From 896a12a0e8cd9339bdcbbe37bd4258cbe6fb1154 Mon Sep 17 00:00:00 2001
From: cneyens <cas.neyens@gmail.com>
Date: Sun, 7 Jul 2024 15:18:36 +0000
Subject: [PATCH] =?UTF-8?q?Deploying=20to=20gh-pages=20from=20@=20cneyens/?=
 =?UTF-8?q?raem@746d28404ead0cde46244cf8e1757de5b6e4a7fb=20=F0=9F=9A=80?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 404.html                                      |   2 +-
 LICENSE-text.html                             |   2 +-
 LICENSE.html                                  |   2 +-
 articles/index.html                           |   4 +-
 articles/overview.html                        | 228 +++++++++++++++---
 .../overview_files/figure-html/well-1.png     | Bin 0 -> 138454 bytes
 authors.html                                  |   2 +-
 index.html                                    |   2 +-
 pkgdown.yml                                   |   2 +-
 reference/add_element.html                    |   2 +-
 reference/aem.html                            |   2 +-
 reference/areasink.html                       |   2 +-
 reference/capzone.html                        |   2 +-
 reference/constant.html                       |   2 +-
 reference/contours.html                       |   2 +-
 reference/dirflow.html                        |   2 +-
 reference/element_discharge.html              |   2 +-
 reference/flow.html                           | 198 ++++++---------
 reference/flow_through_line.html              |   2 +-
 reference/head_to_potential.html              |   2 +-
 reference/headareasink.html                   |   2 +-
 reference/headlinesink.html                   |   2 +-
 reference/headwell.html                       |   2 +-
 reference/index.html                          |   6 +-
 reference/linesink.html                       |   2 +-
 reference/satthick.html                       |   2 +-
 reference/state-variables.html                | 134 +++++-----
 reference/tracelines.html                     |   2 +-
 reference/uniformflow.html                    |   2 +-
 reference/well.html                           |   2 +-
 search.json                                   |   2 +-
 31 files changed, 350 insertions(+), 270 deletions(-)
 create mode 100644 articles/overview_files/figure-html/well-1.png

diff --git a/404.html b/404.html
index ade9f80..e2d5666 100644
--- a/404.html
+++ b/404.html
@@ -39,7 +39,7 @@
 <li class="nav-item dropdown">
   <a href="https://cneyens.github.io/raem/#" class="nav-link dropdown-toggle" data-bs-toggle="dropdown" role="button" aria-expanded="false" aria-haspopup="true" id="dropdown-articles">Articles</a>
   <div class="dropdown-menu" aria-labelledby="dropdown-articles">
-    <a class="dropdown-item" href="https://cneyens.github.io/raem/articles/overview.html">An overview</a>
+    <a class="dropdown-item" href="https://cneyens.github.io/raem/articles/overview.html">An Overview</a>
   </div>
 </li>
       </ul>
diff --git a/LICENSE-text.html b/LICENSE-text.html
index 0b7e0d6..894096c 100644
--- a/LICENSE-text.html
+++ b/LICENSE-text.html
@@ -24,7 +24,7 @@
 <li class="nav-item dropdown">
   <a href="#" class="nav-link dropdown-toggle" data-bs-toggle="dropdown" role="button" aria-expanded="false" aria-haspopup="true" id="dropdown-articles">Articles</a>
   <div class="dropdown-menu" aria-labelledby="dropdown-articles">
-    <a class="dropdown-item" href="articles/overview.html">An overview</a>
+    <a class="dropdown-item" href="articles/overview.html">An Overview</a>
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       </ul><form class="form-inline my-2 my-lg-0" role="search">
diff --git a/LICENSE.html b/LICENSE.html
index 6507b50..b362c59 100644
--- a/LICENSE.html
+++ b/LICENSE.html
@@ -24,7 +24,7 @@
 <li class="nav-item dropdown">
   <a href="#" class="nav-link dropdown-toggle" data-bs-toggle="dropdown" role="button" aria-expanded="false" aria-haspopup="true" id="dropdown-articles">Articles</a>
   <div class="dropdown-menu" aria-labelledby="dropdown-articles">
-    <a class="dropdown-item" href="articles/overview.html">An overview</a>
+    <a class="dropdown-item" href="articles/overview.html">An Overview</a>
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diff --git a/articles/index.html b/articles/index.html
index a8fb36a..aa160a4 100644
--- a/articles/index.html
+++ b/articles/index.html
@@ -24,7 +24,7 @@
 <li class="nav-item dropdown">
   <a href="#" class="nav-link dropdown-toggle" data-bs-toggle="dropdown" role="button" aria-expanded="false" aria-haspopup="true" id="dropdown-articles">Articles</a>
   <div class="dropdown-menu" aria-labelledby="dropdown-articles">
-    <a class="dropdown-item" href="../articles/overview.html">An overview</a>
+    <a class="dropdown-item" href="../articles/overview.html">An Overview</a>
   </div>
 </li>
       </ul><form class="form-inline my-2 my-lg-0" role="search">
@@ -50,7 +50,7 @@
       <h3>All vignettes</h3>
       <div class="section-desc"></div>
 
-      <dl><dt><a href="overview.html">An overview</a></dt>
+      <dl><dt><a href="overview.html">An Overview</a></dt>
         <dd>
       </dd></dl></div>
   </main></div>
diff --git a/articles/overview.html b/articles/overview.html
index bd605e9..7c3eca4 100644
--- a/articles/overview.html
+++ b/articles/overview.html
@@ -6,12 +6,12 @@
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 <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
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+<title>An Overview • raem</title>
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+<!-- bootstrap-toc --><script src="https://cdn.jsdelivr.net/gh/afeld/bootstrap-toc@v1.0.1/dist/bootstrap-toc.min.js" integrity="sha256-4veVQbu7//Lk5TSmc7YV48MxtMy98e26cf5MrgZYnwo=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.11/clipboard.min.js" integrity="sha512-7O5pXpc0oCRrxk8RUfDYFgn0nO1t+jLuIOQdOMRp4APB7uZ4vSjspzp5y6YDtDs4VzUSTbWzBFZ/LKJhnyFOKw==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><!-- search --><script src="https://cdnjs.cloudflare.com/ajax/libs/fuse.js/6.4.6/fuse.js" integrity="sha512-zv6Ywkjyktsohkbp9bb45V6tEMoWhzFzXis+LrMehmJZZSys19Yxf1dopHx7WzIKxr5tK2dVcYmaCk2uqdjF4A==" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/autocomplete.js/0.38.0/autocomplete.jquery.min.js" integrity="sha512-GU9ayf+66Xx2TmpxqJpliWbT5PiGYxpaG8rfnBEk1LL8l1KGkRShhngwdXK1UgqhAzWpZHSiYPc09/NwDQIGyg==" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mark.js/8.11.1/mark.min.js" integrity="sha512-5CYOlHXGh6QpOFA/TeTylKLWfB3ftPsde7AnmhuitiTX4K5SqCLBeKro6sPS8ilsz1Q4NRx3v8Ko2IBiszzdww==" crossorigin="anonymous"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="An Overview">
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@@ -41,7 +41,7 @@
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-    <a class="dropdown-item" href="../articles/overview.html">An overview</a>
+    <a class="dropdown-item" href="../articles/overview.html">An Overview</a>
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@@ -68,7 +68,7 @@
 
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
-      <img src="" class="logo" alt=""><h1>An overview</h1>
+      <img src="" class="logo" alt=""><h1>An Overview</h1>
             
       
       <small class="dont-index">Source: <a href="https://github.com/cneyens/raem/blob/HEAD/vignettes/overview.Rmd" class="external-link"><code>vignettes/overview.Rmd</code></a></small>
@@ -87,58 +87,208 @@ <h2 id="introduction-to-analytic-element-modeling">Introduction to analytic elem
 </h2>
 <p>First developed by Otto Strack and Henk Haitjema in the late 1970’s,
 the analytic element modeling (AEM) approach solves a groundwater flow
-problem by superimposing solutions for features such as wells, streams
-and recharge. Each feature is called <em>an element</em>.</p>
-<p>The governing equation is:</p>
-<p>The main assumption is based on the Dupuit-Forchheimer approximation,
-which states that</p>
-<p>This reduces the governing equation to:</p>
-<p>which described steady-state, single-layer two-dimensional flow in
-the <span class="math inline">\(x-y\)</span> plane.</p>
-<p>When the aquifer is phreatic, the saturated thickness is variable,
-which renders equation X non-linear when solving for <span class="math inline">\(h\)</span>. Therefore, the discharge potential
-<span class="math inline">\(\Phi\)</span> is introduced:</p>
-<p>so that equation X becomes:</p>
-<p>This linear equation can be solved for <span class="math inline">\(\Phi\)</span>. The resulting hydraulic heads can
-then be computed as:</p>
-<p>In addition to the discharge potential <span class="math inline">\(\Phi\)</span>, there exists a streamfunction <span class="math inline">\(\Psi\)</span> which is defined as:</p>
-<p><span class="math inline">\(\Psi\)</span> is only defined for the
-Laplace equation. When areal recharge is applied using area-sinks (see
-paragraph <a href="#area-sink">Area-sink</a> below), the equation
-follows a Poisson equation and <span class="math inline">\(\Psi\)</span>
-is no longer meaningful.</p>
-<p><span class="math inline">\(\Phi\)</span> and <span class="math inline">\(\Psi\)</span> fulfill the Cauchy-Riemann
-conditions, so they can be combined into a complex discharge potential
-<span class="math inline">\(\Omega\)</span>:</p>
-<p>whose real and imaginary terms are <span class="math inline">\(\Phi\)</span> and <span class="math inline">\(\Psi\)</span>, respectively. The flow problem is
-solved in terms of <span class="math inline">\(\Omega\)</span>, which
-then yields <span class="math inline">\(\Phi\)</span> and eventually
-<span class="math inline">\(h\)</span>.</p>
+problem by superposition of analytical solutions for features such as
+wells, streams and recharge. Each feature is called <em>an element</em>.
+By superimposing the individual solutions, the combined effect of all
+elements can be calculated at any point in space. An arbitrary number of
+elements can be placed at any location in the flow field. As such, the
+AEM method is more flexible than single analytical solutions and can be
+used to solve more complex field cases. Compared to numerical solutions
+of the groundwater flow problem, the AEM method does not require a
+spatial grid, is relatively fast and easy to use and does not suffer
+from numerical instability or mass balance errors.</p>
+<p>Flow is governed by the Dupuit-Forchheimer approximation which states
+that the hydraulic head <span class="math inline">\(h\)</span> is
+hydrostatic at each point in the horizontal plane. In other words, there
+is no variation in <span class="math inline">\(h\)</span> along the
+vertical axis and horizontal flow is evenly distributed along the
+vertical axis. This reduces the dimensions of the problem, as the
+solution now only depends on the <span class="math inline">\(x\)</span>
+and <span class="math inline">\(y\)</span> coordinates. Although there
+are no vertical gradients, vertical flow can still be computed from mass
+balance considerations, i.e. areal recharge at the aquifer top or
+leakage through the aquifer bottom. Additionally for phreatic aquifers,
+the curvature of the water-table induces vertical flow components.
+Besides the Dupuit-Forchheimer assumption, the aquifer is assumed be of
+infinite lateral extent, have a horizontal top and base and is
+homogeneous at the scale of interest. In practice, these assumptions
+appear to be (approximately) valid for cases when the groundwater system
+under consideration is much wider than it is thick, which is the case
+for most regional aquifer systems where flow is predominantly
+horizontal. In areas where there is considerable vertical flow, such as
+near groundwater divides or near partially penetrating wells or streams,
+or when the flow system has a similar thickness and width (<span class="math inline">\(width\lt~\approx 3*thickness\)</span>), the
+Dupuit-Forchheimer approximation is not valid and a different method
+should be used, e.g. a numerical model of the 3D groundwater flow
+equation.</p>
+<div class="section level3">
+<h3 id="solution-method">Solution method<a class="anchor" aria-label="anchor" href="#solution-method"></a>
+</h3>
+<p>For steady-state, single layer Dupuit-Forchheimer flow in the
+horizontal plane, the governing equation is:</p>
+<p><span class="math display">\[
+T\frac{\partial^2{h}}{\partial x^2} + T\frac{\partial^2{h}}{\partial
+y^2} + N = 0
+\]</span></p>
+<p>with <span class="math inline">\(T\)</span> the aquifer
+transmissivity <span class="math inline">\([L^2/T]\)</span>, equal to
+<span class="math inline">\(kH\)</span> with <span class="math inline">\(k\)</span> the horizontal hydraulic conductivity
+<span class="math inline">\([L/T]\)</span> and <span class="math inline">\(H\)</span> the saturated thickness <span class="math inline">\([L]\)</span>, <span class="math inline">\(h\)</span> the hydraulic head <span class="math inline">\([L]\)</span> and <span class="math inline">\(N\)</span> a sink/source term <span class="math inline">\([L/T]\)</span>.</p>
+<p>When the aquifer is phreatic, the saturated thickness <span class="math inline">\(H\)</span> is variable, which renders the flow
+equation non-linear when solving for <span class="math inline">\(h\)</span>. Therefore, the discharge potential
+<span class="math inline">\(\Phi\)</span> <span class="math inline">\([L^3/T]\)</span> is introduced so that the
+governing flow equation becomes:</p>
+<p><span class="math display">\[
+\frac{\partial^2{\Phi}}{\partial x^2} + \frac{\partial^2{\Phi}}{\partial
+y^2} + N = 0
+\]</span></p>
+<p>which is a linear equation and can be solved for <span class="math inline">\(\Phi\)</span>. The resulting hydraulic heads can
+then be computed from:</p>
+<p><span class="math display">\[
+\begin{aligned}
+\Phi &amp;= kHh - (\frac{1}{2}kH^2 + kHz_b) &amp;\qquad h \ge z_t \\
+\Phi &amp;= \frac{1}{2}k(h - z_b)^2 &amp;\qquad z_b \lt h \lt z_t
+\end{aligned}
+\]</span></p>
+<p>with <span class="math inline">\(z_t\)</span> and <span class="math inline">\(z_b\)</span> the aquifer top and base elevation
+<span class="math inline">\([L]\)</span>, respectively.</p>
+<p>In addition to the discharge potential <span class="math inline">\(\Phi\)</span>, there exists a stream function
+<span class="math inline">\(\Psi\)</span> <span class="math inline">\([L^3/T]\)</span> which is defined as a function
+that is constant along streamlines and whose difference in stream
+function values between two points is equal to the amount of water
+flowing between those two points. By convention, the stream function
+increases to the right when looking in the direction of flow. It can be
+used to visualize the amount of flow in a groundwater system. <span class="math inline">\(\Psi\)</span> is only defined for the Laplace
+equation, i.e. when <span class="math inline">\(N\)</span> is zero. In
+modeling terms, this means that no area-sinks are active in the model
+(see paragraph <a href="#area-sink">Area-sink</a> below).</p>
+<p>The discharge potential <span class="math inline">\(\Phi\)</span> and
+the stream function <span class="math inline">\(\Psi\)</span> fulfill
+the Cauchy-Riemann conditions and can therefore be combined into a
+complex potential <span class="math inline">\(\Omega\)</span> whose real
+and imaginary terms are <span class="math inline">\(\Phi\)</span> and
+<span class="math inline">\(\Psi\)</span>, respectively. By solving the
+flow problem in terms of <span class="math inline">\(\Omega\)</span>,
+<span class="math inline">\(\Phi\)</span> and <span class="math inline">\(\Psi\)</span> are solved simultaneously in the
+complex plane, which is described by the complex coordinate <span class="math inline">\(\zeta=x+iy\)</span>. The solution in terms of
+<span class="math inline">\(\Omega\)</span> yields <span class="math inline">\(\Phi\)</span> and eventually <span class="math inline">\(h\)</span>.</p>
+<p>The derivative of <span class="math inline">\(\Omega\)</span> with
+respect to <span class="math inline">\(\zeta\)</span> is the complex
+discharge <span class="math inline">\(W\)</span>, whose real component
+is <span class="math inline">\(Q_x\)</span> and whose negative imaginary
+component is <span class="math inline">\(Q_y\)</span>, i.e. the <span class="math inline">\(x\)</span> and <span class="math inline">\(y\)</span> components of the discharge vector
+<span class="math inline">\(Q\)</span> <span class="math inline">\([L^2/T]\)</span>, which represents the first
+derivate of <span class="math inline">\(\Phi\)</span> in the <span class="math inline">\(x\)</span> and <span class="math inline">\(y\)</span> directions. The vertical component
+<span class="math inline">\(Q_z\)</span> is determined from mass balance
+considerations as discussed above. The Darcy flux <span class="math inline">\(q\)</span> <span class="math inline">\([L/T]\)</span> (also called <em>specific
+discharge</em>) is computed as <span class="math inline">\(Q/H\)</span>.
+The average linear flow velocity <span class="math inline">\(v\)</span>
+<span class="math inline">\([L/T]\)</span> is computed as <span class="math inline">\(q/n\)</span> with <span class="math inline">\(n\)</span> the aquifer porosity, which should
+represent the effective porosity.</p>
 <p>Each element gives a solution for the governing flow equation in
-terms of <span class="math inline">\(\Omega\)</span>, which are
-superimposed in space. Since the solution for a given element depends on
-the results of all other elements, the complete system of equations
-needs to be solved simultaneously. This is done by setting up a matrix
-formulation of equation X in the form of <span class="math inline">\(Ax=b\)</span>, which is then solved.</p>
+terms of <span class="math inline">\(\Omega\)</span>, as well as for the
+complex discharge <span class="math inline">\(W\)</span>. An element has
+one or more free parameters, e.g. the discharge for a well element.
+These parameters may be user-specified or need to be computed from other
+conditions, as is the case in head-specified elements. The parameters
+are specified at so called <em>collocation points</em> or <em>control
+points</em>. Since the solution for a given element depends on the
+results of all other elements, the complete system of equations needs to
+be solved simultaneously for the element parameters. This is done by
+setting up the flow equations at the collocation points in a matrix form
+of <span class="math inline">\(Ax=b\)</span>, which is then solved for
+the parameter vector <span class="math inline">\(x\)</span>. Once the
+element parameters are known, the contributions of each element to the
+complex potential <span class="math inline">\(\Omega\)</span> and the
+complex discharge <span class="math inline">\(W\)</span> at any point
+can be calculated and superimposed to form the resulting <span class="math inline">\(\Omega\)</span> and <span class="math inline">\(W\)</span> values, which then yield the variables
+of interest such as <span class="math inline">\(h\)</span> and <span class="math inline">\(Q\)</span>.</p>
 <p>For a more complete overview of analytic element modeling, the reader
-is referred to</p>
+is referred to <a href="https://www.haitjema.com/ModelingofGroundwaterFlow6312.pdf" class="external-link">Haitjema
+(1995)</a>, <a href="https://books.google.be/books/about/Groundwater_Mechanics.html?id=kfFOAQAAIAAJ&amp;redir_esc=y" class="external-link">Strack
+(1989)</a>, <a href="https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2002RG000111" class="external-link">Strack
+(2003)</a> and <a href="https://www.researchgate.net/profile/Randall-Hunt/publication/7367473_Ground_Water_Modeling_Applications_Using_the_Analytic_Element_Method/links/5a2eae43a6fdcc17f91fa2e8/Ground-Water-Modeling-Applications-Using-the-Analytic-Element-Method.pdf" class="external-link">Hunt
+(2006)</a>.</p>
+</div>
 </div>
 <div class="section level2">
 <h2 id="elements">Elements<a class="anchor" aria-label="anchor" href="#elements"></a>
 </h2>
+<p>An overview of the elements available in <code>raem</code> is
+provided. You can specify as many elements as you like, but keep in mind
+that the solution matrix increases in size for every element parameter.
+Currently, every element in <code>raem</code> only supplied one
+parameter to the solution matrix.</p>
+<p>To create an AEM model with <code>raem</code>, first we need load
+<code>raem</code> and specify the aquifer parameters:</p>
+<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://github.com/cneyens/raem" class="external-link">raem</a></span><span class="op">)</span></span>
+<span></span>
+<span><span class="va">k</span> <span class="op">=</span> <span class="fl">10</span>     <span class="co"># hydraulic conductivity, m/d</span></span>
+<span><span class="va">top</span> <span class="op">=</span> <span class="fl">10</span>   <span class="co"># aquifer top elevation, m</span></span>
+<span><span class="va">base</span> <span class="op">=</span> <span class="op">-</span><span class="fl">15</span> <span class="co"># aquifer bottom elevation, m</span></span>
+<span><span class="va">n</span> <span class="op">=</span> <span class="fl">0.2</span>    <span class="co"># aquifer effective porosity, -</span></span></code></pre></div>
 <div class="section level3">
 <h3 id="well">Well<a class="anchor" aria-label="anchor" href="#well"></a>
 </h3>
-<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://github.com/cneyens/raem" class="external-link">raem</a></span><span class="op">)</span></span></code></pre></div>
+<p>The simplest element is a well with a specified discharge <span class="math inline">\(Q\)</span>, which can be created with the
+<code><a href="../reference/well.html">well()</a></code> function. It requires the <span class="math inline">\(x\)</span> and <span class="math inline">\(y\)</span> coordinate of the well and the pumping
+rate <span class="math inline">\(Q\)</span> (positive for withdrawal).
+The well radius <span class="math inline">\(rw\)</span> can also be
+specified (default is <span class="math inline">\(0.3\)</span> length
+units). Inside the well annulus as defined by <span class="math inline">\(r_w\)</span>, the solution is undefined. When a
+output variable is requested inside this circle, its location is
+projected onto the nearest point on the outer annulus.</p>
+<p>Here, we specify two extraions wells. We then create the model with a
+call to <code><a href="../reference/aem.html">aem()</a></code>. This function needs the aquifer parameters
+as well as the elements. You can supply the elements individually or put
+them into a single <code><a href="https://rdrr.io/r/base/list.html" class="external-link">list()</a></code>. The <code><a href="../reference/aem.html">aem()</a></code> function
+automatically solves the system of equations by calling
+<code><a href="../reference/aem.html">solve.aem()</a></code>. Not that by default, the flow system has a
+variable saturated thickness. You can change this by setting
+<code>type = 'confined'</code> to force the model to use a constant
+saturated thickness, set equal to the aquifer thickness. This may be
+useful when you want to force the system of equations to remain linear
+when elements with a hydraulic resistance are supplied (see below).</p>
+<p>Finally, we set-up the contouring grid and plot the head contours in
+blue and the streamlines in orange using <code><a href="../reference/contours.html">contours()</a></code>. Note
+the ugly <em>branch cuts</em> (in AEM jargon) of the streamlines
+extending from the well centers towards the negative x-axis, which is an
+artifact of contouring the stream function.</p>
+<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">w1</span> <span class="op">=</span> <span class="fu"><a href="../reference/well.html">well</a></span><span class="op">(</span>x <span class="op">=</span> <span class="fl">200</span>, y <span class="op">=</span> <span class="fl">0</span>, Q <span class="op">=</span> <span class="fl">300</span><span class="op">)</span>   </span>
+<span><span class="va">w2</span> <span class="op">=</span> <span class="fu"><a href="../reference/well.html">well</a></span><span class="op">(</span>x <span class="op">=</span> <span class="op">-</span><span class="fl">200</span>, y <span class="op">=</span> <span class="fl">0</span>, Q <span class="op">=</span> <span class="fl">1000</span><span class="op">)</span></span>
+<span></span>
+<span><span class="co"># create the model. This automatically solves the system of equations</span></span>
+<span><span class="va">m</span> <span class="op">=</span> <span class="fu"><a href="../reference/aem.html">aem</a></span><span class="op">(</span>k <span class="op">=</span> <span class="va">k</span>, top <span class="op">=</span> <span class="va">top</span>, base <span class="op">=</span> <span class="va">base</span>, n <span class="op">=</span> <span class="va">n</span>, <span class="va">w1</span>, <span class="va">w2</span><span class="op">)</span></span>
+<span></span>
+<span><span class="co"># set-up the contouring grid and plot head contours and streamline </span></span>
+<span><span class="va">xg</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/seq.html" class="external-link">seq</a></span><span class="op">(</span><span class="op">-</span><span class="fl">600</span>, <span class="fl">600</span>, length <span class="op">=</span> <span class="fl">100</span><span class="op">)</span></span>
+<span><span class="va">yg</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/seq.html" class="external-link">seq</a></span><span class="op">(</span><span class="op">-</span><span class="fl">300</span>, <span class="fl">300</span>, length <span class="op">=</span> <span class="fl">100</span><span class="op">)</span></span>
+<span></span>
+<span><span class="fu"><a href="../reference/contours.html">contours</a></span><span class="op">(</span><span class="va">m</span>, <span class="va">xg</span>, <span class="va">yg</span>, col <span class="op">=</span> <span class="st">'dodgerblue'</span>, nlevels <span class="op">=</span> <span class="fl">20</span>, drawlabels <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span>
+<span><span class="fu"><a href="../reference/contours.html">contours</a></span><span class="op">(</span><span class="va">m</span>, <span class="va">xg</span>, <span class="va">yg</span>, variable <span class="op">=</span> <span class="st">'streamfunction'</span>, col <span class="op">=</span> <span class="st">'orange'</span>, nlevels <span class="op">=</span> <span class="fl">20</span>, drawlabels <span class="op">=</span> <span class="cn">TRUE</span>, add <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
+<p><img src="overview_files/figure-html/well-1.png" width="672" style="display: block; margin: auto;"></p>
+<div class="section level4">
+<h4 id="head-specified-well">Head-specified well<a class="anchor" aria-label="anchor" href="#head-specified-well"></a>
+</h4>
+</div>
 </div>
 <div class="section level3">
 <h3 id="line-sink">Line-sink<a class="anchor" aria-label="anchor" href="#line-sink"></a>
 </h3>
+<div class="section level4">
+<h4 id="head-specified-line-sink">Head-specified line-sink<a class="anchor" aria-label="anchor" href="#head-specified-line-sink"></a>
+</h4>
+</div>
 </div>
 <div class="section level3">
 <h3 id="area-sink">Area-sink<a class="anchor" aria-label="anchor" href="#area-sink"></a>
 </h3>
+<div class="section level4">
+<h4 id="head-specified-area-sink">Head-specified area-sink<a class="anchor" aria-label="anchor" href="#head-specified-area-sink"></a>
+</h4>
+</div>
 </div>
 <div class="section level3">
 <h3 id="reference-point">Reference point<a class="anchor" aria-label="anchor" href="#reference-point"></a>
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diff --git a/authors.html b/authors.html
index c188599..318fe60 100644
--- a/authors.html
+++ b/authors.html
@@ -24,7 +24,7 @@
 <li class="nav-item dropdown">
   <a href="#" class="nav-link dropdown-toggle" data-bs-toggle="dropdown" role="button" aria-expanded="false" aria-haspopup="true" id="dropdown-articles">Articles</a>
   <div class="dropdown-menu" aria-labelledby="dropdown-articles">
-    <a class="dropdown-item" href="articles/overview.html">An overview</a>
+    <a class="dropdown-item" href="articles/overview.html">An Overview</a>
   </div>
 </li>
       </ul><form class="form-inline my-2 my-lg-0" role="search">
diff --git a/index.html b/index.html
index 40895fd..ca3c78d 100644
--- a/index.html
+++ b/index.html
@@ -41,7 +41,7 @@
 <li class="nav-item dropdown">
   <a href="#" class="nav-link dropdown-toggle" data-bs-toggle="dropdown" role="button" aria-expanded="false" aria-haspopup="true" id="dropdown-articles">Articles</a>
   <div class="dropdown-menu" aria-labelledby="dropdown-articles">
-    <a class="dropdown-item" href="articles/overview.html">An overview</a>
+    <a class="dropdown-item" href="articles/overview.html">An Overview</a>
   </div>
 </li>
       </ul>
diff --git a/pkgdown.yml b/pkgdown.yml
index d3b8a51..a3b0ac6 100644
--- a/pkgdown.yml
+++ b/pkgdown.yml
@@ -3,7 +3,7 @@ pkgdown: 2.0.9
 pkgdown_sha: ~
 articles:
   overview: overview.html
-last_built: 2024-07-06T19:18Z
+last_built: 2024-07-07T15:17Z
 urls:
   reference: https://cneyens.github.io/raem/reference
   article: https://cneyens.github.io/raem/articles
diff --git a/reference/add_element.html b/reference/add_element.html
index eddee4e..0ee1fb7 100644
--- a/reference/add_element.html
+++ b/reference/add_element.html
@@ -24,7 +24,7 @@
 <li class="nav-item dropdown">
   <a href="#" class="nav-link dropdown-toggle" data-bs-toggle="dropdown" role="button" aria-expanded="false" aria-haspopup="true" id="dropdown-articles">Articles</a>
   <div class="dropdown-menu" aria-labelledby="dropdown-articles">
-    <a class="dropdown-item" href="../articles/overview.html">An overview</a>
+    <a class="dropdown-item" href="../articles/overview.html">An Overview</a>
   </div>
 </li>
       </ul><form class="form-inline my-2 my-lg-0" role="search">
diff --git a/reference/aem.html b/reference/aem.html
index a91ea6d..4c52bdf 100644
--- a/reference/aem.html
+++ b/reference/aem.html
@@ -32,7 +32,7 @@
 <li class="nav-item dropdown">
   <a href="#" class="nav-link dropdown-toggle" data-bs-toggle="dropdown" role="button" aria-expanded="false" aria-haspopup="true" id="dropdown-articles">Articles</a>
   <div class="dropdown-menu" aria-labelledby="dropdown-articles">
-    <a class="dropdown-item" href="../articles/overview.html">An overview</a>
+    <a class="dropdown-item" href="../articles/overview.html">An Overview</a>
   </div>
 </li>
       </ul><form class="form-inline my-2 my-lg-0" role="search">
diff --git a/reference/areasink.html b/reference/areasink.html
index 6edd01c..3cce00a 100644
--- a/reference/areasink.html
+++ b/reference/areasink.html
@@ -24,7 +24,7 @@
 <li class="nav-item dropdown">
   <a href="#" class="nav-link dropdown-toggle" data-bs-toggle="dropdown" role="button" aria-expanded="false" aria-haspopup="true" id="dropdown-articles">Articles</a>
   <div class="dropdown-menu" aria-labelledby="dropdown-articles">
-    <a class="dropdown-item" href="../articles/overview.html">An overview</a>
+    <a class="dropdown-item" href="../articles/overview.html">An Overview</a>
   </div>
 </li>
       </ul><form class="form-inline my-2 my-lg-0" role="search">
diff --git a/reference/capzone.html b/reference/capzone.html
index 5c61a78..3806a08 100644
--- a/reference/capzone.html
+++ b/reference/capzone.html
@@ -26,7 +26,7 @@
 <li class="nav-item dropdown">
   <a href="#" class="nav-link dropdown-toggle" data-bs-toggle="dropdown" role="button" aria-expanded="false" aria-haspopup="true" id="dropdown-articles">Articles</a>
   <div class="dropdown-menu" aria-labelledby="dropdown-articles">
-    <a class="dropdown-item" href="../articles/overview.html">An overview</a>
+    <a class="dropdown-item" href="../articles/overview.html">An Overview</a>
   </div>
 </li>
       </ul><form class="form-inline my-2 my-lg-0" role="search">
diff --git a/reference/constant.html b/reference/constant.html
index 5083f50..1c36190 100644
--- a/reference/constant.html
+++ b/reference/constant.html
@@ -26,7 +26,7 @@
 <li class="nav-item dropdown">
   <a href="#" class="nav-link dropdown-toggle" data-bs-toggle="dropdown" role="button" aria-expanded="false" aria-haspopup="true" id="dropdown-articles">Articles</a>
   <div class="dropdown-menu" aria-labelledby="dropdown-articles">
-    <a class="dropdown-item" href="../articles/overview.html">An overview</a>
+    <a class="dropdown-item" href="../articles/overview.html">An Overview</a>
   </div>
 </li>
       </ul><form class="form-inline my-2 my-lg-0" role="search">
diff --git a/reference/contours.html b/reference/contours.html
index b1621dc..48def4f 100644
--- a/reference/contours.html
+++ b/reference/contours.html
@@ -26,7 +26,7 @@
 <li class="nav-item dropdown">
   <a href="#" class="nav-link dropdown-toggle" data-bs-toggle="dropdown" role="button" aria-expanded="false" aria-haspopup="true" id="dropdown-articles">Articles</a>
   <div class="dropdown-menu" aria-labelledby="dropdown-articles">
-    <a class="dropdown-item" href="../articles/overview.html">An overview</a>
+    <a class="dropdown-item" href="../articles/overview.html">An Overview</a>
   </div>
 </li>
       </ul><form class="form-inline my-2 my-lg-0" role="search">
diff --git a/reference/dirflow.html b/reference/dirflow.html
index c43418d..3ae926d 100644
--- a/reference/dirflow.html
+++ b/reference/dirflow.html
@@ -24,7 +24,7 @@
 <li class="nav-item dropdown">
   <a href="#" class="nav-link dropdown-toggle" data-bs-toggle="dropdown" role="button" aria-expanded="false" aria-haspopup="true" id="dropdown-articles">Articles</a>
   <div class="dropdown-menu" aria-labelledby="dropdown-articles">
-    <a class="dropdown-item" href="../articles/overview.html">An overview</a>
+    <a class="dropdown-item" href="../articles/overview.html">An Overview</a>
   </div>
 </li>
       </ul><form class="form-inline my-2 my-lg-0" role="search">
diff --git a/reference/element_discharge.html b/reference/element_discharge.html
index 442da02..96e67a3 100644
--- a/reference/element_discharge.html
+++ b/reference/element_discharge.html
@@ -26,7 +26,7 @@
 <li class="nav-item dropdown">
   <a href="#" class="nav-link dropdown-toggle" data-bs-toggle="dropdown" role="button" aria-expanded="false" aria-haspopup="true" id="dropdown-articles">Articles</a>
   <div class="dropdown-menu" aria-labelledby="dropdown-articles">
-    <a class="dropdown-item" href="../articles/overview.html">An overview</a>
+    <a class="dropdown-item" href="../articles/overview.html">An Overview</a>
   </div>
 </li>
       </ul><form class="form-inline my-2 my-lg-0" role="search">
diff --git a/reference/flow.html b/reference/flow.html
index fbe11a4..c7d6672 100644
--- a/reference/flow.html
+++ b/reference/flow.html
@@ -1,19 +1,19 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><meta name="description" content="domega() computes the complex discharge for an aem or element object
-at the given x and y coordinates.
-discharge() computes the x, y and z components of the discharge vector for an aem object
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><meta name="description" content="discharge() computes the x, y and z components of the discharge vector for an aem object
 at the given x, y and z coordinates.
 darcy() computes the x, y and z components of the Darcy flux vector (also called specific discharge vector)
 for an aem object at the given x, y and z coordinates.
 velocity() computes the x, y and z components of the average linear groundwater flow velocity vector
-for an aem object at the given x, y and z coordinates."><title>Calculate flow variables — flow • raem</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- bootstrap-toc --><script src="https://cdn.jsdelivr.net/gh/afeld/bootstrap-toc@v1.0.1/dist/bootstrap-toc.min.js" integrity="sha256-4veVQbu7//Lk5TSmc7YV48MxtMy98e26cf5MrgZYnwo=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.11/clipboard.min.js" integrity="sha512-7O5pXpc0oCRrxk8RUfDYFgn0nO1t+jLuIOQdOMRp4APB7uZ4vSjspzp5y6YDtDs4VzUSTbWzBFZ/LKJhnyFOKw==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><!-- search --><script src="https://cdnjs.cloudflare.com/ajax/libs/fuse.js/6.4.6/fuse.js" integrity="sha512-zv6Ywkjyktsohkbp9bb45V6tEMoWhzFzXis+LrMehmJZZSys19Yxf1dopHx7WzIKxr5tK2dVcYmaCk2uqdjF4A==" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/autocomplete.js/0.38.0/autocomplete.jquery.min.js" integrity="sha512-GU9ayf+66Xx2TmpxqJpliWbT5PiGYxpaG8rfnBEk1LL8l1KGkRShhngwdXK1UgqhAzWpZHSiYPc09/NwDQIGyg==" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mark.js/8.11.1/mark.min.js" integrity="sha512-5CYOlHXGh6QpOFA/TeTylKLWfB3ftPsde7AnmhuitiTX4K5SqCLBeKro6sPS8ilsz1Q4NRx3v8Ko2IBiszzdww==" crossorigin="anonymous"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate flow variables — flow"><meta property="og:description" content="domega() computes the complex discharge for an aem or element object
-at the given x and y coordinates.
-discharge() computes the x, y and z components of the discharge vector for an aem object
+for an aem object at the given x, y and z coordinates.
+domega() computes the complex discharge for an aem or element object
+at the given x and y coordinates."><title>Calculate flow variables — flow • raem</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- bootstrap-toc --><script src="https://cdn.jsdelivr.net/gh/afeld/bootstrap-toc@v1.0.1/dist/bootstrap-toc.min.js" integrity="sha256-4veVQbu7//Lk5TSmc7YV48MxtMy98e26cf5MrgZYnwo=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.11/clipboard.min.js" integrity="sha512-7O5pXpc0oCRrxk8RUfDYFgn0nO1t+jLuIOQdOMRp4APB7uZ4vSjspzp5y6YDtDs4VzUSTbWzBFZ/LKJhnyFOKw==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><!-- search --><script src="https://cdnjs.cloudflare.com/ajax/libs/fuse.js/6.4.6/fuse.js" integrity="sha512-zv6Ywkjyktsohkbp9bb45V6tEMoWhzFzXis+LrMehmJZZSys19Yxf1dopHx7WzIKxr5tK2dVcYmaCk2uqdjF4A==" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/autocomplete.js/0.38.0/autocomplete.jquery.min.js" integrity="sha512-GU9ayf+66Xx2TmpxqJpliWbT5PiGYxpaG8rfnBEk1LL8l1KGkRShhngwdXK1UgqhAzWpZHSiYPc09/NwDQIGyg==" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mark.js/8.11.1/mark.min.js" integrity="sha512-5CYOlHXGh6QpOFA/TeTylKLWfB3ftPsde7AnmhuitiTX4K5SqCLBeKro6sPS8ilsz1Q4NRx3v8Ko2IBiszzdww==" crossorigin="anonymous"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate flow variables — flow"><meta property="og:description" content="discharge() computes the x, y and z components of the discharge vector for an aem object
 at the given x, y and z coordinates.
 darcy() computes the x, y and z components of the Darcy flux vector (also called specific discharge vector)
 for an aem object at the given x, y and z coordinates.
 velocity() computes the x, y and z components of the average linear groundwater flow velocity vector
-for an aem object at the given x, y and z coordinates."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
+for an aem object at the given x, y and z coordinates.
+domega() computes the complex discharge for an aem or element object
+at the given x and y coordinates."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
 <script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script>
 <script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
 <![endif]--></head><body>
@@ -38,7 +38,7 @@
 <li class="nav-item dropdown">
   <a href="#" class="nav-link dropdown-toggle" data-bs-toggle="dropdown" role="button" aria-expanded="false" aria-haspopup="true" id="dropdown-articles">Articles</a>
   <div class="dropdown-menu" aria-labelledby="dropdown-articles">
-    <a class="dropdown-item" href="../articles/overview.html">An overview</a>
+    <a class="dropdown-item" href="../articles/overview.html">An Overview</a>
   </div>
 </li>
       </ul><form class="form-inline my-2 my-lg-0" role="search">
@@ -63,28 +63,25 @@
     </div>
 
     <div class="ref-description section level2">
-    <p><code>domega()</code> computes the complex discharge for an <code>aem</code> or <code>element</code> object
-at the given x and y coordinates.</p>
-<p><code>discharge()</code> computes the <code>x, y</code> and <code>z</code> components of the discharge vector for an <code>aem</code> object
+    <p><code>discharge()</code> computes the <code>x, y</code> and <code>z</code> components of the discharge vector for an <code>aem</code> object
 at the given x, y and z coordinates.</p>
 <p><code>darcy()</code> computes the <code>x, y</code> and <code>z</code> components of the Darcy flux vector (also called specific discharge vector)
 for an <code>aem</code> object at the given x, y and z coordinates.</p>
 <p><code>velocity()</code> computes the <code>x, y</code> and <code>z</code> components of the average linear groundwater flow velocity vector
 for an <code>aem</code> object at the given x, y and z coordinates.</p>
+<p><code>domega()</code> computes the complex discharge for an <code>aem</code> or <code>element</code> object
+at the given x and y coordinates.</p>
     </div>
 
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
-    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">domega</span><span class="op">(</span><span class="va">...</span><span class="op">)</span></span>
-<span></span>
-<span><span class="fu">discharge</span><span class="op">(</span><span class="va">...</span><span class="op">)</span></span>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">discharge</span><span class="op">(</span><span class="va">...</span><span class="op">)</span></span>
 <span></span>
 <span><span class="fu">darcy</span><span class="op">(</span><span class="va">...</span><span class="op">)</span></span>
 <span></span>
 <span><span class="fu">velocity</span><span class="op">(</span><span class="va">...</span><span class="op">)</span></span>
 <span></span>
-<span><span class="co"># S3 method for aem</span></span>
-<span><span class="fu">domega</span><span class="op">(</span><span class="va">aem</span>, <span class="va">x</span>, <span class="va">y</span>, as.grid <span class="op">=</span> <span class="cn">FALSE</span>, <span class="va">...</span><span class="op">)</span></span>
+<span><span class="fu">domega</span><span class="op">(</span><span class="va">...</span><span class="op">)</span></span>
 <span></span>
 <span><span class="co"># S3 method for aem</span></span>
 <span><span class="fu">discharge</span><span class="op">(</span></span>
@@ -104,6 +101,9 @@ <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage">
 <span><span class="co"># S3 method for aem</span></span>
 <span><span class="fu">velocity</span><span class="op">(</span><span class="va">aem</span>, <span class="va">x</span>, <span class="va">y</span>, <span class="va">z</span>, as.grid <span class="op">=</span> <span class="cn">FALSE</span>, magnitude <span class="op">=</span> <span class="cn">FALSE</span>, R <span class="op">=</span> <span class="fl">1</span>, <span class="va">...</span><span class="op">)</span></span>
 <span></span>
+<span><span class="co"># S3 method for aem</span></span>
+<span><span class="fu">domega</span><span class="op">(</span><span class="va">aem</span>, <span class="va">x</span>, <span class="va">y</span>, as.grid <span class="op">=</span> <span class="cn">FALSE</span>, <span class="va">...</span><span class="op">)</span></span>
+<span></span>
 <span><span class="co"># S3 method for element</span></span>
 <span><span class="fu">domega</span><span class="op">(</span><span class="va">element</span>, <span class="va">x</span>, <span class="va">y</span>, <span class="va">...</span><span class="op">)</span></span></code></pre></div>
     </div>
@@ -126,14 +126,14 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 <dd><p>numeric y coordinates to evaluate at</p></dd>
 
 
-<dt>as.grid</dt>
-<dd><p>logical, should a matrix be returned? Defaults to <code>FALSE</code>. See details.</p></dd>
-
-
 <dt>z</dt>
 <dd><p>numeric z coordinates to evaluate at</p></dd>
 
 
+<dt>as.grid</dt>
+<dd><p>logical, should a matrix be returned? Defaults to <code>FALSE</code>. See details.</p></dd>
+
+
 <dt>magnitude</dt>
 <dd><p>logical, should the magnitude of the flow vector be returned as well? Default to <code>FALSE</code>. See details.</p></dd>
 
@@ -154,12 +154,6 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
     
 
-<p>For <code>domega()</code>,  vector of <code>length(x)</code> (equal to <code>length(y)</code>) with the complex discharge values at <code>x</code> and <code>y</code>,
-If <code>as.grid = TRUE</code>, a matrix of dimensions <code>c(length(y), length(x))</code> described by
-marginal vectors <code>x</code> and <code>y</code> containing the complex discharge values at the grid points.
-<code>domega()</code> is the derivative of <code><a href="state-variables.html">omega()</a></code> in the x and y directions.</p>
-
-
 <p>For <code>discharge()</code>, a matrix with the number of rows equal to the number of points to evaluate
 the discharge vector at, and with columns <code>Qx</code>, <code>Qy</code> and <code>Qz</code> corresponding to <code>x, y</code> and <code>z</code> components
 of the discharge vector at coordinates <code>x</code>, <code>y</code> and <code>z</code>. If <code>as.grid = TRUE</code>, an array of dimensions
@@ -187,6 +181,12 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
 <p>For <code>velocity()</code>, the same as for <code>discharge()</code> but with the <code>x</code>, <code>y</code> and <code>z</code> components of the
 average linear groundwater flow velocity vector (<code>vx</code>, <code>vy</code> and <code>vz</code>). The values are computed by dividing
 the <code>darcy()</code> values by the effective porosity (<code>aem$n</code>) and the retardation coefficient <code>R</code>.</p>
+
+
+<p>For <code>domega()</code>,  vector of <code>length(x)</code> (equal to <code>length(y)</code>) with the complex discharge values at <code>x</code> and <code>y</code>,
+If <code>as.grid = TRUE</code>, a matrix of dimensions <code>c(length(y), length(x))</code> described by
+marginal vectors <code>x</code> and <code>y</code> containing the complex discharge values at the grid points.
+<code>domega()</code> is the derivative of <code><a href="state-variables.html">omega()</a></code> in the x and y directions.</p>
     </div>
     <div class="section level2">
     <h2 id="details">Details<a class="anchor" aria-label="anchor" href="#details"></a></h2>
@@ -205,126 +205,72 @@ <h2 id="see-also">See also<a class="anchor" aria-label="anchor" href="#see-also"
     <div class="section level2">
     <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span></span></span>
-<span class="r-in"><span><span class="va">w</span> <span class="op">&lt;-</span> <span class="fu"><a href="well.html">well</a></span><span class="op">(</span>xw <span class="op">=</span> <span class="fl">50</span>, yw <span class="op">=</span> <span class="fl">0</span>, Q <span class="op">=</span> <span class="fl">200</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="va">w</span> <span class="op">&lt;-</span> <span class="fu"><a href="well.html">well</a></span><span class="op">(</span>xw <span class="op">=</span> <span class="fl">55</span>, yw <span class="op">=</span> <span class="fl">0</span>, Q <span class="op">=</span> <span class="fl">200</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="va">uf</span> <span class="op">&lt;-</span> <span class="fu"><a href="uniformflow.html">uniformflow</a></span><span class="op">(</span>gradient <span class="op">=</span> <span class="fl">0.002</span>, angle <span class="op">=</span> <span class="op">-</span><span class="fl">45</span>, TR <span class="op">=</span> <span class="fl">100</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="va">as</span> <span class="op">&lt;-</span> <span class="fu"><a href="areasink.html">areasink</a></span><span class="op">(</span>xc <span class="op">=</span> <span class="fl">0</span>, yc <span class="op">=</span> <span class="fl">0</span>, N <span class="op">=</span> <span class="fl">0.001</span>, R <span class="op">=</span> <span class="fl">500</span><span class="op">)</span></span></span>
-<span class="r-in"><span><span class="va">ml</span> <span class="op">&lt;-</span> <span class="fu"><a href="aem.html">aem</a></span><span class="op">(</span>k <span class="op">=</span> <span class="fl">10</span>, top <span class="op">=</span> <span class="fl">10</span>, base <span class="op">=</span> <span class="fl">0</span>, n <span class="op">=</span> <span class="fl">0.2</span>, <span class="va">w</span>, <span class="va">uf</span>, <span class="va">as</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="va">rf</span> <span class="op">&lt;-</span> <span class="fu"><a href="constant.html">constant</a></span><span class="op">(</span>xc <span class="op">=</span> <span class="op">-</span><span class="fl">1000</span>, yc <span class="op">=</span> <span class="fl">1000</span>, hc <span class="op">=</span> <span class="fl">10</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="va">ml</span> <span class="op">&lt;-</span> <span class="fu"><a href="aem.html">aem</a></span><span class="op">(</span>k <span class="op">=</span> <span class="fl">10</span>, top <span class="op">=</span> <span class="fl">10</span>, base <span class="op">=</span> <span class="op">-</span><span class="fl">15</span>, n <span class="op">=</span> <span class="fl">0.2</span>, <span class="va">w</span>, <span class="va">uf</span>, <span class="va">as</span>, <span class="va">rf</span><span class="op">)</span></span></span>
 <span class="r-in"><span></span></span>
-<span class="r-in"><span><span class="fu">domega</span><span class="op">(</span><span class="va">ml</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">50</span>, <span class="fl">0</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">25</span>, <span class="op">-</span><span class="fl">25</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 0.1664214+1.4021609i 0.6507172-0.1007266i</span>
 <span class="r-in"><span></span></span>
 <span class="r-in"><span><span class="va">xg</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/seq.html" class="external-link">seq</a></span><span class="op">(</span><span class="op">-</span><span class="fl">100</span>, <span class="fl">100</span>, length <span class="op">=</span> <span class="fl">5</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="va">yg</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/seq.html" class="external-link">seq</a></span><span class="op">(</span><span class="op">-</span><span class="fl">75</span>, <span class="fl">75</span>, length <span class="op">=</span> <span class="fl">3</span><span class="op">)</span></span></span>
-<span class="r-in"><span><span class="fu">domega</span><span class="op">(</span><span class="va">ml</span>, <span class="va">xg</span>, <span class="va">yg</span>, as.grid <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>                       [,1]                  [,2]                 [,3]</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1,] 0.2611866+0.18880399i 0.3201397+0.25671010i 0.3373044+0.3977459i</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] 0.3036279+0.14142136i 0.4347312+0.14142136i 0.7780411+0.1414214i</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [3,] 0.2611866+0.09403872i 0.3201397+0.02613261i 0.3373044-0.1149032i</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>                         [,4]                    [,5]</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1,]    0.1664214+0.5283345i -0.004461651+0.3977459i</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] -105.9368740+0.1414214i -0.445198416+0.1414214i</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [3,]    0.1664214-0.2454918i -0.004461651-0.1149032i</span>
 <span class="r-in"><span></span></span>
-<span class="r-in"><span><span class="fu">discharge</span><span class="op">(</span><span class="va">ml</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">50</span>, <span class="fl">0</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">25</span>, <span class="op">-</span><span class="fl">25</span><span class="op">)</span>, z <span class="op">=</span> <span class="va">ml</span><span class="op">$</span><span class="va">top</span><span class="op">)</span></span></span>
-<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>Setting Qz values to NA for z above saturated aquifer level or below aquifer base</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>             Qx         Qy Qz</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1,] 0.1664214 -1.4021609 NA</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] 0.6507172  0.1007266 NA</span>
-<span class="r-in"><span><span class="fu">discharge</span><span class="op">(</span><span class="va">ml</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">50</span>, <span class="fl">0</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">25</span>, <span class="op">-</span><span class="fl">25</span><span class="op">)</span>, z <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="va">ml</span><span class="op">$</span><span class="va">top</span>, <span class="fl">5</span><span class="op">)</span>, magnitude <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
-<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>Setting Qz values to NA for z above saturated aquifer level or below aquifer base</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>             Qx         Qy          Qz         Q</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1,] 0.1664214 -1.4021609          NA        NA</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] 0.6507172  0.1007266 -0.01080013 0.6585555</span>
-<span class="r-in"><span><span class="fu">discharge</span><span class="op">(</span><span class="va">ml</span>, <span class="va">xg</span>, <span class="va">yg</span>, z <span class="op">=</span> <span class="va">ml</span><span class="op">$</span><span class="va">top</span>, as.grid <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
-<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>Setting Qz values to NA for z above saturated aquifer level or below aquifer base</span>
+<span class="r-in"><span><span class="co"># Discharge vector</span></span></span>
+<span class="r-in"><span><span class="fu">discharge</span><span class="op">(</span><span class="va">ml</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">150</span>, <span class="fl">0</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">80</span>, <span class="op">-</span><span class="fl">80</span><span class="op">)</span>, z <span class="op">=</span> <span class="op">-</span><span class="fl">10</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>              Qx         Qy           Qz</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1,] 0.02037961 -0.2665091 -0.005060767</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] 0.32717248  0.0887621 -0.005097869</span>
+<span class="r-in"><span><span class="fu">discharge</span><span class="op">(</span><span class="va">ml</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">150</span>, <span class="fl">0</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">80</span>, <span class="op">-</span><span class="fl">80</span><span class="op">)</span>, z <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">2</span>, <span class="fl">5</span><span class="op">)</span>, magnitude <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>              Qx         Qy          Qz         Q</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1,] 0.02037961 -0.2665091 -0.01720661 0.2678405</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] 0.32717248  0.0887621 -0.02039148 0.3396121</span>
+<span class="r-in"><span><span class="fu">discharge</span><span class="op">(</span><span class="va">ml</span>, <span class="va">xg</span>, <span class="va">yg</span>, z <span class="op">=</span> <span class="fl">2</span>, as.grid <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> , , 1, Qx</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>           [,1]      [,2]      [,3]         [,4]         [,5]</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1,] 0.2611866 0.3201397 0.3373044    0.1664214 -0.004461651</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] 0.3036279 0.4347312 0.7780411 -105.9368740 -0.445198416</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [3,] 0.2611866 0.3201397 0.3373044    0.1664214 -0.004461651</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>           [,1]      [,2]      [,3]      [,4]         [,5]</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1,] 0.2578228 0.3171573 0.3438149 0.1945904  0.004180247</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] 0.2967826 0.4195736 0.7201666 6.5326191 -0.515933946</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [3,] 0.2578228 0.3171573 0.3438149 0.1945904  0.004180247</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> , , 1, Qy</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>             [,1]        [,2]       [,3]       [,4]       [,5]</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1,] -0.18880399 -0.25671010 -0.3977459 -0.5283345 -0.3977459</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] -0.14142136 -0.14142136 -0.1414214 -0.1414214 -0.1414214</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [3,] -0.09403872 -0.02613261  0.1149032  0.2454918  0.1149032</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>             [,1]        [,2]        [,3]       [,4]       [,5]</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1,] -0.18443819 -0.24730419 -0.37991259 -0.5264566 -0.4159899</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] -0.14142136 -0.14142136 -0.14142136 -0.1414214 -0.1414214</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [3,] -0.09840452 -0.03553852  0.09706987  0.2436139  0.1331472</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> , , 1, Qz</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>      [,1] [,2] [,3] [,4] [,5]</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1,]   NA   NA   NA   NA   NA</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [2,]   NA   NA   NA   NA   NA</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [3,]   NA   NA   NA   NA   NA</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>             [,1]        [,2]        [,3]        [,4]        [,5]</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1,] -0.01728591 -0.01746242 -0.01775486 -0.01791021 -0.01750075</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] -0.01730880 -0.01756345 -0.01856240 -0.14449874 -0.01783670</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [3,] -0.01721822 -0.01729328 -0.01736962 -0.01728292 -0.01705172</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-in"><span><span class="fu">discharge</span><span class="op">(</span><span class="va">ml</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">50</span>, <span class="fl">0</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">25</span>, <span class="op">-</span><span class="fl">25</span><span class="op">)</span>, z <span class="op">=</span> <span class="va">ml</span><span class="op">$</span><span class="va">top</span> <span class="op">+</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">0.5</span><span class="op">)</span><span class="op">)</span> <span class="co"># NA for z &gt; top</span></span></span>
+<span class="r-in"><span><span class="fu">discharge</span><span class="op">(</span><span class="va">ml</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">150</span>, <span class="fl">0</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">80</span>, <span class="op">-</span><span class="fl">80</span><span class="op">)</span>, z <span class="op">=</span> <span class="va">ml</span><span class="op">$</span><span class="va">top</span> <span class="op">+</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="op">-</span><span class="fl">5</span>, <span class="fl">0.5</span><span class="op">)</span><span class="op">)</span> <span class="co"># NA for z &gt; water-table</span></span></span>
 <span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>Setting Qz values to NA for z above saturated aquifer level or below aquifer base</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>             Qx         Qy Qz</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1,] 0.1664214 -1.4021609 NA</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] 0.6507172  0.1007266 NA</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>              Qx         Qy          Qz</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1,] 0.02037961 -0.2665091 -0.02024307</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] 0.32717248  0.0887621          NA</span>
 <span class="r-in"><span></span></span>
-<span class="r-in"><span><span class="fu">darcy</span><span class="op">(</span><span class="va">ml</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">50</span>, <span class="fl">0</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">25</span>, <span class="op">-</span><span class="fl">25</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">10</span>, <span class="fl">5</span><span class="op">)</span>, magnitude <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
-<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>Setting Qz values to NA for z above saturated aquifer level or below aquifer base</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>              qx         qy           qz        q</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1,] 0.02936046 -0.2473726           NA       NA</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] 0.10643688  0.0164757 -0.001766562 0.107719</span>
-<span class="r-in"><span><span class="fu">darcy</span><span class="op">(</span><span class="va">ml</span>, <span class="va">xg</span>, <span class="va">yg</span>, <span class="fl">10</span>, as.grid <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
-<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>Setting Qz values to NA for z above saturated aquifer level or below aquifer base</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> , , 1, qx</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>            [,1]       [,2]       [,3]         [,4]          [,5]</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1,] 0.03720717 0.04701470 0.05144049   0.02621968 -0.0007083937</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] 0.04441782 0.06621384 0.12721532 -58.35119617 -0.0762653892</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [3,] 0.03892034 0.04932549 0.05418314   0.02771988 -0.0007496139</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> , , 1, qy</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>             [,1]         [,2]        [,3]        [,4]        [,5]</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1,] -0.02689595 -0.037699634 -0.06065810 -0.08323910 -0.06315167</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] -0.02068857 -0.021539862 -0.02312341 -0.07789644 -0.02422640</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [3,] -0.01401304 -0.004026379  0.01845755  0.04089021  0.01930519</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> , , 1, qz</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>      [,1] [,2] [,3] [,4] [,5]</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1,]   NA   NA   NA   NA   NA</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [2,]   NA   NA   NA   NA   NA</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [3,]   NA   NA   NA   NA   NA</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-in"><span><span class="co"># Darcy flux</span></span></span>
+<span class="r-in"><span><span class="fu">darcy</span><span class="op">(</span><span class="va">ml</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">150</span>, <span class="fl">0</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">80</span>, <span class="op">-</span><span class="fl">80</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">5</span><span class="op">)</span>, magnitude <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>               qx           qy            qz          q</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1,] 0.000840556 -0.010992156 -0.0006261932 0.01104202</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] 0.013502552  0.003663251 -0.0008415652 0.01401594</span>
 <span class="r-in"><span></span></span>
-<span class="r-in"><span><span class="fu">velocity</span><span class="op">(</span><span class="va">ml</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">50</span>, <span class="fl">0</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">25</span>, <span class="op">-</span><span class="fl">25</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">10</span>, <span class="fl">5</span><span class="op">)</span>, magnitude <span class="op">=</span> <span class="cn">TRUE</span>, R <span class="op">=</span> <span class="fl">5</span><span class="op">)</span></span></span>
-<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>Setting Qz values to NA for z above saturated aquifer level or below aquifer base</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>              vx         vy           vz        v</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1,] 0.02936046 -0.2473726           NA       NA</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] 0.10643688  0.0164757 -0.001766562 0.107719</span>
-<span class="r-in"><span><span class="fu">velocity</span><span class="op">(</span><span class="va">ml</span>, <span class="va">xg</span>, <span class="va">yg</span>, <span class="fl">5</span>, as.grid <span class="op">=</span> <span class="cn">TRUE</span>, R <span class="op">=</span> <span class="fl">5</span><span class="op">)</span></span></span>
-<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>Setting Qz values to NA for z above saturated aquifer level or below aquifer base</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> , , 1, vx</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>            [,1]       [,2]       [,3]         [,4]          [,5]</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1,] 0.03720717 0.04701470 0.05144049   0.02621968 -0.0007083937</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] 0.04441782 0.06621384 0.12721532 -58.35119617 -0.0762653892</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [3,] 0.03892034 0.04932549 0.05418314   0.02771988 -0.0007496139</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> , , 1, vy</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>             [,1]         [,2]        [,3]        [,4]        [,5]</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1,] -0.02689595 -0.037699634 -0.06065810 -0.08323910 -0.06315167</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] -0.02068857 -0.021539862 -0.02312341 -0.07789644 -0.02422640</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [3,] -0.01401304 -0.004026379  0.01845755  0.04089021  0.01930519</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> , , 1, vz</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>               [,1]          [,2]         [,3]         [,4]         [,5]</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1,] -0.0008624020 -0.0010009501 -0.001244860 -0.001387718 -0.001110515</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] -0.0009070699 -0.0011307663 -0.002184328           NA -0.001404998</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [3,] -0.0008725605 -0.0009590558 -0.001066340 -0.001036064 -0.000871419</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-in"><span><span class="co"># Velocity</span></span></span>
+<span class="r-in"><span><span class="fu">velocity</span><span class="op">(</span><span class="va">ml</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">150</span>, <span class="fl">0</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">80</span>, <span class="op">-</span><span class="fl">80</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">5</span><span class="op">)</span>, magnitude <span class="op">=</span> <span class="cn">TRUE</span>, R <span class="op">=</span> <span class="fl">5</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>               vx           vy            vz          v</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1,] 0.000840556 -0.010992156 -0.0006261932 0.01104202</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] 0.013502552  0.003663251 -0.0008415652 0.01401594</span>
+<span class="r-in"><span></span></span>
+<span class="r-in"><span><span class="co"># Complex discharge</span></span></span>
+<span class="r-in"><span><span class="fu">domega</span><span class="op">(</span><span class="va">ml</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">150</span>, <span class="fl">0</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">80</span>, <span class="op">-</span><span class="fl">80</span><span class="op">)</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 0.02037961+0.2665091i 0.32717248-0.0887621i</span>
 <span class="r-in"><span></span></span>
-<span class="r-in"><span><span class="co"># For elements</span></span></span>
-<span class="r-in"><span><span class="fu">domega</span><span class="op">(</span><span class="va">w</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">50</span>, <span class="fl">0</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="op">-</span><span class="fl">25</span>, <span class="fl">25</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 0.0000000-1.2732395i 0.5092958+0.2546479i</span>
+<span class="r-in"><span><span class="co"># Complex discharge for elements</span></span></span>
+<span class="r-in"><span><span class="fu">domega</span><span class="op">(</span><span class="va">w</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">150</span>, <span class="fl">0</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">80</span>, <span class="op">-</span><span class="fl">80</span><span class="op">)</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] -0.1960417+0.1650878i  0.1857511-0.2701835i</span>
 <span class="r-in"><span></span></span>
 </code></pre></div>
     </div>
diff --git a/reference/flow_through_line.html b/reference/flow_through_line.html
index 170a886..316a015 100644
--- a/reference/flow_through_line.html
+++ b/reference/flow_through_line.html
@@ -24,7 +24,7 @@
 <li class="nav-item dropdown">
   <a href="#" class="nav-link dropdown-toggle" data-bs-toggle="dropdown" role="button" aria-expanded="false" aria-haspopup="true" id="dropdown-articles">Articles</a>
   <div class="dropdown-menu" aria-labelledby="dropdown-articles">
-    <a class="dropdown-item" href="../articles/overview.html">An overview</a>
+    <a class="dropdown-item" href="../articles/overview.html">An Overview</a>
   </div>
 </li>
       </ul><form class="form-inline my-2 my-lg-0" role="search">
diff --git a/reference/head_to_potential.html b/reference/head_to_potential.html
index 3763e10..ffadf4f 100644
--- a/reference/head_to_potential.html
+++ b/reference/head_to_potential.html
@@ -26,7 +26,7 @@
 <li class="nav-item dropdown">
   <a href="#" class="nav-link dropdown-toggle" data-bs-toggle="dropdown" role="button" aria-expanded="false" aria-haspopup="true" id="dropdown-articles">Articles</a>
   <div class="dropdown-menu" aria-labelledby="dropdown-articles">
-    <a class="dropdown-item" href="../articles/overview.html">An overview</a>
+    <a class="dropdown-item" href="../articles/overview.html">An Overview</a>
   </div>
 </li>
       </ul><form class="form-inline my-2 my-lg-0" role="search">
diff --git a/reference/headareasink.html b/reference/headareasink.html
index f63f1ea..663c48f 100644
--- a/reference/headareasink.html
+++ b/reference/headareasink.html
@@ -26,7 +26,7 @@
 <li class="nav-item dropdown">
   <a href="#" class="nav-link dropdown-toggle" data-bs-toggle="dropdown" role="button" aria-expanded="false" aria-haspopup="true" id="dropdown-articles">Articles</a>
   <div class="dropdown-menu" aria-labelledby="dropdown-articles">
-    <a class="dropdown-item" href="../articles/overview.html">An overview</a>
+    <a class="dropdown-item" href="../articles/overview.html">An Overview</a>
   </div>
 </li>
       </ul><form class="form-inline my-2 my-lg-0" role="search">
diff --git a/reference/headlinesink.html b/reference/headlinesink.html
index 034bc39..004418d 100644
--- a/reference/headlinesink.html
+++ b/reference/headlinesink.html
@@ -26,7 +26,7 @@
 <li class="nav-item dropdown">
   <a href="#" class="nav-link dropdown-toggle" data-bs-toggle="dropdown" role="button" aria-expanded="false" aria-haspopup="true" id="dropdown-articles">Articles</a>
   <div class="dropdown-menu" aria-labelledby="dropdown-articles">
-    <a class="dropdown-item" href="../articles/overview.html">An overview</a>
+    <a class="dropdown-item" href="../articles/overview.html">An Overview</a>
   </div>
 </li>
       </ul><form class="form-inline my-2 my-lg-0" role="search">
diff --git a/reference/headwell.html b/reference/headwell.html
index c82d6ff..268cf2f 100644
--- a/reference/headwell.html
+++ b/reference/headwell.html
@@ -28,7 +28,7 @@
 <li class="nav-item dropdown">
   <a href="#" class="nav-link dropdown-toggle" data-bs-toggle="dropdown" role="button" aria-expanded="false" aria-haspopup="true" id="dropdown-articles">Articles</a>
   <div class="dropdown-menu" aria-labelledby="dropdown-articles">
-    <a class="dropdown-item" href="../articles/overview.html">An overview</a>
+    <a class="dropdown-item" href="../articles/overview.html">An Overview</a>
   </div>
 </li>
       </ul><form class="form-inline my-2 my-lg-0" role="search">
diff --git a/reference/index.html b/reference/index.html
index a5fd69f..ab34a52 100644
--- a/reference/index.html
+++ b/reference/index.html
@@ -24,7 +24,7 @@
 <li class="nav-item dropdown">
   <a href="#" class="nav-link dropdown-toggle" data-bs-toggle="dropdown" role="button" aria-expanded="false" aria-haspopup="true" id="dropdown-articles">Articles</a>
   <div class="dropdown-menu" aria-labelledby="dropdown-articles">
-    <a class="dropdown-item" href="../articles/overview.html">An overview</a>
+    <a class="dropdown-item" href="../articles/overview.html">An Overview</a>
   </div>
 </li>
       </ul><form class="form-inline my-2 my-lg-0" role="search">
@@ -99,7 +99,7 @@ <h2 id="all-functions">All functions<a class="anchor" aria-label="anchor" href="
         <dd>Get the discharge in or out of the aquifer from an element</dd>
       </dl><dl><dt>
           
-          <code><a href="flow.html">domega()</a></code> <code><a href="flow.html">discharge()</a></code> <code><a href="flow.html">darcy()</a></code> <code><a href="flow.html">velocity()</a></code> 
+          <code><a href="flow.html">discharge()</a></code> <code><a href="flow.html">darcy()</a></code> <code><a href="flow.html">velocity()</a></code> <code><a href="flow.html">domega()</a></code> 
         </dt>
         <dd>Calculate flow variables</dd>
       </dl><dl><dt>
@@ -139,7 +139,7 @@ <h2 id="all-functions">All functions<a class="anchor" aria-label="anchor" href="
         <dd>Compute the saturated thickness</dd>
       </dl><dl><dt>
           
-          <code><a href="state-variables.html">omega()</a></code> <code><a href="state-variables.html">potential()</a></code> <code><a href="state-variables.html">streamfunction()</a></code> <code><a href="state-variables.html">heads()</a></code> 
+          <code><a href="state-variables.html">heads()</a></code> <code><a href="state-variables.html">omega()</a></code> <code><a href="state-variables.html">potential()</a></code> <code><a href="state-variables.html">streamfunction()</a></code> 
         </dt>
         <dd>Calculate state-variables</dd>
       </dl><dl><dt>
diff --git a/reference/linesink.html b/reference/linesink.html
index 0885633..fd43655 100644
--- a/reference/linesink.html
+++ b/reference/linesink.html
@@ -24,7 +24,7 @@
 <li class="nav-item dropdown">
   <a href="#" class="nav-link dropdown-toggle" data-bs-toggle="dropdown" role="button" aria-expanded="false" aria-haspopup="true" id="dropdown-articles">Articles</a>
   <div class="dropdown-menu" aria-labelledby="dropdown-articles">
-    <a class="dropdown-item" href="../articles/overview.html">An overview</a>
+    <a class="dropdown-item" href="../articles/overview.html">An Overview</a>
   </div>
 </li>
       </ul><form class="form-inline my-2 my-lg-0" role="search">
diff --git a/reference/satthick.html b/reference/satthick.html
index 1da4d1f..0a427e8 100644
--- a/reference/satthick.html
+++ b/reference/satthick.html
@@ -26,7 +26,7 @@
 <li class="nav-item dropdown">
   <a href="#" class="nav-link dropdown-toggle" data-bs-toggle="dropdown" role="button" aria-expanded="false" aria-haspopup="true" id="dropdown-articles">Articles</a>
   <div class="dropdown-menu" aria-labelledby="dropdown-articles">
-    <a class="dropdown-item" href="../articles/overview.html">An overview</a>
+    <a class="dropdown-item" href="../articles/overview.html">An Overview</a>
   </div>
 </li>
       </ul><form class="form-inline my-2 my-lg-0" role="search">
diff --git a/reference/state-variables.html b/reference/state-variables.html
index 56500fd..867c28a 100644
--- a/reference/state-variables.html
+++ b/reference/state-variables.html
@@ -1,17 +1,17 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><meta name="description" content="omega() computes the complex potential for an aem or element object
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><meta name="description" content="heads() computes the hydraulic head at the given x and y coordinates for an aem object.
+omega() computes the complex potential for an aem or element object
 at the given x and y coordinates.
 potential() computes the discharge potential for an aem or element object
 at the given x and y coordinates.
-streamfunction() computes the streamfunction for an aem or element object
-at the given x and y coordinates.
-heads() computes the hydraulic head at the given x and y coordinates."><title>Calculate state-variables — state-variables • raem</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- bootstrap-toc --><script src="https://cdn.jsdelivr.net/gh/afeld/bootstrap-toc@v1.0.1/dist/bootstrap-toc.min.js" integrity="sha256-4veVQbu7//Lk5TSmc7YV48MxtMy98e26cf5MrgZYnwo=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.11/clipboard.min.js" integrity="sha512-7O5pXpc0oCRrxk8RUfDYFgn0nO1t+jLuIOQdOMRp4APB7uZ4vSjspzp5y6YDtDs4VzUSTbWzBFZ/LKJhnyFOKw==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><!-- search --><script src="https://cdnjs.cloudflare.com/ajax/libs/fuse.js/6.4.6/fuse.js" integrity="sha512-zv6Ywkjyktsohkbp9bb45V6tEMoWhzFzXis+LrMehmJZZSys19Yxf1dopHx7WzIKxr5tK2dVcYmaCk2uqdjF4A==" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/autocomplete.js/0.38.0/autocomplete.jquery.min.js" integrity="sha512-GU9ayf+66Xx2TmpxqJpliWbT5PiGYxpaG8rfnBEk1LL8l1KGkRShhngwdXK1UgqhAzWpZHSiYPc09/NwDQIGyg==" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mark.js/8.11.1/mark.min.js" integrity="sha512-5CYOlHXGh6QpOFA/TeTylKLWfB3ftPsde7AnmhuitiTX4K5SqCLBeKro6sPS8ilsz1Q4NRx3v8Ko2IBiszzdww==" crossorigin="anonymous"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate state-variables — state-variables"><meta property="og:description" content="omega() computes the complex potential for an aem or element object
+streamfunction() computes the stream function for an aem or element object
+at the given x and y coordinates."><title>Calculate state-variables — state-variables • raem</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- bootstrap-toc --><script src="https://cdn.jsdelivr.net/gh/afeld/bootstrap-toc@v1.0.1/dist/bootstrap-toc.min.js" integrity="sha256-4veVQbu7//Lk5TSmc7YV48MxtMy98e26cf5MrgZYnwo=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.11/clipboard.min.js" integrity="sha512-7O5pXpc0oCRrxk8RUfDYFgn0nO1t+jLuIOQdOMRp4APB7uZ4vSjspzp5y6YDtDs4VzUSTbWzBFZ/LKJhnyFOKw==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><!-- search --><script src="https://cdnjs.cloudflare.com/ajax/libs/fuse.js/6.4.6/fuse.js" integrity="sha512-zv6Ywkjyktsohkbp9bb45V6tEMoWhzFzXis+LrMehmJZZSys19Yxf1dopHx7WzIKxr5tK2dVcYmaCk2uqdjF4A==" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/autocomplete.js/0.38.0/autocomplete.jquery.min.js" integrity="sha512-GU9ayf+66Xx2TmpxqJpliWbT5PiGYxpaG8rfnBEk1LL8l1KGkRShhngwdXK1UgqhAzWpZHSiYPc09/NwDQIGyg==" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mark.js/8.11.1/mark.min.js" integrity="sha512-5CYOlHXGh6QpOFA/TeTylKLWfB3ftPsde7AnmhuitiTX4K5SqCLBeKro6sPS8ilsz1Q4NRx3v8Ko2IBiszzdww==" crossorigin="anonymous"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate state-variables — state-variables"><meta property="og:description" content="heads() computes the hydraulic head at the given x and y coordinates for an aem object.
+omega() computes the complex potential for an aem or element object
 at the given x and y coordinates.
 potential() computes the discharge potential for an aem or element object
 at the given x and y coordinates.
-streamfunction() computes the streamfunction for an aem or element object
-at the given x and y coordinates.
-heads() computes the hydraulic head at the given x and y coordinates."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
+streamfunction() computes the stream function for an aem or element object
+at the given x and y coordinates."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
 <script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script>
 <script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
 <![endif]--></head><body>
@@ -36,7 +36,7 @@
 <li class="nav-item dropdown">
   <a href="#" class="nav-link dropdown-toggle" data-bs-toggle="dropdown" role="button" aria-expanded="false" aria-haspopup="true" id="dropdown-articles">Articles</a>
   <div class="dropdown-menu" aria-labelledby="dropdown-articles">
-    <a class="dropdown-item" href="../articles/overview.html">An overview</a>
+    <a class="dropdown-item" href="../articles/overview.html">An Overview</a>
   </div>
 </li>
       </ul><form class="form-inline my-2 my-lg-0" role="search">
@@ -61,18 +61,20 @@
     </div>
 
     <div class="ref-description section level2">
-    <p><code>omega()</code> computes the complex potential for an <code>aem</code> or <code>element</code> object
+    <p><code>heads()</code> computes the hydraulic head at the given x and y coordinates for an <code>aem</code> object.</p>
+<p><code>omega()</code> computes the complex potential for an <code>aem</code> or <code>element</code> object
 at the given x and y coordinates.</p>
 <p><code>potential()</code> computes the discharge potential for an <code>aem</code> or <code>element</code> object
 at the given x and y coordinates.</p>
-<p><code>streamfunction()</code> computes the streamfunction for an <code>aem</code> or <code>element</code> object
+<p><code>streamfunction()</code> computes the stream function for an <code>aem</code> or <code>element</code> object
 at the given x and y coordinates.</p>
-<p><code>heads()</code> computes the hydraulic head at the given x and y coordinates.</p>
     </div>
 
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
-    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">omega</span><span class="op">(</span><span class="va">...</span><span class="op">)</span></span>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">heads</span><span class="op">(</span><span class="va">aem</span>, <span class="va">x</span>, <span class="va">y</span>, as.grid <span class="op">=</span> <span class="cn">FALSE</span>, na.below <span class="op">=</span> <span class="cn">TRUE</span>, <span class="va">...</span><span class="op">)</span></span>
+<span></span>
+<span><span class="fu">omega</span><span class="op">(</span><span class="va">...</span><span class="op">)</span></span>
 <span></span>
 <span><span class="fu">potential</span><span class="op">(</span><span class="va">...</span><span class="op">)</span></span>
 <span></span>
@@ -94,18 +96,12 @@ <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage">
 <span><span class="fu">potential</span><span class="op">(</span><span class="va">element</span>, <span class="va">x</span>, <span class="va">y</span>, <span class="va">...</span><span class="op">)</span></span>
 <span></span>
 <span><span class="co"># S3 method for element</span></span>
-<span><span class="fu">streamfunction</span><span class="op">(</span><span class="va">element</span>, <span class="va">x</span>, <span class="va">y</span>, <span class="va">...</span><span class="op">)</span></span>
-<span></span>
-<span><span class="fu">heads</span><span class="op">(</span><span class="va">aem</span>, <span class="va">x</span>, <span class="va">y</span>, as.grid <span class="op">=</span> <span class="cn">FALSE</span>, na.below <span class="op">=</span> <span class="cn">TRUE</span>, <span class="va">...</span><span class="op">)</span></span></code></pre></div>
+<span><span class="fu">streamfunction</span><span class="op">(</span><span class="va">element</span>, <span class="va">x</span>, <span class="va">y</span>, <span class="va">...</span><span class="op">)</span></span></code></pre></div>
     </div>
 
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
-    <dl><dt>...</dt>
-<dd><p>ignored</p></dd>
-
-
-<dt>aem</dt>
+    <dl><dt>aem</dt>
 <dd><p><code>aem</code> object</p></dd>
 
 
@@ -121,18 +117,26 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 <dd><p>logical, should a matrix of dimensions c(<code>length(y), length(x)</code>) be returned? Defaults to <code>FALSE</code>.</p></dd>
 
 
-<dt>element</dt>
-<dd><p>analytic element of class <code>element</code></p></dd>
-
-
 <dt>na.below</dt>
 <dd><p>logical indicating if calculated head values below the aquifer base should be set to <code>NA</code>. Defaults to <code>TRUE</code>. See <code><a href="head_to_potential.html">potential_to_head()</a></code>.</p></dd>
 
+
+<dt>...</dt>
+<dd><p>ignored</p></dd>
+
+
+<dt>element</dt>
+<dd><p>analytic element of class <code>element</code></p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
     
 
+<p>For <code>heads()</code>, the same as for <code>omega()</code> but containing the hydraulic head values
+evaluated at <code>x</code> and <code>y</code>, which are computed from <code>potential()</code> and the aquifer parameters using <code><a href="head_to_potential.html">potential_to_head()</a></code>.</p>
+
+
 <p>For <code>omega()</code>, a vector of <code>length(x)</code> (equal to <code>length(y)</code>) with the complex potential values at <code>x</code> and <code>y</code>.
 If <code>as.grid = TRUE</code>, a matrix of dimensions <code>c(length(y), length(x))</code> described by
 marginal vectors <code>x</code> and <code>y</code> containing the complex potential values at the grid points.</p>
@@ -142,12 +146,8 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
 evaluated at <code>x</code> and <code>y</code>, which are the real components of <code>omega()</code>.</p>
 
 
-<p>For <code>streamfunction()</code>, the same as for <code>omega()</code> but containing the streamfunction values
+<p>For <code>streamfunction()</code>, the same as for <code>omega()</code> but containing the stream function values
 evaluated at <code>x</code> and <code>y</code>, which are the imaginary components of <code>omega()</code>.</p>
-
-
-<p>For <code>heads()</code>, the same as for <code>omega()</code> but containing the hydraulic head values
-evaluated at <code>x</code> and <code>y</code>, which are computed from <code>potential()</code> and the aquifer parameters using <code><a href="head_to_potential.html">potential_to_head()</a></code>.</p>
     </div>
     <div class="section level2">
     <h2 id="details">Details<a class="anchor" aria-label="anchor" href="#details"></a></h2>
@@ -160,60 +160,22 @@ <h2 id="see-also">See also<a class="anchor" aria-label="anchor" href="#see-also"
 
     <div class="section level2">
     <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
-    <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span></span></span>
-<span class="r-in"><span><span class="va">w</span> <span class="op">&lt;-</span> <span class="fu"><a href="well.html">well</a></span><span class="op">(</span>xw <span class="op">=</span> <span class="fl">50</span>, yw <span class="op">=</span> <span class="fl">0</span>, Q <span class="op">=</span> <span class="fl">200</span><span class="op">)</span></span></span>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="va">w</span> <span class="op">&lt;-</span> <span class="fu"><a href="well.html">well</a></span><span class="op">(</span>xw <span class="op">=</span> <span class="fl">55</span>, yw <span class="op">=</span> <span class="fl">0</span>, Q <span class="op">=</span> <span class="fl">200</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="va">uf</span> <span class="op">&lt;-</span> <span class="fu"><a href="uniformflow.html">uniformflow</a></span><span class="op">(</span>gradient <span class="op">=</span> <span class="fl">0.002</span>, angle <span class="op">=</span> <span class="op">-</span><span class="fl">45</span>, TR <span class="op">=</span> <span class="fl">100</span><span class="op">)</span></span></span>
-<span class="r-in"><span><span class="va">ml</span> <span class="op">&lt;-</span> <span class="fu"><a href="aem.html">aem</a></span><span class="op">(</span>k <span class="op">=</span> <span class="fl">10</span>, top <span class="op">=</span> <span class="fl">10</span>, base <span class="op">=</span> <span class="fl">0</span>, n <span class="op">=</span> <span class="fl">0.2</span>, <span class="va">w</span>, <span class="va">uf</span><span class="op">)</span></span></span>
-<span class="r-in"><span></span></span>
-<span class="r-in"><span><span class="fu">omega</span><span class="op">(</span><span class="va">ml</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">50</span>, <span class="fl">0</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">25</span>, <span class="op">-</span><span class="fl">25</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1]  98.92447+39.3934i 124.53947-81.7061i</span>
+<span class="r-in"><span><span class="va">rf</span> <span class="op">&lt;-</span> <span class="fu"><a href="constant.html">constant</a></span><span class="op">(</span>xc <span class="op">=</span> <span class="op">-</span><span class="fl">1000</span>, yc <span class="op">=</span> <span class="fl">1000</span>, hc <span class="op">=</span> <span class="fl">10</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="va">ml</span> <span class="op">&lt;-</span> <span class="fu"><a href="aem.html">aem</a></span><span class="op">(</span>k <span class="op">=</span> <span class="fl">10</span>, top <span class="op">=</span> <span class="fl">10</span>, base <span class="op">=</span> <span class="op">-</span><span class="fl">15</span>, n <span class="op">=</span> <span class="fl">0.2</span>, <span class="va">w</span>, <span class="va">uf</span>, <span class="va">rf</span><span class="op">)</span></span></span>
 <span class="r-in"><span></span></span>
 <span class="r-in"><span><span class="va">xg</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/seq.html" class="external-link">seq</a></span><span class="op">(</span><span class="op">-</span><span class="fl">100</span>, <span class="fl">100</span>, length <span class="op">=</span> <span class="fl">5</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="va">yg</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/seq.html" class="external-link">seq</a></span><span class="op">(</span><span class="op">-</span><span class="fl">75</span>, <span class="fl">75</span>, length <span class="op">=</span> <span class="fl">3</span><span class="op">)</span></span></span>
-<span class="r-in"><span><span class="fu">omega</span><span class="op">(</span><span class="va">ml</span>, <span class="va">xg</span>, <span class="va">yg</span>, as.grid <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>                     [,1]                [,2]               [,3]</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1,] 187.7937+ 88.77717i 171.3677+ 75.98119i 153.8890+ 58.1101i</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] 173.6356+114.14214i 153.6582+107.07107i 124.5236+100.0000i</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [3,] 166.5804- 60.49290i 150.1545- 61.83905i 132.6758- 58.1101i</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>                      [,4]                [,5]</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1,] 140.96545+32.322330i 139.7469+ 6.534558i</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] -45.39471- 7.071068i 110.3814-14.142136i</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [3,] 119.75225-46.464466i 118.5337-34.818830i</span>
-<span class="r-in"><span></span></span>
-<span class="r-in"><span><span class="fu">potential</span><span class="op">(</span><span class="va">ml</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">50</span>, <span class="fl">0</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">25</span>, <span class="op">-</span><span class="fl">25</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1]  98.92447 124.53947</span>
-<span class="r-in"><span><span class="fu">potential</span><span class="op">(</span><span class="va">ml</span>, <span class="va">xg</span>, <span class="va">yg</span>, as.grid <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>          [,1]     [,2]     [,3]      [,4]     [,5]</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1,] 187.7937 171.3677 153.8890 140.96545 139.7469</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] 173.6356 153.6582 124.5236 -45.39471 110.3814</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [3,] 166.5804 150.1545 132.6758 119.75225 118.5337</span>
-<span class="r-in"><span></span></span>
-<span class="r-in"><span><span class="fu">streamfunction</span><span class="op">(</span><span class="va">ml</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">50</span>, <span class="fl">0</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">25</span>, <span class="op">-</span><span class="fl">25</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1]  39.3934 -81.7061</span>
-<span class="r-in"><span><span class="fu">streamfunction</span><span class="op">(</span><span class="va">ml</span>, <span class="va">xg</span>, <span class="va">yg</span>, as.grid <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span>           [,1]      [,2]     [,3]       [,4]       [,5]</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1,]  88.77717  75.98119  58.1101  32.322330   6.534558</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] 114.14214 107.07107 100.0000  -7.071068 -14.142136</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [3,] -60.49290 -61.83905 -58.1101 -46.464466 -34.818830</span>
-<span class="r-in"><span></span></span>
-<span class="r-in"><span><span class="co"># For elements</span></span></span>
-<span class="r-in"><span><span class="fu">omega</span><span class="op">(</span><span class="va">w</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">50</span>, <span class="fl">0</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="op">-</span><span class="fl">25</span>, <span class="fl">25</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 102.460-50.00000i 128.075+85.24164i</span>
-<span class="r-in"><span></span></span>
-<span class="r-in"><span><span class="fu">potential</span><span class="op">(</span><span class="va">w</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">50</span>, <span class="fl">0</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="op">-</span><span class="fl">25</span>, <span class="fl">25</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 102.460 128.075</span>
-<span class="r-in"><span></span></span>
-<span class="r-in"><span><span class="fu">streamfunction</span><span class="op">(</span><span class="va">w</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">50</span>, <span class="fl">0</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="op">-</span><span class="fl">25</span>, <span class="fl">25</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1] -50.00000  85.24164</span>
 <span class="r-in"><span></span></span>
+<span class="r-in"><span><span class="co"># Hydraulic heads</span></span></span>
 <span class="r-in"><span><span class="fu">heads</span><span class="op">(</span><span class="va">ml</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">50</span>, <span class="fl">0</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">25</span>, <span class="op">-</span><span class="fl">25</span><span class="op">)</span><span class="op">)</span></span></span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 4.448021 4.990781</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 8.280544 8.398209</span>
 <span class="r-in"><span><span class="fu">heads</span><span class="op">(</span><span class="va">ml</span>, <span class="va">xg</span>, <span class="va">yg</span>, as.grid <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
-<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>NaNs produced</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>          [,1]     [,2]     [,3]     [,4]     [,5]</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [1,] 6.128518 5.854360 5.547775 5.309717 5.286717</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] 5.892972 5.543612 4.990462      NaN 4.698541</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> [3,] 5.772009 5.480045 5.151230 4.893920 4.868957</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1,] 8.660110 8.591307 8.517038 8.458073 8.448488</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [2,] 8.601056 8.518423 8.400544 8.041392 8.312647</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [3,] 8.570281 8.501215 8.426661 8.367468 8.357846</span>
 <span class="r-in"><span></span></span>
 <span class="r-in"><span><span class="co"># do not confuse heads() with utils::head, which will give an error</span></span></span>
 <span class="r-in"><span><span class="kw"><a href="https://rdrr.io/r/base/try.html" class="external-link">try</a></span><span class="op">(</span></span></span>
@@ -222,6 +184,28 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-out co"><span class="r-pr">#&gt;</span> Error in head.default(ml, c(50, 0), c(25, -25)) : </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>   invalid 'n' - must have length one when dim(x) is NULL, got 2</span>
 <span class="r-in"><span></span></span>
+<span class="r-in"><span><span class="co"># Complex potential</span></span></span>
+<span class="r-in"><span><span class="fu">omega</span><span class="op">(</span><span class="va">ml</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">50</span>, <span class="fl">0</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">25</span>, <span class="op">-</span><span class="fl">25</span><span class="op">)</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 2709.919+45.67669i 2737.381-82.88449i</span>
+<span class="r-in"><span></span></span>
+<span class="r-in"><span><span class="co"># Discharge potential</span></span></span>
+<span class="r-in"><span><span class="fu">potential</span><span class="op">(</span><span class="va">ml</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">50</span>, <span class="fl">0</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">25</span>, <span class="op">-</span><span class="fl">25</span><span class="op">)</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 2709.919 2737.381</span>
+<span class="r-in"><span></span></span>
+<span class="r-in"><span><span class="co"># Stream function</span></span></span>
+<span class="r-in"><span><span class="fu">streamfunction</span><span class="op">(</span><span class="va">ml</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">50</span>, <span class="fl">0</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">25</span>, <span class="op">-</span><span class="fl">25</span><span class="op">)</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1]  45.67669 -82.88449</span>
+<span class="r-in"><span></span></span>
+<span class="r-in"><span><span class="co"># For elements</span></span></span>
+<span class="r-in"><span><span class="fu">omega</span><span class="op">(</span><span class="va">w</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">50</span>, <span class="fl">0</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="op">-</span><span class="fl">25</span>, <span class="fl">25</span><span class="op">)</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 103.0842-56.28330i 130.5466+86.42003i</span>
+<span class="r-in"><span></span></span>
+<span class="r-in"><span><span class="fu">potential</span><span class="op">(</span><span class="va">w</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">50</span>, <span class="fl">0</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="op">-</span><span class="fl">25</span>, <span class="fl">25</span><span class="op">)</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 103.0842 130.5466</span>
+<span class="r-in"><span></span></span>
+<span class="r-in"><span><span class="fu">streamfunction</span><span class="op">(</span><span class="va">w</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">50</span>, <span class="fl">0</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="op">-</span><span class="fl">25</span>, <span class="fl">25</span><span class="op">)</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] -56.28330  86.42003</span>
+<span class="r-in"><span></span></span>
 </code></pre></div>
     </div>
   </main><aside class="col-md-3"><nav id="toc"><h2>On this page</h2>
diff --git a/reference/tracelines.html b/reference/tracelines.html
index 81671a6..1b7da25 100644
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+++ b/reference/tracelines.html
@@ -30,7 +30,7 @@
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diff --git a/reference/uniformflow.html b/reference/uniformflow.html
index 03237ca..e6dd0b7 100644
--- a/reference/uniformflow.html
+++ b/reference/uniformflow.html
@@ -24,7 +24,7 @@
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diff --git a/reference/well.html b/reference/well.html
index 9e744a2..41aecbf 100644
--- a/reference/well.html
+++ b/reference/well.html
@@ -24,7 +24,7 @@
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diff --git a/search.json b/search.json
index 6a0699a..3e19f26 100644
--- a/search.json
+++ b/search.json
@@ -1 +1 @@
-[{"path":"https://cneyens.github.io/raem/LICENSE.html","id":null,"dir":"","previous_headings":"","what":"MIT License","title":"MIT License","text":"Copyright (c) 2023 raem authors Permission hereby granted, free charge, person obtaining copy software associated documentation files (“Software”), deal Software without restriction, including without limitation rights use, copy, modify, merge, publish, distribute, sublicense, /sell copies Software, permit persons Software furnished , subject following conditions: copyright notice permission notice shall included copies substantial portions Software. SOFTWARE PROVIDED “”, WITHOUT WARRANTY KIND, EXPRESS IMPLIED, INCLUDING LIMITED WARRANTIES MERCHANTABILITY, FITNESS PARTICULAR PURPOSE NONINFRINGEMENT. EVENT SHALL AUTHORS COPYRIGHT HOLDERS LIABLE CLAIM, DAMAGES LIABILITY, WHETHER ACTION CONTRACT, TORT OTHERWISE, ARISING , CONNECTION SOFTWARE USE DEALINGS SOFTWARE.","code":""},{"path":"https://cneyens.github.io/raem/articles/overview.html","id":"introduction-to-analytic-element-modeling","dir":"Articles","previous_headings":"","what":"Introduction to analytic element modeling","title":"An overview","text":"First developed Otto Strack Henk Haitjema late 1970’s, analytic element modeling (AEM) approach solves groundwater flow problem superimposing solutions features wells, streams recharge. feature called element. governing equation : main assumption based Dupuit-Forchheimer approximation, states reduces governing equation : described steady-state, single-layer two-dimensional flow \\(x-y\\) plane. aquifer phreatic, saturated thickness variable, renders equation X non-linear solving \\(h\\). Therefore, discharge potential \\(\\Phi\\) introduced: equation X becomes: linear equation can solved \\(\\Phi\\). resulting hydraulic heads can computed : addition discharge potential \\(\\Phi\\), exists streamfunction \\(\\Psi\\) defined : \\(\\Psi\\) defined Laplace equation. areal recharge applied using area-sinks (see paragraph Area-sink ), equation follows Poisson equation \\(\\Psi\\) longer meaningful. \\(\\Phi\\) \\(\\Psi\\) fulfill Cauchy-Riemann conditions, can combined complex discharge potential \\(\\Omega\\): whose real imaginary terms \\(\\Phi\\) \\(\\Psi\\), respectively. flow problem solved terms \\(\\Omega\\), yields \\(\\Phi\\) eventually \\(h\\). element gives solution governing flow equation terms \\(\\Omega\\), superimposed space. Since solution given element depends results elements, complete system equations needs solved simultaneously. done setting matrix formulation equation X form \\(Ax=b\\), solved. complete overview analytic element modeling, reader referred ","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/articles/overview.html","id":"well","dir":"Articles","previous_headings":"Elements","what":"Well","title":"An overview","text":"","code":"library(raem)"},{"path":[]},{"path":[]},{"path":[]},{"path":[]},{"path":[]},{"path":[]},{"path":[]},{"path":[]},{"path":"https://cneyens.github.io/raem/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"Cas Neyens. Author, maintainer.","code":""},{"path":"https://cneyens.github.io/raem/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"Neyens C (2024). raem: Analytic Element Modeling Steady Single-Layer Groundwater Flow. R package version 0.0.0.9000, https://cneyens.github.io/raem/, https://github.com/cneyens/raem.","code":"@Manual{,   title = {raem: Analytic Element Modeling of Steady Single-Layer Groundwater Flow},   author = {Cas Neyens},   year = {2024},   note = {R package version 0.0.0.9000, https://cneyens.github.io/raem/},   url = {https://github.com/cneyens/raem}, }"},{"path":"https://cneyens.github.io/raem/index.html","id":"raem","dir":"","previous_headings":"","what":"Analytic Element Modeling of Steady Single-Layer Groundwater Flow","title":"Analytic Element Modeling of Steady Single-Layer Groundwater Flow","text":"raem R package modeling steady-state single-layer groundwater flow Dupuit-Forchheimer assumption using analytic elements.","code":""},{"path":"https://cneyens.github.io/raem/index.html","id":"installation","dir":"","previous_headings":"","what":"Installation","title":"Analytic Element Modeling of Steady Single-Layer Groundwater Flow","text":"can install development version raem GitHub :","code":"# install.packages(\"devtools\") devtools::install_github(\"cneyens/raem\")"},{"path":"https://cneyens.github.io/raem/index.html","id":"example","dir":"","previous_headings":"","what":"Example","title":"Analytic Element Modeling of Steady Single-Layer Groundwater Flow","text":"Construct analytic element model aquifer uniform background flow, two extraction wells reference point. Specify aquifer parameters create elements: Create model. automatically solves system equations. Find head discharge two locations x = -200, y = 200 x = 100, y = 200. Note vertical flow components model: Plot head contours element locations. First, specify contouring grid: Now plot:  Compute particle traces starting along y = 200 20 intervals per year 5 years add plot:","code":"library(raem)  k = 10 top = 10 base = 0 n = 0.2  hr = 15 # head at reference point, above aquifer top TR = k * (top - base) # constant transmissivity of background flow  uf = uniformflow(TR, gradient = 0.001, angle = -45) rf = constant(xc = -1000, yc = 0, hc = hr) w1 = well(xw = 200, yw = 0, Q = 250) w2 = well(xw = -200, yw = -150, Q = 400) m = aem(k = k, top = top, base = base, n = n,          uf, rf, w1, w2) heads(m, x = c(-200, 100), y = 200) #> [1] 13.64573 13.33314 discharge(m, c(-200, 100), 200, z = top) # [L^2 / T] #>              Qx         Qy Qz #> [1,] 0.15028815 -0.2923908  0 #> [2,] 0.06041242 -0.3347206  0 xg = seq(-500, 500, length = 100) yg = seq(-250, 250, length = 100) contours(m, xg, yg, 'heads', col = 'dodgerblue', nlevels = 20) plot(m, add = TRUE) paths = tracelines(m, x0 = seq(-450, 450, 50), y0 = 200, z0 = top, times = seq(0, 5*365, 365/20)) plot(paths, add = TRUE, col = 'orange')"},{"path":"https://cneyens.github.io/raem/reference/add_element.html","id":null,"dir":"Reference","previous_headings":"","what":"Add element to existing aem object — add_element","title":"Add element to existing aem object — add_element","text":"Add element existing aem object","code":""},{"path":"https://cneyens.github.io/raem/reference/add_element.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Add element to existing aem object — add_element","text":"","code":"add_element(aem, element, name = NULL, solve = FALSE, ...)"},{"path":"https://cneyens.github.io/raem/reference/add_element.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Add element to existing aem object — add_element","text":"aem aem object element analytic element class element name optional name element character. Duplicate names aem allowed. solve logical, model solved adding new element? Defaults FALSE. ... ignored","code":""},{"path":"https://cneyens.github.io/raem/reference/add_element.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Add element to existing aem object — add_element","text":"aem model addition element. solve = TRUE, model solved using solve.aem(). name element taken name argument, object name set element_1 1 index new element element list. See examples.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/add_element.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Add element to existing aem object — add_element","text":"","code":"m <- aem(k = 10, top = 10, base = 0, n = 0.2) add_element(m, constant(xc = 0, yc = 1000, hc = 12), name = 'rf') #> $k #> [1] 10 #>  #> $top #> [1] 10 #>  #> $base #> [1] 0 #>  #> $n #> [1] 0.2 #>  #> $elements #> $elements$rf #> $parameter #> [1] 0 #>  #> $nunknowns #> [1] 1 #>  #> $xc #> [1] 0 #>  #> $yc #> [1] 1000 #>  #> $hc #> [1] 12 #>  #> attr(,\"class\") #> [1] \"constant\" \"element\"  #>  #>  #> $type #> [1] \"variable\" #>  #> $solved #> [1] FALSE #>  #> attr(,\"class\") #> [1] \"aem\"  # if name not supplied, tries to obtain it from object name rf <- constant(xc = 0, yc = 1000, hc = 12) add_element(m, rf) #> $k #> [1] 10 #>  #> $top #> [1] 10 #>  #> $base #> [1] 0 #>  #> $n #> [1] 0.2 #>  #> $elements #> $elements$rf #> $parameter #> [1] 0 #>  #> $nunknowns #> [1] 1 #>  #> $xc #> [1] 0 #>  #> $yc #> [1] 1000 #>  #> $hc #> [1] 12 #>  #> attr(,\"class\") #> [1] \"constant\" \"element\"  #>  #>  #> $type #> [1] \"variable\" #>  #> $solved #> [1] FALSE #>  #> attr(,\"class\") #> [1] \"aem\"  # or else sets it sequentially from number of elements add_element(m, constant(xc = 0, yc = 1000, hc = 12)) #> $k #> [1] 10 #>  #> $top #> [1] 10 #>  #> $base #> [1] 0 #>  #> $n #> [1] 0.2 #>  #> $elements #> $elements$element_1 #> $parameter #> [1] 0 #>  #> $nunknowns #> [1] 1 #>  #> $xc #> [1] 0 #>  #> $yc #> [1] 1000 #>  #> $hc #> [1] 12 #>  #> attr(,\"class\") #> [1] \"constant\" \"element\"  #>  #>  #> $type #> [1] \"variable\" #>  #> $solved #> [1] FALSE #>  #> attr(,\"class\") #> [1] \"aem\" # add_element() is pipe-friendly aem(k = 10, top = 10, base = 0, n = 0.2) |>     add_element(rf, name = 'rf') |>     add_element(headwell(xw = 0, yw = 100, rw = 0.3, hc = 8),                 name = 'headwell', solve = TRUE) #> $k #> [1] 10 #>  #> $top #> [1] 10 #>  #> $base #> [1] 0 #>  #> $n #> [1] 0.2 #>  #> $elements #> $elements$rf #> $parameter #> [1] 377.1432 #>  #> $nunknowns #> [1] 1 #>  #> $xc #> [1] 0 #>  #> $yc #> [1] 1000 #>  #> $hc #> [1] 12 #>  #> attr(,\"class\") #> [1] \"constant\" \"element\"  #>  #> $elements$headwell #> $parameter #> [1] 298.2139 #>  #> $nunknowns #> [1] 1 #>  #> $zetaw #> [1] 0+100i #>  #> $rw #> [1] 0.3 #>  #> $xc #> [1] 0.3 #>  #> $yc #> [1] 100 #>  #> $hc #> [1] 8 #>  #> $resistance #> [1] 0 #>  #> attr(,\"class\") #> [1] \"headwell\" \"well\"     \"element\"  #>  #>  #> $type #> [1] \"variable\" #>  #> $solved #> [1] TRUE #>  #> attr(,\"class\") #> [1] \"aem\""},{"path":"https://cneyens.github.io/raem/reference/aem.html","id":null,"dir":"Reference","previous_headings":"","what":"Create an analytic element model — aem","title":"Create an analytic element model — aem","text":"aem() creates analytic element model elements can added solve.aem() solves system equations constructed elements aem model plot.element() plots location analytic element point line geometry. plot.aem() plots planar locations analytic elements point line geometry aem object calling plot.element() , adds existing plot.","code":""},{"path":"https://cneyens.github.io/raem/reference/aem.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create an analytic element model — aem","text":"","code":"aem(   k,   top,   base,   n,   ...,   type = c(\"variable\", \"confined\"),   verbose = FALSE,   maxiter = 10 )  # S3 method for aem solve(a, b, maxiter = 10, verbose = FALSE, ...)  # S3 method for element plot(   x,   y = NULL,   add = FALSE,   pch = 16,   cex = 0.75,   use.widths = TRUE,   col = \"black\",   ... )  # S3 method for aem plot(x, y = NULL, add = FALSE, xlim, ylim, frame.plot = TRUE, ...)"},{"path":"https://cneyens.github.io/raem/reference/aem.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create an analytic element model — aem","text":"k numeric, hydraulic conductivity aquifer top numeric, top elevation aquifer base numeric, base elevation aquifer n numeric, effective porosity aquifer fraction total unit volume. Used determining flow velocities velocity(). ... ignored type character specifying type flow aquifer, either variable (default) confined. See details. verbose logical indicating information solving process printed. Defaults FALSE. maxiter integer specifying maximum allowed iterations non-linear solution. Defaults 10. See details. aem object b ignored x aem object, analytic element class element plot. point line geometry, nothing plotted. y ignored add logical, plot added existing plot? Defaults FALSE. pch numeric point symbol value, defaults 16. cex numeric symbol size value, defaults 0.75. use.widths logical, line elements non-zero width plotted, plotted polygons including width (TRUE; default) infinitesimally thin lines (FALSE)? col color element. Defaults 'black'. xlim numeric, plot limits along x-axis. Required add = FALSE. ylim numeric, plot limits along y-axis. Required add = FALSE. frame.plot logical, border drawn around plot. Defaults TRUE.","code":""},{"path":"https://cneyens.github.io/raem/reference/aem.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create an analytic element model — aem","text":"aem() returns object class aem list consisting k, top, base, n, list containing elements names objects specified ..., logical solved indicating model solved. solve.aem() returns solved aem object, .e. finding solution system equations constructed contained elements.","code":""},{"path":"https://cneyens.github.io/raem/reference/aem.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Create an analytic element model — aem","text":"default type = 'variable' allows unconfined/confined flow, .e. flow variable saturated thickness. type = 'confined', saturated thickness always constant equal aquifer thickness. solve.aem() called aem object returned, solves system equations. solve.aem() sets system equations, calls solve() solve. head-specified elements supplied, element class constant created constant() (also called reference point), supplied well. Constructing aem object call aem() automatically calls solve.aem(). system equations non-linear, example flow system unconfined (variable saturated thickness) elements hydraulic resistance specified, Picard iteration entered. Picard iteration step (outer iteration), previously solved model parameters used set solve linear system equations. model parameters updated next outer iteration step entered, maxiter iterations reached. linear model, maxiter ignored. analytic element point geometry collocation point (e.g. headwell()), point also plotted. reference point (created constant()) never plotted hydraulic feature. Area-sinks (created areasink() headareasink()) also never plotted clutter plot.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/aem.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create an analytic element model — aem","text":"","code":"k <- 10 top <- 10 base <- 0 n <- 0.2 TR <- k * (top - base)  w <- well(xw = 50, yw = 0, Q = 200) rf <- constant(xc = -500, yc = 0, h = 20) uf <- uniformflow(gradient = 0.002, angle = -45, TR = TR) hdw <- headwell(xw = 0, yw = 100, rw = 0.3, hc = 8) ls <- linesink(x0 = -200, y0 = -150, x1 = 200, y1 = 150, sigma = 1)  # Creating aem ---- m <- aem(k, top, base, n, w, rf, uf, hdw, ls)  # or with elements in named list m <- aem(k, top, base, n,          list('well' = w, 'constant' = rf, 'flow' = uf, 'headwell' = hdw, 'river' = ls),          type = 'confined')  # Solving ---- m <- solve(m)  # solving requires a reference point (constant) element if head-specified elements are supplied try(   m <- aem(k = k, top = top, base = base, n = n, w, uf, hdw) ) #> Error : Please provide an element of class 'constant' when solving for unknown parameters in elements  # Plotting ---- plot(ls) plot(w, add = TRUE)  plot(uf) # empty  plot(m, xlim = c(-500, 500), ylim = c(-250, 250))   xg <- seq(-500, 500, length = 200) yg <- seq(-250, 250, length = 100)  contours(m, x = xg, y = yg, col = 'dodgerblue', nlevels = 20) plot(m, add = TRUE)"},{"path":"https://cneyens.github.io/raem/reference/areasink.html","id":null,"dir":"Reference","previous_headings":"","what":"Create a circular area-sink analytic element with specified recharge — areasink","title":"Create a circular area-sink analytic element with specified recharge — areasink","text":"areasink() creates circular area-sink analytic element constant, uniform specified recharge.","code":""},{"path":"https://cneyens.github.io/raem/reference/areasink.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create a circular area-sink analytic element with specified recharge — areasink","text":"","code":"areasink(xc, yc, N, R, location = c(\"top\", \"base\"), ...)"},{"path":"https://cneyens.github.io/raem/reference/areasink.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create a circular area-sink analytic element with specified recharge — areasink","text":"xc numeric, x location center area-sink yc numeric, y location center area-sink N numeric, uniform constant leakage value (positive aquifer) length per time. R numeric, radius circular area-sink location character, either top (default) base specifying vertical position area-sink. ... ignored","code":""},{"path":"https://cneyens.github.io/raem/reference/areasink.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create a circular area-sink analytic element with specified recharge — areasink","text":"Circular area-sink analytic element object class areasink inherits element.","code":""},{"path":"https://cneyens.github.io/raem/reference/areasink.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Create a circular area-sink analytic element with specified recharge — areasink","text":"Area-sinks can used simulate areal recharge seepage aquifer top, leakage aquifer base. location argument used calculating vertical flow component.","code":""},{"path":"https://cneyens.github.io/raem/reference/areasink.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create a circular area-sink analytic element with specified recharge — areasink","text":"","code":"areasink(xc = -500, yc = 0, N = 0.001, R = 500) #> $parameter #> [1] 0.001 #>  #> $nunknowns #> [1] 0 #>  #> $xc #> [1] -500 #>  #> $yc #> [1] 0 #>  #> $R #> [1] 500 #>  #> $location #> [1] \"top\" #>  #> attr(,\"class\") #> [1] \"areasink\" \"element\"   # flux assuming a constant head difference over a confining unit dh <- 3 res <- 10 / 0.0001 areasink(xc = -500, yc = 0, N = -dh/res, R = 500, location = 'base') #> $parameter #> [1] -3e-05 #>  #> $nunknowns #> [1] 0 #>  #> $xc #> [1] -500 #>  #> $yc #> [1] 0 #>  #> $R #> [1] 500 #>  #> $location #> [1] \"base\" #>  #> attr(,\"class\") #> [1] \"areasink\" \"element\""},{"path":"https://cneyens.github.io/raem/reference/capzone.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate capture zone of a well element — capzone","title":"Calculate capture zone of a well element — capzone","text":"capzone() determines capture zone well element flow field performing backward particle tracking requested time reached.","code":""},{"path":"https://cneyens.github.io/raem/reference/capzone.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate capture zone of a well element — capzone","text":"","code":"capzone(aem, well, time, npar = 15, dt = time/10, zstart = aem$base, ...)"},{"path":"https://cneyens.github.io/raem/reference/capzone.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate capture zone of a well element — capzone","text":"aem aem object well well analytic element class well inherits . time numeric, time capture zone npar integer, number particles use backward tracking. Defaults 15. dt numeric, time step length used particle tracking. Defaults time / 10. zstart numeric value starting elevation particles. Defaults base aquifer. ... additional arguments passed tracelines().","code":""},{"path":"https://cneyens.github.io/raem/reference/capzone.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate capture zone of a well element — capzone","text":"capzone() returns object class tracelines.","code":""},{"path":"https://cneyens.github.io/raem/reference/capzone.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Calculate capture zone of a well element — capzone","text":"capzone() thin wrapper around tracelines(). Backward particle tracking performed using tracelines() setting forward = FALSE. Initial particle locations computed equally spacing npar locations well radius zstart elevation. obtain sharper delineation capture zone, try using particles decreasing dt. Note different zstart values effect models vertical flow components.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/capzone.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate capture zone of a well element — capzone","text":"","code":"k <- 10 top <- 10; base <- 0 n <- 0.3  uf <- uniformflow(TR = 100, gradient = 0.001, angle = -10) rf <- constant(TR, xc = -1000, yc = 0, hc = 20) w1 = well(200, 50, Q = 250) w2 = well(-200, -100, Q = 450)  m <- aem(k, top, base, n = n, uf, rf, w1, w2)  cp5 <- capzone(m, w1, time = 5*365) cp10 <- capzone(m, w2, time = 10*365)  xg <- seq(-800, 800, length = 100) yg <- seq(-500, 500, length = 100)  contours(m, xg, yg, col = 'dodgerblue', nlevels = 20) plot(cp5, add = TRUE) plot(cp10, add = TRUE, col = 'orange')   # model with vertical flow components as <- areasink(0, 0, N = 0.001, R = 1500) m <- aem(k, top, base, n = n, uf, rf, w1, w2, as)  # two different starting levels cp5a <- capzone(m, w1, time = 5*365, zstart = base) cp5b <- capzone(m, w1, time = 5*365, zstart = 8)  contours(m, xg, yg, col = 'dodgerblue', nlevels = 20) plot(cp5a, add = TRUE) plot(cp5b, add = TRUE, col = 'forestgreen') # smaller zone  # plot the convex hull of the endpoints as a polygon endp <- endpoints(cp5b) hull <- chull(endp[, c('x', 'y')]) polygon(endp[hull, c('x', 'y')], col = adjustcolor('forestgreen', alpha.f = 0.7))"},{"path":"https://cneyens.github.io/raem/reference/constant.html","id":null,"dir":"Reference","previous_headings":"","what":"Create a constant-head analytic element — constant","title":"Create a constant-head analytic element — constant","text":"constant() creates analytic element containing constant head, often referred reference point.","code":""},{"path":"https://cneyens.github.io/raem/reference/constant.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create a constant-head analytic element — constant","text":"","code":"constant(xc, yc, hc, ...)"},{"path":"https://cneyens.github.io/raem/reference/constant.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create a constant-head analytic element — constant","text":"xc numeric, x location reference point. yc numeric, y location reference point. hc numeric, hydraulic head reference point. ... ignored","code":""},{"path":"https://cneyens.github.io/raem/reference/constant.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create a constant-head analytic element — constant","text":"Constant-head analytic element point object class constant inherits element.","code":""},{"path":"https://cneyens.github.io/raem/reference/constant.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create a constant-head analytic element — constant","text":"","code":"rf <- constant(xc = -100, yc = 0, hc = 10)"},{"path":"https://cneyens.github.io/raem/reference/contours.html","id":null,"dir":"Reference","previous_headings":"","what":"Plot contours of a computed variable of the analytic element model — contours","title":"Plot contours of a computed variable of the analytic element model — contours","text":"contours() creates contour plot variable computed analytic element model aem, adds contour lines existing plot.","code":""},{"path":"https://cneyens.github.io/raem/reference/contours.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Plot contours of a computed variable of the analytic element model — contours","text":"","code":"contours(   aem,   x,   y,   variable = c(\"heads\", \"streamfunction\", \"potential\"),   asp = 1,   ... )"},{"path":"https://cneyens.github.io/raem/reference/contours.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Plot contours of a computed variable of the analytic element model — contours","text":"aem aem object x numeric x coordinates values z computed. must ascending order. y numeric x coordinates values z computed. must ascending order. variable character indicating variable plot. Possible values heads (default), streamfunction potential. asp y/x aspect ratio, see plot.window(). Defaults 1 (equal unit lengths). ... additional arguments passed contour().","code":""},{"path":"https://cneyens.github.io/raem/reference/contours.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Plot contours of a computed variable of the analytic element model — contours","text":"contours() wrapper around contour(). obtains values variable supplied grid points constructs matrix supplied contour() reversing rows transposing matrix (see also documentation image()).","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/contours.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Plot contours of a computed variable of the analytic element model — contours","text":"","code":"w <- well(xw = 50, yw = 0, Q = 200) wi <- well(xw = -200, yw = 0, Q = -100) uf <- uniformflow(gradient = 0.002, angle = -45, TR = 100) rf <- constant(-1000, 0, hc = 10) ml <- aem(k = 10, top = 10, base = 0, n = 0.2, w, wi, uf, rf)  xg <- seq(-350, 200, length = 100) yg <- seq(-125, 125, length = 100)  contours(ml, xg, yg, nlevels = 20, col = 'dodgerblue', labcex = 1) contours(ml, xg, yg, 'streamfunction', nlevels = 20, col = 'orange',          drawlabels = FALSE, add = TRUE)   # Not to be confused by contour() try( contour(ml, xg, yg, nlevels = 20, col = 'dodgerblue', labcex = 1) ) #> Error in contour.default(ml, xg, yg, nlevels = 20, col = \"dodgerblue\",  :  #>   no proper 'z' matrix specified  # For image() or filled.contour() library(graphics) h <- heads(ml, xg, yg, as.grid = TRUE) h_im <- t(h[dim(h)[1]:1,]) image(xg, yg, h_im, asp = 1) contour(xg, yg, h_im, asp = 1, add = TRUE) # contours() is a wrapper for this  filled.contour(xg, yg, h_im, asp = 1)"},{"path":"https://cneyens.github.io/raem/reference/dirflow.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute flow at a point in the direction of a given angle — dirflow","title":"Compute flow at a point in the direction of a given angle — dirflow","text":"dirflow() computes flow variable given points direction supplied angle","code":""},{"path":"https://cneyens.github.io/raem/reference/dirflow.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute flow at a point in the direction of a given angle — dirflow","text":"","code":"dirflow(   aem,   x,   y,   angle,   flow = c(\"discharge\", \"darcy\", \"velocity\"),   as.grid = FALSE,   ... )"},{"path":"https://cneyens.github.io/raem/reference/dirflow.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute flow at a point in the direction of a given angle — dirflow","text":"aem aem object x numeric x coordinates evaluate flow y numeric y coordinates evaluate flow angle numeric, angle direction evaluate flow, degrees counterclockwise x-axis flow character specifying flow variable use. Possible values discharge (default), darcy velocity. See flow(). .grid logical, matrix returned? Defaults FALSE. See details. ... additional arguments passed discharge(), darcy() velocity()","code":""},{"path":"https://cneyens.github.io/raem/reference/dirflow.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute flow at a point in the direction of a given angle — dirflow","text":"vector length(x) (equal length(y)) flow values x y direction angle. .grid = TRUE, matrix dimensions c(length(y), length(x)) described marginal vectors x y containing directed flow values grid points.","code":""},{"path":"https://cneyens.github.io/raem/reference/dirflow.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Compute flow at a point in the direction of a given angle — dirflow","text":"x y components flow used calculate directed value using angle. z coordinate discharge(), darcy() velocity() set aquifer base. Dupuit-Forchheimer, x y components flow vector change along vertical axis.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/dirflow.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute flow at a point in the direction of a given angle — dirflow","text":"","code":"rf <- constant(-1000, 0, hc = 10) uf <- uniformflow(TR = 100, gradient = 0.001, angle = -45) w <- well(10, -50, Q = 200)  m <- aem(k = 10, top = 10, base = 0, n = 0.2, rf, uf) dirflow(m, x = c(0, 100), y = 50, angle = -45) #> [1] 0.1 0.1  m <- aem(k = 10, top = 10, base = 0, n = 0.2, rf, uf, w, type = 'confined') dirflow(m, x = c(0, 50, 100), y = c(0, 50), angle = -90, flow = 'velocity', as.grid = TRUE) #>           [,1]      [,2]      [,3] #> [1,] 0.1929345 0.1725579 0.1232862 #> [2,] 0.3414225 0.2294467 0.1104284"},{"path":"https://cneyens.github.io/raem/reference/element_discharge.html","id":null,"dir":"Reference","previous_headings":"","what":"Get the discharge in or out of the aquifer from an element — element_discharge","title":"Get the discharge in or out of the aquifer from an element — element_discharge","text":"element_discharge() obtains computed discharge aquifer individual analytic element elements given type.","code":""},{"path":"https://cneyens.github.io/raem/reference/element_discharge.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get the discharge in or out of the aquifer from an element — element_discharge","text":"","code":"element_discharge(aem, name = NULL, type = NULL, ...)"},{"path":"https://cneyens.github.io/raem/reference/element_discharge.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get the discharge in or out of the aquifer from an element — element_discharge","text":"aem aem object name character vector name element(s) available aem$elements. type character type (class) element obtain summed discharge . See details. ... ignored","code":""},{"path":"https://cneyens.github.io/raem/reference/element_discharge.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Get the discharge in or out of the aquifer from an element — element_discharge","text":"numeric named vector length length(name) discharge (negative) (positive) aquifer. type specified, single named numeric value total discharge (negative) (positive) aquifer sum individual elements class type.","code":""},{"path":"https://cneyens.github.io/raem/reference/element_discharge.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Get the discharge in or out of the aquifer from an element — element_discharge","text":"Either name type specified. type specified, one type allowed. Possible values 'headwell', 'well', 'linesink', 'headlinesink', 'areasink' headareasink'. elements add remove water aquifer return non-zero discharge value.","code":""},{"path":"https://cneyens.github.io/raem/reference/element_discharge.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Get the discharge in or out of the aquifer from an element — element_discharge","text":"","code":"k <- 10 top <- 10 base <- 0 n <- 0.2 TR <- k * (top - base)  rf <- constant(xc = -500, yc = 0, h = 20) uf <- uniformflow(gradient = 0.002, angle = -45, TR = TR) w1 <- well(xw = 50, yw = 0, Q = 200) w2 <- well(xw = 0, yw = 100, Q = 400) hw <- headwell(xw = -100, yw = 0, hc = 7.5) hls <- headlinesink(x0 = -200, y0 = -150, x1 = 200, y1 = 150, hc = 8) as <- areasink(xc = 0, yc = 0, N = 0.0005, R = 500) m <- aem(k, top, base, n, rf, uf, w1, w2, hw, hls, as)  element_discharge(m, name = c('hls', 'as')) #>       hls        as  #> 3301.0721 -392.6991  element_discharge(m, type = 'well') #> well  #>  600"},{"path":"https://cneyens.github.io/raem/reference/flow.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate flow variables — flow","title":"Calculate flow variables — flow","text":"domega() computes complex discharge aem element object given x y coordinates. discharge() computes x, y z components discharge vector aem object given x, y z coordinates. darcy() computes x, y z components Darcy flux vector (also called specific discharge vector) aem object given x, y z coordinates. velocity() computes x, y z components average linear groundwater flow velocity vector aem object given x, y z coordinates.","code":""},{"path":"https://cneyens.github.io/raem/reference/flow.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate flow variables — flow","text":"","code":"domega(...)  discharge(...)  darcy(...)  velocity(...)  # S3 method for aem domega(aem, x, y, as.grid = FALSE, ...)  # S3 method for aem discharge(   aem,   x,   y,   z,   as.grid = FALSE,   magnitude = FALSE,   verbose = TRUE,   ... )  # S3 method for aem darcy(aem, x, y, z, as.grid = FALSE, magnitude = FALSE, ...)  # S3 method for aem velocity(aem, x, y, z, as.grid = FALSE, magnitude = FALSE, R = 1, ...)  # S3 method for element domega(element, x, y, ...)"},{"path":"https://cneyens.github.io/raem/reference/flow.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate flow variables — flow","text":"... ignored arguments passed velocity() darcy() discharge(). aem aem object x numeric x coordinates evaluate y numeric y coordinates evaluate .grid logical, matrix returned? Defaults FALSE. See details. z numeric z coordinates evaluate magnitude logical, magnitude flow vector returned well? Default FALSE. See details. verbose logical, TRUE (default), warnings regards setting Qz NA printed. See details. R numeric, retardation coefficient. Defaults 1 (retardation). element analytic element class element","code":""},{"path":"https://cneyens.github.io/raem/reference/flow.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate flow variables — flow","text":"domega(),  vector length(x) (equal length(y)) complex discharge values x y, .grid = TRUE, matrix dimensions c(length(y), length(x)) described marginal vectors x y containing complex discharge values grid points. domega() derivative omega() x y directions. discharge(), matrix number rows equal number points evaluate discharge vector , columns Qx, Qy Qz corresponding x, y z components discharge vector coordinates x, y z. .grid = TRUE, array dimensions c(length(y), length(x), length(z), 3) described marginal vectors x, y z (columns, rows third dimension) containing x, y z components discharge vector (Qx, Qy Qz) fourth dimension. x component discharge() real value domega(), y component negative imaginary component z component calculated based area-sink strengths /curvature phreatic surface. magnitude = TRUE, last dimension returned array expanded include magnitude discharge/darcy/velocity vector, calculated sqrt(Qx^2 + Qy^2 + Qz^2) (sqrt(qx^2 + qy^2 + qz^2) sqrt(vx^2 + vy^2 + vz^2), respectively). darcy(), discharge() x, y z components Darcy flux vector (qx, qy qz). value computed dividing values discharge() saturated thickness x, y z. velocity(), discharge() x, y z components average linear groundwater flow velocity vector (vx, vy vz). values computed dividing darcy() values effective porosity (aem$n) retardation coefficient R.","code":""},{"path":"https://cneyens.github.io/raem/reference/flow.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Calculate flow variables — flow","text":"discharge(), darcy() velocity() method object class element aem object required obtain aquifer base top. z coordinate saturated aquifer level (.e. water-table unconfined conditions aquifer top confined conditions), aquifer base, Qz values set NA warning (verbose = TRUE). Qx Qy values set NA, convenience specifying z coordinate lateral flow interest.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/flow.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate flow variables — flow","text":"","code":"w <- well(xw = 50, yw = 0, Q = 200) uf <- uniformflow(gradient = 0.002, angle = -45, TR = 100) as <- areasink(xc = 0, yc = 0, N = 0.001, R = 500) ml <- aem(k = 10, top = 10, base = 0, n = 0.2, w, uf, as)  domega(ml, c(50, 0), c(25, -25)) #> [1] 0.1664214+1.4021609i 0.6507172-0.1007266i  xg <- seq(-100, 100, length = 5) yg <- seq(-75, 75, length = 3) domega(ml, xg, yg, as.grid = TRUE) #>                       [,1]                  [,2]                 [,3] #> [1,] 0.2611866+0.18880399i 0.3201397+0.25671010i 0.3373044+0.3977459i #> [2,] 0.3036279+0.14142136i 0.4347312+0.14142136i 0.7780411+0.1414214i #> [3,] 0.2611866+0.09403872i 0.3201397+0.02613261i 0.3373044-0.1149032i #>                         [,4]                    [,5] #> [1,]    0.1664214+0.5283345i -0.004461651+0.3977459i #> [2,] -105.9368740+0.1414214i -0.445198416+0.1414214i #> [3,]    0.1664214-0.2454918i -0.004461651-0.1149032i  discharge(ml, c(50, 0), c(25, -25), z = ml$top) #> Warning: Setting Qz values to NA for z above saturated aquifer level or below aquifer base #>             Qx         Qy Qz #> [1,] 0.1664214 -1.4021609 NA #> [2,] 0.6507172  0.1007266 NA discharge(ml, c(50, 0), c(25, -25), z = c(ml$top, 5), magnitude = TRUE) #> Warning: Setting Qz values to NA for z above saturated aquifer level or below aquifer base #>             Qx         Qy          Qz         Q #> [1,] 0.1664214 -1.4021609          NA        NA #> [2,] 0.6507172  0.1007266 -0.01080013 0.6585555 discharge(ml, xg, yg, z = ml$top, as.grid = TRUE) #> Warning: Setting Qz values to NA for z above saturated aquifer level or below aquifer base #> , , 1, Qx #>  #>           [,1]      [,2]      [,3]         [,4]         [,5] #> [1,] 0.2611866 0.3201397 0.3373044    0.1664214 -0.004461651 #> [2,] 0.3036279 0.4347312 0.7780411 -105.9368740 -0.445198416 #> [3,] 0.2611866 0.3201397 0.3373044    0.1664214 -0.004461651 #>  #> , , 1, Qy #>  #>             [,1]        [,2]       [,3]       [,4]       [,5] #> [1,] -0.18880399 -0.25671010 -0.3977459 -0.5283345 -0.3977459 #> [2,] -0.14142136 -0.14142136 -0.1414214 -0.1414214 -0.1414214 #> [3,] -0.09403872 -0.02613261  0.1149032  0.2454918  0.1149032 #>  #> , , 1, Qz #>  #>      [,1] [,2] [,3] [,4] [,5] #> [1,]   NA   NA   NA   NA   NA #> [2,]   NA   NA   NA   NA   NA #> [3,]   NA   NA   NA   NA   NA #>  discharge(ml, c(50, 0), c(25, -25), z = ml$top + c(0, 0.5)) # NA for z > top #> Warning: Setting Qz values to NA for z above saturated aquifer level or below aquifer base #>             Qx         Qy Qz #> [1,] 0.1664214 -1.4021609 NA #> [2,] 0.6507172  0.1007266 NA  darcy(ml, c(50, 0), c(25, -25), c(10, 5), magnitude = TRUE) #> Warning: Setting Qz values to NA for z above saturated aquifer level or below aquifer base #>              qx         qy           qz        q #> [1,] 0.02936046 -0.2473726           NA       NA #> [2,] 0.10643688  0.0164757 -0.001766562 0.107719 darcy(ml, xg, yg, 10, as.grid = TRUE) #> Warning: Setting Qz values to NA for z above saturated aquifer level or below aquifer base #> , , 1, qx #>  #>            [,1]       [,2]       [,3]         [,4]          [,5] #> [1,] 0.03720717 0.04701470 0.05144049   0.02621968 -0.0007083937 #> [2,] 0.04441782 0.06621384 0.12721532 -58.35119617 -0.0762653892 #> [3,] 0.03892034 0.04932549 0.05418314   0.02771988 -0.0007496139 #>  #> , , 1, qy #>  #>             [,1]         [,2]        [,3]        [,4]        [,5] #> [1,] -0.02689595 -0.037699634 -0.06065810 -0.08323910 -0.06315167 #> [2,] -0.02068857 -0.021539862 -0.02312341 -0.07789644 -0.02422640 #> [3,] -0.01401304 -0.004026379  0.01845755  0.04089021  0.01930519 #>  #> , , 1, qz #>  #>      [,1] [,2] [,3] [,4] [,5] #> [1,]   NA   NA   NA   NA   NA #> [2,]   NA   NA   NA   NA   NA #> [3,]   NA   NA   NA   NA   NA #>   velocity(ml, c(50, 0), c(25, -25), c(10, 5), magnitude = TRUE, R = 5) #> Warning: Setting Qz values to NA for z above saturated aquifer level or below aquifer base #>              vx         vy           vz        v #> [1,] 0.02936046 -0.2473726           NA       NA #> [2,] 0.10643688  0.0164757 -0.001766562 0.107719 velocity(ml, xg, yg, 5, as.grid = TRUE, R = 5) #> Warning: Setting Qz values to NA for z above saturated aquifer level or below aquifer base #> , , 1, vx #>  #>            [,1]       [,2]       [,3]         [,4]          [,5] #> [1,] 0.03720717 0.04701470 0.05144049   0.02621968 -0.0007083937 #> [2,] 0.04441782 0.06621384 0.12721532 -58.35119617 -0.0762653892 #> [3,] 0.03892034 0.04932549 0.05418314   0.02771988 -0.0007496139 #>  #> , , 1, vy #>  #>             [,1]         [,2]        [,3]        [,4]        [,5] #> [1,] -0.02689595 -0.037699634 -0.06065810 -0.08323910 -0.06315167 #> [2,] -0.02068857 -0.021539862 -0.02312341 -0.07789644 -0.02422640 #> [3,] -0.01401304 -0.004026379  0.01845755  0.04089021  0.01930519 #>  #> , , 1, vz #>  #>               [,1]          [,2]         [,3]         [,4]         [,5] #> [1,] -0.0008624020 -0.0010009501 -0.001244860 -0.001387718 -0.001110515 #> [2,] -0.0009070699 -0.0011307663 -0.002184328           NA -0.001404998 #> [3,] -0.0008725605 -0.0009590558 -0.001066340 -0.001036064 -0.000871419 #>   # For elements domega(w, c(50, 0), c(-25, 25)) #> [1] 0.0000000-1.2732395i 0.5092958+0.2546479i"},{"path":"https://cneyens.github.io/raem/reference/flow_through_line.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate the total flow passing through a line — flow_through_line","title":"Calculate the total flow passing through a line — flow_through_line","text":"flow_through_line() computes integrated flow passing straight line right angle.","code":""},{"path":"https://cneyens.github.io/raem/reference/flow_through_line.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate the total flow passing through a line — flow_through_line","text":"","code":"flow_through_line(   aem,   x0,   y0,   x1,   y1,   flow = c(\"discharge\", \"darcy\"),   split = FALSE,   ... )"},{"path":"https://cneyens.github.io/raem/reference/flow_through_line.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate the total flow passing through a line — flow_through_line","text":"aem aem object x0 numeric, starting x location line y0 numeric, starting y location line x1 numeric, ending x location line y1 numeric, ending y location line flow character specifying flow variable use. Possible values discharge (default) darcy. See flow(). split logical, flow split positive negative flows summed (default)? See details. ... ignored","code":""},{"path":"https://cneyens.github.io/raem/reference/flow_through_line.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate the total flow passing through a line — flow_through_line","text":"split = FALSE, single value total flow variable flow passing line right angle. split = TRUE named vector total positive total negative value flow passing line.","code":""},{"path":"https://cneyens.github.io/raem/reference/flow_through_line.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Calculate the total flow passing through a line — flow_through_line","text":"flow computed normal line integrated along line length using stats::integrate(). flow value positive going left looking direction line (.e. left going x0-y0 x1-y1). split = FALSE (default), single value returned sum positive negative flows perpendicular line. split = TRUE, positive negative component total flow line returned. line corresponds line element, integration might fail. Try perturbate line vertices slightly case.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/flow_through_line.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate the total flow passing through a line — flow_through_line","text":"","code":"rf <- constant(-1000, 0, hc = 10) uf <- uniformflow(TR = 100, gradient = 0.001, angle = -45) m <- aem(k = 10, top = 10, base = 0, n = 0.2, rf, uf)  xg <- seq(-500, 500, l=100); yg <- seq(-300, 300, l=100) contours(m, xg, yg, col='dodgerblue', nlevels=20)  x0 <- -200 y0 <- -50 x1 <- 300 y1 <- 100 lines(matrix(c(x0, y0, x1, y1), ncol = 2, byrow = TRUE))   flow_through_line(m, x0, y0, x1, y1) #> [1] -45.96194 flow_through_line(m, x1, y1, x0, y0) # reverse direction of line #> [1] 45.96194  w <- well(125, 200, 150) m <- aem(k = 10, top = 10, base = 0, n = 0.2, rf, uf, w) contours(m, xg, yg, col='dodgerblue', nlevels=20) lines(matrix(c(x0, y0, x1, y1), ncol = 2, byrow = TRUE))   flow_through_line(m, x0, y0, x1, y1, flow = 'darcy') #> [1] 0.1633028 flow_through_line(m, x0, y0, x1, y1, flow = 'darcy', split = TRUE) #>  positive  negative  #>  1.369686 -1.206383"},{"path":"https://cneyens.github.io/raem/reference/head_to_potential.html","id":null,"dir":"Reference","previous_headings":"","what":"Convert hydraulic head to potential and vice versa — head_to_potential","title":"Convert hydraulic head to potential and vice versa — head_to_potential","text":"head_to_potential() calculates discharge potential hydraulic head. potential_to_head() calculates hydraulic head discharge potential.","code":""},{"path":"https://cneyens.github.io/raem/reference/head_to_potential.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Convert hydraulic head to potential and vice versa — head_to_potential","text":"","code":"head_to_potential(aem, h, ...)  potential_to_head(aem, phi, na.below = TRUE, ...)"},{"path":"https://cneyens.github.io/raem/reference/head_to_potential.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Convert hydraulic head to potential and vice versa — head_to_potential","text":"aem aem object h numeric hydraulic head values vector matrix. ... ignored phi numeric discharge potential values vector matrix. na.logical indicating calculated head values aquifer base set NA. Defaults TRUE. See details.","code":""},{"path":"https://cneyens.github.io/raem/reference/head_to_potential.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Convert hydraulic head to potential and vice versa — head_to_potential","text":"head_to_potential() returns discharge potentials calculated h, structure h. potential_to_head() returns hydraulic heads calculated phi, structure phi. conversion potential head vice versa different confined (constant saturated thickness) unconfined (variable saturated thickness) aquifers. na.= FALSE, negative potentials can converted hydraulic heads flow unconfined (aem$type = 'variable'). resulting heads aquifer base. may useful use cases, e.g. preliminary model construction internal functions. cases however, values set NA (default behavior) since analytic elements continue extract inject water even though saturated thickness aquifer negative, realistic. cases, setting aem$type = 'confined' might prove useful. Also note heads aquifer base correctly re-converted potentials using head_to_potential(). , caution taken setting na.= FALSE.","code":""},{"path":"https://cneyens.github.io/raem/reference/head_to_potential.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Convert hydraulic head to potential and vice versa — head_to_potential","text":"","code":"k <- 10 top <- 10; base <- 0 uf <- uniformflow(TR = 100, gradient = 0.001, angle = -45) rf <- constant(TR, xc = -1000, yc = 0, hc = 10) w1 <- well(200, 50, Q = 250) m <- aem(k, top, base, n = 0.2, uf, rf, w1, type = 'variable') # variable saturated thickness mc <- aem(k, top, base, n = 0.2, uf, rf, w1, type = 'confined') # constant saturated thickness xg <- seq(-500, 500, length = 100) yg <- seq(-250, 250, length = 100)  h <- heads(m, x = xg, y = yg, as.grid = TRUE) hc <- heads(mc, x = xg, y = yg, as.grid = TRUE) head_to_potential(m, h) #>            [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8] #>   [1,] 462.4030 461.1546 459.8996 458.6378 457.3691 456.0933 454.8101 453.5196 #>   [2,] 461.9708 460.7204 459.4633 458.1993 456.9283 455.6500 454.3644 453.0712 #>   [3,] 461.5403 460.2879 459.0287 457.7626 456.4892 455.2086 453.9206 452.6248 #>   [4,] 461.1115 459.8571 458.5959 457.3276 456.0520 454.7691 453.4786 452.1804 #>   [5,] 460.6844 459.4281 458.1648 456.8944 455.6167 454.3315 453.0386 451.7379 #>   [6,] 460.2589 459.0007 457.7355 456.4630 455.1832 453.8958 452.6006 451.2974 #>   [7,] 459.8352 458.5752 457.3080 456.0335 454.7516 453.4620 452.1645 450.8590 #>   [8,] 459.4132 458.1514 456.8823 455.6059 454.3219 453.0302 451.7305 450.4226 #>   [9,] 458.9930 457.7294 456.4585 455.1802 453.8942 452.6003 451.2985 449.9884 #>  [10,] 458.5745 457.3092 456.0365 454.7563 453.4684 452.1725 450.8685 449.5562 #>  [11,] 458.1579 456.8909 455.6165 454.3344 453.0446 451.7468 450.4407 449.1262 #>  [12,] 457.7430 456.4744 455.1983 453.9145 452.6228 451.3230 450.0150 448.6984 #>  [13,] 457.3300 456.0598 454.7820 453.4965 452.2030 450.9014 449.5913 448.2727 #>  [14,] 456.9188 455.6471 454.3677 453.0805 451.7853 450.4818 449.1699 447.8493 #>  [15,] 456.5095 455.2362 453.9553 452.6665 451.3696 450.0644 448.7506 447.4281 #>  [16,] 456.1020 454.8273 453.5449 452.2546 450.9560 449.6491 448.3335 447.0091 #>  [17,] 455.6964 454.4204 453.1365 451.8446 450.5445 449.2360 447.9187 446.5925 #>  [18,] 455.2928 454.0154 452.7301 451.4368 450.1352 448.8250 447.5061 446.1781 #>  [19,] 454.8910 453.6123 452.3257 451.0310 449.7279 448.4162 447.0957 445.7661 #>  [20,] 454.4912 453.2113 451.9234 450.6273 449.3228 448.0097 446.6876 445.3564 #>  [21,] 454.0933 452.8122 451.5231 450.2257 448.9199 447.6053 446.2818 444.9490 #>  [22,] 453.6973 452.4151 451.1248 449.8263 448.5191 447.2033 445.8783 444.5441 #>  [23,] 453.3033 452.0201 450.7287 449.4289 448.1206 446.8034 445.4772 444.1415 #>  [24,] 452.9113 451.6270 450.3346 449.0337 447.7243 446.4059 445.0784 443.7414 #>  [25,] 452.5213 451.2360 449.9426 448.6407 447.3301 446.0106 444.6819 443.3437 #>  [26,] 452.1333 450.8471 449.5527 448.2499 446.9383 445.6177 444.2878 442.9484 #>  [27,] 451.7472 450.4602 449.1650 447.8612 446.5486 445.2270 443.8961 442.5556 #>  [28,] 451.3632 450.0754 448.7793 447.4747 446.1612 444.8387 443.5068 442.1653 #>  [29,] 450.9812 449.6927 448.3959 447.0904 445.7761 444.4527 443.1199 441.7774 #>  [30,] 450.6012 449.3121 448.0145 446.7083 445.3933 444.0691 442.7355 441.3921 #>  [31,] 450.2233 448.9335 447.6353 446.3285 445.0127 443.6878 442.3534 441.0093 #>  [32,] 449.8474 448.5571 447.2583 445.9509 444.6345 443.3089 441.9738 440.6289 #>  [33,] 449.4736 448.1827 446.8835 445.5755 444.2585 442.9324 441.5967 440.2511 #>  [34,] 449.1018 447.8105 446.5108 445.2023 443.8849 442.5582 441.2220 439.8759 #>  [35,] 448.7320 447.4404 446.1403 444.8314 443.5136 442.1864 440.8497 439.5032 #>  [36,] 448.3644 447.0724 445.7720 444.4628 443.1446 441.8171 440.4800 439.1330 #>  [37,] 447.9988 446.7066 445.4059 444.0964 442.7779 441.4501 440.1127 438.7654 #>  [38,] 447.6352 446.3428 445.0419 443.7323 442.4136 441.0855 439.7479 438.4003 #>  [39,] 447.2737 445.9812 444.6802 443.3704 442.0515 440.7233 439.3855 438.0378 #>  [40,] 446.9143 445.6218 444.3207 443.0108 441.6918 440.3636 439.0257 437.6778 #>  [41,] 446.5570 445.2644 443.9633 442.6534 441.3345 440.0062 438.6683 437.3205 #>  [42,] 446.2018 444.9092 443.6082 442.2983 440.9795 439.6512 438.3134 436.9656 #>  [43,] 445.8486 444.5562 443.2552 441.9455 440.6268 439.2987 437.9610 436.6134 #>  [44,] 445.4974 444.2052 442.9045 441.5949 440.2764 438.9485 437.6111 436.2637 #>  [45,] 445.1484 443.8564 442.5559 441.2466 439.9284 438.6008 437.2636 435.9166 #>  [46,] 444.8014 443.5097 442.2095 440.9006 439.5827 438.2554 436.9186 435.5720 #>  [47,] 444.4565 443.1651 441.8653 440.5568 439.2393 437.9125 436.5761 435.2299 #>  [48,] 444.1136 442.8227 441.5233 440.2152 438.8982 437.5719 436.2361 434.8904 #>  [49,] 443.7728 442.4824 441.1835 439.8759 438.5594 437.2337 435.8985 434.5535 #>  [50,] 443.4340 442.1441 440.8458 439.5389 438.2230 436.8979 435.5634 434.2190 #>  [51,] 443.0973 441.8080 440.5103 439.2040 437.8888 436.5645 435.2307 433.8871 #>  [52,] 442.7626 441.4740 440.1770 438.8714 437.5569 436.2334 434.9004 433.5577 #>  [53,] 442.4300 441.1420 439.8458 438.5410 437.2273 435.9046 434.5726 433.2308 #>  [54,] 442.0993 440.8122 439.5167 438.2128 436.9000 435.5782 434.2471 432.9064 #>  [55,] 441.7707 440.4844 439.1898 437.8868 436.5750 435.2542 433.9241 432.5845 #>  [56,] 441.4441 440.1587 438.8650 437.5629 436.2521 434.9324 433.6035 432.2650 #>  [57,] 441.1195 439.8350 438.5423 437.2413 435.9316 434.6130 433.2852 431.9480 #>  [58,] 440.7968 439.5133 438.2217 436.9218 435.6132 434.2958 432.9693 431.6334 #>  [59,] 440.4762 439.1937 437.9032 436.6044 435.2971 433.9809 432.6557 431.3212 #>  [60,] 440.1575 438.8762 437.5868 436.2892 434.9831 433.6683 432.3445 431.0114 #>  [61,] 439.8407 438.5606 437.2725 435.9761 434.6714 433.3579 432.0356 430.7040 #>  [62,] 439.5259 438.2470 436.9602 435.6652 434.3618 433.0498 431.7290 430.3990 #>  [63,] 439.2131 437.9354 436.6499 435.3563 434.0544 432.7439 431.4246 430.0963 #>  [64,] 438.9021 437.6258 436.3416 435.0495 433.7491 432.4402 431.1225 429.7960 #>  [65,] 438.5931 437.3181 436.0354 434.7447 433.4459 432.1386 430.8227 429.4979 #>  [66,] 438.2859 437.0124 435.7312 434.4420 433.1448 431.8392 430.5251 429.2022 #>  [67,] 437.9806 436.7086 435.4289 434.1414 432.8458 431.5420 430.2297 428.9087 #>  [68,] 437.6772 436.4067 435.1286 433.8427 432.5489 431.2469 429.9365 428.6174 #>  [69,] 437.3756 436.1066 434.8302 433.5460 432.2540 430.9539 429.6454 428.3284 #>  [70,] 437.0758 435.8085 434.5337 433.2514 431.9611 430.6629 429.3565 428.0415 #>  [71,] 436.7779 435.5122 434.2392 432.9586 431.6703 430.3740 429.0696 427.7569 #>  [72,] 436.4817 435.2178 433.9465 432.6678 431.3814 430.0872 428.7849 427.4743 #>  [73,] 436.1874 434.9252 433.6557 432.3789 431.0945 429.8024 428.5022 427.1939 #>  [74,] 435.8947 434.6343 433.3668 432.0919 430.8096 429.5195 428.2216 426.9156 #>  [75,] 435.6039 434.3453 433.0797 431.8068 430.5265 429.2387 427.9430 426.6394 #>  [76,] 435.3147 434.0580 432.7944 431.5235 430.2454 428.9598 427.6664 426.3652 #>  [77,] 435.0273 433.7725 432.5109 431.2421 429.9661 428.6828 427.3918 426.0930 #>  [78,] 434.7415 433.4887 432.2291 430.9625 429.6887 428.4077 427.1191 425.8229 #>  [79,] 434.4574 433.2066 431.9491 430.6847 429.4132 428.1344 426.8483 425.5546 #>  [80,] 434.1750 432.9262 431.6708 430.4086 429.1394 427.8630 426.5794 425.2884 #>  [81,] 433.8942 432.6475 431.3942 430.1342 428.8674 427.5935 426.3124 425.0240 #>  [82,] 433.6150 432.3704 431.1193 429.8616 428.5971 427.3257 426.0472 424.7615 #>  [83,] 433.3374 432.0950 430.8461 429.5907 428.3286 427.0597 425.7838 424.5008 #>  [84,] 433.0613 431.8211 430.5745 429.3215 428.0618 426.7955 425.5222 424.2420 #>  [85,] 432.7869 431.5488 430.3045 429.0539 427.7967 426.5330 425.2624 423.9849 #>  [86,] 432.5139 431.2781 430.0361 428.7879 427.5333 426.2721 425.0043 423.7297 #>  [87,] 432.2424 431.0089 429.7693 428.5235 427.2715 426.0129 424.7479 423.4761 #>  [88,] 431.9725 430.7413 429.5040 428.2607 427.0112 425.7554 424.4931 423.2243 #>  [89,] 431.7040 430.4751 429.2403 427.9995 426.7526 425.4995 424.2400 422.9741 #>  [90,] 431.4369 430.2104 428.9780 427.7398 426.4955 425.2451 423.9885 422.7256 #>  [91,] 431.1713 429.9471 428.7173 427.4816 426.2400 424.9924 423.7386 422.4787 #>  [92,] 430.9071 429.6853 428.4579 427.2248 425.9859 424.7411 423.4903 422.2333 #>  [93,] 430.6442 429.4249 428.2000 426.9696 425.7334 424.4914 423.2435 421.9896 #>  [94,] 430.3827 429.1659 427.9435 426.7157 425.4822 424.2431 422.9981 421.7473 #>  [95,] 430.1226 428.9082 427.6884 426.4633 425.2326 423.9963 422.7543 421.5065 #>  [96,] 429.8638 428.6518 427.4347 426.2122 424.9843 423.7509 422.5119 421.2672 #>  [97,] 429.6062 428.3968 427.1823 425.9625 424.7374 423.5069 422.2709 421.0294 #>  [98,] 429.3499 428.1431 426.9312 425.7141 424.4918 423.2642 422.0313 420.7929 #>  [99,] 429.0949 427.8906 426.6813 425.4670 424.2475 423.0229 421.7930 420.5578 #> [100,] 428.8411 427.6394 426.4328 425.2212 424.0046 422.7829 421.5561 420.3241 #>            [,9]    [,10]    [,11]    [,12]    [,13]    [,14]    [,15]    [,16] #>   [1,] 452.2214 450.9155 449.6016 448.2796 446.9493 445.6104 444.2628 442.9063 #>   [2,] 451.7704 450.4616 449.1447 447.8196 446.4860 445.1438 443.7926 442.4324 #>   [3,] 451.3213 450.0097 448.6899 447.3618 446.0250 444.6794 443.3247 441.9609 #>   [4,] 450.8742 449.5599 448.2372 446.9060 445.5661 444.2172 442.8591 441.4917 #>   [5,] 450.4291 449.1121 447.7866 446.4525 445.1095 443.7574 442.3959 441.0249 #>   [6,] 449.9861 448.6665 447.3382 446.0012 444.6551 443.2998 441.9351 440.5605 #>   [7,] 449.5452 448.2230 446.8920 445.5521 444.2031 442.8447 441.4766 440.0987 #>   [8,] 449.1064 447.7816 446.4480 445.1054 443.7534 442.3920 441.0207 439.6394 #>   [9,] 448.6698 447.3425 446.0063 444.6609 443.3061 441.9417 440.5673 439.1827 #>  [10,] 448.2353 446.9056 445.5669 444.2188 442.8613 441.4939 440.1164 438.7286 #>  [11,] 447.8030 446.4710 445.1297 443.7791 442.4188 441.0486 439.6681 438.2772 #>  [12,] 447.3730 446.0386 444.6950 443.3418 441.9789 440.6059 439.2225 437.8284 #>  [13,] 446.9452 445.6086 444.2626 442.9070 441.5414 440.1657 438.7795 437.3825 #>  [14,] 446.5197 445.1809 443.8326 442.4746 441.1066 439.7282 438.3392 436.9393 #>  [15,] 446.0964 444.7555 443.4051 442.0447 440.6743 439.2934 437.9017 436.4989 #>  [16,] 445.6756 444.3326 442.9800 441.6174 440.2446 438.8612 437.4669 436.0614 #>  [17,] 445.2570 443.9121 442.5574 441.1926 439.8175 438.4318 437.0350 435.6268 #>  [18,] 444.8408 443.4940 442.1373 440.7705 439.3932 438.0051 436.6058 435.1951 #>  [19,] 444.4270 443.0784 441.7198 440.3509 438.9715 437.5812 436.1796 434.7664 #>  [20,] 444.0157 442.6652 441.3048 439.9340 438.5525 437.1601 435.7562 434.3407 #>  [21,] 443.6067 442.2546 440.8924 439.5197 438.1363 436.7418 435.3358 433.9180 #>  [22,] 443.2002 441.8465 440.4826 439.1082 437.7229 436.3264 434.9184 433.4984 #>  [23,] 442.7962 441.4410 440.0755 438.6993 437.3123 435.9139 434.5039 433.0818 #>  [24,] 442.3947 441.0380 439.6709 438.2932 436.9045 435.5044 434.0925 432.6684 #>  [25,] 441.9957 440.6376 439.2691 437.8899 436.4995 435.0977 433.6841 432.2581 #>  [26,] 441.5992 440.2398 438.8699 437.4893 436.0974 434.6940 433.2787 431.8510 #>  [27,] 441.2052 439.8446 438.4735 437.0915 435.6982 434.2934 432.8765 431.4471 #>  [28,] 440.8138 439.4521 438.0798 436.6965 435.3019 433.8957 432.4773 431.0464 #>  [29,] 440.4250 439.0622 437.6888 436.3043 434.9085 433.5010 432.0813 430.6490 #>  [30,] 440.0387 438.6750 437.3005 435.9150 434.5181 433.1094 431.6884 430.2548 #>  [31,] 439.6550 438.2904 436.9150 435.5286 434.1306 432.7208 431.2987 429.8639 #>  [32,] 439.2739 437.9085 436.5323 435.1450 433.7461 432.3353 430.9122 429.4763 #>  [33,] 438.8955 437.5293 436.1524 434.7642 433.3646 431.9529 430.5289 429.0920 #>  [34,] 438.5196 437.1528 435.7752 434.3864 432.9860 431.5736 430.1487 428.7110 #>  [35,] 438.1464 436.7791 435.4009 434.0115 432.6105 431.1974 429.7718 428.3334 #>  [36,] 437.7758 436.4080 435.0294 433.6395 432.2379 430.8243 429.3982 427.9591 #>  [37,] 437.4078 436.0397 434.6607 433.2704 431.8684 430.4543 429.0277 427.5882 #>  [38,] 437.0425 435.6741 434.2948 432.9042 431.5019 430.0875 428.6605 427.2206 #>  [39,] 436.6798 435.3112 433.9317 432.5409 431.1384 429.7237 428.2966 426.8564 #>  [40,] 436.3198 434.9511 433.5715 432.1806 430.7779 429.3632 427.9359 426.4955 #>  [41,] 435.9624 434.5937 433.2141 431.8231 430.4205 429.0057 427.5784 426.1381 #>  [42,] 435.6076 434.2390 432.8595 431.4687 430.0661 428.6514 427.2242 425.7840 #>  [43,] 435.2555 433.8871 432.5077 431.1171 429.7147 428.3003 426.8733 425.4333 #>  [44,] 434.9061 433.5379 432.1588 430.7684 429.3664 427.9522 426.5256 425.0859 #>  [45,] 434.5593 433.1914 431.8127 430.4227 429.0211 427.6073 426.1811 424.7419 #>  [46,] 434.2151 432.8477 431.4694 430.0799 428.6788 427.2656 425.8399 424.4013 #>  [47,] 433.8736 432.5067 431.1290 429.7400 428.3395 426.9269 425.5019 424.0640 #>  [48,] 433.5346 432.1684 430.7913 429.4030 428.0032 426.5913 425.1671 423.7301 #>  [49,] 433.1983 431.8328 430.4564 429.0689 427.6699 426.2589 424.8356 423.3995 #>  [50,] 432.8647 431.4999 430.1243 428.7377 427.3395 425.9295 424.5072 423.0722 #>  [51,] 432.5336 431.1696 429.7950 428.4093 427.0122 425.6032 424.1820 422.7482 #>  [52,] 432.2051 430.8421 429.4684 428.0838 426.6878 425.2800 423.8600 422.4275 #>  [53,] 431.8791 430.5172 429.1446 427.7611 426.3663 424.9598 423.5412 422.1100 #>  [54,] 431.5558 430.1950 428.8236 427.4413 426.0478 424.6426 423.2254 421.7958 #>  [55,] 431.2350 429.8754 428.5052 427.1243 425.7322 424.3285 422.9128 421.4848 #>  [56,] 430.9167 429.5584 428.1896 426.8101 425.4194 424.0173 422.6033 421.1770 #>  [57,] 430.6010 429.2440 427.8767 426.4986 425.1096 423.7091 422.2968 420.8724 #>  [58,] 430.2878 428.9322 427.5664 426.1900 424.8026 423.4038 421.9934 420.5710 #>  [59,] 429.9771 428.6230 427.2588 425.8840 424.4984 423.1015 421.6931 420.2726 #>  [60,] 429.6688 428.3164 426.9538 425.5808 424.1970 422.8021 421.3957 419.9774 #>  [61,] 429.3630 428.0122 426.6514 425.2802 423.8984 422.5055 421.1012 419.6852 #>  [62,] 429.0596 427.7106 426.3516 424.9824 423.6025 422.2118 420.8097 419.3961 #>  [63,] 428.7587 427.4115 426.0544 424.6872 423.3094 421.9209 420.5212 419.1099 #>  [64,] 428.4601 427.1148 425.7597 424.3946 423.0190 421.6328 420.2355 418.8268 #>  [65,] 428.1640 426.8206 425.4676 424.1046 422.7313 421.3474 419.9526 418.5466 #>  [66,] 427.8701 426.5288 425.1779 423.8171 422.4462 421.0648 419.6726 418.2692 #>  [67,] 427.5787 426.2394 424.8907 423.5322 422.1637 420.7848 419.3953 417.9948 #>  [68,] 427.2895 425.9524 424.6060 423.2499 421.8838 420.5076 419.1208 417.7232 #>  [69,] 427.0026 425.6677 424.3236 422.9700 421.6065 420.2329 418.8490 417.4543 #>  [70,] 426.7179 425.3854 424.0437 422.6925 421.3317 419.9609 418.5799 417.1883 #>  [71,] 426.4355 425.1053 423.7661 422.4175 421.0594 419.6914 418.3134 416.9249 #>  [72,] 426.1553 424.8275 423.4908 422.1449 420.7895 419.4245 418.0495 416.6642 #>  [73,] 425.8772 424.5519 423.2178 421.8746 420.5221 419.1600 417.7881 416.4062 #>  [74,] 425.6014 424.2786 422.9471 421.6067 420.2571 418.8980 417.5293 416.1507 #>  [75,] 425.3276 424.0074 422.6786 421.3410 419.9944 418.6385 417.2730 415.8978 #>  [76,] 425.0559 423.7384 422.4124 421.0776 419.7340 418.3813 417.0191 415.6474 #>  [77,] 424.7863 423.4715 422.1483 420.8165 419.4759 418.1264 416.7676 415.3994 #>  [78,] 424.5188 423.2067 421.8863 420.5575 419.2201 417.8738 416.5185 415.1539 #>  [79,] 424.2532 422.9439 421.6264 420.3007 418.9665 417.6235 416.2717 414.9108 #>  [80,] 423.9897 422.6832 421.3687 420.0460 418.7150 417.3755 416.0272 414.6700 #>  [81,] 423.7280 422.4244 421.1129 419.7934 418.4657 417.1296 415.7849 414.4314 #>  [82,] 423.4683 422.1676 420.8592 419.5429 418.2185 416.8859 415.5448 414.1951 #>  [83,] 423.2105 421.9128 420.6075 419.2944 417.9733 416.6442 415.3069 413.9611 #>  [84,] 422.9546 421.6598 420.3576 419.0478 417.7302 416.4047 415.0710 413.7291 #>  [85,] 422.7004 421.4088 420.1097 418.8032 417.4891 416.1671 414.8373 413.4993 #>  [86,] 422.4481 421.1595 419.8637 418.5605 417.2499 415.9316 414.6055 413.2715 #>  [87,] 422.1976 420.9121 419.6195 418.3197 417.0126 415.6980 414.3758 413.0458 #>  [88,] 421.9487 420.6664 419.3771 418.0807 416.7772 415.4663 414.1479 412.8220 #>  [89,] 421.7016 420.4224 419.1365 417.8435 416.5436 415.2364 413.9220 412.6002 #>  [90,] 421.4562 420.1802 418.8976 417.6081 416.3118 415.0084 413.6979 412.3802 #>  [91,] 421.2124 419.9396 418.6604 417.3744 416.0817 414.7822 413.4757 412.1621 #>  [92,] 420.9702 419.7007 418.4248 417.1424 415.8534 414.5577 413.2552 411.9457 #>  [93,] 420.7296 419.4634 418.1909 416.9121 415.6268 414.3349 413.0364 411.7312 #>  [94,] 420.4905 419.2276 417.9586 416.6833 415.4018 414.1138 412.8193 411.5183 #>  [95,] 420.2529 418.9934 417.7278 416.4562 415.1783 413.8943 412.6038 411.3070 #>  [96,] 420.0169 418.7607 417.4986 416.2306 414.9565 413.6763 412.3900 411.0974 #>  [97,] 419.7822 418.5294 417.2709 416.0065 414.7362 413.4599 412.1777 410.8894 #>  [98,] 419.5490 418.2996 417.0446 415.7838 414.5173 413.2451 411.9669 410.6829 #>  [99,] 419.3172 418.0712 416.8197 415.5626 414.3000 413.0316 411.7576 410.4779 #> [100,] 419.0868 417.8442 416.5962 415.3428 414.0840 412.8196 411.5497 410.2743 #>           [,17]    [,18]    [,19]    [,20]    [,21]    [,22]    [,23]    [,24] #>   [1,] 441.5407 440.1658 438.7813 437.3871 435.9830 434.5686 433.1439 431.7085 #>   [2,] 441.0629 439.6839 438.2952 436.8965 435.4876 434.0683 432.6383 431.1974 #>   [3,] 440.5875 439.2045 437.8115 436.4083 434.9948 433.5705 432.1354 430.6891 #>   [4,] 440.1145 438.7275 437.3304 435.9228 434.5046 433.0756 431.6353 430.1836 #>   [5,] 439.6440 438.2531 436.8518 435.4400 434.0172 432.5834 431.1381 429.6811 #>   [6,] 439.1760 437.7812 436.3759 434.9598 433.5326 432.0941 430.6438 429.1816 #>   [7,] 438.7106 437.3120 435.9027 434.4824 433.0509 431.6076 430.1525 428.6851 #>   [8,] 438.2477 436.8455 435.4323 434.0079 432.5720 431.1242 429.6643 428.1918 #>   [9,] 437.7876 436.3817 434.9647 433.5362 432.0961 430.6438 429.1792 427.7017 #>  [10,] 437.3301 435.9206 434.4999 433.0675 431.6232 430.1666 428.6972 427.2149 #>  [11,] 436.8754 435.4624 434.0380 432.6018 431.1534 429.6924 428.2186 426.7314 #>  [12,] 436.4234 435.0071 433.5791 432.1391 430.6867 429.2216 427.7433 426.2514 #>  [13,] 435.9743 434.5546 433.1232 431.6795 430.2232 428.7540 427.2714 425.7749 #>  [14,] 435.5280 434.1052 432.6703 431.2230 429.7630 428.2897 426.8029 425.3020 #>  [15,] 435.0847 433.6587 432.2205 430.7698 429.3060 427.8289 426.3379 424.8326 #>  [16,] 434.6443 433.2153 431.7739 430.3197 428.8524 427.3715 425.8765 424.3670 #>  [17,] 434.2069 432.7749 431.3304 429.8730 428.4022 426.9177 425.4188 423.9052 #>  [18,] 433.7725 432.3377 430.8902 429.4296 427.9555 426.4674 424.9648 423.4471 #>  [19,] 433.3412 431.9036 430.4532 428.9896 427.5122 426.0207 424.5145 422.9930 #>  [20,] 432.9130 431.4728 430.0196 428.5530 427.0725 425.5777 424.0680 422.5428 #>  [21,] 432.4879 431.0452 429.5893 428.1199 426.6364 425.1384 423.6253 422.0966 #>  [22,] 432.0660 430.6208 429.1624 427.6903 426.2040 424.7029 423.1866 421.6545 #>  [23,] 431.6473 430.1998 428.7389 427.2642 425.7752 424.2713 422.7519 421.2164 #>  [24,] 431.2318 429.7821 428.3189 426.8418 425.3501 423.8434 422.3211 420.7826 #>  [25,] 430.8195 429.3678 427.9024 426.4229 424.9288 423.4195 421.8944 420.3530 #>  [26,] 430.4106 428.9569 427.4894 426.0078 424.5113 422.9995 421.4718 419.9276 #>  [27,] 430.0049 428.5494 427.0800 425.5963 424.0976 422.5836 421.0534 419.5065 #>  [28,] 429.6026 428.1453 426.6742 425.1885 423.6878 422.1716 420.6391 419.0898 #>  [29,] 429.2037 427.7448 426.2719 424.7845 423.2819 421.7637 420.2291 418.6775 #>  [30,] 428.8081 427.3478 425.8733 424.3842 422.8799 421.3598 419.8233 418.2696 #>  [31,] 428.4159 426.9542 425.4784 423.9878 422.4819 420.9601 419.4217 417.8661 #>  [32,] 428.0272 426.5643 425.0871 423.5952 422.0879 420.5645 419.0245 417.4672 #>  [33,] 427.6418 426.1779 424.6996 423.2064 421.6978 420.1731 418.6317 417.0728 #>  [34,] 427.2600 425.7950 424.3158 422.8215 421.3118 419.7859 418.2431 416.6829 #>  [35,] 426.8815 425.4158 423.9357 422.4405 420.9298 419.4028 417.8590 416.2976 #>  [36,] 426.5066 425.0402 423.5593 422.0634 420.5518 419.0240 417.4793 415.9169 #>  [37,] 426.1351 424.6682 423.1867 421.6902 420.1780 418.6495 417.1040 415.5407 #>  [38,] 425.7672 424.2998 422.8179 421.3209 419.8082 418.2791 416.7331 415.1693 #>  [39,] 425.4027 423.9350 422.4528 420.9555 419.4425 417.9131 416.3666 414.8024 #>  [40,] 425.0417 423.5739 422.0915 420.5940 419.0808 417.5512 416.0046 414.4402 #>  [41,] 424.6843 423.2164 421.7340 420.2365 418.7233 417.1937 415.6470 414.0826 #>  [42,] 424.3303 422.8626 421.3803 419.8829 418.3699 416.8404 415.2939 413.7296 #>  [43,] 423.9798 422.5123 421.0304 419.5333 418.0205 416.4914 414.9452 413.3813 #>  [44,] 423.6328 422.1658 420.6842 419.1876 417.6752 416.1466 414.6010 413.0376 #>  [45,] 423.2893 421.8228 420.3418 418.8457 417.3340 415.8061 414.2612 412.6986 #>  [46,] 422.9493 421.4835 420.0031 418.5078 416.9969 415.4698 413.9258 412.3641 #>  [47,] 422.6128 421.1477 419.6682 418.1738 416.6639 415.1377 413.5948 412.0343 #>  [48,] 422.2797 420.8156 419.3371 417.8437 416.3348 414.8099 413.2682 411.7090 #>  [49,] 421.9501 420.4870 419.0096 417.5174 416.0098 414.4862 412.9459 411.3882 #>  [50,] 421.6239 420.1620 418.6859 417.1950 415.6888 414.1667 412.6280 411.0720 #>  [51,] 421.3012 419.8406 418.3659 416.8765 415.3718 413.8514 412.3144 410.7603 #>  [52,] 420.9818 419.5227 418.0495 416.5617 415.0588 413.5401 412.0051 410.4531 #>  [53,] 420.6659 419.2083 417.7367 416.2507 414.7497 413.2330 411.7001 410.1503 #>  [54,] 420.3533 418.8974 417.4276 415.9435 414.4444 412.9299 411.3993 409.8519 #>  [55,] 420.0440 418.5899 417.1221 415.6400 414.1431 412.6308 411.1026 409.5578 #>  [56,] 419.7380 418.2859 416.8201 415.3402 413.8456 412.3358 410.8101 409.2681 #>  [57,] 419.4354 417.9853 416.5217 415.0440 413.5519 412.0447 410.5218 408.9826 #>  [58,] 419.1360 417.6880 416.2267 414.7515 413.2619 411.7574 410.2375 408.7014 #>  [59,] 418.8398 417.3942 415.9353 414.4626 412.9757 411.4741 409.9572 408.4243 #>  [60,] 418.5468 417.1036 415.6472 414.1773 412.6932 411.1946 409.6808 408.1514 #>  [61,] 418.2570 416.8163 415.3626 413.8954 412.4144 410.9189 409.4084 407.8825 #>  [62,] 417.9704 416.5323 415.0813 413.6171 412.1391 410.6469 409.1399 407.6177 #>  [63,] 417.6868 416.2514 414.8034 413.3421 411.8674 410.3786 408.8752 407.3568 #>  [64,] 417.4063 415.9738 414.5287 413.0706 411.5992 410.1139 408.6143 407.0998 #>  [65,] 417.1289 415.6993 414.2572 412.8024 411.3344 409.8528 408.3570 406.8467 #>  [66,] 416.8545 415.4278 413.9890 412.5376 411.0731 409.5952 408.1034 406.5973 #>  [67,] 416.5830 415.1594 413.7239 412.2759 410.8151 409.3411 407.8534 406.3516 #>  [68,] 416.3144 414.8941 413.4619 412.0175 410.5605 409.0904 407.6070 406.1096 #>  [69,] 416.0487 414.6317 413.2030 411.7622 410.3091 408.8431 407.3639 405.8712 #>  [70,] 415.7858 414.3722 412.9471 411.5101 410.0609 408.5991 407.1243 405.6362 #>  [71,] 415.5257 414.1156 412.6941 411.2609 409.8158 408.3583 406.8881 405.4048 #>  [72,] 415.2684 413.8618 412.4440 411.0148 409.5738 408.1207 406.6551 405.1766 #>  [73,] 415.0138 413.6108 412.1969 410.7717 409.3349 407.8862 406.4253 404.9518 #>  [74,] 414.7619 413.3626 411.9525 410.5314 409.0989 407.6548 406.1987 404.7303 #>  [75,] 414.5125 413.1170 411.7109 410.2939 408.8659 407.4264 405.9751 404.5118 #>  [76,] 414.2658 412.8741 411.4720 410.0593 408.6357 407.2009 405.7546 404.2965 #>  [77,] 414.0216 412.6337 411.2358 409.8274 408.4083 406.9782 405.5370 404.0842 #>  [78,] 413.7798 412.3960 411.0021 409.5981 408.1836 406.7584 405.3222 403.8748 #>  [79,] 413.5405 412.1607 410.7711 409.3715 407.9616 406.5413 405.1103 403.6683 #>  [80,] 413.3036 411.9278 410.5425 409.1474 407.7423 406.3269 404.9011 403.4646 #>  [81,] 413.0690 411.6974 410.3164 408.9258 407.5255 406.1151 404.6946 403.2637 #>  [82,] 412.8367 411.4692 410.0926 408.7067 407.3111 405.9059 404.4907 403.0653 #>  [83,] 412.6066 411.2434 409.8712 408.4899 407.0993 405.6991 404.2893 402.8696 #>  [84,] 412.3788 411.0198 409.6521 408.2755 406.8898 405.4948 404.0904 402.6764 #>  [85,] 412.1531 410.7985 409.4353 408.0634 406.6826 405.2928 403.8938 402.4856 #>  [86,] 411.9295 410.5792 409.2206 407.8534 406.4777 405.0931 403.6996 402.2971 #>  [87,] 411.7079 410.3620 409.0080 407.6457 406.2749 404.8956 403.5077 402.1110 #>  [88,] 411.4884 410.1469 408.7975 407.4400 406.0743 404.7003 403.3179 401.9270 #>  [89,] 411.2708 409.9338 408.5890 407.2364 405.8758 404.5072 403.1303 401.7453 #>  [90,] 411.0551 409.7226 408.3825 407.0348 405.6793 404.3160 402.9448 401.5656 #>  [91,] 410.8413 409.5133 408.1779 406.8351 405.4848 404.1268 402.7612 401.3879 #>  [92,] 410.6293 409.3058 407.9752 406.6373 405.2921 403.9396 402.5796 401.2121 #>  [93,] 410.4191 409.1002 407.7743 406.4413 405.1013 403.7542 402.3998 401.0383 #>  [94,] 410.2106 408.8962 407.5751 406.2471 404.9123 403.5706 402.2219 400.8662 #>  [95,] 410.0038 408.6940 407.3776 406.0547 404.7250 403.3887 402.0456 400.6959 #>  [96,] 409.7986 408.4934 407.1818 405.8638 404.5394 403.2085 401.8711 400.5272 #>  [97,] 409.5950 408.2944 406.9876 405.6746 404.3554 403.0299 401.6982 400.3602 #>  [98,] 409.3929 408.0969 406.7950 405.4870 404.1730 402.8529 401.5268 400.1948 #>  [99,] 409.1923 407.9010 406.6038 405.3009 403.9921 402.6774 401.3570 400.0308 #> [100,] 408.9932 407.7065 406.4142 405.1162 403.8126 402.5034 401.1886 399.8682 #>           [,25]    [,26]    [,27]    [,28]    [,29]    [,30]    [,31]    [,32] #>   [1,] 430.2623 428.8050 427.3365 425.8565 424.3648 422.8612 421.3456 419.8177 #>   [2,] 429.7454 428.2820 426.8071 425.3202 423.8214 422.3102 420.7866 419.2502 #>   [3,] 429.2313 427.7619 426.2806 424.7870 423.2810 421.7624 420.2308 418.6860 #>   [4,] 428.7202 427.2448 425.7571 424.2569 422.7439 421.2177 419.6782 418.1251 #>   [5,] 428.2121 426.7308 425.2368 423.7300 422.2100 420.6765 419.1291 417.5677 #>   [6,] 427.7070 426.2199 424.7198 423.2064 421.6795 420.1386 418.5835 417.0138 #>   [7,] 427.2051 425.7122 424.2060 422.6862 421.1525 419.6044 418.0416 416.4637 #>   [8,] 426.7064 425.2079 423.6957 422.1695 420.6290 419.0738 417.5034 415.9175 #>   [9,] 426.2111 424.7069 423.1888 421.6564 420.1093 418.5470 416.9691 415.3752 #>  [10,] 425.7191 424.2094 422.6856 421.1470 419.5933 418.0240 416.4388 414.8370 #>  [11,] 425.2306 423.7155 422.1860 420.6413 419.0812 417.5051 415.9126 414.3031 #>  [12,] 424.7456 423.2253 421.6901 420.1395 418.5731 416.9903 415.3906 413.7735 #>  [13,] 424.2642 422.7388 421.1981 419.6417 418.0691 416.4798 414.8731 413.2485 #>  [14,] 423.7865 422.2560 420.7100 419.1480 417.5693 415.9735 414.3599 412.7280 #>  [15,] 423.3126 421.7772 420.2260 418.6584 417.0738 415.4717 413.8514 412.2123 #>  [16,] 422.8424 421.3023 419.7460 418.1730 416.5827 414.9744 413.3476 411.7015 #>  [17,] 422.3762 420.8314 419.2702 417.6920 416.0961 414.4818 412.8486 411.1957 #>  [18,] 421.9140 420.3647 418.7987 417.2153 415.6140 413.9940 412.3546 410.6950 #>  [19,] 421.4557 419.9021 418.3315 416.7432 415.1366 413.5110 411.8655 410.1995 #>  [20,] 421.0016 419.4438 417.8687 416.2756 414.6640 413.0329 411.3816 409.7094 #>  [21,] 420.5516 418.9897 417.4104 415.8127 414.1962 412.5599 410.9030 409.2247 #>  [22,] 420.1058 418.5401 416.9566 415.3546 413.7333 412.0920 410.4297 408.7457 #>  [23,] 419.6643 418.0949 416.5075 414.9013 413.2755 411.6293 409.9619 408.2723 #>  [24,] 419.2272 417.6542 416.0630 414.4528 412.8227 411.1720 409.4996 407.8047 #>  [25,] 418.7944 417.2181 415.6233 414.0093 412.3752 410.7200 409.0430 407.3431 #>  [26,] 418.3661 416.7866 415.1885 413.5708 411.9328 410.2736 408.5921 406.8874 #>  [27,] 417.9422 416.3598 414.7585 413.1374 411.4958 409.8327 408.1470 406.4378 #>  [28,] 417.5229 415.9377 414.3334 412.7092 411.0642 409.3974 407.7078 405.9944 #>  [29,] 417.1081 415.5204 413.9133 412.2861 410.6380 408.9678 407.2745 405.5572 #>  [30,] 416.6980 415.1078 413.4983 411.8684 410.2172 408.5439 406.8473 405.1263 #>  [31,] 416.2925 414.7002 413.0883 411.4559 409.8021 408.1259 406.4262 404.7019 #>  [32,] 415.8917 414.2974 412.6834 411.0487 409.3925 407.7137 406.0113 404.2839 #>  [33,] 415.4957 413.8996 412.2837 410.6470 408.9886 407.3075 405.6025 403.8725 #>  [34,] 415.1043 413.5067 411.8891 410.2507 408.5904 406.9072 405.2000 403.4676 #>  [35,] 414.7178 413.1188 411.4998 409.8598 408.1979 406.5130 404.8039 403.0694 #>  [36,] 414.3360 412.7359 411.1157 409.4744 407.8111 406.1247 404.4140 402.6778 #>  [37,] 413.9591 412.3581 410.7369 409.0946 407.4302 405.7426 404.0306 402.2930 #>  [38,] 413.5869 411.9852 410.3633 408.7203 407.0550 405.3665 403.6535 401.9149 #>  [39,] 413.2196 411.6175 409.9951 408.3515 406.6856 404.9965 403.2829 401.5435 #>  [40,] 412.8572 411.2548 409.6321 407.9882 406.3221 404.6326 402.9187 401.1789 #>  [41,] 412.4996 410.8971 409.2745 407.6305 405.9644 404.2749 402.5609 400.8211 #>  [42,] 412.1468 410.5446 408.9221 407.2784 405.6125 403.9233 402.2096 400.4701 #>  [43,] 411.7989 410.1971 408.5751 406.9319 405.2665 403.5778 401.8647 400.1259 #>  [44,] 411.4558 409.8546 408.2333 406.5908 404.9262 403.2384 401.5262 399.7884 #>  [45,] 411.1175 409.5172 407.8968 406.2553 404.5918 402.9051 401.1941 399.4576 #>  [46,] 410.7841 409.1849 407.5656 405.9254 404.2631 402.5779 400.8684 399.1336 #>  [47,] 410.4554 408.8575 407.2396 405.6009 403.9402 402.2567 400.5491 398.8162 #>  [48,] 410.1316 408.5352 406.9189 405.2819 403.6231 401.9415 400.2361 398.5055 #>  [49,] 409.8125 408.2178 406.6033 404.9683 403.3116 401.6323 399.9293 398.2014 #>  [50,] 409.4981 407.9053 406.2929 404.6601 403.0058 401.3291 399.6288 397.9038 #>  [51,] 409.1884 407.5977 405.9877 404.3572 402.7056 401.0317 399.3344 397.6127 #>  [52,] 408.8833 407.2950 405.6875 404.0597 402.4109 400.7401 399.0462 397.3281 #>  [53,] 408.5829 406.9972 405.3923 403.7675 402.1218 400.4543 398.7640 397.0497 #>  [54,] 408.2870 406.7041 405.1021 403.4804 401.8381 400.1742 398.4877 396.7777 #>  [55,] 407.9958 406.4157 404.8169 403.1985 401.5598 399.8998 398.2174 396.5118 #>  [56,] 407.7089 406.1320 404.5365 402.9218 401.2868 399.6309 397.9529 396.2520 #>  [57,] 407.4266 405.8530 404.2610 402.6500 401.0191 399.3675 397.6942 395.9982 #>  [58,] 407.1486 405.5785 403.9903 402.3832 400.7566 399.1095 397.4411 395.7504 #>  [59,] 406.8750 405.3085 403.7242 402.1213 400.4992 398.8569 397.1936 395.5084 #>  [60,] 406.6057 405.0430 403.4628 401.8643 400.2468 398.6094 396.9515 395.2720 #>  [61,] 406.3406 404.7819 403.2060 401.6120 399.9993 398.3672 396.7148 395.0413 #>  [62,] 406.0796 404.5251 402.9536 401.3644 399.7568 398.1300 396.4834 394.8161 #>  [63,] 405.8228 404.2726 402.7057 401.1214 399.5190 397.8978 396.2572 394.5963 #>  [64,] 405.5700 404.0243 402.4621 400.8828 399.2858 397.6704 396.0360 394.3817 #>  [65,] 405.3212 403.7801 402.2228 400.6488 399.0573 397.4479 395.8197 394.1722 #>  [66,] 405.0763 403.5399 401.9877 400.4190 398.8333 397.2300 395.6084 393.9678 #>  [67,] 404.8352 403.3038 401.7567 400.1935 398.6137 397.0166 395.4017 393.7683 #>  [68,] 404.5979 403.0715 401.5297 399.9722 398.3984 396.8077 395.1996 393.5736 #>  [69,] 404.3643 402.8430 401.3067 399.7550 398.1873 396.6032 395.0021 393.3835 #>  [70,] 404.1344 402.6183 401.0876 399.5417 397.9803 396.4029 394.8089 393.1979 #>  [71,] 403.9079 402.3972 400.8722 399.3324 397.7774 396.2068 394.6200 393.0167 #>  [72,] 403.6850 402.1797 400.6605 399.1268 397.5783 396.0146 394.4353 392.8398 #>  [73,] 403.4654 401.9657 400.4524 398.9249 397.3831 395.8264 394.2545 392.6670 #>  [74,] 403.2492 401.7551 400.2478 398.7267 397.1916 395.6420 394.0777 392.4982 #>  [75,] 403.0362 401.5479 400.0466 398.5319 397.0036 395.4613 393.9047 392.3333 #>  [76,] 402.8264 401.3439 399.8487 398.3406 396.8192 395.2842 393.7353 392.1722 #>  [77,] 402.6197 401.1431 399.6542 398.1526 396.6382 395.1105 393.5695 392.0147 #>  [78,] 402.4160 400.9453 399.4627 397.9678 396.4604 394.9403 393.4071 391.8606 #>  [79,] 402.2152 400.7506 399.2743 397.7862 396.2859 394.7732 393.2480 391.7100 #>  [80,] 402.0173 400.5588 399.0889 397.6076 396.1144 394.6093 393.0921 391.5625 #>  [81,] 401.8221 400.3698 398.9064 397.4319 395.9460 394.4485 392.9393 391.4182 #>  [82,] 401.6297 400.1836 398.7267 397.2591 395.7804 394.2906 392.7894 391.2769 #>  [83,] 401.4399 400.0000 398.5497 397.0890 395.6176 394.1355 392.6424 391.1385 #>  [84,] 401.2526 399.8190 398.3754 396.9216 395.4575 393.9831 392.4982 391.0028 #>  [85,] 401.0678 399.6405 398.2035 396.7567 395.3000 393.8333 392.3566 390.8698 #>  [86,] 400.8854 399.4645 398.0341 396.5943 395.1450 393.6861 392.2175 390.7392 #>  [87,] 400.7054 399.2908 397.8671 396.4344 394.9924 393.5412 392.0808 390.6111 #>  [88,] 400.5275 399.1193 397.7024 396.2767 394.8421 393.3987 391.9464 390.4853 #>  [89,] 400.3519 398.9501 397.5399 396.1212 394.6940 393.2583 391.8142 390.3617 #>  [90,] 400.1783 398.7829 397.3795 395.9678 394.5480 393.1201 391.6842 390.2402 #>  [91,] 400.0068 398.6178 397.2211 395.8165 394.4041 392.9840 391.5561 390.1206 #>  [92,] 399.8372 398.4547 397.0647 395.6671 394.2621 392.8497 391.4299 390.0029 #>  [93,] 399.6695 398.2934 396.9101 395.5196 394.1220 392.7173 391.3056 389.8870 #>  [94,] 399.5036 398.1339 396.7574 395.3739 393.9836 392.5866 391.1829 389.7727 #>  [95,] 399.3394 397.9762 396.6064 395.2299 393.8470 392.4576 391.0619 389.6601 #>  [96,] 399.1769 397.8202 396.4570 395.0876 393.7119 392.3301 390.9424 389.5489 #>  [97,] 399.0160 397.6657 396.3092 394.9468 393.5784 392.2042 390.8244 389.4391 #>  [98,] 398.8567 397.5128 396.1630 394.8074 393.4463 392.0796 390.7077 389.3306 #>  [99,] 398.6989 397.3613 396.0181 394.6695 393.3156 391.9564 390.5923 389.2234 #> [100,] 398.5424 397.2112 395.8747 394.5329 393.1861 391.8345 390.4781 389.1172 #>           [,33]    [,34]    [,35]    [,36]    [,37]    [,38]    [,39]    [,40] #>   [1,] 418.2775 416.7247 415.1594 413.5814 411.9907 410.3874 408.7715 407.1432 #>   [2,] 417.7010 416.1388 414.5634 412.9748 411.3728 409.7574 408.1288 406.4869 #>   [3,] 417.1279 415.5562 413.9707 412.3714 410.7581 409.1308 407.4894 405.8340 #>   [4,] 416.5581 414.9770 413.3816 411.7716 410.1470 408.5077 406.8535 405.1845 #>   [5,] 415.9918 414.4014 412.7960 411.1755 409.5396 407.8883 406.2213 404.5387 #>   [6,] 415.4293 413.8295 412.2142 410.5832 408.9361 407.2728 405.5931 403.8968 #>   [7,] 414.8705 413.2615 411.6364 409.9949 408.3366 406.6614 404.9689 403.2591 #>   [8,] 414.3156 412.6975 411.0626 409.4107 407.7414 406.0543 404.3492 402.6257 #>   [9,] 413.7649 412.1377 410.4932 408.8310 407.1506 405.4518 403.7340 401.9970 #>  [10,] 413.2183 411.5822 409.9281 408.2557 406.5645 404.8539 403.1236 401.3732 #>  [11,] 412.6761 411.0312 409.3677 407.6852 405.9831 404.2610 402.5183 400.7545 #>  [12,] 412.1384 410.4848 408.8120 407.1196 405.4068 403.6732 401.9182 400.1412 #>  [13,] 411.6054 409.9432 408.2613 406.5590 404.8357 403.0908 401.3236 399.5335 #>  [14,] 411.0771 409.4065 407.7156 406.0037 404.2701 402.5140 400.7348 398.9317 #>  [15,] 410.5537 408.8749 407.1752 405.4538 403.7100 401.9430 400.1519 398.3360 #>  [16,] 410.0354 408.3485 406.6402 404.9095 403.1557 401.3779 399.5752 397.7468 #>  [17,] 409.5222 407.8275 406.1108 404.3710 402.6074 400.8191 399.0050 397.1642 #>  [18,] 409.0144 407.3121 405.5871 403.8385 402.0654 400.2667 398.4415 396.5886 #>  [19,] 408.5120 406.8023 405.0693 403.3121 401.5297 399.7209 397.8848 396.0201 #>  [20,] 408.0152 406.2983 404.5575 402.7920 401.0005 399.1820 397.3353 395.4591 #>  [21,] 407.5241 405.8002 404.0520 402.2784 400.4782 398.6502 396.7932 394.9058 #>  [22,] 407.0389 405.3083 403.5528 401.7714 399.9627 398.1256 396.2587 394.3605 #>  [23,] 406.5595 404.8225 403.0601 401.2712 399.4544 397.6085 395.7320 393.8233 #>  [24,] 406.0863 404.3431 402.5741 400.7779 398.9534 397.0990 395.2133 393.2946 #>  [25,] 405.6191 403.8701 402.0948 400.2918 398.4598 396.5974 394.7028 392.7745 #>  [26,] 405.1583 403.4037 401.6224 399.8129 397.9739 396.1037 394.2008 392.2634 #>  [27,] 404.7039 402.9440 401.1570 399.3414 397.4957 395.6183 393.7075 391.7613 #>  [28,] 404.2559 402.4912 400.6988 398.8774 397.0254 395.1412 393.2229 391.2686 #>  [29,] 403.8145 402.0452 400.2479 398.4211 396.5633 394.6726 392.7474 390.7854 #>  [30,] 403.3797 401.6062 399.8043 397.9725 396.1093 394.2127 392.2810 390.3120 #>  [31,] 402.9517 401.1742 399.3681 397.5318 395.6636 393.7616 391.8239 389.8484 #>  [32,] 402.5304 400.7495 398.9396 397.0991 395.2263 393.3194 391.3763 389.3948 #>  [33,] 402.1161 400.3320 398.5186 396.6744 394.7976 392.8863 390.9383 388.9515 #>  [34,] 401.7087 399.9218 398.1054 396.2579 394.3775 392.4622 390.5100 388.5185 #>  [35,] 401.3082 399.5189 397.6999 395.8496 393.9661 392.0475 390.0915 388.0959 #>  [36,] 400.9148 399.1235 397.3023 395.4496 393.5635 391.6420 389.6830 387.6839 #>  [37,] 400.5284 398.7355 396.9126 395.0579 393.1697 391.2460 389.2844 387.2826 #>  [38,] 400.1492 398.3550 396.5307 394.6747 392.7849 390.8594 388.8959 386.8920 #>  [39,] 399.7771 397.9821 396.1569 394.2998 392.4089 390.4822 388.5175 386.5121 #>  [40,] 399.4121 397.6166 395.7910 393.9334 392.0419 390.1146 388.1492 386.1431 #>  [41,] 399.0542 397.2587 395.4330 393.5754 391.6839 389.7566 387.7910 385.7849 #>  [42,] 398.7036 396.9084 395.0831 393.2259 391.3349 389.4080 387.4430 385.4375 #>  [43,] 398.3600 396.5656 394.7411 392.8848 390.9948 389.0690 387.1052 385.1009 #>  [44,] 398.0236 396.2304 394.4071 392.5522 390.6636 388.7394 386.7774 384.7752 #>  [45,] 397.6943 395.9026 394.0810 392.2279 390.3414 388.4194 386.4598 384.4601 #>  [46,] 397.3720 395.5823 393.7628 391.9120 390.0279 388.1087 386.1521 384.1557 #>  [47,] 397.0568 395.2694 393.4525 391.6044 389.7233 387.8074 385.8543 383.8619 #>  [48,] 396.7486 394.9639 393.1499 391.3050 389.4274 387.5153 385.5664 383.5786 #>  [49,] 396.4473 394.6657 392.8551 391.0138 389.1402 387.2324 385.2882 383.3056 #>  [50,] 396.1529 394.3748 392.5679 390.7307 388.8615 386.9585 385.0197 383.0429 #>  [51,] 395.8654 394.0910 392.2882 390.4555 388.5913 386.6936 384.7606 382.7902 #>  [52,] 395.5845 393.8144 392.0161 390.1883 388.3294 386.4375 384.5109 382.5475 #>  [53,] 395.3104 393.5447 391.7513 389.9289 388.0757 386.1901 384.2704 382.3145 #>  [54,] 395.0428 393.2820 391.4939 389.6771 387.8301 385.9513 384.0389 382.0911 #>  [55,] 394.7817 393.0261 391.2436 389.4328 387.5924 385.7208 383.8163 381.8770 #>  [56,] 394.5270 392.7769 391.0003 389.1960 387.3626 385.4986 383.6023 381.6721 #>  [57,] 394.2786 392.5343 390.7640 388.9664 387.1404 385.2844 383.3968 381.4762 #>  [58,] 394.0364 392.2982 390.5344 388.7440 386.9257 385.0780 383.1996 381.2889 #>  [59,] 393.8003 392.0684 390.3116 388.5286 386.7183 384.8794 383.0105 381.1102 #>  [60,] 393.5702 391.8449 390.0952 388.3200 386.5181 384.6883 382.8292 380.9397 #>  [61,] 393.3459 391.6275 389.8852 388.1181 386.3248 384.5044 382.6556 380.7772 #>  [62,] 393.1273 391.4161 389.6815 387.9226 386.1384 384.3277 382.4894 380.6224 #>  [63,] 392.9143 391.2105 389.4839 387.7335 385.9585 384.1578 382.3304 380.4751 #>  [64,] 392.7068 391.0106 389.2921 387.5506 385.7851 383.9947 382.1783 380.3351 #>  [65,] 392.5047 390.8162 389.1062 387.3737 385.6179 383.8380 382.0330 380.2021 #>  [66,] 392.3077 390.6273 388.9258 387.2026 385.4567 383.6875 381.8941 380.0757 #>  [67,] 392.1158 390.4436 388.7509 387.0371 385.3014 383.5431 381.7615 379.9559 #>  [68,] 391.9289 390.2650 388.5813 386.8771 385.1517 383.4046 381.6350 379.8422 #>  [69,] 391.7468 390.0914 388.4168 386.7224 385.0075 383.2716 381.5142 379.7345 #>  [70,] 391.5693 389.9226 388.2573 386.5727 384.8685 383.1441 381.3989 379.6325 #>  [71,] 391.3963 389.7584 388.1025 386.4281 384.7346 383.0217 381.2890 379.5359 #>  [72,] 391.2278 389.5988 387.9524 386.2881 384.6056 382.9044 381.1841 379.4444 #>  [73,] 391.0635 389.4435 387.8067 386.1528 384.4812 382.7918 381.0841 379.3579 #>  [74,] 390.9033 389.2924 387.6654 386.0218 384.3613 382.6837 380.9887 379.2761 #>  [75,] 390.7470 389.1454 387.5281 385.8950 384.2457 382.5800 380.8977 379.1987 #>  [76,] 390.5946 389.0023 387.3949 385.7723 384.1342 382.4804 380.8109 379.1255 #>  [77,] 390.4459 388.8629 387.2655 385.6534 384.0266 382.3848 380.7281 379.0563 #>  [78,] 390.3007 388.7271 387.1397 385.5383 383.9227 382.2930 380.6490 378.9909 #>  [79,] 390.1590 388.5948 387.0174 385.4266 383.8224 382.2047 380.5735 378.9289 #>  [80,] 390.0205 388.4659 386.8985 385.3184 383.7255 382.1197 380.5013 378.8702 #>  [81,] 389.8852 388.3401 386.7828 385.2133 383.6317 382.0380 380.4322 378.8147 #>  [82,] 389.7529 388.2173 386.6701 385.1113 383.5410 381.9592 380.3661 378.7620 #>  [83,] 389.6235 388.0974 386.5603 385.0122 383.4531 381.8833 380.3028 378.7120 #>  [84,] 389.4969 387.9803 386.4533 384.9158 383.3680 381.8100 380.2421 378.6645 #>  [85,] 389.3729 387.8659 386.3489 384.8220 383.2854 381.7392 380.1837 378.6193 #>  [86,] 389.2514 387.7539 386.2470 384.7307 383.2052 381.6707 380.1276 378.5763 #>  [87,] 389.1323 387.6443 386.1474 384.6416 383.1272 381.6044 380.0736 378.5351 #>  [88,] 389.0155 387.5370 386.0500 384.5547 383.0513 381.5401 380.0214 378.4958 #>  [89,] 388.9009 387.4318 385.9547 384.4698 382.9773 381.4776 379.9711 378.4581 #>  [90,] 388.7883 387.3286 385.8614 384.3868 382.9052 381.4169 379.9223 378.4218 #>  [91,] 388.6776 387.2273 385.7699 384.3056 382.8348 381.3577 379.8749 378.3869 #>  [92,] 388.5688 387.1278 385.6801 384.2260 382.7659 381.3000 379.8289 378.3531 #>  [93,] 388.4617 387.0300 385.5920 384.1480 382.6984 381.2436 379.7841 378.3204 #>  [94,] 388.3563 386.9337 385.5053 384.0713 382.6322 381.1884 379.7403 378.2885 #>  [95,] 388.2523 386.8389 385.4200 383.9960 382.5673 381.1343 379.6975 378.2574 #>  [96,] 388.1498 386.7454 385.3360 383.9218 382.5034 381.0811 379.6554 378.2270 #>  [97,] 388.0486 386.6532 385.2531 383.8487 382.4404 381.0287 379.6141 378.1971 #>  [98,] 387.9487 386.5622 385.1713 383.7766 382.3784 380.9771 379.5733 378.1676 #>  [99,] 387.8499 386.4722 385.0905 383.7054 382.3170 380.9261 379.5330 378.1384 #> [100,] 387.7522 386.3832 385.0106 383.6349 382.2564 380.8756 379.4931 378.1095 #>           [,41]    [,42]    [,43]    [,44]    [,45]    [,46]    [,47]    [,48] #>   [1,] 405.5027 403.8503 402.1865 400.5119 398.8271 397.1330 395.4309 393.7218 #>   [2,] 404.8321 403.1644 401.4844 399.7926 398.0895 396.3761 394.6533 392.9225 #>   [3,] 404.1647 402.4817 400.7853 399.0761 397.3545 395.6215 393.8778 392.1248 #>   [4,] 403.5007 401.8022 400.0895 398.3627 396.6225 394.8695 393.1046 391.3291 #>   [5,] 402.8403 401.1264 399.3971 397.6527 395.8936 394.1205 392.3342 390.5357 #>   [6,] 402.1839 400.4544 398.7085 396.9463 395.1682 393.3748 391.5667 389.7450 #>   [7,] 401.5316 399.7866 398.0240 396.2439 394.4467 392.6327 390.8027 388.9575 #>   [8,] 400.8838 399.1231 397.3438 395.5458 393.7293 391.8947 390.0425 388.1734 #>   [9,] 400.2406 398.4644 396.6683 394.8523 393.0165 391.1611 389.2865 387.3933 #>  [10,] 399.6023 397.8106 395.9978 394.1638 392.3086 390.4323 388.5351 386.6177 #>  [11,] 398.9692 397.1620 395.3326 393.4806 391.6060 389.7087 387.7889 385.8469 #>  [12,] 398.3416 396.5190 394.6730 392.8031 390.9091 388.9908 387.0482 385.0815 #>  [13,] 397.7198 395.8819 394.0194 392.1316 390.2182 388.2789 386.3135 384.3220 #>  [14,] 397.1040 395.2510 393.3721 391.4665 389.5338 387.5736 385.5853 383.5690 #>  [15,] 396.4945 394.6266 392.7314 390.8082 388.8564 386.8752 384.8642 382.8230 #>  [16,] 395.8917 394.0090 392.0977 390.1571 388.1862 386.1843 384.1506 382.0846 #>  [17,] 395.2957 393.3985 391.4714 389.5135 387.5239 385.5014 383.4451 381.3544 #>  [18,] 394.7069 392.7954 390.8528 388.8780 386.8697 384.8268 382.7483 380.6330 #>  [19,] 394.1256 392.2001 390.2423 388.2507 386.2242 384.1612 382.0606 379.9210 #>  [20,] 393.5521 391.6129 389.6401 387.6322 385.5877 383.5050 381.3827 379.2190 #>  [21,] 392.9866 391.0341 389.0468 387.0229 384.9608 382.8588 380.7150 378.5277 #>  [22,] 392.4295 390.4640 388.4625 386.4231 384.3439 382.2230 380.0583 377.8478 #>  [23,] 391.8809 389.9030 387.8877 385.8333 383.7374 381.5981 379.4130 377.1798 #>  [24,] 391.3412 389.3512 387.3228 385.2537 383.1418 380.9847 378.7798 376.5245 #>  [25,] 390.8106 388.8091 386.7680 384.6849 382.5575 380.3832 378.1592 375.8825 #>  [26,] 390.2894 388.2769 386.2237 384.1272 381.9849 379.7941 377.5517 375.2544 #>  [27,] 389.7779 387.7549 385.6901 383.5809 381.4245 379.2179 376.9579 374.6409 #>  [28,] 389.2762 387.2434 385.1677 383.0464 380.8766 378.6551 376.3784 374.0426 #>  [29,] 388.7846 386.7426 384.6566 382.5240 380.3416 378.1060 375.8136 373.4601 #>  [30,] 388.3033 386.2527 384.1573 382.0141 379.8199 377.5712 375.2640 372.8939 #>  [31,] 387.8326 385.7740 383.6698 381.5169 379.3119 377.0510 374.7301 372.3446 #>  [32,] 387.3725 385.3067 383.1945 381.0327 378.8178 376.5458 374.2124 371.8128 #>  [33,] 386.9233 384.8510 382.7316 380.5618 378.3379 376.0559 373.7112 371.2988 #>  [34,] 386.4851 384.4071 382.2813 380.1044 377.8726 375.5817 373.2270 370.8032 #>  [35,] 386.0581 383.9751 381.8438 379.6608 377.4221 375.1234 372.7600 370.3263 #>  [36,] 385.6423 383.5551 381.4192 379.2310 376.9865 374.6813 372.3105 369.8685 #>  [37,] 385.2379 383.1473 381.0077 378.8152 376.5661 374.2556 371.8789 369.4300 #>  [38,] 384.8449 382.7518 380.6093 378.4137 376.1610 373.8465 371.4652 369.0112 #>  [39,] 384.4635 382.3686 380.2242 378.0264 375.7713 373.4541 371.0697 368.6122 #>  [40,] 384.0937 381.9979 379.8524 377.6535 375.3971 373.0784 370.6924 368.2331 #>  [41,] 383.7354 381.6395 379.4939 377.2949 375.0384 372.7196 370.3335 367.8739 #>  [42,] 383.3887 381.2936 379.1488 376.9507 374.6952 372.3777 369.9928 367.5348 #>  [43,] 383.0535 380.9600 378.8170 376.6209 374.3676 372.0525 369.6704 367.2156 #>  [44,] 382.7299 380.6388 378.4985 376.3054 374.0554 371.7440 369.3662 366.9163 #>  [45,] 382.4178 380.3299 378.1931 376.0040 373.7585 371.4522 369.0801 366.6365 #>  [46,] 382.1170 380.0332 377.9009 375.7167 373.4768 371.1768 368.8117 366.3762 #>  [47,] 381.8276 379.7485 377.6216 375.4434 373.2101 370.9176 368.5610 366.1351 #>  [48,] 381.5493 379.4758 377.3551 375.1838 372.9583 370.6744 368.3276 365.9127 #>  [49,] 381.2821 379.2149 377.1012 374.9378 372.7210 370.4469 368.1111 365.7088 #>  [50,] 381.0258 378.9657 376.8598 374.7051 372.4980 370.2348 367.9113 365.5229 #>  [51,] 380.7802 378.7279 376.6306 374.4854 372.2890 370.0378 367.7278 365.3545 #>  [52,] 380.5451 378.5013 376.4134 374.2786 372.0938 369.8555 367.5600 365.2031 #>  [53,] 380.3204 378.2857 376.2079 374.0843 371.9119 369.6875 367.4075 365.0681 #>  [54,] 380.1058 378.0808 376.0138 373.9021 371.7430 369.5333 367.2699 364.9491 #>  [55,] 379.9012 377.8865 375.8309 373.7318 371.5867 369.3926 367.1466 364.8454 #>  [56,] 379.7062 377.7025 375.6588 373.5730 371.4426 369.2649 367.0372 364.7563 #>  [57,] 379.5206 377.5284 375.4973 373.4254 371.3104 369.1497 366.9410 364.6814 #>  [58,] 379.3443 377.3639 375.3460 373.2886 371.1895 369.0466 366.8575 364.6198 #>  [59,] 379.1769 377.2089 375.2046 373.1621 371.0796 368.9549 366.7861 364.5710 #>  [60,] 379.0181 377.0630 375.0727 373.0457 370.9802 368.8744 366.7264 364.5344 #>  [61,] 378.8677 376.9258 374.9500 372.9389 370.8909 368.8043 366.6776 364.5092 #>  [62,] 378.7254 376.7971 374.8362 372.8414 370.8112 368.7443 366.6393 364.4948 #>  [63,] 378.5909 376.6765 374.7309 372.7526 370.7407 368.6938 366.6108 364.4906 #>  [64,] 378.4639 376.5638 374.6336 372.6723 370.6789 368.6523 366.5916 364.4960 #>  [65,] 378.3442 376.4586 374.5442 372.6001 370.6254 368.6194 366.5812 364.5102 #>  [66,] 378.2315 376.3606 374.4622 372.5355 370.5798 368.5945 366.5789 364.5328 #>  [67,] 378.1254 376.2694 374.3872 372.4781 370.5416 368.5771 366.5844 364.5631 #>  [68,] 378.0257 376.1848 374.3190 372.4276 370.5104 368.5669 366.5969 364.6005 #>  [69,] 377.9321 376.1065 374.2571 372.3836 370.4857 368.5632 366.6161 364.6444 #>  [70,] 377.8443 376.0340 374.2013 372.3457 370.4672 368.5657 366.6414 364.6944 #>  [71,] 377.7621 375.9672 374.1511 372.3136 370.4545 368.5740 366.6723 364.7499 #>  [72,] 377.6851 375.9058 374.1064 372.2868 370.4471 368.5875 366.7084 364.8104 #>  [73,] 377.6131 375.8493 374.0666 372.2651 370.4447 368.6059 366.7493 364.8754 #>  [74,] 377.5458 375.7976 374.0316 372.2480 370.4469 368.6289 366.7944 364.9444 #>  [75,] 377.4829 375.7504 374.0011 372.2353 370.4534 368.6559 366.8435 365.0171 #>  [76,] 377.4243 375.7073 373.9746 372.2267 370.4638 368.6866 366.8960 365.0929 #>  [77,] 377.3696 375.6681 373.9520 372.2217 370.4777 368.7208 366.9516 365.1715 #>  [78,] 377.3186 375.6326 373.9330 372.2202 370.4950 368.7579 367.0101 365.2526 #>  [79,] 377.2711 375.6004 373.9172 372.2219 370.5151 368.7978 367.0709 365.3356 #>  [80,] 377.2269 375.5715 373.9044 372.2264 370.5379 368.8401 367.1338 365.4204 #>  [81,] 377.1856 375.5454 373.8945 372.2335 370.5631 368.8844 367.1985 365.5066 #>  [82,] 377.1471 375.5220 373.8870 372.2429 370.5904 368.9306 367.2646 365.5939 #>  [83,] 377.1113 375.5010 373.8818 372.2544 370.6196 368.9784 367.3320 365.6819 #>  [84,] 377.0778 375.4823 373.8787 372.2677 370.6503 369.0274 367.4004 365.7705 #>  [85,] 377.0464 375.4656 373.8774 372.2827 370.6824 369.0775 367.4694 365.8594 #>  [86,] 377.0171 375.4507 373.8778 372.2991 370.7157 369.1285 367.5389 365.9483 #>  [87,] 376.9896 375.4375 373.8796 372.3167 370.7498 369.1800 367.6086 366.0370 #>  [88,] 376.9637 375.4257 373.8827 372.3354 370.7847 369.2320 367.6784 366.1254 #>  [89,] 376.9393 375.4153 373.8868 372.3548 370.8202 369.2842 367.7480 366.2132 #>  [90,] 376.9162 375.4059 373.8918 372.3749 370.8560 369.3364 367.8173 366.3002 #>  [91,] 376.8942 375.3975 373.8976 372.3954 370.8920 369.3884 367.8861 366.3864 #>  [92,] 376.8732 375.3899 373.9039 372.4163 370.9280 369.4402 367.9542 366.4714 #>  [93,] 376.8531 375.3829 373.9107 372.4374 370.9639 369.4916 368.0215 366.5553 #>  [94,] 376.8337 375.3765 373.9178 372.4585 370.9996 369.5423 368.0879 366.6378 #>  [95,] 376.8149 375.3704 373.9250 372.4794 371.0348 369.5923 368.1532 366.7189 #>  [96,] 376.7965 375.3646 373.9322 372.5002 371.0696 369.6415 368.2173 366.7983 #>  [97,] 376.7785 375.3590 373.9393 372.5206 371.1037 369.6898 368.2802 366.8761 #>  [98,] 376.7607 375.3533 373.9463 372.5405 371.1370 369.7370 368.3416 366.9522 #>  [99,] 376.7430 375.3476 373.9529 372.5599 371.1695 369.7830 368.4015 367.0263 #> [100,] 376.7254 375.3417 373.9591 372.5785 371.2011 369.8278 368.4598 367.0985 #>           [,49]    [,50]    [,51]    [,52]    [,53]    [,54]    [,55]    [,56] #>   [1,] 392.0075 390.2898 388.5709 386.8534 385.1402 383.4347 381.7409 380.0632 #>   [2,] 391.1851 389.4430 387.6984 385.9539 384.2123 382.4773 380.7527 379.0432 #>   [3,] 390.3639 388.5969 386.8260 385.0536 383.2829 381.5173 379.7608 378.0181 #>   [4,] 389.5442 387.7518 385.9539 384.1530 382.3522 380.5550 378.7654 376.9883 #>   [5,] 388.7264 386.9080 385.0825 383.2524 381.4206 379.5908 377.7670 375.9540 #>   [6,] 387.9109 386.0661 384.2123 382.3522 380.4886 378.6251 376.7658 374.9157 #>   [7,] 387.0982 385.2263 383.3438 381.4529 379.5566 377.6583 375.7623 373.8736 #>   [8,] 386.2885 384.3892 382.4773 380.5550 378.6251 376.6910 374.7571 372.8282 #>   [9,] 385.4825 383.5553 381.6134 379.6590 377.6946 375.7238 373.7506 371.7801 #>  [10,] 384.6806 382.7251 380.7527 378.7654 376.7658 374.7571 372.7434 370.7299 #>  [11,] 383.8833 381.8992 379.8958 377.8750 375.8392 373.7917 371.7363 369.6781 #>  [12,] 383.0912 381.0780 379.0432 376.9883 374.9157 372.8282 370.7299 368.6255 #>  [13,] 382.3048 380.2623 378.1956 376.1061 373.9958 371.8676 369.7250 367.5729 #>  [14,] 381.5247 379.4527 377.3538 375.2291 373.0805 370.9105 368.7225 366.5212 #>  [15,] 380.7515 378.6498 376.5184 374.3581 372.1705 369.9579 367.7234 365.4714 #>  [16,] 379.9859 377.8544 375.6902 373.4940 371.2669 369.0109 366.7288 364.4246 #>  [17,] 379.2286 377.0671 374.8700 372.6375 370.3705 368.0704 365.7397 363.3820 #>  [18,] 378.4801 376.2888 374.0587 371.7898 369.4823 367.1375 364.7573 362.3449 #>  [19,] 377.7412 375.5202 373.2572 370.9517 368.6036 366.2136 363.7831 361.3147 #>  [20,] 377.0126 374.7621 372.4663 370.1242 367.7353 365.2998 362.8184 360.2931 #>  [21,] 376.2951 374.0153 371.6869 369.3084 366.8788 364.3975 361.8646 359.2815 #>  [22,] 375.5893 373.2808 370.9201 368.5054 366.0352 363.5080 360.9235 358.2820 #>  [23,] 374.8961 372.5592 370.1668 367.7164 365.2058 362.6330 359.9967 357.2963 #>  [24,] 374.2161 371.8515 369.4280 366.9424 364.3919 361.7739 359.0859 356.3265 #>  [25,] 373.5501 371.1586 368.7047 366.1846 363.5950 360.9322 358.1931 355.3747 #>  [26,] 372.8989 370.4813 367.9979 365.4443 362.8164 360.1097 357.3200 354.4433 #>  [27,] 372.2632 369.8205 367.3086 364.7225 362.0574 359.3080 356.4688 353.5345 #>  [28,] 371.6437 369.1770 366.6378 364.0205 361.3196 358.5286 355.6413 352.6508 #>  [29,] 371.0411 368.5517 365.9865 363.3395 360.6042 357.7734 354.8396 351.7945 #>  [30,] 370.4561 367.9453 365.3556 362.6805 359.9126 357.0440 354.0657 350.9682 #>  [31,] 369.8893 367.3586 364.7461 362.0446 359.2462 356.3419 353.3217 350.1744 #>  [32,] 369.3414 366.7924 364.1588 361.4330 358.6062 355.6688 352.6094 349.4154 #>  [33,] 368.8129 366.2472 363.5945 360.8465 357.9939 355.0261 351.9307 348.6936 #>  [34,] 368.3044 365.7238 363.0540 360.2862 357.4104 354.4152 351.2873 348.0112 #>  [35,] 367.8162 365.2227 362.5380 359.7528 356.8567 353.8375 350.6810 347.3704 #>  [36,] 367.3489 364.7444 362.0470 359.2471 356.3337 353.2940 350.1130 346.7729 #>  [37,] 366.9027 364.2894 361.5817 358.7697 355.8422 352.7858 349.5848 346.2204 #>  [38,] 366.4779 363.8579 361.1423 358.3212 355.3829 352.3137 349.0973 345.7143 #>  [39,] 366.0749 363.4502 360.7293 357.9019 354.9563 351.8783 348.6514 345.2556 #>  [40,] 365.6937 363.0665 360.3428 357.5122 354.5626 351.4801 348.2476 344.8450 #>  [41,] 365.3344 362.7070 359.9830 357.1521 354.2022 351.1192 347.8862 344.4830 #>  [42,] 364.9970 362.3716 359.6499 356.8217 353.8749 350.7957 347.5673 344.1696 #>  [43,] 364.6814 362.0602 359.3434 356.5208 353.5808 350.5095 347.2906 343.9045 #>  [44,] 364.3876 361.7727 359.0632 356.2493 353.3193 350.2601 347.0556 343.6870 #>  [45,] 364.1152 361.5089 358.8092 356.0067 353.0902 350.0469 346.8615 343.5160 #>  [46,] 363.8641 361.2683 358.5808 355.7925 352.8927 349.8691 346.7073 343.3904 #>  [47,] 363.6339 361.0506 358.3776 355.6061 352.7261 349.7258 346.5918 343.3085 #>  [48,] 363.4242 360.8554 358.1990 355.4469 352.5895 349.6159 346.5137 343.2684 #>  [49,] 363.2345 360.6819 358.0444 355.3139 352.4818 349.5381 346.4712 343.2683 #>  [50,] 363.0643 360.5298 357.9129 355.2064 352.4021 349.4910 346.4627 343.3058 #>  [51,] 362.9131 360.3982 357.8038 355.1232 352.3491 349.4731 346.4863 343.3786 #>  [52,] 362.7802 360.2864 357.7162 355.0634 352.3215 349.4830 346.5401 343.4843 #>  [53,] 362.6651 360.1938 357.6492 355.0259 352.3179 349.5189 346.6221 343.6205 #>  [54,] 362.5670 360.1195 357.6020 355.0096 352.3372 349.5793 346.7304 343.7847 #>  [55,] 362.4853 360.0626 357.5734 355.0132 352.3778 349.6625 346.8628 343.9745 #>  [56,] 362.4192 360.0225 357.5625 355.0357 352.4383 349.7667 347.0174 344.1873 #>  [57,] 362.3680 359.9981 357.5683 355.0758 352.5175 349.8904 347.1922 344.4209 #>  [58,] 362.3310 359.9886 357.5899 355.1324 352.6138 350.0319 347.3853 344.6730 #>  [59,] 362.3074 359.9932 357.6261 355.2043 352.7259 350.1897 347.5948 344.9415 #>  [60,] 362.2965 360.0110 357.6761 355.2903 352.8525 350.3621 347.8189 345.2242 #>  [61,] 362.2975 360.0411 357.7388 355.3894 352.9924 350.5477 348.0560 345.5192 #>  [62,] 362.3097 360.0828 357.8132 355.5003 353.1441 350.7450 348.3044 345.8247 #>  [63,] 362.3323 360.1351 357.8984 355.6222 353.3066 350.9528 348.5626 346.1391 #>  [64,] 362.3647 360.1973 357.9936 355.7538 353.4787 351.1697 348.8292 346.4607 #>  [65,] 362.4061 360.2686 358.0978 355.8943 353.6593 351.3945 349.1028 346.7880 #>  [66,] 362.4559 360.3482 358.2102 356.0428 353.8473 351.6261 349.3822 347.1199 #>  [67,] 362.5133 360.4354 358.3300 356.1982 354.0419 351.8634 349.6662 347.4549 #>  [68,] 362.5778 360.5295 358.4563 356.3598 354.2419 352.1054 349.9538 347.7920 #>  [69,] 362.6488 360.6298 358.5886 356.5268 354.4467 352.3512 350.2441 348.1303 #>  [70,] 362.7255 360.7356 358.7260 356.6984 354.6553 352.5999 350.5360 348.4687 #>  [71,] 362.8076 360.8464 358.8679 356.8739 354.8671 352.8507 350.8288 348.8064 #>  [72,] 362.8944 360.9616 359.0136 357.0526 355.0813 353.1029 351.1218 349.1428 #>  [73,] 362.9854 361.0805 359.1626 357.2339 355.2972 353.3559 351.4142 349.4771 #>  [74,] 363.0800 361.2027 359.3144 357.4173 355.5143 353.6090 351.7055 349.8088 #>  [75,] 363.1780 361.3277 359.4683 357.6021 355.7320 353.8616 351.9951 350.1374 #>  [76,] 363.2787 361.4551 359.6240 357.7879 355.9498 354.1133 352.2825 350.4623 #>  [77,] 363.3818 361.5842 359.7809 357.9742 356.1673 354.3636 352.5673 350.7831 #>  [78,] 363.4869 361.7149 359.9386 358.1606 356.3839 354.6121 352.8491 351.0996 #>  [79,] 363.5936 361.8466 360.0968 358.3467 356.5994 354.8583 353.1275 351.4114 #>  [80,] 363.7015 361.9790 360.2550 358.5321 356.8133 355.1020 353.4022 351.7182 #>  [81,] 363.8104 362.1118 360.4130 358.7165 357.0254 355.3429 353.6730 352.0198 #>  [82,] 363.9199 362.2447 360.5704 358.8996 357.2353 355.5807 353.9395 352.3161 #>  [83,] 364.0297 362.3773 360.7269 359.0811 357.4427 355.8151 354.2017 352.6067 #>  [84,] 364.1396 362.5094 360.8823 359.2608 357.6475 356.0459 354.4593 352.8917 #>  [85,] 364.2492 362.6408 361.0364 359.4383 357.8495 356.2729 354.7121 353.1709 #>  [86,] 364.3584 362.7712 361.1888 359.6136 358.0483 356.4961 354.9601 353.4441 #>  [87,] 364.4670 362.9004 361.3394 359.7864 358.2440 356.7152 355.2031 353.7114 #>  [88,] 364.5747 363.0282 361.4881 359.9565 358.4362 356.9300 355.4411 353.9727 #>  [89,] 364.6814 363.1545 361.6345 360.1238 358.6249 357.1406 355.6739 354.2279 #>  [90,] 364.7869 363.2790 361.7787 360.2882 358.8100 357.3468 355.9014 354.4771 #>  [91,] 364.8910 363.4017 361.9205 360.4496 358.9914 357.5485 356.1238 354.7202 #>  [92,] 364.9935 363.5223 362.0596 360.6077 359.1689 357.7457 356.3408 354.9572 #>  [93,] 365.0945 363.6407 362.1961 360.7626 359.3425 357.9383 356.5526 355.1881 #>  [94,] 365.1936 363.7570 362.3298 360.9141 359.5122 358.1263 356.7590 355.4130 #>  [95,] 365.2908 363.8708 362.4606 361.0622 359.6778 358.3097 356.9602 355.6319 #>  [96,] 365.3861 363.9822 362.5885 361.2069 359.8394 358.4884 357.1560 355.8448 #>  [97,] 365.4792 364.0910 362.7133 361.3479 359.9969 358.6624 357.3466 356.0518 #>  [98,] 365.5702 364.1973 362.8351 361.4854 360.1503 358.8317 357.5319 356.2530 #>  [99,] 365.6589 364.3008 362.9537 361.6193 360.2996 358.9964 357.7119 356.4483 #> [100,] 365.7453 364.4016 363.0691 361.7495 360.4446 359.1564 357.8867 356.6378 #>           [,57]    [,58]    [,59]    [,60]    [,61]    [,62]    [,63]    [,64] #>   [1,] 378.4066 376.7764 375.1786 373.6199 372.1071 370.6473 369.2481 367.9168 #>   [2,] 377.3538 375.6902 374.0587 372.4663 370.9201 369.4280 367.9979 366.6378 #>   [3,] 376.2946 374.5960 372.9291 371.3010 369.7196 368.1931 366.7301 365.3393 #>   [4,] 375.2291 373.4940 371.7898 370.1242 368.5054 366.9424 365.4443 364.0205 #>   [5,] 374.1577 372.3842 370.6408 368.9356 367.2773 365.6755 364.1399 362.6809 #>   [6,] 373.0805 371.2669 369.4823 367.7353 366.0352 364.3919 362.8164 361.3196 #>   [7,] 371.9980 370.1423 368.3145 366.5234 364.7788 363.0915 361.4732 359.9357 #>   [8,] 370.9105 369.0109 367.1375 365.2998 363.5080 361.7739 360.1097 358.5286 #>   [9,] 369.8185 367.8729 365.9517 364.0647 362.2230 360.4388 358.7255 357.0974 #>  [10,] 368.7225 366.7288 364.7573 362.8184 360.9235 359.0859 357.3200 355.6413 #>  [11,] 367.6232 365.5792 363.5549 361.5610 359.6098 357.7152 355.8928 354.1593 #>  [12,] 366.5212 364.4246 362.3449 360.2931 358.2820 356.3265 354.4433 352.6508 #>  [13,] 365.4173 363.2659 361.1280 359.0150 356.9403 354.9197 352.9712 351.1147 #>  [14,] 364.3125 362.1039 359.9050 357.7273 355.5851 353.4949 351.4761 349.5503 #>  [15,] 363.2076 360.9395 358.6766 356.4309 354.2170 352.0524 349.9578 347.9568 #>  [16,] 362.1039 359.7739 357.4441 355.1266 352.8366 350.5925 348.4163 346.3335 #>  [17,] 361.0026 358.6083 356.2086 353.8156 351.4449 349.1156 346.8514 344.6797 #>  [18,] 359.9050 357.4441 354.9715 352.4991 350.0428 347.6227 345.2635 342.9951 #>  [19,] 358.8127 356.2830 353.7343 351.1787 348.6319 346.1146 343.6530 341.2793 #>  [20,] 357.7273 355.1266 352.4991 349.8562 347.2137 344.5928 342.0208 339.5321 #>  [21,] 356.6508 353.9771 351.2678 348.5337 345.7903 343.0589 340.3679 337.7539 #>  [22,] 355.5851 352.8366 350.0428 347.2137 344.3641 341.5151 338.6960 335.9453 #>  [23,] 354.5324 351.7075 348.8268 345.8990 342.9379 339.9641 337.0072 334.1076 #>  [24,] 353.4949 350.5925 347.6227 344.5928 341.5151 338.4093 335.3044 332.2425 #>  [25,] 352.4753 349.4944 346.4337 343.2987 340.0996 336.8544 333.5914 330.3529 #>  [26,] 351.4761 348.4163 345.2635 342.0208 338.6960 335.3044 331.8726 328.4426 #>  [27,] 350.5001 347.3615 344.1159 340.7636 337.3092 333.7649 330.1540 326.5167 #>  [28,] 349.5503 346.3335 342.9951 339.5321 335.9453 332.2425 328.4426 324.5823 #>  [29,] 348.6295 345.3359 341.9056 338.3317 334.6107 330.7448 326.7469 322.6480 #>  [30,] 347.7409 344.3726 340.8520 337.1683 333.3125 329.2805 325.0773 320.7251 #>  [31,] 346.8875 343.4474 339.8393 336.0480 332.0587 327.8595 323.4457 318.8276 #>  [32,] 346.0724 342.5641 338.8724 334.9772 330.8575 326.4925 321.8658 316.9725 #>  [33,] 345.2985 341.7267 337.9563 333.9626 329.7176 325.1913 320.3533 315.1799 #>  [34,] 344.5688 340.9388 337.0959 333.0107 328.6482 323.9680 318.9251 313.4733 #>  [35,] 343.8859 340.2039 336.2961 332.1280 327.6580 322.8354 317.5994 311.8789 #>  [36,] 343.2522 339.5254 335.5611 331.3205 326.7556 321.8059 316.3946 310.4247 #>  [37,] 342.6700 338.9061 334.8949 330.5938 325.9491 320.8912 315.3288 309.1396 #>  [38,] 342.1409 338.3484 334.3008 329.9526 325.2453 320.1019 314.4185 308.0509 #>  [39,] 341.6665 337.8543 333.7816 329.4007 324.6499 319.4466 313.6778 307.1824 #>  [40,] 341.2476 337.4250 333.3390 328.9408 324.1668 318.9315 313.1167 306.5521 #>  [41,] 340.8849 337.0613 332.9741 328.5743 323.7982 318.5600 312.7410 306.1700 #>  [42,] 340.5783 336.7633 332.6869 328.3014 323.5442 318.3323 312.5510 306.0369 #>  [43,] 340.3274 336.5303 332.4767 328.1208 323.4032 318.2457 312.5422 306.1447 #>  [44,] 340.1314 336.3611 332.3417 328.0302 323.3715 318.2946 312.7053 306.4768 #>  [45,] 339.9889 336.2540 332.2795 328.0259 323.4437 318.4707 313.0270 307.0105 #>  [46,] 339.8982 336.2067 332.2868 328.1033 323.6133 318.7639 313.4912 307.7189 #>  [47,] 339.8572 336.2162 332.3598 328.2572 323.8723 319.1626 314.0800 308.5734 #>  [48,] 339.8635 336.2795 332.4941 328.4815 324.2124 319.6545 314.7749 309.5455 #>  [49,] 339.9145 336.3931 332.6852 328.7699 324.6246 320.2269 315.5577 310.6086 #>  [50,] 340.0074 336.5533 332.9281 329.1157 325.1000 320.8675 316.4111 311.7387 #>  [51,] 340.1391 336.7562 333.2178 329.5124 325.6298 321.5643 317.3193 312.9149 #>  [52,] 340.3067 336.9980 333.5494 329.9534 326.2055 322.3065 318.2681 314.1196 #>  [53,] 340.5070 337.2747 333.9179 330.4327 326.8191 323.0840 319.2452 315.3384 #>  [54,] 340.7370 337.5827 334.3185 330.9441 327.4635 323.8879 320.2399 316.5594 #>  [55,] 340.9938 337.9181 334.7469 331.4823 328.1319 324.7103 321.2435 317.7733 #>  [56,] 341.2743 338.2776 335.1986 332.0422 328.8184 325.5444 322.2485 318.9729 #>  [57,] 341.5758 338.6577 335.6699 332.6192 329.5176 326.3845 323.2488 320.1527 #>  [58,] 341.8956 339.0554 336.1570 333.2090 330.2250 327.2254 324.2397 321.3087 #>  [59,] 342.2313 339.4676 336.6566 333.8080 330.9365 328.0632 325.2173 322.4379 #>  [60,] 342.5803 339.8918 337.1658 334.4130 331.6488 328.8944 326.1785 323.5381 #>  [61,] 342.9406 340.3254 337.6818 335.0209 332.3587 329.7162 327.1211 324.6082 #>  [62,] 343.3100 340.7663 338.2021 335.6293 333.0638 330.5264 328.0434 325.6474 #>  [63,] 343.6868 341.2124 338.7248 336.2361 333.7621 331.3231 328.9440 326.6553 #>  [64,] 344.0693 341.6619 339.2478 336.8393 334.4518 332.1049 329.8222 327.6319 #>  [65,] 344.4557 342.1130 339.7695 337.4373 335.1315 332.8708 330.6775 328.5775 #>  [66,] 344.8448 342.5645 340.2885 338.0287 335.7999 333.6199 331.5095 329.4926 #>  [67,] 345.2353 343.0150 340.8035 338.6125 336.4563 334.3517 332.3181 330.3777 #>  [68,] 345.6260 343.4633 341.3134 339.1877 337.0999 335.0657 333.1036 331.2336 #>  [69,] 346.0159 343.9085 341.8174 339.7536 337.7300 335.7619 333.8660 332.0611 #>  [70,] 346.4041 344.3497 342.3146 340.3093 338.3464 336.4400 334.6057 332.8609 #>  [71,] 346.7897 344.7861 342.8043 340.8546 338.9487 337.1000 335.3232 333.6338 #>  [72,] 347.1722 345.2171 343.2861 341.3889 339.5368 337.7422 336.0187 334.3808 #>  [73,] 347.5508 345.6421 343.7594 341.9120 340.1105 338.3666 336.6929 335.1027 #>  [74,] 347.9249 346.0607 344.2239 342.4236 340.6698 338.9735 337.3462 335.8003 #>  [75,] 348.2942 346.4724 344.6793 342.9237 341.2149 339.5630 337.9792 336.4744 #>  [76,] 348.6582 346.8769 345.1255 343.4121 341.7456 340.1357 338.5923 337.1260 #>  [77,] 349.0166 347.2739 345.5621 343.8887 342.2623 340.6917 339.1863 337.7556 #>  [78,] 349.3690 347.6633 345.9891 344.3537 342.7650 341.2313 339.7615 338.3642 #>  [79,] 349.7153 348.0448 346.4064 344.8070 343.2539 341.7551 340.3186 338.9525 #>  [80,] 350.0551 348.4183 346.8140 345.2487 343.7293 342.2632 340.8580 339.5211 #>  [81,] 350.3883 348.7838 347.2119 345.6789 344.1914 342.7562 341.3804 340.0708 #>  [82,] 350.7149 349.1410 347.6000 346.0978 344.6404 343.2343 341.8861 340.6022 #>  [83,] 351.0346 349.4901 347.9785 346.5054 345.0766 343.6980 342.3758 341.1160 #>  [84,] 351.3474 349.8309 348.3474 346.9020 345.5002 344.1476 342.8499 341.6127 #>  [85,] 351.6532 350.1636 348.7067 347.2877 345.9115 344.5835 343.3089 342.0930 #>  [86,] 351.9520 350.4880 349.0567 347.6626 346.3107 345.0060 343.7532 342.5573 #>  [87,] 352.2438 350.8043 349.3972 348.0270 346.6982 345.4154 344.1833 343.0063 #>  [88,] 352.5286 351.1125 349.7286 348.3811 347.0742 345.8122 344.5996 343.4405 #>  [89,] 352.8063 351.4127 350.0509 348.7250 347.4389 346.1967 345.0026 343.8603 #>  [90,] 353.0771 351.7049 350.3643 349.0589 347.7926 346.5692 345.3926 344.2662 #>  [91,] 353.3409 351.9893 350.6688 349.3830 348.1356 346.9300 345.7699 344.6587 #>  [92,] 353.5978 352.2659 350.9647 349.6976 348.4681 347.2795 346.1351 345.0381 #>  [93,] 353.8478 352.5347 351.2520 350.0028 348.7903 347.6178 346.4884 345.4050 #>  [94,] 354.0911 352.7960 351.5309 350.2988 349.1026 347.9455 346.8302 345.7597 #>  [95,] 354.3276 353.0498 351.8016 350.5858 349.4051 348.2626 347.1608 346.1025 #>  [96,] 354.5574 353.2963 352.0642 350.8640 349.6982 348.5695 347.4806 346.4339 #>  [97,] 354.7806 353.5355 352.3189 351.1335 349.9819 348.8665 347.7898 346.7541 #>  [98,] 354.9974 353.7675 352.5658 351.3946 350.2565 349.1538 348.0888 347.0636 #>  [99,] 355.2077 353.9925 352.8050 351.6475 350.5223 349.4317 348.3778 347.3626 #> [100,] 355.4117 354.2106 353.0367 351.8923 350.7795 349.7004 348.6571 347.6515 #>           [,65]    [,66]    [,67]    [,68]    [,69]    [,70]    [,71]    [,72] #>   [1,] 366.6607 365.4866 364.4006 363.4079 362.5126 361.7173 361.0234 360.4304 #>   [2,] 365.3556 364.1588 363.0540 362.0470 361.1423 360.3428 359.6499 359.0632 #>   [3,] 364.0292 362.8079 361.6829 360.6605 359.7456 358.9415 358.2498 357.6700 #>   [4,] 362.6805 361.4330 360.2862 359.2471 358.3212 357.5122 356.8217 356.2493 #>   [5,] 361.3086 360.0328 358.8625 357.8054 356.8675 356.0531 355.3639 354.7996 #>   [6,] 359.9126 358.6062 357.4104 356.3337 355.3829 354.5626 353.8749 353.3193 #>   [7,] 358.4914 357.1520 355.9285 354.8305 353.8656 353.0390 352.3529 351.8068 #>   [8,] 357.0440 355.6688 354.4152 353.2940 352.3137 351.4801 350.7957 350.2601 #>   [9,] 355.5692 354.1551 352.8688 351.7222 350.7251 349.8837 349.2013 348.6771 #>  [10,] 354.0657 352.6094 351.2873 350.1130 349.0973 348.2476 347.5673 347.0556 #>  [11,] 352.5325 351.0301 349.6689 348.4641 347.4280 346.5690 345.8910 345.3931 #>  [12,] 350.9682 349.4154 348.0112 346.7729 345.7143 344.8450 344.1696 343.6870 #>  [13,] 349.3715 347.7635 346.3121 345.0366 343.9530 343.0724 342.3999 341.9342 #>  [14,] 347.7409 346.0724 344.5688 343.2522 342.1409 341.2476 340.5783 340.1314 #>  [15,] 346.0751 344.3400 342.7787 341.4164 340.2741 339.3666 338.7009 338.2751 #>  [16,] 344.3726 342.5641 340.9388 339.5254 338.3484 337.4250 336.7633 336.3611 #>  [17,] 342.6320 340.7424 339.0457 337.5752 336.3591 335.4177 334.7605 334.3850 #>  [18,] 340.8520 338.8724 337.0959 335.5611 334.3008 333.3390 332.6869 332.3417 #>  [19,] 339.0312 336.9515 335.0857 333.4781 332.1676 331.1825 330.5363 330.2256 #>  [20,] 337.1683 334.9772 333.0107 331.3205 329.9526 328.9408 328.3014 328.0302 #>  [21,] 335.2623 332.9467 330.8665 329.0821 327.6482 326.6055 325.9739 325.7482 #>  [22,] 333.3125 330.8575 328.6482 326.7556 325.2453 324.1668 323.5442 323.3715 #>  [23,] 331.3185 328.7068 326.3505 324.3332 322.7339 321.6133 321.0014 320.8906 #>  [24,] 329.2805 326.4925 323.9680 321.8059 320.1019 318.9315 318.3323 318.2946 #>  [25,] 327.1995 324.2126 321.4948 319.1635 317.3356 316.1057 315.5216 315.5710 #>  [26,] 325.0773 321.8658 318.9251 316.3946 314.4185 313.1167 312.5510 312.7053 #>  [27,] 322.9174 319.4520 316.2530 313.4864 311.3313 309.9416 309.3984 309.6805 #>  [28,] 320.7251 316.9725 313.4733 310.4247 308.0509 306.5521 306.0369 306.4768 #>  [29,] 318.5079 314.4309 310.5818 307.1938 304.5491 302.9129 302.4332 303.0709 #>  [30,] 316.2766 311.8343 307.5764 303.7767 300.7921 298.9792 298.5454 299.4353 #>  [31,] 314.0456 309.1942 304.4590 300.1562 296.7383 294.6933 294.3202 295.5382 #>  [32,] 311.8343 306.5286 301.2374 296.3161 292.3361 289.9785 289.6880 291.3425 #>  [33,] 309.6676 303.8638 297.9294 292.2446 287.5224 284.7299 284.5559 286.8073 #>  [34,] 307.5764 301.2374 294.5683 287.9411 282.2201 278.7996 278.7972 281.8899 #>  [35,] 305.5984 298.6997 291.2098 283.4285 276.3390 271.9684 272.2331 276.5557 #>  [36,] 303.7767 296.3161 287.9411 278.7755 269.7869 263.8929 264.6054 270.8002 #>  [37,] 302.1587 294.1654 284.8888 274.1336 262.5123 253.9922 255.5346 264.7036 #>  [38,] 300.7921 292.3361 282.2201 269.7869 254.6458 241.1740 244.4926 258.5474 #>  [39,] 299.7209 290.9159 280.1291 266.1865 246.8878 223.0846 231.0627 253.0098 #>  [40,] 298.9792 289.9785 278.7996 263.8929 241.1740 194.8736 217.4372 249.2830 #>  [41,] 298.5868 289.5677 278.3516 263.3500 240.2501 188.0424 215.2865 248.5893 #>  [42,] 298.5454 289.6880 278.7972 264.6054 244.4926 217.4372 227.1580 251.0745 #>  [43,] 298.8388 290.3025 280.0351 267.2756 251.3314 236.3775 240.2837 255.6451 #>  [44,] 299.4353 291.3425 281.8899 270.8002 258.5474 249.2830 251.0745 261.0342 #>  [45,] 300.2926 292.7219 284.1658 274.6967 265.2470 258.9410 259.7788 266.4604 #>  [46,] 301.3631 294.3514 286.6885 278.6489 271.2280 266.6100 266.9458 271.5805 #>  [47,] 302.5993 296.1497 289.3229 282.4828 276.5220 272.9429 272.9845 276.2860 #>  [48,] 303.9567 298.0486 291.9746 286.1167 281.2183 278.3187 278.1737 280.5702 #>  [49,] 305.3968 299.9948 294.5822 289.5208 285.4089 282.9757 282.7053 284.4643 #>  [50,] 306.8871 301.9485 297.1087 292.6923 289.1736 287.0736 286.7149 288.0102 #>  [51,] 308.4016 303.8811 299.5336 295.6413 292.5784 290.7242 290.3011 291.2497 #>  [52,] 309.9199 305.7733 301.8474 298.3834 295.6769 294.0089 293.5374 294.2206 #>  [53,] 311.4267 307.6123 304.0474 300.9359 298.5125 296.9888 296.4800 296.9559 #>  [54,] 312.9104 309.3903 306.1349 303.3159 301.1206 299.7110 299.1728 299.4839 #>  [55,] 314.3630 311.1032 308.1139 305.5393 303.5302 302.2122 301.6506 301.8285 #>  [56,] 315.7788 312.7492 309.9894 307.6207 305.7654 304.5222 303.9415 304.0103 #>  [57,] 317.1540 314.3282 311.7671 309.5733 307.8462 306.6647 306.0683 306.0468 #>  [58,] 318.4865 315.8412 313.4531 311.4085 309.7896 308.6597 308.0502 307.9530 #>  [59,] 319.7751 317.2901 315.0530 313.1369 311.6099 310.5235 309.9029 309.7418 #>  [60,] 321.0195 318.6772 316.5725 314.7676 313.3193 312.2700 311.6400 311.4243 #>  [61,] 322.2199 320.0050 318.0168 316.3088 314.9285 313.9109 313.2729 313.0102 #>  [62,] 323.3771 321.2761 319.3910 317.7678 316.4464 315.4563 314.8114 314.5081 #>  [63,] 324.4920 322.4932 320.6997 319.1510 317.8812 316.9150 316.2640 315.9253 #>  [64,] 325.5658 323.6589 321.9469 320.4642 319.2397 318.2944 317.6382 317.2685 #>  [65,] 326.5999 324.7758 323.1368 321.7126 320.5281 319.6013 318.9404 318.5433 #>  [66,] 327.5956 325.8464 324.2729 322.9008 321.7519 320.8414 320.1764 319.7551 #>  [67,] 328.5544 326.8731 325.3584 324.0331 322.9159 322.0199 321.3512 320.9084 #>  [68,] 329.4777 327.8580 326.3966 325.1132 324.0244 323.1413 322.4694 322.0073 #>  [69,] 330.3668 328.8034 327.3901 326.1446 325.0812 324.2098 323.5350 323.0555 #>  [70,] 331.2233 329.7111 328.3416 327.1304 326.0900 325.2290 324.5515 324.0565 #>  [71,] 332.0484 330.5831 329.2535 328.0733 327.0537 326.2022 325.5223 325.0133 #>  [72,] 332.8434 331.4211 330.1279 328.9760 327.9753 327.1324 326.4504 325.9285 #>  [73,] 333.6096 332.2268 330.9670 329.8409 328.8573 328.0222 327.3382 326.8048 #>  [74,] 334.3481 333.0018 331.7725 330.6700 329.7022 328.8741 328.1884 327.6443 #>  [75,] 335.0602 333.7475 332.5463 331.4655 330.5120 329.6904 329.0031 328.4493 #>  [76,] 335.7469 334.4652 333.2900 332.2290 331.2887 330.4731 329.7843 329.2216 #>  [77,] 336.4093 335.1563 334.0050 332.9624 332.0342 331.2241 330.5339 329.9630 #>  [78,] 337.0483 335.8220 334.6928 333.6671 332.7501 331.9450 331.2535 330.6752 #>  [79,] 337.6649 336.4633 335.3546 334.3446 333.4379 332.6375 331.9449 331.3595 #>  [80,] 338.2599 337.0814 335.9918 334.9963 334.0992 333.3031 332.6093 332.0176 #>  [81,] 338.8343 337.6773 336.6053 335.6234 334.7351 333.9430 333.2482 332.6505 #>  [82,] 339.3888 338.2518 337.1964 336.2270 335.3469 334.5585 333.8628 333.2596 #>  [83,] 339.9242 338.8060 337.7659 336.8082 335.9358 335.1509 334.4543 333.8459 #>  [84,] 340.4412 339.3405 338.3149 337.3680 336.5028 335.7211 335.0237 334.4105 #>  [85,] 340.9406 339.8563 338.8441 337.9075 337.0489 336.2702 335.5721 334.9544 #>  [86,] 341.4228 340.3540 339.3544 338.4273 337.5750 336.7991 336.1003 335.4784 #>  [87,] 341.8887 340.8343 339.8466 338.9285 338.0820 337.3087 336.6092 335.9834 #>  [88,] 342.3388 341.2980 340.3214 339.4117 338.5707 337.7999 337.0998 336.4703 #>  [89,] 342.7735 341.7456 340.7795 339.8776 339.0418 338.2733 337.5726 336.9397 #>  [90,] 343.1936 342.1778 341.2215 340.3271 339.4961 338.7298 338.0285 337.3923 #>  [91,] 343.5994 342.5951 341.6481 340.7606 339.9342 339.1699 338.4682 337.8289 #>  [92,] 343.9915 342.9980 342.0598 341.1789 340.3568 339.5944 338.8922 338.2501 #>  [93,] 344.3704 343.3870 342.4571 341.5825 340.7644 340.0038 339.3012 338.6563 #>  [94,] 344.7364 343.7627 342.8406 341.9719 341.1576 340.3988 339.6957 339.0483 #>  [95,] 345.0900 344.1255 343.2108 342.3476 341.5370 340.7798 340.0763 339.4264 #>  [96,] 345.4316 344.4757 343.5681 342.7102 341.9030 341.1474 340.4435 339.7913 #>  [97,] 345.7615 344.8140 343.9130 343.0601 342.2562 341.5020 340.7977 340.1434 #>  [98,] 346.0803 345.1405 344.2459 343.3977 342.5969 341.8440 341.1395 340.4831 #>  [99,] 346.3881 345.4558 344.5672 343.7235 342.9256 342.1741 341.4691 340.8108 #> [100,] 346.6853 345.7601 344.8772 344.0378 343.2427 342.4924 341.7872 341.1270 #>           [,73]    [,74]    [,75]    [,76]    [,77]    [,78]    [,79]    [,80] #>   [1,] 359.9366 359.5386 359.2321 359.0112 358.8698 358.8006 358.7964 358.8498 #>   [2,] 358.5808 358.1990 357.9129 357.7162 357.6020 357.5625 357.5899 357.6761 #>   [3,] 357.1999 356.8355 356.5713 356.4005 356.3154 356.3077 356.3687 356.4896 #>   [4,] 355.7925 355.4469 355.2064 355.0634 355.0096 355.0357 355.1324 355.2903 #>   [5,] 354.3572 354.0320 353.8170 353.7040 353.6837 353.7461 353.8809 354.0780 #>   [6,] 352.8927 352.5895 352.4021 352.3215 352.3372 352.4383 352.6138 352.8525 #>   [7,] 351.3972 351.1179 350.9605 350.9148 350.9693 351.1120 351.3309 351.6139 #>   [8,] 349.8691 349.6159 349.4910 349.4830 349.5793 349.7667 350.0319 350.3621 #>   [9,] 348.3065 348.0817 347.9922 348.0251 348.1666 348.4020 348.7168 349.0970 #>  [10,] 346.7073 346.5137 346.4627 346.5401 346.7304 347.0174 347.3853 347.8189 #>  [11,] 345.0694 344.9099 344.9011 345.0269 345.2700 345.6126 346.0373 346.5279 #>  [12,] 343.3904 343.2684 343.3058 343.4843 343.7847 344.1873 344.6730 345.2242 #>  [13,] 341.6676 341.5871 341.6751 341.9113 342.2739 342.7413 343.2924 343.9081 #>  [14,] 339.8982 339.8635 340.0074 340.3067 340.7370 341.2743 341.8956 342.5803 #>  [15,] 338.0790 338.0952 338.3007 338.6692 339.1734 339.7864 340.4831 341.2413 #>  [16,] 336.2067 336.2795 336.5533 336.9980 337.5827 338.2776 339.0554 339.8918 #>  [17,] 334.2773 334.4136 334.7631 335.2917 335.9644 336.7482 337.6130 338.5329 #>  [18,] 332.2868 332.4941 332.9281 333.5494 334.3185 335.1986 336.1570 337.1658 #>  [19,] 330.2305 330.5180 331.0463 331.7702 332.6450 333.6296 334.6885 335.7919 #>  [20,] 328.1033 328.4815 329.1157 329.9534 330.9441 332.0422 333.2090 334.4130 #>  [21,] 325.8997 326.3810 327.1342 328.0986 329.2166 330.4378 331.7204 333.0311 #>  [22,] 323.6133 324.2124 325.1000 326.2055 327.4635 328.8184 330.2250 331.6488 #>  [23,] 321.2372 321.9716 323.0115 324.2745 325.6865 327.1862 328.7256 330.2687 #>  [24,] 318.7639 319.6545 320.8675 322.3065 323.8879 325.5444 327.2254 328.8944 #>  [25,] 316.1850 317.2569 318.6673 320.3035 322.0710 323.8969 325.7286 327.5296 #>  [26,] 313.4912 314.7749 316.4111 318.2681 320.2399 322.2485 324.2397 326.1785 #>  [27,] 310.6727 312.2052 314.1005 316.2048 318.4004 320.6048 322.7643 324.8462 #>  [28,] 307.7189 309.5455 311.7387 314.1196 316.5594 318.9729 321.3087 323.5381 #>  [29,] 304.6192 306.7952 309.3312 312.0210 314.7257 317.3610 319.8801 322.2604 #>  [30,] 301.3631 303.9567 306.8871 309.9199 312.9104 315.7788 318.4865 321.0195 #>  [31,] 297.9421 301.0368 304.4198 307.8312 311.1267 314.2373 317.1370 319.8226 #>  [32,] 294.3514 298.0486 301.9485 305.7733 309.3903 312.7492 315.8412 318.6772 #>  [33,] 290.5942 295.0155 299.4996 303.7694 307.7195 311.3282 314.6096 317.5912 #>  [34,] 286.6885 291.9746 297.1087 301.8474 306.1349 309.9894 313.4531 316.5725 #>  [35,] 282.6779 288.9817 294.8210 300.0399 304.6591 308.7483 312.3825 315.6288 #>  [36,] 278.6489 286.1167 292.6923 298.3834 303.3159 307.6207 311.4085 314.7676 #>  [37,] 274.7529 283.4857 290.7869 296.9164 302.1289 306.6219 310.5413 313.9958 #>  [38,] 271.2280 281.2183 289.1736 295.6769 301.1206 305.7654 309.7896 313.3193 #>  [39,] 268.3971 279.4544 287.9180 294.6991 300.3099 305.0627 309.1607 312.7429 #>  [40,] 266.6100 278.3187 287.0736 294.0089 299.7110 304.5222 308.6597 312.2700 #>  [41,] 266.1176 277.8892 286.6716 293.6212 299.3317 304.1483 308.2894 311.9023 #>  [42,] 266.9458 278.1737 286.7149 293.5374 299.1728 303.9415 308.0502 311.6400 #>  [43,] 268.8807 279.1067 287.1777 293.7452 299.2279 303.8980 307.9396 311.4817 #>  [44,] 271.5805 280.5702 288.0102 294.2206 299.4839 304.0103 307.9530 311.4243 #>  [45,] 274.7100 282.4252 289.1485 294.9309 299.9225 304.2675 308.0836 311.4632 #>  [46,] 278.0129 284.5386 290.5236 295.8384 300.5222 304.6563 308.3227 311.5928 #>  [47,] 281.3215 286.7988 292.0700 296.9044 301.2591 305.1616 308.6605 311.8063 #>  [48,] 284.5386 289.1210 293.7301 298.0920 302.1096 305.7679 309.0865 312.0964 #>  [49,] 287.6133 291.4450 295.4562 299.3677 303.0506 306.4595 309.5897 312.4553 #>  [50,] 290.5236 293.7301 297.2112 300.7025 304.0612 307.2211 310.1592 312.8752 #>  [51,] 293.2642 295.9508 298.9668 302.0725 305.1225 308.0387 310.7846 313.3481 #>  [52,] 295.8384 298.0920 300.7025 303.4581 306.2184 308.8994 311.4558 313.8666 #>  [53,] 298.2543 300.1460 302.4039 304.8440 307.3350 309.7919 312.1639 314.4233 #>  [54,] 300.5222 302.1096 304.0612 306.2184 308.4611 310.7063 312.9005 315.0115 #>  [55,] 302.6526 303.9829 305.6681 307.5723 309.5873 311.6340 313.6582 315.6252 #>  [56,] 304.6563 305.7679 307.2211 308.8994 310.7063 312.5677 314.4306 316.2587 #>  [57,] 306.5432 307.4679 308.7183 310.1950 311.8122 313.5016 315.2120 316.9069 #>  [58,] 308.3227 309.0865 310.1592 311.4558 312.9005 314.4306 315.9975 317.5654 #>  [59,] 310.0033 310.6280 311.5445 312.6801 313.9678 315.3507 316.7832 318.2303 #>  [60,] 311.5928 312.0964 312.8752 313.8666 315.0115 316.2587 317.5654 318.8982 #>  [61,] 313.0982 313.4960 314.1528 315.0148 316.0300 317.1520 318.3413 319.5661 #>  [62,] 314.5260 314.8307 315.3792 316.1250 317.0221 318.0286 319.1085 320.2315 #>  [63,] 315.8818 316.1044 316.5564 317.1974 317.9868 318.8872 319.8651 320.8923 #>  [64,] 317.1708 317.3206 317.6863 318.2327 318.9240 319.7264 320.6094 321.5467 #>  [65,] 318.3978 318.4828 318.7710 319.2318 319.8335 320.5457 321.3403 322.1931 #>  [66,] 319.5670 319.5940 319.8126 320.1958 320.7155 321.3444 322.0568 322.8302 #>  [67,] 320.6823 320.6573 320.8130 321.1256 321.5703 322.1222 322.7582 323.4572 #>  [68,] 321.7471 321.6754 321.7741 322.0225 322.3982 322.8791 323.4439 324.0731 #>  [69,] 322.7647 322.6508 322.6978 322.8875 323.2000 323.6151 324.1135 324.6772 #>  [70,] 323.7381 323.5858 323.5858 323.7218 323.9760 324.3303 324.7669 325.2692 #>  [71,] 324.6697 324.4827 324.4398 324.5266 324.7271 325.0249 325.4038 325.8486 #>  [72,] 325.5622 325.3434 325.2613 325.3029 325.4538 325.6992 326.0243 326.4150 #>  [73,] 326.4177 326.1700 326.0519 326.0519 326.1569 326.3537 326.6285 326.9684 #>  [74,] 327.2383 326.9641 326.8130 326.7745 326.8371 326.9886 327.2164 327.5087 #>  [75,] 328.0259 327.7273 327.5458 327.4719 327.4952 327.6044 327.7883 328.0357 #>  [76,] 328.7823 328.4613 328.2517 328.1450 328.1317 328.2016 328.3443 328.5495 #>  [77,] 329.5090 329.1674 328.9318 328.7947 328.7474 328.7805 328.8847 329.0502 #>  [78,] 330.2076 329.8469 329.5873 329.4219 329.3429 329.3418 329.4097 329.5379 #>  [79,] 330.8795 330.5011 330.2192 330.0276 329.9190 329.8857 329.9197 330.0126 #>  [80,] 331.5260 331.1312 330.8286 330.6124 330.4762 330.4129 330.4149 330.4746 #>  [81,] 332.1482 331.7381 331.4162 331.1773 331.0153 330.9237 330.8956 330.9241 #>  [82,] 332.7472 332.3230 331.9832 331.7229 331.5367 331.4186 331.3623 331.3611 #>  [83,] 333.3242 332.8868 332.5302 332.2500 332.0411 331.8981 331.8151 331.7860 #>  [84,] 333.8802 333.4304 333.0581 332.7592 332.5290 332.3626 332.2544 332.1989 #>  [85,] 334.4159 333.9546 333.5676 333.2512 333.0010 332.8125 332.6806 332.6000 #>  [86,] 334.9324 334.4603 334.0595 333.7266 333.4576 333.2483 333.0940 332.9897 #>  [87,] 335.4303 334.9481 334.5343 334.1859 333.8993 333.6704 333.4948 333.3680 #>  [88,] 335.9105 335.4187 334.9928 334.6299 334.3265 334.0791 333.8834 333.7353 #>  [89,] 336.3736 335.8729 335.4356 335.0589 334.7398 334.4748 334.2601 334.0918 #>  [90,] 336.8204 336.3113 335.8632 335.4735 335.1395 334.8579 334.6252 334.4377 #>  [91,] 337.2514 336.7344 336.2761 335.8743 335.5262 335.2289 334.9790 334.7733 #>  [92,] 337.6673 337.1428 336.6749 336.2615 335.9001 335.5879 335.3218 335.0987 #>  [93,] 338.0687 337.5371 337.0601 336.6358 336.2617 335.9354 335.6539 335.4143 #>  [94,] 338.4559 337.9177 337.4321 336.9974 336.6114 336.2717 335.9755 335.7201 #>  [95,] 338.8297 338.2851 337.7914 337.3469 336.9495 336.5970 336.2869 336.0166 #>  [96,] 339.1904 338.6399 338.1384 337.6846 337.2764 336.9118 336.5884 336.3037 #>  [97,] 339.5385 338.9823 338.4735 338.0108 337.5924 337.2163 336.8802 336.5819 #>  [98,] 339.8744 339.3128 338.7971 338.3260 337.8978 337.5107 337.1626 336.8512 #>  [99,] 340.1986 339.6319 339.1096 338.6305 338.1930 337.7954 337.4357 337.1119 #> [100,] 340.5114 339.9398 339.4112 338.9245 338.4782 338.0706 337.6999 337.3642 #>           [,81]    [,82]    [,83]    [,84]    [,85]    [,86]    [,87]    [,88] #>   [1,] 358.9534 359.1000 359.2830 359.4959 359.7332 359.9894 360.2598 360.5403 #>   [2,] 357.8132 357.9936 358.2102 358.4563 358.7260 359.0136 359.3144 359.6240 #>   [3,] 356.6622 356.8782 357.1301 357.4109 357.7143 358.0346 358.3667 358.7064 #>   [4,] 355.5003 355.7538 356.0428 356.3598 356.6984 357.0526 357.4173 357.7879 #>   [5,] 354.3276 354.6206 354.9484 355.3034 355.6786 356.0680 356.4663 356.8689 #>   [6,] 353.1441 353.4787 353.8473 354.2419 354.6553 355.0813 355.5143 355.9498 #>   [7,] 351.9499 352.3283 352.7398 353.1758 353.6289 354.0927 354.5617 355.0311 #>   [8,] 350.7450 351.1697 351.6261 352.1054 352.5999 353.1029 353.6090 354.1133 #>   [9,] 349.5298 350.0032 350.5067 351.0312 351.5687 352.1124 352.6567 353.1969 #>  [10,] 348.3044 348.8292 349.3822 349.9538 350.5360 351.1218 351.7055 352.2825 #>  [11,] 347.0692 347.6482 348.2530 348.8739 349.5024 350.1316 350.7559 351.3707 #>  [12,] 345.8247 346.4607 347.1199 347.7920 348.4687 349.1428 349.8088 350.4623 #>  [13,] 344.5715 345.2674 345.9835 346.7091 347.4356 348.1560 348.8649 349.5578 #>  [14,] 343.3100 344.0693 344.8448 345.6260 346.4041 347.1722 347.9249 348.6582 #>  [15,] 342.0413 342.8670 343.7048 344.5437 345.3751 346.1922 346.9899 347.7643 #>  [16,] 340.7663 341.6619 342.5645 343.4633 344.3497 345.2171 346.0607 346.8769 #>  [17,] 339.4861 340.4550 341.4253 342.3861 343.3291 344.2480 345.1383 345.9969 #>  [18,] 338.2021 339.2478 340.2885 341.3134 342.3146 343.2861 344.2239 345.1255 #>  [19,] 336.9159 338.0420 339.1557 340.2468 341.3075 342.3326 343.3186 344.2635 #>  [20,] 335.6293 336.8393 338.0287 339.1877 340.3093 341.3889 342.4236 343.4121 #>  [21,] 334.3445 335.6418 336.9094 338.1381 339.3217 340.4565 341.5403 342.5724 #>  [22,] 333.0638 334.4518 335.7999 337.0999 338.3464 339.5368 340.6698 341.7456 #>  [23,] 331.7901 333.2719 334.7026 336.0750 337.3852 338.6315 339.8138 340.9330 #>  [24,] 330.5264 332.1049 333.6199 335.0657 336.4400 337.7422 338.9735 340.1357 #>  [25,] 329.2762 330.9539 332.5545 334.0744 335.5128 336.8707 338.1504 339.3550 #>  [26,] 328.0434 329.8222 331.5095 333.1036 334.6057 336.0187 337.3462 338.5923 #>  [27,] 326.8322 328.7136 330.4877 332.1558 333.7210 335.1881 336.5623 337.8489 #>  [28,] 325.6474 327.6319 329.4926 331.2336 332.8609 334.3808 335.8003 337.1260 #>  [29,] 324.4939 326.5812 328.5274 330.3400 332.0275 333.5986 335.0617 336.4249 #>  [30,] 323.3771 325.5658 327.5956 329.4777 331.2233 332.8434 334.3481 335.7469 #>  [31,] 322.3025 324.5902 326.7008 328.6494 330.4504 332.1169 333.6610 335.0933 #>  [32,] 321.2761 323.6589 325.8464 327.8580 329.7111 331.4211 333.0018 334.4652 #>  [33,] 320.3036 322.7763 325.0360 327.1062 329.0075 330.7576 332.3719 333.8638 #>  [34,] 319.3910 321.9469 324.2729 326.3966 328.3416 330.1279 331.7725 333.2900 #>  [35,] 318.5440 321.1749 323.5602 325.7315 327.7154 329.5336 331.2049 332.7448 #>  [36,] 317.7678 320.4642 322.9008 325.1132 327.1304 328.9760 330.6700 332.2290 #>  [37,] 317.0672 319.8181 322.2973 324.5437 326.5882 328.4563 330.1689 331.7435 #>  [38,] 316.4464 319.2397 321.7519 324.0244 326.0900 327.9753 329.7022 331.2887 #>  [39,] 315.9087 318.7313 321.2662 323.5566 325.6367 327.5338 329.2704 330.8651 #>  [40,] 315.4563 318.2944 320.8414 323.1413 325.2290 327.1324 328.8741 330.4731 #>  [41,] 315.0905 317.9300 320.4781 322.7789 324.8673 326.7712 328.5135 330.1128 #>  [42,] 314.8114 317.6382 320.1764 322.4694 324.5515 326.4504 328.1884 329.7843 #>  [43,] 314.6180 317.4182 319.9358 322.2125 324.2815 326.1696 327.8988 329.4873 #>  [44,] 314.5081 317.2685 319.7551 322.0073 324.0565 325.9285 327.6443 329.2216 #>  [45,] 314.4788 317.1870 319.6329 321.8527 323.8758 325.7263 327.4244 328.9868 #>  [46,] 314.5260 317.1708 319.5670 321.7471 323.7381 325.5622 327.2383 328.7823 #>  [47,] 314.6450 317.2166 319.5550 321.6887 323.6419 325.4350 327.0852 328.6074 #>  [48,] 314.8307 317.3206 319.5940 321.6754 323.5858 325.3434 326.9641 328.4613 #>  [49,] 315.0774 317.4786 319.6810 321.7047 323.5677 325.2861 326.8737 328.3431 #>  [50,] 315.3792 317.6863 319.8126 321.7741 323.5858 325.2613 326.8130 328.2517 #>  [51,] 315.7304 317.9392 319.9854 321.8810 323.6379 325.2675 326.7804 328.1860 #>  [52,] 316.1250 318.2327 320.1958 322.0225 323.7218 325.3029 326.7745 328.1450 #>  [53,] 316.5573 318.5624 320.4403 322.1959 323.8353 325.3656 326.7940 328.1273 #>  [54,] 317.0221 318.9240 320.7155 322.3982 323.9760 325.4538 326.8371 328.1317 #>  [55,] 317.5141 319.3133 321.0180 322.6269 324.1418 325.5656 326.9025 328.1569 #>  [56,] 318.0286 319.7264 321.3444 322.8791 324.3303 325.6992 326.9886 328.2016 #>  [57,] 318.5614 320.1596 321.6916 323.1523 324.5393 325.8527 327.0937 328.2645 #>  [58,] 319.1085 320.6094 322.0568 323.4439 324.7669 326.0243 327.2164 328.3443 #>  [59,] 319.6662 321.0727 322.4372 323.7516 325.0108 326.2123 327.3552 328.4397 #>  [60,] 320.2315 321.5467 322.8302 324.0731 325.2692 326.4150 327.5087 328.5495 #>  [61,] 320.8015 322.0286 323.2335 324.4063 325.5402 326.6308 327.6753 328.6725 #>  [62,] 321.3736 322.5162 323.6449 324.7494 325.8221 326.8581 327.8538 328.8074 #>  [63,] 321.9458 323.0073 324.0624 325.1004 326.1133 327.0955 328.0429 328.9531 #>  [64,] 322.5162 323.5001 324.4843 325.4577 326.4122 327.3416 328.2413 329.1085 #>  [65,] 323.0830 323.9929 324.9089 325.8199 326.7175 327.5951 328.4479 329.2726 #>  [66,] 323.6449 324.4843 325.3348 326.1855 327.0277 327.8548 328.6616 329.4443 #>  [67,] 324.2007 324.9729 325.7607 326.5532 327.3418 328.1197 328.8813 329.6228 #>  [68,] 324.7494 325.4577 326.1855 326.9220 327.6587 328.3886 329.1061 329.8071 #>  [69,] 325.2901 325.9378 326.6081 327.2908 327.9773 328.6606 329.3351 329.9964 #>  [70,] 325.8221 326.4122 327.0277 327.6587 328.2967 328.9348 329.5674 330.1898 #>  [71,] 326.3450 326.8803 327.4435 328.0249 328.6161 329.2105 329.8022 330.3867 #>  [72,] 326.8581 327.3416 327.8548 328.3886 328.9348 329.4868 330.0389 330.5864 #>  [73,] 327.3611 327.7954 328.2610 328.7492 329.2521 329.7632 330.2768 330.7882 #>  [74,] 327.8538 328.2413 328.6616 329.1061 329.5674 330.0389 330.5152 330.9916 #>  [75,] 328.3360 328.6791 329.0562 329.4589 329.8801 330.3135 330.7536 331.1959 #>  [76,] 328.8074 329.1085 329.4443 329.8071 330.1898 330.5864 330.9916 331.4007 #>  [77,] 329.2680 329.5292 329.8258 330.1503 330.4961 330.8572 331.2285 331.6055 #>  [78,] 329.7178 329.9411 330.2003 330.4882 330.7985 331.1255 331.4641 331.8098 #>  [79,] 330.1567 330.3441 330.5676 330.8206 331.0968 331.3909 331.6978 332.0134 #>  [80,] 330.5848 330.7380 330.9276 331.1471 331.3907 331.6531 331.9295 332.2157 #>  [81,] 331.0021 331.1229 331.2801 331.4676 331.6798 331.9117 332.1587 332.4166 #>  [82,] 331.4087 331.4987 331.6250 331.7819 331.9641 332.1667 332.3852 332.6156 #>  [83,] 331.8047 331.8654 331.9623 332.0900 332.2433 332.4177 332.6087 332.8126 #>  [84,] 332.1903 332.2231 332.2919 332.3916 332.5173 332.6645 332.8290 333.0072 #>  [85,] 332.5655 332.5718 332.6138 332.6867 332.7859 332.9069 333.0459 333.1993 #>  [86,] 332.9305 332.9116 332.9280 332.9753 333.0490 333.1449 333.2593 333.3886 #>  [87,] 333.2855 333.2425 333.2345 333.2573 333.3065 333.3783 333.4689 333.5751 #>  [88,] 333.6305 333.5646 333.5334 333.5327 333.5584 333.6069 333.6747 333.7584 #>  [89,] 333.9659 333.8781 333.8246 333.8014 333.8047 333.8308 333.8765 333.9385 #>  [90,] 334.2916 334.1831 334.1083 334.0635 334.0452 334.0498 334.0742 334.1152 #>  [91,] 334.6080 334.4796 334.3845 334.3191 334.2800 334.2639 334.2677 334.2885 #>  [92,] 334.9152 334.7678 334.6532 334.5680 334.5090 334.4730 334.4570 334.4583 #>  [93,] 335.2133 335.0478 334.9146 334.8104 334.7323 334.6771 334.6420 334.6244 #>  [94,] 335.5026 335.3197 335.1687 335.0463 334.9498 334.8761 334.8227 334.7867 #>  [95,] 335.7831 335.5838 335.4156 335.2758 335.1616 335.0702 334.9989 334.9454 #>  [96,] 336.0551 335.8400 335.6555 335.4989 335.3677 335.2591 335.1708 335.1001 #>  [97,] 336.3188 336.0885 335.8883 335.7157 335.5681 335.4431 335.3382 335.2511 #>  [98,] 336.5743 336.3295 336.1143 335.9262 335.7629 335.6220 335.5011 335.3981 #>  [99,] 336.8218 336.5631 336.3335 336.1306 335.9521 335.7959 335.6596 335.5412 #> [100,] 337.0615 336.7894 336.5459 336.3288 336.1358 335.9648 335.8136 335.6803 #>           [,89]    [,90]    [,91]    [,92]    [,93]    [,94]    [,95]    [,96] #>   [1,] 360.8271 361.1170 361.4073 361.6953 361.9793 362.2572 362.5278 362.7897 #>   [2,] 359.9386 360.2550 360.5704 360.8823 361.1888 361.4881 361.7787 362.0596 #>   [3,] 359.0496 359.3933 359.7344 360.0707 360.4001 360.7210 361.0321 361.3322 #>   [4,] 358.1606 358.5321 358.8996 359.2608 359.6136 359.9565 360.2882 360.6077 #>   [5,] 357.2719 357.6720 358.0664 358.4529 358.8295 359.1948 359.5474 359.8865 #>   [6,] 356.3839 356.8133 357.2353 357.6475 358.0483 358.4362 358.8100 359.1689 #>   [7,] 355.4972 355.9565 356.4065 356.8451 357.2704 357.6812 358.0764 358.4552 #>   [8,] 354.6121 355.1020 355.5807 356.0459 356.4961 356.9300 357.3468 357.7457 #>   [9,] 353.7292 354.2504 354.7582 355.2505 355.7258 356.1832 356.6217 357.0408 #>  [10,] 352.8491 353.4022 353.9395 354.4593 354.9601 355.4411 355.9014 356.3408 #>  [11,] 351.9723 352.5579 353.1253 353.6729 354.1994 354.7041 355.1864 355.6462 #>  [12,] 351.0996 351.7182 352.3161 352.8917 353.4441 353.9727 354.4771 354.9572 #>  [13,] 350.2316 350.8837 351.5124 352.1163 352.6948 353.2474 353.7738 354.2743 #>  [14,] 349.3690 350.0551 350.7149 351.3474 351.9520 352.5286 353.0771 353.5978 #>  [15,] 348.5127 349.2331 349.9242 350.5854 351.2162 351.8168 352.3873 352.9282 #>  [16,] 347.6633 348.4183 349.1410 349.8309 350.4880 351.1125 351.7049 352.2659 #>  [17,] 346.8218 347.6117 348.3661 349.0847 349.7680 350.4163 351.0304 351.6112 #>  [18,] 345.9891 346.8140 347.6000 348.3474 349.0567 349.7286 350.3643 350.9647 #>  [19,] 345.1661 346.0261 346.8437 347.6196 348.3547 349.0500 349.7069 350.3267 #>  [20,] 344.3537 345.2487 346.0978 346.9020 347.6626 348.3811 349.0589 349.6976 #>  [21,] 343.5530 344.4828 345.3631 346.1953 346.9811 347.7223 348.4206 349.0779 #>  [22,] 342.7650 343.7293 344.6404 345.5002 346.3107 347.0742 347.7926 348.4681 #>  [23,] 341.9907 342.9892 343.9305 344.8174 345.6521 346.4373 347.1753 347.8684 #>  [24,] 341.2313 342.2632 343.2343 344.1476 345.0060 345.8122 346.5692 347.2795 #>  [25,] 340.4879 341.5525 342.5526 343.4915 344.3728 345.1995 345.9748 346.7016 #>  [26,] 339.7615 340.8580 341.8861 342.8499 343.7532 344.5996 345.3926 346.1351 #>  [27,] 339.0532 340.1805 341.2357 342.2234 343.1479 344.0131 344.8229 345.5805 #>  [28,] 338.3642 339.5211 340.6022 341.6127 342.5573 343.4405 344.2662 345.0381 #>  [29,] 337.6956 338.8806 339.9863 341.0184 341.9821 342.8822 343.7230 344.5084 #>  [30,] 337.0483 338.2599 339.3888 340.4412 341.4228 342.3388 343.1936 343.9915 #>  [31,] 336.4234 337.6599 338.8104 339.8817 340.8800 341.8106 342.6784 343.4880 #>  [32,] 335.8220 337.0814 338.2518 339.3405 340.3540 341.2980 342.1778 342.9980 #>  [33,] 335.2448 336.5251 337.7136 338.8181 339.8453 340.8015 341.6921 342.5218 #>  [34,] 334.6928 335.9918 337.1964 338.3149 339.3544 340.3214 341.2215 342.0598 #>  [35,] 334.1666 335.4820 336.7007 337.8314 338.8817 339.8581 340.7665 341.6121 #>  [36,] 333.6671 334.9963 336.2270 337.3680 338.4273 339.4117 340.3271 341.1789 #>  [37,] 333.1948 334.5352 335.7756 336.9251 337.9917 338.9825 339.9036 340.7604 #>  [38,] 332.7501 334.0992 335.3469 336.5028 337.5750 338.5707 339.4961 340.3568 #>  [39,] 332.3334 333.6884 334.9412 336.1014 337.1774 338.1765 339.1048 339.9681 #>  [40,] 331.9450 333.3031 334.5585 335.7211 336.7991 337.7999 338.7298 339.5944 #>  [41,] 331.5851 332.9434 334.1991 335.3619 336.4400 337.4410 338.3710 339.2358 #>  [42,] 331.2535 332.6093 333.8628 335.0237 336.1003 337.0998 338.0285 338.8922 #>  [43,] 330.9503 332.3008 333.5497 334.7067 335.7798 336.7762 337.7023 338.5637 #>  [44,] 330.6752 332.0176 333.2596 334.4105 335.4784 336.4703 337.3923 338.2501 #>  [45,] 330.4278 331.7594 332.9922 334.1351 335.1960 336.1817 337.0984 337.9513 #>  [46,] 330.2076 331.5260 332.7472 333.8802 334.9324 335.9105 336.8204 337.6673 #>  [47,] 330.0142 331.3167 332.5243 333.6454 334.6872 335.6562 336.5581 337.3979 #>  [48,] 329.8469 331.1312 332.3230 333.4304 334.4603 335.4187 336.3113 337.1428 #>  [49,] 329.7049 330.9687 332.1428 333.2348 334.2512 335.1977 336.0798 336.9019 #>  [50,] 329.5873 330.8286 331.9832 333.0581 334.0595 334.9928 335.8632 336.6749 #>  [51,] 329.4933 330.7101 331.8434 332.8997 333.8847 334.8037 335.6612 336.4616 #>  [52,] 329.4219 330.6124 331.7229 332.7592 333.7266 334.6299 335.4735 336.2615 #>  [53,] 329.3721 330.5348 331.6209 332.6358 333.5844 334.4710 335.2998 336.0745 #>  [54,] 329.3429 330.4762 331.5367 332.5290 333.4576 334.3265 335.1395 335.9001 #>  [55,] 329.3332 330.4359 331.4695 332.4382 333.3458 334.1961 334.9924 335.7380 #>  [56,] 329.3418 330.4129 331.4186 332.3626 333.2483 334.0791 334.8579 335.5879 #>  [57,] 329.3676 330.4062 331.3831 332.3016 333.1646 333.9750 334.7357 335.4493 #>  [58,] 329.4097 330.4149 331.3623 332.2544 333.0940 333.8834 334.6252 335.3218 #>  [59,] 329.4668 330.4380 331.3552 332.2204 333.0359 333.8037 334.5261 335.2051 #>  [60,] 329.5379 330.4746 331.3611 332.1989 332.9897 333.7353 334.4377 335.0987 #>  [61,] 329.6219 330.5239 331.3792 332.1891 332.9548 333.6778 334.3597 335.0022 #>  [62,] 329.7178 330.5848 331.4087 332.1903 332.9305 333.6305 334.2916 334.9152 #>  [63,] 329.8245 330.6564 331.4488 332.2019 332.9163 333.5930 334.2329 334.8372 #>  [64,] 329.9411 330.7380 331.4987 332.2231 332.9116 333.5646 334.1831 334.7678 #>  [65,] 330.0667 330.8287 331.5577 332.2533 332.9157 333.5450 334.1417 334.7066 #>  [66,] 330.2003 330.9276 331.6250 332.2919 332.9280 333.5334 334.1083 334.6532 #>  [67,] 330.3411 331.0340 331.7000 332.3382 332.9481 333.5295 334.0824 334.6071 #>  [68,] 330.4882 331.1471 331.7819 332.3916 332.9753 333.5327 334.0635 334.5680 #>  [69,] 330.6409 331.2662 331.8702 332.4515 333.0091 333.5425 334.0513 334.5354 #>  [70,] 330.7985 331.3907 331.9641 332.5173 333.0490 333.5584 334.0452 334.5090 #>  [71,] 330.9603 331.5198 332.0631 332.5884 333.0944 333.5801 334.0448 334.4883 #>  [72,] 331.1255 331.6531 332.1667 332.6645 333.1449 333.6069 334.0498 334.4730 #>  [73,] 331.2936 331.7898 332.2742 332.7448 333.2000 333.6386 334.0597 334.4627 #>  [74,] 331.4641 331.9295 332.3852 332.8290 333.2593 333.6747 334.0742 334.4570 #>  [75,] 331.6363 332.0716 332.4991 332.9166 333.3223 333.7147 334.0928 334.4557 #>  [76,] 331.8098 332.2157 332.6156 333.0072 333.3886 333.7584 334.1152 334.4583 #>  [77,] 331.9842 332.3613 332.7342 333.1003 333.4579 333.8053 334.1411 334.4645 #>  [78,] 332.1589 332.5080 332.8544 333.1956 333.5297 333.8550 334.1702 334.4741 #>  [79,] 332.3337 332.6555 332.9759 333.2927 333.6037 333.9073 334.2020 334.4867 #>  [80,] 332.5080 332.8032 333.0984 333.3912 333.6796 333.9618 334.2364 334.5021 #>  [81,] 332.6817 332.9510 333.2215 333.4909 333.7570 334.0182 334.2729 334.5199 #>  [82,] 332.8544 333.0984 333.3449 333.5913 333.8357 334.0763 334.3115 334.5399 #>  [83,] 333.0258 333.2453 333.4682 333.6923 333.9154 334.1357 334.3516 334.5619 #>  [84,] 333.1956 333.3912 333.5913 333.7935 333.9958 334.1962 334.3933 334.5856 #>  [85,] 333.3637 333.5361 333.7139 333.8948 334.0766 334.2575 334.4360 334.6107 #>  [86,] 333.5297 333.6796 333.8357 333.9958 334.1576 334.3195 334.4798 334.6371 #>  [87,] 333.6935 333.8216 333.9566 334.0963 334.2387 334.3819 334.5243 334.6646 #>  [88,] 333.8550 333.9618 334.0763 334.1962 334.3195 334.4444 334.5694 334.6929 #>  [89,] 334.0139 334.1001 334.1946 334.2952 334.3999 334.5070 334.6147 334.7219 #>  [90,] 334.1702 334.2364 334.3115 334.3933 334.4798 334.5694 334.6603 334.7513 #>  [91,] 334.3236 334.3704 334.4266 334.4901 334.5589 334.6314 334.7059 334.7810 #>  [92,] 334.4741 334.5021 334.5399 334.5856 334.6371 334.6929 334.7513 334.8109 #>  [93,] 334.6216 334.6313 334.6513 334.6796 334.7143 334.7538 334.7964 334.8408 #>  [94,] 334.7660 334.7580 334.7607 334.7721 334.7903 334.8138 334.8410 334.8706 #>  [95,] 334.9071 334.8820 334.8678 334.8628 334.8650 334.8730 334.8851 334.9001 #>  [96,] 335.0450 335.0032 334.9727 334.9517 334.9383 334.9311 334.9285 334.9292 #>  [97,] 335.1796 335.1216 335.0752 335.0386 335.0101 334.9880 334.9710 334.9577 #>  [98,] 335.3107 335.2371 335.1753 335.1236 335.0802 335.0437 335.0126 334.9857 #>  [99,] 335.4385 335.3497 335.2729 335.2064 335.1486 335.0980 335.0532 335.0129 #> [100,] 335.5628 335.4593 335.3679 335.2871 335.2153 335.1509 335.0926 335.0392 #>           [,97]    [,98]    [,99]   [,100] #>   [1,] 363.0421 363.2839 363.5147 363.7339 #>   [2,] 362.3298 362.5885 362.8351 363.0691 #>   [3,] 361.6204 361.8960 362.1586 362.4076 #>   [4,] 360.9141 361.2069 361.4854 361.7495 #>   [5,] 360.2113 360.5212 360.8159 361.0951 #>   [6,] 359.5122 359.8394 360.1503 360.4446 #>   [7,] 358.8171 359.1617 359.4888 359.7983 #>   [8,] 358.1263 358.4884 358.8317 359.1564 #>   [9,] 357.4402 357.8197 358.1793 358.5191 #>  [10,] 356.7590 357.1560 357.5319 357.8867 #>  [11,] 356.0832 356.4976 356.8896 357.2595 #>  [12,] 355.4130 355.8448 356.2530 356.6378 #>  [13,] 354.7489 355.1980 355.6221 356.0217 #>  [14,] 354.0911 354.5574 354.9974 355.4117 #>  [15,] 353.4400 353.9234 354.3791 354.8079 #>  [16,] 352.7960 353.2963 353.7675 354.2106 #>  [17,] 352.1595 352.6765 353.1630 353.6201 #>  [18,] 351.5309 352.0642 352.5658 353.0367 #>  [19,] 350.9105 351.4600 351.9762 352.4607 #>  [20,] 350.2988 350.8640 351.3946 351.8923 #>  [21,] 349.6960 350.2766 350.8213 351.3318 #>  [22,] 349.1026 349.6982 350.2565 350.7795 #>  [23,] 348.5190 349.1290 349.7006 350.2356 #>  [24,] 347.9455 348.5695 349.1538 349.7004 #>  [25,] 347.3824 348.0199 348.6165 349.1742 #>  [26,] 346.8302 347.4806 348.0888 348.6571 #>  [27,] 346.2892 346.9518 347.5711 348.1495 #>  [28,] 345.7597 346.4339 347.0636 347.6515 #>  [29,] 345.2420 345.9270 346.5666 347.1633 #>  [30,] 344.7364 345.4316 346.0803 346.6853 #>  [31,] 344.2432 344.9477 345.6048 346.2175 #>  [32,] 343.7627 344.4757 345.1405 345.7601 #>  [33,] 343.2951 344.0158 344.6875 345.3133 #>  [34,] 342.8406 343.5681 344.2459 344.8772 #>  [35,] 342.3995 343.1329 343.8160 344.4520 #>  [36,] 341.9719 342.7102 343.3977 344.0378 #>  [37,] 341.5579 342.3002 342.9913 343.6347 #>  [38,] 341.1576 341.9030 342.5969 343.2427 #>  [39,] 340.7713 341.5187 342.2144 342.8619 #>  [40,] 340.3988 341.1474 341.8440 342.4924 #>  [41,] 340.0403 340.7889 341.4857 342.1342 #>  [42,] 339.6957 340.4435 341.1395 341.7872 #>  [43,] 339.3651 340.1110 340.8052 341.4515 #>  [44,] 339.0483 339.7913 340.4831 341.1270 #>  [45,] 338.7453 339.4845 340.1728 340.8136 #>  [46,] 338.4559 339.1904 339.8744 340.5114 #>  [47,] 338.1801 338.9089 339.5878 340.2201 #>  [48,] 337.9177 338.6399 339.3128 339.9398 #>  [49,] 337.6684 338.3831 339.0493 339.6702 #>  [50,] 337.4321 338.1384 338.7971 339.4112 #>  [51,] 337.2086 337.9057 338.5561 339.1627 #>  [52,] 336.9974 337.6846 338.3260 338.9245 #>  [53,] 336.7985 337.4749 338.1067 338.6964 #>  [54,] 336.6114 337.2764 337.8978 338.4782 #>  [55,] 336.4359 337.0888 337.6993 338.2696 #>  [56,] 336.2717 336.9118 337.5107 338.0706 #>  [57,] 336.1183 336.7451 337.3319 337.8808 #>  [58,] 335.9755 336.5884 337.1626 337.6999 #>  [59,] 335.8429 336.4414 337.0024 337.5278 #>  [60,] 335.7201 336.3037 336.8512 337.3642 #>  [61,] 335.6068 336.1751 336.7086 337.2089 #>  [62,] 335.5026 336.0551 336.5743 337.0615 #>  [63,] 335.4070 335.9435 336.4481 336.9217 #>  [64,] 335.3197 335.8400 336.3295 336.7894 #>  [65,] 335.2404 335.7440 336.2183 336.6642 #>  [66,] 335.1687 335.6555 336.1143 336.5459 #>  [67,] 335.1041 335.5739 336.0170 336.4342 #>  [68,] 335.0463 335.4989 335.9262 336.3288 #>  [69,] 334.9950 335.4303 335.8416 336.2294 #>  [70,] 334.9498 335.3677 335.7629 336.1358 #>  [71,] 334.9103 335.3107 335.6898 336.0477 #>  [72,] 334.8761 335.2591 335.6220 335.9648 #>  [73,] 334.8470 335.2126 335.5592 335.8869 #>  [74,] 334.8227 335.1708 335.5011 335.8136 #>  [75,] 334.8027 335.1334 335.4475 335.7449 #>  [76,] 334.7867 335.1001 335.3981 335.6803 #>  [77,] 334.7746 335.0708 335.3526 335.6197 #>  [78,] 334.7660 335.0450 335.3107 335.5628 #>  [79,] 334.7605 335.0226 335.2723 335.5094 #>  [80,] 334.7580 335.0032 335.2371 335.4593 #>  [81,] 334.7581 334.9867 335.2049 335.4122 #>  [82,] 334.7607 334.9727 335.1753 335.3679 #>  [83,] 334.7654 334.9611 335.1483 335.3263 #>  [84,] 334.7721 334.9517 335.1236 335.2871 #>  [85,] 334.7804 334.9441 335.1009 335.2502 #>  [86,] 334.7903 334.9383 335.0802 335.2153 #>  [87,] 334.8015 334.9340 335.0612 335.1822 #>  [88,] 334.8138 334.9311 335.0437 335.1509 #>  [89,] 334.8271 334.9293 335.0275 335.1211 #>  [90,] 334.8410 334.9285 335.0126 335.0926 #>  [91,] 334.8556 334.9285 334.9987 335.0654 #>  [92,] 334.8706 334.9292 334.9857 335.0392 #>  [93,] 334.8859 334.9304 334.9734 335.0140 #>  [94,] 334.9013 334.9320 334.9617 334.9895 #>  [95,] 334.9167 334.9338 334.9505 334.9657 #>  [96,] 334.9320 334.9358 334.9396 334.9425 #>  [97,] 334.9470 334.9377 334.9289 334.9197 #>  [98,] 334.9617 334.9396 334.9184 334.8972 #>  [99,] 334.9759 334.9412 334.9078 334.8748 #> [100,] 334.9895 334.9425 334.8972 334.8526 head_to_potential(mc, hc) #>            [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8] #>   [1,] 962.4030 961.1546 959.8996 958.6378 957.3691 956.0933 954.8101 953.5196 #>   [2,] 961.9708 960.7204 959.4633 958.1993 956.9283 955.6500 954.3644 953.0712 #>   [3,] 961.5403 960.2879 959.0287 957.7626 956.4892 955.2086 953.9206 952.6248 #>   [4,] 961.1115 959.8571 958.5959 957.3276 956.0520 954.7691 953.4786 952.1804 #>   [5,] 960.6844 959.4281 958.1648 956.8944 955.6167 954.3315 953.0386 951.7379 #>   [6,] 960.2589 959.0007 957.7355 956.4630 955.1832 953.8958 952.6006 951.2974 #>   [7,] 959.8352 958.5752 957.3080 956.0335 954.7516 953.4620 952.1645 950.8590 #>   [8,] 959.4132 958.1514 956.8823 955.6059 954.3219 953.0302 951.7305 950.4226 #>   [9,] 958.9930 957.7294 956.4585 955.1802 953.8942 952.6003 951.2985 949.9884 #>  [10,] 958.5745 957.3092 956.0365 954.7563 953.4684 952.1725 950.8685 949.5562 #>  [11,] 958.1579 956.8909 955.6165 954.3344 953.0446 951.7468 950.4407 949.1262 #>  [12,] 957.7430 956.4744 955.1983 953.9145 952.6228 951.3230 950.0150 948.6984 #>  [13,] 957.3300 956.0598 954.7820 953.4965 952.2030 950.9014 949.5913 948.2727 #>  [14,] 956.9188 955.6471 954.3677 953.0805 951.7853 950.4818 949.1699 947.8493 #>  [15,] 956.5095 955.2362 953.9553 952.6665 951.3696 950.0644 948.7506 947.4281 #>  [16,] 956.1020 954.8273 953.5449 952.2546 950.9560 949.6491 948.3335 947.0091 #>  [17,] 955.6964 954.4204 953.1365 951.8446 950.5445 949.2360 947.9187 946.5925 #>  [18,] 955.2928 954.0154 952.7301 951.4368 950.1352 948.8250 947.5061 946.1781 #>  [19,] 954.8910 953.6123 952.3257 951.0310 949.7279 948.4162 947.0957 945.7661 #>  [20,] 954.4912 953.2113 951.9234 950.6273 949.3228 948.0097 946.6876 945.3564 #>  [21,] 954.0933 952.8122 951.5231 950.2257 948.9199 947.6053 946.2818 944.9490 #>  [22,] 953.6973 952.4151 951.1248 949.8263 948.5191 947.2033 945.8783 944.5441 #>  [23,] 953.3033 952.0201 950.7287 949.4289 948.1206 946.8034 945.4772 944.1415 #>  [24,] 952.9113 951.6270 950.3346 949.0337 947.7243 946.4059 945.0784 943.7414 #>  [25,] 952.5213 951.2360 949.9426 948.6407 947.3301 946.0106 944.6819 943.3437 #>  [26,] 952.1333 950.8471 949.5527 948.2499 946.9383 945.6177 944.2878 942.9484 #>  [27,] 951.7472 950.4602 949.1650 947.8612 946.5486 945.2270 943.8961 942.5556 #>  [28,] 951.3632 950.0754 948.7793 947.4747 946.1612 944.8387 943.5068 942.1653 #>  [29,] 950.9812 949.6927 948.3959 947.0904 945.7761 944.4527 943.1199 941.7774 #>  [30,] 950.6012 949.3121 948.0145 946.7083 945.3933 944.0691 942.7355 941.3921 #>  [31,] 950.2233 948.9335 947.6353 946.3285 945.0127 943.6878 942.3534 941.0093 #>  [32,] 949.8474 948.5571 947.2583 945.9509 944.6345 943.3089 941.9738 940.6289 #>  [33,] 949.4736 948.1827 946.8835 945.5755 944.2585 942.9324 941.5967 940.2511 #>  [34,] 949.1018 947.8105 946.5108 945.2023 943.8849 942.5582 941.2220 939.8759 #>  [35,] 948.7320 947.4404 946.1403 944.8314 943.5136 942.1864 940.8497 939.5032 #>  [36,] 948.3644 947.0724 945.7720 944.4628 943.1446 941.8171 940.4800 939.1330 #>  [37,] 947.9988 946.7066 945.4059 944.0964 942.7779 941.4501 940.1127 938.7654 #>  [38,] 947.6352 946.3428 945.0419 943.7323 942.4136 941.0855 939.7479 938.4003 #>  [39,] 947.2737 945.9812 944.6802 943.3704 942.0515 940.7233 939.3855 938.0378 #>  [40,] 946.9143 945.6218 944.3207 943.0108 941.6918 940.3636 939.0257 937.6778 #>  [41,] 946.5570 945.2644 943.9633 942.6534 941.3345 940.0062 938.6683 937.3205 #>  [42,] 946.2018 944.9092 943.6082 942.2983 940.9795 939.6512 938.3134 936.9656 #>  [43,] 945.8486 944.5562 943.2552 941.9455 940.6268 939.2987 937.9610 936.6134 #>  [44,] 945.4974 944.2052 942.9045 941.5949 940.2764 938.9485 937.6111 936.2637 #>  [45,] 945.1484 943.8564 942.5559 941.2466 939.9284 938.6008 937.2636 935.9166 #>  [46,] 944.8014 943.5097 942.2095 940.9006 939.5827 938.2554 936.9186 935.5720 #>  [47,] 944.4565 943.1651 941.8653 940.5568 939.2393 937.9125 936.5761 935.2299 #>  [48,] 944.1136 942.8227 941.5233 940.2152 938.8982 937.5719 936.2361 934.8904 #>  [49,] 943.7728 942.4824 941.1835 939.8759 938.5594 937.2337 935.8985 934.5535 #>  [50,] 943.4340 942.1441 940.8458 939.5389 938.2230 936.8979 935.5634 934.2190 #>  [51,] 943.0973 941.8080 940.5103 939.2040 937.8888 936.5645 935.2307 933.8871 #>  [52,] 942.7626 941.4740 940.1770 938.8714 937.5569 936.2334 934.9004 933.5577 #>  [53,] 942.4300 941.1420 939.8458 938.5410 937.2273 935.9046 934.5726 933.2308 #>  [54,] 942.0993 940.8122 939.5167 938.2128 936.9000 935.5782 934.2471 932.9064 #>  [55,] 941.7707 940.4844 939.1898 937.8868 936.5750 935.2542 933.9241 932.5845 #>  [56,] 941.4441 940.1587 938.8650 937.5629 936.2521 934.9324 933.6035 932.2650 #>  [57,] 941.1195 939.8350 938.5423 937.2413 935.9316 934.6130 933.2852 931.9480 #>  [58,] 940.7968 939.5133 938.2217 936.9218 935.6132 934.2958 932.9693 931.6334 #>  [59,] 940.4762 939.1937 937.9032 936.6044 935.2971 933.9809 932.6557 931.3212 #>  [60,] 940.1575 938.8762 937.5868 936.2892 934.9831 933.6683 932.3445 931.0114 #>  [61,] 939.8407 938.5606 937.2725 935.9761 934.6714 933.3579 932.0356 930.7040 #>  [62,] 939.5259 938.2470 936.9602 935.6652 934.3618 933.0498 931.7290 930.3990 #>  [63,] 939.2131 937.9354 936.6499 935.3563 934.0544 932.7439 931.4246 930.0963 #>  [64,] 938.9021 937.6258 936.3416 935.0495 933.7491 932.4402 931.1225 929.7960 #>  [65,] 938.5931 937.3181 936.0354 934.7447 933.4459 932.1386 930.8227 929.4979 #>  [66,] 938.2859 937.0124 935.7312 934.4420 933.1448 931.8392 930.5251 929.2022 #>  [67,] 937.9806 936.7086 935.4289 934.1414 932.8458 931.5420 930.2297 928.9087 #>  [68,] 937.6772 936.4067 935.1286 933.8427 932.5489 931.2469 929.9365 928.6174 #>  [69,] 937.3756 936.1066 934.8302 933.5460 932.2540 930.9539 929.6454 928.3284 #>  [70,] 937.0758 935.8085 934.5337 933.2514 931.9611 930.6629 929.3565 928.0415 #>  [71,] 936.7779 935.5122 934.2392 932.9586 931.6703 930.3740 929.0696 927.7569 #>  [72,] 936.4817 935.2178 933.9465 932.6678 931.3814 930.0872 928.7849 927.4743 #>  [73,] 936.1874 934.9252 933.6557 932.3789 931.0945 929.8024 928.5022 927.1939 #>  [74,] 935.8947 934.6343 933.3668 932.0919 930.8096 929.5195 928.2216 926.9156 #>  [75,] 935.6039 934.3453 933.0797 931.8068 930.5265 929.2387 927.9430 926.6394 #>  [76,] 935.3147 934.0580 932.7944 931.5235 930.2454 928.9598 927.6664 926.3652 #>  [77,] 935.0273 933.7725 932.5109 931.2421 929.9661 928.6828 927.3918 926.0930 #>  [78,] 934.7415 933.4887 932.2291 930.9625 929.6887 928.4077 927.1191 925.8229 #>  [79,] 934.4574 933.2066 931.9491 930.6847 929.4132 928.1344 926.8483 925.5546 #>  [80,] 934.1750 932.9262 931.6708 930.4086 929.1394 927.8630 926.5794 925.2884 #>  [81,] 933.8942 932.6475 931.3942 930.1342 928.8674 927.5935 926.3124 925.0240 #>  [82,] 933.6150 932.3704 931.1193 929.8616 928.5971 927.3257 926.0472 924.7615 #>  [83,] 933.3374 932.0950 930.8461 929.5907 928.3286 927.0597 925.7838 924.5008 #>  [84,] 933.0613 931.8211 930.5745 929.3215 928.0618 926.7955 925.5222 924.2420 #>  [85,] 932.7869 931.5488 930.3045 929.0539 927.7967 926.5330 925.2624 923.9849 #>  [86,] 932.5139 931.2781 930.0361 928.7879 927.5333 926.2721 925.0043 923.7297 #>  [87,] 932.2424 931.0089 929.7693 928.5235 927.2715 926.0129 924.7479 923.4761 #>  [88,] 931.9725 930.7413 929.5040 928.2607 927.0112 925.7554 924.4931 923.2243 #>  [89,] 931.7040 930.4751 929.2403 927.9995 926.7526 925.4995 924.2400 922.9741 #>  [90,] 931.4369 930.2104 928.9780 927.7398 926.4955 925.2451 923.9885 922.7256 #>  [91,] 931.1713 929.9471 928.7173 927.4816 926.2400 924.9924 923.7386 922.4787 #>  [92,] 930.9071 929.6853 928.4579 927.2248 925.9859 924.7411 923.4903 922.2333 #>  [93,] 930.6442 929.4249 928.2000 926.9696 925.7334 924.4914 923.2435 921.9896 #>  [94,] 930.3827 929.1659 927.9435 926.7157 925.4822 924.2431 922.9981 921.7473 #>  [95,] 930.1226 928.9082 927.6884 926.4633 925.2326 923.9963 922.7543 921.5065 #>  [96,] 929.8638 928.6518 927.4347 926.2122 924.9843 923.7509 922.5119 921.2672 #>  [97,] 929.6062 928.3968 927.1823 925.9625 924.7374 923.5069 922.2709 921.0294 #>  [98,] 929.3499 928.1431 926.9312 925.7141 924.4918 923.2642 922.0313 920.7929 #>  [99,] 929.0949 927.8906 926.6813 925.4670 924.2475 923.0229 921.7930 920.5578 #> [100,] 928.8411 927.6394 926.4328 925.2212 924.0046 922.7829 921.5561 920.3241 #>            [,9]    [,10]    [,11]    [,12]    [,13]    [,14]    [,15]    [,16] #>   [1,] 952.2214 950.9155 949.6016 948.2796 946.9493 945.6104 944.2628 942.9063 #>   [2,] 951.7704 950.4616 949.1447 947.8196 946.4860 945.1438 943.7926 942.4324 #>   [3,] 951.3213 950.0097 948.6899 947.3618 946.0250 944.6794 943.3247 941.9609 #>   [4,] 950.8742 949.5599 948.2372 946.9060 945.5661 944.2172 942.8591 941.4917 #>   [5,] 950.4291 949.1121 947.7866 946.4525 945.1095 943.7574 942.3959 941.0249 #>   [6,] 949.9861 948.6665 947.3382 946.0012 944.6551 943.2998 941.9351 940.5605 #>   [7,] 949.5452 948.2230 946.8920 945.5521 944.2031 942.8447 941.4766 940.0987 #>   [8,] 949.1064 947.7816 946.4480 945.1054 943.7534 942.3920 941.0207 939.6394 #>   [9,] 948.6698 947.3425 946.0063 944.6609 943.3061 941.9417 940.5673 939.1827 #>  [10,] 948.2353 946.9056 945.5669 944.2188 942.8613 941.4939 940.1164 938.7286 #>  [11,] 947.8030 946.4710 945.1297 943.7791 942.4188 941.0486 939.6681 938.2772 #>  [12,] 947.3730 946.0386 944.6950 943.3418 941.9789 940.6059 939.2225 937.8284 #>  [13,] 946.9452 945.6086 944.2626 942.9070 941.5414 940.1657 938.7795 937.3825 #>  [14,] 946.5197 945.1809 943.8326 942.4746 941.1066 939.7282 938.3392 936.9393 #>  [15,] 946.0964 944.7555 943.4051 942.0447 940.6743 939.2934 937.9017 936.4989 #>  [16,] 945.6756 944.3326 942.9800 941.6174 940.2446 938.8612 937.4669 936.0614 #>  [17,] 945.2570 943.9121 942.5574 941.1926 939.8175 938.4318 937.0350 935.6268 #>  [18,] 944.8408 943.4940 942.1373 940.7705 939.3932 938.0051 936.6058 935.1951 #>  [19,] 944.4270 943.0784 941.7198 940.3509 938.9715 937.5812 936.1796 934.7664 #>  [20,] 944.0157 942.6652 941.3048 939.9340 938.5525 937.1601 935.7562 934.3407 #>  [21,] 943.6067 942.2546 940.8924 939.5197 938.1363 936.7418 935.3358 933.9180 #>  [22,] 943.2002 941.8465 940.4826 939.1082 937.7229 936.3264 934.9184 933.4984 #>  [23,] 942.7962 941.4410 940.0755 938.6993 937.3123 935.9139 934.5039 933.0818 #>  [24,] 942.3947 941.0380 939.6709 938.2932 936.9045 935.5044 934.0925 932.6684 #>  [25,] 941.9957 940.6376 939.2691 937.8899 936.4995 935.0977 933.6841 932.2581 #>  [26,] 941.5992 940.2398 938.8699 937.4893 936.0974 934.6940 933.2787 931.8510 #>  [27,] 941.2052 939.8446 938.4735 937.0915 935.6982 934.2934 932.8765 931.4471 #>  [28,] 940.8138 939.4521 938.0798 936.6965 935.3019 933.8957 932.4773 931.0464 #>  [29,] 940.4250 939.0622 937.6888 936.3043 934.9085 933.5010 932.0813 930.6490 #>  [30,] 940.0387 938.6750 937.3005 935.9150 934.5181 933.1094 931.6884 930.2548 #>  [31,] 939.6550 938.2904 936.9150 935.5286 934.1306 932.7208 931.2987 929.8639 #>  [32,] 939.2739 937.9085 936.5323 935.1450 933.7461 932.3353 930.9122 929.4763 #>  [33,] 938.8955 937.5293 936.1524 934.7642 933.3646 931.9529 930.5289 929.0920 #>  [34,] 938.5196 937.1528 935.7752 934.3864 932.9860 931.5736 930.1487 928.7110 #>  [35,] 938.1464 936.7791 935.4009 934.0115 932.6105 931.1974 929.7718 928.3334 #>  [36,] 937.7758 936.4080 935.0294 933.6395 932.2379 930.8243 929.3982 927.9591 #>  [37,] 937.4078 936.0397 934.6607 933.2704 931.8684 930.4543 929.0277 927.5882 #>  [38,] 937.0425 935.6741 934.2948 932.9042 931.5019 930.0875 928.6605 927.2206 #>  [39,] 936.6798 935.3112 933.9317 932.5409 931.1384 929.7237 928.2966 926.8564 #>  [40,] 936.3198 934.9511 933.5715 932.1806 930.7779 929.3632 927.9359 926.4955 #>  [41,] 935.9624 934.5937 933.2141 931.8231 930.4205 929.0057 927.5784 926.1381 #>  [42,] 935.6076 934.2390 932.8595 931.4687 930.0661 928.6514 927.2242 925.7840 #>  [43,] 935.2555 933.8871 932.5077 931.1171 929.7147 928.3003 926.8733 925.4333 #>  [44,] 934.9061 933.5379 932.1588 930.7684 929.3664 927.9522 926.5256 925.0859 #>  [45,] 934.5593 933.1914 931.8127 930.4227 929.0211 927.6073 926.1811 924.7419 #>  [46,] 934.2151 932.8477 931.4694 930.0799 928.6788 927.2656 925.8399 924.4013 #>  [47,] 933.8736 932.5067 931.1290 929.7400 928.3395 926.9269 925.5019 924.0640 #>  [48,] 933.5346 932.1684 930.7913 929.4030 928.0032 926.5913 925.1671 923.7301 #>  [49,] 933.1983 931.8328 930.4564 929.0689 927.6699 926.2589 924.8356 923.3995 #>  [50,] 932.8647 931.4999 930.1243 928.7377 927.3395 925.9295 924.5072 923.0722 #>  [51,] 932.5336 931.1696 929.7950 928.4093 927.0122 925.6032 924.1820 922.7482 #>  [52,] 932.2051 930.8421 929.4684 928.0838 926.6878 925.2800 923.8600 922.4275 #>  [53,] 931.8791 930.5172 929.1446 927.7611 926.3663 924.9598 923.5412 922.1100 #>  [54,] 931.5558 930.1950 928.8236 927.4413 926.0478 924.6426 923.2254 921.7958 #>  [55,] 931.2350 929.8754 928.5052 927.1243 925.7322 924.3285 922.9128 921.4848 #>  [56,] 930.9167 929.5584 928.1896 926.8101 925.4194 924.0173 922.6033 921.1770 #>  [57,] 930.6010 929.2440 927.8767 926.4986 925.1096 923.7091 922.2968 920.8724 #>  [58,] 930.2878 928.9322 927.5664 926.1900 924.8026 923.4038 921.9934 920.5710 #>  [59,] 929.9771 928.6230 927.2588 925.8840 924.4984 923.1015 921.6931 920.2726 #>  [60,] 929.6688 928.3164 926.9538 925.5808 924.1970 922.8021 921.3957 919.9774 #>  [61,] 929.3630 928.0122 926.6514 925.2802 923.8984 922.5055 921.1012 919.6852 #>  [62,] 929.0596 927.7106 926.3516 924.9824 923.6025 922.2118 920.8097 919.3961 #>  [63,] 928.7587 927.4115 926.0544 924.6872 923.3094 921.9209 920.5212 919.1099 #>  [64,] 928.4601 927.1148 925.7597 924.3946 923.0190 921.6328 920.2355 918.8268 #>  [65,] 928.1640 926.8206 925.4676 924.1046 922.7313 921.3474 919.9526 918.5466 #>  [66,] 927.8701 926.5288 925.1779 923.8171 922.4462 921.0648 919.6726 918.2692 #>  [67,] 927.5787 926.2394 924.8907 923.5322 922.1637 920.7848 919.3953 917.9948 #>  [68,] 927.2895 925.9524 924.6060 923.2499 921.8838 920.5076 919.1208 917.7232 #>  [69,] 927.0026 925.6677 924.3236 922.9700 921.6065 920.2329 918.8490 917.4543 #>  [70,] 926.7179 925.3854 924.0437 922.6925 921.3317 919.9609 918.5799 917.1883 #>  [71,] 926.4355 925.1053 923.7661 922.4175 921.0594 919.6914 918.3134 916.9249 #>  [72,] 926.1553 924.8275 923.4908 922.1449 920.7895 919.4245 918.0495 916.6642 #>  [73,] 925.8772 924.5519 923.2178 921.8746 920.5221 919.1600 917.7881 916.4062 #>  [74,] 925.6014 924.2786 922.9471 921.6067 920.2571 918.8980 917.5293 916.1507 #>  [75,] 925.3276 924.0074 922.6786 921.3410 919.9944 918.6385 917.2730 915.8978 #>  [76,] 925.0559 923.7384 922.4124 921.0776 919.7340 918.3813 917.0191 915.6474 #>  [77,] 924.7863 923.4715 922.1483 920.8165 919.4759 918.1264 916.7676 915.3994 #>  [78,] 924.5188 923.2067 921.8863 920.5575 919.2201 917.8738 916.5185 915.1539 #>  [79,] 924.2532 922.9439 921.6264 920.3007 918.9665 917.6235 916.2717 914.9108 #>  [80,] 923.9897 922.6832 921.3687 920.0460 918.7150 917.3755 916.0272 914.6700 #>  [81,] 923.7280 922.4244 921.1129 919.7934 918.4657 917.1296 915.7849 914.4314 #>  [82,] 923.4683 922.1676 920.8592 919.5429 918.2185 916.8859 915.5448 914.1951 #>  [83,] 923.2105 921.9128 920.6075 919.2944 917.9733 916.6442 915.3069 913.9611 #>  [84,] 922.9546 921.6598 920.3576 919.0478 917.7302 916.4047 915.0710 913.7291 #>  [85,] 922.7004 921.4088 920.1097 918.8032 917.4891 916.1671 914.8373 913.4993 #>  [86,] 922.4481 921.1595 919.8637 918.5605 917.2499 915.9316 914.6055 913.2715 #>  [87,] 922.1976 920.9121 919.6195 918.3197 917.0126 915.6980 914.3758 913.0458 #>  [88,] 921.9487 920.6664 919.3771 918.0807 916.7772 915.4663 914.1479 912.8220 #>  [89,] 921.7016 920.4224 919.1365 917.8435 916.5436 915.2364 913.9220 912.6002 #>  [90,] 921.4562 920.1802 918.8976 917.6081 916.3118 915.0084 913.6979 912.3802 #>  [91,] 921.2124 919.9396 918.6604 917.3744 916.0817 914.7822 913.4757 912.1621 #>  [92,] 920.9702 919.7007 918.4248 917.1424 915.8534 914.5577 913.2552 911.9457 #>  [93,] 920.7296 919.4634 918.1909 916.9121 915.6268 914.3349 913.0364 911.7312 #>  [94,] 920.4905 919.2276 917.9586 916.6833 915.4018 914.1138 912.8193 911.5183 #>  [95,] 920.2529 918.9934 917.7278 916.4562 915.1783 913.8943 912.6038 911.3070 #>  [96,] 920.0169 918.7607 917.4986 916.2306 914.9565 913.6763 912.3900 911.0974 #>  [97,] 919.7822 918.5294 917.2709 916.0065 914.7362 913.4599 912.1777 910.8894 #>  [98,] 919.5490 918.2996 917.0446 915.7838 914.5173 913.2451 911.9669 910.6829 #>  [99,] 919.3172 918.0712 916.8197 915.5626 914.3000 913.0316 911.7576 910.4779 #> [100,] 919.0868 917.8442 916.5962 915.3428 914.0840 912.8196 911.5497 910.2743 #>           [,17]    [,18]    [,19]    [,20]    [,21]    [,22]    [,23]    [,24] #>   [1,] 941.5407 940.1658 938.7813 937.3871 935.9830 934.5686 933.1439 931.7085 #>   [2,] 941.0629 939.6839 938.2952 936.8965 935.4876 934.0683 932.6383 931.1974 #>   [3,] 940.5875 939.2045 937.8115 936.4083 934.9948 933.5705 932.1354 930.6891 #>   [4,] 940.1145 938.7275 937.3304 935.9228 934.5046 933.0756 931.6353 930.1836 #>   [5,] 939.6440 938.2531 936.8518 935.4400 934.0172 932.5834 931.1381 929.6811 #>   [6,] 939.1760 937.7812 936.3759 934.9598 933.5326 932.0941 930.6438 929.1816 #>   [7,] 938.7106 937.3120 935.9027 934.4824 933.0509 931.6076 930.1525 928.6851 #>   [8,] 938.2477 936.8455 935.4323 934.0079 932.5720 931.1242 929.6643 928.1918 #>   [9,] 937.7876 936.3817 934.9647 933.5362 932.0961 930.6438 929.1792 927.7017 #>  [10,] 937.3301 935.9206 934.4999 933.0675 931.6232 930.1666 928.6972 927.2149 #>  [11,] 936.8754 935.4624 934.0380 932.6018 931.1534 929.6924 928.2186 926.7314 #>  [12,] 936.4234 935.0071 933.5791 932.1391 930.6867 929.2216 927.7433 926.2514 #>  [13,] 935.9743 934.5546 933.1232 931.6795 930.2232 928.7540 927.2714 925.7749 #>  [14,] 935.5280 934.1052 932.6703 931.2230 929.7630 928.2897 926.8029 925.3020 #>  [15,] 935.0847 933.6587 932.2205 930.7698 929.3060 927.8289 926.3379 924.8326 #>  [16,] 934.6443 933.2153 931.7739 930.3197 928.8524 927.3715 925.8765 924.3670 #>  [17,] 934.2069 932.7749 931.3304 929.8730 928.4022 926.9177 925.4188 923.9052 #>  [18,] 933.7725 932.3377 930.8902 929.4296 927.9555 926.4674 924.9648 923.4471 #>  [19,] 933.3412 931.9036 930.4532 928.9896 927.5122 926.0207 924.5145 922.9930 #>  [20,] 932.9130 931.4728 930.0196 928.5530 927.0725 925.5777 924.0680 922.5428 #>  [21,] 932.4879 931.0452 929.5893 928.1199 926.6364 925.1384 923.6253 922.0966 #>  [22,] 932.0660 930.6208 929.1624 927.6903 926.2040 924.7029 923.1866 921.6545 #>  [23,] 931.6473 930.1998 928.7389 927.2642 925.7752 924.2713 922.7519 921.2164 #>  [24,] 931.2318 929.7821 928.3189 926.8418 925.3501 923.8434 922.3211 920.7826 #>  [25,] 930.8195 929.3678 927.9024 926.4229 924.9288 923.4195 921.8944 920.3530 #>  [26,] 930.4106 928.9569 927.4894 926.0078 924.5113 922.9995 921.4718 919.9276 #>  [27,] 930.0049 928.5494 927.0800 925.5963 924.0976 922.5836 921.0534 919.5065 #>  [28,] 929.6026 928.1453 926.6742 925.1885 923.6878 922.1716 920.6391 919.0898 #>  [29,] 929.2037 927.7448 926.2719 924.7845 923.2819 921.7637 920.2291 918.6775 #>  [30,] 928.8081 927.3478 925.8733 924.3842 922.8799 921.3598 919.8233 918.2696 #>  [31,] 928.4159 926.9542 925.4784 923.9878 922.4819 920.9601 919.4217 917.8661 #>  [32,] 928.0272 926.5643 925.0871 923.5952 922.0879 920.5645 919.0245 917.4672 #>  [33,] 927.6418 926.1779 924.6996 923.2064 921.6978 920.1731 918.6317 917.0728 #>  [34,] 927.2600 925.7950 924.3158 922.8215 921.3118 919.7859 918.2431 916.6829 #>  [35,] 926.8815 925.4158 923.9357 922.4405 920.9298 919.4028 917.8590 916.2976 #>  [36,] 926.5066 925.0402 923.5593 922.0634 920.5518 919.0240 917.4793 915.9169 #>  [37,] 926.1351 924.6682 923.1867 921.6902 920.1780 918.6495 917.1040 915.5407 #>  [38,] 925.7672 924.2998 922.8179 921.3209 919.8082 918.2791 916.7331 915.1693 #>  [39,] 925.4027 923.9350 922.4528 920.9555 919.4425 917.9131 916.3666 914.8024 #>  [40,] 925.0417 923.5739 922.0915 920.5940 919.0808 917.5512 916.0046 914.4402 #>  [41,] 924.6843 923.2164 921.7340 920.2365 918.7233 917.1937 915.6470 914.0826 #>  [42,] 924.3303 922.8626 921.3803 919.8829 918.3699 916.8404 915.2939 913.7296 #>  [43,] 923.9798 922.5123 921.0304 919.5333 918.0205 916.4914 914.9452 913.3813 #>  [44,] 923.6328 922.1658 920.6842 919.1876 917.6752 916.1466 914.6010 913.0376 #>  [45,] 923.2893 921.8228 920.3418 918.8457 917.3340 915.8061 914.2612 912.6986 #>  [46,] 922.9493 921.4835 920.0031 918.5078 916.9969 915.4698 913.9258 912.3641 #>  [47,] 922.6128 921.1477 919.6682 918.1738 916.6639 915.1377 913.5948 912.0343 #>  [48,] 922.2797 920.8156 919.3371 917.8437 916.3348 914.8099 913.2682 911.7090 #>  [49,] 921.9501 920.4870 919.0096 917.5174 916.0098 914.4862 912.9459 911.3882 #>  [50,] 921.6239 920.1620 918.6859 917.1950 915.6888 914.1667 912.6280 911.0720 #>  [51,] 921.3012 919.8406 918.3659 916.8765 915.3718 913.8514 912.3144 910.7603 #>  [52,] 920.9818 919.5227 918.0495 916.5617 915.0588 913.5401 912.0051 910.4531 #>  [53,] 920.6659 919.2083 917.7367 916.2507 914.7497 913.2330 911.7001 910.1503 #>  [54,] 920.3533 918.8974 917.4276 915.9435 914.4444 912.9299 911.3993 909.8519 #>  [55,] 920.0440 918.5899 917.1221 915.6400 914.1431 912.6308 911.1026 909.5578 #>  [56,] 919.7380 918.2859 916.8201 915.3402 913.8456 912.3358 910.8101 909.2681 #>  [57,] 919.4354 917.9853 916.5217 915.0440 913.5519 912.0447 910.5218 908.9826 #>  [58,] 919.1360 917.6880 916.2267 914.7515 913.2619 911.7574 910.2375 908.7014 #>  [59,] 918.8398 917.3942 915.9353 914.4626 912.9757 911.4741 909.9572 908.4243 #>  [60,] 918.5468 917.1036 915.6472 914.1773 912.6932 911.1946 909.6808 908.1514 #>  [61,] 918.2570 916.8163 915.3626 913.8954 912.4144 910.9189 909.4084 907.8825 #>  [62,] 917.9704 916.5323 915.0813 913.6171 912.1391 910.6469 909.1399 907.6177 #>  [63,] 917.6868 916.2514 914.8034 913.3421 911.8674 910.3786 908.8752 907.3568 #>  [64,] 917.4063 915.9738 914.5287 913.0706 911.5992 910.1139 908.6143 907.0998 #>  [65,] 917.1289 915.6993 914.2572 912.8024 911.3344 909.8528 908.3570 906.8467 #>  [66,] 916.8545 915.4278 913.9890 912.5376 911.0731 909.5952 908.1034 906.5973 #>  [67,] 916.5830 915.1594 913.7239 912.2759 910.8151 909.3411 907.8534 906.3516 #>  [68,] 916.3144 914.8941 913.4619 912.0175 910.5605 909.0904 907.6070 906.1096 #>  [69,] 916.0487 914.6317 913.2030 911.7622 910.3091 908.8431 907.3639 905.8712 #>  [70,] 915.7858 914.3722 912.9471 911.5101 910.0609 908.5991 907.1243 905.6362 #>  [71,] 915.5257 914.1156 912.6941 911.2609 909.8158 908.3583 906.8881 905.4048 #>  [72,] 915.2684 913.8618 912.4440 911.0148 909.5738 908.1207 906.6551 905.1766 #>  [73,] 915.0138 913.6108 912.1969 910.7717 909.3349 907.8862 906.4253 904.9518 #>  [74,] 914.7619 913.3626 911.9525 910.5314 909.0989 907.6548 906.1987 904.7303 #>  [75,] 914.5125 913.1170 911.7109 910.2939 908.8659 907.4264 905.9751 904.5118 #>  [76,] 914.2658 912.8741 911.4720 910.0593 908.6357 907.2009 905.7546 904.2965 #>  [77,] 914.0216 912.6337 911.2358 909.8274 908.4083 906.9782 905.5370 904.0842 #>  [78,] 913.7798 912.3960 911.0021 909.5981 908.1836 906.7584 905.3222 903.8748 #>  [79,] 913.5405 912.1607 910.7711 909.3715 907.9616 906.5413 905.1103 903.6683 #>  [80,] 913.3036 911.9278 910.5425 909.1474 907.7423 906.3269 904.9011 903.4646 #>  [81,] 913.0690 911.6974 910.3164 908.9258 907.5255 906.1151 904.6946 903.2637 #>  [82,] 912.8367 911.4692 910.0926 908.7067 907.3111 905.9059 904.4907 903.0653 #>  [83,] 912.6066 911.2434 909.8712 908.4899 907.0993 905.6991 904.2893 902.8696 #>  [84,] 912.3788 911.0198 909.6521 908.2755 906.8898 905.4948 904.0904 902.6764 #>  [85,] 912.1531 910.7985 909.4353 908.0634 906.6826 905.2928 903.8938 902.4856 #>  [86,] 911.9295 910.5792 909.2206 907.8534 906.4777 905.0931 903.6996 902.2971 #>  [87,] 911.7079 910.3620 909.0080 907.6457 906.2749 904.8956 903.5077 902.1110 #>  [88,] 911.4884 910.1469 908.7975 907.4400 906.0743 904.7003 903.3179 901.9270 #>  [89,] 911.2708 909.9338 908.5890 907.2364 905.8758 904.5072 903.1303 901.7453 #>  [90,] 911.0551 909.7226 908.3825 907.0348 905.6793 904.3160 902.9448 901.5656 #>  [91,] 910.8413 909.5133 908.1779 906.8351 905.4848 904.1268 902.7612 901.3879 #>  [92,] 910.6293 909.3058 907.9752 906.6373 905.2921 903.9396 902.5796 901.2121 #>  [93,] 910.4191 909.1002 907.7743 906.4413 905.1013 903.7542 902.3998 901.0383 #>  [94,] 910.2106 908.8962 907.5751 906.2471 904.9123 903.5706 902.2219 900.8662 #>  [95,] 910.0038 908.6940 907.3776 906.0547 904.7250 903.3887 902.0456 900.6959 #>  [96,] 909.7986 908.4934 907.1818 905.8638 904.5394 903.2085 901.8711 900.5272 #>  [97,] 909.5950 908.2944 906.9876 905.6746 904.3554 903.0299 901.6982 900.3602 #>  [98,] 909.3929 908.0969 906.7950 905.4870 904.1730 902.8529 901.5268 900.1948 #>  [99,] 909.1923 907.9010 906.6038 905.3009 903.9921 902.6774 901.3570 900.0308 #> [100,] 908.9932 907.7065 906.4142 905.1162 903.8126 902.5034 901.1886 899.8682 #>           [,25]    [,26]    [,27]    [,28]    [,29]    [,30]    [,31]    [,32] #>   [1,] 930.2623 928.8050 927.3365 925.8565 924.3648 922.8612 921.3456 919.8177 #>   [2,] 929.7454 928.2820 926.8071 925.3202 923.8214 922.3102 920.7866 919.2502 #>   [3,] 929.2313 927.7619 926.2806 924.7870 923.2810 921.7624 920.2308 918.6860 #>   [4,] 928.7202 927.2448 925.7571 924.2569 922.7439 921.2177 919.6782 918.1251 #>   [5,] 928.2121 926.7308 925.2368 923.7300 922.2100 920.6765 919.1291 917.5677 #>   [6,] 927.7070 926.2199 924.7198 923.2064 921.6795 920.1386 918.5835 917.0138 #>   [7,] 927.2051 925.7122 924.2060 922.6862 921.1525 919.6044 918.0416 916.4637 #>   [8,] 926.7064 925.2079 923.6957 922.1695 920.6290 919.0738 917.5034 915.9175 #>   [9,] 926.2111 924.7069 923.1888 921.6564 920.1093 918.5470 916.9691 915.3752 #>  [10,] 925.7191 924.2094 922.6856 921.1470 919.5933 918.0240 916.4388 914.8370 #>  [11,] 925.2306 923.7155 922.1860 920.6413 919.0812 917.5051 915.9126 914.3031 #>  [12,] 924.7456 923.2253 921.6901 920.1395 918.5731 916.9903 915.3906 913.7735 #>  [13,] 924.2642 922.7388 921.1981 919.6417 918.0691 916.4798 914.8731 913.2485 #>  [14,] 923.7865 922.2560 920.7100 919.1480 917.5693 915.9735 914.3599 912.7280 #>  [15,] 923.3126 921.7772 920.2260 918.6584 917.0738 915.4717 913.8514 912.2123 #>  [16,] 922.8424 921.3023 919.7460 918.1730 916.5827 914.9744 913.3476 911.7015 #>  [17,] 922.3762 920.8314 919.2702 917.6920 916.0961 914.4818 912.8486 911.1957 #>  [18,] 921.9140 920.3647 918.7987 917.2153 915.6140 913.9940 912.3546 910.6950 #>  [19,] 921.4557 919.9021 918.3315 916.7432 915.1366 913.5110 911.8655 910.1995 #>  [20,] 921.0016 919.4438 917.8687 916.2756 914.6640 913.0329 911.3816 909.7094 #>  [21,] 920.5516 918.9897 917.4104 915.8127 914.1962 912.5599 910.9030 909.2247 #>  [22,] 920.1058 918.5401 916.9566 915.3546 913.7333 912.0920 910.4297 908.7457 #>  [23,] 919.6643 918.0949 916.5075 914.9013 913.2755 911.6293 909.9619 908.2723 #>  [24,] 919.2272 917.6542 916.0630 914.4528 912.8227 911.1720 909.4996 907.8047 #>  [25,] 918.7944 917.2181 915.6233 914.0093 912.3752 910.7200 909.0430 907.3431 #>  [26,] 918.3661 916.7866 915.1885 913.5708 911.9328 910.2736 908.5921 906.8874 #>  [27,] 917.9422 916.3598 914.7585 913.1374 911.4958 909.8327 908.1470 906.4378 #>  [28,] 917.5229 915.9377 914.3334 912.7092 911.0642 909.3974 907.7078 905.9944 #>  [29,] 917.1081 915.5204 913.9133 912.2861 910.6380 908.9678 907.2745 905.5572 #>  [30,] 916.6980 915.1078 913.4983 911.8684 910.2172 908.5439 906.8473 905.1263 #>  [31,] 916.2925 914.7002 913.0883 911.4559 909.8021 908.1259 906.4262 904.7019 #>  [32,] 915.8917 914.2974 912.6834 911.0487 909.3925 907.7137 906.0113 904.2839 #>  [33,] 915.4957 913.8996 912.2837 910.6470 908.9886 907.3075 905.6025 903.8725 #>  [34,] 915.1043 913.5067 911.8891 910.2507 908.5904 906.9072 905.2000 903.4676 #>  [35,] 914.7178 913.1188 911.4998 909.8598 908.1979 906.5130 904.8039 903.0694 #>  [36,] 914.3360 912.7359 911.1157 909.4744 907.8111 906.1247 904.4140 902.6778 #>  [37,] 913.9591 912.3581 910.7369 909.0946 907.4302 905.7426 904.0306 902.2930 #>  [38,] 913.5869 911.9852 910.3633 908.7203 907.0550 905.3665 903.6535 901.9149 #>  [39,] 913.2196 911.6175 909.9951 908.3515 906.6856 904.9965 903.2829 901.5435 #>  [40,] 912.8572 911.2548 909.6321 907.9882 906.3221 904.6326 902.9187 901.1789 #>  [41,] 912.4996 910.8971 909.2745 907.6305 905.9644 904.2749 902.5609 900.8211 #>  [42,] 912.1468 910.5446 908.9221 907.2784 905.6125 903.9233 902.2096 900.4701 #>  [43,] 911.7989 910.1971 908.5751 906.9319 905.2665 903.5778 901.8647 900.1259 #>  [44,] 911.4558 909.8546 908.2333 906.5908 904.9262 903.2384 901.5262 899.7884 #>  [45,] 911.1175 909.5172 907.8968 906.2553 904.5918 902.9051 901.1941 899.4576 #>  [46,] 910.7841 909.1849 907.5656 905.9254 904.2631 902.5779 900.8684 899.1336 #>  [47,] 910.4554 908.8575 907.2396 905.6009 903.9402 902.2567 900.5491 898.8162 #>  [48,] 910.1316 908.5352 906.9189 905.2819 903.6231 901.9415 900.2361 898.5055 #>  [49,] 909.8125 908.2178 906.6033 904.9683 903.3116 901.6323 899.9293 898.2014 #>  [50,] 909.4981 907.9053 906.2929 904.6601 903.0058 901.3291 899.6288 897.9038 #>  [51,] 909.1884 907.5977 905.9877 904.3572 902.7056 901.0317 899.3344 897.6127 #>  [52,] 908.8833 907.2950 905.6875 904.0597 902.4109 900.7401 899.0462 897.3281 #>  [53,] 908.5829 906.9972 905.3923 903.7675 902.1218 900.4543 898.7640 897.0497 #>  [54,] 908.2870 906.7041 905.1021 903.4804 901.8381 900.1742 898.4877 896.7777 #>  [55,] 907.9958 906.4157 904.8169 903.1985 901.5598 899.8998 898.2174 896.5118 #>  [56,] 907.7089 906.1320 904.5365 902.9218 901.2868 899.6309 897.9529 896.2520 #>  [57,] 907.4266 905.8530 904.2610 902.6500 901.0191 899.3675 897.6942 895.9982 #>  [58,] 907.1486 905.5785 903.9903 902.3832 900.7566 899.1095 897.4411 895.7504 #>  [59,] 906.8750 905.3085 903.7242 902.1213 900.4992 898.8569 897.1936 895.5084 #>  [60,] 906.6057 905.0430 903.4628 901.8643 900.2468 898.6094 896.9515 895.2720 #>  [61,] 906.3406 904.7819 903.2060 901.6120 899.9993 898.3672 896.7148 895.0413 #>  [62,] 906.0796 904.5251 902.9536 901.3644 899.7568 898.1300 896.4834 894.8161 #>  [63,] 905.8228 904.2726 902.7057 901.1214 899.5190 897.8978 896.2572 894.5963 #>  [64,] 905.5700 904.0243 902.4621 900.8828 899.2858 897.6704 896.0360 894.3817 #>  [65,] 905.3212 903.7801 902.2228 900.6488 899.0573 897.4479 895.8197 894.1722 #>  [66,] 905.0763 903.5399 901.9877 900.4190 898.8333 897.2300 895.6084 893.9678 #>  [67,] 904.8352 903.3038 901.7567 900.1935 898.6137 897.0166 895.4017 893.7683 #>  [68,] 904.5979 903.0715 901.5297 899.9722 898.3984 896.8077 895.1996 893.5736 #>  [69,] 904.3643 902.8430 901.3067 899.7550 898.1873 896.6032 895.0021 893.3835 #>  [70,] 904.1344 902.6183 901.0876 899.5417 897.9803 896.4029 894.8089 893.1979 #>  [71,] 903.9079 902.3972 900.8722 899.3324 897.7774 896.2068 894.6200 893.0167 #>  [72,] 903.6850 902.1797 900.6605 899.1268 897.5783 896.0146 894.4353 892.8398 #>  [73,] 903.4654 901.9657 900.4524 898.9249 897.3831 895.8264 894.2545 892.6670 #>  [74,] 903.2492 901.7551 900.2478 898.7267 897.1916 895.6420 894.0777 892.4982 #>  [75,] 903.0362 901.5479 900.0466 898.5319 897.0036 895.4613 893.9047 892.3333 #>  [76,] 902.8264 901.3439 899.8487 898.3406 896.8192 895.2842 893.7353 892.1722 #>  [77,] 902.6197 901.1431 899.6542 898.1526 896.6382 895.1105 893.5695 892.0147 #>  [78,] 902.4160 900.9453 899.4627 897.9678 896.4604 894.9403 893.4071 891.8606 #>  [79,] 902.2152 900.7506 899.2743 897.7862 896.2859 894.7732 893.2480 891.7100 #>  [80,] 902.0173 900.5588 899.0889 897.6076 896.1144 894.6093 893.0921 891.5625 #>  [81,] 901.8221 900.3698 898.9064 897.4319 895.9460 894.4485 892.9393 891.4182 #>  [82,] 901.6297 900.1836 898.7267 897.2591 895.7804 894.2906 892.7894 891.2769 #>  [83,] 901.4399 900.0000 898.5497 897.0890 895.6176 894.1355 892.6424 891.1385 #>  [84,] 901.2526 899.8190 898.3754 896.9216 895.4575 893.9831 892.4982 891.0028 #>  [85,] 901.0678 899.6405 898.2035 896.7567 895.3000 893.8333 892.3566 890.8698 #>  [86,] 900.8854 899.4645 898.0341 896.5943 895.1450 893.6861 892.2175 890.7392 #>  [87,] 900.7054 899.2908 897.8671 896.4344 894.9924 893.5412 892.0808 890.6111 #>  [88,] 900.5275 899.1193 897.7024 896.2767 894.8421 893.3987 891.9464 890.4853 #>  [89,] 900.3519 898.9501 897.5399 896.1212 894.6940 893.2583 891.8142 890.3617 #>  [90,] 900.1783 898.7829 897.3795 895.9678 894.5480 893.1201 891.6842 890.2402 #>  [91,] 900.0068 898.6178 897.2211 895.8165 894.4041 892.9840 891.5561 890.1206 #>  [92,] 899.8372 898.4547 897.0647 895.6671 894.2621 892.8497 891.4299 890.0029 #>  [93,] 899.6695 898.2934 896.9101 895.5196 894.1220 892.7173 891.3056 889.8870 #>  [94,] 899.5036 898.1339 896.7574 895.3739 893.9836 892.5866 891.1829 889.7727 #>  [95,] 899.3394 897.9762 896.6064 895.2299 893.8470 892.4576 891.0619 889.6601 #>  [96,] 899.1769 897.8202 896.4570 895.0876 893.7119 892.3301 890.9424 889.5489 #>  [97,] 899.0160 897.6657 896.3092 894.9468 893.5784 892.2042 890.8244 889.4391 #>  [98,] 898.8567 897.5128 896.1630 894.8074 893.4463 892.0796 890.7077 889.3306 #>  [99,] 898.6989 897.3613 896.0181 894.6695 893.3156 891.9564 890.5923 889.2234 #> [100,] 898.5424 897.2112 895.8747 894.5329 893.1861 891.8345 890.4781 889.1172 #>           [,33]    [,34]    [,35]    [,36]    [,37]    [,38]    [,39]    [,40] #>   [1,] 918.2775 916.7247 915.1594 913.5814 911.9907 910.3874 908.7715 907.1432 #>   [2,] 917.7010 916.1388 914.5634 912.9748 911.3728 909.7574 908.1288 906.4869 #>   [3,] 917.1279 915.5562 913.9707 912.3714 910.7581 909.1308 907.4894 905.8340 #>   [4,] 916.5581 914.9770 913.3816 911.7716 910.1470 908.5077 906.8535 905.1845 #>   [5,] 915.9918 914.4014 912.7960 911.1755 909.5396 907.8883 906.2213 904.5387 #>   [6,] 915.4293 913.8295 912.2142 910.5832 908.9361 907.2728 905.5931 903.8968 #>   [7,] 914.8705 913.2615 911.6364 909.9949 908.3366 906.6614 904.9689 903.2591 #>   [8,] 914.3156 912.6975 911.0626 909.4107 907.7414 906.0543 904.3492 902.6257 #>   [9,] 913.7649 912.1377 910.4932 908.8310 907.1506 905.4518 903.7340 901.9970 #>  [10,] 913.2183 911.5822 909.9281 908.2557 906.5645 904.8539 903.1236 901.3732 #>  [11,] 912.6761 911.0312 909.3677 907.6852 905.9831 904.2610 902.5183 900.7545 #>  [12,] 912.1384 910.4848 908.8120 907.1196 905.4068 903.6732 901.9182 900.1412 #>  [13,] 911.6054 909.9432 908.2613 906.5590 904.8357 903.0908 901.3236 899.5335 #>  [14,] 911.0771 909.4065 907.7156 906.0037 904.2701 902.5140 900.7348 898.9317 #>  [15,] 910.5537 908.8749 907.1752 905.4538 903.7100 901.9430 900.1519 898.3360 #>  [16,] 910.0354 908.3485 906.6402 904.9095 903.1557 901.3779 899.5752 897.7468 #>  [17,] 909.5222 907.8275 906.1108 904.3710 902.6074 900.8191 899.0050 897.1642 #>  [18,] 909.0144 907.3121 905.5871 903.8385 902.0654 900.2667 898.4415 896.5886 #>  [19,] 908.5120 906.8023 905.0693 903.3121 901.5297 899.7209 897.8848 896.0201 #>  [20,] 908.0152 906.2983 904.5575 902.7920 901.0005 899.1820 897.3353 895.4591 #>  [21,] 907.5241 905.8002 904.0520 902.2784 900.4782 898.6502 896.7932 894.9058 #>  [22,] 907.0389 905.3083 903.5528 901.7714 899.9627 898.1256 896.2587 894.3605 #>  [23,] 906.5595 904.8225 903.0601 901.2712 899.4544 897.6085 895.7320 893.8233 #>  [24,] 906.0863 904.3431 902.5741 900.7779 898.9534 897.0990 895.2133 893.2946 #>  [25,] 905.6191 903.8701 902.0948 900.2918 898.4598 896.5974 894.7028 892.7745 #>  [26,] 905.1583 903.4037 901.6224 899.8129 897.9739 896.1037 894.2008 892.2634 #>  [27,] 904.7039 902.9440 901.1570 899.3414 897.4957 895.6183 893.7075 891.7613 #>  [28,] 904.2559 902.4912 900.6988 898.8774 897.0254 895.1412 893.2229 891.2686 #>  [29,] 903.8145 902.0452 900.2479 898.4211 896.5633 894.6726 892.7474 890.7854 #>  [30,] 903.3797 901.6062 899.8043 897.9725 896.1093 894.2127 892.2810 890.3120 #>  [31,] 902.9517 901.1742 899.3681 897.5318 895.6636 893.7616 891.8239 889.8484 #>  [32,] 902.5304 900.7495 898.9396 897.0991 895.2263 893.3194 891.3763 889.3948 #>  [33,] 902.1161 900.3320 898.5186 896.6744 894.7976 892.8863 890.9383 888.9515 #>  [34,] 901.7087 899.9218 898.1054 896.2579 894.3775 892.4622 890.5100 888.5185 #>  [35,] 901.3082 899.5189 897.6999 895.8496 893.9661 892.0475 890.0915 888.0959 #>  [36,] 900.9148 899.1235 897.3023 895.4496 893.5635 891.6420 889.6830 887.6839 #>  [37,] 900.5284 898.7355 896.9126 895.0579 893.1697 891.2460 889.2844 887.2826 #>  [38,] 900.1492 898.3550 896.5307 894.6747 892.7849 890.8594 888.8959 886.8920 #>  [39,] 899.7771 897.9821 896.1569 894.2998 892.4089 890.4822 888.5175 886.5121 #>  [40,] 899.4121 897.6166 895.7910 893.9334 892.0419 890.1146 888.1492 886.1431 #>  [41,] 899.0542 897.2587 895.4330 893.5754 891.6839 889.7566 887.7910 885.7849 #>  [42,] 898.7036 896.9084 895.0831 893.2259 891.3349 889.4080 887.4430 885.4375 #>  [43,] 898.3600 896.5656 894.7411 892.8848 890.9948 889.0690 887.1052 885.1009 #>  [44,] 898.0236 896.2304 894.4071 892.5522 890.6636 888.7394 886.7774 884.7752 #>  [45,] 897.6943 895.9026 894.0810 892.2279 890.3414 888.4194 886.4598 884.4601 #>  [46,] 897.3720 895.5823 893.7628 891.9120 890.0279 888.1087 886.1521 884.1557 #>  [47,] 897.0568 895.2694 893.4525 891.6044 889.7233 887.8074 885.8543 883.8619 #>  [48,] 896.7486 894.9639 893.1499 891.3050 889.4274 887.5153 885.5664 883.5786 #>  [49,] 896.4473 894.6657 892.8551 891.0138 889.1402 887.2324 885.2882 883.3056 #>  [50,] 896.1529 894.3748 892.5679 890.7307 888.8615 886.9585 885.0197 883.0429 #>  [51,] 895.8654 894.0910 892.2882 890.4555 888.5913 886.6936 884.7606 882.7902 #>  [52,] 895.5845 893.8144 892.0161 890.1883 888.3294 886.4375 884.5109 882.5475 #>  [53,] 895.3104 893.5447 891.7513 889.9289 888.0757 886.1901 884.2704 882.3145 #>  [54,] 895.0428 893.2820 891.4939 889.6771 887.8301 885.9513 884.0389 882.0911 #>  [55,] 894.7817 893.0261 891.2436 889.4328 887.5924 885.7208 883.8163 881.8770 #>  [56,] 894.5270 892.7769 891.0003 889.1960 887.3626 885.4986 883.6023 881.6721 #>  [57,] 894.2786 892.5343 890.7640 888.9664 887.1404 885.2844 883.3968 881.4762 #>  [58,] 894.0364 892.2982 890.5344 888.7440 886.9257 885.0780 883.1996 881.2889 #>  [59,] 893.8003 892.0684 890.3116 888.5286 886.7183 884.8794 883.0105 881.1102 #>  [60,] 893.5702 891.8449 890.0952 888.3200 886.5181 884.6883 882.8292 880.9397 #>  [61,] 893.3459 891.6275 889.8852 888.1181 886.3248 884.5044 882.6556 880.7772 #>  [62,] 893.1273 891.4161 889.6815 887.9226 886.1384 884.3277 882.4894 880.6224 #>  [63,] 892.9143 891.2105 889.4839 887.7335 885.9585 884.1578 882.3304 880.4751 #>  [64,] 892.7068 891.0106 889.2921 887.5506 885.7851 883.9947 882.1783 880.3351 #>  [65,] 892.5047 890.8162 889.1062 887.3737 885.6179 883.8380 882.0330 880.2021 #>  [66,] 892.3077 890.6273 888.9258 887.2026 885.4567 883.6875 881.8941 880.0757 #>  [67,] 892.1158 890.4436 888.7509 887.0371 885.3014 883.5431 881.7615 879.9559 #>  [68,] 891.9289 890.2650 888.5813 886.8771 885.1517 883.4046 881.6350 879.8422 #>  [69,] 891.7468 890.0914 888.4168 886.7224 885.0075 883.2716 881.5142 879.7345 #>  [70,] 891.5693 889.9226 888.2573 886.5727 884.8685 883.1441 881.3989 879.6325 #>  [71,] 891.3963 889.7584 888.1025 886.4281 884.7346 883.0217 881.2890 879.5359 #>  [72,] 891.2278 889.5988 887.9524 886.2881 884.6056 882.9044 881.1841 879.4444 #>  [73,] 891.0635 889.4435 887.8067 886.1528 884.4812 882.7918 881.0841 879.3579 #>  [74,] 890.9033 889.2924 887.6654 886.0218 884.3613 882.6837 880.9887 879.2761 #>  [75,] 890.7470 889.1454 887.5281 885.8950 884.2457 882.5800 880.8977 879.1987 #>  [76,] 890.5946 889.0023 887.3949 885.7723 884.1342 882.4804 880.8109 879.1255 #>  [77,] 890.4459 888.8629 887.2655 885.6534 884.0266 882.3848 880.7281 879.0563 #>  [78,] 890.3007 888.7271 887.1397 885.5383 883.9227 882.2930 880.6490 878.9909 #>  [79,] 890.1590 888.5948 887.0174 885.4266 883.8224 882.2047 880.5735 878.9289 #>  [80,] 890.0205 888.4659 886.8985 885.3184 883.7255 882.1197 880.5013 878.8702 #>  [81,] 889.8852 888.3401 886.7828 885.2133 883.6317 882.0380 880.4322 878.8147 #>  [82,] 889.7529 888.2173 886.6701 885.1113 883.5410 881.9592 880.3661 878.7620 #>  [83,] 889.6235 888.0974 886.5603 885.0122 883.4531 881.8833 880.3028 878.7120 #>  [84,] 889.4969 887.9803 886.4533 884.9158 883.3680 881.8100 880.2421 878.6645 #>  [85,] 889.3729 887.8659 886.3489 884.8220 883.2854 881.7392 880.1837 878.6193 #>  [86,] 889.2514 887.7539 886.2470 884.7307 883.2052 881.6707 880.1276 878.5763 #>  [87,] 889.1323 887.6443 886.1474 884.6416 883.1272 881.6044 880.0736 878.5351 #>  [88,] 889.0155 887.5370 886.0500 884.5547 883.0513 881.5401 880.0214 878.4958 #>  [89,] 888.9009 887.4318 885.9547 884.4698 882.9773 881.4776 879.9711 878.4581 #>  [90,] 888.7883 887.3286 885.8614 884.3868 882.9052 881.4169 879.9223 878.4218 #>  [91,] 888.6776 887.2273 885.7699 884.3056 882.8348 881.3577 879.8749 878.3869 #>  [92,] 888.5688 887.1278 885.6801 884.2260 882.7659 881.3000 879.8289 878.3531 #>  [93,] 888.4617 887.0300 885.5920 884.1480 882.6984 881.2436 879.7841 878.3204 #>  [94,] 888.3563 886.9337 885.5053 884.0713 882.6322 881.1884 879.7403 878.2885 #>  [95,] 888.2523 886.8389 885.4200 883.9960 882.5673 881.1343 879.6975 878.2574 #>  [96,] 888.1498 886.7454 885.3360 883.9218 882.5034 881.0811 879.6554 878.2270 #>  [97,] 888.0486 886.6532 885.2531 883.8487 882.4404 881.0287 879.6141 878.1971 #>  [98,] 887.9487 886.5622 885.1713 883.7766 882.3784 880.9771 879.5733 878.1676 #>  [99,] 887.8499 886.4722 885.0905 883.7054 882.3170 880.9261 879.5330 878.1384 #> [100,] 887.7522 886.3832 885.0106 883.6349 882.2564 880.8756 879.4931 878.1095 #>           [,41]    [,42]    [,43]    [,44]    [,45]    [,46]    [,47]    [,48] #>   [1,] 905.5027 903.8503 902.1865 900.5119 898.8271 897.1330 895.4309 893.7218 #>   [2,] 904.8321 903.1644 901.4844 899.7926 898.0895 896.3761 894.6533 892.9225 #>   [3,] 904.1647 902.4817 900.7853 899.0761 897.3545 895.6215 893.8778 892.1248 #>   [4,] 903.5007 901.8022 900.0895 898.3627 896.6225 894.8695 893.1046 891.3291 #>   [5,] 902.8403 901.1264 899.3971 897.6527 895.8936 894.1205 892.3342 890.5357 #>   [6,] 902.1839 900.4544 898.7085 896.9463 895.1682 893.3748 891.5667 889.7450 #>   [7,] 901.5316 899.7866 898.0240 896.2439 894.4467 892.6327 890.8027 888.9575 #>   [8,] 900.8838 899.1231 897.3438 895.5458 893.7293 891.8947 890.0425 888.1734 #>   [9,] 900.2406 898.4644 896.6683 894.8523 893.0165 891.1611 889.2865 887.3933 #>  [10,] 899.6023 897.8106 895.9978 894.1638 892.3086 890.4323 888.5351 886.6177 #>  [11,] 898.9692 897.1620 895.3326 893.4806 891.6060 889.7087 887.7889 885.8469 #>  [12,] 898.3416 896.5190 894.6730 892.8031 890.9091 888.9908 887.0482 885.0815 #>  [13,] 897.7198 895.8819 894.0194 892.1316 890.2182 888.2789 886.3135 884.3220 #>  [14,] 897.1040 895.2510 893.3721 891.4665 889.5338 887.5736 885.5853 883.5690 #>  [15,] 896.4945 894.6266 892.7314 890.8082 888.8564 886.8752 884.8642 882.8230 #>  [16,] 895.8917 894.0090 892.0977 890.1571 888.1862 886.1843 884.1506 882.0846 #>  [17,] 895.2957 893.3985 891.4714 889.5135 887.5239 885.5014 883.4451 881.3544 #>  [18,] 894.7069 892.7954 890.8528 888.8780 886.8697 884.8268 882.7483 880.6330 #>  [19,] 894.1256 892.2001 890.2423 888.2507 886.2242 884.1612 882.0606 879.9210 #>  [20,] 893.5521 891.6129 889.6401 887.6322 885.5877 883.5050 881.3827 879.2190 #>  [21,] 892.9866 891.0341 889.0468 887.0229 884.9608 882.8588 880.7150 878.5277 #>  [22,] 892.4295 890.4640 888.4625 886.4231 884.3439 882.2230 880.0583 877.8478 #>  [23,] 891.8809 889.9030 887.8877 885.8333 883.7374 881.5981 879.4130 877.1798 #>  [24,] 891.3412 889.3512 887.3228 885.2537 883.1418 880.9847 878.7798 876.5245 #>  [25,] 890.8106 888.8091 886.7680 884.6849 882.5575 880.3832 878.1592 875.8825 #>  [26,] 890.2894 888.2769 886.2237 884.1272 881.9849 879.7941 877.5517 875.2544 #>  [27,] 889.7779 887.7549 885.6901 883.5809 881.4245 879.2179 876.9579 874.6409 #>  [28,] 889.2762 887.2434 885.1677 883.0464 880.8766 878.6551 876.3784 874.0426 #>  [29,] 888.7846 886.7426 884.6566 882.5240 880.3416 878.1060 875.8136 873.4601 #>  [30,] 888.3033 886.2527 884.1573 882.0141 879.8199 877.5712 875.2640 872.8939 #>  [31,] 887.8326 885.7740 883.6698 881.5169 879.3119 877.0510 874.7301 872.3446 #>  [32,] 887.3725 885.3067 883.1945 881.0327 878.8178 876.5458 874.2124 871.8128 #>  [33,] 886.9233 884.8510 882.7316 880.5618 878.3379 876.0559 873.7112 871.2988 #>  [34,] 886.4851 884.4071 882.2813 880.1044 877.8726 875.5817 873.2270 870.8032 #>  [35,] 886.0581 883.9751 881.8438 879.6608 877.4221 875.1234 872.7600 870.3263 #>  [36,] 885.6423 883.5551 881.4192 879.2310 876.9865 874.6813 872.3105 869.8685 #>  [37,] 885.2379 883.1473 881.0077 878.8152 876.5661 874.2556 871.8789 869.4300 #>  [38,] 884.8449 882.7518 880.6093 878.4137 876.1610 873.8465 871.4652 869.0112 #>  [39,] 884.4635 882.3686 880.2242 878.0264 875.7713 873.4541 871.0697 868.6122 #>  [40,] 884.0937 881.9979 879.8524 877.6535 875.3971 873.0784 870.6924 868.2331 #>  [41,] 883.7354 881.6395 879.4939 877.2949 875.0384 872.7196 870.3335 867.8739 #>  [42,] 883.3887 881.2936 879.1488 876.9507 874.6952 872.3777 869.9928 867.5348 #>  [43,] 883.0535 880.9600 878.8170 876.6209 874.3676 872.0525 869.6704 867.2156 #>  [44,] 882.7299 880.6388 878.4985 876.3054 874.0554 871.7440 869.3662 866.9163 #>  [45,] 882.4178 880.3299 878.1931 876.0040 873.7585 871.4522 869.0801 866.6365 #>  [46,] 882.1170 880.0332 877.9009 875.7167 873.4768 871.1768 868.8117 866.3762 #>  [47,] 881.8276 879.7485 877.6216 875.4434 873.2101 870.9176 868.5610 866.1351 #>  [48,] 881.5493 879.4758 877.3551 875.1838 872.9583 870.6744 868.3276 865.9127 #>  [49,] 881.2821 879.2149 877.1012 874.9378 872.7210 870.4469 868.1111 865.7088 #>  [50,] 881.0258 878.9657 876.8598 874.7051 872.4980 870.2348 867.9113 865.5229 #>  [51,] 880.7802 878.7279 876.6306 874.4854 872.2890 870.0378 867.7278 865.3545 #>  [52,] 880.5451 878.5013 876.4134 874.2786 872.0938 869.8555 867.5600 865.2031 #>  [53,] 880.3204 878.2857 876.2079 874.0843 871.9119 869.6875 867.4075 865.0681 #>  [54,] 880.1058 878.0808 876.0138 873.9021 871.7430 869.5333 867.2699 864.9491 #>  [55,] 879.9012 877.8865 875.8309 873.7318 871.5867 869.3926 867.1466 864.8454 #>  [56,] 879.7062 877.7025 875.6588 873.5730 871.4426 869.2649 867.0372 864.7563 #>  [57,] 879.5206 877.5284 875.4973 873.4254 871.3104 869.1497 866.9410 864.6814 #>  [58,] 879.3443 877.3639 875.3460 873.2886 871.1895 869.0466 866.8575 864.6198 #>  [59,] 879.1769 877.2089 875.2046 873.1621 871.0796 868.9549 866.7861 864.5710 #>  [60,] 879.0181 877.0630 875.0727 873.0457 870.9802 868.8744 866.7264 864.5344 #>  [61,] 878.8677 876.9258 874.9500 872.9389 870.8909 868.8043 866.6776 864.5092 #>  [62,] 878.7254 876.7971 874.8362 872.8414 870.8112 868.7443 866.6393 864.4948 #>  [63,] 878.5909 876.6765 874.7309 872.7526 870.7407 868.6938 866.6108 864.4906 #>  [64,] 878.4639 876.5638 874.6336 872.6723 870.6789 868.6523 866.5916 864.4960 #>  [65,] 878.3442 876.4586 874.5442 872.6001 870.6254 868.6194 866.5812 864.5102 #>  [66,] 878.2315 876.3606 874.4622 872.5355 870.5798 868.5945 866.5789 864.5328 #>  [67,] 878.1254 876.2694 874.3872 872.4781 870.5416 868.5771 866.5844 864.5631 #>  [68,] 878.0257 876.1848 874.3190 872.4276 870.5104 868.5669 866.5969 864.6005 #>  [69,] 877.9321 876.1065 874.2571 872.3836 870.4857 868.5632 866.6161 864.6444 #>  [70,] 877.8443 876.0340 874.2013 872.3457 870.4672 868.5657 866.6414 864.6944 #>  [71,] 877.7621 875.9672 874.1511 872.3136 870.4545 868.5740 866.6723 864.7499 #>  [72,] 877.6851 875.9058 874.1064 872.2868 870.4471 868.5875 866.7084 864.8104 #>  [73,] 877.6131 875.8493 874.0666 872.2651 870.4447 868.6059 866.7493 864.8754 #>  [74,] 877.5458 875.7976 874.0316 872.2480 870.4469 868.6289 866.7944 864.9444 #>  [75,] 877.4829 875.7504 874.0011 872.2353 870.4534 868.6559 866.8435 865.0171 #>  [76,] 877.4243 875.7073 873.9746 872.2267 870.4638 868.6866 866.8960 865.0929 #>  [77,] 877.3696 875.6681 873.9520 872.2217 870.4777 868.7208 866.9516 865.1715 #>  [78,] 877.3186 875.6326 873.9330 872.2202 870.4950 868.7579 867.0101 865.2526 #>  [79,] 877.2711 875.6004 873.9172 872.2219 870.5151 868.7978 867.0709 865.3356 #>  [80,] 877.2269 875.5715 873.9044 872.2264 870.5379 868.8401 867.1338 865.4204 #>  [81,] 877.1856 875.5454 873.8945 872.2335 870.5631 868.8844 867.1985 865.5066 #>  [82,] 877.1471 875.5220 873.8870 872.2429 870.5904 868.9306 867.2646 865.5939 #>  [83,] 877.1113 875.5010 873.8818 872.2544 870.6196 868.9784 867.3320 865.6819 #>  [84,] 877.0778 875.4823 873.8787 872.2677 870.6503 869.0274 867.4004 865.7705 #>  [85,] 877.0464 875.4656 873.8774 872.2827 870.6824 869.0775 867.4694 865.8594 #>  [86,] 877.0171 875.4507 873.8778 872.2991 870.7157 869.1285 867.5389 865.9483 #>  [87,] 876.9896 875.4375 873.8796 872.3167 870.7498 869.1800 867.6086 866.0370 #>  [88,] 876.9637 875.4257 873.8827 872.3354 870.7847 869.2320 867.6784 866.1254 #>  [89,] 876.9393 875.4153 873.8868 872.3548 870.8202 869.2842 867.7480 866.2132 #>  [90,] 876.9162 875.4059 873.8918 872.3749 870.8560 869.3364 867.8173 866.3002 #>  [91,] 876.8942 875.3975 873.8976 872.3954 870.8920 869.3884 867.8861 866.3864 #>  [92,] 876.8732 875.3899 873.9039 872.4163 870.9280 869.4402 867.9542 866.4714 #>  [93,] 876.8531 875.3829 873.9107 872.4374 870.9639 869.4916 868.0215 866.5553 #>  [94,] 876.8337 875.3765 873.9178 872.4585 870.9996 869.5423 868.0879 866.6378 #>  [95,] 876.8149 875.3704 873.9250 872.4794 871.0348 869.5923 868.1532 866.7189 #>  [96,] 876.7965 875.3646 873.9322 872.5002 871.0696 869.6415 868.2173 866.7983 #>  [97,] 876.7785 875.3590 873.9393 872.5206 871.1037 869.6898 868.2802 866.8761 #>  [98,] 876.7607 875.3533 873.9463 872.5405 871.1370 869.7370 868.3416 866.9522 #>  [99,] 876.7430 875.3476 873.9529 872.5599 871.1695 869.7830 868.4015 867.0263 #> [100,] 876.7254 875.3417 873.9591 872.5785 871.2011 869.8278 868.4598 867.0985 #>           [,49]    [,50]    [,51]    [,52]    [,53]    [,54]    [,55]    [,56] #>   [1,] 892.0075 890.2898 888.5709 886.8534 885.1402 883.4347 881.7409 880.0632 #>   [2,] 891.1851 889.4430 887.6984 885.9539 884.2123 882.4773 880.7527 879.0432 #>   [3,] 890.3639 888.5969 886.8260 885.0536 883.2829 881.5173 879.7608 878.0181 #>   [4,] 889.5442 887.7518 885.9539 884.1530 882.3522 880.5550 878.7654 876.9883 #>   [5,] 888.7264 886.9080 885.0825 883.2524 881.4206 879.5908 877.7670 875.9540 #>   [6,] 887.9109 886.0661 884.2123 882.3522 880.4886 878.6251 876.7658 874.9157 #>   [7,] 887.0982 885.2263 883.3438 881.4529 879.5566 877.6583 875.7623 873.8736 #>   [8,] 886.2885 884.3892 882.4773 880.5550 878.6251 876.6910 874.7571 872.8282 #>   [9,] 885.4825 883.5553 881.6134 879.6590 877.6946 875.7238 873.7506 871.7801 #>  [10,] 884.6806 882.7251 880.7527 878.7654 876.7658 874.7571 872.7434 870.7299 #>  [11,] 883.8833 881.8992 879.8958 877.8750 875.8392 873.7917 871.7363 869.6781 #>  [12,] 883.0912 881.0780 879.0432 876.9883 874.9157 872.8282 870.7299 868.6255 #>  [13,] 882.3048 880.2623 878.1956 876.1061 873.9958 871.8676 869.7250 867.5729 #>  [14,] 881.5247 879.4527 877.3538 875.2291 873.0805 870.9105 868.7225 866.5212 #>  [15,] 880.7515 878.6498 876.5184 874.3581 872.1705 869.9579 867.7234 865.4714 #>  [16,] 879.9859 877.8544 875.6902 873.4940 871.2669 869.0109 866.7288 864.4246 #>  [17,] 879.2286 877.0671 874.8700 872.6375 870.3705 868.0704 865.7397 863.3820 #>  [18,] 878.4801 876.2888 874.0587 871.7898 869.4823 867.1375 864.7573 862.3449 #>  [19,] 877.7412 875.5202 873.2572 870.9517 868.6036 866.2136 863.7831 861.3147 #>  [20,] 877.0126 874.7621 872.4663 870.1242 867.7353 865.2998 862.8184 860.2931 #>  [21,] 876.2951 874.0153 871.6869 869.3084 866.8788 864.3975 861.8646 859.2815 #>  [22,] 875.5893 873.2808 870.9201 868.5054 866.0352 863.5080 860.9235 858.2820 #>  [23,] 874.8961 872.5592 870.1668 867.7164 865.2058 862.6330 859.9967 857.2963 #>  [24,] 874.2161 871.8515 869.4280 866.9424 864.3919 861.7739 859.0859 856.3265 #>  [25,] 873.5501 871.1586 868.7047 866.1846 863.5950 860.9322 858.1931 855.3747 #>  [26,] 872.8989 870.4813 867.9979 865.4443 862.8164 860.1097 857.3200 854.4433 #>  [27,] 872.2632 869.8205 867.3086 864.7225 862.0574 859.3080 856.4688 853.5345 #>  [28,] 871.6437 869.1770 866.6378 864.0205 861.3196 858.5286 855.6413 852.6508 #>  [29,] 871.0411 868.5517 865.9865 863.3395 860.6042 857.7734 854.8396 851.7945 #>  [30,] 870.4561 867.9453 865.3556 862.6805 859.9126 857.0440 854.0657 850.9682 #>  [31,] 869.8893 867.3586 864.7461 862.0446 859.2462 856.3419 853.3217 850.1744 #>  [32,] 869.3414 866.7924 864.1588 861.4330 858.6062 855.6688 852.6094 849.4154 #>  [33,] 868.8129 866.2472 863.5945 860.8465 857.9939 855.0261 851.9307 848.6936 #>  [34,] 868.3044 865.7238 863.0540 860.2862 857.4104 854.4152 851.2873 848.0112 #>  [35,] 867.8162 865.2227 862.5380 859.7528 856.8567 853.8375 850.6810 847.3704 #>  [36,] 867.3489 864.7444 862.0470 859.2471 856.3337 853.2940 850.1130 846.7729 #>  [37,] 866.9027 864.2894 861.5817 858.7697 855.8422 852.7858 849.5848 846.2204 #>  [38,] 866.4779 863.8579 861.1423 858.3212 855.3829 852.3137 849.0973 845.7143 #>  [39,] 866.0749 863.4502 860.7293 857.9019 854.9563 851.8783 848.6514 845.2556 #>  [40,] 865.6937 863.0665 860.3428 857.5122 854.5626 851.4801 848.2476 844.8450 #>  [41,] 865.3344 862.7070 859.9830 857.1521 854.2022 851.1192 847.8862 844.4830 #>  [42,] 864.9970 862.3716 859.6499 856.8217 853.8749 850.7957 847.5673 844.1696 #>  [43,] 864.6814 862.0602 859.3434 856.5208 853.5808 850.5095 847.2906 843.9045 #>  [44,] 864.3876 861.7727 859.0632 856.2493 853.3193 850.2601 847.0556 843.6870 #>  [45,] 864.1152 861.5089 858.8092 856.0067 853.0902 850.0469 846.8615 843.5160 #>  [46,] 863.8641 861.2683 858.5808 855.7925 852.8927 849.8691 846.7073 843.3904 #>  [47,] 863.6339 861.0506 858.3776 855.6061 852.7261 849.7258 846.5918 843.3085 #>  [48,] 863.4242 860.8554 858.1990 855.4469 852.5895 849.6159 846.5137 843.2684 #>  [49,] 863.2345 860.6819 858.0444 855.3139 852.4818 849.5381 846.4712 843.2683 #>  [50,] 863.0643 860.5298 857.9129 855.2064 852.4021 849.4910 846.4627 843.3058 #>  [51,] 862.9131 860.3982 857.8038 855.1232 852.3491 849.4731 846.4863 843.3786 #>  [52,] 862.7802 860.2864 857.7162 855.0634 852.3215 849.4830 846.5401 843.4843 #>  [53,] 862.6651 860.1938 857.6492 855.0259 852.3179 849.5189 846.6221 843.6205 #>  [54,] 862.5670 860.1195 857.6020 855.0096 852.3372 849.5793 846.7304 843.7847 #>  [55,] 862.4853 860.0626 857.5734 855.0132 852.3778 849.6625 846.8628 843.9745 #>  [56,] 862.4192 860.0225 857.5625 855.0357 852.4383 849.7667 847.0174 844.1873 #>  [57,] 862.3680 859.9981 857.5683 855.0758 852.5175 849.8904 847.1922 844.4209 #>  [58,] 862.3310 859.9886 857.5899 855.1324 852.6138 850.0319 847.3853 844.6730 #>  [59,] 862.3074 859.9932 857.6261 855.2043 852.7259 850.1897 847.5948 844.9415 #>  [60,] 862.2965 860.0110 857.6761 855.2903 852.8525 850.3621 847.8189 845.2242 #>  [61,] 862.2975 860.0411 857.7388 855.3894 852.9924 850.5477 848.0560 845.5192 #>  [62,] 862.3097 860.0828 857.8132 855.5003 853.1441 850.7450 848.3044 845.8247 #>  [63,] 862.3323 860.1351 857.8984 855.6222 853.3066 850.9528 848.5626 846.1391 #>  [64,] 862.3647 860.1973 857.9936 855.7538 853.4787 851.1697 848.8292 846.4607 #>  [65,] 862.4061 860.2686 858.0978 855.8943 853.6593 851.3945 849.1028 846.7880 #>  [66,] 862.4559 860.3482 858.2102 856.0428 853.8473 851.6261 849.3822 847.1199 #>  [67,] 862.5133 860.4354 858.3300 856.1982 854.0419 851.8634 849.6662 847.4549 #>  [68,] 862.5778 860.5295 858.4563 856.3598 854.2419 852.1054 849.9538 847.7920 #>  [69,] 862.6488 860.6298 858.5886 856.5268 854.4467 852.3512 850.2441 848.1303 #>  [70,] 862.7255 860.7356 858.7260 856.6984 854.6553 852.5999 850.5360 848.4687 #>  [71,] 862.8076 860.8464 858.8679 856.8739 854.8671 852.8507 850.8288 848.8064 #>  [72,] 862.8944 860.9616 859.0136 857.0526 855.0813 853.1029 851.1218 849.1428 #>  [73,] 862.9854 861.0805 859.1626 857.2339 855.2972 853.3559 851.4142 849.4771 #>  [74,] 863.0800 861.2027 859.3144 857.4173 855.5143 853.6090 851.7055 849.8088 #>  [75,] 863.1780 861.3277 859.4683 857.6021 855.7320 853.8616 851.9951 850.1374 #>  [76,] 863.2787 861.4551 859.6240 857.7879 855.9498 854.1133 852.2825 850.4623 #>  [77,] 863.3818 861.5842 859.7809 857.9742 856.1673 854.3636 852.5673 850.7831 #>  [78,] 863.4869 861.7149 859.9386 858.1606 856.3839 854.6121 852.8491 851.0996 #>  [79,] 863.5936 861.8466 860.0968 858.3467 856.5994 854.8583 853.1275 851.4114 #>  [80,] 863.7015 861.9790 860.2550 858.5321 856.8133 855.1020 853.4022 851.7182 #>  [81,] 863.8104 862.1118 860.4130 858.7165 857.0254 855.3429 853.6730 852.0198 #>  [82,] 863.9199 862.2447 860.5704 858.8996 857.2353 855.5807 853.9395 852.3161 #>  [83,] 864.0297 862.3773 860.7269 859.0811 857.4427 855.8151 854.2017 852.6067 #>  [84,] 864.1396 862.5094 860.8823 859.2608 857.6475 856.0459 854.4593 852.8917 #>  [85,] 864.2492 862.6408 861.0364 859.4383 857.8495 856.2729 854.7121 853.1709 #>  [86,] 864.3584 862.7712 861.1888 859.6136 858.0483 856.4961 854.9601 853.4441 #>  [87,] 864.4670 862.9004 861.3394 859.7864 858.2440 856.7152 855.2031 853.7114 #>  [88,] 864.5747 863.0282 861.4881 859.9565 858.4362 856.9300 855.4411 853.9727 #>  [89,] 864.6814 863.1545 861.6345 860.1238 858.6249 857.1406 855.6739 854.2279 #>  [90,] 864.7869 863.2790 861.7787 860.2882 858.8100 857.3468 855.9014 854.4771 #>  [91,] 864.8910 863.4017 861.9205 860.4496 858.9914 857.5485 856.1238 854.7202 #>  [92,] 864.9935 863.5223 862.0596 860.6077 859.1689 857.7457 856.3408 854.9572 #>  [93,] 865.0945 863.6407 862.1961 860.7626 859.3425 857.9383 856.5526 855.1881 #>  [94,] 865.1936 863.7570 862.3298 860.9141 859.5122 858.1263 856.7590 855.4130 #>  [95,] 865.2908 863.8708 862.4606 861.0622 859.6778 858.3097 856.9602 855.6319 #>  [96,] 865.3861 863.9822 862.5885 861.2069 859.8394 858.4884 857.1560 855.8448 #>  [97,] 865.4792 864.0910 862.7133 861.3479 859.9969 858.6624 857.3466 856.0518 #>  [98,] 865.5702 864.1973 862.8351 861.4854 860.1503 858.8317 857.5319 856.2530 #>  [99,] 865.6589 864.3008 862.9537 861.6193 860.2996 858.9964 857.7119 856.4483 #> [100,] 865.7453 864.4016 863.0691 861.7495 860.4446 859.1564 857.8867 856.6378 #>           [,57]    [,58]    [,59]    [,60]    [,61]    [,62]    [,63]    [,64] #>   [1,] 878.4066 876.7764 875.1786 873.6199 872.1071 870.6473 869.2481 867.9168 #>   [2,] 877.3538 875.6902 874.0587 872.4663 870.9201 869.4280 867.9979 866.6378 #>   [3,] 876.2946 874.5960 872.9291 871.3010 869.7196 868.1931 866.7301 865.3393 #>   [4,] 875.2291 873.4940 871.7898 870.1242 868.5054 866.9424 865.4443 864.0205 #>   [5,] 874.1577 872.3842 870.6408 868.9356 867.2773 865.6755 864.1399 862.6809 #>   [6,] 873.0805 871.2669 869.4823 867.7353 866.0352 864.3919 862.8164 861.3196 #>   [7,] 871.9980 870.1423 868.3145 866.5234 864.7788 863.0915 861.4732 859.9357 #>   [8,] 870.9105 869.0109 867.1375 865.2998 863.5080 861.7739 860.1097 858.5286 #>   [9,] 869.8185 867.8729 865.9517 864.0647 862.2230 860.4388 858.7255 857.0974 #>  [10,] 868.7225 866.7288 864.7573 862.8184 860.9235 859.0859 857.3200 855.6413 #>  [11,] 867.6232 865.5792 863.5549 861.5610 859.6098 857.7152 855.8928 854.1593 #>  [12,] 866.5212 864.4246 862.3449 860.2931 858.2820 856.3265 854.4433 852.6508 #>  [13,] 865.4173 863.2659 861.1280 859.0150 856.9403 854.9197 852.9712 851.1147 #>  [14,] 864.3125 862.1039 859.9050 857.7273 855.5851 853.4949 851.4761 849.5503 #>  [15,] 863.2076 860.9395 858.6766 856.4309 854.2170 852.0524 849.9578 847.9568 #>  [16,] 862.1039 859.7739 857.4441 855.1266 852.8366 850.5925 848.4163 846.3335 #>  [17,] 861.0026 858.6083 856.2086 853.8156 851.4449 849.1156 846.8514 844.6797 #>  [18,] 859.9050 857.4441 854.9715 852.4991 850.0428 847.6227 845.2635 842.9951 #>  [19,] 858.8127 856.2830 853.7343 851.1787 848.6319 846.1146 843.6530 841.2793 #>  [20,] 857.7273 855.1266 852.4991 849.8562 847.2137 844.5928 842.0208 839.5321 #>  [21,] 856.6508 853.9771 851.2678 848.5337 845.7903 843.0589 840.3679 837.7539 #>  [22,] 855.5851 852.8366 850.0428 847.2137 844.3641 841.5151 838.6960 835.9453 #>  [23,] 854.5324 851.7075 848.8268 845.8990 842.9379 839.9641 837.0072 834.1076 #>  [24,] 853.4949 850.5925 847.6227 844.5928 841.5151 838.4093 835.3044 832.2425 #>  [25,] 852.4753 849.4944 846.4337 843.2987 840.0996 836.8544 833.5914 830.3529 #>  [26,] 851.4761 848.4163 845.2635 842.0208 838.6960 835.3044 831.8726 828.4426 #>  [27,] 850.5001 847.3615 844.1159 840.7636 837.3092 833.7649 830.1540 826.5167 #>  [28,] 849.5503 846.3335 842.9951 839.5321 835.9453 832.2425 828.4426 824.5823 #>  [29,] 848.6295 845.3359 841.9056 838.3317 834.6107 830.7448 826.7469 822.6480 #>  [30,] 847.7409 844.3726 840.8520 837.1683 833.3125 829.2805 825.0773 820.7251 #>  [31,] 846.8875 843.4474 839.8393 836.0480 832.0587 827.8595 823.4457 818.8276 #>  [32,] 846.0724 842.5641 838.8724 834.9772 830.8575 826.4925 821.8658 816.9725 #>  [33,] 845.2985 841.7267 837.9563 833.9626 829.7176 825.1913 820.3533 815.1799 #>  [34,] 844.5688 840.9388 837.0959 833.0107 828.6482 823.9680 818.9251 813.4733 #>  [35,] 843.8859 840.2039 836.2961 832.1280 827.6580 822.8354 817.5994 811.8789 #>  [36,] 843.2522 839.5254 835.5611 831.3205 826.7556 821.8059 816.3946 810.4247 #>  [37,] 842.6700 838.9061 834.8949 830.5938 825.9491 820.8912 815.3288 809.1396 #>  [38,] 842.1409 838.3484 834.3008 829.9526 825.2453 820.1019 814.4185 808.0509 #>  [39,] 841.6665 837.8543 833.7816 829.4007 824.6499 819.4466 813.6778 807.1824 #>  [40,] 841.2476 837.4250 833.3390 828.9408 824.1668 818.9315 813.1167 806.5521 #>  [41,] 840.8849 837.0613 832.9741 828.5743 823.7982 818.5600 812.7410 806.1700 #>  [42,] 840.5783 836.7633 832.6869 828.3014 823.5442 818.3323 812.5510 806.0369 #>  [43,] 840.3274 836.5303 832.4767 828.1208 823.4032 818.2457 812.5422 806.1447 #>  [44,] 840.1314 836.3611 832.3417 828.0302 823.3715 818.2946 812.7053 806.4768 #>  [45,] 839.9889 836.2540 832.2795 828.0259 823.4437 818.4707 813.0270 807.0105 #>  [46,] 839.8982 836.2067 832.2868 828.1033 823.6133 818.7639 813.4912 807.7189 #>  [47,] 839.8572 836.2162 832.3598 828.2572 823.8723 819.1626 814.0800 808.5734 #>  [48,] 839.8635 836.2795 832.4941 828.4815 824.2124 819.6545 814.7749 809.5455 #>  [49,] 839.9145 836.3931 832.6852 828.7699 824.6246 820.2269 815.5577 810.6086 #>  [50,] 840.0074 836.5533 832.9281 829.1157 825.1000 820.8675 816.4111 811.7387 #>  [51,] 840.1391 836.7562 833.2178 829.5124 825.6298 821.5643 817.3193 812.9149 #>  [52,] 840.3067 836.9980 833.5494 829.9534 826.2055 822.3065 818.2681 814.1196 #>  [53,] 840.5070 837.2747 833.9179 830.4327 826.8191 823.0840 819.2452 815.3384 #>  [54,] 840.7370 837.5827 834.3185 830.9441 827.4635 823.8879 820.2399 816.5594 #>  [55,] 840.9938 837.9181 834.7469 831.4823 828.1319 824.7103 821.2435 817.7733 #>  [56,] 841.2743 838.2776 835.1986 832.0422 828.8184 825.5444 822.2485 818.9729 #>  [57,] 841.5758 838.6577 835.6699 832.6192 829.5176 826.3845 823.2488 820.1527 #>  [58,] 841.8956 839.0554 836.1570 833.2090 830.2250 827.2254 824.2397 821.3087 #>  [59,] 842.2313 839.4676 836.6566 833.8080 830.9365 828.0632 825.2173 822.4379 #>  [60,] 842.5803 839.8918 837.1658 834.4130 831.6488 828.8944 826.1785 823.5381 #>  [61,] 842.9406 840.3254 837.6818 835.0209 832.3587 829.7162 827.1211 824.6082 #>  [62,] 843.3100 840.7663 838.2021 835.6293 833.0638 830.5264 828.0434 825.6474 #>  [63,] 843.6868 841.2124 838.7248 836.2361 833.7621 831.3231 828.9440 826.6553 #>  [64,] 844.0693 841.6619 839.2478 836.8393 834.4518 832.1049 829.8222 827.6319 #>  [65,] 844.4557 842.1130 839.7695 837.4373 835.1315 832.8708 830.6775 828.5775 #>  [66,] 844.8448 842.5645 840.2885 838.0287 835.7999 833.6199 831.5095 829.4926 #>  [67,] 845.2353 843.0150 840.8035 838.6125 836.4563 834.3517 832.3181 830.3777 #>  [68,] 845.6260 843.4633 841.3134 839.1877 837.0999 835.0657 833.1036 831.2336 #>  [69,] 846.0159 843.9085 841.8174 839.7536 837.7300 835.7619 833.8660 832.0611 #>  [70,] 846.4041 844.3497 842.3146 840.3093 838.3464 836.4400 834.6057 832.8609 #>  [71,] 846.7897 844.7861 842.8043 840.8546 838.9487 837.1000 835.3232 833.6338 #>  [72,] 847.1722 845.2171 843.2861 841.3889 839.5368 837.7422 836.0187 834.3808 #>  [73,] 847.5508 845.6421 843.7594 841.9120 840.1105 838.3666 836.6929 835.1027 #>  [74,] 847.9249 846.0607 844.2239 842.4236 840.6698 838.9735 837.3462 835.8003 #>  [75,] 848.2942 846.4724 844.6793 842.9237 841.2149 839.5630 837.9792 836.4744 #>  [76,] 848.6582 846.8769 845.1255 843.4121 841.7456 840.1357 838.5923 837.1260 #>  [77,] 849.0166 847.2739 845.5621 843.8887 842.2623 840.6917 839.1863 837.7556 #>  [78,] 849.3690 847.6633 845.9891 844.3537 842.7650 841.2313 839.7615 838.3642 #>  [79,] 849.7153 848.0448 846.4064 844.8070 843.2539 841.7551 840.3186 838.9525 #>  [80,] 850.0551 848.4183 846.8140 845.2487 843.7293 842.2632 840.8580 839.5211 #>  [81,] 850.3883 848.7838 847.2119 845.6789 844.1914 842.7562 841.3804 840.0708 #>  [82,] 850.7149 849.1410 847.6000 846.0978 844.6404 843.2343 841.8861 840.6022 #>  [83,] 851.0346 849.4901 847.9785 846.5054 845.0766 843.6980 842.3758 841.1160 #>  [84,] 851.3474 849.8309 848.3474 846.9020 845.5002 844.1476 842.8499 841.6127 #>  [85,] 851.6532 850.1636 848.7067 847.2877 845.9115 844.5835 843.3089 842.0930 #>  [86,] 851.9520 850.4880 849.0567 847.6626 846.3107 845.0060 843.7532 842.5573 #>  [87,] 852.2438 850.8043 849.3972 848.0270 846.6982 845.4154 844.1833 843.0063 #>  [88,] 852.5286 851.1125 849.7286 848.3811 847.0742 845.8122 844.5996 843.4405 #>  [89,] 852.8063 851.4127 850.0509 848.7250 847.4389 846.1967 845.0026 843.8603 #>  [90,] 853.0771 851.7049 850.3643 849.0589 847.7926 846.5692 845.3926 844.2662 #>  [91,] 853.3409 851.9893 850.6688 849.3830 848.1356 846.9300 845.7699 844.6587 #>  [92,] 853.5978 852.2659 850.9647 849.6976 848.4681 847.2795 846.1351 845.0381 #>  [93,] 853.8478 852.5347 851.2520 850.0028 848.7903 847.6178 846.4884 845.4050 #>  [94,] 854.0911 852.7960 851.5309 850.2988 849.1026 847.9455 846.8302 845.7597 #>  [95,] 854.3276 853.0498 851.8016 850.5858 849.4051 848.2626 847.1608 846.1025 #>  [96,] 854.5574 853.2963 852.0642 850.8640 849.6982 848.5695 847.4806 846.4339 #>  [97,] 854.7806 853.5355 852.3189 851.1335 849.9819 848.8665 847.7898 846.7541 #>  [98,] 854.9974 853.7675 852.5658 851.3946 850.2565 849.1538 848.0888 847.0636 #>  [99,] 855.2077 853.9925 852.8050 851.6475 850.5223 849.4317 848.3778 847.3626 #> [100,] 855.4117 854.2106 853.0367 851.8923 850.7795 849.7004 848.6571 847.6515 #>           [,65]    [,66]    [,67]    [,68]    [,69]    [,70]    [,71]    [,72] #>   [1,] 866.6607 865.4866 864.4006 863.4079 862.5126 861.7173 861.0234 860.4304 #>   [2,] 865.3556 864.1588 863.0540 862.0470 861.1423 860.3428 859.6499 859.0632 #>   [3,] 864.0292 862.8079 861.6829 860.6605 859.7456 858.9415 858.2498 857.6700 #>   [4,] 862.6805 861.4330 860.2862 859.2471 858.3212 857.5122 856.8217 856.2493 #>   [5,] 861.3086 860.0328 858.8625 857.8054 856.8675 856.0531 855.3639 854.7996 #>   [6,] 859.9126 858.6062 857.4104 856.3337 855.3829 854.5626 853.8749 853.3193 #>   [7,] 858.4914 857.1520 855.9285 854.8305 853.8656 853.0390 852.3529 851.8068 #>   [8,] 857.0440 855.6688 854.4152 853.2940 852.3137 851.4801 850.7957 850.2601 #>   [9,] 855.5692 854.1551 852.8688 851.7222 850.7251 849.8837 849.2013 848.6771 #>  [10,] 854.0657 852.6094 851.2873 850.1130 849.0973 848.2476 847.5673 847.0556 #>  [11,] 852.5325 851.0301 849.6689 848.4641 847.4280 846.5690 845.8910 845.3931 #>  [12,] 850.9682 849.4154 848.0112 846.7729 845.7143 844.8450 844.1696 843.6870 #>  [13,] 849.3715 847.7635 846.3121 845.0366 843.9530 843.0724 842.3999 841.9342 #>  [14,] 847.7409 846.0724 844.5688 843.2522 842.1409 841.2476 840.5783 840.1314 #>  [15,] 846.0751 844.3400 842.7787 841.4164 840.2741 839.3666 838.7009 838.2751 #>  [16,] 844.3726 842.5641 840.9388 839.5254 838.3484 837.4250 836.7633 836.3611 #>  [17,] 842.6320 840.7424 839.0457 837.5752 836.3591 835.4177 834.7605 834.3850 #>  [18,] 840.8520 838.8724 837.0959 835.5611 834.3008 833.3390 832.6869 832.3417 #>  [19,] 839.0312 836.9515 835.0857 833.4781 832.1676 831.1825 830.5363 830.2256 #>  [20,] 837.1683 834.9772 833.0107 831.3205 829.9526 828.9408 828.3014 828.0302 #>  [21,] 835.2623 832.9467 830.8665 829.0821 827.6482 826.6055 825.9739 825.7482 #>  [22,] 833.3125 830.8575 828.6482 826.7556 825.2453 824.1668 823.5442 823.3715 #>  [23,] 831.3185 828.7068 826.3505 824.3332 822.7339 821.6133 821.0014 820.8906 #>  [24,] 829.2805 826.4925 823.9680 821.8059 820.1019 818.9315 818.3323 818.2946 #>  [25,] 827.1995 824.2126 821.4948 819.1635 817.3356 816.1057 815.5216 815.5710 #>  [26,] 825.0773 821.8658 818.9251 816.3946 814.4185 813.1167 812.5510 812.7053 #>  [27,] 822.9174 819.4520 816.2530 813.4864 811.3313 809.9416 809.3984 809.6805 #>  [28,] 820.7251 816.9725 813.4733 810.4247 808.0509 806.5521 806.0369 806.4768 #>  [29,] 818.5079 814.4309 810.5818 807.1938 804.5491 802.9129 802.4332 803.0709 #>  [30,] 816.2766 811.8343 807.5764 803.7767 800.7921 798.9792 798.5454 799.4353 #>  [31,] 814.0456 809.1942 804.4590 800.1562 796.7383 794.6933 794.3202 795.5382 #>  [32,] 811.8343 806.5286 801.2374 796.3161 792.3361 789.9785 789.6880 791.3425 #>  [33,] 809.6676 803.8638 797.9294 792.2446 787.5224 784.7299 784.5559 786.8073 #>  [34,] 807.5764 801.2374 794.5683 787.9411 782.2201 778.7996 778.7972 781.8899 #>  [35,] 805.5984 798.6997 791.2098 783.4285 776.3390 771.9684 772.2331 776.5557 #>  [36,] 803.7767 796.3161 787.9411 778.7755 769.7869 763.8929 764.6054 770.8002 #>  [37,] 802.1587 794.1654 784.8888 774.1336 762.5123 753.9922 755.5346 764.7036 #>  [38,] 800.7921 792.3361 782.2201 769.7869 754.6458 741.1740 744.4926 758.5474 #>  [39,] 799.7209 790.9159 780.1291 766.1865 746.8878 723.0846 731.0627 753.0098 #>  [40,] 798.9792 789.9785 778.7996 763.8929 741.1740 694.8736 717.4372 749.2830 #>  [41,] 798.5868 789.5677 778.3516 763.3500 740.2501 688.0424 715.2865 748.5893 #>  [42,] 798.5454 789.6880 778.7972 764.6054 744.4926 717.4372 727.1580 751.0745 #>  [43,] 798.8388 790.3025 780.0351 767.2756 751.3314 736.3775 740.2837 755.6451 #>  [44,] 799.4353 791.3425 781.8899 770.8002 758.5474 749.2830 751.0745 761.0342 #>  [45,] 800.2926 792.7219 784.1658 774.6967 765.2470 758.9410 759.7788 766.4604 #>  [46,] 801.3631 794.3514 786.6885 778.6489 771.2280 766.6100 766.9458 771.5805 #>  [47,] 802.5993 796.1497 789.3229 782.4828 776.5220 772.9429 772.9845 776.2860 #>  [48,] 803.9567 798.0486 791.9746 786.1167 781.2183 778.3187 778.1737 780.5702 #>  [49,] 805.3968 799.9948 794.5822 789.5208 785.4089 782.9757 782.7053 784.4643 #>  [50,] 806.8871 801.9485 797.1087 792.6923 789.1736 787.0736 786.7149 788.0102 #>  [51,] 808.4016 803.8811 799.5336 795.6413 792.5784 790.7242 790.3011 791.2497 #>  [52,] 809.9199 805.7733 801.8474 798.3834 795.6769 794.0089 793.5374 794.2206 #>  [53,] 811.4267 807.6123 804.0474 800.9359 798.5125 796.9888 796.4800 796.9559 #>  [54,] 812.9104 809.3903 806.1349 803.3159 801.1206 799.7110 799.1728 799.4839 #>  [55,] 814.3630 811.1032 808.1139 805.5393 803.5302 802.2122 801.6506 801.8285 #>  [56,] 815.7788 812.7492 809.9894 807.6207 805.7654 804.5222 803.9415 804.0103 #>  [57,] 817.1540 814.3282 811.7671 809.5733 807.8462 806.6647 806.0683 806.0468 #>  [58,] 818.4865 815.8412 813.4531 811.4085 809.7896 808.6597 808.0502 807.9530 #>  [59,] 819.7751 817.2901 815.0530 813.1369 811.6099 810.5235 809.9029 809.7418 #>  [60,] 821.0195 818.6772 816.5725 814.7676 813.3193 812.2700 811.6400 811.4243 #>  [61,] 822.2199 820.0050 818.0168 816.3088 814.9285 813.9109 813.2729 813.0102 #>  [62,] 823.3771 821.2761 819.3910 817.7678 816.4464 815.4563 814.8114 814.5081 #>  [63,] 824.4920 822.4932 820.6997 819.1510 817.8812 816.9150 816.2640 815.9253 #>  [64,] 825.5658 823.6589 821.9469 820.4642 819.2397 818.2944 817.6382 817.2685 #>  [65,] 826.5999 824.7758 823.1368 821.7126 820.5281 819.6013 818.9404 818.5433 #>  [66,] 827.5956 825.8464 824.2729 822.9008 821.7519 820.8414 820.1764 819.7551 #>  [67,] 828.5544 826.8731 825.3584 824.0331 822.9159 822.0199 821.3512 820.9084 #>  [68,] 829.4777 827.8580 826.3966 825.1132 824.0244 823.1413 822.4694 822.0073 #>  [69,] 830.3668 828.8034 827.3901 826.1446 825.0812 824.2098 823.5350 823.0555 #>  [70,] 831.2233 829.7111 828.3416 827.1304 826.0900 825.2290 824.5515 824.0565 #>  [71,] 832.0484 830.5831 829.2535 828.0733 827.0537 826.2022 825.5223 825.0133 #>  [72,] 832.8434 831.4211 830.1279 828.9760 827.9753 827.1324 826.4504 825.9285 #>  [73,] 833.6096 832.2268 830.9670 829.8409 828.8573 828.0222 827.3382 826.8048 #>  [74,] 834.3481 833.0018 831.7725 830.6700 829.7022 828.8741 828.1884 827.6443 #>  [75,] 835.0602 833.7475 832.5463 831.4655 830.5120 829.6904 829.0031 828.4493 #>  [76,] 835.7469 834.4652 833.2900 832.2290 831.2887 830.4731 829.7843 829.2216 #>  [77,] 836.4093 835.1563 834.0050 832.9624 832.0342 831.2241 830.5339 829.9630 #>  [78,] 837.0483 835.8220 834.6928 833.6671 832.7501 831.9450 831.2535 830.6752 #>  [79,] 837.6649 836.4633 835.3546 834.3446 833.4379 832.6375 831.9449 831.3595 #>  [80,] 838.2599 837.0814 835.9918 834.9963 834.0992 833.3031 832.6093 832.0176 #>  [81,] 838.8343 837.6773 836.6053 835.6234 834.7351 833.9430 833.2482 832.6505 #>  [82,] 839.3888 838.2518 837.1964 836.2270 835.3469 834.5585 833.8628 833.2596 #>  [83,] 839.9242 838.8060 837.7659 836.8082 835.9358 835.1509 834.4543 833.8459 #>  [84,] 840.4412 839.3405 838.3149 837.3680 836.5028 835.7211 835.0237 834.4105 #>  [85,] 840.9406 839.8563 838.8441 837.9075 837.0489 836.2702 835.5721 834.9544 #>  [86,] 841.4228 840.3540 839.3544 838.4273 837.5750 836.7991 836.1003 835.4784 #>  [87,] 841.8887 840.8343 839.8466 838.9285 838.0820 837.3087 836.6092 835.9834 #>  [88,] 842.3388 841.2980 840.3214 839.4117 838.5707 837.7999 837.0998 836.4703 #>  [89,] 842.7735 841.7456 840.7795 839.8776 839.0418 838.2733 837.5726 836.9397 #>  [90,] 843.1936 842.1778 841.2215 840.3271 839.4961 838.7298 838.0285 837.3923 #>  [91,] 843.5994 842.5951 841.6481 840.7606 839.9342 839.1699 838.4682 837.8289 #>  [92,] 843.9915 842.9980 842.0598 841.1789 840.3568 839.5944 838.8922 838.2501 #>  [93,] 844.3704 843.3870 842.4571 841.5825 840.7644 840.0038 839.3012 838.6563 #>  [94,] 844.7364 843.7627 842.8406 841.9719 841.1576 840.3988 839.6957 839.0483 #>  [95,] 845.0900 844.1255 843.2108 842.3476 841.5370 840.7798 840.0763 839.4264 #>  [96,] 845.4316 844.4757 843.5681 842.7102 841.9030 841.1474 840.4435 839.7913 #>  [97,] 845.7615 844.8140 843.9130 843.0601 842.2562 841.5020 840.7977 840.1434 #>  [98,] 846.0803 845.1405 844.2459 843.3977 842.5969 841.8440 841.1395 840.4831 #>  [99,] 846.3881 845.4558 844.5672 843.7235 842.9256 842.1741 841.4691 840.8108 #> [100,] 846.6853 845.7601 844.8772 844.0378 843.2427 842.4924 841.7872 841.1270 #>           [,73]    [,74]    [,75]    [,76]    [,77]    [,78]    [,79]    [,80] #>   [1,] 859.9366 859.5386 859.2321 859.0112 858.8698 858.8006 858.7964 858.8498 #>   [2,] 858.5808 858.1990 857.9129 857.7162 857.6020 857.5625 857.5899 857.6761 #>   [3,] 857.1999 856.8355 856.5713 856.4005 856.3154 856.3077 856.3687 856.4896 #>   [4,] 855.7925 855.4469 855.2064 855.0634 855.0096 855.0357 855.1324 855.2903 #>   [5,] 854.3572 854.0320 853.8170 853.7040 853.6837 853.7461 853.8809 854.0780 #>   [6,] 852.8927 852.5895 852.4021 852.3215 852.3372 852.4383 852.6138 852.8525 #>   [7,] 851.3972 851.1179 850.9605 850.9148 850.9693 851.1120 851.3309 851.6139 #>   [8,] 849.8691 849.6159 849.4910 849.4830 849.5793 849.7667 850.0319 850.3621 #>   [9,] 848.3065 848.0817 847.9922 848.0251 848.1666 848.4020 848.7168 849.0970 #>  [10,] 846.7073 846.5137 846.4627 846.5401 846.7304 847.0174 847.3853 847.8189 #>  [11,] 845.0694 844.9099 844.9011 845.0269 845.2700 845.6126 846.0373 846.5279 #>  [12,] 843.3904 843.2684 843.3058 843.4843 843.7847 844.1873 844.6730 845.2242 #>  [13,] 841.6676 841.5871 841.6751 841.9113 842.2739 842.7413 843.2924 843.9081 #>  [14,] 839.8982 839.8635 840.0074 840.3067 840.7370 841.2743 841.8956 842.5803 #>  [15,] 838.0790 838.0952 838.3007 838.6692 839.1734 839.7864 840.4831 841.2413 #>  [16,] 836.2067 836.2795 836.5533 836.9980 837.5827 838.2776 839.0554 839.8918 #>  [17,] 834.2773 834.4136 834.7631 835.2917 835.9644 836.7482 837.6130 838.5329 #>  [18,] 832.2868 832.4941 832.9281 833.5494 834.3185 835.1986 836.1570 837.1658 #>  [19,] 830.2305 830.5180 831.0463 831.7702 832.6450 833.6296 834.6885 835.7919 #>  [20,] 828.1033 828.4815 829.1157 829.9534 830.9441 832.0422 833.2090 834.4130 #>  [21,] 825.8997 826.3810 827.1342 828.0986 829.2166 830.4378 831.7204 833.0311 #>  [22,] 823.6133 824.2124 825.1000 826.2055 827.4635 828.8184 830.2250 831.6488 #>  [23,] 821.2372 821.9716 823.0115 824.2745 825.6865 827.1862 828.7256 830.2687 #>  [24,] 818.7639 819.6545 820.8675 822.3065 823.8879 825.5444 827.2254 828.8944 #>  [25,] 816.1850 817.2569 818.6673 820.3035 822.0710 823.8969 825.7286 827.5296 #>  [26,] 813.4912 814.7749 816.4111 818.2681 820.2399 822.2485 824.2397 826.1785 #>  [27,] 810.6727 812.2052 814.1005 816.2048 818.4004 820.6048 822.7643 824.8462 #>  [28,] 807.7189 809.5455 811.7387 814.1196 816.5594 818.9729 821.3087 823.5381 #>  [29,] 804.6192 806.7952 809.3312 812.0210 814.7257 817.3610 819.8801 822.2604 #>  [30,] 801.3631 803.9567 806.8871 809.9199 812.9104 815.7788 818.4865 821.0195 #>  [31,] 797.9421 801.0368 804.4198 807.8312 811.1267 814.2373 817.1370 819.8226 #>  [32,] 794.3514 798.0486 801.9485 805.7733 809.3903 812.7492 815.8412 818.6772 #>  [33,] 790.5942 795.0155 799.4996 803.7694 807.7195 811.3282 814.6096 817.5912 #>  [34,] 786.6885 791.9746 797.1087 801.8474 806.1349 809.9894 813.4531 816.5725 #>  [35,] 782.6779 788.9817 794.8210 800.0399 804.6591 808.7483 812.3825 815.6288 #>  [36,] 778.6489 786.1167 792.6923 798.3834 803.3159 807.6207 811.4085 814.7676 #>  [37,] 774.7529 783.4857 790.7869 796.9164 802.1289 806.6219 810.5413 813.9958 #>  [38,] 771.2280 781.2183 789.1736 795.6769 801.1206 805.7654 809.7896 813.3193 #>  [39,] 768.3971 779.4544 787.9180 794.6991 800.3099 805.0627 809.1607 812.7429 #>  [40,] 766.6100 778.3187 787.0736 794.0089 799.7110 804.5222 808.6597 812.2700 #>  [41,] 766.1176 777.8892 786.6716 793.6212 799.3317 804.1483 808.2894 811.9023 #>  [42,] 766.9458 778.1737 786.7149 793.5374 799.1728 803.9415 808.0502 811.6400 #>  [43,] 768.8807 779.1067 787.1777 793.7452 799.2279 803.8980 807.9396 811.4817 #>  [44,] 771.5805 780.5702 788.0102 794.2206 799.4839 804.0103 807.9530 811.4243 #>  [45,] 774.7100 782.4252 789.1485 794.9309 799.9225 804.2675 808.0836 811.4632 #>  [46,] 778.0129 784.5386 790.5236 795.8384 800.5222 804.6563 808.3227 811.5928 #>  [47,] 781.3215 786.7988 792.0700 796.9044 801.2591 805.1616 808.6605 811.8063 #>  [48,] 784.5386 789.1210 793.7301 798.0920 802.1096 805.7679 809.0865 812.0964 #>  [49,] 787.6133 791.4450 795.4562 799.3677 803.0506 806.4595 809.5897 812.4553 #>  [50,] 790.5236 793.7301 797.2112 800.7025 804.0612 807.2211 810.1592 812.8752 #>  [51,] 793.2642 795.9508 798.9668 802.0725 805.1225 808.0387 810.7846 813.3481 #>  [52,] 795.8384 798.0920 800.7025 803.4581 806.2184 808.8994 811.4558 813.8666 #>  [53,] 798.2543 800.1460 802.4039 804.8440 807.3350 809.7919 812.1639 814.4233 #>  [54,] 800.5222 802.1096 804.0612 806.2184 808.4611 810.7063 812.9005 815.0115 #>  [55,] 802.6526 803.9829 805.6681 807.5723 809.5873 811.6340 813.6582 815.6252 #>  [56,] 804.6563 805.7679 807.2211 808.8994 810.7063 812.5677 814.4306 816.2587 #>  [57,] 806.5432 807.4679 808.7183 810.1950 811.8122 813.5016 815.2120 816.9069 #>  [58,] 808.3227 809.0865 810.1592 811.4558 812.9005 814.4306 815.9975 817.5654 #>  [59,] 810.0033 810.6280 811.5445 812.6801 813.9678 815.3507 816.7832 818.2303 #>  [60,] 811.5928 812.0964 812.8752 813.8666 815.0115 816.2587 817.5654 818.8982 #>  [61,] 813.0982 813.4960 814.1528 815.0148 816.0300 817.1520 818.3413 819.5661 #>  [62,] 814.5260 814.8307 815.3792 816.1250 817.0221 818.0286 819.1085 820.2315 #>  [63,] 815.8818 816.1044 816.5564 817.1974 817.9868 818.8872 819.8651 820.8923 #>  [64,] 817.1708 817.3206 817.6863 818.2327 818.9240 819.7264 820.6094 821.5467 #>  [65,] 818.3978 818.4828 818.7710 819.2318 819.8335 820.5457 821.3403 822.1931 #>  [66,] 819.5670 819.5940 819.8126 820.1958 820.7155 821.3444 822.0568 822.8302 #>  [67,] 820.6823 820.6573 820.8130 821.1256 821.5703 822.1222 822.7582 823.4572 #>  [68,] 821.7471 821.6754 821.7741 822.0225 822.3982 822.8791 823.4439 824.0731 #>  [69,] 822.7647 822.6508 822.6978 822.8875 823.2000 823.6151 824.1135 824.6772 #>  [70,] 823.7381 823.5858 823.5858 823.7218 823.9760 824.3303 824.7669 825.2692 #>  [71,] 824.6697 824.4827 824.4398 824.5266 824.7271 825.0249 825.4038 825.8486 #>  [72,] 825.5622 825.3434 825.2613 825.3029 825.4538 825.6992 826.0243 826.4150 #>  [73,] 826.4177 826.1700 826.0519 826.0519 826.1569 826.3537 826.6285 826.9684 #>  [74,] 827.2383 826.9641 826.8130 826.7745 826.8371 826.9886 827.2164 827.5087 #>  [75,] 828.0259 827.7273 827.5458 827.4719 827.4952 827.6044 827.7883 828.0357 #>  [76,] 828.7823 828.4613 828.2517 828.1450 828.1317 828.2016 828.3443 828.5495 #>  [77,] 829.5090 829.1674 828.9318 828.7947 828.7474 828.7805 828.8847 829.0502 #>  [78,] 830.2076 829.8469 829.5873 829.4219 829.3429 829.3418 829.4097 829.5379 #>  [79,] 830.8795 830.5011 830.2192 830.0276 829.9190 829.8857 829.9197 830.0126 #>  [80,] 831.5260 831.1312 830.8286 830.6124 830.4762 830.4129 830.4149 830.4746 #>  [81,] 832.1482 831.7381 831.4162 831.1773 831.0153 830.9237 830.8956 830.9241 #>  [82,] 832.7472 832.3230 831.9832 831.7229 831.5367 831.4186 831.3623 831.3611 #>  [83,] 833.3242 832.8868 832.5302 832.2500 832.0411 831.8981 831.8151 831.7860 #>  [84,] 833.8802 833.4304 833.0581 832.7592 832.5290 832.3626 832.2544 832.1989 #>  [85,] 834.4159 833.9546 833.5676 833.2512 833.0010 832.8125 832.6806 832.6000 #>  [86,] 834.9324 834.4603 834.0595 833.7266 833.4576 833.2483 833.0940 832.9897 #>  [87,] 835.4303 834.9481 834.5343 834.1859 833.8993 833.6704 833.4948 833.3680 #>  [88,] 835.9105 835.4187 834.9928 834.6299 834.3265 834.0791 833.8834 833.7353 #>  [89,] 836.3736 835.8729 835.4356 835.0589 834.7398 834.4748 834.2601 834.0918 #>  [90,] 836.8204 836.3113 835.8632 835.4735 835.1395 834.8579 834.6252 834.4377 #>  [91,] 837.2514 836.7344 836.2761 835.8743 835.5262 835.2289 834.9790 834.7733 #>  [92,] 837.6673 837.1428 836.6749 836.2615 835.9001 835.5879 835.3218 835.0987 #>  [93,] 838.0687 837.5371 837.0601 836.6358 836.2617 835.9354 835.6539 835.4143 #>  [94,] 838.4559 837.9177 837.4321 836.9974 836.6114 836.2717 835.9755 835.7201 #>  [95,] 838.8297 838.2851 837.7914 837.3469 836.9495 836.5970 836.2869 836.0166 #>  [96,] 839.1904 838.6399 838.1384 837.6846 837.2764 836.9118 836.5884 836.3037 #>  [97,] 839.5385 838.9823 838.4735 838.0108 837.5924 837.2163 836.8802 836.5819 #>  [98,] 839.8744 839.3128 838.7971 838.3260 837.8978 837.5107 837.1626 836.8512 #>  [99,] 840.1986 839.6319 839.1096 838.6305 838.1930 837.7954 837.4357 837.1119 #> [100,] 840.5114 839.9398 839.4112 838.9245 838.4782 838.0706 837.6999 837.3642 #>           [,81]    [,82]    [,83]    [,84]    [,85]    [,86]    [,87]    [,88] #>   [1,] 858.9534 859.1000 859.2830 859.4959 859.7332 859.9894 860.2598 860.5403 #>   [2,] 857.8132 857.9936 858.2102 858.4563 858.7260 859.0136 859.3144 859.6240 #>   [3,] 856.6622 856.8782 857.1301 857.4109 857.7143 858.0346 858.3667 858.7064 #>   [4,] 855.5003 855.7538 856.0428 856.3598 856.6984 857.0526 857.4173 857.7879 #>   [5,] 854.3276 854.6206 854.9484 855.3034 855.6786 856.0680 856.4663 856.8689 #>   [6,] 853.1441 853.4787 853.8473 854.2419 854.6553 855.0813 855.5143 855.9498 #>   [7,] 851.9499 852.3283 852.7398 853.1758 853.6289 854.0927 854.5617 855.0311 #>   [8,] 850.7450 851.1697 851.6261 852.1054 852.5999 853.1029 853.6090 854.1133 #>   [9,] 849.5298 850.0032 850.5067 851.0312 851.5687 852.1124 852.6567 853.1969 #>  [10,] 848.3044 848.8292 849.3822 849.9538 850.5360 851.1218 851.7055 852.2825 #>  [11,] 847.0692 847.6482 848.2530 848.8739 849.5024 850.1316 850.7559 851.3707 #>  [12,] 845.8247 846.4607 847.1199 847.7920 848.4687 849.1428 849.8088 850.4623 #>  [13,] 844.5715 845.2674 845.9835 846.7091 847.4356 848.1560 848.8649 849.5578 #>  [14,] 843.3100 844.0693 844.8448 845.6260 846.4041 847.1722 847.9249 848.6582 #>  [15,] 842.0413 842.8670 843.7048 844.5437 845.3751 846.1922 846.9899 847.7643 #>  [16,] 840.7663 841.6619 842.5645 843.4633 844.3497 845.2171 846.0607 846.8769 #>  [17,] 839.4861 840.4550 841.4253 842.3861 843.3291 844.2480 845.1383 845.9969 #>  [18,] 838.2021 839.2478 840.2885 841.3134 842.3146 843.2861 844.2239 845.1255 #>  [19,] 836.9159 838.0420 839.1557 840.2468 841.3075 842.3326 843.3186 844.2635 #>  [20,] 835.6293 836.8393 838.0287 839.1877 840.3093 841.3889 842.4236 843.4121 #>  [21,] 834.3445 835.6418 836.9094 838.1381 839.3217 840.4565 841.5403 842.5724 #>  [22,] 833.0638 834.4518 835.7999 837.0999 838.3464 839.5368 840.6698 841.7456 #>  [23,] 831.7901 833.2719 834.7026 836.0750 837.3852 838.6315 839.8138 840.9330 #>  [24,] 830.5264 832.1049 833.6199 835.0657 836.4400 837.7422 838.9735 840.1357 #>  [25,] 829.2762 830.9539 832.5545 834.0744 835.5128 836.8707 838.1504 839.3550 #>  [26,] 828.0434 829.8222 831.5095 833.1036 834.6057 836.0187 837.3462 838.5923 #>  [27,] 826.8322 828.7136 830.4877 832.1558 833.7210 835.1881 836.5623 837.8489 #>  [28,] 825.6474 827.6319 829.4926 831.2336 832.8609 834.3808 835.8003 837.1260 #>  [29,] 824.4939 826.5812 828.5274 830.3400 832.0275 833.5986 835.0617 836.4249 #>  [30,] 823.3771 825.5658 827.5956 829.4777 831.2233 832.8434 834.3481 835.7469 #>  [31,] 822.3025 824.5902 826.7008 828.6494 830.4504 832.1169 833.6610 835.0933 #>  [32,] 821.2761 823.6589 825.8464 827.8580 829.7111 831.4211 833.0018 834.4652 #>  [33,] 820.3036 822.7763 825.0360 827.1062 829.0075 830.7576 832.3719 833.8638 #>  [34,] 819.3910 821.9469 824.2729 826.3966 828.3416 830.1279 831.7725 833.2900 #>  [35,] 818.5440 821.1749 823.5602 825.7315 827.7154 829.5336 831.2049 832.7448 #>  [36,] 817.7678 820.4642 822.9008 825.1132 827.1304 828.9760 830.6700 832.2290 #>  [37,] 817.0672 819.8181 822.2973 824.5437 826.5882 828.4563 830.1689 831.7435 #>  [38,] 816.4464 819.2397 821.7519 824.0244 826.0900 827.9753 829.7022 831.2887 #>  [39,] 815.9087 818.7313 821.2662 823.5566 825.6367 827.5338 829.2704 830.8651 #>  [40,] 815.4563 818.2944 820.8414 823.1413 825.2290 827.1324 828.8741 830.4731 #>  [41,] 815.0905 817.9300 820.4781 822.7789 824.8673 826.7712 828.5135 830.1128 #>  [42,] 814.8114 817.6382 820.1764 822.4694 824.5515 826.4504 828.1884 829.7843 #>  [43,] 814.6180 817.4182 819.9358 822.2125 824.2815 826.1696 827.8988 829.4873 #>  [44,] 814.5081 817.2685 819.7551 822.0073 824.0565 825.9285 827.6443 829.2216 #>  [45,] 814.4788 817.1870 819.6329 821.8527 823.8758 825.7263 827.4244 828.9868 #>  [46,] 814.5260 817.1708 819.5670 821.7471 823.7381 825.5622 827.2383 828.7823 #>  [47,] 814.6450 817.2166 819.5550 821.6887 823.6419 825.4350 827.0852 828.6074 #>  [48,] 814.8307 817.3206 819.5940 821.6754 823.5858 825.3434 826.9641 828.4613 #>  [49,] 815.0774 817.4786 819.6810 821.7047 823.5677 825.2861 826.8737 828.3431 #>  [50,] 815.3792 817.6863 819.8126 821.7741 823.5858 825.2613 826.8130 828.2517 #>  [51,] 815.7304 817.9392 819.9854 821.8810 823.6379 825.2675 826.7804 828.1860 #>  [52,] 816.1250 818.2327 820.1958 822.0225 823.7218 825.3029 826.7745 828.1450 #>  [53,] 816.5573 818.5624 820.4403 822.1959 823.8353 825.3656 826.7940 828.1273 #>  [54,] 817.0221 818.9240 820.7155 822.3982 823.9760 825.4538 826.8371 828.1317 #>  [55,] 817.5141 819.3133 821.0180 822.6269 824.1418 825.5656 826.9025 828.1569 #>  [56,] 818.0286 819.7264 821.3444 822.8791 824.3303 825.6992 826.9886 828.2016 #>  [57,] 818.5614 820.1596 821.6916 823.1523 824.5393 825.8527 827.0937 828.2645 #>  [58,] 819.1085 820.6094 822.0568 823.4439 824.7669 826.0243 827.2164 828.3443 #>  [59,] 819.6662 821.0727 822.4372 823.7516 825.0108 826.2123 827.3552 828.4397 #>  [60,] 820.2315 821.5467 822.8302 824.0731 825.2692 826.4150 827.5087 828.5495 #>  [61,] 820.8015 822.0286 823.2335 824.4063 825.5402 826.6308 827.6753 828.6725 #>  [62,] 821.3736 822.5162 823.6449 824.7494 825.8221 826.8581 827.8538 828.8074 #>  [63,] 821.9458 823.0073 824.0624 825.1004 826.1133 827.0955 828.0429 828.9531 #>  [64,] 822.5162 823.5001 824.4843 825.4577 826.4122 827.3416 828.2413 829.1085 #>  [65,] 823.0830 823.9929 824.9089 825.8199 826.7175 827.5951 828.4479 829.2726 #>  [66,] 823.6449 824.4843 825.3348 826.1855 827.0277 827.8548 828.6616 829.4443 #>  [67,] 824.2007 824.9729 825.7607 826.5532 827.3418 828.1197 828.8813 829.6228 #>  [68,] 824.7494 825.4577 826.1855 826.9220 827.6587 828.3886 829.1061 829.8071 #>  [69,] 825.2901 825.9378 826.6081 827.2908 827.9773 828.6606 829.3351 829.9964 #>  [70,] 825.8221 826.4122 827.0277 827.6587 828.2967 828.9348 829.5674 830.1898 #>  [71,] 826.3450 826.8803 827.4435 828.0249 828.6161 829.2105 829.8022 830.3867 #>  [72,] 826.8581 827.3416 827.8548 828.3886 828.9348 829.4868 830.0389 830.5864 #>  [73,] 827.3611 827.7954 828.2610 828.7492 829.2521 829.7632 830.2768 830.7882 #>  [74,] 827.8538 828.2413 828.6616 829.1061 829.5674 830.0389 830.5152 830.9916 #>  [75,] 828.3360 828.6791 829.0562 829.4589 829.8801 830.3135 830.7536 831.1959 #>  [76,] 828.8074 829.1085 829.4443 829.8071 830.1898 830.5864 830.9916 831.4007 #>  [77,] 829.2680 829.5292 829.8258 830.1503 830.4961 830.8572 831.2285 831.6055 #>  [78,] 829.7178 829.9411 830.2003 830.4882 830.7985 831.1255 831.4641 831.8098 #>  [79,] 830.1567 830.3441 830.5676 830.8206 831.0968 831.3909 831.6978 832.0134 #>  [80,] 830.5848 830.7380 830.9276 831.1471 831.3907 831.6531 831.9295 832.2157 #>  [81,] 831.0021 831.1229 831.2801 831.4676 831.6798 831.9117 832.1587 832.4166 #>  [82,] 831.4087 831.4987 831.6250 831.7819 831.9641 832.1667 832.3852 832.6156 #>  [83,] 831.8047 831.8654 831.9623 832.0900 832.2433 832.4177 832.6087 832.8126 #>  [84,] 832.1903 832.2231 832.2919 832.3916 832.5173 832.6645 832.8290 833.0072 #>  [85,] 832.5655 832.5718 832.6138 832.6867 832.7859 832.9069 833.0459 833.1993 #>  [86,] 832.9305 832.9116 832.9280 832.9753 833.0490 833.1449 833.2593 833.3886 #>  [87,] 833.2855 833.2425 833.2345 833.2573 833.3065 833.3783 833.4689 833.5751 #>  [88,] 833.6305 833.5646 833.5334 833.5327 833.5584 833.6069 833.6747 833.7584 #>  [89,] 833.9659 833.8781 833.8246 833.8014 833.8047 833.8308 833.8765 833.9385 #>  [90,] 834.2916 834.1831 834.1083 834.0635 834.0452 834.0498 834.0742 834.1152 #>  [91,] 834.6080 834.4796 834.3845 834.3191 834.2800 834.2639 834.2677 834.2885 #>  [92,] 834.9152 834.7678 834.6532 834.5680 834.5090 834.4730 834.4570 834.4583 #>  [93,] 835.2133 835.0478 834.9146 834.8104 834.7323 834.6771 834.6420 834.6244 #>  [94,] 835.5026 835.3197 835.1687 835.0463 834.9498 834.8761 834.8227 834.7867 #>  [95,] 835.7831 835.5838 835.4156 835.2758 835.1616 835.0702 834.9989 834.9454 #>  [96,] 836.0551 835.8400 835.6555 835.4989 835.3677 835.2591 835.1708 835.1001 #>  [97,] 836.3188 836.0885 835.8883 835.7157 835.5681 835.4431 835.3382 835.2511 #>  [98,] 836.5743 836.3295 836.1143 835.9262 835.7629 835.6220 835.5011 835.3981 #>  [99,] 836.8218 836.5631 836.3335 836.1306 835.9521 835.7959 835.6596 835.5412 #> [100,] 837.0615 836.7894 836.5459 836.3288 836.1358 835.9648 835.8136 835.6803 #>           [,89]    [,90]    [,91]    [,92]    [,93]    [,94]    [,95]    [,96] #>   [1,] 860.8271 861.1170 861.4073 861.6953 861.9793 862.2572 862.5278 862.7897 #>   [2,] 859.9386 860.2550 860.5704 860.8823 861.1888 861.4881 861.7787 862.0596 #>   [3,] 859.0496 859.3933 859.7344 860.0707 860.4001 860.7210 861.0321 861.3322 #>   [4,] 858.1606 858.5321 858.8996 859.2608 859.6136 859.9565 860.2882 860.6077 #>   [5,] 857.2719 857.6720 858.0664 858.4529 858.8295 859.1948 859.5474 859.8865 #>   [6,] 856.3839 856.8133 857.2353 857.6475 858.0483 858.4362 858.8100 859.1689 #>   [7,] 855.4972 855.9565 856.4065 856.8451 857.2704 857.6812 858.0764 858.4552 #>   [8,] 854.6121 855.1020 855.5807 856.0459 856.4961 856.9300 857.3468 857.7457 #>   [9,] 853.7292 854.2504 854.7582 855.2505 855.7258 856.1832 856.6217 857.0408 #>  [10,] 852.8491 853.4022 853.9395 854.4593 854.9601 855.4411 855.9014 856.3408 #>  [11,] 851.9723 852.5579 853.1253 853.6729 854.1994 854.7041 855.1864 855.6462 #>  [12,] 851.0996 851.7182 852.3161 852.8917 853.4441 853.9727 854.4771 854.9572 #>  [13,] 850.2316 850.8837 851.5124 852.1163 852.6948 853.2474 853.7738 854.2743 #>  [14,] 849.3690 850.0551 850.7149 851.3474 851.9520 852.5286 853.0771 853.5978 #>  [15,] 848.5127 849.2331 849.9242 850.5854 851.2162 851.8168 852.3873 852.9282 #>  [16,] 847.6633 848.4183 849.1410 849.8309 850.4880 851.1125 851.7049 852.2659 #>  [17,] 846.8218 847.6117 848.3661 849.0847 849.7680 850.4163 851.0304 851.6112 #>  [18,] 845.9891 846.8140 847.6000 848.3474 849.0567 849.7286 850.3643 850.9647 #>  [19,] 845.1661 846.0261 846.8437 847.6196 848.3547 849.0500 849.7069 850.3267 #>  [20,] 844.3537 845.2487 846.0978 846.9020 847.6626 848.3811 849.0589 849.6976 #>  [21,] 843.5530 844.4828 845.3631 846.1953 846.9811 847.7223 848.4206 849.0779 #>  [22,] 842.7650 843.7293 844.6404 845.5002 846.3107 847.0742 847.7926 848.4681 #>  [23,] 841.9907 842.9892 843.9305 844.8174 845.6521 846.4373 847.1753 847.8684 #>  [24,] 841.2313 842.2632 843.2343 844.1476 845.0060 845.8122 846.5692 847.2795 #>  [25,] 840.4879 841.5525 842.5526 843.4915 844.3728 845.1995 845.9748 846.7016 #>  [26,] 839.7615 840.8580 841.8861 842.8499 843.7532 844.5996 845.3926 846.1351 #>  [27,] 839.0532 840.1805 841.2357 842.2234 843.1479 844.0131 844.8229 845.5805 #>  [28,] 838.3642 839.5211 840.6022 841.6127 842.5573 843.4405 844.2662 845.0381 #>  [29,] 837.6956 838.8806 839.9863 841.0184 841.9821 842.8822 843.7230 844.5084 #>  [30,] 837.0483 838.2599 839.3888 840.4412 841.4228 842.3388 843.1936 843.9915 #>  [31,] 836.4234 837.6599 838.8104 839.8817 840.8800 841.8106 842.6784 843.4880 #>  [32,] 835.8220 837.0814 838.2518 839.3405 840.3540 841.2980 842.1778 842.9980 #>  [33,] 835.2448 836.5251 837.7136 838.8181 839.8453 840.8015 841.6921 842.5218 #>  [34,] 834.6928 835.9918 837.1964 838.3149 839.3544 840.3214 841.2215 842.0598 #>  [35,] 834.1666 835.4820 836.7007 837.8314 838.8817 839.8581 840.7665 841.6121 #>  [36,] 833.6671 834.9963 836.2270 837.3680 838.4273 839.4117 840.3271 841.1789 #>  [37,] 833.1948 834.5352 835.7756 836.9251 837.9917 838.9825 839.9036 840.7604 #>  [38,] 832.7501 834.0992 835.3469 836.5028 837.5750 838.5707 839.4961 840.3568 #>  [39,] 832.3334 833.6884 834.9412 836.1014 837.1774 838.1765 839.1048 839.9681 #>  [40,] 831.9450 833.3031 834.5585 835.7211 836.7991 837.7999 838.7298 839.5944 #>  [41,] 831.5851 832.9434 834.1991 835.3619 836.4400 837.4410 838.3710 839.2358 #>  [42,] 831.2535 832.6093 833.8628 835.0237 836.1003 837.0998 838.0285 838.8922 #>  [43,] 830.9503 832.3008 833.5497 834.7067 835.7798 836.7762 837.7023 838.5637 #>  [44,] 830.6752 832.0176 833.2596 834.4105 835.4784 836.4703 837.3923 838.2501 #>  [45,] 830.4278 831.7594 832.9922 834.1351 835.1960 836.1817 837.0984 837.9513 #>  [46,] 830.2076 831.5260 832.7472 833.8802 834.9324 835.9105 836.8204 837.6673 #>  [47,] 830.0142 831.3167 832.5243 833.6454 834.6872 835.6562 836.5581 837.3979 #>  [48,] 829.8469 831.1312 832.3230 833.4304 834.4603 835.4187 836.3113 837.1428 #>  [49,] 829.7049 830.9687 832.1428 833.2348 834.2512 835.1977 836.0798 836.9019 #>  [50,] 829.5873 830.8286 831.9832 833.0581 834.0595 834.9928 835.8632 836.6749 #>  [51,] 829.4933 830.7101 831.8434 832.8997 833.8847 834.8037 835.6612 836.4616 #>  [52,] 829.4219 830.6124 831.7229 832.7592 833.7266 834.6299 835.4735 836.2615 #>  [53,] 829.3721 830.5348 831.6209 832.6358 833.5844 834.4710 835.2998 836.0745 #>  [54,] 829.3429 830.4762 831.5367 832.5290 833.4576 834.3265 835.1395 835.9001 #>  [55,] 829.3332 830.4359 831.4695 832.4382 833.3458 834.1961 834.9924 835.7380 #>  [56,] 829.3418 830.4129 831.4186 832.3626 833.2483 834.0791 834.8579 835.5879 #>  [57,] 829.3676 830.4062 831.3831 832.3016 833.1646 833.9750 834.7357 835.4493 #>  [58,] 829.4097 830.4149 831.3623 832.2544 833.0940 833.8834 834.6252 835.3218 #>  [59,] 829.4668 830.4380 831.3552 832.2204 833.0359 833.8037 834.5261 835.2051 #>  [60,] 829.5379 830.4746 831.3611 832.1989 832.9897 833.7353 834.4377 835.0987 #>  [61,] 829.6219 830.5239 831.3792 832.1891 832.9548 833.6778 834.3597 835.0022 #>  [62,] 829.7178 830.5848 831.4087 832.1903 832.9305 833.6305 834.2916 834.9152 #>  [63,] 829.8245 830.6564 831.4488 832.2019 832.9163 833.5930 834.2329 834.8372 #>  [64,] 829.9411 830.7380 831.4987 832.2231 832.9116 833.5646 834.1831 834.7678 #>  [65,] 830.0667 830.8287 831.5577 832.2533 832.9157 833.5450 834.1417 834.7066 #>  [66,] 830.2003 830.9276 831.6250 832.2919 832.9280 833.5334 834.1083 834.6532 #>  [67,] 830.3411 831.0340 831.7000 832.3382 832.9481 833.5295 834.0824 834.6071 #>  [68,] 830.4882 831.1471 831.7819 832.3916 832.9753 833.5327 834.0635 834.5680 #>  [69,] 830.6409 831.2662 831.8702 832.4515 833.0091 833.5425 834.0513 834.5354 #>  [70,] 830.7985 831.3907 831.9641 832.5173 833.0490 833.5584 834.0452 834.5090 #>  [71,] 830.9603 831.5198 832.0631 832.5884 833.0944 833.5801 834.0448 834.4883 #>  [72,] 831.1255 831.6531 832.1667 832.6645 833.1449 833.6069 834.0498 834.4730 #>  [73,] 831.2936 831.7898 832.2742 832.7448 833.2000 833.6386 834.0597 834.4627 #>  [74,] 831.4641 831.9295 832.3852 832.8290 833.2593 833.6747 834.0742 834.4570 #>  [75,] 831.6363 832.0716 832.4991 832.9166 833.3223 833.7147 834.0928 834.4557 #>  [76,] 831.8098 832.2157 832.6156 833.0072 833.3886 833.7584 834.1152 834.4583 #>  [77,] 831.9842 832.3613 832.7342 833.1003 833.4579 833.8053 834.1411 834.4645 #>  [78,] 832.1589 832.5080 832.8544 833.1956 833.5297 833.8550 834.1702 834.4741 #>  [79,] 832.3337 832.6555 832.9759 833.2927 833.6037 833.9073 834.2020 834.4867 #>  [80,] 832.5080 832.8032 833.0984 833.3912 833.6796 833.9618 834.2364 834.5021 #>  [81,] 832.6817 832.9510 833.2215 833.4909 833.7570 834.0182 834.2729 834.5199 #>  [82,] 832.8544 833.0984 833.3449 833.5913 833.8357 834.0763 834.3115 834.5399 #>  [83,] 833.0258 833.2453 833.4682 833.6923 833.9154 834.1357 834.3516 834.5619 #>  [84,] 833.1956 833.3912 833.5913 833.7935 833.9958 834.1962 834.3933 834.5856 #>  [85,] 833.3637 833.5361 833.7139 833.8948 834.0766 834.2575 834.4360 834.6107 #>  [86,] 833.5297 833.6796 833.8357 833.9958 834.1576 834.3195 834.4798 834.6371 #>  [87,] 833.6935 833.8216 833.9566 834.0963 834.2387 834.3819 834.5243 834.6646 #>  [88,] 833.8550 833.9618 834.0763 834.1962 834.3195 834.4444 834.5694 834.6929 #>  [89,] 834.0139 834.1001 834.1946 834.2952 834.3999 834.5070 834.6147 834.7219 #>  [90,] 834.1702 834.2364 834.3115 834.3933 834.4798 834.5694 834.6603 834.7513 #>  [91,] 834.3236 834.3704 834.4266 834.4901 834.5589 834.6314 834.7059 834.7810 #>  [92,] 834.4741 834.5021 834.5399 834.5856 834.6371 834.6929 834.7513 834.8109 #>  [93,] 834.6216 834.6313 834.6513 834.6796 834.7143 834.7538 834.7964 834.8408 #>  [94,] 834.7660 834.7580 834.7607 834.7721 834.7903 834.8138 834.8410 834.8706 #>  [95,] 834.9071 834.8820 834.8678 834.8628 834.8650 834.8730 834.8851 834.9001 #>  [96,] 835.0450 835.0032 834.9727 834.9517 834.9383 834.9311 834.9285 834.9292 #>  [97,] 835.1796 835.1216 835.0752 835.0386 835.0101 834.9880 834.9710 834.9577 #>  [98,] 835.3107 835.2371 835.1753 835.1236 835.0802 835.0437 835.0126 834.9857 #>  [99,] 835.4385 835.3497 835.2729 835.2064 835.1486 835.0980 835.0532 835.0129 #> [100,] 835.5628 835.4593 835.3679 835.2871 835.2153 835.1509 835.0926 835.0392 #>           [,97]    [,98]    [,99]   [,100] #>   [1,] 863.0421 863.2839 863.5147 863.7339 #>   [2,] 862.3298 862.5885 862.8351 863.0691 #>   [3,] 861.6204 861.8960 862.1586 862.4076 #>   [4,] 860.9141 861.2069 861.4854 861.7495 #>   [5,] 860.2113 860.5212 860.8159 861.0951 #>   [6,] 859.5122 859.8394 860.1503 860.4446 #>   [7,] 858.8171 859.1617 859.4888 859.7983 #>   [8,] 858.1263 858.4884 858.8317 859.1564 #>   [9,] 857.4402 857.8197 858.1793 858.5191 #>  [10,] 856.7590 857.1560 857.5319 857.8867 #>  [11,] 856.0832 856.4976 856.8896 857.2595 #>  [12,] 855.4130 855.8448 856.2530 856.6378 #>  [13,] 854.7489 855.1980 855.6221 856.0217 #>  [14,] 854.0911 854.5574 854.9974 855.4117 #>  [15,] 853.4400 853.9234 854.3791 854.8079 #>  [16,] 852.7960 853.2963 853.7675 854.2106 #>  [17,] 852.1595 852.6765 853.1630 853.6201 #>  [18,] 851.5309 852.0642 852.5658 853.0367 #>  [19,] 850.9105 851.4600 851.9762 852.4607 #>  [20,] 850.2988 850.8640 851.3946 851.8923 #>  [21,] 849.6960 850.2766 850.8213 851.3318 #>  [22,] 849.1026 849.6982 850.2565 850.7795 #>  [23,] 848.5190 849.1290 849.7006 850.2356 #>  [24,] 847.9455 848.5695 849.1538 849.7004 #>  [25,] 847.3824 848.0199 848.6165 849.1742 #>  [26,] 846.8302 847.4806 848.0888 848.6571 #>  [27,] 846.2892 846.9518 847.5711 848.1495 #>  [28,] 845.7597 846.4339 847.0636 847.6515 #>  [29,] 845.2420 845.9270 846.5666 847.1633 #>  [30,] 844.7364 845.4316 846.0803 846.6853 #>  [31,] 844.2432 844.9477 845.6048 846.2175 #>  [32,] 843.7627 844.4757 845.1405 845.7601 #>  [33,] 843.2951 844.0158 844.6875 845.3133 #>  [34,] 842.8406 843.5681 844.2459 844.8772 #>  [35,] 842.3995 843.1329 843.8160 844.4520 #>  [36,] 841.9719 842.7102 843.3977 844.0378 #>  [37,] 841.5579 842.3002 842.9913 843.6347 #>  [38,] 841.1576 841.9030 842.5969 843.2427 #>  [39,] 840.7713 841.5187 842.2144 842.8619 #>  [40,] 840.3988 841.1474 841.8440 842.4924 #>  [41,] 840.0403 840.7889 841.4857 842.1342 #>  [42,] 839.6957 840.4435 841.1395 841.7872 #>  [43,] 839.3651 840.1110 840.8052 841.4515 #>  [44,] 839.0483 839.7913 840.4831 841.1270 #>  [45,] 838.7453 839.4845 840.1728 840.8136 #>  [46,] 838.4559 839.1904 839.8744 840.5114 #>  [47,] 838.1801 838.9089 839.5878 840.2201 #>  [48,] 837.9177 838.6399 839.3128 839.9398 #>  [49,] 837.6684 838.3831 839.0493 839.6702 #>  [50,] 837.4321 838.1384 838.7971 839.4112 #>  [51,] 837.2086 837.9057 838.5561 839.1627 #>  [52,] 836.9974 837.6846 838.3260 838.9245 #>  [53,] 836.7985 837.4749 838.1067 838.6964 #>  [54,] 836.6114 837.2764 837.8978 838.4782 #>  [55,] 836.4359 837.0888 837.6993 838.2696 #>  [56,] 836.2717 836.9118 837.5107 838.0706 #>  [57,] 836.1183 836.7451 837.3319 837.8808 #>  [58,] 835.9755 836.5884 837.1626 837.6999 #>  [59,] 835.8429 836.4414 837.0024 837.5278 #>  [60,] 835.7201 836.3037 836.8512 837.3642 #>  [61,] 835.6068 836.1751 836.7086 837.2089 #>  [62,] 835.5026 836.0551 836.5743 837.0615 #>  [63,] 835.4070 835.9435 836.4481 836.9217 #>  [64,] 835.3197 835.8400 836.3295 836.7894 #>  [65,] 835.2404 835.7440 836.2183 836.6642 #>  [66,] 835.1687 835.6555 836.1143 836.5459 #>  [67,] 835.1041 835.5739 836.0170 836.4342 #>  [68,] 835.0463 835.4989 835.9262 836.3288 #>  [69,] 834.9950 835.4303 835.8416 836.2294 #>  [70,] 834.9498 835.3677 835.7629 836.1358 #>  [71,] 834.9103 835.3107 835.6898 836.0477 #>  [72,] 834.8761 835.2591 835.6220 835.9648 #>  [73,] 834.8470 835.2126 835.5592 835.8869 #>  [74,] 834.8227 835.1708 835.5011 835.8136 #>  [75,] 834.8027 835.1334 835.4475 835.7449 #>  [76,] 834.7867 835.1001 835.3981 835.6803 #>  [77,] 834.7746 835.0708 835.3526 835.6197 #>  [78,] 834.7660 835.0450 835.3107 835.5628 #>  [79,] 834.7605 835.0226 835.2723 835.5094 #>  [80,] 834.7580 835.0032 835.2371 835.4593 #>  [81,] 834.7581 834.9867 835.2049 835.4122 #>  [82,] 834.7607 834.9727 835.1753 835.3679 #>  [83,] 834.7654 834.9611 835.1483 835.3263 #>  [84,] 834.7721 834.9517 835.1236 835.2871 #>  [85,] 834.7804 834.9441 835.1009 835.2502 #>  [86,] 834.7903 834.9383 835.0802 835.2153 #>  [87,] 834.8015 834.9340 835.0612 835.1822 #>  [88,] 834.8138 834.9311 835.0437 835.1509 #>  [89,] 834.8271 834.9293 835.0275 835.1211 #>  [90,] 834.8410 834.9285 835.0126 835.0926 #>  [91,] 834.8556 834.9285 834.9987 835.0654 #>  [92,] 834.8706 834.9292 834.9857 835.0392 #>  [93,] 834.8859 834.9304 834.9734 835.0140 #>  [94,] 834.9013 834.9320 834.9617 834.9895 #>  [95,] 834.9167 834.9338 834.9505 834.9657 #>  [96,] 834.9320 834.9358 834.9396 834.9425 #>  [97,] 834.9470 834.9377 834.9289 834.9197 #>  [98,] 834.9617 834.9396 834.9184 834.8972 #>  [99,] 834.9759 834.9412 834.9078 834.8748 #> [100,] 834.9895 834.9425 834.8972 834.8526  phi <- potential(m, x = xg, y = yg, as.grid = TRUE) phic <- potential(mc, x = xg, y = yg, as.grid = TRUE) potential_to_head(m, phi) #>            [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8] #>   [1,] 9.616683 9.603693 9.590617 9.577451 9.564195 9.550846 9.537402 9.523861 #>   [2,] 9.612188 9.599171 9.586066 9.572871 9.559584 9.546204 9.532727 9.519152 #>   [3,] 9.607709 9.594665 9.581532 9.568308 9.554991 9.541579 9.528070 9.514461 #>   [4,] 9.603244 9.590174 9.577013 9.563760 9.550414 9.536971 9.523430 9.509788 #>   [5,] 9.598795 9.585698 9.572511 9.559230 9.545854 9.532381 9.518809 9.505134 #>   [6,] 9.594362 9.581239 9.568025 9.554717 9.541312 9.527809 9.514206 9.500499 #>   [7,] 9.589945 9.576797 9.563556 9.550220 9.536788 9.523256 9.509622 9.495883 #>   [8,] 9.585543 9.572370 9.559104 9.545741 9.532281 9.518720 9.505056 9.491287 #>   [9,] 9.581158 9.567961 9.554669 9.541280 9.527793 9.514204 9.500510 9.486710 #>  [10,] 9.576790 9.563568 9.550252 9.536837 9.523323 9.509706 9.495984 9.482154 #>  [11,] 9.572438 9.559193 9.545852 9.532412 9.518872 9.505228 9.491477 9.477618 #>  [12,] 9.568104 9.554835 9.541470 9.528006 9.514440 9.500769 9.486991 9.473102 #>  [13,] 9.563786 9.550495 9.537107 9.523618 9.510027 9.496330 9.482524 9.468608 #>  [14,] 9.559485 9.546173 9.532761 9.519249 9.505633 9.491911 9.478079 9.464135 #>  [15,] 9.555203 9.541868 9.528435 9.514899 9.501259 9.487512 9.473654 9.459683 #>  [16,] 9.550937 9.537582 9.524127 9.510568 9.496905 9.483133 9.469251 9.455254 #>  [17,] 9.546690 9.533314 9.519837 9.506257 9.492571 9.478776 9.464869 9.450846 #>  [18,] 9.542460 9.529065 9.515567 9.501966 9.488258 9.474439 9.460508 9.446461 #>  [19,] 9.538249 9.524834 9.511317 9.497695 9.483965 9.470124 9.456169 9.442098 #>  [20,] 9.534056 9.520622 9.507086 9.493443 9.479692 9.465830 9.451853 9.437758 #>  [21,] 9.529882 9.516430 9.502874 9.489212 9.475441 9.461557 9.447559 9.433441 #>  [22,] 9.525726 9.512256 9.498682 9.485001 9.471211 9.457307 9.443287 9.429147 #>  [23,] 9.521589 9.508102 9.494511 9.480811 9.467002 9.453078 9.439038 9.424877 #>  [24,] 9.517471 9.503968 9.490359 9.476642 9.462814 9.448872 9.434812 9.420630 #>  [25,] 9.513373 9.499853 9.486228 9.472494 9.458648 9.444688 9.430609 9.416408 #>  [26,] 9.509293 9.495758 9.482117 9.468367 9.454504 9.440526 9.426429 9.412209 #>  [27,] 9.505233 9.491683 9.478027 9.464261 9.450382 9.436387 9.422273 9.408035 #>  [28,] 9.501192 9.487628 9.473957 9.460176 9.446282 9.432271 9.418140 9.403885 #>  [29,] 9.497170 9.483593 9.469909 9.456114 9.442204 9.428178 9.414031 9.399760 #>  [30,] 9.493169 9.479579 9.465881 9.452072 9.438149 9.424108 9.409946 9.395660 #>  [31,] 9.489187 9.475585 9.461874 9.448053 9.434116 9.420062 9.405886 9.391584 #>  [32,] 9.485224 9.471611 9.457889 9.444055 9.430106 9.416038 9.401849 9.387534 #>  [33,] 9.481282 9.467658 9.453925 9.440079 9.426118 9.412039 9.397837 9.383508 #>  [34,] 9.477360 9.463726 9.449982 9.436126 9.422154 9.408063 9.393849 9.379508 #>  [35,] 9.473458 9.459814 9.446061 9.432194 9.418212 9.404110 9.389885 9.375534 #>  [36,] 9.469576 9.455923 9.442161 9.428285 9.414293 9.400182 9.385947 9.371584 #>  [37,] 9.465715 9.452053 9.438282 9.424398 9.410397 9.396277 9.382033 9.367661 #>  [38,] 9.461873 9.448205 9.434426 9.420534 9.406525 9.392396 9.378143 9.363763 #>  [39,] 9.458052 9.444377 9.430591 9.416691 9.402675 9.388539 9.374279 9.359891 #>  [40,] 9.454251 9.440570 9.426777 9.412872 9.398849 9.384706 9.370439 9.356045 #>  [41,] 9.450471 9.436784 9.422986 9.409075 9.395046 9.380898 9.366625 9.352224 #>  [42,] 9.446711 9.433019 9.419216 9.405300 9.391267 9.377113 9.362835 9.348429 #>  [43,] 9.442972 9.429275 9.415468 9.401548 9.387510 9.373353 9.359070 9.344660 #>  [44,] 9.439253 9.425553 9.411742 9.397818 9.383777 9.369616 9.355331 9.340917 #>  [45,] 9.435554 9.421851 9.408038 9.394111 9.380068 9.365904 9.351616 9.337200 #>  [46,] 9.431876 9.418171 9.404356 9.390427 9.376382 9.362216 9.347926 9.333509 #>  [47,] 9.428218 9.414512 9.400695 9.386765 9.372719 9.358552 9.344262 9.329844 #>  [48,] 9.424581 9.410873 9.397056 9.383126 9.369079 9.354912 9.340622 9.326204 #>  [49,] 9.420964 9.407256 9.393439 9.379509 9.365462 9.351296 9.337007 9.322591 #>  [50,] 9.417367 9.403660 9.389844 9.375914 9.361869 9.347705 9.333417 9.319003 #>  [51,] 9.413791 9.400085 9.386270 9.372342 9.358299 9.344137 9.329852 9.315440 #>  [52,] 9.410235 9.396531 9.382718 9.368793 9.354752 9.340593 9.326311 9.311903 #>  [53,] 9.406699 9.392998 9.379187 9.365265 9.351228 9.337073 9.322795 9.308392 #>  [54,] 9.403184 9.389485 9.375678 9.361760 9.347727 9.333576 9.319304 9.304906 #>  [55,] 9.399688 9.385994 9.372191 9.358277 9.344249 9.330104 9.315837 9.301446 #>  [56,] 9.396213 9.382523 9.368725 9.354816 9.340794 9.326654 9.312394 9.298010 #>  [57,] 9.392757 9.379072 9.365280 9.351377 9.337361 9.323229 9.308976 9.294600 #>  [58,] 9.389322 9.375642 9.361856 9.347960 9.333951 9.319826 9.305582 9.291215 #>  [59,] 9.385906 9.372233 9.358453 9.344565 9.330564 9.316447 9.302212 9.287854 #>  [60,] 9.382510 9.368844 9.355072 9.341191 9.327198 9.313091 9.298865 9.284518 #>  [61,] 9.379134 9.365475 9.351711 9.337839 9.323855 9.309758 9.295543 9.281207 #>  [62,] 9.375777 9.362126 9.348371 9.334508 9.320534 9.306447 9.292244 9.277920 #>  [63,] 9.372439 9.358797 9.345051 9.331198 9.317235 9.303160 9.288968 9.274657 #>  [64,] 9.369121 9.355488 9.341752 9.327909 9.313958 9.299894 9.285715 9.271418 #>  [65,] 9.365822 9.352199 9.338473 9.324642 9.310702 9.296651 9.282486 9.268203 #>  [66,] 9.362541 9.348929 9.335215 9.321395 9.307468 9.293430 9.279279 9.265011 #>  [67,] 9.359280 9.345679 9.331976 9.318169 9.304255 9.290231 9.276095 9.261843 #>  [68,] 9.356037 9.342448 9.328757 9.314963 9.301063 9.287054 9.272933 9.258698 #>  [69,] 9.352813 9.339236 9.325558 9.311778 9.297892 9.283898 9.269794 9.255575 #>  [70,] 9.349608 9.336043 9.322379 9.308613 9.294742 9.280764 9.266676 9.252476 #>  [71,] 9.346421 9.332869 9.319219 9.305467 9.291612 9.277651 9.263581 9.249398 #>  [72,] 9.343251 9.329714 9.316078 9.302342 9.288503 9.274559 9.260506 9.246343 #>  [73,] 9.340100 9.326577 9.312956 9.299236 9.285414 9.271487 9.257454 9.243310 #>  [74,] 9.336967 9.323458 9.309853 9.296149 9.282344 9.268436 9.254422 9.240299 #>  [75,] 9.333851 9.320357 9.306768 9.293081 9.279295 9.265405 9.251411 9.237309 #>  [76,] 9.330753 9.317275 9.303702 9.290033 9.276264 9.262394 9.248421 9.234340 #>  [77,] 9.327671 9.314210 9.300654 9.287003 9.273253 9.259403 9.245451 9.231393 #>  [78,] 9.324607 9.311162 9.297624 9.283991 9.270261 9.256432 9.242501 9.228465 #>  [79,] 9.321560 9.308132 9.294612 9.280998 9.267288 9.253480 9.239570 9.225558 #>  [80,] 9.318530 9.305119 9.291618 9.278023 9.264333 9.250546 9.236660 9.222672 #>  [81,] 9.315516 9.302123 9.288641 9.275066 9.261397 9.247632 9.233768 9.219804 #>  [82,] 9.312518 9.299144 9.285681 9.272126 9.258479 9.244736 9.230896 9.216957 #>  [83,] 9.309537 9.296182 9.282738 9.269204 9.255578 9.241858 9.228042 9.214129 #>  [84,] 9.306571 9.293235 9.279812 9.266299 9.252695 9.238999 9.225207 9.211319 #>  [85,] 9.303621 9.290305 9.276902 9.263411 9.249830 9.236157 9.222390 9.208528 #>  [86,] 9.300687 9.287390 9.274008 9.260539 9.246981 9.233332 9.219591 9.205755 #>  [87,] 9.297768 9.284492 9.271131 9.257684 9.244149 9.230525 9.216809 9.203001 #>  [88,] 9.294864 9.281608 9.268269 9.254845 9.241334 9.227734 9.214045 9.200264 #>  [89,] 9.291975 9.278740 9.265423 9.252021 9.238535 9.224961 9.211298 9.197544 #>  [90,] 9.289100 9.275887 9.262592 9.249214 9.235751 9.222203 9.208567 9.194842 #>  [91,] 9.286240 9.273048 9.259776 9.246422 9.232984 9.219462 9.205853 9.192156 #>  [92,] 9.283395 9.270225 9.256975 9.243645 9.230232 9.216736 9.203155 9.189487 #>  [93,] 9.280563 9.267415 9.254189 9.240883 9.227495 9.214026 9.200472 9.186834 #>  [94,] 9.277745 9.264619 9.251417 9.238135 9.224774 9.211331 9.197806 9.184196 #>  [95,] 9.274940 9.261838 9.248659 9.235402 9.222067 9.208651 9.195154 9.181574 #>  [96,] 9.272149 9.259070 9.245915 9.232683 9.219374 9.205986 9.192517 9.178968 #>  [97,] 9.269371 9.256315 9.243184 9.229978 9.216695 9.203335 9.189895 9.176376 #>  [98,] 9.266606 9.253573 9.240467 9.227287 9.214031 9.200698 9.187288 9.173799 #>  [99,] 9.263854 9.250845 9.237763 9.224608 9.211379 9.198075 9.184694 9.171236 #> [100,] 9.261114 9.248128 9.235072 9.221943 9.208741 9.195465 9.182114 9.168687 #>            [,9]    [,10]    [,11]    [,12]    [,13]    [,14]    [,15]    [,16] #>   [1,] 9.510220 9.496478 9.482633 9.468681 9.454621 9.440449 9.426164 9.411762 #>   [2,] 9.505476 9.491697 9.477814 9.463822 9.449720 9.435505 9.421175 9.406726 #>   [3,] 9.500750 9.486935 9.473014 9.458983 9.444840 9.430582 9.416207 9.401711 #>   [4,] 9.496043 9.482192 9.468233 9.454163 9.439980 9.425680 9.411261 9.396719 #>   [5,] 9.491355 9.477469 9.463473 9.449365 9.435142 9.420800 9.406337 9.391750 #>   [6,] 9.486687 9.472766 9.458734 9.444588 9.430325 9.415942 9.401437 9.386805 #>   [7,] 9.482038 9.468083 9.454015 9.439832 9.425530 9.411107 9.396559 9.381884 #>   [8,] 9.477409 9.463420 9.449318 9.435098 9.420758 9.406295 9.391706 9.376987 #>   [9,] 9.472801 9.458779 9.444642 9.430386 9.416009 9.401507 9.386877 9.372115 #>  [10,] 9.468213 9.454159 9.439988 9.425697 9.411283 9.396743 9.382072 9.367268 #>  [11,] 9.463647 9.449560 9.435356 9.421031 9.406581 9.392003 9.377293 9.362448 #>  [12,] 9.459101 9.444984 9.430747 9.416388 9.401903 9.387288 9.372540 9.357654 #>  [13,] 9.454578 9.440430 9.426161 9.411769 9.397249 9.382598 9.367812 9.352887 #>  [14,] 9.450076 9.435898 9.421599 9.407174 9.392620 9.377934 9.363111 9.348147 #>  [15,] 9.445596 9.431390 9.417060 9.402603 9.388017 9.373296 9.358437 9.343435 #>  [16,] 9.441139 9.426904 9.412545 9.398057 9.383438 9.368684 9.353790 9.338752 #>  [17,] 9.436705 9.422442 9.408054 9.393537 9.378886 9.364099 9.349171 9.334097 #>  [18,] 9.432294 9.418004 9.403588 9.389041 9.374360 9.359541 9.344580 9.329471 #>  [19,] 9.427906 9.413590 9.399146 9.384572 9.369861 9.355011 9.340017 9.324874 #>  [20,] 9.423542 9.409200 9.394730 9.380128 9.365389 9.350509 9.335483 9.320308 #>  [21,] 9.419201 9.404835 9.390340 9.375711 9.360944 9.346035 9.330979 9.315771 #>  [22,] 9.414884 9.400495 9.385975 9.371320 9.356526 9.341589 9.326504 9.311266 #>  [23,] 9.410592 9.396180 9.381636 9.366956 9.352136 9.337172 9.322059 9.306791 #>  [24,] 9.406325 9.391890 9.377323 9.362620 9.347775 9.332785 9.317644 9.302348 #>  [25,] 9.402082 9.387626 9.373037 9.358310 9.343442 9.328427 9.313260 9.297937 #>  [26,] 9.397863 9.383387 9.368777 9.354029 9.339137 9.324098 9.308907 9.293557 #>  [27,] 9.393670 9.379175 9.364545 9.349775 9.334862 9.319800 9.304584 9.289210 #>  [28,] 9.389503 9.374989 9.360339 9.345550 9.330615 9.315532 9.300294 9.284896 #>  [29,] 9.385361 9.370829 9.356161 9.341353 9.326399 9.311294 9.296035 9.280614 #>  [30,] 9.381244 9.366696 9.352011 9.337184 9.322211 9.307087 9.291807 9.276366 #>  [31,] 9.377153 9.362589 9.347888 9.333044 9.318054 9.302912 9.287612 9.272151 #>  [32,] 9.373088 9.358510 9.343793 9.328933 9.313926 9.298767 9.283450 9.267970 #>  [33,] 9.369050 9.354457 9.339726 9.324851 9.309829 9.294653 9.279320 9.263822 #>  [34,] 9.365037 9.350432 9.335687 9.320798 9.305762 9.290571 9.275222 9.259709 #>  [35,] 9.361051 9.346433 9.331676 9.316775 9.301725 9.286521 9.271158 9.255630 #>  [36,] 9.357091 9.342462 9.327694 9.312781 9.297719 9.282503 9.267126 9.251585 #>  [37,] 9.353158 9.338519 9.323740 9.308817 9.293744 9.278516 9.263128 9.247574 #>  [38,] 9.349251 9.334603 9.319815 9.304882 9.289799 9.274562 9.259163 9.243599 #>  [39,] 9.345371 9.330715 9.315919 9.300977 9.285886 9.270639 9.255232 9.239658 #>  [40,] 9.341518 9.326855 9.312051 9.297102 9.282003 9.266749 9.251334 9.235752 #>  [41,] 9.337691 9.323022 9.308212 9.293257 9.278152 9.262891 9.247469 9.231880 #>  [42,] 9.333891 9.319217 9.304402 9.289442 9.274331 9.259065 9.243638 9.228044 #>  [43,] 9.330118 9.315440 9.300621 9.285657 9.270542 9.255272 9.239841 9.224243 #>  [44,] 9.326372 9.311691 9.296869 9.281901 9.266784 9.251511 9.236077 9.220476 #>  [45,] 9.322653 9.307969 9.293145 9.278176 9.263056 9.247782 9.232347 9.216745 #>  [46,] 9.318960 9.304275 9.289450 9.274480 9.259360 9.244085 9.228650 9.213049 #>  [47,] 9.315294 9.300609 9.285784 9.270814 9.255695 9.240421 9.224987 9.209387 #>  [48,] 9.311655 9.296971 9.282147 9.267179 9.252061 9.236789 9.221357 9.205760 #>  [49,] 9.308043 9.293361 9.278539 9.263573 9.248458 9.233189 9.217761 9.202168 #>  [50,] 9.304458 9.289778 9.274959 9.259996 9.244885 9.229621 9.214198 9.198611 #>  [51,] 9.300898 9.286222 9.271408 9.256450 9.241344 9.226085 9.210668 9.195088 #>  [52,] 9.297366 9.282694 9.267885 9.252933 9.237833 9.222581 9.207171 9.191599 #>  [53,] 9.293860 9.279194 9.264390 9.249445 9.234352 9.219108 9.203708 9.188145 #>  [54,] 9.290380 9.275721 9.260924 9.245986 9.230902 9.215667 9.200277 9.184724 #>  [55,] 9.286926 9.272274 9.257486 9.242557 9.227483 9.212258 9.196878 9.181338 #>  [56,] 9.283499 9.268855 9.254076 9.239157 9.224093 9.208879 9.193512 9.177985 #>  [57,] 9.280097 9.265463 9.250694 9.235785 9.220733 9.205532 9.190178 9.174665 #>  [58,] 9.276721 9.262097 9.247339 9.232442 9.217403 9.202215 9.186876 9.171379 #>  [59,] 9.273371 9.258758 9.244012 9.229128 9.214102 9.198929 9.183606 9.168125 #>  [60,] 9.270046 9.255446 9.240712 9.225842 9.210830 9.195674 9.180367 9.164905 #>  [61,] 9.266747 9.252159 9.237439 9.222584 9.207588 9.192448 9.177159 9.161716 #>  [62,] 9.263473 9.248899 9.234193 9.219353 9.204374 9.189252 9.173982 9.158560 #>  [63,] 9.260224 9.245664 9.230974 9.216151 9.201189 9.186086 9.170836 9.155435 #>  [64,] 9.256999 9.242455 9.227781 9.212975 9.198033 9.182949 9.167720 9.152342 #>  [65,] 9.253799 9.239271 9.224615 9.209827 9.194904 9.179841 9.164634 9.149279 #>  [66,] 9.250623 9.236112 9.221474 9.206706 9.191803 9.176762 9.161578 9.146248 #>  [67,] 9.247472 9.232978 9.218359 9.203611 9.188729 9.173711 9.158551 9.143247 #>  [68,] 9.244344 9.229869 9.215270 9.200542 9.185683 9.170688 9.155553 9.140275 #>  [69,] 9.241240 9.226784 9.212205 9.197499 9.182663 9.167693 9.152584 9.137334 #>  [70,] 9.238159 9.223723 9.209166 9.194482 9.179670 9.164725 9.149643 9.134421 #>  [71,] 9.235101 9.220687 9.206151 9.191491 9.176703 9.161784 9.146730 9.131538 #>  [72,] 9.232067 9.217673 9.203160 9.188524 9.173762 9.158870 9.143845 9.128682 #>  [73,] 9.229055 9.214683 9.200194 9.185582 9.170846 9.155982 9.140986 9.125855 #>  [74,] 9.226065 9.211716 9.197251 9.182665 9.167956 9.153120 9.138154 9.123055 #>  [75,] 9.223097 9.208772 9.194331 9.179772 9.165090 9.150284 9.135349 9.120283 #>  [76,] 9.220151 9.205850 9.191435 9.176902 9.162249 9.147472 9.132569 9.117537 #>  [77,] 9.217227 9.202950 9.188561 9.174056 9.159432 9.144686 9.129815 9.114817 #>  [78,] 9.214323 9.200072 9.185710 9.171232 9.156638 9.141924 9.127086 9.112123 #>  [79,] 9.211441 9.197216 9.182880 9.168432 9.153868 9.139185 9.124382 9.109454 #>  [80,] 9.208579 9.194380 9.180073 9.165654 9.151120 9.136471 9.121701 9.106810 #>  [81,] 9.205738 9.191566 9.177286 9.162897 9.148396 9.133779 9.119045 9.104191 #>  [82,] 9.202916 9.188772 9.174521 9.160163 9.145693 9.131110 9.116412 9.101595 #>  [83,] 9.200114 9.185998 9.171777 9.157449 9.143012 9.128464 9.113801 9.099023 #>  [84,] 9.197332 9.183244 9.169053 9.154756 9.140352 9.125839 9.111213 9.096473 #>  [85,] 9.194568 9.180509 9.166349 9.152084 9.137714 9.123236 9.108647 9.093946 #>  [86,] 9.191824 9.177794 9.163664 9.149432 9.135096 9.120653 9.106103 9.091441 #>  [87,] 9.189097 9.175097 9.160999 9.146800 9.132498 9.118092 9.103579 9.088958 #>  [88,] 9.186389 9.172419 9.158352 9.144186 9.129920 9.115550 9.101076 9.086496 #>  [89,] 9.183699 9.169759 9.155725 9.141592 9.127361 9.113028 9.098593 9.084054 #>  [90,] 9.181026 9.167117 9.153115 9.139017 9.124821 9.110526 9.096130 9.081632 #>  [91,] 9.178370 9.164493 9.150523 9.136459 9.122299 9.108042 9.093686 9.079230 #>  [92,] 9.175731 9.161885 9.147949 9.133919 9.119796 9.105577 9.091261 9.076847 #>  [93,] 9.173108 9.159294 9.145391 9.131397 9.117311 9.103130 9.088855 9.074482 #>  [94,] 9.170501 9.156720 9.142851 9.128892 9.114842 9.100701 9.086466 9.072136 #>  [95,] 9.167911 9.154162 9.140326 9.126403 9.112391 9.098288 9.084094 9.069808 #>  [96,] 9.165335 9.151619 9.137818 9.123931 9.109956 9.095893 9.081740 9.067496 #>  [97,] 9.162775 9.149092 9.135325 9.121474 9.107537 9.093514 9.079402 9.065202 #>  [98,] 9.160230 9.146580 9.132848 9.119033 9.105134 9.091150 9.077080 9.062923 #>  [99,] 9.157699 9.144082 9.130386 9.116607 9.102746 9.088802 9.074774 9.060661 #> [100,] 9.155182 9.141599 9.127938 9.114196 9.100374 9.086470 9.072483 9.058413 #>           [,17]    [,18]    [,19]    [,20]    [,21]    [,22]    [,23]    [,24] #>   [1,] 9.397241 9.382599 9.367832 9.352937 9.337912 9.322753 9.307458 9.292023 #>   [2,] 9.392156 9.377462 9.362640 9.347689 9.332605 9.317384 9.302024 9.286521 #>   [3,] 9.387092 9.372347 9.357473 9.342466 9.327323 9.312041 9.296617 9.281046 #>   [4,] 9.382052 9.367257 9.352330 9.337268 9.322067 9.306724 9.291236 9.275598 #>   [5,] 9.377036 9.362191 9.347212 9.332095 9.316837 9.301434 9.285883 9.270179 #>   [6,] 9.372044 9.357149 9.342119 9.326948 9.311634 9.296172 9.280558 9.264789 #>   [7,] 9.367076 9.352134 9.337052 9.321829 9.306459 9.290938 9.275263 9.259429 #>   [8,] 9.362134 9.347144 9.332013 9.316737 9.301312 9.285733 9.269997 9.254099 #>   [9,] 9.357217 9.342180 9.327000 9.311673 9.296194 9.280559 9.264763 9.248802 #>  [10,] 9.352327 9.337244 9.322016 9.306638 9.291105 9.275414 9.259560 9.243537 #>  [11,] 9.347463 9.332335 9.317060 9.301632 9.286047 9.270301 9.254389 9.238306 #>  [12,] 9.342627 9.327455 9.312133 9.296656 9.281020 9.265221 9.249252 9.233108 #>  [13,] 9.337819 9.322603 9.307235 9.291711 9.276025 9.260173 9.244148 9.227946 #>  [14,] 9.333039 9.317780 9.302368 9.286797 9.271062 9.255158 9.239079 9.222819 #>  [15,] 9.328287 9.312988 9.297532 9.281915 9.266132 9.250177 9.234045 9.217729 #>  [16,] 9.323565 9.308225 9.292727 9.277066 9.261236 9.245231 9.229047 9.212676 #>  [17,] 9.318872 9.303493 9.287954 9.272249 9.256373 9.240321 9.224086 9.207662 #>  [18,] 9.314210 9.298792 9.283213 9.267466 9.251546 9.235447 9.219162 9.202686 #>  [19,] 9.309578 9.294123 9.278505 9.262717 9.246753 9.230609 9.214277 9.197750 #>  [20,] 9.304977 9.289486 9.273830 9.258002 9.241997 9.225808 9.209430 9.192854 #>  [21,] 9.300408 9.284882 9.269189 9.253323 9.237277 9.221046 9.204622 9.187999 #>  [22,] 9.295870 9.280311 9.264582 9.248679 9.232594 9.216322 9.199855 9.183185 #>  [23,] 9.291364 9.275773 9.260010 9.244071 9.227949 9.211637 9.195128 9.178414 #>  [24,] 9.286891 9.271268 9.255473 9.239500 9.223341 9.206991 9.190442 9.173686 #>  [25,] 9.282451 9.266799 9.250972 9.234966 9.218772 9.202386 9.185798 9.169002 #>  [26,] 9.278045 9.262363 9.246507 9.230469 9.214242 9.197821 9.181196 9.164361 #>  [27,] 9.273672 9.257963 9.242078 9.226010 9.209752 9.193297 9.176638 9.159765 #>  [28,] 9.269332 9.253598 9.237685 9.221589 9.205301 9.188815 9.172122 9.155215 #>  [29,] 9.265027 9.249268 9.233330 9.217207 9.200891 9.184374 9.167650 9.150710 #>  [30,] 9.260757 9.244974 9.229012 9.212863 9.196521 9.179976 9.163223 9.146251 #>  [31,] 9.256521 9.240717 9.224732 9.208559 9.192191 9.175621 9.158840 9.141839 #>  [32,] 9.252320 9.236496 9.220490 9.204295 9.187904 9.171309 9.154502 9.137474 #>  [33,] 9.248155 9.232311 9.216285 9.200070 9.183657 9.167040 9.150209 9.133157 #>  [34,] 9.244025 9.228164 9.212120 9.195885 9.179453 9.162815 9.145962 9.128887 #>  [35,] 9.239930 9.224054 9.207993 9.191741 9.175291 9.158634 9.141761 9.124665 #>  [36,] 9.235871 9.219980 9.203905 9.187637 9.171171 9.154497 9.137607 9.120492 #>  [37,] 9.231849 9.215945 9.199856 9.183574 9.167093 9.150404 9.133498 9.116367 #>  [38,] 9.227862 9.211946 9.195846 9.179552 9.163058 9.146356 9.129437 9.112291 #>  [39,] 9.223911 9.207986 9.191875 9.175571 9.159066 9.142353 9.125422 9.108264 #>  [40,] 9.219997 9.204063 9.187944 9.171631 9.155117 9.138394 9.121454 9.104286 #>  [41,] 9.216119 9.200178 9.184052 9.167732 9.151211 9.134481 9.117533 9.100358 #>  [42,] 9.212277 9.196332 9.180199 9.163874 9.147348 9.130612 9.113659 9.096479 #>  [43,] 9.208472 9.192522 9.176387 9.160058 9.143528 9.126789 9.109832 9.092649 #>  [44,] 9.204703 9.188751 9.172614 9.156283 9.139751 9.123011 9.106053 9.088868 #>  [45,] 9.200971 9.185018 9.168880 9.152549 9.136017 9.119277 9.102320 9.085137 #>  [46,] 9.197275 9.181323 9.165186 9.148856 9.132326 9.115589 9.098635 9.081455 #>  [47,] 9.193615 9.177665 9.161531 9.145204 9.128679 9.111945 9.094996 9.077822 #>  [48,] 9.189992 9.174046 9.157916 9.141594 9.125074 9.108346 9.091404 9.074238 #>  [49,] 9.186404 9.170464 9.154339 9.138024 9.121511 9.104792 9.087859 9.070703 #>  [50,] 9.182853 9.166919 9.150802 9.134495 9.117991 9.101283 9.084360 9.067216 #>  [51,] 9.179338 9.163412 9.147304 9.131007 9.114514 9.097817 9.080908 9.063778 #>  [52,] 9.175858 9.159942 9.143845 9.127559 9.111079 9.094395 9.077501 9.060387 #>  [53,] 9.172414 9.156509 9.140424 9.124152 9.107685 9.091017 9.074140 9.057045 #>  [54,] 9.169005 9.153113 9.137041 9.120784 9.104333 9.087683 9.070824 9.053749 #>  [55,] 9.165631 9.149753 9.133697 9.117455 9.101023 9.084391 9.067554 9.050501 #>  [56,] 9.162293 9.146430 9.130390 9.114167 9.097753 9.081143 9.064327 9.047299 #>  [57,] 9.158989 9.143142 9.127121 9.110917 9.094525 9.077936 9.061145 9.044143 #>  [58,] 9.155719 9.139891 9.123889 9.107706 9.091336 9.074772 9.058007 9.041033 #>  [59,] 9.152484 9.136675 9.120694 9.104533 9.088187 9.071649 9.054912 9.037968 #>  [60,] 9.149282 9.133494 9.117535 9.101398 9.085078 9.068568 9.051860 9.034948 #>  [61,] 9.146114 9.130348 9.114413 9.098301 9.082008 9.065527 9.048850 9.031971 #>  [62,] 9.142980 9.127237 9.111326 9.095241 9.078977 9.062526 9.045882 9.029039 #>  [63,] 9.139878 9.124160 9.108275 9.092218 9.075983 9.059565 9.042955 9.026149 #>  [64,] 9.136809 9.121116 9.105259 9.089231 9.073028 9.056643 9.040069 9.023301 #>  [65,] 9.133771 9.118106 9.102277 9.086280 9.070110 9.053759 9.037223 9.020495 #>  [66,] 9.130766 9.115128 9.099330 9.083365 9.067228 9.050914 9.034417 9.017730 #>  [67,] 9.127792 9.112184 9.096416 9.080484 9.064382 9.048106 9.031649 9.015006 #>  [68,] 9.124849 9.109271 9.093535 9.077637 9.061572 9.045335 9.028920 9.012320 #>  [69,] 9.121937 9.106390 9.090687 9.074825 9.058798 9.042600 9.026228 9.009674 #>  [70,] 9.119055 9.103540 9.087872 9.072046 9.056057 9.039901 9.023573 9.007067 #>  [71,] 9.116203 9.100721 9.085088 9.069299 9.053351 9.037237 9.020954 9.004496 #>  [72,] 9.113380 9.097932 9.082335 9.066585 9.050678 9.034608 9.018371 9.001962 #>  [73,] 9.110585 9.095173 9.079613 9.063903 9.048037 9.032012 9.015823 8.999465 #>  [74,] 9.107819 9.092443 9.076921 9.061251 9.045429 9.029449 9.013309 8.997002 #>  [75,] 9.105081 9.089741 9.074259 9.058631 9.042852 9.026919 9.010828 8.994574 #>  [76,] 9.102371 9.087069 9.071626 9.056040 9.040306 9.024421 9.008380 8.992180 #>  [77,] 9.099687 9.084423 9.069022 9.053479 9.037790 9.021954 9.005964 8.989819 #>  [78,] 9.097030 9.081806 9.066445 9.050946 9.035304 9.019517 9.003580 8.987489 #>  [79,] 9.094399 9.079214 9.063896 9.048441 9.032847 9.017110 9.001226 8.985192 #>  [80,] 9.091794 9.076649 9.061374 9.045965 9.030418 9.014731 8.998901 8.982924 #>  [81,] 9.089213 9.074110 9.058878 9.043515 9.028017 9.012382 8.996606 8.980687 #>  [82,] 9.086657 9.071596 9.056408 9.041091 9.025643 9.010060 8.994339 8.978478 #>  [83,] 9.084125 9.069106 9.053963 9.038694 9.023295 9.007765 8.992100 8.976298 #>  [84,] 9.081616 9.066640 9.051543 9.036321 9.020973 9.005496 8.989887 8.974145 #>  [85,] 9.079131 9.064198 9.049147 9.033973 9.018676 9.003253 8.987701 8.972018 #>  [86,] 9.076668 9.061779 9.046774 9.031649 9.016404 9.001034 8.985540 8.969918 #>  [87,] 9.074226 9.059382 9.044424 9.029349 9.014155 8.998840 8.983403 8.967842 #>  [88,] 9.071807 9.057008 9.042096 9.027071 9.011929 8.996670 8.981291 8.965791 #>  [89,] 9.069408 9.054654 9.039790 9.024815 9.009726 8.994522 8.979202 8.963763 #>  [90,] 9.067030 9.052321 9.037505 9.022580 9.007545 8.992397 8.977135 8.961758 #>  [91,] 9.064671 9.050009 9.035241 9.020367 9.005385 8.990293 8.975090 8.959775 #>  [92,] 9.062332 9.047716 9.032997 9.018174 9.003245 8.988210 8.973066 8.957814 #>  [93,] 9.060012 9.045443 9.030773 9.016001 9.001126 8.986147 8.971063 8.955872 #>  [94,] 9.057711 9.043188 9.028567 9.013846 8.999026 8.984103 8.969079 8.953951 #>  [95,] 9.055427 9.040951 9.026380 9.011711 8.996944 8.982079 8.967114 8.952049 #>  [96,] 9.053161 9.038732 9.024210 9.009593 8.994881 8.980072 8.965167 8.950165 #>  [97,] 9.050911 9.036530 9.022058 9.007493 8.992835 8.978084 8.963238 8.948298 #>  [98,] 9.048678 9.034345 9.019922 9.005410 8.990806 8.976112 8.961326 8.946449 #>  [99,] 9.046461 9.032176 9.017803 9.003342 8.988794 8.974157 8.959431 8.944616 #> [100,] 9.044260 9.030022 9.015699 9.001291 8.986797 8.972217 8.957551 8.942799 #>           [,25]    [,26]    [,27]    [,28]    [,29]    [,30]    [,31]    [,32] #>   [1,] 9.276446 9.260724 9.244853 9.228830 9.212652 9.196317 9.179821 9.163162 #>   [2,] 9.270873 9.255075 9.239124 9.223017 9.206752 9.190323 9.173730 9.156967 #>   [3,] 9.265326 9.249453 9.233424 9.217234 9.200881 9.184360 9.167669 9.150803 #>   [4,] 9.259808 9.243861 9.227753 9.211481 9.195041 9.178428 9.161640 9.144672 #>   [5,] 9.254319 9.238298 9.222113 9.205759 9.189233 9.172529 9.155644 9.138574 #>   [6,] 9.248860 9.232766 9.216505 9.200070 9.183458 9.166664 9.149683 9.132512 #>   [7,] 9.243431 9.227266 9.210929 9.194414 9.177717 9.160834 9.143758 9.126486 #>   [8,] 9.238035 9.221799 9.205386 9.188792 9.172012 9.155040 9.137870 9.120499 #>   [9,] 9.232671 9.216365 9.199879 9.183207 9.166343 9.149284 9.132021 9.114551 #>  [10,] 9.227341 9.210966 9.194407 9.177657 9.160713 9.143567 9.126213 9.108644 #>  [11,] 9.222045 9.205602 9.188971 9.172146 9.155121 9.137890 9.120445 9.102781 #>  [12,] 9.216784 9.200275 9.183573 9.166674 9.149570 9.132254 9.114720 9.096961 #>  [13,] 9.211560 9.194985 9.178214 9.161242 9.144060 9.126662 9.109040 9.091188 #>  [14,] 9.206373 9.189734 9.172895 9.155850 9.138592 9.121113 9.103405 9.085461 #>  [15,] 9.201223 9.184522 9.167617 9.150501 9.133168 9.115610 9.097818 9.079783 #>  [16,] 9.196113 9.179349 9.162380 9.145195 9.127789 9.110153 9.092278 9.074156 #>  [17,] 9.191042 9.174218 9.157185 9.139934 9.122456 9.104744 9.086788 9.068579 #>  [18,] 9.186011 9.169129 9.152034 9.134718 9.117170 9.099384 9.081350 9.063056 #>  [19,] 9.181021 9.164083 9.146928 9.129548 9.111933 9.094075 9.075963 9.057588 #>  [20,] 9.176073 9.159080 9.141867 9.124425 9.106744 9.088816 9.070630 9.052175 #>  [21,] 9.171168 9.154122 9.136852 9.119350 9.101606 9.083610 9.065352 9.046820 #>  [22,] 9.166306 9.149209 9.131885 9.114325 9.096519 9.078458 9.060130 9.041523 #>  [23,] 9.161488 9.144342 9.126965 9.109350 9.091485 9.073360 9.054965 9.036286 #>  [24,] 9.156715 9.139521 9.122094 9.104425 9.086504 9.068318 9.049858 9.031110 #>  [25,] 9.151988 9.134748 9.117273 9.099553 9.081576 9.063333 9.044811 9.025997 #>  [26,] 9.147306 9.130023 9.112502 9.094733 9.076705 9.058406 9.039824 9.020947 #>  [27,] 9.142672 9.125347 9.107782 9.089966 9.071888 9.053537 9.034899 9.015961 #>  [28,] 9.138084 9.120720 9.103114 9.085254 9.067129 9.048728 9.030036 9.011042 #>  [29,] 9.133544 9.116144 9.098498 9.080596 9.062427 9.043979 9.025237 9.006189 #>  [30,] 9.129053 9.111617 9.093935 9.075994 9.057784 9.039291 9.020503 9.001404 #>  [31,] 9.124610 9.107142 9.089425 9.071448 9.053199 9.034665 9.015833 8.996687 #>  [32,] 9.120216 9.102719 9.084970 9.066959 9.048674 9.030102 9.011229 8.992040 #>  [33,] 9.115873 9.098347 9.080569 9.062527 9.044209 9.025603 9.006692 8.987463 #>  [34,] 9.111579 9.094028 9.076223 9.058153 9.039805 9.021167 9.002222 8.982957 #>  [35,] 9.107335 9.089761 9.071932 9.053837 9.035462 9.016795 8.997820 8.978523 #>  [36,] 9.103142 9.085548 9.067698 9.049580 9.031181 9.012488 8.993487 8.974161 #>  [37,] 9.099000 9.081388 9.063519 9.045381 9.026962 9.008247 8.989222 8.969872 #>  [38,] 9.094910 9.077282 9.059397 9.041242 9.022804 9.004071 8.985027 8.965655 #>  [39,] 9.090870 9.073230 9.055331 9.037162 9.018710 8.999961 8.980901 8.961512 #>  [40,] 9.086882 9.069231 9.051322 9.033141 9.014678 8.995917 8.976844 8.957443 #>  [41,] 9.082946 9.065287 9.047369 9.029181 9.010709 8.991940 8.972858 8.953448 #>  [42,] 9.079062 9.061397 9.043474 9.025280 9.006803 8.988029 8.968942 8.949526 #>  [43,] 9.075229 9.057561 9.039636 9.021439 9.002960 8.984184 8.965095 8.945679 #>  [44,] 9.071447 9.053780 9.035854 9.017659 8.999180 8.980405 8.961319 8.941906 #>  [45,] 9.067718 9.050052 9.032130 9.013937 8.995463 8.976693 8.957613 8.938206 #>  [46,] 9.064040 9.046379 9.028462 9.010276 8.991809 8.973047 8.953976 8.934580 #>  [47,] 9.060413 9.042760 9.024851 9.006674 8.988217 8.969467 8.950409 8.931027 #>  [48,] 9.056838 9.039194 9.021296 9.003131 8.984688 8.965953 8.946911 8.927548 #>  [49,] 9.053314 9.035682 9.017797 8.999647 8.981221 8.962503 8.943482 8.924140 #>  [50,] 9.049840 9.032223 9.014354 8.996222 8.977815 8.959119 8.940121 8.920805 #>  [51,] 9.046418 9.028818 9.010967 8.992855 8.974470 8.955799 8.936827 8.917542 #>  [52,] 9.043045 9.025464 9.007635 8.989546 8.971186 8.952543 8.933601 8.914349 #>  [53,] 9.039722 9.022163 9.004358 8.986295 8.967963 8.949350 8.930442 8.911226 #>  [54,] 9.036449 9.018914 9.001135 8.983100 8.964799 8.946219 8.927348 8.908172 #>  [55,] 9.033225 9.015716 8.997965 8.979962 8.961694 8.943151 8.924320 8.905187 #>  [56,] 9.030049 9.012569 8.994849 8.976879 8.958648 8.940144 8.921356 8.902269 #>  [57,] 9.026922 9.009472 8.991785 8.973851 8.955659 8.937197 8.918455 8.899418 #>  [58,] 9.023842 9.006425 8.988774 8.970878 8.952727 8.934310 8.915616 8.896633 #>  [59,] 9.020809 9.003427 8.985813 8.967958 8.949851 8.931482 8.912840 8.893912 #>  [60,] 9.017823 9.000478 8.982904 8.965091 8.947030 8.928712 8.910123 8.891255 #>  [61,] 9.014883 8.997577 8.980044 8.962276 8.944264 8.925998 8.907467 8.888659 #>  [62,] 9.011988 8.994722 8.977234 8.959513 8.941552 8.923340 8.904868 8.886125 #>  [63,] 9.009138 8.991915 8.974471 8.956800 8.938892 8.920738 8.902327 8.883651 #>  [64,] 9.006331 8.989152 8.971757 8.954137 8.936284 8.918189 8.899842 8.881235 #>  [65,] 9.003568 8.986435 8.969089 8.951522 8.933726 8.915693 8.897412 8.878877 #>  [66,] 9.000848 8.983763 8.966468 8.948955 8.931218 8.913248 8.895036 8.876574 #>  [67,] 8.998169 8.981133 8.963891 8.946435 8.928759 8.910854 8.892713 8.874326 #>  [68,] 8.995531 8.978546 8.961359 8.943961 8.926348 8.908510 8.890440 8.872131 #>  [69,] 8.992934 8.976001 8.958870 8.941532 8.923982 8.906214 8.888218 8.869988 #>  [70,] 8.990377 8.973497 8.956423 8.939147 8.921663 8.903964 8.886044 8.867896 #>  [71,] 8.987858 8.971033 8.954018 8.936804 8.919388 8.901761 8.883918 8.865853 #>  [72,] 8.985377 8.968609 8.951653 8.934504 8.917156 8.899603 8.881838 8.863857 #>  [73,] 8.982933 8.966222 8.949328 8.932244 8.914966 8.897488 8.879803 8.861907 #>  [74,] 8.980526 8.963874 8.947042 8.930024 8.912817 8.895415 8.877812 8.860003 #>  [75,] 8.978154 8.961561 8.944793 8.927843 8.910708 8.893383 8.875862 8.858141 #>  [76,] 8.975816 8.959285 8.942581 8.925700 8.908638 8.891391 8.873954 8.856322 #>  [77,] 8.973513 8.957043 8.940404 8.923594 8.906606 8.889438 8.872085 8.854543 #>  [78,] 8.971242 8.954835 8.938263 8.921523 8.904610 8.887522 8.870254 8.852803 #>  [79,] 8.969004 8.952660 8.936155 8.919486 8.902650 8.885643 8.868461 8.851101 #>  [80,] 8.966797 8.950517 8.934080 8.917484 8.900724 8.883798 8.866703 8.849435 #>  [81,] 8.964621 8.948405 8.932037 8.915513 8.898831 8.881987 8.864979 8.847805 #>  [82,] 8.962474 8.946324 8.930025 8.913575 8.896970 8.880209 8.863289 8.846207 #>  [83,] 8.960356 8.944272 8.928043 8.911666 8.895140 8.878462 8.861630 8.844642 #>  [84,] 8.958266 8.942248 8.926089 8.909788 8.893340 8.876746 8.860002 8.843108 #>  [85,] 8.956203 8.940252 8.924164 8.907937 8.891569 8.875058 8.858404 8.841603 #>  [86,] 8.954166 8.938283 8.922266 8.906114 8.889826 8.873399 8.856833 8.840127 #>  [87,] 8.952155 8.936339 8.920394 8.904318 8.888109 8.871767 8.855290 8.838678 #>  [88,] 8.950168 8.934420 8.918547 8.902546 8.886418 8.870160 8.853772 8.837254 #>  [89,] 8.948205 8.932526 8.916724 8.900800 8.884751 8.868578 8.852279 8.835855 #>  [90,] 8.946265 8.930654 8.914925 8.899077 8.883108 8.867019 8.850810 8.834480 #>  [91,] 8.944347 8.928805 8.913149 8.897376 8.881488 8.865483 8.849362 8.833126 #>  [92,] 8.942451 8.926978 8.911393 8.895697 8.879889 8.863969 8.847937 8.831794 #>  [93,] 8.940576 8.925171 8.909659 8.894039 8.878311 8.862474 8.846531 8.830481 #>  [94,] 8.938720 8.923384 8.907945 8.892401 8.876752 8.861000 8.845145 8.829187 #>  [95,] 8.936883 8.921617 8.906249 8.890781 8.875212 8.859544 8.843776 8.827911 #>  [96,] 8.935065 8.919867 8.904572 8.889180 8.873690 8.858105 8.842425 8.826652 #>  [97,] 8.933264 8.918135 8.902912 8.887595 8.872185 8.856683 8.841090 8.825408 #>  [98,] 8.931480 8.916420 8.901269 8.886028 8.870697 8.855277 8.839770 8.824178 #>  [99,] 8.929713 8.914721 8.899642 8.884475 8.869223 8.853885 8.838465 8.822963 #> [100,] 8.927961 8.913038 8.898030 8.882938 8.867763 8.852508 8.837173 8.821760 #>           [,33]    [,34]    [,35]    [,36]    [,37]    [,38]    [,39]    [,40] #>   [1,] 9.146338 9.129345 9.112183 9.094849 9.077342 9.059662 9.041808 9.023782 #>   [2,] 9.140033 9.122925 9.105640 9.088176 9.070532 9.052706 9.034697 9.016506 #>   [3,] 9.133760 9.116536 9.099129 9.081536 9.063754 9.045781 9.027618 9.009262 #>   [4,] 9.127520 9.110181 9.092652 9.074928 9.057009 9.038890 9.020571 9.002049 #>   [5,] 9.121314 9.103860 9.086209 9.068357 9.050300 9.032035 9.013560 8.994873 #>   [6,] 9.115144 9.097576 9.079804 9.061823 9.043629 9.025218 9.006587 8.987734 #>   [7,] 9.109012 9.091331 9.073438 9.055328 9.036998 9.018441 8.999655 8.980635 #>   [8,] 9.102919 9.085125 9.067112 9.048875 9.030409 9.011707 8.992766 8.973580 #>   [9,] 9.096866 9.078961 9.060830 9.042466 9.023864 9.005018 8.985922 8.966572 #>  [10,] 9.090856 9.072841 9.054592 9.036102 9.017366 8.998377 8.979127 8.959612 #>  [11,] 9.084890 9.066765 9.048400 9.029786 9.010917 8.991785 8.972383 8.952704 #>  [12,] 9.078969 9.060737 9.042257 9.023520 9.004519 8.985246 8.965692 8.945850 #>  [13,] 9.073096 9.054758 9.036164 9.017306 8.998175 8.978762 8.959058 8.939055 #>  [14,] 9.067272 9.048829 9.030123 9.011145 8.991886 8.972335 8.952483 8.932320 #>  [15,] 9.061498 9.042952 9.024136 9.005041 8.985655 8.965968 8.945970 8.925649 #>  [16,] 9.055776 9.037129 9.018206 8.998995 8.979485 8.959664 8.939522 8.919045 #>  [17,] 9.050108 9.031363 9.012333 8.993009 8.973377 8.953425 8.933141 8.912511 #>  [18,] 9.044495 9.025653 9.006521 8.987085 8.967334 8.947253 8.926830 8.906049 #>  [19,] 9.038938 9.020003 9.000770 8.981226 8.961358 8.941151 8.920592 8.899664 #>  [20,] 9.033441 9.014414 8.995082 8.975433 8.955451 8.935122 8.914430 8.893358 #>  [21,] 9.028002 9.008887 8.989460 8.969709 8.949616 8.929168 8.908347 8.887135 #>  [22,] 9.022626 9.003424 8.983906 8.964055 8.943855 8.923291 8.902344 8.880996 #>  [23,] 9.017311 8.998028 8.978420 8.958473 8.938170 8.917494 8.896426 8.874946 #>  [24,] 9.012061 8.992698 8.973005 8.952965 8.932563 8.911779 8.890594 8.868986 #>  [25,] 9.006877 8.987437 8.967662 8.947534 8.927036 8.906148 8.884850 8.863121 #>  [26,] 9.001759 8.982246 8.962392 8.942180 8.921590 8.900604 8.879199 8.857351 #>  [27,] 8.996709 8.977127 8.957198 8.936906 8.916229 8.895148 8.873640 8.851682 #>  [28,] 8.991728 8.972081 8.952081 8.931712 8.910953 8.889783 8.868178 8.846113 #>  [29,] 8.986818 8.967108 8.947043 8.926602 8.905765 8.884511 8.862814 8.840650 #>  [30,] 8.981979 8.962211 8.942083 8.921575 8.900666 8.879332 8.857550 8.835292 #>  [31,] 8.977212 8.957391 8.937205 8.916634 8.895657 8.874250 8.852389 8.830044 #>  [32,] 8.972519 8.952647 8.932408 8.911780 8.890740 8.869266 8.847331 8.824906 #>  [33,] 8.967899 8.947983 8.927694 8.907013 8.885917 8.864381 8.842379 8.819881 #>  [34,] 8.963355 8.943397 8.923064 8.902336 8.881188 8.859596 8.837534 8.814970 #>  [35,] 8.958886 8.938892 8.918519 8.897748 8.876555 8.854914 8.832797 8.810175 #>  [36,] 8.954494 8.934467 8.914060 8.893251 8.872018 8.850334 8.828171 8.805498 #>  [37,] 8.950178 8.930123 8.909686 8.888846 8.867579 8.845858 8.823655 8.800939 #>  [38,] 8.945940 8.925861 8.905400 8.884533 8.863237 8.841486 8.819250 8.796499 #>  [39,] 8.941779 8.921682 8.901201 8.880313 8.858995 8.837219 8.814958 8.792180 #>  [40,] 8.937696 8.917585 8.897089 8.876186 8.854851 8.833059 8.810779 8.787981 #>  [41,] 8.933692 8.913571 8.893065 8.872152 8.850807 8.829004 8.806714 8.783904 #>  [42,] 8.929765 8.909640 8.889129 8.868212 8.846862 8.825055 8.802761 8.779949 #>  [43,] 8.925917 8.905792 8.885281 8.864365 8.843017 8.821213 8.798923 8.776115 #>  [44,] 8.922148 8.902026 8.881521 8.860611 8.839272 8.817476 8.795197 8.772402 #>  [45,] 8.918456 8.898343 8.877849 8.856951 8.835625 8.813846 8.791584 8.768810 #>  [46,] 8.914842 8.894743 8.874264 8.853383 8.832077 8.810320 8.788084 8.765338 #>  [47,] 8.911305 8.891225 8.870766 8.849908 8.828628 8.806899 8.784695 8.761985 #>  [48,] 8.907846 8.887788 8.867355 8.846525 8.825276 8.803582 8.781417 8.758751 #>  [49,] 8.904463 8.884433 8.864029 8.843232 8.822020 8.800368 8.778249 8.755634 #>  [50,] 8.901157 8.881157 8.860789 8.840030 8.818860 8.797255 8.775189 8.752633 #>  [51,] 8.897925 8.877962 8.857632 8.836917 8.815796 8.794244 8.772236 8.749746 #>  [52,] 8.894769 8.874845 8.854559 8.833893 8.812824 8.791331 8.769389 8.746971 #>  [53,] 8.891686 8.871806 8.851569 8.830955 8.809945 8.788517 8.766646 8.744307 #>  [54,] 8.888676 8.868844 8.848659 8.828104 8.807157 8.785798 8.764005 8.741752 #>  [55,] 8.885738 8.865958 8.845830 8.825337 8.804458 8.783175 8.761464 8.739302 #>  [56,] 8.882872 8.863147 8.843080 8.822653 8.801847 8.780644 8.759022 8.736958 #>  [57,] 8.880075 8.860409 8.840407 8.820050 8.799323 8.778204 8.756676 8.734714 #>  [58,] 8.877347 8.857744 8.837810 8.817528 8.796882 8.775854 8.754423 8.732570 #>  [59,] 8.874687 8.855150 8.835288 8.815085 8.794525 8.773590 8.752263 8.730523 #>  [60,] 8.872093 8.852626 8.832839 8.812718 8.792247 8.771411 8.750191 8.728570 #>  [61,] 8.869565 8.850170 8.830461 8.810426 8.790049 8.769315 8.748207 8.726708 #>  [62,] 8.867100 8.847780 8.828154 8.808208 8.787928 8.767299 8.746307 8.724934 #>  [63,] 8.864698 8.845456 8.825915 8.806061 8.785881 8.765362 8.744488 8.723246 #>  [64,] 8.862357 8.843196 8.823742 8.803983 8.783907 8.763500 8.742749 8.721641 #>  [65,] 8.860075 8.840998 8.821634 8.801973 8.782003 8.761712 8.741087 8.720115 #>  [66,] 8.857852 8.838861 8.819590 8.800029 8.780168 8.759995 8.739498 8.718667 #>  [67,] 8.855686 8.836782 8.817606 8.798149 8.778399 8.758346 8.737981 8.717292 #>  [68,] 8.853574 8.834761 8.815683 8.796330 8.776693 8.756764 8.736532 8.715988 #>  [69,] 8.851517 8.832796 8.813816 8.794571 8.775050 8.755246 8.735149 8.714752 #>  [70,] 8.849512 8.830884 8.812006 8.792869 8.773466 8.753789 8.733830 8.713581 #>  [71,] 8.847557 8.829025 8.810250 8.791224 8.771940 8.752391 8.732571 8.712472 #>  [72,] 8.845652 8.827217 8.808546 8.789632 8.770468 8.751050 8.731370 8.711423 #>  [73,] 8.843794 8.825458 8.806892 8.788091 8.769050 8.749763 8.730224 8.710430 #>  [74,] 8.841982 8.823746 8.805287 8.786601 8.767683 8.748528 8.729132 8.709490 #>  [75,] 8.840215 8.822079 8.803728 8.785158 8.766364 8.747342 8.728089 8.708602 #>  [76,] 8.838491 8.820457 8.802215 8.783761 8.765092 8.746204 8.727095 8.707761 #>  [77,] 8.836808 8.818876 8.800744 8.782408 8.763864 8.745111 8.726146 8.706967 #>  [78,] 8.835165 8.817337 8.799315 8.781096 8.762679 8.744060 8.725239 8.706215 #>  [79,] 8.833561 8.815836 8.797925 8.779825 8.761534 8.743051 8.724373 8.705503 #>  [80,] 8.831993 8.814373 8.796573 8.778592 8.760428 8.742079 8.723546 8.704829 #>  [81,] 8.830461 8.812946 8.795258 8.777395 8.759357 8.741144 8.722754 8.704191 #>  [82,] 8.828962 8.811553 8.793976 8.776233 8.758322 8.740243 8.721997 8.703586 #>  [83,] 8.827497 8.810192 8.792728 8.775103 8.757318 8.739374 8.721271 8.703011 #>  [84,] 8.826062 8.808863 8.791511 8.774005 8.756346 8.738535 8.720574 8.702465 #>  [85,] 8.824657 8.807564 8.790323 8.772936 8.755403 8.737725 8.719905 8.701946 #>  [86,] 8.823280 8.806292 8.789164 8.771894 8.754486 8.736941 8.719262 8.701451 #>  [87,] 8.821931 8.805048 8.788030 8.770879 8.753596 8.736182 8.718642 8.700979 #>  [88,] 8.820606 8.803829 8.786922 8.769888 8.752729 8.735446 8.718044 8.700526 #>  [89,] 8.819307 8.802634 8.785838 8.768920 8.751884 8.734731 8.717466 8.700093 #>  [90,] 8.818030 8.801461 8.784775 8.767974 8.751060 8.734036 8.716906 8.699676 #>  [91,] 8.816775 8.800311 8.783734 8.767048 8.750255 8.733358 8.716363 8.699275 #>  [92,] 8.815541 8.799180 8.782712 8.766140 8.749467 8.732697 8.715835 8.698886 #>  [93,] 8.814326 8.798068 8.781708 8.765249 8.748696 8.732052 8.715321 8.698510 #>  [94,] 8.813130 8.796973 8.780721 8.764375 8.747940 8.731419 8.714819 8.698144 #>  [95,] 8.811950 8.795895 8.779749 8.763515 8.747197 8.730799 8.714327 8.697786 #>  [96,] 8.810787 8.794833 8.778792 8.762669 8.746466 8.730190 8.713844 8.697437 #>  [97,] 8.809638 8.793784 8.777848 8.761834 8.745747 8.729590 8.713370 8.697093 #>  [98,] 8.808504 8.792749 8.776917 8.761011 8.745037 8.728999 8.712902 8.696754 #>  [99,] 8.807382 8.791725 8.775996 8.760198 8.744336 8.728414 8.712439 8.696418 #> [100,] 8.806273 8.790713 8.775086 8.759394 8.743642 8.727836 8.711981 8.696085 #>           [,41]    [,42]    [,43]    [,44]    [,45]    [,46]    [,47]    [,48] #>   [1,] 9.005583 8.987216 8.968684 8.949993 8.931149 8.912161 8.893041 8.873802 #>   [2,] 8.998134 8.979582 8.960853 8.941952 8.922886 8.903663 8.884293 8.864790 #>   [3,] 8.990714 8.971975 8.953048 8.933936 8.914646 8.895184 8.875560 8.855787 #>   [4,] 8.983325 8.964399 8.945272 8.925947 8.906430 8.886726 8.866844 8.846797 #>   [5,] 8.975972 8.956857 8.937529 8.917989 8.898242 8.878293 8.858151 8.837824 #>   [6,] 8.968656 8.949351 8.929821 8.910065 8.890087 8.869890 8.849483 8.828873 #>   [7,] 8.961380 8.941886 8.922152 8.902178 8.881967 8.861520 8.840845 8.819948 #>   [8,] 8.954147 8.934463 8.914525 8.894333 8.873887 8.853188 8.832242 8.811055 #>   [9,] 8.946961 8.927086 8.906945 8.886533 8.865850 8.844898 8.823678 8.802197 #>  [10,] 8.939824 8.919760 8.899413 8.878782 8.857862 8.836654 8.815159 8.793380 #>  [11,] 8.932740 8.912486 8.891935 8.871084 8.849927 8.828462 8.806689 8.784610 #>  [12,] 8.925711 8.905269 8.884515 8.863443 8.842048 8.820326 8.798275 8.775893 #>  [13,] 8.918742 8.898111 8.877155 8.855864 8.834231 8.812252 8.789920 8.767235 #>  [14,] 8.911835 8.891018 8.869860 8.848350 8.826481 8.804244 8.781632 8.758642 #>  [15,] 8.904993 8.883992 8.862634 8.840908 8.818802 8.796308 8.773417 8.750121 #>  [16,] 8.898221 8.877037 8.855481 8.833540 8.811200 8.788450 8.765280 8.741678 #>  [17,] 8.891521 8.870157 8.848406 8.826251 8.803679 8.780676 8.757227 8.733320 #>  [18,] 8.884897 8.863356 8.841412 8.819047 8.796246 8.772991 8.749266 8.725056 #>  [19,] 8.878352 8.856637 8.834503 8.811932 8.788904 8.765400 8.741403 8.716891 #>  [20,] 8.871889 8.850005 8.827685 8.804910 8.781659 8.757911 8.733644 8.708835 #>  [21,] 8.865513 8.843462 8.820961 8.797987 8.774518 8.750529 8.725996 8.700893 #>  [22,] 8.859226 8.837013 8.814335 8.791167 8.767484 8.743260 8.718467 8.693075 #>  [23,] 8.853032 8.830662 8.807812 8.784455 8.760564 8.736110 8.711063 8.685388 #>  [24,] 8.846934 8.824412 8.801395 8.777856 8.753763 8.729086 8.703790 8.677840 #>  [25,] 8.840934 8.818267 8.795089 8.771373 8.747086 8.722192 8.696657 8.670438 #>  [26,] 8.835037 8.812229 8.788898 8.765012 8.740537 8.715436 8.689668 8.663192 #>  [27,] 8.829246 8.806304 8.782826 8.758777 8.734123 8.708822 8.682833 8.656107 #>  [28,] 8.823562 8.800493 8.776875 8.752673 8.727848 8.702357 8.676155 8.649192 #>  [29,] 8.817989 8.794800 8.771051 8.746703 8.721716 8.696046 8.669643 8.642454 #>  [30,] 8.812529 8.789228 8.765355 8.740871 8.715732 8.689893 8.663302 8.635900 #>  [31,] 8.807185 8.783780 8.759792 8.735181 8.709901 8.683905 8.657137 8.629538 #>  [32,] 8.801960 8.778459 8.754365 8.729636 8.704226 8.678085 8.651155 8.623372 #>  [33,] 8.796855 8.773266 8.749076 8.724240 8.698712 8.672438 8.645360 8.617410 #>  [34,] 8.791872 8.768205 8.743927 8.718996 8.693361 8.666968 8.639757 8.611657 #>  [35,] 8.787014 8.763276 8.738922 8.713906 8.688177 8.661679 8.634350 8.606117 #>  [36,] 8.782281 8.758483 8.734062 8.708972 8.683162 8.656574 8.629143 8.600796 #>  [37,] 8.777675 8.753826 8.729349 8.704197 8.678319 8.651655 8.624139 8.595697 #>  [38,] 8.773197 8.749306 8.724784 8.699583 8.673649 8.646924 8.619341 8.590823 #>  [39,] 8.768849 8.744926 8.720369 8.695130 8.669155 8.642385 8.614751 8.586177 #>  [40,] 8.764630 8.740685 8.716104 8.690840 8.664838 8.638037 8.610371 8.581761 #>  [41,] 8.760541 8.736584 8.711991 8.686713 8.660697 8.633882 8.606201 8.577575 #>  [42,] 8.756582 8.732623 8.708029 8.682750 8.656734 8.629921 8.602242 8.573620 #>  [43,] 8.752754 8.728803 8.704217 8.678950 8.652949 8.626152 8.598493 8.569896 #>  [44,] 8.749056 8.725122 8.700557 8.675314 8.649340 8.622576 8.594955 8.566402 #>  [45,] 8.745488 8.721581 8.697047 8.671840 8.645907 8.619190 8.591625 8.563137 #>  [46,] 8.742048 8.718178 8.693686 8.668526 8.642648 8.615994 8.588501 8.560096 #>  [47,] 8.738737 8.714913 8.690473 8.665372 8.639562 8.612985 8.585581 8.557279 #>  [48,] 8.735552 8.711783 8.687406 8.662376 8.636646 8.610161 8.582862 8.554680 #>  [49,] 8.732492 8.708788 8.684483 8.659536 8.633898 8.607519 8.580340 8.552296 #>  [50,] 8.729556 8.705925 8.681703 8.656848 8.631315 8.605055 8.578011 8.550121 #>  [51,] 8.726742 8.703193 8.679062 8.654310 8.628894 8.602765 8.575870 8.548151 #>  [52,] 8.724048 8.700589 8.676559 8.651920 8.626631 8.600645 8.573913 8.546380 #>  [53,] 8.721472 8.698111 8.674190 8.649674 8.624522 8.598691 8.572135 8.544801 #>  [54,] 8.719012 8.695756 8.671953 8.647567 8.622563 8.596899 8.570530 8.543408 #>  [55,] 8.716664 8.693521 8.669843 8.645598 8.620750 8.595262 8.569091 8.542194 #>  [56,] 8.714427 8.691403 8.667858 8.643761 8.619079 8.593776 8.567814 8.541151 #>  [57,] 8.712298 8.689400 8.665995 8.642053 8.617544 8.592435 8.566691 8.540274 #>  [58,] 8.710273 8.687508 8.664249 8.640470 8.616142 8.591235 8.565716 8.539553 #>  [59,] 8.708351 8.685723 8.662616 8.639006 8.614866 8.590168 8.564883 8.538982 #>  [60,] 8.706527 8.684042 8.661094 8.637658 8.613712 8.589230 8.564186 8.538552 #>  [61,] 8.704800 8.682463 8.659677 8.636422 8.612675 8.588414 8.563616 8.538257 #>  [62,] 8.703165 8.680980 8.658362 8.635292 8.611750 8.587715 8.563169 8.538089 #>  [63,] 8.701619 8.679591 8.657146 8.634265 8.610931 8.587127 8.562836 8.538040 #>  [64,] 8.700160 8.678293 8.656023 8.633335 8.610214 8.586645 8.562612 8.538103 #>  [65,] 8.698784 8.677080 8.654989 8.632498 8.609593 8.586261 8.562490 8.538270 #>  [66,] 8.697488 8.675950 8.654041 8.631749 8.609063 8.585971 8.562464 8.538534 #>  [67,] 8.696268 8.674900 8.653175 8.631085 8.608619 8.585769 8.562527 8.538888 #>  [68,] 8.695122 8.673924 8.652387 8.630500 8.608256 8.585649 8.562674 8.539326 #>  [69,] 8.694045 8.673021 8.651672 8.629990 8.607970 8.585607 8.562898 8.539841 #>  [70,] 8.693035 8.672186 8.651026 8.629551 8.607755 8.585636 8.563193 8.540427 #>  [71,] 8.692089 8.671416 8.650447 8.629178 8.607607 8.585732 8.563554 8.541076 #>  [72,] 8.691203 8.670707 8.649929 8.628868 8.607521 8.585890 8.563976 8.541784 #>  [73,] 8.690375 8.670056 8.649470 8.628616 8.607493 8.586104 8.564453 8.542545 #>  [74,] 8.689600 8.669459 8.649065 8.628418 8.607519 8.586371 8.564980 8.543353 #>  [75,] 8.688877 8.668914 8.648712 8.628271 8.607594 8.586686 8.565553 8.544204 #>  [76,] 8.688202 8.668417 8.648406 8.628171 8.607715 8.587044 8.566166 8.545091 #>  [77,] 8.687573 8.667965 8.648145 8.628114 8.607877 8.587441 8.566816 8.546011 #>  [78,] 8.686986 8.667555 8.647924 8.628096 8.608077 8.587874 8.567497 8.546959 #>  [79,] 8.686439 8.667185 8.647742 8.628115 8.608311 8.588338 8.568207 8.547931 #>  [80,] 8.685930 8.666850 8.647594 8.628167 8.608577 8.588831 8.568941 8.548923 #>  [81,] 8.685455 8.666549 8.647479 8.628250 8.608869 8.589347 8.569696 8.549931 #>  [82,] 8.685012 8.666279 8.647393 8.628359 8.609186 8.589885 8.570468 8.550951 #>  [83,] 8.684599 8.666037 8.647333 8.628492 8.609525 8.590441 8.571255 8.551981 #>  [84,] 8.684213 8.665821 8.647297 8.628647 8.609882 8.591012 8.572052 8.553017 #>  [85,] 8.683852 8.665629 8.647282 8.628821 8.610255 8.591595 8.572857 8.554056 #>  [86,] 8.683514 8.665457 8.647286 8.629011 8.610641 8.592188 8.573667 8.555095 #>  [87,] 8.683197 8.665304 8.647307 8.629215 8.611038 8.592788 8.574481 8.556133 #>  [88,] 8.682899 8.665169 8.647343 8.629430 8.611443 8.593393 8.575295 8.557165 #>  [89,] 8.682618 8.665048 8.647391 8.629656 8.611854 8.594000 8.576106 8.558191 #>  [90,] 8.682352 8.664940 8.647449 8.629888 8.612270 8.594607 8.576914 8.559208 #>  [91,] 8.682099 8.664843 8.647515 8.630127 8.612688 8.595213 8.577716 8.560215 #>  [92,] 8.681857 8.664755 8.647589 8.630369 8.613107 8.595816 8.578511 8.561208 #>  [93,] 8.681625 8.664675 8.647667 8.630613 8.613524 8.596413 8.579295 8.562188 #>  [94,] 8.681402 8.664600 8.647748 8.630857 8.613937 8.597003 8.580069 8.563151 #>  [95,] 8.681185 8.664530 8.647832 8.631100 8.614347 8.597585 8.580830 8.564098 #>  [96,] 8.680973 8.664463 8.647915 8.631340 8.614750 8.598157 8.581577 8.565026 #>  [97,] 8.680766 8.664398 8.647998 8.631577 8.615146 8.598718 8.582309 8.565934 #>  [98,] 8.680561 8.664333 8.648078 8.631807 8.615533 8.599267 8.583025 8.566822 #>  [99,] 8.680358 8.664267 8.648154 8.632032 8.615910 8.599802 8.583723 8.567687 #> [100,] 8.680154 8.664198 8.648226 8.632248 8.616276 8.600323 8.584403 8.568530 #>           [,49]    [,50]    [,51]    [,52]    [,53]    [,54]    [,55]    [,56] #>   [1,] 8.854462 8.835042 8.815565 8.796060 8.776562 8.757108 8.737745 8.718523 #>   [2,] 8.845170 8.825452 8.805662 8.785828 8.765984 8.746168 8.726428 8.706816 #>   [3,] 8.835880 8.815860 8.795749 8.775576 8.755374 8.735185 8.715054 8.695035 #>   [4,] 8.826599 8.806268 8.785828 8.765307 8.744738 8.724162 8.703625 8.683183 #>   [5,] 8.817329 8.796681 8.775905 8.755026 8.734079 8.713102 8.692145 8.671263 #>   [6,] 8.808075 8.787105 8.765984 8.744738 8.723401 8.702012 8.680620 8.659280 #>   [7,] 8.798843 8.777543 8.756070 8.734448 8.712710 8.690896 8.669052 8.647237 #>   [8,] 8.789636 8.768001 8.746168 8.724162 8.702012 8.679759 8.657449 8.635140 #>   [9,] 8.780462 8.758486 8.736286 8.713885 8.691313 8.668607 8.645815 8.622994 #>  [10,] 8.771324 8.749002 8.726428 8.703625 8.680620 8.657449 8.634158 8.610806 #>  [11,] 8.762230 8.739556 8.716602 8.693388 8.669939 8.646290 8.622485 8.598582 #>  [12,] 8.753185 8.730155 8.706816 8.683183 8.659280 8.635140 8.610806 8.586332 #>  [13,] 8.744196 8.720807 8.697076 8.673017 8.648651 8.624008 8.599128 8.574064 #>  [14,] 8.735270 8.711518 8.687391 8.662899 8.638061 8.612903 8.587462 8.561790 #>  [15,] 8.726414 8.702297 8.677769 8.652839 8.627520 8.601836 8.575820 8.549520 #>  [16,] 8.717637 8.693151 8.668220 8.642846 8.617040 8.590819 8.564214 8.537267 #>  [17,] 8.708944 8.684091 8.658753 8.632932 8.606631 8.579864 8.552656 8.525046 #>  [18,] 8.700346 8.675123 8.649379 8.623106 8.596306 8.568985 8.541163 8.512872 #>  [19,] 8.691849 8.666259 8.640106 8.613381 8.586077 8.558196 8.529749 8.500762 #>  [20,] 8.683463 8.657507 8.630947 8.603769 8.575959 8.547512 8.518431 8.488734 #>  [21,] 8.675195 8.648877 8.621913 8.594282 8.565965 8.536949 8.507228 8.476810 #>  [22,] 8.667056 8.640379 8.613015 8.584934 8.556111 8.526524 8.496158 8.465010 #>  [23,] 8.659054 8.632024 8.604264 8.575738 8.546412 8.516255 8.485242 8.453357 #>  [24,] 8.651197 8.623822 8.595673 8.566708 8.536884 8.506161 8.474502 8.441877 #>  [25,] 8.643496 8.615784 8.587254 8.557858 8.527544 8.496261 8.463960 8.430596 #>  [26,] 8.635958 8.607919 8.579019 8.549202 8.518408 8.486574 8.453639 8.419540 #>  [27,] 8.628594 8.600239 8.570981 8.540756 8.509494 8.477122 8.443563 8.408739 #>  [28,] 8.621411 8.592753 8.563151 8.532532 8.500818 8.467924 8.433757 8.398223 #>  [29,] 8.614419 8.585473 8.555542 8.524547 8.492398 8.459000 8.424246 8.388021 #>  [30,] 8.607626 8.578407 8.548165 8.516812 8.484251 8.450372 8.415055 8.378165 #>  [31,] 8.601039 8.571565 8.541031 8.509343 8.476393 8.442060 8.406208 8.368684 #>  [32,] 8.594666 8.564956 8.534152 8.502152 8.468840 8.434083 8.397730 8.359610 #>  [33,] 8.588515 8.558589 8.527538 8.495252 8.461607 8.426459 8.389644 8.350971 #>  [34,] 8.582591 8.552472 8.521197 8.488654 8.454708 8.419207 8.381973 8.342796 #>  [35,] 8.576902 8.546610 8.515139 8.482368 8.448156 8.412342 8.374735 8.335111 #>  [36,] 8.571451 8.541012 8.509372 8.476404 8.441963 8.405879 8.367951 8.327939 #>  [37,] 8.566244 8.535682 8.503901 8.470770 8.436139 8.399831 8.361636 8.321302 #>  [38,] 8.561284 8.530626 8.498733 8.465473 8.430693 8.394209 8.355804 8.315218 #>  [39,] 8.556575 8.525845 8.493871 8.460519 8.425631 8.389020 8.350466 8.309700 #>  [40,] 8.552119 8.521344 8.489320 8.455911 8.420958 8.384272 8.345629 8.304758 #>  [41,] 8.547916 8.517124 8.485081 8.451651 8.416676 8.379967 8.341298 8.300398 #>  [42,] 8.543968 8.513185 8.481154 8.447741 8.412787 8.376106 8.337473 8.296621 #>  [43,] 8.540274 8.509527 8.477539 8.444179 8.409290 8.372688 8.334154 8.293425 #>  [44,] 8.536833 8.506147 8.474234 8.440963 8.406180 8.369708 8.331333 8.290802 #>  [45,] 8.533642 8.503045 8.471236 8.438088 8.403454 8.367160 8.329003 8.288740 #>  [46,] 8.530699 8.500215 8.468540 8.435550 8.401103 8.365035 8.327152 8.287224 #>  [47,] 8.528000 8.497654 8.466140 8.433340 8.399120 8.363322 8.325765 8.286235 #>  [48,] 8.525540 8.495356 8.464030 8.431452 8.397493 8.362008 8.324826 8.285752 #>  [49,] 8.523315 8.493314 8.462203 8.429875 8.396212 8.361077 8.324316 8.285750 #>  [50,] 8.521318 8.491523 8.460649 8.428599 8.395262 8.360514 8.324214 8.286202 #>  [51,] 8.519543 8.489973 8.459359 8.427612 8.394630 8.360301 8.324498 8.287081 #>  [52,] 8.517984 8.488656 8.458324 8.426902 8.394301 8.360418 8.325144 8.288357 #>  [53,] 8.516632 8.487565 8.457532 8.426457 8.394259 8.360848 8.326129 8.290000 #>  [54,] 8.515480 8.486689 8.456973 8.426263 8.394488 8.361571 8.327429 8.291981 #>  [55,] 8.514520 8.486020 8.456635 8.426307 8.394972 8.362565 8.329019 8.294269 #>  [56,] 8.513744 8.485546 8.456506 8.426574 8.395693 8.363812 8.330875 8.296834 #>  [57,] 8.513143 8.485258 8.456576 8.427050 8.396636 8.365290 8.332973 8.299649 #>  [58,] 8.512709 8.485147 8.456830 8.427721 8.397783 8.366982 8.335290 8.302687 #>  [59,] 8.512431 8.485201 8.457259 8.428574 8.399118 8.368867 8.337803 8.305919 #>  [60,] 8.512303 8.485411 8.457849 8.429595 8.400626 8.370927 8.340491 8.309322 #>  [61,] 8.512315 8.485766 8.458590 8.430770 8.402290 8.373143 8.343333 8.312872 #>  [62,] 8.512458 8.486257 8.459470 8.432086 8.404096 8.375500 8.346309 8.316547 #>  [63,] 8.512724 8.486874 8.460478 8.433530 8.406029 8.377981 8.349402 8.320326 #>  [64,] 8.513104 8.487606 8.461603 8.435091 8.408076 8.380569 8.352595 8.324190 #>  [65,] 8.513590 8.488446 8.462834 8.436757 8.410224 8.383251 8.355870 8.328122 #>  [66,] 8.514175 8.489384 8.464162 8.438516 8.412459 8.386014 8.359213 8.332105 #>  [67,] 8.514850 8.490411 8.465577 8.440358 8.414771 8.388843 8.362610 8.336125 #>  [68,] 8.515607 8.491519 8.467070 8.442273 8.417148 8.391727 8.366049 8.340168 #>  [69,] 8.516440 8.492700 8.468631 8.444250 8.419581 8.394655 8.369517 8.344223 #>  [70,] 8.517342 8.493946 8.470253 8.446282 8.422058 8.397617 8.373004 8.348277 #>  [71,] 8.518305 8.495251 8.471928 8.448360 8.424572 8.400603 8.376500 8.352322 #>  [72,] 8.519324 8.496606 8.473649 8.450475 8.427114 8.403605 8.379997 8.356349 #>  [73,] 8.520391 8.498006 8.475407 8.452620 8.429676 8.406615 8.383486 8.360349 #>  [74,] 8.521503 8.499444 8.477197 8.454789 8.432251 8.409625 8.386960 8.364315 #>  [75,] 8.522652 8.500915 8.479013 8.456975 8.434833 8.412629 8.390412 8.368242 #>  [76,] 8.523834 8.502412 8.480849 8.459171 8.437415 8.415620 8.393837 8.372124 #>  [77,] 8.525043 8.503931 8.482698 8.461374 8.439992 8.418594 8.397229 8.375955 #>  [78,] 8.526276 8.505467 8.484558 8.463576 8.442558 8.421545 8.400584 8.379733 #>  [79,] 8.527527 8.507016 8.486422 8.465775 8.445110 8.424468 8.403898 8.383453 #>  [80,] 8.528793 8.508572 8.488286 8.467965 8.447643 8.427361 8.407166 8.387112 #>  [81,] 8.530069 8.510133 8.490147 8.470142 8.450152 8.430218 8.410386 8.390707 #>  [82,] 8.531353 8.511694 8.492001 8.472303 8.452636 8.433038 8.413555 8.394237 #>  [83,] 8.532640 8.513252 8.493844 8.474445 8.455090 8.435817 8.416670 8.397699 #>  [84,] 8.533927 8.514804 8.495673 8.476565 8.457512 8.438553 8.419730 8.401092 #>  [85,] 8.535212 8.516347 8.497486 8.478659 8.459899 8.441243 8.422733 8.404414 #>  [86,] 8.536492 8.517878 8.499280 8.480726 8.462250 8.443886 8.425677 8.407665 #>  [87,] 8.537763 8.519395 8.501052 8.482763 8.464561 8.446480 8.428560 8.410843 #>  [88,] 8.539025 8.520895 8.502800 8.484769 8.466832 8.449024 8.431383 8.413949 #>  [89,] 8.540274 8.522376 8.504523 8.486741 8.469061 8.451516 8.434143 8.416982 #>  [90,] 8.541509 8.523837 8.506218 8.488678 8.471246 8.453955 8.436841 8.419942 #>  [91,] 8.542728 8.525276 8.507884 8.490578 8.473386 8.456341 8.439476 8.422828 #>  [92,] 8.543928 8.526691 8.509520 8.492440 8.475481 8.458673 8.442048 8.425642 #>  [93,] 8.545109 8.528080 8.511123 8.494264 8.477529 8.460949 8.444556 8.428382 #>  [94,] 8.546269 8.529443 8.512694 8.496048 8.479531 8.463171 8.447000 8.431050 #>  [95,] 8.547407 8.530777 8.514231 8.497791 8.481484 8.465337 8.449381 8.433646 #>  [96,] 8.548521 8.532083 8.515732 8.499492 8.483389 8.467448 8.451698 8.436170 #>  [97,] 8.549611 8.533359 8.517198 8.501152 8.485245 8.469503 8.453953 8.438624 #>  [98,] 8.550675 8.534603 8.518628 8.502769 8.487053 8.471502 8.456144 8.441007 #>  [99,] 8.551712 8.535817 8.520020 8.504344 8.488811 8.473445 8.458273 8.443320 #> [100,] 8.552723 8.536998 8.521375 8.505875 8.490520 8.475333 8.460340 8.445564 #>           [,57]    [,58]    [,59]    [,60]    [,61]    [,62]    [,63]    [,64] #>   [1,] 8.699501 8.680741 8.662317 8.644304 8.626785 8.609847 8.593580 8.578075 #>   [2,] 8.687391 8.668220 8.649379 8.630947 8.613015 8.595673 8.579019 8.563151 #>   [3,] 8.675190 8.655588 8.636308 8.617436 8.599065 8.581295 8.564229 8.547974 #>   [4,] 8.662899 8.642846 8.623106 8.603769 8.584934 8.566708 8.549202 8.532532 #>   [5,] 8.650522 8.629996 8.609771 8.589943 8.570617 8.551906 8.533931 8.516817 #>   [6,] 8.638061 8.617040 8.596306 8.575959 8.556111 8.536884 8.518408 8.500818 #>   [7,] 8.625520 8.603980 8.582709 8.561815 8.541414 8.521637 8.502625 8.484524 #>   [8,] 8.612903 8.590819 8.568985 8.547512 8.526524 8.506161 8.486574 8.467924 #>   [9,] 8.600215 8.577562 8.555135 8.533050 8.511439 8.490451 8.470248 8.451005 #>  [10,] 8.587462 8.564214 8.541163 8.518431 8.496158 8.474502 8.453639 8.433757 #>  [11,] 8.574651 8.550780 8.527073 8.503658 8.480681 8.458312 8.436738 8.416167 #>  [12,] 8.561790 8.537267 8.512872 8.488734 8.465010 8.441877 8.419540 8.398223 #>  [13,] 8.548887 8.523684 8.498565 8.473665 8.449145 8.425196 8.402038 8.379912 #>  [14,] 8.535953 8.510040 8.484161 8.458455 8.433091 8.408269 8.384225 8.361223 #>  [15,] 8.523000 8.496347 8.469671 8.443115 8.416852 8.391095 8.366096 8.342143 #>  [16,] 8.510040 8.482616 8.455106 8.427653 8.400436 8.373679 8.347650 8.322661 #>  [17,] 8.497088 8.468864 8.440481 8.412082 8.383852 8.356024 8.328882 8.302768 #>  [18,] 8.484161 8.455106 8.425811 8.396417 8.367112 8.338137 8.309796 8.282453 #>  [19,] 8.471277 8.441362 8.411116 8.380676 8.350232 8.320031 8.290393 8.261710 #>  [20,] 8.458455 8.427653 8.396417 8.364881 8.333231 8.301720 8.270680 8.240535 #>  [21,] 8.445719 8.414002 8.381740 8.349056 8.316132 8.283223 8.250671 8.218928 #>  [22,] 8.433091 8.400436 8.367112 8.333231 8.298965 8.264564 8.230382 8.196894 #>  [23,] 8.420598 8.386984 8.352566 8.317439 8.281762 8.245776 8.209838 8.174443 #>  [24,] 8.408269 8.373679 8.338137 8.301720 8.264564 8.226898 8.189071 8.151595 #>  [25,] 8.396134 8.360555 8.323866 8.286117 8.247419 8.207977 8.168125 8.128381 #>  [26,] 8.384225 8.347650 8.309796 8.270680 8.230382 8.189071 8.147056 8.104845 #>  [27,] 8.372576 8.335004 8.295974 8.255466 8.213516 8.170250 8.125934 8.081049 #>  [28,] 8.361223 8.322661 8.282453 8.240535 8.196894 8.151595 8.104845 8.057075 #>  [29,] 8.350203 8.310667 8.269288 8.225955 8.180595 8.133201 8.083897 8.033032 #>  [30,] 8.339555 8.299067 8.256537 8.211800 8.164711 8.115177 8.063216 8.009059 #>  [31,] 8.329315 8.287911 8.244262 8.198146 8.149340 8.097648 8.042956 7.985332 #>  [32,] 8.319524 8.277247 8.232525 8.185074 8.134586 8.080749 8.023289 7.962066 #>  [33,] 8.310217 8.267123 8.221390 8.172669 8.120562 8.064630 8.004415 7.939520 #>  [34,] 8.301431 8.257587 8.210919 8.161013 8.107381 8.049447 7.986553 7.917996 #>  [35,] 8.293201 8.248684 8.201171 8.150190 8.095159 8.035364 7.969936 7.897833 #>  [36,] 8.285557 8.240454 8.192204 8.140277 8.084005 8.022542 7.954804 7.879400 #>  [37,] 8.278526 8.232935 8.184068 8.131344 8.074022 8.011133 7.941395 7.863073 #>  [38,] 8.272133 8.226159 8.176806 8.123455 8.065300 8.001274 7.929925 7.849215 #>  [39,] 8.266396 8.220149 8.170454 8.116659 8.057914 7.993080 7.920578 7.838143 #>  [40,] 8.261327 8.214926 8.165035 8.110990 8.051916 7.986633 7.913491 7.830097 #>  [41,] 8.256935 8.210497 8.160565 8.106471 8.047337 7.981979 7.908742 7.825215 #>  [42,] 8.253221 8.206866 8.157045 8.103103 8.044181 7.979126 7.906339 7.823515 #>  [43,] 8.250181 8.204027 8.154468 8.100874 8.042428 7.978041 7.906228 7.824892 #>  [44,] 8.247805 8.201965 8.152812 8.099755 8.042033 7.978654 7.908291 7.829136 #>  [45,] 8.246077 8.200659 8.152049 8.099702 8.042932 7.980861 7.912358 7.835950 #>  [46,] 8.244977 8.200081 8.152138 8.100658 8.045039 7.984534 7.918222 7.844985 #>  [47,] 8.244479 8.200198 8.153034 8.102558 8.048258 7.989526 7.925654 7.855869 #>  [48,] 8.244556 8.200970 8.154681 8.105326 8.052483 7.995680 7.934418 7.868233 #>  [49,] 8.245174 8.202355 8.157024 8.108882 8.057600 8.002836 7.944278 7.881733 #>  [50,] 8.246300 8.204307 8.160002 8.113146 8.063498 8.010836 7.955013 7.896058 #>  [51,] 8.247898 8.206780 8.163551 8.118034 8.070065 8.019530 7.966421 7.910941 #>  [52,] 8.249929 8.209725 8.167612 8.123465 8.077196 8.028780 7.978322 7.926155 #>  [53,] 8.252357 8.213096 8.172122 8.129362 8.084790 8.038458 7.990559 7.941516 #>  [54,] 8.255144 8.216845 8.177023 8.135652 8.092756 8.048452 8.002999 7.956876 #>  [55,] 8.258254 8.220926 8.182260 8.142264 8.101011 8.058664 8.015529 7.972117 #>  [56,] 8.261650 8.225298 8.187779 8.149138 8.109480 8.069008 8.028057 7.987151 #>  [57,] 8.265299 8.229918 8.193533 8.156214 8.118098 8.079412 8.040508 8.001909 #>  [58,] 8.269167 8.234748 8.199475 8.163443 8.126808 8.089814 8.052822 8.016342 #>  [59,] 8.273225 8.239753 8.205567 8.170778 8.135558 8.100163 8.064952 8.030415 #>  [60,] 8.277443 8.244899 8.211769 8.178178 8.144308 8.110418 8.076862 8.044105 #>  [61,] 8.281794 8.250157 8.218050 8.185608 8.153020 8.120544 8.088524 8.057397 #>  [62,] 8.286254 8.255499 8.224380 8.193038 8.161664 8.130515 8.099918 8.070284 #>  [63,] 8.290800 8.260901 8.230733 8.200440 8.170216 8.140308 8.111030 8.082763 #>  [64,] 8.295411 8.266340 8.237084 8.207792 8.178653 8.149907 8.121850 8.094836 #>  [65,] 8.300069 8.271796 8.243416 8.215075 8.186959 8.159298 8.132373 8.106510 #>  [66,] 8.304755 8.277252 8.249709 8.222271 8.195120 8.168474 8.142597 8.117790 #>  [67,] 8.309456 8.282693 8.255949 8.229369 8.203125 8.177428 8.152523 8.128687 #>  [68,] 8.314156 8.288104 8.262124 8.236355 8.210967 8.186156 8.162151 8.139209 #>  [69,] 8.318845 8.293473 8.268221 8.243222 8.218638 8.194655 8.171487 8.149369 #>  [70,] 8.323510 8.298791 8.274232 8.249962 8.226134 8.202926 8.180535 8.159177 #>  [71,] 8.328142 8.304048 8.280149 8.256568 8.233453 8.210969 8.189300 8.168645 #>  [72,] 8.332733 8.309237 8.285965 8.263037 8.240592 8.218786 8.197789 8.177785 #>  [73,] 8.337275 8.314350 8.291675 8.269365 8.247551 8.226379 8.206009 8.186607 #>  [74,] 8.341762 8.319383 8.297276 8.275550 8.254330 8.233753 8.213966 8.195124 #>  [75,] 8.346188 8.324330 8.302763 8.281590 8.260930 8.240911 8.221668 8.203346 #>  [76,] 8.350548 8.329188 8.308134 8.287485 8.267353 8.247856 8.229123 8.211284 #>  [77,] 8.354838 8.333954 8.313388 8.293235 8.273600 8.254595 8.236337 8.218949 #>  [78,] 8.359055 8.338625 8.318523 8.298840 8.279674 8.261130 8.243318 8.226351 #>  [79,] 8.363196 8.343199 8.323538 8.304300 8.285577 8.267467 8.250073 8.233498 #>  [80,] 8.367259 8.347675 8.328434 8.309617 8.291313 8.273612 8.256609 8.240402 #>  [81,] 8.371241 8.352051 8.333209 8.314793 8.296884 8.279568 8.262934 8.247070 #>  [82,] 8.375140 8.356327 8.337866 8.319829 8.302294 8.285341 8.269052 8.253511 #>  [83,] 8.378957 8.360504 8.342404 8.324727 8.307546 8.290935 8.274972 8.259733 #>  [84,] 8.382689 8.364579 8.346825 8.329490 8.312643 8.296356 8.280699 8.265745 #>  [85,] 8.386336 8.368555 8.351129 8.334118 8.317589 8.301608 8.286240 8.271553 #>  [86,] 8.389899 8.372431 8.355318 8.338616 8.322388 8.306696 8.291601 8.277165 #>  [87,] 8.393376 8.376208 8.359393 8.342985 8.327043 8.311624 8.296786 8.282588 #>  [88,] 8.396768 8.379887 8.363356 8.347228 8.331556 8.316396 8.301803 8.287828 #>  [89,] 8.400075 8.383468 8.367209 8.351347 8.335933 8.321018 8.306655 8.292892 #>  [90,] 8.403298 8.386953 8.370953 8.355344 8.340175 8.325494 8.311348 8.297785 #>  [91,] 8.406437 8.390343 8.374590 8.359223 8.344286 8.329826 8.315888 8.302514 #>  [92,] 8.409492 8.393639 8.378122 8.362985 8.348270 8.334020 8.320278 8.307083 #>  [93,] 8.412465 8.396841 8.381551 8.366634 8.352130 8.338080 8.324523 8.311498 #>  [94,] 8.415356 8.399953 8.384878 8.370171 8.355868 8.342008 8.328628 8.315764 #>  [95,] 8.418166 8.402974 8.388106 8.373599 8.359487 8.345808 8.332597 8.319886 #>  [96,] 8.420895 8.405906 8.391236 8.376920 8.362992 8.349485 8.336433 8.323868 #>  [97,] 8.423546 8.408751 8.394271 8.380137 8.366384 8.353041 8.340142 8.327714 #>  [98,] 8.426119 8.411510 8.397211 8.383253 8.369666 8.356480 8.343726 8.331430 #>  [99,] 8.428614 8.414184 8.400060 8.386269 8.372841 8.359805 8.347189 8.335018 #> [100,] 8.431034 8.416776 8.402818 8.389187 8.375912 8.363019 8.350534 8.338483 #>           [,65]    [,66]    [,67]    [,68]    [,69]    [,70]    [,71]    [,72] #>   [1,] 8.563419 8.549697 8.536986 8.525350 8.514841 8.505496 8.497333 8.490352 #>   [2,] 8.548165 8.534152 8.521197 8.509372 8.498733 8.489320 8.481154 8.474234 #>   [3,] 8.532633 8.518309 8.505092 8.493062 8.482283 8.472798 8.464630 8.457777 #>   [4,] 8.516812 8.502152 8.488654 8.476404 8.465473 8.455911 8.447741 8.440963 #>   [5,] 8.500689 8.485668 8.471865 8.459378 8.448284 8.438638 8.430468 8.423771 #>   [6,] 8.484251 8.468840 8.454708 8.441963 8.430693 8.420958 8.412787 8.406180 #>   [7,] 8.467484 8.451651 8.437162 8.424138 8.412677 8.402844 8.394675 8.388168 #>   [8,] 8.450372 8.434083 8.419207 8.405879 8.394209 8.384272 8.376106 8.369708 #>   [9,] 8.432902 8.416116 8.400819 8.387160 8.375262 8.365211 8.357049 8.350773 #>  [10,] 8.415055 8.397730 8.381973 8.367951 8.355804 8.345629 8.337473 8.331333 #>  [11,] 8.396815 8.378903 8.362641 8.348222 8.335802 8.325491 8.317344 8.311355 #>  [12,] 8.378165 8.359610 8.342796 8.327939 8.315218 8.304758 8.296621 8.290802 #>  [13,] 8.359084 8.339826 8.322404 8.307064 8.294010 8.283386 8.275263 8.269633 #>  [14,] 8.339555 8.319524 8.301431 8.285557 8.272133 8.261327 8.253221 8.247805 #>  [15,] 8.319556 8.298674 8.279839 8.263370 8.249535 8.238527 8.230442 8.225267 #>  [16,] 8.299067 8.277247 8.257587 8.240454 8.226159 8.214926 8.206866 8.201965 #>  [17,] 8.278068 8.255209 8.234630 8.216753 8.201940 8.190454 8.182426 8.177836 #>  [18,] 8.256537 8.232525 8.210919 8.192204 8.176806 8.165035 8.157045 8.152812 #>  [19,] 8.234454 8.209160 8.186399 8.166738 8.150676 8.138581 8.130637 8.126815 #>  [20,] 8.211800 8.185074 8.161013 8.140277 8.123455 8.110990 8.103103 8.099755 #>  [21,] 8.188557 8.160229 8.134697 8.112732 8.095038 8.082147 8.074328 8.071533 #>  [22,] 8.164711 8.134586 8.107381 8.084005 8.065300 8.051916 8.044181 8.042033 #>  [23,] 8.140252 8.108105 8.078992 8.053983 8.034101 8.020140 8.012508 8.011124 #>  [24,] 8.115177 8.080749 8.049447 8.022542 8.001274 7.986633 7.979126 7.978654 #>  [25,] 8.089493 8.052485 8.018664 7.989536 7.966625 7.951172 7.943823 7.944445 #>  [26,] 8.063216 8.023289 7.986553 7.954804 7.929925 7.913491 7.906339 7.908291 #>  [27,] 8.036385 7.993147 7.953025 7.918161 7.890898 7.873267 7.866364 7.869950 #>  [28,] 8.009059 7.962066 7.917996 7.879400 7.849215 7.830097 7.823515 7.829136 #>  [29,] 7.981327 7.930081 7.881393 7.838288 7.804475 7.783481 7.777315 7.785511 #>  [30,] 7.953321 7.897269 7.843168 7.794572 7.756186 7.732777 7.727165 7.738673 #>  [31,] 7.925221 7.863768 7.803320 7.747983 7.703743 7.677152 7.672290 7.688149 #>  [32,] 7.897269 7.829797 7.761925 7.698260 7.646386 7.615490 7.611675 7.633381 #>  [33,] 7.869785 7.795689 7.719189 7.645189 7.583171 7.546256 7.543950 7.573734 #>  [34,] 7.843168 7.761925 7.675523 7.588690 7.512923 7.467256 7.467224 7.508527 #>  [35,] 7.817908 7.729162 7.631642 7.528991 7.434232 7.375207 7.378796 7.437146 #>  [36,] 7.794572 7.698260 7.588690 7.466934 7.345569 7.264887 7.274688 7.359351 #>  [37,] 7.773785 7.670273 7.548361 7.404507 7.245858 7.127302 7.148911 7.276038 #>  [38,] 7.756186 7.646386 7.512923 7.345569 7.136467 6.945128 6.992747 7.190930 #>  [39,] 7.742363 7.627790 7.485039 7.296389 7.026917 6.679589 6.797981 7.113505 #>  [40,] 7.732777 7.615490 7.467256 7.264887 6.945128 6.242973 6.594500 7.060921 #>  [41,] 7.727701 7.610095 7.461255 7.257411 6.931812 6.132575 6.561807 7.051089 #>  [42,] 7.727165 7.611675 7.467224 7.274688 6.992747 6.594500 6.740297 7.086248 #>  [43,] 7.730961 7.619744 7.483784 7.311301 7.089872 6.875718 6.932297 7.150456 #>  [44,] 7.738673 7.633381 7.508527 7.359351 7.190930 7.060921 7.086248 7.225430 #>  [45,] 7.749743 7.651430 7.538778 7.412108 7.283501 7.196402 7.208034 7.300143 #>  [46,] 7.763545 7.672697 7.572166 7.465237 7.365162 7.302191 7.306789 7.369946 #>  [47,] 7.779451 7.696099 7.606877 7.516419 7.436693 7.388409 7.388971 7.433519 #>  [48,] 7.796881 7.720733 7.641657 7.564611 7.499578 7.460813 7.458870 7.490931 #>  [49,] 7.815329 7.745900 7.675704 7.609479 7.555248 7.522975 7.519379 7.542736 #>  [50,] 7.834375 7.771081 7.708549 7.651043 7.604914 7.577250 7.572515 7.589601 #>  [51,] 7.853682 7.795911 7.739943 7.689490 7.649554 7.625276 7.619726 7.632165 #>  [52,] 7.872991 7.820144 7.769780 7.725068 7.689953 7.668232 7.662081 7.670993 #>  [53,] 7.892106 7.843625 7.798043 7.758040 7.726739 7.706994 7.700390 7.706568 #>  [54,] 7.910884 7.866261 7.824767 7.788657 7.760420 7.742234 7.735281 7.739301 #>  [55,] 7.929225 7.888006 7.850018 7.817152 7.791408 7.774474 7.767247 7.769537 #>  [56,] 7.947060 7.908846 7.873873 7.843733 7.820043 7.804129 7.796685 7.797568 #>  [57,] 7.964346 7.928785 7.896419 7.868586 7.846607 7.831535 7.823916 7.823641 #>  [58,] 7.981059 7.947845 7.917740 7.891876 7.871336 7.856968 7.849206 7.847968 #>  [59,] 7.997188 7.966055 7.937921 7.913747 7.894427 7.880653 7.872775 7.870728 #>  [60,] 8.012733 7.983448 7.957041 7.934326 7.916051 7.902784 7.894809 7.892076 #>  [61,] 8.027701 8.000062 7.975172 7.953727 7.936353 7.923520 7.915464 7.912146 #>  [62,] 8.042102 8.015935 7.992384 7.972048 7.955456 7.943001 7.934877 7.931054 #>  [63,] 8.055954 8.031104 8.008741 7.989380 7.973471 7.961344 7.953163 7.948904 #>  [64,] 8.069273 8.045606 8.024300 8.005800 7.990491 7.978652 7.970423 7.965783 #>  [65,] 8.082078 8.059477 8.039115 8.021378 8.006599 7.995015 7.986744 7.981771 #>  [66,] 8.094388 8.072750 8.053234 8.036178 8.021869 8.010511 8.002205 7.996938 #>  [67,] 8.106225 8.085457 8.066702 8.050256 8.036366 8.025209 8.016873 8.011347 #>  [68,] 8.117606 8.097630 8.079562 8.063662 8.050147 8.039171 8.030808 8.025052 #>  [69,] 8.128552 8.109295 8.091849 8.076443 8.063265 8.052451 8.044066 8.038104 #>  [70,] 8.139082 8.120481 8.103599 8.088639 8.075766 8.065098 8.056693 8.050547 #>  [71,] 8.149213 8.131212 8.114844 8.100288 8.087691 8.077155 8.068734 8.062422 #>  [72,] 8.158963 8.141512 8.125613 8.111425 8.099078 8.088663 8.080227 8.073766 #>  [73,] 8.168348 8.151403 8.135932 8.122080 8.109961 8.099657 8.091208 8.084612 #>  [74,] 8.177385 8.160904 8.145827 8.132282 8.120371 8.110168 8.101708 8.094990 #>  [75,] 8.186089 8.170036 8.155321 8.142057 8.130338 8.120227 8.111758 8.104928 #>  [76,] 8.194473 8.178817 8.164435 8.151430 8.139886 8.129860 8.121382 8.114451 #>  [77,] 8.202552 8.187262 8.173188 8.160422 8.149039 8.139092 8.130607 8.123583 #>  [78,] 8.210339 8.195389 8.181598 8.169053 8.157819 8.147945 8.139454 8.132345 #>  [79,] 8.217845 8.203211 8.189684 8.177342 8.166247 8.156440 8.147943 8.140756 #>  [80,] 8.225083 8.210742 8.197460 8.185308 8.174340 8.164595 8.156094 8.148835 #>  [81,] 8.232063 8.217996 8.204942 8.192965 8.182116 8.172429 8.163924 8.156599 #>  [82,] 8.238796 8.224984 8.212142 8.200329 8.189590 8.179958 8.171448 8.164063 #>  [83,] 8.245292 8.231719 8.219075 8.207414 8.196778 8.187196 8.178684 8.171241 #>  [84,] 8.251560 8.238210 8.225751 8.214232 8.203692 8.194158 8.185643 8.178148 #>  [85,] 8.257609 8.244468 8.232182 8.220796 8.210346 8.200856 8.192339 8.184795 #>  [86,] 8.263448 8.250503 8.238379 8.227118 8.216751 8.207303 8.198784 8.191195 #>  [87,] 8.269084 8.256323 8.244351 8.233207 8.222919 8.213510 8.204989 8.197358 #>  [88,] 8.274524 8.261937 8.250108 8.239074 8.228860 8.219487 8.210966 8.203295 #>  [89,] 8.279777 8.267353 8.255659 8.244727 8.234583 8.225245 8.216722 8.209015 #>  [90,] 8.284849 8.272579 8.261011 8.250177 8.240098 8.230793 8.222269 8.214528 #>  [91,] 8.289746 8.277621 8.266173 8.255430 8.245413 8.236139 8.227614 8.219841 #>  [92,] 8.294474 8.282487 8.271152 8.260495 8.250537 8.241291 8.232766 8.224963 #>  [93,] 8.299041 8.287183 8.275955 8.265379 8.255476 8.246258 8.237733 8.229901 #>  [94,] 8.303450 8.291715 8.280587 8.270089 8.260238 8.251046 8.242520 8.234662 #>  [95,] 8.307707 8.296089 8.285057 8.274631 8.264829 8.255662 8.247136 8.239253 #>  [96,] 8.311818 8.300310 8.289368 8.279012 8.269257 8.260113 8.251587 8.243680 #>  [97,] 8.315787 8.304384 8.293528 8.283237 8.273526 8.264405 8.255879 8.247950 #>  [98,] 8.319618 8.308315 8.297541 8.287312 8.277643 8.268543 8.260018 8.252067 #>  [99,] 8.323317 8.312109 8.301412 8.291242 8.281613 8.272534 8.264008 8.256038 #> [100,] 8.326888 8.315769 8.305146 8.295033 8.285442 8.276381 8.267856 8.259866 #>           [,73]    [,74]    [,75]    [,76]    [,77]    [,78]    [,79]    [,80] #>   [1,] 8.484534 8.479842 8.476226 8.473621 8.471951 8.471135 8.471085 8.471715 #>   [2,] 8.468540 8.464030 8.460649 8.458324 8.456973 8.456506 8.456830 8.457849 #>   [3,] 8.452217 8.447905 8.444777 8.442755 8.441747 8.441655 8.442377 8.443810 #>   [4,] 8.435550 8.431452 8.428599 8.426902 8.426263 8.426574 8.427721 8.429595 #>   [5,] 8.418518 8.414654 8.412098 8.410755 8.410514 8.411255 8.412858 8.415200 #>   [6,] 8.401103 8.397493 8.395262 8.394301 8.394488 8.395693 8.397783 8.400626 #>   [7,] 8.383283 8.379951 8.378073 8.377527 8.378177 8.379881 8.382492 8.385868 #>   [8,] 8.365035 8.362008 8.360514 8.360418 8.361571 8.363812 8.366982 8.370927 #>   [9,] 8.346334 8.343641 8.342567 8.342963 8.344658 8.347478 8.351249 8.355801 #>  [10,] 8.327152 8.324826 8.324214 8.325144 8.327429 8.330875 8.335290 8.340491 #>  [11,] 8.307460 8.305539 8.305433 8.306947 8.309873 8.313995 8.319103 8.324997 #>  [12,] 8.287224 8.285752 8.286202 8.288357 8.291981 8.296834 8.302687 8.309322 #>  [13,] 8.266409 8.265435 8.266500 8.269357 8.273741 8.279387 8.286041 8.293469 #>  [14,] 8.244977 8.244556 8.246300 8.249929 8.255144 8.261650 8.269167 8.277443 #>  [15,] 8.222883 8.223080 8.225579 8.230058 8.236181 8.243620 8.252068 8.261250 #>  [16,] 8.200081 8.200970 8.204307 8.209725 8.216845 8.225298 8.234748 8.244899 #>  [17,] 8.176519 8.178185 8.182458 8.188915 8.197127 8.206683 8.217214 8.228401 #>  [18,] 8.152138 8.154681 8.160002 8.167612 8.177023 8.187779 8.199475 8.211769 #>  [19,] 8.126875 8.130412 8.136908 8.145799 8.156531 8.168594 8.181546 8.195022 #>  [20,] 8.100658 8.105326 8.113146 8.123465 8.135652 8.149138 8.163443 8.178178 #>  [21,] 8.073409 8.079368 8.088686 8.100599 8.114390 8.129426 8.145188 8.161264 #>  [22,] 8.045039 8.052483 8.063498 8.077196 8.092756 8.109480 8.126808 8.144308 #>  [23,] 8.015450 8.024607 8.037556 8.053253 8.070768 8.089329 8.108336 8.127346 #>  [24,] 7.984534 7.995680 8.010836 8.028780 8.048452 8.069008 8.089814 8.110418 #>  [25,] 7.952169 7.965638 7.983324 8.003792 8.025845 8.048564 8.071290 8.093572 #>  [26,] 7.918222 7.934418 7.955013 7.978322 8.002999 8.028057 8.052822 8.076862 #>  [27,] 7.882546 7.901964 7.925914 7.952419 7.979980 8.007556 8.034480 8.060350 #>  [28,] 7.844985 7.868233 7.896058 7.926155 7.956876 7.987151 8.016342 8.044105 #>  [29,] 7.805373 7.833202 7.865510 7.899632 7.933798 7.966944 7.998501 8.028205 #>  [30,] 7.763545 7.796881 7.834375 7.872991 7.910884 7.947060 7.981059 8.012733 #>  [31,] 7.719354 7.759340 7.802818 7.846416 7.888304 7.927639 7.964132 7.997782 #>  [32,] 7.672697 7.720733 7.771081 7.820144 7.866261 7.908846 7.947845 7.983448 #>  [33,] 7.623571 7.681348 7.739504 7.794477 7.844992 7.890858 7.932334 7.969833 #>  [34,] 7.572166 7.641657 7.708549 7.769780 7.824767 7.873873 7.917740 7.957041 #>  [35,] 7.519015 7.602391 7.678815 7.746482 7.805884 7.858095 7.904207 7.945172 #>  [36,] 7.465237 7.564611 7.651043 7.725068 7.788657 7.843733 7.891876 7.934326 #>  [37,] 7.412866 7.529750 7.626099 7.706054 7.773403 7.830988 7.880879 7.924593 #>  [38,] 7.365162 7.499578 7.604914 7.689953 7.760420 7.820043 7.871336 7.916051 #>  [39,] 7.326624 7.476020 7.588386 7.677227 7.749966 7.811053 7.863341 7.908766 #>  [40,] 7.302191 7.460813 7.577250 7.668232 7.742234 7.804129 7.856968 7.902784 #>  [41,] 7.295446 7.455055 7.571943 7.663174 7.737334 7.799337 7.852254 7.898130 #>  [42,] 7.306789 7.458870 7.572515 7.662081 7.735281 7.796685 7.849206 7.894809 #>  [43,] 7.333222 7.471367 7.578624 7.664793 7.735992 7.796128 7.847797 7.892803 #>  [44,] 7.369946 7.490931 7.589601 7.670993 7.739301 7.797568 7.847968 7.892076 #>  [45,] 7.412288 7.515653 7.604584 7.680246 7.744967 7.800865 7.849631 7.892569 #>  [46,] 7.456713 7.543720 7.622646 7.692053 7.752705 7.805847 7.852677 7.894210 #>  [47,] 7.500954 7.573623 7.642906 7.705899 7.762205 7.812319 7.856978 7.896914 #>  [48,] 7.543720 7.604223 7.664595 7.721295 7.773153 7.820076 7.862398 7.900587 #>  [49,] 7.584369 7.634723 7.687083 7.737799 7.785250 7.828914 7.868795 7.905129 #>  [50,] 7.622646 7.664595 7.709879 7.755031 7.798220 7.838636 7.876030 7.910439 #>  [51,] 7.658514 7.693514 7.732617 7.772676 7.811818 7.849059 7.883966 7.916415 #>  [52,] 7.692053 7.721295 7.755031 7.790483 7.825834 7.860018 7.892475 7.922961 #>  [53,] 7.723397 7.747851 7.776939 7.808252 7.840090 7.871365 7.901442 7.929984 #>  [54,] 7.752705 7.773153 7.798220 7.825834 7.854439 7.882973 7.910758 7.937399 #>  [55,] 7.780136 7.797216 7.818799 7.843116 7.868765 7.894732 7.920331 7.945127 #>  [56,] 7.805847 7.820076 7.838636 7.860018 7.882973 7.906551 7.930076 7.953096 #>  [57,] 7.829983 7.841784 7.857713 7.876483 7.896989 7.918353 7.939924 7.961242 #>  [58,] 7.852677 7.862398 7.876030 7.892475 7.910758 7.930076 7.949812 7.969509 #>  [59,] 7.874049 7.881979 7.893599 7.907972 7.924238 7.941671 7.959688 7.977848 #>  [60,] 7.894210 7.900587 7.910439 7.922961 7.937399 7.953096 7.969509 7.986215 #>  [61,] 7.913258 7.918282 7.926573 7.937441 7.950221 7.964320 7.979239 7.994574 #>  [62,] 7.931279 7.935121 7.942031 7.951415 7.962689 7.975320 7.988848 8.002893 #>  [63,] 7.948355 7.951156 7.956839 7.964890 7.974796 7.986078 7.998313 8.011146 #>  [64,] 7.964557 7.966437 7.971026 7.977878 7.986539 7.996580 8.007614 8.019310 #>  [65,] 7.979947 7.981012 7.984623 7.990392 7.997919 8.006818 8.016737 8.027366 #>  [66,] 7.994586 7.994924 7.997657 8.002447 8.008939 8.016787 8.025669 8.035300 #>  [67,] 8.008524 8.008213 8.010156 8.014058 8.019604 8.026484 8.034404 8.043099 #>  [68,] 8.021809 8.020915 8.022146 8.025241 8.029922 8.035908 8.042933 8.050752 #>  [69,] 8.034485 8.033066 8.033652 8.036013 8.039900 8.045062 8.051255 8.058254 #>  [70,] 8.046590 8.044697 8.044698 8.046388 8.049547 8.053946 8.059365 8.065596 #>  [71,] 8.058160 8.055838 8.055306 8.056384 8.058872 8.062566 8.067265 8.072776 #>  [72,] 8.069228 8.066516 8.065499 8.066014 8.067885 8.070926 8.074953 8.079790 #>  [73,] 8.079823 8.076757 8.075295 8.075294 8.076595 8.079030 8.082432 8.086636 #>  [74,] 8.089973 8.086582 8.084713 8.084238 8.085013 8.086885 8.089703 8.093314 #>  [75,] 8.099703 8.096016 8.093773 8.092860 8.093147 8.094497 8.096769 8.099823 #>  [76,] 8.109036 8.105076 8.102489 8.101172 8.101008 8.101871 8.103632 8.106165 #>  [77,] 8.117993 8.113783 8.110879 8.109188 8.108605 8.109014 8.110298 8.112339 #>  [78,] 8.126594 8.122154 8.118957 8.116920 8.115946 8.115932 8.116769 8.118348 #>  [79,] 8.134857 8.130204 8.126736 8.124378 8.123041 8.122632 8.123049 8.124194 #>  [80,] 8.142800 8.137950 8.134231 8.131573 8.129898 8.129119 8.129143 8.129879 #>  [81,] 8.150437 8.145405 8.141452 8.138517 8.136526 8.135400 8.135055 8.135405 #>  [82,] 8.157784 8.152583 8.148413 8.145218 8.142932 8.141482 8.140789 8.140775 #>  [83,] 8.164855 8.159496 8.155123 8.151686 8.149124 8.147369 8.146350 8.145993 #>  [84,] 8.171660 8.166155 8.161594 8.157931 8.155109 8.153068 8.151741 8.151060 #>  [85,] 8.178214 8.172572 8.167834 8.163959 8.160895 8.158585 8.156968 8.155980 #>  [86,] 8.184526 8.178756 8.173854 8.169780 8.166488 8.163925 8.162033 8.160756 #>  [87,] 8.190608 8.184718 8.179662 8.175401 8.171894 8.169092 8.166943 8.165391 #>  [88,] 8.196468 8.190467 8.185265 8.180830 8.177121 8.174094 8.171700 8.169888 #>  [89,] 8.202117 8.196011 8.190673 8.186072 8.182173 8.178934 8.176309 8.174250 #>  [90,] 8.207562 8.201357 8.195891 8.191136 8.187057 8.183617 8.180773 8.178481 #>  [91,] 8.212812 8.206515 8.200928 8.196027 8.191778 8.188148 8.185097 8.182583 #>  [92,] 8.217875 8.211490 8.205790 8.200750 8.196342 8.192532 8.189284 8.186559 #>  [93,] 8.222757 8.216290 8.210483 8.205312 8.200753 8.196772 8.193338 8.190412 #>  [94,] 8.227466 8.220921 8.215012 8.209719 8.205016 8.200874 8.197262 8.194146 #>  [95,] 8.232007 8.225389 8.219385 8.213975 8.209135 8.204840 8.201060 8.197763 #>  [96,] 8.236388 8.229701 8.223606 8.218085 8.213117 8.208676 8.204735 8.201265 #>  [97,] 8.240613 8.233860 8.227679 8.222054 8.216963 8.212384 8.208291 8.204656 #>  [98,] 8.244688 8.237874 8.231611 8.225886 8.220679 8.215969 8.211730 8.207938 #>  [99,] 8.248619 8.241746 8.235406 8.229586 8.224269 8.219433 8.215056 8.211114 #> [100,] 8.252410 8.245481 8.239068 8.233158 8.227735 8.222780 8.218271 8.214186 #>           [,81]    [,82]    [,83]    [,84]    [,85]    [,86]    [,87]    [,88] #>   [1,] 8.472938 8.474668 8.476827 8.479339 8.482136 8.485156 8.488343 8.491646 #>   [2,] 8.459470 8.461603 8.464162 8.467070 8.470253 8.473649 8.477197 8.480849 #>   [3,] 8.445853 8.448411 8.451392 8.454714 8.458301 8.462087 8.466011 8.470022 #>   [4,] 8.432086 8.435091 8.438516 8.442273 8.446282 8.450475 8.454789 8.459171 #>   [5,] 8.418167 8.421646 8.425538 8.429750 8.434200 8.438815 8.443534 8.448301 #>   [6,] 8.404096 8.408076 8.412459 8.417148 8.422058 8.427114 8.432251 8.437415 #>   [7,] 8.389873 8.394383 8.399283 8.404473 8.409862 8.415376 8.420946 8.426519 #>   [8,] 8.375500 8.380569 8.386014 8.391727 8.397617 8.403605 8.409625 8.415620 #>   [9,] 8.360978 8.366638 8.372655 8.378917 8.385329 8.391810 8.398294 8.404724 #>  [10,] 8.346309 8.352595 8.359213 8.366049 8.373004 8.379997 8.386960 8.393837 #>  [11,] 8.331497 8.338443 8.345694 8.353130 8.360651 8.368174 8.375631 8.382968 #>  [12,] 8.316547 8.324190 8.332105 8.340168 8.348277 8.356349 8.364315 8.372124 #>  [13,] 8.301463 8.309843 8.318455 8.327173 8.335893 8.344531 8.353022 8.361314 #>  [14,] 8.286254 8.295411 8.304755 8.314156 8.323510 8.332733 8.341762 8.350548 #>  [15,] 8.270929 8.280906 8.291017 8.301129 8.311138 8.320964 8.330545 8.339836 #>  [16,] 8.255499 8.266340 8.277252 8.288104 8.298791 8.309237 8.319383 8.329188 #>  [17,] 8.239977 8.251727 8.263477 8.275097 8.286484 8.297566 8.308289 8.318617 #>  [18,] 8.224380 8.237084 8.249709 8.262124 8.274232 8.285965 8.297276 8.308134 #>  [19,] 8.208726 8.222432 8.235967 8.249203 8.262051 8.274450 8.286358 8.297752 #>  [20,] 8.193038 8.207792 8.222271 8.236355 8.249962 8.263037 8.275550 8.287485 #>  [21,] 8.177341 8.193189 8.208647 8.223602 8.237982 8.251745 8.264869 8.277347 #>  [22,] 8.161664 8.178653 8.195120 8.210967 8.226134 8.240592 8.254330 8.267353 #>  [23,] 8.146043 8.164213 8.181718 8.198475 8.214441 8.229599 8.243952 8.257517 #>  [24,] 8.130515 8.149907 8.168474 8.186156 8.202926 8.218786 8.233753 8.247856 #>  [25,] 8.115124 8.135771 8.155422 8.174037 8.191615 8.208175 8.223751 8.238386 #>  [26,] 8.099918 8.121850 8.142597 8.162151 8.180535 8.197789 8.213966 8.229123 #>  [27,] 8.084952 8.108188 8.130040 8.150531 8.169713 8.187651 8.204417 8.220084 #>  [28,] 8.070284 8.094836 8.117790 8.139209 8.159177 8.177785 8.195124 8.211284 #>  [29,] 8.055978 8.081846 8.105892 8.128223 8.148957 8.168214 8.186107 8.202742 #>  [30,] 8.042102 8.069273 8.094388 8.117606 8.139082 8.158963 8.177385 8.194473 #>  [31,] 8.028730 8.057173 8.083326 8.107397 8.129580 8.150055 8.168978 8.186493 #>  [32,] 8.015935 8.045606 8.072750 8.097630 8.120481 8.141512 8.160904 8.178817 #>  [33,] 8.003795 8.034629 8.062704 8.088340 8.111812 8.133358 8.153182 8.171460 #>  [34,] 7.992384 8.024300 8.053234 8.079562 8.103599 8.125613 8.145827 8.164435 #>  [35,] 7.981779 8.014673 8.044379 8.071326 8.095867 8.118296 8.138856 8.157754 #>  [36,] 7.972048 8.005800 8.036178 8.063662 8.088639 8.111425 8.132282 8.151430 #>  [37,] 7.963256 7.997726 8.028665 8.056596 8.081933 8.105014 8.126117 8.145471 #>  [38,] 7.955456 7.990491 8.021869 8.050147 8.075766 8.099078 8.120371 8.139886 #>  [39,] 7.948694 7.984125 8.015812 8.044335 8.070151 8.093625 8.115053 8.134681 #>  [40,] 7.943001 7.978652 8.010511 8.039171 8.065098 8.088663 8.110168 8.129860 #>  [41,] 7.938394 7.974083 8.005974 8.034661 8.060611 8.084197 8.105720 8.125427 #>  [42,] 7.934877 7.970423 8.002205 8.030808 8.056693 8.080227 8.101708 8.121382 #>  [43,] 7.932439 7.967662 7.999197 8.027608 8.053341 8.076752 8.098133 8.117725 #>  [44,] 7.931054 7.965783 7.996938 8.025052 8.050547 8.073766 8.094990 8.114451 #>  [45,] 7.930684 7.964760 7.995410 8.023125 8.048301 8.071262 8.092273 8.111557 #>  [46,] 7.931279 7.964557 7.994586 8.021809 8.046590 8.069228 8.089973 8.109036 #>  [47,] 7.932780 7.965132 7.994436 8.021081 8.045395 8.067651 8.088080 8.106879 #>  [48,] 7.935121 7.966437 7.994924 8.020915 8.044697 8.066516 8.086582 8.105076 #>  [49,] 7.938229 7.968421 7.996012 8.021281 8.044473 8.065805 8.085465 8.103617 #>  [50,] 7.942031 7.971026 7.997657 8.022146 8.044698 8.065499 8.084713 8.102489 #>  [51,] 7.946451 7.974198 7.999817 8.023478 8.045346 8.065575 8.084310 8.101679 #>  [52,] 7.951415 7.977878 8.002447 8.025241 8.046388 8.066014 8.084238 8.101172 #>  [53,] 7.956850 7.982010 8.005502 8.027401 8.047798 8.066791 8.084478 8.100954 #>  [54,] 7.962689 7.986539 8.008939 8.029922 8.049547 8.067885 8.085013 8.101008 #>  [55,] 7.968865 7.991412 8.012714 8.032769 8.051605 8.069271 8.085821 8.101319 #>  [56,] 7.975320 7.996580 8.016787 8.035908 8.053946 8.070926 8.086885 8.101871 #>  [57,] 7.981998 8.001995 8.021118 8.039307 8.056542 8.072828 8.088186 8.102647 #>  [58,] 7.988848 8.007614 8.025669 8.042933 8.059365 8.074953 8.089703 8.103632 #>  [59,] 7.995827 8.013398 8.030408 8.046758 8.062392 8.077281 8.091418 8.104810 #>  [60,] 8.002893 8.019310 8.035300 8.050752 8.065596 8.079790 8.093314 8.106165 #>  [61,] 8.010012 8.025317 8.040317 8.054891 8.068956 8.082460 8.095373 8.107681 #>  [62,] 8.017152 8.031390 8.045432 8.059148 8.072449 8.085272 8.097578 8.109345 #>  [63,] 8.024286 8.037503 8.050620 8.063503 8.076055 8.088207 8.099912 8.111142 #>  [64,] 8.031390 8.043632 8.055858 8.067933 8.079755 8.091249 8.102362 8.113057 #>  [65,] 8.038445 8.049756 8.061127 8.072421 8.083532 8.094382 8.104911 8.115080 #>  [66,] 8.045432 8.055858 8.066409 8.076949 8.087370 8.097590 8.107547 8.117196 #>  [67,] 8.052337 8.061922 8.071688 8.081500 8.091253 8.100860 8.110257 8.119394 #>  [68,] 8.059148 8.067933 8.076949 8.086062 8.095168 8.104179 8.113028 8.121663 #>  [69,] 8.065855 8.073881 8.082180 8.090622 8.099102 8.107535 8.115850 8.123994 #>  [70,] 8.072449 8.079755 8.087370 8.095168 8.103045 8.110916 8.118711 8.126375 #>  [71,] 8.078923 8.085547 8.092509 8.099690 8.106986 8.114314 8.121604 8.128797 #>  [72,] 8.085272 8.091249 8.097590 8.104179 8.110916 8.117719 8.124518 8.131253 #>  [73,] 8.091491 8.096856 8.102605 8.108627 8.114827 8.121123 8.127445 8.133735 #>  [74,] 8.097578 8.102362 8.107547 8.113028 8.118711 8.124518 8.130378 8.136235 #>  [75,] 8.103530 8.107763 8.112412 8.117375 8.122563 8.127896 8.133310 8.138745 #>  [76,] 8.109345 8.113057 8.117196 8.121663 8.126375 8.131253 8.136235 8.141261 #>  [77,] 8.115023 8.118241 8.121894 8.125888 8.130142 8.134583 8.139146 8.143776 #>  [78,] 8.120564 8.123314 8.126503 8.130046 8.133862 8.137880 8.142040 8.146285 #>  [79,] 8.125967 8.128273 8.131022 8.134132 8.137528 8.141141 8.144911 8.148783 #>  [80,] 8.131233 8.133118 8.135448 8.138146 8.141138 8.144361 8.147754 8.151266 #>  [81,] 8.136364 8.137849 8.139780 8.142083 8.144690 8.147536 8.150567 8.153730 #>  [82,] 8.141360 8.142465 8.144016 8.145943 8.148179 8.150665 8.153345 8.156171 #>  [83,] 8.146223 8.146968 8.148157 8.149724 8.151605 8.153743 8.156086 8.158585 #>  [84,] 8.150954 8.151357 8.152201 8.153424 8.154965 8.156770 8.158787 8.160971 #>  [85,] 8.155556 8.155634 8.156149 8.157043 8.158258 8.159742 8.161445 8.163324 #>  [86,] 8.160031 8.159799 8.160000 8.160580 8.161482 8.162658 8.164059 8.165643 #>  [87,] 8.164379 8.163853 8.163756 8.164034 8.164637 8.165516 8.166626 8.167926 #>  [88,] 8.168605 8.167798 8.167416 8.167407 8.167722 8.168316 8.169146 8.170170 #>  [89,] 8.172709 8.171636 8.170981 8.170696 8.170736 8.171056 8.171615 8.172374 #>  [90,] 8.176694 8.175366 8.174452 8.173904 8.173679 8.173736 8.174034 8.174537 #>  [91,] 8.180562 8.178993 8.177829 8.177029 8.176551 8.176355 8.176402 8.176656 #>  [92,] 8.184316 8.182515 8.181115 8.180073 8.179352 8.178912 8.178716 8.178732 #>  [93,] 8.187958 8.185937 8.184309 8.183036 8.182081 8.181407 8.180978 8.180762 #>  [94,] 8.191490 8.189258 8.187413 8.185919 8.184739 8.183839 8.183186 8.182747 #>  [95,] 8.194914 8.192481 8.190429 8.188722 8.187327 8.186210 8.185340 8.184685 #>  [96,] 8.198233 8.195608 8.193357 8.191446 8.189844 8.188518 8.187439 8.186576 #>  [97,] 8.201449 8.198640 8.196198 8.194092 8.192291 8.190764 8.189483 8.188419 #>  [98,] 8.204564 8.201579 8.198955 8.196661 8.194668 8.192948 8.191472 8.190215 #>  [99,] 8.207580 8.204427 8.201627 8.199153 8.196977 8.195070 8.193407 8.191961 #> [100,] 8.210499 8.207185 8.204218 8.201571 8.199217 8.197131 8.195287 8.193660 #>           [,89]    [,90]    [,91]    [,92]    [,93]    [,94]    [,95]    [,96] #>   [1,] 8.495023 8.498436 8.501850 8.505238 8.508575 8.511841 8.515020 8.518095 #>   [2,] 8.484558 8.488286 8.492001 8.495673 8.499280 8.502800 8.506218 8.509520 #>   [3,] 8.474074 8.478128 8.482151 8.486114 8.489995 8.493775 8.497436 8.500967 #>   [4,] 8.463576 8.467965 8.472303 8.476565 8.480726 8.484769 8.488678 8.492440 #>   [5,] 8.453069 8.457801 8.462464 8.467029 8.471476 8.475787 8.479946 8.483944 #>   [6,] 8.442558 8.447643 8.452636 8.457512 8.462250 8.466832 8.471246 8.475481 #>   [7,] 8.432048 8.437494 8.442826 8.448018 8.453051 8.457910 8.462581 8.467056 #>   [8,] 8.421545 8.427361 8.433038 8.438553 8.443886 8.449024 8.453955 8.458673 #>   [9,] 8.411054 8.417249 8.423279 8.429122 8.434760 8.440180 8.445374 8.450335 #>  [10,] 8.400584 8.407166 8.413555 8.419730 8.425677 8.431383 8.436841 8.442048 #>  [11,] 8.390141 8.397118 8.403872 8.410385 8.416643 8.422637 8.428362 8.433815 #>  [12,] 8.379733 8.387112 8.394237 8.401092 8.407665 8.413949 8.419942 8.425642 #>  [13,] 8.369368 8.377156 8.384657 8.391857 8.398748 8.405324 8.411585 8.417532 #>  [14,] 8.359055 8.367259 8.375140 8.382689 8.389899 8.396768 8.403298 8.409492 #>  [15,] 8.348804 8.357429 8.365694 8.373594 8.381124 8.388287 8.395086 8.401526 #>  [16,] 8.338625 8.347675 8.356327 8.364579 8.372431 8.379887 8.386953 8.393639 #>  [17,] 8.328527 8.338006 8.347048 8.355654 8.363827 8.371575 8.378907 8.385836 #>  [18,] 8.318523 8.328434 8.337866 8.346825 8.355318 8.363356 8.370953 8.378122 #>  [19,] 8.308623 8.318967 8.328790 8.338100 8.346912 8.355238 8.363097 8.370504 #>  [20,] 8.298840 8.309617 8.319829 8.329490 8.338616 8.347228 8.355344 8.362985 #>  [21,] 8.289185 8.300395 8.310994 8.321001 8.330439 8.339332 8.347702 8.355572 #>  [22,] 8.279674 8.291313 8.302294 8.312643 8.322388 8.331556 8.340175 8.348270 #>  [23,] 8.270317 8.282381 8.293739 8.304425 8.314471 8.323909 8.332770 8.341084 #>  [24,] 8.261130 8.273612 8.285341 8.296356 8.306696 8.316396 8.325494 8.334020 #>  [25,] 8.252126 8.265017 8.277108 8.288444 8.299070 8.309025 8.318351 8.327083 #>  [26,] 8.243318 8.256609 8.269052 8.280699 8.291601 8.301803 8.311348 8.320278 #>  [27,] 8.234722 8.248400 8.261183 8.273130 8.284297 8.294735 8.304491 8.313609 #>  [28,] 8.226351 8.240402 8.253511 8.265745 8.277165 8.287828 8.297785 8.307083 #>  [29,] 8.218218 8.232626 8.246045 8.258552 8.270213 8.281090 8.291236 8.300703 #>  [30,] 8.210339 8.225083 8.238796 8.251560 8.263448 8.274524 8.284849 8.294474 #>  [31,] 8.202725 8.217785 8.231773 8.244777 8.256876 8.268138 8.278628 8.288401 #>  [32,] 8.195389 8.210742 8.224984 8.238210 8.250503 8.261937 8.272579 8.282487 #>  [33,] 8.188343 8.203964 8.218438 8.231866 8.244335 8.255926 8.266705 8.276736 #>  [34,] 8.181598 8.197460 8.212142 8.225751 8.238379 8.250108 8.261011 8.271152 #>  [35,] 8.175165 8.191239 8.206104 8.219871 8.232638 8.244490 8.255501 8.265737 #>  [36,] 8.169053 8.185308 8.200329 8.214232 8.227118 8.239074 8.250177 8.260495 #>  [37,] 8.163269 8.179673 8.194823 8.208838 8.221821 8.233863 8.245042 8.255428 #>  [38,] 8.157819 8.174340 8.189590 8.203692 8.216751 8.228860 8.240098 8.250537 #>  [39,] 8.152710 8.169313 8.184634 8.198798 8.211911 8.224068 8.235348 8.245824 #>  [40,] 8.147945 8.164595 8.179958 8.194158 8.207303 8.219487 8.230793 8.241291 #>  [41,] 8.143526 8.160189 8.175562 8.189772 8.202927 8.215120 8.226433 8.236938 #>  [42,] 8.139454 8.156094 8.171448 8.185643 8.198784 8.210966 8.222269 8.232766 #>  [43,] 8.135727 8.152310 8.167616 8.181768 8.194874 8.207024 8.218301 8.228775 #>  [44,] 8.132345 8.148835 8.164063 8.178148 8.191195 8.203295 8.214528 8.224963 #>  [45,] 8.129302 8.145667 8.160787 8.174780 8.187747 8.199777 8.210949 8.221330 #>  [46,] 8.126594 8.142800 8.157784 8.171660 8.184526 8.196468 8.207562 8.217875 #>  [47,] 8.124214 8.140230 8.155052 8.168787 8.181531 8.193366 8.204366 8.214595 #>  [48,] 8.122154 8.137950 8.152583 8.166155 8.178756 8.190467 8.201357 8.211490 #>  [49,] 8.120405 8.135953 8.150372 8.163759 8.176199 8.187768 8.198534 8.208556 #>  [50,] 8.118957 8.134231 8.148413 8.161594 8.173854 8.185265 8.195891 8.205790 #>  [51,] 8.117799 8.132774 8.146698 8.159653 8.171716 8.182954 8.193427 8.203189 #>  [52,] 8.116920 8.131573 8.145218 8.157931 8.169780 8.180830 8.191136 8.200750 #>  [53,] 8.116306 8.130618 8.143966 8.156418 8.168040 8.178887 8.189014 8.198469 #>  [54,] 8.115946 8.129898 8.142932 8.155109 8.166488 8.177121 8.187057 8.196342 #>  [55,] 8.115826 8.129402 8.142107 8.153995 8.165119 8.175525 8.185260 8.194364 #>  [56,] 8.115932 8.129119 8.141482 8.153068 8.163925 8.174094 8.183617 8.192532 #>  [57,] 8.116251 8.129037 8.141046 8.152320 8.162899 8.172821 8.182123 8.190840 #>  [58,] 8.116769 8.129143 8.140789 8.151741 8.162033 8.171700 8.180773 8.189284 #>  [59,] 8.117473 8.129428 8.140703 8.151324 8.161322 8.170724 8.179561 8.187858 #>  [60,] 8.118348 8.129879 8.140775 8.151060 8.160756 8.169888 8.178481 8.186559 #>  [61,] 8.119383 8.130484 8.140998 8.150939 8.160328 8.169183 8.177527 8.185380 #>  [62,] 8.120564 8.131233 8.141360 8.150954 8.160031 8.168605 8.176694 8.184316 #>  [63,] 8.121878 8.132115 8.141852 8.151096 8.159857 8.168145 8.175976 8.183363 #>  [64,] 8.123314 8.133118 8.142465 8.151357 8.159799 8.167798 8.175366 8.182515 #>  [65,] 8.124859 8.134232 8.143190 8.151728 8.159849 8.167557 8.174860 8.181768 #>  [66,] 8.126503 8.135448 8.144016 8.152201 8.160000 8.167416 8.174452 8.181115 #>  [67,] 8.128236 8.136756 8.144937 8.152769 8.160246 8.167368 8.174135 8.180552 #>  [68,] 8.130046 8.138146 8.145943 8.153424 8.160580 8.167407 8.173904 8.180073 #>  [69,] 8.131924 8.139609 8.147026 8.154158 8.160994 8.167527 8.173754 8.179675 #>  [70,] 8.133862 8.141138 8.148179 8.154965 8.161482 8.167722 8.173679 8.179352 #>  [71,] 8.135850 8.142725 8.149394 8.155838 8.162039 8.167987 8.173675 8.179099 #>  [72,] 8.137880 8.144361 8.150665 8.156770 8.162658 8.168316 8.173736 8.178912 #>  [73,] 8.139946 8.146039 8.151984 8.157755 8.163333 8.168704 8.173857 8.178786 #>  [74,] 8.142040 8.147754 8.153345 8.158787 8.164059 8.169146 8.174034 8.178716 #>  [75,] 8.144155 8.149498 8.154743 8.159861 8.164831 8.169636 8.174262 8.178700 #>  [76,] 8.146285 8.151266 8.156171 8.160971 8.165643 8.170170 8.174537 8.178732 #>  [77,] 8.148425 8.153053 8.157624 8.162112 8.166491 8.170744 8.174853 8.178808 #>  [78,] 8.150569 8.154852 8.159098 8.163279 8.167371 8.171352 8.175209 8.178926 #>  [79,] 8.152713 8.156659 8.160587 8.164468 8.168277 8.171992 8.175598 8.179080 #>  [80,] 8.154852 8.158471 8.162088 8.165675 8.169206 8.172659 8.176018 8.179268 #>  [81,] 8.156981 8.160281 8.163596 8.166895 8.170154 8.173350 8.176466 8.179486 #>  [82,] 8.159098 8.162088 8.165107 8.168125 8.171117 8.174060 8.176937 8.179730 #>  [83,] 8.161198 8.163887 8.166618 8.169361 8.172091 8.174787 8.177428 8.179999 #>  [84,] 8.163279 8.165675 8.168125 8.170600 8.173075 8.175527 8.177937 8.180288 #>  [85,] 8.165337 8.167449 8.169625 8.171839 8.174064 8.176277 8.178460 8.180596 #>  [86,] 8.167371 8.169206 8.171117 8.173075 8.175055 8.177035 8.178995 8.180919 #>  [87,] 8.169376 8.170943 8.172596 8.174305 8.176046 8.177798 8.179539 8.181254 #>  [88,] 8.171352 8.172659 8.174060 8.175527 8.177035 8.178562 8.180090 8.181600 #>  [89,] 8.173297 8.174352 8.175508 8.176738 8.178019 8.179327 8.180645 8.181954 #>  [90,] 8.175209 8.176018 8.176937 8.177937 8.178995 8.180090 8.181202 8.182314 #>  [91,] 8.177085 8.177657 8.178345 8.179121 8.179962 8.180848 8.181759 8.182677 #>  [92,] 8.178926 8.179268 8.179730 8.180288 8.180919 8.181600 8.182314 8.183043 #>  [93,] 8.180728 8.180847 8.181092 8.181438 8.181862 8.182344 8.182865 8.183408 #>  [94,] 8.182493 8.182395 8.182428 8.182567 8.182791 8.183078 8.183411 8.183772 #>  [95,] 8.184218 8.183911 8.183738 8.183676 8.183704 8.183801 8.183949 8.184132 #>  [96,] 8.185903 8.185392 8.185019 8.184762 8.184599 8.184511 8.184479 8.184487 #>  [97,] 8.187546 8.186838 8.186272 8.185825 8.185476 8.185206 8.184998 8.184836 #>  [98,] 8.189148 8.188249 8.187495 8.186862 8.186332 8.185886 8.185507 8.185178 #>  [99,] 8.190708 8.189624 8.188686 8.187874 8.187168 8.186550 8.186002 8.185510 #> [100,] 8.192226 8.190962 8.189847 8.188860 8.187982 8.187196 8.186484 8.185832 #>           [,97]    [,98]    [,99]   [,100] #>   [1,] 8.521057 8.523895 8.526602 8.529172 #>   [2,] 8.512694 8.515732 8.518628 8.521375 #>   [3,] 8.504356 8.507597 8.510682 8.513608 #>   [4,] 8.496048 8.499492 8.502769 8.505875 #>   [5,] 8.487771 8.491422 8.494892 8.498178 #>   [6,] 8.479531 8.483389 8.487053 8.490520 #>   [7,] 8.471329 8.475396 8.479255 8.482904 #>   [8,] 8.463171 8.467448 8.471502 8.475333 #>   [9,] 8.455060 8.459547 8.463797 8.467811 #>  [10,] 8.447000 8.451698 8.456144 8.460340 #>  [11,] 8.438995 8.443905 8.448546 8.452923 #>  [12,] 8.431050 8.436170 8.441007 8.445564 #>  [13,] 8.423169 8.428499 8.433530 8.438267 #>  [14,] 8.415356 8.420895 8.426119 8.431034 #>  [15,] 8.407615 8.413363 8.418778 8.423869 #>  [16,] 8.399953 8.405906 8.411510 8.416776 #>  [17,] 8.392372 8.398529 8.404320 8.409757 #>  [18,] 8.384878 8.391236 8.397211 8.402818 #>  [19,] 8.377476 8.384032 8.390187 8.395960 #>  [20,] 8.370171 8.376920 8.383253 8.389187 #>  [21,] 8.362966 8.369905 8.376411 8.382503 #>  [22,] 8.355868 8.362992 8.369666 8.375912 #>  [23,] 8.348880 8.356184 8.363021 8.369416 #>  [24,] 8.342008 8.349485 8.356480 8.363019 #>  [25,] 8.335256 8.342900 8.350047 8.356724 #>  [26,] 8.328628 8.336433 8.343726 8.350534 #>  [27,] 8.322129 8.330088 8.337519 8.344453 #>  [28,] 8.315764 8.323868 8.331430 8.338483 #>  [29,] 8.309536 8.317777 8.325462 8.332627 #>  [30,] 8.303450 8.311818 8.319618 8.326888 #>  [31,] 8.297508 8.305995 8.313902 8.321268 #>  [32,] 8.291715 8.300310 8.308315 8.315769 #>  [33,] 8.286074 8.294767 8.302861 8.310395 #>  [34,] 8.280587 8.289368 8.297541 8.305146 #>  [35,] 8.275258 8.284116 8.292357 8.300025 #>  [36,] 8.270089 8.279012 8.287312 8.295033 #>  [37,] 8.265082 8.274059 8.282407 8.290171 #>  [38,] 8.260238 8.269257 8.277643 8.285442 #>  [39,] 8.255559 8.264608 8.273022 8.280845 #>  [40,] 8.251046 8.260113 8.268543 8.276381 #>  [41,] 8.246700 8.255773 8.264209 8.272051 #>  [42,] 8.242520 8.251587 8.260018 8.267856 #>  [43,] 8.238508 8.247557 8.255971 8.263794 #>  [44,] 8.234662 8.243680 8.252067 8.259866 #>  [45,] 8.230981 8.239958 8.248307 8.256072 #>  [46,] 8.227466 8.236388 8.244688 8.252410 #>  [47,] 8.224113 8.232969 8.241211 8.248880 #>  [48,] 8.220921 8.229701 8.237874 8.245481 #>  [49,] 8.217888 8.226580 8.234674 8.242211 #>  [50,] 8.215012 8.223606 8.231611 8.239068 #>  [51,] 8.212290 8.220775 8.228683 8.236051 #>  [52,] 8.209719 8.218085 8.225886 8.233158 #>  [53,] 8.207295 8.215533 8.223219 8.230387 #>  [54,] 8.205016 8.213117 8.220679 8.227735 #>  [55,] 8.202877 8.210832 8.218263 8.225201 #>  [56,] 8.200874 8.208676 8.215969 8.222780 #>  [57,] 8.199004 8.206645 8.213792 8.220471 #>  [58,] 8.197262 8.204735 8.211730 8.218271 #>  [59,] 8.195644 8.202943 8.209780 8.216177 #>  [60,] 8.194146 8.201265 8.207938 8.214186 #>  [61,] 8.192763 8.199696 8.206200 8.212294 #>  [62,] 8.191490 8.198233 8.204564 8.210499 #>  [63,] 8.190323 8.196872 8.203025 8.208797 #>  [64,] 8.189258 8.195608 8.201579 8.207185 #>  [65,] 8.188290 8.194438 8.200224 8.205660 #>  [66,] 8.187413 8.193357 8.198955 8.204218 #>  [67,] 8.186625 8.192361 8.197768 8.202856 #>  [68,] 8.185919 8.191446 8.196661 8.201571 #>  [69,] 8.185292 8.190608 8.195629 8.200359 #>  [70,] 8.184739 8.189844 8.194668 8.199217 #>  [71,] 8.184256 8.189148 8.193776 8.198142 #>  [72,] 8.183839 8.188518 8.192948 8.197131 #>  [73,] 8.183484 8.187949 8.192181 8.196180 #>  [74,] 8.183186 8.187439 8.191472 8.195287 #>  [75,] 8.182942 8.186982 8.190818 8.194448 #>  [76,] 8.182747 8.186576 8.190215 8.193660 #>  [77,] 8.182599 8.186217 8.189659 8.192920 #>  [78,] 8.182493 8.185903 8.189148 8.192226 #>  [79,] 8.182426 8.185628 8.188679 8.191574 #>  [80,] 8.182395 8.185392 8.188249 8.190962 #>  [81,] 8.182397 8.185190 8.187855 8.190387 #>  [82,] 8.182428 8.185019 8.187495 8.189847 #>  [83,] 8.182486 8.184878 8.187164 8.189338 #>  [84,] 8.182567 8.184762 8.186862 8.188860 #>  [85,] 8.182670 8.184670 8.186586 8.188408 #>  [86,] 8.182791 8.184599 8.186332 8.187982 #>  [87,] 8.182928 8.184547 8.186100 8.187579 #>  [88,] 8.183078 8.184511 8.185886 8.187196 #>  [89,] 8.183240 8.184489 8.185689 8.186832 #>  [90,] 8.183411 8.184479 8.185507 8.186484 #>  [91,] 8.183589 8.184479 8.185337 8.186151 #>  [92,] 8.183772 8.184487 8.185178 8.185832 #>  [93,] 8.183958 8.184502 8.185027 8.185524 #>  [94,] 8.184147 8.184522 8.184885 8.185225 #>  [95,] 8.184335 8.184544 8.184747 8.184934 #>  [96,] 8.184522 8.184568 8.184615 8.184650 #>  [97,] 8.184705 8.184592 8.184484 8.184371 #>  [98,] 8.184885 8.184615 8.184355 8.184096 #>  [99,] 8.185058 8.184634 8.184226 8.183824 #> [100,] 8.185225 8.184650 8.184096 8.183552 potential_to_head(mc, phic) #>            [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8] #>   [1,] 9.624030 9.611546 9.598996 9.586378 9.573691 9.560933 9.548101 9.535196 #>   [2,] 9.619708 9.607204 9.594633 9.581993 9.569283 9.556500 9.543644 9.530712 #>   [3,] 9.615403 9.602879 9.590287 9.577626 9.564892 9.552086 9.539206 9.526248 #>   [4,] 9.611115 9.598571 9.585959 9.573276 9.560520 9.547691 9.534786 9.521804 #>   [5,] 9.606844 9.594281 9.581648 9.568944 9.556167 9.543315 9.530386 9.517379 #>   [6,] 9.602589 9.590007 9.577355 9.564630 9.551832 9.538958 9.526006 9.512974 #>   [7,] 9.598352 9.585752 9.573080 9.560335 9.547516 9.534620 9.521645 9.508590 #>   [8,] 9.594132 9.581514 9.568823 9.556059 9.543219 9.530302 9.517305 9.504226 #>   [9,] 9.589930 9.577294 9.564585 9.551802 9.538942 9.526003 9.512985 9.499884 #>  [10,] 9.585745 9.573092 9.560365 9.547563 9.534684 9.521725 9.508685 9.495562 #>  [11,] 9.581579 9.568909 9.556165 9.543344 9.530446 9.517468 9.504407 9.491262 #>  [12,] 9.577430 9.564744 9.551983 9.539145 9.526228 9.513230 9.500150 9.486984 #>  [13,] 9.573300 9.560598 9.547820 9.534965 9.522030 9.509014 9.495913 9.482727 #>  [14,] 9.569188 9.556471 9.543677 9.530805 9.517853 9.504818 9.491699 9.478493 #>  [15,] 9.565095 9.552362 9.539553 9.526665 9.513696 9.500644 9.487506 9.474281 #>  [16,] 9.561020 9.548273 9.535449 9.522546 9.509560 9.496491 9.483335 9.470091 #>  [17,] 9.556964 9.544204 9.531365 9.518446 9.505445 9.492360 9.479187 9.465925 #>  [18,] 9.552928 9.540154 9.527301 9.514368 9.501352 9.488250 9.475061 9.461781 #>  [19,] 9.548910 9.536123 9.523257 9.510310 9.497279 9.484162 9.470957 9.457661 #>  [20,] 9.544912 9.532113 9.519234 9.506273 9.493228 9.480097 9.466876 9.453564 #>  [21,] 9.540933 9.528122 9.515231 9.502257 9.489199 9.476053 9.462818 9.449490 #>  [22,] 9.536973 9.524151 9.511248 9.498263 9.485191 9.472033 9.458783 9.445441 #>  [23,] 9.533033 9.520201 9.507287 9.494289 9.481206 9.468034 9.454772 9.441415 #>  [24,] 9.529113 9.516270 9.503346 9.490337 9.477243 9.464059 9.450784 9.437414 #>  [25,] 9.525213 9.512360 9.499426 9.486407 9.473301 9.460106 9.446819 9.433437 #>  [26,] 9.521333 9.508471 9.495527 9.482499 9.469383 9.456177 9.442878 9.429484 #>  [27,] 9.517472 9.504602 9.491650 9.478612 9.465486 9.452270 9.438961 9.425556 #>  [28,] 9.513632 9.500754 9.487793 9.474747 9.461612 9.448387 9.435068 9.421653 #>  [29,] 9.509812 9.496927 9.483959 9.470904 9.457761 9.444527 9.431199 9.417774 #>  [30,] 9.506012 9.493121 9.480145 9.467083 9.453933 9.440691 9.427355 9.413921 #>  [31,] 9.502233 9.489335 9.476353 9.463285 9.450127 9.436878 9.423534 9.410093 #>  [32,] 9.498474 9.485571 9.472583 9.459509 9.446345 9.433089 9.419738 9.406289 #>  [33,] 9.494736 9.481827 9.468835 9.455755 9.442585 9.429324 9.415967 9.402511 #>  [34,] 9.491018 9.478105 9.465108 9.452023 9.438849 9.425582 9.412220 9.398759 #>  [35,] 9.487320 9.474404 9.461403 9.448314 9.435136 9.421864 9.408497 9.395032 #>  [36,] 9.483644 9.470724 9.457720 9.444628 9.431446 9.418171 9.404800 9.391330 #>  [37,] 9.479988 9.467066 9.454059 9.440964 9.427779 9.414501 9.401127 9.387654 #>  [38,] 9.476352 9.463428 9.450419 9.437323 9.424136 9.410855 9.397479 9.384003 #>  [39,] 9.472737 9.459812 9.446802 9.433704 9.420515 9.407233 9.393855 9.380378 #>  [40,] 9.469143 9.456218 9.443207 9.430108 9.416918 9.403636 9.390257 9.376778 #>  [41,] 9.465570 9.452644 9.439633 9.426534 9.413345 9.400062 9.386683 9.373205 #>  [42,] 9.462018 9.449092 9.436082 9.422983 9.409795 9.396512 9.383134 9.369656 #>  [43,] 9.458486 9.445562 9.432552 9.419455 9.406268 9.392987 9.379610 9.366134 #>  [44,] 9.454974 9.442052 9.429045 9.415949 9.402764 9.389485 9.376111 9.362637 #>  [45,] 9.451484 9.438564 9.425559 9.412466 9.399284 9.386008 9.372636 9.359166 #>  [46,] 9.448014 9.435097 9.422095 9.409006 9.395827 9.382554 9.369186 9.355720 #>  [47,] 9.444565 9.431651 9.418653 9.405568 9.392393 9.379125 9.365761 9.352299 #>  [48,] 9.441136 9.428227 9.415233 9.402152 9.388982 9.375719 9.362361 9.348904 #>  [49,] 9.437728 9.424824 9.411835 9.398759 9.385594 9.372337 9.358985 9.345535 #>  [50,] 9.434340 9.421441 9.408458 9.395389 9.382230 9.368979 9.355634 9.342190 #>  [51,] 9.430973 9.418080 9.405103 9.392040 9.378888 9.365645 9.352307 9.338871 #>  [52,] 9.427626 9.414740 9.401770 9.388714 9.375569 9.362334 9.349004 9.335577 #>  [53,] 9.424300 9.411420 9.398458 9.385410 9.372273 9.359046 9.345726 9.332308 #>  [54,] 9.420993 9.408122 9.395167 9.382128 9.369000 9.355782 9.342471 9.329064 #>  [55,] 9.417707 9.404844 9.391898 9.378868 9.365750 9.352542 9.339241 9.325845 #>  [56,] 9.414441 9.401587 9.388650 9.375629 9.362521 9.349324 9.336035 9.322650 #>  [57,] 9.411195 9.398350 9.385423 9.372413 9.359316 9.346130 9.332852 9.319480 #>  [58,] 9.407968 9.395133 9.382217 9.369218 9.356132 9.342958 9.329693 9.316334 #>  [59,] 9.404762 9.391937 9.379032 9.366044 9.352971 9.339809 9.326557 9.313212 #>  [60,] 9.401575 9.388762 9.375868 9.362892 9.349831 9.336683 9.323445 9.310114 #>  [61,] 9.398407 9.385606 9.372725 9.359761 9.346714 9.333579 9.320356 9.307040 #>  [62,] 9.395259 9.382470 9.369602 9.356652 9.343618 9.330498 9.317290 9.303990 #>  [63,] 9.392131 9.379354 9.366499 9.353563 9.340544 9.327439 9.314246 9.300963 #>  [64,] 9.389021 9.376258 9.363416 9.350495 9.337491 9.324402 9.311225 9.297960 #>  [65,] 9.385931 9.373181 9.360354 9.347447 9.334459 9.321386 9.308227 9.294979 #>  [66,] 9.382859 9.370124 9.357312 9.344420 9.331448 9.318392 9.305251 9.292022 #>  [67,] 9.379806 9.367086 9.354289 9.341414 9.328458 9.315420 9.302297 9.289087 #>  [68,] 9.376772 9.364067 9.351286 9.338427 9.325489 9.312469 9.299365 9.286174 #>  [69,] 9.373756 9.361066 9.348302 9.335460 9.322540 9.309539 9.296454 9.283284 #>  [70,] 9.370758 9.358085 9.345337 9.332514 9.319611 9.306629 9.293565 9.280415 #>  [71,] 9.367779 9.355122 9.342392 9.329586 9.316703 9.303740 9.290696 9.277569 #>  [72,] 9.364817 9.352178 9.339465 9.326678 9.313814 9.300872 9.287849 9.274743 #>  [73,] 9.361874 9.349252 9.336557 9.323789 9.310945 9.298024 9.285022 9.271939 #>  [74,] 9.358947 9.346343 9.333668 9.320919 9.308096 9.295195 9.282216 9.269156 #>  [75,] 9.356039 9.343453 9.330797 9.318068 9.305265 9.292387 9.279430 9.266394 #>  [76,] 9.353147 9.340580 9.327944 9.315235 9.302454 9.289598 9.276664 9.263652 #>  [77,] 9.350273 9.337725 9.325109 9.312421 9.299661 9.286828 9.273918 9.260930 #>  [78,] 9.347415 9.334887 9.322291 9.309625 9.296887 9.284077 9.271191 9.258229 #>  [79,] 9.344574 9.332066 9.319491 9.306847 9.294132 9.281344 9.268483 9.255546 #>  [80,] 9.341750 9.329262 9.316708 9.304086 9.291394 9.278630 9.265794 9.252884 #>  [81,] 9.338942 9.326475 9.313942 9.301342 9.288674 9.275935 9.263124 9.250240 #>  [82,] 9.336150 9.323704 9.311193 9.298616 9.285971 9.273257 9.260472 9.247615 #>  [83,] 9.333374 9.320950 9.308461 9.295907 9.283286 9.270597 9.257838 9.245008 #>  [84,] 9.330613 9.318211 9.305745 9.293215 9.280618 9.267955 9.255222 9.242420 #>  [85,] 9.327869 9.315488 9.303045 9.290539 9.277967 9.265330 9.252624 9.239849 #>  [86,] 9.325139 9.312781 9.300361 9.287879 9.275333 9.262721 9.250043 9.237297 #>  [87,] 9.322424 9.310089 9.297693 9.285235 9.272715 9.260129 9.247479 9.234761 #>  [88,] 9.319725 9.307413 9.295040 9.282607 9.270112 9.257554 9.244931 9.232243 #>  [89,] 9.317040 9.304751 9.292403 9.279995 9.267526 9.254995 9.242400 9.229741 #>  [90,] 9.314369 9.302104 9.289780 9.277398 9.264955 9.252451 9.239885 9.227256 #>  [91,] 9.311713 9.299471 9.287173 9.274816 9.262400 9.249924 9.237386 9.224787 #>  [92,] 9.309071 9.296853 9.284579 9.272248 9.259859 9.247411 9.234903 9.222333 #>  [93,] 9.306442 9.294249 9.282000 9.269696 9.257334 9.244914 9.232435 9.219896 #>  [94,] 9.303827 9.291659 9.279435 9.267157 9.254822 9.242431 9.229981 9.217473 #>  [95,] 9.301226 9.289082 9.276884 9.264633 9.252326 9.239963 9.227543 9.215065 #>  [96,] 9.298638 9.286518 9.274347 9.262122 9.249843 9.237509 9.225119 9.212672 #>  [97,] 9.296062 9.283968 9.271823 9.259625 9.247374 9.235069 9.222709 9.210294 #>  [98,] 9.293499 9.281431 9.269312 9.257141 9.244918 9.232642 9.220313 9.207929 #>  [99,] 9.290949 9.278906 9.266813 9.254670 9.242475 9.230229 9.217930 9.205578 #> [100,] 9.288411 9.276394 9.264328 9.252212 9.240046 9.227829 9.215561 9.203241 #>            [,9]    [,10]    [,11]    [,12]    [,13]    [,14]    [,15]    [,16] #>   [1,] 9.522214 9.509155 9.496016 9.482796 9.469493 9.456104 9.442628 9.429063 #>   [2,] 9.517704 9.504616 9.491447 9.478196 9.464860 9.451438 9.437926 9.424324 #>   [3,] 9.513213 9.500097 9.486899 9.473618 9.460250 9.446794 9.433247 9.419609 #>   [4,] 9.508742 9.495599 9.482372 9.469060 9.455661 9.442172 9.428591 9.414917 #>   [5,] 9.504291 9.491121 9.477866 9.464525 9.451095 9.437574 9.423959 9.410249 #>   [6,] 9.499861 9.486665 9.473382 9.460012 9.446551 9.432998 9.419351 9.405605 #>   [7,] 9.495452 9.482230 9.468920 9.455521 9.442031 9.428447 9.414766 9.400987 #>   [8,] 9.491064 9.477816 9.464480 9.451054 9.437534 9.423920 9.410207 9.396394 #>   [9,] 9.486698 9.473425 9.460063 9.446609 9.433061 9.419417 9.405673 9.391827 #>  [10,] 9.482353 9.469056 9.455669 9.442188 9.428613 9.414939 9.401164 9.387286 #>  [11,] 9.478030 9.464710 9.451297 9.437791 9.424188 9.410486 9.396681 9.382772 #>  [12,] 9.473730 9.460386 9.446950 9.433418 9.419789 9.406059 9.392225 9.378284 #>  [13,] 9.469452 9.456086 9.442626 9.429070 9.415414 9.401657 9.387795 9.373825 #>  [14,] 9.465197 9.451809 9.438326 9.424746 9.411066 9.397282 9.383392 9.369393 #>  [15,] 9.460964 9.447555 9.434051 9.420447 9.406743 9.392934 9.379017 9.364989 #>  [16,] 9.456756 9.443326 9.429800 9.416174 9.402446 9.388612 9.374669 9.360614 #>  [17,] 9.452570 9.439121 9.425574 9.411926 9.398175 9.384318 9.370350 9.356268 #>  [18,] 9.448408 9.434940 9.421373 9.407705 9.393932 9.380051 9.366058 9.351951 #>  [19,] 9.444270 9.430784 9.417198 9.403509 9.389715 9.375812 9.361796 9.347664 #>  [20,] 9.440157 9.426652 9.413048 9.399340 9.385525 9.371601 9.357562 9.343407 #>  [21,] 9.436067 9.422546 9.408924 9.395197 9.381363 9.367418 9.353358 9.339180 #>  [22,] 9.432002 9.418465 9.404826 9.391082 9.377229 9.363264 9.349184 9.334984 #>  [23,] 9.427962 9.414410 9.400755 9.386993 9.373123 9.359139 9.345039 9.330818 #>  [24,] 9.423947 9.410380 9.396709 9.382932 9.369045 9.355044 9.340925 9.326684 #>  [25,] 9.419957 9.406376 9.392691 9.378899 9.364995 9.350977 9.336841 9.322581 #>  [26,] 9.415992 9.402398 9.388699 9.374893 9.360974 9.346940 9.332787 9.318510 #>  [27,] 9.412052 9.398446 9.384735 9.370915 9.356982 9.342934 9.328765 9.314471 #>  [28,] 9.408138 9.394521 9.380798 9.366965 9.353019 9.338957 9.324773 9.310464 #>  [29,] 9.404250 9.390622 9.376888 9.363043 9.349085 9.335010 9.320813 9.306490 #>  [30,] 9.400387 9.386750 9.373005 9.359150 9.345181 9.331094 9.316884 9.302548 #>  [31,] 9.396550 9.382904 9.369150 9.355286 9.341306 9.327208 9.312987 9.298639 #>  [32,] 9.392739 9.379085 9.365323 9.351450 9.337461 9.323353 9.309122 9.294763 #>  [33,] 9.388955 9.375293 9.361524 9.347642 9.333646 9.319529 9.305289 9.290920 #>  [34,] 9.385196 9.371528 9.357752 9.343864 9.329860 9.315736 9.301487 9.287110 #>  [35,] 9.381464 9.367791 9.354009 9.340115 9.326105 9.311974 9.297718 9.283334 #>  [36,] 9.377758 9.364080 9.350294 9.336395 9.322379 9.308243 9.293982 9.279591 #>  [37,] 9.374078 9.360397 9.346607 9.332704 9.318684 9.304543 9.290277 9.275882 #>  [38,] 9.370425 9.356741 9.342948 9.329042 9.315019 9.300875 9.286605 9.272206 #>  [39,] 9.366798 9.353112 9.339317 9.325409 9.311384 9.297237 9.282966 9.268564 #>  [40,] 9.363198 9.349511 9.335715 9.321806 9.307779 9.293632 9.279359 9.264955 #>  [41,] 9.359624 9.345937 9.332141 9.318231 9.304205 9.290057 9.275784 9.261381 #>  [42,] 9.356076 9.342390 9.328595 9.314687 9.300661 9.286514 9.272242 9.257840 #>  [43,] 9.352555 9.338871 9.325077 9.311171 9.297147 9.283003 9.268733 9.254333 #>  [44,] 9.349061 9.335379 9.321588 9.307684 9.293664 9.279522 9.265256 9.250859 #>  [45,] 9.345593 9.331914 9.318127 9.304227 9.290211 9.276073 9.261811 9.247419 #>  [46,] 9.342151 9.328477 9.314694 9.300799 9.286788 9.272656 9.258399 9.244013 #>  [47,] 9.338736 9.325067 9.311290 9.297400 9.283395 9.269269 9.255019 9.240640 #>  [48,] 9.335346 9.321684 9.307913 9.294030 9.280032 9.265913 9.251671 9.237301 #>  [49,] 9.331983 9.318328 9.304564 9.290689 9.276699 9.262589 9.248356 9.233995 #>  [50,] 9.328647 9.314999 9.301243 9.287377 9.273395 9.259295 9.245072 9.230722 #>  [51,] 9.325336 9.311696 9.297950 9.284093 9.270122 9.256032 9.241820 9.227482 #>  [52,] 9.322051 9.308421 9.294684 9.280838 9.266878 9.252800 9.238600 9.224275 #>  [53,] 9.318791 9.305172 9.291446 9.277611 9.263663 9.249598 9.235412 9.221100 #>  [54,] 9.315558 9.301950 9.288236 9.274413 9.260478 9.246426 9.232254 9.217958 #>  [55,] 9.312350 9.298754 9.285052 9.271243 9.257322 9.243285 9.229128 9.214848 #>  [56,] 9.309167 9.295584 9.281896 9.268101 9.254194 9.240173 9.226033 9.211770 #>  [57,] 9.306010 9.292440 9.278767 9.264986 9.251096 9.237091 9.222968 9.208724 #>  [58,] 9.302878 9.289322 9.275664 9.261900 9.248026 9.234038 9.219934 9.205710 #>  [59,] 9.299771 9.286230 9.272588 9.258840 9.244984 9.231015 9.216931 9.202726 #>  [60,] 9.296688 9.283164 9.269538 9.255808 9.241970 9.228021 9.213957 9.199774 #>  [61,] 9.293630 9.280122 9.266514 9.252802 9.238984 9.225055 9.211012 9.196852 #>  [62,] 9.290596 9.277106 9.263516 9.249824 9.236025 9.222118 9.208097 9.193961 #>  [63,] 9.287587 9.274115 9.260544 9.246872 9.233094 9.219209 9.205212 9.191099 #>  [64,] 9.284601 9.271148 9.257597 9.243946 9.230190 9.216328 9.202355 9.188268 #>  [65,] 9.281640 9.268206 9.254676 9.241046 9.227313 9.213474 9.199526 9.185466 #>  [66,] 9.278701 9.265288 9.251779 9.238171 9.224462 9.210648 9.196726 9.182692 #>  [67,] 9.275787 9.262394 9.248907 9.235322 9.221637 9.207848 9.193953 9.179948 #>  [68,] 9.272895 9.259524 9.246060 9.232499 9.218838 9.205076 9.191208 9.177232 #>  [69,] 9.270026 9.256677 9.243236 9.229700 9.216065 9.202329 9.188490 9.174543 #>  [70,] 9.267179 9.253854 9.240437 9.226925 9.213317 9.199609 9.185799 9.171883 #>  [71,] 9.264355 9.251053 9.237661 9.224175 9.210594 9.196914 9.183134 9.169249 #>  [72,] 9.261553 9.248275 9.234908 9.221449 9.207895 9.194245 9.180495 9.166642 #>  [73,] 9.258772 9.245519 9.232178 9.218746 9.205221 9.191600 9.177881 9.164062 #>  [74,] 9.256014 9.242786 9.229471 9.216067 9.202571 9.188980 9.175293 9.161507 #>  [75,] 9.253276 9.240074 9.226786 9.213410 9.199944 9.186385 9.172730 9.158978 #>  [76,] 9.250559 9.237384 9.224124 9.210776 9.197340 9.183813 9.170191 9.156474 #>  [77,] 9.247863 9.234715 9.221483 9.208165 9.194759 9.181264 9.167676 9.153994 #>  [78,] 9.245188 9.232067 9.218863 9.205575 9.192201 9.178738 9.165185 9.151539 #>  [79,] 9.242532 9.229439 9.216264 9.203007 9.189665 9.176235 9.162717 9.149108 #>  [80,] 9.239897 9.226832 9.213687 9.200460 9.187150 9.173755 9.160272 9.146700 #>  [81,] 9.237280 9.224244 9.211129 9.197934 9.184657 9.171296 9.157849 9.144314 #>  [82,] 9.234683 9.221676 9.208592 9.195429 9.182185 9.168859 9.155448 9.141951 #>  [83,] 9.232105 9.219128 9.206075 9.192944 9.179733 9.166442 9.153069 9.139611 #>  [84,] 9.229546 9.216598 9.203576 9.190478 9.177302 9.164047 9.150710 9.137291 #>  [85,] 9.227004 9.214088 9.201097 9.188032 9.174891 9.161671 9.148373 9.134993 #>  [86,] 9.224481 9.211595 9.198637 9.185605 9.172499 9.159316 9.146055 9.132715 #>  [87,] 9.221976 9.209121 9.196195 9.183197 9.170126 9.156980 9.143758 9.130458 #>  [88,] 9.219487 9.206664 9.193771 9.180807 9.167772 9.154663 9.141479 9.128220 #>  [89,] 9.217016 9.204224 9.191365 9.178435 9.165436 9.152364 9.139220 9.126002 #>  [90,] 9.214562 9.201802 9.188976 9.176081 9.163118 9.150084 9.136979 9.123802 #>  [91,] 9.212124 9.199396 9.186604 9.173744 9.160817 9.147822 9.134757 9.121621 #>  [92,] 9.209702 9.197007 9.184248 9.171424 9.158534 9.145577 9.132552 9.119457 #>  [93,] 9.207296 9.194634 9.181909 9.169121 9.156268 9.143349 9.130364 9.117312 #>  [94,] 9.204905 9.192276 9.179586 9.166833 9.154018 9.141138 9.128193 9.115183 #>  [95,] 9.202529 9.189934 9.177278 9.164562 9.151783 9.138943 9.126038 9.113070 #>  [96,] 9.200169 9.187607 9.174986 9.162306 9.149565 9.136763 9.123900 9.110974 #>  [97,] 9.197822 9.185294 9.172709 9.160065 9.147362 9.134599 9.121777 9.108894 #>  [98,] 9.195490 9.182996 9.170446 9.157838 9.145173 9.132451 9.119669 9.106829 #>  [99,] 9.193172 9.180712 9.168197 9.155626 9.143000 9.130316 9.117576 9.104779 #> [100,] 9.190868 9.178442 9.165962 9.153428 9.140840 9.128196 9.115497 9.102743 #>           [,17]    [,18]    [,19]    [,20]    [,21]    [,22]    [,23]    [,24] #>   [1,] 9.415407 9.401658 9.387813 9.373871 9.359830 9.345686 9.331439 9.317085 #>   [2,] 9.410629 9.396839 9.382952 9.368965 9.354876 9.340683 9.326383 9.311974 #>   [3,] 9.405875 9.392045 9.378115 9.364083 9.349948 9.335705 9.321354 9.306891 #>   [4,] 9.401145 9.387275 9.373304 9.359228 9.345046 9.330756 9.316353 9.301836 #>   [5,] 9.396440 9.382531 9.368518 9.354400 9.340172 9.325834 9.311381 9.296811 #>   [6,] 9.391760 9.377812 9.363759 9.349598 9.335326 9.320941 9.306438 9.291816 #>   [7,] 9.387106 9.373120 9.359027 9.344824 9.330509 9.316076 9.301525 9.286851 #>   [8,] 9.382477 9.368455 9.354323 9.340079 9.325720 9.311242 9.296643 9.281918 #>   [9,] 9.377876 9.363817 9.349647 9.335362 9.320961 9.306438 9.291792 9.277017 #>  [10,] 9.373301 9.359206 9.344999 9.330675 9.316232 9.301666 9.286972 9.272149 #>  [11,] 9.368754 9.354624 9.340380 9.326018 9.311534 9.296924 9.282186 9.267314 #>  [12,] 9.364234 9.350071 9.335791 9.321391 9.306867 9.292216 9.277433 9.262514 #>  [13,] 9.359743 9.345546 9.331232 9.316795 9.302232 9.287540 9.272714 9.257749 #>  [14,] 9.355280 9.341052 9.326703 9.312230 9.297630 9.282897 9.268029 9.253020 #>  [15,] 9.350847 9.336587 9.322205 9.307698 9.293060 9.278289 9.263379 9.248326 #>  [16,] 9.346443 9.332153 9.317739 9.303197 9.288524 9.273715 9.258765 9.243670 #>  [17,] 9.342069 9.327749 9.313304 9.298730 9.284022 9.269177 9.254188 9.239052 #>  [18,] 9.337725 9.323377 9.308902 9.294296 9.279555 9.264674 9.249648 9.234471 #>  [19,] 9.333412 9.319036 9.304532 9.289896 9.275122 9.260207 9.245145 9.229930 #>  [20,] 9.329130 9.314728 9.300196 9.285530 9.270725 9.255777 9.240680 9.225428 #>  [21,] 9.324879 9.310452 9.295893 9.281199 9.266364 9.251384 9.236253 9.220966 #>  [22,] 9.320660 9.306208 9.291624 9.276903 9.262040 9.247029 9.231866 9.216545 #>  [23,] 9.316473 9.301998 9.287389 9.272642 9.257752 9.242713 9.227519 9.212164 #>  [24,] 9.312318 9.297821 9.283189 9.268418 9.253501 9.238434 9.223211 9.207826 #>  [25,] 9.308195 9.293678 9.279024 9.264229 9.249288 9.234195 9.218944 9.203530 #>  [26,] 9.304106 9.289569 9.274894 9.260078 9.245113 9.229995 9.214718 9.199276 #>  [27,] 9.300049 9.285494 9.270800 9.255963 9.240976 9.225836 9.210534 9.195065 #>  [28,] 9.296026 9.281453 9.266742 9.251885 9.236878 9.221716 9.206391 9.190898 #>  [29,] 9.292037 9.277448 9.262719 9.247845 9.232819 9.217637 9.202291 9.186775 #>  [30,] 9.288081 9.273478 9.258733 9.243842 9.228799 9.213598 9.198233 9.182696 #>  [31,] 9.284159 9.269542 9.254784 9.239878 9.224819 9.209601 9.194217 9.178661 #>  [32,] 9.280272 9.265643 9.250871 9.235952 9.220879 9.205645 9.190245 9.174672 #>  [33,] 9.276418 9.261779 9.246996 9.232064 9.216978 9.201731 9.186317 9.170728 #>  [34,] 9.272600 9.257950 9.243158 9.228215 9.213118 9.197859 9.182431 9.166829 #>  [35,] 9.268815 9.254158 9.239357 9.224405 9.209298 9.194028 9.178590 9.162976 #>  [36,] 9.265066 9.250402 9.235593 9.220634 9.205518 9.190240 9.174793 9.159169 #>  [37,] 9.261351 9.246682 9.231867 9.216902 9.201780 9.186495 9.171040 9.155407 #>  [38,] 9.257672 9.242998 9.228179 9.213209 9.198082 9.182791 9.167331 9.151693 #>  [39,] 9.254027 9.239350 9.224528 9.209555 9.194425 9.179131 9.163666 9.148024 #>  [40,] 9.250417 9.235739 9.220915 9.205940 9.190808 9.175512 9.160046 9.144402 #>  [41,] 9.246843 9.232164 9.217340 9.202365 9.187233 9.171937 9.156470 9.140826 #>  [42,] 9.243303 9.228626 9.213803 9.198829 9.183699 9.168404 9.152939 9.137296 #>  [43,] 9.239798 9.225123 9.210304 9.195333 9.180205 9.164914 9.149452 9.133813 #>  [44,] 9.236328 9.221658 9.206842 9.191876 9.176752 9.161466 9.146010 9.130376 #>  [45,] 9.232893 9.218228 9.203418 9.188457 9.173340 9.158061 9.142612 9.126986 #>  [46,] 9.229493 9.214835 9.200031 9.185078 9.169969 9.154698 9.139258 9.123641 #>  [47,] 9.226128 9.211477 9.196682 9.181738 9.166639 9.151377 9.135948 9.120343 #>  [48,] 9.222797 9.208156 9.193371 9.178437 9.163348 9.148099 9.132682 9.117090 #>  [49,] 9.219501 9.204870 9.190096 9.175174 9.160098 9.144862 9.129459 9.113882 #>  [50,] 9.216239 9.201620 9.186859 9.171950 9.156888 9.141667 9.126280 9.110720 #>  [51,] 9.213012 9.198406 9.183659 9.168765 9.153718 9.138514 9.123144 9.107603 #>  [52,] 9.209818 9.195227 9.180495 9.165617 9.150588 9.135401 9.120051 9.104531 #>  [53,] 9.206659 9.192083 9.177367 9.162507 9.147497 9.132330 9.117001 9.101503 #>  [54,] 9.203533 9.188974 9.174276 9.159435 9.144444 9.129299 9.113993 9.098519 #>  [55,] 9.200440 9.185899 9.171221 9.156400 9.141431 9.126308 9.111026 9.095578 #>  [56,] 9.197380 9.182859 9.168201 9.153402 9.138456 9.123358 9.108101 9.092681 #>  [57,] 9.194354 9.179853 9.165217 9.150440 9.135519 9.120447 9.105218 9.089826 #>  [58,] 9.191360 9.176880 9.162267 9.147515 9.132619 9.117574 9.102375 9.087014 #>  [59,] 9.188398 9.173942 9.159353 9.144626 9.129757 9.114741 9.099572 9.084243 #>  [60,] 9.185468 9.171036 9.156472 9.141773 9.126932 9.111946 9.096808 9.081514 #>  [61,] 9.182570 9.168163 9.153626 9.138954 9.124144 9.109189 9.094084 9.078825 #>  [62,] 9.179704 9.165323 9.150813 9.136171 9.121391 9.106469 9.091399 9.076177 #>  [63,] 9.176868 9.162514 9.148034 9.133421 9.118674 9.103786 9.088752 9.073568 #>  [64,] 9.174063 9.159738 9.145287 9.130706 9.115992 9.101139 9.086143 9.070998 #>  [65,] 9.171289 9.156993 9.142572 9.128024 9.113344 9.098528 9.083570 9.068467 #>  [66,] 9.168545 9.154278 9.139890 9.125376 9.110731 9.095952 9.081034 9.065973 #>  [67,] 9.165830 9.151594 9.137239 9.122759 9.108151 9.093411 9.078534 9.063516 #>  [68,] 9.163144 9.148941 9.134619 9.120175 9.105605 9.090904 9.076070 9.061096 #>  [69,] 9.160487 9.146317 9.132030 9.117622 9.103091 9.088431 9.073639 9.058712 #>  [70,] 9.157858 9.143722 9.129471 9.115101 9.100609 9.085991 9.071243 9.056362 #>  [71,] 9.155257 9.141156 9.126941 9.112609 9.098158 9.083583 9.068881 9.054048 #>  [72,] 9.152684 9.138618 9.124440 9.110148 9.095738 9.081207 9.066551 9.051766 #>  [73,] 9.150138 9.136108 9.121969 9.107717 9.093349 9.078862 9.064253 9.049518 #>  [74,] 9.147619 9.133626 9.119525 9.105314 9.090989 9.076548 9.061987 9.047303 #>  [75,] 9.145125 9.131170 9.117109 9.102939 9.088659 9.074264 9.059751 9.045118 #>  [76,] 9.142658 9.128741 9.114720 9.100593 9.086357 9.072009 9.057546 9.042965 #>  [77,] 9.140216 9.126337 9.112358 9.098274 9.084083 9.069782 9.055370 9.040842 #>  [78,] 9.137798 9.123960 9.110021 9.095981 9.081836 9.067584 9.053222 9.038748 #>  [79,] 9.135405 9.121607 9.107711 9.093715 9.079616 9.065413 9.051103 9.036683 #>  [80,] 9.133036 9.119278 9.105425 9.091474 9.077423 9.063269 9.049011 9.034646 #>  [81,] 9.130690 9.116974 9.103164 9.089258 9.075255 9.061151 9.046946 9.032637 #>  [82,] 9.128367 9.114692 9.100926 9.087067 9.073111 9.059059 9.044907 9.030653 #>  [83,] 9.126066 9.112434 9.098712 9.084899 9.070993 9.056991 9.042893 9.028696 #>  [84,] 9.123788 9.110198 9.096521 9.082755 9.068898 9.054948 9.040904 9.026764 #>  [85,] 9.121531 9.107985 9.094353 9.080634 9.066826 9.052928 9.038938 9.024856 #>  [86,] 9.119295 9.105792 9.092206 9.078534 9.064777 9.050931 9.036996 9.022971 #>  [87,] 9.117079 9.103620 9.090080 9.076457 9.062749 9.048956 9.035077 9.021110 #>  [88,] 9.114884 9.101469 9.087975 9.074400 9.060743 9.047003 9.033179 9.019270 #>  [89,] 9.112708 9.099338 9.085890 9.072364 9.058758 9.045072 9.031303 9.017453 #>  [90,] 9.110551 9.097226 9.083825 9.070348 9.056793 9.043160 9.029448 9.015656 #>  [91,] 9.108413 9.095133 9.081779 9.068351 9.054848 9.041268 9.027612 9.013879 #>  [92,] 9.106293 9.093058 9.079752 9.066373 9.052921 9.039396 9.025796 9.012121 #>  [93,] 9.104191 9.091002 9.077743 9.064413 9.051013 9.037542 9.023998 9.010383 #>  [94,] 9.102106 9.088962 9.075751 9.062471 9.049123 9.035706 9.022219 9.008662 #>  [95,] 9.100038 9.086940 9.073776 9.060547 9.047250 9.033887 9.020456 9.006959 #>  [96,] 9.097986 9.084934 9.071818 9.058638 9.045394 9.032085 9.018711 9.005272 #>  [97,] 9.095950 9.082944 9.069876 9.056746 9.043554 9.030299 9.016982 9.003602 #>  [98,] 9.093929 9.080969 9.067950 9.054870 9.041730 9.028529 9.015268 9.001948 #>  [99,] 9.091923 9.079010 9.066038 9.053009 9.039921 9.026774 9.013570 9.000308 #> [100,] 9.089932 9.077065 9.064142 9.051162 9.038126 9.025034 9.011886 8.998682 #>           [,25]    [,26]    [,27]    [,28]    [,29]    [,30]    [,31]    [,32] #>   [1,] 9.302623 9.288050 9.273365 9.258565 9.243648 9.228612 9.213456 9.198177 #>   [2,] 9.297454 9.282820 9.268071 9.253202 9.238214 9.223102 9.207866 9.192502 #>   [3,] 9.292313 9.277619 9.262806 9.247870 9.232810 9.217624 9.202308 9.186860 #>   [4,] 9.287202 9.272448 9.257571 9.242569 9.227439 9.212177 9.196782 9.181251 #>   [5,] 9.282121 9.267308 9.252368 9.237300 9.222100 9.206765 9.191291 9.175677 #>   [6,] 9.277070 9.262199 9.247198 9.232064 9.216795 9.201386 9.185835 9.170138 #>   [7,] 9.272051 9.257122 9.242060 9.226862 9.211525 9.196044 9.180416 9.164637 #>   [8,] 9.267064 9.252079 9.236957 9.221695 9.206290 9.190738 9.175034 9.159175 #>   [9,] 9.262111 9.247069 9.231888 9.216564 9.201093 9.185470 9.169691 9.153752 #>  [10,] 9.257191 9.242094 9.226856 9.211470 9.195933 9.180240 9.164388 9.148370 #>  [11,] 9.252306 9.237155 9.221860 9.206413 9.190812 9.175051 9.159126 9.143031 #>  [12,] 9.247456 9.232253 9.216901 9.201395 9.185731 9.169903 9.153906 9.137735 #>  [13,] 9.242642 9.227388 9.211981 9.196417 9.180691 9.164798 9.148731 9.132485 #>  [14,] 9.237865 9.222560 9.207100 9.191480 9.175693 9.159735 9.143599 9.127280 #>  [15,] 9.233126 9.217772 9.202260 9.186584 9.170738 9.154717 9.138514 9.122123 #>  [16,] 9.228424 9.213023 9.197460 9.181730 9.165827 9.149744 9.133476 9.117015 #>  [17,] 9.223762 9.208314 9.192702 9.176920 9.160961 9.144818 9.128486 9.111957 #>  [18,] 9.219140 9.203647 9.187987 9.172153 9.156140 9.139940 9.123546 9.106950 #>  [19,] 9.214557 9.199021 9.183315 9.167432 9.151366 9.135110 9.118655 9.101995 #>  [20,] 9.210016 9.194438 9.178687 9.162756 9.146640 9.130329 9.113816 9.097094 #>  [21,] 9.205516 9.189897 9.174104 9.158127 9.141962 9.125599 9.109030 9.092247 #>  [22,] 9.201058 9.185401 9.169566 9.153546 9.137333 9.120920 9.104297 9.087457 #>  [23,] 9.196643 9.180949 9.165075 9.149013 9.132755 9.116293 9.099619 9.082723 #>  [24,] 9.192272 9.176542 9.160630 9.144528 9.128227 9.111720 9.094996 9.078047 #>  [25,] 9.187944 9.172181 9.156233 9.140093 9.123752 9.107200 9.090430 9.073431 #>  [26,] 9.183661 9.167866 9.151885 9.135708 9.119328 9.102736 9.085921 9.068874 #>  [27,] 9.179422 9.163598 9.147585 9.131374 9.114958 9.098327 9.081470 9.064378 #>  [28,] 9.175229 9.159377 9.143334 9.127092 9.110642 9.093974 9.077078 9.059944 #>  [29,] 9.171081 9.155204 9.139133 9.122861 9.106380 9.089678 9.072745 9.055572 #>  [30,] 9.166980 9.151078 9.134983 9.118684 9.102172 9.085439 9.068473 9.051263 #>  [31,] 9.162925 9.147002 9.130883 9.114559 9.098021 9.081259 9.064262 9.047019 #>  [32,] 9.158917 9.142974 9.126834 9.110487 9.093925 9.077137 9.060113 9.042839 #>  [33,] 9.154957 9.138996 9.122837 9.106470 9.089886 9.073075 9.056025 9.038725 #>  [34,] 9.151043 9.135067 9.118891 9.102507 9.085904 9.069072 9.052000 9.034676 #>  [35,] 9.147178 9.131188 9.114998 9.098598 9.081979 9.065130 9.048039 9.030694 #>  [36,] 9.143360 9.127359 9.111157 9.094744 9.078111 9.061247 9.044140 9.026778 #>  [37,] 9.139591 9.123581 9.107369 9.090946 9.074302 9.057426 9.040306 9.022930 #>  [38,] 9.135869 9.119852 9.103633 9.087203 9.070550 9.053665 9.036535 9.019149 #>  [39,] 9.132196 9.116175 9.099951 9.083515 9.066856 9.049965 9.032829 9.015435 #>  [40,] 9.128572 9.112548 9.096321 9.079882 9.063221 9.046326 9.029187 9.011789 #>  [41,] 9.124996 9.108971 9.092745 9.076305 9.059644 9.042749 9.025609 9.008211 #>  [42,] 9.121468 9.105446 9.089221 9.072784 9.056125 9.039233 9.022096 9.004701 #>  [43,] 9.117989 9.101971 9.085751 9.069319 9.052665 9.035778 9.018647 9.001259 #>  [44,] 9.114558 9.098546 9.082333 9.065908 9.049262 9.032384 9.015262 8.997884 #>  [45,] 9.111175 9.095172 9.078968 9.062553 9.045918 9.029051 9.011941 8.994576 #>  [46,] 9.107841 9.091849 9.075656 9.059254 9.042631 9.025779 9.008684 8.991336 #>  [47,] 9.104554 9.088575 9.072396 9.056009 9.039402 9.022567 9.005491 8.988162 #>  [48,] 9.101316 9.085352 9.069189 9.052819 9.036231 9.019415 9.002361 8.985055 #>  [49,] 9.098125 9.082178 9.066033 9.049683 9.033116 9.016323 8.999293 8.982014 #>  [50,] 9.094981 9.079053 9.062929 9.046601 9.030058 9.013291 8.996288 8.979038 #>  [51,] 9.091884 9.075977 9.059877 9.043572 9.027056 9.010317 8.993344 8.976127 #>  [52,] 9.088833 9.072950 9.056875 9.040597 9.024109 9.007401 8.990462 8.973281 #>  [53,] 9.085829 9.069972 9.053923 9.037675 9.021218 9.004543 8.987640 8.970497 #>  [54,] 9.082870 9.067041 9.051021 9.034804 9.018381 9.001742 8.984877 8.967777 #>  [55,] 9.079958 9.064157 9.048169 9.031985 9.015598 8.998998 8.982174 8.965118 #>  [56,] 9.077089 9.061320 9.045365 9.029218 9.012868 8.996309 8.979529 8.962520 #>  [57,] 9.074266 9.058530 9.042610 9.026500 9.010191 8.993675 8.976942 8.959982 #>  [58,] 9.071486 9.055785 9.039903 9.023832 9.007566 8.991095 8.974411 8.957504 #>  [59,] 9.068750 9.053085 9.037242 9.021213 9.004992 8.988569 8.971936 8.955084 #>  [60,] 9.066057 9.050430 9.034628 9.018643 9.002468 8.986094 8.969515 8.952720 #>  [61,] 9.063406 9.047819 9.032060 9.016120 8.999993 8.983672 8.967148 8.950413 #>  [62,] 9.060796 9.045251 9.029536 9.013644 8.997568 8.981300 8.964834 8.948161 #>  [63,] 9.058228 9.042726 9.027057 9.011214 8.995190 8.978978 8.962572 8.945963 #>  [64,] 9.055700 9.040243 9.024621 9.008828 8.992858 8.976704 8.960360 8.943817 #>  [65,] 9.053212 9.037801 9.022228 9.006488 8.990573 8.974479 8.958197 8.941722 #>  [66,] 9.050763 9.035399 9.019877 9.004190 8.988333 8.972300 8.956084 8.939678 #>  [67,] 9.048352 9.033038 9.017567 9.001935 8.986137 8.970166 8.954017 8.937683 #>  [68,] 9.045979 9.030715 9.015297 8.999722 8.983984 8.968077 8.951996 8.935736 #>  [69,] 9.043643 9.028430 9.013067 8.997550 8.981873 8.966032 8.950021 8.933835 #>  [70,] 9.041344 9.026183 9.010876 8.995417 8.979803 8.964029 8.948089 8.931979 #>  [71,] 9.039079 9.023972 9.008722 8.993324 8.977774 8.962068 8.946200 8.930167 #>  [72,] 9.036850 9.021797 9.006605 8.991268 8.975783 8.960146 8.944353 8.928398 #>  [73,] 9.034654 9.019657 9.004524 8.989249 8.973831 8.958264 8.942545 8.926670 #>  [74,] 9.032492 9.017551 9.002478 8.987267 8.971916 8.956420 8.940777 8.924982 #>  [75,] 9.030362 9.015479 9.000466 8.985319 8.970036 8.954613 8.939047 8.923333 #>  [76,] 9.028264 9.013439 8.998487 8.983406 8.968192 8.952842 8.937353 8.921722 #>  [77,] 9.026197 9.011431 8.996542 8.981526 8.966382 8.951105 8.935695 8.920147 #>  [78,] 9.024160 9.009453 8.994627 8.979678 8.964604 8.949403 8.934071 8.918606 #>  [79,] 9.022152 9.007506 8.992743 8.977862 8.962859 8.947732 8.932480 8.917100 #>  [80,] 9.020173 9.005588 8.990889 8.976076 8.961144 8.946093 8.930921 8.915625 #>  [81,] 9.018221 9.003698 8.989064 8.974319 8.959460 8.944485 8.929393 8.914182 #>  [82,] 9.016297 9.001836 8.987267 8.972591 8.957804 8.942906 8.927894 8.912769 #>  [83,] 9.014399 9.000000 8.985497 8.970890 8.956176 8.941355 8.926424 8.911385 #>  [84,] 9.012526 8.998190 8.983754 8.969216 8.954575 8.939831 8.924982 8.910028 #>  [85,] 9.010678 8.996405 8.982035 8.967567 8.953000 8.938333 8.923566 8.908698 #>  [86,] 9.008854 8.994645 8.980341 8.965943 8.951450 8.936861 8.922175 8.907392 #>  [87,] 9.007054 8.992908 8.978671 8.964344 8.949924 8.935412 8.920808 8.906111 #>  [88,] 9.005275 8.991193 8.977024 8.962767 8.948421 8.933987 8.919464 8.904853 #>  [89,] 9.003519 8.989501 8.975399 8.961212 8.946940 8.932583 8.918142 8.903617 #>  [90,] 9.001783 8.987829 8.973795 8.959678 8.945480 8.931201 8.916842 8.902402 #>  [91,] 9.000068 8.986178 8.972211 8.958165 8.944041 8.929840 8.915561 8.901206 #>  [92,] 8.998372 8.984547 8.970647 8.956671 8.942621 8.928497 8.914299 8.900029 #>  [93,] 8.996695 8.982934 8.969101 8.955196 8.941220 8.927173 8.913056 8.898870 #>  [94,] 8.995036 8.981339 8.967574 8.953739 8.939836 8.925866 8.911829 8.897727 #>  [95,] 8.993394 8.979762 8.966064 8.952299 8.938470 8.924576 8.910619 8.896601 #>  [96,] 8.991769 8.978202 8.964570 8.950876 8.937119 8.923301 8.909424 8.895489 #>  [97,] 8.990160 8.976657 8.963092 8.949468 8.935784 8.922042 8.908244 8.894391 #>  [98,] 8.988567 8.975128 8.961630 8.948074 8.934463 8.920796 8.907077 8.893306 #>  [99,] 8.986989 8.973613 8.960181 8.946695 8.933156 8.919564 8.905923 8.892234 #> [100,] 8.985424 8.972112 8.958747 8.945329 8.931861 8.918345 8.904781 8.891172 #>           [,33]    [,34]    [,35]    [,36]    [,37]    [,38]    [,39]    [,40] #>   [1,] 9.182775 9.167247 9.151594 9.135814 9.119907 9.103874 9.087715 9.071432 #>   [2,] 9.177010 9.161388 9.145634 9.129748 9.113728 9.097574 9.081288 9.064869 #>   [3,] 9.171279 9.155562 9.139707 9.123714 9.107581 9.091308 9.074894 9.058340 #>   [4,] 9.165581 9.149770 9.133816 9.117716 9.101470 9.085077 9.068535 9.051845 #>   [5,] 9.159918 9.144014 9.127960 9.111755 9.095396 9.078883 9.062213 9.045387 #>   [6,] 9.154293 9.138295 9.122142 9.105832 9.089361 9.072728 9.055931 9.038968 #>   [7,] 9.148705 9.132615 9.116364 9.099949 9.083366 9.066614 9.049689 9.032591 #>   [8,] 9.143156 9.126975 9.110626 9.094107 9.077414 9.060543 9.043492 9.026257 #>   [9,] 9.137649 9.121377 9.104932 9.088310 9.071506 9.054518 9.037340 9.019970 #>  [10,] 9.132183 9.115822 9.099281 9.082557 9.065645 9.048539 9.031236 9.013732 #>  [11,] 9.126761 9.110312 9.093677 9.076852 9.059831 9.042610 9.025183 9.007545 #>  [12,] 9.121384 9.104848 9.088120 9.071196 9.054068 9.036732 9.019182 9.001412 #>  [13,] 9.116054 9.099432 9.082613 9.065590 9.048357 9.030908 9.013236 8.995335 #>  [14,] 9.110771 9.094065 9.077156 9.060037 9.042701 9.025140 9.007348 8.989317 #>  [15,] 9.105537 9.088749 9.071752 9.054538 9.037100 9.019430 9.001519 8.983360 #>  [16,] 9.100354 9.083485 9.066402 9.049095 9.031557 9.013779 8.995752 8.977468 #>  [17,] 9.095222 9.078275 9.061108 9.043710 9.026074 9.008191 8.990050 8.971642 #>  [18,] 9.090144 9.073121 9.055871 9.038385 9.020654 9.002667 8.984415 8.965886 #>  [19,] 9.085120 9.068023 9.050693 9.033121 9.015297 8.997209 8.978848 8.960201 #>  [20,] 9.080152 9.062983 9.045575 9.027920 9.010005 8.991820 8.973353 8.954591 #>  [21,] 9.075241 9.058002 9.040520 9.022784 9.004782 8.986502 8.967932 8.949058 #>  [22,] 9.070389 9.053083 9.035528 9.017714 8.999627 8.981256 8.962587 8.943605 #>  [23,] 9.065595 9.048225 9.030601 9.012712 8.994544 8.976085 8.957320 8.938233 #>  [24,] 9.060863 9.043431 9.025741 9.007779 8.989534 8.970990 8.952133 8.932946 #>  [25,] 9.056191 9.038701 9.020948 9.002918 8.984598 8.965974 8.947028 8.927745 #>  [26,] 9.051583 9.034037 9.016224 8.998129 8.979739 8.961037 8.942008 8.922634 #>  [27,] 9.047039 9.029440 9.011570 8.993414 8.974957 8.956183 8.937075 8.917613 #>  [28,] 9.042559 9.024912 9.006988 8.988774 8.970254 8.951412 8.932229 8.912686 #>  [29,] 9.038145 9.020452 9.002479 8.984211 8.965633 8.946726 8.927474 8.907854 #>  [30,] 9.033797 9.016062 8.998043 8.979725 8.961093 8.942127 8.922810 8.903120 #>  [31,] 9.029517 9.011742 8.993681 8.975318 8.956636 8.937616 8.918239 8.898484 #>  [32,] 9.025304 9.007495 8.989396 8.970991 8.952263 8.933194 8.913763 8.893948 #>  [33,] 9.021161 9.003320 8.985186 8.966744 8.947976 8.928863 8.909383 8.889515 #>  [34,] 9.017087 8.999218 8.981054 8.962579 8.943775 8.924622 8.905100 8.885185 #>  [35,] 9.013082 8.995189 8.976999 8.958496 8.939661 8.920475 8.900915 8.880959 #>  [36,] 9.009148 8.991235 8.973023 8.954496 8.935635 8.916420 8.896830 8.876839 #>  [37,] 9.005284 8.987355 8.969126 8.950579 8.931697 8.912460 8.892844 8.872826 #>  [38,] 9.001492 8.983550 8.965307 8.946747 8.927849 8.908594 8.888959 8.868920 #>  [39,] 8.997771 8.979821 8.961569 8.942998 8.924089 8.904822 8.885175 8.865121 #>  [40,] 8.994121 8.976166 8.957910 8.939334 8.920419 8.901146 8.881492 8.861431 #>  [41,] 8.990542 8.972587 8.954330 8.935754 8.916839 8.897566 8.877910 8.857849 #>  [42,] 8.987036 8.969084 8.950831 8.932259 8.913349 8.894080 8.874430 8.854375 #>  [43,] 8.983600 8.965656 8.947411 8.928848 8.909948 8.890690 8.871052 8.851009 #>  [44,] 8.980236 8.962304 8.944071 8.925522 8.906636 8.887394 8.867774 8.847752 #>  [45,] 8.976943 8.959026 8.940810 8.922279 8.903414 8.884194 8.864598 8.844601 #>  [46,] 8.973720 8.955823 8.937628 8.919120 8.900279 8.881087 8.861521 8.841557 #>  [47,] 8.970568 8.952694 8.934525 8.916044 8.897233 8.878074 8.858543 8.838619 #>  [48,] 8.967486 8.949639 8.931499 8.913050 8.894274 8.875153 8.855664 8.835786 #>  [49,] 8.964473 8.946657 8.928551 8.910138 8.891402 8.872324 8.852882 8.833056 #>  [50,] 8.961529 8.943748 8.925679 8.907307 8.888615 8.869585 8.850197 8.830429 #>  [51,] 8.958654 8.940910 8.922882 8.904555 8.885913 8.866936 8.847606 8.827902 #>  [52,] 8.955845 8.938144 8.920161 8.901883 8.883294 8.864375 8.845109 8.825475 #>  [53,] 8.953104 8.935447 8.917513 8.899289 8.880757 8.861901 8.842704 8.823145 #>  [54,] 8.950428 8.932820 8.914939 8.896771 8.878301 8.859513 8.840389 8.820911 #>  [55,] 8.947817 8.930261 8.912436 8.894328 8.875924 8.857208 8.838163 8.818770 #>  [56,] 8.945270 8.927769 8.910003 8.891960 8.873626 8.854986 8.836023 8.816721 #>  [57,] 8.942786 8.925343 8.907640 8.889664 8.871404 8.852844 8.833968 8.814762 #>  [58,] 8.940364 8.922982 8.905344 8.887440 8.869257 8.850780 8.831996 8.812889 #>  [59,] 8.938003 8.920684 8.903116 8.885286 8.867183 8.848794 8.830105 8.811102 #>  [60,] 8.935702 8.918449 8.900952 8.883200 8.865181 8.846883 8.828292 8.809397 #>  [61,] 8.933459 8.916275 8.898852 8.881181 8.863248 8.845044 8.826556 8.807772 #>  [62,] 8.931273 8.914161 8.896815 8.879226 8.861384 8.843277 8.824894 8.806224 #>  [63,] 8.929143 8.912105 8.894839 8.877335 8.859585 8.841578 8.823304 8.804751 #>  [64,] 8.927068 8.910106 8.892921 8.875506 8.857851 8.839947 8.821783 8.803351 #>  [65,] 8.925047 8.908162 8.891062 8.873737 8.856179 8.838380 8.820330 8.802021 #>  [66,] 8.923077 8.906273 8.889258 8.872026 8.854567 8.836875 8.818941 8.800757 #>  [67,] 8.921158 8.904436 8.887509 8.870371 8.853014 8.835431 8.817615 8.799559 #>  [68,] 8.919289 8.902650 8.885813 8.868771 8.851517 8.834046 8.816350 8.798422 #>  [69,] 8.917468 8.900914 8.884168 8.867224 8.850075 8.832716 8.815142 8.797345 #>  [70,] 8.915693 8.899226 8.882573 8.865727 8.848685 8.831441 8.813989 8.796325 #>  [71,] 8.913963 8.897584 8.881025 8.864281 8.847346 8.830217 8.812890 8.795359 #>  [72,] 8.912278 8.895988 8.879524 8.862881 8.846056 8.829044 8.811841 8.794444 #>  [73,] 8.910635 8.894435 8.878067 8.861528 8.844812 8.827918 8.810841 8.793579 #>  [74,] 8.909033 8.892924 8.876654 8.860218 8.843613 8.826837 8.809887 8.792761 #>  [75,] 8.907470 8.891454 8.875281 8.858950 8.842457 8.825800 8.808977 8.791987 #>  [76,] 8.905946 8.890023 8.873949 8.857723 8.841342 8.824804 8.808109 8.791255 #>  [77,] 8.904459 8.888629 8.872655 8.856534 8.840266 8.823848 8.807281 8.790563 #>  [78,] 8.903007 8.887271 8.871397 8.855383 8.839227 8.822930 8.806490 8.789909 #>  [79,] 8.901590 8.885948 8.870174 8.854266 8.838224 8.822047 8.805735 8.789289 #>  [80,] 8.900205 8.884659 8.868985 8.853184 8.837255 8.821197 8.805013 8.788702 #>  [81,] 8.898852 8.883401 8.867828 8.852133 8.836317 8.820380 8.804322 8.788147 #>  [82,] 8.897529 8.882173 8.866701 8.851113 8.835410 8.819592 8.803661 8.787620 #>  [83,] 8.896235 8.880974 8.865603 8.850122 8.834531 8.818833 8.803028 8.787120 #>  [84,] 8.894969 8.879803 8.864533 8.849158 8.833680 8.818100 8.802421 8.786645 #>  [85,] 8.893729 8.878659 8.863489 8.848220 8.832854 8.817392 8.801837 8.786193 #>  [86,] 8.892514 8.877539 8.862470 8.847307 8.832052 8.816707 8.801276 8.785763 #>  [87,] 8.891323 8.876443 8.861474 8.846416 8.831272 8.816044 8.800736 8.785351 #>  [88,] 8.890155 8.875370 8.860500 8.845547 8.830513 8.815401 8.800214 8.784958 #>  [89,] 8.889009 8.874318 8.859547 8.844698 8.829773 8.814776 8.799711 8.784581 #>  [90,] 8.887883 8.873286 8.858614 8.843868 8.829052 8.814169 8.799223 8.784218 #>  [91,] 8.886776 8.872273 8.857699 8.843056 8.828348 8.813577 8.798749 8.783869 #>  [92,] 8.885688 8.871278 8.856801 8.842260 8.827659 8.813000 8.798289 8.783531 #>  [93,] 8.884617 8.870300 8.855920 8.841480 8.826984 8.812436 8.797841 8.783204 #>  [94,] 8.883563 8.869337 8.855053 8.840713 8.826322 8.811884 8.797403 8.782885 #>  [95,] 8.882523 8.868389 8.854200 8.839960 8.825673 8.811343 8.796975 8.782574 #>  [96,] 8.881498 8.867454 8.853360 8.839218 8.825034 8.810811 8.796554 8.782270 #>  [97,] 8.880486 8.866532 8.852531 8.838487 8.824404 8.810287 8.796141 8.781971 #>  [98,] 8.879487 8.865622 8.851713 8.837766 8.823784 8.809771 8.795733 8.781676 #>  [99,] 8.878499 8.864722 8.850905 8.837054 8.823170 8.809261 8.795330 8.781384 #> [100,] 8.877522 8.863832 8.850106 8.836349 8.822564 8.808756 8.794931 8.781095 #>           [,41]    [,42]    [,43]    [,44]    [,45]    [,46]    [,47]    [,48] #>   [1,] 9.055027 9.038503 9.021865 9.005119 8.988271 8.971330 8.954309 8.937218 #>   [2,] 9.048321 9.031644 9.014844 8.997926 8.980895 8.963761 8.946533 8.929225 #>   [3,] 9.041647 9.024817 9.007853 8.990761 8.973545 8.956215 8.938778 8.921248 #>   [4,] 9.035007 9.018022 9.000895 8.983627 8.966225 8.948695 8.931046 8.913291 #>   [5,] 9.028403 9.011264 8.993971 8.976527 8.958936 8.941205 8.923342 8.905357 #>   [6,] 9.021839 9.004544 8.987085 8.969463 8.951682 8.933748 8.915667 8.897450 #>   [7,] 9.015316 8.997866 8.980240 8.962439 8.944467 8.926327 8.908027 8.889575 #>   [8,] 9.008838 8.991231 8.973438 8.955458 8.937293 8.918947 8.900425 8.881734 #>   [9,] 9.002406 8.984644 8.966683 8.948523 8.930165 8.911611 8.892865 8.873933 #>  [10,] 8.996023 8.978106 8.959978 8.941638 8.923086 8.904323 8.885351 8.866177 #>  [11,] 8.989692 8.971620 8.953326 8.934806 8.916060 8.897087 8.877889 8.858469 #>  [12,] 8.983416 8.965190 8.946730 8.928031 8.909091 8.889908 8.870482 8.850815 #>  [13,] 8.977198 8.958819 8.940194 8.921316 8.902182 8.882789 8.863135 8.843220 #>  [14,] 8.971040 8.952510 8.933721 8.914665 8.895338 8.875736 8.855853 8.835690 #>  [15,] 8.964945 8.946266 8.927314 8.908082 8.888564 8.868752 8.848642 8.828230 #>  [16,] 8.958917 8.940090 8.920977 8.901571 8.881862 8.861843 8.841506 8.820846 #>  [17,] 8.952957 8.933985 8.914714 8.895135 8.875239 8.855014 8.834451 8.813544 #>  [18,] 8.947069 8.927954 8.908528 8.888780 8.868697 8.848268 8.827483 8.806330 #>  [19,] 8.941256 8.922001 8.902423 8.882507 8.862242 8.841612 8.820606 8.799210 #>  [20,] 8.935521 8.916129 8.896401 8.876322 8.855877 8.835050 8.813827 8.792190 #>  [21,] 8.929866 8.910341 8.890468 8.870229 8.849608 8.828588 8.807150 8.785277 #>  [22,] 8.924295 8.904640 8.884625 8.864231 8.843439 8.822230 8.800583 8.778478 #>  [23,] 8.918809 8.899030 8.878877 8.858333 8.837374 8.815981 8.794130 8.771798 #>  [24,] 8.913412 8.893512 8.873228 8.852537 8.831418 8.809847 8.787798 8.765245 #>  [25,] 8.908106 8.888091 8.867680 8.846849 8.825575 8.803832 8.781592 8.758825 #>  [26,] 8.902894 8.882769 8.862237 8.841272 8.819849 8.797941 8.775517 8.752544 #>  [27,] 8.897779 8.877549 8.856901 8.835809 8.814245 8.792179 8.769579 8.746409 #>  [28,] 8.892762 8.872434 8.851677 8.830464 8.808766 8.786551 8.763784 8.740426 #>  [29,] 8.887846 8.867426 8.846566 8.825240 8.803416 8.781060 8.758136 8.734601 #>  [30,] 8.883033 8.862527 8.841573 8.820141 8.798199 8.775712 8.752640 8.728939 #>  [31,] 8.878326 8.857740 8.836698 8.815169 8.793119 8.770510 8.747301 8.723446 #>  [32,] 8.873725 8.853067 8.831945 8.810327 8.788178 8.765458 8.742124 8.718128 #>  [33,] 8.869233 8.848510 8.827316 8.805618 8.783379 8.760559 8.737112 8.712988 #>  [34,] 8.864851 8.844071 8.822813 8.801044 8.778726 8.755817 8.732270 8.708032 #>  [35,] 8.860581 8.839751 8.818438 8.796608 8.774221 8.751234 8.727600 8.703263 #>  [36,] 8.856423 8.835551 8.814192 8.792310 8.769865 8.746813 8.723105 8.698685 #>  [37,] 8.852379 8.831473 8.810077 8.788152 8.765661 8.742556 8.718789 8.694300 #>  [38,] 8.848449 8.827518 8.806093 8.784137 8.761610 8.738465 8.714652 8.690112 #>  [39,] 8.844635 8.823686 8.802242 8.780264 8.757713 8.734541 8.710697 8.686122 #>  [40,] 8.840937 8.819979 8.798524 8.776535 8.753971 8.730784 8.706924 8.682331 #>  [41,] 8.837354 8.816395 8.794939 8.772949 8.750384 8.727196 8.703335 8.678739 #>  [42,] 8.833887 8.812936 8.791488 8.769507 8.746952 8.723777 8.699928 8.675348 #>  [43,] 8.830535 8.809600 8.788170 8.766209 8.743676 8.720525 8.696704 8.672156 #>  [44,] 8.827299 8.806388 8.784985 8.763054 8.740554 8.717440 8.693662 8.669163 #>  [45,] 8.824178 8.803299 8.781931 8.760040 8.737585 8.714522 8.690801 8.666365 #>  [46,] 8.821170 8.800332 8.779009 8.757167 8.734768 8.711768 8.688117 8.663762 #>  [47,] 8.818276 8.797485 8.776216 8.754434 8.732101 8.709176 8.685610 8.661351 #>  [48,] 8.815493 8.794758 8.773551 8.751838 8.729583 8.706744 8.683276 8.659127 #>  [49,] 8.812821 8.792149 8.771012 8.749378 8.727210 8.704469 8.681111 8.657088 #>  [50,] 8.810258 8.789657 8.768598 8.747051 8.724980 8.702348 8.679113 8.655229 #>  [51,] 8.807802 8.787279 8.766306 8.744854 8.722890 8.700378 8.677278 8.653545 #>  [52,] 8.805451 8.785013 8.764134 8.742786 8.720938 8.698555 8.675600 8.652031 #>  [53,] 8.803204 8.782857 8.762079 8.740843 8.719119 8.696875 8.674075 8.650681 #>  [54,] 8.801058 8.780808 8.760138 8.739021 8.717430 8.695333 8.672699 8.649491 #>  [55,] 8.799012 8.778865 8.758309 8.737318 8.715867 8.693926 8.671466 8.648454 #>  [56,] 8.797062 8.777025 8.756588 8.735730 8.714426 8.692649 8.670372 8.647563 #>  [57,] 8.795206 8.775284 8.754973 8.734254 8.713104 8.691497 8.669410 8.646814 #>  [58,] 8.793443 8.773639 8.753460 8.732886 8.711895 8.690466 8.668575 8.646198 #>  [59,] 8.791769 8.772089 8.752046 8.731621 8.710796 8.689549 8.667861 8.645710 #>  [60,] 8.790181 8.770630 8.750727 8.730457 8.709802 8.688744 8.667264 8.645344 #>  [61,] 8.788677 8.769258 8.749500 8.729389 8.708909 8.688043 8.666776 8.645092 #>  [62,] 8.787254 8.767971 8.748362 8.728414 8.708112 8.687443 8.666393 8.644948 #>  [63,] 8.785909 8.766765 8.747309 8.727526 8.707407 8.686938 8.666108 8.644906 #>  [64,] 8.784639 8.765638 8.746336 8.726723 8.706789 8.686523 8.665916 8.644960 #>  [65,] 8.783442 8.764586 8.745442 8.726001 8.706254 8.686194 8.665812 8.645102 #>  [66,] 8.782315 8.763606 8.744622 8.725355 8.705798 8.685945 8.665789 8.645328 #>  [67,] 8.781254 8.762694 8.743872 8.724781 8.705416 8.685771 8.665844 8.645631 #>  [68,] 8.780257 8.761848 8.743190 8.724276 8.705104 8.685669 8.665969 8.646005 #>  [69,] 8.779321 8.761065 8.742571 8.723836 8.704857 8.685632 8.666161 8.646444 #>  [70,] 8.778443 8.760340 8.742013 8.723457 8.704672 8.685657 8.666414 8.646944 #>  [71,] 8.777621 8.759672 8.741511 8.723136 8.704545 8.685740 8.666723 8.647499 #>  [72,] 8.776851 8.759058 8.741064 8.722868 8.704471 8.685875 8.667084 8.648104 #>  [73,] 8.776131 8.758493 8.740666 8.722651 8.704447 8.686059 8.667493 8.648754 #>  [74,] 8.775458 8.757976 8.740316 8.722480 8.704469 8.686289 8.667944 8.649444 #>  [75,] 8.774829 8.757504 8.740011 8.722353 8.704534 8.686559 8.668435 8.650171 #>  [76,] 8.774243 8.757073 8.739746 8.722267 8.704638 8.686866 8.668960 8.650929 #>  [77,] 8.773696 8.756681 8.739520 8.722217 8.704777 8.687208 8.669516 8.651715 #>  [78,] 8.773186 8.756326 8.739330 8.722202 8.704950 8.687579 8.670101 8.652526 #>  [79,] 8.772711 8.756004 8.739172 8.722219 8.705151 8.687978 8.670709 8.653356 #>  [80,] 8.772269 8.755715 8.739044 8.722264 8.705379 8.688401 8.671338 8.654204 #>  [81,] 8.771856 8.755454 8.738945 8.722335 8.705631 8.688844 8.671985 8.655066 #>  [82,] 8.771471 8.755220 8.738870 8.722429 8.705904 8.689306 8.672646 8.655939 #>  [83,] 8.771113 8.755010 8.738818 8.722544 8.706196 8.689784 8.673320 8.656819 #>  [84,] 8.770778 8.754823 8.738787 8.722677 8.706503 8.690274 8.674004 8.657705 #>  [85,] 8.770464 8.754656 8.738774 8.722827 8.706824 8.690775 8.674694 8.658594 #>  [86,] 8.770171 8.754507 8.738778 8.722991 8.707157 8.691285 8.675389 8.659483 #>  [87,] 8.769896 8.754375 8.738796 8.723167 8.707498 8.691800 8.676086 8.660370 #>  [88,] 8.769637 8.754257 8.738827 8.723354 8.707847 8.692320 8.676784 8.661254 #>  [89,] 8.769393 8.754153 8.738868 8.723548 8.708202 8.692842 8.677480 8.662132 #>  [90,] 8.769162 8.754059 8.738918 8.723749 8.708560 8.693364 8.678173 8.663002 #>  [91,] 8.768942 8.753975 8.738976 8.723954 8.708920 8.693884 8.678861 8.663864 #>  [92,] 8.768732 8.753899 8.739039 8.724163 8.709280 8.694402 8.679542 8.664714 #>  [93,] 8.768531 8.753829 8.739107 8.724374 8.709639 8.694916 8.680215 8.665553 #>  [94,] 8.768337 8.753765 8.739178 8.724585 8.709996 8.695423 8.680879 8.666378 #>  [95,] 8.768149 8.753704 8.739250 8.724794 8.710348 8.695923 8.681532 8.667189 #>  [96,] 8.767965 8.753646 8.739322 8.725002 8.710696 8.696415 8.682173 8.667983 #>  [97,] 8.767785 8.753590 8.739393 8.725206 8.711037 8.696898 8.682802 8.668761 #>  [98,] 8.767607 8.753533 8.739463 8.725405 8.711370 8.697370 8.683416 8.669522 #>  [99,] 8.767430 8.753476 8.739529 8.725599 8.711695 8.697830 8.684015 8.670263 #> [100,] 8.767254 8.753417 8.739591 8.725785 8.712011 8.698278 8.684598 8.670985 #>           [,49]    [,50]    [,51]    [,52]    [,53]    [,54]    [,55]    [,56] #>   [1,] 8.920075 8.902898 8.885709 8.868534 8.851402 8.834347 8.817409 8.800632 #>   [2,] 8.911851 8.894430 8.876984 8.859539 8.842123 8.824773 8.807527 8.790432 #>   [3,] 8.903639 8.885969 8.868260 8.850536 8.832829 8.815173 8.797608 8.780181 #>   [4,] 8.895442 8.877518 8.859539 8.841530 8.823522 8.805550 8.787654 8.769883 #>   [5,] 8.887264 8.869080 8.850825 8.832524 8.814206 8.795908 8.777670 8.759540 #>   [6,] 8.879109 8.860661 8.842123 8.823522 8.804886 8.786251 8.767658 8.749157 #>   [7,] 8.870982 8.852263 8.833438 8.814529 8.795566 8.776583 8.757623 8.738736 #>   [8,] 8.862885 8.843892 8.824773 8.805550 8.786251 8.766910 8.747571 8.728282 #>   [9,] 8.854825 8.835553 8.816134 8.796590 8.776946 8.757238 8.737506 8.717801 #>  [10,] 8.846806 8.827251 8.807527 8.787654 8.767658 8.747571 8.727434 8.707299 #>  [11,] 8.838833 8.818992 8.798958 8.778750 8.758392 8.737917 8.717363 8.696781 #>  [12,] 8.830912 8.810780 8.790432 8.769883 8.749157 8.728282 8.707299 8.686255 #>  [13,] 8.823048 8.802623 8.781956 8.761061 8.739958 8.718676 8.697250 8.675729 #>  [14,] 8.815247 8.794527 8.773538 8.752291 8.730805 8.709105 8.687225 8.665212 #>  [15,] 8.807515 8.786498 8.765184 8.743581 8.721705 8.699579 8.677234 8.654714 #>  [16,] 8.799859 8.778544 8.756902 8.734940 8.712669 8.690109 8.667288 8.644246 #>  [17,] 8.792286 8.770671 8.748700 8.726375 8.703705 8.680704 8.657397 8.633820 #>  [18,] 8.784801 8.762888 8.740587 8.717898 8.694823 8.671375 8.647573 8.623449 #>  [19,] 8.777412 8.755202 8.732572 8.709517 8.686036 8.662136 8.637831 8.613147 #>  [20,] 8.770126 8.747621 8.724663 8.701242 8.677353 8.652998 8.628184 8.602931 #>  [21,] 8.762951 8.740153 8.716869 8.693084 8.668788 8.643975 8.618646 8.592815 #>  [22,] 8.755893 8.732808 8.709201 8.685054 8.660352 8.635080 8.609235 8.582820 #>  [23,] 8.748961 8.725592 8.701668 8.677164 8.652058 8.626330 8.599967 8.572963 #>  [24,] 8.742161 8.718515 8.694280 8.669424 8.643919 8.617739 8.590859 8.563265 #>  [25,] 8.735501 8.711586 8.687047 8.661846 8.635950 8.609322 8.581931 8.553747 #>  [26,] 8.728989 8.704813 8.679979 8.654443 8.628164 8.601097 8.573200 8.544433 #>  [27,] 8.722632 8.698205 8.673086 8.647225 8.620574 8.593080 8.564688 8.535345 #>  [28,] 8.716437 8.691770 8.666378 8.640205 8.613196 8.585286 8.556413 8.526508 #>  [29,] 8.710411 8.685517 8.659865 8.633395 8.606042 8.577734 8.548396 8.517945 #>  [30,] 8.704561 8.679453 8.653556 8.626805 8.599126 8.570440 8.540657 8.509682 #>  [31,] 8.698893 8.673586 8.647461 8.620446 8.592462 8.563419 8.533217 8.501744 #>  [32,] 8.693414 8.667924 8.641588 8.614330 8.586062 8.556688 8.526094 8.494154 #>  [33,] 8.688129 8.662472 8.635945 8.608465 8.579939 8.550261 8.519307 8.486936 #>  [34,] 8.683044 8.657238 8.630540 8.602862 8.574104 8.544152 8.512873 8.480112 #>  [35,] 8.678162 8.652227 8.625380 8.597528 8.568567 8.538375 8.506810 8.473704 #>  [36,] 8.673489 8.647444 8.620470 8.592471 8.563337 8.532940 8.501130 8.467729 #>  [37,] 8.669027 8.642894 8.615817 8.587697 8.558422 8.527858 8.495848 8.462204 #>  [38,] 8.664779 8.638579 8.611423 8.583212 8.553829 8.523137 8.490973 8.457143 #>  [39,] 8.660749 8.634502 8.607293 8.579019 8.549563 8.518783 8.486514 8.452556 #>  [40,] 8.656937 8.630665 8.603428 8.575122 8.545626 8.514801 8.482476 8.448450 #>  [41,] 8.653344 8.627070 8.599830 8.571521 8.542022 8.511192 8.478862 8.444830 #>  [42,] 8.649970 8.623716 8.596499 8.568217 8.538749 8.507957 8.475673 8.441696 #>  [43,] 8.646814 8.620602 8.593434 8.565208 8.535808 8.505095 8.472906 8.439045 #>  [44,] 8.643876 8.617727 8.590632 8.562493 8.533193 8.502601 8.470556 8.436870 #>  [45,] 8.641152 8.615089 8.588092 8.560067 8.530902 8.500469 8.468615 8.435160 #>  [46,] 8.638641 8.612683 8.585808 8.557925 8.528927 8.498691 8.467073 8.433904 #>  [47,] 8.636339 8.610506 8.583776 8.556061 8.527261 8.497258 8.465918 8.433085 #>  [48,] 8.634242 8.608554 8.581990 8.554469 8.525895 8.496159 8.465137 8.432684 #>  [49,] 8.632345 8.606819 8.580444 8.553139 8.524818 8.495381 8.464712 8.432683 #>  [50,] 8.630643 8.605298 8.579129 8.552064 8.524021 8.494910 8.464627 8.433058 #>  [51,] 8.629131 8.603982 8.578038 8.551232 8.523491 8.494731 8.464863 8.433786 #>  [52,] 8.627802 8.602864 8.577162 8.550634 8.523215 8.494830 8.465401 8.434843 #>  [53,] 8.626651 8.601938 8.576492 8.550259 8.523179 8.495189 8.466221 8.436205 #>  [54,] 8.625670 8.601195 8.576020 8.550096 8.523372 8.495793 8.467304 8.437847 #>  [55,] 8.624853 8.600626 8.575734 8.550132 8.523778 8.496625 8.468628 8.439745 #>  [56,] 8.624192 8.600225 8.575625 8.550357 8.524383 8.497667 8.470174 8.441873 #>  [57,] 8.623680 8.599981 8.575683 8.550758 8.525175 8.498904 8.471922 8.444209 #>  [58,] 8.623310 8.599886 8.575899 8.551324 8.526138 8.500319 8.473853 8.446730 #>  [59,] 8.623074 8.599932 8.576261 8.552043 8.527259 8.501897 8.475948 8.449415 #>  [60,] 8.622965 8.600110 8.576761 8.552903 8.528525 8.503621 8.478189 8.452242 #>  [61,] 8.622975 8.600411 8.577388 8.553894 8.529924 8.505477 8.480560 8.455192 #>  [62,] 8.623097 8.600828 8.578132 8.555003 8.531441 8.507450 8.483044 8.458247 #>  [63,] 8.623323 8.601351 8.578984 8.556222 8.533066 8.509528 8.485626 8.461391 #>  [64,] 8.623647 8.601973 8.579936 8.557538 8.534787 8.511697 8.488292 8.464607 #>  [65,] 8.624061 8.602686 8.580978 8.558943 8.536593 8.513945 8.491028 8.467880 #>  [66,] 8.624559 8.603482 8.582102 8.560428 8.538473 8.516261 8.493822 8.471199 #>  [67,] 8.625133 8.604354 8.583300 8.561982 8.540419 8.518634 8.496662 8.474549 #>  [68,] 8.625778 8.605295 8.584563 8.563598 8.542419 8.521054 8.499538 8.477920 #>  [69,] 8.626488 8.606298 8.585886 8.565268 8.544467 8.523512 8.502441 8.481303 #>  [70,] 8.627255 8.607356 8.587260 8.566984 8.546553 8.525999 8.505360 8.484687 #>  [71,] 8.628076 8.608464 8.588679 8.568739 8.548671 8.528507 8.508288 8.488064 #>  [72,] 8.628944 8.609616 8.590136 8.570526 8.550813 8.531029 8.511218 8.491428 #>  [73,] 8.629854 8.610805 8.591626 8.572339 8.552972 8.533559 8.514142 8.494771 #>  [74,] 8.630800 8.612027 8.593144 8.574173 8.555143 8.536090 8.517055 8.498088 #>  [75,] 8.631780 8.613277 8.594683 8.576021 8.557320 8.538616 8.519951 8.501374 #>  [76,] 8.632787 8.614551 8.596240 8.577879 8.559498 8.541133 8.522825 8.504623 #>  [77,] 8.633818 8.615842 8.597809 8.579742 8.561673 8.543636 8.525673 8.507831 #>  [78,] 8.634869 8.617149 8.599386 8.581606 8.563839 8.546121 8.528491 8.510996 #>  [79,] 8.635936 8.618466 8.600968 8.583467 8.565994 8.548583 8.531275 8.514114 #>  [80,] 8.637015 8.619790 8.602550 8.585321 8.568133 8.551020 8.534022 8.517182 #>  [81,] 8.638104 8.621118 8.604130 8.587165 8.570254 8.553429 8.536730 8.520198 #>  [82,] 8.639199 8.622447 8.605704 8.588996 8.572353 8.555807 8.539395 8.523161 #>  [83,] 8.640297 8.623773 8.607269 8.590811 8.574427 8.558151 8.542017 8.526067 #>  [84,] 8.641396 8.625094 8.608823 8.592608 8.576475 8.560459 8.544593 8.528917 #>  [85,] 8.642492 8.626408 8.610364 8.594383 8.578495 8.562729 8.547121 8.531709 #>  [86,] 8.643584 8.627712 8.611888 8.596136 8.580483 8.564961 8.549601 8.534441 #>  [87,] 8.644670 8.629004 8.613394 8.597864 8.582440 8.567152 8.552031 8.537114 #>  [88,] 8.645747 8.630282 8.614881 8.599565 8.584362 8.569300 8.554411 8.539727 #>  [89,] 8.646814 8.631545 8.616345 8.601238 8.586249 8.571406 8.556739 8.542279 #>  [90,] 8.647869 8.632790 8.617787 8.602882 8.588100 8.573468 8.559014 8.544771 #>  [91,] 8.648910 8.634017 8.619205 8.604496 8.589914 8.575485 8.561238 8.547202 #>  [92,] 8.649935 8.635223 8.620596 8.606077 8.591689 8.577457 8.563408 8.549572 #>  [93,] 8.650945 8.636407 8.621961 8.607626 8.593425 8.579383 8.565526 8.551881 #>  [94,] 8.651936 8.637570 8.623298 8.609141 8.595122 8.581263 8.567590 8.554130 #>  [95,] 8.652908 8.638708 8.624606 8.610622 8.596778 8.583097 8.569602 8.556319 #>  [96,] 8.653861 8.639822 8.625885 8.612069 8.598394 8.584884 8.571560 8.558448 #>  [97,] 8.654792 8.640910 8.627133 8.613479 8.599969 8.586624 8.573466 8.560518 #>  [98,] 8.655702 8.641973 8.628351 8.614854 8.601503 8.588317 8.575319 8.562530 #>  [99,] 8.656589 8.643008 8.629537 8.616193 8.602996 8.589964 8.577119 8.564483 #> [100,] 8.657453 8.644016 8.630691 8.617495 8.604446 8.591564 8.578867 8.566378 #>           [,57]    [,58]    [,59]    [,60]    [,61]    [,62]    [,63]    [,64] #>   [1,] 8.784066 8.767764 8.751786 8.736199 8.721071 8.706473 8.692481 8.679168 #>   [2,] 8.773538 8.756902 8.740587 8.724663 8.709201 8.694280 8.679979 8.666378 #>   [3,] 8.762946 8.745960 8.729291 8.713010 8.697196 8.681931 8.667301 8.653393 #>   [4,] 8.752291 8.734940 8.717898 8.701242 8.685054 8.669424 8.654443 8.640205 #>   [5,] 8.741577 8.723842 8.706408 8.689356 8.672773 8.656755 8.641399 8.626809 #>   [6,] 8.730805 8.712669 8.694823 8.677353 8.660352 8.643919 8.628164 8.613196 #>   [7,] 8.719980 8.701423 8.683145 8.665234 8.647788 8.630915 8.614732 8.599357 #>   [8,] 8.709105 8.690109 8.671375 8.652998 8.635080 8.617739 8.601097 8.585286 #>   [9,] 8.698185 8.678729 8.659517 8.640647 8.622230 8.604388 8.587255 8.570974 #>  [10,] 8.687225 8.667288 8.647573 8.628184 8.609235 8.590859 8.573200 8.556413 #>  [11,] 8.676232 8.655792 8.635549 8.615610 8.596098 8.577152 8.558928 8.541593 #>  [12,] 8.665212 8.644246 8.623449 8.602931 8.582820 8.563265 8.544433 8.526508 #>  [13,] 8.654173 8.632659 8.611280 8.590150 8.569403 8.549197 8.529712 8.511147 #>  [14,] 8.643125 8.621039 8.599050 8.577273 8.555851 8.534949 8.514761 8.495503 #>  [15,] 8.632076 8.609395 8.586766 8.564309 8.542170 8.520524 8.499578 8.479568 #>  [16,] 8.621039 8.597739 8.574441 8.551266 8.528366 8.505925 8.484163 8.463335 #>  [17,] 8.610026 8.586083 8.562086 8.538156 8.514449 8.491156 8.468514 8.446797 #>  [18,] 8.599050 8.574441 8.549715 8.524991 8.500428 8.476227 8.452635 8.429951 #>  [19,] 8.588127 8.562830 8.537343 8.511787 8.486319 8.461146 8.436530 8.412793 #>  [20,] 8.577273 8.551266 8.524991 8.498562 8.472137 8.445928 8.420208 8.395321 #>  [21,] 8.566508 8.539771 8.512678 8.485337 8.457903 8.430589 8.403679 8.377539 #>  [22,] 8.555851 8.528366 8.500428 8.472137 8.443641 8.415151 8.386960 8.359453 #>  [23,] 8.545324 8.517075 8.488268 8.458990 8.429379 8.399641 8.370072 8.341076 #>  [24,] 8.534949 8.505925 8.476227 8.445928 8.415151 8.384093 8.353044 8.322425 #>  [25,] 8.524753 8.494944 8.464337 8.432987 8.400996 8.368544 8.335914 8.303529 #>  [26,] 8.514761 8.484163 8.452635 8.420208 8.386960 8.353044 8.318726 8.284426 #>  [27,] 8.505001 8.473615 8.441159 8.407636 8.373092 8.337649 8.301540 8.265167 #>  [28,] 8.495503 8.463335 8.429951 8.395321 8.359453 8.322425 8.284426 8.245823 #>  [29,] 8.486295 8.453359 8.419056 8.383317 8.346107 8.307448 8.267469 8.226480 #>  [30,] 8.477409 8.443726 8.408520 8.371683 8.333125 8.292805 8.250773 8.207251 #>  [31,] 8.468875 8.434474 8.398393 8.360480 8.320587 8.278595 8.234457 8.188276 #>  [32,] 8.460724 8.425641 8.388724 8.349772 8.308575 8.264925 8.218658 8.169725 #>  [33,] 8.452985 8.417267 8.379563 8.339626 8.297176 8.251913 8.203533 8.151799 #>  [34,] 8.445688 8.409388 8.370959 8.330107 8.286482 8.239680 8.189251 8.134733 #>  [35,] 8.438859 8.402039 8.362961 8.321280 8.276580 8.228354 8.175994 8.118789 #>  [36,] 8.432522 8.395254 8.355611 8.313205 8.267556 8.218059 8.163946 8.104247 #>  [37,] 8.426700 8.389061 8.348949 8.305938 8.259491 8.208912 8.153288 8.091396 #>  [38,] 8.421409 8.383484 8.343008 8.299526 8.252453 8.201019 8.144185 8.080509 #>  [39,] 8.416665 8.378543 8.337816 8.294007 8.246499 8.194466 8.136778 8.071824 #>  [40,] 8.412476 8.374250 8.333390 8.289408 8.241668 8.189315 8.131167 8.065521 #>  [41,] 8.408849 8.370613 8.329741 8.285743 8.237982 8.185600 8.127410 8.061700 #>  [42,] 8.405783 8.367633 8.326869 8.283014 8.235442 8.183323 8.125510 8.060369 #>  [43,] 8.403274 8.365303 8.324767 8.281208 8.234032 8.182457 8.125422 8.061447 #>  [44,] 8.401314 8.363611 8.323417 8.280302 8.233715 8.182946 8.127053 8.064768 #>  [45,] 8.399889 8.362540 8.322795 8.280259 8.234437 8.184707 8.130270 8.070105 #>  [46,] 8.398982 8.362067 8.322868 8.281033 8.236133 8.187639 8.134912 8.077189 #>  [47,] 8.398572 8.362162 8.323598 8.282572 8.238723 8.191626 8.140800 8.085734 #>  [48,] 8.398635 8.362795 8.324941 8.284815 8.242124 8.196545 8.147749 8.095455 #>  [49,] 8.399145 8.363931 8.326852 8.287699 8.246246 8.202269 8.155577 8.106086 #>  [50,] 8.400074 8.365533 8.329281 8.291157 8.251000 8.208675 8.164111 8.117387 #>  [51,] 8.401391 8.367562 8.332178 8.295124 8.256298 8.215643 8.173193 8.129149 #>  [52,] 8.403067 8.369980 8.335494 8.299534 8.262055 8.223065 8.182681 8.141196 #>  [53,] 8.405070 8.372747 8.339179 8.304327 8.268191 8.230840 8.192452 8.153384 #>  [54,] 8.407370 8.375827 8.343185 8.309441 8.274635 8.238879 8.202399 8.165594 #>  [55,] 8.409938 8.379181 8.347469 8.314823 8.281319 8.247103 8.212435 8.177733 #>  [56,] 8.412743 8.382776 8.351986 8.320422 8.288184 8.255444 8.222485 8.189729 #>  [57,] 8.415758 8.386577 8.356699 8.326192 8.295176 8.263845 8.232488 8.201527 #>  [58,] 8.418956 8.390554 8.361570 8.332090 8.302250 8.272254 8.242397 8.213087 #>  [59,] 8.422313 8.394676 8.366566 8.338080 8.309365 8.280632 8.252173 8.224379 #>  [60,] 8.425803 8.398918 8.371658 8.344130 8.316488 8.288944 8.261785 8.235381 #>  [61,] 8.429406 8.403254 8.376818 8.350209 8.323587 8.297162 8.271211 8.246082 #>  [62,] 8.433100 8.407663 8.382021 8.356293 8.330638 8.305264 8.280434 8.256474 #>  [63,] 8.436868 8.412124 8.387248 8.362361 8.337621 8.313231 8.289440 8.266553 #>  [64,] 8.440693 8.416619 8.392478 8.368393 8.344518 8.321049 8.298222 8.276319 #>  [65,] 8.444557 8.421130 8.397695 8.374373 8.351315 8.328708 8.306775 8.285775 #>  [66,] 8.448448 8.425645 8.402885 8.380287 8.357999 8.336199 8.315095 8.294926 #>  [67,] 8.452353 8.430150 8.408035 8.386125 8.364563 8.343517 8.323181 8.303777 #>  [68,] 8.456260 8.434633 8.413134 8.391877 8.370999 8.350657 8.331036 8.312336 #>  [69,] 8.460159 8.439085 8.418174 8.397536 8.377300 8.357619 8.338660 8.320611 #>  [70,] 8.464041 8.443497 8.423146 8.403093 8.383464 8.364400 8.346057 8.328609 #>  [71,] 8.467897 8.447861 8.428043 8.408546 8.389487 8.371000 8.353232 8.336338 #>  [72,] 8.471722 8.452171 8.432861 8.413889 8.395368 8.377422 8.360187 8.343808 #>  [73,] 8.475508 8.456421 8.437594 8.419120 8.401105 8.383666 8.366929 8.351027 #>  [74,] 8.479249 8.460607 8.442239 8.424236 8.406698 8.389735 8.373462 8.358003 #>  [75,] 8.482942 8.464724 8.446793 8.429237 8.412149 8.395630 8.379792 8.364744 #>  [76,] 8.486582 8.468769 8.451255 8.434121 8.417456 8.401357 8.385923 8.371260 #>  [77,] 8.490166 8.472739 8.455621 8.438887 8.422623 8.406917 8.391863 8.377556 #>  [78,] 8.493690 8.476633 8.459891 8.443537 8.427650 8.412313 8.397615 8.383642 #>  [79,] 8.497153 8.480448 8.464064 8.448070 8.432539 8.417551 8.403186 8.389525 #>  [80,] 8.500551 8.484183 8.468140 8.452487 8.437293 8.422632 8.408580 8.395211 #>  [81,] 8.503883 8.487838 8.472119 8.456789 8.441914 8.427562 8.413804 8.400708 #>  [82,] 8.507149 8.491410 8.476000 8.460978 8.446404 8.432343 8.418861 8.406022 #>  [83,] 8.510346 8.494901 8.479785 8.465054 8.450766 8.436980 8.423758 8.411160 #>  [84,] 8.513474 8.498309 8.483474 8.469020 8.455002 8.441476 8.428499 8.416127 #>  [85,] 8.516532 8.501636 8.487067 8.472877 8.459115 8.445835 8.433089 8.420930 #>  [86,] 8.519520 8.504880 8.490567 8.476626 8.463107 8.450060 8.437532 8.425573 #>  [87,] 8.522438 8.508043 8.493972 8.480270 8.466982 8.454154 8.441833 8.430063 #>  [88,] 8.525286 8.511125 8.497286 8.483811 8.470742 8.458122 8.445996 8.434405 #>  [89,] 8.528063 8.514127 8.500509 8.487250 8.474389 8.461967 8.450026 8.438603 #>  [90,] 8.530771 8.517049 8.503643 8.490589 8.477926 8.465692 8.453926 8.442662 #>  [91,] 8.533409 8.519893 8.506688 8.493830 8.481356 8.469300 8.457699 8.446587 #>  [92,] 8.535978 8.522659 8.509647 8.496976 8.484681 8.472795 8.461351 8.450381 #>  [93,] 8.538478 8.525347 8.512520 8.500028 8.487903 8.476178 8.464884 8.454050 #>  [94,] 8.540911 8.527960 8.515309 8.502988 8.491026 8.479455 8.468302 8.457597 #>  [95,] 8.543276 8.530498 8.518016 8.505858 8.494051 8.482626 8.471608 8.461025 #>  [96,] 8.545574 8.532963 8.520642 8.508640 8.496982 8.485695 8.474806 8.464339 #>  [97,] 8.547806 8.535355 8.523189 8.511335 8.499819 8.488665 8.477898 8.467541 #>  [98,] 8.549974 8.537675 8.525658 8.513946 8.502565 8.491538 8.480888 8.470636 #>  [99,] 8.552077 8.539925 8.528050 8.516475 8.505223 8.494317 8.483778 8.473626 #> [100,] 8.554117 8.542106 8.530367 8.518923 8.507795 8.497004 8.486571 8.476515 #>           [,65]    [,66]    [,67]    [,68]    [,69]    [,70]    [,71]    [,72] #>   [1,] 8.666607 8.654866 8.644006 8.634079 8.625126 8.617173 8.610234 8.604304 #>   [2,] 8.653556 8.641588 8.630540 8.620470 8.611423 8.603428 8.596499 8.590632 #>   [3,] 8.640292 8.628079 8.616829 8.606605 8.597456 8.589415 8.582498 8.576700 #>   [4,] 8.626805 8.614330 8.602862 8.592471 8.583212 8.575122 8.568217 8.562493 #>   [5,] 8.613086 8.600328 8.588625 8.578054 8.568675 8.560531 8.553639 8.547996 #>   [6,] 8.599126 8.586062 8.574104 8.563337 8.553829 8.545626 8.538749 8.533193 #>   [7,] 8.584914 8.571520 8.559285 8.548305 8.538656 8.530390 8.523529 8.518068 #>   [8,] 8.570440 8.556688 8.544152 8.532940 8.523137 8.514801 8.507957 8.502601 #>   [9,] 8.555692 8.541551 8.528688 8.517222 8.507251 8.498837 8.492013 8.486771 #>  [10,] 8.540657 8.526094 8.512873 8.501130 8.490973 8.482476 8.475673 8.470556 #>  [11,] 8.525325 8.510301 8.496689 8.484641 8.474280 8.465690 8.458910 8.453931 #>  [12,] 8.509682 8.494154 8.480112 8.467729 8.457143 8.448450 8.441696 8.436870 #>  [13,] 8.493715 8.477635 8.463121 8.450366 8.439530 8.430724 8.423999 8.419342 #>  [14,] 8.477409 8.460724 8.445688 8.432522 8.421409 8.412476 8.405783 8.401314 #>  [15,] 8.460751 8.443400 8.427787 8.414164 8.402741 8.393666 8.387009 8.382751 #>  [16,] 8.443726 8.425641 8.409388 8.395254 8.383484 8.374250 8.367633 8.363611 #>  [17,] 8.426320 8.407424 8.390457 8.375752 8.363591 8.354177 8.347605 8.343850 #>  [18,] 8.408520 8.388724 8.370959 8.355611 8.343008 8.333390 8.326869 8.323417 #>  [19,] 8.390312 8.369515 8.350857 8.334781 8.321676 8.311825 8.305363 8.302256 #>  [20,] 8.371683 8.349772 8.330107 8.313205 8.299526 8.289408 8.283014 8.280302 #>  [21,] 8.352623 8.329467 8.308665 8.290821 8.276482 8.266055 8.259739 8.257482 #>  [22,] 8.333125 8.308575 8.286482 8.267556 8.252453 8.241668 8.235442 8.233715 #>  [23,] 8.313185 8.287068 8.263505 8.243332 8.227339 8.216133 8.210014 8.208906 #>  [24,] 8.292805 8.264925 8.239680 8.218059 8.201019 8.189315 8.183323 8.182946 #>  [25,] 8.271995 8.242126 8.214948 8.191635 8.173356 8.161057 8.155216 8.155710 #>  [26,] 8.250773 8.218658 8.189251 8.163946 8.144185 8.131167 8.125510 8.127053 #>  [27,] 8.229174 8.194520 8.162530 8.134864 8.113313 8.099416 8.093984 8.096805 #>  [28,] 8.207251 8.169725 8.134733 8.104247 8.080509 8.065521 8.060369 8.064768 #>  [29,] 8.185079 8.144309 8.105818 8.071938 8.045491 8.029129 8.024332 8.030709 #>  [30,] 8.162766 8.118343 8.075764 8.037767 8.007921 7.989792 7.985454 7.994353 #>  [31,] 8.140456 8.091942 8.044590 8.001562 7.967383 7.946933 7.943202 7.955382 #>  [32,] 8.118343 8.065286 8.012374 7.963161 7.923361 7.899785 7.896880 7.913425 #>  [33,] 8.096676 8.038638 7.979294 7.922446 7.875224 7.847299 7.845559 7.868073 #>  [34,] 8.075764 8.012374 7.945683 7.879411 7.822201 7.787996 7.787972 7.818899 #>  [35,] 8.055984 7.986997 7.912098 7.834285 7.763390 7.719684 7.722331 7.765557 #>  [36,] 8.037767 7.963161 7.879411 7.787755 7.697869 7.638929 7.646054 7.708002 #>  [37,] 8.021587 7.941654 7.848888 7.741336 7.625123 7.539922 7.555346 7.647036 #>  [38,] 8.007921 7.923361 7.822201 7.697869 7.546458 7.411740 7.444926 7.585474 #>  [39,] 7.997209 7.909159 7.801291 7.661865 7.468878 7.230846 7.310627 7.530098 #>  [40,] 7.989792 7.899785 7.787996 7.638929 7.411740 6.948736 7.174372 7.492830 #>  [41,] 7.985868 7.895677 7.783516 7.633500 7.402501 6.880424 7.152865 7.485893 #>  [42,] 7.985454 7.896880 7.787972 7.646054 7.444926 7.174372 7.271580 7.510745 #>  [43,] 7.988388 7.903025 7.800351 7.672756 7.513314 7.363775 7.402837 7.556451 #>  [44,] 7.994353 7.913425 7.818899 7.708002 7.585474 7.492830 7.510745 7.610342 #>  [45,] 8.002926 7.927219 7.841658 7.746967 7.652470 7.589410 7.597788 7.664604 #>  [46,] 8.013631 7.943514 7.866885 7.786489 7.712280 7.666100 7.669458 7.715805 #>  [47,] 8.025993 7.961497 7.893229 7.824828 7.765220 7.729429 7.729845 7.762860 #>  [48,] 8.039567 7.980486 7.919746 7.861167 7.812183 7.783187 7.781737 7.805702 #>  [49,] 8.053968 7.999948 7.945822 7.895208 7.854089 7.829757 7.827053 7.844643 #>  [50,] 8.068871 8.019485 7.971087 7.926923 7.891736 7.870736 7.867149 7.880102 #>  [51,] 8.084016 8.038811 7.995336 7.956413 7.925784 7.907242 7.903011 7.912497 #>  [52,] 8.099199 8.057733 8.018474 7.983834 7.956769 7.940089 7.935374 7.942206 #>  [53,] 8.114267 8.076123 8.040474 8.009359 7.985125 7.969888 7.964800 7.969559 #>  [54,] 8.129104 8.093903 8.061349 8.033159 8.011206 7.997110 7.991728 7.994839 #>  [55,] 8.143630 8.111032 8.081139 8.055393 8.035302 8.022122 8.016506 8.018285 #>  [56,] 8.157788 8.127492 8.099894 8.076207 8.057654 8.045222 8.039415 8.040103 #>  [57,] 8.171540 8.143282 8.117671 8.095733 8.078462 8.066647 8.060683 8.060468 #>  [58,] 8.184865 8.158412 8.134531 8.114085 8.097896 8.086597 8.080502 8.079530 #>  [59,] 8.197751 8.172901 8.150530 8.131369 8.116099 8.105235 8.099029 8.097418 #>  [60,] 8.210195 8.186772 8.165725 8.147676 8.133193 8.122700 8.116400 8.114243 #>  [61,] 8.222199 8.200050 8.180168 8.163088 8.149285 8.139109 8.132729 8.130102 #>  [62,] 8.233771 8.212761 8.193910 8.177678 8.164464 8.154563 8.148114 8.145081 #>  [63,] 8.244920 8.224932 8.206997 8.191510 8.178812 8.169150 8.162640 8.159253 #>  [64,] 8.255658 8.236589 8.219469 8.204642 8.192397 8.182944 8.176382 8.172685 #>  [65,] 8.265999 8.247758 8.231368 8.217126 8.205281 8.196013 8.189404 8.185433 #>  [66,] 8.275956 8.258464 8.242729 8.229008 8.217519 8.208414 8.201764 8.197551 #>  [67,] 8.285544 8.268731 8.253584 8.240331 8.229159 8.220199 8.213512 8.209084 #>  [68,] 8.294777 8.278580 8.263966 8.251132 8.240244 8.231413 8.224694 8.220073 #>  [69,] 8.303668 8.288034 8.273901 8.261446 8.250812 8.242098 8.235350 8.230555 #>  [70,] 8.312233 8.297111 8.283416 8.271304 8.260900 8.252290 8.245515 8.240565 #>  [71,] 8.320484 8.305831 8.292535 8.280733 8.270537 8.262022 8.255223 8.250133 #>  [72,] 8.328434 8.314211 8.301279 8.289760 8.279753 8.271324 8.264504 8.259285 #>  [73,] 8.336096 8.322268 8.309670 8.298409 8.288573 8.280222 8.273382 8.268048 #>  [74,] 8.343481 8.330018 8.317725 8.306700 8.297022 8.288741 8.281884 8.276443 #>  [75,] 8.350602 8.337475 8.325463 8.314655 8.305120 8.296904 8.290031 8.284493 #>  [76,] 8.357469 8.344652 8.332900 8.322290 8.312887 8.304731 8.297843 8.292216 #>  [77,] 8.364093 8.351563 8.340050 8.329624 8.320342 8.312241 8.305339 8.299630 #>  [78,] 8.370483 8.358220 8.346928 8.336671 8.327501 8.319450 8.312535 8.306752 #>  [79,] 8.376649 8.364633 8.353546 8.343446 8.334379 8.326375 8.319449 8.313595 #>  [80,] 8.382599 8.370814 8.359918 8.349963 8.340992 8.333031 8.326093 8.320176 #>  [81,] 8.388343 8.376773 8.366053 8.356234 8.347351 8.339430 8.332482 8.326505 #>  [82,] 8.393888 8.382518 8.371964 8.362270 8.353469 8.345585 8.338628 8.332596 #>  [83,] 8.399242 8.388060 8.377659 8.368082 8.359358 8.351509 8.344543 8.338459 #>  [84,] 8.404412 8.393405 8.383149 8.373680 8.365028 8.357211 8.350237 8.344105 #>  [85,] 8.409406 8.398563 8.388441 8.379075 8.370489 8.362702 8.355721 8.349544 #>  [86,] 8.414228 8.403540 8.393544 8.384273 8.375750 8.367991 8.361003 8.354784 #>  [87,] 8.418887 8.408343 8.398466 8.389285 8.380820 8.373087 8.366092 8.359834 #>  [88,] 8.423388 8.412980 8.403214 8.394117 8.385707 8.377999 8.370998 8.364703 #>  [89,] 8.427735 8.417456 8.407795 8.398776 8.390418 8.382733 8.375726 8.369397 #>  [90,] 8.431936 8.421778 8.412215 8.403271 8.394961 8.387298 8.380285 8.373923 #>  [91,] 8.435994 8.425951 8.416481 8.407606 8.399342 8.391699 8.384682 8.378289 #>  [92,] 8.439915 8.429980 8.420598 8.411789 8.403568 8.395944 8.388922 8.382501 #>  [93,] 8.443704 8.433870 8.424571 8.415825 8.407644 8.400038 8.393012 8.386563 #>  [94,] 8.447364 8.437627 8.428406 8.419719 8.411576 8.403988 8.396957 8.390483 #>  [95,] 8.450900 8.441255 8.432108 8.423476 8.415370 8.407798 8.400763 8.394264 #>  [96,] 8.454316 8.444757 8.435681 8.427102 8.419030 8.411474 8.404435 8.397913 #>  [97,] 8.457615 8.448140 8.439130 8.430601 8.422562 8.415020 8.407977 8.401434 #>  [98,] 8.460803 8.451405 8.442459 8.433977 8.425969 8.418440 8.411395 8.404831 #>  [99,] 8.463881 8.454558 8.445672 8.437235 8.429256 8.421741 8.414691 8.408108 #> [100,] 8.466853 8.457601 8.448772 8.440378 8.432427 8.424924 8.417872 8.411270 #>           [,73]    [,74]    [,75]    [,76]    [,77]    [,78]    [,79]    [,80] #>   [1,] 8.599366 8.595386 8.592321 8.590112 8.588698 8.588006 8.587964 8.588498 #>   [2,] 8.585808 8.581990 8.579129 8.577162 8.576020 8.575625 8.575899 8.576761 #>   [3,] 8.571999 8.568355 8.565713 8.564005 8.563154 8.563077 8.563687 8.564896 #>   [4,] 8.557925 8.554469 8.552064 8.550634 8.550096 8.550357 8.551324 8.552903 #>   [5,] 8.543572 8.540320 8.538170 8.537040 8.536837 8.537461 8.538809 8.540780 #>   [6,] 8.528927 8.525895 8.524021 8.523215 8.523372 8.524383 8.526138 8.528525 #>   [7,] 8.513972 8.511179 8.509605 8.509148 8.509693 8.511120 8.513309 8.516139 #>   [8,] 8.498691 8.496159 8.494910 8.494830 8.495793 8.497667 8.500319 8.503621 #>   [9,] 8.483065 8.480817 8.479922 8.480251 8.481666 8.484020 8.487168 8.490970 #>  [10,] 8.467073 8.465137 8.464627 8.465401 8.467304 8.470174 8.473853 8.478189 #>  [11,] 8.450694 8.449099 8.449011 8.450269 8.452700 8.456126 8.460373 8.465279 #>  [12,] 8.433904 8.432684 8.433058 8.434843 8.437847 8.441873 8.446730 8.452242 #>  [13,] 8.416676 8.415871 8.416751 8.419113 8.422739 8.427413 8.432924 8.439081 #>  [14,] 8.398982 8.398635 8.400074 8.403067 8.407370 8.412743 8.418956 8.425803 #>  [15,] 8.380790 8.380952 8.383007 8.386692 8.391734 8.397864 8.404831 8.412413 #>  [16,] 8.362067 8.362795 8.365533 8.369980 8.375827 8.382776 8.390554 8.398918 #>  [17,] 8.342773 8.344136 8.347631 8.352917 8.359644 8.367482 8.376130 8.385329 #>  [18,] 8.322868 8.324941 8.329281 8.335494 8.343185 8.351986 8.361570 8.371658 #>  [19,] 8.302305 8.305180 8.310463 8.317702 8.326450 8.336296 8.346885 8.357919 #>  [20,] 8.281033 8.284815 8.291157 8.299534 8.309441 8.320422 8.332090 8.344130 #>  [21,] 8.258997 8.263810 8.271342 8.280986 8.292166 8.304378 8.317204 8.330311 #>  [22,] 8.236133 8.242124 8.251000 8.262055 8.274635 8.288184 8.302250 8.316488 #>  [23,] 8.212372 8.219716 8.230115 8.242745 8.256865 8.271862 8.287256 8.302687 #>  [24,] 8.187639 8.196545 8.208675 8.223065 8.238879 8.255444 8.272254 8.288944 #>  [25,] 8.161850 8.172569 8.186673 8.203035 8.220710 8.238969 8.257286 8.275296 #>  [26,] 8.134912 8.147749 8.164111 8.182681 8.202399 8.222485 8.242397 8.261785 #>  [27,] 8.106727 8.122052 8.141005 8.162048 8.184004 8.206048 8.227643 8.248462 #>  [28,] 8.077189 8.095455 8.117387 8.141196 8.165594 8.189729 8.213087 8.235381 #>  [29,] 8.046192 8.067952 8.093312 8.120210 8.147257 8.173610 8.198801 8.222604 #>  [30,] 8.013631 8.039567 8.068871 8.099199 8.129104 8.157788 8.184865 8.210195 #>  [31,] 7.979421 8.010368 8.044198 8.078312 8.111267 8.142373 8.171370 8.198226 #>  [32,] 7.943514 7.980486 8.019485 8.057733 8.093903 8.127492 8.158412 8.186772 #>  [33,] 7.905942 7.950155 7.994996 8.037694 8.077195 8.113282 8.146096 8.175912 #>  [34,] 7.866885 7.919746 7.971087 8.018474 8.061349 8.099894 8.134531 8.165725 #>  [35,] 7.826779 7.889817 7.948210 8.000399 8.046591 8.087483 8.123825 8.156288 #>  [36,] 7.786489 7.861167 7.926923 7.983834 8.033159 8.076207 8.114085 8.147676 #>  [37,] 7.747529 7.834857 7.907869 7.969164 8.021289 8.066219 8.105413 8.139958 #>  [38,] 7.712280 7.812183 7.891736 7.956769 8.011206 8.057654 8.097896 8.133193 #>  [39,] 7.683971 7.794544 7.879180 7.946991 8.003099 8.050627 8.091607 8.127429 #>  [40,] 7.666100 7.783187 7.870736 7.940089 7.997110 8.045222 8.086597 8.122700 #>  [41,] 7.661176 7.778892 7.866716 7.936212 7.993317 8.041483 8.082894 8.119023 #>  [42,] 7.669458 7.781737 7.867149 7.935374 7.991728 8.039415 8.080502 8.116400 #>  [43,] 7.688807 7.791067 7.871777 7.937452 7.992279 8.038980 8.079396 8.114817 #>  [44,] 7.715805 7.805702 7.880102 7.942206 7.994839 8.040103 8.079530 8.114243 #>  [45,] 7.747100 7.824252 7.891485 7.949309 7.999225 8.042675 8.080836 8.114632 #>  [46,] 7.780129 7.845386 7.905236 7.958384 8.005222 8.046563 8.083227 8.115928 #>  [47,] 7.813215 7.867988 7.920700 7.969044 8.012591 8.051616 8.086605 8.118063 #>  [48,] 7.845386 7.891210 7.937301 7.980920 8.021096 8.057679 8.090865 8.120964 #>  [49,] 7.876133 7.914450 7.954562 7.993677 8.030506 8.064595 8.095897 8.124553 #>  [50,] 7.905236 7.937301 7.972112 8.007025 8.040612 8.072211 8.101592 8.128752 #>  [51,] 7.932642 7.959508 7.989668 8.020725 8.051225 8.080387 8.107846 8.133481 #>  [52,] 7.958384 7.980920 8.007025 8.034581 8.062184 8.088994 8.114558 8.138666 #>  [53,] 7.982543 8.001460 8.024039 8.048440 8.073350 8.097919 8.121639 8.144233 #>  [54,] 8.005222 8.021096 8.040612 8.062184 8.084611 8.107063 8.129005 8.150115 #>  [55,] 8.026526 8.039829 8.056681 8.075723 8.095873 8.116340 8.136582 8.156252 #>  [56,] 8.046563 8.057679 8.072211 8.088994 8.107063 8.125677 8.144306 8.162587 #>  [57,] 8.065432 8.074679 8.087183 8.101950 8.118122 8.135016 8.152120 8.169069 #>  [58,] 8.083227 8.090865 8.101592 8.114558 8.129005 8.144306 8.159975 8.175654 #>  [59,] 8.100033 8.106280 8.115445 8.126801 8.139678 8.153507 8.167832 8.182303 #>  [60,] 8.115928 8.120964 8.128752 8.138666 8.150115 8.162587 8.175654 8.188982 #>  [61,] 8.130982 8.134960 8.141528 8.150148 8.160300 8.171520 8.183413 8.195661 #>  [62,] 8.145260 8.148307 8.153792 8.161250 8.170221 8.180286 8.191085 8.202315 #>  [63,] 8.158818 8.161044 8.165564 8.171974 8.179868 8.188872 8.198651 8.208923 #>  [64,] 8.171708 8.173206 8.176863 8.182327 8.189240 8.197264 8.206094 8.215467 #>  [65,] 8.183978 8.184828 8.187710 8.192318 8.198335 8.205457 8.213403 8.221931 #>  [66,] 8.195670 8.195940 8.198126 8.201958 8.207155 8.213444 8.220568 8.228302 #>  [67,] 8.206823 8.206573 8.208130 8.211256 8.215703 8.221222 8.227582 8.234572 #>  [68,] 8.217471 8.216754 8.217741 8.220225 8.223982 8.228791 8.234439 8.240731 #>  [69,] 8.227647 8.226508 8.226978 8.228875 8.232000 8.236151 8.241135 8.246772 #>  [70,] 8.237381 8.235858 8.235858 8.237218 8.239760 8.243303 8.247669 8.252692 #>  [71,] 8.246697 8.244827 8.244398 8.245266 8.247271 8.250249 8.254038 8.258486 #>  [72,] 8.255622 8.253434 8.252613 8.253029 8.254538 8.256992 8.260243 8.264150 #>  [73,] 8.264177 8.261700 8.260519 8.260519 8.261569 8.263537 8.266285 8.269684 #>  [74,] 8.272383 8.269641 8.268130 8.267745 8.268371 8.269886 8.272164 8.275087 #>  [75,] 8.280259 8.277273 8.275458 8.274719 8.274952 8.276044 8.277883 8.280357 #>  [76,] 8.287823 8.284613 8.282517 8.281450 8.281317 8.282016 8.283443 8.285495 #>  [77,] 8.295090 8.291674 8.289318 8.287947 8.287474 8.287805 8.288847 8.290502 #>  [78,] 8.302076 8.298469 8.295873 8.294219 8.293429 8.293418 8.294097 8.295379 #>  [79,] 8.308795 8.305011 8.302192 8.300276 8.299190 8.298857 8.299197 8.300126 #>  [80,] 8.315260 8.311312 8.308286 8.306124 8.304762 8.304129 8.304149 8.304746 #>  [81,] 8.321482 8.317381 8.314162 8.311773 8.310153 8.309237 8.308956 8.309241 #>  [82,] 8.327472 8.323230 8.319832 8.317229 8.315367 8.314186 8.313623 8.313611 #>  [83,] 8.333242 8.328868 8.325302 8.322500 8.320411 8.318981 8.318151 8.317860 #>  [84,] 8.338802 8.334304 8.330581 8.327592 8.325290 8.323626 8.322544 8.321989 #>  [85,] 8.344159 8.339546 8.335676 8.332512 8.330010 8.328125 8.326806 8.326000 #>  [86,] 8.349324 8.344603 8.340595 8.337266 8.334576 8.332483 8.330940 8.329897 #>  [87,] 8.354303 8.349481 8.345343 8.341859 8.338993 8.336704 8.334948 8.333680 #>  [88,] 8.359105 8.354187 8.349928 8.346299 8.343265 8.340791 8.338834 8.337353 #>  [89,] 8.363736 8.358729 8.354356 8.350589 8.347398 8.344748 8.342601 8.340918 #>  [90,] 8.368204 8.363113 8.358632 8.354735 8.351395 8.348579 8.346252 8.344377 #>  [91,] 8.372514 8.367344 8.362761 8.358743 8.355262 8.352289 8.349790 8.347733 #>  [92,] 8.376673 8.371428 8.366749 8.362615 8.359001 8.355879 8.353218 8.350987 #>  [93,] 8.380687 8.375371 8.370601 8.366358 8.362617 8.359354 8.356539 8.354143 #>  [94,] 8.384559 8.379177 8.374321 8.369974 8.366114 8.362717 8.359755 8.357201 #>  [95,] 8.388297 8.382851 8.377914 8.373469 8.369495 8.365970 8.362869 8.360166 #>  [96,] 8.391904 8.386399 8.381384 8.376846 8.372764 8.369118 8.365884 8.363037 #>  [97,] 8.395385 8.389823 8.384735 8.380108 8.375924 8.372163 8.368802 8.365819 #>  [98,] 8.398744 8.393128 8.387971 8.383260 8.378978 8.375107 8.371626 8.368512 #>  [99,] 8.401986 8.396319 8.391096 8.386305 8.381930 8.377954 8.374357 8.371119 #> [100,] 8.405114 8.399398 8.394112 8.389245 8.384782 8.380706 8.376999 8.373642 #>           [,81]    [,82]    [,83]    [,84]    [,85]    [,86]    [,87]    [,88] #>   [1,] 8.589534 8.591000 8.592830 8.594959 8.597332 8.599894 8.602598 8.605403 #>   [2,] 8.578132 8.579936 8.582102 8.584563 8.587260 8.590136 8.593144 8.596240 #>   [3,] 8.566622 8.568782 8.571301 8.574109 8.577143 8.580346 8.583667 8.587064 #>   [4,] 8.555003 8.557538 8.560428 8.563598 8.566984 8.570526 8.574173 8.577879 #>   [5,] 8.543276 8.546206 8.549484 8.553034 8.556786 8.560680 8.564663 8.568689 #>   [6,] 8.531441 8.534787 8.538473 8.542419 8.546553 8.550813 8.555143 8.559498 #>   [7,] 8.519499 8.523283 8.527398 8.531758 8.536289 8.540927 8.545617 8.550311 #>   [8,] 8.507450 8.511697 8.516261 8.521054 8.525999 8.531029 8.536090 8.541133 #>   [9,] 8.495298 8.500032 8.505067 8.510312 8.515687 8.521124 8.526567 8.531969 #>  [10,] 8.483044 8.488292 8.493822 8.499538 8.505360 8.511218 8.517055 8.522825 #>  [11,] 8.470692 8.476482 8.482530 8.488739 8.495024 8.501316 8.507559 8.513707 #>  [12,] 8.458247 8.464607 8.471199 8.477920 8.484687 8.491428 8.498088 8.504623 #>  [13,] 8.445715 8.452674 8.459835 8.467091 8.474356 8.481560 8.488649 8.495578 #>  [14,] 8.433100 8.440693 8.448448 8.456260 8.464041 8.471722 8.479249 8.486582 #>  [15,] 8.420413 8.428670 8.437048 8.445437 8.453751 8.461922 8.469899 8.477643 #>  [16,] 8.407663 8.416619 8.425645 8.434633 8.443497 8.452171 8.460607 8.468769 #>  [17,] 8.394861 8.404550 8.414253 8.423861 8.433291 8.442480 8.451383 8.459969 #>  [18,] 8.382021 8.392478 8.402885 8.413134 8.423146 8.432861 8.442239 8.451255 #>  [19,] 8.369159 8.380420 8.391557 8.402468 8.413075 8.423326 8.433186 8.442635 #>  [20,] 8.356293 8.368393 8.380287 8.391877 8.403093 8.413889 8.424236 8.434121 #>  [21,] 8.343445 8.356418 8.369094 8.381381 8.393217 8.404565 8.415403 8.425724 #>  [22,] 8.330638 8.344518 8.357999 8.370999 8.383464 8.395368 8.406698 8.417456 #>  [23,] 8.317901 8.332719 8.347026 8.360750 8.373852 8.386315 8.398138 8.409330 #>  [24,] 8.305264 8.321049 8.336199 8.350657 8.364400 8.377422 8.389735 8.401357 #>  [25,] 8.292762 8.309539 8.325545 8.340744 8.355128 8.368707 8.381504 8.393550 #>  [26,] 8.280434 8.298222 8.315095 8.331036 8.346057 8.360187 8.373462 8.385923 #>  [27,] 8.268322 8.287136 8.304877 8.321558 8.337210 8.351881 8.365623 8.378489 #>  [28,] 8.256474 8.276319 8.294926 8.312336 8.328609 8.343808 8.358003 8.371260 #>  [29,] 8.244939 8.265812 8.285274 8.303400 8.320275 8.335986 8.350617 8.364249 #>  [30,] 8.233771 8.255658 8.275956 8.294777 8.312233 8.328434 8.343481 8.357469 #>  [31,] 8.223025 8.245902 8.267008 8.286494 8.304504 8.321169 8.336610 8.350933 #>  [32,] 8.212761 8.236589 8.258464 8.278580 8.297111 8.314211 8.330018 8.344652 #>  [33,] 8.203036 8.227763 8.250360 8.271062 8.290075 8.307576 8.323719 8.338638 #>  [34,] 8.193910 8.219469 8.242729 8.263966 8.283416 8.301279 8.317725 8.332900 #>  [35,] 8.185440 8.211749 8.235602 8.257315 8.277154 8.295336 8.312049 8.327448 #>  [36,] 8.177678 8.204642 8.229008 8.251132 8.271304 8.289760 8.306700 8.322290 #>  [37,] 8.170672 8.198181 8.222973 8.245437 8.265882 8.284563 8.301689 8.317435 #>  [38,] 8.164464 8.192397 8.217519 8.240244 8.260900 8.279753 8.297022 8.312887 #>  [39,] 8.159087 8.187313 8.212662 8.235566 8.256367 8.275338 8.292704 8.308651 #>  [40,] 8.154563 8.182944 8.208414 8.231413 8.252290 8.271324 8.288741 8.304731 #>  [41,] 8.150905 8.179300 8.204781 8.227789 8.248673 8.267712 8.285135 8.301128 #>  [42,] 8.148114 8.176382 8.201764 8.224694 8.245515 8.264504 8.281884 8.297843 #>  [43,] 8.146180 8.174182 8.199358 8.222125 8.242815 8.261696 8.278988 8.294873 #>  [44,] 8.145081 8.172685 8.197551 8.220073 8.240565 8.259285 8.276443 8.292216 #>  [45,] 8.144788 8.171870 8.196329 8.218527 8.238758 8.257263 8.274244 8.289868 #>  [46,] 8.145260 8.171708 8.195670 8.217471 8.237381 8.255622 8.272383 8.287823 #>  [47,] 8.146450 8.172166 8.195550 8.216887 8.236419 8.254350 8.270852 8.286074 #>  [48,] 8.148307 8.173206 8.195940 8.216754 8.235858 8.253434 8.269641 8.284613 #>  [49,] 8.150774 8.174786 8.196810 8.217047 8.235677 8.252861 8.268737 8.283431 #>  [50,] 8.153792 8.176863 8.198126 8.217741 8.235858 8.252613 8.268130 8.282517 #>  [51,] 8.157304 8.179392 8.199854 8.218810 8.236379 8.252675 8.267804 8.281860 #>  [52,] 8.161250 8.182327 8.201958 8.220225 8.237218 8.253029 8.267745 8.281450 #>  [53,] 8.165573 8.185624 8.204403 8.221959 8.238353 8.253656 8.267940 8.281273 #>  [54,] 8.170221 8.189240 8.207155 8.223982 8.239760 8.254538 8.268371 8.281317 #>  [55,] 8.175141 8.193133 8.210180 8.226269 8.241418 8.255656 8.269025 8.281569 #>  [56,] 8.180286 8.197264 8.213444 8.228791 8.243303 8.256992 8.269886 8.282016 #>  [57,] 8.185614 8.201596 8.216916 8.231523 8.245393 8.258527 8.270937 8.282645 #>  [58,] 8.191085 8.206094 8.220568 8.234439 8.247669 8.260243 8.272164 8.283443 #>  [59,] 8.196662 8.210727 8.224372 8.237516 8.250108 8.262123 8.273552 8.284397 #>  [60,] 8.202315 8.215467 8.228302 8.240731 8.252692 8.264150 8.275087 8.285495 #>  [61,] 8.208015 8.220286 8.232335 8.244063 8.255402 8.266308 8.276753 8.286725 #>  [62,] 8.213736 8.225162 8.236449 8.247494 8.258221 8.268581 8.278538 8.288074 #>  [63,] 8.219458 8.230073 8.240624 8.251004 8.261133 8.270955 8.280429 8.289531 #>  [64,] 8.225162 8.235001 8.244843 8.254577 8.264122 8.273416 8.282413 8.291085 #>  [65,] 8.230830 8.239929 8.249089 8.258199 8.267175 8.275951 8.284479 8.292726 #>  [66,] 8.236449 8.244843 8.253348 8.261855 8.270277 8.278548 8.286616 8.294443 #>  [67,] 8.242007 8.249729 8.257607 8.265532 8.273418 8.281197 8.288813 8.296228 #>  [68,] 8.247494 8.254577 8.261855 8.269220 8.276587 8.283886 8.291061 8.298071 #>  [69,] 8.252901 8.259378 8.266081 8.272908 8.279773 8.286606 8.293351 8.299964 #>  [70,] 8.258221 8.264122 8.270277 8.276587 8.282967 8.289348 8.295674 8.301898 #>  [71,] 8.263450 8.268803 8.274435 8.280249 8.286161 8.292105 8.298022 8.303867 #>  [72,] 8.268581 8.273416 8.278548 8.283886 8.289348 8.294868 8.300389 8.305864 #>  [73,] 8.273611 8.277954 8.282610 8.287492 8.292521 8.297632 8.302768 8.307882 #>  [74,] 8.278538 8.282413 8.286616 8.291061 8.295674 8.300389 8.305152 8.309916 #>  [75,] 8.283360 8.286791 8.290562 8.294589 8.298801 8.303135 8.307536 8.311959 #>  [76,] 8.288074 8.291085 8.294443 8.298071 8.301898 8.305864 8.309916 8.314007 #>  [77,] 8.292680 8.295292 8.298258 8.301503 8.304961 8.308572 8.312285 8.316055 #>  [78,] 8.297178 8.299411 8.302003 8.304882 8.307985 8.311255 8.314641 8.318098 #>  [79,] 8.301567 8.303441 8.305676 8.308206 8.310968 8.313909 8.316978 8.320134 #>  [80,] 8.305848 8.307380 8.309276 8.311471 8.313907 8.316531 8.319295 8.322157 #>  [81,] 8.310021 8.311229 8.312801 8.314676 8.316798 8.319117 8.321587 8.324166 #>  [82,] 8.314087 8.314987 8.316250 8.317819 8.319641 8.321667 8.323852 8.326156 #>  [83,] 8.318047 8.318654 8.319623 8.320900 8.322433 8.324177 8.326087 8.328126 #>  [84,] 8.321903 8.322231 8.322919 8.323916 8.325173 8.326645 8.328290 8.330072 #>  [85,] 8.325655 8.325718 8.326138 8.326867 8.327859 8.329069 8.330459 8.331993 #>  [86,] 8.329305 8.329116 8.329280 8.329753 8.330490 8.331449 8.332593 8.333886 #>  [87,] 8.332855 8.332425 8.332345 8.332573 8.333065 8.333783 8.334689 8.335751 #>  [88,] 8.336305 8.335646 8.335334 8.335327 8.335584 8.336069 8.336747 8.337584 #>  [89,] 8.339659 8.338781 8.338246 8.338014 8.338047 8.338308 8.338765 8.339385 #>  [90,] 8.342916 8.341831 8.341083 8.340635 8.340452 8.340498 8.340742 8.341152 #>  [91,] 8.346080 8.344796 8.343845 8.343191 8.342800 8.342639 8.342677 8.342885 #>  [92,] 8.349152 8.347678 8.346532 8.345680 8.345090 8.344730 8.344570 8.344583 #>  [93,] 8.352133 8.350478 8.349146 8.348104 8.347323 8.346771 8.346420 8.346244 #>  [94,] 8.355026 8.353197 8.351687 8.350463 8.349498 8.348761 8.348227 8.347867 #>  [95,] 8.357831 8.355838 8.354156 8.352758 8.351616 8.350702 8.349989 8.349454 #>  [96,] 8.360551 8.358400 8.356555 8.354989 8.353677 8.352591 8.351708 8.351001 #>  [97,] 8.363188 8.360885 8.358883 8.357157 8.355681 8.354431 8.353382 8.352511 #>  [98,] 8.365743 8.363295 8.361143 8.359262 8.357629 8.356220 8.355011 8.353981 #>  [99,] 8.368218 8.365631 8.363335 8.361306 8.359521 8.357959 8.356596 8.355412 #> [100,] 8.370615 8.367894 8.365459 8.363288 8.361358 8.359648 8.358136 8.356803 #>           [,89]    [,90]    [,91]    [,92]    [,93]    [,94]    [,95]    [,96] #>   [1,] 8.608271 8.611170 8.614073 8.616953 8.619793 8.622572 8.625278 8.627897 #>   [2,] 8.599386 8.602550 8.605704 8.608823 8.611888 8.614881 8.617787 8.620596 #>   [3,] 8.590496 8.593933 8.597344 8.600707 8.604001 8.607210 8.610321 8.613322 #>   [4,] 8.581606 8.585321 8.588996 8.592608 8.596136 8.599565 8.602882 8.606077 #>   [5,] 8.572719 8.576720 8.580664 8.584529 8.588295 8.591948 8.595474 8.598865 #>   [6,] 8.563839 8.568133 8.572353 8.576475 8.580483 8.584362 8.588100 8.591689 #>   [7,] 8.554972 8.559565 8.564065 8.568451 8.572704 8.576812 8.580764 8.584552 #>   [8,] 8.546121 8.551020 8.555807 8.560459 8.564961 8.569300 8.573468 8.577457 #>   [9,] 8.537292 8.542504 8.547582 8.552505 8.557258 8.561832 8.566217 8.570408 #>  [10,] 8.528491 8.534022 8.539395 8.544593 8.549601 8.554411 8.559014 8.563408 #>  [11,] 8.519723 8.525579 8.531253 8.536729 8.541994 8.547041 8.551864 8.556462 #>  [12,] 8.510996 8.517182 8.523161 8.528917 8.534441 8.539727 8.544771 8.549572 #>  [13,] 8.502316 8.508837 8.515124 8.521163 8.526948 8.532474 8.537738 8.542743 #>  [14,] 8.493690 8.500551 8.507149 8.513474 8.519520 8.525286 8.530771 8.535978 #>  [15,] 8.485127 8.492331 8.499242 8.505854 8.512162 8.518168 8.523873 8.529282 #>  [16,] 8.476633 8.484183 8.491410 8.498309 8.504880 8.511125 8.517049 8.522659 #>  [17,] 8.468218 8.476117 8.483661 8.490847 8.497680 8.504163 8.510304 8.516112 #>  [18,] 8.459891 8.468140 8.476000 8.483474 8.490567 8.497286 8.503643 8.509647 #>  [19,] 8.451661 8.460261 8.468437 8.476196 8.483547 8.490500 8.497069 8.503267 #>  [20,] 8.443537 8.452487 8.460978 8.469020 8.476626 8.483811 8.490589 8.496976 #>  [21,] 8.435530 8.444828 8.453631 8.461953 8.469811 8.477223 8.484206 8.490779 #>  [22,] 8.427650 8.437293 8.446404 8.455002 8.463107 8.470742 8.477926 8.484681 #>  [23,] 8.419907 8.429892 8.439305 8.448174 8.456521 8.464373 8.471753 8.478684 #>  [24,] 8.412313 8.422632 8.432343 8.441476 8.450060 8.458122 8.465692 8.472795 #>  [25,] 8.404879 8.415525 8.425526 8.434915 8.443728 8.451995 8.459748 8.467016 #>  [26,] 8.397615 8.408580 8.418861 8.428499 8.437532 8.445996 8.453926 8.461351 #>  [27,] 8.390532 8.401805 8.412357 8.422234 8.431479 8.440131 8.448229 8.455805 #>  [28,] 8.383642 8.395211 8.406022 8.416127 8.425573 8.434405 8.442662 8.450381 #>  [29,] 8.376956 8.388806 8.399863 8.410184 8.419821 8.428822 8.437230 8.445084 #>  [30,] 8.370483 8.382599 8.393888 8.404412 8.414228 8.423388 8.431936 8.439915 #>  [31,] 8.364234 8.376599 8.388104 8.398817 8.408800 8.418106 8.426784 8.434880 #>  [32,] 8.358220 8.370814 8.382518 8.393405 8.403540 8.412980 8.421778 8.429980 #>  [33,] 8.352448 8.365251 8.377136 8.388181 8.398453 8.408015 8.416921 8.425218 #>  [34,] 8.346928 8.359918 8.371964 8.383149 8.393544 8.403214 8.412215 8.420598 #>  [35,] 8.341666 8.354820 8.367007 8.378314 8.388817 8.398581 8.407665 8.416121 #>  [36,] 8.336671 8.349963 8.362270 8.373680 8.384273 8.394117 8.403271 8.411789 #>  [37,] 8.331948 8.345352 8.357756 8.369251 8.379917 8.389825 8.399036 8.407604 #>  [38,] 8.327501 8.340992 8.353469 8.365028 8.375750 8.385707 8.394961 8.403568 #>  [39,] 8.323334 8.336884 8.349412 8.361014 8.371774 8.381765 8.391048 8.399681 #>  [40,] 8.319450 8.333031 8.345585 8.357211 8.367991 8.377999 8.387298 8.395944 #>  [41,] 8.315851 8.329434 8.341991 8.353619 8.364400 8.374410 8.383710 8.392358 #>  [42,] 8.312535 8.326093 8.338628 8.350237 8.361003 8.370998 8.380285 8.388922 #>  [43,] 8.309503 8.323008 8.335497 8.347067 8.357798 8.367762 8.377023 8.385637 #>  [44,] 8.306752 8.320176 8.332596 8.344105 8.354784 8.364703 8.373923 8.382501 #>  [45,] 8.304278 8.317594 8.329922 8.341351 8.351960 8.361817 8.370984 8.379513 #>  [46,] 8.302076 8.315260 8.327472 8.338802 8.349324 8.359105 8.368204 8.376673 #>  [47,] 8.300142 8.313167 8.325243 8.336454 8.346872 8.356562 8.365581 8.373979 #>  [48,] 8.298469 8.311312 8.323230 8.334304 8.344603 8.354187 8.363113 8.371428 #>  [49,] 8.297049 8.309687 8.321428 8.332348 8.342512 8.351977 8.360798 8.369019 #>  [50,] 8.295873 8.308286 8.319832 8.330581 8.340595 8.349928 8.358632 8.366749 #>  [51,] 8.294933 8.307101 8.318434 8.328997 8.338847 8.348037 8.356612 8.364616 #>  [52,] 8.294219 8.306124 8.317229 8.327592 8.337266 8.346299 8.354735 8.362615 #>  [53,] 8.293721 8.305348 8.316209 8.326358 8.335844 8.344710 8.352998 8.360745 #>  [54,] 8.293429 8.304762 8.315367 8.325290 8.334576 8.343265 8.351395 8.359001 #>  [55,] 8.293332 8.304359 8.314695 8.324382 8.333458 8.341961 8.349924 8.357380 #>  [56,] 8.293418 8.304129 8.314186 8.323626 8.332483 8.340791 8.348579 8.355879 #>  [57,] 8.293676 8.304062 8.313831 8.323016 8.331646 8.339750 8.347357 8.354493 #>  [58,] 8.294097 8.304149 8.313623 8.322544 8.330940 8.338834 8.346252 8.353218 #>  [59,] 8.294668 8.304380 8.313552 8.322204 8.330359 8.338037 8.345261 8.352051 #>  [60,] 8.295379 8.304746 8.313611 8.321989 8.329897 8.337353 8.344377 8.350987 #>  [61,] 8.296219 8.305239 8.313792 8.321891 8.329548 8.336778 8.343597 8.350022 #>  [62,] 8.297178 8.305848 8.314087 8.321903 8.329305 8.336305 8.342916 8.349152 #>  [63,] 8.298245 8.306564 8.314488 8.322019 8.329163 8.335930 8.342329 8.348372 #>  [64,] 8.299411 8.307380 8.314987 8.322231 8.329116 8.335646 8.341831 8.347678 #>  [65,] 8.300667 8.308287 8.315577 8.322533 8.329157 8.335450 8.341417 8.347066 #>  [66,] 8.302003 8.309276 8.316250 8.322919 8.329280 8.335334 8.341083 8.346532 #>  [67,] 8.303411 8.310340 8.317000 8.323382 8.329481 8.335295 8.340824 8.346071 #>  [68,] 8.304882 8.311471 8.317819 8.323916 8.329753 8.335327 8.340635 8.345680 #>  [69,] 8.306409 8.312662 8.318702 8.324515 8.330091 8.335425 8.340513 8.345354 #>  [70,] 8.307985 8.313907 8.319641 8.325173 8.330490 8.335584 8.340452 8.345090 #>  [71,] 8.309603 8.315198 8.320631 8.325884 8.330944 8.335801 8.340448 8.344883 #>  [72,] 8.311255 8.316531 8.321667 8.326645 8.331449 8.336069 8.340498 8.344730 #>  [73,] 8.312936 8.317898 8.322742 8.327448 8.332000 8.336386 8.340597 8.344627 #>  [74,] 8.314641 8.319295 8.323852 8.328290 8.332593 8.336747 8.340742 8.344570 #>  [75,] 8.316363 8.320716 8.324991 8.329166 8.333223 8.337147 8.340928 8.344557 #>  [76,] 8.318098 8.322157 8.326156 8.330072 8.333886 8.337584 8.341152 8.344583 #>  [77,] 8.319842 8.323613 8.327342 8.331003 8.334579 8.338053 8.341411 8.344645 #>  [78,] 8.321589 8.325080 8.328544 8.331956 8.335297 8.338550 8.341702 8.344741 #>  [79,] 8.323337 8.326555 8.329759 8.332927 8.336037 8.339073 8.342020 8.344867 #>  [80,] 8.325080 8.328032 8.330984 8.333912 8.336796 8.339618 8.342364 8.345021 #>  [81,] 8.326817 8.329510 8.332215 8.334909 8.337570 8.340182 8.342729 8.345199 #>  [82,] 8.328544 8.330984 8.333449 8.335913 8.338357 8.340763 8.343115 8.345399 #>  [83,] 8.330258 8.332453 8.334682 8.336923 8.339154 8.341357 8.343516 8.345619 #>  [84,] 8.331956 8.333912 8.335913 8.337935 8.339958 8.341962 8.343933 8.345856 #>  [85,] 8.333637 8.335361 8.337139 8.338948 8.340766 8.342575 8.344360 8.346107 #>  [86,] 8.335297 8.336796 8.338357 8.339958 8.341576 8.343195 8.344798 8.346371 #>  [87,] 8.336935 8.338216 8.339566 8.340963 8.342387 8.343819 8.345243 8.346646 #>  [88,] 8.338550 8.339618 8.340763 8.341962 8.343195 8.344444 8.345694 8.346929 #>  [89,] 8.340139 8.341001 8.341946 8.342952 8.343999 8.345070 8.346147 8.347219 #>  [90,] 8.341702 8.342364 8.343115 8.343933 8.344798 8.345694 8.346603 8.347513 #>  [91,] 8.343236 8.343704 8.344266 8.344901 8.345589 8.346314 8.347059 8.347810 #>  [92,] 8.344741 8.345021 8.345399 8.345856 8.346371 8.346929 8.347513 8.348109 #>  [93,] 8.346216 8.346313 8.346513 8.346796 8.347143 8.347538 8.347964 8.348408 #>  [94,] 8.347660 8.347580 8.347607 8.347721 8.347903 8.348138 8.348410 8.348706 #>  [95,] 8.349071 8.348820 8.348678 8.348628 8.348650 8.348730 8.348851 8.349001 #>  [96,] 8.350450 8.350032 8.349727 8.349517 8.349383 8.349311 8.349285 8.349292 #>  [97,] 8.351796 8.351216 8.350752 8.350386 8.350101 8.349880 8.349710 8.349577 #>  [98,] 8.353107 8.352371 8.351753 8.351236 8.350802 8.350437 8.350126 8.349857 #>  [99,] 8.354385 8.353497 8.352729 8.352064 8.351486 8.350980 8.350532 8.350129 #> [100,] 8.355628 8.354593 8.353679 8.352871 8.352153 8.351509 8.350926 8.350392 #>           [,97]    [,98]    [,99]   [,100] #>   [1,] 8.630421 8.632839 8.635147 8.637339 #>   [2,] 8.623298 8.625885 8.628351 8.630691 #>   [3,] 8.616204 8.618960 8.621586 8.624076 #>   [4,] 8.609141 8.612069 8.614854 8.617495 #>   [5,] 8.602113 8.605212 8.608159 8.610951 #>   [6,] 8.595122 8.598394 8.601503 8.604446 #>   [7,] 8.588171 8.591617 8.594888 8.597983 #>   [8,] 8.581263 8.584884 8.588317 8.591564 #>   [9,] 8.574402 8.578197 8.581793 8.585191 #>  [10,] 8.567590 8.571560 8.575319 8.578867 #>  [11,] 8.560832 8.564976 8.568896 8.572595 #>  [12,] 8.554130 8.558448 8.562530 8.566378 #>  [13,] 8.547489 8.551980 8.556221 8.560217 #>  [14,] 8.540911 8.545574 8.549974 8.554117 #>  [15,] 8.534400 8.539234 8.543791 8.548079 #>  [16,] 8.527960 8.532963 8.537675 8.542106 #>  [17,] 8.521595 8.526765 8.531630 8.536201 #>  [18,] 8.515309 8.520642 8.525658 8.530367 #>  [19,] 8.509105 8.514600 8.519762 8.524607 #>  [20,] 8.502988 8.508640 8.513946 8.518923 #>  [21,] 8.496960 8.502766 8.508213 8.513318 #>  [22,] 8.491026 8.496982 8.502565 8.507795 #>  [23,] 8.485190 8.491290 8.497006 8.502356 #>  [24,] 8.479455 8.485695 8.491538 8.497004 #>  [25,] 8.473824 8.480199 8.486165 8.491742 #>  [26,] 8.468302 8.474806 8.480888 8.486571 #>  [27,] 8.462892 8.469518 8.475711 8.481495 #>  [28,] 8.457597 8.464339 8.470636 8.476515 #>  [29,] 8.452420 8.459270 8.465666 8.471633 #>  [30,] 8.447364 8.454316 8.460803 8.466853 #>  [31,] 8.442432 8.449477 8.456048 8.462175 #>  [32,] 8.437627 8.444757 8.451405 8.457601 #>  [33,] 8.432951 8.440158 8.446875 8.453133 #>  [34,] 8.428406 8.435681 8.442459 8.448772 #>  [35,] 8.423995 8.431329 8.438160 8.444520 #>  [36,] 8.419719 8.427102 8.433977 8.440378 #>  [37,] 8.415579 8.423002 8.429913 8.436347 #>  [38,] 8.411576 8.419030 8.425969 8.432427 #>  [39,] 8.407713 8.415187 8.422144 8.428619 #>  [40,] 8.403988 8.411474 8.418440 8.424924 #>  [41,] 8.400403 8.407889 8.414857 8.421342 #>  [42,] 8.396957 8.404435 8.411395 8.417872 #>  [43,] 8.393651 8.401110 8.408052 8.414515 #>  [44,] 8.390483 8.397913 8.404831 8.411270 #>  [45,] 8.387453 8.394845 8.401728 8.408136 #>  [46,] 8.384559 8.391904 8.398744 8.405114 #>  [47,] 8.381801 8.389089 8.395878 8.402201 #>  [48,] 8.379177 8.386399 8.393128 8.399398 #>  [49,] 8.376684 8.383831 8.390493 8.396702 #>  [50,] 8.374321 8.381384 8.387971 8.394112 #>  [51,] 8.372086 8.379057 8.385561 8.391627 #>  [52,] 8.369974 8.376846 8.383260 8.389245 #>  [53,] 8.367985 8.374749 8.381067 8.386964 #>  [54,] 8.366114 8.372764 8.378978 8.384782 #>  [55,] 8.364359 8.370888 8.376993 8.382696 #>  [56,] 8.362717 8.369118 8.375107 8.380706 #>  [57,] 8.361183 8.367451 8.373319 8.378808 #>  [58,] 8.359755 8.365884 8.371626 8.376999 #>  [59,] 8.358429 8.364414 8.370024 8.375278 #>  [60,] 8.357201 8.363037 8.368512 8.373642 #>  [61,] 8.356068 8.361751 8.367086 8.372089 #>  [62,] 8.355026 8.360551 8.365743 8.370615 #>  [63,] 8.354070 8.359435 8.364481 8.369217 #>  [64,] 8.353197 8.358400 8.363295 8.367894 #>  [65,] 8.352404 8.357440 8.362183 8.366642 #>  [66,] 8.351687 8.356555 8.361143 8.365459 #>  [67,] 8.351041 8.355739 8.360170 8.364342 #>  [68,] 8.350463 8.354989 8.359262 8.363288 #>  [69,] 8.349950 8.354303 8.358416 8.362294 #>  [70,] 8.349498 8.353677 8.357629 8.361358 #>  [71,] 8.349103 8.353107 8.356898 8.360477 #>  [72,] 8.348761 8.352591 8.356220 8.359648 #>  [73,] 8.348470 8.352126 8.355592 8.358869 #>  [74,] 8.348227 8.351708 8.355011 8.358136 #>  [75,] 8.348027 8.351334 8.354475 8.357449 #>  [76,] 8.347867 8.351001 8.353981 8.356803 #>  [77,] 8.347746 8.350708 8.353526 8.356197 #>  [78,] 8.347660 8.350450 8.353107 8.355628 #>  [79,] 8.347605 8.350226 8.352723 8.355094 #>  [80,] 8.347580 8.350032 8.352371 8.354593 #>  [81,] 8.347581 8.349867 8.352049 8.354122 #>  [82,] 8.347607 8.349727 8.351753 8.353679 #>  [83,] 8.347654 8.349611 8.351483 8.353263 #>  [84,] 8.347721 8.349517 8.351236 8.352871 #>  [85,] 8.347804 8.349441 8.351009 8.352502 #>  [86,] 8.347903 8.349383 8.350802 8.352153 #>  [87,] 8.348015 8.349340 8.350612 8.351822 #>  [88,] 8.348138 8.349311 8.350437 8.351509 #>  [89,] 8.348271 8.349293 8.350275 8.351211 #>  [90,] 8.348410 8.349285 8.350126 8.350926 #>  [91,] 8.348556 8.349285 8.349987 8.350654 #>  [92,] 8.348706 8.349292 8.349857 8.350392 #>  [93,] 8.348859 8.349304 8.349734 8.350140 #>  [94,] 8.349013 8.349320 8.349617 8.349895 #>  [95,] 8.349167 8.349338 8.349505 8.349657 #>  [96,] 8.349320 8.349358 8.349396 8.349425 #>  [97,] 8.349470 8.349377 8.349289 8.349197 #>  [98,] 8.349617 8.349396 8.349184 8.348972 #>  [99,] 8.349759 8.349412 8.349078 8.348748 #> [100,] 8.349895 8.349425 8.348972 8.348526  # Converting negative potentials results in NA's with warning try( potential_to_head(m, -300) ) #> Warning: NaNs produced #> [1] NaN  # unless na.below = FALSE potential_to_head(m, -300, na.below = FALSE) #> [1] -7.745967"},{"path":"https://cneyens.github.io/raem/reference/headareasink.html","id":null,"dir":"Reference","previous_headings":"","what":"Create a head-specified area-sink analytic element — headareasink","title":"Create a head-specified area-sink analytic element — headareasink","text":"headareasink() creates area-sink analytic element constant specified head. constant leakage flux aquifer area-sink computed solving corresponding aem model.","code":""},{"path":"https://cneyens.github.io/raem/reference/headareasink.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create a head-specified area-sink analytic element — headareasink","text":"","code":"headareasink(xc, yc, hc, R, resistance = 0, location = c(\"top\", \"base\"), ...)"},{"path":"https://cneyens.github.io/raem/reference/headareasink.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create a head-specified area-sink analytic element — headareasink","text":"xc numeric, x location center area-sink yc numeric, y location center area-sink hc numeric, specified hydraulic head center area-sink R numeric, radius circular area-sink resistance numeric, hydraulic resistance area-sink connection aquifer. Defaults 0 (resistance). location character, either top (default) base specifying vertical position area-sink. ... ignored","code":""},{"path":"https://cneyens.github.io/raem/reference/headareasink.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create a head-specified area-sink analytic element — headareasink","text":"Circular head-specified area-sink analytic element object class headareasink inherits areasink.","code":""},{"path":"https://cneyens.github.io/raem/reference/headareasink.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Create a head-specified area-sink analytic element — headareasink","text":"constant leakage flux area-sink computed solving aem model given specified head hc area-sink. head located -called collocation point, placed center area-sink. positive flux aquifer. Note head-dependent flux constant domain computed collocation point. flux therefore determined difference aquifer head specified head location , vary across domain varying aquifer head. resistance can increased area-sink poor connection aquifer, e.g. confining unit low hydraulic conductivity aquifer area-sink. aquifer unconfined (.e. variable saturated thickness), system equations becomes non-linear respect hydraulic head iteration required solve model.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/headareasink.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create a head-specified area-sink analytic element — headareasink","text":"","code":"# using headareasink, the head difference depends on the computed instead of given aquifer head headareasink(xc = -500, yc = 0, hc = 3, R = 500, res = 1000) #> $parameter #> [1] 0 #>  #> $nunknowns #> [1] 1 #>  #> $xc #> [1] -500 #>  #> $yc #> [1] 0 #>  #> $R #> [1] 500 #>  #> $location #> [1] \"top\" #>  #> $hc #> [1] 3 #>  #> $resistance #> [1] 1000 #>  #> attr(,\"class\") #> [1] \"headareasink\" \"areasink\"     \"element\"      headareasink(xc = -500, yc = 0, hc = 3, R = 500, location = 'base') #> $parameter #> [1] 0 #>  #> $nunknowns #> [1] 1 #>  #> $xc #> [1] -500 #>  #> $yc #> [1] 0 #>  #> $R #> [1] 500 #>  #> $location #> [1] \"base\" #>  #> $hc #> [1] 3 #>  #> $resistance #> [1] 0 #>  #> attr(,\"class\") #> [1] \"headareasink\" \"areasink\"     \"element\""},{"path":"https://cneyens.github.io/raem/reference/headlinesink.html","id":null,"dir":"Reference","previous_headings":"","what":"Create a head-specified line-sink analytic element — headlinesink","title":"Create a head-specified line-sink analytic element — headlinesink","text":"headlinesink() creates line-sink analytic element constant specified head. discharge line-sink per unit length computed solving corresponding aem model.","code":""},{"path":"https://cneyens.github.io/raem/reference/headlinesink.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create a head-specified line-sink analytic element — headlinesink","text":"","code":"headlinesink(x0, y0, x1, y1, hc, resistance = 0, width = 0, ...)"},{"path":"https://cneyens.github.io/raem/reference/headlinesink.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create a head-specified line-sink analytic element — headlinesink","text":"x0 numeric, starting x location line-sink y0 numeric, starting y location line-sink x1 numeric, ending x location line-sink y1 numeric, ending y location line-sink hc numeric, specified hydraulic head line-sink resistance numeric, hydraulic resistance line-sink connection aquifer. Defaults 0 (resistance). width numeric, width line-sink. Used resistance calculate line-sink strength, tracelines() determine particle reached line. Defaults zero (infinitesimally narrow line). ... ignored","code":""},{"path":"https://cneyens.github.io/raem/reference/headlinesink.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create a head-specified line-sink analytic element — headlinesink","text":"Head-specified line-sink analytic element object class headlinesink inherits linesink.","code":""},{"path":"https://cneyens.github.io/raem/reference/headlinesink.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Create a head-specified line-sink analytic element — headlinesink","text":"strength line-sink (discharge per unit length line-sink) computed solving aem model given specified head hc line-sink. head located -called collocation point, placed center line-sink. resistance can increased line-sink poor connection aquifer. effect larger smaller wetted perimeter can mimicked adjusting resistance /width accordingly. width = 0 (default) removed conductance calculation. aquifer unconfined (.e. variable saturated thickness), system equations becomes non-linear respect hydraulic head iteration required solve model.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/headlinesink.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create a head-specified line-sink analytic element — headlinesink","text":"","code":"headlinesink(-75, 50, 100, 50, hc = 10) #> $parameter #> [1] 0 #>  #> $nunknowns #> [1] 1 #>  #> $z0 #> [1] -75+50i #>  #> $z1 #> [1] 100+50i #>  #> $L #> [1] 175 #>  #> $width #> [1] 0 #>  #> $xc #> [1] 12.5 #>  #> $yc #> [1] 50 #>  #> $hc #> [1] 10 #>  #> $resistance #> [1] 0 #>  #> attr(,\"class\") #> [1] \"headlinesink\" \"linesink\"     \"element\"      headlinesink(-75, 50, 100, 50, hc = 10, res = 10, width = 4) #> $parameter #> [1] 0 #>  #> $nunknowns #> [1] 1 #>  #> $z0 #> [1] -75+50i #>  #> $z1 #> [1] 100+50i #>  #> $L #> [1] 175 #>  #> $width #> [1] 4 #>  #> $xc #> [1] 12.5 #>  #> $yc #> [1] 50 #>  #> $hc #> [1] 10 #>  #> $resistance #> [1] 10 #>  #> attr(,\"class\") #> [1] \"headlinesink\" \"linesink\"     \"element\""},{"path":"https://cneyens.github.io/raem/reference/headwell.html","id":null,"dir":"Reference","previous_headings":"","what":"Create a analytic element of a well with a constant head — headwell","title":"Create a analytic element of a well with a constant head — headwell","text":"headwell() creates analytic element well constant, specified head. discharge well computed solving corresponding aem model. head can specified well location.","code":""},{"path":"https://cneyens.github.io/raem/reference/headwell.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create a analytic element of a well with a constant head — headwell","text":"","code":"headwell(xw, yw, hc, rw = 0.3, xc = xw, yc = yw, rc = rw, resistance = 0, ...)"},{"path":"https://cneyens.github.io/raem/reference/headwell.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create a analytic element of a well with a constant head — headwell","text":"xw numeric, x location well yw numeric, y location well hc numeric, specified hydraulic head collocation point. rw numeric, radius well. Defaults 0.3 (meter). xc numeric, x location collocation point. See details. Defaults xw. yc numeric, y location collocation point. See details. Defaults yw. rc numeric, radius collocation point. See details. Defaults rw. resistance numeric, hydraulic resistance well screen collocation point. Defaults 0 (resistance). ... ignored","code":""},{"path":"https://cneyens.github.io/raem/reference/headwell.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create a analytic element of a well with a constant head — headwell","text":"Analytic element well constant head object class headwell inherits well.","code":""},{"path":"https://cneyens.github.io/raem/reference/headwell.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Create a analytic element of a well with a constant head — headwell","text":"discharge well location xw yw computed solving aem model given specified head hc. head can specified point, called collocation point. can used compute discharge well specifying head location. collocation point located xc + rc, yc. default, location well collocation point . resistance well screen collocation point can increased well poor connection aquifer. aquifer unconfined (.e. variable saturated thickness), system equations becomes non-linear respect hydraulic head iteration required solve model.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/headwell.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create a analytic element of a well with a constant head — headwell","text":"","code":"headwell(xw = 400, yw = 300, hc = 20, rw = 0.3) #> $parameter #> [1] 0 #>  #> $nunknowns #> [1] 1 #>  #> $zetaw #> [1] 400+300i #>  #> $rw #> [1] 0.3 #>  #> $xc #> [1] 400.3 #>  #> $yc #> [1] 300 #>  #> $hc #> [1] 20 #>  #> $resistance #> [1] 0 #>  #> attr(,\"class\") #> [1] \"headwell\" \"well\"     \"element\"  headwell(xw = 400, yw = 300, hc = 20, rw = 0.3, resistance = 10) #> $parameter #> [1] 0 #>  #> $nunknowns #> [1] 1 #>  #> $zetaw #> [1] 400+300i #>  #> $rw #> [1] 0.3 #>  #> $xc #> [1] 400.3 #>  #> $yc #> [1] 300 #>  #> $hc #> [1] 20 #>  #> $resistance #> [1] 10 #>  #> attr(,\"class\") #> [1] \"headwell\" \"well\"     \"element\"  headwell(xw = 400, yw = 300, hc = 20, rw = 0.3, xc = 500, yc = 500, rc = 0) #> $parameter #> [1] 0 #>  #> $nunknowns #> [1] 1 #>  #> $zetaw #> [1] 400+300i #>  #> $rw #> [1] 0.3 #>  #> $xc #> [1] 500 #>  #> $yc #> [1] 500 #>  #> $hc #> [1] 20 #>  #> $resistance #> [1] 0 #>  #> attr(,\"class\") #> [1] \"headwell\" \"well\"     \"element\""},{"path":"https://cneyens.github.io/raem/reference/linesink.html","id":null,"dir":"Reference","previous_headings":"","what":"Create a strength-specified line-sink analytic element — linesink","title":"Create a strength-specified line-sink analytic element — linesink","text":"linesink() creates line-sink analytic element constant specified strength.","code":""},{"path":"https://cneyens.github.io/raem/reference/linesink.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create a strength-specified line-sink analytic element — linesink","text":"","code":"linesink(x0, y0, x1, y1, sigma, width = 0, ...)"},{"path":"https://cneyens.github.io/raem/reference/linesink.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create a strength-specified line-sink analytic element — linesink","text":"x0 numeric, starting x location line-sink y0 numeric, starting y location line-sink x1 numeric, ending x location line-sink y1 numeric, ending y location line-sink sigma numeric, specific strength line-sink, .e. discharge per length line-sink. Positive aquifer. width numeric, width line-sink. used tracelines() determine particle reached line. Defaults zero (infinitesimally narrow line). ... ignored","code":""},{"path":"https://cneyens.github.io/raem/reference/linesink.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create a strength-specified line-sink analytic element — linesink","text":"Strength-specified line-sink analytic element object class linesink inherits element.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/linesink.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create a strength-specified line-sink analytic element — linesink","text":"","code":"linesink(-75, 50, 100, 50, sigma = 1) #> $parameter #> [1] 1 #>  #> $nunknowns #> [1] 0 #>  #> $z0 #> [1] -75+50i #>  #> $z1 #> [1] 100+50i #>  #> $L #> [1] 175 #>  #> $width #> [1] 0 #>  #> attr(,\"class\") #> [1] \"linesink\" \"element\""},{"path":"https://cneyens.github.io/raem/reference/satthick.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute the saturated thickness — satthick","title":"Compute the saturated thickness — satthick","text":"satthick() computes saturated thickness aquifer aem object given x y coordinates.","code":""},{"path":"https://cneyens.github.io/raem/reference/satthick.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute the saturated thickness — satthick","text":"","code":"satthick(aem, x, y, as.grid = FALSE, ...)"},{"path":"https://cneyens.github.io/raem/reference/satthick.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute the saturated thickness — satthick","text":"aem aem object x numeric x coordinates evaluate y numeric y coordinates evaluate .grid logical, matrix dimensions c(length(y), length(x)) returned? Defaults FALSE. ... additional arguments passed heads() aem$type = 'variable'.","code":""},{"path":"https://cneyens.github.io/raem/reference/satthick.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute the saturated thickness — satthick","text":"satthick() returns vector length(x) (equal length(y)) saturated thicknesses x y. .grid = TRUE, matrix dimensions c(length(y), length(x)) described marginal vectors x y containing saturated thicknesses grid points.","code":""},{"path":"https://cneyens.github.io/raem/reference/satthick.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Compute the saturated thickness — satthick","text":"aquifer confined x y, saturated thickness equals aquifer thickness. flow variable saturated thickness, aquifer unconfined x y, saturated thickness calculated hydraulic head x y minus aquifer base.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/satthick.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute the saturated thickness — satthick","text":"","code":"uf <- uniformflow(100, 0.001, 0) rf <- constant(-1000, 0, 11) m <- aem(k = 10, top = 10, base = 0, n = 0.2, uf, rf, type = 'confined')  satthick(m, x = c(-200, 0, 200), y = 0) # confined #> [1] 10 10 10 satthick(m, x = seq(-500, 500, length = 100),          y = seq(-250, 250, length = 100), as.grid = TRUE) #>        [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] #>   [1,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>   [2,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>   [3,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>   [4,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>   [5,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>   [6,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>   [7,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>   [8,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>   [9,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [10,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [11,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [12,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [13,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [14,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [15,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [16,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [17,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [18,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [19,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [20,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [21,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [22,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [23,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [24,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [25,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [26,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [27,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [28,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [29,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [30,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [31,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [32,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [33,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [34,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [35,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [36,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [37,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [38,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [39,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [40,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [41,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [42,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [43,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [44,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [45,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [46,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [47,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [48,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [49,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [50,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [51,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [52,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [53,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [54,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [55,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [56,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [57,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [58,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [59,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [60,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [61,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [62,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [63,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [64,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [65,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [66,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [67,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [68,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [69,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [70,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [71,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [72,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [73,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [74,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [75,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [76,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [77,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [78,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [79,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [80,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [81,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [82,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [83,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [84,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [85,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [86,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [87,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [88,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [89,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [90,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [91,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [92,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [93,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [94,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [95,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [96,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [97,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [98,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [99,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #> [100,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>        [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] #>   [1,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [2,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [3,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [4,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [5,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [6,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [7,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [8,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [9,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [10,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [11,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [12,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [13,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [14,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [15,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [16,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [17,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [18,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [19,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [20,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [21,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [22,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [23,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [24,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [25,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [26,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [27,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [28,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [29,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [30,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [31,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [32,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [33,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [34,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [35,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [36,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [37,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [38,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [39,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [40,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [41,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [42,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [43,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [44,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [45,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [46,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [47,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [48,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [49,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [50,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [51,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [52,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [53,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [54,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [55,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [56,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [57,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [58,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [59,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [60,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [61,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [62,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [63,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [64,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [65,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [66,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [67,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [68,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [69,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [70,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [71,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [72,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [73,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [74,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [75,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [76,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [77,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [78,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [79,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [80,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [81,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [82,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [83,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [84,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [85,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [86,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [87,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [88,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [89,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [90,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [91,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [92,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [93,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [94,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [95,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [96,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [97,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [98,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [99,]    10    10    10    10    10    10    10    10    10    10    10    10 #> [100,]    10    10    10    10    10    10    10    10    10    10    10    10 #>        [,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] #>   [1,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [2,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [3,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [4,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [5,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [6,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [7,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [8,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [9,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [10,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [11,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [12,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [13,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [14,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [15,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [16,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [17,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [18,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [19,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [20,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [21,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [22,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [23,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [24,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [25,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [26,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [27,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [28,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [29,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [30,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [31,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [32,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [33,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [34,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [35,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [36,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [37,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [38,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [39,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [40,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [41,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [42,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [43,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [44,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [45,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [46,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [47,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [48,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [49,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [50,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [51,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [52,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [53,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [54,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [55,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [56,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [57,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [58,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [59,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [60,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [61,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [62,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [63,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [64,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [65,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [66,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [67,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [68,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [69,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [70,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [71,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [72,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [73,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [74,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [75,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [76,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [77,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [78,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [79,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [80,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [81,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [82,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [83,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [84,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [85,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [86,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [87,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [88,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [89,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [90,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [91,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [92,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [93,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [94,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [95,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [96,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [97,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [98,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [99,]    10    10    10    10    10    10    10    10    10    10    10    10 #> [100,]    10    10    10    10    10    10    10    10    10    10    10    10 #>        [,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] #>   [1,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [2,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [3,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [4,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [5,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [6,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [7,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [8,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [9,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [10,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [11,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [12,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [13,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [14,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [15,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [16,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [17,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [18,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [19,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [20,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [21,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [22,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [23,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [24,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [25,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [26,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [27,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [28,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [29,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [30,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [31,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [32,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [33,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [34,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [35,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [36,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [37,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [38,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [39,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [40,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [41,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [42,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [43,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [44,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [45,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [46,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [47,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [48,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [49,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [50,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [51,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [52,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [53,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [54,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [55,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [56,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [57,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [58,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [59,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [60,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [61,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [62,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [63,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [64,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [65,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [66,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [67,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [68,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [69,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [70,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [71,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [72,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [73,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [74,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [75,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [76,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [77,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [78,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [79,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [80,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [81,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [82,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [83,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [84,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [85,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [86,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [87,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [88,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [89,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [90,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [91,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [92,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [93,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [94,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [95,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [96,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [97,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [98,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [99,]    10    10    10    10    10    10    10    10    10    10    10    10 #> [100,]    10    10    10    10    10    10    10    10    10    10    10    10 #>        [,50] [,51] [,52] [,53] [,54] [,55] [,56] [,57] [,58] [,59] [,60] [,61] #>   [1,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [2,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [3,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [4,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [5,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [6,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [7,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [8,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [9,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [10,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [11,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [12,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [13,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [14,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [15,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [16,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [17,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [18,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [19,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [20,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [21,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [22,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [23,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [24,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [25,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [26,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [27,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [28,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [29,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [30,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [31,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [32,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [33,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [34,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [35,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [36,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [37,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [38,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [39,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [40,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [41,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [42,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [43,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [44,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [45,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [46,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [47,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [48,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [49,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [50,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [51,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [52,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [53,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [54,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [55,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [56,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [57,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [58,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [59,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [60,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [61,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [62,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [63,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [64,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [65,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [66,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [67,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [68,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [69,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [70,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [71,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [72,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [73,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [74,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [75,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [76,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [77,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [78,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [79,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [80,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [81,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [82,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [83,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [84,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [85,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [86,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [87,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [88,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [89,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [90,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [91,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [92,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [93,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [94,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [95,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [96,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [97,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [98,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [99,]    10    10    10    10    10    10    10    10    10    10    10    10 #> [100,]    10    10    10    10    10    10    10    10    10    10    10    10 #>        [,62] [,63] [,64] [,65] [,66] [,67] [,68] [,69] [,70] [,71] [,72] [,73] #>   [1,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [2,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [3,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [4,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [5,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [6,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [7,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [8,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [9,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [10,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [11,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [12,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [13,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [14,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [15,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [16,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [17,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [18,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [19,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [20,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [21,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [22,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [23,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [24,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [25,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [26,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [27,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [28,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [29,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [30,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [31,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [32,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [33,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [34,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [35,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [36,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [37,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [38,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [39,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [40,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [41,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [42,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [43,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [44,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [45,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [46,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [47,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [48,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [49,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [50,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [51,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [52,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [53,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [54,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [55,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [56,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [57,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [58,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [59,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [60,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [61,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [62,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [63,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [64,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [65,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [66,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [67,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [68,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [69,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [70,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [71,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [72,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [73,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [74,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [75,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [76,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [77,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [78,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [79,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [80,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [81,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [82,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [83,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [84,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [85,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [86,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [87,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [88,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [89,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [90,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [91,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [92,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [93,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [94,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [95,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [96,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [97,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [98,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [99,]    10    10    10    10    10    10    10    10    10    10    10    10 #> [100,]    10    10    10    10    10    10    10    10    10    10    10    10 #>        [,74] [,75] [,76] [,77] [,78] [,79] [,80] [,81] [,82] [,83] [,84] [,85] #>   [1,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [2,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [3,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [4,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [5,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [6,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [7,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [8,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [9,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [10,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [11,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [12,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [13,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [14,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [15,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [16,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [17,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [18,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [19,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [20,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [21,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [22,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [23,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [24,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [25,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [26,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [27,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [28,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [29,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [30,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [31,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [32,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [33,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [34,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [35,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [36,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [37,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [38,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [39,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [40,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [41,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [42,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [43,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [44,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [45,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [46,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [47,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [48,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [49,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [50,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [51,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [52,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [53,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [54,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [55,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [56,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [57,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [58,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [59,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [60,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [61,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [62,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [63,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [64,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [65,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [66,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [67,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [68,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [69,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [70,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [71,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [72,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [73,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [74,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [75,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [76,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [77,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [78,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [79,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [80,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [81,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [82,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [83,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [84,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [85,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [86,]    10    10    10  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   10    10    10    10    10    10 #>  [99,]    10    10    10    10    10    10    10    10    10    10    10    10 #> [100,]    10    10    10    10    10    10    10    10    10    10    10    10 #>        [,86] [,87] [,88] [,89] [,90] [,91] [,92] [,93] [,94] [,95] [,96] [,97] #>   [1,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [2,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [3,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [4,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [5,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [6,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [7,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [8,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [9,]    10    10    10    10    10    10    10    10    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#>  [18,]    10    10     10 #>  [19,]    10    10     10 #>  [20,]    10    10     10 #>  [21,]    10    10     10 #>  [22,]    10    10     10 #>  [23,]    10    10     10 #>  [24,]    10    10     10 #>  [25,]    10    10     10 #>  [26,]    10    10     10 #>  [27,]    10    10     10 #>  [28,]    10    10     10 #>  [29,]    10    10     10 #>  [30,]    10    10     10 #>  [31,]    10    10     10 #>  [32,]    10    10     10 #>  [33,]    10    10     10 #>  [34,]    10    10     10 #>  [35,]    10    10     10 #>  [36,]    10    10     10 #>  [37,]    10    10     10 #>  [38,]    10    10     10 #>  [39,]    10    10     10 #>  [40,]    10    10     10 #>  [41,]    10    10     10 #>  [42,]    10    10     10 #>  [43,]    10    10     10 #>  [44,]    10    10     10 #>  [45,]    10    10     10 #>  [46,]    10    10     10 #>  [47,]    10    10     10 #>  [48,]    10    10     10 #>  [49,]    10    10     10 #>  [50,]    10    10     10 #>  [51,]    10    10     10 #>  [52,]    10    10     10 #>  [53,]    10    10     10 #>  [54,]    10    10     10 #>  [55,]    10    10     10 #>  [56,]    10    10     10 #>  [57,]    10    10     10 #>  [58,]    10    10     10 #>  [59,]    10    10     10 #>  [60,]    10    10     10 #>  [61,]    10    10     10 #>  [62,]    10    10     10 #>  [63,]    10    10     10 #>  [64,]    10    10     10 #>  [65,]    10    10     10 #>  [66,]    10    10     10 #>  [67,]    10    10     10 #>  [68,]    10    10     10 #>  [69,]    10    10     10 #>  [70,]    10    10     10 #>  [71,]    10    10     10 #>  [72,]    10    10     10 #>  [73,]    10    10     10 #>  [74,]    10    10     10 #>  [75,]    10    10     10 #>  [76,]    10    10     10 #>  [77,]    10    10     10 #>  [78,]    10    10     10 #>  [79,]    10    10     10 #>  [80,]    10    10     10 #>  [81,]    10    10     10 #>  [82,]    10    10     10 #>  [83,]    10    10     10 #>  [84,]    10    10     10 #>  [85,]    10    10     10 #>  [86,]    10    10     10 #>  [87,]    10    10     10 #>  [88,]    10    10     10 #>  [89,]    10    10     10 #>  [90,]    10    10     10 #>  [91,]    10    10     10 #>  [92,]    10    10     10 #>  [93,]    10    10     10 #>  [94,]    10    10     10 #>  [95,]    10    10     10 #>  [96,]    10    10     10 #>  [97,]    10    10     10 #>  [98,]    10    10     10 #>  [99,]    10    10     10 #> [100,]    10    10     10  mv <- aem(k = 10, top = 10, base = 0, n = 0.2, uf, rf, type = 'variable') satthick(mv, x = c(-200, 0, 200), y = 0) # variable #> [1] 10.000000 10.000000  9.797959"},{"path":"https://cneyens.github.io/raem/reference/state-variables.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate state-variables — state-variables","title":"Calculate state-variables — state-variables","text":"omega() computes complex potential aem element object given x y coordinates. potential() computes discharge potential aem element object given x y coordinates. streamfunction() computes streamfunction aem element object given x y coordinates. heads() computes hydraulic head given x y coordinates.","code":""},{"path":"https://cneyens.github.io/raem/reference/state-variables.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate state-variables — state-variables","text":"","code":"omega(...)  potential(...)  streamfunction(...)  # S3 method for aem omega(aem, x, y, as.grid = FALSE, ...)  # S3 method for aem potential(aem, x, y, as.grid = FALSE, ...)  # S3 method for aem streamfunction(aem, x, y, as.grid = FALSE, ...)  # S3 method for element omega(element, x, y, ...)  # S3 method for element potential(element, x, y, ...)  # S3 method for element streamfunction(element, x, y, ...)  heads(aem, x, y, as.grid = FALSE, na.below = TRUE, ...)"},{"path":"https://cneyens.github.io/raem/reference/state-variables.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate state-variables — state-variables","text":"... ignored aem aem object x numeric x coordinates evaluate y numeric y coordinates evaluate .grid logical, matrix dimensions c(length(y), length(x)) returned? Defaults FALSE. element analytic element class element na.logical indicating calculated head values aquifer base set NA. Defaults TRUE. See potential_to_head().","code":""},{"path":"https://cneyens.github.io/raem/reference/state-variables.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate state-variables — state-variables","text":"omega(), vector length(x) (equal length(y)) complex potential values x y. .grid = TRUE, matrix dimensions c(length(y), length(x)) described marginal vectors x y containing complex potential values grid points. potential(), omega() containing discharge potential values evaluated x y, real components omega(). streamfunction(), omega() containing streamfunction values evaluated x y, imaginary components omega(). heads(), omega() containing hydraulic head values evaluated x y, computed potential() aquifer parameters using potential_to_head().","code":""},{"path":"https://cneyens.github.io/raem/reference/state-variables.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Calculate state-variables — state-variables","text":"heads() confused utils::head(), returns first part object.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/state-variables.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate state-variables — state-variables","text":"","code":"w <- well(xw = 50, yw = 0, Q = 200) uf <- uniformflow(gradient = 0.002, angle = -45, TR = 100) ml <- aem(k = 10, top = 10, base = 0, n = 0.2, w, uf)  omega(ml, c(50, 0), c(25, -25)) #> [1]  98.92447+39.3934i 124.53947-81.7061i  xg <- seq(-100, 100, length = 5) yg <- seq(-75, 75, length = 3) omega(ml, xg, yg, as.grid = TRUE) #>                     [,1]                [,2]               [,3] #> [1,] 187.7937+ 88.77717i 171.3677+ 75.98119i 153.8890+ 58.1101i #> [2,] 173.6356+114.14214i 153.6582+107.07107i 124.5236+100.0000i #> [3,] 166.5804- 60.49290i 150.1545- 61.83905i 132.6758- 58.1101i #>                      [,4]                [,5] #> [1,] 140.96545+32.322330i 139.7469+ 6.534558i #> [2,] -45.39471- 7.071068i 110.3814-14.142136i #> [3,] 119.75225-46.464466i 118.5337-34.818830i  potential(ml, c(50, 0), c(25, -25)) #> [1]  98.92447 124.53947 potential(ml, xg, yg, as.grid = TRUE) #>          [,1]     [,2]     [,3]      [,4]     [,5] #> [1,] 187.7937 171.3677 153.8890 140.96545 139.7469 #> [2,] 173.6356 153.6582 124.5236 -45.39471 110.3814 #> [3,] 166.5804 150.1545 132.6758 119.75225 118.5337  streamfunction(ml, c(50, 0), c(25, -25)) #> [1]  39.3934 -81.7061 streamfunction(ml, xg, yg, as.grid = TRUE) #>           [,1]      [,2]     [,3]       [,4]       [,5] #> [1,]  88.77717  75.98119  58.1101  32.322330   6.534558 #> [2,] 114.14214 107.07107 100.0000  -7.071068 -14.142136 #> [3,] -60.49290 -61.83905 -58.1101 -46.464466 -34.818830  # For elements omega(w, c(50, 0), c(-25, 25)) #> [1] 102.460-50.00000i 128.075+85.24164i  potential(w, c(50, 0), c(-25, 25)) #> [1] 102.460 128.075  streamfunction(w, c(50, 0), c(-25, 25)) #> [1] -50.00000  85.24164  heads(ml, c(50, 0), c(25, -25)) #> [1] 4.448021 4.990781 heads(ml, xg, yg, as.grid = TRUE) #> Warning: NaNs produced #>          [,1]     [,2]     [,3]     [,4]     [,5] #> [1,] 6.128518 5.854360 5.547775 5.309717 5.286717 #> [2,] 5.892972 5.543612 4.990462      NaN 4.698541 #> [3,] 5.772009 5.480045 5.151230 4.893920 4.868957  # do not confuse heads() with utils::head, which will give an error try( head(ml, c(50, 0), c(25, -25)) ) #> Error in head.default(ml, c(50, 0), c(25, -25)) :  #>   invalid 'n' - must have length one when dim(x) is NULL, got 2"},{"path":"https://cneyens.github.io/raem/reference/tracelines.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute tracelines of particles — tracelines","title":"Compute tracelines of particles — tracelines","text":"tracelines() tracks particle locations moving forward backward advective groundwater flow numerically integrating velocity vector. resulting set connected coordinates produces tracelines. endpoints() obtains final time locations tracked particles","code":""},{"path":"https://cneyens.github.io/raem/reference/tracelines.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute tracelines of particles — tracelines","text":"","code":"tracelines(   aem,   x0,   y0,   z0,   times,   forward = TRUE,   R = 1,   tfunc = NULL,   tol = 0.001,   ... )  endpoints(tracelines, ...)  # S3 method for tracelines plot(x, y = NULL, add = FALSE, type = \"l\", arrows = FALSE, marker = NULL, ...)"},{"path":"https://cneyens.github.io/raem/reference/tracelines.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute tracelines of particles — tracelines","text":"aem aem object x0 numeric vector, starting x locations particles y0 numeric vector, starting y locations particles z0 numeric vector, starting z locations particles times numeric vector times locations registered forward logical, forward (TRUE; default) backward (FALSE) tracking performed. R numeric, retardation coefficient passed velocity(). Defaults 1 (retardation). tfunc function list functions additional termination events particles. See details. Defaults NULL. tol numeric tolerance used define particles crossed line element. Defaults 0.001 length units. ... additional arguments passed plot() arrows(). tracelines object class tracelines returned tracelines() x object class tracelines y ignored add logical, plot added existing plot? Defaults FALSE. type character indicating type plot draw. See plot(). Defaults 'l' (lines). arrows logical indicating arrows drawn using arrows(). Defaults FALSE. marker numeric, time interval plot point markers. Defaults NULL (markers). See details.","code":""},{"path":"https://cneyens.github.io/raem/reference/tracelines.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute tracelines of particles — tracelines","text":"tracelines() returns object class tracelines list length equal number particles list element contains matrix columns time, x, y z specifying registered time coordinates particle tracked flow field. final row represents either location maximum times value , particle terminated prematurely, time location termination. matrices ordered increasing time. connecting coordinates, tracelines can produced. endpoints() returns matrix columns time, x, y z specifying final time coordinates particles tracelines object.","code":""},{"path":"https://cneyens.github.io/raem/reference/tracelines.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Compute tracelines of particles — tracelines","text":"deSolve::lsoda() used numerically integrate velocity vector. Particles terminated prematurely reached inner annulus well elements, crossed line element (enter half non-zero width either side) travel saturated aquifer level (.e. water-table unconfined conditions aquifer top confined conditions), aquifer base. Note last two conditions can occur models vertical flow components. returned time value time termination. tfunc argument can used specify additional termination events. function (list functions) takes arguments t, coords parms. , respectively, numeric value current tracking time, numeric vector length 3 current x, y z coordinates particle, list elements aem R. return single logical value indicating particle terminate. See examples. initial particle locations saturated aquifer level, reset elevation warning. Initial particle locations aquifer base reset aquifer base warning. small perturbation added elevations avoid particle tracking algorithm get stuck locations. algorithm get stuck (.e. excessive run-times), try resetting z0 values elevations well inside saturated domain. Backward particle tracking performed reversing flow field (.e. multiplying velocities -1). marker value can used plot point markers given time intervals, e.g. every 365 days (see examples). x y locations particle marked times obtained linearly interpolating computed particle locations.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/tracelines.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute tracelines of particles — tracelines","text":"","code":"k <- 10 top <- 10; base <- 0 n <- 0.2 R <- 5 hc <- 20  uf <- uniformflow(TR = 100, gradient = 0.001, angle = -10) rf <- constant(TR, xc = -1000, yc = 0, hc = hc)  m <- aem(k, top, base, n = n, uf, rf)  x0 <- -200; y0 <- seq(-200, 200, 50) times <- seq(0, 25 * 365, 365 / 4) paths <- tracelines(m, x0 = x0, y0 = y0, z = top, times = times) endp <- endpoints(paths)  xg <- seq(-500, 500, length = 100) yg <- seq(-300, 300, length = 100)  contours(m, xg, yg, col = 'dodgerblue', nlevels = 20) plot(paths, add = TRUE, col = 'orange') points(endp[, c('x', 'y')])  # Backward tracking with retardation; plot point marker every 5 years paths_back <- tracelines(m, x0 = x0, y0 = y0, z0 = top, times = times, R = R, forward = FALSE) plot(paths_back, add = TRUE, col = 'forestgreen', marker = 5*365, cex = 0.5)   # Termination at wells and line-sinks w1 <- well(200, 50, Q = 250) w2 <- well(-200, -100, Q = 450) ls <- headlinesink(x0 = -100, y0 = 100, x1 = 400, y1 = -300, hc = 7)  m <- aem(k, top, base, n = n, uf, rf, w1, w2, ls) contours(m, xg, yg, col = 'dodgerblue', nlevels = 20) plot(m, add = TRUE)  x0 <- seq(-400, 400, 50); y0 <- 200 times <- seq(0, 5 * 365, 365 / 20) paths <- tracelines(m, x0 = x0, y0 = y0, z0 = top, times = times) plot(paths, add = TRUE, col = 'orange')   # User-defined termination in rectangular zone tzone <- cbind(x = c(-300, -200, -200, -300), y = c(150, 150, 100, 100)) termf <- function(t, coords, parms) {   x <- coords[1]   y <- coords[2]   in_poly <- x <= max(tzone[,'x']) & x >= min(tzone[,'x']) &              y <= max(tzone[,'y']) & y >= min(tzone[,'y'])   return(in_poly) } paths <- tracelines(m, x0 = x0, y0 = y0, z0 = top, times = times, tfunc = termf) contours(m, xg, yg, col = 'dodgerblue', nlevels = 20) plot(m, add = TRUE) polygon(tzone) plot(paths, add = TRUE, col = 'orange')   # model with vertical flow due to area-sink as <- areasink(xc = 0, yc = 0, N = 0.001, R = 1500) m <- aem(k, top, base, n = n, uf, rf, w1, w2, as)  # starting z0 locations are above aquifer top and will be reset to top with warning paths <- tracelines(m, x0 = x0, y0 = y0, z0 = top + 0.5, times = times) #> Warning: Resetting z0 values above saturated aquifer level or below aquifer base  contours(m, xg, yg, col = 'dodgerblue', nlevels = 20) plot(m, add = TRUE) plot(paths, add = TRUE, col = 'orange')   # plot vertical cross-section of traceline 4 along increasing y-axis (from south to north) plot(paths[[4]][,c('y', 'z')], type = 'l')    # plot arrows contours(m, xg, yg, col = 'dodgerblue', nlevels = 20) plot(paths, add = TRUE, col = 'orange', arrows = TRUE, length = 0.05)   # plot point markers every 2.5 years contours(m, xg, yg, col = 'dodgerblue', nlevels = 20) plot(paths, add = TRUE, col = 'orange', marker = 2.5 * 365, pch = 20)  # plot point markers every 600 days plot(paths, add = TRUE, col = 'forestgreen', marker = 600, pch = 1)"},{"path":"https://cneyens.github.io/raem/reference/uniformflow.html","id":null,"dir":"Reference","previous_headings":"","what":"Create a uniform-flow analytic element with specified recharge — uniformflow","title":"Create a uniform-flow analytic element with specified recharge — uniformflow","text":"uniformflow() creates analytic element constant uniform background flow.","code":""},{"path":"https://cneyens.github.io/raem/reference/uniformflow.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create a uniform-flow analytic element with specified recharge — uniformflow","text":"","code":"uniformflow(TR, gradient, angle, ...)"},{"path":"https://cneyens.github.io/raem/reference/uniformflow.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create a uniform-flow analytic element with specified recharge — uniformflow","text":"TR numeric, constant transmissivity value used define discharge. gradient numeric, hydraulic gradient. Positive direction flow. angle numeric, angle primary direction background flow, degrees counterclockwise x-axis. ... ignored","code":""},{"path":"https://cneyens.github.io/raem/reference/uniformflow.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create a uniform-flow analytic element with specified recharge — uniformflow","text":"Analytic element constant uniform flow object class uniformflow inherits element.","code":""},{"path":"https://cneyens.github.io/raem/reference/uniformflow.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Create a uniform-flow analytic element with specified recharge — uniformflow","text":"TR gradient multiplied obtain discharge remains constant throughout system, independent saturated thickness aquifer. Groundwater flow direction negative hydraulic gradient. Note gradient specified positive direction flow convenience.","code":""},{"path":"https://cneyens.github.io/raem/reference/uniformflow.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create a uniform-flow analytic element with specified recharge — uniformflow","text":"","code":"uniformflow(TR = 100, gradient = 0.002, angle = -45) # South-eastern direction #> $parameter #> [1] 0.2 #>  #> $nunknowns #> [1] 0 #>  #> $udir #> [1] 0.7071068+0.7071068i #>  #> attr(,\"class\") #> [1] \"uniformflow\" \"element\""},{"path":"https://cneyens.github.io/raem/reference/well.html","id":null,"dir":"Reference","previous_headings":"","what":"Create a analytic element of a constant-discharge well — well","title":"Create a analytic element of a constant-discharge well — well","text":"well() creates analytic element well constant discharge.","code":""},{"path":"https://cneyens.github.io/raem/reference/well.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create a analytic element of a constant-discharge well — well","text":"","code":"well(xw, yw, Q, rw = 0.3, ...)"},{"path":"https://cneyens.github.io/raem/reference/well.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create a analytic element of a constant-discharge well — well","text":"xw numeric, x location well yw numeric, y location well Q numeric, volumetric discharge well (positive aquifer) rw numeric, radius well. Defaults 0.3. ... ignored","code":""},{"path":"https://cneyens.github.io/raem/reference/well.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create a analytic element of a constant-discharge well — well","text":"Analytic element well constant discharge object class well inherits element.","code":""},{"path":"https://cneyens.github.io/raem/reference/well.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Create a analytic element of a constant-discharge well — well","text":"inner annulus well element constitutes singularity equations hydraulic head undefined distance smaller rw well center. state- flow-variable calculated within annulus, location reset nearest location well screen.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/well.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create a analytic element of a constant-discharge well — well","text":"","code":"well(xw = 50, yw = 0, Q = 200, rw = 0.3) #> $parameter #> [1] 200 #>  #> $nunknowns #> [1] 0 #>  #> $zetaw #> [1] 50+0i #>  #> $rw #> [1] 0.3 #>  #> attr(,\"class\") #> [1] \"well\"    \"element\""}]
+[{"path":"https://cneyens.github.io/raem/LICENSE.html","id":null,"dir":"","previous_headings":"","what":"MIT License","title":"MIT License","text":"Copyright (c) 2023 raem authors Permission hereby granted, free charge, person obtaining copy software associated documentation files (“Software”), deal Software without restriction, including without limitation rights use, copy, modify, merge, publish, distribute, sublicense, /sell copies Software, permit persons Software furnished , subject following conditions: copyright notice permission notice shall included copies substantial portions Software. SOFTWARE PROVIDED “”, WITHOUT WARRANTY KIND, EXPRESS IMPLIED, INCLUDING LIMITED WARRANTIES MERCHANTABILITY, FITNESS PARTICULAR PURPOSE NONINFRINGEMENT. EVENT SHALL AUTHORS COPYRIGHT HOLDERS LIABLE CLAIM, DAMAGES LIABILITY, WHETHER ACTION CONTRACT, TORT OTHERWISE, ARISING , CONNECTION SOFTWARE USE DEALINGS SOFTWARE.","code":""},{"path":"https://cneyens.github.io/raem/articles/overview.html","id":"introduction-to-analytic-element-modeling","dir":"Articles","previous_headings":"","what":"Introduction to analytic element modeling","title":"An Overview","text":"First developed Otto Strack Henk Haitjema late 1970’s, analytic element modeling (AEM) approach solves groundwater flow problem superposition analytical solutions features wells, streams recharge. feature called element. superimposing individual solutions, combined effect elements can calculated point space. arbitrary number elements can placed location flow field. , AEM method flexible single analytical solutions can used solve complex field cases. Compared numerical solutions groundwater flow problem, AEM method require spatial grid, relatively fast easy use suffer numerical instability mass balance errors. Flow governed Dupuit-Forchheimer approximation states hydraulic head \\(h\\) hydrostatic point horizontal plane. words, variation \\(h\\) along vertical axis horizontal flow evenly distributed along vertical axis. reduces dimensions problem, solution now depends \\(x\\) \\(y\\) coordinates. Although vertical gradients, vertical flow can still computed mass balance considerations, .e. areal recharge aquifer top leakage aquifer bottom. Additionally phreatic aquifers, curvature water-table induces vertical flow components. Besides Dupuit-Forchheimer assumption, aquifer assumed infinite lateral extent, horizontal top base homogeneous scale interest. practice, assumptions appear (approximately) valid cases groundwater system consideration much wider thick, case regional aquifer systems flow predominantly horizontal. areas considerable vertical flow, near groundwater divides near partially penetrating wells streams, flow system similar thickness width (\\(width\\lt~\\approx 3*thickness\\)), Dupuit-Forchheimer approximation valid different method used, e.g. numerical model 3D groundwater flow equation.","code":""},{"path":"https://cneyens.github.io/raem/articles/overview.html","id":"solution-method","dir":"Articles","previous_headings":"Introduction to analytic element modeling","what":"Solution method","title":"An Overview","text":"steady-state, single layer Dupuit-Forchheimer flow horizontal plane, governing equation : \\[ T\\frac{\\partial^2{h}}{\\partial x^2} + T\\frac{\\partial^2{h}}{\\partial y^2} + N = 0 \\] \\(T\\) aquifer transmissivity \\([L^2/T]\\), equal \\(kH\\) \\(k\\) horizontal hydraulic conductivity \\([L/T]\\) \\(H\\) saturated thickness \\([L]\\), \\(h\\) hydraulic head \\([L]\\) \\(N\\) sink/source term \\([L/T]\\). aquifer phreatic, saturated thickness \\(H\\) variable, renders flow equation non-linear solving \\(h\\). Therefore, discharge potential \\(\\Phi\\) \\([L^3/T]\\) introduced governing flow equation becomes: \\[ \\frac{\\partial^2{\\Phi}}{\\partial x^2} + \\frac{\\partial^2{\\Phi}}{\\partial y^2} + N = 0 \\] linear equation can solved \\(\\Phi\\). resulting hydraulic heads can computed : \\[ \\begin{aligned} \\Phi &= kHh - (\\frac{1}{2}kH^2 + kHz_b) &\\qquad h \\ge z_t \\\\ \\Phi &= \\frac{1}{2}k(h - z_b)^2 &\\qquad z_b \\lt h \\lt z_t \\end{aligned} \\] \\(z_t\\) \\(z_b\\) aquifer top base elevation \\([L]\\), respectively. addition discharge potential \\(\\Phi\\), exists stream function \\(\\Psi\\) \\([L^3/T]\\) defined function constant along streamlines whose difference stream function values two points equal amount water flowing two points. convention, stream function increases right looking direction flow. can used visualize amount flow groundwater system. \\(\\Psi\\) defined Laplace equation, .e. \\(N\\) zero. modeling terms, means area-sinks active model (see paragraph Area-sink ). discharge potential \\(\\Phi\\) stream function \\(\\Psi\\) fulfill Cauchy-Riemann conditions can therefore combined complex potential \\(\\Omega\\) whose real imaginary terms \\(\\Phi\\) \\(\\Psi\\), respectively. solving flow problem terms \\(\\Omega\\), \\(\\Phi\\) \\(\\Psi\\) solved simultaneously complex plane, described complex coordinate \\(\\zeta=x+iy\\). solution terms \\(\\Omega\\) yields \\(\\Phi\\) eventually \\(h\\). derivative \\(\\Omega\\) respect \\(\\zeta\\) complex discharge \\(W\\), whose real component \\(Q_x\\) whose negative imaginary component \\(Q_y\\), .e. \\(x\\) \\(y\\) components discharge vector \\(Q\\) \\([L^2/T]\\), represents first derivate \\(\\Phi\\) \\(x\\) \\(y\\) directions. vertical component \\(Q_z\\) determined mass balance considerations discussed . Darcy flux \\(q\\) \\([L/T]\\) (also called specific discharge) computed \\(Q/H\\). average linear flow velocity \\(v\\) \\([L/T]\\) computed \\(q/n\\) \\(n\\) aquifer porosity, represent effective porosity. element gives solution governing flow equation terms \\(\\Omega\\), well complex discharge \\(W\\). element one free parameters, e.g. discharge well element. parameters may user-specified need computed conditions, case head-specified elements. parameters specified called collocation points control points. Since solution given element depends results elements, complete system equations needs solved simultaneously element parameters. done setting flow equations collocation points matrix form \\(Ax=b\\), solved parameter vector \\(x\\). element parameters known, contributions element complex potential \\(\\Omega\\) complex discharge \\(W\\) point can calculated superimposed form resulting \\(\\Omega\\) \\(W\\) values, yield variables interest \\(h\\) \\(Q\\). complete overview analytic element modeling, reader referred Haitjema (1995), Strack (1989), Strack (2003) Hunt (2006).","code":""},{"path":"https://cneyens.github.io/raem/articles/overview.html","id":"elements","dir":"Articles","previous_headings":"","what":"Elements","title":"An Overview","text":"overview elements available raem provided. can specify many elements like, keep mind solution matrix increases size every element parameter. Currently, every element raem supplied one parameter solution matrix. create AEM model raem, first need load raem specify aquifer parameters:","code":"library(raem)  k = 10     # hydraulic conductivity, m/d top = 10   # aquifer top elevation, m base = -15 # aquifer bottom elevation, m n = 0.2    # aquifer effective porosity, -"},{"path":"https://cneyens.github.io/raem/articles/overview.html","id":"well","dir":"Articles","previous_headings":"Elements","what":"Well","title":"An Overview","text":"simplest element well specified discharge \\(Q\\), can created well() function. requires \\(x\\) \\(y\\) coordinate well pumping rate \\(Q\\) (positive withdrawal). well radius \\(rw\\) can also specified (default \\(0.3\\) length units). Inside well annulus defined \\(r_w\\), solution undefined. output variable requested inside circle, location projected onto nearest point outer annulus. , specify two extraions wells. create model call aem(). function needs aquifer parameters well elements. can supply elements individually put single list(). aem() function automatically solves system equations calling solve.aem(). default, flow system variable saturated thickness. can change setting type = 'confined' force model use constant saturated thickness, set equal aquifer thickness. may useful want force system equations remain linear elements hydraulic resistance supplied (see ). Finally, set-contouring grid plot head contours blue streamlines orange using contours(). Note ugly branch cuts (AEM jargon) streamlines extending well centers towards negative x-axis, artifact contouring stream function.","code":"w1 = well(x = 200, y = 0, Q = 300)    w2 = well(x = -200, y = 0, Q = 1000)  # create the model. This automatically solves the system of equations m = aem(k = k, top = top, base = base, n = n, w1, w2)  # set-up the contouring grid and plot head contours and streamline  xg = seq(-600, 600, length = 100) yg = seq(-300, 300, length = 100)  contours(m, xg, yg, col = 'dodgerblue', nlevels = 20, drawlabels = FALSE) contours(m, xg, yg, variable = 'streamfunction', col = 'orange', nlevels = 20, drawlabels = TRUE, add = TRUE)"},{"path":[]},{"path":[]},{"path":[]},{"path":[]},{"path":[]},{"path":[]},{"path":[]},{"path":[]},{"path":[]},{"path":[]},{"path":[]},{"path":"https://cneyens.github.io/raem/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"Cas Neyens. Author, maintainer.","code":""},{"path":"https://cneyens.github.io/raem/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"Neyens C (2024). raem: Analytic Element Modeling Steady Single-Layer Groundwater Flow. R package version 0.0.0.9000, https://cneyens.github.io/raem/, https://github.com/cneyens/raem.","code":"@Manual{,   title = {raem: Analytic Element Modeling of Steady Single-Layer Groundwater Flow},   author = {Cas Neyens},   year = {2024},   note = {R package version 0.0.0.9000, https://cneyens.github.io/raem/},   url = {https://github.com/cneyens/raem}, }"},{"path":"https://cneyens.github.io/raem/index.html","id":"raem","dir":"","previous_headings":"","what":"Analytic Element Modeling of Steady Single-Layer Groundwater Flow","title":"Analytic Element Modeling of Steady Single-Layer Groundwater Flow","text":"raem R package modeling steady-state single-layer groundwater flow Dupuit-Forchheimer assumption using analytic elements.","code":""},{"path":"https://cneyens.github.io/raem/index.html","id":"installation","dir":"","previous_headings":"","what":"Installation","title":"Analytic Element Modeling of Steady Single-Layer Groundwater Flow","text":"can install development version raem GitHub :","code":"# install.packages(\"devtools\") devtools::install_github(\"cneyens/raem\")"},{"path":"https://cneyens.github.io/raem/index.html","id":"example","dir":"","previous_headings":"","what":"Example","title":"Analytic Element Modeling of Steady Single-Layer Groundwater Flow","text":"Construct analytic element model aquifer uniform background flow, two extraction wells reference point. Specify aquifer parameters create elements: Create model. automatically solves system equations. Find head discharge two locations x = -200, y = 200 x = 100, y = 200. Note vertical flow components model: Plot head contours element locations. First, specify contouring grid: Now plot:  Compute particle traces starting along y = 200 20 intervals per year 5 years add plot:","code":"library(raem)  k = 10 top = 10 base = 0 n = 0.2  hr = 15 # head at reference point, above aquifer top TR = k * (top - base) # constant transmissivity of background flow  uf = uniformflow(TR, gradient = 0.001, angle = -45) rf = constant(xc = -1000, yc = 0, hc = hr) w1 = well(xw = 200, yw = 0, Q = 250) w2 = well(xw = -200, yw = -150, Q = 400) m = aem(k = k, top = top, base = base, n = n,          uf, rf, w1, w2) heads(m, x = c(-200, 100), y = 200) #> [1] 13.64573 13.33314 discharge(m, c(-200, 100), 200, z = top) # [L^2 / T] #>              Qx         Qy Qz #> [1,] 0.15028815 -0.2923908  0 #> [2,] 0.06041242 -0.3347206  0 xg = seq(-500, 500, length = 100) yg = seq(-250, 250, length = 100) contours(m, xg, yg, 'heads', col = 'dodgerblue', nlevels = 20) plot(m, add = TRUE) paths = tracelines(m, x0 = seq(-450, 450, 50), y0 = 200, z0 = top, times = seq(0, 5*365, 365/20)) plot(paths, add = TRUE, col = 'orange')"},{"path":"https://cneyens.github.io/raem/reference/add_element.html","id":null,"dir":"Reference","previous_headings":"","what":"Add element to existing aem object — add_element","title":"Add element to existing aem object — add_element","text":"Add element existing aem object","code":""},{"path":"https://cneyens.github.io/raem/reference/add_element.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Add element to existing aem object — add_element","text":"","code":"add_element(aem, element, name = NULL, solve = FALSE, ...)"},{"path":"https://cneyens.github.io/raem/reference/add_element.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Add element to existing aem object — add_element","text":"aem aem object element analytic element class element name optional name element character. Duplicate names aem allowed. solve logical, model solved adding new element? Defaults FALSE. ... ignored","code":""},{"path":"https://cneyens.github.io/raem/reference/add_element.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Add element to existing aem object — add_element","text":"aem model addition element. solve = TRUE, model solved using solve.aem(). name element taken name argument, object name set element_1 1 index new element element list. See examples.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/add_element.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Add element to existing aem object — add_element","text":"","code":"m <- aem(k = 10, top = 10, base = 0, n = 0.2) add_element(m, constant(xc = 0, yc = 1000, hc = 12), name = 'rf') #> $k #> [1] 10 #>  #> $top #> [1] 10 #>  #> $base #> [1] 0 #>  #> $n #> [1] 0.2 #>  #> $elements #> $elements$rf #> $parameter #> [1] 0 #>  #> $nunknowns #> [1] 1 #>  #> $xc #> [1] 0 #>  #> $yc #> [1] 1000 #>  #> $hc #> [1] 12 #>  #> attr(,\"class\") #> [1] \"constant\" \"element\"  #>  #>  #> $type #> [1] \"variable\" #>  #> $solved #> [1] FALSE #>  #> attr(,\"class\") #> [1] \"aem\"  # if name not supplied, tries to obtain it from object name rf <- constant(xc = 0, yc = 1000, hc = 12) add_element(m, rf) #> $k #> [1] 10 #>  #> $top #> [1] 10 #>  #> $base #> [1] 0 #>  #> $n #> [1] 0.2 #>  #> $elements #> $elements$rf #> $parameter #> [1] 0 #>  #> $nunknowns #> [1] 1 #>  #> $xc #> [1] 0 #>  #> $yc #> [1] 1000 #>  #> $hc #> [1] 12 #>  #> attr(,\"class\") #> [1] \"constant\" \"element\"  #>  #>  #> $type #> [1] \"variable\" #>  #> $solved #> [1] FALSE #>  #> attr(,\"class\") #> [1] \"aem\"  # or else sets it sequentially from number of elements add_element(m, constant(xc = 0, yc = 1000, hc = 12)) #> $k #> [1] 10 #>  #> $top #> [1] 10 #>  #> $base #> [1] 0 #>  #> $n #> [1] 0.2 #>  #> $elements #> $elements$element_1 #> $parameter #> [1] 0 #>  #> $nunknowns #> [1] 1 #>  #> $xc #> [1] 0 #>  #> $yc #> [1] 1000 #>  #> $hc #> [1] 12 #>  #> attr(,\"class\") #> [1] \"constant\" \"element\"  #>  #>  #> $type #> [1] \"variable\" #>  #> $solved #> [1] FALSE #>  #> attr(,\"class\") #> [1] \"aem\" # add_element() is pipe-friendly aem(k = 10, top = 10, base = 0, n = 0.2) |>     add_element(rf, name = 'rf') |>     add_element(headwell(xw = 0, yw = 100, rw = 0.3, hc = 8),                 name = 'headwell', solve = TRUE) #> $k #> [1] 10 #>  #> $top #> [1] 10 #>  #> $base #> [1] 0 #>  #> $n #> [1] 0.2 #>  #> $elements #> $elements$rf #> $parameter #> [1] 377.1432 #>  #> $nunknowns #> [1] 1 #>  #> $xc #> [1] 0 #>  #> $yc #> [1] 1000 #>  #> $hc #> [1] 12 #>  #> attr(,\"class\") #> [1] \"constant\" \"element\"  #>  #> $elements$headwell #> $parameter #> [1] 298.2139 #>  #> $nunknowns #> [1] 1 #>  #> $zetaw #> [1] 0+100i #>  #> $rw #> [1] 0.3 #>  #> $xc #> [1] 0.3 #>  #> $yc #> [1] 100 #>  #> $hc #> [1] 8 #>  #> $resistance #> [1] 0 #>  #> attr(,\"class\") #> [1] \"headwell\" \"well\"     \"element\"  #>  #>  #> $type #> [1] \"variable\" #>  #> $solved #> [1] TRUE #>  #> attr(,\"class\") #> [1] \"aem\""},{"path":"https://cneyens.github.io/raem/reference/aem.html","id":null,"dir":"Reference","previous_headings":"","what":"Create an analytic element model — aem","title":"Create an analytic element model — aem","text":"aem() creates analytic element model elements can added solve.aem() solves system equations constructed elements aem model plot.element() plots location analytic element point line geometry. plot.aem() plots planar locations analytic elements point line geometry aem object calling plot.element() , adds existing plot.","code":""},{"path":"https://cneyens.github.io/raem/reference/aem.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create an analytic element model — aem","text":"","code":"aem(   k,   top,   base,   n,   ...,   type = c(\"variable\", \"confined\"),   verbose = FALSE,   maxiter = 10 )  # S3 method for aem solve(a, b, maxiter = 10, verbose = FALSE, ...)  # S3 method for element plot(   x,   y = NULL,   add = FALSE,   pch = 16,   cex = 0.75,   use.widths = TRUE,   col = \"black\",   ... )  # S3 method for aem plot(x, y = NULL, add = FALSE, xlim, ylim, frame.plot = TRUE, ...)"},{"path":"https://cneyens.github.io/raem/reference/aem.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create an analytic element model — aem","text":"k numeric, hydraulic conductivity aquifer top numeric, top elevation aquifer base numeric, base elevation aquifer n numeric, effective porosity aquifer fraction total unit volume. Used determining flow velocities velocity(). ... ignored type character specifying type flow aquifer, either variable (default) confined. See details. verbose logical indicating information solving process printed. Defaults FALSE. maxiter integer specifying maximum allowed iterations non-linear solution. Defaults 10. See details. aem object b ignored x aem object, analytic element class element plot. point line geometry, nothing plotted. y ignored add logical, plot added existing plot? Defaults FALSE. pch numeric point symbol value, defaults 16. cex numeric symbol size value, defaults 0.75. use.widths logical, line elements non-zero width plotted, plotted polygons including width (TRUE; default) infinitesimally thin lines (FALSE)? col color element. Defaults 'black'. xlim numeric, plot limits along x-axis. Required add = FALSE. ylim numeric, plot limits along y-axis. Required add = FALSE. frame.plot logical, border drawn around plot. Defaults TRUE.","code":""},{"path":"https://cneyens.github.io/raem/reference/aem.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create an analytic element model — aem","text":"aem() returns object class aem list consisting k, top, base, n, list containing elements names objects specified ..., logical solved indicating model solved. solve.aem() returns solved aem object, .e. finding solution system equations constructed contained elements.","code":""},{"path":"https://cneyens.github.io/raem/reference/aem.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Create an analytic element model — aem","text":"default type = 'variable' allows unconfined/confined flow, .e. flow variable saturated thickness. type = 'confined', saturated thickness always constant equal aquifer thickness. solve.aem() called aem object returned, solves system equations. solve.aem() sets system equations, calls solve() solve. head-specified elements supplied, element class constant created constant() (also called reference point), supplied well. Constructing aem object call aem() automatically calls solve.aem(). system equations non-linear, example flow system unconfined (variable saturated thickness) elements hydraulic resistance specified, Picard iteration entered. Picard iteration step (outer iteration), previously solved model parameters used set solve linear system equations. model parameters updated next outer iteration step entered, maxiter iterations reached. linear model, maxiter ignored. analytic element point geometry collocation point (e.g. headwell()), point also plotted. reference point (created constant()) never plotted hydraulic feature. Area-sinks (created areasink() headareasink()) also never plotted clutter plot.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/aem.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create an analytic element model — aem","text":"","code":"k <- 10 top <- 10 base <- 0 n <- 0.2 TR <- k * (top - base)  w <- well(xw = 50, yw = 0, Q = 200) rf <- constant(xc = -500, yc = 0, h = 20) uf <- uniformflow(gradient = 0.002, angle = -45, TR = TR) hdw <- headwell(xw = 0, yw = 100, rw = 0.3, hc = 8) ls <- linesink(x0 = -200, y0 = -150, x1 = 200, y1 = 150, sigma = 1)  # Creating aem ---- m <- aem(k, top, base, n, w, rf, uf, hdw, ls)  # or with elements in named list m <- aem(k, top, base, n,          list('well' = w, 'constant' = rf, 'flow' = uf, 'headwell' = hdw, 'river' = ls),          type = 'confined')  # Solving ---- m <- solve(m)  # solving requires a reference point (constant) element if head-specified elements are supplied try(   m <- aem(k = k, top = top, base = base, n = n, w, uf, hdw) ) #> Error : Please provide an element of class 'constant' when solving for unknown parameters in elements  # Plotting ---- plot(ls) plot(w, add = TRUE)  plot(uf) # empty  plot(m, xlim = c(-500, 500), ylim = c(-250, 250))   xg <- seq(-500, 500, length = 200) yg <- seq(-250, 250, length = 100)  contours(m, x = xg, y = yg, col = 'dodgerblue', nlevels = 20) plot(m, add = TRUE)"},{"path":"https://cneyens.github.io/raem/reference/areasink.html","id":null,"dir":"Reference","previous_headings":"","what":"Create a circular area-sink analytic element with specified recharge — areasink","title":"Create a circular area-sink analytic element with specified recharge — areasink","text":"areasink() creates circular area-sink analytic element constant, uniform specified recharge.","code":""},{"path":"https://cneyens.github.io/raem/reference/areasink.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create a circular area-sink analytic element with specified recharge — areasink","text":"","code":"areasink(xc, yc, N, R, location = c(\"top\", \"base\"), ...)"},{"path":"https://cneyens.github.io/raem/reference/areasink.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create a circular area-sink analytic element with specified recharge — areasink","text":"xc numeric, x location center area-sink yc numeric, y location center area-sink N numeric, uniform constant leakage value (positive aquifer) length per time. R numeric, radius circular area-sink location character, either top (default) base specifying vertical position area-sink. ... ignored","code":""},{"path":"https://cneyens.github.io/raem/reference/areasink.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create a circular area-sink analytic element with specified recharge — areasink","text":"Circular area-sink analytic element object class areasink inherits element.","code":""},{"path":"https://cneyens.github.io/raem/reference/areasink.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Create a circular area-sink analytic element with specified recharge — areasink","text":"Area-sinks can used simulate areal recharge seepage aquifer top, leakage aquifer base. location argument used calculating vertical flow component.","code":""},{"path":"https://cneyens.github.io/raem/reference/areasink.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create a circular area-sink analytic element with specified recharge — areasink","text":"","code":"areasink(xc = -500, yc = 0, N = 0.001, R = 500) #> $parameter #> [1] 0.001 #>  #> $nunknowns #> [1] 0 #>  #> $xc #> [1] -500 #>  #> $yc #> [1] 0 #>  #> $R #> [1] 500 #>  #> $location #> [1] \"top\" #>  #> attr(,\"class\") #> [1] \"areasink\" \"element\"   # flux assuming a constant head difference over a confining unit dh <- 3 res <- 10 / 0.0001 areasink(xc = -500, yc = 0, N = -dh/res, R = 500, location = 'base') #> $parameter #> [1] -3e-05 #>  #> $nunknowns #> [1] 0 #>  #> $xc #> [1] -500 #>  #> $yc #> [1] 0 #>  #> $R #> [1] 500 #>  #> $location #> [1] \"base\" #>  #> attr(,\"class\") #> [1] \"areasink\" \"element\""},{"path":"https://cneyens.github.io/raem/reference/capzone.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate capture zone of a well element — capzone","title":"Calculate capture zone of a well element — capzone","text":"capzone() determines capture zone well element flow field performing backward particle tracking requested time reached.","code":""},{"path":"https://cneyens.github.io/raem/reference/capzone.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate capture zone of a well element — capzone","text":"","code":"capzone(aem, well, time, npar = 15, dt = time/10, zstart = aem$base, ...)"},{"path":"https://cneyens.github.io/raem/reference/capzone.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate capture zone of a well element — capzone","text":"aem aem object well well analytic element class well inherits . time numeric, time capture zone npar integer, number particles use backward tracking. Defaults 15. dt numeric, time step length used particle tracking. Defaults time / 10. zstart numeric value starting elevation particles. Defaults base aquifer. ... additional arguments passed tracelines().","code":""},{"path":"https://cneyens.github.io/raem/reference/capzone.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate capture zone of a well element — capzone","text":"capzone() returns object class tracelines.","code":""},{"path":"https://cneyens.github.io/raem/reference/capzone.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Calculate capture zone of a well element — capzone","text":"capzone() thin wrapper around tracelines(). Backward particle tracking performed using tracelines() setting forward = FALSE. Initial particle locations computed equally spacing npar locations well radius zstart elevation. obtain sharper delineation capture zone, try using particles decreasing dt. Note different zstart values effect models vertical flow components.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/capzone.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate capture zone of a well element — capzone","text":"","code":"k <- 10 top <- 10; base <- 0 n <- 0.3  uf <- uniformflow(TR = 100, gradient = 0.001, angle = -10) rf <- constant(TR, xc = -1000, yc = 0, hc = 20) w1 = well(200, 50, Q = 250) w2 = well(-200, -100, Q = 450)  m <- aem(k, top, base, n = n, uf, rf, w1, w2)  cp5 <- capzone(m, w1, time = 5*365) cp10 <- capzone(m, w2, time = 10*365)  xg <- seq(-800, 800, length = 100) yg <- seq(-500, 500, length = 100)  contours(m, xg, yg, col = 'dodgerblue', nlevels = 20) plot(cp5, add = TRUE) plot(cp10, add = TRUE, col = 'orange')   # model with vertical flow components as <- areasink(0, 0, N = 0.001, R = 1500) m <- aem(k, top, base, n = n, uf, rf, w1, w2, as)  # two different starting levels cp5a <- capzone(m, w1, time = 5*365, zstart = base) cp5b <- capzone(m, w1, time = 5*365, zstart = 8)  contours(m, xg, yg, col = 'dodgerblue', nlevels = 20) plot(cp5a, add = TRUE) plot(cp5b, add = TRUE, col = 'forestgreen') # smaller zone  # plot the convex hull of the endpoints as a polygon endp <- endpoints(cp5b) hull <- chull(endp[, c('x', 'y')]) polygon(endp[hull, c('x', 'y')], col = adjustcolor('forestgreen', alpha.f = 0.7))"},{"path":"https://cneyens.github.io/raem/reference/constant.html","id":null,"dir":"Reference","previous_headings":"","what":"Create a constant-head analytic element — constant","title":"Create a constant-head analytic element — constant","text":"constant() creates analytic element containing constant head, often referred reference point.","code":""},{"path":"https://cneyens.github.io/raem/reference/constant.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create a constant-head analytic element — constant","text":"","code":"constant(xc, yc, hc, ...)"},{"path":"https://cneyens.github.io/raem/reference/constant.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create a constant-head analytic element — constant","text":"xc numeric, x location reference point. yc numeric, y location reference point. hc numeric, hydraulic head reference point. ... ignored","code":""},{"path":"https://cneyens.github.io/raem/reference/constant.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create a constant-head analytic element — constant","text":"Constant-head analytic element point object class constant inherits element.","code":""},{"path":"https://cneyens.github.io/raem/reference/constant.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create a constant-head analytic element — constant","text":"","code":"rf <- constant(xc = -100, yc = 0, hc = 10)"},{"path":"https://cneyens.github.io/raem/reference/contours.html","id":null,"dir":"Reference","previous_headings":"","what":"Plot contours of a computed variable of the analytic element model — contours","title":"Plot contours of a computed variable of the analytic element model — contours","text":"contours() creates contour plot variable computed analytic element model aem, adds contour lines existing plot.","code":""},{"path":"https://cneyens.github.io/raem/reference/contours.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Plot contours of a computed variable of the analytic element model — contours","text":"","code":"contours(   aem,   x,   y,   variable = c(\"heads\", \"streamfunction\", \"potential\"),   asp = 1,   ... )"},{"path":"https://cneyens.github.io/raem/reference/contours.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Plot contours of a computed variable of the analytic element model — contours","text":"aem aem object x numeric x coordinates values z computed. must ascending order. y numeric x coordinates values z computed. must ascending order. variable character indicating variable plot. Possible values heads (default), streamfunction potential. asp y/x aspect ratio, see plot.window(). Defaults 1 (equal unit lengths). ... additional arguments passed contour().","code":""},{"path":"https://cneyens.github.io/raem/reference/contours.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Plot contours of a computed variable of the analytic element model — contours","text":"contours() wrapper around contour(). obtains values variable supplied grid points constructs matrix supplied contour() reversing rows transposing matrix (see also documentation image()).","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/contours.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Plot contours of a computed variable of the analytic element model — contours","text":"","code":"w <- well(xw = 50, yw = 0, Q = 200) wi <- well(xw = -200, yw = 0, Q = -100) uf <- uniformflow(gradient = 0.002, angle = -45, TR = 100) rf <- constant(-1000, 0, hc = 10) ml <- aem(k = 10, top = 10, base = 0, n = 0.2, w, wi, uf, rf)  xg <- seq(-350, 200, length = 100) yg <- seq(-125, 125, length = 100)  contours(ml, xg, yg, nlevels = 20, col = 'dodgerblue', labcex = 1) contours(ml, xg, yg, 'streamfunction', nlevels = 20, col = 'orange',          drawlabels = FALSE, add = TRUE)   # Not to be confused by contour() try( contour(ml, xg, yg, nlevels = 20, col = 'dodgerblue', labcex = 1) ) #> Error in contour.default(ml, xg, yg, nlevels = 20, col = \"dodgerblue\",  :  #>   no proper 'z' matrix specified  # For image() or filled.contour() library(graphics) h <- heads(ml, xg, yg, as.grid = TRUE) h_im <- t(h[dim(h)[1]:1,]) image(xg, yg, h_im, asp = 1) contour(xg, yg, h_im, asp = 1, add = TRUE) # contours() is a wrapper for this  filled.contour(xg, yg, h_im, asp = 1)"},{"path":"https://cneyens.github.io/raem/reference/dirflow.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute flow at a point in the direction of a given angle — dirflow","title":"Compute flow at a point in the direction of a given angle — dirflow","text":"dirflow() computes flow variable given points direction supplied angle","code":""},{"path":"https://cneyens.github.io/raem/reference/dirflow.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute flow at a point in the direction of a given angle — dirflow","text":"","code":"dirflow(   aem,   x,   y,   angle,   flow = c(\"discharge\", \"darcy\", \"velocity\"),   as.grid = FALSE,   ... )"},{"path":"https://cneyens.github.io/raem/reference/dirflow.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute flow at a point in the direction of a given angle — dirflow","text":"aem aem object x numeric x coordinates evaluate flow y numeric y coordinates evaluate flow angle numeric, angle direction evaluate flow, degrees counterclockwise x-axis flow character specifying flow variable use. Possible values discharge (default), darcy velocity. See flow(). .grid logical, matrix returned? Defaults FALSE. See details. ... additional arguments passed discharge(), darcy() velocity()","code":""},{"path":"https://cneyens.github.io/raem/reference/dirflow.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute flow at a point in the direction of a given angle — dirflow","text":"vector length(x) (equal length(y)) flow values x y direction angle. .grid = TRUE, matrix dimensions c(length(y), length(x)) described marginal vectors x y containing directed flow values grid points.","code":""},{"path":"https://cneyens.github.io/raem/reference/dirflow.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Compute flow at a point in the direction of a given angle — dirflow","text":"x y components flow used calculate directed value using angle. z coordinate discharge(), darcy() velocity() set aquifer base. Dupuit-Forchheimer, x y components flow vector change along vertical axis.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/dirflow.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute flow at a point in the direction of a given angle — dirflow","text":"","code":"rf <- constant(-1000, 0, hc = 10) uf <- uniformflow(TR = 100, gradient = 0.001, angle = -45) w <- well(10, -50, Q = 200)  m <- aem(k = 10, top = 10, base = 0, n = 0.2, rf, uf) dirflow(m, x = c(0, 100), y = 50, angle = -45) #> [1] 0.1 0.1  m <- aem(k = 10, top = 10, base = 0, n = 0.2, rf, uf, w, type = 'confined') dirflow(m, x = c(0, 50, 100), y = c(0, 50), angle = -90, flow = 'velocity', as.grid = TRUE) #>           [,1]      [,2]      [,3] #> [1,] 0.1929345 0.1725579 0.1232862 #> [2,] 0.3414225 0.2294467 0.1104284"},{"path":"https://cneyens.github.io/raem/reference/element_discharge.html","id":null,"dir":"Reference","previous_headings":"","what":"Get the discharge in or out of the aquifer from an element — element_discharge","title":"Get the discharge in or out of the aquifer from an element — element_discharge","text":"element_discharge() obtains computed discharge aquifer individual analytic element elements given type.","code":""},{"path":"https://cneyens.github.io/raem/reference/element_discharge.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get the discharge in or out of the aquifer from an element — element_discharge","text":"","code":"element_discharge(aem, name = NULL, type = NULL, ...)"},{"path":"https://cneyens.github.io/raem/reference/element_discharge.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get the discharge in or out of the aquifer from an element — element_discharge","text":"aem aem object name character vector name element(s) available aem$elements. type character type (class) element obtain summed discharge . See details. ... ignored","code":""},{"path":"https://cneyens.github.io/raem/reference/element_discharge.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Get the discharge in or out of the aquifer from an element — element_discharge","text":"numeric named vector length length(name) discharge (negative) (positive) aquifer. type specified, single named numeric value total discharge (negative) (positive) aquifer sum individual elements class type.","code":""},{"path":"https://cneyens.github.io/raem/reference/element_discharge.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Get the discharge in or out of the aquifer from an element — element_discharge","text":"Either name type specified. type specified, one type allowed. Possible values 'headwell', 'well', 'linesink', 'headlinesink', 'areasink' headareasink'. elements add remove water aquifer return non-zero discharge value.","code":""},{"path":"https://cneyens.github.io/raem/reference/element_discharge.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Get the discharge in or out of the aquifer from an element — element_discharge","text":"","code":"k <- 10 top <- 10 base <- 0 n <- 0.2 TR <- k * (top - base)  rf <- constant(xc = -500, yc = 0, h = 20) uf <- uniformflow(gradient = 0.002, angle = -45, TR = TR) w1 <- well(xw = 50, yw = 0, Q = 200) w2 <- well(xw = 0, yw = 100, Q = 400) hw <- headwell(xw = -100, yw = 0, hc = 7.5) hls <- headlinesink(x0 = -200, y0 = -150, x1 = 200, y1 = 150, hc = 8) as <- areasink(xc = 0, yc = 0, N = 0.0005, R = 500) m <- aem(k, top, base, n, rf, uf, w1, w2, hw, hls, as)  element_discharge(m, name = c('hls', 'as')) #>       hls        as  #> 3301.0721 -392.6991  element_discharge(m, type = 'well') #> well  #>  600"},{"path":"https://cneyens.github.io/raem/reference/flow.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate flow variables — flow","title":"Calculate flow variables — flow","text":"discharge() computes x, y z components discharge vector aem object given x, y z coordinates. darcy() computes x, y z components Darcy flux vector (also called specific discharge vector) aem object given x, y z coordinates. velocity() computes x, y z components average linear groundwater flow velocity vector aem object given x, y z coordinates. domega() computes complex discharge aem element object given x y coordinates.","code":""},{"path":"https://cneyens.github.io/raem/reference/flow.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate flow variables — flow","text":"","code":"discharge(...)  darcy(...)  velocity(...)  domega(...)  # S3 method for aem discharge(   aem,   x,   y,   z,   as.grid = FALSE,   magnitude = FALSE,   verbose = TRUE,   ... )  # S3 method for aem darcy(aem, x, y, z, as.grid = FALSE, magnitude = FALSE, ...)  # S3 method for aem velocity(aem, x, y, z, as.grid = FALSE, magnitude = FALSE, R = 1, ...)  # S3 method for aem domega(aem, x, y, as.grid = FALSE, ...)  # S3 method for element domega(element, x, y, ...)"},{"path":"https://cneyens.github.io/raem/reference/flow.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate flow variables — flow","text":"... ignored arguments passed velocity() darcy() discharge(). aem aem object x numeric x coordinates evaluate y numeric y coordinates evaluate z numeric z coordinates evaluate .grid logical, matrix returned? Defaults FALSE. See details. magnitude logical, magnitude flow vector returned well? Default FALSE. See details. verbose logical, TRUE (default), warnings regards setting Qz NA printed. See details. R numeric, retardation coefficient. Defaults 1 (retardation). element analytic element class element","code":""},{"path":"https://cneyens.github.io/raem/reference/flow.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate flow variables — flow","text":"discharge(), matrix number rows equal number points evaluate discharge vector , columns Qx, Qy Qz corresponding x, y z components discharge vector coordinates x, y z. .grid = TRUE, array dimensions c(length(y), length(x), length(z), 3) described marginal vectors x, y z (columns, rows third dimension) containing x, y z components discharge vector (Qx, Qy Qz) fourth dimension. x component discharge() real value domega(), y component negative imaginary component z component calculated based area-sink strengths /curvature phreatic surface. magnitude = TRUE, last dimension returned array expanded include magnitude discharge/darcy/velocity vector, calculated sqrt(Qx^2 + Qy^2 + Qz^2) (sqrt(qx^2 + qy^2 + qz^2) sqrt(vx^2 + vy^2 + vz^2), respectively). darcy(), discharge() x, y z components Darcy flux vector (qx, qy qz). value computed dividing values discharge() saturated thickness x, y z. velocity(), discharge() x, y z components average linear groundwater flow velocity vector (vx, vy vz). values computed dividing darcy() values effective porosity (aem$n) retardation coefficient R. domega(),  vector length(x) (equal length(y)) complex discharge values x y, .grid = TRUE, matrix dimensions c(length(y), length(x)) described marginal vectors x y containing complex discharge values grid points. domega() derivative omega() x y directions.","code":""},{"path":"https://cneyens.github.io/raem/reference/flow.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Calculate flow variables — flow","text":"discharge(), darcy() velocity() method object class element aem object required obtain aquifer base top. z coordinate saturated aquifer level (.e. water-table unconfined conditions aquifer top confined conditions), aquifer base, Qz values set NA warning (verbose = TRUE). Qx Qy values set NA, convenience specifying z coordinate lateral flow interest.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/flow.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate flow variables — flow","text":"","code":"w <- well(xw = 55, yw = 0, Q = 200) uf <- uniformflow(gradient = 0.002, angle = -45, TR = 100) as <- areasink(xc = 0, yc = 0, N = 0.001, R = 500) rf <- constant(xc = -1000, yc = 1000, hc = 10) ml <- aem(k = 10, top = 10, base = -15, n = 0.2, w, uf, as, rf)   xg <- seq(-100, 100, length = 5) yg <- seq(-75, 75, length = 3)  # Discharge vector discharge(ml, c(150, 0), c(80, -80), z = -10) #>              Qx         Qy           Qz #> [1,] 0.02037961 -0.2665091 -0.005060767 #> [2,] 0.32717248  0.0887621 -0.005097869 discharge(ml, c(150, 0), c(80, -80), z = c(2, 5), magnitude = TRUE) #>              Qx         Qy          Qz         Q #> [1,] 0.02037961 -0.2665091 -0.01720661 0.2678405 #> [2,] 0.32717248  0.0887621 -0.02039148 0.3396121 discharge(ml, xg, yg, z = 2, as.grid = TRUE) #> , , 1, Qx #>  #>           [,1]      [,2]      [,3]      [,4]         [,5] #> [1,] 0.2578228 0.3171573 0.3438149 0.1945904  0.004180247 #> [2,] 0.2967826 0.4195736 0.7201666 6.5326191 -0.515933946 #> [3,] 0.2578228 0.3171573 0.3438149 0.1945904  0.004180247 #>  #> , , 1, Qy #>  #>             [,1]        [,2]        [,3]       [,4]       [,5] #> [1,] -0.18443819 -0.24730419 -0.37991259 -0.5264566 -0.4159899 #> [2,] -0.14142136 -0.14142136 -0.14142136 -0.1414214 -0.1414214 #> [3,] -0.09840452 -0.03553852  0.09706987  0.2436139  0.1331472 #>  #> , , 1, Qz #>  #>             [,1]        [,2]        [,3]        [,4]        [,5] #> [1,] -0.01728591 -0.01746242 -0.01775486 -0.01791021 -0.01750075 #> [2,] -0.01730880 -0.01756345 -0.01856240 -0.14449874 -0.01783670 #> [3,] -0.01721822 -0.01729328 -0.01736962 -0.01728292 -0.01705172 #>  discharge(ml, c(150, 0), c(80, -80), z = ml$top + c(-5, 0.5)) # NA for z > water-table #> Warning: Setting Qz values to NA for z above saturated aquifer level or below aquifer base #>              Qx         Qy          Qz #> [1,] 0.02037961 -0.2665091 -0.02024307 #> [2,] 0.32717248  0.0887621          NA  # Darcy flux darcy(ml, c(150, 0), c(80, -80), c(0, 5), magnitude = TRUE) #>               qx           qy            qz          q #> [1,] 0.000840556 -0.010992156 -0.0006261932 0.01104202 #> [2,] 0.013502552  0.003663251 -0.0008415652 0.01401594  # Velocity velocity(ml, c(150, 0), c(80, -80), c(0, 5), magnitude = TRUE, R = 5) #>               vx           vy            vz          v #> [1,] 0.000840556 -0.010992156 -0.0006261932 0.01104202 #> [2,] 0.013502552  0.003663251 -0.0008415652 0.01401594  # Complex discharge domega(ml, c(150, 0), c(80, -80)) #> [1] 0.02037961+0.2665091i 0.32717248-0.0887621i  # Complex discharge for elements domega(w, c(150, 0), c(80, -80)) #> [1] -0.1960417+0.1650878i  0.1857511-0.2701835i"},{"path":"https://cneyens.github.io/raem/reference/flow_through_line.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate the total flow passing through a line — flow_through_line","title":"Calculate the total flow passing through a line — flow_through_line","text":"flow_through_line() computes integrated flow passing straight line right angle.","code":""},{"path":"https://cneyens.github.io/raem/reference/flow_through_line.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate the total flow passing through a line — flow_through_line","text":"","code":"flow_through_line(   aem,   x0,   y0,   x1,   y1,   flow = c(\"discharge\", \"darcy\"),   split = FALSE,   ... )"},{"path":"https://cneyens.github.io/raem/reference/flow_through_line.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate the total flow passing through a line — flow_through_line","text":"aem aem object x0 numeric, starting x location line y0 numeric, starting y location line x1 numeric, ending x location line y1 numeric, ending y location line flow character specifying flow variable use. Possible values discharge (default) darcy. See flow(). split logical, flow split positive negative flows summed (default)? See details. ... ignored","code":""},{"path":"https://cneyens.github.io/raem/reference/flow_through_line.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate the total flow passing through a line — flow_through_line","text":"split = FALSE, single value total flow variable flow passing line right angle. split = TRUE named vector total positive total negative value flow passing line.","code":""},{"path":"https://cneyens.github.io/raem/reference/flow_through_line.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Calculate the total flow passing through a line — flow_through_line","text":"flow computed normal line integrated along line length using stats::integrate(). flow value positive going left looking direction line (.e. left going x0-y0 x1-y1). split = FALSE (default), single value returned sum positive negative flows perpendicular line. split = TRUE, positive negative component total flow line returned. line corresponds line element, integration might fail. Try perturbate line vertices slightly case.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/flow_through_line.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate the total flow passing through a line — flow_through_line","text":"","code":"rf <- constant(-1000, 0, hc = 10) uf <- uniformflow(TR = 100, gradient = 0.001, angle = -45) m <- aem(k = 10, top = 10, base = 0, n = 0.2, rf, uf)  xg <- seq(-500, 500, l=100); yg <- seq(-300, 300, l=100) contours(m, xg, yg, col='dodgerblue', nlevels=20)  x0 <- -200 y0 <- -50 x1 <- 300 y1 <- 100 lines(matrix(c(x0, y0, x1, y1), ncol = 2, byrow = TRUE))   flow_through_line(m, x0, y0, x1, y1) #> [1] -45.96194 flow_through_line(m, x1, y1, x0, y0) # reverse direction of line #> [1] 45.96194  w <- well(125, 200, 150) m <- aem(k = 10, top = 10, base = 0, n = 0.2, rf, uf, w) contours(m, xg, yg, col='dodgerblue', nlevels=20) lines(matrix(c(x0, y0, x1, y1), ncol = 2, byrow = TRUE))   flow_through_line(m, x0, y0, x1, y1, flow = 'darcy') #> [1] 0.1633028 flow_through_line(m, x0, y0, x1, y1, flow = 'darcy', split = TRUE) #>  positive  negative  #>  1.369686 -1.206383"},{"path":"https://cneyens.github.io/raem/reference/head_to_potential.html","id":null,"dir":"Reference","previous_headings":"","what":"Convert hydraulic head to potential and vice versa — head_to_potential","title":"Convert hydraulic head to potential and vice versa — head_to_potential","text":"head_to_potential() calculates discharge potential hydraulic head. potential_to_head() calculates hydraulic head discharge potential.","code":""},{"path":"https://cneyens.github.io/raem/reference/head_to_potential.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Convert hydraulic head to potential and vice versa — head_to_potential","text":"","code":"head_to_potential(aem, h, ...)  potential_to_head(aem, phi, na.below = TRUE, ...)"},{"path":"https://cneyens.github.io/raem/reference/head_to_potential.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Convert hydraulic head to potential and vice versa — head_to_potential","text":"aem aem object h numeric hydraulic head values vector matrix. ... ignored phi numeric discharge potential values vector matrix. na.logical indicating calculated head values aquifer base set NA. Defaults TRUE. See details.","code":""},{"path":"https://cneyens.github.io/raem/reference/head_to_potential.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Convert hydraulic head to potential and vice versa — head_to_potential","text":"head_to_potential() returns discharge potentials calculated h, structure h. potential_to_head() returns hydraulic heads calculated phi, structure phi. conversion potential head vice versa different confined (constant saturated thickness) unconfined (variable saturated thickness) aquifers. na.= FALSE, negative potentials can converted hydraulic heads flow unconfined (aem$type = 'variable'). resulting heads aquifer base. may useful use cases, e.g. preliminary model construction internal functions. cases however, values set NA (default behavior) since analytic elements continue extract inject water even though saturated thickness aquifer negative, realistic. cases, setting aem$type = 'confined' might prove useful. Also note heads aquifer base correctly re-converted potentials using head_to_potential(). , caution taken setting na.= FALSE.","code":""},{"path":"https://cneyens.github.io/raem/reference/head_to_potential.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Convert hydraulic head to potential and vice versa — head_to_potential","text":"","code":"k <- 10 top <- 10; base <- 0 uf <- uniformflow(TR = 100, gradient = 0.001, angle = -45) rf <- constant(TR, xc = -1000, yc = 0, hc = 10) w1 <- well(200, 50, Q = 250) m <- aem(k, top, base, n = 0.2, uf, rf, w1, type = 'variable') # variable saturated thickness mc <- aem(k, top, base, n = 0.2, uf, rf, w1, type = 'confined') # constant saturated thickness xg <- seq(-500, 500, length = 100) yg <- seq(-250, 250, length = 100)  h <- heads(m, x = xg, y = yg, as.grid = TRUE) hc <- heads(mc, x = xg, y = yg, as.grid = TRUE) head_to_potential(m, h) #>            [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8] #>   [1,] 462.4030 461.1546 459.8996 458.6378 457.3691 456.0933 454.8101 453.5196 #>   [2,] 461.9708 460.7204 459.4633 458.1993 456.9283 455.6500 454.3644 453.0712 #>   [3,] 461.5403 460.2879 459.0287 457.7626 456.4892 455.2086 453.9206 452.6248 #>   [4,] 461.1115 459.8571 458.5959 457.3276 456.0520 454.7691 453.4786 452.1804 #>   [5,] 460.6844 459.4281 458.1648 456.8944 455.6167 454.3315 453.0386 451.7379 #>   [6,] 460.2589 459.0007 457.7355 456.4630 455.1832 453.8958 452.6006 451.2974 #>   [7,] 459.8352 458.5752 457.3080 456.0335 454.7516 453.4620 452.1645 450.8590 #>   [8,] 459.4132 458.1514 456.8823 455.6059 454.3219 453.0302 451.7305 450.4226 #>   [9,] 458.9930 457.7294 456.4585 455.1802 453.8942 452.6003 451.2985 449.9884 #>  [10,] 458.5745 457.3092 456.0365 454.7563 453.4684 452.1725 450.8685 449.5562 #>  [11,] 458.1579 456.8909 455.6165 454.3344 453.0446 451.7468 450.4407 449.1262 #>  [12,] 457.7430 456.4744 455.1983 453.9145 452.6228 451.3230 450.0150 448.6984 #>  [13,] 457.3300 456.0598 454.7820 453.4965 452.2030 450.9014 449.5913 448.2727 #>  [14,] 456.9188 455.6471 454.3677 453.0805 451.7853 450.4818 449.1699 447.8493 #>  [15,] 456.5095 455.2362 453.9553 452.6665 451.3696 450.0644 448.7506 447.4281 #>  [16,] 456.1020 454.8273 453.5449 452.2546 450.9560 449.6491 448.3335 447.0091 #>  [17,] 455.6964 454.4204 453.1365 451.8446 450.5445 449.2360 447.9187 446.5925 #>  [18,] 455.2928 454.0154 452.7301 451.4368 450.1352 448.8250 447.5061 446.1781 #>  [19,] 454.8910 453.6123 452.3257 451.0310 449.7279 448.4162 447.0957 445.7661 #>  [20,] 454.4912 453.2113 451.9234 450.6273 449.3228 448.0097 446.6876 445.3564 #>  [21,] 454.0933 452.8122 451.5231 450.2257 448.9199 447.6053 446.2818 444.9490 #>  [22,] 453.6973 452.4151 451.1248 449.8263 448.5191 447.2033 445.8783 444.5441 #>  [23,] 453.3033 452.0201 450.7287 449.4289 448.1206 446.8034 445.4772 444.1415 #>  [24,] 452.9113 451.6270 450.3346 449.0337 447.7243 446.4059 445.0784 443.7414 #>  [25,] 452.5213 451.2360 449.9426 448.6407 447.3301 446.0106 444.6819 443.3437 #>  [26,] 452.1333 450.8471 449.5527 448.2499 446.9383 445.6177 444.2878 442.9484 #>  [27,] 451.7472 450.4602 449.1650 447.8612 446.5486 445.2270 443.8961 442.5556 #>  [28,] 451.3632 450.0754 448.7793 447.4747 446.1612 444.8387 443.5068 442.1653 #>  [29,] 450.9812 449.6927 448.3959 447.0904 445.7761 444.4527 443.1199 441.7774 #>  [30,] 450.6012 449.3121 448.0145 446.7083 445.3933 444.0691 442.7355 441.3921 #>  [31,] 450.2233 448.9335 447.6353 446.3285 445.0127 443.6878 442.3534 441.0093 #>  [32,] 449.8474 448.5571 447.2583 445.9509 444.6345 443.3089 441.9738 440.6289 #>  [33,] 449.4736 448.1827 446.8835 445.5755 444.2585 442.9324 441.5967 440.2511 #>  [34,] 449.1018 447.8105 446.5108 445.2023 443.8849 442.5582 441.2220 439.8759 #>  [35,] 448.7320 447.4404 446.1403 444.8314 443.5136 442.1864 440.8497 439.5032 #>  [36,] 448.3644 447.0724 445.7720 444.4628 443.1446 441.8171 440.4800 439.1330 #>  [37,] 447.9988 446.7066 445.4059 444.0964 442.7779 441.4501 440.1127 438.7654 #>  [38,] 447.6352 446.3428 445.0419 443.7323 442.4136 441.0855 439.7479 438.4003 #>  [39,] 447.2737 445.9812 444.6802 443.3704 442.0515 440.7233 439.3855 438.0378 #>  [40,] 446.9143 445.6218 444.3207 443.0108 441.6918 440.3636 439.0257 437.6778 #>  [41,] 446.5570 445.2644 443.9633 442.6534 441.3345 440.0062 438.6683 437.3205 #>  [42,] 446.2018 444.9092 443.6082 442.2983 440.9795 439.6512 438.3134 436.9656 #>  [43,] 445.8486 444.5562 443.2552 441.9455 440.6268 439.2987 437.9610 436.6134 #>  [44,] 445.4974 444.2052 442.9045 441.5949 440.2764 438.9485 437.6111 436.2637 #>  [45,] 445.1484 443.8564 442.5559 441.2466 439.9284 438.6008 437.2636 435.9166 #>  [46,] 444.8014 443.5097 442.2095 440.9006 439.5827 438.2554 436.9186 435.5720 #>  [47,] 444.4565 443.1651 441.8653 440.5568 439.2393 437.9125 436.5761 435.2299 #>  [48,] 444.1136 442.8227 441.5233 440.2152 438.8982 437.5719 436.2361 434.8904 #>  [49,] 443.7728 442.4824 441.1835 439.8759 438.5594 437.2337 435.8985 434.5535 #>  [50,] 443.4340 442.1441 440.8458 439.5389 438.2230 436.8979 435.5634 434.2190 #>  [51,] 443.0973 441.8080 440.5103 439.2040 437.8888 436.5645 435.2307 433.8871 #>  [52,] 442.7626 441.4740 440.1770 438.8714 437.5569 436.2334 434.9004 433.5577 #>  [53,] 442.4300 441.1420 439.8458 438.5410 437.2273 435.9046 434.5726 433.2308 #>  [54,] 442.0993 440.8122 439.5167 438.2128 436.9000 435.5782 434.2471 432.9064 #>  [55,] 441.7707 440.4844 439.1898 437.8868 436.5750 435.2542 433.9241 432.5845 #>  [56,] 441.4441 440.1587 438.8650 437.5629 436.2521 434.9324 433.6035 432.2650 #>  [57,] 441.1195 439.8350 438.5423 437.2413 435.9316 434.6130 433.2852 431.9480 #>  [58,] 440.7968 439.5133 438.2217 436.9218 435.6132 434.2958 432.9693 431.6334 #>  [59,] 440.4762 439.1937 437.9032 436.6044 435.2971 433.9809 432.6557 431.3212 #>  [60,] 440.1575 438.8762 437.5868 436.2892 434.9831 433.6683 432.3445 431.0114 #>  [61,] 439.8407 438.5606 437.2725 435.9761 434.6714 433.3579 432.0356 430.7040 #>  [62,] 439.5259 438.2470 436.9602 435.6652 434.3618 433.0498 431.7290 430.3990 #>  [63,] 439.2131 437.9354 436.6499 435.3563 434.0544 432.7439 431.4246 430.0963 #>  [64,] 438.9021 437.6258 436.3416 435.0495 433.7491 432.4402 431.1225 429.7960 #>  [65,] 438.5931 437.3181 436.0354 434.7447 433.4459 432.1386 430.8227 429.4979 #>  [66,] 438.2859 437.0124 435.7312 434.4420 433.1448 431.8392 430.5251 429.2022 #>  [67,] 437.9806 436.7086 435.4289 434.1414 432.8458 431.5420 430.2297 428.9087 #>  [68,] 437.6772 436.4067 435.1286 433.8427 432.5489 431.2469 429.9365 428.6174 #>  [69,] 437.3756 436.1066 434.8302 433.5460 432.2540 430.9539 429.6454 428.3284 #>  [70,] 437.0758 435.8085 434.5337 433.2514 431.9611 430.6629 429.3565 428.0415 #>  [71,] 436.7779 435.5122 434.2392 432.9586 431.6703 430.3740 429.0696 427.7569 #>  [72,] 436.4817 435.2178 433.9465 432.6678 431.3814 430.0872 428.7849 427.4743 #>  [73,] 436.1874 434.9252 433.6557 432.3789 431.0945 429.8024 428.5022 427.1939 #>  [74,] 435.8947 434.6343 433.3668 432.0919 430.8096 429.5195 428.2216 426.9156 #>  [75,] 435.6039 434.3453 433.0797 431.8068 430.5265 429.2387 427.9430 426.6394 #>  [76,] 435.3147 434.0580 432.7944 431.5235 430.2454 428.9598 427.6664 426.3652 #>  [77,] 435.0273 433.7725 432.5109 431.2421 429.9661 428.6828 427.3918 426.0930 #>  [78,] 434.7415 433.4887 432.2291 430.9625 429.6887 428.4077 427.1191 425.8229 #>  [79,] 434.4574 433.2066 431.9491 430.6847 429.4132 428.1344 426.8483 425.5546 #>  [80,] 434.1750 432.9262 431.6708 430.4086 429.1394 427.8630 426.5794 425.2884 #>  [81,] 433.8942 432.6475 431.3942 430.1342 428.8674 427.5935 426.3124 425.0240 #>  [82,] 433.6150 432.3704 431.1193 429.8616 428.5971 427.3257 426.0472 424.7615 #>  [83,] 433.3374 432.0950 430.8461 429.5907 428.3286 427.0597 425.7838 424.5008 #>  [84,] 433.0613 431.8211 430.5745 429.3215 428.0618 426.7955 425.5222 424.2420 #>  [85,] 432.7869 431.5488 430.3045 429.0539 427.7967 426.5330 425.2624 423.9849 #>  [86,] 432.5139 431.2781 430.0361 428.7879 427.5333 426.2721 425.0043 423.7297 #>  [87,] 432.2424 431.0089 429.7693 428.5235 427.2715 426.0129 424.7479 423.4761 #>  [88,] 431.9725 430.7413 429.5040 428.2607 427.0112 425.7554 424.4931 423.2243 #>  [89,] 431.7040 430.4751 429.2403 427.9995 426.7526 425.4995 424.2400 422.9741 #>  [90,] 431.4369 430.2104 428.9780 427.7398 426.4955 425.2451 423.9885 422.7256 #>  [91,] 431.1713 429.9471 428.7173 427.4816 426.2400 424.9924 423.7386 422.4787 #>  [92,] 430.9071 429.6853 428.4579 427.2248 425.9859 424.7411 423.4903 422.2333 #>  [93,] 430.6442 429.4249 428.2000 426.9696 425.7334 424.4914 423.2435 421.9896 #>  [94,] 430.3827 429.1659 427.9435 426.7157 425.4822 424.2431 422.9981 421.7473 #>  [95,] 430.1226 428.9082 427.6884 426.4633 425.2326 423.9963 422.7543 421.5065 #>  [96,] 429.8638 428.6518 427.4347 426.2122 424.9843 423.7509 422.5119 421.2672 #>  [97,] 429.6062 428.3968 427.1823 425.9625 424.7374 423.5069 422.2709 421.0294 #>  [98,] 429.3499 428.1431 426.9312 425.7141 424.4918 423.2642 422.0313 420.7929 #>  [99,] 429.0949 427.8906 426.6813 425.4670 424.2475 423.0229 421.7930 420.5578 #> [100,] 428.8411 427.6394 426.4328 425.2212 424.0046 422.7829 421.5561 420.3241 #>            [,9]    [,10]    [,11]    [,12]    [,13]    [,14]    [,15]    [,16] #>   [1,] 452.2214 450.9155 449.6016 448.2796 446.9493 445.6104 444.2628 442.9063 #>   [2,] 451.7704 450.4616 449.1447 447.8196 446.4860 445.1438 443.7926 442.4324 #>   [3,] 451.3213 450.0097 448.6899 447.3618 446.0250 444.6794 443.3247 441.9609 #>   [4,] 450.8742 449.5599 448.2372 446.9060 445.5661 444.2172 442.8591 441.4917 #>   [5,] 450.4291 449.1121 447.7866 446.4525 445.1095 443.7574 442.3959 441.0249 #>   [6,] 449.9861 448.6665 447.3382 446.0012 444.6551 443.2998 441.9351 440.5605 #>   [7,] 449.5452 448.2230 446.8920 445.5521 444.2031 442.8447 441.4766 440.0987 #>   [8,] 449.1064 447.7816 446.4480 445.1054 443.7534 442.3920 441.0207 439.6394 #>   [9,] 448.6698 447.3425 446.0063 444.6609 443.3061 441.9417 440.5673 439.1827 #>  [10,] 448.2353 446.9056 445.5669 444.2188 442.8613 441.4939 440.1164 438.7286 #>  [11,] 447.8030 446.4710 445.1297 443.7791 442.4188 441.0486 439.6681 438.2772 #>  [12,] 447.3730 446.0386 444.6950 443.3418 441.9789 440.6059 439.2225 437.8284 #>  [13,] 446.9452 445.6086 444.2626 442.9070 441.5414 440.1657 438.7795 437.3825 #>  [14,] 446.5197 445.1809 443.8326 442.4746 441.1066 439.7282 438.3392 436.9393 #>  [15,] 446.0964 444.7555 443.4051 442.0447 440.6743 439.2934 437.9017 436.4989 #>  [16,] 445.6756 444.3326 442.9800 441.6174 440.2446 438.8612 437.4669 436.0614 #>  [17,] 445.2570 443.9121 442.5574 441.1926 439.8175 438.4318 437.0350 435.6268 #>  [18,] 444.8408 443.4940 442.1373 440.7705 439.3932 438.0051 436.6058 435.1951 #>  [19,] 444.4270 443.0784 441.7198 440.3509 438.9715 437.5812 436.1796 434.7664 #>  [20,] 444.0157 442.6652 441.3048 439.9340 438.5525 437.1601 435.7562 434.3407 #>  [21,] 443.6067 442.2546 440.8924 439.5197 438.1363 436.7418 435.3358 433.9180 #>  [22,] 443.2002 441.8465 440.4826 439.1082 437.7229 436.3264 434.9184 433.4984 #>  [23,] 442.7962 441.4410 440.0755 438.6993 437.3123 435.9139 434.5039 433.0818 #>  [24,] 442.3947 441.0380 439.6709 438.2932 436.9045 435.5044 434.0925 432.6684 #>  [25,] 441.9957 440.6376 439.2691 437.8899 436.4995 435.0977 433.6841 432.2581 #>  [26,] 441.5992 440.2398 438.8699 437.4893 436.0974 434.6940 433.2787 431.8510 #>  [27,] 441.2052 439.8446 438.4735 437.0915 435.6982 434.2934 432.8765 431.4471 #>  [28,] 440.8138 439.4521 438.0798 436.6965 435.3019 433.8957 432.4773 431.0464 #>  [29,] 440.4250 439.0622 437.6888 436.3043 434.9085 433.5010 432.0813 430.6490 #>  [30,] 440.0387 438.6750 437.3005 435.9150 434.5181 433.1094 431.6884 430.2548 #>  [31,] 439.6550 438.2904 436.9150 435.5286 434.1306 432.7208 431.2987 429.8639 #>  [32,] 439.2739 437.9085 436.5323 435.1450 433.7461 432.3353 430.9122 429.4763 #>  [33,] 438.8955 437.5293 436.1524 434.7642 433.3646 431.9529 430.5289 429.0920 #>  [34,] 438.5196 437.1528 435.7752 434.3864 432.9860 431.5736 430.1487 428.7110 #>  [35,] 438.1464 436.7791 435.4009 434.0115 432.6105 431.1974 429.7718 428.3334 #>  [36,] 437.7758 436.4080 435.0294 433.6395 432.2379 430.8243 429.3982 427.9591 #>  [37,] 437.4078 436.0397 434.6607 433.2704 431.8684 430.4543 429.0277 427.5882 #>  [38,] 437.0425 435.6741 434.2948 432.9042 431.5019 430.0875 428.6605 427.2206 #>  [39,] 436.6798 435.3112 433.9317 432.5409 431.1384 429.7237 428.2966 426.8564 #>  [40,] 436.3198 434.9511 433.5715 432.1806 430.7779 429.3632 427.9359 426.4955 #>  [41,] 435.9624 434.5937 433.2141 431.8231 430.4205 429.0057 427.5784 426.1381 #>  [42,] 435.6076 434.2390 432.8595 431.4687 430.0661 428.6514 427.2242 425.7840 #>  [43,] 435.2555 433.8871 432.5077 431.1171 429.7147 428.3003 426.8733 425.4333 #>  [44,] 434.9061 433.5379 432.1588 430.7684 429.3664 427.9522 426.5256 425.0859 #>  [45,] 434.5593 433.1914 431.8127 430.4227 429.0211 427.6073 426.1811 424.7419 #>  [46,] 434.2151 432.8477 431.4694 430.0799 428.6788 427.2656 425.8399 424.4013 #>  [47,] 433.8736 432.5067 431.1290 429.7400 428.3395 426.9269 425.5019 424.0640 #>  [48,] 433.5346 432.1684 430.7913 429.4030 428.0032 426.5913 425.1671 423.7301 #>  [49,] 433.1983 431.8328 430.4564 429.0689 427.6699 426.2589 424.8356 423.3995 #>  [50,] 432.8647 431.4999 430.1243 428.7377 427.3395 425.9295 424.5072 423.0722 #>  [51,] 432.5336 431.1696 429.7950 428.4093 427.0122 425.6032 424.1820 422.7482 #>  [52,] 432.2051 430.8421 429.4684 428.0838 426.6878 425.2800 423.8600 422.4275 #>  [53,] 431.8791 430.5172 429.1446 427.7611 426.3663 424.9598 423.5412 422.1100 #>  [54,] 431.5558 430.1950 428.8236 427.4413 426.0478 424.6426 423.2254 421.7958 #>  [55,] 431.2350 429.8754 428.5052 427.1243 425.7322 424.3285 422.9128 421.4848 #>  [56,] 430.9167 429.5584 428.1896 426.8101 425.4194 424.0173 422.6033 421.1770 #>  [57,] 430.6010 429.2440 427.8767 426.4986 425.1096 423.7091 422.2968 420.8724 #>  [58,] 430.2878 428.9322 427.5664 426.1900 424.8026 423.4038 421.9934 420.5710 #>  [59,] 429.9771 428.6230 427.2588 425.8840 424.4984 423.1015 421.6931 420.2726 #>  [60,] 429.6688 428.3164 426.9538 425.5808 424.1970 422.8021 421.3957 419.9774 #>  [61,] 429.3630 428.0122 426.6514 425.2802 423.8984 422.5055 421.1012 419.6852 #>  [62,] 429.0596 427.7106 426.3516 424.9824 423.6025 422.2118 420.8097 419.3961 #>  [63,] 428.7587 427.4115 426.0544 424.6872 423.3094 421.9209 420.5212 419.1099 #>  [64,] 428.4601 427.1148 425.7597 424.3946 423.0190 421.6328 420.2355 418.8268 #>  [65,] 428.1640 426.8206 425.4676 424.1046 422.7313 421.3474 419.9526 418.5466 #>  [66,] 427.8701 426.5288 425.1779 423.8171 422.4462 421.0648 419.6726 418.2692 #>  [67,] 427.5787 426.2394 424.8907 423.5322 422.1637 420.7848 419.3953 417.9948 #>  [68,] 427.2895 425.9524 424.6060 423.2499 421.8838 420.5076 419.1208 417.7232 #>  [69,] 427.0026 425.6677 424.3236 422.9700 421.6065 420.2329 418.8490 417.4543 #>  [70,] 426.7179 425.3854 424.0437 422.6925 421.3317 419.9609 418.5799 417.1883 #>  [71,] 426.4355 425.1053 423.7661 422.4175 421.0594 419.6914 418.3134 416.9249 #>  [72,] 426.1553 424.8275 423.4908 422.1449 420.7895 419.4245 418.0495 416.6642 #>  [73,] 425.8772 424.5519 423.2178 421.8746 420.5221 419.1600 417.7881 416.4062 #>  [74,] 425.6014 424.2786 422.9471 421.6067 420.2571 418.8980 417.5293 416.1507 #>  [75,] 425.3276 424.0074 422.6786 421.3410 419.9944 418.6385 417.2730 415.8978 #>  [76,] 425.0559 423.7384 422.4124 421.0776 419.7340 418.3813 417.0191 415.6474 #>  [77,] 424.7863 423.4715 422.1483 420.8165 419.4759 418.1264 416.7676 415.3994 #>  [78,] 424.5188 423.2067 421.8863 420.5575 419.2201 417.8738 416.5185 415.1539 #>  [79,] 424.2532 422.9439 421.6264 420.3007 418.9665 417.6235 416.2717 414.9108 #>  [80,] 423.9897 422.6832 421.3687 420.0460 418.7150 417.3755 416.0272 414.6700 #>  [81,] 423.7280 422.4244 421.1129 419.7934 418.4657 417.1296 415.7849 414.4314 #>  [82,] 423.4683 422.1676 420.8592 419.5429 418.2185 416.8859 415.5448 414.1951 #>  [83,] 423.2105 421.9128 420.6075 419.2944 417.9733 416.6442 415.3069 413.9611 #>  [84,] 422.9546 421.6598 420.3576 419.0478 417.7302 416.4047 415.0710 413.7291 #>  [85,] 422.7004 421.4088 420.1097 418.8032 417.4891 416.1671 414.8373 413.4993 #>  [86,] 422.4481 421.1595 419.8637 418.5605 417.2499 415.9316 414.6055 413.2715 #>  [87,] 422.1976 420.9121 419.6195 418.3197 417.0126 415.6980 414.3758 413.0458 #>  [88,] 421.9487 420.6664 419.3771 418.0807 416.7772 415.4663 414.1479 412.8220 #>  [89,] 421.7016 420.4224 419.1365 417.8435 416.5436 415.2364 413.9220 412.6002 #>  [90,] 421.4562 420.1802 418.8976 417.6081 416.3118 415.0084 413.6979 412.3802 #>  [91,] 421.2124 419.9396 418.6604 417.3744 416.0817 414.7822 413.4757 412.1621 #>  [92,] 420.9702 419.7007 418.4248 417.1424 415.8534 414.5577 413.2552 411.9457 #>  [93,] 420.7296 419.4634 418.1909 416.9121 415.6268 414.3349 413.0364 411.7312 #>  [94,] 420.4905 419.2276 417.9586 416.6833 415.4018 414.1138 412.8193 411.5183 #>  [95,] 420.2529 418.9934 417.7278 416.4562 415.1783 413.8943 412.6038 411.3070 #>  [96,] 420.0169 418.7607 417.4986 416.2306 414.9565 413.6763 412.3900 411.0974 #>  [97,] 419.7822 418.5294 417.2709 416.0065 414.7362 413.4599 412.1777 410.8894 #>  [98,] 419.5490 418.2996 417.0446 415.7838 414.5173 413.2451 411.9669 410.6829 #>  [99,] 419.3172 418.0712 416.8197 415.5626 414.3000 413.0316 411.7576 410.4779 #> [100,] 419.0868 417.8442 416.5962 415.3428 414.0840 412.8196 411.5497 410.2743 #>           [,17]    [,18]    [,19]    [,20]    [,21]    [,22]    [,23]    [,24] #>   [1,] 441.5407 440.1658 438.7813 437.3871 435.9830 434.5686 433.1439 431.7085 #>   [2,] 441.0629 439.6839 438.2952 436.8965 435.4876 434.0683 432.6383 431.1974 #>   [3,] 440.5875 439.2045 437.8115 436.4083 434.9948 433.5705 432.1354 430.6891 #>   [4,] 440.1145 438.7275 437.3304 435.9228 434.5046 433.0756 431.6353 430.1836 #>   [5,] 439.6440 438.2531 436.8518 435.4400 434.0172 432.5834 431.1381 429.6811 #>   [6,] 439.1760 437.7812 436.3759 434.9598 433.5326 432.0941 430.6438 429.1816 #>   [7,] 438.7106 437.3120 435.9027 434.4824 433.0509 431.6076 430.1525 428.6851 #>   [8,] 438.2477 436.8455 435.4323 434.0079 432.5720 431.1242 429.6643 428.1918 #>   [9,] 437.7876 436.3817 434.9647 433.5362 432.0961 430.6438 429.1792 427.7017 #>  [10,] 437.3301 435.9206 434.4999 433.0675 431.6232 430.1666 428.6972 427.2149 #>  [11,] 436.8754 435.4624 434.0380 432.6018 431.1534 429.6924 428.2186 426.7314 #>  [12,] 436.4234 435.0071 433.5791 432.1391 430.6867 429.2216 427.7433 426.2514 #>  [13,] 435.9743 434.5546 433.1232 431.6795 430.2232 428.7540 427.2714 425.7749 #>  [14,] 435.5280 434.1052 432.6703 431.2230 429.7630 428.2897 426.8029 425.3020 #>  [15,] 435.0847 433.6587 432.2205 430.7698 429.3060 427.8289 426.3379 424.8326 #>  [16,] 434.6443 433.2153 431.7739 430.3197 428.8524 427.3715 425.8765 424.3670 #>  [17,] 434.2069 432.7749 431.3304 429.8730 428.4022 426.9177 425.4188 423.9052 #>  [18,] 433.7725 432.3377 430.8902 429.4296 427.9555 426.4674 424.9648 423.4471 #>  [19,] 433.3412 431.9036 430.4532 428.9896 427.5122 426.0207 424.5145 422.9930 #>  [20,] 432.9130 431.4728 430.0196 428.5530 427.0725 425.5777 424.0680 422.5428 #>  [21,] 432.4879 431.0452 429.5893 428.1199 426.6364 425.1384 423.6253 422.0966 #>  [22,] 432.0660 430.6208 429.1624 427.6903 426.2040 424.7029 423.1866 421.6545 #>  [23,] 431.6473 430.1998 428.7389 427.2642 425.7752 424.2713 422.7519 421.2164 #>  [24,] 431.2318 429.7821 428.3189 426.8418 425.3501 423.8434 422.3211 420.7826 #>  [25,] 430.8195 429.3678 427.9024 426.4229 424.9288 423.4195 421.8944 420.3530 #>  [26,] 430.4106 428.9569 427.4894 426.0078 424.5113 422.9995 421.4718 419.9276 #>  [27,] 430.0049 428.5494 427.0800 425.5963 424.0976 422.5836 421.0534 419.5065 #>  [28,] 429.6026 428.1453 426.6742 425.1885 423.6878 422.1716 420.6391 419.0898 #>  [29,] 429.2037 427.7448 426.2719 424.7845 423.2819 421.7637 420.2291 418.6775 #>  [30,] 428.8081 427.3478 425.8733 424.3842 422.8799 421.3598 419.8233 418.2696 #>  [31,] 428.4159 426.9542 425.4784 423.9878 422.4819 420.9601 419.4217 417.8661 #>  [32,] 428.0272 426.5643 425.0871 423.5952 422.0879 420.5645 419.0245 417.4672 #>  [33,] 427.6418 426.1779 424.6996 423.2064 421.6978 420.1731 418.6317 417.0728 #>  [34,] 427.2600 425.7950 424.3158 422.8215 421.3118 419.7859 418.2431 416.6829 #>  [35,] 426.8815 425.4158 423.9357 422.4405 420.9298 419.4028 417.8590 416.2976 #>  [36,] 426.5066 425.0402 423.5593 422.0634 420.5518 419.0240 417.4793 415.9169 #>  [37,] 426.1351 424.6682 423.1867 421.6902 420.1780 418.6495 417.1040 415.5407 #>  [38,] 425.7672 424.2998 422.8179 421.3209 419.8082 418.2791 416.7331 415.1693 #>  [39,] 425.4027 423.9350 422.4528 420.9555 419.4425 417.9131 416.3666 414.8024 #>  [40,] 425.0417 423.5739 422.0915 420.5940 419.0808 417.5512 416.0046 414.4402 #>  [41,] 424.6843 423.2164 421.7340 420.2365 418.7233 417.1937 415.6470 414.0826 #>  [42,] 424.3303 422.8626 421.3803 419.8829 418.3699 416.8404 415.2939 413.7296 #>  [43,] 423.9798 422.5123 421.0304 419.5333 418.0205 416.4914 414.9452 413.3813 #>  [44,] 423.6328 422.1658 420.6842 419.1876 417.6752 416.1466 414.6010 413.0376 #>  [45,] 423.2893 421.8228 420.3418 418.8457 417.3340 415.8061 414.2612 412.6986 #>  [46,] 422.9493 421.4835 420.0031 418.5078 416.9969 415.4698 413.9258 412.3641 #>  [47,] 422.6128 421.1477 419.6682 418.1738 416.6639 415.1377 413.5948 412.0343 #>  [48,] 422.2797 420.8156 419.3371 417.8437 416.3348 414.8099 413.2682 411.7090 #>  [49,] 421.9501 420.4870 419.0096 417.5174 416.0098 414.4862 412.9459 411.3882 #>  [50,] 421.6239 420.1620 418.6859 417.1950 415.6888 414.1667 412.6280 411.0720 #>  [51,] 421.3012 419.8406 418.3659 416.8765 415.3718 413.8514 412.3144 410.7603 #>  [52,] 420.9818 419.5227 418.0495 416.5617 415.0588 413.5401 412.0051 410.4531 #>  [53,] 420.6659 419.2083 417.7367 416.2507 414.7497 413.2330 411.7001 410.1503 #>  [54,] 420.3533 418.8974 417.4276 415.9435 414.4444 412.9299 411.3993 409.8519 #>  [55,] 420.0440 418.5899 417.1221 415.6400 414.1431 412.6308 411.1026 409.5578 #>  [56,] 419.7380 418.2859 416.8201 415.3402 413.8456 412.3358 410.8101 409.2681 #>  [57,] 419.4354 417.9853 416.5217 415.0440 413.5519 412.0447 410.5218 408.9826 #>  [58,] 419.1360 417.6880 416.2267 414.7515 413.2619 411.7574 410.2375 408.7014 #>  [59,] 418.8398 417.3942 415.9353 414.4626 412.9757 411.4741 409.9572 408.4243 #>  [60,] 418.5468 417.1036 415.6472 414.1773 412.6932 411.1946 409.6808 408.1514 #>  [61,] 418.2570 416.8163 415.3626 413.8954 412.4144 410.9189 409.4084 407.8825 #>  [62,] 417.9704 416.5323 415.0813 413.6171 412.1391 410.6469 409.1399 407.6177 #>  [63,] 417.6868 416.2514 414.8034 413.3421 411.8674 410.3786 408.8752 407.3568 #>  [64,] 417.4063 415.9738 414.5287 413.0706 411.5992 410.1139 408.6143 407.0998 #>  [65,] 417.1289 415.6993 414.2572 412.8024 411.3344 409.8528 408.3570 406.8467 #>  [66,] 416.8545 415.4278 413.9890 412.5376 411.0731 409.5952 408.1034 406.5973 #>  [67,] 416.5830 415.1594 413.7239 412.2759 410.8151 409.3411 407.8534 406.3516 #>  [68,] 416.3144 414.8941 413.4619 412.0175 410.5605 409.0904 407.6070 406.1096 #>  [69,] 416.0487 414.6317 413.2030 411.7622 410.3091 408.8431 407.3639 405.8712 #>  [70,] 415.7858 414.3722 412.9471 411.5101 410.0609 408.5991 407.1243 405.6362 #>  [71,] 415.5257 414.1156 412.6941 411.2609 409.8158 408.3583 406.8881 405.4048 #>  [72,] 415.2684 413.8618 412.4440 411.0148 409.5738 408.1207 406.6551 405.1766 #>  [73,] 415.0138 413.6108 412.1969 410.7717 409.3349 407.8862 406.4253 404.9518 #>  [74,] 414.7619 413.3626 411.9525 410.5314 409.0989 407.6548 406.1987 404.7303 #>  [75,] 414.5125 413.1170 411.7109 410.2939 408.8659 407.4264 405.9751 404.5118 #>  [76,] 414.2658 412.8741 411.4720 410.0593 408.6357 407.2009 405.7546 404.2965 #>  [77,] 414.0216 412.6337 411.2358 409.8274 408.4083 406.9782 405.5370 404.0842 #>  [78,] 413.7798 412.3960 411.0021 409.5981 408.1836 406.7584 405.3222 403.8748 #>  [79,] 413.5405 412.1607 410.7711 409.3715 407.9616 406.5413 405.1103 403.6683 #>  [80,] 413.3036 411.9278 410.5425 409.1474 407.7423 406.3269 404.9011 403.4646 #>  [81,] 413.0690 411.6974 410.3164 408.9258 407.5255 406.1151 404.6946 403.2637 #>  [82,] 412.8367 411.4692 410.0926 408.7067 407.3111 405.9059 404.4907 403.0653 #>  [83,] 412.6066 411.2434 409.8712 408.4899 407.0993 405.6991 404.2893 402.8696 #>  [84,] 412.3788 411.0198 409.6521 408.2755 406.8898 405.4948 404.0904 402.6764 #>  [85,] 412.1531 410.7985 409.4353 408.0634 406.6826 405.2928 403.8938 402.4856 #>  [86,] 411.9295 410.5792 409.2206 407.8534 406.4777 405.0931 403.6996 402.2971 #>  [87,] 411.7079 410.3620 409.0080 407.6457 406.2749 404.8956 403.5077 402.1110 #>  [88,] 411.4884 410.1469 408.7975 407.4400 406.0743 404.7003 403.3179 401.9270 #>  [89,] 411.2708 409.9338 408.5890 407.2364 405.8758 404.5072 403.1303 401.7453 #>  [90,] 411.0551 409.7226 408.3825 407.0348 405.6793 404.3160 402.9448 401.5656 #>  [91,] 410.8413 409.5133 408.1779 406.8351 405.4848 404.1268 402.7612 401.3879 #>  [92,] 410.6293 409.3058 407.9752 406.6373 405.2921 403.9396 402.5796 401.2121 #>  [93,] 410.4191 409.1002 407.7743 406.4413 405.1013 403.7542 402.3998 401.0383 #>  [94,] 410.2106 408.8962 407.5751 406.2471 404.9123 403.5706 402.2219 400.8662 #>  [95,] 410.0038 408.6940 407.3776 406.0547 404.7250 403.3887 402.0456 400.6959 #>  [96,] 409.7986 408.4934 407.1818 405.8638 404.5394 403.2085 401.8711 400.5272 #>  [97,] 409.5950 408.2944 406.9876 405.6746 404.3554 403.0299 401.6982 400.3602 #>  [98,] 409.3929 408.0969 406.7950 405.4870 404.1730 402.8529 401.5268 400.1948 #>  [99,] 409.1923 407.9010 406.6038 405.3009 403.9921 402.6774 401.3570 400.0308 #> [100,] 408.9932 407.7065 406.4142 405.1162 403.8126 402.5034 401.1886 399.8682 #>           [,25]    [,26]    [,27]    [,28]    [,29]    [,30]    [,31]    [,32] #>   [1,] 430.2623 428.8050 427.3365 425.8565 424.3648 422.8612 421.3456 419.8177 #>   [2,] 429.7454 428.2820 426.8071 425.3202 423.8214 422.3102 420.7866 419.2502 #>   [3,] 429.2313 427.7619 426.2806 424.7870 423.2810 421.7624 420.2308 418.6860 #>   [4,] 428.7202 427.2448 425.7571 424.2569 422.7439 421.2177 419.6782 418.1251 #>   [5,] 428.2121 426.7308 425.2368 423.7300 422.2100 420.6765 419.1291 417.5677 #>   [6,] 427.7070 426.2199 424.7198 423.2064 421.6795 420.1386 418.5835 417.0138 #>   [7,] 427.2051 425.7122 424.2060 422.6862 421.1525 419.6044 418.0416 416.4637 #>   [8,] 426.7064 425.2079 423.6957 422.1695 420.6290 419.0738 417.5034 415.9175 #>   [9,] 426.2111 424.7069 423.1888 421.6564 420.1093 418.5470 416.9691 415.3752 #>  [10,] 425.7191 424.2094 422.6856 421.1470 419.5933 418.0240 416.4388 414.8370 #>  [11,] 425.2306 423.7155 422.1860 420.6413 419.0812 417.5051 415.9126 414.3031 #>  [12,] 424.7456 423.2253 421.6901 420.1395 418.5731 416.9903 415.3906 413.7735 #>  [13,] 424.2642 422.7388 421.1981 419.6417 418.0691 416.4798 414.8731 413.2485 #>  [14,] 423.7865 422.2560 420.7100 419.1480 417.5693 415.9735 414.3599 412.7280 #>  [15,] 423.3126 421.7772 420.2260 418.6584 417.0738 415.4717 413.8514 412.2123 #>  [16,] 422.8424 421.3023 419.7460 418.1730 416.5827 414.9744 413.3476 411.7015 #>  [17,] 422.3762 420.8314 419.2702 417.6920 416.0961 414.4818 412.8486 411.1957 #>  [18,] 421.9140 420.3647 418.7987 417.2153 415.6140 413.9940 412.3546 410.6950 #>  [19,] 421.4557 419.9021 418.3315 416.7432 415.1366 413.5110 411.8655 410.1995 #>  [20,] 421.0016 419.4438 417.8687 416.2756 414.6640 413.0329 411.3816 409.7094 #>  [21,] 420.5516 418.9897 417.4104 415.8127 414.1962 412.5599 410.9030 409.2247 #>  [22,] 420.1058 418.5401 416.9566 415.3546 413.7333 412.0920 410.4297 408.7457 #>  [23,] 419.6643 418.0949 416.5075 414.9013 413.2755 411.6293 409.9619 408.2723 #>  [24,] 419.2272 417.6542 416.0630 414.4528 412.8227 411.1720 409.4996 407.8047 #>  [25,] 418.7944 417.2181 415.6233 414.0093 412.3752 410.7200 409.0430 407.3431 #>  [26,] 418.3661 416.7866 415.1885 413.5708 411.9328 410.2736 408.5921 406.8874 #>  [27,] 417.9422 416.3598 414.7585 413.1374 411.4958 409.8327 408.1470 406.4378 #>  [28,] 417.5229 415.9377 414.3334 412.7092 411.0642 409.3974 407.7078 405.9944 #>  [29,] 417.1081 415.5204 413.9133 412.2861 410.6380 408.9678 407.2745 405.5572 #>  [30,] 416.6980 415.1078 413.4983 411.8684 410.2172 408.5439 406.8473 405.1263 #>  [31,] 416.2925 414.7002 413.0883 411.4559 409.8021 408.1259 406.4262 404.7019 #>  [32,] 415.8917 414.2974 412.6834 411.0487 409.3925 407.7137 406.0113 404.2839 #>  [33,] 415.4957 413.8996 412.2837 410.6470 408.9886 407.3075 405.6025 403.8725 #>  [34,] 415.1043 413.5067 411.8891 410.2507 408.5904 406.9072 405.2000 403.4676 #>  [35,] 414.7178 413.1188 411.4998 409.8598 408.1979 406.5130 404.8039 403.0694 #>  [36,] 414.3360 412.7359 411.1157 409.4744 407.8111 406.1247 404.4140 402.6778 #>  [37,] 413.9591 412.3581 410.7369 409.0946 407.4302 405.7426 404.0306 402.2930 #>  [38,] 413.5869 411.9852 410.3633 408.7203 407.0550 405.3665 403.6535 401.9149 #>  [39,] 413.2196 411.6175 409.9951 408.3515 406.6856 404.9965 403.2829 401.5435 #>  [40,] 412.8572 411.2548 409.6321 407.9882 406.3221 404.6326 402.9187 401.1789 #>  [41,] 412.4996 410.8971 409.2745 407.6305 405.9644 404.2749 402.5609 400.8211 #>  [42,] 412.1468 410.5446 408.9221 407.2784 405.6125 403.9233 402.2096 400.4701 #>  [43,] 411.7989 410.1971 408.5751 406.9319 405.2665 403.5778 401.8647 400.1259 #>  [44,] 411.4558 409.8546 408.2333 406.5908 404.9262 403.2384 401.5262 399.7884 #>  [45,] 411.1175 409.5172 407.8968 406.2553 404.5918 402.9051 401.1941 399.4576 #>  [46,] 410.7841 409.1849 407.5656 405.9254 404.2631 402.5779 400.8684 399.1336 #>  [47,] 410.4554 408.8575 407.2396 405.6009 403.9402 402.2567 400.5491 398.8162 #>  [48,] 410.1316 408.5352 406.9189 405.2819 403.6231 401.9415 400.2361 398.5055 #>  [49,] 409.8125 408.2178 406.6033 404.9683 403.3116 401.6323 399.9293 398.2014 #>  [50,] 409.4981 407.9053 406.2929 404.6601 403.0058 401.3291 399.6288 397.9038 #>  [51,] 409.1884 407.5977 405.9877 404.3572 402.7056 401.0317 399.3344 397.6127 #>  [52,] 408.8833 407.2950 405.6875 404.0597 402.4109 400.7401 399.0462 397.3281 #>  [53,] 408.5829 406.9972 405.3923 403.7675 402.1218 400.4543 398.7640 397.0497 #>  [54,] 408.2870 406.7041 405.1021 403.4804 401.8381 400.1742 398.4877 396.7777 #>  [55,] 407.9958 406.4157 404.8169 403.1985 401.5598 399.8998 398.2174 396.5118 #>  [56,] 407.7089 406.1320 404.5365 402.9218 401.2868 399.6309 397.9529 396.2520 #>  [57,] 407.4266 405.8530 404.2610 402.6500 401.0191 399.3675 397.6942 395.9982 #>  [58,] 407.1486 405.5785 403.9903 402.3832 400.7566 399.1095 397.4411 395.7504 #>  [59,] 406.8750 405.3085 403.7242 402.1213 400.4992 398.8569 397.1936 395.5084 #>  [60,] 406.6057 405.0430 403.4628 401.8643 400.2468 398.6094 396.9515 395.2720 #>  [61,] 406.3406 404.7819 403.2060 401.6120 399.9993 398.3672 396.7148 395.0413 #>  [62,] 406.0796 404.5251 402.9536 401.3644 399.7568 398.1300 396.4834 394.8161 #>  [63,] 405.8228 404.2726 402.7057 401.1214 399.5190 397.8978 396.2572 394.5963 #>  [64,] 405.5700 404.0243 402.4621 400.8828 399.2858 397.6704 396.0360 394.3817 #>  [65,] 405.3212 403.7801 402.2228 400.6488 399.0573 397.4479 395.8197 394.1722 #>  [66,] 405.0763 403.5399 401.9877 400.4190 398.8333 397.2300 395.6084 393.9678 #>  [67,] 404.8352 403.3038 401.7567 400.1935 398.6137 397.0166 395.4017 393.7683 #>  [68,] 404.5979 403.0715 401.5297 399.9722 398.3984 396.8077 395.1996 393.5736 #>  [69,] 404.3643 402.8430 401.3067 399.7550 398.1873 396.6032 395.0021 393.3835 #>  [70,] 404.1344 402.6183 401.0876 399.5417 397.9803 396.4029 394.8089 393.1979 #>  [71,] 403.9079 402.3972 400.8722 399.3324 397.7774 396.2068 394.6200 393.0167 #>  [72,] 403.6850 402.1797 400.6605 399.1268 397.5783 396.0146 394.4353 392.8398 #>  [73,] 403.4654 401.9657 400.4524 398.9249 397.3831 395.8264 394.2545 392.6670 #>  [74,] 403.2492 401.7551 400.2478 398.7267 397.1916 395.6420 394.0777 392.4982 #>  [75,] 403.0362 401.5479 400.0466 398.5319 397.0036 395.4613 393.9047 392.3333 #>  [76,] 402.8264 401.3439 399.8487 398.3406 396.8192 395.2842 393.7353 392.1722 #>  [77,] 402.6197 401.1431 399.6542 398.1526 396.6382 395.1105 393.5695 392.0147 #>  [78,] 402.4160 400.9453 399.4627 397.9678 396.4604 394.9403 393.4071 391.8606 #>  [79,] 402.2152 400.7506 399.2743 397.7862 396.2859 394.7732 393.2480 391.7100 #>  [80,] 402.0173 400.5588 399.0889 397.6076 396.1144 394.6093 393.0921 391.5625 #>  [81,] 401.8221 400.3698 398.9064 397.4319 395.9460 394.4485 392.9393 391.4182 #>  [82,] 401.6297 400.1836 398.7267 397.2591 395.7804 394.2906 392.7894 391.2769 #>  [83,] 401.4399 400.0000 398.5497 397.0890 395.6176 394.1355 392.6424 391.1385 #>  [84,] 401.2526 399.8190 398.3754 396.9216 395.4575 393.9831 392.4982 391.0028 #>  [85,] 401.0678 399.6405 398.2035 396.7567 395.3000 393.8333 392.3566 390.8698 #>  [86,] 400.8854 399.4645 398.0341 396.5943 395.1450 393.6861 392.2175 390.7392 #>  [87,] 400.7054 399.2908 397.8671 396.4344 394.9924 393.5412 392.0808 390.6111 #>  [88,] 400.5275 399.1193 397.7024 396.2767 394.8421 393.3987 391.9464 390.4853 #>  [89,] 400.3519 398.9501 397.5399 396.1212 394.6940 393.2583 391.8142 390.3617 #>  [90,] 400.1783 398.7829 397.3795 395.9678 394.5480 393.1201 391.6842 390.2402 #>  [91,] 400.0068 398.6178 397.2211 395.8165 394.4041 392.9840 391.5561 390.1206 #>  [92,] 399.8372 398.4547 397.0647 395.6671 394.2621 392.8497 391.4299 390.0029 #>  [93,] 399.6695 398.2934 396.9101 395.5196 394.1220 392.7173 391.3056 389.8870 #>  [94,] 399.5036 398.1339 396.7574 395.3739 393.9836 392.5866 391.1829 389.7727 #>  [95,] 399.3394 397.9762 396.6064 395.2299 393.8470 392.4576 391.0619 389.6601 #>  [96,] 399.1769 397.8202 396.4570 395.0876 393.7119 392.3301 390.9424 389.5489 #>  [97,] 399.0160 397.6657 396.3092 394.9468 393.5784 392.2042 390.8244 389.4391 #>  [98,] 398.8567 397.5128 396.1630 394.8074 393.4463 392.0796 390.7077 389.3306 #>  [99,] 398.6989 397.3613 396.0181 394.6695 393.3156 391.9564 390.5923 389.2234 #> [100,] 398.5424 397.2112 395.8747 394.5329 393.1861 391.8345 390.4781 389.1172 #>           [,33]    [,34]    [,35]    [,36]    [,37]    [,38]    [,39]    [,40] #>   [1,] 418.2775 416.7247 415.1594 413.5814 411.9907 410.3874 408.7715 407.1432 #>   [2,] 417.7010 416.1388 414.5634 412.9748 411.3728 409.7574 408.1288 406.4869 #>   [3,] 417.1279 415.5562 413.9707 412.3714 410.7581 409.1308 407.4894 405.8340 #>   [4,] 416.5581 414.9770 413.3816 411.7716 410.1470 408.5077 406.8535 405.1845 #>   [5,] 415.9918 414.4014 412.7960 411.1755 409.5396 407.8883 406.2213 404.5387 #>   [6,] 415.4293 413.8295 412.2142 410.5832 408.9361 407.2728 405.5931 403.8968 #>   [7,] 414.8705 413.2615 411.6364 409.9949 408.3366 406.6614 404.9689 403.2591 #>   [8,] 414.3156 412.6975 411.0626 409.4107 407.7414 406.0543 404.3492 402.6257 #>   [9,] 413.7649 412.1377 410.4932 408.8310 407.1506 405.4518 403.7340 401.9970 #>  [10,] 413.2183 411.5822 409.9281 408.2557 406.5645 404.8539 403.1236 401.3732 #>  [11,] 412.6761 411.0312 409.3677 407.6852 405.9831 404.2610 402.5183 400.7545 #>  [12,] 412.1384 410.4848 408.8120 407.1196 405.4068 403.6732 401.9182 400.1412 #>  [13,] 411.6054 409.9432 408.2613 406.5590 404.8357 403.0908 401.3236 399.5335 #>  [14,] 411.0771 409.4065 407.7156 406.0037 404.2701 402.5140 400.7348 398.9317 #>  [15,] 410.5537 408.8749 407.1752 405.4538 403.7100 401.9430 400.1519 398.3360 #>  [16,] 410.0354 408.3485 406.6402 404.9095 403.1557 401.3779 399.5752 397.7468 #>  [17,] 409.5222 407.8275 406.1108 404.3710 402.6074 400.8191 399.0050 397.1642 #>  [18,] 409.0144 407.3121 405.5871 403.8385 402.0654 400.2667 398.4415 396.5886 #>  [19,] 408.5120 406.8023 405.0693 403.3121 401.5297 399.7209 397.8848 396.0201 #>  [20,] 408.0152 406.2983 404.5575 402.7920 401.0005 399.1820 397.3353 395.4591 #>  [21,] 407.5241 405.8002 404.0520 402.2784 400.4782 398.6502 396.7932 394.9058 #>  [22,] 407.0389 405.3083 403.5528 401.7714 399.9627 398.1256 396.2587 394.3605 #>  [23,] 406.5595 404.8225 403.0601 401.2712 399.4544 397.6085 395.7320 393.8233 #>  [24,] 406.0863 404.3431 402.5741 400.7779 398.9534 397.0990 395.2133 393.2946 #>  [25,] 405.6191 403.8701 402.0948 400.2918 398.4598 396.5974 394.7028 392.7745 #>  [26,] 405.1583 403.4037 401.6224 399.8129 397.9739 396.1037 394.2008 392.2634 #>  [27,] 404.7039 402.9440 401.1570 399.3414 397.4957 395.6183 393.7075 391.7613 #>  [28,] 404.2559 402.4912 400.6988 398.8774 397.0254 395.1412 393.2229 391.2686 #>  [29,] 403.8145 402.0452 400.2479 398.4211 396.5633 394.6726 392.7474 390.7854 #>  [30,] 403.3797 401.6062 399.8043 397.9725 396.1093 394.2127 392.2810 390.3120 #>  [31,] 402.9517 401.1742 399.3681 397.5318 395.6636 393.7616 391.8239 389.8484 #>  [32,] 402.5304 400.7495 398.9396 397.0991 395.2263 393.3194 391.3763 389.3948 #>  [33,] 402.1161 400.3320 398.5186 396.6744 394.7976 392.8863 390.9383 388.9515 #>  [34,] 401.7087 399.9218 398.1054 396.2579 394.3775 392.4622 390.5100 388.5185 #>  [35,] 401.3082 399.5189 397.6999 395.8496 393.9661 392.0475 390.0915 388.0959 #>  [36,] 400.9148 399.1235 397.3023 395.4496 393.5635 391.6420 389.6830 387.6839 #>  [37,] 400.5284 398.7355 396.9126 395.0579 393.1697 391.2460 389.2844 387.2826 #>  [38,] 400.1492 398.3550 396.5307 394.6747 392.7849 390.8594 388.8959 386.8920 #>  [39,] 399.7771 397.9821 396.1569 394.2998 392.4089 390.4822 388.5175 386.5121 #>  [40,] 399.4121 397.6166 395.7910 393.9334 392.0419 390.1146 388.1492 386.1431 #>  [41,] 399.0542 397.2587 395.4330 393.5754 391.6839 389.7566 387.7910 385.7849 #>  [42,] 398.7036 396.9084 395.0831 393.2259 391.3349 389.4080 387.4430 385.4375 #>  [43,] 398.3600 396.5656 394.7411 392.8848 390.9948 389.0690 387.1052 385.1009 #>  [44,] 398.0236 396.2304 394.4071 392.5522 390.6636 388.7394 386.7774 384.7752 #>  [45,] 397.6943 395.9026 394.0810 392.2279 390.3414 388.4194 386.4598 384.4601 #>  [46,] 397.3720 395.5823 393.7628 391.9120 390.0279 388.1087 386.1521 384.1557 #>  [47,] 397.0568 395.2694 393.4525 391.6044 389.7233 387.8074 385.8543 383.8619 #>  [48,] 396.7486 394.9639 393.1499 391.3050 389.4274 387.5153 385.5664 383.5786 #>  [49,] 396.4473 394.6657 392.8551 391.0138 389.1402 387.2324 385.2882 383.3056 #>  [50,] 396.1529 394.3748 392.5679 390.7307 388.8615 386.9585 385.0197 383.0429 #>  [51,] 395.8654 394.0910 392.2882 390.4555 388.5913 386.6936 384.7606 382.7902 #>  [52,] 395.5845 393.8144 392.0161 390.1883 388.3294 386.4375 384.5109 382.5475 #>  [53,] 395.3104 393.5447 391.7513 389.9289 388.0757 386.1901 384.2704 382.3145 #>  [54,] 395.0428 393.2820 391.4939 389.6771 387.8301 385.9513 384.0389 382.0911 #>  [55,] 394.7817 393.0261 391.2436 389.4328 387.5924 385.7208 383.8163 381.8770 #>  [56,] 394.5270 392.7769 391.0003 389.1960 387.3626 385.4986 383.6023 381.6721 #>  [57,] 394.2786 392.5343 390.7640 388.9664 387.1404 385.2844 383.3968 381.4762 #>  [58,] 394.0364 392.2982 390.5344 388.7440 386.9257 385.0780 383.1996 381.2889 #>  [59,] 393.8003 392.0684 390.3116 388.5286 386.7183 384.8794 383.0105 381.1102 #>  [60,] 393.5702 391.8449 390.0952 388.3200 386.5181 384.6883 382.8292 380.9397 #>  [61,] 393.3459 391.6275 389.8852 388.1181 386.3248 384.5044 382.6556 380.7772 #>  [62,] 393.1273 391.4161 389.6815 387.9226 386.1384 384.3277 382.4894 380.6224 #>  [63,] 392.9143 391.2105 389.4839 387.7335 385.9585 384.1578 382.3304 380.4751 #>  [64,] 392.7068 391.0106 389.2921 387.5506 385.7851 383.9947 382.1783 380.3351 #>  [65,] 392.5047 390.8162 389.1062 387.3737 385.6179 383.8380 382.0330 380.2021 #>  [66,] 392.3077 390.6273 388.9258 387.2026 385.4567 383.6875 381.8941 380.0757 #>  [67,] 392.1158 390.4436 388.7509 387.0371 385.3014 383.5431 381.7615 379.9559 #>  [68,] 391.9289 390.2650 388.5813 386.8771 385.1517 383.4046 381.6350 379.8422 #>  [69,] 391.7468 390.0914 388.4168 386.7224 385.0075 383.2716 381.5142 379.7345 #>  [70,] 391.5693 389.9226 388.2573 386.5727 384.8685 383.1441 381.3989 379.6325 #>  [71,] 391.3963 389.7584 388.1025 386.4281 384.7346 383.0217 381.2890 379.5359 #>  [72,] 391.2278 389.5988 387.9524 386.2881 384.6056 382.9044 381.1841 379.4444 #>  [73,] 391.0635 389.4435 387.8067 386.1528 384.4812 382.7918 381.0841 379.3579 #>  [74,] 390.9033 389.2924 387.6654 386.0218 384.3613 382.6837 380.9887 379.2761 #>  [75,] 390.7470 389.1454 387.5281 385.8950 384.2457 382.5800 380.8977 379.1987 #>  [76,] 390.5946 389.0023 387.3949 385.7723 384.1342 382.4804 380.8109 379.1255 #>  [77,] 390.4459 388.8629 387.2655 385.6534 384.0266 382.3848 380.7281 379.0563 #>  [78,] 390.3007 388.7271 387.1397 385.5383 383.9227 382.2930 380.6490 378.9909 #>  [79,] 390.1590 388.5948 387.0174 385.4266 383.8224 382.2047 380.5735 378.9289 #>  [80,] 390.0205 388.4659 386.8985 385.3184 383.7255 382.1197 380.5013 378.8702 #>  [81,] 389.8852 388.3401 386.7828 385.2133 383.6317 382.0380 380.4322 378.8147 #>  [82,] 389.7529 388.2173 386.6701 385.1113 383.5410 381.9592 380.3661 378.7620 #>  [83,] 389.6235 388.0974 386.5603 385.0122 383.4531 381.8833 380.3028 378.7120 #>  [84,] 389.4969 387.9803 386.4533 384.9158 383.3680 381.8100 380.2421 378.6645 #>  [85,] 389.3729 387.8659 386.3489 384.8220 383.2854 381.7392 380.1837 378.6193 #>  [86,] 389.2514 387.7539 386.2470 384.7307 383.2052 381.6707 380.1276 378.5763 #>  [87,] 389.1323 387.6443 386.1474 384.6416 383.1272 381.6044 380.0736 378.5351 #>  [88,] 389.0155 387.5370 386.0500 384.5547 383.0513 381.5401 380.0214 378.4958 #>  [89,] 388.9009 387.4318 385.9547 384.4698 382.9773 381.4776 379.9711 378.4581 #>  [90,] 388.7883 387.3286 385.8614 384.3868 382.9052 381.4169 379.9223 378.4218 #>  [91,] 388.6776 387.2273 385.7699 384.3056 382.8348 381.3577 379.8749 378.3869 #>  [92,] 388.5688 387.1278 385.6801 384.2260 382.7659 381.3000 379.8289 378.3531 #>  [93,] 388.4617 387.0300 385.5920 384.1480 382.6984 381.2436 379.7841 378.3204 #>  [94,] 388.3563 386.9337 385.5053 384.0713 382.6322 381.1884 379.7403 378.2885 #>  [95,] 388.2523 386.8389 385.4200 383.9960 382.5673 381.1343 379.6975 378.2574 #>  [96,] 388.1498 386.7454 385.3360 383.9218 382.5034 381.0811 379.6554 378.2270 #>  [97,] 388.0486 386.6532 385.2531 383.8487 382.4404 381.0287 379.6141 378.1971 #>  [98,] 387.9487 386.5622 385.1713 383.7766 382.3784 380.9771 379.5733 378.1676 #>  [99,] 387.8499 386.4722 385.0905 383.7054 382.3170 380.9261 379.5330 378.1384 #> [100,] 387.7522 386.3832 385.0106 383.6349 382.2564 380.8756 379.4931 378.1095 #>           [,41]    [,42]    [,43]    [,44]    [,45]    [,46]    [,47]    [,48] #>   [1,] 405.5027 403.8503 402.1865 400.5119 398.8271 397.1330 395.4309 393.7218 #>   [2,] 404.8321 403.1644 401.4844 399.7926 398.0895 396.3761 394.6533 392.9225 #>   [3,] 404.1647 402.4817 400.7853 399.0761 397.3545 395.6215 393.8778 392.1248 #>   [4,] 403.5007 401.8022 400.0895 398.3627 396.6225 394.8695 393.1046 391.3291 #>   [5,] 402.8403 401.1264 399.3971 397.6527 395.8936 394.1205 392.3342 390.5357 #>   [6,] 402.1839 400.4544 398.7085 396.9463 395.1682 393.3748 391.5667 389.7450 #>   [7,] 401.5316 399.7866 398.0240 396.2439 394.4467 392.6327 390.8027 388.9575 #>   [8,] 400.8838 399.1231 397.3438 395.5458 393.7293 391.8947 390.0425 388.1734 #>   [9,] 400.2406 398.4644 396.6683 394.8523 393.0165 391.1611 389.2865 387.3933 #>  [10,] 399.6023 397.8106 395.9978 394.1638 392.3086 390.4323 388.5351 386.6177 #>  [11,] 398.9692 397.1620 395.3326 393.4806 391.6060 389.7087 387.7889 385.8469 #>  [12,] 398.3416 396.5190 394.6730 392.8031 390.9091 388.9908 387.0482 385.0815 #>  [13,] 397.7198 395.8819 394.0194 392.1316 390.2182 388.2789 386.3135 384.3220 #>  [14,] 397.1040 395.2510 393.3721 391.4665 389.5338 387.5736 385.5853 383.5690 #>  [15,] 396.4945 394.6266 392.7314 390.8082 388.8564 386.8752 384.8642 382.8230 #>  [16,] 395.8917 394.0090 392.0977 390.1571 388.1862 386.1843 384.1506 382.0846 #>  [17,] 395.2957 393.3985 391.4714 389.5135 387.5239 385.5014 383.4451 381.3544 #>  [18,] 394.7069 392.7954 390.8528 388.8780 386.8697 384.8268 382.7483 380.6330 #>  [19,] 394.1256 392.2001 390.2423 388.2507 386.2242 384.1612 382.0606 379.9210 #>  [20,] 393.5521 391.6129 389.6401 387.6322 385.5877 383.5050 381.3827 379.2190 #>  [21,] 392.9866 391.0341 389.0468 387.0229 384.9608 382.8588 380.7150 378.5277 #>  [22,] 392.4295 390.4640 388.4625 386.4231 384.3439 382.2230 380.0583 377.8478 #>  [23,] 391.8809 389.9030 387.8877 385.8333 383.7374 381.5981 379.4130 377.1798 #>  [24,] 391.3412 389.3512 387.3228 385.2537 383.1418 380.9847 378.7798 376.5245 #>  [25,] 390.8106 388.8091 386.7680 384.6849 382.5575 380.3832 378.1592 375.8825 #>  [26,] 390.2894 388.2769 386.2237 384.1272 381.9849 379.7941 377.5517 375.2544 #>  [27,] 389.7779 387.7549 385.6901 383.5809 381.4245 379.2179 376.9579 374.6409 #>  [28,] 389.2762 387.2434 385.1677 383.0464 380.8766 378.6551 376.3784 374.0426 #>  [29,] 388.7846 386.7426 384.6566 382.5240 380.3416 378.1060 375.8136 373.4601 #>  [30,] 388.3033 386.2527 384.1573 382.0141 379.8199 377.5712 375.2640 372.8939 #>  [31,] 387.8326 385.7740 383.6698 381.5169 379.3119 377.0510 374.7301 372.3446 #>  [32,] 387.3725 385.3067 383.1945 381.0327 378.8178 376.5458 374.2124 371.8128 #>  [33,] 386.9233 384.8510 382.7316 380.5618 378.3379 376.0559 373.7112 371.2988 #>  [34,] 386.4851 384.4071 382.2813 380.1044 377.8726 375.5817 373.2270 370.8032 #>  [35,] 386.0581 383.9751 381.8438 379.6608 377.4221 375.1234 372.7600 370.3263 #>  [36,] 385.6423 383.5551 381.4192 379.2310 376.9865 374.6813 372.3105 369.8685 #>  [37,] 385.2379 383.1473 381.0077 378.8152 376.5661 374.2556 371.8789 369.4300 #>  [38,] 384.8449 382.7518 380.6093 378.4137 376.1610 373.8465 371.4652 369.0112 #>  [39,] 384.4635 382.3686 380.2242 378.0264 375.7713 373.4541 371.0697 368.6122 #>  [40,] 384.0937 381.9979 379.8524 377.6535 375.3971 373.0784 370.6924 368.2331 #>  [41,] 383.7354 381.6395 379.4939 377.2949 375.0384 372.7196 370.3335 367.8739 #>  [42,] 383.3887 381.2936 379.1488 376.9507 374.6952 372.3777 369.9928 367.5348 #>  [43,] 383.0535 380.9600 378.8170 376.6209 374.3676 372.0525 369.6704 367.2156 #>  [44,] 382.7299 380.6388 378.4985 376.3054 374.0554 371.7440 369.3662 366.9163 #>  [45,] 382.4178 380.3299 378.1931 376.0040 373.7585 371.4522 369.0801 366.6365 #>  [46,] 382.1170 380.0332 377.9009 375.7167 373.4768 371.1768 368.8117 366.3762 #>  [47,] 381.8276 379.7485 377.6216 375.4434 373.2101 370.9176 368.5610 366.1351 #>  [48,] 381.5493 379.4758 377.3551 375.1838 372.9583 370.6744 368.3276 365.9127 #>  [49,] 381.2821 379.2149 377.1012 374.9378 372.7210 370.4469 368.1111 365.7088 #>  [50,] 381.0258 378.9657 376.8598 374.7051 372.4980 370.2348 367.9113 365.5229 #>  [51,] 380.7802 378.7279 376.6306 374.4854 372.2890 370.0378 367.7278 365.3545 #>  [52,] 380.5451 378.5013 376.4134 374.2786 372.0938 369.8555 367.5600 365.2031 #>  [53,] 380.3204 378.2857 376.2079 374.0843 371.9119 369.6875 367.4075 365.0681 #>  [54,] 380.1058 378.0808 376.0138 373.9021 371.7430 369.5333 367.2699 364.9491 #>  [55,] 379.9012 377.8865 375.8309 373.7318 371.5867 369.3926 367.1466 364.8454 #>  [56,] 379.7062 377.7025 375.6588 373.5730 371.4426 369.2649 367.0372 364.7563 #>  [57,] 379.5206 377.5284 375.4973 373.4254 371.3104 369.1497 366.9410 364.6814 #>  [58,] 379.3443 377.3639 375.3460 373.2886 371.1895 369.0466 366.8575 364.6198 #>  [59,] 379.1769 377.2089 375.2046 373.1621 371.0796 368.9549 366.7861 364.5710 #>  [60,] 379.0181 377.0630 375.0727 373.0457 370.9802 368.8744 366.7264 364.5344 #>  [61,] 378.8677 376.9258 374.9500 372.9389 370.8909 368.8043 366.6776 364.5092 #>  [62,] 378.7254 376.7971 374.8362 372.8414 370.8112 368.7443 366.6393 364.4948 #>  [63,] 378.5909 376.6765 374.7309 372.7526 370.7407 368.6938 366.6108 364.4906 #>  [64,] 378.4639 376.5638 374.6336 372.6723 370.6789 368.6523 366.5916 364.4960 #>  [65,] 378.3442 376.4586 374.5442 372.6001 370.6254 368.6194 366.5812 364.5102 #>  [66,] 378.2315 376.3606 374.4622 372.5355 370.5798 368.5945 366.5789 364.5328 #>  [67,] 378.1254 376.2694 374.3872 372.4781 370.5416 368.5771 366.5844 364.5631 #>  [68,] 378.0257 376.1848 374.3190 372.4276 370.5104 368.5669 366.5969 364.6005 #>  [69,] 377.9321 376.1065 374.2571 372.3836 370.4857 368.5632 366.6161 364.6444 #>  [70,] 377.8443 376.0340 374.2013 372.3457 370.4672 368.5657 366.6414 364.6944 #>  [71,] 377.7621 375.9672 374.1511 372.3136 370.4545 368.5740 366.6723 364.7499 #>  [72,] 377.6851 375.9058 374.1064 372.2868 370.4471 368.5875 366.7084 364.8104 #>  [73,] 377.6131 375.8493 374.0666 372.2651 370.4447 368.6059 366.7493 364.8754 #>  [74,] 377.5458 375.7976 374.0316 372.2480 370.4469 368.6289 366.7944 364.9444 #>  [75,] 377.4829 375.7504 374.0011 372.2353 370.4534 368.6559 366.8435 365.0171 #>  [76,] 377.4243 375.7073 373.9746 372.2267 370.4638 368.6866 366.8960 365.0929 #>  [77,] 377.3696 375.6681 373.9520 372.2217 370.4777 368.7208 366.9516 365.1715 #>  [78,] 377.3186 375.6326 373.9330 372.2202 370.4950 368.7579 367.0101 365.2526 #>  [79,] 377.2711 375.6004 373.9172 372.2219 370.5151 368.7978 367.0709 365.3356 #>  [80,] 377.2269 375.5715 373.9044 372.2264 370.5379 368.8401 367.1338 365.4204 #>  [81,] 377.1856 375.5454 373.8945 372.2335 370.5631 368.8844 367.1985 365.5066 #>  [82,] 377.1471 375.5220 373.8870 372.2429 370.5904 368.9306 367.2646 365.5939 #>  [83,] 377.1113 375.5010 373.8818 372.2544 370.6196 368.9784 367.3320 365.6819 #>  [84,] 377.0778 375.4823 373.8787 372.2677 370.6503 369.0274 367.4004 365.7705 #>  [85,] 377.0464 375.4656 373.8774 372.2827 370.6824 369.0775 367.4694 365.8594 #>  [86,] 377.0171 375.4507 373.8778 372.2991 370.7157 369.1285 367.5389 365.9483 #>  [87,] 376.9896 375.4375 373.8796 372.3167 370.7498 369.1800 367.6086 366.0370 #>  [88,] 376.9637 375.4257 373.8827 372.3354 370.7847 369.2320 367.6784 366.1254 #>  [89,] 376.9393 375.4153 373.8868 372.3548 370.8202 369.2842 367.7480 366.2132 #>  [90,] 376.9162 375.4059 373.8918 372.3749 370.8560 369.3364 367.8173 366.3002 #>  [91,] 376.8942 375.3975 373.8976 372.3954 370.8920 369.3884 367.8861 366.3864 #>  [92,] 376.8732 375.3899 373.9039 372.4163 370.9280 369.4402 367.9542 366.4714 #>  [93,] 376.8531 375.3829 373.9107 372.4374 370.9639 369.4916 368.0215 366.5553 #>  [94,] 376.8337 375.3765 373.9178 372.4585 370.9996 369.5423 368.0879 366.6378 #>  [95,] 376.8149 375.3704 373.9250 372.4794 371.0348 369.5923 368.1532 366.7189 #>  [96,] 376.7965 375.3646 373.9322 372.5002 371.0696 369.6415 368.2173 366.7983 #>  [97,] 376.7785 375.3590 373.9393 372.5206 371.1037 369.6898 368.2802 366.8761 #>  [98,] 376.7607 375.3533 373.9463 372.5405 371.1370 369.7370 368.3416 366.9522 #>  [99,] 376.7430 375.3476 373.9529 372.5599 371.1695 369.7830 368.4015 367.0263 #> [100,] 376.7254 375.3417 373.9591 372.5785 371.2011 369.8278 368.4598 367.0985 #>           [,49]    [,50]    [,51]    [,52]    [,53]    [,54]    [,55]    [,56] #>   [1,] 392.0075 390.2898 388.5709 386.8534 385.1402 383.4347 381.7409 380.0632 #>   [2,] 391.1851 389.4430 387.6984 385.9539 384.2123 382.4773 380.7527 379.0432 #>   [3,] 390.3639 388.5969 386.8260 385.0536 383.2829 381.5173 379.7608 378.0181 #>   [4,] 389.5442 387.7518 385.9539 384.1530 382.3522 380.5550 378.7654 376.9883 #>   [5,] 388.7264 386.9080 385.0825 383.2524 381.4206 379.5908 377.7670 375.9540 #>   [6,] 387.9109 386.0661 384.2123 382.3522 380.4886 378.6251 376.7658 374.9157 #>   [7,] 387.0982 385.2263 383.3438 381.4529 379.5566 377.6583 375.7623 373.8736 #>   [8,] 386.2885 384.3892 382.4773 380.5550 378.6251 376.6910 374.7571 372.8282 #>   [9,] 385.4825 383.5553 381.6134 379.6590 377.6946 375.7238 373.7506 371.7801 #>  [10,] 384.6806 382.7251 380.7527 378.7654 376.7658 374.7571 372.7434 370.7299 #>  [11,] 383.8833 381.8992 379.8958 377.8750 375.8392 373.7917 371.7363 369.6781 #>  [12,] 383.0912 381.0780 379.0432 376.9883 374.9157 372.8282 370.7299 368.6255 #>  [13,] 382.3048 380.2623 378.1956 376.1061 373.9958 371.8676 369.7250 367.5729 #>  [14,] 381.5247 379.4527 377.3538 375.2291 373.0805 370.9105 368.7225 366.5212 #>  [15,] 380.7515 378.6498 376.5184 374.3581 372.1705 369.9579 367.7234 365.4714 #>  [16,] 379.9859 377.8544 375.6902 373.4940 371.2669 369.0109 366.7288 364.4246 #>  [17,] 379.2286 377.0671 374.8700 372.6375 370.3705 368.0704 365.7397 363.3820 #>  [18,] 378.4801 376.2888 374.0587 371.7898 369.4823 367.1375 364.7573 362.3449 #>  [19,] 377.7412 375.5202 373.2572 370.9517 368.6036 366.2136 363.7831 361.3147 #>  [20,] 377.0126 374.7621 372.4663 370.1242 367.7353 365.2998 362.8184 360.2931 #>  [21,] 376.2951 374.0153 371.6869 369.3084 366.8788 364.3975 361.8646 359.2815 #>  [22,] 375.5893 373.2808 370.9201 368.5054 366.0352 363.5080 360.9235 358.2820 #>  [23,] 374.8961 372.5592 370.1668 367.7164 365.2058 362.6330 359.9967 357.2963 #>  [24,] 374.2161 371.8515 369.4280 366.9424 364.3919 361.7739 359.0859 356.3265 #>  [25,] 373.5501 371.1586 368.7047 366.1846 363.5950 360.9322 358.1931 355.3747 #>  [26,] 372.8989 370.4813 367.9979 365.4443 362.8164 360.1097 357.3200 354.4433 #>  [27,] 372.2632 369.8205 367.3086 364.7225 362.0574 359.3080 356.4688 353.5345 #>  [28,] 371.6437 369.1770 366.6378 364.0205 361.3196 358.5286 355.6413 352.6508 #>  [29,] 371.0411 368.5517 365.9865 363.3395 360.6042 357.7734 354.8396 351.7945 #>  [30,] 370.4561 367.9453 365.3556 362.6805 359.9126 357.0440 354.0657 350.9682 #>  [31,] 369.8893 367.3586 364.7461 362.0446 359.2462 356.3419 353.3217 350.1744 #>  [32,] 369.3414 366.7924 364.1588 361.4330 358.6062 355.6688 352.6094 349.4154 #>  [33,] 368.8129 366.2472 363.5945 360.8465 357.9939 355.0261 351.9307 348.6936 #>  [34,] 368.3044 365.7238 363.0540 360.2862 357.4104 354.4152 351.2873 348.0112 #>  [35,] 367.8162 365.2227 362.5380 359.7528 356.8567 353.8375 350.6810 347.3704 #>  [36,] 367.3489 364.7444 362.0470 359.2471 356.3337 353.2940 350.1130 346.7729 #>  [37,] 366.9027 364.2894 361.5817 358.7697 355.8422 352.7858 349.5848 346.2204 #>  [38,] 366.4779 363.8579 361.1423 358.3212 355.3829 352.3137 349.0973 345.7143 #>  [39,] 366.0749 363.4502 360.7293 357.9019 354.9563 351.8783 348.6514 345.2556 #>  [40,] 365.6937 363.0665 360.3428 357.5122 354.5626 351.4801 348.2476 344.8450 #>  [41,] 365.3344 362.7070 359.9830 357.1521 354.2022 351.1192 347.8862 344.4830 #>  [42,] 364.9970 362.3716 359.6499 356.8217 353.8749 350.7957 347.5673 344.1696 #>  [43,] 364.6814 362.0602 359.3434 356.5208 353.5808 350.5095 347.2906 343.9045 #>  [44,] 364.3876 361.7727 359.0632 356.2493 353.3193 350.2601 347.0556 343.6870 #>  [45,] 364.1152 361.5089 358.8092 356.0067 353.0902 350.0469 346.8615 343.5160 #>  [46,] 363.8641 361.2683 358.5808 355.7925 352.8927 349.8691 346.7073 343.3904 #>  [47,] 363.6339 361.0506 358.3776 355.6061 352.7261 349.7258 346.5918 343.3085 #>  [48,] 363.4242 360.8554 358.1990 355.4469 352.5895 349.6159 346.5137 343.2684 #>  [49,] 363.2345 360.6819 358.0444 355.3139 352.4818 349.5381 346.4712 343.2683 #>  [50,] 363.0643 360.5298 357.9129 355.2064 352.4021 349.4910 346.4627 343.3058 #>  [51,] 362.9131 360.3982 357.8038 355.1232 352.3491 349.4731 346.4863 343.3786 #>  [52,] 362.7802 360.2864 357.7162 355.0634 352.3215 349.4830 346.5401 343.4843 #>  [53,] 362.6651 360.1938 357.6492 355.0259 352.3179 349.5189 346.6221 343.6205 #>  [54,] 362.5670 360.1195 357.6020 355.0096 352.3372 349.5793 346.7304 343.7847 #>  [55,] 362.4853 360.0626 357.5734 355.0132 352.3778 349.6625 346.8628 343.9745 #>  [56,] 362.4192 360.0225 357.5625 355.0357 352.4383 349.7667 347.0174 344.1873 #>  [57,] 362.3680 359.9981 357.5683 355.0758 352.5175 349.8904 347.1922 344.4209 #>  [58,] 362.3310 359.9886 357.5899 355.1324 352.6138 350.0319 347.3853 344.6730 #>  [59,] 362.3074 359.9932 357.6261 355.2043 352.7259 350.1897 347.5948 344.9415 #>  [60,] 362.2965 360.0110 357.6761 355.2903 352.8525 350.3621 347.8189 345.2242 #>  [61,] 362.2975 360.0411 357.7388 355.3894 352.9924 350.5477 348.0560 345.5192 #>  [62,] 362.3097 360.0828 357.8132 355.5003 353.1441 350.7450 348.3044 345.8247 #>  [63,] 362.3323 360.1351 357.8984 355.6222 353.3066 350.9528 348.5626 346.1391 #>  [64,] 362.3647 360.1973 357.9936 355.7538 353.4787 351.1697 348.8292 346.4607 #>  [65,] 362.4061 360.2686 358.0978 355.8943 353.6593 351.3945 349.1028 346.7880 #>  [66,] 362.4559 360.3482 358.2102 356.0428 353.8473 351.6261 349.3822 347.1199 #>  [67,] 362.5133 360.4354 358.3300 356.1982 354.0419 351.8634 349.6662 347.4549 #>  [68,] 362.5778 360.5295 358.4563 356.3598 354.2419 352.1054 349.9538 347.7920 #>  [69,] 362.6488 360.6298 358.5886 356.5268 354.4467 352.3512 350.2441 348.1303 #>  [70,] 362.7255 360.7356 358.7260 356.6984 354.6553 352.5999 350.5360 348.4687 #>  [71,] 362.8076 360.8464 358.8679 356.8739 354.8671 352.8507 350.8288 348.8064 #>  [72,] 362.8944 360.9616 359.0136 357.0526 355.0813 353.1029 351.1218 349.1428 #>  [73,] 362.9854 361.0805 359.1626 357.2339 355.2972 353.3559 351.4142 349.4771 #>  [74,] 363.0800 361.2027 359.3144 357.4173 355.5143 353.6090 351.7055 349.8088 #>  [75,] 363.1780 361.3277 359.4683 357.6021 355.7320 353.8616 351.9951 350.1374 #>  [76,] 363.2787 361.4551 359.6240 357.7879 355.9498 354.1133 352.2825 350.4623 #>  [77,] 363.3818 361.5842 359.7809 357.9742 356.1673 354.3636 352.5673 350.7831 #>  [78,] 363.4869 361.7149 359.9386 358.1606 356.3839 354.6121 352.8491 351.0996 #>  [79,] 363.5936 361.8466 360.0968 358.3467 356.5994 354.8583 353.1275 351.4114 #>  [80,] 363.7015 361.9790 360.2550 358.5321 356.8133 355.1020 353.4022 351.7182 #>  [81,] 363.8104 362.1118 360.4130 358.7165 357.0254 355.3429 353.6730 352.0198 #>  [82,] 363.9199 362.2447 360.5704 358.8996 357.2353 355.5807 353.9395 352.3161 #>  [83,] 364.0297 362.3773 360.7269 359.0811 357.4427 355.8151 354.2017 352.6067 #>  [84,] 364.1396 362.5094 360.8823 359.2608 357.6475 356.0459 354.4593 352.8917 #>  [85,] 364.2492 362.6408 361.0364 359.4383 357.8495 356.2729 354.7121 353.1709 #>  [86,] 364.3584 362.7712 361.1888 359.6136 358.0483 356.4961 354.9601 353.4441 #>  [87,] 364.4670 362.9004 361.3394 359.7864 358.2440 356.7152 355.2031 353.7114 #>  [88,] 364.5747 363.0282 361.4881 359.9565 358.4362 356.9300 355.4411 353.9727 #>  [89,] 364.6814 363.1545 361.6345 360.1238 358.6249 357.1406 355.6739 354.2279 #>  [90,] 364.7869 363.2790 361.7787 360.2882 358.8100 357.3468 355.9014 354.4771 #>  [91,] 364.8910 363.4017 361.9205 360.4496 358.9914 357.5485 356.1238 354.7202 #>  [92,] 364.9935 363.5223 362.0596 360.6077 359.1689 357.7457 356.3408 354.9572 #>  [93,] 365.0945 363.6407 362.1961 360.7626 359.3425 357.9383 356.5526 355.1881 #>  [94,] 365.1936 363.7570 362.3298 360.9141 359.5122 358.1263 356.7590 355.4130 #>  [95,] 365.2908 363.8708 362.4606 361.0622 359.6778 358.3097 356.9602 355.6319 #>  [96,] 365.3861 363.9822 362.5885 361.2069 359.8394 358.4884 357.1560 355.8448 #>  [97,] 365.4792 364.0910 362.7133 361.3479 359.9969 358.6624 357.3466 356.0518 #>  [98,] 365.5702 364.1973 362.8351 361.4854 360.1503 358.8317 357.5319 356.2530 #>  [99,] 365.6589 364.3008 362.9537 361.6193 360.2996 358.9964 357.7119 356.4483 #> [100,] 365.7453 364.4016 363.0691 361.7495 360.4446 359.1564 357.8867 356.6378 #>           [,57]    [,58]    [,59]    [,60]    [,61]    [,62]    [,63]    [,64] #>   [1,] 378.4066 376.7764 375.1786 373.6199 372.1071 370.6473 369.2481 367.9168 #>   [2,] 377.3538 375.6902 374.0587 372.4663 370.9201 369.4280 367.9979 366.6378 #>   [3,] 376.2946 374.5960 372.9291 371.3010 369.7196 368.1931 366.7301 365.3393 #>   [4,] 375.2291 373.4940 371.7898 370.1242 368.5054 366.9424 365.4443 364.0205 #>   [5,] 374.1577 372.3842 370.6408 368.9356 367.2773 365.6755 364.1399 362.6809 #>   [6,] 373.0805 371.2669 369.4823 367.7353 366.0352 364.3919 362.8164 361.3196 #>   [7,] 371.9980 370.1423 368.3145 366.5234 364.7788 363.0915 361.4732 359.9357 #>   [8,] 370.9105 369.0109 367.1375 365.2998 363.5080 361.7739 360.1097 358.5286 #>   [9,] 369.8185 367.8729 365.9517 364.0647 362.2230 360.4388 358.7255 357.0974 #>  [10,] 368.7225 366.7288 364.7573 362.8184 360.9235 359.0859 357.3200 355.6413 #>  [11,] 367.6232 365.5792 363.5549 361.5610 359.6098 357.7152 355.8928 354.1593 #>  [12,] 366.5212 364.4246 362.3449 360.2931 358.2820 356.3265 354.4433 352.6508 #>  [13,] 365.4173 363.2659 361.1280 359.0150 356.9403 354.9197 352.9712 351.1147 #>  [14,] 364.3125 362.1039 359.9050 357.7273 355.5851 353.4949 351.4761 349.5503 #>  [15,] 363.2076 360.9395 358.6766 356.4309 354.2170 352.0524 349.9578 347.9568 #>  [16,] 362.1039 359.7739 357.4441 355.1266 352.8366 350.5925 348.4163 346.3335 #>  [17,] 361.0026 358.6083 356.2086 353.8156 351.4449 349.1156 346.8514 344.6797 #>  [18,] 359.9050 357.4441 354.9715 352.4991 350.0428 347.6227 345.2635 342.9951 #>  [19,] 358.8127 356.2830 353.7343 351.1787 348.6319 346.1146 343.6530 341.2793 #>  [20,] 357.7273 355.1266 352.4991 349.8562 347.2137 344.5928 342.0208 339.5321 #>  [21,] 356.6508 353.9771 351.2678 348.5337 345.7903 343.0589 340.3679 337.7539 #>  [22,] 355.5851 352.8366 350.0428 347.2137 344.3641 341.5151 338.6960 335.9453 #>  [23,] 354.5324 351.7075 348.8268 345.8990 342.9379 339.9641 337.0072 334.1076 #>  [24,] 353.4949 350.5925 347.6227 344.5928 341.5151 338.4093 335.3044 332.2425 #>  [25,] 352.4753 349.4944 346.4337 343.2987 340.0996 336.8544 333.5914 330.3529 #>  [26,] 351.4761 348.4163 345.2635 342.0208 338.6960 335.3044 331.8726 328.4426 #>  [27,] 350.5001 347.3615 344.1159 340.7636 337.3092 333.7649 330.1540 326.5167 #>  [28,] 349.5503 346.3335 342.9951 339.5321 335.9453 332.2425 328.4426 324.5823 #>  [29,] 348.6295 345.3359 341.9056 338.3317 334.6107 330.7448 326.7469 322.6480 #>  [30,] 347.7409 344.3726 340.8520 337.1683 333.3125 329.2805 325.0773 320.7251 #>  [31,] 346.8875 343.4474 339.8393 336.0480 332.0587 327.8595 323.4457 318.8276 #>  [32,] 346.0724 342.5641 338.8724 334.9772 330.8575 326.4925 321.8658 316.9725 #>  [33,] 345.2985 341.7267 337.9563 333.9626 329.7176 325.1913 320.3533 315.1799 #>  [34,] 344.5688 340.9388 337.0959 333.0107 328.6482 323.9680 318.9251 313.4733 #>  [35,] 343.8859 340.2039 336.2961 332.1280 327.6580 322.8354 317.5994 311.8789 #>  [36,] 343.2522 339.5254 335.5611 331.3205 326.7556 321.8059 316.3946 310.4247 #>  [37,] 342.6700 338.9061 334.8949 330.5938 325.9491 320.8912 315.3288 309.1396 #>  [38,] 342.1409 338.3484 334.3008 329.9526 325.2453 320.1019 314.4185 308.0509 #>  [39,] 341.6665 337.8543 333.7816 329.4007 324.6499 319.4466 313.6778 307.1824 #>  [40,] 341.2476 337.4250 333.3390 328.9408 324.1668 318.9315 313.1167 306.5521 #>  [41,] 340.8849 337.0613 332.9741 328.5743 323.7982 318.5600 312.7410 306.1700 #>  [42,] 340.5783 336.7633 332.6869 328.3014 323.5442 318.3323 312.5510 306.0369 #>  [43,] 340.3274 336.5303 332.4767 328.1208 323.4032 318.2457 312.5422 306.1447 #>  [44,] 340.1314 336.3611 332.3417 328.0302 323.3715 318.2946 312.7053 306.4768 #>  [45,] 339.9889 336.2540 332.2795 328.0259 323.4437 318.4707 313.0270 307.0105 #>  [46,] 339.8982 336.2067 332.2868 328.1033 323.6133 318.7639 313.4912 307.7189 #>  [47,] 339.8572 336.2162 332.3598 328.2572 323.8723 319.1626 314.0800 308.5734 #>  [48,] 339.8635 336.2795 332.4941 328.4815 324.2124 319.6545 314.7749 309.5455 #>  [49,] 339.9145 336.3931 332.6852 328.7699 324.6246 320.2269 315.5577 310.6086 #>  [50,] 340.0074 336.5533 332.9281 329.1157 325.1000 320.8675 316.4111 311.7387 #>  [51,] 340.1391 336.7562 333.2178 329.5124 325.6298 321.5643 317.3193 312.9149 #>  [52,] 340.3067 336.9980 333.5494 329.9534 326.2055 322.3065 318.2681 314.1196 #>  [53,] 340.5070 337.2747 333.9179 330.4327 326.8191 323.0840 319.2452 315.3384 #>  [54,] 340.7370 337.5827 334.3185 330.9441 327.4635 323.8879 320.2399 316.5594 #>  [55,] 340.9938 337.9181 334.7469 331.4823 328.1319 324.7103 321.2435 317.7733 #>  [56,] 341.2743 338.2776 335.1986 332.0422 328.8184 325.5444 322.2485 318.9729 #>  [57,] 341.5758 338.6577 335.6699 332.6192 329.5176 326.3845 323.2488 320.1527 #>  [58,] 341.8956 339.0554 336.1570 333.2090 330.2250 327.2254 324.2397 321.3087 #>  [59,] 342.2313 339.4676 336.6566 333.8080 330.9365 328.0632 325.2173 322.4379 #>  [60,] 342.5803 339.8918 337.1658 334.4130 331.6488 328.8944 326.1785 323.5381 #>  [61,] 342.9406 340.3254 337.6818 335.0209 332.3587 329.7162 327.1211 324.6082 #>  [62,] 343.3100 340.7663 338.2021 335.6293 333.0638 330.5264 328.0434 325.6474 #>  [63,] 343.6868 341.2124 338.7248 336.2361 333.7621 331.3231 328.9440 326.6553 #>  [64,] 344.0693 341.6619 339.2478 336.8393 334.4518 332.1049 329.8222 327.6319 #>  [65,] 344.4557 342.1130 339.7695 337.4373 335.1315 332.8708 330.6775 328.5775 #>  [66,] 344.8448 342.5645 340.2885 338.0287 335.7999 333.6199 331.5095 329.4926 #>  [67,] 345.2353 343.0150 340.8035 338.6125 336.4563 334.3517 332.3181 330.3777 #>  [68,] 345.6260 343.4633 341.3134 339.1877 337.0999 335.0657 333.1036 331.2336 #>  [69,] 346.0159 343.9085 341.8174 339.7536 337.7300 335.7619 333.8660 332.0611 #>  [70,] 346.4041 344.3497 342.3146 340.3093 338.3464 336.4400 334.6057 332.8609 #>  [71,] 346.7897 344.7861 342.8043 340.8546 338.9487 337.1000 335.3232 333.6338 #>  [72,] 347.1722 345.2171 343.2861 341.3889 339.5368 337.7422 336.0187 334.3808 #>  [73,] 347.5508 345.6421 343.7594 341.9120 340.1105 338.3666 336.6929 335.1027 #>  [74,] 347.9249 346.0607 344.2239 342.4236 340.6698 338.9735 337.3462 335.8003 #>  [75,] 348.2942 346.4724 344.6793 342.9237 341.2149 339.5630 337.9792 336.4744 #>  [76,] 348.6582 346.8769 345.1255 343.4121 341.7456 340.1357 338.5923 337.1260 #>  [77,] 349.0166 347.2739 345.5621 343.8887 342.2623 340.6917 339.1863 337.7556 #>  [78,] 349.3690 347.6633 345.9891 344.3537 342.7650 341.2313 339.7615 338.3642 #>  [79,] 349.7153 348.0448 346.4064 344.8070 343.2539 341.7551 340.3186 338.9525 #>  [80,] 350.0551 348.4183 346.8140 345.2487 343.7293 342.2632 340.8580 339.5211 #>  [81,] 350.3883 348.7838 347.2119 345.6789 344.1914 342.7562 341.3804 340.0708 #>  [82,] 350.7149 349.1410 347.6000 346.0978 344.6404 343.2343 341.8861 340.6022 #>  [83,] 351.0346 349.4901 347.9785 346.5054 345.0766 343.6980 342.3758 341.1160 #>  [84,] 351.3474 349.8309 348.3474 346.9020 345.5002 344.1476 342.8499 341.6127 #>  [85,] 351.6532 350.1636 348.7067 347.2877 345.9115 344.5835 343.3089 342.0930 #>  [86,] 351.9520 350.4880 349.0567 347.6626 346.3107 345.0060 343.7532 342.5573 #>  [87,] 352.2438 350.8043 349.3972 348.0270 346.6982 345.4154 344.1833 343.0063 #>  [88,] 352.5286 351.1125 349.7286 348.3811 347.0742 345.8122 344.5996 343.4405 #>  [89,] 352.8063 351.4127 350.0509 348.7250 347.4389 346.1967 345.0026 343.8603 #>  [90,] 353.0771 351.7049 350.3643 349.0589 347.7926 346.5692 345.3926 344.2662 #>  [91,] 353.3409 351.9893 350.6688 349.3830 348.1356 346.9300 345.7699 344.6587 #>  [92,] 353.5978 352.2659 350.9647 349.6976 348.4681 347.2795 346.1351 345.0381 #>  [93,] 353.8478 352.5347 351.2520 350.0028 348.7903 347.6178 346.4884 345.4050 #>  [94,] 354.0911 352.7960 351.5309 350.2988 349.1026 347.9455 346.8302 345.7597 #>  [95,] 354.3276 353.0498 351.8016 350.5858 349.4051 348.2626 347.1608 346.1025 #>  [96,] 354.5574 353.2963 352.0642 350.8640 349.6982 348.5695 347.4806 346.4339 #>  [97,] 354.7806 353.5355 352.3189 351.1335 349.9819 348.8665 347.7898 346.7541 #>  [98,] 354.9974 353.7675 352.5658 351.3946 350.2565 349.1538 348.0888 347.0636 #>  [99,] 355.2077 353.9925 352.8050 351.6475 350.5223 349.4317 348.3778 347.3626 #> [100,] 355.4117 354.2106 353.0367 351.8923 350.7795 349.7004 348.6571 347.6515 #>           [,65]    [,66]    [,67]    [,68]    [,69]    [,70]    [,71]    [,72] #>   [1,] 366.6607 365.4866 364.4006 363.4079 362.5126 361.7173 361.0234 360.4304 #>   [2,] 365.3556 364.1588 363.0540 362.0470 361.1423 360.3428 359.6499 359.0632 #>   [3,] 364.0292 362.8079 361.6829 360.6605 359.7456 358.9415 358.2498 357.6700 #>   [4,] 362.6805 361.4330 360.2862 359.2471 358.3212 357.5122 356.8217 356.2493 #>   [5,] 361.3086 360.0328 358.8625 357.8054 356.8675 356.0531 355.3639 354.7996 #>   [6,] 359.9126 358.6062 357.4104 356.3337 355.3829 354.5626 353.8749 353.3193 #>   [7,] 358.4914 357.1520 355.9285 354.8305 353.8656 353.0390 352.3529 351.8068 #>   [8,] 357.0440 355.6688 354.4152 353.2940 352.3137 351.4801 350.7957 350.2601 #>   [9,] 355.5692 354.1551 352.8688 351.7222 350.7251 349.8837 349.2013 348.6771 #>  [10,] 354.0657 352.6094 351.2873 350.1130 349.0973 348.2476 347.5673 347.0556 #>  [11,] 352.5325 351.0301 349.6689 348.4641 347.4280 346.5690 345.8910 345.3931 #>  [12,] 350.9682 349.4154 348.0112 346.7729 345.7143 344.8450 344.1696 343.6870 #>  [13,] 349.3715 347.7635 346.3121 345.0366 343.9530 343.0724 342.3999 341.9342 #>  [14,] 347.7409 346.0724 344.5688 343.2522 342.1409 341.2476 340.5783 340.1314 #>  [15,] 346.0751 344.3400 342.7787 341.4164 340.2741 339.3666 338.7009 338.2751 #>  [16,] 344.3726 342.5641 340.9388 339.5254 338.3484 337.4250 336.7633 336.3611 #>  [17,] 342.6320 340.7424 339.0457 337.5752 336.3591 335.4177 334.7605 334.3850 #>  [18,] 340.8520 338.8724 337.0959 335.5611 334.3008 333.3390 332.6869 332.3417 #>  [19,] 339.0312 336.9515 335.0857 333.4781 332.1676 331.1825 330.5363 330.2256 #>  [20,] 337.1683 334.9772 333.0107 331.3205 329.9526 328.9408 328.3014 328.0302 #>  [21,] 335.2623 332.9467 330.8665 329.0821 327.6482 326.6055 325.9739 325.7482 #>  [22,] 333.3125 330.8575 328.6482 326.7556 325.2453 324.1668 323.5442 323.3715 #>  [23,] 331.3185 328.7068 326.3505 324.3332 322.7339 321.6133 321.0014 320.8906 #>  [24,] 329.2805 326.4925 323.9680 321.8059 320.1019 318.9315 318.3323 318.2946 #>  [25,] 327.1995 324.2126 321.4948 319.1635 317.3356 316.1057 315.5216 315.5710 #>  [26,] 325.0773 321.8658 318.9251 316.3946 314.4185 313.1167 312.5510 312.7053 #>  [27,] 322.9174 319.4520 316.2530 313.4864 311.3313 309.9416 309.3984 309.6805 #>  [28,] 320.7251 316.9725 313.4733 310.4247 308.0509 306.5521 306.0369 306.4768 #>  [29,] 318.5079 314.4309 310.5818 307.1938 304.5491 302.9129 302.4332 303.0709 #>  [30,] 316.2766 311.8343 307.5764 303.7767 300.7921 298.9792 298.5454 299.4353 #>  [31,] 314.0456 309.1942 304.4590 300.1562 296.7383 294.6933 294.3202 295.5382 #>  [32,] 311.8343 306.5286 301.2374 296.3161 292.3361 289.9785 289.6880 291.3425 #>  [33,] 309.6676 303.8638 297.9294 292.2446 287.5224 284.7299 284.5559 286.8073 #>  [34,] 307.5764 301.2374 294.5683 287.9411 282.2201 278.7996 278.7972 281.8899 #>  [35,] 305.5984 298.6997 291.2098 283.4285 276.3390 271.9684 272.2331 276.5557 #>  [36,] 303.7767 296.3161 287.9411 278.7755 269.7869 263.8929 264.6054 270.8002 #>  [37,] 302.1587 294.1654 284.8888 274.1336 262.5123 253.9922 255.5346 264.7036 #>  [38,] 300.7921 292.3361 282.2201 269.7869 254.6458 241.1740 244.4926 258.5474 #>  [39,] 299.7209 290.9159 280.1291 266.1865 246.8878 223.0846 231.0627 253.0098 #>  [40,] 298.9792 289.9785 278.7996 263.8929 241.1740 194.8736 217.4372 249.2830 #>  [41,] 298.5868 289.5677 278.3516 263.3500 240.2501 188.0424 215.2865 248.5893 #>  [42,] 298.5454 289.6880 278.7972 264.6054 244.4926 217.4372 227.1580 251.0745 #>  [43,] 298.8388 290.3025 280.0351 267.2756 251.3314 236.3775 240.2837 255.6451 #>  [44,] 299.4353 291.3425 281.8899 270.8002 258.5474 249.2830 251.0745 261.0342 #>  [45,] 300.2926 292.7219 284.1658 274.6967 265.2470 258.9410 259.7788 266.4604 #>  [46,] 301.3631 294.3514 286.6885 278.6489 271.2280 266.6100 266.9458 271.5805 #>  [47,] 302.5993 296.1497 289.3229 282.4828 276.5220 272.9429 272.9845 276.2860 #>  [48,] 303.9567 298.0486 291.9746 286.1167 281.2183 278.3187 278.1737 280.5702 #>  [49,] 305.3968 299.9948 294.5822 289.5208 285.4089 282.9757 282.7053 284.4643 #>  [50,] 306.8871 301.9485 297.1087 292.6923 289.1736 287.0736 286.7149 288.0102 #>  [51,] 308.4016 303.8811 299.5336 295.6413 292.5784 290.7242 290.3011 291.2497 #>  [52,] 309.9199 305.7733 301.8474 298.3834 295.6769 294.0089 293.5374 294.2206 #>  [53,] 311.4267 307.6123 304.0474 300.9359 298.5125 296.9888 296.4800 296.9559 #>  [54,] 312.9104 309.3903 306.1349 303.3159 301.1206 299.7110 299.1728 299.4839 #>  [55,] 314.3630 311.1032 308.1139 305.5393 303.5302 302.2122 301.6506 301.8285 #>  [56,] 315.7788 312.7492 309.9894 307.6207 305.7654 304.5222 303.9415 304.0103 #>  [57,] 317.1540 314.3282 311.7671 309.5733 307.8462 306.6647 306.0683 306.0468 #>  [58,] 318.4865 315.8412 313.4531 311.4085 309.7896 308.6597 308.0502 307.9530 #>  [59,] 319.7751 317.2901 315.0530 313.1369 311.6099 310.5235 309.9029 309.7418 #>  [60,] 321.0195 318.6772 316.5725 314.7676 313.3193 312.2700 311.6400 311.4243 #>  [61,] 322.2199 320.0050 318.0168 316.3088 314.9285 313.9109 313.2729 313.0102 #>  [62,] 323.3771 321.2761 319.3910 317.7678 316.4464 315.4563 314.8114 314.5081 #>  [63,] 324.4920 322.4932 320.6997 319.1510 317.8812 316.9150 316.2640 315.9253 #>  [64,] 325.5658 323.6589 321.9469 320.4642 319.2397 318.2944 317.6382 317.2685 #>  [65,] 326.5999 324.7758 323.1368 321.7126 320.5281 319.6013 318.9404 318.5433 #>  [66,] 327.5956 325.8464 324.2729 322.9008 321.7519 320.8414 320.1764 319.7551 #>  [67,] 328.5544 326.8731 325.3584 324.0331 322.9159 322.0199 321.3512 320.9084 #>  [68,] 329.4777 327.8580 326.3966 325.1132 324.0244 323.1413 322.4694 322.0073 #>  [69,] 330.3668 328.8034 327.3901 326.1446 325.0812 324.2098 323.5350 323.0555 #>  [70,] 331.2233 329.7111 328.3416 327.1304 326.0900 325.2290 324.5515 324.0565 #>  [71,] 332.0484 330.5831 329.2535 328.0733 327.0537 326.2022 325.5223 325.0133 #>  [72,] 332.8434 331.4211 330.1279 328.9760 327.9753 327.1324 326.4504 325.9285 #>  [73,] 333.6096 332.2268 330.9670 329.8409 328.8573 328.0222 327.3382 326.8048 #>  [74,] 334.3481 333.0018 331.7725 330.6700 329.7022 328.8741 328.1884 327.6443 #>  [75,] 335.0602 333.7475 332.5463 331.4655 330.5120 329.6904 329.0031 328.4493 #>  [76,] 335.7469 334.4652 333.2900 332.2290 331.2887 330.4731 329.7843 329.2216 #>  [77,] 336.4093 335.1563 334.0050 332.9624 332.0342 331.2241 330.5339 329.9630 #>  [78,] 337.0483 335.8220 334.6928 333.6671 332.7501 331.9450 331.2535 330.6752 #>  [79,] 337.6649 336.4633 335.3546 334.3446 333.4379 332.6375 331.9449 331.3595 #>  [80,] 338.2599 337.0814 335.9918 334.9963 334.0992 333.3031 332.6093 332.0176 #>  [81,] 338.8343 337.6773 336.6053 335.6234 334.7351 333.9430 333.2482 332.6505 #>  [82,] 339.3888 338.2518 337.1964 336.2270 335.3469 334.5585 333.8628 333.2596 #>  [83,] 339.9242 338.8060 337.7659 336.8082 335.9358 335.1509 334.4543 333.8459 #>  [84,] 340.4412 339.3405 338.3149 337.3680 336.5028 335.7211 335.0237 334.4105 #>  [85,] 340.9406 339.8563 338.8441 337.9075 337.0489 336.2702 335.5721 334.9544 #>  [86,] 341.4228 340.3540 339.3544 338.4273 337.5750 336.7991 336.1003 335.4784 #>  [87,] 341.8887 340.8343 339.8466 338.9285 338.0820 337.3087 336.6092 335.9834 #>  [88,] 342.3388 341.2980 340.3214 339.4117 338.5707 337.7999 337.0998 336.4703 #>  [89,] 342.7735 341.7456 340.7795 339.8776 339.0418 338.2733 337.5726 336.9397 #>  [90,] 343.1936 342.1778 341.2215 340.3271 339.4961 338.7298 338.0285 337.3923 #>  [91,] 343.5994 342.5951 341.6481 340.7606 339.9342 339.1699 338.4682 337.8289 #>  [92,] 343.9915 342.9980 342.0598 341.1789 340.3568 339.5944 338.8922 338.2501 #>  [93,] 344.3704 343.3870 342.4571 341.5825 340.7644 340.0038 339.3012 338.6563 #>  [94,] 344.7364 343.7627 342.8406 341.9719 341.1576 340.3988 339.6957 339.0483 #>  [95,] 345.0900 344.1255 343.2108 342.3476 341.5370 340.7798 340.0763 339.4264 #>  [96,] 345.4316 344.4757 343.5681 342.7102 341.9030 341.1474 340.4435 339.7913 #>  [97,] 345.7615 344.8140 343.9130 343.0601 342.2562 341.5020 340.7977 340.1434 #>  [98,] 346.0803 345.1405 344.2459 343.3977 342.5969 341.8440 341.1395 340.4831 #>  [99,] 346.3881 345.4558 344.5672 343.7235 342.9256 342.1741 341.4691 340.8108 #> [100,] 346.6853 345.7601 344.8772 344.0378 343.2427 342.4924 341.7872 341.1270 #>           [,73]    [,74]    [,75]    [,76]    [,77]    [,78]    [,79]    [,80] #>   [1,] 359.9366 359.5386 359.2321 359.0112 358.8698 358.8006 358.7964 358.8498 #>   [2,] 358.5808 358.1990 357.9129 357.7162 357.6020 357.5625 357.5899 357.6761 #>   [3,] 357.1999 356.8355 356.5713 356.4005 356.3154 356.3077 356.3687 356.4896 #>   [4,] 355.7925 355.4469 355.2064 355.0634 355.0096 355.0357 355.1324 355.2903 #>   [5,] 354.3572 354.0320 353.8170 353.7040 353.6837 353.7461 353.8809 354.0780 #>   [6,] 352.8927 352.5895 352.4021 352.3215 352.3372 352.4383 352.6138 352.8525 #>   [7,] 351.3972 351.1179 350.9605 350.9148 350.9693 351.1120 351.3309 351.6139 #>   [8,] 349.8691 349.6159 349.4910 349.4830 349.5793 349.7667 350.0319 350.3621 #>   [9,] 348.3065 348.0817 347.9922 348.0251 348.1666 348.4020 348.7168 349.0970 #>  [10,] 346.7073 346.5137 346.4627 346.5401 346.7304 347.0174 347.3853 347.8189 #>  [11,] 345.0694 344.9099 344.9011 345.0269 345.2700 345.6126 346.0373 346.5279 #>  [12,] 343.3904 343.2684 343.3058 343.4843 343.7847 344.1873 344.6730 345.2242 #>  [13,] 341.6676 341.5871 341.6751 341.9113 342.2739 342.7413 343.2924 343.9081 #>  [14,] 339.8982 339.8635 340.0074 340.3067 340.7370 341.2743 341.8956 342.5803 #>  [15,] 338.0790 338.0952 338.3007 338.6692 339.1734 339.7864 340.4831 341.2413 #>  [16,] 336.2067 336.2795 336.5533 336.9980 337.5827 338.2776 339.0554 339.8918 #>  [17,] 334.2773 334.4136 334.7631 335.2917 335.9644 336.7482 337.6130 338.5329 #>  [18,] 332.2868 332.4941 332.9281 333.5494 334.3185 335.1986 336.1570 337.1658 #>  [19,] 330.2305 330.5180 331.0463 331.7702 332.6450 333.6296 334.6885 335.7919 #>  [20,] 328.1033 328.4815 329.1157 329.9534 330.9441 332.0422 333.2090 334.4130 #>  [21,] 325.8997 326.3810 327.1342 328.0986 329.2166 330.4378 331.7204 333.0311 #>  [22,] 323.6133 324.2124 325.1000 326.2055 327.4635 328.8184 330.2250 331.6488 #>  [23,] 321.2372 321.9716 323.0115 324.2745 325.6865 327.1862 328.7256 330.2687 #>  [24,] 318.7639 319.6545 320.8675 322.3065 323.8879 325.5444 327.2254 328.8944 #>  [25,] 316.1850 317.2569 318.6673 320.3035 322.0710 323.8969 325.7286 327.5296 #>  [26,] 313.4912 314.7749 316.4111 318.2681 320.2399 322.2485 324.2397 326.1785 #>  [27,] 310.6727 312.2052 314.1005 316.2048 318.4004 320.6048 322.7643 324.8462 #>  [28,] 307.7189 309.5455 311.7387 314.1196 316.5594 318.9729 321.3087 323.5381 #>  [29,] 304.6192 306.7952 309.3312 312.0210 314.7257 317.3610 319.8801 322.2604 #>  [30,] 301.3631 303.9567 306.8871 309.9199 312.9104 315.7788 318.4865 321.0195 #>  [31,] 297.9421 301.0368 304.4198 307.8312 311.1267 314.2373 317.1370 319.8226 #>  [32,] 294.3514 298.0486 301.9485 305.7733 309.3903 312.7492 315.8412 318.6772 #>  [33,] 290.5942 295.0155 299.4996 303.7694 307.7195 311.3282 314.6096 317.5912 #>  [34,] 286.6885 291.9746 297.1087 301.8474 306.1349 309.9894 313.4531 316.5725 #>  [35,] 282.6779 288.9817 294.8210 300.0399 304.6591 308.7483 312.3825 315.6288 #>  [36,] 278.6489 286.1167 292.6923 298.3834 303.3159 307.6207 311.4085 314.7676 #>  [37,] 274.7529 283.4857 290.7869 296.9164 302.1289 306.6219 310.5413 313.9958 #>  [38,] 271.2280 281.2183 289.1736 295.6769 301.1206 305.7654 309.7896 313.3193 #>  [39,] 268.3971 279.4544 287.9180 294.6991 300.3099 305.0627 309.1607 312.7429 #>  [40,] 266.6100 278.3187 287.0736 294.0089 299.7110 304.5222 308.6597 312.2700 #>  [41,] 266.1176 277.8892 286.6716 293.6212 299.3317 304.1483 308.2894 311.9023 #>  [42,] 266.9458 278.1737 286.7149 293.5374 299.1728 303.9415 308.0502 311.6400 #>  [43,] 268.8807 279.1067 287.1777 293.7452 299.2279 303.8980 307.9396 311.4817 #>  [44,] 271.5805 280.5702 288.0102 294.2206 299.4839 304.0103 307.9530 311.4243 #>  [45,] 274.7100 282.4252 289.1485 294.9309 299.9225 304.2675 308.0836 311.4632 #>  [46,] 278.0129 284.5386 290.5236 295.8384 300.5222 304.6563 308.3227 311.5928 #>  [47,] 281.3215 286.7988 292.0700 296.9044 301.2591 305.1616 308.6605 311.8063 #>  [48,] 284.5386 289.1210 293.7301 298.0920 302.1096 305.7679 309.0865 312.0964 #>  [49,] 287.6133 291.4450 295.4562 299.3677 303.0506 306.4595 309.5897 312.4553 #>  [50,] 290.5236 293.7301 297.2112 300.7025 304.0612 307.2211 310.1592 312.8752 #>  [51,] 293.2642 295.9508 298.9668 302.0725 305.1225 308.0387 310.7846 313.3481 #>  [52,] 295.8384 298.0920 300.7025 303.4581 306.2184 308.8994 311.4558 313.8666 #>  [53,] 298.2543 300.1460 302.4039 304.8440 307.3350 309.7919 312.1639 314.4233 #>  [54,] 300.5222 302.1096 304.0612 306.2184 308.4611 310.7063 312.9005 315.0115 #>  [55,] 302.6526 303.9829 305.6681 307.5723 309.5873 311.6340 313.6582 315.6252 #>  [56,] 304.6563 305.7679 307.2211 308.8994 310.7063 312.5677 314.4306 316.2587 #>  [57,] 306.5432 307.4679 308.7183 310.1950 311.8122 313.5016 315.2120 316.9069 #>  [58,] 308.3227 309.0865 310.1592 311.4558 312.9005 314.4306 315.9975 317.5654 #>  [59,] 310.0033 310.6280 311.5445 312.6801 313.9678 315.3507 316.7832 318.2303 #>  [60,] 311.5928 312.0964 312.8752 313.8666 315.0115 316.2587 317.5654 318.8982 #>  [61,] 313.0982 313.4960 314.1528 315.0148 316.0300 317.1520 318.3413 319.5661 #>  [62,] 314.5260 314.8307 315.3792 316.1250 317.0221 318.0286 319.1085 320.2315 #>  [63,] 315.8818 316.1044 316.5564 317.1974 317.9868 318.8872 319.8651 320.8923 #>  [64,] 317.1708 317.3206 317.6863 318.2327 318.9240 319.7264 320.6094 321.5467 #>  [65,] 318.3978 318.4828 318.7710 319.2318 319.8335 320.5457 321.3403 322.1931 #>  [66,] 319.5670 319.5940 319.8126 320.1958 320.7155 321.3444 322.0568 322.8302 #>  [67,] 320.6823 320.6573 320.8130 321.1256 321.5703 322.1222 322.7582 323.4572 #>  [68,] 321.7471 321.6754 321.7741 322.0225 322.3982 322.8791 323.4439 324.0731 #>  [69,] 322.7647 322.6508 322.6978 322.8875 323.2000 323.6151 324.1135 324.6772 #>  [70,] 323.7381 323.5858 323.5858 323.7218 323.9760 324.3303 324.7669 325.2692 #>  [71,] 324.6697 324.4827 324.4398 324.5266 324.7271 325.0249 325.4038 325.8486 #>  [72,] 325.5622 325.3434 325.2613 325.3029 325.4538 325.6992 326.0243 326.4150 #>  [73,] 326.4177 326.1700 326.0519 326.0519 326.1569 326.3537 326.6285 326.9684 #>  [74,] 327.2383 326.9641 326.8130 326.7745 326.8371 326.9886 327.2164 327.5087 #>  [75,] 328.0259 327.7273 327.5458 327.4719 327.4952 327.6044 327.7883 328.0357 #>  [76,] 328.7823 328.4613 328.2517 328.1450 328.1317 328.2016 328.3443 328.5495 #>  [77,] 329.5090 329.1674 328.9318 328.7947 328.7474 328.7805 328.8847 329.0502 #>  [78,] 330.2076 329.8469 329.5873 329.4219 329.3429 329.3418 329.4097 329.5379 #>  [79,] 330.8795 330.5011 330.2192 330.0276 329.9190 329.8857 329.9197 330.0126 #>  [80,] 331.5260 331.1312 330.8286 330.6124 330.4762 330.4129 330.4149 330.4746 #>  [81,] 332.1482 331.7381 331.4162 331.1773 331.0153 330.9237 330.8956 330.9241 #>  [82,] 332.7472 332.3230 331.9832 331.7229 331.5367 331.4186 331.3623 331.3611 #>  [83,] 333.3242 332.8868 332.5302 332.2500 332.0411 331.8981 331.8151 331.7860 #>  [84,] 333.8802 333.4304 333.0581 332.7592 332.5290 332.3626 332.2544 332.1989 #>  [85,] 334.4159 333.9546 333.5676 333.2512 333.0010 332.8125 332.6806 332.6000 #>  [86,] 334.9324 334.4603 334.0595 333.7266 333.4576 333.2483 333.0940 332.9897 #>  [87,] 335.4303 334.9481 334.5343 334.1859 333.8993 333.6704 333.4948 333.3680 #>  [88,] 335.9105 335.4187 334.9928 334.6299 334.3265 334.0791 333.8834 333.7353 #>  [89,] 336.3736 335.8729 335.4356 335.0589 334.7398 334.4748 334.2601 334.0918 #>  [90,] 336.8204 336.3113 335.8632 335.4735 335.1395 334.8579 334.6252 334.4377 #>  [91,] 337.2514 336.7344 336.2761 335.8743 335.5262 335.2289 334.9790 334.7733 #>  [92,] 337.6673 337.1428 336.6749 336.2615 335.9001 335.5879 335.3218 335.0987 #>  [93,] 338.0687 337.5371 337.0601 336.6358 336.2617 335.9354 335.6539 335.4143 #>  [94,] 338.4559 337.9177 337.4321 336.9974 336.6114 336.2717 335.9755 335.7201 #>  [95,] 338.8297 338.2851 337.7914 337.3469 336.9495 336.5970 336.2869 336.0166 #>  [96,] 339.1904 338.6399 338.1384 337.6846 337.2764 336.9118 336.5884 336.3037 #>  [97,] 339.5385 338.9823 338.4735 338.0108 337.5924 337.2163 336.8802 336.5819 #>  [98,] 339.8744 339.3128 338.7971 338.3260 337.8978 337.5107 337.1626 336.8512 #>  [99,] 340.1986 339.6319 339.1096 338.6305 338.1930 337.7954 337.4357 337.1119 #> [100,] 340.5114 339.9398 339.4112 338.9245 338.4782 338.0706 337.6999 337.3642 #>           [,81]    [,82]    [,83]    [,84]    [,85]    [,86]    [,87]    [,88] #>   [1,] 358.9534 359.1000 359.2830 359.4959 359.7332 359.9894 360.2598 360.5403 #>   [2,] 357.8132 357.9936 358.2102 358.4563 358.7260 359.0136 359.3144 359.6240 #>   [3,] 356.6622 356.8782 357.1301 357.4109 357.7143 358.0346 358.3667 358.7064 #>   [4,] 355.5003 355.7538 356.0428 356.3598 356.6984 357.0526 357.4173 357.7879 #>   [5,] 354.3276 354.6206 354.9484 355.3034 355.6786 356.0680 356.4663 356.8689 #>   [6,] 353.1441 353.4787 353.8473 354.2419 354.6553 355.0813 355.5143 355.9498 #>   [7,] 351.9499 352.3283 352.7398 353.1758 353.6289 354.0927 354.5617 355.0311 #>   [8,] 350.7450 351.1697 351.6261 352.1054 352.5999 353.1029 353.6090 354.1133 #>   [9,] 349.5298 350.0032 350.5067 351.0312 351.5687 352.1124 352.6567 353.1969 #>  [10,] 348.3044 348.8292 349.3822 349.9538 350.5360 351.1218 351.7055 352.2825 #>  [11,] 347.0692 347.6482 348.2530 348.8739 349.5024 350.1316 350.7559 351.3707 #>  [12,] 345.8247 346.4607 347.1199 347.7920 348.4687 349.1428 349.8088 350.4623 #>  [13,] 344.5715 345.2674 345.9835 346.7091 347.4356 348.1560 348.8649 349.5578 #>  [14,] 343.3100 344.0693 344.8448 345.6260 346.4041 347.1722 347.9249 348.6582 #>  [15,] 342.0413 342.8670 343.7048 344.5437 345.3751 346.1922 346.9899 347.7643 #>  [16,] 340.7663 341.6619 342.5645 343.4633 344.3497 345.2171 346.0607 346.8769 #>  [17,] 339.4861 340.4550 341.4253 342.3861 343.3291 344.2480 345.1383 345.9969 #>  [18,] 338.2021 339.2478 340.2885 341.3134 342.3146 343.2861 344.2239 345.1255 #>  [19,] 336.9159 338.0420 339.1557 340.2468 341.3075 342.3326 343.3186 344.2635 #>  [20,] 335.6293 336.8393 338.0287 339.1877 340.3093 341.3889 342.4236 343.4121 #>  [21,] 334.3445 335.6418 336.9094 338.1381 339.3217 340.4565 341.5403 342.5724 #>  [22,] 333.0638 334.4518 335.7999 337.0999 338.3464 339.5368 340.6698 341.7456 #>  [23,] 331.7901 333.2719 334.7026 336.0750 337.3852 338.6315 339.8138 340.9330 #>  [24,] 330.5264 332.1049 333.6199 335.0657 336.4400 337.7422 338.9735 340.1357 #>  [25,] 329.2762 330.9539 332.5545 334.0744 335.5128 336.8707 338.1504 339.3550 #>  [26,] 328.0434 329.8222 331.5095 333.1036 334.6057 336.0187 337.3462 338.5923 #>  [27,] 326.8322 328.7136 330.4877 332.1558 333.7210 335.1881 336.5623 337.8489 #>  [28,] 325.6474 327.6319 329.4926 331.2336 332.8609 334.3808 335.8003 337.1260 #>  [29,] 324.4939 326.5812 328.5274 330.3400 332.0275 333.5986 335.0617 336.4249 #>  [30,] 323.3771 325.5658 327.5956 329.4777 331.2233 332.8434 334.3481 335.7469 #>  [31,] 322.3025 324.5902 326.7008 328.6494 330.4504 332.1169 333.6610 335.0933 #>  [32,] 321.2761 323.6589 325.8464 327.8580 329.7111 331.4211 333.0018 334.4652 #>  [33,] 320.3036 322.7763 325.0360 327.1062 329.0075 330.7576 332.3719 333.8638 #>  [34,] 319.3910 321.9469 324.2729 326.3966 328.3416 330.1279 331.7725 333.2900 #>  [35,] 318.5440 321.1749 323.5602 325.7315 327.7154 329.5336 331.2049 332.7448 #>  [36,] 317.7678 320.4642 322.9008 325.1132 327.1304 328.9760 330.6700 332.2290 #>  [37,] 317.0672 319.8181 322.2973 324.5437 326.5882 328.4563 330.1689 331.7435 #>  [38,] 316.4464 319.2397 321.7519 324.0244 326.0900 327.9753 329.7022 331.2887 #>  [39,] 315.9087 318.7313 321.2662 323.5566 325.6367 327.5338 329.2704 330.8651 #>  [40,] 315.4563 318.2944 320.8414 323.1413 325.2290 327.1324 328.8741 330.4731 #>  [41,] 315.0905 317.9300 320.4781 322.7789 324.8673 326.7712 328.5135 330.1128 #>  [42,] 314.8114 317.6382 320.1764 322.4694 324.5515 326.4504 328.1884 329.7843 #>  [43,] 314.6180 317.4182 319.9358 322.2125 324.2815 326.1696 327.8988 329.4873 #>  [44,] 314.5081 317.2685 319.7551 322.0073 324.0565 325.9285 327.6443 329.2216 #>  [45,] 314.4788 317.1870 319.6329 321.8527 323.8758 325.7263 327.4244 328.9868 #>  [46,] 314.5260 317.1708 319.5670 321.7471 323.7381 325.5622 327.2383 328.7823 #>  [47,] 314.6450 317.2166 319.5550 321.6887 323.6419 325.4350 327.0852 328.6074 #>  [48,] 314.8307 317.3206 319.5940 321.6754 323.5858 325.3434 326.9641 328.4613 #>  [49,] 315.0774 317.4786 319.6810 321.7047 323.5677 325.2861 326.8737 328.3431 #>  [50,] 315.3792 317.6863 319.8126 321.7741 323.5858 325.2613 326.8130 328.2517 #>  [51,] 315.7304 317.9392 319.9854 321.8810 323.6379 325.2675 326.7804 328.1860 #>  [52,] 316.1250 318.2327 320.1958 322.0225 323.7218 325.3029 326.7745 328.1450 #>  [53,] 316.5573 318.5624 320.4403 322.1959 323.8353 325.3656 326.7940 328.1273 #>  [54,] 317.0221 318.9240 320.7155 322.3982 323.9760 325.4538 326.8371 328.1317 #>  [55,] 317.5141 319.3133 321.0180 322.6269 324.1418 325.5656 326.9025 328.1569 #>  [56,] 318.0286 319.7264 321.3444 322.8791 324.3303 325.6992 326.9886 328.2016 #>  [57,] 318.5614 320.1596 321.6916 323.1523 324.5393 325.8527 327.0937 328.2645 #>  [58,] 319.1085 320.6094 322.0568 323.4439 324.7669 326.0243 327.2164 328.3443 #>  [59,] 319.6662 321.0727 322.4372 323.7516 325.0108 326.2123 327.3552 328.4397 #>  [60,] 320.2315 321.5467 322.8302 324.0731 325.2692 326.4150 327.5087 328.5495 #>  [61,] 320.8015 322.0286 323.2335 324.4063 325.5402 326.6308 327.6753 328.6725 #>  [62,] 321.3736 322.5162 323.6449 324.7494 325.8221 326.8581 327.8538 328.8074 #>  [63,] 321.9458 323.0073 324.0624 325.1004 326.1133 327.0955 328.0429 328.9531 #>  [64,] 322.5162 323.5001 324.4843 325.4577 326.4122 327.3416 328.2413 329.1085 #>  [65,] 323.0830 323.9929 324.9089 325.8199 326.7175 327.5951 328.4479 329.2726 #>  [66,] 323.6449 324.4843 325.3348 326.1855 327.0277 327.8548 328.6616 329.4443 #>  [67,] 324.2007 324.9729 325.7607 326.5532 327.3418 328.1197 328.8813 329.6228 #>  [68,] 324.7494 325.4577 326.1855 326.9220 327.6587 328.3886 329.1061 329.8071 #>  [69,] 325.2901 325.9378 326.6081 327.2908 327.9773 328.6606 329.3351 329.9964 #>  [70,] 325.8221 326.4122 327.0277 327.6587 328.2967 328.9348 329.5674 330.1898 #>  [71,] 326.3450 326.8803 327.4435 328.0249 328.6161 329.2105 329.8022 330.3867 #>  [72,] 326.8581 327.3416 327.8548 328.3886 328.9348 329.4868 330.0389 330.5864 #>  [73,] 327.3611 327.7954 328.2610 328.7492 329.2521 329.7632 330.2768 330.7882 #>  [74,] 327.8538 328.2413 328.6616 329.1061 329.5674 330.0389 330.5152 330.9916 #>  [75,] 328.3360 328.6791 329.0562 329.4589 329.8801 330.3135 330.7536 331.1959 #>  [76,] 328.8074 329.1085 329.4443 329.8071 330.1898 330.5864 330.9916 331.4007 #>  [77,] 329.2680 329.5292 329.8258 330.1503 330.4961 330.8572 331.2285 331.6055 #>  [78,] 329.7178 329.9411 330.2003 330.4882 330.7985 331.1255 331.4641 331.8098 #>  [79,] 330.1567 330.3441 330.5676 330.8206 331.0968 331.3909 331.6978 332.0134 #>  [80,] 330.5848 330.7380 330.9276 331.1471 331.3907 331.6531 331.9295 332.2157 #>  [81,] 331.0021 331.1229 331.2801 331.4676 331.6798 331.9117 332.1587 332.4166 #>  [82,] 331.4087 331.4987 331.6250 331.7819 331.9641 332.1667 332.3852 332.6156 #>  [83,] 331.8047 331.8654 331.9623 332.0900 332.2433 332.4177 332.6087 332.8126 #>  [84,] 332.1903 332.2231 332.2919 332.3916 332.5173 332.6645 332.8290 333.0072 #>  [85,] 332.5655 332.5718 332.6138 332.6867 332.7859 332.9069 333.0459 333.1993 #>  [86,] 332.9305 332.9116 332.9280 332.9753 333.0490 333.1449 333.2593 333.3886 #>  [87,] 333.2855 333.2425 333.2345 333.2573 333.3065 333.3783 333.4689 333.5751 #>  [88,] 333.6305 333.5646 333.5334 333.5327 333.5584 333.6069 333.6747 333.7584 #>  [89,] 333.9659 333.8781 333.8246 333.8014 333.8047 333.8308 333.8765 333.9385 #>  [90,] 334.2916 334.1831 334.1083 334.0635 334.0452 334.0498 334.0742 334.1152 #>  [91,] 334.6080 334.4796 334.3845 334.3191 334.2800 334.2639 334.2677 334.2885 #>  [92,] 334.9152 334.7678 334.6532 334.5680 334.5090 334.4730 334.4570 334.4583 #>  [93,] 335.2133 335.0478 334.9146 334.8104 334.7323 334.6771 334.6420 334.6244 #>  [94,] 335.5026 335.3197 335.1687 335.0463 334.9498 334.8761 334.8227 334.7867 #>  [95,] 335.7831 335.5838 335.4156 335.2758 335.1616 335.0702 334.9989 334.9454 #>  [96,] 336.0551 335.8400 335.6555 335.4989 335.3677 335.2591 335.1708 335.1001 #>  [97,] 336.3188 336.0885 335.8883 335.7157 335.5681 335.4431 335.3382 335.2511 #>  [98,] 336.5743 336.3295 336.1143 335.9262 335.7629 335.6220 335.5011 335.3981 #>  [99,] 336.8218 336.5631 336.3335 336.1306 335.9521 335.7959 335.6596 335.5412 #> [100,] 337.0615 336.7894 336.5459 336.3288 336.1358 335.9648 335.8136 335.6803 #>           [,89]    [,90]    [,91]    [,92]    [,93]    [,94]    [,95]    [,96] #>   [1,] 360.8271 361.1170 361.4073 361.6953 361.9793 362.2572 362.5278 362.7897 #>   [2,] 359.9386 360.2550 360.5704 360.8823 361.1888 361.4881 361.7787 362.0596 #>   [3,] 359.0496 359.3933 359.7344 360.0707 360.4001 360.7210 361.0321 361.3322 #>   [4,] 358.1606 358.5321 358.8996 359.2608 359.6136 359.9565 360.2882 360.6077 #>   [5,] 357.2719 357.6720 358.0664 358.4529 358.8295 359.1948 359.5474 359.8865 #>   [6,] 356.3839 356.8133 357.2353 357.6475 358.0483 358.4362 358.8100 359.1689 #>   [7,] 355.4972 355.9565 356.4065 356.8451 357.2704 357.6812 358.0764 358.4552 #>   [8,] 354.6121 355.1020 355.5807 356.0459 356.4961 356.9300 357.3468 357.7457 #>   [9,] 353.7292 354.2504 354.7582 355.2505 355.7258 356.1832 356.6217 357.0408 #>  [10,] 352.8491 353.4022 353.9395 354.4593 354.9601 355.4411 355.9014 356.3408 #>  [11,] 351.9723 352.5579 353.1253 353.6729 354.1994 354.7041 355.1864 355.6462 #>  [12,] 351.0996 351.7182 352.3161 352.8917 353.4441 353.9727 354.4771 354.9572 #>  [13,] 350.2316 350.8837 351.5124 352.1163 352.6948 353.2474 353.7738 354.2743 #>  [14,] 349.3690 350.0551 350.7149 351.3474 351.9520 352.5286 353.0771 353.5978 #>  [15,] 348.5127 349.2331 349.9242 350.5854 351.2162 351.8168 352.3873 352.9282 #>  [16,] 347.6633 348.4183 349.1410 349.8309 350.4880 351.1125 351.7049 352.2659 #>  [17,] 346.8218 347.6117 348.3661 349.0847 349.7680 350.4163 351.0304 351.6112 #>  [18,] 345.9891 346.8140 347.6000 348.3474 349.0567 349.7286 350.3643 350.9647 #>  [19,] 345.1661 346.0261 346.8437 347.6196 348.3547 349.0500 349.7069 350.3267 #>  [20,] 344.3537 345.2487 346.0978 346.9020 347.6626 348.3811 349.0589 349.6976 #>  [21,] 343.5530 344.4828 345.3631 346.1953 346.9811 347.7223 348.4206 349.0779 #>  [22,] 342.7650 343.7293 344.6404 345.5002 346.3107 347.0742 347.7926 348.4681 #>  [23,] 341.9907 342.9892 343.9305 344.8174 345.6521 346.4373 347.1753 347.8684 #>  [24,] 341.2313 342.2632 343.2343 344.1476 345.0060 345.8122 346.5692 347.2795 #>  [25,] 340.4879 341.5525 342.5526 343.4915 344.3728 345.1995 345.9748 346.7016 #>  [26,] 339.7615 340.8580 341.8861 342.8499 343.7532 344.5996 345.3926 346.1351 #>  [27,] 339.0532 340.1805 341.2357 342.2234 343.1479 344.0131 344.8229 345.5805 #>  [28,] 338.3642 339.5211 340.6022 341.6127 342.5573 343.4405 344.2662 345.0381 #>  [29,] 337.6956 338.8806 339.9863 341.0184 341.9821 342.8822 343.7230 344.5084 #>  [30,] 337.0483 338.2599 339.3888 340.4412 341.4228 342.3388 343.1936 343.9915 #>  [31,] 336.4234 337.6599 338.8104 339.8817 340.8800 341.8106 342.6784 343.4880 #>  [32,] 335.8220 337.0814 338.2518 339.3405 340.3540 341.2980 342.1778 342.9980 #>  [33,] 335.2448 336.5251 337.7136 338.8181 339.8453 340.8015 341.6921 342.5218 #>  [34,] 334.6928 335.9918 337.1964 338.3149 339.3544 340.3214 341.2215 342.0598 #>  [35,] 334.1666 335.4820 336.7007 337.8314 338.8817 339.8581 340.7665 341.6121 #>  [36,] 333.6671 334.9963 336.2270 337.3680 338.4273 339.4117 340.3271 341.1789 #>  [37,] 333.1948 334.5352 335.7756 336.9251 337.9917 338.9825 339.9036 340.7604 #>  [38,] 332.7501 334.0992 335.3469 336.5028 337.5750 338.5707 339.4961 340.3568 #>  [39,] 332.3334 333.6884 334.9412 336.1014 337.1774 338.1765 339.1048 339.9681 #>  [40,] 331.9450 333.3031 334.5585 335.7211 336.7991 337.7999 338.7298 339.5944 #>  [41,] 331.5851 332.9434 334.1991 335.3619 336.4400 337.4410 338.3710 339.2358 #>  [42,] 331.2535 332.6093 333.8628 335.0237 336.1003 337.0998 338.0285 338.8922 #>  [43,] 330.9503 332.3008 333.5497 334.7067 335.7798 336.7762 337.7023 338.5637 #>  [44,] 330.6752 332.0176 333.2596 334.4105 335.4784 336.4703 337.3923 338.2501 #>  [45,] 330.4278 331.7594 332.9922 334.1351 335.1960 336.1817 337.0984 337.9513 #>  [46,] 330.2076 331.5260 332.7472 333.8802 334.9324 335.9105 336.8204 337.6673 #>  [47,] 330.0142 331.3167 332.5243 333.6454 334.6872 335.6562 336.5581 337.3979 #>  [48,] 329.8469 331.1312 332.3230 333.4304 334.4603 335.4187 336.3113 337.1428 #>  [49,] 329.7049 330.9687 332.1428 333.2348 334.2512 335.1977 336.0798 336.9019 #>  [50,] 329.5873 330.8286 331.9832 333.0581 334.0595 334.9928 335.8632 336.6749 #>  [51,] 329.4933 330.7101 331.8434 332.8997 333.8847 334.8037 335.6612 336.4616 #>  [52,] 329.4219 330.6124 331.7229 332.7592 333.7266 334.6299 335.4735 336.2615 #>  [53,] 329.3721 330.5348 331.6209 332.6358 333.5844 334.4710 335.2998 336.0745 #>  [54,] 329.3429 330.4762 331.5367 332.5290 333.4576 334.3265 335.1395 335.9001 #>  [55,] 329.3332 330.4359 331.4695 332.4382 333.3458 334.1961 334.9924 335.7380 #>  [56,] 329.3418 330.4129 331.4186 332.3626 333.2483 334.0791 334.8579 335.5879 #>  [57,] 329.3676 330.4062 331.3831 332.3016 333.1646 333.9750 334.7357 335.4493 #>  [58,] 329.4097 330.4149 331.3623 332.2544 333.0940 333.8834 334.6252 335.3218 #>  [59,] 329.4668 330.4380 331.3552 332.2204 333.0359 333.8037 334.5261 335.2051 #>  [60,] 329.5379 330.4746 331.3611 332.1989 332.9897 333.7353 334.4377 335.0987 #>  [61,] 329.6219 330.5239 331.3792 332.1891 332.9548 333.6778 334.3597 335.0022 #>  [62,] 329.7178 330.5848 331.4087 332.1903 332.9305 333.6305 334.2916 334.9152 #>  [63,] 329.8245 330.6564 331.4488 332.2019 332.9163 333.5930 334.2329 334.8372 #>  [64,] 329.9411 330.7380 331.4987 332.2231 332.9116 333.5646 334.1831 334.7678 #>  [65,] 330.0667 330.8287 331.5577 332.2533 332.9157 333.5450 334.1417 334.7066 #>  [66,] 330.2003 330.9276 331.6250 332.2919 332.9280 333.5334 334.1083 334.6532 #>  [67,] 330.3411 331.0340 331.7000 332.3382 332.9481 333.5295 334.0824 334.6071 #>  [68,] 330.4882 331.1471 331.7819 332.3916 332.9753 333.5327 334.0635 334.5680 #>  [69,] 330.6409 331.2662 331.8702 332.4515 333.0091 333.5425 334.0513 334.5354 #>  [70,] 330.7985 331.3907 331.9641 332.5173 333.0490 333.5584 334.0452 334.5090 #>  [71,] 330.9603 331.5198 332.0631 332.5884 333.0944 333.5801 334.0448 334.4883 #>  [72,] 331.1255 331.6531 332.1667 332.6645 333.1449 333.6069 334.0498 334.4730 #>  [73,] 331.2936 331.7898 332.2742 332.7448 333.2000 333.6386 334.0597 334.4627 #>  [74,] 331.4641 331.9295 332.3852 332.8290 333.2593 333.6747 334.0742 334.4570 #>  [75,] 331.6363 332.0716 332.4991 332.9166 333.3223 333.7147 334.0928 334.4557 #>  [76,] 331.8098 332.2157 332.6156 333.0072 333.3886 333.7584 334.1152 334.4583 #>  [77,] 331.9842 332.3613 332.7342 333.1003 333.4579 333.8053 334.1411 334.4645 #>  [78,] 332.1589 332.5080 332.8544 333.1956 333.5297 333.8550 334.1702 334.4741 #>  [79,] 332.3337 332.6555 332.9759 333.2927 333.6037 333.9073 334.2020 334.4867 #>  [80,] 332.5080 332.8032 333.0984 333.3912 333.6796 333.9618 334.2364 334.5021 #>  [81,] 332.6817 332.9510 333.2215 333.4909 333.7570 334.0182 334.2729 334.5199 #>  [82,] 332.8544 333.0984 333.3449 333.5913 333.8357 334.0763 334.3115 334.5399 #>  [83,] 333.0258 333.2453 333.4682 333.6923 333.9154 334.1357 334.3516 334.5619 #>  [84,] 333.1956 333.3912 333.5913 333.7935 333.9958 334.1962 334.3933 334.5856 #>  [85,] 333.3637 333.5361 333.7139 333.8948 334.0766 334.2575 334.4360 334.6107 #>  [86,] 333.5297 333.6796 333.8357 333.9958 334.1576 334.3195 334.4798 334.6371 #>  [87,] 333.6935 333.8216 333.9566 334.0963 334.2387 334.3819 334.5243 334.6646 #>  [88,] 333.8550 333.9618 334.0763 334.1962 334.3195 334.4444 334.5694 334.6929 #>  [89,] 334.0139 334.1001 334.1946 334.2952 334.3999 334.5070 334.6147 334.7219 #>  [90,] 334.1702 334.2364 334.3115 334.3933 334.4798 334.5694 334.6603 334.7513 #>  [91,] 334.3236 334.3704 334.4266 334.4901 334.5589 334.6314 334.7059 334.7810 #>  [92,] 334.4741 334.5021 334.5399 334.5856 334.6371 334.6929 334.7513 334.8109 #>  [93,] 334.6216 334.6313 334.6513 334.6796 334.7143 334.7538 334.7964 334.8408 #>  [94,] 334.7660 334.7580 334.7607 334.7721 334.7903 334.8138 334.8410 334.8706 #>  [95,] 334.9071 334.8820 334.8678 334.8628 334.8650 334.8730 334.8851 334.9001 #>  [96,] 335.0450 335.0032 334.9727 334.9517 334.9383 334.9311 334.9285 334.9292 #>  [97,] 335.1796 335.1216 335.0752 335.0386 335.0101 334.9880 334.9710 334.9577 #>  [98,] 335.3107 335.2371 335.1753 335.1236 335.0802 335.0437 335.0126 334.9857 #>  [99,] 335.4385 335.3497 335.2729 335.2064 335.1486 335.0980 335.0532 335.0129 #> [100,] 335.5628 335.4593 335.3679 335.2871 335.2153 335.1509 335.0926 335.0392 #>           [,97]    [,98]    [,99]   [,100] #>   [1,] 363.0421 363.2839 363.5147 363.7339 #>   [2,] 362.3298 362.5885 362.8351 363.0691 #>   [3,] 361.6204 361.8960 362.1586 362.4076 #>   [4,] 360.9141 361.2069 361.4854 361.7495 #>   [5,] 360.2113 360.5212 360.8159 361.0951 #>   [6,] 359.5122 359.8394 360.1503 360.4446 #>   [7,] 358.8171 359.1617 359.4888 359.7983 #>   [8,] 358.1263 358.4884 358.8317 359.1564 #>   [9,] 357.4402 357.8197 358.1793 358.5191 #>  [10,] 356.7590 357.1560 357.5319 357.8867 #>  [11,] 356.0832 356.4976 356.8896 357.2595 #>  [12,] 355.4130 355.8448 356.2530 356.6378 #>  [13,] 354.7489 355.1980 355.6221 356.0217 #>  [14,] 354.0911 354.5574 354.9974 355.4117 #>  [15,] 353.4400 353.9234 354.3791 354.8079 #>  [16,] 352.7960 353.2963 353.7675 354.2106 #>  [17,] 352.1595 352.6765 353.1630 353.6201 #>  [18,] 351.5309 352.0642 352.5658 353.0367 #>  [19,] 350.9105 351.4600 351.9762 352.4607 #>  [20,] 350.2988 350.8640 351.3946 351.8923 #>  [21,] 349.6960 350.2766 350.8213 351.3318 #>  [22,] 349.1026 349.6982 350.2565 350.7795 #>  [23,] 348.5190 349.1290 349.7006 350.2356 #>  [24,] 347.9455 348.5695 349.1538 349.7004 #>  [25,] 347.3824 348.0199 348.6165 349.1742 #>  [26,] 346.8302 347.4806 348.0888 348.6571 #>  [27,] 346.2892 346.9518 347.5711 348.1495 #>  [28,] 345.7597 346.4339 347.0636 347.6515 #>  [29,] 345.2420 345.9270 346.5666 347.1633 #>  [30,] 344.7364 345.4316 346.0803 346.6853 #>  [31,] 344.2432 344.9477 345.6048 346.2175 #>  [32,] 343.7627 344.4757 345.1405 345.7601 #>  [33,] 343.2951 344.0158 344.6875 345.3133 #>  [34,] 342.8406 343.5681 344.2459 344.8772 #>  [35,] 342.3995 343.1329 343.8160 344.4520 #>  [36,] 341.9719 342.7102 343.3977 344.0378 #>  [37,] 341.5579 342.3002 342.9913 343.6347 #>  [38,] 341.1576 341.9030 342.5969 343.2427 #>  [39,] 340.7713 341.5187 342.2144 342.8619 #>  [40,] 340.3988 341.1474 341.8440 342.4924 #>  [41,] 340.0403 340.7889 341.4857 342.1342 #>  [42,] 339.6957 340.4435 341.1395 341.7872 #>  [43,] 339.3651 340.1110 340.8052 341.4515 #>  [44,] 339.0483 339.7913 340.4831 341.1270 #>  [45,] 338.7453 339.4845 340.1728 340.8136 #>  [46,] 338.4559 339.1904 339.8744 340.5114 #>  [47,] 338.1801 338.9089 339.5878 340.2201 #>  [48,] 337.9177 338.6399 339.3128 339.9398 #>  [49,] 337.6684 338.3831 339.0493 339.6702 #>  [50,] 337.4321 338.1384 338.7971 339.4112 #>  [51,] 337.2086 337.9057 338.5561 339.1627 #>  [52,] 336.9974 337.6846 338.3260 338.9245 #>  [53,] 336.7985 337.4749 338.1067 338.6964 #>  [54,] 336.6114 337.2764 337.8978 338.4782 #>  [55,] 336.4359 337.0888 337.6993 338.2696 #>  [56,] 336.2717 336.9118 337.5107 338.0706 #>  [57,] 336.1183 336.7451 337.3319 337.8808 #>  [58,] 335.9755 336.5884 337.1626 337.6999 #>  [59,] 335.8429 336.4414 337.0024 337.5278 #>  [60,] 335.7201 336.3037 336.8512 337.3642 #>  [61,] 335.6068 336.1751 336.7086 337.2089 #>  [62,] 335.5026 336.0551 336.5743 337.0615 #>  [63,] 335.4070 335.9435 336.4481 336.9217 #>  [64,] 335.3197 335.8400 336.3295 336.7894 #>  [65,] 335.2404 335.7440 336.2183 336.6642 #>  [66,] 335.1687 335.6555 336.1143 336.5459 #>  [67,] 335.1041 335.5739 336.0170 336.4342 #>  [68,] 335.0463 335.4989 335.9262 336.3288 #>  [69,] 334.9950 335.4303 335.8416 336.2294 #>  [70,] 334.9498 335.3677 335.7629 336.1358 #>  [71,] 334.9103 335.3107 335.6898 336.0477 #>  [72,] 334.8761 335.2591 335.6220 335.9648 #>  [73,] 334.8470 335.2126 335.5592 335.8869 #>  [74,] 334.8227 335.1708 335.5011 335.8136 #>  [75,] 334.8027 335.1334 335.4475 335.7449 #>  [76,] 334.7867 335.1001 335.3981 335.6803 #>  [77,] 334.7746 335.0708 335.3526 335.6197 #>  [78,] 334.7660 335.0450 335.3107 335.5628 #>  [79,] 334.7605 335.0226 335.2723 335.5094 #>  [80,] 334.7580 335.0032 335.2371 335.4593 #>  [81,] 334.7581 334.9867 335.2049 335.4122 #>  [82,] 334.7607 334.9727 335.1753 335.3679 #>  [83,] 334.7654 334.9611 335.1483 335.3263 #>  [84,] 334.7721 334.9517 335.1236 335.2871 #>  [85,] 334.7804 334.9441 335.1009 335.2502 #>  [86,] 334.7903 334.9383 335.0802 335.2153 #>  [87,] 334.8015 334.9340 335.0612 335.1822 #>  [88,] 334.8138 334.9311 335.0437 335.1509 #>  [89,] 334.8271 334.9293 335.0275 335.1211 #>  [90,] 334.8410 334.9285 335.0126 335.0926 #>  [91,] 334.8556 334.9285 334.9987 335.0654 #>  [92,] 334.8706 334.9292 334.9857 335.0392 #>  [93,] 334.8859 334.9304 334.9734 335.0140 #>  [94,] 334.9013 334.9320 334.9617 334.9895 #>  [95,] 334.9167 334.9338 334.9505 334.9657 #>  [96,] 334.9320 334.9358 334.9396 334.9425 #>  [97,] 334.9470 334.9377 334.9289 334.9197 #>  [98,] 334.9617 334.9396 334.9184 334.8972 #>  [99,] 334.9759 334.9412 334.9078 334.8748 #> [100,] 334.9895 334.9425 334.8972 334.8526 head_to_potential(mc, hc) #>            [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8] #>   [1,] 962.4030 961.1546 959.8996 958.6378 957.3691 956.0933 954.8101 953.5196 #>   [2,] 961.9708 960.7204 959.4633 958.1993 956.9283 955.6500 954.3644 953.0712 #>   [3,] 961.5403 960.2879 959.0287 957.7626 956.4892 955.2086 953.9206 952.6248 #>   [4,] 961.1115 959.8571 958.5959 957.3276 956.0520 954.7691 953.4786 952.1804 #>   [5,] 960.6844 959.4281 958.1648 956.8944 955.6167 954.3315 953.0386 951.7379 #>   [6,] 960.2589 959.0007 957.7355 956.4630 955.1832 953.8958 952.6006 951.2974 #>   [7,] 959.8352 958.5752 957.3080 956.0335 954.7516 953.4620 952.1645 950.8590 #>   [8,] 959.4132 958.1514 956.8823 955.6059 954.3219 953.0302 951.7305 950.4226 #>   [9,] 958.9930 957.7294 956.4585 955.1802 953.8942 952.6003 951.2985 949.9884 #>  [10,] 958.5745 957.3092 956.0365 954.7563 953.4684 952.1725 950.8685 949.5562 #>  [11,] 958.1579 956.8909 955.6165 954.3344 953.0446 951.7468 950.4407 949.1262 #>  [12,] 957.7430 956.4744 955.1983 953.9145 952.6228 951.3230 950.0150 948.6984 #>  [13,] 957.3300 956.0598 954.7820 953.4965 952.2030 950.9014 949.5913 948.2727 #>  [14,] 956.9188 955.6471 954.3677 953.0805 951.7853 950.4818 949.1699 947.8493 #>  [15,] 956.5095 955.2362 953.9553 952.6665 951.3696 950.0644 948.7506 947.4281 #>  [16,] 956.1020 954.8273 953.5449 952.2546 950.9560 949.6491 948.3335 947.0091 #>  [17,] 955.6964 954.4204 953.1365 951.8446 950.5445 949.2360 947.9187 946.5925 #>  [18,] 955.2928 954.0154 952.7301 951.4368 950.1352 948.8250 947.5061 946.1781 #>  [19,] 954.8910 953.6123 952.3257 951.0310 949.7279 948.4162 947.0957 945.7661 #>  [20,] 954.4912 953.2113 951.9234 950.6273 949.3228 948.0097 946.6876 945.3564 #>  [21,] 954.0933 952.8122 951.5231 950.2257 948.9199 947.6053 946.2818 944.9490 #>  [22,] 953.6973 952.4151 951.1248 949.8263 948.5191 947.2033 945.8783 944.5441 #>  [23,] 953.3033 952.0201 950.7287 949.4289 948.1206 946.8034 945.4772 944.1415 #>  [24,] 952.9113 951.6270 950.3346 949.0337 947.7243 946.4059 945.0784 943.7414 #>  [25,] 952.5213 951.2360 949.9426 948.6407 947.3301 946.0106 944.6819 943.3437 #>  [26,] 952.1333 950.8471 949.5527 948.2499 946.9383 945.6177 944.2878 942.9484 #>  [27,] 951.7472 950.4602 949.1650 947.8612 946.5486 945.2270 943.8961 942.5556 #>  [28,] 951.3632 950.0754 948.7793 947.4747 946.1612 944.8387 943.5068 942.1653 #>  [29,] 950.9812 949.6927 948.3959 947.0904 945.7761 944.4527 943.1199 941.7774 #>  [30,] 950.6012 949.3121 948.0145 946.7083 945.3933 944.0691 942.7355 941.3921 #>  [31,] 950.2233 948.9335 947.6353 946.3285 945.0127 943.6878 942.3534 941.0093 #>  [32,] 949.8474 948.5571 947.2583 945.9509 944.6345 943.3089 941.9738 940.6289 #>  [33,] 949.4736 948.1827 946.8835 945.5755 944.2585 942.9324 941.5967 940.2511 #>  [34,] 949.1018 947.8105 946.5108 945.2023 943.8849 942.5582 941.2220 939.8759 #>  [35,] 948.7320 947.4404 946.1403 944.8314 943.5136 942.1864 940.8497 939.5032 #>  [36,] 948.3644 947.0724 945.7720 944.4628 943.1446 941.8171 940.4800 939.1330 #>  [37,] 947.9988 946.7066 945.4059 944.0964 942.7779 941.4501 940.1127 938.7654 #>  [38,] 947.6352 946.3428 945.0419 943.7323 942.4136 941.0855 939.7479 938.4003 #>  [39,] 947.2737 945.9812 944.6802 943.3704 942.0515 940.7233 939.3855 938.0378 #>  [40,] 946.9143 945.6218 944.3207 943.0108 941.6918 940.3636 939.0257 937.6778 #>  [41,] 946.5570 945.2644 943.9633 942.6534 941.3345 940.0062 938.6683 937.3205 #>  [42,] 946.2018 944.9092 943.6082 942.2983 940.9795 939.6512 938.3134 936.9656 #>  [43,] 945.8486 944.5562 943.2552 941.9455 940.6268 939.2987 937.9610 936.6134 #>  [44,] 945.4974 944.2052 942.9045 941.5949 940.2764 938.9485 937.6111 936.2637 #>  [45,] 945.1484 943.8564 942.5559 941.2466 939.9284 938.6008 937.2636 935.9166 #>  [46,] 944.8014 943.5097 942.2095 940.9006 939.5827 938.2554 936.9186 935.5720 #>  [47,] 944.4565 943.1651 941.8653 940.5568 939.2393 937.9125 936.5761 935.2299 #>  [48,] 944.1136 942.8227 941.5233 940.2152 938.8982 937.5719 936.2361 934.8904 #>  [49,] 943.7728 942.4824 941.1835 939.8759 938.5594 937.2337 935.8985 934.5535 #>  [50,] 943.4340 942.1441 940.8458 939.5389 938.2230 936.8979 935.5634 934.2190 #>  [51,] 943.0973 941.8080 940.5103 939.2040 937.8888 936.5645 935.2307 933.8871 #>  [52,] 942.7626 941.4740 940.1770 938.8714 937.5569 936.2334 934.9004 933.5577 #>  [53,] 942.4300 941.1420 939.8458 938.5410 937.2273 935.9046 934.5726 933.2308 #>  [54,] 942.0993 940.8122 939.5167 938.2128 936.9000 935.5782 934.2471 932.9064 #>  [55,] 941.7707 940.4844 939.1898 937.8868 936.5750 935.2542 933.9241 932.5845 #>  [56,] 941.4441 940.1587 938.8650 937.5629 936.2521 934.9324 933.6035 932.2650 #>  [57,] 941.1195 939.8350 938.5423 937.2413 935.9316 934.6130 933.2852 931.9480 #>  [58,] 940.7968 939.5133 938.2217 936.9218 935.6132 934.2958 932.9693 931.6334 #>  [59,] 940.4762 939.1937 937.9032 936.6044 935.2971 933.9809 932.6557 931.3212 #>  [60,] 940.1575 938.8762 937.5868 936.2892 934.9831 933.6683 932.3445 931.0114 #>  [61,] 939.8407 938.5606 937.2725 935.9761 934.6714 933.3579 932.0356 930.7040 #>  [62,] 939.5259 938.2470 936.9602 935.6652 934.3618 933.0498 931.7290 930.3990 #>  [63,] 939.2131 937.9354 936.6499 935.3563 934.0544 932.7439 931.4246 930.0963 #>  [64,] 938.9021 937.6258 936.3416 935.0495 933.7491 932.4402 931.1225 929.7960 #>  [65,] 938.5931 937.3181 936.0354 934.7447 933.4459 932.1386 930.8227 929.4979 #>  [66,] 938.2859 937.0124 935.7312 934.4420 933.1448 931.8392 930.5251 929.2022 #>  [67,] 937.9806 936.7086 935.4289 934.1414 932.8458 931.5420 930.2297 928.9087 #>  [68,] 937.6772 936.4067 935.1286 933.8427 932.5489 931.2469 929.9365 928.6174 #>  [69,] 937.3756 936.1066 934.8302 933.5460 932.2540 930.9539 929.6454 928.3284 #>  [70,] 937.0758 935.8085 934.5337 933.2514 931.9611 930.6629 929.3565 928.0415 #>  [71,] 936.7779 935.5122 934.2392 932.9586 931.6703 930.3740 929.0696 927.7569 #>  [72,] 936.4817 935.2178 933.9465 932.6678 931.3814 930.0872 928.7849 927.4743 #>  [73,] 936.1874 934.9252 933.6557 932.3789 931.0945 929.8024 928.5022 927.1939 #>  [74,] 935.8947 934.6343 933.3668 932.0919 930.8096 929.5195 928.2216 926.9156 #>  [75,] 935.6039 934.3453 933.0797 931.8068 930.5265 929.2387 927.9430 926.6394 #>  [76,] 935.3147 934.0580 932.7944 931.5235 930.2454 928.9598 927.6664 926.3652 #>  [77,] 935.0273 933.7725 932.5109 931.2421 929.9661 928.6828 927.3918 926.0930 #>  [78,] 934.7415 933.4887 932.2291 930.9625 929.6887 928.4077 927.1191 925.8229 #>  [79,] 934.4574 933.2066 931.9491 930.6847 929.4132 928.1344 926.8483 925.5546 #>  [80,] 934.1750 932.9262 931.6708 930.4086 929.1394 927.8630 926.5794 925.2884 #>  [81,] 933.8942 932.6475 931.3942 930.1342 928.8674 927.5935 926.3124 925.0240 #>  [82,] 933.6150 932.3704 931.1193 929.8616 928.5971 927.3257 926.0472 924.7615 #>  [83,] 933.3374 932.0950 930.8461 929.5907 928.3286 927.0597 925.7838 924.5008 #>  [84,] 933.0613 931.8211 930.5745 929.3215 928.0618 926.7955 925.5222 924.2420 #>  [85,] 932.7869 931.5488 930.3045 929.0539 927.7967 926.5330 925.2624 923.9849 #>  [86,] 932.5139 931.2781 930.0361 928.7879 927.5333 926.2721 925.0043 923.7297 #>  [87,] 932.2424 931.0089 929.7693 928.5235 927.2715 926.0129 924.7479 923.4761 #>  [88,] 931.9725 930.7413 929.5040 928.2607 927.0112 925.7554 924.4931 923.2243 #>  [89,] 931.7040 930.4751 929.2403 927.9995 926.7526 925.4995 924.2400 922.9741 #>  [90,] 931.4369 930.2104 928.9780 927.7398 926.4955 925.2451 923.9885 922.7256 #>  [91,] 931.1713 929.9471 928.7173 927.4816 926.2400 924.9924 923.7386 922.4787 #>  [92,] 930.9071 929.6853 928.4579 927.2248 925.9859 924.7411 923.4903 922.2333 #>  [93,] 930.6442 929.4249 928.2000 926.9696 925.7334 924.4914 923.2435 921.9896 #>  [94,] 930.3827 929.1659 927.9435 926.7157 925.4822 924.2431 922.9981 921.7473 #>  [95,] 930.1226 928.9082 927.6884 926.4633 925.2326 923.9963 922.7543 921.5065 #>  [96,] 929.8638 928.6518 927.4347 926.2122 924.9843 923.7509 922.5119 921.2672 #>  [97,] 929.6062 928.3968 927.1823 925.9625 924.7374 923.5069 922.2709 921.0294 #>  [98,] 929.3499 928.1431 926.9312 925.7141 924.4918 923.2642 922.0313 920.7929 #>  [99,] 929.0949 927.8906 926.6813 925.4670 924.2475 923.0229 921.7930 920.5578 #> [100,] 928.8411 927.6394 926.4328 925.2212 924.0046 922.7829 921.5561 920.3241 #>            [,9]    [,10]    [,11]    [,12]    [,13]    [,14]    [,15]    [,16] #>   [1,] 952.2214 950.9155 949.6016 948.2796 946.9493 945.6104 944.2628 942.9063 #>   [2,] 951.7704 950.4616 949.1447 947.8196 946.4860 945.1438 943.7926 942.4324 #>   [3,] 951.3213 950.0097 948.6899 947.3618 946.0250 944.6794 943.3247 941.9609 #>   [4,] 950.8742 949.5599 948.2372 946.9060 945.5661 944.2172 942.8591 941.4917 #>   [5,] 950.4291 949.1121 947.7866 946.4525 945.1095 943.7574 942.3959 941.0249 #>   [6,] 949.9861 948.6665 947.3382 946.0012 944.6551 943.2998 941.9351 940.5605 #>   [7,] 949.5452 948.2230 946.8920 945.5521 944.2031 942.8447 941.4766 940.0987 #>   [8,] 949.1064 947.7816 946.4480 945.1054 943.7534 942.3920 941.0207 939.6394 #>   [9,] 948.6698 947.3425 946.0063 944.6609 943.3061 941.9417 940.5673 939.1827 #>  [10,] 948.2353 946.9056 945.5669 944.2188 942.8613 941.4939 940.1164 938.7286 #>  [11,] 947.8030 946.4710 945.1297 943.7791 942.4188 941.0486 939.6681 938.2772 #>  [12,] 947.3730 946.0386 944.6950 943.3418 941.9789 940.6059 939.2225 937.8284 #>  [13,] 946.9452 945.6086 944.2626 942.9070 941.5414 940.1657 938.7795 937.3825 #>  [14,] 946.5197 945.1809 943.8326 942.4746 941.1066 939.7282 938.3392 936.9393 #>  [15,] 946.0964 944.7555 943.4051 942.0447 940.6743 939.2934 937.9017 936.4989 #>  [16,] 945.6756 944.3326 942.9800 941.6174 940.2446 938.8612 937.4669 936.0614 #>  [17,] 945.2570 943.9121 942.5574 941.1926 939.8175 938.4318 937.0350 935.6268 #>  [18,] 944.8408 943.4940 942.1373 940.7705 939.3932 938.0051 936.6058 935.1951 #>  [19,] 944.4270 943.0784 941.7198 940.3509 938.9715 937.5812 936.1796 934.7664 #>  [20,] 944.0157 942.6652 941.3048 939.9340 938.5525 937.1601 935.7562 934.3407 #>  [21,] 943.6067 942.2546 940.8924 939.5197 938.1363 936.7418 935.3358 933.9180 #>  [22,] 943.2002 941.8465 940.4826 939.1082 937.7229 936.3264 934.9184 933.4984 #>  [23,] 942.7962 941.4410 940.0755 938.6993 937.3123 935.9139 934.5039 933.0818 #>  [24,] 942.3947 941.0380 939.6709 938.2932 936.9045 935.5044 934.0925 932.6684 #>  [25,] 941.9957 940.6376 939.2691 937.8899 936.4995 935.0977 933.6841 932.2581 #>  [26,] 941.5992 940.2398 938.8699 937.4893 936.0974 934.6940 933.2787 931.8510 #>  [27,] 941.2052 939.8446 938.4735 937.0915 935.6982 934.2934 932.8765 931.4471 #>  [28,] 940.8138 939.4521 938.0798 936.6965 935.3019 933.8957 932.4773 931.0464 #>  [29,] 940.4250 939.0622 937.6888 936.3043 934.9085 933.5010 932.0813 930.6490 #>  [30,] 940.0387 938.6750 937.3005 935.9150 934.5181 933.1094 931.6884 930.2548 #>  [31,] 939.6550 938.2904 936.9150 935.5286 934.1306 932.7208 931.2987 929.8639 #>  [32,] 939.2739 937.9085 936.5323 935.1450 933.7461 932.3353 930.9122 929.4763 #>  [33,] 938.8955 937.5293 936.1524 934.7642 933.3646 931.9529 930.5289 929.0920 #>  [34,] 938.5196 937.1528 935.7752 934.3864 932.9860 931.5736 930.1487 928.7110 #>  [35,] 938.1464 936.7791 935.4009 934.0115 932.6105 931.1974 929.7718 928.3334 #>  [36,] 937.7758 936.4080 935.0294 933.6395 932.2379 930.8243 929.3982 927.9591 #>  [37,] 937.4078 936.0397 934.6607 933.2704 931.8684 930.4543 929.0277 927.5882 #>  [38,] 937.0425 935.6741 934.2948 932.9042 931.5019 930.0875 928.6605 927.2206 #>  [39,] 936.6798 935.3112 933.9317 932.5409 931.1384 929.7237 928.2966 926.8564 #>  [40,] 936.3198 934.9511 933.5715 932.1806 930.7779 929.3632 927.9359 926.4955 #>  [41,] 935.9624 934.5937 933.2141 931.8231 930.4205 929.0057 927.5784 926.1381 #>  [42,] 935.6076 934.2390 932.8595 931.4687 930.0661 928.6514 927.2242 925.7840 #>  [43,] 935.2555 933.8871 932.5077 931.1171 929.7147 928.3003 926.8733 925.4333 #>  [44,] 934.9061 933.5379 932.1588 930.7684 929.3664 927.9522 926.5256 925.0859 #>  [45,] 934.5593 933.1914 931.8127 930.4227 929.0211 927.6073 926.1811 924.7419 #>  [46,] 934.2151 932.8477 931.4694 930.0799 928.6788 927.2656 925.8399 924.4013 #>  [47,] 933.8736 932.5067 931.1290 929.7400 928.3395 926.9269 925.5019 924.0640 #>  [48,] 933.5346 932.1684 930.7913 929.4030 928.0032 926.5913 925.1671 923.7301 #>  [49,] 933.1983 931.8328 930.4564 929.0689 927.6699 926.2589 924.8356 923.3995 #>  [50,] 932.8647 931.4999 930.1243 928.7377 927.3395 925.9295 924.5072 923.0722 #>  [51,] 932.5336 931.1696 929.7950 928.4093 927.0122 925.6032 924.1820 922.7482 #>  [52,] 932.2051 930.8421 929.4684 928.0838 926.6878 925.2800 923.8600 922.4275 #>  [53,] 931.8791 930.5172 929.1446 927.7611 926.3663 924.9598 923.5412 922.1100 #>  [54,] 931.5558 930.1950 928.8236 927.4413 926.0478 924.6426 923.2254 921.7958 #>  [55,] 931.2350 929.8754 928.5052 927.1243 925.7322 924.3285 922.9128 921.4848 #>  [56,] 930.9167 929.5584 928.1896 926.8101 925.4194 924.0173 922.6033 921.1770 #>  [57,] 930.6010 929.2440 927.8767 926.4986 925.1096 923.7091 922.2968 920.8724 #>  [58,] 930.2878 928.9322 927.5664 926.1900 924.8026 923.4038 921.9934 920.5710 #>  [59,] 929.9771 928.6230 927.2588 925.8840 924.4984 923.1015 921.6931 920.2726 #>  [60,] 929.6688 928.3164 926.9538 925.5808 924.1970 922.8021 921.3957 919.9774 #>  [61,] 929.3630 928.0122 926.6514 925.2802 923.8984 922.5055 921.1012 919.6852 #>  [62,] 929.0596 927.7106 926.3516 924.9824 923.6025 922.2118 920.8097 919.3961 #>  [63,] 928.7587 927.4115 926.0544 924.6872 923.3094 921.9209 920.5212 919.1099 #>  [64,] 928.4601 927.1148 925.7597 924.3946 923.0190 921.6328 920.2355 918.8268 #>  [65,] 928.1640 926.8206 925.4676 924.1046 922.7313 921.3474 919.9526 918.5466 #>  [66,] 927.8701 926.5288 925.1779 923.8171 922.4462 921.0648 919.6726 918.2692 #>  [67,] 927.5787 926.2394 924.8907 923.5322 922.1637 920.7848 919.3953 917.9948 #>  [68,] 927.2895 925.9524 924.6060 923.2499 921.8838 920.5076 919.1208 917.7232 #>  [69,] 927.0026 925.6677 924.3236 922.9700 921.6065 920.2329 918.8490 917.4543 #>  [70,] 926.7179 925.3854 924.0437 922.6925 921.3317 919.9609 918.5799 917.1883 #>  [71,] 926.4355 925.1053 923.7661 922.4175 921.0594 919.6914 918.3134 916.9249 #>  [72,] 926.1553 924.8275 923.4908 922.1449 920.7895 919.4245 918.0495 916.6642 #>  [73,] 925.8772 924.5519 923.2178 921.8746 920.5221 919.1600 917.7881 916.4062 #>  [74,] 925.6014 924.2786 922.9471 921.6067 920.2571 918.8980 917.5293 916.1507 #>  [75,] 925.3276 924.0074 922.6786 921.3410 919.9944 918.6385 917.2730 915.8978 #>  [76,] 925.0559 923.7384 922.4124 921.0776 919.7340 918.3813 917.0191 915.6474 #>  [77,] 924.7863 923.4715 922.1483 920.8165 919.4759 918.1264 916.7676 915.3994 #>  [78,] 924.5188 923.2067 921.8863 920.5575 919.2201 917.8738 916.5185 915.1539 #>  [79,] 924.2532 922.9439 921.6264 920.3007 918.9665 917.6235 916.2717 914.9108 #>  [80,] 923.9897 922.6832 921.3687 920.0460 918.7150 917.3755 916.0272 914.6700 #>  [81,] 923.7280 922.4244 921.1129 919.7934 918.4657 917.1296 915.7849 914.4314 #>  [82,] 923.4683 922.1676 920.8592 919.5429 918.2185 916.8859 915.5448 914.1951 #>  [83,] 923.2105 921.9128 920.6075 919.2944 917.9733 916.6442 915.3069 913.9611 #>  [84,] 922.9546 921.6598 920.3576 919.0478 917.7302 916.4047 915.0710 913.7291 #>  [85,] 922.7004 921.4088 920.1097 918.8032 917.4891 916.1671 914.8373 913.4993 #>  [86,] 922.4481 921.1595 919.8637 918.5605 917.2499 915.9316 914.6055 913.2715 #>  [87,] 922.1976 920.9121 919.6195 918.3197 917.0126 915.6980 914.3758 913.0458 #>  [88,] 921.9487 920.6664 919.3771 918.0807 916.7772 915.4663 914.1479 912.8220 #>  [89,] 921.7016 920.4224 919.1365 917.8435 916.5436 915.2364 913.9220 912.6002 #>  [90,] 921.4562 920.1802 918.8976 917.6081 916.3118 915.0084 913.6979 912.3802 #>  [91,] 921.2124 919.9396 918.6604 917.3744 916.0817 914.7822 913.4757 912.1621 #>  [92,] 920.9702 919.7007 918.4248 917.1424 915.8534 914.5577 913.2552 911.9457 #>  [93,] 920.7296 919.4634 918.1909 916.9121 915.6268 914.3349 913.0364 911.7312 #>  [94,] 920.4905 919.2276 917.9586 916.6833 915.4018 914.1138 912.8193 911.5183 #>  [95,] 920.2529 918.9934 917.7278 916.4562 915.1783 913.8943 912.6038 911.3070 #>  [96,] 920.0169 918.7607 917.4986 916.2306 914.9565 913.6763 912.3900 911.0974 #>  [97,] 919.7822 918.5294 917.2709 916.0065 914.7362 913.4599 912.1777 910.8894 #>  [98,] 919.5490 918.2996 917.0446 915.7838 914.5173 913.2451 911.9669 910.6829 #>  [99,] 919.3172 918.0712 916.8197 915.5626 914.3000 913.0316 911.7576 910.4779 #> [100,] 919.0868 917.8442 916.5962 915.3428 914.0840 912.8196 911.5497 910.2743 #>           [,17]    [,18]    [,19]    [,20]    [,21]    [,22]    [,23]    [,24] #>   [1,] 941.5407 940.1658 938.7813 937.3871 935.9830 934.5686 933.1439 931.7085 #>   [2,] 941.0629 939.6839 938.2952 936.8965 935.4876 934.0683 932.6383 931.1974 #>   [3,] 940.5875 939.2045 937.8115 936.4083 934.9948 933.5705 932.1354 930.6891 #>   [4,] 940.1145 938.7275 937.3304 935.9228 934.5046 933.0756 931.6353 930.1836 #>   [5,] 939.6440 938.2531 936.8518 935.4400 934.0172 932.5834 931.1381 929.6811 #>   [6,] 939.1760 937.7812 936.3759 934.9598 933.5326 932.0941 930.6438 929.1816 #>   [7,] 938.7106 937.3120 935.9027 934.4824 933.0509 931.6076 930.1525 928.6851 #>   [8,] 938.2477 936.8455 935.4323 934.0079 932.5720 931.1242 929.6643 928.1918 #>   [9,] 937.7876 936.3817 934.9647 933.5362 932.0961 930.6438 929.1792 927.7017 #>  [10,] 937.3301 935.9206 934.4999 933.0675 931.6232 930.1666 928.6972 927.2149 #>  [11,] 936.8754 935.4624 934.0380 932.6018 931.1534 929.6924 928.2186 926.7314 #>  [12,] 936.4234 935.0071 933.5791 932.1391 930.6867 929.2216 927.7433 926.2514 #>  [13,] 935.9743 934.5546 933.1232 931.6795 930.2232 928.7540 927.2714 925.7749 #>  [14,] 935.5280 934.1052 932.6703 931.2230 929.7630 928.2897 926.8029 925.3020 #>  [15,] 935.0847 933.6587 932.2205 930.7698 929.3060 927.8289 926.3379 924.8326 #>  [16,] 934.6443 933.2153 931.7739 930.3197 928.8524 927.3715 925.8765 924.3670 #>  [17,] 934.2069 932.7749 931.3304 929.8730 928.4022 926.9177 925.4188 923.9052 #>  [18,] 933.7725 932.3377 930.8902 929.4296 927.9555 926.4674 924.9648 923.4471 #>  [19,] 933.3412 931.9036 930.4532 928.9896 927.5122 926.0207 924.5145 922.9930 #>  [20,] 932.9130 931.4728 930.0196 928.5530 927.0725 925.5777 924.0680 922.5428 #>  [21,] 932.4879 931.0452 929.5893 928.1199 926.6364 925.1384 923.6253 922.0966 #>  [22,] 932.0660 930.6208 929.1624 927.6903 926.2040 924.7029 923.1866 921.6545 #>  [23,] 931.6473 930.1998 928.7389 927.2642 925.7752 924.2713 922.7519 921.2164 #>  [24,] 931.2318 929.7821 928.3189 926.8418 925.3501 923.8434 922.3211 920.7826 #>  [25,] 930.8195 929.3678 927.9024 926.4229 924.9288 923.4195 921.8944 920.3530 #>  [26,] 930.4106 928.9569 927.4894 926.0078 924.5113 922.9995 921.4718 919.9276 #>  [27,] 930.0049 928.5494 927.0800 925.5963 924.0976 922.5836 921.0534 919.5065 #>  [28,] 929.6026 928.1453 926.6742 925.1885 923.6878 922.1716 920.6391 919.0898 #>  [29,] 929.2037 927.7448 926.2719 924.7845 923.2819 921.7637 920.2291 918.6775 #>  [30,] 928.8081 927.3478 925.8733 924.3842 922.8799 921.3598 919.8233 918.2696 #>  [31,] 928.4159 926.9542 925.4784 923.9878 922.4819 920.9601 919.4217 917.8661 #>  [32,] 928.0272 926.5643 925.0871 923.5952 922.0879 920.5645 919.0245 917.4672 #>  [33,] 927.6418 926.1779 924.6996 923.2064 921.6978 920.1731 918.6317 917.0728 #>  [34,] 927.2600 925.7950 924.3158 922.8215 921.3118 919.7859 918.2431 916.6829 #>  [35,] 926.8815 925.4158 923.9357 922.4405 920.9298 919.4028 917.8590 916.2976 #>  [36,] 926.5066 925.0402 923.5593 922.0634 920.5518 919.0240 917.4793 915.9169 #>  [37,] 926.1351 924.6682 923.1867 921.6902 920.1780 918.6495 917.1040 915.5407 #>  [38,] 925.7672 924.2998 922.8179 921.3209 919.8082 918.2791 916.7331 915.1693 #>  [39,] 925.4027 923.9350 922.4528 920.9555 919.4425 917.9131 916.3666 914.8024 #>  [40,] 925.0417 923.5739 922.0915 920.5940 919.0808 917.5512 916.0046 914.4402 #>  [41,] 924.6843 923.2164 921.7340 920.2365 918.7233 917.1937 915.6470 914.0826 #>  [42,] 924.3303 922.8626 921.3803 919.8829 918.3699 916.8404 915.2939 913.7296 #>  [43,] 923.9798 922.5123 921.0304 919.5333 918.0205 916.4914 914.9452 913.3813 #>  [44,] 923.6328 922.1658 920.6842 919.1876 917.6752 916.1466 914.6010 913.0376 #>  [45,] 923.2893 921.8228 920.3418 918.8457 917.3340 915.8061 914.2612 912.6986 #>  [46,] 922.9493 921.4835 920.0031 918.5078 916.9969 915.4698 913.9258 912.3641 #>  [47,] 922.6128 921.1477 919.6682 918.1738 916.6639 915.1377 913.5948 912.0343 #>  [48,] 922.2797 920.8156 919.3371 917.8437 916.3348 914.8099 913.2682 911.7090 #>  [49,] 921.9501 920.4870 919.0096 917.5174 916.0098 914.4862 912.9459 911.3882 #>  [50,] 921.6239 920.1620 918.6859 917.1950 915.6888 914.1667 912.6280 911.0720 #>  [51,] 921.3012 919.8406 918.3659 916.8765 915.3718 913.8514 912.3144 910.7603 #>  [52,] 920.9818 919.5227 918.0495 916.5617 915.0588 913.5401 912.0051 910.4531 #>  [53,] 920.6659 919.2083 917.7367 916.2507 914.7497 913.2330 911.7001 910.1503 #>  [54,] 920.3533 918.8974 917.4276 915.9435 914.4444 912.9299 911.3993 909.8519 #>  [55,] 920.0440 918.5899 917.1221 915.6400 914.1431 912.6308 911.1026 909.5578 #>  [56,] 919.7380 918.2859 916.8201 915.3402 913.8456 912.3358 910.8101 909.2681 #>  [57,] 919.4354 917.9853 916.5217 915.0440 913.5519 912.0447 910.5218 908.9826 #>  [58,] 919.1360 917.6880 916.2267 914.7515 913.2619 911.7574 910.2375 908.7014 #>  [59,] 918.8398 917.3942 915.9353 914.4626 912.9757 911.4741 909.9572 908.4243 #>  [60,] 918.5468 917.1036 915.6472 914.1773 912.6932 911.1946 909.6808 908.1514 #>  [61,] 918.2570 916.8163 915.3626 913.8954 912.4144 910.9189 909.4084 907.8825 #>  [62,] 917.9704 916.5323 915.0813 913.6171 912.1391 910.6469 909.1399 907.6177 #>  [63,] 917.6868 916.2514 914.8034 913.3421 911.8674 910.3786 908.8752 907.3568 #>  [64,] 917.4063 915.9738 914.5287 913.0706 911.5992 910.1139 908.6143 907.0998 #>  [65,] 917.1289 915.6993 914.2572 912.8024 911.3344 909.8528 908.3570 906.8467 #>  [66,] 916.8545 915.4278 913.9890 912.5376 911.0731 909.5952 908.1034 906.5973 #>  [67,] 916.5830 915.1594 913.7239 912.2759 910.8151 909.3411 907.8534 906.3516 #>  [68,] 916.3144 914.8941 913.4619 912.0175 910.5605 909.0904 907.6070 906.1096 #>  [69,] 916.0487 914.6317 913.2030 911.7622 910.3091 908.8431 907.3639 905.8712 #>  [70,] 915.7858 914.3722 912.9471 911.5101 910.0609 908.5991 907.1243 905.6362 #>  [71,] 915.5257 914.1156 912.6941 911.2609 909.8158 908.3583 906.8881 905.4048 #>  [72,] 915.2684 913.8618 912.4440 911.0148 909.5738 908.1207 906.6551 905.1766 #>  [73,] 915.0138 913.6108 912.1969 910.7717 909.3349 907.8862 906.4253 904.9518 #>  [74,] 914.7619 913.3626 911.9525 910.5314 909.0989 907.6548 906.1987 904.7303 #>  [75,] 914.5125 913.1170 911.7109 910.2939 908.8659 907.4264 905.9751 904.5118 #>  [76,] 914.2658 912.8741 911.4720 910.0593 908.6357 907.2009 905.7546 904.2965 #>  [77,] 914.0216 912.6337 911.2358 909.8274 908.4083 906.9782 905.5370 904.0842 #>  [78,] 913.7798 912.3960 911.0021 909.5981 908.1836 906.7584 905.3222 903.8748 #>  [79,] 913.5405 912.1607 910.7711 909.3715 907.9616 906.5413 905.1103 903.6683 #>  [80,] 913.3036 911.9278 910.5425 909.1474 907.7423 906.3269 904.9011 903.4646 #>  [81,] 913.0690 911.6974 910.3164 908.9258 907.5255 906.1151 904.6946 903.2637 #>  [82,] 912.8367 911.4692 910.0926 908.7067 907.3111 905.9059 904.4907 903.0653 #>  [83,] 912.6066 911.2434 909.8712 908.4899 907.0993 905.6991 904.2893 902.8696 #>  [84,] 912.3788 911.0198 909.6521 908.2755 906.8898 905.4948 904.0904 902.6764 #>  [85,] 912.1531 910.7985 909.4353 908.0634 906.6826 905.2928 903.8938 902.4856 #>  [86,] 911.9295 910.5792 909.2206 907.8534 906.4777 905.0931 903.6996 902.2971 #>  [87,] 911.7079 910.3620 909.0080 907.6457 906.2749 904.8956 903.5077 902.1110 #>  [88,] 911.4884 910.1469 908.7975 907.4400 906.0743 904.7003 903.3179 901.9270 #>  [89,] 911.2708 909.9338 908.5890 907.2364 905.8758 904.5072 903.1303 901.7453 #>  [90,] 911.0551 909.7226 908.3825 907.0348 905.6793 904.3160 902.9448 901.5656 #>  [91,] 910.8413 909.5133 908.1779 906.8351 905.4848 904.1268 902.7612 901.3879 #>  [92,] 910.6293 909.3058 907.9752 906.6373 905.2921 903.9396 902.5796 901.2121 #>  [93,] 910.4191 909.1002 907.7743 906.4413 905.1013 903.7542 902.3998 901.0383 #>  [94,] 910.2106 908.8962 907.5751 906.2471 904.9123 903.5706 902.2219 900.8662 #>  [95,] 910.0038 908.6940 907.3776 906.0547 904.7250 903.3887 902.0456 900.6959 #>  [96,] 909.7986 908.4934 907.1818 905.8638 904.5394 903.2085 901.8711 900.5272 #>  [97,] 909.5950 908.2944 906.9876 905.6746 904.3554 903.0299 901.6982 900.3602 #>  [98,] 909.3929 908.0969 906.7950 905.4870 904.1730 902.8529 901.5268 900.1948 #>  [99,] 909.1923 907.9010 906.6038 905.3009 903.9921 902.6774 901.3570 900.0308 #> [100,] 908.9932 907.7065 906.4142 905.1162 903.8126 902.5034 901.1886 899.8682 #>           [,25]    [,26]    [,27]    [,28]    [,29]    [,30]    [,31]    [,32] #>   [1,] 930.2623 928.8050 927.3365 925.8565 924.3648 922.8612 921.3456 919.8177 #>   [2,] 929.7454 928.2820 926.8071 925.3202 923.8214 922.3102 920.7866 919.2502 #>   [3,] 929.2313 927.7619 926.2806 924.7870 923.2810 921.7624 920.2308 918.6860 #>   [4,] 928.7202 927.2448 925.7571 924.2569 922.7439 921.2177 919.6782 918.1251 #>   [5,] 928.2121 926.7308 925.2368 923.7300 922.2100 920.6765 919.1291 917.5677 #>   [6,] 927.7070 926.2199 924.7198 923.2064 921.6795 920.1386 918.5835 917.0138 #>   [7,] 927.2051 925.7122 924.2060 922.6862 921.1525 919.6044 918.0416 916.4637 #>   [8,] 926.7064 925.2079 923.6957 922.1695 920.6290 919.0738 917.5034 915.9175 #>   [9,] 926.2111 924.7069 923.1888 921.6564 920.1093 918.5470 916.9691 915.3752 #>  [10,] 925.7191 924.2094 922.6856 921.1470 919.5933 918.0240 916.4388 914.8370 #>  [11,] 925.2306 923.7155 922.1860 920.6413 919.0812 917.5051 915.9126 914.3031 #>  [12,] 924.7456 923.2253 921.6901 920.1395 918.5731 916.9903 915.3906 913.7735 #>  [13,] 924.2642 922.7388 921.1981 919.6417 918.0691 916.4798 914.8731 913.2485 #>  [14,] 923.7865 922.2560 920.7100 919.1480 917.5693 915.9735 914.3599 912.7280 #>  [15,] 923.3126 921.7772 920.2260 918.6584 917.0738 915.4717 913.8514 912.2123 #>  [16,] 922.8424 921.3023 919.7460 918.1730 916.5827 914.9744 913.3476 911.7015 #>  [17,] 922.3762 920.8314 919.2702 917.6920 916.0961 914.4818 912.8486 911.1957 #>  [18,] 921.9140 920.3647 918.7987 917.2153 915.6140 913.9940 912.3546 910.6950 #>  [19,] 921.4557 919.9021 918.3315 916.7432 915.1366 913.5110 911.8655 910.1995 #>  [20,] 921.0016 919.4438 917.8687 916.2756 914.6640 913.0329 911.3816 909.7094 #>  [21,] 920.5516 918.9897 917.4104 915.8127 914.1962 912.5599 910.9030 909.2247 #>  [22,] 920.1058 918.5401 916.9566 915.3546 913.7333 912.0920 910.4297 908.7457 #>  [23,] 919.6643 918.0949 916.5075 914.9013 913.2755 911.6293 909.9619 908.2723 #>  [24,] 919.2272 917.6542 916.0630 914.4528 912.8227 911.1720 909.4996 907.8047 #>  [25,] 918.7944 917.2181 915.6233 914.0093 912.3752 910.7200 909.0430 907.3431 #>  [26,] 918.3661 916.7866 915.1885 913.5708 911.9328 910.2736 908.5921 906.8874 #>  [27,] 917.9422 916.3598 914.7585 913.1374 911.4958 909.8327 908.1470 906.4378 #>  [28,] 917.5229 915.9377 914.3334 912.7092 911.0642 909.3974 907.7078 905.9944 #>  [29,] 917.1081 915.5204 913.9133 912.2861 910.6380 908.9678 907.2745 905.5572 #>  [30,] 916.6980 915.1078 913.4983 911.8684 910.2172 908.5439 906.8473 905.1263 #>  [31,] 916.2925 914.7002 913.0883 911.4559 909.8021 908.1259 906.4262 904.7019 #>  [32,] 915.8917 914.2974 912.6834 911.0487 909.3925 907.7137 906.0113 904.2839 #>  [33,] 915.4957 913.8996 912.2837 910.6470 908.9886 907.3075 905.6025 903.8725 #>  [34,] 915.1043 913.5067 911.8891 910.2507 908.5904 906.9072 905.2000 903.4676 #>  [35,] 914.7178 913.1188 911.4998 909.8598 908.1979 906.5130 904.8039 903.0694 #>  [36,] 914.3360 912.7359 911.1157 909.4744 907.8111 906.1247 904.4140 902.6778 #>  [37,] 913.9591 912.3581 910.7369 909.0946 907.4302 905.7426 904.0306 902.2930 #>  [38,] 913.5869 911.9852 910.3633 908.7203 907.0550 905.3665 903.6535 901.9149 #>  [39,] 913.2196 911.6175 909.9951 908.3515 906.6856 904.9965 903.2829 901.5435 #>  [40,] 912.8572 911.2548 909.6321 907.9882 906.3221 904.6326 902.9187 901.1789 #>  [41,] 912.4996 910.8971 909.2745 907.6305 905.9644 904.2749 902.5609 900.8211 #>  [42,] 912.1468 910.5446 908.9221 907.2784 905.6125 903.9233 902.2096 900.4701 #>  [43,] 911.7989 910.1971 908.5751 906.9319 905.2665 903.5778 901.8647 900.1259 #>  [44,] 911.4558 909.8546 908.2333 906.5908 904.9262 903.2384 901.5262 899.7884 #>  [45,] 911.1175 909.5172 907.8968 906.2553 904.5918 902.9051 901.1941 899.4576 #>  [46,] 910.7841 909.1849 907.5656 905.9254 904.2631 902.5779 900.8684 899.1336 #>  [47,] 910.4554 908.8575 907.2396 905.6009 903.9402 902.2567 900.5491 898.8162 #>  [48,] 910.1316 908.5352 906.9189 905.2819 903.6231 901.9415 900.2361 898.5055 #>  [49,] 909.8125 908.2178 906.6033 904.9683 903.3116 901.6323 899.9293 898.2014 #>  [50,] 909.4981 907.9053 906.2929 904.6601 903.0058 901.3291 899.6288 897.9038 #>  [51,] 909.1884 907.5977 905.9877 904.3572 902.7056 901.0317 899.3344 897.6127 #>  [52,] 908.8833 907.2950 905.6875 904.0597 902.4109 900.7401 899.0462 897.3281 #>  [53,] 908.5829 906.9972 905.3923 903.7675 902.1218 900.4543 898.7640 897.0497 #>  [54,] 908.2870 906.7041 905.1021 903.4804 901.8381 900.1742 898.4877 896.7777 #>  [55,] 907.9958 906.4157 904.8169 903.1985 901.5598 899.8998 898.2174 896.5118 #>  [56,] 907.7089 906.1320 904.5365 902.9218 901.2868 899.6309 897.9529 896.2520 #>  [57,] 907.4266 905.8530 904.2610 902.6500 901.0191 899.3675 897.6942 895.9982 #>  [58,] 907.1486 905.5785 903.9903 902.3832 900.7566 899.1095 897.4411 895.7504 #>  [59,] 906.8750 905.3085 903.7242 902.1213 900.4992 898.8569 897.1936 895.5084 #>  [60,] 906.6057 905.0430 903.4628 901.8643 900.2468 898.6094 896.9515 895.2720 #>  [61,] 906.3406 904.7819 903.2060 901.6120 899.9993 898.3672 896.7148 895.0413 #>  [62,] 906.0796 904.5251 902.9536 901.3644 899.7568 898.1300 896.4834 894.8161 #>  [63,] 905.8228 904.2726 902.7057 901.1214 899.5190 897.8978 896.2572 894.5963 #>  [64,] 905.5700 904.0243 902.4621 900.8828 899.2858 897.6704 896.0360 894.3817 #>  [65,] 905.3212 903.7801 902.2228 900.6488 899.0573 897.4479 895.8197 894.1722 #>  [66,] 905.0763 903.5399 901.9877 900.4190 898.8333 897.2300 895.6084 893.9678 #>  [67,] 904.8352 903.3038 901.7567 900.1935 898.6137 897.0166 895.4017 893.7683 #>  [68,] 904.5979 903.0715 901.5297 899.9722 898.3984 896.8077 895.1996 893.5736 #>  [69,] 904.3643 902.8430 901.3067 899.7550 898.1873 896.6032 895.0021 893.3835 #>  [70,] 904.1344 902.6183 901.0876 899.5417 897.9803 896.4029 894.8089 893.1979 #>  [71,] 903.9079 902.3972 900.8722 899.3324 897.7774 896.2068 894.6200 893.0167 #>  [72,] 903.6850 902.1797 900.6605 899.1268 897.5783 896.0146 894.4353 892.8398 #>  [73,] 903.4654 901.9657 900.4524 898.9249 897.3831 895.8264 894.2545 892.6670 #>  [74,] 903.2492 901.7551 900.2478 898.7267 897.1916 895.6420 894.0777 892.4982 #>  [75,] 903.0362 901.5479 900.0466 898.5319 897.0036 895.4613 893.9047 892.3333 #>  [76,] 902.8264 901.3439 899.8487 898.3406 896.8192 895.2842 893.7353 892.1722 #>  [77,] 902.6197 901.1431 899.6542 898.1526 896.6382 895.1105 893.5695 892.0147 #>  [78,] 902.4160 900.9453 899.4627 897.9678 896.4604 894.9403 893.4071 891.8606 #>  [79,] 902.2152 900.7506 899.2743 897.7862 896.2859 894.7732 893.2480 891.7100 #>  [80,] 902.0173 900.5588 899.0889 897.6076 896.1144 894.6093 893.0921 891.5625 #>  [81,] 901.8221 900.3698 898.9064 897.4319 895.9460 894.4485 892.9393 891.4182 #>  [82,] 901.6297 900.1836 898.7267 897.2591 895.7804 894.2906 892.7894 891.2769 #>  [83,] 901.4399 900.0000 898.5497 897.0890 895.6176 894.1355 892.6424 891.1385 #>  [84,] 901.2526 899.8190 898.3754 896.9216 895.4575 893.9831 892.4982 891.0028 #>  [85,] 901.0678 899.6405 898.2035 896.7567 895.3000 893.8333 892.3566 890.8698 #>  [86,] 900.8854 899.4645 898.0341 896.5943 895.1450 893.6861 892.2175 890.7392 #>  [87,] 900.7054 899.2908 897.8671 896.4344 894.9924 893.5412 892.0808 890.6111 #>  [88,] 900.5275 899.1193 897.7024 896.2767 894.8421 893.3987 891.9464 890.4853 #>  [89,] 900.3519 898.9501 897.5399 896.1212 894.6940 893.2583 891.8142 890.3617 #>  [90,] 900.1783 898.7829 897.3795 895.9678 894.5480 893.1201 891.6842 890.2402 #>  [91,] 900.0068 898.6178 897.2211 895.8165 894.4041 892.9840 891.5561 890.1206 #>  [92,] 899.8372 898.4547 897.0647 895.6671 894.2621 892.8497 891.4299 890.0029 #>  [93,] 899.6695 898.2934 896.9101 895.5196 894.1220 892.7173 891.3056 889.8870 #>  [94,] 899.5036 898.1339 896.7574 895.3739 893.9836 892.5866 891.1829 889.7727 #>  [95,] 899.3394 897.9762 896.6064 895.2299 893.8470 892.4576 891.0619 889.6601 #>  [96,] 899.1769 897.8202 896.4570 895.0876 893.7119 892.3301 890.9424 889.5489 #>  [97,] 899.0160 897.6657 896.3092 894.9468 893.5784 892.2042 890.8244 889.4391 #>  [98,] 898.8567 897.5128 896.1630 894.8074 893.4463 892.0796 890.7077 889.3306 #>  [99,] 898.6989 897.3613 896.0181 894.6695 893.3156 891.9564 890.5923 889.2234 #> [100,] 898.5424 897.2112 895.8747 894.5329 893.1861 891.8345 890.4781 889.1172 #>           [,33]    [,34]    [,35]    [,36]    [,37]    [,38]    [,39]    [,40] #>   [1,] 918.2775 916.7247 915.1594 913.5814 911.9907 910.3874 908.7715 907.1432 #>   [2,] 917.7010 916.1388 914.5634 912.9748 911.3728 909.7574 908.1288 906.4869 #>   [3,] 917.1279 915.5562 913.9707 912.3714 910.7581 909.1308 907.4894 905.8340 #>   [4,] 916.5581 914.9770 913.3816 911.7716 910.1470 908.5077 906.8535 905.1845 #>   [5,] 915.9918 914.4014 912.7960 911.1755 909.5396 907.8883 906.2213 904.5387 #>   [6,] 915.4293 913.8295 912.2142 910.5832 908.9361 907.2728 905.5931 903.8968 #>   [7,] 914.8705 913.2615 911.6364 909.9949 908.3366 906.6614 904.9689 903.2591 #>   [8,] 914.3156 912.6975 911.0626 909.4107 907.7414 906.0543 904.3492 902.6257 #>   [9,] 913.7649 912.1377 910.4932 908.8310 907.1506 905.4518 903.7340 901.9970 #>  [10,] 913.2183 911.5822 909.9281 908.2557 906.5645 904.8539 903.1236 901.3732 #>  [11,] 912.6761 911.0312 909.3677 907.6852 905.9831 904.2610 902.5183 900.7545 #>  [12,] 912.1384 910.4848 908.8120 907.1196 905.4068 903.6732 901.9182 900.1412 #>  [13,] 911.6054 909.9432 908.2613 906.5590 904.8357 903.0908 901.3236 899.5335 #>  [14,] 911.0771 909.4065 907.7156 906.0037 904.2701 902.5140 900.7348 898.9317 #>  [15,] 910.5537 908.8749 907.1752 905.4538 903.7100 901.9430 900.1519 898.3360 #>  [16,] 910.0354 908.3485 906.6402 904.9095 903.1557 901.3779 899.5752 897.7468 #>  [17,] 909.5222 907.8275 906.1108 904.3710 902.6074 900.8191 899.0050 897.1642 #>  [18,] 909.0144 907.3121 905.5871 903.8385 902.0654 900.2667 898.4415 896.5886 #>  [19,] 908.5120 906.8023 905.0693 903.3121 901.5297 899.7209 897.8848 896.0201 #>  [20,] 908.0152 906.2983 904.5575 902.7920 901.0005 899.1820 897.3353 895.4591 #>  [21,] 907.5241 905.8002 904.0520 902.2784 900.4782 898.6502 896.7932 894.9058 #>  [22,] 907.0389 905.3083 903.5528 901.7714 899.9627 898.1256 896.2587 894.3605 #>  [23,] 906.5595 904.8225 903.0601 901.2712 899.4544 897.6085 895.7320 893.8233 #>  [24,] 906.0863 904.3431 902.5741 900.7779 898.9534 897.0990 895.2133 893.2946 #>  [25,] 905.6191 903.8701 902.0948 900.2918 898.4598 896.5974 894.7028 892.7745 #>  [26,] 905.1583 903.4037 901.6224 899.8129 897.9739 896.1037 894.2008 892.2634 #>  [27,] 904.7039 902.9440 901.1570 899.3414 897.4957 895.6183 893.7075 891.7613 #>  [28,] 904.2559 902.4912 900.6988 898.8774 897.0254 895.1412 893.2229 891.2686 #>  [29,] 903.8145 902.0452 900.2479 898.4211 896.5633 894.6726 892.7474 890.7854 #>  [30,] 903.3797 901.6062 899.8043 897.9725 896.1093 894.2127 892.2810 890.3120 #>  [31,] 902.9517 901.1742 899.3681 897.5318 895.6636 893.7616 891.8239 889.8484 #>  [32,] 902.5304 900.7495 898.9396 897.0991 895.2263 893.3194 891.3763 889.3948 #>  [33,] 902.1161 900.3320 898.5186 896.6744 894.7976 892.8863 890.9383 888.9515 #>  [34,] 901.7087 899.9218 898.1054 896.2579 894.3775 892.4622 890.5100 888.5185 #>  [35,] 901.3082 899.5189 897.6999 895.8496 893.9661 892.0475 890.0915 888.0959 #>  [36,] 900.9148 899.1235 897.3023 895.4496 893.5635 891.6420 889.6830 887.6839 #>  [37,] 900.5284 898.7355 896.9126 895.0579 893.1697 891.2460 889.2844 887.2826 #>  [38,] 900.1492 898.3550 896.5307 894.6747 892.7849 890.8594 888.8959 886.8920 #>  [39,] 899.7771 897.9821 896.1569 894.2998 892.4089 890.4822 888.5175 886.5121 #>  [40,] 899.4121 897.6166 895.7910 893.9334 892.0419 890.1146 888.1492 886.1431 #>  [41,] 899.0542 897.2587 895.4330 893.5754 891.6839 889.7566 887.7910 885.7849 #>  [42,] 898.7036 896.9084 895.0831 893.2259 891.3349 889.4080 887.4430 885.4375 #>  [43,] 898.3600 896.5656 894.7411 892.8848 890.9948 889.0690 887.1052 885.1009 #>  [44,] 898.0236 896.2304 894.4071 892.5522 890.6636 888.7394 886.7774 884.7752 #>  [45,] 897.6943 895.9026 894.0810 892.2279 890.3414 888.4194 886.4598 884.4601 #>  [46,] 897.3720 895.5823 893.7628 891.9120 890.0279 888.1087 886.1521 884.1557 #>  [47,] 897.0568 895.2694 893.4525 891.6044 889.7233 887.8074 885.8543 883.8619 #>  [48,] 896.7486 894.9639 893.1499 891.3050 889.4274 887.5153 885.5664 883.5786 #>  [49,] 896.4473 894.6657 892.8551 891.0138 889.1402 887.2324 885.2882 883.3056 #>  [50,] 896.1529 894.3748 892.5679 890.7307 888.8615 886.9585 885.0197 883.0429 #>  [51,] 895.8654 894.0910 892.2882 890.4555 888.5913 886.6936 884.7606 882.7902 #>  [52,] 895.5845 893.8144 892.0161 890.1883 888.3294 886.4375 884.5109 882.5475 #>  [53,] 895.3104 893.5447 891.7513 889.9289 888.0757 886.1901 884.2704 882.3145 #>  [54,] 895.0428 893.2820 891.4939 889.6771 887.8301 885.9513 884.0389 882.0911 #>  [55,] 894.7817 893.0261 891.2436 889.4328 887.5924 885.7208 883.8163 881.8770 #>  [56,] 894.5270 892.7769 891.0003 889.1960 887.3626 885.4986 883.6023 881.6721 #>  [57,] 894.2786 892.5343 890.7640 888.9664 887.1404 885.2844 883.3968 881.4762 #>  [58,] 894.0364 892.2982 890.5344 888.7440 886.9257 885.0780 883.1996 881.2889 #>  [59,] 893.8003 892.0684 890.3116 888.5286 886.7183 884.8794 883.0105 881.1102 #>  [60,] 893.5702 891.8449 890.0952 888.3200 886.5181 884.6883 882.8292 880.9397 #>  [61,] 893.3459 891.6275 889.8852 888.1181 886.3248 884.5044 882.6556 880.7772 #>  [62,] 893.1273 891.4161 889.6815 887.9226 886.1384 884.3277 882.4894 880.6224 #>  [63,] 892.9143 891.2105 889.4839 887.7335 885.9585 884.1578 882.3304 880.4751 #>  [64,] 892.7068 891.0106 889.2921 887.5506 885.7851 883.9947 882.1783 880.3351 #>  [65,] 892.5047 890.8162 889.1062 887.3737 885.6179 883.8380 882.0330 880.2021 #>  [66,] 892.3077 890.6273 888.9258 887.2026 885.4567 883.6875 881.8941 880.0757 #>  [67,] 892.1158 890.4436 888.7509 887.0371 885.3014 883.5431 881.7615 879.9559 #>  [68,] 891.9289 890.2650 888.5813 886.8771 885.1517 883.4046 881.6350 879.8422 #>  [69,] 891.7468 890.0914 888.4168 886.7224 885.0075 883.2716 881.5142 879.7345 #>  [70,] 891.5693 889.9226 888.2573 886.5727 884.8685 883.1441 881.3989 879.6325 #>  [71,] 891.3963 889.7584 888.1025 886.4281 884.7346 883.0217 881.2890 879.5359 #>  [72,] 891.2278 889.5988 887.9524 886.2881 884.6056 882.9044 881.1841 879.4444 #>  [73,] 891.0635 889.4435 887.8067 886.1528 884.4812 882.7918 881.0841 879.3579 #>  [74,] 890.9033 889.2924 887.6654 886.0218 884.3613 882.6837 880.9887 879.2761 #>  [75,] 890.7470 889.1454 887.5281 885.8950 884.2457 882.5800 880.8977 879.1987 #>  [76,] 890.5946 889.0023 887.3949 885.7723 884.1342 882.4804 880.8109 879.1255 #>  [77,] 890.4459 888.8629 887.2655 885.6534 884.0266 882.3848 880.7281 879.0563 #>  [78,] 890.3007 888.7271 887.1397 885.5383 883.9227 882.2930 880.6490 878.9909 #>  [79,] 890.1590 888.5948 887.0174 885.4266 883.8224 882.2047 880.5735 878.9289 #>  [80,] 890.0205 888.4659 886.8985 885.3184 883.7255 882.1197 880.5013 878.8702 #>  [81,] 889.8852 888.3401 886.7828 885.2133 883.6317 882.0380 880.4322 878.8147 #>  [82,] 889.7529 888.2173 886.6701 885.1113 883.5410 881.9592 880.3661 878.7620 #>  [83,] 889.6235 888.0974 886.5603 885.0122 883.4531 881.8833 880.3028 878.7120 #>  [84,] 889.4969 887.9803 886.4533 884.9158 883.3680 881.8100 880.2421 878.6645 #>  [85,] 889.3729 887.8659 886.3489 884.8220 883.2854 881.7392 880.1837 878.6193 #>  [86,] 889.2514 887.7539 886.2470 884.7307 883.2052 881.6707 880.1276 878.5763 #>  [87,] 889.1323 887.6443 886.1474 884.6416 883.1272 881.6044 880.0736 878.5351 #>  [88,] 889.0155 887.5370 886.0500 884.5547 883.0513 881.5401 880.0214 878.4958 #>  [89,] 888.9009 887.4318 885.9547 884.4698 882.9773 881.4776 879.9711 878.4581 #>  [90,] 888.7883 887.3286 885.8614 884.3868 882.9052 881.4169 879.9223 878.4218 #>  [91,] 888.6776 887.2273 885.7699 884.3056 882.8348 881.3577 879.8749 878.3869 #>  [92,] 888.5688 887.1278 885.6801 884.2260 882.7659 881.3000 879.8289 878.3531 #>  [93,] 888.4617 887.0300 885.5920 884.1480 882.6984 881.2436 879.7841 878.3204 #>  [94,] 888.3563 886.9337 885.5053 884.0713 882.6322 881.1884 879.7403 878.2885 #>  [95,] 888.2523 886.8389 885.4200 883.9960 882.5673 881.1343 879.6975 878.2574 #>  [96,] 888.1498 886.7454 885.3360 883.9218 882.5034 881.0811 879.6554 878.2270 #>  [97,] 888.0486 886.6532 885.2531 883.8487 882.4404 881.0287 879.6141 878.1971 #>  [98,] 887.9487 886.5622 885.1713 883.7766 882.3784 880.9771 879.5733 878.1676 #>  [99,] 887.8499 886.4722 885.0905 883.7054 882.3170 880.9261 879.5330 878.1384 #> [100,] 887.7522 886.3832 885.0106 883.6349 882.2564 880.8756 879.4931 878.1095 #>           [,41]    [,42]    [,43]    [,44]    [,45]    [,46]    [,47]    [,48] #>   [1,] 905.5027 903.8503 902.1865 900.5119 898.8271 897.1330 895.4309 893.7218 #>   [2,] 904.8321 903.1644 901.4844 899.7926 898.0895 896.3761 894.6533 892.9225 #>   [3,] 904.1647 902.4817 900.7853 899.0761 897.3545 895.6215 893.8778 892.1248 #>   [4,] 903.5007 901.8022 900.0895 898.3627 896.6225 894.8695 893.1046 891.3291 #>   [5,] 902.8403 901.1264 899.3971 897.6527 895.8936 894.1205 892.3342 890.5357 #>   [6,] 902.1839 900.4544 898.7085 896.9463 895.1682 893.3748 891.5667 889.7450 #>   [7,] 901.5316 899.7866 898.0240 896.2439 894.4467 892.6327 890.8027 888.9575 #>   [8,] 900.8838 899.1231 897.3438 895.5458 893.7293 891.8947 890.0425 888.1734 #>   [9,] 900.2406 898.4644 896.6683 894.8523 893.0165 891.1611 889.2865 887.3933 #>  [10,] 899.6023 897.8106 895.9978 894.1638 892.3086 890.4323 888.5351 886.6177 #>  [11,] 898.9692 897.1620 895.3326 893.4806 891.6060 889.7087 887.7889 885.8469 #>  [12,] 898.3416 896.5190 894.6730 892.8031 890.9091 888.9908 887.0482 885.0815 #>  [13,] 897.7198 895.8819 894.0194 892.1316 890.2182 888.2789 886.3135 884.3220 #>  [14,] 897.1040 895.2510 893.3721 891.4665 889.5338 887.5736 885.5853 883.5690 #>  [15,] 896.4945 894.6266 892.7314 890.8082 888.8564 886.8752 884.8642 882.8230 #>  [16,] 895.8917 894.0090 892.0977 890.1571 888.1862 886.1843 884.1506 882.0846 #>  [17,] 895.2957 893.3985 891.4714 889.5135 887.5239 885.5014 883.4451 881.3544 #>  [18,] 894.7069 892.7954 890.8528 888.8780 886.8697 884.8268 882.7483 880.6330 #>  [19,] 894.1256 892.2001 890.2423 888.2507 886.2242 884.1612 882.0606 879.9210 #>  [20,] 893.5521 891.6129 889.6401 887.6322 885.5877 883.5050 881.3827 879.2190 #>  [21,] 892.9866 891.0341 889.0468 887.0229 884.9608 882.8588 880.7150 878.5277 #>  [22,] 892.4295 890.4640 888.4625 886.4231 884.3439 882.2230 880.0583 877.8478 #>  [23,] 891.8809 889.9030 887.8877 885.8333 883.7374 881.5981 879.4130 877.1798 #>  [24,] 891.3412 889.3512 887.3228 885.2537 883.1418 880.9847 878.7798 876.5245 #>  [25,] 890.8106 888.8091 886.7680 884.6849 882.5575 880.3832 878.1592 875.8825 #>  [26,] 890.2894 888.2769 886.2237 884.1272 881.9849 879.7941 877.5517 875.2544 #>  [27,] 889.7779 887.7549 885.6901 883.5809 881.4245 879.2179 876.9579 874.6409 #>  [28,] 889.2762 887.2434 885.1677 883.0464 880.8766 878.6551 876.3784 874.0426 #>  [29,] 888.7846 886.7426 884.6566 882.5240 880.3416 878.1060 875.8136 873.4601 #>  [30,] 888.3033 886.2527 884.1573 882.0141 879.8199 877.5712 875.2640 872.8939 #>  [31,] 887.8326 885.7740 883.6698 881.5169 879.3119 877.0510 874.7301 872.3446 #>  [32,] 887.3725 885.3067 883.1945 881.0327 878.8178 876.5458 874.2124 871.8128 #>  [33,] 886.9233 884.8510 882.7316 880.5618 878.3379 876.0559 873.7112 871.2988 #>  [34,] 886.4851 884.4071 882.2813 880.1044 877.8726 875.5817 873.2270 870.8032 #>  [35,] 886.0581 883.9751 881.8438 879.6608 877.4221 875.1234 872.7600 870.3263 #>  [36,] 885.6423 883.5551 881.4192 879.2310 876.9865 874.6813 872.3105 869.8685 #>  [37,] 885.2379 883.1473 881.0077 878.8152 876.5661 874.2556 871.8789 869.4300 #>  [38,] 884.8449 882.7518 880.6093 878.4137 876.1610 873.8465 871.4652 869.0112 #>  [39,] 884.4635 882.3686 880.2242 878.0264 875.7713 873.4541 871.0697 868.6122 #>  [40,] 884.0937 881.9979 879.8524 877.6535 875.3971 873.0784 870.6924 868.2331 #>  [41,] 883.7354 881.6395 879.4939 877.2949 875.0384 872.7196 870.3335 867.8739 #>  [42,] 883.3887 881.2936 879.1488 876.9507 874.6952 872.3777 869.9928 867.5348 #>  [43,] 883.0535 880.9600 878.8170 876.6209 874.3676 872.0525 869.6704 867.2156 #>  [44,] 882.7299 880.6388 878.4985 876.3054 874.0554 871.7440 869.3662 866.9163 #>  [45,] 882.4178 880.3299 878.1931 876.0040 873.7585 871.4522 869.0801 866.6365 #>  [46,] 882.1170 880.0332 877.9009 875.7167 873.4768 871.1768 868.8117 866.3762 #>  [47,] 881.8276 879.7485 877.6216 875.4434 873.2101 870.9176 868.5610 866.1351 #>  [48,] 881.5493 879.4758 877.3551 875.1838 872.9583 870.6744 868.3276 865.9127 #>  [49,] 881.2821 879.2149 877.1012 874.9378 872.7210 870.4469 868.1111 865.7088 #>  [50,] 881.0258 878.9657 876.8598 874.7051 872.4980 870.2348 867.9113 865.5229 #>  [51,] 880.7802 878.7279 876.6306 874.4854 872.2890 870.0378 867.7278 865.3545 #>  [52,] 880.5451 878.5013 876.4134 874.2786 872.0938 869.8555 867.5600 865.2031 #>  [53,] 880.3204 878.2857 876.2079 874.0843 871.9119 869.6875 867.4075 865.0681 #>  [54,] 880.1058 878.0808 876.0138 873.9021 871.7430 869.5333 867.2699 864.9491 #>  [55,] 879.9012 877.8865 875.8309 873.7318 871.5867 869.3926 867.1466 864.8454 #>  [56,] 879.7062 877.7025 875.6588 873.5730 871.4426 869.2649 867.0372 864.7563 #>  [57,] 879.5206 877.5284 875.4973 873.4254 871.3104 869.1497 866.9410 864.6814 #>  [58,] 879.3443 877.3639 875.3460 873.2886 871.1895 869.0466 866.8575 864.6198 #>  [59,] 879.1769 877.2089 875.2046 873.1621 871.0796 868.9549 866.7861 864.5710 #>  [60,] 879.0181 877.0630 875.0727 873.0457 870.9802 868.8744 866.7264 864.5344 #>  [61,] 878.8677 876.9258 874.9500 872.9389 870.8909 868.8043 866.6776 864.5092 #>  [62,] 878.7254 876.7971 874.8362 872.8414 870.8112 868.7443 866.6393 864.4948 #>  [63,] 878.5909 876.6765 874.7309 872.7526 870.7407 868.6938 866.6108 864.4906 #>  [64,] 878.4639 876.5638 874.6336 872.6723 870.6789 868.6523 866.5916 864.4960 #>  [65,] 878.3442 876.4586 874.5442 872.6001 870.6254 868.6194 866.5812 864.5102 #>  [66,] 878.2315 876.3606 874.4622 872.5355 870.5798 868.5945 866.5789 864.5328 #>  [67,] 878.1254 876.2694 874.3872 872.4781 870.5416 868.5771 866.5844 864.5631 #>  [68,] 878.0257 876.1848 874.3190 872.4276 870.5104 868.5669 866.5969 864.6005 #>  [69,] 877.9321 876.1065 874.2571 872.3836 870.4857 868.5632 866.6161 864.6444 #>  [70,] 877.8443 876.0340 874.2013 872.3457 870.4672 868.5657 866.6414 864.6944 #>  [71,] 877.7621 875.9672 874.1511 872.3136 870.4545 868.5740 866.6723 864.7499 #>  [72,] 877.6851 875.9058 874.1064 872.2868 870.4471 868.5875 866.7084 864.8104 #>  [73,] 877.6131 875.8493 874.0666 872.2651 870.4447 868.6059 866.7493 864.8754 #>  [74,] 877.5458 875.7976 874.0316 872.2480 870.4469 868.6289 866.7944 864.9444 #>  [75,] 877.4829 875.7504 874.0011 872.2353 870.4534 868.6559 866.8435 865.0171 #>  [76,] 877.4243 875.7073 873.9746 872.2267 870.4638 868.6866 866.8960 865.0929 #>  [77,] 877.3696 875.6681 873.9520 872.2217 870.4777 868.7208 866.9516 865.1715 #>  [78,] 877.3186 875.6326 873.9330 872.2202 870.4950 868.7579 867.0101 865.2526 #>  [79,] 877.2711 875.6004 873.9172 872.2219 870.5151 868.7978 867.0709 865.3356 #>  [80,] 877.2269 875.5715 873.9044 872.2264 870.5379 868.8401 867.1338 865.4204 #>  [81,] 877.1856 875.5454 873.8945 872.2335 870.5631 868.8844 867.1985 865.5066 #>  [82,] 877.1471 875.5220 873.8870 872.2429 870.5904 868.9306 867.2646 865.5939 #>  [83,] 877.1113 875.5010 873.8818 872.2544 870.6196 868.9784 867.3320 865.6819 #>  [84,] 877.0778 875.4823 873.8787 872.2677 870.6503 869.0274 867.4004 865.7705 #>  [85,] 877.0464 875.4656 873.8774 872.2827 870.6824 869.0775 867.4694 865.8594 #>  [86,] 877.0171 875.4507 873.8778 872.2991 870.7157 869.1285 867.5389 865.9483 #>  [87,] 876.9896 875.4375 873.8796 872.3167 870.7498 869.1800 867.6086 866.0370 #>  [88,] 876.9637 875.4257 873.8827 872.3354 870.7847 869.2320 867.6784 866.1254 #>  [89,] 876.9393 875.4153 873.8868 872.3548 870.8202 869.2842 867.7480 866.2132 #>  [90,] 876.9162 875.4059 873.8918 872.3749 870.8560 869.3364 867.8173 866.3002 #>  [91,] 876.8942 875.3975 873.8976 872.3954 870.8920 869.3884 867.8861 866.3864 #>  [92,] 876.8732 875.3899 873.9039 872.4163 870.9280 869.4402 867.9542 866.4714 #>  [93,] 876.8531 875.3829 873.9107 872.4374 870.9639 869.4916 868.0215 866.5553 #>  [94,] 876.8337 875.3765 873.9178 872.4585 870.9996 869.5423 868.0879 866.6378 #>  [95,] 876.8149 875.3704 873.9250 872.4794 871.0348 869.5923 868.1532 866.7189 #>  [96,] 876.7965 875.3646 873.9322 872.5002 871.0696 869.6415 868.2173 866.7983 #>  [97,] 876.7785 875.3590 873.9393 872.5206 871.1037 869.6898 868.2802 866.8761 #>  [98,] 876.7607 875.3533 873.9463 872.5405 871.1370 869.7370 868.3416 866.9522 #>  [99,] 876.7430 875.3476 873.9529 872.5599 871.1695 869.7830 868.4015 867.0263 #> [100,] 876.7254 875.3417 873.9591 872.5785 871.2011 869.8278 868.4598 867.0985 #>           [,49]    [,50]    [,51]    [,52]    [,53]    [,54]    [,55]    [,56] #>   [1,] 892.0075 890.2898 888.5709 886.8534 885.1402 883.4347 881.7409 880.0632 #>   [2,] 891.1851 889.4430 887.6984 885.9539 884.2123 882.4773 880.7527 879.0432 #>   [3,] 890.3639 888.5969 886.8260 885.0536 883.2829 881.5173 879.7608 878.0181 #>   [4,] 889.5442 887.7518 885.9539 884.1530 882.3522 880.5550 878.7654 876.9883 #>   [5,] 888.7264 886.9080 885.0825 883.2524 881.4206 879.5908 877.7670 875.9540 #>   [6,] 887.9109 886.0661 884.2123 882.3522 880.4886 878.6251 876.7658 874.9157 #>   [7,] 887.0982 885.2263 883.3438 881.4529 879.5566 877.6583 875.7623 873.8736 #>   [8,] 886.2885 884.3892 882.4773 880.5550 878.6251 876.6910 874.7571 872.8282 #>   [9,] 885.4825 883.5553 881.6134 879.6590 877.6946 875.7238 873.7506 871.7801 #>  [10,] 884.6806 882.7251 880.7527 878.7654 876.7658 874.7571 872.7434 870.7299 #>  [11,] 883.8833 881.8992 879.8958 877.8750 875.8392 873.7917 871.7363 869.6781 #>  [12,] 883.0912 881.0780 879.0432 876.9883 874.9157 872.8282 870.7299 868.6255 #>  [13,] 882.3048 880.2623 878.1956 876.1061 873.9958 871.8676 869.7250 867.5729 #>  [14,] 881.5247 879.4527 877.3538 875.2291 873.0805 870.9105 868.7225 866.5212 #>  [15,] 880.7515 878.6498 876.5184 874.3581 872.1705 869.9579 867.7234 865.4714 #>  [16,] 879.9859 877.8544 875.6902 873.4940 871.2669 869.0109 866.7288 864.4246 #>  [17,] 879.2286 877.0671 874.8700 872.6375 870.3705 868.0704 865.7397 863.3820 #>  [18,] 878.4801 876.2888 874.0587 871.7898 869.4823 867.1375 864.7573 862.3449 #>  [19,] 877.7412 875.5202 873.2572 870.9517 868.6036 866.2136 863.7831 861.3147 #>  [20,] 877.0126 874.7621 872.4663 870.1242 867.7353 865.2998 862.8184 860.2931 #>  [21,] 876.2951 874.0153 871.6869 869.3084 866.8788 864.3975 861.8646 859.2815 #>  [22,] 875.5893 873.2808 870.9201 868.5054 866.0352 863.5080 860.9235 858.2820 #>  [23,] 874.8961 872.5592 870.1668 867.7164 865.2058 862.6330 859.9967 857.2963 #>  [24,] 874.2161 871.8515 869.4280 866.9424 864.3919 861.7739 859.0859 856.3265 #>  [25,] 873.5501 871.1586 868.7047 866.1846 863.5950 860.9322 858.1931 855.3747 #>  [26,] 872.8989 870.4813 867.9979 865.4443 862.8164 860.1097 857.3200 854.4433 #>  [27,] 872.2632 869.8205 867.3086 864.7225 862.0574 859.3080 856.4688 853.5345 #>  [28,] 871.6437 869.1770 866.6378 864.0205 861.3196 858.5286 855.6413 852.6508 #>  [29,] 871.0411 868.5517 865.9865 863.3395 860.6042 857.7734 854.8396 851.7945 #>  [30,] 870.4561 867.9453 865.3556 862.6805 859.9126 857.0440 854.0657 850.9682 #>  [31,] 869.8893 867.3586 864.7461 862.0446 859.2462 856.3419 853.3217 850.1744 #>  [32,] 869.3414 866.7924 864.1588 861.4330 858.6062 855.6688 852.6094 849.4154 #>  [33,] 868.8129 866.2472 863.5945 860.8465 857.9939 855.0261 851.9307 848.6936 #>  [34,] 868.3044 865.7238 863.0540 860.2862 857.4104 854.4152 851.2873 848.0112 #>  [35,] 867.8162 865.2227 862.5380 859.7528 856.8567 853.8375 850.6810 847.3704 #>  [36,] 867.3489 864.7444 862.0470 859.2471 856.3337 853.2940 850.1130 846.7729 #>  [37,] 866.9027 864.2894 861.5817 858.7697 855.8422 852.7858 849.5848 846.2204 #>  [38,] 866.4779 863.8579 861.1423 858.3212 855.3829 852.3137 849.0973 845.7143 #>  [39,] 866.0749 863.4502 860.7293 857.9019 854.9563 851.8783 848.6514 845.2556 #>  [40,] 865.6937 863.0665 860.3428 857.5122 854.5626 851.4801 848.2476 844.8450 #>  [41,] 865.3344 862.7070 859.9830 857.1521 854.2022 851.1192 847.8862 844.4830 #>  [42,] 864.9970 862.3716 859.6499 856.8217 853.8749 850.7957 847.5673 844.1696 #>  [43,] 864.6814 862.0602 859.3434 856.5208 853.5808 850.5095 847.2906 843.9045 #>  [44,] 864.3876 861.7727 859.0632 856.2493 853.3193 850.2601 847.0556 843.6870 #>  [45,] 864.1152 861.5089 858.8092 856.0067 853.0902 850.0469 846.8615 843.5160 #>  [46,] 863.8641 861.2683 858.5808 855.7925 852.8927 849.8691 846.7073 843.3904 #>  [47,] 863.6339 861.0506 858.3776 855.6061 852.7261 849.7258 846.5918 843.3085 #>  [48,] 863.4242 860.8554 858.1990 855.4469 852.5895 849.6159 846.5137 843.2684 #>  [49,] 863.2345 860.6819 858.0444 855.3139 852.4818 849.5381 846.4712 843.2683 #>  [50,] 863.0643 860.5298 857.9129 855.2064 852.4021 849.4910 846.4627 843.3058 #>  [51,] 862.9131 860.3982 857.8038 855.1232 852.3491 849.4731 846.4863 843.3786 #>  [52,] 862.7802 860.2864 857.7162 855.0634 852.3215 849.4830 846.5401 843.4843 #>  [53,] 862.6651 860.1938 857.6492 855.0259 852.3179 849.5189 846.6221 843.6205 #>  [54,] 862.5670 860.1195 857.6020 855.0096 852.3372 849.5793 846.7304 843.7847 #>  [55,] 862.4853 860.0626 857.5734 855.0132 852.3778 849.6625 846.8628 843.9745 #>  [56,] 862.4192 860.0225 857.5625 855.0357 852.4383 849.7667 847.0174 844.1873 #>  [57,] 862.3680 859.9981 857.5683 855.0758 852.5175 849.8904 847.1922 844.4209 #>  [58,] 862.3310 859.9886 857.5899 855.1324 852.6138 850.0319 847.3853 844.6730 #>  [59,] 862.3074 859.9932 857.6261 855.2043 852.7259 850.1897 847.5948 844.9415 #>  [60,] 862.2965 860.0110 857.6761 855.2903 852.8525 850.3621 847.8189 845.2242 #>  [61,] 862.2975 860.0411 857.7388 855.3894 852.9924 850.5477 848.0560 845.5192 #>  [62,] 862.3097 860.0828 857.8132 855.5003 853.1441 850.7450 848.3044 845.8247 #>  [63,] 862.3323 860.1351 857.8984 855.6222 853.3066 850.9528 848.5626 846.1391 #>  [64,] 862.3647 860.1973 857.9936 855.7538 853.4787 851.1697 848.8292 846.4607 #>  [65,] 862.4061 860.2686 858.0978 855.8943 853.6593 851.3945 849.1028 846.7880 #>  [66,] 862.4559 860.3482 858.2102 856.0428 853.8473 851.6261 849.3822 847.1199 #>  [67,] 862.5133 860.4354 858.3300 856.1982 854.0419 851.8634 849.6662 847.4549 #>  [68,] 862.5778 860.5295 858.4563 856.3598 854.2419 852.1054 849.9538 847.7920 #>  [69,] 862.6488 860.6298 858.5886 856.5268 854.4467 852.3512 850.2441 848.1303 #>  [70,] 862.7255 860.7356 858.7260 856.6984 854.6553 852.5999 850.5360 848.4687 #>  [71,] 862.8076 860.8464 858.8679 856.8739 854.8671 852.8507 850.8288 848.8064 #>  [72,] 862.8944 860.9616 859.0136 857.0526 855.0813 853.1029 851.1218 849.1428 #>  [73,] 862.9854 861.0805 859.1626 857.2339 855.2972 853.3559 851.4142 849.4771 #>  [74,] 863.0800 861.2027 859.3144 857.4173 855.5143 853.6090 851.7055 849.8088 #>  [75,] 863.1780 861.3277 859.4683 857.6021 855.7320 853.8616 851.9951 850.1374 #>  [76,] 863.2787 861.4551 859.6240 857.7879 855.9498 854.1133 852.2825 850.4623 #>  [77,] 863.3818 861.5842 859.7809 857.9742 856.1673 854.3636 852.5673 850.7831 #>  [78,] 863.4869 861.7149 859.9386 858.1606 856.3839 854.6121 852.8491 851.0996 #>  [79,] 863.5936 861.8466 860.0968 858.3467 856.5994 854.8583 853.1275 851.4114 #>  [80,] 863.7015 861.9790 860.2550 858.5321 856.8133 855.1020 853.4022 851.7182 #>  [81,] 863.8104 862.1118 860.4130 858.7165 857.0254 855.3429 853.6730 852.0198 #>  [82,] 863.9199 862.2447 860.5704 858.8996 857.2353 855.5807 853.9395 852.3161 #>  [83,] 864.0297 862.3773 860.7269 859.0811 857.4427 855.8151 854.2017 852.6067 #>  [84,] 864.1396 862.5094 860.8823 859.2608 857.6475 856.0459 854.4593 852.8917 #>  [85,] 864.2492 862.6408 861.0364 859.4383 857.8495 856.2729 854.7121 853.1709 #>  [86,] 864.3584 862.7712 861.1888 859.6136 858.0483 856.4961 854.9601 853.4441 #>  [87,] 864.4670 862.9004 861.3394 859.7864 858.2440 856.7152 855.2031 853.7114 #>  [88,] 864.5747 863.0282 861.4881 859.9565 858.4362 856.9300 855.4411 853.9727 #>  [89,] 864.6814 863.1545 861.6345 860.1238 858.6249 857.1406 855.6739 854.2279 #>  [90,] 864.7869 863.2790 861.7787 860.2882 858.8100 857.3468 855.9014 854.4771 #>  [91,] 864.8910 863.4017 861.9205 860.4496 858.9914 857.5485 856.1238 854.7202 #>  [92,] 864.9935 863.5223 862.0596 860.6077 859.1689 857.7457 856.3408 854.9572 #>  [93,] 865.0945 863.6407 862.1961 860.7626 859.3425 857.9383 856.5526 855.1881 #>  [94,] 865.1936 863.7570 862.3298 860.9141 859.5122 858.1263 856.7590 855.4130 #>  [95,] 865.2908 863.8708 862.4606 861.0622 859.6778 858.3097 856.9602 855.6319 #>  [96,] 865.3861 863.9822 862.5885 861.2069 859.8394 858.4884 857.1560 855.8448 #>  [97,] 865.4792 864.0910 862.7133 861.3479 859.9969 858.6624 857.3466 856.0518 #>  [98,] 865.5702 864.1973 862.8351 861.4854 860.1503 858.8317 857.5319 856.2530 #>  [99,] 865.6589 864.3008 862.9537 861.6193 860.2996 858.9964 857.7119 856.4483 #> [100,] 865.7453 864.4016 863.0691 861.7495 860.4446 859.1564 857.8867 856.6378 #>           [,57]    [,58]    [,59]    [,60]    [,61]    [,62]    [,63]    [,64] #>   [1,] 878.4066 876.7764 875.1786 873.6199 872.1071 870.6473 869.2481 867.9168 #>   [2,] 877.3538 875.6902 874.0587 872.4663 870.9201 869.4280 867.9979 866.6378 #>   [3,] 876.2946 874.5960 872.9291 871.3010 869.7196 868.1931 866.7301 865.3393 #>   [4,] 875.2291 873.4940 871.7898 870.1242 868.5054 866.9424 865.4443 864.0205 #>   [5,] 874.1577 872.3842 870.6408 868.9356 867.2773 865.6755 864.1399 862.6809 #>   [6,] 873.0805 871.2669 869.4823 867.7353 866.0352 864.3919 862.8164 861.3196 #>   [7,] 871.9980 870.1423 868.3145 866.5234 864.7788 863.0915 861.4732 859.9357 #>   [8,] 870.9105 869.0109 867.1375 865.2998 863.5080 861.7739 860.1097 858.5286 #>   [9,] 869.8185 867.8729 865.9517 864.0647 862.2230 860.4388 858.7255 857.0974 #>  [10,] 868.7225 866.7288 864.7573 862.8184 860.9235 859.0859 857.3200 855.6413 #>  [11,] 867.6232 865.5792 863.5549 861.5610 859.6098 857.7152 855.8928 854.1593 #>  [12,] 866.5212 864.4246 862.3449 860.2931 858.2820 856.3265 854.4433 852.6508 #>  [13,] 865.4173 863.2659 861.1280 859.0150 856.9403 854.9197 852.9712 851.1147 #>  [14,] 864.3125 862.1039 859.9050 857.7273 855.5851 853.4949 851.4761 849.5503 #>  [15,] 863.2076 860.9395 858.6766 856.4309 854.2170 852.0524 849.9578 847.9568 #>  [16,] 862.1039 859.7739 857.4441 855.1266 852.8366 850.5925 848.4163 846.3335 #>  [17,] 861.0026 858.6083 856.2086 853.8156 851.4449 849.1156 846.8514 844.6797 #>  [18,] 859.9050 857.4441 854.9715 852.4991 850.0428 847.6227 845.2635 842.9951 #>  [19,] 858.8127 856.2830 853.7343 851.1787 848.6319 846.1146 843.6530 841.2793 #>  [20,] 857.7273 855.1266 852.4991 849.8562 847.2137 844.5928 842.0208 839.5321 #>  [21,] 856.6508 853.9771 851.2678 848.5337 845.7903 843.0589 840.3679 837.7539 #>  [22,] 855.5851 852.8366 850.0428 847.2137 844.3641 841.5151 838.6960 835.9453 #>  [23,] 854.5324 851.7075 848.8268 845.8990 842.9379 839.9641 837.0072 834.1076 #>  [24,] 853.4949 850.5925 847.6227 844.5928 841.5151 838.4093 835.3044 832.2425 #>  [25,] 852.4753 849.4944 846.4337 843.2987 840.0996 836.8544 833.5914 830.3529 #>  [26,] 851.4761 848.4163 845.2635 842.0208 838.6960 835.3044 831.8726 828.4426 #>  [27,] 850.5001 847.3615 844.1159 840.7636 837.3092 833.7649 830.1540 826.5167 #>  [28,] 849.5503 846.3335 842.9951 839.5321 835.9453 832.2425 828.4426 824.5823 #>  [29,] 848.6295 845.3359 841.9056 838.3317 834.6107 830.7448 826.7469 822.6480 #>  [30,] 847.7409 844.3726 840.8520 837.1683 833.3125 829.2805 825.0773 820.7251 #>  [31,] 846.8875 843.4474 839.8393 836.0480 832.0587 827.8595 823.4457 818.8276 #>  [32,] 846.0724 842.5641 838.8724 834.9772 830.8575 826.4925 821.8658 816.9725 #>  [33,] 845.2985 841.7267 837.9563 833.9626 829.7176 825.1913 820.3533 815.1799 #>  [34,] 844.5688 840.9388 837.0959 833.0107 828.6482 823.9680 818.9251 813.4733 #>  [35,] 843.8859 840.2039 836.2961 832.1280 827.6580 822.8354 817.5994 811.8789 #>  [36,] 843.2522 839.5254 835.5611 831.3205 826.7556 821.8059 816.3946 810.4247 #>  [37,] 842.6700 838.9061 834.8949 830.5938 825.9491 820.8912 815.3288 809.1396 #>  [38,] 842.1409 838.3484 834.3008 829.9526 825.2453 820.1019 814.4185 808.0509 #>  [39,] 841.6665 837.8543 833.7816 829.4007 824.6499 819.4466 813.6778 807.1824 #>  [40,] 841.2476 837.4250 833.3390 828.9408 824.1668 818.9315 813.1167 806.5521 #>  [41,] 840.8849 837.0613 832.9741 828.5743 823.7982 818.5600 812.7410 806.1700 #>  [42,] 840.5783 836.7633 832.6869 828.3014 823.5442 818.3323 812.5510 806.0369 #>  [43,] 840.3274 836.5303 832.4767 828.1208 823.4032 818.2457 812.5422 806.1447 #>  [44,] 840.1314 836.3611 832.3417 828.0302 823.3715 818.2946 812.7053 806.4768 #>  [45,] 839.9889 836.2540 832.2795 828.0259 823.4437 818.4707 813.0270 807.0105 #>  [46,] 839.8982 836.2067 832.2868 828.1033 823.6133 818.7639 813.4912 807.7189 #>  [47,] 839.8572 836.2162 832.3598 828.2572 823.8723 819.1626 814.0800 808.5734 #>  [48,] 839.8635 836.2795 832.4941 828.4815 824.2124 819.6545 814.7749 809.5455 #>  [49,] 839.9145 836.3931 832.6852 828.7699 824.6246 820.2269 815.5577 810.6086 #>  [50,] 840.0074 836.5533 832.9281 829.1157 825.1000 820.8675 816.4111 811.7387 #>  [51,] 840.1391 836.7562 833.2178 829.5124 825.6298 821.5643 817.3193 812.9149 #>  [52,] 840.3067 836.9980 833.5494 829.9534 826.2055 822.3065 818.2681 814.1196 #>  [53,] 840.5070 837.2747 833.9179 830.4327 826.8191 823.0840 819.2452 815.3384 #>  [54,] 840.7370 837.5827 834.3185 830.9441 827.4635 823.8879 820.2399 816.5594 #>  [55,] 840.9938 837.9181 834.7469 831.4823 828.1319 824.7103 821.2435 817.7733 #>  [56,] 841.2743 838.2776 835.1986 832.0422 828.8184 825.5444 822.2485 818.9729 #>  [57,] 841.5758 838.6577 835.6699 832.6192 829.5176 826.3845 823.2488 820.1527 #>  [58,] 841.8956 839.0554 836.1570 833.2090 830.2250 827.2254 824.2397 821.3087 #>  [59,] 842.2313 839.4676 836.6566 833.8080 830.9365 828.0632 825.2173 822.4379 #>  [60,] 842.5803 839.8918 837.1658 834.4130 831.6488 828.8944 826.1785 823.5381 #>  [61,] 842.9406 840.3254 837.6818 835.0209 832.3587 829.7162 827.1211 824.6082 #>  [62,] 843.3100 840.7663 838.2021 835.6293 833.0638 830.5264 828.0434 825.6474 #>  [63,] 843.6868 841.2124 838.7248 836.2361 833.7621 831.3231 828.9440 826.6553 #>  [64,] 844.0693 841.6619 839.2478 836.8393 834.4518 832.1049 829.8222 827.6319 #>  [65,] 844.4557 842.1130 839.7695 837.4373 835.1315 832.8708 830.6775 828.5775 #>  [66,] 844.8448 842.5645 840.2885 838.0287 835.7999 833.6199 831.5095 829.4926 #>  [67,] 845.2353 843.0150 840.8035 838.6125 836.4563 834.3517 832.3181 830.3777 #>  [68,] 845.6260 843.4633 841.3134 839.1877 837.0999 835.0657 833.1036 831.2336 #>  [69,] 846.0159 843.9085 841.8174 839.7536 837.7300 835.7619 833.8660 832.0611 #>  [70,] 846.4041 844.3497 842.3146 840.3093 838.3464 836.4400 834.6057 832.8609 #>  [71,] 846.7897 844.7861 842.8043 840.8546 838.9487 837.1000 835.3232 833.6338 #>  [72,] 847.1722 845.2171 843.2861 841.3889 839.5368 837.7422 836.0187 834.3808 #>  [73,] 847.5508 845.6421 843.7594 841.9120 840.1105 838.3666 836.6929 835.1027 #>  [74,] 847.9249 846.0607 844.2239 842.4236 840.6698 838.9735 837.3462 835.8003 #>  [75,] 848.2942 846.4724 844.6793 842.9237 841.2149 839.5630 837.9792 836.4744 #>  [76,] 848.6582 846.8769 845.1255 843.4121 841.7456 840.1357 838.5923 837.1260 #>  [77,] 849.0166 847.2739 845.5621 843.8887 842.2623 840.6917 839.1863 837.7556 #>  [78,] 849.3690 847.6633 845.9891 844.3537 842.7650 841.2313 839.7615 838.3642 #>  [79,] 849.7153 848.0448 846.4064 844.8070 843.2539 841.7551 840.3186 838.9525 #>  [80,] 850.0551 848.4183 846.8140 845.2487 843.7293 842.2632 840.8580 839.5211 #>  [81,] 850.3883 848.7838 847.2119 845.6789 844.1914 842.7562 841.3804 840.0708 #>  [82,] 850.7149 849.1410 847.6000 846.0978 844.6404 843.2343 841.8861 840.6022 #>  [83,] 851.0346 849.4901 847.9785 846.5054 845.0766 843.6980 842.3758 841.1160 #>  [84,] 851.3474 849.8309 848.3474 846.9020 845.5002 844.1476 842.8499 841.6127 #>  [85,] 851.6532 850.1636 848.7067 847.2877 845.9115 844.5835 843.3089 842.0930 #>  [86,] 851.9520 850.4880 849.0567 847.6626 846.3107 845.0060 843.7532 842.5573 #>  [87,] 852.2438 850.8043 849.3972 848.0270 846.6982 845.4154 844.1833 843.0063 #>  [88,] 852.5286 851.1125 849.7286 848.3811 847.0742 845.8122 844.5996 843.4405 #>  [89,] 852.8063 851.4127 850.0509 848.7250 847.4389 846.1967 845.0026 843.8603 #>  [90,] 853.0771 851.7049 850.3643 849.0589 847.7926 846.5692 845.3926 844.2662 #>  [91,] 853.3409 851.9893 850.6688 849.3830 848.1356 846.9300 845.7699 844.6587 #>  [92,] 853.5978 852.2659 850.9647 849.6976 848.4681 847.2795 846.1351 845.0381 #>  [93,] 853.8478 852.5347 851.2520 850.0028 848.7903 847.6178 846.4884 845.4050 #>  [94,] 854.0911 852.7960 851.5309 850.2988 849.1026 847.9455 846.8302 845.7597 #>  [95,] 854.3276 853.0498 851.8016 850.5858 849.4051 848.2626 847.1608 846.1025 #>  [96,] 854.5574 853.2963 852.0642 850.8640 849.6982 848.5695 847.4806 846.4339 #>  [97,] 854.7806 853.5355 852.3189 851.1335 849.9819 848.8665 847.7898 846.7541 #>  [98,] 854.9974 853.7675 852.5658 851.3946 850.2565 849.1538 848.0888 847.0636 #>  [99,] 855.2077 853.9925 852.8050 851.6475 850.5223 849.4317 848.3778 847.3626 #> [100,] 855.4117 854.2106 853.0367 851.8923 850.7795 849.7004 848.6571 847.6515 #>           [,65]    [,66]    [,67]    [,68]    [,69]    [,70]    [,71]    [,72] #>   [1,] 866.6607 865.4866 864.4006 863.4079 862.5126 861.7173 861.0234 860.4304 #>   [2,] 865.3556 864.1588 863.0540 862.0470 861.1423 860.3428 859.6499 859.0632 #>   [3,] 864.0292 862.8079 861.6829 860.6605 859.7456 858.9415 858.2498 857.6700 #>   [4,] 862.6805 861.4330 860.2862 859.2471 858.3212 857.5122 856.8217 856.2493 #>   [5,] 861.3086 860.0328 858.8625 857.8054 856.8675 856.0531 855.3639 854.7996 #>   [6,] 859.9126 858.6062 857.4104 856.3337 855.3829 854.5626 853.8749 853.3193 #>   [7,] 858.4914 857.1520 855.9285 854.8305 853.8656 853.0390 852.3529 851.8068 #>   [8,] 857.0440 855.6688 854.4152 853.2940 852.3137 851.4801 850.7957 850.2601 #>   [9,] 855.5692 854.1551 852.8688 851.7222 850.7251 849.8837 849.2013 848.6771 #>  [10,] 854.0657 852.6094 851.2873 850.1130 849.0973 848.2476 847.5673 847.0556 #>  [11,] 852.5325 851.0301 849.6689 848.4641 847.4280 846.5690 845.8910 845.3931 #>  [12,] 850.9682 849.4154 848.0112 846.7729 845.7143 844.8450 844.1696 843.6870 #>  [13,] 849.3715 847.7635 846.3121 845.0366 843.9530 843.0724 842.3999 841.9342 #>  [14,] 847.7409 846.0724 844.5688 843.2522 842.1409 841.2476 840.5783 840.1314 #>  [15,] 846.0751 844.3400 842.7787 841.4164 840.2741 839.3666 838.7009 838.2751 #>  [16,] 844.3726 842.5641 840.9388 839.5254 838.3484 837.4250 836.7633 836.3611 #>  [17,] 842.6320 840.7424 839.0457 837.5752 836.3591 835.4177 834.7605 834.3850 #>  [18,] 840.8520 838.8724 837.0959 835.5611 834.3008 833.3390 832.6869 832.3417 #>  [19,] 839.0312 836.9515 835.0857 833.4781 832.1676 831.1825 830.5363 830.2256 #>  [20,] 837.1683 834.9772 833.0107 831.3205 829.9526 828.9408 828.3014 828.0302 #>  [21,] 835.2623 832.9467 830.8665 829.0821 827.6482 826.6055 825.9739 825.7482 #>  [22,] 833.3125 830.8575 828.6482 826.7556 825.2453 824.1668 823.5442 823.3715 #>  [23,] 831.3185 828.7068 826.3505 824.3332 822.7339 821.6133 821.0014 820.8906 #>  [24,] 829.2805 826.4925 823.9680 821.8059 820.1019 818.9315 818.3323 818.2946 #>  [25,] 827.1995 824.2126 821.4948 819.1635 817.3356 816.1057 815.5216 815.5710 #>  [26,] 825.0773 821.8658 818.9251 816.3946 814.4185 813.1167 812.5510 812.7053 #>  [27,] 822.9174 819.4520 816.2530 813.4864 811.3313 809.9416 809.3984 809.6805 #>  [28,] 820.7251 816.9725 813.4733 810.4247 808.0509 806.5521 806.0369 806.4768 #>  [29,] 818.5079 814.4309 810.5818 807.1938 804.5491 802.9129 802.4332 803.0709 #>  [30,] 816.2766 811.8343 807.5764 803.7767 800.7921 798.9792 798.5454 799.4353 #>  [31,] 814.0456 809.1942 804.4590 800.1562 796.7383 794.6933 794.3202 795.5382 #>  [32,] 811.8343 806.5286 801.2374 796.3161 792.3361 789.9785 789.6880 791.3425 #>  [33,] 809.6676 803.8638 797.9294 792.2446 787.5224 784.7299 784.5559 786.8073 #>  [34,] 807.5764 801.2374 794.5683 787.9411 782.2201 778.7996 778.7972 781.8899 #>  [35,] 805.5984 798.6997 791.2098 783.4285 776.3390 771.9684 772.2331 776.5557 #>  [36,] 803.7767 796.3161 787.9411 778.7755 769.7869 763.8929 764.6054 770.8002 #>  [37,] 802.1587 794.1654 784.8888 774.1336 762.5123 753.9922 755.5346 764.7036 #>  [38,] 800.7921 792.3361 782.2201 769.7869 754.6458 741.1740 744.4926 758.5474 #>  [39,] 799.7209 790.9159 780.1291 766.1865 746.8878 723.0846 731.0627 753.0098 #>  [40,] 798.9792 789.9785 778.7996 763.8929 741.1740 694.8736 717.4372 749.2830 #>  [41,] 798.5868 789.5677 778.3516 763.3500 740.2501 688.0424 715.2865 748.5893 #>  [42,] 798.5454 789.6880 778.7972 764.6054 744.4926 717.4372 727.1580 751.0745 #>  [43,] 798.8388 790.3025 780.0351 767.2756 751.3314 736.3775 740.2837 755.6451 #>  [44,] 799.4353 791.3425 781.8899 770.8002 758.5474 749.2830 751.0745 761.0342 #>  [45,] 800.2926 792.7219 784.1658 774.6967 765.2470 758.9410 759.7788 766.4604 #>  [46,] 801.3631 794.3514 786.6885 778.6489 771.2280 766.6100 766.9458 771.5805 #>  [47,] 802.5993 796.1497 789.3229 782.4828 776.5220 772.9429 772.9845 776.2860 #>  [48,] 803.9567 798.0486 791.9746 786.1167 781.2183 778.3187 778.1737 780.5702 #>  [49,] 805.3968 799.9948 794.5822 789.5208 785.4089 782.9757 782.7053 784.4643 #>  [50,] 806.8871 801.9485 797.1087 792.6923 789.1736 787.0736 786.7149 788.0102 #>  [51,] 808.4016 803.8811 799.5336 795.6413 792.5784 790.7242 790.3011 791.2497 #>  [52,] 809.9199 805.7733 801.8474 798.3834 795.6769 794.0089 793.5374 794.2206 #>  [53,] 811.4267 807.6123 804.0474 800.9359 798.5125 796.9888 796.4800 796.9559 #>  [54,] 812.9104 809.3903 806.1349 803.3159 801.1206 799.7110 799.1728 799.4839 #>  [55,] 814.3630 811.1032 808.1139 805.5393 803.5302 802.2122 801.6506 801.8285 #>  [56,] 815.7788 812.7492 809.9894 807.6207 805.7654 804.5222 803.9415 804.0103 #>  [57,] 817.1540 814.3282 811.7671 809.5733 807.8462 806.6647 806.0683 806.0468 #>  [58,] 818.4865 815.8412 813.4531 811.4085 809.7896 808.6597 808.0502 807.9530 #>  [59,] 819.7751 817.2901 815.0530 813.1369 811.6099 810.5235 809.9029 809.7418 #>  [60,] 821.0195 818.6772 816.5725 814.7676 813.3193 812.2700 811.6400 811.4243 #>  [61,] 822.2199 820.0050 818.0168 816.3088 814.9285 813.9109 813.2729 813.0102 #>  [62,] 823.3771 821.2761 819.3910 817.7678 816.4464 815.4563 814.8114 814.5081 #>  [63,] 824.4920 822.4932 820.6997 819.1510 817.8812 816.9150 816.2640 815.9253 #>  [64,] 825.5658 823.6589 821.9469 820.4642 819.2397 818.2944 817.6382 817.2685 #>  [65,] 826.5999 824.7758 823.1368 821.7126 820.5281 819.6013 818.9404 818.5433 #>  [66,] 827.5956 825.8464 824.2729 822.9008 821.7519 820.8414 820.1764 819.7551 #>  [67,] 828.5544 826.8731 825.3584 824.0331 822.9159 822.0199 821.3512 820.9084 #>  [68,] 829.4777 827.8580 826.3966 825.1132 824.0244 823.1413 822.4694 822.0073 #>  [69,] 830.3668 828.8034 827.3901 826.1446 825.0812 824.2098 823.5350 823.0555 #>  [70,] 831.2233 829.7111 828.3416 827.1304 826.0900 825.2290 824.5515 824.0565 #>  [71,] 832.0484 830.5831 829.2535 828.0733 827.0537 826.2022 825.5223 825.0133 #>  [72,] 832.8434 831.4211 830.1279 828.9760 827.9753 827.1324 826.4504 825.9285 #>  [73,] 833.6096 832.2268 830.9670 829.8409 828.8573 828.0222 827.3382 826.8048 #>  [74,] 834.3481 833.0018 831.7725 830.6700 829.7022 828.8741 828.1884 827.6443 #>  [75,] 835.0602 833.7475 832.5463 831.4655 830.5120 829.6904 829.0031 828.4493 #>  [76,] 835.7469 834.4652 833.2900 832.2290 831.2887 830.4731 829.7843 829.2216 #>  [77,] 836.4093 835.1563 834.0050 832.9624 832.0342 831.2241 830.5339 829.9630 #>  [78,] 837.0483 835.8220 834.6928 833.6671 832.7501 831.9450 831.2535 830.6752 #>  [79,] 837.6649 836.4633 835.3546 834.3446 833.4379 832.6375 831.9449 831.3595 #>  [80,] 838.2599 837.0814 835.9918 834.9963 834.0992 833.3031 832.6093 832.0176 #>  [81,] 838.8343 837.6773 836.6053 835.6234 834.7351 833.9430 833.2482 832.6505 #>  [82,] 839.3888 838.2518 837.1964 836.2270 835.3469 834.5585 833.8628 833.2596 #>  [83,] 839.9242 838.8060 837.7659 836.8082 835.9358 835.1509 834.4543 833.8459 #>  [84,] 840.4412 839.3405 838.3149 837.3680 836.5028 835.7211 835.0237 834.4105 #>  [85,] 840.9406 839.8563 838.8441 837.9075 837.0489 836.2702 835.5721 834.9544 #>  [86,] 841.4228 840.3540 839.3544 838.4273 837.5750 836.7991 836.1003 835.4784 #>  [87,] 841.8887 840.8343 839.8466 838.9285 838.0820 837.3087 836.6092 835.9834 #>  [88,] 842.3388 841.2980 840.3214 839.4117 838.5707 837.7999 837.0998 836.4703 #>  [89,] 842.7735 841.7456 840.7795 839.8776 839.0418 838.2733 837.5726 836.9397 #>  [90,] 843.1936 842.1778 841.2215 840.3271 839.4961 838.7298 838.0285 837.3923 #>  [91,] 843.5994 842.5951 841.6481 840.7606 839.9342 839.1699 838.4682 837.8289 #>  [92,] 843.9915 842.9980 842.0598 841.1789 840.3568 839.5944 838.8922 838.2501 #>  [93,] 844.3704 843.3870 842.4571 841.5825 840.7644 840.0038 839.3012 838.6563 #>  [94,] 844.7364 843.7627 842.8406 841.9719 841.1576 840.3988 839.6957 839.0483 #>  [95,] 845.0900 844.1255 843.2108 842.3476 841.5370 840.7798 840.0763 839.4264 #>  [96,] 845.4316 844.4757 843.5681 842.7102 841.9030 841.1474 840.4435 839.7913 #>  [97,] 845.7615 844.8140 843.9130 843.0601 842.2562 841.5020 840.7977 840.1434 #>  [98,] 846.0803 845.1405 844.2459 843.3977 842.5969 841.8440 841.1395 840.4831 #>  [99,] 846.3881 845.4558 844.5672 843.7235 842.9256 842.1741 841.4691 840.8108 #> [100,] 846.6853 845.7601 844.8772 844.0378 843.2427 842.4924 841.7872 841.1270 #>           [,73]    [,74]    [,75]    [,76]    [,77]    [,78]    [,79]    [,80] #>   [1,] 859.9366 859.5386 859.2321 859.0112 858.8698 858.8006 858.7964 858.8498 #>   [2,] 858.5808 858.1990 857.9129 857.7162 857.6020 857.5625 857.5899 857.6761 #>   [3,] 857.1999 856.8355 856.5713 856.4005 856.3154 856.3077 856.3687 856.4896 #>   [4,] 855.7925 855.4469 855.2064 855.0634 855.0096 855.0357 855.1324 855.2903 #>   [5,] 854.3572 854.0320 853.8170 853.7040 853.6837 853.7461 853.8809 854.0780 #>   [6,] 852.8927 852.5895 852.4021 852.3215 852.3372 852.4383 852.6138 852.8525 #>   [7,] 851.3972 851.1179 850.9605 850.9148 850.9693 851.1120 851.3309 851.6139 #>   [8,] 849.8691 849.6159 849.4910 849.4830 849.5793 849.7667 850.0319 850.3621 #>   [9,] 848.3065 848.0817 847.9922 848.0251 848.1666 848.4020 848.7168 849.0970 #>  [10,] 846.7073 846.5137 846.4627 846.5401 846.7304 847.0174 847.3853 847.8189 #>  [11,] 845.0694 844.9099 844.9011 845.0269 845.2700 845.6126 846.0373 846.5279 #>  [12,] 843.3904 843.2684 843.3058 843.4843 843.7847 844.1873 844.6730 845.2242 #>  [13,] 841.6676 841.5871 841.6751 841.9113 842.2739 842.7413 843.2924 843.9081 #>  [14,] 839.8982 839.8635 840.0074 840.3067 840.7370 841.2743 841.8956 842.5803 #>  [15,] 838.0790 838.0952 838.3007 838.6692 839.1734 839.7864 840.4831 841.2413 #>  [16,] 836.2067 836.2795 836.5533 836.9980 837.5827 838.2776 839.0554 839.8918 #>  [17,] 834.2773 834.4136 834.7631 835.2917 835.9644 836.7482 837.6130 838.5329 #>  [18,] 832.2868 832.4941 832.9281 833.5494 834.3185 835.1986 836.1570 837.1658 #>  [19,] 830.2305 830.5180 831.0463 831.7702 832.6450 833.6296 834.6885 835.7919 #>  [20,] 828.1033 828.4815 829.1157 829.9534 830.9441 832.0422 833.2090 834.4130 #>  [21,] 825.8997 826.3810 827.1342 828.0986 829.2166 830.4378 831.7204 833.0311 #>  [22,] 823.6133 824.2124 825.1000 826.2055 827.4635 828.8184 830.2250 831.6488 #>  [23,] 821.2372 821.9716 823.0115 824.2745 825.6865 827.1862 828.7256 830.2687 #>  [24,] 818.7639 819.6545 820.8675 822.3065 823.8879 825.5444 827.2254 828.8944 #>  [25,] 816.1850 817.2569 818.6673 820.3035 822.0710 823.8969 825.7286 827.5296 #>  [26,] 813.4912 814.7749 816.4111 818.2681 820.2399 822.2485 824.2397 826.1785 #>  [27,] 810.6727 812.2052 814.1005 816.2048 818.4004 820.6048 822.7643 824.8462 #>  [28,] 807.7189 809.5455 811.7387 814.1196 816.5594 818.9729 821.3087 823.5381 #>  [29,] 804.6192 806.7952 809.3312 812.0210 814.7257 817.3610 819.8801 822.2604 #>  [30,] 801.3631 803.9567 806.8871 809.9199 812.9104 815.7788 818.4865 821.0195 #>  [31,] 797.9421 801.0368 804.4198 807.8312 811.1267 814.2373 817.1370 819.8226 #>  [32,] 794.3514 798.0486 801.9485 805.7733 809.3903 812.7492 815.8412 818.6772 #>  [33,] 790.5942 795.0155 799.4996 803.7694 807.7195 811.3282 814.6096 817.5912 #>  [34,] 786.6885 791.9746 797.1087 801.8474 806.1349 809.9894 813.4531 816.5725 #>  [35,] 782.6779 788.9817 794.8210 800.0399 804.6591 808.7483 812.3825 815.6288 #>  [36,] 778.6489 786.1167 792.6923 798.3834 803.3159 807.6207 811.4085 814.7676 #>  [37,] 774.7529 783.4857 790.7869 796.9164 802.1289 806.6219 810.5413 813.9958 #>  [38,] 771.2280 781.2183 789.1736 795.6769 801.1206 805.7654 809.7896 813.3193 #>  [39,] 768.3971 779.4544 787.9180 794.6991 800.3099 805.0627 809.1607 812.7429 #>  [40,] 766.6100 778.3187 787.0736 794.0089 799.7110 804.5222 808.6597 812.2700 #>  [41,] 766.1176 777.8892 786.6716 793.6212 799.3317 804.1483 808.2894 811.9023 #>  [42,] 766.9458 778.1737 786.7149 793.5374 799.1728 803.9415 808.0502 811.6400 #>  [43,] 768.8807 779.1067 787.1777 793.7452 799.2279 803.8980 807.9396 811.4817 #>  [44,] 771.5805 780.5702 788.0102 794.2206 799.4839 804.0103 807.9530 811.4243 #>  [45,] 774.7100 782.4252 789.1485 794.9309 799.9225 804.2675 808.0836 811.4632 #>  [46,] 778.0129 784.5386 790.5236 795.8384 800.5222 804.6563 808.3227 811.5928 #>  [47,] 781.3215 786.7988 792.0700 796.9044 801.2591 805.1616 808.6605 811.8063 #>  [48,] 784.5386 789.1210 793.7301 798.0920 802.1096 805.7679 809.0865 812.0964 #>  [49,] 787.6133 791.4450 795.4562 799.3677 803.0506 806.4595 809.5897 812.4553 #>  [50,] 790.5236 793.7301 797.2112 800.7025 804.0612 807.2211 810.1592 812.8752 #>  [51,] 793.2642 795.9508 798.9668 802.0725 805.1225 808.0387 810.7846 813.3481 #>  [52,] 795.8384 798.0920 800.7025 803.4581 806.2184 808.8994 811.4558 813.8666 #>  [53,] 798.2543 800.1460 802.4039 804.8440 807.3350 809.7919 812.1639 814.4233 #>  [54,] 800.5222 802.1096 804.0612 806.2184 808.4611 810.7063 812.9005 815.0115 #>  [55,] 802.6526 803.9829 805.6681 807.5723 809.5873 811.6340 813.6582 815.6252 #>  [56,] 804.6563 805.7679 807.2211 808.8994 810.7063 812.5677 814.4306 816.2587 #>  [57,] 806.5432 807.4679 808.7183 810.1950 811.8122 813.5016 815.2120 816.9069 #>  [58,] 808.3227 809.0865 810.1592 811.4558 812.9005 814.4306 815.9975 817.5654 #>  [59,] 810.0033 810.6280 811.5445 812.6801 813.9678 815.3507 816.7832 818.2303 #>  [60,] 811.5928 812.0964 812.8752 813.8666 815.0115 816.2587 817.5654 818.8982 #>  [61,] 813.0982 813.4960 814.1528 815.0148 816.0300 817.1520 818.3413 819.5661 #>  [62,] 814.5260 814.8307 815.3792 816.1250 817.0221 818.0286 819.1085 820.2315 #>  [63,] 815.8818 816.1044 816.5564 817.1974 817.9868 818.8872 819.8651 820.8923 #>  [64,] 817.1708 817.3206 817.6863 818.2327 818.9240 819.7264 820.6094 821.5467 #>  [65,] 818.3978 818.4828 818.7710 819.2318 819.8335 820.5457 821.3403 822.1931 #>  [66,] 819.5670 819.5940 819.8126 820.1958 820.7155 821.3444 822.0568 822.8302 #>  [67,] 820.6823 820.6573 820.8130 821.1256 821.5703 822.1222 822.7582 823.4572 #>  [68,] 821.7471 821.6754 821.7741 822.0225 822.3982 822.8791 823.4439 824.0731 #>  [69,] 822.7647 822.6508 822.6978 822.8875 823.2000 823.6151 824.1135 824.6772 #>  [70,] 823.7381 823.5858 823.5858 823.7218 823.9760 824.3303 824.7669 825.2692 #>  [71,] 824.6697 824.4827 824.4398 824.5266 824.7271 825.0249 825.4038 825.8486 #>  [72,] 825.5622 825.3434 825.2613 825.3029 825.4538 825.6992 826.0243 826.4150 #>  [73,] 826.4177 826.1700 826.0519 826.0519 826.1569 826.3537 826.6285 826.9684 #>  [74,] 827.2383 826.9641 826.8130 826.7745 826.8371 826.9886 827.2164 827.5087 #>  [75,] 828.0259 827.7273 827.5458 827.4719 827.4952 827.6044 827.7883 828.0357 #>  [76,] 828.7823 828.4613 828.2517 828.1450 828.1317 828.2016 828.3443 828.5495 #>  [77,] 829.5090 829.1674 828.9318 828.7947 828.7474 828.7805 828.8847 829.0502 #>  [78,] 830.2076 829.8469 829.5873 829.4219 829.3429 829.3418 829.4097 829.5379 #>  [79,] 830.8795 830.5011 830.2192 830.0276 829.9190 829.8857 829.9197 830.0126 #>  [80,] 831.5260 831.1312 830.8286 830.6124 830.4762 830.4129 830.4149 830.4746 #>  [81,] 832.1482 831.7381 831.4162 831.1773 831.0153 830.9237 830.8956 830.9241 #>  [82,] 832.7472 832.3230 831.9832 831.7229 831.5367 831.4186 831.3623 831.3611 #>  [83,] 833.3242 832.8868 832.5302 832.2500 832.0411 831.8981 831.8151 831.7860 #>  [84,] 833.8802 833.4304 833.0581 832.7592 832.5290 832.3626 832.2544 832.1989 #>  [85,] 834.4159 833.9546 833.5676 833.2512 833.0010 832.8125 832.6806 832.6000 #>  [86,] 834.9324 834.4603 834.0595 833.7266 833.4576 833.2483 833.0940 832.9897 #>  [87,] 835.4303 834.9481 834.5343 834.1859 833.8993 833.6704 833.4948 833.3680 #>  [88,] 835.9105 835.4187 834.9928 834.6299 834.3265 834.0791 833.8834 833.7353 #>  [89,] 836.3736 835.8729 835.4356 835.0589 834.7398 834.4748 834.2601 834.0918 #>  [90,] 836.8204 836.3113 835.8632 835.4735 835.1395 834.8579 834.6252 834.4377 #>  [91,] 837.2514 836.7344 836.2761 835.8743 835.5262 835.2289 834.9790 834.7733 #>  [92,] 837.6673 837.1428 836.6749 836.2615 835.9001 835.5879 835.3218 835.0987 #>  [93,] 838.0687 837.5371 837.0601 836.6358 836.2617 835.9354 835.6539 835.4143 #>  [94,] 838.4559 837.9177 837.4321 836.9974 836.6114 836.2717 835.9755 835.7201 #>  [95,] 838.8297 838.2851 837.7914 837.3469 836.9495 836.5970 836.2869 836.0166 #>  [96,] 839.1904 838.6399 838.1384 837.6846 837.2764 836.9118 836.5884 836.3037 #>  [97,] 839.5385 838.9823 838.4735 838.0108 837.5924 837.2163 836.8802 836.5819 #>  [98,] 839.8744 839.3128 838.7971 838.3260 837.8978 837.5107 837.1626 836.8512 #>  [99,] 840.1986 839.6319 839.1096 838.6305 838.1930 837.7954 837.4357 837.1119 #> [100,] 840.5114 839.9398 839.4112 838.9245 838.4782 838.0706 837.6999 837.3642 #>           [,81]    [,82]    [,83]    [,84]    [,85]    [,86]    [,87]    [,88] #>   [1,] 858.9534 859.1000 859.2830 859.4959 859.7332 859.9894 860.2598 860.5403 #>   [2,] 857.8132 857.9936 858.2102 858.4563 858.7260 859.0136 859.3144 859.6240 #>   [3,] 856.6622 856.8782 857.1301 857.4109 857.7143 858.0346 858.3667 858.7064 #>   [4,] 855.5003 855.7538 856.0428 856.3598 856.6984 857.0526 857.4173 857.7879 #>   [5,] 854.3276 854.6206 854.9484 855.3034 855.6786 856.0680 856.4663 856.8689 #>   [6,] 853.1441 853.4787 853.8473 854.2419 854.6553 855.0813 855.5143 855.9498 #>   [7,] 851.9499 852.3283 852.7398 853.1758 853.6289 854.0927 854.5617 855.0311 #>   [8,] 850.7450 851.1697 851.6261 852.1054 852.5999 853.1029 853.6090 854.1133 #>   [9,] 849.5298 850.0032 850.5067 851.0312 851.5687 852.1124 852.6567 853.1969 #>  [10,] 848.3044 848.8292 849.3822 849.9538 850.5360 851.1218 851.7055 852.2825 #>  [11,] 847.0692 847.6482 848.2530 848.8739 849.5024 850.1316 850.7559 851.3707 #>  [12,] 845.8247 846.4607 847.1199 847.7920 848.4687 849.1428 849.8088 850.4623 #>  [13,] 844.5715 845.2674 845.9835 846.7091 847.4356 848.1560 848.8649 849.5578 #>  [14,] 843.3100 844.0693 844.8448 845.6260 846.4041 847.1722 847.9249 848.6582 #>  [15,] 842.0413 842.8670 843.7048 844.5437 845.3751 846.1922 846.9899 847.7643 #>  [16,] 840.7663 841.6619 842.5645 843.4633 844.3497 845.2171 846.0607 846.8769 #>  [17,] 839.4861 840.4550 841.4253 842.3861 843.3291 844.2480 845.1383 845.9969 #>  [18,] 838.2021 839.2478 840.2885 841.3134 842.3146 843.2861 844.2239 845.1255 #>  [19,] 836.9159 838.0420 839.1557 840.2468 841.3075 842.3326 843.3186 844.2635 #>  [20,] 835.6293 836.8393 838.0287 839.1877 840.3093 841.3889 842.4236 843.4121 #>  [21,] 834.3445 835.6418 836.9094 838.1381 839.3217 840.4565 841.5403 842.5724 #>  [22,] 833.0638 834.4518 835.7999 837.0999 838.3464 839.5368 840.6698 841.7456 #>  [23,] 831.7901 833.2719 834.7026 836.0750 837.3852 838.6315 839.8138 840.9330 #>  [24,] 830.5264 832.1049 833.6199 835.0657 836.4400 837.7422 838.9735 840.1357 #>  [25,] 829.2762 830.9539 832.5545 834.0744 835.5128 836.8707 838.1504 839.3550 #>  [26,] 828.0434 829.8222 831.5095 833.1036 834.6057 836.0187 837.3462 838.5923 #>  [27,] 826.8322 828.7136 830.4877 832.1558 833.7210 835.1881 836.5623 837.8489 #>  [28,] 825.6474 827.6319 829.4926 831.2336 832.8609 834.3808 835.8003 837.1260 #>  [29,] 824.4939 826.5812 828.5274 830.3400 832.0275 833.5986 835.0617 836.4249 #>  [30,] 823.3771 825.5658 827.5956 829.4777 831.2233 832.8434 834.3481 835.7469 #>  [31,] 822.3025 824.5902 826.7008 828.6494 830.4504 832.1169 833.6610 835.0933 #>  [32,] 821.2761 823.6589 825.8464 827.8580 829.7111 831.4211 833.0018 834.4652 #>  [33,] 820.3036 822.7763 825.0360 827.1062 829.0075 830.7576 832.3719 833.8638 #>  [34,] 819.3910 821.9469 824.2729 826.3966 828.3416 830.1279 831.7725 833.2900 #>  [35,] 818.5440 821.1749 823.5602 825.7315 827.7154 829.5336 831.2049 832.7448 #>  [36,] 817.7678 820.4642 822.9008 825.1132 827.1304 828.9760 830.6700 832.2290 #>  [37,] 817.0672 819.8181 822.2973 824.5437 826.5882 828.4563 830.1689 831.7435 #>  [38,] 816.4464 819.2397 821.7519 824.0244 826.0900 827.9753 829.7022 831.2887 #>  [39,] 815.9087 818.7313 821.2662 823.5566 825.6367 827.5338 829.2704 830.8651 #>  [40,] 815.4563 818.2944 820.8414 823.1413 825.2290 827.1324 828.8741 830.4731 #>  [41,] 815.0905 817.9300 820.4781 822.7789 824.8673 826.7712 828.5135 830.1128 #>  [42,] 814.8114 817.6382 820.1764 822.4694 824.5515 826.4504 828.1884 829.7843 #>  [43,] 814.6180 817.4182 819.9358 822.2125 824.2815 826.1696 827.8988 829.4873 #>  [44,] 814.5081 817.2685 819.7551 822.0073 824.0565 825.9285 827.6443 829.2216 #>  [45,] 814.4788 817.1870 819.6329 821.8527 823.8758 825.7263 827.4244 828.9868 #>  [46,] 814.5260 817.1708 819.5670 821.7471 823.7381 825.5622 827.2383 828.7823 #>  [47,] 814.6450 817.2166 819.5550 821.6887 823.6419 825.4350 827.0852 828.6074 #>  [48,] 814.8307 817.3206 819.5940 821.6754 823.5858 825.3434 826.9641 828.4613 #>  [49,] 815.0774 817.4786 819.6810 821.7047 823.5677 825.2861 826.8737 828.3431 #>  [50,] 815.3792 817.6863 819.8126 821.7741 823.5858 825.2613 826.8130 828.2517 #>  [51,] 815.7304 817.9392 819.9854 821.8810 823.6379 825.2675 826.7804 828.1860 #>  [52,] 816.1250 818.2327 820.1958 822.0225 823.7218 825.3029 826.7745 828.1450 #>  [53,] 816.5573 818.5624 820.4403 822.1959 823.8353 825.3656 826.7940 828.1273 #>  [54,] 817.0221 818.9240 820.7155 822.3982 823.9760 825.4538 826.8371 828.1317 #>  [55,] 817.5141 819.3133 821.0180 822.6269 824.1418 825.5656 826.9025 828.1569 #>  [56,] 818.0286 819.7264 821.3444 822.8791 824.3303 825.6992 826.9886 828.2016 #>  [57,] 818.5614 820.1596 821.6916 823.1523 824.5393 825.8527 827.0937 828.2645 #>  [58,] 819.1085 820.6094 822.0568 823.4439 824.7669 826.0243 827.2164 828.3443 #>  [59,] 819.6662 821.0727 822.4372 823.7516 825.0108 826.2123 827.3552 828.4397 #>  [60,] 820.2315 821.5467 822.8302 824.0731 825.2692 826.4150 827.5087 828.5495 #>  [61,] 820.8015 822.0286 823.2335 824.4063 825.5402 826.6308 827.6753 828.6725 #>  [62,] 821.3736 822.5162 823.6449 824.7494 825.8221 826.8581 827.8538 828.8074 #>  [63,] 821.9458 823.0073 824.0624 825.1004 826.1133 827.0955 828.0429 828.9531 #>  [64,] 822.5162 823.5001 824.4843 825.4577 826.4122 827.3416 828.2413 829.1085 #>  [65,] 823.0830 823.9929 824.9089 825.8199 826.7175 827.5951 828.4479 829.2726 #>  [66,] 823.6449 824.4843 825.3348 826.1855 827.0277 827.8548 828.6616 829.4443 #>  [67,] 824.2007 824.9729 825.7607 826.5532 827.3418 828.1197 828.8813 829.6228 #>  [68,] 824.7494 825.4577 826.1855 826.9220 827.6587 828.3886 829.1061 829.8071 #>  [69,] 825.2901 825.9378 826.6081 827.2908 827.9773 828.6606 829.3351 829.9964 #>  [70,] 825.8221 826.4122 827.0277 827.6587 828.2967 828.9348 829.5674 830.1898 #>  [71,] 826.3450 826.8803 827.4435 828.0249 828.6161 829.2105 829.8022 830.3867 #>  [72,] 826.8581 827.3416 827.8548 828.3886 828.9348 829.4868 830.0389 830.5864 #>  [73,] 827.3611 827.7954 828.2610 828.7492 829.2521 829.7632 830.2768 830.7882 #>  [74,] 827.8538 828.2413 828.6616 829.1061 829.5674 830.0389 830.5152 830.9916 #>  [75,] 828.3360 828.6791 829.0562 829.4589 829.8801 830.3135 830.7536 831.1959 #>  [76,] 828.8074 829.1085 829.4443 829.8071 830.1898 830.5864 830.9916 831.4007 #>  [77,] 829.2680 829.5292 829.8258 830.1503 830.4961 830.8572 831.2285 831.6055 #>  [78,] 829.7178 829.9411 830.2003 830.4882 830.7985 831.1255 831.4641 831.8098 #>  [79,] 830.1567 830.3441 830.5676 830.8206 831.0968 831.3909 831.6978 832.0134 #>  [80,] 830.5848 830.7380 830.9276 831.1471 831.3907 831.6531 831.9295 832.2157 #>  [81,] 831.0021 831.1229 831.2801 831.4676 831.6798 831.9117 832.1587 832.4166 #>  [82,] 831.4087 831.4987 831.6250 831.7819 831.9641 832.1667 832.3852 832.6156 #>  [83,] 831.8047 831.8654 831.9623 832.0900 832.2433 832.4177 832.6087 832.8126 #>  [84,] 832.1903 832.2231 832.2919 832.3916 832.5173 832.6645 832.8290 833.0072 #>  [85,] 832.5655 832.5718 832.6138 832.6867 832.7859 832.9069 833.0459 833.1993 #>  [86,] 832.9305 832.9116 832.9280 832.9753 833.0490 833.1449 833.2593 833.3886 #>  [87,] 833.2855 833.2425 833.2345 833.2573 833.3065 833.3783 833.4689 833.5751 #>  [88,] 833.6305 833.5646 833.5334 833.5327 833.5584 833.6069 833.6747 833.7584 #>  [89,] 833.9659 833.8781 833.8246 833.8014 833.8047 833.8308 833.8765 833.9385 #>  [90,] 834.2916 834.1831 834.1083 834.0635 834.0452 834.0498 834.0742 834.1152 #>  [91,] 834.6080 834.4796 834.3845 834.3191 834.2800 834.2639 834.2677 834.2885 #>  [92,] 834.9152 834.7678 834.6532 834.5680 834.5090 834.4730 834.4570 834.4583 #>  [93,] 835.2133 835.0478 834.9146 834.8104 834.7323 834.6771 834.6420 834.6244 #>  [94,] 835.5026 835.3197 835.1687 835.0463 834.9498 834.8761 834.8227 834.7867 #>  [95,] 835.7831 835.5838 835.4156 835.2758 835.1616 835.0702 834.9989 834.9454 #>  [96,] 836.0551 835.8400 835.6555 835.4989 835.3677 835.2591 835.1708 835.1001 #>  [97,] 836.3188 836.0885 835.8883 835.7157 835.5681 835.4431 835.3382 835.2511 #>  [98,] 836.5743 836.3295 836.1143 835.9262 835.7629 835.6220 835.5011 835.3981 #>  [99,] 836.8218 836.5631 836.3335 836.1306 835.9521 835.7959 835.6596 835.5412 #> [100,] 837.0615 836.7894 836.5459 836.3288 836.1358 835.9648 835.8136 835.6803 #>           [,89]    [,90]    [,91]    [,92]    [,93]    [,94]    [,95]    [,96] #>   [1,] 860.8271 861.1170 861.4073 861.6953 861.9793 862.2572 862.5278 862.7897 #>   [2,] 859.9386 860.2550 860.5704 860.8823 861.1888 861.4881 861.7787 862.0596 #>   [3,] 859.0496 859.3933 859.7344 860.0707 860.4001 860.7210 861.0321 861.3322 #>   [4,] 858.1606 858.5321 858.8996 859.2608 859.6136 859.9565 860.2882 860.6077 #>   [5,] 857.2719 857.6720 858.0664 858.4529 858.8295 859.1948 859.5474 859.8865 #>   [6,] 856.3839 856.8133 857.2353 857.6475 858.0483 858.4362 858.8100 859.1689 #>   [7,] 855.4972 855.9565 856.4065 856.8451 857.2704 857.6812 858.0764 858.4552 #>   [8,] 854.6121 855.1020 855.5807 856.0459 856.4961 856.9300 857.3468 857.7457 #>   [9,] 853.7292 854.2504 854.7582 855.2505 855.7258 856.1832 856.6217 857.0408 #>  [10,] 852.8491 853.4022 853.9395 854.4593 854.9601 855.4411 855.9014 856.3408 #>  [11,] 851.9723 852.5579 853.1253 853.6729 854.1994 854.7041 855.1864 855.6462 #>  [12,] 851.0996 851.7182 852.3161 852.8917 853.4441 853.9727 854.4771 854.9572 #>  [13,] 850.2316 850.8837 851.5124 852.1163 852.6948 853.2474 853.7738 854.2743 #>  [14,] 849.3690 850.0551 850.7149 851.3474 851.9520 852.5286 853.0771 853.5978 #>  [15,] 848.5127 849.2331 849.9242 850.5854 851.2162 851.8168 852.3873 852.9282 #>  [16,] 847.6633 848.4183 849.1410 849.8309 850.4880 851.1125 851.7049 852.2659 #>  [17,] 846.8218 847.6117 848.3661 849.0847 849.7680 850.4163 851.0304 851.6112 #>  [18,] 845.9891 846.8140 847.6000 848.3474 849.0567 849.7286 850.3643 850.9647 #>  [19,] 845.1661 846.0261 846.8437 847.6196 848.3547 849.0500 849.7069 850.3267 #>  [20,] 844.3537 845.2487 846.0978 846.9020 847.6626 848.3811 849.0589 849.6976 #>  [21,] 843.5530 844.4828 845.3631 846.1953 846.9811 847.7223 848.4206 849.0779 #>  [22,] 842.7650 843.7293 844.6404 845.5002 846.3107 847.0742 847.7926 848.4681 #>  [23,] 841.9907 842.9892 843.9305 844.8174 845.6521 846.4373 847.1753 847.8684 #>  [24,] 841.2313 842.2632 843.2343 844.1476 845.0060 845.8122 846.5692 847.2795 #>  [25,] 840.4879 841.5525 842.5526 843.4915 844.3728 845.1995 845.9748 846.7016 #>  [26,] 839.7615 840.8580 841.8861 842.8499 843.7532 844.5996 845.3926 846.1351 #>  [27,] 839.0532 840.1805 841.2357 842.2234 843.1479 844.0131 844.8229 845.5805 #>  [28,] 838.3642 839.5211 840.6022 841.6127 842.5573 843.4405 844.2662 845.0381 #>  [29,] 837.6956 838.8806 839.9863 841.0184 841.9821 842.8822 843.7230 844.5084 #>  [30,] 837.0483 838.2599 839.3888 840.4412 841.4228 842.3388 843.1936 843.9915 #>  [31,] 836.4234 837.6599 838.8104 839.8817 840.8800 841.8106 842.6784 843.4880 #>  [32,] 835.8220 837.0814 838.2518 839.3405 840.3540 841.2980 842.1778 842.9980 #>  [33,] 835.2448 836.5251 837.7136 838.8181 839.8453 840.8015 841.6921 842.5218 #>  [34,] 834.6928 835.9918 837.1964 838.3149 839.3544 840.3214 841.2215 842.0598 #>  [35,] 834.1666 835.4820 836.7007 837.8314 838.8817 839.8581 840.7665 841.6121 #>  [36,] 833.6671 834.9963 836.2270 837.3680 838.4273 839.4117 840.3271 841.1789 #>  [37,] 833.1948 834.5352 835.7756 836.9251 837.9917 838.9825 839.9036 840.7604 #>  [38,] 832.7501 834.0992 835.3469 836.5028 837.5750 838.5707 839.4961 840.3568 #>  [39,] 832.3334 833.6884 834.9412 836.1014 837.1774 838.1765 839.1048 839.9681 #>  [40,] 831.9450 833.3031 834.5585 835.7211 836.7991 837.7999 838.7298 839.5944 #>  [41,] 831.5851 832.9434 834.1991 835.3619 836.4400 837.4410 838.3710 839.2358 #>  [42,] 831.2535 832.6093 833.8628 835.0237 836.1003 837.0998 838.0285 838.8922 #>  [43,] 830.9503 832.3008 833.5497 834.7067 835.7798 836.7762 837.7023 838.5637 #>  [44,] 830.6752 832.0176 833.2596 834.4105 835.4784 836.4703 837.3923 838.2501 #>  [45,] 830.4278 831.7594 832.9922 834.1351 835.1960 836.1817 837.0984 837.9513 #>  [46,] 830.2076 831.5260 832.7472 833.8802 834.9324 835.9105 836.8204 837.6673 #>  [47,] 830.0142 831.3167 832.5243 833.6454 834.6872 835.6562 836.5581 837.3979 #>  [48,] 829.8469 831.1312 832.3230 833.4304 834.4603 835.4187 836.3113 837.1428 #>  [49,] 829.7049 830.9687 832.1428 833.2348 834.2512 835.1977 836.0798 836.9019 #>  [50,] 829.5873 830.8286 831.9832 833.0581 834.0595 834.9928 835.8632 836.6749 #>  [51,] 829.4933 830.7101 831.8434 832.8997 833.8847 834.8037 835.6612 836.4616 #>  [52,] 829.4219 830.6124 831.7229 832.7592 833.7266 834.6299 835.4735 836.2615 #>  [53,] 829.3721 830.5348 831.6209 832.6358 833.5844 834.4710 835.2998 836.0745 #>  [54,] 829.3429 830.4762 831.5367 832.5290 833.4576 834.3265 835.1395 835.9001 #>  [55,] 829.3332 830.4359 831.4695 832.4382 833.3458 834.1961 834.9924 835.7380 #>  [56,] 829.3418 830.4129 831.4186 832.3626 833.2483 834.0791 834.8579 835.5879 #>  [57,] 829.3676 830.4062 831.3831 832.3016 833.1646 833.9750 834.7357 835.4493 #>  [58,] 829.4097 830.4149 831.3623 832.2544 833.0940 833.8834 834.6252 835.3218 #>  [59,] 829.4668 830.4380 831.3552 832.2204 833.0359 833.8037 834.5261 835.2051 #>  [60,] 829.5379 830.4746 831.3611 832.1989 832.9897 833.7353 834.4377 835.0987 #>  [61,] 829.6219 830.5239 831.3792 832.1891 832.9548 833.6778 834.3597 835.0022 #>  [62,] 829.7178 830.5848 831.4087 832.1903 832.9305 833.6305 834.2916 834.9152 #>  [63,] 829.8245 830.6564 831.4488 832.2019 832.9163 833.5930 834.2329 834.8372 #>  [64,] 829.9411 830.7380 831.4987 832.2231 832.9116 833.5646 834.1831 834.7678 #>  [65,] 830.0667 830.8287 831.5577 832.2533 832.9157 833.5450 834.1417 834.7066 #>  [66,] 830.2003 830.9276 831.6250 832.2919 832.9280 833.5334 834.1083 834.6532 #>  [67,] 830.3411 831.0340 831.7000 832.3382 832.9481 833.5295 834.0824 834.6071 #>  [68,] 830.4882 831.1471 831.7819 832.3916 832.9753 833.5327 834.0635 834.5680 #>  [69,] 830.6409 831.2662 831.8702 832.4515 833.0091 833.5425 834.0513 834.5354 #>  [70,] 830.7985 831.3907 831.9641 832.5173 833.0490 833.5584 834.0452 834.5090 #>  [71,] 830.9603 831.5198 832.0631 832.5884 833.0944 833.5801 834.0448 834.4883 #>  [72,] 831.1255 831.6531 832.1667 832.6645 833.1449 833.6069 834.0498 834.4730 #>  [73,] 831.2936 831.7898 832.2742 832.7448 833.2000 833.6386 834.0597 834.4627 #>  [74,] 831.4641 831.9295 832.3852 832.8290 833.2593 833.6747 834.0742 834.4570 #>  [75,] 831.6363 832.0716 832.4991 832.9166 833.3223 833.7147 834.0928 834.4557 #>  [76,] 831.8098 832.2157 832.6156 833.0072 833.3886 833.7584 834.1152 834.4583 #>  [77,] 831.9842 832.3613 832.7342 833.1003 833.4579 833.8053 834.1411 834.4645 #>  [78,] 832.1589 832.5080 832.8544 833.1956 833.5297 833.8550 834.1702 834.4741 #>  [79,] 832.3337 832.6555 832.9759 833.2927 833.6037 833.9073 834.2020 834.4867 #>  [80,] 832.5080 832.8032 833.0984 833.3912 833.6796 833.9618 834.2364 834.5021 #>  [81,] 832.6817 832.9510 833.2215 833.4909 833.7570 834.0182 834.2729 834.5199 #>  [82,] 832.8544 833.0984 833.3449 833.5913 833.8357 834.0763 834.3115 834.5399 #>  [83,] 833.0258 833.2453 833.4682 833.6923 833.9154 834.1357 834.3516 834.5619 #>  [84,] 833.1956 833.3912 833.5913 833.7935 833.9958 834.1962 834.3933 834.5856 #>  [85,] 833.3637 833.5361 833.7139 833.8948 834.0766 834.2575 834.4360 834.6107 #>  [86,] 833.5297 833.6796 833.8357 833.9958 834.1576 834.3195 834.4798 834.6371 #>  [87,] 833.6935 833.8216 833.9566 834.0963 834.2387 834.3819 834.5243 834.6646 #>  [88,] 833.8550 833.9618 834.0763 834.1962 834.3195 834.4444 834.5694 834.6929 #>  [89,] 834.0139 834.1001 834.1946 834.2952 834.3999 834.5070 834.6147 834.7219 #>  [90,] 834.1702 834.2364 834.3115 834.3933 834.4798 834.5694 834.6603 834.7513 #>  [91,] 834.3236 834.3704 834.4266 834.4901 834.5589 834.6314 834.7059 834.7810 #>  [92,] 834.4741 834.5021 834.5399 834.5856 834.6371 834.6929 834.7513 834.8109 #>  [93,] 834.6216 834.6313 834.6513 834.6796 834.7143 834.7538 834.7964 834.8408 #>  [94,] 834.7660 834.7580 834.7607 834.7721 834.7903 834.8138 834.8410 834.8706 #>  [95,] 834.9071 834.8820 834.8678 834.8628 834.8650 834.8730 834.8851 834.9001 #>  [96,] 835.0450 835.0032 834.9727 834.9517 834.9383 834.9311 834.9285 834.9292 #>  [97,] 835.1796 835.1216 835.0752 835.0386 835.0101 834.9880 834.9710 834.9577 #>  [98,] 835.3107 835.2371 835.1753 835.1236 835.0802 835.0437 835.0126 834.9857 #>  [99,] 835.4385 835.3497 835.2729 835.2064 835.1486 835.0980 835.0532 835.0129 #> [100,] 835.5628 835.4593 835.3679 835.2871 835.2153 835.1509 835.0926 835.0392 #>           [,97]    [,98]    [,99]   [,100] #>   [1,] 863.0421 863.2839 863.5147 863.7339 #>   [2,] 862.3298 862.5885 862.8351 863.0691 #>   [3,] 861.6204 861.8960 862.1586 862.4076 #>   [4,] 860.9141 861.2069 861.4854 861.7495 #>   [5,] 860.2113 860.5212 860.8159 861.0951 #>   [6,] 859.5122 859.8394 860.1503 860.4446 #>   [7,] 858.8171 859.1617 859.4888 859.7983 #>   [8,] 858.1263 858.4884 858.8317 859.1564 #>   [9,] 857.4402 857.8197 858.1793 858.5191 #>  [10,] 856.7590 857.1560 857.5319 857.8867 #>  [11,] 856.0832 856.4976 856.8896 857.2595 #>  [12,] 855.4130 855.8448 856.2530 856.6378 #>  [13,] 854.7489 855.1980 855.6221 856.0217 #>  [14,] 854.0911 854.5574 854.9974 855.4117 #>  [15,] 853.4400 853.9234 854.3791 854.8079 #>  [16,] 852.7960 853.2963 853.7675 854.2106 #>  [17,] 852.1595 852.6765 853.1630 853.6201 #>  [18,] 851.5309 852.0642 852.5658 853.0367 #>  [19,] 850.9105 851.4600 851.9762 852.4607 #>  [20,] 850.2988 850.8640 851.3946 851.8923 #>  [21,] 849.6960 850.2766 850.8213 851.3318 #>  [22,] 849.1026 849.6982 850.2565 850.7795 #>  [23,] 848.5190 849.1290 849.7006 850.2356 #>  [24,] 847.9455 848.5695 849.1538 849.7004 #>  [25,] 847.3824 848.0199 848.6165 849.1742 #>  [26,] 846.8302 847.4806 848.0888 848.6571 #>  [27,] 846.2892 846.9518 847.5711 848.1495 #>  [28,] 845.7597 846.4339 847.0636 847.6515 #>  [29,] 845.2420 845.9270 846.5666 847.1633 #>  [30,] 844.7364 845.4316 846.0803 846.6853 #>  [31,] 844.2432 844.9477 845.6048 846.2175 #>  [32,] 843.7627 844.4757 845.1405 845.7601 #>  [33,] 843.2951 844.0158 844.6875 845.3133 #>  [34,] 842.8406 843.5681 844.2459 844.8772 #>  [35,] 842.3995 843.1329 843.8160 844.4520 #>  [36,] 841.9719 842.7102 843.3977 844.0378 #>  [37,] 841.5579 842.3002 842.9913 843.6347 #>  [38,] 841.1576 841.9030 842.5969 843.2427 #>  [39,] 840.7713 841.5187 842.2144 842.8619 #>  [40,] 840.3988 841.1474 841.8440 842.4924 #>  [41,] 840.0403 840.7889 841.4857 842.1342 #>  [42,] 839.6957 840.4435 841.1395 841.7872 #>  [43,] 839.3651 840.1110 840.8052 841.4515 #>  [44,] 839.0483 839.7913 840.4831 841.1270 #>  [45,] 838.7453 839.4845 840.1728 840.8136 #>  [46,] 838.4559 839.1904 839.8744 840.5114 #>  [47,] 838.1801 838.9089 839.5878 840.2201 #>  [48,] 837.9177 838.6399 839.3128 839.9398 #>  [49,] 837.6684 838.3831 839.0493 839.6702 #>  [50,] 837.4321 838.1384 838.7971 839.4112 #>  [51,] 837.2086 837.9057 838.5561 839.1627 #>  [52,] 836.9974 837.6846 838.3260 838.9245 #>  [53,] 836.7985 837.4749 838.1067 838.6964 #>  [54,] 836.6114 837.2764 837.8978 838.4782 #>  [55,] 836.4359 837.0888 837.6993 838.2696 #>  [56,] 836.2717 836.9118 837.5107 838.0706 #>  [57,] 836.1183 836.7451 837.3319 837.8808 #>  [58,] 835.9755 836.5884 837.1626 837.6999 #>  [59,] 835.8429 836.4414 837.0024 837.5278 #>  [60,] 835.7201 836.3037 836.8512 837.3642 #>  [61,] 835.6068 836.1751 836.7086 837.2089 #>  [62,] 835.5026 836.0551 836.5743 837.0615 #>  [63,] 835.4070 835.9435 836.4481 836.9217 #>  [64,] 835.3197 835.8400 836.3295 836.7894 #>  [65,] 835.2404 835.7440 836.2183 836.6642 #>  [66,] 835.1687 835.6555 836.1143 836.5459 #>  [67,] 835.1041 835.5739 836.0170 836.4342 #>  [68,] 835.0463 835.4989 835.9262 836.3288 #>  [69,] 834.9950 835.4303 835.8416 836.2294 #>  [70,] 834.9498 835.3677 835.7629 836.1358 #>  [71,] 834.9103 835.3107 835.6898 836.0477 #>  [72,] 834.8761 835.2591 835.6220 835.9648 #>  [73,] 834.8470 835.2126 835.5592 835.8869 #>  [74,] 834.8227 835.1708 835.5011 835.8136 #>  [75,] 834.8027 835.1334 835.4475 835.7449 #>  [76,] 834.7867 835.1001 835.3981 835.6803 #>  [77,] 834.7746 835.0708 835.3526 835.6197 #>  [78,] 834.7660 835.0450 835.3107 835.5628 #>  [79,] 834.7605 835.0226 835.2723 835.5094 #>  [80,] 834.7580 835.0032 835.2371 835.4593 #>  [81,] 834.7581 834.9867 835.2049 835.4122 #>  [82,] 834.7607 834.9727 835.1753 835.3679 #>  [83,] 834.7654 834.9611 835.1483 835.3263 #>  [84,] 834.7721 834.9517 835.1236 835.2871 #>  [85,] 834.7804 834.9441 835.1009 835.2502 #>  [86,] 834.7903 834.9383 835.0802 835.2153 #>  [87,] 834.8015 834.9340 835.0612 835.1822 #>  [88,] 834.8138 834.9311 835.0437 835.1509 #>  [89,] 834.8271 834.9293 835.0275 835.1211 #>  [90,] 834.8410 834.9285 835.0126 835.0926 #>  [91,] 834.8556 834.9285 834.9987 835.0654 #>  [92,] 834.8706 834.9292 834.9857 835.0392 #>  [93,] 834.8859 834.9304 834.9734 835.0140 #>  [94,] 834.9013 834.9320 834.9617 834.9895 #>  [95,] 834.9167 834.9338 834.9505 834.9657 #>  [96,] 834.9320 834.9358 834.9396 834.9425 #>  [97,] 834.9470 834.9377 834.9289 834.9197 #>  [98,] 834.9617 834.9396 834.9184 834.8972 #>  [99,] 834.9759 834.9412 834.9078 834.8748 #> [100,] 834.9895 834.9425 834.8972 834.8526  phi <- potential(m, x = xg, y = yg, as.grid = TRUE) phic <- potential(mc, x = xg, y = yg, as.grid = TRUE) potential_to_head(m, phi) #>            [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8] #>   [1,] 9.616683 9.603693 9.590617 9.577451 9.564195 9.550846 9.537402 9.523861 #>   [2,] 9.612188 9.599171 9.586066 9.572871 9.559584 9.546204 9.532727 9.519152 #>   [3,] 9.607709 9.594665 9.581532 9.568308 9.554991 9.541579 9.528070 9.514461 #>   [4,] 9.603244 9.590174 9.577013 9.563760 9.550414 9.536971 9.523430 9.509788 #>   [5,] 9.598795 9.585698 9.572511 9.559230 9.545854 9.532381 9.518809 9.505134 #>   [6,] 9.594362 9.581239 9.568025 9.554717 9.541312 9.527809 9.514206 9.500499 #>   [7,] 9.589945 9.576797 9.563556 9.550220 9.536788 9.523256 9.509622 9.495883 #>   [8,] 9.585543 9.572370 9.559104 9.545741 9.532281 9.518720 9.505056 9.491287 #>   [9,] 9.581158 9.567961 9.554669 9.541280 9.527793 9.514204 9.500510 9.486710 #>  [10,] 9.576790 9.563568 9.550252 9.536837 9.523323 9.509706 9.495984 9.482154 #>  [11,] 9.572438 9.559193 9.545852 9.532412 9.518872 9.505228 9.491477 9.477618 #>  [12,] 9.568104 9.554835 9.541470 9.528006 9.514440 9.500769 9.486991 9.473102 #>  [13,] 9.563786 9.550495 9.537107 9.523618 9.510027 9.496330 9.482524 9.468608 #>  [14,] 9.559485 9.546173 9.532761 9.519249 9.505633 9.491911 9.478079 9.464135 #>  [15,] 9.555203 9.541868 9.528435 9.514899 9.501259 9.487512 9.473654 9.459683 #>  [16,] 9.550937 9.537582 9.524127 9.510568 9.496905 9.483133 9.469251 9.455254 #>  [17,] 9.546690 9.533314 9.519837 9.506257 9.492571 9.478776 9.464869 9.450846 #>  [18,] 9.542460 9.529065 9.515567 9.501966 9.488258 9.474439 9.460508 9.446461 #>  [19,] 9.538249 9.524834 9.511317 9.497695 9.483965 9.470124 9.456169 9.442098 #>  [20,] 9.534056 9.520622 9.507086 9.493443 9.479692 9.465830 9.451853 9.437758 #>  [21,] 9.529882 9.516430 9.502874 9.489212 9.475441 9.461557 9.447559 9.433441 #>  [22,] 9.525726 9.512256 9.498682 9.485001 9.471211 9.457307 9.443287 9.429147 #>  [23,] 9.521589 9.508102 9.494511 9.480811 9.467002 9.453078 9.439038 9.424877 #>  [24,] 9.517471 9.503968 9.490359 9.476642 9.462814 9.448872 9.434812 9.420630 #>  [25,] 9.513373 9.499853 9.486228 9.472494 9.458648 9.444688 9.430609 9.416408 #>  [26,] 9.509293 9.495758 9.482117 9.468367 9.454504 9.440526 9.426429 9.412209 #>  [27,] 9.505233 9.491683 9.478027 9.464261 9.450382 9.436387 9.422273 9.408035 #>  [28,] 9.501192 9.487628 9.473957 9.460176 9.446282 9.432271 9.418140 9.403885 #>  [29,] 9.497170 9.483593 9.469909 9.456114 9.442204 9.428178 9.414031 9.399760 #>  [30,] 9.493169 9.479579 9.465881 9.452072 9.438149 9.424108 9.409946 9.395660 #>  [31,] 9.489187 9.475585 9.461874 9.448053 9.434116 9.420062 9.405886 9.391584 #>  [32,] 9.485224 9.471611 9.457889 9.444055 9.430106 9.416038 9.401849 9.387534 #>  [33,] 9.481282 9.467658 9.453925 9.440079 9.426118 9.412039 9.397837 9.383508 #>  [34,] 9.477360 9.463726 9.449982 9.436126 9.422154 9.408063 9.393849 9.379508 #>  [35,] 9.473458 9.459814 9.446061 9.432194 9.418212 9.404110 9.389885 9.375534 #>  [36,] 9.469576 9.455923 9.442161 9.428285 9.414293 9.400182 9.385947 9.371584 #>  [37,] 9.465715 9.452053 9.438282 9.424398 9.410397 9.396277 9.382033 9.367661 #>  [38,] 9.461873 9.448205 9.434426 9.420534 9.406525 9.392396 9.378143 9.363763 #>  [39,] 9.458052 9.444377 9.430591 9.416691 9.402675 9.388539 9.374279 9.359891 #>  [40,] 9.454251 9.440570 9.426777 9.412872 9.398849 9.384706 9.370439 9.356045 #>  [41,] 9.450471 9.436784 9.422986 9.409075 9.395046 9.380898 9.366625 9.352224 #>  [42,] 9.446711 9.433019 9.419216 9.405300 9.391267 9.377113 9.362835 9.348429 #>  [43,] 9.442972 9.429275 9.415468 9.401548 9.387510 9.373353 9.359070 9.344660 #>  [44,] 9.439253 9.425553 9.411742 9.397818 9.383777 9.369616 9.355331 9.340917 #>  [45,] 9.435554 9.421851 9.408038 9.394111 9.380068 9.365904 9.351616 9.337200 #>  [46,] 9.431876 9.418171 9.404356 9.390427 9.376382 9.362216 9.347926 9.333509 #>  [47,] 9.428218 9.414512 9.400695 9.386765 9.372719 9.358552 9.344262 9.329844 #>  [48,] 9.424581 9.410873 9.397056 9.383126 9.369079 9.354912 9.340622 9.326204 #>  [49,] 9.420964 9.407256 9.393439 9.379509 9.365462 9.351296 9.337007 9.322591 #>  [50,] 9.417367 9.403660 9.389844 9.375914 9.361869 9.347705 9.333417 9.319003 #>  [51,] 9.413791 9.400085 9.386270 9.372342 9.358299 9.344137 9.329852 9.315440 #>  [52,] 9.410235 9.396531 9.382718 9.368793 9.354752 9.340593 9.326311 9.311903 #>  [53,] 9.406699 9.392998 9.379187 9.365265 9.351228 9.337073 9.322795 9.308392 #>  [54,] 9.403184 9.389485 9.375678 9.361760 9.347727 9.333576 9.319304 9.304906 #>  [55,] 9.399688 9.385994 9.372191 9.358277 9.344249 9.330104 9.315837 9.301446 #>  [56,] 9.396213 9.382523 9.368725 9.354816 9.340794 9.326654 9.312394 9.298010 #>  [57,] 9.392757 9.379072 9.365280 9.351377 9.337361 9.323229 9.308976 9.294600 #>  [58,] 9.389322 9.375642 9.361856 9.347960 9.333951 9.319826 9.305582 9.291215 #>  [59,] 9.385906 9.372233 9.358453 9.344565 9.330564 9.316447 9.302212 9.287854 #>  [60,] 9.382510 9.368844 9.355072 9.341191 9.327198 9.313091 9.298865 9.284518 #>  [61,] 9.379134 9.365475 9.351711 9.337839 9.323855 9.309758 9.295543 9.281207 #>  [62,] 9.375777 9.362126 9.348371 9.334508 9.320534 9.306447 9.292244 9.277920 #>  [63,] 9.372439 9.358797 9.345051 9.331198 9.317235 9.303160 9.288968 9.274657 #>  [64,] 9.369121 9.355488 9.341752 9.327909 9.313958 9.299894 9.285715 9.271418 #>  [65,] 9.365822 9.352199 9.338473 9.324642 9.310702 9.296651 9.282486 9.268203 #>  [66,] 9.362541 9.348929 9.335215 9.321395 9.307468 9.293430 9.279279 9.265011 #>  [67,] 9.359280 9.345679 9.331976 9.318169 9.304255 9.290231 9.276095 9.261843 #>  [68,] 9.356037 9.342448 9.328757 9.314963 9.301063 9.287054 9.272933 9.258698 #>  [69,] 9.352813 9.339236 9.325558 9.311778 9.297892 9.283898 9.269794 9.255575 #>  [70,] 9.349608 9.336043 9.322379 9.308613 9.294742 9.280764 9.266676 9.252476 #>  [71,] 9.346421 9.332869 9.319219 9.305467 9.291612 9.277651 9.263581 9.249398 #>  [72,] 9.343251 9.329714 9.316078 9.302342 9.288503 9.274559 9.260506 9.246343 #>  [73,] 9.340100 9.326577 9.312956 9.299236 9.285414 9.271487 9.257454 9.243310 #>  [74,] 9.336967 9.323458 9.309853 9.296149 9.282344 9.268436 9.254422 9.240299 #>  [75,] 9.333851 9.320357 9.306768 9.293081 9.279295 9.265405 9.251411 9.237309 #>  [76,] 9.330753 9.317275 9.303702 9.290033 9.276264 9.262394 9.248421 9.234340 #>  [77,] 9.327671 9.314210 9.300654 9.287003 9.273253 9.259403 9.245451 9.231393 #>  [78,] 9.324607 9.311162 9.297624 9.283991 9.270261 9.256432 9.242501 9.228465 #>  [79,] 9.321560 9.308132 9.294612 9.280998 9.267288 9.253480 9.239570 9.225558 #>  [80,] 9.318530 9.305119 9.291618 9.278023 9.264333 9.250546 9.236660 9.222672 #>  [81,] 9.315516 9.302123 9.288641 9.275066 9.261397 9.247632 9.233768 9.219804 #>  [82,] 9.312518 9.299144 9.285681 9.272126 9.258479 9.244736 9.230896 9.216957 #>  [83,] 9.309537 9.296182 9.282738 9.269204 9.255578 9.241858 9.228042 9.214129 #>  [84,] 9.306571 9.293235 9.279812 9.266299 9.252695 9.238999 9.225207 9.211319 #>  [85,] 9.303621 9.290305 9.276902 9.263411 9.249830 9.236157 9.222390 9.208528 #>  [86,] 9.300687 9.287390 9.274008 9.260539 9.246981 9.233332 9.219591 9.205755 #>  [87,] 9.297768 9.284492 9.271131 9.257684 9.244149 9.230525 9.216809 9.203001 #>  [88,] 9.294864 9.281608 9.268269 9.254845 9.241334 9.227734 9.214045 9.200264 #>  [89,] 9.291975 9.278740 9.265423 9.252021 9.238535 9.224961 9.211298 9.197544 #>  [90,] 9.289100 9.275887 9.262592 9.249214 9.235751 9.222203 9.208567 9.194842 #>  [91,] 9.286240 9.273048 9.259776 9.246422 9.232984 9.219462 9.205853 9.192156 #>  [92,] 9.283395 9.270225 9.256975 9.243645 9.230232 9.216736 9.203155 9.189487 #>  [93,] 9.280563 9.267415 9.254189 9.240883 9.227495 9.214026 9.200472 9.186834 #>  [94,] 9.277745 9.264619 9.251417 9.238135 9.224774 9.211331 9.197806 9.184196 #>  [95,] 9.274940 9.261838 9.248659 9.235402 9.222067 9.208651 9.195154 9.181574 #>  [96,] 9.272149 9.259070 9.245915 9.232683 9.219374 9.205986 9.192517 9.178968 #>  [97,] 9.269371 9.256315 9.243184 9.229978 9.216695 9.203335 9.189895 9.176376 #>  [98,] 9.266606 9.253573 9.240467 9.227287 9.214031 9.200698 9.187288 9.173799 #>  [99,] 9.263854 9.250845 9.237763 9.224608 9.211379 9.198075 9.184694 9.171236 #> [100,] 9.261114 9.248128 9.235072 9.221943 9.208741 9.195465 9.182114 9.168687 #>            [,9]    [,10]    [,11]    [,12]    [,13]    [,14]    [,15]    [,16] #>   [1,] 9.510220 9.496478 9.482633 9.468681 9.454621 9.440449 9.426164 9.411762 #>   [2,] 9.505476 9.491697 9.477814 9.463822 9.449720 9.435505 9.421175 9.406726 #>   [3,] 9.500750 9.486935 9.473014 9.458983 9.444840 9.430582 9.416207 9.401711 #>   [4,] 9.496043 9.482192 9.468233 9.454163 9.439980 9.425680 9.411261 9.396719 #>   [5,] 9.491355 9.477469 9.463473 9.449365 9.435142 9.420800 9.406337 9.391750 #>   [6,] 9.486687 9.472766 9.458734 9.444588 9.430325 9.415942 9.401437 9.386805 #>   [7,] 9.482038 9.468083 9.454015 9.439832 9.425530 9.411107 9.396559 9.381884 #>   [8,] 9.477409 9.463420 9.449318 9.435098 9.420758 9.406295 9.391706 9.376987 #>   [9,] 9.472801 9.458779 9.444642 9.430386 9.416009 9.401507 9.386877 9.372115 #>  [10,] 9.468213 9.454159 9.439988 9.425697 9.411283 9.396743 9.382072 9.367268 #>  [11,] 9.463647 9.449560 9.435356 9.421031 9.406581 9.392003 9.377293 9.362448 #>  [12,] 9.459101 9.444984 9.430747 9.416388 9.401903 9.387288 9.372540 9.357654 #>  [13,] 9.454578 9.440430 9.426161 9.411769 9.397249 9.382598 9.367812 9.352887 #>  [14,] 9.450076 9.435898 9.421599 9.407174 9.392620 9.377934 9.363111 9.348147 #>  [15,] 9.445596 9.431390 9.417060 9.402603 9.388017 9.373296 9.358437 9.343435 #>  [16,] 9.441139 9.426904 9.412545 9.398057 9.383438 9.368684 9.353790 9.338752 #>  [17,] 9.436705 9.422442 9.408054 9.393537 9.378886 9.364099 9.349171 9.334097 #>  [18,] 9.432294 9.418004 9.403588 9.389041 9.374360 9.359541 9.344580 9.329471 #>  [19,] 9.427906 9.413590 9.399146 9.384572 9.369861 9.355011 9.340017 9.324874 #>  [20,] 9.423542 9.409200 9.394730 9.380128 9.365389 9.350509 9.335483 9.320308 #>  [21,] 9.419201 9.404835 9.390340 9.375711 9.360944 9.346035 9.330979 9.315771 #>  [22,] 9.414884 9.400495 9.385975 9.371320 9.356526 9.341589 9.326504 9.311266 #>  [23,] 9.410592 9.396180 9.381636 9.366956 9.352136 9.337172 9.322059 9.306791 #>  [24,] 9.406325 9.391890 9.377323 9.362620 9.347775 9.332785 9.317644 9.302348 #>  [25,] 9.402082 9.387626 9.373037 9.358310 9.343442 9.328427 9.313260 9.297937 #>  [26,] 9.397863 9.383387 9.368777 9.354029 9.339137 9.324098 9.308907 9.293557 #>  [27,] 9.393670 9.379175 9.364545 9.349775 9.334862 9.319800 9.304584 9.289210 #>  [28,] 9.389503 9.374989 9.360339 9.345550 9.330615 9.315532 9.300294 9.284896 #>  [29,] 9.385361 9.370829 9.356161 9.341353 9.326399 9.311294 9.296035 9.280614 #>  [30,] 9.381244 9.366696 9.352011 9.337184 9.322211 9.307087 9.291807 9.276366 #>  [31,] 9.377153 9.362589 9.347888 9.333044 9.318054 9.302912 9.287612 9.272151 #>  [32,] 9.373088 9.358510 9.343793 9.328933 9.313926 9.298767 9.283450 9.267970 #>  [33,] 9.369050 9.354457 9.339726 9.324851 9.309829 9.294653 9.279320 9.263822 #>  [34,] 9.365037 9.350432 9.335687 9.320798 9.305762 9.290571 9.275222 9.259709 #>  [35,] 9.361051 9.346433 9.331676 9.316775 9.301725 9.286521 9.271158 9.255630 #>  [36,] 9.357091 9.342462 9.327694 9.312781 9.297719 9.282503 9.267126 9.251585 #>  [37,] 9.353158 9.338519 9.323740 9.308817 9.293744 9.278516 9.263128 9.247574 #>  [38,] 9.349251 9.334603 9.319815 9.304882 9.289799 9.274562 9.259163 9.243599 #>  [39,] 9.345371 9.330715 9.315919 9.300977 9.285886 9.270639 9.255232 9.239658 #>  [40,] 9.341518 9.326855 9.312051 9.297102 9.282003 9.266749 9.251334 9.235752 #>  [41,] 9.337691 9.323022 9.308212 9.293257 9.278152 9.262891 9.247469 9.231880 #>  [42,] 9.333891 9.319217 9.304402 9.289442 9.274331 9.259065 9.243638 9.228044 #>  [43,] 9.330118 9.315440 9.300621 9.285657 9.270542 9.255272 9.239841 9.224243 #>  [44,] 9.326372 9.311691 9.296869 9.281901 9.266784 9.251511 9.236077 9.220476 #>  [45,] 9.322653 9.307969 9.293145 9.278176 9.263056 9.247782 9.232347 9.216745 #>  [46,] 9.318960 9.304275 9.289450 9.274480 9.259360 9.244085 9.228650 9.213049 #>  [47,] 9.315294 9.300609 9.285784 9.270814 9.255695 9.240421 9.224987 9.209387 #>  [48,] 9.311655 9.296971 9.282147 9.267179 9.252061 9.236789 9.221357 9.205760 #>  [49,] 9.308043 9.293361 9.278539 9.263573 9.248458 9.233189 9.217761 9.202168 #>  [50,] 9.304458 9.289778 9.274959 9.259996 9.244885 9.229621 9.214198 9.198611 #>  [51,] 9.300898 9.286222 9.271408 9.256450 9.241344 9.226085 9.210668 9.195088 #>  [52,] 9.297366 9.282694 9.267885 9.252933 9.237833 9.222581 9.207171 9.191599 #>  [53,] 9.293860 9.279194 9.264390 9.249445 9.234352 9.219108 9.203708 9.188145 #>  [54,] 9.290380 9.275721 9.260924 9.245986 9.230902 9.215667 9.200277 9.184724 #>  [55,] 9.286926 9.272274 9.257486 9.242557 9.227483 9.212258 9.196878 9.181338 #>  [56,] 9.283499 9.268855 9.254076 9.239157 9.224093 9.208879 9.193512 9.177985 #>  [57,] 9.280097 9.265463 9.250694 9.235785 9.220733 9.205532 9.190178 9.174665 #>  [58,] 9.276721 9.262097 9.247339 9.232442 9.217403 9.202215 9.186876 9.171379 #>  [59,] 9.273371 9.258758 9.244012 9.229128 9.214102 9.198929 9.183606 9.168125 #>  [60,] 9.270046 9.255446 9.240712 9.225842 9.210830 9.195674 9.180367 9.164905 #>  [61,] 9.266747 9.252159 9.237439 9.222584 9.207588 9.192448 9.177159 9.161716 #>  [62,] 9.263473 9.248899 9.234193 9.219353 9.204374 9.189252 9.173982 9.158560 #>  [63,] 9.260224 9.245664 9.230974 9.216151 9.201189 9.186086 9.170836 9.155435 #>  [64,] 9.256999 9.242455 9.227781 9.212975 9.198033 9.182949 9.167720 9.152342 #>  [65,] 9.253799 9.239271 9.224615 9.209827 9.194904 9.179841 9.164634 9.149279 #>  [66,] 9.250623 9.236112 9.221474 9.206706 9.191803 9.176762 9.161578 9.146248 #>  [67,] 9.247472 9.232978 9.218359 9.203611 9.188729 9.173711 9.158551 9.143247 #>  [68,] 9.244344 9.229869 9.215270 9.200542 9.185683 9.170688 9.155553 9.140275 #>  [69,] 9.241240 9.226784 9.212205 9.197499 9.182663 9.167693 9.152584 9.137334 #>  [70,] 9.238159 9.223723 9.209166 9.194482 9.179670 9.164725 9.149643 9.134421 #>  [71,] 9.235101 9.220687 9.206151 9.191491 9.176703 9.161784 9.146730 9.131538 #>  [72,] 9.232067 9.217673 9.203160 9.188524 9.173762 9.158870 9.143845 9.128682 #>  [73,] 9.229055 9.214683 9.200194 9.185582 9.170846 9.155982 9.140986 9.125855 #>  [74,] 9.226065 9.211716 9.197251 9.182665 9.167956 9.153120 9.138154 9.123055 #>  [75,] 9.223097 9.208772 9.194331 9.179772 9.165090 9.150284 9.135349 9.120283 #>  [76,] 9.220151 9.205850 9.191435 9.176902 9.162249 9.147472 9.132569 9.117537 #>  [77,] 9.217227 9.202950 9.188561 9.174056 9.159432 9.144686 9.129815 9.114817 #>  [78,] 9.214323 9.200072 9.185710 9.171232 9.156638 9.141924 9.127086 9.112123 #>  [79,] 9.211441 9.197216 9.182880 9.168432 9.153868 9.139185 9.124382 9.109454 #>  [80,] 9.208579 9.194380 9.180073 9.165654 9.151120 9.136471 9.121701 9.106810 #>  [81,] 9.205738 9.191566 9.177286 9.162897 9.148396 9.133779 9.119045 9.104191 #>  [82,] 9.202916 9.188772 9.174521 9.160163 9.145693 9.131110 9.116412 9.101595 #>  [83,] 9.200114 9.185998 9.171777 9.157449 9.143012 9.128464 9.113801 9.099023 #>  [84,] 9.197332 9.183244 9.169053 9.154756 9.140352 9.125839 9.111213 9.096473 #>  [85,] 9.194568 9.180509 9.166349 9.152084 9.137714 9.123236 9.108647 9.093946 #>  [86,] 9.191824 9.177794 9.163664 9.149432 9.135096 9.120653 9.106103 9.091441 #>  [87,] 9.189097 9.175097 9.160999 9.146800 9.132498 9.118092 9.103579 9.088958 #>  [88,] 9.186389 9.172419 9.158352 9.144186 9.129920 9.115550 9.101076 9.086496 #>  [89,] 9.183699 9.169759 9.155725 9.141592 9.127361 9.113028 9.098593 9.084054 #>  [90,] 9.181026 9.167117 9.153115 9.139017 9.124821 9.110526 9.096130 9.081632 #>  [91,] 9.178370 9.164493 9.150523 9.136459 9.122299 9.108042 9.093686 9.079230 #>  [92,] 9.175731 9.161885 9.147949 9.133919 9.119796 9.105577 9.091261 9.076847 #>  [93,] 9.173108 9.159294 9.145391 9.131397 9.117311 9.103130 9.088855 9.074482 #>  [94,] 9.170501 9.156720 9.142851 9.128892 9.114842 9.100701 9.086466 9.072136 #>  [95,] 9.167911 9.154162 9.140326 9.126403 9.112391 9.098288 9.084094 9.069808 #>  [96,] 9.165335 9.151619 9.137818 9.123931 9.109956 9.095893 9.081740 9.067496 #>  [97,] 9.162775 9.149092 9.135325 9.121474 9.107537 9.093514 9.079402 9.065202 #>  [98,] 9.160230 9.146580 9.132848 9.119033 9.105134 9.091150 9.077080 9.062923 #>  [99,] 9.157699 9.144082 9.130386 9.116607 9.102746 9.088802 9.074774 9.060661 #> [100,] 9.155182 9.141599 9.127938 9.114196 9.100374 9.086470 9.072483 9.058413 #>           [,17]    [,18]    [,19]    [,20]    [,21]    [,22]    [,23]    [,24] #>   [1,] 9.397241 9.382599 9.367832 9.352937 9.337912 9.322753 9.307458 9.292023 #>   [2,] 9.392156 9.377462 9.362640 9.347689 9.332605 9.317384 9.302024 9.286521 #>   [3,] 9.387092 9.372347 9.357473 9.342466 9.327323 9.312041 9.296617 9.281046 #>   [4,] 9.382052 9.367257 9.352330 9.337268 9.322067 9.306724 9.291236 9.275598 #>   [5,] 9.377036 9.362191 9.347212 9.332095 9.316837 9.301434 9.285883 9.270179 #>   [6,] 9.372044 9.357149 9.342119 9.326948 9.311634 9.296172 9.280558 9.264789 #>   [7,] 9.367076 9.352134 9.337052 9.321829 9.306459 9.290938 9.275263 9.259429 #>   [8,] 9.362134 9.347144 9.332013 9.316737 9.301312 9.285733 9.269997 9.254099 #>   [9,] 9.357217 9.342180 9.327000 9.311673 9.296194 9.280559 9.264763 9.248802 #>  [10,] 9.352327 9.337244 9.322016 9.306638 9.291105 9.275414 9.259560 9.243537 #>  [11,] 9.347463 9.332335 9.317060 9.301632 9.286047 9.270301 9.254389 9.238306 #>  [12,] 9.342627 9.327455 9.312133 9.296656 9.281020 9.265221 9.249252 9.233108 #>  [13,] 9.337819 9.322603 9.307235 9.291711 9.276025 9.260173 9.244148 9.227946 #>  [14,] 9.333039 9.317780 9.302368 9.286797 9.271062 9.255158 9.239079 9.222819 #>  [15,] 9.328287 9.312988 9.297532 9.281915 9.266132 9.250177 9.234045 9.217729 #>  [16,] 9.323565 9.308225 9.292727 9.277066 9.261236 9.245231 9.229047 9.212676 #>  [17,] 9.318872 9.303493 9.287954 9.272249 9.256373 9.240321 9.224086 9.207662 #>  [18,] 9.314210 9.298792 9.283213 9.267466 9.251546 9.235447 9.219162 9.202686 #>  [19,] 9.309578 9.294123 9.278505 9.262717 9.246753 9.230609 9.214277 9.197750 #>  [20,] 9.304977 9.289486 9.273830 9.258002 9.241997 9.225808 9.209430 9.192854 #>  [21,] 9.300408 9.284882 9.269189 9.253323 9.237277 9.221046 9.204622 9.187999 #>  [22,] 9.295870 9.280311 9.264582 9.248679 9.232594 9.216322 9.199855 9.183185 #>  [23,] 9.291364 9.275773 9.260010 9.244071 9.227949 9.211637 9.195128 9.178414 #>  [24,] 9.286891 9.271268 9.255473 9.239500 9.223341 9.206991 9.190442 9.173686 #>  [25,] 9.282451 9.266799 9.250972 9.234966 9.218772 9.202386 9.185798 9.169002 #>  [26,] 9.278045 9.262363 9.246507 9.230469 9.214242 9.197821 9.181196 9.164361 #>  [27,] 9.273672 9.257963 9.242078 9.226010 9.209752 9.193297 9.176638 9.159765 #>  [28,] 9.269332 9.253598 9.237685 9.221589 9.205301 9.188815 9.172122 9.155215 #>  [29,] 9.265027 9.249268 9.233330 9.217207 9.200891 9.184374 9.167650 9.150710 #>  [30,] 9.260757 9.244974 9.229012 9.212863 9.196521 9.179976 9.163223 9.146251 #>  [31,] 9.256521 9.240717 9.224732 9.208559 9.192191 9.175621 9.158840 9.141839 #>  [32,] 9.252320 9.236496 9.220490 9.204295 9.187904 9.171309 9.154502 9.137474 #>  [33,] 9.248155 9.232311 9.216285 9.200070 9.183657 9.167040 9.150209 9.133157 #>  [34,] 9.244025 9.228164 9.212120 9.195885 9.179453 9.162815 9.145962 9.128887 #>  [35,] 9.239930 9.224054 9.207993 9.191741 9.175291 9.158634 9.141761 9.124665 #>  [36,] 9.235871 9.219980 9.203905 9.187637 9.171171 9.154497 9.137607 9.120492 #>  [37,] 9.231849 9.215945 9.199856 9.183574 9.167093 9.150404 9.133498 9.116367 #>  [38,] 9.227862 9.211946 9.195846 9.179552 9.163058 9.146356 9.129437 9.112291 #>  [39,] 9.223911 9.207986 9.191875 9.175571 9.159066 9.142353 9.125422 9.108264 #>  [40,] 9.219997 9.204063 9.187944 9.171631 9.155117 9.138394 9.121454 9.104286 #>  [41,] 9.216119 9.200178 9.184052 9.167732 9.151211 9.134481 9.117533 9.100358 #>  [42,] 9.212277 9.196332 9.180199 9.163874 9.147348 9.130612 9.113659 9.096479 #>  [43,] 9.208472 9.192522 9.176387 9.160058 9.143528 9.126789 9.109832 9.092649 #>  [44,] 9.204703 9.188751 9.172614 9.156283 9.139751 9.123011 9.106053 9.088868 #>  [45,] 9.200971 9.185018 9.168880 9.152549 9.136017 9.119277 9.102320 9.085137 #>  [46,] 9.197275 9.181323 9.165186 9.148856 9.132326 9.115589 9.098635 9.081455 #>  [47,] 9.193615 9.177665 9.161531 9.145204 9.128679 9.111945 9.094996 9.077822 #>  [48,] 9.189992 9.174046 9.157916 9.141594 9.125074 9.108346 9.091404 9.074238 #>  [49,] 9.186404 9.170464 9.154339 9.138024 9.121511 9.104792 9.087859 9.070703 #>  [50,] 9.182853 9.166919 9.150802 9.134495 9.117991 9.101283 9.084360 9.067216 #>  [51,] 9.179338 9.163412 9.147304 9.131007 9.114514 9.097817 9.080908 9.063778 #>  [52,] 9.175858 9.159942 9.143845 9.127559 9.111079 9.094395 9.077501 9.060387 #>  [53,] 9.172414 9.156509 9.140424 9.124152 9.107685 9.091017 9.074140 9.057045 #>  [54,] 9.169005 9.153113 9.137041 9.120784 9.104333 9.087683 9.070824 9.053749 #>  [55,] 9.165631 9.149753 9.133697 9.117455 9.101023 9.084391 9.067554 9.050501 #>  [56,] 9.162293 9.146430 9.130390 9.114167 9.097753 9.081143 9.064327 9.047299 #>  [57,] 9.158989 9.143142 9.127121 9.110917 9.094525 9.077936 9.061145 9.044143 #>  [58,] 9.155719 9.139891 9.123889 9.107706 9.091336 9.074772 9.058007 9.041033 #>  [59,] 9.152484 9.136675 9.120694 9.104533 9.088187 9.071649 9.054912 9.037968 #>  [60,] 9.149282 9.133494 9.117535 9.101398 9.085078 9.068568 9.051860 9.034948 #>  [61,] 9.146114 9.130348 9.114413 9.098301 9.082008 9.065527 9.048850 9.031971 #>  [62,] 9.142980 9.127237 9.111326 9.095241 9.078977 9.062526 9.045882 9.029039 #>  [63,] 9.139878 9.124160 9.108275 9.092218 9.075983 9.059565 9.042955 9.026149 #>  [64,] 9.136809 9.121116 9.105259 9.089231 9.073028 9.056643 9.040069 9.023301 #>  [65,] 9.133771 9.118106 9.102277 9.086280 9.070110 9.053759 9.037223 9.020495 #>  [66,] 9.130766 9.115128 9.099330 9.083365 9.067228 9.050914 9.034417 9.017730 #>  [67,] 9.127792 9.112184 9.096416 9.080484 9.064382 9.048106 9.031649 9.015006 #>  [68,] 9.124849 9.109271 9.093535 9.077637 9.061572 9.045335 9.028920 9.012320 #>  [69,] 9.121937 9.106390 9.090687 9.074825 9.058798 9.042600 9.026228 9.009674 #>  [70,] 9.119055 9.103540 9.087872 9.072046 9.056057 9.039901 9.023573 9.007067 #>  [71,] 9.116203 9.100721 9.085088 9.069299 9.053351 9.037237 9.020954 9.004496 #>  [72,] 9.113380 9.097932 9.082335 9.066585 9.050678 9.034608 9.018371 9.001962 #>  [73,] 9.110585 9.095173 9.079613 9.063903 9.048037 9.032012 9.015823 8.999465 #>  [74,] 9.107819 9.092443 9.076921 9.061251 9.045429 9.029449 9.013309 8.997002 #>  [75,] 9.105081 9.089741 9.074259 9.058631 9.042852 9.026919 9.010828 8.994574 #>  [76,] 9.102371 9.087069 9.071626 9.056040 9.040306 9.024421 9.008380 8.992180 #>  [77,] 9.099687 9.084423 9.069022 9.053479 9.037790 9.021954 9.005964 8.989819 #>  [78,] 9.097030 9.081806 9.066445 9.050946 9.035304 9.019517 9.003580 8.987489 #>  [79,] 9.094399 9.079214 9.063896 9.048441 9.032847 9.017110 9.001226 8.985192 #>  [80,] 9.091794 9.076649 9.061374 9.045965 9.030418 9.014731 8.998901 8.982924 #>  [81,] 9.089213 9.074110 9.058878 9.043515 9.028017 9.012382 8.996606 8.980687 #>  [82,] 9.086657 9.071596 9.056408 9.041091 9.025643 9.010060 8.994339 8.978478 #>  [83,] 9.084125 9.069106 9.053963 9.038694 9.023295 9.007765 8.992100 8.976298 #>  [84,] 9.081616 9.066640 9.051543 9.036321 9.020973 9.005496 8.989887 8.974145 #>  [85,] 9.079131 9.064198 9.049147 9.033973 9.018676 9.003253 8.987701 8.972018 #>  [86,] 9.076668 9.061779 9.046774 9.031649 9.016404 9.001034 8.985540 8.969918 #>  [87,] 9.074226 9.059382 9.044424 9.029349 9.014155 8.998840 8.983403 8.967842 #>  [88,] 9.071807 9.057008 9.042096 9.027071 9.011929 8.996670 8.981291 8.965791 #>  [89,] 9.069408 9.054654 9.039790 9.024815 9.009726 8.994522 8.979202 8.963763 #>  [90,] 9.067030 9.052321 9.037505 9.022580 9.007545 8.992397 8.977135 8.961758 #>  [91,] 9.064671 9.050009 9.035241 9.020367 9.005385 8.990293 8.975090 8.959775 #>  [92,] 9.062332 9.047716 9.032997 9.018174 9.003245 8.988210 8.973066 8.957814 #>  [93,] 9.060012 9.045443 9.030773 9.016001 9.001126 8.986147 8.971063 8.955872 #>  [94,] 9.057711 9.043188 9.028567 9.013846 8.999026 8.984103 8.969079 8.953951 #>  [95,] 9.055427 9.040951 9.026380 9.011711 8.996944 8.982079 8.967114 8.952049 #>  [96,] 9.053161 9.038732 9.024210 9.009593 8.994881 8.980072 8.965167 8.950165 #>  [97,] 9.050911 9.036530 9.022058 9.007493 8.992835 8.978084 8.963238 8.948298 #>  [98,] 9.048678 9.034345 9.019922 9.005410 8.990806 8.976112 8.961326 8.946449 #>  [99,] 9.046461 9.032176 9.017803 9.003342 8.988794 8.974157 8.959431 8.944616 #> [100,] 9.044260 9.030022 9.015699 9.001291 8.986797 8.972217 8.957551 8.942799 #>           [,25]    [,26]    [,27]    [,28]    [,29]    [,30]    [,31]    [,32] #>   [1,] 9.276446 9.260724 9.244853 9.228830 9.212652 9.196317 9.179821 9.163162 #>   [2,] 9.270873 9.255075 9.239124 9.223017 9.206752 9.190323 9.173730 9.156967 #>   [3,] 9.265326 9.249453 9.233424 9.217234 9.200881 9.184360 9.167669 9.150803 #>   [4,] 9.259808 9.243861 9.227753 9.211481 9.195041 9.178428 9.161640 9.144672 #>   [5,] 9.254319 9.238298 9.222113 9.205759 9.189233 9.172529 9.155644 9.138574 #>   [6,] 9.248860 9.232766 9.216505 9.200070 9.183458 9.166664 9.149683 9.132512 #>   [7,] 9.243431 9.227266 9.210929 9.194414 9.177717 9.160834 9.143758 9.126486 #>   [8,] 9.238035 9.221799 9.205386 9.188792 9.172012 9.155040 9.137870 9.120499 #>   [9,] 9.232671 9.216365 9.199879 9.183207 9.166343 9.149284 9.132021 9.114551 #>  [10,] 9.227341 9.210966 9.194407 9.177657 9.160713 9.143567 9.126213 9.108644 #>  [11,] 9.222045 9.205602 9.188971 9.172146 9.155121 9.137890 9.120445 9.102781 #>  [12,] 9.216784 9.200275 9.183573 9.166674 9.149570 9.132254 9.114720 9.096961 #>  [13,] 9.211560 9.194985 9.178214 9.161242 9.144060 9.126662 9.109040 9.091188 #>  [14,] 9.206373 9.189734 9.172895 9.155850 9.138592 9.121113 9.103405 9.085461 #>  [15,] 9.201223 9.184522 9.167617 9.150501 9.133168 9.115610 9.097818 9.079783 #>  [16,] 9.196113 9.179349 9.162380 9.145195 9.127789 9.110153 9.092278 9.074156 #>  [17,] 9.191042 9.174218 9.157185 9.139934 9.122456 9.104744 9.086788 9.068579 #>  [18,] 9.186011 9.169129 9.152034 9.134718 9.117170 9.099384 9.081350 9.063056 #>  [19,] 9.181021 9.164083 9.146928 9.129548 9.111933 9.094075 9.075963 9.057588 #>  [20,] 9.176073 9.159080 9.141867 9.124425 9.106744 9.088816 9.070630 9.052175 #>  [21,] 9.171168 9.154122 9.136852 9.119350 9.101606 9.083610 9.065352 9.046820 #>  [22,] 9.166306 9.149209 9.131885 9.114325 9.096519 9.078458 9.060130 9.041523 #>  [23,] 9.161488 9.144342 9.126965 9.109350 9.091485 9.073360 9.054965 9.036286 #>  [24,] 9.156715 9.139521 9.122094 9.104425 9.086504 9.068318 9.049858 9.031110 #>  [25,] 9.151988 9.134748 9.117273 9.099553 9.081576 9.063333 9.044811 9.025997 #>  [26,] 9.147306 9.130023 9.112502 9.094733 9.076705 9.058406 9.039824 9.020947 #>  [27,] 9.142672 9.125347 9.107782 9.089966 9.071888 9.053537 9.034899 9.015961 #>  [28,] 9.138084 9.120720 9.103114 9.085254 9.067129 9.048728 9.030036 9.011042 #>  [29,] 9.133544 9.116144 9.098498 9.080596 9.062427 9.043979 9.025237 9.006189 #>  [30,] 9.129053 9.111617 9.093935 9.075994 9.057784 9.039291 9.020503 9.001404 #>  [31,] 9.124610 9.107142 9.089425 9.071448 9.053199 9.034665 9.015833 8.996687 #>  [32,] 9.120216 9.102719 9.084970 9.066959 9.048674 9.030102 9.011229 8.992040 #>  [33,] 9.115873 9.098347 9.080569 9.062527 9.044209 9.025603 9.006692 8.987463 #>  [34,] 9.111579 9.094028 9.076223 9.058153 9.039805 9.021167 9.002222 8.982957 #>  [35,] 9.107335 9.089761 9.071932 9.053837 9.035462 9.016795 8.997820 8.978523 #>  [36,] 9.103142 9.085548 9.067698 9.049580 9.031181 9.012488 8.993487 8.974161 #>  [37,] 9.099000 9.081388 9.063519 9.045381 9.026962 9.008247 8.989222 8.969872 #>  [38,] 9.094910 9.077282 9.059397 9.041242 9.022804 9.004071 8.985027 8.965655 #>  [39,] 9.090870 9.073230 9.055331 9.037162 9.018710 8.999961 8.980901 8.961512 #>  [40,] 9.086882 9.069231 9.051322 9.033141 9.014678 8.995917 8.976844 8.957443 #>  [41,] 9.082946 9.065287 9.047369 9.029181 9.010709 8.991940 8.972858 8.953448 #>  [42,] 9.079062 9.061397 9.043474 9.025280 9.006803 8.988029 8.968942 8.949526 #>  [43,] 9.075229 9.057561 9.039636 9.021439 9.002960 8.984184 8.965095 8.945679 #>  [44,] 9.071447 9.053780 9.035854 9.017659 8.999180 8.980405 8.961319 8.941906 #>  [45,] 9.067718 9.050052 9.032130 9.013937 8.995463 8.976693 8.957613 8.938206 #>  [46,] 9.064040 9.046379 9.028462 9.010276 8.991809 8.973047 8.953976 8.934580 #>  [47,] 9.060413 9.042760 9.024851 9.006674 8.988217 8.969467 8.950409 8.931027 #>  [48,] 9.056838 9.039194 9.021296 9.003131 8.984688 8.965953 8.946911 8.927548 #>  [49,] 9.053314 9.035682 9.017797 8.999647 8.981221 8.962503 8.943482 8.924140 #>  [50,] 9.049840 9.032223 9.014354 8.996222 8.977815 8.959119 8.940121 8.920805 #>  [51,] 9.046418 9.028818 9.010967 8.992855 8.974470 8.955799 8.936827 8.917542 #>  [52,] 9.043045 9.025464 9.007635 8.989546 8.971186 8.952543 8.933601 8.914349 #>  [53,] 9.039722 9.022163 9.004358 8.986295 8.967963 8.949350 8.930442 8.911226 #>  [54,] 9.036449 9.018914 9.001135 8.983100 8.964799 8.946219 8.927348 8.908172 #>  [55,] 9.033225 9.015716 8.997965 8.979962 8.961694 8.943151 8.924320 8.905187 #>  [56,] 9.030049 9.012569 8.994849 8.976879 8.958648 8.940144 8.921356 8.902269 #>  [57,] 9.026922 9.009472 8.991785 8.973851 8.955659 8.937197 8.918455 8.899418 #>  [58,] 9.023842 9.006425 8.988774 8.970878 8.952727 8.934310 8.915616 8.896633 #>  [59,] 9.020809 9.003427 8.985813 8.967958 8.949851 8.931482 8.912840 8.893912 #>  [60,] 9.017823 9.000478 8.982904 8.965091 8.947030 8.928712 8.910123 8.891255 #>  [61,] 9.014883 8.997577 8.980044 8.962276 8.944264 8.925998 8.907467 8.888659 #>  [62,] 9.011988 8.994722 8.977234 8.959513 8.941552 8.923340 8.904868 8.886125 #>  [63,] 9.009138 8.991915 8.974471 8.956800 8.938892 8.920738 8.902327 8.883651 #>  [64,] 9.006331 8.989152 8.971757 8.954137 8.936284 8.918189 8.899842 8.881235 #>  [65,] 9.003568 8.986435 8.969089 8.951522 8.933726 8.915693 8.897412 8.878877 #>  [66,] 9.000848 8.983763 8.966468 8.948955 8.931218 8.913248 8.895036 8.876574 #>  [67,] 8.998169 8.981133 8.963891 8.946435 8.928759 8.910854 8.892713 8.874326 #>  [68,] 8.995531 8.978546 8.961359 8.943961 8.926348 8.908510 8.890440 8.872131 #>  [69,] 8.992934 8.976001 8.958870 8.941532 8.923982 8.906214 8.888218 8.869988 #>  [70,] 8.990377 8.973497 8.956423 8.939147 8.921663 8.903964 8.886044 8.867896 #>  [71,] 8.987858 8.971033 8.954018 8.936804 8.919388 8.901761 8.883918 8.865853 #>  [72,] 8.985377 8.968609 8.951653 8.934504 8.917156 8.899603 8.881838 8.863857 #>  [73,] 8.982933 8.966222 8.949328 8.932244 8.914966 8.897488 8.879803 8.861907 #>  [74,] 8.980526 8.963874 8.947042 8.930024 8.912817 8.895415 8.877812 8.860003 #>  [75,] 8.978154 8.961561 8.944793 8.927843 8.910708 8.893383 8.875862 8.858141 #>  [76,] 8.975816 8.959285 8.942581 8.925700 8.908638 8.891391 8.873954 8.856322 #>  [77,] 8.973513 8.957043 8.940404 8.923594 8.906606 8.889438 8.872085 8.854543 #>  [78,] 8.971242 8.954835 8.938263 8.921523 8.904610 8.887522 8.870254 8.852803 #>  [79,] 8.969004 8.952660 8.936155 8.919486 8.902650 8.885643 8.868461 8.851101 #>  [80,] 8.966797 8.950517 8.934080 8.917484 8.900724 8.883798 8.866703 8.849435 #>  [81,] 8.964621 8.948405 8.932037 8.915513 8.898831 8.881987 8.864979 8.847805 #>  [82,] 8.962474 8.946324 8.930025 8.913575 8.896970 8.880209 8.863289 8.846207 #>  [83,] 8.960356 8.944272 8.928043 8.911666 8.895140 8.878462 8.861630 8.844642 #>  [84,] 8.958266 8.942248 8.926089 8.909788 8.893340 8.876746 8.860002 8.843108 #>  [85,] 8.956203 8.940252 8.924164 8.907937 8.891569 8.875058 8.858404 8.841603 #>  [86,] 8.954166 8.938283 8.922266 8.906114 8.889826 8.873399 8.856833 8.840127 #>  [87,] 8.952155 8.936339 8.920394 8.904318 8.888109 8.871767 8.855290 8.838678 #>  [88,] 8.950168 8.934420 8.918547 8.902546 8.886418 8.870160 8.853772 8.837254 #>  [89,] 8.948205 8.932526 8.916724 8.900800 8.884751 8.868578 8.852279 8.835855 #>  [90,] 8.946265 8.930654 8.914925 8.899077 8.883108 8.867019 8.850810 8.834480 #>  [91,] 8.944347 8.928805 8.913149 8.897376 8.881488 8.865483 8.849362 8.833126 #>  [92,] 8.942451 8.926978 8.911393 8.895697 8.879889 8.863969 8.847937 8.831794 #>  [93,] 8.940576 8.925171 8.909659 8.894039 8.878311 8.862474 8.846531 8.830481 #>  [94,] 8.938720 8.923384 8.907945 8.892401 8.876752 8.861000 8.845145 8.829187 #>  [95,] 8.936883 8.921617 8.906249 8.890781 8.875212 8.859544 8.843776 8.827911 #>  [96,] 8.935065 8.919867 8.904572 8.889180 8.873690 8.858105 8.842425 8.826652 #>  [97,] 8.933264 8.918135 8.902912 8.887595 8.872185 8.856683 8.841090 8.825408 #>  [98,] 8.931480 8.916420 8.901269 8.886028 8.870697 8.855277 8.839770 8.824178 #>  [99,] 8.929713 8.914721 8.899642 8.884475 8.869223 8.853885 8.838465 8.822963 #> [100,] 8.927961 8.913038 8.898030 8.882938 8.867763 8.852508 8.837173 8.821760 #>           [,33]    [,34]    [,35]    [,36]    [,37]    [,38]    [,39]    [,40] #>   [1,] 9.146338 9.129345 9.112183 9.094849 9.077342 9.059662 9.041808 9.023782 #>   [2,] 9.140033 9.122925 9.105640 9.088176 9.070532 9.052706 9.034697 9.016506 #>   [3,] 9.133760 9.116536 9.099129 9.081536 9.063754 9.045781 9.027618 9.009262 #>   [4,] 9.127520 9.110181 9.092652 9.074928 9.057009 9.038890 9.020571 9.002049 #>   [5,] 9.121314 9.103860 9.086209 9.068357 9.050300 9.032035 9.013560 8.994873 #>   [6,] 9.115144 9.097576 9.079804 9.061823 9.043629 9.025218 9.006587 8.987734 #>   [7,] 9.109012 9.091331 9.073438 9.055328 9.036998 9.018441 8.999655 8.980635 #>   [8,] 9.102919 9.085125 9.067112 9.048875 9.030409 9.011707 8.992766 8.973580 #>   [9,] 9.096866 9.078961 9.060830 9.042466 9.023864 9.005018 8.985922 8.966572 #>  [10,] 9.090856 9.072841 9.054592 9.036102 9.017366 8.998377 8.979127 8.959612 #>  [11,] 9.084890 9.066765 9.048400 9.029786 9.010917 8.991785 8.972383 8.952704 #>  [12,] 9.078969 9.060737 9.042257 9.023520 9.004519 8.985246 8.965692 8.945850 #>  [13,] 9.073096 9.054758 9.036164 9.017306 8.998175 8.978762 8.959058 8.939055 #>  [14,] 9.067272 9.048829 9.030123 9.011145 8.991886 8.972335 8.952483 8.932320 #>  [15,] 9.061498 9.042952 9.024136 9.005041 8.985655 8.965968 8.945970 8.925649 #>  [16,] 9.055776 9.037129 9.018206 8.998995 8.979485 8.959664 8.939522 8.919045 #>  [17,] 9.050108 9.031363 9.012333 8.993009 8.973377 8.953425 8.933141 8.912511 #>  [18,] 9.044495 9.025653 9.006521 8.987085 8.967334 8.947253 8.926830 8.906049 #>  [19,] 9.038938 9.020003 9.000770 8.981226 8.961358 8.941151 8.920592 8.899664 #>  [20,] 9.033441 9.014414 8.995082 8.975433 8.955451 8.935122 8.914430 8.893358 #>  [21,] 9.028002 9.008887 8.989460 8.969709 8.949616 8.929168 8.908347 8.887135 #>  [22,] 9.022626 9.003424 8.983906 8.964055 8.943855 8.923291 8.902344 8.880996 #>  [23,] 9.017311 8.998028 8.978420 8.958473 8.938170 8.917494 8.896426 8.874946 #>  [24,] 9.012061 8.992698 8.973005 8.952965 8.932563 8.911779 8.890594 8.868986 #>  [25,] 9.006877 8.987437 8.967662 8.947534 8.927036 8.906148 8.884850 8.863121 #>  [26,] 9.001759 8.982246 8.962392 8.942180 8.921590 8.900604 8.879199 8.857351 #>  [27,] 8.996709 8.977127 8.957198 8.936906 8.916229 8.895148 8.873640 8.851682 #>  [28,] 8.991728 8.972081 8.952081 8.931712 8.910953 8.889783 8.868178 8.846113 #>  [29,] 8.986818 8.967108 8.947043 8.926602 8.905765 8.884511 8.862814 8.840650 #>  [30,] 8.981979 8.962211 8.942083 8.921575 8.900666 8.879332 8.857550 8.835292 #>  [31,] 8.977212 8.957391 8.937205 8.916634 8.895657 8.874250 8.852389 8.830044 #>  [32,] 8.972519 8.952647 8.932408 8.911780 8.890740 8.869266 8.847331 8.824906 #>  [33,] 8.967899 8.947983 8.927694 8.907013 8.885917 8.864381 8.842379 8.819881 #>  [34,] 8.963355 8.943397 8.923064 8.902336 8.881188 8.859596 8.837534 8.814970 #>  [35,] 8.958886 8.938892 8.918519 8.897748 8.876555 8.854914 8.832797 8.810175 #>  [36,] 8.954494 8.934467 8.914060 8.893251 8.872018 8.850334 8.828171 8.805498 #>  [37,] 8.950178 8.930123 8.909686 8.888846 8.867579 8.845858 8.823655 8.800939 #>  [38,] 8.945940 8.925861 8.905400 8.884533 8.863237 8.841486 8.819250 8.796499 #>  [39,] 8.941779 8.921682 8.901201 8.880313 8.858995 8.837219 8.814958 8.792180 #>  [40,] 8.937696 8.917585 8.897089 8.876186 8.854851 8.833059 8.810779 8.787981 #>  [41,] 8.933692 8.913571 8.893065 8.872152 8.850807 8.829004 8.806714 8.783904 #>  [42,] 8.929765 8.909640 8.889129 8.868212 8.846862 8.825055 8.802761 8.779949 #>  [43,] 8.925917 8.905792 8.885281 8.864365 8.843017 8.821213 8.798923 8.776115 #>  [44,] 8.922148 8.902026 8.881521 8.860611 8.839272 8.817476 8.795197 8.772402 #>  [45,] 8.918456 8.898343 8.877849 8.856951 8.835625 8.813846 8.791584 8.768810 #>  [46,] 8.914842 8.894743 8.874264 8.853383 8.832077 8.810320 8.788084 8.765338 #>  [47,] 8.911305 8.891225 8.870766 8.849908 8.828628 8.806899 8.784695 8.761985 #>  [48,] 8.907846 8.887788 8.867355 8.846525 8.825276 8.803582 8.781417 8.758751 #>  [49,] 8.904463 8.884433 8.864029 8.843232 8.822020 8.800368 8.778249 8.755634 #>  [50,] 8.901157 8.881157 8.860789 8.840030 8.818860 8.797255 8.775189 8.752633 #>  [51,] 8.897925 8.877962 8.857632 8.836917 8.815796 8.794244 8.772236 8.749746 #>  [52,] 8.894769 8.874845 8.854559 8.833893 8.812824 8.791331 8.769389 8.746971 #>  [53,] 8.891686 8.871806 8.851569 8.830955 8.809945 8.788517 8.766646 8.744307 #>  [54,] 8.888676 8.868844 8.848659 8.828104 8.807157 8.785798 8.764005 8.741752 #>  [55,] 8.885738 8.865958 8.845830 8.825337 8.804458 8.783175 8.761464 8.739302 #>  [56,] 8.882872 8.863147 8.843080 8.822653 8.801847 8.780644 8.759022 8.736958 #>  [57,] 8.880075 8.860409 8.840407 8.820050 8.799323 8.778204 8.756676 8.734714 #>  [58,] 8.877347 8.857744 8.837810 8.817528 8.796882 8.775854 8.754423 8.732570 #>  [59,] 8.874687 8.855150 8.835288 8.815085 8.794525 8.773590 8.752263 8.730523 #>  [60,] 8.872093 8.852626 8.832839 8.812718 8.792247 8.771411 8.750191 8.728570 #>  [61,] 8.869565 8.850170 8.830461 8.810426 8.790049 8.769315 8.748207 8.726708 #>  [62,] 8.867100 8.847780 8.828154 8.808208 8.787928 8.767299 8.746307 8.724934 #>  [63,] 8.864698 8.845456 8.825915 8.806061 8.785881 8.765362 8.744488 8.723246 #>  [64,] 8.862357 8.843196 8.823742 8.803983 8.783907 8.763500 8.742749 8.721641 #>  [65,] 8.860075 8.840998 8.821634 8.801973 8.782003 8.761712 8.741087 8.720115 #>  [66,] 8.857852 8.838861 8.819590 8.800029 8.780168 8.759995 8.739498 8.718667 #>  [67,] 8.855686 8.836782 8.817606 8.798149 8.778399 8.758346 8.737981 8.717292 #>  [68,] 8.853574 8.834761 8.815683 8.796330 8.776693 8.756764 8.736532 8.715988 #>  [69,] 8.851517 8.832796 8.813816 8.794571 8.775050 8.755246 8.735149 8.714752 #>  [70,] 8.849512 8.830884 8.812006 8.792869 8.773466 8.753789 8.733830 8.713581 #>  [71,] 8.847557 8.829025 8.810250 8.791224 8.771940 8.752391 8.732571 8.712472 #>  [72,] 8.845652 8.827217 8.808546 8.789632 8.770468 8.751050 8.731370 8.711423 #>  [73,] 8.843794 8.825458 8.806892 8.788091 8.769050 8.749763 8.730224 8.710430 #>  [74,] 8.841982 8.823746 8.805287 8.786601 8.767683 8.748528 8.729132 8.709490 #>  [75,] 8.840215 8.822079 8.803728 8.785158 8.766364 8.747342 8.728089 8.708602 #>  [76,] 8.838491 8.820457 8.802215 8.783761 8.765092 8.746204 8.727095 8.707761 #>  [77,] 8.836808 8.818876 8.800744 8.782408 8.763864 8.745111 8.726146 8.706967 #>  [78,] 8.835165 8.817337 8.799315 8.781096 8.762679 8.744060 8.725239 8.706215 #>  [79,] 8.833561 8.815836 8.797925 8.779825 8.761534 8.743051 8.724373 8.705503 #>  [80,] 8.831993 8.814373 8.796573 8.778592 8.760428 8.742079 8.723546 8.704829 #>  [81,] 8.830461 8.812946 8.795258 8.777395 8.759357 8.741144 8.722754 8.704191 #>  [82,] 8.828962 8.811553 8.793976 8.776233 8.758322 8.740243 8.721997 8.703586 #>  [83,] 8.827497 8.810192 8.792728 8.775103 8.757318 8.739374 8.721271 8.703011 #>  [84,] 8.826062 8.808863 8.791511 8.774005 8.756346 8.738535 8.720574 8.702465 #>  [85,] 8.824657 8.807564 8.790323 8.772936 8.755403 8.737725 8.719905 8.701946 #>  [86,] 8.823280 8.806292 8.789164 8.771894 8.754486 8.736941 8.719262 8.701451 #>  [87,] 8.821931 8.805048 8.788030 8.770879 8.753596 8.736182 8.718642 8.700979 #>  [88,] 8.820606 8.803829 8.786922 8.769888 8.752729 8.735446 8.718044 8.700526 #>  [89,] 8.819307 8.802634 8.785838 8.768920 8.751884 8.734731 8.717466 8.700093 #>  [90,] 8.818030 8.801461 8.784775 8.767974 8.751060 8.734036 8.716906 8.699676 #>  [91,] 8.816775 8.800311 8.783734 8.767048 8.750255 8.733358 8.716363 8.699275 #>  [92,] 8.815541 8.799180 8.782712 8.766140 8.749467 8.732697 8.715835 8.698886 #>  [93,] 8.814326 8.798068 8.781708 8.765249 8.748696 8.732052 8.715321 8.698510 #>  [94,] 8.813130 8.796973 8.780721 8.764375 8.747940 8.731419 8.714819 8.698144 #>  [95,] 8.811950 8.795895 8.779749 8.763515 8.747197 8.730799 8.714327 8.697786 #>  [96,] 8.810787 8.794833 8.778792 8.762669 8.746466 8.730190 8.713844 8.697437 #>  [97,] 8.809638 8.793784 8.777848 8.761834 8.745747 8.729590 8.713370 8.697093 #>  [98,] 8.808504 8.792749 8.776917 8.761011 8.745037 8.728999 8.712902 8.696754 #>  [99,] 8.807382 8.791725 8.775996 8.760198 8.744336 8.728414 8.712439 8.696418 #> [100,] 8.806273 8.790713 8.775086 8.759394 8.743642 8.727836 8.711981 8.696085 #>           [,41]    [,42]    [,43]    [,44]    [,45]    [,46]    [,47]    [,48] #>   [1,] 9.005583 8.987216 8.968684 8.949993 8.931149 8.912161 8.893041 8.873802 #>   [2,] 8.998134 8.979582 8.960853 8.941952 8.922886 8.903663 8.884293 8.864790 #>   [3,] 8.990714 8.971975 8.953048 8.933936 8.914646 8.895184 8.875560 8.855787 #>   [4,] 8.983325 8.964399 8.945272 8.925947 8.906430 8.886726 8.866844 8.846797 #>   [5,] 8.975972 8.956857 8.937529 8.917989 8.898242 8.878293 8.858151 8.837824 #>   [6,] 8.968656 8.949351 8.929821 8.910065 8.890087 8.869890 8.849483 8.828873 #>   [7,] 8.961380 8.941886 8.922152 8.902178 8.881967 8.861520 8.840845 8.819948 #>   [8,] 8.954147 8.934463 8.914525 8.894333 8.873887 8.853188 8.832242 8.811055 #>   [9,] 8.946961 8.927086 8.906945 8.886533 8.865850 8.844898 8.823678 8.802197 #>  [10,] 8.939824 8.919760 8.899413 8.878782 8.857862 8.836654 8.815159 8.793380 #>  [11,] 8.932740 8.912486 8.891935 8.871084 8.849927 8.828462 8.806689 8.784610 #>  [12,] 8.925711 8.905269 8.884515 8.863443 8.842048 8.820326 8.798275 8.775893 #>  [13,] 8.918742 8.898111 8.877155 8.855864 8.834231 8.812252 8.789920 8.767235 #>  [14,] 8.911835 8.891018 8.869860 8.848350 8.826481 8.804244 8.781632 8.758642 #>  [15,] 8.904993 8.883992 8.862634 8.840908 8.818802 8.796308 8.773417 8.750121 #>  [16,] 8.898221 8.877037 8.855481 8.833540 8.811200 8.788450 8.765280 8.741678 #>  [17,] 8.891521 8.870157 8.848406 8.826251 8.803679 8.780676 8.757227 8.733320 #>  [18,] 8.884897 8.863356 8.841412 8.819047 8.796246 8.772991 8.749266 8.725056 #>  [19,] 8.878352 8.856637 8.834503 8.811932 8.788904 8.765400 8.741403 8.716891 #>  [20,] 8.871889 8.850005 8.827685 8.804910 8.781659 8.757911 8.733644 8.708835 #>  [21,] 8.865513 8.843462 8.820961 8.797987 8.774518 8.750529 8.725996 8.700893 #>  [22,] 8.859226 8.837013 8.814335 8.791167 8.767484 8.743260 8.718467 8.693075 #>  [23,] 8.853032 8.830662 8.807812 8.784455 8.760564 8.736110 8.711063 8.685388 #>  [24,] 8.846934 8.824412 8.801395 8.777856 8.753763 8.729086 8.703790 8.677840 #>  [25,] 8.840934 8.818267 8.795089 8.771373 8.747086 8.722192 8.696657 8.670438 #>  [26,] 8.835037 8.812229 8.788898 8.765012 8.740537 8.715436 8.689668 8.663192 #>  [27,] 8.829246 8.806304 8.782826 8.758777 8.734123 8.708822 8.682833 8.656107 #>  [28,] 8.823562 8.800493 8.776875 8.752673 8.727848 8.702357 8.676155 8.649192 #>  [29,] 8.817989 8.794800 8.771051 8.746703 8.721716 8.696046 8.669643 8.642454 #>  [30,] 8.812529 8.789228 8.765355 8.740871 8.715732 8.689893 8.663302 8.635900 #>  [31,] 8.807185 8.783780 8.759792 8.735181 8.709901 8.683905 8.657137 8.629538 #>  [32,] 8.801960 8.778459 8.754365 8.729636 8.704226 8.678085 8.651155 8.623372 #>  [33,] 8.796855 8.773266 8.749076 8.724240 8.698712 8.672438 8.645360 8.617410 #>  [34,] 8.791872 8.768205 8.743927 8.718996 8.693361 8.666968 8.639757 8.611657 #>  [35,] 8.787014 8.763276 8.738922 8.713906 8.688177 8.661679 8.634350 8.606117 #>  [36,] 8.782281 8.758483 8.734062 8.708972 8.683162 8.656574 8.629143 8.600796 #>  [37,] 8.777675 8.753826 8.729349 8.704197 8.678319 8.651655 8.624139 8.595697 #>  [38,] 8.773197 8.749306 8.724784 8.699583 8.673649 8.646924 8.619341 8.590823 #>  [39,] 8.768849 8.744926 8.720369 8.695130 8.669155 8.642385 8.614751 8.586177 #>  [40,] 8.764630 8.740685 8.716104 8.690840 8.664838 8.638037 8.610371 8.581761 #>  [41,] 8.760541 8.736584 8.711991 8.686713 8.660697 8.633882 8.606201 8.577575 #>  [42,] 8.756582 8.732623 8.708029 8.682750 8.656734 8.629921 8.602242 8.573620 #>  [43,] 8.752754 8.728803 8.704217 8.678950 8.652949 8.626152 8.598493 8.569896 #>  [44,] 8.749056 8.725122 8.700557 8.675314 8.649340 8.622576 8.594955 8.566402 #>  [45,] 8.745488 8.721581 8.697047 8.671840 8.645907 8.619190 8.591625 8.563137 #>  [46,] 8.742048 8.718178 8.693686 8.668526 8.642648 8.615994 8.588501 8.560096 #>  [47,] 8.738737 8.714913 8.690473 8.665372 8.639562 8.612985 8.585581 8.557279 #>  [48,] 8.735552 8.711783 8.687406 8.662376 8.636646 8.610161 8.582862 8.554680 #>  [49,] 8.732492 8.708788 8.684483 8.659536 8.633898 8.607519 8.580340 8.552296 #>  [50,] 8.729556 8.705925 8.681703 8.656848 8.631315 8.605055 8.578011 8.550121 #>  [51,] 8.726742 8.703193 8.679062 8.654310 8.628894 8.602765 8.575870 8.548151 #>  [52,] 8.724048 8.700589 8.676559 8.651920 8.626631 8.600645 8.573913 8.546380 #>  [53,] 8.721472 8.698111 8.674190 8.649674 8.624522 8.598691 8.572135 8.544801 #>  [54,] 8.719012 8.695756 8.671953 8.647567 8.622563 8.596899 8.570530 8.543408 #>  [55,] 8.716664 8.693521 8.669843 8.645598 8.620750 8.595262 8.569091 8.542194 #>  [56,] 8.714427 8.691403 8.667858 8.643761 8.619079 8.593776 8.567814 8.541151 #>  [57,] 8.712298 8.689400 8.665995 8.642053 8.617544 8.592435 8.566691 8.540274 #>  [58,] 8.710273 8.687508 8.664249 8.640470 8.616142 8.591235 8.565716 8.539553 #>  [59,] 8.708351 8.685723 8.662616 8.639006 8.614866 8.590168 8.564883 8.538982 #>  [60,] 8.706527 8.684042 8.661094 8.637658 8.613712 8.589230 8.564186 8.538552 #>  [61,] 8.704800 8.682463 8.659677 8.636422 8.612675 8.588414 8.563616 8.538257 #>  [62,] 8.703165 8.680980 8.658362 8.635292 8.611750 8.587715 8.563169 8.538089 #>  [63,] 8.701619 8.679591 8.657146 8.634265 8.610931 8.587127 8.562836 8.538040 #>  [64,] 8.700160 8.678293 8.656023 8.633335 8.610214 8.586645 8.562612 8.538103 #>  [65,] 8.698784 8.677080 8.654989 8.632498 8.609593 8.586261 8.562490 8.538270 #>  [66,] 8.697488 8.675950 8.654041 8.631749 8.609063 8.585971 8.562464 8.538534 #>  [67,] 8.696268 8.674900 8.653175 8.631085 8.608619 8.585769 8.562527 8.538888 #>  [68,] 8.695122 8.673924 8.652387 8.630500 8.608256 8.585649 8.562674 8.539326 #>  [69,] 8.694045 8.673021 8.651672 8.629990 8.607970 8.585607 8.562898 8.539841 #>  [70,] 8.693035 8.672186 8.651026 8.629551 8.607755 8.585636 8.563193 8.540427 #>  [71,] 8.692089 8.671416 8.650447 8.629178 8.607607 8.585732 8.563554 8.541076 #>  [72,] 8.691203 8.670707 8.649929 8.628868 8.607521 8.585890 8.563976 8.541784 #>  [73,] 8.690375 8.670056 8.649470 8.628616 8.607493 8.586104 8.564453 8.542545 #>  [74,] 8.689600 8.669459 8.649065 8.628418 8.607519 8.586371 8.564980 8.543353 #>  [75,] 8.688877 8.668914 8.648712 8.628271 8.607594 8.586686 8.565553 8.544204 #>  [76,] 8.688202 8.668417 8.648406 8.628171 8.607715 8.587044 8.566166 8.545091 #>  [77,] 8.687573 8.667965 8.648145 8.628114 8.607877 8.587441 8.566816 8.546011 #>  [78,] 8.686986 8.667555 8.647924 8.628096 8.608077 8.587874 8.567497 8.546959 #>  [79,] 8.686439 8.667185 8.647742 8.628115 8.608311 8.588338 8.568207 8.547931 #>  [80,] 8.685930 8.666850 8.647594 8.628167 8.608577 8.588831 8.568941 8.548923 #>  [81,] 8.685455 8.666549 8.647479 8.628250 8.608869 8.589347 8.569696 8.549931 #>  [82,] 8.685012 8.666279 8.647393 8.628359 8.609186 8.589885 8.570468 8.550951 #>  [83,] 8.684599 8.666037 8.647333 8.628492 8.609525 8.590441 8.571255 8.551981 #>  [84,] 8.684213 8.665821 8.647297 8.628647 8.609882 8.591012 8.572052 8.553017 #>  [85,] 8.683852 8.665629 8.647282 8.628821 8.610255 8.591595 8.572857 8.554056 #>  [86,] 8.683514 8.665457 8.647286 8.629011 8.610641 8.592188 8.573667 8.555095 #>  [87,] 8.683197 8.665304 8.647307 8.629215 8.611038 8.592788 8.574481 8.556133 #>  [88,] 8.682899 8.665169 8.647343 8.629430 8.611443 8.593393 8.575295 8.557165 #>  [89,] 8.682618 8.665048 8.647391 8.629656 8.611854 8.594000 8.576106 8.558191 #>  [90,] 8.682352 8.664940 8.647449 8.629888 8.612270 8.594607 8.576914 8.559208 #>  [91,] 8.682099 8.664843 8.647515 8.630127 8.612688 8.595213 8.577716 8.560215 #>  [92,] 8.681857 8.664755 8.647589 8.630369 8.613107 8.595816 8.578511 8.561208 #>  [93,] 8.681625 8.664675 8.647667 8.630613 8.613524 8.596413 8.579295 8.562188 #>  [94,] 8.681402 8.664600 8.647748 8.630857 8.613937 8.597003 8.580069 8.563151 #>  [95,] 8.681185 8.664530 8.647832 8.631100 8.614347 8.597585 8.580830 8.564098 #>  [96,] 8.680973 8.664463 8.647915 8.631340 8.614750 8.598157 8.581577 8.565026 #>  [97,] 8.680766 8.664398 8.647998 8.631577 8.615146 8.598718 8.582309 8.565934 #>  [98,] 8.680561 8.664333 8.648078 8.631807 8.615533 8.599267 8.583025 8.566822 #>  [99,] 8.680358 8.664267 8.648154 8.632032 8.615910 8.599802 8.583723 8.567687 #> [100,] 8.680154 8.664198 8.648226 8.632248 8.616276 8.600323 8.584403 8.568530 #>           [,49]    [,50]    [,51]    [,52]    [,53]    [,54]    [,55]    [,56] #>   [1,] 8.854462 8.835042 8.815565 8.796060 8.776562 8.757108 8.737745 8.718523 #>   [2,] 8.845170 8.825452 8.805662 8.785828 8.765984 8.746168 8.726428 8.706816 #>   [3,] 8.835880 8.815860 8.795749 8.775576 8.755374 8.735185 8.715054 8.695035 #>   [4,] 8.826599 8.806268 8.785828 8.765307 8.744738 8.724162 8.703625 8.683183 #>   [5,] 8.817329 8.796681 8.775905 8.755026 8.734079 8.713102 8.692145 8.671263 #>   [6,] 8.808075 8.787105 8.765984 8.744738 8.723401 8.702012 8.680620 8.659280 #>   [7,] 8.798843 8.777543 8.756070 8.734448 8.712710 8.690896 8.669052 8.647237 #>   [8,] 8.789636 8.768001 8.746168 8.724162 8.702012 8.679759 8.657449 8.635140 #>   [9,] 8.780462 8.758486 8.736286 8.713885 8.691313 8.668607 8.645815 8.622994 #>  [10,] 8.771324 8.749002 8.726428 8.703625 8.680620 8.657449 8.634158 8.610806 #>  [11,] 8.762230 8.739556 8.716602 8.693388 8.669939 8.646290 8.622485 8.598582 #>  [12,] 8.753185 8.730155 8.706816 8.683183 8.659280 8.635140 8.610806 8.586332 #>  [13,] 8.744196 8.720807 8.697076 8.673017 8.648651 8.624008 8.599128 8.574064 #>  [14,] 8.735270 8.711518 8.687391 8.662899 8.638061 8.612903 8.587462 8.561790 #>  [15,] 8.726414 8.702297 8.677769 8.652839 8.627520 8.601836 8.575820 8.549520 #>  [16,] 8.717637 8.693151 8.668220 8.642846 8.617040 8.590819 8.564214 8.537267 #>  [17,] 8.708944 8.684091 8.658753 8.632932 8.606631 8.579864 8.552656 8.525046 #>  [18,] 8.700346 8.675123 8.649379 8.623106 8.596306 8.568985 8.541163 8.512872 #>  [19,] 8.691849 8.666259 8.640106 8.613381 8.586077 8.558196 8.529749 8.500762 #>  [20,] 8.683463 8.657507 8.630947 8.603769 8.575959 8.547512 8.518431 8.488734 #>  [21,] 8.675195 8.648877 8.621913 8.594282 8.565965 8.536949 8.507228 8.476810 #>  [22,] 8.667056 8.640379 8.613015 8.584934 8.556111 8.526524 8.496158 8.465010 #>  [23,] 8.659054 8.632024 8.604264 8.575738 8.546412 8.516255 8.485242 8.453357 #>  [24,] 8.651197 8.623822 8.595673 8.566708 8.536884 8.506161 8.474502 8.441877 #>  [25,] 8.643496 8.615784 8.587254 8.557858 8.527544 8.496261 8.463960 8.430596 #>  [26,] 8.635958 8.607919 8.579019 8.549202 8.518408 8.486574 8.453639 8.419540 #>  [27,] 8.628594 8.600239 8.570981 8.540756 8.509494 8.477122 8.443563 8.408739 #>  [28,] 8.621411 8.592753 8.563151 8.532532 8.500818 8.467924 8.433757 8.398223 #>  [29,] 8.614419 8.585473 8.555542 8.524547 8.492398 8.459000 8.424246 8.388021 #>  [30,] 8.607626 8.578407 8.548165 8.516812 8.484251 8.450372 8.415055 8.378165 #>  [31,] 8.601039 8.571565 8.541031 8.509343 8.476393 8.442060 8.406208 8.368684 #>  [32,] 8.594666 8.564956 8.534152 8.502152 8.468840 8.434083 8.397730 8.359610 #>  [33,] 8.588515 8.558589 8.527538 8.495252 8.461607 8.426459 8.389644 8.350971 #>  [34,] 8.582591 8.552472 8.521197 8.488654 8.454708 8.419207 8.381973 8.342796 #>  [35,] 8.576902 8.546610 8.515139 8.482368 8.448156 8.412342 8.374735 8.335111 #>  [36,] 8.571451 8.541012 8.509372 8.476404 8.441963 8.405879 8.367951 8.327939 #>  [37,] 8.566244 8.535682 8.503901 8.470770 8.436139 8.399831 8.361636 8.321302 #>  [38,] 8.561284 8.530626 8.498733 8.465473 8.430693 8.394209 8.355804 8.315218 #>  [39,] 8.556575 8.525845 8.493871 8.460519 8.425631 8.389020 8.350466 8.309700 #>  [40,] 8.552119 8.521344 8.489320 8.455911 8.420958 8.384272 8.345629 8.304758 #>  [41,] 8.547916 8.517124 8.485081 8.451651 8.416676 8.379967 8.341298 8.300398 #>  [42,] 8.543968 8.513185 8.481154 8.447741 8.412787 8.376106 8.337473 8.296621 #>  [43,] 8.540274 8.509527 8.477539 8.444179 8.409290 8.372688 8.334154 8.293425 #>  [44,] 8.536833 8.506147 8.474234 8.440963 8.406180 8.369708 8.331333 8.290802 #>  [45,] 8.533642 8.503045 8.471236 8.438088 8.403454 8.367160 8.329003 8.288740 #>  [46,] 8.530699 8.500215 8.468540 8.435550 8.401103 8.365035 8.327152 8.287224 #>  [47,] 8.528000 8.497654 8.466140 8.433340 8.399120 8.363322 8.325765 8.286235 #>  [48,] 8.525540 8.495356 8.464030 8.431452 8.397493 8.362008 8.324826 8.285752 #>  [49,] 8.523315 8.493314 8.462203 8.429875 8.396212 8.361077 8.324316 8.285750 #>  [50,] 8.521318 8.491523 8.460649 8.428599 8.395262 8.360514 8.324214 8.286202 #>  [51,] 8.519543 8.489973 8.459359 8.427612 8.394630 8.360301 8.324498 8.287081 #>  [52,] 8.517984 8.488656 8.458324 8.426902 8.394301 8.360418 8.325144 8.288357 #>  [53,] 8.516632 8.487565 8.457532 8.426457 8.394259 8.360848 8.326129 8.290000 #>  [54,] 8.515480 8.486689 8.456973 8.426263 8.394488 8.361571 8.327429 8.291981 #>  [55,] 8.514520 8.486020 8.456635 8.426307 8.394972 8.362565 8.329019 8.294269 #>  [56,] 8.513744 8.485546 8.456506 8.426574 8.395693 8.363812 8.330875 8.296834 #>  [57,] 8.513143 8.485258 8.456576 8.427050 8.396636 8.365290 8.332973 8.299649 #>  [58,] 8.512709 8.485147 8.456830 8.427721 8.397783 8.366982 8.335290 8.302687 #>  [59,] 8.512431 8.485201 8.457259 8.428574 8.399118 8.368867 8.337803 8.305919 #>  [60,] 8.512303 8.485411 8.457849 8.429595 8.400626 8.370927 8.340491 8.309322 #>  [61,] 8.512315 8.485766 8.458590 8.430770 8.402290 8.373143 8.343333 8.312872 #>  [62,] 8.512458 8.486257 8.459470 8.432086 8.404096 8.375500 8.346309 8.316547 #>  [63,] 8.512724 8.486874 8.460478 8.433530 8.406029 8.377981 8.349402 8.320326 #>  [64,] 8.513104 8.487606 8.461603 8.435091 8.408076 8.380569 8.352595 8.324190 #>  [65,] 8.513590 8.488446 8.462834 8.436757 8.410224 8.383251 8.355870 8.328122 #>  [66,] 8.514175 8.489384 8.464162 8.438516 8.412459 8.386014 8.359213 8.332105 #>  [67,] 8.514850 8.490411 8.465577 8.440358 8.414771 8.388843 8.362610 8.336125 #>  [68,] 8.515607 8.491519 8.467070 8.442273 8.417148 8.391727 8.366049 8.340168 #>  [69,] 8.516440 8.492700 8.468631 8.444250 8.419581 8.394655 8.369517 8.344223 #>  [70,] 8.517342 8.493946 8.470253 8.446282 8.422058 8.397617 8.373004 8.348277 #>  [71,] 8.518305 8.495251 8.471928 8.448360 8.424572 8.400603 8.376500 8.352322 #>  [72,] 8.519324 8.496606 8.473649 8.450475 8.427114 8.403605 8.379997 8.356349 #>  [73,] 8.520391 8.498006 8.475407 8.452620 8.429676 8.406615 8.383486 8.360349 #>  [74,] 8.521503 8.499444 8.477197 8.454789 8.432251 8.409625 8.386960 8.364315 #>  [75,] 8.522652 8.500915 8.479013 8.456975 8.434833 8.412629 8.390412 8.368242 #>  [76,] 8.523834 8.502412 8.480849 8.459171 8.437415 8.415620 8.393837 8.372124 #>  [77,] 8.525043 8.503931 8.482698 8.461374 8.439992 8.418594 8.397229 8.375955 #>  [78,] 8.526276 8.505467 8.484558 8.463576 8.442558 8.421545 8.400584 8.379733 #>  [79,] 8.527527 8.507016 8.486422 8.465775 8.445110 8.424468 8.403898 8.383453 #>  [80,] 8.528793 8.508572 8.488286 8.467965 8.447643 8.427361 8.407166 8.387112 #>  [81,] 8.530069 8.510133 8.490147 8.470142 8.450152 8.430218 8.410386 8.390707 #>  [82,] 8.531353 8.511694 8.492001 8.472303 8.452636 8.433038 8.413555 8.394237 #>  [83,] 8.532640 8.513252 8.493844 8.474445 8.455090 8.435817 8.416670 8.397699 #>  [84,] 8.533927 8.514804 8.495673 8.476565 8.457512 8.438553 8.419730 8.401092 #>  [85,] 8.535212 8.516347 8.497486 8.478659 8.459899 8.441243 8.422733 8.404414 #>  [86,] 8.536492 8.517878 8.499280 8.480726 8.462250 8.443886 8.425677 8.407665 #>  [87,] 8.537763 8.519395 8.501052 8.482763 8.464561 8.446480 8.428560 8.410843 #>  [88,] 8.539025 8.520895 8.502800 8.484769 8.466832 8.449024 8.431383 8.413949 #>  [89,] 8.540274 8.522376 8.504523 8.486741 8.469061 8.451516 8.434143 8.416982 #>  [90,] 8.541509 8.523837 8.506218 8.488678 8.471246 8.453955 8.436841 8.419942 #>  [91,] 8.542728 8.525276 8.507884 8.490578 8.473386 8.456341 8.439476 8.422828 #>  [92,] 8.543928 8.526691 8.509520 8.492440 8.475481 8.458673 8.442048 8.425642 #>  [93,] 8.545109 8.528080 8.511123 8.494264 8.477529 8.460949 8.444556 8.428382 #>  [94,] 8.546269 8.529443 8.512694 8.496048 8.479531 8.463171 8.447000 8.431050 #>  [95,] 8.547407 8.530777 8.514231 8.497791 8.481484 8.465337 8.449381 8.433646 #>  [96,] 8.548521 8.532083 8.515732 8.499492 8.483389 8.467448 8.451698 8.436170 #>  [97,] 8.549611 8.533359 8.517198 8.501152 8.485245 8.469503 8.453953 8.438624 #>  [98,] 8.550675 8.534603 8.518628 8.502769 8.487053 8.471502 8.456144 8.441007 #>  [99,] 8.551712 8.535817 8.520020 8.504344 8.488811 8.473445 8.458273 8.443320 #> [100,] 8.552723 8.536998 8.521375 8.505875 8.490520 8.475333 8.460340 8.445564 #>           [,57]    [,58]    [,59]    [,60]    [,61]    [,62]    [,63]    [,64] #>   [1,] 8.699501 8.680741 8.662317 8.644304 8.626785 8.609847 8.593580 8.578075 #>   [2,] 8.687391 8.668220 8.649379 8.630947 8.613015 8.595673 8.579019 8.563151 #>   [3,] 8.675190 8.655588 8.636308 8.617436 8.599065 8.581295 8.564229 8.547974 #>   [4,] 8.662899 8.642846 8.623106 8.603769 8.584934 8.566708 8.549202 8.532532 #>   [5,] 8.650522 8.629996 8.609771 8.589943 8.570617 8.551906 8.533931 8.516817 #>   [6,] 8.638061 8.617040 8.596306 8.575959 8.556111 8.536884 8.518408 8.500818 #>   [7,] 8.625520 8.603980 8.582709 8.561815 8.541414 8.521637 8.502625 8.484524 #>   [8,] 8.612903 8.590819 8.568985 8.547512 8.526524 8.506161 8.486574 8.467924 #>   [9,] 8.600215 8.577562 8.555135 8.533050 8.511439 8.490451 8.470248 8.451005 #>  [10,] 8.587462 8.564214 8.541163 8.518431 8.496158 8.474502 8.453639 8.433757 #>  [11,] 8.574651 8.550780 8.527073 8.503658 8.480681 8.458312 8.436738 8.416167 #>  [12,] 8.561790 8.537267 8.512872 8.488734 8.465010 8.441877 8.419540 8.398223 #>  [13,] 8.548887 8.523684 8.498565 8.473665 8.449145 8.425196 8.402038 8.379912 #>  [14,] 8.535953 8.510040 8.484161 8.458455 8.433091 8.408269 8.384225 8.361223 #>  [15,] 8.523000 8.496347 8.469671 8.443115 8.416852 8.391095 8.366096 8.342143 #>  [16,] 8.510040 8.482616 8.455106 8.427653 8.400436 8.373679 8.347650 8.322661 #>  [17,] 8.497088 8.468864 8.440481 8.412082 8.383852 8.356024 8.328882 8.302768 #>  [18,] 8.484161 8.455106 8.425811 8.396417 8.367112 8.338137 8.309796 8.282453 #>  [19,] 8.471277 8.441362 8.411116 8.380676 8.350232 8.320031 8.290393 8.261710 #>  [20,] 8.458455 8.427653 8.396417 8.364881 8.333231 8.301720 8.270680 8.240535 #>  [21,] 8.445719 8.414002 8.381740 8.349056 8.316132 8.283223 8.250671 8.218928 #>  [22,] 8.433091 8.400436 8.367112 8.333231 8.298965 8.264564 8.230382 8.196894 #>  [23,] 8.420598 8.386984 8.352566 8.317439 8.281762 8.245776 8.209838 8.174443 #>  [24,] 8.408269 8.373679 8.338137 8.301720 8.264564 8.226898 8.189071 8.151595 #>  [25,] 8.396134 8.360555 8.323866 8.286117 8.247419 8.207977 8.168125 8.128381 #>  [26,] 8.384225 8.347650 8.309796 8.270680 8.230382 8.189071 8.147056 8.104845 #>  [27,] 8.372576 8.335004 8.295974 8.255466 8.213516 8.170250 8.125934 8.081049 #>  [28,] 8.361223 8.322661 8.282453 8.240535 8.196894 8.151595 8.104845 8.057075 #>  [29,] 8.350203 8.310667 8.269288 8.225955 8.180595 8.133201 8.083897 8.033032 #>  [30,] 8.339555 8.299067 8.256537 8.211800 8.164711 8.115177 8.063216 8.009059 #>  [31,] 8.329315 8.287911 8.244262 8.198146 8.149340 8.097648 8.042956 7.985332 #>  [32,] 8.319524 8.277247 8.232525 8.185074 8.134586 8.080749 8.023289 7.962066 #>  [33,] 8.310217 8.267123 8.221390 8.172669 8.120562 8.064630 8.004415 7.939520 #>  [34,] 8.301431 8.257587 8.210919 8.161013 8.107381 8.049447 7.986553 7.917996 #>  [35,] 8.293201 8.248684 8.201171 8.150190 8.095159 8.035364 7.969936 7.897833 #>  [36,] 8.285557 8.240454 8.192204 8.140277 8.084005 8.022542 7.954804 7.879400 #>  [37,] 8.278526 8.232935 8.184068 8.131344 8.074022 8.011133 7.941395 7.863073 #>  [38,] 8.272133 8.226159 8.176806 8.123455 8.065300 8.001274 7.929925 7.849215 #>  [39,] 8.266396 8.220149 8.170454 8.116659 8.057914 7.993080 7.920578 7.838143 #>  [40,] 8.261327 8.214926 8.165035 8.110990 8.051916 7.986633 7.913491 7.830097 #>  [41,] 8.256935 8.210497 8.160565 8.106471 8.047337 7.981979 7.908742 7.825215 #>  [42,] 8.253221 8.206866 8.157045 8.103103 8.044181 7.979126 7.906339 7.823515 #>  [43,] 8.250181 8.204027 8.154468 8.100874 8.042428 7.978041 7.906228 7.824892 #>  [44,] 8.247805 8.201965 8.152812 8.099755 8.042033 7.978654 7.908291 7.829136 #>  [45,] 8.246077 8.200659 8.152049 8.099702 8.042932 7.980861 7.912358 7.835950 #>  [46,] 8.244977 8.200081 8.152138 8.100658 8.045039 7.984534 7.918222 7.844985 #>  [47,] 8.244479 8.200198 8.153034 8.102558 8.048258 7.989526 7.925654 7.855869 #>  [48,] 8.244556 8.200970 8.154681 8.105326 8.052483 7.995680 7.934418 7.868233 #>  [49,] 8.245174 8.202355 8.157024 8.108882 8.057600 8.002836 7.944278 7.881733 #>  [50,] 8.246300 8.204307 8.160002 8.113146 8.063498 8.010836 7.955013 7.896058 #>  [51,] 8.247898 8.206780 8.163551 8.118034 8.070065 8.019530 7.966421 7.910941 #>  [52,] 8.249929 8.209725 8.167612 8.123465 8.077196 8.028780 7.978322 7.926155 #>  [53,] 8.252357 8.213096 8.172122 8.129362 8.084790 8.038458 7.990559 7.941516 #>  [54,] 8.255144 8.216845 8.177023 8.135652 8.092756 8.048452 8.002999 7.956876 #>  [55,] 8.258254 8.220926 8.182260 8.142264 8.101011 8.058664 8.015529 7.972117 #>  [56,] 8.261650 8.225298 8.187779 8.149138 8.109480 8.069008 8.028057 7.987151 #>  [57,] 8.265299 8.229918 8.193533 8.156214 8.118098 8.079412 8.040508 8.001909 #>  [58,] 8.269167 8.234748 8.199475 8.163443 8.126808 8.089814 8.052822 8.016342 #>  [59,] 8.273225 8.239753 8.205567 8.170778 8.135558 8.100163 8.064952 8.030415 #>  [60,] 8.277443 8.244899 8.211769 8.178178 8.144308 8.110418 8.076862 8.044105 #>  [61,] 8.281794 8.250157 8.218050 8.185608 8.153020 8.120544 8.088524 8.057397 #>  [62,] 8.286254 8.255499 8.224380 8.193038 8.161664 8.130515 8.099918 8.070284 #>  [63,] 8.290800 8.260901 8.230733 8.200440 8.170216 8.140308 8.111030 8.082763 #>  [64,] 8.295411 8.266340 8.237084 8.207792 8.178653 8.149907 8.121850 8.094836 #>  [65,] 8.300069 8.271796 8.243416 8.215075 8.186959 8.159298 8.132373 8.106510 #>  [66,] 8.304755 8.277252 8.249709 8.222271 8.195120 8.168474 8.142597 8.117790 #>  [67,] 8.309456 8.282693 8.255949 8.229369 8.203125 8.177428 8.152523 8.128687 #>  [68,] 8.314156 8.288104 8.262124 8.236355 8.210967 8.186156 8.162151 8.139209 #>  [69,] 8.318845 8.293473 8.268221 8.243222 8.218638 8.194655 8.171487 8.149369 #>  [70,] 8.323510 8.298791 8.274232 8.249962 8.226134 8.202926 8.180535 8.159177 #>  [71,] 8.328142 8.304048 8.280149 8.256568 8.233453 8.210969 8.189300 8.168645 #>  [72,] 8.332733 8.309237 8.285965 8.263037 8.240592 8.218786 8.197789 8.177785 #>  [73,] 8.337275 8.314350 8.291675 8.269365 8.247551 8.226379 8.206009 8.186607 #>  [74,] 8.341762 8.319383 8.297276 8.275550 8.254330 8.233753 8.213966 8.195124 #>  [75,] 8.346188 8.324330 8.302763 8.281590 8.260930 8.240911 8.221668 8.203346 #>  [76,] 8.350548 8.329188 8.308134 8.287485 8.267353 8.247856 8.229123 8.211284 #>  [77,] 8.354838 8.333954 8.313388 8.293235 8.273600 8.254595 8.236337 8.218949 #>  [78,] 8.359055 8.338625 8.318523 8.298840 8.279674 8.261130 8.243318 8.226351 #>  [79,] 8.363196 8.343199 8.323538 8.304300 8.285577 8.267467 8.250073 8.233498 #>  [80,] 8.367259 8.347675 8.328434 8.309617 8.291313 8.273612 8.256609 8.240402 #>  [81,] 8.371241 8.352051 8.333209 8.314793 8.296884 8.279568 8.262934 8.247070 #>  [82,] 8.375140 8.356327 8.337866 8.319829 8.302294 8.285341 8.269052 8.253511 #>  [83,] 8.378957 8.360504 8.342404 8.324727 8.307546 8.290935 8.274972 8.259733 #>  [84,] 8.382689 8.364579 8.346825 8.329490 8.312643 8.296356 8.280699 8.265745 #>  [85,] 8.386336 8.368555 8.351129 8.334118 8.317589 8.301608 8.286240 8.271553 #>  [86,] 8.389899 8.372431 8.355318 8.338616 8.322388 8.306696 8.291601 8.277165 #>  [87,] 8.393376 8.376208 8.359393 8.342985 8.327043 8.311624 8.296786 8.282588 #>  [88,] 8.396768 8.379887 8.363356 8.347228 8.331556 8.316396 8.301803 8.287828 #>  [89,] 8.400075 8.383468 8.367209 8.351347 8.335933 8.321018 8.306655 8.292892 #>  [90,] 8.403298 8.386953 8.370953 8.355344 8.340175 8.325494 8.311348 8.297785 #>  [91,] 8.406437 8.390343 8.374590 8.359223 8.344286 8.329826 8.315888 8.302514 #>  [92,] 8.409492 8.393639 8.378122 8.362985 8.348270 8.334020 8.320278 8.307083 #>  [93,] 8.412465 8.396841 8.381551 8.366634 8.352130 8.338080 8.324523 8.311498 #>  [94,] 8.415356 8.399953 8.384878 8.370171 8.355868 8.342008 8.328628 8.315764 #>  [95,] 8.418166 8.402974 8.388106 8.373599 8.359487 8.345808 8.332597 8.319886 #>  [96,] 8.420895 8.405906 8.391236 8.376920 8.362992 8.349485 8.336433 8.323868 #>  [97,] 8.423546 8.408751 8.394271 8.380137 8.366384 8.353041 8.340142 8.327714 #>  [98,] 8.426119 8.411510 8.397211 8.383253 8.369666 8.356480 8.343726 8.331430 #>  [99,] 8.428614 8.414184 8.400060 8.386269 8.372841 8.359805 8.347189 8.335018 #> [100,] 8.431034 8.416776 8.402818 8.389187 8.375912 8.363019 8.350534 8.338483 #>           [,65]    [,66]    [,67]    [,68]    [,69]    [,70]    [,71]    [,72] #>   [1,] 8.563419 8.549697 8.536986 8.525350 8.514841 8.505496 8.497333 8.490352 #>   [2,] 8.548165 8.534152 8.521197 8.509372 8.498733 8.489320 8.481154 8.474234 #>   [3,] 8.532633 8.518309 8.505092 8.493062 8.482283 8.472798 8.464630 8.457777 #>   [4,] 8.516812 8.502152 8.488654 8.476404 8.465473 8.455911 8.447741 8.440963 #>   [5,] 8.500689 8.485668 8.471865 8.459378 8.448284 8.438638 8.430468 8.423771 #>   [6,] 8.484251 8.468840 8.454708 8.441963 8.430693 8.420958 8.412787 8.406180 #>   [7,] 8.467484 8.451651 8.437162 8.424138 8.412677 8.402844 8.394675 8.388168 #>   [8,] 8.450372 8.434083 8.419207 8.405879 8.394209 8.384272 8.376106 8.369708 #>   [9,] 8.432902 8.416116 8.400819 8.387160 8.375262 8.365211 8.357049 8.350773 #>  [10,] 8.415055 8.397730 8.381973 8.367951 8.355804 8.345629 8.337473 8.331333 #>  [11,] 8.396815 8.378903 8.362641 8.348222 8.335802 8.325491 8.317344 8.311355 #>  [12,] 8.378165 8.359610 8.342796 8.327939 8.315218 8.304758 8.296621 8.290802 #>  [13,] 8.359084 8.339826 8.322404 8.307064 8.294010 8.283386 8.275263 8.269633 #>  [14,] 8.339555 8.319524 8.301431 8.285557 8.272133 8.261327 8.253221 8.247805 #>  [15,] 8.319556 8.298674 8.279839 8.263370 8.249535 8.238527 8.230442 8.225267 #>  [16,] 8.299067 8.277247 8.257587 8.240454 8.226159 8.214926 8.206866 8.201965 #>  [17,] 8.278068 8.255209 8.234630 8.216753 8.201940 8.190454 8.182426 8.177836 #>  [18,] 8.256537 8.232525 8.210919 8.192204 8.176806 8.165035 8.157045 8.152812 #>  [19,] 8.234454 8.209160 8.186399 8.166738 8.150676 8.138581 8.130637 8.126815 #>  [20,] 8.211800 8.185074 8.161013 8.140277 8.123455 8.110990 8.103103 8.099755 #>  [21,] 8.188557 8.160229 8.134697 8.112732 8.095038 8.082147 8.074328 8.071533 #>  [22,] 8.164711 8.134586 8.107381 8.084005 8.065300 8.051916 8.044181 8.042033 #>  [23,] 8.140252 8.108105 8.078992 8.053983 8.034101 8.020140 8.012508 8.011124 #>  [24,] 8.115177 8.080749 8.049447 8.022542 8.001274 7.986633 7.979126 7.978654 #>  [25,] 8.089493 8.052485 8.018664 7.989536 7.966625 7.951172 7.943823 7.944445 #>  [26,] 8.063216 8.023289 7.986553 7.954804 7.929925 7.913491 7.906339 7.908291 #>  [27,] 8.036385 7.993147 7.953025 7.918161 7.890898 7.873267 7.866364 7.869950 #>  [28,] 8.009059 7.962066 7.917996 7.879400 7.849215 7.830097 7.823515 7.829136 #>  [29,] 7.981327 7.930081 7.881393 7.838288 7.804475 7.783481 7.777315 7.785511 #>  [30,] 7.953321 7.897269 7.843168 7.794572 7.756186 7.732777 7.727165 7.738673 #>  [31,] 7.925221 7.863768 7.803320 7.747983 7.703743 7.677152 7.672290 7.688149 #>  [32,] 7.897269 7.829797 7.761925 7.698260 7.646386 7.615490 7.611675 7.633381 #>  [33,] 7.869785 7.795689 7.719189 7.645189 7.583171 7.546256 7.543950 7.573734 #>  [34,] 7.843168 7.761925 7.675523 7.588690 7.512923 7.467256 7.467224 7.508527 #>  [35,] 7.817908 7.729162 7.631642 7.528991 7.434232 7.375207 7.378796 7.437146 #>  [36,] 7.794572 7.698260 7.588690 7.466934 7.345569 7.264887 7.274688 7.359351 #>  [37,] 7.773785 7.670273 7.548361 7.404507 7.245858 7.127302 7.148911 7.276038 #>  [38,] 7.756186 7.646386 7.512923 7.345569 7.136467 6.945128 6.992747 7.190930 #>  [39,] 7.742363 7.627790 7.485039 7.296389 7.026917 6.679589 6.797981 7.113505 #>  [40,] 7.732777 7.615490 7.467256 7.264887 6.945128 6.242973 6.594500 7.060921 #>  [41,] 7.727701 7.610095 7.461255 7.257411 6.931812 6.132575 6.561807 7.051089 #>  [42,] 7.727165 7.611675 7.467224 7.274688 6.992747 6.594500 6.740297 7.086248 #>  [43,] 7.730961 7.619744 7.483784 7.311301 7.089872 6.875718 6.932297 7.150456 #>  [44,] 7.738673 7.633381 7.508527 7.359351 7.190930 7.060921 7.086248 7.225430 #>  [45,] 7.749743 7.651430 7.538778 7.412108 7.283501 7.196402 7.208034 7.300143 #>  [46,] 7.763545 7.672697 7.572166 7.465237 7.365162 7.302191 7.306789 7.369946 #>  [47,] 7.779451 7.696099 7.606877 7.516419 7.436693 7.388409 7.388971 7.433519 #>  [48,] 7.796881 7.720733 7.641657 7.564611 7.499578 7.460813 7.458870 7.490931 #>  [49,] 7.815329 7.745900 7.675704 7.609479 7.555248 7.522975 7.519379 7.542736 #>  [50,] 7.834375 7.771081 7.708549 7.651043 7.604914 7.577250 7.572515 7.589601 #>  [51,] 7.853682 7.795911 7.739943 7.689490 7.649554 7.625276 7.619726 7.632165 #>  [52,] 7.872991 7.820144 7.769780 7.725068 7.689953 7.668232 7.662081 7.670993 #>  [53,] 7.892106 7.843625 7.798043 7.758040 7.726739 7.706994 7.700390 7.706568 #>  [54,] 7.910884 7.866261 7.824767 7.788657 7.760420 7.742234 7.735281 7.739301 #>  [55,] 7.929225 7.888006 7.850018 7.817152 7.791408 7.774474 7.767247 7.769537 #>  [56,] 7.947060 7.908846 7.873873 7.843733 7.820043 7.804129 7.796685 7.797568 #>  [57,] 7.964346 7.928785 7.896419 7.868586 7.846607 7.831535 7.823916 7.823641 #>  [58,] 7.981059 7.947845 7.917740 7.891876 7.871336 7.856968 7.849206 7.847968 #>  [59,] 7.997188 7.966055 7.937921 7.913747 7.894427 7.880653 7.872775 7.870728 #>  [60,] 8.012733 7.983448 7.957041 7.934326 7.916051 7.902784 7.894809 7.892076 #>  [61,] 8.027701 8.000062 7.975172 7.953727 7.936353 7.923520 7.915464 7.912146 #>  [62,] 8.042102 8.015935 7.992384 7.972048 7.955456 7.943001 7.934877 7.931054 #>  [63,] 8.055954 8.031104 8.008741 7.989380 7.973471 7.961344 7.953163 7.948904 #>  [64,] 8.069273 8.045606 8.024300 8.005800 7.990491 7.978652 7.970423 7.965783 #>  [65,] 8.082078 8.059477 8.039115 8.021378 8.006599 7.995015 7.986744 7.981771 #>  [66,] 8.094388 8.072750 8.053234 8.036178 8.021869 8.010511 8.002205 7.996938 #>  [67,] 8.106225 8.085457 8.066702 8.050256 8.036366 8.025209 8.016873 8.011347 #>  [68,] 8.117606 8.097630 8.079562 8.063662 8.050147 8.039171 8.030808 8.025052 #>  [69,] 8.128552 8.109295 8.091849 8.076443 8.063265 8.052451 8.044066 8.038104 #>  [70,] 8.139082 8.120481 8.103599 8.088639 8.075766 8.065098 8.056693 8.050547 #>  [71,] 8.149213 8.131212 8.114844 8.100288 8.087691 8.077155 8.068734 8.062422 #>  [72,] 8.158963 8.141512 8.125613 8.111425 8.099078 8.088663 8.080227 8.073766 #>  [73,] 8.168348 8.151403 8.135932 8.122080 8.109961 8.099657 8.091208 8.084612 #>  [74,] 8.177385 8.160904 8.145827 8.132282 8.120371 8.110168 8.101708 8.094990 #>  [75,] 8.186089 8.170036 8.155321 8.142057 8.130338 8.120227 8.111758 8.104928 #>  [76,] 8.194473 8.178817 8.164435 8.151430 8.139886 8.129860 8.121382 8.114451 #>  [77,] 8.202552 8.187262 8.173188 8.160422 8.149039 8.139092 8.130607 8.123583 #>  [78,] 8.210339 8.195389 8.181598 8.169053 8.157819 8.147945 8.139454 8.132345 #>  [79,] 8.217845 8.203211 8.189684 8.177342 8.166247 8.156440 8.147943 8.140756 #>  [80,] 8.225083 8.210742 8.197460 8.185308 8.174340 8.164595 8.156094 8.148835 #>  [81,] 8.232063 8.217996 8.204942 8.192965 8.182116 8.172429 8.163924 8.156599 #>  [82,] 8.238796 8.224984 8.212142 8.200329 8.189590 8.179958 8.171448 8.164063 #>  [83,] 8.245292 8.231719 8.219075 8.207414 8.196778 8.187196 8.178684 8.171241 #>  [84,] 8.251560 8.238210 8.225751 8.214232 8.203692 8.194158 8.185643 8.178148 #>  [85,] 8.257609 8.244468 8.232182 8.220796 8.210346 8.200856 8.192339 8.184795 #>  [86,] 8.263448 8.250503 8.238379 8.227118 8.216751 8.207303 8.198784 8.191195 #>  [87,] 8.269084 8.256323 8.244351 8.233207 8.222919 8.213510 8.204989 8.197358 #>  [88,] 8.274524 8.261937 8.250108 8.239074 8.228860 8.219487 8.210966 8.203295 #>  [89,] 8.279777 8.267353 8.255659 8.244727 8.234583 8.225245 8.216722 8.209015 #>  [90,] 8.284849 8.272579 8.261011 8.250177 8.240098 8.230793 8.222269 8.214528 #>  [91,] 8.289746 8.277621 8.266173 8.255430 8.245413 8.236139 8.227614 8.219841 #>  [92,] 8.294474 8.282487 8.271152 8.260495 8.250537 8.241291 8.232766 8.224963 #>  [93,] 8.299041 8.287183 8.275955 8.265379 8.255476 8.246258 8.237733 8.229901 #>  [94,] 8.303450 8.291715 8.280587 8.270089 8.260238 8.251046 8.242520 8.234662 #>  [95,] 8.307707 8.296089 8.285057 8.274631 8.264829 8.255662 8.247136 8.239253 #>  [96,] 8.311818 8.300310 8.289368 8.279012 8.269257 8.260113 8.251587 8.243680 #>  [97,] 8.315787 8.304384 8.293528 8.283237 8.273526 8.264405 8.255879 8.247950 #>  [98,] 8.319618 8.308315 8.297541 8.287312 8.277643 8.268543 8.260018 8.252067 #>  [99,] 8.323317 8.312109 8.301412 8.291242 8.281613 8.272534 8.264008 8.256038 #> [100,] 8.326888 8.315769 8.305146 8.295033 8.285442 8.276381 8.267856 8.259866 #>           [,73]    [,74]    [,75]    [,76]    [,77]    [,78]    [,79]    [,80] #>   [1,] 8.484534 8.479842 8.476226 8.473621 8.471951 8.471135 8.471085 8.471715 #>   [2,] 8.468540 8.464030 8.460649 8.458324 8.456973 8.456506 8.456830 8.457849 #>   [3,] 8.452217 8.447905 8.444777 8.442755 8.441747 8.441655 8.442377 8.443810 #>   [4,] 8.435550 8.431452 8.428599 8.426902 8.426263 8.426574 8.427721 8.429595 #>   [5,] 8.418518 8.414654 8.412098 8.410755 8.410514 8.411255 8.412858 8.415200 #>   [6,] 8.401103 8.397493 8.395262 8.394301 8.394488 8.395693 8.397783 8.400626 #>   [7,] 8.383283 8.379951 8.378073 8.377527 8.378177 8.379881 8.382492 8.385868 #>   [8,] 8.365035 8.362008 8.360514 8.360418 8.361571 8.363812 8.366982 8.370927 #>   [9,] 8.346334 8.343641 8.342567 8.342963 8.344658 8.347478 8.351249 8.355801 #>  [10,] 8.327152 8.324826 8.324214 8.325144 8.327429 8.330875 8.335290 8.340491 #>  [11,] 8.307460 8.305539 8.305433 8.306947 8.309873 8.313995 8.319103 8.324997 #>  [12,] 8.287224 8.285752 8.286202 8.288357 8.291981 8.296834 8.302687 8.309322 #>  [13,] 8.266409 8.265435 8.266500 8.269357 8.273741 8.279387 8.286041 8.293469 #>  [14,] 8.244977 8.244556 8.246300 8.249929 8.255144 8.261650 8.269167 8.277443 #>  [15,] 8.222883 8.223080 8.225579 8.230058 8.236181 8.243620 8.252068 8.261250 #>  [16,] 8.200081 8.200970 8.204307 8.209725 8.216845 8.225298 8.234748 8.244899 #>  [17,] 8.176519 8.178185 8.182458 8.188915 8.197127 8.206683 8.217214 8.228401 #>  [18,] 8.152138 8.154681 8.160002 8.167612 8.177023 8.187779 8.199475 8.211769 #>  [19,] 8.126875 8.130412 8.136908 8.145799 8.156531 8.168594 8.181546 8.195022 #>  [20,] 8.100658 8.105326 8.113146 8.123465 8.135652 8.149138 8.163443 8.178178 #>  [21,] 8.073409 8.079368 8.088686 8.100599 8.114390 8.129426 8.145188 8.161264 #>  [22,] 8.045039 8.052483 8.063498 8.077196 8.092756 8.109480 8.126808 8.144308 #>  [23,] 8.015450 8.024607 8.037556 8.053253 8.070768 8.089329 8.108336 8.127346 #>  [24,] 7.984534 7.995680 8.010836 8.028780 8.048452 8.069008 8.089814 8.110418 #>  [25,] 7.952169 7.965638 7.983324 8.003792 8.025845 8.048564 8.071290 8.093572 #>  [26,] 7.918222 7.934418 7.955013 7.978322 8.002999 8.028057 8.052822 8.076862 #>  [27,] 7.882546 7.901964 7.925914 7.952419 7.979980 8.007556 8.034480 8.060350 #>  [28,] 7.844985 7.868233 7.896058 7.926155 7.956876 7.987151 8.016342 8.044105 #>  [29,] 7.805373 7.833202 7.865510 7.899632 7.933798 7.966944 7.998501 8.028205 #>  [30,] 7.763545 7.796881 7.834375 7.872991 7.910884 7.947060 7.981059 8.012733 #>  [31,] 7.719354 7.759340 7.802818 7.846416 7.888304 7.927639 7.964132 7.997782 #>  [32,] 7.672697 7.720733 7.771081 7.820144 7.866261 7.908846 7.947845 7.983448 #>  [33,] 7.623571 7.681348 7.739504 7.794477 7.844992 7.890858 7.932334 7.969833 #>  [34,] 7.572166 7.641657 7.708549 7.769780 7.824767 7.873873 7.917740 7.957041 #>  [35,] 7.519015 7.602391 7.678815 7.746482 7.805884 7.858095 7.904207 7.945172 #>  [36,] 7.465237 7.564611 7.651043 7.725068 7.788657 7.843733 7.891876 7.934326 #>  [37,] 7.412866 7.529750 7.626099 7.706054 7.773403 7.830988 7.880879 7.924593 #>  [38,] 7.365162 7.499578 7.604914 7.689953 7.760420 7.820043 7.871336 7.916051 #>  [39,] 7.326624 7.476020 7.588386 7.677227 7.749966 7.811053 7.863341 7.908766 #>  [40,] 7.302191 7.460813 7.577250 7.668232 7.742234 7.804129 7.856968 7.902784 #>  [41,] 7.295446 7.455055 7.571943 7.663174 7.737334 7.799337 7.852254 7.898130 #>  [42,] 7.306789 7.458870 7.572515 7.662081 7.735281 7.796685 7.849206 7.894809 #>  [43,] 7.333222 7.471367 7.578624 7.664793 7.735992 7.796128 7.847797 7.892803 #>  [44,] 7.369946 7.490931 7.589601 7.670993 7.739301 7.797568 7.847968 7.892076 #>  [45,] 7.412288 7.515653 7.604584 7.680246 7.744967 7.800865 7.849631 7.892569 #>  [46,] 7.456713 7.543720 7.622646 7.692053 7.752705 7.805847 7.852677 7.894210 #>  [47,] 7.500954 7.573623 7.642906 7.705899 7.762205 7.812319 7.856978 7.896914 #>  [48,] 7.543720 7.604223 7.664595 7.721295 7.773153 7.820076 7.862398 7.900587 #>  [49,] 7.584369 7.634723 7.687083 7.737799 7.785250 7.828914 7.868795 7.905129 #>  [50,] 7.622646 7.664595 7.709879 7.755031 7.798220 7.838636 7.876030 7.910439 #>  [51,] 7.658514 7.693514 7.732617 7.772676 7.811818 7.849059 7.883966 7.916415 #>  [52,] 7.692053 7.721295 7.755031 7.790483 7.825834 7.860018 7.892475 7.922961 #>  [53,] 7.723397 7.747851 7.776939 7.808252 7.840090 7.871365 7.901442 7.929984 #>  [54,] 7.752705 7.773153 7.798220 7.825834 7.854439 7.882973 7.910758 7.937399 #>  [55,] 7.780136 7.797216 7.818799 7.843116 7.868765 7.894732 7.920331 7.945127 #>  [56,] 7.805847 7.820076 7.838636 7.860018 7.882973 7.906551 7.930076 7.953096 #>  [57,] 7.829983 7.841784 7.857713 7.876483 7.896989 7.918353 7.939924 7.961242 #>  [58,] 7.852677 7.862398 7.876030 7.892475 7.910758 7.930076 7.949812 7.969509 #>  [59,] 7.874049 7.881979 7.893599 7.907972 7.924238 7.941671 7.959688 7.977848 #>  [60,] 7.894210 7.900587 7.910439 7.922961 7.937399 7.953096 7.969509 7.986215 #>  [61,] 7.913258 7.918282 7.926573 7.937441 7.950221 7.964320 7.979239 7.994574 #>  [62,] 7.931279 7.935121 7.942031 7.951415 7.962689 7.975320 7.988848 8.002893 #>  [63,] 7.948355 7.951156 7.956839 7.964890 7.974796 7.986078 7.998313 8.011146 #>  [64,] 7.964557 7.966437 7.971026 7.977878 7.986539 7.996580 8.007614 8.019310 #>  [65,] 7.979947 7.981012 7.984623 7.990392 7.997919 8.006818 8.016737 8.027366 #>  [66,] 7.994586 7.994924 7.997657 8.002447 8.008939 8.016787 8.025669 8.035300 #>  [67,] 8.008524 8.008213 8.010156 8.014058 8.019604 8.026484 8.034404 8.043099 #>  [68,] 8.021809 8.020915 8.022146 8.025241 8.029922 8.035908 8.042933 8.050752 #>  [69,] 8.034485 8.033066 8.033652 8.036013 8.039900 8.045062 8.051255 8.058254 #>  [70,] 8.046590 8.044697 8.044698 8.046388 8.049547 8.053946 8.059365 8.065596 #>  [71,] 8.058160 8.055838 8.055306 8.056384 8.058872 8.062566 8.067265 8.072776 #>  [72,] 8.069228 8.066516 8.065499 8.066014 8.067885 8.070926 8.074953 8.079790 #>  [73,] 8.079823 8.076757 8.075295 8.075294 8.076595 8.079030 8.082432 8.086636 #>  [74,] 8.089973 8.086582 8.084713 8.084238 8.085013 8.086885 8.089703 8.093314 #>  [75,] 8.099703 8.096016 8.093773 8.092860 8.093147 8.094497 8.096769 8.099823 #>  [76,] 8.109036 8.105076 8.102489 8.101172 8.101008 8.101871 8.103632 8.106165 #>  [77,] 8.117993 8.113783 8.110879 8.109188 8.108605 8.109014 8.110298 8.112339 #>  [78,] 8.126594 8.122154 8.118957 8.116920 8.115946 8.115932 8.116769 8.118348 #>  [79,] 8.134857 8.130204 8.126736 8.124378 8.123041 8.122632 8.123049 8.124194 #>  [80,] 8.142800 8.137950 8.134231 8.131573 8.129898 8.129119 8.129143 8.129879 #>  [81,] 8.150437 8.145405 8.141452 8.138517 8.136526 8.135400 8.135055 8.135405 #>  [82,] 8.157784 8.152583 8.148413 8.145218 8.142932 8.141482 8.140789 8.140775 #>  [83,] 8.164855 8.159496 8.155123 8.151686 8.149124 8.147369 8.146350 8.145993 #>  [84,] 8.171660 8.166155 8.161594 8.157931 8.155109 8.153068 8.151741 8.151060 #>  [85,] 8.178214 8.172572 8.167834 8.163959 8.160895 8.158585 8.156968 8.155980 #>  [86,] 8.184526 8.178756 8.173854 8.169780 8.166488 8.163925 8.162033 8.160756 #>  [87,] 8.190608 8.184718 8.179662 8.175401 8.171894 8.169092 8.166943 8.165391 #>  [88,] 8.196468 8.190467 8.185265 8.180830 8.177121 8.174094 8.171700 8.169888 #>  [89,] 8.202117 8.196011 8.190673 8.186072 8.182173 8.178934 8.176309 8.174250 #>  [90,] 8.207562 8.201357 8.195891 8.191136 8.187057 8.183617 8.180773 8.178481 #>  [91,] 8.212812 8.206515 8.200928 8.196027 8.191778 8.188148 8.185097 8.182583 #>  [92,] 8.217875 8.211490 8.205790 8.200750 8.196342 8.192532 8.189284 8.186559 #>  [93,] 8.222757 8.216290 8.210483 8.205312 8.200753 8.196772 8.193338 8.190412 #>  [94,] 8.227466 8.220921 8.215012 8.209719 8.205016 8.200874 8.197262 8.194146 #>  [95,] 8.232007 8.225389 8.219385 8.213975 8.209135 8.204840 8.201060 8.197763 #>  [96,] 8.236388 8.229701 8.223606 8.218085 8.213117 8.208676 8.204735 8.201265 #>  [97,] 8.240613 8.233860 8.227679 8.222054 8.216963 8.212384 8.208291 8.204656 #>  [98,] 8.244688 8.237874 8.231611 8.225886 8.220679 8.215969 8.211730 8.207938 #>  [99,] 8.248619 8.241746 8.235406 8.229586 8.224269 8.219433 8.215056 8.211114 #> [100,] 8.252410 8.245481 8.239068 8.233158 8.227735 8.222780 8.218271 8.214186 #>           [,81]    [,82]    [,83]    [,84]    [,85]    [,86]    [,87]    [,88] #>   [1,] 8.472938 8.474668 8.476827 8.479339 8.482136 8.485156 8.488343 8.491646 #>   [2,] 8.459470 8.461603 8.464162 8.467070 8.470253 8.473649 8.477197 8.480849 #>   [3,] 8.445853 8.448411 8.451392 8.454714 8.458301 8.462087 8.466011 8.470022 #>   [4,] 8.432086 8.435091 8.438516 8.442273 8.446282 8.450475 8.454789 8.459171 #>   [5,] 8.418167 8.421646 8.425538 8.429750 8.434200 8.438815 8.443534 8.448301 #>   [6,] 8.404096 8.408076 8.412459 8.417148 8.422058 8.427114 8.432251 8.437415 #>   [7,] 8.389873 8.394383 8.399283 8.404473 8.409862 8.415376 8.420946 8.426519 #>   [8,] 8.375500 8.380569 8.386014 8.391727 8.397617 8.403605 8.409625 8.415620 #>   [9,] 8.360978 8.366638 8.372655 8.378917 8.385329 8.391810 8.398294 8.404724 #>  [10,] 8.346309 8.352595 8.359213 8.366049 8.373004 8.379997 8.386960 8.393837 #>  [11,] 8.331497 8.338443 8.345694 8.353130 8.360651 8.368174 8.375631 8.382968 #>  [12,] 8.316547 8.324190 8.332105 8.340168 8.348277 8.356349 8.364315 8.372124 #>  [13,] 8.301463 8.309843 8.318455 8.327173 8.335893 8.344531 8.353022 8.361314 #>  [14,] 8.286254 8.295411 8.304755 8.314156 8.323510 8.332733 8.341762 8.350548 #>  [15,] 8.270929 8.280906 8.291017 8.301129 8.311138 8.320964 8.330545 8.339836 #>  [16,] 8.255499 8.266340 8.277252 8.288104 8.298791 8.309237 8.319383 8.329188 #>  [17,] 8.239977 8.251727 8.263477 8.275097 8.286484 8.297566 8.308289 8.318617 #>  [18,] 8.224380 8.237084 8.249709 8.262124 8.274232 8.285965 8.297276 8.308134 #>  [19,] 8.208726 8.222432 8.235967 8.249203 8.262051 8.274450 8.286358 8.297752 #>  [20,] 8.193038 8.207792 8.222271 8.236355 8.249962 8.263037 8.275550 8.287485 #>  [21,] 8.177341 8.193189 8.208647 8.223602 8.237982 8.251745 8.264869 8.277347 #>  [22,] 8.161664 8.178653 8.195120 8.210967 8.226134 8.240592 8.254330 8.267353 #>  [23,] 8.146043 8.164213 8.181718 8.198475 8.214441 8.229599 8.243952 8.257517 #>  [24,] 8.130515 8.149907 8.168474 8.186156 8.202926 8.218786 8.233753 8.247856 #>  [25,] 8.115124 8.135771 8.155422 8.174037 8.191615 8.208175 8.223751 8.238386 #>  [26,] 8.099918 8.121850 8.142597 8.162151 8.180535 8.197789 8.213966 8.229123 #>  [27,] 8.084952 8.108188 8.130040 8.150531 8.169713 8.187651 8.204417 8.220084 #>  [28,] 8.070284 8.094836 8.117790 8.139209 8.159177 8.177785 8.195124 8.211284 #>  [29,] 8.055978 8.081846 8.105892 8.128223 8.148957 8.168214 8.186107 8.202742 #>  [30,] 8.042102 8.069273 8.094388 8.117606 8.139082 8.158963 8.177385 8.194473 #>  [31,] 8.028730 8.057173 8.083326 8.107397 8.129580 8.150055 8.168978 8.186493 #>  [32,] 8.015935 8.045606 8.072750 8.097630 8.120481 8.141512 8.160904 8.178817 #>  [33,] 8.003795 8.034629 8.062704 8.088340 8.111812 8.133358 8.153182 8.171460 #>  [34,] 7.992384 8.024300 8.053234 8.079562 8.103599 8.125613 8.145827 8.164435 #>  [35,] 7.981779 8.014673 8.044379 8.071326 8.095867 8.118296 8.138856 8.157754 #>  [36,] 7.972048 8.005800 8.036178 8.063662 8.088639 8.111425 8.132282 8.151430 #>  [37,] 7.963256 7.997726 8.028665 8.056596 8.081933 8.105014 8.126117 8.145471 #>  [38,] 7.955456 7.990491 8.021869 8.050147 8.075766 8.099078 8.120371 8.139886 #>  [39,] 7.948694 7.984125 8.015812 8.044335 8.070151 8.093625 8.115053 8.134681 #>  [40,] 7.943001 7.978652 8.010511 8.039171 8.065098 8.088663 8.110168 8.129860 #>  [41,] 7.938394 7.974083 8.005974 8.034661 8.060611 8.084197 8.105720 8.125427 #>  [42,] 7.934877 7.970423 8.002205 8.030808 8.056693 8.080227 8.101708 8.121382 #>  [43,] 7.932439 7.967662 7.999197 8.027608 8.053341 8.076752 8.098133 8.117725 #>  [44,] 7.931054 7.965783 7.996938 8.025052 8.050547 8.073766 8.094990 8.114451 #>  [45,] 7.930684 7.964760 7.995410 8.023125 8.048301 8.071262 8.092273 8.111557 #>  [46,] 7.931279 7.964557 7.994586 8.021809 8.046590 8.069228 8.089973 8.109036 #>  [47,] 7.932780 7.965132 7.994436 8.021081 8.045395 8.067651 8.088080 8.106879 #>  [48,] 7.935121 7.966437 7.994924 8.020915 8.044697 8.066516 8.086582 8.105076 #>  [49,] 7.938229 7.968421 7.996012 8.021281 8.044473 8.065805 8.085465 8.103617 #>  [50,] 7.942031 7.971026 7.997657 8.022146 8.044698 8.065499 8.084713 8.102489 #>  [51,] 7.946451 7.974198 7.999817 8.023478 8.045346 8.065575 8.084310 8.101679 #>  [52,] 7.951415 7.977878 8.002447 8.025241 8.046388 8.066014 8.084238 8.101172 #>  [53,] 7.956850 7.982010 8.005502 8.027401 8.047798 8.066791 8.084478 8.100954 #>  [54,] 7.962689 7.986539 8.008939 8.029922 8.049547 8.067885 8.085013 8.101008 #>  [55,] 7.968865 7.991412 8.012714 8.032769 8.051605 8.069271 8.085821 8.101319 #>  [56,] 7.975320 7.996580 8.016787 8.035908 8.053946 8.070926 8.086885 8.101871 #>  [57,] 7.981998 8.001995 8.021118 8.039307 8.056542 8.072828 8.088186 8.102647 #>  [58,] 7.988848 8.007614 8.025669 8.042933 8.059365 8.074953 8.089703 8.103632 #>  [59,] 7.995827 8.013398 8.030408 8.046758 8.062392 8.077281 8.091418 8.104810 #>  [60,] 8.002893 8.019310 8.035300 8.050752 8.065596 8.079790 8.093314 8.106165 #>  [61,] 8.010012 8.025317 8.040317 8.054891 8.068956 8.082460 8.095373 8.107681 #>  [62,] 8.017152 8.031390 8.045432 8.059148 8.072449 8.085272 8.097578 8.109345 #>  [63,] 8.024286 8.037503 8.050620 8.063503 8.076055 8.088207 8.099912 8.111142 #>  [64,] 8.031390 8.043632 8.055858 8.067933 8.079755 8.091249 8.102362 8.113057 #>  [65,] 8.038445 8.049756 8.061127 8.072421 8.083532 8.094382 8.104911 8.115080 #>  [66,] 8.045432 8.055858 8.066409 8.076949 8.087370 8.097590 8.107547 8.117196 #>  [67,] 8.052337 8.061922 8.071688 8.081500 8.091253 8.100860 8.110257 8.119394 #>  [68,] 8.059148 8.067933 8.076949 8.086062 8.095168 8.104179 8.113028 8.121663 #>  [69,] 8.065855 8.073881 8.082180 8.090622 8.099102 8.107535 8.115850 8.123994 #>  [70,] 8.072449 8.079755 8.087370 8.095168 8.103045 8.110916 8.118711 8.126375 #>  [71,] 8.078923 8.085547 8.092509 8.099690 8.106986 8.114314 8.121604 8.128797 #>  [72,] 8.085272 8.091249 8.097590 8.104179 8.110916 8.117719 8.124518 8.131253 #>  [73,] 8.091491 8.096856 8.102605 8.108627 8.114827 8.121123 8.127445 8.133735 #>  [74,] 8.097578 8.102362 8.107547 8.113028 8.118711 8.124518 8.130378 8.136235 #>  [75,] 8.103530 8.107763 8.112412 8.117375 8.122563 8.127896 8.133310 8.138745 #>  [76,] 8.109345 8.113057 8.117196 8.121663 8.126375 8.131253 8.136235 8.141261 #>  [77,] 8.115023 8.118241 8.121894 8.125888 8.130142 8.134583 8.139146 8.143776 #>  [78,] 8.120564 8.123314 8.126503 8.130046 8.133862 8.137880 8.142040 8.146285 #>  [79,] 8.125967 8.128273 8.131022 8.134132 8.137528 8.141141 8.144911 8.148783 #>  [80,] 8.131233 8.133118 8.135448 8.138146 8.141138 8.144361 8.147754 8.151266 #>  [81,] 8.136364 8.137849 8.139780 8.142083 8.144690 8.147536 8.150567 8.153730 #>  [82,] 8.141360 8.142465 8.144016 8.145943 8.148179 8.150665 8.153345 8.156171 #>  [83,] 8.146223 8.146968 8.148157 8.149724 8.151605 8.153743 8.156086 8.158585 #>  [84,] 8.150954 8.151357 8.152201 8.153424 8.154965 8.156770 8.158787 8.160971 #>  [85,] 8.155556 8.155634 8.156149 8.157043 8.158258 8.159742 8.161445 8.163324 #>  [86,] 8.160031 8.159799 8.160000 8.160580 8.161482 8.162658 8.164059 8.165643 #>  [87,] 8.164379 8.163853 8.163756 8.164034 8.164637 8.165516 8.166626 8.167926 #>  [88,] 8.168605 8.167798 8.167416 8.167407 8.167722 8.168316 8.169146 8.170170 #>  [89,] 8.172709 8.171636 8.170981 8.170696 8.170736 8.171056 8.171615 8.172374 #>  [90,] 8.176694 8.175366 8.174452 8.173904 8.173679 8.173736 8.174034 8.174537 #>  [91,] 8.180562 8.178993 8.177829 8.177029 8.176551 8.176355 8.176402 8.176656 #>  [92,] 8.184316 8.182515 8.181115 8.180073 8.179352 8.178912 8.178716 8.178732 #>  [93,] 8.187958 8.185937 8.184309 8.183036 8.182081 8.181407 8.180978 8.180762 #>  [94,] 8.191490 8.189258 8.187413 8.185919 8.184739 8.183839 8.183186 8.182747 #>  [95,] 8.194914 8.192481 8.190429 8.188722 8.187327 8.186210 8.185340 8.184685 #>  [96,] 8.198233 8.195608 8.193357 8.191446 8.189844 8.188518 8.187439 8.186576 #>  [97,] 8.201449 8.198640 8.196198 8.194092 8.192291 8.190764 8.189483 8.188419 #>  [98,] 8.204564 8.201579 8.198955 8.196661 8.194668 8.192948 8.191472 8.190215 #>  [99,] 8.207580 8.204427 8.201627 8.199153 8.196977 8.195070 8.193407 8.191961 #> [100,] 8.210499 8.207185 8.204218 8.201571 8.199217 8.197131 8.195287 8.193660 #>           [,89]    [,90]    [,91]    [,92]    [,93]    [,94]    [,95]    [,96] #>   [1,] 8.495023 8.498436 8.501850 8.505238 8.508575 8.511841 8.515020 8.518095 #>   [2,] 8.484558 8.488286 8.492001 8.495673 8.499280 8.502800 8.506218 8.509520 #>   [3,] 8.474074 8.478128 8.482151 8.486114 8.489995 8.493775 8.497436 8.500967 #>   [4,] 8.463576 8.467965 8.472303 8.476565 8.480726 8.484769 8.488678 8.492440 #>   [5,] 8.453069 8.457801 8.462464 8.467029 8.471476 8.475787 8.479946 8.483944 #>   [6,] 8.442558 8.447643 8.452636 8.457512 8.462250 8.466832 8.471246 8.475481 #>   [7,] 8.432048 8.437494 8.442826 8.448018 8.453051 8.457910 8.462581 8.467056 #>   [8,] 8.421545 8.427361 8.433038 8.438553 8.443886 8.449024 8.453955 8.458673 #>   [9,] 8.411054 8.417249 8.423279 8.429122 8.434760 8.440180 8.445374 8.450335 #>  [10,] 8.400584 8.407166 8.413555 8.419730 8.425677 8.431383 8.436841 8.442048 #>  [11,] 8.390141 8.397118 8.403872 8.410385 8.416643 8.422637 8.428362 8.433815 #>  [12,] 8.379733 8.387112 8.394237 8.401092 8.407665 8.413949 8.419942 8.425642 #>  [13,] 8.369368 8.377156 8.384657 8.391857 8.398748 8.405324 8.411585 8.417532 #>  [14,] 8.359055 8.367259 8.375140 8.382689 8.389899 8.396768 8.403298 8.409492 #>  [15,] 8.348804 8.357429 8.365694 8.373594 8.381124 8.388287 8.395086 8.401526 #>  [16,] 8.338625 8.347675 8.356327 8.364579 8.372431 8.379887 8.386953 8.393639 #>  [17,] 8.328527 8.338006 8.347048 8.355654 8.363827 8.371575 8.378907 8.385836 #>  [18,] 8.318523 8.328434 8.337866 8.346825 8.355318 8.363356 8.370953 8.378122 #>  [19,] 8.308623 8.318967 8.328790 8.338100 8.346912 8.355238 8.363097 8.370504 #>  [20,] 8.298840 8.309617 8.319829 8.329490 8.338616 8.347228 8.355344 8.362985 #>  [21,] 8.289185 8.300395 8.310994 8.321001 8.330439 8.339332 8.347702 8.355572 #>  [22,] 8.279674 8.291313 8.302294 8.312643 8.322388 8.331556 8.340175 8.348270 #>  [23,] 8.270317 8.282381 8.293739 8.304425 8.314471 8.323909 8.332770 8.341084 #>  [24,] 8.261130 8.273612 8.285341 8.296356 8.306696 8.316396 8.325494 8.334020 #>  [25,] 8.252126 8.265017 8.277108 8.288444 8.299070 8.309025 8.318351 8.327083 #>  [26,] 8.243318 8.256609 8.269052 8.280699 8.291601 8.301803 8.311348 8.320278 #>  [27,] 8.234722 8.248400 8.261183 8.273130 8.284297 8.294735 8.304491 8.313609 #>  [28,] 8.226351 8.240402 8.253511 8.265745 8.277165 8.287828 8.297785 8.307083 #>  [29,] 8.218218 8.232626 8.246045 8.258552 8.270213 8.281090 8.291236 8.300703 #>  [30,] 8.210339 8.225083 8.238796 8.251560 8.263448 8.274524 8.284849 8.294474 #>  [31,] 8.202725 8.217785 8.231773 8.244777 8.256876 8.268138 8.278628 8.288401 #>  [32,] 8.195389 8.210742 8.224984 8.238210 8.250503 8.261937 8.272579 8.282487 #>  [33,] 8.188343 8.203964 8.218438 8.231866 8.244335 8.255926 8.266705 8.276736 #>  [34,] 8.181598 8.197460 8.212142 8.225751 8.238379 8.250108 8.261011 8.271152 #>  [35,] 8.175165 8.191239 8.206104 8.219871 8.232638 8.244490 8.255501 8.265737 #>  [36,] 8.169053 8.185308 8.200329 8.214232 8.227118 8.239074 8.250177 8.260495 #>  [37,] 8.163269 8.179673 8.194823 8.208838 8.221821 8.233863 8.245042 8.255428 #>  [38,] 8.157819 8.174340 8.189590 8.203692 8.216751 8.228860 8.240098 8.250537 #>  [39,] 8.152710 8.169313 8.184634 8.198798 8.211911 8.224068 8.235348 8.245824 #>  [40,] 8.147945 8.164595 8.179958 8.194158 8.207303 8.219487 8.230793 8.241291 #>  [41,] 8.143526 8.160189 8.175562 8.189772 8.202927 8.215120 8.226433 8.236938 #>  [42,] 8.139454 8.156094 8.171448 8.185643 8.198784 8.210966 8.222269 8.232766 #>  [43,] 8.135727 8.152310 8.167616 8.181768 8.194874 8.207024 8.218301 8.228775 #>  [44,] 8.132345 8.148835 8.164063 8.178148 8.191195 8.203295 8.214528 8.224963 #>  [45,] 8.129302 8.145667 8.160787 8.174780 8.187747 8.199777 8.210949 8.221330 #>  [46,] 8.126594 8.142800 8.157784 8.171660 8.184526 8.196468 8.207562 8.217875 #>  [47,] 8.124214 8.140230 8.155052 8.168787 8.181531 8.193366 8.204366 8.214595 #>  [48,] 8.122154 8.137950 8.152583 8.166155 8.178756 8.190467 8.201357 8.211490 #>  [49,] 8.120405 8.135953 8.150372 8.163759 8.176199 8.187768 8.198534 8.208556 #>  [50,] 8.118957 8.134231 8.148413 8.161594 8.173854 8.185265 8.195891 8.205790 #>  [51,] 8.117799 8.132774 8.146698 8.159653 8.171716 8.182954 8.193427 8.203189 #>  [52,] 8.116920 8.131573 8.145218 8.157931 8.169780 8.180830 8.191136 8.200750 #>  [53,] 8.116306 8.130618 8.143966 8.156418 8.168040 8.178887 8.189014 8.198469 #>  [54,] 8.115946 8.129898 8.142932 8.155109 8.166488 8.177121 8.187057 8.196342 #>  [55,] 8.115826 8.129402 8.142107 8.153995 8.165119 8.175525 8.185260 8.194364 #>  [56,] 8.115932 8.129119 8.141482 8.153068 8.163925 8.174094 8.183617 8.192532 #>  [57,] 8.116251 8.129037 8.141046 8.152320 8.162899 8.172821 8.182123 8.190840 #>  [58,] 8.116769 8.129143 8.140789 8.151741 8.162033 8.171700 8.180773 8.189284 #>  [59,] 8.117473 8.129428 8.140703 8.151324 8.161322 8.170724 8.179561 8.187858 #>  [60,] 8.118348 8.129879 8.140775 8.151060 8.160756 8.169888 8.178481 8.186559 #>  [61,] 8.119383 8.130484 8.140998 8.150939 8.160328 8.169183 8.177527 8.185380 #>  [62,] 8.120564 8.131233 8.141360 8.150954 8.160031 8.168605 8.176694 8.184316 #>  [63,] 8.121878 8.132115 8.141852 8.151096 8.159857 8.168145 8.175976 8.183363 #>  [64,] 8.123314 8.133118 8.142465 8.151357 8.159799 8.167798 8.175366 8.182515 #>  [65,] 8.124859 8.134232 8.143190 8.151728 8.159849 8.167557 8.174860 8.181768 #>  [66,] 8.126503 8.135448 8.144016 8.152201 8.160000 8.167416 8.174452 8.181115 #>  [67,] 8.128236 8.136756 8.144937 8.152769 8.160246 8.167368 8.174135 8.180552 #>  [68,] 8.130046 8.138146 8.145943 8.153424 8.160580 8.167407 8.173904 8.180073 #>  [69,] 8.131924 8.139609 8.147026 8.154158 8.160994 8.167527 8.173754 8.179675 #>  [70,] 8.133862 8.141138 8.148179 8.154965 8.161482 8.167722 8.173679 8.179352 #>  [71,] 8.135850 8.142725 8.149394 8.155838 8.162039 8.167987 8.173675 8.179099 #>  [72,] 8.137880 8.144361 8.150665 8.156770 8.162658 8.168316 8.173736 8.178912 #>  [73,] 8.139946 8.146039 8.151984 8.157755 8.163333 8.168704 8.173857 8.178786 #>  [74,] 8.142040 8.147754 8.153345 8.158787 8.164059 8.169146 8.174034 8.178716 #>  [75,] 8.144155 8.149498 8.154743 8.159861 8.164831 8.169636 8.174262 8.178700 #>  [76,] 8.146285 8.151266 8.156171 8.160971 8.165643 8.170170 8.174537 8.178732 #>  [77,] 8.148425 8.153053 8.157624 8.162112 8.166491 8.170744 8.174853 8.178808 #>  [78,] 8.150569 8.154852 8.159098 8.163279 8.167371 8.171352 8.175209 8.178926 #>  [79,] 8.152713 8.156659 8.160587 8.164468 8.168277 8.171992 8.175598 8.179080 #>  [80,] 8.154852 8.158471 8.162088 8.165675 8.169206 8.172659 8.176018 8.179268 #>  [81,] 8.156981 8.160281 8.163596 8.166895 8.170154 8.173350 8.176466 8.179486 #>  [82,] 8.159098 8.162088 8.165107 8.168125 8.171117 8.174060 8.176937 8.179730 #>  [83,] 8.161198 8.163887 8.166618 8.169361 8.172091 8.174787 8.177428 8.179999 #>  [84,] 8.163279 8.165675 8.168125 8.170600 8.173075 8.175527 8.177937 8.180288 #>  [85,] 8.165337 8.167449 8.169625 8.171839 8.174064 8.176277 8.178460 8.180596 #>  [86,] 8.167371 8.169206 8.171117 8.173075 8.175055 8.177035 8.178995 8.180919 #>  [87,] 8.169376 8.170943 8.172596 8.174305 8.176046 8.177798 8.179539 8.181254 #>  [88,] 8.171352 8.172659 8.174060 8.175527 8.177035 8.178562 8.180090 8.181600 #>  [89,] 8.173297 8.174352 8.175508 8.176738 8.178019 8.179327 8.180645 8.181954 #>  [90,] 8.175209 8.176018 8.176937 8.177937 8.178995 8.180090 8.181202 8.182314 #>  [91,] 8.177085 8.177657 8.178345 8.179121 8.179962 8.180848 8.181759 8.182677 #>  [92,] 8.178926 8.179268 8.179730 8.180288 8.180919 8.181600 8.182314 8.183043 #>  [93,] 8.180728 8.180847 8.181092 8.181438 8.181862 8.182344 8.182865 8.183408 #>  [94,] 8.182493 8.182395 8.182428 8.182567 8.182791 8.183078 8.183411 8.183772 #>  [95,] 8.184218 8.183911 8.183738 8.183676 8.183704 8.183801 8.183949 8.184132 #>  [96,] 8.185903 8.185392 8.185019 8.184762 8.184599 8.184511 8.184479 8.184487 #>  [97,] 8.187546 8.186838 8.186272 8.185825 8.185476 8.185206 8.184998 8.184836 #>  [98,] 8.189148 8.188249 8.187495 8.186862 8.186332 8.185886 8.185507 8.185178 #>  [99,] 8.190708 8.189624 8.188686 8.187874 8.187168 8.186550 8.186002 8.185510 #> [100,] 8.192226 8.190962 8.189847 8.188860 8.187982 8.187196 8.186484 8.185832 #>           [,97]    [,98]    [,99]   [,100] #>   [1,] 8.521057 8.523895 8.526602 8.529172 #>   [2,] 8.512694 8.515732 8.518628 8.521375 #>   [3,] 8.504356 8.507597 8.510682 8.513608 #>   [4,] 8.496048 8.499492 8.502769 8.505875 #>   [5,] 8.487771 8.491422 8.494892 8.498178 #>   [6,] 8.479531 8.483389 8.487053 8.490520 #>   [7,] 8.471329 8.475396 8.479255 8.482904 #>   [8,] 8.463171 8.467448 8.471502 8.475333 #>   [9,] 8.455060 8.459547 8.463797 8.467811 #>  [10,] 8.447000 8.451698 8.456144 8.460340 #>  [11,] 8.438995 8.443905 8.448546 8.452923 #>  [12,] 8.431050 8.436170 8.441007 8.445564 #>  [13,] 8.423169 8.428499 8.433530 8.438267 #>  [14,] 8.415356 8.420895 8.426119 8.431034 #>  [15,] 8.407615 8.413363 8.418778 8.423869 #>  [16,] 8.399953 8.405906 8.411510 8.416776 #>  [17,] 8.392372 8.398529 8.404320 8.409757 #>  [18,] 8.384878 8.391236 8.397211 8.402818 #>  [19,] 8.377476 8.384032 8.390187 8.395960 #>  [20,] 8.370171 8.376920 8.383253 8.389187 #>  [21,] 8.362966 8.369905 8.376411 8.382503 #>  [22,] 8.355868 8.362992 8.369666 8.375912 #>  [23,] 8.348880 8.356184 8.363021 8.369416 #>  [24,] 8.342008 8.349485 8.356480 8.363019 #>  [25,] 8.335256 8.342900 8.350047 8.356724 #>  [26,] 8.328628 8.336433 8.343726 8.350534 #>  [27,] 8.322129 8.330088 8.337519 8.344453 #>  [28,] 8.315764 8.323868 8.331430 8.338483 #>  [29,] 8.309536 8.317777 8.325462 8.332627 #>  [30,] 8.303450 8.311818 8.319618 8.326888 #>  [31,] 8.297508 8.305995 8.313902 8.321268 #>  [32,] 8.291715 8.300310 8.308315 8.315769 #>  [33,] 8.286074 8.294767 8.302861 8.310395 #>  [34,] 8.280587 8.289368 8.297541 8.305146 #>  [35,] 8.275258 8.284116 8.292357 8.300025 #>  [36,] 8.270089 8.279012 8.287312 8.295033 #>  [37,] 8.265082 8.274059 8.282407 8.290171 #>  [38,] 8.260238 8.269257 8.277643 8.285442 #>  [39,] 8.255559 8.264608 8.273022 8.280845 #>  [40,] 8.251046 8.260113 8.268543 8.276381 #>  [41,] 8.246700 8.255773 8.264209 8.272051 #>  [42,] 8.242520 8.251587 8.260018 8.267856 #>  [43,] 8.238508 8.247557 8.255971 8.263794 #>  [44,] 8.234662 8.243680 8.252067 8.259866 #>  [45,] 8.230981 8.239958 8.248307 8.256072 #>  [46,] 8.227466 8.236388 8.244688 8.252410 #>  [47,] 8.224113 8.232969 8.241211 8.248880 #>  [48,] 8.220921 8.229701 8.237874 8.245481 #>  [49,] 8.217888 8.226580 8.234674 8.242211 #>  [50,] 8.215012 8.223606 8.231611 8.239068 #>  [51,] 8.212290 8.220775 8.228683 8.236051 #>  [52,] 8.209719 8.218085 8.225886 8.233158 #>  [53,] 8.207295 8.215533 8.223219 8.230387 #>  [54,] 8.205016 8.213117 8.220679 8.227735 #>  [55,] 8.202877 8.210832 8.218263 8.225201 #>  [56,] 8.200874 8.208676 8.215969 8.222780 #>  [57,] 8.199004 8.206645 8.213792 8.220471 #>  [58,] 8.197262 8.204735 8.211730 8.218271 #>  [59,] 8.195644 8.202943 8.209780 8.216177 #>  [60,] 8.194146 8.201265 8.207938 8.214186 #>  [61,] 8.192763 8.199696 8.206200 8.212294 #>  [62,] 8.191490 8.198233 8.204564 8.210499 #>  [63,] 8.190323 8.196872 8.203025 8.208797 #>  [64,] 8.189258 8.195608 8.201579 8.207185 #>  [65,] 8.188290 8.194438 8.200224 8.205660 #>  [66,] 8.187413 8.193357 8.198955 8.204218 #>  [67,] 8.186625 8.192361 8.197768 8.202856 #>  [68,] 8.185919 8.191446 8.196661 8.201571 #>  [69,] 8.185292 8.190608 8.195629 8.200359 #>  [70,] 8.184739 8.189844 8.194668 8.199217 #>  [71,] 8.184256 8.189148 8.193776 8.198142 #>  [72,] 8.183839 8.188518 8.192948 8.197131 #>  [73,] 8.183484 8.187949 8.192181 8.196180 #>  [74,] 8.183186 8.187439 8.191472 8.195287 #>  [75,] 8.182942 8.186982 8.190818 8.194448 #>  [76,] 8.182747 8.186576 8.190215 8.193660 #>  [77,] 8.182599 8.186217 8.189659 8.192920 #>  [78,] 8.182493 8.185903 8.189148 8.192226 #>  [79,] 8.182426 8.185628 8.188679 8.191574 #>  [80,] 8.182395 8.185392 8.188249 8.190962 #>  [81,] 8.182397 8.185190 8.187855 8.190387 #>  [82,] 8.182428 8.185019 8.187495 8.189847 #>  [83,] 8.182486 8.184878 8.187164 8.189338 #>  [84,] 8.182567 8.184762 8.186862 8.188860 #>  [85,] 8.182670 8.184670 8.186586 8.188408 #>  [86,] 8.182791 8.184599 8.186332 8.187982 #>  [87,] 8.182928 8.184547 8.186100 8.187579 #>  [88,] 8.183078 8.184511 8.185886 8.187196 #>  [89,] 8.183240 8.184489 8.185689 8.186832 #>  [90,] 8.183411 8.184479 8.185507 8.186484 #>  [91,] 8.183589 8.184479 8.185337 8.186151 #>  [92,] 8.183772 8.184487 8.185178 8.185832 #>  [93,] 8.183958 8.184502 8.185027 8.185524 #>  [94,] 8.184147 8.184522 8.184885 8.185225 #>  [95,] 8.184335 8.184544 8.184747 8.184934 #>  [96,] 8.184522 8.184568 8.184615 8.184650 #>  [97,] 8.184705 8.184592 8.184484 8.184371 #>  [98,] 8.184885 8.184615 8.184355 8.184096 #>  [99,] 8.185058 8.184634 8.184226 8.183824 #> [100,] 8.185225 8.184650 8.184096 8.183552 potential_to_head(mc, phic) #>            [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8] #>   [1,] 9.624030 9.611546 9.598996 9.586378 9.573691 9.560933 9.548101 9.535196 #>   [2,] 9.619708 9.607204 9.594633 9.581993 9.569283 9.556500 9.543644 9.530712 #>   [3,] 9.615403 9.602879 9.590287 9.577626 9.564892 9.552086 9.539206 9.526248 #>   [4,] 9.611115 9.598571 9.585959 9.573276 9.560520 9.547691 9.534786 9.521804 #>   [5,] 9.606844 9.594281 9.581648 9.568944 9.556167 9.543315 9.530386 9.517379 #>   [6,] 9.602589 9.590007 9.577355 9.564630 9.551832 9.538958 9.526006 9.512974 #>   [7,] 9.598352 9.585752 9.573080 9.560335 9.547516 9.534620 9.521645 9.508590 #>   [8,] 9.594132 9.581514 9.568823 9.556059 9.543219 9.530302 9.517305 9.504226 #>   [9,] 9.589930 9.577294 9.564585 9.551802 9.538942 9.526003 9.512985 9.499884 #>  [10,] 9.585745 9.573092 9.560365 9.547563 9.534684 9.521725 9.508685 9.495562 #>  [11,] 9.581579 9.568909 9.556165 9.543344 9.530446 9.517468 9.504407 9.491262 #>  [12,] 9.577430 9.564744 9.551983 9.539145 9.526228 9.513230 9.500150 9.486984 #>  [13,] 9.573300 9.560598 9.547820 9.534965 9.522030 9.509014 9.495913 9.482727 #>  [14,] 9.569188 9.556471 9.543677 9.530805 9.517853 9.504818 9.491699 9.478493 #>  [15,] 9.565095 9.552362 9.539553 9.526665 9.513696 9.500644 9.487506 9.474281 #>  [16,] 9.561020 9.548273 9.535449 9.522546 9.509560 9.496491 9.483335 9.470091 #>  [17,] 9.556964 9.544204 9.531365 9.518446 9.505445 9.492360 9.479187 9.465925 #>  [18,] 9.552928 9.540154 9.527301 9.514368 9.501352 9.488250 9.475061 9.461781 #>  [19,] 9.548910 9.536123 9.523257 9.510310 9.497279 9.484162 9.470957 9.457661 #>  [20,] 9.544912 9.532113 9.519234 9.506273 9.493228 9.480097 9.466876 9.453564 #>  [21,] 9.540933 9.528122 9.515231 9.502257 9.489199 9.476053 9.462818 9.449490 #>  [22,] 9.536973 9.524151 9.511248 9.498263 9.485191 9.472033 9.458783 9.445441 #>  [23,] 9.533033 9.520201 9.507287 9.494289 9.481206 9.468034 9.454772 9.441415 #>  [24,] 9.529113 9.516270 9.503346 9.490337 9.477243 9.464059 9.450784 9.437414 #>  [25,] 9.525213 9.512360 9.499426 9.486407 9.473301 9.460106 9.446819 9.433437 #>  [26,] 9.521333 9.508471 9.495527 9.482499 9.469383 9.456177 9.442878 9.429484 #>  [27,] 9.517472 9.504602 9.491650 9.478612 9.465486 9.452270 9.438961 9.425556 #>  [28,] 9.513632 9.500754 9.487793 9.474747 9.461612 9.448387 9.435068 9.421653 #>  [29,] 9.509812 9.496927 9.483959 9.470904 9.457761 9.444527 9.431199 9.417774 #>  [30,] 9.506012 9.493121 9.480145 9.467083 9.453933 9.440691 9.427355 9.413921 #>  [31,] 9.502233 9.489335 9.476353 9.463285 9.450127 9.436878 9.423534 9.410093 #>  [32,] 9.498474 9.485571 9.472583 9.459509 9.446345 9.433089 9.419738 9.406289 #>  [33,] 9.494736 9.481827 9.468835 9.455755 9.442585 9.429324 9.415967 9.402511 #>  [34,] 9.491018 9.478105 9.465108 9.452023 9.438849 9.425582 9.412220 9.398759 #>  [35,] 9.487320 9.474404 9.461403 9.448314 9.435136 9.421864 9.408497 9.395032 #>  [36,] 9.483644 9.470724 9.457720 9.444628 9.431446 9.418171 9.404800 9.391330 #>  [37,] 9.479988 9.467066 9.454059 9.440964 9.427779 9.414501 9.401127 9.387654 #>  [38,] 9.476352 9.463428 9.450419 9.437323 9.424136 9.410855 9.397479 9.384003 #>  [39,] 9.472737 9.459812 9.446802 9.433704 9.420515 9.407233 9.393855 9.380378 #>  [40,] 9.469143 9.456218 9.443207 9.430108 9.416918 9.403636 9.390257 9.376778 #>  [41,] 9.465570 9.452644 9.439633 9.426534 9.413345 9.400062 9.386683 9.373205 #>  [42,] 9.462018 9.449092 9.436082 9.422983 9.409795 9.396512 9.383134 9.369656 #>  [43,] 9.458486 9.445562 9.432552 9.419455 9.406268 9.392987 9.379610 9.366134 #>  [44,] 9.454974 9.442052 9.429045 9.415949 9.402764 9.389485 9.376111 9.362637 #>  [45,] 9.451484 9.438564 9.425559 9.412466 9.399284 9.386008 9.372636 9.359166 #>  [46,] 9.448014 9.435097 9.422095 9.409006 9.395827 9.382554 9.369186 9.355720 #>  [47,] 9.444565 9.431651 9.418653 9.405568 9.392393 9.379125 9.365761 9.352299 #>  [48,] 9.441136 9.428227 9.415233 9.402152 9.388982 9.375719 9.362361 9.348904 #>  [49,] 9.437728 9.424824 9.411835 9.398759 9.385594 9.372337 9.358985 9.345535 #>  [50,] 9.434340 9.421441 9.408458 9.395389 9.382230 9.368979 9.355634 9.342190 #>  [51,] 9.430973 9.418080 9.405103 9.392040 9.378888 9.365645 9.352307 9.338871 #>  [52,] 9.427626 9.414740 9.401770 9.388714 9.375569 9.362334 9.349004 9.335577 #>  [53,] 9.424300 9.411420 9.398458 9.385410 9.372273 9.359046 9.345726 9.332308 #>  [54,] 9.420993 9.408122 9.395167 9.382128 9.369000 9.355782 9.342471 9.329064 #>  [55,] 9.417707 9.404844 9.391898 9.378868 9.365750 9.352542 9.339241 9.325845 #>  [56,] 9.414441 9.401587 9.388650 9.375629 9.362521 9.349324 9.336035 9.322650 #>  [57,] 9.411195 9.398350 9.385423 9.372413 9.359316 9.346130 9.332852 9.319480 #>  [58,] 9.407968 9.395133 9.382217 9.369218 9.356132 9.342958 9.329693 9.316334 #>  [59,] 9.404762 9.391937 9.379032 9.366044 9.352971 9.339809 9.326557 9.313212 #>  [60,] 9.401575 9.388762 9.375868 9.362892 9.349831 9.336683 9.323445 9.310114 #>  [61,] 9.398407 9.385606 9.372725 9.359761 9.346714 9.333579 9.320356 9.307040 #>  [62,] 9.395259 9.382470 9.369602 9.356652 9.343618 9.330498 9.317290 9.303990 #>  [63,] 9.392131 9.379354 9.366499 9.353563 9.340544 9.327439 9.314246 9.300963 #>  [64,] 9.389021 9.376258 9.363416 9.350495 9.337491 9.324402 9.311225 9.297960 #>  [65,] 9.385931 9.373181 9.360354 9.347447 9.334459 9.321386 9.308227 9.294979 #>  [66,] 9.382859 9.370124 9.357312 9.344420 9.331448 9.318392 9.305251 9.292022 #>  [67,] 9.379806 9.367086 9.354289 9.341414 9.328458 9.315420 9.302297 9.289087 #>  [68,] 9.376772 9.364067 9.351286 9.338427 9.325489 9.312469 9.299365 9.286174 #>  [69,] 9.373756 9.361066 9.348302 9.335460 9.322540 9.309539 9.296454 9.283284 #>  [70,] 9.370758 9.358085 9.345337 9.332514 9.319611 9.306629 9.293565 9.280415 #>  [71,] 9.367779 9.355122 9.342392 9.329586 9.316703 9.303740 9.290696 9.277569 #>  [72,] 9.364817 9.352178 9.339465 9.326678 9.313814 9.300872 9.287849 9.274743 #>  [73,] 9.361874 9.349252 9.336557 9.323789 9.310945 9.298024 9.285022 9.271939 #>  [74,] 9.358947 9.346343 9.333668 9.320919 9.308096 9.295195 9.282216 9.269156 #>  [75,] 9.356039 9.343453 9.330797 9.318068 9.305265 9.292387 9.279430 9.266394 #>  [76,] 9.353147 9.340580 9.327944 9.315235 9.302454 9.289598 9.276664 9.263652 #>  [77,] 9.350273 9.337725 9.325109 9.312421 9.299661 9.286828 9.273918 9.260930 #>  [78,] 9.347415 9.334887 9.322291 9.309625 9.296887 9.284077 9.271191 9.258229 #>  [79,] 9.344574 9.332066 9.319491 9.306847 9.294132 9.281344 9.268483 9.255546 #>  [80,] 9.341750 9.329262 9.316708 9.304086 9.291394 9.278630 9.265794 9.252884 #>  [81,] 9.338942 9.326475 9.313942 9.301342 9.288674 9.275935 9.263124 9.250240 #>  [82,] 9.336150 9.323704 9.311193 9.298616 9.285971 9.273257 9.260472 9.247615 #>  [83,] 9.333374 9.320950 9.308461 9.295907 9.283286 9.270597 9.257838 9.245008 #>  [84,] 9.330613 9.318211 9.305745 9.293215 9.280618 9.267955 9.255222 9.242420 #>  [85,] 9.327869 9.315488 9.303045 9.290539 9.277967 9.265330 9.252624 9.239849 #>  [86,] 9.325139 9.312781 9.300361 9.287879 9.275333 9.262721 9.250043 9.237297 #>  [87,] 9.322424 9.310089 9.297693 9.285235 9.272715 9.260129 9.247479 9.234761 #>  [88,] 9.319725 9.307413 9.295040 9.282607 9.270112 9.257554 9.244931 9.232243 #>  [89,] 9.317040 9.304751 9.292403 9.279995 9.267526 9.254995 9.242400 9.229741 #>  [90,] 9.314369 9.302104 9.289780 9.277398 9.264955 9.252451 9.239885 9.227256 #>  [91,] 9.311713 9.299471 9.287173 9.274816 9.262400 9.249924 9.237386 9.224787 #>  [92,] 9.309071 9.296853 9.284579 9.272248 9.259859 9.247411 9.234903 9.222333 #>  [93,] 9.306442 9.294249 9.282000 9.269696 9.257334 9.244914 9.232435 9.219896 #>  [94,] 9.303827 9.291659 9.279435 9.267157 9.254822 9.242431 9.229981 9.217473 #>  [95,] 9.301226 9.289082 9.276884 9.264633 9.252326 9.239963 9.227543 9.215065 #>  [96,] 9.298638 9.286518 9.274347 9.262122 9.249843 9.237509 9.225119 9.212672 #>  [97,] 9.296062 9.283968 9.271823 9.259625 9.247374 9.235069 9.222709 9.210294 #>  [98,] 9.293499 9.281431 9.269312 9.257141 9.244918 9.232642 9.220313 9.207929 #>  [99,] 9.290949 9.278906 9.266813 9.254670 9.242475 9.230229 9.217930 9.205578 #> [100,] 9.288411 9.276394 9.264328 9.252212 9.240046 9.227829 9.215561 9.203241 #>            [,9]    [,10]    [,11]    [,12]    [,13]    [,14]    [,15]    [,16] #>   [1,] 9.522214 9.509155 9.496016 9.482796 9.469493 9.456104 9.442628 9.429063 #>   [2,] 9.517704 9.504616 9.491447 9.478196 9.464860 9.451438 9.437926 9.424324 #>   [3,] 9.513213 9.500097 9.486899 9.473618 9.460250 9.446794 9.433247 9.419609 #>   [4,] 9.508742 9.495599 9.482372 9.469060 9.455661 9.442172 9.428591 9.414917 #>   [5,] 9.504291 9.491121 9.477866 9.464525 9.451095 9.437574 9.423959 9.410249 #>   [6,] 9.499861 9.486665 9.473382 9.460012 9.446551 9.432998 9.419351 9.405605 #>   [7,] 9.495452 9.482230 9.468920 9.455521 9.442031 9.428447 9.414766 9.400987 #>   [8,] 9.491064 9.477816 9.464480 9.451054 9.437534 9.423920 9.410207 9.396394 #>   [9,] 9.486698 9.473425 9.460063 9.446609 9.433061 9.419417 9.405673 9.391827 #>  [10,] 9.482353 9.469056 9.455669 9.442188 9.428613 9.414939 9.401164 9.387286 #>  [11,] 9.478030 9.464710 9.451297 9.437791 9.424188 9.410486 9.396681 9.382772 #>  [12,] 9.473730 9.460386 9.446950 9.433418 9.419789 9.406059 9.392225 9.378284 #>  [13,] 9.469452 9.456086 9.442626 9.429070 9.415414 9.401657 9.387795 9.373825 #>  [14,] 9.465197 9.451809 9.438326 9.424746 9.411066 9.397282 9.383392 9.369393 #>  [15,] 9.460964 9.447555 9.434051 9.420447 9.406743 9.392934 9.379017 9.364989 #>  [16,] 9.456756 9.443326 9.429800 9.416174 9.402446 9.388612 9.374669 9.360614 #>  [17,] 9.452570 9.439121 9.425574 9.411926 9.398175 9.384318 9.370350 9.356268 #>  [18,] 9.448408 9.434940 9.421373 9.407705 9.393932 9.380051 9.366058 9.351951 #>  [19,] 9.444270 9.430784 9.417198 9.403509 9.389715 9.375812 9.361796 9.347664 #>  [20,] 9.440157 9.426652 9.413048 9.399340 9.385525 9.371601 9.357562 9.343407 #>  [21,] 9.436067 9.422546 9.408924 9.395197 9.381363 9.367418 9.353358 9.339180 #>  [22,] 9.432002 9.418465 9.404826 9.391082 9.377229 9.363264 9.349184 9.334984 #>  [23,] 9.427962 9.414410 9.400755 9.386993 9.373123 9.359139 9.345039 9.330818 #>  [24,] 9.423947 9.410380 9.396709 9.382932 9.369045 9.355044 9.340925 9.326684 #>  [25,] 9.419957 9.406376 9.392691 9.378899 9.364995 9.350977 9.336841 9.322581 #>  [26,] 9.415992 9.402398 9.388699 9.374893 9.360974 9.346940 9.332787 9.318510 #>  [27,] 9.412052 9.398446 9.384735 9.370915 9.356982 9.342934 9.328765 9.314471 #>  [28,] 9.408138 9.394521 9.380798 9.366965 9.353019 9.338957 9.324773 9.310464 #>  [29,] 9.404250 9.390622 9.376888 9.363043 9.349085 9.335010 9.320813 9.306490 #>  [30,] 9.400387 9.386750 9.373005 9.359150 9.345181 9.331094 9.316884 9.302548 #>  [31,] 9.396550 9.382904 9.369150 9.355286 9.341306 9.327208 9.312987 9.298639 #>  [32,] 9.392739 9.379085 9.365323 9.351450 9.337461 9.323353 9.309122 9.294763 #>  [33,] 9.388955 9.375293 9.361524 9.347642 9.333646 9.319529 9.305289 9.290920 #>  [34,] 9.385196 9.371528 9.357752 9.343864 9.329860 9.315736 9.301487 9.287110 #>  [35,] 9.381464 9.367791 9.354009 9.340115 9.326105 9.311974 9.297718 9.283334 #>  [36,] 9.377758 9.364080 9.350294 9.336395 9.322379 9.308243 9.293982 9.279591 #>  [37,] 9.374078 9.360397 9.346607 9.332704 9.318684 9.304543 9.290277 9.275882 #>  [38,] 9.370425 9.356741 9.342948 9.329042 9.315019 9.300875 9.286605 9.272206 #>  [39,] 9.366798 9.353112 9.339317 9.325409 9.311384 9.297237 9.282966 9.268564 #>  [40,] 9.363198 9.349511 9.335715 9.321806 9.307779 9.293632 9.279359 9.264955 #>  [41,] 9.359624 9.345937 9.332141 9.318231 9.304205 9.290057 9.275784 9.261381 #>  [42,] 9.356076 9.342390 9.328595 9.314687 9.300661 9.286514 9.272242 9.257840 #>  [43,] 9.352555 9.338871 9.325077 9.311171 9.297147 9.283003 9.268733 9.254333 #>  [44,] 9.349061 9.335379 9.321588 9.307684 9.293664 9.279522 9.265256 9.250859 #>  [45,] 9.345593 9.331914 9.318127 9.304227 9.290211 9.276073 9.261811 9.247419 #>  [46,] 9.342151 9.328477 9.314694 9.300799 9.286788 9.272656 9.258399 9.244013 #>  [47,] 9.338736 9.325067 9.311290 9.297400 9.283395 9.269269 9.255019 9.240640 #>  [48,] 9.335346 9.321684 9.307913 9.294030 9.280032 9.265913 9.251671 9.237301 #>  [49,] 9.331983 9.318328 9.304564 9.290689 9.276699 9.262589 9.248356 9.233995 #>  [50,] 9.328647 9.314999 9.301243 9.287377 9.273395 9.259295 9.245072 9.230722 #>  [51,] 9.325336 9.311696 9.297950 9.284093 9.270122 9.256032 9.241820 9.227482 #>  [52,] 9.322051 9.308421 9.294684 9.280838 9.266878 9.252800 9.238600 9.224275 #>  [53,] 9.318791 9.305172 9.291446 9.277611 9.263663 9.249598 9.235412 9.221100 #>  [54,] 9.315558 9.301950 9.288236 9.274413 9.260478 9.246426 9.232254 9.217958 #>  [55,] 9.312350 9.298754 9.285052 9.271243 9.257322 9.243285 9.229128 9.214848 #>  [56,] 9.309167 9.295584 9.281896 9.268101 9.254194 9.240173 9.226033 9.211770 #>  [57,] 9.306010 9.292440 9.278767 9.264986 9.251096 9.237091 9.222968 9.208724 #>  [58,] 9.302878 9.289322 9.275664 9.261900 9.248026 9.234038 9.219934 9.205710 #>  [59,] 9.299771 9.286230 9.272588 9.258840 9.244984 9.231015 9.216931 9.202726 #>  [60,] 9.296688 9.283164 9.269538 9.255808 9.241970 9.228021 9.213957 9.199774 #>  [61,] 9.293630 9.280122 9.266514 9.252802 9.238984 9.225055 9.211012 9.196852 #>  [62,] 9.290596 9.277106 9.263516 9.249824 9.236025 9.222118 9.208097 9.193961 #>  [63,] 9.287587 9.274115 9.260544 9.246872 9.233094 9.219209 9.205212 9.191099 #>  [64,] 9.284601 9.271148 9.257597 9.243946 9.230190 9.216328 9.202355 9.188268 #>  [65,] 9.281640 9.268206 9.254676 9.241046 9.227313 9.213474 9.199526 9.185466 #>  [66,] 9.278701 9.265288 9.251779 9.238171 9.224462 9.210648 9.196726 9.182692 #>  [67,] 9.275787 9.262394 9.248907 9.235322 9.221637 9.207848 9.193953 9.179948 #>  [68,] 9.272895 9.259524 9.246060 9.232499 9.218838 9.205076 9.191208 9.177232 #>  [69,] 9.270026 9.256677 9.243236 9.229700 9.216065 9.202329 9.188490 9.174543 #>  [70,] 9.267179 9.253854 9.240437 9.226925 9.213317 9.199609 9.185799 9.171883 #>  [71,] 9.264355 9.251053 9.237661 9.224175 9.210594 9.196914 9.183134 9.169249 #>  [72,] 9.261553 9.248275 9.234908 9.221449 9.207895 9.194245 9.180495 9.166642 #>  [73,] 9.258772 9.245519 9.232178 9.218746 9.205221 9.191600 9.177881 9.164062 #>  [74,] 9.256014 9.242786 9.229471 9.216067 9.202571 9.188980 9.175293 9.161507 #>  [75,] 9.253276 9.240074 9.226786 9.213410 9.199944 9.186385 9.172730 9.158978 #>  [76,] 9.250559 9.237384 9.224124 9.210776 9.197340 9.183813 9.170191 9.156474 #>  [77,] 9.247863 9.234715 9.221483 9.208165 9.194759 9.181264 9.167676 9.153994 #>  [78,] 9.245188 9.232067 9.218863 9.205575 9.192201 9.178738 9.165185 9.151539 #>  [79,] 9.242532 9.229439 9.216264 9.203007 9.189665 9.176235 9.162717 9.149108 #>  [80,] 9.239897 9.226832 9.213687 9.200460 9.187150 9.173755 9.160272 9.146700 #>  [81,] 9.237280 9.224244 9.211129 9.197934 9.184657 9.171296 9.157849 9.144314 #>  [82,] 9.234683 9.221676 9.208592 9.195429 9.182185 9.168859 9.155448 9.141951 #>  [83,] 9.232105 9.219128 9.206075 9.192944 9.179733 9.166442 9.153069 9.139611 #>  [84,] 9.229546 9.216598 9.203576 9.190478 9.177302 9.164047 9.150710 9.137291 #>  [85,] 9.227004 9.214088 9.201097 9.188032 9.174891 9.161671 9.148373 9.134993 #>  [86,] 9.224481 9.211595 9.198637 9.185605 9.172499 9.159316 9.146055 9.132715 #>  [87,] 9.221976 9.209121 9.196195 9.183197 9.170126 9.156980 9.143758 9.130458 #>  [88,] 9.219487 9.206664 9.193771 9.180807 9.167772 9.154663 9.141479 9.128220 #>  [89,] 9.217016 9.204224 9.191365 9.178435 9.165436 9.152364 9.139220 9.126002 #>  [90,] 9.214562 9.201802 9.188976 9.176081 9.163118 9.150084 9.136979 9.123802 #>  [91,] 9.212124 9.199396 9.186604 9.173744 9.160817 9.147822 9.134757 9.121621 #>  [92,] 9.209702 9.197007 9.184248 9.171424 9.158534 9.145577 9.132552 9.119457 #>  [93,] 9.207296 9.194634 9.181909 9.169121 9.156268 9.143349 9.130364 9.117312 #>  [94,] 9.204905 9.192276 9.179586 9.166833 9.154018 9.141138 9.128193 9.115183 #>  [95,] 9.202529 9.189934 9.177278 9.164562 9.151783 9.138943 9.126038 9.113070 #>  [96,] 9.200169 9.187607 9.174986 9.162306 9.149565 9.136763 9.123900 9.110974 #>  [97,] 9.197822 9.185294 9.172709 9.160065 9.147362 9.134599 9.121777 9.108894 #>  [98,] 9.195490 9.182996 9.170446 9.157838 9.145173 9.132451 9.119669 9.106829 #>  [99,] 9.193172 9.180712 9.168197 9.155626 9.143000 9.130316 9.117576 9.104779 #> [100,] 9.190868 9.178442 9.165962 9.153428 9.140840 9.128196 9.115497 9.102743 #>           [,17]    [,18]    [,19]    [,20]    [,21]    [,22]    [,23]    [,24] #>   [1,] 9.415407 9.401658 9.387813 9.373871 9.359830 9.345686 9.331439 9.317085 #>   [2,] 9.410629 9.396839 9.382952 9.368965 9.354876 9.340683 9.326383 9.311974 #>   [3,] 9.405875 9.392045 9.378115 9.364083 9.349948 9.335705 9.321354 9.306891 #>   [4,] 9.401145 9.387275 9.373304 9.359228 9.345046 9.330756 9.316353 9.301836 #>   [5,] 9.396440 9.382531 9.368518 9.354400 9.340172 9.325834 9.311381 9.296811 #>   [6,] 9.391760 9.377812 9.363759 9.349598 9.335326 9.320941 9.306438 9.291816 #>   [7,] 9.387106 9.373120 9.359027 9.344824 9.330509 9.316076 9.301525 9.286851 #>   [8,] 9.382477 9.368455 9.354323 9.340079 9.325720 9.311242 9.296643 9.281918 #>   [9,] 9.377876 9.363817 9.349647 9.335362 9.320961 9.306438 9.291792 9.277017 #>  [10,] 9.373301 9.359206 9.344999 9.330675 9.316232 9.301666 9.286972 9.272149 #>  [11,] 9.368754 9.354624 9.340380 9.326018 9.311534 9.296924 9.282186 9.267314 #>  [12,] 9.364234 9.350071 9.335791 9.321391 9.306867 9.292216 9.277433 9.262514 #>  [13,] 9.359743 9.345546 9.331232 9.316795 9.302232 9.287540 9.272714 9.257749 #>  [14,] 9.355280 9.341052 9.326703 9.312230 9.297630 9.282897 9.268029 9.253020 #>  [15,] 9.350847 9.336587 9.322205 9.307698 9.293060 9.278289 9.263379 9.248326 #>  [16,] 9.346443 9.332153 9.317739 9.303197 9.288524 9.273715 9.258765 9.243670 #>  [17,] 9.342069 9.327749 9.313304 9.298730 9.284022 9.269177 9.254188 9.239052 #>  [18,] 9.337725 9.323377 9.308902 9.294296 9.279555 9.264674 9.249648 9.234471 #>  [19,] 9.333412 9.319036 9.304532 9.289896 9.275122 9.260207 9.245145 9.229930 #>  [20,] 9.329130 9.314728 9.300196 9.285530 9.270725 9.255777 9.240680 9.225428 #>  [21,] 9.324879 9.310452 9.295893 9.281199 9.266364 9.251384 9.236253 9.220966 #>  [22,] 9.320660 9.306208 9.291624 9.276903 9.262040 9.247029 9.231866 9.216545 #>  [23,] 9.316473 9.301998 9.287389 9.272642 9.257752 9.242713 9.227519 9.212164 #>  [24,] 9.312318 9.297821 9.283189 9.268418 9.253501 9.238434 9.223211 9.207826 #>  [25,] 9.308195 9.293678 9.279024 9.264229 9.249288 9.234195 9.218944 9.203530 #>  [26,] 9.304106 9.289569 9.274894 9.260078 9.245113 9.229995 9.214718 9.199276 #>  [27,] 9.300049 9.285494 9.270800 9.255963 9.240976 9.225836 9.210534 9.195065 #>  [28,] 9.296026 9.281453 9.266742 9.251885 9.236878 9.221716 9.206391 9.190898 #>  [29,] 9.292037 9.277448 9.262719 9.247845 9.232819 9.217637 9.202291 9.186775 #>  [30,] 9.288081 9.273478 9.258733 9.243842 9.228799 9.213598 9.198233 9.182696 #>  [31,] 9.284159 9.269542 9.254784 9.239878 9.224819 9.209601 9.194217 9.178661 #>  [32,] 9.280272 9.265643 9.250871 9.235952 9.220879 9.205645 9.190245 9.174672 #>  [33,] 9.276418 9.261779 9.246996 9.232064 9.216978 9.201731 9.186317 9.170728 #>  [34,] 9.272600 9.257950 9.243158 9.228215 9.213118 9.197859 9.182431 9.166829 #>  [35,] 9.268815 9.254158 9.239357 9.224405 9.209298 9.194028 9.178590 9.162976 #>  [36,] 9.265066 9.250402 9.235593 9.220634 9.205518 9.190240 9.174793 9.159169 #>  [37,] 9.261351 9.246682 9.231867 9.216902 9.201780 9.186495 9.171040 9.155407 #>  [38,] 9.257672 9.242998 9.228179 9.213209 9.198082 9.182791 9.167331 9.151693 #>  [39,] 9.254027 9.239350 9.224528 9.209555 9.194425 9.179131 9.163666 9.148024 #>  [40,] 9.250417 9.235739 9.220915 9.205940 9.190808 9.175512 9.160046 9.144402 #>  [41,] 9.246843 9.232164 9.217340 9.202365 9.187233 9.171937 9.156470 9.140826 #>  [42,] 9.243303 9.228626 9.213803 9.198829 9.183699 9.168404 9.152939 9.137296 #>  [43,] 9.239798 9.225123 9.210304 9.195333 9.180205 9.164914 9.149452 9.133813 #>  [44,] 9.236328 9.221658 9.206842 9.191876 9.176752 9.161466 9.146010 9.130376 #>  [45,] 9.232893 9.218228 9.203418 9.188457 9.173340 9.158061 9.142612 9.126986 #>  [46,] 9.229493 9.214835 9.200031 9.185078 9.169969 9.154698 9.139258 9.123641 #>  [47,] 9.226128 9.211477 9.196682 9.181738 9.166639 9.151377 9.135948 9.120343 #>  [48,] 9.222797 9.208156 9.193371 9.178437 9.163348 9.148099 9.132682 9.117090 #>  [49,] 9.219501 9.204870 9.190096 9.175174 9.160098 9.144862 9.129459 9.113882 #>  [50,] 9.216239 9.201620 9.186859 9.171950 9.156888 9.141667 9.126280 9.110720 #>  [51,] 9.213012 9.198406 9.183659 9.168765 9.153718 9.138514 9.123144 9.107603 #>  [52,] 9.209818 9.195227 9.180495 9.165617 9.150588 9.135401 9.120051 9.104531 #>  [53,] 9.206659 9.192083 9.177367 9.162507 9.147497 9.132330 9.117001 9.101503 #>  [54,] 9.203533 9.188974 9.174276 9.159435 9.144444 9.129299 9.113993 9.098519 #>  [55,] 9.200440 9.185899 9.171221 9.156400 9.141431 9.126308 9.111026 9.095578 #>  [56,] 9.197380 9.182859 9.168201 9.153402 9.138456 9.123358 9.108101 9.092681 #>  [57,] 9.194354 9.179853 9.165217 9.150440 9.135519 9.120447 9.105218 9.089826 #>  [58,] 9.191360 9.176880 9.162267 9.147515 9.132619 9.117574 9.102375 9.087014 #>  [59,] 9.188398 9.173942 9.159353 9.144626 9.129757 9.114741 9.099572 9.084243 #>  [60,] 9.185468 9.171036 9.156472 9.141773 9.126932 9.111946 9.096808 9.081514 #>  [61,] 9.182570 9.168163 9.153626 9.138954 9.124144 9.109189 9.094084 9.078825 #>  [62,] 9.179704 9.165323 9.150813 9.136171 9.121391 9.106469 9.091399 9.076177 #>  [63,] 9.176868 9.162514 9.148034 9.133421 9.118674 9.103786 9.088752 9.073568 #>  [64,] 9.174063 9.159738 9.145287 9.130706 9.115992 9.101139 9.086143 9.070998 #>  [65,] 9.171289 9.156993 9.142572 9.128024 9.113344 9.098528 9.083570 9.068467 #>  [66,] 9.168545 9.154278 9.139890 9.125376 9.110731 9.095952 9.081034 9.065973 #>  [67,] 9.165830 9.151594 9.137239 9.122759 9.108151 9.093411 9.078534 9.063516 #>  [68,] 9.163144 9.148941 9.134619 9.120175 9.105605 9.090904 9.076070 9.061096 #>  [69,] 9.160487 9.146317 9.132030 9.117622 9.103091 9.088431 9.073639 9.058712 #>  [70,] 9.157858 9.143722 9.129471 9.115101 9.100609 9.085991 9.071243 9.056362 #>  [71,] 9.155257 9.141156 9.126941 9.112609 9.098158 9.083583 9.068881 9.054048 #>  [72,] 9.152684 9.138618 9.124440 9.110148 9.095738 9.081207 9.066551 9.051766 #>  [73,] 9.150138 9.136108 9.121969 9.107717 9.093349 9.078862 9.064253 9.049518 #>  [74,] 9.147619 9.133626 9.119525 9.105314 9.090989 9.076548 9.061987 9.047303 #>  [75,] 9.145125 9.131170 9.117109 9.102939 9.088659 9.074264 9.059751 9.045118 #>  [76,] 9.142658 9.128741 9.114720 9.100593 9.086357 9.072009 9.057546 9.042965 #>  [77,] 9.140216 9.126337 9.112358 9.098274 9.084083 9.069782 9.055370 9.040842 #>  [78,] 9.137798 9.123960 9.110021 9.095981 9.081836 9.067584 9.053222 9.038748 #>  [79,] 9.135405 9.121607 9.107711 9.093715 9.079616 9.065413 9.051103 9.036683 #>  [80,] 9.133036 9.119278 9.105425 9.091474 9.077423 9.063269 9.049011 9.034646 #>  [81,] 9.130690 9.116974 9.103164 9.089258 9.075255 9.061151 9.046946 9.032637 #>  [82,] 9.128367 9.114692 9.100926 9.087067 9.073111 9.059059 9.044907 9.030653 #>  [83,] 9.126066 9.112434 9.098712 9.084899 9.070993 9.056991 9.042893 9.028696 #>  [84,] 9.123788 9.110198 9.096521 9.082755 9.068898 9.054948 9.040904 9.026764 #>  [85,] 9.121531 9.107985 9.094353 9.080634 9.066826 9.052928 9.038938 9.024856 #>  [86,] 9.119295 9.105792 9.092206 9.078534 9.064777 9.050931 9.036996 9.022971 #>  [87,] 9.117079 9.103620 9.090080 9.076457 9.062749 9.048956 9.035077 9.021110 #>  [88,] 9.114884 9.101469 9.087975 9.074400 9.060743 9.047003 9.033179 9.019270 #>  [89,] 9.112708 9.099338 9.085890 9.072364 9.058758 9.045072 9.031303 9.017453 #>  [90,] 9.110551 9.097226 9.083825 9.070348 9.056793 9.043160 9.029448 9.015656 #>  [91,] 9.108413 9.095133 9.081779 9.068351 9.054848 9.041268 9.027612 9.013879 #>  [92,] 9.106293 9.093058 9.079752 9.066373 9.052921 9.039396 9.025796 9.012121 #>  [93,] 9.104191 9.091002 9.077743 9.064413 9.051013 9.037542 9.023998 9.010383 #>  [94,] 9.102106 9.088962 9.075751 9.062471 9.049123 9.035706 9.022219 9.008662 #>  [95,] 9.100038 9.086940 9.073776 9.060547 9.047250 9.033887 9.020456 9.006959 #>  [96,] 9.097986 9.084934 9.071818 9.058638 9.045394 9.032085 9.018711 9.005272 #>  [97,] 9.095950 9.082944 9.069876 9.056746 9.043554 9.030299 9.016982 9.003602 #>  [98,] 9.093929 9.080969 9.067950 9.054870 9.041730 9.028529 9.015268 9.001948 #>  [99,] 9.091923 9.079010 9.066038 9.053009 9.039921 9.026774 9.013570 9.000308 #> [100,] 9.089932 9.077065 9.064142 9.051162 9.038126 9.025034 9.011886 8.998682 #>           [,25]    [,26]    [,27]    [,28]    [,29]    [,30]    [,31]    [,32] #>   [1,] 9.302623 9.288050 9.273365 9.258565 9.243648 9.228612 9.213456 9.198177 #>   [2,] 9.297454 9.282820 9.268071 9.253202 9.238214 9.223102 9.207866 9.192502 #>   [3,] 9.292313 9.277619 9.262806 9.247870 9.232810 9.217624 9.202308 9.186860 #>   [4,] 9.287202 9.272448 9.257571 9.242569 9.227439 9.212177 9.196782 9.181251 #>   [5,] 9.282121 9.267308 9.252368 9.237300 9.222100 9.206765 9.191291 9.175677 #>   [6,] 9.277070 9.262199 9.247198 9.232064 9.216795 9.201386 9.185835 9.170138 #>   [7,] 9.272051 9.257122 9.242060 9.226862 9.211525 9.196044 9.180416 9.164637 #>   [8,] 9.267064 9.252079 9.236957 9.221695 9.206290 9.190738 9.175034 9.159175 #>   [9,] 9.262111 9.247069 9.231888 9.216564 9.201093 9.185470 9.169691 9.153752 #>  [10,] 9.257191 9.242094 9.226856 9.211470 9.195933 9.180240 9.164388 9.148370 #>  [11,] 9.252306 9.237155 9.221860 9.206413 9.190812 9.175051 9.159126 9.143031 #>  [12,] 9.247456 9.232253 9.216901 9.201395 9.185731 9.169903 9.153906 9.137735 #>  [13,] 9.242642 9.227388 9.211981 9.196417 9.180691 9.164798 9.148731 9.132485 #>  [14,] 9.237865 9.222560 9.207100 9.191480 9.175693 9.159735 9.143599 9.127280 #>  [15,] 9.233126 9.217772 9.202260 9.186584 9.170738 9.154717 9.138514 9.122123 #>  [16,] 9.228424 9.213023 9.197460 9.181730 9.165827 9.149744 9.133476 9.117015 #>  [17,] 9.223762 9.208314 9.192702 9.176920 9.160961 9.144818 9.128486 9.111957 #>  [18,] 9.219140 9.203647 9.187987 9.172153 9.156140 9.139940 9.123546 9.106950 #>  [19,] 9.214557 9.199021 9.183315 9.167432 9.151366 9.135110 9.118655 9.101995 #>  [20,] 9.210016 9.194438 9.178687 9.162756 9.146640 9.130329 9.113816 9.097094 #>  [21,] 9.205516 9.189897 9.174104 9.158127 9.141962 9.125599 9.109030 9.092247 #>  [22,] 9.201058 9.185401 9.169566 9.153546 9.137333 9.120920 9.104297 9.087457 #>  [23,] 9.196643 9.180949 9.165075 9.149013 9.132755 9.116293 9.099619 9.082723 #>  [24,] 9.192272 9.176542 9.160630 9.144528 9.128227 9.111720 9.094996 9.078047 #>  [25,] 9.187944 9.172181 9.156233 9.140093 9.123752 9.107200 9.090430 9.073431 #>  [26,] 9.183661 9.167866 9.151885 9.135708 9.119328 9.102736 9.085921 9.068874 #>  [27,] 9.179422 9.163598 9.147585 9.131374 9.114958 9.098327 9.081470 9.064378 #>  [28,] 9.175229 9.159377 9.143334 9.127092 9.110642 9.093974 9.077078 9.059944 #>  [29,] 9.171081 9.155204 9.139133 9.122861 9.106380 9.089678 9.072745 9.055572 #>  [30,] 9.166980 9.151078 9.134983 9.118684 9.102172 9.085439 9.068473 9.051263 #>  [31,] 9.162925 9.147002 9.130883 9.114559 9.098021 9.081259 9.064262 9.047019 #>  [32,] 9.158917 9.142974 9.126834 9.110487 9.093925 9.077137 9.060113 9.042839 #>  [33,] 9.154957 9.138996 9.122837 9.106470 9.089886 9.073075 9.056025 9.038725 #>  [34,] 9.151043 9.135067 9.118891 9.102507 9.085904 9.069072 9.052000 9.034676 #>  [35,] 9.147178 9.131188 9.114998 9.098598 9.081979 9.065130 9.048039 9.030694 #>  [36,] 9.143360 9.127359 9.111157 9.094744 9.078111 9.061247 9.044140 9.026778 #>  [37,] 9.139591 9.123581 9.107369 9.090946 9.074302 9.057426 9.040306 9.022930 #>  [38,] 9.135869 9.119852 9.103633 9.087203 9.070550 9.053665 9.036535 9.019149 #>  [39,] 9.132196 9.116175 9.099951 9.083515 9.066856 9.049965 9.032829 9.015435 #>  [40,] 9.128572 9.112548 9.096321 9.079882 9.063221 9.046326 9.029187 9.011789 #>  [41,] 9.124996 9.108971 9.092745 9.076305 9.059644 9.042749 9.025609 9.008211 #>  [42,] 9.121468 9.105446 9.089221 9.072784 9.056125 9.039233 9.022096 9.004701 #>  [43,] 9.117989 9.101971 9.085751 9.069319 9.052665 9.035778 9.018647 9.001259 #>  [44,] 9.114558 9.098546 9.082333 9.065908 9.049262 9.032384 9.015262 8.997884 #>  [45,] 9.111175 9.095172 9.078968 9.062553 9.045918 9.029051 9.011941 8.994576 #>  [46,] 9.107841 9.091849 9.075656 9.059254 9.042631 9.025779 9.008684 8.991336 #>  [47,] 9.104554 9.088575 9.072396 9.056009 9.039402 9.022567 9.005491 8.988162 #>  [48,] 9.101316 9.085352 9.069189 9.052819 9.036231 9.019415 9.002361 8.985055 #>  [49,] 9.098125 9.082178 9.066033 9.049683 9.033116 9.016323 8.999293 8.982014 #>  [50,] 9.094981 9.079053 9.062929 9.046601 9.030058 9.013291 8.996288 8.979038 #>  [51,] 9.091884 9.075977 9.059877 9.043572 9.027056 9.010317 8.993344 8.976127 #>  [52,] 9.088833 9.072950 9.056875 9.040597 9.024109 9.007401 8.990462 8.973281 #>  [53,] 9.085829 9.069972 9.053923 9.037675 9.021218 9.004543 8.987640 8.970497 #>  [54,] 9.082870 9.067041 9.051021 9.034804 9.018381 9.001742 8.984877 8.967777 #>  [55,] 9.079958 9.064157 9.048169 9.031985 9.015598 8.998998 8.982174 8.965118 #>  [56,] 9.077089 9.061320 9.045365 9.029218 9.012868 8.996309 8.979529 8.962520 #>  [57,] 9.074266 9.058530 9.042610 9.026500 9.010191 8.993675 8.976942 8.959982 #>  [58,] 9.071486 9.055785 9.039903 9.023832 9.007566 8.991095 8.974411 8.957504 #>  [59,] 9.068750 9.053085 9.037242 9.021213 9.004992 8.988569 8.971936 8.955084 #>  [60,] 9.066057 9.050430 9.034628 9.018643 9.002468 8.986094 8.969515 8.952720 #>  [61,] 9.063406 9.047819 9.032060 9.016120 8.999993 8.983672 8.967148 8.950413 #>  [62,] 9.060796 9.045251 9.029536 9.013644 8.997568 8.981300 8.964834 8.948161 #>  [63,] 9.058228 9.042726 9.027057 9.011214 8.995190 8.978978 8.962572 8.945963 #>  [64,] 9.055700 9.040243 9.024621 9.008828 8.992858 8.976704 8.960360 8.943817 #>  [65,] 9.053212 9.037801 9.022228 9.006488 8.990573 8.974479 8.958197 8.941722 #>  [66,] 9.050763 9.035399 9.019877 9.004190 8.988333 8.972300 8.956084 8.939678 #>  [67,] 9.048352 9.033038 9.017567 9.001935 8.986137 8.970166 8.954017 8.937683 #>  [68,] 9.045979 9.030715 9.015297 8.999722 8.983984 8.968077 8.951996 8.935736 #>  [69,] 9.043643 9.028430 9.013067 8.997550 8.981873 8.966032 8.950021 8.933835 #>  [70,] 9.041344 9.026183 9.010876 8.995417 8.979803 8.964029 8.948089 8.931979 #>  [71,] 9.039079 9.023972 9.008722 8.993324 8.977774 8.962068 8.946200 8.930167 #>  [72,] 9.036850 9.021797 9.006605 8.991268 8.975783 8.960146 8.944353 8.928398 #>  [73,] 9.034654 9.019657 9.004524 8.989249 8.973831 8.958264 8.942545 8.926670 #>  [74,] 9.032492 9.017551 9.002478 8.987267 8.971916 8.956420 8.940777 8.924982 #>  [75,] 9.030362 9.015479 9.000466 8.985319 8.970036 8.954613 8.939047 8.923333 #>  [76,] 9.028264 9.013439 8.998487 8.983406 8.968192 8.952842 8.937353 8.921722 #>  [77,] 9.026197 9.011431 8.996542 8.981526 8.966382 8.951105 8.935695 8.920147 #>  [78,] 9.024160 9.009453 8.994627 8.979678 8.964604 8.949403 8.934071 8.918606 #>  [79,] 9.022152 9.007506 8.992743 8.977862 8.962859 8.947732 8.932480 8.917100 #>  [80,] 9.020173 9.005588 8.990889 8.976076 8.961144 8.946093 8.930921 8.915625 #>  [81,] 9.018221 9.003698 8.989064 8.974319 8.959460 8.944485 8.929393 8.914182 #>  [82,] 9.016297 9.001836 8.987267 8.972591 8.957804 8.942906 8.927894 8.912769 #>  [83,] 9.014399 9.000000 8.985497 8.970890 8.956176 8.941355 8.926424 8.911385 #>  [84,] 9.012526 8.998190 8.983754 8.969216 8.954575 8.939831 8.924982 8.910028 #>  [85,] 9.010678 8.996405 8.982035 8.967567 8.953000 8.938333 8.923566 8.908698 #>  [86,] 9.008854 8.994645 8.980341 8.965943 8.951450 8.936861 8.922175 8.907392 #>  [87,] 9.007054 8.992908 8.978671 8.964344 8.949924 8.935412 8.920808 8.906111 #>  [88,] 9.005275 8.991193 8.977024 8.962767 8.948421 8.933987 8.919464 8.904853 #>  [89,] 9.003519 8.989501 8.975399 8.961212 8.946940 8.932583 8.918142 8.903617 #>  [90,] 9.001783 8.987829 8.973795 8.959678 8.945480 8.931201 8.916842 8.902402 #>  [91,] 9.000068 8.986178 8.972211 8.958165 8.944041 8.929840 8.915561 8.901206 #>  [92,] 8.998372 8.984547 8.970647 8.956671 8.942621 8.928497 8.914299 8.900029 #>  [93,] 8.996695 8.982934 8.969101 8.955196 8.941220 8.927173 8.913056 8.898870 #>  [94,] 8.995036 8.981339 8.967574 8.953739 8.939836 8.925866 8.911829 8.897727 #>  [95,] 8.993394 8.979762 8.966064 8.952299 8.938470 8.924576 8.910619 8.896601 #>  [96,] 8.991769 8.978202 8.964570 8.950876 8.937119 8.923301 8.909424 8.895489 #>  [97,] 8.990160 8.976657 8.963092 8.949468 8.935784 8.922042 8.908244 8.894391 #>  [98,] 8.988567 8.975128 8.961630 8.948074 8.934463 8.920796 8.907077 8.893306 #>  [99,] 8.986989 8.973613 8.960181 8.946695 8.933156 8.919564 8.905923 8.892234 #> [100,] 8.985424 8.972112 8.958747 8.945329 8.931861 8.918345 8.904781 8.891172 #>           [,33]    [,34]    [,35]    [,36]    [,37]    [,38]    [,39]    [,40] #>   [1,] 9.182775 9.167247 9.151594 9.135814 9.119907 9.103874 9.087715 9.071432 #>   [2,] 9.177010 9.161388 9.145634 9.129748 9.113728 9.097574 9.081288 9.064869 #>   [3,] 9.171279 9.155562 9.139707 9.123714 9.107581 9.091308 9.074894 9.058340 #>   [4,] 9.165581 9.149770 9.133816 9.117716 9.101470 9.085077 9.068535 9.051845 #>   [5,] 9.159918 9.144014 9.127960 9.111755 9.095396 9.078883 9.062213 9.045387 #>   [6,] 9.154293 9.138295 9.122142 9.105832 9.089361 9.072728 9.055931 9.038968 #>   [7,] 9.148705 9.132615 9.116364 9.099949 9.083366 9.066614 9.049689 9.032591 #>   [8,] 9.143156 9.126975 9.110626 9.094107 9.077414 9.060543 9.043492 9.026257 #>   [9,] 9.137649 9.121377 9.104932 9.088310 9.071506 9.054518 9.037340 9.019970 #>  [10,] 9.132183 9.115822 9.099281 9.082557 9.065645 9.048539 9.031236 9.013732 #>  [11,] 9.126761 9.110312 9.093677 9.076852 9.059831 9.042610 9.025183 9.007545 #>  [12,] 9.121384 9.104848 9.088120 9.071196 9.054068 9.036732 9.019182 9.001412 #>  [13,] 9.116054 9.099432 9.082613 9.065590 9.048357 9.030908 9.013236 8.995335 #>  [14,] 9.110771 9.094065 9.077156 9.060037 9.042701 9.025140 9.007348 8.989317 #>  [15,] 9.105537 9.088749 9.071752 9.054538 9.037100 9.019430 9.001519 8.983360 #>  [16,] 9.100354 9.083485 9.066402 9.049095 9.031557 9.013779 8.995752 8.977468 #>  [17,] 9.095222 9.078275 9.061108 9.043710 9.026074 9.008191 8.990050 8.971642 #>  [18,] 9.090144 9.073121 9.055871 9.038385 9.020654 9.002667 8.984415 8.965886 #>  [19,] 9.085120 9.068023 9.050693 9.033121 9.015297 8.997209 8.978848 8.960201 #>  [20,] 9.080152 9.062983 9.045575 9.027920 9.010005 8.991820 8.973353 8.954591 #>  [21,] 9.075241 9.058002 9.040520 9.022784 9.004782 8.986502 8.967932 8.949058 #>  [22,] 9.070389 9.053083 9.035528 9.017714 8.999627 8.981256 8.962587 8.943605 #>  [23,] 9.065595 9.048225 9.030601 9.012712 8.994544 8.976085 8.957320 8.938233 #>  [24,] 9.060863 9.043431 9.025741 9.007779 8.989534 8.970990 8.952133 8.932946 #>  [25,] 9.056191 9.038701 9.020948 9.002918 8.984598 8.965974 8.947028 8.927745 #>  [26,] 9.051583 9.034037 9.016224 8.998129 8.979739 8.961037 8.942008 8.922634 #>  [27,] 9.047039 9.029440 9.011570 8.993414 8.974957 8.956183 8.937075 8.917613 #>  [28,] 9.042559 9.024912 9.006988 8.988774 8.970254 8.951412 8.932229 8.912686 #>  [29,] 9.038145 9.020452 9.002479 8.984211 8.965633 8.946726 8.927474 8.907854 #>  [30,] 9.033797 9.016062 8.998043 8.979725 8.961093 8.942127 8.922810 8.903120 #>  [31,] 9.029517 9.011742 8.993681 8.975318 8.956636 8.937616 8.918239 8.898484 #>  [32,] 9.025304 9.007495 8.989396 8.970991 8.952263 8.933194 8.913763 8.893948 #>  [33,] 9.021161 9.003320 8.985186 8.966744 8.947976 8.928863 8.909383 8.889515 #>  [34,] 9.017087 8.999218 8.981054 8.962579 8.943775 8.924622 8.905100 8.885185 #>  [35,] 9.013082 8.995189 8.976999 8.958496 8.939661 8.920475 8.900915 8.880959 #>  [36,] 9.009148 8.991235 8.973023 8.954496 8.935635 8.916420 8.896830 8.876839 #>  [37,] 9.005284 8.987355 8.969126 8.950579 8.931697 8.912460 8.892844 8.872826 #>  [38,] 9.001492 8.983550 8.965307 8.946747 8.927849 8.908594 8.888959 8.868920 #>  [39,] 8.997771 8.979821 8.961569 8.942998 8.924089 8.904822 8.885175 8.865121 #>  [40,] 8.994121 8.976166 8.957910 8.939334 8.920419 8.901146 8.881492 8.861431 #>  [41,] 8.990542 8.972587 8.954330 8.935754 8.916839 8.897566 8.877910 8.857849 #>  [42,] 8.987036 8.969084 8.950831 8.932259 8.913349 8.894080 8.874430 8.854375 #>  [43,] 8.983600 8.965656 8.947411 8.928848 8.909948 8.890690 8.871052 8.851009 #>  [44,] 8.980236 8.962304 8.944071 8.925522 8.906636 8.887394 8.867774 8.847752 #>  [45,] 8.976943 8.959026 8.940810 8.922279 8.903414 8.884194 8.864598 8.844601 #>  [46,] 8.973720 8.955823 8.937628 8.919120 8.900279 8.881087 8.861521 8.841557 #>  [47,] 8.970568 8.952694 8.934525 8.916044 8.897233 8.878074 8.858543 8.838619 #>  [48,] 8.967486 8.949639 8.931499 8.913050 8.894274 8.875153 8.855664 8.835786 #>  [49,] 8.964473 8.946657 8.928551 8.910138 8.891402 8.872324 8.852882 8.833056 #>  [50,] 8.961529 8.943748 8.925679 8.907307 8.888615 8.869585 8.850197 8.830429 #>  [51,] 8.958654 8.940910 8.922882 8.904555 8.885913 8.866936 8.847606 8.827902 #>  [52,] 8.955845 8.938144 8.920161 8.901883 8.883294 8.864375 8.845109 8.825475 #>  [53,] 8.953104 8.935447 8.917513 8.899289 8.880757 8.861901 8.842704 8.823145 #>  [54,] 8.950428 8.932820 8.914939 8.896771 8.878301 8.859513 8.840389 8.820911 #>  [55,] 8.947817 8.930261 8.912436 8.894328 8.875924 8.857208 8.838163 8.818770 #>  [56,] 8.945270 8.927769 8.910003 8.891960 8.873626 8.854986 8.836023 8.816721 #>  [57,] 8.942786 8.925343 8.907640 8.889664 8.871404 8.852844 8.833968 8.814762 #>  [58,] 8.940364 8.922982 8.905344 8.887440 8.869257 8.850780 8.831996 8.812889 #>  [59,] 8.938003 8.920684 8.903116 8.885286 8.867183 8.848794 8.830105 8.811102 #>  [60,] 8.935702 8.918449 8.900952 8.883200 8.865181 8.846883 8.828292 8.809397 #>  [61,] 8.933459 8.916275 8.898852 8.881181 8.863248 8.845044 8.826556 8.807772 #>  [62,] 8.931273 8.914161 8.896815 8.879226 8.861384 8.843277 8.824894 8.806224 #>  [63,] 8.929143 8.912105 8.894839 8.877335 8.859585 8.841578 8.823304 8.804751 #>  [64,] 8.927068 8.910106 8.892921 8.875506 8.857851 8.839947 8.821783 8.803351 #>  [65,] 8.925047 8.908162 8.891062 8.873737 8.856179 8.838380 8.820330 8.802021 #>  [66,] 8.923077 8.906273 8.889258 8.872026 8.854567 8.836875 8.818941 8.800757 #>  [67,] 8.921158 8.904436 8.887509 8.870371 8.853014 8.835431 8.817615 8.799559 #>  [68,] 8.919289 8.902650 8.885813 8.868771 8.851517 8.834046 8.816350 8.798422 #>  [69,] 8.917468 8.900914 8.884168 8.867224 8.850075 8.832716 8.815142 8.797345 #>  [70,] 8.915693 8.899226 8.882573 8.865727 8.848685 8.831441 8.813989 8.796325 #>  [71,] 8.913963 8.897584 8.881025 8.864281 8.847346 8.830217 8.812890 8.795359 #>  [72,] 8.912278 8.895988 8.879524 8.862881 8.846056 8.829044 8.811841 8.794444 #>  [73,] 8.910635 8.894435 8.878067 8.861528 8.844812 8.827918 8.810841 8.793579 #>  [74,] 8.909033 8.892924 8.876654 8.860218 8.843613 8.826837 8.809887 8.792761 #>  [75,] 8.907470 8.891454 8.875281 8.858950 8.842457 8.825800 8.808977 8.791987 #>  [76,] 8.905946 8.890023 8.873949 8.857723 8.841342 8.824804 8.808109 8.791255 #>  [77,] 8.904459 8.888629 8.872655 8.856534 8.840266 8.823848 8.807281 8.790563 #>  [78,] 8.903007 8.887271 8.871397 8.855383 8.839227 8.822930 8.806490 8.789909 #>  [79,] 8.901590 8.885948 8.870174 8.854266 8.838224 8.822047 8.805735 8.789289 #>  [80,] 8.900205 8.884659 8.868985 8.853184 8.837255 8.821197 8.805013 8.788702 #>  [81,] 8.898852 8.883401 8.867828 8.852133 8.836317 8.820380 8.804322 8.788147 #>  [82,] 8.897529 8.882173 8.866701 8.851113 8.835410 8.819592 8.803661 8.787620 #>  [83,] 8.896235 8.880974 8.865603 8.850122 8.834531 8.818833 8.803028 8.787120 #>  [84,] 8.894969 8.879803 8.864533 8.849158 8.833680 8.818100 8.802421 8.786645 #>  [85,] 8.893729 8.878659 8.863489 8.848220 8.832854 8.817392 8.801837 8.786193 #>  [86,] 8.892514 8.877539 8.862470 8.847307 8.832052 8.816707 8.801276 8.785763 #>  [87,] 8.891323 8.876443 8.861474 8.846416 8.831272 8.816044 8.800736 8.785351 #>  [88,] 8.890155 8.875370 8.860500 8.845547 8.830513 8.815401 8.800214 8.784958 #>  [89,] 8.889009 8.874318 8.859547 8.844698 8.829773 8.814776 8.799711 8.784581 #>  [90,] 8.887883 8.873286 8.858614 8.843868 8.829052 8.814169 8.799223 8.784218 #>  [91,] 8.886776 8.872273 8.857699 8.843056 8.828348 8.813577 8.798749 8.783869 #>  [92,] 8.885688 8.871278 8.856801 8.842260 8.827659 8.813000 8.798289 8.783531 #>  [93,] 8.884617 8.870300 8.855920 8.841480 8.826984 8.812436 8.797841 8.783204 #>  [94,] 8.883563 8.869337 8.855053 8.840713 8.826322 8.811884 8.797403 8.782885 #>  [95,] 8.882523 8.868389 8.854200 8.839960 8.825673 8.811343 8.796975 8.782574 #>  [96,] 8.881498 8.867454 8.853360 8.839218 8.825034 8.810811 8.796554 8.782270 #>  [97,] 8.880486 8.866532 8.852531 8.838487 8.824404 8.810287 8.796141 8.781971 #>  [98,] 8.879487 8.865622 8.851713 8.837766 8.823784 8.809771 8.795733 8.781676 #>  [99,] 8.878499 8.864722 8.850905 8.837054 8.823170 8.809261 8.795330 8.781384 #> [100,] 8.877522 8.863832 8.850106 8.836349 8.822564 8.808756 8.794931 8.781095 #>           [,41]    [,42]    [,43]    [,44]    [,45]    [,46]    [,47]    [,48] #>   [1,] 9.055027 9.038503 9.021865 9.005119 8.988271 8.971330 8.954309 8.937218 #>   [2,] 9.048321 9.031644 9.014844 8.997926 8.980895 8.963761 8.946533 8.929225 #>   [3,] 9.041647 9.024817 9.007853 8.990761 8.973545 8.956215 8.938778 8.921248 #>   [4,] 9.035007 9.018022 9.000895 8.983627 8.966225 8.948695 8.931046 8.913291 #>   [5,] 9.028403 9.011264 8.993971 8.976527 8.958936 8.941205 8.923342 8.905357 #>   [6,] 9.021839 9.004544 8.987085 8.969463 8.951682 8.933748 8.915667 8.897450 #>   [7,] 9.015316 8.997866 8.980240 8.962439 8.944467 8.926327 8.908027 8.889575 #>   [8,] 9.008838 8.991231 8.973438 8.955458 8.937293 8.918947 8.900425 8.881734 #>   [9,] 9.002406 8.984644 8.966683 8.948523 8.930165 8.911611 8.892865 8.873933 #>  [10,] 8.996023 8.978106 8.959978 8.941638 8.923086 8.904323 8.885351 8.866177 #>  [11,] 8.989692 8.971620 8.953326 8.934806 8.916060 8.897087 8.877889 8.858469 #>  [12,] 8.983416 8.965190 8.946730 8.928031 8.909091 8.889908 8.870482 8.850815 #>  [13,] 8.977198 8.958819 8.940194 8.921316 8.902182 8.882789 8.863135 8.843220 #>  [14,] 8.971040 8.952510 8.933721 8.914665 8.895338 8.875736 8.855853 8.835690 #>  [15,] 8.964945 8.946266 8.927314 8.908082 8.888564 8.868752 8.848642 8.828230 #>  [16,] 8.958917 8.940090 8.920977 8.901571 8.881862 8.861843 8.841506 8.820846 #>  [17,] 8.952957 8.933985 8.914714 8.895135 8.875239 8.855014 8.834451 8.813544 #>  [18,] 8.947069 8.927954 8.908528 8.888780 8.868697 8.848268 8.827483 8.806330 #>  [19,] 8.941256 8.922001 8.902423 8.882507 8.862242 8.841612 8.820606 8.799210 #>  [20,] 8.935521 8.916129 8.896401 8.876322 8.855877 8.835050 8.813827 8.792190 #>  [21,] 8.929866 8.910341 8.890468 8.870229 8.849608 8.828588 8.807150 8.785277 #>  [22,] 8.924295 8.904640 8.884625 8.864231 8.843439 8.822230 8.800583 8.778478 #>  [23,] 8.918809 8.899030 8.878877 8.858333 8.837374 8.815981 8.794130 8.771798 #>  [24,] 8.913412 8.893512 8.873228 8.852537 8.831418 8.809847 8.787798 8.765245 #>  [25,] 8.908106 8.888091 8.867680 8.846849 8.825575 8.803832 8.781592 8.758825 #>  [26,] 8.902894 8.882769 8.862237 8.841272 8.819849 8.797941 8.775517 8.752544 #>  [27,] 8.897779 8.877549 8.856901 8.835809 8.814245 8.792179 8.769579 8.746409 #>  [28,] 8.892762 8.872434 8.851677 8.830464 8.808766 8.786551 8.763784 8.740426 #>  [29,] 8.887846 8.867426 8.846566 8.825240 8.803416 8.781060 8.758136 8.734601 #>  [30,] 8.883033 8.862527 8.841573 8.820141 8.798199 8.775712 8.752640 8.728939 #>  [31,] 8.878326 8.857740 8.836698 8.815169 8.793119 8.770510 8.747301 8.723446 #>  [32,] 8.873725 8.853067 8.831945 8.810327 8.788178 8.765458 8.742124 8.718128 #>  [33,] 8.869233 8.848510 8.827316 8.805618 8.783379 8.760559 8.737112 8.712988 #>  [34,] 8.864851 8.844071 8.822813 8.801044 8.778726 8.755817 8.732270 8.708032 #>  [35,] 8.860581 8.839751 8.818438 8.796608 8.774221 8.751234 8.727600 8.703263 #>  [36,] 8.856423 8.835551 8.814192 8.792310 8.769865 8.746813 8.723105 8.698685 #>  [37,] 8.852379 8.831473 8.810077 8.788152 8.765661 8.742556 8.718789 8.694300 #>  [38,] 8.848449 8.827518 8.806093 8.784137 8.761610 8.738465 8.714652 8.690112 #>  [39,] 8.844635 8.823686 8.802242 8.780264 8.757713 8.734541 8.710697 8.686122 #>  [40,] 8.840937 8.819979 8.798524 8.776535 8.753971 8.730784 8.706924 8.682331 #>  [41,] 8.837354 8.816395 8.794939 8.772949 8.750384 8.727196 8.703335 8.678739 #>  [42,] 8.833887 8.812936 8.791488 8.769507 8.746952 8.723777 8.699928 8.675348 #>  [43,] 8.830535 8.809600 8.788170 8.766209 8.743676 8.720525 8.696704 8.672156 #>  [44,] 8.827299 8.806388 8.784985 8.763054 8.740554 8.717440 8.693662 8.669163 #>  [45,] 8.824178 8.803299 8.781931 8.760040 8.737585 8.714522 8.690801 8.666365 #>  [46,] 8.821170 8.800332 8.779009 8.757167 8.734768 8.711768 8.688117 8.663762 #>  [47,] 8.818276 8.797485 8.776216 8.754434 8.732101 8.709176 8.685610 8.661351 #>  [48,] 8.815493 8.794758 8.773551 8.751838 8.729583 8.706744 8.683276 8.659127 #>  [49,] 8.812821 8.792149 8.771012 8.749378 8.727210 8.704469 8.681111 8.657088 #>  [50,] 8.810258 8.789657 8.768598 8.747051 8.724980 8.702348 8.679113 8.655229 #>  [51,] 8.807802 8.787279 8.766306 8.744854 8.722890 8.700378 8.677278 8.653545 #>  [52,] 8.805451 8.785013 8.764134 8.742786 8.720938 8.698555 8.675600 8.652031 #>  [53,] 8.803204 8.782857 8.762079 8.740843 8.719119 8.696875 8.674075 8.650681 #>  [54,] 8.801058 8.780808 8.760138 8.739021 8.717430 8.695333 8.672699 8.649491 #>  [55,] 8.799012 8.778865 8.758309 8.737318 8.715867 8.693926 8.671466 8.648454 #>  [56,] 8.797062 8.777025 8.756588 8.735730 8.714426 8.692649 8.670372 8.647563 #>  [57,] 8.795206 8.775284 8.754973 8.734254 8.713104 8.691497 8.669410 8.646814 #>  [58,] 8.793443 8.773639 8.753460 8.732886 8.711895 8.690466 8.668575 8.646198 #>  [59,] 8.791769 8.772089 8.752046 8.731621 8.710796 8.689549 8.667861 8.645710 #>  [60,] 8.790181 8.770630 8.750727 8.730457 8.709802 8.688744 8.667264 8.645344 #>  [61,] 8.788677 8.769258 8.749500 8.729389 8.708909 8.688043 8.666776 8.645092 #>  [62,] 8.787254 8.767971 8.748362 8.728414 8.708112 8.687443 8.666393 8.644948 #>  [63,] 8.785909 8.766765 8.747309 8.727526 8.707407 8.686938 8.666108 8.644906 #>  [64,] 8.784639 8.765638 8.746336 8.726723 8.706789 8.686523 8.665916 8.644960 #>  [65,] 8.783442 8.764586 8.745442 8.726001 8.706254 8.686194 8.665812 8.645102 #>  [66,] 8.782315 8.763606 8.744622 8.725355 8.705798 8.685945 8.665789 8.645328 #>  [67,] 8.781254 8.762694 8.743872 8.724781 8.705416 8.685771 8.665844 8.645631 #>  [68,] 8.780257 8.761848 8.743190 8.724276 8.705104 8.685669 8.665969 8.646005 #>  [69,] 8.779321 8.761065 8.742571 8.723836 8.704857 8.685632 8.666161 8.646444 #>  [70,] 8.778443 8.760340 8.742013 8.723457 8.704672 8.685657 8.666414 8.646944 #>  [71,] 8.777621 8.759672 8.741511 8.723136 8.704545 8.685740 8.666723 8.647499 #>  [72,] 8.776851 8.759058 8.741064 8.722868 8.704471 8.685875 8.667084 8.648104 #>  [73,] 8.776131 8.758493 8.740666 8.722651 8.704447 8.686059 8.667493 8.648754 #>  [74,] 8.775458 8.757976 8.740316 8.722480 8.704469 8.686289 8.667944 8.649444 #>  [75,] 8.774829 8.757504 8.740011 8.722353 8.704534 8.686559 8.668435 8.650171 #>  [76,] 8.774243 8.757073 8.739746 8.722267 8.704638 8.686866 8.668960 8.650929 #>  [77,] 8.773696 8.756681 8.739520 8.722217 8.704777 8.687208 8.669516 8.651715 #>  [78,] 8.773186 8.756326 8.739330 8.722202 8.704950 8.687579 8.670101 8.652526 #>  [79,] 8.772711 8.756004 8.739172 8.722219 8.705151 8.687978 8.670709 8.653356 #>  [80,] 8.772269 8.755715 8.739044 8.722264 8.705379 8.688401 8.671338 8.654204 #>  [81,] 8.771856 8.755454 8.738945 8.722335 8.705631 8.688844 8.671985 8.655066 #>  [82,] 8.771471 8.755220 8.738870 8.722429 8.705904 8.689306 8.672646 8.655939 #>  [83,] 8.771113 8.755010 8.738818 8.722544 8.706196 8.689784 8.673320 8.656819 #>  [84,] 8.770778 8.754823 8.738787 8.722677 8.706503 8.690274 8.674004 8.657705 #>  [85,] 8.770464 8.754656 8.738774 8.722827 8.706824 8.690775 8.674694 8.658594 #>  [86,] 8.770171 8.754507 8.738778 8.722991 8.707157 8.691285 8.675389 8.659483 #>  [87,] 8.769896 8.754375 8.738796 8.723167 8.707498 8.691800 8.676086 8.660370 #>  [88,] 8.769637 8.754257 8.738827 8.723354 8.707847 8.692320 8.676784 8.661254 #>  [89,] 8.769393 8.754153 8.738868 8.723548 8.708202 8.692842 8.677480 8.662132 #>  [90,] 8.769162 8.754059 8.738918 8.723749 8.708560 8.693364 8.678173 8.663002 #>  [91,] 8.768942 8.753975 8.738976 8.723954 8.708920 8.693884 8.678861 8.663864 #>  [92,] 8.768732 8.753899 8.739039 8.724163 8.709280 8.694402 8.679542 8.664714 #>  [93,] 8.768531 8.753829 8.739107 8.724374 8.709639 8.694916 8.680215 8.665553 #>  [94,] 8.768337 8.753765 8.739178 8.724585 8.709996 8.695423 8.680879 8.666378 #>  [95,] 8.768149 8.753704 8.739250 8.724794 8.710348 8.695923 8.681532 8.667189 #>  [96,] 8.767965 8.753646 8.739322 8.725002 8.710696 8.696415 8.682173 8.667983 #>  [97,] 8.767785 8.753590 8.739393 8.725206 8.711037 8.696898 8.682802 8.668761 #>  [98,] 8.767607 8.753533 8.739463 8.725405 8.711370 8.697370 8.683416 8.669522 #>  [99,] 8.767430 8.753476 8.739529 8.725599 8.711695 8.697830 8.684015 8.670263 #> [100,] 8.767254 8.753417 8.739591 8.725785 8.712011 8.698278 8.684598 8.670985 #>           [,49]    [,50]    [,51]    [,52]    [,53]    [,54]    [,55]    [,56] #>   [1,] 8.920075 8.902898 8.885709 8.868534 8.851402 8.834347 8.817409 8.800632 #>   [2,] 8.911851 8.894430 8.876984 8.859539 8.842123 8.824773 8.807527 8.790432 #>   [3,] 8.903639 8.885969 8.868260 8.850536 8.832829 8.815173 8.797608 8.780181 #>   [4,] 8.895442 8.877518 8.859539 8.841530 8.823522 8.805550 8.787654 8.769883 #>   [5,] 8.887264 8.869080 8.850825 8.832524 8.814206 8.795908 8.777670 8.759540 #>   [6,] 8.879109 8.860661 8.842123 8.823522 8.804886 8.786251 8.767658 8.749157 #>   [7,] 8.870982 8.852263 8.833438 8.814529 8.795566 8.776583 8.757623 8.738736 #>   [8,] 8.862885 8.843892 8.824773 8.805550 8.786251 8.766910 8.747571 8.728282 #>   [9,] 8.854825 8.835553 8.816134 8.796590 8.776946 8.757238 8.737506 8.717801 #>  [10,] 8.846806 8.827251 8.807527 8.787654 8.767658 8.747571 8.727434 8.707299 #>  [11,] 8.838833 8.818992 8.798958 8.778750 8.758392 8.737917 8.717363 8.696781 #>  [12,] 8.830912 8.810780 8.790432 8.769883 8.749157 8.728282 8.707299 8.686255 #>  [13,] 8.823048 8.802623 8.781956 8.761061 8.739958 8.718676 8.697250 8.675729 #>  [14,] 8.815247 8.794527 8.773538 8.752291 8.730805 8.709105 8.687225 8.665212 #>  [15,] 8.807515 8.786498 8.765184 8.743581 8.721705 8.699579 8.677234 8.654714 #>  [16,] 8.799859 8.778544 8.756902 8.734940 8.712669 8.690109 8.667288 8.644246 #>  [17,] 8.792286 8.770671 8.748700 8.726375 8.703705 8.680704 8.657397 8.633820 #>  [18,] 8.784801 8.762888 8.740587 8.717898 8.694823 8.671375 8.647573 8.623449 #>  [19,] 8.777412 8.755202 8.732572 8.709517 8.686036 8.662136 8.637831 8.613147 #>  [20,] 8.770126 8.747621 8.724663 8.701242 8.677353 8.652998 8.628184 8.602931 #>  [21,] 8.762951 8.740153 8.716869 8.693084 8.668788 8.643975 8.618646 8.592815 #>  [22,] 8.755893 8.732808 8.709201 8.685054 8.660352 8.635080 8.609235 8.582820 #>  [23,] 8.748961 8.725592 8.701668 8.677164 8.652058 8.626330 8.599967 8.572963 #>  [24,] 8.742161 8.718515 8.694280 8.669424 8.643919 8.617739 8.590859 8.563265 #>  [25,] 8.735501 8.711586 8.687047 8.661846 8.635950 8.609322 8.581931 8.553747 #>  [26,] 8.728989 8.704813 8.679979 8.654443 8.628164 8.601097 8.573200 8.544433 #>  [27,] 8.722632 8.698205 8.673086 8.647225 8.620574 8.593080 8.564688 8.535345 #>  [28,] 8.716437 8.691770 8.666378 8.640205 8.613196 8.585286 8.556413 8.526508 #>  [29,] 8.710411 8.685517 8.659865 8.633395 8.606042 8.577734 8.548396 8.517945 #>  [30,] 8.704561 8.679453 8.653556 8.626805 8.599126 8.570440 8.540657 8.509682 #>  [31,] 8.698893 8.673586 8.647461 8.620446 8.592462 8.563419 8.533217 8.501744 #>  [32,] 8.693414 8.667924 8.641588 8.614330 8.586062 8.556688 8.526094 8.494154 #>  [33,] 8.688129 8.662472 8.635945 8.608465 8.579939 8.550261 8.519307 8.486936 #>  [34,] 8.683044 8.657238 8.630540 8.602862 8.574104 8.544152 8.512873 8.480112 #>  [35,] 8.678162 8.652227 8.625380 8.597528 8.568567 8.538375 8.506810 8.473704 #>  [36,] 8.673489 8.647444 8.620470 8.592471 8.563337 8.532940 8.501130 8.467729 #>  [37,] 8.669027 8.642894 8.615817 8.587697 8.558422 8.527858 8.495848 8.462204 #>  [38,] 8.664779 8.638579 8.611423 8.583212 8.553829 8.523137 8.490973 8.457143 #>  [39,] 8.660749 8.634502 8.607293 8.579019 8.549563 8.518783 8.486514 8.452556 #>  [40,] 8.656937 8.630665 8.603428 8.575122 8.545626 8.514801 8.482476 8.448450 #>  [41,] 8.653344 8.627070 8.599830 8.571521 8.542022 8.511192 8.478862 8.444830 #>  [42,] 8.649970 8.623716 8.596499 8.568217 8.538749 8.507957 8.475673 8.441696 #>  [43,] 8.646814 8.620602 8.593434 8.565208 8.535808 8.505095 8.472906 8.439045 #>  [44,] 8.643876 8.617727 8.590632 8.562493 8.533193 8.502601 8.470556 8.436870 #>  [45,] 8.641152 8.615089 8.588092 8.560067 8.530902 8.500469 8.468615 8.435160 #>  [46,] 8.638641 8.612683 8.585808 8.557925 8.528927 8.498691 8.467073 8.433904 #>  [47,] 8.636339 8.610506 8.583776 8.556061 8.527261 8.497258 8.465918 8.433085 #>  [48,] 8.634242 8.608554 8.581990 8.554469 8.525895 8.496159 8.465137 8.432684 #>  [49,] 8.632345 8.606819 8.580444 8.553139 8.524818 8.495381 8.464712 8.432683 #>  [50,] 8.630643 8.605298 8.579129 8.552064 8.524021 8.494910 8.464627 8.433058 #>  [51,] 8.629131 8.603982 8.578038 8.551232 8.523491 8.494731 8.464863 8.433786 #>  [52,] 8.627802 8.602864 8.577162 8.550634 8.523215 8.494830 8.465401 8.434843 #>  [53,] 8.626651 8.601938 8.576492 8.550259 8.523179 8.495189 8.466221 8.436205 #>  [54,] 8.625670 8.601195 8.576020 8.550096 8.523372 8.495793 8.467304 8.437847 #>  [55,] 8.624853 8.600626 8.575734 8.550132 8.523778 8.496625 8.468628 8.439745 #>  [56,] 8.624192 8.600225 8.575625 8.550357 8.524383 8.497667 8.470174 8.441873 #>  [57,] 8.623680 8.599981 8.575683 8.550758 8.525175 8.498904 8.471922 8.444209 #>  [58,] 8.623310 8.599886 8.575899 8.551324 8.526138 8.500319 8.473853 8.446730 #>  [59,] 8.623074 8.599932 8.576261 8.552043 8.527259 8.501897 8.475948 8.449415 #>  [60,] 8.622965 8.600110 8.576761 8.552903 8.528525 8.503621 8.478189 8.452242 #>  [61,] 8.622975 8.600411 8.577388 8.553894 8.529924 8.505477 8.480560 8.455192 #>  [62,] 8.623097 8.600828 8.578132 8.555003 8.531441 8.507450 8.483044 8.458247 #>  [63,] 8.623323 8.601351 8.578984 8.556222 8.533066 8.509528 8.485626 8.461391 #>  [64,] 8.623647 8.601973 8.579936 8.557538 8.534787 8.511697 8.488292 8.464607 #>  [65,] 8.624061 8.602686 8.580978 8.558943 8.536593 8.513945 8.491028 8.467880 #>  [66,] 8.624559 8.603482 8.582102 8.560428 8.538473 8.516261 8.493822 8.471199 #>  [67,] 8.625133 8.604354 8.583300 8.561982 8.540419 8.518634 8.496662 8.474549 #>  [68,] 8.625778 8.605295 8.584563 8.563598 8.542419 8.521054 8.499538 8.477920 #>  [69,] 8.626488 8.606298 8.585886 8.565268 8.544467 8.523512 8.502441 8.481303 #>  [70,] 8.627255 8.607356 8.587260 8.566984 8.546553 8.525999 8.505360 8.484687 #>  [71,] 8.628076 8.608464 8.588679 8.568739 8.548671 8.528507 8.508288 8.488064 #>  [72,] 8.628944 8.609616 8.590136 8.570526 8.550813 8.531029 8.511218 8.491428 #>  [73,] 8.629854 8.610805 8.591626 8.572339 8.552972 8.533559 8.514142 8.494771 #>  [74,] 8.630800 8.612027 8.593144 8.574173 8.555143 8.536090 8.517055 8.498088 #>  [75,] 8.631780 8.613277 8.594683 8.576021 8.557320 8.538616 8.519951 8.501374 #>  [76,] 8.632787 8.614551 8.596240 8.577879 8.559498 8.541133 8.522825 8.504623 #>  [77,] 8.633818 8.615842 8.597809 8.579742 8.561673 8.543636 8.525673 8.507831 #>  [78,] 8.634869 8.617149 8.599386 8.581606 8.563839 8.546121 8.528491 8.510996 #>  [79,] 8.635936 8.618466 8.600968 8.583467 8.565994 8.548583 8.531275 8.514114 #>  [80,] 8.637015 8.619790 8.602550 8.585321 8.568133 8.551020 8.534022 8.517182 #>  [81,] 8.638104 8.621118 8.604130 8.587165 8.570254 8.553429 8.536730 8.520198 #>  [82,] 8.639199 8.622447 8.605704 8.588996 8.572353 8.555807 8.539395 8.523161 #>  [83,] 8.640297 8.623773 8.607269 8.590811 8.574427 8.558151 8.542017 8.526067 #>  [84,] 8.641396 8.625094 8.608823 8.592608 8.576475 8.560459 8.544593 8.528917 #>  [85,] 8.642492 8.626408 8.610364 8.594383 8.578495 8.562729 8.547121 8.531709 #>  [86,] 8.643584 8.627712 8.611888 8.596136 8.580483 8.564961 8.549601 8.534441 #>  [87,] 8.644670 8.629004 8.613394 8.597864 8.582440 8.567152 8.552031 8.537114 #>  [88,] 8.645747 8.630282 8.614881 8.599565 8.584362 8.569300 8.554411 8.539727 #>  [89,] 8.646814 8.631545 8.616345 8.601238 8.586249 8.571406 8.556739 8.542279 #>  [90,] 8.647869 8.632790 8.617787 8.602882 8.588100 8.573468 8.559014 8.544771 #>  [91,] 8.648910 8.634017 8.619205 8.604496 8.589914 8.575485 8.561238 8.547202 #>  [92,] 8.649935 8.635223 8.620596 8.606077 8.591689 8.577457 8.563408 8.549572 #>  [93,] 8.650945 8.636407 8.621961 8.607626 8.593425 8.579383 8.565526 8.551881 #>  [94,] 8.651936 8.637570 8.623298 8.609141 8.595122 8.581263 8.567590 8.554130 #>  [95,] 8.652908 8.638708 8.624606 8.610622 8.596778 8.583097 8.569602 8.556319 #>  [96,] 8.653861 8.639822 8.625885 8.612069 8.598394 8.584884 8.571560 8.558448 #>  [97,] 8.654792 8.640910 8.627133 8.613479 8.599969 8.586624 8.573466 8.560518 #>  [98,] 8.655702 8.641973 8.628351 8.614854 8.601503 8.588317 8.575319 8.562530 #>  [99,] 8.656589 8.643008 8.629537 8.616193 8.602996 8.589964 8.577119 8.564483 #> [100,] 8.657453 8.644016 8.630691 8.617495 8.604446 8.591564 8.578867 8.566378 #>           [,57]    [,58]    [,59]    [,60]    [,61]    [,62]    [,63]    [,64] #>   [1,] 8.784066 8.767764 8.751786 8.736199 8.721071 8.706473 8.692481 8.679168 #>   [2,] 8.773538 8.756902 8.740587 8.724663 8.709201 8.694280 8.679979 8.666378 #>   [3,] 8.762946 8.745960 8.729291 8.713010 8.697196 8.681931 8.667301 8.653393 #>   [4,] 8.752291 8.734940 8.717898 8.701242 8.685054 8.669424 8.654443 8.640205 #>   [5,] 8.741577 8.723842 8.706408 8.689356 8.672773 8.656755 8.641399 8.626809 #>   [6,] 8.730805 8.712669 8.694823 8.677353 8.660352 8.643919 8.628164 8.613196 #>   [7,] 8.719980 8.701423 8.683145 8.665234 8.647788 8.630915 8.614732 8.599357 #>   [8,] 8.709105 8.690109 8.671375 8.652998 8.635080 8.617739 8.601097 8.585286 #>   [9,] 8.698185 8.678729 8.659517 8.640647 8.622230 8.604388 8.587255 8.570974 #>  [10,] 8.687225 8.667288 8.647573 8.628184 8.609235 8.590859 8.573200 8.556413 #>  [11,] 8.676232 8.655792 8.635549 8.615610 8.596098 8.577152 8.558928 8.541593 #>  [12,] 8.665212 8.644246 8.623449 8.602931 8.582820 8.563265 8.544433 8.526508 #>  [13,] 8.654173 8.632659 8.611280 8.590150 8.569403 8.549197 8.529712 8.511147 #>  [14,] 8.643125 8.621039 8.599050 8.577273 8.555851 8.534949 8.514761 8.495503 #>  [15,] 8.632076 8.609395 8.586766 8.564309 8.542170 8.520524 8.499578 8.479568 #>  [16,] 8.621039 8.597739 8.574441 8.551266 8.528366 8.505925 8.484163 8.463335 #>  [17,] 8.610026 8.586083 8.562086 8.538156 8.514449 8.491156 8.468514 8.446797 #>  [18,] 8.599050 8.574441 8.549715 8.524991 8.500428 8.476227 8.452635 8.429951 #>  [19,] 8.588127 8.562830 8.537343 8.511787 8.486319 8.461146 8.436530 8.412793 #>  [20,] 8.577273 8.551266 8.524991 8.498562 8.472137 8.445928 8.420208 8.395321 #>  [21,] 8.566508 8.539771 8.512678 8.485337 8.457903 8.430589 8.403679 8.377539 #>  [22,] 8.555851 8.528366 8.500428 8.472137 8.443641 8.415151 8.386960 8.359453 #>  [23,] 8.545324 8.517075 8.488268 8.458990 8.429379 8.399641 8.370072 8.341076 #>  [24,] 8.534949 8.505925 8.476227 8.445928 8.415151 8.384093 8.353044 8.322425 #>  [25,] 8.524753 8.494944 8.464337 8.432987 8.400996 8.368544 8.335914 8.303529 #>  [26,] 8.514761 8.484163 8.452635 8.420208 8.386960 8.353044 8.318726 8.284426 #>  [27,] 8.505001 8.473615 8.441159 8.407636 8.373092 8.337649 8.301540 8.265167 #>  [28,] 8.495503 8.463335 8.429951 8.395321 8.359453 8.322425 8.284426 8.245823 #>  [29,] 8.486295 8.453359 8.419056 8.383317 8.346107 8.307448 8.267469 8.226480 #>  [30,] 8.477409 8.443726 8.408520 8.371683 8.333125 8.292805 8.250773 8.207251 #>  [31,] 8.468875 8.434474 8.398393 8.360480 8.320587 8.278595 8.234457 8.188276 #>  [32,] 8.460724 8.425641 8.388724 8.349772 8.308575 8.264925 8.218658 8.169725 #>  [33,] 8.452985 8.417267 8.379563 8.339626 8.297176 8.251913 8.203533 8.151799 #>  [34,] 8.445688 8.409388 8.370959 8.330107 8.286482 8.239680 8.189251 8.134733 #>  [35,] 8.438859 8.402039 8.362961 8.321280 8.276580 8.228354 8.175994 8.118789 #>  [36,] 8.432522 8.395254 8.355611 8.313205 8.267556 8.218059 8.163946 8.104247 #>  [37,] 8.426700 8.389061 8.348949 8.305938 8.259491 8.208912 8.153288 8.091396 #>  [38,] 8.421409 8.383484 8.343008 8.299526 8.252453 8.201019 8.144185 8.080509 #>  [39,] 8.416665 8.378543 8.337816 8.294007 8.246499 8.194466 8.136778 8.071824 #>  [40,] 8.412476 8.374250 8.333390 8.289408 8.241668 8.189315 8.131167 8.065521 #>  [41,] 8.408849 8.370613 8.329741 8.285743 8.237982 8.185600 8.127410 8.061700 #>  [42,] 8.405783 8.367633 8.326869 8.283014 8.235442 8.183323 8.125510 8.060369 #>  [43,] 8.403274 8.365303 8.324767 8.281208 8.234032 8.182457 8.125422 8.061447 #>  [44,] 8.401314 8.363611 8.323417 8.280302 8.233715 8.182946 8.127053 8.064768 #>  [45,] 8.399889 8.362540 8.322795 8.280259 8.234437 8.184707 8.130270 8.070105 #>  [46,] 8.398982 8.362067 8.322868 8.281033 8.236133 8.187639 8.134912 8.077189 #>  [47,] 8.398572 8.362162 8.323598 8.282572 8.238723 8.191626 8.140800 8.085734 #>  [48,] 8.398635 8.362795 8.324941 8.284815 8.242124 8.196545 8.147749 8.095455 #>  [49,] 8.399145 8.363931 8.326852 8.287699 8.246246 8.202269 8.155577 8.106086 #>  [50,] 8.400074 8.365533 8.329281 8.291157 8.251000 8.208675 8.164111 8.117387 #>  [51,] 8.401391 8.367562 8.332178 8.295124 8.256298 8.215643 8.173193 8.129149 #>  [52,] 8.403067 8.369980 8.335494 8.299534 8.262055 8.223065 8.182681 8.141196 #>  [53,] 8.405070 8.372747 8.339179 8.304327 8.268191 8.230840 8.192452 8.153384 #>  [54,] 8.407370 8.375827 8.343185 8.309441 8.274635 8.238879 8.202399 8.165594 #>  [55,] 8.409938 8.379181 8.347469 8.314823 8.281319 8.247103 8.212435 8.177733 #>  [56,] 8.412743 8.382776 8.351986 8.320422 8.288184 8.255444 8.222485 8.189729 #>  [57,] 8.415758 8.386577 8.356699 8.326192 8.295176 8.263845 8.232488 8.201527 #>  [58,] 8.418956 8.390554 8.361570 8.332090 8.302250 8.272254 8.242397 8.213087 #>  [59,] 8.422313 8.394676 8.366566 8.338080 8.309365 8.280632 8.252173 8.224379 #>  [60,] 8.425803 8.398918 8.371658 8.344130 8.316488 8.288944 8.261785 8.235381 #>  [61,] 8.429406 8.403254 8.376818 8.350209 8.323587 8.297162 8.271211 8.246082 #>  [62,] 8.433100 8.407663 8.382021 8.356293 8.330638 8.305264 8.280434 8.256474 #>  [63,] 8.436868 8.412124 8.387248 8.362361 8.337621 8.313231 8.289440 8.266553 #>  [64,] 8.440693 8.416619 8.392478 8.368393 8.344518 8.321049 8.298222 8.276319 #>  [65,] 8.444557 8.421130 8.397695 8.374373 8.351315 8.328708 8.306775 8.285775 #>  [66,] 8.448448 8.425645 8.402885 8.380287 8.357999 8.336199 8.315095 8.294926 #>  [67,] 8.452353 8.430150 8.408035 8.386125 8.364563 8.343517 8.323181 8.303777 #>  [68,] 8.456260 8.434633 8.413134 8.391877 8.370999 8.350657 8.331036 8.312336 #>  [69,] 8.460159 8.439085 8.418174 8.397536 8.377300 8.357619 8.338660 8.320611 #>  [70,] 8.464041 8.443497 8.423146 8.403093 8.383464 8.364400 8.346057 8.328609 #>  [71,] 8.467897 8.447861 8.428043 8.408546 8.389487 8.371000 8.353232 8.336338 #>  [72,] 8.471722 8.452171 8.432861 8.413889 8.395368 8.377422 8.360187 8.343808 #>  [73,] 8.475508 8.456421 8.437594 8.419120 8.401105 8.383666 8.366929 8.351027 #>  [74,] 8.479249 8.460607 8.442239 8.424236 8.406698 8.389735 8.373462 8.358003 #>  [75,] 8.482942 8.464724 8.446793 8.429237 8.412149 8.395630 8.379792 8.364744 #>  [76,] 8.486582 8.468769 8.451255 8.434121 8.417456 8.401357 8.385923 8.371260 #>  [77,] 8.490166 8.472739 8.455621 8.438887 8.422623 8.406917 8.391863 8.377556 #>  [78,] 8.493690 8.476633 8.459891 8.443537 8.427650 8.412313 8.397615 8.383642 #>  [79,] 8.497153 8.480448 8.464064 8.448070 8.432539 8.417551 8.403186 8.389525 #>  [80,] 8.500551 8.484183 8.468140 8.452487 8.437293 8.422632 8.408580 8.395211 #>  [81,] 8.503883 8.487838 8.472119 8.456789 8.441914 8.427562 8.413804 8.400708 #>  [82,] 8.507149 8.491410 8.476000 8.460978 8.446404 8.432343 8.418861 8.406022 #>  [83,] 8.510346 8.494901 8.479785 8.465054 8.450766 8.436980 8.423758 8.411160 #>  [84,] 8.513474 8.498309 8.483474 8.469020 8.455002 8.441476 8.428499 8.416127 #>  [85,] 8.516532 8.501636 8.487067 8.472877 8.459115 8.445835 8.433089 8.420930 #>  [86,] 8.519520 8.504880 8.490567 8.476626 8.463107 8.450060 8.437532 8.425573 #>  [87,] 8.522438 8.508043 8.493972 8.480270 8.466982 8.454154 8.441833 8.430063 #>  [88,] 8.525286 8.511125 8.497286 8.483811 8.470742 8.458122 8.445996 8.434405 #>  [89,] 8.528063 8.514127 8.500509 8.487250 8.474389 8.461967 8.450026 8.438603 #>  [90,] 8.530771 8.517049 8.503643 8.490589 8.477926 8.465692 8.453926 8.442662 #>  [91,] 8.533409 8.519893 8.506688 8.493830 8.481356 8.469300 8.457699 8.446587 #>  [92,] 8.535978 8.522659 8.509647 8.496976 8.484681 8.472795 8.461351 8.450381 #>  [93,] 8.538478 8.525347 8.512520 8.500028 8.487903 8.476178 8.464884 8.454050 #>  [94,] 8.540911 8.527960 8.515309 8.502988 8.491026 8.479455 8.468302 8.457597 #>  [95,] 8.543276 8.530498 8.518016 8.505858 8.494051 8.482626 8.471608 8.461025 #>  [96,] 8.545574 8.532963 8.520642 8.508640 8.496982 8.485695 8.474806 8.464339 #>  [97,] 8.547806 8.535355 8.523189 8.511335 8.499819 8.488665 8.477898 8.467541 #>  [98,] 8.549974 8.537675 8.525658 8.513946 8.502565 8.491538 8.480888 8.470636 #>  [99,] 8.552077 8.539925 8.528050 8.516475 8.505223 8.494317 8.483778 8.473626 #> [100,] 8.554117 8.542106 8.530367 8.518923 8.507795 8.497004 8.486571 8.476515 #>           [,65]    [,66]    [,67]    [,68]    [,69]    [,70]    [,71]    [,72] #>   [1,] 8.666607 8.654866 8.644006 8.634079 8.625126 8.617173 8.610234 8.604304 #>   [2,] 8.653556 8.641588 8.630540 8.620470 8.611423 8.603428 8.596499 8.590632 #>   [3,] 8.640292 8.628079 8.616829 8.606605 8.597456 8.589415 8.582498 8.576700 #>   [4,] 8.626805 8.614330 8.602862 8.592471 8.583212 8.575122 8.568217 8.562493 #>   [5,] 8.613086 8.600328 8.588625 8.578054 8.568675 8.560531 8.553639 8.547996 #>   [6,] 8.599126 8.586062 8.574104 8.563337 8.553829 8.545626 8.538749 8.533193 #>   [7,] 8.584914 8.571520 8.559285 8.548305 8.538656 8.530390 8.523529 8.518068 #>   [8,] 8.570440 8.556688 8.544152 8.532940 8.523137 8.514801 8.507957 8.502601 #>   [9,] 8.555692 8.541551 8.528688 8.517222 8.507251 8.498837 8.492013 8.486771 #>  [10,] 8.540657 8.526094 8.512873 8.501130 8.490973 8.482476 8.475673 8.470556 #>  [11,] 8.525325 8.510301 8.496689 8.484641 8.474280 8.465690 8.458910 8.453931 #>  [12,] 8.509682 8.494154 8.480112 8.467729 8.457143 8.448450 8.441696 8.436870 #>  [13,] 8.493715 8.477635 8.463121 8.450366 8.439530 8.430724 8.423999 8.419342 #>  [14,] 8.477409 8.460724 8.445688 8.432522 8.421409 8.412476 8.405783 8.401314 #>  [15,] 8.460751 8.443400 8.427787 8.414164 8.402741 8.393666 8.387009 8.382751 #>  [16,] 8.443726 8.425641 8.409388 8.395254 8.383484 8.374250 8.367633 8.363611 #>  [17,] 8.426320 8.407424 8.390457 8.375752 8.363591 8.354177 8.347605 8.343850 #>  [18,] 8.408520 8.388724 8.370959 8.355611 8.343008 8.333390 8.326869 8.323417 #>  [19,] 8.390312 8.369515 8.350857 8.334781 8.321676 8.311825 8.305363 8.302256 #>  [20,] 8.371683 8.349772 8.330107 8.313205 8.299526 8.289408 8.283014 8.280302 #>  [21,] 8.352623 8.329467 8.308665 8.290821 8.276482 8.266055 8.259739 8.257482 #>  [22,] 8.333125 8.308575 8.286482 8.267556 8.252453 8.241668 8.235442 8.233715 #>  [23,] 8.313185 8.287068 8.263505 8.243332 8.227339 8.216133 8.210014 8.208906 #>  [24,] 8.292805 8.264925 8.239680 8.218059 8.201019 8.189315 8.183323 8.182946 #>  [25,] 8.271995 8.242126 8.214948 8.191635 8.173356 8.161057 8.155216 8.155710 #>  [26,] 8.250773 8.218658 8.189251 8.163946 8.144185 8.131167 8.125510 8.127053 #>  [27,] 8.229174 8.194520 8.162530 8.134864 8.113313 8.099416 8.093984 8.096805 #>  [28,] 8.207251 8.169725 8.134733 8.104247 8.080509 8.065521 8.060369 8.064768 #>  [29,] 8.185079 8.144309 8.105818 8.071938 8.045491 8.029129 8.024332 8.030709 #>  [30,] 8.162766 8.118343 8.075764 8.037767 8.007921 7.989792 7.985454 7.994353 #>  [31,] 8.140456 8.091942 8.044590 8.001562 7.967383 7.946933 7.943202 7.955382 #>  [32,] 8.118343 8.065286 8.012374 7.963161 7.923361 7.899785 7.896880 7.913425 #>  [33,] 8.096676 8.038638 7.979294 7.922446 7.875224 7.847299 7.845559 7.868073 #>  [34,] 8.075764 8.012374 7.945683 7.879411 7.822201 7.787996 7.787972 7.818899 #>  [35,] 8.055984 7.986997 7.912098 7.834285 7.763390 7.719684 7.722331 7.765557 #>  [36,] 8.037767 7.963161 7.879411 7.787755 7.697869 7.638929 7.646054 7.708002 #>  [37,] 8.021587 7.941654 7.848888 7.741336 7.625123 7.539922 7.555346 7.647036 #>  [38,] 8.007921 7.923361 7.822201 7.697869 7.546458 7.411740 7.444926 7.585474 #>  [39,] 7.997209 7.909159 7.801291 7.661865 7.468878 7.230846 7.310627 7.530098 #>  [40,] 7.989792 7.899785 7.787996 7.638929 7.411740 6.948736 7.174372 7.492830 #>  [41,] 7.985868 7.895677 7.783516 7.633500 7.402501 6.880424 7.152865 7.485893 #>  [42,] 7.985454 7.896880 7.787972 7.646054 7.444926 7.174372 7.271580 7.510745 #>  [43,] 7.988388 7.903025 7.800351 7.672756 7.513314 7.363775 7.402837 7.556451 #>  [44,] 7.994353 7.913425 7.818899 7.708002 7.585474 7.492830 7.510745 7.610342 #>  [45,] 8.002926 7.927219 7.841658 7.746967 7.652470 7.589410 7.597788 7.664604 #>  [46,] 8.013631 7.943514 7.866885 7.786489 7.712280 7.666100 7.669458 7.715805 #>  [47,] 8.025993 7.961497 7.893229 7.824828 7.765220 7.729429 7.729845 7.762860 #>  [48,] 8.039567 7.980486 7.919746 7.861167 7.812183 7.783187 7.781737 7.805702 #>  [49,] 8.053968 7.999948 7.945822 7.895208 7.854089 7.829757 7.827053 7.844643 #>  [50,] 8.068871 8.019485 7.971087 7.926923 7.891736 7.870736 7.867149 7.880102 #>  [51,] 8.084016 8.038811 7.995336 7.956413 7.925784 7.907242 7.903011 7.912497 #>  [52,] 8.099199 8.057733 8.018474 7.983834 7.956769 7.940089 7.935374 7.942206 #>  [53,] 8.114267 8.076123 8.040474 8.009359 7.985125 7.969888 7.964800 7.969559 #>  [54,] 8.129104 8.093903 8.061349 8.033159 8.011206 7.997110 7.991728 7.994839 #>  [55,] 8.143630 8.111032 8.081139 8.055393 8.035302 8.022122 8.016506 8.018285 #>  [56,] 8.157788 8.127492 8.099894 8.076207 8.057654 8.045222 8.039415 8.040103 #>  [57,] 8.171540 8.143282 8.117671 8.095733 8.078462 8.066647 8.060683 8.060468 #>  [58,] 8.184865 8.158412 8.134531 8.114085 8.097896 8.086597 8.080502 8.079530 #>  [59,] 8.197751 8.172901 8.150530 8.131369 8.116099 8.105235 8.099029 8.097418 #>  [60,] 8.210195 8.186772 8.165725 8.147676 8.133193 8.122700 8.116400 8.114243 #>  [61,] 8.222199 8.200050 8.180168 8.163088 8.149285 8.139109 8.132729 8.130102 #>  [62,] 8.233771 8.212761 8.193910 8.177678 8.164464 8.154563 8.148114 8.145081 #>  [63,] 8.244920 8.224932 8.206997 8.191510 8.178812 8.169150 8.162640 8.159253 #>  [64,] 8.255658 8.236589 8.219469 8.204642 8.192397 8.182944 8.176382 8.172685 #>  [65,] 8.265999 8.247758 8.231368 8.217126 8.205281 8.196013 8.189404 8.185433 #>  [66,] 8.275956 8.258464 8.242729 8.229008 8.217519 8.208414 8.201764 8.197551 #>  [67,] 8.285544 8.268731 8.253584 8.240331 8.229159 8.220199 8.213512 8.209084 #>  [68,] 8.294777 8.278580 8.263966 8.251132 8.240244 8.231413 8.224694 8.220073 #>  [69,] 8.303668 8.288034 8.273901 8.261446 8.250812 8.242098 8.235350 8.230555 #>  [70,] 8.312233 8.297111 8.283416 8.271304 8.260900 8.252290 8.245515 8.240565 #>  [71,] 8.320484 8.305831 8.292535 8.280733 8.270537 8.262022 8.255223 8.250133 #>  [72,] 8.328434 8.314211 8.301279 8.289760 8.279753 8.271324 8.264504 8.259285 #>  [73,] 8.336096 8.322268 8.309670 8.298409 8.288573 8.280222 8.273382 8.268048 #>  [74,] 8.343481 8.330018 8.317725 8.306700 8.297022 8.288741 8.281884 8.276443 #>  [75,] 8.350602 8.337475 8.325463 8.314655 8.305120 8.296904 8.290031 8.284493 #>  [76,] 8.357469 8.344652 8.332900 8.322290 8.312887 8.304731 8.297843 8.292216 #>  [77,] 8.364093 8.351563 8.340050 8.329624 8.320342 8.312241 8.305339 8.299630 #>  [78,] 8.370483 8.358220 8.346928 8.336671 8.327501 8.319450 8.312535 8.306752 #>  [79,] 8.376649 8.364633 8.353546 8.343446 8.334379 8.326375 8.319449 8.313595 #>  [80,] 8.382599 8.370814 8.359918 8.349963 8.340992 8.333031 8.326093 8.320176 #>  [81,] 8.388343 8.376773 8.366053 8.356234 8.347351 8.339430 8.332482 8.326505 #>  [82,] 8.393888 8.382518 8.371964 8.362270 8.353469 8.345585 8.338628 8.332596 #>  [83,] 8.399242 8.388060 8.377659 8.368082 8.359358 8.351509 8.344543 8.338459 #>  [84,] 8.404412 8.393405 8.383149 8.373680 8.365028 8.357211 8.350237 8.344105 #>  [85,] 8.409406 8.398563 8.388441 8.379075 8.370489 8.362702 8.355721 8.349544 #>  [86,] 8.414228 8.403540 8.393544 8.384273 8.375750 8.367991 8.361003 8.354784 #>  [87,] 8.418887 8.408343 8.398466 8.389285 8.380820 8.373087 8.366092 8.359834 #>  [88,] 8.423388 8.412980 8.403214 8.394117 8.385707 8.377999 8.370998 8.364703 #>  [89,] 8.427735 8.417456 8.407795 8.398776 8.390418 8.382733 8.375726 8.369397 #>  [90,] 8.431936 8.421778 8.412215 8.403271 8.394961 8.387298 8.380285 8.373923 #>  [91,] 8.435994 8.425951 8.416481 8.407606 8.399342 8.391699 8.384682 8.378289 #>  [92,] 8.439915 8.429980 8.420598 8.411789 8.403568 8.395944 8.388922 8.382501 #>  [93,] 8.443704 8.433870 8.424571 8.415825 8.407644 8.400038 8.393012 8.386563 #>  [94,] 8.447364 8.437627 8.428406 8.419719 8.411576 8.403988 8.396957 8.390483 #>  [95,] 8.450900 8.441255 8.432108 8.423476 8.415370 8.407798 8.400763 8.394264 #>  [96,] 8.454316 8.444757 8.435681 8.427102 8.419030 8.411474 8.404435 8.397913 #>  [97,] 8.457615 8.448140 8.439130 8.430601 8.422562 8.415020 8.407977 8.401434 #>  [98,] 8.460803 8.451405 8.442459 8.433977 8.425969 8.418440 8.411395 8.404831 #>  [99,] 8.463881 8.454558 8.445672 8.437235 8.429256 8.421741 8.414691 8.408108 #> [100,] 8.466853 8.457601 8.448772 8.440378 8.432427 8.424924 8.417872 8.411270 #>           [,73]    [,74]    [,75]    [,76]    [,77]    [,78]    [,79]    [,80] #>   [1,] 8.599366 8.595386 8.592321 8.590112 8.588698 8.588006 8.587964 8.588498 #>   [2,] 8.585808 8.581990 8.579129 8.577162 8.576020 8.575625 8.575899 8.576761 #>   [3,] 8.571999 8.568355 8.565713 8.564005 8.563154 8.563077 8.563687 8.564896 #>   [4,] 8.557925 8.554469 8.552064 8.550634 8.550096 8.550357 8.551324 8.552903 #>   [5,] 8.543572 8.540320 8.538170 8.537040 8.536837 8.537461 8.538809 8.540780 #>   [6,] 8.528927 8.525895 8.524021 8.523215 8.523372 8.524383 8.526138 8.528525 #>   [7,] 8.513972 8.511179 8.509605 8.509148 8.509693 8.511120 8.513309 8.516139 #>   [8,] 8.498691 8.496159 8.494910 8.494830 8.495793 8.497667 8.500319 8.503621 #>   [9,] 8.483065 8.480817 8.479922 8.480251 8.481666 8.484020 8.487168 8.490970 #>  [10,] 8.467073 8.465137 8.464627 8.465401 8.467304 8.470174 8.473853 8.478189 #>  [11,] 8.450694 8.449099 8.449011 8.450269 8.452700 8.456126 8.460373 8.465279 #>  [12,] 8.433904 8.432684 8.433058 8.434843 8.437847 8.441873 8.446730 8.452242 #>  [13,] 8.416676 8.415871 8.416751 8.419113 8.422739 8.427413 8.432924 8.439081 #>  [14,] 8.398982 8.398635 8.400074 8.403067 8.407370 8.412743 8.418956 8.425803 #>  [15,] 8.380790 8.380952 8.383007 8.386692 8.391734 8.397864 8.404831 8.412413 #>  [16,] 8.362067 8.362795 8.365533 8.369980 8.375827 8.382776 8.390554 8.398918 #>  [17,] 8.342773 8.344136 8.347631 8.352917 8.359644 8.367482 8.376130 8.385329 #>  [18,] 8.322868 8.324941 8.329281 8.335494 8.343185 8.351986 8.361570 8.371658 #>  [19,] 8.302305 8.305180 8.310463 8.317702 8.326450 8.336296 8.346885 8.357919 #>  [20,] 8.281033 8.284815 8.291157 8.299534 8.309441 8.320422 8.332090 8.344130 #>  [21,] 8.258997 8.263810 8.271342 8.280986 8.292166 8.304378 8.317204 8.330311 #>  [22,] 8.236133 8.242124 8.251000 8.262055 8.274635 8.288184 8.302250 8.316488 #>  [23,] 8.212372 8.219716 8.230115 8.242745 8.256865 8.271862 8.287256 8.302687 #>  [24,] 8.187639 8.196545 8.208675 8.223065 8.238879 8.255444 8.272254 8.288944 #>  [25,] 8.161850 8.172569 8.186673 8.203035 8.220710 8.238969 8.257286 8.275296 #>  [26,] 8.134912 8.147749 8.164111 8.182681 8.202399 8.222485 8.242397 8.261785 #>  [27,] 8.106727 8.122052 8.141005 8.162048 8.184004 8.206048 8.227643 8.248462 #>  [28,] 8.077189 8.095455 8.117387 8.141196 8.165594 8.189729 8.213087 8.235381 #>  [29,] 8.046192 8.067952 8.093312 8.120210 8.147257 8.173610 8.198801 8.222604 #>  [30,] 8.013631 8.039567 8.068871 8.099199 8.129104 8.157788 8.184865 8.210195 #>  [31,] 7.979421 8.010368 8.044198 8.078312 8.111267 8.142373 8.171370 8.198226 #>  [32,] 7.943514 7.980486 8.019485 8.057733 8.093903 8.127492 8.158412 8.186772 #>  [33,] 7.905942 7.950155 7.994996 8.037694 8.077195 8.113282 8.146096 8.175912 #>  [34,] 7.866885 7.919746 7.971087 8.018474 8.061349 8.099894 8.134531 8.165725 #>  [35,] 7.826779 7.889817 7.948210 8.000399 8.046591 8.087483 8.123825 8.156288 #>  [36,] 7.786489 7.861167 7.926923 7.983834 8.033159 8.076207 8.114085 8.147676 #>  [37,] 7.747529 7.834857 7.907869 7.969164 8.021289 8.066219 8.105413 8.139958 #>  [38,] 7.712280 7.812183 7.891736 7.956769 8.011206 8.057654 8.097896 8.133193 #>  [39,] 7.683971 7.794544 7.879180 7.946991 8.003099 8.050627 8.091607 8.127429 #>  [40,] 7.666100 7.783187 7.870736 7.940089 7.997110 8.045222 8.086597 8.122700 #>  [41,] 7.661176 7.778892 7.866716 7.936212 7.993317 8.041483 8.082894 8.119023 #>  [42,] 7.669458 7.781737 7.867149 7.935374 7.991728 8.039415 8.080502 8.116400 #>  [43,] 7.688807 7.791067 7.871777 7.937452 7.992279 8.038980 8.079396 8.114817 #>  [44,] 7.715805 7.805702 7.880102 7.942206 7.994839 8.040103 8.079530 8.114243 #>  [45,] 7.747100 7.824252 7.891485 7.949309 7.999225 8.042675 8.080836 8.114632 #>  [46,] 7.780129 7.845386 7.905236 7.958384 8.005222 8.046563 8.083227 8.115928 #>  [47,] 7.813215 7.867988 7.920700 7.969044 8.012591 8.051616 8.086605 8.118063 #>  [48,] 7.845386 7.891210 7.937301 7.980920 8.021096 8.057679 8.090865 8.120964 #>  [49,] 7.876133 7.914450 7.954562 7.993677 8.030506 8.064595 8.095897 8.124553 #>  [50,] 7.905236 7.937301 7.972112 8.007025 8.040612 8.072211 8.101592 8.128752 #>  [51,] 7.932642 7.959508 7.989668 8.020725 8.051225 8.080387 8.107846 8.133481 #>  [52,] 7.958384 7.980920 8.007025 8.034581 8.062184 8.088994 8.114558 8.138666 #>  [53,] 7.982543 8.001460 8.024039 8.048440 8.073350 8.097919 8.121639 8.144233 #>  [54,] 8.005222 8.021096 8.040612 8.062184 8.084611 8.107063 8.129005 8.150115 #>  [55,] 8.026526 8.039829 8.056681 8.075723 8.095873 8.116340 8.136582 8.156252 #>  [56,] 8.046563 8.057679 8.072211 8.088994 8.107063 8.125677 8.144306 8.162587 #>  [57,] 8.065432 8.074679 8.087183 8.101950 8.118122 8.135016 8.152120 8.169069 #>  [58,] 8.083227 8.090865 8.101592 8.114558 8.129005 8.144306 8.159975 8.175654 #>  [59,] 8.100033 8.106280 8.115445 8.126801 8.139678 8.153507 8.167832 8.182303 #>  [60,] 8.115928 8.120964 8.128752 8.138666 8.150115 8.162587 8.175654 8.188982 #>  [61,] 8.130982 8.134960 8.141528 8.150148 8.160300 8.171520 8.183413 8.195661 #>  [62,] 8.145260 8.148307 8.153792 8.161250 8.170221 8.180286 8.191085 8.202315 #>  [63,] 8.158818 8.161044 8.165564 8.171974 8.179868 8.188872 8.198651 8.208923 #>  [64,] 8.171708 8.173206 8.176863 8.182327 8.189240 8.197264 8.206094 8.215467 #>  [65,] 8.183978 8.184828 8.187710 8.192318 8.198335 8.205457 8.213403 8.221931 #>  [66,] 8.195670 8.195940 8.198126 8.201958 8.207155 8.213444 8.220568 8.228302 #>  [67,] 8.206823 8.206573 8.208130 8.211256 8.215703 8.221222 8.227582 8.234572 #>  [68,] 8.217471 8.216754 8.217741 8.220225 8.223982 8.228791 8.234439 8.240731 #>  [69,] 8.227647 8.226508 8.226978 8.228875 8.232000 8.236151 8.241135 8.246772 #>  [70,] 8.237381 8.235858 8.235858 8.237218 8.239760 8.243303 8.247669 8.252692 #>  [71,] 8.246697 8.244827 8.244398 8.245266 8.247271 8.250249 8.254038 8.258486 #>  [72,] 8.255622 8.253434 8.252613 8.253029 8.254538 8.256992 8.260243 8.264150 #>  [73,] 8.264177 8.261700 8.260519 8.260519 8.261569 8.263537 8.266285 8.269684 #>  [74,] 8.272383 8.269641 8.268130 8.267745 8.268371 8.269886 8.272164 8.275087 #>  [75,] 8.280259 8.277273 8.275458 8.274719 8.274952 8.276044 8.277883 8.280357 #>  [76,] 8.287823 8.284613 8.282517 8.281450 8.281317 8.282016 8.283443 8.285495 #>  [77,] 8.295090 8.291674 8.289318 8.287947 8.287474 8.287805 8.288847 8.290502 #>  [78,] 8.302076 8.298469 8.295873 8.294219 8.293429 8.293418 8.294097 8.295379 #>  [79,] 8.308795 8.305011 8.302192 8.300276 8.299190 8.298857 8.299197 8.300126 #>  [80,] 8.315260 8.311312 8.308286 8.306124 8.304762 8.304129 8.304149 8.304746 #>  [81,] 8.321482 8.317381 8.314162 8.311773 8.310153 8.309237 8.308956 8.309241 #>  [82,] 8.327472 8.323230 8.319832 8.317229 8.315367 8.314186 8.313623 8.313611 #>  [83,] 8.333242 8.328868 8.325302 8.322500 8.320411 8.318981 8.318151 8.317860 #>  [84,] 8.338802 8.334304 8.330581 8.327592 8.325290 8.323626 8.322544 8.321989 #>  [85,] 8.344159 8.339546 8.335676 8.332512 8.330010 8.328125 8.326806 8.326000 #>  [86,] 8.349324 8.344603 8.340595 8.337266 8.334576 8.332483 8.330940 8.329897 #>  [87,] 8.354303 8.349481 8.345343 8.341859 8.338993 8.336704 8.334948 8.333680 #>  [88,] 8.359105 8.354187 8.349928 8.346299 8.343265 8.340791 8.338834 8.337353 #>  [89,] 8.363736 8.358729 8.354356 8.350589 8.347398 8.344748 8.342601 8.340918 #>  [90,] 8.368204 8.363113 8.358632 8.354735 8.351395 8.348579 8.346252 8.344377 #>  [91,] 8.372514 8.367344 8.362761 8.358743 8.355262 8.352289 8.349790 8.347733 #>  [92,] 8.376673 8.371428 8.366749 8.362615 8.359001 8.355879 8.353218 8.350987 #>  [93,] 8.380687 8.375371 8.370601 8.366358 8.362617 8.359354 8.356539 8.354143 #>  [94,] 8.384559 8.379177 8.374321 8.369974 8.366114 8.362717 8.359755 8.357201 #>  [95,] 8.388297 8.382851 8.377914 8.373469 8.369495 8.365970 8.362869 8.360166 #>  [96,] 8.391904 8.386399 8.381384 8.376846 8.372764 8.369118 8.365884 8.363037 #>  [97,] 8.395385 8.389823 8.384735 8.380108 8.375924 8.372163 8.368802 8.365819 #>  [98,] 8.398744 8.393128 8.387971 8.383260 8.378978 8.375107 8.371626 8.368512 #>  [99,] 8.401986 8.396319 8.391096 8.386305 8.381930 8.377954 8.374357 8.371119 #> [100,] 8.405114 8.399398 8.394112 8.389245 8.384782 8.380706 8.376999 8.373642 #>           [,81]    [,82]    [,83]    [,84]    [,85]    [,86]    [,87]    [,88] #>   [1,] 8.589534 8.591000 8.592830 8.594959 8.597332 8.599894 8.602598 8.605403 #>   [2,] 8.578132 8.579936 8.582102 8.584563 8.587260 8.590136 8.593144 8.596240 #>   [3,] 8.566622 8.568782 8.571301 8.574109 8.577143 8.580346 8.583667 8.587064 #>   [4,] 8.555003 8.557538 8.560428 8.563598 8.566984 8.570526 8.574173 8.577879 #>   [5,] 8.543276 8.546206 8.549484 8.553034 8.556786 8.560680 8.564663 8.568689 #>   [6,] 8.531441 8.534787 8.538473 8.542419 8.546553 8.550813 8.555143 8.559498 #>   [7,] 8.519499 8.523283 8.527398 8.531758 8.536289 8.540927 8.545617 8.550311 #>   [8,] 8.507450 8.511697 8.516261 8.521054 8.525999 8.531029 8.536090 8.541133 #>   [9,] 8.495298 8.500032 8.505067 8.510312 8.515687 8.521124 8.526567 8.531969 #>  [10,] 8.483044 8.488292 8.493822 8.499538 8.505360 8.511218 8.517055 8.522825 #>  [11,] 8.470692 8.476482 8.482530 8.488739 8.495024 8.501316 8.507559 8.513707 #>  [12,] 8.458247 8.464607 8.471199 8.477920 8.484687 8.491428 8.498088 8.504623 #>  [13,] 8.445715 8.452674 8.459835 8.467091 8.474356 8.481560 8.488649 8.495578 #>  [14,] 8.433100 8.440693 8.448448 8.456260 8.464041 8.471722 8.479249 8.486582 #>  [15,] 8.420413 8.428670 8.437048 8.445437 8.453751 8.461922 8.469899 8.477643 #>  [16,] 8.407663 8.416619 8.425645 8.434633 8.443497 8.452171 8.460607 8.468769 #>  [17,] 8.394861 8.404550 8.414253 8.423861 8.433291 8.442480 8.451383 8.459969 #>  [18,] 8.382021 8.392478 8.402885 8.413134 8.423146 8.432861 8.442239 8.451255 #>  [19,] 8.369159 8.380420 8.391557 8.402468 8.413075 8.423326 8.433186 8.442635 #>  [20,] 8.356293 8.368393 8.380287 8.391877 8.403093 8.413889 8.424236 8.434121 #>  [21,] 8.343445 8.356418 8.369094 8.381381 8.393217 8.404565 8.415403 8.425724 #>  [22,] 8.330638 8.344518 8.357999 8.370999 8.383464 8.395368 8.406698 8.417456 #>  [23,] 8.317901 8.332719 8.347026 8.360750 8.373852 8.386315 8.398138 8.409330 #>  [24,] 8.305264 8.321049 8.336199 8.350657 8.364400 8.377422 8.389735 8.401357 #>  [25,] 8.292762 8.309539 8.325545 8.340744 8.355128 8.368707 8.381504 8.393550 #>  [26,] 8.280434 8.298222 8.315095 8.331036 8.346057 8.360187 8.373462 8.385923 #>  [27,] 8.268322 8.287136 8.304877 8.321558 8.337210 8.351881 8.365623 8.378489 #>  [28,] 8.256474 8.276319 8.294926 8.312336 8.328609 8.343808 8.358003 8.371260 #>  [29,] 8.244939 8.265812 8.285274 8.303400 8.320275 8.335986 8.350617 8.364249 #>  [30,] 8.233771 8.255658 8.275956 8.294777 8.312233 8.328434 8.343481 8.357469 #>  [31,] 8.223025 8.245902 8.267008 8.286494 8.304504 8.321169 8.336610 8.350933 #>  [32,] 8.212761 8.236589 8.258464 8.278580 8.297111 8.314211 8.330018 8.344652 #>  [33,] 8.203036 8.227763 8.250360 8.271062 8.290075 8.307576 8.323719 8.338638 #>  [34,] 8.193910 8.219469 8.242729 8.263966 8.283416 8.301279 8.317725 8.332900 #>  [35,] 8.185440 8.211749 8.235602 8.257315 8.277154 8.295336 8.312049 8.327448 #>  [36,] 8.177678 8.204642 8.229008 8.251132 8.271304 8.289760 8.306700 8.322290 #>  [37,] 8.170672 8.198181 8.222973 8.245437 8.265882 8.284563 8.301689 8.317435 #>  [38,] 8.164464 8.192397 8.217519 8.240244 8.260900 8.279753 8.297022 8.312887 #>  [39,] 8.159087 8.187313 8.212662 8.235566 8.256367 8.275338 8.292704 8.308651 #>  [40,] 8.154563 8.182944 8.208414 8.231413 8.252290 8.271324 8.288741 8.304731 #>  [41,] 8.150905 8.179300 8.204781 8.227789 8.248673 8.267712 8.285135 8.301128 #>  [42,] 8.148114 8.176382 8.201764 8.224694 8.245515 8.264504 8.281884 8.297843 #>  [43,] 8.146180 8.174182 8.199358 8.222125 8.242815 8.261696 8.278988 8.294873 #>  [44,] 8.145081 8.172685 8.197551 8.220073 8.240565 8.259285 8.276443 8.292216 #>  [45,] 8.144788 8.171870 8.196329 8.218527 8.238758 8.257263 8.274244 8.289868 #>  [46,] 8.145260 8.171708 8.195670 8.217471 8.237381 8.255622 8.272383 8.287823 #>  [47,] 8.146450 8.172166 8.195550 8.216887 8.236419 8.254350 8.270852 8.286074 #>  [48,] 8.148307 8.173206 8.195940 8.216754 8.235858 8.253434 8.269641 8.284613 #>  [49,] 8.150774 8.174786 8.196810 8.217047 8.235677 8.252861 8.268737 8.283431 #>  [50,] 8.153792 8.176863 8.198126 8.217741 8.235858 8.252613 8.268130 8.282517 #>  [51,] 8.157304 8.179392 8.199854 8.218810 8.236379 8.252675 8.267804 8.281860 #>  [52,] 8.161250 8.182327 8.201958 8.220225 8.237218 8.253029 8.267745 8.281450 #>  [53,] 8.165573 8.185624 8.204403 8.221959 8.238353 8.253656 8.267940 8.281273 #>  [54,] 8.170221 8.189240 8.207155 8.223982 8.239760 8.254538 8.268371 8.281317 #>  [55,] 8.175141 8.193133 8.210180 8.226269 8.241418 8.255656 8.269025 8.281569 #>  [56,] 8.180286 8.197264 8.213444 8.228791 8.243303 8.256992 8.269886 8.282016 #>  [57,] 8.185614 8.201596 8.216916 8.231523 8.245393 8.258527 8.270937 8.282645 #>  [58,] 8.191085 8.206094 8.220568 8.234439 8.247669 8.260243 8.272164 8.283443 #>  [59,] 8.196662 8.210727 8.224372 8.237516 8.250108 8.262123 8.273552 8.284397 #>  [60,] 8.202315 8.215467 8.228302 8.240731 8.252692 8.264150 8.275087 8.285495 #>  [61,] 8.208015 8.220286 8.232335 8.244063 8.255402 8.266308 8.276753 8.286725 #>  [62,] 8.213736 8.225162 8.236449 8.247494 8.258221 8.268581 8.278538 8.288074 #>  [63,] 8.219458 8.230073 8.240624 8.251004 8.261133 8.270955 8.280429 8.289531 #>  [64,] 8.225162 8.235001 8.244843 8.254577 8.264122 8.273416 8.282413 8.291085 #>  [65,] 8.230830 8.239929 8.249089 8.258199 8.267175 8.275951 8.284479 8.292726 #>  [66,] 8.236449 8.244843 8.253348 8.261855 8.270277 8.278548 8.286616 8.294443 #>  [67,] 8.242007 8.249729 8.257607 8.265532 8.273418 8.281197 8.288813 8.296228 #>  [68,] 8.247494 8.254577 8.261855 8.269220 8.276587 8.283886 8.291061 8.298071 #>  [69,] 8.252901 8.259378 8.266081 8.272908 8.279773 8.286606 8.293351 8.299964 #>  [70,] 8.258221 8.264122 8.270277 8.276587 8.282967 8.289348 8.295674 8.301898 #>  [71,] 8.263450 8.268803 8.274435 8.280249 8.286161 8.292105 8.298022 8.303867 #>  [72,] 8.268581 8.273416 8.278548 8.283886 8.289348 8.294868 8.300389 8.305864 #>  [73,] 8.273611 8.277954 8.282610 8.287492 8.292521 8.297632 8.302768 8.307882 #>  [74,] 8.278538 8.282413 8.286616 8.291061 8.295674 8.300389 8.305152 8.309916 #>  [75,] 8.283360 8.286791 8.290562 8.294589 8.298801 8.303135 8.307536 8.311959 #>  [76,] 8.288074 8.291085 8.294443 8.298071 8.301898 8.305864 8.309916 8.314007 #>  [77,] 8.292680 8.295292 8.298258 8.301503 8.304961 8.308572 8.312285 8.316055 #>  [78,] 8.297178 8.299411 8.302003 8.304882 8.307985 8.311255 8.314641 8.318098 #>  [79,] 8.301567 8.303441 8.305676 8.308206 8.310968 8.313909 8.316978 8.320134 #>  [80,] 8.305848 8.307380 8.309276 8.311471 8.313907 8.316531 8.319295 8.322157 #>  [81,] 8.310021 8.311229 8.312801 8.314676 8.316798 8.319117 8.321587 8.324166 #>  [82,] 8.314087 8.314987 8.316250 8.317819 8.319641 8.321667 8.323852 8.326156 #>  [83,] 8.318047 8.318654 8.319623 8.320900 8.322433 8.324177 8.326087 8.328126 #>  [84,] 8.321903 8.322231 8.322919 8.323916 8.325173 8.326645 8.328290 8.330072 #>  [85,] 8.325655 8.325718 8.326138 8.326867 8.327859 8.329069 8.330459 8.331993 #>  [86,] 8.329305 8.329116 8.329280 8.329753 8.330490 8.331449 8.332593 8.333886 #>  [87,] 8.332855 8.332425 8.332345 8.332573 8.333065 8.333783 8.334689 8.335751 #>  [88,] 8.336305 8.335646 8.335334 8.335327 8.335584 8.336069 8.336747 8.337584 #>  [89,] 8.339659 8.338781 8.338246 8.338014 8.338047 8.338308 8.338765 8.339385 #>  [90,] 8.342916 8.341831 8.341083 8.340635 8.340452 8.340498 8.340742 8.341152 #>  [91,] 8.346080 8.344796 8.343845 8.343191 8.342800 8.342639 8.342677 8.342885 #>  [92,] 8.349152 8.347678 8.346532 8.345680 8.345090 8.344730 8.344570 8.344583 #>  [93,] 8.352133 8.350478 8.349146 8.348104 8.347323 8.346771 8.346420 8.346244 #>  [94,] 8.355026 8.353197 8.351687 8.350463 8.349498 8.348761 8.348227 8.347867 #>  [95,] 8.357831 8.355838 8.354156 8.352758 8.351616 8.350702 8.349989 8.349454 #>  [96,] 8.360551 8.358400 8.356555 8.354989 8.353677 8.352591 8.351708 8.351001 #>  [97,] 8.363188 8.360885 8.358883 8.357157 8.355681 8.354431 8.353382 8.352511 #>  [98,] 8.365743 8.363295 8.361143 8.359262 8.357629 8.356220 8.355011 8.353981 #>  [99,] 8.368218 8.365631 8.363335 8.361306 8.359521 8.357959 8.356596 8.355412 #> [100,] 8.370615 8.367894 8.365459 8.363288 8.361358 8.359648 8.358136 8.356803 #>           [,89]    [,90]    [,91]    [,92]    [,93]    [,94]    [,95]    [,96] #>   [1,] 8.608271 8.611170 8.614073 8.616953 8.619793 8.622572 8.625278 8.627897 #>   [2,] 8.599386 8.602550 8.605704 8.608823 8.611888 8.614881 8.617787 8.620596 #>   [3,] 8.590496 8.593933 8.597344 8.600707 8.604001 8.607210 8.610321 8.613322 #>   [4,] 8.581606 8.585321 8.588996 8.592608 8.596136 8.599565 8.602882 8.606077 #>   [5,] 8.572719 8.576720 8.580664 8.584529 8.588295 8.591948 8.595474 8.598865 #>   [6,] 8.563839 8.568133 8.572353 8.576475 8.580483 8.584362 8.588100 8.591689 #>   [7,] 8.554972 8.559565 8.564065 8.568451 8.572704 8.576812 8.580764 8.584552 #>   [8,] 8.546121 8.551020 8.555807 8.560459 8.564961 8.569300 8.573468 8.577457 #>   [9,] 8.537292 8.542504 8.547582 8.552505 8.557258 8.561832 8.566217 8.570408 #>  [10,] 8.528491 8.534022 8.539395 8.544593 8.549601 8.554411 8.559014 8.563408 #>  [11,] 8.519723 8.525579 8.531253 8.536729 8.541994 8.547041 8.551864 8.556462 #>  [12,] 8.510996 8.517182 8.523161 8.528917 8.534441 8.539727 8.544771 8.549572 #>  [13,] 8.502316 8.508837 8.515124 8.521163 8.526948 8.532474 8.537738 8.542743 #>  [14,] 8.493690 8.500551 8.507149 8.513474 8.519520 8.525286 8.530771 8.535978 #>  [15,] 8.485127 8.492331 8.499242 8.505854 8.512162 8.518168 8.523873 8.529282 #>  [16,] 8.476633 8.484183 8.491410 8.498309 8.504880 8.511125 8.517049 8.522659 #>  [17,] 8.468218 8.476117 8.483661 8.490847 8.497680 8.504163 8.510304 8.516112 #>  [18,] 8.459891 8.468140 8.476000 8.483474 8.490567 8.497286 8.503643 8.509647 #>  [19,] 8.451661 8.460261 8.468437 8.476196 8.483547 8.490500 8.497069 8.503267 #>  [20,] 8.443537 8.452487 8.460978 8.469020 8.476626 8.483811 8.490589 8.496976 #>  [21,] 8.435530 8.444828 8.453631 8.461953 8.469811 8.477223 8.484206 8.490779 #>  [22,] 8.427650 8.437293 8.446404 8.455002 8.463107 8.470742 8.477926 8.484681 #>  [23,] 8.419907 8.429892 8.439305 8.448174 8.456521 8.464373 8.471753 8.478684 #>  [24,] 8.412313 8.422632 8.432343 8.441476 8.450060 8.458122 8.465692 8.472795 #>  [25,] 8.404879 8.415525 8.425526 8.434915 8.443728 8.451995 8.459748 8.467016 #>  [26,] 8.397615 8.408580 8.418861 8.428499 8.437532 8.445996 8.453926 8.461351 #>  [27,] 8.390532 8.401805 8.412357 8.422234 8.431479 8.440131 8.448229 8.455805 #>  [28,] 8.383642 8.395211 8.406022 8.416127 8.425573 8.434405 8.442662 8.450381 #>  [29,] 8.376956 8.388806 8.399863 8.410184 8.419821 8.428822 8.437230 8.445084 #>  [30,] 8.370483 8.382599 8.393888 8.404412 8.414228 8.423388 8.431936 8.439915 #>  [31,] 8.364234 8.376599 8.388104 8.398817 8.408800 8.418106 8.426784 8.434880 #>  [32,] 8.358220 8.370814 8.382518 8.393405 8.403540 8.412980 8.421778 8.429980 #>  [33,] 8.352448 8.365251 8.377136 8.388181 8.398453 8.408015 8.416921 8.425218 #>  [34,] 8.346928 8.359918 8.371964 8.383149 8.393544 8.403214 8.412215 8.420598 #>  [35,] 8.341666 8.354820 8.367007 8.378314 8.388817 8.398581 8.407665 8.416121 #>  [36,] 8.336671 8.349963 8.362270 8.373680 8.384273 8.394117 8.403271 8.411789 #>  [37,] 8.331948 8.345352 8.357756 8.369251 8.379917 8.389825 8.399036 8.407604 #>  [38,] 8.327501 8.340992 8.353469 8.365028 8.375750 8.385707 8.394961 8.403568 #>  [39,] 8.323334 8.336884 8.349412 8.361014 8.371774 8.381765 8.391048 8.399681 #>  [40,] 8.319450 8.333031 8.345585 8.357211 8.367991 8.377999 8.387298 8.395944 #>  [41,] 8.315851 8.329434 8.341991 8.353619 8.364400 8.374410 8.383710 8.392358 #>  [42,] 8.312535 8.326093 8.338628 8.350237 8.361003 8.370998 8.380285 8.388922 #>  [43,] 8.309503 8.323008 8.335497 8.347067 8.357798 8.367762 8.377023 8.385637 #>  [44,] 8.306752 8.320176 8.332596 8.344105 8.354784 8.364703 8.373923 8.382501 #>  [45,] 8.304278 8.317594 8.329922 8.341351 8.351960 8.361817 8.370984 8.379513 #>  [46,] 8.302076 8.315260 8.327472 8.338802 8.349324 8.359105 8.368204 8.376673 #>  [47,] 8.300142 8.313167 8.325243 8.336454 8.346872 8.356562 8.365581 8.373979 #>  [48,] 8.298469 8.311312 8.323230 8.334304 8.344603 8.354187 8.363113 8.371428 #>  [49,] 8.297049 8.309687 8.321428 8.332348 8.342512 8.351977 8.360798 8.369019 #>  [50,] 8.295873 8.308286 8.319832 8.330581 8.340595 8.349928 8.358632 8.366749 #>  [51,] 8.294933 8.307101 8.318434 8.328997 8.338847 8.348037 8.356612 8.364616 #>  [52,] 8.294219 8.306124 8.317229 8.327592 8.337266 8.346299 8.354735 8.362615 #>  [53,] 8.293721 8.305348 8.316209 8.326358 8.335844 8.344710 8.352998 8.360745 #>  [54,] 8.293429 8.304762 8.315367 8.325290 8.334576 8.343265 8.351395 8.359001 #>  [55,] 8.293332 8.304359 8.314695 8.324382 8.333458 8.341961 8.349924 8.357380 #>  [56,] 8.293418 8.304129 8.314186 8.323626 8.332483 8.340791 8.348579 8.355879 #>  [57,] 8.293676 8.304062 8.313831 8.323016 8.331646 8.339750 8.347357 8.354493 #>  [58,] 8.294097 8.304149 8.313623 8.322544 8.330940 8.338834 8.346252 8.353218 #>  [59,] 8.294668 8.304380 8.313552 8.322204 8.330359 8.338037 8.345261 8.352051 #>  [60,] 8.295379 8.304746 8.313611 8.321989 8.329897 8.337353 8.344377 8.350987 #>  [61,] 8.296219 8.305239 8.313792 8.321891 8.329548 8.336778 8.343597 8.350022 #>  [62,] 8.297178 8.305848 8.314087 8.321903 8.329305 8.336305 8.342916 8.349152 #>  [63,] 8.298245 8.306564 8.314488 8.322019 8.329163 8.335930 8.342329 8.348372 #>  [64,] 8.299411 8.307380 8.314987 8.322231 8.329116 8.335646 8.341831 8.347678 #>  [65,] 8.300667 8.308287 8.315577 8.322533 8.329157 8.335450 8.341417 8.347066 #>  [66,] 8.302003 8.309276 8.316250 8.322919 8.329280 8.335334 8.341083 8.346532 #>  [67,] 8.303411 8.310340 8.317000 8.323382 8.329481 8.335295 8.340824 8.346071 #>  [68,] 8.304882 8.311471 8.317819 8.323916 8.329753 8.335327 8.340635 8.345680 #>  [69,] 8.306409 8.312662 8.318702 8.324515 8.330091 8.335425 8.340513 8.345354 #>  [70,] 8.307985 8.313907 8.319641 8.325173 8.330490 8.335584 8.340452 8.345090 #>  [71,] 8.309603 8.315198 8.320631 8.325884 8.330944 8.335801 8.340448 8.344883 #>  [72,] 8.311255 8.316531 8.321667 8.326645 8.331449 8.336069 8.340498 8.344730 #>  [73,] 8.312936 8.317898 8.322742 8.327448 8.332000 8.336386 8.340597 8.344627 #>  [74,] 8.314641 8.319295 8.323852 8.328290 8.332593 8.336747 8.340742 8.344570 #>  [75,] 8.316363 8.320716 8.324991 8.329166 8.333223 8.337147 8.340928 8.344557 #>  [76,] 8.318098 8.322157 8.326156 8.330072 8.333886 8.337584 8.341152 8.344583 #>  [77,] 8.319842 8.323613 8.327342 8.331003 8.334579 8.338053 8.341411 8.344645 #>  [78,] 8.321589 8.325080 8.328544 8.331956 8.335297 8.338550 8.341702 8.344741 #>  [79,] 8.323337 8.326555 8.329759 8.332927 8.336037 8.339073 8.342020 8.344867 #>  [80,] 8.325080 8.328032 8.330984 8.333912 8.336796 8.339618 8.342364 8.345021 #>  [81,] 8.326817 8.329510 8.332215 8.334909 8.337570 8.340182 8.342729 8.345199 #>  [82,] 8.328544 8.330984 8.333449 8.335913 8.338357 8.340763 8.343115 8.345399 #>  [83,] 8.330258 8.332453 8.334682 8.336923 8.339154 8.341357 8.343516 8.345619 #>  [84,] 8.331956 8.333912 8.335913 8.337935 8.339958 8.341962 8.343933 8.345856 #>  [85,] 8.333637 8.335361 8.337139 8.338948 8.340766 8.342575 8.344360 8.346107 #>  [86,] 8.335297 8.336796 8.338357 8.339958 8.341576 8.343195 8.344798 8.346371 #>  [87,] 8.336935 8.338216 8.339566 8.340963 8.342387 8.343819 8.345243 8.346646 #>  [88,] 8.338550 8.339618 8.340763 8.341962 8.343195 8.344444 8.345694 8.346929 #>  [89,] 8.340139 8.341001 8.341946 8.342952 8.343999 8.345070 8.346147 8.347219 #>  [90,] 8.341702 8.342364 8.343115 8.343933 8.344798 8.345694 8.346603 8.347513 #>  [91,] 8.343236 8.343704 8.344266 8.344901 8.345589 8.346314 8.347059 8.347810 #>  [92,] 8.344741 8.345021 8.345399 8.345856 8.346371 8.346929 8.347513 8.348109 #>  [93,] 8.346216 8.346313 8.346513 8.346796 8.347143 8.347538 8.347964 8.348408 #>  [94,] 8.347660 8.347580 8.347607 8.347721 8.347903 8.348138 8.348410 8.348706 #>  [95,] 8.349071 8.348820 8.348678 8.348628 8.348650 8.348730 8.348851 8.349001 #>  [96,] 8.350450 8.350032 8.349727 8.349517 8.349383 8.349311 8.349285 8.349292 #>  [97,] 8.351796 8.351216 8.350752 8.350386 8.350101 8.349880 8.349710 8.349577 #>  [98,] 8.353107 8.352371 8.351753 8.351236 8.350802 8.350437 8.350126 8.349857 #>  [99,] 8.354385 8.353497 8.352729 8.352064 8.351486 8.350980 8.350532 8.350129 #> [100,] 8.355628 8.354593 8.353679 8.352871 8.352153 8.351509 8.350926 8.350392 #>           [,97]    [,98]    [,99]   [,100] #>   [1,] 8.630421 8.632839 8.635147 8.637339 #>   [2,] 8.623298 8.625885 8.628351 8.630691 #>   [3,] 8.616204 8.618960 8.621586 8.624076 #>   [4,] 8.609141 8.612069 8.614854 8.617495 #>   [5,] 8.602113 8.605212 8.608159 8.610951 #>   [6,] 8.595122 8.598394 8.601503 8.604446 #>   [7,] 8.588171 8.591617 8.594888 8.597983 #>   [8,] 8.581263 8.584884 8.588317 8.591564 #>   [9,] 8.574402 8.578197 8.581793 8.585191 #>  [10,] 8.567590 8.571560 8.575319 8.578867 #>  [11,] 8.560832 8.564976 8.568896 8.572595 #>  [12,] 8.554130 8.558448 8.562530 8.566378 #>  [13,] 8.547489 8.551980 8.556221 8.560217 #>  [14,] 8.540911 8.545574 8.549974 8.554117 #>  [15,] 8.534400 8.539234 8.543791 8.548079 #>  [16,] 8.527960 8.532963 8.537675 8.542106 #>  [17,] 8.521595 8.526765 8.531630 8.536201 #>  [18,] 8.515309 8.520642 8.525658 8.530367 #>  [19,] 8.509105 8.514600 8.519762 8.524607 #>  [20,] 8.502988 8.508640 8.513946 8.518923 #>  [21,] 8.496960 8.502766 8.508213 8.513318 #>  [22,] 8.491026 8.496982 8.502565 8.507795 #>  [23,] 8.485190 8.491290 8.497006 8.502356 #>  [24,] 8.479455 8.485695 8.491538 8.497004 #>  [25,] 8.473824 8.480199 8.486165 8.491742 #>  [26,] 8.468302 8.474806 8.480888 8.486571 #>  [27,] 8.462892 8.469518 8.475711 8.481495 #>  [28,] 8.457597 8.464339 8.470636 8.476515 #>  [29,] 8.452420 8.459270 8.465666 8.471633 #>  [30,] 8.447364 8.454316 8.460803 8.466853 #>  [31,] 8.442432 8.449477 8.456048 8.462175 #>  [32,] 8.437627 8.444757 8.451405 8.457601 #>  [33,] 8.432951 8.440158 8.446875 8.453133 #>  [34,] 8.428406 8.435681 8.442459 8.448772 #>  [35,] 8.423995 8.431329 8.438160 8.444520 #>  [36,] 8.419719 8.427102 8.433977 8.440378 #>  [37,] 8.415579 8.423002 8.429913 8.436347 #>  [38,] 8.411576 8.419030 8.425969 8.432427 #>  [39,] 8.407713 8.415187 8.422144 8.428619 #>  [40,] 8.403988 8.411474 8.418440 8.424924 #>  [41,] 8.400403 8.407889 8.414857 8.421342 #>  [42,] 8.396957 8.404435 8.411395 8.417872 #>  [43,] 8.393651 8.401110 8.408052 8.414515 #>  [44,] 8.390483 8.397913 8.404831 8.411270 #>  [45,] 8.387453 8.394845 8.401728 8.408136 #>  [46,] 8.384559 8.391904 8.398744 8.405114 #>  [47,] 8.381801 8.389089 8.395878 8.402201 #>  [48,] 8.379177 8.386399 8.393128 8.399398 #>  [49,] 8.376684 8.383831 8.390493 8.396702 #>  [50,] 8.374321 8.381384 8.387971 8.394112 #>  [51,] 8.372086 8.379057 8.385561 8.391627 #>  [52,] 8.369974 8.376846 8.383260 8.389245 #>  [53,] 8.367985 8.374749 8.381067 8.386964 #>  [54,] 8.366114 8.372764 8.378978 8.384782 #>  [55,] 8.364359 8.370888 8.376993 8.382696 #>  [56,] 8.362717 8.369118 8.375107 8.380706 #>  [57,] 8.361183 8.367451 8.373319 8.378808 #>  [58,] 8.359755 8.365884 8.371626 8.376999 #>  [59,] 8.358429 8.364414 8.370024 8.375278 #>  [60,] 8.357201 8.363037 8.368512 8.373642 #>  [61,] 8.356068 8.361751 8.367086 8.372089 #>  [62,] 8.355026 8.360551 8.365743 8.370615 #>  [63,] 8.354070 8.359435 8.364481 8.369217 #>  [64,] 8.353197 8.358400 8.363295 8.367894 #>  [65,] 8.352404 8.357440 8.362183 8.366642 #>  [66,] 8.351687 8.356555 8.361143 8.365459 #>  [67,] 8.351041 8.355739 8.360170 8.364342 #>  [68,] 8.350463 8.354989 8.359262 8.363288 #>  [69,] 8.349950 8.354303 8.358416 8.362294 #>  [70,] 8.349498 8.353677 8.357629 8.361358 #>  [71,] 8.349103 8.353107 8.356898 8.360477 #>  [72,] 8.348761 8.352591 8.356220 8.359648 #>  [73,] 8.348470 8.352126 8.355592 8.358869 #>  [74,] 8.348227 8.351708 8.355011 8.358136 #>  [75,] 8.348027 8.351334 8.354475 8.357449 #>  [76,] 8.347867 8.351001 8.353981 8.356803 #>  [77,] 8.347746 8.350708 8.353526 8.356197 #>  [78,] 8.347660 8.350450 8.353107 8.355628 #>  [79,] 8.347605 8.350226 8.352723 8.355094 #>  [80,] 8.347580 8.350032 8.352371 8.354593 #>  [81,] 8.347581 8.349867 8.352049 8.354122 #>  [82,] 8.347607 8.349727 8.351753 8.353679 #>  [83,] 8.347654 8.349611 8.351483 8.353263 #>  [84,] 8.347721 8.349517 8.351236 8.352871 #>  [85,] 8.347804 8.349441 8.351009 8.352502 #>  [86,] 8.347903 8.349383 8.350802 8.352153 #>  [87,] 8.348015 8.349340 8.350612 8.351822 #>  [88,] 8.348138 8.349311 8.350437 8.351509 #>  [89,] 8.348271 8.349293 8.350275 8.351211 #>  [90,] 8.348410 8.349285 8.350126 8.350926 #>  [91,] 8.348556 8.349285 8.349987 8.350654 #>  [92,] 8.348706 8.349292 8.349857 8.350392 #>  [93,] 8.348859 8.349304 8.349734 8.350140 #>  [94,] 8.349013 8.349320 8.349617 8.349895 #>  [95,] 8.349167 8.349338 8.349505 8.349657 #>  [96,] 8.349320 8.349358 8.349396 8.349425 #>  [97,] 8.349470 8.349377 8.349289 8.349197 #>  [98,] 8.349617 8.349396 8.349184 8.348972 #>  [99,] 8.349759 8.349412 8.349078 8.348748 #> [100,] 8.349895 8.349425 8.348972 8.348526  # Converting negative potentials results in NA's with warning try( potential_to_head(m, -300) ) #> Warning: NaNs produced #> [1] NaN  # unless na.below = FALSE potential_to_head(m, -300, na.below = FALSE) #> [1] -7.745967"},{"path":"https://cneyens.github.io/raem/reference/headareasink.html","id":null,"dir":"Reference","previous_headings":"","what":"Create a head-specified area-sink analytic element — headareasink","title":"Create a head-specified area-sink analytic element — headareasink","text":"headareasink() creates area-sink analytic element constant specified head. constant leakage flux aquifer area-sink computed solving corresponding aem model.","code":""},{"path":"https://cneyens.github.io/raem/reference/headareasink.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create a head-specified area-sink analytic element — headareasink","text":"","code":"headareasink(xc, yc, hc, R, resistance = 0, location = c(\"top\", \"base\"), ...)"},{"path":"https://cneyens.github.io/raem/reference/headareasink.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create a head-specified area-sink analytic element — headareasink","text":"xc numeric, x location center area-sink yc numeric, y location center area-sink hc numeric, specified hydraulic head center area-sink R numeric, radius circular area-sink resistance numeric, hydraulic resistance area-sink connection aquifer. Defaults 0 (resistance). location character, either top (default) base specifying vertical position area-sink. ... ignored","code":""},{"path":"https://cneyens.github.io/raem/reference/headareasink.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create a head-specified area-sink analytic element — headareasink","text":"Circular head-specified area-sink analytic element object class headareasink inherits areasink.","code":""},{"path":"https://cneyens.github.io/raem/reference/headareasink.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Create a head-specified area-sink analytic element — headareasink","text":"constant leakage flux area-sink computed solving aem model given specified head hc area-sink. head located -called collocation point, placed center area-sink. positive flux aquifer. Note head-dependent flux constant domain computed collocation point. flux therefore determined difference aquifer head specified head location , vary across domain varying aquifer head. resistance can increased area-sink poor connection aquifer, e.g. confining unit low hydraulic conductivity aquifer area-sink. aquifer unconfined (.e. variable saturated thickness), system equations becomes non-linear respect hydraulic head iteration required solve model.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/headareasink.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create a head-specified area-sink analytic element — headareasink","text":"","code":"# using headareasink, the head difference depends on the computed instead of given aquifer head headareasink(xc = -500, yc = 0, hc = 3, R = 500, res = 1000) #> $parameter #> [1] 0 #>  #> $nunknowns #> [1] 1 #>  #> $xc #> [1] -500 #>  #> $yc #> [1] 0 #>  #> $R #> [1] 500 #>  #> $location #> [1] \"top\" #>  #> $hc #> [1] 3 #>  #> $resistance #> [1] 1000 #>  #> attr(,\"class\") #> [1] \"headareasink\" \"areasink\"     \"element\"      headareasink(xc = -500, yc = 0, hc = 3, R = 500, location = 'base') #> $parameter #> [1] 0 #>  #> $nunknowns #> [1] 1 #>  #> $xc #> [1] -500 #>  #> $yc #> [1] 0 #>  #> $R #> [1] 500 #>  #> $location #> [1] \"base\" #>  #> $hc #> [1] 3 #>  #> $resistance #> [1] 0 #>  #> attr(,\"class\") #> [1] \"headareasink\" \"areasink\"     \"element\""},{"path":"https://cneyens.github.io/raem/reference/headlinesink.html","id":null,"dir":"Reference","previous_headings":"","what":"Create a head-specified line-sink analytic element — headlinesink","title":"Create a head-specified line-sink analytic element — headlinesink","text":"headlinesink() creates line-sink analytic element constant specified head. discharge line-sink per unit length computed solving corresponding aem model.","code":""},{"path":"https://cneyens.github.io/raem/reference/headlinesink.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create a head-specified line-sink analytic element — headlinesink","text":"","code":"headlinesink(x0, y0, x1, y1, hc, resistance = 0, width = 0, ...)"},{"path":"https://cneyens.github.io/raem/reference/headlinesink.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create a head-specified line-sink analytic element — headlinesink","text":"x0 numeric, starting x location line-sink y0 numeric, starting y location line-sink x1 numeric, ending x location line-sink y1 numeric, ending y location line-sink hc numeric, specified hydraulic head line-sink resistance numeric, hydraulic resistance line-sink connection aquifer. Defaults 0 (resistance). width numeric, width line-sink. Used resistance calculate line-sink strength, tracelines() determine particle reached line. Defaults zero (infinitesimally narrow line). ... ignored","code":""},{"path":"https://cneyens.github.io/raem/reference/headlinesink.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create a head-specified line-sink analytic element — headlinesink","text":"Head-specified line-sink analytic element object class headlinesink inherits linesink.","code":""},{"path":"https://cneyens.github.io/raem/reference/headlinesink.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Create a head-specified line-sink analytic element — headlinesink","text":"strength line-sink (discharge per unit length line-sink) computed solving aem model given specified head hc line-sink. head located -called collocation point, placed center line-sink. resistance can increased line-sink poor connection aquifer. effect larger smaller wetted perimeter can mimicked adjusting resistance /width accordingly. width = 0 (default) removed conductance calculation. aquifer unconfined (.e. variable saturated thickness), system equations becomes non-linear respect hydraulic head iteration required solve model.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/headlinesink.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create a head-specified line-sink analytic element — headlinesink","text":"","code":"headlinesink(-75, 50, 100, 50, hc = 10) #> $parameter #> [1] 0 #>  #> $nunknowns #> [1] 1 #>  #> $z0 #> [1] -75+50i #>  #> $z1 #> [1] 100+50i #>  #> $L #> [1] 175 #>  #> $width #> [1] 0 #>  #> $xc #> [1] 12.5 #>  #> $yc #> [1] 50 #>  #> $hc #> [1] 10 #>  #> $resistance #> [1] 0 #>  #> attr(,\"class\") #> [1] \"headlinesink\" \"linesink\"     \"element\"      headlinesink(-75, 50, 100, 50, hc = 10, res = 10, width = 4) #> $parameter #> [1] 0 #>  #> $nunknowns #> [1] 1 #>  #> $z0 #> [1] -75+50i #>  #> $z1 #> [1] 100+50i #>  #> $L #> [1] 175 #>  #> $width #> [1] 4 #>  #> $xc #> [1] 12.5 #>  #> $yc #> [1] 50 #>  #> $hc #> [1] 10 #>  #> $resistance #> [1] 10 #>  #> attr(,\"class\") #> [1] \"headlinesink\" \"linesink\"     \"element\""},{"path":"https://cneyens.github.io/raem/reference/headwell.html","id":null,"dir":"Reference","previous_headings":"","what":"Create a analytic element of a well with a constant head — headwell","title":"Create a analytic element of a well with a constant head — headwell","text":"headwell() creates analytic element well constant, specified head. discharge well computed solving corresponding aem model. head can specified well location.","code":""},{"path":"https://cneyens.github.io/raem/reference/headwell.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create a analytic element of a well with a constant head — headwell","text":"","code":"headwell(xw, yw, hc, rw = 0.3, xc = xw, yc = yw, rc = rw, resistance = 0, ...)"},{"path":"https://cneyens.github.io/raem/reference/headwell.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create a analytic element of a well with a constant head — headwell","text":"xw numeric, x location well yw numeric, y location well hc numeric, specified hydraulic head collocation point. rw numeric, radius well. Defaults 0.3 (meter). xc numeric, x location collocation point. See details. Defaults xw. yc numeric, y location collocation point. See details. Defaults yw. rc numeric, radius collocation point. See details. Defaults rw. resistance numeric, hydraulic resistance well screen collocation point. Defaults 0 (resistance). ... ignored","code":""},{"path":"https://cneyens.github.io/raem/reference/headwell.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create a analytic element of a well with a constant head — headwell","text":"Analytic element well constant head object class headwell inherits well.","code":""},{"path":"https://cneyens.github.io/raem/reference/headwell.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Create a analytic element of a well with a constant head — headwell","text":"discharge well location xw yw computed solving aem model given specified head hc. head can specified point, called collocation point. can used compute discharge well specifying head location. collocation point located xc + rc, yc. default, location well collocation point . resistance well screen collocation point can increased well poor connection aquifer. aquifer unconfined (.e. variable saturated thickness), system equations becomes non-linear respect hydraulic head iteration required solve model.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/headwell.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create a analytic element of a well with a constant head — headwell","text":"","code":"headwell(xw = 400, yw = 300, hc = 20, rw = 0.3) #> $parameter #> [1] 0 #>  #> $nunknowns #> [1] 1 #>  #> $zetaw #> [1] 400+300i #>  #> $rw #> [1] 0.3 #>  #> $xc #> [1] 400.3 #>  #> $yc #> [1] 300 #>  #> $hc #> [1] 20 #>  #> $resistance #> [1] 0 #>  #> attr(,\"class\") #> [1] \"headwell\" \"well\"     \"element\"  headwell(xw = 400, yw = 300, hc = 20, rw = 0.3, resistance = 10) #> $parameter #> [1] 0 #>  #> $nunknowns #> [1] 1 #>  #> $zetaw #> [1] 400+300i #>  #> $rw #> [1] 0.3 #>  #> $xc #> [1] 400.3 #>  #> $yc #> [1] 300 #>  #> $hc #> [1] 20 #>  #> $resistance #> [1] 10 #>  #> attr(,\"class\") #> [1] \"headwell\" \"well\"     \"element\"  headwell(xw = 400, yw = 300, hc = 20, rw = 0.3, xc = 500, yc = 500, rc = 0) #> $parameter #> [1] 0 #>  #> $nunknowns #> [1] 1 #>  #> $zetaw #> [1] 400+300i #>  #> $rw #> [1] 0.3 #>  #> $xc #> [1] 500 #>  #> $yc #> [1] 500 #>  #> $hc #> [1] 20 #>  #> $resistance #> [1] 0 #>  #> attr(,\"class\") #> [1] \"headwell\" \"well\"     \"element\""},{"path":"https://cneyens.github.io/raem/reference/linesink.html","id":null,"dir":"Reference","previous_headings":"","what":"Create a strength-specified line-sink analytic element — linesink","title":"Create a strength-specified line-sink analytic element — linesink","text":"linesink() creates line-sink analytic element constant specified strength.","code":""},{"path":"https://cneyens.github.io/raem/reference/linesink.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create a strength-specified line-sink analytic element — linesink","text":"","code":"linesink(x0, y0, x1, y1, sigma, width = 0, ...)"},{"path":"https://cneyens.github.io/raem/reference/linesink.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create a strength-specified line-sink analytic element — linesink","text":"x0 numeric, starting x location line-sink y0 numeric, starting y location line-sink x1 numeric, ending x location line-sink y1 numeric, ending y location line-sink sigma numeric, specific strength line-sink, .e. discharge per length line-sink. Positive aquifer. width numeric, width line-sink. used tracelines() determine particle reached line. Defaults zero (infinitesimally narrow line). ... ignored","code":""},{"path":"https://cneyens.github.io/raem/reference/linesink.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create a strength-specified line-sink analytic element — linesink","text":"Strength-specified line-sink analytic element object class linesink inherits element.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/linesink.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create a strength-specified line-sink analytic element — linesink","text":"","code":"linesink(-75, 50, 100, 50, sigma = 1) #> $parameter #> [1] 1 #>  #> $nunknowns #> [1] 0 #>  #> $z0 #> [1] -75+50i #>  #> $z1 #> [1] 100+50i #>  #> $L #> [1] 175 #>  #> $width #> [1] 0 #>  #> attr(,\"class\") #> [1] \"linesink\" \"element\""},{"path":"https://cneyens.github.io/raem/reference/satthick.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute the saturated thickness — satthick","title":"Compute the saturated thickness — satthick","text":"satthick() computes saturated thickness aquifer aem object given x y coordinates.","code":""},{"path":"https://cneyens.github.io/raem/reference/satthick.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute the saturated thickness — satthick","text":"","code":"satthick(aem, x, y, as.grid = FALSE, ...)"},{"path":"https://cneyens.github.io/raem/reference/satthick.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute the saturated thickness — satthick","text":"aem aem object x numeric x coordinates evaluate y numeric y coordinates evaluate .grid logical, matrix dimensions c(length(y), length(x)) returned? Defaults FALSE. ... additional arguments passed heads() aem$type = 'variable'.","code":""},{"path":"https://cneyens.github.io/raem/reference/satthick.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute the saturated thickness — satthick","text":"satthick() returns vector length(x) (equal length(y)) saturated thicknesses x y. .grid = TRUE, matrix dimensions c(length(y), length(x)) described marginal vectors x y containing saturated thicknesses grid points.","code":""},{"path":"https://cneyens.github.io/raem/reference/satthick.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Compute the saturated thickness — satthick","text":"aquifer confined x y, saturated thickness equals aquifer thickness. flow variable saturated thickness, aquifer unconfined x y, saturated thickness calculated hydraulic head x y minus aquifer base.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/satthick.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute the saturated thickness — satthick","text":"","code":"uf <- uniformflow(100, 0.001, 0) rf <- constant(-1000, 0, 11) m <- aem(k = 10, top = 10, base = 0, n = 0.2, uf, rf, type = 'confined')  satthick(m, x = c(-200, 0, 200), y = 0) # confined #> [1] 10 10 10 satthick(m, x = seq(-500, 500, length = 100),          y = seq(-250, 250, length = 100), as.grid = TRUE) #>        [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] #>   [1,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>   [2,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>   [3,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>   [4,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>   [5,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>   [6,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>   [7,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>   [8,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>   [9,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [10,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [11,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [12,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [13,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [14,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [15,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [16,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [17,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [18,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [19,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [20,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [21,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [22,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [23,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [24,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [25,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [26,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [27,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [28,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [29,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [30,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [31,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [32,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [33,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [34,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [35,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [36,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [37,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [38,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [39,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [40,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [41,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [42,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [43,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [44,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [45,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [46,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [47,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [48,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [49,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [50,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [51,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [52,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [53,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [54,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [55,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [56,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [57,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [58,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [59,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [60,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [61,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [62,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [63,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [64,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [65,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [66,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [67,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [68,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [69,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [70,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [71,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [72,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [73,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [74,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [75,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [76,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [77,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [78,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [79,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [80,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [81,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [82,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [83,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [84,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [85,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [86,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [87,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [88,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [89,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [90,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [91,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [92,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [93,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [94,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [95,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [96,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [97,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [98,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>  [99,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #> [100,]   10   10   10   10   10   10   10   10   10    10    10    10    10 #>        [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] #>   [1,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [2,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [3,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [4,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [5,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [6,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [7,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [8,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [9,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [10,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [11,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [12,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [13,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [14,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [15,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [16,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [17,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [18,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [19,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [20,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [21,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [22,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [23,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [24,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [25,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [26,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [27,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [28,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [29,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [30,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [31,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [32,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [33,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [34,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [35,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [36,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [37,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [38,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [39,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [40,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [41,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [42,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [43,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [44,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [45,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [46,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [47,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [48,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [49,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [50,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [51,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [52,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [53,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [54,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [55,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [56,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [57,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [58,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [59,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [60,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [61,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [62,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [63,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [64,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [65,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [66,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [67,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [68,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [69,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [70,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [71,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [72,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [73,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [74,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [75,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [76,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [77,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [78,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [79,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [80,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [81,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [82,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [83,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [84,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [85,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [86,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [87,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [88,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [89,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [90,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [91,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [92,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [93,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [94,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [95,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [96,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [97,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [98,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [99,]    10    10    10    10    10    10    10    10    10    10    10    10 #> [100,]    10    10    10    10    10    10    10    10    10    10    10    10 #>        [,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] #>   [1,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [2,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [3,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [4,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [5,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [6,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [7,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [8,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [9,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [10,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [11,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [12,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [13,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [14,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [15,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [16,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [17,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [18,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [19,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [20,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [21,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [22,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [23,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [24,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [25,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [26,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [27,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [28,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [29,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [30,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [31,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [32,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [33,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [34,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [35,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [36,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [37,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [38,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [39,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [40,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [41,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [42,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [43,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [44,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [45,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [46,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [47,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [48,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [49,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [50,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [51,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [52,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [53,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [54,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [55,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [56,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [57,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [58,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [59,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [60,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [61,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [62,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [63,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [64,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [65,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [66,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [67,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [68,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [69,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [70,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [71,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [72,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [73,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [74,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [75,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [76,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [77,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [78,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [79,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [80,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [81,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [82,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [83,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [84,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [85,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [86,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [87,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [88,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [89,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [90,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [91,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [92,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [93,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [94,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [95,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [96,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [97,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [98,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [99,]    10    10    10    10    10    10    10    10    10    10    10    10 #> [100,]    10    10    10    10    10    10    10    10    10    10    10    10 #>        [,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] #>   [1,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [2,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [3,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [4,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [5,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [6,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [7,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [8,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [9,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [10,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [11,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [12,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [13,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [14,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [15,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [16,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [17,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [18,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [19,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [20,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [21,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [22,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [23,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [24,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [25,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [26,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [27,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [28,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [29,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [30,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [31,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [32,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [33,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [34,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [35,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [36,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [37,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [38,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [39,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [40,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [41,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [42,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [43,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [44,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [45,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [46,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [47,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [48,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [49,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [50,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [51,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [52,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [53,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [54,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [55,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [56,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [57,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [58,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [59,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [60,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [61,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [62,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [63,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [64,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [65,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [66,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [67,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [68,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [69,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [70,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [71,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [72,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [73,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [74,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [75,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [76,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [77,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [78,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [79,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [80,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [81,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [82,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [83,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [84,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [85,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [86,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [87,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [88,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [89,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [90,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [91,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [92,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [93,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [94,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [95,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [96,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [97,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [98,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [99,]    10    10    10    10    10    10    10    10    10    10    10    10 #> [100,]    10    10    10    10    10    10    10    10    10    10    10    10 #>        [,50] [,51] [,52] [,53] [,54] [,55] [,56] [,57] [,58] [,59] [,60] [,61] #>   [1,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [2,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [3,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [4,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [5,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [6,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [7,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [8,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [9,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [10,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [11,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [12,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [13,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [14,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [15,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [16,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [17,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [18,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [19,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [20,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [21,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [22,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [23,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [24,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [25,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [26,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [27,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [28,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [29,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [30,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [31,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [32,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [33,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [34,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [35,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [36,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [37,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [38,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [39,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [40,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [41,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [42,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [43,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [44,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [45,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [46,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [47,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [48,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [49,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [50,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [51,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [52,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [53,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [54,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [55,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [56,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [57,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [58,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [59,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [60,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [61,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [62,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [63,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [64,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [65,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [66,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [67,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [68,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [69,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [70,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [71,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [72,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [73,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [74,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [75,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [76,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [77,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [78,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [79,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [80,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [81,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [82,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [83,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [84,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [85,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [86,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [87,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [88,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [89,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [90,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [91,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [92,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [93,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [94,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [95,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [96,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [97,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [98,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [99,]    10    10    10    10    10    10    10    10    10    10    10    10 #> [100,]    10    10    10    10    10    10    10    10    10    10    10    10 #>        [,62] [,63] [,64] [,65] [,66] [,67] [,68] [,69] [,70] [,71] [,72] [,73] #>   [1,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [2,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [3,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [4,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [5,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [6,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [7,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [8,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [9,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [10,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [11,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [12,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [13,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [14,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [15,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [16,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [17,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [18,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [19,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [20,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [21,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [22,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [23,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [24,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [25,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [26,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [27,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [28,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [29,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [30,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [31,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [32,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [33,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [34,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [35,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [36,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [37,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [38,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [39,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [40,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [41,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [42,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [43,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [44,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [45,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [46,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [47,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [48,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [49,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [50,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [51,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [52,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [53,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [54,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [55,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [56,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [57,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [58,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [59,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [60,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [61,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [62,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [63,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [64,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [65,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [66,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [67,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [68,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [69,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [70,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [71,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [72,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [73,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [74,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [75,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [76,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [77,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [78,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [79,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [80,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [81,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [82,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [83,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [84,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [85,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [86,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [87,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [88,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [89,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [90,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [91,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [92,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [93,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [94,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [95,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [96,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [97,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [98,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [99,]    10    10    10    10    10    10    10    10    10    10    10    10 #> [100,]    10    10    10    10    10    10    10    10    10    10    10    10 #>        [,74] [,75] [,76] [,77] [,78] [,79] [,80] [,81] [,82] [,83] [,84] [,85] #>   [1,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [2,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [3,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [4,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [5,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [6,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [7,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [8,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [9,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [10,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [11,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [12,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [13,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [14,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [15,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [16,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [17,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [18,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [19,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [20,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [21,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [22,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [23,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [24,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [25,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [26,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [27,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [28,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [29,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [30,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [31,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [32,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [33,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [34,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [35,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [36,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [37,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [38,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [39,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [40,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [41,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [42,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [43,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [44,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [45,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [46,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [47,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [48,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [49,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [50,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [51,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [52,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [53,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [54,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [55,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [56,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [57,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [58,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [59,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [60,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [61,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [62,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [63,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [64,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [65,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [66,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [67,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [68,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [69,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [70,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [71,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [72,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [73,]    10    10    10    10    10    10    10    10    10    10    10    10 #>  [74,]   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   10    10    10    10    10    10 #>  [99,]    10    10    10    10    10    10    10    10    10    10    10    10 #> [100,]    10    10    10    10    10    10    10    10    10    10    10    10 #>        [,86] [,87] [,88] [,89] [,90] [,91] [,92] [,93] [,94] [,95] [,96] [,97] #>   [1,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [2,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [3,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [4,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [5,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [6,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [7,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [8,]    10    10    10    10    10    10    10    10    10    10    10    10 #>   [9,]    10    10    10    10    10    10    10    10    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#>  [18,]    10    10     10 #>  [19,]    10    10     10 #>  [20,]    10    10     10 #>  [21,]    10    10     10 #>  [22,]    10    10     10 #>  [23,]    10    10     10 #>  [24,]    10    10     10 #>  [25,]    10    10     10 #>  [26,]    10    10     10 #>  [27,]    10    10     10 #>  [28,]    10    10     10 #>  [29,]    10    10     10 #>  [30,]    10    10     10 #>  [31,]    10    10     10 #>  [32,]    10    10     10 #>  [33,]    10    10     10 #>  [34,]    10    10     10 #>  [35,]    10    10     10 #>  [36,]    10    10     10 #>  [37,]    10    10     10 #>  [38,]    10    10     10 #>  [39,]    10    10     10 #>  [40,]    10    10     10 #>  [41,]    10    10     10 #>  [42,]    10    10     10 #>  [43,]    10    10     10 #>  [44,]    10    10     10 #>  [45,]    10    10     10 #>  [46,]    10    10     10 #>  [47,]    10    10     10 #>  [48,]    10    10     10 #>  [49,]    10    10     10 #>  [50,]    10    10     10 #>  [51,]    10    10     10 #>  [52,]    10    10     10 #>  [53,]    10    10     10 #>  [54,]    10    10     10 #>  [55,]    10    10     10 #>  [56,]    10    10     10 #>  [57,]    10    10     10 #>  [58,]    10    10     10 #>  [59,]    10    10     10 #>  [60,]    10    10     10 #>  [61,]    10    10     10 #>  [62,]    10    10     10 #>  [63,]    10    10     10 #>  [64,]    10    10     10 #>  [65,]    10    10     10 #>  [66,]    10    10     10 #>  [67,]    10    10     10 #>  [68,]    10    10     10 #>  [69,]    10    10     10 #>  [70,]    10    10     10 #>  [71,]    10    10     10 #>  [72,]    10    10     10 #>  [73,]    10    10     10 #>  [74,]    10    10     10 #>  [75,]    10    10     10 #>  [76,]    10    10     10 #>  [77,]    10    10     10 #>  [78,]    10    10     10 #>  [79,]    10    10     10 #>  [80,]    10    10     10 #>  [81,]    10    10     10 #>  [82,]    10    10     10 #>  [83,]    10    10     10 #>  [84,]    10    10     10 #>  [85,]    10    10     10 #>  [86,]    10    10     10 #>  [87,]    10    10     10 #>  [88,]    10    10     10 #>  [89,]    10    10     10 #>  [90,]    10    10     10 #>  [91,]    10    10     10 #>  [92,]    10    10     10 #>  [93,]    10    10     10 #>  [94,]    10    10     10 #>  [95,]    10    10     10 #>  [96,]    10    10     10 #>  [97,]    10    10     10 #>  [98,]    10    10     10 #>  [99,]    10    10     10 #> [100,]    10    10     10  mv <- aem(k = 10, top = 10, base = 0, n = 0.2, uf, rf, type = 'variable') satthick(mv, x = c(-200, 0, 200), y = 0) # variable #> [1] 10.000000 10.000000  9.797959"},{"path":"https://cneyens.github.io/raem/reference/state-variables.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate state-variables — state-variables","title":"Calculate state-variables — state-variables","text":"heads() computes hydraulic head given x y coordinates aem object. omega() computes complex potential aem element object given x y coordinates. potential() computes discharge potential aem element object given x y coordinates. streamfunction() computes stream function aem element object given x y coordinates.","code":""},{"path":"https://cneyens.github.io/raem/reference/state-variables.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate state-variables — state-variables","text":"","code":"heads(aem, x, y, as.grid = FALSE, na.below = TRUE, ...)  omega(...)  potential(...)  streamfunction(...)  # S3 method for aem omega(aem, x, y, as.grid = FALSE, ...)  # S3 method for aem potential(aem, x, y, as.grid = FALSE, ...)  # S3 method for aem streamfunction(aem, x, y, as.grid = FALSE, ...)  # S3 method for element omega(element, x, y, ...)  # S3 method for element potential(element, x, y, ...)  # S3 method for element streamfunction(element, x, y, ...)"},{"path":"https://cneyens.github.io/raem/reference/state-variables.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate state-variables — state-variables","text":"aem aem object x numeric x coordinates evaluate y numeric y coordinates evaluate .grid logical, matrix dimensions c(length(y), length(x)) returned? Defaults FALSE. na.logical indicating calculated head values aquifer base set NA. Defaults TRUE. See potential_to_head(). ... ignored element analytic element class element","code":""},{"path":"https://cneyens.github.io/raem/reference/state-variables.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate state-variables — state-variables","text":"heads(), omega() containing hydraulic head values evaluated x y, computed potential() aquifer parameters using potential_to_head(). omega(), vector length(x) (equal length(y)) complex potential values x y. .grid = TRUE, matrix dimensions c(length(y), length(x)) described marginal vectors x y containing complex potential values grid points. potential(), omega() containing discharge potential values evaluated x y, real components omega(). streamfunction(), omega() containing stream function values evaluated x y, imaginary components omega().","code":""},{"path":"https://cneyens.github.io/raem/reference/state-variables.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Calculate state-variables — state-variables","text":"heads() confused utils::head(), returns first part object.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/state-variables.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate state-variables — state-variables","text":"","code":"w <- well(xw = 55, yw = 0, Q = 200) uf <- uniformflow(gradient = 0.002, angle = -45, TR = 100) rf <- constant(xc = -1000, yc = 1000, hc = 10) ml <- aem(k = 10, top = 10, base = -15, n = 0.2, w, uf, rf)  xg <- seq(-100, 100, length = 5) yg <- seq(-75, 75, length = 3)  # Hydraulic heads heads(ml, c(50, 0), c(25, -25)) #> [1] 8.280544 8.398209 heads(ml, xg, yg, as.grid = TRUE) #>          [,1]     [,2]     [,3]     [,4]     [,5] #> [1,] 8.660110 8.591307 8.517038 8.458073 8.448488 #> [2,] 8.601056 8.518423 8.400544 8.041392 8.312647 #> [3,] 8.570281 8.501215 8.426661 8.367468 8.357846  # do not confuse heads() with utils::head, which will give an error try( head(ml, c(50, 0), c(25, -25)) ) #> Error in head.default(ml, c(50, 0), c(25, -25)) :  #>   invalid 'n' - must have length one when dim(x) is NULL, got 2  # Complex potential omega(ml, c(50, 0), c(25, -25)) #> [1] 2709.919+45.67669i 2737.381-82.88449i  # Discharge potential potential(ml, c(50, 0), c(25, -25)) #> [1] 2709.919 2737.381  # Stream function streamfunction(ml, c(50, 0), c(25, -25)) #> [1]  45.67669 -82.88449  # For elements omega(w, c(50, 0), c(-25, 25)) #> [1] 103.0842-56.28330i 130.5466+86.42003i  potential(w, c(50, 0), c(-25, 25)) #> [1] 103.0842 130.5466  streamfunction(w, c(50, 0), c(-25, 25)) #> [1] -56.28330  86.42003"},{"path":"https://cneyens.github.io/raem/reference/tracelines.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute tracelines of particles — tracelines","title":"Compute tracelines of particles — tracelines","text":"tracelines() tracks particle locations moving forward backward advective groundwater flow numerically integrating velocity vector. resulting set connected coordinates produces tracelines. endpoints() obtains final time locations tracked particles","code":""},{"path":"https://cneyens.github.io/raem/reference/tracelines.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute tracelines of particles — tracelines","text":"","code":"tracelines(   aem,   x0,   y0,   z0,   times,   forward = TRUE,   R = 1,   tfunc = NULL,   tol = 0.001,   ... )  endpoints(tracelines, ...)  # S3 method for tracelines plot(x, y = NULL, add = FALSE, type = \"l\", arrows = FALSE, marker = NULL, ...)"},{"path":"https://cneyens.github.io/raem/reference/tracelines.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute tracelines of particles — tracelines","text":"aem aem object x0 numeric vector, starting x locations particles y0 numeric vector, starting y locations particles z0 numeric vector, starting z locations particles times numeric vector times locations registered forward logical, forward (TRUE; default) backward (FALSE) tracking performed. R numeric, retardation coefficient passed velocity(). Defaults 1 (retardation). tfunc function list functions additional termination events particles. See details. Defaults NULL. tol numeric tolerance used define particles crossed line element. Defaults 0.001 length units. ... additional arguments passed plot() arrows(). tracelines object class tracelines returned tracelines() x object class tracelines y ignored add logical, plot added existing plot? Defaults FALSE. type character indicating type plot draw. See plot(). Defaults 'l' (lines). arrows logical indicating arrows drawn using arrows(). Defaults FALSE. marker numeric, time interval plot point markers. Defaults NULL (markers). See details.","code":""},{"path":"https://cneyens.github.io/raem/reference/tracelines.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute tracelines of particles — tracelines","text":"tracelines() returns object class tracelines list length equal number particles list element contains matrix columns time, x, y z specifying registered time coordinates particle tracked flow field. final row represents either location maximum times value , particle terminated prematurely, time location termination. matrices ordered increasing time. connecting coordinates, tracelines can produced. endpoints() returns matrix columns time, x, y z specifying final time coordinates particles tracelines object.","code":""},{"path":"https://cneyens.github.io/raem/reference/tracelines.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Compute tracelines of particles — tracelines","text":"deSolve::lsoda() used numerically integrate velocity vector. Particles terminated prematurely reached inner annulus well elements, crossed line element (enter half non-zero width either side) travel saturated aquifer level (.e. water-table unconfined conditions aquifer top confined conditions), aquifer base. Note last two conditions can occur models vertical flow components. returned time value time termination. tfunc argument can used specify additional termination events. function (list functions) takes arguments t, coords parms. , respectively, numeric value current tracking time, numeric vector length 3 current x, y z coordinates particle, list elements aem R. return single logical value indicating particle terminate. See examples. initial particle locations saturated aquifer level, reset elevation warning. Initial particle locations aquifer base reset aquifer base warning. small perturbation added elevations avoid particle tracking algorithm get stuck locations. algorithm get stuck (.e. excessive run-times), try resetting z0 values elevations well inside saturated domain. Backward particle tracking performed reversing flow field (.e. multiplying velocities -1). marker value can used plot point markers given time intervals, e.g. every 365 days (see examples). x y locations particle marked times obtained linearly interpolating computed particle locations.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/tracelines.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute tracelines of particles — tracelines","text":"","code":"k <- 10 top <- 10; base <- 0 n <- 0.2 R <- 5 hc <- 20  uf <- uniformflow(TR = 100, gradient = 0.001, angle = -10) rf <- constant(TR, xc = -1000, yc = 0, hc = hc)  m <- aem(k, top, base, n = n, uf, rf)  x0 <- -200; y0 <- seq(-200, 200, 50) times <- seq(0, 25 * 365, 365 / 4) paths <- tracelines(m, x0 = x0, y0 = y0, z = top, times = times) endp <- endpoints(paths)  xg <- seq(-500, 500, length = 100) yg <- seq(-300, 300, length = 100)  contours(m, xg, yg, col = 'dodgerblue', nlevels = 20) plot(paths, add = TRUE, col = 'orange') points(endp[, c('x', 'y')])  # Backward tracking with retardation; plot point marker every 5 years paths_back <- tracelines(m, x0 = x0, y0 = y0, z0 = top, times = times, R = R, forward = FALSE) plot(paths_back, add = TRUE, col = 'forestgreen', marker = 5*365, cex = 0.5)   # Termination at wells and line-sinks w1 <- well(200, 50, Q = 250) w2 <- well(-200, -100, Q = 450) ls <- headlinesink(x0 = -100, y0 = 100, x1 = 400, y1 = -300, hc = 7)  m <- aem(k, top, base, n = n, uf, rf, w1, w2, ls) contours(m, xg, yg, col = 'dodgerblue', nlevels = 20) plot(m, add = TRUE)  x0 <- seq(-400, 400, 50); y0 <- 200 times <- seq(0, 5 * 365, 365 / 20) paths <- tracelines(m, x0 = x0, y0 = y0, z0 = top, times = times) plot(paths, add = TRUE, col = 'orange')   # User-defined termination in rectangular zone tzone <- cbind(x = c(-300, -200, -200, -300), y = c(150, 150, 100, 100)) termf <- function(t, coords, parms) {   x <- coords[1]   y <- coords[2]   in_poly <- x <= max(tzone[,'x']) & x >= min(tzone[,'x']) &              y <= max(tzone[,'y']) & y >= min(tzone[,'y'])   return(in_poly) } paths <- tracelines(m, x0 = x0, y0 = y0, z0 = top, times = times, tfunc = termf) contours(m, xg, yg, col = 'dodgerblue', nlevels = 20) plot(m, add = TRUE) polygon(tzone) plot(paths, add = TRUE, col = 'orange')   # model with vertical flow due to area-sink as <- areasink(xc = 0, yc = 0, N = 0.001, R = 1500) m <- aem(k, top, base, n = n, uf, rf, w1, w2, as)  # starting z0 locations are above aquifer top and will be reset to top with warning paths <- tracelines(m, x0 = x0, y0 = y0, z0 = top + 0.5, times = times) #> Warning: Resetting z0 values above saturated aquifer level or below aquifer base  contours(m, xg, yg, col = 'dodgerblue', nlevels = 20) plot(m, add = TRUE) plot(paths, add = TRUE, col = 'orange')   # plot vertical cross-section of traceline 4 along increasing y-axis (from south to north) plot(paths[[4]][,c('y', 'z')], type = 'l')    # plot arrows contours(m, xg, yg, col = 'dodgerblue', nlevels = 20) plot(paths, add = TRUE, col = 'orange', arrows = TRUE, length = 0.05)   # plot point markers every 2.5 years contours(m, xg, yg, col = 'dodgerblue', nlevels = 20) plot(paths, add = TRUE, col = 'orange', marker = 2.5 * 365, pch = 20)  # plot point markers every 600 days plot(paths, add = TRUE, col = 'forestgreen', marker = 600, pch = 1)"},{"path":"https://cneyens.github.io/raem/reference/uniformflow.html","id":null,"dir":"Reference","previous_headings":"","what":"Create a uniform-flow analytic element with specified recharge — uniformflow","title":"Create a uniform-flow analytic element with specified recharge — uniformflow","text":"uniformflow() creates analytic element constant uniform background flow.","code":""},{"path":"https://cneyens.github.io/raem/reference/uniformflow.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create a uniform-flow analytic element with specified recharge — uniformflow","text":"","code":"uniformflow(TR, gradient, angle, ...)"},{"path":"https://cneyens.github.io/raem/reference/uniformflow.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create a uniform-flow analytic element with specified recharge — uniformflow","text":"TR numeric, constant transmissivity value used define discharge. gradient numeric, hydraulic gradient. Positive direction flow. angle numeric, angle primary direction background flow, degrees counterclockwise x-axis. ... ignored","code":""},{"path":"https://cneyens.github.io/raem/reference/uniformflow.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create a uniform-flow analytic element with specified recharge — uniformflow","text":"Analytic element constant uniform flow object class uniformflow inherits element.","code":""},{"path":"https://cneyens.github.io/raem/reference/uniformflow.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Create a uniform-flow analytic element with specified recharge — uniformflow","text":"TR gradient multiplied obtain discharge remains constant throughout system, independent saturated thickness aquifer. Groundwater flow direction negative hydraulic gradient. Note gradient specified positive direction flow convenience.","code":""},{"path":"https://cneyens.github.io/raem/reference/uniformflow.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create a uniform-flow analytic element with specified recharge — uniformflow","text":"","code":"uniformflow(TR = 100, gradient = 0.002, angle = -45) # South-eastern direction #> $parameter #> [1] 0.2 #>  #> $nunknowns #> [1] 0 #>  #> $udir #> [1] 0.7071068+0.7071068i #>  #> attr(,\"class\") #> [1] \"uniformflow\" \"element\""},{"path":"https://cneyens.github.io/raem/reference/well.html","id":null,"dir":"Reference","previous_headings":"","what":"Create a analytic element of a constant-discharge well — well","title":"Create a analytic element of a constant-discharge well — well","text":"well() creates analytic element well constant discharge.","code":""},{"path":"https://cneyens.github.io/raem/reference/well.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create a analytic element of a constant-discharge well — well","text":"","code":"well(xw, yw, Q, rw = 0.3, ...)"},{"path":"https://cneyens.github.io/raem/reference/well.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create a analytic element of a constant-discharge well — well","text":"xw numeric, x location well yw numeric, y location well Q numeric, volumetric discharge well (positive aquifer) rw numeric, radius well. Defaults 0.3. ... ignored","code":""},{"path":"https://cneyens.github.io/raem/reference/well.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create a analytic element of a constant-discharge well — well","text":"Analytic element well constant discharge object class well inherits element.","code":""},{"path":"https://cneyens.github.io/raem/reference/well.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Create a analytic element of a constant-discharge well — well","text":"inner annulus well element constitutes singularity equations hydraulic head undefined distance smaller rw well center. state- flow-variable calculated within annulus, location reset nearest location well screen.","code":""},{"path":[]},{"path":"https://cneyens.github.io/raem/reference/well.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create a analytic element of a constant-discharge well — well","text":"","code":"well(xw = 50, yw = 0, Q = 200, rw = 0.3) #> $parameter #> [1] 200 #>  #> $nunknowns #> [1] 0 #>  #> $zetaw #> [1] 50+0i #>  #> $rw #> [1] 0.3 #>  #> attr(,\"class\") #> [1] \"well\"    \"element\""}]