11_god_spiked_the_integers-2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/ksachdeva/rethinking-tensorflow-probability/blob/master/notebooks/11_god_spiked_the_integers.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 11. God Spiked the Integers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "import arviz as az\n",
    "import pandas as pd\n",
    "import xarray as xr\n",
    "import matplotlib.pyplot as plt\n",
    "from collections import namedtuple\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "import random\n",
    "import jax\n",
    "import jax.numpy as jnp\n",
    "\n",
    "import tensorflow as tf\n",
    "from tensorflow_probability.substrates import jax as tfp\n",
    "tfd = tfp.distributions\n",
    "tfb = tfp.bijectors\n",
    "# to use 'sample_distributions'\n",
    "import tensorflow_probability as xtfp\n",
    "xtfd = xtfp.distributions\n",
    "xtfb = xtfp.bijectors\n",
    "\n",
    "key = tfp.util.SeedStream(1004, salt=\"ch-11\")\n",
    "plt.rcParams['figure.figsize'] = [6, 5]\n",
    "\n",
    "# TFP often requires 64-bit precision (float64) for certain computations \n",
    "# to ensure numerical stability and accuracy, e.g., tfd.Possion.\n",
    "# However, jax.config.update(\"jax_enable_x64\", True)\n",
    "# converts all 32 to 64, so that sometimes errors occur.\n",
    "# e.g., TypeError: Tensor conversion requested dtype \n",
    "#   <class 'jax.numpy.int32'> for array with dtype int64\n",
    "jax.config.update(\"jax_enable_x64\", True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 11.1 Binomial regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 11.1.1 Logistic regression: Prosocial chimpanzees"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.1\n",
    "\n",
    "Authors start the chapter by highlighting one key difference between **Generalized Linear Models** and **Gaussian Linear Models**. He says, that unlike Gaussian Linear Models where we had some interpretation of parameters, in the case of **GLM** it is the combination of parameters that matter.\n",
    "\n",
    "Most common & **useful** GLM models are about **counts** but they are also difficult to model. What is the reason for that ?\n",
    "\n",
    "He says - \"When we *wish* to predict the outcome in the form of counts, the scale of parameters is **never the same** as the scale of outcome. This is another way of saying that it is the combination of parameters that help in prediction and hence some where we lose human intution that could have connected the parmaeters with the outcome.\n",
    "\n",
    "\n",
    "**Binomial Regression** -: model the outcome (count) when both of the categories are known.\n",
    "\n",
    "**Poisson Regression** -: model the outcome (count) when the maximum count is unknown.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "d = pd.read_csv(\"./data/chimpanzees.csv\", sep=\";\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.2\n",
    "\n",
    "\n",
    "We aim to build index variables instead of using dummy variables. Below is a quick way to do it. Treatment here is about the 4 possible situations.\n",
    "\n",
    "1. prosoc_left= 0 and condition= 0: Two food items on right and no partner. \n",
    "2. prosoc_left= 1 and condition= 0: Two food items on left and no partner.\n",
    "3. prosoc_left= 0 and condition= 1: Two food items on right and partner present.\n",
    "4. prosoc_left= 1 and condition= 1: Two food items on left and partner present."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# In the book there is an additional 1 in the code snippet.\n",
    "# That is because of R as in R index does not starts with 0\n",
    "\n",
    "d[\"treatment\"] = d.prosoc_left + 2 * d.condition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "condition  prosoc_left  treatment\n",
       "0          0            0            126\n",
       "           1            1            126\n",
       "1          0            2            126\n",
       "           1            3            126\n",
       "dtype: int64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d.groupby([\"condition\", \"prosoc_left\", \"treatment\"]).size()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>actor</th>\n",
       "      <th>recipient</th>\n",
       "      <th>condition</th>\n",
       "      <th>block</th>\n",
       "      <th>trial</th>\n",
       "      <th>prosoc_left</th>\n",
       "      <th>chose_prosoc</th>\n",
       "      <th>pulled_left</th>\n",
       "      <th>treatment</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>504.000000</td>\n",
       "      <td>252.00000</td>\n",
       "      <td>504.000000</td>\n",
       "      <td>504.000000</td>\n",
       "      <td>504.000000</td>\n",
       "      <td>504.000000</td>\n",
       "      <td>504.00000</td>\n",
       "      <td>504.000000</td>\n",
       "      <td>504.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>4.000000</td>\n",
       "      <td>5.00000</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>3.500000</td>\n",
       "      <td>36.500000</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>0.56746</td>\n",
       "      <td>0.579365</td>\n",
       "      <td>1.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>2.001987</td>\n",
       "      <td>2.00398</td>\n",
       "      <td>0.500497</td>\n",
       "      <td>1.709522</td>\n",
       "      <td>20.803253</td>\n",
       "      <td>0.500497</td>\n",
       "      <td>0.49592</td>\n",
       "      <td>0.494151</td>\n",
       "      <td>1.119145</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.00000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>2.000000</td>\n",
       "      <td>3.00000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>18.750000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>4.000000</td>\n",
       "      <td>5.00000</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>3.500000</td>\n",
       "      <td>36.500000</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>1.00000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>6.000000</td>\n",
       "      <td>7.00000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>54.250000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.00000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>7.000000</td>\n",
       "      <td>8.00000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>72.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.00000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>3.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            actor  recipient   condition       block       trial  prosoc_left  \\\n",
       "count  504.000000  252.00000  504.000000  504.000000  504.000000   504.000000   \n",
       "mean     4.000000    5.00000    0.500000    3.500000   36.500000     0.500000   \n",
       "std      2.001987    2.00398    0.500497    1.709522   20.803253     0.500497   \n",
       "min      1.000000    2.00000    0.000000    1.000000    1.000000     0.000000   \n",
       "25%      2.000000    3.00000    0.000000    2.000000   18.750000     0.000000   \n",
       "50%      4.000000    5.00000    0.500000    3.500000   36.500000     0.500000   \n",
       "75%      6.000000    7.00000    1.000000    5.000000   54.250000     1.000000   \n",
       "max      7.000000    8.00000    1.000000    6.000000   72.000000     1.000000   \n",
       "\n",
       "       chose_prosoc  pulled_left   treatment  \n",
       "count     504.00000   504.000000  504.000000  \n",
       "mean        0.56746     0.579365    1.500000  \n",
       "std         0.49592     0.494151    1.119145  \n",
       "min         0.00000     0.000000    0.000000  \n",
       "25%         0.00000     0.000000    0.750000  \n",
       "50%         1.00000     1.000000    1.500000  \n",
       "75%         1.00000     1.000000    2.250000  \n",
       "max         1.00000     1.000000    3.000000  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_11_1(a_scale):\n",
    "    def _generator():\n",
    "        a = yield tfd.Normal(loc=0., scale=a_scale, name='a')\n",
    "        logit = a\n",
    "        yield tfd.Binomial(total_count=1., logits=logit, name='pulled_left')\n",
    "\n",
    "    return tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_11_1 = model_11_1(a_scale=10.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "prior = jd_11_1.sample(1000, seed=key())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = jax.nn.sigmoid(prior[0])\n",
    "az.plot_kde(p)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Most of the probability mass in the above plot is piled up near zero or one. A flat prior in the logit space is not a flat prior in the outcome probability space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "jd_11_1b = model_11_1(a_scale=1.5)\n",
    "prior_with_1_5 = jd_11_1b.sample(1000, seed=key())\n",
    "\n",
    "p = jax.nn.sigmoid(prior_with_1_5[0])\n",
    "\n",
    "az.plot_kde(p)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A more concentrated Normal(0,1.5) prior produces something more reasonable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# simply showing both of the above plots\n",
    "# at the same time to reproduce figure 11.3\n",
    "\n",
    "p1 = jax.nn.sigmoid(prior[0])\n",
    "p2 = jax.nn.sigmoid(prior_with_1_5[0])\n",
    "az.plot_kde(p1)\n",
    "az.plot_kde(p2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.7 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d.treatment.unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_11_2(treatments):\n",
    "    treatments = jnp.array(treatments, dtype=jnp.int32)\n",
    "\n",
    "    def _generator():\n",
    "        a = yield tfd.Normal(loc=0.0, scale=1.5, name='a')\n",
    "        b = yield tfd.Normal(loc=[0., 0, 0, 0], scale=10.0, name='b')\n",
    "        logit = a + jnp.take(b, treatments)\n",
    "        yield tfd.Binomial(total_count=1.0, logits=logit, name='pulled_left')\n",
    "\n",
    "    return tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_11_2 = model_11_2(d.treatment.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "prior_a, prior_b, _ = jd_11_2.sample(1000, seed=key())\n",
    "\n",
    "p = jax.nn.sigmoid(prior_a[..., jnp.newaxis] + prior_b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.8 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# az.plot_kde(p[:, 0])\n",
    "az.plot_kde(jnp.abs(p[:, 0] - p[:, 1]))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.9 \n",
    "\n",
    "Sample model as 11_2 but with a different scale for beta_treatment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_11_3(treatments):\n",
    "    treatments = jnp.array(treatments, dtype=jnp.int32)\n",
    "\n",
    "    def _generator():\n",
    "        a = yield tfd.Normal(loc=0.0, scale=1.5, name='a')\n",
    "        b = yield tfd.Normal(loc=[0., 0, 0, 0], scale=.5, name='b')\n",
    "        logit = a + jnp.take(b, treatments)\n",
    "        yield tfd.Binomial(total_count=1.0, logits=logit, name='pulled_left')\n",
    "\n",
    "    return tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array(0.09510462, dtype=float32)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jd_11_3 = model_11_3(d.treatment.values)\n",
    "\n",
    "prior_a, prior_b, _ = jd_11_3.sample(1000, seed=key())\n",
    "\n",
    "p = jax.nn.sigmoid(prior_a[..., jnp.newaxis] + prior_b)\n",
    "\n",
    "np.mean(jnp.abs(p[:, 0] - p[:, 1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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l8ng8Ki0tjdr995c+v1TLdhTp7in9dctk1ikAALSMPx3q9wnevXv31ooVKzR9+nStXLlSTz75pLZu3apbbrlFy5Yta3HRo8GloxtOP3xrRa78fN8FAECL+D2zDyRm9tLBmjqNvn++Kmvq9eaNY3Ryr1SrIwEAwkBQZ/YIrPgYR/M592+t2G1xGgBAJKLsQ0DTpvyP1+5ReXWtxWkAAJGGsg8BJ2Ymq096oqpq6/Xhmj1WxwEARBjKPgQYhqHLRjXM7l9ftsviNACASEPZh4iLR3ZTjMOmtXmlWpNbYnUcAEAEoexDRIeEGJ07tIsk6R9f77Q4DQAgklD2IWTamB6SpA/X5KvkYI3FaQAAkYKyDyEjuidrYBe3vHU+/Wslp+EBAAKDsg8hhmHoqjHdJUn//GaXfD5W1AMAtB1lH2IuHN5VSS6HcvZXatGWQqvjAAAiAGUfYhJcDl3WuMjOi4u3W5wGABAJKPsQNH1clmyGtCT7gDbuKbM6DgAgzFH2IahbSrzOajwN76+LcyxOAwAId5R9iLp+fE9J0ger81VQXm1xGgBAOKPsQ9SJ3VM0skeKaup9enUpi+wAAFqPsg9hTbP7f3y9U9W19RanAQCEK8o+hJ05uLO6pcSp+GCt3maRHQBAK1H2IcxuM5pn939etE119T6LEwEAwhFlH+IuG91dqQkx2l1cpQ+/y7c6DgAgDFH2IS4uxq7rJjTM7p/9fBtL6AIA/EbZh4GrxvRQUqxDWwsqNG/DPqvjAADCDGUfBtyxTl1zSpYk6dmF2TJNZvcAgJaj7MPEteOyFOu06bvdpVqcvd/qOACAMELZh4nURJeuOKnh8rdP/mcrs3sAQItR9mHkplN7K8Zh0/IdxczuAQAtRtmHkc6eWE07uWF2/9i8LczuAQAtQtmHmZsn9Vas06bVuSVauLnQ6jgAgDBA2YeZ9KRYXd14ZP7jnzG7BwAcH2Ufhm46tZfiY+xam1fKefcAgOOi7MNQaqJL08dmSZL+9NkWVtUDABwTZR+mbjy1l5JcDm3aW653V+VZHQcAEMIo+zCVHB+jX0zuI0l6bN5mrncPADgqyj6MXTsuSxmeWOWXVuulJTlWxwEAhCjKPozFOu26a0p/SQ1XxDtQ4bU4EQAgFFH2Ye7C4V01OMOtCm+dnvzPVqvjAABCEGUf5mw2Q/ecPVCS9M9vdml7YYXFiQAAoYayjwDj+nTU5P5pqvOZenTuZqvjAABCDGUfIWacPVA2Q5q7fq9W7CiyOg4AIIRQ9hGiX6ckXToqU5L04McbWUYXANCMso8g/++Mfopz2vXtrhJ9sm6v1XEAACGCso8g6e5Y3XBqL0nSw59sYqEdAIAkyj7i3HRqL3Vyu7Sr6KD+upiFdgAAlH3ESXA5NOOshlPxnvk8W3tLqy1OBACwGmUfgS4YnqGRPVJ0sKZeD3+y0eo4AACLUfYRyDAMzTpvsAxDem91PqfiAUCUo+wj1NBuHl3WeCrerA/Xq55r3gNA1KLsI9hdU/orKdahdXllentFrtVxAAAWoewjWMdEl24/ra8k6dFPN6vkYI3FiQAAVqDsI9w1Y7PUNz1RRZU1eoR18wEgKlH2Ec5pt+n+C4dIkl5ftkvf7iq2OBEAoL1R9lHg5F6pumRkN0nSve+uU129z+JEAID2RNlHiRlnDZAnzqmNe8r0ytKdVscBALQjyj5KpCa69JuzBkiSHp+3mZX1ACCKUPZR5LJRmRrRPVmVNfW6798brI4DAGgnlH0UsdkM3X/hUNlthj5au0cLNxdYHQkA0A4o+ygzKMOt6WOzJEm/f389l8EFgChA2UehO87op87uWO0qOqhnP8+2Og4AIMgo+yiU6HJo5nmDJEnPL9qubYUVFicCAAQTZR+lpg7prEn901RT79M9c9bKx4VyACBiUfZRyjAM3XfBEMU57fomp0hvLOdCOQAQqSj7KJbZIV53TekvSXro442cew8AEYqyj3LTx2ZpeGayyr11+u1762SabM4HgEhD2Uc5u83QIxefIKfd0PyN+/TR2j1WRwIABBhlD/XvnKSbJ/WRJM36YL2KK7nuPQBEEsoekqRbJvdWn/RE7a+o0f0fbbQ6DgAggCh7SJJcDrseufgEGYb0zre79eXWQqsjAQAChLJHs5E9UnTNKVmSpBlz1upgTZ21gQAAAUHZ4xB3TemvDE+sdhdX6fF5W6yOAwAIgDaX/aOPPirDMGQYhr7++utAZIKFEl0OPfDjoZKkl5bkaE1uibWBAABt1qay37hxo37/+98rISEhUHkQAib3T9cFwzPkM6Vfv/Odaut9VkcCALRBq8u+vr5e11xzjYYNG6aLLrookJkQAn5/7iClxDu1aW+5/rxom9VxAABt0Oqyf+SRR7RmzRq99NJLstvtgcyEEJCa6NLvG6+M9+R/spVdwJXxACBctars161bp9mzZ+u3v/2tBg8e3OKv83q9KisrO+SG0HXh8K6a2I8r4wFAuPO77Ovq6jR9+nQNHDhQv/nNb/z62oceekgej6f5lpmZ6e+3RzsyDEMPXDRE8TF2LdtRpNeW7bI6EgCgFfwu+wcffLB5873T6fTra2fMmKHS0tLmW24ul1UNdd1S4nV345XxHv5kE1fGA4Aw5FfZr1mzRvfff7/uuusujRgxwu9v5nK55Ha7D7kh9F19SsOV8Sq4Mh4AhCW/yv6aa65R7969NWvWrCDFQSiy2ww9esn3V8b7eO1eqyMBAPzg98x+06ZNio2NbV5IxzAMvfLKK5KkU045RYZh6L333gtGVlioX6fvr4w384N1KjnIlfEAIFw4/Hnyddddd8T7v/jiC23dulXnn3++0tLSlJWVFYhsCDG3TO6tj9fuUXZBhR74aKP+8JNhVkcCALSAYQZgB+z06dP1yiuvaOnSpRozZkyLv66srEwej0elpaXsvw8TK3cW6ZLnl8o0pVevO1nj+3a0OhIARCV/OpQL4cAvI3t00NVjekiSZrz7napq6i1OBAA4Hsoefrt76gBleGKVW1Slxz/bbHUcAMBxBKTsX375ZZmm6dcmfISvRJdD9180RJL018U5WpdXanEiAMCxMLNHq/xoQCede0IX+Uzpfz/cwLn3ABDCKHu02j1nD1Ss06ZlO4r00do9VscBABwFZY9Wy0iO080TG869f+jjTRysBwAhirJHm9x4ai91TY5TXkmV/vLFdqvjAACOgLJHm8TF2HXP2QMlSc8tylZ+SZXFiQAA/42yR5udPbSzTurZQdW1Pj38ySar4wAA/gtljzYzDEMzzxskw5A+WJOvFTuKrI4EAPgByh4BMTjDo8tHZ0pquO49p+IBQOig7BEwvzy9n1wOm1bsLNaCTQVWxwEANKLsETCd3LG6dlxPSdKjczer3sfsHgBCAWWPgLp5Ym+5Yx3avK9c76/OszoOAECUPQLME+/UzZMaFtp5/LMt8tax0A4AWI2yR8BNH5ulTm6XdhdX6bVvdlkdBwCiHmWPgIuLsev20/pJkp5duE3VtczuAcBKlD2C4pKR3dQ1OU6F5V5m9wBgMcoeQRHjsOmWyQ377p9fxOweAKxE2SNommb3BeVevbGM2T0AWIWyR9DEOGy6eVJvSdJzzO4BwDKUPYLqJ6O6qYsnVvvKvHprRa7VcQAgKlH2CCqXw65fNM3uF27jvHsAsABlj6C7dHSmOrtjtae0Wm+t2G11HACIOpQ9gs7lsH+/7/7zbNXU+SxOBADRhbJHu7hsdKbSklzKL63We6tYMx8A2hNlj3YR67TrhgkNV8R7btE2rogHAO2Iske7mXZyDyXHO5Wzv1Ifrd1jdRwAiBqUPdpNgsuhnzVe7/6ZBdnyMbsHgHZB2aNdXXNKlhJdDde7n79xn9VxACAqUPZoV554p64+pYck6ZnPs2WazO4BINgoe7S768b3VKzTpjW7S7U4e7/VcQAg4lH2aHepiS5dcVJ3SdJTC7ItTgMAkY+yhyVuPLWXnHZDy3KKtHxHkdVxACCiUfawRBdPnC4ZmSlJeprZPQAEFWUPy9w8sbfsNkOLthTqu90lVscBgIhF2cMy3VPjdf6wDEkNR+YDAIKDsoelmi5/++n6fdqyr9ziNAAQmSh7WKpvpySdNaSzJGb3ABAslD0sd8vkPpKkD9fka8f+SovTAEDkoexhuSFdPZrUP00+U3p+0Tar4wBAxKHsERJubZzdv/PtbuWXVFmcBgAiC2WPkDAqq4PG9Oqg2npTf/liu9VxACCiUPYIGbdO7itJen3ZLhWWey1OAwCRg7JHyBjXJ1XDMpPlrfPpr4tzrI4DABGDskfIMAyjed/9P5buUMnBGosTAUBkoOwRUk4bkK4BnZNUWVOvl5bssDoOAEQEyh4hxWYzdNuPGvbdv7Q4R0WVzO4BoK0oe4Scs4Z01qAublV46zjvHgACgLJHyLHZDN09pb8k6ZWvdmhvabXFiQAgvFH2CEmT+qdpdFaKvHU+PbVgq9VxACCsUfYISYZh6O4pAyRJby7P1c4DrJkPAK1F2SNkndSzgyb2S1Odz9Tjn22xOg4AhC3KHiGtad/9+6vztWpXscVpACA8UfYIaUO6enTxiG6SpNkfbpDPZ1qcCADCD2WPkPfrqf2VEGPX6twSvbsqz+o4ABB2KHuEvHR3rG5tXGjnkbmbVOGtszgRAIQXyh5h4Wfjs9QjNV4F5V4983m21XEAIKxQ9ggLLoddvz1nkCTpr1/maHthhcWJACB8UPYIG6cPTNfEfmmqqffpN3PWcrAeALQQZY+wYRiG7r9wiOJj7FqWU6TXlu2yOhIAhAXKHmEls0N887n3D3+ySfklVRYnAoDQR9kj7Fx9SpZG9khRhbdOv37nOzbnA8BxUPYIO3aboUcuPkGxTpu+3Lpff/5iu9WRACCkUfYIS33SEzX7/MGSpD/O26yVO1lKFwCOhrJH2Lp0VKbOG5ahep+p/3l9lYora6yOBAAhibJH2DIMQw9cNETdO8Qrr6RKN/1jpbx19VbHAoCQQ9kjrLljnXrxmlFKcjm0bEeRZsxZK9PkgD0A+CHKHmGvX6ckPT1thOw2Q3O+zdMT87daHQkAQgplj4gwsV+aZjUesPd//9mqZxeyfj4ANPGr7PPy8vTEE0/ozDPPVPfu3RUTE6POnTvr4osv1jfffBOsjECL/HRMj+YFdx6du1kvcEoeAEjys+yfeuop3XHHHdq+fbvOOOMM3XnnnRo/frzef/99jR07Vm+99VawcgItcsvkPrrj9H6SpAc+3qhH525i0R0AUc8w/Tiaac6cOUpLS9OECRMOuf/LL7/UaaedpqSkJOXn58vlcrXo9crKyuTxeFRaWiq32+1fcuAYnvrPVj322RZJ0vnDMvSHn5wgl8NucSoACBx/OtSvsj+WKVOmaN68eVq+fLlGjRoV8KCAv/61crd+8853qvOZOqGbR09dcaJ6pCZYHQsAAsKfDg3YAXpOp1OS5HA4AvWSQJtcMrKbXr72JHninPpud6nOfXKxPliTz6l5AKJOQGb2u3btUr9+/ZSSkqLdu3fLbj/y5lKv1yuv19v8eVlZmTIzM5nZI6jySqp0++urtKJxSd3TBqRr1vmDldkh3uJkANB67Tqzr62t1U9/+lN5vV49+uijRy16SXrooYfk8Xiab5mZmW399sBxdU2O0xs3jtH/nNZXTruh/2wq0Bl/WqTH5m1WaVWt1fEAIOjaNLP3+Xy65ppr9Oqrr+qGG27QX/7yl2M+n5k9rJZdUK57312nb3KKJElJsQ7dMKGXrh2XpaRYp8XpAKDl2uUAPdM0df311+ull17SVVddpVdeeUU2m38bCjhAD1YwTVOfrt+nP322RZv3lUuSPHFOTR+bpWvHZSk5PsbihABwfEEve5/Pp+uvv15/+9vfdMUVV+gf//jHMTffByIoEGg+n6mP1u7RE/O3aFthpSQpIcauaWN66PrxPZXujrU4IQAcXVDL/odFf9lll+mf//xnq4re36BAsNT7TM1dt1fPfJ6tDXvKJEkxDpsuG5WpG0/txYF8AEJS0Mre5/Ppuuuu08svv6yf/OQneu2119p0qh1lj1BimqYWbi7U059na2XjkfsOm6ELhnfVzZN6q096osUJAeB7QSv7WbNmafbs2UpMTNTtt99+xKK/8MILNXz48IAHBdqLaZr6enuRnvk8W4uz90uSbIZ01Zge+n9n9GOfPoCQ4E+H+jUt37FjhySpoqJCDzzwwBGfk5WV1eKyB0KRYRg6pXeqTumdqtW5JXp6wVbN31igvy/dqQ/W5OvOM/rpypN7yG4zrI4KAC0SsOVyW4OZPcLFV9n7NfvDDc1H75/Us4P+dNlwdU2OszgZgGhlyXK5QCQb26ejPvqf8frfCwYrIcauZTlFOuuJL/Tv7/KtjgYAx0XZAy3ksNt09SlZ+vj2CRqemayy6jrd+toqzZjznbx19VbHA4CjouwBP/VITdDbPz9Ft07uI8OQXl+Wqytf+EYF5dVWRwOAI6LsgVZw2m26a0p//W36aCXFOrRyZ7EueHqJvttdYnU0ADgMZQ+0waT+6Xr/lnHqnZagPaXVuvTPS/X5pgKrYwHAISh7oI16pSXqvVvGaVL/NFXX+nTD31fo/dV5VscCgGaUPRAASbFOvXD1KF0wPEN1PlO/fHO1/vnNTqtjAYAkyh4IGKfdpj9dOlzXnNJDpind++46vfjldqtjAQBlDwSSzWZo1vmDdfOk3pKk+z/aqKcXbLU4FYBoR9kDAWYYhn41pb/uPKOfJOmP87bo0bmbZOFilQCiHGUPBIFhGLrttL767TkDJUnPLtym2R9uoPABWIKyB4Lo+gm9dN+FQyRJL3+1Q/e8u1b1PgofQPui7IEg++mYHvrDJSfI1rja3l1vr1Fdvc/qWACiCGUPtIOfjMrU/11+ohw2Q++uytNtr69STR2FD6B9UPZAOzlvWIaenTZCMXabPlm3Vz9/daWqa7mADoDgo+yBdnTm4M564ZpRcjlsWrCpQD97ebkqvXVWxwIQ4Sh7oJ1N7JemV352khJi7Ppq2wFd8vxS7S4+aHUsABGMsgcsMKZXql69/mR1TIzRxj1lOv/pJfp6+wGrYwGIUJQ9YJETu6fo/VvHa0hXt4oqa3TlC1/r0bmbOHAPQMBR9oCFuibH6e2bxuriEd3kMxsW37ngmSVaubPI6mgAIghlD1gsLsauxy4dpuevGqEOCQ2b9S9+bqlufnWlthdWWB0PQAQwTAvX7ywrK5PH41FpaancbrdVMYCQUVju1WPzNuutFbnymZJhSKcP7KTrxvfUyT07yDAMqyMCCBH+dChlD4SgzXvL9YdPN2v+xn3N93VNjtO5J3TRGYM6aVhmspx2NswB0YyyByJEdkGFXlqSo/dW5elgzfcL8CTE2DWmV6pO6Z2qk3p20KAubjkofyCqUPZAhKmurdfnmwr00do9Wpy9XyUHaw95PD7GrhHdUzQ6q4NGZ6VoePdkxcc4LEoLoD1Q9kAE8/lMbdhTpiXZ+/VNTpFW7ChSWfWhq/A5bIZGZaXo7KFdNHVwZ6W7Yy1KCyBYKHsgivh8prYUlGv5jmItzynS8h1F2lNa3fy4YUgn9+yg6WOzdMagzrLbOMgPiASUPRDldh04qHkb9uqjtXu0aldJ8/1dk+N046m9dNnoTMU67dYFBNBmlD2AZnklVXr9m1365zc7Vdy4r7+zO1a3/qiPrjipOzN9IExR9gAOU11br7dX7tazn2c3b+Y/oZtHD140VEO6eixOB8BflD2Ao/LW1eu1b3bp8c+2qLy6TjZDmj62p+6a0o8j+IEw4k+HcmIuEGVcDruuHddT/7lzos4bliGfKb20JEfnPrVY6/JKrY4HIAgoeyBKpSfF6qkrTtQrPztJnd2x2l5YqYueXaLnF22Tz2fZBj8AQUDZA1FuYr80fXL7BE0d3Fm19aYe/mSTrvnbMhVX1lgdDUCAUPYAlJIQo+euGqFHLh6qWKdNX27dz2Z9IIJQ9gAkSYZh6LLR3fXuL8apR2q88kqqdPFzX+lfK3dbHQ1AG1H2AA4xsItbH9w6Xj8akC5vnU93vb1Gsz9cr7p6n9XRALQSZQ/gMJ44p168epRuP62vJOlvS3bo6pfYjw+EK8oewBHZbIbuOKOfnr9qpOJj7Ppq2wGd/8xibdpbZnU0AH6i7AEc09QhnTXnF2OV2SFOuUVV+vGzX2nuur1WxwLgB8oewHEN6OzWB7eM17g+qTpYU6+fv7pST8zfwvn4QJig7AG0SEpCjF659iT9bFxPSdIT87fq5n+uVIW3zuJkAI6HsgfQYg67Tb8/b5AeveQExdht+nT9Pl387FfadeCg1dEAHANlD8Bvl47K1Bs3jVFakkub95Xr/GcWa0n2fqtjATgKyh5Aq4zonqIPbx2vYZnJKjlYq6tfWqa/fMG6+kAoouwBtFpnT6zevHGMfjyiq+p9ph78eJOmv7xcBeXVVkcD8AOUPYA2iXXa9dhPhun+C4fI5bDpiy2FOuuJL/WfjfusjgagEWUPoM0Mw9BVY3ro37eN14DOSTpQWaPrXlmh//fmahWx6h5gOcoeQMD07ZSk924Zp+vG95RhSHNW5emMxxfp/dV5Mk325QNWoewBBFSs067fnTtIc24eq/6dGmb5t7+xWpf+eam+3VVsdTwgKhmmhW+3y8rK5PF4VFpaKrfbbVUMAEFSU+fT84u26ZnPs+Wta7hq3tTBnXXnmf3Ut1OSxemA8OZPh1L2AIJub2m1/vTZFr29MldNZ+adPjBdN03srVE9UmQYhrUBgTBE2QMISVv2levxeVv06Ya9avrL069Toi4b3V0/PrGrUhJirA0IhBHKHkBI21ZYoRe+2K73VuepurZh836M3aZxfVJ15uDOOm1gutKTYi1OCYQ2yh5AWCitqtUHq/P0+rJcbdhT1ny/YUjDM5M1oW+axvTsoBE9UhTrtFuYFAg9lD2AsGKaprbsq9BnG/bqsw37tGZ36SGPx9htGp6ZrNE9UzQqq4NGdE+RJ85pUVogNFD2AMLavrJqLdhUoK+3H9DX2w9oX5n3kMcNQ+qXnqRRWSkNtx4d1C0ljgP9EFUoewARwzRN7TxwUF9vP6DlO4q1cmeRdhzhkrqd3C6NyuqgUT1SNDqrgwZ0TpLDzlIiiFyUPYCIVlju1cqdRVqxo1jLdxZrfV6p6v7ransJMXad2D1FIxvLf3j3ZCW6HBYlBgKPsgcQVapq6rU6t0QrdxZp+Y5ifbuzWOXeukOeYzOkgV3cGp3VQWN6perknh041Q9hjbIHENXqfaa27CvXip3FWrGjYQtAXknVIc8xDGlAZ7fG9Pq+/JPjKX+ED8oeAP7LntIqLd9RrOU5Rfp6+wFtLag45HHDkAZ2dmtMr1SN6dVBJ/dMlSeeI/4Ruih7ADiOwnKvvsk50HjEf5Gyj1L+J3ZP1pCuHg3J8Khf50S5HJzvj9BA2QOAnwrKq/XN9qLm0/22FVYe9hyHzVDfTknqm56oXmkJ6tkxQb06JiqrY7ySYtkKgPZF2QNAGxWUV2tZTpHW5pVqfV6Z1uWXquRg7VGf74lzqosnVp09seriiVUnd2zj53FKT3IpPcmllPgY2WysBYDAoOwBIMBM01R+abXW55Vq+/5K5RRWKmd/pbbvr9T+Cu/xX0CS024oLdGlNHesOiW5lO52KT0pVp0aP6YludTJHavUBN4U4Pj86VBOOgWAFjAMQ12T49Q1Oe6wx8qra7W3tFp7Squ//1hW1fx5QblXRZU1qq1veMOQX1p9zO9ltxnqmBijTu5YpSe5lNb4hiCj8ft3TY5Tl+RYjh9Ai1H2ANBGSbFOJcU61bdT0lGfU1PnU2GFVwVlDeX//UevCsqrta/Mq4Jyrw5UelXvM7WvzHvYMsH/LS2p4Q1At+Q4ZSTHqmtyXMMbgpQ4dUuOlzvOwRLCkNTKsl++fLlmzpyppUuXqqamRoMHD9Yvf/lLXXnllYHOBwARIcZhO+qWgR+qq/dpf0WNCsqrG98IeLWvrFr7yhq2COQVH1ReSZWqa30qLPeqsNyrNbklR3ythBi7uqbENW8RyEiOU7cffJ6e5GJJ4Sjhd9kvXLhQU6ZMUUxMjC6//HJ5PB7NmTNH06ZN044dO3TPPfcEIycARAWH3abOjQf6HY1pmio+WKv8kirtLq5SfkmV8kqqlFdcpfzSho8HKmtUWVOvLfsqtGVfxRFfx24z1NndsEWg4U1BrNISXYqPcSguxq74GLviYuxy2m2qqzflM03V+Uz5fKaqa+tV7q1TRXWdKrwNt/LqOpVX16rSW6fKmnodrKnTQW+9Khs/eut8ktGwmqEhQzZDcjpscsc65Yn7/paS4FRGcpwyPA1vTDKSGw54dIbJG5OaOp9KqmpUXeNTTb1Ptc03UyN7pFiSya8D9Orq6jRgwADt3r1bS5cu1YknnihJKi8v1ymnnKLNmzdrw4YN6tu3b4tejwP0ACA4qmvrlVfS+Eag8Q3B7pLv3xjsKak+7HoCocxmSOlJsYdsqeia/P3nGclxcgf49Eefz1RZda2KD9aq+GCNSg7WqORgw+clB2sa76ttvK/p3w1vso7EMKTtD54dsF0rQTtAb8GCBdq2bZuuvfba5qKXpKSkJP3ud7/T5Zdfrr/97W968MEHW5ccABAQsU67eqclqnda4hEfr/eZKiz3NmwR+MEbgqLKmoYZeU29qmrrdbCmXnX1Ptlthhw2m2w2Q3ab5HLYlRTrUKLL8YOPTiW6Gv6d4HIo3mVXQoxD8Y1bCVxOu0zTVNMU02eaqqnzqay6oTBLqxpuBypqlF/akCe/pOEgx5p6n/aWVWtvWbVW7iw+4s+UEGNXSkKMkuOdSomPUXJ8jJJiHYqx2+Ry2OS022S3GarzNcyym2bc3lqfyqvrVFpVq7LqxltVw1aK1r4fMgwpztmwVSTGYVOM3San3VC9z5TD3v7HUfhV9gsXLpQknXnmmYc91nTfokWL2p4KABBUdpvRvLvAqk3LLeXzmdpf4W08ZuEHuy1+sKWi5GCtKmvqVVnTsGsjkBJdjubdC01vIpLjnEqJdyo5PkYpCU4lx/3wTYZT7lhnSJ0+6VfZb926VZKOuJk+JSVFHTt2bH7OkXi9Xnm93x9dWlZW5s+3BwBEIZvNULo7VunuWA3PTD7icyq9dSoo9zZvbi+urFVJVa3Kq2tVW+9TTd33s3ln4yzbabfJ0Tjrd8c55Y51NH50yhPX8O/kuBjFOMLjWIFj8avsS0tLJUkej+eIj7vdbu3evfuoX//QQw9p9uzZ/nxLAACOK8HlUE+XQz2VYHWUkNSub1dmzJih0tLS5ltubm57fnsAAKKSXzP7phl90wz/vzUdGXg0LpdLLpfLn28JAADayK+ZfdO++iPtly8uLtb+/ftbfNodAABoH36V/cSJEyVJ8+bNO+yxpvuangMAAEKDX2V/2mmnqVevXnrttde0evXq5vvLy8t13333yeFwaPr06QGOCAAA2sKvffYOh0MvvviipkyZogkTJuiKK66Q2+3WnDlzlJOTo/vvv1/9+vULVlYAANAKfq+NP3nyZC1evFgzZ87UW2+91XwhnPvuu0/Tpk0LRkYAANAGfq2NH2isjQ8AQOv406HhvywQAAA4JsoeAIAIR9kDABDhKHsAACIcZQ8AQISj7AEAiHCUPQAAEc7vRXUCqekU/7KyMitjAAAQdpq6syXL5Vha9uXl5ZKkzMxMK2MAABC2ysvLj3l5ecniFfR8Pp/y8/OVlJQkwzAC8pplZWXKzMxUbm4uq/K1AeMYOIxlYDCOgcNYBobV42iapsrLy5WRkSGb7dh75S2d2dtsNnXr1i0or+12u/klDgDGMXAYy8BgHAOHsQwMK8fxeDP6JhygBwBAhKPsAQCIcBFX9i6XSzNnzpTL5bI6SlhjHAOHsQwMxjFwGMvACKdxtPQAPQAAEHwRN7MHAACHouwBAIhwlD0AABGOsgcAIMJR9gAARLiQL/vly5fr7LPPVkpKihISEnTSSSfptdde8+s1fD6fnn76aZ1wwgmKi4tTWlqaLr30Um3dujVIqUNTW8eyoKBADz30kC655BL17NlThmEEbJnjcNLWcVy8eLHuvPNOjRw5UqmpqYqNjdWAAQP061//WiUlJcELHoLaOpYLFy7UlVdeqYEDByo5OVnx8fHq37+/fvazn2nz5s1BTB5aAvF38odqa2s1fPhwGYahAQMGBDBp6AvE72TT38Yj3b7++usgpj86S5fLPZ6FCxdqypQpiomJ0eWXXy6Px6M5c+Zo2rRp2rFjh+65554Wvc7Pf/5zvfDCCxo0aJBuu+027du3T2+++abmzZunr776SoMGDQryT2K9QIzlhg0bdM8998gwDPXt21fx8fE6ePBgO6QPHYEYx0suuUT79+/X+PHjdfXVV8swDC1cuFCPPvqo3nnnHX311VdKT09vh5/GWoEYy/nz52vx4sU6+eSTm19r48aN+vvf/67XXntNn3zyiSZPntwOP411AvV38ofuu+8+ZWdnByFtaAvkWE6cOFGTJk067P5gLRF/XGaIqq2tNXv37m26XC7z22+/bb6/rKzMHDx4sOlwOMwtW7Yc93UWLFhgSjInTJhgVldXN98/f/580zAM89RTTw1K/lASqLHcu3evuWjRIrOsrMw0TdPs37+/GcK/QgEXqHF8+OGHzfz8/EPu8/l85s0332xKMn/xi18EPHuoCdRYVlVVHfH++fPnm5LMUaNGBSxzKArUOP7QypUrTYfDYT755JOmJLN///6Bjh2SAjWWn3/+uSnJnDlzZhDT+i9k/1J/+umnpiTz2muvPeyxN954w5Rkzpgx47ivc8UVV5iSzEWLFh322NSpU01J5ubNmwOSOVQFaiz/W7SVfbDGsUl+fr4pyRw8eHBbYoaFYI+laZpmSkqKmZyc3KbXCHWBHkev12sOHTrUHD9+vOnz+aKq7AM1lqFa9iG7GX/hwoWSpDPPPPOwx5ruW7RoUYteJyEhQePGjTvssSlTpmju3LlatGiR+vXr17bAISxQYxntgj2OTqdTkuRwhOx/y4AJ9lguXbpUxcXFGj9+fKtfIxwEehxnzZqlrVu3as2aNVF3PE6gx3Lr1q168skndfDgQfXo0UNnnHGGOnbsGJCsrRGyf1WaDp7r27fvYY+lpKSoY8eOxz3ArrKyUnv27NGQIUNkt9sPe7zptSP9QL1AjCWCP44vvfSSpCP/sYk0gR7LhQsXauHChfJ6vdq6dav+/e9/q2PHjvrTn/4UsMyhKJDjuHz5cj366KN68MEHI3ryczSB/p187bXXDjmwLy4uTrNnz9bdd9/d9rCtELJH45eWlko6+rV63W5383Pa8ho/fF6kCsRYIrjjuHr1as2ePVvp6en61a9+1eqM4SLQY7lw4ULNnj1bDz/8sN555x1lZmZq7ty5GjVqVEDyhqpAjaPX69X06dN14okn6s477wxoxnARqLFMS0vTH/7wB23cuFGVlZXKy8vTq6++qg4dOuhXv/qV/vznPwc0d0uFbNkD0SInJ0fnnnuu6uvr9cYbb1i6qS9czZo1S6ZpqqKiQsuWLdOAAQM0bty4Np1+Fk1+97vfaevWrXrppZeOuBUULTd48GDdddddGjBggOLj45WRkaFp06Zp7ty5iomJ0cyZM+Xz+do9V8iWfdO7q6O9kyorKzvqOzB/XuOHz4tUgRhLBGccd+7cqcmTJ6uwsFD/+te/Iv40sSbB+p1MSEjQ6NGj9e6772rAgAG68cYbVVhY2KasoSwQ4/jtt9/q8ccf17333quhQ4cGPGO4CPbfySFDhujkk0/Wvn37LDmtMWTL/lj704uLi7V///4j7lv5oYSEBHXp0kU5OTmqr68/7PFj7aOJJIEYSwR+HHfs2KFJkyYpPz9fb731ls4999yAZQ11wf6ddDgcmjx5siorK7VixYpWv06oC8Q4fvfdd6qvr9esWbMOWwBGkjZv3izDMJScnBzw/KGkPf5ONm21s2J9kpAt+4kTJ0qS5s2bd9hjTfc1Ped4r1NZWaklS5Yc9tinn37a4tcJZ4Eay2gXyHFsKvq8vDy9+eabuuCCCwIXNAy0x+9kfn6+pMg+uyEQ49ivXz9dd911R7xJDTPe6667TldffXWA04eWYP9O1tXV6dtvv5VhGOrevXurX6fVrD7372hqa2vNXr16mS6Xy1y1alXz/T9c4OCH58cXFhaaGzduNAsLCw95nR8uquP1epvvj7ZFdQIxlv8t2s6zD9Q45uTkmD169DAdDof5zjvvtFf8kBKosVy0aJHp8/kOe/1PP/3UdDqdpsfjMSsqKoL2c1gtWP+3myiKzrMP1Fh+9dVXh/1O1tbWmr/85S9NSebUqVOD+nMcTUj/pV6wYIHpdDrNxMRE84YbbjDvvPNOs2fPnqYk8/777z/kuTNnzjzqQgbXX3+9KckcNGiQeffdd5tXX3216XK5TI/HY65fv76dfhprBWosr7nmmuab2+02JR1yX0v/iISrQIxjjx49TEnmmDFjzJkzZx7xFg0CMZYej8fs3bu3efnll5t33323eeutt5qnnnqqKcl0Op3m22+/3Y4/kTUC9X/7SKKp7E0zcP+/s7KyzCuvvNK8++67zRtuuKF5YtS9e3dzx44d7fgTfS+ky940TfObb74xp06dano8HjMuLs4cNWqU+eqrrx72vGP9EtfX15tPPvmkOXjwYNPlcpmpqanmJZdcEvEr5/23QIylpGPecnJygv+DWKyt43i8MYymrSVtHcsnnnjCnDp1qtmtWzfT5XKZsbGxZt++fc3rr7/eXLduXTv9FNYLxP/tI4m2sjfNto/lww8/bE6aNMnMyMgwY2JizPj4ePOEE04w7733XrOoqKidforDGaZpmsHYPQAAAEJDyB6gBwAAAoOyBwAgwlH2AABEOMoeAIAIR9kDABDhKHsAACIcZQ8AQISj7AEAiHCUPQAAEY6yBwAgwlH2AABEOMoeAIAI9/8BQtevx85te4EAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_kde(jnp.abs(p[:, 0] - p[:, 1]))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4, 5, 6, 7])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d.actor.unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "d[\"actor_id\"] = d.actor.values - 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_11_4(actors, treatments):\n",
    "    actors = jnp.array(actors, dtype=jnp.int32)\n",
    "    treatments = jnp.array(treatments, dtype=jnp.int32)\n",
    "\n",
    "    def _generator():\n",
    "        a = yield tfd.Sample(tfd.Normal(loc=0.0, scale=1.5), sample_shape=7, name='a')\n",
    "        b = yield tfd.Normal(loc=[0., 0, 0, 0], scale=.5, name='b')\n",
    "        logit = jnp.take(a, actors) + jnp.take(b, treatments)\n",
    "        yield tfd.Binomial(total_count=1.0, logits=logit, name='pulled_left')\n",
    "\n",
    "    return tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_11_4 = model_11_4(d.actor_id.values, d.treatment.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_11_4_pin = jd_11_4.experimental_pin(\n",
    "  pulled_left=jnp.array(d.pulled_left.values, dtype=jnp.float32))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# https://www.tensorflow.org/probability/examples/Modeling_with_JointDistribution\n",
    "@jax.jit\n",
    "def run_chain(init_state, seed, step_size=1e-3, num_steps=500, burnin=300):\n",
    "\n",
    "#   def trace_fn(_, pkr):\n",
    "#     return (\n",
    "#         pkr.inner_results.inner_results.target_log_prob,\n",
    "#         pkr.inner_results.inner_results.leapfrogs_taken,\n",
    "#         pkr.inner_results.inner_results.has_divergence,\n",
    "#         pkr.inner_results.inner_results.energy,\n",
    "#         pkr.inner_results.inner_results.log_accept_ratio)\n",
    "\n",
    "  def target_log_prob(*states):\n",
    "    return jd_11_4_pin.unnormalized_log_prob(states)\n",
    "  \n",
    "  bijectors = [tfb.Identity(), tfb.Identity()]\n",
    "\n",
    "  kernel = tfp.mcmc.NoUTurnSampler(\n",
    "      target_log_prob_fn=target_log_prob,\n",
    "      step_size=step_size)\n",
    "  \n",
    "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
    "    inner_kernel=kernel,\n",
    "    bijector=bijectors)\n",
    "\n",
    "  kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "    inner_kernel=kernel,\n",
    "    num_adaptation_steps=burnin,\n",
    "    # step_size_setter_fn=lambda pkr, new_step_size: pkr._replace(\n",
    "    #     inner_results=pkr.inner_results._replace(step_size=new_step_size)),\n",
    "    # step_size_getter_fn=lambda pkr: pkr.inner_results.step_size,\n",
    "    # log_accept_prob_getter_fn=lambda pkr: pkr.inner_results.log_accept_ratio\n",
    "  )\n",
    "\n",
    "  chain_state = tfp.mcmc.sample_chain(\n",
    "      num_results=num_steps,\n",
    "      num_burnin_steps=burnin,\n",
    "      current_state=init_state,\n",
    "      kernel=kernel,\n",
    "      seed=seed,\n",
    "      trace_fn=None)\n",
    "  \n",
    "  return chain_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state = jd_11_4_pin.sample_unpinned(num_chains, seed=key())\n",
    "\n",
    "post_4 = run_chain(init_state=init_state, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_4_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_4._asdict().items()}\n",
    "dict_4 = dict(posterior=post_4_dict)\n",
    "idata_4 = az.from_dict(**dict_4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a[0]</th>\n",
       "      <td>-0.444</td>\n",
       "      <td>0.322</td>\n",
       "      <td>-0.964</td>\n",
       "      <td>0.052</td>\n",
       "      <td>0.008</td>\n",
       "      <td>0.006</td>\n",
       "      <td>1568.0</td>\n",
       "      <td>1561.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a[1]</th>\n",
       "      <td>3.888</td>\n",
       "      <td>0.730</td>\n",
       "      <td>2.739</td>\n",
       "      <td>5.031</td>\n",
       "      <td>0.024</td>\n",
       "      <td>0.017</td>\n",
       "      <td>973.0</td>\n",
       "      <td>1020.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a[2]</th>\n",
       "      <td>-0.739</td>\n",
       "      <td>0.331</td>\n",
       "      <td>-1.288</td>\n",
       "      <td>-0.226</td>\n",
       "      <td>0.009</td>\n",
       "      <td>0.006</td>\n",
       "      <td>1470.0</td>\n",
       "      <td>1403.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a[3]</th>\n",
       "      <td>-0.746</td>\n",
       "      <td>0.333</td>\n",
       "      <td>-1.263</td>\n",
       "      <td>-0.204</td>\n",
       "      <td>0.008</td>\n",
       "      <td>0.006</td>\n",
       "      <td>1568.0</td>\n",
       "      <td>1702.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a[4]</th>\n",
       "      <td>-0.448</td>\n",
       "      <td>0.326</td>\n",
       "      <td>-0.950</td>\n",
       "      <td>0.094</td>\n",
       "      <td>0.008</td>\n",
       "      <td>0.006</td>\n",
       "      <td>1645.0</td>\n",
       "      <td>1436.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a[5]</th>\n",
       "      <td>0.485</td>\n",
       "      <td>0.329</td>\n",
       "      <td>0.004</td>\n",
       "      <td>1.059</td>\n",
       "      <td>0.009</td>\n",
       "      <td>0.006</td>\n",
       "      <td>1465.0</td>\n",
       "      <td>1681.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a[6]</th>\n",
       "      <td>1.958</td>\n",
       "      <td>0.418</td>\n",
       "      <td>1.307</td>\n",
       "      <td>2.660</td>\n",
       "      <td>0.011</td>\n",
       "      <td>0.008</td>\n",
       "      <td>1476.0</td>\n",
       "      <td>1471.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b[0]</th>\n",
       "      <td>-0.050</td>\n",
       "      <td>0.279</td>\n",
       "      <td>-0.474</td>\n",
       "      <td>0.413</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.005</td>\n",
       "      <td>1520.0</td>\n",
       "      <td>1575.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b[1]</th>\n",
       "      <td>0.477</td>\n",
       "      <td>0.278</td>\n",
       "      <td>-0.008</td>\n",
       "      <td>0.883</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.005</td>\n",
       "      <td>1491.0</td>\n",
       "      <td>1384.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b[2]</th>\n",
       "      <td>-0.380</td>\n",
       "      <td>0.290</td>\n",
       "      <td>-0.884</td>\n",
       "      <td>0.058</td>\n",
       "      <td>0.008</td>\n",
       "      <td>0.006</td>\n",
       "      <td>1490.0</td>\n",
       "      <td>1565.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b[3]</th>\n",
       "      <td>0.362</td>\n",
       "      <td>0.282</td>\n",
       "      <td>-0.087</td>\n",
       "      <td>0.801</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.005</td>\n",
       "      <td>1502.0</td>\n",
       "      <td>1415.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "a[0] -0.444  0.322    -0.964      0.052      0.008    0.006    1568.0   \n",
       "a[1]  3.888  0.730     2.739      5.031      0.024    0.017     973.0   \n",
       "a[2] -0.739  0.331    -1.288     -0.226      0.009    0.006    1470.0   \n",
       "a[3] -0.746  0.333    -1.263     -0.204      0.008    0.006    1568.0   \n",
       "a[4] -0.448  0.326    -0.950      0.094      0.008    0.006    1645.0   \n",
       "a[5]  0.485  0.329     0.004      1.059      0.009    0.006    1465.0   \n",
       "a[6]  1.958  0.418     1.307      2.660      0.011    0.008    1476.0   \n",
       "b[0] -0.050  0.279    -0.474      0.413      0.007    0.005    1520.0   \n",
       "b[1]  0.477  0.278    -0.008      0.883      0.007    0.005    1491.0   \n",
       "b[2] -0.380  0.290    -0.884      0.058      0.008    0.006    1490.0   \n",
       "b[3]  0.362  0.282    -0.087      0.801      0.007    0.005    1502.0   \n",
       "\n",
       "      ess_tail  r_hat  \n",
       "a[0]    1561.0   1.00  \n",
       "a[1]    1020.0   1.00  \n",
       "a[2]    1403.0   1.00  \n",
       "a[3]    1702.0   1.00  \n",
       "a[4]    1436.0   1.00  \n",
       "a[5]    1681.0   1.00  \n",
       "a[6]    1471.0   1.00  \n",
       "b[0]    1575.0   1.00  \n",
       "b[1]    1384.0   1.00  \n",
       "b[2]    1565.0   1.00  \n",
       "b[3]    1415.0   1.01  "
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_4, hdi_prob=0.89)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly interpretation of all these varying parameters is difficult now. The alphas above represent intercepts unique to each chimpanzee. Each of these expresses the tendency of each individual to pull the left lever. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([<Axes: title={'center': '89.0% HDI'}>], dtype=object)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x470 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p_left = jax.nn.sigmoid(idata_4.posterior['a'].values)\n",
    "az.plot_forest({'p_left' : p_left}, combined=True, hdi_prob=0.89)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What above plot shows is that 0,2,3,4 show preference for right lever.\n",
    "Two chimps (1 & 6) show strong preference for left lever and it is also reflected in the data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.13\n",
    "\n",
    "Here we are now considering treatment effects and hoping that they are estimated more precisely"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x440 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "labs = [\"R/N\", \"L/N\", \"R/P\", \"L/P\"]\n",
    "az.plot_forest(idata_4, combined=True, var_names=\"b\", hdi_prob=0.89);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* L/N => prosocial on left / no partner\n",
    "* R/P => proscoial on right / partner\n",
    "\n",
    "What we are looking for is evidence that the chimpanzees choose the prosocial option more when a partner is present. This implies comparing the first row with the third row and the second row with the fourth row"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x520 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "diffs = {\n",
    "    \"db13\": idata_4.posterior[\"b\"][..., 0] - idata_4.posterior[\"b\"][..., 2],\n",
    "    \"db24\": idata_4.posterior[\"b\"][..., 1] - idata_4.posterior[\"b\"][..., 3],\n",
    "}\n",
    "az.plot_forest(diffs, combined=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "db13 is the difference between no-partner/partner treatments when the prosocial option was on the right.\n",
    "\n",
    "There is a weak evidence that individual pulled left more when the partner was absent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code 11.15\n",
    "\n",
    "Compute proportion in each combination of actor & treatment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>treatment</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>actor</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>0.277778</td>\n",
       "      <td>0.555556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.277778</td>\n",
       "      <td>0.611111</td>\n",
       "      <td>0.166667</td>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>0.111111</td>\n",
       "      <td>0.444444</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.555556</td>\n",
       "      <td>0.277778</td>\n",
       "      <td>0.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.777778</td>\n",
       "      <td>0.611111</td>\n",
       "      <td>0.555556</td>\n",
       "      <td>0.611111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.777778</td>\n",
       "      <td>0.833333</td>\n",
       "      <td>0.944444</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "treatment         0         1         2         3\n",
       "actor                                            \n",
       "1          0.333333  0.500000  0.277778  0.555556\n",
       "2          1.000000  1.000000  1.000000  1.000000\n",
       "3          0.277778  0.611111  0.166667  0.333333\n",
       "4          0.333333  0.500000  0.111111  0.444444\n",
       "5          0.333333  0.555556  0.277778  0.500000\n",
       "6          0.777778  0.611111  0.555556  0.611111\n",
       "7          0.777778  0.833333  0.944444  1.000000"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pl = d.groupby([\"actor\", \"treatment\"])[\"pulled_left\"].mean().unstack()\n",
    "pl"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "the cells contain proportions of pulls that were of the left lever"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.16\n",
    "\n",
    "Plotting observed proportions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plt.subplot(\n",
    "    xlim=(0.5, 28.5),\n",
    "    ylim=(0, 1.05),\n",
    "    xlabel=\"\",\n",
    "    ylabel=\"proportion left lever\",\n",
    "    xticks=[],\n",
    ")\n",
    "plt.yticks(ticks=[0, 0.5, 1], labels=[0, 0.5, 1])\n",
    "ax.axhline(0.5, c=\"k\", lw=1, ls=\"--\")\n",
    "for j in range(1, 8):\n",
    "    ax.axvline((j - 1) * 4 + 4.5, c=\"k\", lw=0.5)\n",
    "for j in range(1, 8):\n",
    "    ax.annotate(\n",
    "        \"actor {}\".format(j),\n",
    "        ((j - 1) * 4 + 2.5, 1.1),\n",
    "        ha=\"center\",\n",
    "        va=\"center\",\n",
    "        annotation_clip=False,\n",
    "    )\n",
    "for j in np.delete(range(1, 8), 1):\n",
    "    ax.plot((j - 1) * 4 + np.array([1, 3]), pl.loc[j, [0, 2]], \"b\")\n",
    "    ax.plot((j - 1) * 4 + np.array([2, 4]), pl.loc[j, [1, 3]], \"b\")\n",
    "x = np.arange(1, 29).reshape(7, 4)\n",
    "ax.scatter(\n",
    "    x[:, [0, 1]].reshape(-1),\n",
    "    pl.values[:, [0, 1]].reshape(-1),\n",
    "    edgecolor=\"b\",\n",
    "    facecolor=\"w\",\n",
    "    zorder=3,\n",
    ")\n",
    "ax.scatter(\n",
    "    x[:, [2, 3]].reshape(-1), pl.values[:, [2, 3]].reshape(-1), marker=\".\", c=\"b\", s=80\n",
    ")\n",
    "yoff = 0.01\n",
    "ax.annotate(\"R/N\", (1, pl.loc[1, 0] - yoff), ha=\"center\", va=\"top\")\n",
    "ax.annotate(\"L/N\", (2, pl.loc[1, 1] + yoff), ha=\"center\", va=\"bottom\")\n",
    "ax.annotate(\"R/P\", (3, pl.loc[1, 2] - yoff), ha=\"center\", va=\"top\")\n",
    "ax.annotate(\"L/P\", (4, pl.loc[1, 3] + yoff), ha=\"center\", va=\"bottom\")\n",
    "ax.set_title(\"observed proportions\\n\")\n",
    "plt.tight_layout()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.17"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "dat = {\"actor\": np.repeat(np.arange(7), 4), \"treatment\": np.tile(np.arange(4), 7)}\n",
    "\n",
    "def compute_p_for_given_actor_treatment(params):\n",
    "    a = params[0]\n",
    "    t = params[1]\n",
    "    p = idata_4.posterior[\"a\"].values[0][:, a] + idata_4.posterior[\"b\"].values[0][:, t]\n",
    "    return jax.nn.sigmoid(p)\n",
    "\n",
    "params = zip(dat[\"actor\"], dat[\"treatment\"])\n",
    "\n",
    "p = np.array(list(map(compute_p_for_given_actor_treatment, params))).T\n",
    "\n",
    "p_mu = np.mean(p, 0)\n",
    "p_ci = np.percentile(p, q=(4.5, 95.5), axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.18"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "d[\"side\"] = d.prosoc_left  # right 0, left 1\n",
    "d[\"cond\"] = d.condition  # no partner 0, partner 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.19"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_11_5(actor, side, cond):\n",
    "  actor = jnp.array(actor, dtype=jnp.int32)\n",
    "  side = jnp.array(side, dtype=jnp.int32)\n",
    "  cond = jnp.array(cond, dtype=jnp.int32)\n",
    "\n",
    "  def _generator():\n",
    "    a = yield tfd.Sample(tfd.Normal(loc=0.0, scale=1.5), sample_shape=7, name='a')\n",
    "    bs = yield tfd.Sample(tfd.Normal(loc=0.0, scale=0.5), sample_shape=2, name='bs')\n",
    "    bc = yield tfd.Sample(tfd.Normal(loc=0.0, scale=0.5), sample_shape=2, name='bc')\n",
    "    logits = jnp.take(a, actor) + jnp.take(bs, side) + jnp.take(bc, cond)\n",
    "    yield tfd.Binomial(total_count=1.0, logits=logits, name='pulled_left')\n",
    "\n",
    "  return tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_11_5 = model_11_5(d.actor_id.values, d.side.values, d.cond.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_11_5_pin = jd_11_5.experimental_pin(\n",
    "  pulled_left=jnp.array(d.pulled_left.values, dtype=jnp.float32))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def run_chain(init_state, seed, step_size=1e-3, num_steps=500, burnin=300):\n",
    "\n",
    "  def target_log_prob(*states):\n",
    "    return jd_11_5_pin.unnormalized_log_prob(states)\n",
    "  \n",
    "  bijectors = [tfb.Identity(), tfb.Identity(), tfb.Identity()]\n",
    "\n",
    "  kernel = tfp.mcmc.NoUTurnSampler(\n",
    "      target_log_prob_fn=target_log_prob,\n",
    "      step_size=step_size)\n",
    "  \n",
    "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
    "    inner_kernel=kernel,\n",
    "    bijector=bijectors)\n",
    "\n",
    "  kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "    inner_kernel=kernel,\n",
    "    num_adaptation_steps=burnin)\n",
    "\n",
    "  chain_state = tfp.mcmc.sample_chain(\n",
    "      num_results=num_steps,\n",
    "      num_burnin_steps=burnin,\n",
    "      current_state=init_state,\n",
    "      kernel=kernel,\n",
    "      seed=seed,\n",
    "      trace_fn=None)\n",
    "  \n",
    "  return chain_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state = jd_11_5_pin.sample_unpinned(num_chains, seed=key())\n",
    "\n",
    "post_5 = run_chain(init_state=init_state, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_5_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_5._asdict().items()}\n",
    "dict_5 = dict(posterior=post_5_dict)\n",
    "idata_5 = az.from_dict(**dict_5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a[0]</th>\n",
       "      <td>-0.653</td>\n",
       "      <td>0.444</td>\n",
       "      <td>-1.292</td>\n",
       "      <td>0.127</td>\n",
       "      <td>0.015</td>\n",
       "      <td>0.011</td>\n",
       "      <td>828.0</td>\n",
       "      <td>930.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a[1]</th>\n",
       "      <td>3.784</td>\n",
       "      <td>0.826</td>\n",
       "      <td>2.509</td>\n",
       "      <td>5.121</td>\n",
       "      <td>0.031</td>\n",
       "      <td>0.022</td>\n",
       "      <td>736.0</td>\n",
       "      <td>859.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a[2]</th>\n",
       "      <td>-0.949</td>\n",
       "      <td>0.445</td>\n",
       "      <td>-1.633</td>\n",
       "      <td>-0.198</td>\n",
       "      <td>0.015</td>\n",
       "      <td>0.011</td>\n",
       "      <td>866.0</td>\n",
       "      <td>1143.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a[3]</th>\n",
       "      <td>-0.950</td>\n",
       "      <td>0.445</td>\n",
       "      <td>-1.636</td>\n",
       "      <td>-0.204</td>\n",
       "      <td>0.016</td>\n",
       "      <td>0.011</td>\n",
       "      <td>797.0</td>\n",
       "      <td>1037.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a[4]</th>\n",
       "      <td>-0.652</td>\n",
       "      <td>0.447</td>\n",
       "      <td>-1.325</td>\n",
       "      <td>0.084</td>\n",
       "      <td>0.015</td>\n",
       "      <td>0.011</td>\n",
       "      <td>849.0</td>\n",
       "      <td>1093.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a[5]</th>\n",
       "      <td>0.270</td>\n",
       "      <td>0.450</td>\n",
       "      <td>-0.471</td>\n",
       "      <td>0.975</td>\n",
       "      <td>0.016</td>\n",
       "      <td>0.011</td>\n",
       "      <td>827.0</td>\n",
       "      <td>1201.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a[6]</th>\n",
       "      <td>1.765</td>\n",
       "      <td>0.514</td>\n",
       "      <td>1.003</td>\n",
       "      <td>2.648</td>\n",
       "      <td>0.017</td>\n",
       "      <td>0.012</td>\n",
       "      <td>968.0</td>\n",
       "      <td>1244.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bc[0]</th>\n",
       "      <td>0.273</td>\n",
       "      <td>0.327</td>\n",
       "      <td>-0.287</td>\n",
       "      <td>0.755</td>\n",
       "      <td>0.010</td>\n",
       "      <td>0.007</td>\n",
       "      <td>1141.0</td>\n",
       "      <td>1322.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bc[1]</th>\n",
       "      <td>0.024</td>\n",
       "      <td>0.327</td>\n",
       "      <td>-0.474</td>\n",
       "      <td>0.567</td>\n",
       "      <td>0.010</td>\n",
       "      <td>0.007</td>\n",
       "      <td>1080.0</td>\n",
       "      <td>1330.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bs[0]</th>\n",
       "      <td>-0.183</td>\n",
       "      <td>0.333</td>\n",
       "      <td>-0.675</td>\n",
       "      <td>0.393</td>\n",
       "      <td>0.010</td>\n",
       "      <td>0.007</td>\n",
       "      <td>1064.0</td>\n",
       "      <td>1272.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bs[1]</th>\n",
       "      <td>0.511</td>\n",
       "      <td>0.339</td>\n",
       "      <td>-0.019</td>\n",
       "      <td>1.058</td>\n",
       "      <td>0.010</td>\n",
       "      <td>0.007</td>\n",
       "      <td>1072.0</td>\n",
       "      <td>1194.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "a[0]  -0.653  0.444    -1.292      0.127      0.015    0.011     828.0   \n",
       "a[1]   3.784  0.826     2.509      5.121      0.031    0.022     736.0   \n",
       "a[2]  -0.949  0.445    -1.633     -0.198      0.015    0.011     866.0   \n",
       "a[3]  -0.950  0.445    -1.636     -0.204      0.016    0.011     797.0   \n",
       "a[4]  -0.652  0.447    -1.325      0.084      0.015    0.011     849.0   \n",
       "a[5]   0.270  0.450    -0.471      0.975      0.016    0.011     827.0   \n",
       "a[6]   1.765  0.514     1.003      2.648      0.017    0.012     968.0   \n",
       "bc[0]  0.273  0.327    -0.287      0.755      0.010    0.007    1141.0   \n",
       "bc[1]  0.024  0.327    -0.474      0.567      0.010    0.007    1080.0   \n",
       "bs[0] -0.183  0.333    -0.675      0.393      0.010    0.007    1064.0   \n",
       "bs[1]  0.511  0.339    -0.019      1.058      0.010    0.007    1072.0   \n",
       "\n",
       "       ess_tail  r_hat  \n",
       "a[0]      930.0    1.0  \n",
       "a[1]      859.0    1.0  \n",
       "a[2]     1143.0    1.0  \n",
       "a[3]     1037.0    1.0  \n",
       "a[4]     1093.0    1.0  \n",
       "a[5]     1201.0    1.0  \n",
       "a[6]     1244.0    1.0  \n",
       "bc[0]    1322.0    1.0  \n",
       "bc[1]    1330.0    1.0  \n",
       "bs[0]    1272.0    1.0  \n",
       "bs[1]    1194.0    1.0  "
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_5, hdi_prob=0.89)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.20\n",
    "\n",
    "We need to compute likelihoods in order to use arviz's compare method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_11_4x(actor, treatment):\n",
    "  actor = tf.convert_to_tensor(actor, dtype=tf.int32)\n",
    "  treatment = tf.convert_to_tensor(treatment, dtype=tf.int32)\n",
    "\n",
    "  def _generator():\n",
    "    a = yield xtfd.Sample(xtfd.Normal(loc=0.0, scale=1.5), sample_shape=7, name='a')\n",
    "    b = yield xtfd.Normal(loc=[0., 0, 0, 0], scale=.5, name='b')\n",
    "    logits = tf.gather(a, actor) + tf.gather(b, treatment)\n",
    "    yield xtfd.Binomial(total_count=1.0, logits=logits, name='pulled_left')\n",
    "\n",
    "  return xtfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_4x = model_11_4x(d.actor_id.values, d.treatment.values)\n",
    "ds_4, _ = jd_4x.sample_distributions(value=post_4)\n",
    "ll_4 = ds_4[-1].log_prob(d.pulled_left.values)\n",
    "ll_4 = np.moveaxis(ll_4, 0, 1) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "dict_4.update(log_likelihood={'ll': ll_4},\n",
    "              dims={\"ll\": [\"obs\"]},\n",
    "              coords={\"obs\": np.arange(len(d.pulled_left.values))})\n",
    "idata_4 = az.from_dict(**dict_4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_11_5x(actor, side, cond):\n",
    "  actor = tf.convert_to_tensor(actor, dtype=tf.int32)\n",
    "  side = tf.convert_to_tensor(side, dtype=tf.int32)\n",
    "  cond = tf.convert_to_tensor(cond, dtype=tf.int32)\n",
    "\n",
    "  def _generator():\n",
    "    a = yield xtfd.Sample(xtfd.Normal(loc=0.0, scale=1.5), sample_shape=7, name='a')\n",
    "    bs = yield xtfd.Sample(xtfd.Normal(loc=0.0, scale=0.5), sample_shape=2, name='bs')\n",
    "    bc = yield xtfd.Sample(xtfd.Normal(loc=0.0, scale=0.5), sample_shape=2, name='bc')\n",
    "    logits = tf.gather(a, actor) + tf.gather(bs, side) + tf.gather(bc, cond)\n",
    "    yield xtfd.Binomial(total_count=1.0, logits=logits, name='pulled_left')\n",
    "\n",
    "  return xtfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_5x = model_11_5x(d.actor_id.values, d.side.values, d.cond.values)\n",
    "ds, _ = jd_5x.sample_distributions(value=post_5)\n",
    "ll_5 = ds[-1].log_prob(d.pulled_left.values)\n",
    "ll_5 = np.moveaxis(ll_5, 0, 1) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "dict_5.update(log_likelihood={'ll': ll_5},\n",
    "              dims={\"ll\": [\"obs\"]},\n",
    "              coords={\"obs\": np.arange(len(d.pulled_left.values))})\n",
    "idata_5 = az.from_dict(**dict_5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>rank</th>\n",
       "      <th>elpd_loo</th>\n",
       "      <th>p_loo</th>\n",
       "      <th>elpd_diff</th>\n",
       "      <th>weight</th>\n",
       "      <th>se</th>\n",
       "      <th>dse</th>\n",
       "      <th>warning</th>\n",
       "      <th>scale</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>m11.5</th>\n",
       "      <td>0</td>\n",
       "      <td>530.592546</td>\n",
       "      <td>7.726895</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>19.128082</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>False</td>\n",
       "      <td>deviance</td>\n",
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       "    <tr>\n",
       "      <th>m11.4</th>\n",
       "      <td>1</td>\n",
       "      <td>532.427182</td>\n",
       "      <td>8.567087</td>\n",
       "      <td>1.834636</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18.919016</td>\n",
       "      <td>1.270507</td>\n",
       "      <td>False</td>\n",
       "      <td>deviance</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       rank    elpd_loo     p_loo  elpd_diff  weight         se       dse  \\\n",
       "m11.5     0  530.592546  7.726895   0.000000     1.0  19.128082  0.000000   \n",
       "m11.4     1  532.427182  8.567087   1.834636     0.0  18.919016  1.270507   \n",
       "\n",
       "       warning     scale  \n",
       "m11.5    False  deviance  \n",
       "m11.4    False  deviance  "
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.compare({\"m11.5\": idata_5, \"m11.4\": idata_4}, ic='loo', scale=\"deviance\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 11.1.2 Relative shark and absolute penguin"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.23"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9265165"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(np.exp(post_4_dict['b'][:, :, 3] - post_4_dict['b'][:, :, 1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Aggregated binomial: Chimpanzees again,condensed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.24"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "d = pd.read_csv(\"./data/chimpanzees.csv\", sep=\";\")\n",
    "d[\"treatment\"] = d.prosoc_left + 2 * d.condition\n",
    "d[\"side\"] = d.prosoc_left  # right 0, left 1\n",
    "d[\"cond\"] = d.condition  # no partner 0, partner 1\n",
    "d_aggregated = (\n",
    "    d.groupby([\"treatment\", \"actor\", \"side\", \"cond\"])[\"pulled_left\"].sum().reset_index()\n",
    ")\n",
    "d_aggregated.rename(columns={\"pulled_left\": \"left_pulls\"}, inplace=True)\n",
    "\n",
    "d_aggregated[\"actor_id\"] = d_aggregated[\"actor\"].values - 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.25"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_11_6(actor, treatment):\n",
    "  actor = jnp.array(actor, dtype=jnp.int32)\n",
    "  treatment = jnp.array(treatment, dtype=jnp.int32)\n",
    "\n",
    "  def _generator():\n",
    "    a = yield tfd.Sample(tfd.Normal(loc=0.0, scale=1.5), sample_shape=7, name='a')\n",
    "    b = yield tfd.Sample(tfd.Normal(loc=0.0, scale=0.5), sample_shape=4, name='b')\n",
    "    logits = jnp.take(a, actor) + jnp.take(b, treatment)\n",
    "    yield tfd.Binomial(total_count=18.0, logits=logits, name='left_pulls')\n",
    "\n",
    "  return tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_11_6 = model_11_6(d_aggregated.actor_id.values, d_aggregated.treatment.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_11_6_pin = jd_11_6.experimental_pin(\n",
    "  left_pulls=jnp.array(d_aggregated.left_pulls.values, dtype=jnp.float32))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def run_chain(init_state, seed, step_size=1e-3, num_steps=500, burnin=300):\n",
    "\n",
    "  def target_log_prob(*states):\n",
    "    return jd_11_6_pin.unnormalized_log_prob(states)\n",
    "  \n",
    "  bijectors = [tfb.Identity(), tfb.Identity()]\n",
    "\n",
    "  kernel = tfp.mcmc.NoUTurnSampler(\n",
    "      target_log_prob_fn=target_log_prob,\n",
    "      step_size=step_size)\n",
    "  \n",
    "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
    "    inner_kernel=kernel,\n",
    "    bijector=bijectors)\n",
    "\n",
    "  kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "    inner_kernel=kernel,\n",
    "    num_adaptation_steps=burnin)\n",
    "\n",
    "  chain_state = tfp.mcmc.sample_chain(\n",
    "      num_results=num_steps,\n",
    "      num_burnin_steps=burnin,\n",
    "      current_state=init_state,\n",
    "      kernel=kernel,\n",
    "      seed=seed,\n",
    "      trace_fn=None)\n",
    "  \n",
    "  return chain_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state = jd_11_6_pin.sample_unpinned(num_chains, seed=key())\n",
    "# StateTuple = namedtuple(\"StateTuple\", ['a', 'b'])\n",
    "# init_state = StateTuple(jnp.zeros((num_chains, 7)), jnp.zeros((num_chains, 4)))\n",
    "post_6 = run_chain(init_state=init_state, seed=key(), burnin=500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_6_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_6._asdict().items()}\n",
    "dict_6 = dict(posterior=post_6_dict)\n",
    "idata_6 = az.from_dict(**dict_6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a[0]</th>\n",
       "      <td>-0.442</td>\n",
       "      <td>0.339</td>\n",
       "      <td>-0.992</td>\n",
       "      <td>0.090</td>\n",
       "      <td>0.009</td>\n",
       "      <td>0.007</td>\n",
       "      <td>1446.0</td>\n",
       "      <td>1290.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a[1]</th>\n",
       "      <td>3.890</td>\n",
       "      <td>0.757</td>\n",
       "      <td>2.658</td>\n",
       "      <td>4.997</td>\n",
       "      <td>0.022</td>\n",
       "      <td>0.016</td>\n",
       "      <td>1169.0</td>\n",
       "      <td>877.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a[2]</th>\n",
       "      <td>-0.741</td>\n",
       "      <td>0.336</td>\n",
       "      <td>-1.222</td>\n",
       "      <td>-0.136</td>\n",
       "      <td>0.009</td>\n",
       "      <td>0.006</td>\n",
       "      <td>1410.0</td>\n",
       "      <td>1547.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a[3]</th>\n",
       "      <td>-0.736</td>\n",
       "      <td>0.341</td>\n",
       "      <td>-1.318</td>\n",
       "      <td>-0.251</td>\n",
       "      <td>0.009</td>\n",
       "      <td>0.006</td>\n",
       "      <td>1385.0</td>\n",
       "      <td>1541.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a[4]</th>\n",
       "      <td>-0.440</td>\n",
       "      <td>0.332</td>\n",
       "      <td>-1.001</td>\n",
       "      <td>0.050</td>\n",
       "      <td>0.008</td>\n",
       "      <td>0.006</td>\n",
       "      <td>1588.0</td>\n",
       "      <td>1689.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a[5]</th>\n",
       "      <td>0.491</td>\n",
       "      <td>0.334</td>\n",
       "      <td>-0.082</td>\n",
       "      <td>0.999</td>\n",
       "      <td>0.008</td>\n",
       "      <td>0.006</td>\n",
       "      <td>1541.0</td>\n",
       "      <td>1431.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a[6]</th>\n",
       "      <td>1.975</td>\n",
       "      <td>0.420</td>\n",
       "      <td>1.357</td>\n",
       "      <td>2.689</td>\n",
       "      <td>0.012</td>\n",
       "      <td>0.009</td>\n",
       "      <td>1295.0</td>\n",
       "      <td>1347.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b[0]</th>\n",
       "      <td>-0.054</td>\n",
       "      <td>0.285</td>\n",
       "      <td>-0.531</td>\n",
       "      <td>0.388</td>\n",
       "      <td>0.008</td>\n",
       "      <td>0.006</td>\n",
       "      <td>1320.0</td>\n",
       "      <td>1560.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b[1]</th>\n",
       "      <td>0.472</td>\n",
       "      <td>0.298</td>\n",
       "      <td>-0.027</td>\n",
       "      <td>0.934</td>\n",
       "      <td>0.008</td>\n",
       "      <td>0.006</td>\n",
       "      <td>1386.0</td>\n",
       "      <td>1419.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b[2]</th>\n",
       "      <td>-0.391</td>\n",
       "      <td>0.285</td>\n",
       "      <td>-0.836</td>\n",
       "      <td>0.083</td>\n",
       "      <td>0.008</td>\n",
       "      <td>0.005</td>\n",
       "      <td>1376.0</td>\n",
       "      <td>1423.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b[3]</th>\n",
       "      <td>0.358</td>\n",
       "      <td>0.286</td>\n",
       "      <td>-0.084</td>\n",
       "      <td>0.824</td>\n",
       "      <td>0.008</td>\n",
       "      <td>0.005</td>\n",
       "      <td>1453.0</td>\n",
       "      <td>1363.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "a[0] -0.442  0.339    -0.992      0.090      0.009    0.007    1446.0   \n",
       "a[1]  3.890  0.757     2.658      4.997      0.022    0.016    1169.0   \n",
       "a[2] -0.741  0.336    -1.222     -0.136      0.009    0.006    1410.0   \n",
       "a[3] -0.736  0.341    -1.318     -0.251      0.009    0.006    1385.0   \n",
       "a[4] -0.440  0.332    -1.001      0.050      0.008    0.006    1588.0   \n",
       "a[5]  0.491  0.334    -0.082      0.999      0.008    0.006    1541.0   \n",
       "a[6]  1.975  0.420     1.357      2.689      0.012    0.009    1295.0   \n",
       "b[0] -0.054  0.285    -0.531      0.388      0.008    0.006    1320.0   \n",
       "b[1]  0.472  0.298    -0.027      0.934      0.008    0.006    1386.0   \n",
       "b[2] -0.391  0.285    -0.836      0.083      0.008    0.005    1376.0   \n",
       "b[3]  0.358  0.286    -0.084      0.824      0.008    0.005    1453.0   \n",
       "\n",
       "      ess_tail  r_hat  \n",
       "a[0]    1290.0    1.0  \n",
       "a[1]     877.0    1.0  \n",
       "a[2]    1547.0    1.0  \n",
       "a[3]    1541.0    1.0  \n",
       "a[4]    1689.0    1.0  \n",
       "a[5]    1431.0    1.0  \n",
       "a[6]    1347.0    1.0  \n",
       "b[0]    1560.0    1.0  \n",
       "b[1]    1419.0    1.0  \n",
       "b[2]    1423.0    1.0  \n",
       "b[3]    1363.0    1.0  "
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_6, hdi_prob=0.89)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.26 (Find a way to get the comparison even if different number of obs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_11_6x(actor, treatment):\n",
    "  actor = tf.convert_to_tensor(actor, dtype=tf.int32)\n",
    "  treatment = tf.convert_to_tensor(treatment, dtype=tf.int32)\n",
    "\n",
    "  def _generator():\n",
    "    a = yield xtfd.Sample(xtfd.Normal(loc=0.0, scale=1.5), sample_shape=7, name='a')\n",
    "    b = yield xtfd.Sample(xtfd.Normal(loc=0.0, scale=0.5), sample_shape=4, name='b')\n",
    "    logits = tf.gather(a, actor) + tf.gather(b, treatment)\n",
    "    yield xtfd.Binomial(total_count=18.0, logits=logits, name='left_pulls')\n",
    "\n",
    "  return xtfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:5 out of the last 5 calls to <function pfor.<locals>.f at 0x38015d620> triggered tf.function retracing. Tracing is expensive and the excessive number of tracings could be due to (1) creating @tf.function repeatedly in a loop, (2) passing tensors with different shapes, (3) passing Python objects instead of tensors. For (1), please define your @tf.function outside of the loop. For (2), @tf.function has reduce_retracing=True option that can avoid unnecessary retracing. For (3), please refer to https://www.tensorflow.org/guide/function#controlling_retracing and https://www.tensorflow.org/api_docs/python/tf/function for  more details.\n"
     ]
    }
   ],
   "source": [
    "jd_6x = model_11_6x(d_aggregated.actor_id.values, d_aggregated.treatment.values)\n",
    "ds, _ = jd_6x.sample_distributions(value=post_6)\n",
    "ll_6 = ds[-1].log_prob(tf.convert_to_tensor(d_aggregated.left_pulls.values, dtype=tf.float32))\n",
    "ll_6 = np.moveaxis(ll_6, 0, 1) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "dict_6.update(log_likelihood={'ll': ll_6},\n",
    "              dims={\"ll\": [\"obs\"]},\n",
    "              coords={\"obs\": np.arange(len(d_aggregated.left_pulls.values))})\n",
    "idata_6 = az.from_dict(**dict_6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# in order to use comparison the number of observations should be same\n",
    "# which is not the case with m11.4 (504) and m11.6 (28)\n",
    "# az.compare({\"m11.6\": idata_6, \"m11.4\": idata_4}, ic='loo', scale=\"deviance\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.27"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "11.790481\n",
      "20.652117\n"
     ]
    }
   ],
   "source": [
    "# deviance of aggregated 6-in-9\n",
    "print(-2 * tfd.Binomial(total_count=9.0, probs=0.2).log_prob(6))\n",
    "# deviance of dis-aggregated\n",
    "print(\n",
    "    -2\n",
    "    * np.sum(tfd.Bernoulli(probs=0.2).log_prob(np.array([1, 1, 1, 1, 1, 1, 0, 0, 0])))\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 11.1.4 Aggregated binomial: Graduate school admissions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.28\n",
    "\n",
    "Evaluate if there is a gender bias in admissions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dept</th>\n",
       "      <th>applicant.gender</th>\n",
       "      <th>admit</th>\n",
       "      <th>reject</th>\n",
       "      <th>applications</th>\n",
       "      <th>gid</th>\n",
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       "  </thead>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>A</td>\n",
       "      <td>male</td>\n",
       "      <td>512</td>\n",
       "      <td>313</td>\n",
       "      <td>825</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>A</td>\n",
       "      <td>female</td>\n",
       "      <td>89</td>\n",
       "      <td>19</td>\n",
       "      <td>108</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>B</td>\n",
       "      <td>male</td>\n",
       "      <td>353</td>\n",
       "      <td>207</td>\n",
       "      <td>560</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>B</td>\n",
       "      <td>female</td>\n",
       "      <td>17</td>\n",
       "      <td>8</td>\n",
       "      <td>25</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>C</td>\n",
       "      <td>male</td>\n",
       "      <td>120</td>\n",
       "      <td>205</td>\n",
       "      <td>325</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>C</td>\n",
       "      <td>female</td>\n",
       "      <td>202</td>\n",
       "      <td>391</td>\n",
       "      <td>593</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>D</td>\n",
       "      <td>male</td>\n",
       "      <td>138</td>\n",
       "      <td>279</td>\n",
       "      <td>417</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>D</td>\n",
       "      <td>female</td>\n",
       "      <td>131</td>\n",
       "      <td>244</td>\n",
       "      <td>375</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>E</td>\n",
       "      <td>male</td>\n",
       "      <td>53</td>\n",
       "      <td>138</td>\n",
       "      <td>191</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>E</td>\n",
       "      <td>female</td>\n",
       "      <td>94</td>\n",
       "      <td>299</td>\n",
       "      <td>393</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>F</td>\n",
       "      <td>male</td>\n",
       "      <td>22</td>\n",
       "      <td>351</td>\n",
       "      <td>373</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>F</td>\n",
       "      <td>female</td>\n",
       "      <td>24</td>\n",
       "      <td>317</td>\n",
       "      <td>341</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   dept applicant.gender  admit  reject  applications  gid\n",
       "1     A             male    512     313           825    0\n",
       "2     A           female     89      19           108    1\n",
       "3     B             male    353     207           560    0\n",
       "4     B           female     17       8            25    1\n",
       "5     C             male    120     205           325    0\n",
       "6     C           female    202     391           593    1\n",
       "7     D             male    138     279           417    0\n",
       "8     D           female    131     244           375    1\n",
       "9     E             male     53     138           191    0\n",
       "10    E           female     94     299           393    1\n",
       "11    F             male     22     351           373    0\n",
       "12    F           female     24     317           341    1"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = pd.read_csv(\"./data/UCBadmit.csv\", sep=\";\")\n",
    "d[\"gid\"] = (d[\"applicant.gender\"] != \"male\").astype(int)\n",
    "d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are 12 rows in the above dataset however they collectively represent 4526 applications. Counting the rows in the data table is not a sensible way to assess sample size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.29\n",
    "\n",
    "We will model the admission as the outcome that depends on the gender"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_11_7(gid, applications):\n",
    "  gid = jnp.array(gid, dtype=jnp.int32)\n",
    "  applications = jnp.array(applications, dtype=jnp.float32)\n",
    "  \n",
    "  def _generator():\n",
    "    a = yield tfd.Sample(tfd.Normal(loc=0.0, scale=1.5), sample_shape=2, name='a')\n",
    "    logits = jnp.take(a, gid)\n",
    "    yield tfd.Binomial(total_count=applications, logits=logits, name='admit')\n",
    "\n",
    "  return tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_11_7 = model_11_7(d.gid.values, d.applications.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_11_7_pin = jd_11_7.experimental_pin(\n",
    "  admit=jnp.array(d.admit.values, dtype=jnp.float32))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def run_chain(init_state, seed, step_size=1e-3, num_steps=500, burnin=300):\n",
    "\n",
    "  def target_log_prob(*states):\n",
    "    return jd_11_7_pin.unnormalized_log_prob(states)\n",
    "  \n",
    "  bijectors = [tfb.Identity()]\n",
    "\n",
    "  kernel = tfp.mcmc.NoUTurnSampler(\n",
    "      target_log_prob_fn=target_log_prob,\n",
    "      step_size=step_size)\n",
    "  \n",
    "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
    "    inner_kernel=kernel,\n",
    "    bijector=bijectors)\n",
    "\n",
    "  kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "    inner_kernel=kernel,\n",
    "    num_adaptation_steps=burnin)\n",
    "\n",
    "  chain_state = tfp.mcmc.sample_chain(\n",
    "      num_results=num_steps,\n",
    "      num_burnin_steps=burnin,\n",
    "      current_state=init_state,\n",
    "      kernel=kernel,\n",
    "      seed=seed,\n",
    "      trace_fn=None)\n",
    "  \n",
    "  return chain_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state = jd_11_7_pin.sample_unpinned(num_chains, seed=key())\n",
    "post_7 = run_chain(init_state=init_state, seed=key(), burnin=400)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_7_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_7._asdict().items()}\n",
    "dict_7 = dict(posterior=post_7_dict)\n",
    "idata_7 = az.from_dict(**dict_7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a[0]</th>\n",
       "      <td>-0.221</td>\n",
       "      <td>0.040</td>\n",
       "      <td>-0.289</td>\n",
       "      <td>-0.160</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>1603.0</td>\n",
       "      <td>1615.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a[1]</th>\n",
       "      <td>-0.829</td>\n",
       "      <td>0.051</td>\n",
       "      <td>-0.919</td>\n",
       "      <td>-0.754</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>1657.0</td>\n",
       "      <td>1285.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "a[0] -0.221  0.040    -0.289     -0.160      0.001    0.001    1603.0   \n",
       "a[1] -0.829  0.051    -0.919     -0.754      0.001    0.001    1657.0   \n",
       "\n",
       "      ess_tail  r_hat  \n",
       "a[0]    1615.0   1.01  \n",
       "a[1]    1285.0   1.00  "
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_7, hdi_prob=0.89)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.30\n",
    "\n",
    "Posterior of males is higher than females, here we compute the contrast"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a[0]</th>\n",
       "      <td>-0.221</td>\n",
       "      <td>0.040</td>\n",
       "      <td>-0.289</td>\n",
       "      <td>-0.160</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>1603.0</td>\n",
       "      <td>1615.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a[1]</th>\n",
       "      <td>-0.829</td>\n",
       "      <td>0.051</td>\n",
       "      <td>-0.919</td>\n",
       "      <td>-0.754</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>1657.0</td>\n",
       "      <td>1285.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diff_a</th>\n",
       "      <td>0.609</td>\n",
       "      <td>0.065</td>\n",
       "      <td>0.505</td>\n",
       "      <td>0.707</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.001</td>\n",
       "      <td>1658.0</td>\n",
       "      <td>1423.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diff_p</th>\n",
       "      <td>0.141</td>\n",
       "      <td>0.015</td>\n",
       "      <td>0.117</td>\n",
       "      <td>0.162</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1659.0</td>\n",
       "      <td>1423.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "a[0]   -0.221  0.040    -0.289     -0.160      0.001    0.001    1603.0   \n",
       "a[1]   -0.829  0.051    -0.919     -0.754      0.001    0.001    1657.0   \n",
       "diff_a  0.609  0.065     0.505      0.707      0.002    0.001    1658.0   \n",
       "diff_p  0.141  0.015     0.117      0.162      0.000    0.000    1659.0   \n",
       "\n",
       "        ess_tail  r_hat  \n",
       "a[0]      1615.0   1.01  \n",
       "a[1]      1285.0   1.00  \n",
       "diff_a    1423.0   1.00  \n",
       "diff_p    1423.0   1.00  "
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff_a = idata_7.posterior[\"a\"][:, :, 0] - idata_7.posterior[\"a\"][:, :, 1]\n",
    "idata_7.posterior[\"diff_a\"] = diff_a\n",
    "\n",
    "# to add diff_p have to do lot of massaging to make xarray happy !\n",
    "diff_p = jax.nn.sigmoid(idata_7.posterior[\"a\"][:, :, 0].values) - jax.nn.sigmoid(\n",
    "  idata_7.posterior[\"a\"][:, :, 1].values)\n",
    "\n",
    "coords = [idata_7.posterior.coords[\"chain\"], idata_7.posterior.coords[\"draw\"]]\n",
    "idata_7.posterior[\"diff_p\"] = xr.DataArray(\n",
    "    diff_p, coords=coords, dims=[\"chain\", \"draw\"])\n",
    "\n",
    "az.summary(idata_7, hdi_prob=0.89)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Log odds difference is certainly positive, corresponding to a higher prob of admissions for male applicants. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.31"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(500, 12)"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute the posterior predictive given the posterior parameters\n",
    "N = jnp.array(d.applications.values, dtype=jnp.float32)\n",
    "gid = d.gid.values\n",
    "\n",
    "# only picking the first chain\n",
    "a = post_7_dict['a'][0]\n",
    "\n",
    "# jnp.take(a, gid, axis=1)\n",
    "sample_logits = jnp.take(a, gid, axis=1)\n",
    "\n",
    "dist = tfd.Binomial(total_count=N, logits=sample_logits)\n",
    "\n",
    "# taking the samples from first chain\n",
    "predictive_samples = dist.sample(seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "admit_rate = predictive_samples / N\n",
    "\n",
    "plt.errorbar(\n",
    "    range(1, 13),\n",
    "    np.mean(admit_rate, 0),\n",
    "    np.std(admit_rate, 0) / 2,\n",
    "    fmt=\"o\",\n",
    "    c=\"k\",\n",
    "    mfc=\"none\",\n",
    "    ms=7,\n",
    "    elinewidth=1,\n",
    ")\n",
    "plt.plot(range(1, 13), np.percentile(admit_rate, 5.5, 0), \"k+\")\n",
    "plt.plot(range(1, 13), np.percentile(admit_rate, 94.5, 0), \"k+\")\n",
    "# draw lines connecting points from same dept\n",
    "for i in range(1, 7):\n",
    "    x = 1 + 2 * (i - 1)\n",
    "    y1 = d.admit.iloc[x - 1] / d.applications.iloc[x - 1]\n",
    "    y2 = d.admit.iloc[x] / d.applications.iloc[x]\n",
    "    plt.plot((x, x + 1), (y1, y2), \"bo-\")\n",
    "    plt.annotate(\n",
    "        d.dept.iloc[x], (x + 0.5, (y1 + y2) / 2 + 0.05), ha=\"center\", color=\"royalblue\"\n",
    "    )\n",
    "plt.gca().set(ylim=(0, 1), xticks=range(1, 13), ylabel=\"admit\", xlabel=\"case\")\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What above plot shows is that only for departments C & E, there was a lower rate of admissions for females. Now this is not in sync with what we observed earlier where the model was telling that females should expect an overall 14% lower chance of admission. \n",
    "\n",
    "What is going on ?\n",
    "\n",
    "Problem here is that male and females do not apply to same departments & departments also vary in their rate of admissions. Females do not apply to A & B that has higher rate of acceptance. Instead they applied to departments that have lower rate (10% of applicants) of acceptance.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.32\n",
    "\n",
    "Changing the question to be asked -\n",
    "\n",
    "Instead of asking - \n",
    "\n",
    "*What are the average probabilities of admission for females and males across all departments?* \n",
    "\n",
    "we are now going to ask -\n",
    "\n",
    "*What is the average difference in probability of admis- sion between females and males within departments?*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_11_8(gid, dept_id, applications):\n",
    "  gid = jnp.array(gid, dtype=jnp.int32)\n",
    "  dept_id = jnp.array(dept_id, dtype=jnp.int32)\n",
    "  applications = jnp.array(applications, dtype=jnp.float32)\n",
    "  \n",
    "  def _generator():\n",
    "    a = yield tfd.Sample(tfd.Normal(loc=0.0, scale=1.5), sample_shape=2, name='a')\n",
    "    delta = yield tfd.Sample(tfd.Normal(loc=0.0, scale=1.5), sample_shape=6, name='delta')\n",
    "    logits = jnp.take(a, gid) + jnp.take(delta, dept_id)\n",
    "    yield tfd.Binomial(total_count=applications, logits=logits, name='admit')\n",
    "\n",
    "  return tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_11_8 = model_11_8(d.gid.values, d.dept.factorize()[0], d.applications.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_11_8_pin = jd_11_8.experimental_pin(\n",
    "  admit=jnp.array(d.admit.values, dtype=jnp.float32))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def run_chain(init_state, seed, step_size=1e-3, num_steps=500, burnin=300):\n",
    "\n",
    "  def target_log_prob(*states):\n",
    "    return jd_11_8_pin.unnormalized_log_prob(states)\n",
    "  \n",
    "  bijectors = [tfb.Identity(), tfb.Identity()]\n",
    "\n",
    "  kernel = tfp.mcmc.NoUTurnSampler(\n",
    "      target_log_prob_fn=target_log_prob,\n",
    "      step_size=step_size)\n",
    "  \n",
    "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
    "    inner_kernel=kernel,\n",
    "    bijector=bijectors)\n",
    "\n",
    "  kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "    inner_kernel=kernel,\n",
    "    num_adaptation_steps=burnin)\n",
    "\n",
    "  chain_state = tfp.mcmc.sample_chain(\n",
    "      num_results=num_steps,\n",
    "      num_burnin_steps=burnin,\n",
    "      current_state=init_state,\n",
    "      kernel=kernel,\n",
    "      seed=seed,\n",
    "      trace_fn=None)\n",
    "  \n",
    "  return chain_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state = jd_11_8_pin.sample_unpinned(num_chains, seed=key())\n",
    "post_8 = run_chain(init_state=init_state, seed=key(), burnin=400)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_8_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_8._asdict().items()}\n",
    "dict_8 = dict(posterior=post_8_dict)\n",
    "idata_8 = az.from_dict(**dict_8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a[0]</th>\n",
       "      <td>-0.522</td>\n",
       "      <td>0.534</td>\n",
       "      <td>-1.387</td>\n",
       "      <td>0.261</td>\n",
       "      <td>0.031</td>\n",
       "      <td>0.023</td>\n",
       "      <td>290.0</td>\n",
       "      <td>225.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a[1]</th>\n",
       "      <td>-0.425</td>\n",
       "      <td>0.534</td>\n",
       "      <td>-1.260</td>\n",
       "      <td>0.388</td>\n",
       "      <td>0.031</td>\n",
       "      <td>0.023</td>\n",
       "      <td>300.0</td>\n",
       "      <td>211.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>delta[0]</th>\n",
       "      <td>1.103</td>\n",
       "      <td>0.537</td>\n",
       "      <td>0.260</td>\n",
       "      <td>1.937</td>\n",
       "      <td>0.032</td>\n",
       "      <td>0.022</td>\n",
       "      <td>293.0</td>\n",
       "      <td>208.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>delta[1]</th>\n",
       "      <td>1.060</td>\n",
       "      <td>0.539</td>\n",
       "      <td>0.267</td>\n",
       "      <td>1.945</td>\n",
       "      <td>0.031</td>\n",
       "      <td>0.022</td>\n",
       "      <td>308.0</td>\n",
       "      <td>219.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>delta[2]</th>\n",
       "      <td>-0.162</td>\n",
       "      <td>0.536</td>\n",
       "      <td>-0.941</td>\n",
       "      <td>0.742</td>\n",
       "      <td>0.031</td>\n",
       "      <td>0.028</td>\n",
       "      <td>300.0</td>\n",
       "      <td>231.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>delta[3]</th>\n",
       "      <td>-0.192</td>\n",
       "      <td>0.539</td>\n",
       "      <td>-1.088</td>\n",
       "      <td>0.594</td>\n",
       "      <td>0.031</td>\n",
       "      <td>0.028</td>\n",
       "      <td>298.0</td>\n",
       "      <td>210.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>delta[4]</th>\n",
       "      <td>-0.632</td>\n",
       "      <td>0.539</td>\n",
       "      <td>-1.460</td>\n",
       "      <td>0.211</td>\n",
       "      <td>0.031</td>\n",
       "      <td>0.026</td>\n",
       "      <td>301.0</td>\n",
       "      <td>217.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>delta[5]</th>\n",
       "      <td>-2.187</td>\n",
       "      <td>0.545</td>\n",
       "      <td>-3.034</td>\n",
       "      <td>-1.314</td>\n",
       "      <td>0.031</td>\n",
       "      <td>0.023</td>\n",
       "      <td>307.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "a[0]     -0.522  0.534    -1.387      0.261      0.031    0.023     290.0   \n",
       "a[1]     -0.425  0.534    -1.260      0.388      0.031    0.023     300.0   \n",
       "delta[0]  1.103  0.537     0.260      1.937      0.032    0.022     293.0   \n",
       "delta[1]  1.060  0.539     0.267      1.945      0.031    0.022     308.0   \n",
       "delta[2] -0.162  0.536    -0.941      0.742      0.031    0.028     300.0   \n",
       "delta[3] -0.192  0.539    -1.088      0.594      0.031    0.028     298.0   \n",
       "delta[4] -0.632  0.539    -1.460      0.211      0.031    0.026     301.0   \n",
       "delta[5] -2.187  0.545    -3.034     -1.314      0.031    0.023     307.0   \n",
       "\n",
       "          ess_tail  r_hat  \n",
       "a[0]         225.0   1.01  \n",
       "a[1]         211.0   1.01  \n",
       "delta[0]     208.0   1.01  \n",
       "delta[1]     219.0   1.01  \n",
       "delta[2]     231.0   1.01  \n",
       "delta[3]     210.0   1.01  \n",
       "delta[4]     217.0   1.01  \n",
       "delta[5]     242.0   1.01  "
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_8, hdi_prob=0.89)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.33\n",
    "\n",
    "Computing the contrast"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>diff_a</th>\n",
       "      <td>-0.097</td>\n",
       "      <td>0.080</td>\n",
       "      <td>-0.233</td>\n",
       "      <td>0.025</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.001</td>\n",
       "      <td>2413.0</td>\n",
       "      <td>1759.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diff_p</th>\n",
       "      <td>-0.022</td>\n",
       "      <td>0.018</td>\n",
       "      <td>-0.051</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2365.0</td>\n",
       "      <td>1778.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "diff_a -0.097  0.080    -0.233      0.025      0.002    0.001    2413.0   \n",
       "diff_p -0.022  0.018    -0.051      0.007      0.000    0.000    2365.0   \n",
       "\n",
       "        ess_tail  r_hat  \n",
       "diff_a    1759.0    1.0  \n",
       "diff_p    1778.0    1.0  "
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff_a = post_8_dict['a'][..., 0] - post_8_dict['a'][..., 1]\n",
    "diff_p = jax.nn.sigmoid(post_8_dict['a'][..., 0]) - jax.nn.sigmoid(post_8_dict['a'][..., 1])\n",
    "\n",
    "diffs = az.from_dict(**dict(posterior={'diff_a': diff_a, 'diff_p': diff_p}))\n",
    "az.summary(diffs, hdi_prob=0.89)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.34"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "      <th>D</th>\n",
       "      <th>E</th>\n",
       "      <th>F</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>male</th>\n",
       "      <td>0.88</td>\n",
       "      <td>0.96</td>\n",
       "      <td>0.35</td>\n",
       "      <td>0.53</td>\n",
       "      <td>0.33</td>\n",
       "      <td>0.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>female</th>\n",
       "      <td>0.12</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.65</td>\n",
       "      <td>0.47</td>\n",
       "      <td>0.67</td>\n",
       "      <td>0.48</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           A     B     C     D     E     F\n",
       "male    0.88  0.96  0.35  0.53  0.33  0.52\n",
       "female  0.12  0.04  0.65  0.47  0.67  0.48"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dept_id = d.dept.factorize()[0]\n",
    "\n",
    "pg = np.stack(\n",
    "    list(\n",
    "        map(\n",
    "            lambda k: np.divide(\n",
    "                d.applications[dept_id == k].values, d.applications[dept_id == k].sum()\n",
    "            ),\n",
    "            range(6),\n",
    "        )\n",
    "    ),\n",
    "    axis=0,\n",
    ").T\n",
    "pg = pd.DataFrame(pg, index=[\"male\", \"female\"], columns=d.dept.unique())\n",
    "pg.round(2)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Department A receives 88% of its applications from males. Department E receives 33% from males. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 11.2 Poisson regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.35\n",
    "\n",
    "\n",
    "Binomial is good when the count is known but quite often it is not the case.\n",
    "\n",
    "When the count goes extremely high then mean and variance of Binomial starts to become same and this is known as Poisson Distribution\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Array(0.9982, dtype=float32), Array(0.98779696, dtype=float32))"
      ]
     },
     "execution_count": 197,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = tfd.Binomial(1000, probs=1 / 1000).sample(10000, seed=key())\n",
    "jnp.mean(y), jnp.var(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Useful for binomial events for which the number of trials N is unknown or uncountably large."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.36\n",
    "\n",
    "Counts of unique tool types for 10 historical Oceanic societies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>culture</th>\n",
       "      <th>population</th>\n",
       "      <th>contact</th>\n",
       "      <th>total_tools</th>\n",
       "      <th>mean_TU</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Malekula</td>\n",
       "      <td>1100</td>\n",
       "      <td>low</td>\n",
       "      <td>13</td>\n",
       "      <td>3.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Tikopia</td>\n",
       "      <td>1500</td>\n",
       "      <td>low</td>\n",
       "      <td>22</td>\n",
       "      <td>4.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Santa Cruz</td>\n",
       "      <td>3600</td>\n",
       "      <td>low</td>\n",
       "      <td>24</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Yap</td>\n",
       "      <td>4791</td>\n",
       "      <td>high</td>\n",
       "      <td>43</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Lau Fiji</td>\n",
       "      <td>7400</td>\n",
       "      <td>high</td>\n",
       "      <td>33</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Trobriand</td>\n",
       "      <td>8000</td>\n",
       "      <td>high</td>\n",
       "      <td>19</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Chuuk</td>\n",
       "      <td>9200</td>\n",
       "      <td>high</td>\n",
       "      <td>40</td>\n",
       "      <td>3.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Manus</td>\n",
       "      <td>13000</td>\n",
       "      <td>low</td>\n",
       "      <td>28</td>\n",
       "      <td>6.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Tonga</td>\n",
       "      <td>17500</td>\n",
       "      <td>high</td>\n",
       "      <td>55</td>\n",
       "      <td>5.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Hawaii</td>\n",
       "      <td>275000</td>\n",
       "      <td>low</td>\n",
       "      <td>71</td>\n",
       "      <td>6.6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      culture  population contact  total_tools  mean_TU\n",
       "0    Malekula        1100     low           13      3.2\n",
       "1     Tikopia        1500     low           22      4.7\n",
       "2  Santa Cruz        3600     low           24      4.0\n",
       "3         Yap        4791    high           43      5.0\n",
       "4    Lau Fiji        7400    high           33      5.0\n",
       "5   Trobriand        8000    high           19      4.0\n",
       "6       Chuuk        9200    high           40      3.8\n",
       "7       Manus       13000     low           28      6.6\n",
       "8       Tonga       17500    high           55      5.4\n",
       "9      Hawaii      275000     low           71      6.6"
      ]
     },
     "execution_count": 198,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = pd.read_csv(\"./data/Kline.csv\", sep=\";\")\n",
    "d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To remember - Number of rows in count based models is not same as the sample size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.37\n",
    "\n",
    "Here the outcome variable is **total tools**\n",
    "\n",
    "We want to establish a relationship between **log population** and our outcome variable.\n",
    "\n",
    "We also want to see the interaction between **contact** and **log population**\n",
    "\n",
    "So first and foremost let's create a column for **log population**\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [],
   "source": [
    "d[\"P\"] = d.population.pipe(np.log).pipe(lambda x: (x - x.mean()) / x.std())\n",
    "d[\"contact_id\"] = (d.contact == \"high\").astype(int)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.38"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = jnp.linspace(0, 100, 200)\n",
    "plt.plot(x, tfd.LogNormal(loc=0.0, scale=10.0).prob(x))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.39"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array(1.0910003e+11, dtype=float32)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = tfd.Normal(loc=0.0, scale=10.0).sample(1000, seed=key())\n",
    "lambda_ = jnp.exp(a)\n",
    "jnp.mean(lambda_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.40"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0, 100, 200)\n",
    "plt.plot(x, tfd.LogNormal(loc=3.0, scale=0.5).prob(x))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.41"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 100\n",
    "a = tfd.Normal(loc=3.0, scale=0.5).sample(N, seed=key())\n",
    "b = tfd.Normal(loc=0.0, scale=10.0).sample(N, seed=key())\n",
    "plt.subplot(xlim=(-2, 2), ylim=(0, 100))\n",
    "x = np.linspace(-2, 2, 100)\n",
    "for i in range(N):\n",
    "    plt.plot(x, jnp.exp(a[i] + b[i] * x), c=\"k\", alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.42"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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yZYs8ufPgwYMMDg4aeIUzh0KhIDk5mb1792JiYkJFRQXff/89PT09hl6aQCAQCGaQe/fu0dLSgrW19Yzba7+IaRcUGo2G//v//r8JCAjA0tKSwMBA/v2///ejQvCSJPH3f//3eHp6YmlpyerVq6etoHD58uX4+/szNDTE1atXOXDgANbW1jQ1NXHo0CHUavW0PM9cJSQkhE8++QQrKysaGhr4+uuvaWlpMfSyBAKBQDADNDU1ce/ePWB4kqiVlZXB1jLtguIf//Ef+Zd/+Rf++Mc/UlZWxj/90z/xn/7Tf+K//bf/Jj/mn/7pn/jnf/5n/vjHP5KdnY27uzvr1q2blqtpfSuppaUljY2NFBQU8NFHH2FhYUFNTQ1Hjx5Fq9W+9vPMZXx8fPj1r3/NggUL6O7u5ptvvqGystLQyxIIBALBNKLT6Thz5ow8STQkJMSg65l2QZGens6OHTvYsmUL/v7+vPfee6xfv56cnBxgODrxX//rf+X/+r/+L959913CwsL44Ycf6O/v59ChQ9OyBjs7O3bu3CmvR6lU8sEHH8gOkydOnHjjixb1baV+fn6oVCp++uknuTdZIBAIBPOftLQ0GhsbsbCwYPPmzQafZTXtgmLFihXcuHGDR48eAVBYWMj9+/fZvHkzMGy60dTUxPr16+W/MTc3Z9WqVXKF6lhUKhVKpXLU7WUEBweTmJgIwKlTp7C3t+f999/H2NiY0tJSuYDlTcbKyoqPPvqIiIgIdDodZ8+e5dq1a2/86xYIBII3ndbWVm7dugXAxo0bsbW1NfCKZkBQ/O3f/i379+9nyZIlmJqaEh0dzW9+8xv2798PDOd7AHkGhx43Nzf5d2P5wx/+gL29vXzz8fGZ1FrWrVuHh4cHAwMDnDhxgoCAAPbs2YORkRGFhYVcvHjxjT+5mpiYsGvXLlavXg3AgwcP+OWXX974WhKBQCB4U9HpdJw6dQqtVsvixYuJjIw09JKAGRAUR48e5aeffuLQoUPk5eXxww8/8J//83/mhx9+GPW4saEZSZKeG675u7/7O7q7u+VbbW3tpNZiYmLCnj17MDc3p7q6mtu3b7NkyRJ27dqFQqEgOzub69evv/GiQqFQsHr1at59912MjY0pKysTHSACgUAwT3nw4AENDQ1YWFiwbds2g6c69Ey7oPg//8//k9/+9re8//77hIeH89FHH/HXf/3X/OEPfwDA3d0dYFw0oqWlZVzUQo+5uTl2dnajbpPFycmJbdu2AcOtNZWVlYSHh7N161Zg+B9z9+7dKb/O+UhERAQff/wxVlZW1NfX8/XXXz83KiQQCASCuUdLSwu3b98GYNOmTVM6H8400y4o+vv7x81dNzY2losgAwICcHd359q1a/Lvh4aGuHPnDsuWLZvu5QAQFhZGbGwskiRx8uRJent7iY2NlY2gbt26RXp6+ow891zDz8+PX//617Lp17fffktFRYWhlyUQCASCl6DVajl9+jRarZagoCAiIiIMvaRRTLug2LZtG//xP/5HLly4wLNnzzh16hT//M//zK5du4Dh8PtvfvMbfv/733Pq1ClKSkr49NNPsbKy4sCBA9O9HJmNGzfi6upKb28vJ0+eRKfTkZycLBthXblyhezs7Bl7/rmEvgMkMDCQoaEhjhw5ImaACAQCwRxHn+qwtLScU6kOPQppms8iPT09/D//z//DqVOnaGlpwdPTk/379/P//r//L2ZmZsBwvcTvfvc7/vSnP9HZ2UliYiL//b//d8LCwib1HEqlEnt7e7q7u6cU7mltbeWrr75CrVazevVqVq9ejSRJ3Lx5UzYG2bFjB9HR0VN/4fMQrVbLpUuX5JbemJgYtmzZgrGxsYFXJhAIBIKRNDc389VXX6HVann33XdfKzrxqufQlzHtgmI2eJ2dUVRUxMmTJ1EoFHz00UcEBgYiSRJXrlwhIyMDhULBu+++S3h4+Aytfm4hSRKZmZlcuXIFSZLw9/dn7969BnVbEwgEAsFf0Gq1/PnPf6apqYklS5awb9++14pOzJSgeKNmeUyGiIgIYmJikCSJEydO0NPTg0KhYMOGDcTFxSFJEqdOnaK0tNTQS50VFAoFSUlJHDhwAHNzc549e8af//xnWltbDb00gUAgEDA8lrypqQkrKyu2bt0651Idet46QQHDlbFubm709fVx/PhxdDodCoWCLVu2EBUVhU6n4/jx45SXlxt6qbPG4sWL+fzzz3F0dKSzs5Ovv/6ax48fG3pZAoFA8FZTV1fH/fv3Adi6dSs2NjYGXtHzeSsFhampKXv37pX9KfRuYwqFgu3btxMeHo5Op+PYsWOy4+fbgKurK1988YVs133o0CHS09NFsaZAIBAYgKGhIU6dOoUkSURERBh8VsfLeCsFBcCCBQvYvn07MOxPoRcORkZG7Nq1i9DQULRaLUePHuXJkyeGXOqsYmVlxccffyynha5cucKZM2fQaDSGXppAIBC8VVy/fp329nbs7Ozk8RVzmbdWUACEhoaSkJAADM/76OrqAv4ysXTp0qVotVqOHDnyVk3rNDY2Ztu2bWzcuBGFQkFBQQE//PADvb29hl6aQCAQvBVUVlaSlZUFDHcfWlhYGHhFL+etFhQA69evx9vbm4GBAX755Rf5StzY2Jj33nuP4OBgNBoNhw8fpqqqysCrnT30xZoffvghFhYW1NbW8tVXX9HY2GjopQkEAsEbzeDgIKdPnwYgPj6ehQsXGnZBk+StFxT6eR9WVlY0NDRw6dIl+XfGxsbs2bOHoKAg1Go1hw4d4tmzZ4ZbrAFYuHAhX3zxBc7OziiVSr799ltKSkoMvSyBQCB4Y7lw4QJKpRInJyfWrVtn6OVMmrdeUADY29uze/duFAoFubm5FBQUyL8zMTFh7969LF68GLVazc8///zWiYoFCxbw61//Wt4Hx48f58aNG7KdukAgEAimh+LiYoqLi+XUu94Qcj4gBMX/ZOHChfKI7/Pnz9Pc3Cz/zsTEhH379rFo0aK3VlRYWFiwf/9+li9fDgwXsh4+fJjBwUEDr0wgEAjeDLq7u7lw4QIAK1euxNvb28ArmhpCUIxg5cqVLF68GI1Gw9GjR0edLE1MTHj//fffalFhZGTEunXr2L17NyYmJjx+/Jivv/6atrY2Qy9NIBAI5jWSJHH69GkGBwfx9vYmJSXF0EuaMkJQjEChULBr1y4cHBzo6Ojg5MmTozwYhKgYJjw8nM8++ww7Ozva2tr485//LCaWCgQCwWuQnp5OVVUVpqam7Nq1a17OVBKCYgxWVlbs27cPExMTHj16xN27d0f9fiJR8Ta1lOrx9PTkr/7qr/D19UWlUnH48GHu3LkjTLAEAoFgijQ3N3Pjxg1geDL2ggULDLyiV0MIignw8PBg69atwLCH+lgLar2o0BcpHjp0iKdPnxpiqQbFxsaGTz75hPj4eABu3brF0aNHUalUBl6ZQCAQzA/UajUnTpxAq9USHBxMTEyMoZf0yghB8RyioqKIj4+Xh4h1dHSM+r2+UDMoKEj2qXibHDX1GBsbs2XLFnbs2IGxsTHl5eV8/fXXtLe3G3ppAoFAMOe5du0aLS0t2NjYsH379jk7+GsyCEHxAjZu3IiPjw+Dg4McPXqUoaGhUb/Xt5QuWbJEFhVv60Ct6OhofvWrX2Fra0traytfffWVqKsQCASCF/Do0SPZDXPnzp1YW1sbeEWvhxAUL0BvbGVjY0NzczNnz54dVyOgN8YaadP9Nk0pHYm3tzdffvnlqLqKW7duiboKgUAgGENPT4/shpmUlMSiRYsMu6BpQAiKl2BnZ8eePXswMjKipKSE9PT0cY/R23TrB4r98ssvPHz40ACrNTz6uorExEQA7ty5w6FDhxgYGDDwygQCgWBuoG8R7e/vx93dnbVr1xp6SdOCEBSTwM/Pj02bNgHD+a6JCjCNjY3ZvXs3ERER6HQ6jh8/TlFR0WwvdU5gbGzMpk2b2LVrl+xX8ec//3mUWZhAIBC8rWRkZPD06VNMTU1lX583ASEoJklcXJw80vv48ePjijRh2Php586dREdHI0kSp06dIj8/3wCrnRtERkby+eefy74eX3/99VsrsgQCgQCgsbGR69evA7BhwwZcXFwMvKLpQwiKSaJQKNi8ebM8mfTIkSPjijRhWFRs375d7hA5c+YM2dnZBljx3MDDw4O/+qu/kn07Tp48ycWLF9FqtYZemkAgEMwqQ0NDHD9+HK1Wy5IlS4iNjTX0kqYVISimgL5V1MbGhpaWFk6fPj1hwaFefCQlJQHDk+PS0tJme7lzBisrKw4cOCDPSsnKyuK7775DqVQadmECgUAwi1y8eJH29nbs7OzmfYvoRAhBMUVsbW3Zt28fxsbGlJaWcu/evQkfp1Ao2LBhg+zHfvXqVW7fvv3WdjwYGRmxevVqDhw4gIWFBXV1dfzpT3+iqqrK0EsTCASCGaewsJCCggIUCgW7d+/GysrK0EuadoSgeAV8fHzYsmULADdv3qSsrGzCxykUClJTU0lNTQWGXTevXbv21ooKgKCgIL788kvc3d3p6+vjxx9/5N69e2/1PhEIBG827e3t8hTR1atX4+fnZ+AVzQzzWlAUFxcb7LljYmLk1shTp069sIMhJSWFjRs3ApCWlsbFixff6hOoo6Mjn3/+uVy8euPGDQ4fPixaSwUCwRuHRqPh+PHjDA0N4e/vPy+niE6WeS0oLly4YFATqQ0bNhAYGMjQ0BCHDx+mr6/vuY9NSkpi27ZtKBQKsrOzOX36NDqdbhZXO7cwNTVlx44d7NixQx7E9qc//YmGhgZDL00gEAimjevXr9PY2IiVlRXvvvsuRkbz+rT7Qub1K5MkiWPHjhls2qeRkRF79uzBycmJrq4ufvnllxd2L8TGxspvqMLCQn755Rc0Gs0srnjuER0dzeeff46joyNdXV188803ZGdnv9URHIFA8GZQXl5ORkYGMGytbWdnZ+AVzSzzWlAEBQXJdtd1dXUGWYOlpSX79+/H3Nyc6urql6YzwsPD5fHo5eXlHDp0aML207cJDw8PvvzyS5YsWYJWq+XChQucPHnyrd8vAoFg/tLV1SVbaycnJxMUFGTYBc0C81pQ7Nixg4ULFzI0NMTPP/9sMCdGFxcXdu/ejUKhIDc3Vx728jyCg4P54IMPMDMzo7KykoMHD7719QMWFhbs27eP9evXY2RkRHFxMV999RUtLS2GXppAIBBMCa1Wy7FjxxgcHMTLy+uNsdZ+GfNaUOh9IXx8fBgYGODgwYMGG5sdFBTEunXrALh8+fJLR5kHBATw8ccfY2lpSW1tLd9//z29vb2zsdQ5i0KhYNmyZXz66afY2dnR1tbGn//8ZwoKCgy9NIFAIJg0169fp76+HgsLC/bs2YOxsbGhlzQrzGtBAWBmZsaBAwdwc3Ojt7eXH3/8ke7uboOsJTk5We5cOHbsGK2trS98vLe3N59++qk8zfTbb7+ls7NzllY7d/H19eXLL79k4cKFqNVqTp8+zenTp0UKRCAQzHnKy8vlIZK7du3CwcHBsAuaRea9oIDhOoaPPvoIZ2dnuru7+eGHH+jp6Zn1dSgUCrZu3Yqfnx8qlYpDhw69sPMDwM3Njc8++wxHR0c6Ojr49ttvRZgfsLa25oMPPmDNmjUoFAoKCgr485///FKRJhAIBIais7NTrptYtmwZwcHBhl3QLPNGCAoYHpv98ccfy4OoDh48SH9//6yvw9jYmH379uHo6EhnZydHjx59aSeHk5MTn332Ga6urvT09PDdd99RW1s7SyueuxgZGbFq1So++eQTbGxsaG1t5auvvhIpEIFAMOfQ+00MDg7i7e0tGxq+TbwxggLAzs6OTz75BFtbW1paWjh48CCDg4Ozvg797Apzc3Nqamo4f/78S9sgbW1t+dWvfiXXg/z4448vrcN4W/D39+df/at/RWBgoJwCOXXqlEiBCASCOcOVK1eor6/H0tKS9957762pmxjJGyUoYNiF8ZNPPsHa2prGxkZ+/vlng5x4XFxc2LNnD0ZGRhQUFDx35sdI9Kkb/WTOQ4cOGdQNdC5hY2PDhx9+KKdACgsL+eqrrwzW2SMQCAR6iouL5anS77777ltVNzGSN05QADg7O/PRRx9hYWFBbW0thw4dQq1Wz/o6Fi1axKZNm4DhmR8lJSUv/RszMzP2799PeHg4Op2OEydOkJmZOdNLnRfoUyCffvoptra2chdITk6OMMISCAQGobW1lbNnzwKwcuVKFi9ebOAVGY43UlAAuLu789FHH2Fubs6zZ884cuSIQVwp4+PjSU5OBuD06dOTqo0wNjbm3XfflWeFXLp0iRs3boiT5v/Ez8+Pf/2v/zVBQUFoNBrOnz8v5y4FAoFgtlCpVBw9ehS1Wk1gYCCrV6829JIMyhsrKAC8vLxkA6mnT5++1Bp7pli3bh3BwcFoNBoOHz48qdZQhULBxo0b5cKee/fuce7cubd6/sdIrKys2L9/Pxs2bMDIyIiHDx/yL//yLwZzTBUIBG8XkiRx7tw52trasLOzY/fu3fNmTsdMXZzOj1f/Gvj6+nLgwAFMTU159OgRx48fn3VRYWRkxO7du/Hw8KC/v5+ff/55Us6YCoWClJQUtm/fjkKhIC8vT1bDguH9k5ycPGoWyLfffsv9+/dFNEcgEMwoWVlZlJSUyDOdrK2tDb2klyJJEk+ePOH777+fke2/8YIChrsE3n//fUxMTCgrK+PkyZOzfqWvN+DSO0BOpp1UT0xMjDz/o6Kigh9//NEgLbFzFS8vL7788kvCwsLQ6XRcv36dgwcPGsSLRCAQvPnU1NRw5coVYDgC7ePjY+AVvZzq6mq+++47fvrpJ5qammbkOd4KQQGwcOFC9u7di7GxMQ8fPuTUqVOzLipsbW354IMP5LqOM2fOTPpKesmSJXz88cdyoem3335LV1fXzC54HmFhYcHu3bvZsWMHpqamVFZW8j/+x//g0aNHhl6aQCB4g+jp6eGXX35Bp9MRFhZGUlKSoZf0QhoaGvjpp5/47rvvqKmpwcTEhPj4+Bl5LoU0D2PDSqUSe3t7uru7pzwOtqKiQq6liIiIYOfOnbOe93r69Ck///wzOp2OlJSUKRmgtLa28tNPP9Hd3S0LFHd39xlc7fyjtbWVEydOyCo8MTGRdevWYWJiYuCVCQSC+YxWq+WHH36gpqYGV1dXfv3rX2NmZmboZU1Ic3Mzt27dory8HBhOvcfExLBy5UqAVz6Hvoi3TlDAsNe6XmFGRkayY8eOWRcV+fn5nDlzBoBt27YRGxs76b9VKpX89NNPtLS0YG5uzr59+wgMDJyppc5LNBoN169fJyMjAxi2OH/vvfdwcXEx8MoEAsF85dKlS2RmZmJubs5f/dVfsWDBAkMvaRxtbW3cvn2bhw8fIkkSCoWCiIgIVq1ahZOTE/D659Dn8VYKCoDS0lKOHz+OTqcjOjpaLnycTW7fvs3t27cxMjJi//79U+pfHhwc5PDhw1RXV2NsbMz27duJjIycwdXOTx4/fszp06fp6+vDxMSEDRs2EBcXN+v/a4FAML8pKiri5MmTAOzfv3/Ozeno7Ozkzp07FBYWyqn00NBQVq9ePe5CSgiKEUzXznj48CEnTpxAp9MRFRXF9u3bZzVSIUkSZ86coaCgADMzMz799FM8PT0n/fcajYbTp0/LhlmpqamsWLFCnCzH0Nvby6lTp3j69CkAwcHBbN++fV5UZQsEAsPT1NTEN998g1qtZuXKlbzzzjuGXpJMd3c3d+/eJT8/X64LDAoK4p133nluOlwIihFM584oKSmRuz4MISq0Wi0///wzlZWVWFtb8+tf/xpHR8dJ/70kSVy7do20tDQA4uLi2Lx587zph54tJEkiMzOTa9euodVqsbGxYefOnSxatMjQSxMIBHOY/v5+vvrqK7q6uli0aBEHDhyYE8dXpVLJ/fv3yc3Nla0QFi1axJo1a/Dy8nrp3wpB8T/R74z8/HxCQ0MxNTV9re2NjFQYoqZCpVLx3Xff0dTUxIIFC/jss8+mfPWcmZnJ5cuXkSSJoKAg3nvvvTlbLGRImpubOX78uDwGPSkpibVr14qCTYFAMA6dTsfBgwepqqrCycmJL774AktLS4OuqaenRxYSeuuBgIAA1qxZg6+v76S2IQTFCPQ747e//S1WVlb4+PgQGBhIYGAgnp6eryQGRooKQ3R/9PT08M0339DV1YWXlxeffPLJlAVBWVkZJ06cQKPR4OHhwYEDB7C1tZ2hFc9f1Go1165dIysrCwBXV1feffdd0S0jEAhGceXKFdLT0zEzM+PXv/41rq6uBltLb28vDx48IDs7WxYSfn5+rF69moCAgElvp7+/nxs3brB9+3YhKOAvguL3v/89KpVq1O/Mzc3x9/cnICCAgIAAXF1dJ11TMLJQMzw8nF27ds2qqGhra+Obb75hYGCAoKAg3n///Sk/f11dHYcPH6avrw97e3s++OADg34I5jKPHz/mzJkz9Pb2YmxsTGpqKsnJyaIGRSAQUFhYyKlTpwDYt28fS5cuNcg69EIiJydHdkn28fFhzZo1BAQETPp41d/fT0ZGBpmZmSiVSv7hH/5BCAr4i6Do6upCo9FQWVlJVVUVVVVV4yytra2tCQgIIDAwkICAgJfWJ5SVlXHs2DF0Oh2hoaG8++67szrXvra2lh9++AGNRkNMTAzbtm2b8gmuo6ODn3/+mfb2dtFW+hL6+vo4d+6c3KsdEBDAzp07sbe3N/DKBAKBoWhoaODbb79Fo9EYrAizr69PjkjohYSXlxdr1qxh4cKFUxIS6enpZGVlyRfg9vb2/M3f/I0QFPD8/I8kSTQ1NckCo7q6etzcC0dHRzl6ERAQgI2Nzbjtl5eXc+zYMbRaLUuWLGHPnj2zKirKy8s5evQokiRN2fhKz8DAAEeOHKG6uhojIyO2bdtGdHT0DKx2/iNJEvn5+Vy6dAm1Wo2FhQVbtmwhLCxMRCsEgreM3t5evvrqK5RKJUFBQezfv39WjwO9vb2kpaWNExKrV69m0aJFUxISaWlpZGVlMTQ0BAxP4V69ejUeHh44ODgIQQGTLyjRaDTU1dXJ0Yu6urpxdtsuLi6yuPD395cLbh4/fizP2wgKCmLv3r2zWriXl5fH2bNnAdi4ceMr2btqNBrOnDlDcXExACtWrCA1NVWcJJ9De3s7p06dkieWhoaGsnXrVoMXYQkEgtlBo9Hwww8/UFtbi7OzM7/+9a+xsLCYleeeKLXh6enJmjVrpiQk+vr6ZEEyUkisWrWKJUuWoFAoRFHmSF51Z6hUKmpqamSB0dTUNGqWhkKhwMPDQxYXGo1GLnJcuHAh77///mt3lEyFu3fvcvPmTQB2795NeHj4lLchSRK3b9/mzp07wPBJcufOnbP6OuYTOp2Oe/fucefOHXQ6Hba2tuzYsUO0lwoEbzgjfYEsLCz44osvZsUJs6enh7S0tFFC4lUiEhNFNjw8PFi9ejVBQUGjtiMExQima2f09/fz7NkzWWC0tbWN+r2RkRFmZmY8evQIW1tbIiIi+Oijj2atHVOSJC5fvkxmZiZGRkYcOHDglU9shYWFnD17Fq1Wi7e3N++///6E6R7BMA0NDZw8eVJ+T8THx7Nu3TrRiisQvKGkp6dz5coVFAoFH374IQsXLpzR51MqlTx48GBU+6e3tzerV6+eUo3ERNvx9PRk9erVLF68eMLtCEExgpnaGT09PbK4qKqqkqd5dnd3U1RUhCRJ+Pv7y7arXl5eM15bIUkSJ0+epLi4GFNTUz755BO8vb1faVvV1dUcOXKEgYEBHBwcOHDggOgAeQFqtZrr16+TmZkJgJOTE7t27ZoXo4oFAsHkefz4MYcOHUKSpFdOMU+W7u5u7t+/T15enmxI5ePjw6pVq6YkJLq6unjw4MGo7UxGkAwNDZGWlsaaNWuEoICZExRj6ezslCMYBQUFpKWlodFosLGxITIyEisrK3x9feUUyat6YLwMrVbLoUOHePr0KZaWlvzqV796ZSHQ3t7OoUOH5A6Q9957b0ozRN5GKisrOX36NEqlEoVCwfLly1m9erUwwxII3gDa2tr485//jEqleuXOusnQ0dHB/fv3KSwslAWAn58fq1atmlL7Z0dHB/fu3aOwsFCuCZzMdrq6usjKyiIvL4/u7m7RNqpntgTFSCRJorS0lD/96U80Njai0WhYunTpqBC4ubn5KIHh7u4+bQJjaGiIH3/8kbq6Omxtbfnss8+mZNE9kv7+fn755ReePXuGQqFg/fr1JCUliWLNFzA4OMilS5coLCwEhqeX7tq1S5hhCQTzmP7+fr7++ms6Ojrw9fXlk08+mfaoc1tbG/fu3aO4uFgWAAEBAaxatQp/f/9Jb6e1tVXejv60HRgYyMqVK5+7HUmSePbsGZmZmVRUVMh/Z2lpyW9/+1shKMAwgkJPa2srP/74I0qlEjMzM5KSkmhtbaW6unqcB4aFhQV+fn74+/vLAuN1TtoDAwN89913tLS04OTkxGefffbKdRBarZYLFy6Ql5cHQGxsLJs3b57V9tj5SFlZGefPn6evrw8jIyNWrVrFihUrxH4TCOYZWq2WgwcP8uzZMxwcHPjiiy+mdWBgc3Mzd+/epbS0VD6RL1q0iFWrVk0pbdrY2Mi9e/coKyuTt7N48WJWrlz53O0MDQ1RVFREVlYWLS0t8v0LFy4kMTERV1dXHB0dhaAAwwoKGA45/fjjj3R1dWFvb8/HH3+Mo6Mjzc3Ncoqkurp6nIunpaXlKIHh5uY2ZYHR09PDt99+S2dnJ25ubnz66aev3NYoSRIZGRlcvXoVSZIICAhgz549WFlZvdL23hb6+vo4f/48ZWVlwHAB1M6dO0U9ikAwT5AkibNnz5Kfn4+5uTmff/75tH1+6+vruXv3LhUVFfJ9wcHBrFy58qVDu0ZSW1vL3bt3efz4sXzf0qVLSUlJee5U6o6ODrKzs8nPz2dwcBAAMzMzIiMjSUhIkMeYi6LMERhaUMBwYc3Bgwdpa2vD2tqajz76aFT4W6fT0dTURFVVFc+ePaOmpmbaBEZHRwfffvstvb29+Pj4vHbnyaNHjzh+/DhDQ0M4Ojpy4MAB+Y0nmBhJkigpKeHixYsMDAxgbGzMmjVrWLZs2ZyYRCgQCJ5PWloaV69eRaFQcODAgdeuI5Mkierqau7du8fTp0+BYRuC0NBQUlJScHNzm/R2KisruXfvHs+ePZO3ExYWRkpKyoSiR5Iknjx5QlZWFk+ePJGjGE5OTiQkJBAVFTXOS0MIihHMBUEBw1eqBw8epKmpCQsLCz744IPnhqB0Oh2NjY1yBKOmpkY2HdEzFYHR3NzMd999x+DgIIGBgRw4cOC1igRbWlo4dOgQXV1dolhzCvT09HDu3DkePXoEDPeP79y5UwgygWCOUlFRwZEjR5AkiU2bNpGYmPjK29KfzO/evUttbS0wbDcQERHBihUrcHZ2nvR2KioquHfvHvX19QAYGxsTGRnJihUrcHJyGvc3AwMDFBQUkJ2dTUdHh3z/4sWLSUhIeKGHhRAUI5grggKGi/V+/vlnamtrMTMz4/3335/U3AytVjtKYNTW1k5ZYNTV1fHjjz8yNDREcHAwe/fufa1c/thizXXr1olhWZNAkiQKCwu5fPkyg4ODmJiYsGbNGpKTk0W0QiCYQzQ1NfHtt98yNDREXFwcW7ZseaXjm06no6ysjPv379PY2AgMC4Do6GiWL18+6YJ5rVZLSUkJ9+/fp7W1FQBTU1NiY2NJTk6ecKZQU1MTWVlZFBcXywZWFhYWREdHEx8fP6H4GIsQFCOYS4IChgtgjh49ytOnTzE2Nua9996b8mS6kQJDnyIZKzBGFnn6+fnh7u5OdXU1P//8MxqNZlompGq1Wi5evEhubi4AkZGRbNu2TbRITgKlUsm5c+fknKe3tzc7duwQ0QqBYA6gVCr585//TE9PD4GBgXzwwQdTvgDTarUUFRVx//592tvbgeEahbi4OJKTk7G1tZ3UdtRqNfn5+aSlpcl+R+bm5iQkJJCUlDSuOFSj0VBWVkZWVpYcCYHhbrOEhATCw8OnlPYWgmIE+p3R2Ng4Z9r2NBoNJ0+epLS0FIVCwbZt24iJiXnl7ekFRnV19XNrMPRtqkZGRuTm5mJlZUVcXNxr91FLkkR2djaXL19Gp9Ph5eXFvn375oR4m+tIkkRBQQFXrlxhcHAQY2NjVq9ezfLly0W0QiAwECqViu+++46mpiZcXFz4/PPPpzSjY2hoiLy8PNLS0lAqlcBwBDkhIYHExMRJF7IPDg6SnZ1NRkYGfX19wPBE7KSkJOLj48etqbu7m5ycHPLy8uTHGxkZERISQnx8PL6+vq90rBeCYgT6nfHv//2/Z/fu3YSEhBh6ScBwGOz8+fNyK+a6detYvnz5tG17rMDQV/HCcA1ERUUFdnZ2LFu2jL179+Ll5fVakYXKykqOHTvGwMAANjY27Nu3T7hETpKx0QoPDw927tw56eIsgUAwPeh0Og4fPszjx4+xsbHh17/+NQ4ODpP624GBAbKyssjMzKS/vx8AW1tbkpOTiY2NxdzcfFLb6enpISMjg5ycHPnC0MHBgWXLlhEdHT1qtpK+MDM7O3uUd4StrS2xsbHExsZOOhLyPISgGIF+Z/z2t7/F3NyckJAQtmzZMq09xK+KJEncuHGD+/fvA7B8+XLWrl077XUIOp1OblOtrq6murqaqqoqysvLAfD19WXx4sX4+PjIKRJvb+8pDwXr7Ozk8OHDtLS0YGxszNatW8UY9EkiSRJFRUVcvnxZ7gRJSUkhJSVF+FYIBLOAJElcvHiR7OxsTE1N+fTTTyfVuqlUKklPTyc3N1dOPTs6OrJ8+XKioqImfaHW3t5OWloaBQUFsjumq6sry5cvJywsbNRxoL+/n4KCAnJyckYVWQYEBBAfH09wcPC0HTeEoBiBfmfo+4h1Oh1WVlZs2rSJsLCwOVFE+ODBA65duwZAdHQ027Ztm9GQtyRJtLS0cPHiRS5evEhXVxdeXl6jHNSMjY3x9PSUBYaPj8+kFPbQ0BCnTp2SfRcSEhLYsGGDOClOkp6eHi5cuCCLPVdXV3bs2DGlnnSBQDB1Rg782rt370tr21pbW0lLS6OoqEgWAO7u7qxYsYKQkJBJH8Pr6+t58ODBKDMqX19fVqxYMWpglyRJ1NfXk52dzcOHD+XhXubm5kRFRREXFzcjNVjzSlDU19fzt3/7t1y6dImBgQGCgoL45ptviI2NBYZ34u9+9zu++uorOjs7SUxM5L//9/9OaGjopLY/cmf09fVx+vRpmpubgWEDkS1btsyJfH9+fj5nz55FkiSCgoLYs2fPrIwNT09Pl6+Kg4ODcXBwoLq6Ws796dGPa/fz88PPzw9fX9/n5gIlSeLOnTvcvn0bGPaO37Nnj5hYOkkkSeLhw4dcunSJvr4+FAoFycnJrFmzRoySFwhmgNLSUo4dO4YkSWzYsIHk5OTnPrauro779+/Loh+Gj3EpKSmTHtglSRJPnz7lwYMHVFVVyfcHBQWxfPly/Pz85Pv0TpY5OTk0NTXJ97u7uxMfHz/lIsupMm8ERWdnJ9HR0axZs4Z//a//Na6urjx9+hR/f395HOw//uM/8h//43/k+++/JygoiP/wH/6D7Cw2mdzQ2J2h1Wq5d+8e9+7dQ6vVYmFhwfr164mOjjZ4tKKiooJjx46h0Wjw9fVl//79r+xsORXu3bvHjRs3ANi0aRMJCQl0dXXJNRjV1dV0dnaO+ztXV1d8fX1lkTH2zVZRUcHJkydRqVTY2dmxb98+caU9Bfr7+7l8+TJFRUXAcBh1+/btBAQEGHhlAsGbQ01NDT/++CMajYaEhAQ2bdo07lwgSRKPHz/mwYMHVFdXy/cvWbKEFStWTHqqs1ar5eHDh6SlpcniwMjIiPDwcJYvXz7KjKq5uZmcnByKiorkWgoTExNCQ0OJi4vD29t7xs9ZkiTR1NSEp6fn3BcUv/3tb3nw4AH37t2b8PeSJOHp6clvfvMb/vZv/xYYrsB1c3PjH//xH/nyyy9f+hzPU1ctLS2cOXNGNgYJCAhg+/btrzxEa7qorq7m8OHDDA4O4urqyocffjgrEZRbt25x584dALZu3UpcXNyo3yuVSqqrq6mpqeHZs2dyH/RIHB0d5eiFn58fTk5OtLe3c+TIEdra2jAxMWHr1q1ERUXN+Ot5k3j06BHnz5+Xo0YxMTGsW7duVsSmQPAm09bWxjfffMPAwABLlixh7969o1IVWq2W4uJi0tLS5DkXxsbGREREsGzZskmnGPSdH+np6XR3dwPDLaQxMTGjPCTUajWlpaXk5OSMavlcsGABcXFxREVFTfvnXqfT0d3dTUdHB52dneO+9vT0zI9poyEhIWzYsIG6ujru3LmDl5cX/+bf/Bu++OILYLhzYOHCheTl5Y0q7tuxYwcODg788MMP47apUqlGtUwqlUp8fHwm3Bk6nY6MjAxu3bqFWq3G1NSUNWvWkJSUZNC2vZaWFg4ePEhPTw/29vZ8+OGHM+5PIEkS169f58GDBwBs27ZNTjtNRH9/PzU1NXKRZ2NjI2PfHjY2Nvj6+uLu7k5JSQnNzc0oFAri4+PZuHGjqKuYAoODg1y/fp2cnBxgeN9u3rx5znQtCQTzjd7eXr7++mu6urrw9vbmk08+kVOKKpWK3NxcMjIyZCFvbm5OXFwciYmJkz6x9vb2kpmZSU5OjjwQ0tramsTEROLj42Vx0NraSm5uLoWFhfLjjIyMWLp0KbGxsVMaWT4RKpWKzs7OUUJB/313d7c82fR5fzsvBIW+j/Zv/uZv2LNnD1lZWfzmN7/hT3/6Ex9//DFpaWksX76c+vr6UQNO/uqv/orq6mquXLkybpt///d/z+9+97tx979oZ3R0dHD27FnZD93T05MdO3YYtG2vq6uLn376iba2NiwtLdm/fz++vr4z+pySJHH16lXS09MB2L59+6T9MVQqFbW1tbLIqK+vl4uG9NtuaGigvb0de3t7li5dyhdffGHwiNB8o7q6mrNnz8pGOUuXLmXz5s2v3RomELxNqFQqvv/+exobG1mwYAGff/45VlZWKJVKWQDoL0xtbGxISkoiLi5u0n4Ura2tpKenU1hYKBdsOjk5sXz5ciIjIzExMUGj0VBaWkpubu6oNIqDgwOxsbFER0dPuu5MkiR6enpkoTBWOOh9KZ6HiYkJjo6O8s3JyUn+amRkxIIFC+a+oNC7hqWlpcn3/e//+/9OdnY26enpsqBoaGjAw8NDfswXX3xBbW0tly9fHrfNqUQoRiJJEvn5+Vy9epXBwUGMjIxYvnw5q1atMpjzY39/P4cOHaKurg4TExN27949ZVfNqSJJEleuXCEjIwOFQsGOHTteKUWh0Wior6+XBUZtbS0qlYr29nbKysrQaDSYm5uzdu1aoqOj5U6SqRjIvK1oNBru3r3L/fv30el08n6Mi4szeB2QQDDX0Wq1HD58mCdPnmBtbc3nn3+ORqMhLS2N4uJiWQA4OzuzbNkyIiIiJnUO0A/9SktLk+f1APj4+LBs2TKCg4MxMjKira2N3NxcCgoKRkUjgoKCiI2NZeHChRNGyNVqNV1dXaOEwsjbyAu4ibCysholFkZ+b2trO/9nefj5+bFu3Tq+/vpr+b7/8T/+B//hP/wH6uvrXynlMZap7oyenh4uXrwotz0uWLCAbdu2jWqpnE3UajXHjx+noqIChUIhF03OJJIkcenSJbKyslAoFOzcuZPIyMjX2qbeC6OmpoaHDx9y/vx5Ojo6UCgULFy4EC8vL4yMjEYVevr6+s6JDpy5SnNzM2fPnpXrgHx8fNi2bZsYjS4QPAdJkjh9+jSFhYWYmJjwzjvvUFlZyZMnT+TH+Pn5sWzZMoKCgiYl0HU6HaWlpaSlpdHQ0AAMd8UFBwezfPlyfHx8nhuNsLe3JyYmhujoaGxtbenr6xsnFEbWMrwIIyMj7O3tx4kG/e1VL9bmjaA4cOAAtbW1o4oy//qv/5rMzEzS0tLkosy//uu/5t/9u38HDBe3uLq6vnZR5ssoKyvj4sWL8j/RkIVwOp2OixcvyvnzFStWkJqaOqNXoyNNXl4nUvE8VCoVhw8flouUrK2t8fT0HFdX4eDggK+vr3xzcXERV+Ej0Ol0ZGdnc+PGDYaGhjA2NmbFihWkpKSImSoCwRiuXbvGvXv3aGtrw93dXa4dUCgULF26lGXLlk26Y0OlUpGXl0dGRoZcaGliYkJUVBTJycksWLCAlpYW8vLy5NoIrVaLSqXC3d0dHx8frK2t6e7ulsWDfoDX8zA3N8fJyQkHB4dxkQY7O7sZqUubN4IiOzubZcuW8bvf/Y69e/eSlZXFF198wVdffcUHH3wADLeN/uEPf+C7775j8eLF/P73v+f27duv3DY6FSYqhNu4cSOhoaGzflKTJIl79+5x8+ZNAMLDw9mxY8eMnjQkSeLChQvk5OTMiKiQJImsrCyuXLmCTqfDzs6OhIQEent7qampmbDQ09LSEh8fH1lgeHp6ihMnwzVCFy9epKKiAhiOrG3dulW0mAoE/5Pbt2/z448/Ul9fT0BAAO7u7piamhIdHU1SUtKkJm/C8GctIyODvLw8Ob1ubW1NQkICsbGxqFQqMjMzycrK4tmzZwwMDMijDxwdHfHw8HiuSaBCoZCjDBPdLC0tZ/3cM28EBcD58+f5u7/7Ox4/fkxAQAB/8zd/I3d5wF+Mrf70pz+NMrYKCwub1PanY2fU1NRw9uxZ2tragOEZ8lu2bJm0x/t0UlBQwNmzZ9HpdPj7+7Nv374ZjZqMjVRs37592u20a2tr+eWXX+jp6cHMzIwdO3YQGhqKSqWivr5ersGora0dp+D1jp56geHj4zPp4TtvGpIkUVZWxqVLl+TIWmRkJOvXr58TVvMCgSHo7OzkyJEjHD9+HK1WS2BgICEhISQkJBAXFzfp40V9fT3p6ekUFxfT19fH4OCgPNXZwcGBmpoaysvLaWhokOswFAoFCxYswNPTE0dHRxQKBebm5s8VDA4ODnOu+21eCYqZZrp2hkaj4f79+7IhlqmpKatXryYpKWnW3wCVlZUcPXoUlUqFi4sLH3zwwYyKm5E1FTC17o/J0tfXx/Hjx2XXuMTERNavXz9q32q1WrkOQy8yent7x23L2dl5lMBwcnJ6q9Ikg4OD3Lx5k+zsbCRJwtLSkvXr1xMVFfVW7QfB24skSdTV1ZGens6DBw8oKipCkiRCQ0P5/PPPX1hoqdPpUCqVdHZ20t7eTlFREdnZ2dTX1zMwMIBarcbR0RFvb2/s7OxoaWmhsbFRPhYpFAocHBwICQkhPDwcLy8vg0cZXgchKEYw3Tujra2N8+fPyy2mbm5ubNu2bdJ5t+miubmZn3/+GaVSiY2NDQcOHBjVWjvdSJLE5cuXyczMBCY2v3pddDodN2/elIeleXt7s2fPHtn0ZaI1dXZ2UlNTI9/0UaSRWFtbj0qTeHh4zLmrgJmgrq6Oc+fOyVbzfn5+bNmyRRRtCt5Y9AWSGRkZ1NXVoVQqKSwsxM7OjnfeeYf/5X/5X1AoFAwMDMh1C11dXaOKILu7uxkaGqKxsZH6+no5XaFQKHBzc5MnM+tFh5mZGRYWFlhbWxMVFcXy5csnbcE9HxCCYgQzsTMkSaKwsJArV64wMDCAQqEgLi6O1NTUWW17VCqV/PzzzzQ3N2Nqasru3btZsmTJjD3fyJZSGLbpTkxMnPbnqaio4NSpUwwODmJpacm7777L4sWLJ/W3/f39sh9GTU3NqPCjHhMTE7y8vPDx8ZFvb2qaRKvVkpmZKZu3GRkZsWzZMlatWiXmggjeGAYHB8nNzSUrK4vu7m60Wi1dXV3U1dVhZWWFp6cn0dHRcgGkfiroWAYGBqirq5OPqZaWlnInRkREBJ2dnVRWVo6adeTq6ir//k08jghBMYKZ2hkwHKa/evUqhYWFwPCV8MaNG2d1iqlKpeKXX37h6dOnKBQKNmzYQGJi4ow9vyRJXLt2TfYOWb9+PcuWLZv25+ns7OTYsWNyG9bKlStZvXr1lB1MNRoNDQ0Ncg1GTU0N/f394x7n7OwsiwtfX18WLFjwxlxhwHAh2aVLl+SBRg4ODmzevJmgoCADr0wgmDp6u+iqqiru379PYWEhPT09DA4OotPpsLW1paWlBa1Wi52dHZGRkeOikra2tnLdgkqlorq6mubmZiwsLDAzM8PV1VV2sywuLubJkydyV4iZmRnh4eHExMTg6en5Rh0rxiIExQhmUlDoefbsGefPn5fD7YGBgWzZsoUFCxbMyPONRavVcunSJbkbJSEhgY0bN86YfbgkSdy6dYu7d+8C8M4777By5cppfx6NRsOVK1fIzs4GwN/fn927d7+WK6QkSXR0dFBTUyOLjInmkui7SfQ3Ly+vN+KKvry8nEuXLsltbkuWLGHjxo0GKTAWCJ6HJEn09vbK6YiRX/Wf35qaGtkxFoYv6Ly9vXF0dKSwsBC1Wo2LiwubN2/G1dV1VB2Dvb09CoWC4uJiMjIy5LQgDBfdL168mK6uLoqKikbVafn6+hIdHU1oaOiMTvicSwhBMYLZEBSA7LR29+5dNBqN7AewYsWKWTkRSZJEeno6165dQ5IkFi9ezHvvvffc9qTp4O7du3Ib68qVK1mzZs2MKPWSkhLOnj3L0NAQ1tbWvPvuu/I02umgv7+furo6OYIx1jYchk1jPDw8RomM+Wq6NTQ0xJ07d0hPT0en02FqasqqVatITk5+K2pLBIZHkiQGBwdlkTCRcBj7GdRqtbS0tFBXV0dfXx9GRkZyl0VcXBzBwcFYW1tz5coVenp6cHFx4bPPPhv3Oe3p6SE7O5vc3FzZktrU1JSQkBDs7Ox49uzZqMFc+tqI6OhonJ2dZ37nzDGEoBjBbAkKPR0dHVy8eFF2XnN0dGTz5s2TrgF4XcrKyjh58iRqtRo3Nzf2798/o1efDx484Nq1awAsW7aMdevWzYioaG9v59ixYzQ1NaFQKEhJSXmlFMhk0Gq1NDU1jUqTTORSZ2dnN0pguLu7z6sTcktLCxcuXJCd+/RXc8K7QjAdDA0NTSgY9N+PHJEwEXpPBnNzc1pbW6mvr5dFhN6zJikpSY4EDw0NcfDgQWpra7G2tuazzz4bFSWuq6sjMzOThw8fyqkLOzs7fH190Wg0PH36VG5LNzIyYvHixURHR7N48eJ59bmeboSgGMFsCwoYVt/60LK+eGfp0qVs3LjxuR0L00l9fT2HDx+mt7cXa2tr9u/fP6NdKJmZmVy6dAmAuLg4tmzZMiOiQq1Wc+XKFTm14+fnx+7du2f8/ypJEt3d3dTW1sqRjKampnET+kxMTPD09JQFhre396SH+xgKSZIoKiri6tWr8tVaWFgY69evn7cRGMHsoFar5SJHvVAYKRwmqlUai42NDQ4ODnItg/6rg4MDSqWS7OxsysrK5M+ag4MDCQkJxMTEjCqA12g0HDp0iMrKSiwsLPj0009xd3dHq9Xy8OFDMjMzZYt6GK6ZsrGxkdc88v7o6GgiIyPn/Gd3thCCYgSGEBR6DBla7u7u5vDhwzQ1NWFiYsLOnTsnbQb2KuTl5XHu3DkkSSIiIoKdO3fOWA1HcXEx586dY2hoCCsrK3bu3DnrxYVDQ0PU19fLAqO2tlYe9DMSR0dHWVz4+Pjg5uY2Y/vldRgYGODWrVuyd4WZmRmrV68mMTHxrb46e5vRarV0d3ePiy7of57IA2YslpaW44TCyO/HpoM1Gg0lJSVkZWXJBdkwXD+VmJgoD9gau85jx45RXl6OmZkZH3/8Mfb29uTm5pKTkzNqnQ4ODhgZGdHZ2Sm78JqbmxMWFkZUVBTe3t5vdIHlq1BUVERkZKQQFGBYQaFnbGjZ2dmZzZs3ExgYOKPPOzQ0xIkTJ2Q75tWrV7Nq1aoZ+8CUlJRw8uRJdDodS5cuZffu3TNmi93e3s7x48dpbGwEhtMtqampBjv5SZJEe3v7qChGa2vrOOtwU1NTvLy8ZIHh7e09p1wsGxsbuXjxopxDdnFxYdOmTTP+XhXMPlqtFqVSOaFg6OrqoqenZ9z7dyxmZmYTRhf0t8m20SuVSnJyckbVNZiYmBAeHk5iYiLu7u4T/p0kSZw6dYqioiKMjY1Zs2YNzc3NlJaWotVqkSQJnU6HlZXVuBRLQEAAUVFRhISEvBEF19PN0NAQ165d4/79+/zDP/yDEBQwNwQFDL/xi4uLuXr1qqyYQ0NDWb9+/YymQXQ6HdevX5fbPENDQ9m5c+eMfYAqKir45Zdf0Gq1LFq0iH379s3Yc2k0Gq5duyabbXl5efHee+/h6Og4I883VQYHB6mvr5dFRl1dnWySMxInJye8vb3nTBRDkiQKCgq4du2aHLaejfeqYHoZKRgmuimVypcKBlNT01ECYaxoeB3XR0mSqKmpISsra1RaQ18fERMT80JfB/2soaysLFpbW3F3d5dfz+DgIJIkYWRkhKmpqfx5cnR0JCoqisjISNHZ9AKqqqo4c+YMXV1dqFQqISj0zBVBoWdwcJDbt2+TmZmJJEmYmpqycuVKkpOTZ3TIVV5eHhcuXECr1eLh4cH+/ftnbH9UVlZy+PBh1Go1vr6+HDhwYEYNv8rLyzlz5gwDAwOYm5uzdetWwsPDZ+z5XhVJkmhtbZUjGHV1dRO2rJqamuLp6TkqimGIfO7YNIipqSkpKSksW7ZMDGSbA+gtoscKBX20YTKCwcTEBAcHB3kg1VjxYGVlNe0RTbVaTXFxMVlZWTQ1Ncn3+/n5kZiYyJIlS14qqCVJ4uTJk5w5c4bGxkYWLVqEs7MzHR0dmJqaYmJiIn9mzMzMCAkJISoqCj8/P5HSeAH6qIS+Vd/BwYE1a9YQFRUlBAXMPUGhp7m5mYsXL8ppECcnJzZt2jSj3SDV1dUcPXqU/v5+bGxseP/992esWLO2tpaff/6ZwcFB3N3d+fDDD2f0pNjd3c2JEyeoqakBICoqis2bN8/5XvGBgQG5FuNFUQwHB4dRUYzZ7Chpamri0qVLo96rGzZsICgoSBycZ5DpiDAYGxuPS0OMFAzW1taz9j/s6OggJyeH/Px8ud7I1NSUiIgI4uPjn5vWGIkkSTx9+pTvvvuOBw8eIEkSnp6eWFpaYmJigouLixwRDQgIIDIykpCQkDl/HJgLVFZWcvbsWblINS4ujnXr1qFSqURRpp65Kihg4jRIUFAQGzdunPQo3anS1dXFoUOHaGlpwcTEhO3btxMRETEjz9Xc3MzBgwfp7e3FycmJjz/+eEbDjDqdjjt37nD37l0kSWLBggW89957eHh4zNhzTjeSJNHW1iaLi+fVYpiYmODh4SHXY3h7e8tmPTO1rpKSEq5evSq30C5atIiNGze+lb3504FGo6G7u1sufBx56+7unnSEwd7e/rmiwcbGxqCiT5Iknjx5QlZWFk+ePJFfj6OjI/Hx8URHR09qWvLg4CAFBQWyf8Tjx4/p7e3F3d2dxYsXy862Tk5OREZGipTGFBgcHOTatWvk5uYCwxcv27dvl+umRJfHCOayoNCjUqm4c+cOGRkZ6HQ6jI2NWbZsGSkpKTOirFUqFSdPnpSLNZctW8batWtnJG/f3t7OwYMH6erqws7Ojo8++ggXF5dpf56RPHv2jJMnT6JUKjE2NiY1NZXk5OR5ezWtH+M+MooxUUuejY0N3t7essjw9PScdmMzlUrFvXv3SE9PR6vVYmRkRFJSEitXrpzVOTbzAX1b5UiRMLbo8WWMTUmMFQ+GFgzPY2BggPz8fLKzs+ns7JTvX7RoEQkJCSxatGhSx5umpiaysrIoLi6mv7+foqIinjx5gomJCRERESxevFju0oiMjMTHx2dO7o+5yuPHjzl37pxsb5CQkEBqauqo44YQFCOYD4JCT1tbG5cuXeLp06fAcHHSunXrZmQ2iCRJ3Lx5k3v37gHDH/Tdu3dP6mphqiiVSg4ePEhraytWVlZ88MEHeHl5TfvzjGRgYIAzZ87IsysWLlzIzp07X8u2e66gn7I6UmBM5IuhUChwdXUdFcVwdnaeFuHY3t7OlStXePToETDsJpiamkpUVNScbIudCVQq1YRiQf+9vlvhRZiamj5XLDg4OMxqSmI6aGhoIDs7m+LiYtnp0sLCgqioKOLj4yc1jkCj0fDw4UNycnKorq6mvb2d5uZmmpqa5HTt4sWLSU1NJTIykqCgINGlMUX6+/u5cuWKPIfKycmJHTt24OfnN+6xxcXFRERECEEB80tQwPDJoqKigitXrsjK3tfXl40bN87IePKSkhLOnDmDWq3GycmJ/fv3z0gEob+/n59//pn6+nrMzMzYt2/ftNpnT4QkSeTl5XH58mXUajVWVlbs2LGD4ODgGX1eQ6BWq2lqaholMvTzOkZibm6Op6enLDK8vLxeS2Q9fvyYy5cvyzMVPDw82LRpE76+vq+8zbmAJEkMDAw8Vyx0dXVNWOsyFnNzcznCMFIo6H+eiaLH2UatVvPw4UOys7NHmUe5u7uTkJBAWFjYpCKtHR0d5ObmkpeXR1NTE83NzbS2tuLo6IiRkRGNjY3Y2tqyceNGPv30U2E89QpIkkRpaSkXL16kr68PhUJBUlIS77zzzjhRJkkSmZmZnD17lj/84Q9CUMD8ExR69LNB7t27h1qtRqFQEBUVRWpq6rR/kJqamjh8+DDd3d2Ym5vz7rvvzshJd2hoiKNHj/L06VOMjY3ZuXPnrHRjtLW1ceLECdmzIi4ujvXr17/xhVo9PT2jUiUNDQ0Tjm22t7cfJTA8PDymtG+0Wi1ZWVncvn1b7vUPCwtj3bp1c7bNVKfTycOn9CJh7Fe9DfOL0Bs3PU8wWFhYzHvB8Dza29vJycmhoKBALrI0NjYmNDSU+Pj4SZlE6XQ6Hj16RE5ODkVFRTQ3N9Pc3CwXW7q7uzMwMEB7ezvu7u5s2LCB1NTUN3afziQ9PT1cuHBBjtq6urqyffv2CQvzh4aGOHfuHMXFxaJtdCTzVVDoUSqVXL9+naKiImD4imflypUkJiZOa+teX18fv/zyi1zJP1MmWFqtllOnTlFSUgLApk2bSExMnNbnmAiNRsPNmzdlP44FCxawe/fuGYn6zFV0Op08E6Guro76+npaWlrGFf4ZGRnJqRK90JhMqqSvr4+bN2+Sl5eHJEmYmJiwfPlyli9fPuviTaPRyB0SIwsf9V+VSiVarfal29FbQ48UCSO/zuTwvbmIVquloqKCnJwcKisr5fsdHByIi4sjOjp6UkZtSqWS/Px80tLSqKyspLm5GaVSiZOTE56ennh4eBASEoKRkRF5eXkoFAqWL1/O2rVrhZiYIpIkkZuby7Vr11CpVBgbG5OSkkJKSsqEnWIdHR0cPXqU5uZmjIyMWLFiBampqUJQwPwXFHpqa2u5dOmSbEfr5OTE+vXrCQ4OnrYPmFar5cqVK2RlZQHDHSfvvvvutBfbSZLE5cuXZUOqlJQU3nnnnVk5UFRWVnL69GmUSiVGRkasWbOG5cuXvzV5/7GoVCoaGxtlgVFXVzdhsaCZmdmEqZKJ/meNjY1cvnxZFqe2trasXbuWiIiIafsfDw4OykJhoghDb2/vSzskjIyMsLOzm1Ao6L8Kv41huru7ycvLIy8vT35/KBQKuchy4cKFk/KOqKysJCMjg7S0NBobG+ns7MTExAR3d3e8vLzk4srg4GB5yjDM7ODBN5m2tjbOnTsnfxa9vLzYsWMHrq6uEz7+0aNHnDx5ksHBQWxsbNizZ49c3yMEBW+OoIC/OBjeuHFDbjMNCAhg48aNuLm5TdvzFBQUcP78eTQaDQsWLOD999+f9roKSZK4d++ePP48KiqKbdu2zYq3wsDAAOfPn+fhw4fAcI3Krl275ozDpqFRKpWjohjPS5XY2trKUQwvLy88PT1l8SlJEmVlZVy7dk2uBfL09GTDhg0TFn6NRJIkent7RwmEsd9Ppn5BX/A4ViTov7e1tX1rheRk0Ol0PH36lJycHB49eiQLNGtra2JiYoiNjZ1Ua2ZfXx+5ublcvXqVx48f09bWhlarxd7eHk9PTyIiIoiOjiYsLExO546cDZSUlMSGDRuEmJgCWq2WBw8ecOfOHbRaLWZmZqSmphIfHz/he16n03H79m3u3r0LDH9Wk5KSaGtro6ysjP/1f/1fhaCAN0tQ6FGpVNy/f5/09HQ0Gg0KhYKYmBjWrFkzbfUVDQ0NHDlyBKVSiZmZGTt37iQkJGRatj2SvLw8zp8/j06nY9GiRezdu3dWwuP6KZsXL15EpVJhZmbGpk2biIqKEgeuMeh0Otra2mSR0dDQQHNz87iuEhieU6OPZHh5eeHs7ExOTg737t2T6yuCgoJISEhAoVCMijJMNR1hZWU1SiCMFQ1vQsGjIejp6SE/P5/c3NxRhb3+/v7Ex8ezZMmSlwp/SZKoqqri6tWrPHjwgKamJtRqNSYmJri5ubF06VKWL19OeHj4OB+T3Nxczp07B0BiYiIbN24U/8cpUFtby7lz52hpaQFg8eLFbNmy5bnir6+vj6NHj1JYWEhXVxdOTk44ODjIArK/v5//9J/+kxAU8GYKCj1dXV1cu3ZNvtI2NzcnJSWFpKSkaQnV9vX1cezYMZ49ewbA8uXLSU1NnfarukePHnHs2DHUajWenp588MEHszYwq7Ozk9OnT8shweDgYLZv3z6nBnbNRdRqNY2NjdTX18s3/QRHtVqNSqVicHCQoaEhLC0tMTY2loWIfsaCt7c3fn5+E75XFQrFuHTE2O/f9KLa2UTvQJmbm0tFRYUsFi0tLYmKiiI2NnZSBmZ9fX3cvn2by5cv8+TJE7lY09bWlsDAQFJTU4mOjn5uwWZ2djYXLlwAIDk5mfXr1wsxMUkGBwe5fv06OTk5wHAkacOGDYSHh4/bh2q1mtraWrKzszl16hTNzc0oFAqCg4PlaLe1tTVarZbq6mr+5V/+RQgKeLMFhZ6amhouX74s11c4ODiwdu1aQkNDX/vDqNVquX79Ounp6cBwiuW9996b9hNuXV0dhw4dor+/HycnJz788MMZcwsdi06nIz09nZs3b6LVarG2tmbbtm0sWbJkVp5/PqEvdhwbWeju7qalpYW6ujo6Ozvp6elBqVSO65QYGhqiq6sLSZKwtbXFycmJ5cuXs2LFChYsWCCLBTs7O5GOmAV6enooKCggLy9vlAGVj48PcXFxk5rEqY/2nTt3jqysLNkkydjYGC8vL1auXMmqVasIDAx8YWQjKyuLixcvAqJmYiroW0EvXbokp8Kjo6NZt26dPFxtaGiI2tpanj17RnV1NXV1ddTU1PD06VMkScLS0pKkpCTCw8Px8fGRo1Q9PT2iy2Mkb4OggL/YeF+/fl3+QHt7e7N+/fpp8QR4+PAhZ86cYWhoCDs7O/bt2zft5lTt7e389NNPdHZ2YmVlxf79+/Hx8ZnW53gRzc3NnDx5kubmZmC4rmPjxo1vjQOkJEn09/dPKBb0N/0B62XY2Nhgb2+PqakpQ0NDDA4O0tfXh1KpRKFQoFQqqayslB0/7e3tWbZsGXFxcbLL55tgQjYX0el0VFZWjotGWFhYEBkZSWxs7HOL9kbS0tLC2bNnuXnzpnwxA8OGfImJiWzatGnSHhQZGRlcvnwZQO4qEGLi5XR2dnLx4kUeP34MDHevbdu2DQ8PD2pqamQB0dDQIP+fNRoNFRUVKJVKHBwciI6O5pNPPsHV1ZXi4mLu3Lkji0s7Ozs5nS4EBX8RFJ2dnW+Ft7tarSYtLY0HDx7IhXQhISGsXbv2ta/4W1tbOXLkCO3t7RgbG7Nx40bi4uKm9YPf29vLoUOHaGhowMTEhN27d7N06dJp2/7L0Gg03Lp1i7S0NCRJwt7enh07dsi+9vMZtVr93OiCfnbEZLwX9MWOz7vZ2dk9N+Wm0+lob2+Xx7pnZGSQk5Mj11fY29uzcOFC7OzssLOzw9PTU67J0A+BErwa+lbN/Px8eQAUDBclx8TEEBoa+tJoxMDAANevX+fKlSuUlpbKJyljY2PCw8PZuHEjK1eufOHY8bE8ePCAa9euAbPb8TWf0Wq1pKenc+fOHdRqNTqdjoULF+Li4kJdXR2NjY3jupz06UK9D4WVlZV8DC8tLeX27duyQZ2NjQ0pKSnExsbS398vujz06AXFP/zDP/DOO+8QFRX1Vti09vT0cPv2bdkTwNjYmPj4+Cl/2MeiUqk4ffo0ZWVlAERERLB169ZpzWcPDQ1x/PhxHj16hEKhYMOGDSQlJU3b9idDTU0Np0+fpqOjAxj2uF+7du2czduP7Ix4nliYjBU0/CW68LzbdBc79vX1ceHCBW7duiWnS6ytrQkICBgnIBwdHWVxofcreNu8IKaC3jgqLy+Px48fyycZS0tLIiMjiYmJeWk0Qq1Wk5eXx8WLF8nKypLrImBYjLzzzjts2bJlyp1gkiRx584dbt++DcCqVatYvXq1EBMvoaamhhMnTvD48WO6u7sxNjbG3d193HHdyckJPz8//P398fX1paqqiosXL6LRaLC3t+e9995DqVRy+/ZtWltbgWGRsXz5cuLj4+VjnZjlMQL9zvjtb3+Lubk5VlZWJCQkkJCQ8Fon1vlCS0sLV69e5cmTJ8BwWDMlJeW1jLEkSSI9PZ3r16+j0+lwcXFh37590zp1UqfTcfHiRbnAKCkpifXr189qXn1oaIhr166RnZ0NDH9Ad+7cOeu20pIkoVKpxgmEsT9P1HUxFjMzMzmKMLLAUV8A+aLowkyjVCq5efMmhYWFaDQa+vv78fLyws3Njfb2dlncjUShULBgwYJRIsPd3f2tuGh4ER0dHeTn51NQUDDKV8TPz4/Y2FiWLl36wn2k1Wp59OiR3KWh7xiA4TD4ihUr2LZt2ytHDyVJ4saNG9y/fx+A1NRUUlJSXmlbbwPd3d2Ul5dz9uxZ8vPz6e/vx9TUlIULF+Lm5oZCocDZ2VkWEH5+fvLJf2hoiPPnz8vmiIsWLWLp0qVkZmbK/1dLS0uWLVtGQkLCOIEuBMUI9Dvjyy+/pLm5mcHBQRQKBSYmJvj5+bFw4UK5H93Y2BgjI6NRt7H3TfXnsfc97/upbEuhUExZxT99+pSrV6/K9QH29vakpqZOWAE8Waqrqzl+/Dg9PT2YmZmxfft2wsLCXmlbEyFJEmlpaXI4NDg4mN27d896lODp06ecOXNGzv8/z/v+VdGnIiYSCfrvJ/KBGIuRkRG2trajxIJeKOhv88EKurm5mWvXrski2NzcnBUrVhAZGUlraysNDQ3ybaJ5JfqhaB4eHqNExptuUqVWqykrKyMvL0/uzILhav2oqChiYmJeOJxLp9Px7Nkz7t+/z507d6ipqZFTYObm5kRERLB582ZWrFjxWu/9scZ2GzdunPUI5FxGkiQ6Ojqorq6murqaZ8+eUV5eztOnT+WBax4eHiQlJREUFISfnx++vr4TWgY0Nzdz7Ngx2traUCgUBAYG0tPTIwsJCwsLkpKSSEpKem6tmBAUIxgZoTAzM6O1tZWamppRxWUuLi74+PjMq6LNVxElAPX19VRUVMjCytHRkaioKDw9PV9JJA0ODnLz5k0aGxtRKBRERESQkpKCubn5lITWRD/rT3wlJSWcPn0ajUaDh4cHBw4cmPWCvcHBQa5cuUJ+fj4wXPy0c+fOlxaN6nQ6enp6RgmEkUJhKqkIKyurcQJBLx7s7OzeOKOmyspKrl27Js9gsbW1Zc2aNaMmmvb19Y0SGPX19RMWjurtxEemStzc3N4IkdHY2Eh+fj5FRUWy4ZdCoWDhwoXExMQQHBz83O4KSZKoqakhLy+P27dvU1lZKUc0zMzM8PPzIzU1lfXr109L15VOp+PChQvk5uYCsHXrVuLi4l57u/MZnU5Hc3MzNTU1sojQHxN6e3t59OgRPT092NjY4O/vz+7du0lMTHxhPZF+MOKlS5dQq9UMDAxgb28/SiAmJSWRnJz80qJzIShGoN8ZFRUVWFtbo9Pp5N7anJwcnj17hiRJ6HQ6PDw8iIiIwMfHB51ON+qm1Won/Hns/S967FQeM/Ln6Uar1VJfX091dbVsIOTo6EhgYOArnaj1JjY1NTXAcA4+NDT0tQvoRooLpVJJUVERGo0GS0tL4uPjsbe3n7FI0vN+rq2t5fbt2wwMDKBQKAgNDSUsLEzuYujv76e3t5fe3l56enrkiX5jbyMFk0KhGFfoOFI46L9/G8P4kiRRUlLCjRs35EJCFxcXUlNTn2s7rx+K1tjYKAuNiUSbsbHxuEiGq6vrvBAZAwMDFBcXk5+fLwsuGI48RkdHEx0d/dzBbJIkUVdXR0lJCffv3+fJkye0trai0+lk46mkpCTWrVtHUFDQtInUkXN8FAoFO3bsICoqalq2PZ/QaDQ0NDRQXV1NTU0NNTU1clGyHkmSUCqVdHZ2Ymdnh7OzM+vWrSMxMfGl/w+VSiWnONra2ujv78fT0xNTU1PMzc1JTEwkOTl5Usfnvr4+SktLSUhIEIICXq6uWlpaSEtLo7i4WD65LliwgOTkZCIjIw1+EJckCUmSpixKJvN4vSXuw4cP0Wq1SJKEv78/UVFRo8TXZMVRY2MjOTk5DA4OYmJiQkREBK6urpNa52TQH0T7+/sxNjYmJCTkhSHc193vGo0GlUolmzTpv+/v75f9FgBMTExwdnZ+rtJXKBSYm5vLNwsLi1HfW1paYmZmhomJyZRF0Eym6qZTnL1Kmm4kGo2GnJwc7t69K7ea+vj4sHbt2klZeSuVSllc6IWGfjsj0YsMfRRjLokMvXDPz8+nrKxMDn8bGxuzZMkSYmJiCAgImPCEI0kS9fX1PHz4kNzcXB4/fkxjY6P8WXV2dmbJkiWkpqYSExMz7T4zarWaY8eO8ejRI4yNjXn33XcJDQ2d1ueYqwwODlJXVycLiPr6evl/p8fc3BwfHx98fX3p7++nqKhIfn+GhoayYcOGSZ3MGxoaOHr0KI8fP6ampgZXV1d8fHxGpTZeJCSUSqUcJamurqa1tVX4UIxksuGanp4eMjMz5RMiDIeY4+PjiY+Pn/aR4XOJzs5Obt68SXFxMTB8gIqLi2PlypVTPrB0d3dz/PhxamtrgWHr3HXr1r30gDxZ0dLX18eZM2dkZ8uUlBQiIiImFF3P245Wq0WlUtHT00NPT48cUejt7aWvr4++vj56e3vRaDSyoNPpdPL3+ltPT4/s/Ki/svP398fS0hJzc3NMTU1loaDfxtvMdAgbjUbDkydPePz4MTqdDoVCgZeXF9HR0SxYsGBKoquvr4/29nba29tpbW2lra0NlUo1LppkYmKCi4sLHh4esshwd3fHzMxs3HO8rnCaiM7OTgoLC8nPzx9VM+Lm5kZ0dDQRERETFphLkkRDQwOlpaUUFRXx9OlTeSCXsbExzs7OsvFUbGzspMaNvwoqlYojR45QVVWFiYkJ+/btY/HixdP+PHOFnp4eOfJQXV0tHyNGYm1tja+vL35+fvj5+eHm5kZrayuXLl2S618WLFjA5s2bWbhw4UufU19vdvjwYSorK9HpdCxduhRXV9fnCglJkujs7BwlIEaam+mxtbXl3/7bfysEBUw9/zM0NER+fj7p6elyiNXY2JiIiAiSkpKmdQjXXKOxsZHr16/z9OlTYDiHumzZMpKTk6fUmqfVarlx44Y8KtzDw4M9e/ZMm/OlVqvl/Pnzcj1DXFwcmzZtkvPEKpVqVJHj2O8nW+QIwx/8kR0QI7/XpyFu3LhBXl4eMJw62r59OwEBAeO29bxo03SkyKYrvTYd256Nw4RKpaK6unpUv72rq+uEraaTRd9Noxea+tvYq0kYjjpZW1tjY2ODra0tNjY22NjYvLDoeipCSi8GampqaG1tlYWKmZkZgYGBLF68GGdnZ/nv9F8VCgXt7e1UV1dTVVVFS0sL7e3tsi26o6MjCxYsIDQ0lMjISBYvXoyFhcUrRb8mIz4GBgb4+eefqaurw9zcnP379+Pv7/9K/5+5iCRJtLe3y+KhpqZmwpOyo6OjXDzp5+eHk5OTvP8GBwe5ffs2WVlZ6HQ6TE1NWblyJcnJyZOKjCmVSv74xz9y7949BgYGcHFxkWvZRtZaSJI0rlZjbL2RQqHA3d1d7hTx9fWV20yFoODVC0p0Oh1lZWWkp6dTV1cn3x8YGEhycjKLFi2a89Xyr0plZSXXr1+X3e+sra1JSUkhLi5uSqHfR48ecfr0afr7+zE3N2fbtm2v3QUyNDQkFzTqq9EHBwext7dnyZIlDA4OTmoSJQy3So0VCGNFw2Rf79OnTzl79qx8BRkTE8P69evfGpfNkeijMdMtdCa6v7Ozk9zcXNlCWF+MGBISgoWFxYRiZyqpQa1WS39/P11dXfLgMr0gnehwOJHImOx7SJ+aaWpqoqWlZdSANEdHR9zd3XFxcRmX0tBHy1pbW2ltbZUjbfoom5WVFVZWVjg4OMjRlekwCNPXAj1PfAwNDZGbm0tvb69cBPiiKNLrpvkmm357FcGnP9ZrtVoaGxvlCERNTc241JlCocDNzU0WD76+vhPWpkmSRGFhIdeuXZNrfEJCQli/fv2kTBg1Gg0XLlzg22+/pbu7GyMjI0JDQ9mzZw8JCQmYmprKtRrV1dXU1taOOzbq7dH1kRIfHx/RNvoipmNn6B39SktL5YOIs7MzSUlJc6LOYibQ+8PfvHlTdk+zt7dn9erVREZGTpinnQilUsmJEyfkFEVMTAybNm2acJ+NjCyMvI2MMoz9QOjH62q1WiwtLQkPD8fKygoLC4tx4mDsz9PdfqpSqbh+/brsW2Fra8vWrVsJDg6e1ucRjKexsZEbN27IraampqYkJCSwfPnyafebGVuToXcm7OnpGZcW00cFXFxccHFxwdnZGWdnZ8zMzGTR0tXVRXl5OaWlpXR1dcnpNVtbWxYtWsSiRYuwtLQcJ3qam5tla2V9J1FnZyd9fX2yqLG1tcXb2xtvb285QqgXVlMRelNFXwcwODiImZkZkZGR83Lg3siWbn3ESi9cR6bEHBwcWLBggXyzsLB4oVjp6uoiPz+fjo4OFAoFDg4OxMfH4+3t/VKBo9PpKC8v59y5c/JxVe/ou2jRIjo6OmhsbKS5uRmtVjuqENzMzEweyufn54e3t/e4jryxF8pCUIxgOndGZ2cnWVlZ5OXlyVW5lpaWxMXFER8fP6/aTieLVquloKCA27dvy+1kzs7OvPPOOyxdunRSURqdTse1a9e4ceMGg4ODsrmYiYnJKNEwttL5eZibm48SBhqNhgcPHqBWq7G3t2f//v0zMmp9slRXV3P27FlZiIWGhrJp06Y3ug5nrlBdXc3169flGh5zc3OWLVtGUlLSjDtq9vT0yAWfjY2NNDY2ynN1xmJnZ4dWq5XFso2NDWZmZpiZmRESEkJUVBR+fn6jPl+SJFFbW0tpaSmlpaV0d3fT09NDU1MT7e3t2Nvb4+LigpOTk1xcHRoaOi1RsqnUKDU1NXH8+HH6+vqws7Nj586d2NraTkq8TCWi9bL7p/I3+toq/Swb/TFpou6gsR1ZNjY2k77AGhoaoqqqSu7MMTY2xt/fHy8vr5duQ98dUllZSUNDA4ODg0iShIuLC66urhNGZkeu1cHBARsbm5ces0dGnoyNjenv7+f/+//+PyEoYGbUlUqlIj8/n8zMTDlfpg83JSYm4u3tPS3PM5dQq9VkZ2fLeToYro1455138PLykqdLPu+mUqno7OykrKyMoaEhjIyMWLhwIZ6enqPe4CMjCxNFF+zs7CY8MfT29nL06FFqa2tlu+7ExESDpaXUajV37twhLS0NnU6HpaUl69evJyoq6o1Nlc0VJEni8ePH3Lx5k6amJmC4wHrFihXEx8fPakSxt7eXpqYmWWg8fPiQx48fj0tpODg4EBgYSFRUFN7e3nIBqK2tLTU1NZSVlVFWVkZPTw+Dg4M0NzfT1taGpaWlLCIcHR2JjIwkMjJyWl1rp0J1dTWHDh1CpVLh7u7Ohx9+OGeFtF781NTUUFtbS21trSwARxZjj7R79/LywsHB4bmdd88TMUNDQ5SUlJCVlSWny/Q+IWNTc2O3MTAwQHl5OUVFRdTW1tLU1IRGo8HCwkJ2xNSv19LSEgcHB9nYztLScsIU5GQiTyqVivr6empqarhz544QFDCz00Z1Oh0VFRVkZGTIoScYnvKZlJTE0qVLXziud66jnz45Uhi0tbWRnZ1NUVERfX19qFQqbG1tCQgIeGneT98e+fjxYzo7OzE3N2fJkiVs3boVd3d3bG1tX+sqUqPRcP78eQoKCoDhEb5btmwxaMtfQ0MD586dk69IAgIC2LZt26yNZn+bkSSJhw8fcuvWLTlaZGtrS0pKCjExMbP2vtB3aRQWFtLZ2Ylaraa3t1c2lrO0tGRgYEBOp+rTIK2trXR3d2NmZoaVlRVqtRqVSjVKRJibm7N06VKioqLw9/ef9JXyTFBeXs7x48fRaDT4+fmxf//+OVVDNDAwIAuH2tpa6uvrxw3DMzY2xsPDA19fX3x8fPDx8XltQfTkyRMuX75MW1sbAJ6enmzatOmFpnh663O9o2hLSwtNTU1yFNbLy4uQkBC5RkN/m8o5bqRoGikyGhoayMzMlO0EBgcH+W//7b8JQQGzN768sbGRzMzMUX4Wtra2xMfHExsbO+fyhzqdjt7e3hdGFXp6ep6rYoeGhqipqZHH4pqamuLt7U1sbCz+/v7jogojaxYkSSIzM5Nr166h1Wqxs7Nj165dE3ZGTBVJksjIyODq1atIkoSvry979+416FWSTqcjPT2dW7duodFoMDExYfXq1SQnJ89rwTlf0Ol0FBYWcufOHblzy97enlWrVhEZGTkj/4PBwUFKS0spKCiQDd9guHMqNDSUqKgofH195WhVX18fWVlZZGdnU1JSQkdHB729vQwMDMhiw9LSEktLS4yNjfHz8yM6Opr4+Hj8/PwM7pWRk5PDhQsXkCSJ4OBg3nvvPYPWlum7L0YKCP0ArJFYWlrK/g8+Pj6yAdR00N7ezpUrV3j06BEwXLCbmpo6yulVz0ixU1paSmZmJvX19UiSxMDAAEqlUp6++84777Bx40bZX2I60OmGh8hlZGSMsm338/MjPDyc+Ph4IShg9gSFnt7eXnJycsjJyZFbckxMTAgLCyMxMREPD48ZX4NarR6Xghj7c29v76Ta+/TtcfrUg35WhP4GUFBQQFFRETrdsM9CcHAwa9aswd3d/YXbbmxs5Pjx47S3t6NQKFi+fDlr1qyZlgP8kydPOH78OIODg9jZ2bFv3z68vLxee7uvQ0dHB+fPn6eyshIY9hHYtm3bG5kim4toNBry8/O5e/euXA/k5OTEqlWrCA8Pf+2re61Wy9OnTyksLKSiokJuN9XPUIiMjBw1lEulUvH48WPKysp4/Pix3MqsF/pqtVrOZff39yNJElZWVhOaqBkZGeHs7IyHhwfu7u7ybabHvY+dGBoTE8PWrVtnPVKiVqupr6+XT8p1dXUTGpctWLBgVPTB2dl52lOQg4OD3L17l4yMDHQ6HUZGRiQmJrJq1SosLCxk/4fa2lo53dLS0kJvby81NTXynA1jY2PMzc2xtLTE19eXwMBA9uzZ89Lj6lRQqVQUFBSQmZkpD9/Tp++Tk5Px9PQURZkjmW1BoUer1fLw4UNZaerx9fUlISHhldIhkiQxODj4UrEwcrzwizAyMppQJIy86XvrX0ZnZyd37tyhsLBQFiqhoaGsXr36hWONh4aGuHLliuzt7+npye7du6fFAbOtrY0jR47Q1taGiYkJ27ZtIzIy8rW3+zroW8WuXr1Kf38/CoWC+Ph4UlNTxRjuWUKtVpOTk8P9+/flojtnZ2dWrVpFaGjolE6Ger+IoqIiSkpKRhXxubq6EhkZSXh4uHzs6evro6KigrKyMiorK+UIoEqloq+vTzZJs7OzQ6FQYGlpSVhYGJGRkXh5ecmDoxobG+XajKampglPnjBcmzFWZOi3/brodKPncszW+HF9l83I6ENTU5N8QaPHxMQELy8vfHx88Pb2xsfHZ0YjxTqdjtzcXG7duiX/P4KCgkhNTUWtVo8SEPqLTUmS6O7upqamRp63YW9vT0BAAENDQ/Jrio+PZ/369dMWPXleg0FsbCwJCQmjzpVCUIzAUIJCj943Pysri4cPH8pvEH06JCYmBhsbm1EpiJECQf+9/uvYnN/zMDU1HScOxgoHa2vraf/wt7W1cfv2bUpKSoDhq7OwsDBWrVr1wkKxsrIyzp49y8DAAGZmZmzcuJHo6OjXXp9KpeLkyZNUVFQAyDMKDJ1q6O/v58qVKxQWFgLD74dNmzZNunNG8PoMDQ2RlZXFgwcPZBHu4uLC6tWrCQkJeeH/oauri6KiInlegh5ra2siIiKIiIjA3d0dhUJBd3c3ZWVllJeXU11dLQtujUYjf541Go1cgW9sbExQUJBsPPWy96reh0IvLvRCQ5/eGYulpeUogeHh4SH7Q0wWtVrNiRMnKC8vR6FQsGXLlhkb8qXRaGhsbKSurk4WECNHsuuxtbWVow/6wtbZ+pw/ffqUK1eu0NLSglqtxtjYmMDAQNnyfKw5mj7y1NHRwdDQkFxsHhISgqmpqRzxtbGxYceOHdPiLCpJEtXV1WRmZlJeXi6/DxcsWCBbIEzUSi8ExQgMLShg+MDV09MjF7vk5+fT1dWFSqVCrVbj6OiIk5MTtra2kzqZ6A2ZnicUbG1tDT6murm5mdu3b1NWVgYgTyJdtWrVcwsSlUolp06doqqqCoAlS5awbdu2176qGBuW9ff3Z8+ePXOirqWyspLz58/L4cbFixezefNmHB0dDbyytweVSkVmZiZpaWly652rqyurV68eJfAGBgZkG+uRRdimpqYsWbKEiIgIFi5ciEKhoLW1lfLycsrLy2WDOBi+itXXOgwODmJqaipv39fXl4iIiGkZrKdfr15g6G/6IWBjMTExwdXVFXd3d9zc3GSxMVHUrK+vj8OHD1NXV4eJiQm7d+9m6dKlr71ePfrog15ANDY2jqvlMjIywt3dXRYP+oLE2T7mtbS0cPLkSdkWfWBgQB44NzLSZWVlhY+PDx4eHvT398uF6TC876Ojo1m6dCm3bt2SW55DQkLYunXra/uoqNVqSkpKyMzMlLueABYuXEhSUtJLTRofPnxIWFiYEBQw810efX19o6IIYyMK+javsX/X2tpKfX39qD51Ozs7Fi1aRFBQEE5OTuPEgt6oZj4ZaTU2NnL79m05QmBkZERERAQrV66cUFjoCxhv3ryJVqudVoVeXl7OyZMn5SuCuVBXAcMf+Pv373P//n20Wi2mpqasWrVKFG3OMoODg2RkZJCRkSF/ZhcsWICfnx99fX08efJEPrEpFAr8/f3luggzMzPq6upkEaHvKtFja2uLJElyWkPPggUL5IjGbIhIjUZDS0sLzc3No4TG8zxg9A6d+puZmRlnz56ls7MTS0tL9u/fj6+v72utp6mpaZSAmMi7w9raWk5bTHfx5FQYGhqivr6eR48ece3aNQoLC1Gr1fJMGT8/P0xNTXF2dh5Vq2FtbU1eXh4ZGRlydMXCwoK4uDgSExMpLy/n6tWrqNVqzM3N2bx5MxEREa8lkJRKJdnZ2eTm5sopGFNTUyIjI0lMTHxhKlqSJJ49e8adO3eoqKgQw8H0vKqgGBoaeqFI0Bc2TqT2J8LMzGzCiMLAwABPnz6lsrJSdimztLQkOjqauLi4N6a9sKGhgVu3bvH48WNgWFhERkaSkpIy4Wtsamri5MmTcoFSfHw869ate213y9bWVo4cOUJ7ezvGxsZs2bKFmJiY19rmdNHW1sb58+flKmsXFxe2bNnyRs0+mA/09/dz5swZLl68SGNjIxqNBmtra/z8/AgLCyMqKoqwsDCsrKyoqqqioqKC8vLyUXMR9MO3gHF1TTY2NoSFhREREYGHh4fBU1ySJNHV1TVKYExkyqVUKikuLkaSJFxdXdmxYwdBQUGyJfjLukz0tQ964aB3GJ0o+uDm5iY7fPr4+ODo6Djr+0m/X0YWejY0NFBbW0t1dbW8bjc3N1asWEFISIgcMdFHFZRKJRkZGeTm5sqizc7OjqSkJGJjY1GpVJw5c0aen+Tv78/OnTsnZb39vDXX1NSQlZVFWVmZfH6yt7cnISGBmJiYF0a/JEni0aNHXLp0iUePHtHX14dSqeT06dNCUMB4QaGvVRgrFMaKhcm6NioUCtnmdqRYGPv1ZQV3/f395Ofnk52dLec+FQoFixYtIj4+nkWLFhm0x3y6qK+v5/bt26OExfMiFhqNhuvXr5ORkQEMX83t2rXrtbsiVCoVp06dory8HIDY2Fg2bdo0Z0ZUFxUVceXKFfmqIjIyknXr1s1Zg6A3AUmSaGpqori4mOLiYnp6euTOgdbWVpycnOSTnI+PDxqNhsrKylHHCXNzc7y8vFAoFHR1dY2KUpiZmbF06VLCw8MJDAycF5/l/v5+OZKRk5PDtWvX6OnpwcbGhvDw8FHiXt9lMjJl4uTkJAsI/W2i2gd99EG/bz09PafdFn8yqNVq2UpdLyBGFk+2tLRQVVWFJEnY29sTGBjIrl27iIuLGxdJbGlp4cGDBxQXF8sndRcXF5YvXy53FBUXF3Px4kV5hPy6detISEh4JeGkVqspLi4mKytrVFrD39+fxMREgoODx73ntFotHR0dtLa20tzcTGFhoZwWkSQJIyMjPDw8cHV15b/+1/8qBAX8RVD8l//yX9BqtZNul4ThA4Q+zfA8sTAV29XJoNPpePLkCVlZWfJcAhiu1o6LiyM6OnpO5P5fl7q6Ou7cuTNKWISHh7Ny5cpxHR6VlZWcPn0apVKJQqEgJSWFVatWvVY6QJIk7t+/z82bN5EkCS8vL/bs2fPKVwbTzcDAADdu3CA3NxdJkrCwsCA1NZXY2Nh5cTKaL7S3t1NSUkJxcfGo4koLCwtCQ0MJDw/HwsKCU6dOcevWLVpbW+X2TV9fXxYtWiQLBL3vgR5jY2MWLVpEeHg4wcHB8ypVqWesr8vChQtZtWoVHR0do9Im/f39sl+C/tbX14epqak8ME1/4RUYGIivr68sIgwVfeju7h6VapmoU8TY2FgesqWfuuni4kJqauq4lIQkSVRVVZGWljbq2O3v78+yZctYvHgxCoWC3t5ezp8/L1/QeHl5sWvXrldyN+3s7CQnJ4e8vDw5CmZqakpERAQJCQm4ubmh0+no6OigpaVFHiCnn0KrT4HV1NTIHUpGRkb4+fkRFxcnp2vWrl0rBAX8RVCsWbMGZ2dnnJyc5AEuEwmEkd8buo2vo6ODnJwc8vPz5TeLsbExISEhxMXFjTLGma+MFRYKhYLw8HBSUlJG5fgGBga4dOkSRUVFwLDt965du3B1dX2t53/y5AknTpxgYGAAS0tLdu/ezaJFi15rm9NJfX0958+fl502PTw82LJli/CueA16enooKSmhpKRkVEu3iYkJwcHBhIWFYWNjw9OnT6moqJD3vUajob6+ns7OTqytrWVhZ21tjaurq5yy1JsBhYSEzLgPxEyi0+m4dOmSPOwuLi6OzZs3Y2RkxMDAAPX19fLJuLKykra2Nnp7e+WbvmNrpI2+fmaJi4uLHM3QRzSme4jbSF4UfRiJfpiaj48PlpaWlJSUyOkIc3NzVqxYQVJS0ihxqNVqKSkpIT09XY4OKBQKli5dyvLly+U6Lb1z64ULFxgYGMDY2JhVq1axYsWKKbcqP336lKysLB4/fixfINvb2xMcHIyHhwdKpXKUcBibVtLpdDQ3N1NfXy97DTk4OLBs2TLWrl07KhUnujxGoN8ZX3zxBba2tvIAHhcXFwIDAwkMDMTf339OWcSORa1W8/DhQ7Kzs0cdAF1dXYmLiyMyMtLg4ud1qa+v586dO7KrnEKhICQkhJUrV+Lm5iY/7uHDh5w/f17+QL7zzjskJye/1lV7V1cXv/zyCw0NDSgUClatWsWqVavmjFjT6XTk5ORw8+ZNuVgwJiaG1NTUNyJaNRv09/dTVlZGSUkJz549kw/CRkZGBAYGsnTpUiwtLeWaiJH1AwqFAh8fHxYtWoSJiQlVVVXcunWL6upque3TxcWFjRs3smvXrjei7kmlUnH8+HH5hBUTE4O7uzv19fXU19ePKzqFYUHm4eEhRx70A6v0ttHNzc00Nzc/N51sa2srCwz9zdnZ+ZX8ejo7O0elWiaKPuhD+noB4e3tjb29Pb29vdy+fZu8vDw59B8bG8vq1atHfd4GBgbIzc0lKytLfr+YmpoSExNDUlLSqCLbvr4+Lly4QGlpKTB8YbBz585Rx7aXMTAwQEFBAdnZ2dTV1dHX10dfXx+2trY4OTlhZGT03Oi7qakpLi4uODo60tHRIX8GzM3Nsba2JikpiYSEhAnPg0JQjEC/M44ePcqCBQuoqqqSLU31KBQKPD09ZYHh4+MzJ/LpE9HQ0EBOTg7FxcXywczMzIywsDDi4uLw9PQ08Apfj4aGBu7evSuHA2G4fXTlypXya+vp6eHs2bNyVMPHx4edO3e+lhmWRqPh8uXL5OTkALBo0SLefffdGb1qmiq9vb1cv35dnlUi0iAvRqVSUVFRQUlJCU+ePBl1QtGnK8zMzKipqeHJkyeyUyUMH4D1o8NNTEyorKykvLx81MnQwcEBU1NT2tra5OOJra0tycnJxMXFGaQO4HXRF/V9/fXXVFVV0dfXh4+Pz4QiacGCBXh5eckCws3NbVKeGV1dXXK6RC8y9G3TYzE2NsbFxWWc0BjpoTM4OChHH/S3iYy+Ro5y17dwjow0qFQqHjx4QHp6unxsXbJkCWvXrh2Vjujo6CAjI4OCggL5PWNjY0NiYiJxcXGjolKSJFFSUsKlS5fo7+/HyMhIjkq8bF9ptVra29spLS3lwYMHlJSUoFQq5e14eHjg6ek56hilFw76CaT6r2ZmZuTk5JCRkSHvG1tbW5YtW0ZsbOwL36tCUIxAvzN++9vfsmjRIrZs2YKDgwPPnj2jsrJSDtWNxMTEBF9fXwICAggMDBzXUzwXGBwcpLCwkJycnFEe9Z6ensTGxo4rmppvNDc3c/fuXUpLS+WD9aJFi0hJScHPzw9JkigoKODy5cuoVCpMTU1Zu3btKxc16SksLOT8+fOo1Wrs7OzYs2fPC4f4GIKamhouXrwoh1fd3d3ZvHnza7XvvSmo1WoeP35MSUkJjx49GmUo5ObmJl8sNDY2UlNTM+rCwtbWlqCgIDnXrXe0HNmhYW9vT1hYGGFhYbJxlVqtJj8/nwcPHtDd3Q0M+w686KpvrtDf3y+fjOvr6yktLSU7O5uhoSFMTU1ll09LS8tR4sHLy2ta0zkqlUpuZx15GxvN0Lfe6ls11Wo1Wq0Wa2trrKys5JO0fsiXPvLg5eWFvb39hMcGjUZDTk4Od+/elU+2Pj4+rFu3Tv5M6YVWeno6FRUV8vvGzc2N5ORkwsLCxl2E9vT0cOHCBfniyM3NjV27do2zzlar1bS3t8v1Da2trTQ1NVFRUUFdXd2oaJm1tbX8f/Dw8JDFg/7m4OAw6jXqu0xycnJk8ePo6MiKFSuIjIx84YVzX18fZWVl5Obm8q/+1b8SggL+Iig+/fRTuXo4ISGBNWvWyB90pVIpi4uqqqpxlcgWFhb4+/vLAmMm/N9fFf0bPScnh9LSUjlXZm5uTnh4OHFxcdPq/T7btLW1ce/evVHV0n5+fqxcuZLAwEC6u7s5e/asPB/D39+f7du3v1bYubm5mV9++YX29naMjIxYt24dSUlJc+Z/DhOnQSIiIli3bh22trYGXt3sotFoePr0KSUlJVRUVIyKNDg6Osr1Dfp88kjc3NwIDg4mKCgIjUZDaWkppaWlo/LrNjY2hISEEB4ejre393PfB1qtlsLCQu7fvy9fcZubmxMfH09SUpLBu3T0ng968VBfXz8qMtDS0iI7KHp6erJz506Cg4MNWjhZV1dHcXEx5eXlPH36lJqamgk7RSwsLLC3t8fb25vFixfLtQRubm7jTrIjt19cXMzNmzflzjpnZ2fWrl1LcHAwCoVCHqGQnp4u19LAsAFdcnIyAQEB47at79S6fPmynJpduXIl8fHxdHZ20traSltbmyweOjs7ZYEyMDBAQ0OD3K5sbGyMra0twcHBJCYmEhYWhqur63PFkZ62tjbS0tIoLCwc1976Inv53t5eysrKKC0tldMiKpVK+FDo0QuKv/7rv6ahoQFJkvDw8MDLy4sNGzYQHh4+rlK3ra1NFhfPnj0bZ0xlY2NDQECAfJsrrob9/f0UFBSQk5Mz6kDh5eVFbGwsYWFh8zZq0dnZyf379ykoKJA/IJ6enqSkpBAcHExubq5sDDMd0QqVSsW5c+dkC/ElS5awY8eOOVdk19fXx40bN8jPz0eSJMzMzFi1ahVJSUlvtCmWVqulqqqKkpISysvLR31Grays5JNIW1vbqKtcY2NjAgIC5EhEb28vDx8+5OHDh6NOVJaWloSEhBAWFoafn9+UIpQ6nY6HDx9y79492UfFxMSEmJgYli1bNiudRDqdjra2NhoaGmTxMFEdAQwPSOvu7qa6uho7Ozuio6PZu3fvrNdlDQ0NyRbb+jXrIz4jMTExwcbGBgsLC0xMTNBqtXR3dz93nomZmRmurq64ubnh6uqKq6srPT09PHjwgObmZmA4OrV69Wqio6MxMjKir6+P3NxcsrOz5feFiYkJkZGRJCUlPdcUqru7m+PHj8tzXSwsLAgKCkKtVk/4WmD4nNPb20t3dzd9fX1ytMXDw4Ply5fL4xkmQ11dHQ8ePBhlre3n58eKFSue64ipVCplETE2aufp6Ymfnx8bN24UggJGt412dXXR0dHB48eP5bqJuLg4du7c+dyreJ1OR2NjI1VVVVRWVlJTUzPOl93BwWGUwDD0FaK+fSkvL4+ysrJRUYuwsDBiY2PnhKHOq6BUKklLSyM3N3dUQdyKFSvw8vIaZQzl5+fHjh07XjlaIUkSOTk5XL58Ga1Wi4ODA3v27JkT7ppjqa+v59KlS9TV1QHD+e0NGzbI4fs3AZ1Ox7Nnz3j48CFlZWXyCUSSJNkPBhhXvW9lZUVQUBBBQUEEBgbS1tbGw4cPKS0tHXWQt7CwYMmSJYSGhhIYGPjagkxvEnT37l25mFrfHr18+fLX7lAa+Tzd3d2jxENDQ8OoSI0efchcHzZ3cXHh2rVrFBcXA5CcnMy6detmPMWrFzz6TpH6+npaWlrGCR6FQoGrq+uodIuzs/O49elPyvoCUH36pLW1dVSHQ3d3N5WVlXR3d2NmZoajoyOJiYmkpKTg7e0tD/gqKiqSj/P6uUtxcXFyvYJ+foo+2tDS0kJ2djbZ2dkMDAzIrZdjO/FsbGzk9ISFhQVNTU08e/YMlUqFQqF4Je8hSZJ48uQJDx48GDV6PDg4mBUrVkyYsu3q6pJFxMhWZxi+AA0JCSEkJARHR0dRQzGSkTtDP1q8oKCAqqoq2Y/f1dWVTZs2sXfv3pdegWo0Gurq6qiqqqKqqoq6urpxHwJnZ2cCAgLw9/fH39/foJX4fX19FBYWkpubOyrc6+7uLtdazOUc7/Po6+sjMzOTrKws+erUwcGB5ORkdDodt27dkvPA77zzDomJia98kGxoaODYsWN0dnbO2RQI/GWS6fXr1+WT6qJFi9i4ceMr9bjPBXQ6HdXV1bKI0PfK63Q6BgcHsbKyQqfTyQdjPW5ubrKI8PT0pKmpSY5EjBQR5ubmBAcHExoaysKFC2ekGFtvY3zv3j05NQfDUa8VK1ZMuQW4v79fFg16ATFyyqkeMzMzORqrv40MlSuVSo4cOUJDQwNGRkZs2bKF2NjY13uxE6A/+erXql/7RN0e+sJJ/Xo9PT1fK1KiN296+PAh165do7y8nL6+PoaGhvDy8sLX1xcTExPa29upq6ujq6sLKysr2Rl12bJlhIaGjjKBamtrGxX56u/vp6KiQn5f2dvbEx8fj7+/Py4uLjg7O8siwtzcnCdPnpCbm8ujR4/kaIC1tTUxMTHExMRMOuKtb1d98ODBqJHnesE6NorS3t4ui4iR82VguGYkJCSEpUuXYm1tTWdnJ11dXXK3zHvvvScEBfxFUJSVlREUFISRkRGDg4MUFxdz//590tLS5KJGR0dHduzYMaXBUUNDQ9TU1MgCo7GxcVzrjpubm1yD4efnZ5CwuX7SXG5u7qhaC1NTU0JDQ4mJicHHx2fOnSRfxuDgIDk5OaSnp8sHVWtra0JDQ+WDF4C3tzc7dux4oX/9y57n7NmzcttXUFAQO3funFNdIHpUKhV3794lIyMDrVaLkZERiYmJrFy5cs6lbCbieSJicHCQ/v5+zMzMkCRJns4Jw+HokakMe3t7uciwtLR01ORNMzMzWUTouzhmi/r6eh48eEBZWZl8nPD392f58uUThqRVKhWNjY2jBMREU0T1dtUjxcNEV/J66urqOHr0KD09PVhZWbFnzx4CAgKm5TXquy5GCoiJ6h7MzMzw9PQcFTGZ7nlL7e3t8vRjfQtodHQ0SUlJdHV1cf/+fTIyMmhsbKSzs1MWqTY2NkiSxMDAgPx31tbWo242Njb09fXR2Ngo13Bs3LiRtWvXjhNBSqWS/Px88vLyRglaf39/4uLiWLp06aQjYiqVitzcXDIyMuSCTTMzM2JjY0lOTpb3od7dUy8i9KJDXxexYMEC3NzccHR0ZGhoSBYQYyN8fX19/Of//J+FoIDRXR52dnb4+Pjg7++Pn58fHh4eNDc3c+HCBc6dOye/6e3t7dm8eTPr1q2bsOjmRQwMDFBdXS0LDP0/UY9CocDd3V0WGL6+vrMeIejv76eoqIjc3NxRHSLOzs7ExPz/7L15cGTndR1+ekN3Y2sA3ehGY9/3Gcw+5HATKYmSJUuiw8ilVCpekrKdxEnFjiuR7FTF1q+sOKokFf8RuxJXXHb+cMVOaGu1KFKiSVHDIYezAzPY931fG2j0/vsDOnfue3gNYBZuynxVr7qBwfTy3ve+79xzzz33FLq6uj5y/gZU2l+6dEkW3JycHPh8PiwuLkpb6GeeeQZPPPHEfdHZmUwG165dw/e//30kk0kUFhbixRdfRE1NzUP+Ng9nrKys4NVXX5XGbLm5uXj22Wc/lGWmViCCvR+2trbgcrngcrkM4sDCwkI0NTWhubkZdXV1cLlcmJ6eFhChF+6cnBw0NzcLiPigXSuXl5fx1ltvobu7W8B9IBBAc3Mz8vPzxXRoZWXF0lsgEAgYNuOysrIjA6Pu7m58+9vfRjKZRDAYxD/4B//gvnVgFHpqAGGumgP2AA9TFzxKS0vfs3m4sbGBH/3oR7h586YwyB0dHTh//rwIvW/cuCFlmMlkEuFwGIFAAKlUSjweIpEIdnd34fF4kJubK+xFMpnE1NQU4vE48vLy0NTUhM9+9rNoaGhAaWkpvF6vuB6b2Qiv14sTJ07g9OnT98Qcbmxs4PLly4a+IPn5+Xjsscdw5swZeDweEbLeuHEDN2/exNzcHHZ3d7G7u4tYLCZgqaSk5EA9HQNvpnX+6q/+6hGgAO4Cit/93d/d928ul0sARjAYxI9//GN873vfk7ayZWVlOHnyJB5//HGcOHHivk7m9vY2xsfHMT4+jrGxsX03m81mQzgclhRJdXX1+yaG4uS7fv06bt++LZoEu92OlpYWnDx58iPXQ4SCuIsXL4rgKplMYmdnB06nE7m5uQiFQvjCF75w354d8/PzeOmll7C8vCxGWE8//fSH9jwNDw/jlVdeEfAYDAbxqU99Cg0NDR/o50qn0xgbG0Nvb6+Bil5dXUUkEoHdbkdRURGKiorEhZIq/ubmZoRCIWQyGUxNTaG3txd9fX2GErsPG4jQI5VKYWFhAYODg/jRj36E69evY3NzU8yG6JPgcDjg8/mE/q+oqEA4HL6vICSdTuOHP/whLl26BGAv5fJzP/dzR15vtO6BAGJhYWGfCyOwx/bqtEU4HH5fBOGRSAQ/+tGPcPHiRUQiEezs7KCoqAjl5eWYnZ3F6OiorO/AXU1JKBRCQUGBpCcCgYA8LygowPr6OhYXFzE1NYXXX38dt27dws7OjviVBINBgy/G5uYmNjY2DMxGW1sbzp07h/b29ntixebn53Hp0iXcvn1bwFFRURE6OjoQDoexvr6OwcFB9PX1YWRkBOvr6/J3drsdJSUlCAQC8Pv9cg84HA4UFRWhuLhYHp1OJ5aWlqTKhNv9oyoPNQgoSGeNj49jYmICExMT+1TBTqcTgUBATGy2trZEXFNZWYnW1lacOnUKTU1N9y3Y2traEoAxPj6+r4yNhiXUX7xfACMWi+H27du4fv26wY2zoKAAJ06cwMmTJz9SDoCZTAZDQ0N46623MDExIfTfxsaGlJI99thjePbZZ+9roYvH4/je974nJlPV1dV48cUX4fP5HvI3eTiDYrPXX39d5n1TUxOef/75+04D3c9IpVIYHR1FX1+fgIitrS2srq5ia2sLbrcbgUBAQITX60VjYyOam5vR0NAgmonx8XH09fWhr6/PQNFSE9He3o6GhoYPBYhIpVKGhdpqI6Y19NLSkvQQCgQC+NjHPoaPfexjD1xyGo1G8dJLL4mN9FNPPYXnnnsuK/tKt0kCB352K6Fnbm6ugXkoLy9/XxjOWCyGlZUVLC8vY3p6GpcuXUJ3dze2traQyWRQVFSEyspK8dqg1opz6syZM+jo6BB9w0Hpy0wmg/7+frz88ssCWo8dO4YTJ04gEolgbm4O3d3d6O7uFmE0sBe0hkIhhMNh5Ofno7i4WMymePj9/n0AIx6P48aNG3jjjTcwPDwsLENeXh4CgQA8Hg/W1tawvLwsPTk42Om2pqYGTU1NCAQCKC4uNoCHgoICqYLq7+9HX1+fYd0H9io82traUFlZKSX6jwBFFoVqJpPB0tKSAWDohWlzcxNDQ0PY3NxEPB6H0+lER0eHINmuri6cPHnygcVum5ubBgZDo2fACDCoGn6vUySLi4u4fv06uru7DaCrpqYGJ0+eRHt7+0eq/HRqakpKqeLxuNyg1dXVaGhowOc///n7jtZ7enrw3e9+F7FYDB6PB5///OfR3t7+kL/BwxvRaBRvvvkmLl++jHQ6ndVW+GGORCKBkZER9PX1YWBgQAAEQYTP55Paes73pqYmNDU1oaKiAna7fR8Q0fPS4/EYQMQH6XKbTqextLSEubk5zM7OYnZ2FvPz8/sqw4C9ja28vFyYh/Lycni9Xty6dQtvv/22BBsOhwNdXV14/PHH7wv8LSws4C//8i+xtrYGl8uFF154AR0dHYa/2dzclM9LAKENvTioe9CfOZvPw8MYTHtRCMljZWUFm5ubknqYnp4WgFZYWCimY5ubm3C73cjNzUVJSYn04riX0t2NjQ1873vfk9RhcXExPve5z6G+vh4rKyuSXuD+kUwmUVJSgoqKCuTl5WFlZQWLi4sG4Ww6nUYsFpNUhMvlEm0QwWcymRSxMXufxONxLC8vY3V1FQ6HAx6PBx6PB8XFxWhpacGJEyfQ2dlpCVJ4Pufm5uQ+0ilvm82G6upqtLa2oq2tTc7RoyoPNY56MjKZjHicE2DQInZ0dFTyaS6XC9XV1SgrK4PP50NjYyNOnTqF9vb2h8IksB6cIMNsScsUSU1NjTAY75XQLplMYmBgADdv3sTw8LBQYLT6PnHixEdKyKnz1ouLixgcHITdbkdVVRWef/55/MzP/Mx9bapra2t46aWXBOGfOnUKn/70pz/UoGtlZUVU78BeZP/000/j/PnzD2VDjsfjGBoaQm9vLwYGBgRArKysIBaLCZ1cVFQEj8eDhoYGNDU1obGxUcquE4kEhoeHBYjoqoDc3Fy0traivb0ddXV1H4jnhvZ6IICYn5+X1KEebrdbNmIeB23E6XQaAwMDuHTpkqGsr7m5GRcuXEBNTc2R7rs7d+7gm9/8JhKJBIqLi/GlL30J+fn5Ah54WIkmHQ4HysrKDODhIKHngwy6RWrAwEcrVoTVdouLi9LRtKKiAg0NDdjd3cXa2pqcn3A4jHPnzqGzs/OeGKt0Oo3Lly9LxZjdbhdAMjw8jOvXrxvKNPPz84XNZbnl+vq6iB1pKjY7O4vFxUVsbW2JfiOVSoleiOkKp9MpVuMulwvpdBo+nw8+nw9erxeBQEA2/6qqqqzXJZVKYXJyEv39/ejv7zdoi+jL0tbWhpaWFksm7BGgUONBTsb6+jomJiYwPDyM119/XaojotEonE4nHA4H8vPz4fP5EAgE8Nhjj+Gpp556qF1AjwIwQqGQAIyampr3pPJgc3MTt27dwo0bNwyfwe/348SJE+jq6nroCu33amxtbeHy5ct45513hOpzuVxoaGjAL/7iL95XSWgqlcLrr7+Ot956C5lMBn6/Hy+++OKHvrfK+Pg4XnnlFXEBLCoqwsc//nF0dnbe8zmIRqOSy71z5w6Wlpawuroq5baBQADBYFAiyMbGRjQ1NaGqqkoAwe7urrzG8PCwYXPOz89HW1sb2traUFtb+75qVu4FPLBcU4OHkpKS+14TJicncenSJYPlc3l5OS5cuJC1OiCdTuO1117DG2+8gUgkgoKCArS2tmJpacnSYIl+Dxo8BIPBh8r2kG2wAg7ZTJ8Aow6gsLAQc3NzGB4eht1uh8vlklTC8vKyoStzR0cHzp07h4qKins+99PT0/jud78r9vZVVVU4e/Yspqam0NPTg2g0ilgshlgshtLSUlRWVqKgoAAbGxtYX1/H5uampYmYHgQ3FLOm02kBFy6XC6lUap+pYl5enpREU7vBnh3FxcVyT8TjcYyMjKC/vx+Dg4MGtiknJweNjY1oa2tDU1PToYz3I0ChxsM8GVNTU3jppZdw9epV8bXIy8szXPicnBxUVlbi/PnzePbZZx+6qHFzc9MAMKy6/gWDQdTU1MjxMI22aPV948YN9Pb2SvRgs9nQ0NCAEydOoKWl5UORuz5sxGIx3LhxAy+//DKuXr2K7e1t2O12dHV14Z//83+Opqame37NsbExfOMb38Dm5ibsdjuee+45XLhw4UMr2ATu+le89tprEqmWl5fj+eefR21t7YH/NxKJoL+/H3fu3MGtW7ewvLyMtbU1bG1tSRRFkRubbTU2NhruxUgkIn0zxsbGDNqCoqIiARHvFxuWSqUM4GFubu5Q8KABhN/vf08+58rKCt555x3cuHFDUig+nw/nz5/HqVOnAABzc3MYGRnBN7/5TYyMjCAajaKqqgr19fWGz8QqER5lZWUPjVEjLa9ZBj5anUOO3Nxc+P1+EUT6/X5hsZLJJN59911cunRJSjkzmQzy8vL29Vo5c+YMTp48eV+6k2g0itdeew1XrlxBLBZDIpFAUVERVldXDRUTDOTKysqybsgUPuqjuLgYhYWFWFpaQnd3NyYmJpBOp7GxsQGbzQaPxyNMdywWw87ODvLz81FYWAi3242dnZ2s5zCdTiOVSmFnZwdbW1tSmeL1epGXl4eWlha0traivr7+ntbnR4BCjffiZExMTOCVV17B5OQkNjY2kEwmkZeXh9nZ2X1iq2AwiJMnT+L8+fNoaGhAeXn5Q91st7a2JEUzMTGxr0wV2LPW1QzGYT7wRx3xeBy9vb24ceOGmIQBezntjo4OnDhx4sDeBx+WkU6n0dPTg7/4i7/A1atXRVvw5JNP4hd+4RfQ0NBwz6XD3/nOd8Szora2Fi+88ML7Yrn8ICORSODtt9/GxYsXBSi2tLTgE5/4hCF3v7q6iv7+fly7dg23b9/GysoK1tbWpEmTBhBaC6Ej6bW1NcnjTk1NGUojS0tLBUQwF/5ejVQqhcXFRWEd5ubmsLCwYKl5sAIPbBv9fo6dnR289dZb+Lu/+zuhzqPRKHw+HwoLCzEyMoJYLAaHwyGbiBk8PKgOK51OY319HSsrK/uAg1X6hINsgxk4BAIBS2Y1FosZgEQ8HhcvEq/XK3OjoaEB586dQ1NT05GuRzqd3peSoHZlY2MDa2trcDgccDqd8npk2cLhMIqKiuB0OuHz+faBBh4UPnLs7u7ixo0bePfdd4W9oxYiFArJ/kS2lD1mdBqW3VoXFxextLSEkZER3LlzB0NDQ/v0dx6PB4FAAGVlZaivr0coFDI0Ejvq3H0EKNR4r05Gtqiura0Ng4ODuHz5MkZGRgRcOJ1OoRRbW1tFYFlVVfVQUxTb29uYnJwUgDE/P7+vjr2wsNDAYDyMZmerq6u4desWbt26ZTDe8fv96OrqwvHjxz/0Gyqb+vz3//7f0dfXB2BPOPfkk0/ic5/7HDo6Oo6cq2c31JdffhnxeBxutxuf/exn9/WO+TAOlt5du3ZNaNv6+nr4fD7cvHkTg4ODWFtbM7RBLi0tRVVVFY4fP47GxkY0NDQYIsRMJoOFhQUBESzp5aioqJB88Hvl6plIJLCwsCCsw9zcHBYXFy3LHt1utwAHgoj3ink4bOzu7orXA4HPysoK0uk0FhYWMD09jUgkgkgkgs3NTfj9fnR0dODXfu3XcOzYsfvWWGUyGezs7OwDDSsrK1hdXbU8bxx5eXkCFDR4KCoqOtI9FIvFcPnyZbz99tvY2dnB+vq6gfWy2Wzwer04efIkTp8+Db/fb/j/1CQQMKyvr0s6wpySiEQiGBoawvLyMiKRCOLxuOgUPB4PysrK0NHRga6uLoRCIfh8PhQXFyM/P/9IG/LKyoqAovn5eSwvL2N7e1v0KR6PB3l5eWhubj6UQWCp/8DAAAYGBkRUmclkxJSrpKQEeXl5whRZgWPgbjWIuWNpSUmJ4Ro9AhRqvFcngyMej+PSpUt46623hIrq7OzExz/+caRSKbzxxhu4ePGiNLqJx+PihVBWViZlctXV1XI8zM5+u7u7mJqawvj4OCYnJyVXp0dubi6qq6sF5DxIu3baDN+8eRN9fX0GQVVdXR26urrQ1tb2vjceupeRyWRw8eJF/Nmf/RnGx8eRTqcRCoXQ1dWFp556CqdPnz4yCFxdXcXf/M3fSClZR0cHfvZnf/ZD71iZTqdx8+ZN/Nmf/RneffddmbsFBQVC3QaDQXR1daGzsxONjY375k06nTaIwTTQZDl2a2srWltbH3q5bSwWw/z8vAE8LC8vW+a1vV6vgAYeD6J5eJCxu7trYEvm5uYs05rAHr1fXl6O0tJS/PjHP8a1a9ewubkpYr3q6mo89thjhwJhen8QLGgAYc7h6+F0Og0eB3z0+/33Pb+j0ajom7a2tjA/Py/fiV4PlZWVOHHiBCoqKrC9vW0ACnzO0tGDRiaTwfz8PIaGhqQlOtdBv9+P06dP4/Tp0/fVrZn9NV5++WVcu3ZNQERubi4qKytFbNnS0iIdXbOtuYlEAqOjowIidLWI3W5HbW0tWltb0dLSsu8+YjqFjIY+sqVO7Ha7pJuKi4sxPz+PX/iFX/joAYo/+IM/wO/8zu/gX/2rf4U//MM/BLB3Yb761a/iT/7kT7C2tobz58/jj/7oj/aVPWUb7zWg4Nja2sLf/d3f4ebNm8hkMnA4HDh37hyefvppeDwejI+Pi/UqRUibm5vIyckRKoo3fV5enoALbXDzMEYikcD09LQwGNPT0/smFnUgBBiVlZX3laZhSuTWrVsYGxuT37tcLrS1teH48eOor6//0OoLdnd38b3vfQ/f+c53BIjRPv3EiRM4f/78kcr40uk0Ll68iDfeeAPpdBoFBQV44YUXPnBjKfNIJBLo7u7GxYsXce3aNczPzyMej2N3dxfr6+tiNFVfX4/Pfvaz+NznPrcvT32QGIxUbmtrK5qbmx8aM7e9vb0PPJjFyxx5eXkG1qGsrOw9LXs8aOzs7Bg+8+zs7D7amoPggZ+9vLwcubm5WFlZwV/91V+JG+ypU6eEadPNrU6dOiUVEGbgoM3AzMNms8Hn8wlQ0MDhYaVOeS7eeecdvPPOO1haWsLU1BQ2NjYQCAREpxYKhYSJsOpdYh5Op1PSDzo1UVhYiKtXr+Lb3/42pqamkE6nUVpaisbGRnR2duLkyZNobm6+L0Hq1tYWXn75Zfzwhz/E+Pi4BFR+vx+VlZXo6uqSzd/MqphfZ3BwEIODgxgdHTWs0W63W1q0H0VUaTXYUI5AQ7dTp0Mm52QkEhHL8I8MoLhy5Qp+/ud/HoWFhXj22WcFUHz961/H1772Nfz5n/85mpub8fu///t48803MTAwcCSx4fsFKDjm5+fx6quvShMgj8eDp59+GufOnYPT6UQsFkNvby9u3ryJiYkJaWu7s7OD3Nxc5OTk7Mu9OZ1OaWRTVVWFqqqqhxbhplIpzM3NCcCYnJzcF5U4HA6Ew2FB7/eTpllfX0d3dzdu3bpliLgKCgpw7NgxHD9+/L4igfdjzMzM4Fvf+paY1thsNjQ1NaGwsBCNjY04f/581tbAeszOzuJv/uZvxC317Nmz+OQnP/mBlpeur69L34/bt28bNheWrZ04cQKPPfYYnE4nrl69KtfP5/Ph2WefRX19PYaGhjAwMIDR0VEDxcpOn62trQ9sNMVFkOCBj9k2xMLCwn3gwXxvvV+D5kf6sOrJAewJUc3pFqty5t7eXnzrW99CLBZDfn4+XnzxRfj9fqysrGBmZgbvvPMObt68idXVVUSjUankqKys3AcEmUrQwMHv96OkpOShC6yZSllfX8fc3BwuXryIK1euiLFXMplEQUEBcnNzUVBQkLXiJCcnZx9Y0D/n5eUZrvXKygpef/11/PVf/7VUNXm9Xpw7dw7PP/88jh8/fl8C9s3NTVy+fBmvvPIKbt26JZu/w+FAdXW1sJpNTU1Z102mBAcHBzEwMLDPZKqoqEjYjJqamodeJr2zs4PR0VG8/fbbePvttzExMYGNjQ3s7u4ilUpJuelHAlBEIhGcOnUKf/zHf4zf//3fx4kTJ/CHf/iHyGQyKC8vx2/8xm/gy1/+MoA9KjMUCuHrX/86fu3Xfu3Q1yag+Ou//mtUVVXJTfIw0bXVGB4exg9+8APJFRcVFeG5554z5NDX1tZkk2VERUq2pKQEXq8X6+vrlgYzzFlXVVWhurr6oVG0dJSkDmNyctJywS4tLTWkaY4a5WUyGczMzKC7u1vKrzhCoRCOHz+OY8eOfehKUNPpNK5evYrXXntN8tZutxu1tbVwuVwIBAI4f/48urq6DgQIiUQCP/jBD/Duu+8C2LvOL7zwAqqrq9+X75HJZNDb24sf//jHuHr1KkZHRw1pALfbjebmZpw7dw6PP/44amtrDQt5Op3GjRs38Ld/+7cYHx/H8vIyUqkU6urqRGNAkx3S7vfDQLFMc35+3gAgrO4FYC8CJGjgJvxBNG4j6NGAZ25uLqtQsaSkZB94OChYYOfOb33rW3jrrbews7MjCn7S9nrQaGt6ehrb29vwer3Izc1FbW2t9IA4zCXyXgcFj0w/WD1GIhFMTk5ifHxcAiqXywWfz4eCggIEg0E0NDSgqqoKxcXFAhI0ePB4PIeuOdFoFHfu3MG7776Lt956SzbqnJwcPPfcc/jSl750ZE8PDq5h/f39uHjxIm7dumVglgKBAJ588kk8//zzaGlpybr5J5NJjI2NCRNhLp2trKxEc3MzWlpaDNbeDzKSySSWlpawsLCAxcVFzM7O4s6dOxgdHcXq6qqkiex2O0pLS6Vp22/91m99dADFL/7iL6KkpAT/9b/+V3zsYx8TQDE6OoqGhgZcv34dJ0+elL//whe+gKKiIvyv//W/9r0Wa4M5Njc3UVVVha985SuGvL3T6URxcbEBifPxYUUx6XQat27dwuuvvy6bcllZGT7xiU8YKgfYj+DWrVu4c+eOgSEgM1BQUICVlRVMTk5a5lRzc3MFYFRVVT20ahKqiicnJ+XQ7mocBQUFBoARCoUO3UhSqRSGhobQ3d2NgYEBEXnZbDbU1tbi+PHjaGtr+1C1V49EIvjBD36AW7duIRqNYnl5GV6vVzZTj8eDkydP4ty5cwc2XBodHcW3vvUtKRe7cOECnn322ffE5XFtbQ3vvPMO3n77bXR3d++LjAOBAE6cOIELFy7g3LlzluV21ENoMdjMzAwmJyclomxvb8ff//t/H2fOnLmn+ycej2NxcdEAHLJVWrDJlAYOoVDoA9HkZDIZrKys7Eu3WIEem80mFQKaMck2t5ma0NqG1dVV6b1DgGIuCbXb7VnXtc3NTbz77rvo7e0VEMlW26dOnToyqIjH49jY2DAABP2cPUmsRjQaxejoqJgFZjIZaVne0tKCc+fO4ezZsw9UxppKpTA8PIxbt26hv78f09PTGBsbQzKZRHFxMZ588kn84i/+4oEpB/PY3d3F6OgoBgcHcefOHQwPDxtasPt8Ppw8eRKf+cxncObMmaxr30GpDJfLhfr6eqnueBC79XQ6jbW1NSwuLgp4WFxcFDEv9SmLi4tyn3k8HlRXV8v6xUB1e3v7oyPK/Mu//Et87Wtfw5UrV+DxeAyA4tKlS3jiiScwMzNjMAj61V/9VSndNI/f+73fw1e/+tV9v//rv/5r7O7uitHOQQpll8tluBH1c90y+agjkUjg8uXLuHjxooCFuro6fPKTn9xnfJRMJjE4OIhbt25haGjI0OSloaEBx48fR1VVFRYWFjA1NYXJyUmxadWDFsYEGJWVlQ9N+LazsyPvPTExgbm5uX3nkzoMpmkqKysPXPSj0Sh6e3ulNpvD6XSipaUFx44de6AeKg97TExM4G//9m/lhkylUtJhENjbQBjpmz0AOHZ3d/H9739f+oGUlpbihRdeQEVFxQN9NppDvf3227h27RrGxsYMC5fT6URTUxPOnDmDZ555JmtZ7O7uLoaHhzE4OIihoSHDRulwOFBfX4+amhqsrKwYmss1NDTg4x//uKWpVyQSEdaBR7aOmjk5OSgrK5MjHA6jtLT0A7HWZnmpBj3UmJgHQQ9BQ3l5OUKh0L4NMh6PG0CDBg/mPkMAsLS0hIGBASSTSeTn5+Opp55CZ2enrE9+v/9IVRSbm5u4evUqrl27JloEp9OJY8eO4ezZsygsLNwHFvTP2VgiPdjUjEcqlcKVK1fQ09MjHi3FxcVobGzEU089hTNnzqC8vPy+A7lMJoPZ2Vl0d3fj9u3bItYcGhpCJpORSo0XXngB9fX1R3q9lZUVDA0NYXBwEOPj41hfXxeXS5a/VlRU4BOf+ASefPJJyyo2fi7eQ7Ozs4Z/LywsFBaCbOe9fu+trS0DaKAuwrwnxGIxLCwsCBvOpmVlZWV4/PHHce7cOUuQ9ZGp8piamsKZM2fw6quvoqurCwAsAcXs7CzC4bD8v1/5lV/B1NQUvv/97+97zWwMhT4ZVL5aRQC6U5vVyMnJEZBhBh2HgY2dnR38+Mc/xrvvvisbcEdHB5599lnLUrnt7W3cuXNnX8OZnJwcETXW1dWJP/vU1JQcVhQr27dXVlY+VLFnIpHAzMyMgIypqal9Ogy2bddpmmwAZ319HT09Peju7jawIV6vF+3t7Th27Ng905TvxeAi+frrr8ucKysrg8vlMtglBwIBnDt3Dl1dXZagqr+/H9/97nelw+YTTzyBZ5555sgbJ22Ie3p6cPnyZfT392N1ddUwj/1+P44dO4YLFy7giSeeyGoxvrq6Knlcmu5w5ObmihisoaHB8F22trbw5ptvSqlpJpORqDORSMhGrPvl6JGfn28ADmVlZR9YpQUrRDR4WFpasgxCdPMnHhr0sIJCW4/zMdu54MjPzxeQwKg+NzcXjY2N+NKXvnRfAUIikZB0xPLyMrq7u3H9+nWJtnd3d1FQUHBoe3GPxyNgQaci+DuuhXfu3MFf/uVf4sqVK7Im+P1+0Q91dnY+ELtEbVZ3d7dok2KxmIioy8rKpMna2bNnD1zvkskkxsfHBUQw8FxYWMDs7CzS6bSs+e3t7VJBY75PY7EYRkZGBERoAanNZkNFRQWam5ulY+5R5/j29jaWlpYMwGFxcTFrJQ6rcGKxGNbW1rCxsSE6vZycHLS2tuLEiROoq6s7kE3+yACKb37zm/i5n/s5w0VOpVKw2Wyw2+0YGBhAY2PjPaU8zONeT0YqlcL6+rrh5ufz9fX1A0uRzGBDHzqNsr6+jtdffx3d3d3IZDKw2+04ceIEPvaxj2X9jCsrK3Lj6Hxdfn4+Ojs7cezYMUH4zONqgLGwsLAPKDmdTmExCDIehqum1mEQZFgJ0AhwyGKEQiHDXKBQiXoLDZIKCwtx7NgxdHZ2vufmR4cNnQYBIGmPeDyOnp4eiWLdbje6urpw7ty5fQByZ2cHL7/8Mnp6egDsGaK98MILllE+y91GRkZw/fp13Lp1CwsLC4YNyuv1orq6GmfOnMFTTz2Vld1Jp9OYmpoSEMFFmSMQCBxa2haPx7GwsICFhQUMDw+LaJobcCgUQm1trRgR+f1+KZsmgHjQbpr3MzKZjIExIXjIViHi9XoNgIfeFMlkEmtra5ZrxkEmT8BelKgDEx2guN1urK6u4qWXXpLI9oknnsBzzz1neS0zmYxE5tkOq+oIWmLPzMxgaWlJWqj7fD60t7fj5MmTKC8vN4CGg0AAdULf+MY3MDQ0JL+vqKjAZz7zGXz84x9/IAF2NjZTr6+FhYWw2+04deoUnnvuuawAen19HUNDQxgaGjIweawcisViKCwshN/vFwH5mTNnDCxiJpPB8vKyvI4ZiLvdbulV09TUdOhc393dtQQO2SpbWOZJG+5AIIBYLIaxsTEMDAwYWLSamhp0dXWho6PjUCAXj8dlXpw4ceLDDyjo8qjHL//yL6O1tRVf/vKX0dHRgfLycvzmb/4m/u2//bcA9r5kMBi8Z1HmwzgZqVRKFg5zxHEY2HC5XCguLjaAjHQ6je7ubkxNTcFms8HpdOLcuXN48sknD1QDT09Po7u7G3fu3DFQo4xCjx07to+6isfjmJmZwfT0tHTns6JVfT6fgIvKykqUlZU9FIp5a2vLADDm5+f3ARyXy4WKigqDFoQCtXQ6jYmJCfT09KC3t9eAygOBgHzvD7LF+uTkJF5++WVRkAeDQTz77LPY2trCu+++a9is6+vrce7cOTQ3Nxs26b6+Pnz3u98VG/ALFy7gmWeewebmpgi4rl27JuZGXCxycnJQXFyM1tZWPPbYYzh9+jRKS0stgVY0GpVUxvDwsIHCpj8E87j6fHLjWVhYkE2YFKp57m9vb2NqakqsgwsKCnD+/Hn87M/+LILB4MM54fcw0uk0VldX94GHbIt0YWGhAIeysjL4/f599z/v/cNAAzU2ZlbT7/cfqA/q7u7Gd7/7XfGu+cxnPoNQKLQPJJBx2NjYODCVy6GrI3gUFhZKumRwcBA3btyQ72W329HS0oKzZ8+irq4uK3ifm5vDt771Lbz66qsCymw2G7q6uvDiiy/iscceu29dVzKZFL3V4OCgQW/F/kUTExNyPaurq/EzP/MzBmabrzM5OYnh4WEMDQ0ZGNB0Oi1unKlUCsXFxXA4HCgpKcHZs2dx4sQJWY8SiYSwGVYulX6/H83NzWhqaspalRGPx6VUUwOHg8p46f9i1f5cB1/6NUpKSsRckLouggXOHT7XP3ONjcVi+I//8T9++AGF1dApD2CvbPQP/uAP8Gd/9mdoamrCf/gP/wFvvPHGh65slMyGjlB4HJZGoUBmd3cXXq8XhYWFEokEg8GsNF0qlcLIyAh6enrQ399vyJOXl5fj2LFj6OjosPze7K5KcDE9PY2FhYV9GwNZjMrKSjkKCwsfmBGIx+OYnZ0VkGGVJgGM1SyVlZUIBAIi5uzp6cHg4KAhV3jY936vB6sgXnvtNQFsbW1t+OQnP4n19XW8++67hiZP7D1w6tQpiaJ2dnbw0ksv4dKlS1hfX5fmTrFYTOYS+wSUlpbi9OnTOHPmzD6bXg62RCYFOzk5abjOTGWw26fH4xE1OEEDH7PlzwsKClBWVibMAz0D5ufn8frrr0uk6nA4cOrUKTz11FPv2fXRIk8NfKyMfCiWLCsrQ3FxMXJzc+F0OhGNRg338mHpCa/Xu49h4M9HKfFOpVLY2tqSVt3f//73cfv2bSkJra+vP9Soid+noKDAABbMx1GqI1gqeOXKFUNHzUAggDNnzuDEiRPweDyIRqO4efMmvv3tb+PGjRtyD+fm5uJjH/sYfv7nf/7QfjDZBk3yrIIImqqVlJQYOrL6fD588pOfREdHh3xHaimGh4cxOjpqiNip5Ugmk1hdXYXdbheGvKWlBWfOnBEN1OrqqgARijw5HA4HamtrBURoIJ5IJLC8vCzaBj5m8xwB9gAtm37pBmBmHc7W1pakh9nIjG3Pq6urUVFRAa/XK3OLx0GGZXq43W64XC78m3/zb346AAWNrf7H//gfBmOrzs7OI73e++1DYTUINszRzdramuTpuMGPjY3J4uVyuVBTU4P29naxRC0pKRGmo7i4WBB/PB5Hf38/enp6MDIyYhAH1tTU4NixY2hvbz9wcYvFYpidnT2UxaAqm0c4HH5gLwXShhpgWFWzeL1eA4Pi9/sxNjaGnp4ejI6OyqLLG+rYsWNoa2u7r7bkDzKi0SjeeOMNXLlyRQDA448/jqeeegrRaBRXr17F9evX5fymUikxCyIbQVU5mxGVlZWhqakJ9fX1OHPmDNra2lBTU2PJICUSCYyNjUkEZU45BYNBWfyKiopEDc4jm6sky8k0cCgrKzv0/E5OTuKNN94Qfxan04nTp0/jySefvO80mxakafBgxZjwPYuLi5GXlycLJVmX1dXVQ82SaGtspZ86rNRzZ2fHklHgczo7bm1tobe3V4Ab++9wc9TahcLCwn06hvz8/IcuXF5cXMSVK1dw69YtxONx+Zw2mw2zs7NYXl5GIpGAzWZDeXk5PvOZz+CFF164r3uO6byenp59vihMcx4/fhwejwc//OEPJUWYk5ODJ598Eo8//jhsNhsmJycFRJir0vLz81FXVwen0ykltfo9Tp06JVUvZCGGh4f3rUc+n0+AOJmblZUVS+CQbevMy8szAAY+t2KuaK+9tLSEGzdu4ObNmxgbG8Pu7q40MisoKJC5eViVndvtRmFhocwjPte/c7vdHx0NxfsxeDL+/b//98jNzYXdbrc8iEodDofl7x/0yPY6AKQ7HFHk4OAgenp6JBplxQQ1BjabTQ5OIHNEtLCwgJGREUmnAHsouqGhAZ2dnWhtbT0UBGQyGaytrQmDMT09bZmqoKqdAKOiouKh9AdhNQnBzczMzL4ok2Y99BhhfbsWRdrtdtTX16Ojo+N9L0NdXFzEK6+8gpGREQB7i9nHP/5xtLa2YnR0FD/60Y9w6dIlTExMIBqNYmdnB6lUSkSKPp9PqOfS0lLU19fjS1/6EhobG/e919ramqQyzBGU0+lEdXU1SktLkZ+fj+3tbQEPVqARuKsZ0ODhQassxsfH8frrr0uq0+l04syZM3jiiScOBBapVErq5zVrYv7smUwG8XgcdrsdXq8XOTk58nnNgm2rwVbYGizw54NKPK1AgqaSs/VT0J97ZmYGs7OzkpL41Kc+hebmZgN4+CAt62dnZ/GNb3wD3//+9zE+Po5IJCJln8ePH8c//sf/GE8//fR9pTVWV1dx+/Ztg7gS2ANQ7e3tOH78OGpqahCPx3Hx4kW8/fbbEol3dXXh5MmTouExVzXRrrupqQmlpaWYmZnBzZs3JXCz2WxobGzE6dOnEQgEMDIyguHhYYyPjxtex263o7q6GnV1dZKypsPk4uLigcAhNzdXAIMGDkxtp9NpbG9v72MSdBpibGwMMzMzUvrJ4fP55N7kufd6vcJUaZCgf3fUufQIUKjBk2H2ofiwD1ZujI6OIhKJSARQXFwMt9uN3d3dQxcpp9MJp9Mp9snJZBIulwsulwtutxuhUEhc6Fwu15GAEStkyLisrKxIBK0P9ijRuT46190vKGMpl24pzUhJH6Sfk8kkNjY2EIvF4HQ6YbPZ4HA40NjYiI6ODrS0tLwvcyKTyeD27dv4q7/6K0xMTIjepqysDMlkUqqM4vE4EokE3G438vPzEQ6H8fjjj+Mzn/kM0uk0vvOd74j5zYkTJ/Dcc88ZxGBciDOZDGKxGOx2uzQ5olDXinUg7c/+AgQP75WrZCaTwdjYGF5//XUBfk6nE2fPnsUTTzwBm81mAA4LCwuGKgtGatFoFLFYTOY0Abrb7T4QLBcWFu4DC3xung9WuWbz42EgBdg7x2xDbdYuOBwO/OhHP8LMzAxsNhva2trw+c9//kPR72V3dxd37tzBzZs3cefOHUxNTUlJIu+1hoYGBINBeL1edHV14fTp00fSyWxtbeH27du4ffu2wRnS6XSiublZSsWdTifS6TSuX7+O119/Hdvb29LZtrKyUlhfPfLz86XbbU1NDSYmJnD9+nUB9vybzs5OBAIBLC4uYnh42PA6qVRKykPz8/Phcrlk3cu2FXq9XgENBA4EHxosmIHD1tbWvntT22NrvwiXyyUajfb2dpSXl+9jFx6m++4jQKEGT8bY2Bjy8/ORTqfv68hkMtJvns8f9utY/S6ZTGJiYgLDw8PY3d1FJpOBx+NBTU0NiouLEY1Gsb29jZ2dHUSjUVlorerj4/E4tre35YZ0Op1wuVzIyckR051QKCRMzlFHLBY79OYA9qINouTCwsKHQs/q96YDn/m9E4mEnEt+jpycHDgcDpSWlsr3zsnJuS+WKRvwYt50cXERq6urSCQS4hsSjUZlsaqtrYXf75deDbRD39zcFJBUVlaGtrY2zMzMSIvlnZ0dVFRUIDc3V659Tk6OAJK8vDz53Dxyc3NFaEgAoSOb93Mkk0lcv34d3/ve9zAyMoLt7W1Eo1E5F5lMBtFoVI5kMgmn0wmHw4Hc3FzDd9TDZrNJAzO/328QQ+s0YTKZPBQsHMVzAYBon8xgQUeIVnO9v78f3/72t8Up8md+5mdw8uTJD7RqKZ1OY3R0VBr80fNmY2MDfr8fZWVlOHfuHJ566ikEg0HcunULV69eNWgCqqurcfr0abS3txvm1s7ODvr6+tDT04OJiQlDirK+vl5SlAR2mUwGg4OD+MEPfoDx8XGsrq4iHo9LOa029KqurkZjYyMaGxsRCoWwsrIiVVA6nRUMBlFUVIR4PI6pqSnEYjHs7OzIGurxeASUmu27OQgcioqKpCtpTk4OEomEdH3lcZS+IzwHTBPRlCqVSsHtdsPtdkvDshMnTiAcDr9vc+QRoFDjw6CheBgjkUjg2rVr+PGPfywT1O/345lnnkFnZ6dE8AQi0Wh0XzUKNRxcLNkUhgIdNjUrKSkRnQLzsgUFBSgoKEB+fj5ycnL2gSQNhhKJBFZXV4UKXF5elqhcHzabTdTlzAMT9B0FtFkBsmQyue+G1gIkgiqyKrxZNSVpbt97lGFul8z2yPF4XDbEVCoFj8cDl8slNf8ejwe5ubloaGhAY2OjLL6MTpjq2d7eltbKdrtdGKdMJiN5WN1OmeCBm25eXp5cu6MCo3tlkw76e7O7oma34vE41tfXpTROR4YVFRUoLCwU3QPfh42fiouLUVRUZAAM7NbLc6aPra0tedzZ2TnSopyTk5MVJPD5vUaEsVgMr7zyCq5fvw5gzxH3xRdffM9atx9lLCws4NatW5JuJZCw2+0CQs+cOYMLFy4gFAoZ/m8mk8Ho6CiuXLmCwcFBAfVerxdtbW0oKCjA7OysQd8F7Dl9UkRt1lwMDw/jf//v/43bt28LK1BTU4Py8nIRU/K+qaurg9vtRiKRQG9vL65fvy5ptUQigXg8Dq/Xi2g0KmCcgZjNZpP5U1RUBKfTKakzh8Mhc8/tdktKPBaLIRKJHImdAvbSzWYWgYFVYWGh2HD39vYaNB9ut1s8h2pra+8p0HtY4xGgUOOnBVBwxONxXLlyRXz8gT3l9TPPPIOOjo4jTbhUKoWNjQ1Z1IeGhnD79m0MDg5ifX1dqGX2qCAS18IwLQzVh8/ns/wMu7u7IvicmZnBzMyMpXLe7XajvLwcFRUVctwr9a6BBjd6akCmpqYwNzeHWCwmRjEEVR6PB3l5efD5fGhra8PJkydRW1sLh8OxD8jEYjHMzc1J3puUJNMsBDKMckiZshqCBljd3d2YnZ1FJpOBy+VCc3MzCgsLMTY2hqmpKczPz8sGSFDCVJbD4UAmk4HX64XX60VVVRXq6uqQl5d3JCX/ezHS6TR2dnZkA6ehTjQaRSKRkHOUTCaRTqdhs9nEaMflckkuOZFIwG63w+VyobS0VJxevV4v3G63LPjURehjd3c3a2tm83A4HHC73XIO9ZGbmyvv9zBAFY+VlRVcunQJ29vbsNls6OzsxOnTpw1px4cJ5g76m52dHdy5cwc9PT1SCUM/iuLiYjGGOnPmDM6fP3+kNZRl0q+88or0iEin0/D5fAiHwzh+/DiOHz+Ozs5Og7tkMpnE1NQUbty4gVdeeQUDAwMA9tiHyspK8XIgiKDxGdPD169fR3d3t5Q263vSZrMZUsS8J+mNwnngdDrlXHm93iMxdx6PxwAOzGChsLBQ3kePzc1NSfloB02rlM8HOR4BCjV+2gAFRywWw7vvvotLly4JLXuvwMI86PVw/fp1XL9+XboURqNRabtdUFBwYCMw5u2twEZxcbEI26iu1wBjdnbWciOgcx+BRnl5+QPll9PpNBYXFwVk0EKcqmwyGvwu7e3tOHHiBKqrq8VPY2ZmRliZra0tOVcADM2L3G436uvrhYrVC+ju7i4WFxdx+fJlfOMb38Do6KhU/bCEkRtuSUmJ1Jzv7OxgbW1N/n1qagputxvhcBiNjY343Oc+h4qKCmGCjpqmu5dUHssc5+bmMD4+jtnZWbHRpuo8FovJZwD2In2PxyPnheZJZFByc3PhdrulRI8+AYlEAolEQjQI/KyHHZqBom7I7XYb3p/amvdj8P5i5Mzo08qy+b0cqVQKy8vLBhvmeDwuqUpej7y8PNTU1KCystKQDswGXpjmm5mZkc2cXUUTiYSwkYWFhaitrUVjY6P4JywsLMgawCodVmo9/vjjaGlpkf4eXNuWl5el/9H09DTW1tawvr6OeDwuqVybzYZUKiWAIS8vT9Ktubm58j1dLtc+LRZF72aAYP7dvbBTkUgEvb29uHPnjsGDyW63S8qnpaXlQ9W/6BGgUOOnFVBwxGIxXL58GW+//bYBWDz99NOSCrmfkU6nMT4+jjt37qCvr89Q3mi328Vi2OPxCIW9vr5+qFDU6/VaAo3i4mLk5+dLA6TZ2VlZmKz0GKTDCTLC4fAD6QCi0ajYh9++fRvXr1/H8PCwiDpjsZgsMH6/XzY/Rie6+2EwGBRBWHV1tZTE6tLM0dFRTExMSAoqlUohEolIZU9BQQHq6urwmc98Bk8//TTKysoMQG5raws3b97EtWvXsLa2Js6ZXq9XSvc+9alPPfDCRPBF9TzBFAWxVgDQ6XRKBFhYWIiKigrpSEsmgt9jZ2fHkJ4yV22sr69jYmLCkJ8PhUKor69HOBzOWu5mjgoJlg4DTUcFXoeBNPPfrKys4Ec/+hGWl5eRyWRQV1eHM2fOiODQzKpZvfZRAZ/Va9FnYW5uTnLz1KhQ8J2XlyfUfFVV1ZEqtdLpPcMwNp7Sxloej0cE2QQOU1NTWF9fF60XUwrpdFp6fHi9XoRCIXR0dMDn8wnjxV4iy8vLWF5extbWloHtstvtUgXndDqFZSJjp4W7DodD9EY8rH5+EIaIv0smk5ifn8fMzIwIpwlYgsEgampqxJzrXting1ipwxire/n3SCSCQCDwCFAAP/2AgsMKWPj9fjz11FM4duzYA4kfU6kUxsfH0dvbawAXwF45VFtbG9rb21FTUyPRs9VxmDmQ3W5HYWGhAWTk5eUhkUhge3sbq6urEsFY/d/S0lIDi2G28j5oRKNRiR4nJiYwOzuLnZ0dzM/PY2pqal+Khpsm9QttbW04duyYdAnkIktBJv302ZyOuVdGTcFgEO3t7ejo6EA8Hsf169dls25pacEnPvEJlJaW7vvczF1fu3ZNXAQXFxfhcDhQXV2Nf/gP/yGee+65A4Hl7u4u1tbWsLy8jPHxcUxMTEhqaGlpKaswkTqN4uJihEIhBAIBsZnn+yUSCVG0H9VMx+Vy7QMJ0WgUAwMDmJubE2ahvb0dTz31lKU9+YdlpNNpvPPOO/i7v/s7JJNJeL1e/OzP/iw6Ojre8/fOZLGup84okUjA4/EI20c3zHA4fCCAicfj4to6MjJiYKJowlVfXw+/3y8pFLKBy8vLYt61vr6OnZ0d0TPRUTQYDIp3Dz9nPB5HJBLBzs6OiKyBvfuQzBe1XoFAQAy8mE7TB4GF/n4PeySTSQkizFUhbM8eDAY/EpWHH2mnzIc9/l8BFBxMhbz99tuy8bNl74kTJx64quIgcOH1etHa2or29nbU19fvey+K7zTIoJPo2traoewG6/Nzc3NlYWPtNmlNPZxOp5TGEmQEAgHY7XZJXRBALCwsyP9j5MbPE4/HkZeXJ6rwmZkZSQNpvYnL5YLH4xGw4XQ6kUqlxMpXU8k+n098MRoaGvZFg1tbW3jjjTdw48YN0RqcPHkSzz77bFa/hu3tbdy8eROvvvoq3n33XQEC1dXV+NznPoe2tjbpuEuXUgI0CtTMtzgX3by8PEnlkAHIy8uTc2VVVZTtGvL/W9XJFxYWHqj/mJubw5tvvon+/n75rA0NDXjqqac+FA3j9FhbW8M3vvENTE5OAgCamprw+c9//qH0yznsfXt6etDT02MQ+FF0vb29LefY4/Hg9OnTOHv27IGpl0QigZGREdy5cweDg4MGMWJhYSE6OjrQ0dGBcDiM+fl5DA8Po6+vDyMjIzI/dnd3RVAeiUQwOzuL9fV1uZfIIlB3lJOTI1VjsVgMDocDLpcLXq8XpaWlaG5uRldXF1paWtDa2opAIGAQJt/LOCrrdBAztLu7K03BxsfHRTSdyWTg9/tRV1eH+vp6FBQU3NfrH8ZiPchnt3otjkeAQo3/1wAFB8WbFH8BewYoFy5cwKlTpx5KmSDTIgQXujzK4/FInXRDQ8Oh75fJZETEx/SJBh50Esw2YrGYUJ9cvOx2u+TLqXWgGQ/TFwUFBfB6vQIeHA6H/F+32y2ghWkI5ksp6FxYWMDa2ppQuDs7O7LwUdTH/H1FRYU0Wzp9+jT8fv+hG+Dy8jJ++MMfor+/H8AecDl//jyeeOIJiSwzmb2mUPp89fX14dVXX0V3dzd2d3elvXpxcbFEagCk9TqFaRSOak0DUxWHjdzcXEtBmgYPDysiW1pawsWLF9HT0yMRZlVVFZ588kk0Nzd/oMAik8ng6tWr+MEPfoB4PI6cnBx8+tOffk/LQbe3t6VhljZ1o0V7LBYTzxZgLy16/vx5dHV1Zb22iUQCQ0ND6O3txeDgoLhkJpNJ5OTkoKqqCmVlZQI2xsfHMT09Lakr+qoAkDQXUxv8vcPhMDCRrJwgE5Gbmwufz4eCggKUl5fj7NmzeOqpp9Dc3Py+a0+sRiwWw8DAAHp7ezE8PGwIikpLS9HZ2YmOjo4PtHrnfoZOEa6vr6O0tPQRoADuAoqXXnoJJ06cyGpV/NM6WG761ltvCeWZl5eHCxcu4MyZMw9tgU+n05icnBRwoRsmuVwuNDU1ob29HU1NTff1nqye0JumBh2aTucGS83C8vKylCM6HA6pkiD9yQ3f6/VKdMP67/z8fJSUlOyrR2eumfoIijpZzhmPx5FMJqWksaqqat8CmJ+fv09smq0p3NDQEL7zne9gdHRUIrrq6mr4/X6pAKHHCKtCqEtYWFgwfH9qP4qLi8XYTJdmmjc9bcqUDSwUFhZ+IF4Wa2treOutt3Dz5k1ZzIPBIJ544gl0dnY+dBvqw8b6+jq+9a1vYWxsDMBed8cXXnhBmjI9zMHNzMpuv6qqCm63G8vLywb9SWNjI86fP4/GxkbDdaZZ2PLyslQeDA4OCjCgURoFjaT0l5aWpCqHB71y6DvDv19dXUUymRQL81OnTqGlpQXp9F7H276+PszNzUlr93g8Ljb/nZ2deO6553Dq1KkPpLmcHjzvd+7cwcjIiAFEBAIBYWuyNef7qI1Hokw1eDK++MUvCt3Mze348eMIBoM/FRf9sJFMJnHz5k1cvHhR+jp4vV6cP38e586dy7qR3c/IZDKyQPT29oq7I7CXhqivr0dbWxtaWloeyvumUimMjo6it7cXAwMDGB8fF+EXj0wmg5ycHLFJZk4/FosJfciUhdfrRX5+voCB2tpatLa2oqamBun0nuMdVfL6lnA4HOKhT7Ehz8f29jacTqeUj/IzcZAyJd3r9XqlAiESiSAajUqfg/7+fgFRqVRKxGMUUgF7mhIal7FdMhd/dq9ki+yysjKhjamB0GBBayI+rGNrawuXL1/GlStXhI4nI3fy5MmH6hxoNTKZDK5du4ZXX31Vqgw+8YlP4Ny5cw91fUkmkxgeHpbGeOaGgDU1Ndje3pYeMJlMBna7Xfq2uFwugxcHK5TGxsYwPz+PtbU1g6aA8zGdTguDSPM4iiCpeTEbiVHbMjY2ho2NDXi9XqTTaYTDYeTl5WFmZkZEylwj8vPzEQwG8dhjj+HkyZNYW1tDd3e3Qb9UXl6OkydPorOz831zE93d3TUwEVp8GggERP/007ifPAIUavBkvPjii9jc3NyX6/X5fKioqEBdXR2qqqoEUXMhpZkTS/Q+6iOVSqGnpwcXL14UxXFOTg5Onz6Nxx9//KGnhVgjTuZCN9ix2WyyWbe2tsLn8x3pNXd3d6Xcc3JyEtPT04YogdPU7XZjZ2dH1O3Ly8uijWB+kw2iuDiS6qMKnJFbPB4XLQErCYqLi9HY2Ci9UWpraw0b19bWFvr7+9Hf3y+5ZAIcloOy/FKbOtGgi54KuhTSbrfL/6PmgemZYDCIUCgkZlZ+vx/hcFhK9TweD4aHh9Hb2yuqeZ/Ph+rqavm+HR0dUiL7UZzvu7u7uHLlCt555x1JwXm9Xpw7dw7nz59/qMCZY21tTdgjYI+V+MIXvmDoOPkgI51OSwO8vr4+EUFSl8NKoqGhIRFJ0pQpGAwiEAjsY2Xj8bhUS5A5ILtA9g6A3C+8P+h/Qvtyln/SryIQCMDv92N9fR2vvfYabt68KV4k+fn5KC8vRyQSEeYwJydHAMjJkydx/vx5tLa2GtiuVCqF4eFh3Lx5EwMDAwJ4HA4HWltbceLECTQ0NIgnhabrj/rc6t92dnYwNDSEwcFBTE5OSuCRyWTk3q+vr5frnO317uU9H/Qzvxf/JxqN4nd+53ceAQrgLqD49re/jVQqhampKYyOjmJycnJf9zh6pNM1Td+EDodDgIbZOVI/ZrNq/bCNdDqNvr4+XLx4EXNzcwD2vmNXVxeeeOIJ+P3+h/6emcxeG+2+vj709/fL+3KUl5ejra0Nra2thoqGzc1NAQ+Tk5PCDGQyGYPGIScnB9FoFGtra5YliPSVqKmpQXNzM5qbm2XBzcnJEaEmc9FDQ0MiWGT+2OFwCItBfQbLRrmYUhjGRX9nZwfLy8uYn5832HATOOgF227fc5WkkJOfmwwEr1NJSQlCoZC4AxYVFSEvLw8VFRX45Cc/eWBUvrS0hJdffhmjo6PY3d1FJBKRlAXfo6SkBF1dXejq6vpQ5KrvdSQSCdy6dQuXLl2SqiCXy4WTJ0/i8ccffygpiHQ6jXfffRc//OEPkUgk4HQ68eyzz+Ls2bNHWsCt/i2dToub48jICHp7ezE0NCQpgHg8LikoNnlbWloSkAHsiSQJLLnJ0t2WzrksTyaQIKC02WyGoIsAgw2o6KBbUlIiQZb+7FNTU3j33XcxMTEh9yWDNLpT5uTkiL6ouLhYOhZT63TQ+drd3cXc3BxmZ2cNuiqXyyVW8mTk7mfEYjFJ5WxsbBhYxLy8POnR8dMSYB5lPBJlqnEQXbOxsSHGKIODg3LTshUsa+lZy3yUCWS325GXl2cJNszA4/3O71qNTCaDkZER/PjHPxajFTYoevLJJ9/Tkry1tTX09/ejr68PU1NTsmjQQVBHkxRqsRoBgEHvwI6teorSk6GlpQUdHR04duzYPr+K7e1tjI2NSbtwnW8GIOKzkpIS8aoYGhoSF0v2e2ApG6MnnYJgXbzdbpeStVQqJf4W5vp50sdlZWXSkZCLvbnEjSK5mZkZrK2tCcBpbGzEpz/9aTQ0NBgWZL34DwwM4PXXXxebcBoP0WCMf19ZWYmWlhbU19cLo3MvG+WDRmv3+148N7OzsxgaGrL0svD5fPcV3UUiEfT19QlVX1RUhJaWlqwUfCaTQSKREPaAh/55d3cXW1tbhn47HFxXuJFFIhG5TwgG6GrrdrsFLGixLqt+CHTphcDXp56IqTk2jAsEApa6J27w6+vrmJ+fx9jYmKHdOAE37wNdxREMBlFWViag535GJBIRXw2d+mGn3mAwuA9U8zvr+5MtwQki+HfAHoNdVlaGcDiMwsLCff//oOcH/XzU/3Ovzx/0/1s9j0QiaG1tfQQogKPnf1KpFCYnJ6Vzoy63SqfTotIPBoPw+XziLKfzkdvb2zjqKeKGaQYdjDz0794vsdvk5CQuXryIwcFB+V1dXR2efPJJ1NXVAcBD3whoYT0yMoIbN27gzp07WFxcFFEjNzbWl9MpMRqNirOfdj9keVZDQwMqKysl6tERzvz8vEQ5rBHnAkzPf/r2JxIJQ+kaPxNtpPmcivZUKrWvDIvvrQWhfE5QxJvY6XQavk9JSYkBWFBrwbnHg+9NfQjnIRmZsrIyAbJaD8F5PzU1hXR6rzyVnUaXlpZEbwPc9fowm2x9FEYms6dWn5qaMviY+Hw+VFVVHaniBoBE4RMTE6IjIODUQMEMGLjh8T14vcmy0byJNtEUz/r9foRCIfj9fkQiEaysrCAajQq4ZJTPPhVscKXnBQCZpxQgcy5wnhUVFSEcDostfGFhoeXmsrOzg4WFBen2S+ZtbW3NwG4xzcJAzOVyoa6uTrRI1Ac96AZMh86RkRHcvn3bIE5lZ+Guri5Jo/AzkimlEFSPyspKtLW1oa2t7aGlrT7K45GGQg2ejL6+PkPjqcM2v/X1dTH5mZmZkRszk9nLWZP+q6ioEEo4mUwa1PaMpnVkrRtF8fX4mO250+k02AVnc3djU5v7ieT0862tLYyPj2N+fl5+l5+fj6qqKpSWlj6QQI8RDZ312P6ZCx4HFwpulMxf2u12YYy4KGqbb3OEmE6npTpkaWkJq6uroomwek++b7aprgEBB9kFvh/Pp05p8Hrzb/n3usqE0dTu7q6o6zkIQJmOKykpMaRdKJrb2trC2toapqenDWCALd29Xq9BdFlUVISCggLE43ExxQL29CctLS0IBoOYm5vD9PS0RMQ2m016h9TU1MDn893T5vBeRGX38rdra2u4fv06BgcH5ToXFxfjzJkz6OjogMvlkuie9+/Ozg4mJydx6dIlLC8vSwVCTU2NzDl9Xa0ebTabCMNTqRRWVlYEPOsuscePHxc2bWxsDBcvXsTNmzfFs2F3d1c6srLSaH19XTQRBCVkIjweD0pLS1FRUSGfNS8vD7W1tairq5Nut1aAimvB2NiYdPsE9pi9iYkJLC0tSYqPQIJNvmy2PY3UsWPH0N7e/r7YSe/s7OD27du4deuWoSU6xccul0t6GHHYbDbU1NRIuvWoWq7/V8YjQKEGT8ZXvvKV+y6RZDOtlZUVQ88GDkaS3NgOK0sl/WlFe5p/Z6a4Dxo2m00WJiuHOH0cBRRQ/Dg7Oyufw+12o6qqCuFweF/KxryAJxIJoRLZ7ZT15fx7AGJWo/s80E9CMxnMyRJQ5Ofno7KyUkof2eV0ZmZGqND19XUBLAQl2naXbcz1+eNBlohUrcPhkFQFNwGmMPTGwfng9/tFk+NyuRCNRiU/y54hNptNzK/4uqw24bzb2NgwsF+M+PR7MMrURzQaxdWrV3Hnzh1Eo1HRStTW1hoWBrvdjmAwKA6Jvb292N3dFVHfpz71KdTX12NmZgY3b96U1+MIh8Po6upCZ2fnA+Wv3+tBoR1Zxfn5eVy9elXaW3O+sess14tUKoWxsTFMT08D2JuvjY2Noui30leZmcb8/Hxsbm5K5RPTL6lUColEQlgIr9eL1dVV9Pf3Y3R01FAh5fF4UF5ejnA4LJbOuldGIpGQyiVqeqgFy83NRU1NjQCIbCWNBBA8zDozGsmxSyftsysqKuTah0Ihaf71QW7OCwsLePXVV/Hmm29icnLS4E5bXl4uQt2WlpZ9nU4fjbvjEaBQgyfjP/yH/yD5xweNoGjJvLCwgKWlJaGKgb0INBAIIBwOG5wZ7zXK0tbFrAwgw6Gfk+Zkrwlgf6Rk9VxvylaLHzUfHo8Hu7u7uHnzJq5evSr6Ba/XizNnzuDs2bOw2/c6KE5NTclCyOjFDIhsNpvkZ1lZ43K5xLLb3FI6k8nIwpiTk4Pl5WX09fVheHhYqjZYVslBBkFfE7YJZ3UGS9y4eRQVFUlkytekOj3boGMfDwo8j9IdNZPZa47G9AsPnYPmILsRjUaxubkpPRMItCjKJLgwR4LRaFSofnZOZS8URrIej0fmXCaTEUCmo+YXX3wRlZWVSCaTGBoawq1btzA0NCSfz2azoaGhAcePH0dra+t7XqrJQVtm3Z7cqmV5tpRkKpUSFoZ+JjabDRUVFSgtLcX8/LyU57a3t+O5555DaWmp3C9WnSSBvfM4OzuLW7du4dq1a5ifn5d7NhaLyX1WUlICh8OBnZ0dSSUQdHs8HtTV1eHkyZOoqamROTM6Oor19XWsr69jc3NT1p1AICAC3draWgER2coZDwMQNptNeqbMzs5ibGxMbOUJTvPz8+Hz+XDs2DEcO3ZsX2vz93PE43EMDw+jv7/fUDrLHiDpdFrKwZ1Op3Q/7ezsfM8dTD9qI53ea2Z37do1fPGLX3wEKIC7gOKNN96QvCDV9A/6nOK6yclJDA8PyyanR15ennSbbGhoeM8iOPrzH2VhvRfWgwKt3Nxcg86EUXM0GhXVttX0YFlbXV0dWlpaUFNTg2QyienpaQwODmJ2dhaxWEw28e3t7X0lnDoHzZwzbXwppCXNy5K3oqIi1NfX48SJE3jsscdQU1ODUCgEm80miwuZAhpfZRv5+fkoLS0V0RufvxcVPdvb2wIy+MjuixxM4zBdlMlkDE238vPzpdma3W4X0SX7lczPz8trlZSUIBwOw2azSWqGm6rT6cTKygqWl5dF79Ha2io21xSqjY2Nobu7WyJ4YE/M2traiuPHj6O+vv6e02TpdFqu72Hz+qi23wAk7WAFpPPy8jA/P487d+5gZmYGY2NjWFpaQlFREdra2vDLv/zLaG5utnzdVCol/VD6+vrQ09OD/v5+rKysSGRst9ulVwVBBFNV7GvBhlalpaV44oknUF1djcnJSbz77rsYGhoSAEGmjiAiGAyirq7uUACxsbGBiYkJARDmvjg2mw1lZWWora1FbW0tXC4XfvCDH+DSpUtYXFxENBpFaWkpampqUFpaKn4+H2SZ8dbWFgYHB9Hf34+xsbF9bcrpsVJfX49MJoPBwUHcunULw8PDBjOwuro6HDt2DG1tbR+qbp/v50gmkxgbG5NKPAarj6o8fjIIKP7JP/knKCoqgtfrfejVFRpssNESD62mttlsKCoqQigUkrptUumHAZeDfrZ6bv57XUlAfwMzy7G9vY2NjQ3ZZDc2NuTfIpGI0KnczOkKyXOQm5uLsrIyVFdXIxwOo6KiAnl5eVhZWZH21myURRDAkkkKEXWkDNxVpGsdBV0tuTH4/X40NTXB5/NJS/CNjQ3JfUejUbGRph+D1fD5fMI2BAIBef5+medkG/F43CCEIzvG87Gzs4OVlRXRpFDsS5MgburFxcWIxWKYmJjA22+/jb6+PmG/ioqKDKmQWCwmG/jKygomJiYQiURELFheXi7Onn6/H7W1tSgpKZGW5pppysvLQ2dnJzo7O+H3+y2Bgvmw6ity0KBluAYKZtaNoOEgcJNOp3HlyhV885vfxMjICJaXl1FRUSHfr729HRUVFYhEIlhdXRXARUZuaWnJAHBodlZRUSFlyizJnpmZwfj4uCEFWFdXh5KSEszMzODGjRvCWmmRbSAQQFVVlTTkq62ttQQQ1FYQQJi7tvI9NYCoqamBx+NBT08P/s//+T+4fv26gO1gMIiGhgacOXMGx44dQ0NDwwdSqZbJ7JWfDwwMYGBgwABkgT2QTG+bysrKrNd7Z2cHd+7c2WdX7nQ60dzcjGPHjqGpqemn0lk5kUjI2r+xsSHVdiMjI8L40oPE5XLh+9///iNAAdwFFJ///Ocl6uVmxDIs7UzIDYyiOir1+fO9jHR6z7eeHSa1HTWwtwmTfisuLn7faptZ7aAFZzxYVUEWgD0qmF/Wn483KhkELfjUojDztGGFQ05OjmgncnJyxN6ZZZJkgChKZZTMiptwOCwujhQj0o57Y2MD6+vrAmAASCopGAyiqakJHR0daG9vl9K494uifxgjlUqJwl4fnG/U+xDwEUw1NDTg2LFjOHfuHIqKivDWW2/h1q1bcr1LS0ul/JHnkOBscXERfX19WF9fF30PKX/eKwSyml2iNsXhcEhr6mAweGjemmyCFVAwA4aHce1mZ2fxne98R0zICgoKUFtbK34QvH+pLcnPz0ckEsHy8rJ4OXi9XhQWFkrjquPHj6OsrAy5ublIJpPo7e3FtWvXpGEYvyewxx5QN8F7hr0uqqurxaq6trbWsrV4JpMR8EcQYU6hMYVBAFFdXS0Ae319HT/4wQ/wve99T6zD+fcf+9jH8Pjjj6OlpeUDuU/S6T1rf4IIM7NSUVGB1tZWtLS03JflNRuqdXd3G1hmj8eDtrY2dHZ2oq6u7oEE6Q97UIvHzT/bwaBqe3tb7ueNjQ0sLi5K11eykwzwcnNzkZubK1qut9566xGgAO4Civ/23/7bvly7eXg8HqEQaVLE/D3BiFbwW4EO8+/030UiEUOLbOZ0+Zq5ubkIh8NSvuV2uy1f66D30c9jsZiUEZrLW9lIK5lMCrgggGD6gDclAQIrHKjzyPykzp+Mw+7urqFqAoAIIFnNYBaNkvbVojJzSoYaCC2iJGPhcDjk0J9Z3xQOh0N8LFhyx+FyuYSNCAQCwpDcK0v0sBimB/nZZrNJD5OlpSXMz89jYGAAY2NjWFlZ2Wf0lZ+fj4aGBtTV1QkLwvNVUVGBs2fPCqOwvr6OhYUFzM/P4/bt2+jp6RHzMJbuZjIZ0XRwcI7w+mo9SzAYREtLCzo7OyUlVVpaCp/PJ0DlvVjAk8mkdLpdXV3F/Pw83nrrLdy+fVvEqPX19SgvL5e5kkqlMDs7i9HRUXHcZQqDKb3jx4+jo6MD9fX1EtVSj3L9+nX09PQIwzc/Py8s0ObmpmFOut1uVFdX4+TJkzhz5gwaGxtRXFy8b5NMp9NYWFgwdM01p+7sdjsqKiqEyWCPD46trS3cuXMHP/zhD3H58mUBTXa7HV1dXXjhhRdw7ty5D4Sl293dxfDwMAYGBjA8PGxYu3mNWlpa0Nzc/NA2ukxmr+U7u7VqQJaXlyd+NpWVlQ8t+ON9kw0QmNlkfTBg0x4n+lE/18CCQRbXDo/Hg6KiIhQXF4sRGfVmHo8Hv/mbv/kIUAB3AUV3dzcCgYBs7IxoWWpl7lmvh91uR3FxsQFk8LhfK99MJoPFxUWMjIxgZGQEExMT+9p3h8Nh1NfXo6GhAdXV1ZbUWzqdljIofhfm3tfW1izNczY3N6WhD8GH3ow5SVkrTjbB7XbDbrfL5sDNw263G0pbySxQy5CXl4fm5mZ0dHTA5/NhenpaOhPOzc2JSI03iTknbhZp6pJaDVjcbrfQ/ezySaMePnLT5Yaiz7nNZkNhYaGIG39a3PBSqRSi0SiWlpYwOzsr1S/aShiAXDeyQvQRKCsrQ3FxsQG0MRpeXl4WwMkmaBTyMo3GFAdTXEyd8f+xF0QwGER5eTkqKysFWPh8PkPlis/nk7SFPszXKR6PG0CDPphC4D04PDwsICgUCqG1tRXhcFiawkUiEQFpLDudmZnB1taWgNH6+nqcP38eJ06cgMfjQTQaRU9PD65duyZCRvqeJJNJKfPmKC8vF+bo9OnTlu6kNOkigJiamjI0xQP26PrKykoBEJWVlft8bGjK1dPTgytXrmBiYkLAZklJCZ555hl88YtffE9N7bKN1dVVDAwMYHBwULw+OHJzc9HU1ISWlhY0Nja+L/1ZJiYmcPv2bfT29hoAuc/nkzReWVkZbDabeMQcxhhYAQYrXRsZ3mwAQZsw8n41r3eJRALb29uit+I67fV6EQ6Hpa9VdXW1oX+PnjOPqjzUOKhslCZCvLlpbKRbUZNF0GZE+jnz1BposFTwXvKLiUQCk5OTGBkZwejoqEE4pxkMOs9Fo1HxcqCvgrnUlJ4IjBD573xNvXlwI+YiXlBQIOdLd9BMJBICHPhYUVGBpqYmEYUVFBSIE+PFixdx584dUaSnUin4fD6DEU88HpeyR743b1BqLQgWdAmnw+EQhf9RhHk6JcMbKx6PY2NjA6urq9jZ2ZEb0el0il9/Q0MDysvL4XQ674mdOiqTdNTXsvqZ15WgzMpciSXKGjxpYK3BpdmXhPPc7XbL5smFx+fzwW63Y3Z2FktLSwJMSKnr+43+JrR9ZqUADcP4nXhfejweMV4im0VASJaDP3Po86JZNquKqnQ6Lakbt9uN4uJinD59WgzcFhYWMDMzYwBMdrtd0iA1NTXIy8vD4OAghoaGkEgkpAKMAmlarkejUdjtdknv2e17XTubmppw8uRJPPbYYygrK9vHPiUSCczMzGBmZgbT09OYmZnZF3SwjLumpgY1NTUyT82DIKK3txcjIyOYnZ3F1NQUYrEYCgsLUVFRgc985jN47rnn3tcSShqFDQ4OYmBgYJ+oPRAIoKWlBS0tLQfqIR7W4Hpp3vQjkQhGR0fR19cnHX+5rubk5Eja+qjnzgwUaLXPe4BrMwM6M1Dgc5at2+12SePHYjEJltlqnut1Q0OD+G0cZKmvfZj6+/vxla985RGgAO4Cit/4jd9AYWEhnE7nPWkhqCcwaw2ILAHIQqCBhsvlgs/nE38KXSVAGokImxE/BW2MQkZGRjA9PS3qaj2oJWAawePx7PO30D0i9OH1eoXeYvlkSUmJnB/W6rNjJ1kHjmAwKItqTU2NoXIlFothbGwMt2/fRn9/P8bHx7G4uChtiekuSKOshoYGoXO5aZmPo3h7EFhowZ9Z/MefzWkZjt3dXRE3stcBz7XH4xHxWkNDA8LhsEHox0er9t/3OhKJhOHzHvRobtsO7G9SpA9ubPrweDzSw2B2dlYqbxiZr6+vC6goKChAeXk5ioqK5DoWFRXB6XSKmRbvg6amJjQ3N8s9ZwWYWILN/jrLy8sSsXGuUJNhZtMILqzON5krc3l0bm6u6Ex4bWtqalBSUoLV1VUsLy/v0zrl5eUJmDJX9iSTSczNzeHOnTuScuDn5LmmRqugoADhcFicOc2bYywWk/z2xsaGocMmB8EP71ves1apsEQiIWJe3nsUi+fk5IitdFdXF5qamgTsZBN0H/a7o/6/WCyG8fFxjI6OYnR0VHQ2vJ61tbWSyrhfp8psbIH+XTY24bD9IZVKCSDmeeXweDwIBoOiEeJ9p03udBM2DRKyBaBsA68bVuojJycHc3NzGBoawvDwsGFNoGdKa2srmpqaLBn1TCaD1dVVQzpem+I9qvJQw8xQsNKiuLhYujAWFBRIWSTp2KMcWvSigQY3LV2doLtI6sVV0/eMCLVGAYAhOmX0qLUCwF1DJaJUUlYOhwOlpaUoLy9HVVUVamtrUV5eDp/Ph8LCQsRiMSwtLQmNal5MqQInhVpdXS0loltbW5iampJeKKOjo5LC0IOpj9zcXKHCNSty8uRJPPvss2hqanrPUwwEiObN2bxRb2xsYGpqysAC6eHxeAxmZlwMmCbQQEMzS7yujIR0SkCXwd7LcDgc+95Tb6L6ucfjOfQc7+7uYmRkBMPDwxgaGsLKygpGR0cxPj4uGhSPx4Pq6mo0NTUZqGeWJSaTSeTn56OkpATPPvssnn/+ecs6/1QqJYzF2toaJiYmcOvWLfT09GB2dlb6pJAZI0PF88drQb1MTk6OMChklHjPcJ7z/Pp8Pvj9ftH+aJ0P043V1dXSvjud3mtdPz8/j5mZGQwODmJsbAxra2uGKJNRJT08qBXhps37mcCG311rqvQ8I3NHZu+g66ebW3FToH18IpGQstSCggJUV1cLM/Jejkxmrz+PrkTSQ5u00QROr4E8X1wDuYaanWi1Hb65ui6b70+2g4EX5xx76fAzkeWKxWJYXFwUG3L9vrqZGIGoPgjQDzusWi+srq4Kq2NODeXn56O5udnQf8d8PZaWlgwAwqpgoLy8XFxUT5069QhQAHcBxR//8R+Lw5vVsNv3rGPpM8BHv98vwkGWT/LY3NyUygLWh1MASY3G1taWiNdIS5sjNfPnIHIlTcUKFIoXtXhSR23aATIQCKC6uhrNzc2orKxEfn4+XC4XIpGIUPyrq6sibCRCzsnJQWVlpXhnlJWVyWKwvLyM8fFx0XyQzjUPWv2ytTGd+bhg2O129Pb24vLly4aSr4qKCpw7dw4dHR0fmlIt9myZmppCX1+f5HZ1REN3S5azMjrUKQerHCn1A6T09XOv17vPhEv7JejHo4CE+x0UqQ0NDaGvr09y7tw8M5kM6uvr0dTUBK/Xi52dHbGVHhsbE3dTu92O6upqVFdXC7giKMj22be3t4UxSCaTIowG9qyyqafQkR1ZukwmI1Vc0WgUfX19op+IRqMCTDjMOilWGdlsNlHS856mOp5gh8LeqqoqtLa24tSpUygvL8fa2hpu374t3i+RSESAAe9hPQjeq6urUVVVJWXX3FA1S6OPtbU1qX6YnZ2VTZhpFxqfsYEYRbCAMU10WOruqKk6sgPLy8si5GUqiEAgJyfHEPwQHBAU8HjQLcfhcOxLE5g1Vfo8aPCi0xHmVJPV4B7BNUGzwnl5eQgGgwiFQnItdLriMGaH/jlLS0tYWFhAJBIxgCSfz4eKigpUVlYiGAwa/j+wl8JgWTNLmzW4cTqdCIVCqKioQEVFBcrLy+F2uxGLxXDr1i380i/90iNAARgFJQUFBQYV/MLCglhLb21tZc0/c/KZy0xJ2ZqZCjIUGvmbqS9Oai6GrLoAsC+vRtTLzYa6D7oj5ufnS952c3NTqFIiaLpo0sNBpzCYz9WdAcm+sJcB9RMEQ5zEzGWXlpaisrISDQ0NYiCj0zpMzVhtHDMzM3j33Xdx+/ZtoRpzc3Nx6tQpnDlz5n1tnU0rY7IFZvaAzzc2NjA7O4vl5WXpDcLzTU0KmQlGpNS26AhHAwgzoLCi8jn3eBBUWP38XgnWdnd3MTg4iNdeew1vvvmmiJkzmQyKi4sN/SV2dnYwPDyM8fFxg1kWhbpczAoKChAMBqU1Nh1U/X6/6DQWFxdx584d3L5921AymMlkJC3mdruxsrKCpaUl2RAGBgYwPj4uBj0UflKjUVdXJ4K0jY0NjI+PY2ZmBvPz89ja2hLWcnV1FRsbG1LdQcBfUlKCpqYmNDY2orGxEXV1dfD5fHA4HAKIbt68iZs3bxo8ILxer5SCNjU1obq6GpWVlUc2VFpZWRFNxOzsrOF85OTkSI6fr9fY2IgnnngCtbW19ww+ta6AaQLzYzQaxcLCgohFFxYWpJkeU206vcrPZZWWM6fs6H1iXv94DXjf8JH3TjweNxjm8ZH3OPVb2d7XfJBVsGpvQHaLIEEzFysrKwZgZGYuso1kMmkoAdepWoIIavd0FU4qlZKUNQ3wzGkcu91uED3T9BGAaHempqakGd3g4OAjQAHcBRTf/OY3AWBfTp2TiDS4bupFsZruLqkpNrvd2PJXi8ZImZFi1I/sZFlQUCBK3FgsZvBN4IJIoMK/17k0bhqkDL1er+gAJicnMTs7ayjtI2hxOp2GPhX8N54DXULKxUA3saK5TmlpqVhWHzZ4M2ZrbEZF9cjIiJTuMf939uxZtLS0CEA5KnuRyWTEhMvqMAMHc8R4lMGFUdd487Pz+9XU1KC9vR2tra0oLy+XagorTUS2z3avt57L5bIEHVbg4yjlmRR66WN5eRk3btzAtWvXRPuQyWTE4pzeF0VFRVIVQrbG4/EgHA6jtLRU6GQ93G43SktLxbOCR25uLubn59Hb24s7d+4YwIXT6URjYyOKiopw5coVvPHGG1haWkIikZD0A23fyUJQlMrolBVC0WhUwEU0GjXoFHw+H8LhsDhe0jqe2geyIBzcEHWVVEFBgTRm6+rqwoULFw50myRTxA6ZbOIG7N1blZWVcDqdWFpakoDCbrejs7MTFy5cQCgUOhQUWIEEPrfSFdAdlGyn+f5hQzq/3y/OrUwj6Mdsz/nI9SWTyQhTZHZONXd+zqaTshraFE2nGsw/368+igwZu6Fq8bPf70dzczOamprg9/uxvLyM4eFhjIyMYGpqyvC3OTk5wvJVVFQgJydHWJHZ2Vmx7yegNovQdXm8z+eTXkH07pmamsLk5CSWlpaEkclkMnC5XOjt7X0EKICjNQfjxsxaXS7onKDa4IlUNk8FNw+CCjaVKisrQygUEkdBlm8RHbP+3WoTc7vd4jTJ/2+32wWtanc+Cmjoasm0CAEQFzMAIm7jBMv8pP45Ho+Lsr64uFjACRfh8vJyMX/y+XzCfOhSJvPBahl9ro4yuPHMzMzsi+i4iDMCMUcQ5ryqbgWt0zr6uXkj1Wppq83Y/DuzkCqRSGBiYiKrFbvX65VS4IaGhiM1T2K0bwU4GGlpAHIviykA0UTwu+gKEl5H0tRk1cylvFtbW8L6cV7k5uaitrYW4XBYAHcymcTy8rJUcNB90uPxYHFxUdIJ2YRxeXl5AjJKS0sB7BlSXb58GSMjI5icnBQXUQrknn/+eTz++ONwOp2YnZ3FwMAARkdHsbq6KiJKslME8AQhzKHX1dXhmWeewec+9zmUl5dLXwvqKFitog/qhFgRw9RUKpXC4uIiZmZmZPOno2Zrays6OjpQWlqK/Px8Ea1OTU0hEonIZ02n09LWnikPpoYAoKqqCpWVlQBwICi413nC6JfgSVe+0T+DIsBwOCwgIRtDCUDAdTagoIPAe/kOXL8OAwtWgPa9GtFoFAMDA7hz5w5GR0eRSCQkkIxGo8Je5Ofnw2azIRAIoLm5Gc3NzQI4NzY2MDk5KYcGlxzshEvwYbfbDe0GqA2LRCJYWFiQ+1b//9bWVpw8eRJlZWX4+Mc//ghQAHcBxZ/+6Z9KqdzGxoZQQtQ8sC7eajCnTeGX3+9HUVGRLBDUNbAPhcvlkqoDIuetrS3JpZG65mLDjpnl5eWoqKiwdMHTNNTQ0BCGhoZEyEXtBhcn3ryMqABjbplVKyx142JAqj4UCqGzsxMnTpzAiRMnZELez+D7mmuoebCihJGdjjSWl5cxOTkpJkBcSOmeeNSIgdoQTYvyUVt4c6E5iEnJ9pysk3msr6+LwHFsbGwfgCwtLRVwUVNT81BSFWbRKZ+vrq4aur+Sxtds1EGDXVDz8vKEvtZRT0FBAXZ3d9HX14fx8XFJw/GasTIkkUgInUqdSGdnJz796U+jrq5ONBiLi4vSgG9hYcEAMGOxmIDrtbU10RIwTeF2u1FZWYmSkhLEYjHROdARNZlMYmtrC5lMRqzMWUbK+6S4uFg666bTaVk3qM/QILOgoACVlZWif2D6goLIzc1NiQb5uVdXVzE5OYnx8XGJCllOqAGz1loVFhZKeSI3Yd7n7CiarXQUuFuxZMUEWD3abDbMz89jdnbW0nmzqKgITU1NaGpqQm1trcxfrjNWPVjMz7Pp2rINikrNbqnmxw+r8+3m5iaGh4dx+/ZtXLlyRfxJmBItKipCdXU1nnzySZw5cwY5OTmYmZkRAGHVQDAQCKC8vBwFBQXCVBNAmHsB0XKAIIKi8fz8fLS0tKC9vR1lZWUioF9eXsY/+kf/6BGgAO4CCrrXWSl9CQJYTklxZigUQjgcFiFNSUkJioqKJG/HFMfW1hZmZ2eloRAjUx1VMlrmZsiDC61emEtLS5HJZDA2NoaBgQEpH6VGg1EI0yDMhRUWFkq5akFBgSEHR0qak4RolJEiAKk6oH87owufzyf6iGPHjqG2tjYrwMiWZjBH2Dyi0eihG5mO6GhK5HQ6pdthdXW19GjRnUZ5cJHWoOZeo/ijDE1tWwEPl8slwipGCFq4xfQIKVAyU0cdjHaYkuBzPtIdTw9dapxKpeD1egVw8X6x2+2iAznqedvd3cXMzAxmZ2cNtfQ0i2KvDm6uzAl3dnbiC1/4Ah577DHDpphOpzE+Pi7txlmiubGxISI1nkeCQlZvkLZlyk739GF6gu8fDofR2tqKUCiEhYUFDA8PY2VlxXAfp9NpERUyyOB9Qu0MGT4AkjqwEmICe+BoZmZG/CHINDLdyHs8NzcXsVhM9F7af4DpF1a5sIqNlUi6DLuwsDBriWI6ncbc3JyA4OnpaYOg2OFwoKysTNJVTqczaxO3e7nHWIKcrf27/t0H0T/kQQa9Nlg1pT2GgL2qDIKx1dVV9PT0YGVlRYIssldMMfP/kF2x2++2HmD6WqfqyVazb8fOzo5BsMn+UhTMm8ejslE1CCgqKirk5jdHFrxZD4t4mSIw21hTT6HVuRSf6Zs4JycHu7u78v+pOmclgbbIpk2xFurl5eVJVEg3vNLSUilbjEb32lubjYY4GLVVVVWhrKwMXq9XKjh0OoXRGjcjXQJLDQYXKbI1BFfaWOtehr4uLCfVUSB/t7Gxge7ubty5c0cWLJfLhY6ODpw5c0Zach82sqVtrNI4Vi51DwOcaLpzbW3NsNkwDREMBsWOvaioyLBYsMRZV5togKJTPDwnBQUFstmwgoTHUdqum7VG2QCjFr2xNbjuuqkZjaWlJczNzSESicgmSuOnUCgEp9Mpm6xuMb+xsSGt3DOZjOgSWJXBjYcN+8jYcI66XC4xc6uvr4ff7zeUH+pKA23jrs/DYY3MdDWDnst2u12qxDY3Nw3VXbxmqVRKNlACQoL8ZDIpQlZqQcieHGXk5eVJea3dbsfa2pr0g+F1IhCnFoYi43sBuezRYwUM9POfFldajq2tLUl7UhfGYbPZUFFRgcbGRoRCIWHsKGalNTw1Ebu7uwY3WPY8Yp8NDRyAu2spqzS4r+jzW1xcLGlDAnfNwmuwnMlk8Pzzzz8CFMBdQPGrv/qrOHfuHDo7O4V21YuzFarjgkWjIy765g3TZrMJDaeZB4fDYdm8JRKJSLqCv2Pko8uwGFFpwRJpek3nUSuhG2hRPFZWVibplGAwaKjh52Zo9oFnukGzG3Q4pIDN/P35OWl0RFMvImtGUFYCQS6w9zJ2d3fR3d2Nq1evGnKIwWAQp0+fxvHjx9+3/gNW4OQgq1yr37OSYGZmBouLiyLO1WY4BBmko60iNWph9N/RGIebglmpftCj1e+ymUmZh2arNjc30dPTg8uXL2N2dlZYEVaG2Gw2aZs8NTUlpXoERtxwqeInKMhkMvB4PCgvL0dpaamUeLNKKR6PY319XTZ+fZ8RvHCxphEVu85q1tCcQtDXgikUzQCyb5A2LeLizmZM+h6oqqrC6dOn0dHRIaB4bm4OL730El5//XURn1J4+tnPfhZPPfWUoQqKpaJMsaytrWFhYUEs+Zke2tnZMZS6m1lCpkXInnJz0of2jWDvB4IE3dDtw5p2eNgjlUphenpazKXMLITX60VVVZVUB87NzWF8fFza1usKFF2iypJaanuoIWEal2w6Aw5q7dggUWv8wuEwmpub0dnZidLSUgEMZNSyrcGPrLfV4Mn4rd/6LUHCzzzzDM6cOWPQF6ysrEiuUCND87Db7ft8KjweD9bX1/fduBR97ezsiMYhEolI+SVLorgJsAyUUf/u7i42NjbktRjNaPGMNsJxOp3wer0S3etGVxRr3otIUtcyE8i4XC7RPvD7MPfL70PVNNMwpOY8Ho98P03BhkIh+Hy++4pQMpkMpqence3aNdy+fVtuRqfTifb2dpw6dQo1NTUfiugnk8kgEonIYq5ZIAprddc/XVGhS7+YPigqKpLUXDAYNIiLdZnvwx50abUCIYcBFJfLhaWlJVy7dg1DQ0PScyMWi0m5HbUF7LXCjd/hcMj54TwjSCKo43kmSNYiPl2CyMoBDeB1GSIrFGirHwqFhOpnrb7f7z+w4igajeL69eu4fv06bt++jcXFRQE5wJ4eQvcEstlsKC4uRiaTEYdSnT7Jy8sTzQHL2oPBoJTY7u7uGtIO+nwwiGFFhq5WS6VShqogaifMpZFah6SN9QgkeK/rSjQ+zyaI/ygO6kPm5ubQ19cnDfjMVYG6r1EkEsHKyorBxZiPug+SuccL2SECOK6/dDHW/Ymou6GJYDqdRlFRkbQPoL2AuVrR/Dvz77e2tvDrv/7rjwAFcBdQ/Mqv/Aq2t7cNDo11dXVwu937FK4cDodDFpLCwkJBcdrhTrfHBvaoUEYIPLjR66OqqgpNTU2or69HVVWVCDF3dnbEknZsbAwTExPY2NgwRLLa3lc/clO3qqc2l7iae2MQOOh6al1fnS1vmclkpGSSpYRE2Zo6JoNCJsOMhilY1SwPAQlLEK2MafR3SqfTGB0dRX9/P9bW1gQQBQIBnDhxAqdOnZIy1/cCYHDhpvjODBwIGA4arA/Xbq5cIDY3N7GwsICxsbF9ym6HwyEeDuyUabfbDR4i2R4P+jdzczl+T+Zq7/VIJBKiBWKOWANsRv7UQejPSD8WziWth+L1B2AAt8BdoO3xePY1G2OjsUQiIQ6Y1BvpDqmcjxRjc3MtLS01sIClpaXY2NgQLZVeG1wul7hvFhcXiyfO/Py8VAZRK8X7mYwJzZDsdrusMdxE+B2DwSDKyspQUFAgZb4bGxvydxoU0D+jpaUFbW1tCAQChvJvnYYlZW5+vJcUi3aFzAY88vPz33PXTvMgi6adjrM939rakoaGS0tLkurSwlmy0iz51+w356SZQWTqzbzuMa1BRtl8H3HOzM7OGoJfp9MpXXArKytRWFh45DSwVQ+g7e1t/N//+38fAQrgLqB48cUXpW0w1eJerxd+vx8dHR0Ih8OGPCFd+egqabURaIqRC3cmkzEAB26ENN9hPTZRK3t3zM/PS1RiPs2MAvREMyN++jNoTwlOaqrcrQCCw+EQ9Mt6cYo8XS6XZUpIgwWz8Ccej2N1dRVzc3NYWFjA4uKilHvFYjEpJdXsBzeJbIPRUraadXOUyDLGubk5LC4uSpRqs9ng9/tRVlaG0tJSS5BiBVj0I7UL2sxMawg0ja41NbyhbTabQTSnD+oYjrKobm1tYWxsTIDnxsbGvvlQU1ODuro61NXVSUdEnh+CU16ToxxMIzASM1sgW1nM87ozOt7c3BSXVwIIplC4IDMypniQmxhTCASErLAi2NDnmbR8XV0dWltbUVFRIZ4XOuXBFIhuoEYV/Pz8vPgr6H/nfGD6hWlNmmeR0WPagLb3bB2uy3LX1tYwPj6Oubk5WcRTqZT4g/Bn8/3Ae5i6Ln0OCRgqKirEqtvtdksfGupFHhRUp9NpSWeZwYcGHlZiYKuhRetWvSsIOtxut6X1NtO11LZpjQvvUQ0QeGRzBGXqTKcjCB54/bTTJu8tDXQ5D3Q6WOsTDks3mM/32toalpaWpPEXB1lDAk6m8IC9tYDpKdrf63Q3QXsymbR07UwkEvjTP/3TR4ACMDYH29zclEWCk02X6jQ1NaGqqkpqgPXg5GCExZsGuNv2WVNdzDtS6EIHSvNNZ1VX7fF4JBVQXl6OcDgs/UbMZad8PIh6TSQSkophWoY/HyQoZFMkpij4WFRUdGSldSaTwfr6usE3nvlgHelyA2GOnsBkfX19n1252fpX37SaOnS5XEin09JZUTe8ycnJkSoeNszh4nzQRnuUW0D7F/DQ/TQIZA5jXLI9UiegWQIa00xNTWF2dtbgr8CFggszF7EH3VCYa+c853dlGmpiYkLq5PVixWoP9riora0VwD0yMoJXXnkFly9fNlgEczNh6pAbCjdvAhOee/ZA0G6cBG0HVTnoQeCltVQUTHOj0VoO/Zn4PbXXCYEAgb8GKDSbo9iaFWWsKuO1ojsvNxUCNVqUc9Nj86/W1lY888wz+NSnPoXy8vL7rpAws1JmqtyKOtf+HrxuBBrmHjpa36I3bLNAln+jdS8cnAPmSq+jDKbQKCzX1XDak4VrD6+vfn2mLgoLC8WUjW6vrLzTJoi6maT+mfOG6Yy5uTkJHrheJ5NJ8f2oqqpCYWGhAP719XVht+fn5w17jHYs9fv9+wJT3ReIBwB84QtfeAQogLuA4pd+6Zck1ZGTk4ONjQ3Mz89jeHgYS0tLgjDz8vJQVlaGsrIyEVaSnrVSc1vpBWjgo62wtUpdswW5ublSv15fX4/6+noEg8H3hfojA2MFNKxqnTnsdruB1SDY8Pv9+7oxWo2trS1pRjYxMYHFxcV95zU/P19uFuYOyRZpTclhNezUGpSUlCCVSmFsbAxjY2Ni9BOLxWQRoAbhoF4FmUxGNi2zdoALASNeK7CoI5zD0gMH5TcPGroUlODIHDlx3nJxYeMpK3dXM4Dl4eI2WgAAjL9JREFUQkPR6/LyMkZGRnDr1i0RVZoZvby8PNTX1+P48ePo6uqSCqXd3V1MTExgbGwM/f39uHTpEiYmJuTeoaskFz6CRfaLcLvdKC8vx7Fjx/C5z30ObW1t2NjYwPDwsDQ0Y88ank8AIhr2+XxSRaJ9EeicSqZPBxEs29TXQXdjJQAg2NA0tfa5AO6KO6nc1+dcs6UA5HNtbW0Jxa03eg02ydzwejscDhQVFaGiogJlZWWG6gqWjR8EEsjo3OswlzFasZrmuUoGy8x68TAPsw0AN+ecnBzD/CW7S4aQETsDHrpE8hwT5GgBrk4PB4NB1NTUoLGxUZq/lZaWHtk+XQ96dhAQDA4Ooq+vD8PDw6K7IbimduoourN0Oi2Vg+vr6xKA8aioqEBbWxs6OztRX1+/L9DIZPYaiYVCoUeAArgLKJ544gk5iVrpztbNQ0NDmJmZkUnEXBfVtLzRuYGyJwB91Jlrooo7Eonsa0Jjs9mk1IuNXAKBwPueNzzK0MZBmt04jNXQwkvzkU3xvbu7i6mpKbmpZ2Zm9i0cnPy0nq2srBSvAQoXmQNnuoUNnMguaA0AF2c6GhLkMWpua2tDWVnZvrREfn6+pD2smAz9s7kTrfYRMQOV+/lZbxbmxVQf3Nx0VAjAEMHl5OQY0jBWDceY4qMpHKtRmBLga5K5KCsrQ1VVFerr68XoKZPJYG1tDSsrK5iensbCwgK2t7fFbIueEUVFRRJRU8xI6j4vLw9dXV34xCc+gYKCAly9elWAZV5eHs6cOYOWlhYkk3u+KnNzc5IaojEQF2ieR1qEs68BADECW1lZETZR6zwYcSYSiX0ujmSE8vLykEwmpTSbGyW/J1Mm2TRR+rrzvfV110yXrr7hRs45SSaWc0RXqGhdGTVLnOtkPnUen/bpZGU0W2aV8tL0OeeH1WH+NwZcusyfKU5+F4InplspTDUL6pnK2t7eFkaHxm68Hjzv1Nywcq+wsBB+vx8NDQ1oampCa2sr2tvbLVuBc1CbYTaXs3K6JXjV6Qw9l3JycmTPIYig30q2LsNWHYYp9h0YGEB/fz/GxsYMmgmHwyFMIZvq8fM98qH4ySCgOHPmjKAvLZIhM0EamqCAi4fP50NtbS2CwaDoH8LhsNSHb25uYm5uzlJjQf8L3cHto15GlclksLm5aQk2NjY2DoxieGOaD3MKJZlMYnZ21mAvS4GTBgdsW800CRdcDir/CSrYo4SLHwejYe1QaLfbUVRUJDa4moY8qGzzqEOX2mqxarafdWqB/2Z+fy7wVjoXvRnQdIopkvn5edkkdMkyc7sEEouLi5Kf1lbOBN9FRUUiUCwpKZF7jZ0O6XapG9/p3C1TFhSRaVqZiyivPzcrOkSmUilhNHj9KHQzn6dkMilCT84Hbmh8XaY4ea1zcnLEACgQCOxLi6ZSKYMLJhkNVkHxtdiFt+gn/U1SqZREpwRaDEi0WJVzxmwfb6bHdeWa1oro8nUNVHiedcqU/5e/J6uq28RzHjJI0312tBcKPxs3OXNfo4Mej9IjSI90Oi3XYG5uDjMzM5iZmcH4+DimpqYESOgqGQIenZ7WFXfUlGkhLr+nBkL6fMdiMcvyevNIJpMCWulmydcvLCwU5qOurm5fp2ErzySmbM0mY1YOpdT7aLdZcxBHQOJ0OvEXf/EXjwAFcBdQfOITnxCRIm9wnWsjBcz8qnZxjEQihpI83ojAnrCzuLgY4XAYHR0dqKmpEQBBAcz/K4M3iBlscIHNNhjNERxwE2FUtLGxgZmZGSwtLUnVBBuemRXWFD7RC4PKeB5cePnaugnS6uoqFhYWsLq6aqj6YVSse3fY7XZDnwa+J8VPfr/foCvQIIG0/QdZyqqp8u3tbdy8eVNSFkw5EIzFYjEkEgkBU0zvBQIB1NXVoaKiAiUlJVLxMz4+jtHRUUxPTwtLxNw3QR81BHa7XTZM6g240WZ+4ojK+5SKem7C5hJozhst+KS3BFOdeqNjFYwW7/H/Anc3cJozad8IBiBcR8hE7uzsyMZFdiCVSonFOPU0LDt1u93Y3NzE8vKy9NTRpeRlZWWyqQGQKJaVIDpVQKBGQMhND4CkQLa2tgyeMppR0KJdDWT0ILgj2NPsntYycY7zZ23Op1Nn3MCzlahalazqtgY0htObIkuR2aOCjBQBKAW7jMbZsZnzJ51OS6UW7dY5h48yyGpz3eBaRNE1TdlWV1flbymkbW9vR1tbG6qqquR66Dl62HGYyR7PjwbyfB9+JlYu8j7JZDJ4++23HwEKwJjyIAonZcncORebWCwmWgkKKLkwcOgNwul0ykSherehoQHNzc1oaGh4oB4YP00jnd6z8x0aGsLY2BimpqakAkNHDGatgvbqMFOguo8KbxAtgAPuAhVdHcNNxbzB64XQ5XJJjTlNlkhL81ofVo1Bt0dW9nBRYdRMlztznvqgxwf9GzIUXCypB2A0lUqlDMZM3LB5DRhlE1QEAgFJO5GFoGmTLqcjkCOIYoqEUbIGkTbbXZM4lnRq9kIzNC6XS9IlLAmnuLGoqEgiMoKLsrIyVFZWSokoRZ9c1jKZjERl9MSgTsdK48Nr6vF4pLJJrxWFhYUoLy+Hz+eTDW5ubk4obkaEevPlesR0hL52ZsEiRZ1mTYJZU6BBAOc5I16Caor8eI2ZVtRGSRSBsueJ9lQgwwVgn+Mnf852v5iFyNQpmO8PDSJ11RQAAz2vPwvnHuct+9AQyDAlYAaaZh0BN+JEIiFzUq9vvM90eS6/RywWE30aq/h4FBQUiDicxlRWOqvDgg8yIwyEdApJzxsAln4iejAlzL1wfX0df/u3f/sIUAB3AcWnP/1p5OXlCahgVKpz3kR3+oJyQdQIlzmtUCiETOZuS11eTI1OmUNmtzifz2comTxqPtHq39+PwbSBufpB/455Se27oBuWsZrGamiaXv+NZh101MYFgqCA7ADPK5X5LOU1n2uW09EMitRzto14a2sLQ0NDGBwcxOrqqnwum80mYka73W5oasaeD5o9MX9/vbibXS11nvhBr53u4qg3WH1tmU7SQJsbNsGYzWZDJBLBzMwM5ufnJU+tBYZckN1utwDt0tJS+Hw+aQfOslGbzWaw/K6trUVzczPq6+sltXgvbqrz8/O4du0auru7pUzR4djrgTA/P4/R0VFJJfh8PhH7er1eyY03NDRYsopUzVOHsbKyIroIlqFzIy4oKJDvEY/HMT09jdnZWSwsLEh/C1Y1kAHVc5ypBUb1hwUkZFd1BZCezwQZ2vbcvCFynjItol8zPz9fNF/FxcWyCWlXUAJQfj/zvOdn0Skavj/vf/P6YgZQ+rDSaphBhgbAum261X3Fv9VieSsRMufkQYZfBNd0zRwdHcXi4qJhvSTzxbROtvtcn0cCcl3Bplkosj9HScWSjc/Wpp1aGlZPLS4uPhJlchBQfPGLXxS1NsV4VgpijVI1RQ7cNa1i3pXCKu2Ipic7cFekxklOVKz7h+hDC6sOGvp1rUAIaX0zONI3ufn3VqrqbJGuzs1nq2bgZ+DgudKRJnOm2rND5ye1sEx7IbBqBsA+RkNvcFyw+Jn52jzHzLXrI1sJLjvvmYWpbrdbKl28Xq/krM09QTQtzffW0aN+zEYPa+dBHVVlfuK9QYp2dXVVjIe0PkBT+0xj6FQBrwkXJTr8Mc3E763nhM5BszwuNzcXxcXFiEQimJ+fl43K7XajoqJCms01NjaioqLCsAg+CJCKxWK4evUq3nrrLQEwvK/5HXn/1dTU4KmnnkJnZ6fk67n5mkW2fFxeXkZvby8GBgawuroquhymKFi3TzCr3Q/t9r1GXgRp+fn5Upa6ubkpTZsIDFjaTAE3za109K+FiVb3K39PIMP5oUvXmT7hvcIgwQx42FqbzrbmtB1z+NrjgVoSggQzm2IWm/J1OA/4/fR3IROgh05P6RQK13KCNW7G5uos3iNmtoRrkPZsMLdo4O9ZzUeArj8biwHIhvNc63On12fN4On10GrN0GuZNge08vIguOK9wHSmlaEVj0gkgv/yX/7LI0AB3AUUp06dkoUXgAhgtMiIUZDO1eqTy82Ai6zuCkjBEgCZ9LpHBvNvZhStnSm5QJgnkDmq0CAg23OdAzU/8rkGHOZN2bw5m4fVDW3+rPpmNk/+Bx3mG9B8WH0+APvOi/mzEu2b0yBmIy6Kn2hmpel6Rt7m/8f34c1sdqEk4NCGOVaP5mvORU0DJUapmjrVIjz+HTcuzi2Cbi74WovABTc/P1+aC5WXl8vGyPuCToKbm5sG6rmoqEi6w1ZUVNyz6C7bSCbv2pSvrq7KRkjmkBu+vsd4vvj5CNisGIF0Oi1RuC7XBO7qNrSbp66o0NoBLfIjONDMghZ2snpGD4/HI91Di37SkO9hjHQ6va8iidUIdNrUAJ6BFAEuy3h1yk2b2FkxC3qNMa8L5jUJsC4N5X3K9JD5Htf3iR7mtc9qHdQHYAT/+vPq+0uvlVzfdYBk/nerNVGvTfxM5qE/Vzati5mxMT/nWmRmgM0H5+Vbb731CFAAdwHF3/t7f08ETqTIj+Ivb96o9M2wtLSEgYEBzM/PC4olfcRFiKkVRtqMaLRmQE8cLnhWxix6IvBvzBuV+abSi4AVYODrmt/HPAH1xNOTkc/5t+abJtukzva+Vs/N3998Y1vd6Drvao6MODR7oSMm83ckPUlK0ev1ymKeTt8tpSS44GfVDeMOo641k6TZDS0aJdgwL17Zzrc+Z5oB0VGZVvzzdfn3BLoFBQUiYtORKd+DvQWWl5extLRk8GmgjoU2wjwPNptNBGs8GDmZQVE2HQhBhDa64rxmgEAhLTdHDQh4L2vAS/0F9QW8trw+yWRSqHFz7t3pdMr6woWYehUzi0eApTU2ugIsk8mIPoRVAHpzsdn2Uka6m/HDAOuMjglyWfW2srKCqampfdeX4EkzJvx8PK+k65l20KwN18mNjQ1DGk2nMThnzVUgZjEnr6E5wqZwVQN4PV/MQMIqGON30ukhDTr4b/caQB20jul7RX+WbGusGYxYBYR6fTKvSeb/r3/PEttHgOIngOLnfu7n9k1qrT7m5Db3NrCiEs20Irtzbm9vy/vm5ubK4qs3Lr2B6Y1CC9l4mKNiwAgqrNIcXOxIQ5tvOiv9hrlTKisXWJuvFfIazepH8/OHxURwHMZImBcGKwCYTqeFYqbQjCIz0s6MtHXNuGaXSJfm5+ejtLQU4XBY+jikUimMj49jYmICS0tLhrlCTUFeXp6UbprpdC58WqPCz89zwEfzgqXz5fysOvXDvzVHbpw/XORzc3MRCAQM1QVmJiGT2TNEY/qHOg2mF6ihaGlpQXV1NdLpPXMd3QhNWx7z8+hctmYTCCy0p4g5cqP2QJf0agU9j2QyKV4xPDcU+pGxZEqI9xkDAl5Dbvwul0tSAGVlZdLN13xfZjIZ8e2gHT1LlHmtbLY9TQ7nEjULuhpldnZW5tfGxobh/1MQ3tDQgMbGRmlLTvaBqUKzVbxmJAjSzNbUrPThSKVSAjQ0c+FwOESzUFpaaug4qs2rUqmUlK9qDwSKJwsKChAIBFBTU4NQKITc3FxEIhE5d2yypYGDOQWpDcJ0p2bON/19zEwf132dXqX+iJ9f3z96Ldb3Zrbgx3x/cvD/aG8RsxGiTtdoDQXfl/en/j6a/dTgKhqNGsCV/l7mvYg9ih4Bip8AitbWVgPCtGIHSKVlo4D0ZmmlW6Bd9Pb2tvxtSUkJqqurxUHNXFXABTCRSGBxcRGzs7OYmZmRaEoLRjUSBu6mVrhxmZEraUHtfhgIBBAOh1FVVSUlrvSCoLDx/9VBylk3fmNkNjExISptmhxpwRijYlYnsN8AqyV4szscDhEdssxQC1fNmyr1GeFwGOFwWMoH19fXMTc3JxVJXPCoVeBrUSRGgSxz+/r1CRopOuNGyp/JHGxubkplDhenlZUVaZNMoBUKhVBQUGBgU8wHUyuk2s2pBK1D4nkjqCWwo6VxSUkJ8vLyDLbG3NgPutbLy8uYm5uTe5bRN3P0NptN0gws8eR7UityGPNkNZiO2djYkCMaje77O/oRaBfeTGZPn8MKNJ5/szkW730yKVyrtFZKM3P8/9zwzAED5wqrpeg+6/V6EY1GpQKEACYSichr6XYF3MTMzAZTKGR4dQ8SBnz8/AQkGmBqa3zzoRkH/X3MKScd6ZNNZgWMZizz8/MNjB2Fw2ThdDBlFeBoPQg3ew1EzHuUZhC1aZ4ORs17gZllyZbi0feXWT+o2d6+vr5HgAK4Cygef/xxg78BsN8GWS9GVo/0xydVyZxoaWkpAoEASktLkZeXh9XVVbz11lu4ffu2XLTq6mpcuHABVVVVhkY6Vgepbh3RafU0NzBaJ3NSJ5NJ2WCIUnXUa47qbLa7OV5GqPw+7KIYDofFoc0qWv0oDr1gmJsGZftZpyAikYihnTzV7VaDgl193QCIcRRFdzRLCofDct5DoRDsdruY84yPj2NpaclQd76zsyPVLmxZTHFmMpkUkRYpYpqLkZ1Lp9MGK3N+HzICGqhwkPLlgk8gVVVVJb1R+L2Bw5u7eb1epFIpDA4OYnh4GCMjI1hYWJD/S9Be9JNWzMePH8eJEydQVVUl6cXDmCnzsb6+jhs3buDy5cvo6ekRx04t4HQ6ndJMrqSkBB0dHejo6EBxcfE9v6fV77UAlJ1k6cxJkKBZrnQ6bRA267mlnVl17xt+Jm1HbRYr6uf0yTBbsDPNpzfLeDwuzBPLSldXVyWS159bp011GlXfk3qz04Pvaf68+jBvmnoj5qMe3DDNqVwNqLRwnKwdO09rQSe/k/kzmRlEKy1JMpnc12BNW39r4MT0rRUgMDPCmsk2H1r0m610nvclGfb/7//7/x4BCuAuoKCS28wqaCQOwDJvpVG/pqHMVBQAgwd/LBbDxMQEZmZm5DXy8vJQXV19aL8OCp4YmaRSKbl5l5aWAMBwQ7rdbtTU1KC2thbl5eXIzc01TFRS1LSkpqhUo3srARDfh5GCz+eD3+9HaWkpgsGg1FDTHfEoupSHPRgBHQQM9O80TXsvw+Fw7OttwWNrawvDw8PSgnpubk46LZp1LDwo1vN6vQgEAmhtbZVNcmNjA9PT06L+J4DgHGLDOea5dckyNw/+zMiP/TqypaMymb1KEbpaEpToWnjSxUxJ5ObmSvdWzRBwrrD6RWuXCICXlpakHHN2dnbfNeF9ZLfbhX42D5aA8giFQvtYtnQ6jcXFRUxOTqK3txdXrlzB6OioASS53W40NTWhpqYGmcyePbjT6cTi4iLm5uaQk5MjwKKurg7nzp1Da2urvBeZAyur9WwgleJRq6GB4ebmpgAMvhfXjpycHAGMTHVSf6E7Ietr7PV6EQ6HDfb/3Fw4B3TJN6uGWO3Df9OOpZr50EyqZn+5aWs9kl4DzToZc7SdTZPFe9Ps6Mn0i3bTBe7qqwik6auhzxHBFQEFAbhZRM/PbU5pm3069HnS4MKsrTnK4H6l7zczWNApTitAawY95vOqj1Qqhddff/0RoADuAoonn3wSAAyo2ZwvAqxPqBbiaIGfvgHM5iM6sqL4jVEdJz37egSDQQSDQYTDYVRWVkpZlu45osGL3W7H4uIixsfHpaucuUUwO9HV1taipqYG4XDYsNCm03fFhFy4lpaWpI06QQdV8sznHzToKMjGO2amg71PDqOirRTnVgs1j8Pc4bINLhZmgJDtOcWIzOfymJ+f3+e/n8lkhOZlBMm0RiaTEdtbam80ZQ0Y/QI0SODCyahf+xVQVEianE6hHJopYATicDjElIpdQTVTV1NTg7KyMmxubmJ6elrmTmlpKTo6OlBSUmKg7qlH0ZsY/w+dDcmEmHU+wWAQjY2NaG1tRUdHhzA0HBsbG5iamsLk5CSmpqawsLBgqaXQDZpisZikEQmSeC6KiorQ2dmJp59+Go899pjBg2JrawtXr17FtWvXMDk5ifX1dUlFUhtARqm0tFTWgvsZ3AD1XKOoU7eMX1pawuzsLBYXF8V0yMyAME1DU7WioiIAkOvCa6M3N26e3CTNGyJTFPpa6jQr2RyuUSyhpSZLm58RRHF9JOhkTyRzNM3rr10s9abNQEj/vZkNYNrX6XTKWkfWF4DoJcyurGQlNSNgBgUADJ+TQ6cvOLKxGJot0H40ZjbPbPmfLX1/GENmBm5WVv36+e7uLl577bVHgAK4Cyi+8pWvSPTMCULKkbQSqV3mdLmR8oYyAxGr47Chc+4ADDejBiFaw6FFZaQ6db211+tFOn1XUMp6dg1CcnNzEQ6HUVNTg5qaGlRXV4snvLbONdOazM9vbm5iaWlJGm+xiQ2pcitrWqub0Gaz7btBtPOhVoDfi7BTswdWDIL533SlRraRTCaF1SFwmJmZkajPHEmxokGzVBSkMWc+Pj6O6elpLC0tiU5GL1A6ouNc4DXkYqKrMAoKCqR8k1odNhKiqZSmLwFgZWVFzLomJiYM89btdqOxsRHNzc1wOBy4du0axsbG5N+bmprw5JNPoqamJut5Y5Q7NDQkHRPHx8clqqXoLSfnbkMy2lLrwfOpdQv68Hq9WFpaQn9/P7q7uzE4OCgpIQI6sjfUP/j9frS2tqKrqwvl5eVZWQUN0Le3tzE/P4+FhQVD11Hm06kbCYVCItrU0axZh8XNh2k3bvRkIniesq0nGnQyUNGbK/9Gi131usHNkmkS8/zjXCOLwHtBiw7NKRev1ysghnPOauzs7GBxcRGLi4uIRqOGqDoQCKCqqgrV1dXiGsnzpcWF+pHfgeu2WUxKUaVZWMp7jClBCuh5b/Hf9R6hg0ga8Vlp6ficpcK8H8vKyhAKhYTN1Y287keLc79DsxaHpekSiQSmp6dx9uzZR4ACuAso/uf//J9SxqVdA83Obtme8yYyq8bNdrHaiMnKJIQLFr3nzbXrWtluFtXoYUa65kltpuA49EbFDVw7I+pIQ1sC87talUORvdH2t5o90DbBmlrTj/o5FzTaG1MAxY2TDZpKS0ulckLXoR80tLBJC5wo0KOSfGlpCWtra/K5zcJX0qnaSY8MBjUajPxpSa1toHmdtAiT0SEZCy5avP7UXFRVVaGystLQWyTb4ILJ6obV1VUkEgm55qwuaG5uRlNTEyorK9Hb24u3335bdAx2ux3Hjh3DhQsXEAqFLN8nk8lgfn5etB4TExP7fBRyc3NRW1sr/T+cTqdsolaH1YaaSqUExPKcMsq22+2iRtd22YzAeb1o0qRBp9Pp3EdFp9PpfUBga2tLgDRTUbFYTF4/GAyiqqoKwWAQNptN0oo6vcjNjZ9PR44afOsNlfNDCwo11a2rQbSegs6MWmdAYS5fiyJZGv5xnnOz0bQ/gT5trKmzIDVuJWTXm7SuRqMlNT1L9MjPzxfmIi8v70j3Nt+D6Rna+us1mOdUrz/mqgydDjezBOzXQ0ZFMyHaOZgBxkH3JT1FzIfX6z30uz6sQYEwdTDmg0HPo26jPxkEFD//8z8vPRS0vTFwd9GlXsHq0azePWjoxUHnz8ybfDKZxPDwMK5duyYtu+PxOHw+H8LhMJxOp2GBZe5Sb3Is+9HiLQ1QABjU3ea8pN6wzOAEMOb9OazSQgfl4Mz0pX5dM4OhmRtgv5skgH3sjRaQ6YVPL2ZcSDXg4yOjNKvv4XQ6DcBBl9eS5WCkxH4Ni4uLstGYQV9hYSFCoRBKSkqktE9XgQCQCCwnJ0cqK1ZWVgwbLCM6tnMvLCyUxX5rawszMzOYnZ2VHLFZwFVUVIRAIIDa2lpUVlYiNzcXCwsLGB8fRyqVkg3y9OnTePzxx6W6RM/xhYUFTExMCIAwVyq43W7U1tYKiAiFQoZ7KJVKGSo99HNqOSYnJzE+Po7Z2VlhdbRDq974dHUGD6sKAT1/GAzopmfamCzbPZ9MJrGwsIDp6WnMz8+LmC6VSslrcv1g2skcqAAwzGHm/Ql0tHjS/DnojWL+O3OlEktV2QxMm/FZ0fH62vAckyXj56QmhgZbZsfJow6+Lo2xCALW1tYMLC27NldWVqK4uNiw9sViMSwtLYnF+fLysuF7ORwOCUooRtbXUPdU4RrJNVXr5LTXBT87mbWSkhLDI0W75moxPrfSAunh9XoNAIOvTVbjXphbYC+lQ3G/Bgv82czcmEcymcTXvva1R4ACuAsoXnjhBSnn41FYWIhgMChlk+YjG233Xozp6Wm8/fbb6O3tlRsiEAjg8ccfx/Hjx0X0yZIxggx2yGRXTzoFaptYbeqirVbNoAS467DG6ExHQNkABIfOGZpV1/ydXlQ5rKpuNADToMPM3Jg/g/4sVuyHlfqZmwvFi9q+lnPG5XJJjTqp1LW1NTH50RoTvgfLKJlzZykpwZuOioqLi4U2Lysrg9/vN0Sl0WgUfX19uHPnDoaGhrC2tiaaHIfDITQzI0WmgDSLxnLVnJwcKSHd2dmR/hz8/Dk5OaisrERVVRVKS0tFTEndDQW+eiGmlwMp74KCArhcLkMbb7Mexmx/z/SDrlaw0u0wsub9wDnLc2+OpjVI1qlOfR9oVk5vnOzXkpeXJzoQCp1pWU02iiXFTD1Qz1BUVISKigqEw2GJ6skIAhAgpCswrPLd2nOBFThkSnQZYbZlmvczX1ezYHouUgPBklxWA1G4qO8dj8cj+ijqwbS/j5nV1Y3gGM2bj5WVFembMjs7axBMspTW6XQimUxKMzo9mN6trq5GVVWV2JzrFIN+bpX65GuTDTM/HqYnIwNBgKEPl8sljqh8TR5bW1sHvi7ThBpo0DU1nb7bJVUDhsNeE8C+Rob6s6dSKRQVFT0CFMBdQPGNb3xDkBrNWw4bXAy4oFoBjntFi9kGafK5uTlcunQJN27cEOrbbrejpqYGlZWVsNlshkXXSreg6TdzYy8tNNIRGgBDiWkikYDD4TDoHYqKiqSMNBQKobCwEKlUShTlelHQOU39aKbxzc8Pyu3x9wQZWlluLhEzT1UzuDDX2JtdQHkuzcCGn1WDB/0a5ly1TnEQ5DB61XoA5m+PMp8ymYzoMcbGxgwaFn1dmYqhHTgXVqZAJicnsbCwIJuqw+FAQUGBLPa8bpw/vCYa1DFlozcLTXcfBELJyOlNk+dTgz5qH8iSUGPAf8/JyZHmYrW1tQZFPrVFupEVN4WVlRUROJLJYVWNTkVyaD0Lr7G5xC6VShnSLropV25uroBGmmzpeavFcObrbTZx0kEAX1+nR+iLwM9ot9ulI6+e73T3pHjSbrcL8LMqN2R7AfYG4TVm2tPpdKK0tFSCNIJKM2g4qoA1lUphaWlJXDq55vF7FBcXo6ysDKdPn8bx48fR3t6+T4D+sEcmk8Hm5qbB7l1H/oftLU6n0+CSqo+8vDxptqi7vFLHZa7M0+kzAlgrMSfFrwQLZpfWg/Rk3EMfAQrcPRm/8zu/g/z8fEOJqNlFzGwkdZBGgRGoGWyQNqUzm3Zf0wublZBIn95kMom5uTnMzMxILtpmsyEQCKCystJgtcuNX9vS6hQAf2aZFvNmmmLUOTOr9tZ0ttODuVRdWWDV8IwRCXCXhbBSc5tzmxz8Pzs7O+LVQS0MW29rUELRVOYn5V+a+dAiSkZ92tjHTAVb0cI6/6wbmjG6M38vs0hUgw0zWOLGa964uamwlG9zc1PAGQGkVt0DMLAhPLd6M9JpAdK5enPX51WzQVYgQZ8fnYPWUapmCahL4nnTES/p3dLSUuTm5kpXz62tLYP2hI6SgUBA7md9v0WjUZkrTBdSpMn73kq7oIV35rJFnUbj59DaI4IZh8OBWCwmpdu6TTrZI23TrXUGBBrA3TQJwarWNrEyprKyUjQ1wJ7wcW5ubh/9D+xFuBUVFYZSWysmdnt7G6OjoxgdHcX4+DgmJydlzhHUUABOYEimR9/HLpfLsEZqyp5l02bmIDc3F7u7u1K+zDL5TCYjrEE8HpfUQEFBARwOB6qrq9HS0oKWlhb4/f593+n9Gkx/WgEOK20Qg0DuPQAMQI3Xn6kzLUTVoIJCfatKEafTKRb6VkCGVvNWTqpLS0v4whe+8AhQANZVHkcZzO/q6FsDAO1lb64A0Yuv2XXTnJczL1CcFHoy7OzsYGFhAZubm/L3JSUlaGxsRE1NjdBdeiHkTa4XWeZDzRuB1SDFqdXgujW5tifWh1ZNFxYWimBS5wEZbdJng39HsMMSVooj+WguD+VmypQBQQ1TFU6nE7u7u9jY2DCUwi4vL2N5eVn0KNx8+D01jW6lJTHrTnituaFq5oMLrI4gzYwFsF9ky39jyoqfz5xG0vXo+u8JMHieCD7Mn5Wfn6+ro1GmBbnxkZUjWNZCPzIBpOLp/qi7L5rBiZ4vOr2kc77mPh36nJr1SGY26aCqK6vrZQVytf6GqUMz0DC/Ll9TszW8H3U0yfudltuFhYVSkcXzy7ng8XjE5jsUCqGoqEjy9AsLC5ibmxM7bz2vioqKRMQbCoWQn5+/z4bb6mBJKgcZVHOnUvPf8OB8ZCtsOpkWFhaioaEBzc3NaGxslNLgjY0NjI6OYmRkBGNjY/t0Bj6fDw0NDaivr0d9fT28Xi/m5uYwMDAg/ZT0CAQCaG5uRnNzM6qrq9/XKgrzYABHMDQzM4OZmRlDxRwrDA9ibiiOJdime25VVZV07I3H4wJiqJ/R/Vf0fqDBYSqV2gdI+Giz2fCf/tN/egQogLuAYmBgQARruhKBuV0tCiN40A28zNQ7o0LdLdJMR5oXbivhogYYXHzM1LeOpin+0osyF+TDyiA5tFJcU/TaE8Dc98TcZtzhcIj50uzsLGZnZyWC0bXMFCLqzV5vfvrcczPQZW76yM3NlXJIencEg0GptWetPulB3rAUy/HgpsfeE6RqtbCNFUDcBLhhaVranM4ArFupmwGEFf2v/4/eQDWw4XzR5+QgkMK+JTy3nDPckHXlDiNiXc5LZonlkZrtogkSq1L0JsP0iLm+nd+X95FmK/Tfm9MMjM74WXm+zJS/+Rzw3GkGQfc/4HkyV0GZH833sAaB/Oy6RwI/n2bM+DsAArzMege73S4eEj6fzyACdjqdwgrwfXgOtKDZXJnF+0yff6uqhmyP2quFglEeXq9XPhPTPGtrawaWjK6PBLQsL/V6veLNAkDEl7QzZxqL/Un8fv+BQdD6+joGBwcxMDAgwmIOj8eDpqYmATEPu4pCA4Zsh9aBZBs6EOI1YDBA3xqCczMg0HoYnQrUBQgaGGuwb9VBVwcbiUTikbEVBwHFl7/85fsWWWqLVXP1AG88Di4k3Pw5obRwio9mStnqYE7UvChyUyR1bLfbUVxcjHA4jOLiYsMmxM9nroN/2CMWi+2rSNGLre5JojUIuiKFw+xGqhkepjG0mI8bkf5ufE0CG+BuDT8ZIl4rnmtG6VrRDewt9lzguZiS1tYdDXmwZI9gRNeu64Of3wpA8H113w3e7GbQxYUjJydHaEoKLxm5Ohx7Zkmk+vk96dFAsZsWRzLVpUGO3qDM1SP8Xbb0DwdTODx/BGia3dOpGisgxvfgteT3d7vdwnx4vV5LlsjqkZUtTOHl5+fvi9Z0sz0CMV7DtbU1TE1NYWhoCBMTE5iampJGYFp7w7lKHQWDG54XUtwEdXp+66BGp920f4s+7+bgROtAzI9Wv7vXtYLCXYJLpkzT6bQwHIzGOQf5man7YNRNwTyB81GPVColLMD09DTi8bjhfqJgs6amBn6/3wAUNeOoU3RMn+kUGpk4Aiar9ZvXlGCPwFxXovG9zGuIuVEg7z2rAJaAgu/HR30f8VHvA/ze5tJXzVykUilJ1zwCFD8BFOfOnTNEVzoS1wsRN27A2OL4YQxSlzp6MEe+nFTciKxqunVUS/FOJBIxOA6ePXsW586dQzgchsfj2Scw1DSx1c/6s/DQn81cOcLFgtoLLiqkvnkD6GoS4O6GqZkSiunMbn3ZBJccVmwAAMOGovPY+t/NGxavEzUhBKM61WBOU5h1NgRLOkpn3lk3S+Lc4OKlmSGHwyHXQkeiepNgpQHZNu2XwQif84ebLwD5PGbamosON0ytM9GpBL25W0VF5vQIo2VGrRQs6nPOz0fgo7Ut+jNqIJ0tcrXZbPscCLWuiIBB+4DoodNWGtQzHapTomxxbk6V6PPFOa0NqOj/sLGxIZ1bzakLiiyLiopEOMnNXjMwOl3F57rSiMyAeb3j/ZZtLTA/WqWX9L9z4+MGzKCK11OnX7UAmiBVp4mpD9NzSt/H2TZxPVfICFm56hK4MWjhdzEfek7p+1WvxVbpMg2I9RqsX88KKJt/1p9X358aqPOe0WyZZtEJeg4aev3i/Lfb7ZicnHwEKIC7gOLChQtSzXCUoXUO2jlO05A6/2/VXMX8qMWJRxk64tdiSaJklkyRop+dncXCwoJh4hQVFYkRFBdPvXHrHK+ZRrPKQevFVC+qB/UlsNvtIhJlBMHSN0YvWizJxYblezx3WjTHia41Bjs7OwYqWL+eTj9oOpwLsnkj1EJLnY4w6yeswIReFPSCpsW3ekHUG5bD4TB8Tz7nYDRhFhRroMYNXjM6msY0Ay7qH3jd+TqaIdMbEB0U+f3IaJjLQM2VOhoYcBHUGz4/qxYgap2RGfzz/fkeZu2QvmZW55Tz2xy1aU0KF2mdCtUsm5k10FQxX1dvOuYS0GxaDA1E9OLOEtRQKCRpJz3XdUqOaVcddWcbel0wiz/5XH8X88hk9lpcs4puY2Njn4hbi9jz8vIEdJDJ4P2rgxSuBbwmFHJy3dVln+Z7VKentVaKaWOmAjVbaq5QMrPFZlaa91E2Qbn+nRkE8dqa70nzvZlt7mbT7en3NgMSHVBZMe387vqe2t3dxdjY2CNAAdwFFL/9278Nr9crJ9R8obQfg15gsuka9NAufHwkrcXNkBs4o7RsOTD9c7bnWqdhZg2i0ahY23KzBvYAEv0QrGhMszOmOa2gGQMzhcbnHo8HxcXF0hCKWodAIACHw2FgLZhvZUtwvRDpboncaHU/DQDCiHDhNFODjGDJElgtHBrp8/eAkTLkRmYuFeRGp/8/34MROAVuerMnzasXa4IIXiu9iHGzN5f96pJDfnaCML0gcq7ztfizfh9zqkVvlvq8WEVP+pHDvNnqoSMgTbWbNQ7ZRJJW7281+L00oNT3vPn3minUkbZmg/Tia/7MOlLk/9NVOHxN/bn5Wjq9wehbV4ZRb6HPJSN3imV5X5vBrJ77+hzoe5sbohXjpu91GoBxI+daRqBMBpZzz+PxoLy8XDwqWNGi54DezBKJhPjpLC8vY3FxEfPz87JubG5uivOnw+GQ9Ywgq7y8HPn5+XA6ndjZ2RERJFN/vLa6Eog9TnTbeq75Xq9X+hGVlJQAgOwTGrjxtTUboe8vfS/Y7XZ5bvZD0es7X9ccxJgDI84nrlWa0c52aMBAwEzmlFVQmoXi+voIUCB7DS3Rl/ngidP5MR4Uc2ohp7mW3Lx5mcdBOUzNiGgActjQUaRelHd2djA2NoapqSlZkDKZjKiEnU6noV5el87y5tKTlu+Rl5cnYMHc+GtjYwPz8/P7mozRxlqr5PXE1RE186208mYrZL0B6s2OiwA3Z97YXKh1zxMCgGwpIH1D641Xv5c5QtFRKjcN8+ZDsEnthVmXwPfRG4m5OZEGknpT9vl8YpijwYOOrrWpmXmhstr4rahj8++sNga+nvk8aZCu563+Oz5apRnM0aK+JmZNipkR0Qu7Lok1MxXm19YpNB5mLQ8BHJkTne7QDBvnJjt9sj0922EDxq6VnEsbGxsiMKax2dLSkqFahPOLrxsIBCSgMadxzEPPOc0OmH/W62O27sQMKgoKCgy+CtSz0BdFO4haXWv9cywWw/T0NCYnJ8U1dWJiQiqAzIJjgg0z82WlfzOnj5k2ZPWXeb7rUnzd94OvYU4Pmtk6DeyygTfzfLNKI+p0vdnF04qh0UyNLmMlU6PXBH5nvZ84HA7cuXPnEaAA7gKKr371q1JWw5vDTEGZF5ODfgcYrVrN7IHOm+toyExvHfac6ZZsaRSmMazK+DiRdnZ2MDIyIjeiprapK+GE4+JiFhmZkbf+bhrNAtn7dOhF2Zxf1JurOadvtfCbqUduWOyxwUUrm6BLsytW/wbsRSPa2IkgR7d3pmjRvOGao1eeC11SasUC6eiXmwEXJ6YC3G63lI35/X6Zg5pypkOe9lrQYNcclXLo80+QRnbG4XAYQJc5VaU/X05OjmwgVO7z9TnXdA29jsI1K8DrrfUfOl3H19R/qzVAGsTqjUdvQBrEaDbK5XIZ0hQ6XcEcNQGemXLW15uLMytorFwktbbKqsJJs4fb29vo7+/H7du3MTs7K+Jnp9Mp/hbV1dUIhUKoqamRlKff70dJSQk8Ho/hOupzpaNVtm5ntRQ3Wv29zSBR0+/Z1k+zrsR8j+t5akXr602Sa45V2ojXgcGFTm1qJk8f+vvoagir6iNeOwJeMxiwAglc+whCtfmU2TuITLcVa6fTE/pIJpNSvbi4uCgW/LTvtwoUCQJpcV5XV4dgMCieFS6XCy0tLR9+QPEHf/AH+Ju/+Rv09/fD6/XiwoUL+PrXv46Wlhb5m0wmg69+9av4kz/5E6ytreH8+fP4oz/6I3R0dBzpPQgonnjiiaxllWbq3orOP+j5Qb/TC7bO7+pHq9+ZxUM8F2Y6XD8nyjSLK7UiX38GDRbMpXm8qTRla0bZ5sVCn0/zhq3TRmZq0Iz0dbpD32jM4xYVFUmEY7fvCQd1xYumfN1ut/goUPNis9lk8TRHZUwt6LG7u2tQeGvqmuBG9xEhC2FFscfjcUPvCg2S9Pe22WwGKpWpF6aQAAhzxjy0NrfSg2JErQGiex59Qbjh0PabJYE00eL7TE9PY3h4WJgvfhe9oeXm5gprwv45XMg4d8xaAp2yM98T5rJLPec5n/RmQDBgBiCcC+xFQaOlvLw8A4OhmYxIJGIwJqK1vb4X+LdmQGrWc1gd+jtlWzvM4Fvfd9SvsHeMjjR5bnSEzo1IAxmeL53WJAOiUxROp3Ofd4xeewgSWeWkXXPNHh7ZAjbzWmIOZqxSMfxueo3TTJSZYQTuCm6tejuZP5cOMPTarMECDf6Y6mVAU1BQILoRMjc0ANTA2JzuyzZSqZTBpZMH++rQc4Il/Obv43Ds9QAKhULCLPv9fvEL0nOAx8bGBv7pP/2nH35A8elPfxpf+tKXcPbsWSSTSfy7f/fv0NPTg97eXnF9+/rXv46vfe1r+PM//3M0Nzfj93//9/Hmm29iYGAABQUFh74HAcWv//qvG9AeL6JW62skaaZhj/I7TX2ZFw4rIQ0nvF7ItJ5Dm8yYW/PqygvzRmJ1mayQs5kaBoypDb3waDTOxZmd95hnpLkUAKnLZtvnpaUlrK6u7vPt4IahhXgUwNJ3IhwOo6ysDGVlZQgGg/B6vZJz1Y6jzLmyQdfq6uo+WhbYE4fpJl/sO8Fzt729LdUq9PzQN77H40FFRYW0gg8Gg8I2ZDJ7Isy1tTVMT0+LgQ2dHnnNNFNAtiKZTIo4TdPynGN6PvGa6s2U1HdhYSFKS0tRW1uLpqYmVFRUoKSkxGD1TdfYw0YymcT4+LjQ7cvLy4bIltUSmUwGi4uL0ppdt3tOp9NCPzNCz5bK43fSGx11KWaLdytGjBsQmSqyVRQCahbFXFmUSqVkc2bKkxurWYeiwRmBpGZs9Hcn62duSqcV+VroaY7A9c88R1YsoK7M0sBf/52+/zlfzX9n9bdmMJPt4D2k16BsmhsdYOi1VP+sdWya8bMKVLROQN9TbBFPYGwlIM9kMvtYA23hbl4DGRhQc6BTrQ6Hw2BtzW6shw1eZw2wzQ7OXOt1MGQWU2uQxXlKbRvt0K3SPtlGLBb7aHYbXVpaQjAYxI9+9CM8/fTTyGQyKC8vx2/8xm/gy1/+MoC9LxcKhfD1r38dv/Zrv3boa2oNBXsYPKgo8qDn+qayKj/Sufpsvze/rplmBrLn8/XGp9MjdrtdXpMpDQ1qtO0rX1OLLLkws2243+8XTwb6+zOaZQnc2tqa5CT5b5FIRBYCfn6CGk0Ta5W9FVsDYF8Nvlmd7nK5BHCQxo3FYgYw6XDslWXyvePxOHJycpCbmyugJZ1OG6IMt9stND3PnxaObW5u7uu8yQ1BU90EzRSncpMkONTpEk0La1aE1UZaPc/0hB7c+PPz8w1ly5w7ejFbXl7GxMQEpqenxYFRszKMugoLCw1ASqczrGr0ea0dDofBKC2Tycj8M6crzLldDr3ZWEXu+medjuPmoDdUAngr8Mno01zhZRZb89DpI/PQbIqZvs5kMgZ2wFztoBuOWQU3HJyPbBy2srJi8ETh+dFC4cMAAP9OpzytvpvV/zczCWathBkcmM8lAbSV3k0f+vOZKX2roQM8XVmmmS6dQqJLKXUhbrdb5lUkEhEh6crKikEYzvnO+46VObwmGlxqNpmfnfNXM8VkYq20FhoImb10OJ/N888cNJrXVAD43d/93YcOKI5mw/gAY2NjAwBEUTs2Nob5+Xk8//zz8jdutxvPPPMMLl26ZAkoeHE4Njc3AQD/+T//Z1n8jjI0BXo/B4WG2dIlXFw1YNCLKBcfHUFxA/X5fLKp0y2yrKwMRUVFQjdGIhFpgESHNfN3482YSqXEn4M21aurq5JOiEajYuZkt9sxMzMjIh0CCNbPa7qaFJsZ5FAoReqUKQxSjuY0hC6N1ODDvDhxIdCiTqdzr/kRI4tkcq/tNEWjZE3MCyq7LRJA8Yam7bhONUQiEcOizIVE52tZCUQPiNXVVUxOTmJ5edmQk6ZTIlM61IUwLcGUB50G2VWQn2VqasrAbDH61eyXeQMxz3XzxsWFleyH3W6XkmYrIZ3L5UI4HJZ/293dlc1tcXFRukyyFTnva9LO3EzIGpjTZHpOWemOOLd1JRTnD2l5vQFpTQuBF9M2eXl5Btrf6pFALJFIGJwkdadZAhFzXxe73S4RpwYQ5lTT1taWdBPWFvj6WmsNCoGSDk60GJfzXDMAem3S/25OwTCSZ6OpQCCAQCAAn89n0AHQ/0ZH3GaRu2Zq9EFwbWY9eGgNgzl9xGFOJ+r72wy4NdWvmxjy7zWrwjmq+ybxs/DvyF6QLdIAQwd+ZsEx9w5+br4n56YGAea5ZMU8aAZCAzSz5oPvzbJafS2O0kjzfsZ7ylBkMhl84QtfwNraGn784x8DAC5duoQnnngCMzMzKC8vl7/91V/9VUxMTOCVV17Z9zq/93u/h69+9av7fv/P/tk/EwrMrODXh05L6IjCSi9xkI6CF0nnWnlz8ybS1JSeYE6nE/n5+QiFQob8tt/vR2FhobT45QLD5we1qbXZbMIw6JbM9NjXOezd3V0sLy+jr68Pt2/fxuLioqFJGL8fIzsuVHoCZ0O/uqbdDAYYtXMR1h4UjLq5sfOGpXGO3tw1NcgNRR+87vrc6IWVqF5/T74OFzN9w/J3ZpaEAJbvqxvD6U2bzo4EbdpsSRugmdm1bJVE5vvKLHLTaTUN1vQiQ92FtgPm4qfTEroRnQades5TyEpQy0WL6Qu+L5mAqqoqNDU1oaOjA+3t7dL8ifcWaWxtKrW1tYW1tTWxgV9cXMT6+rqheZy5LI8LrU6z6ejO6/UaGigxXWSz2WTD58ESZq3B0GDGPAfNwnDOQ14zs07AvNmbr7H2ytCMkhY/ZlvvGEVrSp8ivZKSEtnI+H8Iunhv8jpT3EcwweiWn0unqfTcNGvHzMzDYWkXAg8r8GQ+T3pNtrpeOvWsP1s20TjXCX42AjMdBDocxqou80av10ZqK/Q4KEV71KFZaLP1tlkQbd4Ld3d30d/f/9FiKP7Fv/gX6O7uxsWLF/f9m/km0tGFefz2b/82/vW//tfy8+bmJqqqqgw0drYb02qQ8jSX7WhqSUfEeqGLRCIyyayG0+kUoEBxHNv+xuNxA8MwMTGBlZUVbGxsGCJhcwqF0aReGPl94/G45MO5OepcrW4OxIoB/b0Y2fG80IWvtLTU0BCMNDwXFHP0xU2Vm7+OorV24Cj41bzwAti3efIG1pGYLkckctebrNY66BtNR8kEIex3oHOuvBF1HlSnbkiDUqDFOcUowxwJM4K3+jf+X3OXWUYvfKRHCdkZwJjeqqmpQXl5OUKhEDKZjAA0fWgDIl5HlgprsGS+RpyL1Hd0dnairKwMgUBAKOC5uTlhFLe2tvDOO+/gxo0bqKmpQX19vajPeQ0YvbNMeWVlBZlMRhZdXk8AstHxfqC4jU6znPdkoJhiMOufNDtm1mDojUNvVub/z+dWc1lHjWaQq+cw2U3OV+BuZ0/+DTt8UttEcEq9x8rKChYWFsShk/4pHLFYDHNzcwKuCJJZ8aF78HDj13NTs6w8T7rE1hx0EEBrweK9rNUcZhCtgx2ryJ33gU4H8VyQfdVrOtkgzcRagVZzOkent7RglMGlzWaD2+2G3+9HOBxGTU0N6urqxGNEg3ozo5ROpw1ib66vep3Vn5NpEwYATqfToMPgekig/16M9wxQ/Mt/+S/x7W9/G2+++SYqKyvl92VlZQCA+fl5hMNh+f3i4iJCoZDla+m8jx7l5eXSLTHboS2PtfYglUpJnvv/b+9KY+w6z/J7l7l39hmPZ7XHy9hO4iih4Li0SdR0hZC0VC1CVaFVlEhQaIGgECQUWqlpkSALpZVoSZNKlX8ApRUkoaCGCKPGSUldSIpLl9ROvY49+7547Jm5cw8/zPPNc977nnPvndXX+R7p6C5z595zzvd97/u86wcF39/f77K/4R7TsWRMZOQfIIYNdo/vPX36tLz66qvOfY24sw6h4BGLlwWO5T6LArv3lpaWzJACW9CZTMaVD+G7FxcXQ9nVIsuW0tzcnPT19blrsGLTerw4VqitARZQLASYCHCOCbvIrdgtxpTj57gXIuJIGeL7nJyK/0VSFoQ6lDXA1hQSOaFMkcypLREuLeTqFn7U74FkWEC58MmTJ+V//ud/3EZMIleUT3t7u1x33XWyb98+2blzZ4EbeHFxudEQvGHcJwRhCVS1QBmA2OK+8/nCslpYWHC9BRhBEDiLFls9Hzt2TBYXF52Sh0cBngsmj7CuQaKampoklUq5JkbsocC8wToFOcRrECeQQXaDM3huao9bbW2tC+mBaKPCpL6+3nX8RLUGwpWcdwSlBkWmc4ogD/L55W3OEV6DclxcXAyV2uL6M5mMNDc3u89h3BGO4NAt5jMrR/ZqiUgBAeN7w2sQVnd9fb2bQzBMNMHg51b1TtRno0jJwsKCa2iF8BE/n52ddd4o1kdMVJDDlEqlnPE1Ojoq/f39MjU1FdqhmnPTdCgR95LzJbAb8o9//GPnreY9QNizxKQ1CvicSDg/jT0kmC88tpxHcvTo0cjvXynWnFAEQSD333+/PPvss3LkyBHp6ekJ/b2np0c6Ozvl8OHDcuDAARG5MhlefPFFeeyxx8r6rVdeecU1euGB5IWgs2m5ikLE7hgI4aObjHDCX29vb2hzMLZ+oxQ/x9nwyN30eIHo7GZ+zTFMsFUIGE4kZbc9zp33ssDv4x7CwpuYmHAx34sXL0oqlXKleRDmUPBQiHCNW5Y0Fg6UAivMyclJOXHihJw8eVJOnTolZ8+eda50TjzjPgLJZNKdH6xpvvc8lljkCFlwy28oHxbonEkOxQQCpa1MkIpEIiHj4+OSy+Wkvb3dNQRraWkJKR6Ov0d5uDSWlq5sigQS0d/fH5pfmUxG9uzZI/v27ZN9+/Y5RTIxMSEnT54Mhc/Gxsact8ACemHg3BFKa21tlcbGRkdUuewSQhvJmggVwPrj9tZcvYOwmq5kAonhLdBrampCa0O7xXnNaOsRhE4n5uERHiTMA5wfPDk8B9i4QCnsxMREKKzBYQi2Njn3Aa5ozl3AGoTHACQZuRgoI2RvX6lgQo/f5HNF9QzWcEtLi+uHUldX58IfMFIQEgLpxvuwqnHv+vv7nfGFXKHOzk7Zvn27dHd3uxJkHJr88nijwqy/vz9EFvCoE6YtgGjBy6OPbDYrY2NjzjuGSq7rr78+tPsurp/1BcYXxArhpFwu57whvHcSvEaYO7rEFAYsh9t1+AzkCmOsx1wTYpxXMpks2Ep+rbDmORS/93u/J1/72tfkm9/8Zqj3BJJ7RK6UjT7yyCNy6NAhue666+Qv/uIv5MiRI2WXje7YscNNYrZ+me3FudY4dsyP+B9OuuHvtkgIJ8nopjfcvps3MtOWK0gLlM3i4qKrSR4ZGZHBwUEZGRlxMVUkB2EI2epGrBhWE87BitOBGLDFvLCwIP39/dLX1xeqomhoaJA3velNcuDAAdm7d2+kJY1MaQgXWGUXLlyQ8+fPy/nz56Wvr08mJydD9xdCj0MNIuKUEPcwYIGtwwggHmwlgvxpFzSeI+8BiZ4QkhDssGCy2axLMuNzxznBokaCKqwRJhEgWFaSXy6Xk5GRERkYGHAdURkdHR3S09MjbW1tUltbK9PT06Hcm8nJyYKEMPaGwUIC6eP5l8/nza6KXO2kAeWu8w9AKOA9sJJEIZB5/PWagpDmtvdYZyDIuM+cFIy+CgjVMeHgXBrkf3DeDh4RPoGVq5sisbzhR50bAGXJskNbjbpCwsrax/fgN7SxwXOaDSPuS4H21UiYR6iLrXSsv5qaGtm2bZvs2rVLdu/eLe3t7SGvFCfFshIeGhqS0dHR2OQ/yEb8Fu/jwZ6DhYUFtz7jqm6QVKoJA14zMb18+bJL5OaydK7IAFKplGs6h1L3mpoa6e3tlZMnT8rZs2fl/PnzMjQ0FNqNlUs/Mf8Q2oLXFyEIztHDuGJdwuPF6w3yhskxy0wQGowP99kAQXv++eev/rLRKAV+6NAhue+++0RkubHVU089FWpsdfPNN5f0GyAU+/btM+OaHB7QCxePOA8ruY0FgpVExYKMM7+RFInvBrO3ykr5OSd5sccD7knL68GCUcfbQVysciEO/3CMX7vF+PtRvQDlBmFaVVXlvBZIasMBy0X33dC5FBB4uIew1HBvoEzh0gNQ6dHa2ipbtmxxCw+KfnZ21p0je3mwcKFw4D3BZjknTpwIudFFrmzG1t7e7hpoAfl83rmzuUkWvCXa+ubcDCYScMXz3gYcLkqlUs5SR1gN9wXClWOkcJWi+kaHWCxSycKHD6sUGqEKTvhdWFgocP/iXqMahkMEdXV1zqXP82FxcdHtCQMFr8NmyI7n69G5DPx5KAlW8nzP2JvABJXBBgruOeYnE3z2DuI3ME469wDvQQFwXopet7BguRIDJc9ssPAjl+8iD4w3AJyYmJCf/exncvr0ablw4UKoGgVl1yAVuB8ouYT3jb0KPC4YG+R1IMcHvWtwzyyyypVFuhoOlVpY++z5QNk7E/ggCFzvHBCHwcFBmZycLFgDWDNtbW1OLiAfgY0irmRi5HK5gooXzD32TnG5MCdow0PGpBrXzv1RQEpAtqAfovJ6tMGN9XnixImrn1BsBHSnTLguuXEOXPjIDWCLC4MGMOPjWJgOdUCY6MRJLhPFgFleDyw+7V7V4RK20CBwoHSRnQ5lyDvzRTH3OGAickKebrTFYSK4r3WNPyfG8uTWygWWBgtJLChYSOy2xjiAAGCcoYTROljHfnHvuAwOCbJbtmyRdDotMzMzcvr0aTl16pRMTk66/89ms3L99dfLTTfdJHv27JGqqipH/LjGHJYtW7Wzs7MyOjoqIyMjoRJAnRCI72GPC7vLmczq2LaeG1BAnAiKXCHON2GPD7vvWVkysUTIEAoIpaFcqojvgRuWtxHXXjHMTygnHaq0jJFcLufc2uiBwsmLUHxMOCGcOYdG5wXgPc6LYlLBMXsOS+D7dTk4ezWXlpZC45LJZByh1IoS1w1PCsaOXd+chFcOkslkqNzVesTzdDotZ86ckZ/+9Kfy05/+1K0r5CBgTSPer0vT4T3RawReVC1zkPMF4wRzij02LEMTiYSr2gGJguEEuQqvKAwKzA8QNdxXjHtdXV2oORp7rEoBfl/PPYwXPBXcgAvGFpN/9mLxOsA90t5xNiJBnizPDa9xXc2Sy+Xk5Zdf9oRCZJlQfO5zn5OWlpZQzBuDiT4CUVYXFr1WbGw5RzWqijpYwcLlxNYcex3Y2oFAggBrbm6W1tZWtzEQulYi8VN7GZCwyoKWM9zZbcsKEJ9BDgFbVdrK0hYXWz7o+YDrqaqqcgsexAeKY2lpKRR60EoEVg6Xei4tLbmQRxQgbPhABRAQBFe2Y4a1BOWEa2LrGb/LB3vCOCZtWeasrBYXF51LHfkhWpgwUdAkjF3h+rt18hYTNz50Tgm+E8KQrw8CSMdw+WDPHLdtXgmp5WvUVpbu6YJYOixuFv4YS91PAJYy583gnnNoiMt2MW4c9oFy0sYCept0dXXJjh07ZOfOnS4PhUOdSIzk3TfR/CwKqVTKVYvBEwfXNtYF5B13HS1VKQKJxHIn0pqaGpmbm5ORkRHp6+tznsVcLudyB3CvcB8hz+Ah4CZyIF3cUwHzEPILycyQXdzmG6EBVo4syzncxCElnhfsBQKhAxFBSIlz5urq6tz9hheBQxXo1ImQHhuWGrqkHnKaPUe6pxCuh2WgDhWy/KyurpaWlha310t3d7eruMJ4oJ1AIpGQqakpOXDggCcUIsuE4sYbb3QDrWPZIuGJopUwGu6woNYuf04u1K5ELjvN5a40Vjp//rwLDaBcjhkmu5ygdOG2REYurLliLmerQVRc2CdK0bAViyxtlIqivXFtba0TuiBsnPUfBIGL4XMPAgib5uZmaWtrc9sji1xZNHCncpY6iA4Eh75+WOJQFtzKWcf9oRCmp6dldHTU7dnAUx79+iEA+d7puHixpQJBofM22JvD36Hd6/xbGDcmd5p48P/h0TrHqL9bc0QkXIMP0o01wE3LmLxxDhD37WCPCAiLJgkQrPA26LwPXgfcrwPjpcddh+wymYyLo6NFOTxRmEsi4pQzOsKCeDDpgFxALkdUXlIUQMYgW3TODisstIiPCiNXV1c7r5suVU+n0yGCwe3NQUDY0ODkSg7fwErmuYz5guuBgsY6wtHV1SU33XST/MIv/ILs37/fEXWA1wm+Xz8fHx+X4eFhl3c1PDwsU1NTBSXgbMFj3OHdBGmGrMN54zr0+mMPtL7/mqBbHkDtgdIVaRzSYWMWZa3wbiwsLIQ+A8KNA17S+fn5gk66aJa4detW2b17t+zZs8c10GttbXXhak8oZJlQ7Nq1K5SUwglKOllJvy72OcsFOz8/75KZYOlzPbAGvA7cUKalpUUaGxud+5QFZBAETsDqI6rDpCZScWRB504gD4QFZD6fd9fEfe35PmOBQjDiNdos83a6UA5wWSJJFF6lKOsfpYksePFbpeDixYsyMjIiIyMjrrQSigE5ER0dHSE3KBQUWwNM4LDg2argqgWQGPY8ABC8HBfXScD4PI8p5whhTuFRK32dfKdbPmsBzETJ8oxE5RPgXPlc+H9Y4IJAsyAWCbdJ5lCQzmfQVRm8XvX5gsjoPA/ce17j8PaJSGiOao8htiPv7Ox0Zeqci8Muft1giPuzIOxVDkBiOD+G55mVawClYvV+wNyam5tzuSn4HQ4hcaMuJCPjgJdFN8TDfeRkTVZwUGDd3d2yc+dO2bVrl9vIDblPCBUODQ1Jf3+/DA0Nub1XQGRA2vP5vJMFmOtcscVJs1YOmg53WWtPJ9iyhwNkhYkCz0/t8YDhwn1EsPMnPAhswNbU1MjS0pLb5h4Jr8PDwwUhpEuXLsno6Ghoq3ZcN8YmlUo5A7GpqUmy2az85V/+pScUIsuE4pvf/Ka0t7eHMmi55IpdmVxSqTu3IZYHATA2Nibnz593jXWQ4Q3iYB2cUMUVHJj02lVuHRwGYeWtCQ8OVApgkoKooBKBGydxzI7LTbGAYcFzGACLiq0SK3bOn8fncHBzK/4b8l54kydOHoQyY4XEeSysnDDW2N4XJAIhgSAIXP8CbLtteX1YiGrvkJVzw/+POYADRLKlpcW1VOccB51Eywdna+NIJpMyNzfnMvTR8rq/vz/kGsZjEAQhwoijoaHBnQ/vEwILCVVFEO6wYEGi8f0YVxbY1sHQVh3PcS2YkVDKuVFY51qQc6M3BsJyCHGNjo66hFuNbDbrQo3oZlvqBlDFAGWkvS+8NrRMYi+Mzv+AV4ZJCxsdmsRpjw1XniGpkcOrqI5AWScTAxg92AbgxIkTcvz4cTl58qTzyILMQf6CBOFacZ64Fp28rMkqzxEo5sbGRifnWL5xd1Hsv8P5LnquioQ3NGOCBg8W1gfLavbC8nlDhnMCLhMLy1sBJY+qPE4sxTjBM57P513FH5e3ciXY0tKSC7GyPMB5gnj5HIr/B28OxjcDpKCU49KlSzI0NOQ2SxoZGXHEwYrV4zZBkXO5JzeyAXtmy1u7qFlIaeuUiQkLWCZKXBZWClHBeXBLViwybYFaCVQQZKxI2YWv45fanYgFxuerwzCcTMj3BNeq75vIsmCFFcgLnWPCICh87jxGmvBoixakkOPFqVQqFA5rbGyUvXv3yvXXXy/79++XnTt3luxNKQY0oxoZGXGKfmRkRMbGxpzbmF3aSJzE+XHnR1jeOkcFlqdFuEGaeE5AMHNOB4ilRZQ58ZOVnPZs8HiLLCdugqizx4rLbeFOR3IskglR+ov5gkRTXAfCGojhYz5zi+7m5mYXFtHXZb1eqUjFfOakX3gCMMe5yirqdzEGIoVhMxHbbY/x4MogzG0oPJBdTqRGOAQ5FyBu2IWX8xyiCCiPNStieFYga3it8nzTRpj2ZnHyIrccZ3mwsLDgCAX/L+4XjB8ofBiLqVQqlGDPHTdxcPiV/2YRW85x0p4PdKWFEcaejnQ67fpboEoKZcFBELjkUDRUW1hYkP/4j//whEJkmVD89V//tXO1Y/Jq6DI0NOCB0AX0BEeSn048y2Qysri4aGaos2DVgkbH2DjRjv8fAk9vAKXzCXRugY43c0kfJjEvZhZA2nXNCp0/w+RAu8Otv+nvYoWjQwQMXkDsQscj7gUn1+GAVwZleTpHQI8Bx/oRk25tbZVsNuu8OTMzMy60gOtJpVLS3d0tu3fvlt27d0t3d3dZsXQLly9fDpEGPCLLnucqzm1xcTFEEHCfL168KMPDw24/GN5ULGrJ455AoeidTDnHBpVGvJERKyJ+DwRhcXFRJicnnecD3hCsS6xNrE8oT72u2fJlIa3DJVAy9fX1snXrVuno6JCuri7XVAm5H7lcTiYnJ12y5NTUVEg5iVwJIXR3d0t3d7fs2LFDuru7I9sXa+WZy+UKyg51zw6MUbEcHpZPTMI5dIc1giRWrtji0m6E6mCxavJnhccAXnPWGmdZYyVLahmiQw7s8WOSyaSJPaJMiiyFzLKajUJOdIf8xZixZ0UTMPa0gmiAfGJdpNPpEEHXJANVU5gbmO+WB13LSAs65IISfNxfyE0k9H7961/3hEJkmVC8973vdRYtLHCwL51YJBLu7Y5HDlGAOCDGr4mBPnhy8YS1vAkiElqg5TzH4tKxZUwWLosFgeBJxNn7OlkJgkf3sOdFivvF4R1ddcDnYxERXoTahQvBh42G+LPcihpdGtlCC4IgFNPWAkr/JucbsCsdSirqPFKpVEgpdXV1uW3P9XdZfT84b2JmZsZl+I+Ojsrw8LAMDAzI6OhoZNku5huPD7vSiwEJynAP495gXoJQ4XwhnLLZrLS2tsq2bdvcniDoprlaAhUHhCump6fl3LlzcurUKTl9+rT09fVJf39/wa6WmBM6D4o9MRpWm2eEl3gtoSxZ53AgPNLW1ubCA6yIUFaMTcZKARQUDjZmSqmmYU+k3jAKjbpA4kCiQOhANEA8mbRpeaQJjl7nWi5iTDnfC/+nc2+wrjk8lk6HNzdDzwmUsULGcR6IFeYuRTFraJLH4U6WfXwdeK57wOBRey/ZY8IJyDokazWd04YnrlGHrlmfgdx7QiHLhGLnzp0hFmmxeyAqpmgpQP1ZnVSmX/N72nMRlQSqwxn60EpbRJylg7gp3NxsrfL9ABvHeXLyEhaszlBmgqCtTRxRrvxEIhGqpuGwjb4vfA9ZkFy4cEGOHz8ux48fl97eXme5QSDDgkYMFd0dgVQq5Qgixy1ZsKF9MOcFcCgECps9GLpbnZ4rWrGzp4kz6CGcWSCz6xbniXvH4Qrt+cHnOOyi3aHNzc1uR1v2GqAUTuSKMJuZmXEua4RURkZGIhMJE4mEyzkAwcDjSjcemp+fD3UvRO6DpYzT6XQo9o820dxMDeEP7QUBKbWEtn7O1ipi9Oyu5rAPh+50NVk6nXZl1AghoEcKDuQvZLPZUJ6ERQ74NSxclNPqRFw+Z510aHkl2HvJf4MHjA0VTmjV+QQsU7WXgMMynLtQVXWlGy88YNXV1a7Mmr0O2WxWOjs7Zffu3dLT0yN79+6VhoYGl7TJXkz27iIsgPmhm31xlYnesVPfO/wWy17Ow4oypHjt6vyKdHq5aZUOOXLODeficH6c5VWKOpaWljyhEFkmFNpC0soe7JZf43M6wc8KP2i2bbm9+Hc0IbBIiVY81ufY46InelRs2wq9YKFDMXJuBu4FFFJdXZ1LxsLuqIi/s5WtN1rjRw4JWJifny/owY/nY2Nj0tfX59zOCGHhuhHXZqHc09Mj+/fvl5tuukk6OjpCJXh8j8bHx+X8+fNy4cIF6evrk5GRkYJciqqqqpDLMpvNFhA3lHRxG29u+sQueo4TW9CeGu221VUO7DHA/eZcHt2XhF3i1gZknFGOkI+27kXEJe4iNg6iEddSGcl+TDKwHwjmJnYUZQIxPj5ufh+UB1ofd3V1SWtrayhZsFTk81f2mhgeHnbXhIRk3asFXk728LGFyvFwtqpFll366GnAnRet89ZKQ4cMQZpZ2eikYCYBVohAZDlHi+UQu/r5OzhnAeeEucHl+JyTwApPhy44PILfZcXJ1Rwsn0HK8Pmo8DbfaxBoJio6qZ1JehSQZ1MssZ+NOVy/JnQ8vtqY0HJC6ybWHVaoic/X+g4O9+D7/vd//9cTCpFlQrFt27aC/RAgSLkbHIQmxxt5grEi17E+AIOuJz+Xeeq22RBI2k2lczeY3bIbS1sN7KrW54dEQs32oYw4Ls4WLBKMdBZyKY/6OSdosRKGZaib7aAMF3X/8KpAWe7evVtuuOEGufnmm6Wjo0PGx8fl3LlzcvLkyZBCSyQSsn37drnuuutkz549kkwm5cKFC3L27Fk5ffq0jI+PFzB9LmFFTJFb5rLVwcSB38cYYRz5EQKAPQjcfwBCXYeO8Hu6BI4tkLVeslZCG1tQuuQYmfW4l9w/YX5+viDUx/MfVm5V1XLzMzQ+SyQS0tjYKB0dHdLR0eFKe5uamkwLUbugYanzFu16u3bemhvjFXWILBMDEHRWmrxuucEUJ09a36tljPas8nnpz8Y9RhkvLCu0HOFH/C6TV54D2jNphfX4OQw+y9OCR00MlpaWQoYUl62y5xQeQ9x7TqTH9SCMx6Qbc5LlPctKzH++Hzw2HDJgjwQeOezA85PJA5MuTVZ5zHGefOhKQux0y12A0RUY7dEhe7B+8/m8DAwMyN69ez2hEFkmFCdOnHAZrqzsdHwRIQFW2Cs9VgNk0sMViyQ0jpmxIOIcBggMDifobGhtofLfSomzxwEuWF1zz+9x6IHBwo0trKWlpZClA6/Dzp07ZefOnS6hj2OkiJMODw9Lb2+vnD17Vvr6+kJlk1BYmA8iEnIvVlVd2bKdk52s+CXHI3lRcyikpqZGtm7dKm1tbW4XxZ07d8r27dvd5l1R8W4RMRUlCyC2fDA/EA/nBkDcF4PDLCibQz4Rf5cmrVHkyHpP/03HgNndrMOPIoV77HCZKJMXjJXlpmfrGRa0ZcFhfPnctUeSvQF8XcXWDSsabcHivvO80oSB10icJW8RCB0StRSYBc6/0V4wfB9XezDx49wOLk/n8kgobnij+Lr0OSDpGXKRN2YDOePkVSYgS0tXWoHD+wWjBl5PnVPBFXe49zw/dZggbszjPNjsEeB7wjLZCnfguzlhkw/IK5ZLPKfZI6HnEBNi4MyZM55QiCwTiueee85NojgSUGpCVKnARIlKwkMJz+zsbGhjGjRpgTLgZDKOi2ezWZd8xVn09fX10tbW5pKSEHtFT4EoxRWV7MOJV4g1IxTBhEd3r4yLwYLt434kk0mnAKenpwsSKlmRpFKpEHPXih3EkL1D+D7+XpHC2nIoJ164IhJyVbPXRVfiINSCcAuXofECjiMH1rGZ0G5tK8OcQ0d4ZItTe9RYGOu8JHbRMiHQXgH9PC70qKFDSVY4Uce18X+YBywSLZIVpXyskKsmOBzvhpDX5wkFz7sTi4jLD9GudFYwfI5ayXAYBgnCVg4XkndB5q0x0e9pWNUVxe4/7jdyveB9YK+GLp/V52XNDz1Geo7g3KwEXosI6Tw3nYxvebwBHX7RFSns8cW5g6wiX4Y7n8KTE5Uwy0RaEw40DvOE4v8JxV133eWSBEtxzVu7+IElsqtOv9bvcTInYsGnTp2SU6dOOYt5YmJCpqenXd4DBDIUF5Qu77IJxdre3u6SkvhAox1LScUpLV0uppkvu4GLHXw/LTYMCwFWAm/EhgXPCwgLhg/L+tQKWLsFeUGzotRMnu8/J6Gy+1PPHbjjGZb1zkKqlEdLuPJrXSnE16ktfMv6s6xaVpyWwNNWPefvYK5YnjrMP3Yd85xgb5Ymguyx0smxlguYzzMqroxz0sokagzjoO+j9V1RVr9OzOZQAkIpnC/Fe+vwWmBlyfOBz00n9GIs+G+l5AzEkV1NqHRYVq9hJk5RxLEYCbXWBuaBzvPQ5IJDd/BW8nlpb2N9fb10dnbKjh07ZNeuXdLV1RUKlYhIgRfK6juhQ+Js8FgGk5UUzPOqmI5j+YX5EQSBI/pa3i0uLspTTz215oRibTrvbBJmZmZczJaFtX7NbihMMFiumklrxg6hvrCwIBMTE66hEPaugEvZqhLA4meLHS4urvEHUUEuA6y/vr4+EYm2DkSWd1a0JrVOGNOWlXb38b0TKczVYNcqHqEMdCa5tpJY+YFYaSGh3dmwTrUS1RUkImHBwuBwFxYpXyMsQXSi42vULD/qNe4VHuF+ByzFbj1GvVcMlmUcdVgVNiLLO+By7g96O2hyp5MGLauI51kUYA1rBcnWKtzWCP8w6cB3W8+t+QXoc7KsV35tWbGQI1xyypapvm/slcE+Dboc07ImcX5YC1qZIBcI5e6QITwOXLHC56S9gVYoTN8j/ag9ODyOkH18L/VnWFFHkX7uGcMJ5hzShVJFLguMOZZvCLFyInIQBKHGYXNzc3LmzBk5d+6cvPzyy5LJZKS1tVW2b9/uKkp27dolLS0toT1gdLdafSB/RyeMWx5Afg/3UO8ToueeFdpOJBJuPjCZWVy8slnheqCiCQUsXChNLfS0cmJYFqbIctfAqDiw/h4WOpq0cCKothqSyeWd+LDboFbkmtFG1VVbngQsdBawrJxxsFuflWWci56FFOd7MEPm6gL2ZuA68Rsc39SKJQiCgqY9cIfGQf8+t3C+fPmya19tLSreIr6pqakgxq4tJswfHbfW5M2K0+rnOpErLrQE0or5oh9Z0fM6wJ4SEH5W90U93lGhA/4tvRZ0wrO2nFkA4v+tDHzcY20FIwkUuSOcXW8ZFnxgbwV4/jhBmSsg8L86B6vYI4eBdBiJ3fS4v1CgUIyYq1ydk8lkZGFhwSkmXHcul3P7PTAhsaqFotZ2lGy0QjpabmqZyHKGvZpRnr90Oh3qgIrwri6lhAyB7GTCxsq4rq5O2traJJm80m+Fq8nQjh9KHkYUPBONjY1y8eJF512F51bfG/YYoH8Rzl1fC1f1wCOtN5zk0Da/V1tbK/l8PlQujBAQl7ZaB1oDcJUcwtuLi4uxO9yuBhVNKLC5kxZolgsU7lUoMexbgLp0DBR7GjRYqEJA6rJJHQ4QkQIBCcVoEQYWQNbC15YrCyKdrayVs1ZEABa+dtVyxjMEOO4T7rfIlYRHJCZiy1wIwmw26+438iiwMZF2ETLByWazUldXV6B08IjteqEMcGDLaMtdijHEe/Pz83Lu3Dk5c+aMnDlzRiYnJ909geLZtWuX7NmzR3p6eqSjo6Msz8FqAHelToTFo07GnJmZcWG2yclJt28F8nUQqtDWPSsEeAz4nrF1zJYnrwWLrGovCM/BxcVF16xLEwUmZMU8L5ifSMiD9Qmlw6QKawzXyGskl8vJ8PCwDA0NhSxY/lwQBC53JJfLhZLmdCkx+sDwXAKgXKwYPBNUuMrHxsZMr4+WHzrEpz00yWQyZNkj61+vdauiB9Y8ysKjvAtQWOwRjMvHwXOEYstBMpkMyVsmKpwAjs+i2oG7lKKHD5NoDpOggZjO2WIjDt+PecU6AefElXXNzc0hIsNeukQi4eaWyBXvM8ZKhyUWF8M7tXJIEpu/oboOOo5LV8vd3r5UVHQOxX/+539KQ0NDgeKAIBkdHXVd9np7e6W/v98JWmuHUCz8dDottbW10tzcHGrX29ra6txccJWxxTA3N+eUJre25eRQTMhSoeOvYPQ6E167Ea39QFjQRgHfjWsDs+eFizbE+/fvD+1bkc/nZXR0VPr7+6W/v98pazTj4mY8+Xw+1NYc1iEDm2uBKPDzlTZPisPExIScPn1aTp8+LWfOnCnotYBS1p6eHtm9e7e0traa9xIKwSodtsiB9QgrQ5elcakacmN4a2luXGaFZeBFgrtcKw5+D6QQnUr5+qDMdKiEf1snfOqEWSZ3IC1aecIqZaVnuXxZKOM74Mbnuce5RJxYyqE6kXCXQX7EfcR1MIGyvJUWybKMHr1+QTz09/I4gnRxaBDjwwp8fn6+gBTiOXtqGhoaXPdXa15j7jAx4bHQMkffG00wRZYTTRGq4JCBDkUg/4tDM9oY08nZGpoI6xCQiITOu6qqqqDsG0of8h6N8fh7EBbUofUoT6eVwBoVCowKf1mHzuVBL59EIiH333+/T8oUWSYUfX19Mjk5Kb29vXL69Gk5deqU2yUU+Q06UYcFbCaTcV3ZWlpa3DbFzc3NLu6kY8q6p4R+rntMMPvlmmORcDklC2yR5eY0Ue7bUoDFAJce703CLX3r6+tlfv5K0yk0MWKBLyKydetWZ6n39PRIJpORwcFBOXHiRCgZlckDL1D8Jg4QIb2VL543Nze7+OtGAu7ty5cvy4ULF+TkyZNuXsE6hdBIp9MuNNLQ0CDpdNrNA2tZcYiHHy3iASuXk9qsZC5Au2LR5wGuXE3cYG1qwFMlUrhxHeYuzoFbUpdKWBHXhVsX7n1WRiyAQc64DJPd0roSiUMgXAERFULSioA9JsVyZVghQHHoeD+HOLVChxfMEvyWp1C/z7lZ2jOpQxPYfZM7xMIVro9kMunkBshlfX29abiUI4/4fNhTwfIZ91zne+Tz+YIcFSt8w/+HHBV4HjgnLorogXRiPum8K9wblqGc9wayygYk57axLNBeJ+vgdaP1gU741UncTGZ4XoIw/uM//qMnFCLLhGLPnj2hXAKRwsxhdl+hCUhbW5u0t7e7G6lddVGPENpRbnhekLzIOd7GORWaRDDYAlxaWgolg7F7VP82FhR/RmNpaXl7W7jFdYgnm82GttNF9Ybun6Hd0FVVVaH2wp2dnbJ9+/YC0oCY9VqFEJBbEaWco97XryFArO+fmZmRyclJF1qwrBuO/bKlbHmmtNDQ7n9OgGThx8Iwm82GiBr2OmhqanIuVb7HLMS0dQcSE0U0orL4WTFalpEmw5wLhPumXeZ6LxMeLw4HFstL4dAJE3eWD3yu2luQzS5vYY3wH/4G8pnL5QoULT6H8WIyz50cdbk0J55aRznezWJAXxxdihiVU4GcMPaQptPpgioFK3eES9RB3KJC1HGHTkpkL4kmdNxmnnOwcE2ahODg+QnyBZkH7yr/L+Y/k3kYozqErYloEAQFzaqwPwmHWTR54vnAuTk8t/k5v4fzHh0d9YRCZJlQNDY2hiwDMEfuHIaMZ3Zr4uBMawZPOghSDChn3epOchx3jVKUVVXLuzmW+oid8EoFLAAI46mpKTl79qycOXNGent7ZWBgwN0PCO58Ph9aCLozpAVYmxwjbGxsDCVCopJFu9M570QTJFggIhJrwfNRLFEz6j7pHBbe6dXKceGDewLoMi+QAL23iTW38Bsch9XzqampybVEZxd1VVWV+46FhSubrCFmivbRUUTAOqCErVwInWmPx2QyGfLAaStRl4zqqiTcTz23tCWsLTQW4iyg+d7yeFgVXJlMJhTfbm1tdftqtLa2ulwDHg94cABUgE1MTIR2UcUeIsVIQE1NTSgXiPdhaW5udkQG88YiGXFEhBW+9Rm8Nz9/ZfM9tCTHxmEIEfPnea5Yc0LfI2vtWR4DbaBoQlFs3opIwTzRRpdFQFlR8xqxFLkmTlqBiyz3KmKyw2OH/9XygPWMDoHg//lzeMSa0eehvT+4j/l8XsbHxz2hEFkmFB/5yEekvb3dKSUIVChJCCkOPfCA8qVbJMF6xOTkSgLeU6HY641w41+8eFF6e3vl1KlT8vrrr0tvb68jB1CYekGzguQJi3tTW1vrSBqaatXW1rrmM1wyhd4b2oLXCWS8oKKgXb7aktQuV3bzAazc2AXJBBPCQ4d6SgEnrMFqhSUDYDFzCKKuri5Ealg46woHxJG1QNeC1VrOUR4ES4jjuvX3Wr/LSkkLZo5js0UW9ygioRwJrBlOdMbn8vm8U3JRycR4jv1p2Du2Hl4yC/BsYZ8QJhsTExMlZds3NDQUkAzed0YrbxhQnH/AVQJRj3GkfGFhwXkxOCQApaZzRmpra0Mt/nEgHwcklL0BOoTMoQKsXfZaMRmN8pDo+cmKWCvmqJAD5ALfX01SMNZx8kx7tDl0owlA1P/pELhFvKJC5EzcREROnz7tCYXIMqHYt29fpDBgxa/jTByKYJcmxyN1K1ltNULA4besEIj1vvW6lOf6NbwQMzMzMjQ0JBcuXJD+/n4ZGhqSycnJAncy52vAO4PJz4oa7lmEh5DvkEwu792gBQ+PgaWQNJHT5a9sFbBC4u/UsW9rIWo3JlsscQd7uRAe45wT7lPBxHBpacnF9CcmJpxVh/4o3ESMK4hwTQiNFdvJVQs+jBnHS7VFxrkN7OYXEWcB4bBi0pYVaHkSNCyFjnI5zt9BeKa+vj4k5EBQ4WFBqV8c0ItBW/d43AgSr++fjo9b74MUTU1NhbYU583zYBhZShKkXYeVRMIdGfn8LEWq111UMqlFPGHE6cZnOjcA58CEn+eqRUat11GWdxQh0HIibvw0tDzXv2v9nzUP8J7WVSx/eC2yJ4a/yzoPfI8mEnwNTDSAfD7vO2UCnEPBTaqsTHXEPnVGrGX1XE2AsNFb6s7Nzbl4Hpeo8US24uDsFuaJbGVr69wL7V7jhaIJj0i06409AFrQaMGhPRk6R4aFC7/PvwlYCtd6rb+fFau+fuv3LEuCBTLGlRPNtEsX85KJKxS0TrxDWMUS+CJS4FmwnuM6eE7EPcdvIubLSb/W3g7wHHKrYH7k7dH1XAFg8SK+zM9B7qwx0fOkGBGNUkTatazfsxSGXn9MyJiYs+fMsrCLefksZcmvMV5sNGBOgUBbSaOlQMscDguwF5ANB0vB8/zT8zrqXHhO6kRW7c2MSo7Va0cnM1p7lFghbi4vhj7S+RRTU1NuC4bBwUGZnJx094G9tXV1dc57Cf3FbQ6QvwWyrUM0eM3XxkYFxmhxcVFOnTrlCYXIMqH49re/LVu3bnWtUaOUGD+3Xq/k/6zn2oWnFxSXcfFunFw/zCEbTBQduxcJu9dYOXIM0woF6IXCihTQglL/BrupsSAsF3lUrJbP2yIilhDBeVhCwFJ87I2xzoHPEQLdco9a4HO0PElW/JbfY4sc99q6LxC0uhRMz3VNdHSoQZ8nP/I18b0rJnRxDlHjXWpIC+eiFUE5lSNRY1RszZfyN4v0WhZ0nGciykIt9prf02tPW6JxRKjYb+H+8xjzGsc60vdArxE2JHBO+ve01a0JLf8u5r42FEEi8Z1xHmj9mteR/rsm8CvxHpf6efQYGRsbk9HRURkdHQ2Ra/xPKpVyu4e2tbVJW1ubbNmyRVKplCwtLcnk5KTbrRkeUoS0tWxOp9PO45pMJuXxxx/3hEJkmVCs9maAAHC8Lq6FtfVcf56/M66awLrtcKEjPsi9MvQjYswI0UDAJxKJUEIkl2lyXN6ydqw4JhOiqNi9iO2V0EpWEwjLPW5VM7Dy0tYdJ09arnr8n/Y2aBcqQ5OAqNi89uRgTlneEyYaUS5UJqRMbvQ54pys+nZWAjqUozPkdZ8SPYaYE/pgwsxWu74mHmctyPm1JrXaG8AKkt+zvAqWe1iPK88J/h+LJOjPRRGDKMWtyad2cetyUEs5spLX9wr3BOeqSZ1OXLbWjuXl0LBCHhaptzxm2pOg552ImOHQXC4XmtOaaHBIEiFD3TOlUhAEV/JeUAKNA2FrRjKZDIUQmSTge7hyBz1XGLlcTl5++WVPKESWCcWnP/1pVwHBVh1gMWq2WLXLsBQLRScQWRnsrGQ1LILAXgjL4mSlxgqJhRIvXLYOdThExyFLIQH8fhS0sLHc/vr8LcHNSl8L9LjzscYZ/8uf1+cH64wtIAgnlJyxAuAQGytIFvQ8zzCuunEVC/Mo6y+fL+yDks/nC+51KpVy543QAwikNb9Fll3w+n5pomndL4w3Hjn8oKt4uNxyrRAE4UoHJmDWa52jY3nbLOs/6jW3xebEaz5Q1cPbVWNt8tzgXiS6UZ5OqOQmXPo6IXNwf6LumwbLQz1H8GiFjDlcgso1zotpbm4OJWWitw9/b5SXCM/n5+dlYmLC7ZuEKpqpqamCc8TzRCIRqtpBCXtzc7Nks9nY3yvlnFbyPOo3ij3P5/OuA+74+Li7B7qgADqCy/Vx7ShfR74dSv9HR0flb//2bz2hEFkmFDt27CiLjVqDKxLeiEd/Vlsw2kLQSg7va5aO72FBwIqTzyfKra8teD4PtlT4vCyLia+P/84KSltRHIuzfp+Vt753bBFq6zHOFW8RBh1KwO+x2xKCjpNssci2bt0qra2t7ujs7HSZ/hxf5DAUP9fd/PCcXbmavEU9Fwm3ZefqCyaQ/DeUKCJxDxtN8ffjXHS4AKWBuilWHJjMWtY0h9a0soElyrFm3dLaIqGYT1gj3MMA514uEdAAOdTub74+6/xwblYHU+4Ea4X8LKLDR7miWHsH0ul0KCzARIf3itAHmttxWSxfq27jrI9SSrYTieUKJyg+/RwJusWQy+VCoQI+4pKGUamGEAJXrK016V0vBEEg4+PjMjAwIAMDA9Lf3y8DAwOhcAmQSCSkpaVFurq6XNPGzs5Oqa+vXzMvf8FvVjKh2Ldvn2NgrFi1AtNWr+Uqtdx+UbdGW+A42B2uXZBcdcDfo61fjuOxRRwVt+P3NLSCwvmxgNdCly0WnVHOj3HThq9Lu0HZokbYRlvTfA5wreP/MC5aSXPiHm8GBpc6stG5tTWHoTjPpVRlq6E9F1bXRH6t81xKAdzYPC4zMzOuAQ/27mCPDg6U/7KSQTiMm64xEUsmk87C5/mAe4hz4XUWpzTZYxAFWFxxXi+Rws3EOKwDcoO5j3lprXOA591KDuuatIcuKqyH1xgjkAHePMpyczOBiGqZvZ6AJwHkgjtx8mMpa0qTDu63onuvRJ0LrG9NOOJ214RXQ5MM9H252kMoQRDI1NSUIxkDAwMyODgoMzMz5ufRN+h3fud3PKEQWSYU27Ztc5YlW4cAW+H6YCHFVo3O0tV9D7TLGFYJlJMu19SeDI4lcr8BnIPlqbASilhw8vlZIQUW9EwMILijQgFRbm5+jXNgpaktPFwXlx9yTwxsFFUM2qJkQayJ0GrJQTKZDClXFtx6rwtWxjofxMoPsT6TTCZDJXi6FA8x0cXFxaJKI5/Pu6Rebiyly55FROrq6pzgRAvxZDJZ0KWSX6M0kMeTM/l1EnKUhY6xseL4OkavCYblpYoKG/EatMQdr00rh8HK+4giBCC2Oq7P80bvl8KvOafkWkEQBK46jYkGtwKfmZkpea3q/Uesx5qamtB9XFhYkPHxcUc2OCFyfn4+8reSyaTr8guigedNTU1XNdmYnZ0NVZYMDg66zebm5+fl0Ucf9YRCZJlQtLe3h5S8ZcmwO5YFOQsshvZeaMuME5rYza/BxAEKV7uIRaJL0CxvSdQR5b2w3reEs0VWtOuavRqsPHH/obgsBQTlxteCe833nO+TzrZmEqNJoOX+1t4jbZnzNsFs9cFCKrc7aRRwb+A90Ae/H2e1M7jpk97pFvMZXVBBSmC5jY6Oyvj4uGsjrOddPp8PhY44cRKkkOdmVJleXNWGJuq8znRCNHsXdXWO9oZErQ3LeGBPhx7nuOvBa503AQIBr0FUe+io90px9V/LCILwfiNYF/x6enq6aB8UIJ1Oh/bb0HsJ4aiqqpK5uTm3LphsjI+Pm0mRAJMNPpAzcjWGURYXF2V4eFhOnjwp73znOz2hEFkmFDfddJNbiPBURGVv63IlrcT5/3Q8PMpNqpU0K0SdzKfjsDp3gT/HeRfa8oqK02vSoF9bsW9dmx2lqIMgKLD+OR7Piy5KCTNhgEDmBMja2tqQ5ReFVCoVEualPF8rcqCxsLDgyAC6B1oHqnowD3X1DFv3PP5876z5bCW0lgMdluNz0OQzk8mY7mgOm2lYYUi+D7pSKCpMVg4QToNS5yqYuJwNvs+68ourudYLHPK0jqidPeOOlYTUrmYEQSCXL18OEQ3rud4lOA7V1dUm0YBxIXJlR9Tp6WmXGIkjjmwkEglpbGwMkQzez6i6unrV92M18DkUBNyM7u7uWGZvue21+xMJVlZVAX+eY5w63CAiof+J+m3rOV5DmLI1BJcou0/17pGNjY3S3NwcUqS890A6nTbL/3gvj7GxMRkaGgpZsMgGRkxeu6xxvxjFSuCiLEHtVkb3SI4jc3kYZ85bZZBRr3musFWsmw1hN0vtntU7XGKL8aiYOicWYsx1ro0OgZSjACwXPb4LjaewoZNVlWCVbM7Pz8vk5GRoTwrEwC3CXV1dHYrv19XVuWz+coEwk7WduvU8qondeilRkI24cvKottFR7600JFcKQASLrZGoI6rM+Gr3puRyuUgvIL8u1dshEiYemOuJRCIU8rt06ZKryihGPmtqasxW8Fu2bDHbqa81PKEg4Gb8+q//unNbYbKzNQ03PG90pcs9kUuQSCRCyi2bzbqdG1taWtxEirKYEolEKEvaCi0ATFZYseHc4phvFLQXAY/IONd9BDgZUedSWNnyVVVVIUEP4Y0kMiiSqCx5EQl5k3C+ule/Vfa5mudsgfPuf1D0fHDyrCaUOhcGz1mpx+VJsHudBb1WlAhjwLOi3eooZQUZYCXPoQFcb9xRaogln8+HatqRz6E9U7gPyMtAM5729nZpb29312QRApDEa8miLgVRvT7iDsgti6RwDtd6wfKmxBH5qOcW4d+o8Y8KRcLTiE6UUb0gopDJZEKkGvIIYwN5HDfXk8mk2/rAaidfV1e36vvkCQUBN+O+++5zShOJkVaiGB7hdtc11XV1dS7RBkIQm19Zwt5KrspkMqseZCTTzc7OFiQuYbLz5jywmvEeb8FdrmBBOCJuV1AoM74PnIhohU6i3MoW+VlYWAgpRauZkm5+A9LIn9NeA+09ioLO1YjKztelkFyup/tYwGqHV4Dd8LrUlwkRzpvvDcZ3LQEirMkiewis15lMJrQPxejoqAwNDcn4+Lj5O8lkUrZu3Srt7e3S0dHhSEYlZNFXGliB8Tph2RB1gKhYnyuVgK4UiUSigGhYTdms58UeV0pWEGbhkCae68dSQ2IIe3LyPOssTdj0uafT6YJN4viora0teq2eUBBwM2699VbHNNnS1PXYEPCNjY3S0dEhXV1d0tXVJd3d3dLd3S1btmxZE+sILlFORgTRiXqPn3OsnbtV6gZa/Fn2csDToOPEWFiwAnXSHFx3lmvWKneNu34r30M/12C3O3+OCQm8SOUk3WlvAuLrcdvEgziiXJLDF+zZ4eoUHd6wnq8GnM/AHhAdGtB7Xeg+BPpoaGiQ2traNXWvzs/Py8jIiAwNDYUOq05e5ErpZ2trqyMYaC/c3Nz8hvNWXO3Q3hSLdOj3rG0I9Ov19qiISEG4Ou6x2HvW31GlpYmGfo4+NlEylRPcoRvgRYY8iSNWMAy5uRee47G+vl5mZ2fXhVBcfWmoZQDsDBYgLOdUKuU8DbCGOjo6ZMuWLbHWECdkaRLABICbGunNu3T3Qe1+51BD1GIUKcyxsMrmkKColYjevCYuUVKXleoQgLb0+VEr06jyv0QiURBOsIgGEw6dtGqFYaBkQR6RYa+VKHeP5GvX+QAIPc3OzkZaG7ivjY2NofvH9zHqNUhSHOnBueG6dUKtVfmiAY9dqYDXJUp4Wq/j/pbNZmXv3r1y4403upj77OysDA8Py9DQkAwPD8vw8LCMjIzI4uKiq51nVFVVOXKBo7W1tega3kzwvI8KmUU9btT/rPV3sgxa6e/qCh/2ynFlneWh1F5OXa6MHBWtwFf7Wr9n5TNFJcPX1tYWyFhdcg0dwd1qU6mU+x9sN6/1Ry6XM9se6HNbr6TQiiYUN910kwtTsLsnk8m4eNX09LQMDAzI3NxcqJMd2J9ucGQRAiYG1kTTmevsYteVGZZi5AoRdG2E24td6/AssDvMOhf8LjYf05Us7FaPy5tASEjX/FultLyodQKfSHhzI3wXEwx9blavAV2hw+QEloBGKd4VTYCiSmo57wE5JXiNLbqtZEEeO2us+Bx4/DjkwR0j+T3996jGUla5pfX7cfdtNULXauaUTCZDyoHzO3gsdMVSbW2ty2niRDnkUFn3cyOUssfmAkm92WzWvWdVRlnE3zIMSnm+3rBkXlyFosiVpFSU6luGrcj6zdmKDnns27dPkslkwQ1di0vSygzgAWGlYCll6/+5jDMqkQ8WmJ48HAZYS8QpAvw+KyO+B9a5RE18SznoAwqn2DVqQqG9I1a4xPp/fm71tFiL+23lYVgNr8o51iI8x0S4mPCME7hR76005o75pi1SvYeBRjqdLsj1AKGzSlKtEtVS/rYea7BUaG+W9Z7+Wzn/s9LHjfqfjTyPYn9nDyV7abXXFkYqe4D5PR0e5deWxzbqNX9f1AFvxtzcnJw4ccKHPBjz8/Nm/JxL87Srh6sO2MXMLE538ivmrmOFpEmFJg9xAgmTlMsM9bXhfcudxp/higme6FGHRQBYUVvnqxVjlJtPn5v1HTpZ1kqe1X+P62DI48vPox5x37W1r61+6+/abckhoqhxtl5DkVqWj74WfS84fsqPHFvVJc9WGGMtBbkmolGeFf3c8sKgagUdF2dnZ10mPjLnGUEQOG8H584gsRihMd18KG5dskeP7791z3lusoeKxwBeyLgxAXncLALjsbmAjGFPnibZ1nvWZzgsNDU1JZ/+9KfX/Hwr2kPxta99TZqamkLCg7dunZmZCW3ghLCHZU2J2MIklUqF+h7oBjNcQmkJVxEpKJWCQNKWsKUIMQF0Uia3Z+YQTjErLg5xyUdw8XNPiKgOgLoKwjrwuauxm9xaAAoorrxPZ97HfW6jMu2LlfbFvY7LxF+vunoQwampKRkcHHRJoOipMjExEfKs6UeUPev8I5ArFsSbISo1edFkxSLcUSS8lMco4u9xbcFXeRBwM37pl37JCe5ykEgkCgQiFCA3kUI+hlU5ge/Bo3afc3wLyZhI3tRsUTdXKtXFG3d9KPPEwdfV0NDgsvzRIAvxf0thcPmSx+YB86mUXgVMUqJKBfn99YZO/CxGRMp5jAsBLS0tFbRUxjE7Oxt7zvX19a4PDe910tDQIOl0OrRei63nuM9arzdLLEN2lENEVvM3eDM9NhaeUBBwM97+9re7xETdHVB32gNpYG+Cdu2z+zUK7BovJjD0expxvQ74vUwmU1C1wAlpDQ0Nbgvg5uZmaWhoKEjY9PCIQhAsd4CMK/srpywQz9fboyISLgksp+QvCILQtvRc8nf58uWC3iqM6urqUCtlbq/c2Ni4qkqUYjKmXLkT93/F5N1GgCskLCIS97ycv+n3r9ZqoY3AehGKivY333jjjU556pCDBc4g55wCvcD4ORMOrkCwiABKGC1SgNe8bTR7DeL2pODYtofHWoM9dmsJVoy6OZn1GPW3qM8j1ySfz6950690Oh0KJeoQVVTVCnKCQO5R2t7S0iKtra2ydetWtweKlSshEu46uhGwCEwxubiSz+rnQD6f3zBPGSOKyJRCSFb6uWI5ZZWOiiYUzc3Nrp4WYQdddqe9D5x9y4IAOQI6uztq0DmkoBsJWfsm4Ll373m8UcCKsaamZs2/H4ooinRYCWvWZ6Jep9NXdqzUWFpaCpWg6wZ1xbwy3DuFG/DB24hQq06Y5UMnI5f6OSs8tNEERiScsBtHOixSspLXnOQLbBaREQmHllZyWAUH5fzfegUmKppQMLhcUGS57r0YOPsbDVqszZT0ca0mE3p4VApYMa8HUPIXlUkf9R52psRGcmifj2Rx5MFg+/i464raFG2l1q3OkShGUvR7xRJD+XlcbgvOo6qqakXXsVLEEZm493SFV1zFHD6nv4vJTBAEm0ZmRGTNW/gDFa0VMVl162Hr0SIM2Wz2DR1H8/DwiIbVKGm1yOVyMjU1JZOTkzIxMeG2wh4bG3MkRDciQmL3zMyM+zvniHFiOSzRRCIRypng3jEbpch0efNKqlLKSRAtpT/LZhEZkUIyU+xgYlLKEVeCrcNM64WKTsocGBiQ9vZ2Two8PDyuCeRyObfpH4gHPB04SunQiDwOHGg/j/ArEtVZecVVnpRTtbKZKmU1VShxlShxrytF/yBXJpfLyfj4uGzfvt1XeYisX4aqh4eHx9WMIAhCuxEz0cDrYuWwQCqVcmXjUY9oaV7O+XGoqJQKk1I+E5dXsRGVRHFADt5KKk1Wm+S50tCXr/Lw8PDweIMjkUi45M0o5HI5Fx5B/oY+kMsxOTkpk5OTsb/JCaP6QPl6fX29U3DIX1uv3BYNna9QSlXKap/r5M61rjIqFStN6vQ5FB4eHh4eRZFOp11PjCgsLS259uXT09MyMzNjPuZyOVfNMjw8HPu7IB7cJwfP+fVqkkotgMCsZa5LMVhbGZRaaRKXM1FKEigHFVaaG+EJhYeHh4fHmiCVSklTU5M0NTVFfiYIArl8+bLMzMxEHmgEtrS0VDLxSKfToQZ9aOVvPa41+VgrJJPJdendUgwIKcUlb1pJmfq9qampdTk/Tyg8PDw8PAqQSCRcRVx7e3vk54IgkEuXLoW6jernOC5fvuwUWilKLZVKhToE4zkf3EX4Wi/n55DSajwy09PTa3hWy6jouw/GpRG3HbcF/bfV/n+p37kW57Da61rt763Xda32HK7V8droMdzM61rPMVzLe/VGmmvlfGcymSzI91hcXCxoBMYNwvi9qJbgcefAWyzoLRis95H38Uabo3Nzc5G/uxpUNKF4/PHHNzRu5uHh4eGxPoCSRxiGO6HGtWbH42o2Ulxtt9FKg8+huMZgTUirJe5q/r/c71iP7yz1d1Z7Dht9r0o9h6vxXpX7vZVyr8r9jkr5ztX8zmq/s9zf26zfwQZ3ly5dkvn5+ZC3A6/5/fn5+QLvtv7OqOoNbnhmeT74PX6OPZk2Yj4V+43Z2Vl59NFHIz+zUlR0H4qhoSFpbGysSAXl4eHh4bF5WFxcdLvNWselS5cKnkeFYUoBWqrrjs36udXtOZPJrKk+8X0oDKxnH38PDw8Pj2sXVVVVRStdNHK5XIhgIP8Dh/XepUuXXAMuEJRykUgkCsiGPnjfF/06k8lsSEfPiiYUHh4eHh4eGwVuaV4OEI7hJFS9U61OVMXj0tKSq6S5dOmSTExMrOjcOQzjdxv18PDw8PCoQCChcyXhBVTGRB1W3gjnjCBXBPkg09PTPinTw8PDw8PjjQaQkbh263HI5XIFyamjo6PrkpTpCYWHh4eHh8c1inQ67TqSAq2trevyW5Wx76qHh4eHh4fHVQ1PKDw8PDw8PDxWDU8oPDw8PDw8PFYNTyg8PDw8PDw8Vg1PKDw8PDw8PDxWjU0lFE888YT09PRIdXW1HDx4UL7zne9s5ul4eHh4eHh4rBCbRii+8Y1vyAMPPCCf+tSn5NixY3LHHXfI3XffLb29vZt1Sh4eHh4eHh4rxKZtDvbWt75VbrnlFvnyl7/s3rvxxhvlgx/8oDzyyCOx/7teG5t4eHh4eHhc67imNgdbWFiQ73//+/LQQw+F3r/zzjvlu9/9bsHn9RayU1NTInLlpnh4eHh4eHiUDujOtfYnbAqhGB0dlaWlJeno6Ai939HRIYODgwWff+SRR+Szn/1swfs7duxYt3P08PDw8PC4ljE2NlbWbqvFsKmtt/X+7kEQmHu+/+mf/qk8+OCD7vXk5KTs2rVLent71/RmXG2Ynp6WHTt2yPnz56/50M4b5Vr9dV5b8Nd5beGNcp1TU1Oyc+dOaWlpWdPv3RRC0draKqlUqsAbMTw8XOC1EFnedlWjqanpmh50YCXb5VYq3ijX6q/z2oK/zmsLb5TrTCbXti5jU6o8MpmMHDx4UA4fPhx6//Dhw3L77bdvxil5eHh4eHh4rAKbFvJ48MEH5Z577pE3v/nNctttt8lXvvIV6e3tlY9//OObdUoeHh4eHh4eK8SmEYoPf/jDMjY2Jn/2Z38mAwMDcvPNN8tzzz0nu3btKvq/2WxWHn74YTMMci3hjXKdIm+ca/XXeW3BX+e1BX+dq8Om9aHw8PDw8PDwuHbg9/Lw8PDw8PDwWDU8ofDw8PDw8PBYNTyh8PDw8PDw8Fg1PKHw8PDw8PDwWDUqglCcPXtWfuu3fkt6enqkpqZG9u7dKw8//LAsLCzE/l8QBPKZz3xGtm3bJjU1NfLOd75TfvKTn2zQWa8Mf/7nfy6333671NbWSnNzc0n/c99990kikQgdt9566/qe6CqxkuusxPGcmJiQe+65R5qamqSpqUnuuecemZycjP2fShnPJ554Qnp6eqS6uloOHjwo3/nOd2I//+KLL8rBgwelurpa9uzZI08++eQGnenqUM51HjlypGDsEomEHD9+fAPPuHy89NJL8v73v1+2bdsmiURC/vmf/7no/1TieJZ7nZU4no888oj84i/+ojQ0NEh7e7t88IMflBMnThT9v7UYz4ogFMePH5d8Pi9PPfWU/OQnP5EvfOEL8uSTT8onP/nJ2P97/PHH5fOf/7x86UtfkldeeUU6Ozvll3/5l2VmZmaDzrx8LCwsyIc+9CH5xCc+Udb/3XXXXTIwMOCO5557bp3OcG2wkuusxPH8yEc+Ij/4wQ/k+eefl+eff15+8IMfyD333FP0/6728fzGN74hDzzwgHzqU5+SY8eOyR133CF333239Pb2mp8/c+aMvPe975U77rhDjh07Jp/85CflD//wD+Xpp5/e4DMvD+VeJ3DixInQ+F133XUbdMYrw8WLF+Xnf/7n5Utf+lJJn6/U8Sz3OoFKGs8XX3xRfv/3f1++973vyeHDhyWXy8mdd94pFy9ejPyfNRvPoELx+OOPBz09PZF/z+fzQWdnZ/Doo4+69y5fvhw0NTUFTz755Eac4qpw6NChoKmpqaTP3nvvvcEHPvCBdT2f9UKp11mJ4/naa68FIhJ873vfc+8dPXo0EJHg+PHjkf9XCeP5lre8Jfj4xz8eem///v3BQw89ZH7+T/7kT4L9+/eH3vvd3/3d4NZbb123c1wLlHudL7zwQiAiwcTExAac3fpARIJnn3029jOVOp6MUq7zWhjP4eHhQESCF198MfIzazWeFeGhsDA1NRW7scmZM2dkcHBQ7rzzTvdeNpuVd7zjHeYW6ZWOI0eOSHt7u1x//fXysY99TIaHhzf7lNYUlTieR48elaamJnnrW9/q3rv11lulqamp6DlfzeO5sLAg3//+90NjISJy5513Rl7X0aNHCz7/K7/yK/Lqq6/K4uLiup3rarCS6wQOHDggXV1d8p73vEdeeOGF9TzNTUEljudqUMnjOTU1JSISqy/XajwrklCcOnVKvvjFL8a26cbGY6VukV7JuPvuu+Xv//7v5dvf/rb81V/9lbzyyivy7ne/W+bn5zf71NYMlTieg4OD0t7eXvB+e3t77Dlf7eM5OjoqS0tLZY3F4OCg+flcLiejo6Prdq6rwUqus6urS77yla/I008/Lc8884zccMMN8p73vEdeeumljTjlDUMljudKUOnjGQSBPPjgg/K2t71Nbr755sjPrdV4biqh+MxnPmMmvPDx6quvhv6nv79f7rrrLvnQhz4kv/3bv130N0rdIn09sZLrLAcf/vCH5X3ve5/cfPPN8v73v1/+7d/+TV5//XX51re+tYZXURzrfZ0ilTee1rkVO+erZTyLodyxsD5vvX+1oZzrvOGGG+RjH/uY3HLLLXLbbbfJE088Ie973/vkc5/73Eac6oaiUsezHFT6eP7BH/yB/PCHP5R/+Id/KPrZtRjPTdvLQ+TKxf7Gb/xG7Gd2797tnvf398u73vUut5lYHDo7O0XkCvPq6upy70dtkb6eKPc6V4uuri7ZtWuX/OxnP1uz7ywF63mdlTieP/zhD2VoaKjgbyMjI2Wd82aNZxRaW1sllUoVWOlxY9HZ2Wl+Pp1Oy9atW9ftXFeDlVynhVtvvVX+7u/+bq1Pb1NRieO5VqiU8bz//vvlX/7lX+Sll16S7u7u2M+u1XhuKqFobW2V1tbWkj7b19cn73rXu+TgwYNy6NChovu49/T0SGdnpxw+fFgOHDggIldioi+++KI89thjqz73clDOda4FxsbG5Pz58yHFuxFYz+usxPG87bbbZGpqSv77v/9b3vKWt4iIyH/913/J1NSU3H777SX/3maNZxQymYwcPHhQDh8+LL/2a7/m3j98+LB84AMfMP/ntttuk3/9138Nvffv//7v8uY3v1mqqqrW9XxXipVcp4Vjx45dNWO3VqjE8VwrXO3jGQSB3H///fLss8/KkSNHpKenp+j/rNl4lpXCuUno6+sL9u3bF7z73e8OLly4EAwMDLiDccMNNwTPPPOMe/3oo48GTU1NwTPPPBP86Ec/Cn7zN38z6OrqCqanpzf6EkrGuXPngmPHjgWf/exng/r6+uDYsWPBsWPHgpmZGfcZvs6ZmZngj//4j4Pvfve7wZkzZ4IXXnghuO2224Lt27dfU9cZBJU5nnfddVfwpje9KTh69Ghw9OjR4Od+7ueCX/3VXw19phLH8+tf/3pQVVUVfPWrXw1ee+214IEHHgjq6uqCs2fPBkEQBA899FBwzz33uM+fPn06qK2tDf7oj/4oeO2114KvfvWrQVVVVfBP//RPm3UJJaHc6/zCF74QPPvss8Hrr78e/PjHPw4eeuihQESCp59+erMuoSTMzMy4NSgiwec///ng2LFjwblz54IguHbGs9zrrMTx/MQnPhE0NTUFR44cCenKubk595n1Gs+KIBSHDh0KRMQ8GCISHDp0yL3O5/PBww8/HHR2dgbZbDZ4+9vfHvzoRz/a4LMvD/fee695nS+88IL7DF/n3NxccOeddwZtbW1BVVVVsHPnzuDee+8Nent7N+cCSkS51xkElTmeY2NjwUc/+tGgoaEhaGhoCD760Y8WlKBV6nj+zd/8TbBr164gk8kEt9xyS6gs7d577w3e8Y53hD5/5MiR4MCBA0Emkwl2794dfPnLX97gM14ZyrnOxx57LNi7d29QXV0dbNmyJXjb294WfOtb39qEsy4PKI/Ux7333hsEwbUznuVeZyWOZ5SuZFm6XuPpty/38PDw8PDwWDUqsmzUw8PDw8PD4+qCJxQeHh4eHh4eq4YnFB4eHh4eHh6rhicUHh4eHh4eHquGJxQeHh4eHh4eq4YnFB4eHh4eHh6rhicUHh4eHh4eHquGJxQeHh4eHh4eq4YnFB4eHh4eHh6rhicUHh4eHh4eHquGJxQeHh4eHh4eq4YnFB4eHh4eHh6rxv8BS/8autXRmyEAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 100\n",
    "a = tfd.Normal(loc=3.0, scale=0.5).sample(N, seed=key())\n",
    "b = tfd.Normal(loc=0.0, scale=0.2).sample(N, seed=key())\n",
    "plt.subplot(xlim=(-2, 2), ylim=(0, 100))\n",
    "x = np.linspace(-2, 2, 100)\n",
    "for i in range(N):\n",
    "    plt.plot(x, jnp.exp(a[i] + b[i] * x), c=\"k\", alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.43"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_seq = np.linspace(np.log(100), np.log(200000), num=100)\n",
    "lambda_ = np.array(list(map(lambda x: np.exp(a + b * x), x_seq)))\n",
    "\n",
    "plt.subplot(\n",
    "    xlim=(np.min(x_seq).item(), np.max(x_seq).item()),\n",
    "    ylim=(0, 500),\n",
    "    xlabel=\"log population\",\n",
    "    ylabel=\"total tools\",\n",
    ")\n",
    "\n",
    "plt.plot(x_seq, lambda_, c=\"k\", alpha=0.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.44"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(\n",
    "    xlim=(np.min(np.exp(x_seq)).item(), np.max(np.exp(x_seq)).item()),\n",
    "    ylim=(0, 500),\n",
    "    xlabel=\"population\",\n",
    "    ylabel=\"total tools\",\n",
    ")\n",
    "plt.plot(np.exp(x_seq), lambda_, c=\"k\", alpha=0.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.45"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [],
   "source": [
    "# intercept only\n",
    "def model_11_9():\n",
    "\tdef _generator():\n",
    "\t\ta = yield tfd.Sample(tfd.Normal(loc=3.0, scale=0.5), sample_shape=1, name='a')\n",
    "\t\tyield tfd.Poisson(log_rate=a, name='T')\n",
    "\n",
    "\treturn tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_11_9 = model_11_9()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [],
   "source": [
    "total_tools = jnp.array(d.total_tools.values, dtype=jnp.float32)\n",
    "jd_11_9_pin = jd_11_9.experimental_pin(T=total_tools)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def run_chain(init_state, seed, step_size=1e-3, num_steps=500, burnin=300):\n",
    "  # To avoid\n",
    "  # TypeError: Tensor conversion requested dtype <class 'jax.numpy.int32'> \n",
    "\t#   for array with dtype int64\n",
    "  burnin = jnp.array(burnin, dtype=jnp.int32)\n",
    "\n",
    "  def target_log_prob(*states):\n",
    "    return jd_11_9_pin.unnormalized_log_prob(states)\n",
    "  \n",
    "  bijectors = [tfb.Identity()]\n",
    "\n",
    "  kernel = tfp.mcmc.NoUTurnSampler(\n",
    "      target_log_prob_fn=target_log_prob,\n",
    "      step_size=step_size)\n",
    "  \n",
    "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
    "    inner_kernel=kernel,\n",
    "    bijector=bijectors)\n",
    "\n",
    "  kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "    inner_kernel=kernel,\n",
    "    num_adaptation_steps=burnin)\n",
    "\n",
    "  chain_state = tfp.mcmc.sample_chain(\n",
    "      num_results=num_steps,\n",
    "      num_burnin_steps=burnin,\n",
    "      current_state=init_state,\n",
    "      kernel=kernel,\n",
    "      seed=seed,\n",
    "      trace_fn=None)\n",
    "  \n",
    "  return chain_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state = jd_11_9_pin.sample_unpinned(num_chains, seed=key())\n",
    "post_9 = run_chain(init_state=init_state, seed=key(), burnin=400)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_9_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_9._asdict().items()}\n",
    "dict_9 = dict(posterior=post_9_dict)\n",
    "idata_9 = az.from_dict(**dict_9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a[0]</th>\n",
       "      <td>3.54</td>\n",
       "      <td>0.055</td>\n",
       "      <td>3.458</td>\n",
       "      <td>3.632</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.001</td>\n",
       "      <td>935.0</td>\n",
       "      <td>1504.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "a[0]  3.54  0.055     3.458      3.632      0.002    0.001     935.0   \n",
       "\n",
       "      ess_tail  r_hat  \n",
       "a[0]    1504.0    1.0  "
      ]
     },
     "execution_count": 212,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_9, hdi_prob=0.89)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {},
   "outputs": [],
   "source": [
    "# interaction model\n",
    "def model_11_10(cid, P):\n",
    "\tdef _generator():\n",
    "\t\ta = yield tfd.Normal(loc=[3.0, 3.0], scale=0.5, name='a')\n",
    "\t\tb = yield tfd.Normal(loc=[0.0, 0.0], scale=0.2, name='b')\n",
    "\t\tlog_lambda = jnp.take(a, cid) + jnp.take(b, cid) * P\n",
    "\t\tyield tfd.Poisson(log_rate=log_lambda, name='T')\n",
    "\n",
    "\treturn tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_11_10 = model_11_10(d.contact_id.values, d.P.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_11_10_pin = jd_11_10.experimental_pin(T=d.total_tools.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def run_chain(init_state, seed, step_size=1e-3, num_steps=500, burnin=300):\n",
    "\n",
    "  def target_log_prob(*states):\n",
    "    return jd_11_10_pin.unnormalized_log_prob(states)\n",
    "  \n",
    "  bijectors = [tfb.Identity(), tfb.Identity()]\n",
    "\n",
    "  kernel = tfp.mcmc.NoUTurnSampler(\n",
    "      target_log_prob_fn=target_log_prob,\n",
    "      step_size=step_size)\n",
    "  \n",
    "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
    "    inner_kernel=kernel,\n",
    "    bijector=bijectors)\n",
    "\n",
    "  kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "    inner_kernel=kernel,\n",
    "    num_adaptation_steps=burnin)\n",
    "\n",
    "  chain_state = tfp.mcmc.sample_chain(\n",
    "      num_results=num_steps,\n",
    "      num_burnin_steps=burnin,\n",
    "      current_state=init_state,\n",
    "      kernel=kernel,\n",
    "      seed=seed,\n",
    "      trace_fn=None)\n",
    "  \n",
    "  return chain_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state = jd_11_10_pin.sample_unpinned(num_chains, seed=key())\n",
    "post_10 = run_chain(init_state=init_state, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_10_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_10._asdict().items()}\n",
    "dict_10 = dict(posterior=post_10_dict)\n",
    "idata_10 = az.from_dict(**dict_10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a[0]</th>\n",
       "      <td>3.322</td>\n",
       "      <td>0.088</td>\n",
       "      <td>3.188</td>\n",
       "      <td>3.462</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.001</td>\n",
       "      <td>1822.0</td>\n",
       "      <td>1604.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a[1]</th>\n",
       "      <td>3.610</td>\n",
       "      <td>0.072</td>\n",
       "      <td>3.493</td>\n",
       "      <td>3.720</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.001</td>\n",
       "      <td>2138.0</td>\n",
       "      <td>1584.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b[0]</th>\n",
       "      <td>0.377</td>\n",
       "      <td>0.052</td>\n",
       "      <td>0.301</td>\n",
       "      <td>0.467</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>2216.0</td>\n",
       "      <td>1588.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b[1]</th>\n",
       "      <td>0.185</td>\n",
       "      <td>0.156</td>\n",
       "      <td>-0.064</td>\n",
       "      <td>0.432</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.004</td>\n",
       "      <td>925.0</td>\n",
       "      <td>939.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "a[0]  3.322  0.088     3.188      3.462      0.002    0.001    1822.0   \n",
       "a[1]  3.610  0.072     3.493      3.720      0.002    0.001    2138.0   \n",
       "b[0]  0.377  0.052     0.301      0.467      0.001    0.001    2216.0   \n",
       "b[1]  0.185  0.156    -0.064      0.432      0.005    0.004     925.0   \n",
       "\n",
       "      ess_tail  r_hat  \n",
       "a[0]    1604.0   1.00  \n",
       "a[1]    1584.0   1.00  \n",
       "b[0]    1588.0   1.00  \n",
       "b[1]     939.0   1.01  "
      ]
     },
     "execution_count": 219,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_10, hdi_prob=0.89)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.46  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [],
   "source": [
    "# intercept only\n",
    "def model_11_9x():\n",
    "\tdef _generator():\n",
    "\t\ta = yield xtfd.Sample(xtfd.Normal(loc=3.0, scale=0.5), sample_shape=1, name='a')\n",
    "\t\tyield xtfd.Poisson(log_rate=a, name='T')\n",
    "\n",
    "\treturn xtfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_9x = model_11_9x()\n",
    "ds_9, _ = jd_9x.sample_distributions(value=post_9)\n",
    "ll_9 = ds_9[-1].log_prob(d.total_tools.values)\n",
    "ll_9 = np.moveaxis(ll_9, 0, 1) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [],
   "source": [
    "dict_9.update(log_likelihood={'ll': ll_9},\n",
    "              dims={'ll': ['culture']},\n",
    "              coords={'culture': d.culture.values})\n",
    "idata_9 = az.from_dict(**dict_9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [],
   "source": [
    "# interaction model\n",
    "def model_11_10x(cid, P):\n",
    "\tdef _generator():\n",
    "\t\ta = yield xtfd.Normal(loc=[3.0, 3.0], scale=0.5, name='a')\n",
    "\t\tb = yield xtfd.Normal(loc=[0.0, 0.0], scale=0.2, name='b')\n",
    "\t\tlog_lambda = tf.gather(a, cid) + tf.gather(b, cid) * P\n",
    "\t\tyield xtfd.Poisson(log_rate=log_lambda, name='T')\n",
    "\n",
    "\treturn xtfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:6 out of the last 6 calls to <function pfor.<locals>.f at 0x35610cc20> triggered tf.function retracing. Tracing is expensive and the excessive number of tracings could be due to (1) creating @tf.function repeatedly in a loop, (2) passing tensors with different shapes, (3) passing Python objects instead of tensors. For (1), please define your @tf.function outside of the loop. For (2), @tf.function has reduce_retracing=True option that can avoid unnecessary retracing. For (3), please refer to https://www.tensorflow.org/guide/function#controlling_retracing and https://www.tensorflow.org/api_docs/python/tf/function for  more details.\n"
     ]
    }
   ],
   "source": [
    "jd_10x = model_11_10x(d.contact_id.values, d.P.values)\n",
    "ds_10, _ = jd_10x.sample_distributions(value=post_10)\n",
    "ll_10 = ds_10[-1].log_prob(d.total_tools.values)\n",
    "ll_10 = np.moveaxis(ll_10, 0, 1) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [],
   "source": [
    "dict_10.update(log_likelihood={'ll': ll_10},\n",
    "              dims={'ll': ['culture']},\n",
    "              coords={'culture': d.culture.values})\n",
    "idata_10 = az.from_dict(**dict_10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jun/miniforge3/envs/dl/lib/python3.12/site-packages/arviz/stats/stats.py:795: UserWarning: Estimated shape parameter of Pareto distribution is greater than 0.70 for one or more samples. You should consider using a more robust model, this is because importance sampling is less likely to work well if the marginal posterior and LOO posterior are very different. This is more likely to happen with a non-robust model and highly influential observations.\n",
      "  warnings.warn(\n",
      "/Users/jun/miniforge3/envs/dl/lib/python3.12/site-packages/arviz/stats/stats.py:795: UserWarning: Estimated shape parameter of Pareto distribution is greater than 0.70 for one or more samples. You should consider using a more robust model, this is because importance sampling is less likely to work well if the marginal posterior and LOO posterior are very different. This is more likely to happen with a non-robust model and highly influential observations.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>rank</th>\n",
       "      <th>elpd_loo</th>\n",
       "      <th>p_loo</th>\n",
       "      <th>elpd_diff</th>\n",
       "      <th>weight</th>\n",
       "      <th>se</th>\n",
       "      <th>dse</th>\n",
       "      <th>warning</th>\n",
       "      <th>scale</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>m11.10</th>\n",
       "      <td>0</td>\n",
       "      <td>84.304236</td>\n",
       "      <td>6.452423</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.962789</td>\n",
       "      <td>12.279325</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>True</td>\n",
       "      <td>deviance</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>m11.9</th>\n",
       "      <td>1</td>\n",
       "      <td>141.002675</td>\n",
       "      <td>7.921044</td>\n",
       "      <td>56.698439</td>\n",
       "      <td>0.037211</td>\n",
       "      <td>31.811849</td>\n",
       "      <td>31.553552</td>\n",
       "      <td>True</td>\n",
       "      <td>deviance</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        rank    elpd_loo     p_loo  elpd_diff    weight         se        dse  \\\n",
       "m11.10     0   84.304236  6.452423   0.000000  0.962789  12.279325   0.000000   \n",
       "m11.9      1  141.002675  7.921044  56.698439  0.037211  31.811849  31.553552   \n",
       "\n",
       "        warning     scale  \n",
       "m11.10     True  deviance  \n",
       "m11.9      True  deviance  "
      ]
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.compare({\"m11.9\": idata_9, \"m11.10\": idata_10}, ic='loo', scale=\"deviance\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.47"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jun/miniforge3/envs/dl/lib/python3.12/site-packages/arviz/stats/stats.py:795: UserWarning: Estimated shape parameter of Pareto distribution is greater than 0.70 for one or more samples. You should consider using a more robust model, this is because importance sampling is less likely to work well if the marginal posterior and LOO posterior are very different. This is more likely to happen with a non-robust model and highly influential observations.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": 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VV17J9OnT+30wAWKHQhAEwStqamqora0lOzs7ZN9cjEYj1dXVQT0ttaSkhL/+9a8+eWyn08mrr77KunXrUCgUzJo1izPOOMMnz9UXBedPhCAIQh/S3t7O/v37UalUREZGBno5PuF0OqmpqcFmswVdX42mpibsdjuFhYU+ew673c7zzz/Pb7/9RlhYGDfffLOYK/UHIqAQBEE4Bg6Hg71792K320lLSwv0cnymsbGR1tZWMjIyAr2Ubux2O8899xzNzc3ccccdjBw50uvPYbFYePrpp9mzZw+RkZHceeedjBgxwuvP09eJgEIQBOEY1NTU0NzcHLKDvwB0Oh21tbWoVKqga9K1bNky6urqSExMpKSkxOuPbzAYePLJJ6mqqiI6Opp7772X4447zuvPEwpEQCEIgnCUdDodBw4cICkpKejeaL3FbrdTXV2NLMtBV9WxefNmvv/+ewBuueUWkpKSvPr4arWaxx9/nKamJhISEpg7dy5FRUVefY5QIgIKQRCEo+Byudi/fz9WqzVkjzpkWaauro729vagy5toa2vj1VdfBeC8887j+OOP9+rjNzQ08Pjjj9Pe3k5qaipz584lJyfHq88RakRAIQiCcBQaGhpoaGjwaeOkQFOr1TQ0NJCSkhJUTbqcTicvvPACZrOZsrIyLr74Yq8+fkVFBU899RQmk4mcnBzmzp0b0qXA3iICCkEQhF4ymUzs37+fuLi4kK3qsFgsVFdXExkZiVKpDPRyuvnpp584cOAAsbGxXm+tvX37dp555hlsNhulpaXcd999ITt63ttEQCEIgtALsixz4MABDAYD+fn5gV6OT7hcLmpqajCZTEF31AEwceJETCYTubm5Xj1uWr9+PUuWLMHlcnH88cdz1113hWzHU18QAYUgCEIvNDc3U1NTQ0ZGRsg2sGptbaWpqYnU1NSg/B7DwsKYNm2aVx/z66+/ZtmyZQCMHTuWm266KWibdwWr4DkUEwRBCHIWi4V9+/YRFRUVsleuXbthBtNxjtPpZMWKFdhsNq8+riRJvPvuu55g4uyzz+aWW24RwcRREAGFIAhCD8iyTGVlJRqNJmSrOrp2wwy2vIEPPviADz/8kCeeeAJZlr3ymE6nkyVLlvDVV18BcPnllzNz5sygSkDtS0QIJgiC0AOtra1UVlaG9FFHc3MzbW1tpKenB3op3WzZsoWvv/4a6BwT7o2/f4vFwrPPPsuOHTsICwvjxhtv5JRTTjnmx+3PREAhCILwJ2w2G/v27SM8PJyYmJhAL8cnTCYTdXV1xMXFBVWTrtbWVl555RUAzjnnHEaPHn3Mj6nT6XjyySepqakhKiqKO++8kxNOOOGYH7e/EwGFIAjCn6isrKStrS3kqzqCbfCX3W7n2WefxWw2U15ezmWXXXbMj9nY2MgTTzyBWq0mMTGR++67zyctu/sjEVAIgiAcQVtbG5WVlaSlpYXs2Xprayutra1BlxvyzjvvUFNTQ0JCAnfccccxJ0ru27ePf/7zn5hMJrKysrj//vuDKoDq60RAIQiCcBhWq5U9e/YAEBcXF+DV+EZHRwe1tbXExsYGVWWDXq9n8+bNKBQKbr31VlJSUo7p8X7++WcWL16Mw+GgtLSUe++9l8TERC+tVgARUAiCIBySLMvs27cvpI86JEmirq4Oi8USdFfqKpWKRx55hB07dhzTnA5Zlvnmm2949913kWWZkSNHcuutt4Zs2W8giYBCEAThEBoaGqiqqiIzMzOkjzqam5tJTk4O9FIOKSUlhdNOO+2ov16SJN5++21WrVoFwKRJk7jqqqtC9t8z0MTfqiAIwh8YDAb27NlDTExMyF7JmkwmqquriY6OJioqKtDLATp3E1555RW2bNlyzI9ltVp55plnPMHEjBkzuPrqq0Uw4UPib1YQBKELp9PJ3r176ejoCNkJk+6qDqvVikqlCvRyPL7++mt++uknXnjhBdrb24/6cXQ6HQsWLODXX38lMjKSO+64g3POOSdk+4cEC3HkIQiC0EVVVRV1dXXk5uYGeik+09TUFHRVHXv27OH9998HYObMmUedhFlXV8dTTz2FRqMhISGBOXPmMGDAAG8uVTgMEVAIgiD8R1tbG/v37yc1NTWoKh68yWAwUFdXR3x8fNB8j1qtlueffx5Jkhg/fjxnnnnmUT3O77//znPPPYfVaiU7O5v77rsv6JJNQ1lw/DQJgiAEmNVqZe/evciyTHx8fKCX4xPuWR12u52kpKRALwfoXNNzzz2HXq8nPz+f66677qiOJr7//nvefPNNJEli0KBB3H333SH77xisREAhCEK/J8syFRUVtLS0UFBQEOjl+Ex9fT1tbW1kZGQEeike77zzDvv37yc2Npa7774bpVLZq6+XJIlly5bx7bffAjB+/Hhmz54dVJNS+wsRUAiC0O81NTVRWVkZ0iWi7e3t1NfXo1KpgmZWhyRJhIWFeZpX9fZ4wmKx8OKLL7J161YALr74Yi644AKRfBkgIqAQBKFfM5lM7N69G6VSGbKDv6xWK1VVVQDExsYGeDX/FRYWxtVXX83EiRN73TxMo9Hw1FNPUVdXR2RkJDfffDNjxozx0UqFnhABhSAI/ZbL5WL//v0YjUby8vICvRyfkGWZuro6DAZD0Bx1WCwWIiMjPUmhvQ0mKioqWLRoEXq9HpVKxZw5cygrK/PFUoVeEAGFIAj9Vl1dHdXV1WRlZYXsNnlraysNDQ0kJycHxXGOy+XimWeeweVycccdd/S6D8a6det47bXXcDgc5Ofnc++99wZV+Wt/JgIKQRD6JZ1Ox969e0lMTAyaTpHe1rUbZm+THX3lgw8+YOfOnURFRWEwGHocUEiSxPLly1mxYgWAmMkRhERAIQhCv+NwONizZw9WqzVkjzrcJaLBNPhrw4YNfPXVVwDcdNNNPT7qsFqtLF68mF9++QWA8847j0svvTQodlyE/xIBhSAI/U5VVRWNjY0h2w1TlmXq6+tpbW0lPT090MsBoKamhldffRXoDAh6mkDZ2trKokWLqKurIyIigtmzZ3PKKaf4cqnCURIBhSAI/Up/6Iap0Wiora0NmhJRo9HIokWLsNvtDBs2jEsvvbRHX7d7926effZZTCaTSL7sAwK+X9TQ0MBVV11FamoqsbGxnHDCCZ5tLeiMtOfPn09OTg4xMTFMnDiRnTt3BnDFgiD0VVarlT179gCEbBfFjo4OKisriYyMDJoy2Ndeew21Wk1GRga33XZbj44qfvjhBxYuXIjJZKK4uJh//OMfIpgIcgENz7VaLePHj+f000/n66+/JiMjgwMHDnRrCfv444/z9NNP88YbbzBgwAAeeeQRJk2axN69e0lISAjc4gVB6FMkSWLfvn20tbX1ukyxr3A6nVRVVWE2m4OmRBTg0ksvRa1Wc/PNNxMXF3fE+zqdTt566y1++OEHAE4++WRuuOGGoEkqFQ4voAHFwoULyc/P5/XXX/fcVlRU5Pl/WZZZtGgRDz74INOnTwdg6dKlZGZmsmzZMm6++WZ/L1kQhD6qrq6OqqqqkO2G2TVvIiMjI6jKYHNzc/nf//3fP12TXq/n2WefZd++fSgUCi655BLOP//8oPpehMML6G/VihUrGD16NJdeeikZGRmMGDGCV155xfP5qqoqmpubmTx5suc2pVLJhAkTWL9+fSCWLAhCH6TRaNizZw/x8fEhW2bozptISkoKiryJffv2sXv3bs+f/ywoqKys5KGHHmLfvn3ExMRw7733Mm3aNBFM9CEB3aGorKzkpZde4t577+WBBx7g559/5q677kKpVHLNNdfQ3NwMcFDJU2ZmJjU1NYd8TJvNhs1m8/zZYDD47hsQBCHoWa1Wdu/ejd1uD9kGSBaLherqasLDw4Mib0KtVvPMM8/Q0dHBvffey7Bhw454/7Vr1/Kvf/0Lh8NBdnY299xzD9nZ2X5areAtAQ0oJEli9OjRLFiwAIARI0awc+dOXnrpJa655hrP/f4YocqyfNio9dFHH+Xhhx/23aIFQegzJEliz549tLa2hmzehMvloqamBqPRGBT9Jmw2G8888wwGg4GCggIGDBhw2Ps6nU6WLVvGqlWrADjhhBO49dZbg2reiNBzAT3yyM7OZvDgwd1uO+6446itrQUgKysLwLNT4dba2nrYX5x58+ah1+s9H3V1dT5YuSAIfUFNTY2ntXYo5k1A5+tjU1MTqampAT8ekCSJl19+merqahISErjnnnsOe8Sk1+t57LHHPMHEhRdeyD333COCiT4soDsU48ePZ+/evd1u27dvH4WFhQAUFxeTlZXFqlWrGDFiBAB2u53Vq1ezcOHCQz6mUqkU2cCCINDW1saePXtITEwM2dcEvV5PbW0tcXFxREZGBno5fPrpp2zevJnw8HDuvvvuwx4xHThwgGeeeQatVkt0dDS33norI0eO9PNqBW8LaEBxzz33MG7cOBYsWMBll13Gzz//zJIlS1iyZAnQedQxZ84cFixYQHl5OeXl5SxYsIDY2FhmzJgRyKULghDEOjo62LVrF5Ik9Xr4VF9ht9uprq7G4XB0K7UPlE2bNvHJJ58AcN111zFw4MCD7iPLMv/+97956623cDqd5OTkMGfOHJEvESICGlCceOKJfPLJJ8ybN49//OMfFBcXs2jRImbOnOm5z9y5c7FYLNx2221otVrGjBnDypUrRQ8KQRAOyel0snv3brRabcjO6ZBlmdraWjQaTdD0m9i1axcA55xzDhMmTDjo83a7nTfeeIM1a9YAMHr0aG666aagSCIVvEMhy7Ic6EX4knuanV6vJzExMdDLEQTBh2RZZu/evezevZucnJyQba3d3NzMnj17SEpKCprjHFmW2bRpEyeddNJB+Sqtra08++yz1NTUoFAouOyyy5g6dWrAcz5Czc6dO5k2bRpjx4712mP25j00NH/bBEHolxobG0N+TofBYKCqqoqYmJiABxN2u52IiAjCwsJQKBScfPLJB91n69atLF68mI6ODhISErj99tsZMmRIAFYr+Fpo/sYJgtDv6PV6du3ahVKp/NP2zn2V3W6nqqoKu90e8KMOSZJ46aWXkCSJW2+99aBqDkmS+OSTT/j0008BKCkp4c477wzZXiCB5nK5cLlcAV2DCCgEQejzHA4Hu3fvxmw2h2zehCRJ1NbWolarg6LfxEcffcSWLVuIiIigvr6+2+Aug8HASy+9xI4dOwA488wzmTlzZlBUooQiu92ORqMhJSUloAm6IqAQBKFPk2WZAwcO0NjYSG5ubqCX4zMtLS3U19eTmpoa8Nbaa9as4fPPPwdg9uzZ3YKJffv28cILL9De3k5UVBTXX38948ePD9RSQ15HRwdGo5Hc3FwiIiICujsnAgpBEPq05uZm9u/fT1paWsjmTeh0Oqqrq4mNjQ143sSePXt47bXXAJg2bRqnnHIK0BnYffPNN7z//vu4XC6ysrK46667QrZDaaDJsoxWq0WWZcrLy8nOzqaxsTGgawrN3z5BEPoFk8nE7t27iYyMDNm8CavVSlVVVVD0m2hqauKZZ57B5XJx0kkncfHFFwOdV8mvvPIKv/zyCwBjxoxh9uzZoiTUR1wuF2q1mtjYWEpKSoImL0UEFIIg9ElOp5O9e/ei1+tD9irY5XJRXV2NVqsNeN6EJEk899xzmEwmSktLufnmmwkLC6Oqqornn3+e1tZWIiIimDlzJmeeeaYoCfURm81Ge3s7GRkZFBUVER8fH+gleYiAQhCEPsedN1FbW0t2dnbIvnk1NjbS1NREWlpawGeRhIWFMXv2bN5++23mzJlDZGQkq1atYtmyZTidTtLS0rjzzjspKSkJ6DpDmdFoxGw2U1hYSEFBQdAluYqAQhCEPqepqYl9+/aRkpISdC+q3qLRaKipqSEhISFovsfS0lIeeughzGYzzz77LFu2bAFg1KhR3HjjjSF77BRokiTR3t5OeHg4AwcOJDMzM+AB5qGIgEIQhD5Fr9eze/duoqKigmq715tMJhMHDhxAoVAE/E36yy+/ZPDgwRQXFwN4jjja2toIDw/nyiuvZPLkySG7SxRoDocDjUaDSqWipKQk4Hk0RyICCkEQ+gybzcauXbswmUwh22/CZrNRWVmJ2WwOePOqH3/8kffee4+oqCgee+wxNm/ezAcffIDL5RJHHH5gNpvR6/Xk5ORQVFR02FHwwUIEFIIg9AmSJLFv3z6amppCNphwuVxUVVWhVqvJyMgI6FX/77//zuuvvw7A6aefztKlS9m2bRvQOdhx9uzZAd89CVWyLKPT6XC5XJSVlZGbmxvw3iM9IQIKQRD6hJqaGiorK8nMzOwTL669JcsydXV1NDY2kpaWFtDvsaamhueeew5Jkhg6dCg///wzWq2WyMhIZs6cyRlnnCGOOHyka0nogAEDgqYktCdEQCEIAgCyDN99Bx9+CO3tkJwMF18MZ58NgX7vaG5uZteuXSQkJAT9tu/RamlpoaamhqSkpIAmYarVap588kmsViupqans3LkTWZbJycnh9ttvp6CgIGBrC3VWqxWtVktGRgbFxcV9bgdIBBSCIPDLLzBjBuzb1/32V1+FsjJ4+20YMyYwa9PpdOzYsYPw8HBUKlVgFuFjWq2WqqoqoqOjA9oMqqOjg6eeegqdTkdUVBQajQaA0047jauvvjpkg7lgoNfrsdlsFBUVUVBQ0Ce7vva9FQuC4FW//Qannw5G46E/X1EBZ54JP/4Io0f7dWmYzWa2b9+O2WwO2Tkd7ooOl8sV8Az+8PBwz1GL3W4nJiaG66+//pBjyQXvcB9xREdHM2jQoIDnzhwLEVAIQj93yy2HDybcOjrgppvg11/9syboLJfbuXMnarU6ZJMwrVYrBw4cwGQyBbyiw2Kx8NZbb1FTUwNAWVkZt956a8DXFcrcXS/T0tIoLi4mISEh0Es6JiKgEIR+bMsW+Pnnnt33t99g40bwx8WqJEns2bOHuro6cnNzg7KJz7FyOp1UVVWh0WgCflX67bffsnLlSlpbW1EoFJx//vlcdNFFfXLbva8wGAxYLBYKCgooKCggKioq0Es6ZuKnRRD6sS+/7N39P//cPwFFVVUVBw4cIDMzMyTf1CRJoqamhqamJtLT0wNW0SFJEk8//bSnHDQlJYVbb72VQYMGBWQ9/YHL5UKj0aBUKhk0aBCZmZl99ojjj0LvN1UQhB4zmXx7/6PR1NTEnj17UKlUIZsE2NTURF1dHSkpKQELmNra2njiiSdoamoCID8/nwcffLDPVRb0JV2POIqKikhMTAz0krxKBBSC0I+lp/fu/r4+TtfpdOzatYuIiIiQe7F102g0VFVVERcXh1Kp9Pvzy7LM+vXr+de//oXdbgdgyJAhzJ07NySPloJFKB5x/JH46RGEfuyKK6Cn7yEKBVx5pe/WYrFY2LlzJx0dHX2qmU9vdJ3REYg5JB0dHbzwwgssXrzYE0wMGzZMBBM+5HK5aG1tRZZlBg0aRGlpaUgGEyB2KAShXysogGnT4NNP//y+554Lvhrb4HQ62bNnDy0tLeTn5/vmSQIs0DM6duzYwZIlS9BqtZ7bjjvuOObMmSOCCR8J9SOOPxIBhSD0c0uWwK5dBze16qq0FF57zTfPL8syBw4coLq6mpycnJB8c3O5XFRXVwdkRofNZuP9999n1apVACQlJaHX6ykoKOCee+4JmtHooUav12O1WkP6iOOPREAhCP1cejqsWwf33Qfvvw82238/p1TCpZfCU0/5Ln+isbGRffv2kZKSEpJvboGc0VFZWcnLL79MY2MjAGeeeSZXXHEF+/fvJz8/P6BdOUOVJEmo1eqQrOL4MyKgEASBtDRYuhSefrqzNNQ9y+O883qfuNkb7iTMqKiogOQU+ENrayu1tbUkJib6LWByOp189tlnrFixAkmSUKlUzJw5k7FjxwJw/PHH+2Ud/Y3T6aStrY2UlBRKSkpC/ojjj0RAIQiCR2oqzJrln+eyWq3s2rULi8USsm21dTodlZWVREVFERsb65fnrK+v5+WXX6a6uhroHDVutVr56KOPKCkpITMz0y/r6G/cg71ycnIoKioK2ZLnIxEBhSAIfudyudizZw/Nzc0h21bbbDZz4MABnE6nX6pWJEni66+/Zvny5TgcDuLi4rjmmmvYvn07mzdvJjIyEp1OJwIKHzAYDFitVkpKSsjLywvJZmw90T+/a0EQAkaWZSoqKqiqqiIrKytgXSJ9yeFwUFlZidFo9EtFR3NzM0uWLGH//v0ADB8+nOuvv55vvvmGtWvXEhYWxh133MHAgQN9vpb+RJZlNBoNERERDBw4sF/lSxyKCCgEQfCrmpoa9uzZQ2pqakAaO/mau6KjtbXV5xUdkiSxatUqPvjgA+x2O9HR0cycOZMJEybw2Wef8fXXXwNw4403MnLkSJ+toz9yTwlNSEigtLQ04JNig4EIKARB8JvGxkZ27txJQkJCSLZ4dld01NfXk5qa6tPdl5aWFl555RX27t0LdHa7vOGGG0hLS2PlypUsX74cgKuuuopTTjnFZ+voj9z9JTIzMykpKRHVMv8hAgpBEPxCrVazY8cOIiIiUKlUgV6OTzQ0NFBdXU1SUpLP+g78cVdCqVRy5ZVXcsYZZ6BQKHA4HPzwww8AXHTRRZx99tk+WUd/ZTQaMZvNFBYWUlhY2G/zJQ5F/E0IguBzBoOBHTt2YLfbyc7ODvRyfKKlpYWqqiri4+N9luHf3NzMK6+8wr7/dCE77rjjuOGGG7rlaURGRvLAAw+wbt06pkyZ4pN19EeSJKHRaIiMjOx3/SV6SgQUgiD4lM1mY+fOnej1+pAtD21vb+fAgQNERkb65ChHkiS++eYbPvroIxwOB9HR0VxxxRWcfvrpns6iBoPB0/cgMTGRc845x+vr6K/sdjsajYaUlBSKiopEvsRhiIBCEASfkSSJvXv30tTURF5eXkhe0RkMBioqKpAkieTkZK8/fn19Pa+88gqVlZVA91wJt7179/Lkk08yY8YMTj/9dK+voT9zH3Hk5uZSWFjYL/tL9JQIKARB8Jnq6moqKyvJzMwMyfJQs9nM/v37sVqtpHu5pajT6eTzzz/ns88+w+VyERMTw4wZM5gwYUK3wKyyspInn3wSq9XKL7/8woQJE0JyHoq/2Ww2tFotMTExlJWVkZ2dHZI/w94kAgpBEHyipaWF3bt3o1KpQvKqzmazceDAAZ/0mqisrOTVV1+lrq4OgBEjRjBr1ixSUlK63a+uro4nnngCq9XKcccdx1133SWCiWMkSRI6nQ6n00lOTg65ubkh2xbe20RAIQiC1xmNRnbt2oVCoQjJeQZOp5Oqqira2tq82mvCarWyfPlyvv32W2RZJiEhgauvvpqTTz75oOdoampi4cKFmEwmSktLueeee/rFREtfMpvN6PV6kpOTyc/PJzU1NSSP6XxFBBSCIHiVxWJhx44d6PX6kGyrLUkS1dXVNDY2kp6e7rVt8O3bt/Ovf/0LtVoNwLhx45g5c+YhA7LW1lYeffRRzxjyv/zlL6IXwjFwuVy0t7cTHh5OSUkJOTk5Ijg7CiKgEATBa6xWK7///jvNzc3k5uaG3NWdJEnU1tZSV1dHSkqKV3oQGAwGli1bxrp16wBITU3luuuuY/jw4Yf9mp9//tkziGru3Lkh2STMX4xGIyaTifT0dAoKCkK2R4o/iIBCEASvsNls7Nixg4aGBnJzc0MugU2WZU/jKpVKdcxtw2VZZu3atSxbtgyTyYRCoeCss87i0ksv/dPdhqlTpxIZGcmYMWPEG+BRcjqdaDQaoqOjGTBgAFlZWaJJ1TEKaPbO/PnzUSgU3T6ysrI8n5dlmfnz55OTk0NMTAwTJ05k586dAVyxIAiH4nA42LVrF7W1teTm5obkC3NDQwOVlZUkJCQc8/FCc3Mzjz32GEuWLMFkMpGfn89DDz3ENddcc9jHNhgM2O12ABQKBWeffbboh3CUDAYDarWazMxMhg4d2q8nhHpTwP8GhwwZwnfffef5c9ermscff5ynn36aN954gwEDBvDII48wadIk9u7dS0JCQiCWKwjCHzgcDnbu3ElVVRU5OTkh+cLc3NxMZWUlcXFxxMbGHvXjOBwOvvzyS1asWIHD4SAyMpLp06czZcqUI/69GQwGHn30UVQqFXPmzAnJqhl/cDgctLe3Ex0dzaBBg8jIyAi5nbRACvhvfkRERLddCTdZllm0aBEPPvgg06dPB2Dp0qVkZmaybNkybr75Zn8vVRCEP3AHE5WVlWRnZxMZGRnoJXlda2srFRUVREdHH1Ouwu7du3njjTdobGwEYOjQocyaNYvMzMwjfp3RaOSxxx6jvr4ek8mEwWAQAUUvybKMwWDAarWSmZlJfn6+KAX1gYAHFPv37ycnJwelUsmYMWNYsGABJSUlVFVV0dzczOTJkz33VSqVTJgwgfXr1x82oLDZbNhsNs+fDQaDz78HQeiP7Ha7Z2ciOzs7JLPitVotBw4cICIi4qh3RQ0GA++99x5r1qwBQKVSMXPmzEOWgv6RyWRi4cKF1NXVoVKpeOCBB7ze8yLUuRtUxcXFeXYlRK8O3whoQDFmzBjefPNNBgwYQEtLC4888gjjxo1j586dNDc3AxwUvWdmZlJTU3PYx3z00Ud5+OGHfbpuQejv7HY7O3bs8BxzhGIwYTQaqaiowOVykZqa2uuvlySJn376iffffx+TyQTAGWecwWWXXdajnY6Ojg4WLlxITU0NiYmJzJs3L2QHq/mCLMvodDocDge5ubnk5+eL0lofC2hA0XV4zfHHH8/YsWMpLS1l6dKlnHzyyQAHRfCyLB8xqp83bx733nuv588Gg4H8/Hwvr1wQ+i93NUdNTQ25ubkhecxhsVg4cOAAHR0dR7UjUFtby+uvv05FRQUABQUFzJo1i/Ly8h59vTuYqK6uJiEhgXnz5oXsYDVfsNlstLe3k5iYyIABA0SDKj8J+JFHV3FxcRx//PHs37+fCy+8EOhMhuoalbe2th7xzFGpVB5zOZcgCIdmsVjYvn079fX1IVvNYbfbOXDgAFqtttddMC0WC8uXL2fVqlVIkkR0dDTTp09n8uTJvUr+U6vVtLS0EB8fz7x580KyQZgvyLKMXq/HZrORn59Pfn6+yDfxo6B6NbDZbOzevZtTTz2V4uJisrKyWLVqFSNGjAA6f9FXr17NwoULA7xSQeh/TCYT27dv9zStCsVgwuFwUFlZSWtra6/O2mVZZuPGjSxbtgydTgfAiSeeyFVXXXXQ/I2eKCws5K9//SsRERFih7WH3LkSCQkJlJWVkZaWJnYl/Cygrwj3338/559/PgUFBbS2tvLII49gMBi49tprUSgUzJkzhwULFlBeXk55eTkLFiwgNjaWGTNmBHLZgtDvGAwGtm3bhkajCcmmVdAZTBw4cIDGxkbS0tJ6/D02NDSwdOlSdu/eDUBWVhZXX301w4YN69Xzd3R00NbWRlFREQAlJSW9+vr+quuuRE5ODgUFBSJXIkACGlDU19dz5ZVXolarSU9P5+STT2bjxo0UFhYCMHfuXCwWC7fddhtarZYxY8awcuVK0YNCEPyovb2d33//Hb1eT25ubkhmyLuPOZqamkhPT+/R7ovFYuGTTz5h5cqVuFwuIiMjueCCCzj33HN7nVfiruZoaWnhr3/9K6WlpUf7rfQr7l2J+Ph4SktLSUtLC8mfz74ioAHFe++9d8TPKxQK5s+fz/z58/2zIEEQumlra+P333/HYrGE5GwO6AwmKioqaG5u7lEwIcsy69at47333kOv1wMwatQoZsyYcVQJnEaj0VPNkZCQEJIVM94mdiWCU+gdggqC4BXNzc38/vvvOByOkC1XtNlsVFRU0NLS0qOuidXV1bz11lvs27cPOPrjDTe9Xt+tz8Tf/vY3kYD5J7rmSohdieAiAgpBEA5SX1/P9u3bCQsLO2Qn21BgtVqpqKjwJGAeKZgwGo189NFH/Pvf/0aWZaKiorjgggs455xzjrpsVqfT8eijj9LY2EhSUhLz5s0jJyfnaL+dkNe1r0ReXp6o4AhCIqAQBMFDlmVqamrYuXMnUVFRR1Wh0Bf0NJhwuVz88MMPLF++nI6ODgDGjh3LFVdccUx/N3q9nv/7v/+jubmZlJQU5s2bF7KBmzd0dHRgMBhITEykvLxcVHAEKRFQCIIAdFY57N+/n/3795OQkBCyY7GtViv79u1Do9EcMZjYsWMHb7/9Ng0NDUBnc6qrr76aQYMGHfMaYmNjSU9Px+FwiHbaR2Cz2dDpdCiVSkpKSsjKyhK7EkFMBBSCINDR0cGuXbuoq6sjIyMjZBPcLBYL+/fvR6PRkJ6efshgoqWlhWXLlvHrr78CEB8fz8UXX8wZZ5zhtbP6yMhI7r77bkwm01G19Q51LpcLnU6Hy+UiKyuLvLw8McyrDxABhSD0cxqNhh07dtDe3h6yDaugM2jav38/Op3ukMGE2Wzms88+Y+XKlTidTsLCwpg0aRIXXXTRMU0ZdWtoaODnn3/mwgsvRKFQiK6+hyBJEgaDAZvNRkpKCrm5uaSkpIjjjT4iNF85BEHokZaWFrZt24bdbic/Pz9kX7hNJhN79+7FaDSSnp7ebafB5XKxevVqPvroI4xGI9A5W2jmzJlem59RU1PDwoULMRqNxMXFdZuiLHQyGo10dHSQmJhISUlJr5qLCcFBBBSC0E+1traybds2JEkK2bJQ6EyA3L9/v2fQV9egafv27bz77rvU1dUBkJ2dzYwZMxg+fLjXgquKigqeeOIJzGYzRUVFjB071iuPGyqcTicajYbo6GjKy8vJzMwMyYFz/YEIKAShH2pra2Pbtm24XK6QTgjU6XTs27cPq9VKenq6J0hoaGjg3XffZdu2bUDnYMLp06dzxhlnePXIZ9euXTz99NPYbDbKysq4//77vXJ8EiqMRiNms5nMzEzy8/NFnkQfJwIKQehn2tra2Lp1Kw6H44iTe/s6jUbD/v37cTqdpKenA50zST7++GP+/e9/I0kS4eHhnHXWWVxwwQVeb+m/detWnn32WRwOB0OGDGHOnDmiQuE/XC4XarUapVLJgAEDyMzMFMcbIUAEFILQj6jVak/ORCj3PVCr1ezfvx9JkkhNTcVms/Htt9/y+eefY7Vagc522ZdffrlPjnu0Wq0nmBg5ciS33367aKn9H+5ciYyMDAoKCsRsphAiAgpB6Cfcxxw2my2kg4nW1lb2799PWFgYSUlJrFmzho8++oj29nYAioqKmDFjBscdd5zP1pCcnMysWbPYuXMnN954Y8hWzvRG11wJ966E+HsJLeJfUxD6AXcCZqjvTDQ3N1NRUUFERAS1tbW8//771NTUAJCamsqll17K2LFjfTb7wWKxeHp4nHbaaZx66qkhWznTGwaDAbPZTFZWlsiVCGEioBCEEOcuDXU3CQpV7mCiubmZzz//nJ07dwKdXSmnTZvGpEmTfHbsIMsyH3zwAVu2bOHvf/+7p8tofw8m7HY7Wq2WmJgYBg0a1KMBbELfJQIKQQhhTU1N/P7778iyHNLVHM3NzWzatIlvvvmGzZs3A/g04bIrSZJ44403+Pe//w10lqKecsopPnu+vqDreHH3roSobgl9IqAQhBAkyzJ1dXXs2LGD8PBwT5VDKNqzZw8vv/wy69evx+VyAZ0DvC655BKfB1EOh4OXXnqJzZs3o1AouP766/t9MCHGi/dfIqAQhBAjSRIHDhxg9+7dxMXFkZSUFOgl+URHRwdLlizho48+wmazATB06FAuv/xyioqKfP78FouFRYsWsWvXLsLDw7n11lsZM2aMz583mOn1eqxWKzk5ORQWFooy2X5GBBSCEEKcTid79+5l3759pKSkhGTym91uZ/ny5bz66qvo9XoAiouLueyyyxg6dKhf1qDX63nqqaeoqqoiOjqaOXPmMGTIEL88dzByV3DExsZy3HHHHdTeXOgfREAhCCHCarWye/duqqqqyMzMDLmrQ6fTyVdffcWSJUtobm4GID09ncsvv5wTTzzR729gZrOZhIQE/vKXv1BcXOzX5w4mBoMBi8VCZmYmBQUFIleiHxMBhSCEAIPBwM6dO2lubiYnJyekZiFIksQPP/zA4sWLqa6uBkClUjF16lQmTZoUkF4GKpWKuXPn4nK5QnoOypE4HA7a29uJjo5m4MCBooJDEAGFIPR1ra2t7NixA6PRSG5ubsi8qMuyzLp163jppZfYu3cvAPHx8UycOJHJkyeTnJzs1/Xs2rWL9vZ2T9JlKFfNHIksyxgMBqxWq6jgELoRAYUg9FHuSo6dO3ciyzK5ubkh0/dg8+bNvPTSS/z+++9AZy+JqVOnMmzYMDIyMoiNjfXrejZt2sTixYuRJIm0tDQGDRrk1+cPFu4Kjri4OJErIRxEBBSC0Ac5HA7279/P/v37iY+PD5lKjq1bt7J48WK2bNkCgFKp5JJLLmHChAno9XpUKpWnE6W/fPvtt7zzzjvIssyJJ55ISUmJX58/GEiShE6nw+VykZeXR15ent//HYTgd8wBhcvlYvv27RQWFvp9C1IQ3Kqr4eWXYeNGcLlg6FC45RYYNizQK/M+o9HIrl27aGhoICMjIyRe2Hfs2MGSJUtYv349AJGRkVx00UXMmDEDo9FIU1MTKSkpKJVKv61JkiTef/99vvrqKwDOOussrr766n53RW6xWNDpdKhUKgoLC0lNTQ2ZnTDBu3odUMyZM4fjjz+e2bNn43K5mDBhAuvXryc2NpYvvviCiRMn+mCZgnBosgwPPACPPw6S9N/b16yBl16CK66AN94AP74P+VRzczO7du3CYDCQm5vb54cr7d69m5dffpm1a9cCnd0tp02bxuzZs1GpVFRUVNDW1kZ6erpfv1eHw8GSJUvYuHEjAJdeeinnn39+v3ojdblcaLVaFAoFRUVF5Obm+jWgE/qeXv+GfvTRR1x11VUAfP7551RVVbFnzx7efPNNHnzwQdatW+f1RQrC4fy//wePPXb4z7/3Hjid8OGH/luTL1itVqqrqzlw4ADh4eHk5eX16Te3PXv2sGTJEn766SegM5A499xzmT17Nnl5eZhMJvbs2YNerw9I9cDGjRvZuHEj4eHh3HDDDf2u+6XJZMJoNJKWlkZBQUHIHKkJvtXrgEKtVnsGDH311VdceumlDBgwgNmzZ/Pss896fYGCcDitrbBw4Z/f76OPOo9CTj7Z92vyNkmSaGpqoqKiAo1GQ2pqap9uVrV7926WLFnCmjVrAAgLC+Occ87hhhtuID8/HwCdTkdFRQUmkylgSX+nnHIKtbW1DB8+3G/NsoKBuxRUqVQyYMAAsrKy+vwumOA/vf5JyczMZNeuXWRnZ/PNN9/w4osvAp1NXkKlXE3oG/71L7Dbe3bfF1/sewGFVqulsrKS+vp6oqOjyc/P77Pn97t27eKVV17pFkicffbZzJ49u1ubbI1GQ0VFBXa7nYyMDL/uwtTW1pKRkUF0dDQKhYKZM2f67bkDreswr8zMTDFiXDgqvQ4orrvuOi677DKys7NRKBRMmjQJ6Cyr6q+lVEJg/PZbz++7davPluF17uON6upqbDYbGRkZPhu77Wu///47r776qifZMiwsjClTpjB79mwKCwu73be1tZWKigpkWSYtLc2v69y6dSvPP/88gwYN4p577ulXF0c2m4329nYSEhIoKSkRpaDCUet1QDF//nyGDh1KXV0dl156qSdJJzw8nL/97W9eX6Ag9Bcul8tzvNHe3k5qamqfnRL622+/8eqrr7Jp0yag8/XBvSPxx0BCkiQaGxuprq4mIiIClUrl17V+9913vPnmm8iyjMvlwuFw9IuAwuVyodPpkGWZgoIC8vLyQq5du+BfR3U4dskllxx027XXXnvMixGE3hg1Cj74oOf3DWYajYYDBw7Q2NhITExMnzzekGWZTZs28a9//Ytff/0V6AwkzjvvPK677jry8vIO+hqn00lNTQ11dXXEx8f7teOiJEm89957fP311wCcdtppXHfddf0iZ8CddJmamkp+fj7Jycl9OslXCA49+s3pTbLlXXfdddSLEYTeuP56eOgh+M/k6iO69Vbfr+dodHR0eI43JEkiKyurz83hkGWZNWvW8Nprr7Fz506gs4/E+eefz6xZs8jJyTnk11mtVqqqqgLSY8JqtbJ48WJ++eUXAC6++GIuuOCCkH9TtdvtaLVaoqOjRdKl4HU9+kn65z//2aMHUygUIqAQ/CYtrbMHxf/7f0e+3xVXwEkn+WdNPWW326mvr6eystJTnufvdtLHyul08t133/HGG29QUVEBdHa2nD59OldfffURZ12YTCYqKirQarV+7zEB8OKLL/Lbb78RGRnJjTfeyNixY/36/P4mSRJ6vR673U5WVhZ5eXki6VLwuh79FldVVfl6HYJwVB56qLMz5oIFnf0m/uiaa+CVV/y/rsNxOBw0NTVRVVWFRqNBpVKRn5/fp66M7XY7X375JUuXLqW+vh6AuLg4LrnkEmbOnElKSsoRv75rWWhGRkZAjnYuuugi6urquPXWWxkwYIDfn9+fzGYzOp2OpKQkysvLSU1N7XPHaULfoJBlWT7aL3Z/aTC/GBoMBlQqFXq9nsTExEAvR/CRhobOwGHDhu6tt4Ol8MjhcNDS0kJVVRVqtZrY2FhSUlL61At7R0cHH3/8Me+88w5qtRroHOM9Y8YMLrvsMhISEv70Mdra2jhw4ABOp5OUlBS/vna4Z4G4OZ3OkN7ud7lcqNVqIiMjyc3NJScnp89WCwk9U1dXx8iRIykoKPDaY/bmPfSofpvefPNNnnjiCfbv3w/AgAED+Mtf/sLVV199NA/X51itVtRqNS6XC0mSkCQJWZaJjIzs9hEdHY1SqQzqgCtU5ObC/PmBXkV37tbFarWaxsZGDAYDMTExfW7EuFar5d133+XDDz/EaDQCnaO7r7rqKi666KIezRKRZZmmpiYqKysJDw8nNTXV18vu9txfffUVH3/8MQ888AClpaUAIR1MGAwGLBYLaWlp5Ofn+71yRuifev0b9fTTT/M///M/3HHHHYwfPx5Zllm3bh233HILarWae+65xxfrDCoajYYtW7Z0CxS6bvQoFArCw8OJiopCqVSSmJhIYmIiSqWS8PBwIiIiiIiIIDIyktjY2D51lSocmd1ux2AwoNVqaWxsRK/XI0kSCQkJ5OTk9KlAor6+nnfeeYcVK1Zg+0/ma0FBAddeey3nnHNOj692XS4XdXV1VFdXExcX59eze6fTyeuvv+5p8f3rr796AopQZLPZ0Ol0xMTEMHDgwIC0LRf6r14HFM899xwvvfQS11xzjee2Cy64gCFDhjB//vx+EVC4HaoMDvDUs9tsNux2O42NjdTU1HS7jzuwiI6OJikpiaSkJGJjY4mKivJ89LVs//7IbrdjNpvp6OhArVajVqvp6OhAkiRiY2PJzMzsc1fCe/bsYenSpXz//fdI/5m4NnjwYGbNmsWECRN69QZlt9upqqqioaGBpKQkv05GNRqNPPPMM+zdu9fT+XLy5Ml+e35/kiQJrVaLy+UiOzub/Pz8PpfkK/R9vX6la2pqYty4cQfdPm7cOJqamryyqL5OoVB4diEOV1fvbqBjtVo9TX3cOxtdj03cb0YKhQKFQkFMTAxJSUmeKz3RiMa/3FeAOp0OrVaLyWTCarXidDoJCwsjPj6erKysPndVKMsyGzZs4K233mLz5s2e28eNG8c111zDqFGjen10ZzabOXDgAG1tbaSmpvr1/L6uro6nn34atVpNdHQ0d9xxB8OHD/fb8/tTR0cHBoOB5ORk8vPzxXhxIWB6HVCUlZXxwQcf8MADD3S7/f3336e8vNxrCwt14eHhhIeHHxQQOJ1OnE4nDocDu92O1WrtdpyiVquprKwkLCyMmJgYYmNjSUhIID4+HqVSSVRU1EEvJhERESiVSs+Ri9BzkiRhtVrR6/Wo1WpaW1sxmUwAREdHEx0dTUJCQp/bhXBzOBx8++23vPXWWxw4cADo/NmcNGkS11xzzVFXQOj1eioqKjAYDH7fdq+vr+cf//gHVquVjIwM7r33XnJzc/32/P7i7imhVCopLy/vkz1MhNDS61fBhx9+mMsvv5yffvqJ8ePHo1AoWLt2Ld9//z0f9LRt4SE8+uijPPDAA9x9990sWrQI6Lxqevjhh1myZAlarZYxY8bwwgsvMGTIkKN+nmDn3tn4s50Hl8uF1WrFbDaj1+txOByez7kDClmWUSgUhIWFeY5QYmNjiY+PJyEhgZiYGM+bYkRERL/O5ZAkCZvNhs1mw2q1YrFYMBgM6HQ6z5/DwsI8uRBH83dVUQFvvAE//thZ4jp6NFx9NYwZ4/Vv508ZDAY+/vhj3n//fdra2gCIjY3lwgsvZMaMGZ6JwkfDXclht9vJzMz0+9VyTk4OgwcPxmq1cscdd/So+qQvkSQJnU6Hw+EQPSWEoNLrgOLiiy9m06ZN/POf/+TTTz9FlmUGDx7Mzz//zIgRI45qEZs3b2bJkiUMGzas2+2PP/44Tz/9NG+88QYDBgzgkUceYdKkSezduzfkXiR6Kzw8nLi4uB61Ku6646HX62lra8PlcgGdHQ2VSiVhYWGEhYV5kkVlWfZUsLirWNxkWfbskLg/3Mcz7g/3Doz7cd1vwO7HdQc77smO3iTLMk6nE5fL5flv1+/H5XJht9ux2+10dHRgNpuxWCye25z/aWjhTqqNi4s75hLPrVvhjjvAav3vbRs3dn78z//ABRcc4zfdQ/X19bz77rusWLECi8UCQFpaGldccQUXX3zxMf1edZ3JER4e7tc5JDabDYVCQVRUFGFhYdx6662en8VQ0tHRgdFoJCkpifz8/D5XeiyEtqP6bRs1ahRvv/22VxZgMpmYOXMmr7zyCo888ojndlmWWbRoEQ8++CDTp08HYOnSpWRmZrJs2TJuvvlmrzx/f+B+Yf1jQpwsy9jtdhwOBy6Xy5PX0dHRAfw3b8P9ht/1jd/hcGA2mz1f6+a+j3vHIywsrNvjuIOJrgFFcnIyKpWKmJgYFApFt6DDHci4/7/rB3S+iblzUdw7DA6HA0mScDqd3YKiPwZG7nW681Xi4uJISkryyZvQY491Dya6evJJOOss8NUYC1mW2bp1K8uWLePHH3/0/B2Ul5czc+ZMzj777GPeKg/kTA61Ws2iRYvIy8vj5ptv9vxchRJ3TwmlUklZWRmZmZmip4QQdI7qldPlcvHpp5+ye/duFAoFgwcPZtq0aUd1Tnr77bczdepUzjrrrG4BRVVVFc3Nzd2yspVKJRMmTGD9+vWHDSjcbypuBoOh12vqLxQKhSe3wpvcuwDuN3D3m7n7Od1BhvuYoba21rMr0JM1w6HLdLt+REREEBUV5fkz0G2nxJ/27Ok87jgciwW+/x6mTfPu8zocDr7//nuWLVvGrl27PLePGzeOmTNnctJJJ3lld8g9br2xsdHvMzl2797Nc889h9FopL293TOlNZS4dyUyMjIoKCjo97uzQvDqdUBRUVHB1KlTqa+vZ+DAgciyzL59+8jPz+fLL7/sVY33e++9x6+//totq9ytubkZgMzMzG63Z2ZmHlSC2dWjjz7Kww8/3OM1CN7Xmzfu/lDaptX++X3a2733fDqdjuXLl/PRRx958iOUSiXnnnsuM2bMoLi42GvPpdfrqaysRKfT+XUmhyzLfP/997z99tu4XC4KCwuZM2dOSAUTLpeL9vZ2IiIiPEmXoXaEI4SWXv903nXXXZSUlLBhwwZPz36NRsNVV13FXXfdxZdfftmjx6mrq+Puu+9m5cqVR9ye/OMVlHur/HDmzZvHvffe6/mzwWAgPz+/R2sSBF/oyY9fYeGxP8/+/ft57733+Oabbzy7dKmpqVx66aVcfPHFJCcnH/uT/Icsy7S2tlJZWYnD4fDrTA673c7SpUs9zapOPvlkbrjhBr/ujPia1WpFq9WSlpZGYWGh6HQp9Am9DihWr17Nxo0buw0ASk1N5bHHHmP8+PE9fpxffvmF1tZWRo0a5bnN5XLx008/8fzzz7N3716gc6ciOzvbc5/W1taDdi268sUWviAci7w8OPnkzgTMQ8nIgFNPPbrHdv/OvPfee55R3NDZiOqKK65g0qRJXi8ldDqd1NfXU1NTg1Kp9GvyJcCzzz7Ltm3bUCgUXH755Zx77rkh1XfBXcFRVFREfn6+KAUV+oxeBxRKpdLTz78rk8nUqyShM888k+3bt3e77brrrmPQoEH89a9/paSkhKysLFatWuWpHrHb7axevZqFCxf2dtmCEFB//3vnsLL/DOf0iI/vTNjs7U62Tqfjs88+46OPPvI0lAsPD+eMM87g8ssvZ/jw4T55k7VarVRVVdHU1ERycnJAkh/PPfdcqqurueWWWxg6dKjfn99X3ImXsbGxlJaWkp6eHlKBkhD6eh1QnHfeedx000289tprnHTSSQBs2rSJW265hWm9yCpLSEg46MUgLi6O1NRUz+1z5sxhwYIFlJeXU15ezoIFC4iNjWXGjBm9XbYgBFRWFrzzDnz5Zfc+FNOnQ1pazx9n7969vP/++3z77beeYw2VSsX06dO55JJLjrh7d6wMBgMHDhwISL5ES0uLpzfG4MGDeeqpp0JqJ9Ld7TIjI4OioiLRV0Lok3r9ivDss89y7bXXMnbsWM9WnNPpZNq0aZ6GVN4yd+5cLBYLt912m6ex1cqVK0WWs9AnxcXBZZd1fvSGu1rjww8/ZNu2bZ7bBwwYwOWXX87ZZ5/t050CWZZpa2ujsrISu93u13wJq9XKq6++yrZt2/jHP/7hOf4MlWDC6XSi0Wg83S6zs7NF4qXQZ/X6JzcpKYnPPvuMiooKdu/e7WlsVVZWdsyL+fHHH7v9WaFQMH/+fOYH21xqQfCD5uZmPv74Yz799FPa/1MG4o9jja5cLhcNDQ1UV1cTFRXl13yJpqYmnnnmGRoaGggPD6eqqqpbPlVfJssyBoMBq9VKenq6KAcVQkKvA4p//OMf3H///ZSVlXULIiwWC0888QQPPfSQVxcoCP2JJEn8/PPPfPjhh6xZs8bTvyMtLY3p06dz0UUX+e1N3d1foqmpicTERL+W+Lq751qtVpKSkrjzzjuPeq5IsLHZbGi1WuLi4hg0aBDp6elixo4QEhTyH1sH/onw8HCamprIyMjodrtGoyEjI6Nb18RgYDAYUKlU6PV6EhMTvfKYDQ0NbN68WZSjCl6j0+n4/PPPWb58OfVdMjdHjhzJZZddxsSJE/26FW4wGKisrKS9vZ20tDS/VRo4nU4++OADvv76awAGDhzIHXfcQVJSkl+e35fcMzicTqdnxLg/x7kLoa+uro6RI0dSUFDgtcfszXtor1+hDtcHYtu2bd1KSQVBODJZltm2bRvLly/n+++/x263A53Jyeeddx4XX3wxJSUlfl9T13yJzMxMv3YX/f777z3BxLnnnsull14aEjkF7r4SKpWKwsJCMWJcCEk9/k1NTk72zGMYMGBAt18Gl8uFyWTilltu8ckiBSGUGI1GvvrqKz7++GPPyHDovBq/5JJLmDJlSkCuXB0OB7W1tdTX1wekvwT8t5x84sSJjB492u/P722SJKHVapFlmaKiInJzc0MmoVQQ/qjHAcWiRYuQZZnrr7+ehx9+uFvntqioKIqKihg7dqxPFikIfZ0sy2zfvp1PPvmElStXeko+lUolZ599NhdffDGDBw8O2FWrwWCguroatVrt13kckiSxZs0axo8f7xlid99994XE1bvNZqO9vR2VSkVRUREpKSkh8X0JwuH0OKC49tprASguLvb88guCcGR6vZ6vv/6aTz75pNtuRGlpKRdddBFTp04NaHa/JEm0tLRQXV3tKQn1V4KgwWBg8eLFbN++ncbGRq688krg4Hb7fY0kSej1ehwOBwUFBeTl5YXc9FNBOJReRwUTJkzwxToEIWTIsswvv/zCp59+yg8//ODJjVAqlUyaNInp06dz/PHHB/yN0z3ptaGhgdjY2IMSrX1p3759PP/882i1WqKiosjNzfXbc/uS2WxGr9ejUqkoLy8nLS0t4P/OguAvYptBELykra2NL774ghUrVlBXV+e5fcCAAVx44YVMmTLFa5VGx0qv11NVVUV7e7vfjzi++OILli9fjiRJZGdnc+edd/b5iimHw0F7eztRUVGUlJSQnZ0tciWEfkcEFIJwDJxOJ2vXruWzzz5j/fr1nrLp2NhYzj77bC688MKA5kb8kSRJtLa2UlVV5ZkS6q8jDr1ez8svv+yZ4TNu3DhmzZrV50snjUYjZrOZzMxM8vLyRIMqod8SAYUgHIXKyko+//xzvvzyS08XS4Dhw4dzwQUXcNZZZ/m1EVRPWK1WamtraWxsJCYmxu9VHGazmf379xMVFcU111zDaaedFjSB1tFwuVy0t7cTGRnJoEGD/NqSXBCCkQgoBKGHjEYjK1eu5PPPP2fHjh2e21NSUpg6dSrTpk2juLg4gCs8NFmW0Wg0VFdXYzQaSU5O9tt2fNe+NdnZ2dx6661kZGSQl5fnl+f3FXcFR2pqKsXFxUFzlCUIgdSjgGL69Ok9fsCPP/74qBcjCMHG5XKxefNmPv/8c3788UdPuWd4eDinnHIK06ZNC+qqJ5vNRl1dHY2NjURERJCZmem3XQGNRsPixYu58MILGTJkCNDZ+bMv6zqDo6CggIKCAqKiogK9LEEICj16Fezac0IQ+oPq6mq++OILvvrqK1pbWz23l5SUMG3aNKZMmUJab+aOB4BOp6OqqgqtVuvXxEuAX375hVdeeYWOjg6WLl3KY4891uePA7rO4DjuuONIT0/v89+TIHhTjwKK119/3dfrEISA0+l0rFy5ki+//JKdO3d6bk9MTOTss8/m/PPP57jjjgv6c3+Xy0VTUxM1NTXIsuzX9tk2m413332X77//HujsW3P77bf36TdeWZbR6/XYbDZycnIoKCjo84mkguALwblPKwh+YrfbWb9+PV988QVr167F6XQCnUca48aNY+rUqZx22ml9ZlvbYrFQU1NDU1MTCQkJxMXF+e25a2trefHFF2loaABCYxaHe1ciISGB0tJS0tLS+nRwJAi+dFS/6R999BEffPABtbW1nqY9br/++qtXFiYIvuIeyvX111+zatUqDAaD53MDBw7k3HPPZcqUKaSmpgZwlb3zx8TL1NRUv00IBWhqamL+/Pk4HA5UKhU333wzxx9/vN+e39vck0FdLhd5eXnk5+eLbpeC8Cd6HVA8++yzPPjgg1x77bV89tlnXHfddRw4cIDNmzdz++23+2KNguAV1dXVfP3113zzzTeeq2iA9PR0pkyZwtSpUykrKwvgCo+OzWajvr6ehoYGvydeumVlZTFq1CisVis33nhjn656EJNBBeHo9DqgePHFF1myZAlXXnklS5cuZe7cuZSUlPDQQw91q8cXhGCgVqv59ttv+eabb9i9e7fn9tjYWM444wzOOeccRo8e7bfmTt6m1Wqprq72lDD6M/Fy69atlJaWkpCQgEKh4MYbbyQyMrJPv/m6KzjEZFBB6L1eBxS1tbWMGzcOgJiYGIxGIwBXX301J598Ms8//7x3VygIvWQ0Gvnhhx/49ttv2bJlC5IkAZ15EWPHjmXKlClMnDixT29hOxwOGhoaqK+vBzp3CPyZeLls2TJ++OEHRo0axd13341CoegzeSaHIssy7e3thIWFMXDgwIDs8ghCX9frgCIrKwuNRkNhYSGFhYVs3LiR4cOHU1VVhSzLvlijIPwpq9XK2rVr+fbbb1m3bl233J5hw4YxZcoUJk2aRHJycgBX6R06nY7a2lrUajUqlcqvHTkPHDjA4sWLaW5uBiAjIwNJkvrsDg905ku0tbURFxdHaWkpKSkpgV6SIPRJvQ4ozjjjDD7//HNGjhzJ7Nmzueeee/joo4/YsmVLrxpgCcKxcjgcbNq0iW+//ZbVq1djNps9nyspKWHKlClMnjy5z3dldHM6nTQ2NlJXV4fL5fLrHA6Xy8WKFSv49NNPkSSJ5ORkbrrpJoYOHeqX5/cVd8fLlJQUysrKiI+PD/SSBKHP6nVAsWTJEs8W8i233EJKSgpr167l/PPP55ZbbvH6AgWhK6fTyZYtW1i1ahX//ve/u1Vo5OTkMHnyZM4++2zKyspCastar9dTU1ODRqPxezmoRqPh2WefpbKyEoAxY8Ywa9asPv3ma7PZ0Ol0REREkJ+fL6o4BMELeh1Q1NfXdxs1fNlll3HZZZchyzJ1dXUUFBR4dYGC4HK5+O2331i1ahU//PADWq3W87nU1FQmTZrE2WefzdChQ0MqiIDOAKqpqYna2lpcLhfp6el+P16IiYnBYDAQGxvLrFmzGDt2rF+f35scDgc6nQ7oPL7Nzs4mMTEx5H5uBCEQeh1QFBcX09TUREZGRrfb29vbKS4u9oxvFoRj4XK52LZtmyeI0Gg0ns+pVCrOPPNMJk+ezIgRI/r0+f2RBHJXQqfToVKpUCgUxMbGctddd5GYmNinenN05XK50Ol0OJ1O0tPTycnJISkpSQQSguBFvQ4ouk4P7MpkMoktQ+GYuFwutm7dynfffXdQEJGYmMjEiRM566yzOOmkkwLefdFohB9+AK0WcnNhwgTwVpGDe1eirq7O8wbor6BJlmXWrVvHW2+9xeWXX84ZZ5wBEJRTVHvCPczLYrGQnJxMXl4eKSkpotulIPhAj1+V7733XgAUCgX/8z//0y2z3OVysWnTJk444QSvL1AIbU6nk99++43vv/+ef//7392CiPj4eCZOnMikSZM46aST/Nr58UhefRXeeAOs1v/elpQEc+fC5MnH9thGo5GamhpaW1tJTEz0a1WKTqfj9ddf93S7/fnnnzn99NP77FV8R0cHBoOBhIQEBg0aRHp6esADUUEIZT3+7frtt9+Azoh/+/bt3WrOo6KiGD58OPfff7/3VyiEHIfDwebNm/nhhx/48ccfPWfa0LkTMWHCBM4880zGjBkTNEGE29KlsHjxwbfrdPDggxAXB+PH9/5xnU4nzc3N1NXVYbPZ/FrBIcsyGzdu5M0338RkMhEeHs706dOZOnVqnwwm3AmXSqWSkpISsrKyxO6pIPhBjwOKf//73wBcd911PPPMM326ta7gf1arlY0bN/L999+zZs0aTCaT53MqlYrTTz+dM844gxNPPDHoggg3qxWONHhXlmHJkt4HFHq9nrq6Ok8vhMzMzGNbaC+fe+nSpWzevBmAwsJCbr755m6J132Fy+XyNKfKzc0lOzu7T1eiCEJf0+v9v66jzOvr61EoFOTm5np1UUJoMBqNrF27lh9++IENGzZg7XJGkJqayumnn86ZZ57JiBEj+sRW9IYN0CUOOqSdO6GhoTOv4s/Y7XYaGxtpaGjwe66Em0ajYcuWLYSHh3PBBRdw/vnn94l/iz8ymUyYTCbS0tLIz8/3JJQKguA/vX7lkCSJRx55hKeeespzlZmQkMB9993Hgw8+KJKd+rm2tjZWr17Njz/+yObNm7tV/WRnZ3t2IoYNG9bnflb+LJjo6f3cbZ7r6upob2/3e7dLh8Ph2QUqKSnhmmuuoaysjKKiIr+twVtcLhdqtRqlUkl5eTlZWVl9MiAShFDQ69+8Bx98kNdee43HHnuM8ePHe7LC58+fj9Vq5f/+7/98sU4hSMmyTHV1tSeI2LFjR7fPl5SUcPrpp3P66aczcODAPn3VWFj45/eJjITs7MN/3mKxUF9fT1NTE2FhYWRmZvotsHL/rr733nv87W9/83QQPeuss/zy/N7UtXojIyODgoICEhISAr0sQejXeh1QLF26lFdffZVp06Z5bhs+fDi5ubncdtttIqDoB1wuF9u3b2f16tWsXr2a2trabp8fNmwYEyZMYOLEiRT25F24jxg2DMrKoKLi8Pc56yw4VHqRy+Wira2N2tpaOjo6SE5O9uskS7Vazeuvv87vv/8OwDfffMMNN9zgt+f3pq7VG8cdd1xAjooEQThYrwOK9vZ2Bg0adNDtgwYNEuPLQ5jZbGbTpk389NNPrFmzpltlRmRkJCeeeCITJkxgwoQJpKWlBW6hPvb3v8Ott4LFcvDnsrLgzjsPvt1gMHiSLqOjo/06yVKSJL7//ns++OADrFYrkZGRXHjhhUydOtUvz+9NXas3SktLycrKEuPFBSGI9DqgGD58OM8//zzPPvtst9uff/55hg8f7rWFCYHX3NzM2rVr+emnn9iyZUu3CZ4JCQmccsopTJgwgZNPPrnfZNMPHdpZ6fHqq/Djj+B0QmwsnHsu3HADdI2luiZdOhwOUlNTvX6+L0kSDocDp9Pp+S909otpa2vj3Xff9czgKC8vZ/bs2eTk5OByubDb7bhcLiRJIjIyksjIyKA8kpJlGa1Wi8vlIjc3l5ycHL92DRUEoWd6/er2+OOPM3XqVL777jvGjh2LQqFg/fr11NXV8dVXX/lijYKfSJLErl27WLNmDWvWrGHfvn3dPp+bm8tpp53GhAkTOOGEE/pt8ltZGTz2GJjNnQmYSUndu2TKsoxGo6Gmpga9Xo9KpTrqkdiSJGGz2TwfXZ9DoVCgUCiIjIwkIiKCuLg4YmJigM4jlg0bNlBZWYlSqeSCCy5g7NixSJJEa2sr4eHhhIWFef5rMplwOBxAZzCiVCqJjo4mKioqoEGGexqoSqWisLCQ1NTUoAx6BEE4ioBiwoQJ7Nu3jxdeeIE9e/YgyzLTp0/ntttuIycnxxdrFHzIZDKxadMm1q5dy7p167odWykUCo4//nhOO+00Tj31VEpKSsSLeRexsZ0fXZlMJurr62lpaSEiIqJHSZeSJHXbYXC5XDidTmRZBkCpVBIbG0tubi7R0dGEhYV1+3DvLkRERGC1Wj1NnMrKyggPD+eKK64gPT3d8/iSJBEeHk5ERIQnoLDb7Z6gpaOjA71eT0dHB1qttlvQ4v4a9399xT17w+VyUVBQQF5enmhOJQhBrtcBRW1tLfn5+YdMvqytrRXTRoOcuypj3bp1rF27lt9++61baWdcXBwnn3wyp556KuPHj/dr6+e+zN3psr6+HqvVSnJycrdusn9kNBrp6OgA8LxhR0ZGEhUVRUxMDDExMSiVSk8woVQqjxjMmUwmXnjhBbZs2cLbb7+NUqkkIiLC0zIfOGLDsIiIiG6lq5IkYbVaMZvNdHR0YDKZsNlsOBwObDabJ/Bx75JEREQQFRVFVFTUMR+dmEwmjEYjycnJ5Ofni10JQegjvDZtVKPRiGmjQcpqtbJlyxbWrVvH+vXraWho6Pb5goICTj31VE455RROOOGEoO1UGYzcPSXq6+vRaDTEx8cfsdOl1WpFp9MRExNDaWkpsbGx3d6Me3uMJMsyP/zwA08++SRtbW0ArFu3zjPU62iFhYURGxtLbGysJ8lWlmVcLhcOhwOHw4HdbsfhcHgCD7PZ7Dk6kWXZcwwTHR3do4DAnXQZHR3NgAEDyMzMFD+LgtCHiGmjIUiWZWpqatiwYQPr16/nl19+6ZZQGRUVxahRoxg/fjzjx4/vk22Wg4HJZKKhoYHm5mbCw8OPOH/D6XSi1WoJCwsjLy+P3NzcY25m1dzczMKFC1mzZg3QGRjOmzePE0888Zge93DcOxERERGeXI2uXC5Xt3wPrVaLXq9Hr9cTFhZGTEyMZxem6zGQ++8GOpuf5ebm9pskX0EIJWLaaIjo6Ohgy5YtbNy48ZC7ENnZ2YwfP55x48Zx4oknHvINQegZm81GS0sLDQ0N2Gw2kpKSDlu+KEkSBoMBq9XqtbbQkiTxzjvv8PLLL2O1WomIiGDWrFlcd911AS2jDA8P9+xqAGRlZWG1WjGZTJ7gwmq1YjAYkCQJSZKwWCwoFAqysrIoKCggLS1NHG8IQh8V0GmjL730Ei+99BLV1dUADBkyhIceeohzzjnH81wPP/wwS5YsQavVMmbMGF544QWGDBnSq+cJRZIksX//fjZs2MCGDRvYtm2bp2QQOs/LR4wYwbhx4xg3bhzFxcXihfoYuds819fXo9frSUxMJCkp6bD3dzdgUqlUlJSUkJaW5pVERoVCwebNm7FarYwYMYJ58+ZRUlJyzI/rC9HR0URHR5OWloYkSZ7kT7VajVqtJjU11dN63G63U19fD3QeuURFRXlySPprRZEg9CUBnTaal5fHY489RllZGdDZhfOCCy7gt99+Y8iQITz++OM8/fTTvPHGGwwYMIBHHnmESZMmsXfv3n7ZZletVrNp0yY2btzIpk2bDmoklpeXx9ixYxk3bhyjRo3y63yIUCbLMnq9nvr6es/ciMNVbzgcDk8+QUxMDOXl5WRmZh4xQbMndDodYWFhJCYmolAomDt3Lr/++ivnn39+nwkUw8LCiIiIQK1Wo1KpGD16NPn5+YSHh2O1WrFarZ7jErPZjNFoxGQy0dbWhsPhIDw8nJiYGE+Q0tdmwQhCqFPI7tq0IJGSksITTzzB9ddfT05ODnPmzOGvf/0r0LnVnJmZycKFC7n55pt79HjuK0T3FaU3NDQ0sHnzZp/nHlitVrZu3eoJIPbv39/t8zExMYwePZqxY8cyduxYkQvhA0ajkebmZlpaWpAkieTk5IOulu12Ox0dHdhsNiIjI4mLiyMtLY3k5ORjzgWQJIkVK1bw3HPPcfrpp/P3v//9mB4vkIxGI+3t7eTm5jJgwIAeVRA5HA5PlYler0ej0WCxWLBarUiSREREhCfAEEGG0N/V1dUxcuRIr1Zb9uY9NGj2EV0uFx9++CEdHR2MHTuWqqoqmpubmTx5suc+SqWSCRMmsH79+h4HFH2JJEns3buXTZs28fPPP7N169ZuyZTQ2eJ87NixjBkzhuHDh4sseB8xmUyeQMLhcByUJ+F0Ouno6MBisRAZGUlCQgKFhYUkJiYSFxfnlTe2vXv38thjj7F9+3YAdu3a1a3PRF/hcrk8zbSGDRtGYWFhj39uIyMjSUpKIikpiby8PGRZxmKxeHaB9Ho9Wq0Ws9lMe3u7J8joWnrbV3ZwBKGvC3hAsX37dsaOHYvVaiU+Pp5PPvmEwYMHs379eoCDSvAyMzOpqak57OP9saOgwWDwzcK9QJZl6uvr+fnnn9m8eTObN29Gr9d3u09mZiZjxoxhzJgxnHTSSaIvhI91dHR4Agm73U5iYmK3LpfuigRZlklISCA3N5ekpCSvBRHQ+TP70ksvsXz5ciRJIjY2lptvvpnLL7+8z+USmM1m2trayMrKYuDAgaSmph7T4ykUim6Jn8BBQYZOp0Or1WI0Gmlra0OhUJCYmEhCQoIILgTBhwL+6jRw4EC2bt2KTqdj+fLlXHvttaxevdrz+T++AByubNXt0Ucf5eGHH/bZeo+VWq1my5YtniCiqamp2+fj4uIYNWqUJ4goLCwUL4J+YLFYaGlpoampCavVSmJiYrfgTZIkdDodDoeD9PR0cnJySExM9Hq3yG3btnH//fd7yignTZrEPffcc1Dfl2AnyzJtbW04nU4GDRpEWVnZMeeRHM4fg4yCggJPBYnJZEKj0dDY2EhdXR1KpRKVStXndnkEoS8IeEARFRXlScocPXo0mzdv5plnnvHkTTQ3N5Odne25f2tr6xEbB82bN69bd0CDwRDQ3AK9Xs+vv/7K5s2b2bJli2dQk1tERATDhg3jpJNO4sQTT2TIkCF97iq0L3OXgDY2NmKxWEhISOhWuSFJEkajEYvF4tl2T01N9dlZfVFREZIkUVJSwl/+8hef9ZTwJavVSmtrK8nJyQwaNMiv01XdwsLCiIuLIy4ujszMTEpKSjwVOhqNxrP7lJCQIEafC4KXBN07lyzL2Gw2iouLycrKYtWqVYwYMQLoTH5bvXo1CxcuPOzXu9sVB4rJZGLr1q1s2bKFLVu2sHfvXrrmvSoUCgYMGMBJJ53E6NGjGTlypOgJEQDuEtC6ujoMBgMJCQlkZWV1+7zBYMBms5GYmEhhYSHp6eleD/ba29v58ssvueqqq1AoFKhUKhYvXkxxcXGfDCzdSZPFxcUMGDAgaCqNoqOjPQ3FdDodra2tNDQ00NjYSHh4OElJSUGzVkHoqwL6ivXAAw9wzjnnkJ+fj9Fo5L333uPHH3/km2++QaFQMGfOHBYsWEB5eTnl5eUsWLCA2NhYZsyYEchld9PR0cG2bdvYsmULv/zyC3v27Dmo/XhRUREnnngio0ePZtSoUUfsXSD4nk6nO2wJqCRJaLVanE4nKpWK0tJSUlJSvJ786nQ6+eCDD3j55Zfp6OggNzfX0y67vLzcq8/lDw6Hg+bmZhISEhg1ahQ5OTlBWXGhUChITk4mOTmZ4uJiNBoNTU1NtLa20tbWRlxcHCqVSiQ7C8JRCGhA0dLSwtVXX01TUxMqlYphw4bxzTffMGnSJADmzp2LxWLhtttu8zS2WrlyZUB7UDidTn744Qc++eQT9u3bd8gAIi8vj1GjRnmCCPcsBCFwZFn2lIC2trYiSRKpqanddgHcjahSU1M9yZa+2CXYsGEDTz/9NFVVVUBn5c6x5EjU1sJnn3X+NzISRo6Ec86BuDhvrfjwJEmivb0di8VCfn4+AwYM6DM9YqKiosjOziY7Oxuj0YhGo6Guro7W1lZkWSYxMZH4+PigDIwEIRgFXR8Kb/N2HwqXy0Vqamq3aozc3FxGjhzp2YHounUuBJYsyxgMBpqbmz1Jgn9MynM6nbS3txMVFUVeXh7Z2dk+CSRqampYtGiRZ/ZGUlISt99+O9OmTTuqc3yHAx59FFasgMREGDwYrFbYtq1zrPoDD8DZZ3v7u/gvnU6HXq8nNTWVkpIScnJy+nw+gsvlQqvV0traSmNjI0ajkaioKFQqlTiaFIKe6EPRx4SHh3PhhRdSX1/PaaedJgKIIOXubtnc3IxarcbpdB7US8IdbFgsFjIyMigoKPDZ1bUsy8ybN499+/YRHh7OFVdcwQ033HDUzyfL8P/+H/zwA/ztb3DeeeCOkZqb4fnn4cEHISoKTj/di98InTs57smqw4cPJy8vL6B5S94UHh5OWloaaWlplJSUeCpE1Go1ra2txMXF+WznShD6OrFDcRT81SlT6D13eWdTUxMajQZZllGpVAe94XV0dGA0GklISCAvL4/09HSvX107nU5kWfacx2/cuJF3332Xe+65h6KiomN67G3bYPZs+N//7Tze+CNJgvvug4oK+PRT8Ma3ZrVaUavVREVFUVBQQGFhYb+YCuo+LlOr1TQ0NHj6kMTExHjGswtCMBA7FILgBe6z/ObmZjQajadi4o+9D9xjtaOjoyktLSUzM9MnV9fr169n0aJFTJ06lWuvvRaAk08+mZNPPtkrj//RR5CXd/gjjbCwzoBj1izYsAFOOeXon8tut9PW1kZ4eDiFhYUUFRX1q8Rid2Msd7WPVqtFo9HQ0tKCXq+ntbWViIgIIiMjCQ8P98wsUSqVIrlT6FdEQCH0ae5Awr0jER4eTnJy8kEv5O4OlwqFwpMn4Yur64qKChYtWsTGjRsB+Pjjj5k5c6bXt8j37oVx4zoDh8MZMgSSkjrve7QBhVarxWQykZubS3FxMampqf260VrXI5Hy8nJMJhMGgwGtVovFYsFut+NwOHA6nRgMBpxOJ3FxcSQkJPissZcgBAsRUAh9kjt5zh1IREREHFS1Af/NpbBYLKSnp5OXl0dSUpLX3xTVajWLFy9mxYoVnnkSl19+ObNnz/bZeXtPDiuP9kDT6XTS3NxMbGwsI0aMIC8vr88nXHqbe/prYmIieXl5ntslScLlcnmGobl/Rh0OB7GxsSQkJIRMzokgdCUCCqFPcVdkNDU1odVqDxtIQPc8ieLiYtLS0nzy5v7dd9/x8MMPY7FYADjzzDO58847u73JeNtxx8G6dZ25Eofbpdi+HfT6zvv2hl6vR6fTecpAVSrVsS+4HwkLCyMsLIyUlBRSUlIoKSlBr9d3+7m12+0iuBBCjggohD7B4XB4mhDpdDqioqJIS0s75FWz1WpFp9MRHR1NSUkJmZmZPk2cKysrw263M3ToUObMmcMJJ5zgs+dyu+QS+PJL+OqrzgqPP3K54NVXITcXepq2YbfbaW1tJTo6muHDh1NYWCiqGbwgLCysWzMt9xFJ1+AiJiaGhIQEkeAp9Gni1UIIana73VO6ZzAYiI6OPmxFhsvlor29nbCwMJ/lSciyzE8//cS+ffu48cYbgc5OqG+88QaDBg3yW37B0KFw7rnwyCNgMMBFF4G7TUJ9PTz3XGcy5tNPHznPAjq/J41Gg9VqJS8vj7KyMrEr4SNhYWGeceyFhYUYjcZuwUVraytKpZLExETR90Loc0RAIQQlq9XqCSSMRiOxsbFHLO20Wq1otVrS09PJz89HpVJ5/c1969atPPfcc2zbto2wsDBOP/10z2C743p7rnCMFAp46KHOIOKf/4SXX4ZBgzobW+3cCQkJ8NhjcOqpR34c93jxpKQkhgwZErQts0NRWFgYKpUKlUrlCS50Oh2NjY2eeSNKpZKEhARiY2P7dTKs0DeIgEIIKlarlba2NpqamjCZTMTGxnabtfFH7qRLh8NBUVER+fn5Xi/Vq6ys5IUXXmD16tVA5wC6GTNmBLyhWUQEzJvXWRratfX2xRfD5Mn/bXR1KE6nk9bWVsLCwhg4cCDFxcViOFYAdS1Nzc/Pp6OjA61WS0tLCxqNhvb2dsLDwz3BhUiQFYKRCCiEoGAymVCr1TQ3N2M2m4mPjycrK+uIV2VOpxONRkNsbCxlZWWkpaV59SpOq9Xy7LPP8uWXXyJJEuHh4UybNo2bbrqJ9PR0rz3PscrOhltu6dl93ccbZrOZnJwcSktLxayZIKNQKIiPjyc+Pp78/HzMZjNarZa2tjbUajVNTU1IkoRSqSQuLo7Y2FixqyQEBRFQCAEjSRIGg8FzFWaz2TxjxP8sMDCbzej1ejIzMykqKiLOB5OwIiMj+emnn5AkidNPP53bb7/9mDtcBpLVaqWlpYXk5GQGDx4cErM3+oPY2FhiY2PJzc3FZrNhNBoxGo20tbWh1+s9/VViY2OJj48X/S6EgBEBheB37iZTzc3NaLVaJEkiMTGR5OTkP/1a93hx6KyuyMnJ8Volgslk4uuvv+aSSy7xXCU+8MADZGZmMnToUK88RyDIsuyZCFpaWkp5ebk43uijlEolSqWStLQ0iouLsVqtnjLf5uZm2tvbsdvtREZGenYvRKWO4C/iJ03wG6vV6qnFNxqNREREkJSU1OOcB3fFR1JSEkVFRaSkpHhlXRaLhffff58333wTg8FAeno6EydOBDp7SvRldrud5uZmEhMTGTVqlEi6DDHR0dFER0eTmZlJeXk5RqMRg8GARqPxtAd3uVxERUURHR1NTEyM6Hsh+IwIKASfcg9Wcs/ZMJvNxMbGHraHxOG4p4Lm5eVRUFDglXp9m83GJ598wuuvv45GowGguLg4JMr1JEnyHCMVFBQwYMAAn01SFYJD16qR/Px87HY7RqMRk8mETqejvb3d0/dCoVB4Aozo6GixiyF4hfgpEnzC6XSi0+loaWlBq9XidDp7lGj5Ry6XC41Gg1KpZNCgQWRkZBzzFbbT6eTTTz/l9ddfp6WlBYDc3FxuuukmpkyZ0qfzCtxVL3q9nvT0dIYNG0ZmZmaf/p6EoxMVFUVqaiqpqakUFhbicrno6Oigo6MDk8mERqPBaDSi1+txuVxEREQQExNDTEwMUVFRYidL6DURUAhe5e4f0dzc7DnWiI+PP6ptVovFgk6nIz09naKiIq9dYYeFhbF8+XJaWlrIzMzk+uuvZ9q0aX1+MqTFYqGtrY2EhAROOOEE8vLyRIKe4BEeHu4pTQUoLy/HZrN5ggy9Xu8JMmw2G/J/BsFERkaiVCqJjY0VxyXCEYmAQjhm7mMNtVpNa2srFouFmJiYXh9rdH08nU6Hy+WiuLiY/Pz8Y9qSdTqdfPPNN5x55pnExMQQFhbGXXfdRU1NDRdddFGff5F0uVy0tbUhyzJlZWWUlJT4pOpFCD3uJM+UlBTy8/ORJAmLxYLFYsFms3mqSnQ6nee4JCIiwlN5IgJWoSsRUAhHzX2s0dbWhkaj8RxrZGZmHnU/CKfTiVqtJj4+ngEDBhzTuGx3IPHqq69SX1+PRqPh2muvBWDs2LGMHTv2qB43mOh0OvR6PVlZWZSVlZGeni46KgpHLSwsjLi4uIMCUkmSPOWq7oRPd0VJWFgYsbGxnoRPcVTSf4mAQui1P1ZruDv49fZKX5bh11/hu+9gzx5wuTrIyjIweXI2M2cWkpJydKWNTqeTr776in/961/U19cDkJycHFJJiSaTifb2duLi4jjhhBN80iFUENy6Jnzm5eXhdDo9uRjuo5KOjg40Gg2SJHmqSqKjo1EqlSLI7SdEQCH0iMvl8pSjqdVqzGbzMR1ruKdhrl0LJSUy557bTlQU1NaWs3RpNps2RfD885CU1LvHXbFiBa+99hoNDQ0AJCUlcfXVV3PZZZeFRPVGR0cH7e3txMTEMHDgQAoKCrw+AE0Q/kxERIQnwMjNzUWWZSwWiycfw31EYjAYsNlsQGeSqLuqRByVhCYRUAhH5B661dLSgl6vR5blHnezPJLPPusMJm66yUFZmRqVSkVxcTEpKSns3Qu33w4PPggvvNC7x92wYQMNDQ2kpKRw9dVXc8kll4RUIKFUKiktLaWwsNCTXCcIgebu1Oke4gedFyFms5mOjg7MZjPt7e3o9Xra29txOBzAf/toxMTEiNLVECD+BYVDcs/WaGlpoaOjg5iYGFJTU71SfmizwbffwplndlBebiQ7O4eioiJPb4mBAzuHXv31r51HIYMGHfpxrFYrH3/8Maeeeir5+fkAzJ49myFDhnDJJZd4pVdFoJlMJrRaLdHR0ZSWlpKfn09Sb7dtBCEA3Eeh7qPGkpISz1GJ2Wz2lK6aTCba2tpwOByEhYV5ggzRH6PvEf9agofT6USv13uSLO12+1H1jvgz27dLmM3tnHyywtM++4+ByoQJkJoK33xzcEBhNBr58MMPWbZsGTqdjgMHDvA///M/QGc7bvdI8b7MXQIaGxtLeXk5eXl5qFSqQC9LEI5J16MS6Cxdtdvtnp0Md26QyWTCYDDgdDq7BRkxMTGip0oQEwGF4Jlm6O4dERYWRkJCgtdaW3dlt9upr9cASUyYUExKyqHnd0REQG4u6HT/vU2r1bJs2TI++OADOjo6gM6GVMOHD/f6OgPFPVZcoVBQWlpKUVGRONoQQlpUVBRRUVHddt7c/THcOxnuIEOv1yNJ0kGdPkWQERxEQNFPuZMs1Wo1arX6mHtH9ITRaKSjo4P8/DygAIvl8EcSLhc0NcHxx3f++eWXX+bNN9/0JHiVlJRw3XXXMWnSpJDYFnUP8DKbzWRlZXnGiovseKE/6tofw81qtXp2Mtzt/M1ms6dnTVhYmCfAEEFGYPT9V2KhV6xWq6cltk6n8yRZ+vJc3j1XIiIiggEDBnDSSdm8+moYy5fDXXcd+mvWrYO2Npg8+b+32Ww2Bg8ezPXXX89pp50WMvXu7rPkpKQkRo4c6dUJqoIQKtyBgjvIkGUZm8122CBD7GT4n3jV6gckScJgMNDe3k5bWxtms9kT/fv6jctms9He3k5ycjLFxcWewOWSS+Ctt2DYMPjPYE+g80Xim2+28b//u5SSkosZMuQUAC6//HJGjBjBiSeeGDJX7Tabjba2NpRKJYMHD6awsDAkKlIEwR/cwcLhggyz2YzBYECr1XpKWcVOhm+JgKKPsNmgoQEkCbKyoCetB2w2G1qtltbWVs8AoGPtZNkber0eq9VKfn4+BQUF3Rpf3XIL1NbC/ffD6NFw5pkS1dU/8e23b6LT/Q5AXFwH0BlQJCUlcdJJJ/l8zf7g7gbqcrkoKCjoFmgJgnD0DhVkwOGPS7RaLZIkER4e3q26RAQZR0cEFEGurQ3efhtWrACjsfO2qKjOo4Crr4bS0u737zouvKWlBbPZTFRUFCqVym+dFB0OB+3t7URHRx92QmhEBDz6KHz1lY3XXvuShQvfBmoBCA+P4txzpzJr1lV+Wa+/OJ1ONBoNDoeDzMxMiouLSU9PD5mjG0EIVofbyXAnfh4qyFAqlcTFxREbGyt+R3tIBBRBrLISbrsN7Ha48EI47TQID+9sV/3RR50tq594AsaO7SwzdJd86vV6nE4ncXFxftuNgM5ET/e2YkZGBvn5+Udsdx0eDt98cy/19ZsAiI+P59JLL+Xyyy8nLS3NL2v2B0mSaG9vx2KxkJ6eTnFxsRgpLggB1HUnIzU1FegMMtw7Ge5hh1qt1pNrFhMTQ3x8fEj0t/EVEVAEKau1M2ExKamzW+R/fuaBzryDK66AuXMd3H+/jkcf1RAZqcVisRAVFUVCQoJfW9vKsuw53khJSSE3N5eUlJRDRvXV1dWkp6d7hg+dd9551NTUMGPGDC644IKQmpLp/nvR6/WkpqYyZMgQsrKyRMKlIAQhhUJBTEyMp4lfUVERVqvVM221paUFg8FAa2srERERniFq4vf5v8TfRJBatQqam2H58u7BBPy3DfNllzXz228mVqwIZ8aMeFQqld8TFt2tuRMTEykuLiYtLe2gXzBZlvnll1945513WLNmDffeey8zZswAYNKkSSFT+tmVu3IjMTGRE044gdzc3D4/Jl0Q+hv3LkZ6ejplZWXdhqGp1Wqam5uRZZno6Gji4uKIiYkJmaTxoxFar+Ih5LPP4OSTobCw889Op9PTN0Kj0WCxWIiLi2PChAzWrAnj+uvBnz/HkiR5jjcKCwvJzc09aCvQbrezcuVKli1bxr59+zy319bWev4/1AIJq9WKWq1GqVQyaNAgCgsLQ2rXRRD6K4VC4WklnpeXh8PhwGAwoNfrPYnvGo0GhULh2b3ob0PQQuvVPIQ0NcE557jQ6Tq329RqNSaTCYDExERPVUBpaWd7aqsV/FVx6M7XSEpKoqCggJSUlIOi8tdff5333nsPjUYDdDaqOe+885gxYwaF7igphNjtdtRqNQqFgsLCQoqKikTlhiCEsMjISFJTU0lNTaW4uLhbmWpbWxvt7e3Y7XbCwsI8uxehPspdBBRBRpIkTCYTCoWBuro2fv/diCRJh+1i+Z/GkfjjQt/lctHe3k5YWBhFRUXk5uYeNgLfu3cvGo2GjIwMLrvsMi666KKQnEXhLgF1Op3k5ORQXFxMampqSL9oCILQXdddiezsbFwuFyaTCZPJ5LkgNBgM2O12ZFkmMjLSc5wSSkGGCCiCgCzLdHR0eKo0TCYTeXkOfvklmiuvTEapPPw/08aNUFICvq4INZlMGI1G0tLSKCgo8Fx9O51OfvzxRz744AMefPBBz+7DrFmzmDhxImeddVbIHWvAf4Mrq9XqKQE9VHmsIAj9T3h4uGcIWm5uLpIkeZptuZts6XS6kAsyQu+Vvg+xWq2eIEKn02G324mJiSExMZFp0yJ56KHOFtRnnHHor9+7F3bsgJtu8t0a3T0llEol5eXlZGdnExERQXt7O5988gnLly+ntbUVgPfff5+5c+cCMGjQIAYdbu54HyZJkqfzXlpaGscffzyZmZkhGTQJguAdYWFhxMfHE9+lI6HL5cJisXgCDXeQYTQaaWtrO2SQEewXLOJV0M/cI8Lb29s9yZWRkZHEx8d3qwIoLu5sSf3GG519KE4/HdyfdrlgyxZ47TUYOLCzD4W3uUsebTYbmZmZ5OfnExcXx86dO/nggw9YtWoVDocDgJSUFC666CIuvvhi7y8kSMiy7LmiSElJYeDAgeTk5PitWZggCKElPDz8oCCj606G2WxGr9ej0+k8VWOSJBEREdEtyAimfjYioPADWZY9Z2ktLS3/yZFQEB8fT2Ji4mG3tmbN6syNeOcd+Pjjzsmb4eGdOxPt7XDCCXDrrd7Pn+haCuqeehkWFobNZuPuu+9Gr9cDMGTIEC6//HLOOuuskM5mdv9Sq1QqUQIqCILPHGonQ5KkbjsZXbt6tre3I0kSYWFhREdH43K5Arh6EVD4lDvCbGtrw2Aw4HA4iI2N7fGI8PBwuPZamDIF/v3vzs6ZsgzDh3fuWBQXe3e9TqcTnU7nqVRwuVysWLGC66+/Huis1Lj00ktpamri0ksvZejQod5dQJBxXxUkJCQwbNgwcnNzxfAuQRD8yl0l0rX8vGtXT3eQodVqiYiICOiORUADikcffZSPP/6YPXv2EBMTw7hx41i4cCEDBw703EeWZR5++GGWLFmCVqtlzJgxvPDCCwwZMiSAKz88q9WKwWBAo9Gg0+mwWCwolcpj6l6ZmdnZGdNX3PM/zGYzSUlJ1NfXs2zZMn7++WcAhg4dysknnwzALbfc4ruFBAmr1UpbW5tnFonoJSEIQjD5Y1dPN5vNFtBj2IAGFKtXr+b222/nxBNPxOl08uCDDzJ58mR27drleQF//PHHefrpp3njjTcYMGAAjzzyCJMmTWLv3r1HnBPhTzabDaPRiEajQavtbIEdERFBfHx80PcisFqt6HQ6bDYb27dv5/vvv0etVgOdP7Tjxo3rtv0Wyux2O21tbYSHh1NUVCR6SQiC0KcE+ihWIcuyHNAVdNHW1kZGRgarV6/mtNNOQ5ZlcnJymDNnDn/9618BPEmCCxcu5Oabb/7TxzQYDKhUKvR6PYmJiV5ZZ0NDA+vXrycxMZH29nZPENG1gUmwl/w4nU60Wi1hYWHY7Xb+9re/IUkS0JlkOW3aNC666CJyc3MDvFLf6zpOPDs7W/SSEARB+I/evIcGVQ6FO9nPPWK2qqqK5uZmJk+e7LmPUqlkwoQJrF+//pABhc1mw+bu9kTnX4a3tbe3s3v3buLi4jwNTfrKGGpJkqiurqampoZTTz2V/Px8VCoVRUVFpKamMn36dCZOnNgvqhecTift7e2eIPVYe0n89BN89RWYzZCfD1ddBdnZXl60IAhCkAqagEKWZe69915OOeUUT7Jfc3MzAJmZmd3um5mZSU1NzSEf59FHH+Xhhx/26VptNhsdHR0UFRX1iSACOvtJbNiwgZ9++ol9+/YRGxvLtdde6zlaWrp0ab9JOHQHElarlfT0dIYNG0ZWVtZRJzP99ltn8uz27d1vf+ABuPpqePFFEBOPBUEIdUETUNxxxx38/vvvrF279qDP/XHrWZblw25Hz5s3j3vvvdfzZ4PBQH5+vncX+5819YVgorGxkVWrVrFx40bPLBCAwYMHo9PpPAFFfwgmuu5IpKWlMWzYsGNuSvX77539Qg61EeZ0wuuvQ0MDfPmlf9qjC4IgBEpQvMTdeeedrFixgp9++om8vDzP7VlZWUDnTkV2l73j1tbWg3Yt3JRKZcATU4LFN998wzvvvOP5c2pqKtOmTWPatGk+CbKClc1m8zSFSU9Pp6CggKysLK90t7zzzkMHE12tXAnLlsE11xzz0wmCIAStgAYUsixz55138sknn/Djjz9S/IfGCsXFxWRlZbFq1SpGjBgBdGbir169moULFwZiyUFLlmX27duHUqkkNzcXrVZLcXEx4eHhjBkzhosvvpjx48f3qxbRHR0daLVawsPDycrKoqCgoMc9QHpix47OvImeePFFEVAIghDaAvrucvvtt7Ns2TI+++wzEhISPDkTKpXKUykxZ84cFixYQHl5OeXl5SxYsIDY2FhmzJgRyKUHDY1Gw9q1a1mzZg0tLS0MGzaMa665hoyMDEaMGMHEiRP7VemjLMsYDAb0ej0xMTEUFxeTm5t7yBHrx+rHH3t+302bOpM1Y2O9ugRBEISgEdCA4qWXXgJg4sSJ3W5//fXXmTVrFgBz587FYrFw2223eRpbrVy5Mmh6UASCzWZjy5YtrF27lp07d+Ku/I2KikKlUnHcccf1maoTb3F3+ezo6CAxMZHBgweTnZ3ttVLhQ7Hbe39/EVAIghCqAn7k8WcUCgXz589n/vz5vl9QH/HEE0+wd+9ez59LSkoYN24c5557LkVFRSE9V+OPbDYbWq0Wp9NJUlISgwYNIiMjwy9JpmVlPb9vejqoVL5biyAIQqD1nwP1PqqpqYn169dzzjnnEPufy9sTTzyR9vZ2Ro4cyejRoxkyZAg5OTn9pqMl4Bm2Fh4eTkZGBvn5+aSnp/s1R+TccyE3t7OK48/ccAOIPlmCIIQyEVAEIYPBwKZNm1i7di2VlZVAZ4WG+2hozJgxDB06lNTUVAoKCnySHxCMJElCr9djMBiIi4ujpKSEnJycgH3/EREwbx7ccceR75eaCrff7p81CYIgBIoIKIKE3W7nl19+Yf369fz++++eNthhYWEcf/zxpKenY7fbaW9vJzo6moEDB5KVldUvOlo6HA60Wi1WqxWVSsXw4cPJzMwMih2Z22+H5mZ45JFDfz49vbMHRT/oYC4IQj8nAoogYTabeemllzx5JcXFxYwfP54xY8aQmJiITqdDp9ORnZ1NXl5eULyZ+prFYkGr1SLLMunp6eTn55ORkRF0OSL/+79w4YWdpaFffvnf1tvXXQfXXw//6SQvCIIQ0kRA4WeSJLF//342bNhAR0cHt/9nLzwpKYlTTz2VlJQUxo0b52nkZTQaaWlpITk5mfz8fFJSUkK+esNkMqHVaomMjCQvL4/c3FxSU1O91j/CF0aNgtdeC/QqBEEQAkcEFH4gyzI1NTVs2LCBTZs2odFogM4KlhkzZpCcnAzAjTfe6Pka91jxmJgYysvLQ/54w90/wt0OvLy8nJycHJKSkvpFfoggCEJfJwIKH1u3bh2ffvqpp2kXQHR0NKNHj2bs2LEH9UlwjxVXKBTk5eWRk5PjmbcRiro2okpISPBUrPTnPiOCIAh9kQgovKyxsZGEhATPG6LT6aS5uZnIyEhOOOEExo4dy/Dhww/KA5AkCYPBgNVqJS0tjby8vJC/OjcYDGi1WhISEhg6dCi5ubme0lhBEAShbxEBhRc0NTWxadMmfv75Z+rq6pg5cyZTpkwBYPTo0URGRjJixIjDNlsymUwYjUYSExMpKSnx6ryJYNO19LNrIBHKuzCCIAj9gQgojpJareaTTz7h559/pr6+3nN7eHg4Wq3W8+e4uDjGjRt3yMf4Y55EZmZm0FUweEvX0s/k5GSGDx9OVlaWCCQEQRBChAgojoLZbOaNN97A5XIBnUHEkCFDGDNmDCNHjvzTkk673e7p8uiuYgjVrX73xE+FQkFaWhrHH398UJZ+CoIgCMdGBBRHITY2lrKyMmJiYjjxxBMZNWpUj6603QOsZFkmIyODnJwcVCE44OGPHS0LCws9Ez9D9ShHEAShvxMBxVG64IILOP7443t0X5fLhV6vx263k5aWFtB20b7kcDhob2/HZrN5jjUyMjJExYYgCEI/IAKKo9STYKBr5UZSUhLl5eVB36DpaJjNZk/eSDB3tBQEQRB8RwQUPvDHQKKkpITU1FS/TsL0NVmWPcca0dHR5Ofnk5ubS1paWsh38hQEQRAOFjrvcEFAkiSMRiNmsxmVSkVxcTFpaWkhFUiYzWaMRqNnUNfgwYPJysoKyVwQQRAEoedC550ugGRZxmQyYTKZSEhI4LjjjiMtLS0kWmXLsuwJIux2OzExMaSlpZGdnU16ejrR0dGBXqIgCIIQBERAcQxkWaajowOTyeSZP5GRkYFSqQz00o5J1yDCZrMRFxdHZmYmmZmZJCcn94tJp4IgCELviIDiKEmSRHNzM3FxcZSVlYXE1bq7P4bVaiU2NpasrCxPECEaUAmCIAhHIgKKoxAWFkZCQgKlpaVkZGQctqV2X+DO+zAYDERERJCamkpeXh4pKSkiiBAEQRB6TAQURyEtLY2BAwdSWFgY6KUcNXfbb4fDQXx8PAMGDCArK4ukpCRRpSEIgiD0mggojkJ4eHif7LHgLmc1Go1ERkaSlpbmKfXs68c1giAIQmCJgKIf6LobkZiYyJAhQ0hPT0elUoVct05BEAQhMERA4QOyDL/8Al////buPiiq634D+LOCy/vuytsuCAIWghirRkG6qFVJpSWZBEhbtU0tVpMpIgilCRpNK01FLM1oovgSTaLOdETptKgz0VYmI0ikGlHQVOUtxUAzWIJaWJEXWc7vD8r+XAEFL3AXeD4zO8M9995zvtwY9/Hcu2dPAbdvA46OwKJFwIIFwHAtSdHR0QGDwQCDwQClUgl3d3fTbMRInF0hIiLLxkAxyOrrgTfeAK5fByZNAnx9ga++AtatA3Q6IDMTmDp1aMbuXg+jsbERAKBWqzFt2jTORhAR0ZBjoBhETU1AXBzQ3g7s3g2EhADd7+GVlUB6OhAfDxw82BU0BkP3WhhNTU0wGo1wcHDA5MmTodVq4ezsPKpW6SQiIsvFd5tBlJMD/Oc/wNGjgJeX+b6AACArC3j1VWDvXmDrVmlj3b9/H01NTWhvb4eDgwO8vLxMa0aM5I+xEhHRyMRAMUg6O4G//hWIjOwZJro5OgI/+QmwfTvQ0AC4ug5sjNbWVjQ1NaGlpQX29vbQarXQ6XRwdnaGvb299F+CiIjoKTFQDJLGxq7nJ+bOffxx8+YB774L/Otf/QsUra2tMBgMaGlpgVKphLOzM6ZOnQpnZ2c4OTkNTvFEREQSMVAMMiGk7QeAtrY200yEjY0NJkyYgClTpmDChAlQqVR8uJKIiCwOA8UgUau7PsXx2WdAeHjfxxUWdn109FvfMm9/8OABmpqa0NzcDKVSyRBBREQjCgPFIBk3DnjlFeDDD4HYWKC3VbkNBiA7uytwuLh0rRXR1NSEe/fuwdraGiqVCpMnT4aLiwvUajWXwCYiohGDgWIQLVkCnDzZ9dHRt98G9PquoAF0rUuxZQtgMDzAsmUG1NY2Y9y4caa1IrpDhJWVlby/BBER0VNgoBhEjo5dHwlNTQWSkgBPz67Frb75ph1fftkEd/cWbN5shcmTVfD09IWzszM0Gg1DBBERjXgMFIPM1RX46CPg4sVWfPKJAQ0NLfD1VeK111SIifkW3NycORNBRESjDgPFIBFC4P79+zAYDGhra4OPjy02bpwAD48p0Gg0UKlUfCaCiIhGLQYKCYxGI5qbm2EwGNDZ2Qk7OztotVq4u7tDo9HAycmJn84gIqIxgYHiKRmNRtTV1cHR0RE+Pj5wc3ODRqPhipVERDQmMVA8BScnJ0yfPh1qtRoajYZfB05ERGMeA8VTUKlUUKlUcpdBRERkMWR9SvDs2bN46aWX4OnpCYVCgWPHjpntF0IgLS0Nnp6esLOzw8KFC3Ht2jV5iiUiIqI+yRoompubMWPGDGRlZfW6PzMzE9u2bUNWVhYuXrwInU6HxYsXw2AwDHOlRERE9Diy3vKIjIxEZGRkr/uEEHjvvfewceNGvPLKKwCAQ4cOQavV4vDhw/jlL385nKUSERHRY1jswgjV1dW4desWIiIiTG02NjZYsGABioqK+jyv+5s6H34RERHR0LLYQHHr1i0AgFarNWvXarWmfb3JyMiAWq02vby9vYe0TiIiIrLgQNHt0YWhhBCPXSzqrbfeQmNjo+lVW1s71CUSERGNeRb7sVGdTgega6bCw8PD1F5fX99j1uJhNjY2sLGxGfL6iIiI6P9Z7AyFn58fdDod8vLyTG3t7e0oKChAWFiYjJURERHRo2Sdobh37x6qqqpM29XV1SgtLYWzszMmTZqE5ORkbNmyBQEBAQgICMCWLVtgb2+Pn/70pzJWTURERI+SNVAUFxdj0aJFpu2UlBQAQGxsLA4ePIjU1FS0tLQgPj4ed+/eRWhoKE6fPg0nJye5SiYiIqJeKIQQQu4ihlJTUxPUajUaGxu5XDYREdEADOQ91GKfoSAiIqKRg4GCiIiIJGOgICIiIskYKIiIiEgyBgoiIiKSjIGCiIiIJGOgICIiIskYKIiIiEgyBgoiIiKSjIGCiIiIJGOgICIiIskYKIiIiEgyBgoiIiKSjIGCiIiIJGOgICIiIskYKIiIiEgyBgoiIiKSjIGCiIiIJGOgICIiIskYKIiIiEgyBgoiIiKSjIGCiIiIJGOgICIiIskYKIiIiEgyBgoiIiKSjIGCiIiIJGOgICIiIskYKIiIiEgyBgoiIiKSjIGCiIiIJGOgICIiIskYKIiIiEgyBgoiIiKSjIGCiIiIJGOgICIiIskYKIiIiEgyBgoiIiKSjIGCiIiIJGOgICIiIskYKIiIiEiyEREodu/eDT8/P9ja2mL27NkoLCyUuyQiIiJ6iMUHiqNHjyI5ORkbN25ESUkJ5s+fj8jISNTU1MhdGhEREf2PQggh5C7icUJDQzFr1izs2bPH1BYUFITo6GhkZGQ88fympiao1Wo0NjZCpVINZalERESjykDeQy16hqK9vR2XLl1CRESEWXtERASKiopkqoqIiIgeZS13AY/T0NAAo9EIrVZr1q7VanHr1q1ez2lra0NbW5tpu7GxEUBXyiIiIqL+637v7M/NDIsOFN0UCoXZthCiR1u3jIwM/O53v+vR7u3tPSS1ERERjXYGgwFqtfqxx1h0oHB1dYWVlVWP2Yj6+voesxbd3nrrLaSkpJi2Ozs7cefOHbi4uPQZQkaTpqYmeHt7o7a2ls+MyIDXX168/vLi9ZfXUFx/IQQMBgM8PT2feKxFBwqlUonZs2cjLy8PMTExpva8vDxERUX1eo6NjQ1sbGzM2jQazVCWaZFUKhX/h5YRr7+8eP3lxesvr8G+/k+amehm0YECAFJSUrB8+XIEBwdDr9dj3759qKmpQVxcnNylERER0f9YfKBYunQpbt++jXfeeQd1dXWYNm0aTp48CR8fH7lLIyIiov+x+EABAPHx8YiPj5e7jBHBxsYGmzZt6nHbh4YHr7+8eP3lxesvL7mvv8UvbEVERESWz6IXtiIiIqKRgYGCiIiIJGOgICIiIskYKIiIiEgyBopRLD09HWFhYbC3tx+Ti3sNt927d8PPzw+2traYPXs2CgsL5S5pzDh79ixeeukleHp6QqFQ4NixY3KXNGZkZGQgJCQETk5OcHd3R3R0NMrLy+Uua0zZs2cPpk+fblrQSq/X49SpU8NeBwPFKNbe3o4f//jHWL16tdyljHpHjx5FcnIyNm7ciJKSEsyfPx+RkZGoqamRu7Qxobm5GTNmzEBWVpbcpYw5BQUFWLNmDc6fP4+8vDx0dHQgIiICzc3Ncpc2Znh5eWHr1q0oLi5GcXExwsPDERUVhWvXrg1rHfzY6Bhw8OBBJCcn47///a/cpYxaoaGhmDVrFvbs2WNqCwoKQnR0NDIyMmSsbOxRKBTIzc1FdHS03KWMSd988w3c3d1RUFCA7373u3KXM2Y5Ozvjj3/8I1atWjVsY3KGgkii9vZ2XLp0CREREWbtERERKCoqkqkqInk0NjYC6HpDo+FnNBpx5MgRNDc3Q6/XD+vYI2KlTCJL1tDQAKPR2OMbcLVabY9vyiUazYQQSElJwbx58zBt2jS5yxlTvvjiC+j1erS2tsLR0RG5ubmYOnXqsNbAGYoRJi0tDQqF4rGv4uJiucsckxQKhdm2EKJHG9FolpCQgKtXryI7O1vuUsacwMBAlJaW4vz581i9ejViY2Nx/fr1Ya2BMxQjTEJCApYtW/bYY3x9fYenGAIAuLq6wsrKqsdsRH19fY9ZC6LRKjExESdOnMDZs2fh5eUldzljjlKphL+/PwAgODgYFy9exPvvv48PPvhg2GpgoBhhXF1d4erqKncZ9BClUonZs2cjLy8PMTExpva8vDxERUXJWBnR0BNCIDExEbm5ucjPz4efn5/cJRG6/ru0tbUN65gMFKNYTU0N7ty5g5qaGhiNRpSWlgIA/P394ejoKG9xo0xKSgqWL1+O4OBg6PV67Nu3DzU1NYiLi5O7tDHh3r17qKqqMm1XV1ejtLQUzs7OmDRpkoyVjX5r1qzB4cOHcfz4cTg5OZlm6tRqNezs7GSubmzYsGEDIiMj4e3tDYPBgCNHjiA/Px9/+9vfhrcQQaNWbGysANDjdebMGblLG5V27dolfHx8hFKpFLNmzRIFBQVylzRmnDlzptc/67GxsXKXNur1dt0BiAMHDshd2pixcuVK0989bm5u4vnnnxenT58e9jq4DgURERFJxk95EBERkWQMFERERCQZAwURERFJxkBBREREkjFQEBERkWQMFERERCQZAwURERFJxkBBJIOFCxciOTlZ7jKGzc2bN6FQKEyrtcrdT3+0t7fD398f586dG9R+09LSMHPmTNP2G2+8gbVr1w7qGERyYKAgIou0YsUKREdHm7V5e3ujrq5uWL4ae9++ffDx8cHcuXP7dbxCocCxY8cGPE5qaioOHDiA6urqAZ9LZEkYKIhoxLCysoJOp4O19dB/DdHOnTvx2muvDfk47u7uiIiIwN69e4d8LKKhxEBBZAHu3r2Ln//855gwYQLs7e0RGRmJyspKs2P2798Pb29v2NvbIyYmBtu2bYNGo+mzz+7bA0eOHEFYWBhsbW3x7LPPIj8/3+y4goICzJkzBzY2NvDw8MD69evR0dFh2r9w4UIkJCQgISEBGo0GLi4uePvtt/Hwqv29/etco9Hg4MGDvdZmNBqxatUq+Pn5wc7ODoGBgXj//fdN+9PS0nDo0CEcP34cCoUCCoUC+fn5vd7y6E/9a9euRWpqKpydnaHT6ZCWltbndQOAy5cvo6qqCi+++KKprb29HQkJCfDw8ICtrS18fX2RkZEBAPD19QUAxMTEQKFQmLYBYOvWrdBqtXBycsKqVavQ2traY7yXX34Z2dnZj62JyNIxUBBZgBUrVqC4uBgnTpzAP/7xDwgh8MILL+DBgwcAgHPnziEuLg5JSUkoLS3F4sWLkZ6e3q++33zzTfz6179GSUkJwsLC8PLLL+P27dsAgK+//hovvPACQkJCcOXKFezZswcfffQRNm/ebNbHoUOHYG1tjQsXLmDHjh3Yvn07Pvzww6f+fTs7O+Hl5YWcnBxcv34dv/3tb7Fhwwbk5OQA6HquYMmSJfjBD36Auro61NXVISwsrEc/A6nfwcEBFy5cQGZmJt555x3k5eX1Wd/Zs2fxzDPPQKVSmdp27NiBEydOICcnB+Xl5fjTn/5kCg4XL14EABw4cAB1dXWm7ZycHGzatAnp6ekoLi6Gh4cHdu/e3WO8OXPmoLa2Fl999dXALiSRJRn2ryMjIrFgwQKRlJQkhBCioqJCABDnzp0z7W9oaBB2dnYiJydHCCHE0qVLxYsvvmjWx6uvvirUanWfY1RXVwsAYuvWraa2Bw8eCC8vL/GHP/xBCCHEhg0bRGBgoOjs7DQds2vXLuHo6CiMRqOp1qCgILNj1q1bJ4KCgkzbAERubq7Z+Gq12vSNk921lJSU9FlvfHy8+OEPf2jajo2NFVFRUb3+Tt399Lf+efPmmfUTEhIi1q1b12ctSUlJIjw83KwtMTFRhIeHm431sN6ugV6vF3FxcWZtoaGhYsaMGWZtjY2NAoDIz8/vsyYiS8cZCiKZ3bhxA9bW1ggNDTW1ubi4IDAwEDdu3AAAlJeXY86cOWbnPbrdF71eb/rZ2toawcHBpn5v3LgBvV4PhUJhOmbu3Lm4d+8e/v3vf5vavvOd75gdo9frUVlZCaPROIDf1NzevXsRHBwMNzc3ODo6Yv/+/aipqRlQH/2tf/r06WbneXh4oL6+vs9+W1paYGtra9a2YsUKlJaWIjAwEGvXrsXp06f7Xd/DHt0GADs7OwDA/fv3n9gnkaVioCCSmXjoWYRH27vfKB/++Unn9Ud/+n20/Un9PVpP9+2a3uTk5OBXv/oVVq5cidOnT6O0tBS/+MUv0N7e3u8xu2vtT/3jx4/vUW9nZ2ef/bq6uuLu3btmbbNmzUJ1dTV+//vfo6WlBUuWLMGPfvSjAdXblzt37gAA3NzcBqU/IjkwUBDJbOrUqejo6MCFCxdMbbdv30ZFRQWCgoIAAFOmTMHnn39udl5xcXG/+j9//rzp546ODly6dAlTpkwxjV1UVGQWBoqKiuDk5ISJEyf22kf3dkBAAKysrAB0vRHW1dWZ9ldWVj72X9uFhYUICwtDfHw8nnvuOfj7++PLL780O0apVD5xBqS/9Q/Uc889h7Kysh4hSaVSYenSpdi/fz+OHj2Kv/zlL6YwMH78+B71BgUF9XrtHvXPf/4T48ePx7PPPvvUNRPJjYGCSGYBAQGIiorC66+/js8++wxXrlzBz372M0ycOBFRUVEAgMTERJw8eRLbtm1DZWUlPvjgA5w6dapfswi7du1Cbm4uysrKsGbNGty9excrV64EAMTHx6O2thaJiYkoKyvD8ePHsWnTJqSkpGDcuP//66G2thYpKSkoLy9HdnY2du7ciaSkJNP+8PBwZGVl4fLlyyguLkZcXFyPWYGH+fv7o7i4GH//+99RUVGB3/zmN6YHGbv5+vri6tWrKC8vR0NDQ68zHv2tf6AWLVqE5uZmXLt2zdS2fft2HDlyBGVlZaioqMCf//xn6HQ60ydtfH198emnn+LWrVum2Y2kpCR8/PHH+Pjjj1FRUYFNmzaZ9dmtsLAQ8+fPN936IBqR5Hl0g2hse/ihTCGEuHPnjli+fLlQq9XCzs5OfP/73xcVFRVm5+zbt09MnDhR2NnZiejoaLF582ah0+n6HKP7AcbDhw+L0NBQoVQqRVBQkPj000/NjsvPzxchISFCqVQKnU4n1q1bJx48eGBWa3x8vIiLixMqlUpMmDBBrF+/3uzhxK+//lpEREQIBwcHERAQIE6ePPnYhzJbW1vFihUrhFqtFhqNRqxevVqsX7/e7GHF+vp6sXjxYuHo6CgAiDNnzvT6cGd/6n/4WgshRFRUlIiNje3z2gkhxLJly8T69evNrv/MmTOFg4ODUKlU4vnnnxeXL1827T9x4oTw9/cX1tbWwsfHx9Senp4uXF1dhaOjo4iNjRWpqak9Hsp85plnRHZ29mPrIbJ0CiEk3IglItm8/vrrKCsrQ2FhYa/7b968CT8/P5SUlJgt9TxQCxcuxMyZM/Hee+89dR8j0RdffIHvfe97qKqqgpOT05CN88knn+DNN9/E1atXh2XBLqKhwlseRCPEu+++iytXrqCqqgo7d+7EoUOHEBsbK3dZo9a3v/1tZGZm4ubNm0M6TnNzMw4cOMAwQSMe/wQTjRCff/45MjMzYTAYMHnyZOzYsWNYloYey4YjsC1ZsmTIxyAaDrzlQURERJLxlgcRERFJxkBBREREkjFQEBERkWQMFERERCQZAwURERFJxkBBREREkjFQEBERkWQMFERERCQZAwURERFJ9n/dPgp8QS5xCgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k = az.loo(idata_10, pointwise=True).pareto_k.values\n",
    "\n",
    "cex = 1 + (k - np.min(k)) / (np.max(k) - np.min(k))\n",
    "plt.scatter(\n",
    "    d.P,\n",
    "    d.total_tools,\n",
    "    s=40 * cex,\n",
    "    edgecolors=[\"none\" if i == 1 else \"b\" for i in d.contact_id],\n",
    "    facecolors=[\"none\" if i == 0 else \"b\" for i in d.contact_id],\n",
    ")\n",
    "plt.gca().set(xlabel=\"log population (std)\", ylabel=\"total tools\", ylim=(0, 75))\n",
    "\n",
    "P_seq = np.linspace(-1.4, 3, num=100)\n",
    "\n",
    "jd_10_cid0 = model_11_10x(cid=np.repeat(0, 100), P=P_seq)\n",
    "ds_cid0, _ = jd_10_cid0.sample_distributions(value=post_10)\n",
    "lambda_0 = ds_cid0[-1].mean()\n",
    "lmu0 = np.mean(lambda_0, axis=(0, 1))\n",
    "lci0 = np.percentile(lambda_0, (0.55, 94.5), axis=(0, 1))\n",
    "plt.plot(P_seq, lmu0, \"k--\", lw=1.5)\n",
    "plt.fill_between(P_seq, lci0[0], lci0[1], color=\"k\", alpha=0.2)\n",
    "\n",
    "jd_10_cid1 = model_11_10x(cid=np.repeat(1, 100), P=P_seq)\n",
    "ds_cid1, _ = jd_10_cid1.sample_distributions(value=post_10)\n",
    "lambda_1 = ds_cid1[-1].mean()\n",
    "lmu1 = np.mean(lambda_1, axis=(0, 1))\n",
    "lci1 = np.percentile(lambda_1, (0.55, 94.5), axis=(0, 1))\n",
    "plt.plot(P_seq, lmu1, \"k\", lw=1.5)\n",
    "plt.fill_between(P_seq, lci1[0], lci1[1], color=\"k\", alpha=0.2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Open points are low contact societies and closed points are the high contact ones. Dashed curve is the posterior mean for low contact societies."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 11.2.2 Negative binomial (gamm-poisson) models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 11.2.3 Example: Exposure and the offset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_days = 30\n",
    "y = tfd.Poisson(rate=1.5).sample(num_days, seed=key())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code 11.51"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_weeks = 4\n",
    "y_new = tfd.Poisson(rate=0.5 * 7).sample(num_weeks, seed=key())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.52"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_all = np.concatenate([y, y_new])\n",
    "exposure = np.concatenate([np.repeat(1, 30), np.repeat(7, 4)])\n",
    "monastery = np.concatenate([np.repeat(0, 30), np.repeat(1, 4)])\n",
    "d = pd.DataFrame.from_dict(dict(y=y_all, days=exposure, monastery=monastery))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.53"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {},
   "outputs": [],
   "source": [
    "# compute the offset\n",
    "d[\"log_days\"] = d.days.pipe(np.log)\n",
    "\n",
    "def model_11_12(log_days, monastery):\n",
    "\tdef _generator():\n",
    "\t\ta = yield tfd.Normal(loc=0.0, scale=1.0, name='a')\n",
    "\t\tb = yield tfd.Normal(loc=0.0, scale=1.0, name='b')\n",
    "\t\tlog_lambda = log_days + a + b * monastery\n",
    "\t\tyield tfd.Poisson(log_rate=log_lambda, name='y')\n",
    "\treturn tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_11_12 = model_11_12(d.log_days.values, d.monastery.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_11_12_pin = jd_11_12.experimental_pin(y=d.y.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def run_chain(init_state, seed, step_size=1e-3, num_steps=500, burnin=400):\n",
    "\n",
    "  def target_log_prob(*states):\n",
    "    return jd_11_12_pin.unnormalized_log_prob(states)\n",
    "  \n",
    "  bijectors = [tfb.Identity(), tfb.Identity()]\n",
    "\n",
    "  kernel = tfp.mcmc.NoUTurnSampler(\n",
    "      target_log_prob_fn=target_log_prob,\n",
    "      step_size=step_size)\n",
    "  \n",
    "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
    "    inner_kernel=kernel,\n",
    "    bijector=bijectors)\n",
    "\n",
    "  kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "    inner_kernel=kernel,\n",
    "    num_adaptation_steps=burnin)\n",
    "\n",
    "  chain_state = tfp.mcmc.sample_chain(\n",
    "      num_results=num_steps,\n",
    "      num_burnin_steps=burnin,\n",
    "      current_state=init_state,\n",
    "      kernel=kernel,\n",
    "      seed=seed,\n",
    "      trace_fn=None)\n",
    "  \n",
    "  return chain_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state = jd_11_12_pin.sample_unpinned(num_chains, seed=key())\n",
    "post_12 = run_chain(init_state=init_state, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_12_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_12._asdict().items()}\n",
    "dict_12 = dict(posterior=post_12_dict)\n",
    "idata_12 = az.from_dict(**dict_12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a</th>\n",
       "      <td>0.257</td>\n",
       "      <td>0.157</td>\n",
       "      <td>0.018</td>\n",
       "      <td>0.513</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.004</td>\n",
       "      <td>1058.0</td>\n",
       "      <td>1393.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>-0.744</td>\n",
       "      <td>0.274</td>\n",
       "      <td>-1.185</td>\n",
       "      <td>-0.323</td>\n",
       "      <td>0.010</td>\n",
       "      <td>0.007</td>\n",
       "      <td>758.0</td>\n",
       "      <td>921.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  ess_bulk  ess_tail  \\\n",
       "a  0.257  0.157     0.018      0.513      0.005    0.004    1058.0    1393.0   \n",
       "b -0.744  0.274    -1.185     -0.323      0.010    0.007     758.0     921.0   \n",
       "\n",
       "   r_hat  \n",
       "a   1.01  \n",
       "b   1.01  "
      ]
     },
     "execution_count": 231,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_12, hdi_prob=0.89)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.54"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>lambda_new</th>\n",
       "      <td>0.631</td>\n",
       "      <td>0.145</td>\n",
       "      <td>0.407</td>\n",
       "      <td>0.858</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>1097.0</td>\n",
       "      <td>1462.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>lambda_old</th>\n",
       "      <td>1.308</td>\n",
       "      <td>0.205</td>\n",
       "      <td>0.954</td>\n",
       "      <td>1.596</td>\n",
       "      <td>0.006</td>\n",
       "      <td>0.005</td>\n",
       "      <td>1058.0</td>\n",
       "      <td>1393.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "lambda_new  0.631  0.145     0.407      0.858      0.004    0.003    1097.0   \n",
       "lambda_old  1.308  0.205     0.954      1.596      0.006    0.005    1058.0   \n",
       "\n",
       "            ess_tail  r_hat  \n",
       "lambda_new    1462.0   1.00  \n",
       "lambda_old    1393.0   1.01  "
      ]
     },
     "execution_count": 233,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# using only the first chain\n",
    "sample_a = post_12_dict['a']\n",
    "sample_b = post_12_dict['b']\n",
    "\n",
    "lambda_old = jnp.exp(sample_a)\n",
    "lambda_new = jnp.exp(sample_a + sample_b)\n",
    "\n",
    "az.summary(\n",
    "    az.from_dict({\"lambda_old\": lambda_old, \"lambda_new\": lambda_new}), hdi_prob=0.89)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 11.3 Multinomial and categorical models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 11.3.1 Predictors matched to outcomes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.55\n",
    "\n",
    "Here we simulate career choice from three different careers, each with its own income trait. These traits are used to assign a score to each type of event. Then when the model is fit to the data, one of these scores is held constant, and the other two scores are estimated, using the known income traits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 500  # number of individuals\n",
    "income = np.array([1., 2, 5])  # expected income of each career\n",
    "career = tfd.Categorical(logits=income).sample(N, seed=key())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.56\n",
    "\n",
    "\n",
    "Categorical likelihood is a multinomial logistic regression distribution.\n",
    "\n",
    "Each possible career will gets its own linear model with its own features. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 365,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_11_13(career_income):\n",
    "\tcareer_income = jnp.array(career_income, dtype=jnp.float32)\n",
    "\tK = jnp.size(career_income)\n",
    "\n",
    "\tdef _generator():\n",
    "\t\ta = yield tfd.Sample(tfd.Normal(loc=0.0, scale=1.0), sample_shape=K-1, name='a')\n",
    "\t\t# fix-one-to-zero constraint (for intercept, not a whole category)\n",
    "\t\ta = jnp.concatenate([a, jnp.array([0.])])\n",
    "\t\tb = yield tfd.Normal(loc=0.0, scale=0.5, name='b')\n",
    "\t\ts = a + b*career_income\n",
    "\t\tyield tfd.Sample(tfd.Categorical(logits=s), sample_shape=500, name='career')\n",
    "\n",
    "\treturn tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.57"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 366,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_11_13 = model_11_13(income)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 367,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_11_13_pin = jd_11_13.experimental_pin(career=career)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 368,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def run_chain(init_state, seed, step_size=1e-3, num_steps=500, burnin=400):\n",
    "\n",
    "  def target_log_prob(*states):\n",
    "    return jd_11_13_pin.unnormalized_log_prob(states)\n",
    "  \n",
    "  bijectors = [tfb.Identity(), tfb.Identity()]\n",
    "\n",
    "  kernel = tfp.mcmc.NoUTurnSampler(\n",
    "      target_log_prob_fn=target_log_prob,\n",
    "      step_size=step_size)\n",
    "  \n",
    "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
    "    inner_kernel=kernel,\n",
    "    bijector=bijectors)\n",
    "\n",
    "  kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "    inner_kernel=kernel,\n",
    "    num_adaptation_steps=burnin)\n",
    "\n",
    "  chain_state = tfp.mcmc.sample_chain(\n",
    "      num_results=num_steps,\n",
    "      num_burnin_steps=burnin,\n",
    "      current_state=init_state,\n",
    "      kernel=kernel,\n",
    "      seed=seed,\n",
    "      trace_fn=None)\n",
    "  \n",
    "  return chain_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 369,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state = jd_11_13_pin.sample_unpinned(num_chains, seed=key())\n",
    "post_13 = run_chain(init_state=init_state, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 371,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_13_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_13._asdict().items()}\n",
    "dict_13 = dict(posterior=post_13_dict)\n",
    "idata_13 = az.from_dict(**dict_13)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 372,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_5.5%</th>\n",
       "      <th>hdi_94.5%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a[0]</th>\n",
       "      <td>-0.803</td>\n",
       "      <td>0.755</td>\n",
       "      <td>-1.989</td>\n",
       "      <td>0.431</td>\n",
       "      <td>0.037</td>\n",
       "      <td>0.028</td>\n",
       "      <td>416.0</td>\n",
       "      <td>365.0</td>\n",
       "      <td>1.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a[1]</th>\n",
       "      <td>-0.153</td>\n",
       "      <td>0.581</td>\n",
       "      <td>-1.105</td>\n",
       "      <td>0.703</td>\n",
       "      <td>0.026</td>\n",
       "      <td>0.018</td>\n",
       "      <td>500.0</td>\n",
       "      <td>522.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>0.878</td>\n",
       "      <td>0.190</td>\n",
       "      <td>0.581</td>\n",
       "      <td>1.183</td>\n",
       "      <td>0.009</td>\n",
       "      <td>0.006</td>\n",
       "      <td>491.0</td>\n",
       "      <td>576.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean     sd  hdi_5.5%  hdi_94.5%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "a[0] -0.803  0.755    -1.989      0.431      0.037    0.028     416.0   \n",
       "a[1] -0.153  0.581    -1.105      0.703      0.026    0.018     500.0   \n",
       "b     0.878  0.190     0.581      1.183      0.009    0.006     491.0   \n",
       "\n",
       "      ess_tail  r_hat  \n",
       "a[0]     365.0   1.02  \n",
       "a[1]     522.0   1.01  \n",
       "b        576.0   1.01  "
      ]
     },
     "execution_count": 372,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_13, hdi_prob=0.89)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 11.3.3 Multinomial in disguise as Poisson"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.60\n",
    "\n",
    "Multinomial in disguise as Poisson. The author shows a technique here on how to fit a multinomial/categorical model as a series of Poisson Likelihoods.\n",
    "\n",
    "\n",
    "It is computationally easier to use Poisson rather than multinomial likelihoods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 373,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dept</th>\n",
       "      <th>applicant.gender</th>\n",
       "      <th>admit</th>\n",
       "      <th>reject</th>\n",
       "      <th>applications</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>A</td>\n",
       "      <td>male</td>\n",
       "      <td>512</td>\n",
       "      <td>313</td>\n",
       "      <td>825</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>A</td>\n",
       "      <td>female</td>\n",
       "      <td>89</td>\n",
       "      <td>19</td>\n",
       "      <td>108</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>B</td>\n",
       "      <td>male</td>\n",
       "      <td>353</td>\n",
       "      <td>207</td>\n",
       "      <td>560</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>B</td>\n",
       "      <td>female</td>\n",
       "      <td>17</td>\n",
       "      <td>8</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>C</td>\n",
       "      <td>male</td>\n",
       "      <td>120</td>\n",
       "      <td>205</td>\n",
       "      <td>325</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>C</td>\n",
       "      <td>female</td>\n",
       "      <td>202</td>\n",
       "      <td>391</td>\n",
       "      <td>593</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>D</td>\n",
       "      <td>male</td>\n",
       "      <td>138</td>\n",
       "      <td>279</td>\n",
       "      <td>417</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>D</td>\n",
       "      <td>female</td>\n",
       "      <td>131</td>\n",
       "      <td>244</td>\n",
       "      <td>375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>E</td>\n",
       "      <td>male</td>\n",
       "      <td>53</td>\n",
       "      <td>138</td>\n",
       "      <td>191</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>E</td>\n",
       "      <td>female</td>\n",
       "      <td>94</td>\n",
       "      <td>299</td>\n",
       "      <td>393</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>F</td>\n",
       "      <td>male</td>\n",
       "      <td>22</td>\n",
       "      <td>351</td>\n",
       "      <td>373</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>F</td>\n",
       "      <td>female</td>\n",
       "      <td>24</td>\n",
       "      <td>317</td>\n",
       "      <td>341</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   dept applicant.gender  admit  reject  applications\n",
       "1     A             male    512     313           825\n",
       "2     A           female     89      19           108\n",
       "3     B             male    353     207           560\n",
       "4     B           female     17       8            25\n",
       "5     C             male    120     205           325\n",
       "6     C           female    202     391           593\n",
       "7     D             male    138     279           417\n",
       "8     D           female    131     244           375\n",
       "9     E             male     53     138           191\n",
       "10    E           female     94     299           393\n",
       "11    F             male     22     351           373\n",
       "12    F           female     24     317           341"
      ]
     },
     "execution_count": 373,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = pd.read_csv(\"./data/UCBadmit.csv\", sep=\";\")\n",
    "d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code 11.61\n",
    "\n",
    "Using Poisson regression to model rate of admission & rate of rejection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 376,
   "metadata": {},
   "outputs": [],
   "source": [
    "def m_binom(applications):\n",
    "\tdef _generator():\n",
    "\t\ta = yield tfd.Normal(loc=0.0, scale=1.5, name='a')\n",
    "\t\tyield tfd.Binomial(total_count=applications, logits=a, name='admit')\n",
    "\n",
    "\treturn tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 388,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_binom = m_binom(d.applications.values.astype(np.float32))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 389,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_binom_pin = jd_binom.experimental_pin(admit=d.admit.values.astype(np.float32))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 390,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def run_chain(init_state, seed, step_size=1e-3, num_steps=500, burnin=400):\n",
    "\n",
    "  def target_log_prob(*states):\n",
    "    return jd_binom_pin.unnormalized_log_prob(states)\n",
    "  \n",
    "  bijectors = [tfb.Identity()]\n",
    "\n",
    "  kernel = tfp.mcmc.NoUTurnSampler(\n",
    "      target_log_prob_fn=target_log_prob,\n",
    "      step_size=step_size)\n",
    "  \n",
    "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
    "    inner_kernel=kernel,\n",
    "    bijector=bijectors)\n",
    "\n",
    "  kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "    inner_kernel=kernel,\n",
    "    num_adaptation_steps=burnin)\n",
    "\n",
    "  chain_state = tfp.mcmc.sample_chain(\n",
    "      num_results=num_steps,\n",
    "      num_burnin_steps=burnin,\n",
    "      current_state=init_state,\n",
    "      kernel=kernel,\n",
    "      seed=seed,\n",
    "      trace_fn=None)\n",
    "  \n",
    "  return chain_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 391,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state = jd_binom_pin.sample_unpinned(num_chains, seed=key())\n",
    "post_binom = run_chain(init_state=init_state, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 392,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_binom_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_binom._asdict().items()}\n",
    "dict_binom = dict(posterior=post_binom_dict)\n",
    "idata_binom = az.from_dict(**dict_binom)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 402,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array(0.38746039, dtype=float64)"
      ]
     },
     "execution_count": 402,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jax.nn.sigmoid(az.summary(idata_binom, hdi_prob=0.89)['mean']['a'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 412,
   "metadata": {},
   "outputs": [],
   "source": [
    "def m_pois():\n",
    "\tdef _generator():\n",
    "\t\ta = yield tfd.Sample(tfd.Normal(loc=0.0, scale=1.5), sample_shape=2, name='a')\n",
    "\t\tyield tfd.Sample(tfd.Poisson(log_rate=a[0]), sample_shape=12, name='admit')\n",
    "\t\tyield tfd.Sample(tfd.Poisson(log_rate=a[1]), sample_shape=12, name='rej')\n",
    "\n",
    "\treturn tfd.JointDistributionCoroutineAutoBatched(_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 413,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_pois = m_pois()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 414,
   "metadata": {},
   "outputs": [],
   "source": [
    "jd_pois_pin = jd_pois.experimental_pin(\n",
    "  admit=d.admit.values.astype(np.float32), rej=d.reject.values.astype(np.float32))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 415,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def run_chain(init_state, seed, step_size=1e-3, num_steps=500, burnin=400):\n",
    "\n",
    "  def target_log_prob(*states):\n",
    "    return jd_pois_pin.unnormalized_log_prob(states)\n",
    "  \n",
    "  bijectors = [tfb.Identity()]\n",
    "\n",
    "  kernel = tfp.mcmc.NoUTurnSampler(\n",
    "      target_log_prob_fn=target_log_prob,\n",
    "      step_size=step_size)\n",
    "  \n",
    "  kernel = tfp.mcmc.TransformedTransitionKernel(\n",
    "    inner_kernel=kernel,\n",
    "    bijector=bijectors)\n",
    "\n",
    "  kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "    inner_kernel=kernel,\n",
    "    num_adaptation_steps=burnin)\n",
    "\n",
    "  chain_state = tfp.mcmc.sample_chain(\n",
    "      num_results=num_steps,\n",
    "      num_burnin_steps=burnin,\n",
    "      current_state=init_state,\n",
    "      kernel=kernel,\n",
    "      seed=seed,\n",
    "      trace_fn=None)\n",
    "  \n",
    "  return chain_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 416,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chains = 4\n",
    "init_state = jd_pois_pin.sample_unpinned(num_chains, seed=key())\n",
    "post_pois = run_chain(init_state=init_state, seed=key())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 417,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_pois_dict = {k: jnp.moveaxis(v, 0, 1) for k, v in post_pois._asdict().items()}\n",
    "dict_pois = dict(posterior=post_pois_dict)\n",
    "idata_pois = az.from_dict(**dict_pois)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 421,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3881726309982628"
      ]
     },
     "execution_count": 421,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k = az.summary(idata_pois, hdi_prob=0.89)['mean']\n",
    "np.exp(k['a[0]']) / (np.exp(k['a[0]']) + np.exp(k['a[1]']))"
   ]
  }
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