03. Linear models/3.5 Polynomial regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regresión polinomial\n",
    "\n",
    "La regresion lineal tanto univariante como multivariante asumen que existe una relación lineal entre las variables dependientes e independientes, pero es habitual encontrar que los datos reales que recopilamos presentan relaciones que no son lineales. En estos casos es posible realizar una regresión polinomial. Por ejemplo, podemos estudiar cómo se relacionan el número de millas que una persona camina cada día y la edad de dicha persona usando una ecuación cuadrática."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comenzamos como siempre cargando las librerías que necesitaremos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import statistics as s\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "plt.rcParams['figure.figsize'] = (12, 8)\n",
    "sns.set()\n",
    "sns.set(font_scale=1.5)\n",
    "\n",
    "import statsmodels.formula.api as sm\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "np.random.seed(1234)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora creamos un conjunto de datos ficticio, en el que el número de millas recorridas crece con la edad hasta 40, y luego comienza a decrecer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "kms = np.random.normal(5, 2, 50)\n",
    "ages = np.random.normal(40,13,50)\n",
    "ages = [a if a > 0 else -a for a in ages]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "first_kms = sorted(kms[0:int(round(len(kms)/2,0))])\n",
    "second_kms = sorted(kms[int(round(len(kms)/2,0)):len(kms)], reverse=True)\n",
    "\n",
    "ages = sorted(ages)\n",
    "kms = first_kms + second_kms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame({\"age\": ages, \"kilometers\": kms})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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>age</th>\n",
       "      <th>kilometers</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6.325717</td>\n",
       "      <td>0.514630</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>8.794103</td>\n",
       "      <td>0.957490</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>21.204469</td>\n",
       "      <td>1.906189</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>21.774347</td>\n",
       "      <td>2.618049</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>25.015432</td>\n",
       "      <td>3.558823</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         age  kilometers\n",
       "0   6.325717    0.514630\n",
       "1   8.794103    0.957490\n",
       "2  21.204469    1.906189\n",
       "3  21.774347    2.618049\n",
       "4  25.015432    3.558823"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hacemos un breve análisis exploratorio:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "g = plt.hist(df['age'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "g = plt.hist(df['kilometers'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Scatter plot of kilometers walked in a day vs age')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot kilometers vs. age\n",
    "ax = sns.regplot(x='age', y='kilometers', data=df, fit_reg=False)\n",
    "ax.set_title('Scatter plot of kilometers walked in a day vs age')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Evidentemente, la relación entre ambas variables es no lineal (hemos obligado a que sea así). Intentemos ajustar a los datos un modelo basado en una parábola, que es un polinomio de grado 2:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:             kilometers   R-squared:                       0.756\n",
      "Model:                            OLS   Adj. R-squared:                  0.743\n",
      "Method:                 Least Squares   F-statistic:                     57.38\n",
      "Date:                Thu, 13 Feb 2020   Prob (F-statistic):           4.57e-12\n",
      "Time:                        15:08:03   Log-Likelihood:                -52.635\n",
      "No. Observations:                  40   AIC:                             111.3\n",
      "Df Residuals:                      37   BIC:                             116.3\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "====================================================================================\n",
      "                       coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------------\n",
      "Intercept           -4.1822      0.881     -4.749      0.000      -5.967      -2.398\n",
      "np.power(age, 2)    -0.0065      0.001    -10.069      0.000      -0.008      -0.005\n",
      "age                  0.5157      0.048     10.650      0.000       0.418       0.614\n",
      "==============================================================================\n",
      "Omnibus:                        1.853   Durbin-Watson:                   2.009\n",
      "Prob(Omnibus):                  0.396   Jarque-Bera (JB):                1.734\n",
      "Skew:                           0.424   Prob(JB):                        0.420\n",
      "Kurtosis:                       2.432   Cond. No.                     1.15e+04\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.15e+04. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "pd.options.mode.chained_assignment = None  # default='warn'\n",
    "\n",
    "# Define our dependent variable\n",
    "y_column = 'kilometers'\n",
    "y = df[y_column]\n",
    "# Define our independent variables\n",
    "x_columns = ['age']\n",
    "X = df[x_columns]\n",
    "\n",
    "# Split our data into training and test data sets\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)\n",
    "training = pd.concat([pd.DataFrame({'kilometers' : y_train}), X_train], axis=1)\n",
    "\n",
    "model = sm.ols(formula = 'kilometers ~ np.power(age, 2) + age', data = training).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjQAAAHQCAYAAAC2tvAKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAAIABJREFUeJzs3Xl4VNX5wPHvbElmsieEJSyKikcBpYZFUaRaLO67WK3VWq1ba631p7buWrV1X6rWra6otS5QtCpF0RY3QMFicTlaAZOAQMgCSSYhs/3+OHfCzGQSJpMJk0nez/PwhLlz586ZO3fufe9733OuLRQKIYQQQgiRyezpboAQQgghRE9JQCOEEEKIjCcBjRBCCCEyngQ0QgghhMh4EtAIIYQQIuNJQCOEEEKIjCcBTS9RSp2plAoppQ7qalpfopRao5T6V7rbEY9S6iBr3Z2Z7rb0JUqp9Uqp+THTFiulvkxXm/ojpdT51va3X7rb0pcopS5WSn2llGqz1s/QdLeptyil7rE+Y1GSry+yXn9PqtsmDGe6G5AqVpDwTszkZkADTwP3a60DO7pdqWJ9voOAe7TWDeltTd/UyTbQmW+11jv3XmuSo5R6HvgRkK+1boqYbgceAM4H/gacrrX2paeVqaWUGgRcCLyltX4v3e3pa5RS+wDLrYdTtNYfpbM9YUqpw4G7gZeAPwB+oNf2TUqpHKClGy8ZprVe31vtyVRKqYsx31uYH9gMrAaWAE9qrT/u4XscBuwH3KK1bu3Jsrqj3wQ0Ef4KvA7YgHLgTOAeYBxwbvqaBcBs4HmgLYnXHgRcBzxJL+40MtwXwOkx084FDgR+A2yKmN5EhlBKuYCngFOBh4FfaK2D1tM7AcHOXpshBmG27VZAApqOzgbqrf+fBfSJgAb4ofX3TK118w54vzY6/r5/APwME+wvjnku1fvJS4HfJXuA1lo3KKXcmACiL7gF+AxzpaYY2Av4MfBLpdQjmP1MskmAw4BfY469EtD0wHKt9TPhB0qpBzEHup8rpa7RWm+I9yLroOHozWjS2jgyNkvU11nf7TOR05RSh2ACmr9rrdckshylVBZg01pvTXkju8naAb4IHIk527ki8vm+0Ma+TimVr7VuTHc7kmFlJU4DnsOcpP1YKXWJ1ro7mYreMhTYmupgRinlsZYbta+0gvjY33ceJqB5T2v9fILLtwPu7rZba+2nh8HIjsxWJGCh1vqtyAlKqUsw6/hcoA64It4L+6r+GNBE0VpvUUp9CJwI7AJsUEpdjzkjHI85+zkZGAbMAP4F7QfCy4EpQA7wFfBnrfVDse+hlDoH+D9gNFAF3I9J4cXOdybwBHCw1vpfEdOzgIsx0fHugA/4GpP6u18p9STwU2v21Uqp8Etv0Fpfby2jELjS+pwjgS3AW8BVWutVMe0YCdwJHIrZSf7bev+EWDuEK6zX7w6UAOuB14Crtda1EfPujEll3gB8jFnve2HOOJ8BrrB2FJHLPxa4HtgTqMFkpRYl2r7uUErdAvwWUJjLHididtQHKKUaMMHwFVrrWzp5XVRaWyk1ArgWOBwYYrV/HnBN5HpJsG0FwKvAdOByrfXtceZZD/xHa31YAsv7AXAVMBnz2/8c+JPW+umY+RYDRZgg6m7g+5hA/GXMWddW4GrMgWQo8F/gl1rrpTHLcQC/tOZT1jKWYLbbd615DgPesF7yR6XUH63/a631HhHLOg3z/eyFOaP8D3Cr1npexDzhSxIPA3/HfA8TgHeBw5RSZda0IzHZ2yZgDTBba33v9tafJUspdTNwBlAGfAn8Xms9J6IdX2JOjsbEvlgpdTrmEviPtNYvJPB+J2C+i6esxxdgttFnYme0Du5/wLpkiVlHvwN+ARyntc6JmX9P4BrMfq8YqAZewHw/nQZMSqk9ML+L8OPw/XP+Gd4OlVIVmN/wNMAD/A94DLg3IrsYvsR6HLAzcBvmzH4Q5vvp8eUipdRxwFy27f/PxeynLwPuUUpNt6ZNtd7Th7m890et9T9jlnUPZvsvDl/2j5g2ApPBOQWzP/wUuCxmP1+E2e/dq7W+OHYa5rd+I7AP0Ij5Li6NDYKsS303Yo5ftZjM/1xMhuo3Wuuka3Ss4+WpwDfAxUqpO7XWm6z3nYD5DR5ofV4bsNL6PM9FtO/vwLHWw/qI49VvtNb3KKVGYzLmBwOjgCzM8e4vwH1a66Tvx9TvAxqllA3YzXq4KebpZzE7wDuBEPCd9ZpzgYcwG8jNmFqcHwIPKqV21VpfFrH88PXIFZiAwoPZsDcm2L4s4J+YS0oLMDuqVsyO+wRMcPQwUAAcT/Slk0+tZRQCH2A2jscxacRhmB3ZEqXUJK31t9a8RZjgYKT1GT/HHLDeAdyJtBmzAV6GOcDNs9bPZExwOE0pNVFrHXtZ7QirPQ9ZbTwWs57qMTvh8Po43lruGuD3mDOin2EOQr3pBcxO5HbMD7UGcHVnAUqpXTHfA5id92pMwHcBcJBSakpkXcx2DMLUJuwDnKO1/kt32hKnbSdham+qMZ+xGRNAP6WU2klrfWPMSwox28QCTOA2Ffg5Zp0EMDvTezHbzKXAq0qp0Vprr/V+Nszl1ROs9/2LNe8ZwNtKqaOsA8YKzInDbdZ8/7Dev/2EQCl1B+aE4R+YgAzgJODvSql46+YA67M9gjmBCJ/p/x2YhNkG/wvkAmMxv71EA5q7gWzgT5j951nAS0qpH0dkCP4C3K6U+r7W+t8xrz8b8/v9e4LvdzbwZThYVEp9Yb1nbKbChvkt/gCT0fsXZr/3KlAZu1CruPlNzHb+ACZ42Ae4BNhPKTWji8sN6zCXfn4JTLTaE56OUmp/YCHgtZZdgwla7mLbSWQkuzX/asxvPp/u1cok4logD7M9bMKcoIK5jDsScyyoAgZbn+cNpdTRWuvXElz+y5j9xx+t97kE+IdSahetdSLHgmnAT4BHMQHvYZj168X8PoD2YOZVzLq+yXr+NOCQBNu5XVrrZivQ/DUm2P2b9dThmO97Dmb/XGi997NKqUKt9YPWfHdjkgCHAudZbQRzQguwr/X55gGrMPuFYzC/weGY/U1S+mNA47GKDG2Yg/qvMGdpi7XWX8fM2wAcEpkhUEoNw+ysntda/zhi3j8rpe4FLlFKPai1XmUFBzdjzlb2j9iZP4E5c0vExZgd6h+11ldGPmFlQtBaf6iU+hQT0MS7dPJ7zNnHflrrFRGvfxKz474BU0sE5sexM3CW1vqJiM8WPtNIxFZMZiJyp/OQUuoDzM78OEyAEGkcMC7cdqVU+KDyK6yAxjqjvxeT6pwScWbwMFbw1os2AEdE7sStM9Hu+DPm4FkRk7X5OyZLcCHmunUiFmLOgk7RWr/YzXZEsYLm+zDB4+TwDlYp9WerXdcppZ4OB72WocBFWuv7rMcPWRmOMzCB/gHh341S6n+Ynd4stmUSTsEEHT+NzAAppf6E2bHdC+yhtf5OKfUqJqD5T+TlYmv+/THBzHVa69/HLOcN4Dal1LMx2+J4YHo4C2TNPxjYH7hba31Jd9ZfjAJgn3Bgam3HnwP3KqXmWIH8k5j9wtmY7Ge4Dbthsm33xAn4O7DOZA/GnCiFPYXJZO0Sk3k9HhPM3K+1/lXEMt7DHGy3RkyzYw7sazD7jOaI5xZhLm/NwgSkHWittwDPKKWOstZFbLboPsABTNNaf2Et935MFuEspdTjWuv3I+Z3AR9qrX++nVXSE2XAWK11bOb80thLT1ZbV2KC50QDmm+01qdFLOMjzMnAz4BbE3j93ph1+Zn1+CGl1PuYepbfRWS17sEECFPC+xjrd7y0wxJ7Jry/3T1i2n1xMtX3YPYH1wAPAmit/22dmB4KvKA7dmJ5Jc7lwbuUUq8Av1ZK3WxtY93WH7tt34A5I9iIOfs7C3gFc5CNdU/s5Q7MTjgbeEwpNSjyHyYytrMtGp6Jycg8EA5mALTW1ZiIPxGnYQ40v499IjI12xnrzOw0TNZlbUx7mzEb28yIlxyHOXg/HbOoRH504XaFwgcQpZRDme6Ig4C3rVn2jfOyqEDMSiu+Awy1UuVgov+RwBPhYMaadzPmrLo33d3FGel2WQfMmZidtj/me9DAt0R/D9szDHOWujrZNkXYDxOgPBJ5tmilsu/AHHyOjnnNVqwdVIR3MScKf4753YQDh8hLLD/BpMPfiFkXBZiDhFJKjUqg7adhip6fiVlOKeYMrxiTHYy0JDKYsTRjsn37J/i+nXkgMsumta7HZIIGYzJDWNvuXOAkK3sadhZm/T2W4Hv9DJM5nh0xbTZmffwsZt7w93dX5ETrUtiqmHknAntgsjzumPX6Nqb4tjvbajtr3VYAL4WDGasdQbZlYo+P89I7knm/bng0TjBDTDCXq5QqxQRY7wKTwyeVCYi9zPMvzPfU4bJjJ96MCGbC3sYcX8qt9ilMgPHXyBMm63d8f4Lvk6hwQFEQ8T6R68ptratCTGnDMGVKGbYr8liplMpWSpVY294/McfeCck2uj9maB7BpFxDmJ3YV1rruk7m/SrOtD2tv2/FeS5siPV3F+tvvGzM59tpZ9gYzJlpssViZZid+0xMIBdPZGC0C/BR7MHbOlNOuFeAUupkzJnzPnS8NFMc5yWxO1UwBzww7W8iNeszWfG2he4IZ3N+Yf2Lx9vJ9HhOwGzHbyqlZuqeddUdbf2N3WFGTtslZnpVnGA/3NMmNsgKTy+NmLan9birdPsQ4lwOibEn5iTim+0sJ1KH79JKo1+Kudy2Rin1GeaAMSfOZaGufBFnWnjb3IVtwwY8gqllORVztu3A1MEtjnPg6sA6kJ6JyWa5rexO2FLgTKXUdREnPaMxgciaOIv7CpPKDwvv426h84xh7DpNVDLbWpCuv99UiPv7Vqbm7WbMJe3SOLPkse3g3pWo/ZvW2qeUauxkmdt9vSVy/1jNtnWr48wbb1pPhAOZ9s+ulCrGnHifiDnhilWMuWzXJaVUNiaj82O2fabY5SSlPwY0X+uYyu0uxDvA2Ky/Z2DV1MQRb+NLl3B736IbWZaeUEqF6yKWYi5TVWHqfhzAfOJn/rrKfti6eG5HibctdFWcFvvbCX+GxzFDB8TTnV4V72GuM8/HBDWHaq2XdOP1PdXV99XZc7aY/69l26XOeBLZCdswhZpH0vn38d+Yx3EDR631vUqpl61lTcdcFrtIKfWU1rqrdibjHUyh49mY7OLhmDPtaxN8/UxMtnKktZzO5pnfyXNdCX9Pf2RbVjVWbL1hb/Lp3h9TqcM2YV2KfQfzvdyDKaLejAmwfoWp60g0Q5PIbyKZ13dnGam0t/U38jc6D3PZ9gHgQ8yJTADTqeYcEl9Xj2JqsJ7C/B42YbKn0zGBTtJXjvpjQNNT4Z3HpgQCo3Bgswem5iHS2ATf7ytgD6VUtu66C25nO/MaTC1QQYKB3CpgjFLKEVMvMgzTmyIRp2MCmINj0ofdrTmJ1zbYlu2IlOj6TKVwZq8kznOxZ5nh7cbZjYC6S1rr95VSh2IOWgusoCZ2rI1EhNfruDjPjY2ZJ1W+xhSbv5dA9rGrwPFrTI3Z/7TWPb78Zl0Ofhh4WCnlxATmP1WmN0dsYBTPnpjUeKQO61BrHVJK/QW4VSm1NyawaWJbgeX2nIUJgM/s5PnHrWWGA5o1mPW9Mx0zaLvHPA5vq75UbasR0rGtJWsqpnD6Eq115EBzWNm8vmaN9VfFeS7etKQopXIxwX4r1nFNKbUTpnfTn7TWv46Z/6Q4i4n7m7Z+c6dg6mjOjHluUk/b3h9raHrqBUz9wA3KjAESRSlVaKXMwPQSaMEUbnki5hmBSacl4llMiu3qOO8VGZmHr9tHHVytlPOzwJRONqxwfUfYPEw6+YyY2bpTWR7AbLDt24/V1g6foZuWYVKrP7OuqYaXXYAZIXeH0lqHg8UZkdOtwO3ImHnXYX78pyjTZZWY19gjP1M32vAB27rX/1MpNbW7y8B0lV4PnGMV9obblI25bBjA1Iel0tOY3nCxvafC7x15SSPutm0J14/cEq+eIWY5nbLqI6J+z9YltXAQE++94/llRM1XOA1/LubE4oOYeZ/EZJeuBI4C/qYT6OVm1SYcC7yutX4p3j9MHdIx1ryw7fu7JGZZJ9Ax+F6COZG6MF7dg1LKZX2ubtNaV2G6PZ+olGoPpKz9w++sh3OTWXYvCJ/QRWVAlOkBlrJeQymkMcHoqSriFhPKDFdwYSreQCmVj8kwDwHu0tuGmuhsXY3G1LnF6uw3HcJkwGKXU4zp1dUjkqGJobWuVkpdgOmt84VSajamoLMM05X6OMyZxhqtdb1S6hpMQdsHSqmnMUVc52M2vH0SeMt7MQV9VyulJmMq41sxZziKbT+s8Jn5rUqpZ615Vmqtw9X4BwAvKKVesOZtw4wiewQmUDjTev1tmGDrUaXURMx17YMwZyuJpplfwlxHfdv6zC5rvXi6fNV2aK0DSqnfYILKpUqpRzGpyLMw15N7UsyZrPsx382rmIPISExXxE8xXYAjnYO5VPShUuopTArbiTmgHIe59JBoL6d2Vi+3cKbmn0qpw6xAJ9HXtymlfoXJDnxkrVcvZjuYBFwb08MpFZ7FXGa5VCk1BdMjqRbTc+tATJHyWKt9a5VSVcDp1t8aYIvW+nWt9bvKjE1zBaYu8mXMpeByq+0HY7r5bs9ewHyl1BzMNt+A6Q11Aebgnmjmawuw2Pp+HZgsyVDgJ7EZVq31RqXUPEwtDZh9SiJOxwSDL3cxz8uYM93TMZdL5mIKUS+0grx3MPV5Z2N67LTX4Fi/s59gLlN/ppR6HFMblGu95kTgIjrp5ZSAX2GC+w+U6YFTgwnQZgCxPZzSaRnW8BBWoL+Kbd3K/wt8L31N68jK+l2COSldqkzvz3C37fC2150xXGZYgZEdU9y7N6Z2rwSzr7om4r2rlVJLgAtMbTKfArtijnVf0nFfGP493WP9ZrdiBr39Splenz9Sphfu+5jf8jmY3/WIbrS/A8nQxKFNd+bpwCeYg9efMT/SYZgvObLC/E7Ml+rGXJM+ExPg3EcCrO6bMzHZjZGYngB/wAzoNydivvcxWZRdMdcg/4rpkRXuBXQAZtC6cVY7bsVcA15MRG8Vq1fGgZhxMM6w5vNgDgwJ1XhYXe7OxRTM3YHpCq4xmYQesc4+T8IcOK7H7FhfogdjE/TQjZhxFaZgDhwzMT14Yi8xYl0S2Qdzjflg63U3WP+fQ8T32V1a6w8x6zeEOTAf0M3Xv2S1fRXmTPkPmN//mbrjGDQ9ZvVi+wnm4ODEBN1/wmxztXTM5p2KObjcitm274pY1pWYgHATJgPxAGZMHAeJDwi5CpM1moT5Dd+HyZo8ABy4ncu9kX6DOaBchPluvcAsrXVnvRofsf5+1o3LhWdhDgBddRl+A5MdPgvaM7XHYD7PQZj1tx/mZOlbYsZ1sYrM98EEucdj1seVmPXzCD0YyNIKtg/A1FlchNlHDMNkA89JdrmpZvXUPBRTR3Qu5vc6CRPQdadQfIfRWv8D8z3XYOpPLsMEpuHsV3fG7/kdJgP6GGZfW4Hpsj9Za31BnF62x2OC3JMx28thmMxQh21fm/F7fo/psfQY5jd9hPX0uZjt9BBrOadgivX/ELuc7rKFQkkPyieEEKILyoxE+2/i1GnswDZ8BXi11n0q4yBSRyl1NiYDeLjWOplC8X5BMjRCCNF7LsRcHo4d9ynlOqn5OxFzGenN3n5/0fuUGffLFTMtB9Pb1EvHOq4BRWpohBAihazCyiMxNRizMPe66dZ9vJJ0szIFDv/GDMNfgRmAbwPm9i4i85UBHyulnsPcH2sw5tKuwtxzLqkRdvsLCWiEECK1hmNqBpqsv1d1PXvK/BtT6/VbzMBotZiah2siR5YVGa0RU/A9i22DH35G9K1sBiypoRFCCCFExusPGZpszL1cvqPr0RaFEEII0fc5MD3jPiLixqrb0x8CmslsuzmeEEIIIfqHAzFjeyWkPwQ03wHU1zcTDPavy2elpXnU1m53YFGBrKvukHWVOFlXiZN1lThZV12z220UF+dC5/dTjKs/BDQBgGAw1O8CGqBffqbeIusqcbKuEifrKnGyrhIn6yoh3SojkXFohBBCCJHxJKARQgghRMaTgEYIIYQQGU8CGiGEEEJkvLQWBSulxgA3Ye7MWoy5K+zTwN3duPutEEIIIQa4tAU0SqnhwFJgM3A/UIfpc/5HYBxwerraJoQQonMtLc00NTUQCPjbp23caCcYDKaxVZljIK8rh8NJXl4RbnduypedzgzNT4AiYJrW+jNr2iPWHWNPUUqdpbX2pa95QgghYrW0NNPYWE9RURkuVxY2mw0Ap9OO3z8wD9LdNVDXVSgUwudro6GhBiDlQU06a2gKrL8bYqavB3zIbQyEEKLPaWpqoKiojKys7PZgRohE2Gw2srKyKSoqo6mpIeXLT2eG5t/AlcBjSqlrMZecpgNnArdqrQde+CqEEH1cIODH5cpKdzNEBnO5sqIuV6ZKWu+2rZS6GhPUuCMmX6u1vrEbi9kZWJ3KdgkhhIjvs88+p7x8p3Q3Q2S4deu+Zdy4sdubbTSwJtFlpvvWB6uBfwFzgVrgSOAGpVSN1vqh7iyotrap3w0lXVaWT01NY7qbkRFkXSVO1lXiZF11FAwG49Z/DNS6kGTIujLbUWe/LbvdRmlpXreXmc5eTqcADwO7a63XWZPnKKXswB1Kqb9prevT1T4hhIintaqSpuXL8NfV4iwpJa9iIjkjR6W7WUIMeOksCv4FsCwimAl7BcgFJuz4JgkhROdaqyqpXzCfgLcZR3EJAW8z9Qvm01pVme6miR567LGHmTZtEo2NnWfkTjrpaG6++fr2x6+//irTpk3iu+9iD2MiHdIZ0AwBHHGmu6y/6b4cJoQQUZqWL8Pu8eDw5GKz2XB4crF7PDQtX5bupgkR1+LFH/DYYw+nuxk7RDoDmq+ASUqpXWOmn4rpsv3pjm+SEEJ0zl9Xi93tiZpmd3vw19WmqUViR3ruuZf57W+vTnczumXJkg954olH092MHSKdWZDbgcOB95VS4ZGCj7KmPaS13pjGtgkhRAfOklJzucmzbUCwYIsXZ0lpGlsldpSsLOmuDhAIBAgEAn1ufaQtoNFaL1JK7Q9cD/wSKMX0eroCE+wIIUSfklcxkfoF8wGTmQm2eAl6vRROm57mloneUF1dxUUXnU9JSSl33XU/Z511GvvsM5Grrrq+y9e9/PLfmDPnRdatW0tRUTE/+MEPOeecC8jJyWmf56STjmbMmN054YRZPPjgfaxZs4add96ZSy+9grFjx/PGG//gqaceZ+PG9YwdO54rr7yO8vLhUe/z3/+u4LHHHubzzz8jGAwwbtzeXHDBr9hjjz0BuPnm63njjX8AMG3apPbXvffex4DpafT888/y2mvzWLduLQUFBRx00AzOO+9CPJ5tmchp0yYxa9ap7L67YvbsJ1i7tpq7736AiopJvPXWP3nuudlUVVVis9kYOnQoRx11HCeffGqP1n0y0lqnorVeChyRzjYIIUSickaOonjmYVG9nAqnTZdeTv1QZeUaLrroAoYMGcqdd95HXl5i3Ygfe+xhnnjiUaZMmcoJJ8xi1apveOGF51i16n/cddf9UaMrf/vtGm666TqOO+4kZs5088wzT3H55b/h/PN/ybPPPs2xx56A19vMs88+xa233sS99z7Y/tqPPlrCZZf9mnHj9uLnPz+PYDDIK6/M5cILz+HRR59m9OhdOPbYE6itrWXp0g+55prfd2jrLbfcyJtvzufII49h1qxTqa6uYs6cF1izZjX33PPnqLZ+9NFi3n57AccfP4v8/HwGDRrERx8t5vrrr+L73z+YY445nkAgwJo1q/nvf1cMvIBGCCEyTc7IURLApFhf6wq/atU3XHzxLxgxYiR33HEvHk9i9xyqr6/nmWeeZOrUA7jttnvaA4KhQ8t5+OH7ef/9d5kWkc2rrPyWRx55krFjxwNQVjaE6667ggce+BPPPz+HwsIiAPx+P7NnP8GGDesZMmQowWCQO++8hSlTpnLbbXe3L++oo47jtNNO5MknH+WGG/7I+PF7s9NOO7N06Yccemh07mDFik94/fVXuemmWznooBnt0/fccyzXXXclS5Z8yH777d8+vaqqktmzX2DUqG2DKs6d+zKjR+/CzTf3jYsq6SwKFkIIMcD1ta7w//vfV1x00XnstNPO3HnnfQkHMwAff7wEn8/HySefGpXdOPHEk3E6nXz44XtR8++665j2YAZg3Djz/2nTprcHMwBjx44DaO8e/r//fUV1dRWHHHIoDQ0N7f/8fj97770Pn3yyfLttfeedhRQUFPK9702MWsaECRU4HA4++SS6515FxaSoYAYgLy+PjRs38NlnKxNZPb1OMjRCiAGvqwxBX8se9DeRXeGB9r9Ny5elZT1ffvlvGDJkCHfccS/Z2Tnbf0GE9evXAzBy5M5R0z0eD2Vlg9ufDxsyZGjU49xcc1lr8OAhcac3Nm4BoKqqCoDf/z5+jyu7ffu5iurqSrZs2cxRRx0S9/mGhuhxbYcNK+8wzwknzOKdd97ivPPOZNiw4UyePIWDDz6EyZP33e779wYJaIQQA1o4Q2D3eKIyBMUzD6OpKbfT5ySoSQ1/XS2O4pKoaensCn/QQT9g/vzXePvttzj88KN69b0cjviBR2cBSfjWi6GQuW3CRRddwujRsSOfJCYYDFFaOoirr74h7vODBpVFPY4X3BUXl/DEE8+xdOliFi/+gMWLP+CVV+Zy5JHHcMUV1ybVrp6QgEYIMaB1lSEI5Wb1qexBf9TXusL/6leXAKZg1uPJ5fvfPzjh1w4dajIuVVVr2v8P0NLSQk3NRqZM2S8lbRw+fAQAeXn5282GRFz56rCMTz75mAkT9ulR92uXy8UBBxzIAQccSCgU4u67b2POnBc544yz2tu5o0gNjRBiQOtqsLytNZtkIL1ellcxkaDXS8DbTCgUIuBtJuj1klcxMS3tsdls/O531zBt2nRuuOEqPvpoScKvnTRpX1wuFy+++DdCoW03S54790X8fj9Tp05LSRt3330PysuH89e/zqa1tbXD8/X12y4X5eS4ATqlUERQAAAgAElEQVTc0uHgg2fg8/l45pknO7y+ra2N5uam7bZj8+aGqMc2m41ddx0DwNatW7f7+lSTDI0QYkDrKkOQnZvF1pr6PpM96I/6Yld4h8PB9df/gcsvv5grr7yUu+/+M+PH77Xd1xUXF/OTn5zJE088ymWX/ZqpU6exevU3vPLKXCZP3pcDDjgwZe27/PKruPzyiznjjB9x+OFHUVo6iJqajSxdupgRI0ZwzTU3AqCUGZPmnntuZ999p2K32znkkEOpqJjE0Ucfx+OPP4LWXzBx4hTsdhtVVZW8/fZbXHvtjdvN/txyy000Nm6homISgwcPZsOGDbz00t8YM2Z3dt55dEo+a3dIQCOEGNC6GiyvuDiXhr+9HPc5kTp9sSu8y+XiD3+4g0su+SWXXfZr7r//kYRed/bZ51FYWMicOS9y3313UVRUzKxZp/Dzn18Q1fOppyZNmsKDDz7Ok08+yosvPk9rawulpWXstdfeHHvsie3zHXjg95k161TefHM+Cxa8QSgU4pBDDgXg8suvQqk9eOWVuTz00P1kZbkYNqyco48+jjFj1HbbcOihh/PKK3OZO/clmpoaKSkp5Qc/OISzzjo3ocLkVLNFpsUy1M7A6traJoLBjP8sUcrK8qmp6fzOr2IbWVeJk3XVUWc9mcrK8qla/pn0coqwfv23DB26U4fpTqcdvz+YhhZlHllXnW9HAHa7jdLSPIDRwJpElykZGiHEgNdVhqAvZg+EEB1JUbAQQgghMp4ENEIIIYTIeBLQCCGEECLjSUAjhBBCiIwnAY0QQgghMp70chJCDEhy00kh+hfJ0AghBpzwDSkD3uaom062VlWmu2lCiCRJQCOEGHAib0hps9lweHKxezw0LV+W7qYJIZIkAY0QYsDp6oaUQojMJAGNEGLAcZaUEmzxRk2Tm04KkdkkoBFCDDh5FRMJer0EvM2EQiEC3maCXi95FRPT3TQxgE2bNonHHns43c3IWBLQCCEGnJyRoyieeRgOTy6B+jocnlyKZx4mvZyEyGDSbVsIMSDJTSeF6F8koBFCiF4WHvOmtfJbgi0tODweskeOkrFv+oFAIEAgECArKyvdTRnwJKARQoheFB7zJhgI4N+0CWwQaG7ClpVF/YL5cqmrj3jssYd54olHee65l3nkkQdYsmQx2dnZHHHEUZx77i9xOs3hctq0ScyadSq7766YPfsJ1q6t5u67H6CiYhLBYJDnn3+W116bx7p1aykoKOCgg2Zw3nkX4vFs61XX1tbG/fffy4IFb7B1axsVFRP5v//7XYc2eb3NPProQ7z77r+ord1Ebm4eu+02hgsuuAil9thh6yZTSEAjhBC9KDzmja+qCrJc2F1ZhHxt+BsayB45kqblyySg6UOuuea3lJeP4PzzL+TTT//Dc8/Nxutt4dJLtwUcH320mLffXsDxx88iPz+fQYMGAXDLLTfy5pvzOfLIY5g161Sqq6uYM+cF1qxZzT33/BmbzQbAH/7we+bPf51DDz2csWP3Yvnyj7jssos7tOX22//IBx+8ywknnMzw4SNoaKjn00//w5o1qySgiUMCGiGE6EX+ulocxSUEW7zYctwA2Jwugi1eGfumDxoxYiQ333w7ACeeeDLZ2dnMm/cyP/7x6ZSXDwegqqqS2bNfYNSondpft2LFJ7z++qvcdNOtHHTQjPbpe+45luuuu5IlSz5kv/325+uvv2L+/Nc56aRTuPjiS9vf54Ybruabb76OasuHH77HT396Nj/+8Rm9/bH7BenlJIQYcFqrKtk0by7rn/gLm+bN7dVbHoTHvLG7PYT8PgBCfh92t0fGvrFUN67jtVULmP35C7y2agHVjevS1pYTTji5w+NQKMTSpR+2T6uomBQVzAC8885CCgoK+d73JtLQ0ND+b8KEChwOB598YkahXrz4fQBmzTol6vUnn3xqh7bk5eXzySfL2Ly5ISWfrb+TDI0QYkAJ17TYPZ6o+zj1Vi1LXsVE6hfMx1FURHDtWoI+H6FQiOyywQS9XgqnTU/5e2aS6sZ1LKxchMfppji7EK+vhYWVi5gxajoj8st3eHtGjBgZ9XjkSPP4u+++a582bFjHdlVXV7Jly2aOOuqQuMttaKgHYP3673A4nB2WERsgAVxwwUXcfPP1HHPMoYwdO4799juAQw89gqFDh3XvQw0QEtAIIQaUyPs4Ae1/e6uWJTzmTdPyZYS2bm3v5ZQ1ZKj0cgJW1KzE43TjcZnLceG/K2pWpiWgSUR2dk6HacFgiNLSQVx99Q1xXzNoUFm332fGjB8yYcI+vPvuv1i6dDHPPPMks2c/wc03386++07t9vL6OwlohBADSrimJVJv17LImDedq2ttoDi7MGqa25lDXWt6LrNUV1cxZMjQ9sdVVVUA282KDB8+gk8++ZgJE/bpsgv30KHDCAT8fPfdOoYPH9E+vbLy27jzDxo0iOOPP4njjz+JhoYGzjrrNJ566jEJaOKQGhohxIAi93HqW0pyimjxt0ZNa/G3UpJTlJb2zJnzQofHNpuNKVP26/J1Bx88A5/PxzPPPNnhuba2NpqbmwDYb7/9AXjxxeej5nnhhb9GPQ4EAjQ1NUVNKyoqYvDgIbS1tSX0WQYaydAIIQaUcE0L0F6YK7Us6TOhbDwLKxcBJjPT4m/F629havnktLSnurqKK664lMmT92XFik9YuHABxx57QlQ2JZ6KikkcffRxPP74I2j9BRMnTsFut1FVVcnbb7/FtdfeyOTJ+zJmjGLmzMN46aXnaWzcwrhxe7Fs2VKqq6ujluf1ejnhhCP4/vd/wG67jcHjyWXZso9YufJTLrywYxdvIQGNEGKAiaxp8dfV4iwppXDadLkklCYj8suZMWo6K2pWUtfaQElOEVPLJ6etfubGG2/l4Yfv58EH7yM7O4tTTvkJ559/YUKvvfzyq1BqD155ZS4PPXQ/WVkuhg0r5+ijj2PMGNU+31VXXUdBQRFvvvkGixa9Q0XFJG6//R5OOOHI9nlycnI4/viTWLp0CYsW/YtQKMjw4SP5v//7Hccff1LKP3d/YAuFQuluQ0/tDKyurW0iGMz4zxKlrCyfmprGdDcjI8i6Spysq8TJuupo/fpvGTq0Y48cp9OO3x9MQ4tSIzxS8BtvvEN+fn6vvlemr6tU6Gw7ArDbbZSW5gGMBtYkukzJ0Agh+qXw/ZPCWRjpUSRE/yZFwUKIfic81kzA2xw11kxvDqAnhEgvydAIIfqdHT3WTLIkiyRE6kiGRgjR7/jrarG7PVHT+tp9kySL1LecffZ5vPfex71ePyN6jwQ0Qoh+JxPGmonMItlsNhyeXOweD03Ll6W7aUJkJAlohBD9Tl7FRIJeLwFvM6FQiIC3maDXS17FxHQ3rV0mZJGEyCQS0Agh+p3wWDMOTy6B+jocntxeu/lksjIhi9SZfjDch0ij3tp+pChYCNEv9fX7J2XqiMUOhxOfr42srOx0N0VkKJ+vDYcj9eGHZGiEECINMiGLFE9eXhENDTW0tW2VTI3ollAoRFvbVhoaasjLS/29uiRDI4QQadLXs0jxuN2mC/zmzZsIBPzt0+12O8HgwB79NlEDeV05HE7y84vbt6NUkoBGCCH6qL46To3bndvhgCS3iUicrKveIZechBCiD5JxaoToHglohBCiD5JxaoToHglohBCiD5JxaoToHglohBCiD8rkcWqESAcJaIQQog/KhNGOhehLJKARQog+KFPHqREiXaTbthBC9FGZOE6NEOkiGRohhBBCZDwJaIQQQgiR8SSgEUIIIUTGk4BGCCGEEBlPAhohhBBCZDwJaIQQQgiR8SSgEUIIIUTGk3FohBB9RmtVJU3Ll+Gvq8VZUkpexUQZh0UIkRDJ0Agh+oTWqkrqF8wn4G3GUVxCwNtM/YL5tFZVprtpQogMkPYMjVJqMnA9sD/gAr4B7tZaP5nGZgkhdrCm5cuwezw4PLkA7X+bli+TLI0QYrvSGtAopQ4H5gH/Aq4BfMDuwMg0NksIkQb+ulocxSVR0+xuD/662qSWV924jhU1K6lrbaAkp4gJZeMZkV/e/ty7az9kzZZKQiEoyyklLzsXfzAQd97I5Qz1DGG9d0Pc5Qoh0idtAY1SqhB4EnhQa/3rdLVDCNE3OEtKzeUmKzMDEGzx4iwp7fayqhvXsbByER6nm+LsQry+FhZWLmLGqOkAvLpqPhu9m8hx5OALtvFF/dd4nDmMLVVR83qduVHL2eitYcl3y9m5YCSDPYOi5pWgRoj0SmeG5sdAEXAtgFIqH2jSWofS2CYhRJrkVUykfsF8wGRmgi1egl4vhdOmd3tZK2pW4nG68bjcAO1/V9SsBKCxrQm3043L7qTR10SWw0mQEBu8NexevOu2ZXizo5bTsHUL2c5sNrdtYUhuWdRyuwpousoWCSFSI50BzSHAl8ARSqnbgBFAg1LqYeAqrXUgjW0TQvSyeD2aimceFjWtcNr0pOpn6lobKM4ujJrmduZQ19oAgC/gbw9G/EE/DhwEQkFa/K1R83px4XZ62pfR4m/F7cimNdAad7nxRGaLHNj5rFazdP1y9igZw4HDp0pgI0SKpDOg2Q1TK/MkcBvwCXAU8FsgB7i4OwsrLc1LcfP6hrKy/HQ3IWPIukpcutdV0+o11C9aSHZuLp7hQwl4vbQsWkjgkP34734lbGqGQbkl7Du8kLLi7rd1ROkQmtu8eLK2BSPNbV5G5A0BoKZtExDC5XCR7cuize/DaXdQ4MnDk5sdNW/kcgqa8/C2ecl3m/kil9vZOn1nw9eUFhTiC/hYVbsWl8tFoTOf71o38M/qhZS4C/EHA9bn/R47FY/o9uftK9K9XWUSWVepl86AJg8oBn6ntb7VmjZHKZUH/EIpdZPWelOiC6utbSIY7F9Xq8rK8qmpaUx3MzKCrKvE9YV1tWnhIgJ2FwGbC1p8YHOxNsvPkk9epXi0wu30sKmhgRc3vZFUfcoYzxgWblpEi7MNtzOHFn8rXn8L3xs1AYAvbd+019C4Qk4a/c14nDmUOIvZ1NDQPm9JcS4vrnijfTm5Ng8bW2sZlDWI5qbWqOV2tk6razdQnF3Imoa12II2bNgAG1u2NtLY0kRtUwNjS3bv0eftC/rCdpUpZF11zW63JZWkSGdA02L9/WvM9GeBWcAU4PUd2iIhxA7hr6ulpjSbL51VNNi3UhTMpjGrjaxWX9y6l+4e4EfklzNj1PSoupWp5ZPbl3P0Loe193Ky2x3sWTymvZdTocvdPm9ZcX7UcgZ7yth70PioXk6Ry42nJKcIr6+F1kAr2XaT1fEF/fhCfvKdeQRCfmw2W9zPK7U3QiQunQHNd8A4YEPM9PDj4h3bHCFEbwsfoL8pr6EeL4NDuZSG3LTY/KxyNLBLTud1L901Ir+804P/iPxyTt3jxB4vJxETysazsHIRDpsTf8gPIRu+oA+X3YnNBjn2nPZ5Iz9vVz21JKgRoqN0jhS8zPo7PGZ6+AJyzQ5sixCil1U3rmPBl29Qq1fS3NZEsHUrG0ONNNnayPYFcfthY54t6jUt/lZKcorS1OLUCGeLRuaV0+zzAiFGF4zC7cyh1b+VoZ7B7fNGft7InlrhDI7H6W7vqSWEiJbOgOZF6+/Z4QlKKRvwc6AZWJyORgkheseyb97HXv0d2b4gvhwXbmc29q0+NrY1YHdlMapsN1rsfry+FkKhEF5fC15/CxPKxqe76T02Ir+cU/c8kXP2OoNxpXsQCAUZmT+cQe5SnHZn3M9b19qA25kTtZyeZKyE6O/SdslJa71MKfU0cIVSajCwHDgSOBS4XGu9JV1tE0Kk3sb1a8h3ZGN3ZZETcuB32XA57PjsNjy77QG+FvYI5uNxuROuT8k0sZevYmtkIj9vuPYmXFsDXWespN5GDHTpvpfTOUAl8FPr3yrgfK31w2ltlRAiId05iBZ4A7S6XXiAsqCbKkcjITvk+ILt2YmBVh/SVX1OuPYGiOqpNbV8cod5pd5GiDQHNFrrNsw9nK5JZzuEEN3X3YPoONcI3g9WYrPbyA25GBzwsMHWRI5VJ9LfsjE9tb2eWpG6GhlZ1qkYKNKdoRFCZJhwVubTTZ/hsDkZmVfeabfjSLt9bzr+d/6OLmpjc1aA4jYH+zWUscfBx8ndtDuRaA+rutYG8reCd/23BFu82N0eXEOHUpe9lWXrV7Bo7QdsbttCYVYB04fvz8ShE3ZA64XYsSSgEUIkLDIrEwyGcDhCrN7yLaMLdqIgO7/LotWckaPY4+DjGLF8Gf7vrNsdHDxRgpkUKGizUb9G43bkYHO7CfraaFjzFVuHDWJe/RtkO7MpcOXj9bcy75s3ACSoEf2OBDRCiIRFXtrwuNz4gn6cdifrvRspyM7fbjfrnJGjJIDpBbtWbeX9LDt2u50cYKvLzlaHnZot68kuLMRj9ZbyOHPwBXzM/eY1Pq/TUjws+pV0dtsWQmSYyK7EQ3MH4wv6CIVM75v+1M060wza1Mr+gZG4Q04229pwh5zsHxhJa9CH25HdPt/WQBtev5cWf0tU3VN147o0tl6I1JAMjRAiYZFdiQuy8tmlcCeqGtdCCCnsTSNnSSmDm5sZ5hnZPi3gbaYgO4eWwNb2DE2Tr5kQ4Ha6E6p7EiKTSEAjhEhYbFdip83JEM9g6R6cZnkVE6lfMB8Au9tDsMVL0Otl+t7783rDRwC4Hdm0+luBEDvlb7ujd7juScaxEZlOLjkJIRIW7krscbmp37oZj8stwUwfkDNyFMUzD8PhySVQX4fDk0vxzMPYb9wMjt31cDzOHLb4Gslx5jC6YBTleUPbX9vib8Vpd7CwchFen1yKEplLMjRCiG7p6c0aRe/orOB6nK+YnaqH4q9zsWlQDkuztuL1tUQN1pdld8k4NiLjSYZGCCH6qdaqSuoXzCfgbcZRXEJZE1R80UxWS1tUhs0fCsh9o0TGkwyNEEL0U03Ll2H3eHB4cgFweHIZ5oUR3zoZdOzx7fNt775RUl8jMoFkaIQQop/y19USbPPh1V/S9J/lePWXBNt8+Otqo+abUDYer78l7p3Ow4MpSn2N6OskQyNEPxd7dn2wc188FKZk2a1VlTQtX4a/zhr5t0JG/u1THE5av/oSm9uNLceMINz6tca9+x5Rs3V136jXVi2Q+hqRESSgEaIfi3cDyVf1WxwweGqPD0bh+gy7x4OjuISAt5n6BfMpnnmYBDV9hW3bH+u/hCKmR+qs2LuutYHi7OgAWOprRF8kAY0Q/Vi8uzCHXIGUnF3Hq88IT5eApo/w+8nZXeFbv779ppU5I0eB35/wIrqqr4nM/o0oHcIYzxjJ2oi0kRoaIfqxyFsVhHlc7pScXfvrarG7PVHT7G5Ph/oMkT7OklLsLhcetQd536vAo/bA7nLhLClNeBmd1dcM9QyJqq1pbvNKbY1IKwlohOjHSnKKaPG3Rk3z+lq6vIFkopwlpQRbvFHTgi3ebh0sRe/Kq5hI0Osl4G0mFAoR8DYT9HrJq5iY8DI6G0xxvXdDe/bPZrORm+XB43SzomZlL34iITonl5yE6Mdib1XQ4m8lGPJzwOCpPV52Z8PtF06b3uNli9QIjyAcWbhdOG16ty8JxquveafqPamtEX2KBDRC9GPxeq8cvPu+ePw97+WUqoOl6F2xIwi3VlWyad7cHvdM66y2xml38NqqBTJmjdjhJKARop+LPbsuK86npqYxJcvubLh90TelsmdabPavuc3LptZaQiFw2pxRY9bI/b7EjiA1NEIIMUBE9kyz2Ww4PLnYPR6ali/r9rJia2tyszwUZRVS5i5tr6vxB/1s8NYw+4u/8dqqBVIwLHqVZGiEyBAy/LzoKX9dLY7ikqhp4Z5pyQySGJn9KyvL565/P0a+Mw+ALVsbWb3lW5x2J8FgSLI1otdJhkaIDCDDz4tU6KxnGk5n1E0sw5eiWqsqu7X8yF51670bcdqdgA2Py/SGkl5QojdJQCNEBogcIM9ms8nBQSSls27chEjJpajIMWta/K2EQuAL+hiaOxiQXlCid0lAI0QGiDdAnhwcRHeFe6Y5PLkE6utweHIpnnkYBPxdDpIY7hm1/om/sGne3E4zN5F1NQA2G+xSuBMFWflA9B28hUg1qaERoo+KrJnZ1FKLP+hjsKes/Xk5OIhkxOuZ5iwpNZebrNtXwLZBErvbMypcVxPuBeW0OQmFQrT4W/H6W5haPrnXP6MYmCSgEaIPir2ppC/gY/XmKgDK3IPSenCQO2z3P10NkpjsPbu6uoO3EL1BAhoh+qDYm0oOyTWZmYatW3DaXd06OMQGIO4Z0yEvudsTyB22+6euBklseGtBpz2jtqezO3gL0RskoBGiD6prbegwrPxgzyBcDhenjz054eXEC0DWzXsF9/QZSQUgcoft/quzQRK7uhwlRF8iRcFC9EHxbiqZTM1MvIHUnLm5SQ2kBnKH7YEoFTe4FGJHkAyNEGkWb8C8eDeVTKZmJt5Aag6PB//a9Um1Vc7WBx65Z5fIFBLQCJFGscW/kaOppqKgMl4AEvAmH4DIHbYHph19zy4ZFVskQwIaIdIotvg3/HdFzUqO3GVmj3fi8QIQf9BH3vQZSS1PztZFb+sqyJegRnRFAhohdrDIs8/qprXslD8ScLc/n8oB8+IFIOUzptOSZC+n8DIlgBG9pasgXwIa0RUJaITYgWLPPr9r3sDXDavYvXjXXhtNNTYAySvLp6WmMWXLFyKV4vXwk1GxRSKkl5MQO1DsPZlG5pVjw0ZV41pCIXNHYq+/hQll49PdVCHSIl4Pv5qWTWxqqWX25y/w2qoFclNWEZcENELsQLH3ZCrIzme3wtH4gwHqt27G43JLrYDIGJH3eKr86/Pdvjt3PJE3uAyFQmz01rB6cxWFWQVyp3nRJbnkJMQOVJJThNfX0l4XAOByuJhQNo4jd5mZxpYJ0T2xgzb6m5ppWjAfz97fw7dubdK3xoi9ZULD1i3sXDCyfbRsqakRnZEMjRA7UOzZp1xiEpkqdtBGZ14eoUCA+tdeMUMFRNwao7uZmxH55Ry5y0xOH3syg9ylDPYMinpeampEPBLQCLEDhc8+PS63XGISGS3eqNG++npCgUDUyNR2jyfpkakhdaNmi/5PLjkJ0Qu6GhhMbtgn+oO4o0Y3NeLIy4+ar6e3xkjVqNmi/5MMjRAptmz9Cp7+/HmWbVhBjXcTG701UsQo+p3Yezz5m5qwORw4iovb5/Fv3oz3s//SWvktm+bNTapoWLKaIlGSoREihaob1zH/24WAjfysPHxBP+uaN1CeO6THRYytVZVRA+R1t9hSiFTqMGjjyGEUH3kM3k//Y25g2eaj9Wtt5t1dtdfTFM88rNvbrWQ1RSIkoBEihVbUrCQYCpLrNLUFLrv5idW3bsZpdyW93NgeJT05OAiRKpGDNpaV5VNT00j20KE0LV9Gy1fLsbnd5IzaCWfBtoHympYvk21W9AoJaIRIobrWBvJcufiCPlw2E8C47E4a25pQObslvdzIHiVA+185OIi+JhzkhO/0brPZ2p/raT2NEF2RGhohUqgkp4jCrAL8QT++oM90zfa34rQ7etQ1O16PEjk4iL7MWVJKsMUbNS3Ykvyd3oXYHglohEihCWXjcdgdDPUMwWV30ez3AiEO3WlGj2oA5OAgMk1s0XDA20zQ6yWvYmK6myb6KQlohEihcI+MIbllDHKXUjF4b3469hQmDp3Qo+XKwUFkmnDRsMOTS6C+DocnV2q+RK+SGhohUqw3emR06FFSUkrhtOlycBB9Wuyd3oXoTRLQCJEh5OAghBCd63ZAo5QqBQZrrb+ImDYauAQoAZ7WWv8zdU0UQgghhOhaMhmae4HdgSkASqk84F0gnGP/kVLqB1rrRalpohADkwykJ4QQiUsmoJkKzI54/CNMMHME8B/gTeByQAIaIRIQL3ABZCA9MWBJMC+SkUwvpyFAVcTjw4GPtdbztdbrgSeBfVLQNiH6vfAIwAFvc1Tg0vDO2+0D6aXqrsVCZILOfhPJ3AdKDCzJBDQ+wB3x+PvAvyMeNwAyOIYQCYgcATgycGld/Y0MpCcGpM5+ExLMi+1JJqD5CjhRKWVTSh2DKQReGPH8SKAuFY0Tor/rbARgQAbSEwOSjIotkpVMQPMAJitTD7wErCI6oDkQ+G/PmyZE/9fZCMA5u+wqA+mJAUlGxRbJ6nZAo7V+GvgpJoh5Bjhca+2D9i7dRcALqWykEP1VZyMAFx30AxllVQxI8X4Tvpoa/Js3s/6Jv7Bp3lyppxFxdauXk1LKAQwHXtNaz459XmtdC8gppBAJ2t4IwBLAiIEm9jeB00mIEDaXE3tBgfT4E53qbrdtF+YS0xXA7alvjhADj4wALES0yN/EpnlzsTmdODy5AO1/m5Yvk9+NiNKtS05a61ZgE9DcO80RQgghtpEiYZGoZIqCXweOSnVDhBBCiFhSJCwSlUxAczkwTCn1lFJqL6VUTqoao5S6XCkVUkr9J1XLFEIIkbk6K5yXHn8iVjK3PtgIhIAJwE8AlFKx84S01t0tOB4KXI1czhJCCGHZXuG8EGHJBDRPYwKaVLsF+BiTNSrqheULIYTIQFI4LxLR7YBGa31mqhuhlJqCyfZMAu5J9fKFEEII0b8lU0OTUkopG3Af8JTWWmpnhBBCCNFtyVxyCg+wdxowE3P37cu11p8opYqBo4GFWuu1CS7uDGAscFwybRGiu6ob17GiZiV1rQ2U5BQxoWw8I/LL090sIYQQPdDtgEYp5QEWAPtjCng9QLH19BZMLczjmALf7S0r35r/Fq31d91tS6TS0ryevLzPKivLT3cTMkYi6+rb+mre3/ghuVkehnsG4/W18P7GDzm6+BB2Kh6xA1rZN8h2lThZV4mTdZU4WVepl0yG5npMrcvxwAfAhvATWuuAUmoOcCgJBDTWPG3AXUm0I0ptbRPBYG/UKqdPWfSqpbwAAB8fSURBVFk+NTWN6W5GRkh0Xb2zagl2vxObzUGLrw0bDux+J+98tYQjdyncAS1NP9muEifrKnGyrhIn66prdrstqSRFMgHNLOARrfU862aUsf4H/Gh7C1FKDQMuBq4BhkR0/c4BspRSOwObtdb1SbRRiLjqWhsozo4OXNzOHOpaG9LUIiFEJmmtqozqQp5XMVF6YPURyRQFlwMrunjeCySSSxsCZAG3Aqsj/u0L7Gn9/7dJtE+ITpXkFNHib42a1uJvpSRHRgoQQnSttaqS+gXzCXibcRSXtN8oU+7+3Tckk6GpxdxxuzPjgHUJLGc15rJVrJuAXOA3wFfdbp0QMSKLgJ12B/WtmymjFLczhxZ/K15/C1PLJ6e7mUKIPq5p+TI2Ftj4KreOBvt3FGVls7vTjUtulNknJBPQLAR+ppS6I/YJpdRo4Cxg9vYWorXeDPw9zjIuBvxa6w7PCdFd1Y3rWFi5CI/TTXF2IS3+Vmw28Af91G/dTElOEVPLJ0svJyHEdq1tXMviQV7cISeFoSxabH4W59ez36atDEp340RSAc0NmBF9PwL+ihk1+DCl1A+B84GtwB9T1kIhemBFzUo8TjcelxsAj8vNIErxuNwcucvMNLdOCJFJvioJku0L4XaaQ6cbJ0Gfj69KgkxIc9tEciMF/08pNQPTNfv31uRLrb8rgdO11lXJNkhrfVCyrxUiVl8sApaiQiEyU/PgPLK/bSIYasPmchHy+cj2BWjeqX8OG5JpkhpYT2u9DJiglBqPKeC1AV9rrT9JZeOE6KmSnCK8vpb2DA2ktwg4XFRo93iiigqLZx4mQY0QfVxZyQi22LKwb6wj2OLF7vYQHD6UsuLB6W6aILmB9aYDX2ita7TWKzFZmcjnBwFjtdaLUtRGIZI2oWw8CyvNprgji4A7y8I0LV9mghlPLkD73yYpKhSiz5tQNp6FLYtw7rITudb+pM3fwoSy8elumiC5btvvAD/s4vkZ1jxCpN2I/HJmjJqOx+WmfutmPC43M0ZN79Ui4K66dvrrarG7PVHz290e/HW1vdYeIURqpGN/IhKXzCUn23aedwDBJJYrRK8YkV++Q3c4XWVhnCWlJtCxpgEEW7w4S+KNUSmE6Gt29P5EJC7Zu213dY+B/YFNSS5XiIzXVRYmr2IiQa+XgLeZUChEwNtM0Oslr2JimlorhBD9Q0IZGqXUr4FfR0y6Ryl1c5xZi4ECTA8oIQakrrIwOSNHUTzzsKj6msJp06V+RggheijRS04NwLfW/3fGjBa8IWaeEKZAeDFwdyoaJ0QmcpUPp+m1VwgFAtjz8nEVF2NzOCicNh2AnJGjJIARQogUSyig0Vo/BTwFoJRaDfxOa/1KbzZMiEzUWlWJ99P/4CofTqC+nkBTI20tXoqPPEaCGCGE6EXJDKw3ujcaIkR/EC4IdnlyYchQAALeZnzr1qa5ZUII0b8lNbAetI9HMxNz1+w7tdZfKqXygArgU611+oZiFSJN/HW1OIpLoqZJt2whhOh9yQys5wCeA07CdOEOYe7p9CXgx9xw8g7gD6lrphCZQbplCyFEeiTTbfu3wInAJWy77QEAWutWYC5wREpaJ0SGkW7ZQgiRHskENGcAT2ut7yX+eDNfALv2qFVCZKhwt2yHJ5dAfR0OT67cp0kIIXaAZGpodgbu7OL5Bsx4NEIMSNItWwghdrxkMjSNQEkXz+8G1CTXHCGEEEKI7ksmQ/Me8BOl1G2xTyilioGzgPk9bZgQQgjRn1Q3rmNFzUq8q5rxkMuEsvFyX6gUSiZDczMwBngbOMqaNkEpdR6wHMgFbklN84QQQojMV924joWVi/D6Wij1FOP1tbCwchHVjevS3bR+o9sBjdb6Y0wvpz2AJ6zJdwAPAm7geK315ylroRBCCJHhVtSsxON043G5sdlseFxuPE43K2pWprtp/UZSA+tprV9TSu0M/JBtXbe/Bv6ptfamrnlCCCFE5qtrbaA4uzBqmtuZQ12rjEGbKkmPFKy13gr8w/onhBBCiE6U5BSxpX4jzo11tPq2EnRl4x9cQknx4HQ3rd9IpoZGCCGEEN2wZ2AQm6tX0+xvwe7Jodnfwubq1ewZGJTupvUbSWVolFI/Bn6JKQ6ON6Z7SGuddPZHCCGE6E8KPv+WqW1D+Sq3hQZ85Dnc7NNaQsHn38KYinQ3r19I5l5OVwM3ABuAD4D6VDdKCCGE6E/8dbWUF5cy3GcjNyubZt//t3f/UXbX9Z3Hn/MjZuYmMcmEWSAmEViPb+lGgURQu5BKsYgWf9HS48FfIOpadKHWVrcrVURt/S3WFtaqraDbHqRYVqxiJIgpcqhrgtF41s+KwiY5wRpnEszkzoRMZvaP7/fGm2Eyc2cyc7/3O/N8nHPP5H6+3xne98Pk5nU/38/n+znI6IJRN66dQdMZRbkKuBe4KKV0aGbLkSRp7nHj2tk3nTk0Twa+ZJiRJKkxR21cOzLixrWzYDqB5kFg9UwXIknSXFW/ce3jfX1uXDsLpnPJ6Vrg9oi4PaX04EwXJEnSXFTbuLa3dwl79uwvupw5Z8qBJqX07Yi4EnggIh4AHgEOjzltNKV05QzUJ0mSNKnprHJ6DnAzsAA4L3+MNQoYaCRJUlNM55LTJ4HHgZcB/5pS8r7NkiSpUNMJNM8Crksp3TnTxUiSJE3HdFY5/YJshEaSJKklTCfQ/B3w6ohwawNJktQSphNK7gMuJlvldCPwME9c5URKafNx1iZJktSQ6QSau+v+/FmyFU312vK2jukWJUmSNBXTCTRXzHgVkiRJx2E6N9a7eTYKkSRJmq7pTAqWJElqKdNaqRQRi4B3AK8ATsubfwZ8GfhISunAzJQnSZI0uSmP0ERED/Bd4M+BE8l2334w//O7ge/m50iSJDXFdC45XQ88A3grsDKldF5K6TxgJfAWIIDrZqxCSZKkSUznktNLgc+mlG6sb0wpHQZuioizgJcDV89AfdKMG9q5g4GtWxju76OzZwWL162na/WaosuSJB2H6YzQ1C4zHcvW/Byp5Qzt3MHejXdxuHqAjuU9HK4eYO/GuxjauaPo0iRJx2E6gebfgbMmOH5Wfo7Ucga2bqG9UqGjsoi2tjY6Kotor1QY2Lql6NIkScdhOpec7gT+S0RsBT6TUhoBiIh24A3A64FPz1yJ0swZ7u+jY/nRc9bbuysM9/cVVJEkaSZMJ9C8G/gd4EbgvRGR8vYAeoGHgPfMTHnSzOrsWZFdbqosOtI2Mlils2dFgVVJko7XlC85pZT6gGcDHwT6gLPzxy+BvwTOzs+RWs7idesZqVY5XD3A6Ogoh6sHGKlWWbxufdGlSZKOw7RurJdS+hXwrvwhlUbX6jUsv/Cio1Y5LT13g6ucJKnkphVopDLrWr3GACNJc8ykgSYiNkznB6eUNk/n+yRJkqaqkRGae4HRKfzMtvz8jukUJEmSNFWNBJorZr0KSZKk4zBpoEkp3dyMQiRJkqZrOncKliRJaimNTApeA5BS2lH/fDK18yVJkmZbI3NoHgFGI6I7pfR47XkD3+ekYEmS1BSNBJrryQLM8JjnE2k7nqIkSZKmopFJwddFxNraJpQppesm+56I+NQM1CZJktSQRicFfyMiTmnkxIj4K+CqaVckSZI0RY0GmsXA3RFx4kQnRcQNwFuBbxxvYZIkSY1qNNC8FFgJbIyIZeOdEBEfB64mCzMvn5nyJEmSJtdQoEkpfRv4A+B04GsRUak/HhEfA/4I2Ai8LF8NJUmS1BQN77adUvpqRFwOfAG4IyJ+N6V0KCI+ArwN+CZTCDMRcTZwOXA+8FSgD7gfuDal9NCUXoUkSZrXpnSn4JTSP5DNkXkB8I8R8WHg7cAmsjBzcAo/7p3AJcDdwDXA3wLPBx6MiNOnUpckSZrfGh6hqUkp3ZTPo/kA2f1oNgEXTzHMAHwcuKx+RCcibgV+SBZ2Lp9qbZIkaX5qKNBExB+PaToI/Aw4Cfg28JaIqD8+mlL6xEQ/M6V0/zhtP4mIH5HN1ZEkSWpIoyM0H53g2PXjtI0CEwaa8UREG3AisG2q3ytJkuavRgPN+bNaxa+9CngK8K4m/fckSdIc0DY62sg+k7MvIp4B/BvwA+C3alstNOAU4OHZqkvlN/DwI/Q/8AAH9/yShb0n0PPc57L41FOKLkuSNLFTyTbEbkhLBJqIOAn4DtkO3c9NKf18Ct9+CvBwX98AIyPFv5aZ1Nu7hD179hddRikcq6+Gdu5g78a7aK9UaO+uMDJYZaRaZfmFF9G1ek0BlRbP36vG2VeNs68aZ19NrL29jRUrFsMUA82Ulm3PhohYCnwdWAq8cIphRprQwNYttFcqdFQW0dbWRkdlEe2VCgNbtxRdmiRpBhUaaCKiC7gTeDrZ0u9UZD2ae4b7+2jvPurG1rR3Vxju7yuoIknSbCgs0EREB3Ar8Dzg0pTSA0XVormrs2cFI4PVo9pGBqt09qwoqCJJ0myY8o31ZtDHyDa9vBPoiYhX1x0bSCndUUxZmksWr1vP3o13ARw1h2bpuRsKrkySNJOKDDRn5l9fkj/q/T/AQKPj1rV6DcsvvIiBrVsY7u+js2cFS8/dMG8nBEvSXFVYoEkpPb+o/7bml67VawwwkjTHFb7KSZIk6XgZaCRJUukZaCRJUukZaCRJUukZaCRJUukZaCRJUukZaCRJUukZaCRJUukZaCRJUukZaCRJUukZaCRJUukZaCRJUukZaCRJUukVttu2JEkqj137d7Ntz3b6h/bR07WMM3rXsmrJyqLLOsIRGkmSNKFd+3ezacdmqocGWb5wKdVDg2zasZld+3cXXdoRBhpJkjShbXu2U+nsprKgm7a2NioLuql0drNtz/aiSzvCQCNJkibUP7SP7s6uo9q6O7voH9pXUEVPZKCRJEkT6ulaxuDw0FFtg8ND9HQtK6iiJzLQSJKkCZ3Ru5bq8CDVQ4OMjo5SPTRIdXiQM3rXFl3aEQYaSZI0oVVLVnLBmg1UFnSz9+BjVBZ0c8GaDS21ysll25IkaVKrlqxsqQAzliM0kiSp9Aw0kiSp9Aw0kiSp9Aw0kiSp9Aw0kiSp9Aw0kiSp9Aw0kiSp9LwPTZMN7dzBwNYtDPf30dmzgsXr1tO1ek3RZUmSVGqO0DTR0M4d7N14F4erB+hY3sPh6gH2bryLoZ07ii5NkqRSM9A00cDWLbRXKnRUFtHW1kZHZRHtlQoDW7cUXZokSaVmoGmi4f4+2rsrR7W1d1cY7u8rqCJJkuYGA00TdfasYGSwelTbyGCVzp4VBVUkSdLc4KTgJlq8bj17N94FZCMzI4NVRqpVlp67oeDKJEmaWKsvanGEpom6Vq9h+YUX0VFZxOG9/XRUFrH8wota6hdCkqSxyrCoxRGaJutavcYAI0kqlfpFLcCRrwNbt7TMv2mO0EiSpAmVYVGLgUaSJE2oDItaDDSSJGlCi9etZ6Ra5XD1AKOjoxyuHmCkWmXxuvVFl3aEgUaSJE2oDItanBQsSZIm1eqLWhyhkSRJpWegkSRJpWegkSRJpWegkSRJpeek4Aa0+v4VkiTNd47QTKIM+1dIkjTfGWgmUb9/RVtbGx2VRbRXKgxs3VJ0aZIkKWegmUQZ9q+QJGm+M9BMogz7V0iSNN8ZaCZRhv0rJEma7ww0kyjD/hWSJM13LttuQKvvXyFJ0nznCI0kSSo9A40kSSo9A40kSSo9A40kSSo9A40kSSo9A40kSSo9A40kSSo9A40kSSo9A40kSSq9Qu8UHBELgeuB1wDLgW3Au1JKm4qsS5IklUvRIzSfB94GfBG4BhgBvh4RzyuyKEmSVC6FjdBExDnAK4G3pZRuyNtuAbYDHwI2FFWbJEkqlyJHaH4fOAR8ttaQUhoCPgecGxEnF1WYJEkqlyIDzVnAj1NKA2Pavwu0AWc2vyRJklRGRQaak4FHx2mvta1sYi2SJKnEilzl1A0cHKd9qO54w1asWHzcBbWi3t4lRZdQGvZV4+yrxtlXjbOvGmdfzbwiA80gsHCc9q664w3r6xtgZGT0uItqJb29S9izZ3/RZZSCfdU4+6px9lXj7KvG2VcTa29vm9YgRZGXnB4lu+w0Vq1tdxNrkSRJJVbkCM33gWsiYvGYicHPyb9uK6CmWbdr/2627dlO/9A+erqWcUbvWlYtcbqQJEnHo8gRmn8CFgBvqDXkdw6+AvhOSmnOjdDs2r+bTTs2Uz00yPKFS6keGmTTjs3s2j/nXqokSU1V2AhNSunfIuI24MP5PWd+CrwOeCpweVF1zaZte7ZT6eymsiCb71z7um3PdkdpJEk6DoXu5QS8Fnhf/nU58APgxSml7xRa1SzpH9rH8oVLj2rr7uyif2hfQRVJkjQ3FBpo8jsD/2n+mPN6upZRPTR4ZGQGYHB4iJ6uZQVWJUlS+RW9OeW8ckbvWqrDg1QPDTI6Okr10CDV4UHO6F1bdGmSJJWagaaJVi1ZyQVrNlBZ0M3eg49RWdDNBWs2OH9GkqTjVPQcmnln1ZKVBhhJkmaYIzSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0DDSSJKn0OosuoAx27d/Ntj3b6R/aR0/XMs7oXcuqJSuLLkuSJOUcoZnErv272bRjM9VDgyxfuJTqoUE27djMrv27iy5NkiTlDDST2LZnO5XObioLumlra6OyoJtKZzfb9mwvujRJkpQz0Eyif2gf3Z1dR7V1d3bRP7SvoIokSdJYBppJ9HQtY3B46Ki2weEherqWFVSRJEkay0AziTN611IdHqR6aJDR0VGqhwapDg9yRu/aokuTJEk5A80kVi1ZyQVrNlBZ0M3eg49RWdDNBWs2uMpJkqQW4rLtBqxastIAI0lSC3OERpIklZ6BRpIklZ6BRpIklZ6BRpIklZ6BRpIklZ6BRpIklZ6BRpIklZ6BRpIklZ6BRpIklZ6BRpIklZ6BRpIklZ6BRpIklZ6BRpIkld5c2G27A6C9va3oOmbFXH1ds8G+apx91Tj7qnH2VePsq2Or65uOqXxf2+jo6MxX01znAv9adBGSJGlGnQfc1+jJcyHQLATOBh4FDhdciyRJOj4dwMnA/wYONvpNcyHQSJKkec5JwZIkqfQMNJIkqfQMNJIkqfQMNJIkqfQMNJIkqfQMNJIkqfQMNJIkqfQMNJIkqfTmwl5OpRQRJwPXAM8Bng0sBs5PKd07zrkvBa4DfgP4BfA54AMppeFm1VuUiDgbuBw4H3gq0AfcD1ybUnpozLm/CXwYWAf8CrgV+LOUUrWZNRclIp4NvIvs9f8H4DHg+8D1KaX7x5w7r/tqPBHxDuBDwLaU0pljjs3b/oqI5wPfOsbh01NKP647d972U738fes64DeBBcBPgU+klD5fd868fV+fLQaa4gTwTuAh4Adkv/hPPCniRcAdwD3AfwWeCbwbOCF/Pte9E/jPwG1k/XQS8FbgwYg4J6X0fwAi4kxgE/Aj4I+BVcCfAKcBLymg7iL8R7K/058h2wpkGfAqYHNEvCil9E2wr8YTEScB1wIHxjlmf2VuALaMadtd+4P9lMnfs/8XcC/w58Ah4OnA6jHnzOf39VlhoCnOFuCElFJfRLwc+OdjnPdR4EHghSmlwwAR8SvgzyLir1JKP2lOuYX5OHBZSunxWkNE3Ar8kCzsXJ43/wXZ6M3zU0oD+XmPAJ+JiN9OKd3TxJoLkVK6lewT8RERcRPwM7LRwG/mzfO+r8bxQeB7ZJfhl405Zn9lvp1SumOC4/O+nyJiKfB54KaU0jUTnDrf39dnhXNoCpJS2p9S6pvonIj4DbLhyE/XfulzN5L9v/u9WSyxJaSU7q8PM3nbT8g+BZ4OEBFPBn4HuKX2Rpq7BRgA/qBJ5bacfKh/D/k/0vbVE0XEOcCryUYVxh6zv+pExJKIeMIHYfvpiMvI/q69G470V1v9Cb6vzx4DTWs7K//6vfrGlNJuYFfd8Xklf4M4Efhl3vRMstHGsf30ONkcknnVT/mb6AmR+QtgLdmlALCvjpL/Ln0KuDml9P1xTrG/fu0LZPNiBiNiY0Q8s+6Y/ZR5AfBj4MURsZOsv/oj4oMR0ZGf4/v6LDHQtLaT86+PjnPsUWBlE2tpJa8CngJ8KX9uPx3t78lGZX4MvB34H2SXA8C+Guu1ZJ+Wrz3GcfsLHgf+ieyy5cuA9wLnAPdFxNPzc+ynzNPI5sp8Pn/8Htl0gncCH8vPsa9miXNoWlt3/vXgOMeGgEoTa2kJEfEM4G+A+8g+McLk/dQ9Tvtc9l7g02STMl8DLCRbaXEQ++qIiFhCNnfmgyml8f5xAfuLfIVc/Sq5r0TEnWQjDO8h+4Ax7/sptxhYDvy3lNKH8rYvR8Ri4KqIeD++r88aR2ha22D+deE4x7rqjs8L+UqUfwH2ApemlEbyQ/ZTnZTSD1NK30wp/T3wQmA92adFsK/qXUs2+vDxCc6xv8aRUtoG3A1ckDfZT5na6/zHMe3/k+xDxTnYV7PGQNPaap8aTx7n2MnULZmc6/LVA18HlpKtDPh53WH76RhSSofIlpBeEhHd2FfAkftA/RHZaN+JEXFKRJxC9g/Kk/Lny7G/JrIT6Mn/bD9lav3w72Paa8/9nZpFBprWVpuk+Oz6xohYSXY5YbxJjHNORHQBd5Ldy+HilFIac8p2YJgn9tOTgDOZJ/00gW6gDViCfVVzIvAkshvpPVz3eA7Z6rmHyeY92F/HdhrZXC2wn2pq9+l5ypj2VfnXPfi+PmsMNC0spfQjsomdb6qbIQ/wh8AIcHshhTVR/rpvBZ5HdpnpgbHnpJQeIxv+fk1+rbrmNWTXtG9rRq1Fi4jecdqeDFwK7Ewp/cK+OuJh4BXjPH4EPJL/+Rb765i/V+eS3b37G+DfwTq113llrSFfSfcGsps2PuD7+uxpGx0dLbqGeSsiaisrTie7f8Hfkb3R7ksp/XV+zsXAV8juKHkr2RLct5Ldw+CqphfdZBFxA9nqijv59aqmmoHajb4iYh3ZxMXtwGfJPum8HfhWSunFzau4OBFxD9mkwvuBn5OttriCrC9emVL6Un7evO+rY4mIe4Fl9VsfzPf+yn+vqmR98Euy96A3kW2tcXZKaUd+3rzup5qIuJksyH0O2Ar8bv54R0rpI/k58/p9fbY4QlOs9+WPy/Lnr8+f/0nthJTSV4FLgBVk98u4BHg/cHVTKy1O7R+Wl5Ctaqp/3FA7KaW0leweEAeBTwBvJNsC4NJmFluwL5KtkLgauAm4CthGtkfYkTBoX02N/cUdQC9ZOPkbsqXI/0BdmAH7qc4bgQ+QTcj/JNlS7jfXwgz4vj5bHKGRJEml5wiNJEkqPQONJEkqPQONJEkqPQONJEkqPQONJEkqPQONJEkqPQONJEkqPQONJEkqvc6iC5A0P+W7We8m2+H6tSmlLxRckqQSc4RGUlFeBSwk27/s9QXXIqnkDDSSinIl8C2yPbl+KyJOK7geSSXmJSdJTZfvzHwm8Drga8BHyUZprh1zXgfw34E3ACcC/5ds47/TgfcAp6aUHqk7/2Tg3WS7G59Etjv0V4FrU0q/mNUXJalQjtBIKsKVwABwe0qpFjpeFxFj35P+Grge+Cnwp2Q7P98IXDz2B0bEGuB7wO+T7Qb9FrJd2V8JfCcils7OS5HUChyhkdRUEdEFXEYWZg7kzTcDrwBeCHw9P+8/AW8GvgG8OKU0krffBnx/nB/9KWABcFZKaVfdf+824AHgbcB1s/CSJLUAR2gkNdslwDKyEFPzNWAPR08Oro3CfLIWZgBSSj8kCzlH5KMvFwNfAYYi4oTaA3gEeAi4cIZfh6QW4giNpGa7kiy87IqIp9W1bwQujYgT8stQp+btaZyfkYAX1T0Psg9oV+aP8fzsuKqW1NIMNJKaJiJOBc4H2sgm+I7n1WQrn6aiLf/6RY4e+ak3OMWfKalEDDSSmukKsvDxRmDfOMffT3bZ6QayS0WQjb6MHV2JMc8fAkaBJ6WU7p6pYiWVR9vo6GjRNUiaB/IVTI8A+1JKzzrGOe8hm7h7DlAFtvPEScHPJJsU3E7dsu2I+CrZpOLzUkoPjPm5bcAJKaU9M/7CJLUER2gkNcuFwGrgcxOccztZoLkypfTmiPhb4E3A3RHxz0Av2XLsB4H1ZKMyNX8I3Adsjohb8nPagdOAlwG34Conac5ylZOkZqlN1v3ysU5IKW0nm1vzyojoBq4iCyFPI7v53svJgsu9+bcM1n3vTrKQ80lgA/Ax4H3AC4A7gS/N2CuR1HK85CSpdCLiTuC3gSenlA4XXY+k4jlCI6ll5aM0Y9ueRbZk+x7DjKQa59BIamWvi4jXAv9Cdu+aZ5DNqXmcbM8mSQIMNJJa21ayLRGuBnqA/cA9wHtTSg8WWZik1uIcGkmSVHrOoZEkSaVnoJEkSaVnoJEkSaVnoJEkSaVnoJEkSaVnoJEkSaX3/wGueqSJpAlteQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 648x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Get predictions for the training data and plot\n",
    "training['preds'] = model.predict(training['age'])\n",
    "\n",
    "plt.figure(figsize=(9,7))\n",
    "plt.scatter(training['age'], training['kilometers'], alpha=0.5, c='r')\n",
    "plt.scatter(training['age'], training['preds'], alpha=0.5, c='g')\n",
    "plt.title('Predicted and True Kilometers by Age for Training Data')\n",
    "plt.xlabel('Age')\n",
    "plt.ylabel('Kilometers')\n",
    "plt.legend()\n",
    "plt.show();\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept          -4.182212\n",
       "np.power(age, 2)   -0.006509\n",
       "age                 0.515704\n",
       "dtype: float64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vemos que el modelo se adapta mucho mejor a los datos, aunque aún hay margen de mejora. Podemos emplear un modelo más complejo, con un polinomio de grado 5 con un término logarítmico y una raiz cuadráda (un número elevado a 0.5):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:             kilometers   R-squared:                       0.952\n",
      "Model:                            OLS   Adj. R-squared:                  0.941\n",
      "Method:                 Least Squares   F-statistic:                     90.42\n",
      "Date:                Thu, 13 Feb 2020   Prob (F-statistic):           2.94e-19\n",
      "Time:                        15:08:04   Log-Likelihood:                -20.183\n",
      "No. Observations:                  40   AIC:                             56.37\n",
      "Df Residuals:                      32   BIC:                             69.88\n",
      "Df Model:                           7                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "======================================================================================\n",
      "                         coef    std err          t      P>|t|      [0.025      0.975]\n",
      "--------------------------------------------------------------------------------------\n",
      "Intercept          -2296.4742    676.221     -3.396      0.002   -3673.891    -919.058\n",
      "np.log(age)        -1742.4847    537.069     -3.244      0.003   -2836.458    -648.511\n",
      "np.power(age, 5)   -2.994e-06   7.58e-07     -3.951      0.000   -4.54e-06   -1.45e-06\n",
      "np.power(age, 4)       0.0008      0.000      3.914      0.000       0.000       0.001\n",
      "np.power(age, 3)      -0.0872      0.023     -3.820      0.001      -0.134      -0.041\n",
      "np.power(age, 2)       5.8616      1.602      3.658      0.001       2.598       9.125\n",
      "age                 -418.5504    121.303     -3.450      0.002    -665.637    -171.464\n",
      "np.power(age, 0.5)  3158.9882    944.255      3.345      0.002    1235.604    5082.373\n",
      "==============================================================================\n",
      "Omnibus:                        0.049   Durbin-Watson:                   2.769\n",
      "Prob(Omnibus):                  0.976   Jarque-Bera (JB):                0.249\n",
      "Skew:                           0.018   Prob(JB):                        0.883\n",
      "Kurtosis:                       2.615   Cond. No.                     5.68e+12\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 5.68e+12. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjQAAAHQCAYAAAC2tvAKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAAIABJREFUeJzs3Xt8U+X9wPFPLr0kbeldbi2CTh4FHLNcFEWm4g/vIirO25zTzcvmnHPq5l3n3HTqxKnzNq+oc6igbipDUYcXEAWHw8uDikgrIqUXaJuUJk1+fzwnJUnTNk3TJm2/79eLV8nJyck3JyfnfM9ztQWDQYQQQggh+jN7qgMQQgghhOgpSWiEEEII0e9JQiOEEEKIfk8SGiGEEEL0e5LQCCGEEKLfk4RGCCGEEP2eJDS9RCl1plIqqJQ6qLNl6UQptUEp9Uaq44hFKXWQte/OTHUs6UQptVkptThq2Qql1KepimkgUkqdZx1/+6U6lnSilLpIKbVOKdVi7Z9hqY6ptyil5lmfsSDB1xdYr5+X7NiE4Ux1AMliJQmvRy1uAjTwGHCX1rq1r+NKFuvzHQTM01rXpzaa9NTBMdCRr7TWo3svmsQopZ4CfgDkaa0bw5bbgbuB84B/AD/UWvtSE2VyKaVKgAuAV7XWb6U6nnSjlNoHWG09nKq1fi+V8YQopY4AbgeeAf4A+IFeOzcppbIBbzdeMlxrvbm34umvlFIXYb63ED+wDfgSeBd4RGv9fg/f43BgP+AmrXVzT7bVHQMmoQnzd+AlwAaMAM4E5gHjgXNSFxYA84GngJYEXnsQcC3wCL140ujnPgF+GLXsHOBA4FfA1rDljfQTSqkM4FHgFOA+4Gda64D19K5AoKPX9hMlmGO7GZCEpr2zgTrr/2cBaZHQAP9n/T1Ta93UB+/XQvvf9yHAjzHJ/oqo55J9nrwE+G2iF2itdb1SyoVJINLBTcBHmJqaQmBv4FTg50qp+zHnmUQLAQ4Hfom59kpC0wOrtdaPhx4ope7BXOh+opS6Wmv9bawXWRcNR29mk9bB0W9LidKd9d0+Hr5MKXUoJqF5Tmu9IZ7tKKUyAZvWekfSg+wm6wT4NHAU5m7n8vDn0yHGdKeUytNaN6Q6jkRYpRKnAU9ibtJOVUpdrLXuTklFbxkG7Eh2MqOUclvbjThXWkl89O87F5PQvKW1firO7dsBV3fj1lr76WEy0pelFXFYqrV+NXyBUupizD4+B6gFLo/1wnQ1EBOaCFrr7Uqp5cAJwG7At0qp6zB3hBMwdz8nAcOBmcAb0HYhvAyYCmQD64C/aq3vjX4PpdRPgV8DY4BK4C5MEV70emcCDwMHa63fCFueCVyEyY7HAj7gM0zR311KqUeAH1mrf6mUCr30eq31ddY28oErrM9ZDmwHXgWu1Fqvj4qjHLgNOAxzkvyP9f5xsU4Il1uvHwsUAZuBF4GrtNY1YeuOxhRlXg+8j9nve2PuOB8HLrdOFOHbnw1cB+wFVGNKpZbFG193KKVuAn4DKEy1xwmYE/UBSql6TDJ8udb6pg5eF1GsrZQqA64BjgCGWvE/D1wdvl/ijG0I8E9gBnCZ1vqWGOtsBv6rtT48ju0dAlwJTMH89j8G/qK1fixqvRVAASaJuh34PiYRfxZz17UDuApzIRkG/A/4udZ6ZdR2HMDPrfWUtY13Mcftm9Y6hwMvWy/5o1Lqj9b/tdZ6z7BtnYb5fvbG3FH+F7hZa/182DqhKon7gOcw38NE4E3gcKVUqbXsKEzpbSOwAZivtb6jq/1nyVRK3QicAZQCnwK/01ovDIvjU8zN0R7RL1ZK/RBTBf4DrfWCON7veMx38aj1+HzMMfp49IrWxf0PWFWWmH30W+BnwHFa6+yo9fcCrsac9wqBKmAB5vvpMGFSSu2J+V2EHofmz/l36DhUSlVgfsPTATfwOfAgcEdY6WKoivU4YDTwJ8ydfQnm++lxdZFS6jhgETvP/+dgztOXAvOUUjOsZdOs9/Rhqvf+qLX+d9S25mGO/8JQtX/YsjJMCc7JmPPhh8ClUef5Asx57w6t9UXRyzC/9RuAfYAGzHdxSXQSZFX13YC5ftVgSv4XYUqofqW1TriNjnW9PAX4ArhIKXWb1nqr9b4TMb/BA63PawPWWp/nybD4ngNmWw/rwq5Xv9Jaz1NKjcGUmB8MjAIyMde7vwF3aq0Tno9pwCc0Sikb8B3r4daop5/AnABvA4LAN9ZrzgHuxRwgN2La4vwfcI9Sanet9aVh2w/VR67BJBRuzIG9Jc74MoF/Y6qUlmBOVM2YE/fxmOToPmAIMIfIqpMPrW3kA+9gDo6HMMWIwzEnsneVUpO11l9Z6xZgkoNy6zN+jLlgvQ644okZcwBeirnAPW/tnymY5HC6UmqS1jq6Wu1IK557rRhnY/ZTHeYkHNofc6ztbgB+h7kj+jHmItSbFmBOIrdgfqjVQEZ3NqCU2h3zPYA5eX+JSfjOBw5SSk0NbxfThRJM24R9gJ9qrf/WnVhixHYipu1NFeYzNmES6EeVUrtqrW+Iekk+5phYgkncpgE/weyTVszJ9A7MMXMJ8E+l1Bittcd6PxumevV4633/Zq17BvCaUupo64KxBnPj8CdrvX9Z7992Q6CUuhVzw/AvTEIGcCLwnFIq1r45wPps92NuIEJ3+s8BkzHH4P+AHGAc5rcXb0JzO5AF/AVz/jwLeEYpdWpYCcHfgFuUUt/XWv8n6vVnY36/z8X5fmcDn4aSRaXUJ9Z7RpdU2DC/xUMwJXpvYM57/wQ2Rm/Uatz8CuY4vxuTPOwDXAzsp5Sa2Ul1wyZM1c/PgUlWPKHlKKX2B5YCHmvb1Zik5c/svIkMZ7fW/xLzm8+je21l4nENkIs5HrZiblDBVOOWY64FlcAu1ud5WSl1jNb6xTi3/yzm/PFH630uBv6llNpNax3PtWA6cDrwACbhPRyzfz2Y3wfQlsz8E7Ovf289fxpwaJxxdklr3WQlmr/EJLv/sJ46AvN9L8Scn/Ot935CKZWvtb7HWu92TCHAYcC5VoxgbmgB9rU+3/PAesx54VjMb3Ak5nyTkIGY0LitRoY2zEX9F5i7tBVa68+i1q0HDg0vIVBKDcecrJ7SWp8atu5flVJ3ABcrpe7RWq+3koMbMXcr+4edzB/G3LnF4yLMCfWPWusrwp+wSkLQWi9XSn2ISWhiVZ38DnP3sZ/Wek3Y6x/BnLivx7QlAvPjGA2cpbV+OOyzhe404rEDUzIRftK5Vyn1DuZkfhwmQQg3Hhgfil0pFbqo/AIrobHu6O/AFHVODbszuA8reetF3wJHhp/ErTvR7vgr5uJZEVVq8xymlOACTL11PJZi7oJO1lo/3c04IlhJ852Y5HFK6ASrlPqrFde1SqnHQkmvZRhwodb6TuvxvVYJxxmYRP+A0O9GKfU55qQ3l50lCSdjko4fhZcAKaX+gjmx3QHsqbX+Rin1T0xC89/w6mJr/f0xycy1WuvfRW3nZeBPSqknoo7FCcCMUCmQtf4uwP7A7Vrri7uz/6IMAfYJJabWcfwxcIdSaqGVyD+COS+cjSn9DMXwHUxp27wYCX871p3swZgbpZBHMSVZu0WVvM7BJDN3aa1/EbaNtzAX2x1hy+yYC/sGzDmjKey5ZZjqrbmYhLQdrfV24HGl1NHWvoguLboTcADTtdafWNu9C1OKcJZS6iGt9dth62cAy7XWP+lil/REKTBOax1dcn5JdNWTFetaTPIcb0Lzhdb6tLBtvIe5GfgxcHMcr/8uZl9+ZD2+Vyn1NqY9y2/DSrXmYRKEqaFzjPU7Xtluiz0TOt+ODVt2Z4yS6nmY88HVwD0AWuv/WDemhwELdPtOLC/EqB78s1LqBeCXSqkbrWOs2wZit+3rMXcEWzB3f2cBL2AustHmRVd3YE7CWcCDSqmS8H+YzNjOzmx4FqZE5u5QMgOgta7CZPzxOA1zofld9BPhRbMdse7MTsOUunwdFW8T5mCbFfaS4zAX78eiNhXPjy4UVzB0AVFKOZTpjlgCvGatsm+Ml0UkYlax4uvAMKuoHEz2Xw48HEpmrHW3Ye6qe9PtndyRdsm6YM7CnLT9Ud+DBr4i8nvoynDMXeqXicYUZj9MgnJ/+N2iVZR9K+bic0zUa3ZgnaDCvIm5Ufhr1O8mlDiEV7GcjikOfzlqXwzBXCSUUmpUHLGfhmn0/HjUdooxd3iFmNLBcO+GJzOWJkxp3/5xvm9H7g4vZdNa12FKgnbBlAxhHbuLgBOt0tOQszD778E43+vHmJLj+WHL5mP2x4+j1g19f38OX2hVha2PWncSsCemlMcVtV9fwzS+7c6x2sbatxXAM6FkxoojwM6S2DkxXnprIu/XDQ/ESGaISuZylFLFmATrTWBK6KYyDtHVPG9gvqd21Y4deCUsmQl5DXN9GWHFpzAJxt/Db5is3/Fdcb5PvEIJxZCw9wnfVy5rX+VjmjYMV6YpQ5fCr5VKqSylVJF17P0bc+2dmGjQA7GE5n5MkWsQcxJbp7Wu7WDddTGW7WX9fTXGcyFDrb+7WX9jlcZ83EWcIXtg7kwTbSxWijm5z8IkcrGEJ0a7Ae9FX7ytO+W4ewUopU7C3DnvQ/uqmcIYL4k+qYK54IGJv5Hk7M9ExToWuiNUmvMz618sng6Wx3I85jh+RSk1S/esq+4Y62/0CTN82W5RyytjJPuhnjbRSVZoeXHYsr2sx50Vtw8lRnVIlL0wNxFfdLGdcO2+S6sY/RJMddsGpdRHmAvGwhjVQp35JMay0LG5GzuHDbgf05blFMzdtgPTDm5FjAtXO9aF9ExMaZbLKt0JWQmcqZS6NuymZwwmEdkQY3PrMEX5IaFz3E10XGIYvU/jlcixFqDz7zcZYv6+lWnzdiOmSrs4xiq57Ly4dybi/Ka19imlGjrYZpevt4SfH6vYuW91jHVjLeuJUCLT9tmVUoWYG+8TMDdc0Qox1XadUkplYUp0TmXnZ4reTkIGYkLzmY5qud2JWBcYm/X3DKw2NTHEOvhSJRTvq3SjlKUnlFKhdhErMdVUlZh2Pw5gMbFL/jor/bB18lxfiXUsdNY4Lfq3E/oMD2GGDoilO70q3sLUMy/GJDWHaa3f7cbre6qz76uj52xR//+anVWdscRzErZhGmoeRcffx/+iHsdMHLXWdyilnrW2NQNTLXahUupRrXVncSbidUxDx7MxpYtHYO60r4nz9bMwpZXl1nY6WmdxB891JvQ9/ZGdparRotsb9iaf7v0xldodE1ZV7OuY72UephH1NkyC9QtMu454S2ji+U0k8vrubCOZvmv9Df+NPo+ptr0bWI65kWnFdKr5KfHvqwcwbbAexfwetmJKT2dgEp2Ea44GYkLTU6GTx9Y4EqNQYrMnps1DuHFxvt86YE+lVJbuvAtuRyfzakxboCFxJnLrgT2UUo6o9iLDMb0p4vFDTAJzcFTxYXfbnMSKDXaWdoSLd38mU6hkryjGc9F3maHjxtmNhLpTWuu3lVKHYS5aS6ykJnqsjXiE9uv4GM+Ni1onWT7DNDZ/K47Sx84Sx88wbcw+11r3uPrNqg6+D7hPKeXEJOY/UqY3R3RiFMtemKLxcO32odY6qJT6G3CzUuq7mMSmkZ0NLLtyFiYBPrOD5x+ythlKaDZg9vdo2pegjY16HDpWfck6VsOk4lhL1DRMw+mLtdbhA81hlealmw3WXxXjuVjLEqKUysEk+81Y1zWl1K6Y3k1/0Vr/Mmr9E2NsJuZv2vrNnYxpR3Nm1HOTexr7QGxD01MLMO0HrldmDJAISql8q8gMTC8BL6bhljtsnTJMcVo8nsAUsV0V473CM/NQvX3ExdUqcn4CmNrBgRVq3xHyPKY4+Yyo1brTsrwVc8C2HT9WrO0+QzetwhSt/tiqUw1tewhmhNw+pbUOJYszw5dbidtRUetuwvz4T1amyypRr7GHf6ZuxPAOO7vX/1spNa2728B0ld4M/NRq2BuKKQtTbdiKaR+WTI9hesNF954KvXd4lUbMY9sSaj9yU6z2DFHb6ZDVPiLi92xVqYWSmFjvHcvPw9p8hYrhz8HcWLwTte4jmNKlK4CjgX/oOHq5WW0TZgMvaa2fifUP0w7pWGtd2Pn9XRy1reNpn3y/i7mRuiBWuwelVIb1ubpNa12J6fZ8glKqLZGyzg+/tR4uSmTbvSB0QxdRAqJMD7Ck9RpKIo1JRk9RYVNMKDNcwQXJeAOlVB6mhHko8Ge9c6iJjvbVGEw7t2gd/aaDmBKw6O0UYnp19YiU0ETRWlcppc7H9Nb5RCk1H9OgsxTTlfo4zJ3GBq11nVLqakyDtneUUo9hGnGdhznw9onjLe/ANOi7Sik1BdMyvhlzh6PY+cMK3ZnfrJR6wlpnrdY61Br/AGCBUmqBtW4LZhTZIzGJwpnW6/+ESbYeUEpNwtRrH4S5W4m3mPkZTD3qa9ZnzrD2i7vTV3VBa92qlPoVJqlcqZR6AFMUeRamPrknjTkTdRfmu/kn5iJSjumK+CGmC3C4n2KqipYrpR7FFGE7MReU4zBVD/H2cmpj9XILldT8Wyl1uJXoxPv6FqXULzClA+9Z+9WDOQ4mA9dE9XBKhicw1SyXKKWmYnok1WB6bh2IaaQ8zorva6VUJfBD6281sF1r/ZLW+k1lxqa5HNMu8llMVfAIK/aDMd18u7I3sFgptRBzzNdjekOdj7m4x1vytR1YYX2/DkwpyTDg9OgSVq31FqXU85i2NGDOKfH4ISYZfLaTdZ7F3On+EFNdsgjTEPUCK8l7HdM+72xMj522NjjW7+x0TDX1R0qphzBtg3Ks15wAXEgHvZzi8AtMcv+OMj1wqjEJ2kwguodTKq3CGh7CSvTXs7Nb+f+A76UutPasUr+LMTelK5Xp/Rnqth069rozhstMKzGyYxr3fhfTdq8Ic666Ouy9q5RS7wLnm7bJfAjsjrnWfUr7c2Ho9zTP+s3uwAx6u06ZXp8/UKYX7tuY3/JPMb/rsm7E346U0MSgTXfmGcAHmIvXXzE/0uGYLzm8hfltmC/VhamTPhOT4NxJHKzum7MwpRvlmJ4Af8AM6LcwbL23MaUou2PqIP+O6ZEV6gV0AGbQuvFWHDdj6oBXENZbxeqVcSBmHIwzrPXcmAtDXG08rC5352AazN2K6QquMSUJPWLdfZ6IuXBchzmxPkMPxibooRsw4ypMxVw4ZmF68ERXMWJVieyDqWM+2Hrd9db/FxL2fXaX1no5Zv8GMRfmA7r5+mes2Ndj7pT/gPn9n6nbj0HTY1YvttMxFwcnJun+C+aYq6F9ad4pmIvLzZhj+89h27oCkxBuxZRA3I0ZE8dB/ANCrseUGk3G/IbvxJSa3A0c2EV1b7hfYS4oF2K+Ww8wV2vdUa/G+62/H3WjuvAszAWgsy7DL2NKh8+CtpLaYzGf5yDM/tsPc7P0FVHjuliNzPfBJLlzMPvjCsz+uZ8eDGRpJdsHYNpZXIg5RwzHlAb+NNHtJpvVU/MwTDuiczC/18mYhK47DcX7jNb6X5jvuRrT/uRSTGIaKv3qzvg9v8WUgD6IOddWYLrsT9Fanx+jl+0cTJJ7EuZ4ORxTMtTu2Ndm/J7fYXosPYj5TR9pPX0O5jg91NrOyZjG+n+I3k532YLBhAflE0II0QllRqL9DzHaafRhDOsAj9Y6rUocRPIopc7GlAAeobVOpKH4gCAlNEII0XsuwFQPR4/7lHQdtPk7AVON9Epvv7/ofcqM+5URtSwb09vUQ/t2XIOKtKERQogkshpWHoVpgzEXM9dNt+bxStCNyjRw+A9mGP4KzAB832KmdxH9XynwvlLqScz8WLtgqnYVZs65hEbYHSgkoRFCiOQaiWkz0Gj9vbLz1ZPmP5i2Xr/BDIxWg2nzcHX4yLKiX2vANPiey87BDz8iciqbQUva0AghhBCi3xsIJTRZmLlcvqHz0RaFEEIIkf4cmJ5x7xE2sWpXBkJCM4Wdk+MJIYQQYmA4EDO2V1wGQkLzDUBdXROBwMCqPisuzqWmpsuBRQWyr7pD9lX8ZF/FT/ZV/GRfdc5ut1FYmAMdz6cY00BIaFoBAoHggEtogAH5mXqL7Kv4yb6Kn+yr+Mm+ip/sq7h0qxmJjEMjhBBCiH5PEhohhBBC9HuS0AghhBCi30tpGxql1B7A7zETmRViJlF7DLi9G5PFCSGEEGKQS1lCo5QaCawEtgF3AbWYLlp/xMwY/cNUxSaEEEKI/iWVJTSnAwXAdK31R9ay+60J1k5WSp2ltfalLjwhhBCxeL1NNDbW09rqb1u2ZYudQCCQwqj6j8G8rxwOJ7m5BbhcOUnfdioTmiHW32+jlm8GfMiov0IIkXa83iYaGuooKCglIyMTm80GgNNpx+8fnBfp7hqs+yoYDOLztVBfXw2Q9KQmlQnNf4ArgAeVUtdgqpxmAGcCN2utB9+3LYQQaa6xsZ6CglIyM7NSHYroZ2w2G5mZWRQUlLJt29akJzQpnZxSKXUVJqlxhS2+Rmt9Qzc2Mxr4MplxCSGEiO2jjz5m+PBRbSUzQnRXMBjkm282Mn78uK5WHQNsiHe7qR4p+EvgDWARZqr7o4DrlVLVWut7u7OhmprGATfyYmlpHtXVDakOo1+QfRU/2Vfxk33VXiAQoLU1CESebwdrNUoiZF+Z46ij35bdbqO4OLfb20xlL6eTgfuAsVrrTdbihUopO3CrUuofWuu6VMUnhBBCiP4jlSU0PwNWhSUzIS9g2tFMxJTeCCFE2miu3Ejj6lX4a2twFhWTWzGJ7PJRqQ5LiEEvlSMFDwUcMZZnWH9TXR0mhBARmis3UrdkMa2eJhyFRbR6mqhbspjmyo2pDk300IMP3sf06ZNpaOi4ivHEE4/hxhuva3v80kv/ZPr0yXzzTfR9uUiFVCY064DJSqndo5afgumy/WHfhySEEB1rXL0Ku9uNw52DzWbD4c7B7nbTuHpVqkMTIqYVK97hwQfvS3UYfSKVpSC3AEcAbyulQiMFH20tu1drvSWFsQkhRDv+2hochUURy+wuN/7amhRFJPrSk08+i93ev6ZAfPfd5Tz99N85++xzUx1Kr0vZN6O1XgbsD6wGfg7MA3YHLgcuSFVcQgjREWdRMQGvJ2JZwOvBWVScoohEX8rMzMTplNYQra2ttLS0pDqMdlL6zWitVwJHpjIGIYSIV27FJOqWLAZMyUzA6yHg8ZA/fUaKIxO9oaqqkgsvPI+iomL+/Oe7OOus09hnn0lceeV1nb7u2Wf/wcKFT7Np09cUFBRyyCH/x09/ej7Z2dlt65x44jHsscdYjj9+LvfccycbNmxg9OjRXHLJ5YwbN4GXX/4Xjz76EFu2bGbcuAlcccW1jBgxMuJ9/ve/NTz44H18/PFHBAKtjB//Xc4//xfsuedeANx443W8/PK/AJg+fXLb6956633AdJ1+6qknePHF59m06WuGDBnCQQfN5NxzL8DtdretP336ZObOPYWxYxXz5z/M119Xcfvtd1NRMZlXX/03Tz45n8rKjdhsNoYNG8bRRx/HSSed0qN9nwhJNYUQIk7Z5aMonHV4RC+n/OkzpJfTALRx4wYuvPB8hg4dxm233Ulubnzjojz44H08/PADTJ06jeOPn8v69V+wYMGTrF//OX/+810RAxJ+9dUGfv/7aznuuBOZNcvF448/ymWX/Yrzzvs5TzzxGLNnH4/H08QTTzzKzTf/njvuuKftte+99y6XXvpLxo/fm5/85FwCgQAvvLCICy74KQ888BhjxuzG7NnHU1NTw8qVy7n66t+1i/Wmm27glVcWc9RRxzJ37ilUVVWycOECNmz4knnz/hoR63vvreC115YwZ85c8vLyKCkp4b33VnDddVfy/e8fzLHHzqG1tZUNG77kf/9bIwmNEEKku+zyUZLAJFm6dYVfv/4LLrroZ5SVlXPrrXfgdsc3RH9dXR2PP/4I06YdwJ/+NK8tIRg2bAT33XcXb7/9JtPDSvM2bvyK++9/hHHjJgBQWjqUa6+9nLvv/gtPPbWQ/PwCAPx+P/PnP8y3325m6NBhBAIBbrvtJqZOncaf/nR72/aOPvo4TjvtBB555AGuv/6PTJjwXXbddTQrVy7nsMMiK0PWrPmAl176J7///c0cdNDMtuV77TWOa6+9gnffXc5+++3ftryyciPz5y9g1Khd25YtWvQsY8bsxo033hLvru1V/at1kxBCiAEl3brCf/75Oi688Fx23XU0t912Z9zJDMD777+Lz+fjpJNOiSjdOOGEk3A6nSxf/lbE+rvvvkdbMgMwfrz5//TpM9qSGYBx48YDtHUP//zzdVRVVXLooYdRX1/f9s/v9/Pd7+7DBx+s7jLW119fypAh+Xzve5MitjFxYgUOh4MPPojsuVdRMTkimQHIzc1ly5Zv+eijtfHsnl4nJTRCCCFSJrwrPND2t3H1qpSU0lx22a8YOnQot956B1lZ2V2/IMzmzZsBKC8fHbHc7XZTWrpL2/MhQ4cOi3ick2OqtXbZZWjM5Q0N2wGorKwE4He/uypmHPH0xKqq2sj27ds4+uhDYz5fXx85UP/w4SParXP88XN5/fVXOffcMxk+fCRTpkzl4IMPZcqUfbt8/94gCY0QQoiUSbeu8AcddAiLF7/Ia6+9yhFHHN2r7+VwxE48OkpIQnNJB4NmHqgLL7yYMWOih3KLTyAQpLi4hKuuuj7m8yUlpRGPYyV3hYVFPPzwk6xcuYIVK95hxYp3eOGFRRx11LFcfvk1CcXVE5LQCCEGvc7acKRb+46BxllUbKqbwqp2UtkV/he/uBgwDWbd7hy+//2D437tsGGmxKWyckPb/wG8Xi/V1VuYOnW/pMQ4cmQZALm5eV2WhnQ0KfrIkWV88MH7TJy4D5mZmQnHkpGRwQEHHMgBBxxIMBjk9tv/xMKFT3PGGWe1xdlXpA2NEGJQ66wNR+OXG9KqfcdAlFsxiYDHQ6uniWAwSKuniYDHQ27FpJTEY7PZ+O1vr2b69Blcf/2VvPfeu3G/dvLkfcnIyODpp/9BMLhzNvJFi57G7/czbdr0pMQ4duyejBgxkr//fT7Nzc3tnq+r21ldlJ3tAmg3pcPBB8/E5/Px+OOPtHt9S0sLTU2NXcYSV841AAAgAElEQVSxbVt9xGObzcbuu+8BwI4dO7p8fbJJCY0QYlDrrA1HMCczrdp3DETp2BXe4XBw3XV/4LLLLuKKKy7h9tv/yoQJe3f5usLCQk4//UwefvgBLr30l0ybNp0vv/yCF15YxJQp+3LAAQcmLb7LLruSyy67iDPO+AFHHHE0xcUlVFdvYeXKFZSVlXH11TcAoJQZk2bevFvYd99p2O12Dj30MCoqJnPMMcfx0EP3o/UnTJo0FbvdRmXlRl577VWuueaGLkt/brrp9zQ0bKeiYjK77LIL3377Lc888w/22GMso0ePScpn7Q5JaIQQg1pnbTh2eDKwu/JiPieSJx27wmdkZPCHP9zKxRf/nEsv/SV33XV/XK87++xzyc/PZ+HCp7nzzj9TUFDI3Lkn85OfnB/R86mnJk+eyj33PMQjjzzA008/RXOzl+LiUvbe+7vMnn1C23oHHvh95s49hVdeWcySJS8TDAY59NDDALjssitRak9eeGER9957F5mZGQwfPoJjjjmOPfZQXcZw2GFH8MILi1i06BkaGxsoKirmkEMO5ayzzknJFBG28GKxfmo08GVNTSOBQL//LBFKS/Ooru545lexk+yr+Mm+irT1+UXt2nCEHufkZLK9ui7mcyWz56Qi3JTbvPkrhg3btd1yp9OO3x9IQUT9j+yrjo8jALvdRnFxLsAYYEO825Q2NEKIQa2zNhxF++2XVu07hBAdk4RGCDGohdpwONw5tNbV4nDnUDjrcLLLR5E7ZnSHzwkh0ou0oRFCDHqdteFIx/YdQoj2pIRGCCGEEP2eJDRCCCGE6PckoRFCCCFEvycJjRBCCCH6PUlohBBCCNHvSUIjhBBCiH5PEhohhBBC9HuS0AghhBCi35OERggxKDVXbmTr84vY/PDf2Pr8IporN6Y6JDHITZ8+mQcfvC/VYfRbktAIIQad5sqN1C1ZbCaaLCyi1dNE3ZLFktQI0Y9JQiOEGHQaV6/C7nbjcOdgs9lwuHOwu900rl6V6tCEEAmShEYIMej4a2uwu9wRy+wuN/7amhRFJPqr1tZWWlpaUh2GQCanFEIMQs6iYlPd5M5pWxbwenAWFacwKpFKDz54Hw8//ABPPvks999/N+++u4KsrCyOPPJozjnn5zid5nI5ffpk5s49hbFjFfPnP8zXX1dx++13U1ExmUAgwFNPPcGLLz7Ppk1fM2TIEA46aCbnnnsBbvfOBLqlpYW77rqDJUteZseOFioqJvHrX/+2XUweTxMPPHAvb775BjU1W8nJyeU739mD88+/EKX27LN9019IQiOEGHRyKyZRt2QxYEpmAl4PAY+H/OkzUhyZSLWrr/4NI0aUcd55F/Dhh//lySfn4/F4ueSSnQnHe++t4LXXljBnzlzy8vIoKSkB4KabbuCVVxZz1FHHMnfuKVRVVbJw4QI2bPiSefP+is1mA+APf/gdixe/xGGHHcG4cXuzevV7XHrpRe1iueWWP/LOO29y/PEnMXJkGfX1dXz44X/ZsGG9JDQxSEIjhBh0sstHUTjrcBpXr8JfW4OzqJj86TPILh+V6tBEipWVlXPjjbcAcMIJJ5GVlcXzzz/Lqaf+kBEjRgJQWbmR+fMXMGrUrm2vW7PmA1566Z/8/vc3c9BBM9uW77XXOK699grefXc5++23P599to7Fi1/ixBNP5qKLLml7n+uvv4ovvvgsIpbly9/iRz86m1NPPaO3P/aAIG1ohBCDUnb5KEpmz2HYj39Cyew5ksykUFXDJl5cv4T5Hy/gxfVLqGrYlLJYjj/+pHaPg8EgK1cub1tWUTE5IpkBeP31pQwZks/3vjeJ+vr6tn8TJ1bgcDj44APT4HzFircBmDv35IjXn3TSKe1iyc3N44MPVrFtW31SPttAJyU0QgghUqaqYRNLNy7D7XRRmJWPx+dl6cZlzBw1g7K8EX0eT1lZecTj8nLz+JtvvmlbNnx4+7iqqjayffs2jj760Jjbra+vA2Dz5m9wOJztthGdIAGcf/6F3HjjdRx77GGMGzee/fY7gMMOO5Jhw4Z370MNEpLQCCFEL2uu3BhRvZVbMUlKhCxrqtfidrpwZ7gA2v6uqV6bkoQmHllZ2e2WBQJBiotLuOqq62O+pqSktNvvM3Pm/zFx4j68+eYbrFy5gscff4T58x/mxhtvYd99p3V7ewOdJDRCCNGLQoP42d1ugnYHTWs/ZPuKd3CPG0/BQYcM+sSmtrmewqz8iGUuZza1zampZqmqqmTo0GFtjysrKwG6LBUZObKMDz54n4kT9yEzM7PD9YYNG05rq59vvtnEyJFlbcs3bvwq5volJSXMmXMic+acSH19PWeddRqPPvqgJDQxpLQNjVLqEaVUsJN/I1MZnxBC9FRoEL+gz8+OL78gCNhzcmje+JWMTgwUZRfg9TdHLPP6mynKLkhJPAsXLmj32GazMXXqfp2+7uCDZ+Lz+Xj88UfaPdfS0kJTUyMA++23PwBPP/1UxDoLFvw94nFrayuNjY0RywoKCthll6Ey7k0HUl1Ccx/watQyG3AvsEFr/XXfhySEEMnjr63BUViEt1JDRgb2jEwIBgk0e9tGJx7MpTQTSyewdOMywJTMeP3NePxepo2YkpJ4qqoqufzyS5gyZV/WrPmApUuXMHv28RGlKbFUVEzmmGOO46GH7kfrT5g0aSp2u43Kyo289tqrXHPNDUyZsi977KGYNetwnnnmKRoatjN+/N6sWrWSqqqqiO15PB6OP/5Ivv/9Q/jOd/bA7c5h1ar3WLv2Qy64oH0Xb5HihEZrvRxYHr5MKTUdcANPpCQoIYRIotAgfgGvB1u2aR8S9Puwu9wyOjFQljeCmaNmsKZ6LbXN9RRlFzBtxJSUtZ+54Yabue++u7jnnjvJysrk5JNP57zzLojrtZdddiVK7ckLLyzi3nvvIjMzg+HDR3DMMcexxx6qbb0rr7yWIUMKeOWVl1m27HUqKiZzyy3zOP74o9rWyc7OZs6cE1m58l2WLXuDYDDAyJHl/PrXv2XOnBOT/rkHAlswGEx1DBGUUn8FzgN201pviOMlo4Eva2oaCQTS67P0VGlpHtXVDakOo1+QfRU/2VemZ82bXy9nw/aNBINQml1MblYO/kArRdkFTCydQFneiKTsq1AbmpbN3xAMgs0GQZ+P7N2/g83pxOHOoWT2nCR9st63efNXDBvWvkeO02nH7w+kIKLkCI0U/PLLr5OXl9er79Xf91UydHQcAdjtNoqLcwHGABvi3Waqq5wiKKUygJOAd+JMZoQQIqaqhk0Rd/2hJKWqYRPPffQc1Q3fkOEP4nfa+cSzFXeGm3HFKqLbcGmp6vqNuhAaxK/+9dfwfvIx5OaQtdvu2JxOGZ1YiCRKq4QGOAwoRqqbhBA90NnYJqu+eJtttZvItDvIcDjxBL04fK202nx866lmbOHugOk2vM9uqsPEqDuyy0cx7IwzI7pvO/ILZHRiIZIo3RKaUwEfsKCrFaNZxVMDTmlp7xZ9DiSyr+I30PfV699+RvGQfHIyzYSAOWTT1JLJZ57PqN26kUCGHZc9Axs2WrHhDDoItPrw4cOdk4UrmEmNp46v6qp4e8tycjLdjHTvgsfn5e0tyzmm8FB2Ley8kWhMpeOhYnySP23f2rLFjtMZu4NsR8v7A7vdzLPkdHb8+ZKpP++rZLDb7Uk/D6VNGxqlVC7wLfCa1vqYbrx0NNKGZtCTfRW/wbCv5n+8gMKs/LbJAAGCwSB1O7aR+el6Ps/dgQ1wYqfevgMfAeyBAMOKd2Vs4e54fF7cGS7cOVlsra9vG+wNYIunmvod2ylxFSdcYtOfDdQ2NH1J9lXvtKFJpxTxOKR3kxAiCTob22R8Rhk5fjs7bH58tJIZtOMPtuKw2RnqLsXj8+Lxe5lYOoGtTbW4nDtHhd3e0sDXjZtp9DVFVGWlcu4hIYSRTgnNaUAj8EKqAxFC9G8TSyfg8Xvx+LwEg8GIJOU735vBQVvzGbUjh1bA3gq7ebIZV6hoDQZwZ7ja5hEqySmKSIw2N23BZrOTm5GDzWYzpThOF2uq16buwwohgDRpQ6OUKgUOBf6utfakOh4hRP/W6dgmebDnwcdRtnoV/q87n1tp35Hf4+mtLwNm0LeGlkYcdgfD3Lu0rZPKYfpTJRgMRlTnCdEdvdXUJS0SGuAHmFikukkIkRRleSM6bNuSXT4qrt5FuxaWRSRGeZm55GcOYUjWzsaMqRymPxUcDic+XwuZmVmpDkX0Uz5fCw5H8tOPdEloTgO20H4aBCGESKnwxCjUHdzj86bFMP2pkJtbQH19NQUFpWRkZEpJjYhbMBjE52uhvr6avLzCpG8/LRIarbVMGyqESKrwMV86q1bqjnQbpj8VXK4cALZt20prq79tud1uJxAY3D134jWY95XD4SQvr7DtOEqmtEhohBAimULTDdjdbhyFRbR6mqhbspjCWYcnJakZTAlMLC5XTrsL0mAYDiBZZF/1jnTq5SSEEEnRuHqVSWbcpjeSw53TNrO1EGJgkhIaIcSA46+twVFYFLEsHWe27o1qMSEGK0lohBADjrOomFZPEw73zmqRgNeDs6g4JfHEmg+qpN7fa9ViQgxGUuUkhBhwcismEfB4aPU0EQwGafU0EfB4yK2Y1OexhPeMCh9d+PP/LpNqMSGSSEpohBBpIxkzW4MZZ6Zw1uER1Tmpmtl6TfVa3E4X7gwX23c0sNmzhUZfE9/at3NEzh4MDxtjLB2rxYToLyShEUKkhVBJhtvpiijJCE1D0F3xDp7X22qb6ynMymf7jga+3P4VTruTHKebbZnbeaelkgMCoxgWMFVjqawWE6K/kyonIURaCC/JGEjzJIUmytzs2YLT7iTDnoE/2MqQnCKyWgJ8FNyc8moxIQYCSWiEEGmhtrk+YmZrGBjzJIUmymz0NeG0OfEF/PgCPkYUlVMweizbM4O01tXicOdIg2AhekASGiFEWgiVZIQbCPMkhUYXzs3IodHXRIbdyW75uzIkM4+6DB+Npbm8su8Q3t07h60F0gpAiERJQiOESAuhkgyPz0swGMTj8+Lxe5lYOiHVofVYWd4I5o6dza5DyinLHUFeRi5bPNV8ua2S/MwhEW2Gqho2pTpcIfoluR0QQqRErB5NA3mepOh5oOp3bGf0kHKG5pQC4M5wAaYt0UD5zEL0JUlohBB9rrMeTUftNivV4fWa8Hmg5n+8gMKs/Ijno9sMyUjCQsRPqpyEEH1uoPZo6o6u2gyFJths9TRFjCTcXLkxFeEKkfYkoRFC9LmB2qOpO7pqMyQTbArRPZLQCCH63EDt0dQdoTY17gwXdTu24c5wRQwi6K+twe5yR7xGRhIWomPShkYI0WdCDYErGzdR461luHsou7hL8Pqb8fi9TBsxJdUh9qnwNjXR0m2CTSHSnZTQCCH6RPgkjWU5wxmRM5TNnm+pavimXemESK8JNoXoD6SERgjRJ8IbAgPs4i4lNyMXd4ZrQPdsSlQ6TbApRH8gCY0Qok+EJmkMN9gaAndXukywKUR/IAmNEKJPFGUX4PF520poYPA1BO6uWIMPSrWcELFJGxohRJ8YyFMb9IbwNkcyNYIQXZOERgjRJ7rqpiwiyeCDQnSPVDkJIfpMZ92URSRpcyRE90gJjRBCpCEZfFCI7pGERggh0pC0ORKieyShEUKINCRtjoToHmlDI4QQaUraHAkRPymhEUIIIUS/JwmNEEIIIfo9SWiEEEII0e9JGxohRNportwYMRljbsUkmctICBEXKaERQqSF5sqN1C1ZTKunCUdhEa2eJuqWLKa5cmOqQxNC9AMpL6FRSk0BrgP2BzKAL4DbtdaPpDAsIUQfa1y9CrvbjcOdA9D2t3H1KimlEUJ0KaUJjVLqCOB54A3gasAHjAXKUxiWECIF/LU1OAqLIpbZXW78tTUpikgI0Z+kLKFRSuUDjwD3aK1/mao4hBCJq2rYxJrqtdQ211OUXcDE0gkJj5viLCo21U1WyQxAwOvBWVScrHCFEANYKtvQnAoUANcAKKXylFK2FMYjhOiGqoZNLN24DI/PS2FWPh6fl6Ubl1HVsCmh7eVWTCLg8dDqaSIYDNLqaSLg8ZBbMSnJkQ9MVQ2beHH9EuZ/vIAX1y9J+HsQor9KZUJzKPApcKRSqhLYDtQqpW5SSjlSGJcQIg5rqtfidrpwZ7iw2Wy4M1y4nS7WVK9NaHvZ5aMonHU4DncOrXW1ONw5FM46XNrPxCHZyaUQ/VEq29B8B9NW5hHgT8AHwNHAb4Bs4KKURSaE6FJtcz2FWfkRy1zObGqb6+N6fUddtCWB6b7w5BJo+7umeq1MnSAGjVQmNLlAIfBbrfXN1rKFSqlc4GdKqd9rrbfGu7Hi4tzeiDHlSkvzUh1CvyH7Kn7J2FdlxUNpavHgznS3LWtq8VCWO7TL7Td+uYG6ZUvJysnBPXIYrR4P3mVLKZx9LLljRvc4tmTqD8eVZ30TxfmF2Gw7a+1dwUxqPHV9Gn9/2FfpQvZV8qUyofFaf/8etfwJYC4wFXgp3o3V1DQSCASTFFp6KC3No7q6IdVh9Auyr+KXrH21h3sPlm5dhtfZgsuZjdffjMfv5XujJna5/a1Ll9Fqz6DVlgFeH9gyaLVnULl0GSWz06cRcH85rtzkULNtW1vJDIDH58WdkdNn8feXfZUOZF91zm63JVRIkco2NN9Yf7+NWh56XNiHsQghuqksbwQzR83AneGiboe5mM4cNSOuKg5/bQ12lztimXTRTtzE0gl4/F48Pi/BYBCPz4vH72Vi6YRUhyZEn0llCc0qTMPgkcD6sOVl1t/qPo9ICNGlZHTVli7ayRVKLsO/l2kjpkj7GTGopDKheRrTAPhs4EoAq9v2T4AmYEXqQhNCxBLqTeN2uiJ608RbMhOSWzGJuiWLAVMyE/B6CHg85E+f0VuhD3hleSMkgRGDWsoSGq31KqXUY8DlSqldgNXAUcBhwGVa6+2pik0IEVtPe9OE92yyZWYS9Plpba7FWVRM/vQZ0sNJCJGwVM/l9FNgI/Aj69964Dyt9X0pjUoIEVNPumqHJp+0u904CovaSmVkrJnelczRnIVIZylNaLTWLZg5nK5OZRxCiPgUZRdYvWd29qbx+pspyi7o8rUy+WTfq2rYxAtfLKbR14Q/4Oebpm/5ansVx+5+uCQ1YsBJZS8nIUQ/05PeNNKzqe+9WbWcrd4aIEi2IwsIstVbw5tVy1MdmhBJJwmNECJuPemq7SwqJuD1RCyTnk2968vtG8l2ZpFhz8Bms5FhzyDbmcWX2zemOjQhki7VbWiEEP1Mor1ppGdT37PZIBg13mgwaJYLMdBICY0Qok/I5JN9b/SQUTS3NuML+AHwBfw0tzYzeojsczHwSAmNEKLPyOSTvSfWZJ8HjpxG/Y5tNLQ04vF5yXA42cVdwoEjp6U6XCGSThIaIYTo56K7xLd6mqhbspiSWYdzzG6HR3TbHuYeyprqtbxe+ZZ04xYDiiQ0QgjRz3XWJb5s9py2hCVZIz0LkY6kDY0QQvRz8XaJDx/p2Waz4c5w4Xa6WFO9ti/DFaJXSEIjhBD9XLxd4mub63E5syOWxTvSsxDpThIaIYTo53IrJhHweGj1NBEMBmn1NBHweMitmBSxXlF2AV5/c8SyeEd6FiLdSUIjhBD9XLxd4nsy0rMQ6U4aBQshxAAQT5f40EjP4b2epo2YIg2CxYAgCY0QQgxg0ePTlFRM4qjdZqU6LCGSTqqchBBigAqNT9PqaYoYn6a5UuZyEgOPJDRCCDFAhY9PY7PZcLhzsLvdNK5elerQhEg6qXISQogByl9bQ9DuYEflpwS8HuwuNxlDhxFsrmm3blXDpoi2NTKCsOhvpIRGCCEGKoeT5s80AV8LtmwXAV8LzZ9pcETey4ZGEPb4vBEjCFc1bEpR4EJ0n5TQCCESFmtCRJl8Mo3Ydv6x/kswbHlI+AjCQNvfNdVrpZRG9BtSQiOESIg0OO0H/H6yxypsGZkEmr3YMjLJHqvA749YTUYQFgOBlNAIIRLS2YSIUkqTHpxFxbR6mnCrPduWtXqacORHjgxclF2Ax+dtK5kBGUFY9D9SQiOESEi8EyKK1Il3SgQZQVgMBJLQCCESEu+EiCJ14p0SITSCsDvDRd2ObbgzXMwcNUPaz4h+RaqchBAJya2YRN2SxYApmQl4PQQ8HvKnz0hxZCJcPFMigElqJIER/ZmU0AghEhLv3b8QQvQFKaERQiQs3rt/kT6kq70YqKSERgghBgnpai8GMklohBBikJC5ncRAJlVOQggxSPhra3AUFkUsi6ervczzJPoDSWiEEGKQCA20FxoEEXZ2te+obU1onie30xUxz5N06xbpRqqchBBikOhooL2MESM7bFsTPs+TzWbDneHC7XSxpnptqj+OEBEkoRFCiEGio672vk1fd9i2RuZ5Ev2FVDkJIcQgEqurff2rSzpsW1OUPUrmeRL9giQ0QggxyHXWtmZi6QSWfPoy3q3byPTuoMWVhb8kn2l7HpHCiIVor9sJjVKqGNhFa/1J2LIxwMVAEfCY1vrfcWznIOD1Dp7eS2v9aXdjE0II0X2dTWORW++n4pMmdEGA7W4nQ1oCfPeTJkqG+SEvxYELESaREpo7gLHAVAClVC7wJhBq7v4DpdQhWutlcW5vHhA9CMKmBOISQvQBGWl24Am1rQn/XvOnzyC7fBRbn1/E8IwiyoI5sMOs35rRROPqVfK9i7SSSEIzDZgf9vgHmGTmSOC/wCvAZUC8Cc1/tNbPJRCHECIO0QmIa+YMyE1sRuzQSLN2tzuiN4zM4dT/dTSNRaJj1wjR1xLp5TQUqAx7fATwvtZ6sdZ6M/AIsE93NqiUylNKSXseIZIs1lD3m55/IeGh7mWk2cHHWVRMwOuJWBZqXyNEOkkkofEBrrDH3wf+E/a4HujOkT4f2A54lVJLlFJ7JxCTECKGWAmIMycn4QTEX1uD3eWOWCZ36wNbR2PX5FZMoqphEy+uX8L8jxewYO2/qGqQ1gIidRIpFVkHnKCUuhs4BtMQeGnY8+VAbRzbaQGeAV4GtgLfBS4B3lJKTdFar+tOUMXFud1Zvd8oLZVWd/GSfdVevWc79cVZrLVvoo4dFJLFhEAxJTXbE9pf3vLh+BubcObs/L35Gxtxlg8fsPt/oH6uuJWOp7Awh9oVK9hRvZWs0hKK9juCmgInb+tXycl0M9K9C00tHt5uXM4xhYeya2FZqqNOe4P+uOoFiSQ0d2OqleoAN7CeyITmQOB/XW1Ea/0O8E7YoheUUv8E3geuBU7rTlA1NY0EAsHuvCTtlZbmUV3dkOow+gXZV7FV5Tp427celz2bHBxsZwdv2DawX24ZBQnsL5vam8Yli7F7WyJ6wxRO2m9A7n85riy5xbgOPaqtaN4LvL5uCXa/E5vNgdfXQk6OG6+nhdfXvctRu+WnMtq0J8dV5+x2W0KFFN2uctJaPwb8CJPEPA4cobX2QVuX7gJgQbcjMdteA7wKzEzk9UKISF+UZ5HVEiDLFwAgyxcgqyXIF+VZCW2vo5FmpUHw4CMjCIt0060SGqWUAxgJvKi1nh/9vNa6BpjUw5gqkYRGiKTYnhmkYPRYfJs3E/B6sLvclI7+DtXBloS32VFvGDG4FGUXyAjCIq10t4QmA1PFdHYvxBKyG1Ddi9sXYtAoyi7A587CrfYk93sVuNWe+HOz5KIjemxi6QQ8fi8en5dgMEhTiweP38vE0gmpDk0MUt1KaLTWzZgGvE09fWOlVGmMZdOBg4EuRxoWQnQt+qLj8XlpavHIRUf0WFneCGaOmoE7w0Xdjm3kZLqZOWoGZXkjun6xEL0gkUbBLwFHA3/t4Xv/QynlwTQM3gpMAM6x/n9dD7cthGDnRWdN9Vpqm+spyi7g4LH74vZLo03Rc2V5I9oSGGnoKlItkYTmMuAVpdSjwK3AZ1bJTXc9h+nJ9GtgCLAFeBK4Tmud2KhfQoh2wi86AKWFcuERvaeqYVNEAj2xdIKU2og+kUhCswUIAhOB0wGUUtHrBLXWnW5ba/0X4C8JvL8QQog0VNWwiaUbl+F2uijMysfj87J04zKpihJ9IpGE5jFMQiOEEGIQC58nzFs+nFUlHtwuV1vPp9DfNdVrJaERva7bCY3W+sxeiEMIIUQ/Ej1Rqb+xic1NmuKikXgaG9uGCcgYNozarB2pDlcMAonM5SSEEGKQi54nzJmbS36Lg20bNAFfCzaXi+2tTXz0zYdsrN3Ai+uXyFxPolclNMO1NcDeacAszOzbl2mtP1BKFWLmd1qqtf46eWEKIYRIJ/7aGhyFRRHLdv/Gz8riIBkZdvy2Fr7K8kIARjfapD2N6HXdLqFRSrkxs2s/AswGDgEKrae3AzcB5ycpPiGEEGnIWVRMwOuJWFZS7WXfmlxcQSdV9kaygg5GBwvI8bTiznDhdrpYU702RRGLgS6RKqfrgMnAHMyovrbQE1rrVmAhcFgyghNCCJGecismEfB4aPU0EQwG8Tc2YnM4GJ5dysG+coYHctndk03Wt3X4t23Doz8lw7ND5noSvSaRhGYucL/W+nkgEOP5z4HRPQlKCCFEeoueqNSZm0PhUcdidzho9TQxxBukcVsNQb8PR2EhAV8L9RvWMaTF1vXGhUhAIm1oRgBrOnneA+QlFo4QoiPhXWSdRcXkVkySSSJFSoVPVBoaKThr2DAaV69izLp63it34CwYQmZmFs20ssNhZ/fKHfC9FAcuBqRESmhqMDNud2Q8IE3ZhUiiUBfZVk8TjsIiWj1N1C1ZTHOlDKot0kt2+ShKZs9hVMluzHCPIycjh222FlxBJ/u3llOyNZGB5YXoWiIlNEuBHyulbo1+Qik1BjgLmN/TwIQQO4V3kQXa/jauXiWlNCItOYuK2aWpieHu8rZlrZ4mHEXFKYxKDGSJlNBcj+nV9B6mNzQoa90AACAASURBVFMQOFwp9UdgNbAD+GPSIhRC4K+twe5yRyyzu9z4a2tSFJEQnYtuNNzqaSLg8ZBbMSnVoYkBqtsJjdb6c2Am4Ad+h+nldAnwG6ASmKm1rkxmkEIMdrG6yAa8HpxytyvSVHSjYYc7h8JZh0uJoug1CQ2sp7VeBUxUSk0A9sIkNZ9prT9IZnBCCCO3YhJ1SxYDpmQm4PUQ8HjInz4jxZEJ0bHwRsNC9LZuJzRKqRnAJ1rraq31WmBt1PMlwDit9bIkxSjEoBe62w3v5ZQ/fYZcLIQQwpJICc3rwA+BJzt4fqb1nCPRoIQQ7cndrhBCdCyRRsFdjYrkIPaAe0IIIYQQvSLR2baDnTy3P7A1we0KIYQQQnRbXFVOSqlfAr8MWzRPKXVjjFULgSHAQ0mITYhBTUYGFkKI+MXbhqYe+Mr6/2jMaMHfRq0TxDQQXgHcnozghBisQiMD293uiJGBpdurGAwkmReJiCuh0Vo/CjwKoJT6Evit1vqF3gxMiMEi1slbRgYWg5Uk8yJR3e7lpLUe0xuBCDEYdXTybvV4yIo6ecvIwGIwkGReJCqhgfWgbTyaWcBQ4Dat9adKqVygAvhQa12fpBiFGLA6Onn7amoIeD1tj0FGBhaDg7+2BkdhUcQySeZFPBIZWM+BGWfmREwX7iDwd+BTzHQIzwG3An9IXphCDEwdnbwdbjcBj6ftsYwMLAYLZ1ExX7dsZV2Ol3r7DgoCWYxtcjGyqCTVoYk0l0i37d8AJwAXs3PaAwC01s3AIuDIpEQnxADX0RxNWTHmwfHOmMxS36fM/3gBL65fQlXDphRFLUTv2T5uV5Znbqap1cuQYAZNrV6WZ25m+7hdUx2aSHOJJDRnAI9pre8g9ngznwC79ygqIQaJzmYkzi4fRcnsOQz78U9oPmRf3mxZh8fnpTArH4/Py9KNyySpEQPOJ46t5JeNIcfpAm8zOU4X+WVj+MQhw5uJziXShmY0cFsnz9djxqMRQnQh3jma1lSvxe104c5wAbT9XVO9lrK8EX0etxC9pba5nsKCUmyFu7Qt822rZ9O6NWz+z0bpxi06lEhC0wAUdfL8d4DqxMIRYvCJZ46m2uZ6CrPyI5a5nNnUNkvbezGwFGUX4PF525J2//Zt1G9YxxBHtnTjFp1KpMrpLeB0pVS7OZ2UUoXAWZgJLIUQSVKUXYDX3xyxzOtvpii7IEURCdE7JpZOwOP34vF5CQaDbPumkh2ZdsbbhmGz2XC4c7C73TSuXpXqUEWaSSShuRHYA3gNONpaNlEpdS6wGsgBbkpOeEIIaH+S9/i8ePxeJpZOSHVoQiRVWd4IZo6agTvDRd2ObWR5WxgbLOETRy2Lsj7n9YxKtuQEpRu3aKfbCY3W+n1ML6c9gYetxbcC9wAuYI7W+uOkRSiEaHeSd2e4mDlqhrSfEQNSWd4IjtptFj8cdxLjM8pYZ9uK1+YnP5iJ1+bnHUclW0uyUx2mSDMJDayntX5RKTUa+D92dt3+DPi31trT2WuFEIkpyxshCYwYdL4ozyLrywBZjgBkOMjyBQi0BvhiTBZSPinCJTxSsNZ6B/Av658QQgiRdNszgxSMHotv82YCXg92l5uC8lFszwymOjSRZhJOaHqDUuoy4GZgjdb6e6mORwghRGoVZRfgcXhxqz3blnl8XoqsXlBChCSU0CilTgV+jmkcHGtymaDWulvbVkoNA64CmhKJSYiBpqphE2uq11LbXE9RdgETSydIlZMYdCaWTmDpxmWAGarA62/G4/cybcSUFEcm0k0iczldBVwPfAu8A9QlKZabgPcxDZWlL6oY1KoaNrF04zLcTlfEyMDSEFgMNqEG8eHJ/bQRU+R3INpJpITmZ8AbwOFaa18yglBKTQVOByYD85KxTSH6MxkZWIidpEG8iEci49AMARYkMZmxAXcCj2qt/5uMbQrR39U21+NyRnZLlZGBhRCiY4mU0HwAlCcxhjOAccBxSdymEP1a9PDvICMD/3979x4lZ1knePxb1fdKdy6ddICQDhfRBwQFEpFFMWtGJ6KDgjrO8ah4Y3Qdx0UdZ3VmZRTxsjrex9s4XlF35qCrw4gKRqIYgWVnTTBjPMsDKjEJARM6F5JUd6e7q/aPt6rtNJ2k0re33urv55w63fW+T3X96pfuyq+e97lI0rFMpqC5Fvh2COHbMcZ7pvLkIYQukrEzH4wxPjSVn7V4cedUHl63enq60g4hMxopV2uaL+bmeBvllhEKLR0Uh/oplYdZ84SL6Vk09dfZSLmaaeaqduaqduZq+p1wQRNj/GkI4Wrg7hDC3cBWYGRcs3KM8eoafty1wGHgYycax3h9fQcplRprXYKeni527z6QdhiZ0Gi5KrCApy+9hM27t/DggV10ty/k6UsvoTC8YMqvs9FyNZPMVe3MVe3M1bHl87lJdVJMZpbTxcANQAvwjMptvDJwzIImhHAK8Bbg74CTQgjVU+1Aa2Ul4v0xxumaRSVligMhJal2k7nk9EmSXpUrgJ/FGCc7SvEkoJVkIb0PTXD+gcrxv5nkz5ckaVoNbN/GwU0bGd7TR3P3YjpXrqK9d0XaYYnJFTRPBq6LMd48xed+AHjhBMffR7Jj91uB+6b4HJIkTYuB7dvYu+5W8oUCTYu6GSkeYu+6W1m09jKLmjowmYJmF0kPzZTEGPcDN40/HkJ4CzAcY3zMOUmS0nJw08akmCnMAxj9enDTRguaOjCZdWi+DLwihFBX+0BJkjSThvf0ke8oHHEs31FgeE9fShFprMkUJXcAl5PMcvosyaWj8bOciDFumExAMcZnTuZxUla5Z5OUDc3dixkpHhrtmQEo9Rdp7p5oS0PNtskUNLeN+f6LJDOaxspVjjVNNihprnDPJik7OleuYu+6W4GkZ6bUX6RULLLg0tUpRyaYXEHzmmmPQpqj3LNJyo723hUsWnvZEbOcFly62vEzdWIyC+vdMBOBSHPF2GmfO0/ZS89Jp8GCP2xx4J5NUv1q711hAVOnJjMoWNIkVad9jhQP0bSom/mHc+zbeh/Dj+4fbeOeTZJ04iY1UymEMA94O8k6MmdWDv8W+A7w4RjjoekJT8qmoy2+NX7a57m5k7mzdRv7H9pOd9d8+ocHKA73c8myi1J+BZKULSfcQxNC6Ab+ncqWBSS7b99T+f5dwL9X2khz0vhemOriWwPbtz1m2ufJpXk8baSXtv7D7B3cT6GlwwHBkjQJk+mhuR44G3gT8PkY4whACKEJeD3wKeA64JppilHKlGMtvjXRtM+lh3KcUggseeJEC2dLkmoxmYLmBcAXY4yfHXuwUth8LoRwIXAlFjSao4b39NG06MhOyuriWwufvZZ7f3ITMfcwj7aWmX84Rxhq5eyVTvuUpKmYzKDg6mWmo9lUaSPNSc3diyn1F484Vl1865GFzWw6Zx6DLXm6isMMtuTZdM48HlnowtuSNBWTeRf9PXDhMc5fWGkjzUnHWnzr/+zeQtf8JRQW9462Lw71u+6MJE3RZHpobgauDiH8lxDC6ONDCPkQwuuB1wLfna4ApSzKtbTSf1/k0OZ7KA8Pj+7Gu2dgHx3N7Ue0dd0ZSZq6yfTQvAv4Y+CzwHtCCLFyPAA9wK+Bd09PeFK2VGc45QsF5p1/4WjvTFV3+0KKQ/2jKwKD685I0nQ44R6aGGMf8BTgg0AfcFHl9gjwP4CLKm2kOWfsDKdcLkdTYR75QoGDmzYCcH7PeRSH+ykO9VMulykO9VMc7uf8nvNSjlySsm1SIxFjjI8C76zcJFUca4YTwPKuZTxrxeojdte+ZNlFjp+RpClyaoU0jSZaZ6Y6w6lqedcyCxgpo3Yc2HnEB5Lze87z77lOHLegCSFMaoGMGOOGyTxOyrJjzXCSlG07Duxk/bYNFJo7WNS2gOJQP+u3bXB17zpRSw/N7UD5BH5mrtK+aTIBSVnW3ruCRWsvO2IfpwWXrnZ3XqkBbN69hUJzx+ig/upXl12oD7UUNK+Z8SikBtLeu8ICRmpAewb2sahtwRHHXHahfhy3oIkx3jAbgUiSVM9cdqG+TWZhPUmS5hyXXahvtQwKXgEQY9w29v7xVNtLktQIXHahvtUyhmYrUA4hdMQYD1fv1/A4BwVrznJqp9SYXHahftVS0FxPUsAMj7t/LLmpBCVlmVM7JWn21TIo+LoQwnkxxlL1/vEeE0L41DTEJmXSzx783/y+uIvh0ggdze2cPG8pheYOp3ZK0gyqdVDwD0MIp9fSMITwD8AbJx2RlGE7Duzk3j33Uy4n0zmHSsP8dv/vGCoNObVTkmZQrVsfdAK3hRCeHmP8/dEahRA+AbwJuHU6gpOyZvPuLcxrmUf1qmxLPvkT23FwJ+cuPjvFyCSlrTq2rvjbQxSY59i6aVZrD80LgGXAuhDChBPuQwgfA64BfghcOT3hSdmyZ2Afy+edwnBpmKHSEOVyGShzaKjo1E5pDttxYCfr7r2FvriF3Jb76YtbWHfvLew4sDPt0BpGTQVNjPGnwJ8B5wA/CCEUxp4PIXwUeAuwDriiMhtKmnO62xfS0tTCGfNPoyXfwmBpEMhx9qLH+0lMmsM2/uZO8jseom2oRHOhQNtQifyOh9j4mzvTDq1h1LywXozxe8CrgYuBm0IILQAhhA8DbwV+hMWM5rjqwlvN+WYev/BMzlpwJicVenjG8kvSDk1SinY9vJX2pjbyLa2Qy5FvaaW9qY1dD29NO7SGcUIrBccY/5lkjMyzgX8JIfw98DZgPUkxMzj9IUrZUV14q9DSwd7B/RRaOpyuLYn5xREGW478L3ewJc/84khKETWeWgcFj4oxfq4yjub9JCMf1wOXW8xICRfekjTeuS3LubO0jVw+RzN5+hlmoDTIqhY3sp0uNRU0IYS/GndoEPgtcDLwU+AvQwhjz5djjB+flgglScq4sy5YzfBPbiIuPMy+5kEKQ2WevK+Ts9asTju0hlFrD81HjnHu+gmOlQELGkmSgPbeFZy95kqWb9pI8yOPMlyYT+eaVbT32kMzXWotaNZM9xOHEJ4CvBNYCSwF9gO/AK6PMd413c8nSVKa2ntX0N67gp6eLnbvPpB2OA2npoKmMm17uj2u8vxfAB4CFgIvBzaEEJ4bY/zRDDynJElqQCc8KHi6xBhvBG4ceyyE8DmSsTlvJpkGLkmSdFwnNG17psUYi8Bukt4aSZKkmqTWQ1MVQugC2oDFwKuA85h4oLEkSdKEUi9ogK8AL658fxj4R+AD6YUjSZKyJpdsnpeeEMKTSNazWQ5cBWwFrokxHqzxR5wOPDAjwUmSpLScQVIT1CT1gmasyv5QPwfujzH+aY0POx14oK/vIKVS/byW6eDUvtqZq9qZq9qZq9qZq9qZq2PL53MsXtwJJ1jQ1Nug4CHg34AXhRA60o5HkiRlQ10VNBUdQA7oSjsQSZKUDakVNCGEngmOzQdeAmyPMe6a/agkSVIWpTnL6cYQwgBwF/Aw0Au8hmRw8EtTjEuSJGVMmgXNN4BXAtcAi4B9wN3AVTO01YIkSWpQaW598GXgy2k9vyRJahz1OChYkiTphFjQSJKkzLOgkSRJmWdBI0mSMs+CRpIkZV497LYtzaodB3ayefcW9gzso7t9Ief3nMfyrmVphyVJmgJ7aDSn7Diwk/XbNlAc6mdR2wKKQ/2s37aBHQd2ph2aJGkK7KFRwxvbI/NIfx+dw80U9uziUH+RfEeB1qXdbN69xV4aScowe2jU0Mb3yDxa3MvOPVt5dOQQuY4OSkOHYes2du/ZkXaokqQpsKBRQ9u8ewuF5g4KLR3kcjk6+kcgl6evdZgcOfItrQy2NjFv18G0Q5UkTYEFjRranoF9dDS3j95f3J+j3JTjEMOUKdPPMIMtOZ6wxz8FScoy38XV0LrbF9I/PDB6f37rfJYebmNeuZn9ucN0lJv5TwcWcWrXqSlGKUmaKgsaNbTze86jONxPcaifcrnM8NJu8sMlnvPoyVw58DhW7+9m6aNlOleuSjtUSdIUWNCooS3vWsazVqym0NLB3sH9zF+0lLVP/BNObV3CyN49NBXmsWjtZbT3rkg7VEnSFDhtWw1vedeyx07JfvzKdIKRJM0Ie2gkSVLmWdBIkqTMs6CRJEmZZ0EjSZIyz4JGkiRlngWNJEnKPAsaSZKUeRY0kiQp8yxoJElS5lnQSJKkzLOgkSRJmWdBI0mSMs+CRpIkZZ4FjSRJyjwLGkmSlHkWNJIkKfMsaCRJUuZZ0EiSpMxrTuuJQwgXAa8G1gCnAX3AXcC1McZfpxWXJEnKnjR7aN4BvAi4DXgz8E/AM4F7QgjnpBiXJEnKmNR6aICPAS+LMR6uHggh3Aj8kqTYeXVKcUmSpIxJraCJMd41wbH7Qwi/AuyhkSRJNaurQcEhhBxwEvBI2rFIkqTsSPOS00ReDpwKvPNEH7h4cef0R1MHenq60g4hM8xV7cxV7cxV7cxV7czV9KubgiaEcDbwGeAO4Osn+vi+voOUSuVpjytNPT1d7N59IO0wMsFc1c5c1c5c1c5c1c5cHVs+n5tUJ0VdFDQhhJOB7wN7gZfEGEsph6QGMrB9Gwc3bWR4Tx/N3YvpXLmK9t4VaYclSZpGqY+hCSEsAG4BFgDPiTE+nHJIaiAD27exd92tjBQP0bSom5HiIfauu5WB7dvSDk2SNI1SLWhCCO3AzcATgMtjjDHNeNR4Dm7aSL5QoKkwj1wuR1NhHvlCgYObNqYdmiRpGqVW0IQQmoAbgUtILjPdnVYsalzDe/rIdxSOOJbvKDC8py+liCRJMyHNMTQfBV5A0kPTHUJ4xZhzB2OMN6UTlhpJc/fi5HJTYd7osVJ/kebuxSlGJUmabmkWNBdUvj6/chvrd4AFjaasc+Uq9q67FUh6Zkr9RUrFIgsuXZ1yZJKk6ZTmSsHPTOu5NXe0965g0drLjpjltODS1c5ykqQGUxfTtqWZ1N67wgJGkhpc6tO2JUmSpsqCRpIkZZ4FjSRJyjwLGkmSlHkWNJIkKfMsaCRJUuZZ0EiSpMyzoJEkSZlnQSNJkjLPgkaSJGWeBY0kSco8CxpJkpR5FjSSJCnzLGgkSVLmWdBIkqTMs6CRJEmZZ0EjSZIyz4JGkiRlngWNJEnKPAsaSZKUeRY0kiQp8yxoJElS5lnQSJKkzLOgkSRJmWdBI0mSMs+CRpIkZZ4FjSRJyjwLGkmSlHkWNJIkKfMsaCRJUuZZ0EiSpMyzoJEkSZnXnOaThxBOAd4MXAw8BegE1sQYb08zLkmSlC1p99AE4B3AcuA/Uo5FkiRlVNoFzUZgSYzx8cCHU45FkiRlVKqXnGKMB9J8fkmS1BhSLWjmooHt2zi4aSPDe/po7l5M58pVtPeuSDssSZIyrWEKmsWLO9MO4bgOPrCVvRvW0zZvHoVTT2akWKR/w3oWXfECOs84fcLH9PR0zWqMWWauameuameuameuameupl/DFDR9fQcplcpph3FMj6zfwIOtw9zX+jD7SoMsbG3jCUMdjKzfwJIrFj+mfU9PF7t3e1WuFuaqduaqduaqduaqdlnN1Y4DO9m8ewt7BvbR3b6Q83vOY3nXsml/nnw+N6lOirQHBc8pDx54kLu79tKfG2ZBuZX+3DB3d+3lwQMPph2aJElHtePATtZv20BxqJ9FbQsoDvWzftsGdhzYmXZooyxoZtF93SXahsp00EyOHB000zZU5r7uUtqhSZJ0VJt3b6HQ3EGhpYNcLkehpYNCcwebd29JO7RRDXPJKQsOLe2k7XcHKZUPk2tpoTw0RNvQCIdOq//xP5KkuWvPwD66BqH48O8o9RfJdxRoOflk9rQNph3aKHtoZlFP93I4fQX5llbK/f3kW1rh9BXJcUmS6tT8wzn2bb2P0tBhch0dlIYOs2/rfcw/nEs7tFGp99CEEK6tfHtO5etVIYRLgX0xxk+nFNaMOL/nPNb3b6D5zNOY19xO//AAh4f7Ob/nvLRDkyTpqB63fZA7W/Pk83nagcGWPINNeR63fRAuSDu6ROoFDfDecfdfW/n6O6ChCprlXct41orVR4wSv2TZRTMySlySpOmy5JEBnra4l3tze9mXH2RhqY0LR3pZ0jeQdmijUi9oYoz10181C5Z3LbOAkSRlSnP3YpYeOsQphd7RYyPFQzR1P3bJkbQ4hkaSJB1T58pVlIpFRoqHKJfLjBQPUSoW6Vy5Ku3QRlnQSJKkY2rvXcGitZfRVJjHyN49NBXmsWjtZXW1dU/ql5wkSVL9a+9dUVcFzHj20EiSpMyzoJEkSZlnQSNJkjLPgkaSJGWeBY0kSco8CxpJkpR5FjSSJCnzXIemBjsO7Dxi/6Xze85z+wJJkuqIBc1x7Diwk3X33kLzI/tp7R+kr6ONdX3bWXv2cy1qJEmqE15yOo6Nv7mT/I6HaBsqke8oJF93PMTG39yZdmiSJKnCHprj2PXwVrqa2si3tAKQa2mlnTK7Ht6abmCSJGmUPTTHMb84wmDLkWkabMkzvziSUkSSJGk8C5rjOLdlOQOlQfoZpkyZfoYZKA1ybsvytEOTJEkVFjTHcdYFq7m4r5O2oRL7c4dpGypxcV8nZ12wOu3QJElShWNojqO9dwVnr7mS5Zs2MvxQH83di+lcs6qut1CXJGmusaCpQXvvCgsYSZLqmJecJElS5lnQSJKkzLOgkSRJmWdBI0mSMs+CRpIkZZ4FjSRJyjwLGkmSlHkWNJIkKfMsaCRJUuZZ0EiSpMyzoJEkSZlnQSNJkjLPgkaSJGVeI+y23QSQz+fSjmNGNOrrmgnmqnbmqnbmqnbmqnbm6ujG5KbpRB6XK5fL0x/N7LoU+FnaQUiSpGn1DOCOWhs3QkHTBlwEPASMpByLJEmamibgFOD/AoO1PqgRChpJkjTHOShYkiRlngWNJEnKPAsaSZKUeRY0kiQp8yxoJElS5lnQSJKkzLOgkSRJmWdBI0mSMq8R9nLKpBDCKcCbgYuBpwCdwJoY4+0TtH0BcB3wRGAX8CXg/THG4dmKNy0hhIuAVwNrgNOAPuAu4NoY46/HtX0a8PfASuBR4Ebgb2OMxdmMOS0hhKcA7yR5/UuB/cAvgOtjjHeNazunczWREMLbgQ8Bm2OMF4w7N2fzFUJ4JvCTo5w+J8Z475i2czZPY1Xet64Dnga0AL8BPh5j/OqYNnP2fX2mWNCkJwDvAH4N/AfJL/5jG4XwXOAm4MfAfwWeBLwLWFK53+jeATwd+BZJnk4G3gTcE0J4aozx/wGEEC4A1gO/Av4KWA78NXAm8PwU4k7D40j+pr9AshXIQuDlwIYQwnNjjD8CczWREMLJwLXAoQnOma/EJ4CN447trH5jnhKV9+x/A24H/g4YAp4A9I5rM5ff12eEBU16NgJLYox9IYQrgX89SruPAPcAz4kxjgCEEB4F/jaE8A8xxvtnJ9zUfAx4WYzxcPVACOFG4Jckxc6rK4c/QNJ788wY48FKu63AF0IIfxRj/PEsxpyKGOONJJ+IR4UQPgf8lqQ38EeVw3M+VxP4IPBzksvwC8edM1+Jn8YYbzrG+TmfpxDCAuCrwOdijG8+RtO5/r4+IxxDk5IY44EYY9+x2oQQnkjSHfn56i99xWdJ/u1ePIMh1oUY411ji5nKsftJPgWeAxBCmA/8MfC16htpxdeAg8CfzVK4dafS1b+byn/S5uqxQghPBV5B0qsw/pz5GiOE0BVCeMwHYfM06mUkf2vvgtF85cY28H195ljQ1LcLK19/PvZgjHEnsGPM+Tml8gZxEvBI5dCTSHobx+fpMMkYkjmVp8qb6JKQ+ABwHsmlADBXR6j8Ln0KuCHG+IsJmpivP/g6ybiY/hDCuhDCk8acM0+JZwP3As8LIWwnydeeEMIHQwhNlTa+r88QC5r6dkrl60MTnHsIWDaLsdSTlwOnAt+s3DdPR/oKSa/MvcDbgH8kuRwA5mq8V5J8Wr72KOfNFxwG/hfJZcsrgPcATwXuCCE8odLGPCXOIhkr89XK7cUkwwneAXy00sZczRDH0NS3jsrXwQnODQCFWYylLoQQzgY+A9xB8okRjp+njgmON7L3AJ8nGZR5FdBGMtNiEHM1KoTQRTJ25oMxxon+cwHzRWWG3NhZct8NIdxM0sPwbpIPGHM+TxWdwCLgb2KMH6oc+04IoRN4Ywjhffi+PmPsoalv/ZWvbROcax9zfk6ozET5PrAXeEmMsVQ5ZZ7GiDH+Msb4oxjjV4DnAKtIPi2CuRrrWpLeh48do435mkCMcTNwG/CsyiHzlKi+zn8Zd/x/knyoeCrmasZY0NS36qfGUyY4dwpjpkw2usrsgVuABSQzAx4ec9o8HUWMcYhkCumLQggdmCtgdB2ot5D09p0UQjg9hHA6yX8orZX7izBfx7Id6K58b54S1Tz8ftzx6n1/p2aQBU19qw5SfMrYgyGEZSSXEyYaxNhwQgjtwM0kazlcHmOM45psAYZ5bJ5agQuYI3k6hg4gB3RhrqpOAlpJFtJ7YMztYpLZcw+QjHswX0d3JslYLTBPVdV1ek4dd3x55etufF+fMRY0dSzG+CuSgZ2vHzNCHuAvgBLw7VQCm0WV130jcAnJZaa7x7eJMe4n6f6+qnKtuuoqkmva35qNWNMWQuiZ4Nh84CXA9hjjLnM16gHghRPcfgVsrXz/NfN11N+rS0lW7/4h+Dc4RvV1Xl09UJlJ9+ckizbe7fv6zMmVy+W0Y5izQgjVmRXnkKxf8GWSN9p9McZPV9pcDnyXZEXJG0mm4L6JZA2DN8560LMshPAJktkVN/OHWU1VB6sLfYUQVpIMXNwCfJHkk87bgJ/EGJ83exGnJ4TwY5JBhXcBD5PMtngNSS5eGmP8ZqXdnM/V0YQQbgcWjt36YK7nq/J7VSTJwSMk70GvJ9la46IY47ZKuzmdp6oQwg0khdyXgE3An1Rub48xfrjSZk6/r88Ue2jS9d7K7WWVzmZfiQAAA9RJREFU+6+t3P/raoMY4/eAFwGLSdbLeBHwPuCaWY00PdX/WJ5PMqtp7O0T1UYxxk0ka0AMAh8HXkeyBcBLZjPYlH2DZIbENcDngDcCm0n2CBstBs3ViTFf3AT0kBQnnyGZivzPjClmwDyN8Trg/SQD8j9JMpX7DdViBnxfnyn20EiSpMyzh0aSJGWeBY0kSco8CxpJkpR5FjSSJCnzLGgkSVLmWdBIkqTMs6CRJEmZZ0EjSZIyrzntACTNTZXdrHeS7HD9yhjj11MOSVKG2UMjKS0vB9pI9i97bcqxSMo4CxpJabka+AnJnlz/OYRwZsrxSMowLzlJmnWVnZkvAF4F/AD4CEkvzbXj2jUB/x34c+Ak4D6Sjf/OAd4NnBFj3Dqm/SnAu0h2Nz6ZZHfo7wHXxhh3zeiLkpQqe2gkpeFq4CDw7Rhjteh4VQhh/HvSp4Hrgd8A/41k5+fPApeP/4EhhBXAz4E/JdkN+i9JdmV/KXBnCGHBzLwUSfXAHhpJsyqE0A68jKSYOVQ5fAPwQuA5wC2VducCbwB+CDwvxliqHP8W8IsJfvSngBbgwhjjjjHP9y3gbuCtwHUz8JIk1QF7aCTNthcBC0mKmKofALs5cnBwtRfmk9ViBiDG+EuSImdUpfflcuC7wEAIYUn1BmwFfg2snebXIamO2EMjabZdTVK87AghnDXm+DrgJSGEJZXLUGdUjscJfkYEnjvmfiD5gHZ15TaR304pakl1zYJG0qwJIZwBrAFyJAN8J/IKkplPJyJX+foNjuz5Gav/BH+mpAyxoJE0m15DUny8Dtg3wfn3kVx2+gTJpSJIel/G966Ecfd/DZSB1hjjbdMVrKTsyJXL5bRjkDQHVGYwbQX2xRiffJQ27yYZuPtUoAhs4bGDgp9EMig4z5hp2yGE75EMKn5GjPHucT83ByyJMe6e9hcmqS7YQyNptqwFeoEvHaPNt0kKmqtjjG8IIfwT8HrgthDCvwI9JNOx7wFWkfTKVP0FcAewIYTwtUqbPHAmcAXwNZzlJDUsZzlJmi3VwbrfOVqDGOMWkrE1Lw0hdABvJClCziJZfO9KksLl9spD+sc8djtJkfNJYDXwUeC9wLOBm4FvTtsrkVR3vOQkKXNCCDcDfwTMjzGOpB2PpPTZQyOpblV6acYfezLJlO0fW8xIqnIMjaR69qoQwiuB75OsXXM2yZiawyR7NkkSYEEjqb5tItkS4RqgGzgA/Bh4T4zxnjQDk1RfHEMjSZIyzzE0kiQp8yxoJElS5lnQSJKkzLOgkSRJmWdBI0mSMs+CRpIkZd7/B0P+X6I+lucNAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 648x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = sm.ols(formula = 'kilometers ~ np.log(age) + np.power(age, 5) + np.power(age, 4) + np.power(age, 3) + np.power(age, 2) + age + np.power(age, 0.5)', \n",
    "               data = training).fit()\n",
    "print(model.summary())\n",
    "\n",
    "# Get predictions for the training data and plot\n",
    "training['preds'] = model.predict(training['age'])\n",
    "\n",
    "plt.figure(figsize=(9,7))\n",
    "plt.scatter(training['age'], training['kilometers'], alpha=0.5, c='r')\n",
    "plt.scatter(training['age'], training['preds'], alpha=0.5, c='g')\n",
    "plt.title('Predicted and True Kilometers by Age for Training Data')\n",
    "plt.xlabel('Age')\n",
    "plt.ylabel('Kilometers')\n",
    "plt.legend()\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vemos que conforme el modelo se hace más complejo va adaptándose mejor a los datos. Pero hay que tener en cuenta que el modelo que hemos elegido es totalmente arbitrario: ¿por qué un polinomio de grado 7 y no uno de grado 17? Además, conforme vaya aumentando la complejidad del modelo se va incrementando el riesgo de *overfitting*, pudiendo tener modelos polinómicos con un error prácticamente cero de entrenamimento pero enorme en la validación. Por tanto, hay que usar este tipo de modelos con prudencia, solo cuando sepamos perfectamente lo que estamos haciendo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}