{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Régression linéaire\n",
    "\n",
    "Ce notebook s'intéresse à la façon d'interpréter les résultats d'une régression linéaire lorsque les variables sont corrélées puis il explore une façon d'associer arbre de décision et régression linéaire pour construire une régression linéaire par morceaux."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Un cas simple\n",
    "\n",
    "Une façon d'interpréter des résultats statistiques est de les calculer dans un cas où la réponse cherchée est connue. On simule un modèle simple $Y=\\alpha X_1 + 0.X_2 + \\epsilon$ et on cale une régression linéaire. On suppose que $X_1, X_2, \\epsilon$ sont des variables aléatoires gaussiennes de même variance et moyenne."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((1000, 3), (1000,))"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy.random as npr\n",
    "\n",
    "eps = npr.normal(1000)\n",
    "X = npr.normal(size=(1000, 3))\n",
    "alpha = 2\n",
    "Y = alpha * X[:, 0] + X[:, 2]\n",
    "X.shape, Y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        ,  0.02585011, -0.00808406],\n",
       "       [ 0.02585011,  1.        ,  0.00338766],\n",
       "       [-0.00808406,  0.00338766,  1.        ]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from numpy import corrcoef\n",
    "\n",
    "corrcoef(X.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.regression.linear_model import OLS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared (uncentered):</th>      <td>   0.803</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared (uncentered):</th> <td>   0.802</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>          <td>   2029.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 07 Oct 2024</td> <th>  Prob (F-statistic):</th>           <td>  0.00</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>11:29:03</td>     <th>  Log-Likelihood:    </th>          <td> -1417.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1000</td>      <th>  AIC:               </th>          <td>   2840.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   998</td>      <th>  BIC:               </th>          <td>   2849.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</td>      <th>                     </th>              <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>              <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "   <td></td>     <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th> <td>    1.9922</td> <td>    0.031</td> <td>   63.680</td> <td> 0.000</td> <td>    1.931</td> <td>    2.054</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th> <td>    0.0041</td> <td>    0.032</td> <td>    0.130</td> <td> 0.896</td> <td>   -0.058</td> <td>    0.067</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 4.685</td> <th>  Durbin-Watson:     </th> <td>   2.126</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.096</td> <th>  Jarque-Bera (JB):  </th> <td>   4.706</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.167</td> <th>  Prob(JB):          </th> <td>  0.0951</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.972</td> <th>  Cond. No.          </th> <td>    1.03</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] R² is computed without centering (uncentered) since the model does not contain a constant.<br/>[2] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/latex": [
       "\\begin{center}\n",
       "\\begin{tabular}{lclc}\n",
       "\\toprule\n",
       "\\textbf{Dep. Variable:}    &        y         & \\textbf{  R-squared (uncentered):}      &     0.803   \\\\\n",
       "\\textbf{Model:}            &       OLS        & \\textbf{  Adj. R-squared (uncentered):} &     0.802   \\\\\n",
       "\\textbf{Method:}           &  Least Squares   & \\textbf{  F-statistic:       }          &     2029.   \\\\\n",
       "\\textbf{Date:}             & Mon, 07 Oct 2024 & \\textbf{  Prob (F-statistic):}          &     0.00    \\\\\n",
       "\\textbf{Time:}             &     11:29:03     & \\textbf{  Log-Likelihood:    }          &   -1417.8   \\\\\n",
       "\\textbf{No. Observations:} &        1000      & \\textbf{  AIC:               }          &     2840.   \\\\\n",
       "\\textbf{Df Residuals:}     &         998      & \\textbf{  BIC:               }          &     2849.   \\\\\n",
       "\\textbf{Df Model:}         &           2      & \\textbf{                     }          &             \\\\\n",
       "\\textbf{Covariance Type:}  &    nonrobust     & \\textbf{                     }          &             \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lcccccc}\n",
       "            & \\textbf{coef} & \\textbf{std err} & \\textbf{t} & \\textbf{P$> |$t$|$} & \\textbf{[0.025} & \\textbf{0.975]}  \\\\\n",
       "\\midrule\n",
       "\\textbf{x1} &       1.9922  &        0.031     &    63.680  &         0.000        &        1.931    &        2.054     \\\\\n",
       "\\textbf{x2} &       0.0041  &        0.032     &     0.130  &         0.896        &       -0.058    &        0.067     \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lclc}\n",
       "\\textbf{Omnibus:}       &  4.685 & \\textbf{  Durbin-Watson:     } &    2.126  \\\\\n",
       "\\textbf{Prob(Omnibus):} &  0.096 & \\textbf{  Jarque-Bera (JB):  } &    4.706  \\\\\n",
       "\\textbf{Skew:}          & -0.167 & \\textbf{  Prob(JB):          } &   0.0951  \\\\\n",
       "\\textbf{Kurtosis:}      &  2.972 & \\textbf{  Cond. No.          } &     1.03  \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "%\\caption{OLS Regression Results}\n",
       "\\end{center}\n",
       "\n",
       "Notes: \\newline\n",
       " [1] R² is computed without centering (uncentered) since the model does not contain a constant. \\newline\n",
       " [2] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                                 OLS Regression Results                                \n",
       "=======================================================================================\n",
       "Dep. Variable:                      y   R-squared (uncentered):                   0.803\n",
       "Model:                            OLS   Adj. R-squared (uncentered):              0.802\n",
       "Method:                 Least Squares   F-statistic:                              2029.\n",
       "Date:                Mon, 07 Oct 2024   Prob (F-statistic):                        0.00\n",
       "Time:                        11:29:03   Log-Likelihood:                         -1417.8\n",
       "No. Observations:                1000   AIC:                                      2840.\n",
       "Df Residuals:                     998   BIC:                                      2849.\n",
       "Df Model:                           2                                                  \n",
       "Covariance Type:            nonrobust                                                  \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "x1             1.9922      0.031     63.680      0.000       1.931       2.054\n",
       "x2             0.0041      0.032      0.130      0.896      -0.058       0.067\n",
       "==============================================================================\n",
       "Omnibus:                        4.685   Durbin-Watson:                   2.126\n",
       "Prob(Omnibus):                  0.096   Jarque-Bera (JB):                4.706\n",
       "Skew:                          -0.167   Prob(JB):                       0.0951\n",
       "Kurtosis:                       2.972   Cond. No.                         1.03\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] R² is computed without centering (uncentered) since the model does not contain a constant.\n",
       "[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = OLS(Y, X[:, :2])\n",
    "results = model.fit()\n",
    "su = results.summary()\n",
    "su"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(np.float64(0.8026213180783517), np.float64(0.8022257696175868))"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.rsquared, results.rsquared_adj"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On vérifie que le coefficient devant $X_1$ est non nul (P-value nulle, 0 n'est pas l'intervalle de confiance). Le coefficient devant $X_2$ n'est pas nul mais presque, la P-value est élevée, le coefficient $R^2$ est élevé. Dessinons."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_21413/1827909711.py:6: UserWarning: \n",
      "\n",
      "`shade_lowest` has been replaced by `thresh`; setting `thresh=0.05.\n",
      "This will become an error in seaborn v0.14.0; please update your code.\n",
      "\n",
      "  seaborn.kdeplot(x=X[:, 0], y=Y, cmap=\"Reds\", shade=True, shade_lowest=False, ax=ax[1])\n",
      "/tmp/ipykernel_21413/1827909711.py:6: FutureWarning: \n",
      "\n",
      "`shade` is now deprecated in favor of `fill`; setting `fill=True`.\n",
      "This will become an error in seaborn v0.14.0; please update your code.\n",
      "\n",
      "  seaborn.kdeplot(x=X[:, 0], y=Y, cmap=\"Reds\", shade=True, shade_lowest=False, ax=ax[1])\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn\n",
    "\n",
    "fig, ax = plt.subplots(1, 2, figsize=(10, 4))\n",
    "ax[0].plot(X[:, 0], Y, \".\")\n",
    "seaborn.kdeplot(x=X[:, 0], y=Y, cmap=\"Reds\", shade=True, shade_lowest=False, ax=ax[1])\n",
    "ax[0].set_title(\"nuage de points\")\n",
    "ax[1].set_title(\"estimation de la densité\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evolution de R2\n",
    "\n",
    "Dans la régression précédente, le coefficient $R^2$ transcrit en quelque sorte la part du bruit $\\epsilon$ par rapport au terme $\\alpha X_1$. Faisons varier $\\alpha$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "alphas = []\n",
    "r2s = []\n",
    "for a in [0.1 * i for i in range(50)]:\n",
    "    Y = a * X[:, 0] + X[:, 2]\n",
    "    model = OLS(Y, X[:, :2])\n",
    "    results = model.fit()\n",
    "    alphas.append(a)\n",
    "    r2s.append(results.rsquared)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(alphas, r2s, \".\", label=\"observed\")\n",
    "ax.plot(alphas, [a**2 / (1 + a**2) for a in alphas], label=\"theoretical\")\n",
    "ax.set_xlabel(\"alpha\")\n",
    "ax.set_ylabel(\"r2\")\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dans ce cas de régression simple, la valeur à prédire est $y_i$, la valeur prédite est $\\hat{y_i}=\\alpha X_{1i}$ et la moyenne $\\bar{y} = \\alpha \\bar{X_1} + \\bar{\\epsilon} = 0$.\n",
    "\n",
    "$$R^2 = 1 - \\frac{\\sum_{i=1}^n (\\hat{y_i}-\\bar{y})^2}{\\sum_{i=1}^n (y_i - \\bar{y})^2}=1-\\frac{\\mathbb{V}\\epsilon}{\\alpha^2\\mathbb{V}X_1+\\mathbb{V}\\epsilon} = 1 - \\frac{1}{1+\\alpha^2}=\\frac{\\alpha^2}{1+\\alpha^2}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Deux variables corrélées\n",
    "\n",
    "On ne change pas le modèle mais on fait en sorte que $X_2=X_1$. Les deux variables sont corrélées."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared (uncentered):</th>      <td>   0.803</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared (uncentered):</th> <td>   0.802</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>          <td>   4062.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 07 Oct 2024</td> <th>  Prob (F-statistic):</th>           <td>  0.00</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>11:29:04</td>     <th>  Log-Likelihood:    </th>          <td> -1417.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1000</td>      <th>  AIC:               </th>          <td>   2838.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   999</td>      <th>  BIC:               </th>          <td>   2843.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>              <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>              <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "   <td></td>     <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th> <td>    0.9961</td> <td>    0.016</td> <td>   63.736</td> <td> 0.000</td> <td>    0.965</td> <td>    1.027</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th> <td>    0.9961</td> <td>    0.016</td> <td>   63.736</td> <td> 0.000</td> <td>    0.965</td> <td>    1.027</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 4.681</td> <th>  Durbin-Watson:     </th> <td>   2.126</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.096</td> <th>  Jarque-Bera (JB):  </th> <td>   4.705</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.167</td> <th>  Prob(JB):          </th> <td>  0.0951</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.971</td> <th>  Cond. No.          </th> <td>3.15e+16</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] R² is computed without centering (uncentered) since the model does not contain a constant.<br/>[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[3] The smallest eigenvalue is 2.06e-30. This might indicate that there are<br/>strong multicollinearity problems or that the design matrix is singular."
      ],
      "text/latex": [
       "\\begin{center}\n",
       "\\begin{tabular}{lclc}\n",
       "\\toprule\n",
       "\\textbf{Dep. Variable:}    &        y         & \\textbf{  R-squared (uncentered):}      &     0.803   \\\\\n",
       "\\textbf{Model:}            &       OLS        & \\textbf{  Adj. R-squared (uncentered):} &     0.802   \\\\\n",
       "\\textbf{Method:}           &  Least Squares   & \\textbf{  F-statistic:       }          &     4062.   \\\\\n",
       "\\textbf{Date:}             & Mon, 07 Oct 2024 & \\textbf{  Prob (F-statistic):}          &     0.00    \\\\\n",
       "\\textbf{Time:}             &     11:29:04     & \\textbf{  Log-Likelihood:    }          &   -1417.8   \\\\\n",
       "\\textbf{No. Observations:} &        1000      & \\textbf{  AIC:               }          &     2838.   \\\\\n",
       "\\textbf{Df Residuals:}     &         999      & \\textbf{  BIC:               }          &     2843.   \\\\\n",
       "\\textbf{Df Model:}         &           1      & \\textbf{                     }          &             \\\\\n",
       "\\textbf{Covariance Type:}  &    nonrobust     & \\textbf{                     }          &             \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lcccccc}\n",
       "            & \\textbf{coef} & \\textbf{std err} & \\textbf{t} & \\textbf{P$> |$t$|$} & \\textbf{[0.025} & \\textbf{0.975]}  \\\\\n",
       "\\midrule\n",
       "\\textbf{x1} &       0.9961  &        0.016     &    63.736  &         0.000        &        0.965    &        1.027     \\\\\n",
       "\\textbf{x2} &       0.9961  &        0.016     &    63.736  &         0.000        &        0.965    &        1.027     \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lclc}\n",
       "\\textbf{Omnibus:}       &  4.681 & \\textbf{  Durbin-Watson:     } &    2.126  \\\\\n",
       "\\textbf{Prob(Omnibus):} &  0.096 & \\textbf{  Jarque-Bera (JB):  } &    4.705  \\\\\n",
       "\\textbf{Skew:}          & -0.167 & \\textbf{  Prob(JB):          } &   0.0951  \\\\\n",
       "\\textbf{Kurtosis:}      &  2.971 & \\textbf{  Cond. No.          } & 3.15e+16  \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "%\\caption{OLS Regression Results}\n",
       "\\end{center}\n",
       "\n",
       "Notes: \\newline\n",
       " [1] R² is computed without centering (uncentered) since the model does not contain a constant. \\newline\n",
       " [2] Standard Errors assume that the covariance matrix of the errors is correctly specified. \\newline\n",
       " [3] The smallest eigenvalue is 2.06e-30. This might indicate that there are \\newline\n",
       " strong multicollinearity problems or that the design matrix is singular."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                                 OLS Regression Results                                \n",
       "=======================================================================================\n",
       "Dep. Variable:                      y   R-squared (uncentered):                   0.803\n",
       "Model:                            OLS   Adj. R-squared (uncentered):              0.802\n",
       "Method:                 Least Squares   F-statistic:                              4062.\n",
       "Date:                Mon, 07 Oct 2024   Prob (F-statistic):                        0.00\n",
       "Time:                        11:29:04   Log-Likelihood:                         -1417.8\n",
       "No. Observations:                1000   AIC:                                      2838.\n",
       "Df Residuals:                     999   BIC:                                      2843.\n",
       "Df Model:                           1                                                  \n",
       "Covariance Type:            nonrobust                                                  \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "x1             0.9961      0.016     63.736      0.000       0.965       1.027\n",
       "x2             0.9961      0.016     63.736      0.000       0.965       1.027\n",
       "==============================================================================\n",
       "Omnibus:                        4.681   Durbin-Watson:                   2.126\n",
       "Prob(Omnibus):                  0.096   Jarque-Bera (JB):                4.705\n",
       "Skew:                          -0.167   Prob(JB):                       0.0951\n",
       "Kurtosis:                       2.971   Cond. No.                     3.15e+16\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] R² is computed without centering (uncentered) since the model does not contain a constant.\n",
       "[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[3] The smallest eigenvalue is 2.06e-30. This might indicate that there are\n",
       "strong multicollinearity problems or that the design matrix is singular.\n",
       "\"\"\""
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[:, 1] = X[:, 0]\n",
    "Y = 2 * X[:, 0] + X[:, 2]\n",
    "model = OLS(Y, X[:, :2])\n",
    "results = model.fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.int64(1)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.rank"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les variables corrélées n'ont pas l'air de déranger l'algorithme de résolution car il utilise la méthode [SVD](https://en.wikipedia.org/wiki/Singular-value_decomposition) pour résoudre le même problème dans un espace de moindre dimension. Le problème survient que les deux variables ne sont pas complétement corrélées. On étudie le modèle $Y \\sim X_1 + X'_2$ avec $X'_2 = \\alpha X_1 + (1-\\alpha) X_2$ et on réduit la variance du bruit pour en diminuer les effets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_ = npr.normal(size=(1000, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "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>r2</th>\n",
       "      <th>rank</th>\n",
       "      <th>c1</th>\n",
       "      <th>c2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.90</th>\n",
       "      <td>0.997328</td>\n",
       "      <td>2</td>\n",
       "      <td>1.013974</td>\n",
       "      <td>0.986445</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.91</th>\n",
       "      <td>0.997353</td>\n",
       "      <td>2</td>\n",
       "      <td>1.015480</td>\n",
       "      <td>0.984939</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.92</th>\n",
       "      <td>0.997379</td>\n",
       "      <td>2</td>\n",
       "      <td>1.017363</td>\n",
       "      <td>0.983056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.93</th>\n",
       "      <td>0.997403</td>\n",
       "      <td>2</td>\n",
       "      <td>1.019783</td>\n",
       "      <td>0.980636</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.94</th>\n",
       "      <td>0.997428</td>\n",
       "      <td>2</td>\n",
       "      <td>1.023011</td>\n",
       "      <td>0.977409</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.95</th>\n",
       "      <td>0.997453</td>\n",
       "      <td>2</td>\n",
       "      <td>1.027529</td>\n",
       "      <td>0.972890</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.96</th>\n",
       "      <td>0.997477</td>\n",
       "      <td>2</td>\n",
       "      <td>1.034306</td>\n",
       "      <td>0.966113</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.97</th>\n",
       "      <td>0.997501</td>\n",
       "      <td>2</td>\n",
       "      <td>1.045602</td>\n",
       "      <td>0.954817</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.98</th>\n",
       "      <td>0.997525</td>\n",
       "      <td>2</td>\n",
       "      <td>1.068193</td>\n",
       "      <td>0.932226</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.99</th>\n",
       "      <td>0.997548</td>\n",
       "      <td>2</td>\n",
       "      <td>1.135968</td>\n",
       "      <td>0.864452</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.00</th>\n",
       "      <td>0.997571</td>\n",
       "      <td>1</td>\n",
       "      <td>1.000861</td>\n",
       "      <td>1.000861</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             r2  rank        c1        c2\n",
       "alpha                                    \n",
       "0.90   0.997328     2  1.013974  0.986445\n",
       "0.91   0.997353     2  1.015480  0.984939\n",
       "0.92   0.997379     2  1.017363  0.983056\n",
       "0.93   0.997403     2  1.019783  0.980636\n",
       "0.94   0.997428     2  1.023011  0.977409\n",
       "0.95   0.997453     2  1.027529  0.972890\n",
       "0.96   0.997477     2  1.034306  0.966113\n",
       "0.97   0.997501     2  1.045602  0.954817\n",
       "0.98   0.997525     2  1.068193  0.932226\n",
       "0.99   0.997548     2  1.135968  0.864452\n",
       "1.00   0.997571     1  1.000861  1.000861"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alphas = [0.9 + i * 0.01 for i in range(11)]\n",
    "res = []\n",
    "for a in alphas:\n",
    "    X = X_.copy()\n",
    "    X[:, 1] = a * X[:, 0] + (1 - a) * X[:, 1]\n",
    "    Y = X[:, 0] + X[:, 1] + 0.1 * X[:, 2]\n",
    "    model = OLS(Y, X[:, :2])\n",
    "    results = model.fit()\n",
    "    res.append(\n",
    "        dict(\n",
    "            alpha=a,\n",
    "            r2=results.rsquared,\n",
    "            rank=model.rank,\n",
    "            c1=results.params[0],\n",
    "            c2=results.params[1],\n",
    "        )\n",
    "    )\n",
    "\n",
    "import pandas\n",
    "\n",
    "df = pandas.DataFrame(res)\n",
    "df = df.set_index(\"alpha\")\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(10, 4))\n",
    "df[[\"r2\"]].plot(ax=ax[0])\n",
    "df[[\"c1\", \"c2\"]].plot(ax=ax[1])\n",
    "ax[0].set_title(\"R2\")\n",
    "ax[1].set_title(\"coefficients\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le $r^2$ augmente quand la corrélation augmente mais les coefficients sont moins fiables. Les résultats devraient être sensiblement identiques en théorie mais en pratique, plus le déterminant devient proche de zéro, plus l'ordinateur est limité par sa précision numérique. Pour en savoir plus, vous pouvez lire un examen écrit que j'ai rédigé, en python bien sûr : [Examen Programmation ENSAE première année\n",
    "2006](https://sdpython.github.io/doc/teachpyx/dev/_downloads/f9f86ad8c2bcfcba777d6ed8caafb5f6/td_note_2006.pdf). Cette précision est aux alentours de $10^{-15}$ ce qui correspond à la précision numérique des [double](https://en.wikipedia.org/wiki/Double-precision_floating-point_format)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "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>r2</th>\n",
       "      <th>rank</th>\n",
       "      <th>c1</th>\n",
       "      <th>c2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>-1.000000e-10</th>\n",
       "      <td>0.806651</td>\n",
       "      <td>2</td>\n",
       "      <td>1.355493e+08</td>\n",
       "      <td>-1.355493e+08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-1.000000e-11</th>\n",
       "      <td>0.806651</td>\n",
       "      <td>2</td>\n",
       "      <td>1.355632e+09</td>\n",
       "      <td>-1.355632e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-9.999779e-13</th>\n",
       "      <td>0.806651</td>\n",
       "      <td>2</td>\n",
       "      <td>1.355997e+10</td>\n",
       "      <td>-1.355997e+10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-1.000311e-13</th>\n",
       "      <td>0.806651</td>\n",
       "      <td>2</td>\n",
       "      <td>1.357117e+11</td>\n",
       "      <td>-1.357117e+11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-9.992007e-15</th>\n",
       "      <td>0.806648</td>\n",
       "      <td>2</td>\n",
       "      <td>1.410632e+12</td>\n",
       "      <td>-1.410632e+12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-9.992007e-16</th>\n",
       "      <td>0.806616</td>\n",
       "      <td>2</td>\n",
       "      <td>1.008605e+00</td>\n",
       "      <td>1.008605e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-1.110223e-16</th>\n",
       "      <td>0.806616</td>\n",
       "      <td>1</td>\n",
       "      <td>1.008605e+00</td>\n",
       "      <td>1.008605e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.000000e+00</th>\n",
       "      <td>0.806616</td>\n",
       "      <td>1</td>\n",
       "      <td>1.008605e+00</td>\n",
       "      <td>1.008605e+00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     r2  rank            c1            c2\n",
       "alpha_1                                                  \n",
       "-1.000000e-10  0.806651     2  1.355493e+08 -1.355493e+08\n",
       "-1.000000e-11  0.806651     2  1.355632e+09 -1.355632e+09\n",
       "-9.999779e-13  0.806651     2  1.355997e+10 -1.355997e+10\n",
       "-1.000311e-13  0.806651     2  1.357117e+11 -1.357117e+11\n",
       "-9.992007e-15  0.806648     2  1.410632e+12 -1.410632e+12\n",
       "-9.992007e-16  0.806616     2  1.008605e+00  1.008605e+00\n",
       "-1.110223e-16  0.806616     1  1.008605e+00  1.008605e+00\n",
       " 0.000000e+00  0.806616     1  1.008605e+00  1.008605e+00"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alphas = [1 - 10 ** (-i) for i in range(10, 18)]\n",
    "res = []\n",
    "for a in alphas:\n",
    "    X = X_.copy()\n",
    "    X[:, 1] = a * X[:, 0] + (1 - a) * X[:, 1]\n",
    "    Y = X[:, 0] + X[:, 1] + X[:, 2]\n",
    "    model = OLS(Y, X[:, :2])\n",
    "    results = model.fit()\n",
    "    res.append(\n",
    "        dict(\n",
    "            alpha_1=a - 1,\n",
    "            r2=results.rsquared,\n",
    "            rank=model.rank,\n",
    "            c1=results.params[0],\n",
    "            c2=results.params[1],\n",
    "        )\n",
    "    )\n",
    "\n",
    "import pandas\n",
    "\n",
    "df = pandas.DataFrame(res)\n",
    "df = df.set_index(\"alpha_1\")\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On fait un dernier test avec [scikit-learn](http://scikit-learn.org/stable/) pour vérifier que l'algorithme de résolution donne des résultats similaires pour un cas où le déterminant est quasi-nul."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "    }\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>c1</th>\n",
       "      <th>c2</th>\n",
       "      <th>r2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.90</th>\n",
       "      <td>1.140599</td>\n",
       "      <td>0.863675</td>\n",
       "      <td>0.791250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.91</th>\n",
       "      <td>1.155746</td>\n",
       "      <td>0.848528</td>\n",
       "      <td>0.792821</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.92</th>\n",
       "      <td>1.174680</td>\n",
       "      <td>0.829593</td>\n",
       "      <td>0.794384</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.93</th>\n",
       "      <td>1.199024</td>\n",
       "      <td>0.805250</td>\n",
       "      <td>0.795940</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.94</th>\n",
       "      <td>1.231482</td>\n",
       "      <td>0.772791</td>\n",
       "      <td>0.797489</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.95</th>\n",
       "      <td>1.276924</td>\n",
       "      <td>0.727350</td>\n",
       "      <td>0.799029</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.96</th>\n",
       "      <td>1.345087</td>\n",
       "      <td>0.659187</td>\n",
       "      <td>0.800562</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.97</th>\n",
       "      <td>1.458691</td>\n",
       "      <td>0.545583</td>\n",
       "      <td>0.802087</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.98</th>\n",
       "      <td>1.685900</td>\n",
       "      <td>0.318374</td>\n",
       "      <td>0.803603</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.99</th>\n",
       "      <td>2.367526</td>\n",
       "      <td>-0.363252</td>\n",
       "      <td>0.805111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.00</th>\n",
       "      <td>1.008682</td>\n",
       "      <td>1.008682</td>\n",
       "      <td>0.806575</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             c1        c2        r2\n",
       "alpha                              \n",
       "0.90   1.140599  0.863675  0.791250\n",
       "0.91   1.155746  0.848528  0.792821\n",
       "0.92   1.174680  0.829593  0.794384\n",
       "0.93   1.199024  0.805250  0.795940\n",
       "0.94   1.231482  0.772791  0.797489\n",
       "0.95   1.276924  0.727350  0.799029\n",
       "0.96   1.345087  0.659187  0.800562\n",
       "0.97   1.458691  0.545583  0.802087\n",
       "0.98   1.685900  0.318374  0.803603\n",
       "0.99   2.367526 -0.363252  0.805111\n",
       "1.00   1.008682  1.008682  0.806575"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import r2_score\n",
    "\n",
    "alphas = [0.9 + i * 0.01 for i in range(11)]\n",
    "res = []\n",
    "for a in alphas:\n",
    "    X = X_.copy()\n",
    "    X[:, 1] = a * X[:, 0] + (1 - a) * X[:, 1]\n",
    "    Y = X[:, 0] + X[:, 1] + X[:, 2]\n",
    "    model = LinearRegression()\n",
    "    model.fit(X[:, :2], Y)\n",
    "    r2 = r2_score(Y, model.predict(X[:, :2]))\n",
    "    res.append(dict(alpha=a, c1=model.coef_[0], c2=model.coef_[1], r2=r2))\n",
    "\n",
    "import pandas\n",
    "\n",
    "df = pandas.DataFrame(res)\n",
    "df = df.set_index(\"alpha\")\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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phLBPWq2WIUOG8OOPP7Jz584y7yuKwj333ENsbCzbtm2zLc/NzWXhwoUEBwfbmlw+8sgjJCYm8umnn5bZT35+Prm5uVUSs6+vL7fffjuLFy8mISGhTLxXM2DAANzd3XnnnXcoLCws8355I01fj4uLC1D2xiwvL892/S4REhKCm5tbuVMrCVETKvJ9B+Q7fw019Z2v6Gc7ZMgQtFotb775Zpnp026kVviRRx5h27Zt/Prrr2Xeu3jxIkVFRRXe181+/q6urrbjVlRF/3Yrqlu3bvj6+rJgwYJS0xfGxMSUiaskAb+8H7/ZbC7TbD0sLIyQkBBmzZpFTk5OmWOWfC46nY6HHnqIb775ptwfqW7k7/dmSRWhEMArr7zC0KFDiYmJ4cknn2TAgAFcuHCBV155pcxckCEhIfTs2VOlSIUQtd0777zDb7/9Rt++fW3TACUlJbFy5Uq2bNnCxIkT+d///sfdd9/NCy+8gJeXF0uXLuXkyZN88803tgGMhg0bxooVK3jmmWfYuHEjvXv3xmw2ExcXx4oVK2zz3VaF//znP/Tp04euXbvy9NNP07x5c06dOsXq1avZu3dvudu4u7szf/58hg0bRteuXXnsscfw9fUlISGB1atX07t3bz766KNKxeHs7Ey7du1Yvnw5rVq1wsvLiw4dOlBUVES/fv145JFHaNeuHQ4ODnz33XekpKTw2GOPVcEnIMSNud733dPTU77z13Cz3/mYmBiio6NZsmQJUVFRVz1ORT/b0NBQXn/9dWbMmMFtt93Ggw8+iMFgYMeOHTRq1Mg2HV5FvfLKK/zwww/ce++9tqnbcnNz2b9/P19//TWnTp2q8LTAN/v5d+7cGZ1Ox3vvvUdmZiYGg4E777wTPz+/q25T0b/ditLr9bz11luMHTuWO++8k0cffZSTJ0+yZMmSMn3U27dvz6233sqkSZPIyMjAy8uLr776qsyPG1qtls8++4y7776b9u3bEx0dTePGjUlMTGTjxo24u7vz448/Atbp4zZu3EiPHj0YM2YM7dq1IyMjg927d7Nu3ToyMjIqdT43rUbHmBdCRSXTOJQ3RYrZbFZCQkKUkJAQ5dixYwpw1TJixIiaD14IUaecPn1aGT58uG16yBYtWijPPfecbTqa48ePKw8//LDi6empODk5KeHh4cpPP/1UZj8mk0l57733lPbt2ysGg0Fp2LChEhYWprzxxhtKZmambb2bnapJURTlwIEDygMPPGCLqXXr1sqUKVNs719rqpwBAwYoHh4eipOTkxISEqJERUUpO3futK0zYsQIxdXVtUx806ZNU668Vdm6dasSFhamODo62qYrSk9PV5577jmlTZs2iqurq+Lh4aH06NFDWbFiRZl9ClHTrvd9VxT5zpeo6u/8hx9+WO60YuWp6GerKIqyePFipUuXLrb1+vbtq6xdu9b2fnmfs6JY/10un2JMUazTmU2aNEkJDQ1VHB0dFR8fH6VXr17KrFmzFJPJZFuv5NxL3MznfzWffvqp0qJFC0Wn05Wa4uxq56MoFfvbLZkybeXKlaWWX+1v7+OPP1aaN2+uGAwGpVu3bsrmzZvL/eyOHz+uREZGKgaDQfH391dee+01Ze3ateVOM7dnzx7lwQcfVLy9vRWDwaA0a9ZMeeSRR5T169eXWi8lJUV57rnnlKCgIEWv1ysBAQFKv379lIULF17386tqGkW5gXYaQgghhBBCCGHHHnnkEU6dOkVsbKzaoYibFBERAcCmTZtUjaMmSdN3IYQQQgghRJ2iKAqbNm2SwSRFrSWJuhBCCCGEEKJO0Wg0NT7vtRBVSUZ9F0IIIYQQQggh7Ij0URdCCCGEEEIIIeyI1KgLIYQdmTlzJt27d8fNzQ0/Pz+GDBlCfHz8NbeJiYlBo9GUKk5OTjUUsRBCCCGEqGqSqAshhB35/fffee655/jrr79Yu3YthYWF9O/fn9zc3Gtu5+7uTlJSkq2cPn26hiIWQgghhBBVTQaTE0IIO7JmzZpSr2NiYvDz82PXrl3cfvvtV91Oo9EQEBBQ3eEJIYQQQogaUG8SdYvFwrlz53Bzc0Oj0agdjhCiFlIUhezsbBo1aoRWWzMNkjIzMwHw8vK65no5OTk0a9YMi8VC165deeedd2jfvv1V1zcajRiNRttri8VCRkYG3t7eco0UQlSaGtfHmiL3kEKIm3Gj18d6M5jc2bNnCQoKUjsMIUQdcObMGZo0aVLtx7FYLNx3331cvHiRLVu2XHW9bdu2cfToUW655RYyMzOZNWsWmzdv5uDBg1eNc/r06bzxxhvVFboQop6qqetjTZJ7SCFEVajs9bHeJOqZmZl4enpy5swZ3N3d1Q5HCFELZWVlERQUxMWLF/Hw8Kj24z377LP88ssvbNmypVIX9sLCQtq2bcvjjz/OjBkzyl3nyhr1zMxMmjZtKtdIIcQNqenrY02Se0ghxM240etjvWn6XtJUyd3dXS6yQoibUhNNH8eNG8dPP/3E5s2bK107pdfr6dKlC8eOHbvqOgaDAYPBUGa5XCOFEDejLjYNl3tIIURVqOz1sW51IhJCiFpOURTGjRvHd999x4YNG2jevHml92E2m9m/fz+BgYHVEKEQQgghhKhu9aZGXQghaoPnnnuOZcuW8f333+Pm5kZycjIAHh4eODs7AzB8+HAaN27MzJkzAXjzzTe59dZbCQ0N5eLFi/z73//m9OnTjB49WrXzEEIIIYQQN04SdSGEsCPz588HICIiotTyJUuWEBUVBUBCQkKpUUMvXLjAmDFjSE5OpmHDhoSFhbF161batWtXU2ELIYQQQogqJIn6ZRRFoaioCLPZrHYoNUqn0+Hg4FAn+5UJUdtUZHzPTZs2lXo9Z84c5syZU00RXWI2myksLKz249gjuU4KIYQQV1df86gSer0enU5XpfuURL2YyWQiKSmJvLw8tUNRhYuLC4GBgTg6OqodihDCDuXk5HD27NkK/ZBQV8l1UgghhCirvudRYB0orkmTJjRo0KDK9imJOta5ik+ePIlOp6NRo0Y4OjrWm1oTRVEwmUykpaVx8uRJWrZsWapJrRBCmM1mzp49i4uLC76+vvXm+lhCrpNCCCFE+epzHlVCURTS0tI4e/YsLVu2rLKadUnUsf4KZLFYCAoKwsXFRe1wapyzszN6vZ7Tp09jMplwcnJSOyQhhB0pLCxEURR8fX1tA9rVN3KdFEIIIcqq73lUCV9fX06dOkVhYWGVJepSJXCZ+lxDUp/PXQhRMfXtF/IryXVSCCGEKF99/z+yOu6R6vcnKoQQQgghhBBC2BlJ1IUQ9VJ2QSFz1x2h0GxROxQhhKiUY6nZZOSa1A5DCCFENZJEvY7JyMjg+eefp3Xr1jg7O9O0aVNeeOEFMjMz1Q5NCLtRUGhmzOc7mbvuKBO/2a92OEIlb7/9Nr169cLFxQVPT0+1wxGiQg4kZjJw7h8888UutUMRQog6yx7uESRRr2POnj3LuXPnmDVrFgcOHCAmJoY1a9YwatQotUMTwi4UmS2MW7aHv05k0MDgQHTvYLVDEioxmUwMHTqUZ599Vu1QhKiwr3edpciisCvhAsai+jlfsRBCVDd7uEeQUd9ruYiICDp06ICDgwNffvklHTt2ZOPGjbb3Q0JCePvtt3nqqacoKirCwUH+yUX9ZbEovPrNPtYdTsHRQctnI7rRobGH2mGJamSxWJg1axYLFy7kzJkz+Pv7M3bsWF5//XXeeOMNAGJiYtQNUogKKjRb+PHvcwCYLQrHUnNo30iuYUIIcSPs/R5BsrarUBSF/EJ1fql21usqNXLg0qVLefbZZ/nzzz/LfT8zMxN3d3dJ0kW9pigKb/50iG93J6LTavj4ia7c2sJb7bBqpdp0fZw0aRKffvopc+bMoU+fPiQlJREXF1eNEQpRfbYcS+f8ZX3T45KyJVEXQtgVuUeoOpK5XUV+oZl2U39V5diH3hyAi2PF/2latmzJv/71r3LfS09PZ8aMGTz99NNVFZ4QtdJ/1h8jZuspAGYNvYXIdv7qBlSL1ZbrY3Z2Nh988AEfffQRI0aMAKytjPr06VOdIQpRbb7fkwiAVgMWBeKSs1SOSAghSpN7hKojfdTrgLCwsHKXZ2VlMWjQINq1a8f06dNrNigh7EjMnyeZs+4IANMHt+OBLk1UjkjUhMOHD2M0GunXr5/aoQhx0/JMRfx2KAWAh8Os17C45Gw1QxJCiFqrNtwjSI36VTjrdRx6c4Bqx64MV1fXMsuys7MZOHAgbm5ufPfdd+j1+qoKT4ha5bs9Z5n+4yEAXopsRVTv5ipHVPvVluujs7NzNUYiRM1aeyiFPJOZZt4uPNq9KSt2npVEXQhhd+QeoercUI36vHnzCA4OxsnJiR49ehAbG3vN9efOnWubLiwoKIiXXnqJgoKCSu9z27Zt3Hnnnbi6uuLu7s7tt99Ofn7+jZzCdWk0GlwcHVQplelbUZ6srCz69++Po6MjP/zwA05OTlX0qQhRu6w7lMI/Vu4DILp3MC/0C1U5orqhtlwfW7ZsibOzM+vXr6/GT0OImrGquNn7/Z0a0SbADYC0bCPnc4xqhiWEEKXIPULVqXSN+vLly5kwYQILFiygR48ezJ07lwEDBhAfH4+fn1+Z9ZctW8bEiRNZvHgxvXr14siRI0RFRaHRaJg9e3aF97lt2zYGDhzIpEmT+PDDD3FwcODvv/9Gq5XW+5crSdLz8vL48ssvycrKIivL2ofN19cXna5ytfVC1Fbbjp/n/5btxmxReLBrY6YManfTP4KJ2sXJyYl//vOfvPrqqzg6OtK7d2/S0tI4ePAgo0aNIiEhgYyMDBISEjCbzezduxeA0NBQGjRooG7wQlzmfI6RzUfTAbi/S2NcDQ4083bh9Pk84pOz6RVqUDlCIYSoXWrDPUKlE/XZs2czZswYoqOjAViwYAGrV69m8eLFTJw4scz6W7dupXfv3jzxxBMABAcH8/jjj7N9+/ZK7fOll17ihRdeKHWM1q1bVzb8Om/37t22zzY0tHTt4cmTJwkODlYhKiFq1v6zmYz5fCemIguRbf3510O3oNVKkl4fTZkyBQcHB6ZOncq5c+cIDAzkmWeeAWDq1KksXbrUtm6XLl0A2LhxIxEREWqEK0S5Vu9PwmxRuKWJByG+1hvE1v5unD6fx+HkbHqF+qgcoRBC1D72fo9Qqepok8nErl27iIyMvLQDrZbIyEi2bdtW7ja9evVi165dtqbsJ06c4Oeff+aee+6p8D5TU1PZvn07fn5+9OrVC39/f/r27cuWLVuuGqvRaLTVJl9eq1zXbNq0iblz59peR0REoChKuUWSdFEfHEvNYcSSWHKMRfRs4c1HT3TBQSctb+orrVbL66+/zqlTpzCZTJw+fZpJkyYB1rlRy7tWSpIu7I2t2XvnxrZlbQLdAYhLqpv3N0IIUd3s/R6hUnev6enpmM1m/P1LT2vk7+9PcnJyuds88cQTvPnmm/Tp0we9Xk9ISAgRERG89tprFd7niRMnAJg+fTpjxoxhzZo1dO3alX79+nH06NFyjztz5kw8PDxsJSgoqDKnKoSohRIv5jNs0XYyck3c0sSDT0d0w6mSgzMKIYQ9STifx+6Ei2g1MLhToG152+J+6vEpMqCcEELURdVezbRp0ybeeecdPv74Y3bv3s23337L6tWrmTFjRoX3YbFYABg7dizR0dF06dKFOXPm0Lp1axYvXlzuNpMmTSIzM9NWzpw5UyXnI4SwT+k5RoZ9tp2kzAJCfF2JiQ6ngUEmthBC1G7f77XWpvcO9cHP7dLgsK1LEvXkbMwWRZXYhBBCVJ9KJeo+Pj7odDpSUlJKLU9JSSEgIKDcbaZMmcKwYcMYPXo0HTt25IEHHuCdd95h5syZWCyWCu0zMND6C3K7du1KrdO2bVsSEhLKPa7BYMDd3b1UEULUTVkFhYxYHMuJ9Fwaezrz5egeeLk6qh2WEELcFEVRWLW3bLN3gGberjjptRiLLJw6n6tGeLXSu+++i0ajYfz48WqHIoQQ11SpRN3R0ZGwsLBSw9hbLBbWr19Pz549y90mLy+vzMjsJSOPK4pSoX0GBwfTqFEj4uPjS+3nyJEjNGvWrDKnIISoYwoKzYyO2cnBc1n4NHDki1HhBHrY/9yYQghxPQcSszielovBQcuA9qW7COq0Glr7X6pVF9e3Y8cOPvnkE2655Ra1QxFCiOuqdNP3CRMm8Omnn7J06VIOHz7Ms88+S25urm3E9uHDh9s64QMMHjyY+fPn89VXX3Hy5EnWrl3LlClTGDx4sC1hv94+NRoNr7zyCv/5z3/4+uuvOXbsGFOmTCEuLo5Ro0ZVxecghKiFCs0W/u+/u4k9lYGbwYGlI8Np4SvTagkh6oaS2vTIdv64OenLvF/S/F0GlLu+nJwcnnzyST799FMaNmyodjhCCHFdle7A+eijj5KWlsbUqVNJTk6mc+fOrFmzxjYYXEJCQqka9MmTJ6PRaJg8eTKJiYn4+voyePBg3n777QrvE2D8+PEUFBTw0ksvkZGRQadOnVi7di0hISE3c/6lKEr97eNVn89d1E4Wi8I/Vv7NhrhUnPRaFkd3p30jD7XDEkKIKmG2KPz49zkAhlzR7L1EmwBrt77DUqN+Xc899xyDBg0iMjKSt956S+1whBDium5opKVx48Yxbty4ct/btGlT6QM4ODBt2jSmTZt2w/ssMXHixHLnar9Zer31V+q8vDycnetnk9m8vDzg0mchhD1TFIXpPx7k+73ncNBqmP9kGN2DvdQOSwghqsy24+dJzTbi6aKnbyvfctdpE1hco54sNerX8tVXX7F792527NhRofWNRiNGo9H2uq5O8SuEsG8yJDLWPvOenp6kpqYC4OLigkajUTmqmqEoCnl5eaSmpuLp6WnrjiCEPZuz9gifbzuNRgPvP9KJO9r4qR2SEEJUqZJm7/d0DMTRofyeiiU16mcy8skxFslMF+U4c+YML774ImvXrsXJyen6G2Cd4veNN96o5siEEOLa5IperGSE+ZJkvb7x9PS86sj9QtiTz/44wX82HAPgzfs7lBkJWQgharuCQjNrDiQDV2/2DuDl6oifm4HUbCPxydmENZO+11fatWsXqampdO3a1bbMbDazefNmPvroI4xGY5lKikmTJjFhwgTb66ysLIKCgmosZiGEAEnUbTQaDYGBgfj5+VFYWKh2ODVKr9dLTbqoFb7edZa3Vh8G4JUBrRl2q8z6IISoe9YfTiXHWERjT2e6XSf5bhPoTmp2GnHJWZKol6Nfv37s37+/1LLo6GjatGnDP//5z3LvfwwGAwaDoaZCFEKIckmifgWdTidJqxB26NeDyfzzm30AjLmtOf8XUXUDSYr659SpU8yYMYMNGzaQnJxMo0aNeOqpp3j99ddxdHRUOzxRz12aO70RWu21u+K1DXBj85E0maLtKtzc3OjQoUOpZa6urnh7e5dZLoQQYD/3CJKoCyHs3tZj6Ty/bA9mi8Ij3Zrw2j1t6804EqJ6xMXFYbFY+OSTTwgNDeXAgQOMGTOG3NxcZs2apXZ4oh67mGdiU7y1G96QLtfv2nNpijZJ1IUQoirYyz2CJOpCCLv295mLjPl8JyazhYHtA3jngY6SpIsKs1gszJo1i4ULF3LmzBn8/f0ZO3Ysr7/+OgMHDrSt16JFC+Lj45k/f74k6kJVP+9PptCs0DbQnVb+btdd/9IUbVkoiiLXxwq4coYiIUT9ZO/3CJKoCyHs1tGUbKKWxJJrMtM71JsPHu+Mg6780Y9FDVIUKMxT59h6F6hEIjJp0iQ+/fRT5syZQ58+fUhKSiIuLq7cdTMzM/Hykmn+hLpKmr0P6dyoQuuH+LnioNWQXVBEUmYBjTzr5zSzQgg7IfcIVUYSdSGEXTqTkcewRbFcyCukc5AnC4d1w+Ag40fYhcI8eKdiSUSVe+0cOLpWaNXs7Gw++OADPvroI0aMGAFASEgIffr0KbPusWPH+PDDD6U2Xagq8WI+sScz0Gjgvgom6gYHHS18XTmSkkNccpYk6kIIdck9QpWRqikhhN1JyzYybNF2krMKaOXfgCVR3XGV+YFFJR0+fBij0Ui/fv2uuV5iYiIDBw5k6NChjBkzpoaiE6Ks74tr03s09yLQo+IJt635u/RTF0KICqkN9why5yuEsCvZBYVELYnl1Pk8mjR05otRPWjoKqNw2xW9i/VXa7WOXUHOztdPdM6dO8cdd9xBr169WLhw4c1EJsRN+36P9Xt1rbnTy9Mm0I0f/kZGfhdCqE/uEaqMJOpCCLthLDLzzJe7OHguC29XR74c1QN/dye1wxJX0mgq3LRMTS1btsTZ2Zn169czevToMu8nJiZyxx13EBYWxpIlS9BqpZGZUM/hpCziU7Jx1Gm5u2NgpbZtUzLye3JWdYQmhBAVJ/cIVUYSdSGEXbBYFF5e8Td/HjuPq6OOmOhwgn3s/0Iv7JeTkxP//Oc/efXVV3F0dKR3796kpaVx8OBBBg4cSEREBM2aNWPWrFmkpaXZtgsICFAxalFflQwid0cbXzyc9ZXatqTp+/G0XIxFZhnPQwghrqM23CNIoi6EUJ2iKMxYfYif9iWh12lYMCyMjk081A5L1AFTpkzBwcGBqVOncu7cOQIDA3nmmWdYu3Ytx44d49ixYzRp0qTUNoqiqBStqK8sFoUf995Ys3eAQA8n3J0cyCoo4nhqLu0auVd1iEIIUefY+z2CJOpCCNUt+P0ES/48BcCsoZ24raWvugGJOkOr1fL666/z+uuvl3kvKiqq5gMSohyxpzI4l1mAm5MDd7Txq/T2Go2GNgHuxJ7KIC45SxJ1IYSoAHu/R5AOeUIIVX296yzvrbHOWTl5UFvuv4HaJCGEqM1KRnu/p0MgTvoba7beJrCkn7oMKCeEEHWBJOpCCNVsjEvln9/sA2Ds7S0YfVsLlSMSQoiaZSwys3pfEgD3d7nxuYdL+qlLoi6EEHWDJOpCCFXsSbjA//13N2aLwoNdGvPPgW3UDskuzJw5k+7du+Pm5oafnx9DhgwhPj7+ututXLmSNm3a4OTkRMeOHfn5559rIFohxM3aFJ9GVkERAe5O3Nrc+4b3Y6tRT5KR34UQoi6QRF0IUeOOp+UwMmYH+YVm+rby5b2Hb0Gr1agdll34/fffee655/jrr79Yu3YthYWF9O/fn9zc3Ktus3XrVh5//HFGjRrFnj17GDJkCEOGDOHAgQM1GLkQ4kaUNHu/r3Ojm7oOtvK3Juqp2UYyck1VEpsQQgj1SKIuhKhRKVkFDF8Uy4W8Qjo18eDjJ7ui18mlqMSaNWuIioqiffv2dOrUiZiYGBISEti1a9dVt/nggw8YOHAgr7zyCm3btmXGjBl07dqVjz76qAYjF0JUVlZBIesOpwJwf+cbb/YO0MDgQFMvF0DmUxdCiLpA7o6FEDUmM7+QEYtjSbyYT3MfVxZHdcfVIJNPXEtmZiYAXl5eV11n27ZtREZGllo2YMAAtm3bdtVtjEYjWVlZpcr11Pdpy+r7+Yuqt2Z/MqYiCy39GtAu8OZHam8TUNL8XfqpCyFqVn3/P7I6zl8SdSFEjSgoNDPm853EJWfj52bg85HheDcwqB2WXbNYLIwfP57evXvToUOHq66XnJyMv79/qWX+/v4kJydfdZuZM2fi4eFhK0FBQVddV6ezjkJtMtXv5rR5eXkA6PV6lSMRdcWq4mbvQ7o0RqO5+e4/tkRdatSFEDWk5P/Ekv8j66uSe6SSe6aqIFVZQohqZ7YojP9qL7EnM3AzOLB0ZDhBxU00xdU999xzHDhwgC1btlT5vidNmsSECRNsr7Oysq6arDs4OODi4kJaWhp6vR6ttn79xqsoCnl5eaSmpuLp6Vml/wmL+is5s4BtJ84DcF+nm2v2XqJNoIz8LoSoWTqdDk9PT1JTrd14XFxcquSHx9rEYrGQlpaGi4sLDg5Vl15Loi6EqFaKojD1+wOsOZiMo07LwuHdaFsFTTzrunHjxvHTTz+xefNmmjRpcs11AwICSElJKbUsJSWFgICAq25jMBgwGCrWokGj0RAYGMjJkyc5ffp0hbapizw9Pa/5mQpRGT/+fQ5FgW7NGlbZD5clNepHUrIxWxR0MkinEKIGlPzfWJKs10darZamTZtW6Y8UkqgLIarVf9Yf47/bE9BoYO5jnekZcuPTD9UHiqLw/PPP891337Fp0yaaN29+3W169uzJ+vXrGT9+vG3Z2rVr6dmzZ5XF5ejoSMuWLett83e9Xi816aJKlTR7v79L4yrbZzNvV5z0WgoKLZw+n0sL3wZVtm8hhLiakh/0/fz8KCwsVDscVTg6OlZ5i0NJ1IUQ1WbZ9gTmrDsCwJv3teeejoEqR2T/nnvuOZYtW8b333+Pm5ubrZ+5h4cHzs7OAAwfPpzGjRszc+ZMAF588UX69u3L+++/z6BBg/jqq6/YuXMnCxcurNLYtFotTk5OVbpPIeqjY6nZHDyXhYNWw71VeF3UaTW08ndj39lM4pKzJVEXQtQonU4nP2pXoRtK++fNm0dwcDBOTk706NGD2NjYa64/d+5cWrdujbOzM0FBQbz00ksUFBTc0D4VReHuu+9Go9GwatWqGwlfCFEDfj2YzORV+wF4/s5QhvUMVjegWmL+/PlkZmYSERFBYGCgrSxfvty2TkJCAklJSbbXvXr1YtmyZSxcuJBOnTrx9ddfs2rVqmsOQCeEUM+qPecAiGjtS0NXxyrd96UB5aSfuhBC1GaVrlFfvnw5EyZMYMGCBfTo0YO5c+cyYMAA4uPj8fPzK7P+smXLmDhxIosXL6ZXr14cOXKEqKgoNBoNs2fPrvQ+586dW+8GKBCittlxKoMX/rcHiwKPdQ9iwl2t1A6p1qjI9B6bNm0qs2zo0KEMHTq0GiISQlQlRVH4/u/iZu+dq67Ze4nWAcUDyiXJyO9CCFGbVbpGffbs2YwZM4bo6GjatWvHggULcHFxYfHixeWuv3XrVnr37s0TTzxBcHAw/fv35/HHHy9VY17Rfe7du5f333//qscSQqgvPjmbUTE7MBZZiGzrz1tDOsiPa0IIUWx3wgXOZOTj6qgjsq3/9TeopLZSoy6EEHVCpRJ1k8nErl27iIyMvLQDrZbIyEi2bdtW7ja9evVi165dtsT8xIkT/Pzzz9xzzz2V2mdeXh5PPPEE8+bNk1F3hbBTiRfzGbE4lqyCIsKaNeTDx7vgoKtfU3kJIcS1lDR7H9AhAGfHqu/L2bo4UU/IyCPXWFTl+xdCCFEzKtX0PT09HbPZjL9/6V+A/f39iYuLK3ebJ554gvT0dPr06YOiKBQVFfHMM8/w2muvVWqfL730Er169eL++++vUKxGoxGj0Wh7nZUlTcCEqE4X80yMWBxLclYBLf0asGhEt2q5CRVCiNqq0Gxh9X7r+BJDqqHZO4B3AwN+bgZSs43Ep2TTtWnDajmOEEKI6lXtVV2bNm3inXfe4eOPP2b37t18++23rF69mhkzZlR4Hz/88AMbNmxg7ty5Fd5m5syZeHh42EpQUNANRC+EqIh8k5mRMTs4lppDoIcTS0eG4+lStQMkCSFEbffH0TQyck34NDDQqxqnqiypVY9LkubvQghRW1UqUffx8UGn05GSklJqeUpKylWbo0+ZMoVhw4YxevRoOnbsyAMPPMA777zDzJkzsVgsFdrnhg0bOH78OJ6enjg4OODgYG0I8NBDDxEREVHucSdNmkRmZqatnDlzpjKnKoSooCKzhXHLdrM74SLuTg4sHRlOI09ntcMSQgi7811xs/fBnQKrtVtQ20DrgHLxydKaUAghaqtK/S/h6OhIWFgY69evty2zWCysX7+enj17lrtNXl5emcnfS+bXUxSlQvucOHEi+/btY+/evbYCMGfOHJYsWVLucQ0GA+7u7qWKEKJqKYrCa9/tZ31cKgYHLYujutPK303tsIQQwu7kGItYeygZqL5m7yVKpmg7LAPKCSFErVXp6dkmTJjAiBEj6NatG+Hh4cydO5fc3Fyio6MBGD58OI0bN2bmzJkADB48mNmzZ9OlSxd69OjBsWPHmDJlCoMHD7Yl7NfbZ0BAQLk19k2bNqV58+Y3fPJCiJvz/m9HWLHzLFoNfPREV7oFe6kdkhBC2KXfDiZTUGihuY8rtzTxqNZjXWr6noWiKDLzhhBC1EKVTtQfffRR0tLSmDp1KsnJyXTu3Jk1a9bYBoNLSEgoVYM+efJkNBoNkydPJjExEV9fXwYPHszbb79d4X0KIezP0q2n+GjjMQDeeaAjd7WT76sQQlzNqr3WZu/3d25U7YlzqF8DdFoNWQVFJGcVEOgh3ZGEEKK20SiKoqgdRE3IysrCw8ODzMxMaQYvxE36ad85nv/fHhQFJtzVihf6tVQ7pBpRl68jdfnchFBbWraRHu+sw6LApn9EEOzjWu3H7D/nd46k5LAkqjt3tPGr9uPV5WtIXT43IUT1u9FriExwLISolK3H05mw/G8UBYbd2ozn7wxVOyQhhLBrP+07h0WBzkGeNZKkA7QOsN4MHpYB5YQQolaSRF0IUWGHzmUx9vNdmMwW7u4QwPT72kvfRyGEuI6SZu9DOjeqsWOWDCgXLwPKCSFErSSJuhCiQs5k5BG1JJZsYxHhzb2Y82hndFpJ0oUQ4lpOpufy95mL6LQa7u1Uc4l620CZS10IIWozSdSFENd1IdfEiCWxpGYbae3vxqfDu+Gk16kdlhBC2L3v9yYC0CfUB58Ghho7bknT9+NpORiLzDV2XCGEEFVDEnUhxDXlm8yMXLqDE2m5NPJwYunIcDyc9WqHJYQQdk9RFL4vafbepeZq0wEaeTjh5uRAkUXheGpujR5bCCHEzZNEXQhxVUVmC+OW7WZPwkU8nPUsHRlOgIeT2mEJIUStsO9sJifTc3HW6+jfLqBGj63RaGhbXKsenyIDygkhRG0jiboQolyKovD6dwdYH5eKwUHLohHdaOnvpnZYQghRa3y3x9rs/a52/rgaHGr8+G2kn7oQQtRakqgLIco1Z91Rlu88g1YDHz7ehW7BXmqHJIQQtUaR2cJP+9Rp9l6idfHI74dl5HchhKh1JFEXQpTx5V+n+c/6owC8NaQj/dvXbJNNIYSo7f48fp70HBNero7c1tJXlRjalDR9l7nUhRCi1pFEXQhRypoDyUz9/gAAL/ZryRM9mqockRBC1D7fFzd7H9QxEL1Ondutkhr1lCwjGbkmVWIQQghxYyRRF0LY7DiVwQtf7cGiwOPhQYyPbKl2SEIIUevkm8z8ejAZgCFdGqsWRwODA0FezgDESa26EELUKpKoCyEAOJKSzaiYHZiKLES29WfG/R3QaDRqhyWEELXO2sMp5JrMNPVyoWtTT1VjudT8XfqpCyFEbSKJuhCCpMx8RiyOJaugiK5NPfnw8S44qNRUUwgharuSZu/3d26k+g+ebQNk5HchRP2RYyzifI5R7TCqhNyJC1HPZeYVMmJxLEmZBYT4urJoRHecHXVqhyWEELVSRq6J34+kAXB/Z/WavZdoXVyjLk3fhRB13eYjafR8Zz13vv87Zy/kqR3OTZNEXYh6rKDQzJjPd3IkJQd/dwNLR4bT0NVR7bCEEKLWWr0/iSKLQofG7oT6NVA7HNtc6kdScjBbFJWjEUKI6vHFtlNEx+wg21hEZn4hb68+rHZIN00SdSHqKbNFYfxXe4k9lYGbkwNLR4bTpKGL2mEJIUStVtLsfYgd1KYDBHu7YnDQkl9oJiGj9tcwCSHE5YrMFqb/cJAp3x/EbFG4q50/Oq2GXw4k88fRNLXDuymSqAtRDymKwvQfDrLmYDKOOi0Lh3WzDTgkhBDixszfdJydpy+g0cDgTo3UDgcAnVZDK/+SfurS/F0IUXdkFxQy+vOdxGw9BcCrA1uzcFgYw3s2A2D6DwcxFVlUjPDmSKIuRD00b+MxvvjrNBoNzHm0Mz1DvNUOSQghai1FUXhvTRzvrYkD4MV+LfF3d1I5qkvalAwoJyO/CyHqiDMZeTw0fyub4tNw0muZ/2RX/i8iFI1Gw/jIVvg0cOR4Wi4xW0+qHeoNk0RdiHpmxY4zzPrtCADT7m3HoFsCVY5ICCFqL4tFYfKqA8zfdByASXe3YXxkK5WjKq1NoAwoJ4SoO3advsCQeX9yJCUHPzcDK8f24u6Ol+5nPZz1/HNgGwA+WHeUlKwCtUK9KZKoC1GPbIhLYdJ3+wH4v4gQono3VzkiIYSovQrNFl5asZf/bk9Ao4GZD3ZkbN8QtcMqQ2rUhRB1xfd7E3n80784n2uifSN3vh/Xm45NPMqs91DXJnRp6kmuyczMn2vnwHKSqAtRT+xJuMD//Xc3ZovCQ12b8MqA1mqHJIQQtVZBoZlnvtjF93vP4aDV8J/HuvB4eFO1wypXSaKekJFHrrFI5WiEEKLyFEVh9tojvPjVXkxFFu5q58+KsT0J9HAud32tVsOM+zug0cCqvefYfuJ8DUd88yRRF6IeOJ6Ww8iYHRQUWoho7cu7D3VEo9GoHZYQQtRK2QWFjFgcy/q4VAwOWj4d3s1uBo8rj3cDA75uBhQFjqTUr1r1mTNn0r17d9zc3PDz82PIkCHEx8erHZYQohIKCs08/789/Gf9UQDG9m3BJ0+F4WpwuOZ2HRp78ETxD6jTfjhIkbl2DSwniboQdVxKVgHDF8VyIa+QTk08mPdEV/Q6+eoLIcSNyMg18eRn29l+MoMGBgc+HxnOHW381A7ruupr8/fff/+d5557jr/++ou1a9dSWFhI//79yc3NVTs0IUQFpGYX8NjCv/hpXxIOWg3/eugWJt3dFq22YhVO/+jfGk8XPXHJ2fx3e0I1R1u1rv0zhBCiVssqKCRqyQ4SL+YT7O3C4qju1/31UQghRPmSMwsYtmg7R1Nz8HJ1ZGl0eLl9I+1RmwA3/jiaXu+maFuzZk2p1zExMfj5+bFr1y5uv/12laISQlTE4aQsRi/dSeLFfDxd9Mx/MqzSMxU1dHXklQGtef27A8z6LZ5BtwTi08BQTRFXLalWE6KOMhZZ+08eTsrCp4GBz0f2wLuWXJiEEMLeJJzPY+gnWzmamkOAuxMrxt5aa5J0gDYBJSO/168a9StlZmYC4OXlddV1jEYjWVlZpYoQomZtiEvh4flbSbyYTwsfV777v943PJ3wY92b0qGxO9kFRfyreBrN2kASdSHqIItF4eUVf7P1+HlcHXXERHenqbeL2mEJIUStFJ+czcMLtnImI59m3i6sfKYnoX5uaodVKW0CLzV9VxRF5WjUYbFYGD9+PL1796ZDhw5XXW/mzJl4eHjYSlBQUA1GKUT9pigKi7acZPTSneSazPRs4c23/9eL5j6uN7xPnVbDG/dZv/Mrdp5lT8KFqgq3Wt1Qoj5v3jyCg4NxcnKiR48exMbGXnP9uXPn0rp1a5ydnQkKCuKll16ioKD0fHbX2mdGRgbPP/+8bR9NmzblhRdesP0qKoS4RFEUZqw+xE/7ktDrNCwYFkaHxrWn1kcIIezJ3jMXeeSTbaRmG2kT4MbKsT0J8qp9P3yG+jVAp9WQmV9Ici2dU/hmPffccxw4cICvvvrqmutNmjSJzMxMWzlz5kwNRShE/VZotvD6qgPM+OkQFgUeDw/i81HheLo43vS+w5o15OGwJgBM/f4gZov9/2BZ6UR9+fLlTJgwgWnTprF79246derEgAEDSE1NLXf9ZcuWMXHiRKZNm8bhw4dZtGgRy5cv57XXXqvwPs+dO8e5c+eYNWsWBw4cICYmhjVr1jBq1KgbPG0h6q6Fm0+w5M9TAMwa2onbWvqqG5AQQtRSW4+n8+Snf5GZX0iXpp589fSt+Lk7qR3WDTE46GhRXCNVH5u/jxs3jp9++omNGzfSpEmTa65rMBhwd3cvVYQQ1Sszv5DoJTtYtj0BjQYmD2rLOw90rNIBkP85sA1uBgf2J2ayYqf9/wBX6TOfPXs2Y8aMITo6mnbt2rFgwQJcXFxYvHhxuetv3bqV3r1788QTTxAcHEz//v15/PHHS9WYX2+fHTp04JtvvmHw4MGEhIRw55138vbbb/Pjjz9SVCTzgQpRYtWeRGb+Yu17M3lQW+7v3FjliIQQonZaeyiFqCU7yDWZ6R3qzZejelRJrY6a2gQW91NPqj+JuqIojBs3ju+++44NGzbQvHlztUMSQlzh9PlcHvz4T7YcS8fFUcenw7ox+rYWVT6VsK+bgZfuagXAv9bEcTHPVKX7r2qVStRNJhO7du0iMjLy0g60WiIjI9m2bVu52/Tq1Ytdu3bZEvMTJ07w888/c88999zwPsE6GIi7uzsODuWPYC0DgYj65o+jafxj5d8AjO7TnNG3tVA5IiGEqJ2+23OWZ77chanIwl3t/Fk0om7MmHFpirb6c0/03HPP8eWXX7Js2TLc3NxITk4mOTmZ/Px8tUMTQgDbT5xnyLw/OZ6WS6CHE18/04vIdv7VdrzhPZvR2t+NC3mFvP/bkWo7TlWoVKKenp6O2WzG37/0h+fv709ycnK52zzxxBO8+eab9OnTB71eT0hICBEREbam7zeyz/T0dGbMmMHTTz991VhlIBBRnxxIzOSZL3ZRZFEY3KkRr93TVu2QhBCiVvpi2yleWv43ZovCg10bM//JrjjpdWqHVSVKEvX4etT0ff78+WRmZhIREUFgYKCtLF++XO3QhKj3Vu48w1OLtnMhr5BOTTz4/rnetGtUvV1NHHRa3ri/PQD/3X6aA4n2O+ZZtY/6vmnTJt555x0+/vhjdu/ezbfffsvq1auZMWPGDe0vKyuLQYMG0a5dO6ZPn37V9WQgEFFfnMnIszXP7NnCm1lDb0GrrdqmQqLmbN68mcGDB9OoUSM0Gg2rVq265vqbNm1Co9GUKVf7oVMIUT5FUZi38RhTvj8IQFSvYGY93AmHKuwfqbaSpu/HUnMwFVlUjqZmKIpSbomKilI7NCHqLYtF4b01cbzy9T4KzQqDOgayfGzPGhsD5NYW3tzXqREWBab9cNBuZ8KoVDsuHx8fdDodKSkppZanpKQQEBBQ7jZTpkxh2LBhjB49GoCOHTuSm5vL008/zeuvv16pfWZnZzNw4EDc3Nz47rvv0Ov1V43VYDBgMMic0aJuy8g1MWJxLOk51tGIPxkehsGhbtT81Fe5ubl06tSJkSNH8uCDD1Z4u/j4+FIDHvn5+VVHeELUSYqi8O6aOD75/QQAL9wZykt3tary/pFqa+ThhJuTA9kFRRxPy6FtoAySJoSoWXmmIiYs/5s1B60VCs/fGcpLka1qvJLptXvasu5wCrtOX+C7PYk82PXag0yqoVI/Ezs6OhIWFsb69ettyywWC+vXr6dnz57lbpOXl4dWW/owOp01kVAUpcL7zMrKon///jg6OvLDDz/g5FQ7R10Voqrkm8yMWrqDE+m5NPZ0ZunIcNydrv7jlagd7r77bt566y0eeOCBSm3n5+dHQECArVx53RVClM9sUXjtuwO2JP31e9oyoX/rOpekA2g0mnrZ/F0IYR/OZOTx6Cd/seZgMo46LXMe7cTL/Vur0hI0wMOJF/q1BOCdn+PILiis8Riup9Ijo0yYMIERI0bQrVs3wsPDmTt3Lrm5uURHRwMwfPhwGjduzMyZMwEYPHgws2fPpkuXLvTo0YNjx44xZcoUBg8ebEvYr7fPkiQ9Ly+PL7/8stTgcL6+vrb9CFFfFJktPP+/3exJuIiHs56lI7vjX0unDBJVo3PnzhiNRjp06MD06dPp3bu32iEJYfdMRRYmrNjLT/uS0Gpg5oMdebR7U7XDqlZtAtzZceoCh5OzGILMDCKEqD6mIgu7Tl/g9yNp/H4kjcNJ1vzNy9WRhcPC6BbspWp8I3s3Z8WOM5xIz2XuuqNMubedqvFcqdKJ+qOPPkpaWhpTp04lOTmZzp07s2bNGttgcAkJCaVqciZPnoxGo2Hy5MkkJibi6+vL4MGDefvttyu8z927d7N9+3YAQkNDS8Vz8uRJgoODK33iQtRWiqIw5fsDrDucisFBy6IR3Qj1c1M7LKGSwMBAFixYQLdu3TAajXz22WdERESwfft2unbtetXtjEYjRqPR9lpmxhD1Tb7JzP/9dxcb49PQ6zTMfbQLg24JVDusatcmsHjk93o0RZsQouacycizJeZbj6WTazLb3tNooHuwF7Me7kRTbxcVo7RydNAy/b72DF8cS8zWUzzaPYhW/vZzT61R7LX3fBXLysrCw8PDNq2bELXVB+uOMmfdEbQamP9UGAPalz8+hKh6NX0d0Wg0fPfddwwZMqRS2/Xt25emTZvyxRdfXHWd6dOn88Ybb5RZLtdIUR9kFxQyaulOYk9m4KTXsuCpMCJa149xHXadzuCh+dsIcHfir9f6Vdl+6/J9Vl0+NyFuVkGhmb9OnLcl5yfScku979PAkdtb+tK3tS99Qn3wbmB/Y4iN/WInvx5MoWcLb5aN6VHlXZ9u9BpS+ycFFaIe+So2gTnrrHM+vnF/B0nSRbnCw8PZsmXLNdeZNGkSEyZMsL3OysqSaSxFvXA+x8iIJbEcSMzCzeDA4ujudFe5+WVNKqktSs4q4EKuiYaujipHJISoTRRF4Xhari0x337iPMbLZpHQaTWENW1I39a+9G3lS7tAd7ufjWjyoHZsik9j24nzrN6fxL23NFI7JEASdSFqjfWHU3h91QEAxt0RyrBbm6kckbBXe/fuJTDw2k14ZWYMUR8lZebz1GfbOZ6Wi7erI0tHhtOhsYfaYdUoNyc9QV7OnMnIJy45m54h3mqHJISwc9kFhWw9XlxrHp9G4sX8Uu838nCyJea9Qn1q3eDGQV4u/F9EKHPWHeHt1Ye5o7Ufrgb102T1IxBCXNeehAs8t2w3ZovCw2FNeLl/K7VDEtUkJyeHY8eO2V6fPHmSvXv34uXlRdOmTZk0aRKJiYl8/vnnAMydO5fmzZvTvn17CgoK+Oyzz9iwYQO//fabWqcghN3JyDURs/UUS7eeIjO/kEAPJ74c3YMQ3wZqh6aK1v7unMnIJz45SxJ1IUQZiqJwOCmbTUdS+T0+jV2nL1BkudRb2lGnpUcLL/q2sibnoX4Nav1MGWP7tuDr3Wc4k5HPvI3HeHVgG7VDkkRdCHt3Ii2HUUt3UlBooW8rX2Y+2LHWXwzF1e3cuZM77rjD9rqkefqIESOIiYkhKSmJhIQE2/smk4mXX36ZxMREXFxcuOWWW1i3bl2pfQhRX529kMdnf5zkqx0JFBRam2a29ndjUVQ3mjRUfyAjtbQNdGPd4RTiZIo2IQRQaLZw9kI++xMz2VzcpD0t21hqneY+rrbEvEcLL1wc61Ya6aTXMfXe9oz5fCef/nGCh8Oa0ELlH3Pr1icsRB2Tml3AiCWxZOSauKWJBx8/2RW9TubHrssiIiK41hifMTExpV6/+uqrvPrqq9UclRC1S3xyNp/8fpwf/j5nqwXq2NiDZyNCGNA+AJ2d95esbm0CrIMZHZZEXYh6o6DQzNkLeZxKz+PU+VxOn7/0mHgxH7Ol9L2Hs15H71Bv+rby5fZWvjTzdlUp8poT2daPO1r7sjE+jTd+PERMdHdVK8ckURfCTuUYixgZs4MzGfk083ZhcVR3u+gvI4QQ9mrX6QzmbzrOusOptmW9Q715tm8ovUO9pTVSsdYB1gHljiRnY7Eodj/QkxCiYvJNZk5n5HIqPY/T53M5dd76ePp8Hucy87nWXF/Oeh0tfF3pHepDRCtfwoIbYnDQ1VzwdkCj0TB1cHv+PLaZ34+kse5wKne181ctHrnrF8IOmYosPPvlLg4kZlkHPIoOx8cOp7MQQgi1KYrCpvg05m86TuypDMA6V+/A9gE80zeETkGe6gZoh4K9XTA4aMkvNJOQkUewT92vKROirsgxFnEq/fIa8UsJeUqW8ZrbNjA4EOzjQjNvV4K9Sx6tz33dDPJjJtYm/mNub868jcd586eD3NbSBye9Oj9YSKIuhJ1RFIWJ3+zjj6PpOOt1LI7qLjdRQghxhSKzhdX7k5i/6bitr7Vep+Ghrk0Yc3uLejtQXEU46LS08ndjf2ImcclZ8n+MECozWxQu5pk4n2siPcdIRq6J8znW1+dzjJzPMZGaXUBCRh7pOaZr7svDWU+wz+WJ+KVHL1dHScYr4Lk7Qvl2dyJnMvJZ8PtxxkeqM4izJOpC2Jl//RrPt3sS0Wk1fPxUV6kNEkKIyxQUmlm58wyfbD7B2QvWKYJcHXU8eWszRvZuToCHk8oR1g6tA6yJ+uGkbAZ2uPZ0jkKIyrFYFLIKCosT7eJk25Z8G20JeElCfiHPhOUazdKv5O3qSDNvF4K9Xa1J+GW15J4ujtV3YvWEi6MDkwe147llu5m/6TgPdW1CkFfND0AqiboQdmTp1lPM33QcgHcf7Mgdrf1UjkgIIexDZn4hX/51msVbTnI+11qj5O3qSHTvYIbdGoyHS+2at1dtbYr7qcfLgHJClMtYZCa7oIicgiJyjEVkFRSSU1BkXWYsuyzjstrwjFxTqenMKsrTRY+3qyPeDQzFj454uxrwbuCITwMDTb1caOrtUuvmKa+N7ukYQK8Qb7YeP8+Mnw6xcHi3Go9BEnUh7MQv+5OY/uNBAP7RvxVDuwWpHJEQQqgvJauARVtOsmx7AjnGIgAaezoztm8LhoYF4exYvwY7qiptA60jv8clZ6kciRBVw2JRKCgyk28yk19opqDQTJ7J+vpSYl2SeBfakvCs4tc5xiLbsuyCIkxmy03H5ObkcNXE28vVmnyXPG/o4igz+9gRjUbDG/e15+4P/uC3Qylsik8looYr0CRRF8IOxJ7M4MXle1EUeLJHU567I1TtkIQQQlUn0nJYuPkE3+5OtN0wt/Z349mIEAbdEig3tDepZOT30xl55JmK6tycyMI+KIqCschSXMyYSp4XWjCZLRgLLyXV+YVm8k0W8kxFttd5puL3TFe8LllWvNy6j5tPrMvTwOBgLU4OuDlZn7s76csssybc1oTcp4GBhq76ejdqel3T0t+NqF7BfLblJG/8eIieId41+m8qV2UhVHYkJZvRS3dgKrLQv50/b97fQQb6EELUW/vOXmTB78f55UCybSqh7sENeTYihDta+8n1sYr4NDDg08BAeo6RIyk5dJbxUGo1RVEoNCsUmi0Umq1JcKFZobDoitdmC4VFV7w2WzAVWcpuX6RgMpsvS6qLk23b8yuS7yJr4n35+1VRK30jnPRanPU6nPU6nBx1uJUk1QY9DWzJdkmifSnpdndyoEHxOm5ODrg6OqCT6QvrtRcjW7Jq7zlOpueyeMspno0IqbFjS6IuhIqSMvMZsTiWrIIiwpo15D+Pd5H/EIQQ9U5mfiFbjqbzv9gEthxLty2PbOvHM31D6BbspWJ0dVfbQDf+OGokLilLEvUqtGpPIilZBRRZrIlvkVmh0GLBbFbKLrMo1udmS6n3zBbr+5e/V2R7VCiylE6sC82V7w9d0zQaMDhocdRpMeh11ucOlxJqZ8fSj056HS6XLyt5Xpx8u5SzjbOjDicHHVq5lxJVxM1Jz2v3tGHCir/5cMNRhnRpRKCHc40cWxJ1IVSSmV9I1OIdJGUWEOLrymfDu6k2T6MQQtQki0XhwLlMfo9P4/cjaew5cxFz8cBLOq2G+zs1YmzfEFvzbFE92gS48cfRdNv0dqJqLP7zJPvOZqodBo7FSbFep0Gv06LXWRPjUq91WvQOV7wued+WVGsxOFgT65Li6HDZMr0WR52ueL0r3rvstV6nkRYxolZ6oEtjlm1PYOfpC7zzcxwfPt6lRo4riboQKigoNPP05zuJT8nGz83A0pHhNHSV6TSEEHVXeo6RP46m8Xt8GpuPppORW3ou4BBfV/q19WfYrc1UmQanPmodIAPKVYeI1n6E+jVAr9XiUJz06rQa6/PiZQ5aDQ46LQ5a6/u2ZZdt41C8jcMV+7m0Xw2OOl25ibZOK0mxEFVFo9Hwxv3tGfzhFn78+xxPhDelZ4h3tR9XEnUhapjFovDyir/ZfjKDBgYHYqLDadJQbkqFEHVLkdnCnjMXbbXm+xNL1zC6OuroHepD39a+3N7SV5JzFZRM0RaXnI2iKJLYVZEJd7VSOwQhRBVr38iDp25txufbTjP9h4P89EKfah/UVBJ1IWqQoijMWH2I1fuT0Os0LBwWRrtG7mqHJYQQVeLcxXw2H7Em5luOpZNdUFTq/XaB7vRt7UvfVr50bdoQRwcZuV1NoX4N0Gk1XMwrJCXLSICHk9ohCSGE3ZpwVyt+2pfEnen/Zc2aiwwedF+1Hk8SdSFq0Kd/nGDJn6cAmDW0E71CfdQNSAghbkJBoZkdpzJsyfmRlJxS73u66Lm9pS+3t/Ll9pY++LlLImhPnPQ6mvu4ciw1h7jkLEnUhRDiGjxdHHm3h5H+W7/CHLuc9Fv+wieoTbUdTxJ1IWrI93sTeefnOABev6ct93durHJEQghROYqicOp8Hr/Hp/L7kTS2nThfau5irQY6B3nSt5UffVv70rGxh8xkYefaBLgVJ+rZRLT2UzscIYSwXxYLd516H4DDfvfQwj+0Wg8niboQNeDPY+n8Y+XfAIzs3Zwxt7dQOSIhhLi+IrOFE+m5HDqXxa7TF/j9SBoJGXml1vFzM9C3lS99W/vSJ9QHTxcZGLM2aRvozk/7kohLkgHlhBDimvb+F8253SiObnQYPgccqzeVlkRdiGp2OCmLZ77YRaFZYdAtgUwe1FbtkIQQoozsgkLikrM5dC7LWpKyiE/JxlRkKbWeXqehWzMvW1/zNgFuMghZLdba/9KAckIIIa4i/yKsmw6AJuKf4OZf7YeURF2IapR4MZ+oJbFkG4sIb+7F+0M7oZVmoEIIFSmKQnJWQamE/FBSFqfP55W7fgODA20D3WjfyIPeoT70DPGmgUFuH+qKNoHWRP14Wg6mIosM8FcVPr8fkvaBTg9aPegcrI9ah0vPS97T6squpyteV+twlX2UPDoWF30lnl/jffnBTYir2/Qu5KWDTysIH1sjh5T/aYWoJpl5hYxYHEtKlpFW/g34dFg3nPQ6tcMSQtQjhWYLJ9JyOZSUeSkpP5fFhbzCctcP9HCiXaA77Rq52x6DGrrID4x1WGNPZ9wMDmQbiziRnkObAJmJ5KblX4D8DLWjqDxb8n95Au8IDk7gYLisOF22/FrvGa54v/i57vLXjqB3Ab2z9VGnV/tTEKKs1MMQu9D6/O73rH+3NUASdSGqQUGhmTGf7+RYag4B7k7ERIfj4SL/+Qghqk9Fm64D6LQaQn0blErI2wa64+Uq/cvrG41GQ+sAN3aevkBcUrYk6lXhkS+gMA/MhWApBHMRWIoue15ofW2+/LHkecl6xa8vf//K/ZhNl9Y1m4rL9Z4XPxYZAaV03CXHK/93vJqh1V+WuDuDo+ul53rXSwm93hkcXUon+Zc/v/I9g5u1OBhUPDlRKykK/PIqKGZocy+E3Fljh76hRH3evHn8+9//Jjk5mU6dOvHhhx8SHh5+1fXnzp3L/PnzSUhIwMfHh4cffpiZM2fi5ORU4X0WFBTw8ssv89VXX2E0GhkwYAAff/wx/v7V3z9AiMqwWBQmrNhL7KkM3AwOxIzsTiNPZ7XDEkLUATnGIhLO55GQkceZDOvj6Yw8TqXnlhnkrURJ0/VLNeUetPRvIC18hE2bwOJEXfqpV42GzdSOoGIs5msn9UVG6/OiguLXBdZlRcbLnl/5XgEUlby+1ntGMBuhsACK8kEp/kHRUgjGTGupDjqDNWF3ci9O3t2Ly5XLih+vXObkDo5u1q4Ion449D2c3GxtATLg7Ro9dKX/ypYvX86ECRNYsGABPXr0YO7cuQwYMID4+Hj8/MpO67Fs2TImTpzI4sWL6dWrF0eOHCEqKgqNRsPs2bMrvM+XXnqJ1atXs3LlSjw8PBg3bhwPPvggf/75501+BEJUHUVRmLH6ED/vT0av0/DJ8DCpnRBCVJjFopCSXcDpK5Px89bn53NN19y+kYeTrXZcmq6Liir5fyouWUZ+r1e0OtAW11arSVGsCX1hHpjyoDDf+txW8q3FlHvFe/mXbXPZeoW55bxX/EOm2Qh5Rmtf45uhdymb4Lv4gGtxcfEBV9/iUrzM4C7jANQ2pjz4bbL1ee8XoWFwjR6+0on67NmzGTNmDNHR0QAsWLCA1atXs3jxYiZOnFhm/a1bt9K7d2+eeOIJAIKDg3n88cfZvn17hfeZmZnJokWLWLZsGXfeaW1usGTJEtq2bctff/3FrbfeWvkzF6IafPbHSZb8eQqA9x/pTK8QH3UDEkLYnTxTEWcy8jl9PteWjJ8uTsjPZuRjMpdtqn65hi56mnq50NTblaZeztbnXq60CXCjoTRdFzegbfGAcnFJUqMuVKDRXOrH7tyweo5hMYMxG4xZxY/ZUJBV/PrKZdmXlhdc9p4xy9oaAC4l/znJFY9B51g6mXf1vey172XLvK2Pjq6S2Kvtz7mQeQY8gqD3+Bo/fKUSdZPJxK5du5g0aZJtmVarJTIykm3btpW7Ta9evfjyyy+JjY0lPDycEydO8PPPPzNs2LAK73PXrl0UFhYSGRlpW6dNmzY0bdqUbdu2SaIu7MIPf5/j7Z8PA/DaPW24r1MjlSMSQtS0IrOF87kmUrIKSM0ykpJdQEpmAWculCTm+aTnGK+5DwethsYNSxLwSyXIy4Wm3i64O8l4F6JqtSqeoi05q4CLeSY8XeQHH1HHaHXg7GktN6PIdEXCX/xYkAl55yE3DXLTi0uateY+Nx1MOdZWA9nnrKUiHJxL19A38LPW6Hq1AK/m1sfq+mFDwIVTsGWu9Xn/t6zjHtSwSiXq6enpmM3mMv3C/f39iYuLK3ebJ554gvT0dPr06YOiKBQVFfHMM8/w2muvVXifycnJODo64unpWWad5OTyf8kyGo0YjZduhrKypDmXqD5bj6fz8oq9AET3DmbMbS3UDUgIUaXMFoXzOUZSsozWJDy75PGyhDzLyPkcIxbl+vvzcNZfSsK9SyfkgR5OOOhkiixRc9yc9DRp6MzZC/nEJWdzawtvtUMSwj45OIKDN7hW8jtSmG9N2PMuS+JtyXxJgp8GucXPi/KtJfOMtVyNc8PixP3KEgIuXlIjfzN+fd3aVaL57dDuflVCqPaREDZt2sQ777zDxx9/TI8ePTh27BgvvvgiM2bMYMqUKdV23JkzZ/LGG29U2/6FKBGXnMXYz3dRaFa4p2MAUwa1QyMXRiFqBbNF4Xyu0ZpsX5aAp2QZSStOvlOyCkivYAIO1hHVfRo44u/uhJ+bE37uBoIalk7GZRYIYW/aBLhbE/WkLEnUhahqemfwDLKWijDllq2dz0mGjFOQccJacpKtUwEm7rKWKxk8LtW8X1ka+EkSfy3HN0DcT6DRwd3/Uu2zqlSi7uPjg06nIyUlpdTylJQUAgICyt1mypQpDBs2jNGjRwPQsWNHcnNzefrpp3n99dcrtM+AgABMJhMXL14sVat+reNOmjSJCRMm2F5nZWURFFTBL4cQFXTuYj5Ri3eQbSwiPNiL2Y90lkGbhFCJoihkG4u4kGsiI9fEhTwTGbmF1td5piuWm7iQV8jFPFOFE3CtBnzdDPi5OeHvbsDP3Qk/NwP+7sWvi5Nyb1cDOrkOiFqmTYAb6w6nEJ8i/dSFUJ2jq7Vca/AyUy5knLyUuNvKScg6ax05P2mvtVxJ71q6CX1J8WkJbuXnVvWGuRB++af1efjT4NdWtVAqlag7OjoSFhbG+vXrGTJkCAAWi4X169czbty4crfJy8tDqy3dhE+ns04JoyhKhfYZFhaGXq9n/fr1PPTQQwDEx8eTkJBAz549yz2uwWDAYJC5EkX1ycwvJGpJLMlZBbT0a8Cnw7vJdEdCVBFFUcg1mbmYZ+JCbuFVEu3ix8veL6po1n0ZrQZ8GhiKa8CtCXhJ4u3vfmm5dwNJwEXd1aZ4QLnDMqCcELWDoysEdLCWKxXmw4XTVyTwx62PmWetI+On7LeWK/m2gdBICO0HTXuB3qnsOnXZ9k8g/Yh1XICIsgOl16RKN32fMGECI0aMoFu3boSHhzN37lxyc3NtI7YPHz6cxo0bM3PmTAAGDx7M7Nmz6dKli63p+5QpUxg8eLAtYb/ePj08PBg1ahQTJkzAy8sLd3d3nn/+eXr27CkDyQlVGIvMPP35To6k5ODvbiBmZLg0ZRXiMiWJdlZ+IVkFhWTlF132vJCsgqLS7xWUfp5dUIT5BpJuAFdHHQ1dHfFydaShy+WPeutyF0fb+54ueqkBF4JLU7QdScnGYlGkdZgQtZneGfzaWMuVioxwMaGcmvgT1gHU0uKsZdtH1gHtmt9WnLhHWmvd63KT+ewU2PSu9XnktJsffPAmVTpRf/TRR0lLS2Pq1KkkJyfTuXNn1qxZYxsMLiEhoVQN+uTJk9FoNEyePJnExER8fX0ZPHgwb7/9doX3CTBnzhy0Wi0PPfQQRqORAQMG8PHHH9/MuQtxQywWhQkr/mb7yQwaGBxYEhVOY0+V5yAVogYVFJpZuPlEtSXal3N00NoSa2/X4gTbRX+VRNyaeEvLFiEqL9jbBUcHLXkmM2cu5NHM21XtkIQQ1cHBYG3i7tOy7Hv5F+DEJji6Do6ts/aDP/qbtYC1KX5J0h58Gxga1GTk1W/9G2DKhkZdofNTakeDRlGUm7+TqgWysrLw8PAgMzMTd3d3tcMRtdiMnw6xaMtJ9DoNMdHh9A6VudLri7p8HanMuRUUmmkzZU2F9qvXafBw1uPupMfNWY+7kwPuJY9O+kvPi9dxd7603M3JAWe9TgZnFKKG3PvhHxxIzGLBU2EM7FC5fqpyfRSijlEUSDloTdiPrYOEv8BSeOl9rR6a9SxO3O+y9uWuzf9fn9kBi4qnAh+9Hpp0q7Jd3+g1pNpHfReiLvnsjxMs2nISgFlDO0mSLuolJ72OJ3s0pcFVkm2Py5Jtg4NWEm0haok2Ae4cSMwiLjmr0om6EKKO0Wgu9YHvM946X/zJP4oT97XW5vMnN1vL2qng1sjarz00ElpEqN5svFIsFvjlFevzzk9WaZJ+MyRRF6KCfvz7HG+tPgzAxLvbcH/nxipHJIR63n6go9ohCCGqWJsA64By8ckyoJwQ4goGN2hzj7UoCpw/fqm2/dQfkH0O9nxhLRodNOl+aVC6wM5wxeDidmXvl3BuDxjcIXK62tHYSKIuRAVsO36el1f8DUBUr2DG3t5C5YiEEEKIqlUyoFycJOpCiGvRaMAn1FpufcY6yvzprXBsvTVxT4+HM39Zy8a3wMUbQvpd6t/u6q32GVySfxHWvWF9HjHROse8nZBEXYjriE/O5ukvdmIyWxjYPoAp97aTprxCCCHqnJIp2k6dzyXPVISLo9wmCiEqQO9c3Oy9H/COtVl8SdJ+4nfIOw/7V1iLgzMM+Rg6PKh21FabZkJeOvi0ts6bbkfkCizENSRl5hO1JJbsgiK6NWvI3Mc6yzROQggh6iSfBgZ8GhhIzzFyNCWHTkGeaockhKiNPJtCt2hrMRfCmVhr0h7/C6Qdhq+j4fwxuP0VdQegSzkEsZ9an9/9Hujsa6plO+4sIIS6MvMLiVq8g6TMAkJ8XflsRDeZ9kkIIUSdVtJPPS45S+VIhBB1gk4Pwb2t85I/+yf0HGddvvFt+PZpKCxQJy5FgV9eBcUMbQdDyB3qxHENkqgLUQ5jkZmxX+wkPiUbPzcDS0eG4+niqHZYQgghRLUqSdQPJ0k/dSFEFdPqYMDbMPgD0DpYm8IvHQw5aTUfy6FV1kHwHJyg/9s1f/wKkERdiCtYLAr/WLmPv05k0MDgwJLo7jRp6KJ2WEIIIUS1axNYMqCc1KgLIapJWBQ89S04ecDZWPjsTmsz9JpiyoNfJ1uf9x4PDZvV3LErQRJ1Ia7w7po4fvz7HA5aDfOf6kr7Rh5qhySEEELUiMunaFMUReVohBB1Vou+MHo9eLWwDj63qD8cXVczx94yB7LOgkdT6xzxdkoSdSEus3jLSRZuPgHAvx6+hdta+qockRBCCFFzQv0aoNXAhbxCUrONaodTZebNm0dwcDBOTk706NGD2NhYtUMSQvi0tCbrzfqAKRuWDYXtn1TvMS+cgj8/sD4f8JZ1xHo7JYm6EMV+3p/EjNXWZjevDmzNg12bqByRqI82b97M4MGDadSoERqNhlWrVl13m02bNtG1a1cMBgOhoaHExMRUe5xCiLrJSa+jhW8DAA4n1Y3m78uXL2fChAlMmzaN3bt306lTJwYMGEBqaqraoQkhXLxg2HfQ+SlQLNYB3lb/A8xF1XO8X18HsxGa94W291XPMaqIJOpCALEnMxi/fC+KAsNubcazfUPUDknUU7m5uXTq1Il58+ZVaP2TJ08yaNAg7rjjDvbu3cv48eMZPXo0v/76azVHKoSoq9r7GXChgPjkujGg3OzZsxkzZgzR0dG0a9eOBQsW4OLiwuLFi9UOTQgB4OAI938EkW8AGtjxqbV2vSCzao9zbD3E/QQanXU6NjWnhqsAmUdd1HvHUrMZ8/lOTEUW+rfzZ/p97dHY+RdX1F133303d999d4XXX7BgAc2bN+f9998HoG3btmzZsoU5c+YwYMCA6gpTCFGH9XOK4wOnFzkcGw5916odzk0xmUzs2rWLSZMm2ZZptVoiIyPZtm2bipEJIUrRaKz9xb1D4dsxcHyDtd/641+BV/Ob33+RCX75p/V5j7Hg1/bm91nNpEZd1GspWQWMWLyDzPxCujb15D+Pd0GnlSRd1B7btm0jMjKy1LIBAwZc9wbUaDSSlZVVqgghBEBb7VkA0oucVI7k5qWnp2M2m/H39y+13N/fn+Tk5HK3keujECpqey9E/wJugZAWB5/1g9NV8KNa7Cdw/ii4+kLExJvfXw2QRF3UWznGIqKX7CDxYj7NfVz5bER3nPQ6tcMSolKSk5PLvQHNysoiPz//qtvNnDkTDw8PWwkKCqruUIUQtURz8ykAeve6Xd1AVCLXRyFU1qgzjNkAgZ0g7zx8fh/8/dWN7y87GTa9Z33eb5p1WrhaQBJ1US8Vmi08++UuDiVl4dPAkaXR4Xi5OqodlhA1ZtKkSWRmZtrKmTNn1A5JCGEnHNLjAND6t1c5kpvn4+ODTqcjJSWl1PKUlBQCAgLK3Uauj0LYAfdG1pr1toPBbILvxsL6GWCxVH5f696wjirfOAw6P1n1sVYTSdRFvaMoCpO+3c8fR9Nx1utYNKI7Tb1d1A5LiBsSEBBQ7g2ou7s7zs5Xn3LEYDDg7u5eqgghBOZCa3NTAP926sZSBRwdHQkLC2P9+vW2ZRaLhfXr19OzZ89yt5HroxB2wtEVhn4OfSZYX/8xC76OAlNexfdxJhb+XmZ9fve/QVt70t/aE6kQVWTOuqN8vessOq2GeU92oVOQp9ohCXHDevbsWeoGFGDt2rVXvQEVQohrOn8MLIXg6AYeTdWOpkpMmDCBTz/9lKVLl3L48GGeffZZcnNziY6OVjs0IcT1aLUQOQ2GzAetHg59DzH3WJuzX4/FDD+/Yn3e+SloEla9sVYxGfVd1CtfxSbwn/VHAXhrSAfubON/nS2EqFk5OTkcO3bM9vrkyZPs3bsXLy8vmjZtyqRJk0hMTOTzzz8H4JlnnuGjjz7i1VdfZeTIkWzYsIEVK1awevVqtU5BCFGbpRy0Pvq1rVU1T9fy6KOPkpaWxtSpU0lOTqZz586sWbOmzPgeQgg71vkJ8GwGy5+Ec3vg0zutI8IH3nL1bfZ8CUl7weBuTfZrmbpxBRaiAjbGpfL6qgMAvHBnKI+H142aAlG37Ny5ky5dutClSxfAWhPUpUsXpk6dCkBSUhIJCQm29Zs3b87q1atZu3YtnTp14v333+ezzz6TqdmEEDcm9ZD1sQ40e7/cuHHjOH36NEajke3bt9OjRw+1QxJCVFZwbxi9HrxbQlYiLB4IcT+Xv27+BVj/hvV5xCRo4FdzcVYRqVEX9cK+sxf5v//uxmxReKhrE166q5XaIQlRroiICBRFuer7MTEx5W6zZ8+eaoxKCFFv2GrUa/9AckKIOsg7BEavhRUj4OTv8NUTcNeb0Ot561zsJTbOtI4Y79sGwseoF+9NkBp1UeclnM9jZMwO8gvN3NbSh3cf6ohGI3OlCyGEEGWklNSoS6IuhLBTzg3hqW8gLBpQYO0U+PEFKDJZ3085CDs+sz6/+z3Q6VUL9WZIoi7qtIxcEyOWxJKeY6JdoDsfP9kVvU7+7IUQQogyCrIgs7hrTR1r+i6EqGN0erh3Dgx8FzRa2P05fPkg5GXAL/8ExQxt74MWEWpHesOk6buoswoKzYxeuoOT6bk09nRmSXR33Jxq5y9qQgghRLVLPWx9dGtkrbESQgh7ptHArc+CVwv4eiSc+gM+6g556eDgBP3fUjvCmyJVi6JOMlsUXvxqD7sTLuLu5EBMdHf83Z3UDksIIYSwXynWAVelNl0IUau0GgAjfwWPIGuSDtDnJWjYTN24bpLUqIs6R1EU3vzxIL8eTMFRp+XT4d1o6e+mdlhCCCGEfUuV/ulCiFoqoIN1RPgfngdLIfR+Ue2IbtoN1ajPmzeP4OBgnJyc6NGjB7GxsVddNyIiAo1GU6YMGjTItk5KSgpRUVE0atQIFxcXBg4cyNGjR0vtJzk5mWHDhhEQEICrqytdu3blm2++uZHwRR336R8nWLrtNABzHu1MjxbeKkckRB2UfhSyU6CwQO1IhBBVpWQgORnxXQhRG7n5w5MrYNh3oHdWO5qbVuka9eXLlzNhwgQWLFhAjx49mDt3LgMGDCA+Ph4/v7Lz03377beYTCbb6/Pnz9OpUyeGDh0KWGs/hwwZgl6v5/vvv8fd3Z3Zs2cTGRnJoUOHcHV1BWD48OFcvHiRH374AR8fH5YtW8Yjjzxim3NYCIDv9ybyzs9xAEwe1JZBtwSqHJEQdZDFDB91u/RaZwAnjwoWz+JH90vLHJxKT6kihKh5igKpxVOzSdN3IYRQXaUT9dmzZzNmzBiio6MBWLBgAatXr2bx4sVMnDixzPpeXl6lXn/11Ve4uLjYEvWjR4/y119/ceDAAdq3t/6CO3/+fAICAvjf//7H6NGjAdi6dSvz588nPDwcgMmTJzNnzhx27doliboAYOvxdP6x8m8ARvZuzujbWqgckRB1lCnHmnAXZAIKmI2Qm2otN0LnePXE3rkhuHhfUbysjwZ3SfCFqCpZidbvtEYHPq3UjkYIIeq9SiXqJpOJXbt2MWnSJNsyrVZLZGQk27Ztq9A+Fi1axGOPPWarKTcajQA4OV0a6Eur1WIwGNiyZYstUe/VqxfLly9n0KBBeHp6smLFCgoKCoiIiCj3OEaj0bZvgKysrMqcqqhl4pOzGfvFLgrNCvd0DGDyoLZqhyRE3eXkARNPg8ViTdoLMitQLpZdZswCxQJmE+SmWUtlaB3KT+CvtUzvIsm9EOUpafbu0wocDOrGIoQQonKJenp6OmazGX9//1LL/f39iYuLu+72sbGxHDhwgEWLFtmWtWnThqZNmzJp0iQ++eQTXF1dmTNnDmfPniUpKcm23ooVK3j00Ufx9vbGwcEBFxcXvvvuO0JDQ8s91syZM3njjTcqc3qilkrOLCBqSSzZBUV0D27I7Ec6o9XKjbgQ1U6rLW7C7g4EVX776yb6FyH/IuSdv6xkWB8Lc8FSBDkp1lJRDk5lE3hXP3ALALdAa/82t0Dra6mxF/WJNHsXQgi7UqOjvi9atIiOHTvamq8D6PV6vv32W0aNGoWXlxc6nY7IyEjuvvtuFEWxrTdlyhQuXrzIunXr8PHxYdWqVTzyyCP88ccfdOzYscyxJk2axIQJE2yvs7KyCAq6gRtJYdeyCgqJWhJLUmYBIb6ufDq8G056ndphCSEq4mYS/cL8S0n7lUl8ucvSrTX3RQXWJr5Zidc/ht4FGlyWuNtK8esGxa8NbpLQi9rPNpCcJOpCCGEPKpWo+/j4oNPpSEkpXXuRkpJCQEDANbfNzc3lq6++4s033yzzXlhYGHv37iUzMxOTyYSvry89evSgWzfrYEXHjx/no48+KtWPvVOnTvzxxx/MmzePBQsWlNmnwWDAYJCmW3WZqcjCs1/uIi45G183AzHR4Xi6OKodlhCiJuidwaOxtVSEooApt/wEPicFspMhO8k6kn12MhgzoTAPLpy0lmvG4lq6Jt4t8IoEPxA8moDe6dr7EUJNKSU16jLiuxBC2INKJeqOjo6EhYWxfv16hgwZAoDFYmH9+vWMGzfumtuuXLkSo9HIU089ddV1PDw8AOsAczt37mTGjBkA5OXlAda+65fT6XRYLJbKnIKoIxRF4Z/f7OPPY+dxcdSxJKo7QV4uaoclhLBXGg0YGlhLw2bXX9+UBznJlyXwyZeVpEvJvTHL2gw/44S1XItbI2gYDF7NrY+20hxcfaRWXqjHXAjpR6zPJVEXQgi7UOmm7xMmTGDEiBF069aN8PBw5s6dS25urm0U+OHDh9O4cWNmzpxZartFixYxZMgQvL3Lzmm9cuVKfH19adq0Kfv37+fFF19kyJAh9O/fH7D2Yw8NDWXs2LHMmjULb29vVq1axdq1a/npp59u5LxFLTfrt3i+25OITqvh4ye70qGxh9ohCSHqEkcX8GphLddiyi0ngb8isc86Z03ms89ZS8LWsvvRu149ifcMksG9RPVKPwqWQuu4DB7STVAIIexBpRP1Rx99lLS0NKZOnUpycjKdO3dmzZo1tgHmEhISytR8x8fHs2XLFn777bdy95mUlMSECRNISUkhMDCQ4cOHM2XKFNv7er2en3/+mYkTJzJ48GBycnIIDQ1l6dKl3HPPPZU9BVHLffnXaeZtPA7AzAc7EtHaT+WIhBD1lqMreIdYy9UoirWp/YVTl5rSXzgFF05Dxklrf/nCXOtgXiUDepWiAffGxYl88KUEvmFxUu/iJbXx4uaklvRPbyt/S0IIYSc0yuUjttVhWVlZeHh4kJmZibu7u9rhiBu09lAKY7/YiUWBlyJb8WJkS7VDEvVIXb6O1OVzs3tFRrh45rJE/tSlknHSmsRfi6ObNYH372AtAR2txcWr2kMXdcS66bBlDoRFw+C5N7SLunwNqcvnJoSofjd6DanRUd+FuBl7Ei7w/P92Y1Hg0W5BvNCv/Kn5hBCiVnEwgE+otVxJUSA3/bLk/YpEPisRTNmQvN9aLufe5FLSXlIaBkuNqSirZMR36Z8uhBB2QxJ1USucSs9l1NKdFBRaiGjty1sPdEAjN5tCiLpOo4EGvtYS1L3s+4UFcDEBzh+zjtqdvM+asF84CVlnreXIL5fWN7iXrnUP6Ght7ix94Ou3VEnUhRDC3kiiLuze+RwjUUtiycg10aGxO/Oe6Ipep73+hkIIUdfpncC3lbW0uWzMloKs4sR9/6XkPfWQdZT6hK2lB7TTOoBP67K179J0vn4oyITMM9bnfm3VjUUIIYSNJOrCruWbzIxaupNT5/No0tCZxVHdcTXIn60QQlyTkzs062ktJcyF1tG9L0/ek/dB/oVLA9nt++rS+lc2nQ+8BTybSdP5uqak2bt7Y3BuqG4sQgghbCTjEXbLbFF44as97D1zEQ9nPTHR4fi5OakdlhBC1E46Pfi3s5ZOj1qXKYp1+riSPu7XazrfMBhCI60l+DbrvPSidiuZaUCavQshhF2RRF3YJUVRePPHg6w9lIKjg5bPRnQj1E9uCIUQokppNODR2FpaD7y0vLym8ykHrQPY7fjMWrR6a419SeLu105q22ujkhp1v3bqxiGEEKIUSdSFXfr0jxMs3XYajQbmPNKZ7sHSV1IIIWpMeU3njdlw8g84ts5aLp6Gk5utZe1UcAuE0H7WpL1FhDSjri1SpEZdCCHskSTqwu78+Pc53vk5DoDX72nLoFsCVY5ICCEEBjfrgHVt7rE2mc84AUfXWpP2U1sgOwn2fGktGi006V5c294PAruAVgYBtTuKAqmHrc+lRl0IIeyKJOrCrmw/cZ6XV/wNQFSvYEb1aa5yREIIIcrQaMA7xFpufQYK8+H0Vji+wZq4p8XBme3WsvFtcPGGkDshpJ81cW/gp/YZCIDMs2DMLB75v5Xa0QghhLiMJOrCbhxLzWbM5zsxmS0MaO/PlHvbyVzpQghRG+idi5u994MBb8PFM3B8vTVpP/E75J2H/SutBSDglkt924PCrQPdiZpXMn+6TytwcFQ3FiGEEKVIoi7sQmpWASMW7yCroIiuTT354LEu6LSSpAshRK3kGQRhUdZiLoSzOy71bU/6u3iAun2wZTY4ukGLvtakveVd4NFE7ejrj5QD1kdp9i6EEHZHEnWhulxjESOX7iDxYj7NfVz5bER3nPQ6tcMSQghRFXR6aNbLWvpNhZzUS03kj62H/AyI+8la0EC7+6HPeGjURe3I676SEd/9JVEXQgh7I4m6UFWR2cJzy3ZzIDELb1dHYqK74+Uqze+EEKLOauAHnR6zFosZkvZaE/aja+FsLBxaZS0t7rAm7M37yrRv1aWk6bt/B3XjEEIIUYYk6kI1iqIwedUBNsWn4aTXsiiqO828XdUOSwghRE3R6qBxmLX0fRWSD8CfH8CBb+DERmtp1AX6vARt7rWuL6pGkQnSj1ifS9N3IYSwOzJXilDNRxuO8dWOM2g18OHjXekc5Kl2SEIIIdQU0AEe+hRe2A3dx4CDE5zbAyuGw7xw2P05FBnVjrJuSD8CliIweMi4AEIIYYckUReq+GbXWd5fa/0l/4372nNXO3+VIxJCCGE3GgbDoFkw/gDc9g9w8oDzx+CH5+GDTrD1QzBmqx1l7VbS7N2vrXQtEEIIOySJuqhxW46m889v9gEwtm8LhvUMVjcgIYQQ9qmBL/SbAi8dhP5vgVsgZCfBb5NhTnvY8BbkpqsdZe2UctD66N9e3TiEEEKUSxJ1UaMOJ2XxzJe7KLIoDO7UiH8OaKN2SEIIIeydwQ16PQ8v/g33fQjeoVCQCZv/DXM6wM+vwIXTakdZu6TKiO9CCGHPJFEXNSYpM5/oJTvIMRbRo7kXs4beglbmShdCCFFRDgboOhyei4VHPrcONFeUD7EL4T9d4NunL9UUi2sr+Zz8pEZdCCHskSTqokZkFRQStXgHyVkFtPRrwMJh3TA4yOi9QgghboBWZ51vfcxGGP69dSo3xQz7lsP8XvDfR+D0NrWjtF/5FyAr0frcr626sQghhCiXJOqi2pmKLDz75S7iU7LxdTOwJLo7Hi56tcMSQghR22k00CIChq+CpzdBuyGABo7+CksGwqIBEL8GLBZVw7Q7qYetjx5B4OypaihCCCHKJ4m6qFaKojDxm338eew8ro46lkR1p0lDF7XDEkIIUdc06gKPLIVxO6HrCNA5wpm/4H+PwoLe8PdyMBeqHaV9sDV7l/7pQghhryRRF9Xq/d+O8O2eRHRaDR8/FUaHxh5qhySEEKIu8wmF+/4DL+6DXi+Ao5t14LTvnob/dIVdMaAoakepLtuI75KoCyGEvZJEXVSbZdsT+GjjMQBmPtCRvq18VY5ICCFEveEeCP1nwEsHoN9UcPWFzAT48UVYM7F+N4e3zaEuA8kJIYS9kkRdVIuNcalM+f4AAC/0a8kj3YNUjkiI2mXevHkEBwfj5OREjx49iI2Nveq6MTExaDSaUsXJyakGoxXCjjl7wm0vw/j91oQdYPsC+P45MBepGpoqFOVSH3WZQ10IIeyWJOqiyu0/m8lzy3Zjtig8HNaElyJbqh2SELXK8uXLmTBhAtOmTWP37t106tSJAQMGkJqaetVt3N3dSUpKspXTp2VOaSFK0TtbE/YHPgGNDv5eBitHQJFR7chqVuYZMGaBVg8+8v+zEELYqxtK1CtT0xMREVGmpkej0TBo0CDbOikpKURFRdGoUSNcXFwYOHAgR48eLbOvbdu2ceedd+Lq6oq7uzu33347+fn5N3IKopqcycgjOmYHeSYzt7X0YeaDHdFoZK50ISpj9uzZjBkzhujoaNq1a8eCBQtwcXFh8eLFV91Go9EQEBBgK/7+/jUYsRC1SKfHrHOw6xwh7idY9iiYctWOquaU9E/3aQU6mYFFCCHsVaUT9crW9Hz77belankOHDiATqdj6NChgHVU8CFDhnDixAm+//579uzZQ7NmzYiMjCQ399J/nNu2bWPgwIH079+f2NhYduzYwbhx49BqpVGAvbiYZ2LEkljSc4y0DXTn4ye7otfJv48QlWEymdi1axeRkZG2ZVqtlsjISLZtu/q80Dk5OTRr1oygoCDuv/9+Dh48eM3jGI1GsrKyShUh6o2298KTK0HvCic2wudDrHOL1wcykJwQQtQKlc6iKlvT4+XlVaqWZ+3atbi4uNgS9aNHj/LXX38xf/58unfvTuvWrZk/fz75+fn873//s+3npZde4oUXXmDixIm0b9+e1q1b88gjj2AwGG7w1EVVKig0M+bznZxIyyXQw4klUd1xc5Jf6oWorPT0dMxmc5kacX9/f5KTk8vdpnXr1ixevJjvv/+eL7/8EovFQq9evTh79uxVjzNz5kw8PDxsJShIxpEQ9UyLCBj+PTh5wtlYiLkXslPUjqr6lQwkJ/3ThRDCrlUqUb/Rmp7LLVq0iMceewxXV1fAWqsDlBr4SKvVYjAY2LJlCwCpqals374dPz8/evXqhb+/P3379rW9Xx6pLao5FovCyyv/ZsepC7g5ORATHU6AhwxkJURN6dmzJ8OHD6dz58707duXb7/9Fl9fXz755JOrbjNp0iQyMzNt5cyZMzUYsRB2Iqg7RP8MDfwh5QAsGQgXE9SOqnqlyIjvQghRG1QqUb+Rmp7LxcbGcuDAAUaPHm1b1qZNG5o2bcqkSZO4cOECJpOJ9957j7Nnz5KUlATAiRMnAJg+fTpjxoxhzZo1dO3alX79+pXblx2ktqgmvbsmjtX7ktDrNHwyLIzWAW5qhyREreXj44NOpyMlpXTNXkpKCgEBARXah16vp0uXLhw7duyq6xgMBtzd3UsVIeol//YQ/Qt4NIWME7B4IKQdUTuq6lFkhPTic5Om70IIYddqtAPxokWL6NixI+Hh4bZler2eb7/9liNHjuDl5YWLiwsbN27k7rvvtvU/txTPdTp27Fiio6Pp0qULc+bMsTX3LI/UFtWMpVtPsXCz9YeUfz18C71CfFSOSIjazdHRkbCwMNavX29bZrFYWL9+PT179qzQPsxmM/v37ycwMLC6whSibvEOgVG/gk9ryEq01qyf26t2VFUv/QgoZjB4gHtjtaMRQghxDZVK1G+mpic3N5evvvqKUaNGlXkvLCyMvXv3cvHiRZKSklizZg3nz5+nRYsWALabzXbtSv/627ZtWxISym+iJrVF1e+3g8m88aN1UJpXBrTmgS5NVI5IiLphwoQJfPrppyxdupTDhw/z7LPPkpubS3R0NADDhw9n0qRJtvXffPNNfvvtN06cOMHu3bt56qmnOH36dKnWS0KI63BvZK1ZD+wMeedh6WA4vVXtqKpWymX902VGFiGEsGuVStRvpqZn5cqVGI1Gnnrqqauu4+Hhga+vL0ePHmXnzp3cf//9AAQHB9OoUSPi4+NLrX/kyBGaNWtWmVMQVWTvmYu88NUeLAo8Hh7E/0WEqB2SEHXGo48+yqxZs5g6dSqdO3dm7969rFmzxtbtKCEhwdY1CODChQuMGTOGtm3bcs8995CVlcXWrVvL/LgphLgOV28Y8SM0622da/yLB+HoOrWjqjqpMuK7EELUFg6V3WDChAmMGDGCbt26ER4ezty5c8vU9DRu3JiZM2eW2m7RokUMGTIEb2/vMvtcuXIlvr6+NG3alP379/Piiy8yZMgQ+vfvD1jnB37llVeYNm0anTp1onPnzixdupS4uDi+/vrrGzlvcRMSzucxKmYHBYUW+rbyZcb9HWSudCGq2Lhx4xg3bly5723atKnU6zlz5jBnzpwaiEqIesDJHZ76BlYMh6O/wf8eg4c+hfYPqB3ZzSuZms2vfiTqp06dYsaMGWzYsIHk5GQaNWrEU089xeuvv46jo6Pa4QkhxDVVOlF/9NFHSUtLY+rUqSQnJ9O5c+cyNT1Xzm0eHx/Pli1b+O2338rdZ1JSEhMmTCAlJYXAwECGDx/OlClTSq0zfvx4CgoKeOmll8jIyKBTp06sXbuWkBCpya1JF3JNRC2J5XyuifaN3Jn3ZFccZK50IYQQdYneGR79L6x6Bg58A1+PhIIsCBuhdmQ3x9b0vYO6cdSQuLg4LBYLn3zyCaGhoRw4cIAxY8aQm5vLrFmz1A5PCCGuSaMoiqJ2EDUhKysLDw8PMjMzpb/6DSooNPPUZ9vZefoCjT2d+fb/euHvLtOwifqjLl9H6vK5CXHDLGZY/TLsWmJ93f8t6PW8ujHdqPwL8F6w9fnEM9aWA1WotlxD/v3vfzN//nzbjEIVUVvOTQhhn270GlLpGnVRP1ksCi+v+Judp61zpS+J7i5JuhBCiLpNq4N751iT2j8/gN8mQ0Em3PF67RuMraQ23aNplSfptUlmZiZeXl7XXMdoNGI0Gm2vs7KyqjssIYQoQ9osiwp5d00cq/dfmiu9lb/MlS6EEKIe0Gjgrjeh3zTr683/hl9eheKpY2uNFBlI7tixY3z44YeMHTv2muvNnDkTDw8PWwkKCqqhCIUQ4hJJ1MV1XT5X+r8f7iRzpQshhKh/bpsAg94HNBC7EFY9C+YitaOqONuI7+3VjaMKTJw4EY1Gc80SFxdXapvExEQGDhzI0KFDGTNmzDX3P2nSJDIzM23lzJkz1Xk6QghRLmn6Lq7pyrnSh3RprHJEQgghhEq6jwaDO3z3DOz7CozZ8PBi0NeCrmAlTd/rwIjvL7/8MlFRUddcp0WLFrbn586d44477qBXr14sXLjwuvs3GAwYDIabDVMIIW6KJOriqmSudCGEEOIKtzwCBjdYMQLiV8OyofDY/8DQQO3Irs5igdTD1ud1oEbd19cXX1/fCq2bmJjIHXfcQVhYGEuWLCkzM5EQQtgruVqJcslc6UIIIcRVtL4bnvoaHBvAyc3w+f2Ql6F2VFeXmQCmbNDqwTtU7WhqTGJiIhERETRt2pRZs2aRlpZGcnIyycnJaocmhBDXJYm6KONCromoGOtc6e0CZa50IYQQoozmt8PwH8C5ISTuhJhBkG2nCWBJs3ffNqDTqxtLDVq7di3Hjh1j/fr1NGnShMDAQFsRQgh7J9mXKKWg0MzTX+zkRFoujTycWBLdnQYG6SEhhBBClNEkDKJ/gQYBkHoIFg+EC6fVjqqs1Po54ntUVBSKopRbhBDC3kmiLmwsFoWXV/7NjlPWudJjRobLXOlCCCHEtfi1hZFrwLMZXDhpTdbT4tWOqrQ6NJCcEELUF5KoC5v31sSxel/xXOlPyVzpQgghRIV4NYeRv1qblmefgy8eBHOh2lFdklJ3pmYTQoj6QhJ1AcDn207xSfFc6f96+BZ6hcpc6UIIIUSFuQdam8G7+kLWWTixSe2IrIqMcP6Y9bkk6kIIUWtIoi5YeyiF6T9Yf23/R/9WPNClicoRCSGEELWQixd0eMj6fN9ydWMpkRYPihmcPMFNBlETQojaQhL1eu7vMxd5/n+7sSjwWPcgnruj/kzbIoQQQlS5jo9YH+NWgzFH3VigdLN3mWZVCCFqDUnU67GE83mMWnrZXOlDZK50IYQQ4qY07gpeLaAwD+J/VjuaSyO+y0ByQghRq0iiXk+VzJWennNprnS9zJUuhBBC3ByN5lKt+r4V6sYCl0Z8l/7pQghRq0hmVg/JXOlCCCFENbqlOFE/vgFy0tSNJVUSdSGEqI0kUa9nZK50IYQQopp5h0CjrtZB3A5+p14ceRmQnWR97tdWvTiEEEJUmiTq9YzMlS6EEELUgJJa9f0qNn8vGUjOsykY5P97IYSoTSRRr0e+uGyu9PcekrnShRBCiGrT/kHQaOHsDsg4oU4MtmbvHdQ5vhBCiBsmiXo9se5QCtOK50p/+a5WPNhV5koXQgghqo2bP7SIsD7f/7U6MaTIiO9CCFFbSaJeD1jnSt+DRYFHuwUx7k6ZK10IIYSodpeP/q4oNX982xzqkqgLIURtI4l6HXcmwzpXen6hmdtb+fLWAzJXuhBCCFEj2t4LDs5w/igk7a3ZY1sskHrY+txPRnwXQojaRhL1OuxinokRSy7Nlf6xzJUuhBBC1ByDG7S+2/q8pudUv3gaCnNB5wje0pJOCCFqG8na6ihjkZmnv9jFibRcAj2cWBwlc6ULIYQQNe6WR62PB74Bi7nmjlsykJxva9DJ//9CCFHbSKJeB1ksCq+s3EfsyQzcDA4sie5OgIfMlS6EEELUuNB+4OwFOSlw8veaO65tIDlp9i6EELXRDSXq8+bNIzg4GCcnJ3r06EFsbOxV142IiECj0ZQpgwYNsq2TkpJCVFQUjRo1wsXFhYEDB3L06NFy96coCnfffTcajYZVq1bdSPh13vtr4/nh73M4aDXMfyqMNgHuaockhBBC1E86PbR/wPp838qaO64MJCeEELVapRP15cuXM2HCBKZNm8bu3bvp1KkTAwYMIDU1tdz1v/32W5KSkmzlwIED6HQ6hg4dClgT7yFDhnDixAm+//579uzZQ7NmzYiMjCQ3N7fM/ubOnSuDoV3D/2ITmLfxOAAzH+xIn5YyV7oQQgihqluKR38//CMU5tfMMW1zqEuNuhBC1EaVTtRnz57NmDFjiI6Opl27dixYsAAXFxcWL15c7vpeXl4EBATYytq1a3FxcbEl6kePHuWvv/5i/vz5dO/endatWzN//nzy8/P53//+V2pfe/fu5f3337/qseq7TfGpTF51AIAX+rVkaLcglSMSQgghBEE9wLMpmLIh/pfqP15hAZw/Zn0uTd+FEKJWqlSibjKZ2LVrF5GRkZd2oNUSGRnJtm3bKrSPRYsW8dhjj+Hq6gqA0WgEwMnpUh9qrVaLwWBgy5YttmV5eXk88cQTzJs3j4CAgOsex2g0kpWVVarUZQfPZfLcf3djtig82KUxL0W2VDskIYQQQvD/7d15fFT12ffx72RPhCRmIawhBCNbgoEEaNTeWIuGpdzGWqTeyhIVn/JIRdNiodaltRb7FHdRKw1LqTbII1hRG+UJUEoLQgipRFkioEFIJqxJDJhA5vf8ETIaSSAJmZmTyef9ep0XM2d+55zrgsxFrjlnfkeSzSYl1Z+g0E43XP5+ZLdkHFLw5VLXi//OBACwnlY16kePHlVdXZ1iYmIarY+JiVFZWdlFt9+6dauKiop09913O9cNHDhQsbGxmjdvnk6cOKHa2lr9/ve/1xdffKHS0lLnuAceeEBXX321brrpphbFOn/+fIWFhTmXPn289+zy4ZOndefSbaqurVNafKSevGUoXw8AAMBKks5d/l68Vjp13LXHarjsvduQ+g8JAAAdjltnfc/OzlZSUpJGjhzpXOfv769Vq1Zp7969ioiIUEhIiNavX69x48bJx6c+vLffflvr1q3Ts88+2+JjzZs3TxUVFc7l4MGD7Z2OJVR+dUZ3Lt0me2WNErp10StTUhTgx2T+AABYSreBUvckyXFG+uQt1x7LOZEcl70DQEfVqo4uKipKvr6+stvtjdbb7faLXo5eXV2tnJwc3XXXXee9lpKSosLCQp08eVKlpaXKzc3VsWPHFB8fL0lat26d9u3bp/DwcPn5+cnPr/5+oLfccouuu+66Jo8XGBio0NDQRou3OVPn0L2vFWh3WZWiuwZqSeYIhQX7ezosAADQlIaz6q6e/d05kRwzvgNAR9WqRj0gIEApKSnKy8tzrnM4HMrLy1NaWtoFt125cqVqamp0xx13NDsmLCxM0dHRKi4uVn5+vvMy97lz5+qjjz5SYWGhc5GkZ555RkuWLGlNCl7DGKOHVu/UP4uPKtjfV4unjVDvy0M8HRYAAGhO0o8k2aSSf0snS1x3HO6hDgAdnl9rN8jKytK0adOUmpqqkSNH6tlnn1V1dbUyMzMlSVOnTlWvXr00f/78RttlZ2crIyNDkZGR5+1z5cqVio6OVmxsrHbu3KnZs2crIyNDN954oyQ5Z4z/ttjYWPXr16+1KXiFF9d9qjfyv5CPTXrxf4YpqXeYp0MCAAAXEtpTirtW+uyf9ZPKffdn7X+M6mPSl+eufOw2sP33DwBwi1Y36pMnT9aRI0f0yCOPqKysTMnJycrNzXVOMFdSUuL8bnmDPXv2aNOmTfrggw+a3GdpaamysrJkt9vVo0cPTZ06VQ8//HAb0ukcVu/4Qk+t3StJ+vV/D9H3B8VcZAsAAGAJQ2+tb9Q/Wildm9X+k72VnzubfnmcFNi1ffcNAHAbmzHGeDoId6isrFRYWJgqKio69PfV/73vqKYt3qozdUb3/Fe8fjl+kKdDAjoNb6kjTfHm3ABLOX1SWnClVFcj/WRT/QRz7WnLK1LuL6QBE6TbXm/ffV+AN9cQb84NgOu1tYYwPXgHUmyv0v9avl1n6owmJPXQ3LFc0gYAQIcSHC5dmV7/+KM32n//9qL6P5lIDgA6NBr1DqK86itNX7JNVV+dVUrfy/XUrVfJx4d7owIA0OEMPTf7e9GbksPRvvt23kOdRh0AOjIa9Q7gVO1Z3bU0X4dOnla/qMu0aGqqgvx9PR0WABdauHCh4uLiFBQUpFGjRmnr1q0XHL9y5UoNHDhQQUFBSkpK0nvvveemSAG0WsKNUlCYVHlI+vxf7bdfh0Mq313/OCax/fYLAHA7GnWLq3MY3ffXHdp5qEIRlwVoyfQRirgswNNhAXChFStWKCsrS48++qgKCgp01VVXKT09XeXl5U2O//e//63bbrtNd911l3bs2KGMjAxlZGSoqKjIzZEDaBG/QGlw/S1otbMdL38/+Zl0plryDZQi4ttvvwAAt6NRtzBjjH695mP9v13lCvDz0aKpqYqLuszTYQFwsaefflozZsxQZmamBg8erFdeeUUhISFavHhxk+Ofe+45jR07VnPmzNGgQYP0+OOPa/jw4XrxxRfdHDmAFks6d/n7J3+Tzta0zz4b7p8ePUDybfWNfQAAFkKjbmF/+ucB/Xnz57LZpGcnJyul7+WeDgmAi9XW1mr79u0aM2aMc52Pj4/GjBmjzZs3N7nN5s2bG42XpPT09GbHS1JNTY0qKysbLQDcqO81Umgv6asKqbjp29e2mv3c99NjhrTP/gAAHkOjblHv7SzVE+/tkiT9ctwgjU/q4eGIALjD0aNHVVdXp5iYmEbrY2JiVFZW1uQ2ZWVlrRovSfPnz1dYWJhz6dOnz6UHD6DlfHykxFvqH7fX7O8N91CnUQeADo9G3YK2f35c968olCRNTeuru7/bz7MBAfA68+bNU0VFhXM5ePCgp0MCOp+G2d/3vl9/f/VLZWfGdwDwFjTqFnPgaLXuXpav2rMOjRnUTY9OHCKbjduwAZ1FVFSUfH19ZbfbG6232+3q3r17k9t07969VeMlKTAwUKGhoY0WAG4WkyhFD5LqaqRdb1/avs6clo7vO7dfzqgDQEdHo24hx6trlblkq06cOqOhvcP0/G3D5Mu90oFOJSAgQCkpKcrLy3OuczgcysvLU1paWpPbpKWlNRovSWvXrm12PACLsNmkoZPqH1/q5e9HdkvGIQVHSF1iLj4eAGBpNOoW8dWZOs34c74+O3ZKvcKD9adpqQoJYMZWoDPKysrSokWLtGzZMu3atUszZ85UdXW1MjMzJUlTp07VvHnznONnz56t3NxcPfXUU9q9e7cee+wx5efna9asWZ5KAUBLJZ1r1D/bJFUebvt+vjmRHFfiAUCHRydoAQ6H0c/e+I+2f35CoUF+WnbnCHXrGuTpsAB4yOTJk3XkyBE98sgjKisrU3JysnJzc50TxpWUlMjH5+vPWa+++mq9/vrr+tWvfqVf/vKXSkhI0FtvvaXExERPpQCgpcJjpdirpZJ/Szv/r3TNfW3bTzkzvgOAN6FRt4Anc3fr3Z2l8ve16ZUpKbqiW1dPhwTAw2bNmtXsGfENGzact27SpEmaNGmSi6MC4BJDJ51r1N9oe6NuL6r/k4nkAMArcOm7hy3f/Jle3bhfkvR/fjRUV/eP8nBEAADArQZnSD7+UtlOqXx32/bBPdQBwKvQqHtQ3i67Hn27/p6nP7vhSt08rLeHIwIAAG4XEiEl3FD/eGcbJpWrPipVl0uySdED2zU0AIBn0Kh7yM4vKjTr9R1yGOnW1N6adf0Vng4JAAB4SsOkcjtXSsa0blt7/Yf+ujxOCuzSrmEBADyDRt0DDp08rTuXbdPpM3W69oooPXFzEvdKBwCgMxswTgroKp0skQ5+2LptGxp1LnsHAK9Bo+5mlV+d0Z1LtulIVY0GxHTVS3cMl78v/wwAAHRq/sHSoIn1j1t7T/Xyc406E8kBgNegQ3SjM3UO/e+/FGiPvUrdugZqceYIhQb5ezosAABgBUPPXf7+8WrpbG3Lt2MiOQDwOjTqbmKM0UOrd2rTp0cVEuCrxdNHqFd4sKfDAgAAVtFvtNQlRjp9XNqX17JtHHVS+a76xzTqAOA1aNTdZOH6T/VG/hfysUkv/s8wJfYK83RIAADASnx8pcRb6h+39PL3E59JZ09LfkFSRLzLQgMAuBeNuhv8rfCQFnywV5L06/8eousHxng4IgAAYEkNs7/v+btUU3Xx8Q0TyUUPqG/0AQBegUbdxT7cf0xzVn4kSZrx3X6akhbn2YAAAIB19RwmRV5Rf5Z81zsXH1/e8P30RNfGBQBwKxp1F9p35Evds3y7auscGpfYXfPGDfJ0SAAAwMpsNinp1vrHO1tw+bu9qP5PZny/oJqaGiUnJ8tms6mwsNDT4QDARdGou8jRL2uUuWSbKk6f0bDYcD0zOVk+PtwrHQAAXETD7O/7N0hV9guPdc74TqN+IQ8++KB69uzp6TAAoMVo1F3gqzN1untZvkqOn1JsRIgWTU1VkD/fGwMAAC0QES/1HiEZh/TxqubH1Z6Sju+vf9yNGd+b8/e//10ffPCBFixY4OlQAKDF2tSoL1y4UHFxcQoKCtKoUaO0devWZsded911stls5y0TJkxwjrHb7Zo+fbp69uypkJAQjR07VsXFxc7Xjx8/rp/+9KcaMGCAgoODFRsbq/vuu08VFRVtCd+lHA6jB1YUqvDgSYUF+2tJ5ghFdQn0dFgAAKAjabj8/UKzvx/ZLclIIVFSl25uCaujsdvtmjFjhpYvX66QkJAWbVNTU6PKyspGCwC4W6sb9RUrVigrK0uPPvqoCgoKdNVVVyk9PV3l5eVNjl+1apVKS0udS1FRkXx9fTVpUv1lXcYYZWRkaP/+/frb3/6mHTt2qG/fvhozZoyqq6slSYcPH9bhw4e1YMECFRUVaenSpcrNzdVdd911Cam7xpO5u/X3ojIF+Pro1Skp6h/dxdMhAQCAjmbIzZLNVzpcIB3b1/SYhhnfYwbXf7cdjRhjNH36dP3kJz9Rampqi7ebP3++wsLCnEufPn1cGCUANK3VjfrTTz+tGTNmKDMzU4MHD9Yrr7yikJAQLV68uMnxERER6t69u3NZu3atQkJCnI16cXGxtmzZopdfflkjRozQgAED9PLLL+v06dP661//KklKTEzUm2++qYkTJ6p///66/vrr9cQTT2jNmjU6e/bsJaTfvpZv/kyvbqy/BO0Pk4ZqVHykhyMCAAAdUpdoqf/19Y+bO6veMON7J7vsfe7cuU1erfnNZffu3XrhhRdUVVWlefPmtWr/8+bNU0VFhXM5ePCgizIBgOb5tWZwbW2ttm/f3qjg+fj4aMyYMdq8eXOL9pGdna0f//jHuuyyyyTVX14kSUFBQY32GRgYqE2bNunuu+9ucj8VFRUKDQ2Vn1/TKdTU1Dj3Lcnlly2t223Xo2/Xf7L98xuv1E3JvVx6PAAA4OWG3ip9urZ+9vfr5p5/1vybZ9Q7kZ/97GeaPn36BcfEx8dr3bp12rx5swIDG38FMTU1VbfffruWLVvW5LaBgYHnbQMA7taqRv3o0aOqq6tTTExMo/UxMTHavXv3RbffunWrioqKlJ2d7Vw3cOBAxcbGat68efrjH/+oyy67TM8884y++OILlZaWNhvH448/rnvuuafZY82fP1+//vWvW5jZpSk6VKFZr++Qw0i3pvbWvd+7wi3HBQAAXmzAeMk/pH7CuEPbpd7funzbeQ/1znVGPTo6WtHR0Rcd9/zzz+u3v/2t8/nhw4eVnp6uFStWaNSoUa4MEQAumVtnfc/OzlZSUpJGjhzpXOfv769Vq1Zp7969ioiIUEhIiNavX69x48bJx+f88CorKzVhwgQNHjxYjz32WLPHctdlS4dPntadS7fpVG2drr0iSk/cnCQb3xMDAACXKrCLNPDc5Lvfvvz9y3Kp+ogkmxQ9yO2hdQSxsbFKTEx0LldeeaUkqX///urdu7eHowOAC2tVox4VFSVfX1/Z7Y3v6Wm329W9e/cLbltdXa2cnJwmJ4BLSUlRYWGhTp48qdLSUuXm5urYsWOKj49vNK6qqkpjx45V165dtXr1avn7+zd7vMDAQIWGhjZa2lvlV2eUuWSbyqtqdGVMF710x3D5+3LHOwAA0E4aZn//eJVU9415eRoue4/oJwW0bDZzAEDH0aquMiAgQCkpKcrLy3OuczgcysvLU1pa2gW3XblypWpqanTHHXc0OyYsLEzR0dEqLi5Wfn6+brrpJudrlZWVuvHGGxUQEKC333670XfaPeFMnUP3vlagPfYqRXcN1JLMkQoNav6DAwAAgFbr/z0pJLL+7Pn+DV+vd04k17m+n34p4uLiZIxRcnKyp0MBgItq9enfrKwsLVq0SMuWLdOuXbs0c+ZMVVdXKzMzU5I0derUJmfXzM7OVkZGhiIjz58JfeXKldqwYYPzFm033HCDMjIydOONN0r6ukmvrq5Wdna2KisrVVZWprKyMtXV1bU2hUtmjNGvVhfpn8VHFRLgqyXTR6hXeLDb4wAAAF7O118a8sP6xzu/cfm7veH76YnujwkA4HKtmkxOkiZPnqwjR47okUceUVlZmZKTk5Wbm+ucYK6kpOS875bv2bNHmzZt0gcffNDkPktLS5WVlSW73a4ePXpo6tSpevjhh52vFxQU6MMPP5QkXXFF44naDhw4oLi4uNamcUle2rBPK/IPyscmvXDbMCX2CnPr8QEAQCcy9FZp2yJp1ztSbbUUcJlkL6p/rZPN+A4AnYXNGGM8HYQ7VFZWKiwszHlbt7b6W+Ehzc4plCQ9ftMQTUmLa58AAVhee9URK/Lm3IAOzxjp+WTpxGfSLdnSkJul3/WUzn4lzdouRXn+bjPeXEO8OTcArtfWGsLMZ62w9cBxzVn5kSTp7mv70aQDAADXs9m+nlTuozek4wfqm3S/4PrJ5AAAXodGvYX2HflS9yzPV22dQ2OHdNcvx3MrFAAA4CZDzzXq+/KkzzbWP+42UPLx9VxMAACXoVFvgWNf1ihzyTadPHVGyX3C9czkZPn4cK90AADgJlEJUo9kyXFW2rigfl23IR4NCQDgOjTqF/HVmTrN+HO+So6fUp+IYP1pWqqCA/j0GgAAuFnDWfXKQ/V/MpEcAHgtGvULcDiMst4oVEHJSYUF+2vJ9JGK6hLo6bAAAEBnlHiLZPvGr27cQx0AvBaN+gX8Pne33ttZJn9fm/44JUVXdOvi6ZAAAEBn1bW71O+/vn7OPdQBwGvRqDfjjfyD+uPG/ZKkP/zoKn0nPtLDEQEAgE6vYfb3y6KlLtGejQUA4DJ+ng7Aqv4rIVqDe4RqXGJ3ZQzr5elwAAAApKQfSYcLpD7f8XQkAAAXolFvRvewIL0582oF+XPRAQAAsAi/QGnCU56OAgDgYjTqF8Ds7gAAAAAAd+N0MQAAAAAAFkKjDgAAAACAhdCoAwAAAABgITTqAAAAAABYCI06AAAAAAAWQqMOAAAAAICF0KgDAAAAAGAhNOoAAAAAAFgIjToAAAAAABZCow4AAAAAgIX4eToAdzHGSJIqKys9HAmAjqqhfjTUE29CjQRwKaiPANC0ttbHTtOoV1VVSZL69Onj4UgAdHRVVVUKCwvzdBjtihoJoD1QHwGgaa2tjzbjjR99NsHhcOjw4cPq2rWrbDZbi7aprKxUnz59dPDgQYWGhro4Qtfxhjy8IQeJPKykLTkYY1RVVaWePXvKx8e7vjnU2hrpDT8Dknfk4Q05SORhNa3Ng/r4tc76M2BV3pCHN+Qgdd482lofO80ZdR8fH/Xu3btN24aGhnboH6YG3pCHN+QgkYeVtDYHbztT1KCtNdIbfgYk78jDG3KQyMNqWpMH9bGxzvgzYGXekIc35CB1zjzaUh+96yNPAAAAAAA6OBp1AAAAAAAshEb9AgIDA/Xoo48qMDDQ06FcEm/IwxtykMjDSrwhB0/ylr8/b8jDG3KQyMNqvCUPT/CWvzvysA5vyEEij9bqNJPJAQAAAADQEXBGHQAAAAAAC6FRBwAAAADAQmjUAQAAAACwEBp1AAAAAAAspFM16gsXLlRcXJyCgoI0atQobd26tdmxZ86c0W9+8xv1799fQUFBuuqqq5Sbm3tJ+2wv7Z3H/PnzNWLECHXt2lXdunVTRkaG9uzZ4+o0XPLv0eDJJ5+UzWbT/fff74LIv+aKHA4dOqQ77rhDkZGRCg4OVlJSkvLz812ZRrvnUVdXp4cfflj9+vVTcHCw+vfvr8cff1yunLty48aNmjhxonr27Cmbzaa33nrrotts2LBBw4cPV2BgoK644gotXbr0vDGeeI97ijfUSOqjdeqj5B01kvpIfZSoj9TH9ucN9VHq+DXS0vXRdBI5OTkmICDALF682Hz88cdmxowZJjw83Njt9ibHP/jgg6Znz57m3XffNfv27TMvvfSSCQoKMgUFBW3ep1XzSE9PN0uWLDFFRUWmsLDQjB8/3sTGxpovv/yyQ+XRYOvWrSYuLs4MHTrUzJ49u0PlcPz4cdO3b18zffp08+GHH5r9+/eb999/33z66acdKo8nnnjCREZGmnfeecccOHDArFy50nTp0sU899xzLsvjvffeMw899JBZtWqVkWRWr159wfH79+83ISEhJisry3zyySfmhRdeML6+viY3N9c5xhPvcU/xhhpJfbROfXRVHu6ukdRH6qMx1EfqY8fIg98h28bK9bHTNOojR4409957r/N5XV2d6dmzp5k/f36T43v06GFefPHFRut++MMfmttvv73N+2wPrsjj28rLy40k849//KN9gm6Cq/KoqqoyCQkJZu3atWb06NEuLbSuyOEXv/iFufbaa10TcDNckceECRPMnXfeecExrtSSQvvggw+aIUOGNFo3efJkk56e7nzuife4p3hDjaQ+fs3T9dEY76iR1MevUR+pj9TH9uMN9dEY76uRVquPneLS99raWm3fvl1jxoxxrvPx8dGYMWO0efPmJrepqalRUFBQo3XBwcHatGlTm/d5qVyRR1MqKiokSREREe0Q9flcmce9996rCRMmNNq3K7gqh7ffflupqamaNGmSunXrpmHDhmnRokWuSUKuy+Pqq69WXl6e9u7dK0n6z3/+o02bNmncuHEuyKJtNm/efN7PSXp6ujNvT7zHPcUbaiT10Tr1UfKOGkl9pD5K1MfmcmgK9bFlvKE+Sp23RrqzPnaKRv3o0aOqq6tTTExMo/UxMTEqKytrcpv09HQ9/fTTKi4ulsPh0Nq1a7Vq1SqVlpa2eZ9WzOPbHA6H7r//fl1zzTVKTExs9xwk1+WRk5OjgoICzZ8/3yVxf5Orcti/f79efvllJSQk6P3339fMmTN13333admyZR0qj7lz5+rHP/6xBg4cKH9/fw0bNkz333+/br/9dpfk0RZlZWVN5l1ZWanTp0975D3uKd5QI6mP1qmPknfUSOoj9VGiPlIf25831EdX5mH1GunO+tgpGvW2eO6555SQkKCBAwcqICBAs2bNUmZmpnx8OtZfWWvzuPfee1VUVKScnBw3R3phF8vj4MGDmj17tl577bXzPqmzipb8WzgcDg0fPly/+93vNGzYMN1zzz2aMWOGXnnlFQ9G3lhL8njjjTf02muv6fXXX1dBQYGWLVumBQsWuOw/C7ifN9RI6qO1eEONpD5Coj5aCfXROvVRoka2VsepGJcgKipKvr6+stvtjdbb7XZ17969yW2io6P11ltvqbq6Wp9//rl2796tLl26KD4+vs37tGIe3zRr1iy98847Wr9+vXr37u2SHCTX5LF9+3aVl5dr+PDh8vPzk5+fn/7xj3/o+eefl5+fn+rq6iyfgyT16NFDgwcPbrTdoEGDVFJS0q7xN3BVHnPmzHF+IpqUlKQpU6bogQcecNun1S3RvXv3JvMODQ1VcHCwR97jnuINNZL6aJ366Ko8JPfWSOoj9VGiPlIfqY/N6aw10p31sVM06gEBAUpJSVFeXp5zncPhUF5entLS0i64bVBQkHr16qWzZ8/qzTff1E033XTJ+7RSHpJkjNGsWbO0evVqrVu3Tv369XNJ/A1ckcf3v/997dy5U4WFhc4lNTVVt99+uwoLC+Xr62v5HCTpmmuuOe/WJnv37lXfvn3bNf4Grsrj1KlT533q7uvrK4fD0b4JXIK0tLRGeUvS2rVrnXl74j3uKd5QI6mP1qmPrspDcm+NpD5SHyXqI/WR+ticzloj3VofWzX1XAeWk5NjAgMDzdKlS80nn3xi7rnnHhMeHm7KysqMMcZMmTLFzJ071zl+y5Yt5s033zT79u0zGzduNNdff73p16+fOXHiRIv32VHymDlzpgkLCzMbNmwwpaWlzuXUqVMdKo9vc/Wsna7IYevWrcbPz8888cQTpri42Lz22msmJCTE/OUvf+lQeUybNs306tXLeWuNVatWmaioKPPggw+6LI+qqiqzY8cOs2PHDiPJPP3002bHjh3m888/N8YYM3fuXDNlyhTn+Ibba8yZM8fs2rXLLFy4sMnba7j7Pe4p3lAjqY/WqY+uysPdNZL6SH00hvpIfewYefA7ZNtYuT52mkbdGGNeeOEFExsbawICAszIkSPNli1bnK+NHj3aTJs2zfl8w4YNZtCgQSYwMNBERkaaKVOmmEOHDrVqnx0lD0lNLkuWLOlQeXybOwqtK3JYs2aNSUxMNIGBgWbgwIHm1VdfdWkOrsijsrLSzJ4928TGxpqgoCATHx9vHnroIVNTU+OyHNavX9/kz3FD7NOmTTOjR48+b5vk5GQTEBBg4uPjm/yZ98R73FO8oUZSH61TH43xjhpJfaQ+GkN9pD62P2+oj67Iw9010sr10WaMMa07Bw8AAAAAAFylU3xHHQAAAACAjoJGHQAAAAAAC6FRBwAAAADAQmjUAQAAAACwEBp1AAAAAAAshEYdAAAAAAALoVEHAAAAAMBCaNTRKXz22Wey2WwqLCxs8TZLly5VeHi4y2ICACugPgJA06iP8CQadQAAAAAALIRGHQAAAAAAC6FRh9fIzc3Vtddeq/DwcEVGRuoHP/iB9u3b1+TYDRs2yGaz6d1339XQoUMVFBSk73znOyoqKjpv7Pvvv69BgwapS5cuGjt2rEpLS52vbdu2TTfccIOioqIUFham0aNHq6CgwGU5AkBbUB8BoGnUR1gVjTq8RnV1tbKyspSfn6+8vDz5+Pjo5ptvlsPhaHabOXPm6KmnntK2bdsUHR2tiRMn6syZM87XT506pQULFmj58uXauHGjSkpK9POf/9z5elVVlaZNm6ZNmzZpy5YtSkhI0Pjx41VVVeXSXAGgNaiPANA06iMsywBe6siRI0aS2blzpzlw4ICRZHbs2GGMMWb9+vVGksnJyXGOP3bsmAkODjYrVqwwxhizZMkSI8l8+umnzjELFy40MTExzR6zrq7OdO3a1axZs8Y1SQFAO6A+AkDTqI+wCs6ow2sUFxfrtttuU3x8vEJDQxUXFydJKikpaXabtLQ05+OIiAgNGDBAu3btcq4LCQlR//79nc979Oih8vJy53O73a4ZM2YoISFBYWFhCg0N1ZdffnnBYwKAu1EfAaBp1EdYlZ+nAwDay8SJE9W3b18tWrRIPXv2lMPhUGJiompra9u8T39//0bPbTabjDHO59OmTdOxY8f03HPPqW/fvgoMDFRaWtolHRMA2hv1EQCaRn2EVdGowyscO3ZMe/bs0aJFi/Td735XkrRp06aLbrdlyxbFxsZKkk6cOKG9e/dq0KBBLT7uv/71L7300ksaP368JOngwYM6evRoGzIAANegPgJA06iPsDIadXiFyy+/XJGRkXr11VfVo0cPlZSUaO7cuRfd7je/+Y0iIyMVExOjhx56SFFRUcrIyGjxcRMSErR8+XKlpqaqsrJSc+bMUXBw8CVkAgDti/oIAE2jPsLK+I46vIKPj49ycnK0fft2JSYm6oEHHtAf/vCHi2735JNPavbs2UpJSVFZWZnWrFmjgICAFh83OztbJ06c0PDhwzVlyhTdd9996tat26WkAgDtivoIAE2jPsLKbOabX5gAOokNGzboe9/7nk6cOKHw8HBPhwMAlkF9BICmUR/hTpxRBwAAAADAQmjUAQAAAACwEC59BwAAAADAQjijDgAAAACAhdCoAwAAAABgITTqAAAAAABYCI06AAAAAAAWQqMOAAAAAICF0KgDAAAAAGAhNOoAAAAAAFgIjToAAAAAABZCow4AAAAAgIX8fxDUtFtId1h9AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1200x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 3, figsize=(12, 4))\n",
    "df[[\"c1\", \"c2\"]].plot(ax=ax[1])\n",
    "df[[\"c1\", \"c2\"]].plot(ax=ax[2])\n",
    "df[[\"r2\"]].plot(ax=ax[0])\n",
    "ax[0].set_title(\"R2\")\n",
    "ax[1].set_title(\"coefficients\")\n",
    "ax[2].set_ylim([-5, 5])\n",
    "ax[2].set_title(\"coefficients, échelle tronquée\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le second graphe est trompeur mais il ne faut pas oublier de regarder l'échelle de l'axe des ordonnées."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Indicatrices\n",
    "\n",
    "$X_1$ est une variable aléatoire gaussienne. On teste maintenant un modèle $Y = X'_1 + X'_2 + \\epsilon$ avec $X'_1 = X_1 \\mathbb{1}_{X_1 < 0}$ et $X'_2 = X_1 \\mathbb{1}_{X_1 \\geqslant 0}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        ,  0.48561838,  0.0042644 ],\n",
       "       [ 0.48561838,  1.        , -0.01058737],\n",
       "       [ 0.0042644 , -0.01058737,  1.        ]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = npr.normal(size=(1000, 3))\n",
    "X[:, 1] = X[:, 0]\n",
    "X[X[:, 0] >= 0, 0] = 0\n",
    "X[X[:, 1] < 0, 1] = 0\n",
    "Y = X[:, 0] + X[:, 1] + X[:, 2]\n",
    "corrcoef(X.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pandas import DataFrame\n",
    "\n",
    "names = [\"X%d\" % i for i in range(X.shape[1] - 1)]\n",
    "ax = (\n",
    "    DataFrame(X[:50, :2], columns=names)\n",
    "    .sort_values(names)\n",
    "    .reset_index(drop=True)\n",
    "    .plot()\n",
    ")\n",
    "ax.set_title(\"Représentation des features tronquées\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared (uncentered):</th>       <td>   1.000</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared (uncentered):</th>  <td>   1.000</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>           <td>1.581e+33</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 07 Oct 2024</td> <th>  Prob (F-statistic):</th>            <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>11:29:06</td>     <th>  Log-Likelihood:    </th>           <td>  33532.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1000</td>      <th>  AIC:               </th>          <td>-6.706e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   997</td>      <th>  BIC:               </th>          <td>-6.704e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     3</td>      <th>                     </th>               <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>               <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "   <td></td>     <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th> <td>    1.0000</td> <td> 2.98e-17</td> <td> 3.35e+16</td> <td> 0.000</td> <td>    1.000</td> <td>    1.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th> <td>    1.0000</td> <td> 2.73e-17</td> <td> 3.66e+16</td> <td> 0.000</td> <td>    1.000</td> <td>    1.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th> <td>    1.0000</td> <td> 2.09e-17</td> <td> 4.79e+16</td> <td> 0.000</td> <td>    1.000</td> <td>    1.000</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>20.214</td> <th>  Durbin-Watson:     </th> <td>   1.267</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  30.796</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.179</td> <th>  Prob(JB):          </th> <td>2.05e-07</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.781</td> <th>  Cond. No.          </th> <td>    1.43</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] R² is computed without centering (uncentered) since the model does not contain a constant.<br/>[2] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/latex": [
       "\\begin{center}\n",
       "\\begin{tabular}{lclc}\n",
       "\\toprule\n",
       "\\textbf{Dep. Variable:}    &        y         & \\textbf{  R-squared (uncentered):}      &     1.000   \\\\\n",
       "\\textbf{Model:}            &       OLS        & \\textbf{  Adj. R-squared (uncentered):} &     1.000   \\\\\n",
       "\\textbf{Method:}           &  Least Squares   & \\textbf{  F-statistic:       }          & 1.581e+33   \\\\\n",
       "\\textbf{Date:}             & Mon, 07 Oct 2024 & \\textbf{  Prob (F-statistic):}          &     0.00    \\\\\n",
       "\\textbf{Time:}             &     11:29:06     & \\textbf{  Log-Likelihood:    }          &    33532.   \\\\\n",
       "\\textbf{No. Observations:} &        1000      & \\textbf{  AIC:               }          & -6.706e+04  \\\\\n",
       "\\textbf{Df Residuals:}     &         997      & \\textbf{  BIC:               }          & -6.704e+04  \\\\\n",
       "\\textbf{Df Model:}         &           3      & \\textbf{                     }          &             \\\\\n",
       "\\textbf{Covariance Type:}  &    nonrobust     & \\textbf{                     }          &             \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lcccccc}\n",
       "            & \\textbf{coef} & \\textbf{std err} & \\textbf{t} & \\textbf{P$> |$t$|$} & \\textbf{[0.025} & \\textbf{0.975]}  \\\\\n",
       "\\midrule\n",
       "\\textbf{x1} &       1.0000  &     2.98e-17     &  3.35e+16  &         0.000        &        1.000    &        1.000     \\\\\n",
       "\\textbf{x2} &       1.0000  &     2.73e-17     &  3.66e+16  &         0.000        &        1.000    &        1.000     \\\\\n",
       "\\textbf{x3} &       1.0000  &     2.09e-17     &  4.79e+16  &         0.000        &        1.000    &        1.000     \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lclc}\n",
       "\\textbf{Omnibus:}       & 20.214 & \\textbf{  Durbin-Watson:     } &    1.267  \\\\\n",
       "\\textbf{Prob(Omnibus):} &  0.000 & \\textbf{  Jarque-Bera (JB):  } &   30.796  \\\\\n",
       "\\textbf{Skew:}          &  0.179 & \\textbf{  Prob(JB):          } & 2.05e-07  \\\\\n",
       "\\textbf{Kurtosis:}      &  3.781 & \\textbf{  Cond. No.          } &     1.43  \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "%\\caption{OLS Regression Results}\n",
       "\\end{center}\n",
       "\n",
       "Notes: \\newline\n",
       " [1] R² is computed without centering (uncentered) since the model does not contain a constant. \\newline\n",
       " [2] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                                 OLS Regression Results                                \n",
       "=======================================================================================\n",
       "Dep. Variable:                      y   R-squared (uncentered):                   1.000\n",
       "Model:                            OLS   Adj. R-squared (uncentered):              1.000\n",
       "Method:                 Least Squares   F-statistic:                          1.581e+33\n",
       "Date:                Mon, 07 Oct 2024   Prob (F-statistic):                        0.00\n",
       "Time:                        11:29:06   Log-Likelihood:                          33532.\n",
       "No. Observations:                1000   AIC:                                 -6.706e+04\n",
       "Df Residuals:                     997   BIC:                                 -6.704e+04\n",
       "Df Model:                           3                                                  \n",
       "Covariance Type:            nonrobust                                                  \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "x1             1.0000   2.98e-17   3.35e+16      0.000       1.000       1.000\n",
       "x2             1.0000   2.73e-17   3.66e+16      0.000       1.000       1.000\n",
       "x3             1.0000   2.09e-17   4.79e+16      0.000       1.000       1.000\n",
       "==============================================================================\n",
       "Omnibus:                       20.214   Durbin-Watson:                   1.267\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               30.796\n",
       "Skew:                           0.179   Prob(JB):                     2.05e-07\n",
       "Kurtosis:                       3.781   Cond. No.                         1.43\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] R² is computed without centering (uncentered) since the model does not contain a constant.\n",
       "[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = OLS(Y, X[:, :3])\n",
    "results = model.fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On découpe en trois."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        , -0.0221138 ,  0.15312241, -0.01158589],\n",
       "       [-0.0221138 ,  1.        ,  0.02182757,  0.03734989],\n",
       "       [ 0.15312241,  0.02182757,  1.        ,  0.01263351],\n",
       "       [-0.01158589,  0.03734989,  0.01263351,  1.        ]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy\n",
    "\n",
    "X = npr.normal(size=(1000, 4))\n",
    "for i in range(3):\n",
    "    X[:, i] = X_[:, 0]\n",
    "X[:, 3] = X_[:, 2]\n",
    "X[X_[:, 0] > -1, 0] = 0\n",
    "X[(X_[:, 0] < -1) | (X_[:, 0] > 1), 1] = 0\n",
    "X[X_[:, 0] < 1, 2] = 0\n",
    "Y = X[:, 0] + X[:, 1] + X[:, 2] + X[:, 3]\n",
    "corrcoef(X.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pandas import DataFrame\n",
    "\n",
    "names = [\"X%d\" % i for i in range(X.shape[1] - 1)]\n",
    "ax = (\n",
    "    DataFrame(X[:50, :3], columns=names)\n",
    "    .sort_values(names)\n",
    "    .reset_index(drop=True)\n",
    "    .plot()\n",
    ")\n",
    "ax.set_title(\"Représentation des features tronquées\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared (uncentered):</th>       <td>   1.000</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared (uncentered):</th>  <td>   1.000</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>           <td>3.030e+31</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 07 Oct 2024</td> <th>  Prob (F-statistic):</th>            <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>11:29:06</td>     <th>  Log-Likelihood:    </th>           <td>  31722.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1000</td>      <th>  AIC:               </th>          <td>-6.344e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   996</td>      <th>  BIC:               </th>          <td>-6.342e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     4</td>      <th>                     </th>               <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>               <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "   <td></td>     <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th> <td>    1.0000</td> <td> 2.07e-16</td> <td> 4.84e+15</td> <td> 0.000</td> <td>    1.000</td> <td>    1.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th> <td>    1.0000</td> <td> 2.87e-16</td> <td> 3.49e+15</td> <td> 0.000</td> <td>    1.000</td> <td>    1.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th> <td>    1.0000</td> <td> 2.01e-16</td> <td> 4.97e+15</td> <td> 0.000</td> <td>    1.000</td> <td>    1.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th> <td>    1.0000</td> <td>  1.3e-16</td> <td> 7.66e+15</td> <td> 0.000</td> <td>    1.000</td> <td>    1.000</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>457.510</td> <th>  Durbin-Watson:     </th> <td>   1.879</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>1715.476</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 2.280</td>  <th>  Prob(JB):          </th> <td>    0.00</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 7.514</td>  <th>  Cond. No.          </th> <td>    2.20</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] R² is computed without centering (uncentered) since the model does not contain a constant.<br/>[2] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/latex": [
       "\\begin{center}\n",
       "\\begin{tabular}{lclc}\n",
       "\\toprule\n",
       "\\textbf{Dep. Variable:}    &        y         & \\textbf{  R-squared (uncentered):}      &     1.000   \\\\\n",
       "\\textbf{Model:}            &       OLS        & \\textbf{  Adj. R-squared (uncentered):} &     1.000   \\\\\n",
       "\\textbf{Method:}           &  Least Squares   & \\textbf{  F-statistic:       }          & 3.030e+31   \\\\\n",
       "\\textbf{Date:}             & Mon, 07 Oct 2024 & \\textbf{  Prob (F-statistic):}          &     0.00    \\\\\n",
       "\\textbf{Time:}             &     11:29:06     & \\textbf{  Log-Likelihood:    }          &    31722.   \\\\\n",
       "\\textbf{No. Observations:} &        1000      & \\textbf{  AIC:               }          & -6.344e+04  \\\\\n",
       "\\textbf{Df Residuals:}     &         996      & \\textbf{  BIC:               }          & -6.342e+04  \\\\\n",
       "\\textbf{Df Model:}         &           4      & \\textbf{                     }          &             \\\\\n",
       "\\textbf{Covariance Type:}  &    nonrobust     & \\textbf{                     }          &             \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lcccccc}\n",
       "            & \\textbf{coef} & \\textbf{std err} & \\textbf{t} & \\textbf{P$> |$t$|$} & \\textbf{[0.025} & \\textbf{0.975]}  \\\\\n",
       "\\midrule\n",
       "\\textbf{x1} &       1.0000  &     2.07e-16     &  4.84e+15  &         0.000        &        1.000    &        1.000     \\\\\n",
       "\\textbf{x2} &       1.0000  &     2.87e-16     &  3.49e+15  &         0.000        &        1.000    &        1.000     \\\\\n",
       "\\textbf{x3} &       1.0000  &     2.01e-16     &  4.97e+15  &         0.000        &        1.000    &        1.000     \\\\\n",
       "\\textbf{x4} &       1.0000  &      1.3e-16     &  7.66e+15  &         0.000        &        1.000    &        1.000     \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lclc}\n",
       "\\textbf{Omnibus:}       & 457.510 & \\textbf{  Durbin-Watson:     } &    1.879  \\\\\n",
       "\\textbf{Prob(Omnibus):} &   0.000 & \\textbf{  Jarque-Bera (JB):  } & 1715.476  \\\\\n",
       "\\textbf{Skew:}          &   2.280 & \\textbf{  Prob(JB):          } &     0.00  \\\\\n",
       "\\textbf{Kurtosis:}      &   7.514 & \\textbf{  Cond. No.          } &     2.20  \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "%\\caption{OLS Regression Results}\n",
       "\\end{center}\n",
       "\n",
       "Notes: \\newline\n",
       " [1] R² is computed without centering (uncentered) since the model does not contain a constant. \\newline\n",
       " [2] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                                 OLS Regression Results                                \n",
       "=======================================================================================\n",
       "Dep. Variable:                      y   R-squared (uncentered):                   1.000\n",
       "Model:                            OLS   Adj. R-squared (uncentered):              1.000\n",
       "Method:                 Least Squares   F-statistic:                          3.030e+31\n",
       "Date:                Mon, 07 Oct 2024   Prob (F-statistic):                        0.00\n",
       "Time:                        11:29:06   Log-Likelihood:                          31722.\n",
       "No. Observations:                1000   AIC:                                 -6.344e+04\n",
       "Df Residuals:                     996   BIC:                                 -6.342e+04\n",
       "Df Model:                           4                                                  \n",
       "Covariance Type:            nonrobust                                                  \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "x1             1.0000   2.07e-16   4.84e+15      0.000       1.000       1.000\n",
       "x2             1.0000   2.87e-16   3.49e+15      0.000       1.000       1.000\n",
       "x3             1.0000   2.01e-16   4.97e+15      0.000       1.000       1.000\n",
       "x4             1.0000    1.3e-16   7.66e+15      0.000       1.000       1.000\n",
       "==============================================================================\n",
       "Omnibus:                      457.510   Durbin-Watson:                   1.879\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1715.476\n",
       "Skew:                           2.280   Prob(JB):                         0.00\n",
       "Kurtosis:                       7.514   Cond. No.                         2.20\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] R² is computed without centering (uncentered) since the model does not contain a constant.\n",
       "[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = OLS(Y, X[:, :4])\n",
    "results = model.fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Régression linéaire par morceaux\n",
    "\n",
    "On se place dans un cas particulier où le problème est linéaire par morceaux :\n",
    "\n",
    "$$Y = -2 X_1 \\mathbb{1}_{X_1 + \\epsilon_1 <0} + 4 X_1 \\mathbb{1}_{X + \\epsilon_1 > 0} + \\epsilon_2$$\n",
    "\n",
    "La régression donne de très mauvais résultat sur ce type de problèmes mais on cherche une façon systématique de découper le problème en segments linéaires."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = npr.normal(size=(1000, 4))\n",
    "alpha = [4, -2]\n",
    "t = (X[:, 0] + X[:, 3] * 0.5) > 0\n",
    "switch = numpy.zeros(X.shape[0])\n",
    "switch[t] = 1\n",
    "Y = alpha[0] * X[:, 0] * t + alpha[1] * X[:, 0] * (1 - t) + X[:, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(X[:, 0], Y, \".\")\n",
    "ax.set_title(\"Nuage de points linéaire par morceaux\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared (uncentered):</th>      <td>   0.107</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared (uncentered):</th> <td>   0.106</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>          <td>   119.3</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 07 Oct 2024</td> <th>  Prob (F-statistic):</th>          <td>2.56e-26</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>11:29:06</td>     <th>  Log-Likelihood:    </th>          <td> -2555.7</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1000</td>      <th>  AIC:               </th>          <td>   5113.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   999</td>      <th>  BIC:               </th>          <td>   5118.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>              <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>              <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "   <td></td>     <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th> <td>    1.0940</td> <td>    0.100</td> <td>   10.924</td> <td> 0.000</td> <td>    0.897</td> <td>    1.290</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 3.084</td> <th>  Durbin-Watson:     </th> <td>   1.111</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.214</td> <th>  Jarque-Bera (JB):  </th> <td>   2.960</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.088</td> <th>  Prob(JB):          </th> <td>   0.228</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.801</td> <th>  Cond. No.          </th> <td>    1.00</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] R² is computed without centering (uncentered) since the model does not contain a constant.<br/>[2] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/latex": [
       "\\begin{center}\n",
       "\\begin{tabular}{lclc}\n",
       "\\toprule\n",
       "\\textbf{Dep. Variable:}    &        y         & \\textbf{  R-squared (uncentered):}      &     0.107   \\\\\n",
       "\\textbf{Model:}            &       OLS        & \\textbf{  Adj. R-squared (uncentered):} &     0.106   \\\\\n",
       "\\textbf{Method:}           &  Least Squares   & \\textbf{  F-statistic:       }          &     119.3   \\\\\n",
       "\\textbf{Date:}             & Mon, 07 Oct 2024 & \\textbf{  Prob (F-statistic):}          &  2.56e-26   \\\\\n",
       "\\textbf{Time:}             &     11:29:06     & \\textbf{  Log-Likelihood:    }          &   -2555.7   \\\\\n",
       "\\textbf{No. Observations:} &        1000      & \\textbf{  AIC:               }          &     5113.   \\\\\n",
       "\\textbf{Df Residuals:}     &         999      & \\textbf{  BIC:               }          &     5118.   \\\\\n",
       "\\textbf{Df Model:}         &           1      & \\textbf{                     }          &             \\\\\n",
       "\\textbf{Covariance Type:}  &    nonrobust     & \\textbf{                     }          &             \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lcccccc}\n",
       "            & \\textbf{coef} & \\textbf{std err} & \\textbf{t} & \\textbf{P$> |$t$|$} & \\textbf{[0.025} & \\textbf{0.975]}  \\\\\n",
       "\\midrule\n",
       "\\textbf{x1} &       1.0940  &        0.100     &    10.924  &         0.000        &        0.897    &        1.290     \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lclc}\n",
       "\\textbf{Omnibus:}       &  3.084 & \\textbf{  Durbin-Watson:     } &    1.111  \\\\\n",
       "\\textbf{Prob(Omnibus):} &  0.214 & \\textbf{  Jarque-Bera (JB):  } &    2.960  \\\\\n",
       "\\textbf{Skew:}          &  0.088 & \\textbf{  Prob(JB):          } &    0.228  \\\\\n",
       "\\textbf{Kurtosis:}      &  2.801 & \\textbf{  Cond. No.          } &     1.00  \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "%\\caption{OLS Regression Results}\n",
       "\\end{center}\n",
       "\n",
       "Notes: \\newline\n",
       " [1] R² is computed without centering (uncentered) since the model does not contain a constant. \\newline\n",
       " [2] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                                 OLS Regression Results                                \n",
       "=======================================================================================\n",
       "Dep. Variable:                      y   R-squared (uncentered):                   0.107\n",
       "Model:                            OLS   Adj. R-squared (uncentered):              0.106\n",
       "Method:                 Least Squares   F-statistic:                              119.3\n",
       "Date:                Mon, 07 Oct 2024   Prob (F-statistic):                    2.56e-26\n",
       "Time:                        11:29:06   Log-Likelihood:                         -2555.7\n",
       "No. Observations:                1000   AIC:                                      5113.\n",
       "Df Residuals:                     999   BIC:                                      5118.\n",
       "Df Model:                           1                                                  \n",
       "Covariance Type:            nonrobust                                                  \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "x1             1.0940      0.100     10.924      0.000       0.897       1.290\n",
       "==============================================================================\n",
       "Omnibus:                        3.084   Durbin-Watson:                   1.111\n",
       "Prob(Omnibus):                  0.214   Jarque-Bera (JB):                2.960\n",
       "Skew:                           0.088   Prob(JB):                        0.228\n",
       "Kurtosis:                       2.801   Cond. No.                         1.00\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] R² is computed without centering (uncentered) since the model does not contain a constant.\n",
       "[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = OLS(Y, X[:, :1])\n",
    "results = model.fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "yp = results.predict(X[:, :1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(X[:, 0], Y, \".\", label=\"expected\")\n",
    "ax.plot(X[:, 0], yp, \".\", label=\"predicted\")\n",
    "ax.legend()\n",
    "ax.set_title(\"Régression linéaire sur un nuage linéaire par morceaux\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Passons à un arbre de décision qui n'est pas le meilleur modèle mais on va détourner ses résultats pour revenir à un problème de régression par morceaux."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.tree import DecisionTreeRegressor\n",
    "\n",
    "model = DecisionTreeRegressor(min_samples_leaf=10, max_depth=3)\n",
    "model.fit(X[:, :1], Y)\n",
    "yp = model.predict(X[:, :1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(X[:, 0], Y, \".\", label=\"expected\")\n",
    "ax.plot(X[:, 0], yp, \".\", label=\"predicted\")\n",
    "ax.legend()\n",
    "r2 = r2_score(Y, model.predict(X[:, :1]))\n",
    "ax.set_title(\"Arbre de décision sur un nuage linéaire par morceaux\\nR2=%f\" % r2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'tree_dot.gv.pdf'"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import graphviz\n",
    "from sklearn.tree import export_graphviz\n",
    "\n",
    "dot = export_graphviz(model)\n",
    "\n",
    "src = graphviz.Source(dot)\n",
    "src.render(\"tree_dot.gv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On extrait tous les seuils de l'arbre et on ajoute les milieux de segments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[np.float64(-2.0),\n",
       " np.float64(-1.85539710521698),\n",
       " np.float64(-1.71079421043396),\n",
       " np.float64(-1.3022041469812393),\n",
       " np.float64(-0.8936140835285187),\n",
       " np.float64(-0.2086283266544342),\n",
       " np.float64(0.47635743021965027),\n",
       " np.float64(0.6395495533943176),\n",
       " np.float64(0.802741676568985),\n",
       " np.float64(0.942541167140007),\n",
       " np.float64(1.082340657711029),\n",
       " np.float64(1.310522198677063),\n",
       " np.float64(1.538703739643097),\n",
       " np.float64(1.6980005204677582),\n",
       " np.float64(1.8572973012924194)]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "th = list(sorted(set(model.tree_.threshold)))\n",
    "th += [(th[i] + th[i - 1]) / 2 for i in range(1, len(th))]\n",
    "th = list(sorted(th))\n",
    "th"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On fait une régression sur les variables $W_{i>0} = X_1 \\mathbb{1}_{X_1 > t_i}$, $W_0 = X_1$ où les $(t_i)$ sont les seuils."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "W = numpy.zeros((X.shape[0], len(th) + 1))\n",
    "x = X[:, 0]\n",
    "W[:, 0] = x\n",
    "for i in range(len(th)):\n",
    "    W[x > th[i], i + 1] = x[x > th[i]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared (uncentered):</th>      <td>   0.858</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared (uncentered):</th> <td>   0.855</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>          <td>   370.4</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 07 Oct 2024</td> <th>  Prob (F-statistic):</th>           <td>  0.00</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>11:29:07</td>     <th>  Log-Likelihood:    </th>          <td> -1637.5</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1000</td>      <th>  AIC:               </th>          <td>   3307.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   984</td>      <th>  BIC:               </th>          <td>   3385.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    16</td>      <th>                     </th>              <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>              <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "   <td></td>      <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>  <td>   -1.8183</td> <td>    0.119</td> <td>  -15.303</td> <td> 0.000</td> <td>   -2.051</td> <td>   -1.585</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>  <td>   -0.4155</td> <td>    0.260</td> <td>   -1.600</td> <td> 0.110</td> <td>   -0.925</td> <td>    0.094</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>  <td>    0.2157</td> <td>    0.320</td> <td>    0.673</td> <td> 0.501</td> <td>   -0.413</td> <td>    0.845</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th>  <td>    0.1368</td> <td>    0.247</td> <td>    0.553</td> <td> 0.581</td> <td>   -0.349</td> <td>    0.622</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x5</th>  <td>   -0.2634</td> <td>    0.166</td> <td>   -1.589</td> <td> 0.112</td> <td>   -0.589</td> <td>    0.062</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x6</th>  <td>    1.0105</td> <td>    0.196</td> <td>    5.164</td> <td> 0.000</td> <td>    0.627</td> <td>    1.395</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x7</th>  <td>    3.3282</td> <td>    0.356</td> <td>    9.357</td> <td> 0.000</td> <td>    2.630</td> <td>    4.026</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x8</th>  <td>    1.3866</td> <td>    0.454</td> <td>    3.051</td> <td> 0.002</td> <td>    0.495</td> <td>    2.278</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x9</th>  <td>    0.3655</td> <td>    0.403</td> <td>    0.907</td> <td> 0.365</td> <td>   -0.425</td> <td>    1.156</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x10</th> <td>    0.1177</td> <td>    0.334</td> <td>    0.353</td> <td> 0.724</td> <td>   -0.537</td> <td>    0.773</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x11</th> <td>   -0.3147</td> <td>    0.307</td> <td>   -1.023</td> <td> 0.306</td> <td>   -0.918</td> <td>    0.289</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x12</th> <td>    0.2972</td> <td>    0.255</td> <td>    1.166</td> <td> 0.244</td> <td>   -0.203</td> <td>    0.797</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x13</th> <td>   -0.0456</td> <td>    0.197</td> <td>   -0.231</td> <td> 0.817</td> <td>   -0.433</td> <td>    0.342</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x14</th> <td>    0.2807</td> <td>    0.252</td> <td>    1.112</td> <td> 0.266</td> <td>   -0.215</td> <td>    0.776</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x15</th> <td>   -0.3102</td> <td>    0.303</td> <td>   -1.024</td> <td> 0.306</td> <td>   -0.904</td> <td>    0.284</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x16</th> <td>   -0.0231</td> <td>    0.237</td> <td>   -0.097</td> <td> 0.923</td> <td>   -0.489</td> <td>    0.443</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>207.506</td> <th>  Durbin-Watson:     </th> <td>   1.993</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 673.510</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.999</td>  <th>  Prob(JB):          </th> <td>5.61e-147</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 6.489</td>  <th>  Cond. No.          </th> <td>    37.1</td> \n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] R² is computed without centering (uncentered) since the model does not contain a constant.<br/>[2] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/latex": [
       "\\begin{center}\n",
       "\\begin{tabular}{lclc}\n",
       "\\toprule\n",
       "\\textbf{Dep. Variable:}    &        y         & \\textbf{  R-squared (uncentered):}      &     0.858   \\\\\n",
       "\\textbf{Model:}            &       OLS        & \\textbf{  Adj. R-squared (uncentered):} &     0.855   \\\\\n",
       "\\textbf{Method:}           &  Least Squares   & \\textbf{  F-statistic:       }          &     370.4   \\\\\n",
       "\\textbf{Date:}             & Mon, 07 Oct 2024 & \\textbf{  Prob (F-statistic):}          &     0.00    \\\\\n",
       "\\textbf{Time:}             &     11:29:07     & \\textbf{  Log-Likelihood:    }          &   -1637.5   \\\\\n",
       "\\textbf{No. Observations:} &        1000      & \\textbf{  AIC:               }          &     3307.   \\\\\n",
       "\\textbf{Df Residuals:}     &         984      & \\textbf{  BIC:               }          &     3385.   \\\\\n",
       "\\textbf{Df Model:}         &          16      & \\textbf{                     }          &             \\\\\n",
       "\\textbf{Covariance Type:}  &    nonrobust     & \\textbf{                     }          &             \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lcccccc}\n",
       "             & \\textbf{coef} & \\textbf{std err} & \\textbf{t} & \\textbf{P$> |$t$|$} & \\textbf{[0.025} & \\textbf{0.975]}  \\\\\n",
       "\\midrule\n",
       "\\textbf{x1}  &      -1.8183  &        0.119     &   -15.303  &         0.000        &       -2.051    &       -1.585     \\\\\n",
       "\\textbf{x2}  &      -0.4155  &        0.260     &    -1.600  &         0.110        &       -0.925    &        0.094     \\\\\n",
       "\\textbf{x3}  &       0.2157  &        0.320     &     0.673  &         0.501        &       -0.413    &        0.845     \\\\\n",
       "\\textbf{x4}  &       0.1368  &        0.247     &     0.553  &         0.581        &       -0.349    &        0.622     \\\\\n",
       "\\textbf{x5}  &      -0.2634  &        0.166     &    -1.589  &         0.112        &       -0.589    &        0.062     \\\\\n",
       "\\textbf{x6}  &       1.0105  &        0.196     &     5.164  &         0.000        &        0.627    &        1.395     \\\\\n",
       "\\textbf{x7}  &       3.3282  &        0.356     &     9.357  &         0.000        &        2.630    &        4.026     \\\\\n",
       "\\textbf{x8}  &       1.3866  &        0.454     &     3.051  &         0.002        &        0.495    &        2.278     \\\\\n",
       "\\textbf{x9}  &       0.3655  &        0.403     &     0.907  &         0.365        &       -0.425    &        1.156     \\\\\n",
       "\\textbf{x10} &       0.1177  &        0.334     &     0.353  &         0.724        &       -0.537    &        0.773     \\\\\n",
       "\\textbf{x11} &      -0.3147  &        0.307     &    -1.023  &         0.306        &       -0.918    &        0.289     \\\\\n",
       "\\textbf{x12} &       0.2972  &        0.255     &     1.166  &         0.244        &       -0.203    &        0.797     \\\\\n",
       "\\textbf{x13} &      -0.0456  &        0.197     &    -0.231  &         0.817        &       -0.433    &        0.342     \\\\\n",
       "\\textbf{x14} &       0.2807  &        0.252     &     1.112  &         0.266        &       -0.215    &        0.776     \\\\\n",
       "\\textbf{x15} &      -0.3102  &        0.303     &    -1.024  &         0.306        &       -0.904    &        0.284     \\\\\n",
       "\\textbf{x16} &      -0.0231  &        0.237     &    -0.097  &         0.923        &       -0.489    &        0.443     \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lclc}\n",
       "\\textbf{Omnibus:}       & 207.506 & \\textbf{  Durbin-Watson:     } &     1.993  \\\\\n",
       "\\textbf{Prob(Omnibus):} &   0.000 & \\textbf{  Jarque-Bera (JB):  } &   673.510  \\\\\n",
       "\\textbf{Skew:}          &  -0.999 & \\textbf{  Prob(JB):          } & 5.61e-147  \\\\\n",
       "\\textbf{Kurtosis:}      &   6.489 & \\textbf{  Cond. No.          } &      37.1  \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "%\\caption{OLS Regression Results}\n",
       "\\end{center}\n",
       "\n",
       "Notes: \\newline\n",
       " [1] R² is computed without centering (uncentered) since the model does not contain a constant. \\newline\n",
       " [2] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                                 OLS Regression Results                                \n",
       "=======================================================================================\n",
       "Dep. Variable:                      y   R-squared (uncentered):                   0.858\n",
       "Model:                            OLS   Adj. R-squared (uncentered):              0.855\n",
       "Method:                 Least Squares   F-statistic:                              370.4\n",
       "Date:                Mon, 07 Oct 2024   Prob (F-statistic):                        0.00\n",
       "Time:                        11:29:07   Log-Likelihood:                         -1637.5\n",
       "No. Observations:                1000   AIC:                                      3307.\n",
       "Df Residuals:                     984   BIC:                                      3385.\n",
       "Df Model:                          16                                                  \n",
       "Covariance Type:            nonrobust                                                  \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "x1            -1.8183      0.119    -15.303      0.000      -2.051      -1.585\n",
       "x2            -0.4155      0.260     -1.600      0.110      -0.925       0.094\n",
       "x3             0.2157      0.320      0.673      0.501      -0.413       0.845\n",
       "x4             0.1368      0.247      0.553      0.581      -0.349       0.622\n",
       "x5            -0.2634      0.166     -1.589      0.112      -0.589       0.062\n",
       "x6             1.0105      0.196      5.164      0.000       0.627       1.395\n",
       "x7             3.3282      0.356      9.357      0.000       2.630       4.026\n",
       "x8             1.3866      0.454      3.051      0.002       0.495       2.278\n",
       "x9             0.3655      0.403      0.907      0.365      -0.425       1.156\n",
       "x10            0.1177      0.334      0.353      0.724      -0.537       0.773\n",
       "x11           -0.3147      0.307     -1.023      0.306      -0.918       0.289\n",
       "x12            0.2972      0.255      1.166      0.244      -0.203       0.797\n",
       "x13           -0.0456      0.197     -0.231      0.817      -0.433       0.342\n",
       "x14            0.2807      0.252      1.112      0.266      -0.215       0.776\n",
       "x15           -0.3102      0.303     -1.024      0.306      -0.904       0.284\n",
       "x16           -0.0231      0.237     -0.097      0.923      -0.489       0.443\n",
       "==============================================================================\n",
       "Omnibus:                      207.506   Durbin-Watson:                   1.993\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              673.510\n",
       "Skew:                          -0.999   Prob(JB):                    5.61e-147\n",
       "Kurtosis:                       6.489   Cond. No.                         37.1\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] R² is computed without centering (uncentered) since the model does not contain a constant.\n",
       "[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = OLS(Y, W)\n",
    "results = model.fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dessinons les résultats de la prédictions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/4sUL/v9BQUE4c+YMrly5wrclJSXhjz/+MHn/ffr0wZkzZ3Do0CG991JSUpCZmQlAHUmijUwm45eDNEshun1sbW1RqVIlvZBnbTQ3Su3oHAD4+eefAcCkaJyCwNTzJpfLwXGc4Mk6OjoaO3fuzPa+g4KCYGdnh7lz5+Lt27d672tfI4ZYuXKlYPtly5YhMzMTwcHB/NwBocUjIyMDS5cuzfbcc4uOHTvi33//xZkzZ/i21NRUrFy5Et7e3qhRo4bB7Rs0aAAfHx8sWLBAT0hojjcr30W5XK5nGfrrr7/0smdrRJO2T5RSqcTKlSv1xo+KisLEiRPRs2dPfPXVV/jxxx+xe/fubKcGIIoOZHkhigQTJ05E7969ERYWhs8++wxLlixBQEAAateujaFDh6JixYp49uwZzpw5gydPnvC5IyZNmoTff/8d7du3x+jRo/lQ6QoVKiApKcmkpZiJEydi9+7d6Ny5Mx8OnJqaiuvXr2Pr1q2Ijo6Gi4sLhgwZgqSkJLRp0wbly5fHo0eP8Ouvv6JevXq8xaRGjRpo1aoV/Pz84OTkhAsXLmDr1q0YNWqU5P7r1q2LkJAQrFy5kl+m+Pfff7F+/Xp069ZNYBkoTJh63jp16oSff/4ZHTp0QP/+/fH8+XMsWbIElSpVwrVr17K1bzs7OyxbtgyffPIJGjRogL59+8LV1RUxMTHYt28fmjdvblKByIyMDLRt2xZ9+vTB3bt3sXTpUgQEBKBr164AgGbNmsHR0REhISEYM2YMOI7Db7/9lqtLdNllypQp2LRpE4KDgzFmzBg4OTlh/fr1iIqKwrZt24wmoJPJZFi2bBm6dOmCevXqYdCgQXB3d8edO3dw8+ZNXpSa+l3s3LkzZs+ejUGDBqFZs2a4fv06/vjjD956o6FmzZpo2rQppk6diqSkJDg5OeHPP//kxa4Gxhg+/fRTWFlZYdmyZQCA4cOHY9u2bRg7dizatWuX5fBroghRUGFOBKGLJkRSLMxRqVQyX19f5uvry4fERkZGsgEDBjA3NzdWqlQp5uHhwTp37sy2bt0q2Pby5cssMDCQWVhYsPLly7PQ0FC2aNEiBoDFx8fz/by8vCTDmP/77z82depUVqlSJWZubs5cXFxYs2bN2I8//siH0m7dupV98MEHrEyZMszc3JxVqFCBDR8+nMXFxfHjfPvtt6xx48bMwcGBWVlZsWrVqrHvvvtOEI6rGyrNGGNv375ls2bNYj4+PqxUqVLM09OTTZ06VRCeaugYWrZsyVq2bCl6bNrAxFBpU/dhynljjLE1a9awypUrMwsLC1atWjW2bt060fMgFSotFRp77NgxFhQUxOzt7ZmlpSXz9fVlAwcOZBcuXDB4HjTjnjhxgg0bNow5OjoyW1tb9tFHH7HExERB39OnT7OmTZsyKysrVq5cOTZp0iR26NAhvbDeli1bspo1axrcrzYhISHMxsZGr11qHLHPJTIykvXq1Ys5ODgwS0tL1rhxY7Z3715BH00I8l9//SU6j/DwcNa+fXtWunRpZmNjw+rUqcN+/fVXvf0Y+y6+efOGjR8/nrm7uzMrKyvWvHlzdubMGdHrJjIykrVr145ZWFiwsmXLsq+++oodPnxYcE4XLlzIALBt27YJto2JiWF2dnasY8eOosdDFA84xgrBIwJB5DPjxo3DihUr8OrVq1xJf08UL8LCwjBo0CCcP3+ewm4JohBCPi9EsSctLU3wOjExEb/99hsCAgJIuBAEQRRByOeFKPb4+/ujVatWqF69Op49e4Y1a9bg5cuXlA+CIAiiiELihSj2dOzYEVu3bsXKlSvBcRwaNGiANWvWCEJbCYIgiKID+bwQBEEQBFGkIJ8XgiAIgiCKFCReCIIgCIIoUpB4IQiiUHHt2jXMnDkTjx8/LuipEARRSCHxQhBElhg4cCC8vb0FbRzHYebMmTkeW6FQoHv37khOToanp2e2xpg5c6bJRSwJgiiakHghCKLQMGjQINSvXx+//PJLQU+FIIhCDIkXgiByTFpaGr755pscjREdHY2GDRvi999/N1p3xxDffPONXmJCgiCKFyReiGLBmzdvoFKpCnoaJRZLS0uYmeUsbZS3tze++uorWFpa5mgcMzMzo2OoVCq8efMmR/vJL1JTUwt6CqIwxkgkEgUGiRciX/jvv/8wbtw4eHt7w8LCAmXKlEH79u1x6dIlvo+3tzcGDhyot22rVq3QqlUr/vXx48fBcRz+/PNPfPPNN/Dw8IC1tTVevnwpum9N/+PHjwvao6OjwXEcwsLC+LaBAwfC1tYWsbGx6NatG2xtbeHq6ooJEyZAqVQaPU5vb2907twZ4eHhaNy4MSwtLVGxYkVs2LBB0E/KLyMsLAwcxyE6Oppv27VrFzp16oRy5crBwsICvr6+mDNnjuh8lixZgooVK8LKygqNGzfGqVOn9M4fAKSnp2PGjBmoVKkSLCws4OnpiUmTJiE9Pd3oMYqh6/OiOb4HDx5g4MCBcHBwgL29PQYNGoTXr1/rbf/777/Dz88PVlZWcHJyQt++ffUcdk+dOoXevXujQoUK/Jy/+OILvRuo2LnlOA6jRo3CH3/8gZo1a8LCwgIHDx4EAMTGxuLTTz9F2bJlYWFhgZo1a2Lt2rUmH7dm3KpVq8LS0hJ+fn44efKkoN+jR48wYsQIVK1aFVZWVnB2dkbv3r0FnzPw/vM/ceIERowYgTJlyqB8+fKS+9dc21u2bMGsWbPg4eGB0qVLo1evXlAoFEhPT8e4ceNQpkwZ2NraYtCgQXqfcWZmJubMmQNfX19YWFjwIlK3n+baPnToEBo2bAgrKyusWLECAJCSkoIvvviC/36XL18eAwYMQEJCAr+9qdfcunXr0KZNG5QpUwYWFhaoUaMGXzVa99yL+Vlp/44wxtC6dWu4urri+fPnfJ+MjAzUrl0bvr6+hVYcEoahDLtEvvDZZ59h69atGDVqFGrUqIHExESEh4fj9u3baNCgQbbGnDNnDszNzTFhwgSkp6fD3Nw8V+aqVCoRFBSEJk2a4Mcff8SRI0fw008/wdfXF59//rnR7R88eIBevXph8ODBCAkJwdq1azFw4ED4+fmhZs2aWZ5PWFgYbG1t8eWXX8LW1hZHjx7F9OnT8fLlS/zwww98v2XLlmHUqFEIDAzEF198gejoaHTr1g2Ojo6CG6BKpULXrl0RHh6OYcOGoXr16rh+/Tp++eUX3Lt3Dzt37szyHKXo06cPfHx8EBoaikuXLmH16tUoU6YM5s+fz/f57rvvMG3aNPTp0wdDhgzBixcv8Ouvv6JFixa4fPkyHBwcAAB//fUXXr9+jc8//xzOzs74999/8euvv+LJkyf466+/jM7l6NGj2LJlC0aNGgUXFxd4e3vj2bNnaNq0KS9CXF1dceDAAQwePBgvX77EuHHjjI574sQJbN68GWPGjIGFhQWWLl2KDh064N9//0WtWrUAAOfPn0dERAT69u2L8uXLIzo6GsuWLUOrVq1w69YtWFtbC8YcMWIEXF1dMX36dJNurqGhobCyssKUKVPw4MED/PrrryhVqhRkMhmSk5Mxc+ZMnD17FmFhYfDx8cH06dP5bYcMGYL169ejV69eGD9+PM6dO4fQ0FDcvn0bO3bsEOzn7t276NevH4YPH46hQ4eiatWqePXqFQIDA3H79m18+umnaNCgARISErB79248efIELi4uWbrmli1bhpo1a6Jr164wMzPDnj17MGLECKhUKowcOdLoudCG4zisXbsWderUwWeffYbt27cDAGbMmIGbN2/i+PHjsLGxydKYRCGhIEtaEyUHe3t7NnLkSIN9vLy8WEhIiF57y5YtWcuWLfnXx44dYwBYxYoV2evXr43uW9P/2LFjgvaoqCgGgK1bt45vCwkJYQDY7NmzBX3r16/P/Pz8jO7Ly8uLAWAnT57k254/f84sLCzY+PHj+bYZM2Ywsa/funXrGAAWFRXFt4kd4/Dhw5m1tTV78+YNY4yx9PR05uzszBo1asTevn3L9wsLC2MABOfvt99+YzKZjJ06dUow5vLlyxkAdvr0aYPHGBISwry8vARtANiMGTP0ju/TTz8V9OvevTtzdnbmX0dHRzO5XM6+++47Qb/r168zMzMzQbvYeQgNDWUcx7FHjx7p7Vt3fjKZjN28eVPQPnjwYObu7s4SEhIE7X379mX29vZGry8ADAC7cOEC3/bo0SNmaWnJunfvbnDuZ86cYQDYhg0b+DbN5x8QEMAyMzMN7pux99d2rVq1WEZGBt/er18/xnEcCw4OFvT39/cXfHZXrlxhANiQIUME/SZMmMAAsKNHj/Jtmmv74MGDgr7Tp09nANj27dv15qdSqRhjWbvmxM5VUFAQq1ixoqBN95rTnqfu78iKFSsYAPb777+zs2fPMrlczsaNG6e3LVF0oGUjIl9wcHDAuXPn8PTp01wbMyQkBFZWVrk2njafffaZ4HVgYCAePnxo0rY1atRAYGAg/9rV1RVVq1Y1eXtdtI/xv//+Q0JCAgIDA/H69WvcuXMHAHDhwgUkJiZi6NChAt+Tjz76CI6OjoLx/vrrL1SvXh3VqlVDQkIC/9emTRsAwLFjx7I1TzHEzmNiYiK/xLd9+3aoVCr06dNHMBc3NzdUrlxZMBft85CamoqEhAQ0a9YMjDFcvnzZ6FxatmyJGjVq8K8ZY9i2bRu6dOkCxphg/0FBQVAoFIJlTSn8/f3h5+fHv65QoQL+97//4dChQ/zSnvbc3759i8TERFSqVAkODg6i+xg6dGiWKp4PGDAApUqV4l83adIEjDF8+umngn5NmjTB48ePkZmZCQDYv38/AODLL78U9Bs/fjwAYN++fYJ2Hx8fBAUFCdq2bduGunXronv37nrz0izfZeWa0z5XCoUCCQkJaNmyJR4+fAiFQmHC2dBn2LBhCAoKwujRo/HJJ5/A19cXc+fOzdZYROGAlo2IfOH7779HSEgIPD094efnh44dO2LAgAGoWLFitsf08fHJxRm+x9LSEq6uroI2R0dHJCcnm7R9hQoV9Nqysr0uN2/exDfffIOjR4/q+fVofswfPXoEAKhUqZLgfTMzM72cLPfv38ft27f1jlGDtm9ATtE9FxohlZycDDs7O9y/fx+MMVSuXFl0e+0bckxMDKZPn47du3frnUtTbmq618uLFy+QkpKClStXYuXKlaLbmHIuxOZepUoVvH79Gi9evICbmxvS0tIQGhqKdevWITY2FkyrpJzY3LN6beueZ3t7ewDQy5Vjb28PlUoFhUIBZ2dnPHr0CDKZTO+6cXNzg4ODA39dGZpXZGQkevbsaXB+WbnmTp8+jRkzZuDMmTN6/lEKhYI/tqyyZs0a+Pr64v79+4iIiMizBx8ifyDxQuQLffr0QWBgIHbs2IG///4bP/zwA+bPn4/t27cjODgYACQTiymVStGnUFN/fAyNK0ZWnnizsr32DcvUOaWkpKBly5aws7PD7Nmz4evrC0tLS1y6dAmTJ0/OVoSVSqVC7dq18fPPP4u+n93kcGIYOxcqlQocx+HAgQOifW1tbQGoz0v79u2RlJSEyZMno1q1arCxsUFsbCwGDhxo0nnQvV4023z88ccICQkR3aZOnTpGxzWF0aNHY926dRg3bhz8/f1hb28PjuPQt29f0bln9cYqdZ5NuRYB6esxp/PSYOo1FxkZibZt26JatWr4+eef4enpCXNzc+zfvx+//PKLSZ+z1Pf6+PHjvHPw9evX4e/vn61jIQoHJF6IfMPd3R0jRozAiBEj8Pz5czRo0ADfffcdL14cHR2RkpKit92jR49yZKHRPO3rjq37VJmfaM9J45AK6M/p+PHjSExMxPbt29GiRQu+PSoqStDPy8sLgNpZuHXr1nx7ZmYmoqOjBTdhX19fXL16FW3bti3wTLS+vr5gjMHHxwdVqlSR7Hf9+nXcu3cP69evx4ABA/j2w4cPZ3vfrq6uKF26NJRKJdq1a5ftce7fv6/Xdu/ePVhbW/OWhq1btyIkJAQ//fQT3+fNmzei13t+4uXlBZVKhfv376N69ep8+7Nnz5CSksJfV4bw9fXFjRs3jPYx5Zrbs2cP0tPTsXv3boE1SWwpU+z3IiMjA3FxcXp94+LiMHr0aHzwwQe8k39QUJBJx0cUTsjnhchzlEqlnmm8TJkyKFeunCBM0tfXF2fPnkVGRgbftnfv3hzXuPHy8oJcLtcLX126dGmOxs0Jvr6+ACCYU2pqKtavXy/op3ly1n5SzsjI0Jt7w4YN4ezsjFWrVvH+DADwxx9/6C2x9OnTB7GxsVi1apXevNLS0vI1dLRHjx6Qy+WYNWuWnjWAMYbExEQA4ueBMYaFCxdme99yuRw9e/bEtm3bRG++L168MGmcM2fOCPxWHj9+jF27duGDDz7g5y2Xy/WO79dffzUp/D4v6dixIwBgwYIFgnaNhaRTp05Gx+jZsyeuXr2qF5kEvP+8TL3mxD5nhUKBdevW6W3n6+ur951euXKl6DkdOnQoVCoV1qxZg5UrV8LMzAyDBw/W+0yIogNZXog857///kP58uXRq1cv1K1bF7a2tjhy5AjOnz8veBIdMmQItm7dig4dOqBPnz6IjIzE77//zt/os4u9vT169+6NX3/9FRzHwdfXF3v37s1V346s8sEHH6BChQoYPHgwJk6cCLlcjrVr18LV1RUxMTF8v2bNmsHR0REhISEYM2YMOI7Db7/9pveja25ujpkzZ2L06NFo06YN+vTpg+joaISFhcHX11fwtPvJJ59gy5Yt+Oyzz3Ds2DE0b94cSqUSd+7cwZYtW/g8HvmBr68vvv32W0ydOpUP7S5dujSioqKwY8cODBs2DBMmTEC1atXg6+uLCRMmIDY2FnZ2dti2bVu2/Yg0zJs3D8eOHUOTJk0wdOhQ1KhRA0lJSbh06RKOHDmCpKQko2PUqlULQUFBglBpAJg1axbfp3Pnzvjtt99gb2+PGjVq4MyZMzhy5AicnZ1zNP+cUrduXYSEhGDlypX8EuW///6L9evXo1u3bgIrnhQTJ07E1q1b0bt3b3z66afw8/NDUlISdu/ejeXLl6Nu3bomX3May0iXLl0wfPhwvHr1CqtWrUKZMmX0LCpDhgzBZ599hp49e6J9+/a4evUqDh06BBcXF0G/devWYd++fQgLC+NTBvz666/4+OOPsWzZMowYMSL3TiiRf+RvcBNREklPT2cTJ05kdevWZaVLl2Y2Njasbt26bOnSpXp9f/rpJ+bh4cEsLCxY8+bN2YULFyRDpf/66y+T5/DixQvWs2dPZm1tzRwdHdnw4cPZjRs3REOlbWxs9LaXCm3WxcvLi3Xq1EmvXfcYGGPs4sWLrEmTJszc3JxVqFCB/fzzz6Kh0qdPn2ZNmzZlVlZWrFy5cmzSpEns0KFDouHfixYtYl5eXszCwoI1btyYnT59mvn5+bEOHToI+mVkZLD58+ezmjVrMgsLC+bo6Mj8/PzYrFmzmEKhMHiMWQmVfvHihaCf2PExxti2bdtYQEAAs7GxYTY2NqxatWps5MiR7O7du3yfW7dusXbt2jFbW1vm4uLChg4dyq5evar3GUqFSkuF6j979oyNHDmSeXp6slKlSjE3NzfWtm1btnLlSoPnQXvc33//nVWuXJlZWFiw+vXr630uycnJbNCgQczFxYXZ2tqyoKAgdufOHb2wXs35OX/+vNF9Myb9XZAaR+xzefv2LZs1axbz8fFhpUqVYp6enmzq1Kl8GL4GqWubMcYSExPZqFGjmIeHBzM3N2fly5dnISEhghB0U6+53bt3szp16jBLS0vm7e3N5s+fz9auXat33SiVSjZ58mTm4uLCrK2tWVBQEHvw4IHgnD5+/JjZ29uzLl266M25e/fuzMbGhj18+NDwSSYKJRxjZDcjiOKKSqWCq6srevToIWqyJ3IGx3EYOXIkFi9eXNBTIYgSBfm8EEQx4c2bN3rLSRs2bEBSUpJeeQCCIIiiDPm8EEQx4ezZs/jiiy/Qu3dvODs749KlS1izZg1q1aqF3r17F/T0CIIgcg0SLwRRTPD29oanpycWLVqEpKQkODk5YcCAAZg3b16u1X0iCIIoDJDPC0EQBEEQRQryeSEIgiAIokhB4oUgCIIgiCIFiReCIAiCIIoUJF4IopgRFhYGjuP4PzMzM3h4eGDgwIGIjY3l+6lUKoSFhaFr167w9PSEjY0NatWqhW+//RZv3rzJtfmoVCp8//338PHxgaWlJerUqYNNmzaZvP3FixfRuXNnuLm5wdbWFnXq1MGiRYv00sB7e3sLjlvz99lnnwn6tWrVSrQfx3GCKtYa/vvvP0yaNAk+Pj6wsLCAh4cHevXqJah4HBcXhylTpqB169YoXbo0OI7D8ePHRY9Hav8dOnQw+ZwQREmHoo0Iopgye/Zs+Pj44M2bNzh79izCwsIQHh6OGzduwNLSEq9fv8agQYPQtGlTfPbZZyhTpgzOnDmDGTNm4J9//sHRo0dzpXDj119/jXnz5mHo0KFo1KgRdu3ahf79+/NVlQ1x8eJFNGvWDJUrV8bkyZNhbW2NAwcOYOzYsYiMjNSrbVSvXj2MHz9e0KZb8PHrr7/GkCFDBG2pqan47LPP8MEHHwjaFQoFWrZsiSdPnmDYsGGoVKkSXrx4gVOnTiE9PR3W1tYAgLt372L+/PmoXLkyateujTNnzhg8rvLlyyM0NFTQVq5cOYPbEAShRYHm9yUIIteRSg0/efJkBoBt3ryZMaYu23D69Gm97WfNmsUAsMOHD+d4Lk+ePGGlSpUSpOZXqVQsMDCQlS9fnmVmZhrcfujQoczc3JwlJiYK2lu0aMHs7OwEbYbS1xvjt99+YwDYH3/8IWj//PPPmYODg9EU8i9fvuTn+Ndff4mWbtDQsmVLVrNmzWzNkyAINbRsRBAlhMDAQABAZGQkAHUxx2bNmun16969OwDg9u3bOd7nrl278PbtW0HxO47j8Pnnn+PJkydGLRQvX76EpaUlHBwcBO3u7u6wsrIS3SYjIyPLlbE3btwIGxsb/O9//+PbUlJSsG7dOgwbNgw+Pj7IyMgQVEHXpnTp0nBycsrSPjMzM/Hq1assbUMQhBoSLwRRQoiOjgYAODo6GuwXHx8PAHrVeRMSEkz6077BX758GTY2NqhevbpgrMaNG/PvG6JVq1Z4+fIlhg8fjtu3b+PRo0dYvnw5tm/fjqlTp+r1P3r0KKytrWFrawtvb2+9ZSUxXrx4gcOHD6Nbt26wsbHh28PDw/HmzRtUqlQJvXr1grW1NaysrNC8eXNcuXLF6LiGuHfvHmxsbFC6dGm4ublh2rRpePv2bY7GJIiSBPm8EEQxRaFQICEhAW/evMG5c+cwa9YsWFhYoHPnzga3+/7772FnZ4fg4GBBu6urq0n7XbduHQYOHAhA7chatmxZPd8Zd3d3AMDTp08NjjV06FDcvHkTK1aswOrVqwEAcrkcixcv1nPErVOnDgICAlC1alUkJiYiLCwM48aNw9OnTzF//nzJfWzevBmZmZn46KOPBO33798HAEydOhW+vr7YsGEDFAoFZs2ahTZt2uDmzZv8cWQFX19ftG7dGrVr10Zqaiq2bt2Kb7/9Fvfu3cPmzZuzPB5BlERIvBBEMaVdu3aC197e3vj9999Rvnx5yW3mzp2LI0eOYOnSpXpLNYcPHzZpvzVr1uT/n5aWBgsLC70+lpaW/PuGkMvl8PX1RVBQEHr37g1LS0ts2rQJo0ePhpubG7p168b33b17t2DbQYMGITg4GD///DNGjx4tedwbN26Eq6sr2rdvL2jXLOlwHId//vkHtra2AID69evD398fS5Yswbfffmtw/mKsWbNG8PqTTz7BsGHDsGrVKnzxxRdo2rRplsckiJIGiReCKKYsWbIEVapUgUKhwNq1a3Hy5ElRIaFh8+bN+OabbzB48GB8/vnneu/riiFTsLKyEvUT0YRiS/mtaJg3bx4WLlyI+/fv8+KhT58+aN26NUaOHInOnTvDzEz8Z4zjOHzxxRc4dOgQjh8/jo8//livz8OHD3HmzBmMGjVKbxzN3Lp06cLvGwCaNm0KHx8fREREGJx7Vhg/fjxWrVqFI0eOkHghCBMg8UIQxZTGjRujYcOGAIBu3bohICAA/fv3x927dwU3Y0BtVRkwYAA6deqE5cuXi46n8YUxhr29PX/jd3d3x7Fjx8AYEywdxcXFATAeHrx06VK0adNGb75du3bFl19+iejoaFSqVElye09PTwBAUlKS6PsbN24EAL0lI+25lS1bVu+9MmXKIDk52eDcs4KxeRIEIYQcdgmiBCCXyxEaGoqnT59i8eLFgvfOnTuH7t27o2HDhtiyZYukJcPd3d2kP22/jXr16uH169d6kUvnzp3j3zfEs2fP9JLRAeCdWzMzMw1u//DhQwDS/jobN26Er6+vqLXDz88PAASJ/TQ8ffrUZB8gUzA2T4IghJDlhSBKCK1atULjxo2xYMECjBs3DpaWlrh9+zY6deoEb29v7N271+AyTnZ8Xv73v//hiy++wNKlS3nRxBjD8uXL4eHhIQjVjouLg0KhgK+vL5/ptkqVKjh8+DASExPh7OwMAFAqldiyZQtKly4NX19fAGqLhb29PeRyOT/e27dvMW/ePJibm6N169Z687x8+TJu376NadOmiR5H1apVUbduXezatQsJCQl89NXff/+Nx48fY/To0SadD21evnwJCwsLwfIdY4z3nQkKCsrymARREiHxQhAliIkTJ6J3794ICwvDRx99hKCgICQnJ2PixInYt2+foK+vry/8/f3519nxeSlfvjzGjRuHH374AW/fvkWjRo2wc+dOnDp1Cn/88YdAbEydOhXr169HVFQUvL29AQBTpkzBxx9/jCZNmmDYsGGwsrLCpk2bcPHiRXz77be8yNm9eze+/fZb9OrVCz4+PkhKSsLGjRtx48YNzJ07F25ubnpz++OPPwCILxlp+OWXX9C+fXsEBARg+PDhUCgU+Pnnn1GlShU9vyCNALl58yYA4LfffkN4eDgA4JtvvgEAXLp0Cf369UO/fv1QqVIlpKWlYceOHTh9+jSGDRuGBg0aZPkcE0SJpICT5BEEkctIZdhljDGlUsl8fX2Zr68ve/DgAQMg+RcSEpIr81EqlWzu3LnMy8uLmZubs5o1a7Lff/9dr19ISAgDwKKiogTtBw8eZC1btmQuLi7M3Nyc1a5dmy1fvlzQ58KFC6xLly7Mw8ODmZubM1tbWxYQEMC2bNkiOScPDw/WoEEDo/M/fPgwa9q0KbO0tGROTk7sk08+YXFxcXr9DJ1LDQ8fPmS9e/dm3t7ezNLSkllbWzM/Pz+2fPlyplKpjM6FIAg1HGOM5b9kIgiCIAiCyB7ksEsQBEEQRJGCxAtBEARBEEUKEi8EQRAEQRQpSLwQBEEQBFGkIPFCEARBEESRgsQLQRAEQRBFimKXpE6lUuHp06coXbq0oJYKQRAEQRCFF8YY/vvvP5QrVw4ymWHbSrETL0+fPuWLnBEEQRAEUbR4/Pgxypcvb7BPsRMvpUuXBqA+eDs7uwKeDUEQBEEQpvDy5Ut4enry93FDFDvxolkqsrOzI/FCEARBEEUMU1w+yGGXIAiCIIgiBYkXgiAIgiCKFCReCIIgCIIoUhQ7nxdTYIwhMzMTSqWyoKdC5IBSpUpBLpcX9DQIgiCIfKbEiZeMjAzExcXh9evXBT0VIodwHIfy5cvD1ta2oKdCEARB5CMlSryoVCpERUVBLpejXLlyMDc3p0R2RRTGGF68eIEnT56gcuXKZIEhCIIoQZQo8ZKRkQGVSgVPT09YW1sX9HSIHOLq6oro6Gi8ffuWxAtBEEQJokQ67BpLO0wUDchqRhAEUTKhuzhBEARBEEUKEi8EQRAEQRQpSLwQhY7jx4+D4zikpKQU9FQIgiAIXRSxQNRJ9b8FBIkXIlcgwUEQBFECuLQBWFALWN9F/e+lDQUyDRIvOSBOkYaIyATEKdIKeioEQRAEkbcoYoE9YwGmUr9mKmDPuAKxwJB4ySabz8eg+byj6L/qHJrPO4rN52PydH8qlQqhoaHw8fGBlZUV6tati61bt4Ixhnbt2iEoKAiMMQBAUlISypcvj+nTpwN4bxXZt28f6tSpA0tLSzRt2hQ3btwQ7CM8PByBgYGwsrKCp6cnxowZg9TUVP799PR0TJ48GZ6enrCwsEClSpWwZs0aREdHo3Xr1gAAR0dHcByHgQMHGpy3Nvv370eVKlVgZWWF1q1bIzo6Oo/OIkEQBJFtkiLfCxcNTAkkPcz3qZB4yQZxijRM3X4dKrVWgIoBX22/kacWmNDQUGzYsAHLly/HzZs38cUXX+Djjz/GyZMnsX79epw/fx6LFi0CAHz22Wfw8PDgxYuGiRMn4qeffsL58+fh6uqKLl264O3btwCAyMhIdOjQAT179sS1a9ewefNmhIeHY9SoUfz2AwYMwKZNm7Bo0SLcvn0bK1asgK2tLTw9PbFt2zYAwN27dxEXF4eFCxcanPeJEycAAI8fP0aPHj3QpUsXXLlyBUOGDMGUKVPy7DwSBEEQ2cTJF+B0ZAMnB5wq5v9cWDFDoVAwAEyhUOi9l5aWxm7dusXS0tJytI/TD14wr8l79f4iHiTkaFwp3rx5w6ytrVlERISgffDgwaxfv36MMca2bNnCLC0t2ZQpU5iNjQ27d+8e3+/YsWMMAPvzzz/5tsTERGZlZcU2b97MjzVs2DDB+KdOnWIymYylpaWxu3fvMgDs8OHDonPU7CM5OTlL8546dSqrUaOG4P3JkyfrjSVGbn2eBEEQhIlcXM/YTEfGZtip/724PteGNnT/1qVEZdjNLXxcbCDjwFteAEDOcfB2yZusvQ8ePMDr16/Rvn17QXtGRgbq168PAOjduzd27NiBefPmYdmyZahcubLeOP7+/vz/nZycULVqVdy+fRsAcPXqVVy7dg1//PEH34cxxpdUuH79OuRyOVq2bJmr8759+zaaNGkiOU+CIAiiENFgAODbVr1U5FQRsPcokGmQeMkG7vZWCO1RG19tvwElY5BzHOb2qAV3e6s82d+rV68AAPv27YOHh/BCsbCwAAC8fv0aFy9ehFwux/3797O1j+HDh2PMmDF671WoUAEPHjzIk3kTBEEQRQx7jwITLRpIvGSTDxtVQIsqrohOeA1vF+s8Ey4AUKNGDVhYWCAmJkbS8jF+/HjIZDIcOHAAHTt2RKdOndCmTRtBn7Nnz6JChQoAgOTkZNy7dw/Vq1cHADRo0AC3bt1CpUqVRMevXbs2VCoVTpw4gXbt2um9b25uDgBQKpVZmnf16tWxe/duvXkSBEEQhBQkXnKAu71VnooWDaVLl8aECRPwxRdfQKVSISAgAAqFAqdPn4adnR1cXFywdu1anDlzBg0aNMDEiRMREhKCa9euwdHRkR9n9uzZcHZ2RtmyZfH111/DxcUF3bp1AwBMnjwZTZs2xahRozBkyBDY2Njg1q1bOHz4MBYvXgxvb2+EhITg008/xaJFi1C3bl08evQIz58/R58+feDl5QWO47B371507NgRVlZWRucdEhKCzz77DD/99BMmTpyIIUOG4OLFiwgLC8vzc0oQBEEUYbLrWHPixAnWuXNn5u7uzgCwHTt28O9lZGSwSZMmsVq1ajFra2vm7u7OPvnkExYbG2twzBkzZjAAgr+qVatmaV754bBbEKhUKrZgwQJWtWpVVqpUKebq6sqCgoLY8ePHWdmyZdncuXP5vhkZGczPz4/16dOHMfbemXbPnj2sZs2azNzcnDVu3JhdvXpVsI9///2XtW/fntna2jIbGxtWp04d9t133/Hvp6WlsS+++IK5u7szc3NzVqlSJbZ27Vr+/dmzZzM3NzfGcRwLCQkxOO8TJ07w2+3Zs4dVqlSJWVhYsMDAQLZ27Vpy2CUIgihhZMVhl2OMMUllY4ADBw7g9OnT8PPzQ48ePbBjxw7+KV6hUKBXr14YOnQo6tati+TkZIwdOxZKpRIXLlyQHHPmzJnYunUrjhw5wreZmZnBxcXF5Hm9fPkS9vb2UCgUsLOzE7z35s0bREVFwcfHB5aWllk74CLM8ePH0bp1ayQnJ8PBwaGgp5NrlNTPkyAIojhi6P6tS7aXjYKDgxEcHCz6nr29PQ4fPixoW7x4MRo3boyYmBje70J0QmZmcHNzy+60CIIgCIIo5uRbkjqFQgGO44w++d+/fx/lypVDxYoV8dFHHyEmxnDm2vT0dLx8+VLwRxAEQRBE8SVfxMubN28wefJk9OvXz6ApqEmTJggLC8PBgwexbNkyREVFITAwEP/995/kNqGhobC3t+f/PD098+IQijStWrUCY6xYLRkRBEEQJZc8Fy9v375Fnz59wBjDsmXLDPYNDg5G7969UadOHQQFBWH//v1ISUnBli1bJLeZOnUqFAoF//f48ePcPgSCIAiCIAoReRoqrREujx49wtGjR4064Oji4OCAKlWqGEyQZmFhQQnPCIIgCKIEkWeWF41wuX//Po4cOQJnZ+csj/Hq1StERkbC3d09D2ZIEARBEERRJNvi5dWrV7hy5QquXLkCAIiKisKVK1cQExODt2/folevXrhw4QL++OMPKJVKxMfHIz4+HhkZGfwYbdu2xeLFi/nXEyZMwIkTJxAdHY2IiAh0794dcrkc/fr1y/4REgRBEARRrMj2stGFCxfQunVr/vWXX34JAAgJCcHMmTP5lO/16tUTbHfs2DG0atUKABAZGYmEhAT+vSdPnqBfv35ITEyEq6srAgICcPbsWbi6umZ3mgRBEARBFDOyLV40ESxSmJL7Ljo6WvD6zz//zO50iFzE29sb48aNw7hx4wAAHMcJkhDmFzNnzsTOnTt56x5BEARBAPmY54UousTFxUkmJNRl5syZetY2giAIgshNqDBjMSUjI4Ov9JxTKOMxQRAEUZggy0tOUMQCUSfV/+YxrVq1wqhRozBq1CjY29vDxcUF06ZN45fnvL29MWfOHAwYMAB2dnYYNmwYACA8PByBgYGwsrKCp6cnxowZg9TUVH7c58+fo0uXLrCysoKPjw/++OMPvX1zHIedO3fyrzW+SU5OTrCxsUHDhg1x7tw5hIWFYdasWbh69So4jgPHcXyF6JSUFAwZMgSurq6ws7NDmzZtcPXqVcF+5s2bh7Jly6J06dIYPHgw3rx5k8tnkSAIgigOkHjJLpc2AAtqAeu7qP+9tCHPd7l+/XqYmZnh33//xcKFC/Hzzz9j9erV/Ps//vgj6tati8uXL2PatGmIjIxEhw4d0LNnT1y7dg2bN29GeHg4Ro0axW8zcOBAPH78GMeOHcPWrVuxdOlSPH/+XHIOr169QsuWLREbG4vdu3fj6tWrmDRpElQqFT788EOMHz8eNWvWRFxcHOLi4vDhhx8CAHr37o3nz5/jwIEDuHjxIho0aIC2bdsiKSkJALBlyxbMnDkTc+fOxYULF+Du7o6lS5fm0ZkkCIIgijR5Wd66IDBUUjstLY3dunWLpaWl5WwnKU8Ym+nA2Ay7938zHdXteUTLli1Z9erVmUql4tsmT57MqlevzhhjzMvLi3Xr1k2wzeDBg9mwYcMEbadOnWIymYylpaWxu3fvMgDs33//5d+/ffs2A8B++eUXvg0A27FjB2OMsRUrVrDSpUuzxMRE0XnOmDGD1a1bV2+fdnZ27M2bN4J2X19ftmLFCsYYY/7+/mzEiBGC95s0aaI3lja59nkSBEEQBY6h+7cuZHnJDkmRAFMJ25gSSHqYp7tt2rQpOI7jX/v7++P+/ftQKpUAgIYNGwr6X716FWFhYbC1teX/goKCoFKpEBUVhdu3b8PMzAx+fn78NtWqVTNYA+nKlSuoX78+nJycTJ731atX8erVKzg7OwvmEhUVhcjISADA7du30aRJE8F2/v7+Ju+DIAiCKDmQw252cPIFOJlQwHBywKliwc0JgI2NjeD1q1evMHz4cIwZM0avb4UKFXDv3r0s78PKyirL27x69Qru7u44fvy43ntULJIgCILIKmR5yQ72HkCXhWrBAqj/7bJA3Z6HnDt3TvD67NmzqFy5MuRyuWj/Bg0a4NatW6hUqZLen7m5OapVq4bMzExcvHiR3+bu3btISUmRnEOdOnVw5coV3ldFF3Nzc94SpD2P+Ph4mJmZ6c3DxcUFAFC9enXR4yMIgiAKF3GKNEREJiBOkVZgcyDxkl0aDADGXQdC9qr/bTAgz3cZExODL7/8Enfv3sWmTZvw66+/YuzYsZL9J0+ejIiICIwaNQpXrlzB/fv3sWvXLt5ht2rVqujQoQOGDx+Oc+fO4eLFixgyZIhB60q/fv3g5uaGbt264fTp03j48CG2bduGM2fOAFBHPWlKRSQkJCA9PR3t2rWDv78/unXrhr///psv//D111/jwoULAICxY8di7dq1WLduHe7du4cZM2bg5s2buXj2CIIgiJyy+XwMms87iv6rzqH5vKPYfD6mQOZB4iUn2HsAPoF5bnHRMGDAAKSlpaFx48YYOXIkxo4dy4dEi1GnTh2cOHEC9+7dQ2BgIOrXr4/p06ejXLlyfJ9169ahXLlyaNmyJXr06IFhw4ahTJkykmOam5vj77//RpkyZdCxY0fUrl0b8+bN460/PXv2RIcOHdC6dWu4urpi06ZN4DgO+/fvR4sWLTBo0CBUqVIFffv2xaNHj1C2bFkAwIcffohp06Zh0qRJ8PPzw6NHj/D555/n0pkjCIIgckqcIg1Tt1+H6l0CfRUDvtp+o0AsMBxjJuTxL0K8fPkS9vb2UCgUsLOzE7z35s0bREVFwcfHB5aWlgU0w+zRqlUr1KtXDwsWLCjoqRQaivLnSRAEUdSIiExA/1Xn9No3DW0Kf1/nHI9v6P6tC1leCIIgCIIwio+LDWScsE3OcfB2sc73uZB4IQiCIAjCKO72VgjtURvydyk75ByHuT1qwd0+61GoOYVCpYsIYmHGBEEQBJGffNioAlpUcUV0wmt4u1gXiHABSLwQBEEQBJEF3O2tCky0aKBlI4IgCIIgihQlUrwUswCrEgt9jgRBECWTEiVeSpUqBQB4/fp1Ac+EyA0yMjIAQDLDMEEQBFE8KVE+L3K5HA4ODnj+/DkAwNraWlDokCg6qFQqvHjxAtbW1jAzK1GXMUEQRImnxP3qu7m5AQAvYIiii0wmQ4UKFUiAEgRRvFDEAkmR6iLA+ZTBvahR4sQLx3Fwd3dHmTJl8Pbt24KeDpEDzM3NIZOVqJVPgiCKO5c2AHvGAkwFcDJ1EeB8qJ1X1Chx4kWDXC4nXwmCIAii8KCIfS9cAPW/e8YBvm3JAqMDPbYSBEEQRGEgKfK9cNHAlEDSw4KZTyGGxAtBEARBFAacfNVLRdpwcsCpYsHMpxBD4oUgCIIgCgP2HmofF+6dSwMnB7osoCUjEUqszwtBEARBFDoaDFD7uCQ9VFtcSLiIQuKFIAiCIAoCqZBoew8SLUYg8UIQBEEQRohTpCEqIRU+Lja5U5SQQqJzBIkXgiAIgjDA5vMxmLr9OlQMkHFAaI/a+LBRhewPSCHROYYcdgmCIAhCgjhFGi9cAEDFgK+230CcIi37g1JIdI4h8UIQBEEQEkQlpPLCRYOSMUQnZL/A77NSHlAyYVmTTCbDs1Llsj1mSYPEC0EQBEFI4ONiA5lO+TQ5x8HbxTrbY0am22Nq5hBkMvUtOJPJ8FXmYDxMd8jBTEsW5PNCEARBEBK421shtEdtfLX9BpSMQc5xmNujVo6cdn1cbLBV1Ron0+vAW/YM0aqyeMG54IscCKKSBokXgiAIgjDAh40qoEUVV0QnvIa3i3WOo420BVG8yllPEOV6ZFMxhMQLQRAEQRjB3d4qV4WElCDK9cimYkq2fV5OnjyJLl26oFy5cuA4Djt37hS8zxjD9OnT4e7uDisrK7Rr1w737983Ou6SJUvg7e0NS0tLNGnSBP/++292p0gQBEEQhRZ3eyv4+zoLLC65HtlUTMm2eElNTUXdunWxZMkS0fe///57LFq0CMuXL8e5c+dgY2ODoKAgvHnzRnLMzZs348svv8SMGTNw6dIl1K1bF0FBQXj+/Hl2p0kQBEEQRYK8iGwqrnCMMWa8m5FBOA47duxAt27dAKitLuXKlcP48eMxYcIEAIBCoUDZsmURFhaGvn37io7TpEkTNGrUCIsXLwYAqFQqeHp6YvTo0ZgyZYpJc3n58iXs7e2hUChgZ2eX00MjCIIgiHwhTpGG5vOOCgSMnOMQPqV1ifB9ycr9O09CpaOiohAfH4927drxbfb29mjSpAnOnDkjuk1GRgYuXrwo2EYmk6Fdu3aS2xAEQRBEcUHjyCvn1LHZuRHZVFzJE4fd+Ph4AEDZsmUF7WXLluXf0yUhIQFKpVJ0mzt37kjuKz09Henp6fzrly9fZnfaBEEQBFGg5HZkU3GlyCepCw0Nhb29Pf/n6elZ0FMiCIIgiGyj68hL6JMn4sXNzQ0A8OzZM0H7s2fP+Pd0cXFxgVwuz9I2ADB16lQoFAr+7/HjxzmcPUEQBEEQhZk8ES8+Pj5wc3PDP//8w7e9fPkS586dg7+/v+g25ubm8PPzE2yjUqnwzz//SG4DABYWFrCzsxP8EQRBEMWLOEUaIiITKGyYAJADn5dXr17hwYMH/OuoqChcuXIFTk5OqFChAsaNG4dvv/0WlStXho+PD6ZNm4Zy5crxEUkA0LZtW3Tv3h2jRo0CAHz55ZcICQlBw4YN0bhxYyxYsACpqakYNGhQ9o+QIAiCKNIUysRtilh1dWgnX8Deo2DnUgLJtni5cOECWrduzb/+8ssvAQAhISEICwvDpEmTkJqaimHDhiElJQUBAQE4ePAgLC0t+W0iIyORkJDAv/7www/x4sULTJ8+HfHx8ahXrx4OHjyo58RLEARBlAykEre1qOJacD4hlzaA7RkLjqnAOBm4LguBBgMKZi4llFzJ81KYoDwvBEEQxYeIyAT0X3VOr33T0Kbw93XO/wkpYsF+qQUOKr5JxckgG3eDLDA5pMDzvBAEQRBEbuDjYgMZJ2yTcxyszWUF4gOT+PiWQLgAgIypkPj4dr7Oo6RDhRkJgiCIQot2BWYlY5BzHLrVL4fuSyPyzwdGEQs8Vlt/nryyhwPjIOfeL1pkMhmiVW4oADtQiYXEC0EQBFEoiFOkISohFT4uNgJ/Fu3EbdbmMl64APngA3NpA7B7NP+yDjhsUwagm/w0zDgVMpkM32QOwVgv39zfNyEJiReCIAiiwDEWUeRubwV3eytERCZIFi/MdfGiiBUIFwDgwNDD7DR6pM+CJZeOx8wNY3q0pIRy+QyJF4IgCKJAyUpEkcYHRrd4obeLde5P7LG+ozAAyKDCmo9q4J5VfUrhX0CQwy5BEARRoEQlpEpaU3ST0+WkeGGuJbrjZHD2rE4p/AsQsrwQBEEQBYqUNeVabAo+Wn1WbykpO8ULs5XozrMJAA6AjrJqN4vCogsYsrwQBEEQBYqYNWVSh6qYf+CO3lKStgXGFMtHnCINe67Gii5LGbXA2HsAXReBcepbJQMHtJ8NNB+T/YMlcgWyvBAEQRAFjq41xdBSkqlLNdrWFl1ExxJJ+b9Z2QoL3yxEBe4ZYlhZjDVvhQ+ze5BErkHihSAIgigUaCKKNOTEMVfXCVgXvbEubQD2jAWYCuBkQJeFiPPt/W4MZzxl6iwuBV6agABAy0YEQRBEIcRUx1wxJ9w4RRr2XntqULgIxlLEvhcugPrfPeMQ++iBpPWHKFjI8kIQBEEUSow55oo54QKQtLjIAPzavz4aeDkKx0qKfC9cNDAlfGTP8i8sm8gSJF4IgiCIQovuUpImC6+NuVzPCXfqtuuAjtjQoLG2dKpTTv9NJ1/1UpG2gOHkcPasjtAeSkFpAlPDsom8hcQLQRAEUSTQtrRwHMB0RIoK0ItqBoBpnaqjYx13adFh7wF0WQjsGQcwJcDJgS4LAHsPfNgIWQ7LJvIeEi8EQRBEviJVw8jYNtqWFl3hAqgzsnAiyzx6wkUkqggNBgC+bYGkh4BTRUEeF13rD1HwkHghCIIg8o3sJIsz5oCrTff6Hth5+an0Ms/pRcCR6Wr18y6qCA0GqN+z96Dkc0UEjjEx/Vp0efnyJezt7aFQKGBnZ1fQ0yEIgiDecfVxMrotiRCs7Mg5DuFTWktaNgzlapG9WzrSHW/7CH+8zlDpL/P8Mxs49ZNwEE4OjLtOoqUQkJX7N4VKEwRBEHnO5vMx6LY0Qs8lxVDosaFcLXKOw+AAH9HxXmeo9LPvnl6kL1wAtY9L0sMsHQtR8NCyEUEQBJGnaESIlJ+KVOixWJZd4L0DLgCsCY8yHsqsiFUvFYnBydQ+LsieLw5RMJB4IQiCIPIUKRECQK1eJJAq2KjtgBvao7ZeKDMAREQmqEUIkoCbO8Q9fAG+yGK2CjcSBQaJF4IgCCJPERMhGhiDZL0iTZZdQ3lWdBPZnbz3As3nHYWKAX3lxxBaag04qPTGBgAEjgeaj9FbntIUbqQyAIUXEi8EQRBEnqIRIWL+K8Yy1hrLsqsZ393eihchZVgiGsju4TuzVeKGHU6mtri8qw6dG0UgifyFxAtBEASR6+j6j2hEyLrTUVh9MgoqSNcr0sXUPCtRCanoJTuGULNVkEstRwXNBWp0E0QXSS1PaUQV+cIUPihUmiAIgshVjPmPxCnS8iRj7bMnkXBd1QAyKeFiICx68/kYveWpDxtVIF+YfCQr92+yvBAEQRC5hin+I3mVsbZsylVpB2CtlP9iiC1PkS9M4YXEC0EQBJFrFEr/kRaTAb8Qo4nodEVVoTwWAgCJF4IgCCIXMeY/Yohs+5Y8uQjEnAGcK0FtetHaOceZJFzEyMmxEHkLiReCIAgi1zAlvFmDtlg5ee9F9nxLtoQAt3a+f12+CRB7HmCq97WLspn6PyvHQuQv5LBLEARB5DrGnHK1HWE1bipZqXkEQLxWEQD02wyY2+hVh9bMKzsVrfPCwZgQQg67BEEQRIFiyClX1xFW7AnaoG+JIha4e0BcuABAUiTgP1KvObuRQ3nlYExkHxIvBEEQRL5isFzAOyR9Sy5tAHaPgbjkeYdnU70mihwqXlBVaYIgCIInTpGGiMgExCnS8mwfGkdYbTiAb5P0LVHEGhcuNboB5f30mg1FDhFFD7K8EARBEACyv6ySVfhyAduuQwX1U3Roz9qGywAoYoG9X8KgcAkcD7QVrx4tFjkkg3RFa6JwQ5YXgiAIQnJZxVQLTLYsNpzwX3d7K/j7OusLl9OLgF9qAPcPSg805KikcNGMHdqjtiCHHQNw8t4L0+dLFBpIvBAEQRA5WlbZfD4GzecdRf9V59B83lFsPh9jsH+WhNLphcDhaYYn0HWR6FKRLi2quILTUi8MWRNoROGBxAtBEAQh6odiSkK27FhsTBZKiljgsLQ1hbe4NBhgcI5Z3i9R6MlT8eLt7Q2O4/T+Ro7UD2EDgLCwML2+lpaWeTlFgiAIAu+XVeTvTBOmJmTLjiAwWSid/MHwpNvPNsnikuX9EoWePHXYPX/+PJRKJf/6xo0baN++PXr37i25jZ2dHe7evcu/5jipKlsEQRBEbiJWnNAY2Umhb1LmWkUscDFMeseB44HmY0w4qizulygS5Kl4cXV1FbyeN28efH190bJlS8ltOI6Dm5tbXk6LIAiCEEEq+6yhrLTZFQRGhVJSJCQjiwInAG2N+MFkd79EkSDfQqUzMjLw+++/48svvzRoTXn16hW8vLygUqnQoEEDzJ07FzVr1pTsn56ejvT0dP71y5cvc3XeBEEQJQGpMGlTwqezKwgMZq518lXXJmIqYXvg+GwLF5P2SxQJ8s1hd+fOnUhJScHAgQMl+1StWhVr167Frl278Pvvv0OlUqFZs2Z48uSJ5DahoaGwt7fn/zw9PfNg9gRBEMUXKafbq4+TTXbGlQxzNhVFLHDiR2D7MODuQXVNoi4LAU6ufp+TAe3nGAyHJkoO+VaYMSgoCObm5tizZ4/J27x9+xbVq1dHv379MGfOHNE+YpYXT09PKsxIEARhIhGRCei/6pxe+zedquPbfbf12jcNbQp/X2e99uwUPQTwLuX/aGFb+SbAkL/VoibpoWiRRaJ4UegKMz569AhHjhzB9u3bs7RdqVKlUL9+fTx48ECyj4WFBSwsLHI6RYIgiBKDrsiQcrpt5O0IDkLPE457n5VWe5yT915kLzsvn/Jfhyfn1BaYqh1ItBB65It4WbduHcqUKYNOnTplaTulUonr16+jY8eOeTQzgiCIkoWUD4uY020ZO5FUFUx/HE74FlQMWLT9BNpZucHZs4a0+FDEAjd3QNIx98FhtXghCB3yXLyoVCqsW7cOISEhMDMT7m7AgAHw8PBAaGgoAGD27Nlo2rQpKlWqhJSUFPzwww949OgRhgwZktfTJAiCKPYYqqws5nQbEZmgJysYgH9uP8O0nTf593T79JEfQ6jZasi3MrWvSpeF+onkLm0A9ozVd8jVplL77B8sUazJc/Fy5MgRxMTE4NNPP9V7LyYmBjLZe5/h5ORkDB06FPHx8XB0dISfnx8iIiJQo0aNvJ4mQRBEscdQQjlNBI62r4rYchIHCISLLm5IVAsX7l0PpgL2jAN82763wNw9qO/jokv5JmR1ISTJN4fd/CIrDj8EQRAliThFGprPO6rn2xI+pbWkg+3m8zH8cpIMaiuL2E2DA1CHe4Ce8hMYYPaPfoeQvYBPILDjc+DqRvEJVg4GrB2AGt1IuJRACp3DLkEQBFHwZCehnPZyUmJqOkZtvKzXRwbguPc6eMYf5h18Bdm8OLk6WujyH9LCBQDK1QFaf5XNoyNKEiReCIIgShCmJpTTjUhyt7dCnCJNbxlJxgFn6x1CmduH+TZt4cI4GRTtfoDD0W8NCxcAqByUgyMjShIkXgiCIEoYxjLMSkUkiVlu/q74J8rc3iU6zvrMdliW+T+U3ZuMnRYbYbBSXd3+WSqySJRsSLwQBEEQPIYiktztrQSWm3q72sEy9qHoOIwBWzNbIB7O6Cs7Ki1cyjUAOv5oknDJdhI8othB4oUgCKIEYOqN31hEEqC23GB9V1gqHkKsVB1jwD5lE7yAI/xlN/GGSdxqmo0DPphl0tzXhkdhTXhU1pPgEcUSEi8EQRDFHEPFFU3NtqvJqgsAyRHr4Jb4r6RwWZcZhDuogNMWYyDnGJRM3a7Xv8kwk+Y+Zdt1QYSTrjWIKHmQeCEIgigiZGfZJE6RJrj5qxgwdft1VHMrjTvx/5mcbZff347P4XB1o6Rw2ZzZAiuVnXnhAgByDlCBe7d09C4Wqesio2n/NUtYYqHZutYgomRB4oUgCKIIYMh6Yoi14VF6N38VA/63JEJQt0gq2661uQypGUrEKdLgHn8C7Kq44y1jwH2VO6YoP4O/7Ob7JHXvkIEBvcIAGxeTiyyKLWG9Hw8CaxBRsiDxQhAEUcgx5kRraLs14VGS7+vqAiVjuBidjM511dFI2sUW+8qPIbTUaknhcs+6PjqmTALAEMPcwSADB63U/5wc8GycpSKLPi42eoUhNQxp4UNWlxIMiReCIIhCjilOtKZuZ4wxf15GakYmWlRx5YWLGxLxndlqcCIygjHgSoO5qP+/kQhXpPH5Y7hIpi4LwJRq4dJlQZarQ7vbW2FKcDWEHrgjaJdxwKDmPlk7MKJYQeKFIAiikGOKE62p22mjWw0aeG/VWdivHr+djyxebxkIUAuXbcoWqNygPyIiE+DjYgN/X2f1mw0GqOsZJT3kl4my47MzvKUvwAHzD9yBisGkrMBE8YfEC0EQRCEnO2n9xbbj3q3BMLwXATYWZnop/5VM3UkjfKJUblAyTiBgVIzD0IzxcKjfBZOWRoj74th78NYWYz47hoTN8Ba+6Fq3HG/VAcCLJRIxJRMqzEgQBFGI0b6pAzCa1l9qDO0bv/YYYsUaAWBqcDU4WJfihU8f+THMNVsDM06FTCbDN5mD0f7jCRi64aLRQo/GCkJmxRk5u47LROGHCjMSBEEUMcQsD7l1o9YtB6D7/w613LD/erxgm+8P3kX4lNYIn9Ia+67F4dt9wEllHXjLniFaVRbxcMarS7Em+eIY8tkBYLIzcnYdl4nih6ygJ0AQBFHS2Xw+Bs3nHUX/VefQfN5RbD4fI3mjjlOk5dp+4xRp2HM1Fgd0hAsgFCGd6rhDxgHxcMZZVQ3EwxkyDtgrsp2M0w9h1vjeaKPx2TEmbLTJSl+ieEPihSAIogCREikXHyXn6Y1aI5hGb7oiGoqsnUdF4ztTj4vEYPk+1OMi0beRp+i4fd8VcNRGs738XWY7bZ8dQ8JGl6z0JYo3tGxEEARRgEhZE7QdZjXk1o1aVzCJEVTLTSBCPnw4DX0sdvJ5V56kdMNG9NHbrnklZ9HxPmxUAdXcSuN8dDIaeTuirqcjgKw5I2fXcZkofpB4IQiCKEBszOWi7Z5O+jfqScFVEZWQCgA5umGbkv/l75vP+CWqzMOzUf72Tj60mgNQPmYn6qABrqESvw3HAQ28HEXHM+S/o53R15gzclb6EsUXEi8EQRAFSGqGUrT9dYZKcKO+9iSFz3ViyHnXlFwqxvK/AGrrz7rwaDwI/wtrzJfq1TLiAEyr+gQf3qskmJPYPk1xtNV1KjZEVvoSxRMSLwRBEAWIsQR0mpv0R6vPGo2yMTU6SbP8YmjpSAagypmJmGp+SrQIIwA4lfHE6R5tjFpBspshmCCkIIddgiCIAsSQM6uGdeFRRp13sxqd9GGjCljYt57oezIO+LhCAnrKpYULY4Bt3U7q/4u6/L6HHG2J3IYsLwRBEAWMIT+OOEUaVp3SL66oG5KcHetGQ28nPauPDMCqAX6oubExOHF3HDAG3Ko0FDfiSmHqkqMmW3rI0ZbILUi8EARBZJHs1OgxhpQfR1RCqnhV5YCKgv7ZqX8kJip+CXZBo0PdUFqmEN2GMeC8sjIsWn2Nqe/KAgDGE8blpaNtXnweROGGxAshCv0YEIQ4+Z2eXkyUyAAMCvAW9MuOdSNOkQZPJ2tsH+GP1xkq1Ly7CHZHF6jfFFkuYgy4rfJEn8xZ+CZaOg+N1D7zwtGWygWUTEi8EHrQjwFBiFMQ6emzIkqyYt3Q/Z6fLL8Mdi9OSfZnDPglvRsWoQ/kHIdG3o55lofGVKhcQMmFxAshIDs/BmSlIUoKBRU1IyVK4hRpuPgoGYwxNPR24i0bxuai+z0fJ9sMj+enRK0tgDop3W2VJxahDzgOmBRcFXU9HQvcj4WimEouJF4IAVn9MSArDVGSyI5fSW6hK0pWnIhE6IE7/GsOwLyepn3/tL/nbkjEaLNdklFFABDv1Bgdn44DoLbAzNt/Bw5WpXLdjyWrD0IF+XkQBQuFSuczcYo0REQm5GpxtdwkKyGN+VE4jiAKE6aENecHK04KhQugto5M3Xbd6PcvTpGGpNQM3sjyW6m5BoVL4v82oHncOMl9udtbwd/XOcfnQKw4pTEKy+dB5D9keclHioKVIivr62SyJUoi+Z2eXtcacfVxMkL33xHtqwIkv39xijSsDY/Cmnc5YzgAK+Tfo5IsTnrnjYfhrl1zqNi5LO0rq+TEd4XKBZRMSLxkk6yaN4uSY5mpPwZksiVKKvmVnl73gad7fQ9svxwr2Z8DRL9/m8/HYMq263zItRsSsd98Chy5VFGrC2NApl15JDSfjcToJHCcuk0b7arTOSWnD0JULqDkQeIlG2THglLUrBSm/BhQ4imiJFBQDuliDzzbLkkLFw27rz5FbQ97fr6acTQ/P33kxzDfbJXBzLlJzAY/+fyJP+cd5a00mmrSePf/0J7idYyyAz0IEVmFxEsWyYoFRftHr7h+OclkSxRnCnKp15TKz7owgF9S0szX08la4JxrTLhcUVZE98xvgX/f+5wwqC0tE4KqIP2tCm2rl0FdT/Hq0dmBHoSIrELiJYuYakER+9Errl/OvDLZUgg2UZAU9FKvKZWfxZZzNKiY2ql2VreakHFAC3YRq8x/Nihc/s6sh+HKSeLjAfjx73tgDFh87EGuCzl6ECKyAomXrKCIRdW0WyjHJeIpc+abdS0oUj964VNaI3xKa/pymkBRcG4mijcFvdSra43QRc5xmBRcFfMP3JEUOCoA03bexN+lxqOyLM6gcHnG7HnhoummOyzLYyFHviuEqVCotKlc2gAsqAXnrb1w2mIs+sqPAxAPzTP2o5cbYYWFkdwKA6cQbKIwkJeVkE39rnzYqAK2j/DXyx0nA7B9hD+Gt/AVhArr4oZEnDIfbVi4AHhWujqaZSzjx57Xszbm9Xw/rtiNQreqNUHkJ2R5MQVFLLBnLMBUAAAOKoSar8aggFpwqBqAsuWFFoHi6t9iiNy0lBT0Ey9BAFn3wzB1mTOr35XUDKWeBUQF4HWG+vdIs9xy6VEyRm68zPfpIz+GeWar9ASYNowBJzJr4NPEbzC5YzXU8XAQWIWruZXG+ehk+LhYY+iGiyXqN40o3OSp5WXmzJngOE7wV61aNYPb/PXXX6hWrRosLS1Ru3Zt7N+/Py+naBpJkbxw0cAxFaqeGoOyaxqqrTJalLTESbltKcnLJ16CyAofNqqA8CmtsWloU4RPaS0pMkxNsJad74op3wd3eys42pjzr92QaJJwecmsMFD5DVQM+P7AXYFw2Xw+Bt2XRuDbfbcxdMNFdK/vUWJ+04jCT55bXmrWrIkjR46836GZ9C4jIiLQr18/hIaGonPnzti4cSO6deuGS5cuoVatWnk9VWmcfAFOpidgAKjb9owDfNsC9h58c0lyPsttSwlFHhCFCWN+GKY49mqsMomv0rNVibl7fQ9BmHS3+uX4MOgL0UngOA6ejla8xXeuCcLlitIb3TPnCuZx6VEyHG1SYWMu1zumnZef8tWni/tvGlH4yXPxYmZmBjc3N5P6Lly4EB06dMDEiRMBAHPmzMHhw4exePFiLF++PC+naRh7D6DLQrA948Axpf77TAkkPRSIF6DkOJ8ZWibLbsRQSRJ/RNHGmHjXXiaS8juxNpc2gscp0rBDJzHdzstPUaVsacw7cEeQe6VHAw80vjodreXXRMdiDHjO7DAkYwKuo5Le+6M2XgaDeBSTkjG8zlDB39dZbzuCyG/y3GH3/v37KFeuHCpWrIiPPvoIMTHS9SrOnDmDdu3aCdqCgoJw5swZyW3S09Px8uVLwV9esFnZCs3fLMCIjDFQ6i5Ac3LAqaL+RopYIOqk+t9ijNQy2cl7L7Jcq0R33OLq3EwUH8SWdWScWpDoWmWkwpo1/ivaaJx6L0QniYqjUC3hAqgdb0de740+pU5IZs39Jb0bmmQsFxUumjGk5pkXS7eFvdYbUXjJU8tLkyZNEBYWhqpVqyIuLg6zZs1CYGAgbty4gdKlS+v1j4+PR9myZQVtZcuWRXx8vOQ+QkNDMWvWrFyfuzbvf4Cc8ZQ5wzYzDXPN1sCMU6mFS5cFelYXXNrw3smXkwFdFgINBuTpPAsSXUsJADR/l50TKNzlEAgiJ4iFNKsY0H1pBIYE+BhNNCcmCnSderWz2wIQzf9yutRIlJMl60UmAWoxclXljUXok+Xj0zCpQ9Vc/e5SOgQiJ+Sp5SU4OBi9e/dGnTp1EBQUhP379yMlJQVbtmzJtX1MnToVCoWC/3v8+HGuja1B1yy8RdkaAekLcbP9RmDcdX1RohOdxPvFKGKLtTVG21JiyJRuKvRURhQVxEKaVQxYfSpKzyrDce9/eMX8ucR8aKCzzeetfAVjHi01Ti1cJCwumzNboNvb9/4trau6ZvkY65R3yPI2UlA6BCKn5GuotIODA6pUqYIHDx6Ivu/m5oZnz54J2p49e2bQZ8bCwgIWFha5Ok9dxHw6XnAucKrVGhB7EhGJTgJTAueWA2cWF7g1Jj8y1+Y0XJyeyoiihlRI87CAilgTHiVwPpfy54pTpGHvtad6wp8xYHH/+nCyscC12BTMP/C+qvRu+WT4yJ4bFC5TlJ8J2k/eS8Co1r5YejwSKqb+bnarXw47Lz+VTIiXm0tGlA6ByCn5Kl5evXqFyMhIfPLJJ6Lv+/v7459//sG4ceP4tsOHD8Pf3z+fZihOlqNfRKOTZO+FCyAZpZRTjAmT/BIFOYkYKui07ASRHaQE+6AAbwwK8NYTK7qiZW14FNaER4kuM8k5Dg281LWEPlp9lu9zz/wjlOKYuHABkGZbATYfLAc2XRG8p2QMzSu54qOmXohOeA1rcxlSM5QY4O+F1xkqXHuSgu8P3s2zaL+SmAuLyF3yVLxMmDABXbp0gZeXF54+fYoZM2ZALpejX79+AIABAwbAw8MDoaGhAICxY8eiZcuW+Omnn9CpUyf8+eefuHDhAlauXJmX0zSJLEW/vItOwp5xaosLJwf8RwARvwr7SUQpZRdjwiS/RUF2I4boqYwoihgS7HGKNDA9u4yazedjMGXbdYl3hUtLc/fd4r8bV80HSQsXBryyKIPSE6+joSJN1Ecm/P4LMLjgeqyCLzGg+d0Y3tIXXeuVE/iwRUQm5Jq1ltIhEDklT8XLkydP0K9fPyQmJsLV1RUBAQE4e/YsXF3V660xMTGQyd673TRr1gwbN27EN998g6+++gqVK1fGzp07CzbHixZZCn1uMEBtVUl6+D4S6cwSoTVGKkopG5giTApCFGQnXDw/n8qo+CORU7SvoRZVXLGwXz2AAX7ejnqh0roPFZrvrSGf3hZVXPBhowq4+jgZK09FAQBWyL+HHZcuKVyiVGWwrcEeTIT6Ozg5uBpfbVrDkuORWHI8UtCm+7thbP45gdIhEDkhT8XLn3/+afD948eP67X17t0bvXv3zqMZ5TP2HkKriq41RixKSRtFrNp/xsnXqHXGFGEiJgpkHJDw6g3iFGn5/uMhJRzy66mM/GoIDdkVsYIcLu/aGN5fTy2quBp8qBD73upy7O4L/HDwDpaeUAuN38y+RYD8lmTOmIdKV7TNXAD5iYf42N8L7vZW8HAw/Zg0yeo61bESfSiauu16rllrS0ouLCL3odpG+YmuNcaQIMliqLUp1gpdUaBJRDV60xVwHDAluBqGt/AVGR14cTcCr+6dgm2VQLhWbZblQ9fFmHDI66cy8qshNGRXxOrlcNF6T3M9Lehb1+BDhY+LjV4YtBgaC8kOs69RTx5lsDr0R5nT+f1cjE5G57pWYFIJZiQYtfEyXqVnwtPJWm/+KgDrwqPxVafqWRqTIHITqiqd39h7AD6Bxi0uYqHWTy5KhlmbWk9JU6tlSf/6ABMmpQrdfwcrTkRCl4erPoHLxmD4XJwLl43BiFscnKNQb1PDJPMySV1uhHITRZ+chOwas5ooGYOM43KtTld4qZFGhcvczH6Ix/sMuGP+vIzN52PQ0NtJNP+LFAzA1O3XYWMuF91udfhDCmsmChQSL4URqVDr1W2B9V2ABbX0ikECpheR0xRxE/vdnX/gjuBH6cXdCPg82c3/YHIc4J4QAfZLDdE5mEJhEA5U/JEAsnctavIP2ZjLDdYP0kQIhfaozf/QygDBQ0VUQqpRqwsAnDX/HB4SeVwAtXD5NbMbVim7CNo1YgwA5vV8Pw8O70sVyDkO/Rt76o2pYsC+63EYGugj+h4JfaIgoWWjwohkIUiNfVorzBoQ+MWYuobs42IjWr9EBQj8ZF7dOwVXkR9MDsh2qHdBhEnq+jRQtAMBZP1a1F1i6l7fg8+Nwr1b/2EQsXxq1oZ0vks25nKjc+yO4yjLKYwKlwXKPmhbzRX/3HkheF8jxsSyYGv//8/zj/WE3OqTUdgxshlW64Rwk9AnChoSL4URvVBrESGTw6R37vZWCK7phv03hKUXdH+UbKsEgl2QKCinCfUGTHYs1uw7P4WDlE8DRTsQWbkW4xRpgpBmsUrLAATXk5TDazW30qjr6YjUDJFCrzp0KHVeWrgAiPL9GPG2nwHnY/SECyD8Tus+3Gj/f3CAD1a9i2bSoIK67hIJfaKwQeKlsKLl3PsiQw6njR0h594/+iiZDLKIX8GJWWO0BIRUFEWcIg0Hb+rXjJoULKxf4lq1GR6W7ypYOuLh5MDTy8CGrgBTgQHIcPODRetJQNUOBiM48ks4GHPMlbJUUQh1ycHYtai5FvZcfaq3xKOptOztYs1fL5qqy1LZclUAui2NwLwetZGS9tbo/A6+bYQPZJf1vn8MwP7Mxhh5qyMA8aKnWREanwb4YPWpKMExaoSPv68zCX2iUEHipTDzLtT6fmQCdmYO4YtBZjIZ1iiDMdxsn7A/UwKP/wWSnAEnX2y+pxRYHCYHV0NtD3v4uNhIOhvW8XDQa6s49De8uBsBnF4Ml5j9asHEyYF2M4AjM3irEAfAIv4i2KYPkeBQF82fTTYYwWHKEpe2iACQZUGRndw2FEJd8pC6FrWvBSlOP3iBj1ZHCq4XAAa3Y8zw+9rsQCuMYTvhDXUJAAbgP5UlPsr4SrI6NABM61QdDb3V1h1TUiG421thXk9pCwuFNROFCY5lNYaukPPy5UvY29tDoVDAzs6uoKeTK8Qp0tB83lGUYYnwlj1DtKos5ByHcMsx4ATLSZx6fYepwDgZpmYMxnFlHfjI4hGlcuOjEDRCRpNVU4Oc4xA+pTUAAyJBEfs+1DspUu1ALAJjwKD08TgOP36fp6e0ydUcGqaGszYLPSp4muQAREwVn4vmXIudF/rhLv7oimXda0EMXd8x2bvXuf3D2h3HEVTqAg69bYgdaGW0f8fabjh4I15PhBuzKsYp0sjCQhQIWbl/k+WlCKC9Lh+vcuafiDi5ll8MZFB7C76zgjAVvjNbDZgBco5ByThMzRyCLcrWUDHg+wN3MblDNb36JSfvvRC1Orz/wXOCu8/7ZSkG7v3SlRYcB7Q2u4rjmWrxomLAutNR+KpjDZOO2ZQcGtnOyWIgQiS/shDTslThQ9fiNiTAx7hwgYjTu4mqRcxh3hDJKI3nzBHJKG1S//3X3y8La74zKWlv9UoBZMciShAFDYmXIoL4urxW0rvUF8DWQYJttH1k5BxDqNlqpDJLxKhcYculo6GjOrRaO+JA+0mT/8F7/RbzD4r84Nl74GXgNNidnK2/Hs+AY5l1BW2rT0ZhUHMfk34YTcmhYYqgEAtFZQyS2+ZHJBQtSxU+xHyjVp+KEq0JpIEDMKK1L5a9q8yswdA22n1GtPLF4mP6eZV06Y7jmGb+Oxy51+A44BP5P7igqozeb2cJ5mJMBykZw7z9dwQOx5SYkSiqUJ6XIoRo0jZN0jvPJuqIIwPIOYYl5r9it8V0bDL/Dg22B8D9xip+TCmrwzyt5SXVu7X6q4+T1btvOx5Xq38peIJkAJ7Y1uaXjDRowrBNQSwPi/BYhIJCk3tDN3FWVvO5mJrsL7vkJCkakXeIXfsqAEMCKgquhakdq/E5URiAZccj0b2+h6DP4AD9vCjayADsGNEMzSq5SPd5d81GmI/EzxYr4SR7Lci11FB2H61wETIOGBZYETtHNjMpCZ2YwzHlayGKImR5KS7ohldrlpEklnQAqJd7Dk8DHvwDVO8C33KtRWsf6f2oM6DbkgjM66m2GNTrOwPPnnyMpNO/wea/h7Dx6wmzih+A0/E1yYoFQ6yUgVQODUOWjOyEZX/YqAKquZXG+ehkNPJ2RF1PR5PmbApUMbtwImVxGxTgjUEB3ohOeA1rcxkeJ6dhnlaBQ91waWtzGa4+STG4r9CetVHX0xFxijRRi4mMAz5v6Yvg8F5w58QT03EcEFrnGdCpDR+SnR0oXwtRVCHxUpzQrZ0U+Y+WmDFA1HEg6jjKAviz4Sz0u1CFv9FPCq6q59gLqH9wtU3Ox+NKYeqVRlCxRpBFAqE9XhiMXDAFQ0m1NOOYUqMoq2HZebmsUxAJ+gjjGBO52r5gumjCpWOSUk2KIGpRxZXf58KOrth08DjvUM+9c6Zv/HcP1JQ/lszvAgDufl2Ad8Jl7zX9MG5jUL4WoihD4qW4oV3JWiNmHv/7zh/G+M9b4+szcXbgfjxPSIKLVzWULe8LB6tSoj/K2iZnMQGxfYQ/FvarBzDAz9sxW/lUNM6DUv1MtWSY6oSY1wUbKbNv4UVK5OpeE7rIOQ7W5jKTQ5811+bL/TPQ5d8F6GoOMMhwvcEsuLYcCvtVjWEljzGYmC7JqR7OpNdB7MlI0YcLQ8gA/Nq/Php4iX8nCaIoQOKluGPvAdh3BzL+A3aPhXol3xAMrn92hKvGiaVaZ3wY/D2qjWiGbksiRJeBdAWEGxLRgLuHlcsicFFVBc85Z1HrhakWDkP9xCwZMg5IePXGpNwWulx8lJznyzqmWIIoGil/0T7fmiRzGow5j3/YqDxikl6bJCA4qK/NxwvaoXzyea0lXBXqXJ4JPPkT7JUB4cKAWen9Efa0M7DxsuR+5ByHbvXLYcflWD0r39wetdCpTjnjkyWIQgzleSlJKGLVJQUiFmV9266/YrOylZ7FQBNGrYlS6iM/hnlmqyF7F+mkYsBOZTP8pOyPrVN6CZ5mTcmnYkq/zedjRH1jsrrks/l8jCD9u6F55SUUjZS/GDvfYtegLlnJ7bLa7Hu0lV8xuCQkBmPAP8p6GJI5yWC/aZ2qo2Mdd5y890JwPQ9r4WNytB9BFARZuX9TtFFJwt4D+GAO8MUtoFcY4NXc9G13j8GHVeSiVas1SyEeXBJCtYQLoP5R72EWgVPmo6A6NE0toGB6NV9T+mmqaS/pX58XLkDWInk0SwNizpP5uaxD0Uj5iynnW3N9G4p+UzEAHATVo8W6D8ReSeFiSPgwBoQraxgVLnKOQ8c67gCgdz2vORVtcFuCKErQslFJRLOUVKs78OQicO8QYFsWKFcPWN1GYiMGJD2Eu4+H6I38w0YV0M7KDfKt4j/BMg7wuLUKuLUa6LoIPr69RR1Xrc1liIhM4JdLrscq9MYSc3B1t7eCo41+Tpes5IMRe7Je1Lc+OtcVmtjzckmHopHyD6naQ2LnW7PUt+50FFafjBJdfGUMWNy/PpxsLHDtSQrmHXgflcQB2FdqMqrLpJ1wpbSRigGLM/+Hn5UfGjweTktoR0Qm0HVEFGtIvJR0yvup/97xqt5g2FxeI1IEjgPnVNHgUM6eNcQrYOuMhN1j4d7LFguCy2PcgRe8ub5b/XLovjTifS2mDtUw/+AdvREmdagqWH7SCAlDkTzGBIfUtn7ejoL9XH+iEE/Yl0uYGo1EPjE5Q2qJEBCeb815tjGXIzVDiU613VGnvAOSUzMwY/dNvc+pgZf6evlo9VnB2AfMvkRVWXyWlooYgEilGz5++zVf2sPYBppIJopqI4o7JF4IAddqfwWbi0dRRxbF/9CqGBDlPxe+WtWqRdHkmtk92sheVMDWQegC4KW8DRZndkc8c8b2S7GCJZ95B+6I3lzqlHcAIO6rIBbJI1XyQBtDUUBSxfk0SwzV3EojNUOZK0LClGgk3eOe3KEaape3JyFjInGKNIPCxdjnDqjPe/f6Hth5+ane56Rr9ThvPhwu3H9Z9nF561ARF5vvwovtN0yqI8DwPpKJotqI4g457BICNM6JLdhFdDI7hweqctjLWgicbY2iiAW2DABiL5jUXcWAKZlDsUXZ2mhf7eKRUo68APikYlefpGDGrlt6UVJSDri6RelMcdbU1KjJTUuMVHE8Q/Mh517T2HM1FqM3XdFrH9umEvo2qWDy5y7nOKwc0ABRCa8FyQy1t91sNgON5fezLFxUDLjc8zT86tRCnCIN605HYeXJKIPbyACc1ik4SkUWiaIEFWYkss37JzYOxzP9IIM6aVaWfvjsPYCh/wD/zAZO/WS0u4wD5pqtxkllHaPm8W71yxld0/f3ddaLtBDrZyivjAZjYbLA+4fi3MwJI5WXxtB8qFaNaXASSqKKW2n+vJnyuSsZw5D1F0Uj2wYH+EAZ/qtB4cLeOfnqvq1iwFeZwzDWy5dvW31KX7hoZ+floM7cq/u5U5FForhC4qUQU1B+DR82qoCUtLd8TaP5B+/AwbpU1p/o204HGg5WZ/wtZQ2kxEgmyzPjGLxlz/CcORu8aey8/BQTgqoa9W+REi7a/XQRO99i+9Egg37WHCVj2HQuBv3ePcHnNobmo9k/OWUaxs/LUS8tP8eB91cBjJ9nDbqRbZoippvNZqChuWHhsjuzCcrJktBQdp+33iUwW3TJCMWg4OZGhRQD0L+JJ5pVdJFMAkkQxRUKlS6kbD4fg+bzjqL/qnNoPu8oNp+Pybd9xynSMP/AHT2LQrbCdd8VjowrXQMRVoFQBE4TFRWZjEP/Di1xekobLOlfXzLyQvvmPDm4Gh++qr2mL1ZJWoNu6LMm4uSr7ddEz7dYocapHath09Cm2DGymWj47KKjD+Afmjefme58dCGnTOO421thXs/3oc8yDpjXQ2i1cLe3MlpgURdNEdMW7CIvSMRgDLit8sRY5Vj0fjsLg9LHY31mOwxKH49GGSsRD2ferwswXKR0879PSLgQJRKyvBRC8jpFvTFyO1xX6PhYDUPl/fGV2Ub+x50xIN25BrrW9QDsrdDACxga6INVp6JEE8Z5u1hj8/kYPi06B3UEknbWXbGCd4C6mq/GN0Eq4kT3fBvKiBvaozambrsuGjo7Zdv1PPnMtOdzLTYF3x+4W+KcMnNqlTQly/GnAT5YLXINGoIBGGy236jFZaxyLN92HH44nvk+4k9XgGoEq9h1RpY2oqRC4qUQUtC5PnIzzFKsLswepT+mmG2E/N1rjgNskm4Cv9RAvGNDfB3fEkeZH2QcEFjJBeH3E6DCe+sKIKylxAB8f/AuutYrx6/xTwmuhtADwjBrjgPK2FkK5iV1Y1Iyhn3X4tCpjjs/plR+GxsLM4wSSdXOAFyMTkbnurn/mWnm4+/rjK51y5Uop8zcykCs+5nqCiKNhYbP3gwAGudsiBfa4AB4c/Gi+2MMuKksLxAuukgJUE2l825LIwSBR2K5kQiiJEDipRBS0DkashtmKfY0LCbEfGTxkEs8mbolX8Aa8wt4yNzwUcbXCH8AzOpWE45W5rx53JQEXLXL2+uNzdj7UFJTHDK/3Xcb3+27jXk9398ctY9Rc3yejlaSlh7tJ3Cx85Mbfk0lySkzr6ySUoJIqrK5tbmMz0mkQc5xWOO4DuVTk/XGZwx4zczROfN7vk1zzWiqt9fxcDAoQOt6OmKezvdSNzcSRZsRJQUSL4WQrIiH7Nz8TNnGFLO6NlI//mJCLErlxvcTg+MAXy4eERajcVZVDSt3dsJJzs/gmLrizlgfG3M5TIHh/fKPdr4YTut9GQcE13LD/hvCJ25tJ1Cx8wOAahhlkbywSkoJIk3+HhtzOZiWNGVgKGNnqfcdPeM8G67/3RZdMnrJLFA3Y52g7V2wESZ1qIrhLXz1NxJB+3upK6Ao2owoSZB4KaSYIh6yYz7PyjamPtEbexrW/pHnADzjnBGW+QEGmf1tMP+FjAOaye/AX3YHqawUftsRhGfus+Fe3teouJMSgAAQEZmApNQMo8elgQH45/YzTN91U7BUpUHFgEM3n2Fka18sOx4pOLeanCG652fKtuvgtMRVbt54inP23bywSkoJIt0q6rqCNbRHbYRPaY3ohNeo/mgD7E+KCxcAmJo5XLRdd8nTFDTfSyoBQJRkSLwUYgyJh+yYz/PK5G7saVjc9N4Ubw91Q6nn1yQjizRwHGDLvcXn5nvBVu/Ff43HwbPqaGwf4Y/XGSpJcae735P3XvDJw7KYMwzPX74xuMykZAwBlVzxcVMvPcEpdn4Y9JOm5saNpzBXpM6uqNLdLqeZY3XHkwqL1v24dQXr1O3XsWNEM/hf+wa4ulFyf4wBl1SVJd/P7ude0MvLBFGQkHgpomTHfJ5XjsCm/IjqCjF3eyvEffQ3vp73A4Ll59BcdhPuXLLRTKQcANtzC+B8ZjMmZX6O/j26w9/3fWI7MadLMetHViJIOABtq5fF4mORkgJGc7xiTqB7r8WZtJ+c3ngKOkrNENkVVVLbmbKkKeafdD1WwUepaZdWmBxcjY/aMiW/C6DuM23JBuyy3CgphhkDNme2MJp88fSDF4Lr2BSoBABRkiHxUkTJzlOX1BPmtScpWf7h1EbsR3RScFVEJaTy74sRlZCKo8wPR9+FiU6Xh2Gg2d+SvjAaOA6oKo/DTtl03N+9HK+edoKtXz9sjnOVvEFqC7dWuIg2ZldwNLMejsPPwJ7UDA2siLqejnrLX8B7h0uxm4ah4n8aNJ+HsRuPKVaLgo5SkyK7osrYdoa21RY92p+VNioGPiJNI2TqlHcQdcYVoxUuYon5IoPCJZ7ZY4ryM8MDAVh8LBKlLUtheEvTfF80ZNU3jSCKCyReiijZeerSJHYL3S8MIc7qmrsYgtwjT1IET7dST9m6Ymq2ciBWKruggew+vjHbAHdZisHlHY4DqsifApdXgV1eBS9lNZRhIxEPZ70bnWZfm81m8AnEPpH/g0cqV/R9O13yyVgGYFCAN3+MmszD7N1NcVgLHwxq7qN37oyFYgNqwaK79CUmUky1WhTWZYTsiqrsbpcdK5uKAfMP3MGqED8wmGFyh2r4/qDaEqONJkJoV6mvBcVLdWEMuKL0RvfMuQDUn9uo1pWw6OgDyTnMP3AnW9/DkhRtRhAaSLwUYbLz1FXbQz+EOLeezjXbf7T6rElP2WLJt+LhjP0qZ+zPaIqbZb6BzcuHJu2bA9BUfgdnZKNxRFkfizK74zqrxB/X7qtP9TKfchzgLX+BM7LRiFSWxReZI3EdlQQhrLrZeLUzDzMAa05FY1BzYSZWTdZeQ0/uMqgz/WoS5gHiIqVFFVeTrRa6glYGYPA74aU7v/x06M2uqMruduvCo0xa9tFFBWDw+osA3lligqsh8b8MrAp/KPjM58mXGxUu2onoNNdRNbfSBsWLCihwKxlBFBVIvBRxsvrUlddP51l9WjaUfOvl4AjYxJ8ADn4NlvzAJCdbjgPam11GO/llXFb5wsPiL6w4kYLQA3fwo9k50RsOxwGVzJ5ht3w6tilboPLwDaKOwMaOLU6RhnXhUaKZgTXIOGBIQEUMCvDW840REykz/1fD6D61hYhG0K4Lj8bq8IdYeSoKq8OjeGtNQTj0Ztc3IzvbxSnSsEqkiGFWUTFg3v47fFI6DfPky/Gh2UmDwuW+yh1jlWMh44BFfesL8hMZojBYyQiiqJCn4iU0NBTbt2/HnTt3YGVlhWbNmmH+/PmoWrWq5DZhYWEYNGiQoM3CwgJv3rzJy6mWGPLayS874kgs+RY/J/sOQNUO2HPyX7z9eyZ6yE8bdeoF3uVYkUeCrW6A6pm1UBt98EDlbnSbnmYnwV2cBjQcBNj7IU6RhgvRSeA4Dp6OVpLHJiyBoI8MwBCJJSZAWhhN23lTr6/YPnWFyOrwh6J5SwrKoTe7vhlZ3c5QXSsxpJILQtOu9eb+UpNRXfbYoHC5q3RHh8yf1FWee9RG57rl+PeNFXucFFyVrC4EYSJ5Kl5OnDiBkSNHolGjRsjMzMRXX32FDz74ALdu3YKNjY3kdnZ2drh79y7/WqqEPZE98tLJL7viyNCc4hRpGHfgBVRsJH7I7IvWskv4WH4ENQzcSDRwAFqY3UCg/AaSmI3aV8XANhwAXPkNuPIb0mU2WPn6f1iHzvx7PRp4YMflWF4wiJUr0BuTE9ZUEsPUKsZS+9QWIlJC6Hx0coE69GbXNyMr25l6HgG1CFw5oAGGbLioF7auy3R5mFHh8oKV5oXLzpH6n7e7vRUmd9AvW6GhjocDAPEoqeKYs4cgckKeipeDBw8KXoeFhaFMmTK4ePEiWrRoIbkdx3Fwc3PLy6mVePLSyS+74khqTto343g4Y5OqPTap2qM2HmCWWRjqyx8aFzEc4MylgjEYFTAaLFSpmG6xEaPYLvhlrAIDsP1SLP8wrpmTsVIDjAGvM8Qq4bxHz19F4ga8qG99dK5bzmCCMinrVyNvx0Lp0JubaM7j5G3XDfbTiOq21d0wJbga72AuhhsSMdBAQkVtiwvwPjpNzLdIrGwFoLbM6VrTxJLiFZacPQRR0Mjyc2cKhQIA4OTkZLDfq1ev4OXlBU9PT/zvf//DzZv6pnOicONury4amBsCSXMz1kYG4CZXCT0yv8U+ZWOjT84aOE79pxExpvR34lJxsdRQ/CJfhFoQOlxO3nYdaRmZBv1xTBUIHzaqgPAprbFpaFPsGNFM9JiTX2dgz9VY2JjL9d7XzjUzuUM1/sutuVFrwr3l7+7CUlaxOEUaIiITEKdIMzrnwsiHjSpg4gdVRN+bGFQFm4Y2RfiU1rwPkCHhAgBtZJckw/cZA56rbHnhwgHoVMcNc/fdgn/oUfRfdQ7NQo9i8/kYAOLXMqB2Dgb0C45qC+Wvtt8osp8JQeQ2HGOm/uznDJVKha5duyIlJQXh4eGS/c6cOYP79++jTp06UCgU+PHHH3Hy5EncvHkT5cuX1+ufnp6O9PR0/vXLly/h6ekJhUIBOzu7PDkWInfIStTL5vMxoqn+NW218QBt5FfQWRaBSrJ4kywrjAExSmdUkCea1F+zzQlVbUx5O4wPrzbkN6GZq9gTs7Hj1z5m3X1olrB2Xn4qOCe6TrkcB0wJriaonROnSJO0ihXmDL1ZYc/VWIzedEWvfXE/teUqTpGGi4+SMXrjZaM+MuPkf2FcqR167QzAWxWHKhl/AFCf6x713y8rasMBiJjaBu72VoLPVRPVNLyFLyIiE9B/1TmDc9k0tGmOcjIRRGHm5cuXsLe3N+n+nW/i5fPPP8eBAwcQHh4uKkKkePv2LapXr45+/fphzpw5eu/PnDkTs2bN0msn8VK4kQoLNnQzF7vpatpeZ7zl37v5+ySMMttlNNkdABxUNsDMt4Mw0Owghsv3ZUnEXMr0Rk/lXMk+/Zt4YnSbyjmqSxWnSMPF6GSM/vOynqVIBmDHyGZ6eWI0JRA0yDkO4VNaGxWIOdm2MKERJqM2Xha0awSEdoFNU6iNB9htMV1wbTAGKDkZXnzxFBej1ZmhyztaGUxut7ifOvIoKiEVNuZyvYg2sfOvjYwDFvath4beTkXq8yAIU8mKeMmXZaNRo0Zh7969OHbsWJaECwCUKlUK9evXx4MH4vkRpk6dCoVCwf89fvw4N6ZM5CFShQqbz1Ob2ZvPe29m10Z3KUpjufB2sUbb6m4YHFgRNcrZ4xflh2iW/iu2ZTZ/b4IXuSEwBhx62xDxcMa8zI/gn/4rnqicTIpW4TiggVk0Is37oxUuivbZdE78WoxTpGHKNuHxT91+HXuuxuotC7jbW8HJ1lx0/iqAvwFefJSMPVdjcSE6SdIXxhiGQsGLCpvPx6D5vKMYtfGyYCmPAzCvp7CSt6lcRyWEK2u8z/XCgJvK8qjy5ndcfJQMP29HdKpTDqkZSoPjHrkdz1/j3ZdGICYpVa9khvayHof3vlmapc7Rm65Ifj8IoiSRpw67jDGMHj0aO3bswPHjx+Hj42N8Ix2USiWuX7+Ojh07ir5vYWEBCwuLnE6VyEeMFSo0JYRXynKhCZWNhzPGZ6qjk7xlz7DM7Cc4II2/GTAGRLMy2IFW/JjxcMa+dkcw/NVy4N+VRo+D4wA5B6yz+AkvmQVmZoQIxmMALj1KRqc6wmNYG66fB0b17sYkZoWRiqDhAIQ/eIH+qyL58TiIL2OZUgKisGboNRVDmXU1n7sx52pd3JCIveaT4cy9fn/tANjAgqECMGrjZYHl0FCk084r72tcSV3jLaq4YkHfupBxHBp4qaOVLr2zIun6vxSGmlUEUVDkqeVl5MiR+P3337Fx40aULl0a8fHxiI+PR1ra+6fLAQMGYOrUqfzr2bNn4++//8bDhw9x6dIlfPzxx3j06BGGDBmSl1Ml8hEpp0VtNE/8Ys6jUgnd4hRpemPHwxlnVTXwVZV9mJAxDNeUXriqrIAv04ehdcYCwT7bVndV+4Z0/AH44hbgN8hkK4y9LB0/W6zELfMQdMdx/j1di0mcIg1rwqWTqIk5ZmqeyHWXtBiAJcciBXPUdvLU5vuDd01y9hwS4KPn6FsYb5Bi14WY1UmD5ryKOTpr0G0eKt+DMxaj4SJ7LTj3Mg6Ya7YKbkgUjA1AYDkxhq5VS2M1Gr3pCkZvuoyT917A3d4Kjjbmep9pUbOIEURuk6eWl2XLlgEAWrVqJWhft24dBg4cCACIiYmBTPZeQyUnJ2Po0KGIj4+Ho6Mj/Pz8EBERgRo1auTlVIlcxJgjqlgae92brpzjcO1JCl9qQNvx1NDyhr+vs17IscYhMk5RA+tOD8LKk+LiYUybyu9f2HsAXRbgduVh4P7ojWqyJyaFY1tzb/GzxUp8zf5Ao4xV8PMW5vow5clfLPeKJvz8n9vP8I1I4jpjGMvnomvJGiaSBbiwIGZ1A9TLQYZQMoYnyWkYHOAjmoWX4f3yzFD5XnxltknyMzfjAG/ZM8SrnPmxoxNeC9IEPHjxn2iSQQ3aVi1DRSiLukWMIPKCPF82Msbx48cFr3/55Rf88ssveTQjwlSyW//GVEdU3VwwJ++90KtKrR3CyhjUBSUZ0LVeOckf8zhFGjydrPmCh9bmMqRmKBGnSIO7vRV8XW1F592zgYdoErmUUmXQ/+33qI0HGFpqP7rIzpqWUwapeGD5MeTxm9RZgt9hShI1qRuTu70VKkrMX7D/d//qikGpm53YjXNNeBRfkLIg0b0OxeY6ddt1wMTEdCN1nHi10Qjdfw9sxFdmGw1+zpkMiFaV5V9rn19NviJvF2vM2HVTdF66Vq2sCPLCbBEjiPyCahsRemQ3XNbQ06OUBUbTritmpCwUmsq7Yj/m2lEkMg7oXl+YDXdycDV1vRoRBvh7ibZrxMZ1Vglj3o7BXHyE9WbfoYrccDg2xwFyqMA2fQjOyRcI2QPYe4hmIO5Wv5xeyLPUjcnGXG4wNFvbMdXUm112qzfnNWLXoaeTtd5cVYBppaONMCSgIobHz8Ywi50G8/aoGPBV5lA8excqL3V+Nfl25h+4A9W7fpOCq6KOh4NemLox60peZsUmiKJIvoVK5xdZCbUi9MlJuKxUnors5KaIU6Sh2byjolE2mvG0Q6cBGAwzBWDQ4jGtU3UMDqwo+p5uXg4VUztyriz1I2rLHpkcXg2/QUCLiYC9h17Yt1TuFW3Lg1iIr5zjMKlDVZR3tAJj4JeppMJxxcYF9M+d7meuXePJz8sxz2+eUtfh9hH+euHIhsScqXAA/qkQBp/nf0sKF8YAJQMCMn7lc/z0b+yJ0W2Nh8OL5dsR668rOItijh2CyC5ZuX+T5YUQkJOn8JyuzesuEUwJrqZeKtJCznGwNpchIjIBPi42vCgSS5evi6H3G3rrLxlpqOZWGiPb+MLV1gJ1ytuj+9IIxDNndH0bitp4gLmlVqOWPMZ41euL64CLYUDXRXBvMIAXLbrHomHz+RhM2XZdEEmkfQgyDtg+wl+w3CVmrRAbV7ePoWUJsXnM6ym0xokt7+SkJo/Udfg6Q6U318EB3liZg0rSHAccNxuDCs8SDJYAUDAL1MtYJ2jf+O9jjG5bWa+/XuQTA74/cBdd65aTPB9kXSEI0yHxQgjIiQDJScVqsRvq8Ba+uBqTgv034vl+dT3t+Sdv7RDVpNQMo0/gGiuFbmE8XX8X7Rvvj4fuYtulWEFf7WO8yVVCRPudqC3fB3Z4mnEBAwbsGQv4tsXme0rJ5TlNLhjdSCJtVExYM8mUZTupPuFTWiN8SmvRJIBi85i6/To/ru5np7tcl5UsvZpzr4kK0r0Orc1lAp8mzXW5OjwqSyHQAFDP0x5DAyui2db6cODeGBQuZzMro59SPxkmIB4On92HgLysOUYQxQkSL4SAnAgQIHtPj1I31GpupXHwZryg76WYFP7/muR2nAnOmtpm+K71yuGf28/w/GU62lYvI2m5EGPbpVh0rO0myMWhPsYx4Gr1RMryYNi/NrKUxFRIfHwbU7alC3J3TN52HdbmcjT0dsKF6CSjSyEyDrA2fx+pZ8oN05hjqO7npcmbo4uKgQ/V1f3stMVeVnKS6Iqgep4Ogs9bTLhq/KMmi1jpjHHtiQJttteDJZcuLVwApNuWg/ewU+j/z31s/Fc/8aDY0iZFCBFE3kLihdAjp+brrD49St1Qz0cnGxUlDMYLLE7rVB0d67jzc3K3t8LHTb31+umKKCkGr1dn1JVxwOQO1VC7vP275REPOEy+hhd3I1DqyDTYv7ggbonhZDj+ojQY0vXe0iSq69vY0/AkoL4xdlsSwS/hGLthxinSkPgqPUs3VR8XG1GLloyDQcdqbZSMYd+1OHTS+gx0EROw2sIFEBGu268D7F2IMwA/LwdcfCTcxhC3Sn0CC6Y0KFy4D76DZbNRcAfwYSNPPfHCQe1npG0xSs1QwsfFhiKECCIPIfFCiJKf5mupm24jb0ejYcXGkHOcQLgYIqvZV1UM/BKUjAMGB/jg0wAfuFdtBlT9B1DEAid/UPu6aOA4/FtrBsYfSjA47p/nHpvkiMqgtj5VcyuNMnaWaF7JBafuvx+7W/1yAIC5+25h1ako/kavyWeiWUqLSkgFAFFn4Skd9a0a3et78H1N+Yy+3Xcbc/fflqxhldVzDwhFKwOyJFxum38CC86IcOn6K9BgAID3ViFtOABDA32w+8pTzD8orEytsQyJLcURBJFzKNqIKBRIRVrotmuHFYslt9MmO/4WxiKWjCHmzApFLPD4XyS9zsDRVC9MPJRoUnTMsMCKWHnqocn7BfTPhZQAkgH4tX99PElJ4/PpaJ8v3SUc3XOiHY1k6DMSm6dmmU97fytOROr5IuUVY7AFX1jsNCxchhwFyvsByP51URSLWhJEQULRRkSRQ2qpSqx9QlBVQXI7saUeGYAdI5pJOuKakvlXcyPefinW5FBchvc+HgDe7c8JJ9P8MGX7dbB3KeVNoZQZZ3IYsFQfqXYV1JYL7USA2r5Guks4umj70kh9RvuuxeHbfbf15qNbw6qaW2nMP5g/wgUAPrK/Ak5/xU49PwZcazAHqele8HmX2DA7ViGgcOTKIYjiCokXotAgtVSl2y6W3G7d6SisPhnFJwOb26OWQLisOBmJeQfugBmJgPmwUQVUcyuN89HJaOTtiLqejqjiVprfVsrCoY2SMawLj8bq8Id8jo/s2DeX6tQtyk3kHCealdZUXyMAuBb7vtij2GfUqY475u6/bXCsrOxPl8bejvg3Olnyfdm78y4ILweQ5BWMMneXCSwvjAFvGYeWGYvw7KwzVGfOmVxwUQpy0CWIvCNPCzMSRH7gbm+FrzrWwOmpbbBpaFOET2ktECYrTkQidP8dvSd+sUKFm8/HoPvSCHy77za6LY3AD4fuYP6B99syqMXImDaVJOcjA3jhAmRPuMg44xYXU3PjiTG3Ry34eTnqFSnU9jUyxvcHjBd71C70KIP+nDX7y+qxyDgYFC5j2vhix4hmmNeztmBsBuBk+aF4xSzef6YMeMPkqJLxB+LhrGeJAtSO2VmBHHQJIm8h8UIUG9ztrfTCfeMUaZgn4kshVpVXLLHYkmOR+uno372WusEPCfTJliVBMxzHqcsVGLuh58Qq829UEr9MpqmCrG2x0m0fFuijN4ahysaaCskrT0UBnNp/5/TUNpjXU39/ZewsTave/e5fOcehbyPxaCzu3d+io5HotjQCMUnCitAMatEVWu8IfknvhttKD/yS3g3VM37j3xc7Rg9HwyJkZGtfbBraFLtGNhMV0ARB5C60bEQUa6TylGhCfXX7mio6Fh19INou44BOddyznDRN27eFMSAs4pHgfe0yAIaKC5rKtkuxGODvZbKvEaCfCE5qWcRQoUex/UVESkdeaeAA7BzZDE+S06BiDClpb0X7aZ9yjfjURckYmldywejzfbDobR++XfZuR2LHmPDqjeTcpnY0nPafIIjch8QLUaCYmkY+u+nmpao4Tw6upjeOj4uNpH+KqT4Pmqy3oT1qm5QzRoOhbhyAIYHeSM3IxO4rsQZ6vqeBpwMuPU4x2OdCdDLqejqa5GsUp0jDkAAfrD713q9IE2L9/OUbPreJlIOrtvOq7v6kcsno8tPf93DqfgIf7p1d5O+SC+oWTZzboxYA6FU3j0pIRQUna705agSVWDVygiDyFhIvRIFhavXq7Fa5BvQjiGRQCxexJ2Wpekoc1JFL56OT9aJndNE8qXu7WGNRv/qIiEzAn+ceS94gZQDaVS+Lv28/kxyTAVhxMsqk49Vw+XEK+jf2RDNfF6S9zcTErdf1+qhMdMbRPf/DAirCubS5IFIJgEEHV0POq+72VpjXszYmb9OfowYG4KRW/hqxpHmTO1TDvIN3DIpP7Qrk8w+qhQsH4MNG5fkswC2quOLSo2ScfpCAefvvgL3bvkcDDz7yTBMST8KFIAoGyvNCFAimVq/OSZVr3f2ZkiwsTpEG/9CjgjaOAyKmtMHzl2/wvyURktvKAIT2rA0Agpv95OBqqOPhoFczKDrhNa7FpmQ5rX1W0CTPWyVRuLBnAw/81KeepGVL7PyLRfFo0Hw2J++9EAi0IYE+GBTgY/DcX32cjEX/PMDRO8+z5M8j496Hxa84GSl6Pke28kVAZVeDFcg1ggSAqNVMO9JMNJ8PQRA5Iiv3b3LYJQoEQ0sL2elnDDFnXgB8VWdN1Iwm06w2jKnr+KRmKCXHl3HAjpHN0KKKq56/x/cH7uqJJnd7K3i7WGN+LiRm4wDM6VZT9D2Nv4nUMsu2S7H48dAdNJ93FP1XnUPzeUex+XwM/77Y+VdJCBdA/dlcepTMF08cFlgR4ICVp6L4sXXPOfA+yuufO8/BcUD3euVMXhrSLlA5vIUvRrbWt6otP/GQ/wykfJsYgKnbrksu92knRNTk8zEWbUUQRN5Ay0ZEgWBq4bq8LHAnthxlbMlDqs5PaA/1EkJEZILR4ogaK0fiq3RJn5hRrX1Rzc0OozYZd85lAJyszSX9clQM6FTbDfuux+u/CbVTK9PqO3W7utxAXU9HRDww7kyrDccBozZeFvilaI+tXY9Is9Tj4WglqFytYsCOK09N3qfu9ZCRqdLro/0ZSPlBAerkfaaafbTH1LVcZddHiyAI0yDxQhQIplavzmmVaymkKlmHT2ktuT+pp2ztTL4GxdaTi7gcfgAzr5bGVVYJMk46fb+nkzU61y2HWEWa0WUljQNqaI/amLrtOnRv3XKOw7AWFSXFi+7+NQUfpwRXw5Lj+tE6UuguJ4kdl/YitXZtqKyi68OiLQxXSyyRvc54i4jIBFx/okBLdhGdzM7igaocdqpaIB7qZHtiEUfvmkSP6VpsCmKSUgUiuHt9D+y4HJstHy2CIEyDfF6IAiUrvii5WeAuIjIB/Ved02vfNLQp/H2dRfdnbBsNonWanoSCXd2oFisMeKpyQBossDvTH7+yPno3RY3vyIXoJIzedEVvn5qbt6Ag5DuBpZ3dV7dOlK5TbHAtNxy6GS9qhZABekJIl2mdqr+rLv0aFqVkmLbzppEtcofF/erD2dZC73qQ+ow0tMJF/Gr+K2y5DD7/C2PA5Myh+EvZmvd54f11OGBIQEUMCvDG7itP9cSWIf8fDVTjiCBMg2obEUUGU6tX53aVa2PLUWL7M3UJS6/EAPcQ2LdRkITOQ54CAPhCthNjuZ24mFkJx1QNsEMViHg4Q8kYvtt3C/uu6VtL5ByH7SP8se96HFadjMKqU1FYEx7FP+F/1ak6BgV449KjZKgYQ0NvJ35eLaq44sitZ0h4lY421cqgrqejYPlMG2PCBQAuPErGd+9KAGgSxOX105Cc4+Dn7ai3DOfjYgMbc7noNgOxF1PN/4Q5p9IryMhxQKjZaoSr6ggijqITXsPaXMb7OtUub683rimh8FTjiCByHxIvRInElOUoXb8FU7dZF64WFBq/jv1V90EquTzHAXIAjc0eoDEeYBLbAoXKAsdV9bHmWkcwCMsQyAA+K+3qd/sA3i97aW6+2gUrtZcu3O2t8Im/t2BMjdjqtiQiy8LjwI334krj56JtFdK1SmhXlZaiVVVXnLj7QjK5oPY5165Grc6HI8wEPAZbMMZ8J+QcJKtIA4CcY6jAPRPkotE9h5M7VNMTr6ZaXqjGEUHkLrRsRJRopJajDOWWMWUbbabL/9/e3YdFVeZ9AP+eQQZBcQREgQRBNKkUNXxDS0F9Vs0yjS03dzcz17LUNtldRbey2m1BtzafNS3L1vYllG0T7cm0XM3MMEXU1SwoWAlFMFAEQ2SAOc8f44zzcs68McOcGb6f6/K6Yjgz3B69PL/u+/fyNzwSuNvptYkicEHXAw0IwX910VjfNgsL59yP6ckxsscjrz44HCnxYZLl5dueSDVrJmfJ9LirPTsov595G6616GSPkQxHPicrL1v1irHnd/feZgy+pMqiDfHJYJRim3oVugiizaDFoE0UMF67Dv/K+rHx+E3qHi6bNghrdpWYBa8ArCaRbz9+3vzYkDkvRHY58/xm8EJkwZXeMlLvMRiCUrzf9dl2dYUF9MGMThDQGjYQX8U/jPsOxUtWPsn1dTF0DzYNxqSqZMprr+Kj01VWIwocIVyPemz9o7LjeldaqRwce9bPGY7pyTGoqm/C2Ox9Vj9nCEqxpetqdBMbHQpaAP09WdH6KIbPXGIMMmzlN8X3CrEKXi0DWnfnaBF1Bsx5IWoHe+3tHX2PwVfCQDTd+gBCvvpnu9alP2ISEVD3DYZdWolv1cD+1mRswwQc091snIgsV21jOVX7clOLcefDcnfpb4fsBy7GyppjlcZOtfYCF0Dfk8VQ7eWsc5f1FV9F39VZ/Zy/d/k97gj4Sr8OBwIXUQSaxQBsHfs+xkUnGHODANv5TVL5UJavuTtHi4jMMXihTsPR3huu9JaR6x1iyFEJGXkXcG4hcOpdHCr+DnGXChCjuuzw7oAlQQC6CMBk9UlMxkmIIvCtLgp/aPkp9iPF7vvbRBE5u4qtAprxN0c6NKByzuhYzB4Ri50nq8yHIdr5uYb76MwQTFM5u4oBEWaTwlfir3hY/REC7eS1GNco6n+//6udiT/jAWB/PYATVrlBrpTos78LUcfgsRF1Cs7OR5Isd7aTt2D6HtMSW7l2+0NQikcCPsRo1deIDqhv97ESoH8wXxJDIIg6qNGGcrEPXmqd7VBAA9w4FpE7AjO4c2AvHCytlZwjZMo0Qdf0Psod+zhjCEqxTf0sujgYtAD6dexpHYbH2pZJft/yeNCZ45/2zOAiIua8MHghM67OR3Ilb8Hee+RyKd6b0w+3FD2NgLNHoGptdOqBbI8oAnViMN5ovdusIZsl03uSV1iBrG2n7AYnthgmT8f07ArV9UZ6hnuSV1hh1lXXWfldfothAWecymupE7vhLm2O7O/fwLJvjyPcNYOLqDNjzguRCVdyWADX8hbsvUfuSCqmXyJCkrcbg5tZ2I97Aw9hmPAtNMK1dgUyggCEC03IUr+L5eK7uKYLQB1CcbDtVvxJ96DxYb5s6iDj2sffHNmuhi0qAXg8rb9+cvP1z5k5LAaTbumNuPAQrNjmfOAShYv4ueojLOjygcNHRNdXgy+Sn8PPjg5EG/SDIkXID5Z0pazZ1b9jROQaBi/k9zw5H8lZ9nIpDGvNF9OQ35IGQN8VdlWXzYgR6hAgiAhQOZSPKkkQgOCANgTjMh4IKMD9YgHKdRG4gAg0Vf0UVfWPGYcXtmdLVicC6/eXme3cbD9xHtudmFlkKidgIx7o8ilUTuy0iAKguncDMPynSAVwcPKNXTHTqdcG7Rk9oaS/Y0SdAY+NqFMwy0cBsHxaEh6bYD19uKPYOl6yd2TzMD7Ao4E70Ueo189HcuPxklYMwNneE3Cw+xQ8Vxzr8mc5MlrAEbOwHznqN6B2Ihm3WQzACu18PLAgy+bxj+HPIEStwlWtrt1lza7kSRHRDcx5YfBCEjYeKDNW2CgxobKqvglHyy9BEATEhgXjXF0T9nx1weZuxSzsx7zA3YjGJfRS/eDWQKZFBK6KQTgnRkom/co1sjMEh64OXQT0R0R71L8ym0HkyJrzWscjq22hMd8EQIdW/7C/C5HrGLwweCELSk+otExgFQDkZAxBbHiIzUGDpqJxETvvC0J42QdAyfvGdv3uYAhmmkQ1yuMycHXiiyituSLZQXfO6Fj0i+hmdxq2KcNOzSzsx4rAdxCpcqzJnH63SMCm1un4u24KqhFhDJ56hgRKVv+wnJlImRi8MHghC45OhPYGubJhlQDkPzEW964vsPsZKgDZGRY7SfteBE7mAUE9oLtwCoLoniMmEUAbAjCw+e/tqkYymDMqDj+7NQDxuXciWGh1vOxZCMR3w36Nhtsfw1WtDgdLa7D+kzLj9y13hgzVT4YkYiXuvhF1Zqw2IrKg5IRKueRYnQicq2uSPZ4RAGTdlYTkm3pKH1NM/C0w8bfGXad/iM8hJfBbiIKIoHbkyggAAsQ2HA98BMO0f3HtQ0wMKPodbjn5EQSVY9eLAITY0VDN/xiGMYxV9U2Y82aZ1XWmjI35rn9tOcySiHyHg/9cEPk2Q5VPwPUndnsqS9wtoVc3yeMdfbAlylb9CALQMzgQqYkRkr+PqvomFJTVoui7OuhEYA6ew6CWd5CkzcWM5heQ3zIGDeju0u6JIAAa4RpmYb/zb75uFvbjS/VczOvykUPHW6II6HTAjhF/B+Z/bPa9PV9V262OUgnSAU157VVnlk1ECtAhwcv69esRHx+Prl27YvTo0Thy5IjN6999910kJSWha9euGDJkCD788MOOWCb5udkj43AwKx1bFozBwax0xRwXRGuCkZMxxOwBLlw/0hgRHy5bHmzYOaiqb7L6Xl5hBcbl7MOcNw9jSe5xq+DgFAZgaduTSL72BmY0v4DPW25GTVs3tOrgcDAjCMCUwKOOXWwiChfxpfph/CnoDXRXtTic23JFVKO/NhehiaPMvpdXWIFVO76y+f4AQcDyaUlW91Ipu29E5ByPHxvl5eUhMzMTr7/+OkaPHo21a9diypQpKCkpQe/eva2uLygowIMPPojs7GzcfffdyM3NxcyZM3Hs2DEMHjzY08slP6fUgXmzR8Zh/M2RKCqvgyDArBtt9n1DjImnlqQaoRmGHhqul0vcNRxHncIA/LTtOaBN//pK/BWzAj9DuHDVZim2KAIftYxw+PcYhYtY1/0vGNFy3KkKomYRWKF9FPlIAwCEqAON3zf8Xm3FW89MvwUj4sPQqG3D8qlJWLO7xKl5RUSkPB5P2B09ejRGjhyJV199FQCg0+kQGxuLJUuWICsry+r62bNno7GxER988IHxtTFjxmDYsGF4/fXX7f48JuySL3G08mXltpPIPXLW6nUVgM9XTDR7r1xysisexgd4MPATRKIOPVXXjDsXogiUi72Rrl1r9zOicBHPdvkrpgYcdbzJHIBrugCs1M43Bi0GOxaNRe8eXXGmthGXGrVYnHtc9nNUgr7yyHR69vJpNvKErmNFElHHU0zCrlarRVFREVasWGF8TaVSYfLkyTh06JDkew4dOoTMzEyz16ZMmYLt27dLXt/c3Izm5mbj1w0NDe1fOFEHcHSQX1V9E7YWWgcugP5BbPlwlUpOVgnXu86aXCfXSO6WqO74uvoHAMDbuBtvt9wNQB+ErE04gsjGErz6/TCroMLwmQ+Pi8dfPi8HAPw14EWM73LaqZ2WVhEonfgm/n4pCfkSAdvOU1XY9NkZ6MTrgx8hP8lgxtAYY+AC6O/Jml0lNkvkOWCRSPk8mvNSW1uLtrY29OnTx+z1Pn36oLq6WvI91dXVTl2fnZ0NjUZj/BUb63pXUKKOYnm0Yyt/RWpuDqDvpyLVJVgqOTn7viHIyTB/TSoHRCXAGLhYuoAI/CdpKSZ9/5Rk4CJAX669YHx/CAC+Uc9xKnDRicD7raOR1LIFPYffgyWTBkqu780DZ8yOxAyvS9lx4rzszCEpzvy5EJH3+Hyp9IoVK8x2ahoaGhjAkOI5M8hPbidlycSBsp9vyKGx7PZq+VrPkECzlvZjB0Tgs29rJT9z7th+yLHTNTctugXd338EZV0/dLivjAhgd+sIPN86FxcQgaxpNwZEzhp+E947Vmm8dtyAXlbrEwG8MOM2PLvjtNUOjGQHYAGySbpyfy47T1ZhenI0j5CIFMKjwUuvXr0QEBCACxcumL1+4cIFREVFSb4nKirKqeuDgoIQFBTkngUTdRBn+s7YG+YoRyo52fI10yAnRK3CrA3yDfF6dO0iezwThYtY1mULem8quJEc7MiOS9ee+L+x7+LJD2uML+XsKgYE/ZFP/vFKs8s/L62VbD4X1k3t8CBJnQgc+KZG8ihI6s8FAH6/82v84cOveYREpBAePTZSq9VISUnB3r17ja/pdDrs3bsXqampku9JTU01ux4A9uzZI3s9kS9ytu+MJ8u8ozXBSE2MQKO2TfJ4yqB3j66S8cjGgDU4FLQE93UpcLhfS4sO+DRlHaoeL8YvTQIXQB+YZH9YjHV7v7Vaj04EFoxPMN43FYBlUwchpV+Yw8nAALDivVOSR0GWfy6WP5tHSETK4PFjo8zMTMydOxcjRozAqFGjsHbtWjQ2NmLevHkAgIceegg33XQTsrOzAQC//OUvMWHCBLz88suYPn06tm7diqNHj+KNN97w9FKJOpTc0Y4l08oXT4wyMHx+k7ZV9hoBwJCbNFhwZwLe+OwMACANRXhT/TK6ODHxWRSBtdqZ+DMegOpz4PleF2R3THKPnJXcZZk3LgER3YOQcz0Rd/XuYvQMCdQPg3RwnpIOkDyiA278uew8WYXf7/za7HtyR3tE1LE8HrzMnj0bNTU1ePbZZ1FdXY1hw4Zh9+7dxqTciooKqFQ3NoDGjh2L3NxcPP3001i5ciUGDhyI7du3s8cL+SV7fWc8WflSVd+Evxw8g7cO3qjckXPf7Tdh1oYC6ETgEeEDZAX9E4FodXjwoygCZW29Mbl1rfE1HYBndlgPdjR7n8l/qwRg2bRBAIDV16eDAzd2RNb+ZKjkZ0hVI6kgn/cC6P9cpidH4w8ffq3IkRJEnR0HMxIplKuTsB3pUZJXWIHl751yaB2zR/TFu0XnoBOBQvVj6CVccar0uVrU4FHtr3AKAxx7kw0qAfjFHTd2f0ytnzMcS7Yct7pfy6YOQs7uG8GOYWK3IxOm8worrHKNmPNC5BmK6fNCRK5zpiLJQGqnZvzNkWYP6Kr6JmQ5GLgAQIi6C3SivmGdo4GLKAItogoZ2ufcErQY6ERg02dnJJOdb+8XZtaQzjTYmDEsBse+q4MoAinx+u7FjuxqOXq0R0Qdi8ELkUI5OwlbqkeJIUgRceMBHaIOcLgyBwA2F5QDAB4I/Mxu4CKKgFZUIVv7E7wNfXM7W03kXKED8Ogd/fHWwTNmOyIHvqkxa0i3cEJ/jL85EgVltUjo1Q3Tk2OMnyHXz0VqwrRSR0oQdWYMXogUyrJE2lBZI/cgldqpMf3S8IB+7t5bJd8vXI8y5AKN73S9cGuAdKdfUQSuiQJWahcYG9gZ4hx3n0urBGDeHfGYd0e8cUcEgNUR2/r9ZVi/v8z4HtOdFVd2tYhIOTpkqjQR6f9vv6Cs1qlS29kj47Bs2iAIgn7HYfXuYuQVVkhea9ipsaVNFBEeopZMtH1+xq02A40NbbMkJ06LInCw7Vbcon0H+UiDCsDvZ94GQXB/4GL4eQe+qTGWeEdrgmW7EBtYljlL3Ssm4xL5DgYvRB0gr7AC43L2Yc6bhzEuZ59sAGKpqr5JsrLG2R4lBqrrE6tzMoYYH94qAVidMQT/c2uUzeDnFAbgX213GtciisDZtjDMaH4BP299Wv9ZAH5xZwI0wYE2g4n2EGF9DxJ6dbNb+WQ6FsDZPjtEpCysNiLyMGerhkwrYM7UNkpOiN6yYIxsz5eq+iYUldfhya3HrQKIFXcl4bHxicbrLBNRTatr5AxBKUYGfIPCtpvNknHnjIrD1sIKYwKs5SBIW6S62tpjuAeG+/V5aS3Wf1Im/zMA5JtMpE7o1Q0AmIxLpBCsNiJSEGfyKywrYAzDE53pNRKtCcbdQ4PRqG01y5dZPu1G4GK4zvLnG6prjn1Xh8W5xyWDj1MYgFNt1hVEWworzHaInGh4i+dn3Ib3jp3DibP1Vt+TCoQM98DyfqUPisQnJTVWnwHoj91mrtePPzBNYGbpM5HvYfBC5GGOVg1JVcCs2VWC5VOTsGZ3iVNzjQDrMl8AxsobQ8m0VI8TfYO2YPzQ3Iqs9045tHsiAFb5MM5spMg1q5szOhZLJg7EgW9qrPqtALC6X59+Ix24SK3JVoURESkbgxciD4vWBFtNR545PMbqgSm3Q5PctycOZqW7dLxh2F3JK6wwBiIC9B1z849Xmu3wDLlJY7OxnS1PpCUaK3vcqVe3IBwtv4TxN0di2xOpKCyvw8j4MAyNDUNBWa3k7CNnSrNZYUTkmxi8EHlYVX2T1XTk7cfP49dTzMuebe3QONtrxHRXBYDZDooImAVSOhHGmUCmje1WbHNs10UlAEnRoQ6vzRl/3lcq+fMMa5S6Xw+M7IstR6RLui0Z7q/cLpQj3YqJqOOx2ojIw2zlvJhyVwWMZWXTur3fOrwTYThKKfquzuEEWv3ujeBUjkt7GNYIQPJ+PTlpoOxaBOFGLo5pczupSjBXK8SIyPO480LkYc50ym1vO3qpvBlHdyEM2q5nxzp6/KISgK6B7vn/oLsGR+H2fmFW05yl1lhee1X2fuVkDDHLkVk2dRCS+/Y03nO55naGwCgpKtThDrxE1PEYvBB5mGWnXHs7Ku1pRy/XZdeZPBAVgNhw658v9xk6EfjFX4vc0pDuo9MX8NiE/voGdzY+0HQqtK2qKbkg0PC1VN5MmyiisNx654n5MUTKweCFqAN01IA/uV2ehWn9seGTMskAw7KNvwhg58kqq2ttBSeSn2tn3ICUNlHEzpPVdt+0fFqS8R7aqpqyd5/l7tfI+DCnS9SJqOMw54Wog5i2s/fkz7DMA5k5PAav7S8z7sBYkgpSDJObTdkbPWB6TYAgIOe+Idi+aKxT61cB2HTwv1ZrMvxolXC90d4Efb8aV/JSTMc0yOUZDY0NYwdeIgVjh10iP2TonhuiVmHWhgKbybcq6Bu4WXr0TvPJzcumDTKb2mwpQBCw7YlUXNXqjLtLBWW1kh2C5Ywf2AsHvq21ev3VB4cjonuQ2a6VXOfibU+kolHbJlkhZNnUztCkTqrbsOFnsAMvUcdgh12iTs5wZCKV0wHcCFgCBAFTbuuDD7+sNvt+gCBYTW6O1gSjZ3CgMXfH9FjIdMfClNSxjC0HS2utcmsCBAEp8WEO98WZuaEAomjdQVcqmdk0CVcqOGlP/hEReQ6DFyI/JpfTYdghMezMWFo29UYPGtOHt+n4AJ0oIi48xGynBbDOQTFNVlYBmD0qVrYCSicCj45PwFuflUsmN5t+tlxgZDnE0hCcODOmgYiUjcELkR+TqnRaNm2Q8VhF6oEOAMl9e8p+5oFvaqyOXgxDIuWOZSzHFOQVnpX8uQGCgHnjEjBvXAKKyusAAUjpF2b8bNMuwTkZQ6w6F1tqE0UUldchvHsjuqkDmIRL5CcYvBD5OdPg4eS5y8a8FZUALJ9qPfhRBSBELZ3Lb+voBbCeNSR3LLN8WpJV/ozpLovUgMqcD4vNKqKy3jsFwU4SsQAYp2urBGBYbE8cq7hs/L7UmAYiUj5WGxH5INOKGUdEa4IR3ysEq3cXmwUXa3aXYPm0JGNVDaDPhZm1oUCycsfW0YujnYTzCiuMgYsAYFFaIrYsGIODWenG5FnLIChnV7FkVZRkPs/134rhHzfTzzENXAD9mAZH7yERKQeDFyIf42rbetnBjzf1xLYnUs12MQy7JpYPdkOeiSnD0Yut7xlYBiYigNc//a9Zzoxkoz2ZhF/LjReVAOQ/MRZbFozBn+cMt9tjRiq4IiLlY/BC5EPkjm0c2T2QCi5UAlD7wzWcrWuyChAM+SKmbM1fitYE64+hrl8r1RvFkd2ZbuoAyaDEkiAAWdOSzIIuUQSKq68gNTECKf3C7PamaU/Oi7O7X0TkPsx5IfIh7amYsUzeNbTgX7LlBADp9v9Pbj2ORm2rsdwYkO8WvPFAGXJ26493BAFYNm2Q2fsA+3OeDLkulqXSf7hvMABYJQOPvzkSObuKjdeKMM+zsUxWnjk8BtuPn3doTIMtconJRNQxGLwQ+RBnhjxKMS11Xpx73CxIkJtbZJqQa1oCbfrQ3/hpGbJNgwgRWLOrBDOGmifE2przVFXfZKwmMhAAbHsi1dg/xjJoKiirtVq3aTAnFWj9esqgdjWes9cvhog8j8ELkQ9xdsij3GeEdWt0eOZQmyhi8+dnsOmzM5I7DVX1TWa7H6bvk9oRmj0yDklRoSgsr8PI+DBjYFL0XZ1kUu65uibjNZZBkyPBnOV7HGk8JzcvCWjf7hcRuQeDFyIfUlXfhNjwEKs2/M5K6NXN4WtVAvDmgTPGwEKq+ZtUIKQSILkjJHfkIjepxNYAk2hNsFnZtTtmENk7Emrv7hcRtR8Tdol8hGmV0awNBai41OjyQzpaE4xFaYl2r1MJwE9GxsoezQDSicAAMHVwlNX6bCUcj4gPt0rUFQCkxIdBjmXZ9bKp1nk2ziTWSq1vxbZT+L//VBrfbytpmYg6BoMXIh/QniojOb+ZmoS7hkTZvOYno2KxtdC6lb/pToOhysjSR19esFqfvSOXnIwhxn+UVNB30ZULCqTKrtfsLjH7mc6WlUutT3c9qdn0/bNHxuFgVrpZf5r2YOUSkXN4bETkAzyVZ7Hhpyn4z9k67Cv+Hv+7t9TseyoB2HL4rNWuiwqw2mkY0ldj9dlS67N35CJXySTF3j1xJbHW1iBJqY7B7thtYeUSkfO480LkAxxpAOeqobFhWPo/g7A6w/woZP4dCZK5LOvmDJctgba3PkeOXKI1wUhNjLAbGNj7mY52/LW1PkvubmrniR01os6AOy9EPsAdVUb2SA1QfOvgGatdktv7Weeg2CuBNq3ccWZ3xRZ798TQ7M6yZ4y9gM9WObm7E3NZuUTkGgYvRF5mqyzXlLse+rZYHoU4EzBJrU/uSMRdRy5y98RWsztHfm60JhjTk4PxQ3OrRwNGVi4RuUYQ5eoTfVRDQwM0Gg3q6+vRo0cPby+HyCal5DvYCqCq6ptcCpiq6pswLmef1YP5YFa6R3cVpH6uYeaRoV+Ms5/nyYAxr7DCKkBizgt1Rs48v7nzQuQlSunUai+AcnWXxFtHInIVQ1e1Opc+z127RHI6YkeNyN8wYZfIS1xJKHWUo6W3nkwY9WSSsRJ/bns4mqRMRHoeCV7Ky8sxf/58JCQkIDg4GImJiVi1ahW0Wq3N96WlpUEQBLNfCxcu9MQSibzOUw/ZvMIKjM3W9zYZm227t4knAyhvNXNjEzki/+eRY6Pi4mLodDps3LgRAwYMwJdffokFCxagsbERL730ks33LliwAC+88ILx65AQ5f7fElF7eKKCyHK4oQgg671TkoMVAc8njHrrSIRHMUT+zSPBy9SpUzF16lTj1/3790dJSQlee+01u8FLSEgIoqJsd/0k8hfufsgeLb8kOdxw3d5SbC2skKz68XQJtqdzRpT2c4nI8zosYbe+vh7h4eF2r3vnnXfwj3/8A1FRUbjnnnvwzDPP2Nx9aW5uRnNzs/HrhoYGt6yXqKO48yEryDRX23Kkwmyw4optp5AUFYqhsWFuCaCkqpUcLQEnInJWhwQvpaWlWLdund1dlzlz5qBfv36IiYnByZMnsXz5cpSUlGDbtm2y78nOzsbzzz/v7iUT+aSUfmFWjdkg8bVOBGauL0BORvv7rkhVKwFQRAk4Efknp/q8ZGVlYfXq1Tav+frrr5GUdGNIW2VlJSZMmIC0tDRs2rTJqcXt27cPkyZNQmlpKRITpSfgSu28xMbGss8L+T25nQ3LYGL51CSs3l0sOa+nvX1XJHuqABAFQOzg/i5E5Ns81uflV7/6FR5++GGb1/Tv39/43+fPn0d6ejrGjh2LN954w5kfBQAYPXo0ANgMXoKCghAUFOT0ZxP5EstAxVZvFqljoJ4hgWYl0Qbt7bsi2VMFsNrqYct7InInp4KXyMhIREZGOnRtZWUl0tPTkZKSgs2bN0Olcr4q+8SJEwCA6Ohop99L5C+sdlKmJWH1rmKbze0sj4Fmj4xDUlQoZq4vcOusHltTmE2pBCi6zwoR+RaP9HmprKxEWloa4uLi8NJLL6GmpgbV1dWorq42uyYpKQlHjhwBAJSVleF3v/sdioqKUF5ejvfffx8PPfQQxo8fj+TkZE8sk0jxpJrImQYuBpa9WaSa1A2NDUNOhnv7n1j2VJH7B+WOAb2460JEbuORhN09e/agtLQUpaWl6Nu3r9n3DCk2LS0tKCkpwdWr+n9w1Wo1/v3vf2Pt2rVobGxEbGwsMjIy8PTTT3tiiUQ+Qa7Vva1pyc4eKbWX6WeGqFWYtaHAas0Hv9UHUgxgiMgdOJiRSMHkhhsumzoIa3aXWA3z89YwRFMv7vwKb352xur1LQvGIDUxokPWQES+h4MZifyEXBO52SPjMGNYjNUOireGIZp65I4EbPrsjFtza4iITDF4IVI4uaMeqd4sttr9d1TTuGhNMHIyPNu1l4g6Nx4bEfmZvMIKq8ABcL1pnKtBT1V9E2cLEZHDnHl+M3gh8kOmgQMAl/NgbCX/EhG5kzPPb4+UShORd0VrgpGaGIFoTbDNPBhbpMq0V2770qz8mojIGxi8EPk5Qx6MKUcSaF0NenyBVB8cIvIdTNglUhB3JdVafo5UxZK9z7eV/OvLeBRG5PsYvBAphLseqnKf42xzOleDHiWTOwozHa1ARMrH4IVIAdz1ULX3Oc4+oD3RkdeblNAHh4jaj8ELkQK466HqiYezK0GPUvnrURhRZ8OEXSIFOHWu3uo1Vx6qribndhaWgyT94SiMqDPizguRl1XVN2H17mKr15dNG+T0Q9Uf81Tczd+Owog6IwYvRF4mddQDAMk39XTp8/hwts+fjsKIOiMGL0Re5ok8DD6cicifMeeFyMuYh0FE5BzuvBApgKeOejpqkjQRUUdi8EKkEO4+6mEnWSLyVzw2IvJDHKpIRP6MwQuRH/LnoYpERAxeiPwQm9URkT9j8ELkh1jBRET+jAm7RH6KzeqIyF8xeCHyY2xWR0T+iMdGRERE5FMYvBApXFV9EwrKalnmTER0HY+NiBSMjeaIiKxx54VIodhojohIGoMXIoViozkiImkMXogUio3mCGDOE5EUBi9ECsVGc5RXWIFxOfsw583DGJezD3mFFd5eEpEiCKIoivYv8x0NDQ3QaDSor69Hjx49vL0conarqm9io7lOqKq+CeNy9pkdHQYIAg5mpfPvAfklZ57frDYiUjg2muucbOU88e8DdXY8NiIiUiDmPBHJY/BCRKRAzHkiksdjIyIiheJwTSJpHtt5iY+PhyAIZr9ycnJsvufatWtYtGgRIiIi0L17d2RkZODChQueWiKRIrE0lkxFa4KRmhjBwIXIhEd3Xl544QUsWLDA+HVoaKjN65cuXYqdO3fi3XffhUajweLFi3Hffffh888/9+QyiRSD4wCIiOzzaPASGhqKqKgoh66tr6/HW2+9hdzcXEycOBEAsHnzZtxyyy344osvMGbMGE8ulcjr5MYBjL85kv/XTURkwqMJuzk5OYiIiMDw4cPxxz/+Ea2trbLXFhUVoaWlBZMnTza+lpSUhLi4OBw6dMiTyyRSBI4DICJyjMd2Xp588kncfvvtCA8PR0FBAVasWIGqqir86U9/kry+uroaarUaPXv2NHu9T58+qK6ulv05zc3NaG5uNn7d0NDglvUTdTRDaaxlUzKWxhIRmXNq5yUrK8sqCdfyV3FxMQAgMzMTaWlpSE5OxsKFC/Hyyy9j3bp1ZoGGO2RnZ0Oj0Rh/xcbGuvXziToKS2OJiBzj1HiAmpoaXLx40eY1/fv3h1qttnr99OnTGDx4MIqLizFo0CCr7+/btw+TJk1CXV2d2e5Lv3798NRTT2Hp0qWSP09q5yU2NpbjAchncRwAEXVGHhsPEBkZicjISJcWdeLECahUKvTu3Vvy+ykpKQgMDMTevXuRkZEBACgpKUFFRQVSU1NlPzcoKAhBQUEurYlIiTgOgIjINo/kvBw6dAiHDx9Geno6QkNDcejQISxduhQ/+9nPEBYWBgCorKzEpEmT8Le//Q2jRo2CRqPB/PnzkZmZifDwcPTo0QNLlixBamoqK42IiIjIyCPBS1BQELZu3YrnnnsOzc3NSEhIwNKlS5GZmWm8pqWlBSUlJbh69UYlxSuvvAKVSoWMjAw0NzdjypQp2LBhgyeWSERERD7KqZwXX+DMmRkREREpgzPPbw5mJCIiIp/C4IWIiIh8CoMXIiIi8ikMXoiIiMinMHghIiIin8LghYiIiHwKgxciIiLyKQxeiIiIyKd4pMOuNxl67jU0NHh5JUREROQow3Pbkd65fhe8XLlyBQAQGxvr5ZUQERGRs65cuQKNRmPzGr8bD6DT6XD+/HmEhoZCEAS71zc0NCA2NhZnz57lOAEZvEeO4X2yj/fIPt4j+3iP7PPFeySKIq5cuYKYmBioVLazWvxu50WlUqFv375Ov69Hjx4+8wfsLbxHjuF9so/3yD7eI/t4j+zztXtkb8fFgAm7RERE5FMYvBAREZFP6fTBS1BQEFatWoWgoCBvL0WxeI8cw/tkH++RfbxH9vEe2efv98jvEnaJiIjIv3X6nRciIiLyLQxeiIiIyKcweCEiIiKfwuCFiIiIfAqDFwszZsxAXFwcunbtiujoaPz85z/H+fPnvb0sxSgvL8f8+fORkJCA4OBgJCYmYtWqVdBqtd5emqK8+OKLGDt2LEJCQtCzZ09vL0cR1q9fj/j4eHTt2hWjR4/GkSNHvL0kRTlw4ADuuecexMTEQBAEbN++3dtLUpzs7GyMHDkSoaGh6N27N2bOnImSkhJvL0tRXnvtNSQnJxub06WmpmLXrl3eXpbbMXixkJ6ejn/+858oKSnBe++9h7KyMvz4xz/29rIUo7i4GDqdDhs3bsTp06fxyiuv4PXXX8fKlSu9vTRF0Wq1uP/++/H44497eymKkJeXh8zMTKxatQrHjh3D0KFDMWXKFHz//ffeXppiNDY2YujQoVi/fr23l6JYn376KRYtWoQvvvgCe/bsQUtLC370ox+hsbHR20tTjL59+yInJwdFRUU4evQoJk6ciHvvvRenT5/29tLcSySbduzYIQqCIGq1Wm8vRbHWrFkjJiQkeHsZirR582ZRo9F4exleN2rUKHHRokXGr9va2sSYmBgxOzvbi6tSLgBifn6+t5eheN9//70IQPz000+9vRRFCwsLEzdt2uTtZbgVd15suHTpEt555x2MHTsWgYGB3l6OYtXX1yM8PNzbyyCF0mq1KCoqwuTJk42vqVQqTJ48GYcOHfLiysjX1dfXAwD//ZHR1taGrVu3orGxEampqd5ejlsxeJGwfPlydOvWDREREaioqMCOHTu8vSTFKi0txbp16/DYY495eymkULW1tWhra0OfPn3MXu/Tpw+qq6u9tCrydTqdDk899RTGjRuHwYMHe3s5inLq1Cl0794dQUFBWLhwIfLz83Hrrbd6e1lu1SmCl6ysLAiCYPNXcXGx8frf/OY3OH78OD7++GMEBATgoYcegujnjYidvUcAUFlZialTp+L+++/HggULvLTyjuPKPSIiz1i0aBG+/PJLbN261dtLUZxBgwbhxIkTOHz4MB5//HHMnTsXX331lbeX5VadYjxATU0NLl68aPOa/v37Q61WW71+7tw5xMbGoqCgwO+23Uw5e4/Onz+PtLQ0jBkzBm+//TZUKv+Pg135e/T222/jqaeewuXLlz28OuXSarUICQnBv/71L8ycOdP4+ty5c3H58mXubEoQBAH5+flm94tuWLx4MXbs2IEDBw4gISHB28tRvMmTJyMxMREbN2709lLcpou3F9ARIiMjERkZ6dJ7dTodAKC5udmdS1IcZ+5RZWUl0tPTkZKSgs2bN3eKwAVo39+jzkytViMlJQV79+41Pox1Oh327t2LxYsXe3dx5FNEUcSSJUuQn5+P/fv3M3BxkE6n87tnWKcIXhx1+PBhFBYW4o477kBYWBjKysrwzDPPIDEx0a93XZxRWVmJtLQ09OvXDy+99BJqamqM34uKivLiypSloqICly5dQkVFBdra2nDixAkAwIABA9C9e3fvLs4LMjMzMXfuXIwYMQKjRo3C2rVr0djYiHnz5nl7aYrxww8/oLS01Pj1mTNncOLECYSHhyMuLs6LK1OORYsWITc3Fzt27EBoaKgxZ0qj0SA4ONjLq1OGFStWYNq0aYiLi8OVK1eQm5uL/fv346OPPvL20tzLu8VOynLy5EkxPT1dDA8PF4OCgsT4+Hhx4cKF4rlz57y9NMXYvHmzCEDyF90wd+5cyXv0ySefeHtpXrNu3ToxLi5OVKvV4qhRo8QvvvjC20tSlE8++UTy78zcuXO9vTTFkPu3Z/Pmzd5emmI88sgjYr9+/US1Wi1GRkaKkyZNEj/++GNvL8vtOkXOCxEREfmPzpGsQERERH6DwQsRERH5FAYvRERE5FMYvBAREZFPYfBCREREPoXBCxEREfkUBi9ERETkUxi8EBERkU9h8EJEREQ+hcELERER+RQGL0RERORTGLwQERGRT/l/56s2N7ZGiGYAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "yp = results.predict(W)\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(X[:, 0], Y, \".\", label=\"expected\")\n",
    "ax.plot(X[:, 0], yp, \".\", label=\"predicted\")\n",
    "ax.legend()\n",
    "ax.set_title(\n",
    "    \"Régression linéaire par morceaux\\nsur un nuage linéaire par morceaux\\nR2=%f\"\n",
    "    % results.rsquared\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le modèle nous suggère de ne garder que quelques seuils. En s'appuyant sur les p-values :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 5, 6, 7])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "keep = numpy.arange(len(results.pvalues))[results.pvalues < 0.05]\n",
    "keep"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "W2 = W[:, keep]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared (uncentered):</th>      <td>   0.856</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared (uncentered):</th> <td>   0.855</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>          <td>   1481.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 07 Oct 2024</td> <th>  Prob (F-statistic):</th>           <td>  0.00</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>11:29:08</td>     <th>  Log-Likelihood:    </th>          <td> -1642.9</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1000</td>      <th>  AIC:               </th>          <td>   3294.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   996</td>      <th>  BIC:               </th>          <td>   3314.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     4</td>      <th>                     </th>              <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>              <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "   <td></td>     <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th> <td>   -1.9657</td> <td>    0.062</td> <td>  -31.604</td> <td> 0.000</td> <td>   -2.088</td> <td>   -1.844</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th> <td>    0.8316</td> <td>    0.163</td> <td>    5.106</td> <td> 0.000</td> <td>    0.512</td> <td>    1.151</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th> <td>    3.3282</td> <td>    0.355</td> <td>    9.363</td> <td> 0.000</td> <td>    2.631</td> <td>    4.026</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th> <td>    1.7842</td> <td>    0.327</td> <td>    5.455</td> <td> 0.000</td> <td>    1.142</td> <td>    2.426</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>225.520</td> <th>  Durbin-Watson:     </th> <td>   2.011</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 775.424</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-1.066</td>  <th>  Prob(JB):          </th> <td>4.16e-169</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 6.750</td>  <th>  Cond. No.          </th> <td>    17.4</td> \n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] R² is computed without centering (uncentered) since the model does not contain a constant.<br/>[2] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/latex": [
       "\\begin{center}\n",
       "\\begin{tabular}{lclc}\n",
       "\\toprule\n",
       "\\textbf{Dep. Variable:}    &        y         & \\textbf{  R-squared (uncentered):}      &     0.856   \\\\\n",
       "\\textbf{Model:}            &       OLS        & \\textbf{  Adj. R-squared (uncentered):} &     0.855   \\\\\n",
       "\\textbf{Method:}           &  Least Squares   & \\textbf{  F-statistic:       }          &     1481.   \\\\\n",
       "\\textbf{Date:}             & Mon, 07 Oct 2024 & \\textbf{  Prob (F-statistic):}          &     0.00    \\\\\n",
       "\\textbf{Time:}             &     11:29:08     & \\textbf{  Log-Likelihood:    }          &   -1642.9   \\\\\n",
       "\\textbf{No. Observations:} &        1000      & \\textbf{  AIC:               }          &     3294.   \\\\\n",
       "\\textbf{Df Residuals:}     &         996      & \\textbf{  BIC:               }          &     3314.   \\\\\n",
       "\\textbf{Df Model:}         &           4      & \\textbf{                     }          &             \\\\\n",
       "\\textbf{Covariance Type:}  &    nonrobust     & \\textbf{                     }          &             \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lcccccc}\n",
       "            & \\textbf{coef} & \\textbf{std err} & \\textbf{t} & \\textbf{P$> |$t$|$} & \\textbf{[0.025} & \\textbf{0.975]}  \\\\\n",
       "\\midrule\n",
       "\\textbf{x1} &      -1.9657  &        0.062     &   -31.604  &         0.000        &       -2.088    &       -1.844     \\\\\n",
       "\\textbf{x2} &       0.8316  &        0.163     &     5.106  &         0.000        &        0.512    &        1.151     \\\\\n",
       "\\textbf{x3} &       3.3282  &        0.355     &     9.363  &         0.000        &        2.631    &        4.026     \\\\\n",
       "\\textbf{x4} &       1.7842  &        0.327     &     5.455  &         0.000        &        1.142    &        2.426     \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lclc}\n",
       "\\textbf{Omnibus:}       & 225.520 & \\textbf{  Durbin-Watson:     } &     2.011  \\\\\n",
       "\\textbf{Prob(Omnibus):} &   0.000 & \\textbf{  Jarque-Bera (JB):  } &   775.424  \\\\\n",
       "\\textbf{Skew:}          &  -1.066 & \\textbf{  Prob(JB):          } & 4.16e-169  \\\\\n",
       "\\textbf{Kurtosis:}      &   6.750 & \\textbf{  Cond. No.          } &      17.4  \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "%\\caption{OLS Regression Results}\n",
       "\\end{center}\n",
       "\n",
       "Notes: \\newline\n",
       " [1] R² is computed without centering (uncentered) since the model does not contain a constant. \\newline\n",
       " [2] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                                 OLS Regression Results                                \n",
       "=======================================================================================\n",
       "Dep. Variable:                      y   R-squared (uncentered):                   0.856\n",
       "Model:                            OLS   Adj. R-squared (uncentered):              0.855\n",
       "Method:                 Least Squares   F-statistic:                              1481.\n",
       "Date:                Mon, 07 Oct 2024   Prob (F-statistic):                        0.00\n",
       "Time:                        11:29:08   Log-Likelihood:                         -1642.9\n",
       "No. Observations:                1000   AIC:                                      3294.\n",
       "Df Residuals:                     996   BIC:                                      3314.\n",
       "Df Model:                           4                                                  \n",
       "Covariance Type:            nonrobust                                                  \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "x1            -1.9657      0.062    -31.604      0.000      -2.088      -1.844\n",
       "x2             0.8316      0.163      5.106      0.000       0.512       1.151\n",
       "x3             3.3282      0.355      9.363      0.000       2.631       4.026\n",
       "x4             1.7842      0.327      5.455      0.000       1.142       2.426\n",
       "==============================================================================\n",
       "Omnibus:                      225.520   Durbin-Watson:                   2.011\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              775.424\n",
       "Skew:                          -1.066   Prob(JB):                    4.16e-169\n",
       "Kurtosis:                       6.750   Cond. No.                         17.4\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] R² is computed without centering (uncentered) since the model does not contain a constant.\n",
       "[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = OLS(Y, W2)\n",
    "results = model.fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "yp = results.predict(W2)\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(X[:, 0], Y, \".\", label=\"expected\")\n",
    "ax.plot(X[:, 0], yp, \".\", label=\"predicted\")\n",
    "ax.legend()\n",
    "ax.set_title(\n",
    "    \"Régression linéaire par morceaux\\nsur un nuage linéaire par morceaux\\n\"\n",
    "    + \"réduction du nombre de segments\\nR2=%f\" % results.rsquared\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le coefficient $R^2$ est quasiment identique pour un nombre de segments moindre. Je me suis amusé à rendre ce code plus générique pour comparer la première étape, le découpage en morceaux, via deux modèles, un arbre de décision et le nouvel objet [KBinsDiscretizer](https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.KBinsDiscretizer.html) qui segmente une variable sans tenir compte de la cible. La régression n'est plus nécessaire linéaire : [Piecewise linear regression](https://sdpython.github.io/doc/mlinsights/dev/auto_examples/plot_piecewise_linear_regression.html). Je me suis également amusé à faire de même pour une classification par morceaux [PiecewiseClassifier](https://sdpython.github.io/doc/mlinsights/dev/api/mlmodel.html#piecewiseclassifier). Celle-ci pose quelques soucis pratiques car toutes les classes ne sont pas forcément représentées dans chaque compartiment..."
   ]
  },
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   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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