diff --git a/DESU_regression2.ipynb b/DESU_regression2.ipynb
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+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "ef2a766b-a3a1-431f-8dac-6c57c1157312",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import scipy.stats as stt\n",
+    "import statsmodels.api as sm\n",
+    "import statsmodels.formula.api as smf\n",
+    "from patsy import dmatrices\n",
+    "import pandas as pd\n",
+    "\n",
+    "import matplotlib.pyplot as plt\n",
+    "%matplotlib inline\n",
+    "import seaborn as sb\n",
+    "from statsmodels.graphics.factorplots import interaction_plot\n",
+    "\n",
+    "sb.set_style('whitegrid')\n",
+    "sb.set(font_scale=1.5)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "393f8324-fb25-41e1-b9dd-6e80ebc9c137",
+   "metadata": {},
+   "source": [
+    "## ANOVA and categorical predictor variables\n",
+    "\n",
+    "First we start with synthetic data"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "id": "0ab81d81-5613-4269-8767-750493d848ce",
+   "metadata": {
+    "tags": []
+   },
+   "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>x1</th>\n",
+       "      <th>x2</th>\n",
+       "      <th>y</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>0.0</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>-0.219803</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>0.0</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>-0.707458</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>0.0</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>-2.078523</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>1.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.161505</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>1.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>-1.280134</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "    x1   x2         y\n",
+       "0  0.0  1.0 -0.219803\n",
+       "1  0.0  1.0 -0.707458\n",
+       "2  0.0  1.0 -2.078523\n",
+       "3  1.0  0.0  0.161505\n",
+       "4  1.0  0.0 -1.280134"
+      ]
+     },
+     "execution_count": 38,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# number of samples\n",
+    "n = 50\n",
+    "\n",
+    "# exogeneous variables\n",
+    "x1 = stt.bernoulli.rvs(p=0.4, size=n)\n",
+    "x2 = stt.bernoulli.rvs(p=0.5, size=n)\n",
+    "\n",
+    "# error\n",
+    "e = stt.norm.rvs(size=n)\n",
+    "\n",
+    "# endogenous variable scaled by factor a\n",
+    "a1 = -1.5\n",
+    "a2 = -1.2\n",
+    "a12 = 0.0\n",
+    "y = a1 * x1 + a2 * x2 + a12 * x1 * x2 + e\n",
+    "\n",
+    "# build dataframe\n",
+    "df = pd.DataFrame(np.column_stack((x1,x2,y)), columns=['x1','x2','y'])\n",
+    "df.head()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "id": "02584a51-7b0e-4881-87c6-270357bf0e4f",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "                            OLS Regression Results                            \n",
+      "==============================================================================\n",
+      "Dep. Variable:                      y   R-squared:                       0.181\n",
+      "Model:                            OLS   Adj. R-squared:                  0.127\n",
+      "Method:                 Least Squares   F-statistic:                     3.382\n",
+      "Date:                Sat, 22 Jul 2023   Prob (F-statistic):             0.0260\n",
+      "Time:                        12:53:46   Log-Likelihood:                -65.914\n",
+      "No. Observations:                  50   AIC:                             139.8\n",
+      "Df Residuals:                      46   BIC:                             147.5\n",
+      "Df Model:                           3                                         \n",
+      "Covariance Type:            nonrobust                                         \n",
+      "=============================================================================================\n",
+      "                                coef    std err          t      P>|t|      [0.025      0.975]\n",
+      "---------------------------------------------------------------------------------------------\n",
+      "Intercept                    -0.5981      0.272     -2.198      0.033      -1.146      -0.050\n",
+      "C(x1)[T.1.0]                 -1.1373      0.371     -3.067      0.004      -1.884      -0.391\n",
+      "C(x2)[T.1.0]                 -0.7414      0.365     -2.031      0.048      -1.476      -0.006\n",
+      "C(x1)[T.1.0]:C(x2)[T.1.0]     1.4799      0.544      2.722      0.009       0.386       2.574\n",
+      "==============================================================================\n",
+      "Omnibus:                        0.166   Durbin-Watson:                   1.339\n",
+      "Prob(Omnibus):                  0.920   Jarque-Bera (JB):                0.151\n",
+      "Skew:                          -0.115   Prob(JB):                        0.927\n",
+      "Kurtosis:                       2.858   Cond. No.                         6.57\n",
+      "==============================================================================\n",
+      "\n",
+      "Notes:\n",
+      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Fit and summarize OLS model with/without interaction\n",
+    "#lm = smf.ols('y ~ C(x1) + C(x2)', df)\n",
+    "lm = smf.ols('y ~ C(x1) * C(x2)', df)\n",
+    "lmf = lm.fit()\n",
+    "\n",
+    "print(lmf.summary())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "id": "f81b9991-0e47-4751-bfaf-4ced6bf83124",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "                sum_sq    df         F    PR(>F)\n",
+      "C(x1)         2.432021   1.0  2.736386  0.104895\n",
+      "C(x2)         0.066287   1.0  0.074583  0.785999\n",
+      "C(x1):C(x2)   6.585679   1.0  7.409870  0.009131\n",
+      "Residual     40.883474  46.0       NaN       NaN\n"
+     ]
+    }
+   ],
+   "source": [
+    "table = sm.stats.anova_lm(lmf, typ=2) # Type 2 ANOVA DataFrame\n",
+    "print(table)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "id": "cadc3f11-921a-4160-981e-d16158878061",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# prediction and residuals\n",
+    "resid = lmf.resid\n",
+    "\n",
+    "sm.graphics.qqplot(resid, line='r')\n",
+    "plt.tight_layout()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "id": "301432e0-8f9d-47b8-9023-3af30adf8c2f",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "resid = lmf.resid\n",
+    "\n",
+    "cat = 2 * df['x1'] + df['x2']\n",
+    "labels = ['00','01','10','11']\n",
+    "\n",
+    "plt.scatter(cat, resid)\n",
+    "plt.xticks(range(len(labels)),labels)\n",
+    "plt.xlabel('category (x1,x2)')\n",
+    "plt.ylabel('residuals')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cf7b9e8a-a66e-4cb9-b891-79142c8a5def",
+   "metadata": {},
+   "source": [
+    "The interaction plot is a visualization to check whether the means for a categorical variable have similar trends for different values of another categorical variable. The more unparallel lines are, the stronger the interaction between the two categorical variables."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "id": "58685548-0cf1-444b-b4da-7eadb50e5572",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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xCc6LLiHx6+VkdusBQMjE8UTdeTPmI4e9HJmIiEj5UWEmviMoiLRXJ5Ay7QNc4RHYNn5PdHxrAr5d4u3IREREyoUKM/E52Xd0IXHZdziaXoE5MZHIrvcSOux5OK2PqYiISEWkwkx8kuuCC0n68hsyHstdXiRk6iSi7uiE+eAfXo5MRETEc1SYie8KDCR91Kskv/8RrsgobFs2E92+LQGLv/R2ZCIiIh6hwkx8nv2W20hcvgZHs+aYk5OI7PYgoc8/A9lnXxtHRETE36gwE7/gqlOXpM+XktGnPwAh094m6tYbMe//3cuRiYiIuI8KM/EfAQGkjxhF8qw5uKKjsf20jegO1xLw+UJvRyYiIuIWKszE79g73kTiinU4Wl2FOTWFyJ6PEPbMAMjK8nZoIiIiZaLCTPySK64WSQu/IuPJpwEI/uA9om7ugOX3fV6OTEREpPRUmIn/stlIf2E4SbPn44qNxbZzO1HtryVwwTxvRyYiIlIqKszE7znibyBxxTrsV7fGnJ5GxOM9CHu6P2RkeDs0ERGRElFhJhWC67yaJM//gvSnn8EwmQj+30yib4rHsvcXb4cmIiJSbCrMpOKwWsl47gWS536Gq2o1rD/vJvrGdgTO/sjbkYmIiBSLCjOpcBztridhxTrsbdthysgg4sk+hPd/HNLTvR2aiIjIWVm9HYCIJxjVq5M89zNC3niNkHGjCZrzMdZtW0iZNhPnpQ29HZ6IiJzD1q2bmT37f+zevZOMjExq1KjB9dd34P/+rxvBwcE+M6a7acZMKi6LhYyBz5I8/wuc1Wtg3fsL0R2vI+ijD8EwvB2diIicwaefzuapp/qwfv1aAgICOf/88zl27E9mznyPxx57mJSUZJ8Y0xNUmEmF52jdNveuzeviMWVlET6gH+F9H8OUlurt0EREPMq2eiXRbVpiW73S26EU2549PzNx4ngABg0awvz5XzJjxkfMnbuI+vUv5cCB/YwdO9LrY3qKCjOpFIyqVUmevYC0F4ZjWCwEzZ9L1A3tsOzc4e3QREQ8wzAIHTUC695fCB01wm/OFMycOR2Xy0XHjjdzxx1dMJlMAFSpUpXhw0dhNptZvXol+/b96tUxPUWFmVQeZjOZTz5N0sLFOGvGYf1tH9E3xRP0wXt+8wtLRKS4bCuXY/txa+7XP27FtnK5lyM6t4yMDH74YQMAt9/eudD22rXr0KxZCwBWrlzmtTE9SYWZVDo5V11N4oq1ZN/QEVN2NuHPDCC816OYfOT6AhGRMjMMQseMxLBYcr+1WAgdM9Ln/wj99ddfsNvtBAQE0LBhoyL3adr0CgB27SreGQ9PjOlJKsykUjJiYkmZNYe04aMwrFaCFi0gusO1WH/a5u3QRETKLG+2zOR0AmByOv1i1uzQoT8AqFatBlZr0QtHxMXVAuDgwT+8NqYnabkMqbzMZjL79sfR6koienfHcmA/UbfcQNrwkWT16A1/X4MgIuJRhuHeFnKGQegrIzDMFkwu5z8Pmy2EvjKCpFZXue/3W0iIW39XpqSkABAREXHGfcLDc7elphbvBi5PjOlJKsyk0stp0YrE5WsIf+oJAr/+kvAhzxCwdg2pb7yFERXt7fBEpCIzDKJuvRHbph88fiiTy4lt+09UvbCm28Z0tLqKpC+Wuq04s9vtANhstjPuExAQ8Pe+2V4b05N0KlMEMKKiSfngI9JGjcWw2Qhc/EXuqc0tm7wdmohUdJqdz5dXIDkcjjPuk1doBQQEem1MT9KMmUgek4nMx/rgaHklEY91w/LHAaJu60j6iy+R+fgT+uUpIu5nMuXOOLnpVKZt9Uqiuj14zv2SPvgYR7vry35AN5/KzDulmHf6sSipqSl/7xvutTE9SYWZyL/kXN4s99TmgP4EfvEZYcOGYFv3HakTp2LExHo7PBGpaEwmCA0t+ziGQegbr2FYLPkX/Re5m8VC6BuvkXTTLT73B2ft2nUAOH78GDk5OUVerH/kyOG/963rtTE9SacyRYpgRESSMn0mqWPHYwQGEvjNEqLbt8W60fPXgYiIlMa/78Q8E1++Q7NevQbYbDbsdju7d+8scp+f/r57vlGjxl4b05NUmImciclE1qM9SVy8nJwLL8Jy5DBRd3QieOIEcLm8HZ2IyD/+tW7ZOXf30XXNQkJCaNXqKgA+/3xhoe2HDh1k69bNAFx3XXuvjelJKsxEzsHZuAlJy74jq8vdmJxOwkYOI/LBuzGdPOnt0EREgOLPluXx5Vmzbt16YjKZWLp0MYsWLcD4u3g8efIkw4c/j8vlom3b67jkknoFntenTw/uvvs25s792G1jeoPJMHysXJZzcjpdJCSkezuMM7JazURHh5KYmE5OTgWaWTIMgj76kLAhgzBlZeGscR6p78zAcXVrjx2ywuaynCmP7qNclozDYefUqT+JjT0Pmy2g0Har1Vz2PBoGUR2vx/rTj5iM4o9lmMzkNL2cpKUrfe5as7lzP2bSpAkYhkG1atWJioriwIH92O126tSpy5Qp7xEVFZW/v9Vq5s47b+HYsT959NHH6NGjd5nHPJdz/dv+W0xMKBbLuefDNGMmUlwmE1n/9wiJS1aSc0k9LMf+JLLzLYSMfxWK+VeqiIjb2e2YjxwuUVEGYDJcmI8ehr+XivAl9977IBMmTOaqq64hKyuLAwf2U716DR566FGmT59VogLKk2N6gmbM/JBmzHxAWhrhzw0kaO4nANivvZ6UKdMwqlVz62EqRS7LgfLoPsplyZTLjBlgPnIY86mSX17hqlIVV824Mh/f29yVx5Lw1IyZlssQKY2wMFLfegd7m2sJf24gAd+tJOb6a0iZOh3Htdd5OzoRqWRccbVw/d3vUfybTmWKlEH2/V1JXLqKnAaXYj5xnMh77iBk7Cid2hQRkVKptIXZoUOHGDx4MNdeey2NGjWiXbt2DBkyhEOHDpV6zJycHD755BO6du1Kq1atuOyyy7jyyit56KGH+PTTT3FpiYUKyVm/AYlLVpLZ9WFMhkHo62OJvPt2zMf+9HZoIiLiZyplYbZt2zZuv/12FixYQFZWFvXq1SMjI4P58+dzxx13sH379hKPmZWVRbdu3Rg+fDibN28mICCA+vXrY7PZ2LhxI88//zy9evU6a68u8WMhIaRNeCv3OrOQUALWrSE6vjW2Fcu8HZmIiPiRSleYZWZm0r9/fzIyMrjrrrtYs2YNCxYsYO3atXTp0oX09HT69+9PVlZWicZ977332LRpE4GBgUyZMoW1a9fmjzt58mQCAgJYs2YNs2fP9tArE1+Qffd9JC7/jpzLGmM+eZKo+7sQOmoE5OR4OzQREfEDla4wmzNnDidOnKBu3boMHz6cwMDcTvKBgYGMGDGCOnXqcOzYMebNm1eicVesWAHAAw88QPv2BVcO7tChA/fffz8Aq1atKvuLEJ/mvOgSEhcvI/ORHgCEvPk6UZ1vwXz0iJcjExERX1fpCrMlS5YA0LlzZwICCt7eGhAQQJcuXQD4+uuvSzRudnY2ALVr1y5ye506uU1UczRzUjkEB5M2bgIp0z7AFRaO7YcNRMe3JuDbJd6OTEREfFilKsycTic7d+Y2MG3RokWR++Q9vmPHDpwluLOuYcOGAGzdurXI7Vu2bAGgadOmxR5T/F/2HV1IXL4GR5PLMSckENn1XkKHvwC61lBERIpQqQqzI0eO5F98nzeD9W95j9vtdo4ePVrssfv06UN4eDhfffUV48aN49ChQ2RnZ3Pw4EHGjh3L119/zfnnn0/37t3L/kLEr7guuJCkr74lo2dui5CQKROJur0T5kMHvRyZiIj4mkq1wGxSUlL+12dqvRAZGZn/dXJy8hlPTf7bBRdcwJw5cxg/fjzvv/8+06dPz99mtVrp3r07vXv3dlvLB6vVd2vqvJWNi7PCcaVhDSb71ddxtb2WkP59sW3ZRHR8GzLemorjltvO+DTl0j2UR/dRLkvG5TpzD8q89pQmE6gHT+l5O48Wi8mtn8mVqjCzn9YPzGazFbnP6dedlfTOzKNHj5KQkIDT6SQmJoYaNWpw7NgxEhIS+OKLL7jwwgu55557Shf8acxmE9HRoWUex9MiIoK9HYLvefhBaHs13H8/5o0bCXvoAXjqKXj1VQg4c0sP5dI9lEf3US6LJyvLwsmT5rN+eKvIdY/yzqPLZcJsNhMZGUJQUJDbxvWbwmzo0KHMmTOnxM9r1aoVs2bNAgoWXQ6HI/+OzNOdXryVJNGLFy9m4MCBhIeHM3nyZDp06JC/bfny5QwePJgXXngBu91O165dS/w6TudyGaSkZJRpDE+yWMxERASTkpKJ06lFdQuJqgafLyH4pWEETZkEb75JzndrSH9vJq7zLyiwq3LpHsqj+yiXJWO3Z+NyuXA6jUK9HE2m3Hw6nS7NmJWBt/LodBq4XC6SkzPIzDz3NekREcEVq1dmeHg4VapUKfHzTj81efrXSUlJVK9evdD+ycnJRe5/Ng6Hg1deeQWXy8XgwYMLFGUA7du357nnnmPw4MG88cYb3HPPPYXuCC0pf2ge7HS6/CJOrzBbSR0+iuyr2xDevzfWbVsJb9ea1Dfewn7bnYV2Vy7dQ3l0H+WyeJzOM1cKeUWEirKy8XYeiyq6y8JvCrNBgwYxaNCgMo0RFxeHzWbD4XBw8ODBIguzgwdzL8gOCAigZs2axRr3jz/+4MSJEwBce+21Re7Trl07AFJSUjhw4AD16tUrzUuQCsbe8SYSV6wjond3bJt+ILLHw2Q+2pO0Ea+AG6fGRUTEP1SqE9tWq5VGjRoBsHnz5iL3yXu8cePGWCyWYo2bnp5eojjy1jwTAXDVqk3SZ4vJ6D8AgOD3pxN1cwcsv+/zcmQiIlLeKlVhBtCxY0cAFi5cWKhvpd1uZ8GCBQB06tSp2GPWqVMHszk3lWvWrClyn++++w4Ai8VC3bp1Sxy3VHA2G+kvjiD5k09xxcZi27mdqPbXYps/19uRiYhIOap0hdl9991H1apV+eOPPxg2bFj+7FV2djbDhg3j4MGDVKtWrci7J8eOHUt8fDwDBgwo8Hh0dHT+qcrRo0cXaru0atUqxowZA0B8fDwREREeeGVSEdjb30jiinXYr7oGc3oaYY91h169IDPT26GJiEg58JtrzNwlJCSEN998k549ezJ//nyWLVtGrVq1OHz4MMnJyYSEhDBp0iSCgwvfCp6YmMiRI0eIi4srtG3EiBH8/vvv/PHHH/Tu3ZvY2Nj85TJOnToF5K51NmzYMI+/RvFvrvNqkrzgS0JeG03IhNcwTZtG+Lr1pEybifMSXZsoIoUdPmwiIeHMa6adSUyMQa1avnX3walTJ9m8eSM//7ybX37Zzd69v5CdnU39+pfy3nuzyjT21q2bmT37f+zevZOMjExq1KjB9dd34P/+r1uRn/veUOkKM4DmzZuzaNEipkyZwrp169i7dy/R0dF06dKFvn37FntR2dNVr16dzz77jI8++ohly5bx22+/sWfPHkJCQrjiiivo0KEDXbt29Zl/ePFxVisZz72Iq821hD/eA+vuXUTfcC2pY8eTfd+D3o5ORHzI4cMmrr46lOzskhdmgYEGGzak+1Rxtnz5N0ycON7t43766WzefPN1DMOgWrXqVKtWnQMH9jNz5nusXr2CKVOmExFRvNUYPMlkGLpR1984nS4SEkp2w0F5slrNREeHkpiYrtvpy8hqNROdlYLj/gewfbcagKz7u5I6+jUI9f1Fhn2F3pPuo1yWjMNh59SpP4mNPQ+brfAySVarucx53L7dTIcOpf99sGxZOk2a+M6/5ZdfLmLZsqU0aNCQBg0u5dChg7zzzuSzzpidK4979vxMr16PYBgG//3vYG6/vTMmk4mTJ0/w7LNP88svP9Ou3fWMGjWu2HGe69/232JiQou1jlmlu8ZMxO+cdx5p8z8n/ZkhGGYzQbM/IrrT9Vj2/OztyERE3O7WW+/gjTem8Pjj/bjuuvbExpZ8DdN/mzlzOi6Xi44db+aOO7pg+ruPU5UqVRk+fBRms5nVq1eyb9+vZT5WWakwE/EHFgsZ/32O5Plf4KxeA+sve4jueB1BH32o1SlFRM4iIyODH37YAMDtt3cutL127To0a9YCgJUrl5VrbEVRYSbiRxyt2+betXldPKbMTMIH9CO872OY0lK9HZqIiE/69ddfsNvtBAQE0LBhoyL3adr0CgB27dpRnqEVqVJe/C/iz4yqVUmevYDgSRMIHTOSoPlzsf64NfeuzUaNvR2eiJSQYUBGGdofl3U1ncxMKOE66flCQnJ7VfqyQ4f+AKBatRpYrUWXPXFxtQA4ePCPcovrTFSYifgjs5nMpwbiuPIaIno/ivW3fUTfFE/ayLFkPfyo7/+mFBEgtyi79dYQNm0qXqcZT7jtttLfONCqVQ5ffJHp079yUlJSAM66hmh4eO621FTvn33QqUwRP5Zz1dUkrlhHdocbMWVnEz7oP4T3ehRTaoq3QxORYjKZdJ2oJ9ntdgBsNtsZ9wkICPh7X++3TNSMmYifM2JjSfnfXIKnvkXoqOEELVqA7adtpEyfSU6Ty70dnoichckEX3yRWaZTmTt3mss06/XFF+k0alS65TL84VRmXtH17zaMp8sr3gICAsslprNRYSZSEZjNZD7xJI5WVxLRuzuWA/uJurkDaSNGkdW9l+//5hSpxEymsi1LWNZ1y4ODK/ayiHmnKfNOaRYl9e+zDOHh4eUS09noVKZIBZLT8koSl68hu9MtmOx2wgcPIqL7Q5iSk7wdmoiIV9SuXQeA48ePkZOTU+Q+R44c/nvfuuUW15moMBOpYIzoGFJmfkzayDEYNhuBX31OdPu2WLdu9nZoIiLlrl69BthsNux2O7t37yxyn59+2gZAIx+4s12FmUhFZDKR2asvSV9+g7PO+VgO/kHUrTcSPPUtLUgrIpVKSEgIrVpdBcDnny8stP3QoYNs/fsP1+uua1+usRVFhZlIBZZzRXMSl39H9q13YMrJIWzYECIevh9TYoK3QxMRcas+fXpw9923MXfux4W2devWE5PJxNKli1m0aAF5bcJPnjzJ8OHP43K5aNv2Oi65pF55h12ILv4XqeCMyChS3vuQoPenEzZ0MIFLv8Ya34aUd94np9WV3g5PRMooJsYgMNAgO7vkN/kEBhrExPjWLPpffx2je/eu+d/b7bl3U+7bt5dbbvlnRuvBBx+ma9dH8r8/ceI4x479WeRaZJdeehn9+w9g0qQJjBv3CjNnvkdUVBQHDuzHbrdTp05dnn32BQ++quJTYSZSGZhMZHV/jJyWrQjv+QjW/b8TdUcn0ocMI/OJJ8GsyXMRf1WrlsGGDekkJJS8MIuJMahVy7cKM5fLRXJycqHHnU5ngcezsrJKNO699z7IhRdezOzZ/2P37l0cOLCf6tVrcN117XnooUcJCQkpc+zuYDIMXXDib5xOFwkJpeyfUQ6sVjPR0aEkJqaTk1O6tXEklydyaUpNIey/TxG0cD4A2e1vIHXSOxhVqrhlfF+k96T7KJcl43DYOXXqT2Jjz8NmCyi03Wo1K49u4I08nuvf9t9iYkKxWM79R7D+TBapZIzwCFLfnkHq6xMxgoIIXP4t0fGtsW1Y5+3QREQqPRVmIpWRyUTWQ91I/HoFORdfguXYn0R2voWQCePApb/eRUS8RYWZSCXmvKwRid+sJuue+zG5XISOfpnI+zpjOn7c26GJiFRKKsxEKruwMFInv0vKxKkYwcEErF6Ze2pzzWpvRyYiUumoMBMRALLv70riN6vJaXApluN/EXn37YS8+go4nd4OTUSk0lBhJiL5nPUbkLhkJZkPPoTJMAh9bQyRd9+O+dif3g5NRKRSUGEmIgWFhJD2xmRSJr+LERJKwLo1uac2Vy73dmQiIhWeCjMRKVL2PfeTuOw7cho2wnzyJJH3dyHklZcgJ8fboYmIVFgqzETkjJwXX0Li18vJfLh77qnNN14jqvMtmI8e8XZoIn5Ga7lXPJ75N1VhJiJnFxxM2mtvkPLu+7jCwrH9sIHo+NYELFvq7chEfJ7ZbAEgJ8fh5UjE3ZzO3LMHZje3tFNhJiLFkn3nXSQu+w5Hk8sxJyQQ+eA9hI54ERz6wBE5E4vFQkBAEOnpqbi0eHOFYRgGGRnpWK0BWCzubTuuJuYiUmyuCy8i6atvCRv+PMHvvUvI5Dexfb8+dzatdh1vhyfik8LCokhMPM6pU38SFBRKQEDg37MsJlwuE06nTnOWVfnl0cDpzCEjIx27PZPISPf3GFZhJiIlExhI2ujXsF/TlvAB/bBt2UR0+zakvjkV+023eDs6EZ8TEBBIbGwN0tKSyMhIJT09OX+b2WzWTJoblHcerdYAIiOrEBwc6v6xS/vEzMxMgoOD3RmLiPgR+213kNikKRG9umHbtpXIRx4go3df0l98CQICvB2eiE+xWm1ERVXFMHJnXAzDwGIxERkZQnJyhmbNyqC882g2m91++vJ0pR65TZs23Hrrrdx33300bNjQnTGJiJ9w1T2fpC++IfTlYYS8M5mQd6Zg2/g9Ke9+gKvu+d4OT8TnmEwmrFYbAFarmaCgIDIzneTkaNastCpaHkt98X96ejpz587lrrvu4u6772bevHlkZma6MzYR8QcBAaS/PJrkD2fjiorCtm0r0e3bEvDFIm9HJiLid0pdmL388ss0adIEwzDYuXMnQ4cOpU2bNgwfPpzdu3e7M0YR8QP2TjeTuGIdjhatMKckE9njIcKeGwhZWd4OTUTEb5gMwyjTCdm9e/cyZ84cvvjiC1JSUjCZTAA0atSIe++9l1tvvVXXormZ0+kiISHd22GckdVqJjo6lMTE9AoxrexNfplLh4PQ0S8T8tYbud82bkrqtPdxXnix10Lyyzz6KOXSfZRL9/CXPMbEhGKxnHs+rMyFWR673c7ixYuZO3cuW7duzR3cZCIkJITbbruNe++9V9eiuYkKs8rDn3MZsGwp4f16Y05IwBUWTtrrb5Ld+W6vxOLPefQ1yqX7KJfu4S95LPfC7HS///47c+fOZdGiRSQmJubPol122WXcd999mkUrIxVmlYe/59J89Ajhj/cg4Pv1AGQ+9ChpI8dAOf/8+3sefYly6T7KpXv4Sx69WpjlOXnyJAMGDGDTpk3/HNBkIiwsjAceeIBevXoRFhbmqcNXWCrMKo8KkcucHELGvULIG69jMgxyLr2MlOkzcV5Sr9xCqBB59BHKpfsolyVz+LCJhARTocctFjMREcGkpGTidBbOY0yMQa1a3l+OxKuF2ebNm5k3bx5Lly4lOzsbwzAIDg6mTZs2bNq0iaSkJEwmE+eddx4zZ86kdu3a7g6hQlNhVnlUpFzaVq0gou9jmE+ewAgJJfXV8WTf+0C5HLsi5dHblEv3US6L7/BhE1dfHUp2duHC7FwCAw02bEj3enFW3MLMbSukJSUl8dlnnzFv3jx+//138uq9Sy65hPvvv5877riDsLAw7HY7X375JRMnTuTPP/9k3LhxTJw40V1hnFNWVhZr165lx44d7Ny5k507d5KUlATA1q1bCQ0t2yq+hw4dYsqUKaxbt46EhARiY2Np3bo1ffr0UQEqlZrjungSV64jvE9PAtZ+R0S/3mSuW0PaK+OgjD93IlKxJSSYSlWUAWRn5860ebswK64yF2YbN25kzpw5LFu2DLvdjmEYBAQEcOONN/LAAw/QvHnzAvsHBATQpUsXWrRoQadOnQqc5iwP+/fv54knnvDI2Nu2baN79+5kZGQQGRlJvXr1OHToEPPnz2fJkiV88MEHNGnSxCPHFvEHruo1SJ63iJDxrxLy2hiCP/kftq2bSZk2E2eDS70dnoiI15W6MHvvvfeYN28ef/zxB5Dbab1OnTrce++93HXXXURHR5/1+XXq1KFKlSqcOHGitCGUitVqpUmTJjRu3JhGjRoRGxtLr169yjxuZmYm/fv3JyMjg7vuuothw4YRGBhIdnY2w4cPZ8GCBfTv35+lS5cSFBTkhlci4qcsFjIGDcZxdWvCH++B9Zc9RHe8jtQxr5N9f1cwle6vYhGRiqDUhdm4ceNyB7Baue6663jggQdo3bp1icaIi4vDai3fPuqXXHIJ8+bNy//+8OHDbhl3zpw5nDhxgrp16zJ8+HAC/u4VGBgYyIgRI9i8eTMHDx5k3rx5PPTQQ245pog/c7S5lsSV64no25OA1SuJeKovWWtWk/rqBNBNQSJSSZV65f9q1arRr18/li9fzltvvVXiogzgk08+YcWKFaUNwacsWbIEgM6dO+cXZXnyTt8CfP311+Uem4ivMqpWJXnOQtKHDMUwmwn6dA7RN1yLZddOb4cmIuIVpZ6uWrVqFWZzqeu6CsXpdLJzZ+4HSYsWLYrcJ+/xHTt24HQ6sVgs5RafiE8zm8n4z39xXHUN4b27Y/1tH9Gdridt5FiyHn5UpzZFpFIpdWGmouwfR44cweFwALnXzhUl73G73c7Ro0fLfIem1eq7+c+7Hbg4twXL2VWmXBpt2pD63XpC+/TCtuwbwgf9h8D1a0ifMAkiIso0dmXKo6cpl+6jXBZfWXNksZgp5yunSs1PwvRtecttAERFRRW5T2RkZP7XycnJZSrMzGYT0dG+v7xARIS6O7hLpclldCgs/Rpefx0GDyZg4XwCdvwEc+ZAs2ZlHr7S5LEcKJfuo1wWlpMDO3fChg2wfj2sWlW28SIigjnHPYk+Q4WZG9jt9vyvbTZbkfucft1ZVlZWmY7nchmkpGSUaQxPOtcqzFJ8lTaXPftiadKc0J7dsOzbh3H11WS+/ArZPXuX6tRmpc2jByiX7qNc/iMxETZvtrBxo5lNmyxs3WomLc19lzGkpGSSmOjdHEdEBJfvArOeNnToUObMmVPi57Vq1YpZs2Z5IKJ/nF50ORwOAgMDC+1zevHmjuUy/GGVaKfT5Rdx+oPKmMucZi2xL19D+FN9CVyymJBn/4tlzRpSJ0zCiIwq1ZiVMY+eoly6T2XLpcsFe/ea2bzZwqZNFjZvNvPrr4Wvuw4PN2je3EmLFk5iY10MHlz6mUV/yrHfFGbh4eFUqVKlxM87/RSip5x+jKSkJKpXr15on+Tk5HKNSaQiMKJjSJn5CcHvTiH0paEEfrkI6/afSJn2PjlXND/3ACLidampsGWLJb8Q27LFQkpK4dmwiy5y0bJlbiHWsqWTevVc5N0nt3175bkOz28Ks0GDBjFo0CBvh1GkuLg4bDYbDoeDgwcPFlmYHTx4EMidXatZs2Z5hyjiv0wmMns/gaPVVUQ89iiWgweIuvVG0oe+RGavvrprU8SHGAb8/ruJTZvyZsMs7NljxjAK/pyGhBg0a5ZbhLVo4aR5cxexsf7RMsnT/KYw82VWq5VGjRqxbds2Nm/eTMuWLQvts3nzZgAaN26spTJESiHniuYkLv+O8AH9CfxyEWEvDsa2bg2pb07BiI7xdngilVJ6Ovz44+mzYWZOnSo8u1Wnzj+zYa1aObn0Upff3CVZ3oqVltGjRxMWFkb//v09HY/f6tixI9u2bWPhwoX07NmzwE0AdrudBQsWANCpUydvhSji94zIKFLe+5CgGdMIGzaEwCWLsbZvS8o7M8hpeaW3wxOp0AwDDh40nXZtmIVdu8w4nQVnwwIDDZo2ddKypSt/Rqx69bLNhsXEGAQGGqVqZB4YaBAT4z+zcSbDMM4ZbYMGDahSpQpr164t8FjVqlVZs2aNRwP0tMOHD9O+fXsAtm7dSmjomZehGDt2LEuXLqVp06ZMmDChwLaMjAxuvPFGTpw4ccZemdWqVeObb74hOLhst0Y7nS4SEtLLNIYnWa1moqNDSUxM95uLLX2Vcnlm1u0/EtHzESwH9mNYLKQPGUbmE09CEWssKo/uo1y6j6/nMisLfvop9+L8vELs+PHCP181a7ryrwtr0cJJ48Yu/tUAxy0OHzaRkFC4MDvX3a0xMQa1anm/MIuJCXXfXZkmk4mi6rdi1HQ+qXPnzhw9ehQo+Bri4+Pzv27WrBlTp04t8LzExESOHDlCXFxcoTFDQkJ488036dmzJ/Pnz2fZsmXUqlWLw4cPk5ycTEhICJMmTSpzUSYiuXKaXE7i8jWEDXySoM8WEPbyUGzr15D61rsYsbHeDk/E7xw9WnA2bPt2Mw5HwULIZjNo3Pif05ItWjiJiyufWqBWraILLKsVoqMhMdF/7rw8m2IVZuHh4SQlJZGdnV3kUhD+Jjk5ucCisHlOfywtLa3E4zZv3pxFixYxZcoU1q1bx969e4mOjqZLly707du3zKv9i0hBRngEqe+8j6NNO8Kef4bA5d9ijW9N6jszcFx1jbfDE/FZdjvs3GkuUIgdOVJ4Nqdq1dNnw1w0bepE8wueVaxTmQ8//DCbNm2iY8eOdO7cmZCQEB566CEiIyOZPHlyiWbOirowXkpGpzIrD+Wy+Cy7dhLx2CNY9/2KYTaT8ezzZDw1EMxm5dGNlEv3Kc9cHj+eOxuWd1ryp58sZGUVnA2zWAwaNix4WrJuXcPnb3z2l/dkcU9lFqswW758OU888QSm0/51DMMo8H1xmEwmdu/eXaLnSGEqzCoP5bKE0tIIf2YAQZ/mLkZtb3c9KZOnYalZQ3l0E70n3cdTuczJgZ9//ue6sE2bLPzxR+GCIDraKFCEXX65k7Awt4VRbvzlPenWa8zat2/Pm2++yYwZM9i7dy+ZmZlnvO7sbPz1mjQR8RNhYaROfhd723aEPzeQgNUriY5vTca0GXD7zd6OTsQjEhL+WcB18+bcBVwzMgpOnJhMBg0aFJwNu+gi358Nq4yKNWNWlKLu1JTyoRmzykO5LD3Lnp9zT23+sgfDbMY0dCiJTwwgx9AnUVnoPek+pcllXjujf2bDzOzbd/Z2Ri1bOmne3ElEhLtfgW/wl/ekW2fMRET8jbPBpSQuWUnYkEEEf/I/GD6csOUrSJkyHVf1Gt4OT6RY8toZ5RViZ2pndPHFuRfn582Gnd7OSPxLqQuz5cuXawV7EfFtoaGkvTkF17XtCP3vf7Ct+Y7o61uTMmUajuviz/18kXJUmnZGebNhMWp+UWGUujArai0vERFfZL/vAUKva0POXXdj3b2LyPs6k/GfgWQMGoL6woi3pKfDTz/B8uU2Nm40s3mzmYSEwqe66tb9ZwV9tTOq+NzyT7tr1y6+/PJLdu7cSUJCAiaTiejoaBo3bsytt95Kw4YN3XEYEZHSa9CA1G9XETT4WYI/nEHohNewbVhP6tvv4aqpPzTFs/LaGeXNhP3Tzgjgn2XyAwMNLr/8n9OSzZuXvZ2R+JdSX/wPuW2IXnzxRRYvXgwUvusybzmNm2++mZdffpmQkJAyhCp5dPF/5aFcuse/8xi48FPCBj6FOS0VV0wMqW+9g71DR2+H6Rf0niyevHZGmzb9s4jriROFZ8Nq1YIWLXJo3jyHli2dNGrkmXZGFZm/vCc9fvG/y+Wib9++/PDDDxiGQdWqVbnqqquoUSP3otpjx47xww8/cPz4cRYvXkxCQgIzZswo8dpnIiLult35bnKaXk74Y49i2/ETkQ/eQ8YTT5E+ZCjYbN4OT/xQadoZXXmlQePGISQmZvt0QSHlq9SF2Weffcb333+P1Wrlueee48EHH8T8r+bBLpeLTz75hNGjR/P999+zaNEi7rzzzrLGLCJSZs4LLybpq28JG/48wTOmETL5TWw/bCDl3fdx1VL7NDmzkrQzyivCWrZ00aRJwXZGVuu5Z0+k8il1Yfb5559jMpl45pln+L//+78i9zGbzXTt2hWXy8WoUaP47LPPVJiJiO8ICiJtzOvYW19L+IB+2DZvJDq+NakT38beSQvSSq68dka5RZj5rO2M/inEnNSpowVcpeRKXZjt2bMHi8XCvffee85977nnHsaOHcvPP/9c2sOJiHiM/bY7SGzchIjej2LbtpXIh+8no/cTpL84Al3wU7mc3s4obzbsTO2M8oowf25nJL6n1IVZeno6oaGhBAUFnXPfoKAgQkNDycjIKO3hREQ8ynX+BSR98Q2hLw8l5J0phLwzGdvGDaS8+wGuuud7OzzxkNPbGW3aZGHr1nO3M2rZ0smFF2o2TDyj1IVZdHQ0J0+e5NSpU8TGxp5131OnTpGSkkKVKlVKezgREc8LCCD95TE4Wl9L+JOPY9u2lej2bUl9YzL2W2/3dnRSRi4X/PKLucBpybO1M8qbEavI7YzE95S6MLv88sv59ttvmTRpEsOHDz/rvhMnTsQwDJo1a1baw4mIlBt7p5tJXL6WiF6PYtuyicju/0dmj16kDR8FgYHeDk+KKSWl8GxYcdoZ1a/vwqzr8sVLSl2Yde3alW+++YY5c+aQnp5Ov379qFu3boF9/vjjDyZNmsSXX36JyWSia9euZQ5YRKQ8uGrXIenzJYSOfpmQt94g+L13sW7amHvX5oUXeTs8+RfDgN9+K7hkxdnaGZ0+G6Z2RuJLSl2YXXnllTzyyCPMnDmTL7/8ki+//JLzzjuPatWqYTKZOHbsGMeOHcvfv1u3brRq1cotQYuIlAubjfShL+G4pjXh/Xpj2/4j0R2uJW38RLLvvMvb0VVqaWnw44//zIZt2XL2dkZ514apnZH4ujK9PQcPHkzt2rWZNGkSycnJHD16lKNHjxbYJyoqiv79+2u2TET8lr1DRxJXrCOid3dsP2wgotejZK5dQ9rLoymwMJV4hGHAH3+Y8lsZbdpkYfduM05nwdmwoCCDpk0LnpasVk3tjMS/lKklU57s7GzWrVvHzp07OXXqFACxsbE0atSI1q1bE6hrMtxKLZkqD+XSPdyWx5wcQl59hZA3X8dkGOQ0bETK9Jk4L77EfcH6uPJ4T2Zm5rYz2rzZnH9asqh2RnFx/8yGtWjhf+2M9PPtHv6Sx+K2ZHJLYSblS4VZ5aFcuoe782hbuZyIJx7DfPIkRkgoqeMmkH3P/W6I1Pd54j159Og/zb03bbKwY0fR7YyaNClYiNWs6d8fX/r5dg9/yaPHe2WKiFRWjuvbk7hyPeGP9yBg3RoinuhF5ro1pL0yDkJCvB2eT8trZ3R6IXb06LnbGTVt6qQYy2aK+D0VZiIipeCqXoPkTz8n5PWxhLw+luCPZ2HbsomU6R/irN/A2+H5jL/+Ov3aMDPbtxfdzuiyywrOhqmdkVRWKsxERErLYiHjmSE4rm5NeJ+eWH/ZQ/SN7Ugd8zrZ93elslUWee2MNm78Zzbs4MGztzNq2TK3nVFoqBcCFvFBKsxERMrI0bZd7l2bfR8j4LuVRDzVl6y135E6djwVuYFiXjujvNOSamckUnYqzERE3MCoVo3kuQsJefN1QsaOImjebKw/biXl3Q9wXtbI2+GVWV47oy1brGzfDmvXBrNvX+HZsPBwI7+xd8uWTpo1UzsjkZJQYSYi4i5mMxkDBuG46hrCe3fH+uteom+KJ23kWLIe6uZXpzbz2hnlzYZt2WIhNfX0+HOLsosvzr04P68Qq1dP7YxEykKFmYiImzmubk3iinWE9+9N4PJvCf/vU9jWfUfaa29ihPve9FFeO6O8Iuxs7YyaN3dx7bUWGjfO4vLLHWpnJOJmKsxERDzAqFKFlI/mETx5IqGvjCBo4XysP24jdfpMcho39Wpsee2MTi/EEhMLz+bVresqcJH+pZe6CArKWzPKSU6OF4IXqeBUmImIeIrZTGb//+C48moiej+Kdf/vRN3UnrQRr5DV/bFyObV5ejujvEJs1y4zLlfR7YxyCzGX2hmJeIkKMxERD8tpdSWJK9YS/mQfApd+Tfjg/xKwfi2p4ydiREa59Vh57Yxyi7DchVxPnqx47YxEKqoyF2Y//PADX331Fb/88gtJSUnknGVu22QysWzZsrIeUkTE7xjRMaR8OJvgdyYT+vIwAr/4DOtPP5Iy7X1yrmhe6nGPHCk4G1ZZ2hmJVFSlLswMw2DIkCF89tln+d+fi8mP7kgSEXE7k4nMx/vhaHUVEb0exXLwAFG33kj60JfI7NX3nKc27XbYscNcoBArqp1RtWqnF2FqZyTiT0pdmM2aNYuFCxcCcNlllxEfH0+1atWwWnV2VETkbHKatSBx+RrC/9OPwK8+J+zFwdjWrSX1zckY0f/c5pjXzijvtORPP1nIzlY7I5GKrNRV1IIFCzCZTNxzzz289NJL7oxJRKTCMyKjSJkxi6AZ7xI27HksS5awv20fVt01ge//upDNm4tuZxQT46JFi3/ullQ7I5GKpdSF2YEDBwAYOHCgu2IREak0Tp0ysWWLhc1/9WfzpT3Zuj2AjOMhMPWffdTOSKTyKXVhFhgYSGBgIJGRke6MR0SkwnE6c9sZnX5t2G+/nT4bFghApDWdq3LWcDUbaNHMzqVvP074+VrBVaQyKXVhVq9ePbZu3Up6ejqhfjSPnpWVxdq1a9mxYwc7d+5k586dJCUlAbB169ZSv5YDBw7w7bff8sMPP/DLL7+QmJhIYGAgF1xwATfeeCNdu3b1qzyJSOklJ+e2M8orxLZu/Xc7o1yXXOIscFqy3iVOQv73C2EvjMW0NRvnHR+S+s4MHFdd44VXISLeUOrCrGvXrmzatIn58+fz8MMPuzMmj9q/fz9PPPGEW8d0Op107Ngx//uqVatSv359Tp48yY4dO9ixYwfz5s3jgw8+IC4uzq3HFhHvMgzYt8/M5s3/zIj98suZ2hn9s4p+8+ZOoqP/PZqJrEe642jekojHHsH62z4iO99CxrPPk/Hk06gJpUjFV+rCrFOnTnTt2pXXXnuNiIgI7rzzTjeG5TlWq5UmTZrQuHFjGjVqRGxsLL169SrTmIZhEBYWxv3330+XLl246KKL8rf9+OOPDBw4kIMHDzJgwADmzp1b1pcgIl6Ulgbbtv0zG7ZlS/HbGRX3pnVno8Ykfvsd4c8MIOjTOYS+8hK29WtJmTwNo2pVN78iEfElJqM4C5AVYfDgwQCsWLGClJQUzjvvPBo1anTW03Umk4lXXnmldJF6yOHDh2nfvj1Q+lOZhmGQnJxMVFRUkdu3bt3KAw88AMBnn33GpZdeWup4AZxOFwkJ6WUaw5Os1rxeeunk5Li8HY5fUy7do7R5zGtnlHdd2KZNFnbvLrqd0eWX5xVhLpo3d1M7I8Mg6JP/ETb4v5gyM3FWr0Hq2+/haN227GOXkt6T7qNcuoe/5DEmJhSL5dyz3qWeMVu4cCEmkyl/YdmjR49y9OjRIvfN288XCzN3MJlMZyzKAJo1a0Z4eDipqans37+/zIWZiHhGSdoZnT4bdtllHmpnZDKR9eBDOJq1IKLnw1j3/kLkXbeRMfBZMp5+BiwWDxxURLyp1IXZnXfeqZX8i8npdOa3qgrS8tsiPuPIkYKzYTt2mMnJ8b12Rs4Gl5K4dBVhQwYR/Mn/CB03Gtv360mZMh2jevVyjUVEPKvUhdmYMWPcGUeFtnz5cjIzM7FarVx++eVuGdNq9d2LgPOmaoszZStnp1y6h8ViJjsbtm618P33VjZtsrBxo5k//yyc1+rVXbRsmTsj1qqVi6ZNXf9qZ2T6+79yFhlO1uS3cV3bjpCBTxGwZjUx8deQ/s4Mcq67vtzC0HvSfZRL96hoeVT/JA9LS0tj7NixANx1113ExJR9TSKz2UR0tO8vvREREeztECoM5bLk/vwTNmzI/W/9etiyBbKzC85YWyzQtClccw1cfXXu/+vWNWMymfHZX4+P94Tr2sC992LesYPwu26HIUNg+HCKfXeBG+g96T7KpXtUlDz66G+eisHpdPL0009z+PBh4uLiGDRokFvGdbkMUlIy3DKWJ1gsZiIigklJycTp9N0LMf2Bclk8OTmwa5eZjRvN+bNhRbczMvJnwlq2dHLFFa5C7Yz+XtbQt1WvDUtWEDLkGQJnvg+jRuFYuYr0d9/HqFnTo4fWe9J9lEv38Jc8RkQEe/bi//I2dOhQ5syZU+LntWrVilmzZnkgorMzDIMXX3yR1atXExkZydtvv014eLjbxvflO0/yOJ0uv4jTHyiXBeW2MzLnXx+2bZuFjIyCpxfz2hm1bOnkyisNbrghkNjYjEK/uP++/NP/2AJJGfcmgde0JezpJ7GtX0dEu6tJmfwujvgbPH54vSfdR7l0j4qSxzIXZidOnGD+/Pls2bKFY8eOkZmZyZlW4DCZTCxbtqxUxwkPD6dKlSolfp63WkaNHDmS+fPnExoayvTp06lXr55X4hDxd3ntjE6/SP/33wv/1RkRkbuAa94F+s2bO8n7Wyj3dvpAEhPLOfhykN35bnKaXk54z27Ydm4n6v67yOg/gPTnXgCbzdvhiUgJlakw+/bbb3n22WfPWYzlbSvLXZyDBg1y26lATxs7diz/+9//CA4O5t1336VJkybeDknEb+S1M8orxLZssZCWVox2RvVclXZhfOeFF5O0eBlhw58neMY0QiZNyL1r850ZuGrV9nZ4IlICpS7M9u3bx8CBA7Hb7Vx33XW0a9eOESNGEB4ezrPPPsvJkydZv349GzduJDo6mn79+hESEuLO2H3ShAkTmDFjBoGBgUydOpUWLVp4OyQRn+VywW+/mfPXDNu8+eztjE6fDSvczqiSCwoibczr2Fu3Jfw//bBt+oHo+NakTnoHe8ebvB2diBRTqQuzDz74ALvdzu23386rr74KwIgRIwgMDOTuu+8G4PHHH2f16tX85z//4bPPPuPjjz92T9Q+6u233+btt9/GZrMxadIkrr76am+HJOJT8toZ5RVhmzdbSEoqPBt2/vkF1w0rSTujys5+250kNm5KRK9u2H7cRuRD95HxeD/SXxiOZ1bBFRF3KvWvuo0bN2Iymejdu/dZ92vXrh3PPvssw4cPZ+bMmfTs2bO0h/S6sWPHsnTpUpo2bcqECRMKbPvwww+ZMGECVquVCRMm0K5dOy9FKeIbDAMOHDDlXxe2eXPx2hm1aOGkatXyXcC1onGdfwFJX3xD6MhhhLwzhZC338K2cQMp77yPq+753g5PRM6i1IXZX3/9hcViKdCw22Qy4XA4Cu17xx138PLLL7N48WKfKMw6d+6c3z7q9Gvj4uPj879u1qwZU6dOLfC8xMREjhw5QlxcXIHH//rrr/xWU6GhocyYMYMZM2YUeey77rorf0ZRpCLJa2e0cWNuO6PNm4tuZ1SrVsHZMI+1M6rsAgNJf3kMjmvaEv5kH2xbtxDdvi2pb0zGfuvt3o5ORM6g1IWZzWYj4F+/TUNCQkhNTSUnJwfraecdgoODCQ0N5eDBg6WP1I2Sk5NJKmKxotMfS0tLK/Z4Docjv8BLTk5m69atZ9z3mmuuKfa4Ir7KMHLbGZ0+G3audkatWuUWYuedp9mw8mS/6RYSV6wlotej2LZsIrL7/5HZoxdpw0dBYKC3wxORfyl1YVatWjX2799PVlZWfv/HuLg4fv31V/bs2UOjRo3y901OTiYlJYVAH/klsGLFilI9b8yYMUW2oqpVqxa//PJLWcMS8VnZ2bBjh7lAIVZUO6Nq1Qo2927S5N/tjMQbXLXrkPT5EkJHjSBkykSC33sX66aNpLz7Pq4LLzr3ACJSbkpdmF100UXs37+fAwcO0KBBAyD39N/evXuZMWMG48ePz9/3jTfeAOCCCy4oW7QiUi7++iu3uXdeEbZ9u5ns7IKzYRaLQaNGBU9L1q5tUIZVccSTbDbSh4/E0boN4f0fx7b9R6I7XEvahElk39HF29GJyN9KXZi1a9eOb7/9lm+++Sa/MLv//vuZO3cuX3/9NXv37qV+/frs3buXffv2YTKZuOuuu9wWuIi4h8MBu3cXnA0rup2RK//i/JYtnTRt6izUzkh8n/2GTiSuWEdE7+7YfthAxGPdyFy7hrSXXoHgitFrUMSflbowi4+Pp3PnzlgslvzHGjRowJAhQxg9ejT79u1j3759+dtuueUWHnroobJFKyJlduqUKf/i/E2bLPz4Y9HtjC69NLcIy7s+7IILNBtWUbhqxpG08CtCx44i5M3XCZ75HrZNP5AyfSbOiy/xdngilZrJONOS/WXw22+/sXTpUo4dO0ZYWBht27bVml5u5HS6SEhI93YYZ5Tb/iaUxMT0CtG3zJvKmkunE/bsKTgbdqZ2RnlFWMuWTpo1+6edUUWg9+SZ2VYsI6JfL8wnT2KEhJL62htk333fGfdXLt1HuXQPf8ljTExosZqYe6QwE89SYVZ5lDSXp7cz2rTJwtatZ25nlHtdWO7F+pdcUrHbGek9eXbmY38S3qcnAevWAJDZ9WHSRr0KRXRrUS7dR7l0D3/JY3ELM62lLeKn8toZbdr0z4zYL79YCu0XGmrQrJnaGcmZuWqcR/KnnxPy2hhCxr9K8EcfYtuyiZRpM3HWb+Dt8EQqFbcUZgkJCfzwww8cPXqUzMxM+vXr545hReQ0aWmwdaslvwjbsuXM7YxOX7Li0ktdWArXayIFWSxkPPs8jmvaEPF4D6x7fia643Wkjnmd7Pu7ejs6kUqjTIVZTk4Or732Gh9//HGBFf9PL8ySk5O54YYbyMzMZPny5VSrVq0shxSpFPLaGW3damX7dlizJuis7YzyTkuqnZGUlaNtOxJWriei72MEfLeSiCf7kLX2O1LHvA5hYd4OT6TCK1Nh9tRTT+Uv1nrxxRezf/9+nE5ngX0iIyO59dZb+fjjj1m+fDkPPPBAWQ4pUiFlZOS2M8q9QL+odka5U15qZyTlwahWjeQ5Cwh583VCXn2FoLmfYN22hZRpM6FJY2+HJ1KhlbowW7x4McuXL6dKlSq8++67NGzYkDZt2nDq1KlC+3bq1ImPP/6YVatWqTCTSi+vnVHeXZKbNlnYubNwO6OAgNx2Rtdea6Fx4yyaNctROyMpPxYLGU8/g+Oqawh/vAfWX/cS3el6MkaPg6ee8HZ0IhVWqQuz+fPnYzKZGDRoEA0bNjzrvk2aNMFkMrF3797SHk7Eb+W1Mzq9EDt27MztjPJmw5o0cREWlne3kZOcHBVlUv4c17TJXZC2Xy8CViwjdEB/2LgexoyHYK0wLOJupS7Mdu/eDUDHjh3PuW9QUBDh4eEkJCSU9nAifuPf7Yx++smM3a52RuK/jCpVSP74U4LfepPQ0S9h+uQTIn7YSMq0D8hp3NTb4YlUKKUuzFJTUwkPD89vYH4uLpfvri0iUlp57YxOnw07dKjwbFhsrCt/zbAWLdTOSPyQ2UzmkwNwtW5NRK9Hsfz+G1E3dyBtxCtkPdoT/VUh4h6lLswiIyNJSEggOzubwMDAs+577Ngx0tLSqFmzZmkPJ+IT8toZ5RVi27ZZyMw8czujvFOTamckFYXzyqtg2zbs//cwAUsWE/7cQALWrSF1wiSMiEhvhyfi90pdmDVo0ID169ezceNG2rZte9Z9Z8+eDeReaybiL/LaGeUVYWdqZxQZadC8ecVtZyRSSGws6R/Nwf7WJEJfHkrgF59h/elHUqZ/QM7lzbwdnYhfK3Vhdsstt7Bu3TrefPNNWrRoQXBwcJH7LV68mOnTp2MymbjjjjtKHaiIp+W1M9q4MbcIO1M7o3r18oqw3Fmxit7OSKRIJhOZffrhaHVl7qnNgweIuuUG0oe9TOZjfXRqU6SUSl2Y3XnnncyePZsdO3Zw33338cADD+QvMrtjxw5++eUXFi9ezIYNGzAMg6uvvprrr7/ebYGLlIXLBfv2mQucljxXO6O82TC1MxL5R07zliQuX0P4f/oRuPgLwl54Dtu6taS+ORkjSj8sIiVVpibmp06donfv3uzcuRPTGf46MgyDpk2b8s477xAVFVXaQ8lp1MS85PLaGeUVYWdqZ3TBBbmzYL7SzsgXc+mPlEf3OWMuDYOg994hbPgLmOx2nLXrkPLODHJatPJesD5O70v38Jc8lksT89jYWD755BPmzp3LvHnz2Lt3b4G7Ly+++GLuvfde7r//fgK0PLmUE8OA/ftN+XdJbt5s4eefi25ndMUV/xRhzZu71M5IpLRMJrJ6Pk5OyyuJ6PkIlj8OEHV7J9KfH05mn37ofL9I8ZRpxuzf0tPTOXnyJE6nkypVqhAREeGuoeU0vjJjdviwiYSEwrNOFouZiIhgUlIycToL//USE2NQq5b7CqBztzPKVatWwebel13mwmZzWxge4S9/Cfo65dF9ipNLU0oyYQOfImjRAgCyb+hI6qS3MWJiyzNUn6f3pXv4Sx7LZcbs30JDQwnV4kyVwuHDJq6+OpTs7LNd4Fv0DSGBgQYbNqSXqjgzjNxjnz4bdrZ2Rqcv4Kp2RiLlw4iIJPXd93G0bkvYi88R+O1SrPFtSHl7BjlXXe3t8ER8mlsLM6k8EhJM5yjKziw7O3emrTiFWXY2bN9uLlCIFdXOqHr1grNhjRu7KObaxyLiCSYTWd164GjRiojHHsH62z6iOt9M+nMvkNl/gE5tipyBWwozp9PJgQMHSElJIScn56z7tmzZ0h2HlArq2LGCzb23bz9zO6PTC7FatbSAq4gvcjZqTNK3qwkbNICg+XMJGzWCgPVrSXnrXYyqVb0dnojPKVNhduzYMcaPH8+3335LVlbWOfc3mUz5PTZFHA7YtavgbNiZ2hnlFmEutTMS8UNGWDipU6bhaHMtYUMGEbByOdHxrUl9ZwaOa9p4OzwRn1LqwuzQoUM88MADnDp1iuLeP+DG+wzEzw0YEMi+fYXbGZnNBg0aFJwNUzsjkQrAZCKr68M4mrXIPbW59xciu9xKxn+fI2PAILy6Lo2IDyl1YTZ+/HhOnjxJTEwMAwcOpE2bNlSpUgWLfrikGHbsyH3r5bUzyivE1M5IpGJzXtqQxKWrCB/8X4Jmf0Toq69g27COlCnTMapX93Z4Il5X6sJs/fr1mEwmxo8fz1VXXeXOmKQSePrpbDp3zlE7I5HKKDSU1IlTsbduS/izTxOwZjUx8a1JmTINRzt1iJHKrdQfiXa7naCgIBVlUio335xD/foqykQqs+z7HiTxm9XkXNoQ84njRN57JyFjXoZz3EQmUpGV+mOxVq1aumZMRETKxFmvPolLVpL5UDdMhkHo+HFE3nUb5j+Pejs0Ea8odWF20003kZ2dzYYNG9wZj4iIVDbBwaS9PpGUqdNxhYYRsGEd0fGtsa341tuRiZS7Uhdm3bt3p0GDBrz44oscOnTInTGJiEgllH3XvSQtW03OZY0xnzpF1P13ETpyeO7aOiKVRKkv/g8KCuL999/nxRdf5Pbbb6djx440btz4nC2Z7rzzztIeUkREKjjnRZeQ+PVywoYNIfj96YRMHJ971+a77+OKq+Xt8EQ8rkwLzB45coSTJ0+SmZnJokWLWLRo0Vn3N5lMKsxEROTsgoJIGzs+967NAf2xbfohd0HaSW9jv/Emb0cn4lGlLsz27NnDQw89RGZmJgA2m43o6GitYyYiIm5hv70ziY2bEtHrUWw/bSPy/+4j4/F+pL8wHAICvB2eiEeUujCbNGkSGRkZ1K5dm5dffplWrVph1toHlUZMjEFgoFGqRuaBgQYxMbqjV0TOzXXBhSR9+Q2hLw8l5N2phLz9FrZN35Pyzvu46tT1dngiblfqwmzbtm2YTCYmTJhAo0aN3BmT+IFatQw2bEgnIaFwYWaxmImICCYlJROn01Voe0yMQa1aKsxEpJgCA0kfORbHNW0Jf6ovti2biW7fltQ3JmO/5TZvRyfiVqUuzDIzMwkODva7oiwrK4u1a9eyY8cOdu7cyc6dO0lKSgJg69at57x5oST++usvbrnlFlJTUwFYvnw5tWpVnItXa9UqusCyWiE6GhITXeTkFC7MRERKw37zrSQ2akxE70exbdlM5KNdyejZm/RhIyEw0NvhibhFqQuzunXr8vvvv+N0Ov3qurL9+/fzxBNPlMuxRowYkV+UiYhI2bnq1CVp0RJCR40gZOokQqa/g23Txty7Ni+40NvhiZRZqS8Ku/POO7Hb7axYscKd8Xic1WqlSZMmdO3aldGjR/Puu+965DiLFy9m+fLldOjQwSPji4hUWgEBpI8YRfL/5uCKjsb20zaiO1xLwOcLvR2ZSJmVujB7+OGHufrqqxk6dCjbtm1zZ0wedckllzBv3jyGDh1Kly5duOiii9x+jKSkJEaNGsV5553HU0895fbxRUQE7DfeROKKdThaXYU5NYXIno8Q9swAyMrydmgipVbqU5lTpkyhadOm7Nq1iwcffJDmzZsXa4HZfv36lfaQfmP06NGcPHmSqVOnEhIS4u1wREQqLFdcLZIWfkXoq68Q8ubrBH/wXu6pzekf4LzoEm+HJ1JipS7M3nrrLUym3DvyDMNg8+bNbNmy5ZzPq+iF2dq1a/nss8/o2LEj8fHxHD582NshiYhUbDYb6c8Pw351ayL69cK6awdRHdqR9tobZN91r7ejEymRUhdmLVu2dGccFUJGRgZDhw4lLCyM559/3tvhiIhUKo74DiSuWEf44z0IWL+WiD49yVy3hrSRY0FnL8RPlLowmzVrljvjqBDGjx/PkSNHGDp0KNWrV/fosaxW313M12IxF/i/lJ5y6R7Ko/v4fC5rxZH+2Zc4x40h6LWxBP9vJgFbNpE240Nc9Rt4O7oCfD6XfqKi5bFMvTLlH9u2beOjjz7i8ssv54EHHvDoscxmE9HR7ltvzVMiIoK9HUKFoVy6h/LoPj6fy1dHQ8cO0LUrlp93E9n+WpgyBR55xNuRFeLzufQTFSWPflOYDR06lDlz5pT4ea1atfL47J7dbueFF17AbDbz0ksvebw1lctlkJKS4dFjlMW5Vv6X4lMu3UN5dB+/ymWzqzCtWk/o4z2wrV4F3bqRveQbMsZNADcuJl5afpVLH+YveYyICC7WrJ7fFGbh4eFUqVKlxM+LjIz0QDQFTZs2jX379tGrVy/q16/v8eMBfrGivtOplf/dRbl0D+XRffwml7FVSZq9kJA3XiNk3GgCZ3+MZctmUqbNxNnwMm9HB/hRLn1cRcmjyTCMSt208PDhw7Rv3x4ofUumvn37snz5cqKiorBaC9a6TqeTxMREAKKjo7FYLHTv3p0ePXqUOman00VCQnqpn+9pVquZ6OhQEhPTK8QPiTcpl+6hPLqPP+fStn4t4Y/3wHLsT4ygINJeGUdW14fBVLjnb3nw51z6En/JY0xMaLFmzCrGlXI+IikpiZMnTxb4L68oA0hMTOTkyZNkZPjuaUgRkYrKcU0bElesw359e0xZWYQ/3Z/wPj0xpal1nvgOvzmV6cumTJlyxm2nz8hVtCbmIiL+xqhSheRP5hP81huEjn6ZoAXzsP64NffUZuMm3g5PRDNmJTF27Fji4+MZMGCAt0MREZHSMpvJfPJpkj77GmfNOKy//0b0ze0Jen86VO6re8QHVMoZs86dO3P06FEgt2tBnvj4+PyvmzVrxtSpUws8LzExkSNHjhAXF1c+gYqIiMfkXHkViSvWEv5kHwK/WUL4s09jW7eGtPETMSI8f+OYSFEq5YxZcnIySUlJJCUlkZycnP943mNJSUmkpaV5MUIRESkPRkwsKbPmkDbiFQyrlaDPFxLdvi3WH7d6OzSppCr9XZn+SHdlVh7KpXsoj+5TkXNp3bKJiF6PYjl0EMNmI334SDJ7Pu6xuzYrci7Lk7/kUXdlioiIlEBO85YkLl9D9k23YnI4CHv+WSIe/T9MSYnnfrKIm6gwExER+ZsRFU3KBx+RNmoshs1G4OIvck9tbtnk7dCkklBhJiIicjqTiczH+pD01bc4656P5dBBom7rSPCUSbprUzxOhZmIiEgRci5vRuLyNWTd3hlTTg5hw58n4qH7MCWc8nZoUoGpMBMRETkDIyKS1GkfkDp2PEZgIIHfLCE6vg3WH773dmhSQakwExERORuTiaxHe5K4eDk5F16E5egRou68ieCJ48Hlu3cBin9SYSYiIlIMzsZNSFr2HVld7sHkdBI2cjiRD96N6eRJb4cmFYgKMxERkWIywsJJnTqd1PGTMIKCCFixjOj41tjWr/V2aFJBqDATEREpCZOJrP97hMQlK8m5pB6WY38S2eVWQl4fC06nt6MTP6fCTEREpBScDS8j8ZvVZN33ICaXi9Cxo4i8tzOmv/7ydmjix1SYiYiIlFZoKKmT3iZl4lSMkBAC1qwiJr41tu9WeTsy8VMqzERERMoo+/6uJC5dRc6lDTGfOE7kPXcQMnaUTm1KiakwExERcQNn/QYkfr2CzP97BJNhEPr6WCLvug3zsT+9HZr4ERVmIiIi7hISQtr4SaRMnY4rNIyA9WuJvv4abCuWeTsy8RMqzERERNws+657SVq2mpzLGmM+dYqo+7sQOnI45OR4OzTxcSrMREREPMB50SUkfr2czG49AAiZOJ6oO2/GfOSwlyMTX6bCTERExFOCgkh7dQIp0z7AFRaObeP3RMe3JuDbJd6OTHyUCjMREREPy76jC4nL1+BoegXmxEQiu95L8ItDwOHwdmjiY1SYiYiIlAPXBReS9OU3ZDz2OABBkydC27aYD/7h5cjEl6gwExERKS+BgaSPepXk9z/CFRkFP/xAeLvWBCz+0tuRiY9QYSYiIlLO7LfcRurqddCqFebkJCK7PUjoC89Cdra3QxMvU2EmIiLiBa46dWHNGrKeeBKAkHenEnXrjZj3/+7lyMSbVJiJiIh4S0AAmS+/QvKsObiio7H9tI3oDtcS8PlCb0cmXqLCTERExMvsHW8iccU6HC2vxJyaQmTPRwh7ZgBkZXk7NClnKsxERER8gCuuFkmfLSbjyacBCP7gPaJu7oDl931ejkzKkwozERERX2Gzkf7CcJJmz8cVG4tt53ai2l9L4IJ53o5MyokKMxERER/jiL+BxBXrsF/dGnN6GhGP9yDs6f6Qment0MTDVJiJiIj4INd5NUme/wXpTw/CMJkI/t9Mojtdj2XvL94OTTxIhZmIiIivslrJeO5Fkud+hqtqNaw/7yb6xnYEzvnY25GJh6gwExER8XGOdteTsGId9rbtMGVkENH/ccKf7APp6d4OTdxMhZmIiIgfMKpXJ3nuZ6Q/+zyG2UzQ7I+I7ngdlp93ezs0cSMVZiIiIv7CYiFj4LMkz/8CZ/UaWPf+QnSn6wn66EMwDG9HJ26gwkxERMTPOFq3zb1r87p4TJmZhA/oR3jfxzClpXo7NCkjFWYiIiJ+yKhaleTZC0h7YTiGxULQ/LlE3dAOy84d3g5NykCFmYiIiL8ym8l88mmSFi7GWTMO62/7iL4pnqAP3tOpTT+lwkxERMTP5Vx1NYnL15J9Q0dM2dmEPzOA8F6PYkpJ9nZoUkJWbwdQ3rKysli7di07duxg586d7Ny5k6SkJAC2bt1KaGhomY/x66+/MmvWLNavX8/x48cJCgqievXqtGzZkh49ehAXF1fmY4iIiJzOiI0lZdYcgqe+Reio4QQtWoDtp22kTPuAnKZXeDs8KaZKV5jt37+fJ554wmPjz5o1i7Fjx+JwOIiMjOTiiy8mKyuLw4cPs3fvXtq2bavCTEREPMNsJvOJJ3FceRURvbtjObCfqFtuIG34SLJ69AaTydsRyjlUusLMarXSpEkTGjduTKNGjYiNjaVXr15uGfvzzz9n5MiRREZG8tJLL3HjjTdiNueeLXa5XGzbto3q1au75VgiIiJnktOiFYnL1xD+ZF8Cl3xF+JBnCFi7htQ33sKIivZ2eHIWla4wu+SSS5g3b17+94cPH3bLuElJSYwcORKz2czbb79Ns2bNCmw3m800b97cLccSERE5FyMqmpSZHxM8bSqhI14kcPEXWHduJ+Xd98lp1sLb4ckZ6OJ/N1mwYAHJyclcf/31hYoyERERrzCZyOzVl6SvvsVZ93wsB/8g6tYbCZ76lu7a9FGVbsbMU5YvXw5A+/bt+fPPP5k9eza7d+/GMAwuuOACbrvtNpo0aeLlKEVEpDLKubxZ7qnNAf0J/OIzwoYNwbbuO1InTsWIifV2eHIaFWZuYBgGu3btAuDUqVPceuutpKWl5W9fs2YNH374Id27d+fZZ5/1VpgiIlKJGRGRpEyfSdAH7xE2dDCB3yzB2r4tKe+8T06rK70dnvxNhZkbpKamkpmZCcDEiROJiYlh3LhxXHPNNaSlpTFnzhwmTZrEjBkzqF27Ng8++GCZj2m1+u5ZaIvFXOD/UnrKpXsoj+6jXLqPt3KZ81gvUq+6itDuD2P5bR9Rd3Qi84VhZPf/D5j979+1or0nTYZRuU8yHz58mPbt2wOlX8fs2LFjtGvXLv/72bNnc8UVBdeMGTlyJLNmzaJq1aqsWrUKq7X0NbFhGJh0y7OIiJRFair07g2ffJL7fadO8OGHULWqd+Oq5Pxmxmzo0KHMmTOnxM9r1aoVs2bN8kBE/wgICMj/+oorrihUlAF0796dWbNmceLECfbs2UOjRo1KfTyXyyAlJaPUz/c0i8VMREQwKSmZOJ0ub4fj15RL91Ae3Ue5dB/v59IMb71LQKtrCBk8CNOSJbiaNiV92vvkXNPGC/GUjvfzWDwREcHFmtXzm8IsPDycKlWqlPh5kZGRHoimoPDwcMxmMy6Xi4suuqjIfWrWrElISAgZGRkcPny4TIUZQE6O77758jidLr+I0x8ol+6hPLqPcuk+3s5lTtdHyL6iBRGPPYL1172E3X4zGc8MIeOpgWCxeC2ukvJ2Ht3FbwqzQYMGMWjQIG+HUSSbzUbt2rX5448/CAwMPON+AQEBZGRk4HL5/xtHREQqDmfDy0hcuorw5wYSNPcTQseMxLZ+HSlTpmFUq+bt8CqVinGlnA/IW7vs4MGDRW5PTU3N78lZTW9yERHxNWFhpL71DikTp2KEhBDw3Upirr8G25rV3o6sUlFh5iY33XQTAN9//z1HjhwptP3TTz8FICwsjMaNG5drbCIiIsWVfX9XEpeuIqfBpZhPHCfy7tsJGTsKnE5vh1YpqDArgbFjxxIfH8+AAQMKbWvXrh3NmjXD4XDw7LPPcurUqfxtP/zwA5MnTwbg0UcfPevpThEREW9z1m9A4pKVZHZ9GJNhEPr6WCLvvh3zsT+9HVqF5zfXmLlT586dOXr0KJC79ESe+Pj4/K+bNWvG1KlTCzwvMTGRI0eOEBcXV+S4EyZM4MEHH2TTpk20a9eOevXqkZ6ezoEDBwDo0KEDjz/+uJtfjYiIiAeEhJA24S0crdsS/t//ELBuDdHxrUmZPA3H9e29HV2FVSlnzJKTk0lKSiIpKYnk5OT8x/MeS0pKKrByf3HVqFGDzz//nMcff5xatWqxb98+Tpw4QbNmzRg1ahSTJk0q0/plIiIi5S377vtIXP4dOZc1xnzyJFH3dSZ01AjIyfF2aBVSpV9g1h85nS4SEtK9HcYZWa1moqNDSUxMrxC3LnuTcukeyqP7KJfu43e5zMwkbOgQgme+B4DjyqtJeWcGrppFn0UqL/6Sx5iY0GKtY1YpZ8xERESkhIKDSRs3gZRpH+AKC8f2wwai41sT8O0Sb0dWoagwExERkWLLvqMLicu+w9HkcswJCUR2vZfQ4S+Aw+Ht0CoEFWYiIiJSIq4LLyLpq2/J6NkbgJApE4m6vRPmQ0Wv5SnFp8JMRERESi4wkPRXxpE843+4IiKxbdlEdHwbAr7+ytuR+TUVZiIiIlJq9ltvJ3H5GhxXNMOcnETkIw8Q+sKzYLd7OzS/pMJMREREysRV93ySvviGjMf7ARDy7lSibr0B84H9Xo7M/6gwExERkbILCCD9pVdInjUHV1QUth+3Ed2+LQFffObtyPyKCjMRERFxG3vHm0hcsQ5Hyysxp6YQ2eNhwp59GrKyvB2aX1BhJiIiIm7lqlWbpM8Wk9E/t7d08PvTibrlBiy/7/NyZL5PhZmIiIi4n81G+osjSP7kU1yxsdh2/ERU+2sJXDDP25H5NBVmIiIi4jH29jeSuGId9quuwZyeRsTjPQgb+CRkZno7NJ+kwkxEREQ8ynVeTZIXfEn604MwTCaCZ31AdKd4LL/u9XZoPkeFmYiIiHie1UrGcy+SPGchripVsf68i+gbriVwzsfejsynqDATERGRcuO4Lp7Eleuwt7kWU0YGEf0fJ/zJPpCe7u3QfIIKMxERESlXruo1SJ63iPRnhmCYzQTN/ojoTtdj2fOzt0PzOhVmIiIiUv4sFjL++xzJ87/AWa061l/2EN3xOoI+ngWG4e3ovEaFmYiIiHiNo3VbEleux35dPKbMTML/8wThfR+DtDRvh+YVKsxERETEq4yqVUmevYC054dhWCwEzZ9L9A3XYtm5w9uhlTsVZiIiIuJ9ZjOZTw0kaeFinOfVxPrbPqJviido5oxKdWpThZmIiIj4jJyrriZxxTqyO9yIKTub8EH/IbzXo5hSU4rc37pqJTRsmPv/CkCFmYiIiPgUIzaWlP/NJW3YSAyrlaBFC4hu3xbr9h//taNB8MvD4Oefc/9fAWbWVJiJiIiI7zGbyXziSZIWfY2zVm0sB/YTdXMHgt57J78As61cjnXbVgCs27ZiW7ncmxG7hQozERER8Vk5La8kcfkasjvdjMluJ3zwICK6P4QpKZHQMSMxLBYADIuF0DEj/X7WTIWZiIiI+DQjOoaUmZ+QNnIMhs1G4FefE926JbYft2JyOgEwOZ3YfvT/WTMVZiIiIuL7TCYye/Ul6ctvcNaui+XEcf49N1YRZs1UmImIiIjfyLmiOWkjRgJg+te2ijBrpsJMRERE/IdhEDJxQv61ZYU2+/msmQozERER8Ru2lcsLXFv2b/4+a6bCTERERPyDYRS4E/OMu/nxrJkKMxEREfEL55oty+PPs2YqzERERMT3FXO2LH93P501U2EmIiIiPq+4s2V5/HXWTIWZiIiI+La82TJTycoWw2T2u1kzFWYiIiLi2+x2zEcOYzJcJXqayXBhPnoY7HYPBeZ+Vm8HICIiInJWgYEkfbMK86mThTZZLGYiIoJJScnE6SxcuLmqVIXAwPKI0i1UmImIiIjPc8XVwhVXq/AGqxmiQ3EmppOTU7IZNV9U6QqzrKws1q5dy44dO9i5cyc7d+4kKSkJgK1btxIaGlrqsXNycpg3bx5ffvklv/76K+np6YSFhVGvXj3uuOMOunTpgtmss8ciIiJStEpXmO3fv58nnnjC7eNmZWXRs2dPNm3aBEDVqlWpVasWx48fZ+PGjWzcuJElS5YwdepUbDab248vIiIi/q/SFWZWq5UmTZrQuHFjGjVqRGxsLL169SrzuO+99x6bNm0iMDCQCRMm0L59+/xty5YtY8CAAaxZs4bZs2fz0EMPlfl4IiIiUvFUusLskksuYd68efnfHz582C3jrlixAoAHHnigQFEG0KFDB+6//34+/PBDVq1apcJMREREiqQLntwkOzsbgNq1axe5vU6dOkDudWgiIiIiRVFh5iYNGzYEcm8gKMqWLVsAaNq0abnFJCIiIv6l0p3K9JQ+ffqwYsUKvvrqK8477zzuv/9+qlWrxl9//cUnn3zC119/zfnnn0/37t29HaqIiIj4KBVmbnLBBRcwZ84cxo8fz/vvv8/06dPzt1mtVrp3707v3r2Jiopyy/GsVt+d7LRYzAX+L6WnXLqH8ug+yqX7KJfuUdHyqMLMjY4ePUpCQgJOp5OYmBhq1KjBsWPHSEhI4IsvvuDCCy/knnvuKfNxzGYT0dGlX2+tvEREBHs7hApDuXQP5dF9lEv3US7do6Lk0W8Ks6FDhzJnzpwSP69Vq1bMmjXLAxEVtHjxYgYOHEh4eDiTJ0+mQ4cO+duWL1/O4MGDeeGFF7Db7XTt2rVMx3K5DFJSMsoassecqz2GFJ9y6R7Ko/sol+6jXLqHv+QxIiK4WLN6flOYhYeHU6VKlRI/LzIy0gPRFORwOHjllVdwuVwMHjy4QFEG0L59e5577jkGDx7MG2+8wT333ENAQECZjukPbSecTpdfxOkPlEv3UB7dR7l0H+XSPSpKHv2mMBs0aBCDBg3ydhhF+uOPPzhx4gQA1157bZH7tGvXDoCUlBQOHDhAvXr1yi0+ERER8Q8V40o5L0tPTy/R/nlrnomIiIicToWZG9SpUye/OfmaNWuK3Oe7774DwGKxULdu3XKLTURERPyHCrMSGDt2LPHx8QwYMKDA49HR0fmnKkePHs2qVasKbF+1ahVjxowBID4+noiIiHKJV0RERPyL31xj5k6dO3fm6NGjABiGkf94fHx8/tfNmjVj6tSpBZ6XmJjIkSNHiIuLKzTmiBEj+P333/njjz/o3bs3sbGx+ctlnDp1Cshd62zYsGGeeEkiIiJSAVTKwiw5OZmkpKRCj5/+WFpaWonGrF69Op999hkfffQRy5Yt47fffmPPnj2EhIRwxRVX0KFDB7p27UpwcMVYZ0VERETcz2ScPmUkfsHpdJGQULIbDsqT1WomOjqUxMT0CnHrsjcpl+6hPLqPcuk+yqV7+EseY2JCi7WOma4xExEREfERKsxEREREfIROZfohwzBwuXz7n81iMft0awx/oly6h/LoPsql+yiX7uEPeTSbTZhMpnPup8JMRERExEfoVKaIiIiIj1BhJiIiIuIjVJiJiIiI+AgVZiIiIiI+QoWZiIiIiI9QYSYiIiLiI1SYiYiIiPgIFWYiIiIiPkKFmYiIiIiPUGEmIiIi4iNUmImIiIj4CBVmIiIiIj5ChZmIiIiIj1BhJiIiIuIjrN4OQHzb999/z/vvv89PP/1ERkYGNWvWpFOnTvTq1YuQkBCfGdMfuOt1G4bBtm3bWLFiBVu2bOH3338nLS2N8PBwGjZsyJ133sltt92GyWTy4KvxHk+/f1avXk2vXr0AiIuLY8WKFWUe01d5KperV69m3rx5/PjjjyQlJREREUGdOnW48sor6d+/P1ZrxfvocXcuk5KSeP/991m1ahUHDx7E4XAQHR3N5ZdfTteuXbnqqqs88Cq868SJE6xfv54dO3awc+dOfv75Z7KysrjssstYsGBBmcb2p88dk2EYhreDEN80a9YsRo0ahWEY1KhRg5iYGPbt24fdbueiiy7i448/Jioqyutj+gN3vu4NGzbQrVu3/O9r165NREQER44cISkpCYDrrruOSZMmERAQ4P4X40Wefv+kpaVx66238ueffwIVuzDzRC5zcnIYPHgwn3/+OQA1atSgatWqJCUlcezYMRwOB1u3biU0NNQDr8h73J3LAwcO8NBDD3H8+HHMZjNxcXGEh4dz8OBB0tLSAHjqqafo27evh16Rd3zwwQeMHj260ONlLcz87nPHECnCjh07jAYNGhj169c3Zs+ebbhcLsMwDOPYsWNG586djXr16hn9+vXz+pj+wN2ve926dUZ8fLwxc+ZM4+TJkwW2LVy40GjUqJFRr149Y9y4cW59Hd5WHu+fYcOGGfXq1TP69u1r1KtXz7j++uvdEbrP8VQun3/+eaNevXrG7bffbvz0008FtmVkZBjLli0z7Ha7W16Dr/BELh9++GGjXr16xo033mjs3bs3//Hs7GzjjTfeMOrVq2fUr1/f+Pnnn936Wrxt3rx5Rrdu3YzXXnvNWLJkifH2228b9erVMzp37lzqMf3xc0eFmRSpT58+Rr169Yxnnnmm0Lb9+/cbDRo0MOrVq1eiXwyeGNMfuPt1p6amnvXDberUqUa9evWMVq1aGU6ns9Rx+xpPv382bdpk1K9f33jiiSeM+fPnV+jCzBO53LBhg1GvXj2jTZs2RmJiohuj9W2e+PmuX7++Ua9ePWPZsmVF7nPHHXcY9erVM955550yxe7r8n4Oy1KY+ePnji7+l0LS09NZs2YNAPfee2+h7eeff37+9Q1Llizx2pj+wBOvOywsDJvNdsbt1157LZB7jUpCQkJJQ/ZJnn7/ZGdn88ILLxASEsKLL75YtmB9nKdy+cEHHwDQo0cP3zot5EGeyKXdbsf4+wqj2rVrF7lP3uMOh6PEMVcm/vq5o8JMCvn555+x2+0EBATQpEmTIvdp3rw5AD/99JPXxvQH3njd2dnZ+V8HBQW5ZUxv83QeJ0+ezP79+3n66aepXr16mWL1dZ7IZXZ2NmvXrgWgffv2bN++neHDh/Poo4/y+OOP89Zbb3Hs2DH3vAAf4olcxsTEcN555wGwdevWQtuzs7PZuXMnAE2bNi1N2JWGv37uVLxbY6TM9u/fD0DNmjXPODNTp06dAvt6Y0x/4I3X/dVXXwHQoEEDwsLC3DKmt3kyjz///DPvvfceTZo04cEHHyxboH7AE7ncs2cPDoeDkJAQli5dyuuvv47L5crfvnLlSqZNm8aYMWO46aabyvgKfIen3peDBg1i4MCBjBs3DrPZzPXXX09YWBi//fYbb775JkePHqVjx460adOm7C+iAvPXzx0VZlJIcnIyAJGRkWfcJ29b3r7eGNMflPfr3rVrF7NnzwbIX/KhIvBUHp1OJ88//zwAL7/8MmZzxT+J4IlcnjhxAsg9DTdu3DiaN2/O888/zyWXXMLRo0eZMGECS5YsYdCgQVxwwQU0aNCgjK/CN3jqfXnLLbcQGhrKW2+9VejUenR0NEOHDuWBBx4oRcSVi79+7lT830JSYnmnws52HVPeMgynnzYr7zH9QXm+7pMnT9KvXz8cDgc33HADt9xyS5nG8yWeyuN7773Hrl276NatW4UpFs7FE7lMT08HcpfLiI6O5t133+Wyyy4jICCA888/nwkTJnDppZficDiYOnVqGV+B7/Dkz/fBgwdJTk7GZDJRs2ZNGjRoQEhICImJicyZM8enTr35Kn/93FFhJoUEBgYCZ7+w1G63F9jXG2P6g/J63ampqTz22GMcPXqUyy67jDFjxpR6LF/kiTweOHCAt956i1q1atGvX7+yB+knPPnzDXDfffcVOoVuNpvz195bu3ZtgdOc/sxTP98jRoxg1KhRhISEsGjRIlauXMmiRYvYuHEjAwcO5JdffuGRRx5h165dZXsBFZy/fu6oMJNCijO1W5wpYk+P6Q/K43Wnp6fTs2dPdu/ezSWXXMJ7771XYa4ty+OJPA4bNozs7GyGDx9OcHBw2YP0E578+Qa48MILi9wn7/G0tLT8hZD9nSdyuWfPHj755BOsViuTJk2ifv36+dtsNhu9evWic+fOZGdn88Ybb5Q++ErAXz93dI2ZFHL++ecDcPToURwOR5HTwAcPHiywrzfG9Aeeft2ZmZn07t2bH3/8kfPPP5/333+f6OjosoTskzyRx127dmEymXjuuecKbcvKygLgzz//pHXr1gBMmjSJZs2alSJ63+KJXJ5ejJ1p5uH0xyvKjJkncrllyxYMw6Bu3br5F6b/27XXXsvChQvZvn17qeKuLPz1c0czZlJIw4YNsdls2O32M/7gb9myBYDLL7/ca2P6A0++7uzsbPr27cumTZuIi4tj5syZVK1atawh+yRP5dEwDE6ePFnov7y2Ny6XK/+xirJmlCdyWb16deLi4oB/Puj+7dChQ0DuNT0VZZ0zT+Qy73q94vS6zTsNJ0Xz188dFWZSSGhoaP5t2HPnzi20/cCBA3z//fcAdOrUyWtj+gNPvW6Hw0H//v1Zv349NWrUYObMmdSoUcM9QfsgT+Rx8+bN/PLLL0X+l9evLy4uLv+xK6+80k2vxrs89Z7MWwbjs88+K3JG7NNPPwWgVatWFaaJuSdyecEFF+Q/N6+Y/be8RVPz9pWi+evnjgozKVLfvn0xmUwsWrSIOXPm5K9Effz4cZ5++mlcLhcdOnQodCfbAw88QHx8fP4q4O4Y09+5O5dOp5P//ve/rF69mqpVqzJz5swzrhBekXjiPVlZeSKXPXr0IDw8nN9++41XXnklfzbHMAxmzpzJypUrMZlMFWoZF3B/Ltu0aUOVKlXIycnhySef5Ndff83f5nA4mD59en5D7zvvvNOjr81fVLTPHZORF6XIv3zwwQeMGTMGwzA477zziI6OZt++fdjtdi644AI+/vhjYmJiCjwnPj6eI0eO0K9fP/r37++WMSsCd+byyy+/ZODAgUDujM7ZVqp/8cUXadiwoWdelBd44j1ZlAULFjB48GDi4uJYsWKFJ16K13kil+vXr6dPnz5kZWURGRlJ3bp1+fPPPzlx4gQmk4lBgwbRo0eP8nqJ5cbdudywYQN9+/YlIyMjf7mMiIgIDh48mH+q88Ybb+SNN97AYrGU2+v0tD///LNAsWm328nIyMBqtRa4oalnz5489thj+d9XtM+dijGfLB7RrVs36tevz4wZM9i+fTunTp2iZs2adOrUiV69ehEaGuoTY/oDd77u068rOXLkCEeOHDnjvqmpqWWK29dU1vePJ3gil9dccw2LFi3inXfeYf369fz888+EhYURHx/Po48+SqtWrTzwSrzP3bm8+uqr+fLLL5k5cybr16/n8OHD/PXXX0RGRtKsWTM6d+5codYpzON0Oou8YzcnJ6fA43k35xSXv/3e0IyZiIiIiI/QNWYiIiIiPkKFmYiIiIiPUGEmIiIi4iNUmImIiIj4CBVmIiIiIj5ChZmIiIiIj1BhJiIiIuIjVJiJiIiI+AgVZiIiIiI+QoWZiIiIiI9Qr0wRER9z4sQJNm3axO7du9m1axe7d+/O7xX44YcfcuWVV3o3QBHxGBVmIiI+Zvbs2bz11lveDkNEvECFmYiIjzGZTJx33nk0bNiQhg0bUr16dV544QVvhyUi5UCFmYiIj+nTpw/9+vXL//7w4cNejEZEypMu/hcR8YB3332X+vXr06hRI7Zv317kPqtXr6ZBgwbUr1+fL774Iv9xi8VSXmGKiI9RYSYi4gGPPfYY11xzDQ6Hg6effpq0tLQC248fP85zzz2HYRjceeed3HbbbV6KVER8iQozEREPMJlMvPrqq8TGxnLo0CGGDRuWv80wDJ599lkSEhKoW7cuQ4cO9WKkIuJLVJiJiHhI1apVGT16NCaTiS+//JKFCxcCMG3aNNavX4/NZuP1118nNDTUy5GKiK9QYSYi4kHt2rWjW7duALz00kssWrSIiRMnAjBgwAAaN27sxehExNeoMBMR8bCnn36ayy67jIyMDJ555hkcDgdt2rShe/fu3g5NRHyMCjMREQ8LCAhgzJgx+d+Hh4czZswYTCaTF6MSEV+kwkxEpBzMnTs3/+u0tDR+/vlnL0YjIr5KhZmIiIetXLmSWbNmAVC/fn0Mw+C5557j5MmTXo5MRHyNCjMREQ86fvw4gwcPBqBLly589NFHxMXFcerUKZ599lkMw/ByhCLiS1SYiYh4iMvl4plnniExMZHzzz+fF198kfDwcF5//XWsVitr167l/fff93aYIuJDVJiJiHjI9OnT2bBhQ/56ZSEhIQBcccUVPPHEEwCMHz+eXbt2FXiey+UiISEh/7+UlJT8bampqQW22e328ntBIuJxJkPz6CIibrd9+3YefPBBHA4HzzzzDD169Ciw3eVy8cgjj7Bx40bOP/98Fi5cmF+4HT58mPbt2xfrOKNHj6ZLly5uj19EvEMzZiIibpaWlsbTTz+Nw+GgdevWRa5XZjabGTduHFFRURw4cICXX37ZC5GKiK/RjJmIiIiIj9CMmYiIiIiPUGEmIiIi4iNUmImIiIj4CBVmIiIiIj5ChZmIiIiIj1BhJiIiIuIjVJiJiIiI+AgVZiIiIiI+QoWZiIiIiI9QYSYiIiLiI1SYiYiIiPgIFWYiIiIiPkKFmYiIiIiPUGEmIiIi4iP+H8WhLJRKMa4VAAAAAElFTkSuQmCC",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig = interaction_plot(\n",
+    "    x=df['x1'],\n",
+    "    trace=df['x2'],\n",
+    "    response=df['y'],\n",
+    "    colors=['red', 'blue'],\n",
+    "    markers=['^', 's'],\n",
+    "    ms=10\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "818048ec-b365-4141-af93-34100b40b62b",
+   "metadata": {
+    "tags": []
+   },
+   "source": [
+    "### Exercices:\n",
+    "\n",
+    "- change the interaction terms $a_{12}$ to see study the match between the data and the model"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6aa1f3f8-7265-4b0c-a686-edfb53411b95",
+   "metadata": {},
+   "source": [
+    "## Mixed-effect model\n",
+    "\n",
+    "We now create a new response variable $y3$ that is sensitive to a group index (first and second half of indices)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 177,
+   "id": "0b29074e-18d7-48f7-892e-e7365831056d",
+   "metadata": {
+    "tags": []
+   },
+   "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>x1</th>\n",
+       "      <th>y</th>\n",
+       "      <th>gp</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>2.494329</td>\n",
+       "      <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>0.020408</td>\n",
+       "      <td>0.088026</td>\n",
+       "      <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>0.040816</td>\n",
+       "      <td>3.858834</td>\n",
+       "      <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>0.061224</td>\n",
+       "      <td>1.663404</td>\n",
+       "      <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>0.081633</td>\n",
+       "      <td>0.787157</td>\n",
+       "      <td>1</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "         x1         y  gp\n",
+       "0  0.000000  2.494329   1\n",
+       "1  0.020408  0.088026   1\n",
+       "2  0.040816  3.858834   1\n",
+       "3  0.061224  1.663404   1\n",
+       "4  0.081633  0.787157   1"
+      ]
+     },
+     "execution_count": 177,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# number of samples\n",
+    "n = 50\n",
+    "\n",
+    "# define the groups and add an effect on the intercept\n",
+    "gp = np.array(np.arange(n)<n/2, dtype=int)\n",
+    "\n",
+    "# exogeneous variables\n",
+    "x1 = np.linspace(0,1,n)\n",
+    "\n",
+    "# error\n",
+    "e = stt.norm.rvs(size=n)\n",
+    "\n",
+    "# endogenous variable scaled by factor a\n",
+    "a1 = 2.0\n",
+    "a_gp = 2.0\n",
+    "y = a1 * x1 + a_gp * gp + e\n",
+    "\n",
+    "# build dataframe\n",
+    "df = pd.DataFrame(np.column_stack((x1,y)), columns=['x1','y'])\n",
+    "df['gp'] = gp\n",
+    "df.head()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 178,
+   "id": "badf4303-57f2-44b3-bef8-b5684b551ca5",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "                            OLS Regression Results                            \n",
+      "==============================================================================\n",
+      "Dep. Variable:                      y   R-squared:                       0.099\n",
+      "Model:                            OLS   Adj. R-squared:                  0.080\n",
+      "Method:                 Least Squares   F-statistic:                     5.280\n",
+      "Date:                Fri, 07 Jul 2023   Prob (F-statistic):             0.0260\n",
+      "Time:                        18:05:52   Log-Likelihood:                -82.524\n",
+      "No. Observations:                  50   AIC:                             169.0\n",
+      "Df Residuals:                      48   BIC:                             172.9\n",
+      "Df Model:                           1                                         \n",
+      "Covariance Type:            nonrobust                                         \n",
+      "==============================================================================\n",
+      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
+      "------------------------------------------------------------------------------\n",
+      "Intercept      3.1332      0.358      8.740      0.000       2.412       3.854\n",
+      "x1            -1.4195      0.618     -2.298      0.026      -2.662      -0.177\n",
+      "==============================================================================\n",
+      "Omnibus:                        1.928   Durbin-Watson:                   1.790\n",
+      "Prob(Omnibus):                  0.381   Jarque-Bera (JB):                1.143\n",
+      "Skew:                           0.330   Prob(JB):                        0.565\n",
+      "Kurtosis:                       3.335   Cond. No.                         4.31\n",
+      "==============================================================================\n",
+      "\n",
+      "Notes:\n",
+      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
+     ]
+    }
+   ],
+   "source": [
+    "# model with ols\n",
+    "lm = smf.ols('y ~ x1', df)\n",
+    "\n",
+    "# fit model to data\n",
+    "lmf = lm.fit()\n",
+    "\n",
+    "# summary\n",
+    "print(lmf.summary())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 179,
+   "id": "3eb0babb-3759-4568-80d9-42736b5a39fe",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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dp5YmeFtagqvwDuyH58B+lFy6RGnb/sbr6Pn0k8FSBmXDCeVWKwQ1f3WiOWa6BUdONWd1vhYRZQ6+21NWya2tQ25tnXJbliT42tqC03YOO1QGg3LMc2A/vE3B6uQ9I08iitCUWFB1x13Kyjt/pxtiTi5EHROVAeZrEWU7u70Vf/jD09i4cQM6O90wm4tx8smn4Yorvo/CwiIAwPXXX43a2nr86Ec3RTzHJ598jOeeewZffbUbHo8HJSUWzJo1G7fffjfUCfyyykCJspogitBardBarWHHLN/+brCIZktzyAiU1N+PQKcbol6vtHX86QX0fLIJ6uJiaG1l0JWWDo5ABf+oRrQlIspkTU2NuOaa76Gysgr33nsfSkvLsXfvV/jtb3+DjRs34Omnn0NBQeGo59iz5yvcfPMP8Y1vXIqbb74NarUWDQ0H8M47/0Kit6hloEQUxVAhTcw+UrlPlmX43W74nR0hRTD9nZ3Bv9vb4W9vR9+W4W08BI0Ghy1/SkkY793yRbBMQmkZVIWFKVtMk4gyh8/phM9hh8ZihSbOJVQeeeRX0Gg0ePTRJ6DTBXdnsNlsqKurx6WXXoSnn/4tbr75jlHP8fHH/4HZXIzrrvuRsilueXkFjj/+xLheeyQMlIjGQRAEaIxGaIyh00pVd9wFf3cXvC0twWm8lpbgSFRLC1T5+SGr6tpeewXexgYAgJibC21pKbS24MiTrqIC+iNmg4goGskzStFWUYCo0Ya07dqwHo6V/xusVScIsCz9NgpOnA8IQsjuCdHOO56Ugq6uTnz44Qe4+urrlCBpiNlcjLPOOhf/+tc/cdNNt496HpPJjI6Odnz22Sc4+ugoS54ThIESUYyoDQVQGwqQV1cfcr/s94fc1pWWQvZ54XM4IPX3h5Qy0JaVhQRKbX9+FYJaPRhMBf+MfGMjouzz5bIfRD2mP2I2yn9043DbH18P+HzDDWQZjj+9AMefXkBuXT0qbx0e2dl7280I9HSHnbPu98+P+doaGhogyzKmTKmJeLy6uhrd3V1wu12jnuf00xfgww834vrrr4bZXIwZM2bh6KOPwcKF50OvT+yuDAyUiOLs4BVypT+4DgAg+XzwOezKyJO3pRlq4/CQuCzLcL/9L8ieEQUcBQEaczE0tlLk1U+H6dzzEvIciChNJTif51CG84tGTzlQqVT46U/vwVVXXYvPPvsYmzd/gT/+8Q/405/+iKefXoHi4uL4X+wgBkpESSJqNNCVV0A3osp4iEAA5q99PWQaT+rrha+9Db72NggqEUAwUJJlGfvuuh3qgkJobDboSsugsZVCW1rKgppEGeaw5U9FP3hQGY7qe/8f9t19R2jAJIqo/vn9Yds91fzPQ5O+toqKCgiCgH379uCUU04LO75//34YDAUoKioa0/lKSiw499wLcNZZ5+Gqq67F0qWLsXr1n3HlldFH1WKNgRJRihLUapjOOVe5LcsyAt3d8LYOjj4NLrEFgEBXF3x2O3x2O/p37wo9j0aDgpNOhvXb31Xu8zQcgMZiZTkDojQ0nt9brc0G63cvh/2FFYAkAaII63cuC+63OYnzRlNYWIRjjjkOq1a9hksvXRqSp9TR0Y5//vMfWLjw/AktYikoKIDZXIz+/v5JX+d4MFAiShOCIEBdUAB1QXgelEqvR9XP/nt49Km1Bd6WFvjsrZB9PggajdI20NOD/f/9MwCA2mQOyX/SlpZCW14OtaEgoc+NiOKn8ORTkTfziIStevvJT27Ftdd+DzfeeAOuuupalJaWYe/ePfjtb3+D4mILrr76OqWt2+3C7t07Qx5vMpnx3nvv4ssvd+GUU05HVVUl+voGsGbN37F37x78+Me3xPX6D8ZAiSgDCGo1cqqmIKdqSsj9siTB194esumw3+2CKt+AQE83/M4O+J0d6Nu6RTleePqZsH7rOwAAaaAfrrX/VIIpjcUKcUTQRUTpQWMyxT1AGlJZWYXf//4F/OEPT+Oee+5AZ2cnTCYzTjnlNFxxxVUhNZT++c81+Oc/14Q8/oorrsLJJ5+KL774DA8++Et0dLQhNzcXNTXTcP/9D2Hu3HkJeR5DBDnRlZtSWCAgwensjcu51Wox4pYaFB/s70MLTuO1wts6PALlbW2F8axzUHT6GQCAgb17cOC+nw8/SBCgKS6B1maDxlaK/LlHKaNb7PPEYn8nXiL73OfzoqOjBWZzKTSa7F7pOlRHaSJG60eTSQ+V6tD5mxxRIspSKoMBuQYDcmtro7YRtFoUnHBSMJBqDVYl97U54GtzAF9shsZoUgKlgYYGfH7f81CVWKC2WAen82zQWK0hdV2IiNIJAyUiikpXXgHblVcBGEwm7+oMjjzZW+FtaQkJsjxNTejZvRvYvTv0JIIAtdmMkm9cAsPRxwIApIEBBPr7oS4qYmVyIkppDJSIaEwEQYC6sAjqwiLkTT887Lh++nTU33YznLv3YWCwnIHP3gqpvx/+9nYI6uHcpt4tX6Dld8sh6HKCe+0po082aG02aEvLWFiTiFICAyUiigl1URGMNeVQHT5bySdQRqFaW0PqRQW6OgFRhOwZgOfAfngO7A85V+m118MwL7htgafhAPq2b4fGZoXWWgpNcXFIcjoRUTwxUCKiuBk5CjVS0RkLUHjKafC1OQYTylvhtbfCZ2+Ft7UlpMZL75YtaP/zK8MPVqmgLbFAY7NBa7Wh8LTToS2xJOgZESUW11tNTiz6j4ESESVFcA+74GbABxv55qaxWpE/72h47XalLtRQcnkvAMNxxytt3e+8jc717wWn86yDU3nWYEK5Kjc3EU+LKCZUg6OmXq8HWi0Lw06U1xvc6Felmni4w0CJiFLOyARvw1HzYDgqWDdFliT4Xa7g6FNrC7x2O7TW4dEnT8MBePbthWff3rBzqgoLUXnL7dDaSgEA3jYHZJ8fmpIS1oailCOKKuTm5qOnJ7h5rFary9qFD5IkIBAY38iQLMvwej3o6XEhNzcf4iS2cWKgRERpQxBFaMxmaMxmYMbMsOPGhecFKxDbh6by7PC2tiLQ3YVAZydUI6YAXW+tQee6t4c3GrZaobValVGo3Pp6ljWgpCooCBaIHAqWspUoipCkidVRys3NV/pxohgoEVHG0JZYIuYrBfp64XO0hU6/yYCYkwNpYEDZaHhkhfJpv1kODAZKnf9+F97WlsFgygaNxRosbcDNhimOBEFAYaEZBoMRgYA/2ZeTFCqVgMLCPHR29o17VEmlUk9qJGkIAyUiyniqPD1U1fqQ+6zf/i4s3/oOAl1dw4nkdju89lYEuruh0g+37/7kY/Rt+SLk8YJWC40lOApl+/7VyuiT5PFA0GqzdpqEYk8URYhido5uqtUicnJy0N8fSFoFegZKRJS1gqvyCqEuLAQO2mh4pIITToTWZgtO5Tns8LW1QfZ64W1sgN/pDKkR1fLUb9G/a6cSRGmsVmgtNmgslmBSeb6BQRRRGmGgRER0CAXHnYCC405Qbst+P3wd7fDa7ZD6+0MCH5/DAWkgcn0oMTcX0x77rXK76z8fAJIUDKosVoj5+QyiiFIMAyUionES1GpoB5O+D1Z1z8/ha2uDz2EfTih32OFz2KEqKAwJhJx/+yu8Lc3KbTEvTwmadBUVMJ13QUKeDxFFx0CJiCiGRI0GurIy6Moi1IcKBEJu5x0+A6rCQvjsdvhdTkh9fUp5A29LVUigdOCB+yD7fMHpPIsFOTYbVIdVw59bADmPI1FE8cJAiYgoQQ7eesWy9NvKvyWvF742x+BIlB3iiBV6siTBc2A/ZK8Xnv37lPuHxqJypk5F1U9/ptzfveljqAwGaEosUBcWcnUe0SQwUCIiSgGiVgtdeUXInngKQUDVnffA52iF1xEMpvxtDvjb2+Bpa4e60Kg0lWUZrc8+DdnrDT5Uq4WmxAKNxQKtxYKcmmkwHH1Mop4WUdpjoERElOIEQYCuvBy68nLlPrVahNGoR4fDDV9Pn3K/7PEgt7YOPocDvo724Oq8pkZ4mxrRC0A/Z64SKMmyjAO/uBfqwsLBYMoKjaUEWosVanMxK5YTgYESEVFaEzUaqAyG4ds5Oaj4yc0AhlbndcDXZofP4YDX4YCuYnjEKtDdHVydF+nEgoCCE+fDdsWVwXPJMno+2QRNSQk0JRbunUdZg4ESEVGGCq7OC9ZzikTMzUHFTbfC2+YIjkAN5Ug52iB7BkLypKSeHrQ8+YRyeygHamhaL6+uHnmHz4j7cyJKNAZKRERZStRokXf4jLAAR5ZlBLq6AAxvGRHo70fO1GnwtTkQ6O5W/gzs+QoAIJ2xQDlPoKcHDQ8+AE1JCbSDgdTQSJTGXAxBzY8eSh98tRIRUYihiuUjaS0WVP30bgDBoMnXNjQCFfw7d/rhSltfmyMkL+qgk8N0/oUovmgxgOCWL71ffD44OlUCVZ7+4EcQJRUDJSJKCkmSsavBDXevB0V6HeoqiyCKrAWUDlS5uVBVTUFO1ZSIxzVWG8p/dGMwYGprGw6o2oNbv4zcR8/b0oyW3w1XKxf1+mDQVFwCTUkJ8mfPQW5tbdyfU6rg70XqYaBERAm3aacDK9fuhqt7OI3YaNBh6YJazKu3JPHKKBZUeXnQHzE77H5ZlhHo7AyZepMlCTnTDgtO6XV1Qerthac3WHQTANQGgxIoDRzYj5Ynlw9P45WUKAFVJoxG8fciNTFQIqKE2rTTgeWrtoTd7+r2YPmqLVi2aBY/FDKUIAhQFxWF3Jc7dRqq7rgLQHAaLjil1wZfWxu8bQ7kTJ2mtFUSztscALaGnb/km0thXHB2sK3Tid4vNg8HUyZTSudG8fcidaXuq4aIMo4kyVi5dveobV5cuxtza0s43ZCFRJ0OuopK6CoqIx7PmzEDFbfcHgyW2tuUgMrX1oZAdxfUJrPSdmDvHjheeH74wYIAtck0OK1XjMKTT0XutMMABEe1IAhJ2waGvxepjYESESXMrgZ3yLRCJM5uD3Y1uDF9inHUdpR9VHl65NVPB+qnhx2TBgYAlTiibR70s49UAirZ54O/owP+jg70AyFTgz2ffYrW3z8VHHkqLh6ezise/GO1QtRq4/a8+HuR2hgoEVHCuHtH/zAYbzuiIWJOTsjtkWUPhnKjlFGo9jbkVFUrbX1tjmAF8+YmeJubws5des0ypZp59+4vYX/731CZzEogpTabJ1XFnL8XqY2BEhElTJFeN652XAFEsTCUG6UuKkLuYeEr6IxnnoX8OXPha28PCaZ87e3wtTmgKS5R2nZt246O//v7wT8A6qIiaIpLUHzxN5E7dSqAYD0pyTMAtdE06sbE4/29oMRioERECVNXWQSjQTfqNIPJEAyIuAKIEiVYwdwGrdUW8bgsDxfezJ9aA9OCs+BxOJTASvZ64Xe54He5IIwI5Ls+eB9tL78IqFTQGE1QD03rFRdDU1wM/cwjoDIYxvV7QYnHQImIEkYUBSxdUBtxdc+QJQtq8enuNq4AopQxMsm78IhZkCpq4PdLAAan9bq7B0eg2qC1lSptpYEBCGp1cM+9weP92K4cr7rrHqgMBoiigO+WdqF1x7/RqcmHW52PTk0+OtX56NTo0avKxZIFtRxNTRIGSkSUUPPqLVi2aFbYaJHJoMOSBbWYW1uCW57cMOo5uAKIUoUgCFAXFEBdUIDcEaUMAMB84ddhOv9C+N1u+Nrb4O9oHxyFaoevoz1kSq/U60RufwvQH/4zZJUa1XnDU4YDe/fA2+aAxhwcmVIVFCZtxV42YKBERAk3r96CubUlEfOPdux3cQUQZQxBFKExmaAxmQDUR21XOP8U6Cqr4G1rh/NAM/wd7VD3uCF0uSEE/FCNqD/V9Z+NcK99a/hnqNVQDwZNGnMxzF+7SKlXJXm9ENTqUXOkaHQMlIgoKURRiBjocAUQZaOR9aNKRtwv+/3wuZxQ5RuU+zTFxcitrYOvox1+lyvYxt4Kn70VAGAe3EcPANpffw2d77wNtckMjdkcDKjMZmiKi6E2FyOnZuqkVuxlAwZKlLECkozt+5zo6Brgiqk0whVARMMEtRraktB8POOCs5UK5LLfD7/LBV9HcDrP39EBlWE4qPJ3dAQDKYcdPoc97PxTH3lMCZTc6/6F/j1fBQMpc7ESVKlNkyt/kO4YKFFG+miHAyv/uQsdnQPKfVwxlR64Aoho7AS1WtnrLpLSa66D3+2Cr6MD/sHcqKGAyt/ZGRJU9W3bhp5PN0U8j6qwENU/v1/Z0Lh/924E+nqVUSpVbm7sn1yKYKBEGYd7JqW3sa6M4+gg0aEJKlUw6dtcDNRFz5ECgMJTT0NOTc1gMBWsYu7raIfs9ULq64OYl6e0df1zDXo+GQ6qxLw8ZXpPYzaj+OJLIWqC1cylgQEIWm3a5kkxUKKMwj2TMsOhVsYx0CWKPf2sI6CfdUTIfbIsQ+rpgb+rM2RlnaakBLqqKfB1tEPq7YXU1wdvXx+8jQ0QNBqULPm20rb1D8+gd/PnUBtNUJvN0JjMwb8Hp/hy66endBDFQIkyCvdMyhyjrYwjosQQBAEqgyFkig4ASi7+pvJvaWAAPufwCJTk8YQEVT6nM5gn1eaAr80RUgFBUKtx2JPPKLfbXnsFvjZHcHTKZIJ+2lQYjzsqbs9vLBgoUUbhiqmJS8XtQqKtjCOi1CHm5EBXVg5dWXnE41W33xnMk3I6g7WkOjrgd3bA19EBCEJIUNW3Yzs8+/Yqt70nzUc5AyWi2OGKqYnhdiFEFC+CWq1sIDxaLSkAKL5oMbytrcFAytmBvLq6xFzkKBgoUUbhiqnxY/I7EaWKg/Ok1Ork5y4l/wqIYmhoxdRouGJq2FiT3yVJHrUNEVGmYqBEGWdevQU3fGM2zIU5IfebDDqOjhxkPMnvRETZiFNvlJGOmW7BmcdV4z+fN7Iy9yiY/E5ENDoGSpSxVKKAw6tN8PulZF9KymLyOxHR6Dj1RpTFhpLfR8PkdyLKZgyUiLIYk9+JiEbHQIkoyw1tF3LwyBKT34mImKNEROB2IURE0TBQIiIA3C6EiCiStJ56e/fdd1FfX4/6+nqcccYZyb4cIiIiyjBpGyj19PTgnnvuSfZlEBERUQZL20DpoYceQktLCxYsWJDsS6E0Jkkydux3YeO2VuzY7+JWHUREFCItc5Q+/vhjvPTSSzjrrLNwxhlnYO3atcm+JEpDm3Y6sHLt7pAtPIwGHZYuqOVKLyIiApCGI0oejwd33XUX8vLycPfddyf7cihNbdrpwPJVW8L2OXN1e7B81RZs2ulI0pUREVEqSbtAafny5di7dy9uvPFGWK3WZF8OpSFJkrFy7e5R27y4djen4YiIKL0Cpe3bt+PZZ5/F7NmzsXTp0mRfDqWpXQ3usJGkgzm7PdjV4E7MBRERUcpKmxylQCCAO++8EwDwi1/8AqIYnxhPrY7PeVUqMeRviq/R+ru73zemc3T3++L2eshEfI0nFvs78djniZcKfZ42gdKzzz6LrVu34vvf/z6mT58el58higKMRn1czj2koCA3ruenUJH6u7K0cEyPrSwtjPvrIRPxNZ5Y7O/EY58nXjL7PC0CpX379uGJJ55ARUUFrr/++rj9HEmS0dXVF5dzq1QiCgpy0dXVj0BAisvPoGGj9XeZMQcmgw7OUabfTAU6lBlz4HL1xvtSMwZf44nF/k489nnixbPPCwpyxzRSlRaB0j333AOPx4N7770XubnxjSr9/vi++AMBacI/Q5Jk7sU1TtH6e8mCWixftSXq45acWQtJkpnQPQGTeY3T+LG/E499nnjJ7PO0CJS2bt0KQRBw++23hx0bGBgAALS0tOCkk04CADz++OM46qijEnqN8caaP7E1r96CZYtmhfWpyaDDEvYpERENSotACQBkWUZ7e3vU45IkKcd9vrEl66aLoZo/Bxuq+bNs0Sx+sE/AvHoL5taWcJSOiIiiSotA6eOPP4567PXXX8cdd9yB8vJyvP322wm8qsQYa82fubUl/ICfAFEUMH2KMdmXQUREKYprHFMca/4QERElDwOlFOfuHT1IGm87IiIiGjsGSimuSK+LaTsiIiIau7TIURrN4sWLsXjx4mRfRtzUVRbBaNCNOv1mMgSTkImIiCi2OKKU4kRRwNIFtaO2WbKgloncREREccBAKQ0M1fwxGkKn10wGHUsDEBERxVHaT71lC9b8ISIiSjwGSmmENX+IiIgSi1NvRERERFEwUCIiIiKKglNvNCpJkpkXRUREWYuBEkW1aacDK9fuDqnhZDTosHRBLVfaERFRVuDUG0W0aacDy1dtCSt06er2YPmqLdi005GkKyMiIkocBkoURpJkrFy7e9Q2L67dDUmSE3RFREREycFAicLsanCPumUKADi7PdjV4E7MBRERESUJAyUK4+4dPUgabzsiIqJ0xUCJwhTpdYduNI52RERE6YqBEoWpqywK21fuYCZDsFQAERFRJmOgRGFEUcDSBbWjtlmyoJb1lIiIKOMxUKKI5tVbsGzRrLCRJZNBh2WLZrGOEhERZQUWnKSo5tVbMLe2hJW5iYgoazFQolGJooDpU4zJvgwiIqKk4NQbERERURQMlIiIiIiiYKBEREREFAVzlCilSJLM5HEiIkoZDJQoZWza6cDKtbtD9pkzGnRYuqCW5QgmgcEnEdHEMVCilLBppwPLV20Ju9/V7cHyVVtYu2mCGHwSEU0Oc5Qo6SRJxsq1u0dt8+La3ZAkOUFXlBmGgs+RQRIwHHxu2ulI0pUREaUPBkqUdLsa3GEf5gdzdnuwq8GdmAvKAAw+iYhig4ESJZ27d/QgKVI7SZKxY78LG7e1Ysd+Fz/wD8Lgk4goNpijRElXpNcdutGIdsy7ObSJBJ9ERBSOI0qUdHWVRWGb7x7MZAiu1mLezdiMN/gkIqLIGCgliM/phHvzF/A5ncm+lJQjigKWLqgdtc2SwePMuxmb8QSfREQUHQOlBOh8713svukn2Hr3vdh900/gfuftiO18Tif6dmzPymBqXr0FyxbNCvtwNxl0SmkA5t2M3ViDT9ZTCsf8NyIaiTlKceZzOmH/4/OAPPhmK8tw/O8f0fG3v0BXVg6N1Qqt1QY5IKH9tZeD7QQB1u9ejsKTT414Pp/DDo3FCo3JlNgnE2fz6i2YW1sStTgi827GZyj4PDify2TQYQnzuSJi/hsRHYyBUpz5HPbhIGmEgNuNPrcb2LY1eIcghART9hXPYWDvXuimTIHWaoPGakPvF5vheOH5QwZT6UwUBUyfYox4jHk34Q5VdftQwScNY9FTIoqEgVKcaSzW0CAIAAQBpddcD6m/D157K/q/3I2B3bvCHtv573ein1iWYX9hBXRV1dCYzVDl54cczsSRp6G8m9Gm37Ip72asox+jBZ8UNNa6U3NrSxhkEmUZBkpxpjGZYP3u5bC/sAKQJEAUYf3OZTDMm6e08Tmd2HvbTWHBVMFJJyPQ1QmvvRU+hyN8ZEqS0PHXN9D72acQ9XporVZorDZI/QPo/fzTjJvGG8q7ifStf0i25N1w9CO2xpP/xqCTKLswUEqAwpNPRcGRR0LX1wlPXiGEgqKQ49GCqZHBjbfNgX0/vS00WBJFAMHbUm8vBvbswcCePaE/fHDkKW/mERj4cjd8Lie0Vhs8jQ3oWL0q7abxmHfD0Y94YP4bEUXDQClBNCYTCqdVwuXqhd8vhR0vPPlU5M08IuoIj7bEEjWYkjwe+BwOeO2t6N2yGV3r3ws9uSTB57Cjc8P76NuyOfziBnOicqcfDm1JeKCRaiNP2Z53w9GP2GP+GxFFw0AphWhMplEDkWjBlKjTQVdZCV1lJXKmTkPX++vDRp40Fiv0RxwBVV4uBvbtCyaZH8TX0aEESs1PPgFvSzOgUsPbcCDYQBBQfPGlMJ51DgQhNChJdDCVzXk3HP2IPea/EVE0DJTSzKGCqWjTeBqTCcYzzwLOPCtqTpTWYlVuehob4bO3hp5cltH+yktwvbkG0x7+tXJ326svwfXWm2Oaxku10al0xNGP2GP+GxFFw0ApAx1qGm+0YGpIxY9vQvfHH6L9z6+GnV/MGf4A9jmdcL25Zvjg4DRe75YtyJkyBdqycuTPmQsgWHhTqSmVRnlRqYajH/HB/DciioSBUoaa6DSe8viSEhiOOwHtr78WNo1XetW1yk3vwaNOg3o2fYSeTR9BV1mJ/DlzIxbetP/xeWgsNuROmwZBPfxS5KjT6Dj6ET/Znv9GROEYKGWxiU7j5VRXK220VlvEOlFFZ5+DQFcXNCYzgCiFN2UZjQ/+MphDVVIC/cxZ0FVWhYw6Wb5zGYpOOS3i9WVzQMXRj/jJ5vw3IgrHQIlGNdFpvIOn1CIW3gQAjQbw+eCz2+EtscC97u3Q7V7++Dxcb60Z3O7FBq3VBq3Viv59e9H+yktZPY3H0Q8iovhjoESHNNlpvKFzRAqoCuafAr/bDZ+9FZ7mZvRt+SLssb7WVvhaI0/xAVCm8SSvD7nTDoPGaoXaoA8+1ulEf3NLxo46cfSDiCi+GChRTBwqmAKiB1QaozH4x2JF24v/GzaNZ7vi+wj09cJrt8Nnb8VAYwOkrq7Qk8ty8LGDVAWF0OjzMNDSopwnUyqUExFR4jBQooQaLaCKOup04kkh7SKWNwCQU10Dn7MDga4uBLo6EejqHD44WKE8p2Yqmh7/tbLRcKCnBz0ff8jSBkREFBEDJUopk5nGGwpwAn196P34P2j944rQB0oS+nbthL+jA/6ODmDb1tDjg1N4eTOPgMZkguTxYGDvHmisNvR+sRmOF55PWE6UJMnMPSKiSeH7SGwwUKKUM5lpPABQ5eXBMGcuWl/4Y1hpA/2MWci57c7gdi/btqDnw/+EnliWg+c0meBtbkLjQ/8T/sOHShvYSpFXWxdyKBajTpt2OsJWsxkNOizlajYiGiO+j8SOmOwLIJoojcmEvOmHRx11OmzZNYMbB0MZddLabMitrUXh/JNR8o1LgyvxRhKC270AgOTxQGO1hrcBAFlG94cblZvelmbsv/8X2HvrjWh86H+w97ab4H77X1Gv3ed0om/HdviczpD7N+10YPmqLWHFJF3dHixftQWbdjpG6xIiIr6PxBhHlChjWc9aAGFqfdRVb4eqUJ43/XDU3Pc/8LY5sO+nt4XlROXW1Sv/7t2+DZ49Xw0flGU4Vr6A9r+thq60DKbzLoB+5iwAgPudt+H40wth03iSJGPl2t3KKQz+Xhi93XBpDehWB1fxvbh2N+bWlnD4nIgiOvh9JBK+j4wPAyXKaBqTCUJBUdTjY8mJ0pZYIieZH3Oc0kbURt5XTerqQn9XF+SzzgEQHElSgiRA2fLF1+lGe54FkrMDgjoPR3R/hYWOjRAhQ4KANZbjsbmgFs5uD3Y1uFkSgIgi2tXgHnV7IwB8HxknBkqU9SabEwUAeTNmRqhQLqJ02Q8h9/chp2YqgCgVygE431gFEcC1AP5RcjzOafsPRATbiZCx0PEBWrUmOHQmuHtD3wS5Go+Ihhz8/jDZdsRAiWjMJlLawDBnTmi7KBXKc2fOQp+9DYH2NkgQlSBpiAjge41/h0dQQ7vShpaqYKVyUatD++uvHnI1HoMpouxQpI88uj3RdsRAiShmJlvaQJJk3Prb9fC5XJAghARL8uAfnewHWhvR3doYPDAy6BqcxuvdsgW6qqrB7V5s6P9yFxwr/zert3shyhZ1lUUwGnSjTr+ZDMFSATQ2DJSIYmgy03iiKGDJWfVYvmoL1liOD8tR2mqYiutOtaE2zw+vvRX9O3egd/PnYefv2fQRejZ9FPmHDxbe1JaWQZVvgKa4GIJ6+G2AI09E6U0UBSxdUIvlq7ZEbbNkQS0TuceBgRJREkQLqObVW7Bs0SysXKvDk3llyqo3jdGEaxbUYu6I+ie+Y44Lr1AuCCg6+xwEurqC++c1NUH2HPTNUpLgXPN/6P3sU0AUoSkugdZqheT3o3/7dgCcxiNKZ8PvI6F1lEwGHZawjtK4MVAiSjHz6i2YW1tyyIq6h6pQDgDejg7su/3msMKbok4HQauF7PXC57AHk8xHGhx5ypt5BPq2bYHXbofWaoO3tRWuN/+PW74Qpbixvo/QoTFQSgBJkrF9nxO+vS5oBBnTygr5YqVRiaIwpqW7h8qL0prNUYMpWZbhd7vhs7ei5/NP4f7nW6EnlyT4HHZ0f/wR+rZ8Ef7DB3OicuunQztYpFMOBAAAne+9C/sfn2deFNEIid5SZKzvIzQ6BkpxxjLyFG+HyouKFkwJggCN0Rj8Y7HCvfafYSNPGosVBcceD02JBQN7voJn/76w8/ucTiVQ2n7//6Bzxy5IPd3DDQa3fBkZUI18LEedKBvwsyB9cQuTOGIZeUoVo233MnTc+t3Lw7Z80ZhMKDjxJFi/9R2ULfthhC1fhJDgp7+5OTRIGiLL2P/fP4M8IhCzr3wBe2+7SdnypfO9dyNeW7TtXojSBT8L0tukRpTOOussXHzxxfiv//ovmM3mWF1TRmAZeUo3h5rGO9SWLwBw5MO/QvOHn6Lh14+G1YrSFJdAGAy0fE4nOkfuhTc4jdf14X+QU1EJbUUlCk+azyk8Snv8LEh/kwqUGhoa8Oijj+Kxxx7DmWeeiUsvvRQnnnhirK4trbGMPKWjQ03jGU46BS1FVehpbkZ+WRkMM6tDjqvz8mA4ck5YQGX59mUoOHZ4y5ew5PFB/du3oX/7Nugqq5B3+IzhIAkYDKaeR6B/ALnTpkFrtUGVnz98zjSdxkt03golFj8L0t+kAqVrrrkGq1atgt1ux5tvvom33noLFRUVuOSSS7B48eKsHmViGXnKNGE5Fp/uhfHfzRFzLA45OhWpQrkgwHzRYgS6u6EuKIiy3YuM9ldeVG6JeXroj5iNvOnTQ0aeLEu+jaIzzgx7DqkWTDFvJfPxsyD9CbIcYeOpcZAkCe+++y5efvllvPfeewgEAhAEASqVCgsWLMAll1ySNqNMgYAEp7M3Jufasd+FX7346SHb3bpkLr9FxIFaLcJo1MPl6oXfLyX7ctLeUI5FNMsWzcJxM23j6vPO994dtbSBz+kMrxMFIGfaYfA7nfC7gjlLeUfMDq7KO6idWFAAXWkZtFYbNFYrfB3t6Fz3dsqUNhhLn44WLPE1nngT6XN+FkxOPF/nJpMeKtWhU7UnvepNFEWcfvrpOP3002G32/Haa6/hz3/+M5qbm7FmzRq8+eabWTnKxDLylCnGmmNxzOHWUdscbKI5UUPBjeTxwOdwYGD/XvR9sTn8uru60N/Vhf6dO8J/+GCdqIE9e6CtrBzc7sUKtcmMrvffO2Re1GSny5i3kj5G/l+bC3JwXGHeuB7Pz4L0N+kRpUhkWcb69evxyiuvYN26dfD7/WkxyhTLESVg8t8YaeL4bTt2xvqN+I5vH4UT51bGvM8PNboTceRJEFG67IeQB/rgtdvRv3sn+ndECJgOplIBg7WgFKKI6l8+CI3JBEEQlOkyv8upVE5XG03jmi6LxSgDX+PxF2lq1FyYg6Vn1WHuYcXjOg8/CyYmI0aUIhEEASeffDJOPvlk2O123Hzzzfjoo4/g9/vx5ptv4s0330RVVRW+973v4Rvf+AZUKlU8LiPpsqWMPJNRxyfd+mvMORY93rj8/EMlmEcbeTLMmaO0iRxMCSg85VT4OzsHq5M7IPv94T9AkuA9sB/7f3Yn/EVmNPRqcIbkx2F9jRAASADW9J2A5as8ET/wIgV6zFtJfdGCm47OATz+2uZxBTfZ8lmQqeJWcLK5uVmZhnM4gjUiBEHA4Ycfjl27dmH//v2499578corr+CZZ56BKQUSK+NhqIz8V82d8MlCxlXmZjLq+KRjfxXpdWNrl6+N85VEN9lpPACQJQkDe79CwwP3hxXelGUZsmcAKnsTZhz0s0UA5zo+wN68Mry4djeOrCpA/9YvoLXa0P/lLjhW/m/YNN6Y+3SM7VJdun05iMfUKLcUSV8xDZQCgQDWrVuHl19+GRs2bIAkSZBlGUVFRVi0aBGWLFmCqqoqtLe348UXX8Rzzz2Hbdu24eGHH8Z9990Xy0tJKaIo4PBqU8YNk0f7xjVURI3DyaHStb/GmmNRX5XcRNSJVigfIogicqfVRgyo8mcfCema27HqjY2o6WvGUV27Qh8LwOjtxoFuPb78dAfEPywPv4DBCuVqkxl1h88M6VODv1eZxutW6wFkTt5KOn45iNeSfm4pkp5iEig1Njbi1VdfxZ///Gd0dHQo1Xfnzp2LJUuWYOHChdBqh79tFhcX44YbbsBpp52Giy++GP/+979jcRmUQExGHZ907i9RFLB0Qe2oORZLFtSm3HVHcqhgCogeULnzirA7vwqtOWbM6doNEcOjThIEuLQGAEBP7wAsU6fC09QE2XPQh60so+ezT6GfOQtLF9Ti5ZfW40L7v2HxuiEAkAG8YzoK/zHOjNinI6fx1Jax58gkS7p+OeDUKI00qUBpzZo1eOWVV7Bx48bg0LQsIz8/HxdeeCGWLFmCurq6UR9/xBFHoLi4GO3t7ZO5DEoCFlEbn3Tvr2zLsYgUUA1Ng3Wr9VhjOR4LHRshQoYEAWssxysjQfl19ag663h4Ozqw7/abw8oW5E0/HECwT9V1InIb3MoxAcDpzk9wWufn0K0sRc+i/0L+nLkAAPe6f4VM45Ve/j0YLzov7NoPlfyeqGmwdP5ykG1TozS6SQVKP/7xj5V/z5gxA9/85jdxwQUXIC9v7MsnR440UfrgN67xyYT+yvYci5FTkJsLarE3r2zU6TKt2Rw5yXze0co5q2ssiFSjXAgE4G1qVG77nM7hIAkAZBktzz0LOB0QSyugKrZAW1qG7g83jlraIJHTYOn85YBL+mmkSQVKOp0O5513HpYsWYLZs2dP6Bxvv/32ZC6BkoTfuMYnU/orm3MsDp6C7FbrlQBpyMHTZYfKi8qrmx5eoVwUUXHL7ZAHBpBTXQMAUaqUAy2r/6r823rZFeFbvvzxeajNJcitPQyf7nEr1z4yJ8rVjbhMg6Xzl4NMmm6myZtUoPTee++hoKAgVtdCaYTfuMaH/ZV8sZhymsgU5Gh5UdFW4+XVhqYtRN3y5aQT0Odoh7e1FRDE8GBKltH0yK+Cj9XocanKAAESqvrtEAFl2nBzQW3EabDJVCgf75eDVFsZF+3/urgoF0sW1I6rjlImSLX/n0SaVKDEICl7TeQbVzb/ovEbanLFcsop1lOQhxp1AiIHVKWXXYGpF52nrKT1OZ3hwRQAIScH8sAADN4eGNATckyEjHMdH+B45xZ0aAux+w+7Ya2thtZqxcD+fWh/7ZUxbfkSyXi+HKTqyriD/6/NBTk47sgKdHX2Zczq5bFI1f+fRIlLZe50FevK3CNlahXdSL9Akb5dJ/oXLVX7e6z9lY6S2eejBeGZVBV55AhPrqU4rL8j7Z9XMP8UfLjpK/z9rx/hsN5GHO/eOrEfLooo/8ktELUaaK02qPLzw67p4CBvLH0PIG3+f1L1fSWekv37k7GVuSl7jOXbdbouEY6HbE+IjofRgvC5tSVpu/IqkonWiiosMaMx14pOTT6OdW8LK23wF+t85EpenD1Vh/w+NwYaGxBwuUJPLklwr30LvZ8Ht14R9XqIubnwD61aFgRYln4bRaefqTxk5PTVyC1fNEZTcPqqtgS3PLlh1OecTv8/mSadVy7GEgMlmrTREnz5ixYumxOiY+1QQfhF86vTduXVREUKpoanwRCxtMEOQw1MBh1qrzwRoihE3vJFFKEuKoTaZILf6YTU2wupd8QIvCzDsfJP0B85FxqTCa6318Lb2IAaqw23FrbD/dnbEGQZsiDAesrlKKq3YMd+V8j/T6TCm5n2/5NO0nnlYiylRaAkyzI+/fRTvP3229i0aRP27NmDnp4eGAwGzJgxAxdddBEuvPBCCEJ2fNCmE/6iUbyMJQj/58eNox4fkoorr2JpZI5ctNIGI3PkDrXli+TxoPs/G2H/43OhP0iWgqNZJhN6P/8MfVuHg9ihd2dBluH443PImz4d7t5gIKYLeDG9Zx/OaftPSAC3uaAWQOb//6SqdF65GEtpESht3LgRl19+uXK7srIS5eXlaGpqwvvvv4/3338ff//73/H444+zLlOK4S8axctYgvDegQib3EaQ6mUZYiF0FRdCaj9FypEbLclc1OmQN+uIiKUNNBYrAKDo9DORM3Ua+nfvRP+OHWHX43c6UaS3AQAuankH1QOtSjAlQsZCxwcYELVoyrGgKC/0fX0yq/Fo7DKlrMlkpUWgJMsyKioqcNlll+H888+H2WxWjr3xxhu4++678c477+Cxxx7DzTffnMQrpYPxF43iZazBtT5HPWrAlE1lGcabIzeR0gZD7fPnzEX+nLmRp/EEARqLFXVFwSlBk68bB1+BCGBx67vwihrUVp6r3N+64g/oWv/eIVfjMZiaPJY1CUqLQGn27NlYs2YNNBpN2LGLLroIra2tePTRR/Hqq6/ixhtvhCgeOoudEoO/aBQvYw2uzzq6Em+s3xv1eLaVZYhljtxESxuMDKiWLqjFC86zcc3+VRj5zi0D6FTlwWApVlYm+ZxOdL03Ym9QWYZ9xXNwv7MOuvIK6CorYTzrnODqv1EqlNPYsKxJUFoESvmDy1CjOeWUU/Doo4/C7XbD6XSiuDi7CoGlMv6iUbyMNQi/4MRqlJfoM7YsQ7JNZqNhIDjKhUtOwL9fbscpB9YrOUrvVc3HUZdeiOm1w+/nPkekDV8Az/598OzfB13VFOTPOya8QvmK5+DrcCKnpgZaqw2a4mII6uDHH0eeRpdt+zxGkhaB0qF4RuzQnZOTk8QroUj4i0bxMJ4gnGUZkm+0gGpevQVz7/oedm09A13NzcgvK8OVM6vD/n+iVSi3LP0OAr09UOXlRd3uxfm31cM3RBH6WUcgf+5RISNPxYsvhvGchRAOmpUYCqZyy0oBY+i2Ndkg239/MiJQ+vvf/w4AmD59+iFHnyg5sv0XjeJjPEE4yzKkNlEUMP2IGuCImqhtDrUaD0DkCuWCgLwjZiPgcsFrb4Xs9UIe3Atv5MhT+59fQfvq16G12qC1WqGx2hDo7ETXB+8rwZS87Bpojz4h4vVl8uhUNv/+pH1l7q1bt+LSSy+Fz+fDI488gvPPP3/C5woEJHR19cfw6oapVCIKCnLR1dWPQCA7KromE/s78ZLZ55IkY+cBF9w9XhTla1FfZcz4IDybX+M+pxNeuz0YzEQISFzvvouWFc+FbPdiPDUYTMmyDL/bhd4dO9H81JPj/+GiiMKjj4a2rBxamy34x2pD14cfouX5PygBVenl31N+Jk1cPF/nBQW5Y6rMndaBUnt7Oy6++GI0NzfjrLPOwhNPPDGp88myzFpMREQZwNPegYGWFuSUlkJXbI54/OPv/yCsvMGs+34Oqb8f/c3NcG/eAteHH03sAkQR855+EtrCAogjytZ42jvQ39yM3LKyiNdFqSdtp966u7tx1VVXobm5GTNnzsQDDzww6XNKkoyurr4YXF24bP72lwzs78RjnycW+/sQVDlARQ36APS5IuzhqcpB6eXfCxt5kkqrAAC5U+uhnnEkXB99HBZMlZx/PnydXfC2tsLT2opAV2f4+SUJ9s+3ovGJx6ExmaG12SAHAujbsT14XBBQetnlMJ52ethDgyNmrcHE8wybwhuvVBhRSstAqbe3F9///vexbds21NbW4tlnn41ZblK8NzoMBKSs2UwxFbC/E499nljs74kznHQycg6fGZJXNLIvhYKisJyow677AbRHnxDSztPcjP333BkWUAUkALIMX0c7fB3toT9cltHy/HPImXEENCYTpIF+dP3nP/A5WuF6681DljaQJBm7tu5DT1Mz8svLUBch+T2TJPN1nnaBUn9/P37wgx/gs88+Q3V1NZ577jkYjdmZYEZERJMzno2Gc8tKYZlWCddBI1S6srKISeb5c+Zi6iOPwWe3o+ezT+B68x9h5x/a8sXT3AzHC8+HHhwsbeA5cACG409A7rTDAAT3ONz08l9xyoH1KBgsp/D7qvmYd+mFXEUcB2kVKHk8Hlx33XX46KOPUF5ejhUrVqCkpCTZl0VElBIkSebK0jgYCqbU6ujTNNFqRakLCoJ/zGa43loTdcsXQRSRM3UaBvZ8FXZu97p/QWO1IXfaYdi004G//++buLTlvZAtX045sB7PvGwCLj0pJFjK5JV4iZI2gZLP58MNN9yADRs2wGazYcWKFbDZbMm+LCKilLBppyOsTILRoMNS1ipLmMls+ZJTXYPSa5ZF3O7FcNzxyJk6TdkIetaAI8KWLzJ+cGA1eh/9Jzqv+C4Kjzt+XBXKGVBFlxaBUiAQwM0334x3330XJSUlWLFiBSorK5N9WUREKWHTTkfEwpuubg+Wr9qCZYtmMVhKAYfa8uVQdaJ27HfB1e3BTn0lTnR9ERIsyQAEAHp/H1q6/MhzOiNWKO/8YANyKiqhsdmgtViRU12Dnk83ccuXUaRFoPSPf/wDa9asAQBotVrccccdUdvefffdmDFjRqIujYgoqYZGGUbz4trdmFtbwmm4FDCenKiDg6mhjaAdOcX4h+UELHRsVLZ8WWM5Hjv1VTD5uvE1c3nUCuUDu3ZiYNdO5bb1sivCA6o/Pg8hLw95h9VCVVColM3J1lGntAiUvF6v8u+mpiY0NTVFbdvd3Z2ISyIiSgk7D7hG3e8OAJzdHuxqcGdtZeV0Ey2YGrkR9OaCWuzNK4PR2w2X1oBudXBrlRaVDoXmImgMcsQK5cWLL0agtwdeeyt89lZAFMMDKllG65PLAQBiTk4wj0olwrNvnzLqZPnOZSg65bSI1x+rgEqSZGzf54RvrwsaQca0ssKkBPtpESgtXrwYixcvTvZlEBGlHHeP99CNMDwaQenr4I2gu9V6JUAaYjIMJ/EfarsXIMqWLwDUJhP8LhekgQF4DuwPvRBZhuOFFWh/7VVoS0uD9Z6sVmitNniamoL76h1iGu9QwVQq5dylRaBERESRFeVrD90IoaMRlJ7GsxE0cOicKGD0vCjJ54OvrQ09n3yMjjdeD32gLEPq68XAV19i4KsvI1+MLMP+wgqoiooASQ4GVMXF6Prg/VFzolIt546BUgbiEmGi7FFfZQwZZYhkaJSB0t94NoIGDp0TBUQPqESNBrqyMog589GxelVYaYOyH/4Ycl8/vA47vPZWDOzbC19LS+jJJQmd76xD7+efBW8fPHo1GEzlzRwsvHlQzp3B3xs2vZjonDsGShkmlYYrMwmDT0pV4x1loPQ3r96CubUlMX1Pmkhpg/xZs0Pa+ZzO8PIGogiN1QZdZSW8djtkb4SpYklSCm/ueunPOG3XZjg1BdAH+jCrew9EQElY31xQm/CcOwZKGSTVhiszBYNPSnXjHWWg9CeKQkKT88cyjbe5zY9NlfNxyoH1ymq8f1echHlHnoF5l3wTsixjYN8+NNz/86iFNwNf7UR974Gwc4uQsdCxEXvzytCt1ic0546BUobgEuH4YPBJ6SIeowxEI4026qS8V2prsLXaEjJdtnHEe2VuTc2ohTdVp56Ntf9XhMr+VtT3NoT8DBEyjN5udKv1Cc25Y6CUIXY1uLlEOMYYfFK6SfQoAxEQ/l4ZaTXeyPfK0Uan6uYfjWe+8GKny4na3kaIGB55kiDApTUkPOcu+sY1lFbGOgzJJcJjN57gk4goW03kvVJjMiFv+uFhI1RDOXfdaj3WWI6HNFh/fChHqVutT3jOHUeUMsRYhyG5RHjsGHwSER1arN8rh3PudHhyRFFNjdGEZayjRBN1cCGySLhEeHwYfBKNjqtBh2VzX8TjvXIo5+6r5k74ZIGVuWnyuEQ49hh8EkXH1aDDsr0v4vVeKYoCDq82wWjUw+Xqhd8vTfJKJ4Y5ShlkaLjSaAiN2k0GHVdnTcBQ8DkaBp+UjYZWOB38wTi0GnTTTkeSrizx2BeZ/17JEaUMwyXCscX6NEShuBp0GPtiWCa/VzJQykBcIhxbDD6JhiW7FEkq5QIluy9STaa+VzJQIhoDBp9EQclcDZpquUBcGRsuE98rmaNERERjlqzVoKmYC8SVsdmBgRIREY3Z0Aqn0cR6NehYc4EkSR61TaTz7tjvwsZtrdix3zXuxyejLyjxOPVGRERjloxSJPHIBYrFNB7LsmQHjigREdG4JLoUSaxzgWI5jceyLJmPI0pERDRuiVzhFMtcoHgs6c/U1V4UxECJiIgmJFErnGJZ+TleS/ozcbUXBXHqjYiIUlosKz9zST+NFwMlIiJKebHKBeKSfhovTr0REVFaiEUuEDe7pvHiiBIREaWNoVyg42fYMH2KcdwJ05m+gSvFHgMlIiLKKlzST+PBqTciIso6XNJPY8VAiYiIshKX9NNYcOqNiIiIKAoGSkRERERRMFAiIiIiioKBEhEREVEUDJSIiIiIomCgRERERBQFAyUiIiKiKBgoEREREUXBQImIiIgoCgZKRERERFEwUCIiIiKKgoESERERURTcFJeIiMJIkoxdDW64ez0o0utQV1kEURSSfVlECcdAiYiIQmza6cDKtbvh6vYo9xkNOixdUIt59ZYkXhlR4nHqjYiIFJt2OrB81ZaQIAkAXN0eLF+1BZt2OpJ0ZUTJwUCJiIgABKfbVq7dPWqbF9fuhiTJCboiouRjoJSlJEnGjv0ubNzWih37XXzjIyLsanCHjSQdzNntwa4Gd2IuiCgFMEcpCzH/gCj9HJxcPaPGFPOf4e4dPUgab7tkYSI6xRIDpSwzlH9wsKH8g2WLZjFYIkoxkb7cmAw6/GDxbBxeWRizn1Ok18W0XTLwiyDFGqfesgjzD4jST7Tkame3B79c8RE+2hG75Oq6yiIYDaMHQSZDcIQmFTERneKBgVIWYf4BUXoZy5ebP721M2ZfbkRRwNIFtaO2WbKgNiWnsfhFkOKFgVIWyZT8A6JsMaYvN12x/XIzr96CZYtmhY0smQy6lJ6a5xdBihfmKGWRTMg/IMomyfpyM6/egrm1JWmVEM0vghQvDJSyyFD+wWjfulI5/4Ao2yTzy40oCpg+xRjz88YLvwhSvHDqLYukc/4BUTYaU3J1Ab/cAOmfiE6pi4FSlknX/AOibDSWLzffOrueX27AL4IUP4Isy1wCMCgQkOB09sbl3Gq1CKNRD5erF36/FJefMR6ZXpAt1fo7G7DP4ydiHaUCHX6wKFhHif09LFrNqSUxqKPE13jixbPPTSY9VKpDjxcxRylLpVv+AVE2i5RcPaPGBLM5Hy5XfL7cpat0TESn1MZAiYgoDRz85YYf/NHxi2BqS7cZDQZKRERElBDpuMUMk7mJiIgo7tJ1ixkGSkREcSJJMnbsd2Hjtlbs2O/i9hmUtdJ5ixlOvRERxUE6TjEQxct4tphJtfwyjigREcVYuk4xEMVLOm8xw0CJiCiG0nmKgShe0nmLGQZKREQxxF3sicKl8xYzDJQSxNvWhs4vtsDrcED2+5N9OUQUJ+k8xUAUL+m8xQyTuROk6+OP8OXLLwVvCAJUhYXQmMzQmM1Qm8woOu0MaEpKAACyJAGCAEFIvRcMEY0unacYiOJpaK/ReG0xEy8MlBJE1GiQU1YKj6Mdst+HgNuNgNuNgT1fAQAMxx0PzWBb1z/fRMdfVitBlMY8GFCZzdCYiqGrqoKo45ssUSoammIYbfotVacYiOItHbeYYaCUIKYFZ2HaxRfB6eyBx9UJv7MDvo4O5W9NcbHS1t/RAdkzAG9zE7zNTWHnqvrZfyOnagoAoPvjD9Hz+WfBYMpUHAymzMVQm00QNdqEPT8iChqaYli+akvUNqk6xUCUCOm2xQwDpQQTBAHqggKoCwqQU10TsU3xf12MojPODAZSHR3wOdtH/LsDGpNZadu/axe6P9gQ8TwqQwEqb70d2tIyAMDAgf3wO52DgZQZqry82D9BIkrbKQYiCsdAKQWJOh20tlJobaWHbJt/9DFQFxXB1xE6QiV7BhDo7oLKUKC07Vr/Htxvrx3+Obm50BQXQ20uhsZkhumCr0FdEGwv+/2ASsU8KaIJSscpBiIKx0ApzeXV1SOvrj7kPlmWIfX2wufsgKjXK/eri4qgq5oCX0c7pN5eSP398DQ0wNPQAAAwX/h1pW3bqy+jc/2/B/OkiqEpLobGXKwEVjlVVRDUfPkQjSbdphiIKBw/6TKQIAhQ5edDlZ8fcr/pvAtgOu8CAIA0MDA4CtUOf0cH/C4nxBHtfR3tkD0eeJub4W1uDvsZ0x59HCqDAQDgfncdPAf2B6f0RgRUqoJCjkgREVFaY6CUpcScHOjKy6ErL494vPQH18Lf4YSvox2+9nb4O9qVwCrQ3RUSVPV+sRm9n30adg5Bo4HGXIzKO38GVW4ugGCelOz3Q2MuhqqggIEUERGlNAZKFJGo0UJrs0Frsx2ybeFJJ0NXUTEYUA2OUrlckH2+4PRfTo7StuMvbyhBlaDVDiaWF0NTEhyJMi44m1N6RESUMviJRJOWP/co5M89KuQ+2e+Hz+VEoKsrZNRIlZ8PtckUDKS8XnhbmuFtCU7tCVotjOecq7RtefZpeA4cCOZHFZcEp/RKgv9Wm4u5ao+IiOKOgRLFhaBWQ1tiAUpCl0HbLr8SwGAg5XTC194Gf3t7MCfK7wsJqryNjfA2Bf+EnV+rxWHLn1Lad76/HrLXExydKi6BaLMA0Ic9joiIaDwYKFFSCGo1tBYLtJbo9WRKr7kOvjYHfO3tg3/agtN77e1QGQwhQZV77VvwNBwIebzGWBQMnErLYLvse8r9gZ4eiHl5EERudUhERKNjoEQpS2u1QWuNnCMl+Xwht/VHHgm12TwYSLUFV/W53PC53Aj09Ia0bXzkQXiaGoN77RWXKNN5muISaKxW5EypjtdTIiKiNMNAKUVIkszCdOMgajQht4sv+i/l37IsQ/D0IWegB849DQhIUkhbv9sFBALB0ao2B7B9+JjGZkPN/3tAud32ykuALENTUgJ1cQm0JSVQFxdzexgioiyRdoHSxo0b8dxzz+Hzzz9HX18fysrKsHDhQlx99dXIS9Pk3k07HWFbHRgNOizlVgcTIggC1PkGGCpt8BeXwu8PDZSmPvRr+N3u4FReW9vglF4wV0pTXBLStvP99yD1ho5IAYDaaERu3XSUXvUD5T5PwwGoDAVQFbJ+FBFRpkirQOmFF17AfffdB1mWYbPZUFpaii+//BJPPvkk3nrrLaxcuRJFRUXJvsxx2bTTEXHzTFe3B8tXbcGyRbMYLMWYIIrQmEzQmEzAQVXNR5IlCeavL4K/rW0wR8oBX1twWs/vciHQ0x3SvuHhX0Hq6QmWPRhaqWexQFNsga6iAnnTD4/3UyMiohhLm0Bpy5YtuP/++wEAP//5z3HJJZdAEATY7XZce+212Lp1K+6++248/vjjSb7SsZMkGSvX7h61zYtrd2NubQmn4ZJAEEUYz1gQcp+yPUybAxCGk8ElrxdiTg6k3t5g2YODKprnzZwVEig1PfYoRL0e2hILNCUWaEpKoCmxsAgnEVGKSZtA6be//S0kScJFF12ESy+9VLnfarXikUcewbnnnou33noLO3bswPTp05N4pWO3q8EdMt0WibPbg10Nbu4XlSKibQ8jarWY+sBDwbIHHR3KdJ7P4YCvvS0kQVwa6Efv5s8jn1+nQ8Fxx8P63SuU+/q2b4PaZIbGbGYxTiKiBEuLd93e3l689957AIBLLrkk7Hh1dTWOP/54bNiwAWvWrEmbQMndO3qQNN52lHyCWg2t1Qqt1TpKIxG2q68J5ke1tQ0mlbfB73JC9ngADI8oSQMDaHz4V4OPE6A2m0eMQlmQM21a2KbIREQUO2kRKG3fvh1erxdarRazZ8+O2GbevHnYsGEDPv888jf1VFSk18W0HaUHUadDwbHHh90v+Xzwd3RAUKmU+wK9PdCWlcPX3gbZ64V/sI4Utm8DABSecqoSKEkeDxof/lUwiBqsUTUUUHFKj4hoYtIiUNq7dy8AoKysDJqDloUPqaqqCmmbDuoqi2A06EadfjMZgqUCKPOJGk3Y3noaczGqfx5cwBDo7ISvzQGvw6GUNsitHR5N8rW3YWDPVxjY81XYuQVdDoxnn4Piry8CEKyM3r97FzQWC9RGE4tvEhFFkRaBUmdnJwCgsLAwapuhY0NtJ0qtjs8Hhkolhvw95Nvn1OPx1zZHfdy3zqmHVquKepwii9bf6UxTbEJOsQk4PPLUslBsRsWy6+F1OJQ/PocdPqcTsmcAap1WeX17HG3KlJ6gVkNTXKJUStdYrdDXT0fO4JePscrEPk9l7O/EY58nXir0eVoESh5PcMQl2mgSAGi12pC2EyGKAozG+O4PVlCQG3L77BNqkK/X4ek3vkBH54Byf3FRLq76+iycOLssrteT6Q7u74xm1KO4IryUhOTzYcDugDovD9rB13e3A8gtL8OA3QHZ74e3tQXe1hblMVXfWgLjkcFVegOtrfjyt08ht9SGnNJS5JTakFtqg85qhUoXPi2cVX2eAtjficc+T7xk9nlaBEq6wTdj30HbVozk9XpD2k6EJMno6uqb8ONHo1KJKCjIRVdXPwKB0AKIh1cW4uFlJ2HnARfcPV4U5WtRX2WEKApwucKLHdKhjdbfWUlfBA+A3qHXk6UcNfc9AFmSgpsTOxzwOuzw2u3wOhyArVx57XVv/wqdn29G5+fhI59qkwmWxf+FovknQ6USkacGOvYcgLq4BOIkfhfp0PgaTzz2eeLFs88LCnLHNFKVFoHSWKbVxjI9NxYHV3GOtUBAivozaiuKlH9LkgxJkuN6LdlgtP6mILHIBF2RCbq60Cm9oX5Tl1XAesWVwVIHg8GUr80Bqb8ffqcTkiAqbbu/3IUv//v/AQBUhUXBqTxLcBWgxmJB7mG1UBex1EUs8TWeeOzzxEtmn6dFoFRdXQ0AaG5uhs/nizgFd+DAgZC2RBQbGpMJhSedHHKfLMuQenrgddihsQxP9wX6+qDKz0egpweBTjf6O93o371LOW678ioUnHASAGBg7x6431mnBFEaixVaixViTk5inhgR0RikRaA0Y8YMaDQaeL1ebN68GfPmzQtrs2nTJgDAnDlzEnx1RNlHEASoDAbkGgwh9xfPPwmqmXPg6ewOjj4NjUI57PA5HNCWlittB/btRdf774Wde2gkqnjxxcitrQUQLH0AgNN5RJRwaREo6fV6zJ8/H+vWrcMrr7wSFijt27cPGzduBAAsXLgwGZdIRCOo9HqoaqYip2Zq1DY5U6fB/PVFSn6Uz25HoKdbGYkaqWvjBjheWAFVURG0Fis0Viu0Flvwb6sVWquNVcuJKC7S5p3luuuuwzvvvIPVq1fjqKOOUvZ6czgcuPHGGyFJEhYsWJA2VbmJsl3OlOqQrV0AINDXC589OAKlLR8effJ3dASPu93od7vRv2tnyOMqbr1DKbzZv3s3BvbuGQyibNAUFzOIIhqFJMnY1eCGu9eDIn2wdh/3Fx0myLKcNhnDzz//PB544AHIsozS0lIYjUZ8+eWX8Hq9qKmpwcqVK2EymSZ8/kBAgtMZn1VmarUIo1EPl6uXSYAJwP5OvHj3eWAwJ2ookPLZ7fDaW+Fz2FH9i19CXVQEAGh79WW43vzH8ANFEZriEiWp3LjwPGiM6Z9Qztd44mVin2/a6cDKtbtDCh8bDTosXVCLefXh5UYSLZ59bjLpM2fV25DLL78c9fX1+MMf/oDNmzejo6MDZWVlWLhwIa6++mro9fGtgUREyaPKz0dufj5yp04Luf/g73q6ykrkzztaWaEne73BwpsOO/q2AMZzzlXadvx1Nbo/+jA48jQ4jaex2qC12rjtC2W8TTsdWL5qS9j9rm4Plq/agmWLZqVEsJRsaRUoAcAJJ5yAE044IdmXQUQp4uBgpuD4E1Fw/IkAgkGU3+2Gz96qlDUYGnkCAE9jA7zNTfA2N4WdV8zNDRmp8jQ2QPYHoLFaocplwUFKb5IkY+Xa3aO2eXHtbsytLcn6abi0C5SIiMZKEARojEZojEbkTT887HjJpUtQePKpwSm8oak8ux2+jnbIPh9UBQVKW+ff/4rujz4EAKgKC0eMQgVHoPRHzGYuFKWNXQ3uUfcZBQBntwe7GtyYPiX9p6ong7/VRJS1NCYzNCYz9LOOCLlf8vngd7lCNgsWdDlQFRQg0NWFQGcn+js7h5PKVSrU/vZppa3zzX/A73YrK/I0tlKoi4o4lUcpw907tu2+xtoukzFQIiI6iKjRQGsJzc2wXf49AMGimsH8p1Z4W1vhs7dC9vshqIY3r+7+6EN49u0Nebyg0wVHn0rLYPv+1UrQJPv9HImihCvSj60m2VjbZTL+dhIRjYMqLw+q6hrkVNdEbWM8cwE8Bw4Egyl7K3xtbZA9HngO7Ic0MBAystTw4APwtbdDa7MF/1hLobHZoLWVBksbiNypnmKvrrIIRoNu1Ok3kyFYKiDbMVAiIoqxghNOAga3agGCo0a+9jZ4W1shB/whbb2tLZB6e4PbvezcEXJMY7Wi5r7/UW73bP4cKr0eWqsN6qICEE2UKApYuqA24qq3IUsW1GZ9IjfAQImIKO4EtRpaWym0ttKwYzW//BW8rXb47C3wtrbC2xr82+ewQ1NcEtLW/tyzCHR3AQBUBgP0lRUQiy1QW23IqZqCvMNnJOT5UGaYV2/BskWzwuoomQw6LEmROkqpgIESEVESqfL0yJ06FblTQ7d7kSUJ0kD/8G2/H7qKCnhbW+F3ORHo7kbXtu0AtgMAcqcfHhIotT73LFQFBYMBmg3a0lKo8lhrjkLNq7dgbm0JK3OPgoESEVEKEkQxJLAR1GpU3HQrAEAaGECg3QFNtxPOL/fB09wMXWWV0lYa6I+84fBg4KQ/cg5MIwpvypLEXKgsJopC1pcAGA0DJSKiNCPm5EBbXQ2jcSbURxwVcWuHkiXfCk7jtbTAZ2+F3+VCoKsL/V1d0NpsSjvJ48FXP7kBmhILtKXB6UHlb6sNYk5OIp8aUcphoERElGHEnFwYzzwr5D5poF/JgdKYh3OffI7gNi/epkZ4mxrDzlV01jmwXLoEQHD6r//L3dDaSqEqLGRdKMoKDJSIiLKAmJOLnAhlDbTlFaj+5a+CI0+tLcoolLe1BYHubqgLCpW2XocdjQ8FV+GJubnDI0+2UmhLy6CrrsmIDYeJRmKgRESUxQRRhLbEAm2JBZh9ZMixQE8PMGLUSOrrg8Ziha/NAam/HwN79mBgzx7luPmixTBf8DUAgM/lQue6f0FbWjb4pxSijsULKf0wUCIioohU+fkht3MPq0XN/f8DyeeFz+FQRp68Lc3wtrRAV1GptPXs3wfn//0t5PFqk0kJmgqOOwE5NaEr/YhSEQMlIiIaF1Gjha68Arryiqht1EVFKDz1tGAw1dKCQHcX/E4n/E4n+rZuQU7NNCVQ6tuxHe1vvA5taSl0QyNQZWVQG01cjUdJx0CJiIhi7uB8qEBPz2DQ1AxvS3PIMc+BAxj4cjcGvtwdcg5Bq4XWVoqSby5FXl09AEDyeiGIIvfHo4ThK42IiOJOlZ+P3Npa5NbWhh3LP+ooqAoLQgIprz24Gs9zYD9EjUZp27X+33C8/CK0Vutw/lNZGXSl5dDYrBA12kQ+LcoCDJSIiCipNMUlYdu1DO2P52luhrasXLnf67ADgQC8zc3wNjeHnkgQUPXTu5UpPa+9FVJfXzCRPCc37s+DMhMDJSIiSjnR9scruWQJjGedExx1am6GZ/Bvb0tzcFVeyfD+ZO531sH9zzcBAGqTeXDkacQo1JTqkNEqokgYKBERUdoQRBEaczE05mLoZ81W7pdlGYGurpCVeoJKBVVBAQJdXfA7O+B3dqBvyxfK8akP/xpiYREAoOezT+F3u6AtK4eurDxsxR9lLwZKRESU9gRBgLqwMOS+km9cgpJvXDKYSB46+uR3u6EaUUyzc/2/0fvZp8ptlaEA2rLBkaeychSefCqgZv5TNmKgREREGS2YSF6H3Nq6qG1ya+uAQACelmb429sR6O5C/84u9O/cAUGXg8LTzlDaOla9Dp+7E9ry8uBUXlk5VAUF3NIlQzFQIiKirGc651zgnHMBBDcK9ra0wNvcBE9zE+RAICQI6v7oI3iam0IeL+bnQ1daBt2UKbB881sJvXaKLwZKREREI4g6HXKqq5FTXR3xePHXvo6+/fuDCeVNTfC1t0Hq6UH/7l0I9PWFtG18+EHIAX8wgbw8mP+kLSuHuqAgAc+EYoGBEhER0TgUHn889Ecfq9yWvN7gVi5NTYBquJK4LEno/3IXZJ8P/bt2hpxDlW+A/ojZsF15lXJfoL8fqlyWMUg1DJSIiIgmQdRqkVM1BTlVU8KOVd5xF7xNwSm8kSNQgZ5uSAMDSjtZlrH31hshqDWDI09l0JZXKCNQKr0+kU+JRmCgREREFAeCKEYMoCSPB97WFmBE3lOg0w2pvx9AP/p3dKF/x/aQxxiOOwGlV/1AuT2wdw8LaSYIAyUiIqIEEnU65EypDrlPXWTEYU/8LljGoLkpmEje1AxvcyP8TifURqPS1t/VhQP3/Tz4OLMZuvKKYP2n8nJoyyugtZVC1LKUQawwUCIiIkoBYk4OcmqmKluwDAn09wN+v3Lb73ZBVViEQKcb/o4O+Ds60Lv5c+V40RkLYFn6bQDB0avezz+DtqICWouVmwlPAHuMiIgohR2c4J1TNQXTHv41Aj09wdGnoRyopkZ4mpugrahQ2noaG9Dy9JODJ1JBaysNjkCVl0NXXoGcmhqoB6uTU2QMlIiIiNKQKj8feXX1yKurV+6TZRmQ5eHbgQBypk6Dt7kJ0sAAvE2N8DY1KsdLlnwLxjPPAgD42tvQvelj6CoqoSsvh6qwiEU0wUCJiIgoYwiCEJIknldXj6qf3g1ZluF3OuFpahwcgQr+rausUtr2796F9ldfVm6Len3I6JN+9pHQmMwJfT6pgIESERFRhhMEARqzGRqzGZh9ZMQ2qsIi5M87Gp6mRvjsdki9vejftVOpAVX2w58ogVL/7l3o+ezTYCBVURFcgafJzARyBkpEREQE/YyZ0M+YCQCQfN7gNi5NjfA0NcHT2Bgy+tS7bStcb/5j+MGCAI3VCl15BXTlFSg85VSoi4wH/4i0xECJiIiIQoia6EU0ASD3sFoUnn5mMJBqbITU1wtfayt8ra3o2fQxDMcer7Tt+uB99O3YoYw+6coroC4sTNRTmTQGSkRERDQu+pmzoJ85C0AwgTzQ6YansTGYA9XcDI3ForTt3fIFuv+zMeTxKoMhWHm8ogLmCy9K6crjDJSIiIhowgRBgLrICHWREfpZR4QdL5x/CjQW6+A0XiN8DgcC3d3o37Ed/bt2ovi/LlHatr/xOrxNTcrIk35qDWCsSeTTCcNAiYiIiOIm7/AZyDt8hnJb8niCFcgbGxHo6oSo0SjH+rZuwcDePcCnmwAAhqOPgfXu2xN+zSMxUCIiIqKEEXU65FTXIKc6fKSo+OJL4dm/T5nGy506NcIZEouBEhEREaWEgwtoqtViEq8mKPlXQERERJSiGCgRERERRcFAiYiIiCgKBkpEREREUTBQIiIiIoqCgRIRERFRFAyUiIiIiKJgoEREREQUBQMlIiIioigYKBERERFFwUCJiIiIKAoGSkRERERRMFAiIiIiikKQZVlO9kWkClmWIUnx6w6VSkQgIMXt/BSK/Z147PPEYn8nHvs88eLV56IoQBCEQ7ZjoEREREQUBafeiIiIiKJgoEREREQUBQMlIiIioigYKBERERFFwUCJiIiIKAoGSkRERERRMFAiIiIiioKBEhEREVEUDJSIiIiIomCgRERERBQFAyUiIiKiKBgoEREREUXBQImIiIgoCgZKRERERFGok30B6Wjjxo147rnn8Pnnn6Ovrw9lZWVYuHAhrr76auTl5aXMOTNFrPpGlmV8+umnePvtt7Fp0ybs2bMHPT09MBgMmDFjBi666CJceOGFEAQhjs8mPcT79fjuu+/i6quvBgCUl5fj7bffnvQ50128+vzdd9/Fq6++is8++wxutxsFBQWoqqrCcccdhxtuuAFqdXZ+DMS6v91uN5577jm88847OHDgAHw+H4xGI+bMmYNvfetbOP744+PwLNJDW1sbNmzYgC+++AJbtmzB9u3bMTAwgJkzZ+L111+f1LkT8dkpyLIsx+RMWeKFF17AfffdB1mWYbPZYDKZ8OWXX8Lr9WLatGlYuXIlioqKkn7OTBHLvvnggw9w+eWXK7crKytRUFCApqYmuN1uAMBpp52Gxx9/HFqtNvZPJk3E+/XY09ODCy64AC0tLQAYKAHx6XO/34877rgDf/nLXwAANpsNJSUlcLvdaG1thc/nwyeffAK9Xh+HZ5TaYt3f+/btw3e+8x04HA6Ioojy8nIYDAYcOHAAPT09AIAf/ehHuO666+L0jFLb888/j1/+8pdh9082UErYZ6dMY/bFF1/I06dPl+vr6+WXXnpJliRJlmVZbm1tlRctWiTX1dXJ119/fdLPmSli3Tfvv/++fMYZZ8grVqyQ29vbQ46tWrVKnjVrllxXVyc/+OCDMX0e6SQRr8d77rlHrqurk6+77jq5rq5OPv3002Nx6WkrXn1+5513ynV1dfLXvvY1+fPPPw851tfXJ69du1b2er0xeQ7pJB79/d3vfleuq6uTzz77bHnXrl3K/R6PR/71r38t19XVyfX19fL27dtj+lzSxauvvipffvnl8kMPPSSvWbNG/t3vfifX1dXJixYtmvA5E/nZyUBpHK699lq5rq5OvvXWW8OO7d27V54+fbpcV1c3rl+GeJwzU8S6b7q7u0f9YHjyySfluro6+dhjj5UDgcCErzudxfv1+NFHH8n19fXysmXL5D//+c8MlOT49PkHH3wg19XVyfPnz5ddLlcMrzb9xeN9pb6+Xq6rq5PXrl0bsc3Xv/51ua6uTn7qqacmde2ZYuh3fzKBUiI/O5nMPUa9vb147733AACXXHJJ2PHq6mplDnrNmjVJO2emiEff5OfnQ6PRRD1+yimnAAjmGjidzvFectqL9+vR4/HgrrvuQl5eHu6+++7JXWyGiFefP//88wCAK6+8Mmun7SOJR397vV7IgxkslZWVEdsM3e/z+cZ9zRQu0Z+dDJTGaPv27fB6vdBqtZg9e3bENvPmzQMAfP7550k7Z6ZIRt94PB7l3zk5OTE5ZzqJd58vX74ce/fuxY033gir1Tqpa80U8ehzj8eD9evXAwDOPPNMbN68Gffeey+uuOIKXHPNNXjiiSfQ2toamyeQZuLR3yaTCaWlpQCATz75JOy4x+PBli1bAABHHnnkRC6bDpLoz4fsXO4wAXv37gUAlJWVRR2VqKqqCmmbjHNmimT0zd///ncAwPTp05Gfnx+Tc6aTePb59u3b8eyzz2L27NlYunTp5C40g8Sjz3fs2AGfz4e8vDy8+eabePjhhyFJknJ83bp1eOaZZ/DAAw/g3HPPneQzSC/xeo3fcsstuOmmm/Dggw9CFEWcfvrpyM/Px1dffYXf/OY3aG5uxjnnnIP58+dP/klQwj8fGCiNUWdnJwCgsLAwapuhY0Ntk3HOTJHovtm6dSteeuklAFCWrWebePV5IBDAnXfeCQD4xS9+AVHkQPaQePR5W1sbgOCU0IMPPoh58+bhzjvvRG1tLZqbm/Hoo49izZo1uOWWW1BTU4Pp06dP8lmkj3i9xs8//3zo9Xo88cQTYdPKRqMRP/vZz7BkyZIJXDFFkujPB75jjdHQtMxoOS5DS8pHTuEk+pyZIpF9097ejuuvvx4+nw9nnXUWzj///EmdL13Fq8+fffZZbN26FZdffnlWfSiPRTz6vLe3F0CwPIDRaMTTTz+NmTNnQqvVorq6Go8++igOP/xw+Hw+PPnkk5N8Buklnu8rBw4cQGdnJwRBQFlZGaZPn468vDy4XC68/PLLWZc+EU+J/uxkoDRGOp0OwOjJeF6vN6RtMs6ZKRLVN93d3bjqqqvQ3NyMmTNn4oEHHpjwudJdPPp83759eOKJJ1BRUYHrr79+8heZYeL5vgIAl156adg0siiKSj2x9evXh0zLZbp4va/893//N+677z7k5eVh9erVWLduHVavXo0PP/wQN910E3bu3InLLrsMW7dundwTIACJ/+xkoDRGYxnGG8twYLzPmSkS0Te9vb34/ve/j23btqG2thbPPvtsVuYmDYlHn99zzz3weDy49957kZubO/mLzDDxfF8BgKlTp0ZsM3R/T0+PUmw1G8Sjv3fs2IEXX3wRarUajz/+OOrr65VjGo0GV199NRYtWgSPx4Nf//rXE794UiT6s5M5SmNUXV0NAGhubobP54s45HfgwIGQtsk4Z6aId9/09/fjBz/4AT777DNUV1fjueeeg9FonMwlp7149PnWrVshCAJuv/32sGMDAwMAgJaWFpx00kkAgMcffxxHHXXUBK4+PcWjz0cGR9G+TY+8P5tGlOLR35s2bYIsy5gyZYqSQHywU045BatWrcLmzZsndN0UKtGfnRxRGqMZM2ZAo9HA6/VGfbFv2rQJADBnzpyknTNTxLNvPB4PrrvuOnz00UcoLy/HihUrUFJSMtlLTnvx6nNZltHe3h72Z2hrB0mSlPuyrc5MPPrcarWivLwcwPCHxcEaGhoABPM4sqnOUjz6eygnbCx7RA5NB9HkJPqzk4HSGOn1emVp5yuvvBJ2fN++fdi4cSMAYOHChUk7Z6aIV9/4fD7ccMMN2LBhA2w2G1asWAGbzRabi05z8ejzjz/+GDt37oz4Z2jvp/LycuW+4447LkbPJj3E63U+tOz/jTfeiDhi9NprrwEAjj322KzaFDce/V1TU6M8digAPdhQccShtjQ5if7sZKA0Dtdddx0EQcDq1avx8ssvK9VYHQ4HbrzxRkiShAULFoSt7FmyZAnOOOMMpVpuLM6ZDWLd34FAADfffDPeffddlJSUYMWKFVEr6WareLzGaXTx6PMrr7wSBoMBX331Fe6//35lJEOWZaxYsQLr1q2DIAhZWQoj1v09f/58FBcXw+/344c//CF2796tHPP5fPj973+vbPx60UUXxfW5ZZpU+ewU5KGz05g8//zzeOCBByDLMkpLS2E0GpXdimtqarBy5UqYTKaQx5xxxhloamrC9ddfjxtuuCEm58wWsezvv/3tb7jpppsABEcxRqsOfffdd2PGjBnxeVIpLh6v8Uhef/113HHHHSgvL8fbb78dj6eSNuLR5xs2bMC1116LgYEBFBYWYsqUKWhpaUFbWxsEQcAtt9yCK6+8MlFPMaXEur8/+OADXHfddejr61PKAxQUFODAgQPK1NzZZ5+NX//611CpVAl7nqmipaUlJEj0er3o6+uDWq0OWUDz/e9/H1dddZVyO1U+O7NnzDVGLr/8ctTX1+MPf/gDNm/ejI6ODpSVlWHhwoW4+uqrodfrU+KcmSKWfTMyP6CpqQlNTU1R23Z3d0/qutMZX4+JF48+P/HEE7F69Wo89dRT2LBhA7Zv3478/HycccYZuOKKK3DsscfG4Zmkh1j39wknnIC//e1vWLFiBTZs2IDGxkbY7XYUFhbiqKOOwqJFi7K2PhsQHM2PtLrS7/eH3D+0wGOsEvVexRElIiIioiiYo0REREQUBQMlIiIioigYKBERERFFwUCJiIiIKAoGSkRERERRMFAiIiIiioKBEhEREVEUDJSIiIiIomCgRERERBQFAyUiIiKiKLjXGxERgLa2Nnz00UfYtm0btm7dim3btin7UP3xj3/Ecccdl9wLJKKkYKBERATgpZdewhNPPJHsyyCiFMNAiYgIgCAIKC0txYwZMzBjxgxYrVbcddddyb4sIkoyBkpERACuvfZaXH/99crtxsbGJF4NEaUKJnMTUcZ4+umnUV9fj1mzZmHz5s0R27z77ruYPn066uvr8de//lW5X6VSJeoyiSiNMFAiooxx1VVX4cQTT4TP58ONN96Inp6ekOMOhwO33347ZFnGRRddhAsvvDBJV0pE6YKBEhFlDEEQ8Ktf/QpmsxkNDQ245557lGOyLOO2226D0+nElClT8LOf/SyJV0pE6YKBEhFllJKSEvzyl7+EIAj429/+hlWrVgEAnnnmGWzYsAEajQYPP/ww9Hp9kq+UiNIBAyUiyjinnnoqLr/8cgDAz3/+c6xevRqPPfYYAOAnP/kJjjjiiCReHRGlEwZKRJSRbrzxRsycORN9fX249dZb4fP5MH/+fHzve99L9qURURphoEREGUmr1eKBBx5QbhsMBjzwwAMQBCGJV0VE6YaBEhFlrFdeeUX5d09PD7Zv357EqyGidMRAiYgy0rp16/DCCy8AAOrr6yHLMm6//Xa0t7cn+cqIKJ0wUCKijONwOHDHHXcAABYvXow//elPKC8vR0dHB2677TbIspzkKySidMFAiYgyiiRJuPXWW+FyuVBdXY27774bBoMBDz/8MNRqNdavX4/nnnsu2ZdJRGmCgRIRZZTf//73+OCDD5R6SXl5eQCAuXPnYtmyZQCARx55BFu3bg15nCRJcDqdyp+uri7lWHd3d8gxr9ebuCdEREklyByDJqIMsXnzZixduhQ+nw+33norrrzyypDjkiThsssuw4cffojq6mqsWrVKCaQaGxtx5plnjunn/PKXv8TixYtjfv1ElHo4okREGaGnpwc33ngjfD4fTjrppIj1kkRRxIMPPoiioiLs27cPv/jFL5JwpUSUTjiiRERERBQFR5SIiIiIomCgRERERBQFAyUiIiKiKBgoEREREUXBQImIiIgoCgZKRERERFEwUCIiIiKKgoESERERURQMlIiIiIiiYKBEREREFAUDJSIiIqIoGCgRERERRcFAiYiIiCgKBkpEREREUfx/x10oD6SX/dgAAAAASUVORK5CYII=",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "pred_ols = lmf.get_prediction()\n",
+    "iv_l = pred_ols.summary_frame()[\"obs_ci_lower\"]\n",
+    "iv_u = pred_ols.summary_frame()[\"obs_ci_upper\"]\n",
+    "\n",
+    "x = df['x1']\n",
+    "y = df['y']\n",
+    "\n",
+    "plt.figure()\n",
+    "plt.scatter(x, y, label='data')\n",
+    "plt.plot(x, lmf.fittedvalues, 'r--.', label=\"OLS\")\n",
+    "plt.plot(x, iv_u, 'r--')\n",
+    "plt.plot(x, iv_l, 'r--')\n",
+    "plt.xlabel('x1')\n",
+    "plt.ylabel('y')\n",
+    "plt.legend(fontsize=10)\n",
+    "plt.tight_layout()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 180,
+   "id": "71aba0ad-c064-4610-918a-cac03c828a5a",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "        Mixed Linear Model Regression Results\n",
+      "======================================================\n",
+      "Model:            MixedLM Dependent Variable: y       \n",
+      "No. Observations: 50      Method:             REML    \n",
+      "No. Groups:       2       Scale:              1.4079  \n",
+      "Min. group size:  25      Log-Likelihood:     -80.1312\n",
+      "Max. group size:  25      Converged:          Yes     \n",
+      "Mean group size:  25.0                                \n",
+      "------------------------------------------------------\n",
+      "              Coef. Std.Err.   z   P>|z| [0.025 0.975]\n",
+      "------------------------------------------------------\n",
+      "Intercept     1.778    1.153 1.541 0.123 -0.483  4.038\n",
+      "x1            1.292    1.187 1.088 0.276 -1.034  3.617\n",
+      "Group Var     1.901    2.561                          \n",
+      "======================================================\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "# model with mixed model\n",
+    "mem = smf.mixedlm('y ~ x1', df, groups=ind_gp)\n",
+    "\n",
+    "# fit model to data\n",
+    "memf = mem.fit()\n",
+    "\n",
+    "# summary\n",
+    "print(memf.summary())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 181,
+   "id": "debbc6c8-7113-4806-b0c1-db72f8a4ad5f",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "x = df['x1']\n",
+    "y = df['y']\n",
+    "\n",
+    "pred_mem = memf.predict(x)\n",
+    "\n",
+    "plt.figure()\n",
+    "plt.scatter(x, y, label='data')\n",
+    "plt.plot(x, memf.fittedvalues, 'r--.', label=\"MEM\")\n",
+    "plt.xlabel('x1')\n",
+    "plt.ylabel('y')\n",
+    "plt.legend(fontsize=10)\n",
+    "plt.tight_layout()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 175,
+   "id": "12bf3347-729f-45eb-a62c-581929cbb523",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(DesignMatrix with shape (50, 1)\n",
+       "          y\n",
+       "    1.12359\n",
+       "    1.26403\n",
+       "    2.35548\n",
+       "    2.37509\n",
+       "    2.88171\n",
+       "    3.15566\n",
+       "    2.20136\n",
+       "    1.76819\n",
+       "    1.80392\n",
+       "    0.90444\n",
+       "    4.38990\n",
+       "    3.05902\n",
+       "    3.17022\n",
+       "    5.61056\n",
+       "    3.12959\n",
+       "    0.80367\n",
+       "    1.77260\n",
+       "    2.35809\n",
+       "    2.41295\n",
+       "    3.21103\n",
+       "    2.52541\n",
+       "    3.07791\n",
+       "    2.57623\n",
+       "    2.36746\n",
+       "    3.99027\n",
+       "    0.60022\n",
+       "    2.55591\n",
+       "    1.08885\n",
+       "   -0.77351\n",
+       "    0.98839\n",
+       "   [20 rows omitted]\n",
+       "   Terms:\n",
+       "     'y' (column 0)\n",
+       "   (to view full data, use np.asarray(this_obj)),\n",
+       " DesignMatrix with shape (50, 3)\n",
+       "   Intercept       x1  gp\n",
+       "           1  0.00000   1\n",
+       "           1  0.02041   1\n",
+       "           1  0.04082   1\n",
+       "           1  0.06122   1\n",
+       "           1  0.08163   1\n",
+       "           1  0.10204   1\n",
+       "           1  0.12245   1\n",
+       "           1  0.14286   1\n",
+       "           1  0.16327   1\n",
+       "           1  0.18367   1\n",
+       "           1  0.20408   1\n",
+       "           1  0.22449   1\n",
+       "           1  0.24490   1\n",
+       "           1  0.26531   1\n",
+       "           1  0.28571   1\n",
+       "           1  0.30612   1\n",
+       "           1  0.32653   1\n",
+       "           1  0.34694   1\n",
+       "           1  0.36735   1\n",
+       "           1  0.38776   1\n",
+       "           1  0.40816   1\n",
+       "           1  0.42857   1\n",
+       "           1  0.44898   1\n",
+       "           1  0.46939   1\n",
+       "           1  0.48980   1\n",
+       "           1  0.51020   0\n",
+       "           1  0.53061   0\n",
+       "           1  0.55102   0\n",
+       "           1  0.57143   0\n",
+       "           1  0.59184   0\n",
+       "   [20 rows omitted]\n",
+       "   Terms:\n",
+       "     'Intercept' (column 0)\n",
+       "     'x1' (column 1)\n",
+       "     'gp' (column 2)\n",
+       "   (to view full data, use np.asarray(this_obj)))"
+      ]
+     },
+     "execution_count": 175,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "dmatrices('y ~ x1 + (gp)', df)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}