{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Weighted Least Squares"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-18T11:13:26.284266Z",
     "iopub.status.busy": "2024-04-18T11:13:26.284037Z",
     "iopub.status.idle": "2024-04-18T11:13:27.139752Z",
     "shell.execute_reply": "2024-04-18T11:13:27.139095Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-18T11:13:27.143238Z",
     "iopub.status.busy": "2024-04-18T11:13:27.142829Z",
     "iopub.status.idle": "2024-04-18T11:13:29.138218Z",
     "shell.execute_reply": "2024-04-18T11:13:29.137445Z"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import statsmodels.api as sm\n",
    "from scipy import stats\n",
    "from statsmodels.iolib.table import SimpleTable, default_txt_fmt\n",
    "\n",
    "np.random.seed(1024)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## WLS Estimation\n",
    "\n",
    "### Artificial data: Heteroscedasticity 2 groups \n",
    "\n",
    "Model assumptions:\n",
    "\n",
    " * Misspecification: true model is quadratic, estimate only linear\n",
    " * Independent noise/error term\n",
    " * Two groups for error variance, low and high variance groups"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-18T11:13:29.141801Z",
     "iopub.status.busy": "2024-04-18T11:13:29.141365Z",
     "iopub.status.idle": "2024-04-18T11:13:29.147577Z",
     "shell.execute_reply": "2024-04-18T11:13:29.146906Z"
    }
   },
   "outputs": [],
   "source": [
    "nsample = 50\n",
    "x = np.linspace(0, 20, nsample)\n",
    "X = np.column_stack((x, (x - 5) ** 2))\n",
    "X = sm.add_constant(X)\n",
    "beta = [5.0, 0.5, -0.01]\n",
    "sig = 0.5\n",
    "w = np.ones(nsample)\n",
    "w[nsample * 6 // 10 :] = 3\n",
    "y_true = np.dot(X, beta)\n",
    "e = np.random.normal(size=nsample)\n",
    "y = y_true + sig * w * e\n",
    "X = X[:, [0, 1]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### WLS knowing the true variance ratio of heteroscedasticity\n",
    "\n",
    "In this example, `w` is the standard deviation of the error.  `WLS` requires that the weights are proportional to the inverse of the error variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-18T11:13:29.154759Z",
     "iopub.status.busy": "2024-04-18T11:13:29.153680Z",
     "iopub.status.idle": "2024-04-18T11:13:29.185471Z",
     "shell.execute_reply": "2024-04-18T11:13:29.184864Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            WLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.927\n",
      "Model:                            WLS   Adj. R-squared:                  0.926\n",
      "Method:                 Least Squares   F-statistic:                     613.2\n",
      "Date:                Thu, 18 Apr 2024   Prob (F-statistic):           5.44e-29\n",
      "Time:                        11:13:29   Log-Likelihood:                -51.136\n",
      "No. Observations:                  50   AIC:                             106.3\n",
      "Df Residuals:                      48   BIC:                             110.1\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          5.2469      0.143     36.790      0.000       4.960       5.534\n",
      "x1             0.4466      0.018     24.764      0.000       0.410       0.483\n",
      "==============================================================================\n",
      "Omnibus:                        0.407   Durbin-Watson:                   2.317\n",
      "Prob(Omnibus):                  0.816   Jarque-Bera (JB):                0.103\n",
      "Skew:                          -0.104   Prob(JB):                        0.950\n",
      "Kurtosis:                       3.075   Cond. No.                         14.6\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "mod_wls = sm.WLS(y, X, weights=1.0 / (w ** 2))\n",
    "res_wls = mod_wls.fit()\n",
    "print(res_wls.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## OLS vs. WLS\n",
    "\n",
    "Estimate an OLS model for comparison: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-18T11:13:29.189707Z",
     "iopub.status.busy": "2024-04-18T11:13:29.188639Z",
     "iopub.status.idle": "2024-04-18T11:13:29.207210Z",
     "shell.execute_reply": "2024-04-18T11:13:29.206605Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5.24256099 0.43486879]\n",
      "[5.24685499 0.44658241]\n"
     ]
    }
   ],
   "source": [
    "res_ols = sm.OLS(y, X).fit()\n",
    "print(res_ols.params)\n",
    "print(res_wls.params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare the WLS standard errors to  heteroscedasticity corrected OLS standard errors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-18T11:13:29.277217Z",
     "iopub.status.busy": "2024-04-18T11:13:29.276917Z",
     "iopub.status.idle": "2024-04-18T11:13:29.283823Z",
     "shell.execute_reply": "2024-04-18T11:13:29.283252Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=====================\n",
      "          x1   const \n",
      "---------------------\n",
      "WLS     0.1426  0.018\n",
      "OLS     0.2707 0.0233\n",
      "OLS_HC0  0.194 0.0281\n",
      "OLS_HC1  0.198 0.0287\n",
      "OLS_HC3 0.2003  0.029\n",
      "OLS_HC3  0.207   0.03\n",
      "---------------------\n"
     ]
    }
   ],
   "source": [
    "se = np.vstack(\n",
    "    [\n",
    "        [res_wls.bse],\n",
    "        [res_ols.bse],\n",
    "        [res_ols.HC0_se],\n",
    "        [res_ols.HC1_se],\n",
    "        [res_ols.HC2_se],\n",
    "        [res_ols.HC3_se],\n",
    "    ]\n",
    ")\n",
    "se = np.round(se, 4)\n",
    "colnames = [\"x1\", \"const\"]\n",
    "rownames = [\"WLS\", \"OLS\", \"OLS_HC0\", \"OLS_HC1\", \"OLS_HC3\", \"OLS_HC3\"]\n",
    "tabl = SimpleTable(se, colnames, rownames, txt_fmt=default_txt_fmt)\n",
    "print(tabl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate OLS prediction interval:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-18T11:13:29.301085Z",
     "iopub.status.busy": "2024-04-18T11:13:29.300783Z",
     "iopub.status.idle": "2024-04-18T11:13:29.305257Z",
     "shell.execute_reply": "2024-04-18T11:13:29.304671Z"
    }
   },
   "outputs": [],
   "source": [
    "covb = res_ols.cov_params()\n",
    "prediction_var = res_ols.mse_resid + (X * np.dot(covb, X.T).T).sum(1)\n",
    "prediction_std = np.sqrt(prediction_var)\n",
    "tppf = stats.t.ppf(0.975, res_ols.df_resid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-18T11:13:29.312377Z",
     "iopub.status.busy": "2024-04-18T11:13:29.311960Z",
     "iopub.status.idle": "2024-04-18T11:13:29.325467Z",
     "shell.execute_reply": "2024-04-18T11:13:29.324870Z"
    }
   },
   "outputs": [],
   "source": [
    "pred_ols = res_ols.get_prediction()\n",
    "iv_l_ols = pred_ols.summary_frame()[\"obs_ci_lower\"]\n",
    "iv_u_ols = pred_ols.summary_frame()[\"obs_ci_upper\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Draw a plot to compare predicted values in WLS and OLS:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-18T11:13:29.328419Z",
     "iopub.status.busy": "2024-04-18T11:13:29.327858Z",
     "iopub.status.idle": "2024-04-18T11:13:29.979340Z",
     "shell.execute_reply": "2024-04-18T11:13:29.978588Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f9588322740>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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p3Lkz3t7eODg4UKBAAQYMGEBwcHDiOfXr12fgwIHPvcbOnTtp2LAhHh4eODs7U6RIETp27EhsbGw6vAIhhBAic7kQfAGjyQiAXqenV+VeVMtbjQ3tNnCi5wk+KvORBJppkOpgc9euXbRs2RJvb290Oh3r169Pcc7Zs2d5++23cXNzI2vWrFSpUoUbN26YY7w27cqVK1SuXJmLFy/yww8/cOnSJebPn8/WrVupUaMGISEh/3mNM2fO0LRpUypXrsyuXbs4efIks2bNwsHBAaPRmA6vQgghhMgcjgQe4b2f3qP47OKsPbs28fjA6gPZ12UfLYu1RK+Tebm0SnWYHhkZSbly5ejcuTPvvPNOivsvX75M7dq16dKlC2PGjMHV1ZXTp0/j5ORklgG/YGDPv89ggCef/0Xn6vWQJct/n5s1a+rGB/Tp0wcHBwe2bNlClsfPkT9/fipUqEDhwoX5v//7P+bNm/fCa2zZsgVPT08mTpyYeKxw4cI0bdo01eMRQgghXjeaprH7xm7G7h7LX5f/Sjx+OPAw75d6H0BmMc0s1X+bzZo1o1mzZs+9///+7/946623UgRDFpct2/Pve+st2LQp6Xbu3BAV9exz69WDHTuSbhcsCPfvpzxP01I1vJCQEP766y++/fbbxEAzgaenJx9//DE//vgjc+fOfeF1PD09CQoKYteuXdStWzdVYxBCCCFeV5qm8eelPxm7eyz+N/0B1e3nwzIfMrLWSErlLmXlEWZeZp0bNplMbNq0iaJFi9KkSRNy585NtWrVnrnUniAmJoawsLBkX5nRxYsX0TSNEiVKPPP+EiVK8ODBA+7du/fC67z//vt8+OGH1KtXDy8vL9q0acPs2bMz7d+bEEIIYS7/2/k//G/642BwoGelnlzod4EVbVZkjkAzPt7aI3guswabd+/eJSIigvHjx9O0aVO2bNlCmzZteOedd9i5c+czHzNu3Djc3NwSv/Lly/dqTx4R8fyvX399eqDPP/fPP5Ofe+3as897RVoqZ0SfZjAYWLp0KQEBAUycOJG8efMyduxYSpUqRVBQUJquLYQQQmQWscZYlhxbwoNHDwDQ6XSMrjeaoTWGcm3ANea1mEeh7IWsPEoz2bgR8ueHixetPZJnMvvMJkCrVq0YNGgQ5cuXZ+TIkbRo0YL58+c/8zGjRo0iNDQ08evmzZuv9uRZsz7/6+n9oi8696kl7ueel0p+fn7odDrOnj37zPvPnj1L9uzZyZUr10tdL2/evHTo0IHZs2dz+vRpoqOjn/t3LIQQQrwuErr9FJ5ZmC4bujDn0JzE+5oVaZZ5uv08OXlVsCAEBcF331ltOC9i1h2wOXPmxM7OjpIlSyY7XqJECfbs2fPMxzg6OuLo6GjOYWRIOXLkoHHjxsydO5dBgwYl27d5+/ZtVq1axSeffIJOp0v1tbNnz46XlxeRL0p8EkIIITKxZ3X78crmRZ6smazLz6VLMGmSSmhOSCouUwb++QcyaC6HWYNNBwcHqlSpwvnz55Mdv3DhAgUKFDDnU9mk2bNnU7NmTZo0acI333yDr68vp0+fZtiwYeTNm5dvv/028dx79+5x/PjxZI/38vJi/fr1HD9+nDZt2lC4cGGio6NZvnw5p0+fZtasWen8ioQQQgjr+3L7l0zfP/2Z3X4c7TLJhNbRozBhAvzyC5hMYGcHo0eDp6e6/403rDu+F0h1sBkREcGlS5cSb1+9epXjx4/j4eFB/vz5GTZsGG3btqVu3bo0aNCAzZs3s3HjRnY8meH9mipSpAiHDx9m9OjRfPDBB4SEhODp6Unr1q0ZPXo0Hh4eieeuXr2a1atXJ3v8119/TfPmzdmzZw89e/YkMDCQbNmyUapUKdavX0+9evXS+yUJIYQQVnc99DrhseGZr9uPpqkKOePHw5YtScebN4eRI5MCzQxOp6UyY2XHjh00aNAgxfGOHTuybNkyAJYsWcK4ceMICAigWLFijBkzhlatWr3U9cPCwnBzcyM0NBRXV9dk90VHR3P16lV8fX0tX7fzNSB/n0IIIWzN2XtnmeA/gWE1hyVmkV8IvsC5++doUbRF5irCvnAh9OihvtfroV07GDECypa17rh4cbz2tFQHm5YmwWb6kb9PIYQQtuJw4GHG7RnHurPr0NBoX7Y9K9qssPawzCs2Fu7cgYTKPCEhUKwYfPABDBkChTJO9nxqgs1MMMcshBBCiMxI0zR2Xt/J2N1j+fvK34nH2xRvQ/+q/a04MjOLiFCZ5FOnQoECkJBU7eEBN2+mrKpjYyTYFEIIIUSG1ObHNvx2/jdAdfv5qMxHjKg1InMUYQfVoXD2bJg1S81igirOfvt20n5MGw80QYJNIYQQQmQQRpMRnU6XuO+yat6qbL60mS4VujC05lB8s/taeYRmcvMmTJmiZjMT2mf7+cHw4dChQ6YIMJ+UiXbRCiGEEMIWxcTHsOjoIorPKc7G8xsTj/et2pdrA68xp/mczBNoAuzdCzNmqECzYkX46Sc4dw66dct0gSbIzKYQQgghrCQyNpKFRxYyed9kAsMDAZh3eB6tiqsKNq6Orrg6vjj5xCbs369aZb/9trr97rtqBrNDB2jUCF6hoYstkWBTCCGEEOnqwaMHzD44mxkHZhD8KBiAvC55GVJjCN0rdbfy6MxE02DzZlWIfedO8PaGJk3A0VEVZF++3NojTDcSbAohhBAiXbX5sQ07r+8EwM/DjxG1RtChbIfM0e0nPh5+/lkFmSdOqGP29tC0KURGqmDzNSPBphBCCCEs6sqDK+RyzoWLowsA/ar240H0Az6r/RnvlXwPg95g5RGayd9/qyLsV6+q21mzQs+eMHAg+PhYdWjWJAlCQgghhLCI03dP02FdB4rOKsq8w/MSj7cp0YbjPY7TtnTbzBNoAuTIoQLNnDnh66/hxg2YPPm1DjRBgs10MX/+fFxcXIiPj088FhERgb29PfXr10927o4dO9DpdFy+fJmCBQsyffr051533bp1VK9eHTc3N1xcXChVqhQDBw60zIsQQgghXtKBgAO0XtOa0vNKs/LflRg1I6fvnU68X6/To7P1pJjAQFWqaOjQpGMVK8Kvv8L16/D556oou5Bl9PTQoEEDIiIiOHz4MNWrVwdg9+7deHp6cuDAAaKjoxPbRW7fvp38+fNTuHDhF15z69attG3blm+//Za3334bnU7HmTNn+Pvvv1/4OCGEEMJStl3dxre7v2Xb1W0A6NDxTol3GFV7FJW8K1l5dGZy4QJMmqQSfGJjwcFBBZwJRdjfece648uAMk2wGRkb+dz7DHoDTnZOL3WuXqcni32W/zw3q0PWlx5bsWLF8PLyYseOHYnB5o4dO2jVqhXbtm1j//79iTOcO3bsoEGDBv95zY0bN1KrVi2GDRuWeKxo0aK0bt36pcclhBBCmNOio4vYdnUbdno72pdtz4haIyies7i1h2UeR47A+PFq5lLT1LHatWHkSMiTx7pjy+AyTbCZbVy25973VpG32PTRpsTbuSfnJiou6pnn1itQjx2f7ki8XXBGQe5H3U9xnjZaS9X4GjRowPbt2xk5ciSgZjCHDx+O0Whk+/bt1K9fn0ePHnHgwAE6d+78n9fz9PRk9erVnDp1itKlS6dqLEIIIURaxZviWXNqDdV9quPn4QfAyNojyemckyE1hlDAvYCVR2hGS5ZAly5Jt1u2hBEjoFYt643JhsiezXTSoEED/P39iY+PJzw8nGPHjlGvXj3q1q3Ljh07ANi3bx8xMTEvNbPZr18/qlSpQpkyZShYsCDt2rVjyZIlxMTEWPiVCCGEeJ1Fx0cz79A8is4qSod1HRi/Z3zifWXzlGVms5m2H2gajXDnTtLtli3BxUUVYT95EjZskEAzFTLNzGbEqIjn3vd0ptvdoXefe25CP9YE1wZcS9O4EtSvX5/IyEgOHTrEgwcPKFq0KLly5aJevXp06tSJ6OhoduzYQaFChcifP/9/Xi9r1qxs2rSJy5cvs337dvbv38+QIUOYMWMG+/btw9nZ2SzjFkIIIQDCY8KZf3g+U/dP5XbEbQByOeeiRM4SVh6ZGcXEqL2YkyZB3rywfbs6nisXBASAayboZmQFmSbYTM0eSkud+yJ+fn74+Piwfft2Hjx4QL169QDw9vYmX7587N27l+3bt9OwYcNUXbdw4cIULlyYrl278n//938ULVqUH3/8kU6dOpll3EIIIcSUvVP4Zvc3PIx+CEB+t/wMqzmMzhU642yfCSY3wsJg/nyYPh2CgtSx+/fV915e6rYEmq8s0wSbtqBBgwbs2LGDBw8eJEvsqVu3Ln/++ScHDx6kV69er3z9ggUL4uzsTGTk8xOghBBCiNQKjw3nYfRDiuUoxsjaI/m4zMfYG+ytPay0u3MHZsyAuXMhNFQd8/GBwYOhWzfI9vx8EPHyJNhMRw0aNKBPnz7ExcUlzmwC1KtXj759+xIbG5tiv+atW7c4fvx4smMFChRgxowZREVF8dZbb1GgQAEePnzIzJkziYuLo3HjxunxcoQQQmRCF4MvMsF/Au+XfJ8mfk0A1fGndO7StCneJnMVYd+yBcaNU98XL66Sfj76SJUzEmYjwWY6atCgAY8ePaJ48eLkeaJMQr169QgPD08skfSkyZMnM3ny5GTHVqxYQb169ZgzZw6ffPIJd+7cIXv27FSoUIEtW7ZQrFixdHk9QgghMo8Tt08wbs84fj7zMybNxPng84nBZg7nHLxX8j0rj9AMjh1Ts5lNm6rb7drB+vXwyScqCUgvedOWIMFmOipYsCCalrJkUoECBZ55/Nq1ay+83stkrQshhBAv4n/Dn7F7xvLHxT8Sj7Uo2oJRtUdZcVRmpGmwYwdMmAB//QX588OlS2Bvr75+/dXaI8z0JNgUQgghXlM9NvZg4dGFgKrG8kGpDxhZayTlPMtZeWRmYDKpWcsJE+DgQXVMr1eF2MPCVB9zkS4k2BRCCCFeE0aTEaNmxMGg9iTWL1ifpceX8mn5Txlea3hicXabt3Ur9OkD58+r205O0KmTaitZqJB1x/YakmBTCCGEyORijbGs/HclE/wn0KtyLwZWHwjA+6Xep26BuuR1zWvdAZpbtmwq0HR3V0Fn//6QO7e1R/Xasslg81n7G0Xqyd+jEEJkblFxUSw6uohJeycREBYAwJJjSxhQbQA6nQ47vZ3tB5p37sDMmer7b79Vf1arBqtXQ4sWqvOPsCqbCjbt7VVNr6ioKLJkyWLl0di+qCjVHz7h71UIIUTm8DD6IXMOzmH6gencj7oPgFc2LwbXGEyPSj3Q6XRWHqEZXLkCkyervuUxMWqpfOBA1e0H4MMPrTo8kcSmgk2DwYC7uzt376p2k87OzpnjH0w60zSNqKgo7t69i7u7OwZDJqqZJoQQgr5/9GXVyVUAFMpeiOE1h9OxfEec7JysPDIzOH5cJf389JNKAgKoWhVGjpSknwzKpoJNAE9PT4DEgFO8Ond398S/TyGEELbr2sNrOBgc8HbxBmBQ9UH8e+dfRtYeyQelPsBOb3O/7p9t8WLo2jXpdpMmKsisVw9k8inD0mkZbONeWFgYbm5uhIaG4vqCPqRGo5G4uLh0HFnmYm9vLzOaQghh487cO8P4PeNZfXI13Sp2Y16LeYn3aZpm+6t/JhMEByctjQcFgZ8fvP02DB8OFSpYd3yvsZeN18AGZzYTGAwGCZaEEEK8lg7eOsi4PeNYf2594rFb4beSBZg2HWjGxMDKlTBpkirCvmWLOu7lBQEBkD27dccnUsVmg00hhBDidbPr+i7+t/N/bL26FQAdOtqUaMOo2qOo7F3ZyqMzg7AwWLgQpk2DwEB17M4duHs3qXSRBJo2R4JNIYQQwkZsvrSZrVe3Yqe34+MyHzOi1ghK5Cph7WGlXUL5orlz4eFDdczbGwYPhu7dpXyRjZNgUwghhMiA4k3xrDm1hkLZC1EzX00ABlYfSGRsJINrDKaAewErj9CMNm2CsWPV98WKqf2YH38Mjo7WHZcwC5tNEBJCCCEyo+j4aJYeW8rEvRO59vAaDX0bsvWTrdYelnkdOwb370Pjxup2bCx88AF07AitWqke5iJDey0ShIQQQojMJCwmjPmH5zN131TuRN4BIJdzLt7wfQOTZkKvs/EATNNg2zZVI/Pvv1WP8vPnwc4OHBxg/Xprj1BYiASbQgghhJXNPzyfUVtH8TD6IQD53fIzrOYwOlfojLO9s3UHl1ZGI6xbp4LMw4fVMYMBqleH8HBJ+HkNSLAphBBCWFkWuyw8jH5I8ZzFGVlrJB+V+Qh7QyZoJfzXX9CvH1y8qG5nyQJdusCQIVCwoFWHJtKPBJtCCCFEOroQfIEJeyZQzaca3St1B+CjMh/h7uROy2ItbX+5/EnOzirQzJ4d+vZVgWdCgXbx2pAEISGEECIdHA06yrg94/j1zK9oaBRwK8Cl/pcyTyvJoCCYPl1lkP/vf+qYpsHq1SrpJ1s2qw5PmJckCAkhhBAZgKZp7L6xm7G7x/LX5b8Sj7cs2pJRtUdljkDz4kXV6ef771VWedasMHAgeHiofuUff2ztEQorywQ/5UIIIUTG9NnWzxjvPx4Ag85Au9LtGFFrBGXylLHyyMzg0CGV9LN2rZrBBKhZE0aMAHd3qw5NZCwSbAohhBBmEm+K51HcI1wcVcebVsVbMW3/NDqV78SwWsMolL2QlUdoJnPnQp8+SbdbtFBBZu3a1hvTcxhNGgevhnA3PJrcLk5U9fXAoLfhvvE2SPZsCiGEEGkUEx/D9ye+Z4L/BJoXac7MZjMT7wuOCiaHcw4rjs4M4uMhJCSpP3lAgOr08+67qttP6dLWHd9zbD4VxJiNZwgKjU485uXmxOiWJWla2suKI7N9qYnXJNgUQgghXlF4TDgLjixg6r6pBEUEAZDPNR+X+1/OHKWLHj2CpUth8mQoUUK1lUzw8GGGXi7ffCqIXiuP8nSQkzCnOa99RQk400AShIQQQggLCo4KZuaBmcw6OIsH0Q8AyOuSl2E1h9G1YlfbDzRDQtRS+cyZcO+eOhYRoY57eKjbGTjQNJo0xmw8kyLQBNBQAeeYjWdoXNJTltTTgQSbQgghRCpN2juJCf4TACiaoygjao2gfdn2OBgcrDyyNAoIgKlTYeFCiIxUxwoWVEXYO3dWdTNtwMGrIcmWzp+mAUGh0Ry8GkKNwja+xeGxgLAALgZfpEiOIvi4+lh7OMlIsCmEEEL8h4vBF4kzxVEyV0kABlQbwK7ruxhUfRDvlHgHg95g5RGayaZNMG2a+r5sWZX088EHqn+5Dbkb/vxA81XOMwdLJiotPrqY7r93x6SZ0Ov0LGyxkC4Vu5jl2uZgWz89QgghRDo6fvs44/eM5+czP9O4UGM2t98MgJeLF3u77LXy6Mxg7141g9m4sbrdsSNs2QJdu0LTpqpOpg3K7eJk1vPSypKJSpdDLtNtYze0x5sGTJqJHr/3oIlfkwwzw5mJemIJIYQQ5rHnxh6ar25OhQUV+PH0j5g0E/YGe2LiY6w9tLQzmeD336FOHahVS7WQNJnUfU5O8Ouv0KyZzQaaAFV9PfByc+J5r0CHCvaq+npYfCwJiUpPL+vfDo2m18qjbD4V9ErXfRT3iKn7plJtUbXEQDOBUTNyKeTSK4/Z3CTYFEIIIR7beW0ndZbWoc7SOvxx8Q/0Oj0flv6QEz1PsPHDjTjaOVp7iK8uLg6WL1fL4y1bwp494OCgamNGRFh7dGZl0OsY3VJteXg64Ey4PbplSYsnB/1XohKoRCWjKfWFgUyaiW93f0vwo+AU9xl0Bvw8/FJ9TUtJdbC5a9cuWrZsibe3NzqdjvXr1z/33J49e6LT6Zg+fXoahiiEEEKkj4shF9lzYw8OBge6V+zO+b7nWf3uasrmKWvtoaXNb79B4cJqmfz0aXBxUfUxr16FRYsgE5YabFrai3ntK+Lplnyp3NPNKd3KHqUmUelZAsIC2H51OwFhAdwIvcHY3WNJqFiZ1SErYxuOZVHLRcxrPg+DTu0bNugMLGixIMMsocMr7NmMjIykXLlydO7cmXfeeee5561bt479+/fj7e2dpgEKIYQQlhATH8OKf1fg7uTOeyXfA6BD2Q7cCL1Bz8o98XbJRL+/XF3h5k3w9FR9y3v2BDc3a4/K4pqW9qJxSU+rdRBKS6LSk0k/OnTodDpMmomyecrSomgLAHpU7pF4fouiLbgUcgk/D78MFWjCKwSbzZo1o1mzZi8859atW/Tr14+//vqL5s2bv/DcmJgYYmKS9sCEhYWldkhCCCHES4uIjWDhkYVM3TeVW+G3KJy9MK2Lt8ZOb4ejnSP/a/A/aw8xba5cgSlTIFcu+Oordax+ffjpJ7V87pQ+STEZhUGvs1p5o1dNVAoIC0gMNAE0NDRNo1a+WuRyzvXMa/i4+mS4IDOB2bPRTSYTHTp0YNiwYZQqVeo/zx83bhxjxowx9zCEEEKIZEIehTDrwCxmHpxJyCO1bOnt4k3vKr0xmozY6W28QMuxYzBhAvz8s0r4cXWFwYPVnzodvP++tUf42klIVLodGv3MfZs61LL+k4lKIY9CaLG6RWKg+aRvGn5DNZ9qlhuwhZg9QWjChAnY2dnRv3//lzp/1KhRhIaGJn7dvHnT3EMSQgjxmlt6bCn5p+Xnq51fEfIoBD8PP75r+R1X+l9hcI3Btpv4o2mwdSu8+SZUrAg//qgCzSZNYP16tTdTWM2rJCpld8pOrDE25bVelPTj7w/16sGdO2YYtfmZNdg8cuQIM2bMYNmyZehesmSCo6Mjrq6uyb6EEEKItEpIpAAo7FGYyLhIyuUpx5p313Cuzzm6Vuxqu0FmgokToVEj+PtvMBjgo4/UDOfmzdCggU2XL8osXpSoNOPDUgTEbqL6oupExKqKADqdjhVtVjCx0cSXT/rRNNi1C2bPtuhreVU67cl/jal9sE7HunXraN26NQDTp09n8ODB6PVJMazRaESv15MvXz6uXbv2n9dMTWN3IYQQ4mknbp9gvP948rvmZ0Jj1VJS0zT8b/pTK1+tl54MyZAePYKHD8HrcSb1tWuqlFHHjmrJ3NfXmqNLZMluObbKaNL4/dQpTt45S+Ec+bj5aA/T908jKELV2ZzeZDoDqg9I9piAsICUST/376u+9TodfPGFOqZpMH8+vPMO5MmTLq8nNfGaWYPN4OBggoKSFydt0qQJHTp0oFOnThQrVsysgxdCCCES7Lmxh3F7xvHHxT8AyOaQjaAhQWRzyGblkZnBgwcwbx7MmAE1a8K6dUn3RUZC1qzWG9tTLNktJ6NJTVD9ZHb5k/K65GVIjSF0q9TtxT+rV66ovvVLlqgPHVmzqgoD2bOb8yW9tNTEa6neDR0REcGlS0lV6a9evcrx48fx8PAgf/785MiRPOPL3t4eT0/Plwo0hRBCiNTQNI3NlzYzbs84dt/YDYBep+eDUh8wstZI2w80b91SvcoXLEgqvH78uPo+2+PXlsECzV4rj6ZIhknolpNe9S3TQ2qC6qezyxNMajyJ/tX642BweP4THToEkyapzk4JnZ4qVlR1Um1kT26q92wePnyYChUqUKFCBQAGDx5MhQoV+PLLL80+OCGEEOJFJvhP4K3Vb7H7xm4cDA50q9iN833P88O7P1DOs5y1h/fqzp2DTp3UsviUKSq4LFMGVqyACxeSAs0MxJLdcjKal21BGRgeCMDF4IvPzC6v7F35xYHmnDlQtWpShYGmTVVC2OHD0LYt2NlGBYU0LaNbgiyjCyGEeJ6Y+BgeRD/AM5snADdDb1Jufjk6le/E4BqDyeua18ojNJNZsyChqku9emoWK4P3K993OZgPv9v/n+f90K261epemoPRpFF7wrbndgbSAVldrlCo0D/8eekPzvY5i5OdEwWmF0gWcBp0Bq4NvJY86Sc2FoKDk/bk3rwJxYvDu+/C0KFqf24GYdFldCGEECK9PVmIvYJXBTZ+uBGAfG75uDX4Flnss1h5hGlgMsGmTapPeZMm6ljnzmr5tE8fqGYbdRXT0i3HljzdgjKe+8TrAzGYvIjX3yDU7mdi4k9x+gLo0LH1ylZ6VO7BwhYL6fF7D4yaMWV2eWgoLFyo9uSWLw+//66O58sHgYE23+1Jgk0hhBAZ1rMKsQOERofi5qR+AdtsoBkbC6tXq/14Z85AqVLQuDHo9Wof5vLl1h5hqrxqtxxb82SwHG7YQoj9LNBpaq9AwsSzZscbBd5lTssxFMupcla6VOxCE78mybPLAwJUgLlgAYSHP36spoLPhADTxgNNkGBTCCFEBnQr7BZT901lwZEFRMZFAuDn4ceIWiPoULaDbdfHDA9Xs1jTpqkEIFBdflq0gJgYyGKbwfOrdMuxRQnBcjz3kwJNUC9Qg6zxTXCP/5Cv67agWM7k2wUSW0qePQv9P1UfNuLi1J0lS6ql8o8+Akcb/vl+Bgk2hRBCZDi/nf+NqfunAlDeszyjao/i3RLvYtAbrDyyNFq2DAYOVDNXoPbmDRwIPXrY/AxWQrecXiuPJsRdiZ7XLccWFfe2w5BtO9FRHkmBZgIdZDPVI5+bz4uD6l274Pvv1fd16ybtydWbvbFjhiDBphBCCKs7cfsED6MfUq9gPQA6le/E31f+pkelHjQp3MS2C7FrWlJij5eXCjSLFYNhw6B9+0w1i5XQLefpkkCemaDO5t3Iu8zYP4M5h+YQagwlJ0NA0yUPODU99ibv5EF1fDysXatmrFu2VMc++QQOHICePVW2eSYn2ehCCCGs5slC7MVzFud079PodZlkdufQIdVOsmRJGDNGHdM01VqyUaNMO4sFmauD0LWH15i8dzKLjy0mOl4F0MVzFqd9sS9Zsv8IV+Kngc4Emp5CdoOY03qICqojI2HpUlWI/epV9QHjzJlM875LNroQQogMS9M0/rz0J+P2jGPPjT2AKsRe3rM8YTFhuDu5W3eAaaFp8NdfKsjcvl0dy54dRo0CJyc1w/nmm9YdYzow6HU2W94oICyAi8EX8czmybe7v2XNqTUYNSMAVbyrMKr2KFoVb4Vep2dkw3b8fqojJ++eo0zu4rQoXRpD8H0YPVrVyAwOVhfNkQPatVNJYU62nSD1KiTYFEIIkW62X93OoL8GceLOCQAcDA58Wu5ThtUahp+Hn5VHlwbx8fDTTyrIPKFeG3Z2Ktlj2LDXMsCwRU+2lNTr9OTJmgejZqRxocaMqj2K+gXrJ9vSYdDraFW2DK0oow7Mm6d61Ec/3kJQqJC63akTODtb4RVlDBJsCiGESDdGzciJOyfIap+VnpV7MrjGYLxdvK09rLT74gsYP159nzUrdO+uEn/y57fqsMTL0TSNlf+upOvGronHTJqJO5F32PThJt4q+tbzHxwfn9TJp1gxFWhWqaI+ZLzzDhhsPKnNDCTYFEIIYTH3o+7z0+mf6F2lNwBv+L7BvObz+KDUB3hkseESOPfvQ1RUUjDZpYvKNO/bF3r1Ag8bfm2vkXhTPD+f/pnx/uP5986/Ke43aSacHZ4xI2kywR9/qJnsGjVgwgR1vEED2LdPFeK35aQ2M5MEISGEEBYz//B8Rvwzgh0dd1DBq4K1h5N2V6+qhI/Fi1Vm8Y8/Jt335AyXyNCi46NZdnwZk/ZO4sqDKwBksctCdHw02hNFm1K0lIyJgVWrYPJkVSsTIGdOVS/V4QU9zjMhSRASQgiRIRwJPEJYTBg/n/nZtoPNY8fULNZPP6lZLYBr11TCR0KQIYFmhpWQ9FMkRxFcHV0pPrs4QRFBAOTIkoMB1QbQp2of1p1d9+yWkg8fqi4/M2ZAkHocrq6qPuqAAa9doJla8i9DCCGExRwJOgJAJa9KVh7JK9qzB/73P1WuKEGTJqoId4MGslRqA55O+lnYYiHVfKpxJPAIQ2sOpUuFLmR1yAo8p6UkqJ+BadPU93nzqv243brZfCH+9CLBphBCCIuIiY/h1N1TAFTyttFg8+BBFWgaDNC2rUr6KF/e2qMSL2nvjb1029gtcWncpJno8XsPDnc/TMlcJXEwpJyR9HH1wedaCDwKh4TV4X79YNs2GDQIPvxQZjJTSYJNIYQQFnHy7kniTHF4ZPGggFsBaw/nv0VFqSSfAgWgeXN1rFs3tR+vXz8oWNCaoxOpcPLOScb7j2fNyTXJ9mCCqojwMPphykBT01Rt1IkTVa3U1q1h3Tp1n6+v2kohM9mvRIJNIYQQFnEkMGkJPUO3mwwOhrlzYeZMlWVerhy89ZYKLFxcYMoUa48wQ7CFrkD+N/wZt2ccmy5ueu45Bp0heU3X+Hj45ReYNAmOHlXH9HpVG9VoTCpdlJF/hjM4CTaFEEJYRIbfr3n9usosX7RIzWqCmr3s1k0FGZLwk2jzqaAU/c69rNjv/MmEn4R9leEx4TRb1Yzw2HB06Hiv5HuMrD2SY0HHnp30Ayqz/PPPVbIXqP7lXbqo5fJChdL9dWVW8i9JCCGERdQtUJewmDDqF6xv7aGkNH68CjKMqg0hFSqopJ/33pMg8ymbTwXRa+VRnq6TeDs0ml4rjzKvfcV0DTifTPjRoWNhy4V0rdgVF0cXBlYfSFB4EMNrDadIjiIAVPSq+OykH4CQEBVo5syptkr07q2+F2YldTaFEEJkfpqmlkvt7dXt339XdTIbNVJBZqNGskz6DEaTRu0J25LNaD5JB3i6ObFnRMN0WVIPCAugwPQCmDRT4jG9Ts/1gdeTB5HPcuGC2hJRv75K8gGIjISVK+GTT9SspnhpqYnX9Ok0JiGEECL9GY1qP161ajB2bNLxt96C48dVpnnjxhJoPsfBqyHPDTQBNCAoNJqDV0MsPpbQ6FDG7BiTLNAElWF+KeTS8x+4b59qG1m8OCxcqH4OEubZsmZVtTIl0LQoWSsQQghhdpdDLmPSTBT2KIxeZ4V5jUeP4PvvVaeXy5fVsdu31dK5waASQMqVS/9x2Zi74c8PNF/lvFcRFRfF1zu/Zu7huYTFhKW4P0XCD6jC+7//rjLL/f2TjrdsqcpXiXQlM5tCCCHMboL/BIrOLspXO75K3ycOCYFvvlHli3r1UoGmhwd8+SUcOZKUWSxeSm4XJ7Oe9yocDY6sPbeWsJgwSuYqSZfyXTDo1PuYIuEnQbdu0KqVCjQdHKBzZzh9GjZsgDp1ZCY7ncnMphBCCLNLyEQvlyedZw8/+0y1FQTInx+GDFHZxVmzpu84Momqvh54uTlxOzQ6RYIQJO3ZrOrrkebnSsgwjzPGsfbcWqY3nY6TnRMGvYGpb04l3hRPy2It0ev0fNXgq+QJPw8eqADS3V1d7P334ddf1QeOfv3A2zvN4xOvToJNIYQQZhUTH8PJOyeBdOgcdPKk2m/n93gZdeBAOHBALZW+/35SQpB4JQa9jtEtS9Jr5VF0kCzgTJgbHN2yZJqTg57MME9Q0asi3St1B6B50ebJzvdx9VFB5vXrMHoQfPedeu+/+Uad0KQJ3Lyp6qQKq5NldCGEEGZ16u4py3YO0jTYsQOaNYOyZeGrr5LuK15cFeb+6CMJNM2kaWkv5rWviKdb8qVyTzenNJc90jSNZceX0XVj12SBpg4dvu6+z3yM0aRx4ved3Gz+DlrhwjB9usoq9/dPSvxJKMgvMgSZ2RRCCGFWhwMPAxboHGQ0qvaBEyfCoUPqmF6vAgyTSX0Psh/PApqW9qJxSU+zdhCKjI2kxuIanLx7MsV9Ghr2hpQfFg4u/hlt/ASqXTqSeOxQ4Qrohg2jcvd28t5nUBJsCiGEMCuLdA5avVol+SRkljs5qaSPIUOk00s6Meh11CicI03XMJqMGPQquSerQ1byueXj8oPLPIp7lKyH+bMyzDefCiJ49hI+vnSEeJ2eTcXrsLBqG854+sFVmHf6tlW6GYn/JsGmEEIIs0oMNs25X/PmzaTM8r591VeuXOa7vjC7J1tKZnPIxrxD85h7eC77uuxLzB6f3Ww27k7urD27NmVLSb27WiKvVw9jufKM2XgGxyptiDXYs7hKawLc8iQ+lw4Ys/EMjUt6Zrh+7UKCTSGEEGb2Vb2v2B+wnxo+NV7tAjduqJ7lDRvC22+rYz16gLOzms2UzPIM7+mWko52jkTHq1qc3x35jjENxgDgm13ty+xSsUtSS8l4V3yW/ALz8sHDh/DBBxwcO1cVl/fIy5hGPVI835PF5dM6+2pLTCa4eFHlxCV8LVsGpUtbe2TJSbAphBDCrFoWa0nLYi1T/8B//4VJk+CHH9T+zL17VRHuhJI2/fqZfazC/ALCApJllmtoRMdHU9SjKF/U+4K2pdo+83E+gRH4TF4JK1ZAbKw6WLQovPlmhigunxHcvw8HD8L+/SqwPHhQxeNP2rdPgk0hhBAiSUJm+cSJsHlz0vE33pBOLxZmNGlmTfhJcPLOyRQtJQHmtZhHQ9+Gz35Q794wb17S7Ro1VM/6t98GvZ7cl4Nf6rktWVw+vcXGwrFjyWctE7YsP8nJCSpWVB1Zq1WDevXSf6z/RYJNIYQQZvPHxT/QoaNGvhq4O7n/9wO6d4dFi9T3er2qjTlsGFSycH3O19zmU0GM2XgmWd9zLzcnRrcsmeokG03TOHb7GBW9KgJQJk8ZdOhSJPwUzVE06UFG4+M7Hnd08vNTM9hvv63e/1q1kj1HehaXt5bAQDUrmfB15AjExKQ8r1ixpMCyWjVV/UtvSPrgcDXSiVwm83xwMBedpmnPet+sJiwsDDc3N0JDQ3F1dbX2cIQQQqRC5YWVORJ0hJ/e+4n3S72f8oSoKDWbmbDvcu1aaN9e7cUcPFgyy9PB5lNB9Fp5NEXQlhCavGztTJNmYtOFTYz3H8/em3vZ3Wk3tfPXBtS+zF6beiVL+OlSsYvqWb98OUyZAmPGwIcfqouFh6toq1ix/xw3PLu4fFprfqanuDg4fjx5cHn9esrzcuSA6tWTAssqVSB79uTnmPODQ2qkJl6TYFMIIYRZxBpjcRnnQqwxliv9ryQmfwAQHAxz5sCsWSqoHDVKHTcaVT9zySxPF0aTRu0J25IFJk9KmCHcM6LhM2fGAsICOHvvLGfvn+W7o99x6u4pABwMDkxvMp1eVXolOzexpWRcFrVMPmsW3L2rTmjQALZtS9X4rRVYpVVIiNqCvGeP+vPQIYh+6i3Q69Vey5o11S6CGjWSJnyfx1wfHF5FauI1WUYXQghhFqfuniLWGEt2p+wUdC+oDl67pjLLFy9Ws5oAGzbAyJHqt6jBIIFmOjp4NeS5gSa8OKt7weEF9NrUK9nyuIuDC72r9GZAtQF4uSQPanxcffAJjoPPJyZ///Pnh0GDVM/6VLJEcXlz0zS4ckUFlv7+6s+zZ1Oelz17UlBZowZUrZq6pkdGk8aYjWeeua1AI2OVg5JgUwghhFkkdg7yroTu+HGVWf7TT0n78ypUUEkf770nnV6s5FWzugPCAuj9R+9kgaYOHfu67KNU7lLPv1DnzioBDKB8ebP0rDdHcXlziotTiTwJgaW/P9y5k/K84sXVVtRatVRwWbRoUtOrV5GWDw7pTYJNIYQQZnEk8InOQdOmqRJGAI0bqyCjUSMJMq3sZbO1c7s4ERQexMIjCxlVZxQXgy+myDDX0LgXde+JAxps2aKSu3LmVMeGDAEHB/X+v/FGpnj/o6JUZviuXbB7t9pvmTBpm8DBASpXVoFl7dpqaTzhr8RcbKkclASbQggh0iY+Hn75hSN3/YHHweawj9XxYcPUjKbIEF4mq9vdNZilZ0bx/Q/fE2uMJZ9bPt4s/CZ6nT5ZwJnYUjIuDtasgcmTVa3UMWNUa1GAFi3Ulw0LDVWzlbt2qa/Dh9VLfpKHhwooE4LLypVVSSJLSs0HB2uTYFMIIcSriYyEJUtg6lRib17j5Od60EFl78qQ3Vf1MxcZikGvY3TLkvRaeRQdEMd94vWB2Jm8MelCCbX7hRtx/hw/qoLKmvlq4uvui4+rDwtbLEzeUrLRdHy++1G1lAwIUE+QNavNz17evZs0a7lrF5w4oSZtn5Q3L9StC3XqqD9LlEjbkvirsKVyUBJsCiGESJ1792D2bPUVEgKAXa6cHHL8mONvVUxKDhIZUtPSXsxrX5E+66dwK34q6LSkjJLHmhdpzsjaIxNLGcFTLSWX/obPW5+raT+APHlgwADo2TNlbZ4M7s4d2LlTfe3YAWfOpDzHz08FlQkBpq+v9WPqpz84PKsc1OiWJa2eHAQSbAohhEiNL75Qy6UJdVsKF4ahQ9F37EjZLFkoa93RiZdUOr+Ra6ZpKtCExOikdfHWjKk/hrJ5nv1O+rj64OPqAwErVKBZrBgMHapqpVp63dhMbt9OHlw+K1O8TJnkwaVXBq2qlPDB4elyUJ4ZrByUBJtCCCFeTNOSpnEcHFSgWbkyjBgBbdokdYERGV6cMY41p9bwza5vntlSckC1AckDTU1T68mTJsE330C5cur4yJHQqpXaj5ne68epdOeOCioTvs6dS3lOuXKqzWP9+irAzJFxkt3/ky2Ug5JgUwghREqapnqVT5yoaiK+/bY63qePmuqpVy/ZOuJXO74iR5YcfFjmQ3I6mzntVqRZVFwUi48uZvK+ydwIvQHwzJaSfh5+6obRCOvXq/f/4EF1zN0dVqxQ3xcpor4yoIcP1azltm3q69Sp5PfrdMmDyzp1bCu4fJaMVg7qaRJsCiGESBIbqzKLJ01K+i2taUnBpoeH+g395EOMsYzbM45YYyzNizaXYNPKAsICuBh8kSI5ipDVPitzDs1hxoEZ3I+6D0CerHkYVH0QzvbODPprULKWkj72OVSnn6lT4dIldUFHR/j0U1XGKAOKjFT1LROCy6NHwfTUpG25cqphUUJw6WH9nJnXigSbQgghICwMvvsueWZxtmzQo4dK/HiBJzsH+br7vvBcW2E0aRl6WfJ5Fh9dTPffu2PSTOh1erLaZyU8NhyAQtkLMazmMDqW60gW+ywAtCnRJqmlpEteVXj933/VxTw81Ex2376QO7eVXlFKsbGwfz9s3aqCywMHUpYiKlYMGjZUX/Xrm7/GpUgdCTaFEEJA69awfbv63tMzKbPY3f0/H5pQzL2iV0V01k7RNQNb7b8dEBaQGGgCmDQTEbERFM9ZnC/rfsn7pd7HTp/8175PcBw++esk7bv98EP1wWPwYNX9J2vW9H4ZKWiammT/+2/45x+1RP50EfX8+VXN+IYN1Qxm3rzWGat4Ngk2hRDidXTuHHh7g6urut2jBwQGqiLs7durpdOXdCToic5BNm7zqSB6rTyaom7h7dBoeq08yrz2FTNkwHk06CiD/xr8zC4/c9+aSwPfBskfcPiw2irxyy+qpei776rjAweq7HI764YHN2+qwPKff9QM5tPtH3PlUsFlQoCZEUoRieeTYFMIIV4n/v4qyPjtN/Xn0KHq+HvvqZ7Vr5BZnBhsett2sGk0aYzZeOaZBbITylCO2XiGxiU9M8SSuqZp7Ly+k3F7xrHl8pZnnmPQGSiSo0jCA+DPP9X7ntCvHNSadEKwaaXyRWFhamI9Yfby/Pnk9zs7qyzxRo1U99PSpTN8Erx4QqqDzV27djFp0iSOHDlCUFAQ69ato3Xr1gDExcXx+eef88cff3DlyhXc3Nxo1KgR48ePx9vb29xjF0II8TJMJti4UWUW792rjul0cOVK0jmvWL4o1hjLv3fUHj9bn9k8eDUk2dL50zQgKDSag1dDrJr5a9JMbDy/kXF7xnHg1gFABZXtSrejiEcRvt71dfKkn2ze8P33Ksg8fVpdxM4OPvpIfdgoUybdX4PRCEeOwF9/qXbq+/apYwn0eqhSRQWWjRpB9eqpmmx/9XHZ6F7djC7VwWZkZCTlypWjc+fOvPPOO8nui4qK4ujRo3zxxReUK1eOBw8eMGDAAN5++20OHz5stkELIYR4SUuXwoQJSVNFDg7QsaPKLC5WLM2Xvxh8kThjHO5O7hTKXijN17Omu+HPDzRf5TxzeTK73MfVh3hTPP3+7MfNsJs42TnRpUIXhtQYgm92lZzVpWKXpKQfVx81ozlvngo0XVyge3e1JzdfvnR9HTdvqsByyxY1e/m4+VSiIkVUcNm4sUrqeYntwmZlq3t1bUGqg81mzZrRrFmzZ97n5ubG33//nezY7NmzqVq1Kjdu3CB//vyvNkohhBCvZssWFWi6u0Pv3tCvn0oAMpNSuUsROjKUaw+v2XxyUG6Xl1tCftnzzOHp7PKFLRbSpWIXRtcbzZUHV+hfrT95suVJ9hifMPCZv1kV3Qc1iz16tMoy79Ej3aK4qCiVzLNli5rBfLpTj5ub2nP55pvqy9eKhQxsda+urbD4ns3Q0FB0Oh3uz/nhjomJISYmJvF2WFiYpYckhBCZ040bqnRRz55QtKg6NnIkVK0KXbuqWS0LcHF0oUye9F+KNbeqvh54uTlxOzT6mfs2dag2gFV906dI48m7J+m2sVti4XWTZqLH7z1o4teELhW7pHzAqVOqlejq1aoWkJsbjBql7mvWTH1ZkKapzzWbN6utoTt3whO/3tHr1Y/im29CkybqeyvnIQG2t1fXFln0bY6OjmbEiBF8+OGHuCZkPD5l3LhxjBkzxpLDEEKIzO3ff9V+vDVrID5eVblesEDdV65cUotB8UIGvY7RLUvSa+VRdJAs+EgIMUa3LGnxgCMgLIBp+6Yx99DcZB1+AIyakUshl9TyOKgIb8cO9f7/+WfSiXXrqk2PFhYRoWpdJgSY164lvz9fPhVYNmmissYzYjF1W9mra8ssFmzGxcXxwQcfoGka8+bNe+55o0aNYvDgwYm3w8LCyJfO+0iEEMLmaJr6LT9pklqjTNCwocosTwexxliarGxC2dxlGddoHM72zunyvJbUtLQX89pXTLF3zzMd9u7FGmPpvak3y08sJ84U98xzkrWUjI9XQeW+feq2Xg/vvKOSfqpVs8gYNQ3OnFGB5ebNqm16bGzS/Q4OakjNmkHTplCiRMYvSZRR9+qmyrlzMG2a+v/gOZN71mSRYDMh0Lx+/Trbtm177qwmgKOjI47pkWImhBCZSdOmajMcqCDjgw9UjcyKFdNtCKfvnmbHtR0cv32c6U2np9vzWlrT0l40Lulp0azkp5N+ABwMDlwKuUScKY66BeoyqvYoAsIC6Pl7z6Ts8mZzkmY17eygcGE4dgw6dVKF2P38zDbGBJGR6nPNpk3wxx8q0edJhQolBZcNGmSIOvCpkhH36qbamTOwcKGK7gcOtPZoUjB7sJkQaF68eJHt27eTw9a72wshREYQGamKDSZME1WrphpCd+kCgwZZJbsiob5mZukc9CSDXmexJdMnk34ApjWZxsDqAwGY1HgScaY4auarmXh+U7+mXLp8CL91O/F563PYWQdKllR3jhun+pjnymXWMV65ooLLTZvUKv2Tey+dnFS2eMI2UD+/jD97+SIZba/uf4qOhlWr1F96587qWKtWqrVonTrWHdtzpDrYjIiI4NKlS4m3r169yvHjx/Hw8MDLy4v33nuPo0eP8vvvv2M0Grl9+zYAHh4eODg4mG/kQgjxOrh7F2bNgjlz1C+YhCSPwYNV+RorfqBPaFNp6/U109ON0BvJkn4ABv81mPdKvoePqw9V8j61z/LSJXymTMFn2TIVZAAsWaISgQB8fMwyrthY9dnljz9UgHnuXPL7CxaE5s3VV/36kCWLWZ42Q8goe3X/0927qoTVnDlw756qKvHxx6oAqcEAs2dbd3wvkOpg8/DhwzRokNT2KmG/ZceOHfnqq6/YsGEDAOXLl0/2uO3bt1O/fv1XH6kQQrxOLl6EKVNg2bKkaaUffkgKNtO7COEzJMxsVvaubOWR/DdrF+uONcay6t9VjN4xOkXSj4aWPOkH4MABtf9u7Vq1URJUws+wYWpfphncvauCy99/VzsywsOT7rOzg9q14a23VIBpC3sv08Kae3X/09mzaj/m8uVJ/xfky6c+bJpML35sBpHqYLN+/fpo2rMmmpUX3SeEEOI/7N+vgox165KCjKpVYfhweNytLSOwpc5B1i7WHWeMo+Scklx+cPmZ9ydL+gEVULRsqWavQEV8w4ZBvXppivg0TdV137hRfe3fn/QjBpA7t/os07y5Kk/k5vbKT2WT0mOvbqpNm6ZWMRJUqaIaMrz7bsaoG/WSbGekQgiR2WmaKrr9rwriaN5cBZl16mS4aaXTd08TY4zJ8J2DrFWsOzwmHBdHVdfU3mBPQ9+GRMZFMrj6YLLYZ2Hg5oFJST9NZ+Pzxx6V5KXXq2XRwYNV0cqhQ6FUqVceR2ysqneZEGA+XZqoYkVo0UJ9Vaok/cYtuVf3pcTGqinmhO0xb7yh3pRWrdTPRK1aGe7/gpeh0zLYVGRYWBhubm6Ehoa+MItdCCFsXkyMKsD9/vuQLZs6tmaNKmWUxiDD0v669BedfutEiVwl2PrJVmsP55mMJo3aE7Y9t4ZiQuLHnhEN0zx7lZBdns0hG6tPrua7o9+xu9NuKnhVACDkUQjO9s442Tklnn/pxnH8ft+Lz8xlEBQEv/0Gb7+dpnEABAer5fGNG1V5oieXxx0dVfzSsqUKMM205VOkVUiIqo07a5YqSrp0adJ9t25B3rzWG9tzpCZek5lNIYRIbw8fwvz5MHOmCjLCwtT+K4B27dRXBtfErwmBQwKJiouy9lCeK72KdT+dXZ5gzak1icGmR5YnMplv3sRn+nR8Fi5UVdFBBRPRr17H8fJlFav+9ptK9HlyK1+ePCqwbNkSGjWyvdJEmdqlS6rr19Klqr8nqPT/2FhVtBQyZKCZWhJsCiFEerl5U/1ieTrIsOFVnIxcyD09inX/fuF3um7smuL4ijYr+LjMx8kPRkZCr14q0Ss+Xh0rXVrNYn/4YVJw8YTnJTaZTHDkiAou169XezGfVK6cCi5btoTKlWV5PMM5cADGj1dvYMICc7lyaj9m27bP/FmwZRJsCiGEpZlMqh7eqlXJg4xhw9Qspo39YtE0zSbqalq6WHecMY5P13/6zPt8XH1S/h05O6v+5fHxhFavzZmPu0PTZlQtlOOZy/hPJzZp8Xqcgz0pFFWU43uyEhiYdK7BoPKHWrVSXwUKvNJLEunl77/VpwRQCWBDhqiK+Dbw7+pVSLAphBCWpterjXPx8eoXyrBhqt2Kjf5iOXHnBM1WNeMN3zdY+c5Kaw/nucxdrNtoMrLp4iaaF2mOQW/A3mBPv6r9GLNzTLJyRgadAT/XgmoGc+FCNXvl6go6HfsHfsmCA4FsdykAAcCiA8/MjE9IbDLG2PHosjdRF/Pw6EoutFh7EkpgZsumfoxatVLxSkbsOy6A0FBYtAjKlFFp/qBmuAMCoH//pAL9mZgEm0IIYU7x8fDzz6pkyQ8/qHaCAF9/DaNGqTVNG3ck8Ai3I24TFBFk7aG8UFqLdSck/RRwL8COazuY6D+R88HnWfPuGtqWbqseX380Pq4+9Pi9R1J2eZb38alYH65fVxf67jsYMkQFkGfs0VySTzs+nRkfdFuj95cPuX2iCtHXc4DRkPSaskaTpcgd8pZ7wJG55cjqbJsfWF4L16/DjBkq0AwPV4VLE4LNHDnUvu3XhASbQghhDhERsHixCjITgowZM1QSEGSq2YvENpWe6deH/VW9arHu5yX9uDu5ExoTmuxYl4pdaOJWkUvLpuL3/UZ8bq5Rd+TKBX37QseOGE0aYzaeeeYMqwYYQ7PQc2Q4+cI82esPJlOJxPvtPCJwLnob5yJ3cPB6iE4H0cC/QfmsW6ZHPNvBg6ohw6+/gtGojpUoAR07qv2ZFlrROH77OOXylMuQW1wk2BRCiLS4fVuVK5k3Dx48UMdy5YJ+/aB3b+uOzcwuBl9kgv8Elp9YDkAl74xdzD1Baot1X3t4LUVLSYDP63zO8FrDE+tnJnr4EJ9ydfCJjFS3/fzUHryOHRP7Oh68HJws2NU0iLufjaiLnjy64EnsHVVB/fHHFBw8HyYGmPY5I545zrQkNgkL6d1b/V+QoFEjVR+zSROLZGlpmsafl/5kgv8Edl3fxbZPttHAt8F/PzCdSbAphBCvKi4OypeHO3fU7WcEGZlF/z/7M+fQnMSZvreKvEWb4m2sPKqXl5pi3VdCrqQINAHeKPRGUqB5/jwUK6a+d3dXBfivX1dF+Fu1Uhk7T7gbHo2mQewdV6LOexF1wZP4kGxJJ+g0HH1C6NDOwFstNQZt2vuf43zVxCZhRgkfMBLqSdWtq5bNP/oIBg1SGeYWEGeMY82pNUzcO5FTd08BYK+358SdExJsCiGEzTt8WLVa0enA3h4+/RR27VJJP2+/nSLIsGVPZp17u3hj0kw0L9Kcz+p8Rs18Na08OvM5e+8s0/ZPY3yj8Xhk8aBozqLodfpkS+gGnQE/90Iq2WfSJNi7F86dg6JF1QlLl6oPGE8tYZpMalX1p8Ue3Pq5AcbQJ0pFGYxkKXgf56K3yeJ3F4NzLJ27VaeqrwcT95gvsUlYQGAgzJ6t9l1+9pkqXwXw3nsq4PT2tthTx5viKTOvDOeDzwOQzSEbPSr1YGD1gfi4Zswq/RJsCiHEfzEaYcMGFWTs2wf//KPasIBK/LG3t+74zEjTNLZd3ca3u7+lX9V+tCmhZi97V+lNU7+mlPcsb90BpkFCwk+RHEXwcfXh4K2DjN8znvXn1qOhkc81H1/U+wIfVx8WtliYPOnH7WN8qr+pZjRBlas6cCAp2HROCiKNRhWL/vqr+goIAFAz3To7I1kK38W5aBBZCt9F76j29D0ZQKY1sUlY0IkTMHWqSv6Li1PHNm1KCjbt7CwSaD6Mfoi7k7t6Cr0db/i+wcPohwyoNoCelXuSPUt2sz+nOUm7SiGEeJ5Hj2D5crXZ/+JFdczBASZPVnsyMxGTZmLj+Y2M3TOWg7cOAlDDpwZ7u/z3cq4teDLhR4+eIjmKJM4MAbQu3prPan9GlbxVEo8FBJ3n0pLJ+C1Zj8+V++qgm5sqW9O/P3glJRfFx6sJ7l9/hbVr1VbeBNmyqeLqhao8YMXNA+gdjM8MIJ/u0/50nU3gmWWSRDrYskV92Pznn6RjtWur/ZgWXNG4+uAqU/ZNYcmxJez4dAdV81YF4MGjB2Sxz5LY/tQaUhOvSbAphBBPi4lRv1hmzoR799Qxd3e1+b9fP/D0tOrwzCneFM+Pp35kvP/4xL1fWeyy0K1iN4bUHEJ+t/xWHmHaBYQFUGB6gRSZ5QadgfZl2zOi1ghK5CqR8oGRkZA/v+pbnS+f2oPXtSu4qH2bRiPs3KkqXf36a9KPCqiYtFUrePddVe3G6XFMkNoA8nkdhEQ6+/BDWLNGJfm8957am121qsWe7ljQMSbtncRPp3/CqKnZ7+E1hzOh8QSLPWdqSW90IYRIC3t71e3n3j0VbAwaBF26JAYZmUm7X9rx69lfAXB1dKVPlT4MrD6Q3FlzW3lk5hFviudi8MUUgSbAqndWJdbLBOD4cbU8On682nuZNSuMG6eWyNu2BXt7jEbYvQN++kkFmHfvJj3cwwPatFEB5htvPLsxVGoz41OT2CTM5P59mDtXvecJSWBDh6qZ7P79oWBBizxtwhaWiXsnsuXylsTjTQo3YUStEdQvWN8iz5seJNgUQogjR1S5kpkzVWCh18PEiaoQ8/vvZ6o9mRGxEejQkdVBZc9+XOZjdl7fyaDqg+hdpXfivjBbFx4TzsIjC5m2fxrLWi97ZsJPrfy1VA2iv/9OvkTaoIFqzQPQvTtGI+zZo2Ywf/klqfgAQPbs8M478MEH6mEv86MiAWQGdf68qpP7/fcQHQ23bsGCBeq+SpXUlwXFm+LpvKEzN0JvYNAZaFu6LcNqDrPpfdIJJNgUQryeNA02b1ZBxvbt6lilSmo/HqhNdpnIg0cPmH1wNjMOzGBozaGMrD0SgFbFW/Fm4TcTg09bdy/yHrMOzmL2wdk8iFZ1T9edXZcy4afZXHw27lTv/4kT6sEGg/pwkT8/JhP4+6sZzF9+Sb4HM3t2NYP5wQfQsGGm+izy+tE0tRdi6lTYuDHpeKVK0LixRZ/6Udwj1pxaQ/uy7bE32GNvsOez2p9x6u4pBtcYjG92X4s+f3qSYFMI8XqJjYXVq1WSz+nT6pidHbRrB3XqWHdsFnA74jbT9k1j7uG5RMSq4uC/X/idEbVGoNPp0Ov0Nh1oJmSYO9s7s/rkar47+h2P4h8BUDRHUYbXHE77su1xtHOkiV8TLoVcwi/aGZ8m78ONG+oizs7QtSvawEEcvl+QNYvhxx/VxFYCd3cVYL7//vOXyIUNatYM/vpLfa/TqQ+ZQ4ao/wss1InnwaMHzDs8jxkHZnA38i72Bnval20PQI/KPSzynNYmwaYQ4vURHq7aRqpaNCpNuHt3GDhQJYBkItceXmOS/yQWH1tMjDEGgLJ5yvJZ7c94r+R7GbKlXWp9d2QRPX/vgYnk+zEreVViZO2RtCneBoP+cZZwTAw+rj6qDqGmqQye3LnR+vXnbP1erPrTgzWN4MqVpOu4ukLr1mrrXqNGEmBmCqGhau91QjefqlXVzOann6q92QmlrCwgICyAafumsfDowsQPfvnd8mOvz/xT45KNLoTI3B4+VNNSCVq2VHs0BwyAHj2S35eJdFjXgZX/rgSguk91/q/O/9G8SPNMEWQC/O/vlYze2xGeCjRHVJnDuGa9kl7nuXOqdNWmTap81eNOL9f+vsjq3flY9asTZ84kPd7ZWVWyaddObdt0dEynFyQs6/p1mDFDdfdZswbeeksdf/BAlRXImdNiTx1rjKXH7z1Y9e8q4kyqNmeZ3GUYXms4bUu1xd5gm8GmZKMLIcS//6ql8l9+UQFH/sclfBYuVGnDmSyKOBJ4BI8sHon7vEbUGsGdiDt8Vucz6hWolymCTE3T+PvK3wz7awz/3nt2/c9le0Kpny+IpqFX1H7MDRsS7wteuoGl0R/yww9w9GiRxOMODir2aNcOWrRI6jwoMoGDB9WHjV9/VUElwLp1ScFmdssXQ3cwOHDlwRXiTHHUK1CPEbVG0NSvaab4N/myJNgUQmQemgZbt6ogY0tS6RA2bIC+fdX3XpmnGLamaey+sZuxu8fy1+W/6FS+E0taLQGgdO7SbOmw5T+uYBuMJiNrz65lvP94jgYdVQc1PaCB7onFOU3PG5cDydu8Edw8qw7pdFwr+zaTGcbcfrUSTzUYVP5Hu3ZqqdzNLf1ej7AwTVNtRadMUWUEEjRqpEoYvfmmxZ7apJnYdGETMw7M4Id3fyBX1lwATG48GZNmoppPNYs9d0YmwaYQwvbFxam6NJMmqVqJoPZkvf+++uVSubJVh2dumqbx56U/Gbt7LP43/QFVykeHLlk/c1v0ZEtJbxdvlhxbwkT/iVwMUR2cnAzO2Mc0xjW+NY/0xwixnw06E2h6ioS2Z8VPc9CjEW/nyD/enzDk1hDOnFC1EnU6lffx0UeqFqYFV06FtY0erVY37O3VGz54MJQta7GnizXGsvrkaibtncSZe2pfxuyDsxnTYAxAss5UryMJNoUQti8yUu2/jIhQm+66dFGb/X0zT+mQBBvPb+SL7V9w4o4q1+NocKRzhc4MqznM5kulJGspqdOzoMUCFh5ZyMWQi2R3yk7/av0pnOVdvlinssjzRVSnWZCRf/zyYojPS2hAcZa7xxIYVpCZ8QO4c0N1eqpQQcUbbdtmujwwARAUBPPnw7BhKulPp4MvvoCjR9WKhgV6lScIjwnnu6PfMW3/NALCVOKhq6MrPSv1zLSZ5a9Cgk0hhO0JDFR7Mfv1U79Y3N1h5Ei1fNarF+TIvAWzj98+zok7J8jmkI1elXsxqPogvFxsf2tAQFhAYqAJajmy5+89Wdp6Kfcj79OtUjeyOWRj3+VgfB4epMvh32j77xYc4+MoV2IHZ69WxfTIkU78AIB3PiOfd1RBZolndKIUmcCpU6o+5qpVqqRZjhyqww+olpLvvWfRp4+Oj6bo7KLcjlBFWL2yeTGw+kB6VOqBm5Psy3iSBJtCCNtx5oxK+lm5Ui2dly8Pdeuq+/7v/6w6NEuIjI1k0dFFlM5dmjcKvQFA36pq72mfqn3wyOKR7mOyRK/u6w+vM+ivQSlaSho1I/lc89GhbAd14MgRqk2cxM6ff8bw+NxjlCfLGSdMOKJ3jiFriUDyV73P8VmVsTOkaVgiI9I01elpypSk+pgANWtC8eIWf/rA8EC8XdRMqZOdEy2KtGD3jd0MrTmUDmU74GiXuRIPzUWCTSFExpbQ4WPyZFW+JkGtWqoYeyb0MPohsw/OZvr+6QQ/CqaGTw3qFWjAoWsPuBseTSOf3rg5Wj6L9mmbTwUxZuMZgkKjE495uTkxumVJmpZO/ezq6bunmeA/gdUnV2PUjCnuN+gM+Hn4wZUrxHbshsOebTyujshfvMkkhrHNvh7Oxe6Qu+QBshQIRqfXmNy+InaG9Nu3aokAXDxDTAzUqAHHjqnber3qFTpkCFSvbtGnPhJ4hIl7J/LLmV843O0wFbwqADC1yVSyOmRFr9P/xxVeb5nzf2ohROYQGAitWsHhw+q2TqfauAwdqn7pZDJ3Iu4wff905hyaQ3hsOACFsheicq421J6wldthsYnnpiXIexWbTwXRa+VRni7MfDs0ml4rjzKvfcWXHotJM/H+z++z9uzaxGNv+L5BuTzlmHFgRmJLyVlvLmDPHz78siSMxXsOo8fAGtoxTT8Uu9rFCfG6hE/ef9Dbq1nO9P47AfMH4OIpUVFqHzaocmW+vnDhgtqXPWAAFCpksafWNI1/rvzDBP8JbL26NfH4lstbEoNNF0cXiz1/ZiJF3YUQGYumJbWJMxrV0lhAgOrwMXgwFCnywofbqil7p/D59s+JjldBS+ncpRlVexRuWh36rv43RZCXMG+WmiDvVRlNGrUnbEsWUD09Fk83J/aMaPjMGb0nM8x9XH0AaL+2PatPrqZNiTaMrDUyMVv3+o2z7J48k5xbLvPBrb8Ij1DXa87v6MqW5c2u+WnbFnLntv6M4vMC8PR8bzKty5dh+nRYvlzNZCYElTduqA5AFqyPaTQZ+eXML0zwn8Cx22oW1aAz0K50O4bXGk7ZPJbLarclqYnXJNgUQmQMd+7ArFmwfr3q8JNQdP3QIShYEHLlsuboLOLJMkU/nvqRdr+2o1reaqrbT9HmaJouTUGeuey7HMyH3+3/z/N+6FadGoWTJ2d9d+Q7evzeAw0NvU7PwhYL6VKxC1ceXCHWGEvxnGqf3cWdgdwaOZMKB+bjpoUC0JCtXC3YkPbtoX17KFbM/K/tVaU1ABfPsXev2o+5bp364Anw7bfw2WfpNoSY+BgKzSxEYHggzvbOdK3QlcE1BlPAvUC6jcEWSAchIYTtOH9e/XJZvlztyQJVM7N9e/V9lcxXn+5w4GHG7RlHnfx1GFh9IADvlXyPnS47qZO/TmIAuu9K8HODGQANCAqN5uDVkBRBnjndDX/+GJ53Xkx8DNP3T2fk1pGJx0yaiR6/96CJXxMKZS9EcDCs/vwM2RZMpun9lRRBtfI7ry/OgTpD+frLWtRskDTRnZEcvBqSId6bTMFoVB8yJ0+G/U98qGnWTO3HbNjQok8f8iiE5SeW069qPwx6A452jnxZ90tuR9ymT9U+5HSWgqxpJcGmECL9aRr4+6doJ0i1aqpWXuvWVhuapWiaxs7rOxm3ZxxbLqvOPgcCDtC3al/s9HYY9AbqFqib7DGvEuRZQm4Xp5c+LywmjAWHFzBt/zSCIoJSnGPUjCzbcImja324u2E/e4xJe29Pe9QmtPtwKn3ZnGJZMnbCRUZ5bzKFqCi1BzM0VPUObd9ebZkpVcqiT3sz9CbT9k9j4ZGFRMZF4u3izQelPgCQGplmJsGmECL9XbyoWrkkePttFWTWqpUxp7HSQNM0Nl3cxNjdY9kXsA9Q+78+KvMRI2qNwE7//P+GUxPkWVJVXw+83Jy4HRqdYn8iJC0ZVy7oTsm5xbkUcgkAz2ye3Im4g/bko0x6vujjB2GgoyqXnUqiFS2Ox7hhlHrLshnF5pRR3hubFBgIa9aoxgs6ndqDOXKkas7Qpw94elr06c/cO8NE/4msOrmKeFM8AGXzlMXVUbbuWYoEm0IIy4uKUstjCcthRYuqLPPcudUyWUbajGdmw/8ezuR9k4HUd/t52SCvqq9l620a9DpGtyxJr5VH0QFx3CdeH4idyRudzoRBy8XoliWxNxjoULYDP5z6gRG1RtAw10cMWb6CX6J7gN6I3gSTNzozM0sO3usOn3yip7DfYciSxaLjt4SM8t7YlH//VVtmfvhB1cktW1b1KwcVbFpYZGwkH/76IRsvbEw8Vr9gfUbUGkGTwk1sus1rRifBphDCcu7dgzlz1FdoKFy7ltQ6bt26TDeLCWqvYlRcFNmzqGzZj8p8xIIjC1S3nxqD8Mz28rM2Twd5TwY1CX9zo1uWTJcElKalvZjXviJ91k/hVvxU0GlqQDodY2p+n5h1PbDKcEre/5zvv9Az4o/79DQFcNzVlQceD/ALgdyaA/3+OoVdjYS9uLYXaELGem8yNE2DLVtUkPn330nH69RJ9w8ZzvbO3I+6jw4dbUq0YUStEVTNWzVdx/C6kmx0IYT5Xbig2sh9/z1EP96z5uurOv/UrGndsVlIRGwEC48sZMq+KbQo0oIFLRckuy+bQ7ZXvnZGqeUYEBZAgekFUnT66VGxB73yz2fpUtU50OH+LUYxjs4swZlHABjzF8QwdDB07gxZs6bbmC0to7w3GVJgIDRpotpKgirC/t57ajWjqmWDvFhjLD+c/IG5h+fy58d/JnbbOhp0lKz2WSmWM/OupqQXKX0khLCOa9fUPqzffksqW1KlitqP2aZNpuz4E/IohFkHZjHz4ExCHoUAUDh7Yc70OYODwcFsz2PNmpKaprH50mZG/DOCk3dPpri/8J7tXP6nfuLtujnPsPP+4+SOihXV+//ee5ny/Qfr1/vMUOLjk95nk0kl+QQEQNeuqgh7wYIWffrwmHC+O/od0/ZPIyAsAIBvG37LZ3XSr3TS60KCTSGEdQQHQ7588OgRtGihOv3UrZspl8sDwwOZum8q8w/PJzIuEgA/Dz9G1hpJ+7LtM1WPZE3TqLCgAifunEh5p8lAg+mLqR55h4tthtOpE7z5JtiN/R/Urg0NMmjtImFely/DtGnw++9w5kxS158TJ6BAAXB3t+jT3428y8wDM5lzaA4Pox8C4JXNi4HVB9KjUg/cnNws+vyvIwk2hRCW9+iRWibft0/9mWD1aihfHkqWtNrQ0sOX27/k611fA1AuTzk+q/MZ75Z4F4PeYOWRpV10fDTLTyznw9IfJrbjm7djHd9v8+fsIU/Cqo4EvRGdSc+3mz0ZdTAQzc4O3ZUr6sOGeH08qwj7qlXw0UfpNoTwmHB8pvkQFhMGQNEcRRlWcxgdynbIVB/6Mhop6i6EsJwnk37u31fHevWC6o/L1qTjL5n0dPLOSeJN8Yk9kftX68++gH0Mrj6Ypn5NbT6TNSAsgOO3j7P3xl6WHF/Cncg7hESEky9gCIsXw/btbYA2uBLKoKMhNPRYSPnAYHzCAsHFBV337kldn0TmZuUi7ACXQy5T2KMwoPqTtynehrP3zzKi1ghaFWuVKT70ZSYysymEeDkXL6qkn2XLkpJ+ChaEgQNVQeZsr54Ak5Htu7mPcXvGsfHCRuoVqMeOT3dYe0hmN23fNIZsGZKsHmY2Yz6M/3zNo30dAbUSPrTSdr493Qr7R+HqJG9vtQ+vRw9wk2XK18aFC0nlytKxCLumaWy7uo0J/hP4+8rfnOx1ktK5SwPwKO4RTnZONv+hz5bIzKYQwrx274Z69ZKWySpVUkkf776bKZM+NE3j7yt/M3b3WHZe3wmADh15suUhOj4aJ7vMUahb0zS6bOjC0uNLk99h0hMxcyeE+lI03yM+7pqFTz+F/C7lIZ9JbZEYOlTNYstsZuYXFAS7dkHbtup20aLQsSP4+EDfvmYpwv6iJCujycivZ39lov9EjgQdAVRjBP8b/onBZhZ72yyh9brIfL8lhBBpZzSqzPLCapmKGjXUJv9SpVSQUa9epk36+OfKP4z4ZwRHg44CYK+3p0PZDoyoPYKiOYpaeXTmpuPo1SspD+tNdGqwnom3/iaH4QG6L/Y+fr+zw6FDalZLn7HbSQozOHVK7cdcvVr9n1CjBuTPr+5btsxsT/O88lGj3ipMYNxmJu+dzOUHlwHIYpeFrhW7MrjGYAq6FzTbGIRlSbAphEiSkPQzdarq+nPliloms7NT3T9cXKw9Qou7HXGbo0FHcbZ3pnvF7gyuMZh8bi+X9JLRS+D43/Bngv8E/q/yVHat92PRIrgQMxo6NgJ9Uu1Mgwn+t20wOcNQQeW5c1CihLoz4U+ROWkabN2q9mP+9VfS8Vq14MGDpGDTTDafCqLXyqMpujDdDo2m3w9HCXP/gocx9/HI4kG/qv3oW7UvOZ1zmnUMwvIk2BRCqKSfuXNh9uykpB93d1XCpHx5dTsTBppRcVEsOroIjywetC/bHoB2pdtxK+wWXSp2SdUvtYxW3DsgLICLwRfx8/Dj5N2TjNs9jj039wCwaY0Xpg2q6Hy2bA2oHDKLXTn6YtJpGEywYCP4xGWB3p3UXryEGW6RuZ0+rbZG/Puvuq3XwzvvqKSf6ubvW280aYzZeCYx0IznPpF223CNfw/Qo8eR7PHtGd2kIN0qdiWrQ+ZpBvC6kWBTiNfZjRswfjwsXZqU9FOggCrMnomTfh5GP2TOwTlMPzCd+1H3yeeajw9KfYCDwQE7vR0jao9I1fVeNDvTa+VR5rWvmK4B5+Kji+n+e/cUnX6Id4ATHTH5D6VKFejeHTzK3ObQzDusWK5xyQNyRGXjQOk2bN08nDfqlk63MQsr0bSkLTF586rVjKxZ1b//AQOgUCGLPfXBqyEEhUYTp7tJqN2vRBp2gC4ee5MPzqaaaIAW0YhquapLoGnjJNgU4nV27x7Mm6e+z+RJP6CWyKfvn87cQ3MJj1UZ1b7uvoyolbrg8klPz848SUP1yR6z8QyNS3qmy5L6zdCbKQNNDTjcA5djX/JJG2/6dLtECYe/2Jy3rOrtnbcSzTwqsLVINX4u04gYeyf44zrzPHJIy8XM6to1mDFDzWL+848KON3dVUmjihUhe3aLD2HXdX/uOozjkSGpfJKjsRR6klc2uBse/fRDhY3JnL9RhBApGY2qjeS1a2ppFFSA+X//B40bZ9pOPwkWHV1E3z/6EmOMAaB07tKMqj2KD0p9gJ3+1f8rTJideR4NCAqN5uDVEGoUzvHKz/NfwmLCiAh2YfTiiylnNHUwokU7vhp2E6dZ/aHVWrQ8eRjbe4maPdIb+KTt108/JF2DZJFODh1SST8//6zaSQIcOJC0TP7GGxYfwoNHD2i1phW7b+yGx+Uwsxir4xb3Ho5a8RTn53bJHNUfXmepTifctWsXLVu2xNvbG51Ox/r165Pdr2kaX375JV5eXmTJkoVGjRpx8eJFc41XCJFaUVFq9rJ4cTVr+dlncPdu0v3ffJNps8ufDLrK5ilLjDGGGj412NBuAyd6nuCjMh+lKdCEl591sdTsTGDYbdotGkWOb/ORr8EWlk4uCqbk/7Ub0NP31xE41a8Ov/4KmsbD4qWJvn3vudd9MkgWNs5kgg0b1L/zqlXhxx/VscaNVRJQtWoWH8KTJb3dndyJiovCXm9PLn0TvKPnkTv28xSBpg6177mqr4fFxycsK9XBZmRkJOXKlWPOnDnPvH/ixInMnDmT+fPnc+DAAbJmzUqTJk2IjpZpcCHS1d278NVXag9m795w6ZJaGhs6NNMukyfYH7CfVmtaMeDPAYnHquatytHuR/Hv7E/LYi3R68xTuudlZ13MMTsTEBbA9qvbCQgL4NClK9T4pjc+kwvy463xxBvCMJX4kZqlfeiUawF6nZoyMphgwW8mfP45CPb28OmncOoUu6Yt467Lf8+0yhKmbTGaNPZdDua347fYdzkYo0mDzZuhVStVK9PeHj75BI4fhy1bVCN7C37QjIyNZOaBmZRfUJ7Q6FAAdDodi95exJUBV1jeZikOWj6eHkHC7dEtS8rMeiaQ6t84zZo1o1mzZs+8T9M0pk+fzueff06rVq0AWL58OXny5GH9+vW0a9cubaMVQrycDRtUAeYnO/0MHgydO6vN/5lQQiH2cXvGsePaDgCc7Z359o1vcXVU3S0SWk2aU1VfD7zcnLgdGv3MfZs6wNMMszPJkn40QNOBXgMDGAKr0yTrKMb+rwVB+iDGbPTFK2ox3qFHWLt6Fu4xzlzp1JFCX/+fSgIBcl8OfqnnlSVM25FQESE28DaFQgI4lK+0qojwVlmaVq6slsj79Uv8GbCk+1H3mX1wNrMPzib4kfpZW3xsMYNrqC085T3LA+BTGua1r5iikoOnFSs5CPMz6/TG1atXuX37No0aNUo85ubmRrVq1di3b98zg82YmBhiYmISb4eFhZlzSEK8HjQNwsMhoWVYtWrqWJUqaibznXcy7WymSTOx7uw6xu0Zl9hdxE5vpwqx1xqRGGhaikGvY3TLkirRBpIFnOaanTl9M4BuG7ujYUq6sE7D5X59epb4ii+H1CXbgwCuft6bI6eDCGrUHTtyctetCePrZ2FXoUqEO2Zl3gM9TR/HGekVJIv0sflUEJNmbKDv4fW8e2ob4Y7O1Oq5lNuh0OuHE8xb8htNy3hbfBzXH15nyr4pLDq6iEfxjwAonL0ww2oOo2P5js98TNPSXjQu6Zmha9SKtDHrb5/bt28DkCdPnmTH8+TJk3jf08aNG8eYMWPMOQwhXh9Go8oenTwZnJ1VMWaAPHlU94/ChTPlXswnTfSfyKitowDVXaR7pe4MqTHkpQuxm0PT0l4WmZ05ckTjs2V/sH2bHu0DU4r7NwwZTf2w7NDrE7Q1a/CNj8fbYMe86u9zL5vKJv69RF0gZcJPegTJIh1oGsadu3DuPYqtZ/clHj6XqwC5I4IJcPdU7/3vZ2lcysui72fIoxCKzS6WmIRX0asiI2qN4N0S72LQG174WINeZ9EEOmFdVp/qGDVqFIMTMmNRM5v58qXfLwkhbFJkpGoXN3WqqosHqkd1QIDqVwzg52e14VlSZGwk96PuU8C9AACflv+UGQdm0LVCV/pX60+urLmsMi5zzc48egQ//BjP2A0/ctlzAuQ5CTnHgKYH3RNdftDj1/8r2JjQux325i/LwqrvcC+re4rrPisr3lJBskgnBw5Av34YDh2iLmBCx1a/qiys2oZDPqUSP2haqiKCpmmcuXeGUrlLAeCRxYN3SrzDvah7jKg1gjd830CXyT/sipdj1mDT09MTgDt37uDllfSf1J07dyif0IXkKY6Ojjg6OppzGEJkXnfuqC4/c+dCyOMsYQ8P6NNHfT21qpCZPHj0gNkHZzPjwAwqeFXg7w5/A+CZzZObg26mOavcHNIyO3P5Msya/4jvDi0lqvwkKHcNADujCz26Z6V8iYX0/L0HRs2IAb1K+jm2U3V5ee89dr7dkY4nn7UgntzTCT+yhGnDsmSBQ4cwOjqypkQDFlduzZUcPs893VzJXibNxIbzG5jgP4EDAQc40+cMxXOqTPJlrZfhYHAwy/OIzMOs/zv7+vri6enJ1q1bE4PLsLAwDhw4QK9evcz5VEK8nrZsUaWKQC2RDx4MHTtm2qQfgKDwIKbum8r8I/OJiI0A4MqDKzyMfoi7kztAhgg0X8X1BwGs+OMif//ox64Hq6DGVGigyhFlJRf9qw5keIPeuBvt4c4dmg68xqWQS/jhgc/sN6BvO9XtqVAhHC4Hw8n9//GMz074kSVMG3DrFsyapZL+pk9Xx8qWhWXLOFqiOv+39tJ/XiKtyV4x8TGsOrmKSXsnce7+OQAcDY4cDjycGGxKoCmeJdX/Q0dERHDpUtIP9dWrVzl+/DgeHh7kz5+fgQMH8s0331CkSBF8fX354osv8Pb2pnXr1uYctxCZn6apUiXh4dCihTrWti2sXQsffwxt2oDhxfugbNmVB1eY6D+RpceXEmuMBVStzJG1RvJ+qfdtNsAE1bip58LFrI3tDnoTVNDD7bKQ9R65HQrwecNhdKnYCeeQcPh2CsyZA6VL47NrFz6uj2eubt4Ep6TgQRJ+Mql//1VF2H/4AeLiVOmi4cPB+3GyT8eOVDRpeG0NsNh7HxUXxdxDc5m2fxqB4YGAqpXZu3Jv+lfrT55smXdFRZhHqv+3Pnz4MA0aNEi8nbDfsmPHjixbtozhw4cTGRlJ9+7defjwIbVr12bz5s04OUn5DCFeSny8Krw9eTIcPqzKFjVtqrLJHRxg3TprjzBd7Li2gwVHFgBQK18tRtUexVtF3rLpPWCHDqldED/s2UNch26qdBGA3oQ+779MazKDXpV7YX/5KvQdBN9/DwnVOoKC1NYJj8cBw1P/p0rCTyaiaaqF5OTJajUjQd26MGQIPN6ylsDS772maYzfM57gR8F4u3gzqPogelTqgYujyytdT7x+dNqTZf0zgLCwMNzc3AgNDcXV1bIlS4TIUMLDYckSmDYNrl9Xx5ycVBHu8ePBze2FD7d1/jf8CYsJo1kRVcc31hhL1w1d6VaxG3UK1LHy6F5ddLTqDDh7Nhy8cRxqTYBSPyYFmk/YXnMh9ef9qSoMJPzXXK2amslq1eqlZrITai0+mfDjJQk/tmXePNWIARL35DJkiOr+8wLmeu8vhVxixYkVjK4/OrH5wcIjC7HT2/FxmY9xtJM8C5G6eE2CTSEygtWrVYLPw4fqds6c0Lev+oWTyzrZ1elB0zT+vPQn4/aMY8+NPfi6+3Kh3wWLLpEbTVq6JMPcvAnz58PC7zTuO++G2uOhyJ/PPd+gM3Ct4HR8OvZTB1q2hGHDoHbtVJevSq/XKMzk4UPV8atoUXU7OBhKloQPP4QBA8DX96UvlZb3/mjQUSb4T+CXM79g0kxs/HAjLYq2eIUXJF4HqYnXbHfTkxC2zmhMmqny9VW/cIoUUTMYn3yiMk0zqXhTPL+c+YXxe8Zz4s4JQCUWNCrUiMjYSNycLDOLa+lZP02DnzYHMHv1Rfw3FkELzQsfvwVFNgOg1+lpW6otI2qN4PD1ffTY3AcjJgw6AwtaLMCnbEf49xp06QIlSrzyOCThx0Zcv66SfRYtgvLlYfdudTxHDvVpxSH1yTapfe81TWPb1W2M9x/PP1f+STzezK8ZXtlkJlyYh8xsCpGeNE0VXp88WQWWs2Yl3bd9O9Srp5bNMrG/Lv1Fnz/6cPnBZQCy2melZ+WeDK4xGG8Xy3U42XwqiF4rj6ZIoEiY85nXvuIrB5yRkbBqFYzZsJjASo+Tfkx6il1cSIlaF/jzwQw6le/E0JpDKUx2tUw6axYBj+5wqVgu/P48gE+Ol5+9Ejbu8GGV9PPzz+pDJ0CpUirYzJ493YZxL/IezVY1S+y8ZdAZaFe6HcNrDadsnrLpNg5hm2RmU4iMJi4OfvxRBZkn1Ewee/fChAmq8w/AE4l3mVlWh6xcfnCZHFly0L9af/pW7YtHFstmSBtNGmM2nnlmpq5Gyu46L+vaNVXydNEieKC7CP26gS4p6edS8R78/N4x5joPxCskFv43TZ0cGQmAT758+LQbCFltZwbJpJn44+If3Iu8x6flPzVrwlamX/7fvRu+/BJ27Eg61qiRain75pvp0u1L07TE9yync07iTfFksctClwpdGFJzCAXdC1p8DOL1I8GmEJYUGgrffQczZqjuPqCCyy5dYODApEAzk7oXeY+ZB2Zi0Bv4qv5XANTOX5vV76zm7WJvk9Uh7fVBXyZAOXg1JNnS+dNS02FF02DnTpg5E377DUwOD6DKXHS1J6HpkoezRs1I8KNgyvy8U73fCbNYZcuq/Zht26pSNjbgWTUW82TLw1tF3jLL9V+LxKbAQBVo2tlBu3Zqy8xzGp6Y28Poh8w7NI8V/67gYLeDZHPIhk6nY3mb5Xhl87Ja5y3xepBgUwhLmjgRxo5V3+fJA/37Q8+eSeVrMqkboTeYsncK3x39jkfxj3C2d6Zf1X7kcFaB3IdlPjTL87xsgPKynVNedF5UlMrjmjkTTp4EXALhjekYqs3HaBf+zFlTg86An4cfVM+mAs1GjVSQ2bixTfWsD4sJo9TcUgSEBSQ7vvXKVrMEm8/b4nA7NJpeK4+maYuD1QQHq+0SefJAt27q2Lvvwpgx0LlzUltZCwsMD2TavmksOLKA8NhwAJafWE7vKirbXZbLRXqQYFMIczp2TO25LFdO3e7dG/74A/r1U4XYM3lr1rP3zjLBfwKrTq4i3hQPQGXvyoyqPSqx24+5pCZAednOKc8678YNtVT+3XdJHUKzOGs4929GsP2/GIHSuUszstZIIqPD6P1nX5X0o+lY0HKBKsJe2QfOnYNixdLwitNXeEx4Yh1FV0dXynuWx6SZGFR9ENkcstFrUy92Xt+Z5uex1BYHq7l8WZUvW7JENbrPm1d1+XJwUDOaX36ZLsM4f/88k/ZOYsW/KxKbIpTKVYoRtUbQrnS7dBmDEAkk2BQirTQNNm9W+zG3bYMmTdRtUL9ojh2z7vjSydJjS+myoQva47DhDd83GFl7JG/4vmH2QuypDVBS211H02D/fpUo/MuWAEzuFyF7DPmz16d/Lyc6d9ax9mp/lh5fqorNe9ZBt3gxTJ/OWw9NXPIAP80dn5EfJz2JjQSa5++fZ/Leyfxw6gfO9DlDfrf8ACxssRCPLB442jlyK+wW0/dPp2reqsn2AL4Kc25xsKp9+1TSz9q1STVSK1RQ+zHTOenvdsRtSs8rnfiBr3b+2oyoNYK3iryVWDdTiPQkwaYQryomRq2rTpkCp0+rYwaDKluS0FYuE9M0jfDYcFwdVRZi48KNcTA48FaRtxhZeyRV8764AHVapDZAedkOKyajjp9+VEHmwYNAhUXQv4fKLgfqlO7AkHeXA9DJvRNdvN5SFQXmtU+skeqTOzc+XftDr14puvxkZAcCDjDBfwLrz61P/MDw65lfGVRjEABeLknL2Hld83Ku7zmzPK85tjhY3ejR8L//Jd1+6y21H7NBg3RL+vn3zr+U81QrKp7ZPHmnxDtEx0czotYIauarafExCPEiEmwK8SqWLoXPPoPbt9VtFxe1L2vAAMif37pjszCTZmLd2XWM9x9P7qy52fTRJgB8XH24PvB6uvRJfpUApWlpL+a1r5hij6enmxOD6pTi+O+edG0Kt24BOhOGyksxNu+WFI0Cq0+tZHzjsfi4+qgZorlzYdw4dWfRomoWq0MHmwkyE4rqT/CfwK7ruxKPtyzakhG1RlArfy2LjyEtWxysJipKfeXMqW63bKm6fH38sQoyS5VKl2HEm+L5+fTPTPCfwMm7J7nQ9wKFPQoDsOqdVRZtjiBEashPohCvwmRSgWbevCrLuFu3TN9OMtYYy6p/VzHBfwLng88D4GzvzO2I23hmU72a0yPQhFcPUJqW9qJxSc/E7PWoO1nZsdaNT7/W8eiROse1zgoc3xjPPc6kuJ6GxqV9m/Bp0kMd6NsX/P1V4tfbb9tcjdTQmFDa/tKWiNgI7PX2fFz2Y4bVHEbJXCVf6vFxxjjO3T9HmTxlXnkMqd3iYFV378KcOerr3XdhwQJ1vHJllWmeI32W+aPiolh6bClT9k3h6sOrgKpXe+z2scRgUwJNkZHIT6MQ/+XAAbUf8803k7JKP/5Ydfh5771X6vJhSyJiI1h0dBFT9k1JzEZ2d3KnX9V+9Kva76VKppi7fmJaAhS9TkfYpRzMn560tRZUBZqBA2GNYQ2bL58hm0M2ImMjE5eUAQwm8JuxAhKCzTx51D5dGxERG8Fv537jozIfodPpcHdyZ0iNIUTERjCw+kCVzPSS7kXeo+CMgsTEx/Bw5EOyOWR7pTG97BYHqyYHnT8PU6fC99+r7TOgambGx6ukH0iXQDMiNoLp+6cz88BM7kXdA1StzP5V+9Onah+L16sV4lVJByEhnsVohI0bVZDp76+OFSmifunYUMkac/juyHd0/707AF7ZvBhcYzA9KvVIzFT+L5aqn5iQjQ7PDlCeLpcTHa26/EydCmcCAsDjIkTlokSb9Yxp8ynvvemDTgf7bu5j5/Wd9Cr9KT8tGUav0JUY9SrQnP+nHV3Ld1IzW2nck5ueBczvRd5j1sFZzD44mwfRD9j56U7qFqib5usWnF6Q66HX+av9X7xZ+M00XStD1tnct08tj2/YkHSsShVVvqpNm6RAM52Ex4STf3p+HkY/pKB7QYbWGEqnCp1wts/c9XpFxiQdhIR4VVFRavZi6lS4dEkds7dXM5mDB78WgWZAWAABYQFU96kOQIdyHVjx7wo6lO3AJ+U+wdHu5cs3WbJ+4ov2YD4ZoNy7p8odzpmjVkGpsBgGdk9M+jkL7OcB7+umAFAjXw1q/H2WmFal6RYSTDNXOO7pxFHvxqxt9Ak+H9WiaRoDzfQKrK48uMKUvVNYcnwJ0fHqufw8/IiKizLL9esVrMfyE8vZeW1nmoPNp7c4ZIgOQn/+mRRovv222pNbu3a6/T9w9t5Zfjj1A2Pqj0Gn0+Hi6ML4N8bj6ujK+6Xel6VyYTPkJ1WIJ3XrpjLMAdzdVUZx377gbbme3RnF+fvnmeg/kRX/rsA3uy9nep/BoDfgZOfErk67/vsCT0mP+okvClDOnVPlDpcvV7OaADkr7eZ+y27w1KiK5UhelujfoHDKhgQT4JqbxVVa8WPZN4lyyILORJqD5PQoYP7g0QN6/9Gbn07/hElTQXUV7yqMqDWC1sVbY9Ab0nT9BPUKPA42zVBvE9SSutXKG0VGqsS/0qWhfn11rE8f9Qll4EAoXjzdhrLv5j7G+49nw3kV6NbOXzsxmO9RuUe6jUMIc5FgU7zezp5VQaXX41/uPXqopbNBg6BTJ8j2avvQbMnhwMOM3zOetWfXJu5P9Hbx5n7U/TQl/KRX/cQnAxRNg+3b1cT0pk1J51SqBNk+7syusGU8HWgCFJ23BioboVcvjCaNPqZilH17BJuL1cT4RGCW1iA5vQqYuzq6cjjwMCbNRFO/pgyvOZz6Beubvd5pvQL1ADh46yBRcVG2uZx7+zbMnq0qCzx4oMoVJQSbefLA/PnpMoyEygDj94xn943dAOjQ0bp4a7yy2Vj3JCGeIsGmeP1oGuzapfZj/v67Wh6fopZQqVMHLl5U9TIzuSOBRxi5dST/XPkn8djbxd5mZK2R1MhXI83XT8/6ibGx8OOPKsg8fvzxQZ1Gq7d1DBmiVj4H/+XGzgMpwzyDCfx+2Q7br0GPHhy8+oCbkUZulqjzzOdKS5BsiQDcaDLy69lf+f7E96z9YC2Odo4Y9AbmN59PTuecibUXLaFQ9kJ4u3gTGB7I/oD9NPRtaLHnMruzZ9UPzPLl6gcIoHBhlfSnaem6ZSYoPIgmK5tw8u5JAOz19nQo24FhtYZRPGf6zagKYSkSbIrXR1wc/PKLCiyPHFHHdDq1qS+BTvdaBJqg+l3/c+UfDDoDH5X5iBG1RlAqt/nqA6ZH/cTQUFi4EKYuCuB27EUIKUIWZ2/q99jArULjGPr2FGrnrw3A8FrD6VymAwfXz6XH3cWJST8LNunwefvjxE4vlgySzXntR3GPWHZ8GZP3TebKgysArPh3BV0rdgXgjUJvpHp8qaXT6ahXoB4/nPqBndd22k6wOWSICjQTVK+ukn5atUq3f/9Pdl7Kky0PRs1INods9KzUk4HVB5LXNW+6jEOI9CDBpng9LFgAY8eqRtegim536qT2YhUtatWhpYeEGplhMWEMqD4AgPoF6zOx0UQ+KPUBBdwLpPqa/5VNbcn6iTdvwowZKtAM91sM7RISfnS4OnvyZ1QQBMOUfUnBppeLF16DvqDM4sU0cYVLeZ3wa9Yen7VfJCvEb8kg2RzXfvDoAXMPzWXmwZncjbwLgEcWD/pV7Ufr4q1TPaa06lC2A6Vzl6ZF0Rbp/twvLT5eVZhwfJzcVr68+mDZurX6kFEz/TrsBEcFM/vgbNacXsOR7kdwtndGr9Pzw7s/kM81H9mzZE+3sQiRXqT0kXg9DB6sskVy5YJ+/VTiT0L3j0zs6RqZ2RyycWPgjTT/QnvZbOrUlif6LydOqN0Pa9ao+AHXABhUAHSmZOe5OLjQr2o/+hf4QO079VRF59m7VxXj7t8fevaE7Cn/HowmjdoTtv1nkLxnRMNX2rOZlmvfjbxL4ZmFiYiNAKCAWwGG1BhC5wqdyeqQNVVjeS1ERMCSJerf/qBB6n0HtWx+7Vq6ftC8EXqDqfum8t3R7xKrASxquYguFbuk2xiEMKfUxGsSbIrM5/hxtVTevbvagwlqRnPLFmjf3mZaCaZFcFQwsw7OYtbBWYQ8CgGSamT2qtwrTYHJ87KpnxdAprXMj6bB1q0waZJ6CxPUrw9v9tjOZ+dTLt1urDWHFqsOqcKaPXvCzJlJd8bG/mchfnMHyWm59p2IO8kStZqubEpQRBDDaw7ng1IfYG9IWxmmTCko6HHP+nmJPeupXBkOHUr3oZy6e4qJ/hP54dQPxJviAajgWYERtUbwbsl3pXyRsFkSbIrXj6apdjBTpqjIBFS/4ieLMb8m1p5dS4d1HRJnT/w8/BhWcxgdy3VMVY3MZ0mYmXteksvzZuZepYB5XBz89JOayUxI+tHrofmHtxjVPxc1qjoQEBZA/mn5k3f50XRcm6bhE/b4QJMmql5iKhM+LFkL82Wu7X/Dnwn+E9hyeQtXBlzB20WV33rw6AHuTu5mzyxPi3uR99h2dRuujq40K9LMegM5c0b9wKxalZT04+en9mh+8gk4p2+2/M3QmxScUTCx/FRD34aMrDWSRoUaZaj3T4hXIUXdxesjWVuYx72sDQb44AP1C+Y1EW+KT5whqeRViZj4GCp4VmBk7ZG8W+Jds9VVfNVs6tTUT4yIgEWL1Ft686Y65uwM73Y/T0zlSay7spw29guoQSd8XH2Y33w+vTf1wohJJfxs1PAJ18E7bVTSR/Xqr/RaLVlk/HnX1uk0Np7fyAT/CfjfVJ2rdOj4+/LfdCzfESBD7un76fRP9P2zL2/4vmHdYPOLL2DtWvV9zZrq/W/ZMt2SfkyaiRO3T1DBqwIA+dzy0apYKwx6A8NrDqdK3irpMg4hMhoJNoVta9wY9uxR37u4qKLs/ftDgdQnvNiiQ7cOMW7POADWtlW/ZAu4F+BYj2OUzl3a7LMnFs3UvqtWPufMUeUOcQ0ge4WLtHznEQ8KLmHl5bVol9QM5u4bu+lUoRMA3St3562fj3Hpp/n4RTri824n+HGwai+aRpYsMv7ktWONsaz493sm7Z3EmXvqQ5ODwYFPyn7C0JpDKZaz2IsuZXX1Cqp6m3tv7iXWGIuD4cXbFMwiPl5Vl6hWDXx91bFhw9SfQ4aka9JPnDGOH079wET/iZy7f47L/S8nJt39/P7PZvuwJ4StkmBT2JZLl8DHJ2nf5UcfwdWrKqu8Wzdwc7Pq8NKDpmn8c+UfxvuPZ9vVbQDodXoCwgLwcfUBoEyeMhZ5bktkal+5onY/LFmS1Oknd9PF3KvenQeYWG4ELqvjLYu2ZGTpntRcewg8difuyfXp/zk+jrlUt6fcuVPzkjKEsJgwem/qzaP4R7g6utKzUk8GVB+QuHSe0ZXMVZIcWXIQ/CiYI4FHzFKn9bkiImDxYpX0c/26es9nzVL3Va8Ov/5qued+SmRsJIuOLmLq/qncCFWVLlwcXDhx50RisCmBphASbApbsXev2ou1fr1aY+3cWR3v0gW6dlX9yzM5o8nIunPrGL9nPEeCVJ1QO70d7cu2Z3jN4YmBpiWZs5zRsWMwcaLal2l6nExepQp0HRxArwvd0bSkDHMdOra88T2NftgPXd6DR49g/361FxMgb1743//S/gLTyd3Iu6w7uy6x9WBO55yMqj0KB4MDPSv3xM3Jtj406XV66haoy7pz69h5fadlgs1nJf3kypWsbFV6CYsJY+q+qckS8PJkzcPA6gPpWbkn7k7u6T4mITIyCTZFxmU0quByyhTVQjLBiRNJ3/9HVnFm8v2J7+myQZVJcbZ3plvFbgyuMZj8bun3y9ag1zG6ZUl6rTyKjmdnU49uWfK5+xo1DbZtgwkT4O+/k46/2SyWch1WMahFM87dv4jpfPJSRhoadp90hKuPn7FSJVUn1cZceXCFKXunsOT4EqLjoymbp2xiYPZFvS+sPLq0qVegXmKwObL2SPNefMgQ1VIyIemnSJGkpJ8sWcz7XC/BpJmYum8q4bHhFM5emOG1hvNJuU9wssv8lS6EeBUSbIqMR9PUxr1p09QaK6igskMHVS+zZEnrji+dhMWEcSP0BqVzlwagXel2TPSfSNtSbelXrR85na1TJ7RpaS/mta+YIpva8wWZ2kajytuYMCGpeZPBAO+0i6BAm0WsuTGFLRcC0B8YQd+qfdHr9IkZvPC4pWSwBk2bwvDhqu6RDWXzHgs6xsS9E/np9E+Jr6uKd5Vkr9HWJezb3HNjT7KEtVeSUCQl4T22t1eBZq1aSUk/en0aR/zyTt45yS9nfuGr+l+h0+lwd3JnfKPx5HLOxTsl3pGlciH+gwSbIuPR6WDjRhVoenhA797Qp09SYe5M7m7kXWYemMmcQ3PwdvHmZK+T6HV6nO2dOdPnDHpd+v2SfZ6XzdSOjYUVK9Ry+YXbAeBxEafcRfi4bRZcGs5m+YWZhJxSy5Ce2TzJn9UbH6fczG++gJ6bemLSjBhMMO9+DXz2LIAyltmLail3Iu7wyfpP2HI5qUBok8JNGFFrBPUL1s9U5W/K5C6Du5M7D6MfcvLOycSM7FRJSPqZPBnGj4dGjdTxgQNVK8kaFtwL+hRN09hzYw8T/Cew6eImABr4NqB+wfoA9K7SO93GIoStk2BTWN/Jk2oW85tvwPtxQsQXX6hWch07pnttPGu59vAak/dOZvGxxUTHqxnDPFnzEBgemLgfMyMEmglelKkdEQHffad2QNy6BVRYDANVS8kYdKww2BN7Qi2JFs5emOEV+/GJfwRO703gdJdolmSphFfU4v9v777jm6y+B45/knRSaIECLaWUvfceBRciIEtFEQTZe++CyhfRH6MsUUCGIoggCioiKChDEcqesimbQlkFOuhOnt8fl6YU2kIhadL2vF8vX5KnT5Pb9Glycu8956DTLlPwvhvf+FajqK4AzTPx57MEz1yenAk7g16n591K7zLGfwzVvavbelhWYdAbWPPuGkrnL53x/cOPJv2A6keaFGx6e2fah02TZuL3M78zNWgqO6/sBNSe4XYV21EwV8FMGYMQ2Y0UdRe2oWlq097MmcltYcaOhSlTbDsuGzgTdoZPtn3CD8d+wKgZAbXEOq7RONqWb2tXAeaT3Lmjcji++EL9G6BQ6RBudS6GRsol40oFK/G/ygNpt+4shoVfQWQkALuLVqbDe1NTnGuJzj3WFpcYx7Ijy/jh+A9s7LTR3Nln28VtFPUoSsl8JW08QjuUWtJPgQIqw3zAAJUAlImuhF+h+YrmKcpPda3WldENR1PG8/lLaQmRnUhRd2G/4uNh5UoVZB49qo7p9fD226pndQ506d4lVhxdAUDTkk0Z12hclltivXpVFWFfuBDu31fHSpeG9sP2sc1lJDdDHt+bOOe/Irw8dMiDJuegVazIpAqvs6y4/2PnaqiAc+K6EzSt6G2RwuqWEh4bzoL9C5i9ZzbXo64D8MOxH3i/2vtA8l5GkYrXX09uD5XU6adr10xN+tE0zfy35pPHhwRjAu7O7vSv3Z+h9YZSOI99frgRIiuRYFNkHqMRKlVStTIB3NxU2aKhQ5OLMmdzmqbxR/Af3Lx/01yU/NWSr5r7XNfyqWWzsT1LS8ngYLUfc9my5EThqtU0Wg/Zwi7DVCZf3JLq9xk0HWVW/gWJwIsvwujR7C5bl68X703zsdLqTmQroZGhzN49mwUHFhARp3pj+rr7MqL+CN6s8KaNR2c78/bO44+zfzClyRSqelVN/oKmwb//qvpWSVtjBg1SBVZHjYI2bTKt0w/A7ejbzNkzh59O/sSBPgdwcXDBoDew+p3VFM9bPMuVnxLCnkmwKawrJEQVYQf1RtKsGURHw+DB0Lcv5LO/1nvWkGhK5MdjPxIYFMjRm0fJ65KXdhXb4e7sjk6nI7BpoE3Hl9E+4EePwuTJKWtkNmps4oW+a/greiqTruwHwKAz0KlyR0qFxvFJ2C8YNSMGnYGF5Ubg+9oFlVlcty4ANw9ffaqxPkt3Iku7HH6ZMnPKEG9UEXbFghUZ03AMHat0zJzuOXbs9+Df2XB2A01LNlXBZmKiKkUwYwbs26eWzPv1Uyd3765q5WaiS/cuMXPXTL4++DUxiTGAarfZpVoXAKp5V8vU8QiRE0iwKaxj5061VP7rrxAUlNyf+v/+T6235pD6mNEJ0Sw5tIQZu2Zw8d5FQHUY6VOzD0aT0baDe2DjsVD6Lz/4WJH26+Gx9F9+MMU+yb17YdIk+O23Bye5h1CvRTBjepVh4fWeTD6r9t+6OrjSq0pXRl4oTLFRS+HCBXqM6sPZgR2TE0g6pHw8a3QnsqSHOzT5efjhX9SfOGMcY/3H0rJsyyy1t9aaXiz2IhvObmDbuS0M22dQf+8XL6ovurhAWFjyyZlcvmjazmmsPLrSvDe6ZuGajPUfy1sV3sq0cQiRE0mwKSwnrSLsW7cmB5t589piZDaxIXgDXX/tyq3oWwAUcivEsHrD6F+nv910GDGaNCauO5FqN6CH90k63/ZmymSduRC7TgfVe8/jiM8Q9mDinZ0q2zqvS14GVerBkH06CnZfkpwl5OmJr1cZfB+UjUmNJbsTWYqmaWw6v4nAoEB2XtnJxaEX8crtBcDaDmvJ45wn08aSVbxY7AUA/j36O6Zp69FrgKenWjIfODDTk35AVXqotqAa2oMrq0mJJoxtNJYmJZpkqb3RQmRVEmyK5xcfD4sWPV6EvXNnVYS9UiXbji8TPZxsUMazDGExYZTIW4LRDUfTrXo3XB0zv9tJevZeuJNi6fxhmgYxFwpyaFdpXvlA/UwGA7R7PwzX1ybx7ZnPzOeaNBOrjq/i2P2ulH/ny+Qm5yVLqqSPbt2eWMLqebsTWVKiKZGfT/xMYFAgh64fAlRr0H8v/cs7ld4BkEAzDbV8auNmNHDH1cjxmr5U6flBppcwM2kmjt44al4SL563OC3LtsTVwZUx/mOo7VM708YihJBgU1iCXq/2Y126pIqw9++vZjFySBF2gNO3TzN953TijHF89+Z3AJTOX5pt3bZR37f+83VTsaLU9j9qGsQEexG+qzTx1/MC4OCo0aF3CI4vzuLHs4uIPhP92PcZNSPXTeGUj41VSSCjR8Nbb2Uo6eNZuhNZUmxiLEsPL2X6zumcv6s+ONmqNWiWoGmwY4daKv/8c/Dzw9HgSEOv2my6vYdtc0dTpX7/TBtOgjGB749+z7Sd0wgOC+b80PPmrQ9r3l1jt3+HQmR38pcnMu6//1QB5unT1Qymg4PayBcermYw3NxsPcJMs+/qPqYGTWXNyTVoaOh1eia9MskclDTya2TjEabv4f2PmgmiT/kQvqs0CbfVrJ3OMRHXhn/T4L2l/HhjNQknEwBVI/PErRPmZUlQyUClewVAy0Eqw/wZlyeftjuRNYTHhjNs4zDijHF4unoypN4QBtYZiGcu22e/2xWjEdasUR8y9+xRx0qUUEEn8GKV1mz6ew/brmxnUP0hVh9OVHwUXx/8mlm7ZnEl4goA7s7uHLl+xBxsSqAphO3IX594Opqmiq/PnIl5416dOmqpHKBTJ9uNLZNpmsbm85uZGjSVrRe2mo+3KdeGAP+ALDX7VbdEfrxyu3J+V37u7SpNovEe5N8PWnHcyybiUfsi4QXGsCX0MAAv+73I2JiaNJ27gW9cNPq2BqNeBZoLWy3Et1wdKPf840qvO5ElXYu8xm+nf6NfbZUd7ZXbi3GNxpHfNT89avTAzSnnfHB6KtHRsHSpCirPnVPHnJ2hSxfo08d82gvFXsDFwcXqSVPhseF8tvsz5uydw50YtT/Yy82L4fWH0692PylfJISdkA5CIn1xcfD99+rN5dgxdSypCPu4cVC9uk2HZwtLDy+l+1pVI9NB70CnKp0Y4z+GigUr2nhkGRMfr+pjjv84ketXHVRLydaqpSSaDs+EweQxvkavphHsD13B2CvFqDdnjer6AuDuTkj/Tpxt9zKlyzXIeItCG0ra9vDdf98Rb4xnX+99so/vSYxGKFMGLlxQt/PnV11+Bg0CL6+Up5qMJJoScXZwtuqQwqLD8JvtR3RCtGp76j+GLtW64OJgm4oFQuQk0kFIWEZYGFSuDNdVVxRy504uwl68uE2HlpliE2MJiQihdP7SALxd8W3G/z2edhXaZfo+vmcpvP6ouDhVR3vqVLh8GcCB3H7niWrTG3QPPnvqNMKc5vJZiy68X7cl1JwOh35XXytSBIYPh9698XV3J+uEmLD36l4CgwLN2x4AGvs1xs4+c9uPS5fAz09tiTAY4I03VMWJESNUjcw0tswY9AYMessXaD928xhrTq5h/IvjAdV7fkqTKXjn9qZdhXZWeUwhxPOTmU2RUliYKlOS5OWXVZuYIUPUMlkOKl0UHhvO/P3zmb17Nt65vTnU95A50zzBmGDufZ1ZMlp4/VExMfDVVxAYCNeuqWNePnG8OGQ5QQ4fczUq5LHv+bvr37xU/CX48ktVjHv0aOjQIcvVSb0acZX317zP3xf/Nh9rXbY1YxuNpWHRhjYcmZ3atUvtx1yzBv75B15Q5YyIilK1Mh2efp4iOiGaXI7Pl4kedDmIqUFTWX9mPQDbu2+3+/3QQmR3MrMpMkbTVOH1mTPhzz/VMlnSstjy5aouXhYLLp5HaGQon+/5nPn755vbEDoZnAiJCKGoR1EAmwSaT1t4/VH378OCBSqf68YNdczXFxoMnUeQbgqrolLv3GNAb57NpU8fVWUgi9YkLOhWkOA7weZtD6MbjqZSoZxTkuupmEywbp26UIKCko//+29ysJk791Pf3dk7Z3njhze4F3uPVW0OcysqLkOz8SbNxB/BfzB1x1SCrqjx6NDRrmI78rtmXq1VIcTzk2AzJ0tqIzdzpmoNk+Svv+D999W/ixSxzdhs4MLdC0zdMZWlR5amaEMY4B9Ax8odMz3ATPK0hdebVvRO8SYeFQXz5kHg/BDu6oIhpgzFivkybpwqeznkr/+4dvAqPrl9GOn6Ms5btjG0cohK+DHBQmOz5H2YGZjJsrWk8kU/n/yZDZ024KB3wMngxHdvfkfJfCWzVAJXpkhIUEk/M2fC6dPqWFKd3JEjoeKz7UUukqcIp8OCSTTF887iNThqPsDTzcZfuneJVitbceym2ifuZHCia7WujGo4irKeZZ9pPEII28k67yDCcu7fV+upn3+e3EYuKaN0+HCoUMGmw7OVE7dOsOjgIgAaFm1oN20I0yu8DirgDA2PZe+FOzQo5WkOMqdPhzC/xdD1QdIPOjo3Gk/fJhMBGNNwNHVPR9L5y504n18BQNsdLpzt1JzS3UfhW8U/E346y3l428ON+2oK96cTP9GhsuqL+VI63YtyNL0epk2Ds2fBw0PNYA8ZAoWfr6bpttP3MCSUJtFwglj9MRyNKthMazb+4YYIRdyLEJ0QTR6nPPSv3Z+h9Yfik8fnucYjhLAdCTZzovv3YexYlSlSoIBqITdgABQqZOuRZRpN09h6YSs37t/gvSrvAfB6mdcZWGcgHSp3sKv9YKkVXk/NpetxbFutttqFhQHuIdCmD+hMD87QmLzjU/rV6Y2vuy+lPEtT6q/bcP6S2ioxeDC+Awbg65m1akqGRoYye/ds5u+fT2R8JKB6l49qMIrWZVvbeHR26MIFWLgQJk5UHzINBvjkE5UI2KsX5Hn+zkhJs/HOpirEGU4Qpz9KHuNrwOOz8fdi7zBv3zx+OfkLe3vvxcnghIPegdXvrKZkvpJ209pVCPHsJNjMCQ4ehA0b4MMP1e1CheCjj9T/338fXO2rhaI1GU1G1pxaQ2BQIPuv7cfT1ZO25dri5uSGTqdj7utzbT3ExzxceD01pjgDkQeL03ehNxH31LGi9fdgbD6Ua5hSnKuhsXrLRoa/2UsdmDAB2rVTs9pZ8Dq4cPcC5eeVN297qFSwEgH+AXSo3MFm2x7s1v79arr7p5/U/swyZaBnT/W1jh0t+lBJs/Eu+spE8COx+mMpvq4BVyKu0Gl1f9ad+47oBNWRavXx1XSqqmr21ixc06JjEkLYjgSb2ZXJBH/8ofZh/fOPOtaiBdR88AL+0Uc2G5otxCXGsezIMqbvnE7wnWAAXB1c6Vi5I3HGONyw3+LddUvkp7CHC9fDY1Ps2zTFORB5sBgRe0tiilUJXGXLQoE+ndkZpZbFzdNIDxhMcP/zX9lYpqVawvT3V/9lIaGRoRTOo5ZfS+QrQb0i9dDQCPAP4PUyr9t824Nd0TT1QXP69OTXAYDXXrPqdpmk2XhnUwXQDBj1t0jU3cBB8yJed5kIh5+5b/iHH08ZAajhXYMA/wDaVWxntTEJIWzH4sGm0Wjk448/Zvny5Vy/fh0fHx+6devGRx99ZN6PI6woJga++w4++wxOnVLHDAZ4990MZZJmJxvPbqTH2h6ERqli5Plc8jGo7iAG1x1MQbeCFn88S9TCfJhBr2NC64r0X34QHWB8NMjUGfEpEce0T53p0AFm7a7Ors0/UOZOJV45d42vat02J/0M2VOCQ74v8XsqCUX2TNM0tlzYQmBQILuu7OLSsEvmFpLr31uPu7OUSXtMVBQ0aJDcjMHBQc1gjhwJ1apZ9aGTZuP1uOCklSZed5pY/TGcTSZCnQea67nW9GrElKbjaVqyqbw/CJGNWTzYDAwMZP78+Xz77bdUqlSJ/fv30717dzw8PBgyxPo9cnO0o0ehSRO4dUvddndXJWuGDIGiRW07tkz2cLJB8bzFuR51HV93X0bUH0HvWr3J7WSdwPt5a2GmpXnlwsx6qxZDx0cRckiP5nYJXBxxqLuRPE0+Y8Ybk+hY9V0AauZrx1/L5vLq+f8AGBVk4Nsa1dlSph2/VK+q7vChhCJ7lrTtYeqOqRwIPQCo1pjbLm3jrQpvAUig+bD4+OQyZblzg4+PKszep49qxpBJrwMPz8a7GRvhaCqKg+aNo1YYF1N19LhS0vk99vYZkGU+8Aghnp3Fg82dO3fStm1bWrZsCUDx4sVZuXIlex8urfOQuLg44uLizLcjIiIsPaTsLSoqecayfHn1RlOsGAwbpvZjWWCzf1Zy9s5ZZuycQYIxgcVtFwNQvkB5Nr2/icbFGuNksF690OephZme+/dVTfVp07y5XXQx9E/KLodE4K4GX+3/0hxsRsU7Ee5RmQjn2yyv0YIltdpwK/fjdQmfNvHIFuIS4/juv++YFjQtxbaHXjV7MaLBCIrnLW7bAdqbK1dg9mz49lv47z8VZIIqxJ8/f6Y3Y3h4Nt4j8c0UfxNe8RPQ4cD09jUl0BQih7D45qaGDRuyZcsWzpw5A8CRI0fYsWMHLVq0SPX8KVOm4OHhYf6vaA6bgXsmmgZbt0LLllC1qqqXCeDoqI6fPauCzRwUaB64doD2q9tTbm45Fh5YyNIjSwmJSO6I06RkE6sGmk+qhQkq+9ZoevqGXTExajdEyZIwZgzc1h+BNr3NgWaS/8XU5beR+2HPHkAtYX7W6D0a9F/CtBe7pRpoJp1nr25F32LA7wMIvhNMPpd8/O+F/3Fp2CW+aPGFBJoPO3JEJfmVLAmzZqkyBCtWJH+9ZEmbdf1qXrkw8zvXxNsj5XVW2CP3M3/wEkJkTRaf2Rw7diwRERGUL18eg8GA0Whk0qRJdOrUKdXzx40bx4gRI8y3IyIiJOBMS3w8/PijelM5fFgd0+lg925o9KBUT9mcU/A4qXzR1KCpbD6/2Xy8RekWjG00liJ5Mq8gfUZrYaYnNhYWLYIpU5Lb0pcsCcae3bmU8Hiw+vKPe8l9D1i1CurVo26J/LgU9uJeGuPRAd4eai+pvbgRdYM/gv+ge43uAPi6+zK64Wg8c3nSp1Yfq217yJI0DbZsUUk/f/2VfPyll1Q70TQ+2NtC88qFaVrR26J7mIUQWY/Fg81Vq1axYsUKvv/+eypVqsThw4cZNmwYPj4+dO3a9bHznZ2dcXZ2tvQwspd791RdvC++SG5qnSsX9Oih9mGVLm3T4dnKksNL6PmbKt1i0BnoULkDY/zHUNWraqaP5WmXpNM7Ly4OFi+GyZPh6lWg4Al8yxTm44B8dOkCK44NpvtvPVJ8j8EEpSs2goXjoWlTdeyRhKKHw9Okt/gJrSvaxRv++bvnmbFzBt8c+oY4Yxw1C9ekmrdKXpnUZJKNR2en7t6FNm3U1LdeD2+/rYLM2rVtPbJUGfQ6u98bLISwLosHm6NHj2bs2LF06KC6dlSpUoVLly4xZcqUVINN8RROn1ZF2EF19Rg8GPr2VXuxcpDYxFiuRV6jZL6SALSr0I6Ptn5EuwrtGNlwpE2XV592STq18+Lj4bPFIcxcGsytU2XAPQSXblOJLb6Wno0/oecr4wHoWrkziaNH0s//rsou13QsrDEe34kTH7vPpCXMR5OVvC2QrGQJR64fITAokB+P/4hJU9sC6hWpR5wx7gnfmQNFRame5Um1MPPnV68B0dGq41fJkrYdnxBCPIHFg83o6Gj0+pRbQQ0GAyaTKY3vEI/ZuVOVLerxYBarXj2V7NO4MXTooLp+5CDhseEs2L+A2Xtm4+vuy95ee9HpdHi4eHBx2EWr7sV8WmnVwkyS2tJ1YqLaXjdqxWJuN+gDr5ughTo5FtChI3TfX9B4LDg6onN0pNc7U2h+ai9n321K6YqNknuXp8IelzCvRV6j12+92HB2Q/I4SzdnrP9YXij2gpS/edj162o1Y/58tbpRogTUr6++Fhho06EJIURGWDzYbN26NZMmTcLPz49KlSpx6NAhZs2aRY8ePZ78zTlZYiKsWaP2Y+7erZbJ33gjefby669tOjxbSGpDuODAAiLiVJUCR70joVGh5j7J9hBoQsaWrk0mWL1aNe85HRoCw3ub6w4mnfyusTwTl1+l3IUdUORH6NxZfaFvX3zpS9oh5uPjsqclTE9XTw5fP4xep6d9pfYE+AdQ3bu6rYdlX06dUs0Yli1T096guv1IpQ4hRBZl8WBzzpw5jB8/ngEDBnDz5k18fHzo27cv//vf/yz9UNlDZKTaqPf553Dxojrm5KRmMONy5pLiuTvnCAwK5Nsj36ZoQzjGfwwdK3e0SBtCSxdehycvXTerVJi1a2H8eFUSFcC10mlidI/Phfb77hTlLqISvtzst7tRehKMCaw8tpKfTvzEmnfXYNAbcHZw5ts3vqVkvpKUyl/K1kO0L7duqd7kv/2WfKxBA7Ufs00b1ZxBCCGyIJ2maU9fiyUTRERE4OHhQXh4OO7u2bxY88aNKqgMD1e3PT1hwAAYOBC8vGw7Nhv69dSvvPnjmwD4F/UnwD+AlmVbWqwNobUKryd5NJCtUzw/Wzbr+Ogj2H80AmotxC30dd5s4cdW57Vcc++SPLOJSvpZ+0NpCg8YR83B3VQSSBZyP/4+iw8tZsbOGVyJuALA6ndW83bFt208MjuXmKhmMC9ehLZtVZCZxVqJCiFyjozEaxJsZraYGHB1Vf++dg2KF1cb/IcPV/XycuWy6fAym6Zp/HXuL+7G3qVDZZVUZtJMDPx9IJ2qdqKRXyOLPl5ahdeT5jQtXf9v2zbVhn7HoZtQ7wuoOw9c7tGubCeuXuxOaHgskYa/uOfwBSa9KqFZ/dbb3HHvhreHCzsCXrGLrPGnERYdxrx98/hizxeExYQB4OXmxfD6w+lXux8eLh42HqEdiYlRy+Q//qg+dCZ1/dmyBYoUUQ0ahBDCjkmwaW9MJvj9d7UPy8VFvbkkOXxYFWbPYrNXzyvRlMjq46uZtnMah68fppBbIS4OvYiro6vVHtNo0mgUuDXNephJSTyWCPDWbQvh4znBHNzjAlVXQI3F4Kget7zBm5FBBuaXDiTMLS8AJW4f4J7LPW7lroYDBcz3s7J3fbvac5mWC3cvUGV+Fe4n3AegZL6SjGk4hq7Vu+LiYL/F4zNdWJhqBzVnTnJb2WXL1AdNIYTIQjISr1l8z6Z4SHS0eiP57DN40FEJR0dVRLHIg4Lj1avbbHi2EJMQw5LDS5ixcwYX7l0AIJdjLjpW7kicMc6qwaYlC6+n5ehR6PLZYg4X7QNVTFAZ87RpHYow7o9I2u67jl6D8EYbmOOvytlcKFALePwP0p5bSt6JuUN+V5XAVjxvcSoXqkycMY6x/mNpV7EdDnp5eTG7eFEl/y1erF4XAPz8YMQIePNNmw5NCCGsTd4NrOH6dZg3T5UsCVPLiXh4qNqYgwcnB5o5zLrT6+j5W09uRasZnQK5CjC47mAG1hmIZy7rz95ZovB6Ws6dU9nlK9ZdgWHJvcuTUtN/+M2J9oeuqrizWDEudOnL4qgyT7xfe2wpuffqXqbumMqWC1u4OPQi+VzzodPpWP/eejxdPaV80aMuXlSNF4xGdbt6dbUf85131IdPIYTI5iTYtIY//oD/+z/17xIlVJefHj1yVK/yJJqmmYOPEvlKcCv6FsXzFmdkg5H0qNGDXI6Zt0f1eQqvp+XqVfjkU42v/9mIqeEUqNHksd7l6MDrbjy6GjXMQYaf3oBH4FZiMlCX05Y0TWPT+U1M3TGVvy/+bT6+6fwm2ldqD6gPDwLVTvLkSahYUd0uXhxefFFlk48eDa++qtrMCiFEDiHB5vPSNNWfOCEBWrVSx957T9XM7NpVLZHlwJIlx28eZ9rOaTgbnFnUehEAlQtVZmuXrTQu1tgmS6zPUng9Lbdvw5TAROZsWU1CvanQ8T8AKpe5xYkEvbkrDoBBg9Jzv4fXO5iDDANkiZaSRpORX07+wtSgqRwMPQiAg96BzlU7M6bhGCoUrGDT8dmV+Hj44QeYMUNtm7l0KbmqxPr1yYmBQgiRw0iC0LOKi1PtX2bNguPH1TLZqVM5MrB82I7LO5gWNI11Z9YBKjAJGR6CV277KOWUlI0OqQd46WWjh0SEcORKMH/+VJRFmzYTV2s65D8PQC7Nmf7BeRi+7jYbl42n73+TMWpGDDoDC1stpGfNnmmOx5plmJ7X5fDLlPqiFImmRHI55qJ3zd6MaDACPw8/Ww/NfkREwFdfwezZEBKijrm5qcr9LVrYdGhCCGEtkiBkTbdvq72Y8+bBjRvqWO7c0LKlKmeSO7dtx2cDJs3E72d+JzAokKArQYBqtfhmhTcJ8A+wm0ATnr1n+II9ixmwsQ8aJhWlNlXH8xpzMfyQgUFbIskfEwe5c9PzfjmaDbvI2TtnKZ2/dJZqKRkZF8mm85t4q8JbAPh5+DGwzkA8nD0YXG+wLJU/LCwMpk+HBQuSa+V6e8OQIdCvH+TLZ9vxCSGEnZCZzYxYtEjtv4x9EKT4+qo3lt69IW9emw7NlubtncegDYMA1T6yS9UujGo4inIFytl4ZGl72g5CiYnw6deH+CS0dsq9mBp8vMuJUX/H45aACjKGDlVJYFkwyLh1/xaf7/mcefvmcS/2HscHHKdiwYq2HpZ9u3EDihVTqxzlyqn9mJ07g7OzrUcmhBBWJzOblqJpah9W0ptH+fIq0KxZE0aOzLHZpFHxUVyPuk7p/KUB6FilI5N3TKZzlc4MrT/U3Lfcnj2pZ7imwcJVF/hg3QzulvgKHB5P+nnxTDxupcrDqFFZNsi4dO8SM3bOYPGhxcQkxgBQzrMct6Nv23hkdkbTYMcO2LQJPvlEHfPygilToFQptV87h9XKFUKIpyUzm6mJj4dVq9R+zJdeUv8H9Yazbx/UqZMjs0lv3r/JF3u+4Mt9X1K+QHmCegSZM80TTYnZpq7iN+uPMmbdVMK8fwT9g3I1GskbOwEDei5W/hrfN7tmySDj5v2bjPprFN8f/R6jpn7GOj51GNdoHG3Lt7VYa9Asz2iEtWth2jTYs0cd278fatWy7biEEMLGZGbzWd29q5bK58xRNW1AtZQMDFQzmDod1K1r2zHawLk755i5ayZLDi8hNlFtIQiLCSMsJsy8hy8rBpohESEEhwVTxrMMvu6+LNkcRMD6KdzK9zs8mJx94Yo7E7dEcDYf9Gurx4jJnPTjW7O7bX+A55DbKTcbz27EqBl5teSrjGs0jpeLvyw1MpMktZOcMQPOnlXHnJ1VhQlP++/oJIQQ9iTrRQjWcO4cfP45fPMN3Fft9vD2hkGD1Eb/HLhUDnDs5jE+/fdTfjrxk7mUT90idQnwD6BtubYY9Fk3837xwcX0Wd8Hk2ZCj55aoYvYd+tvqPo7aDranMnFhH/uUzM0ApydeaFZN4rUbc0Bx2iqFCpPq8qVbf0jPDVN09h4diOrTqxicZvF6HV6cjnmYkGrBfh5+FHbp7ath2hfjh6FJk2S20nmywcDBqiGDF72k+wmhBBZhSyjg9pzN3Om+neVKmo/ZocOWXIPniWtOr6Kd396F4AWpVsQ4B/AC8VeyPKzXyERIRSbXSxFLUxMBvJ+t4I21bry0b9xlLkD5M8PAweytck7fLjzpt2WJ0pLoimRn078xNQdUzly4wgAazuspU25NjYemR2KjQWXB8X84+OhZElVxmzECOjZM0dWmRBCiPTIMnpGDR6sOn4MH65mNLJ4MPUsjCYjP5/8mURTIu9VeQ+AdhXaMazeMLrX6E5Vr6o2HqFlxCTEMPmfGSkDTQC9kemLvOg1oRa4X4OJI6F7dzZeiKD/8oOPFYG/Hh5L/+UH063LaSuxibF8e/hbpu2cxvm7qg6om6MbfWv1pVZh2WuYwqFDqnzRvn3qNcDBAZycYPNmlfiTQ1c1hBDCkmRmM4eLSYhh6eGlzNg1g/N3z+OTx4fzQ87j7JC9ZnXDY8OZu2c+gdtmE6ndeOzrBp2Bi8Mu4hupU0ulDg4YTRqNAremmNF8WFLHoR0Br9i800+SK+FXqPt1Xa5HXQfA09WTIfWGMKjuIPK72kfrS5vTNJVVPn26CiqTbN6sPmwKIYR4IpnZFE90N+YuX+77ki/2fsHN+zcBFZj0qdmHRFMizmSfYHPq9kA++WcyMaYIALzuOfPK5ThWVQajXmWWL2y1UBVff+jvZe+FO2kGmqAS1EPDY9l74U66ZZSsLd4Yj5PBCQBfd1988vjgoHdgVINR9KrZCzcnN5uNza4kJKgqE9OnwxG1rQCDQW2ZGTUKqle36fCEECK7kmAzB1rx3wr6ru/L/QSVDFU8b3FGNhhJ9+rds3RgYjRprD92jKM3TlLFqwKtKldm2z865i6KJqZCBKVuOjNhRxwdjsXhoHdgmkdbznZ+ndK1X0u1y8/NyLQDzWc5z9Iu3rvIjJ0z+OXkL5wadAp3Z3d0Oh0/t/8Znzw+5gBUPHDwoKqHCqqdZK9eautMsWK2HZcQQmRzEmzmEEaT0Zw9XrFgRe4n3KeaVzXG+I+hfaX2WbJ00cM2Hgtl4K8zOZ84C3QaaDpcAz4jZuNQvF3fYfXhSbx1Jg5d7jzoRvSFoUPx9fUl7UaSUCiPy1M99tOeZynHbh4jMCiQlUdXmmtk/nziZ7rXUKWYiuctnqnjsVs3bqi9mK1aqdv16sFbb6mmDP37qwQwIYQQVpe1IwyRLk3T2HF5B4FBgfjk8WFR60UA1Chcgz299lDHp06WzywHFWh2+X4Ot5xmJhde12nE1B0Ju96kbssStMg/En0PT9VO0sPjqe63bon8FPZw4Xp47GMJQpC8Z7NuicwJWnZd2cWUHVNYd2ad+VjTkk0Z22gsLxd/OVPGkCWcOaOqS3z7rVomv3w5uTbmzz/bdmxCCJEDSbCZDZk0E7+d/o1pQdPYFbILAFcHV6Y3nY6Hiwq06hbJ+sXpNU3jt9Pref+XcUQ6H3/8BL2RAu//zE2fqrgETIUMJvEY9DomtK5I/+UH0UGKgDPpnia0rpgpyUEhESE0WtIIk2ZCh463KrzF2EZjpUbmw3bvVvsx16xRSUAA9eurGU4pxC6EEDYjwWY2EpcYx/L/ljN953ROh50GwNngTNdqXRnVcJQ50MwuOv3SiZXHVgJgSASTAbSH4z5Nh7Nb/udK4mleuTDzO9dk4roTKZKFvK1cZ9NoMrI7ZDf+fv6ASvzpXLUzDjoHxviPoVyBclZ53Czp+HG1LL59e/Kx1q1hzBjw98+RpcyEEMKeSLCZjczaNYsPtn4AgIezBwPqDGBIvSF45/a28cie3cMtJT1dVbDo6uiKyQQ+5+qRK+5HBu43MXwXrC+jo19rDZMe0PTkTxiEA6qd5vMk8TSvXJimFb3Ze+EONyNjKZRHLZ1bY0YzLjGOb498y7QgVSPz1KBTlPUsC8DStkuzxbYHi8uXT81qOjrC+++rpgwVK9p6VEIIIR6QYDMLC40M5W7sXSoWVG+svWr2YsnhJfSt1ZfetXrj7py165Q+3FJShw43JzcmvvgxtRJGMno0HDnQkyNOk/CLjWKlXxuW1XqVwnGOJOqv4WDyMQea8PxJPAa9zqrljSLjIll4YCGzds0iNCoUgPyu+Tl1OznYlEATCA+HhQvh1CnVXhbAxweWL4dGjdS/hRBC2BUp6p4Fnb59muk7p/Pdf99R37c+27ptM39N07RsEZSk2lISqHzdjRMLwjFhIHdumNN+G9973iFY75RuEo89FV5/WERcBDN2zmDu3rncjb0LQJE8RRjZYCS9a/Umt5O0SQTg6lWYPVsFmpGR6tiRI1A1e3S2EkKIrEaKumdTu0N2ExgUyNpTa9EehFZGk5HIuEjyOOcBssfs17k75xj257DHW0oCn/15nzn6DRTp24oJE8DL60W8j4XaRRLPs9Dr9MzbN4+7sXcp61mWAP8AOlftLDUykxw/DjNmwIoVqig7qCXyMWOgfHnbjk0IIcRTkWAzC/j30r98tPUjtl9OToBoW64tY/zH0LBoQxuOzDo+2PoB68+sf+y43gRbi8wncF0LyldKPm6rJJ5ncer2KZb/t5xPX/4UnU5HbqfcqkqAswdvlH/DXAtVABs2wOuvJ99+4QUVZLZoAXq97cYlhBAiQyTYzAKuhF9h++XtOOod6Vy1M6MbjqZCwQq2HpZFaJrG9svb8fPwMxcjH523DRHBq6h6A2Y2VC0ldSY9oyosZPLEXqneT2Ym8TyLfVf3MTVoKmtOrkFDw7+oPy3KtACgR40eNh6dnTAaISQkuaPPyy+rPZgNGsDo0aoouxBCiCxHgk07ExkXyVcHv8LT1ZOu1bsC8G7ldzl39xw9a/SkiHsRG4/w+YVEhHD69mkuh1/m60Nfs/PKTvoWfZMFPX5h61YYOeo95hyZTzBlaHipMy+NNdC7XWmKeqTX78f6STwZpWkaWy9sZcqOKWy5sMV8vG25ttni92gxsbGwbJlaLgc4eVIVY3dxgdOnIbfsWxVCiKxMEoTsxI2oG3yx5wu+3P8l92Lv4efhx9nBZ3E0OGb6WIwmzWozhIsOLKLf+n7mPacATkboe9iRG/G3WPWnqgWaz93IuI8MDB6sYo6s5ub9m7T6vhX7ru0DwKAz0KlqJwL8A8zVA3K8O3dg/nz44gu4eVMdy5cPgoKgQvaYuRdCiOxKEoSykOCwYGbsnMG3R74lzhgHQFnPsoxuONom49l4LPSxvY+FLbT3cdauWYz8a2SKYzoNdn4FXtcL8RanMRjq0r8/TJhgoECBNO7ITj1cCaBgroLEJsbi6uBKr5q9GNlgJMXyFrPxCO3E1atqFvOrr+D+fXXMzw9GjICePWUmUwghshkJNm1o1q5ZjPprlHmWr75vfcY0HEPb8m3R6zI/AWLjg6zuR6e6r4fH0n/5QeZ3rvlcAefB4H8fO6bpYJzLWP5hIi3aOHF8GpR70BzHmjOslhSdEM3XB79m6eGlbO++HTcnN3Q6HcveXIZPHh8KuRWy9RDty7lzqowRqNJFY8ZA+/aqKLsQQohsR4LNTKRpGtEJ0bg5uQHQ2K8xGhqtyrZiTMMxNPJrZLPSRUaTxsR1J1KtVamhyghNXHeCphW9UwR8aQWE1yKvMXv3bJqXbs4rJV4BYHTlPnx/fm3KlpImA6E+A/nzGydefjn5sDVnWC3lbsxd5u2bx+d7Pud29G0Alh5eysC6AwGo7l3dhqOzE5oGf/8NFy9CjweJUI0bw+DB0LIlvPaatJMUQohsTvZsZoIEYwIrj61k+s7pvOD3AvNazjN/7fzd85TMV9KGo1N2nQuj41e7n3jeyt71zUk4SQHhlfAQc9eegu46vIv8xdYrq4k3xvOy0Y+tn1wCVEfBWeM7sbrhD6qOkclAj0IL+ap/zxSVbNKaYU0KSZ53hvV5hUaG8tnuz1iwfwGR8arAeIm8JRjjP4Zu1bvh4pAFN5laWmIi/PILTJsGBw6opfErVyBvXluPTAghhAXInk07ERUfxVcHvuKz3Z9xJeIKoBJHZjWbhbODM4BdBJrw9L3Dk85LCggjDH9xx2WO2nypwdV44KI6t+FlGLHjMldfPMnoxRVYuRJgBa5HA+k48Cxj+5WmjFfKDPNnnWHNLLejb1Pqi1LEJMYAULlQZcY1Gkf7Su1x0MufE9HRsHQpzJwJ58+rY66u0LVrclF2IYQQOYq8O1rBjagbzNk7h3n75nEv9h4AXm5eDKs/jH61+5kDTXvytL3DC+VxMQeECdzmjuODQBPMU4+vnIeJ/0DD6IL8XWkwdVp6ERqnVku7dYNJk3wpXDj1MkZ7L9xJsXT+KA0IDY9l74U7mVbm6GrEVXOpogK5CtCiTAtCI0MZ12gcLcu2tMn+Wrv011/QqRPcVlsK8PRUy+UDB5Llsr2EEEJYjASbVvDFni+YvGMyAGXyl2FUw1F0qdbFrpdX65bIT2EPF66Hx6bbY7xuifzsPn+ba+FRJOqvJQeaD+l1MD9r8gygY8xYQrap/akvvgizZkHNmumPI6MzrNa088pOpuyYwsazGzk96LR5FnrZG8vI5ZgrW7QGfW4mU3I3n/Ll4e5dKFECRo6E7t0hVy7bjk8IIYTNSbBpAXuv7sVR70iNwjUAGFxvMDuu7GBYvWG0KdcmS7QgNOh1TGhdMd0e4x+2LMOKo9/x0ZZJJGoNcTC9pNLJHwo4dZqO7vf/Ie5CFQBKloTp0+HNN58uDyQjM6zWoGkaf577kyk7pvDvJZU9r0PHlvNbKFlLBZtJCV452qFD6hcbFwc//6yO+fnB9u1Qpw44yEuLEEIIRRKEnpGmaWw4u4FpQdPYdmkbTUs25a/3/7L1sJ5balnghdyhVsVD/HHxKy6HXwag3G1HYnP9RKTDFu44zgWdSvhh3UI41BOdUwIDR8Qz42M3nDOwa8Bo0mgUuPWJM6w7Al6x6J5No8nIzyd/ZuqOqRy6fggAR70jXap1YYz/GMp6lrXYY2VZmgZbt0JgIGzapI7pdHDhQnKLSSGEEDmCJAhZUbwxnh+O/cD0ndM5dvMYAA56B3zy+JBgTLBJxx9LSuoxvv7YMfZe3c+FyANsuvgj+46ofXiFomD4buh5UKPLu5c57vE68QffISokDm6Xg8gi5Kl+ibKvX2L2p40xZHA749PMsE5oXdHiyUFR8VH0XtebiLgIcjnmom+tvoxoMAJf9/RbZOYIiYlq9nLaNDh4UB3T6+Hdd1XPcgk0hRBCpEOCzQxY8d8Kxm4ZS0hECAC5nXLTt1ZfhtUflq2CkqWHv6HP+j6YNJP5WIm7MCYIup53x7XPADZPeJd9M/Xc/bEcpmg1delS/Bb53/4Xp4JR/F/Hms8cEDavXJj5nWs+NsPqbcE6m1HxUfx84me6VOuCTqfDw8WDDxt/SHRCNIPrDsYzl/30WLe5ZctUZx9QmeW9esHw4WpvphBCCPEEEmxmQLwxnpCIkBSZ5Xld8tp6WBYTHBZMRFzEY4Gm3gRb//SmeJ8x0KsX2w/nYcxQCFOrzTjkjyLfKydxLXkTn7wuTGj9/HUwk2ZYLd1B6E7MHebuncvnez7nTswdfPL40LRUUwDG+I95rvvONm7fVjUxa6g9yHTooNpLdugAAwZIZrkQQogMkWAzDadvn2bmrpnULVKXXjV7AfBelffQ6XR0qNzBrjPLM+pg6EGm7pjKTyd+om3u2ikCTQCTHi6u+w6d46uM6QWrVqnjHh7w0XiNuq/HcTfOh0J5Slq0paRBr7NYeaNrkdeYtWsWCw8sJCo+CoDS+UuTYJLaj2YXL6qSAV9/DcWLw7Fjark8Vy44flw6/QghhHgmEmw+YnfIbqYFTePXU7+iobHlwha6V++OQW/A2cGZbtW72XqIFqFpGtsubWPK9in8dT45sSnxv0PoS+lTBJwGnYFfl5Vn4XSIjVUxR58+8OmnULCgDrDfJefIuEhG/TWKpUeWEm+MB6CaVzXGNRrH2xXfzhKVAqwuKbN81SowGtUxV1e4cQMKP5ihlkBTCCHEM5JgEzBpJv4I/oNpQdPYfnm7+Xjrsq0Z4z8mWxTtDokIITgsmDKeZTh64ygT//mYPdf2AmAwQYdjELBLT5WX3mFx41r03R6AUTOix0CebQv5fKvak/rSSzB7NlSrZrufJSPcnNz49/K/xBvjaeTXiHGNxtGidAupkQmwfz988EFyZjmoXuVjxsArr0iAKYQQwiIk2ASGbhjK3H1zAVXupnPVzoxqOIqKBSvaeGSWsfjgYvM+TL1Oz2setdhzbx8uCdDzEIw87EqJd/rAzGFQvDg9AS/DuwQEnuXEjtLci/CleHG1be+tt+w7Btl5ZSdf7vuSr1p/haujK3qdnrkt5uJkcKJxsca2Hp59uXdPBZoGQ3JmefXqth6VEEKIbEbqbAJBl4NosaIF/Wr3Y2i9oebWhNnBmdtnKD+vPNpDRYQMOj39d5v46EQBvHoPg/79IX9+AK5fh3HjVHtrADc3Nfk1YgS42Ok2VU3T+OvcX0zeMdlciH1ui7kMrDvQxiOzI9HRsGSJ6k8+bJg6pmmqZmaHDmqPphBCCPGUMhKvSbD5QGRcJHmc82Ta41nbnZg7zNs7jxk7AolIvP/Y1/+uNJ2XWg0yR5Dx8fDFF/DJJxAZqc7p0gWmTAEfn8wc+dMzmoysObWGKTumcDBU1X9MKsQe4B9AGc8yNh6hHbh9G+bNgzlzICxMZXVdvgx23DBBCCGE/bN5UferV68SEBDAhg0biI6OpnTp0ixZsoTatWtb4+EswhqBptGkWbx0z5NcjbjKZ7tmsXDffKKMMeqgRnJFdFTCT+nXOpgDzQ0b1GTXmTPq63XqqNikXj2rDvW53I+/T+2vanPq9ikAKcT+qKTM8sWL1awmJPcsd8zajQeEEEJkLRYPNu/evYu/vz8vv/wyGzZsoGDBggQHB5MvXz5LP5RdS63tY2ELFiU3mjTWHzvG0RsnqeJVgVaVKzP530/49N//I0FLBKDadRi3A8LrVmOA31GMmDDoDCxstRBfd1/OnlW1udevV/dZqBBMnQpdu6qKN/Ym0ZSIg15dsm5ObpT1LMuNqBsMrjuYwfUGUyCX1H8E1B6IXr2SM8tr1FBJP2+/LT3LhRBCZDqLL6OPHTuWoKAgtm/f/uSTU5FVeqOnZ+OxUPovP/hYb++kycX5nZ+v6PnGY6EM/HUm5xNngU4DTUdJhxF0S7jM//SreeEijNvjSLPG3dCNGAnlyhESEcLZO2cpnb80HjpfJk2Czz5Ty+cODjB0KIwfr1ZZ7c3dmLvM2zeP+fvns6vnLvw8/AC4En6FvC55s9X2h2eiaXD/PuTOrW6fOwdly0KTJirIbNLEvrO6hBBCZDk23bNZsWJFmjVrRkhICNu2baNIkSIMGDCA3r17p3p+XFwccXFxKQZftGjRLBtsGk0ajQK3ppjRfJgO1XZxR8Arz7SkvvFYKL2W/8lVlx4q0Eyi6Skd8TmLtk3i5RY9YfBg8PJK8b2aBitWqPgjNFQda9ZMlTIqXz7DQ7G661HX+WzXZ8zfP5/IeLWRdPwL4/nk5U9sPDI7YTTCL7+onuXFisFPPyV/7eJFSfoRQghhNTbds3n+/Hnmz5/PiBEj+OCDD9i3bx9DhgzBycmJrl27Pnb+lClTmDhxoqWH8dQsva9y74U7aQaaoLZPhobHsvfCnQx3x0kwGhm6dhFhDgtSBpoAOhORLpF8+NYyto979bGf4cABFX/u2qVulyqlZjZbtbK/Sa+L9y4yPWg6iw8tJs6oPohULlSZcY3G0b5SexuPzg7ExKil8pkz1SwmwMmTcOeOuaqABJpCCCHshcWDTZPJRO3atZk8eTIANWrU4NixYyxYsCDVYHPcuHGMGDHCfDtpZjMzWGNf5c3ItAPNZzkPVE/2749+zycbJ3Ah8TI48ljSD5oeB5MP1yLjUwSyt2/Dhx/CV1+pmU03N/joI7VX09n56X+uzBKTEEONhTW4F3sPgPq+9fmg0Qe0LNsyWxTXfy537sCXX6qyAbduqWP586tPEQMHJgeaQgghhB2xeLBZuHBhKlZMWQy9QoUK/Pzzz6me7+zsjLMNop609lVeD4+l//KDz7yvslCepytG+eh56c2w9vnmTb699gcAHrEwaC/ccynCl3Wuoek00PTkTxiEAypB5mZkLEYjLFqkAs27d9VjvPeeWnEtYmdlRI/dPEalgpXQ6XS4OrrSq0Yv/rv5H+MajePFYi9Kt58k332nNtaCWjYfORJ69FCfIIQQQgg7ZfFg09/fn9OnT6c4dubMGYoVK2bph3pmRpPGxHUnHgs0IXnCcOK6EzSt6J3hJfW6JfJT2MOF6+Gxqd5/0p7NuiWSZ6GSZlivhIeQqL+GzpSHIu4+/F+bBjSvXJheeV7gz8g/GL5Hh09kI1bUfIeThUriE3ubRP01HEw+5kAT4EZwbmp3h8OH1e2qVWHuXGhsRw10NE3j74t/M2XHFDaf38y2btt4odgLAEx9dar0LAc4ehQiIsDfX93u2RN+/RV694b27SWzXAghRJZg8Xer4cOH07BhQyZPnkz79u3Zu3cvixYtYtGiRZZ+qGdmzX2VBr2OCa0r0n/5QXQP7itJUtg6oXVFcxCbNMMaYfiLOy5zHmSXQ66bvvRfvkDNsLYfzaVzcRi+60qjlWe5/mDsDhTAwZQcZBqjnIndWYm+gSqlPG9e+PRT6NfPfuISk2Zi3el1TNkxhT1X9wCq7ueBawfMwWaODjQ1Df79V3X22bBBfVI4fFhtrM2dG/7+29YjFEIIITLE4pvg6tSpw5o1a1i5ciWVK1fm008/Zfbs2XTq1MnSD/XMrLGv8mHNKxdmfueaeHukXCr39nBJsTyfNMMaozvKHccvkpN+dHA+bwj6xBAmrjuBER1OH/4PQ/FiTGhdMekUM82oI2JfCa5+9SK3DxVGp1NlFs+cgUGD7CPQNJqMrPhvBVXnV+WNH99gz9U9OBlcGFhnIOeGnGN4g+G2HqJtGY3w889Qvz689JIKNPV6VSYgqaWTEEIIkQVZJQxp1aoVrVq1ssZdW8Sz7qvMiOaVC9O0one6me7f7t/CuXujueV6OGX0CKCDWIdbhIb7pphhTQpkkxKbYi55cndTJRLCVK3JunXVknmdOs88dKsZ89d4rt2/gE5zJU9iS9xj2nLgSGFO+jlRLK+tR2dDv/+uMraCg9VtFxfo3l01pC9d2rZjE0IIIZ6THcx5Zb5n2Vf5LAx6XbrL8P/89j9u5TqsbqSSXa5DZeU/OsPavHJhKrh707N/PFv+UMlVBQpoBAbq6NbNPrr/RMZFsuTwEvrW6ouzgzObTtwk/u7b5NXdIE/i6+hRBcifNyErW9DpVKCZL5/KKh88WLVzEkIIIbIBOwhLMl/SvkpIdUIRSLmv8nmERITw94W/uRx+mV+O/8SB08l77jrVDeD9wzD/9+pUv/kOaA9+HY9klz88wxofrzLKK1XUseUPZ/R6FZucOaOjRw/bB5ph0WF8/M/HFJtdjKEbh7LsyDLzdgE344t4JLY3B5qQvKd14roTGE0W7S9gn65ehdGjYfr05GMtWqge5pcvq022EmgKIYTIRnLkzCY8vhydxNuC/csXH1xMn/V9MGkm87GWUT6sn34VgFdbtWHOrh8JLOeGBhSJbZkiu/zRGdYtW9QezFOn1H01agTz5qkckvRYunB9aq5GXGXWrlksPLCQ+wn3ASjrWZYCuQpYNSEryzh5UgWYy5dDQoKqiTlggCpbpNOpEkZCCCFENpRjg014un2Vz+r07dP0Xtcb7eGFeg1Kn72DKSoSfe48GPQ6BnVqbM5cfzi7/OEZ1tBrOkaOhFWr1LFChWDGDOjc+cndf6xRuP5hiaZEBv0xiCWHlxBvjAeghncNPmj8AW+WfxOD3sDaw1ef6r6eNSHLru3cqTLLf/st+VjjxhAQAK6uthuXEEIIkUly5DL6w5L2VbatXoQGpTwtEmh++cdEas+pkjLQBNDBG5N/QZ87j/lQepnrX7xbk6MbClO+vAo09XoYMgROn4b333+6QLP/8oOPzSom7ZPceCz0uX5OAAe9A5fCLxFvjOeFYi+wodMGDvQ5wNsV3zaXMMqMhCy7NHWqqpH522/ql/XGGyr4/PdfaNnS9nsehBBCiEyQo2c2rUV/6DBR+oTHkn4MOgOli1R57PzUZlijLuRnaCcdJ0+qcxo2VEvm1as/3RisVbh+d8hupgVNY+7rc/HJ4wPAlCZT+LDxhzTya5Tq92RWQpbNxcerIuwFHtQ+festmDgROnWCUaNUGSMhhBAih5Gpled08sZxus9tyrIfxpmPdes7n9UX67Ko7AgMOjW7Z9AZWNhqIb7uvqneT9IMa+2CRfjiI09ea6oCzYIFYckS2L796QNNyFjh+ifRNI3N5zfzyrev0GBxA9acWsNnuz4zf726d/U0A82kny2zErJsIjISZs2CUqXU1HOSsmUhNBS+/loCTSGEEDmWzGxmUEhECMFhwUTdv8uSPybxa/RBNB3svLSdzu3/D73egEsBb95eorrjtIgYztk7Zymdv3SagSaonJEvvoCPP4aoKLXC2r+/Sk7Oly/j47RE4XqTZuK3078xeftk9l3bB6hl8y5Vu9CrZq8MjSczErIy3Y0b6pf25Zdw7546tmMHREdDrlzqdt68thqdEEIIYRck2MyArw9+Td91fTA9vBisgzeCHQgo0g59QiI4p2y16Ovum26QCSo+GTBAtcIG1URm3jyoWfPZx/q8+yRNmon6X9c3B5muDq70rtmbkQ1H4ufh90xjsmZCVqY6d05lli9dCnFx6ljZsqqk0fvvg7OzTYcnhBBC2BMJNp9SSEQIfdb1TtnrXIPNzr15Zd508PDI8H3euqWSkpcsUbfz51eJy5aol/ks+yTjjfE4GZwA0Ov0NCzakNNhpxlUZxDD6g+joFvB5xsUTy50nyX88gssXKj+Xa+e+iW2bSsJP0IIIUQq5N0xHXGJcUTGRgAQHBb8WNCm6UDf8b0MB5omEyxaBOXKJQeaPXuqLPNevSwTs2Rkn2RkXCQzds6g2Oxi7Lqyy3ze+BfGc3nYZSY1mWSRQDNL0jT46y/455/kY337wttvq2O7dsGbb0qgKYQQQqRB3iFTERkbwczv+lNyggeTprcGoIxnGfS6lE+XQWegdP6M9a4+dEhllvftC3fvqoLsQUEqhyQpidlS0iurNL9zTeqWcjZ3+xm9aTTXo66z6OAi83meuTzxcMn4jG22kJgIP/wAtWpBs2Yqm1x78HHD3R1Wr4YXX3xy/SkhhBAih5NldJKTfvI7uvPzr5OZG7qWu05GcILfwnYyOSEeX3dfFrVaRN/1fTFqxidmlz8qIgL+9z+YM0fNbObOrZJ/Bg0CByv+FlLbJ1m0QByf75nF27/NT9HtZ6z/WDpV7WS9wWQFMTFqunnGDLhwQR3LlUu1a4qLA5dsVgtUCCGEsDKdpml21ZA6IiICDw8PwsPDcXd3t/rjpWgp+VBdzDJ3dAQ4vEjnvvNwLlvRfH5IRMhTZZcn0TT48UcYMUJVwQF4912YOROKFLHCD/TE8WhUmFeB02GnAVW26INGH/BWhbfMRdhzrO++g5Ej1WZaUFPNgwfDwIHgmcX3mQohhBAWlJF4LUfPbIZEhKTsXa4DNFiga0mvDxdjKOSV4nyjSePKLVfCI8twxehC4dxaupnUZ86oOGXzZnW7TBmVZd60qZV+oDScuHWCMvnL4GhwRKfTMaTeEL4/+j0fNv6Q5qWbo5OlYMXdXQWaxYuroLNHj+QSRkIIIYR4Jjk62AwOC04ONJPooFzXUY8FmhnpMR4bq7LKJ09WTWWcneHDD1VlnMxchd13dR+Td0zm11O/srTtUrpW7wpAv9r9GFBnQOYNxB4dOwbTpkGlSiqbHKB1a5Vp3rq1dfc2CCGEEDlIjn5HTUr6eTjgTC3pJ6nH+KP7DZJ6jM/vXNMccG7erGpmBgerc5o3h7lzVXOZzKBpGtsubWPy9slsOr8JAB06jt08Zj7n0USnHEPTVFHTwED4/Xd1rGBBGDZMfSLQ61VmuRBCCCEsJodGHUpS0k96LSWf1GMcVI/xa6EanTurJfLgYChcGFatgj/+yLxAc/2Z9fh/48/L377MpvObMOgMdK3WleMDjjP9temZMwh7ZDLB2rXg7w8vvKACTZ1OlS/6/Xcpwi6EEEJYUY6e2QToWbMnzUo3SzPp50k9xk0anNlWiPJTNSIjdOh0KsP800+fqc77c/ls92fsCtmFs8GZnjV6Mtp/NMXzFs/cQdijDz5Qs5kATk7QrZsqZVSmjE2HJYQQQuQEOT7YhPRbSqbXOzz+Zh7C/qxC/DXVvLxmTdVYpnZtqwwz5WMb41n+33JalW1FIbdCgCrCXqtwLYbXH07hPFmw17ilREbC/fvg7a1ud+mifjH9+sHQocnHhRBCCGF1Emw+QWq9w03xBsJ3lCVif3HQ9OicEhgaEM+MCW4YrFw9KDohmq8Pfs30ndMJiQhhXKNxTG4yGYCXir/ES8Vfsu4A7NmNG/D55/Dll9CmDSxbpo5XrAjXroGrq23HJ4QQQuRAEmw+waM9xqODvbizqRLGSBW45CoXSvk3zjHjY38MVtwBGx4bzpf7vuSz3Z9xK1rVgSycuzB+Hn7We9Cs4uxZVYR96VJVeB1Uq6b4eLVsDhJoCiGEEDYiweYTJPUY7/3lCe5srkR0sFqCNXhE49n0GLlK3WJS55rp1tt8Xp9u+5QZu2YQEaf6tJfIW4IA/wC6Vu+Ki0MO7mhz+DBMmQI//aSSgADq1VOljNq2lX7lQgghhB2QYPMJjEYI/rswYcu8iLmvB70J9zrn8fAPpkgBJya0rvlYnU1LuxZ5jYi4CCoWrMgHjT7g3crv4qCXXx2//65S/gFatFBB5gsvSL9yIYQQwo5IxJKOw4ehTx/Ytw9AT/0GGgM/iiCPjyuF8tSlbon8Fp/RPHvnLIE7AulXux+1fGoBMLbRWJqVbkabcm1ybo1MoxF+/hkKFYKXXlLHBgxQS+jDh0PVqjYdnhBCCCFSJ8FmKu7fh48/hs8+UzGOuztMnQp9++rQ6/MCeS3+mEdvHGXKjin8ePxHTJqJO7F3+Ln9zwAUy1uMYnmLWfwxs4TYWLUXc8YMOHcO6teHnTvV7GW+fLBkia1HKIQQQoh0SLD5iD/+UBNmly6p2++8oxKcC1tppXxPyB4m75jMb6d/Mx97vczrjGww0joPmFXcu6eyyj//HG7eVMfy54dmzSAxERwdbTo8IYQQQjwdCTYfCA1VJRhXr1a3ixWDefOgZUvrPWbXX7uy7Igqz6NDx9sV32Zco3HUKFzDeg+aFXz5pdp/GRWlbvv5wciR0LMnuLnZdmxCCCGEyJAcugEwmckECxZAhQoq0DQYVFxz/LjlA01N01L0Ya/hXQMHvQPdqnfjxMATrHpnVc4NNLWHGoIWLKgCzcqV4bvv1L7MIUMk0BRCCCGyIJ2maam1/baZiIgIPDw8CA8Px93d3eqPN3q02g4IqvPPokVQw8LxntFkZPWJ1UzZMYUA/wDeq/IeoAq037p/K+fuxwTYs0e1kmzYULWQBLVRdssW1WheMsuFEEIIu5OReC3HB5vnzqk458MPYeBALNoBKKml5NQdUwm+EwxAA98G7Oy503IPkhVpGmzcqILMbdvUMR8ftVHWQXZ2CCGEEPYuI/Fajn9nL1VKxTguFqyNHpMQY24peSXiCgD5XfMztN5QBtcdbLkHymoSE1VdzGnT4MgRdczRETp1UlPMEmgKIYQQ2Y68u2PZQBOg488dWXt6LQDeub0Z1WAUfWv3JbdTbss+UFYzYgTMmaP+nTu3KmI6fDj4+tp2XEIIIYSwGgk2LeB29G0c9Y54uHgA0LdWX47cOEKAfwDdqnfLuS0l79xR/cm9VYtPevSAH39UyT79+6tSRkIIIYTI1nL8ns3ncS3yGjN2zmDhgYWMajCKiS9PBFTWeaIpEUdDDq0FeeUKzJoFX30FHTrA118nfy0+HpycbDc2IYQQQjw32bNpZefvnmda0DSWHF5CvDEegKArQWiahk6nQ6fT5cxA88QJtR9zxQq1PxPg6FGVXZ6UeSWBphBCCJGjSLCZASdunWDKjimsPLoSo2YEoJFfIz5s/CHNSjVDl1PL9OzdC5MmwW/JXZB4+WVVmP2116R8kRBCCJGDSbCZAbN2zWL5f8sBaFaqGR82/pDGxRrbeFR24I8/VKCp08Gbb6ogs25dW49KCCGEEHZAgs107Li8g0JuhSjrWRaAAP8A7sbeZVyjcdT2qW3j0dlIQgL88IPq5/nCC+rYoEFw/brKLC9XzrbjE0IIIYRdkQShR2iaxqbzm5i0fRL/XvqXDpU7sLLdykwfh925fx8WL4aZM+HyZWjcGP7919ajEkIIIYQNSILQMzBpJtaeWsvkHZPZf20/AE4GJ/K55DMn/uRIYWEwd66qjxkWpo4VKgTNm6dM/BFCCCGESIUEm8Cvp37lo60fcfzWcQBcHVzpW6svoxqOooh7ERuPzoZmz1Z9PKOj1e2SJVWnn65dwdXVpkMTQgghRNYgwSZwJuwMx28dx93ZnUF1BjGs/jAKuhW09bBsQ9OSs8cLFVKBZo0aKumnXTtpKSmEEEKIDJHIAehfuz+aptG3dl/yuuS19XBsIygIAgPhlVdg2DB1rH178PJSx3LqNgIhhBBCPBdJEMrJTCZVtigwEHbsUMf8/OD8edmLKYQQQog0ZSRe02fSmIQ9SUiA776DatWgdWsVaDo5Qa9e8NdfEmgKIYQQwmJkGT0nGjIEFixQ/86TB/r1U0vnPj42HZYQQgghsh8JNnOCsDDVq9zLS93u2RPWrIGhQ6F/f8ib16bDE0IIIUT2ZfVl9KlTp6LT6RiWlHQiMs+VK6qrj58fTJyYfLx2bVWYfdw4CTSFEEIIYVVWndnct28fCxcupGrVqtZ8GPGoEydg2jRYsULNaAIcPqwSgvQPPl84OdlseEIIIYTIOaw2sxkVFUWnTp346quvyJcvn7UeRjxs71544w2oVAm+/VYFmi+/DH/+qUob6SUfTAghhBCZy2rRx8CBA2nZsiWvvvpquufFxcURERGR4j/xjNauVf/pdPDWW7BnD2zdCq+9JnUyhRBCCGETVllG/+GHHzh48CD79u174rlTpkxh4sP7CcXTSUyEVaugeHFo2FAdGzIEbt2CkSOhXDmbDk8IIYQQAqwws3nlyhWGDh3KihUrcHFxeeL548aNIzw83PzflStXLD2k7CU6GubNgzJloFMn+N//kr/m5QWLFkmgKYQQQgi7YfGZzQMHDnDz5k1q1qxpPmY0Gvn333+ZO3cucXFxGB4qGu7s7Iyzs7Olh5H93L0LX34Jn3+uZi8BChaEl15KmfgjhBBCCGFHLB5sNmnShKNHj6Y41r17d8qXL09AQECKQFM8pc8/h48+gqgodbt4cRg1Crp3h1y5bDo0IYQQQoj0WDzYzJMnD5UrV05xzM3NDU9Pz8eOi6eUN68KNKtUgbFjoX17cJB6/EIIIYSwfxKx2Jt9+2DqVHj1VdXdB6BjR7Ufs1kzySoXQgghRJai0zRNs/UgHhYREYGHhwfh4eG4u7vbejiZQ9Ng82YVZG7dqo6VKAFnz8peTCGEEELYnYzEaxLJ2JLRqMoX1aqlamFu3aqWx7t2hXXrJNAUQgghRJYny+i2NHAgLFyo/p0rF/TuDSNGqF7mQgghhBDZgEydZaaICAgLS77dtSvkzw8ffwyXL8Ps2RJoCiGEECJbkWAzM9y4AR98oALJTz5JPt6gAYSEwIQJ4Olpu/EJIYQQQliJLKNb0/nzMGMGfPMNxMWpYzt3pizC7upqu/EJIYQQQliZzGxaw5EjqlxRmTIwf74KNOvXh19/hT17JPFHCCGEEDmGzGxaw/Ll8MMP6t/Nm6tC7C+8IDUyhRBCCJHjSLD5vEwmWL8efHygdm11bPhwCA1VLSWrV7fp8IQQQgghbEnWc59VQgJ8+61qIdm2LYwfn/w1Hx81uymBphBCCCFyOJnZzKj79+Hrr2HmTLhyRR1zd4caNVIm/gghhBBCCAk2M2ThQlXC6M4dddvbWy2Z9+0LHh62HZsQQgghhB2SYDMj9HoVaJYqBWPGQJcu4OJi61EJIYQQQtgtCTbTcuoUTJsGjRtD9+7qWJcukC8fvPkmGAy2HZ8QQgghRBYgGwwftXcvvPUWVKwIS5bA5MlqLyaAszO8/bYEmkIIIYQQT0mCTQBNg02boEkTqFcP1qxRx954A777TpJ+hBBCCCGekSyjAwwdCnPmqH87OEDnzmpPZoUKth2XEEIIIUQWJ1N2AO3aQa5cKug8d04tn0ugKYQQQgjx3GRmE1QryZAQlfwjhBBCCCEsRmY2QfUsl0BTCCGEEMLiJNgUQgghhBBWI8GmEEIIIYSwGgk2hRBCCCGE1UiwKYQQQgghrEaCTSGEEEIIYTUSbAohhBBCCKuRYFMIIYQQQliNBJtCCCGEEMJqJNgUQgghhBBWI8GmEEIIIYSwGgk2hRBCCCGE1UiwKYQQQgghrEaCTSGEEEIIYTUSbAohhBBCCKuRYFMIIYQQQliNBJtCCCGEEMJqJNgUQgghhBBW42DrATxK0zQAIiIibDwSIYQQQgiRmqQ4LSluS4/dBZuRkZEAFC1a1MYjEUIIIYQQ6YmMjMTDwyPdc3Ta04SkmchkMnHt2jXy5MmDTqfLlMeMiIigaNGiXLlyBXd390x5zKxAnpe0yXOTOnleUifPS9rkuUmdPC9pk+cmdZn9vGiaRmRkJD4+Puj16e/KtLuZTb1ej6+vr00e293dXS7cVMjzkjZ5blInz0vq5HlJmzw3qZPnJW3y3KQuM5+XJ81oJpEEISGEEEIIYTUSbAohhBBCCKuRYBNwdnZmwoQJODs723oodkWel7TJc5M6eV5SJ89L2uS5SZ08L2mT5yZ19vy82F2CkBBCCCGEyD5kZlMIIYQQQliNBJtCCCGEEMJqJNgUQgghhBBWI8GmEEIIIYSwGgk2hRBCCCGE1eSYYHPevHkUL14cFxcX6tWrx969e9M9f/Xq1ZQvXx4XFxeqVKnCH3/8kUkjzRxTpkyhTp065MmTh0KFCvHGG29w+vTpdL9n6dKl6HS6FP+5uLhk0ogzz8cff/zYz1m+fPl0vye7Xy8AxYsXf+x50el0DBw4MNXzs/P18u+//9K6dWt8fHzQ6XT8+uuvKb6uaRr/+9//KFy4MK6urrz66qsEBwc/8X4z+jplb9J7XhISEggICKBKlSq4ubnh4+NDly5duHbtWrr3+Sx/j/boSddMt27dHvs5mzdv/sT7zc7XDJDqa45Op2P69Olp3md2uGae5j06NjaWgQMH4unpSe7cuWnXrh03btxI936f9bXpeeWIYPPHH39kxIgRTJgwgYMHD1KtWjWaNWvGzZs3Uz1/586ddOzYkZ49e3Lo0CHeeOMN3njjDY4dO5bJI7eebdu2MXDgQHbv3s2mTZtISEjgtdde4/79++l+n7u7O6Ghoeb/Ll26lEkjzlyVKlVK8XPu2LEjzXNzwvUCsG/fvhTPyaZNmwB455130vye7Hq93L9/n2rVqjFv3rxUvz5t2jS++OILFixYwJ49e3Bzc6NZs2bExsameZ8ZfZ2yR+k9L9HR0Rw8eJDx48dz8OBBfvnlF06fPk2bNm2eeL8Z+Xu0V0+6ZgCaN2+e4udcuXJluveZ3a8ZIMXzERoayjfffINOp6Ndu3bp3m9Wv2ae5j16+PDhrFu3jtWrV7Nt2zauXbvGW2+9le79Pstrk0VoOUDdunW1gQMHmm8bjUbNx8dHmzJlSqrnt2/fXmvZsmWKY/Xq1dP69u1r1XHa0s2bNzVA27ZtW5rnLFmyRPPw8Mi8QdnIhAkTtGrVqj31+TnxetE0TRs6dKhWqlQpzWQypfr1nHK9ANqaNWvMt00mk+bt7a1Nnz7dfOzevXuas7OztnLlyjTvJ6OvU/bu0eclNXv37tUA7dKlS2mek9G/x6wgteema9euWtu2bTN0Pznxmmnbtq32yiuvpHtOdrxmHn2Pvnfvnubo6KitXr3afM7Jkyc1QNu1a1eq9/Gsr02WkO1nNuPj4zlw4ACvvvqq+Zher+fVV19l165dqX7Prl27UpwP0KxZszTPzw7Cw8MByJ8/f7rnRUVFUaxYMYoWLUrbtm05fvx4Zgwv0wUHB+Pj40PJkiXp1KkTly9fTvPcnHi9xMfHs3z5cnr06IFOp0vzvJxyvTzswoULXL9+PcU14eHhQb169dK8Jp7ldSo7CA8PR6fTkTdv3nTPy8jfY1b2zz//UKhQIcqVK0f//v0JCwtL89yceM3cuHGD33//nZ49ez7x3Ox2zTz6Hn3gwAESEhJS/P7Lly+Pn59fmr//Z3ltspRsH2zevn0bo9GIl5dXiuNeXl5cv3491e+5fv16hs7P6kwmE8OGDcPf35/KlSuneV65cuX45ptvWLt2LcuXL8dkMtGwYUNCQkIycbTWV69ePZYuXcrGjRuZP38+Fy5coHHjxkRGRqZ6fk67XgB+/fVX7t27R7du3dI8J6dcL49K+r1n5Jp4lteprC42NpaAgAA6duyIu7t7mudl9O8xq2revDnLli1jy5YtBAYGsm3bNlq0aIHRaEz1/Jx4zXz77bfkyZPniUvF2e2aSe09+vr16zg5OT32Qe1JsU3SOU/7PZbiYNV7F1nCwIEDOXbs2BP3tDRo0IAGDRqYbzds2JAKFSqwcOFCPv30U2sPM9O0aNHC/O+qVatSr149ihUrxqpVq57qE3VOsHjxYlq0aIGPj0+a5+SU60VkXEJCAu3bt0fTNObPn5/uuTnl77FDhw7mf1epUoWqVatSqlQp/vnnH5o0aWLDkdmPb775hk6dOj0x0TC7XTNP+x5tz7L9zGaBAgUwGAyPZWjduHEDb2/vVL/H29s7Q+dnZYMGDWL9+vX8/fff+Pr6Zuh7HR0dqVGjBmfPnrXS6OxD3rx5KVu2bJo/Z066XgAuXbrE5s2b6dWrV4a+L6dcL0m/94xcE8/yOpVVJQWaly5dYtOmTenOaqbmSX+P2UXJkiUpUKBAmj9nTrpmALZv387p06cz/LoDWfuaSes92tvbm/j4eO7du5fi/CfFNknnPO33WEq2DzadnJyoVasWW7ZsMR8zmUxs2bIlxazLwxo0aJDifIBNmzaleX5WpGkagwYNYs2aNWzdupUSJUpk+D6MRiNHjx6lcOHCVhih/YiKiuLcuXNp/pw54Xp52JIlSyhUqBAtW7bM0PfllOulRIkSeHt7p7gmIiIi2LNnT5rXxLO8TmVFSYFmcHAwmzdvxtPTM8P38aS/x+wiJCSEsLCwNH/OnHLNJFm8eDG1atWiWrVqGf7erHjNPOk9ulatWjg6Oqb4/Z8+fZrLly+n+ft/ltcmi7Fq+pGd+OGHHzRnZ2dt6dKl2okTJ7Q+ffpoefPm1a5fv65pmqa9//772tixY83nBwUFaQ4ODtqMGTO0kydPahMmTNAcHR21o0eP2upHsLj+/ftrHh4e2j///KOFhoaa/4uOjjaf8+jzMnHiRO3PP//Uzp07px04cEDr0KGD5uLioh0/ftwWP4LVjBw5Uvvnn3+0CxcuaEFBQdqrr76qFShQQLt586amaTnzekliNBo1Pz8/LSAg4LGv5aTrJTIyUjt06JB26NAhDdBmzZqlHTp0yJxVPXXqVC1v3rza2rVrtf/++09r27atVqJECS0mJsZ8H6+88oo2Z84c8+0nvU5lBek9L/Hx8VqbNm00X19f7fDhwyled+Li4sz38ejz8qS/x6wivecmMjJSGzVqlLZr1y7twoUL2ubNm7WaNWtqZcqU0WJjY833kdOumSTh4eFarly5tPnz56d6H9nxmnma9+h+/fppfn5+2tatW7X9+/drDRo00Bo0aJDifsqVK6f98ssv5ttP89pkDTki2NQ0TZszZ47m5+enOTk5aXXr1tV2795t/tqLL76ode3aNcX5q1at0sqWLas5OTlplSpV0n7//fdMHrF1Aan+t2TJEvM5jz4vw4YNMz+HXl5e2uuvv64dPHgw8wdvZe+++65WuHBhzcnJSStSpIj27rvvamfPnjV/PSdeL0n+/PNPDdBOnz792Ndy0vXy999/p/r3k/Tzm0wmbfz48ZqXl5fm7OysNWnS5LHnrFixYtqECRNSHEvvdSorSO95uXDhQpqvO3///bf5Ph59Xp7095hVpPfcREdHa6+99ppWsGBBzdHRUStWrJjWu3fvx4LGnHbNJFm4cKHm6uqq3bt3L9X7yI7XzNO8R8fExGgDBgzQ8uXLp+XKlUt78803tdDQ0Mfu5+HveZrXJmvQPRiMEEIIIYQQFpft92wKIYQQQgjbkWBTCCGEEEJYjQSbQgghhBDCaiTYFEIIIYQQViPBphBCCCGEsBoJNoUQQgghhNVIsCmEEEIIIaxGgk0hhBBCCGE1EmwKIYQQQgirkWBTCCGEEEJYjQSbQgghhBDCav4f90fTp+CvVtoAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pred_wls = res_wls.get_prediction()\n",
    "iv_l = pred_wls.summary_frame()[\"obs_ci_lower\"]\n",
    "iv_u = pred_wls.summary_frame()[\"obs_ci_upper\"]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "ax.plot(x, y, \"o\", label=\"Data\")\n",
    "ax.plot(x, y_true, \"b-\", label=\"True\")\n",
    "# OLS\n",
    "ax.plot(x, res_ols.fittedvalues, \"r--\")\n",
    "ax.plot(x, iv_u_ols, \"r--\", label=\"OLS\")\n",
    "ax.plot(x, iv_l_ols, \"r--\")\n",
    "# WLS\n",
    "ax.plot(x, res_wls.fittedvalues, \"g--.\")\n",
    "ax.plot(x, iv_u, \"g--\", label=\"WLS\")\n",
    "ax.plot(x, iv_l, \"g--\")\n",
    "ax.legend(loc=\"best\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feasible Weighted Least Squares (2-stage FWLS)\n",
    "\n",
    "Like `w`, `w_est` is proportional to the standard deviation, and so must be squared."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-18T11:13:29.982819Z",
     "iopub.status.busy": "2024-04-18T11:13:29.982597Z",
     "iopub.status.idle": "2024-04-18T11:13:30.015010Z",
     "shell.execute_reply": "2024-04-18T11:13:30.014420Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            WLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.931\n",
      "Model:                            WLS   Adj. R-squared:                  0.929\n",
      "Method:                 Least Squares   F-statistic:                     646.7\n",
      "Date:                Thu, 18 Apr 2024   Prob (F-statistic):           1.66e-29\n",
      "Time:                        11:13:29   Log-Likelihood:                -50.716\n",
      "No. Observations:                  50   AIC:                             105.4\n",
      "Df Residuals:                      48   BIC:                             109.3\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          5.2363      0.135     38.720      0.000       4.964       5.508\n",
      "x1             0.4492      0.018     25.431      0.000       0.414       0.485\n",
      "==============================================================================\n",
      "Omnibus:                        0.247   Durbin-Watson:                   2.343\n",
      "Prob(Omnibus):                  0.884   Jarque-Bera (JB):                0.179\n",
      "Skew:                          -0.136   Prob(JB):                        0.915\n",
      "Kurtosis:                       2.893   Cond. No.                         14.3\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "resid1 = res_ols.resid[w == 1.0]\n",
    "var1 = resid1.var(ddof=int(res_ols.df_model) + 1)\n",
    "resid2 = res_ols.resid[w != 1.0]\n",
    "var2 = resid2.var(ddof=int(res_ols.df_model) + 1)\n",
    "w_est = w.copy()\n",
    "w_est[w != 1.0] = np.sqrt(var2) / np.sqrt(var1)\n",
    "res_fwls = sm.WLS(y, X, 1.0 / ((w_est ** 2))).fit()\n",
    "print(res_fwls.summary())"
   ]
  }
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