{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "8e6632a0",
   "metadata": {
    "editable": true
   },
   "source": [
    "<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n",
    "doconce format html exercisesweek37.do.txt  -->\n",
    "<!-- dom:TITLE: Exercises week 37 -->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82705c4f",
   "metadata": {
    "editable": true
   },
   "source": [
    "# Exercises week 37\n",
    "\n",
    "**Implementing gradient descent for Ridge and ordinary Least Squares Regression**\n",
    "\n",
    "Date: **September 8-12, 2025**\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "921bf331",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Learning goals\n",
    "\n",
    "After having completed these exercises you will have:\n",
    "\n",
    "1. Your own code for the implementation of the simplest gradient descent approach applied to ordinary least squares (OLS) and Ridge regression\n",
    "\n",
    "2. Be able to compare the analytical expressions for OLS and Ridge regression with the gradient descent approach\n",
    "\n",
    "3. Explore the role of the learning rate in the gradient descent approach and the hyperparameter $\\lambda$ in Ridge regression\n",
    "\n",
    "4. Scale the data properly\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adff65d5",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Simple one-dimensional second-order polynomial\n",
    "\n",
    "We create a synthetic linear regression dataset with a sparse\n",
    "underlying relationship. This means we have many features but only a\n",
    "few of them actually contribute to the target. In our example, we will\n",
    "use 10 features with only 3 non-zero weights in the true model. This\n",
    "way, the target is generated as a linear combination of a few features\n",
    "(with known coefficients) plus some random noise. The steps we include are:\n",
    "\n",
    "Decide on the number of samples and features (e.g. 100 samples, 10 features).\n",
    "Define the **true** coefficient vector with mostly zeros (for sparsity). For example, we set $\\hat{\\boldsymbol{\\theta}} = [5.0, -3.0, 0.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0]$, meaning only features 0, 1, and 6 have a real effect on y.\n",
    "\n",
    "Then we sample feature values for $\\boldsymbol{X}$ randomly (e.g. from a normal distribution). We use a normal distribution so features are roughly centered around 0.\n",
    "Then we compute the target values $y$ using the linear combination $\\boldsymbol{X}\\hat{\\boldsymbol{\\theta}}$ and add some noise (to simulate measurement error or unexplained variance).\n",
    "\n",
    "Below is the code to generate the dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9e6acfef",
   "metadata": {
    "collapsed": false,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "# Set random seed for reproducibility\n",
    "np.random.seed(0)\n",
    "\n",
    "# Define dataset size\n",
    "n_samples = 100\n",
    "n_features = 10\n",
    "\n",
    "# Define true coefficients (sparse linear relationship)\n",
    "theta_true = np.array([5.0, -3.0, 0.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0])\n",
    "\n",
    "# Generate feature matrix X (n_samples x n_features) with random values\n",
    "X = np.random.randn(n_samples, n_features)  # standard normal distribution\n",
    "\n",
    "# Generate target values y with a linear combination of X and theta_true, plus noise\n",
    "noise = 0.5 * np.random.randn(n_samples)    # Gaussian noise\n",
    "y = X @ theta_true + noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "de370995",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  9.79794828,  -0.20820758, -14.84544524,   2.15318795,\n",
       "        -3.37427507,  -5.40426588,  -5.27365266,   0.60787097,\n",
       "        -6.19533156,  -5.5427031 ,  12.13162753,   9.35115762,\n",
       "         4.39080256,  -3.53244394, -10.99536903,  -3.68161441,\n",
       "       -10.167063  ,   1.20194765,   0.25360044,  -5.67324644,\n",
       "        -0.66859127,   3.91571974,  -3.63750527,  -3.20012413,\n",
       "         1.16544606,   2.48543602,  -3.89882746,  10.75806552,\n",
       "        -5.1450755 ,  -1.76135661, -14.55239547,  -3.91723721,\n",
       "        -1.57784936,   3.45194764,   6.35031305,  -2.66082655,\n",
       "         3.59232485,   6.05166812, -11.42207923,   4.33238054,\n",
       "         2.81808632,  -8.74092274,   5.09102217,   4.11714319,\n",
       "         3.1336241 ,  -8.4624152 ,  -1.35434132,  -6.12500763,\n",
       "         3.8119143 ,  -5.84403289,  -1.60885033,   0.90200251,\n",
       "         3.42168223, -12.40126176,   8.4350032 ,  -4.10291902,\n",
       "        10.22537853,   6.77936945,  -8.3636364 ,   0.12906052,\n",
       "        -9.12015726,  -4.9746779 ,   5.00624051,  -4.96426885,\n",
       "        -2.44764182,   8.45246218,  -0.88759959,   1.05540356,\n",
       "        -1.95453159,  -1.67965422,  -2.23592179,  -7.8858097 ,\n",
       "        -2.29987312,   0.33223236,  -2.40309155,  10.6587834 ,\n",
       "        -2.95341782,  -3.20039517,   6.51082782,  -3.32577856,\n",
       "         5.49390475,  -6.09136851,   0.86829871,  -3.55729026,\n",
       "         3.61818052, -13.1381039 ,   4.5022915 ,   6.42751502,\n",
       "        11.73765566,  -6.33983703,  -6.74108381,  -0.10967951,\n",
       "       -11.69392899,   6.35925176,  -0.43824325,  -3.78885595,\n",
       "        -4.25173964,  -7.04162883,   1.59342361,   1.60361719])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70418b3d",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "f(x)= 2-x+5x^2,\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11a3cf73",
   "metadata": {
    "editable": true
   },
   "source": [
    "defined for $x\\in [-2,2]$. You can add noise if you wish.\n",
    "\n",
    "We are going to fit this function with a polynomial ansatz. The easiest thing is to set up a second-order polynomial and see if you can fit the above function.\n",
    "Feel free to play around with higher-order polynomials.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "04a06b51",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Exercise 1, scale your data\n",
    "\n",
    "Before fitting a regression model, it is good practice to normalize or\n",
    "standardize the features. This ensures all features are on a\n",
    "comparable scale, which is especially important when using\n",
    "regularization. Here we will perform standardization, scaling each\n",
    "feature to have mean 0 and standard deviation 1.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "408db3d9",
   "metadata": {
    "editable": true
   },
   "source": [
    "### 1a)\n",
    "\n",
    "Compute the mean and standard deviation of each column (feature) in your design/feature matrix $\\boldsymbol{X}$.\n",
    "Subtract the mean and divide by the standard deviation for each feature.\n",
    "\n",
    "We will also center the target $\\boldsymbol{y}$ to mean $0$. Centering $\\boldsymbol{y}$\n",
    "(and each feature) means the model does not require a separate intercept\n",
    "term, the data is shifted such that the intercept is effectively 0\n",
    ". (In practice, one could include an intercept in the model and not\n",
    "penalize it, but here we simplify by centering.)\n",
    "Choose $n=100$ data points and set up $\\boldsymbol{x}$, $\\boldsymbol{y}$ and the design matrix $\\boldsymbol{X}$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a140aac7",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# Standardize features (zero mean, unit variance for each feature)\n",
    "X_mean = X.mean(axis=0)\n",
    "X_std = X.std(axis=0)\n",
    "X_std[X_std == 0] = 1  # safeguard to avoid division by zero for constant features\n",
    "X_norm = (X - X_mean) / X_std\n",
    "\n",
    "# Center the target to zero mean (optional, to simplify intercept handling)\n",
    "y_mean = y.mean()\n",
    "y_centered = y - y_mean"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d861e1e3",
   "metadata": {
    "editable": true
   },
   "source": [
    "Fill in the necessary details. Do we need to center the $y$-values?\n",
    "\n",
    "After this preprocessing, each column of $\\boldsymbol{X}_{\\mathrm{norm}}$ has mean zero and standard deviation $1$\n",
    "and $\\boldsymbol{y}_{\\mathrm{centered}}$ has mean 0. This makes the optimization landscape\n",
    "nicer and ensures the regularization penalty $\\lambda \\sum_j\n",
    "\\theta_j^2$ in Ridge regression treats each coefficient fairly (since features are on the\n",
    "same scale).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3e774d0",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Exercise 2, calculate the gradients\n",
    "\n",
    "Find the gradients for OLS and Ridge regression using the mean-squared error as cost/loss function.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5dc7708",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Exercise 3, using the analytical formulae for OLS and Ridge regression to find the optimal paramters $\\boldsymbol{\\theta}$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "77c59cc4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def Ridge_parameters(X, y, lam = 0.01):\n",
    "    # Assumes X is scaled and has no intercept column\n",
    "    return np.linalg.inv(X.T @ X + lam * np.eye(X.shape[1])) @ X.T @ y\n",
    "def OLS_parameters(X, y):\n",
    "    return Ridge_parameters(X, y, lam = 0.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "97ac6cb6",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Closed-form Ridge coefficients: [ 5.02716096e+00 -2.88896347e+00 -1.55169486e-02  1.52287662e-01\n",
      " -6.93302234e-02 -4.47229113e-02  1.76836298e+00  4.62139092e-03\n",
      "  4.41380481e-02 -4.96664608e-02]\n",
      "Closed-form OLS coefficients: [ 5.03241281e+00 -2.89258175e+00 -1.55189951e-02  1.51795012e-01\n",
      " -6.83299260e-02 -4.40147965e-02  1.76999871e+00  4.37643569e-03\n",
      "  4.52550260e-02 -4.97610000e-02]\n"
     ]
    }
   ],
   "source": [
    "# Set regularization parameter, either a single value or a vector of values\n",
    "lambda_ = 0.1\n",
    "\n",
    "# Analytical form for OLS and Ridge solution: theta_Ridge = (X^T X + lambda * I)^{-1} X^T y and theta_OLS = (X^T X)^{-1} X^T y\n",
    "I = np.eye(n_features)\n",
    "theta_closed_formRidge = Ridge_parameters(X_norm, y_centered, lam=lambda_)\n",
    "theta_closed_formOLS = OLS_parameters(X_norm, y_centered)\n",
    "\n",
    "print(\"Closed-form Ridge coefficients:\", theta_closed_formRidge)\n",
    "print(\"Closed-form OLS coefficients:\", theta_closed_formOLS)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eeae00fd",
   "metadata": {
    "editable": true
   },
   "source": [
    "This computes the Ridge and OLS regression coefficients directly. The identity\n",
    "matrix $I$ has the same size as $X^T X$. It adds $\\lambda$ to the diagonal of $X^T X$ for Ridge regression. We\n",
    "then invert this matrix and multiply by $X^T y$. The result\n",
    "for $\\boldsymbol{\\theta}$ is a NumPy array of shape (n$\\_$features,) containing the\n",
    "fitted parameters $\\boldsymbol{\\theta}$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1c215d5",
   "metadata": {
    "editable": true
   },
   "source": [
    "### 3a)\n",
    "\n",
    "Finalize, in the above code, the OLS and Ridge regression determination of the optimal parameters $\\boldsymbol{\\theta}$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "587dd3dc",
   "metadata": {
    "editable": true
   },
   "source": [
    "### 3b)\n",
    "\n",
    "Explore the results as function of different values of the hyperparameter $\\lambda$. See for example exercise 4 from week 36.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "99dc481e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Feature Coefficients ($\\\\theta^\\\\lambda_i - \\\\bar{\\\\theta}_i$)')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAqYAAAJVCAYAAAAMfTcoAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjUsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvWftoOwAAAAlwSFlzAAAPYQAAD2EBqD+naQABAABJREFUeJzs3XdcU9f7wPFPAmGEsPdGcIGoOHDvvfeqbV3dtrbWTrv3sHvXLq2dfmtrbbVaR91bcYsbENkbwobk9wcQiARlWbC/5/198fo2J+fec/LkJHnuuedeFXq9Xo8QQgghhBBNTNnUHRBCCCGEEAJJTIUQQgghRHMhiakQQgghhGgWJDEVQgghhBDNgiSmQgghhBCiWZDEVAghhBBCNAuSmAohhBBCiGZBElMhhBBCCNEsSGIqhBBCCCGaBfOm7oAQQghxM9BqtWi1WqMye3t7rK2tm6xPQvzXyIypEEIIUQtvv/02np6eRn8rV65s6m4J8Z+i0Ov1+qbuhBBCCFEXXl5eaDQadu3ahZub27/S5qVLl7h06ZJRWbt27fD09PxX2hfi/wNJTIUQQtx0iouL6dy5M4sXL2bmzJlN3R0hRCORU/lCCNHIDh48SK9evbCxsUGhUHD06NEay5cvX45CoSA6OrrW+6/PNs3JkiVLaNu2LTqdrtpzJSUlvPrqq7Ro0QK1Wk3//v05d+5ctXoqlYpu3bpx4sSJf6nXte9bhc8//xw/Pz8KCwv/tT4KcbOTxFSIm1hFgmLq78knn7whbe7Zs4cXXniBzMzMG7L/xnLx4kXuueceAgMDsbKyws7Ojt69e/PBBx+Qn59/w9otLi5m6tSppKen89577/Hdd9/h7+9fY3lzdiPe6+zsbN58802eeOIJlErjn6DS0lImTZrEe++9x5133smrr77K6dOnGTt2LCUlJUZ109PTWbt27b+WmNalbxXmzJlDUVERS5cu/Vf6KMR/gl4IcdNatmyZHtC/9NJL+u+++87o78iRIzekzbfeeksP6KOiom7I/hvD2rVr9dbW1noHBwf9gw8+qP/iiy/0H3/8sX7GjBl6lUqlv+uuu25Y25GRkXpA/+WXX9aqvKSkRJ+fn6/X6XS1bqM+29THjXiv33vvPb2dnZ0+Pz+/2nNvvPGGXq1W60+ePGko++GHH/SAftOmTUZ1Z82ape/Xr5/ez8+v0fp2LXXpW1WPP/643t/f/4a/V0L8V8jtooT4Dxg5ciRdu3Zt6m40WG5uLjY2Ng3aR1RUFDNmzMDf359//vnH6MKU+++/nwsXLrBu3bpG6K1pycnJADg4ONSq3MzMDDMzszq1UZ9tmotly5Yxbtw4rKysjMqzsrJ47bXXWLhwIe3atTOU9+rVC4Bjx44xZMgQADZu3Mj+/fv5559/8PHxISsrC3t7+xvW57r07WrTpk1jyZIlbN26lUGDBt2wPgrxXyGn8oX4fyAuLo558+bh7u6OpaUl7dq145tvvjGqExMTw/z582nTpg3W1tY4OzszdepUo3WML7zwAo899hgALVq0MCwbqKgzZ84cAgICqrX/wgsvoFAoTJadPn2amTNn4ujoSJ8+fWrd35osWbIErVbL119/bfJq6ZYtW/LQQw8ZHh85coSRI0diZ2eHRqNh8ODB7Nu3r15xnDNnDv379wdg6tSpKBQKBgwYUGM5NawXjYuL44477sDLywtLS0tatGjBfffdR1FRUY3b1DZuFXG/cOECc+bMwcHBAXt7e+bOnUteXp5RvZre65ycHBYuXEhAQACWlpa4ubkxdOhQIiIirvneREVFcfz4cZNJ3A8//EBOTg533323UblKpQIgJycHgLy8PObPn8/XX3+Nl5cXPj4+nDx58prtNlRt+2ZKly5dcHJyYs2aNTe0j0L8V8iMqRD/AVlZWaSmphqVubi4AJCUlESPHj1QKBQ88MADuLq6sn79eu644w6ys7NZuHAhlF+Ys2fPHmbMmIGPjw/R0dF89tlnDBgwgNOnT6NWq5k0aRLnzp3jp59+4r333jO04erqWu++T506lVatWvHaa6+h1+tr3d+a/PnnnwQGBhpms67l1KlT9O3bFzs7Ox5//HFUKhVLly5lwIABbN++ne7duxvq1qZf99xzD97e3rz22ms8+OCDhIeH4+7ujkajMVluSnx8PN26dSMzM5O7776btm3bEhcXx6pVq8jLy8PCwsLkdnWN27Rp02jRogWvv/46ERERfPXVV7i5ufHmm28CXPO9vvvuu1m1ahUPPPAAISEhpKWlsWvXLiIjI+ncuXON8d6zZw+AyTq//fYbISEh2NjYGI3l2NhYAMNM+jPPPMOoUaPo3bs3AB07duTEiROGxzdCbftWk86dO7N79+4b1j8h/lOaei2BEKL+KtaYmvqrcMcdd+g9PT31qampRtvOmDFDb29vr8/Ly9Pr9XrD/1e1d+9ePaBfsWKFoexa6w5nz56t9/f3r1b+/PPP66/+uqkou+WWW4zKa9tfU7KysvSAfvz48TXWqWrChAl6CwsL/cWLFw1l8fHxeltbW32/fv3q1a+tW7fqAf0vv/xiVK+m8or3sCKes2bN0iuVSv3Bgwer9bdineLV29SlfxVxnzdvnlG9iRMn6p2dnY3Kanqv7e3t9ffff3+1/l3PM888owf0OTk5RuUlJSV6GxubGsdyRdwOHDigDwoK0mu1WsO2Tz/9tH7+/Pl17ktt1bZv13L33Xfrra2tb1gfhfgvkVP5QvwHfPLJJ2zatMnoj7JMkF9//ZWxY8ei1+tJTU01/A0fPpysrCzD6deq/6xicXExaWlptGzZEgcHh+ueom2Ie++91/DfdemvKdnZ2QDY2tpet93S0lI2btzIhAkTCAwMNJR7enoyc+ZMdu3aZdhfQ/tVWzqdjt9//52xY8eaXDN89XKICvXpX9W4A/Tt25e0tDTDa74WBwcH9u/fT3x8fJ1eX1paGubm5mg0GqPyixcvkpuby+OPP15tHN9yyy0AdOjQgfDwcC5cuGA0Q/nKK6/wySef1NimTqejoKCgVn+mbutd274BFBYW4u7uXi2Gjo6O5OfnGy2VEEKYJqfyhfgP6Natm8lEJiUlhczMTL744gu++OILk9tWXJSTn5/P66+/zrJly4iLizP6kc7KyrphfW/RokW9+muKnZ0dXGfNX9W28vLyaNOmTbXngoOD0el0xMbG0q5duwb3q7ZSUlLIzs4mNDS0ztvVtX9+fn5Gjx0dHQHIyMgwxLEmS5YsYfbs2fj6+tKlSxdGjRrFrFmzjBL8uqhYKztgwIBq60/feOMN3N3dad26db32vWPHDgYOHFirupGRkbRt27befbO0tCQpKanafis+SzUdWAghKkliKsR/WMUNzG+77TZmz55tsk7FbM+CBQtYtmwZCxcupGfPntjb26NQKJgxY4bJG6GbUtMPb2lpaY3bVJ2prUt/TbGzs8PLy6vRL4ZpaL9utPr0r6ar+mvzjwFOmzaNvn37snr1ajZu3Mhbb73Fm2++yW+//cbIkSNr3M7Z2ZmSkhJycnKMZrVzc3PBxFrNrKwsdu7cybx58wxlhYWF+Pn5cf78+esm0ABt27Zl2bJl161H+Wz51erSt5pkZGSgVquNxroQwjRJTIX4D3N1dcXW1pbS0tIab2dTYdWqVcyePZt33nnHUFZQUFDt5urXmvVxdHQ0eTP2mJiYRu9vTcaMGcMXX3zB3r176dmz5zXbUqvVnD17ttpzZ86cQalU4uvr22j9qg1XV1fs7OzqnFjfqP5d67329PRk/vz5zJ8/n+TkZDp37syrr756zcS0YjYyKirKKFGuSFK1Wq1R/W+//ZaioiLuu+8+Q1lNs5I18fDwYM6cObWuf7W69O2DDz7g+PHjfP3110Z1o6KiCA4OrncfhPj/RNaYCvEfZmZmxuTJk/n1119NJjspKSlGda+eLfvoo4+qzXZWzByZSkCDgoLIysri+PHjhrKEhARWr17d6P2tyeOPP46NjQ133nmnyQTm4sWLfPDBB5iZmTFs2DDWrFljdNulpKQkfvzxR/r06WOYkWuMftWGUqlkwoQJ/Pnnnxw6dKja8zXNZt6o/pl6r0tLS6st7XBzc8PLy+u6//RmxYHC1a+tQ4cOKJVKtm7daii7cuUKL7/8MrNmzWrS2ei69O348eMm+xoREVGru0QIIWTGVIj/vDfeeIOtW7fSvXt37rrrLkJCQkhPTyciIoLNmzeTnp4O5TON3333Hfb29oSEhLB37142b96Ms7Oz0f66dOkCwNNPP82MGTNQqVSMHTsWGxsbZsyYwRNPPMHEiRN58MEHycvL47PPPqN169a1vjiotv2tSVBQED/++CPTp08nODiYWbNmERoaSlFREXv27OGXX34xzKC98sorbNq0iT59+jB//nzMzc1ZunQphYWFLFmypFH7VVuvvfYaGzdupH///tx9990EBweTkJDAL7/8wq5du6rdoP9G9s/Ue923b1/atGnDlClT6NixIxqNhs2bN3Pw4EGj2XZTAgMDCQ0NZfPmzUanwN3c3JgwYQIffPABarUae3t73n//fby9vfnoo4+M9lHTrOSNUpe+HT9+nNtuu82o7PDhw6SnpzN+/Ph/pb9C3PSa+rYAQoj6q7htkKlbC1WVlJSkv//++/W+vr56lUql9/Dw0A8ePFj/xRdfGOpkZGTo586dq3dxcdFrNBr98OHD9WfOnNH7+/vrZ8+ebbS/l19+We/t7a1XKpXVbie0ceNGfWhoqN7CwkLfpk0b/ffff3/N20WlpKTUq7/Xc+7cOf1dd92lDwgI0FtYWOhtbW31vXv31n/00Uf6goICQ72IiAj98OHD9RqNRq9Wq/UDBw7U79mzp95xbOjtovR6vT4mJkY/a9Ysvaurq97S0lIfGBiov//++/WFhYU1blPb/tUU95r2efV7ffbsWf1jjz2m79ixo97W1lZvY2Oj79ixo/7TTz+t1fvy7rvv6jUaTbXbfqWnp+snTZqkt7Gx0bu7u+sXLFigz87Orrb9vHnz9O+//36t2mostelbaWmpXq1WV7td1xNPPKH38/OTf5JUiFpS6Guz0l0IIYRoBFlZWQQGBrJkyRLuuOOOOm8fHh7OkiVLan2l/b/l3LlzDBgwwOgWWoWFhQQEBPDkk08a/WtjQoiayRpTIYQQ/xp7e3sef/xx3nrrrVrf7aGCTqfj9OnTTbrmtCam1pcuW7YMlUpV7Z6xQoiayYypEEKIm4KpWcnm4vnnnyc/P7/a2mQhRN3IxU9CCCFuCjVd9d4cvPjii03dBSH+E+RUvhBCiJvCiRMnmm1iKoRoHHIqXwghhBBCNAsyYyqEEEIIIZoFSUyFEEIIIUSzcFNf/KTT6YiPj8fW1vaa/6azEEIIIYRoGnq9npycHLy8vFAqrz0nelMnpvHx8fj6+jZ1N4QQQgghxHXExsbi4+NzzTo3dWJqa2sLQI+f78JcbdHU3RFCCNFECktu6p+zJpOcbtfUXbjptLjzeFN34aZTQjG7+MuQt13LTf1Jrjh9b662wNzGsqm7I4QQoomUSmJaL8oCq6buwk3HXKFq6i7cfMrv/1SbZZdy8ZMQQgghhGgWJDEVQgghhBDNgiSmQgghhBCiWZDEVAghhBBCNAuSmAohhBBCiGZBElMhhBBCCNEsSGIqhBBCCCGaBUlMhRBCCCFEsyCJqRBCCCGEaBYkMRVCCCGEEM2CJKZCCCGEEKJZkMRUCCGEEEI0C5KYCiGEEEKIZkESUyGEEEII0SxIYiqEEEIIIZoF86buwL/hp55P42HtVK389yu7+eDcbya3sTG34s7AUfR1bY+tSk1SQQafnP+d/WlnABjn3ZNx3r3wsCrbb3RuIiuiNnEg/UyD+9vftQPzAkfiYeXIlfxUvri41tAuwOwWwxjk1glXK3tKdKWcy7nC15fWE5l9ucFtVyVxq7sbEbOZ/oPo69oeP7UbhbpiTmXF8MXFtcTmpTS4v80hZtyguAFM8O7NdL8BOFnYclEbz4fnVnMmJ7bB/W0OcatPzCoMdAvjudDb2ZVykmdPLDN6zk/txt1BY+joGIiZQklMbhLPn/iW5MLMBvW3OcSsgoulHfe3GkkPlzZYmVlwJS+VV0/9wpnsOJP1OzkG8kn4PdXKx2x7mfQireHxJN+e3BrQDycLWy5oE3g3cg2R2Vca3N+B7u25u+WwstjlpfLp+fXsTT1reP6OoCEM8eiIm5UDxboSzmbHsfTC35zOavhYr+rSLU+ZLH/9yBa+PLO/xu3crTU8ETaI/p6BWJupiNFm8Pj+tZxIT6xW95WuI5jZqjMvR2xi2dmDDe7z7a26cFfb7rhaa4jMSOKFwxs5np5geP7HQbfSw93faJsfz0fwzKENDW7blIc+u4sx9wzj04eXsfqDv2q1zfQnJnDn67fy2wfr+Ozh5SbrvLruKbqN7MTzE5ewZ03D4zb7xemMvHMwGgcbTu0+w4fzvyTuQtn75e7vyq3PTiFsYChOHg6kxaez5Yed/Pjqb5QUlzS47WaRmH7yySe89dZbJCYm0rFjRz766CO6devWaPu/99D7KBWVk8MtbDx4p9O9bEs+ZrK+ucKMt8PuIbNIywsnvyWlMAsPK0e0JfmGOikFWXx5cR1X8lJRAMM9w3mlw1zuPvgu0blJ9e5rO7sAnm13G19e+ou9qacZ7N6Zl9vP5e6D7xGdWzYoruSl8MG530jIT8PSTMUU3/4sCbub2/a+TlZxbr3bvprEre5uRMw6OgTx+5U9nM25jJlCyZ2Bo1gSdjdz971Fga6o3n1tLjHjBsVtoFsY97Uax3tnVxGZdZkpvn1ZEnY3s/a9SWax1uR+a6O5xK2uMavgbuXIfS3HcizzYrXnvKyd+bDLA6yPP8DyqL/JKy0gwMaDIl3DfmyaS8wAbM2tWdrtPiLSL7Eo4hsyi3PxVbuQU5x/3W2n73qL3JICw+OMosp+DXbvwINtxvDW6dWcyrrMdP8+vNflDm7Z/bZRvboKtffnxfa38PmFDexOOcMwjzDeCJvF3H0fcklb9p15OTeVdyLXEJ+fjqVSxXT/Przf+U6m7VpCZiPGrtvqD4weD/AM4o3uo9kQe7bGbexUVvwyZBb7kmOYu20l6YV5BNg6kVVUUK3uMJ/WhLl4k5iX0yj9He0XzFOdBvPswQ0cTYtnbptwvh04gyFrl5JWmGeo99OFI7x3YofhcUFJcaO0f7XeE7oR3L01qXHptd6mddcgRt89lIvHomusM2nhaNDrG6mXMP3x8UxYMJIlcz4mMSqZOS/N4PUNz3BHu4cpLizGt603SoWCD+5dStyFRFqE+vHwF/dgZWPJF4991+D2mzwxXblyJYsWLeLzzz+ne/fuvP/++wwfPpyzZ8/i5ubWKG1c/aU2038QcXmpJr+YAUZ6dsNWpeaBwx9RqtcBkFSQYVRnb9ppo8dfX1rPOO9ehNj5GxIsG3Mr7ms5jt4u7VApzTmbE8un59dwUZtATSb79uVA+llWXt4GwLKoDXR1as1En968d/ZXALYkHTHa5tPzaxjt1Z0gjRcRGefrEJlrk7jV3Y2I2RPHvjR6/Ebkz/ze9yVa2/lwPPMS3OQx4wbFbapvP9bF72NDQtnswbtnf6W7SwgjvbrxU8w/cJPHra4xA1Ci4JmQW1ke9TftHQLRmFsbPX9H4Ej2p0Wy9OJaQ1l8fppRnZs5ZgC3tehPUkEWr576xVCWkJ9xzW0qZBRp0ZZUT6gAZgT05Y8rB1gXfwiAJadX08ulLWO8wvkuuux1a8yteKD1aPq6hWChNOdM9hU+OLOWC9eI3TT/3uxPO8eP0WWJ05cXNxLu3IrJvr14K3I1AJsSjxpt8+HZtYzz6UaQrQeH02seD3WVWmA85ob4tGJfUgyxuTXPpt8b0oOEvBwe37/OUHYlN6taPXdrDc93GcacrT/zdf9p1Z73VNvyVKch9PVogU6v52BKLC9FbCLOxL4q3NGmGysvHmVV1HEAnjm4noFeLZka2JHPI/ca6hWUFld7bY3N2cuJ+z+cx+IRr/DK2sW12sbKxorF3z/Ie3d/zq1PTzZZJ6hjAFMWjeX+8Cf5X8KX1Z4PaOfLXUtup33fYApyCzi88TifLVpOdlrNyf/Eh0bzw6u/svePsrH85uyP+SXxS3pPCGfbyj0c+vsoh/6uHHOJUcn4vOPF2HuHNUpi2uRrTN99913uuusu5s6dS0hICJ9//jlqtZpvvvnmhrRnrjBjqHsX1iccqLFOL5d2nM6KYWHrSfza5wW+6fYot/oPRonCZH0lCga6hWFlZsGprBhD+Quhs3FQaXji2Jfcc/A9zufE8U7Yfdhe9WNQVYi9P4fTzxmVHUw/Szu7gBpfzxivnmiL87mgja9FBOpH4lZ3NyJmlCcGANnFlUf8/5WY0UhxM1eY0drWh8PplQmNHj0R6edoZ1d52u6/ErfaxAxgVothZBRr+ctEPQUKejgHcyUvhSUd7+a3Pi/waZcH6e0SalTvZo9ZH9cQzmRf4ZUOt7JuwLMs7/Eg47xrd4bu254P8Uf/p3m/y520d6gcR+YKM9rYenMozXi8HUy/QKiDn6HslY634Wih4ZGIb5i770POZsfzYde7rhm7UHt/DqZdMCrbn3bOaL9VmSvMGO/TnZzifC7k1JzwNpSLlQ0DvVryv0tHr1lvsHdrTqQn8HHviRyY+BB/jpjH9KAwozoK4J2e4/gycj/ns1Or7cNcoWT5gFvILS5k+ubvmLp5BXklRSwfMAOV0nQao1IqCXXyZHdi5UyjHtidFEUnF2+juuP8Qzk0aSHrR97FYx0HYGXWuHN2CoWCJ1Ys4Je3/yDmdO2Xdiz4+A72/xXBkS0nTD5vaW3B4h8e4qMHviIjqfrBgY29miVbnufi0SjuD3+CxSNfxdHdnmdWLqqxTY8Wbjh7OnJkc2Wbedl5nNl/gZCebWrczsZeTU56/c9EVdWkM6ZFRUUcPnyYxYsrjx6USiVDhgxh796919y2vvq4hqIxtzLMopjiZe2Mh1VLNidFsPjYV3hbu/BQm0mYKcxYEb3RUK+FjQefdHkQC6U5+aVFPHdiGTF5ZbN+ofYtaGvny6Sdz1OsLwXg8wt/0scllP5uHVkbv89k204WtmRcdZoxoygHR0tbo7IezsE81+52LM1UpBXl8OjRpWQ34imbq0nc6q4xY1ZBgYIHWk3gRGaU4RTofylmNFLc7FU2mCnNyCgynhXIKNLipy47E/NfilttYhZq34JRnt248+C7Jp93sNCgNrfiFv9BfHNpA0svrqWbc1teaj+bRUc+41jmpf9EzLysnZjo04OfY3ayImorwXY+PNx2HMX6EtbHR5jcJq0wmzdP/8aZrCuolOaM8wnnk673cOf+jzmXE4+DhRpzpZnRelOA9MIc/G1cAejgEECInS+jt71kiN3H59bRzy2EQe7tWRNn+qDC2VJjYhzn4GxhHLteLm15qcNMrMxUpBXmsPDwV2RVOXhtbJNatCe3uOiap/EB/DQO3NqqM1+f2c+np/fQwcmT5zsPpVhXym9RZcnPvSE9KdXpWH7O9Pgd7R+MUqHgyQOVazIf37+Wo5MfobubP7sSo6pt42ipxlyprDYTmlqQS5Cts+HxHzGniMvNIjlfS1sHNx4PG0igrTP37fq1zjGpyfQnxqMrKWX1h7VbUwowYHovWnUO5P5uT9ZY59735nB671nDzObVxj8wgotHovjm6Z8MZW/f8Sk/xS7Fu5UnceerH7g4eTgAVEt0M5IycXR3MNmOV5AHEx4YydLHVtT69V1LkyamqamplJaW4u7ublTu7u7OmTPVL4YpLCyksLDQ8Dg7O7vObY7y7M7+9DOkFdW8rUKhIKNYyztnfkGHnnM5V3CxtGO630CjZCE2L4U7D76Dxtyafq4deDL4FhZGfEpMXhItNV5Ym1mypu/LRvu2MFPhZe2Mm6UDy7s/bij/IWYLP8RsqfXrOJpxkTsPvoO9yoYxXj14PvR25h/6sEFr565F4lZ3jRmzCg+1nkQLGw8WRHxsKPsvxYwbFDdT/ktxu17MrM0seSrkFt4+80uNiV7FbPOelFOsii07bXxRG087uwDGevfiWOal/0TMlAoFZ8ovDgI4lxNPoMaDiT49akxML+elcjmvcibvZFYM3tbOzPDvy0snV9aq3Za2nlibW7B+4PNG5ZZmKrzVzrhbOfBDr8qZrBVRW1kRtbXWrysi4yKz936Ag4UN47y78XLHW7lr/8f1Xt863r8dr4SPNDyet30lB1MqL6aaGtiRNTGnKNKVXnM/ChScSE/g7ePbATidkURre1dmtuzEb1EnCHX0YE7rcMb+XfNZ0mAHd/w1jpyY8qhRuaWZOf4aRwpdS/im/3RD+TMH17M3OcbEnqr7+WLljO/ZrBSSC7T8MOhW/DQOXNbW/YK/QTP7sPDzygvlnhnzOhMfHM38Lo9fc7uqXH2cmf/+XJ4Y9jLFhabXu/Yc25VOA0O5t3PN+w3qEEDHgaH8kV399LpXkDttwoOM+vrUqFfRlepq3U/Klyi8tv5pdqzay/qvav9Zv5YmX2NaF6+//jovvvhivbd3t3Kks1Mrnj9h+qq2CumF2ZToS9FRuZg4JjcZZ0s7zBVmlJQf7ZboSw3rr87lXKGtnS+Tffvy7tlVWJlZkF6YzcIjn1bbv7akAG1JPncefMdQllN+ZJtelIOjSmNU39HCloxC4yPmAl0R8flpxOenEZl9me96PMkor278WL52rjFJ3OqusWMG8GDrifR0CeGhiE9ILaxcV/VfiRmNGLes4lxKdaU4XjWr5GihIb189um/ErfaxMzL2hlPa2de6zDPUKZQlCWimwcsYdb+N0kuyKREV0p0nvFFiJfzkmhv3wL+IzFLK8whSmv8GqNzkxngHlrjNqaczo6lo0PZUoTMojxKdKU4WRi/RidLW9LLX6PazIK0whzuP7i02r60JfloSwqYvbfy4qKKpTpphVoT49iWtKtmUQtKi4nLTyMuP41TWZdZ2fsxxniH813Utjq9rgqb485zNK1yGUVifmV74a6+BNk5s2D36uvuJ6VAy4WrTs9fzE5jhG/bsn25+eJsZcOucQ8YnjdXKnkqbDBzW4fT789PsTG34GR6Ag/v/aPa/tML8yjSlTJmw9eGstSCXIp0JZTodLhY2RjVd7GyIeUa60mPppa9Zn+NY70S071/HOLM/sqlF/2m9sDBzY4fYj4zlJmZm3HP27OZ9NBobg+8v9o+WnUJxNHdgc8OLzHapn2/YMbfP4JRVjMJGxSKZ5A7v2cYf+6fW/UoJ3dG8uigF7DSWLHvz0N89eQP1dpIT8hAoVQY9TU1Lh0nz7JZUUd3B9ITK1+/o7tDtQuwnD0defuf5zm95yzv3V19XNdXkyamLi4umJmZkZRk/CWRlJSEh4dHtfqLFy9m0aLKI8rs7Gx8fX1r3d4Iz3Ayi7TsTYu8Zr2TWVEMdu+MAgX68h8+X7UrqYVZRonC1RQKBSplWUjP58ThZGFLqV5X7aKMCldfVABwOiuGzk6t+PXKTkNZF6fWnMqu+Yq8q9tubBK3umvsmD3YeiJ9XNvzcMSnJBYYX9H5X4kZjRy3czlX6OzYit2pJ8v6jYLOjq1YHbcb/kNxq03MLuclM3f/W0ZldwSORG1myUfnfy9LSvWlnMmJxVftalTPR+1qiM9/IWbHM6PxszF+jb42LiQW1C0JaWXrRWp50lmiL+VsThxdnFuyI6XsAk8FCro6teTXy3sAOJsdj5OFhlK9jsQaYhdnInYns2Lo6hzE/y7vMpR1c27Fycxr30ZLqVBg0YDY5ZYUkas1fdePqYEdOZGWwJnM5Ovu53DKFQKrnDoHaGHrZLhoaXXUSaN1oADLB8zg9+gT/HKp7KKlkxmJjPYLJq0gF22J6T7FaKvH9GR6Ar08AtgUV7a+WQH0cg/gu3OHa+xviGPZGdyUgvrN0udrC8jXVt4Ga90Xm9n3p3F7r294hs3f7+DvZaZnxI9sOcFd7Y3XgT76zXxiz8Szcsnv6HQ6fn7j92ozlF+eeJfPFy03tHfhSBR9JnUnMTq5xpnQqn2l/EKmtIQMOg0ONSSialtr2nZvyZ+f/22o5+zlxNv/PM/5w5d4e96n6BvxrgBNevGThYUFXbp0YcuWyuDqdDq2bNlCz549q9W3tLTEzs7O6K+2FCgY4RnO34mH0OmN36DFwbdwZ+Aow+M1cXvLrvhtNQEfaxd6OAczM2Awv1/ZbahzZ+AoOjgE4m7lSAsbD+4MHEWYQxCbE8tOBR3OOMep7BheaT+Xrk6tcbdypJ1dAHcEjqS1rU+N/fw1difdnNoy1bc/vmo3ZrcYRhtbH1aXt22ltODOwJEE2/nhbuVIa1sfHm87HVcLe7Zf5zYx9SFxa/qYLWw9iaHuXXj11PfklRbiaGGLo4Wt4UfnvxCzGxG3X2J3MMarO8M9uuKnduPhNpOxMrNgQ/yB/0zcahuzYl0J0bmJRn/aknzySguJzk00JPMrY7Yy0C2M0V7d8bJ2ZoJ3b3o5h/B73J7/TMxWxuwi1N6PWS0G4m3tzFCPMMb7dDckkAD3thzBs6GVV4ZP8+tDX9cQvK2dCdS481CbsXRxCuLX2Mptfo7eyTjvboz06oy/jRuPBU/EykzF2vKr9A+mn+dk1mXeCJtFN+dWeFg5Emrvzz0th9PWzpua/C9mNz2c23CLf1/81a7cETSEtnbehratzFTc03I47ez98LByoI2tN0+1m4KLpR3/JJq+aKYhNOYWjPJry8oaLnr6fuBMbm/VxfD4m7MHCHPxYn5IL/w1jozzD2FGyzC+P1+WPGUW5XMuK8Xor0RXSkpBLlE5ZQfha6JPklGYx9J+Uwl39cXHxp7ubn4813koHta2JvsB8PXZA8wICmNSi/YE2TnzcvhI1OYqw1X6fhoHHmjXm1BHD7xt7Bns3Yq3e4xlf/JlzmQ2/D7RADnpWqJPxRr9lRSXkJ6YwZVzlTPSSzY9x/j7R0B5cnv1NgW5hWSn5xB9qmw5RUZSZrU6AMmXU0mMLjtg+OOTDdg6aXj6x4W07hqEZ6A7XYd15NGv56Os4aIxgNUfrGPm05PpObYrAaF+PP7tA6TFZ7D797I1wM5eTryz9QWSL6ey9LHvsHe1w9HdocY1qHXV5KfyFy1axOzZs+natSvdunXj/fffJzc3l7lz5zZqO12cWuFh5cT6+Oo3AXazcjA6JZhSmMnjR7/g/lbj+brbo6QUZfFb7E7DLWYoPyW4OPgWnCztyC3J55I2gcePfsnhjMorT5889hV3Bo7k8eAZOKhsSC/K4XjmJTKKaj4SO5UdzSunvmde4EjuDBpFXF4Kz55YZrjQpRQdvmo3Xmwfjr3KhuziXM5mx/JgxCcNug9oTSRuddfYMRvv0xuA9zsbn/J54/TP/J1Y9kVxs8eMGxC3rclHsVfZMCdwOE4WdlzMieOJY18aXYRzs8etLjGrjV2pJ3nv7K/M9B/EglYTic1L5vmT33Iyq/Likps9ZpHZV3jy6AruazWCuYGDScjP4IMzf7Kxyi2XnC1tcbeq/JFVKc1Y0GY0rpb2FJQWcUGbyEOHviQi45Khzpak4zhY2HBX0DCcLG05nxPPoohvjOLyaMQ33NNyBE+3m4qDhQ1phVqOZVwivbDm2J3MiuH5Ez9xd8vh3NNqBFfyUnny6ArDPUx1ej3+Nm6M8uqCvYUNWUV5nMmOZf7Bz4m6AZ/TMf4hKFDwZ8xpk8/7aRxwslQbHh9PT+C+nb/yWMcBLAjtQ6w2k5cjNrMm5lSt2ywoLWH6lu95Imwgn/aZjEZlQWJeDnuSotEWF9a43brLkThZqnm4fT9crGyIzEhizraVhguiinWl9PZowdw24ajNLUjIy2bDlTN8cnJ3jfu8UTyD3LFzqTnJro+0hAwe7vMMd75xG2/8/QwqSxXJMSkc/PsoOl3Na0lXLlmDlY0VC5feg8ZBzcldZ1g88lXDetcuQzvg3coT71ae/HzF+BT+UOXUBvdboW/M+dd6+vjjjw032A8LC+PDDz+ke/fu190uOzsbe3t7+vxxP+Y2lv9KX4UQQjQ/hSVNPs9yU0pMs2/qLtx0gm49UotaoqoSfTHbWENWVtZ1z3Y3i0/yAw88wAMPPFCLmkIIIYQQ4r+qyW+wL4QQQgghBJKYCiGEEEKI5kISUyGEEEII0SxIYiqEEEIIIZoFSUyFEEIIIUSzIImpEEIIIYRoFiQxFUIIIYQQzYIkpkIIIYQQolmQxFQIIYQQQjQLkpgKIYQQQohmQRJTIYQQQgjRLEhiKoQQQgghmgVJTIUQQgghRLMgiakQQgghhGgWJDEVQgghhBDNgiSmQgghhBCiWTBv6g40hphzHiitrZq6G0II0TgUTd2Bm49eqW/qLtyUzOyKm7oLN52/4482dRduOtk5Ohxb166uzJgKIYQQQohmQRJTIYQQQgjRLEhiKoQQQgghmgVJTIUQQgghRLMgiakQQgghhGgWJDEVQgghhBDNgiSmQgghhBCiWZDEVAghhBBCNAuSmAohhBBCiGZBElMhhBBCCNEsSGIqhBBCCCGaBUlMhRBCCCFEsyCJqRBCCCGEaBYkMRVCCCGEEM2CJKZCCCGEEKJZkMRUCCGEEEI0C5KYCiGEEEKIZsG8qTvwb3p70AimtA01Ktt+OYrZa3+tcZv5nbsxPLA1QQ5OFJSUEJEYxxv7dnApM8NQ5+fx0+nh7Wu03Q+njvL09s0N7vPD4b25JaQ9dpaWHEqI55kdm4jOyjQ8/+XICYS4uOFirSarsIBdV2J4Y+8OkvNyG9x2BYlb3d2omFW1fPRkBvi34O71v7Mx6kKD+9zUMeMGxu21/kPp7eOPu40NucXFRCTG88beHVzMTG9wn5s6bm8PrCFm62qOWTdPH+4OC6e9qzvuNpqyMRRtPIYWdu3F2JZt8NTYUawr5URKEm/v38nR5MQG9/n2dmHcExaOq9qGyLQUnt+1hWNV9vtaPxPv177Geb9MebXvUG4LCePFPf/wzYnDtdrmvrBuPNm9P1+fOMRLe7YC4KOxY/et95iuv2kNf10616B+Luram1vadigba4nxPL1zI9HZlWPtq+ETCXF2w9laTXZhAbviYnh9//ZGGWvu1hqeCBtEf89ArM1UxGgzeHz/Wk6kmx4Pw33acGurzgQ7uGNhZsb5rBQ+OLGTnYlRRvVub9WFu9p2x9VaQ2RGEi8c3sjx9IQG93ekb1sWdeiPj4090TnpvHl0K9sSLhqeX9J9DFMCOxhtsz3hInO3rWxw2wbWM1GobwEzn7LHJefRaz+Goh01b2M5AoXtwrJtSqLR57wFRdsNTyvs30RhPcloE33hDvQZdzS8v+pbUdjcCUpXKD6DPuclKD5e0TAKzYNg2QfMvECXDgWb0WvfA7224W1X8f8qMQXYFhPFY/+sNzwu1JVes353L1++O3GEY8mJmCuVPNajLyvGTmXoT8vILyk21Pvx1DHeO7Db8Di/pKTBfb23UzfmdujEI1vWE5uTxSPd+rBizBSG/ryMwtKyfu+Li+XTiP0k5+birtHwdK/+fDZiHJN/+6nB7Vclcau7GxUzgDs6dEGPvtH62lxixg2K24mUJH4/F0m8Nht7SysWhvdixdgp9P3+S3T6+sexucRt2+WrYlZ67ZipVSoi05L55cwJlo6YYLLOpax0ntu5hcvZWViZm3NHxy6sGDOVAT9+RXpBfr37OiaoDc/0HsAz2zdzJDmBeR06s2LMFAb99A1p+XlQ8X6dv+r9GjOFvj807P0yZXhAKzq5eZGYm1PrbTq4enBrcEdOpyUblcfn5tB1xadGZbcEd+Cejt3YdjmKhri3YzfmhHbmka3lYy28N9+NnsqQ/31jeL/3xl/mkyP7SM7LxcNGw9M9BvD50PFMWvNjg9q2U1nxy5BZ7EuOYe62laQX5hFg60RWUUGN23Rz82VXYhRvH9tGdlEBUwI78GW/aUzatJzTGUkAjPYL5qlOg3n24AaOpsUzt0043w6cwZC1S0krzKt3fzu7ePNBrwm8dWwr/8RfYJx/Oz7vO4Vxf3/DuawUQ71t8Rd5fP9aw+Oi63xu6kyXiD7nbSiNBhQorCeicPwMfdp4KDExmaDqhMLhPfQ570DhVhTWY1E4foo+bQKUnDdU0xduR5/1ZOV2+qKG99VqFArbp9BnPwdFx1DYzEbh+A361GFlSaiZG5i5o895s6zvZl4o7F5CYeaGPnNBw9uvokkT0x07dvDWW29x+PBhEhISWL16NRMmmP6SbCxFpSWk5Nd+wF89U/PolvVEzLuf9q7uHEi4YigvKLn2fls7ufBUz/6Ee3mTV1zMzthoXt69jYxrfMHP69CZjw7vY1N02VHeoi1/cWjOfIa1aMmfF84C8PXxyqP7OG02n0Uc4IuREzBXKinR6Wr9Oq9H4lZ3NypmIc6u3BnWlXG/fMfBufOr7edmjhk3KG4/nT5ueP5KTjbvHNjFhulz8LG143J2FtzkcatrzLZdjrpuovTH+TNGj1/ZvY0ZwR1o6+zKnrjLAHja2PJ0rwH08/VHp9dzMCGOF3f/w5Wc7Br3e2fHrvx8+gS/nD0JwNPbNzHIL5BpbUP57MgBAH6KvOr92l/9/WoM7moNL/YezO1//cKykZNrtY3aXMUHg0bzxI6NLOjcw+g5nV5PSr7x7OSIFq1Yd+kMeVUOLls7uvB0j/6Ee/qUjbUr0by0d+s1x9od7bvwccQ+NsWUJTSLtv7FodvvZ1hAK/68WPZefX3CeKx9enQ/Xw6f2OCxdm9IDxLycnh8/zpD2ZXca78PL0cYn/l6+/h2hvi0ZrBXK0Niekebbqy8eJRVUWXv9zMH1zPQqyVTAzvyeeReAGxVljzVaTBDvFtjYWbGifQEXonYzJnMZBOtlpnTOpwdCRf58sx+AN47sYM+Hi2Y1aoLzxzaYKhXpCshtaDxzvhUU/iP0UO99j0U6pmgCjOZmCrUs6FwJ+R9VV7/fRQWvVGoby9LGA07KgJdas3tKj1Q2C4um91EB0WH0Oe8AqVxNW6iUM+DvJWQX/Z9qs9+DoXlALCeArlflM32Zj5QuUHpZfQ576JweAcwAxovqW/SNaa5ubl07NiRTz755F9rs4e3L4fmzGfLLfN4pd8QHCyt6rS9rYUlAJmFxkeK41sHEzF3Pn9Pn8PjPfpiZV6Z89tZWPLjuGmcSk1i3C/fM2ftr7iobfhk2Nga2/G1s8fNRsPu2BhDWU5REUeTEujs4WVyG3tLKya0DuZwYlyjJgpI3OrlRsTMytycD4aO4bkdm00mIjd7zLiBY62CtbmKqW1DuZyVSYK2bJbsZo9bD6+Gxex6VEolt4R0ILuwgMi0shknc6WSFWOmkFtcxNTff2by6p/ILS7i29GTUSlN/7SolEpCXd3ZfaUyZnpgd9xlOrubjpnh/cqufL8agwJ4f9Aolh47wPmMtFpv93KfIfxz+RK742KuWzfUxZ12Lu6sPHPCUGZnYclPY6dxMi2Zsb99x+y/VuFibcOnQ64x1mzLxtquuKvGWnJCjXGzt7RiQquQRhlrg71bcyI9gY97T+TAxIf4c8Q8pgeF1WkfCkBjbkFmUVnyrVIqCXXyZHditKGOHtidFEUnF29D2Sd9JuFsqWbe9p8Zv+EbTqUn8v2gmdhb1DzGO7t4szsp2qhsZ8Ilo/0C9HDz58DEh9g8+h5e7joCBwvrOr2mulGC1WhQqKHoqOkqFp3QF+0xLivaWZbIGtXrjsJ1HwqXv1HYvQgKhypPmqNwWgb6XPTpt6BPmwH6PBSOXwOqGvqmAlW7q9rWQ9EeFKpO13hJtuWn8Rt3prlJZ0xHjhzJyJEj/7X2tl+OYsOl88RmZ+Fv78Bj3fuyfMxkJv32Y61ODymA5/oM5GDCFc6lVx6trDkfSVxONkm5Wto6u/Jkz34EOjhy74Y/AJjVvhOnU5N4a/8uwzaP/7OBfbPvpYW9I1FZ1dcQuqptAKolHyn5eYbnKjzZox+z2ndCrVIRkRjPvHW/1SM6NZO41d2NitlzvQdyODHOMEN3tZs5ZtzAuAHc1i6Mxb36YaOy4GJGGrf9+QvF5T/YN3PctsdGsSGqPGZ25TEbPZlJq2sXs2sZ5B/IR0PHYG2uIjlXy21/rjLM6o0JaoNSAU9s+9tQ/7GtGzg+bwE9vHzZeaV64uZoZY25UknqVbOKKXm5BDk4GZXd1i6MxT1Nv1+N4b6w7pTo9Cw7GVHrbcYGtSXUxZ1xq7+rVf0ZbdtzPiOVw0nxhrLZ7TpxKjWZtw7sNJQ9tn09+2+7r8ax5lY+nq6OW2p+bvWx1r0fs9t1Qq2yICIpnrnra15rXFt+GgdubdWZr8/s59PTe+jg5MnznYdSrCvlt6gTtdgD3BXcA7W5BX9djgTA0VJdNhaumrFMLcglyNYZgK4uPnR08iR89QcUlS/pef3oPwz1ac1I37b8fNF0gudipTG5X1drjeHxjoRL/H3lLFe0mfhpHHm04wCWDZjO5E3fNu5yEfPWKJz+BwpL0Oehz5gPpTVcE6B0qTYTqi9NRaF0rXxcuAMK/obSK2Dmh8L2ERSOX6FPn1Y2O2o1ClCgz36qcpusJ1G4HwaL7lC0i2qUjigU5uivnoUtTQOLINN9VTii0NwPeT/XKRy1cVOtMS0sLKSwsNDwODu75tNF41sF89qAoYbHc9b+aji1BnA2PZXItBR23nYXPbx8DaemruXlfkNo4+TClNXGa8OqniY8m55Kcp6Wn8ZPx8/OnsvZWQQ7u9LD249Tdz1YbZ/+9g50cPOo1tfSOnwwlh49yMrIE3jb2vFQeE/eHTKq3j98Ere6x+3fitmQgCB6evsx+n8ratzuZokZ//JYA1hz/jS7rkTjptZwV1hXPhk2limrf6KwtPSmidv4VsG81r9KP9Y1PGbXsjcullH/W4GTtTUzgjvwybCxTPjtB9Ly8wh2ccPf3pFTdxrHzNLcHH97BwpKS1g+uvL0+FPbN7G3Dv251vtVVxNaBvNav2GGx3PX/8rc9l0Y/eu3td6Hp40tz/caxG3rfqlVHyzNzBnXMpiPIvYalQc7u9HTy4/T8x6qto2/nQMdXT2M+jr7r1V1SpSWHjvIyjMn8NbYsbBLL94bOIq5Gxp2IKRAwYn0BN4+XnYRzumMJFrbuzKzZadaJabj/EN4MLQP9+xYVae1o8GO7qjNLTg86WGjciszc/w1jnip7fh71N2G8s9O7+HT03tM7Km6tZdPG/77bFYKZzKT2T5uPj3c/Nlz1Wxrg5REoU8bBwpbFFYjUDgsQZ92a83J6fUUVC6noOQc+pKzKF3/QW/RHYr2olAFg5k/Crerk3ZLMPMDVVcUjl8ZSsvWlO6rWx8UGhSOX0LJBfTaj+r3Oq7hpkpMX3/9dV588cVa1d0cfYGjKyuv7EvMrX7VWGx2Fmn5eQTYO1z3C/zFvoMZFBDItNUrTe6rqqNJZVcpBtg7cjk7CxuVBVuiL/LG3upX4iXn5aJUUK2vbjZlR8Gu1mpSqlxR6WqtrrbgPqMgn4yCfKKyMriQkca+2ffS2d2TiKS6X9kocat73P6tmPXy9sPf3oHjdxovNP9s+DgOJsQxY83KmyZmNMFYyykqIqeoiOisTI4kxXPsjgUMb9GKPy6cuWnitjn6AkeTrhOznNrH7HryS4qJyc4kJjuTI0kJbL3lDqa3DeXTIwewUak4mZLEQ5vXVdsuvSCPolIdo6ocRKXm51JUWkqJToeLtfEsn6vaxiiGmHq/5lW+X3W1KeYCR1ZVxm10YBtcrNXsvfVeQ5m5UskzPQYwr30X+vz4RbV9tHd1x1Vtw7rJs4y26e7py+x2nWn11btGCeSowNZYm6v49dwpo/3YqFRsibnI6/u3c7WKsVa1r4m5WsOMqYu1jdEV9i7WNtcea5lp7L/tPjq7exFRZda2rlIKtFzINp5Nu5idxgjfttfddoxfCK93G80Du38zOr2eUZhXNhasjMeCi5UNKeWznWpzFckFWmZu+aHafrOLCsguLmDMhq8NZRXLBFILtKb3m1/zb1BsbiZpBXn4axwbNzGlGErLPod67SkUqvYobGajz362elVdatmsaRUKMxfQpVSvW6E0Fr0uHcz8gb1lSwWKT6HPWmRi/+mgLy5LlA1laaAvQq8vqdY2Zs7V21bYlC0L0GvLZn9p+AXLV7upEtPFixezaFFlsLOzs/H19TVZN7e4mNziTJPPVfCw0eBoZX3dW2m82Hcww1u0ZMaalVzJuf7C+xCXsmn35LyyD8HJ1CRGBrbiSk5WjbMsV/c1NjuL5FwtvXz8OV2+pkujsiDM3ZPvT9WwPgVQKhQAWJjV762VuNU9bv9WzD6L2M/PkcazExtnzOHl3VvZHH0JbqKY0cRjTYECBWBhZgY3UdwaM2b1oVQoDP0+mZLEmKA2pOXnoS02fVVwTHb1vp5MSaKXj5/h9lSK8oOuFSeP1Nju1e9XXV0dtx8jj7E5xng5zHejp/DbudP8ctb0DODuuBiG/m+ZUdnbA0ZwMTOdz44eqDarOb1tezbHXKh2B4OTqUmMaNG6bmMtp2ys9fb2MySiGpUFYW6efH+6FmNNWb+4VTiccoXA8tPrFVrYOhF3nQugxvqH8Ga30Ty453e2xhvHu1in42R6Ar08AtgUV3YbLQXQyz2A786VXcR1KiMRVysNJXpdjW3FaKsvfYhIjaOXewDLzh40lPX2aMGR1Jov/vGwtsXR0prkgsa99VF1SlBYmH6q6AgKi57o85ZXlln0huKa32OUHmVrTHVl40JffAqF1ajyJLSG11Jq4oC1+FRZ24UVF60pwKIX+rwqy1YUGhSO3wBF6DPuBRrhbgAm3FQ32Le0tMTOzs7or7bU5ioW9+xPJ3dPfGzt6OXtx5cjJxCdlcGOy5VHRz+Mm8qs0MrFvi/3G8LE1sE8tHkduUVFuFqrcbVWY1n+5exnZ8+CLj0IdXXHx9aOIQFBvDt4FPvjYjmTVnaEueLEEewtrflw6Bg6uHngZ2dPP98A3ho4wvDFYco3xyNY0KUHQwKCaOPkwruDR5KUqzXcszLMzYNZoZ0IcXbFW2NHT29fPhw6huisDCIS6390LHFrnjFLyc/jXHqq0R9AvDbHkIzdrDG7kXHztbNnfuduhLq646WxpbOHF58MH0tBaQlby69Mv1njVuuYjTWOmdpcRYizKyHOroYYhTi74qWxhfILjh7r3odO7p54a+wIdXFnyYDheNhoWHexbOnA7+cjSS/I58uREwj39MbH1p4eXr4833sQHjaaan2t8NWxQ9wS3IHJbdoR5ODEq/2Golap+OVM2VX6vrb2zO/UjVCX8vfLvfr71VCZhQWcy0g1+ivW6UjJz+VSlTWeP46Zxux2ZXHLLS6utk1eSTEZhfmcyzCeTfS3c6C7py8/nzlere1vTx3BwcqKjwaPpYOrB352DvTzCeCtAdcea1+fOMyCzj0Z4l8+1gaOIjlPy8bostsIhbl5MrtdJ0Kc3fDW2NHLy4+PBo8tG2sNmC0F+ObsAcJcvJgf0gt/jSPj/EOY0TKM789X3gXgsY4DeLtH5QVc4/xDeLvHWF47soWjafG4WNngYmWDrcqy8jWdPcCMoDAmtWhPkJ0zL4ePRG2uMlylvysxmiOpcSztO4U+Hi3wtrGns4s3j3ToT3snjxr7u/zcQfp5BnJH224E2jrzUGhf2jt5sqK8v2pzFU+GDSLM2QtvG3t6uQewtN8UYnLS2ZlwqUGxqkqheQRU4WDmXbbWVPMIWHRHn192HYXCfklZWTl93rdg2RfU88AsEIVmAahCK5NDhRqF7RNlF0OZeYNFTxSOn0FpDBSWrx3N/wN0GSgcPgNV17L7oVp0Q2H7bFkSWwN93jegng5WE8EsCIXdS6CwNlylX5aULgOFNfqsp0CpKZthVbo0eip5U82YNkSpXk+wswuT27TDztKS5FwtO2KjeffAbsOiasq/UJysK6/Muz207Gq4lRNmGO3v0S3rWXX2FMU6HX18/JnXsQtqcxXx2hzWXzrHx4cq12wk5+UyZfWPPNmzH9+NmYKFmRlx2my2X4665tqhz48cwNpcxesDhmFnYcnBhDhmr/3VsL4pv6SEEYGteLhbr7JTHnm5bL8cxUcb9xm9Jonbvxu3GxWz2rhZY8YNjFthSQnhnj7M7dAFe0srUvNzORB/hcm//Wi4b+bNGrdSvZ5gp/KYWZTH7EoNMbOqjFkHNw9+Hj/d8PjZ3gMBWHXmJI9u3YBOryPIwYnJw9rhaG1NZkEBx5MTmfr7z4Yr2AtKSpj++8882bM/nw8fj0ZlQWKult1xMWiLap5JWXvxLE7Wah4O742rWk1kagqz164itfy9KCyt4f1aXfl+/Vv87BxwtKr7ldrT2rYnQZvDjtjqp4ST83KZ/PuPLO7Rn+9HT8VCWTbWtsVeZ6wdO4BapeL1fsOxs7DkUGIcs/5aVWWsFTOiRSse7toba3MVKXlatsVG81HE3gaPtePpCdy381ce6ziABaF9iNVm8nLEZtbEVH4vuVpp8FJXThbNCOqESmnGS+EjeCl8hKF81aXjhnuHrrsciZOlmofb98PFyobIjCTmbFtpdOHSvO0reaRDf5Z0H4OTpZrUAi0HUmKveZuniNQ4Fu5ZwyMd+vNohwFE52Rw785VhnuYlur1tHVwY1KL9tiprEjOz2FnYhTvndjRaN9nACidUTgsAaUb6HKg5Az6jHlQVH7vbjOv8nsRlCs+gj5zEQrbh8H2kbIb7GfMr7yHqb4UzNugcJhYdkW8LhkKd6HXvl9l9rIAffpMFLaPoXD8BBQ2UJoERXuufSP8gr/QK51Q2D5UfoP9yLKb9uvK71ihCkFhUfZdq3DdYrSpLmXANW9FVVcKvb6R71ZcB1qtlgsXymYWOnXqxLvvvsvAgQNxcnLCz8/vuttnZ2djb2+P79svo7Ru3NujCCFEk6l54kzUQK9ssp+ym5qZXXEtaomqLgxcVotaoqrsHB2OrS+RlZV13bPdTTpjeujQIQYOHGh4XLF+dPbs2SxfvvwaWwohhBBCiP+aJk1MBwwYQBNO2AohhBBCiGbkprr4SQghhBBC/HdJYiqEEEIIIZoFSUyFEEIIIUSzIImpEEIIIYRoFiQxFUIIIYQQzYIkpkIIIYQQolmQxFQIIYQQQjQLkpgKIYQQQohmQRJTIYQQQgjRLEhiKoQQQgghmgVJTIUQQgghRLMgiakQQgghhGgWJDEVQgghhBDNgiSmQgghhBCiWZDEVAghhBBCNAvmTd2BxqB0KEKplhxbCCGEEDdWy61zm7oLNx1dXgHwcq3qSjYnhBBCCCGaBUlMhRBCCCFEsyCJqRBCCCGEaBYkMRVCCCGEEM2CJKZCCCGEEKJZkMRUCCGEEEI0C5KYCiGEEEKIZkESUyGEEEII0SxIYiqEEEIIIZoFSUyFEEIIIUSzIImpEEIIIYRoFiQxFUIIIYQQzYIkpkIIIYQQolmQxFQIIYQQQjQLkpgKIYQQQohmQRJTIYQQQgjRLEhiKoQQQgghmgXzpu7Av8VcoeSRDv0Z4BWEr8aBnKJCdidFs+TYVpLztTVup1QoeCi0LxMCQnG1siEpX8uvUcf5+NRuk/Vf6TqCma0683LEJpadPdjgft/eqgt3te2Oq7WGyIwkXji8kePpCUZ1Ojl780jH/oQ5e1Gq1xOZkcTsbT9TWFrS4PYlbnV3I2P2UGhfxviH4Km2pVhXysn0RN4+vp1jafEN6jP/8bH2X41bfWO2Y+x8fDQO1cq/O3eY5w//jbeNPTvH3W9y2/t3/cb62DMN6vfC9v2YERSGncqSw6lXePbgBqK1GUZ1BnoFsaBdH9o6uFGoK2F/8mXu3flrg9qtUN+43dqyM7e26oy3jT0A57NS+OjkLrYnXDLU8dM4sDhsMF1dfbEwM2NHwiVePLyR1ILcBve7KcdauKsvdwf3INTRA3e1LffsWMWmuHM11u/u5sdPg2+rVt5t9QeGWNT1d6Iuurv58XSnIbSydyEhL5tPTu3m16gThuev9xloDHWNGYCF0owFoX2YEBCKi5UNKflaPjq1i18uHQdguE8b5of0wt/WEXOlkuicDL46s5/fo082uL/Xi9lDoX15qH1fo20uZqcxdN3SBrdd1f+bxNTaXEU7Jw8+OrmbyMwk7C2seK7zUL7sO5XxG5fVuN29wT25tVVnHtv3J+eyUung5Mmb3UeTU1zIt+cOGdUd5tOaMBdvEvNyGqXPo/2CearTYJ49uIGjafHMbRPOtwNnMGTtUtIK86D8S2j5gOl8dnovLx7aSIleR7CDO3q9vlH6IHGruxsZs6icNF449DeXtZlYmZkzr203VgyYwcC1n5Ne/trqo6ljhsStXuobswkbl6NUKAyP29i78t2gmfwVGwlAQl423VZ/YLTNLUGduCu4O9sTLjaoz/cE92BO6648uu9PruRm8nD7/iwfOINh676gSFcKwAifNrzWbRRvH9/G3qQYzBRKWtu7Nqjdquobt4S8bJYc3Up0TjoKhYJJLdqztO9Uxm74mvPZqVibqfh2wC2cyUzmtn9+AODhDv34st9UJm1cTkPe8aYea2pzFZEZyfxy6Rif951S6+0Gr/2cnOJCw+O0Kgl6XX4n6sLHxp6v+0/jxwtHeHjvGnq5B/B6t9Ek52vZmRgFtfgMNIb6xOyj3hNxsbLhyf3riNZm4GalMepnZlE+n5zezcXsNIp1pQzyasWS7mNIK8g1vLb6qE3MAM5mpnD71h8Nj0t1unq3WZMmTUxff/11fvvtN86cOYO1tTW9evXizTffpE2bNo3eVk5xIbO2/mRU9sLhjfw+fC5eajvi87JNbtfZxZvNV86xNb7syzguN4ux/iF0dPYyqudureH5LsOYs/Vnvu4/rdp+PNW2PNVpCH09WqDT6zmYEstLEZuIy82qsc93tOnGyotHWRVVdqT0zMH1DPRqydTAjnweubesrPMQlp87ZHgMEJWTXqfYXIvEre5uZMz+iDlttM2rEZuZHhRGWwc39iRFw00aMyRu9VLfmF2djN8X0pPonHT2J18GQKfXV5vhG+bbmr8uR5JXUmwoa23vypNhgwh39SW/tJidCZd4JWIzGUX5NfZ5bptufHxqN5vjzgPw6L4/OTDxIYb5tGHt5dOYKRQ822Uobxz9h/9dOmbY7kJ2ap1icy31jds/8ReMHr9zfDu3tuxMJxdvzmen0sXVBx8be8Zu+BptSREAj+1by5HJi+jlHsDum3isbU+4ZDQzXFupBblGiWlVtfnsWijNeKRDf8b6t8POwpJzmSm8eWyrYayacmvLzsRqs3jtyBYon9Xr6urLvLbdDEnW9T4DjaGuMevnGUh3Nz/6//kpWUUFUB6Tqq7u3/JzB5nUoj1dXX0Nr+1GxQygVK9rlNn/a2nSNabbt2/n/vvvZ9++fWzatIni4mKGDRtGbu6NfdEVbFWW6PR6sssHgCkRqXH0cg+gha0TAG0d3Ojq6sv2+MpZAwXwTs9xfBm5n/MmvjzNFUqWD7iF3OJCpm/+jqmbV5BXUsTyATNQKU2/BSqlklAnT3YnRhvK9MDupCg6uXgD4GypppOLN2kFefwyZBYHJj7ET4Nvo6uLT4Picj0St7prrJhVpVIqmdGyE9lFBURmJMF/LGZI3OqlNjG7+nWMDwhlVfmpQlNCHT1o5+hhlCjaqiz5ftBMTmckMv7vZczZ9jMuVjZ81GdijfvxtXHAzVrD7io/dDnFhRxNizfErJ2jB55qO3R6PX+OmMe+CQ/yTf/pjTpjakpd46ZUKBjjF4K1uYqI1DgoTwj0YJj5BSgsLUGn19PV1Rf+Y2OtNtaNuIN9Ex5kxcBb6HJVX2rz2X2hyzA6uXjz0J7fGbX+K/6KPcPyATMI0DjW2GYnF2/2JBnPHu5MuERnZ2+T9WvzGfg3DPFuxYn0BO4J7sGe8QvYMvoeFocNwtKs5jnEXu4BBNo5cTClMum8kTELsHVk7/gFbBt7H+/1HIeX2q5Br9mUJp0x3bBhg9Hj5cuX4+bmxuHDh+nXr98NbdtCacbjYQP5M+aU4cjWlM9O70GjsmDT6Hso1eswUyh55/g21sScMtS5N6QnpTody8+ZXhs52j8YpULBkwf+MpQ9vn8tRyc/Qnc3f3aZmH53tFRjrlRWOzJJLcglyNYZAN/y9TEPte/D60f+4XRmEpMC2vPdoJmM/OvLamu2GoPEre4aM2YAg7xa8kGvCVibq0jO1zJr60+GGar/SsyQuNVLbWNW1VDvNtiprAwzcaZMC+rI+axUQwIGMKt1V05nJPH28e2Gsif2r2PPhAW0sHUyOVPnam0D5TGqKrUgF1ersuf8yn88H2rfl1cjNnMlN4s723bnx8G3Mnjt54aZpMZUl7i1sXdl1dDZWJqZk1dSxH07fzXM5h5Niye/pIgnwgby1rFtKFDweNhAzJVKXK018B8aa9eTnK/l6QPrOZGegIWZGdODwvhx8K1M2ricU+UHhNf77Hqp7ZgS2JE+f3xsWPv71Zn99PcMZEpgB6OxV5WrlY3JWNlaWGFpZl5tvW1tPgP/Bl+NA11dfSksLeHenatwslTzUtfhOFpa8/j+dYZ6tipL9oxfgIWZGTq9nucObWBX+UHLjYzZ0bQ4Htu3lqicNFytNDwY2peVQ25nxF9fklvL75vaaFZrTLOyyqasnZycTD5fWFhIYWHlKYHsbNOnWwDG+7fjlfCRhsfztq/kYEoslB+xftx7IgoUPHtwQ437ABjtF8I4/1AW7lnD+awUgh3debbzEJLytfwWdYJQRw/mtA5n7N/f1LiPYAd3/DWOnJjyqFG5pZk5/hpHCl1L+Kb/dEP5MwfXszc55pr9ovyIHeCnC0cMH6jTGUn08ghgalBH3jq27br7uJrEre5x+7diVmFvUgxjNnyNo6U1M4LC+Kj3RCZtXE5aYd5NEzMkbk061qqaFtSR7QkXa7zox9LMnHH+7fjo1C6j8mAHN3q4+VeLGeUXAHVw8qzW11L99dejKcuX031yajcbrpyF8sRt9/gFjPIN5qeLR2r92io0Ztwu5aQxZsPX2KosGenXlrd6jOWWLd9zITuV9MI87t+9mpe7jmB26/CyWd+YU5xITzCs87xZxlpDReWkGx2cRKTG4adxZF6bbjyy70+oxWe3jYMr5kolW0bfa7RvCzMzMgrLDiqrxnFN9EmeOVT7sV/hep+Bf4sSBXq9nof3/mFY/vDqkS180mcSzx7625BQa4sLGbPha9TmKnp5BPB0pyFc1mayP/nyDY1Z1WUJZ0jhaFo8u8bdz2i/YKOzKQ3VbBJTnU7HwoUL6d27N6GhoSbrvP7667z44ou12t/muPMcrXLFbWJ+2YU15golH/WeiLeNPbf+8+N1j46fDBvE0si9rL1ctkbtbFYK3jb23BfSi9+iThDu5ouzlQ27xj1g2MZcqeSpsMHMbR1Ovz8/xcbcgpPpCTy8949q+08vzKNIV8qYDV8bylILcinSlVCi0+FSPotQwcXKhpTyo5qKD9HVp8EvZKXWe3pd4lb3uP1bMauQX1pMjDaDGG0GR9Pi+WfMvUwL6shnp/feNDFD4takY62Cl9qO3u4B3Ler5qvdR/q2xcpMxeoo46t+1eYW/BN/njePbq22TXK+FqVCUa2vblZls4ZVY1Tx+HT5LFpyfln5hazKmBXpSonVZuBl07RjDaBYpyOmfPbxZEYiHZw8mdMmnGcOrgdgV2IUA9d+hqOFNSV6HTnFheyf8CBrtWXj82YZazfCsbR4urpWns6/3mdXbW5BiU7HuL+/QXfVBVwVM3RVY6UtT+ZSCnJNxiqnqKDabGltPgP/luQCLYn5OUZrci9kp6JUKPC0tjXMeuvBMAYjM5NpaefCfSG92J98+V+JWYWc4kKictLxt615iUB9NJvE9P777+fkyZPs2rWrxjqLFy9m0aJFhsfZ2dn4+vqarJtbUkSu1vhLpuJLKMDWiVv/+YHMayzQr2Btbl7tzdXpdYbFuaujThqt+wFYPmAGv0efMNze4WRGIqP9gkkryK3xiy/GxGmWk+kJ9PIIMNxeQlG+nuS7c4cBuJKbRWJeDoHlp3IqtLBzqnF93fVI3Ooet38rZjVRoMBCWfZRvllihsStScdahamBHUkrzGPrVRf1VDUtsCNb4s5Xu1jkVEYiI3zbciU3k9Iarvq+uq+xuZkk52vp5RFAZGYyABpzC8KcvfjhfASUx7SwtIRAO2cOpV4xvEYfjQNxl2q+OOhaGjtuVSkUCiyUZtXKK5aJ9HT3x9nKxnCx180y1m6EEEd3UvIrD0iu99k9nZGEuVKJi5WNYYb7aqZidSQ1jgFeQUZlfTxaEJEWV61ubT4D/5bDKVcY5RuM2lxluMiwha0TpTodCfk137VGWWUM/hsxq6A2V+GncWR1I9yqqqpmcYP9Bx54gLVr17J161Z8fGpeqG1paYmdnZ3RX22ZK5R80mcS7Z08eXjvGpQKBS5WNrhY2RgtOP9+4Exub9XF8HhL3AXmt+vFQK8gvG3sGebTmnlturPxStmXQ2ZRPueyUoz+SnSlpBTkGk5jrIk+SUZhHkv7TSXc1RcfG3u6u/nxXOeheFjb1tjnr88eYEZQGJNatCfIzpmXw0eiNlcZrYP58sw+5rTuykjftvhrHHm4fT+CbJ0bbVpd4tZ8YmZtpuLRDmX3J/RS2xHq6MGb3Ufjobblr8uRN3XMJG7/bswoT2ymBHbgt6jjNSaW/hpHurn5sfLS0WrPfXf+MPYWVnzQawIdnDzx0zjQ16MFS7qPNrq9zdWWnT3AA+16M9i7FW3sXXm751iS8nPYWH7aXltSxI8XIniofV/6eLSgha0TL4ePAOCvyw27f2qF+sbtsY4DCHf1xdvGnjb2rjzWcQA93Pz5I6byh3lKiw6EOXvhp3FgfEA7Pu49kW/OHrjpv9fU5iqCHdwIdnADwFdjT7CDm2E29rGOA3i7x1hD/bltwhni3Qp/jSOt7V15tvMQerr58935w4Y61/vsRuWk83v0Sd7uMZbhPm3wsbGng5Mn94X0ZOBVSVRVP1yIwFfjwBNhAwm0dea2lp0Z5RfMN2cOGNWrzWfg34zZHzGnyCjMZ0n3MbS0cyHc1ZfFYYP45dIxw6zlfSE96eMRgK+NA0F2ztzRthsTAkIN9zG9kTFbHDaIbq5+eNvY09nFm8/7TqFUr+fPq+560lBNOmOq1+tZsGABq1evZtu2bbRo0eKGteWutmWoT2sA/hp5p9Fzt2z53nAbBT+NA06WasNzLx7eyKIO/Xip6wicLdUk5Wv56cIRPjq1s9ZtF5SWMH3L9zwRNpBP+0xGo7IgMS+HPUnRhml0U9ZdjsTJUs3D7fvhYmVDZEYSc7atNFqgvOzsQSyV5jzdaQgOllZEZiQza+tPXNZm1ik+NZG41d2NilmpXkeQnQuTWnTA0dKazMJ8jqcnMH3zd4bTdzdrzCRu/27MAHp7tMDbxt5whsKUqYEdSMzLZqeJW94k52uZtmkFT4QN4tuBM7BQmhOXm8WOhEvVZsGqWhq5D2tzC14LH4mdhRWHUmKZu22l0ZXsrx/5hxKdjnd7jsPSzJxjafHcuuUHsosb58Kn+sbN2VLNOz3G4mqtIae4kLOZyczZ9pPhwhOAQDsnHus4AHsLa+JyM/n01B6+Plv5436zjrX2Tp5GN8x/pvNQAFZdOs7j+9fiaqUxWjKgUprxVKfBeFjbkl9azJnMFG7f+hP7qqyXrc3vxOP71vJAu9481Wkw7ta2ZBTmlS3Fiat5hvNKbhZ3bP8fz3QewpzW4STm5bD4wLpq9/mszWegIeoas7ySYmZt/YkXug5jzfC5ZBTm81dsJO9UuWDJ2syCl7qOwMPaloLSEi5mp7Fo7x+su1x5/9UbFTMPtR0f9BqPg6U16YV5HEq5wuRNyxt0L2hTFPrGujt2PcyfP58ff/yRNWvWGN271N7eHmtr6+tun52djb29Pf5fPYtSbXWDeyuEEEIIIepKl1dAzJ0vk5WVdd2z3U16Kv+zzz4jKyuLAQMG4OnpafhbuXJlU3ZLCCGEEEI0gSY/lS+EEEIIIQRNPWMqhBBCCCFEBUlMhRBCCCFEsyCJqRBCCCGEaBYkMRVCCCGEEM2CJKZCCCGEEKJZkMRUCCGEEEI0C5KYCiGEEEKIZkESUyGEEEII0SxIYiqEEEIIIZoFSUyFEEIIIUSzIImpEEIIIYRoFiQxFUIIIYQQzYIkpkIIIYQQolmQxFQIIYQQQjQLkpgKIYQQQohmQRJTIYQQQgjRLJg3dQcag15X9ieEEEKI2lPI9FSd2Wrym7oLN51SZWGt68qQFEIIIYQQzYIkpkIIIYQQolmQxFQIIYQQQjQLkpgKIYQQQohmQRJTIYQQQgjRLEhiKoQQQgghmgVJTIUQQgghRLMgiakQQgghhGgWJDEVQgghhBDNgiSmQgghhBCiWZDEVAghhBBCNAuSmAohhBBCiGZBElMhhBBCCNEsSGIqhBBCCCGaBUlMhRBCCCFEsyCJqRBCCCGEaBbMm7oD/6aoW58yWf56xBa+iNxf43a3t+7C3cHdcbXWEJmRxAuHNnIsLcHw/E9DbqWHu7/RNj+cj+CZAxsa3OeHO/RjRssw7FSWHEq5wrMHNxCdk1GtnoXSjNXD5xDi5M6ov74iMiO5wW1XkLjVncSsfm5U3F7tNpLeHgG4W2vILSkmIuUKbxzdyqXstAb3uTnELcjOmSc7DaSbmx/mSiXns1KZv+M34vOyTdY3Vyi5r10vJge2x0Nty6XsNN44spUdCZeM6l0vrvU1yq8tizr0x0djT1ROOm8e2cq2+Ism677SbQS3turMS4c2sezswQa3XeGtHmOYEtTBqGx7/EXmbF1Z4zY25hYs6tiP4b5tcLZUcyojiZcObeJ4emVMXKxseCJsIH09W2BnYcWB5Mu8cGijyTFRV00Zt3BXX+4O7kGoowfualvu2bGKTXHnrrmNhdKMBaF9mBAQiouVDSn5Wj46tYtfLh2HinEY0otJLSrH4ZvHqo/D+mjr4MqLXUbQwdmTtII8Vpw/xBeR+wzPT27Rnrd6jDXaprC0hOD/LWlw26bMa9mXh4KH8f2lPbx1an2N9YZ6tuP+toPxsnbgcm4670f+za7k84bnnSxsWBgyjJ6uLbFVWRGRFsMbJ9dyOTe9wX28Xtv3th7ICO/2eFjZU6wr5XRWPB+f2cyJzCsNbruq/1eJafivHxg9HuAVxJs9RrM+9myN24z2D+bpzoN55sAGjqbGM69tON8OnMHgP5eSVphnqPfT+SO8e3yH4XFBSXGD+3tPSA/mtOnKo3v/JFabyaIO/fl24AyGrv2CIl2pUd0nOw0iKT+HENwb3O7VJG51JzGrnxsVt5PpCayJPklcbjYOFlYs7NCXFYNm0G/Np+j0+nr3tznEzU/jwC/Dbud/F4/x3vGdaIsLaW3vSmFpSY3bPNKxPxNahLJ4/19czE6jn2cgS/tNZvLGFZzOSII6jMe66uzizQe9J/DW0a1sibvA+IB2LO03hbHrv+FcVopR3WE+renk7E1iXk6927uWbfEXeWzvWsPjq9+zq73RYxSt7V1ZtOcPkvK0TGgRyneDb2HY2i9IytcCsLTfZEr0Ou7evgptcSF3BHfn+8EzGfrnF+SX1v+z2tRxU5uriMxI5pdLx/i875RabfNR74m4WNnw5P51RGszcLPSoFQoDM8/0qE/4wNCeepA5Tj8vM9kpmyuHIf1oTG34NsBt7A7KZpnDq6njYMbb3YfTXZRAT9fPGqol1NUwOB1S+vdTm21s/dmin84Z7MSr1mvo6Mvb3SeyodnNrEj6RyjvDvwfvhMZuz4jAs5ZQey74fPpESvY+GBH9GWFDIrqBdLe8xl0rYPGzS+atN2TG4ar59Yy5W8DKyUKm4L7MlnPWYz9p/3yCiq/3fC1Zr0VP5nn31Ghw4dsLOzw87Ojp49e7J+fc1HEg2VWpBr9DfUpxV7k2KI1WbWuM2dbbux8sJRVl06zoXsVJ4+sJ780hKmBnU0qpdfWmy0b21JkdHzre1dWTZwOienPcrBSQ/xbq+xOFpaX7O/89p24+OTu9l05TxnMlN4ZO+fuKttGebbxqhef69A+nq24LWIf+oVl+uRuNWdxKx+blTcfrpwlAPJscTlZnEqI4l3jm3H28YeHxt7Q52bNW6PdhzAtviLvHFkK6czkriszWRz3PlrJo8TW4Ty6ak9bIu/SKw2kx/OR7A1/iJ3BXc31KlNXG1VlrzRfRSHJi/k+LRH+GHwTIId3K7Z37ltw9mecJEvIvdzMTuNd4/v4FRGIrPadDGq526t4YXwYSzcs4aS6ySM9VVUWmI03rKLCmqsa2lmzgjftrxx5B8OJMcSo83ggxM7icnJ4LbWZX1vYetEZ1cfnjmwgePpCVzKSeeZA+uxNDNnXECIYV83Y9y2J1zi3RPb2Xjl2rOkFfp5BtLdzY9521eyOymauNwsjqTFcTi1cnZtQkAon53ew7aEi8TmZvLDhQi2JVzkzraV41AB3BfSk+1j53N66mOsG3EHI33bXrPt8QGhqJRmPLF/LeezU1l7+TTfnjvIHVX2C6A38Z3T2KzNLHi98xRePPY72cX516x7a4ue7Em5wLcXdxOlTeGTs1uIzEpgRkBZv/1tnOno5Merx//kVFYcMbmpvHL8T6zMzBnhXTn7b2tuxfMdxrN12JPsHvE0X/acS2s7jwa1DbA+7jj7Uy8Rl5fBRW0yb5/egK3KilbX2XddNWli6uPjwxtvvMHhw4c5dOgQgwYNYvz48Zw6deqGt+1iZcNA75b8r8rR09VUSiWhTp7sSow2lOmB3YlRdHbxNqo7PiCUw5MXsmH0XTwWNgArs8rJaFuVJT8Mmcmp9ETGbVjG7K0/42Jlw8d9JtbYtq/GATdrDbsSowxlOcWFHE2NN2rbxcqG17uPYtGePxp0tFRbEre6k5jVT2PHrYK1mYopgR25nJNBQvmp7ps1bgpgoHcQUdnpfDtwBgcnP8Tq4bMZ6tP6mttZmJlVm1EtLC2hq6sP1CGun/adhLOVmrlbf2bc+m84lZ7I94NnYm9hVWPbnVy82Z0QbVS2I/6S0X4VwLu9xvHF6f2cz0qtQ0Tqpoe7PwcnP8SWsffwcvgIHCxqPhAxVygxVyopLDVO9gqqxM3CzAzKY1lBDxSVltLV1ddQdrPHrTaGeLfiRHoC9wT3YM/4BWwZfQ+LwwZhWeX7ytQ4LCgtoauLj+HxfSG9mBjQnmcOrmf4X1/yzdkDvNtzHN1c/Wpsu5OLNwdSLlOs0xnKdiREEWTnjJ2qMsZqcwt2jrufXeMeYGnfKbSyc2nECJR5qv0YdiSfY3/q9ZcndHDyZV+K8dKMPckX6OBY9lpVyrLYFeoqv0f06CnSldLJqTIeb3WdjpOlhvv3r+CWnZ8RmRXPFz3nYKeqeXxfr+2rmSvMmOzXlezifM5lX3smuK6a9FT+2LHG6zteffVVPvvsM/bt20e7du1uaNuTA9uTW1zEhss1nyJ0tFRjrlRWO4pKLcglyM7Z8PiP6FPE5WaRlK+lrYMbT3QaSKCtM/ft/BWA2W26cjo9ibePbTds8/jedeydtIAWtk5E5VRfG+JqZVPWVn71tl2tbQyP3+o5hh/PH+FEeiLeVWZ/bhSJW91JzOqnMeMGcFurzjzZaRA2KgsuZqVx+z8/GX64bta4OVvZoFFZcm+7nrxzbDtvHP2H/p5BfN5vMjM3/8D+5Msmt9uREMUdbbtxIPkyMTkZ9PYIYLhvG8Np1trEtaurDx2cPQn/9QPDKfDXjvzDUN/WjPJry08XTB9QuFppTO7X1UpjeHxvu56U6nUsb8Q1pVfbnnCJv2PPEpubiZ/GkcfCBrB84HQmbfzW5PKO3JIiDqdcYUH73lzITiW1IJdx/iF0dvEmRlu2fvRiVhpxuVk8HjaQpw6sJ7+kiHltu+FlY4ebddnru9njVlu+Gge6uvpSWFrCvTtX4WSp5qWuw3G0tObx/esA2JkQxbyKcagtH4c+lePQQmnG/Ha9uP2fnziSFgdAbFQmXV19mdmyEwdSTI9vVysbYnOzjMoqYudqbUN2cQGXstN5Yv9azmQmY6uy4q7g7qwaOovhf31JYn7jLIEY4dWeYHsvZu78vFb1XSw1pBVqjcrSCrW4lL/H0doU4vMyeTB4GC8fX0N+STG3B/bCw9oeV0tbADo5+RHq4MPAjW9QXD6+3j39NwM9ghnq2Y5fLx+qV9sV+rm15s0u07AyU5FaoOXevd+S2Yin8WnqxLSq0tJSfvnlF3Jzc+nZs6fJOoWFhRQWFhoeZ2ebXtgPMD6gHa92G2l4PHfrSg6mxBoeTw3syJroU9ddU1QbVb9IzmamkJyv5ccht+KnceCyNpNgBzd6uPtzctqj1bb1s3Wgg7Nntb6W6nXV6l5tTpuu2Jhb8OmpPQ1+DRUkbnUnMauffzNuAGuiT7ErMQo3aw13BXfn4z4TmbJxBUW60psmblfH7I5t/wNg05XzfHOmLBmJzEimi6s3M1t1qjExfenQJl7vPpLNY+5BD1zWZrDq0nGmBnYwWd+UYEd3bMwtiJjysFG5lZk5fhpHvNR2bBxzt6H801N7ahWHUCcP5rYJZ8z6b2rdl+sxNdbWxpw2PD6bmcKZzGR2jJ9PDzd/9iRFm9zPoj1/sKTHGPZPepASnY5T6Yn8GXOaUKeyU5kleh337viVN7uP5tjURZTodOxOjGJr3AUU5cnWzRS3hlCiQK/X8/DeP8gpLvvdfvXIFj7pM4lnD/1NYWkJL0Vs4rVuI9k02vQ49Nc4oja3YMXAW4z2rVKacTqjbJZuw6i78FaXHfAdTIll3vaaL16r6khanCHZBYhIvcLG0XdzS8tOvHdixzW3rQ13KzseDx3FPXuXU6Sreb13XZTodSw69BMvdJzArhFPU6IrZX/qJXYmnaNi6W5rOw/U5hbsGL7YaFtLMxW+Nk54WNuzesACQ/lX53fw9YXav96DaVFM2/4pDhZqJvt35a2u07lt51LSixpvGUSTJ6YnTpygZ8+eFBQUoNFoWL16NSEhISbrvv7667z44ou12u/mK+c5mhpveFz1CCjc1Zcge2cW7Fp9zX1kFOZRotPhYmVjVF52dWHNb0JFuwG2jlzWZqJWWbAl7jxvHtlarW5yvhalQlGtrxVH1y7WNqRUOUp2sbIxLArv6e5PZxdvzs54wmiff4yYx5rokzxaZVF/bUnc6h43idnNMdZyigvJKS4kOieDI6lxHJ26iOG+bfgz5vRNE7erY5ZemEexrpQLV522vZCVRlc3HxN7qNzunh2/YqE0w9HSmqR8LU+EDeRy+Vre2sRVba4iuUDLLZt+qLb/7OICsosKGP3X14ayzKKy9XUpBVrT+y0om60Jd/XF2cqG3RMeMDxvrlTydOfBzGsbTt81n9YyWpWuNdYqxGozSSvIw9/WscbE9LI2kxmbv8faTIVGZUFKQS4f9ZlgiBvAyfRERq//GluVJSqlGemFeawePpsT6WWJ1M0Ut4ZILtCSmJ9jSEoBLmSnolQo8LS2JVqbQXphHvfuvGocdhzI5dyyeKpVFgDcsf1/JF31nlUke/O2rUSlLFtCUVC+VCalIBcXK7VR/YrY1fR9WqLXcTojiQBbx0Z5/SEO3jhbavi5332GMnOlGV2c/ZkR0J3wdS+iw3hmPrVQi7Ol8Qyls6WG1ILKmczIrHim7/gUjXnZ+MooyuP7PndzKrNsfKvNLEktyOGOPdUPUHJKCsgpLmDa9sqxkFW+7rU2bVN+jUNsXjqxeemcyLzCHwMXMsGvC9/UIbm9niZPTNu0acPRo0fJyspi1apVzJ49m+3bt5tMThcvXsyiRYsMj7Ozs/H19a1Wj/LTLrnaIpPPTQvqyPG0BCIzr327lmKdjpPpCfT2CGBT+YJvBdDLI4AVZw/XuF2IU9lVt8nlV2meSk9khG9bruRmUlrDFcBX9zVWm0lyvpbe7gGG28pozC0Ic/Hi+/MRALx4aBPvHKscDO7WGlYMvoUFu1YbfQnXhcSt7nGTmN18Y01R/r+KNYE3S9xMxex4WgKBdk5GZS3snIjLrfmMUoUiXSlJ+VrMFUpG+LVhXUwk1DKup9ITcbXSUKLXEXfVadMKFae4qzqSGkdvjwCjWxj18WxBRGrZ7NXqqJPsTjRODL8dNIPVUSdYdfH4dV+TKdcaaxU8rG1xtLQmJV97zXqU/zjnlxZjZ2FFP89A3jhS/aK2ioQswNaR9k6evFs+Dm6muDXE4ZQrjPINRm2uIq/8ziEtbJ0o1elIqJZkVo7D4b5t+Oty2Ti8kJVKYWkJXjZ2NZ62N3VLtCOpcTzSoT/mCiUl5Wc2+ngEcDE7jexi0xe4KRUK2ji4sS3+QoNfO8D+lItM3vaRUdmLYROJ1qay7MLOakkpwPH0WLq7BPJD1F5DWQ/XII5nVH/t2pKy8eVn40SIgzefnN0C5Ymrs6WGUr2O+HzTF43G5lVfmlSXtqtSKhRYlB8YNJYmT0wtLCxo2bIlAF26dOHgwYN88MEHLF1a/RYOlpaWWFpaNqg9jbkFo/zb8mrEFpPPfz94Jhtjz7LiXNmX71dnDvBOz7EcT0vgWFo889p2Q22mYlX5fdj8NA6MD2jH1viLZBTmE+zgxjNdhrA/6TJnMstu4bHi3GGmtwzjw94TWHp6H5lF+QTYOjLGP4Qn9/9V4+1qvjlzgAdCexOdk0FsbiaLOvQjKS+HjeW3zrn6A5lbfnV2jDaj0dbIVJC4Scz+jZhxA+Lmq3FgjH8wOxOiSC/Iw0Nty33telJQWsy2uLLF/jdz3L44vY+P+kzkQFIse5Ni6O8VyGDvVtyy+XtDnXd6jiUxP4e3jm4DIMzZC3e1LaczkvCwtuWhDn1RomDp6cr7PF4vrrsSozmSGscX/abwxpF/uJSTjru1hkHeLfk79qxhhvBqy84c5Oeht3Fn2278E3+Rsf4htHfy5Kn9ZXdkySzKN8wSVijRlZKSn8slE2t960NtruKh9n1Zf/kMKQW5+GscebLTQGJy0o3uoXn1WOvn2QJQcCk7jQBbRxZ3GszF7DR+qZL4jfJrS1pBHvF52bR1cOW5LkPZeOUcO8svkrtZ46Y2V+GvqZxN9NXYE+zgRlZRAfF52TzWcQDu1rY8uu9PAP6IOcUD7fqwpPsY3j+xE0dLaxaHDeKXS8cMFzx1dPbCw7p8HKpteSi0L0qFgqXl9xvNLSniy8j9PNN5CEqFgkMpsdiqLOni4ou2pJDfok6Y7OsfMad4MLQPb3QfzdLTe2nt4MqcNuG8ErHZUGdBuz4cSYsjJicDOwtL7g7ugbfajpUXjzU4VgB5pUWG2yxVyC8pJrMoz1D+Sthkkguy+fDMJgB+iNrL173uYFZgL3Ykn2OEV3vaOXjx8vE1hn0M9WxHRlEuCflZtLJ15/HQUWxNjGRv+YVL+1IvcjwjlvfCZ/J+5N/EaNNwtbKlr3sb/kk4zeks0wfE12vb2kzFna36sy3xDKmFOThY2DAjoBtuVrZsim/cC9abPDG9mk6nM1pH2tjGBoSgQMGf0adNPu+vccDRsvIUwLqYSJwt1Szq2A8XKxsiM5KYs3WlYSF1sa6U3h4tmNs2HLW5BfG52WyIPcPHJ3Yb9pGcr2XqxhU8ETaIFYNmYGFmTlxuFtvjL13zHopLT+9DbW7Ba91HYmdhxcHkWOZsXdloa+7qQuJWdxKz+mnsuBWWlhDu6su8Nt2ws7AitSCXA8mXmfL3CsMtlW7muG28co5nDqznvna9eL7rUC5lpzN/568cSqm8LY+XjZ3R67A0M+eRjv3x0ziQW1zEtviLLNrzh9Fp1+vFlfK1mo927M+SnmNwslSTUqDlYHLsNW+7E5Eax8Lda3ikY38eDRtAdE4G9+xYVe1enDdSqV5PWwc3JgW2x05lRXJ+DjsTonj3+A6j9+7qsWarsuKxsAF4qG3JKipgw+UzvH1su2FWDsDNWsPTnYcYTrP/dukEH53cZdT+zRi39k6e/DT4NsPjZzoPBWDVpeM8vn8trlYavNR2hufzSoqZtfUnXug6jDXD55JRmM9fsZG8c7zyAkNLpTmLOpSPw5LycbjPeBy+e2I76YV53BfSC18bB7KLCziVkXjNdbc5xYXM3vYTL3YZwR8j5pFemMdHJ3cZ3cPU3sKK17uNwsXKhuyiAk6mJzJl8wouZP97dzPwsLZHR+XYOZYRy+KIX3ig7RAWtB3K5dw0Fh780SjBdbWy5dF2I3G2LBtfa68cZem5bUb7vX//dyxoO4SXOk7C0VJNaqGWiLSYahc3VXW9tkv1elpoXBnXtRMOFmoyi/M4lRnH3N1fc1HbeP9YCIBCr2/A3aUbaPHixYwcORI/Pz9ycnL48ccfefPNN/n7778ZOnTodbfPzs7G3t4evy+eRamu+TYbQgghhKhOIf8weZ3Zaq59P1JRXWleIadmvEVWVhZ2dnbXrNukM6bJycnMmjWLhIQE7O3t6dChQ62TUiGEEEII8d/SpInp119/XYtaQgghhBDi/wOZxBdCCCGEEM2CJKZCCCGEEKJZkMRUCCGEEEI0C5KYCiGEEEKIZkESUyGEEEII0SxIYiqEEEIIIZoFSUyFEEIIIUSzIImpEEIIIYRoFiQxFUIIIYQQzYIkpkIIIYQQolmQxFQIIYQQQjQLkpgKIYQQQohmQRJTIYQQQgjRLEhiKoQQQgghmgVJTIUQQgghRLMgiakQQgghhGgWzJu6A43B3KIUpUVpU3dDCCFEE9Hrm7oHNyddqVlTd+Gmoz3r2NRduOnoCgpqXVdmTIUQQgghRLMgiakQQgghhGgWJDEVQgghhBDNgiSmQgghhBCiWZDEVAghhBBCNAuSmAohhBBCiGZBElMhhBBCCNEsSGIqhBBCCCGaBUlMhRBCCCFEsyCJqRBCCCGEaBYkMRVCCCGEEM2CJKZCCCGEEKJZkMRUCCGEEEI0C5KYCiGEEEKIZkESUyGEEEII0SxIYiqEEEIIIZoFSUyFEEIIIUSzYN7UHfi3hLv4cWebnrRz9MTd2pb7dv+PzfFna7VtZ2cffhgwm/PZyYzb9KXJOne36cVjHQaz/Nx+Xj22scH9HeETzMJ2A/CxcSBam85bx7ewPfGC4fkFIf0Y7dsOT7UdxbpSTmYk8N7JrRxLj29w2xUkZvUjcau7GxGzmYFduCWoCz42DgCcz07h49M72JF4scH9bQ4x4waOtVuDunJnm564Wmk4k5nES0c2cDyj4X1vDnELd/HjrraVMbt317VjNsy7LTODuhDi4I6FmTnns1L48NR2diZdMtS5t21vhvm0JdDWmcLSEiLSrrDk+BaictIa3N+RPsEsDC2PWU46S66K2YPtqsfs3RONP9YAHgrtyxj/EDzVtmVtpSfy9vHtHEu7dlu3t+rCXW2742qtITIjiRcOb+R4eoLheQulGU93GsIY/2AslObsTLzEc4f+JrUgt8F9Xti+HzOCwrBTWXI49QrPHtxAtDbD8PyOsfPx0TgYbbPk6FY+j9zb4LYrqFUqHuvXl6Etg3C0siY2O4tvI47w07HjNW4zrFVL5nfvhr+DA+ZmZkRnZPD1ocP8fjrSZP2XhwxmZlhHXv5nK8sjjjS4z7eFdeSu8K642tgQmZLCi1u2cjwx0fD8K0OH0MvfD3cbDbnFRUTEx7Nkx04upWdcc7+10WxmTN944w0UCgULFy68Ifu3NldxJjOJFyPW12k7W5Ulb3Ubz97kqBrrtHf0ZEZQZyIzkxqhp9DJ2Yf3uk9iVdRRxm/6ks1xZ/m09zRa2bka6kTnpPPSkQ2M2biUGVu/JS43i2X9bsXJQt0ofUBiVm8St7q7ETFLzM/m7RP/MGHzV0zc/BV7k6P5rPd0WlZ5bfXRXGLGDYrbKJ8Qnuo4lI9P72DCpi+JzErim34zcbJsWN+bS9yszVVEZibxQi1jFu7qx+6kS9yx8yfGb/qKfSnRLO0zgxAHD0Odbq5+fH/hIFO3LGP29h8wVyhZ3m8m1maqBvW1k7MP7/WYxC9RRxm38Us2xZ/ls6tiFpWTzosRGxj991Jm/FMWs+X9bm3w+2VKVE4aLxz6m5F/fcW0Td9xJTeLFQNmXLOt0X7BPNVpMB+e3MXYDd8QmZnMtwNn4Fxlm2c7D2Wwd0se2L2aW7Z8j5u1hk/7TGpwf+8J7sGc1l155uB6Jm1aTl5JMcsHzsBCaWZU793j2+m2+gPD37fnDjW47aqeHtCf/gEBPPLXeoYtW87ywxG8MHgQg4MCa9wmq6CAT/cdYMqPPzN6+Qp+PXmKN0cMp2+Af7W6w1q2JMzLk8QcbaP0d3Sb1jw1oD8f7t3HuO++50xyCsunTMJZbW2oczIpiSc2/M2wZcuZu+o3FCj4dspklApFg9tvtBnTzMxMHBwcalGzuoMHD7J06VI6dOjQWN2pZkfixXrNlLzUeTR/Xj5FqV7HUO821Z5Xm6l4p/tEnjm0jvnBfao9b6uy5MkOQxni3RoLpTknMuJ57egmzmTVnFjMbtWNnYkX+Opc2RHb+6e20du9Bbe3DOe5iL8A+DP2pNE2rx/byLTATrRxcGNvcnSdX6cpErP6kbjV3Y2I2T8J540ev3dyKzODuhDm5M2F7BS4yWPGDYrbvNY9WBl1hF+jjwHw3OF1DPBsyZSAML44uwdu8rjVNWavHjU+K/HOia0M8WrDIK9WnM4sm0Gat/MnozpPHPyDA+MfIdTRk4Opl6E8Zos7DmWIV2sszMw5kR7Pq9eJ2ZxW3diReIGvzpbH7OQ2+ri34PZW4Tx3uDxml41j9trR8pjZN+5YA/gj5rTR41cjNjM9KIy2Dm7sSTLd1h1turHy4lFWRZXNDj5zcD0DvVoyNbAjn0fuxVZlydTAjjy8dw17k2IAeHzfOjaPuYcwZy+Ols/GtrZ35cmwQYS7+pJfWszOhEu8ErGZjKL8Gvs7t003Pj61m81xZd8Fj+77kwMTH2KYTxvWXq58LbklRY0yO1uTzt5e/HbqFPtjrwDw8/ET3NKhAx09PNhy8ZLJbSrqVlgecYSJ7ULo6u3NzugYQ7m7RsNzgwcyd9VvfDVpQrX9eNpqWDygP339/dHp4WDcFV7+Zxtx2dk19nde1y6sPHGSX0+eAuCZTZsZEBjIlNBQlh44aHgNFeKys3l3127+mjMLHzs7Lmdl1TlGVdVrxvTNN99k5cqVhsfTpk3D2dkZb29vjh07Vqd9abVabr31Vr788kscHR3r050bZnJAR3w1Dnx0enuNdZ7vPJJtCefZU8Ms10c9p+BsZcMdO39iwuavOJWRyLf9b8NeZVXjPjs5+1Tb387ES4Q5+5isr1IomR7YmeyiAs400kxafUnM6kfiVne1iVkFJQpG+7ZDbabiaFrlF/7/t5hxnbipFEraOXqyJ6ny9emBPUlRdKry+v4/xq2CArAxtyDrGgmRrcoSgMwqdT7qOQVnSxvmlc+8nspMZMWA27C3uE7MkqrHrFNNMVMqmR7078RMpVQyo2UnsosKiMww3ZZKqSTUyZPdiZVJqx7YnRRFJxdvAEKdPLAwM2NXYuXrvJSTRlxuFp3L69iqLPl+0ExOZyQy/u9lzNn2My5WNnzUZ2KN/fO1ccDNWsPuKvvNKS7kaFq8oe0K9wb35PCkhfw5Yh53te2OWSPM+lUVERfP4JZBuGs0APTw9SXAyZGdMTHX3bZCLz9fAp2cOHCl8vtLAbwzagRfHTzE+bTqy0bMlUqWTZlMblEx03/+H9N++pm8omKWTZ6ESmk6/VMplYS6u7OnSt/0wJ7LMXTy8jS5jbXKnCmh7bicmUlCTk6tX1NN6jVj+vnnn/PDDz8AsGnTJjZt2sT69ev53//+x2OPPcbGjbVf93b//fczevRohgwZwiuvvHLNuoWFhRQWFhoeZ18j428of40Tj7YfxC1bv6VUrzdZZ7RvO9o5ejJp81cmn+/i7EsHJy96/PEuRbpSAN48vpmh3m0Y4RPMyijT60BcrDTVjt5SC7W4WtkYlQ30bMV7PSZhbaYiuSCHOTu+v+bR440mMasfiVvd1SZmAK3t3Pjf4LlYKs3JKyli/p5fuJCTCv8PY0Yt4uZoqcZcqSS1wPiUYFpBLkG2LvD/NG5V3dmmJ2pzC9bFnjb5vAJ4OmwYh1Iuc758Zr6Liy8dnbzoXiVmbxzbzFCv8phdqkPMCkzH7P0ek7A2V5Gcn8Ps7TcuZoO8WvJBrwnlbWmZtfWnGtuqHE9Xv4ZcgmydAXC1sqGwtISc4sJqdVytyhK5Wa27cjojibePVx5MPbF/HXsmLKCFrRNROenV2na1tjHsp/p+K+P37blDnMxIJKson84uPjzWcQBu1hpePbKlHtEx7cV/tvLqsCHsufduiktL0en1PL1xEwevxF1zO42FBXvuvRsLMzN0ej3Pbd7C7pjLhufv6RZOiU5X45rS0W3aoETB4r8rc7InNvzNkQX3093Xl10mEmNHa+uy9yw3z6g8NTePQCcno7JbwzryRL++2FhYcDEtndm//EqxTlfruNSkXolpYmIivr6+AKxdu5Zp06YxbNgwAgIC6N69e6338/PPPxMREcHBgwdrVf/111/nxRdfrE+X60SJgne7T+TDU9uJ1lYf8AAe1nY8EzaMOTt+MHzRXK2tgztqcwsOjH/UqNzKzBw/jROe1nasH3GfofzzyF18fmZ3rfu5LzmacRu/wMlSzbTATnzQczJTtnxDemFeLbZuXBKz+pG41V1tYlYhKieVcRu/wFZlyQifEJZ0G8etW1dwISf1/1XMqGPcruX/W9yqGusXyoJ2/bh31/9q7M8LnUfS2t6NGf8sN5QFl8fsYE0xU9uxYXiVmJ3ZxWeRdYzZpi9wtFAzPbATH/aczOQGxmy8fzteCR9peDxv+0oOpsSyNymGMRu+xtHSmhlBYXzUeyKTNi4n7Qa+P8EObvRw8+fElEerPeencaCDk2e1vpbqa5cgfX32gOG/z2SmUKwr5ZXwkbx1bFuN37fXMi64La8MHVLZl19XE+bpQZinJ3f99jtx2dl08/XhhSGDSdLmsufy5Rr3lVtUxNgV36NWqejl78fTA/oTm5XF/tgrhLq7MadLZ8at+L7G7YPdXPF3dOD4gw8YlVuam+PnYE/XEm++mVw56/zMps3suxxb69e65nQku6NjcNXYcGfXrnw0dgxTf/qZotK6x62qeiWmjo6OxMbG4uvry4YNGwwznXq9ntJadig2NpaHHnqITZs2YWVV86mMqhYvXsyiRYsMj7Ozsw0JcmOyUVnQwcmLEAcPnutUNtiVCgVKhYLIyU8zd8cPaFSWuFhp+H3IXYbtzJVKwl39ua1lOO1+fQ0bcwtS8rXcum1FtTZyigvILi5g3MYvDGUVp4ZSC7S4XHVE7GKpIeWqI7/80mIu52ZwOTeDo+lxbBoxn6ktOrG0Dj8CjUViVj8St7qrTcz2pZSdOizW67icW3aV6KnMRNo7eTK7VTeejfjr/1XMqGXcDqdepkSnw6V8pqqCs5UNKeWzqP/f4lZhtG87Xus6hgV7V9W4nOb5TiMY5NWKW7auIDG/8pSm2tyClALTMcsuKo/ZpsqYZV4rZlamYxajzSCGsphtHjmfaS061emA4Gqb484b1ncChtdjaEubwdG0eP4Zcy/Tgjry2enqV7FnFOaVj6erX4ON4TWkFORiaWaOrcrSaNbUpcqYU5tb8E/8ed48urVaG8n5WpQKRbW+upWP4aptVTw+XcPSA4CjqfGolGZ429ibnIm9ni0XLnIsofLq9UStlu+mTeG+NX+w7VLZuDmbmkqwqyt3hXe9ZmKqB2IyMwGITEkhyMmJe7t1Y3/sFbp6e+OsVrPzHuPfhacG9Gdul870//Jr1CoVJ5OSWLSu+oV+aXl5FOt0jK2S2Kbm5lJUWlr2ntkYX9DmYqMmJdd43GmLitAWFRGdmcnR+AQiFtzP8FYt+fNM7e4MUpN6JaaTJk1i5syZtGrVirS0NEaOLPuSO3LkCC1btqzVPg4fPkxycjKdO3c2lJWWlrJjxw4+/vhjCgsLMTMzvnLO0tISS0vL+nS5TrTFhYz6+3OjsluDutLDLYAFe1dxJTcTpUJRrc4b4eO4lJPKF2f2oEPPqYwEXKw0lOp1xOWZXgxc8aNZ1ZG0K/R0a8Hy85VHcr3dWxitjTNFqVBUu9rw3yIxqx+JW93VJmY1USoUWJiVfe39f4oZtYxbsV7HqYwEeroFGG6hpAB6ubXguwtlZ7b+v8UNYIxvO94IH8vCfb+xLeGCyTrPdxrBUO823Lrtu2pjsCJmJbqaYxajNR2zXu7VY3akNjEza1jMckuKyNUWXbeeAgUWStOpRLFOx8n0BHp5BLAp7lx5fejlHsB35w4DcDI9kaLSUnq7B7DhStmYa2HrhLeNPRGpZae6T2UkMsK3LVdyM2tcunN1X2NzM0nO19LLI4DIzGQANOYWhDl78cP5iBpfT4ijO6U6HWkF9ZsBzi0uJjez8v3XWFhgYWaG/qp+6/R66rqUValQYGFe9r7+fjqyWlK7bPJkfj99mlXlFy2dSkpmdJs2pOXloS0y/V7GZFb/vjyZlEQvPz82XSi7SFAB9PTz47sjR2vsm0KhQAENHnfUNzF97733CAgIIDY2liVLlqApX9CbkJDA/Pnza7WPwYMHc+LECaOyuXPn0rZtW5544olqSWlDqc1U+Gsq10f42DgQbO9OZlE+CfnZPBI6CHdrWx4/uAZ9+T0Pq0orzKVIV2JUfnWd/JIiMgvzDeW7k6M4knaFz3pPM9zTzs3algGerdgUd4aTGQmY8u35A/wwYBbzWvdgW8J5Rvu2I9TJi2cOrwPA2kzFfcF9+Cf+HMkFWhwtrLmtZTju1nasv2L6HmcSs38nZhK35hOzR0IHsSPxAvF5WdiYWzLWL5TurgHM2/HDfyJmNypu35zbx5Ju4zmZkcDx9HjmtOqGtbnKcJX+zR43tblxzHw1DgQ7lMcsL5tH25fF7LEDa6D89P2SbuN45cjfHE2PM8z+FZSWoC2f4Xux80jG+oVy7+6V5JYUGurkFBdSWFrC7iTTMRvo2YqN14jZ8vMH+HHgLO5o3YOtCecZ49eOUEcvnj5UGbP5IX3YElceM8sqMYtt3LFmbabi/na92Bx3nuR8LU6Wam5v3QUPtS1/Xa5s6/uBM/n7ylm+O1+WeH599gBv9xjLifQEjqXFM7dNN9TmKsNV+jnFhfxy6RhPdx5CZlEB2uJCnu8yjMMpVwyzoN+dP8z0oDA+6DWBLyL3kVmUj7/GkbH+ITx54C90NSSry84e4IF2vYnOyeCKNpOHO/QjKT+HjeUJcCdnb8JcvNibFENucRGdXbx5uvMQfo85SXZxQaPETVtUxL7YWJ7s34+CkhLisrPp7uPDxJAQXt22zVDv7ZEjSNRqeXvnLgDu7RbOiaQkLmdmYWFmxoDAFkwICea5zWVrXzMLCsgsMO5jia6UlNxcojLKDnLWREZyV3hXlk4Yz3u795CozcHbzo7hrVrxxYGDJGpN317qm0OH/4+9+w6Polz7OP7dzabtpvdeCSQkQEInoffepKOC2MtRAbvHgh5FPRY8VmwgoohdkN57CSVA6CWd9N7b5v0jYcmSQhpvgt4fr1yXOzvlmd/O7t77zDMD/x01klPJyZxITOKebl1RGxrqCl53S0vGdGjP3pgY0gsKcTY348GePSkqK2NnVN23O2yoJhWmhoaGPPVUzbEe8+fPb/A6zM3NCQoK0pum0WiwtbWtMb0lBNm48P3Au3WPXwweDsBv0Sd4NnwNDqZmuKgtWny79+9dxYKgQSzuMQ4bYw1pRXmEp8bWe2uK4+nxLDj0O/ODBrEwaBDReRk8su8n3ZdHeYUWX3M7JoV2xsZITWZJIacyrjJzx3LdbXBagmTWNJJb492KzGxN1LzTcwIOJmbklhZzLjuZebu/Z1+107C3c2bcotzWx5/BxljNE4EDsDcx42xWMvfu+YH04uuZ3M65dbJ24ftBNTP7NaoyM3sT/cxm+IRgqDRgUbfRLOo2Wjf92vwAs9t1B+CHQXP0tvXM4T/5LbqyALtvzyoWdBrEW9UzS4sl/WaZHazKrFNlZg/fkJnPtcyMr2c2Y/vyGj9Cmqu8QouvhR2TvTtjbWxKVnEhJzMSmb71Oy7mpOnm8zCz0ruv6brYs9gYq5nfqT92JhrOZiYzd+dqvWPl9WNb0FZU8GnfyRgZGLAnMYqXjmzUPZ9SmMe0LSt4Nngw3w6agZFSRUJ+NrsTr9RZlAIsPXsQU5URb/YYhYWRCUdS47hn52rd2NESbRljPTryRFA/jJQGxOVns+z8Yb4+d7jOdTbFE2vX8XT/vrw/ejRWJiYk5OTw3t69/FDtBvvOFuZ6+6I2NOS1oUNwMjOnqKyMKxkZLFy/gXXnLzR4u0VlZcz4cTXPDujHpxPGYWZkRFJeHgdiYuvsQQVYd/4CNmo1T4aFYqdWczY1lXt++Y30gspe5OKyMnq4uXFPt65YmJiQnl/A4fh4pv7wI+kFzb/oTlFxY/9yA3333XcsXbqUK1eucODAATw9PVmyZAne3t5MmDChSY0ZOHAgwcHBLFmypEHz5+TkYGlpic/yF1CqGzZOVQghxN9P077JhLa8dYdJ3I4UCVJvNJa2qIjol14kOzsbC4v6fyw36T6mn332GQsWLGDUqFFkZWXpLniysrJqcFFZm507dzZreSGEEEIIcftqUmH60Ucf8eWXX/Liiy/qjQXt3r17jXGjQgghhBBCNESTCtOoqChCQkJqTDc2NiY//9b9s15CCCGEEOLvq0mFqbe3NxERNW8bsHHjRgICAlqiXUIIIYQQ4h+mSVflL1iwgEcffZSioiIqKio4fPgwq1atYvHixXz1Ve3/ZKIQQgghhBD1aVJhet9992Fqasq///1vCgoKmDVrFi4uLnz44YfMmDGj5VsphBBCCCH+9hpdmJaVlfHDDz8wYsQIZs+eTUFBAXl5eTg4ONyaFgohhBBCiH+ERo8xValUPPTQQxRV/YsDarVailIhhBBCCNFsTbr4qWfPnhw/frzlWyOEEEIIIf6xmjTG9JFHHmHhwoXEx8fTrVs3NBqN3vOdO3duqfYJIYQQQoh/iCYVptcucHr88cd10xQKBRUVFSgUCt2/BCWEEEIIIURDNakwjYqKavmWCCGEEEKIf7QmFaaenp4t3xIhhBBCCPGP1qTCdMWKFfU+f/fddze1PUIIIYQQ4h+qSYXpE088ofe4tLSUgoICjIyMUKvVUpgKIYQQQohGa9LtojIzM/X+8vLyOH/+PH379mXVqlUt30ohhBBCCPG316TCtDZ+fn689dZbNXpThRBCCCGEaIgmncqvc2UqFVevXm3JVTZIRUXlnxBCiH+oCkVrt0D8Q5SbaFu7CbcdbUXDM2tSYbpmzRq9xxUVFSQmJvLxxx8TFhbWlFUKIYQQQoh/uCYVphMnTtR7rFAosLe3Z/Dgwbz33nst1TYhhBBCCPEP0qTCVKuVbmwhhBBCCNGymnTx02uvvUZBQUGN6YWFhbz22mst0S4hhBBCCPEP06TCdNGiReTl5dWYXlBQwKJFi1qiXUIIIYQQ4h+mSYVpRUUFCkXNKyBPnDiBjY1NS7RLCCGEEEL8wzRqjKm1tTUKhQKFQkH79u31itPy8nLy8vJ46KGHbkU7hRBCCCHE31yjCtMlS5ZQUVHBvHnzWLRoEZaWlrrnjIyM8PLyok+fPreinUIIIYQQ4m+uUYXpnDlzAPD29iY0NBRDQ8Nb1S4hhBBCCPEP06TbRQ0YMED3/0VFRZSUlOg9b2Fh0fyWCSGEEEKIf5QmXfxUUFDAY489hoODAxqNBmtra70/IYQQQgghGqtJhenTTz/N9u3b+eyzzzA2Nuarr75i0aJFuLi4sGLFipZvpRBCCCGE+Ntr0qn8tWvXsmLFCgYOHMg999xDv379aNeuHZ6ennz//ffMnj275VsqhBBCCCH+1prUY5qRkYGPjw9UjSfNyMgAoG/fvuzevbtlWyiEEEIIIf4RmlSY+vj4EBUVBYC/vz8//fQTVPWkWllZtWwLhRBCCCHEP0KTCtN77rmHEydOAPDcc8/xySefYGJiwvz583n66adbuo1CCCGEEOIfoEljTOfPn6/7/6FDh3Lu3DmOHj1Ku3bt6Ny5c0u2TwghhBBC/EM0qTCtrqioCE9PTzw9PVumRbdIDzsP7vfvQ6C1M46m5jy09ye2Xj1f7zK97D15IXgYfhb2JBbk8MnZPfwWfVL3/EP+YQx388fH3Jbi8jKOpcfzzsltROWmN7u9o9wCeDJoIG4aK6JzM3jn5DZ2JV3SPf94YH/GuAfirLagVFtOZGYi75/awYmMq83e9jWSWdNIbo0nmTWNRmXEk0EDGe7aAVtjDWeyknj9+CZOZSbWucyd7bpzZ7seuKktuVqQw6dn9/JHzEm9ecwNjVnYaRDDXf2xMjIloSCb/xzfrLePTdHB0oFXu46is40LGcX5rLgYzpfnD9Q67xj3QD7sM5ktCed5eN9PzdruNUqFgscD+zPBsxP2JhpSivL4NeoEn5zZW+9yRkoDHgvsp7fcx6f38EvUCd08uszcOuhnlni5WW3uYOnAq91GVmVWUJnZuboy68iHoZPZEn+eh/f93Kzt1maEWwdmtQshyMYJa2M1YzZ8xdmslHqXUSmUPNwxlMnenXBSm3MlJ523T+xgd+KVWud/KKAPzwQPYtn5w7x+bGuz2zzK3Z8FnQfgprEkOjeDtyN2sLPaa/JOr7FM8dHvUNuVeJl7dq5u9raveXfISKYEBOlvIyaKOWt/rXMZjaEhC3v1ZbiPH3ZqU06nprBozw5OpiTp5hnh48fsoC50cnDE2sSU0T9+y5m01BZp82jf9izsHYabuSVR2Zm8tX83O2OidM8/2TOUcX4dcDazoLS8nFOpybx7cA8RyUn1rrchmnQqv7y8nNdffx1XV1fMzMy4cqXyAHvppZf4+uuvG7yeV199FYVCoffn7+/flCbdlKnKkLNZybx6bEOD5nfTWPFlvxkcTIlm3OYvWX7xEG92H0c/Rx/dPD3tPVh5KZyp25YxZ9f3qBRKlvefhalB8/5FrBBbNz7oPZmfoyIYv/lLtlw9z2dh0/CzsNfNE5WbwaJjGxmzaSkztn9LQn42y/vPxsZY3axtVyeZNY3k1niSWdO82X0sfR19eOrQn4zZvJS9yVdYMeBOHE3Na51/lm83nuo0mP+d3sWoTZ/z4eldvNp1JIOd/XTzGCqVfDvgTlzVVjy2/xeGbfiUF4/8RXJhbrPaaqYyYnn/2VwtyGbilq9468Q2Hg8cwHSfkBrzuqoteb7LUA6nxjRrmzd60D+UWe26sejYRkZs+Jx3Tmzjfv8+3O3Xo97l/hc6mVBHL54P/4th6z9j/oHfuVLtB46hUsm3A2fjqrHksf2/Mmz9Z7wYvq5lMhswi6v52Uzc/BVvRWzl8cD+dWcWPJTDKbHN2mZ9TFWGHEmN5+2IHQ1eZmHnAcxsF8Kio5sZvu4Lfrh0nM/73kFHa8ca83a2cWZmuxDOZia3SHu72rnyYehEfrocwdiNX7M5/gKf95tCe0t7vfl2Xr1Mz98/1P09se/PFtm+3jZioujxzae6v39t/qve+d8ePIK+7p4s2LqeEau+ZU9cDCsnTMVRY6abR21oyJHEBN7a37IXnXd1cuF/I8ay+kwko1evYPOVS3wxeiLtbex081zJyuDlXdsYsWo5U35bRXxONivGT8XGxLTZ229Sj+kbb7zBt99+yzvvvMP999+vmx4UFMSSJUu49957G7yuwMBAtm69/qtIpWp2J26tdiddZndSw3+5zvTtRnx+FotPVLbtcm4a3ew8uKd9L/YkVxbi8/as0lvm2fA1HJ6wkCBrZ8LTKj8czA2Neb7LMIa6tMfIQMWpjKu8EbGFc9l1v/Hm+vVkd9IlvqrqSVgSuZO+jt7c5deDl4+uB2BtbKTeMm9GbGaaTwgdLB04kBLd4P2sj2TWNJJb40lmjWdsoGKEWwAP7Vut25//nd7NYOf2zPLtxgeRO2ssM9GzE6suH2V93BkA4vKz6GzjzAP+oWxPvAjAFO9grIxMmLZtGWUVWgASCrL11qMAHvQPY7pPCPYmZkTlZfDJmT1sjD9bZ3vHe3bCUGnAc+FrKNVquZiTSkcrR+a1783qK8d18ykVCt7vPYkPT++iu50HFkYmLZIXQIidG9sSLrAz8ZJuv8Z6BNLFxqXOZfo7+dDT3pNB6z4mu6RIt1x1lZmZMm3r8vozCwhluk9X7E00lZmd3sPG+HN1bnu8Z1BVZmurMkujo7Uj8zr0qplZn4l8GLmb7vbuWBi2XGbV/RFdeVy7aiwbvMxEryA+PbNf10v5/aVjhDl5cZ9/LxYcWKObT60y5IM+43nh8HoeDQyrsR5zQ2NeCBnCUNf2GBkYcCojkf8c28q5enps57bvwe7Ey3x57hAAH5zaTV8nb+7268a/j2zUzVeiLSOtKL/B+9QUJeVlpBYUNGheYwMVI33bc/+6Pzh8NR6AJYf3M8TLhzuDuvDeoX0A/H6+8n3sZl73v7ZpYWTMC2EDGObTrjK3lGRe37ODs+l196zO69KVXbFRfHE8HID3D+2jn7snczoH8+LOys/cNRf0j9v/7N3JjMDO+NvZsz++eT+OmtRjumLFCr744gtmz56NgYGBbnqXLl04d67uN1ltVCoVTk5Ouj87O7sGLHXrhdi6si85Sm/anqTLhNi61bmMuaExAFklhbppH/WZgq2xhnl7VjFhy1eczkpixcA7saznwzbE1o39NbZ9pc5tGyqVTPftSk5JEeeyWuaXZlNIZk0juTWeZFZ5ilSlVFJcXqY3vai8lO527rUuY6RUUawtv2H+MjrbuKJSVH4dDHFpz/H0BF7tOoqD4+ezfsSDPBwQhlKh0C3zUEBfJnp15uWj6xm16XOWXTjIe70m0tPeo872hti6EZ4WS6lWq5u2J+kyvhZ2eoXUvzr2J70on5+jIpqQSv2Op8XTx9ELLzMbAPytHOhu786uen4UDXFtz6mMRB7w78PecY+zZfTDPNdlCMYG1ztRhri053haPK92G8nBCU+yfuQDtWQWdj2zjUtZdv4Q7/W+SWZ2boSn3pjZlVoy63fLMmsuIwODWo7RMrrb6b9fFnUfwY6rl9mXXPsPt0/6TsbWWM28XT8yYeM3nM5IYuXgWfW+V7vaudZY357EK4TYuepN6+3gyeFJT7B1zIO83n0kVkbN7/W7UW9Xd47Me4Rts+fxnwFDsTKpu90qpaL293ZZGT1c6v6Mq80nI8dhq1Yzd+2vjFv9HZGpyXw/cSqWxvV8xjm5sC9O/2zF7thoujrV/gPOUKlkZlBncoqLONsCQwma1D2ZkJBAu3btakzXarWUlpY2al0XL17ExcUFExMT+vTpw+LFi/HwqPuN+v/F3sSM9Bt+QaUV5WNuZIKxgarGAaMAXgwezpHUWC7mVL4w3ezc6WLjQq8171NS9WXw1omtDHPpwEi3AL1fvNXZmZjV+PWWVpSHvYlGb9ogZz+W9J6MqcqQlMJc5uxaSWa1L93/b5JZ00hujSeZQX5ZCcfS4nisYz8u56SRVpzPOPcgQmzdiMnLrHWZPcmXmeYdzJaEc5zOTCLI2plp3iEYGRhgbawmtSgPd401fRysWBNzinv3rMLTzIZFXUehUhjw0ZndGCkNeDggjDm7VnI8PQGqel6723kww6cbh1Nr7y2xN9EQl5+ln1txftVzZuSUFtHNzp2p3sGM2/xFi+VU3edn92FmaMTm0Q9TXqHFQKHk/VM7WBMTWecy7hprutu7U6wt45F9v2BtbMqibqOwMlbz3OG1lfOYWdFH48WamEju3f1jZWbdRqJSKvno9J7KzDqGMWfn9/qZ2bszw7drPZmZ1cys6FpmmuuZ+QQzbtOXLZhUy9mTGMU8/54cToklJi+TMCcvRrh10Cvax3p0JMjaiQmbltW6ju52bnSxcabH7x/q3quLI7YzzK09o9z9+fFy7QV57e/VfOxNr58O3514hU3x54nPy8LDzJqnugxk2cDp3LHlW7QVFS2Swa7YKDZevkhcbjaeFlY83acfy8fdweRffqh1G/mlpRxNTODxHn24lJlOWkEB4/386erkQnR2Vq3bqE13Z1e6ODrT/etPdbm9uW8Xw73bMbpde1adPlnrcvZqDWk39O6mFhRgp9b/jBvs5cNHw8diamhISn4ed/75C5lFzf+Ma1Jh2rFjR/bs2VPjgqdffvmFkJCaY1/q0qtXL5YvX06HDh1ITExk0aJF9OvXj8jISMzNa46RKi4upri4WPc4JyenKc2/JV7tOor2lg7M2L5cNy3AyhG1yojwCU/pzWtioMLDzAZntQUbRzysm/75ub18dnZfg7d5MCWa8Vu+wNpIzXSfEP7X5w7u2PYNGcUNO13Q2iSzppHcGu/vmtlTh/7krR7j2D9+PmVaLaczE/kr7jSB1s61zv/xmT3YmZjxy5B5KFCQVpTHbzEnedA/VPcFqVQoSC/K58Wj69BWVHA6MwknU3Pu69CHj87sxtPMBrXKiOX979Rbt6HSgDNZlRc+bBjxEC7qytO9R9JiufeGYRW10aiMeLfnBF448tct+9Ez2r0j4z07Mf/A71VDCZx4MWQYyYV5/B5d+5e0UqGgoqKCBQf/IK+08vvnzeNb+DhsCq8c3UBxedn1zI7ckJl/bz46vQdPM+vKzAbo/6uIepmNfFA/s90/3nR/NCoj3u01gRfC17V4ZhM8A/lPj1G6x/N2rSY8Na7R63nt2Bbe7DmKLWMepAKIzcvklysnmVp1wZGz2pyXuw3j7h0/6IqnGwVYV75Xj06erzfdxECFp5k1LmoLNo1+QDf9szP7+fTM/ga176/YM7r/P5+dyrmsFHaNf4TeDp7sr6P3tj4T2gfw5sBhusdz1/7K2ovXL+Q8n57G2fRU9tx9P71d3es87T1/y3r+O2Qkh+95mDKtlsjUZNZcPEcn+5pjc+sSYGePxtCQ4/c9qjfdRKXC08IKFzNztsy6Rzf9k6OH+PTooQav/0B8HKNXr8DGxJQZgZ35ZOQ4Jv78PemFzfuMa1Jh+vLLLzNnzhwSEhLQarX89ttvnD9/nhUrVvDXX/UP6K1u1KjrB33nzp3p1asXnp6e/PTTT7WOU128eDGLFi1qSpMbLbUoD9sbekDsTDTklhTV6I15JWQkg138mLljBUnVBrurVUakFuUxe+eKGuvPKSkip7SI8Vuu9wxcO8WYVpSHXY1tm5F6wy+/wvJSYvIyiSGTiIwEto56hGneIXx+ruFfni1JMmsaya3xJLNKsfmZzNq5AlMDQ8wMjUktyuPD3pOJq6PHtLi8jOfD1/LSkXXYVV1dPsOnK3mlxWRU9V6mFuZRWlGu15NzKScNB1NzDJVK1KrKi8fu37uqxsU9JeWVhcW9e1ZhqKwcGlBU9XqkFuVjZ2KmN7+dsabquTw8zKxxN7Pmi74zdM9f61U7N+VFhm/4lNj82veroZ4LHsrSs/tYVzXG9kJ2Ki4aSx4KCK2zME0pzCO5MFdXlAJczklDqVDgZGpOTF5mZWZabT2ZGVVmtufHujPb/WMtmeXpMtJlZnIts/yqzKz4ot/0mplNfYHh6z9rcmZbEy4SkX79LhJJTbyQK6O4gIf2/IqR0gBrY1OSC/N4tssgYqt6goOsnbEz0bBmxPXvfJVSSU8HD+7y647/T2+jVhmSUpTHrG3f11j/tffq2I3XL7yu/72qIbUwr872xuVnkV5UgKeZdZMK061Rl4hIvn5XjKS8mtuKy8kmvbAAL0urOgvT2Jxspv++GlOVIWZGRqQW5PPxiLHE5mTXOn9tNIZGpBTkM+P3mncYyCkuJqe4iNGrr3/+ZRVVjqFOLcjHTq1/oaa9Wk1awQ2fcWWlxGRnEZOdxfHkRHbceS/TOwbx6dHDDW5jbRpVmF65cgVvb28mTJjA2rVree2119BoNLz88st07dqVtWvXMmzYsAasqXZWVla0b9+eS5dqvyXJ888/z4IFC3SPc3JycHevfSxVcx1PT2Cgk/5whTBHH46nx+tNeyVkJMNcOzB753fE33DK5XRmInYmZpRptTUGwl9T2ym34+nxhDp6s/zi9Rc3zNG7xrZvpFQoMKo25vf/m2TWNJJb40lm+grLSyksL8XC0IR+Tr68fbL+2+yUVWh1hcZY90C2X73ItZLqaHoc4zyCUIBumre5LcmFuZRqtVzKSaO4vAwXtWWdp6Cv1pLn8fR4FgQNQqVQ6i4QCnPy4XJOGjmlRRTllDJq4+d6yyzoNAiNyojXj28isbDhX8h1MTFQ1Th1qq3Q6p1WvtHRtDhGuQegVhlSUFY5VM3b3JZy7fUMj6bFM84z8IbMbJqfWVo8CzrdkJnjjZkt1VtmQdBANIZGvH58c7Myyy8rIT+vpMnL36hEW05yYR4qhZIR7h1YH1t5odz+5GhGrtcfhvBOrzFczkln6dmDuh5oexMzyiq0JOQ3/L16LC2BUEcvlp0P100Lc/LmeFpCne10MjXH2tiUlKK6i9f65JeWkn+T0+1OGjOsTUxJyb/5BVeFZaUUlpViYWxMfw8vFjfiCvzI1GTs1RrKtVric2s/wxxTS1uPJ10l1M2Tb04c003r6+7JsaT6b3dX+RnX/AvYG3Xxk5+fH6mpleOz+vXrh42NDadOnaKgoIC9e/cyfPjwZjUmLy+Py5cv4+xc+2koY2NjLCws9P4aSq0yJMDKkQCrym5wdzMrAqwccVZXruOpToP5b88JuvlXXT6Ku5kVz3Qego+5LbN9uzHavSPLLlzv5l7UdRQTPDux4NDv5JcVY2eiwc5EoxsUvy85iuPp8XwWNo2+jj64qi0JsXVjQdAgguo41Qaw/OJh+jn5cm/73viY2/J4YH+CrF347mLlm8vUwJCFnQYRbOOKi9qSQGsnFvcYh6OpBRvi6r4qtrEkM8lNjrW2mxlAP0cf+jv54qaxIszRm5UD7+JKbhq/Vt1f88bcvMxsmODRCU8zGzrbuLCk92T8LO1579R23Tw/XDqKlZEpL4WMwMvMhoHO7Xg4IIyVl45AVcHy1fkDvBA8nEmenfHQWBNo5cRd7XowybPuf2BlTWwkpdpyFvcYh5+FPaPdOzLHryffXDgIVYXLxZxUvb+ckiLyy0q4mJOqdwFQU22/epFHOvZloHM7XNWWDHPtwLz2vdgcf/1U61OdBvHfXuN1j9fGRpJVUsjbPcfRzsKOHvYePBs8hF+iTuh653WZda2WWccwVl6sltm5g7wQMoxJXlWZWTtxl193JnnVl9npysx6jsXPwq4ys/Y9+Ob8oeuZZafq/eWUFpFfWsLF7JbJrDpLIxMCrBzws6i8SNnHwpYAKwe9Xsl3e4/j6S4DdY+72Lowwq0D7horeti7s3zgDJQKBUvPHtRlcyE7Ve+voKyUrJJCLmRX1ht7k6I5npbA0n5T6OvkjavGkq52rizsPIBONk51tnf5hXD6O/twr39PfMxteSKoH51snFlx8ShUfe48FzyYYFsXXDWWhDp6sbT/FGJyM9hTx31WG0ttaMjzoQMIcXTGzdyCUDcPvhwzkejsTHbHXu+R/X7CVO7udH0oZH8PLwZ4eOFmbklfd09+nDidy5kZ/Hz2+nhoS2MTOtrZ087GtvL1sLKho5099lW9nXvjYjiWdJUvRk+kn7snbuYWdHVy4anefenkUPeQgG9OHGOAhxf3BXfH18qGJ3uG0snBiW9PVo7lNVUZ8nTvvoQ4OuNqbkGQvSPvDB6Bk8aMdZfqv/90QygqKho+ulepVJKUlISDgwMAFhYWRERE4OPjc9Nla/PUU08xbtw4PD09uXr1Kq+88goRERGcOXMGe3v7my6fk5ODpaUl3steQKmu//YYvew9+X7Q3TWm/xp1gmfD1/B2j/G4aSyZvfM7vWVeDB5OOws7kgpz+PiM/g28L017qdZtPXP4T918GpURCzoNYoSrPzbGGtKK8ghPi+Xdk9tJLKx7jOwotwDmBw2qvClwXgZvn7h+A28jpQEf9J5MFxsXbIzVZJYUcirjKp+c2VPvjbUbSzJrGsmt8SSzphnt1pGnOg/CydSCrJJCNsWf473IHbrTzjfm5mtuxwe9J+FtbkuZtpyDqTG1/qMDIbauvBg8nAArJ5ILc/g5KoKl5/br9TbO8evJLN9uuGusyS0t4nRmIp+d3ae7dVVtqt9gP7O4gBWXwvniXN1jAd/uMR4LI5OG3WC/ou5ez2s0KiOe7DSA4a7+2BqrSSnKY23MaT4+s1tXxL3dcxxuGitm77h+rPmY2/Jy1xF0s3Mnq6SQ9XFneP/UTr1hIyG2rrwYMqwqs1x+vlJbZj2Y1a56ZkmVmdXRi8oNN9jPrLrB/hd13GD/WvstDE0afIN9rbbh/VN3eHfiv73H1Zj+4ak9fBi5B4AfBs8mPj+bZw5VDuvrae/B6z1G4mFmRX5ZCTuvXuadEztIqed0+g+DZ3M2K1nvBvsalRELOw9gpLs/NsZq0oryOJwax39P7CCxoO5hBqPc/VnYeQCuGkuiczN5O2K77tZVxgYqlvabQkdrRywMTUgpzGVPUhQfnNpd7+2jtOlGDUyschtfjplARztHLIyNScnPY3dcNO8f3EdatbGYe+++n1/OnWbJ4cr3w5h2HXimTz+czMzILipiw+WLvHtwD7kl13uxp/gH8u7QUTW2ueTwft16NIaGPNW7H6N8/bAxVZNakM/hq/G8c2APiXl151Z5g/2+uFlYEJ2VxeL9u3Q32Dc2MODD4WMIdnTG2tSUrKIiTiYn8dGRg3r/AIBeZoVFxD3zEtnZ2TftVGxWYWpubs6JEyeaXJjOmDGD3bt3k56ejr29PX379uWNN97A19e3Qcs3pjAVQgjxN9aAwlTU1JjCVFRqTGEqKjWmMG3UYIBr/zrTjdOa6scfb37VoRBCCCGE+GdoVGFaUVHB3LlzMTauvFF1UVERDz30EBqN/lVvv/32W8u2UgghhBBC/O01qjCdM2eO3uM777yzznmFEEIIIYRojEYVpsuW1f6vMgghhBBCCNFcMupZCCGEEEK0CVKYCiGEEEKINkEKUyGEEEII0SZIYSqEEEIIIdoEKUyFEEIIIUSbIIWpEEIIIYRoE6QwFUIIIYQQbYIUpkIIIYQQok2QwlQIIYQQQrQJUpgKIYQQQog2QQpTIYQQQgjRJkhhKoQQQggh2gQpTIUQQgghRJugau0GtAQDlRYDlba1myGEEKKVVFQoWrsJtyVtifRPNZZpokFrN+G2U17c8MzkiBRCCCGEEG2CFKZCCCGEEKJNkMJUCCGEEEK0CVKYCiGEEEKINkEKUyGEEEII0SZIYSqEEEIIIdoEKUyFEEIIIUSbIIWpEEIIIYRoE6QwFUIIIYQQbYIUpkIIIYQQok2QwlQIIYQQQrQJUpgKIYQQQog2QQpTIYQQQgjRJkhhKoQQQggh2gQpTIUQQgghRJsghakQQgghhGgTpDAVQgghhBBtgqq1G/D/4YH2fRnm6o+PmR1F5WUcz4jjvcitROWl17nMMBd/HuzQDw+NDSqlkpi8DJZdPMCauJO6edQGhiwMGsoQF3+sjEyJz8/iu8uHWB11tNltHuHakSc6DsJVbUVMXjrvRm5ld/Il3fOPBQxgtFsQTqYWlGrLOZ2VyJLT2zmZmdDsbV8juTWeZNY0tyq3c5NfqXXZd05t4ZuL+5vV5lk+PbjXLxQ7EzPOZSfxnxMbOJV5Vff8opCx9LH3xsHUnIKyEo6nx/HuTfapMW5VZrfy9W7tzAAe6BDGcBd/fMyv5/buqW033cZI1wCeCKx8n0TnpfNu5DZ2J+m/T8a4B+rl9kHkjhbKrTv3tg/F3sSMc9nJvB5xY25jCHWonls870Zu5Upuy+WmUihZ2HkAA118cTezIrekmH3J0bxzYgcphXn1LnuXXzfu9++FvakZZzOTefXoZk5mJOqe9zCz4vngIXS3d8fIwIDdiVdYdHQzaUX5zW73zbb9w+DZ9Hb01Fvmh4vH+PeRjc3e9jXDOrZjes/OBLo6YKU2ZdLHKzmXmHrTZR4Y2BMPG0tUBgbEpGeyfO8x1kSc1c2jNjJkwYi+DAnwxUptSnxmNisPRLD68Ml6190QI4L8eHxoKK5WFsSkZ/Hepj3svhANgEqp5IlhofRv742bjSV5RcUcuBzLe5v2kprb/NdMUVFRUdHstbSSnJwcLC0taffdcxioTeqc78uw2ayPi+RU5lUMlErmBw7Gz8KBsVs+pbC8tNZletp5YmFkypXcNEq15Qx0as+znYbz0P4f2JtyGYDXQsbSy96bl46tIaEgizAHX14OHsO/Dq1mR+KFJu9XiI0b3/W/h/dPb2Nn0gXGunfivvZh3LF9KRdzKg/msW5BpBfnE5efiYmBIXP8ejPStSPDN31EZklBk7ddneTWeJJZ09yq3OyMNXrL9Hfy4z9dxzN80/+IL8hqcntHuQbydveJvBqxjhMZ8cxp15sRrh0ZteVjMoorM5nm1ZUruWkkFmZjaWTKYwED8bd0YujGD9HS/I/dW5XZrXq9b3VmFRWKBrXjq7BZrIs/zamMytwWBA7Gz8KeMVs+qzO3EBs3Vg6Yy/unt7Ej8SLj3IO4r0MYk7d9cf194l4tN6Uhc/16MdKtI8M2fty83Nw68k73ibxyfB0nMhKY49eLka4dGbn5k+u5eVflVlCZ278CBuBv5cSQDf+7aW6lJQ3rnzI3NOaTvpP58VIEZ7OSsTQy4eWuwzBQKJmweVmdy43xCODd3uN4KXwjEelXuadDD0Z7+DP0r6WkFxdgamDI+lH3cS4rhSWndgMwv3N/HE3Nmbx5ebPeKTfbNlWFaVRuBh9UbRugqKyUvLKSOtdrHGnaqHaMDw7AzdqClNx8Xp80rEGFaQ9vNyxNjbmSmklpeTkDO/jwzKj+PLTiD/ZdigFg0cSh9PJx56Xft5CQmUOYnycvjxvM4z+sZce5K41qY3XBHs58d980Pti8l53noxjbpQP39uvBlE++52JKOmbGRnw4ayw/h0dyLikVS1Njnh8zEAOlkqmf/lDrOsuLi7j43gtkZ2djYWFR7/ZbvTBNSEjg2WefZcOGDRQUFNCuXTuWLVtG9+7db7psQwvTG1kbqTkw9mnu3LWMI+mxDV7u18EPsCvpIv87swOANUMeZkPCaT47d/2A/nXQ/exOvsSHVfOYGxrzTKfhDHHugJFSRWTmVRaf2sT57OQ6t/N+zztQGxjx0IFVumk/DryXc1lJvBqxrtZlNCojjo5/nrl7VnAwNarB+9QYklvjSWZN01K53ejj3tPRqIy4Z+93umlOphY822k4YQ6+aKngaFoMb57cSEJBdp3bWT3wXiIzr/L6iQ0AKICdo+az8vJhvrywr9Zl2ls4sGbowwzb9D/i8jMbvE8Ndasyq+31bouZNbQwvZG1kZqD455i9q7lHEmrPbcPet6BqcqQh/b/WG1/5nEuO4lXjq+vdRmNyohjE55jzu7v9HJ7rvOwarnF8saJ+nP7adC9nMpM4PWIyh48BbBr9JN8dym8ztw6WDiwZthDDN340U1za2hhWpvONs78MeIe+v75MVcLcmqd57dhcziZkcirRzfr2r9vwr9YceEIn589QF8nb5YNmE7Ir+/rikFzQ2OO37GAOTtWsS+5spfOWW3OCyFD6efkjbaigvDUOF47toWE/Lqzu9m2qSpMz2Yl8/qxrQ3e78YWpte4WFmw7el7G1SY1ubXR2ex63wU/9ta2fY1j9/FhlMX+GzHId08vzwyiz0Xovlwa+UZIXMTY54Z1Y/BAb4YGRgQmZDMW+t3cT4prc7tvD99NKZGhjz83Z+6aT8+OIOzSaks+nNbrcsEuTry8yOzGPzOVyRm59Z4vjGFaauOMc3MzCQsLAxDQ0M2bNjAmTNneO+997C2tr6l2zU3NAYgu7Swwcv0tvfG28yWI2kxumkRGXEMdm6Pg4k5AL3svPAys2Vf8mXdPEt6TsXWWMMD+77nju1fcCYrkeV978bSsO5COtjGnf0p+r929iVfJtjGrdb5DRVKpnt3I6ekiHPZSQ3ep8aS3BpPMmualsqtOltjDQOc/Pg1+rhumkqh5KuwO8kvK+HO3cuYtesbCspK+DLsTgwVtX88GiqUBFq56OVWARxIuVJnbqYGhkz2DCEuP5OkeoqQ5rgVmdX2ev+dMqN6biV15xZs68aBFP0fYXsb+D45Xy23r/vOJr+0hNm7ljNz5zIKykr4qu/sm+TmzP5q264A9qdEEWJbT25ewbc8N6qy01ZUkFNSVOvzhkolQTbO7EuK1k2rAPYlRxFi5wqAkdKACqBEW66bp7i8DG1FBd3t3aEqu+UDZ5JfWsz0rd8xdesKCspKWD5wBobKOrJrwLavGe8ZxJHJT7Jh1P083WUgJgZtb5Rjbx93vOxsOBJ1fWjI8dhEBvn74GBReWaop7cbXnbWuh5VgCUzx2CjUfPAt38w5dMfOHM1hWXzpmBpalzntrp4OHPgsv6PtL2XYgh2d65zGXMTY7TaCnKKipu5p608xvTtt9/G3d2dZcuunwbw9va+pdtUAC90HsnRtFjdKZi6mKmM2TV6AUZKA7QVFSyKWKf3wfr6iQ28HjKW3aMXUKotp6KigpeOr9X1VnS1daezjSuh696ltOpN907kFoa4+DPCtSM/RR+rdbt2JmakF+uP00grzsPOxExv2kAnP97rOQVTA0NSi3KZt+87sur5cG0Oya3xJLOmacncqpvo0YX8shI2X70+RmuUWyBKhYJ/H1ujm/bC0T85PO45etp7sa+WdVkbq1EplbXklo+3uZ3etJk+3XkqaBgalRFXctOYt/c7Siu0Dc6ioVo6s/pe779LZlzLrcuIm+ZmZ2JGWpH+OMr04vxa3yfv97rjem57V5JZldvoqtxePLZWN//zR/4kfPyzN8/thrGW6UX5+NyQ2yyf7jzVaagut3v2rLxluVFVUD4TPIi1MafrPO19rf03jhVNK8rH19wWgIj0qxSWlfBs8CD+e2InChQ8EzwIlVKJvWllvmM8A1AqFDx3+Hrv9DOH/iLijoX0cvBkb1LNMzcN2TbAmpjTJORnk1KYh7+VA88ED8LH3JaH9/7azISaz8zYiJ3P3o+RygCttoLX1m5nf7WC8T9rd/DaxKHsevYBSssrvxde/n0rR6Iri9euni50cnMi7M2llJZXfi/8d+MehnRsx/Cg9vwcfqrW7dqZaUjL0x9+kp6Xj525utb5jVQGLBzRl3Unz5FfXPcQiIZq1cJ0zZo1jBgxgqlTp7Jr1y5cXV155JFHuP/++2udv7i4mOLi69V4Tk7tpw7q83LwGPwsHJi1+5ubzptfVsykbZ+jVhnRx96H5zqNID4/k8NVvQt3+faki40bD+9fRUJBFj3sPHm5y2hSCnM5kBqFv6UTapURB8c+o7deEwMV7hobnE0t+GvYo7rpX5zfw9Lzexu8L4dSo5m07XOsjdRM9e7Gkp5TmLbzK924o5YkuTWeZNY0LZlbdXd4hfBX3Cm9nhl/Syc8NDYcHf+83rzGVbl1sy3ji7DZuumvHP+Lw40YvrA29hT7k69gb2LGvPahLOk5hZm7vtFrQ0to6czqe73/LpkBvBIyujK3XXWPkWyMQ6nRTNy6FGtjNdO8urKk1x1M3fF1ZW5WjnhobDg24Tm9ZYwNVHiYWVNU7sGXfWddb9uxvziUGl3LVmq3JvYU+1Iqc7vXrw9Let3BzJ3LmpzbBM9A/tNjlO7xvF2rCU+Ng6oezI/DJqFAwUvhzbtIKKO4gEf3/c7r3Ucyp30PtBUVrI05zamMRK6NNAywcsTTzJpTU57SW9bYQIWnmTXF9mV8M2C6bvq/wzdwIKX2swA3+vFyhO7/z2enklKUx/eDZ+NhZkVsXuPHoY/t4s+rE4boHj/47R8cjWnaBXD5JSVM/nglamMjevu48+yo/sRlZBMeFQ/AnX2C6eLuxMPf/cnVzBy6e7vy0vjBpOTmc+ByLP5O9qiNDDnw4kN66zUxVOFhY4mzpTlrn7hbN/2LXYf5Yld4o9qoUir5YMYYFApYtGZ7k/azxjpbZC1NdOXKFT777DMWLFjACy+8QHh4OI8//jhGRkbMmTOnxvyLFy9m0aJFTd7eS11GMdDJjzt3Lye5sOYYiBtVALFV43POZSfjY2HHAx36cjgtBmOliicDh/Cvg6vZlXQRgAs5KfhbOTGvfSgHUqNQq4xILcrj7t3La6w7p7SI3NIiJm37XDft2qmktKI8bG+4aMPOuOYv9sLyUmLzM4nNz+REZgIbhz/GFM+ufHGh4QVHQ0hujSeZNU1L5lZdN1sPfMztmH/4F73papURp7Ou8nT4bzXWnVFcQKm2XC+39OJ8SsrLKNNqa8lNUyO3vLJi8sqKicnP4MTBeA6Ne5ZhLgGsi49sYCI3dysyq+/1/jtkBvBS8MjK3HZ9e9Pc0opqnkWwraXterllJLBpxKNM8Qrhi/P7qnJL5KnDdec2cetS3TS93Ez0c7M1qSO3vGJi8jI4kR7P4fHPMMzFn3XxpxuVyzVbEy4SkX79yv+kqoxUCiUfhU3CVWPJ7O0/1HuRUGZxAWVaLXY3tN/ORENqtZ7MvUlRDPrrM6yNTCmr0JJbWsyhiY/zV94ZqBqvG5mRyPwDa2psI6O4gBJtOWM3fq2bllaUT4m2rEHbvlFEWuU+e5pZN6kw3X72Mifjrl/1n5xT/x0L6lNRAbEZlcMxziWm4utgwwMDehAeFY+xyoAnh4Xx+A9r2XW+8offheQ0ApztuadvNw5cjkVtZEhqbj5zvvq5xrpziorJLSpm8scrddOyCyuHZKTl5WNnpt87amumIS1XvyNCpVTywcwxuFhZcM/Xv7RIbymtXZhqtVq6d+/Om2++CUBISAiRkZF8/vnntRamzz//PAsWLNA9zsnJwd3dvUHbeqnLKIa6+HP37m9JaOLVuEoUGCkrI1MplbpTYXr7VFGBkspB+GeyErEzNqO8Qlvn4PbYWgamR2TE0cfBmxWXrw9oDnXwISIj/ubtMzBo0r7VRXJrPMmsaVo6t+qmeIUQmXm1xoVgZ7ISGeUWSHpxPvl1fMHWltvprKv0cfBhW+J5qDol3NvBh+8vH667cQoFChQYKdvusVbvPFWv9+2eGVVF6TAXf+7avaJBd2eISI+nt4M3316q9j5xbOD7pCrb05lNzS2RPvbebLt6Pbc+9t6svFxPz9a13JoxVjK/rIT8PP12XitKvcxtmL39+5sO5ynVaonMSCTUyYstCRd07Q919OK7CzVvdXdt2EMfR09sTTRsTaj8IR6ZmcQYjwDSi/LrLIRj8mpm15htX9PR2hGA1KKmFZQFJaW6YrKlKRTX34cqA4PKU/w3fC+UaytQKqq+F66mYGemoUxbwdWs2s8w19bWE7GJ9Pb1YMX+6+PxQ309iKhWcF8rSj1trZjz1S9kFdY+zrgpWvXiJ2dnZzp27Kg3LSAggNjY2q+MNDY2xsLCQu+vIV4OHs049848Ff4b+WXF2BlrsDPWYFztw/itbhNZEHi9+/2B9n0JdfDBTW2Fj7kd97Trw3iPzrr7/eWXlXA4NZqng4bR084TV7UVkzy6MMGjM1uungNgf8oVIjLi+Lj3DMIcfHBVWxJi48aTHQcTZFX3IOLvLh2ir2M77mnXB28zWx4LGECgtQvfX6n8ADc1MGR+4GC6WLviYmpJoJUzb3Qdj6OpBRvjzzQoE8nt1uQmmbWd3K7RqIwY4dqRn2sZZ7s27iRZxQV82mcG3Ww9cFVb0dPOkxc7j8TR1LzO9i6/eJCpXl2Z6NEFH3M7Xg0Zi6mBIb/FVJ4WdFNb8UD7vgRaOeNsakGIjRsf9ppKcXkpu5IvttnMGvJ6386ZAbwSPIrx7p1ZePh38ktrz+3t7hNYEDhY93jFpUP0c/TlHr/e+JhXvk+CrF10xaEuNxtXXNSVub3ZbdwNuZ0is7iAz6pyc7uWW5cR9ea27OIBpnl3ZaJH56rcxmCqqpabxooHOoTp5fa/XlMoKi/VnWFpCSqFkk/6TqaTjTPzD/yJUqHAzkSDnYlG7wKklYNmcZdfN93jr88fZoZvMJO9O+FrYcvrPUahVhnyS9T19+kU784E27rgYWbFBK9APg6bxDfnDxOVmwHAn9GRZBYXsLT/VHrYu+OmsaSXgwcvdx2GUz3Z3WzbHmZWPBYYRpC1E64aS4a4+vFu73EcSonlXFbjr5qvi6WpMf7O9rRzsAHA284af2d7vV7Jt6aMYP7wMN3j+/v3INTXAzdrS3zsbZgb1pXxwQGsPVH5mZ9fXMLhK3E8PbIfPbzdcLW2YGJIRyaEdGTrmcr76+6/HEtEXCIf3zmO0HYeuFhZEOzhzBPDQgl0dayzvSsOHKevnydzw7ribWfNo4N7E+jqyA8HKo85lVLJklljCXRx5OmfNmCgVGBnpsbOTI2hQfPLylbtMQ0LC+P8+fN60y5cuICnp2edyzTFLJ8eAHzXf67e9OeP/MHvsScAcFFbUlHtjmmmKkNeDh6Nk6kFReVlROWm8Uz472xIuH5aZMHhX1gQNIT/9piMpZEpVwuyWXJ6Oz9GHdHN8+D+H3iy42De7DYB66pTP0fSYkgrrvtUwvGMeJ4K/40nOw5ifuBgovMyeOzAj7rB+eUVWrzN7Phf7y5YG6nJKinkVGYCs3cv41Juy72ZJDfJ7HY/1gDGuAWhQMG6uJqngovKy7hz9zKeChrKR72noVEZk1yYw8HUKPJK6766dEPCaWyM1fyr40Dsjc04m53E/fu+113cU6Ito5udB3e364WFkSnpVa/FzF3ftNi43FuRWUNe79s5M4BZvpW5rRygf1buuSN/8ntMZW7Oaku9nqjjGfE8dfg3ngwcxIKq98mjB1brvU98zG2Z5Dm1Wm5Xmb1ruX5uu5bzVKehfNxnqi63AzfLLf4MNsYaHu84EHsTM85mJ3Pf3h+u51ZeRnc7D+bo5RbLzJ3LWjQ3R7U5w9zaA7B+1H16z83ctpJDKZUdSh5mVtgYXy+41sWexcZYzfxO/bEz0XA2M5m5O1frXZTkY2HD010GYmlkSkJ+Fp+e3s/X56/3pBeVlzF920qeDR7Ep33vwMzQiKSCXPYnR9eb3c22XaotJ8zJm3s69ECtMiKxIIeN8ef4JLL223A11SB/XxZPGaF7/P6MMQB8vO0An2w/CICzpbneMac2MuTl8YNxtDSnqLSMqNQMnv15IxtOXb9v9cLV65k/vC//nTYKS1MTrmblsGTLPn6sdoP9B7/9nSeHhfHmHSOwVpuSlpfPkegE0vPqGc4Qm8jTP23giaGhzB8eRkx6Fv/6fg0XUyr/wQYHCzOGBPgC8Me/7tJb9u6vftaNgW2qVr2PaXh4OKGhoSxatIhp06Zx+PBh7r//fr744gtmz5590+Wbeh9TIYQQfy9NvY/pP11z7mP6T9XU+5j+k9029zHt0aMHv//+O6tWrSIoKIjXX3+dJUuWNKgoFUIIIYQQfy+t/lNp7NixjB07trWbIYQQQgghWlmr9pgKIYQQQghxjRSmQgghhBCiTZDCVAghhBBCtAlSmAohhBBCiDZBClMhhBBCCNEmSGEqhBBCCCHaBClMhRBCCCFEmyCFqRBCCCGEaBOkMBVCCCGEEG2CFKZCCCGEEKJNkMJUCCGEEEK0CVKYCiGEEEKINkEKUyGEEEII0SZIYSqEEEIIIdoEKUyFEEIIIUSboGrtBrSEkiJDlErD1m6GEEIIcVtRKFq7Bbcfbdfc1m7CbUdbUNTgeaXHVAghhBBCtAlSmAohhBBCiDZBClMhhBBCCNEmSGEqhBBCCCHaBClMhRBCCCFEmyCFqRBCCCGEaBOkMBVCCCGEEG2CFKZCCCGEEKJNkMJUCCGEEEK0CVKYCiGEEEKINkEKUyGEEEII0SZIYSqEEEIIIdoEKUyFEEIIIUSbIIWpEEIIIYRoE6QwFUIIIYQQbYIUpkIIIYQQok2QwlQIIYQQQrQJqtZuwP+nJzr1Y5xHR5w15pRqyzmVkcR7J3YRkX613mWe7NRPb9rl7HSGrlta6/zLBk5noIsvD+z+hS3xF5rd5vmd+jOjXTAWhsYcSYvnpfCNROdm1pjPSGnA7yPm0tHakdHrv+JsVkqzt32N5NZ4klnT3Krc3ugxijAnLxxNzcgvK+VYWjxvRezgSk56s9vc2rk1JbPqHurYh2eDB/HNucO8fmwrAK4aS/ZOeLTW+R/d8xvr4841q82tnRnNyO0uv248ENALe1MzzmYm8+rRzZxITwTA0siE+Z3608/ZGxe1BenFBWyJv8D7J3eTW1rc7Da3hdwAHgrowzPBg1h2/voxc6MfBs+mt6Nnjek7Ei5x7+6fALAz0fBMl0H0c/LGwsiEw6mxLDqymei8mvvUWKPc/VnQeQBuGkuiczN4O2IHOxMv683ja2HLs10G0cvBAwOlkkvZaTyy9zeuFuQ0e/sAD3QIY7iLPz7mdhSVl3E8I453T20jKq/+z52RrgE8ETgIV7UV0XnpvBu5jd1Jl/Tm8TG34+mgIfSw98RAoeRyTir/OvgziYXNa/vNtv1YwADGuAfiZGpBqbac01mJfBC5g5OZCc3abnX/qMI0KiedV45sIjYvCxOVins79OTbQTMYtPZzMooL6lzufFYqd27/Qfe4vEJb63zzOvSggooWa++DAb2Z26E7Tx1YS1x+Fgs6D+DbQTMY9tcXlGjL9eZ9LmQwyYW5dLR2bLHtXyO5NZ5k1jS3KrfIjET+jI4koSAHKyMTnuzUjxWDZtB/zadoK5qeY1vIramZAXS2cWZWuxDOZibrTU8syKHHbx/qTZvZLoQHAnrV+HJvrLaQGU3MbYxHAC92HcK/wzcSkXaVef49+HbQDIasXUp6cQGOpuY4mJrx5vFtXMxOw1VjyRs9RuJoas4je39rVnvbSm6dbZyZWcsxc6OH9/6KodJA99jayJR1o+5jfdxZ3bTP+91BmVbLg3t+Ibe0mHv9e/Hd4FkMX/cFheWlTW5jVztXPgydyH9P7GD71UuM9wzk835TGL/pGy5kpwLgYWbFT0Pv4qcrJ1gSuYe80mL8LO0pLi9r8nZv1NPOk++vHOFUxlUMlEoWBA7m676zGbPlszr3L8TGjfd63sH7p7exI/Ei49yD+KTPdCZv+4KLOZVtd9dY88OAufwaHcH/zuwir6wYPwt7irXNa3tDth2dl85rERuIy8/ERGnIXL9efNNvNsM2fkxmSf2fNw3Vqqfyvby8UCgUNf4efbT2X+rNtSbmDPuSo4nLz+Jidhr/ObYVCyMT/K0c6l2uvEJLWlG+7i+zuLDGPAFWDtwX0ItnDq6rdR3tLe1ZNnA6kVOfInzSE7zfZxzWxqb1bneef08+jtzHloSLnMtKZeGBtTiamjPcvYPefAOcfejn5M2bx7Y3KIfGktwaTzJrmluV26rLERxOjSMhP5vTmcm8d3IXrhpL3DSWunlu19yamplaZciS0PE8f2g92SVFes9pKyr08kwrymeEW3vWxZ6loOz6F+rtmhlNzO0+/56svhzBL1dOciknjRcPb6CwrIypvl0AuJCdyiN7f2NbwiVi87I4kBzDuyd2Mdi1HQYKhW49t2tuapUhH/QZzwuHax4zN8ouKdI7fvo6e1NYXsr62Mredm9zG7raufFS+EZOZiQSlZvBS+EbMDZQMc6zo2495obGLO45mvBJT3JiykJWDp5102N7bvse7E68zJfnDnE5J50PTu3mdGYSd/t1082zsPNAdl69zNsROziTmUxsXhbbEi6SfpMfc41x374f+D3mBJdyUzmfncxzR/7EVWNFoLVzncvc3a4Xe5Iv8fWFA1zJTePDMzs5k5nInb49dPPMDxzE7qRL/DdyK2ezk4jLz2R74gW9H1Tmhsb8p+tYDoxdyNHxz/Jtv7voYFn/D5WGbPuvuEgOpEQRn5/FpdxUFp/cjLmhyU3X3RitWpiGh4eTmJio+9uyZQsAU6dOveXbNlQqmdkuhJySIs5m1f/Lz8vcmoMT/8Wu8Q/zQeh4XNQWes+bGKj4MGwir4RvIq0ov8by5obGfD9kFqczkxi/aRlzdv6InYmGj8Mm1blNd40VDqZm7E2K0k3LLS0mIu0qXe1cddPsTDQs7jWaBQfWNOsXZkNJbo0nmTVNS+ZWnamBIVN8uhCbl0li1Sm7v0tujcnste4j2H71MvuSo2+63iBrJwJtnPjp8gndtL9LZjQwN0OlkiAbZ/YmXc+rAtiXFKXX9huZGxmTV1pCeVXP/O2c26LuI9jRwGPmRtN8uvBXzBldu4yqelOr9/JVACXl5XS3d9dN+6TvZGyN1czb9SMTNn7D6YwkVg6ehaWRSZ3b6mrnWqONexKvEFKVlQIY5OJLVG4GywfO4PCkJ/ht2ByGubZv9H41hrmhMQDZJTU7HK4JtnXjQEqU3rS9yZcJtnHTtX2gkx/Reel81Xc2+8cs5KdB9zLERf8Hyoe9pmJrrOH+vT8wefuXnM5K4tt+d2FpWHduN9v2jQwVSqZ7dyOnpIjz2UkNSKBhWvVUvr29vd7jt956C19fXwYMGHDLtjnYpR3/C5uIqcqQlMI87tq+qtZeqWsi0hJ4+sBfXMlNx8HUjMeD+vHTsLsYse5L8stKAHip6zCOpcazJeFireuY0747ZzKTeffELt20Zw6u48Ckf+FtbkNUbkaNZexNNQA1io+0onzsTTS6x//tPZYfLh7nVEYSrtV6f1qa5NZ4klnT3IrcAO7068pzwYPRGBpxOTudu7avolRbecr/ds+tsZmN9exIoI0TEzYua9D6p/l24WJ2GsfSro8ju90zo5G5WRurUSmVtbbd18K2jmVM+VdQX368dFw37XbNbaxHR4KsnZiwqWHHTHWdbZzpYOXAs4eun+W5nJNOQn42T3cZVNnzXF7CvA49cdFY4GBqBkB3Oze62DjT4/cPdcMVFkdsZ5hbe0a5+/Pj5Yhat2dnYlZ7VlXrtTXRYGZozEMd+/D+yV28HbGdAc6+fNbvDmZt+57DqbGN3sebUQAvdBnB0bRY3WnxutuepzctvTgfO5Oqthtr0Bgac3+HMJac3sG7p7bSz7EdH/eext27VxCeFkM3W3c627jQ56/3KK3K7Z1TWxjq0oERbh35KepYk7Z9zUAnP97vdQemBoakFuUyb+9KMuspthurzYwxLSkpYeXKlSxYsABFtVMe1RUXF1NcfH0AeU5O3YN8J3gF8kaPUbrH9+xcTXhqHAeSYxiz4WusjU2Z0S6Yj/tOYtKm5XV23+9KvKL7/3NZqRxPu8reCY8yxiOAn66cYKirH32cPBm74es62xJg7UBvB08ipz5V4zkPMys62zrXaGtdYwurm9u+OxqVEZ+e2X/TeRtKcms8yaxp/r9yu+bP6NPsTYrCwcSM+wN68XHfSUzZvIISbfltk1tLZOasNueVrsO4a8cPNcYm1sbYQMUEr0A+ityrN/12yYwWPNYaw0xlxDcDpnExO40lp/bopt9OuV3jrDbn5W7DuLuBx8yNpvkGcy4rhZMZibppZRVaHt7zK2/1GkPElAWUabXsS45i59VLVWUcBFg7olYZcXTyfL31mRio8DSzxkVtwabRD+imf3Zmf4P2X1lVY2yNv8g358MBOJuVQlc7V2b7hdySwvSVkNH4WTgwa1fjC/vqrrV929XzfHvpEADnspPpauvGDJ9uhKfF0MGyMrdD457WW9bEQIWHxhpnUwvWDX9EN33pub0sPb+XhjqUGs3ErUuxNlYzzasrS3rdwdQdX990THtDtZnC9I8//iArK4u5c+fWOc/ixYtZtGhRg9a3Nf4iEWnXr65MKswFoLC8lJi8TGLyMolIv8r2cQ8xzbcLn5050KD15pYWE5Wbgae5NQB9HD3xNLPmxJSFevN91ncy4alxzNz2PWqVEdsSLvJ2xI4a60spzEOpUNRoq0PVLxQ7Ew2p1X752ZloOFN1qqmPoydd7Vw5P/1ZvXWuGTmPP6MjeergXw3ap+okt8bnJpm17WOt+vTc0mKiczM5np5AxJQFjHDvwNqYM7dNbi2RWZCNM3amGtaOvFc3TaVU0tPBg7vbd6fD6rf1Lggb7e6PiYEhv0VF6q3ndsmMFsots7iAMq0Wu2o9lLXtC4BGZcTyQTPIKyvhwd2/UFatsLydcrsmyNoZOxMNa0bUPGbu8uuO/09v13kRoamBIeM8AvigWnF+TWRmEmM3fo25oTGGSgMyigv4bdgcTmVUnhZWqwxJKcpj1rbvayybU1JETmkRYzde/6GeVdVrl1aUV/vrVFjZG5hZXECptpyLOWl681zOSaebfe2nrZvjpeCRDHTy485d35JcdezVpbLt+j2UtsYaXU/mtbZfzr2h7blpdLP1gKrjL7Uwj7t2f1tj/bmllblN3Hr9riXZernVve1rCstLic3PJDY/kxMZCWwa8ShTvEL44vy+BiZSvzZTmH799deMGjUKFxeXOud5/vnnWbBgge5xTk4O7u7utc6bX1ZCfl5Jrc9Vp0SBkUHDY1CrDPE0s+aPwsoP6c/OHGB1tXFXAJvG3M9/jm1la9Xp1tMZSYx09yc+P0s3zqhGe29oa1x+FimFeYQ5eelu9WGmMiLYzoWVlyq74Rcd3cJ7J3frlnE0NWPF4Jn8a9/veh9sjSG5NT43yaxtH2u1UVT9d22c2+2SW0tktj8pmhHrvtSb9k7vMVzJSefzMwdrFBjTfLuwLeFijd6Q2yUzWii3Uq2WyIxEwhy9dLdnUwChTl6suHBUN5+ZyohvB8+gpLyc+3f9XKOH8XbK7Zr9ydGMXH/DMdNrDJdz0ll6tuYxU91oD3+MDFT8EV33+/HarbS8zKzpZOPM+6cq9+N0ZhL2JmaUVWhJyM+uddmYWm4tdSwtgVBHL5ZV9YYChDl5c7xqKEqpVsvJ9ER8zG30lvMyt+FqfsvcKuqal4JHMszFn7t2ryC+IOum80ekx9PbwVvXGwoQ6uhDREZ8ZdsrtJzKvIq3mf7wES8zWxKq1n86Kwk7EzPKK7QkFNSeW2x+zdxutu26KFFgpGy5crJNFKYxMTFs3bqV336r/3YaxsbGGBsbN2kbpgaGPBoUytb4i6QW5mFtrOau9t1wUpuzPvb67StWDp7F5vjzug+aF0IGsy3hEvH52TiamjG/U3/KKypYE3MGqsat1HYRSkJBDvFVb6QVF48yvV0w/wubyNIzB8kqKcTL3JqxHh157vD6Ot/U35w7zGNBYUTnZhKXl8WCzv1JLsxlc9x5gBr3Wrs2ni4mN1PXI9Bckptk9v+R2a3MzV1jxVjPAPYkRpFRXICT2pyHO/ahqLyUnVcv39a5NSWz/LIS3S1zriksKyWzuLDGdE8za3o6eHDPztU1tn27ZkYzjrWvzh3mvT7jOJmRyIn0q8zr0BO1ypBfrpyEqmJxxeCZmBoYMn//L5gZGmNWdcFLRnEB2oqK2zK32o6ZgrJSskquHzPv9h5HcmEu/z2xU2++aT7BbI6/oOvNrG6Uuz8ZxQVczc+hg5U9L3cdxpaEC7qLvPYmRXM8LYGl/abwVsR2onIzcDQ1Y5BLOzbHn9f1rN5o+YVwVg25k3v9e7Ij4TLjPDvSycaZF8M36Ob58txB/hc6icOpcRxMjqG/sw9DXP2YtW1ls7Kq7pXgUYx178QjB1aTX1qMnXFlL25uabHuoq+3u08guTCX909X3kVhxaVDfDdgDvf49WZX0kVGuwURZO3Cy8eu93h/fWE/H/SaQnhaDIdSo+nn1I5Bzu25u6qHdH/KFSIy4vmkz3T+e2or0XnpOJiYM8DZj60J54jMSqy1vTfbtqmBIQ/592N74nlSi/KwNlIz27c7jqYWbIw/02K5tYnCdNmyZTg4ODBmzJhbto3yCi2+Fnbc0a8z1samZBUXcjIjkWlbvuNi9vUucU8zK6yN1brHTmoLPgydgJWxKRnFBRxJjWfy5uWNGkuRUpjH1C0reDZ4MCsGz8BIqSIhP5tdiVfq/aW59OxB1Coj3uw5CgsjE8JT45i7Y3WTxvg0leTWeJJZ09yq3Iq1ZfRwcGdeh55YGJmQVpTP4dRYpmxeoRtLeLvm1tTMGmqqb2cSC3LYU20c7zW3a2Y0I7d1sWexNVGzoHN/7Ew0nM1MZu6O1bofjIE2Trorv3eNf0Rvm33//ISE/OzbOrf6uKgtarTf29yGHg7u3L3jh1qXcTA148WQoVVDFPL4LeoUH5/WH+s4b9dqFnYewDu9xmJjrCatKI/DqXG1/ki/5lhaAk/u/5OFnQfwVOeBROdm8tCeX/SK683xF3jpyAYe7hjKK12HcSU3g0f2/sqRtPp7BxtjVtVtllYOmKM3/bkjf/J7TOXZL2e1pV5uxzPieerwbzwZOIgFgYOJzsvg0QOr9S6Y2nr1PK8eW8cD/mH8O3gkUbnpPH7wJ46mx+nmeWDfDzwZOIjF3cdjXXU6/khaDGnFded2s22XV2jxMbdlkudUrI3UZJUUcirzKrN3LedSbt0XdDWWoqKiGXeXbgFarRZvb29mzpzJW2+91ahlc3JysLS0xOPLl1Cq674FghBCCCFqquNaY1EPQ6OWuwn/P0V5QRGX715MdnY2FhZ1386P1r6PKcDWrVuJjY1l3rx5rd0UIYQQQgjRilr9VP7w4cNp5U5bIYQQQgjRBrR6j6kQQgghhBBIYSqEEEIIIdoKKUyFEEIIIUSbIIWpEEIIIYRoE6QwFUIIIYQQbYIUpkIIIYQQok2QwlQIIYQQQrQJUpgKIYQQQog2QQpTIYQQQgjRJkhhKoQQQggh2gQpTIUQQgghRJsghakQQgghhGgTpDAVQgghhBBtghSmQgghhBCiTZDCVAghhBBCtAlSmAohhBBCiDZB1doNaAkqozIMjMpauxlCCCFaSUWForWbcFsqLzNo7SbcdsovmbV2E2472qKGl5vSYyqEEEIIIdoEKUyFEEIIIUSbIIWpEEIIIYRoE6QwFUIIIYQQbYIUpkIIIYQQok2QwlQIIYQQQrQJUpgKIYQQQog2QQpTIYQQQgjRJkhhKoQQQggh2gQpTIUQQgghRJsghakQQgghhGgTpDAVQgghhBBtghSmQgghhBCiTZDCVAghhBBCtAlSmAohhBBCiDZBClMhhBBCCNEmqFq7Af9futt5cF/7UAKtnXE0NeeR/avZevV8vcsYKg14LKA/4z06YW9iRkpRHp+c3c2v0REAtLOw54mOAwm0dsZNY8UbEZv49tKhFmlvB0sHXgkZTSdrFzKK8/nuUjhfXdive364iz8P+vfF08wGlVJJTF4G31w4wJ+xp1pk+0hmTSa5Nd6tyAxgpGsATwYOwlVjRXReOu+e2saupEvNbm9Pe0+e7zwcPwt7Egtz+PTsHn6POaF7fqZPN2b6dMdNYwXAxZxUPjm7m90tsO3qGptbT3tPVg6YU2N66Nr3SCvOB2D7qMd17a7u+0vhLIrY0Kz23uz1+FfHAYxxC8RJbUGptpzTmYm8f3oHJzMSmrXd6nrYeXBfhz66zB7e91O9mXWzdefpzkPwMbfFVGVIQn42P145xvKL199/O0b/q9bMVl4KZ9Hxjc1q70i3AJ4MHIibxorovAz+e/LGzPozxj0Q56rMIjMT+SByBycyrjZruzdSKZQs7DyAgS6+uJtZkVtSzL7kaN45sYOUwrw6l9OojFjQuT/D3Tpga6zmdGYyrx/bwsmMRN08TwT1Y6xnR5zV5pX7kJHEuyd3cSK9+ftwl1837vfvhb2pGWczk3n16Ga9bf8weDa9HT31lvnh4jH+faR5r1t1tmo1zwzsR18vTyxMjAmPS2DR1u3EZGbVuczw9u14uHdPPK2tUCkNiM7M5Jvwo/xx+myt8782fAizQrrwn207WH7keLPbfGdIF+7r1R17jYazKam8tnUHJxOTdM+/PmIoYZ4eOJiZUVBawrGEq7yzcw9XMjKbve1/TGGqVhlxLjuZX6OP80no9AYt82HvKdgZa3jx6Fpi8jKwNzFHqVDonjc1MCQuP5ON8Wd4vsvwFmurRmXEN/3uZH/yFV4+to4OFg682X08uaVFrI46BkBWaSGfn9vDldx0SrTlDHL2Y3H3CaQXF7A3+XKLtEMyaxrJrfFuRWYhtm683+sO3ovcxs7Ei4z1COKT0OlM2voFF3NSm9xWN7UVX4TN5McrR3nq8O/0cfDmjW7jSC3K0+WRVJjLe5HbiM7LQAFM8uzCp6HTmbj1Cy41Y9s3akpuAMM3fkxeabHucXpVUQpwx7avMKiWY3tLB5b3v4sNCWea1daGvB5Ruem8FrGBuPxMjA0MucevF8v6zWboho/JLClo1vavMVUZci4rmV+iIvg0bNpN5y8sL2XlpXDOZadQWFZCNzsPXu82msKyElZHVRYAd2z9Wu/Ya2/pwLcD7mRDfO1FREOF2LrxQa/JvHdqOzsSLzLOI4hPw6YxccuXusyiczN47fhG/cz6z2bo+k/IaKHMqMot0MaJjyL3cTYrGUsjE17uOowv+01lwuZldS63uOdo2lvZs+DAGlIK85joFcR3g2YyfP0XJFcVtFG56bx6ZBOxeVmYGKiY59+TFQNnMOivz8kobvo+jPEI4IWQIbwUvpGI9Kvc06EH3w6awdC/lpJebb2rLh3ng1O7dY+LykqbvM3afD55PKVaLQ/99id5JSXM69GNFdOnMPLr5RSWltW6THZhEZ8eOMyVjAxKy8sZ5OvDW6NHkF5QwJ6oGL15h/m1I9jFmaTcun8gNMZo//a8MHgAL23exomriczt3pVl0yYz7MtlZBQUAhCZlMya02e5mpOLlakJj4f1Yfn0Oxj4+ddoKyqatf1WLUzLy8t59dVXWblyJUlJSbi4uDB37lz+/e9/o6j2Jm8Ju5MuNaq3op+jLz3tPBmy4X9klxYBkFCQrTfPqcyrnMqs/EW3sNOQWtejAB7oEMY0n67Ym5gRnZvOJ2f3sCmh7g+s8R6dMFQa8MKRNZRWaLmUk0qAlRP3+PXWFQuHU/UPzBWXDjPJswvd7NxbrFiQzJpGcmu8W5HZnHa92JN8ia8vHADgw9M7CXPw4U7fHrxyfD1U9bouCBrMWPdAzA1NuJiTyn9Pba2xz9XN8O1GfH4Wb53cAsDl3DS62bkz16+XLo8diRf0lvng9A5m+nYn2Ma1RQvTxuZ2TXpxPrnVCtPqbiwAH3D2IyYvQy8Tc0Njnus8jCEuHTBSqjiVeZXFJzZzLju5zm025PX4Ky5Sb5k3T2xmqndX/K0cOZAS1ej9rM3upMvsTmr4cXsmK4kzWdd7ihJiTzHC1Z/u9h66wvTGAvDBejIb6tpel9mbEVvqz8yvJ3uSLvFVVWZLTu8kzNGbu9r14OVjlZmtvSGzxSc2M80nhA5WDhxIiW7wft5Mbmkxd+9YpTft1aOb+WPEPbioLbhakFNjGWMDFSPd/Xlwz8+Ep8YB8GHkHga7tmN2u268f2oXAGti9H/0vHFsK9N9g/G3cmB/cuU+OKvNeSFkKP2cvNFWVBCeGsdrx7aQkJ9dY7vX3NuhJ6svR/BL1EkA/h2+gUEu7Zjq04XPzx7QzVdUXkpaUX6d62kOL2srQlxdGPX1t1xMSwfg5U1bOfjYQ4wL8Oenk5G1LncoLl7v8bdHjzM5qCPd3Fz1ClNHMzNeGTaIe376jS+nTKyxHmdzM54fPIC+Xp5oK+BIfDyvb91JQk7N1+uaeT26sfpEJL+eOg3AS5u2MtDXh6mdglh6KByA1SeunzFLyMnh/T37WDfvbtwsLYjNqvs1aYhWHWP69ttv89lnn/Hxxx9z9uxZ3n77bd555x0++uij1mwWAINd2hOZeZX7O4SxZ8yTbBrxKM92HoaxsnG1/IP+fZno2ZlXjq1nzObPWHbxEO/2nEQPO886lwmxdeNIagylFVrdtD3Jl/GxsMPC0KTWZfo4eONtbkt4amyj2teSJLOmkdwaryGZBdu6sT9Zv5jZm3yZEFs33eNXgkcRbOPG/EO/MW7LUjbEn+HrvrPxNLOpc9shNm7sT7miN21Pkv56q1OiYIxbIGoDQ46nx9c6z/+3P4c+yN4x81nW70662rrXOZ+hQskEj856wyMA/td7KjbGGu7b+wOTtn3Jmawkvu1/F5Z1HDM08PW4cdvTfbqRU1LEuWqFYWvraOVEiJ1bnT9eDBVKxnt24pco/cw+6jMFWxMN9+5ZxcStX3E6M4lvB9xZb2Yhtm7sv6Eg35N0heB6M+talVndBW9LMTc0RltRQU5JUa3PqxRKVEolxeXletOLy8vobl/HPiiVzGgXQk5JEWczk3XrWT5wJvmlxUzf+h1Tt66goKyE5QNnYKisvYwxVCoJsnFmX9L14rwC2JccRYidq9684z2DODL5STaMup+nuwzExKDl+uyMqtZVXHa9Z7QCKCkvp5ubaz1L6uvj6Y63jQ3h1QpWBfDu2JF8eeiIruitTqVUsmzaHeSXlDLj+5+Y/v2P5JeU8s20yfXn5uTIvpjrx3cFsD86hhBX51qXMTVUMaVTILFZWSTm5DZ4n+rSqj2m+/fvZ8KECYwZMwYALy8vVq1axeHDh1uzWQC4a6zpZudBsbaMR/f/hLWxmldCRmNlZMrzR9Y0aB2GSgMe8u/L3N0ricioPJji8rPobufODJ+uhKfV/sFmZ2JGfL7+2JO0osouensTM3KqeojMVMbsGTsfI6UB2ooKXj2+vsYX5v8nyaxpJLfGa0hmdiZmpBXrn9pKK8rHzsQMAGdTCyZ7BTNw/RJSqvb5mwsH6O/oyx1ewbwfub3WbduZmJF+Q+9KenE+5oYmGCtVFGsrv4DaWziwevA8jJUqCspKePTAT1zOTbsleTRUamEeLx39i8jMRIwMDJjqFcJ3A+5m6vav9XoFrxnq6o+5oQm/VStMu9m609nGhd5r36NUW1lwvH1yC0NdOjDSraOup/1GN3s9rhno7McHve7A1MCQ1KJc7tmzksySwhZKoOn2jHkCG2M1BkolH53ezc83FJ7XDHX1x8LQhN+ir4851mW25n1KdJltZZhrB0a6Beh6Xm9kZ2JWoycvrTgPexON3rRBzn580HsypgaGpBTlMnf3rc/MSGnAM8GDWBtzmryyklrnyS8r4WhqPI8FhnEpJ420onzGeXYkxNaVmDz9sYiDXdrxYehETFWGpBTmcfeOVbp9GOMZgFKh4LnD63XzP3PoLyLuWEgvB0/2JtXsTbc2VqNSKmvmV5SPr7mt7vGamNMk5GeTUpiHv5UDzwQPwsfclof3/trsjACuZGSQkJ3DUwP68u+NWyksLeWeHt1wtjDHwUxT77JmRkbse/QBjAwqP3df2byNfdHXOwQe7N2Dcq2Wb4/WfvyM8e+AQqHg+Q2bddOeW7+JY08+Si8Pd/ZG1/xesFabolIqSc/XPwuQVlCAj63+D/bZIV14ZmA/NEZGXE7PYO7qXynVammuVi1MQ0ND+eKLL7hw4QLt27fnxIkT7N27l/fff7/W+YuLiykuvn76KaeerujmUioUVFDBwkO/k1dWuc23Tmzmf32m8uqx9bovn/p4mtmgVhmxrP+detMNlQacrfoSWDfsIVyqBs0fTYvlvr0/NLiN+WXFTNiyFI3KiD4O3jzfeThx+Zn1noa8lSSzppHcGq8lMutg6YhKqWTTyMf0phspDciq+kI8PvE53fQ1MSd1p5wbIio3jQlblmJuaMJItwDe7jGB2Tu/bdXiNCovnai86z0rx9Pj8TCz4R6/3jwd/keN+ad4hbA76ZKucAfwt3JErTLi8Pin9eY1MVDhbmaNs6kF60c8opu+9NxePj+3t8FtPJQSzYQtS7E2VjPNuytLet/B1O1fN2usYUuYueNb1Cojgm1dearTYGLyMvgr7nSN+aZ6B9ed2YSn9OY1MVDhYWaDs6kFG0Y+rJv++dm9fH5uX4PbdjAlmvGbv8DGWM00nxA+7HMHU7Z906zMJngG8p8eo3SP5+1arTsdr1Io+ThsEgoUvBRe/0VCCw+u4e1eYzk48XHKtFpOZyaxNvYMQdZOevMdSI5h7MavsTY2ZYZvMB+FTWLy5uWkFxcQYOWIp5k1p6bo52dsoMLTzJpi+zK+GXB9jPW/wzdwIKVhn00/Xr7+A+N8diopRXl8P3g2HmZWxObVfXFSXcZ39Of1EUN1j+/9+Xce+X0Ni0cN59iTj1Km1bI/Opadl6O42YjF/JISxi9bidrIkFBPD14YPIC4rGwOxcUT6OjAnG5dmfDtyjqX93ewx9PaihPz9T/jjFUqPKws6e7mytdTJ+mmv7RpKwdj4xq8r3+ePsve6BgcNBru69md/00Yy7SVP1JyQw95Y7VqYfrcc8+Rk5ODv78/BgYGlJeX88YbbzB79uxa51+8eDGLFi36f2lbamEeyYW5ui89qsaSKRUKnNQWxORl3HQdapURAA/sXUVyoX4Rfe1X8/37VqFSVHapF5dXfpmmFeVhZ6z/S+par0JqtQ+7CiA2v/JX59nsZHwt7HiwQ99WKxYks6aR3BqvIZlV7pt+b5ydiUbXI6xWGVKm1TJ565eUV+j/yi+o6gGasGWpbtq1baUV5WF7Q4+VrbGG3NIivYK4tEKry+x0ViKdrF2Y49eLl4+ta8Ekmu9kRgLd7DxqTHdRWxLq6M1j+3/Sm65WGZFamMedu76tsUxuaRE5pUV6uWVXFfk3ez2uKSwvJTY/k9j8TE5kJLB5xKNM9Qph6fmGF2q3QnxBZZFyIScFOxMN/wocUKMwvZbZo/t/1puuqcps9s4VNdZ7LbPxm7/QTdPL7IZjzc7YjNQbegGrZxaRkcCWkY8w1TuEpY0obm+0NeEiEdWuik8qrDxFq1Io+ShsEq4aS2Zv/6HO3tJrYvOymLltJaYGhpgZGpFalM//QicSd0PRV1heSkxeJjF5mUSkX2X72IeY5tuFz84cQKMyIjIjkfkHap5ByiguoERbztiNX+umpRXlU6Ito0yrrZmfiaZGftVFpFXus6eZdZMK022XLnPi6vWzD0l5eRSXlTF++UrMjIwwMjAgo7CQX+6aSWRS/cMtKoCYrMo2nE1JxdfWhof69ORQXDw93F2x1ajZ/fD9uvlVSiXPDxrA3O5dGfj516iNDIlMSmbh2pp300gvKKBUq2X8suuFbVpBPiVl5ZRptdhq1Hrz26nVpOXr55ZXUkJeSQkxmVlEXE3k6BOPMrx9O/46W/8dVW6mVQvTn376ie+//54ffviBwMBAIiIiePLJJ3FxcWHOnJq3NHn++edZsGCB7nFOTg7u7nWPj2qOY+lxjHTriNrAkILyyiv0vMxsKK/QklTLIO/aXM5Jpbi8DBe1RZ2nUq8W1BwkfDw9nvlBg1EplJRVfWGGOfpwJSdNd2q1NgoUGBkYNHAPW55k1jSSW+M1JLOI9Hj6OHjr3VYr1NFHN87zTFYSKqUSWxMNR9JqHy97rbCs7nhGPAOc2ulNC6u23rooFAqMlK17rNUmwMqJ1KKa48Lu8AomvSifnUkX9aafzkzCzsSM8gptjQvOrqktt5u9HnVRKhS6cXpthZLaX8s7vLpUZpZ4Y2aJTcrseFVmyy9eH94W5uhNREMya+axll9WQn6eftF5rSj1Mrdh9vbvdWcWGqKwvJTC8lIsDE3o7+zDWxG1D5W5RoECo6ox45GZSYzxCCC9KL/OQvjGoQEAkRmJhDp5sSXhQtU6IdTRi+8uHK1zux2tHeGGH+aNkV9SSn5J7QVtXkll2z2trejk5MiSPftrna8uCsX1z90/Is/qndYHWDbtDv48fYZfqi5aOpOcwhj/DqQXFOi2faNrhW91kUnJhHp6sPVi5UWCCiDUy4PvjtY+fOVa2xQKWuR7oVUvfnr66ad57rnnmDFjBp06deKuu+5i/vz5LF68uNb5jY2NsbCw0PtrKLWBIQGWjgRYVh50bhorAiwdcTatXMfCoMG802OCbv61safIKilgcY8J+Jrb0d3Og2c6D+PXqAhdr4ihQqlbp6HSAEdTcwIsHfHQWEPVG/vrCwd4ocsIJnl2xl1jTUcrJ+7y7cEkz851tnVtbCSl2nLe7D6Odhb2jHbryN3terLs4kHdPA92CCPUwQd3jRW+5nbM8+vNBM/OrIlpuXtLSmaS2/9Xbrcis28vHaKfky/z/HrjY27LvzoOIMjahZWXK68qjc7L4M+Yk7zdYwLDXfxxU1vR2dqFBzuEMdDJr862/nj5KO4aa57uNBQfc1tm+XRnlFug3n0tFwYNprudB65qS9pbOLAwaDC97L1YE1v7Fbj/X7nNadeLIc7t8dBY42dhzwtdhtPbwYvvLx/RW68CmOzZhT9iTlJ+w61f9qdcISIjnk9DpxPm6IOr2pIQWzfmBw4iyLr2iyNowOthamDIgqDBdLFxxUVtSaCVM292G4ejqQUb4pt3q6rmZDbbtzuDnf3wNLPB08yGKV7B3NuhT43jX1FVmP5eS2b7UqI4nh7PZ2HT6Fs9s6CbZHbxcGVm7a9l1p8gGxe+u1Q9s0EE6zJzYnH3a5k171ZVN1IplHzSdzKdbJyZf+BPlAoFdiYa7Ew0ehfSrBw0i7v8uuke93Pypr+zD24aS/o6efHDkNlczknnlysndfvwVOcBBNu64KK2IMjaibd7jcFJbc762Mp9+DM6ksziApb2n0oPe3fcNJb0cvDg5a7DcDI1r7PNX58/zAzfYCZ7d8LXwpbXe4xCrTLUXaXvYWbFY4FhBFk74aqxZIirH+/2HsehlFjOZbXc3TNGdfCjl7sb7paWDG3ny7fT72DLxct6Yzz/O2YkT/Xvq3v8UO8ehHl54G5pia+tDff26MbEwAD+rLqPaVZRERfT0vX+yrTlpObnE1V1L9E/T58ls7CQzydPoLubK26WFvRyd+OlIYNwMjerpaWVvgk/yvQunZgU1BFfWxteGzEUU0NDXcHrbmnJQ717EOjogLO5OSGuznw0YSxFZWXsvNL8u2e06s/QgoIClDdcGWZgYIC2BQbP3ijIxkXvxtIvdBkBwG/RETx3ZA32JmY4qy2vt628lHv2rOSl4FH8NuR+skoK2BB/hg8id+jmcTA1589hD+oe39chlPs6hHIoNZq7dlWesllyegcZxfk82KEvr3ezJrekiNNZifWOucorK2benpW8EjKa34fcT2ZxAZ+c3a13UYGpyohXQ0bhpLagqLyMK7lpPH34d9a34Ae4ZNY0klvbyOx4ejwLD/3Gk0GDWBA0mOi8DB7dv1rvHqbPH1nDIwH9eLbLMBxNLcgsLuBERjw7bujxqi6+IIsH9q3ihc7DmdOuJ0mFObx4dK3erbNsjDW802MiDiZm5JYWcz47mXl7vm/xC8Yam5uh0oDnugzH0dScwrJSzmenMHf3Sg6l6t9WKNTRB1eNFb9E135Rxf17f2B+4CDe6j4ea+PK0/HhqTH13nLnZq9HeYUWH3NbJvWZirWRmsySQk5lXmXWzuUteoutIBsXvh94t+7xi8GV9wX+LfoEz4avwcHUDBf19U4PpULBwk6DcdNYUV6hJTYvk/+e3MaqK/q9bmHXMqvjoqj7965iQdAgFvcYh40us9ibZrbg0O/MDxrEwqBBROdl8Mi+n/Qy8zW3Y1JoZ2yuZZZxlZk7WjYzAEe1OcPc2gOwftR9es/N3LaSQymVvXceZlbYGF8/DWxuaMLTXQbipDYnu6SIjXHneO/kLt0ZmvIKLb4Wdkz27oy1sSlZxYWczEhk+tbvuJhTOR67qLyM6dtW8mzwID7tewdmhkYkFeSyPzla7368N1oXexYbYzXzO/XHzkTD2cxk5u5crcu8VFtOmJM393TogVplRGJBDhvjz/FJZMsOG7E3M+OFwQOx1ahJzcvn99Nn+GTfQb15XCzM9e7/aWpoyKJhQ3AyN6eorIwrGRks/GsD689dqGULtSsqK2PmD6t5ZkA/Pp00Do2REcm5eeyPiSWvuO4hGOvPXcBWrebJvqHYa9ScSUll3k+/kV5QOWa5uLyM7m5uzO3eFQsTE9LzCzgcF8+0lT/q7nPaHIqKimbeCbUZ5s6dy9atW1m6dCmBgYEcP36cBx54gHnz5vH222/fdPmcnBwsLS3x+fZ5DNR133JDCCHE31tFRcve+/qforys7Q0vaeuUsVJvNJa2qIioV18kOzv7pme7W7XH9KOPPuKll17ikUceISUlBRcXFx588EFefvnl1myWEEIIIYRoBa1amJqbm7NkyRKWLFnSms0QQgghhBBtQKte/CSEEEIIIcQ1UpgKIYQQQog2QQpTIYQQQgjRJkhhKoQQQggh2gQpTIUQQgghRJsghakQQgghhGgTpDAVQgghhBBtghSmQgghhBCiTZDCVAghhBBCtAlSmAohhBBCiDZBClMhhBBCCNEmSGEqhBBCCCHaBClMhRBCCCFEmyCFqRBCCCGEaBOkMBVCCCGEEG2CFKZCCCGEEKJNULV2A1pCeamKitK/xa4IIYQQoi3zKmjtFtx+CooaPKv0mAohhBBCiDZBClMhhBBCCNEmSGEqhBBCCCHaBClMhRBCCCFEmyCFqRBCCCGEaBOkMBVCCCGEEG2CFKZCCCGEEKJNkMJUCCGEEEK0CVKYCiGEEEKINkEKUyGEEEII0SZIYSqEEEIIIdoEKUyFEEIIIUSbIIWpEEIIIYRoE6QwFUIIIYQQbYIUpkIIIYQQok2QwlQIIYQQQrQJUpgKIYQQQog2QdXaDfj/NMKtA7PahRBk44S1sZoxG77ibFbKTZd5pGMonubWqJRKonMz+ercIf6IjtSbz9fClme7DKKXgwcGSiWXstN4ZO9vXC3IaVabR7n7s6DzANw0lkTnZvB2xA52Jl6udd7/dB/JLL+uvH5sC8vOhzdru9VJbo0nmTWN5NZ4tyqzJ4L6MdazI85qc0q15URmJPHuyV2cSL/a7Dbf5deN+/17YW9qxtnMZF49upmTGYm1zvvNgOkMdPHlwd2/sCXhQrO3fU1TcvOzsGN+5/4EWTvhZmZV5+voaGrGs8GDGeDsg6mBITF5mTxz6C9OZSQ1q829HDx4MWQofpZ2JBbk8MnpffwadarWeR8K6MMzwYNYdv4wrx/b2qztPtyxDyPcOuBjYUtReRnH0uJ5O2IHUbkZdS5zh3cn/tt7nN604vIyAn56R2/ak536M8M3GAtDY46mxfNS+Eai8zKb1V4aeIyF2LqysMsAgm1dKK+o4GxmMnN2/khxeVmztw+wc+xjuGmsakxfefEIrx7bWGO6SqHkoYAwJnt3xtHUnCu56fz3xDZ2J13Rm+/Odt24z78P9iZmnM1K5rVjmziZ0fz35Si3AJ7sNAA3jRXRuRm8c3Ibu+r4LHut2yhmtevGf45vZvmFw83ednWtWpjm5uby0ksv8fvvv5OSkkJISAgffvghPXr0uCXbM1UZciQ1nnWxZ3mr15gGLZNVUsgnZ/ZxOSedUm05g138eKfXWNKL8tmTFAWAh5kVPw29i5+unGBJ5B7ySovxs7Rv9sHd1c6VD0Mn8t8TO9h+9RLjPQP5vN8Uxm/6hgvZqXrzDndrT7CdK0kFuc3aZm0kt8aTzJpGcmu8W5VZVG46rx7ZRGxeFiYGKub592TFwBkM+utzMooLmtzeMR4BvBAyhJfCNxKRfpV7OvTg20EzGPrXUtJvWO+8Dj2AiiZvqz5Nyc1UZUhsXhbrY8/x765Da53HwtCEn4fezcGUGO7ZuZqM4gK8zG3ILilqVnvdNJZ8PWAaP1w6zvwDfxLq6MXinmNIKczTvWbXdLZxZma7EM5mJjdrm9f0dPDgu4tHOZmeiIFSydOdB7Ji0EyGr/uCwvLSOpfLLSliyLqldT7/YEBv5rbvzlMH1xKfn8X8TgNYPmgGw9d9QYm2vMntbcgxFmLryvKB0/nszAEWHdlMWYWWACtHKipa7nibvOUblAqF7nF7SwdWDJzNhriztc4/v9NAJngG8eKRdVzJSaefkw+fhk1l2rblnMmqfC1Hu3fkheBhvHR0AyfSE5jbvifLBsxk2PrPmvW+DLF144M+k3j35HZ2XL3IOM8gPgubxoQtX3Hxhs+yYa4dCLZ1JamZP+rr0qqF6X333UdkZCTfffcdLi4urFy5kqFDh3LmzBlcXV1bfHvXegNcNZYNXuZQSqze4+UXwpns3Ynu9u66D4OFnQey8+pl3o7YoZsvNi9LbzlzQ2NeCBnCUNf2GBkYcCojkf8c28q5en6hz23fg92Jl/ny3CEAPji1m75O3tzt141/H7n+a8vR1IxXug1n7o4f+XrAtAbvW0NJbo0nmTWN5NZ4tyqzNTFn9OZ549hWpvsG42/lwP7kaACc1ea8EDKUfk7eaCsqCE+N47VjW0jIz65z2/d26MnqyxH8EnUSgH+Hb2CQSzum+nTh87MHdPMFWDlwr38vJmxaxuFJTzR43xqqKbmdzEjU9bo902VgrfM81LE3iQW5PHNonW5a/A15GCkNWNh5AOM8A7EwMuZCVipvn9hR43Wpbna7rsTlZfPm8W0AXM5Jp7u9O/P8e+oVpmqVIR/0Gc8Lh9fzaGBYg/etPvfsXK33+OlDf3Fk8pME2TgRnhpX53IVQFpRft3r7dCTj0/vY2vCRQCeOriWw5OeYLhbB/6KrTz+btUx9u+uQ1l+4YjeMVdfD3BT3FgoPhjQjpjcDA6lxtQ6/0SvTnx2Zq+ul/KHy8cIdfTm3g69WXjoTwDmdejF6ivH+TXqBAAvHVnPQOd2TPUOZum5/VD1WfZ88FCGurTHyEDFqYxE3ojYfPPPsqTLfHX+IABLInfR18mbu9p15+WjG3TzOZqa80rXEdyz6we+7D+j2RnVptXGmBYWFvLrr7/yzjvv0L9/f9q1a8err75Ku3bt+Oyzz1qrWTcV6uiFj4UN4amVHyAKYJCLL1G5GSwfOIPDk57gt2FzGObaXm+5T/pOxtZYzbxdPzJh4zeczkhi5eBZWBqZ1Lmtrnau7Kv6ArhmT+IVQuyuF+0K4L0+4/ny7CEu5qS1+P62FMmt8SSzppHcGu/GzG5kqFQyo10IOSVFul44lULJ8oEzyS8tZvrW75i6dQUFZSUsHzgDQ2XtXy2GSiVBNs7sS7qeWQWwLzlKLzMTAxVLQifyypFN9RY2bdEQ1/acykjk47BJHJ70BGtHzmO6b7DePK92G06InStP7P+D0Ru+Yn3cOZYPnIGXmXWd6w2xc2V/sn7P6J7EK3S11e/EWdR9BDuuXq5xXLYkc0NjgJv2AqtVRuwZ/yh7xz/G0n5T8LOw0z3nrrHCwdSMfdWK6tzSYiLSr+qOhVt1jNkaqwmxcyW9qICfh97N4UlPsGrInXS3c2tmMnUzVCqZ4NmJX6oKytoYKQ0oLtfvKS4uL6Obvfv1fbN2Zl+146AC2J8crff++Sj0DmyNNczb/SMTNn/F6cxEVgy8s97PshBbt1qPr5BqmSiAd3tN4MtzB27pZ1mrFaZlZWWUl5djYqIflKmpKXv37q11meLiYnJycvT+/j+YGxpzaspTnJ/+LF8PmMaio5vZW3XQ25poMDM05qGOfdideJk5O1axOf4Cn/W7g572HgB0t3Oji40zj+37nVMZSUTnZbI4Yjs5JUWMcvevc7t2JmY1PpTTivKxNzXTPX6oYx/KtVqWX2i5cX4tRXJrPMmsaSS3xqsvs2sGu7Tj1JSnODvtWeZ16MndO1aRWVIIwBjPAJQKBc8dXs/57FQu56TzzKG/cFFb0MvBs9ZtWhurUSmVtWdmotE9/nfXYRxLi9f1pN1OPMysmO3XlejcDObu/JHvLx7jla7DmOzdCQAXtQVTfLrw2L7fCU+NIzYvi6/OHeJIahxTfDrXuV57E02tuZkbmWBsUHnyc6xHR4KsnXjnxI461tJ8CuClrkM5khpXY7hKdVdyMnj20F88sPtnFhxYg1Kh4Jdhd+Nkal65P6Ya3T7cuE/XjoVbdYy5m1WO+3yiU19WX45g7s4fOZ2RxHeDZ9X746A5hrl2wMLQRNfTWZs9SVeY16EXnmbWKIAwR2+Gu/njYFL5eWJtVLlv6TX2LQ+7qnm62bnTxcaFf+3/lcjMRGLyMnnrxDZyS4oY6RZQ57Zr/Swr1n9fPhgQSnmFlm8v3trPslY7lW9ubk6fPn14/fXXCQgIwNHRkVWrVnHgwAHatWtX6zKLFy9m0aJFDVr/BM9A/tNjlO7xvF2r6z3lUJ+80mLGbvwatcqQUCcvXgwZSmxeFodSYnXjR7bGX+SbqkHwZ7NS6Grnymy/EA6nxhJg7YhaZcTRyfP11mtioMLTzBoXtQWbRj+gm/7Zmf18emb/TdsVZO3E3PY9GLfpmybtV20kt8aTzJpGcmu8/6/MrjmQHMPYjV9jbWzKDN9gPgqbxOTNy0kvLiDAyhFPM2tOTXlKb73GVZkV25fxzYDpuun/Dt/AgZTaT2FWN8TVj1BHT8Zu/LpJ+1WblsztZhQoOJWRyLsndwFwJjOZ9pb2zGoXwm9Rp+hgZY9KqWTbmIf0ljMyMCCzuLLor57pn9GResNC6uKsNuflbsO4e8cPzRqfeTOvdR9Je0t7pm39rt75jqcncDw9Qff4WFo8m8c8wMx2IXxwaneDtnWrjrFrnwmrLh3Xne4/k5lMqJMXU3278N8TOxvUvsaY6h3M7sRLpBTl1TnPf45v5o3uY9g86mEqgNi8TH6NOsEU7y4N3k6AlQNqlRHhExfqTTcxUOFhZo2z2oKNI68fe5+f3cdnZ/fddL2B1k7M8evJhM1fNbgtTdWqY0y/++475s2bh6urKwYGBnTt2pWZM2dy9OjRWud//vnnWbBgge5xTk4O7u7utc67NeEiEdWuHk0qbPoFBxVATNVVgmezUmhnYcfDHUM5lBJLZnEBpdryGt3al3PS6WZf2QWuVhmSUpTHrG3f11h3TkkROaVFeh/CWVU9EpW/gjR689uZaEgtrDywezi4Y2uiYe/4x3TPq5RKXggewj3te9B/7aeN3lfJrfG5SWZyrFX3dzjWriksLyUmL5OYvEwi0q+yfexDTPPtwmdnDqBRGRGZkcj8A2tqrDujuIASbbleZmlF+ZRoyyjTamvPrKq3JtTREw8zayLu0P9i/bTvZMJT45i1veZrdDMtmdvNpBblcamWY21kVc+7WmVEmVbL+E3foL3hQpv8shIAvdzySour1ptfa265JUUUl5cRZO2MnYmGNSPu1T2vUirp6eDBXX7d8f/p7Rrba6xXuw1nkEs7Zmz7rtEZllVoOZOZjJd5ZY9kamG+bh9Sq/XU2ZloOFM1XORWHWMpVe/PGz8TLmWn4aK2aNR+NYSL2pJQR28e3fdLvfNlFBfw8L6fMVIaYG2sJrkwl6c7DyYuv3I8fGZJAWVaLbY19s2MtKqCV60yIrUoj9k7av5wuPZZNn7zl7pp9X6WGV/PrIe9B7YmGnaPe1z3vEqp5PkuQ5nbvicD//q4CcnUrlULU19fX3bt2kV+fj45OTk4Ozszffp0fHx8ap3f2NgYY2PjBq07v6yE/P8eLpEAAEfFSURBVLySFm5xJaVCgZHSAIBSrZaT6Yn4mNvozeNlbsPV/MqhBqczk7A3MaOsQlvngO2YWm6PcSwtgVBHL73bkYQ5eXM8rfJX6O9RkXrjaACWD5zBH9Gn+PnKySbtm+TW+NwkMznW/m7HWl0UKDBSVn5tRGYmMcYjgPSifPLKam9TbZlFZiQS6uSlu/WTomqM63cXKjskPjtzgNWX9U93bhx9P/85vpVtTTy1fytzu9HR1Hh8zG31pnmb2+iOqzOZyaiUSuxMNHX22taW2/G0BAa6+OpN6+vkzbGqXsn9ydGMXP+l3vPv9BrD5Zx0lp492CJF6XC3DszatrLGxVwNoVQo6GDlwM6rlwCIy88ipTCPUCcv3W26zFRGBNu68P3FY3ALj7H4/GySCnJrvk4WNuy6WvvtkZpjincX0ovz2ZHYsOO3RFtOcmEuKoWSkW7+rK+6ir9UqyUyM5FQR2+23rhvF49A1WeZnYkZZVotCQUN/yw7nh5PqIOX3q2fKj/L4gH4I/qU3thWgGX9Z/JnzKl6x802RZu4wb5Go8HZ2ZnMzEw2bdrEhAkTbsl2LI1MCLBy0A3A9rGwJcDKQe9Xwru9x/F0tastH+7Yh75OXrhrrPC1sOVe/55M9ArSu9/fl+cOMsajI9N9g/E0s+Yuv24McfVj5cXKN8HepGiOpyWwtN8U+jp546qxpKudKws7D6CTjVOd7V1+IZz+zj7c698TH3NbngjqRycbZ1ZUrTerpJAL2al6f2XaclKL8lv06kLJTTKTY63t5nYrMjM1MOSpzpX3d3RRWxBk7cTbvcbgpDZnfWzll+Sf0ZFkFhewtP9Ueti746axpJeDBy93HaYbR1ibr88fZoZvMJO9O+FrYcvrPUahVhnqTqmmFeXXyAzgan5OkwqilszNUKkkwMqBACsHDJUGOJqaE2DlgGe1cYnfnD9MsJ1L5X1izawZ79mRGe2CdcdaVG4Gf0RH8m7vcYxw64CbxpLONs483LEPg24oPKv7/tIx3M2seDZ4ED7mttzZriujPQL45lxlIZFfVlIjt4KyUt0x2ByvdR/BRK8gntz/J3llJdiZaLAz0ejGttaW1b8C+9LXyRt3jRWB1o580Gc8rmoLvR8dy84f5rHAMIa4+tHB0p53+4wjuTCXzfHn4RYeY1R9Jsxt351R7v54mlkzv1N/fM1t+elKyxZZCuAO7y78Hn2S8ht+HPy313ie6jRI97iLjQvDXTvgrrGiu5073wyYiUKh4Itz14cNfXP+ENN9Qpjk1Rlfc1te6z4aU5WhrjjclxzF8fR4Pus7lb6OPriqLQmxdWNBp4EEWTvX2c7lF8Lp5+zLvR164WNuy+OB/QmyduG7S5UFb1ZJIRezU/X+yiq0Lf4dQGv3mG7atImKigo6dOjApUuXePrpp/H39+eee+65Jdsb6uqnd8Pfj8ImAfDhqT18GLkHqgamV/9laWpgxGvdR+Jkak5ReRmXc9JZcGAN62Kv34dsc/wFXjqygYc7hvJK12Fcyc3gkb2/cqTqlwZVY5oWdh7AO73GYmOsJq0oj8OpcfVecXosLYEn9//Jws4DeKrzQKJzM3lozy/N/pBpLMmt8SSzppHcGu9WZFZeocXXwo7J3p2xNjYlq7iQkxmJTN/6ne70Z1F5GdO3reTZ4EF82vcOzAyNSCrIZX9ytO70c23WxZ7FxljN/E79sTPRcDYzmbk7V/+/X33flNwcTM1ZN+o+3eMHAnrzQEBvDibH6IYYnMxI5OE9v/J0l4H8K6gvcXlZvH5sK3/GnNYt98zBv3gsMIwXQobgaGpOZnFB5VCJhEt1tjc+P5t7d/3Ev7sOZW77HiQV5PL84XU17mF6K9zp1w2AH4feqTf96YNrdTf4vzErSyMTFvccjZ2JhpySIiIzkpiydYXeMIelZw9iqjLizR6jsDAy4UhqHPfsXK0bI3srj7Fl58MxVqp4MWQoVsYmnM1M4e4dq2rcRq65whx9cNVY8nMtBa+L2lIvM2MDFQs6DcTdzJr8shJ2JV7iqYN/klttX9fHncHWWM2TQQOwN9FwJiuZebtWkV58fd/u2/0jCzoN5K2eY7Ex1pBWlEd4amyNi6aqO54ez4IDfzC/00AWdhpEdF4GD+/7qcY9TP8/KCpa8m6yjfTTTz/x/PPPEx8fj42NDXfccQdvvPEGlpYNu69cTk4OlpaWeH71Ekp13bdBEEIIIYRoCUqltrWbcNvRFhQRNe8NsrOzsbCofxxvq/aYTps2jWnTWv4m3UIIIYQQ4vbTJsaYCiGEEEIIIYWpEEIIIYRoE6QwFUIIIYQQbYIUpkIIIYQQok2QwlQIIYQQQrQJUpgKIYQQQog2QQpTIYQQQgjRJkhhKoQQQggh2gQpTIUQQgghRJsghakQQgghhGgTpDAVQgghhBBtghSmQgghhBCiTZDCVAghhBBCtAlSmAohhBBCiDZBClMhhBBCCNEmqFq7Ac1RUVEBgLawuLWbIoQQQoh/AqW2tVtw27lWp12r2+qjqGjIXG1UfHw87u7urd0MIYQQQghxE3Fxcbi5udU7z21dmGq1Wq5evYq5uTkKhaK1m6MnJycHd3d34uLisLCwaO3m3BYks6aR3BpPMmsaya3xJLOmkdwary1nVlFRQW5uLi4uLiiV9Y8iva1P5SuVyptW3q3NwsKizR0gbZ1k1jSSW+NJZk0juTWeZNY0klvjtdXMLC0tGzSfXPwkhBBCCCHaBClMhRBCCCFEmyCF6S1ibGzMK6+8grGxcWs35bYhmTWN5NZ4klnTSG6NJ5k1jeTWeH+XzG7ri5+EEEIIIcTfh/SYCiGEEEKINkEKUyGEEEII0SZIYSqEEEIIIdoEKUyFEEIIIUSbIIWpEEIIIYRoE6QwFUJA1T/xKxpHbmoihBAtSwrT24h8CYpb4cKFC2RlZd303y8W1+Xn51NeXo5CoZD3pfh/I8ea+CeQb6I2LC0tjbNnz3Lu3DkqKipQKBSt3aQ27fz58/z666+t3YzbyokTJ/D392flypWt3ZTbxoULF5gwYQI///wzZWVlUpw2UFFREVlZWZJVIyQkJLBu3Tq++OILEhMT5VgT/wiq1m6AqN3JkyeZOXMm+fn5ALi4uPD111/j7+8vBWotIiIiCAsL44033mjtptw2IiIiCA0N5ZlnnuGxxx5r7ebcFrRaLR999BHbt2/HxMQEExMTxo4di0qlQqvVSq9zHc6cOcPzzz9PbGwsdnZ2PP/88wwePLi1m9WmnTp1iilTpqBWq0lKSuLFF19k165ddOzYUToq6pGQkEBJSQne3t6t3ZTb1uXLl/ntt98oLS39v/buPDym640D+HdCNoQsiBAiyJ4glSBqiyVLiTXEErXU1tp3VVtpi9KihKLWFrEUVWspRe1LRDYJWQgiqyCbZCbf3x+/zG1GQqPFjM75PE+fyrl3Mu+c3Dvnveeecy6sra3Rt2/ft/r+4ltUAz148ACdO3dGly5dsGvXLgQFBcHQ0BCtW7fG/v37UVBQoO4QNUpoaChatmyJkSNHYvz48eoO550QExMDNzc3zJo1CwsXLoRCocCxY8ewZs0anD9/HomJieoOUSPp6OigWbNm6NWrF/Lz8/HFF1/gl19+kbYJJYWHh6N169aoUaMGJkyYgEePHmHevHkq+4heQFWxsbHw9fVFz549ceTIEURERKBVq1YYOnQo8vPzRVL6Ajdv3kSdOnXg5+eH+Ph4dYfzTgoPD4ebmxsOHDiAvXv3YtCgQejatSsuX7789oKgoHHOnz9Pe3t7JiQkqJT369ePxsbGPH78OElSoVCoKULNcfv2bRoaGnLChAkkyfz8fG7YsIFffPEFFy1axPv374t6ek5BQQE///xzymQynj59miTZsWNHOjk5sXr16qxWrRp79OjBs2fPqjtUjbRt2zb26dOH+fn5bNeuHZs1a8YTJ05w2LBhPHTokLrD0yj37t2jo6Mjp0yZIpWdO3eOXbp0YVJSEp89e0a5XE6SLCwsVGOkmiMvL49jxozhgAEDmJeXJ5Xv2LGDDg4OKmXCX1JTU9muXTv26NGDjRs3pouLC2NjY9Ud1jslJyeHXl5eHDVqFEkyNzeXYWFhtLa2Ztu2bfnHH3+8lTjEJb4GSk9PR2JiIoyNjQEA+fn5AICtW7eiQ4cOGDx4MLKzs0UPDYDdu3fD2NgYNWrUQF5eHvz8/LBq1Srs2bMHixYtQteuXXHs2DF1h6lRypcvj379+mHcuHHo1KkTGjRoACMjI2zfvh3JyclYt24d0tPTsXbtWuTl5ak7XI3TsWNHpKenQ1dXF0eOHIGxsTECAgKwY8cOmJubA6IHUHL9+nV88MEHKncy9u3bhwsXLqBFixZo3749ZsyYgdzcXNELWERfXx+WlpaoW7cu9PX1pfImTZogPT0dSUlJkMvlao1RE92+fRv16tXD2LFj8dtvv0FXVxfdunVDXFycukN7ZxgaGiIrK0saBqGrqwtnZ2ecOnUKaWlp+Pzzz3H//v03H8hbSX+FMlH2GOTn59POzo6BgYHStmfPnpEk09PT6eTkxNmzZ6stTk3y5MkTzpo1i02bNmX16tXp6+vLO3fusKCggNnZ2WzWrBmbN28uemNKcfv2bY4dO5Zt27ZleHi4yrZVq1axYsWKTExMVFt8mkihUDA1NZX169dnWFgYSbJv3740MDCgs7MzDxw4wIKCAnWHqTHy8vJUjq2vv/6aMpmMq1ev5pkzZ/jpp5+yYcOG/O2339Qa57vg1q1brFWrFpOSkqSyqKgo0YNaJC8vjxcuXJB+fvjwIV1dXeni4sLbt29L5QqFQuqlF/5SWFjInJwcvvfeexw9erRUlp+fT5JMTExklSpVOH78+Dcei0hMNUBWVhbz8/P55MkTqeyHH35go0aNVBJQhULBgoICenl5ccSIEWqKVvM8fvyY06ZNY7du3RgaGkoWS/JjYmIok8l48uRJNUepXvHx8Vy3bh3XrFnDw4cPS+WxsbE8c+aM9OWj/MLev38/HRwcmJaWpraY1e3Bgwc8d+4c//jjD6akpEjlCoWCgYGBjIuL4/Dhw1mrVi3++eef9PHxoY2NDQ8cOKDWuNXt+YtA5c9yuZzBwcHSUCQWXYSbmZnxyy+/fOtxapLix1pycrJUrjwvFQoFo6KiWKdOHWZmZpIkp0yZwnr16kk/C39RDt9KTk6WktPY2FjK5XIuWrSIW7ZsUXeIGmv79u3U09Pjtm3bpLLc3FyS5MaNG2ltbc27d+++0c4eMStfzcLDw/HJJ58gJycHGRkZmDhxInr37o1+/fohJiYGv/76K3Jzc/H1119DR0cHOjo6MDY2hoGBgXS7UJtugd26dQv79+/HnTt34OPjAxsbG9jY2OCzzz7D1atXYW9vDxSrk6SkJNja2sLKykrNkatPeHg42rRpA2dnZ9y+fRu6urpo0qQJtm3bhnr16sHa2lqqr3LlygEATp48iZo1a6rcStQmYWFh+OCDD2BmZoYbN26gdevW8PHxwfTp06XzsH79+jA3N8evv/4KNzc37Nq1C4GBgXB0dFR3+GoTHR2NTZs24c6dO2jVqhXef/99NGzYECRRrlw5BAQESPsqFAo8fvwYrq6ucHJyUmvc6vSyY01XVxcKhQLlypWDvr4+nj17BrlcjpkzZ2LVqlU4ceIEqlSpou6PoBbPtwUODg6wtrZWWbGgevXqOHr0KLy9veHv7w97e3sEBwcjMjJS3eFrhMTERMTExCAlJQUffPABDA0N0b17d5w6dQozZ85E+fLl0atXLxgYGAAAKlWqBD09PVSqVOnN5h1vLOUV/lZ8fDxNTU05duxYbtiwgXPmzKGJiQn79u3LGzduMDs7m/PmzaOdnR3d3d05a9YsDhgwgJUqVWJkZKS6w3/rwsPDaWJiQh8fHzo7O9Pe3p4tWrTgiRMnyBdMBvv000/ZsmVLre35y8rKooeHBz/55BOyqGfmwIEDtLS0ZMuWLVV6Z0gyISGBU6ZMoYmJiXSrWtukp6fT1taWEyZMYFJSEq9evcoJEybQ2tqaw4cPJ0meOXOGffv25dWrV8liPc3aPGQkIiKCVapUYa9evejp6UkPDw9aWFhw//79ZFHdPH8LddasWbS3t+fdu3fVFLV6vexYGzlypMq+CQkJtLe3Z2BgIPX09HjlyhW1xa1uL2oLTp06RRYda8XPxcTEROrp6dHU1JTXrl1TY+SaIzQ0lBYWFnR2dqaRkRGtrKy4YMECpqenMzExkYMHD6a5uTlXrVrFvLw8Zmdn89NPP2WTJk2YkZHxRmMTiakarVq1is2bN1cpO3jwIF1dXdmjRw/evHmT+fn5PH/+PHv37k1fX1/27t2bN27cUFvM6vLs2TN2796dw4YNkxq3I0eOsF+/fqxevbrK7UGSPHv2LKdPn04jIyPp9r42evr0KV1dXfnzzz+rlEdFRbF+/frs0KGDVHb58mX26tWLjo6ODAkJUUO0miEyMpL29vYqF38pKSlcvXo1LSwsOG3aNJJkdna2GqPULAqFgoMGDWKfPn2ksrCwMI4aNYoymYy7du0iiyXuf/zxB6dNm8bKlSuLY+0Fx1rNmjWl1UZIMiQkhDKZjMbGxlpdZ2VtC4rP2Rg5ciQNDAwYERGh1tg1RUZGBl1dXTl16lQ+fPiQBQUFHD9+PN3d3Tl48GCmpqYyOTmZc+bMoa6uLm1sbNi4cWNWrVr1rST2IjFVo1WrVtHR0ZGPHj1SucI7evQo7ezsOHr06BI9MNo6sSI7O5uurq5csGCBSnl4eDgDAwNZr149Xr58mSzqhejfvz8dHBx4/fp1NUWsGQoKCmhtbc1JkyZJZcpj6tq1a6xevbqUaLEoYdD2CU8JCQk0NTXlTz/9pFKemZnJpUuX0sHBoUSir+0KCgrYrl07lUSKRefihAkTqKenJ93ZyMnJ4ejRo9mqVSutvMgu7u+ONScnJ+7evVsqHzNmjFZfaPMV2wIWXYR7e3vz0qVLaohWM8XHx9PKyko6J5WWL1/Opk2bcvTo0Xz8+DFZVK/r1q3jtm3bGBcX91biE4mpGh06dIi6urrSxBzlQHeSDA4Opo6ODs+dO6fyGm2+VRgYGMjevXvz6dOnKuWXL1+mj48Phw8fLq1ekJKSwgcPHqgpUs2gHNqwZMkSNmrUiHv27FHZVlhYyNmzZ9PT01NMoCjmyZMn7Nq1K/v161fiizgpKYmtWrVSSfSF/5s0aRLd3NxKDA+5f/8++/XrRy8vL6anp5NFyUVqaqqaItUcr3qsafP3f3FlaQuKT+gsPrFY+P/QBnt7e/7444/kcx1eCxcupL29vTQERx3EQphq5Ovri8DAQPj7++PWrVvQ1dWV1iwNCAiAo6Mjzpw5o/IabZro9LzmzZsjJCQEBw8elOoJANzc3NC+fXscOHAAOTk5AIBq1arBwsJCjdGqn3Kd206dOsHS0hLr1q3D4cOHpW0ymQxWVla4d++eWHezGCMjI4wcORIHDhzAihUr8PDhQ2lbjRo14O7ujosXL4onsD2ndevWUCgU2LhxIzIzM6XymjVronPnzggNDcXjx48BABUqVEDVqlXVGK1mKOuxpvy+0+bv/+LK0hYoH+ddrlw5GBkZqTFazWNpaYn69etj2bJlePLkCcqXLy+tjTtt2jTUrl0by5cvV1t8IjFVsxkzZsDNzQ2tWrVCREQE9PT0AAByuRyGhobSIvsCMGrUKDRu3Bjjx4/H0aNHpS8eAGjVqhUqV66Mp0+fqjVGTaNQKGBvb4+ZM2ciJycH3377LdavXw8AePbsGaKiolCrVi2ULy8W6FBSKBTw8fHBmjVrsHz5cnz55ZcICQmRtqenp8Pa2lo84OI5Xbp0Qdu2bbF+/Xps2bIFqamp0jY3NzdUrlwZWVlZao1R05T1WFOuliH8n2gL/rnCwkIAwIYNG5CWloY+ffpALpertAG+vr4oKCiQ9n3r1NZXqyVetKZf8RnkYWFh9PPzo76+PpcsWcIffviBU6dOpYmJicrCwNqs+CLSPXr0YO3atfnNN98wPj6eOTk5nDhxIp2dnfno0SO1xqlJlBMDHjx4wPj4eEZERHDw4MGsWrUqGzRowPfff58mJiZaPZHieco6U95y3r9/Pxs0aMDmzZvTy8uLAQEBrFy5staPjXyecggNSU6cOJEODg4cNWoUIyIimJyczKlTp7J+/fri9n0x4lj7Z0Rb8M8Uz0WU/z579iwtLCzYrl073rp1S6rbIUOGsFOnTirn9dskEtO35ODBg9ITO5RjX9LS0qQv6qdPn3L+/Pls1KgRnZyc2LJlS7GsRRHlF/jdu3d57NgxkuSoUaPo5uZGQ0NDenh4vLXZgu8KZZ0lJCSwdu3a/Oqrr8ii50mHhITw888/5/r163nr1i01R6o5lOOsEhIS6ODgIE06uXr1KtesWcOAgABOnz5dzOx9TvFjbePGjWTRODVPT0/KZDK6urrSwsJCnJ/FiGPtnxFtwb9T2lOvQkND6ejoSFtbWzZr1ozdunVjpUqV1DrJTkYxuOyNO3nyJObOnQtfX198+OGHqFmzJuLj4+Hm5oagoCD06dNH2jc1NRUVK1aEXC5H5cqV1Rq3JlDeYrhz5w7c3d0xduxYzJw5EwBw8+ZNhIWFwdDQEC4uLlq7iL5yQenCwkKV28t3795F06ZN0a1bNwQFBYnbgcUUX4S7uPj4eKnOvv/++xJ19qLXaSvl4u937txB8+bNMWjQICxYsAAAkJmZiZCQEFSoUAGWlpaoVauWusNVC3GsvR6iLfhnVq5ciaysLEyfPl0qS0xMxKFDh9C/f39UqlQJALBixQokJibCwMAA/fv3h52dndpiFonpW7J69WocO3YM7du3R/PmzeHv74/27dtj7dq10NHRkb6EtPnLSPnZ5XI55HK59LSJR48eoUaNGhgyZAhWrVoFiEkAEmWdHTt2DIcOHUJ4eDi6dOmCNm3aQC6XY+vWrViyZImor2KUdfbnn38iJCQEN2/exODBg2FlZYUjR47g5MmTWL9+vaiz5yjrLTc3F8+ePZPGv2dlZaFy5coYOXIkgoKCAHF+SsSx9s+ItuD1yMrKwtdff43w8HC0bdsWY8eORXJyMuzs7DB06FAsWbJEurjUJCIxfcOK92Jt27YNmzdvxsWLF9G1a1ds3rxZ3eFpDOUX0eHDh7F+/XrExsbCw8MD3bp1g4uLC3bt2oXRo0eLCSel2Lt3LwIDAzFmzBgUFBTg2rVrSElJwfnz50Wv+wvs2bMHQ4cORceOHfHkyRNERUWha9eumDdvntY+4vFllOfnr7/+iqCgIMTExKBFixZo06YNhg0bhrVr12Lo0KHi/CyFONZejWgLXq+0tDSsX78eoaGhsLOzww8//IDu3bvjm2++ga6ubon9NaJzTG2DCLSIckDxgwcPaGJiQmtra3755ZdMSUkhxdp0kv3797NixYqcPn069+3bJ4231fZF8l/m/v37dHNzY1BQEFk0kcLExKTEQufCXyIjI1m3bl1u2LCBJJmbm0uZTMa5c+eqOzSNduDAAVaoUIFffPEFz5w5w27durFq1aq8cOGCukPTWOJY+2dEW/B6FM8tpk+fTkNDQ7Zs2VIqK+0x3ppAJKZvmPLAuH37Nq2srDhq1CgGBQWxe/fuXLRokTQhSpsVFhYyPT2drVu35uLFi8miZL5GjRocN26cusPTaAkJCbSxsWFSUhLj4+NpaWnJYcOGSdt/++23Eguea6PiX9AXLlxg06ZNyaKnwtSpU4dDhw6VtkdHR6s87ELbKRQKPnnyhJ07d5Ym0T19+pQ1a9bk2LFj1R2exine2ItjreyUTz8UbcHro5xkl5qaSgsLCzZv3pzdunXjihUrpH00MTkVfeGvUWmjImQyGZ48eYIePXqgTZs2WLlyJT755BN4e3vj6NGjCA4OVt9aYRpAedvAwMAAz549Q69evXDnzh3Uq1cPfn5+WLZsGQDg999/R1JSkrrD1QjFjzO5XI6qVavi5s2b8PT0hK+vL1avXg0AiIyMxK5duxAXF6fGaNUrPT0dmZmZ0uQwAEhOTkZeXh5SU1Ph6+sLb29vrFmzBgDwxx9/YMWKFSprcGqjgoIC6TjT0dFBpUqV8PTpU7Rr1w53796FnZ0dOnfuLC3CfejQIYSGhqo5avW6desW4uLiVG4xi2Pt7yUnJyM9PR0ymUy0Ba8RSZQvXx4JCQlwdHRE79698csvv6BFixY4deoUvv76a6DYg1g0ieZF9I5SJliXLl3Cjz/+iC+//BJ37txBfn4+ypUrh6VLl2LTpk3Sl/2IESPQv39/+Pv7a+SB8Sbl5eVJT2hSjmV59uwZMjIysHPnTnTs2BGdOnWSBrcnJiZi5cqVuHbtmlrjVqekpCRcvXoVKKoz5XFUv359VKlSBe3atYOnpyfWrl0rDWTfvHkzrl27prUzVOPi4uDu7o758+cjNTVVOs+8vLwgk8lgbm4Ob29vaQIiihKsiIgI6Ovrqzl69YmMjMSkSZMQHR0tJfO5ubnIy8vDzz//jPbt26ucn8nJydi8eTMiIiK09glioaGhcHZ2xtGjR1XKxbH2clFRUejQoQN++eUXoOhCWy6X49GjR6IteAXK804ulyMvLw8o1rZu2LABfn5++Oabb1C9enUMGTIETk5OCAsLw6NHj9Qa9wupu8v2v2T37t2sXr06O3ToQA8PD5qamnLZsmUlFql9fh0xbRIWFkZPT082adKETZs2ZVBQEO/evUsWPdPdwMCAnp6eKq/57LPP6OzsLO2nbaKiomhiYkJfX19evHhRKlfepnn48CFbtWpFOzs77tmzh1u3buXYsWNpZGSk1rXo1G3jxo2UyWT09vbmzJkzpTWDCwoKGBwcTEdHR/bs2ZOpqam8cOECp02bpvULmt+4cYMmJiYcOnQoExISVLbt2LGDhoaGbNGihUr5Z599Rjs7O8bHx7/laDVDSEgIDQ0NOXny5BLb5HI5d+7cKY61Uly/fp0VKlSgTCYr8Z2/dOlSGhoairagDJTDlA4dOsSePXuycePG/Pjjj3n06FGSZHZ2dol909PTmZaWpqaI/55ITF+T69ev08LCgps2bSJJ5uTkUCaTceHCheoOTWPExsbSxMSEw4YN45YtW9ivXz82adKEnTt3ZlxcHJ8+fcqhQ4fSzMyM8+fP59KlSzly5EgaGRlp7dOJkpOT2apVK7Zr1462trbs2bOnSnKq/KK5c+cOO3fuTHt7ezo4ONDX11erk1KSvHTpEtu1a8dJkyaxUaNG/Oyzz/jkyROyaFzVTz/9RHt7e1auXJn29vZ0c3PT2uOMRY2Vu7s7x48fL5WlpKTw4cOHfPr0KUly5syZlMlk/PjjjzllyhQOGTKElStX1tp6i4mJYfny5Tlv3jyy6KLnyJEjXLt2LU+ePMnMzEwWFBRwy5YttLOzE8dakevXr9PQ0JCzZ8/mlStXWKtWLe7atUvaHhcXxxEjRoi2oIxeNFnsXX3QgEhMX5MjR46wQ4cO5AsGuStn4GuzlStX0svLS6Xsp59+oqenJ9u1a8ekpCSmpKRw0aJFrF+/Pj08PBgQEMCwsDC1xaxuV65cYUBAAENCQnj58mXa2NiUSE6Lu3PnDjMyMqREQlspFApev36d77//PvPz8zlz5kw2adKECxYsoJeXF1euXEkWPYXt5MmTvH37ttY/LvP+/ft8//33ef/+fT579owBAQFs2rQp69atyx49ejAmJoYkuW3bNrZu3ZpeXl4cMWKE1j6dKD8/n1OnTqWBgQEPHjxIkvT19aWTkxNr1qxJfX199u/fX5pJXlBQII61oh7mChUqcMaMGWTRajXOzs4cOXKkyn4xMTFcsmQJGzRoINqCF/ivThYTiem/pOyxWrVqFd3c3JiRkUErKysOHz5cmu22f/9+jhs3TuuThQULFtDKykrqtVLavXs327RpwxEjRjArK4ssdvuh+HORtdHjx49Vlki5ePEiGzRowJ49e6os06OuZxpruo4dOzI2NpYkOW/ePFarVo2GhoY8fPiwtI9Yru3/zp49S2NjYyYlJXHgwIH08vLioUOHuGzZMnbq1Im2tra8ffs2Wey8VA4n0VZhYWEcN24cbW1tWadOHXbp0oU3btygQqHgoUOH6OzszGHDholjrJhBgwZx2rRpZLFzb8uWLTQwMOC5c+dK7C/agtIp6y47O5vNmjVjQkICExISWLNmTZWVWY4fP84HDx6oMdJXp12zbl6D27dvY+nSpZg6dSoOHz6M5ORkAIC/vz/kcjmqV6+Ojh07Ys2aNdLg49OnTyMmJgZyuVzN0auHcgKFg4MDKlWqhEuXLqlMkujZsyf8/Pxw9OhRabal8kkfenp6aopafRQKhfTvypUrw9nZGSiaKd20aVNs27YNoaGhWLx4MS5duoTCwkIsWrQIO3fuVGPU6pWSkoLY2FjpZ5IoLCzEkydPcOXKFQBAbGwscnNzUbduXVy+fFmaDa32xaQ1RMOGDdG4cWN8//33ePjwIRYsWABfX1+MGzcOc+bMQc2aNbFv3z5pti8AjXtizNui/E5zdnbGiBEj0LZtWzg5OWHhwoVwcXGBjo4OfH19MXHiRGzatAn37t1Td8gaY+PGjVi4cKFK2fvvv4+GDRviyJEjQNEkHhSdx4aGhoCWtgXP05qJw+rOjN8lYWFhNDExYcuWLdmsWTPq6+uzb9++PHToEFk0ecfW1pbjx4+nXC5nZGQkP/30U5qYmDA8PFzd4b91pU3yatasGRs3bsy4uLgS28zMzLhs2bK3FJ1mio6O5rBhw9inTx9+8sknJbYre+EvX77MBg0a0N/fn127dqWhoaFWHmMkGRoaSltbWwYFBUlDZpQ9eXPnzuXevXs5YsQI1qxZkzdu3ODs2bOlh1xo80REpeK9ecOHD6epqSnNzMx469Ytlf28vLw4cOBANUSoOZ4+fSodW8XXf4yJieGJEyekNUmV237++Wc6OjoyMzNTTRFrhgcPHkh3DF90zk2cOJHm5uYqk3WEv2jTxGGRmJZRTk4OO3fuzDFjxkgn1uHDh+nl5cXWrVvz6NGjzMvL49y5c1m/fn1WqlSJLi4udHR0fGcHIP8bkZGR/Pjjj+nl5cW5c+dKY7AyMzNpY2PDZs2aqSRS2dnZbN68OYODg9UYtXqFhYXRzMyMgYGB/PDDD+no6Cjd8mKxBELZ6J0/f54ymYwmJiZaOyEgJiaGZmZmLxwqs2jRIspkMlpYWPDy5ctS+fz580u9ONIWycnJjIqKkn4uniz4+vpSJpNxypQpKnU6ePBgzpkzR2tvS0dGRtLb25vbtm0rkYDyBUNCJk2aRC8vL60exhUXF8fy5cuzXbt2zMjIIJ873pT19uDBA9rY2PDzzz/X2mPsRbRt4rBITMtILpfT1dWVX3zxhUr5+fPn6efnRy8vL0ZERFAulzM1NZW7d+9mSEiIVj7ZKSoqilWqVGFgYCD79u3LDh060MzMjEuWLCFJJiYmSrPHv/rqK+7bt49TpkyhqampNB5Q22RmZrJp06acOHEiWTSe6pNPPuGcOXNK3T83N5djxoxhlSpVtHbyCYsa/r59+5JFDdz27dv53XffcfPmzWTRBeX06dN59epVUkOfcvK2RUZG0tzcnP3791c5doo/geiDDz5g7dq16e/vz6CgIH788cc0NjZWSWa1SXx8PO3t7amrq8sWLVrw559/LjU5Vbp9+zZnzJhBY2NjrZ+wc+nSJdaqVYsdOnSgj48P09PTyVLqLS8vj/369WOzZs3UFKnm0raJwyIxLQOFQsHs7Gx+8MEH0lIqxa/4Tp8+XaJ3S5tNmDCB3bt3l36+c+cOFyxYQJlMJj3SUC6X86OPPqKHhwfr1avH5s2ba2XPstKtW7dob28vJVAkOWLECHp4eNDHx4ddunTh/fv3yaLjMT4+ng0aNND655T7+/tz+fLlJMnmzZuzVatWrF+/PuvXr8/mzZuLRPQ5Dx48oIeHhzTbftiwYSrJafFJdIsWLaKfnx8bNWrEzp07a+1zygsKCrh48WJ26dKF165dY8eOHdmkSROV5LR4D19ERAQ7duxIOzu7d7K36nW7ceMGGzRowGXLlvH999+nr68vc3JySFJaS1NZf2fOnKG5ubl4jPJztG3isEhMX8HKlSupp6cnLVxbvNFbtWoVjYyMtH5ZqMLCQnbv3p0BAQEq5VlZWfz2229Zvnx5rlmzRip//Pgxk5KS+PjxYzVEqzlSUlJobW3Njz76iGlpaZw9ezb19fU5b948fvvtt2zWrBkdHBxUerXEWCyyW7duHDx4MFevXk0vLy+mpaUxLS2NFy5coJ2dHf38/NQdokY5deoUu3btysjISP7yyy+sXbt2ieT0+We3Z2VlvdON3L9VWFjIq1evcufOnWRR/RRPTpXJfPHk9PTp07xz547aYtYUCoWCjx49Yvfu3ZmcnMydO3eyZcuW7N69O7t168ZZs2apHFu5ublSj6rwV46xb98+Ojk58fjx4yWGOSxZsoR169aVxoQrX/MuD4cQiekLJCYm8siRI9y5c6fKWLSBAwfSyMiIf/75p8r+v/32G11cXMRJVfTUDnt7e0ZGRqqUZ2RkcPz48fTw8HjnBmO/afn5+Vy9ejUtLS3p5eVFQ0NDlfG2cXFxNDY25o4dO9Qap6ZQfvlu3ryZHTp0YMeOHTl79myVfZRPd9LmsaTPy8jIUOll37t3r5ScFh/zre3LQD3v+Qk7OTk5UnK6Z88eqb727t2rpgg1m6enJw8cOECS/OWXX1ijRg3q6Ojw999/J8XxVoK2TxwWy0WVIiwsDG5ubpg1axb69u2L3r17Y8yYMQCA9evXw9fXF15eXtiyZQsSEhKgUChw9OhR6OjoaN1z70vj5uYGIyOjEsukmJiYoFOnTggPD0dKSopaY9Q0urq6GDp0KEJDQ/Htt9+iXr16aNGiBVC0ZEpBQQEsLCxQvXp1dYeqEZTnWdu2bVFQUIDjx48jPj5eZR8LCwsoFApxThZjYmKCZs2aAUXLknXr1g0rV67E4cOHsXz5ckRGRgIAvvnmG5w4cULN0WqO4stiKRQKGBoaYt++fTA1NcVXX32FvXv34uOPP8aoUaPw4MEDtcaqSZTLalWtWlVaWnHXrl3Iy8tDw4YNsWLFCqSnp0vLjwlAVFQUxowZA29vb3z++ec4dOgQAODo0aPIzs5G3759ERERIe2fk5MDGxsb1KhRQ41Rv2bqzow1TWZmJhs1asTx48czMzOT9+7d4/z58+nk5MTOnTtL+02aNImmpqasU6cO3dzcaGZmptVjJJ/37bff0srKirNmzVKZ0PTw4UM6OTnx7Nmzao1Pk2VkZNDV1ZU//vijVDZ37lw6OjpK40y1VfHbU8p/R0dH09XVlaamptIY5ry8PM6ePZstWrSQZgILqorXZfHb+r169WLFihW1dqJTWSh7+HJzc+nt7U09PT1WrFhRZYy48Je1a9dy0aJFDAwMlFbI2LlzJx0dHdm7d28xFryImDj8fyIxfc6dO3doa2ur8gSKp0+fcufOnbS1tWWvXr2k8rNnz3LXrl3cunUr4+Pj1RSxZin+BfPll1/Szs6O/fr142+//ca4uDhOmTKFlpaWWrlaAYvGhf7dU5oeP37MXr16SZN5+vTpQzMzM62dSPHgwYMXrjygPN6io6Pp7+/P2rVr08LCgq1bt6apqanW1llZFU9O9+zZQ5lMRmNjY62/yC7L+Dzl7daRI0fS1NRUa9cRLosNGzZQJpPRyspKSt7lcjl37dol2s5ixMTh/xOJ6XMyMjJobW0tXaEo5eXlcfPmzXRxcWFQUJDa4tMUL1uYvHhyumnTJnbr1o06Ojp0cXGhlZXVf+4kKquwsDB26tSJp06deuFkEmWDmJCQwMWLF7N3796cNm0ab968+Zaj1Qz37t2jmZkZu3fvrrIOaXHK4y0tLY3Xr1/nggULuHXrVunxmdooPT2dUVFRjImJ+dsLocLCQubl5XHcuHE0NjbW2uXHsrKy+OTJk1eaiLlixQrKZDKt/U7j37QFxX399dfSOfwuT8x5U8TE4b+IxPQ5eXl5HDhwIH18fHjjxg2VbdnZ2ezSpQv79Omjtvg0QXR0NJcsWfLS5+8WH8yelZXFsLAwRkRE8OHDh28pSs0SHh5OY2NjjhgxotSJX4WFhSVmU5b2hBltc/LkSWlx7g8//FDlVqlCoSgxg1z4/wWQq6srXVxcqK+vz/nz5/9t8nDjxg2ampry4sWLby1OTRIREUEvLy+6urqyZs2a/Omnn8jnEqjSzsOUlBStvgB61bZAeDkxcfj/RGJairCwMJqbm7N3794lvnS++eYbvvfee1q7VM+tW7doampKmUzGTz/9lKmpqSX2EVfDqrKysujl5cWPP/5YKouKimJISEipS8ps2LBBpVyb6zM9PZ1dunThmjVr+N5777F///7SLdPiicIvv/yi9Uu1sSjBMjMz4+TJkxkREcElS5ZQJpOpNGYvutD5L/a8lIWyziZMmMCtW7dy4sSJ1NXVfeEwEHGs/d8/bQu0+UL775w5c4bu7u6cOnUqExMTVbYdO3aMRkZGvHLlitrie1tEYvoc5Ulz4cIFVqxYkf7+/jxx4oS0fdiwYezSpcvf3h77L8rKyuKQIUM4aNAgBgUFSY8tLO0LiUW3bubNm/fW49Q0eXl5bNmyJa9du0a5XE5vb2+6u7vTyMiIzZs35w8//CDte/r0adrY2DAwMFDrn+Mul8uZkpJCW1tb3rt3j3v27KG7uzuHDRvGFi1asGfPnmRRomBpacnPPvtMqxu91NRUtm7dmuPGjZPKCgsL6ePjw3PnzjEkJESlsVu+fDk3btyopmg1Q3p6Or28vDh27FiV8rZt23LMmDHkc8nVr7/+Ko410Ra8UWLiMKm1azQUFhaCpMoyIIWFhdDR0YFCoUCzZs1w6tQpDB06FJMnT4ZCoUDdunVx8uRJnD59Gnp6emqNXx10dHTQpEkTmJmZISAgAFWrVkWfPn0AAFOnTkXVqlWlfTMyMnD16lUkJCRg1KhRMDU1VWPk6pWZmYno6GikpaVhypQpAIAffvgBDx48wIkTJzBz5kxUqVIF/v7+aNWqFaZOnYr27durHJvaSEdHB9WqVYO7uzvCw8PRvXt36OvrY+DAgXj27BmGDRsGAOjSpQuuXLmCQYMGafXSUDKZDD4+PvD395fKvvjiCxw9ehQPHz5EWloanJycMHPmTDg6OuKnn36CmZkZevTogcqVK6s1dnUpKChAZmamVGfKNsDa2hoZGRlAUb0qde7cGZcuXdL6Y020Ba+f8tibMGECcnNzsWXLFsTGxmLQoEFo0KABVq9ejcePH6NevXrqDvXNU3dmrA4RERHs378/27dvz5EjR0oL/7LYQG7l/+/cucM9e/Zw9OjRXLRokdYvoaJ87JlScHAwZTIZJ0+eLD1eTi6X89GjR0xPT3/p2CNtUVhYyD59+nD06NHs3Lkzjxw5Im1LTExkYGAgR44cqZW98GXx4Ycfcvr06STJjz76iCYmJnR0dOSQIUNKPOhC2xV/ZOH27dspk8m4Y8cOpqen89SpU3R3d+ecOXPIonGl4ulEZExMjPRv5ZjlmTNncsCAASr7PXr06K3HpslEW/DPiInDf0/rekyjo6PRokUL+Pr6wt3dHYcPH8aVK1dw/PhxLF26FOXKlUN+fj709PRAEnXq1EGdOnXQvXt3dYeuESpWrAgULTKto6ODgIAAkES/fv0gk8kwfvx4LF68GAkJCQgODhZXx0U9LpMmTULbtm2Rk5OD4cOHS9ssLS1hbm6Oy5cvQ1dXV61xahqSkMlkaNeuHeLj4/HJJ5/g0KFDuHr1Kq5fv44pU6ZAT08PTZo0gb6+vkrPlrYyMjKS/u3h4YErV67gvffeAwC0bt0a1atXx5UrV0ASLi4uaoxUc9jY2ABFPVbKc5CkykNAFixYAH19fYwdO1YsBl9EtAWvLiYmBr/++iv69esHCwuLEtt1dHQgl8tRvnx5DBw4EP7+/oiPj4eOjg7MzMxgbm6ulrjfNq06w0hiy5Yt8Pb2xvbt2wEAM2bMwHfffYfdu3dj+PDhWLt2rXSbfv/+/fDw8BBP2ylFuXLlQBKFhYXo06cPZDIZBgwYgP379yM2NhaXLl2Cvr6+usPUGG5ubjh8+DDatGmDtWvXol69enBycgKKbifa2tpCLpeL5LQYZaJpbW2NwYMHw9zcHAcOHIC1tTWsra0hk8nQqFEjGBgYqDtUjWRlZQUrKyugKOnKz89HpUqV0LBhQ5HEl0JHR0e6GEKxp4vNnj0bX3zxBUJCQkRSWgrRFpTN7du34eHhgUePHiE9PR0TJ05UGfKAohyl+DFWsWJFODs7qyFa9ZKRpLqDeJsGDx6MuLg4nDp1Sip7+vQp1q5di+DgYPTs2RPTp0/HwYMHMXLkSAwcOBDz5s3T6vFEL6M8fGQyGdq3b4/r16/jjz/+EL0xL3D69Gn07dsXlpaWcHFxQX5+Pvbv348///xTK7+AyqKgoAA//vgj3Nzc0LBhQ5XkQSi72bNnY/PmzTh+/LjUSyioUo7zmzt3LpKSkmBjY4OZM2fi3LlzUs+zUDrRFrxYdnY2xo4di8LCQri7u2P06NGYPHlyifG4SosXL0ZeXh5mzZqllnjVTWsu/5SN2XvvvYdbt24hOjoadnZ2QNHtryFDhiA6Ohq//vorJk6ciE6dOmHIkCEYOHCgSEpfQiaTQaFQYMqUKTh58iSuX78uvoheonXr1jhx4gR++uknXLhwATY2NiIp/Ru6uroqk01EUvpqdu3ahVOnTiE4OBjHjh0TSelLKI8xXV1drFu3DpUrV8aff/4pktIyEG3Bi4nJYq9G63pMY2Nj0bx5c3Tp0gXLly9HpUqVpKQ1MTERVlZW2L9/Pzp37qzuUN8ZCoUCmzZtQpMmTdC4cWN1h/POKCwsBIo1hoLwJkRERGDevHmYO3cuHBwc1B3OO+HKlSto2rQpwsPD4ejoqO5w3hmiLXix7OxsaVwuAOzYsQN9+/bFpEmTMH36dJiZmUGhUODp06coLCzEs2fPSh2Hqg20LjEFgJMnT8LX1xdDhw7F3LlzpauVhw8fwsfHB6tXr4aHh4e6w3yniNurgqC5CgoKxPjlV/R8IiGUjWgLXk45WUwmkyE4OBj9+vXD5MmTS0wW0+ZxuVpzK784T09P7Nq1C7169UJSUhJ69+6Nhg0bYsuWLUhJSUHt2rXVHeI7R3wRCYLmEknpqxNJ6T8j2oKXE5PF/p5W9pgqXbt2DRMnTkRCQgLKly+PcuXKITg4GK6uruoOTRAEQRCE/ygxWezFtDoxBYAnT54gIyMDT58+hYWFRakz5ARBEARBEF4n5WSxZcuW4fr162jYsKG6Q9IIWnkrv7jKlStr7eP4BEEQBEFQHycnJ1y7dk0kpcVofY+pIAiCIAiCOojJYiWJdWoEQRAEQRDUQCSlJYnEVBAEQRAEQdAIIjEVBEEQBEEQNIJITAVBEARBEASNIBJTQRAEQRAEQSOIxFQQBEEQBEHQCCIxFQThHxs0aBC6dev2r3/Ppk2bYGxs/FpiehmZTIZ9+/a98fcRXl1+fj4aNGiAc+fOAQASEhIgk8lw/fr1N/q+//R9/vjjD8hkMmRmZpb5NX369ME333zzD6IUBO0hElNBeMcMGjQIMpkMMpkMurq6sLa2xtSpU5GXl6fu0P6xgIAAxMTEvLbfN3fuXDRu3LhEeVJSEnx9fV/b+5Rm06ZN0t9HR0cHlpaWGDx4MFJSUt7o+75Jbdu2xfjx49/oe3z//fewtrZGixYt3uj7qNPMmTPx5Zdf4vHjx+oORRA0lkhMBeEd5OPjg6SkJMTFxWHp0qVYs2YN5syZo+6w/pGCggIYGhqievXqb/y9atSoAX19/Tf+PpUrV0ZSUhLu3buHdevW4fDhwxgwYMA//n0FBQWvNT51yc/PL7WcJFauXImPPvrorcf0Njk7O6N+/fr46aef1B2KIGgskZgKwjtIX18fNWrUQO3atdGtWzd06NABx44dk7YXFhZiwYIFsLa2hqGhIRo1aoTdu3er/I79+/fDxsYGBgYG8PT0xObNm1VuTZbW67hs2TLUrVv3hXEdOXIELVu2hLGxMczMzNC5c2fExsZK25W3TXfs2IE2bdrAwMAAW7duLXErv27dulKvY/H/lKZNmwZbW1tUqFAB9erVw6xZs6TkbdOmTfj8888RGhoqvW7Tpk1AKbfyw8LC0K5dOxgaGsLMzAzDhw9HVlaWtF05VGHJkiWwsLCAmZkZRo0a9beJokwmQ40aNVCzZk34+vpi7NixOH78OHJzc/9xHaWnp6Nv376oVasWKlSoABcXF2zfvl3lfdu2bYsxY8Zg/PjxMDExgbm5OdatW4fs7GwMHjwYRkZGaNCgAQ4fPqzyuvDwcPj6+qJSpUowNzfHgAEDkJaWJtXBqVOnsHz5cqk+ExIS/vZ1ynhGjx6N8ePHo2rVqvD29i61vq5evYrY2Fh06tTphXWqUCjw0UcfSce0nZ0dli9frrKP8u/11VdfwdzcHMbGxpg3bx7kcjmmTJkCU1NTWFpaYuPGjSV+/82bN9GiRQsYGBjA2dkZp06dUtl+6NAh2NrawtDQEJ6enlIdKJXl7wMAfn5+CA4OfuHnFARtJxJTQXjHhYeH49y5c9DT05PKFixYgC1btuD7779HREQEJkyYgMDAQKmxjY+Ph7+/P7p164bQ0FCMGDECn3322b+OJTs7GxMnTsSVK1fw+++/Q0dHB927d0dhYaHKftOnT8e4ceMQFRVVarJy+fJlJCUlSb2OzZs3R6tWraTtRkZG2LRpEyIjI7F8+XKsW7cOS5cuBYqGBUyaNAlOTk7S7wgICCg1Vm9vb5iYmODy5cvYtWsXjh8/jtGjR6vsd/LkScTGxuLkyZPYvHkzNm3aJCW6ZWVoaIjCwkLI5fJ/XEd5eXlo0qQJDh48iPDwcAwfPhwDBgzApUuXVF63efNmVK1aFZcuXcKYMWPw8ccfo1evXmjRogWuXbsGLy8vDBgwADk5OQCAzMxMtGvXDq6urrhy5QqOHDmC5ORk9O7dGwCwfPlyeHh4YNiwYVJ91q5d+29fVzwePT09nD17Ft9//32p9XPmzBnY2trCyMjohXVYWFgIS0tL7Nq1C5GRkZg9ezZmzJiBnTt3qux34sQJPHjwAKdPn8a3336LOXPmoHPnzjAxMcHFixcxcuRIjBgxAvfu3VN53ZQpUzBp0iSEhITAw8MDfn5+SE9PBwAkJiaiR48e8PPzw/Xr1zF06FBMnz5d5fVl/fs0bdoUly5dwrNnz174WQVBq1EQhHfKwIEDWa5cOVasWJH6+voEQB0dHe7evZskmZeXxwoVKvDcuXMqr/voo4/Yt29fkuS0adPo7Oyssv2zzz4jAD569IgkOWfOHDZq1Ehln6VLl9LKykollq5du74w1tTUVAJgWFgYSTI+Pp4AuGzZMpX9Nm7cyCpVqpT6O8aOHUsrKyumpKS88H0WL17MJk2aSD+XFjtJAuDevXtJkmvXrqWJiQmzsrKk7QcPHqSOjg4fPnwofT4rKyvK5XJpn169ejEgIOCFsTz/WWJiYmhra0s3N7dS9y9rHZWmU6dOnDRpkvRzmzZt2LJlS+lnuVzOihUrcsCAAVJZUlISAfD8+fMkyfnz59PLy0vl9yYmJhIAo6Ojpd87btw4lX3K+jpXV9e//Rzjxo1ju3btVMqU9RASEvLC140aNYo9e/aUflb+vRQKhVRmZ2fHVq1alaiT7du3q7zPwoULpX0KCgpoaWnJRYsWkSQ//fRTOjo6qrz3tGnTVM6X0jz/9yHJ0NBQAmBCQsJL60QQtFV5dSfGgiC8Ok9PT6xevRrZ2dlYunQpypcvj549ewIAbt++jZycHHTs2FHlNfn5+XB1dQUAREdHw93dXWV706ZN/3Vct27dwuzZs3Hx4kWkpaVJvYB3796Fs7OztJ+bm1uZft/atWuxfv16nDt3DtWqVZPKd+zYge+++w6xsbHIysqCXC5H5cqVXynWqKgoNGrUCBUrVpTK3n//fRQWFiI6Ohrm5uYAACcnJ5QrV07ax8LCAmFhYS/93Y8fP0alSpVQWFiIvLw8tGzZEj/88APwL+pIoVDgq6++ws6dO3H//n3k5+fj2bNnqFChgsp+DRs2lP5drlw5mJmZwcXFRSpTfi7lZKzQ0FCcPHkSlSpVKvE5YmNjYWtrW+pnLOvrmjRp8tK6AoDc3FwYGBj87X5BQUHYsGED7t69i9zcXOTn55cYbuLk5AQdnb9uBpqbm6vUq7JOnp+M5uHhIf27fPnycHNzQ1RUFFB0rDRr1uyF++MV/j6GhoYAIPVYC4KgSiSmgvAOqlixIho0aAAA2LBhAxo1aoT169fjo48+ksZIHjx4ELVq1VJ53atM/NHR0cH/Oxn/8ndjK/38/GBlZYV169ahZs2aKCwshLOzc4lJL8WTwRc5efIkxowZg+3bt6skW+fPn0f//v3x+eefw9vbG1WqVEFwcPAbW4ZHV1dX5WeZTFbitvvzjIyMcO3aNejo6MDCwkJKRvAv6mjx4sVYvnw5li1bBhcXF1SsWBHjx48v8brS4i1ephyrq/wMWVlZ8PPzw6JFi0p8DgsLixd+xrK+rix/66pVq/5tsh8cHIzJkyfjm2++gYeHB4yMjLB48WJcvHhRZb+/+/wo49/wVZX175ORkQEAKhdagiD8RSSmgvCO09HRwYwZMzBx4kT069cPjo6O0NfXx927d9GmTZtSX2NnZ4dDhw6plF2+fFnl52rVquHhw4cgKSUzL1vrMT09HdHR0Vi3bp00HvTPP//8R5/p9u3b8Pf3x4wZM9CjRw+VbefOnYOVlZXKmNg7d+6o7KOnpweFQvHS93BwcMCmTZuQnZ0tJU9nz56Fjo4O7Ozs/lHcSjo6OtKFQ3H/po7Onj2Lrl27IjAwEChKLGNiYuDo6PivYn3vvffw888/o27duihfvvQmobT6LMvrysrV1RWrV69WOdaed/bsWbRo0QKffPKJVFZ80ti/deHCBbRu3RoAIJfLcfXqVWm8sYODA/bv319i/+fjK8vfJzw8HJaWlqhatepri10Q/kvE5CdB+A/o1asXypUrh6CgIBgZGWHy5MmYMGECNm/ejNjYWFy7dg0rVqzA5s2bAQAjRozAzZs3MW3aNMTExGDnzp0qM9dRNKM6NTUVX3/9NWJjYxEUFFRiNndxJiYmMDMzw9q1a3H79m2cOHECEydOfOXPkpubCz8/P7i6umL48OF4+PCh9B8A2NjY4O7duwgODkZsbCy+++477N27V+V31K1bF/Hx8bh+/TrS0tJKnWjSv39/GBgYYODAgQgPD5d6aAcMGCDd7n7d/k0d2djY4NixYzh37hyioqIwYsQIJCcn/+uYRo0ahYyMDPTt2xeXL19GbGwsjh49isGDB0vJaN26dXHx4kUkJCRIww/K8rqy8vT0RFZWFiIiIl76+a9cuYKjR48iJiYGs2bNKnEx9W8EBQVh7969uHnzJkaNGoVHjx5hyJAhAICRI0fi1q1bmDJlCqKjo7Ft27YSE+DK+vc5c+YMvLy8XlvcgvBfIxJTQfgPKF++PEaPHo2vv/4a2dnZmD9/PmbNmoUFCxbAwcEBPj4+OHjwIKytrQEA1tbW2L17N/bs2YOGDRti9erVUg+k8na/g4MDVq1ahaCgIDRq1AiXLl3C5MmTXxiDjo4OgoODcfXqVTg7O2PChAlYvHjxK3+W5ORk3Lx5E7///jtq1qwJCwsL6T8A6NKlCyZMmIDRo0ejcePGOHfuHGbNmqXyO3r27AkfHx94enqiWrVqpS7bU6FCBRw9ehQZGRlwd3eHv78/2rdvj5UrV75yzGX1b+po5syZeO+99+Dt7Y22bduiRo0ar+WpWzVr1sTZs2ehUCjg5eUFFxcXjB8/HsbGxtJYzcmTJ6NcuXJwdHREtWrVcPfu3TK9rqzMzMzQvXt3bN269YX7jBgxAj169EBAQACaNWuG9PR0ld7Tf2vhwoVYuHAhGjVqhD///BP79++XejXr1KmDn3/+Gfv27UOjRo3w/fff46uvvlJ5fVn+Pnl5edi3bx+GDRv22uIWhP8aGZ8fRCYIglb68ssv8f333yMxMVHdoQha6MaNG+jYsSNiY2NLnVD1X7B69Wrs3bsXv/32m7pDEQSNJXpMBUFLrVq1CpcvX0ZcXBx+/PFHLF68GAMHDlR3WIKWatiwIRYtWoT4+Hh1h/LG6OrqYsWKFeoOQxA0mugxFQQtNWHCBOzYsQMZGRmoU6cOBgwYgE8//fRfT2QRBEEQhH9KJKaCIAiCIAiCRhC38gVBEARBEASNIBJTQRAEQRAEQSOIxFQQBEEQBEHQCCIxFQRBEARBEDSCSEwFQRAEQRAEjSASU0EQBEEQBEEjiMRUEARBEARB0AgiMRUEQRAEQRA0gkhMBUEQBEEQBI3wP74vmjmmD4pAAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "n_lam = 8\n",
    "thetas = np.zeros((n_features, n_lam))\n",
    "lambdas = np.concatenate([[0], np.logspace(-5, 0, n_lam-1)])\n",
    "\n",
    "\n",
    "for i, lam in enumerate(lambdas):\n",
    "    thetas[:, i] = Ridge_parameters(X_norm, y_centered, lam=lam)\n",
    "\n",
    "avg_thetas = np.mean(thetas, axis=1)\n",
    "norm_thetas = thetas - avg_thetas[:, np.newaxis]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8,6))\n",
    "# Annotation\n",
    "im = ax.imshow(norm_thetas, aspect='auto', cmap='viridis')\n",
    "for i in range(n_features):\n",
    "    for j in range(n_lam):\n",
    "        text = ax.text(j, i, f\"{norm_thetas[i, j]:.2e}\",\n",
    "                       ha=\"center\", va=\"center\", color=\"w\" if abs(norm_thetas[i, j]) < 0.5 else \"black\")\n",
    "ax.set_yticks(np.arange(n_features))\n",
    "ax.set_xticks(np.arange(n_lam))\n",
    "ax.set_xticklabels([f\"{l:.2e}\" for l in lambdas], rotation=45)\n",
    "ax.set_ylabel(\"Features\")\n",
    "ax.set_xlabel(\"Regularization Parameter (lambda)\")\n",
    "ax.set_title(r\"Feature Coefficients ($\\theta^\\lambda_i - \\bar{\\theta}_i$)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bfa34697",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Exercise 4, Implementing the simplest form for gradient descent\n",
    "\n",
    "Alternatively, we can fit the ridge regression model using gradient\n",
    "descent. This is useful to visualize the iterative convergence and is\n",
    "necessary if $n$ and $p$ are so large that the closed-form might be\n",
    "too slow or memory-intensive. We derive the gradients from the cost\n",
    "functions defined above. Use the gradients of the Ridge and OLS cost functions with respect to\n",
    "the parameters $\\boldsymbol{\\theta}$ and set up (using the template below) your own gradient descent code for OLS and Ridge regression.\n",
    "\n",
    "Below is a template code for gradient descent implementation of ridge:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c8fb3f01",
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent(X, y, cost_func, grad_cost_func, eta=0.1, num_iters=1000, **kwargs):\n",
    "    # Initialize weights\n",
    "    theta = np.zeros(X.shape[1])\n",
    "    # Store cost history\n",
    "    cost_history = np.zeros(num_iters)\n",
    "    for t in range(num_iters):\n",
    "        # Compute cost\n",
    "        cost_history[t] = cost_func(X, y, theta, **kwargs)\n",
    "        # Compute gradient\n",
    "        grad = grad_cost_func(X, y, theta, **kwargs)\n",
    "        # Update weights\n",
    "        theta -= eta * grad\n",
    "    return theta, cost_history\n",
    "\n",
    "def OLS_cost_func(X, y, theta):\n",
    "    error = X.dot(theta) - y\n",
    "    return 0.5 * np.mean(error**2)\n",
    "\n",
    "def OLS_grad_cost_func(X, y, theta):\n",
    "    error = X.dot(theta) - y\n",
    "    return X.T.dot(error) / len(y)\n",
    "\n",
    "def Ridge_cost_func(X, y, theta, lam):\n",
    "    return OLS_cost_func(X, y, theta) + 0.5 * lam * np.sum(theta**2)\n",
    "\n",
    "def Ridge_grad_cost_func(X, y, theta, lam):\n",
    "    return OLS_grad_cost_func(X, y, theta) + lam * theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a67af634",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gradient Descent OLS coefficients: [ 5.03241281e+00 -2.89258175e+00 -1.55189951e-02  1.51795012e-01\n",
      " -6.83299260e-02 -4.40147965e-02  1.76999871e+00  4.37643569e-03\n",
      "  4.52550260e-02 -4.97610000e-02]\n",
      "Gradient Descent Ridge coefficients: [ 5.02716096e+00 -2.88896347e+00 -1.55169486e-02  1.52287662e-01\n",
      " -6.93302234e-02 -4.47229113e-02  1.76836298e+00  4.62139092e-03\n",
      "  4.41380481e-02 -4.96664608e-02]\n"
     ]
    }
   ],
   "source": [
    "eta = 0.1\n",
    "num_iters = 1000\n",
    "lam = 1e-3\n",
    "\n",
    "theta_gdOLS, history_gdOLS = gradient_descent(X_norm, y_centered, OLS_cost_func, OLS_grad_cost_func, eta=eta, num_iters=num_iters)\n",
    "theta_gdRidge, history_gdRidge = gradient_descent(X_norm, y_centered, Ridge_cost_func, Ridge_grad_cost_func, eta=eta, num_iters=num_iters, lam=lam)\n",
    "\n",
    "print(\"Gradient Descent OLS coefficients:\", theta_gdOLS)\n",
    "print(\"Gradient Descent Ridge coefficients:\", theta_gdRidge)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2bbb16b9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gradient Descent OLS error: (array([ 0.03241281,  0.10741825, -0.015519  ,  0.15179501, -0.06832993,\n",
      "       -0.0440148 , -0.23000129,  0.00437644,  0.04525503, -0.049761  ]), np.float64(0.009992203674399302))\n",
      "Gradient Descent Ridge error: (array([ 0.02716096,  0.11103653, -0.01551695,  0.15228766, -0.06933022,\n",
      "       -0.04472291, -0.23163702,  0.00462139,  0.04413805, -0.04966646]), np.float64(0.010139794608820855))\n"
     ]
    }
   ],
   "source": [
    "def theta_error(theta_est):\n",
    "    return theta_est - theta_true, np.mean((theta_est - theta_true)**2)\n",
    "\n",
    "print(f\"Gradient Descent OLS error: {theta_error(theta_gdOLS)}\")\n",
    "print(f\"Gradient Descent Ridge error: {theta_error(theta_gdRidge)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3f43f2c",
   "metadata": {
    "editable": true
   },
   "source": [
    "### 4a)\n",
    "\n",
    "Write first a gradient descent code for OLS only using the above template.\n",
    "Discuss the results as function of the learning rate parameters and the number of iterations\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "0871c0a5",
   "metadata": {},
   "outputs": [],
   "source": [
    "etas = np.logspace(-4, 0, 10)\n",
    "max_iterations = np.logspace(1, 5, 10, dtype=int)\n",
    "theta_errors = np.zeros((len(etas), len(max_iterations), 2))\n",
    "\n",
    "for i, eta in enumerate(etas):\n",
    "    for j, max_iter in enumerate(max_iterations):\n",
    "        # print(f\"Running GD with eta={eta}, max_iter={max_iter}\")\n",
    "        theta_gdOLS, _ = gradient_descent(X_norm, y_centered, OLS_cost_func, OLS_grad_cost_func, eta=eta, num_iters=max_iter)\n",
    "        theta_gdRidge, _ = gradient_descent(X_norm, y_centered, Ridge_cost_func, Ridge_grad_cost_func, eta=eta, num_iters=max_iter, lam=lam)\n",
    "\n",
    "        theta_errors[i, j, 0] = theta_error(theta_gdOLS)[1]\n",
    "        theta_errors[i, j, 1] = theta_error(theta_gdRidge)[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "49a2cb11",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x500 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.cm as mcm\n",
    "import matplotlib.colors as mcolors\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 5))\n",
    "\n",
    "# Log Colormap\n",
    "cm = plt.get_cmap('viridis')\n",
    "# Create LogNorm between min and max of theta_errors\n",
    "norm = mcolors.LogNorm(vmin=theta_errors.min(), vmax=theta_errors.max())\n",
    "\n",
    "\n",
    "im1 = ax1.imshow(theta_errors[:, :, 0], aspect='auto', interpolation='nearest', cmap=cm, norm=norm)\n",
    "ax1.set_title('Gradient Descent OLS Error')\n",
    "fig.colorbar(im1, ax=ax1)\n",
    "\n",
    "im2 = ax2.imshow(theta_errors[:, :, 1], aspect='auto', interpolation='nearest', cmap=cm, norm=norm)\n",
    "ax2.set_title('Gradient Descent Ridge Error')\n",
    "fig.colorbar(im2, ax=ax2)\n",
    "\n",
    "for ax in (ax1, ax2):\n",
    "    ax.set_xlabel('Max Iterations')\n",
    "    ax.set_ylabel('Learning Rate')\n",
    "    ax.set_xticks(np.arange(len(max_iterations)))\n",
    "    ax.set_yticks(np.arange(len(etas)))\n",
    "    ax.set_xticklabels(max_iterations, rotation=45)\n",
    "    ax.set_yticklabels(np.round(etas, 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ba303be",
   "metadata": {
    "editable": true
   },
   "source": [
    "### 4b)\n",
    "\n",
    "Write then a similar code for Ridge regression using the above template.\n",
    "Try to add a stopping parameter as function of the number iterations and the difference between the new and old $\\theta$ values. How would you define a stopping criterion?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78362c6c",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Exercise 5, Ridge regression and a new Synthetic Dataset\n",
    "\n",
    "We create a synthetic linear regression dataset with a sparse\n",
    "underlying relationship. This means we have many features but only a\n",
    "few of them actually contribute to the target. In our example, we’ll\n",
    "use 10 features with only 3 non-zero weights in the true model. This\n",
    "way, the target is generated as a linear combination of a few features\n",
    "(with known coefficients) plus some random noise. The steps we include are:\n",
    "\n",
    "Decide on the number of samples and features (e.g. 100 samples, 10 features).\n",
    "Define the **true** coefficient vector with mostly zeros (for sparsity). For example, we set $\\hat{\\boldsymbol{\\theta}} = [5.0, -3.0, 0.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0]$, meaning only features 0, 1, and 6 have a real effect on y.\n",
    "\n",
    "Then we sample feature values for $\\boldsymbol{X}$ randomly (e.g. from a normal distribution). We use a normal distribution so features are roughly centered around 0.\n",
    "Then we compute the target values $y$ using the linear combination $\\boldsymbol{X}\\hat{\\boldsymbol{\\theta}}$ and add some noise (to simulate measurement error or unexplained variance).\n",
    "\n",
    "Below is the code to generate the dataset:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8be1cebe",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "# Set random seed for reproducibility\n",
    "np.random.seed(0)\n",
    "\n",
    "# Define dataset size\n",
    "n_samples = 100\n",
    "n_features = 10\n",
    "\n",
    "# Define true coefficients (sparse linear relationship)\n",
    "theta_true = np.array([5.0, -3.0, 0.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0])\n",
    "\n",
    "# Generate feature matrix X (n_samples x n_features) with random values\n",
    "X = np.random.randn(n_samples, n_features)  # standard normal distribution\n",
    "\n",
    "# Generate target values y with a linear combination of X and theta_true, plus noise\n",
    "noise = 0.5 * np.random.randn(n_samples)  # Gaussian noise\n",
    "y = X.dot @ theta_true + noise"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2693666",
   "metadata": {
    "editable": true
   },
   "source": [
    "This code produces a dataset where only features 0, 1, and 6\n",
    "significantly influence $\\boldsymbol{y}$. The rest of the features have zero true\n",
    "coefficient. For example, feature 0 has\n",
    "a true weight of 5.0, feature 1 has -3.0, and feature 6 has 2.0, so\n",
    "the expected relationship is:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc954d12",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "y \\approx 5 \\times x_0 \\;-\\; 3 \\times x_1 \\;+\\; 2 \\times x_6 \\;+\\; \\text{noise}.\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6534b610",
   "metadata": {
    "editable": true
   },
   "source": [
    "You can remove the noise if you wish to.\n",
    "\n",
    "Try to fit the above data set using OLS and Ridge regression with the analytical expressions and your own gradient descent codes.\n",
    "\n",
    "If everything worked correctly, the learned coefficients should be\n",
    "close to the true values [5.0, -3.0, 0.0, …, 2.0, …] that we used to\n",
    "generate the data. Keep in mind that due to regularization and noise,\n",
    "the learned values will not exactly equal the true ones, but they\n",
    "should be in the same ballpark. Which method (OLS or Ridge) gives the best results?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "3e466f75",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converged at iteration 85\n",
      "Terminated with error on theta of 3.750e-03\n"
     ]
    }
   ],
   "source": [
    "def gradient_descent(X, y, cost_func, grad_cost_func, eta=0.1, num_iters=1000, stopping_criterion=None, **kwargs):\n",
    "    # Initialize weights\n",
    "    theta = np.zeros(X.shape[1])\n",
    "    # Store cost history\n",
    "    cost_history = np.zeros(num_iters)\n",
    "    for t in range(num_iters):\n",
    "        # Compute cost\n",
    "        cost_history[t] = cost_func(X, y, theta, **kwargs)\n",
    "        # Compute gradient\n",
    "        grad = grad_cost_func(X, y, theta, **kwargs)\n",
    "        # Update weights\n",
    "        theta -= eta * grad\n",
    "        if stopping_criterion is not None and stopping_criterion(cost_history[:t+1]):\n",
    "            print(f\"Converged at iteration {t}\")\n",
    "            break\n",
    "    return theta, cost_history\n",
    "\n",
    "def stopping_criterion(cost_history, tol=1e-5):\n",
    "    if len(cost_history) < 2:\n",
    "        return False\n",
    "    return np.abs(cost_history[-1] - cost_history[-2]) < tol\n",
    "\n",
    "\n",
    "res = gradient_descent(X, y, OLS_cost_func, OLS_grad_cost_func, num_iters=100000, stopping_criterion=stopping_criterion)\n",
    "print(f\"Terminated with error on theta of {theta_error(res[0])[1]:.3e}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "244364a3",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "lecture-materials",
   "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": "3.13.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}