Sparse-Identification-with-SINDy-on-Lorenz-system-with-control.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Test SINDy on Lorenz System with Control Inputs\n",
    "\n",
    "This code demonstrates three methods to identify the governing equations of a non-linear dynamical system with a forced input.\n",
    "\n",
    "The system used in these examples is the [Lorenz system](https://en.wikipedia.org/wiki/Lorenz_system) of ordinary differential equations.\n",
    "\n",
    "Contents:\n",
    "1. Generate data by simulating forced Lorenz system\n",
    "2. Identify system dynamics using sparse regression\n",
    " 1. Using SINDy recursive least-squares method\n",
    " 2. Using L1-regularized feature selection in Scikit-Learn\n",
    " 3. Using L1-regularized feature selection in Scikit-Learn with cross-validation\n",
    "\n",
    "References:\n",
    "\n",
    "1. Brunton, S. L., & Kutz, J. N. (2019). Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control (1st ed.). Cambridge University Press. http://www.databookuw.com"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from functools import partial\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import odeint\n",
    "from scipy.interpolate import interp1d\n",
    "\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression, Lasso, LassoCV, \\\n",
    "                                 MultiTaskLassoCV\n",
    "from sklearn.feature_selection import SelectFromModel\n",
    "\n",
    "# Local modules\n",
    "from examples.lorenz_forced import lorenz_forced_odes, \\\n",
    "                                   lorenz_forced_odes_vectorized, \\\n",
    "                                   scatter_plot_3d\n",
    "from dynopt.models.sindy import sparsify_dynamics_lstsq\n",
    "from dynopt.preprocessing.utils import polynomial_features, polynomial_feature_labels\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Generate data by simulating forced Lorenz system"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "dt = 0.01\n",
    "T = 50\n",
    "t = np.arange(0, T + dt, dt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Lorenz system parameters\n",
    "beta = 8 / 3\n",
    "sigma = 10\n",
    "rho = 28\n",
    "n = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initial condition\n",
    "x0 = (-8, 8, 27)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array(0.), array(-5.44021111))"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Control input\n",
    "u = 10*np.sin(t/5)\n",
    "uf = interp1d(t, u, kind='previous')\n",
    "u = u[:-1]\n",
    "assert u.shape == (5000,)\n",
    "\n",
    "# u is a function defined in this range\n",
    "uf(t[0]), uf(t[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x180 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,2.5))\n",
    "plt.plot(t, uf(t))\n",
    "plt.title('Input $u(t)$')\n",
    "plt.xlabel('$t$')\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 49.8 s, sys: 974 ms, total: 50.7 s\n",
      "Wall time: 50.2 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# THIS CAN TAKE ABOUT A MINUTE\n",
    "\n",
    "# Simulate using scipy.integrate.odeint method\n",
    "# Produces same results as Matlab\n",
    "fun = partial(lorenz_forced_odes, u=uf, sigma=sigma, beta=beta, rho=rho)\n",
    "rtol = 10e-12\n",
    "atol = 10e-12 * np.ones_like(x0)\n",
    "x = odeint(fun, x0, t[:-1], tfirst=True, rtol=rtol, atol=atol)\n",
    "assert x.shape == (5000, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-8.        ,  8.        , 27.        ],\n",
       "       [-6.48640305,  7.80317052, 25.72552262],\n",
       "       [-5.13782726,  7.56259206, 24.60881802],\n",
       "       [-3.94095236,  7.31300704, 23.62896269],\n",
       "       [-2.88097253,  7.07823176, 22.76580088]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lufD3EaB34f97gWEAKaUphIgvPL8X+MGiYy5+TV1RQr/FrBZ+sxE0TVsxyrVe1LrILzbc3Xfffate8OopFo3qYmzXpYDlwm/bdjmu9+zZs6TTac6ePVsWfrfbXbf3buaKvtGt9c1u3ZdGMN/w1Nd1PyOlvKfqWwnxFmBKSvm8EOLBa2ewArnKY7VeU1eU0G8RpQlqQN1zrzVNWzJVq17UWgcvGe4OHTpEW1tb3d9bURtN0wiFQoRCIQCOHz9OT08PsViM8+fPk8vl8Pv9S4R/o4KqKvrqbHbrXlX019jE1v39wMNCiDcBbopr9J8GwkIIY6Gq7wPGFp4/AvQDI0IIAwgBc4v+vcTi19QVJfRbQCn85uTJkxw+fLjuv6iNat1XqppLhrtsNlvRcNcolgtNI30J26F1v16EEGXh3717N7Ztk0wmicViDAwMkM1m8fl85bx+j8ezZvFu5oq+2c1+y1Fr9JuPlPJXgF8BWKjoPyalfLcQ4kvAoxSd9+8BvrbwkicW/v7MwuPfllJKIcQTwN8JIf6QohnvAHC8EeeshH4TqbQW3whB3iyhTyQSnDp1ir6+vqqGu83kRmrdrxdN0wgGgwSDQXbt2oWUsiz8pSjixcLv9Xqrfu3NLvSNDCfa7NZ9KpVSrXuKPXBt639XPwF8QQjx28AJ4HML//454K8XzHZzFJ32SClfEkJ8ETgDmMAHG+G4ByX0m0alCNvSKMt604jpdXDtBmKx4e7222/H7/fX/b3Wy04R5HqwlhseIQSBQIBAIEB/fz9SSlKpFLFYjEuXLpXXfkuufp/Pt+QzbtbWfbMffzlqjX6BLUrGk1I+DTy98P+XKLrmlz8nCzxW5fW/Q9G531CU0DeYWuE3zVbRa5pGJpPh5MmT+P3+NRnuNovtsKWwmRFC4Pf78fv99PX1lT0k0WiUy5cvl9eCw+EwlmU1rPLeCa37zd5ep4ResRpK6BvIahG2jXLHa5rWENHL5/OcPHmSI0eObLnhbrkgqIr+GvUQSyEEPp8Pn89XFv5MJkM0GiWfz3P8+HE8Hk+54g8EAnX5HjT79DpV0W8NAoGusu6rooS+AZSq+NXCbxrVuq93Rb/YcHf06FHC4XDdjr1RKn2eyoxXpFFeBa/Xi9frZWxsjHvuuYdMJkMsFmNkZIRkMonL5Sq7+v1+/4YEr9mn123FGn1pcNKNjhpqUx0l9HVmeYRtrV/6ZmjdLzbc5fP5bTFlbTNS9mq9VzPQ6PNeLPw9PT0AZeEfHR0lkUjgdDrLwh8IBNYkgM2+hm7b9qbGE6uKXrEWtv6qvYNYb/jNdq7oKxnuYrFY01W3NyJblfnv8XjweDx0d3cDkM1micVijI+Pc/78eRwOR1n4g8FgRcFt9uQ6tb1uaxBiW7juty1K6OvARiNsG7lGfz1Cn81mOX369ArD3XYZllMJZcbbfrjdbrq6uujq6gKKyYmxWIzJyUkGBgbK6X7hcJhgMIiu601vxlPJeFuHat1XRwn9dVJp29xa2Y6t+1oJd9tZTFVgzjW26xQ/l8tFZ2cnnZ2dQNHcGYvFmJqaYnBwEF3XEUIQDAYbNpVtp7nuS/kHCiX0tVBCv0HqMYimUVG1GxH65Ql3Z8dSfP77Z7mlP8SP3dldM+BHSsnVmTQ+l0FbcHOmqG2WmG1HwdwpOJ1OOjo6ymayfD7PwMAAyWSSEydOIIQou/pDoVBd/CE7rXWvAnMUa0EJ/Qa4nip+Mbquk81m63x2669u5+fnOX369JKEu6/84BwC+Lez0xzd20Jn2F31uN8+Ncl3z0yha4L3ve4melvWt2a4EdHezAjcZmO7VvSr4XQ68Xg8BINB2traKBQKxGIx5ubmGBoaAigLfzgc3pDw78TW/XYIrNpqhIBtEumxLVFCvw5qhd9shM1s3Usp+d8/GOZHV2K89rZOHryls2bCXVfEw8hMCrfTwO8u/phUS9y7MpNCE1AwbabjuXUJfa1BOYqN0cyf5+JzdzgctLe3097eDoBpmsRiMWKxGFeuXEFKSSgUKgu/w+FY9fhqH/1ORaA36c/8ZqCEfo2sFn6zERop9Mur25lEjmcHZ3EaGl9/fox79wY5c+alFYY7kR5BZIf5hVfu59JcB90RD74FoV9xXDMJdp7X39bFV54dJuJ3crg3WPPcRmfTfPPkBL2tHh66ratulbiq6HcGtYTSMAza2trK3hHTNInH48RiMa5evYqUkmAwWDb4VRL+nTi9TlX0itVQQr8K9a7iF6PresPmxi8n6HEQ9DhIZEw6AzonTryw0nBnpdFnvg3Sxp++zM19jxd7YgssEdP8HMb0P4O02R28kw+/5eY1nccTz40ym8hxZTrF/s5AUwh9s91ANHroTCNZz7kbhkFrayutra1AsW1eEv7h4WEsy1oi/E6ns+ld/cvJ5XK4XJvji9nOCJQZrxZK6GsgpSQWi5FKpWhra6v7BWLTtqtZGTypc3zkQR/PDFgEjQJ33lFtpKwA5MJ/l7L4fEUhCtIEoSNy48DahL7F72QylsVhCPweg+ltXok3Ywu8kZ/ndk6u03WdlpYWWlpagKLwz8/Pl9P7LMsim80yNTVFOBxuiEBu9ho9sG3mTWwpWzTUpllQQl+FUhWfSqWYnZ0trxPWk3oIvS0lE9EsEb8Dj7Pyt1Of+Vdk6jKuvMntPffTvuuuyhdr3YvV8TpEZhTbd9OSah6WVs3S04dMdSCsFHbw9prnKFIX0edPYrt7eOuxu7ilP0RrwEV70M3lJqjom5FmHiNbz45ZJBIhEomwd+9ebNvm2WefJZ1OMzY2RqFQIBgMltf43W73db/nZrbu1c+7Yq0ooV/G8m1zhmE0rOquRzLeF/79Cs9fnMPnNvj4I0fwe5auS0opSSbiOEyzuI+5ow1Z40Iq3d1Id3fFx5bcmGgurI43rOkc9fgJpNDQ0kO4fAe5dVek/Fg1gc4VLL51coK8afP627sqfl3Lh9qoC1+RZp4X38jja5qGYRjs3bsXKIpyIpEgGo1y7tw58vk8gUCgLPwej2dD77OZXaB6LiU2M9tkHv22RQn9IipF2DZyHb0eyXhnhuMYuiCVMxmPZTmwSBBLCXdh/0EOtHUjnS1Id++G32ujYmq7utCyI0jdA8ZSR361Y/7ocoznL84hhMDj1Hnj0WKeum3bDA4OMj4+jtvtLldsjW5XK4rspDVuTdMIhUKEQqHyeyeTSaLRKBcuXCCXy+H3+5cI/3YSVfVzuRTVuq+OEnpqh980Wuivt6L/saPdfO34CHs6fOxuv7bNplAo8Pzzz5cNd5Liyvt6kfkciS/9Dfb8PNqrX4/lD1R+nmWSP/Uiwh/Auf/QksfslpcjC1GkEQBt6broCqGXJqDjc+tomkDKopEQiilgJ0+epK2tjfvuu49CoUA0GmVsbIyZmRkSiQQdHR3l6Wn1uCg3Y6dAVfQbQ9M0gsEgwWCQ3bt3I6UkkUgQi8UYHBwkk8mUhT8SiWy58Ofz+U0doKNoXm54oV8t/KaRQn+9rXuRvsprQj/kgYf7sMMHQQgsy+LcuXMUCgVe9rKXrWo4kpaFqLGmmH3m30h/8xsIASKdRr7j3RWfl3riy6T+8WsITSP0oU/gunnRur3Qkc7K8+sXC6k2fxoteQbb1cnNva/Eef9uTMvmUE+wHM178803Ew6HyefzuFyucpb64OAgfr8fKSXDw8Mkk8klFb/P59tW1Vgzs13NePWmFMcbDAbZtWtXcRksmSQWi3Hx4sXyHvaS8G/2cJlUKqUG2pQQQlX0NbhhhX6t2+Ya6Yy/3ta9PvM0yAJ6Por07iWec3P69Gn6+/uJx+M1A0SkaRL9w98mf/pFfD/xKIHHfrri84Q/gNA1pG1DKFy1ujUnxgCJNE3s2Zmq72vNzlC4chHnwZvR/Eu312mpc0jdi5abwrYSHOgOY9s258+fI5PJcOzYsfIWqUo4nU5aWlro7u5GSkkmkyEajXL58uVyVGhpq5XX692xwt/MFX0jA22utzMjhCAQCBAIBOjv70dKSSqVIhaLMTQ0RCqVIpvNMjIyQjgcbvjNpYq/vYYAdCX0VbkhhX494TeNrOiv9yIgHSG03BRS6FwZnWFsar6ccDc2NlZzvdMcGyF/5hTCFyD19f+N/9F3Vzwf1133Ev5PH8dOJYnt2Y+dy1c8nv/t70KmU2ihMK5jr6j4HDuTJvp7v4GdmMfo6SPyq//3EqG3PXvR0peQjjDoflKpFKdOnaKrq4vDhw9XPL+peJbnLkVx5E0ikWsX8sXz0nt7e5FSkk6niUajXLp0qTwMpFTxb9R4tR1ppBg3c7JcvY8thMDv9+P3++nr68O2bY4fP44Qonxz6fF4yjeX9VpOKqFG1CrWyg0l9BsJv9nOo1mtzjeSi1/k3NAMDp/Ovffeu+aRskZnF0ZnF+bEOO57Xlb1cxBC4Dp6DIDE1BR2pnI2v9HZTeSjv17zfGU6jZ1MItwezMlxWBCNstCH7sIOHAHNzfjEJENDQ9xyyy1ls1QlnnhunPlMgXQmx95uk4XslIpfh8/nw+fz0dfXV27DLjZelRzXkUhkyVarZlujbyTNvEbfaKOflBKHw0Fvb2/55jKTyZST+5LJJB6Pp2zu8/v913U+Kv52Kcp1X50bRuillBQKBSzLWteWlK1q72byFv9ycgKv2+DBmzsqrj9NTscYHIxy+PAt5XSwEhpg5fNQxawjXG5a/9sfYs3OoHdW3k634jXXaUzTW9vwv+2dZI9/H+8b3oJYGEtaPqYQWLg4e/olrFxxil7F5QfbBGmBMHA5NApJiSYE6+ncLW7D7tq1a4njurTVKhgMIoRoOsNTM7fum1nolx9/cVepp6cHKSXZbJZoNMrIyAjJZBKXy1UW/kAgsK7zU2v01xAqMKcmN4TQlxz1i7fNbXe++uww3z8/gxDgdui84tA1M1vJcJfP58vr1ospjFyl5Y9+h6gA7Zd/C9ctd1R8D+F0YXSvfbtdPRzo3te9Ce/r3lTxmIlEgtOnTtF38jiul14kffvdBN/7QcTii2d2Ej36fTQpyIdfyVvv7WVgLIGZmiXg3vhFfLnj2rZt5ufnGR4eZm5ujpmZmfIAlUgksqYBKjsRJfQbP74QAo/Hg8fjoaenuF20VPGPjY2RSCRwOp3ln7HVhF9V9Iq1sqOFvh4z47cKS14Lol0srqWRsv39/fT19VW8KGaPfx8tlUS6XaSeerKq0K+XRixjlI45MjLC8PAwtxw6RPbvPovW2k7u1AvY8Sh65Fq3QmSuFj8YO4eWnyTgPcBd+yIMDcXqfl7hcJhMJkM4HKanp4f5+Xmi0SjDw8PlyWml9dd6zEqvF81c0UPjumiN9hdYlrXuVLyS8Hd3F7tquVyOaDTK+Pg458+fx+FwlCv+UCi05BqmhH4pqqKvzva5OtWZSuE325VKF8+3HevCq2Xxen3cd6AVKSWXL19mcnJyxUjZ5bjuuAu+6AYh8LzigXqdJZpmI2V9hb4UgOPxeMoeA3n0GLkfPYfzwGG0YHjpWXj3ILIjoLmwnZ3lf1+t23A9AiWlXBKnCsWLeiwWK7v6gXIlFg6HN3WCWSWaWegbxWZMrrve4y/eMgpF4Y/FYkxNTTE4OIiu64RCIQYGBojFYhsSesuyuOeee+jt7eXJJ59kaGiIxx9/nLm5Oe666y7++q//uumWq4TaXleTHSf0jariG3WBqziPXUpCc0/yzr45pBEgmX+YE6fPEAwGlxjuquG86SCJj/5Xejs78ezavcYzKYlkpa9RoulXCEcSFMxqOxAshIgjcYL0VTnOUuLxOFNTU/T393PgwIHyvwd/4T9ix2NogeCKPf7S1Y7Z8RYKZnGgzqpflZR869QUL43Mc+ymCPcfqryfvxrVvue6ri+ZnFaalT43N8fQ0FC5IxCJRAgGg5sq/M081KaRbHXrfiO4XC46Ozvp7Cze1ObzeSYnJ/nyl7/Mc889h6ZpzM/P88ADD/Dyl798TcL/R3/0Rxw5coT5+XkAPvGJT/CRj3yExx9/nPe///187nOf4wMf+EBdvw7F1tI8vew1UNo2VxL5ZhgnW7EdLk1EfgbQsXNRTr14nH379nHo0KE1X0g0nx8CtWfDXyOHZgygG+dBpEHgDKAAACAASURBVCs8ngeRxpY6obBFpYw9oU0i9Ak0fbjKMa5R6k6cPXuWjo6O8rSx8rGEQA9Hqgb52Lk8qS/8Fcm//FPsudnyayoJXDJncXp4noDb4NmBOQpWY3ZQlGalHzhwgHvuuYfbbrsNv9/P9PQ0L7zwAidOnGBoaIhYLNbwXRzN3rpvFI0W+o207teL0+mkv7+fv/iLv+Dnfu7n+MhHPsLdd9/Nk08+yac//elVXz8yMsLXv/513ve+9wHF7+e3v/1tHn30UQDe85738NWvfrWhX0OjKBpyr//PTmRHVfSlC1C9f5kbucWuYjqe5qAQuB059yKzZht33PUKnOscqbmecxbaPJBHIhBiDimvOXlNaZOzNZyEcGhzROcEnR1iyeNZ28YhDTyaWKjjK72vBJHANAucOnkFt7vYqh8YGFj3Z5t74Tj5H34fNJ1sIIT3sZ9eIvTCSqLlZ7GdbXidXjpDLibjOfZ2+DA2qb3ncDjo6Oigo6MDKFZi0WiUiYkJLly4gNPpJJfLMT8/f93brDYTJfRbd/zlpNNpDh8+zFvf+lbe+ta3ruk1H/7wh/m93/s9EokEALOzs0s8Jn19fYyOjjbsnBuFmkdfmx0l9NCYbPLNHmwzPz/P6QvQ3/8TFQ132RefI/2PT+B+1WvxvvLBqsddKqDVW/NS+tAWmjtSBhb9uyRpmUgkebMNRz7A+NhFOjuuvTZlm9gSClYIQ7MxhAHSv+QYJhJNJBD2CLlchn03tRIK7i2f53q/X3q4BQwHSBut7dr4YCklSAtn7HsIO4fU3MiWh/jJl/cRTxcI+5xbJlJOp3NJCzabzfLCCy8wOjpKIpHA5XKVPQDXG6yiKvrK7EShr+XVWc6TTz5JR0cHd999N08//TRQeZmnWb+/iuoooV8Dm9W6X4vhTubzRD/1m0jbIvej53Hddid6KLzieUuFPotuDAESy9oDiyr2nG2RsQ0c5n68GghRzYQjEBgs/2iLNbxEIBB254oRuCnbpCBtCgUbH4ViLCj+8nE2clFx3Hwbgf/jw8hcDuPwLUuPI22ENEEYCFkAJIau0xpYX0dkMY1Y83a73TgcDo4cOQJQjustBat4vd6y8K83rlet0VdmO7rur4f1uu6/973v8cQTT/CNb3yDbDbL/Pw8H/7wh4nFYpimiWEYjIyMlLf+NRVCReDWYscJfSPYjME22WyWU6dOrW640zWE24Ocj4HHi6iyrWux0AstDhTPf3lrPm0X19zzUuDCWPIDIYQgoBvkbRuHpmFq9tIugbTwizwF4Uavsr5VsGySqSQOh4HL14sQNtJuWfIexWNKIEOx41A7jlYIgb7vwJKLdvkGT3OQD9yNnh3Gcu8CsbYf8WoCtlmitnh/9eKc/lKG+vK43tXOS1X0K7Ftu7YQy4UZj2JjVflWVPTrEfpPfvKTfPKTnwTg6aef5g/+4A/427/9Wx577DG+/OUv8/jjj/P5z3+eRx55pFGn3DDUPPraKKFfA41Yo7elJJrMA4Lp6WnGx8c5fPjwioS75QjdoO23/5DM8e/juv2uoumuyjmXKjsp/cDCoBm51KBnCIEpZfEXZVlbX8g4LussLhyY3Iq9uM0uLQzrBEJmcWgtWNrNK85hbnaKK6Nj9O/fj9flRieItK+9h5QSh9+H8HnJy3ncxmTxs7F7F5z7G6OQ0In//bdBN/D91C+ghSNVn2tLyVM/muTCWJL79kd42cHan/9mUCmnP5VKEY1GGRwcJJvNrhiXuphmbd03PGrYzOIoJCu+7+TMLK0v/RWBwhz5oz+L3XZwxXmt9nVvd6Gvxqc+9Skef/xxfu3Xfo2jR4/y3ve+tw5np9hOKKFfA42o6D/7zUFOX43j0/I8ciRZMeGuGkZvP4G3vbPmc65VymDaHgr2QQzkita8X+iYwkLHWHFHrFnDC+3vHJqcRYj2RTc8OYTMInGg2XNYmizmUFK84I0Nn6QtOMXdhwPYDq1iZW0DTr8XEGRsDWf5EHlgfRewxUs2uWe+izlyFaQk//wPcD/041VfN58ucH4sQcjj4AeDc9x7oGXF57DVWfeLh6eUpqZVyulfvM+/UTTrTYRIzdB/+jNodgFL/jjm/teVH/uXwSgvjc5jWG/gF+QThIaeJr8g9DOpAv/fiyOQS/COlmFabn8jaJW7ApZlbWpwUiqVWtca/WIefPBBHnzwQQD27dvH8ePH63hmW4HaR1+LHSf0jbhQ1FvoLVvyo6EoQlrE0Qh19NUpoMKiuGNSlLsQBWmTsIpDfDxCx7P4GiUlhn0Gp5xFiiCmuGNJ21KKFpDR4jx5sXSkLHiwtTY0ewZL2120+pkmOdPk5MmTHNlnFk1lWCDj2GJlJrcAsCXoGhoOBF6Q2oquQzUWC8PiGxu9b3cxNlcItN7+Fa/T8tMIK4nl6sHvcdIRdDE1n+NAl3+FyG/HNnWlnP5EIkE0GuXMmTNkMhkcDke56q9n+Emjhb4RFfHF2QzRsQnutDU8aOSmLqDd9FD567gczWILnYIw+EHoQXZ3tLN34es8M5kik8sBBidnbV4bu4zdclPF91l1aaDOrNeMt6MR0CQbV7aEHSf0jaCeQi+l5OqVy9wUtrkY1+kL6kS81/9tENo4mj6DlG5s8yY0TSsO8VlUjZor9r/baHIGcCFkcYsdXJvaZus92FoI0LHzGuOf/Rz2S2fI7dqDq7sTSz+MpYOZSHLpEx8jeekymTc9xM0/8y6CIYmwzyFxYtkBrFQSI7BwUZIWuhzAkFlk0o+lBfB5OpB234rPykSiIdBFAUQOpBchlg3DWYbr6DH0ji6ErqN3LTUWCTOOc/44SAstPwOhY/zky/tIZExCvubMr9c0jVAoRCgUYs+ePUxOTjI3N0cqlWJkZATLspbE9V5PTv92HYGrj76AFr+CuefVSO+15ZfReI6vvTSDZQcYdL6J/p4IcV8vnbM57m4r/qy/ck+Ibw1EcbgDpDp7uKDruNIWvT6D3RE3p64KpA39WgzpKfpL5rMmL02m6PQ72dfqKZ//Zrfu1VAbxVpQQr8GKu513wCLDXcfe1M71sS3EdjM2kGg67qOrWlzIDUEORDZckXvFBoFoSGReJe3HIWOrXWj2ePYohVwIS0LaZpopX37woeUkolnnmHq334Ao6OM/flfsvc3fwWAZMHi3MQ86aP34BgepeVHZ4l8KIIE8txLKpVl9Dd/l9yFQToffwed734MQRRNRpFohDw5ZhOuikaajG2RlzYCScA5XhR76VlxQwArd1sYFSp5oDj1Dlm8fZD54nN1jYi/uSI/a1EanrJnzx727t2LZVnE4/Gyq/96cvq3Y0Wvxa7gPPl3YJtoM+fJvfqXy49lzYUdLQjm3P0EfC3ommAibWLL4tTDwx0+Dnf4ODmXZTRlLhi7iq/fHXHz47f3cS6W47LzESKajxbgH8+MM5vIous6jx7tp9Xn2HShtyzrhh2utBxlxqvNjhP6RlyEKu11Xy+Tk5MMDg6WDXfG+BM4DAvLKuAyx4ADS54vpQTbQuhr+xbZdgRNn0VKF0g3mpYoXniEIKhl0axhpB3B1peOpLX0Q1jafkAjPzPHwH/+vzDnouz6xIeJPFTMyZ/ImAztPUT+Ix/D8Sf/A0f7tRjZwViGeSHgzqN4Bi7Qcsc1U97VtM1YNE/hTQ8TSf49s19/is53P0bRVa8hkOSyTqxYHPpXCrOFXNi8t2CIFhqIwpo+j6qfkxYidUUiCjHEkXvWENTbfCwXY13XaWlpKScQmqZZFv7Lly8jhCgb+0KhUM3283ar6E1LYizchM8723im6zHERJp72tx4DI19LW6O9QWYTObZ60iQ1CUpW9DnW+lJORJ24dU1XLqga9EaVxodh9OFBcxmLVpcOsxPIGw3wpLI9Cz4ujZ9e51iKWqJvjo7Tugbga7r5PP5Db3WNE3OnTtHoVBYYriz/AcxsmNIHKRoZfGqtDU3y8wv/2es6Czh//RxvA88tOr7SLsby+4AdBav0QMY5ikgD3IaWwuCWGZ0W8iMnz19lnQghDORZPorT5SFPp63EB43Rk839mNvo+fHXwvA+Pg48dkkrtYujECA/g+9n0jXtZuAaM7CcDnJh8PkPV56X/Wy4rkKH3H7NuZiCSZ+578jLl3E//730vYTbyy21OUwgjwesZsMGgYamgyCTC/ZmrfkS1hjfoJ5/gypLz0FSBxDJr53/XzN558cSfHCUIK75id56LaObblmv14Mw1iS018oFIjFYszOznLx4kV0XV8i/Iur1O1kxjs7meIfzs7iMgx+/sCjXLIDzLs6IG9zOVngSNiFEIJX7SvmTAwMxNnjMQlGIjgqqIJDE+wPrezs9PsdTGdtNAHdC8tsb3G/xIvpCD3EaPe+uThQcRMr+mbe5qjYfJTQr4GNrtHH43Feeukldu3aRW9v75JfTBk4TMGzi7GJKfLm0tflXvwh1twsCEHya19cVeillCRsE0vaeDSBW9OXBvEIHSFtijcBlS9EyYLN0KHbyH2gE9d3vkPvwWsVdp/PQcqUGH43l7t6eXokgS81icvO8/KbbyYlNUbjWb4zJ3HEZnjD/laCboNen8HlhMTX243vo79EqKt4wbWl5GwcskmNwtvegf/P/4zot79L20+8EcEcuhwHBC6hYej7F86iZYnISyQWoJfCetYalGQYIATSkghH7Xa9bUtOXEnjdgpeGp7n2P4WQt7t3ypdrwg4HA7a29tpby+mDObz+SUT0wzDKDv6G2k4qySUIhPDGPxn7EAX1u5XlXd2APxwJIEtJTlTcs51M60hN1q8eEMeckrQsmC7KKVBSinRDVHMcpDamj+jkFPnwe7iOnzpNfFDb8UfmyPk0ZC+4s2tZW1u637x+dzoqNZ9bZTQr4H1rtFLKRkaGmJqaoo77rij+l5Xw4tmuLHzS4fAOA/finC7kbks3le/dtX3M5GYC+Njs7a1QuhN/Q40exIpQiA8TH3lHxj//N8TeeB++j/yAYSmkbFs0A1cPd343v04kY5AeQ3T79A52upmMJZlTvOTmJ0i6NV56x0RTFsnlZEMzKawzQx5WWAmWSDo7qHVZSCk4NuDs1i2zWB6jjcfbCtWPxIMj5uCxwOFAm0Pl7bAOZCyKNqZ0Sls4cK9e2VbPwdYAoSQ+PVpWtsSTE+vfpE1DhzG+66fx47HcN3zshWPi8IcmpXCcnahaQ76W1wMTafY1enC52qOtuz1bgd0Op1LcvoXz0ifnZ3FMAwKhQKRSIRAIFA3sal0g+J84X+iRYdAdzDr6sToOIhTLz7n1i4vk4k8mgZ7Im7afQ5CTh1EHlPPM1WQtDnyaHaxX+b0QNTlYiJtE9Btet3XbtrshSyJal/L4n/PmjbnMw6Eq4uohAek5PtX4pyY8zDpTPPQwdUDja6XRqf8NSNK6Kuz44R+q9fo15xwV+PYRk8fnX/+t9ipJEbHcpOeufDnWqWiF2taJBLHwva4JRnywo2tF8fVSttm5I//HM3tYebJf6Lj0Ydx7+4n4tQJOXWylsQjBP/rR1dx6gXedDhJwN3KXKabRN5EGAYWHvzOBLqWJGdHyNoe+v0mZ7IOwq4cvcFRNKExme1kOpMnaxZw2UkyOQ8g0YXGoZCLy/EsY/4w2V//TY7eUdyylDYDnJ+/mfz0DM4//jMcs3Ps++Rv4Nl7bdyulBJrYfFeChuh5dB0SSi0+vq9EALn7XdVfsycxxX/AWChOXspBO/iwcNBDrXDrQf7MPTm2b9Tz9+DxTPSr169ihCiHJeaTCZxu93lit/n8234vSub8Yo/w2da7+dMvhsxluJVXV4CDrhrb5oDPToO4cBNsTvT5taZyGvM5RYq8FyC/Mc/iOb14fql9xG3DDRhM29q8NFfgnwW72/9OlPudnQ0drnBucpir64JdCEwbYlH18gXCpwbi+KWOS7HcqQLNj5nY28KleNesR52nNA3grW27icmJrh48eKaEu5KVEvd03z+Cql3OXRjEISNbbUj7eJNgCYEId2BlEkMew4p25fsK19M0pKkP/lJ5MQkgS99CUdb8TwNTXBLxE3GsnlqYIa8DabUGJkrcHPvNOOjeVzBDm7pdOC04tzWOQuEMXDg1QUEg7zRPUBvJArOIBY2tpR4DJt9EUEmD3d0jGHoGjmzj4QluRrNkCpIEpaD0fkcu8Ju5vIWeVsnlzKRt92J8c9PUZiaxrN3N5o9gSZHsEUYp+ynABhSIpBomiSXFXhrp+fWxsxhZ9PgcILMAcWLetij4zCaR+QbvY5empHe3d1djuuNxWJcuXLlunL6F1epV2NZbAm7j74Hx+A3uRq8HxsNIWEuayE0mJoP4TUKdHiTpL/3Q/RwGNeBAwjpoDRBMfODFzEHBoqZEd/8Fu7H3kPGcuKZGCZ/7hyR972duNMF2JgSYlfG8E+P47n7nqpjkh2a4O42N/G8TYtbw3vpX+jPCa5aLXS4fHg24WcllUqtSES8oRHKjFcLJfRrYDWhr2a4WwvrGicrMiDshTju+bLQA2iYOKwXABPMYTTtjorHHU4V0Pbuxe7ro/1V9yI9bqScxWFMYdstRPOtdAWdRNN5HJpJjz/L3Kwg7O4kEPRy8eII+/d1kHN0I0wPIhGne34Ss30/Od8e4lofXpmHtI+27BRzzhC3ekZp65lHGD6kmCdp2mQtiVvLg8zjwMTrLF4cg06dsXSBfDiCrumEHrwf/523F79GOQwY6HIOJ+0Y0o3AgVnoJhadIRbLcD3BcKknn0KLnsXRGUB7zc+XW7nVWuGmZQMCQ79xrjDLbyIWx/WWcvrT6TTRaJRLly6VQ11KW/lq5fSXKvpT40n+6fwcCHjwgMaxY6/mpqifF2ckLl3Q6dG5kgVLCrKWgePcWeZ//b8C0PcrH6DLlUI/+AaEvxVtZpqYYdB5NIDXPIV46vcx3/hxcsl5ppxOHGE3IT1FVvrRcllSv/8p0tOTuN7/QXwPPEhAr9wd8Tk0fI6F7llmljfpo0xmLSI9D29KQlu94m93CgLQVeu+KjtO6Dc7Ga+W4e56j70cKQNI6UaIHNLsWPZocX940WxnFZcE8nlS5wdw9/Wi+4ptvqBDI54XGC4n87bNd56/iMdt85aDcfy+DF49QnvQR9ijEU4PMhsN0dqyh15fCi7/OyFnBNvhxgbyuSzu734GYRUw73krsucQFgaFtI7zu3+G08oTufVN5PsOExcZgsYMMhvCVUghpIO9Yclub4IOX5SIL4i1cOPisG1mUhbi5a+hty+E5nJiS8nFVC+ZfJ72y8eZ/Zsv0f2hD+Lq6wHpwDQdSJnBRlLaH3FtcWNt35PCwDlAkL0ygf9oFiNQ/bljcxm+9sMxdE3w9vt6aQtufDpevdlKZ7wQAp/Ph8/no6+vr2pOf0vIT/fcsxiYFA49DE5fuaKfSOQx7eLN1fi8DWj0hTL0eFrLN1/OvE1GFrdo6mMXCD90M/P/+hKeoaeQvgDurv3YIR++R9+B66b9BM//DRmHB5eUGMkZ9DvvZPeHH8WYOoO87CLQfy/JH54lQQ77XY8RO3QbiZzEdECLs/ZnObvrIaT2PHlzFK1tf83n1gsl9Ir1sOOEvhFUqrrXaribjGVJZgvs66w8Y3x9A3N0bPNA5YeEG0s7gpBT2FofmqWT/9O/5Nylqzg72rj5rz+D7vHQ6y0almwJ3xqYwdTcpPIFxuYFB706YaeOU9pcmRjH6OnH63ah2xriO5+FfJq2zsOwZ08xXjafAdsEXceYHsLsOYRAoCVmwcyB5sByGsVgHnxk4xLn9z6H17bovfMxbFcaT0sCy5Lo2gyJQifTOZvZTB7TKmDoBomFLQnxvM1ULow5O83c5QCBkUniT/8bHT99LfNfSkmBokkPwBYJPI4olhXAMiOsJvjuH3+E7Ne/iuO2u9B7ems+99xoAsuW5E2boanUuoV+q/PzN8p6byIq5fQnEgnEhX/COfU9BJKrKZjoewMtuokQgnv7g1yJZclZkj1dAUw7Rf7ZU+ixYbz33Yscm2LfwPeZvfURMt0HyL72cdpecRhH79MIbZzErQ+R7D1ajFNOTeK5aT+5yDuJRm4Cw0XQ68cNOMgURxqfPA6u3QRe9So8d7YTd7WRcQQASXZyGtMpMDo7K3590ZzFqYwP2fpqbHuYbm1zLqlqjX4lqnVfHSX0a2B51V0y3IVCoZqGu0uTST795Dkk8Prbu3j42MpEt/VOxstYJnlsXGi4l4Xp2HonULwgCZHDOjOAs62F/NQM+bFJPDftQRNpgg7JdM5Ne8hNPFvAIaBdmuTNQ8RmZ5l67p/oPnQrursUrmODVQDNQL96Cue970QznOgBP/LgqxHTl3D0H0MXPkCgtezGbt2HlpzEcLdilWJsZ69AIQe6A8sJduQgCTuFWxvGSthIK47EQ683h51K4hV59rcWOxdFp7UkqblxxZMIXcdzy+HiZ0iKsG8CWZDFzYMSEBJDTyGlga7PY5nFKN9auO48huvOYxUfE+Y8WmEW29GGNAIc7AlwbnQew6Gzu317VVaNyowvHft6ugVCCILBIEZrO9qMxvyhB3hBfy2WJRjJCyLj45imyasP7iJvOBHA9LlZnBcv0PljN+EQVyE7iBUfxzd6glzPIcBi3thDIS1w3/8uRIuruIXStshfvsjQr/4Fh776u0gZRkhJ9PIYrSEv1p2PwNnv4DCz2P23o0Wv4vILWmQU2xki/aPLFD77p4ybFl2//ds4Ksxpz1oSKYu7P2zDxWyqwEQiR1/YTcjduMtraXSxooig8phsRREl9GtgsRivx3B3dSaFaRcvBBfGExWfs56te7aUZGTxhiONhUvqVS+6ltAofOZPyQudtueexb13F0LOYBiXAYFX30tvJEC7302rM4t0tzGTmif73Fc5lLwAJ14iH/wP2JFenLoTee+7YfgFhhIebtbdaEIjmsrzD7OHcLuO8LrBMVxnr+C67xV88YUpLk7fx/27/LzsyjSe/S3g9XFF343P2UeHiGIHOwCBabuYPzFE2+w5/LqTwrGfwbbHOHJTAkPXsBxRCnYrpi3JZfJMZ2wcR1/GTa99Bf6ehXAeeRXdyNEaSEEhgdsRACmKuxFEAdsuJvFtGGkV8/HtHGgucpHX0Nfq4b0P7S22kbeZUW87hdpUw9z9aqQG2f6DyJGF4+kO9u1tp68rx1AiTtZsASQpTwD79T/FiNugr/AMhlH0wDjnxwEdK5+n8NyzDP/Pb5Od97PrI/+BFjFH/Ac/ZOJ/fAkrk8LPBPN2CGyIfub/Je4J0PIbn4BjP4VX2Pg1iX7xOFKmcXT30OkwGf/KlymYJoXeXaSnZwhVEPp2t07Mq5O3JIl0lH8e8JA3JWen0rzjtvaGfR+U0CvWw44T+kb8YpUMWadPn16X4e7ufS08c36GWCLB2w7OgpUF3b3kOXJ6EuPUCewjR9BWcdEKKG+jWz47fjkJU2K3teNxuzB3vY0zI6OMz09x9+4cHSGDgHMehxYBD2TsLKlkGsOh093Xi7gwCFLiTMxBa3Hb24hrN8/rQUTsNB1/+Hu4Dx7iX3vv5fJMCjudxv/8N7ht5CT5sVkueW7G59T512fOsf/7f4HR2cW5X/gvPHMxjsYDPNaaons6iez2InMFjJmroBtITeBy6chAP7Y2ijR0hEgwl4uQMG3m0gV0bKThIB8s7kiI5y2uZnogn2bX2PeJf/H36fnYRzEiYcxCJwgTpAELnxsLn+FaEUJgnHoOs2McraUNrf1aC9flaI599fXkeoQ+W7D56kvTpAs2D9/cRmTXA/icsxxqzTORNGg3c+zqjuJy2hyxJ5l9cQq7/2XEWvdhZ7PIjE1iOoPP4yZ39DVoPa+kU8ujpf8d0RfF+aFXYfn3o5HDaydJpSyy8xatr3kVGJ20pI4z+8VnYXyEnv/y0+TIYeUk6UQSX0cYe9edGM/+L5ieRD74i0R+9mcYPXWBwj33MtPZiduWuJb1hw1NcCTsAin50blpbDuCYbiLN/is1R2yftQa/UpURV+dHSf0sPY41LUSj8dJpVLs3r17XYa7gMfBrz5ko8++AEjsuTxW+7UAHGtulujHP0gonWL27Iu0/+4f1zyeWNhGV5AmbvsSupXG1A+ujLSl6F4XtoUEnFJyfEoiZJjopQI/dcsMltGFA4v4xR8xYet07N2F03Ch3/RKZCYBLj/03wkUOwl/+/2r5E1JYUJw4MWT+J8/Tvj9+9BME01k6Oh3g2M3rlyK1lCOufk0BwtXEF4P5sQ4E3NpBJCPRrnynSdxRYcIfOzX+IcZB5OZB3gsdJ6+fbuwPcX2f44eHPNnkAMnkHsfAWGwN1RgbHKGcLCDbr8TkMRNiY2H3OwcQy+k8F6ZJDt0BX8kDAiQxVCUApK8AF2CayFNby3IXBbj375L4mAPjmAcx5tfW44MrkQmbzE8m6Y94NqyQTlbXtHbFiI3j3SHiy30hfHJJ8YSxZGwEv7xwix3HWhHT7eyW8Tx/tkfYN7/GuaCe+jSRtCETWuvhZ1/BmHsZd7nI/Ov38W7L4aVK+Du0nn2wmX8HpNDeyTfnbmD+K338cp9e3HZJzDtNN/rOcjUb/0ud3b7MWWAF86N0dZ6F10/10vrfg9z9izzw3Gmfv+z2D/xetoe/jHkm/eCZoCRwx3K4dr7erC9SKBgg6tK80ZEhzicfJYu7wSX3Hdz074DDRUeJfRLEWp7XU12pNDXi8WGO4/HQ1/fyjX2VVkiCkuvEtbMNBQKICXmlaFlL7QR2jQgkXZH+bWaEHjkDLocBcCwBjCNO5G2jRmfxwiHitPLDB3n+EXuvvdeLifySM3AsgVOO0vKPoywddL//Ge45y5y0BeEXR8FhxfhEcwdeTtDMyk6nnwK8dW/x33fy9F3vQ47n8AdcRD+j4+S9vaxq62Fn3R/D5fHS/hNDzOU7cLWHDwcfQZXbg7XA4cYmE6ISAAAIABJREFUST1ATro5piXIRkfxOmLsjl1FFkyGRmcZSbdgSwffHOvh0cmLOPtuB4eBFs9h/eAZ0Axa8t9Av+ke2owYRw/EkIZGVmvFsiCka5ycSJHMuugZHCfc043nQGleuInAQuKiIIrVlYWNMKI49AxmoRVpr2JocjiRrW3kR2JY7Z0Yvq6atwhPPDfGRDSLx6nz06/ejbdKml6zZpWvet62ifvfP4VIT2O1HSZ57N2gp3BoGhGPF00IdCHxugEsLKkxd2EE681vR9t/kHjeJvet59h1IImIBNCcHoJiDK/eR9zrYHzezYT3EL16gLvvPohp5jk7OcCZ+RZsCf9wdpqfPZRiIutjNFU0wJ6ajPPyzkEmNS/n9u7GZ5g86piiJXmWiT/9CugezKNHidoaAYcftyYh/hKYGdpcSabYg33mPPnzp7Hf/v+z997hcV73ne/nvHV6Re8g2MDeRauTlq1i2bLlIrnFjktsr9OcunezeVJ89z7ZZK+TbJKbxF5n1/HGcbxySRxLsqqtSokUOwkQBAESHZjB9PbWc/8ASYuSKNGyKMcKv8+DBxi8gxcz78yc7zm/8/19v+9GeQmClfUSAkmPmqcjPI8XWXvZXgNYKt1fqlfHFVzBFaK/CF4ouNuzZ8+rOo8fXQ3SAd/Cj2+64Ji+fCWhN99C7okfEP/0r1xwTCgZFHV+6RxIpP+j1Dl5vnFMIkUA33EY+Q+/SeXocVI372bZ7/9HQNKccgnqs0TMFjZ2J6g0XFam49QViVXLEfMqBEIR8GxkZRGCCRzP53/8cJya5WJMSz7c1YZdy/OeAY/TUxO0pwMoyzZRtJsRQiHZvpoudYqMGsPXDRQpKIf6aAla5CNdVLUmFCGwa3U+tnqBeqydqS2/Rb4miLW1Enh2kmq9SsvwXmpTB8CT7N92O6emG1zrtLNWn8MZ2IqZbMXEQ0gHTInXcJlzNXI1F8tyCegq2XffxXWbehCKgi8bKHIMQ7Fx6UCTzTgCVMVHV6pLe/hqCfcViF4oCo13foDWgI7a3vmKaYKFqoOpK1iuj+16FyX6y4mfantdNYOoZcH3yFbrPHYGIMyOzgar2lTeqzVjuxnaUxWmGkmE8GhfUSVvtVBXBL4rmfxfj8PVUbru3oYaDuKLpS0tuXEb3z3Wh92QhKsqu1rz9LalMMPLQeQRUmJoKrlyD0XpoCoKjidJRTzqTpWs0gwSqo7KXLWfpHTQBo6RXj2A1tKElBILCABichTZO0CwtkhqzxHy37qPqgQ1FiN+xztfdE2y0eWU4ptYmVTxul5a0Plaol6vX1nRvwBXSvcXxxWifwmcE9wNDg6ej/aEVzmACgU/vvEihxQSn/kcxzdexbKrr37h0XP/lRfu9EklhctGBDa+aMGenqF6fBg1FiN3/8P0/+ffQNGrDCwDVczQEbQIqr0YyQCOV6DRsDFNE33LHbD/W9A8AOlevGIBWzFo2B66V8FNJzDf+2FmRTe+ZrI8WKepdoySqiOUs4qBxAoUJUUkEML0wPFUWlLdCN/AMCMoNkhfIaxInGCMaqSPktaMIhTqjQyf6tpHJtJAf2YYLxSmEExy4HQBU9e4v7GR/kQrfrIToahYtBCws4j5cWxbx4v1ExIVFOng+hDXJUJRcHzJaMXH9VpJLw6TGPsOLLuJ4PL+s1dSQQgfz7s0ZzFpGGjLXqI/2rfRq8dBejiRtaAEuHVzK/tG8yxri/zUAnB+mkQvwy340Q6U0iTjbW/Gk0sT0qmiRjpp0pJQMWSKhPcEaWMKZqfRu5oJmlXmija5Qxnc4RGGsk3MXv8hAloPveEwpgp118c/m1lsWS6z9z5Ksr+NZRuWs96aZjHcQvsD96Ks7KVtzXKWU8EN6GxOzTBeayYR0ZkvesR0SaMm+c68h9x9O7v66yj1LOWT81Se3EP0sx9FSa5F3f84frofws1LtWEBajT2oue8UPcYqUCtaSfRzhQt5uUfVq+I8V6MK6X7i+MNSfSvdo/+nMOd67rs2LEDXf/RQH1OHf965U1Lvwn/rHhM+s0vPq6kOPcM9bYW/F/4JJXmFpqmzoDwcWafxkxrIBU0xSOhCUZGRnA8h/5VfRiKidq+Fv+2NSxWbLz7vo/9v/4WpbmZ2z/9nzl8eoKtfQ5quB3fNlAUKETXUlq06CFGT0TH9RRUX3KinqZTN1kTU6k7Hk9Nl7HdGFd1RVgdUyjbMO20Y2kJWkwFxQZfCoJukWA8Rmr5TiY2fBC34dMU0gntnaJSsGg6eZjcvQ8Rbe6k1tNPpWATPn0Yr27jVA5jbf0QAUNwY/QEDTdK0VpyuKl7koanQr1BXmnCf+oM2vgPCS1fBlLHsTvOOgxq+Gcz7y+2Z3/RroZcFnnsAYwOHxFPotbDeOHV9DSF6Wl64w7AL0X0F4gcFRXr6l/HshsYlotSWLq+iQcfInPVFryOZQgiqN/bg16cQetqg84WVAWkZxNZtxLn7/6aA3UTt6bQvWCRPbmfvgN7aPutX2VjtMho2aDbzhB/+F6qm9eTnHuQ6zJzeJUqY8/UCXbcSPDB73FVoc70SYG/bR36u99H2oS2Xp0BY4bnJmIUG4Kw4XMyA5snv8f8lw/gFks0br+J0Iq1eJ1L5ffAag85sBpf1dCfF8N8DtZZ4R1CYHmvjz/ClRX9Ffw4eEMS/avBKzncnQufeb2IHhSk3/q8VK2L37MuVJxbbkH3fSrbt/DY6CzjhWW0zpW5vXeGSmAtQ/seZs3iEwR1Ddnx85Bc0hs8fiLLo0MZ1KzJB975VkLX34gRjLO7dRU9C9/FdtoJ663UXZXWoMaoiFO2BO1hE9vzuXc0h+P5jObqvG1FmpmKQ6HuoCiCk4sWO7ti7M8Wma3YCKGwMxRmRUxlpuSxKFsIRCSeH8NVDbSwQqM2ycc6nmHe1OC+RwBB8Yn9/HNvFMt2Gai1cZPYT2j9TXQnNYLuCcw4FCo1Th2uc3I8QCAa5/SiT83SaTtwAuNMgbbbn79tooJUcZA4Z6+rKSXqj6GRrn3za6iNGUySqGYAIi8/6FqOj6GJ12Vf/vVc0Us8pL7Ig0MWJ+bhmt44W7tiTPs6vqLTn/Lp08fwpp/Abr0JHw/p+syM+LQpVRYX6oR2vQmBpGpnCYYkmVgav1FDSknF9unbMoj1+IPI0jg7+y3Wqe34Cx7iIzcRvnEb1cUa4ocPYooxmj78LoL+CATDmMUSIcUlnnAJ/uXvEHzvO9GqKpWuQYLNaZS5GhKX3liVM0cr1MJhUr/0aXJNTfjVKuFQAFGfp+YaOC3tCKDgn3Oq+BHaQxrFWgPFbxBSYGyxTmvUuKzBNldW9BfiSkzty+PfPdFfqsPdq82k/0nQ8D1qvosAYqqOKl5a8qsrAkWApyjoCI6UNTRdZdZWmaoJGlaOVSlJcK4MroI4+Thyx/sBODZdQpUObtgkt34rVaMFRxgs6m0kVn2WmKGy8uz/Gc3VGZNxpmZr3GAGiJkavpSo0sNtlCC3QDK4Ak1IpFWiTcyCu21pkiJ9kD4aKho6xxbKSKkxXW9ne3sDQ0psV5Kun8JMNJHq6GTid25A5PKYLe00jhWwyyVO5wL4TX24y7YhhcAOrcasnyIWhtb2GFpzOwtVi1qtiuo5FNdvpOnGTUR6upHSR6WIEA4eKXzU81URlBK6VsZzk/j+Kw+gQtexT9cp7oXwwCDCvLhQ8+mRRfaO5uhKh3jHtg409bXtCnk9EalPEVjIQ+/OJXW6arFYdTk05eP68MBIni2dUTQUwF8S31VtlOYosfo+cqFNiHKZU998hkndQPmtT9LIqgjpMxisEg24LNdMTi2CLz1WNQXpSEeRv/IrEPOouw6uGkLGWjHffCvluo/fvBx5cz/IadzhBUb+T46B3jLa6k203bwZ/fB9qEEX7cgzBLesJuOHCRo6g11xloVVpvIx5nZ/gP47DSLJEK7nMzk7RWsoR9y00X0TXB0CUQIv8RHUFUGP6TPl1nhsrIDl+kRNldtWpy/bhOuK6v6FuGKY83J4QxL9pX646vU6R48efUWHO/jpEL191hzHBxwpuVh2iqkqbEgFqbo+uiKYjJpkyhaRQAAlGSFtBpDxjXDiEcBHtq7Cr5SxR09yXV8n3z5YoiVgsSqYZT6wHMcTKAg0BQoNl5CuYKgK2dpSDKzvNCid+gGt3T1c1dHH9NhelsvTaJN50oMd3BwawWucIF4r4y8G2dI0SCp3iIhXoDWXwurcjXL2OelCsHA6T/eKNp5eKDPtrmNbU52q2oSbMiHZTKJ0nB6ZYaEMO8aeojq8SHD3Lcx4QYLCJm6W8DI5oqU0TudKmgMNsmGouSG6Az6z1Rwj+w+gtHURDEr6asfR5ktoG27FM3QEHoZWAgSqlse3LxxAX4qUQ+/+IPbBfSgtbYiONS/7Oh4cL5AI6Uwv1slXbZrP2uX+Wze1eSGUzHFWZu5DySpY5SlG++5EVyEdAVVZqjpFDI28Z5GsTxM7+RwGFsG+nVRar0JZLNEensBqXsvqf/h/+E4hTVWaaDMlBpoNsmYraiCJ4cFd60LYj3wJf/3PIXyPxZpkaMymjRlSgzGsQg2jVUUNBvEaDgSDOEoH6rYVxLrXcegP/4wVt96JnBgmoRloqRTZE4t4AY/Inm9R33IDkZ5laFLhVK6MoboMLbpco0pUz2N5Tze6a0G1QUA0CO7/HovPnsEKBai+572kmpoIBH7kieF7HgIX15PoqsByL+9E7lxY0BVcwaXgDUn0l4KLCe4uhstJ9OciZV840TCFiitdFCDgT6JKB0/pB/Hily2kCSJ6Bk96rG1PU0roePl5QoG2JYMdM4J862+C7yJDKeZ++TPISICW97+Hj928mWS+TMRZUomXFRNTVTg0W2aqZBFQBW/tkKxOJ5jJZol78/RwBuXMCTo3/iLd+inGCj6zsplVUiUQjPCDXJopq48bk1G6wwXS1iSnGymCco5Uj8J1gZPM53K0BjzGnHamyw6ulEglxKwToi2oUnIkfqOEWTzOXcssKiGN7BkJNY8jJ0rsKdRRPIv3iNN0iyxaSBJoTOFJyS3RYbzoOpRID9BG1vIYK9WwG0XmrRjR43uYO16j+aYbSafjKLoA4eF7F5L8xQhTicYIXLf7xQekRLh5EApSSwCwtjvOwdN52pMBkuHLL9C7XNUCpbYIUoJ0OKQNcDpvI4TPDq3ML15TYzzbQzgepoGBFe2hhYcxDjxJdaZM+J2foeGDq4CozsGyNLUDJkJAw/KQlTJ2tYEbiiMcj2/ff5D7720m/tV/5Ld+cxNfvGee+YxLMBTks7c+wd/ck0fqAT73m7toMfIYMYkfTyMaAi0ZZuAPfp7JL36T0lOH6bljJ823XoP57L2E8odI3biBDnsv8xWb0cAgLoAHHXqGxd/7B2S5gvq+d9D81m0IdxGlVMDYN0o6k8Op1bFPnmQ4m8W2bWKxGMlEgsj8XlbkThJr2saZyHpWNIcv6zbNFa/7C3Glj/7l8e+O6F3XZWhoCM/zXiS4ezn8uJ70Pw7OnftFRK+oGEJB8SbQ5SicVTC7ygrm/v7rVIdG6PzkR8562OdQlSnwXKL1MzSHNjA0nsOUfaCAjgaRMHvHcjxw6ARda67ljtuXcyawCsdSyYS3szYRQFcEibP/f7Ziowlo1PLURp8gFW9hrd7NSn8f07UQNb2PAQljydv41ulZPKEzO1ZnVdsq9tsGqgL3Txh8tLOZr2c20LA9nqmH+ZTn4S4MMVHthGoe3YzTEVY5s9gARaMnmiKouDw7naHh+USCPQQ7mzjd1oW70ieGS2nBRRTK2KU602VBausWxMqthIIQYxQ1GcGSCraEhg/5msOpBQtclY0Tp+GpGVo/eCN1y+LYsRNI6ZJKxwiHg8SSLrqqvqL74AvhnBxGWThCqF8DI4AT24ZvNHPdYJptAwkCuvq6RJjCa1stkMIFtYzTt47y2DPENY9yYiW+A0IqlOwAPd5p0v/tL+D3/gRHW/pMCdfGqnhU0jrTtQpTNR2tVqXzf/53mn7jP9CbDjKZs1gfXOTeLx9gJivobznOb/z2Rp58YopwWFBS0tjVEfIZBVNVaFQd9p+yqaNAscj3/ulJJoZnSBgOv/jptegbdqJHwA310vyLH0fr+yHF48MkO1Zj2t9AhMNLjOBLZsxOAprCstYgPcEsLbkMQ/MLS40ungdmEtl2DbIN1K4ccnIOPRyiZc0a+lpb8X2fUqlEYTFDZO4YeQK0ZPcRSPUQNy/vartarV5Z0b8AV0r3F8e/K6I/J7jr7e2lo6PjxxoML+eK/uUmEUKIs10E4nxrWPm5g8x88Sv4roc1Oc3af/gifnUWEagg0WlrbUPKMOnyGOpwBXXltXA2O/vBo/NI6TKeGiBbt/Ej+tmOfHB9n3zdI6yrhA2Vtc1hjswVaWeehGIhSmMQXMEh7TYenKvjC42dJ7M0RQP4ahAhoWy5xAI6mm7iuB5NURMPFVdPouoS9+xz+U5+I5W6xTElyaYUrM8+ztbyLFHDQ629mT0jC9iRTuJRkxFvFS2GwHU0tLBC3S5zbXAvRbUDzhymfe4ojd5W3OWCim8QVOOI8gQao8wGOmn4gsmKQ1gTuEJHtqym7TOrCa1fgxCCvr4+PM+jWCxiK4LFahnf83EKJVRVvaQVsp/PUf3alwkNhHC1JPrACoRXBZb8zkMvaLnyfIl3eeaNr33pXiuC4oAKc8vehto+QLujUC3aqIog4AgWv72Hyr5TmJ//PKn/8tuISp6D/+n7KDdfy+iaW6iPN+hsUhC+g7Ohh7/8/w5jxlt43wc2IguLzC4qhIOSkfES8f1f47YdvfzTQyrx4jy9huRX707wrfstNi33WbdKYc9REz9qUKxXsHSTibLK3kdOsHN8P9Gbb6IcHkQoCqFNayiPnGT0d79A4PpNrDTzWIUwtLYSsTwKqiBkBNGVJo4pTYR+NU40GiSxeuCCSxC662607TsIJuLnk+wURSGRSBCOxqhWN5LKDyOTyyg1PCaOHMH3feLxOMlkkkQigaa9dsOtZVkEX8Ey+wqu4BzekET/ovYfKRkbGyOTybys4O7lcClEX2m4/Mu+KUKGyu1bO9HUF+/5S8/Fr1RQ44nzvzvXuidEDkT9bDvdj+xTfeWc0MvHV7pRw6fw43Hc3l5EKEAhO0PxzH6a0wbxiIaTvgqmj9C78DRqToX6ImxbinPtbw5zYtompPt0NYaw/SSZ4CAJXePofJXTxQaatLlZPMnqWBsrB69BjD/L4Zk4k/ogzSrUFR1vqeBJoeZwzfI0C+ka5fwCNyZTRPQEtyeOU69VWNU6iJApdjfPM1GE9asH0TUFLdyEKxtoigIiz4MTGscLyzFw2FY+xuYNb+JApkbZdehJhjAND1FxmS15rLKPk1BLvK+3wtT+BTTfpTRf5Ht7CzhS4ab2Bbb2avjDw7iDb0L1q7QHfE5VPSKmSd/y1YQNlYLtsWg3aPIniBQKxFs3YwWW9s996WLEy1RLRaanixw8WCOZTJJKpYhEXjpyGAmNiRpaUwzFbMczXxyCArBYtvjmnmkWc9A1UKcj9W93wLZcn3sO1ik1PG7foBIwHTyhYOoeHTEDRTokTw+R+Ycnl4h163YCWjMk29nwL//AdycrZKogcSlUXbqweGA8xsFDeaRSoZ953n69wY7NJk/va3BLfJTGYyd4+2CeNcuCZB8fofC/YdXGLu6amiYRShHt6uF3tjtE17Sxd1jhnkwQEdD49kmT7x5S+djMg6z+cAwl2YphxCggqBwZpuK7LP/8ryDu+2vs799PZEYhtOudpN7xNu4fWQqgEulebljRRFURJPChVqAqFbJKFNGzAtW4cNCsuz7HCzaV+FW0xNcy2NPFsrOiWc/zKBQKFAoFzpw5g5SSRCJxnvh/0g6ey5VQ+LOKK6X7i+MNSfTPR71e58iRIyQSiVcU3L0cLoXo73l6gj0jWRQhiIcMdq27sBHHr1TI/Non8TILhO+8m/iHPwmc+8BWULQZkBKp1C7MnRcKvtpz/mZw9Qq8v/pLHCnJaSqHRxeoK9egLzjcIcZR0jWUaBT1LBkJ18Ytlag8cB9vW7OSzcu6aSZMUAkRSK0hpi6R27N1ByHAtWqU8IguPAepVcw03cx9JyfwpSRYcHnPRpNyrUE9e4rd3gJu/TbCeoVgWwxzYQ+HZJppfSVawmdZZj/7ynHKIkk8VqanfpiJuZWsCU5gq5Ku/vXMn84xanciyFL2Q7QMbiGQ20/LwjyrA5L2vptx/DiTuQK+53HUaSfVk2TC7cL+mIZWrdBoeBSHciRMnSPHbTZM7sdvX0Fa5qjYJZIUWZes47ZcjxACT0rOVD2EX6VSDTFYOEjp8RMkPvgRHCCo1DANBVML0tunk0r2kc/nmZiYoFKpEA6HSSaTJJNJgsEgSjJF+IMfwz19CrlpO070pfPLAcbna9RsF1/C8Ez5NSf6V7ui10a/jzp/CHfgZry2JZOn4/NVpgseri956LjFx7dWmPc0QCVheDQ7w0SKz7J44y10fuJOMokAB4tlWrILlH7hc/hvv4vncr2UsjV+7iMb2Fx9mDOmj6KFENKldeRB5Ow8n3rz+9k0doqOmcNMNjUzdSzM6u1baMpMcFLG2BBaRvMKi2BtDm1/Df+0TbwTbtmaZHBA8uxxlfsOGBCMcGBBYZt1ilrZoxHqJP2J9+P8eR23vRmRnUDRLEJ37KSz6nDyuXnmaja+dAAFiYrvuUsOiI0JRH4Ut6RC+xakGcH2IfQ8fq66cmmCgKSqhOB5nTGqqpJOp89b1bquS6FQIJfLMT4+jhDi/HsoFotdMvH/rHZsXE5caa97ebyhif7HFdy9HC4lTlZTxNl+dx+jdhJhKUjzR2Y39shxvFwOVI3a9//1AqL3/Uv/8PoS3FAQz7LxFQUrkMD3fCxpMh/fRisSP5qksGwXTbKGvuntLP6/X8ApZeBNG6lpJmdoR0T6SD3P0nVja4TnZsuktDJtzjxFGUYXoaXnBUjfIygqGK7O1vAEk3qEhj3HXHaRea0dIT1GA2spEEURFq4UFOPrKTVMTEqUlBhZEeBotorUmkkoeTrVBcalT4ucY1xPMtjRTGcqwtcPqGQbPRjC5aN9JfREfMmQRahIM4kXcLGrJqop8NUQffIwUSVIY2KW/vGnyS2LYtzyNgQuzeYsAbWK60RxETR8qDY8RubKuJ6kL+AhGy718RmaEGiAgooiltzybVsQCARob2+nvb0dKSW1Wo1cLsfo6CiNRoNoNEoqlSJ5wwDqC5MNfQvhN5BqDISgtyXEvlMKNQEr2v6N7LNWZlEqJ5Gqj3r4f/OUspKC7RM7O3gaqqQzamHVJJoJDgoKDmpxjsbR0yw+Wqbptz/CcDaIjyAf7uKatzRz5sRBipUAiqrxyLf2s62zwG27d9O+KUDpK19me3SOU8Fu/vxrVVRjNZ++1uUvjg5guxqrjilM1W7EcgQDe2yCwW0E7BwfikzScXUKZ99p3OgMvW/ZSGi9y7NDCplKjMVYB89+/xRr37sK4bkY7W0kb72RfGYeN9pOcFUfKDZOPEbh7Teheg06mhQiTh7vm09S9D2CN+2AVUGkoROO+DTqOQhGiLxgxIwbCmFNoYEkpb7C+KBpNDU10dS0ZLrjOA6FQoFMJsPo6Ciqql5A/K+0KPlZzEq4nLhYV9IVvEGJ3vM8jhw58mML7l4O5wxzXg7vflMP8SBEq3u5LrWAOjuE0/vx87N8Y+Ua1FQKL7NA6Obbz/+dqqo4joHvdj2vdH9xVEpFvLkZAi2ddMeCmIrKaKZKIqjTFDEBFyEUcrEVBDt7eHK4ykzzBt527TyNYATfX1KpVl1J3WqQq7ssk2foqo3T0bkdAut4dijIoxMCM7/AR6/u5d2bmlk49gCDyhjGVJhHUu9GqGUywRY2hOMorga+Q6RpCy1mkENSkDIkrZ1puufKTBYkAyEHo3UAqjNIz0NDciwvKJlx1KDgXXKUng3r8KSgrDShqUUcEcYyW2F2P8uLMziJZXR2DaBqFYqVBpmqzxpxirQ3yofafapPD6E3qthaKwdGS1QbLtf3hzCtaVTToyhdKkJjruqiArqmYc8VWdyXo+n97z9/jX0/gmOblEpl1ICNg2Qp7HZJMxEOhwmHw3R3d+P7PuVymVwux/T0NJ7nkUgkSEydJjB2jOQNHaiJKF6wFze8huaYyUdu6OHwkSN0N732yulXs6KXER1r860gJdmhE2QbHq4EVxFcN5iktbqPlqefYOL3D9Pzd1swzSCinqP00FHGvrHA8O/+CXv2NnCKRWaGsgxubuPawXX0zx3FLDaQQmN5fYx0di8jfzvOvembmFO2ohNmRO3H1TSqDY/DxjKkYaAbkC2UcYIBDMPnWFknWHLwRAvFUwH6Ex5v62gloIFzcJz08g7++NOCX/6Cx/SUxlen0vzusv1EVq9CXyxy6ot/j1WuM1Wqs+zTt6DLMQxpolYiSCxiAYX1RoZjRw7haQbFgEJsw20Is4K2OIP+/X/CrXnIj3wEnpdLryuCtUmD0XwJTw3TcH0C2qVVDXVdp7m5mebmpc+7bdvk83nm5uYYGRnBMIzzxB+JRK6U6q/gVeMNSfSVSoVUKvVjC+5eDqqqYtv2y94naKi8fUsL+uTikrrtBSU2JRKh5a+/+qI9+nOTCClTSF/iIVGQLypFnTP3yWQybF+/nlDIRFWmSQc0uhLNhDWFmCLw8VBQkT6MzFV55lQOGe3g3gWd9y8+Sy21C6EGMYXkh1MlPN9j1q5zqz+EWpnC2/BpjhVCqKqNZdnMTI2xrLOFqaYBnmYNm2rPoupBHMXAVAUdTWkabpb8zGlaDYXn6m0cH5+nUyvSJJfz5FAeXJsNywOMz0fJ5hr0xCEhAkyWlxzzQOABx+ZynFksMpBsUPHbWN6WwFR9vnaoSs1vYUUonU8yAAAgAElEQVRxgnV9A2TqYXKVMgF8Tttx+jrWMJfsxP2ldxIeOkQ13sqBsQoC0EuL3LEphDcxjdNloVAloflkNIkvFQY3raXl2s00PEnWcomKOronUIIRfD2AGTGwOVfYlbwwhVBRFOLxOPF4nP7+fjzPIz87g33vt3HTAUKTVTx1EN2dRgZXoygKuqagn12C+FJyZqGGqgq608Gf+D37qkr3ugIiCMInNjgAE0tRvoYqiIUDLJcF3L4EcnYBubBAqD+BH7cwP/4Bosu2ULZVnGyeh/5pFF0RnDkyy7tvbdCxeSOf33Ijj33/MabLzRxpWYfbZrIwZBMMCh4q9HPnFp9Dp31CmsfVq20iEcH4nMZ7dlbYNx5gaEqnO2HxxFGdWllypBBhrOziyzbeN1BAKGFUU8UvV0k1pZidWSTU1UNweRDFALt/De2feC+n/+ofsTOL+DOLNJ68n9pElqaBt6De+mbCSoXxfD9+awdifp7E1TtBtiDjTVQOV6mfnkHRdapPPE7ifXddcOmEEJwsSsrSZaya58aBJOYlkv3zYRgGra2ttJ4V+1mWRT6fZ3p6mnK5jGmanDp1iqamph9b2NdoNLj++uuxLAvXdXnPe97DH/zBHzA+Ps7dd99NLpdjy5YtfPWrX8V4YUXqZwBL7XVXlvQXwxuS6BOJxGvuGnXJqnstjNtyC0ptDD+69oI9OwChaheQPFyouq/6Lrb0EUBcNc6/eW3b5siRI0QiEbZv346iKChiFlWZJ25KIrqL5/dAvYjiexBOLcXVGsqSa55qkApLYvYs6yKAGSDfWDLAWYpvVUB6oCxVP67qT/Gvh6ZJePMsyzzHgreDYmAF2FWGEzdyTVecifk5YtlDVE438cCIiuMqTGTzzAmdEA1m3CjDYxO4bgAhBMMTU5z0PDSvztGCwGiPMlpSca06u3p8ujq38OB0laBXoKEFuSU1j2jvYaFYpyYDBITFlJ0E1SBECUN42FKjJZGgHori1GKYAQN721XEamXUbAl7ehpKR6kXysh1u4iLIuVGlahfY2XKxk5uQ1OW9uxHKw6eW0Nv5BiYeAxbrEJsWrLOFcJD0zJowsV1WpHy4oOhqqqkW9sot7Xjl/LIqoFmGEyWYsxN7MM0TeLx+NnJneTw6QI/PJ5FCLhtcxvL26OX8I587eB4PioRhGGjUiNpVNjVvcBIsQdDhaDqETA9Zp4awV65CtHZxTOZBlWvhYDl0LFmC8GDkzhCRbfrqCro0mN+soxzZha96TSPjZuo0uWvMyv4412jRM5AsSi5sXmGZ55Ls6wryvr8Mf7k6wPEo4IV2jxfui/FO9YXuHp3kNa0z451kuFR+N7jULU07jsdo1AX/PyqLNLcgWFM8tnrc3z3niJ29yDlukIo3YHiNtA3bCR6/RjdH3oXyvF/pjY2ha5KlMfuI7ZtK49ZYeqOT+Cjv8DuvigB/ezQKFWMrm4Uw0R6Hsbylwg3AooOhIIKdcen4fiviuhfCNM0aWtro62tDfiRwdef//mfc+rUKe6880527drF7t27WbNmzctO7kzT5JFHHiESieA4Dtdeey233norX/jCF/jc5z7H3Xffzac//Wm+/OUv85nPfOYnfuw/DVwh+ovjDUn0lwOXskd/DjLcjxfuv+RzP5/oHbn0XQK+X0YTVbJ5laHhkyxrbiHm+j/q7va9pR5nsbTWZGEU8fgXAYm86kMoikF7XOeD13aQqTRY29yHFwyBtuTolQzobO+Ikqk5rDKbODC9mwemYnTWJnnP1k5+LRhg8lSWKXUFaWsKNboOSyrEyGNVy/zg6BSen2ZtdhJX9qHiU/BDDDarHF0waVKqbOzrYGI4j+97rG3WOTNTp+4rpNQ6U2UDakVcTyD0Jp6cM1jIV0kGg7QoRapqmv2jk0inQU9zgsU6XLeyhYX5aR45NEJY9di2aoBkaxNF22Is20DBYoc2TJc3zttifWSeeIJ+N0dh9XXYLWsJqA7t+ml0Uceqp1CEwPIhW7U5Ol1BFw69JqixANUf7iU4uIZapUxTNIYmHISQCKWG9F5+1SN0ncgnfglv6gxKTz9KNEYP0MPSgJ3NZmk0Gjz77LOMlwM0GgqarlO1fvIWzout6EVpClGZw2tdA2oQgeCfj2UZWqjSkwjwwY1BgoHTCAEhNUJLSAPHQs/PYOVreKu2UO2PsWj51GzJ0HNTPHzPccIBlf/7Ew2m/us36fWilK6/lolClc8PbWaw2+WjkSKBoEap6NEc9Tg14VP3NEzRoBRJcWQqBgKm1dWoisNcQTDtpEkqdf5oMk1LyKGvA37p9gprbjBpD7n8j/sCxGWVY7kAE5NFBh5+DGt9J3oswBE/hPPUcWZyA/zmZyo4SghF9zFW9KJGwoiVA0RaferHJqiZ7XiRJFatgVAVao6kgo7+PCdKo6+P5t/+bXCc8611Zy80ytwRlNIky0UT80oPPekgscDl8bgPBoN88IMf5IYbbuBzn/scf/RHf8Sjjz7Kn/7pn/KlL33pZf9WCHG+795xHBzHQQjBI488wte+9jUAPvKRj/D7v//7P7NEfwUXxxuS6C+L/ecl7NG/Wjy/WhAUKjXpoeMR8J/Dc22ErbK+cwWnPv4rTNfrNN9xG72/9csoY49CSIBi4DZvhMXHUT0bhIKYPoqajVH5mz8j9p9+nXK8g1Fb0KtrpFWJ7UnMwnEGFvbRn16HTG/jBwcdhPA5kykxO3QK0bySI+GrQLosi+nsak9wbN8jyOIkM7MmjlyFik3Oi7KjL81ktsg1XSbtPSvZXq8T0gSqGeJjHXVko8CZhSqbIyeJag16Wps5tlhnoaJhYlMtFzk8V0JIj2YtxOZVPRzNK3hWHiEEq4MzrNqxG1/Cvzx9mqwdYEEKVuTnaWntZjLnYNdqBDWfOi71UCva8n7SOwrw6P0cSa7gwBPzhEz40EaVJBaKu0jGARcYydsEVbAcQag8TfXkPMF12wCwKlVU2QwIfF/B90MvER78Eu+ZeALledUbP59DWg1CSYWupMdiNsTGTVvoz5V45PAstlWjOjfCcCO2JOxLJl+VvuSlVNmiuoC5969oXHMX6PMsNOKUaoLjC1WQMFW0qOaGCQbLSNNEqGHSKngThwnO7sfdtJV6W5JDYyYHDk3T4jcY2jeHKsCqNxh6Yoq2mwbZ8pYuDCPJx/5EIZGUDE9p6BGF9avjPL53EaTDPrUPRZXYhsmCJ1A0BcuT9CY9pkphAgEPXfVpVIL4rkLIqvLkyTRn/l7nrpscdq+tM57RefiZEFVpcNhuZ1mwiN6Zwj+VQYkmUXIWimcRyjyHnF2k+OAPKR6C8eeOsP4PdyObN2N3baHkr0Uogq6UQbEOnYnAkqmR7yLyUxQDScp6lGgsSUy78BUXjSLa3EGkZrK6PsHgmrWvi4nNOfvblStXsnLlSj71qU9d0t95nsfWrVsZHR3ls5/9LAMDAxf093d1dTE9PX05H/plw5Lq/qf9KP7t4g1J9JcDr5dhTkDVCKDhNGZw3AaKqtDcHCX71DRevY5UFIpP76VuOxwttRGqOAzGStSoIVdsIZg/g74wjlx+Lcrf/xfCfRoVxVhKwROCou1xZK7MQtWmp5HhGpFHnXwUN7mageYwR6YKhJxFmgt7yVoZiO0GIfA1yOcyPLEYw5VrWSYXaYsHKFoBdq7soLurl53Pe07R522duFLlyMgMkUiELdfcfF5UtLWjwIDxQxazC+ihTajSwUch6uX5+tEQpYZD1HDpjXu0mjZPnMlSbVhogSi+sFCFT7S5F6taJOyUkL6CqgcJt3Qxo8apehG4/i3o113H6aESpmpRLdbIZ4okW1W8XBk36KA5RVJBnUpdEDMNujp2EB7Ygh0MUS6XAZDSxLY7sRC4QkFDYvLKZH/+GkxPUv27v0JLKCRuWYOIJ2gyDYQQtKTj3L0rDoDv++QLRWYXFpmYmAReXe/1Cye7op5HhhPIQJh8TbAvo+P7PpGgTq3hEjI1lHweX1rIShWafUxVYPVvJ9O9Dk2HR55b4PjRebpXxqAyyVWPf4f7W64mptU4POzyT3IFyRmP//Y7gqt6JQ+eFBgBhTNnZjhxppnmhEfJCjBd8ihXJa6ncDpngrpUdp0sh3BQCOuSYFilPeWzXS/z9NEQQWmjFOt849EYy98T4P1Xlzi6T6FAiMcWkqwLzLN2Q5F0Z5iPD04xMq6z8zN92IqD1X0tsh5GHf0B9al5fN9EVcvIUAtKfWly2xRq0PSNe/GiCdRdV6GaC8iJE5Rbt6M06RRlgLAqz7esAtiqiaIFUJ06DTVC5HVKtny1yXWqqnLw4EEKhQLvete7GBoaetF9fnaV/K9fqI0QIgA8Bpgsceg9UsrfE0L0A18HUsB+4MNSSlsIYQJ/D2wFFoG7pJSnz57r/wI+DnjAL0spv385HvMVor9EvJ7OeJlMhpGRMbZtaCese3jqSqLbVLR33E7h5lvxIyEenyxzxl29VEo2fLqFAFXgvun9aIQ4MFHkiR3v5pr4MKunH6bccTu+HiOmKyxUHUxVMKF08yZvP7YSxvY0bl3fytauIN7JvYxpa+nyZxhMmTSqRdIj/0rDF/jKdhTPwdWj3L1zBagvX8IuFoscPXqUFStW0NLScsExEUiQ3HgHQ089xZu6+7gj+z0ansBMruLoWIaIcBAiwrbWGGPONkq5LAEsAjq8ffsqDE1FOHW+9tQIni8ZDBfYvHYXuqExMg25Rp3OkEfEO8a2jgEeeGSSRH6WwLG9VO94C37v9aSqxyhraVbJU6zqXI4aTKCrCkVb40zZwa9bpBaGyB0/ROLtd+LqS06CroCAqII0QL7yqtufn0FaDRQjhqxVEPEEqnBffD8JDw1XmC9I1vd0c93q1Pne67GxMTRNO6/EjkajL6nEfqnSvZ9egTffh1LKYQf74GxNYnlnlGRwKVK1NNuPfOgePCNO7P1lPBf2ZXQcX1DO1bj3q4cp1xxmhgNc23uE4AaFD/+6gllz+fDnkwQTHgsVjYPDDrfe3ML+XIGA7vM/98RRA4KJRYNExGehqBIOSqqWQkBzWKzp4HlI4VN3JOG4ZGTWoCMpGPdCvPWqRY4+U+CI206iYPPf74vxh3c06O8T7D+joUiXaCyMNZyh5rnsPWSwP2uiPLPIdbdtRrHrWGuvwxycpfe2G3AfeQprYRy/qNH90Y9hawFa6lOcHBlFUQzEtnZIhGDZMoxcmYbnYWgXSjDn6y7TVYHZfhur9CKz43Osep1U8dVq9SfyuU8kEtx4443s2bOHQqGA67pomsbU1BQdHS9t8nQFF8ACdkspK0IIHXhCCHEf8GvAn0opvy6E+BuWCPyvz37PSymXCyHuBv4rcJcQYg1wN7AW6AAeEkKslFK+5kTzhuzXuByz0stJ9OfO7fs+w8PDTExMsH37DszoJlxtK1JEUUMhxC98AqOjHTcWp+75SKEAKg0tzVLenIKOSd3x+ef9M2SCzfxLYzuak2dD9Wk2JIOkAxrNYR3Lg65kgrmmW/izhd38xQ8mGJmcJaFbHEi+lVOh9TydfDsDyRDDExm+UdnED+sr2Raaoz2Z4C1vuuplSV5KycTEBENDQ2zevPlFJP9CiHAzXW/6AMuvfh/tqSgdWhFLamwI5/nGsMsTJzJM5FwcYdDtT4GmMFv3GMuWsT2BQFCwIKTp5Koa+ZqP4jlUc7NE7GkG9FPc2TjOLZOPY9thnjM2sj8r0UIm/YHjRK3TnPnTrzJ7/+M0HI9npyscmylRrFvQkiYQzVMfHUOTEgnoShlNy6Lr8yxNxl8e2so1aP3LceoB3PRmbLOXjPXiNspizWW+0CAR0jk+VT7fe71ixQq2b9/O2rVrCQQCzMzMsG/fPg4fPszU1BTVavUFJXuJFC7yXBCvUHDX3oWMXUWL2sSK6CJtoTI7mhZoC0iSioNuF1n85/0EbryacgPydhHHsxBOFatSA88jqnnEKxme+c4Uf1y4il/7MyhLkzu3FMgsSiqWwt9+x2O2UqZmKyxUdFCgUvNIJSAYhIW6Sb6uIVXBRCmIKxQ806CsBFACOpmSiulaZEsqlTo8Oplm0xqffrlAAIeFvGChpPGO9SUMt4brC06XFAKb2vGWdXFE66Yp5PLD743j54r4NQ8loNPyyfcRX96ONzNBYyyDXpxDf+wghudxvNCOFWvCazTQm9IQb0XoAVKVDMnCIk36hePKYsNDV6CBRi3YjuuL16397dVE1GYyGQqFArCkEXnooYcYHBxk165d3HPPPQB85Stf4Y477njNH+/rgrOhNq/F1ytBLqFy9qZ+9ksCu4F7zv7+K8A7z/58x9nbnD3+ZrH0ZroD+LqU0pJSjgOjwI7X4Gq8CFdW9JeIyxdqI4nGarhunQMH9pJKtbBq1aqXnKykTJWK46MI2NYZ41imhqkpLEsGCbNUNhRCoKs+QUOl5KgEdBOtcyd+8+al5yEEu9oV7GoVI97F06cFlpdBxWHo6HMMpEch/j7QQoAHQ99mqrqSoOJTlGF62lO0C0EydPFVrOu6HDt2DFVV2b59+6VbfaoGqKA1reTOgQlkY4p5s489I3lMXBQzwg5znkJgDcNzWRS3BsIkFjKwbIdUMEA2l6dSraISwZeCeFgl07yTGSuFfO8W4s89xVSwiadO1YEa6oDg2pSDEgxg7NxCvb2H0aJD1XIxVUG+5rPVn8GrugTSKTTAkD6GUkCggPCBVzY7UiJRIh//xfO3HcfB84+cTYOzQRggBImwTm9zmDOZGjuWJ190HsMwziuxpZTU63Xy+TxjY2PUqxW61QyGKzBjKdBrzBcUDk5U6Ewq9KZaiKoBFOGzOTa25AwgPQrDJ/ErJcwjP2Bi3setN/Pdox4HHjhFXLO57e4VDI4/waf6TnHM6OWduyRf+PIGRNVioRjhSw9HeedOya2qyw+GDWoNeOKoxAypCEcSD0vOTGsIAcGgIB3zyNV1FFVihBQcT8XQlqoQuu7hmgGE46A1LIgYLBRVHvG72R49ysPlKOGgwz/ujXFLOItEkAwLns4kuUFVSaUk/e0wXomxenmE+JP/iNvw8Y6fYMHcQOsvfxAxsBp1do5SwUTGu3h2KgISzJ/7KDekVYymOCg2VsUh951vg/c44u23E975pvOvQ0tQZaLy/7P33lFyXde55++cmyrHrs4JaORMEASYxSBSpESKsgItyX6ixnLQc5D97FnL9hq/WTPznufNvPGLSx7LGsm2HGU5SKJEiaQkBoliBkDk1Gh0o3Os6kq36oZz5o8CIZIAmASCNB++tbDQVXXvrXPvrXu+s/f+9t4BcVMQM1vdJ3/akravF2+G6Kenp7nvvvvOGhT33nsvd911Fxs2bODjH/84f/AHf8AVV1zBZz7zmbdo1G8tLnJlvDYhxPMvef1FrfUXX/Z9QhjAbmAV8MfASaCktX7RTTcB9Jz5uwcYB9BaB0KIZSB/5v2nX3LYl+5zUfGuJfpWI5iLVyryrbLohSySTFUIw5AtW3NY5oXV+n1xm7xjYsomcesYHQmHIOwnYpjQrIE0wXIwDckv3TTIvrEJ8vkYi5kMbWakVd2uuYx56M8xlYfOrGJNxwd4dqSI32xwRew0pvLZpQ8zk7mWyMmHOForsVMeZLe1nfVdWWIZzloG50O1WmX//v0MDAzQ0/Mmf7OGhVp1JwCFiWfZ6kxyOsiyMd/gn2b6aIY+MTugM22TCxe47pot+Aqe272Hbzx/Eq0127tM+ldtJBWTDC/CXEPSFjMwrtuFuaDh0HTLhb5QhIKJKtUJnAjRtMS2AyKmxA81fSmL4kSatqtvQuXzLaW1EIRBG8Ko0lRJNCYWrz9er4MA96t/QX7v8wjnDuyOCKHTSZDYhiEFH9zRRag0piEJQkXFDUjHrXMmMiEEsViMWCxGT08P5pFvYJ5+giCaoqa2MLIY4Vsv1Gn4gv3TgvdsgjazgfXlP6Fri0Xm5vX4spPIthyBV+fE6tuI3l1lYq7Jid1TzJwqsiA0E99+DP3Vf+JHW+4gNmSTibncdZvBXz7ssFwTPHfM4MhYhvdurlDxTIQURKhTdJMoLZguQyQq0UrTDARuaIPWeL4glAYRQ+EGBlJoig2JZWgQDtmMRdj0yCVDln2LSauNgqjiO3maFY+hGzLk9voU64I7uxdo7C4TBFVuX6wjP3g9ffdsIyz14z/0PYJKHW/8GLKyB/u6jTQ37mSxUUDEE+iZGp7WmJaFmT8jnlRRwtlFtO8hTItgavpl174tYpJzDAQ/mWsuVXz7zbjut2zZwt69e895f+XKlTz77LMXa2jvFixorXe82gZn3OvbhBAZ4OvA+vNtdub/8/0wLqTnfUvqG79rif5i462w6MMwZHpygq5uhWFIDCuCeo21RMyUGHIBaBA1mig5SzhWQjzz12BY6Jt/A6/swTM/pPfW91FScU5XFToa8MJ0hWW3wS7VwQoxhahO0bbK4TduHaJeXebp0w4HsNiWj9MRMfm74iBh2Msqe47P7cxAop3FxcULXoepqSlGR0fZvHkzyeTFyQUXnVu5wVsGHTJcruNXwRGKKJKN3gyJWJynp6r4SlFWNoEKMYSgVqtSiNnMex5jyx5e6IG7xFbzOdrjg9ROHSaslOnde4xK9qPonivpj06wbGusYJJbu9N4ZoHArXK6vpLlSBa1VCd99HkSS2Vyd95J0yoQiFbvP3mmct7roftwdorw+BFIJZDLI+junRjNGYK4D6Il0DMNQRBq/vHpSeaWm6zujHPn9q5XPa6szyN0iKyVOD5ncboZwwubZz/XSEKhce77BcY+dDfH/2OW9d/6Ima0ybCbZ6IhETpOZ6ZINue0OtPpgJ4OwdKnPsSxH5pERiX/9f4Yq3sV//5TZf7dN/IsVBS1pqDUtHCikronOblgY5mghKDYtNEIAmFgWAIhTRQaLWWL8IUBEhSQiGpcV4FWFJuSeDSB77pYBCxG86SWJjld1zRjBsXJGsI3sewYmZSB7EpwfF/IP04VyO9t8ombJE5uHf5NBcafWCTabmHEbMBgyUniGUkUmqGOOE1fU0g6+AicM3Ots34Dka1b0dUq8RtvPOd6V5shlWZIIW5dUqJ/Mxb9ux8awVvUDvLVvlXrkhDiMeBqICOEMM9Y9b3A1JnNJoA+YEIIYQJpYOkl77+Il+5zUXGZ6F8nfpqHWLl1iv/P/0E4N0Pmc7+HvWYd1WqVAwcO0NPTTcPV1OvLFNpenxBGhVGkDFv58zqJGPseoMF3YfYYC//lr7AKAn3jzQgjBkgW6j6lRoA0TA7Y2+kIKjzYuA69d4rbBwJKrofrtGMIwal6yODED1CyD2HYLMdXQ6Lj7HV4padEKcWRI0fwfZ+dO3de1HacmA5q5W0A9O/9S/rsdopBhDWdnTw034aoCTqSS8SkTyouSViaptdky6oVjEwt4AuB1Aa29knrEn60nQna6bwlQ+pvvshy20q+Nd2HtVDnrnVxVtgH0FUXV96ENg1cJCe9GO5Ema6IS7QnR9Q9QnXvC1g7zyz6ZYhlzGMAgV8AXt2Fa+QLiHwbjI0SyHbMsNrqdCdeHg6pNgLml1vx+uGZGkqfp1oiGmSrYqO37h4cGeKaFtUgjtaCFd0ptLtEX84hFxXEdIDlVmjKkNpShZEn9uHvuI6jx5f52z/dje1Ifu9fx/l3iQf4Tm+EyewKdmwSHB8ziKYsfCSHJ01OzSvGFk2uWKf4/m4DhWR6AbxAICVMlW1CIQmRaNNAmhIJaCHQopVSp9WLvyfQWiEU1JoC05KtnEel8AONkAbSUJQaFhKHFUmXmoqx+5CmqKJEgybP6S62dhm8sC+DjteZnPIZPlFhw/YcRqGL2Cc/TC7lIKaOolQDJ381wo5iYpBvBMhIBNOWrcqHWqERiEiE7Mc/wfng+iFPjS3jK017/Kcvsf1G4LruT927490IIS4N0QshCoB/huSjwHtpCeweBT5KS3l/H/DNM7vcf+b1U2c+f0RrrYUQ9wN/K4T4z7TEeKuBt8S98q4l+ovtuv9p4D7xKM0XnkeHiuUvfx7vc7/P2NgYmzZtIpVKUSqVmJutkchqICAijZctLLTWqFodGY8hhEBO7YbGKEpI6r0rCXfchfOcj7U0ie5cT7Uty+A1ktTxv2ai93Yi7ZtJW5JjCwI/1PR29PBk8Wc4OL0Iqkhm7hDXpKdw0vfgWWl6lp4jUTrKVbLMbHo7N6wfODuWV3o26vU6+/fvp6uri/7+/rfUqjFX3sQ98hGItvHtySmEa9E0kjQtRTRu0RecJr7xTqKm4MjJUQ5MzCDRXL2uh1guTUcsx3C9i2oYI9brwK/9DmNzHvVFD+U2GVkK6ClISKRYJk7Zh1Jo0Qgh4ggWGgabGyNYuShE4jiA1BpTFjEIETJESA+tXr0bnYhEif7i5zi953n6dt5IQwdAyw2MDgEJQpCKmaztSXF8qsLO1bnzxyClC9aZFMBkFG/HDQR+yLZwlr1LfTgxk6tWNImKUfzaXqonXZyVXbh/+YeEf/xdnksPUhmusPtbxxChorFY5fDXTzBwUy9fX8ziTksOzhvcdqXPjdtDerIuX302y2zFojxs8uEriggrT9MX7JuMY5mKJhZNYSAdAxBIQyIM2fJVGuKsz0MYAAKURiBbVrFSBD6YBmgtMaTGMQWhJ0lHIe14TPntbExWuPoqh91jmoaw2FaooY08G/p9jozmiFkmA9N7sQ7NYYQ+IttJnArugz8iqLrk74bEmusQQZ3JP7kfvwnZ916P3eXTrBaZX3UTRrKNNuvlKXUAqIAgVASqVeve9TWXstHwZYv+bUcX8JUzcXoJfE1r/W0hxGHgq0KIfw/sBb58ZvsvA38lhBimZcl/HEBrfUgI8TXgMK2l7a+9FYp7eBcT/aXETMnlvz1wjDDU/Pr719Df9vKH0OzphzPkXUpmcBcXX2b5GgxA14EAACAASURBVIaBk0xQP3OPtQpJMA0iSkiB4d/93yg9/mMy77mOVf/xf6fq1vAaDqmogW8AVpTGdZ/EJMH9L8yxZ+unyFQX+Gz6WfqKT2KvuBKA9w+laS5Pkoyb7HbNVjc4rUgaLqb2uC18ksqKe/n7HxaoeXk22lN8ZH0Cks7Zc3npAmpubo4TJ06wceNGMpmXl/V9S5DuR239NKI0ytDUDznNKqK6zioroFbxOCmHsGbmkYZFrVJHoFEa4v4Sg7kOxqpJTiyFeKFHX9xlpT3NQOcghw8fRuqQ3s4FaI+hm5pmRGMES8RMG8cAE8H6vCSvclTdldiDaxGADUhshHDxVBSlrNew51sQto1KZdANl9pXvoBamCfziZuxM4ow0ksQ34QUgtu3dnDblnY0cHSyTLPhsXXpG0TcGbxNHycstDM8F3BsVrGuwyAwh9BAxJAMRAOsY0cp+j5q61qkahLtnmI2toJDXobSz69ifKxMttOjc00b5dFFTNNg/dY4buARGBaWGTBbFPzjU1GUr7j5SsmWIZ9njgoayuDbR3N0RBucJo4bgnRstDAQUiAcA6EFWgJSIo1WQyApW1a8EGcCkrrlFSJULfbXAUFgYMqQWgM8KUjZAhXCpJ8mJ10W/ChTh8dZIQUbB6KsX5qg9K1T9JUVn+pbSc9nPkHy6W9Qf+wFvKVFGv03ot93PaHrISwTd3gRY6hGaTGkUW7gZJPEegx0UlGJrkYuzxLE22i+oi2tKI5iTjxLNpJmc+EaFpqCoXyUY4sX/+d+IbzZPPp3M0QrMHVJvktrvR+44jzvj3Ae1bzWugF87ALH+kPgDy/2GF+Jy0R/EfCjw/MUqx4a+MGz+/jFnQFh7mqQrfQzZ8Nmov/2/+LUC7tpv/l2Vvf3v2x/KVsW3IsQeh5TDwOSwF1J6fEnMZIJSo8/yczMEg+XdxIoxZZInfXCarVZESYIk4MTy9iOzbLfxkRsO2Ykx4vyvujp7xIvHkNLi+0bPk3c6UargGLZ4AEVoy8dpb1cpCaT2BGfE3I9tye7zxlrGIYcO3aMarXKVVdddcmbYOh4O+uTDXrM56mm1vGN2XaU4eD5DdbHahDAtv400ZESSVuRyAxxYqqCKyUSQUS75GqniHnTtGfz3DHyKI7voU4FvPCvPkNbIU++vJtFZ4BMs0zPg48SUXF6730fC13XMB4JkfMVsk89SjpXIP2ea6mHCQLRuo8xrV9X3qoQgnD0JGpmGpGMI0sn0PmtGI0JgtjalhL/zHYjM1UefGEWGmVcfG5OlDCOfJMnvV/h8aMhAs3xGZf3bUshJHihJGJDw7SY+p3/hciGtaz9k/8EopORomTsxALf+tIeCDw2vaeHu9csIG+f4k8ezfL5h1P81odcrt0UcmLKZs1KeGyfZKlh8t09FlsHG9iOoFYXVD1JYDgIy0BLibYk0jTQQoAhEVJgmBLTECDANA1aWWgtbUOoWiQf+IAhCZoBGAYiDFEKDAmdWU2xJHDCEMcGYZoENY+vnspjSc3JiQibb/cZO1Dl4JTNhg/1EzGruDfeQ333f8ENCvh79mHcexvqjl+h+vhjkNnBvqkemr4iduudbIkt46xcgXZnic0s0MhuQAqwX3EjjcXjaCuCcIsMdNbob+u65J7Dyxb9+XGpXPf/EnGZ6N8gzie6WdeT4vHDc6ADNqdOIcsltDBQ+evQWjM+Ps5kvcHmj3z8vCUypZRUFhbpOlOsIq4Xz0ovjXiE5M7tzF9zA+qKbYz4Bk0lkBiMeXm2kUCgMc7cyutW53nkyDyd2QjOyu3UZpcIlGay0iRbrZIVEpSP4S2zvmuQanWZ4Xo7jiEZrwdsGfkz+oOtjMteblzbec5Yfd9ncXGRgYEBtm/fftFc9W9IzGTF8Dd/CstdJnbkfoQfA69OEo+2MCRNHdfaRce6q+h0NPc/cxTfD2hPRRhYOYQIanRm2zjcXI0mgbzvl4n93Rd5eOtHWDqpiY4vct9mi0HrAO7sAseXXew1g4zuH+aEF6OpFH1OnbZN7XiP/BBvzRCqqxMQIAKkUURqGxUmuZA470VyMLp6W8rvag0V7cIKq4R2+znx+lDp1jWKODS6dhA2y0x3X82c24rPK93KAY6YAhXWiButhZ994HHWfvFzWNkEE8tzjI5Ok+hdzfx4mcBXWOUy2T2nuOa6OH9/IkVgW4h6k7993GamahH6mrVBkx1rFE8ecXBDg+dG42QcH8Oy0FLStCxMSxIKAyyJEBLDlEhTYFsG0hBkEw7tWYfOTJS+thimFNQaAYfGywxPV6iLgMBXGJZB0AzQGiwDAg+ml6CQECR8iEVNko7PB7eW+drDFpWmSbYzjrXK4sH9BpWwyuGnLX5pV45kW4baNffiPvQdVn1qPXF7kvqGXspDv4EKFd5MDduy0Bs2kB+KgVGD6CBmOU7eC7Hsn6RshVoz74aI5Hq65p5GOkl0NHv2Xl7KFrLvJKL/whe+wBe+8AWgVRxrcHCQRx999G0e1WW8Eu9aon+riuacL19280CG//Vjm9ClQ/SGZ1LPhInv+xw8eBDbttm5c+cF82xfTN2LG63bofRaRGihRRQtO+j+oz9ksehiSomvNEnHpBkoBttiGMJ4Wez2pvXtXLU6ynBFMx9IRKaDJ8eXma56GMZN3CEeZX+9l2ef8dmW3sMt4UPkY7eyGF1Bh6jyfKOXdeYUH85MIvo2v2yci4uLHD58mHg8ztDQ0EW7rm8qPcmw0HaStOHz/vhRpsIMw34Hzy7lSEQs8sUSUhpUDJsw8LEMScOtcGVXnKbU7BmPMFU3yEZCetJxUr/zuyw/dhoraOD64CnQ2kSk24ndsxMRj7PsxJGBRqBpKk2qNIGxKo+MRHAAX2sso4QpmkijjhfGeK1HTGZzJD/3u+hGA5VIUps+hbAKGKoOykebaRCCVZ0JbtycpBHU2TqQYaL8MTwnhrVksKIrTrPhcfNgjN6YRfXxvyNvV/AnFyjSzkJ2BSWZ4aEfF5k8WqN3zWk+eGOOuQNxyjMNZnD4/77V4JZrQh54HkJp0teumKwIFuomDx8wiUUgk9Q0liHEYCkwMCIGoTTQ0iA0W3F4w2qRvGMbJOMW/W0xbtvWRW9blELKOece372zhyeOzPPn3x+hphRatSx/YYDnC2xT05aAelUjKz7aVPhJh2LV4GejLzCT6mHDriyWjBJxLIr5bmxhIgOFWK6Qu/YKrDUZlHkS4TWYVpKG1gQK2tIRqs2A9blIq8JhYNI4dozlr/0DIEh9+MNEN24EYKkRMlMPwCggV9xFIWaDbD3PSqlLTvQ/TWW8i4nPfvazfPazn8X3fW655RZ++7d/+20aydujuv+Xgnct0b8VeNFtfT7Cbk9HILWNcNkAFEu6n0PPPsvQ0NDZNpOvddyzEBFCc8PZlzHbxDJNAqUpRA2u2+xRC0wcaSEbZTj5FKS70L1bKP3Fl2iKJsFd9yGEJtCSctNHAEpYLPV/lMeeHMMxNU9NhuzqiHJj/XvUO+/h+7NZjoQbkX5IJJ/lRSrXWjMyMsLi4iKbN29mZGTkp7+YL8GbXpQJibfmQ/QsHae3WWHPiZBkpEKxHicZNYmYgvZIwHUdLuPlgI1dGY7P1ojFFUVPkrI1lVqVXn2QSDPNjcpn7+gSK80SGT+FthM0rDZSQzkcAwyZoD7vEkWwq90llumiFO7CTqcxAAONKXyUEPiqle3wes5MRKKISBT3gX+m+eyTmG0J8h+9EtmYRZWbeCvuQaZ62dCbQRnw3efKjMwK0mmPnZtT9KRs8pE4ptAc+9zvU+tvZ/tHdyL7Ynht2zhZDnHdgCf/6Rn8hsfYgTn+tXWMP7xR8//u72PfKZupw4Joxsd0DIRlUA9C1vcFvDAqUUKyUJUYtiRuN6kIG0wDZUqE3RLcmY6BYUlsU5CJSdZ2Oly3Ps+6gXai0VeXql2/vsCTRxfYO7zUUt8LgVIQsTV+U7NQ0mzoCpmvtLwgQdnloe818djENalZIvtHmDoW5+aaYmbLbawedCgceBAVTWG29yNSGbyDR1BRC6snj0qnkEIykIsRMcSZamgakIQLi6A1Gk24+JPA+0srpknTOkvycOmJvlarXZLmOW8Ev/mbv8ktt9zC3Xff/baN4bLr/sK4TPRvAK9ZNEcYhOmtjI6OMjs7zBVXXPG6Vt6vlaNvSsH2fJRGqEhai5jmDBEDlK6hHv8uzI+ANAjKH6X64P10fGyIcOEZFrJb0BWXXb1d7J2pko+YdKds2hI2S1WPdDzCKXsVVbuN9fE+tHu6pStwIoTxVjqd53kcOHCARCLBjh078DzvosckWxP7G5ssX/QC6GgbQU8bzr4vs8bIcsLroyPuka9PkrQV9dR2SoUdbF0JTxwco3jqMLYdYe3qfkquxxp7BuEkOUYv9sYItz3+f1MLBH915NNEMklu6q5SqO7FS62gjSWGVrbqYlS9FM/U+rCkwNx7mOz3H6Tj5z+J6unAlWcU4/CG1NjBqZOIaAzD8KG+iFYeQdcgYuYJnq1+gMeHi6ACdNklHkuxWGoimgGZlI0UAh34VPcfoX1TAbGij9CwaRw8AbmVmIbANgRSecTcOj/69iLr7hokHw8JQ4VC4wWC0FcUGyZPHZOYTiu/XSsQUhMgqZpxDNtACYmwJNIyEQZEHZOOXJTr1he4dm2euBVSLBY5fvw4zWaTVCp1tkb/+TQdQ+0xXji5BLQWlhpNowGZmEYHgkbNJ5lz2FJoMJgLeOjHCfJWwF65gvc6B/DGpmnvzrNmcALZvorgB0cIK1XCa+/Bdus0nzyAsaaf7sw+2vqiuBPg1+KEhTYiL+lKF926DX9qGrQmun372fdzjnFWfZ9+ReD+Qov/twqu675jXPcAf/EXf8HY2Bif//zn3+6hXMYF8K4l+rej3v2LpBiPx9m5c+frJC6NlAGvVRDJlIKENEC0mqpoAWi7JXoSrZQlEY/i9fVA3KZr7Pv0eQfZo26iEBvgfdl55Mi3oZjlvp0/y1QVpCnZN9+NBrzpErfV7ifBEMlkD6sKK8/bkOatKBz0ZlMhX3qPg8ImdhV/wPVZl281tnKg2Y/2DPrsZRJWiZO6jWq1jC0NgmadjSlwehLMVTp5fMEm5li0J2OYv/KbDI+VWfAswpkaJ5OC67uB6gGq8gpKoUCHimdOlyl5iig+Kwpx2m4oUHroYdp+4T60AoQGo4kplwn8PK/nUYu8727cB76O7upHJToIMjmUnWAx5bD3YI0g1GgtyadNPLfCxv4siVPP0147jD+0Hfefv4tuNGHNKp6divP8KZ8D94/iVY5xx72b+L1f7eaxLz1NfH2efzh0JXytyWffV+FH0RhNw+DkjE9nQdOY05iWpNiQOEaIJywMG7RhtPLeTKMVgzckjmOQSTlcOZTltiu66Gv7ycI2kUjQ19eHUopyuUyxWGRychKl1IU78unWpUNrLBN8ryVsrJQgbTY4vhBlU9cyK8wip60u3rtLcyixk28fLpLwOvhU5wDxnl4mxy1kkKLxwB5W/danqNRMItEUaIu4V2Lh/seonSqR3HUl+dt3tKz4TBcykSDzsXMF0kIIMs75yfztcN2/Uyz63bt380d/9Ef86Ec/uqTX4JW4lKr7f4l41xL9W4FXI/qlpSWOHDly3i5trwZpnEbIZTZttmjVBnv1h0U3JWrhJIIQN9dN84ZPYFQWiS7O80ilgyeu/lWS1RK/vmIPKrsNNd8iZTn1JADCXSBSP82K7CqK4y8ggi60GUGEPk/7Q2SEy9ZkkfHxcaamps7xSrwV9QkuxjHD7l0cHA+4Rp4grC1iqBjKjGAog0CZdFKmr9fj4LyiP6+YdyU5J+TIUituvFjzKRizpDKajnqaY4dnMGyTDsfDK7nYqRSLsh8vCGkEGs8PsSpVgrhF+8JR7JggtrYPSSvlTgmPqLGEEAGGUSYMzy1w8rLFaNDEWjmE9Vu/j6qUKX3rH4ncWUBGbQJhk044FGseBnDNlgEKSZv9h07y3WFFwU1y7/J3SfziJ6jc+QmOJ3sYnnRZmq4xNeWRDkr8+Cs/ZFv8aX7tuhx/NpcEI4IvbUYmBEJo4lHNnrEIHXmNL00ansYUioawENLANw2EYyIMgbQMLNsgGjXpbYvx4Wv6uGLluXX5X4SUkkwmQyaTYcWKFQRBwPLy8tmOfIZhMDYt0GFLcKiURpxJvwsC2NLdZGqkiVdrIpqC0aemudkYp+s6SK7J8mePWSQ6c1R0kvGwh6FIAXHFtTSefpr01i7M9gJTV99NMpdmId/P6RGwGwkKkTp2uIA+9D2KudU0dYR0OkvUONdICJVmse4TtSRJ5+XT5qUm+iAILnmmy4Xw+c9/nqWlJW6++WYAduzYwZe+9KVLPxBx2XX/arhM9G8A57NmtdacPHmSpaUlrrzySiKRyBs4okbIZdCSaAzAA159f1kdheU5tDDw8wFIgzDdTpheyQvfOYllW1TDNsZ6fp6BXJxw9hCjpQZGbBuD7vc47ed57KjNoLWHG7yHuc7soFLYxZ56gZNsQirF/JJHd1g5b0Oad5JF/0qEwoLQ4/bkKfY12qnFB5hfqNAXrbMY3YSXvIKtXT7PHZthft8JnEicVUPtVBqKbDjPUHOMsmqjPdbDrXvvx444NJNrObmqnxUigu2O4RtpomaM3ulxpqeLDKhZ8ncMMivX4zjt2LPz2O1tSBRCg6sSCB05J7f+pecr5w5iH/g7dCRJY9d9NE+NUD1xgmBpityvfgAp2hnIW7Ql83QuniJn5UEpjk5qODXFeDJH8RO/QCFv0tAxyuMutdkqdsLCciS4ASuHTP7Mv4niE/DRnWVOJm1O1QyemGkjEw+ZWLJIxKEeSIKQVqqcaLnmlZQIy0DaEsNskXwyZnLj5g5+7saBN+w9M02TfD5PPp8HoOY2+IcDh1BKowKFUBp0K0Yfj8NiGYZ6NVsLPseOK/YUezkgurjv0ElUGLLWVIwZa+jsSNGdBF0sUrj1auLXx7FzCQI1SnPVWqorhzgxWSUakyxd+x425EokuxN4i/M0SSODBrUQoucx3I/P15lYbmIYgl19KeL2TzYKw/BttWbfTvz5n//52z2Ey3gduEz0bwCvtOgbjQYHDhwgk8mwY8eON/GwC1SYQxpLVCqabNo5ZwsdBCw88DA6VLTd/T6WjS7Gg/V0mMukQ00TkEgMDK5Znefhg7PkEpKGbXC66TEvYoxMloEe/L5P88CBEjU/4LTvMJRO0SZL5MwK+4M4WikaCtL5djau7T9nLPDOtejPHAhv1d2k5/ZzfX2RL892EI1lONxMs6JaJG4JJo02SpUKDgLfLbE+PUCY9Qm8CM9XtmILi2QmQ+49NzB+aISn6htQBwW3rjHYLp4kYnRj2a1egfb+PRS7uvnO/CrSKYfU1DjZ732L1MAq8h+9B1e3qqZrJDEU8gLeGnPyWdAKb+0uFgOfv6n007zhl9k1v5f3yzIpYZGJ5VoZAssn8Sbq+LkeVh19hr1BjPzCHIdmDRbGTPK2x9f/+Dk8T7FpfYI/umOG8e8cwLzuRr58f0DE1jx9xGawS+IGmsWqQbFpYlrgKYnXFCgp0LSsdwwDI2IiDIk0W676oZ4kv3L7Krrz0YsSIlusKmZLPmHQsui1UhgoarUQKwzxqx71vObwbIRUqoHlWoROmnJzgszuY6wVJhv654mtWk94qtV8xlixgUgC9PI8c5EkfjTFvKewTEndVxT620kN5BGqJaKU1ThBokDqlbfId0Fr6r5q9R9QGi9UZ7tFApe0c907pdrnOxGXVfcXxruW6N/qGP38/DzHjx9n3bp1Zy2TNwOteglVF0ePPMe2q0KkENgIJCUQDjNf+y4T//1P0Rr8coXHrriJur8BwxfcJQoUaKmehRBcv6aNq1ZmGXMrlD0L34fAjp+dHJpGgmTUpdx0sawoR9vex7JMkifCTaU/JR12k4vAxlU/f8HxvqOJHtCJLpQKMI9/k3azypwrSBs+MkzgSZMuy+eGjgpHliw645qSG1LICp6eS9EMwW8I1jg14jfcgOrbjD4+B0FAzYtiDXSSC+os+kME1w2S3LiekZk6mCazyw0yGZuOO1ex/MARWq2mDTQKKRpY1gI6yKDUubHVoPsq7KWTYDnsno7QDBogJft6dnBLdYJqZICkJYmGC3R0NWh888/wwxg7uq9kx72r+avDKb75TBnLkmQdExk2STeKTI9Kgvwcu4d2kD9cJJnIMLWgKVlJhqIBxYp5ZmqUVP2W+lybEsMQBIaBtk2kKRFnrPhM0mJ1QfJzt6+mK3vxir4+eWwBpRQqVBAodKCJR0BLwcqky5EFje03qGmLD/j7eDoySM/mNrL5Pp56RLB2azsDa/Ko0EEf3ouMJxErNuM9sweikjBqIjIbAMGqriRSadodgdANkD5a58nYBjJqYr60cFV9CXPsCdCKdZ1XMWykSdoGmcjb67q/lA10/uVAX3bdvwretUT/VsAwDIIg4NixY1QqFXbs2IHjnGuFnw/B3AzCMDHybec7MvmeLuo6bGm4mMXWw4BAmi5KSrw7389M/wq8ULdS5bSmEijaX1JYJVxaZPnz/w3r7jsQfZsRQpIJKhQKGQzls1qdZGBzN8dKaQoJh92LdRxDMF1p0B6myDsBq+2lV51E3ooJ5mIvHlQki7Ci3B07xElrLT8qdzI+X2cwDWPRNsju5KrOEg8fXqax7yRtuQyZQgIZKmLhMr2VUxiqwJCKMD1zHNpybIktENYDpBOnYuUwwgo6kyThCupeSMYJWeEPY6ommdtvRAARrQmlj20ugRYIWQHfwTr2TczKHFFzI1rWCXv6cfO/D9KgO6xzUAqCELpyUaYePEp44xqstCaQGVSoaHgW1kd/m86OCCdLmqq7SH2+xvTBOQbW5LjxSoujT/n8zC0p/mrvIHNFgRY2v/F+xX//riCXDjkxaxFNSPwAGqEkUIAUKMNAGa0UO2FLTMvEtCSxmMnVa3NsbW9cVJKfWnJ57vgibiNEKwVaYxsK39e0JTRRGfKRDUssjtURvmYmlueTNwUEGZfPP5LGjW7kwFyaX/ngamrPj7B8IEAbVfq3NmDvcayOLLkuQTJWoC3SQdyULQGr1KBiNE8OU/76NwBI/czPYJ6pDxFqDW4JU7XCY0lvka1d52+7fCld90qpyyR/GW8Yl4n+DSAIAsbHx+nt7eXKK6983Q9c/cePU/qv/ycIQf4P/gPOlnPKJCPPuP5art7GmXc17XfdyLzO4F55FW48zlqlmas0aU/ZdEVNmD6MOPYoum875cf2o6YOMjBTJ8dxjMJq9ruCa3qSGAf+FLwyjhHhii2fhcoMM/VxTotubGnzgHwvYdDkkBPjXnnpUoXgLfAS2AmaGz6OOfYI9sIsoZfGiGWZdOv0ugsoO0UR8Jp1HKmpLGtu39zN/PIiMvQY8Vbi6ARmZ4JdM3/DyLDiK/a9JLJRPrKuSab2DIvJTVja49q+HOVGQNS0mXY34eoo5myRtr/9B/K33YxVyOKHMTwiGFoSnT+MMf0CWof0ZyMcmF1L0dVc1W8TI8/WfB29KUEtsMk4mkKhm4pTpu61ERt/kqXjJ5gcidCWjDE8phGGxYbVbez71jGEHzC+f5o7ho5x7cYqJ6ck0UiaUEPNFfzx9yTxmOLUrAUSXF/gehIpNdr4idBOWxbCEBimiWFJ2jIOH7m2n51DCUZHRy/abdJa88zxBRZLdfxmSOiF4CkMQxMxNWHZZ9YSWPEY+W7JqdMWM2KAtskpBnIRtJVCJttQjoUb7aLRETK3/H1s06cSSoTZR259F9JMMJhYINi3D3/NGux04qzjPZiZhTOak2B2FmdoCF9pRio+vm6nL9pLXpVQ2cELnseldN03Go3XrEvwPyrEZdX9BfGuJfqLveqdmZlhcnKSzs5OVq5c+Yb2bT7zBNoPQCuae589L9GXpmfpaG/HEBKLdtCLKBGDaA/t9/RQWm6i0RTikvf0T4AIUSqNeuoroBVi4RRW+07CuIOQkGmOI5pxoKeVCO1XQZiUm3B6apme8QfY5M6wJRpnvvfDnJyRSMOiEl7alpvwxolea83o6CgLCwvkcjlyudy5ecVWHOnX6HXq9DWLzKgYWUo03Ax5o0QkkeHKbJGJWoTOXIylikc6HeG58Ry1wCAZSvrzBvYv/zonnhnFsCxKpSbjy5or8i7xhe/RyGynEmkj7pg8PV5nvipw6vOsSAf4aoG5v/57ev7Nr9FQGSSaQCh0Jg2mBb7moB7kkcMeSsOpJfjQpgUyZoRV6RozXhJDeRgN6Go8Re2pYeaPupSbDdTv/c9847BPvRHiLiyxMhqyaWWUfYeKWI7DiUgfP5iVlGuCRELyyS2z/PWBDrLJkPFFi0RKgoBlVxIxAuraRhuS0HjRVS8wbBPbMejKR/n0rSvYPJChVqtd1Ofq2FSFHx2eP2PNawwEwtCkY5LA9Wi6Hjk7oBaapHyfoNbAEprw0DDhVIO7ajFmtr6fvh1DxJaXiPR14fzse3l+RvPIg1OsKGzh9oxJI9NOdd8x5I+eR3z/h/T9xmeQqVYIJbJ5M/74eOvvTZsAaIQaP1SYpsVi2zbSqVdXuF9K132tVnvHVMV7J0GgkZdd9xfEu5boLxZebODSbDYZGhrC9/03fIz4B36GxvNPg2kSvfl9591GK4WjwLZNIINvXHP2szZHEyZtfK3pjjWAELRAihpBqh0ay0jf5+jaG3jYXcWQV+Te9jKi5z3o2aNM1UKcnntILz7Llxe2sDw3R4Yt/FJbnbJdoBCFa9nNRJDmOrsGDL6pa/Vm8UaIPggCDhw4gOM4rF69muXlZUZHR6nVajSbTWZmZsjlcti2TdBzPdbpR3l/ZpSvVtuYD9Lo5QAZy1BpRIh2X8VgeYKnpoClcXasy6OFQUSGCL9GvnISOzZAX2WSI2E/QbsKVgAAIABJREFUsahJT6qJxkJmc8xF1hGGimagaQQKu1rDT0SJhlMU1kapSQOaFSKzB/DyA5jJODIladzyC6hQMXcgRNda51X3YLYZx2iMEfpxYklQDWgYWezTR6juniASa6P7M7fyuJ9Ca5daqcEz3zjCC0KzsbvG1rU2fhjixhKUXI+oHVKqSb59qoBhaEbnLHwl8IF6aKKBpmGjDQNpnvlnSQzbxIkYZFI2P3/TIFsGf1LT/WIRfa0R8P29M8wttKx55YcQBkRlqzf91UOKxKkJJsoWPSmfO+QRxjf3kekKSY0aGNU67bEIa8Qe1OQCYaMX0w6xru1m5CvTFApxRpeTTCVWcWquTnkhT4c7TK6ySGHPt5GFAsaa6zFSKTIf//jLxhY1BDFT0gg1bZHXttSVUmc7Ub7VuNy57jLeDC4T/augVquxf/9+uru7Wb9+PfPz8zQajfNuq7XGCxSOde7EYK/dQOff3A9c2NPwamlrQgg6Yy9a2iYqiCJ1iWbYS/3m/wkdNIn4gocfKaGcKEeDCMPpzfRYFkUzxeTpZYTIsDl/F8UTp7FNQd0s8Fj+k/jSIlkJud48ySbDJhk4l1y7+nqJvlqtsn//fgYHB+ns7MT3feLxON3d3S038DPP0Gg0OHjw4NmiLD2xlWRKe7G8ZULZjtQK7dexRAM/1kmtPAdhBh02Mf0c6/JRyqVJ4tSZ1XkM7dDekWbtI19ltG89DyWvZPuKblYnG8jGFFpGcawca/JRJhouXYsvkO2OMZO/hmTOhEMPES/uJbbQSWPzrRxaLJCMaTrjmiv761RElFIjYFNfAqUFzUDSEe5jPojg15oc+dUvEl0eJ3vDFhbu/TkOBxEcw6crH6UyXSYSuCSjitJMwK8VHuU/1G7j+ISBaVqsyblMVgWGZUADIlFBZ0IxsuDQnvCYqzsYhsY3ZCsubwjkmZh8MmHzr25awfahn+T/X0yif+zgHPtPLeEHqpVSFygM1crdTzVd9h8L2NmbYltsln0zOfZ1r+H2GxwOTsX4Z7+LVAI++V4H7RmomSms6iHkjl3EyyPkrIAT81Ha+wosKQfHkYieXvrXtNPrLNAozjOhYtROHMewIuTPFO55kaxNKViZsl/3+YZh+Lq1Oj8t3kkNbd5puKy6vzAuE/0FMDk5ydjYGJs2bSKVSgE/aWrzSiil+fyDxzkyUeaqoRS/eMUSmBlUct3Z9rOvNWFc6NjnQAvE8FPooE6Y99FtW8GOENoOAwWP4ZkqtgVLvkO5KAjjKTTgByEjo2NcvzLH6HLIlv40M77CEIJFD74c3k3dC7m6I801rzmIi4vXQ/Szs7MMDw+zefNmUqnUOddKCIFhGAwODjI4OEgQBJRKJYpTpzEqVW6Qe3jWvJrxhs3cUp1VOYWZ7CCbjbMmKOFqh1BJ8jFBqZnj6HIaTxmsdCTBmg1EDIN9lSx2I8JDR2Bo9Qid3jDVxCqEBe3ZdroTnTx5+moOBor+us/iwhzqBz+md0cEpQRfO5LldNFFSsFtG2PEjCwf2Fgia9UZqeXwPIUv2vDFFH21H1BV/cxpRdi1kuGf+zfsW2j1cbe8Mse+d5LlUoMr14W4ZYMPOkdRA71UngTLFjSbmjE3TsPXlIuasmtiRiRF10QLmHWdVjOaM9Y8psSItEg+n4nwiRv6uXrty4WjF4PotdbsHi7y4O4pissNQk+D1hhSEzHBCDVLNUUhoZgomhwvd9CrSjwTrONqUWbPXJRYT5alumSsbZC2yWHmnzqEnUky2LuMnD7GPSuTvJDfSm5oBUjwpcbICFZs7cdspGjMFYh5GruwAhmGLC8tMDo6ihDibJnedDr9ut3xl9J1/05qaPPOwrtfdS+E2AHcAHQDLnAQ+L7Weum19n3XEv2bnZCCIODIkSNordm5c+fLXHLnNJ85g6Wqx7GpCrYpeG54kfv69hGxBNqMoWMDr+t7L3Tsc6FBBSAkduU0zbatgMTC5md39jJRdFFWSDFoNVTJxS0WK01sr8atyaNEbRO1/k60V+PoiT1MyG5SkTSnRQIrEnKkZLyjiF5rzfDwMOVymauuuup1VwQzTZO2tjbI34yxUCA+9gjR6iKh7qXWDJiu26ScMuXIBtb0T/G9E01OD89wupyhvT2GYYJsBoTNEjF3gcSuq3G+sxcXTT5jIts6cEQZvbDAlLwK5cNyxaMRavBdSqZgqNfCXjvIYtBB7KrrmX0iAFpV1k6XJKvbLabqBRJiH2k1S91pR4cW3skZFg7tw9+wls3//GW0UeLR0xJw0WjmJyqUF5aI2Ypm0eVj44+wr3cDP9w7SMQIcAyNE40wVzdwTEXM8OlLKRbqEhSYyqeKg2EJtCFbKXW2gWlKEjGTW7Z0cO36wnnvxU9L9MWaz8MvTFMqNwg8hWqGEIRETCjEFTevhtozo4yGOXKRgK5ggZlmhN7pPfjfHmetbucH8mpSQz0UOtP4lU6sdBq/XKV2agH79Cx2bIm16QVcZxVR28SKmUSqIaYBxLM4+RRNHcOwIuQs6MimgVYL5mKxyMjUPEtHT5GLSAr5HNlslkQiccFzv9Qx+ssW/f9YEEJ8GvgccArYDRyjVVnteuB3hRAHgX+rtT59oWO8a4n+zaBSqXDgwAH6+/vp6ek558G+UAncbMKmJxdlasllQ8HDMRRgtERwrweiTm9fiGGWgeSrbhpoeMa6i4rnsSkXo0NkfjJOA9pP7qd6ZDfVOz5CICMEs+Osz6RZlxxDzp+COsj5TghDNtWfY5MwcJ3NnAwLFD3YJUcg7Abj0pXYvBDRe57H/v37SafTbN++/c2RjBAgLaRhsTruMlKVeNIiInzwargBFJeHCfwChmji1x3W53OcmF3GCuaIeSHNRIH5QHPb4YeYXbedMjn2Txhs67ZpJjvAKyGsxP/P3psH23VdZ36/vc9wz52HNw94GB5mAgRFkCApDqJE0dRgkbJkS23Lg9yy1e2kHKVciaMknTiVim25K67Y7U6qlbS6JcuW3ZZtWZLllinLJEWTNElwhDBPD28e73zvGffe+eOCIEWCBEACsBriV/UKhXfvPm/fc+45315rr/V9ZD0Hz0TY0RrbKgEF3eH7wzcSnGpxc0dx26YUj56IyKctNvbbGCNQRrAst1Fa+0esgc2YIGD5G/tZ+94pRv/nDvunG6y1AjakO6wf6OfZvz9Ba66JQ0ySCN61uc6GW9fzp0+NkEr1zs+2SpOH5lNEkcY3oLIO1UiijUBICHExtoUSNuLs3rzlWjiuZOu6Ah/YO4KUrz3Xb5Xop1c7/NFDUxycquF3EtAGtMEVBhUrkmqbv3vS8NPbbK479By5bJHxzS2apX7yi7OIRpsdhOzclie5cxLZWMMtZQiKeSp334o7XEZnu9iDWYa2lmime+c4VqC0DSpH0qhhr7bpHy8gHX7A4tlxHNLFCu22g+MN4HgCR/pMT0/TbrfJZrOUy2UqlcoPVL5fTVObt4vxzg/BNV11nwVuN8b453tRCHEDsAX40ST6i937NcYwMzPD3Nwc119//esaRrwe0VtS8D98eCe1dkTFizAN0G4Jk9lwUfO0rClKZY0lVzG6H/jB/b7aI49z5nd+j8zWScL/7tc5UBMYkyK0Xe7KG/Jn3bdUvcbq//nbDLx/jP4XponLFY5Hm9m69aOw3AJhccov8ZcvFil6Nh9zC1SdYdz8Dj7pfgWT9rCUjwpqcNa97mrgfNep2Wxy4MCBN/QOuOg91Pw4VqrAhmSaW8sj/EOtyGIbNoo62cFh/NQubpcHONbM0mw6HDwUMr6hj0PhAEFkUdYJbsFi5IEHOPD8LKfbZY5MW6Qdh23+o3T77iCOMgy2VxiZ2M7SwdMcqW7mdDBOPdGICQgOJezdM8AHCi6OpRnwQoKwRVSTmCy08jsYrT5G7I2xYvfT96EtLFy/h6On2wghaAY5bkmv8FcvLJESPumgza/uPM3Qhhy//ehOpusSpQU7+3yOrXmMV2Kmqw6JkVhpCDoGywJlBNqyweoV3mGJXgGeJRkopfnZd20gnTr/Y+GtEP1KI+Q7LyxzZqlFEiToWCESRTltyLoQdxIaTYvJUpe/PtVHNnSwqml+5n0VyrLDI/YW8vEUN49EuBkLdfRJVGkAp6/Ewn238mffazHhCz74ntvQxiGuLtF88Buk7roTWciCUqh6l8Yf/zk6DPF27CD/vvedm5/wa4jWIsYdAiRCgGXZjAyPMDIygjGGTqdDrVbj+PHjBEFAPp+nUqkQx/FVTd2/HdGfD9du6t4Y838DCCFuN8Y89srXzve78+GaJvqLQRzHHDx4EMdx2Ldv3xuuzN9oH92Sgv5CCkihBu6+pDmYs8p2Pap7xYPUhIBi9g8+j2p1qK/U0LPzCKeEoVc0JI1BPP0nsHgEMfnungFJPSA1liXtuqAyxErTzO2mNFnh0e+HJMJi2Ye/7/tJSDmIrsVo5UMcnK2yviC5M91/AWudy1uY9Wqin5+fZ2pqihtuuOENH2rn+/vnnZebQw28AxE+hOkug+wDI2hqSV9cp+v2Mzq2nXqzCZbDkWaGcmKRaI0wCo2Gzgr2lu24izE6iJFJjEx5OCMbGZ79B6pmPauZzbj1OQ6U7kYZQ6PewZy9nr7l0ghcLAlRIogSQd5VdMoZjNZ4SYMzX36OdmuGTb/5P9KKYprdOlIalBaYdsDTR+oYv0EiNZO5LhP5Gi/Ux1htWwz1gWdp7CCiGuXQgQatsRxBtS5IpcRZsZWelbqxBEYILEdi2QIvJbn3hiHG+l4/Wnyz17zRjfmTR6d47kSVZiNEK42OFZZSdCLDWL/h3g2rHDzawfcq+J0YKw4xSNbmW+xv5Znr5oj7Rph4d4UBbSHPHMSRBmfY5sk/OUkmneHQcZjYNk5dx8THNOtXasRf+DJ9v/qLCAHa99FRhPBSJNVXbGvqBGu2J0NcEdNsG7oLP4HRwssLbiEEuVzuBxz5Wq0W1WqVWq1Gp9M51+pZLBavWBX+D5tF7du4qvgD4MaL+N1r8CNN9C/ZsG7atImRkZELvv/i99EvDTrZRLV6HCmLpAsSQ4yHj6ueAzSjn7iD4989RfDLv4Td38d1CBzZZevAKnk1g5l+tpeePvq3PPtT/5LZWsI9pRzbNm8kPL7Mw1N1GpEi6xaZHIX5E2u4tiCb9egkCmMU/1AtItIFqpFhWztmuPD6Cx4p5RUheq01R44cIYqi19RHnG/MpcDInlTwDmeRudQWTtYVQQx+GGLbmpSq4ghBkAR4qTQbSnkS1abdqOKFLVR6iEPLNUZe+DtSm2+gVe6n1lD4nsbJDdMUW7C7dZ7qjnCy0SXr2YyULJpdhefabPPalN06tTiDrTWJTtFMSvSJM9jxGmb+BHNTHdI3XM/fT7c4vtwlZWv2DhhCK813/vgo8zMNhID3Dy3zbv0UB44W+ENRYbHa02D/sS1NHjxaZMtwxHTVRccG4wjCBBIkCImwJAgbcbbKXkiBZUsGS2nuveGN74E3c80Pzzb5m2fmOTZdx+9GqEghtCHngkgMJopZWgp5sOHwqfwJZD0mnXf5nlfBVSuse6HOgprAL96IzOfRuQEWv/Ft/OOLDH/wnQwsTjFZ1jx02iU7kGJOZchbhm6cohkoJjZUsFZPYRmJPTRE9vZ3Es8vkL31VgAaoWLJTyjJPkbiRYRtM5xze6uhN4CUkmKxSLFYpNVqsWnTJsIwpFarcfr0aaSU5wr7CoXCZYv4O50OxWLxshzrWoO8RqvuhRC3Ae8EBoQQv/aKlwrwGr+s8+KaJvrXS92/JLiytLT0GhvWN8KF/OjfPFLUa2lypTSYGANoElwSQDL44zezdt2PsZwvI6RFf9piR+U4GAuICYc2kAiX+ZU2zzCKPWDz1UXDJ3dnyW9Yx/G5mJRl0Q4V75qw2FIq4+XKWGsHOLJUJW0CAm8r89Umjg7JL0xB4Z7Xna0Q4rIWIEkpiaKI/fv3MzAwwI4dO97UIuKl632+sbqyFd04TWr1IMVoAdceoxv6lPwmJj/MEbWBe4efZv9qkTUxwMmlgNEBm2daJZZkmXIsGe2rMPDPfo72n3+Tk3KYqThDqCV3icfI5Ac4KSc4vGaItUYZmOhzqRQ8Cpk03SiNVZ9mq12jLscJ2IC20wSmH/X338YevZGBn9tBZt+N/N3hGlIogkRiWS7lZp3W6ioyCnE8iy1qlpSleMrdAUoy3AfvvynmqUM56qFDfd6QThnK2YT5poXtWiAkWoCwbbB650rYAmkJXEfynusHce0LWCRfAtEnSnN6ucM3n57j+EydWj1EJb1IXiYabRnu2SOZP5MwvybIyIT/FOym0qzx43uyfPwdDaJDs5hmizt0h/FNO8jtvY5y2mIlXUTYK/hHjtE+coIbCzlSd2wlvW07gdJ0ujH9129lcleJwvLz+AtHKYgsQuwmc/O+H5jnkq+whGStuI0Sfbj5/guS/Gu+W1rjui65XO6c70UURdRqNRYXFzl27BipVIpKpVfYl81m3/QiudvtMjZ2fineH3Vcw+11LpCjx9evLOJqAj95MQe4pon+fIiiiAMHDpDNZtm3b98lkdWVsGh9CZZloY2ml7o3aNJAGojR1nrWTxYJGiEaGMs4GJNF0CbRWZo3/xQqichoD++hVcJE4aUkS10XQ4qhQkCtY9ic7lI49hcUAbXpAUTjKDdFZ0AnTA6lmekco99JKCw3UNten+hfiugvF4IgYH5+nl27dr0lg6A3hJCQ+Oh0H4OdOsbaRBTHaGNwglWS9CBJboKluZA0NZ48ZXFfsYSRDrYISZTBSjpkR4bJ3bYPsSIgClFWjtbAdpbnavgyj6EM9AxiIgVBR2PLmFLOJVYeq5k9CL+LCLo4nsCywNu9GX8tw8p1uzg+3aaSSpgPBRlXYHV8/t1/PELQTMiXUny88n3WNRZ4ojPKM/Egyw2YHFekO1VmGyOsH0xo+ZLllk1bSWwbHEfTii0c52y5kuwp40nZs531XIvbtp3Pg+EHcbFE70eKfzy2xvcOLnNyroHfTVChAmPwLI3QGkslnNhf5wPpkzxf3kg1cFFNn5ztsN/bRP6GHKfy72Bg/5MMlQS7zWm6cgdU22RLGcJNE6S3jNN8fAanEzA21ESlbcYdSabPw3JayLhA195EPUoR4hBrg/OqIsOcK2mECtdJYRU2nGuHvRScb9Hrui5DQ0MMDfVqXXzfp1arnRN3yuVy5wr7LsXa+u09+h89GGMeAR4RQnzRGHPmzRzjR4roq9Uqhw8ffsMCrzfClTSTkFKS+CFexUIDaWETW+8EY0AIUsD1lVdU+jZzWMtPECYOevwe3HQOKST//F0bmFrpMFBJUTcCozWj+TTvnsgipw+AUTQSlyeOrFIu38RW2eZQZg/5zEYG0rMcbNlMjmzjjc7OSxH9W8VLRZBra2tMTk6+ZZK/UPGlGtyDe/zrbJVVDqX3MBsaljsCL+1jPJBhlWIqQzVIKJQ0AxmbjfmQ+ZUGOSOJIlhYbXBd/a+Jyu/kpB6i1fH598sb6BqPvkKaLWMOngVJoqj7Pd4oOAH90kemCphmC5PJUPCPIlMDqHZInB7C3rWFhw83UVohBfz4jhweiheemKPbbJDzNGVPsbtzFJlxeKyzlUJB4qXhJ3fX+Otn8kRKcGbFpr9kGC1ErIYplLGIEoMlNEq4IM5+j3s7GQh65jnF7IW7LC6UxTHGsNwI+frT8xyba7C82sXvxi9H8saQzwrWDUnOnIlZVh6nRZGP1x6mli7yt+E4oTaMdE7y53/ZTyfVT6rvPn7x7ixy6SSZY0+D6+Lc9R6WmymstCFTbmM5mtzE9XQ8F4whFhpHAE6OqG8DqtYlsrIo4NUCzyNpi0pK4kiB9Sbv74vJbqXTadLp9Dlxp3a7Ta1WO6e6WSwWz6X6Hef1ZajfJvrzQ4hrtxhPCPH/Av/GGPP987yWBT4OhMaYP369Y1zTRP8SMRtjOHnyJNVqlb17917SCvpywn/yMTrf/AvSd99L9r3v/4HXXtr/T8tX3eSv8/BJqsdIGlVcyyYXV0m8PCnSZIs2fa0V2l/7I7K3bSFwsgx4LpRvQw9cj1U/zn+uTnIiKSIbmul1H8JOOSw2Dd8J70BZimeqNp9O9Oumci+HCY1SikOHDgEwPj7+hg+3i8WF5mXSfRgnA9Imrq3hpcqosEVgcmSl5piznXv6H+ebixM0Inj+jM+6QYfALtFMJKWuZMzqEPdN0DfzPI/Z7+V0O0OIJJuFbhCTGciwfdCmG1mstROWam1W2gphF2lqwaBRuCJBzhzGOFlMYR2quI6l2svubQJwLMnUC2f4q79dIIw0AyXBT+eegYbiwWMDTGXKrKwIdm+Myc5Oc6q2h3QByjlDJ5bUOg4IyOU0ja7AkpDAOaKXluz9K2CkdHEmKW8U0fuR4tvPLXJousFyvctq1SfwE1Sk6bnbaxyjidqa4bKPKSgG3S4nGxWeNBvYI2p8YvgkYaNDcS7DM7WdyM2DJAKSQpbmyQrFiU2kxwR/850XmF5yyBeLfOKntoKwSWorJHEWu5DrFUDqFMiEXKZMI/SwggD3PFMXQuBZb10E6FIyg0II8vk8+XyeiYkJtNY0m02q1SozMzMYYyiVSucK+15ZIPx2H/3r4xpur/t/gP9VCLGbnkjOCr0++i309un/A/C6JA/XONFDLy184MABSqUSN91001X1jX4lTBxT+93/A4wmOnYI78absSovp0sty7poHf3l5WXmZxN2lSoE6QFcewhXvLx1s/qvfxPHqTM0OkNS6sMuDmHMrVRNEW/7LyHiRVhuA+DZkjgJEFr1HlhJFxN0EUdfgJ0PnHeh8Va3MLrdLi+++CJjY2OMj48zNTV1xbZEXgkjHZA2hE3eWVjia80+YpNCR12SsIt0sgQmRawNBVPnxLLNxFAeLSS2DiABaUWkghpP5G5jvuliJZDLSXIebB2GiXxAPSwjkSSRT5JExMpmrQODeQcvnKXsT2EympXjS5jBLI900jR8hWPDWFaxfqCEIwTHTzXwW036yza7hn3Gm7OYVIpD6Y14aVifg/v3Bnz3OxVKOU0rhi3rNM+etsl6mhiLIBEkyJcXbVbvXyEEQvTcEsNEXXRa/pXvMcbQ9GOePlHjxakaq62IWt1nrRGiIo1OFCbWOJZhqGQIWwnp2Gfu4Ap3ru/wdDRCNxKcDEs0tu/mZ+7L0P3qg6RqC9xXWuTU5O1s3DlKd22NtUeeJhgvsfGDFRZPBsjiIHO1mCdnbMJ2h+LRo5Tqz9P34feT7q+gu4b2Q9/DhCHuddchPO8HeuahJ1z0UvfKPyWklJRKJUqlEsA5Vce1tTVOnjyJbdsIIWg0GpfcRz8zM8PP//zPs7i4iJSST3/603zmM5+hWq3y8Y9/nKmpKTZs2MCf/dmfUS6Xr9RHfBtvAcaY54GPCSFywE3ACD1lvMPGmKMXc4xrmuhXV1c5dOgQ27dvv3J7vxcLKZG5HLpRR3hphOu96uULV/RrrTl+/Djtdpt49Ga+tLqLEi7v0EU2GINsLvVEemwbf65N0oqRZYNf3MOplQ6HV7tIIbhtSx+DhRTljMv21DKLU0+T1U1uKo9xcClkR6FBenWWJHoPpAqvmcdbiehXV1c5evQo11133bkH25Vq03sNnCwqP4EdHsBRHRwLiqZLrWnhlSSJ0kR2hmEv5mTbZftAipJl2JRuMxeG6NgmdCwOXfcvWH1mmkJO0vI1uZTFvdsNk/kmh7ubEMagtGKoM01LpvDJkXbAERqVSaFON4jtCie+vp+RD7jU3U3YFkSJYWe6RTZb4dT+kzz+1DKtLvQXYt6lD2DimCenskynKyysSCaHFev1Kl8M+lmIPIYrmmoTMk5CqGyUJdEaLAxYFsLwmoWbVnBwus6fPjbNndsHGKmksV6H+F46ty8V2h2ebTK10mF2tQvaMLfSJQoVKkpQscbC4AqNHWv8lmbvaMiBKYGo5FjXPMo2eZy/8HegbJu8rvP92RzRzT/B9lNPsSErGdkkwVRp1bu9uVarhAeq3Lp7PY/M2Gy5YYSayZFdWmFelyguTWO328iBCsHp00QnT4JjE0uBuHHvD3yWTqT4/mIHg+G6oSz519EO+KfAS6qO/f29QCAMQ1544QU+//nPs3//fn7913+dBx54gHvuuYdt27a94f1j2za/+7u/y4033kir1WLv3r3ce++9fPGLX+See+7hs5/9LJ/73Of43Oc+x+/8zu9crY94BXDtu9cZY9rAw29m7A/Pt/sKwLIsbrrppstuOPFm2oyEZdH/239AsP8JUrtuQL5KlOdCUXIQBLzw7QfxXjjE5H338vW1AFsK6t2YZqjQjeNYT/4hAIWf/yjfPhAis31sq2QZHaiwMNdGIFHGENWnuNt/BONtw4hR1idTJEaS84Z4z7DPyVXFbG4Lw875U4RvJqI3xnD69GlWV1dfc00u157/xUAoH+MUKCgfz7FZ9rMMOl1k3MHJDbCsN7I59Tyz4RZOr3YZsRsIz0W7eWqhxbH5mIgaIpdD1XykgY6fcGrJJuX2I+Muscwgo4iJyira3sWRZc1yI8ElYNkpkXPStI+s4u/YziPOBoSARMF4WZIeXI/SDoeONQiDgNEhm5vWNykvL2DsNHP2AF1js27IcPMuWJ0zaMtmpJgwkFUsdFK0ugLHAynOlnhYEqTEKPOaqBagGxqeP1XjwJkGg0WPbWN5xippimkH25IkWhNEimNnOiw2YhrPtJFCMLvWxbMFCysdokChYoVKDEJrZKLwHENfwRC2QipBA+Y7bKkUqLUsnhHruSe3yk/Ys9Q6Ctcb5zsPucj+dYQ7Psidfau4S2dIKqMULB/rPbfD6jzt4wcYSR3l3e+5GYaHqLdDovXrGTMnGbx9G2m3A0mEVS4jHAejFJQrL2fyggYiaFDXRZTurXvWuvEPFdG/GqlopOh7AAAgAElEQVRUin379vGVr3yFD3/4w/zGb/wGL774Iv/qX/0rPvOZz3DnnXe+7tiRkZFzrcP5fJ4dO3YwNzfH17/+dR5++GEAfuEXfoG77777v3Civ6ar7t8yfni/3ZcBlUqFJEku6zFfEs15M5KX9tAwuQ/+xOseV6kEIVcBg9F9cFa2Zm1tjSOHD+N9/svEjSbHj59h6LP/CwsRZFzJRH6ZlLWINgoMPLWieTG7DhFC3HAJWjnS6YRuFFFwHcZXHgQJ8zPHWBrazPjwfewPysR2nq4fMkcXqyv4eL3FUKX0mrleakT/krWs53nn3T65HHv+F3sc1bcLa/U/4UmHwbSh2dZ0jEcpaNNxKkyKkEikENqHEJKgSznvYgJDN4joxAItNP1Zh3J/imrDRwqF7eTpqt64ol/FaIu10g4C30KrBAE0fU0lJQnm23TnFcvv2kOMxBjYPuJx47AiRrDy4gmefX6JasuQcmP2JUdxRMSxFxNeLI4TG0GtKbhna5t/+MuIauyRNGz27UiYOgCWUXi2IBAGY8TZRamBXl0nxvQWXlqBZfUyRcv1gLG+DGdWOsxXfVxHEicGz7WwpaAdJKRtTStQpFyHRivCjxK6nRidJMSRAa3PpurBEgoRafI5hTAxtcDh3cwQDY7yj7Uiy4HLIxvu4IGNLQb+7pvMHQkx9mDPlz6ricd24NgncJIAdd1NWHYaPTNF88FFjLEYL5cga7M1Z6NJ44yuRx6ewcwfhCTAWf8OSh//OEYpfN9HCEkY+nizT2OZhH67zLy9A2OgP/PW5J4vZwfKhdDtdrn++uu5/fbb+ZVf+ZVLGjs1NcVzzz3HLbfcwtLS0rkFwMjICMvLy1dium/jhwTXNNFfCbyUYr9ooje619p1EcctFGOktUCvvS5Bq2FOnTpFq7HMLTeNcnJ9marcRPjLv0y+kmVrxmWyfAxbaoybJ7j1w8T5IexZF3G0Z3RupAPCkHFttm/I0J9ykUGF1UaDr6xeT9xo01/oY3Aoj4VmqR0hMOhuje7zDyH2vAvTt/U1c73Yh9srrWVHR0fP+56rSfQiamG8CkgLGTaRlouKO0CerCNZivK8IxdxvFZlplsiWJrBKrmcWPUIEokyvUg55dlMuiFx0eHJM4pjsz7lvEPGaGTKRqTSBFaZrO3jGoUJmxSyklinWRvdzVyjiW8slDHYGAbzNqFVQis4dbqLH8Zs3uAyUexSWlsgsdN0bMNiksFyDSP9hnLS4VQ8ABIKGcNAwWC0xhiD52o6gUBrQL4kJiJ7LI84t1jVWkMsidEsrHXJeDbGgOdIokQhMMRS0A1ifKNodhIgIgwSkqQXwaMURoHUGkcYMrYmLRMGXJ9kucN4n0tpMKbeHuTO6Wc52dyBKmTJ2lVy+yZZm9pF+eRx7rt3HZ3iGJNDDjNf/CqZ9esYvGcdf/2tJ1hq5Lnj9gF2f/o+DDYNUUEbSSAMGbsNRtMY2UwQO6TcDHljsM7uOeszZ2hbDp2OJiP6mGCVjIjYO96razlfluNicTVJHnqZvVfq7F8s2u02H/3oR/m93/u9c26c1xLENSyB+2oIIbLGmM6ljHmb6C8RFxLN8SPFt56ZQ0rBh9afJuMfRKfXo4be94aE34tyzdkfUCrh+eeeI5vNcNNug2CK6373p3jmUZukrwKWjZESKQrAGlq4xKNbAMnubZpspoAQAlvVSaIA13QpWgJSE+itH6M7P42qKywhSJQmbQKioMV7nYMc1Ovod6bYaK0gVg6+hugvNtW+tLTEyZMn2b17N/n865v1XM3Uvc4OIcIm6IjtIx4Hmxoh0qg4gCRGWFlSqkk9KTHitvm+Ws9SvUKoeqSc82yGKhl2DmbYWjJ8/ck6tu3QCjSNZsDO7ncQE+uZE3t7aggmYbJ5nBNuhbl2PyMktK1Bjq4bx0QJjm1z91CLvnSBBDBhi6dfXKLRhnY34peuWyFzKubkM22WBm8gowwdS7JrUmM36yx3hvBkgiUt8p4iOCvd61oGKUAKgxYaIazew9AojLAhBi00JGAsA1ioRBFFCse16HTDszLBPRvZWGmiuLeQULHqLSC07qXqlcaR4EiNlSTIMGEgF7G4Ytiqawx4eQ4uphmysnQ33MD9azM081kiG/7tlxaZ3HwPN2YcNva7iHKEX+vg9A9j5o9SO9Zi4TR4g5KnnzcMrx/H6daJZB2nWD6brDVoJ0e3nMX1A4JcPzleFpNWWhNikXFduoUNxCaDLI69JYI/9326is510FtYXGo2MY5jPvrRj/KJT3yCj3zkIwAMDQ2xsLDAyMgICwsLb6rd+IcN13DVPQBCiHcC/56eeM6EEGIP8C+MMf/VhcZe00R/JfreL0T0335unocPLgOGTGuFD212kf40KmmB8/rSlVJKVlcM4+ODBEGXE2faTOzahmNZGL2GQCJcyfb37uNIs+dLPppxUPEoYuEpRNBEjpfQqRIp6fCO9Vm633uI5l9/kYEPbMQdGEA0szQzP8/pWky5MMbtm7vM1X3u3NLP8OLfQPc0lgnZOVFkZbbGgXgdG/re8Ro/vQsRszGG48eP02q1uPnmmy/YOndVI/rEx7g5EBZ+c5mMM0AqbpOEBoHECht0As2oVedINELLKtCqG9TZSDiTssinDGk3JpEw3J/lVN3HGEPeiihuG6WqBtF4GC3pRgJL+EjbwpUJHe2CK1B2r+Q9rULGCh18y8UYm25osVAN2TBmoaOEEbVGENpETh/NdI7F5RQpFzYORJhmRMuk6SiXrBIU8j1f9xiDMAZLahItsJTBaLCEQUVgpzQKiYkN2ulF+lolSClIEggj3dvfP3stMaCSXuufTnrHTpRGaoN7djGRtxS21FRSPim/Q7tp887Nivpiln3tw6xFG8iamCfFVt7t1BjpnOFLyxVKGw3HF6E0eSt7mmuo/AD26gz+ydOUBxS55gJOcQsLNcnw9YM8P+Vj5hqMzx6m/8fuJj8ygDAeQijSqRSBUyQlf8AxAqM1JduQaEM5l0emL191+dUkemPMJd8nxhg+9alPsWPHDn7t115WT73//vv50pe+xGc/+1m+9KUv8cADD1zu6b6Ny4//C7gP+AaAMeYFIcRdFzPwmib6K4E3MraBXv8zgEBgp4pgVjFuGezzO+K98rhJopk6HbKwsMzWvdcjZK+8JJC7SJsptBggZWXYU3l5nPDr0KkihEt+5rtEm38BiYUQgtoXPo+2FaLVhEIOXdzM4zMNan7voX7voM8dyaPQnsAM3UDYnOfF9K3EYjPPmk1EKMqH2nxy+0EY3HmuYvuNUvdvxlr2ahK9cXKIxAcdMzJoE1UlK0mJPZkqTtzEiprUrQojqRrPJluJjUUYQ3/JwUvZZGSCYzSBlix0MpTzMRknJIxjDhxd45Z1KdpJXy+6UAbZWmPEXablFpkxOZq+odp1MFKTSULubDyFE0/Q1RqhOhw8sEQYC46fifmpO2LSC9PMz7QIViQzJY+xcoJxHNaN2CQHFaCxUaRsQTEDnmsIA+h2DPmcJmrbaNMjZUtIlDI9vXlHY7AxkUFZ6mxWX57bz09eOo9a99yWtUGp3kJCJz1rWSkFg3lNvZaQtiNklOCrBNUK2LFJsLhkUS44FANBJvYJSyV2D6xRuX0P4dcW2FiE46HH8LhFYTCHcLNk1qZhz15yt93D8h/8W+IZxW0TBrVrN/PKQS8uEdRi1GoNZ3kZZ2yQ8PgM/vPP4W3bTm7Xrp5l6Su+d1prKo6gXLj81stvtl7nreBSApjHHnuML3/5y+zevZsbbrgBgN/6rd/is5/9LB/72Mf4whe+wMTEBF/96lev1HSvEn40UvfGmJlXXf+LSmO8TfSXiAu1wf3YDSOkHIklBXftuIFY7wUnD+KNHwZaaxqNBul0mn379hGiCIxCApYskIg95x1nUv3o9DBBokmK15HG6kUzSYS7bSet/U8x861F1v3vv0w0MEh8KjxL2BZi9lFIVjiykrBSGcMZ/VmWfEXoa/xYk1JdfL+JPPIQRoIZuO7cOTgfoV6Mtez5cLmI/qL+VtLFSBchLIJYkZaKvlSd1cBmMOzQtgqMhwHfi/cQaJvYaFJAPpsCY7BNjBIplIbIWChbEsWKTOITZAosxv0kdh6ZgGm1cDIOwh2kZKdYbHsstzWx0tgSMkmX0XGbpDKGFimMgKlTVaQlGRly2Fis488pAqefwS2KuskwX7fJZQUD2QCr20XyUvRqqOQUli0wGDodw76NXR5tFxBSYgcdAiuNZdso1dvTtN0YjY1ODAaBQr2kwAz0lHIx9ArkhAZtsAxYQjBQ1KwsJwRaUbAThhyftZZm0zAkWZtteoE1PUhrVfDiur18JPweyd5NTLcK7F8ZYs/Nt/Hu8SHeMbwVN+Ux+9W/YXl4gnUfvptGM8ZWgvQ7bqT17PNUBlxEf5FBbVhLDSPDJkODO8hu34RRis7DDyFzOTpPPIG7aRPiVYIylypocylQSv2TaXNcDO64447Xvbe++93vXuXZXFkIc80T/czZ9L0RQrjAfwMcvpiBbxP9JeJCqXvXlty755UuYBdOE7ZaLV588UUcx2Hnzp0ApJGkjP2a6OTVCDQ8Et1FN9FslXlGIkXf01+EpaPk33srX9n6Pqomxfu7/WQaKSp5l2wUsD6fo7TsMrea4Zu1bSTtiL56g+HBDGnV4DbvJNUky032c0h0bw/7LM6Xup+bm2N6evqC1rLnw9WM6AGECsEY8q5ACZspv8CkvYSrXdykw1PJdT1hGQECybqyy6Y+G9VeZSlMkyjTK8yzLOwk5CavxdNNh4I0rPklBrJNVGRhtavYOUE7P0lWG9pVQRAZEOC5FpsXT+BtzFCLMtjJErUlxcyZOt2uQWQsdvV3EEIz+8hJtn1wkmBNk/M0xVxPrlWkM3hSE0WCji/ohoLtYwmPVy18bZHqNCh4WZq+JJYOWd0lSNJYtkOsIfJBygTbAW0AKRAGtO5dX8eGKAbHFqBBGsN4STG/ounWFYNewvpsh5OLFnHXZ9eQotGVOGmXXBRgrTRw0xb1wCOkSOtYg6c6Jey2jbn+DvbZc+SEJlpaJDIOcuEgpx/v8tBzAqswzoc/tInxuyaJ5DARLo4wDGYdcAewzjwHxx9BbbsLa3CQZGGh11L3qlbaWGlakWbgCq0jr2bqPo7jK2Z/+zb+i8C/BH4fGANmgQeB//piBv7wLkUvA/4p9ugvFXNzcxw4cIDdu3e/5iaWQlzwMxxZ6TLfDFnrRExXuyRJA/x5SOWZOXOaukhj25LHj9VRWpByJKPFLBtKafTk/cQjd2LcEkJIso7kZnmKW7qPcqd8lvtHm5zK3MAf8SHOWBMQ9wo9X0moWmsOHTrEysoKN99885uS57yqe/Rhs5fREBDZRUhCBkSDlnZRwuZgOMhK7NHSKQySfNqm1k5YXxS0yFFKg58IItUr8hILc7iHn8FLSWLjcmAmoquLpKqn8Yqg0kUcz2GklEcKgTY9Us24ILZsQfWPoVM5YrefuOVTXfPxMhaVikdqZIxuPSYxFlIHYDtowCBw0xKUz0iqi8SQxIZTSw733Rhiub1Q/ImTWX5s8xopxyAkBCKFJyJE3MVVMRmpsAUkEagYVGjQkQGlcaVAxYKBrEHGCaNeF0dHVNdiJgoBG9Jt3CiguRow1qcZG7Vw44SsrUk6iqY3yi2jHTZtT/P+d4YU946gGxF4eZSAbMnBDTvIRg25MEdw6DjlccGZ0x1iA7VWm5nlJqEw+CQkBnwDRrYxokGQ6yPSBuE3KLzv/RQ+dD+F+x/oufMB6AStEg4udZj1LU43Lm+b7Uu4mqn7t3XuLwCjL8/PDymMMavGmE8YY4aMMYPGmJ81xqxdzNi3l4eXiMtF9EopDh8+jFKKffv2YVnWJZHd8te+Re07DyF++hPYuWEAyl7EYG4R645baa14FDKjeE+EdAPF7vEiLhoVdhiqPQfeHfgiS2VsC++1O6w2fW5en6cUx+iVGgfdPazo63guUNgm5jvPHuHT+cfQ133snGBOEAS88MILDA4OvmlrWbi6qXuUD1phpIMjDYRdairNoNVgpuvRDg2WsEilJEIHRJFisqQopQVDecOJVQlWTyOeKMb72p/i3rQbKTVNH7a4CbbqMlB7nGb2VhqyRFeUaHTSrHbrQG91nZMat69Ip74AlZjoxBlmDszh2Aa/rRmfqCBGijQDD5I1vLQkWlMERtD1ACGQ2TTbCx32NzVxInjmmMV/+xM+m0YUJ84IWqT4/tN13nN9jYenykQJxFikHINREVpJXK3xpIURkJUJbe1gCY0jDb62CNuanA3NjmZbJSDsJshQs9qGTf0xOjQMFdo04xRb0w0eP56i4CQc9Yt8rG+V1miRJ45l2bR9BzvfWyYzvJXQyrNxSKHFLXhRk9T6nbgNTTB9gPENFV6sZRClEtNxjupzK6yzmpS2bsFK24AhyA7TirKIrCCf6cNzXZyzrZvKGOjWcJeeR+ESsh0HRVeZNyV0dSFczYj+UuVvf7RgfqhJ+nJACLER+FVgA6/gbmPM/Rca+zbRXyIuh1Vtt9vl2J/8IX1/9y3SW7Yit/3my5HIRSBaXmH29/8denCA7soqmzZuYjTrsqXvGEJo4uwoyh0mJx0++e6QhakaW1YP48w/izvoYEvN0toEjzaG0AZuGbTZW/8GHOuQTNzL1OZPcqKmiBJDopoIFdInWmAUYu0owt5Bu93m9OnTl0Ve+GpG9LK91HuvUUS1WYQp4IletN6O3F4NhhGM5xQzoU0la7PWClBGYUkLx4FQgR/E2LGPNXuciTvL5LLvoNUwnFhW7Bqo4rgC4ToIW2BwWGolvUSC6InUxEajhWQpP0nRymCNjBHUjlKrhhhhUenLEdkWqd3bsJ9Yxc2nSYuIvB1jW5J2B0qlPLv6FWLWYJTm+WOStm/45Ht9/vVXM9SbhkPJIPL5BT64u8Mjy6M0AgttQFoSV0KiJAaDZRnaykbKnja9UoJN5YBaV9LvhXQ7Bn8toh3ajNstCpU0aE0qZ9Nda5MIyaqVZmNfzLJX5q4NPtGsx7ceNTiDhtNUGNibZ3isDx0rqk8dI56qMvHpf4awLHAcup0s1nzMu+/eyFpphHBpmc5cl9baaQrSIn/91t62kZuFcgUjLPQrgulYG+a6CbrZZVBkKKkWG3IBa2uGybJ3RTJ8V3OP/u2I/g3QaxH5p57FlcZfAV8AvgmXJgN4TRP9D2PqfmlpiRMnTrDxye8hBMTHjhB9/3m8m249z7sNENIz1zz7RDMGOxNSvmOSuYlb0Fs2YzkWrmuhzCas+AiytYjIDWIwuEiysyep/cf/j/TGDH33bsQMj7Eo+oi1QgrJQr3O+qjNQ82NPPWEz8hQl0LZI6Vb3J07RlEk9EezHFbrGCnupDWzQK0VcvO+fW9KvOPVuKrFeEH1rDycwl49RmRuoWXSxDqFScBxDLmMQ3/BYrXaRGuJZQuE1CAFsQatDUYprOUlcmMFnJ1b6RwT5DxDHCuclcPIcomSmKMlJ2jEKY5XGyS650xXMT5BkqKjXWQsELpJeGKWRrpIf2WFIBIMDXroYj+5e+4g971pLEtSsGJmAkkhDfWupNKfZjTfZjJV51C3QrNp+NojDr/4gYifvNPmTx928TuaI3qY1eea3N7/fapDYxxrFmmHFq4NlgBtBGPlhPmqxUBBEYUGyzXEfoLTNSQdHxubtIzIVySek2IgG5C1NUNuyJPzNnm7zenY5lO7Fkhdn0e7OZRXJn+6n6qTJ+sZUjrEtALixRX0cp1cZpnTT3yTw0tltFtgxwfuQ3W69G2cYFBaTHcyhK0muXadTF8JaQTxdAPHcfAqvcjWewXHRrrXQmd7edphmqKTMNRXYXRxlb6LsOF9M7iaqfu3net+5BEYY/7Nmxl4TRP9lYBlWURRdMnjXmlIs2/fPjrf34//0IMIz8Nev/G8Y4ScR1o1MDYq2QzYCLNKKnWCLf/TBxEzFeYLfQghSNsSE9twYj8SQV6eId78s4Rhu6f3DXRPNKFoKP73P4PXjXEaCQLD5EAZ1c7ydHOEbNZjse5z05hDrvEUY3YNE7X5D/JjdOIY7+lpPiG+TTyw57KQPFy9iF74a73WuriDSEL8MEcibLomjWcZpGORzzj0ZS36klnKlmFN98yHlDI4ltOTGUajwgj8Nt5Nk0SFQXZuLPLw86ukLYWxJLJYQCrR8xeINUGsSDkSozRRqLCTmCDxcF2PJgK3kMVvzjG/EGPbimIWlHbQuQFy24YQbpPRjM8h39D2YWpRsHlnAakWuX8UTpwqESrJd5602Ls14YGbuhht+MvHPTqthCp5/nM1S2W1zbh7mmwGEjdLU6QJtUS1bIaIUFVBKonRoSaSFpvSbWbtCoO5GNtNsbXYJpcRHDgQsZbAGSXYklllIdXPPmeFWsfhu9+ThIU+3nP9Jj60L8NsM83wZIWMSKOnj2HiGLo+2RtyfP2xLpmiYsn3eODH16PFBLHxyAKD20dQI7cjwjayf4Dg0CE6jz+OsCT5D3wQZ2TkB66vJwWeJYlEhsLoTpRrgZBXNL1+NVP33W73st1z1ySu8dQ98PtCiN+gV4QXvvRLY8yzFxp4zRP95Y4W30xEHwQBL774Iv39/ed6y4u//Ktk3vt+rL4BrNL5K/OlbIKRQIImQJk0rgkBg3BsNk2mKaosloCCa4HSIB2MijDSwxIOVtzFq1h4v/gp/mbJRY+t5+aaIJIeE/2GdVlNxSvC7k+xKZnn1FrIQD7F5HA/TsvhYHc9pwo7qS7GiLCN0BYmVybXOvbWT+ZZXDWiDxsIfwURdTHCoeNUWI2KaKCrHUqWJJd2ScmQ9WaeA3qUgmeRGEU7tmjGNhYRFoa43cHKeojxrbR1PzpJKGYsPBFzvFNgnV7Bdg2puMbxNYsw6e0Rj+cl/skZ8jvHWG1myKYhDDpYa2u0/ZjxURsTRjgmQKgIa3SUwY/ejX7uUXYMKh5rKHwFzx0T3Ls3hSzabGsFXJ9Z5ZnOIO1A8nt/6vC//fOQj9zcZf1AzB8/kmVhTRAHmobO0Yk9kpokU/NJ0aVLiiGqLFoltnirHGeEuyZWebI6iK4INnqK7bk29cjm5BlD2tKgrF5mJAp41z4o7E6TdPp49sFFlpqKlA545mSBD+4YYqKgCWeWWTxRZej+e8kJQbz6DfTsYZLMIDPdDHYxzVzTJp9TaARSGLImxF54FtltYppDqKZB2BYmTtDd7muuryUF41n7NXvxV5KMr2bq/u2I/o3Q81q4xrEb+DngPbycujdn//+GuOaJ/nLjQoI5r8ba2hpHjhxhx44dVCovK90IKXEnt77BSNB6EGktoFWWlrLRxNj0U5ItMAna2kTZfkXa0HLpjn+Ead8gUjmKoaK8/0uk21We827kTOFGREdjnWywe0sFoRWyuYBx0tQiwb27R4n8Nv8/e+8ZbNl1X/n99j75npvDy6Fz7kaOTGASSYmkRFGU6NHI8ihYljTyOM+4ylN2uabK9sxI5VClGWtsaUoljWZkJUpMoggSDCCARmx0fJ27X04333vy3v7wAAgAuwE00IAksNenV/fdu9874e51/mv/91rl1UcwLz7JcPajXF5KMbKEeq6NKwJut5fYDB2S/B52b85tucwVJm/4PL4c75R0b6w8jYgHICDMBF/Vd5EIE4EmZ0smah6mlBRVh3G1jGtNcqkXMV6WRJmFaRioTBPFCXlTIIoFqFaJnCrlkkmStOhGCm9SgGkhkhgzC+kFCYaxtYPCH7QRImaQGihTE6cwNFysMCG6PM/isIJrQyFdgahOYpcxZvegmlfZu3EMgyksU3LmqkFvGJM7MEF87Dg/U22zkuRYjHzWewb/9N84/PKPhtxzMOa2n4n53pzDN4+7XNlwsDDoDSVIE8NKUZGNVzUxOi6i0WAiyGiaJT51uM14LuPpOZjr2ujuEMfx6XVi3jveRpU9RuI23dDiG49DY9tODj5U59zFAl2dY++0IFhbRw0ieoubDI+eovqeQ9j1CbIoobVe4M49ZZqlGdqmZu7sGnXXY3qbi/JtEH3SgocyHJz+Jt7hD6CjEOF52LOzr3k/vRxvRxPei3gnK/ogCG4R/Q82PgPs0FrfsKR8i+hvEG8kNx62JpeLFy/SbDZvKCr35ZOSVjUyVSXTGsVW2EyKIJX7rjlxDeKML11IGCQZOxsmsmIxMl0jWTYo5ksYm4CAHVWPRrqK1b/AyPAMJwcfZS6uYwj4gHsJOpf4i9Yu1q+eI1dtYBsJ+9wN3sN3Oeq8n6/FR5CdPvkTDzNp9sgO/zQUp27oPL4cb5boX30OXmsc0VvGXH0WoRJSLB6338NmUEK+4P0+UnJQSDKlmGGRRMFAeWwfMWkPNd1QolWGSUwx2yRQBRwzoWVMY2UxealxTEHR1Bxf9bh/Ww8RBrQ6Q+JUEaeKsm9Rm7tI9dSjXNk1SyKgO4yxchaxlKTdPsVyBdMAEa4iNhvIKohiEfYcpLFykenzfU6HHu2BwWOnLT56u0/l9horj7X5hfyT/Ja6m5UkTy80+PU/zHHHzJBPvy/j/p0RD24b0Ikki22H+YWMEJvhUOEaIaYt+aS3QaoFnpHR62oeP2NyTmnC0KBgJGSpIo3aNFTI3l2Syq48KpD80ZczWp7JfOoy+r4JPn33CNKUuLaLnp+nfXGJ+PnTTL6/wDe//DU2ohKHD22n4blMzkxg10ZpPT9H2BuQBMskpkVp/zhaOLTLu1Cyi1vfQ6FQIP/B7y9elNL04wzHlDjmtUn37SR623571v9fjVsV/evg3S/dHwPKwA1HDb7rif5vQrqP45jjx49TKBS46667/vqJX2fI3hlAoAp7v88t78WO/lc29wgk4AiDRGe4wrzupLUxiIkzhSEFS52Aw2Md5MEDqF11ps0qn+sbkDrUH/4LrMFJSndUkADR7eIAACAASURBVI7DauYCGakSdIwK63GVubBOojWFrMdPH5IUrj7OJWsHc1EZLQRKadrKZ1K1EVEHrcZBvrmmpJsp3V/z9eEG9onfAxWhhcVRbue4sY9+lqKlwDQEhbyLMKAiAkhAGBbSkswtJ0zUPLQwMQkhDmiqPAXfIfDL5CyIjSLIGKvfpm3nGHVNyBQ6jgkGPVKlsUyJYxmYi1coVAwW0QSZYhCllD2DQbGMJRUqUSAhjRT2hecICz8MrkM2vgvjgQf46IWnuXC2RJzl+YtHFQ8eyvDv2UFl9QTGmuRX1eP8bu82LmY1TKF56nKOE/MZE+WM7SOwfTxjZCRhJheAmxDaKcNYsNI0ePqSoDMQqMRirQd7qrDZV1jpgGGWcf9El3s+MoZoRcwtm3z9qRz79k8wdaDH6rKDZRrYtgODLrEy2PjOUSY/+0nK22/DdTIWBxtcXHKxi5K1oaJwaIq19U1ySUQlatFYW6MaDigU78TCIiVC2SVkvc41S5h4gEgGXBp6bAQK25AcGvNfsqF+J3BLuv9bAv3u314HjAJnhBBP8so1+lvb6242Xo/o2+02J0+efIUNbKsfs9GL2OWcxeg8tfVGnaBKr7S1vV7WvRCCnLDY6r7/fqg4YeX3/5AsSsk9+FGGSnDnmMWIu4RSOVLlIyyPiarAuLzKxhf/FCwT1Rul+LM/z6Tp011TFBzF6Og21tKMeKOHtHLsna5RGmuwJFxO9FzcROCFazTsPoZX5pvs4uDSRUbm/hw1eS96+4dv+JzeSOztK477GrLpq8cRgzWsM3+CjJoINE+rPXzPupsg0gilENKgYGkMKRAIBqlgVK/Rkz5aGuwcNWgHGsfISIMAL9jEMV1i5eCaCUGSo2xFiF6X6miRfjsjShSbkUe9fZ75eD/qhfz3Us7COHWCamGFqhmRSEWYapJMIIpFLNdhECjCTBJkAnf1OOvmDrxDu0gLJYLxAzxwzxxfmB+ypHIsbBj80SMWP/sJKH18P/rLZwk7Dv+oepS/7O/k0WgGUxiEymK1lbHRsfnOnGAsl9GOS9TdjCBzycmUMBWM5jIWOpK9hT6+NuluBIw5CT90t8ZUMVbJIshM/LEa3346Tz4P3znp85Of3sZ4ZFCs58mtrjFcCEn7McH5eeJWB9My6J5aINs1SmAX6VDgQC3HzLYSo7OjxGFMt9uB6jZWooho0KX4zBK+1rj7DpLakHvZZR4mGZtBjN88Sz1rMUzGcYrTxGlGkmmsd9B6/p1uxrte1PMt/EDgf3yzH7xF9DeI663Ra625evUqy8vL3HHHHS8ZW2z2Iv75n50myRS3jyX8/N4XPqC+36nrxWWB10t7ezU2vvQ1ln/n3xF96lPUHU1tpMLuskOWxoj2szhrp2D2o0inhsgVEZZFnCjW4ilU/gCDQcR0DepuSnNjnauLm/y9+/ehdMa2jS+SHYsIxz4JhoObdnlPYYHJ7kn+Q/gplLS42Fb8XKWIXHySbPahrTjeG5RKb4TotdYopVBKkaZb5/HFh6OXjyN6y1in/ggRrEEWMSd38oi8j2K+wLDVwzAMpCFxPYucbeAIgQi6KCuPHJmhu6RoNzNmxwpkCirhKleFpG/4uLbFgDwF0yLSJmLtLGyGWF6FWJnEYYZSFu3YRMutaFEDcGZnceWQkp2xojRJmtINYuq2jTMxQmU5QTuSzb4J+Tzu1dNEE1M4nkvs1bHufT+fO/0w/+qYR2xV+NLjml2TivcezlH99AHsJxc4+23NJ4tX+XA2z9PBCE+H46xrH0enhCqHEQ1IszwM+yQ6hyUHpNpCDgNudyLsJOHD0yEjIxamlVE8Mo0KAv70cYvVq0V27SgwPhawOHApyATDL9HwFQQB1sw+5PHT9I8+xfSdFt3L38OaugtZqCAHOe6+e5rlXJnASzi5qNk+pjE8n7wjud3rgZeyGfdpPvx11sMI9dxzFD/0IYxaDbtQQAjBZrR17Ts4FAyPHaLPVUPQyLt41jtr9vlObq+7tUb/OniXV/Ra62+92c/eIvobxLXW6NM05cSJE9i2zb333vuKJ/y1TkiSbd2AF9oeWfEgIFGlI9cc+82Y8RiugbejTu9DH8JOEnqJIswgN+ghli9DGJNbeZxs249DTlL+b/8bfuc09OwcO59fY+/OKqiIaPUC7Y0W8cSdLKcmd5rztAYR/379IPHSKnft386Y2WQ8muOMt4colJgIpGnRCRN0aRfl534bkQzJ9n/2Da/b30ge/ctJ3rIstNZkWUaapgyHw62fkxizOYd1+ZvI/gJCCi6IGR5W94Djs9KL0AhSBbZQTBRMTCFoRzFVNEUr4EJaxLWgYRsYZNgqxlt8BiH24ckUxVa4iyTBiDTphXPMHLqdCxcyPFPRDSRWKMmkubX0Ygo8S5J1umhvyL5il/O9cfKGST/MqBQFhUPbaJ89h4wVSysaOSspOj3m/uxhRn7202DlCep7uOtzHR5cPsEj6y6Zl+P//nOI04gPHrHIv3cbB2eLZG2f+Ml53hs2eV+4SE97bCQGG6JKlGYEiY3rgR1G+G5Cw7OwrYDR3WWESvAObUdHAZdbLt86WWTHZI2r7R7jxYSzSy4//bkddDOXctqHtU3iNKXzxFmq9xsU77oLL7jE6c2AZ7/Xxyyc4OM//GmmRIjhlQkWWmTnL9HL5wmUJDczwmjdQCsT2Y0oixBqNdAgt20j9DwWFhbo9Xr4vo9RqiNyBbx8AyMFvzLNfudvhgDfaWe8W0T/GniXdt0LIb6rtX6vEKLHS5FTW78CtNa6+HpjvOuJ/mY34bxauu/1ehw/fpxt27ZdU1bbNV5g/2SRK+sDPnPfDKp2/ZCbG+3oB0CnjH6kRP3en4RuRidXxzMljiHQbgMMm8gtkxQPk1s9h/H479LLCvSMj+I5JlfW+jyw2ydpnmS8f5JTzj7aUUorTGlURuklVYLMxHQdmr2I9x46zDPaYz7xGc8JKp05pvwe/y75EWglfIxH2emkyMWjKCHB8sEtveYhvNGJ8kVSf7Fh8cVr+6KdcLVapVLMY1/4Csb6ia2kOtPifNrgG+IBNkUFT5oUjZRuoil6EpTm0ESZ892YshHi6wg1tp+kK1nrJ2idMVmvUGjOYxoCbVpE0sMUBqk2yLSEq1cRtosOQ4qejdaSVk/jywK91CV9saLXCnHkCGJpGUNrSiJiKbGIU8FQWVSnajjeZSIFF5aB233sZguxMqT98FFqH7uPpFxFTN3FT/98RPNfX+VYVzIUHv/2q5KrqxGfeSCmNFtDT2mmt82StaeIBhb2Ro9GoogX58EQmLYi0xlOvQD5OlbVwsznUNpgkMBjiznKXoHvnAEnVSz0y8wcybPcdDi4PY/tF6lpjWOP03v6DJ2TF0lWmggyostXGJye55I9S9csYCqHhBb+xBQ7tIWxHLO81qR26SJm0cLblmdN2bTKDSy1QW5sB/nCFKrXw965k7LrMjY2htaa4XDIZrPJxuIlOlFAVCpRMUIqFe9vJPDlnXbGu2WB+wMJH0BrXXizA7zrif5m4+VV9+LiIleuXOHIkSPk89fOm7cMyS9+dNcbGtsIhiTzl9H7Dl7nAUUj5DJCDlHZKOgCggBBjFksc6SwQU/uxTEEUghwKqxO/BRXezElu0ghvsLYWIUyVaZCi/lOyr2jJpv/729y+AETp+STdx10qhASvLxP5fDH8J9ZI9aSI8U2cuE42PtQqUneHHIk3+JKV5BphZAWC2mDmorwkhTn+O+DtMiO/H3I1a973G8oR/46JN/r9Th58iQ7d2xjxBxgHP+3iM4VVHEG0evxXLaXb8u7GCiLYs7GsCSG1gSZRMWKgw2TQaaJM02YCPYUMzKnzLkNk4ovSDJFwUjIpX3SziaiqjAsiRASKbac5YLvPIqZl4xNluktDSDTDGObNTxcmZBJTd4xMFGoUhkuBUjHYm9Bs7FkkDM0rUFCY/sodj6Hl/ZpdiSDQhU3W2Hbx+/m2X/5J1gTI5Tutkn8HOaeB/nVXzb41791mefbNQKR4y+fMnjyjMUP3RVyzz4Yr0gsb2spSPU0wrVQURVhgFYCIUEnmr6wSdfbfG+5Sn89oB9JVlcUmV/E9Wx6Efi25AMf2E6u5KCbEfHFeVJMmnOrTHz2RzBJcQ9Ar38SJXYTxnka28ZZXwFdr6ByJrEeoHWFmb0z1FWACmPyB/aAztCFGirfIMhNYdsmdv77bZWFEPi+j+/7zExPvxTt3Gw2uXLlClJKKpUK1WqVYrH4jmzbvCXd/22Bfjdb4L7lA7tF9DeIFyePEydOvBRIczMqiXRlifz/+b8wVBnGj36O4ud/9hp/fIiUra0f5TJRmgPtIUQDQzdRxna8l3UcL3VDvnmpT5wpDkoHv+wjiwdQ5j4+K/KEmWb1f/3f8U6eZPWMy+h/8UsUx/Yy0oOirajlwBYlfuEDRVTQQs79AV9qztJKz1MemeJwLUWFKSvl20m7JpW0SZQb5ffTQ+Q3NvlJZwUvC5BXv4vor6DGbkdPfb/V7+tJ91mWoZRCCPHKZZG1NS5dOMdt2xsUlr+GaF5EGzYYHqq/yjfFfTyV7aYqB0SWj2k7FPOCK4sBtoCiE3JkehtLQYokIy8DvEKBOErYDGzWuzGebTC+eRlRAScvyNwCqTKwhURpidQw+Naj1H/pcwx0StmXCKXZGBhYvk8n89AIDENioRD5PGmpgZsmlMwerlFhY5hhSLBLilLd58r5gJLKuLIu2etZ+OFVag/cwfKv/w7GP/0V8rftQdkOYtcD/No/rvCF/+cZHr5cIXYKbA5tfu9hybeOKaqFlN3jKROjgophYOYNjFgRIYj6sNiT6DDl/LpAqDJRmGDbeUIzj+lpDJHxQx8ZIREWRdfBFBlZIDCkR+/UcZJ2jECghkPkyimeGrqc2QjxR9b4yCc+wZRt09vr4aQdzq9m2JbEyQl8NPnZOlgeSmuiC8t0W22KR6YQxtbD07UQZwrJ1i4J4CVir1S2VLI4jmm1WiwtLXHmzBlyuRyVSuVtJftb0v3fEmjezWv0I0KI/+p6v9Ra/8brDfCuJ/qbLd0Ph0OGwyHT09NMT0/ftPGTi+cRcYS2baKnn4BrEb22eGFZhiAtE6hk62W5B0d+/6Vc7sVblXCaMghjRt11kCMYmaQfpKRpRtW2iaXBILLoZjU2YpeSm5JlGfH6JZ6NpumlcHtVshlUmRtWEUIy3Iz44TsP86gYI5fBHrvJXcF5/rI5iedl9I0Kl/Q42s4xs36Ogmshr34HPWxC0kNt//BLVf71zuHL1+NfXsVrrbl87iRsnOd+t4l54VEI2+jcKGKwzIYzxdfjAywmRXwZsy5q1Ap5GiWLYWudJDPQWUypWMB1DZIwQaUxbs4m76csDKs0ex3GKy5pHNOYqqDnniDKOwhTorSJaUiEALmyhg5DLF9S9h2GccygD5WyxWbsUbBiQmFhGwKJQtcbKGNrz77nSKZ8iCJNBqz3M2Zvn2L+SodBpHlizmLfNgdWF9n56U/z/Nwl5v+n/4upf/ILFO6/A9PKiBq38aP/3Ti3f/MJvvD1VVbCPKuZwXq/QChNTj0xZHoU1jYiphqCdldRKwk2O5pdExYnFwT37HRZGNiYvkAkXe67w6NYcvEKJeqTeSxDES5sMlzpEs13qOzfR3HPHvTZxyjsniWYO8WwIzgdNYjyOeLIQVXLTNdKNC9usHZ6HqdcIIxinMNFaF5ALp0FJL3FlHBpFavVpnTwIIbrYLxwnROlSdMEd7BKN7M4F+aQQrB/JId3jdZ627YZHR1ldHT0JZl/Y2ODMAw5evQopVJpa3mnUrlpMv87Ld1fTzm8hXc1DCDP1uT/pvCuJ/qbidXVVS5cuIDruszMzNzUsZ0jd6LHp2BznfxP/PR13mWTpTsRIkJpF15IJ79WvRItrzIyv8wlf4wkS7h9NI/BCLp/ErnwHNI9RGP6LvQv/jInv/gwX3F3YS44vK8S4bnghst0W3OsyCLSznGibbB7+4MYvQ6JsKgaHeTZP2LS2s0ZPYMjt6obv+BzZQgzLPPddAexrlKOy3xePA6Gg7l+AqSBPPNniDRAe1XkxHsohPOQHNj65w0LjUSpFyr5NEAIieguoMIevXPfYTrr43oeYmMVXdmJDFqkmeJJ7308PWhgkBEID8sSTFaLNIo23cGQy22DNEmpuXD79gYbMfRjhWtoGl7KMNKs9yVhlNLqpezxI8RGF8dPSEZGiUMLhUQCaEiPHSMb9nGm6gRC4duCYjGjExqYTo5u4iJNsC2JgYBOh6g+Q0FnSEvQKFic72QEsYIkZfuuEs+WfKK+4ujJmM/fO4I9fwrn6mPs+NXPc+5f/g4L/+xfMfYPf4bKh+7H9DWRbjD5kY/wK3cvsXDqCk8+usS5tSEycuhhI5RLJkwwHSKRYjoG2s4IwohdMzadQcy+bTb3HM4xEONMThQwjYykNSRd3SDoJ2TtjItf/R4Vy6Zy+CDOcJFkyubZpS6Foolj1Zlp1DnRtBiZ8qmU20hcDlRt3NVFrPkQ+/BecuYQaUSktTrm+hr02wjXQ6QbGEmM4W1lC6RKszhI0f11iuEqw2GCkd9BIj0Gsbom0b8cL8r8lmXRarU4cuTIdWX+QqHwpsn6nd5ed6uifw28eyv6Za31//xWBrhF9G8ASinOnj3LcDjknnvu4cknn7zpf0Pm86T/6L/H8X28sbHXeKeD1g6u0C/45G2Z6bwc8fomc//Zf0mwYycj/+DnqDU8fMeitTrAXTiG7RUZCY+TDnciTv0JK/VJ0D5Jphn0Qo7kh3idRxjgIE2DTCtKnmJ8ZJyfKozR7A6oX/oGf3ZlJwtRj/v3tjiya5bHr3r42mJf2ObwcJUvN21sK6JnVvk9/XHi1OJjfJdZsYkIWmB5iO4iTvsPmApCjOcW0UkMpoMSJmYyQJs+Iukj0pAME7pL5AqT5NI+SuTAKZImMeerH+bxVp52aqKFRayh5kKlUcd3TQZxRLPVw0xjSnZGrTrGZNnjyZUBZWtIhsFkWbIc1VjtphhS0nA04yULk5Sc1WLR2otMTHQmsS0DKSB84mm8nZPgmLi2DQxYakkaOQjTDNfO0NJAAgINk9PEgyvoOIN+n7wdM+EZLGsI4gSZcynXfRa6Q7qB5MmlIvd7Dsb6PNXaBbb/2t/n0v/xuyz/xm8TnL5I/bMfwdk2iRAOurKDifsm+Mz9GaK9wkY7Zri0SrMniIYxIZKCnRKZHjvHUvrONJN1sHM+wnYhTSglGbrVJDI9ukcvINwcw+NnmfypH6Gyr8iOsTIqbjE4dYbviTrLbYVZUfzQxz5Cw7HZPYjxCDjfcZisGDjlEjs+9UGSzRbezmkkim5+hlgM8K1xvCmP9NjzqFoNo/jXzcOZBoXGFIoYixF7SBOJbxkUnTe+Jv4iEb+WzN/tdsnlclSrVarV6g0Fx7yTa/S3KvrXgka/e4n+LcvGt4j+dfDyQJq9e/e+Qj6+2csCN7K9TgqBL6693z5eXSMLIuKHPogOhlDMc35hmeHyCvdW6oRmnlZ+P7mrz+N1lzhoS44ns0jTZvr577L5G39O9VP34t13gG12gX4iGC0kxJkiVFDNOyxnNa6EBRyZ8fRSxp2TTQoW9BMT03SIDZditUQYZexJz3NqOIaVr/E9+QDfyKBqxvxQ+i2UyOEx2CLx3jI6NwaDza072y0iWxfQ9b3o1eN0dJmy423lpRemWPZ2skSD403BStdhxOzT1y5VGVAtFik3RkgBmfUIO0PCXo9IeViOz/3bK5zvhAziGC0cdhUGtEOXQDmsbnYZhgmpTpkK1rEKIWatTITDILUAvSXbRxHRuQuUHpzE9BwwEkxDUPMVSSLJhEGkDFwjwzPBSEFfOEdUGoN0DeFPYJMynmYsY5EzFEol7L13goXLLfqx4s+/Dff9vZ0kjzyLdfZJRu6oYP7TX+Piv/gtun/5CIOnjlH55Ecof+xB7JKNtn2k6pJWdlKvBGTTO5gxUnQKwlCoWGM4gixQjFoalWQow0YvrZC5PoPnziNzRQbPPkn5tv10H3sCf8c2RG+DUWuDdqmObp5naNZoG9O0XCjaPrmSjevmWLu0TJoNCUKfzK+SWBqvaOPUt4PlkKmEWGisfJ6hluRsgfue98D586+4h20JZdsgpEHVEbjWBEf8+g1/565XcV9L5m82m5w9e5Yoit6wzP92+ui/GnEcv2N2u7fwtwo37kL2Krzrif6tfAmvF0hzPQe7t4q3mnX/Ivx9OzjwGz/Fhi+5ajYYxilp0OXOex4gzu5iPlAIw6LrjLFrsk/d2sEvUgHDYfAvnkPbDhv/37cpPfQfo5VJwUpod0MubsyzaUwgpaBW2E1OeQwyycGypHnyS0RBiW2jO5jafpinlzzGhEE8bDHRTzmdGsRhnyDrgTRYckb4D+LDhNphT66POZyj1phlR/sJ+s4EFTEkyRRmZSe91gZtYydmdZpNf4orgc3aUNHbjOgkJnkRYAibQJmMuimVxjS275JmGj9rkXY32dxUdLIctYLLndvqOI7B8saQvJ0gVMZIXtLNfOJ0y+SoIgI8R1KfqpFvPoFojLC20cC1DOJsq7JU66tYrkX57lmU4YL0yIkOKwONZwrCzEAbAi0lqQYLTbxzF2nQIQ1WsFSG7SR4pSIzQca5tgVJSmU2z9hUicUrLS6sar5yssCn9k0Qn5zHfvavqB56H+6v/xOu/vYf0z95jrV/8wd0vvIIuTsP4t97GHuygTtqoIVC2BYqjlGGhwjaKLtMtraKyhUIFjfRcUZw+gLkisQXnsLO5xgszeGM1KnuKDBiNdBWzNo3HmGlXuN7fzXErpW54/aD7KpWUSshozVJpdxB4zF15RypYZKPy2TTU3jdC4jl8whp0d0wSZttjA98kKRYecntTmv9fWQshKDqGOAYwBSaN1fWvBFp/eXd/NPX6OYXQrxU7b8Vmf9m4J16qPg7B827dh+91rr5Vsd41xP9m8HrBdK8aJpz04heRYjhFRxiQvWmt0q+BCn75PeO4SmB1z7JsYsGRz7wfqJU8fWLPTaClN0jeSbLJtoZwZAmJg5amxhens14mWfu/jFGr/QZn66gk4hq/xxLaRlpJChMxmYq3Fmeph8qyuFFfueJXQTKxAlS/sFMyKgZMZ/kcHJlVsQ+pvN5zGxIvr3EseEIRthkoBRls8UzYQU7m0FulHnU+CgkAt+1GUQhcZhCFiNtD92OSZqKTEVINImWeIYiykyqTka91sDyiwRa4IuEIB3itC9wplUlUYKS57CtXuLwZJ7HlnrYMqGfmOwuRHSTPKH0uLTcQQQDesLkgBfiDvvYIxaZYdKJHAbJCxarUqCvzGNZEWapAKaGLMSyJZYliWJNRSfYRoYtNJbQ2Gji1VV0ziJMDYw4xjSGENtMOjarrkmWBHQzya57J+k0+/R7mj951GPvT25nZ71DvNrEOvYIfmuF3f/pj9BdGLLy51+n88wJwufPsPnFhzGP7MPuBxTuPoyKIpzZCZJmC3dmit4Tz1K84wjdx55BGhLD9zA8j7Qzj10tM/mhQ8j5k2T+KMOv/BnxbIWmWcYeLXI+HqfjG/hWDlGoY1SKTLs9DBWzNMxR9QTT999O+5uP4jQKlEoZcmOIHhlBnz1HeqkP+QrGU0cpf+xjW1tA4aVmy7cDb6bivhGZ/53CO5Hu+HcbPxBe928at4j+VbhuIM3LcLMq75fGW3sYGS4xmmkWxANvYoQIITtonQedQ4s8cQJJ3Cfvb8OxtrbkrQ9iumGGawhW2gF3j9lIw8CLlzEGARQPkvvFX+Jb37vMQuSwcLXDJ2s59vo93I05XKPMU844BdcgZwlaYUKYCHL+NjJziJFlZFaR4NxXCDsw69lsv+0TPLZqY2cKndhkpXEmSwUKqk2rFbIc+4yKdbrSIQ1a9LSkbgy43K8yKTdo6zJ5IyUOh2QIHKlJNbgmlAkwPJ9KbQzDyTFUEsMQ5JIeTn8Vv7/O45sVPCOhJytsK/m8Z2eZ080enTAFBFUrxjYtUumjM8Xl+XXCVFN1EqZrNjmWMWo1VvQESIucZSCkJKcV8fnz1D54CHeqylD6aCRuvIxIEgwsusqBzMC1JSpTeI5Fv1ZDpxGRLlCwLaRIsTyD4UaPvaU8z6yaNLwYuS3PyPYq8dw6rb7mN79S5B//+G1Ue0+QNlvI8DmMzibVyd2U/+GPEST/Ee0nn2f96DG6i8tIJOHJOdJ2n+TyEmmnQzaxhA5Chkefwx2pkpuokyWK8btnkZuXiZ0a2Tf/GLFzCqO5Rj9f5ytzZdJU4o9PUt9eo1428dyMg3thrZtw8tQlxGgVrRPinQ38bdNM/tznAYWSA7r+LGnQozDjwsop1HBIbt++l0hea00/0aQoVHuBpaxINzOYKjoU3bc+Pd2MZrnXkvmHwyFzc3M3vZv/erhV0d/Cm8G7nuhv5ItxrUCaa+FmEL3WmjOLXQwp2J/10EgEKUKFNzoS0rwMpAjdpB9vo9Xusj6f4+CB27CsIkI8jlKKas7CtSRhqthT87BlgWyxjexdxEaTRRk8+zXK3Rm0dRBpuKhvfJW173yV8o99Av3+j9OILbROWWlusDBYIrOKjBUlP3LfTs4ux+xueHz7uctcDosYHcVPTK1ye3Cay4xRrm/nbHc7RUMSRXmKVgdPuBTjjJW+ACmxgxZXkxI7jGU2dJmyEYAG05LU5YC+WWBXwWIofcxcEWkYZFqg0OR0QD7YoB5eZbUvebZTIsFhgM+OkTyfPFxlcdjnaielKAfEwqXuRGCUSTC4eHUFMRhQ9nPUcoppq41bc9CmzVqnTC/eirGtFkyiIEQuzJP/WIUo8ZEkaKVxixaDRchSQZ4UpAJhoFAYUkKviy6VGVJHpxEYGX4BomGOXByzo2RwvgOOlXLooRlaqwMGrYCrayn//C9q/Oc/5Or0JgAAIABJREFU/H7GTz+JaLWIzp/DWl1AXHyeXG2c3LZdlPa8h6VuwnRjjCQREA1JY3BzgiiCQkGRRjFSxVjtqySRJvnmn2Jtn4ELxxm4Po+e1AypMz47QWszxqrl8AyP0PeZniriGSmRVIzIgMGls9hiBiFGkUmIsXwCYfvo8T0kqUNkushCmWFRUhzfgw4CZLn80t3bTxSbcQYqZGNjhbWwjVndxnw75ODYW288u9ld8a+W+Y8ePcrIyMjbLvO/k70Af2dxS/W4Lt71RP9GcL1AmuvhTVnVvgrfPb3OF55cBODz997NfZXTDNI8g+GNS/fihS12YebSDQNMz2H34SNYxlbjjpSScHGJK//s15m4/0HUhz9MreC+cDAeWkPX24ZKJAUTHjpsUzU9cvk89aMZiePQ+vd/SuFDn0EkGSIO0INNyKpgpSSZZKSsGStWMYTBk/40Iu6jzQKttcs8u2zgyGU+5guE6XB1aNIolFkyRrAE9Byfgp8gDIskKDOTpFjeBMV0iJAOcZah04TImKQkFQPTwzUNQJNlCk8PqMaL1ONFgtTiyXWXLmWa5Knkc2wruXz0QJG1sM+FZoojFd3UZTKXoO0yQ3IMmi3Wrm7SlTbOMGT/COTtNQxHEFBgJczjWZJYaSq2gb46j+8GeLO7UI0SgfAQUmH225TRBMIjyTykEtjE2LjkSiWEUujNDbK8JA4VnkhwvD4SHyVNZl1JHG+yHHvYrsV9n97Dd//wFEkEV5dS/rcvlPjc+9/Hg+PnkJfmCdc6OHFEsNAkd+EERn6EyXiAPT6LHYeIQgXV7yLzRazmJkqBNCTpyhJJfRxDDUgKOZ5fTUnM7QxyE5xeTRmpWyzIOrs/WGdjqcWH78px4koLcyUgK+YYVEuISoXGXYcI5xcp33MALziHMAKYv0jvsadJjTw89BFULoctQbouuO6r7l3QbH2XTCm2wmmzjIZ3c5rO3s7tby+S78tl/iRJaDabLC0t0ev18DzvpWr/rdjXhmGI+6pzdwuvwi3p/rr4gSf61wqkuR6uFWxzo1jrhGRKAYK1wCPb/0mCzU1Uf/0V74vnTtH7o9/HPnCE/I/95DWe6gVZNkuSrHBloU95rI5pmS9Jo7BVhWx++esMN1qE+w9gtdvMey4jngmN++i4s2zKKiCRd2f41oD9Xh6tc4TlMivK4bvv/U9oPLvMQ4dGsdMezuBJcrkDLLh1qnmLK82Acxub5ByLBw9PcGohZCTvMb+saKVdMu1xdiNBd+awtWCX9vCdWVphTKnY4GKUIxj2SZVFvlQhVQJh5TAlRImimJf04xSpM6y4ixoG+AzZmV6koNqsy0me2XBZyup0lYe0POq+zZGpPAenLFaHQy40MwYxeCKjbis8rwAZZElItDlgM9Y08hLf8zgw1sGpuCjHYT2cpB1bDOMMIbbC+RgOGH9wiqyfoOwKQmikisgVbDZjQYaBhYGNIBEWCQJDSpwoIBidIFIxkU7xTI0R93HLNQbtiDQz2VWwSPsBnUyjqx7v+4mDPPaF04SBZH095re/6vDdbbfxsdv3s2fmHEa3i7i8QJrZpJcvIz2TYL2LlTMJgsvkcpqB9rHdDGwXUS+Q7NjFqY5DR08ReuOcvhCRK7g0CnXMYkQngcPjNXTJolwpYucVM9kK4Ykeudv2oS/GqMMNyg/cjXjwbpB9VLuLsl1EFJP1AzDBu3gW947bMa9TjfqWpCwFfdOjUvTIjzWIjRw5++aQ89tJ9Nca27Ksa8r858+fJwzDl7r5y+XyDaVUDgaDWz73t/Cm8QNN9C8G0mzfvp3x8fE3/LmbId1/6PAYq50I0xC8b3/jpXFfrRS0f/PXUe028dnTOEfuwN655/vGWlnucPHiMocOH8Z1PDRg89cTkJQSd99uylefR5cgzfvkzC3Tl34Cz7V8DDNlvOyi/DqGZeDpDglF3Lvfx1+FE2SZy0IzYPXMJXaunOayOU5t/33UMpc0CVhY72OlEX1RJ8XgPXsNDF1AilnOdpcwhaStDU50JhBak9oRRnyWBIt94XOYfYFtaHLVSeajKuV4iV5+L8NhlwNqnU01zoHoElIrHB1gJX02Q835ZIrzgxrtzMcyJS1VYKToUnAt7t7mM9NImdsIWegoggR8meDJjEbOJsi2tJCKIXnswjJOoUJ7GPPh6YiCv4GMQ3qiSjspMowzLGPLftXpdpDLV7CmwZmqM8AGYYJhYKZ9/BgSu4hUKZbMkEi0zsi0JgyH6G4XUS4yiD3KOkBKRTGXEvUE8TBC+FUOm6c4ZTQQCETd5QM/dYinvnaBzmqPaJhw7jJcWTCoVI9waDvsvS+gQR9n0MQxMowgQJXzDDtDovoY6+tDQrvEYt/j8lyKN15jfSMjV7Axezbaz5EJRVIssXNPjgl3yLa64MSpDZQniKoVRHmcarQMFy9hPnAP7sYl5GADPbGfzLFoe1NoK8HeM4FefASUwh4fuy7Jw9ZDqCcVkeUi6juwgZu5geydJvqX441081cqFWq12uvK/Lfsb18Pt5rxXgvveqK/3rrW4uIiV69efc1AmuvhZhB9JW/zKx/f/YrXrqUUGNU6WXMTYdnI/CvTCJVSnDt3jsFgwD333HPdCkFKSf7e2xi7OyJV6wRmiONUEULwxEKHtUGC0poR3yLvVxDds9iddazsNGplwM5+woI4jJHL4y2fpf2nf4zMFPZDn0VkGSILmRRrXKa6Fd0qBU/Mp/TDDXbXDT59bw1HeCxtJujVCK0zVowxlnproDLWBoqWKmCbJg/p87SiAMNTVPrfIVNFXDcgXW+x6RZY7is201EGepYYi2biMFW2GXQMKq6gqhRjRoc7d/jYnubogslaX1CxYhIkriEYyVkMZAELxZTn8sUvPsamVcGJYvaN2RwYX8YwFZlboxVNsz6UGBKiJKPmO6TdmKnqEH/3CMoukgkftEakMVacECoXpQWRNjEyiVApRmZy+sxZnJyL1Bo6PcKKTaoDTBR2uEqxvofWapM0TJD2Nu5QZ5izxplXEBVdHvzRPVw+sc6Vk+u01wfkCxbz8yG9nsVjJxwMLCrVMZIwplCwSS+luI5JcD7FdExUJonjlNndFebnB7i5HGGqKE43mKl57C5rQtcnb/bIhEtDNxk7/hzWkSMYZ5dQIyOM/cxPoMMQp5Qi2osQDUiPfp1BZRfZjl0YloeuFyl95sdBa+QL5jNaa3qJQmUpRZEQCAcpJZ5lXHN73c3C20n0N2p/++pu/iRJXurm7/V6uK770vr+q6v3W654r4N38fa6m4F3PdG/Gi9GmiqluOeee95Ul+zN7rp/EdcyzKn81/8D4VOPY81uxxz9a8e8OI45duwY1WqVO+644zUbdbbG1QjHx9YxlkhJxdYEZUqJ1hpDCKq2gdA+rFxFGzliFSNb89y3a5LRER/HK2OvTbK5bQdPZXWmLmxy5646tmWTHyyTL9To5AostgO6nT45EXOlU+P+aYP1fsBIJc9799dRWmNJhyubIUk6pO3vIw37xGnIl/t3opMhqp+BMY1UEYkWWJZD2EvAsPBsh40QZuoFNloRgbDYN2Gwb8xhqiawTMXcasbipkbpFE9kdCKDqgvFYpFBEOHbglnH4htf+jbzVoOxskUaJ3xif4BTVKhAsx6O0dNl1oYxQZJhSoEjwei2KFU1weIA+84aWzXoENOMsEyBUoIUgVYaKTSpMAnSjJFSkR17dnHuW4+Szu4gUYphZFF0Y2CAb2mCcoGg3SPOBAM1w232eRoj4xzbrCBtk9kjY2zfV+Py2SarF9oUsoAoSimUTZorQ0Yni1y91KMxW+PMMyvsuq3MoNXFtUy0IXEqPmtr6Ra576rSsDJk0ccyhoyXNMOFyyyvZ8zsqDOwx8mrZ1FLS4hDB9DDLtZEDVH20ekGmTIQhmA4d57EaCKEgdyzl9yL6/EvwyBRrA8TZG+B7rDLBiXIj7C77r2t2+ve7rHfyhZby7IYGRlhZGQErTVBELxC5i8Wi1SrVXzfZzgc3pBj3y3cwsvxA0H0LybODYdDjh07xtTUFFNTU296ArgRB7sbwbWke5kvkHvoo694rdPpcOLECfbs2UOj0XiNESOECLAsQaYgNW5D6jZKlEBsVVKHNucxDR93fIScY4KUqOpdbMQp3dwujFKfWfs4E54itiWKcU5sv49LssralQ7FjQW2n3gU+dAHEaM7MVKNR0hOxATapG4Lji2ntPsxUibcM2tiSsHaWpt95YTxqQk8y+GROQtTbMW5tgY+Wm1Zx5oGxGGK4VgY1gs2sqZgR9ECqfjUbUXKeSh5kihTLHQyFrqaYayoWBHrgYVh2YyXTBw04SDAjAOcQZOjJy9zwRvB1pJWL+HHDiZUjCXox/TlCD1GGSaKOFUULAMtBbmNNQps4NdsrHqFoRhDCYXAQMYBemUDLyiSeQ5SuJgyQ2kTKQ1qo2NI28BH8f+z9+YxkiX3nd8n4l2ZL+/Muqu6uqrv6WOmZ3qmObyHEkWKokRql1hyZaxEWhIhQdZitVgb4i5WMlZr2KM11vAalg3LK2FHkC1LhGSRK1IHTWl4n0NOX9P3WdV15328O8J/ZFVN90wf1d3VLQ6nvkChql6+jHyZGS++8bu+v0YQEjs2zShHLlVDSIFcPkV55CmWNQT1BiF5qv4OxpKLDI95nOuWsY00Dd/hyNFRao8Po7shi4s9vLpHYTig2QkZ3jnAwnLExMFxep5i+MA45YIDSManczgiIpV20NpjshAzc20eJQSZUp7s8jWy5jaSi4tElXEGP/YhVL1FKhvBiW9hRFdIdr2dtp0jGNiP0WiguIpIFK7fxbVuc08JQMeIJMIXDiLsEmtNEKuHatG/UbwFQghc18V1XSYmJlBK0Wq1qNVqfPKTn2RhYYFCocDXvvY1jh49uqH4/s///M/zF3/xFwwNDXHy5EkAarUaH/vYx7hy5QpTU1P8yZ/8ybqH4Y2NLdf9nfCmIHp4tSHNgQMHKBQKDzTWw7To7zbu7OwsMzMzG6gOiJDmZUAxNp0lMiUdJcnI4fUNTu2vvsjVP/oz4l/6ZcKex/mWyRPlNEnlMM1ujBSaxMoQpNukRRs7mkPJEQZHBNZKgiZBOhFRu8bS7/yvDPz7/wVpGzja5IB1nNO5d6KdDNdWmsiohzZMlrs5Llcj4hD27x2hkjHohoqPHCljWD5Kw6WFNKWMxotj5muaXcM2i20f13IYLoIXJQzmLKTQdEKoeYrr8z7NUNDwBYNWl3Zs08Kh4goGszZaC8IwYXqwiFsN+c6LxzlV3EnN0xSzBm+diHi8NIvMungdh2qyHe2kmVnpl821lWYsZxHHFqPFkKgeYW0bIBRZJBFSRNhWRLLUxHfGiTBJK0GcgJ0oDB0TJwowKO2cornURJOlG7mEysIxI1A1TK9BOV+kCgS1BgF5VoI95Jevcjjfpj00wGKUZq7t0kssCkMWIlNge77C5WbCuBMz20kYL6QJkQgSymmTRuDhGAJBwHg2ZmGhjmVIShlIV8/hudtJlmyYeJLoxW/gPPs0lm3gpLOIgotonCa1bZyk3ab7xb+m9/R7SFVKRMUs2R97HyIMcKanbzsbM6ZkOONAlMIWK8xktiHSFsWUxXLr4VrdD6u2/WF2rpNSUiwWKRaLfOYzn+HTn/40n/3sZ3nhhRf4lV/5FT784Q/zW7915z4nn/jEJ/jVX/1Vfu7nfm792PPPP8+P/uiP8qlPfYrnn3+e559/nt/+7d9+KO/hkWOL6G+LNwXRnzlz5q5x7HuBYRiEYbgJV3Yz7uQpUEpx+vRp4jjm6NGjG3AZJvQDVxJtFyHWxIYiQWOuiokG1+fRSYKRNoEYSd8C+sZMk2tNn0o2xcGRDFZchNpJjE4H2e7ytrBJbvtBzKlxRhot5p94hr8uCNxvzPIP9uTILM0QTv84pkwTa824GxGGdQJnhIUmhGGCm7RZbsLleoo4jilZXSoFl4WOYjIvSKckiW/x9E5FL4YRK0XWVMx1BWmh+N5sgBcL4ijC0DH12GFAdpAqRSPJkE/DYMYkY9u0A40RhxwYKSNmr/Dlly5wPLsTL7EZzCY8Nq55944FRAJhM2Ap2YmfHqQbSJpehNaQsiUZr03eaCIuXCJ1cIrAmgbZ7yFoiQgdxqi5KrIYgVIkiUIKSJAkGARx/7t1p6exjn+ecN8B4nZI1c0zZlYhn4ULf4tz4ENU8hnqhoFfrRFGGapqD93qEgW7yiQBOypF/LJLNU4xkTepeWmmCyGtbsx02UYJRVoqUkLT9WL2FwXB/BLaNBk0LEqdeXr2OH5Yxuu4KBGhRIrs9DbKk+OI9hzGuS+gpYPa/RZ8dwTf6GDVFoh6Fnznm8Q/9n5c0yC9/eZOjonSRFrjyFdbCwshyNoWDE0D0+y84fyHWSP+sJPxHlVDGyklR44c4Td+4zf6+Q7t9l2f8653vYsrV67cdOwzn/kML774IgAf//jHee655354iH4Lt8WbguiHh4cpFAqbtpg8LIv+da57rZDVr0BvhvMrJTLlA2zfvn2D78NBq0GE6OC3PJyMg0T0W6WuYvAffBDTbWEOzBHkNRVX4sU211sBOdug0Q0YsPMQWdDu0jEH8Eq7ycorPD5p4xcMkqHtXJ63MLal6AUxx7/+XQ5e+BbCC9n2m/+Wdqxx7SI+LS6pNDlbEoUgsBDCphNoskmbZihYiRxSeJxuhpDKobXiWtIjNrMorRCxj5A2oQYRR6RkRFtlSRsmllB0RZZS1qKSgpSTJhE2rXqViqmZHCxS/du/4SuqxCk5xpirUZFi72jCj47PYYVtYmWypKbx7RG8rs+FagRRhDYsyobAEjHDapbc3hFIDxEbxb5XA4WpIwg1anYRIxNgxQGmzGCSoBQkaHphBDgIIRiaHGfW8yDt0u5IvJRL2uzBQA5e/hzO4Q9SyaZo2sMEjSZR16OXDOF7RexUTGpuCceqUvY9Risp2tcbONuytNsx5cEC9dN1MjsrhNfbkHNJWkVSKsQLcnSkQ9jJou0Ea9il8LZnEa0WViWD1ashswUENfTwICwu4l29RmdiB1VnEm0rrO45UrZDwZYIefNcTLRmrhcThz3coI60MhhukVLavO28/fvMjP9BHfu16PV66x48IQT5fP4uz7g1FhcX1yuMRkdHWVpa2rRr/HvHlmDObfGmIPpyubypMfWHFaMXQtw0rgir6NYFekHE7lICU1P3MhpaDaAZoL18Fps0uVLmpsXWqpQZ+dhPYairQI1EZomlZChrs9QJGcnZGAJwBgiG3sGiLqGNDJ3SAYbk98mKBVTscFie5Up3CFkcYfvuAXp7PsgXvjJL7tuzvC/XZfn4SywNjzLwzE4iYfAWq0UjdvHtPJFqk/Q0GTfNQijxIoFtWPQiia0DPG0TKbCISHBQysBQIcpI0RUuFUfjkGBn8uQsjTBcLAkqjqmdP8Gu8TEyzQbHz57lpWSYlrLIGTErocnT2yLeN3wJO5sh6pgsxTuJnAo4BbwwAqNDJMESAkskZB0Pe2GBSOYxJg4QCY0kRhLhmC38WkKYKEIrRWKnMFaljDQKrSR+FK9/9vlDB3D+5kWC6d1EISz1ckxmfESxBEsL8L3/jPXkByk7Nr2BMr18RNTtEc3OEeg8oXbQjTb2UBk1v4Ac3o7X7GKNZVle7mFMDNGoxpAqABmiy4uI8jC652MOjuLuLSLiGHugSMo0MGULMfctiGL05JOE2WFYvEpSb9Ge+T6RzBGgyTx1BGd6O+bAAOIWJJfofi95u32dOd9A+Q1UyWTPUI7CbSRt38gW/aMi+m63Sy734H0wfmih9SPLuhdCbAP+ABih79D7Xa31fxBClIE/BqaAK8BHtdZ10Z/c/wH4CaAHfEJr/b3VsT4O/OvVof87rfULD+Oa3xREv9l4WBb9jS1wm72I+kKNkTAhm3YgM8GNr5jUVuh89k8xBofIfODDt1x01yClRMXJLRdTJccQhOt/E4Ts+OLnMQ88gVXZxtVuzHTOJnB30OtGpIQEK091LiTbu4aoLTPJCr+0y8d/bBvSGOFvv13DG5uiW+tybO4K+4yI3MsnGHz7u0mrCBiArMu8rxgvl6jkI+ZFiZSS6G4H07TxsWn6ipLZT+rzEknZ8gmFg5A2GVOhjAymACFNTEOQNQSGFESNKleOH2PvYIX6+Vf4spfhkl+iICNasWC8aPMT4ys8MemhA4NwocqScwg/PUbsFFExLDQ9upHGNCSVtKAoWxRmT5AZclhIilQvXGd4YoSUa2LJgCQxOP/SBSx0PwSCAK3QGpIEtFJ48avfoLQshnZMMtOoQ6lMp2NRSxWpmHXYuQuOv4z48n9CPvmTZEtjpA0Lzyng5zIkfkDshyRLiiAy8K41yVUmCU9fxX56G/HleczpSXTQwxooo7s9sk8+jpVOY4Y+sljE0gquHUOc/C5JZQeq4CAKOfADunPz9HYcQhdS0FjGCOvI+Rl0vkDGnUBmJm471ywBRVvgSYOCalOXNgh5R2PrjZIw91psamOru6DX692T1sftMDw8zPz8PKOjo8zPz99R6nsLt0UM/Aut9feEEDngJSHEF4BPAF/UWj8vhPgU8Cng14EPALtXf94C/O/AW1Y3Bv8t8DT9OOtLQojPaq3rm33Bbwqi32xr4WER/Rr+32/N8OWT8xRdya//9M+gZA/tDNx0TusP/k+C738HpMQcGSN15C23He/1HogAIXwS5fYdz3LnupJe/Ut/y/LXv0289yDGwjz1bZMMOQZ/e6lGkGimSikeH8lxreqRqDb1zGPEYwnlXAtHVImdAXYOCS4vdFGJYnTXEOe6I7yc9Ei9eIEfO/835JIemXe9j91PPknSaiMzQ5SVQag0lfx2lgKFTDQj+Qyh1qSUZFT2CSFEkDcFSvfvjAFbEgOOFBCHzH7lS/SaTQZHR/nCfMR8WMS1BJ6WpFJp9rkBH9xXoyI66G6Av9JjufRWvPQ2LDOFRHKt1l4VyAHbkJSkR1bXGBpOSOICo/veQx5FoiPQPqFXZbnaxOhEyCTCiCOk0JhoDKGJBYQKQpUQJhrb6H/Whcf20vjCi7QzGbQQLDcc7IEiOaOBPnQYfeok4ku/D1OHMXa8hWx+kIw0iR2TMONwLeiQTruM/tSPoTyf3Ifeh+r5GO97DkMnICSmZWFrhdYxhpCIxbOImRpq4iDQgKkpxPIC3ugzRKHCqF+ifaVG7AxjDQ9jTu3CTi/g7NsLV67cpLiotaYVKTSQtyRS9GPypZRFaXQ7qtfETdKYdopC6vaE+LC7170RNxGvxWaV133oQx/ihRde4FOf+hQvvPACH/7whzfh6n5A8IiS8bTW88D86t9tIcRpYBz4MPDc6mkvAC/SJ/oPA3+g+y0IvymEKAohRlfP/cJaG9rVzcKPA3+02df8piD6zcbDJHqlFF87fZ1MyiZQBktdyfbB4dedJ1LpvrtKCIR1Zy2xm4k+RppX+l3DkmGUTmMgyUoLIQRmIY9Rq1EwmsTDOxlPLdLwRvoEJQVNL8aWgpoeplXcQ80ahZKLEl1GnbOY3XMcqh8nLQwKzxwlNbyT499skyo7BJ5P+9m3cjk0eeVSxN6Zr3L42jehPEDuJz9CfnmRpN1i/OAhEsdERhHCsQkV2LJfoRUrjZHECNsiujaDTiKIfRa+/i2q09P0DJfjdoXOvCafMfG0QBgG24oRb5+ss8NZwTUFenGBmrOL5tC70GYG00whhKTW6NHwI8JEIQ1JOaVJWxHlq+eI7Qjr0I8Qib5L3hQRggjL8jBKe8C6TCeOSYQkjCGrEwQgVEKUGESJphcr7BuswIl3vY2LX/0W4egEcU8zX3OhqMnYHTj0BLp0HXn2JcS1E1Aah9G9qMwA5y7NMDq1i5FKAS0lZBy0NBAyAiJEHEJjETIluPp98DvoyiRKtxCDBXTzKklxAGYuE2ibZkMj7RHizjJOu4rRquNMjJHasxuxZxdxHK/PzzVy60SKFS9C9Gr9lsDFUQoZF0MKMFPIfIoR7o6HTcZvxLDAa9Hr9e5Z2OtnfuZnePHFF1lZWWFiYoJ/82/+DZ/61Kf46Ec/yu/93u8xOTnJpz/96Yd0xX8P+HvIuhdCTAFPAt8Chlc3AWit54UQa+6ScWDmhqfNrh673fFNxxbR3wc2o6nNrbC8vEyv1+Od+3fxjQtNxitpRku33sXnf/YXMSenMCoD2IcO33Hcm4leARqNgUYggL5NtjruW44w/a9+jcL0MiI/jxQhnhihnDap+zHDeRs/TtDCpGWMo80MQgqEUUBfm6XrRcTpYSYmItLZHrHZ5Z3TLb7wtTrDpRzjUxW+/N2QfCnF6fmAqXe9ly9dh/jLl3jrxa+SP/o4i989xeiZk7hhnd4zbyfbrKOOvUT43vfjzF6jd/kanXe8m9zydU75LpGVoj7yBH5T00gMxnKSFgIfyWgx4JmRBpNug4oborstuksOzdw78NxhLNPBl1lSUlBv+8y2AlpBXxynktYUaVOZfwXX8qD8FrBdIvpkmiCwkyqOPYxlDJE4Do1UGgwDYRr9kjoFCIUfabJJQs2PKDqvEr3h2Gw/fIBLZy+RlAcI2yFzZCjnJGXHQ2ybRA2PwNWLUG+jT/4NXsfjwOAEzrkLcNUFO42IQ7SdRkQB/fyMCFwXHYboQh4xNIH2euh0BlWr0clM4NmTqLTGnlsk7F4m/eRT2GPbSBsG7t7dGGkbpRRJknDu3DlKpRJJkqxvcpXSEHQJuk0WujF2b5Gh4TEmi/fWfOWNSsZJkjz0trRruB9lvD/6o1sbhl/84hc345J+mDEghPjuDf//rtb6d197khAiC/wp8Gta69Yd5vCtHtB3OL7p2CL6+8BmNLW5EVprLl68SL1ex3Vd3vfWHXzg6QTLlDe5Sm+6hkyW7E/89Iav91Wit9HJEEJ0cLCIkDhC3lQGlX/mCCL9sx3bAAAgAElEQVS5iKEXUaKIkRhM/fWfYz/xNN3sOBcMg+LoJH93sQaixt68JFVIM9fNkWSKRMNTCJFiPL1AKpxhuneBXxgLEFMT+ANDTI0YzM40GRswadgWvgEWmitTh1iuZwmFiW2MMbr3ANdmNWlyDB98jmuXE1xrgnj7OOHlAG2NoGOFkIJOYjLqhHjaIhQRU8WQZ4frVNIRBaODSEKCpZCWu49OZQrTMEjsCoYwKBiw0vI4V+3RDRWmKSjbirL0qYglCr05QjVK7ulD+EQkWqN1jNRdsimTJB4EBEmnA3EIWmMYEstIMCRo3RfdUUpx/voCnastBgYGqFQqOI6DUymzfVfCzKVZokKJqOmxHDv0XJuy65BJB7DnACrwCRtN8r0W2HmShctQGYTF8zC8G7pVKGQRmRza7yByRZQGZaTg+jXa4/vxyGFpgb/Qw9JtwrbGmF0mP2aStiWpPTuRe3etz50kSTh+/DiDg0NURscJkoSM2U8aTeuEigVe0qSrTIQsEKt7X6feyMl4jzJGvyWBewdsbjLeitb66TudIISw6JP8/6W1/rPVw4tCiNFVa34UWCtpmAW23fD0CWBu9fhzrzn+4oNf/uvxpiD6H+QYfRRFnDhxgkwmw5EjR/jmN7+J1hrH2rwFREpJFEXr/2tdBl0mJeF2tpeSO1BsBwy6Lx+n8Z3vow49hW6uELsDeNhkspJYgzJizp87Rxw7DO6ewtYZTNsh9HNYSwu0GSMuQV4buKzwkR2LVL0l8pUs1fGnOL0cEjVb7BuDpW6q3wQlZbIYSDIlG68bcrUdkBtM0Qk0cb1NbqRAx1cYSQcz5fJ4ukegNW8t19he8LD9Nralwevi9Qw6hf30BkeQhknkDIO0SEnIS83Fmscryz1SpkALQcWOKLoGBb9K/tpJOrOSwX/8k8QkhCohiTuYpqaQ7oLqd/kDoN1CaNXPtRcCWyQYQKwVftSvqbfyJSZyFZq1FU6cOIFSinK5TKVSYfv+nVw/cxE/lUU1u3Q8C99P41g2KdnDMU3SAzkQCQgNhTykU1BwwbHQQRbt2OilOv7YftS1q4TZIQLDRboG4byPJSK6HYl1+TJ6YieFvXvJjg1hDQwgzJsJ0fd9jh07xvT0NG6xwnw3hMhDWQnFfBnbtnEch5xjILoBvsgwkBaEYYhhGAghNkSyb9TM+B901/2bDo8u614Avwec1lr/Tzc89Fng48Dzq78/c8PxXxVC/D/0k/Gaq5uBvwb+eyHEmjTh+4B/+TCu+U1B9JuNzSqvW+uet2PHDkZGRm4ae8OWglarfVNvjzUJ4LsjALoEKk2MQUqYGEJgjwxhBQHlV75O6gNvY9y9TMOocL2TAZ3QbLfYvWMn5cogV2od/CBGN2ocW7zGzoFBuuUDYBcJTIPRhc+jGjWyWZCxYixd5ZOHV4guL2LmcxS3Z7i00GNPaobWWIavX0o4ONRlgIRvd2z2l7qMDvtc6CqeG6iTTUlUvMy2QYWuNyDw0F0b3apTd/fh5w8RlCoYQhGmRjCFhSMgb/at1WPzPWbbARlbUvViBjJQSkuyCxcZ0+dpnGoz9F/8AloKupFPELZIZxzSRguhDOJkiDUPXNJp9zPMhUQjMXSMbcREyiSJFXHST8EPLZfp6Wmmp6eJ45harcb8/DzNZhM3lcYNO0TSQmuI4oRIJXQdEyuTxxYhIomxUga652BoE+Wnkcog9hN0aIORRl3voeUQuqUxGvOEUmI0GohnjpJpt8iW8qRGKkjThOzrs7nb7TYnT57kscceo1gs0g4TCDv49UVO9SIKRZ+928awTYmdqzCe6xOf1pokSdbvjyRJ1gn/dqT4RrXoH6Yy3mux1b3uBwpvB34WOCGEeHn12L+iT/B/IoT4BeAa8I9WH/s8/dK6C/TL6/5LAK11TQjxb4HvrJ73W2uJeZuNLaK/D2zGojQ/P8/ly5df1z3vXohe1r+NbJ9BuVOoyjvhdm7+DW1MFNKcIVYCX0nQKXo6JistzJEhpv+H30QEc+SGOwgEKVOx6+Q3WRzfjjs+RtfNcGamRS9OsKTgvTsmMCbHWWm26WESd0MaXgc3VLQHnyORaSynzNjC50haLWIzDZHLVHqBqZEW6to8o/YwB4700H5AcnmFJw8Mg2Xin73IvpyLVS6ilhYRYYSXDJNIF7RDPXsEig5K2ggpiKwBkBJbQF6CKTRz7ZBzKz0ipfFjRawTBrMGo0mNbOgxWD1G43SHgY9+HKOQp95tEyY+bj6NJXwcGaKSQdCvJkLqdqv/W0iEBCE0LiEdYYOOCCIbw0643o0YXhWQMU3zpsYm3W6XlZUVWitVdLOOaTqYmQyy1+sTeeChbBvTTaMaPYxKBVVtY6ZsEiTG7AXUxCSy00VojdFqYh55GrdVJzs+jDVYRA4W7ziHq9Uqpy7PMLz7IMLt54hkLUkiQ66FHhkUfhjTDhMqN3gB1khvbe6uxffXyH/NCyalvMnaf6Na3Y/adb9l0d8Jj66OXmv9VW4dXwf40Vucr4H/6jZj/T7w+5t3dbfGm4LoH5a1cD9QSnHu3Dl6vd4tJXk3nOinY2T7DBgusncFVXwKzCxaKVr/6f8gOP4S2Q/9I9wfef89eCAUAolAo+jPZKX6sWVnbATBCLFeAh1x4RtXaH7289if/CSiVYVsRJwoDGGTKPBjTc6WhIaDSDTj5Txm5LBSPYKvc4Regk1MNszTGnqKRKYwUhVG5/+cujlJuO1x8rZFaubLtOwJ5PAY2bnj1MUIevApCuESNX8b4cgzuFGdrl1BGym0mcVUPpFVAGkhgJyElARLQtOLuFDzWeyGKK1pBQmuLRhMa4qiRUlVSX/7G9TPBoz98i9hDZZZqq+AJcjkHUwiXLPVd9mrV9XJdJKQtJtonaBFP+URYNxpsBTn0SrG9yMyqYhmkNCKEgr2zbefEIJsNks2m2VsbIyXX34ZO5dDJ4puq4ulE4Q0kFGEbkZILVErdQzDQrc9bNtG7t6LtbJI+rHHMLQiZRkY2SxiaGONS+bn57k6O8vwzv24SY+lpQZupYSVzlIsDyFDjwstsDNFMvadSe5GK37N2l+bT2ubgBsfexh4oyb6vRae5211r7sTNHAf+SFvFrwpiP4HBRtpLbvxRD8DnRpH+NfRdgWMfpw4npvF/+ZXEJks7U//4T0QvUQlY0jRwpUWiTKRSvelZ1frozWaSA9w5swZtIaCTgj+7guUf+49jGUCxq2YE4tjJNLgci/CaCdcqnqrivuCXWUXN7WdVgJeArrX4mo4iY6yIAxskdAsHKFr5pBmmqbh4A3GeGaByCiwGNqkKiMIK0NspoijLlJatLNToCMQJoY0SHQWU0BhdXbbAmpexMW6z0InxJGChh+TsiCfFkylWkhhUrp+iuSL38KzBtn2L/45Iu0wsziHW8iQSmkEirTZRGqbOBkEXl3kte+B54Nci033DYxtqQYv9yZJNHjdHjpvEyaKy82QJwaMW86BbrfLiRMn2L17N5VKpT/+avfFlWqVaq1O2OtRGByklE5TGh5GSoG5Sjpi99QG5s+r0FpTC2Jm5hdJmlWefvJJFjoejeUllnuaTqPBnj37ydgm+bGdPD7cnxOG3DiB3sraV0rheR7tdns9j+S11v5m4IfBdf8wm/Ns4YcfWzPnEWGjrWXvRsphrPjmuRVMQ/KWXc9hqC6YmfU4vVEZQJbKqEYd+8ATGxpzHTqL1lkMrUElq2X6AiFDEF06UYpGs0OhXGJ8/378sXGC2esMjEgMw8MBsn/2aTpvewdJVMTL2ggNCItWmNAOE04tdal6EQcGM0yVi1Au0o01rSDEb9Q4t9zFHirgOIKsGWEW9uH5Ab2ex+j44wSGhUJiSlCGS6IhIwHhkOh+7F0AcaIIY1jqhFxtBbT8GNeCVhDhmIK0LZhKt8FIke61sb/8dySzDdyDz1D54PtRtsnM9RnyAwXcVILCJCXrSG0RJ6O89tZRrSY68NCk+zF63Xfdj1pNHAPi2CSII+IwxLJDVgLJkhcx7N6sgVCv1zlz5gwHDx68SfJUCEEmkyGTybB9cpIkSajX61SrVa68NIPjOOuZ/HfuanjD170aG+9GCWeuzSOSkKmpaUzTZMw1iOIOPoKEHG0/XrfgTePByU1Kied5nDp1iscee4xsNntLa/9hEP9m4VG57h+Wt+OHDo/Idf9GxBbRPwA2mkS08dayd3fdf+nUIl88sYgQIAU8u+dmxTyZdqn85vPEC/NY2/ttQ+8leXAtkerVxVVjWnP0QpNEQzabIV12EAjSO6dJ75wm1hGKLq0LlzHOncfcfwBjPMuhYps5UzBXK6Iig1fqkuWuT9oyOV/zGM/ZvLLSY7ETsrfiMj0+ytjwMO0gIuy1qV9fYnmlipPLMzo8jCsFGUuidN8Vr1lVBVAaDWgBl+sBhoBrzYAg0bTDmHJK0YlWO6pZku3pDmDiqhjzuy+SmbmGf91j+Gc/RvbQfvwwZG7hOqWBInZKoBGkZLtP2NEo8PoOiPHyEjqKwRZo01z9vDVpI2HMVZyP7X5SXm0Jy3FIjBTnGiEZyyC7WmExPz+/Pk9SqTvXohuGwcDAAAMD/e+/1+tRrVY5e/YsQRBQLBYZGBigVCq9joyU1iz0YrxEMWALLpw9g5N2kTpg8dpFsnqCfGmQ4cm9NJfaSCdLMb25S0Wj0eD06dMcOnRoPfZ8o7X/2qS+OI7XQwE/KKT/KF33a161LdwGj1Dr/o2INwXRP4wbZCNJc0opXnnlFZRSG2wte3fXfaz0es5dcpuYlMxksXfuft213gk3xk9fu6j4vkcYKsxUDrBu6oAHoIVJQgF332Pk9uzE/qu/YueRnyLt2GRbdRrn54jyZZxdY7imjx8ZuOkCx+sB1xs+WRtOr3TJpQxemmsTJ7CzlKYVKjrFbbjFHJHf5ksnLxBqwY68jZ8qEkqLqWKKc1WPUGlSBnTDhEhBmMRkbEWQSOqBJutItlktlLZwkxBOfI/i9Yu0X1nGee97GPonz2INVmh1OtS7TQZGikhTYhBgywBbKuL41iQPkCzMo+MIbWmEaaF0f/MhhGD/kMPlnkEcCZYii929FQLHxYttTtZ8niinmJ+5SrPZ5KmnnrovF63ruriuy7Zt21BKrVv7Fy5cwLZtSpUBnEKJvJvGkJJulGCEHU5cmmPH0AAFI+D710MyhFxY6fFkUePmijyRLQCbew8tLy9z8eJFDh8+fMu48+2S+tZ+r6n03UsJ38PAoyT6LWzhQfCmIPqHgbVa+tuR91oN8sjICJOTkxteKO9Gyu85MIwUAsuQHN1d2ZQxb0fyWmvOnz+P1iF7942gtYXGQq4TfUhESICNRJJOOUz+N/90ddCYiCYr3/w70i9+H+/oUUZ3S45sk1yf6zE734B8AcO08KMAy8pwthHSCRMyhs/puQZWehDTsFgJIoxskSifw0Qxh0+96aGDGnMNB2FYuJbFYhAjBAjdrwrwYsGkG5PRXQytMZsdzPOv4Fy8QjDTRr7tLUz804+Q2bcbhabarOPFHuWhPIaIkUKTNlpInSK5A8kDhJcugFIoIcEwQau+7qAwGC/mKLkxS4GNlyREi1ewU3kCd4hWoPjq1RUGEs0TTzyxKcQhpaRSqZArlhmdUhAHXF5pMTNfJYxChiyFNi2Wl5fI21BMD+NkRshWe4QqhesW1sfa7E3y3Nwc169f56mnnsK27yzdfOP7eW1S372W8D0MPCqif5S5AG9obFn0t8UW0d8n7iSaU61WOXPmDPv376dU2li2843j3omUU7bB+w9voIuVipCtE6A1wtyJ1hqtNcFL30L1uqSffQfCdtYXzbUwxNrCvibkUywWmZ5+AnRfLvfVZV9hWtfx4iJSJyhcFPpVa1+YKCrk3/Ej9C4sUFxZZKTwJEaygPGdlzAGjqJVwjsP2fRqXRbDmPDyAqnBQeLQY7iUoRsZtMIQU0T4icJPTBwZYNkmlgKcAq4ZE0aKThgy4gQkcYLpWOQTH2lDauYyYWhiv/wt9HwPDJPMu9/OwE9Pk9m3B4Um1DGNThNpJxQLGUwRY4oAW3oIneuX0d22mqaP+PIF0BptO2jD7Gvwa4USJoaT5+nxmL/phsR+yCU5xrtmvsLi1HO0RBbDsmmlhzjbDJjI2mRNed8E68WKXqxwTcF8ry/BmzJMSuUSabNK5EdkEsXslVOEIk3LU3z/0hxP7M2wd/c+vEj1BXA2meC11ly5coVGo8FTTz1137Htey3he5h4mPX/N2Krhn6D2CL62+JNQfQP42a8FdFrrbl69SqLi4scOXLkrnHWW2Gz5HVl5xyydQoAJ61QyiB4+SWa//F3QCuSxQUyH/mZmxbGNaxlfe/YseMObSz7EXJLBAS4CM26pa9JCFBoBM5AiW3/9a+uPyuKx/DPfAn36h+SPXyA8tH3Yi1/n2pzDC+0eazSoGJ1uRrvQq7UmZjMQrtOGGUZ0zYlt0cYGFQcAyKJg49yTIxmC7oeqlxCf+Ev6dUj0iKkd2UJ23LIvv0o6XdPkZrahj00iEIRkxCoCC9o4aRMbEsACY7oYgrQyShK372kSbWaJEtLfc+I7ZLQ7yYAgJEBabNjwGZyxeXyUoIfa76R7OXd5/+C+R3vx0+PkGhY6CXUfI+sKSmnDHKOgS0EliEQq30JhIBktfYxUpowUQgNK0FCyhD0+uL61Pq1kRhhmwjNRCbFyeUF6p7C7c6x/5l3cmFumSBKsJ0Uly5dotvtUigUiCoVKpXKpmV5a605e/YsSZJsmtdiDXcq4fN9H601URStbwzeiJZxt9vdcILlFrZwK7wpiP5h4LWWdxzHnDx5Etu2eeaZZ+57Qdks1T0trT4raBCGjVIROvZXOzwJkl533eV540ZoLX568ODBuwh0GCTJMLZoYygDMFepKEQbyyQqi9Y2IYIU/UVWo9GmwcSv/zPi5RXs4SFiw6R95RX8P/2/kbksY//uX9P63B+Tbl9F1yLGPvhWorlj1Iq70C9dplSRRJNlulWFu9IhaS6gKiXkco/w4hWkgMKzz9CbvQAjQ8S/+OPUFxZoDVYYGCxRzqbROiIWCRAQRBGOmWBYJpYMsaQClUMleWBjVmd05RKq1+u/w3KlT/F6VYfAqYAQSOCd00Xq3Yh6O6Sts3zDeJwfufw5WlNvZ7mwj0hrIiVoxYpmW2F2Y9KmQClImRKl9TrZ919CYAoIEkXONmlFCrTGjNoYAvI65ML8Mll8kpEhWh0Px6/B4A4K+SIH3DxBosg7Jobs69e3Wi1WVla4evXqeghgYGCAbDZ7XxtmpRQnT57EdV327t37UC3gG619z/N45ZVX2Llz5/rmec0C/0HO5L8Ver3eFtHfDVvJeHfEm4boNy4DuzHcaHl3u12OHz/O5OQk4+MP1mVw04g+s4u+0rpG2RModZzU088SLy2i2k1SH/jQ6+LxV65coVarbTh+qlUWTfYmp7aUPkL0dfWFSJCrH7kiwidGYWDbBs74GABRHDG3cxvZf/7L7Dp0CCPlkHn2J/H+819SfHI/mf2Hmf/6CZJjn2XsA+8ltXOa+d99AaeQZ/AXf5ba57+AqvoM/5OPEi4sgdZkDu1HSLluVccowjim227jJx3ioIsUoFWE7Vg4Jtiyh1BpdNLfoNzNVX8jvO99Bx0FCCExd+wFFaMBQ2hUamz9vELK4skBwd+1JcIwaVDg8/LtPHXtDAfdl1mZfCcr1ihKmCj63eEEEk8pRJKgtECgMaTAlIIoUVgywUYQtpdxYp+cobm03KAsfHpuDqKANoIzs0toK4M5NMV4pYiUAtc2cG/YzEgpKRaLFItFAIIg6JfvXblCp9Mhn89TWbX2Xyv0dCvEccyxY8cYHBxkcnJyw5/ng6LT6XDixAn2799PodDPN7iTYM8POvFvWfQbxJZgzm3xpiH6zcaa635paYnz589z8ODB9UXlQcd9EKKfrfb43uU6j43n2D26EwC5lrhkGKR/4sOvi8cnScKpU6dwHIcnn3zygRY8pdKYBmSNOnE8iKRfoifNJXSSQQKxzmIDPa9HtddgYu8OSukcRr8dDPaObYz/s19aDwWM/tLHIUqQdp9cdv6Pv4UwJMIwGPvlTwAgEJhDAySrIYOIhIgYSb8Nr2F5ZEo2UkjiRKPCBkJKwtYyCysK1y2SzxfIZOx7sjp1HBO89O3+Ndg27NiOutovrUOATr+68bt27RpBdZmfOrSHL19p0e50CBP4tjjA6aDH7nPHmDK/ilkYJiqM0XMGiEIbS9qIpL+ImSpEqwQr6mIkMb7fo6LbXPQzWKakoyKElixrizE7j87kqdaqjBYyvOfgPrQGuUGhG8dxGBsbY2xsDK31urU/M9Nvob1G+vl8/nWfWRAEHDt2jO3btzM8PLzhz/NB0Ww2X1e2B7eO7b8RSvigr4q3FaPfwoNgi+jvE1JKZmdnieOYZ555ZsMZxBsZ98ZOc/cCpTR/+OUrRInixNUGv/bBvWRS5rqXYK0s6cZFzPM8Tpw4wfjYGEORj66twMDt4vIbgUUcbQc0xrpynMIkwBAplDaw0DQadfxkgVJlBIkmIsHAJCAgQSMwSGORoAhEgrQFKTQxisjWSBQ2YvXsBBO5GhsPiPp2L6bokmAitEAhMEVIEraJfZ9iLoMUg5Aaw01pqtUqFy9eotfrrdegl8vluyaNBadPkSz3u1HKQglZTqGv9tBCYpkWWFm01pw7d44oitY3UpVsiq9dtrheb5MEHl0Fx8UOTitNttEj01zBFctkRYAQGtPJEAY+YTqP1/NQmSFUr4rIVJgPXVwjIYwEVqZMJFKYAsoDw8ydPsPusQH27pgCbtsO4a4QQlAoFCgUCuzcuZMwDKlWq8zMzNBut8nlcuvEH8cxx48fZ8+ePZTL5ft7wftAtVrl/PnzPPHEE3eVi33QEr6HKa37Wmwl420Ami3X/R3wpiH6zXTdR1HEwsLCemvZzbzhH9R1bxgCP9IYpuiH6FfdlVprTp48uS6ykkqWCGunuLKg2bPnWaxvfInmFz6HMC0Kv/YvMccmHuBd3JyfD5JEDZIRLRKdZ25umdnZWZ55dgBf95X1Ta3QhGjhIVFobLS2iOkiRYymL20b4yNEgMIg0enV8/shAbSBEP0F2tIhEQamiLBRaJnQbta4PhP1Y8Wk0Lq/eKdSMD4+zvj4OEopGo0G1WqVS5cuYVnWuuLcrRbb3l9/DsIAAThH30rUm0erAlprTCdPkiScOHGCXC7Hnj171udKLmXxvr2DXK1nObXYotHuooIeKglpk0MCSzpLRgfYRHhhngG1QjPMkRcJOo4JrTJFHWO4OVRmAIuEXRMDJBgkUcjpUyfYOTX1UCxq27YZHR1ldHQUrTXtdpuVlRW+973v0e12GR0dRUr5yDLTFxcXuXr16j2V7d2Iey3he9QtareI/m7YitHfCW8aot8srLWWLRaLlEqlh9Lr/n6JXkrBz717mtMzTXaN5kjbxno88ujRo+ud0Y4f+z77syfRCPYPplC5FK2L58Ew0WFAsjj/gET/emiVI9ZZLly4QK/X48iRIxi0yRoNEpUFbSFEiCO7RDqNiYfQWSzZJdAukgSDGC08IiykiDF1hBIRSps4sodQLrHol+NJVcQSvb63IC5y6tRpMpkM+/YduON3JqWkXC6vW6Ke561bir7v36Q4p+ZmCV/+LloIpJsh967D+PNzKF3qZwdYOV566SUmJiYYGxu7xWsJpisu20tp6n7MUttnsenR9nzMpEAmUZg6wZAaV4OypylKgbSHSRkwXMoTaoOxvINtiHX9+U6nw6mTJ9i3b989l3feD4QQ5PN5oihiaWmJo0eP0uv1uH79OqdP9z/3tc2S4zib/vqzs7MsLi7et9jQa7GREr4wDB8Z4W9Z9Ft4UGwR/T3gxtayjUZjU8rgXosHLa8bLqQYLqRuWR+fy+XIZDL4fg+MFBlb0fMVx7/9EoXHHqewtEB6917sxw5t4jvqY60qIZvN8vjjjyOEQKkiqOL6OVrbGLqAKXxUUgIEhs6QNeqgHJQuYeFgGw2ENlGUcHSClO1VKzqDjQdaonUKdJae73P8+LHbku3dkE6nmZiYYGJiYl1xbmVlhQvnz1P58z8m1e0g0diPP4WTXqQXCvp+RJNmo86uQ7vu6r6WUlBxLSquxWPDOZTSBIkiVn3tA6XBlAIN2IbEkgIEyFtsWGq1GufOnePxxx9/pOQwPz/P7OzsukWdy+UYHh5Ga02n02FlZYUTJ06glKJcLlOpVCgUCg9EkmsJpK1Wi8OHDz803fnXWvtKKc6fP0+hUFh38wshHloJ35ZFvzFovWXR3w5bRL8BrLWW9TyPo0ePYpom7XabMAw3/bU2I+v+diI4YRhy4sQJKpUK6YkPI8Nl0vYgz+xyaTabrExOc61Ww3rllXUXv+u66CRGd7uI3OuTrjYCz/M4fvw427dvZ2Rk5A5nCrTKoXm1mQs6j4pzrIcCdA4dZ1fz6UX/8eSGdrH61ezkdrvNyZMnN82yXSs3q1Qq+N/6GtWrF1FAaKcInxpjoDtLM9iGRpBozfbRofuKUUspSMt7J60btfIfhuV8O1y9epVqtcqTTz75Oot6bYOZy+WYnp4mjmNqtRrz8/OcOXMG13XXrf170Z1Yy3uI45hDhw490uS5V155hWw2y/T09E2Z/A+rhK/b7T7ShMY3JLbK6+6INw3R36+LPQgCjh8/TrlcvqkO+E7KeA+CB826f31Tmj7a7TanTp1iYvsO3FwRDAvl9rOSJVAqldbJ0PM8qsuLnD17hqDbY/SLn8NpVMm880fI/cN/fE/Xs9aN7cZSp3vHa7+7u3+Xa3oATzzxxKaXJsXz12n+wX9EJArDNCn9w5+kuMtEh5JGZBEpgRAGIgnxff++hJPuBWtCTWulkY+qnemaRHIYhhw+fHhDpGaaJkNDQwwNDRmAf94AACAASURBVKG1Xg8nnTp1ijiO1639YrF42/HWekg4jsP+/fsfWVJckiQcP36cSqWyXi544332sEr4tiz6DWKL6G+LNw3R3w8ajQanTp1i7969613C1rBZ9e6vxf267u/UlGZxcZHLly+zbec+Pv3tJYKoxrsPDPLsbbTyXdGgYH+f6XGHrr+Tan2FIJWm+//9JZd37V+39u+W9HT9+nWuX7++oW5smwWtNdeuXWNlZYUjR45sqN77XpA06jR+59+jlpdACux9uyg+W8JI6oQo6kEawzARAmyTmwhsYGDggd3Vr8WNqnMbJdvNwBrZ2rbNgQN3znu4HYQQZLNZstksU1NTxHFMvV5ncXGRs2fPkk6n1639tSz6teTGYrHI1NTUJr+r22NNE2B0dPS2IaCHVcK3VV63hQfFFtHfBjMzM8zOzt62tezDsujvZwNxp6Y0Fy9epN1uc+TIES4seXhhgmNJzs61b0v0Ru8yGolIejglE/exA9gXzpH6qY+gpqdZWVnh2LFjaK3XST+Xy930uufOnSMIgn7S3SPo2Q39hfXMmTMAD6wHcCvEK0s0/7f/+f9n783DoyrvPu7vmSUzmZlksg3ZQ8hCCAlJSETBBXArSkZ8tA+L9VEqYF1qpa1asVWL2rq0T99XrX0fl0vRPuqjoiUJoChaN0oVFbKShOwJWWcmk8k26zn3+0e4D5N9O3MGkvO5Lq5LA5xzz0k4v/v+Ld8v3HW1gEKBgNhILPivVZCxNjhcLNyMBgNMGAAP5DIZUhNjsMigG5WuFqo5jWVZvu/B16pz3tDxufDwcCxcuFCw6yoUChgMBhgMBhBCeOvdyspKuFwu6PV62Gw2xMbGIj4+XrD7TobL5UJxcfG0NQGEcuGTTvRTRBLMGRcp0I+AZVlUVlZOai17rqTux6vH0+Y3rVaLnJwcMAyDhREMokLU6O534ZLF4zvfcYELoXB1gsjUIIGRCP7ZTsDtAhMwFJRovXWg5Dh633wFnYZIVGStQPCZSYT29naEhIQMGyfzNdSEJywsDAsXLhT8vq76WvS9/hLcTQ1gFAooY8Jg2Hop5EoH7A43ZPJAsIYrYXdbQQDIGCBUM5TxGC9d7d2cRk/7U123y+VCSUkJYmJiZq3GOB3ofePi4hAdPQVzpRnCMAy0Wi20Wi0SEhIwODiIEydOQKPRoLW1FWazmd8s+VI1zul0ori4GMnJyaOyetNlpi58UqCfAlKNfkLmTaCfygvUbrfzL8/4+PgJ/44vT/RTva73S2Lki6GsrGxU85tGpcBtly+adLaZC4yFS5UPMDKAUQxVxM8EeRAOMkcbCCOH6+A/oAJBQHM9EvP/A5YANaqrq/nNUUtLC9/Q50vo5120aNEEJjwzg7As7F/9EwP7PwDbbQHDMFAtiUTYDSsgCySw2wehVGmBqCvR0R8Cl8cMQgCVQoZgzeiywch0tdvtRnd3Nz+KptPp+AA2XmlkcHAQpaWlSElJmXXwmQ7030dqairCw6dmkSzUfUtLS5Gens43N9LTfnV1NZxO57CxR6EySPTzpqWlCT6mOB0XPmm8TmK2zJtAPxnTtZadbdPceEwldT9RPZ7OfC9duhTBwcFj/v2JgrzTzUIpl0EmGzvIyAZqoOirABgGgcsWYuBoGRitDr1g0NDQgOXLl0OnVGKgqgI9th5UWyxwOp0IDQ3lX8RCptRps19GRsa4n3cmEJaFu7EOAwf3wV15EpzLBUVIIHQrEqBbmQxOLsegfQABOgNguBxEHYH6+g54OAAgCNOpxhx/G4lSqURkZOSoUTRaGqGmMlRm1maz4eTJk4J/3smgEwxi35fq1o+8r0ajgUajQXx8PD/2aLFYUFtbi4CAgGGn/Zlkd6h/hVifdzwXvt7eXhw5csQnEz5zDulEPy7zPtDTWdyurq5pWcsKZSc71nUnCvT0BcCy7DDPbdqEZjKZZjxe9e9TZvyr2oJIvQqbL05AgGJ0QGY45xlXPILAtZdDvnQNOt0s2ju7kJubC5VKhd7X/j946mug02gRe++DIIEaWK1WmEwmnDp1ih+pioiImFWN2nucTKhmP0IIPA11sH/9TzgrK0D6esHIOehyYqDJjoUqwQAXCzgGHQgMTQYMF4MohqYXKlpsYDkChgApUdM/gY0cRXO73cNkZpVKJex2O3JychAUFDT5BQWCzub7YoJhInp6elBVVTWpJoD32CNwVuSIijN5n/anMpHQ29uLioqKUXr5YkEDfn9/P26++WY888wzyM3NFX0d5xWSBO6EzJtAP9aufjbWsr5K3U90+vCux3sHeY7jUFlZCYZhkJubO+MT84nGHujUCnTaHDD1OhEbNlovnNUuBggLMAqwmgTUuevhdnuGxrrcFsi7a6CQm8EGakDsdpDBAch1QUOnUnMnWM4JT9QiWOwOvkY98tQ6GbTJsL+/X5BmP8JxIIMDcFWdhPOHb+Hp6gTbVA/5okQEhLsRuCwOqoRIMMHBcDoH0O+UIyh6FaBPA2RD6fk+uxvNpkGAAxQKBukxsz8FKpVKREVFISoqCi0tLWhtbUVkZCT/vaabpZlayE4FKi0r9my+2WxGXV0dcnJypr2JGyly5C1prFAo+J83rVY76rnRzYXYm5qRdHd3Y9OmTdi5cyc2b97st3VIzA3mTaAfyWytZX01XjcehJAxTWnonH9UVBTi4uJm9cLPXhiCf5+yICJIhYigcUbn5Gqw+uVDzW8lZQgNDeU7vhWWHwAwCL4sBT1fmSBPyoTMMNSl7DndjP533gBYD5QZTUjcshWJiYlw9ffDUl+Llv4+9A3aERwczKddxzp9Uac9tVqN7OzsWX1e1tQFd9tpuGtPwVN3CmxnB2RRBqC3A8FrU6E0BEAWkYKA8ABwagPsve2wcQaEJV8CRjW8vPN1VRccHg4MAH2gAosWCHMSJISgvr4e/f39WLFiBb+poaYy3hayEz23mUAzRGLO5gNAR0cHn6mZrVnUSEljh8PBB/2BgQHo9Xo+G2Cz2VBbWzujzYWQmEwmbNq0Cbt27cINN9zgt3WcX0jNeBMxLwM9tZZdtmzZjOtvYnWTT1SPp/XatLQ0QVzCLkmLwPLEEKiUcsjHsDJ1ulnIZQycjiHHu6SkpGHNb0QRBMbVDSYoHLpb/xOgdX5PP5SecmiXaDB4ahDwDLnzEY8Hjrdfg7qzHQuTUqG96afo7e2FpbYGrUePgMTGIyIykj990U1NdHQ04uKmpsVPWA/AyECcDniaGsDoguH89ghYswncQB9AAE/jKWguvxgeVzu0GRrIL0yHLHQBFGFaQK4CBwatZgc8gXmITV026nvfZ3fjSJUFHAHkDHBhchgU8tn3IdBMjVwu52WDKd6mMrSWazab0dTUBLlcPuGpddJndiZjMjg46JMxxYloaWnhy0++2Fyo1ephBkb0udXW1sLpdCIhIQFutxsqlUq0f+PedHR0YOPGjXjiiSewfv160e9/XiMF+nGZN4GeutfV1tbCZrMJai3rKyYK8m1tbTh9+jRycnImteScDhrV2D8SdZ39OHi8HTLiQbquBxcuzxxVJ/aEXAiZywxOoT8b5AHI+09BFgholieBiQmEIvvqoc/Xb4WcmCGLDYe7oRYMxyGI84D88yOEOh2QgUV/TAzqv/oC8m+PwB5ugCH/PxCl02Lwq39CblgAVXomPK0tcDfUISAtHVAoYf/6c8jDwiGPjcfggX2QaXVglEp4ujoBpx2yYCWIXAuFohvq5FiwUQlQBvVCkZ8NBEdCrlGBAQei1MEhi0BlvQWGuDTEjSHfSwjB3n+3oNfuhowBggKVWJMxe7lSOqs+lXFBmUyGkJAQhIQM+QY4nU4+9T1d2126uVAoFFi2bPSmxlcQQtDQ0IC+vj7RhH/ocxscHIRKpUJOTg5sNtuwLAk97QstvDQWra2t2Lx5M/70pz/hqquu8vn9JOYP8ybQu91uHD9+HEFBQYJby/qC8ebjOY5DbW0t7Ha7qGI05S02uBwO9NsdCFuSOnYzmCwAnHq0ahhR6gFnO2ShBqiSVoIohwKSkq2FYmUcWIsVrqVXgVEowNl6EBDBQhaghbvHhLi4OCje/Tv6iAsh3e3oazuNqvffhsbcBZVGjZCf3Ab3R4UgHg/cJ4+DMcSCbagHq2ShOB0GyGWQubuhDAIYgxoKFaAMVYJwHOSGDABKBC6NBXSRAPEAjAJQaOHWJKHfwaHsZC2WLMkadxLjwA9tKG3pgeyMc9w1OdEICpxdUHA6nSgpKUFCQsIk3gBjo1KpJrTdpaf9kR3pVOKVqs6JGeSrq6vBcdyozIWv8c4gyOVyaLVaxMTEgBDCn/ZbWloAgA/6U+0lmQ5NTU246aab8Pzzz2P16tWCXnteIM3RT8i8CfQMwyAhIQEGg8HfS5kStB7vHeSpKExISIioL0SO46DzdMPldiNmQRgWRY4ud7hZDgoZM+aaOE0SiDIUkClAFGf/LgM3ZFEJkEfFQRa+YsidzSBHQG4ciN0OdewFaG5uhidcjaTMcDByJaKXpaC/vRmyWA6KUAbt7cVwdpqwYIkOgTEsoOMw2OKBLk0FRXQwBsr7oV4QCHnCIgRYzZAFx4EJiwHjtIEJ1AEg4ALCAUYFotCCqKIBmexMOrdu3I5vN8vhwx/acKTaDMIRyBgGWQl6XLpkdnPtdJxMqHLMWDVqs9mMmpoa2O12fuxRq9WivLwcsbGxM3L5mykcx6GiogKBgYFITk4WNcg3NDTwzncjMwgMw0Cv10Ov1yM5OZnviaATEEFBQXzgn21msKamBrfeeiteeuklrFy5clbXmtdIynjjwhAy4cOZM0+OECL4LOrRo0exatUqwV5ONFV/6tQpdHd3IywsDAaDAXq9HoODgygvLx9VF/c13opzUbHxUMiYUfXn4w1WHK02IyokENeviIFyqvVpTx/kAw0gAWHg1LEAw0BmPw1579AMeZNND6s7FJmxHGTdtZCpFODCcuDxBELRdAhEHQKFPhB9AwmQWb5ErzwYjNyFPksgYqJZqEMjAFkQGMYDhjgAeSBYdRzk9hZw6mhw6mgwnGNo88GcXfPp06fR3t6O7OzsMV/iXTYHin5oQ3V7LzgWICBIjtRh+xVJUCtnnmGhmgBijXXR+fOOjg50dHRAp9MhJiYGERERgpaDxoNmEGh5QixoCc/pdGLp0qXTLhMQQtDX1wez2QyLxcLrHVDr3em8DyorK3Hbbbdhz549yMvLm+5HOV/w+e7tglQDOfb/3ijIteTXvfwDIeQCQS52jjCvTvRCQzvvhUife9fjU1NTwXEcr49eXl4Oj8eDRYsWCa7QNREDAwNjNt2NpLjBiqBAJTp67DD3OhEdOsUgoQgCq88a9iVOHQMPS1BXVwNFUAwyFieB8fRBxnYDjAKcygBZoApM3BLI3D1g1dFQG1IhC3dD62gHq46GIiEGPeZSuDqtsLjVCA1bgAWhKqh0BjCKQHg0Z3XSifxsdzUNAHa7Hbm5uaO+rwNOD76pseDfpywYcLgBAshkQFZCKP5zZfysgrz3GJtYHd8ymWxI96C3FxdccAGUSiUvHOVLkSNgaANJVSjFzCAQQlBVVQWGYWZlxhMcHIzg4GAkJSWNUjecqpdBWVkZbr/9drz55pvIysoa989JTAFpjn5C5k2g9wV0ln7Wc9xjNN3J5XJERESgv78fGo0GixYtgtVqxYkTJ/jfoylXX0AV9jIyMiYVZ1kar8f3dd0I0wUgTHf2BOxwsfi60gQPR7A63QCtevIfN7vDidKKNiQmZvAGIkQZDE/E2mF/jg3JAzgnIFMDDAMuOAOcbjEgU0IPACFrAAARZ8apqpvMGBxsHRa8vL9vdGwvMDBwVBOaqdeB0mYbSht70Gt3w8MN9U3oAxVYs9SAi9MMY04pTBXq5y72GJvVakV1dfWw8gRVm2NZdpjIEXWSi4iImPVGhPYgJCYmipqdoo57arVa0DLBeOqG3l4G9LRPN0zHjx/H3XffjXfffRfp6emCrGN+I9XoJ2LepO6BodnjST7vtDh+/DjS09NnleYcr+mOBh6VSoXU1NRhJypaZzWbzXA4HLwpykQe3tNZT0tLC7q6upCVlTWl+iMhBIMuFiqFbFhav7ixB0eqTJAxQE5iKC5OO1u/HnR6IGMYqAPOBtuenh5UVlbO0rt+fGiq2mw2w2q1Qq1W82YyVVVVw8b2uvtdaLPaUXnahvYeO/rsLGQyBi43B6WcwaJILa7IjESkfuZBj7r8ud3uGaWQZ0NXVxcaGhqQnZ09aeCmTnI0Ve12u6fkGz8WVKd/8eLFgvQgTBV/2tt2d3fDbDajsrISe/bsQU5ODg4dOoTCwkKkpqaKthY/4vvUfUoEOfbf1wtyLfkNr0mpe4mzzFYdbzxTGrt9aE49Li5uzLSmWq3mlb9YlkV3dzfv4U1NUSIiIqY9EkRtXgkh01LYYxgG2jHG8vSBCshkDECAEO3ZDUOTeQCHSzqhkDPIz42BIViFjo4ONDU1I3NZFoJ0vslSjJRKHRgYQFtbG06dOgUiV8Ft6ketpQVmO9Bvd6Oz1wW9RoFeuwdKuQyBSjlSInVYkRKKhHDt0GebIdRiVqvViuryBwz1IHR2diI3N3dKPyPeTnILFy4c5Rs/VUljf+nlsyyLkpISGAwGUe1tgeHOhUuWLMHg4CBefPFFhIWF4eabb8bll1+OO+64A0lJSaKua04inejHRQr0s2CmxjYTzcfThqz09HR+LnqyNXh7ePf398NkMuHEiROQyWSIiIiAwWCY1NzD5XKhrKwMERERSEhIECTwJC7Q4oYVsWA5MkxOt9k0CIYBnG4OHVY7ek2nYe2xwaKIxXvHOnFBUhiyE4c++4DDg167G4Zg1axFaAadZycZmkwDYJ2D+LbKAk1oIjhOhr7OQXTZuqCReWBzy6HXquD2MIgNDURaTBBSooIQETw1s5qJoPVpqmYoFt4qezk5OTMuOY30jae2u+Xl5WBZdkzb3anq1guN2+1GcXGxz211p8IXX3yBl19+Gfv370dcXBz6+/vxxRdfnPOjvucFBCDsnEpAC8q8CvRUNEcoZmJsM54pDXC223umDVnepihJSUm8cAptMAsNDYXBYBiVbu3v70d5eTmSk5MFHT9kGGbMxry0mCA0dA0gUAkMmpsRoFMhcXEGir9rRUigEiVNPchODMGg04P9P7TB7mKRFKnFmqULYOp14kiVCUGBSly2JAIsR3CisQdKOYPliaGwDrhQ1mxDTFgg4sICcaTKDIYBlsQE4bs6KwAgMECGTksvzD19WGAwgJEp0GWzIz4iCAMeOWJDAxHpdkInd0HN2aBXyxCtkkEjDwSD2em9U+tToZ/1ZBBCeI18IUczR9ruejweWCyWYba7AQEB6O7uFrXREBjavBYXF4veCzAWhw4dwlNPPYWDBw/y2gg6nQ5Go9Gv65KYH8yrQC80003dT2RKU11dDZZlx+z2ninewim0uaqrqwvV1dXQarUwGAxgGAaNjY3IzMwUzalrgV6NTSujUVZahqgFkYiPj4eb5WAIUsHc50Rm/FB9ftDFwu5mERggh6nXCQAobeqBw83BNjiIjh4HzH1O1HX2gxAgVBuA8hYbOI6gs8eBnn4negZdAGFQ0dILlhCAELR0WMF6XIhaYIBaKYeMGdokyGQMVi2OgEohQ6g2gE/Nj1SaG6+hbzKoK5qvehDGg5YJqCueL0+QCoViWGNaQ0MDWltboVKpUFpaOm0Do5nicDhQXFyM1NRUvlTjL4qKivDcc8/hww8/PG90PM5LpDn6cZEC/SyYTup+PFMaX6TMx1srraPSFH9NTQ1sNhu0Wi1MJhMAzEgbfbrQDIL3S1gpl8GYFwPnmcAOAGG6AGTG6dFmteOCpKGxwuhQNVq77VApZdBrlLC72KExN2ZIvlevUaLN6kCgUoao0EA0m+2ADEiPC0blaRu6TCZkRSmhC09GWJAKhmAVPCyBboKJgJFKc7Shr7a2FiqVCgaDYdJudPrnxXZF81eZABhSnevp6cGqVaugUChG2e4GBQXxY2hCSszShr8lS5ZMqfzlS/bu3YtXXnkFBw8eFLX5cN5BCCCl7sdFCvSzYCon+onq8X19faioqEBKSgoiImanqDYdqHe9Wq1GTk4OPB7PqBOrwWDwyfw0HdsbK4MglzHDtPZlDIMVKcNfjkvj9IgKCYRKKYNWpUCwRomgQCUUcgaRejUMwSp02RzQn/m6IVgNBkCAnKCntRMZS8bQjp9GjBnZ0Ee70SsqKuDxeIaJHNF7tLa2oq2tDbm5uaL6KzgcDpSUlGDRokWipq5pL8DAwMAw1Tlv211vidnm5mbBbHdpw19m5mgvBjEhhOCtt97CW2+9hYMHD4qawZGQGMm8Gq/zeDyCeshTp7DxTkoTBfnOzk4+ZS5mc5LL5UJpaSkWLFiA+Pj4US9UemI1mUywWq3QaDT8iXW2QaqlpQUdHR3jKs75CrvdjtLSUiQmJvKz+b6AjlKZTCb09vZCp9Px/RjZ2dmi+RIAZ22Yp9rUKRRUt54QgiVLlkw5YFOJWbPZPMx2NywsbMqnfermKHbD30gIIdizZw8KCgpQWFjo17WcI/i82zAvKZx8+7gwbn/KW96UxuskzjLRiX68+XhqAdrX14e8vDxRBVJoynyiDIL3iZV2VJtMJpSUlAAA38U/nRQ/nRd3uVyC9iBMBVoXFyPgeY9S0bltp9MJhmFw/PjxGT27mUD1CMSS0qXMRrfe23aXEAKbzcbb7tLpkYlsd7u7u3Hq1CnB3RynCyEEL730Ej799FPs37/fr2uZVxBIqfsJkAL9LJDL5WPq53vX472DvMfjQXl5OXQ6HXJyckQdqzGZTKirq8OyZcumfMLw7qhetGgRXC4XzGYzn5alTWlhYWHjpvg9Hg/KysoQHBws+rw4/cxi18XpZ/Z2gRv57KZjHTsdTCYT6uvrRe9wp7PqtNdkNjAMM8p2l7rvDQwMQK/X889OoVAM+8wTzfH7GkIInnvuOXz77bfYt2+fX9ciIeHNvAr0QgeZkSf6iVL1g4ODKCsrw8KFC2dkPTpTCCG8xGpeXt6smp4CAgJ4bfKRTWneEqn0BedwOFBaWjpju9XZ0NLSgs7Ozll/5ulC5V3j4+OHzW2PfHY9PT18X4RKpeKf3WxOgK2trWhvb5+yEI5Q0Fl1XznfqVSqYc+OnvYbGhrAcRw8Hs+UVRx9BSEETz/9NKqrq7F3716/rmVeQgCwkmDOeMyrQC801NQGmDjI0wa0pUuXiqoIRrW95XI5li9fLmhj3cgU/+DgIEwmE8rKykAIgU6ng8ViQUZGhqhGPCPLBGLKylIToMnkXUdax9KGvsrKSl5elgrOTGX9hBA0NjbCZrPxvupiQRv+kpKSRBkdk8lkCA0NRWhoKE6fPo22tjbExsaioaFhmO3udEcfZwPHcXjsscfQ0dGBt99+W9RynASFgEjjdeMi/UTOAnqin6ge39zcDJPJJHrHNW26i4yM9Lnsp7dEamJiIlpbW9HQ0ACtVouqqiqEhITwXfy+fPl6y8pmZmaKWiagdfGZdHtrNBokJCQgISGBb+hrb29HVVUVL2k8nu85bX5jWRZZWVmibmzoGFtaWpqomzlgqBG2u7sbeXl5kMvlSEhIGHP0kc7t+6p0w3Ecfvvb32JgYACvv/66qJssCYmpMq8Cva9S9+OZ0lRWVkImk4l+sqRje2KLhdCTpdVqxUUXXQSlUsmnqU0mE2pra6FWq/kufiFrmE6nE6WlpT5LH08ENYgRoi7u3dDnLWns3QxJR9AIISgvL4dGo0FaWpqoGxt/jbF5j+5lZ2cP+3c1cvTRbrfDbDajurraJ7a7LMvivvvug1KpxCuvvCLqv3GJEUjNeBMyrwK90MhkMlitVrS2tsJgMAyrTZeVlSEqKkp0E42uri7U19dPq+lOCGiZQKFQDJudHpmmpl381MIzPDwcBoMBQUFBMw5UYwnwiIV3xkbouvhISWPa0NfQ0ID+/n54PB5ERET4XO1uJNTeVuwmR1qWYVl2lJXwWAQGBiI+Pn6U7W5NTQ3vXBgeHj6jvgiPx4N7770X4eHh+POf/ywF+XMBKXU/LvNqjp7jOLjd7llfx7seT+urZrN5WG06PT3db6fpZcuWidqMRdX9DAbDtDquqVKayWRCf38/9Ho9DAbDtDrR6ViVmBK+wNDzrqmpgdPpREZGhqgveqfTieLiYkRERIDjOFgsFgQEBPCZEl+OdNEO96nY2woJIQQnT56EUqlEamrqrDc2AwMD/Nz+dG133W437rzzTiQnJ+Pxxx8X7Hvf0tKCW2+9FR0dHZDJZPjZz36GnTt3oru7G5s3b0ZjYyMSExPx3nvviV4qmSW+n6NfGEa+2XW1INcKuPu9OTdHLwX6aTJR011zczOam5uh0WjgdDp5lTQhfOIngmVZ/iW4ePFivzSgzdakhXZTm0wmdHd3T0latq2tDadPn0Z2draoo0wcx6G8vByBgYFISUkR9TQ9XsMfTVObTCa4XC6+oU/In722tja0trYiJydH1I0kfd50zFPo502tns1mM3p6eia03XW5XNi+fTtycnLw8MMPC7qW9vZ2fmqC6mwUFBTg9ddfR1hYGHbt2oWnn34aVqsVzzzzjGD3FQHfB/qEMPLv31wlyLVUv9grBfrzGULImHPv0/n7Y9XjOY4bdrqjtXuaKuzp6YFOp4PBYBBc15vWpqOjo0XXMqen6YyMDMHrtLSL32w2g2XZYWYoAFBfX4++vj4sW7ZM1AYot9s9TFlQTKjy22R18ZGBS6vV8oFrpg2htPktKytL1OfNsixvhjPb+fyp4G27a7FY4PF4oFKpYDKZsHLlSmzfvh1r167Ffffd5/MN3vXXX4977rkH99xzD7744gtER0ejvb0da9euRXV1tU/vLTAiBPpQ8u/7rxTkiJBDvQAAIABJREFUWqqdH8y5QC/V6KcIlTIFhpvSuN1uXhzFWxBmpIlMX18fTCYTmpqahvl5zybNSlXf0tLSRDfMoPrtvhIp0Wg0WLhwIRYuXDjKDIVlWWi1WtGDPJXSFVs7Hjg7ojkV5Te5XD7ML76/vx9ms5lv6KN9EVPRlKdKjna7fVTzm6/xeDy8IU9sbKwo9xzLdreiogKvvfYa7rzzTsTExGDBggUwm80+HSdsbGzEiRMncNFFF6Gzs5PXZIiOjkZXV5fP7isxN5EC/SRMlKqnTWBJSUkTvvgZhkFwcDCCg4ORnJwMh8MBk8nEz03TF+90rDupVr4/GqJqamrgcDhEk7OlZijh4eEoKSnhx/S+//57XmzGYDD4tGZMu8zF1o4HhlK6p0+fntGIpndDH1U3tFgsaGxs5PsivFXmvCGEoKqqCgzDiD6u6HK5UFJSgoSEBJ/6E0yGQqFAcnIy+vr6sHv3bqxcuRIfffQRNm7ciIcffhhXXSVMutib/v5+/PjHP8azzz4rqu7GeY3UdT8h8yp1DwyluqfKREGeyqvOtgnM4/HwDWl9fX2TNqRRj2+bzYbMzExRa6Xec+rT1TKfLXa7nRdm8d5U0WZIk8kEj8czo03TZNDTtNiTDAD4BktfpMy9Vea6u7uhVCr5LJRarea/10lJSaJ+r2mzYXJysqiujmNhs9mwefNm7NixA7feeqvP7+d2u2E0GrFu3Tr8+te/BgCkpaVJqftJyIsPJUd/ebkg11Lfv09K3c8XJhLBaWhoQE9PjyDyqgqFApGRkYiMjBzWkFZXV8fPnBsMBgQEBIBlWVRUVEClUomulU/lbOPi4kSfU6e16YyMjFEnnJFiM94p/uDgYH7TNFO1MtqAJrbgEc2cuFwun6XMvVXmgLMNfVVVVejp6UFwcDDi4uL4fwNiQDd0/hDhGUl3dzc2bdqEnTt3YvPmzT6/HyEE27dvR3p6Oh/kAWDDhg144403sGvXLrzxxhu4/vrrfb4WibnFvDvRu1wuTPKZh5nSeL9gvQNtamqqT+uV3rKyJpMJHMfB5XIhNjZW9Llp2guwZMkS0V++VIwmKytrWv0M1AGNdvErlcppjZ/RccWenh7RG9CoJoFKpRK9q5+mzGNiYhAQEDCsE10ou+LxoNa6S5cu9bt/u8lkwsaNG/HQQw/hhhtuEOWeR44cwWWXXYZly5bx75Ynn3wSF110ETZt2oTm5mYkJCRg7969ovfkzBLfn+jjQsnRe9cKci31gwVz7kQvBXovJkrV2+12lJWV+e1EW1FRAYPBgMHBQV7TW4zRPSrAk5WVJXovQHNzMywWiyC6AN7jZ7QvgurJjwykHMcN81QXuwGNdpkvXLhQtPsC4+vWe9sVWywWwYSOvKGbSbGtdceio6MDGzduxOOPP478/Hy/rmWOIEKgDyFHf75WkGupf1s45wK9lLo/w0RB3mq1oqqqyi8njY6ODjQ1NWH58uX8SZSOT3V0dKC6uhpBQUH86J5QhhrU9Y7qiYs9N00V0LxV9maDt0oa1ZNvbW1FZWUlgoODeZU0hmF4W12xMyculwvFxcV+cfuj8/lLliwZ1Ww40q6YTkE0NzcLUiLp6elBVVWV6I2lY9Ha2orNmzfjT3/6k08a7SQk/IEU6DF+PR4YUqvq6OgQ3d+banr39vYiLy9v2At05PhUb28vTCYTGhsbp52iHguO41BZWQmGYQQLtFOFernr9XqfBdqRevL0+VEHtIiICERHR4sa5KlBjD9kfOlpeqq69XQKIioqii+RUGlehULBT0FMJWhbLBbU1tYiJydH1H9fY9HU1ISbbroJzz33HNasWePXtUhMEwLJvW4C5l2gZxhmWOp+IhGcqqoqcBwn2hgZhfYCqNXqSZvuGIaBXq+HXq9HSkoK7HY7TCYTTp48yWuhTyfFSgVhIiIikJCQ4JeGv5Fe7r6EPj+lUgmz2YwlS5bA4/GgsrISLpeLT1GPleIXChpox2o29DVU9Gimp2mGYRASEoKQkBCkpKTA4XBM2Uimq6sLjY2NWL58ud/922tra3HLLbfgpZdewsqVK/26FokZIvnRj8u8q9G73W7eQ55l2TFT9dTilWq3n6/d7SO15Cezi6Wnysl0AXwBnVP3R8PfeIpzLMvyeug2m40vkYSFhQlWyqCBVuweCOBso2NOTo5PRI+oOqTZbIbVah0mLWuxWNDW1obs7GxRy0JjUVlZidtuuw179uxBXl6eX9cyR/F9jT42hPzrjssEuVbg7w9INfq5wET1+N7eXpw8edIvKVQacIQSZfFOsXrbxdbU1IzqoqZ9CGLbjgJn59SzsrJEn1P3DnYjSx1yuXxUit9sNqOpqYkvn8zG67yjowPNzc0+UxeciLa2NrS1tfnEdY8yUh2SSst+//33cLlciIuLw+DgoKCaB9OlvLwcO3bswJtvvomsrCy/rEFi9hApdT8h8zLQjxfkaeObP05X7e3taGlpmZLE6Uzwtov17qIuKSmBy+UCx3E+0ayfjNOnT/NGHmKnb1taWtDZ2TmlYOddIqHqht4pampgpNfrp9TT0NzcDLPZjNzcXMEaKKcKFeFZvny5aCUp2tBnMpmg0+mwZMkSWK3WYZoHtCFSrOdx/Phx3H333Xj33XeRnp4uyj0lfAWRlPEmYF6l7gkhuPXWW7Fq1Spce+21WLBgARiG4WviHMchMzNT1Bcv1RLv7+/3y71ra2vR39/Pp1MdDse0g9Zs7m2323kjILEQ+t50CsJkMsFms01oYETv7XA4RLe3pfd2Op1YunTpOXNv74a+7u7uYZkAX2V4vv32W/zyl7/E+++/j9TUVJ/cQ4LH5+ma3Bg9+df2SwW5luYPH8651P28CvTAUD2uoKAABw4cAMMwuPLKK/HJJ59gw4YNuPfee0VNIVLDDI1GI7owCpWzHXnvkUHLF6N7dGPlD5tXKkYTEBAgiK/5SLwNjCwWy7CgFRgYiMrKSigUimEGSGJACEFlZSVkMhnS0tJEvzfVzJ/KvWm2xGw2w+FwTNjQNxOOHDmCBx98EPv27UNiYuKsrycxKb4P9NF68q9tlwhyLc2TH0mBfq5ACMHRo0dx8803IzExEb29vbjyyiuRn5+PvLw8n58wqQCPmB3mFGptGxMTM6ErmPfomcVi4Uf3ZmMgQxsdo6KiRLfVpRMFtMlSDGjQMplMsFqtCAoKQlJSkmBBaypwHIeysjLe2MYfGyu1Wj0jfwSO44bZPavV6mF6/NPl888/x6OPPorCwkLRf/7mMaIE+iNbLxbkWtpnDkmBfq5QXFzMd9rm5OSgr68Phw4dQmFhIUpKSnDRRRfBaDRi9erVgs/39vT0oLKy0i9OaLS7fSbWtnR0z2Qy8R7x0xndo6IsKSkpopuVUNW3xMRE0d3QqKxsdHQ0VCoVLyur0+n4oOWrhjiqtGcwGBAfH++Te4wH3WDo9XpBTs5UFpqe9lmW5ctMU2no+/jjj/Hkk09i//79ggoSbdu2DQcOHMCCBQtQXl4OYGiaYvPmzWhsbERiYiLee+89v2v3+xEp0PuZeRvoHQ4H+vr6xvSUdrvd+Prrr7Fv3z58+eWXSE1NRX5+PtatWzfrf6xtbW04ffo0srKyRBcIoWY5QriwjTe6FxYWNuZJlW5u/NHV39/fj7KyMr9srKhJy8jNDfWJN5lMMJvNkMlkw4RmhDh10w1GfHy86Ep7LMuipKTEpxsMt9uN7u5umM1m9Pb2Tjj+WFRUhGeffRb79+8X3Ef+q6++gk6nw6233soH+t/85jcICwvDrl278PTTT8NqteKZZ54R9L7nEb4P9FF6cuTWVYJcS/vnj6VAP9/gOA6lpaXYt28fPv74Y2g0GuTn58NoNCIuLm7KL2TajDQ4OIjMzEzRm89ol3dWVpbgp0fv0b3u7u5Ro3t0jMwfm5vu7m5UV1f7ZXSPZk+mIp3sdDr5k6oQXgYOhwPFxcV+yZ643W6UlJQgNjZWtLKU9/ijxWKBTCbjZavr6urwyiuvoKioyGdmMI2NjTAajXygnwPWskIiQqAPJkduFkboSPv/HJYC/XyG6r8XFhZi//796O3txbp165Cfn4/MzMxxX8gejwfl5eXQ6XSi+7hTgxaO45Cenu7zurD36J7JZILT6YRMJsOyZctEV32jI4vZ2dmiz6lbrVZUV1fPKHsyUmhGq9XyDZFTGUGcSLfe11C9/sTERNFFl7xxOp34+9//jrfeegs1NTXYtGkTbrzxRqxZs8Ynm82RgT4kJAQ9PT3874eGhsJqtQp+3/OEORXoGYZ5DYARQBchJPPM18IAvAsgEUAjgE2EECsz9LJ/DsB6AIMAfkoIOX7m72wF8PCZy/6BEPKGIB9gDOblHP1MYRgGiYmJ2LlzJ3bu3Inu7m4cPHgQf/nLX1BdXY3LLrsMRqMRF198MX9qpoIsCxcuFD196na7UVZWhtDQUCQmJoqywaDz0hqNBna7HRqNBnq9HnV1dXA6naJIynob8vhjTp1Ku85Uv32k0Ex/fz/MZjNKSkoAgE/xa7XaUc+Qii75wwWOZhH8ITY1koCAAMjlcgQHB6Ourg7Hjx/HwYMH8eqrr+K9997z69okfIC4gjmvA3gBwN+9vrYLwGeEkKcZhtl15v8fBHAtgNQzvy4C8D8ALjqzMfg9gAuGVo8fGIYpIoT4ZDconegFwuFw4J///CcKCwtx9OhRLFu2DKmpqXj77bdx8OBB0Tt8BwcHUVZW5pfmM9oAFhYWhoULFw4b3aN1/d7e3lm7no0FIQTV1dVgWVaUDMZIWlpa0NXV5ZMSCTB0YqZd/IODg3yKPzQ0FD09PbxuvS9ElyaCyif7I4swEkIIXnrpJXz66af44IMPRHkWUup+Qnx/oo8MJl9vvlCQa+n++tmkqXuGYRIBHPA60VcDWEsIaWcYJhrAF4SQNIZhXjrz3//n/efoL0LIHWe+PuzPCY10ohcItVqN9evXY/369WBZFr///e/x2muvIS4uDjt37kR+fj7Wr1+PyMhIn5+saeObP2x1J+puHykpa7PZYDKZUF9fD5VKxdf1Z5papdoAOp3OL7Pi9fX16O/vR05Ojs96MAICAhATE4OYmJhho2fUxCgpKUnU/g/gbLOjPxotR0IIwXPPPYdvv/0W+/btE71kQ9mwYQPeeOMN7Nq1C2+88Qauv/56v6xj3iDsiT6CYZjvvf7/ZULIy5P8nUhCSDsAnAn2tG4VC6DF68+dPvO18b7uE6RA7wOefPJJ1NTUoLq6GoGBgTh16hQKCgqwdetWcByHa665Bvn5+T4JRrQuLbatLnDWhW0q3e3ermepqakYHByEyWRCRUUFWJbl09M6nW5Kz4h2mE+mDeALqBgNwzDIysoSbYMhk8kQHh7OT5CkpqbCarUOS/FHRERM+RnOBFoq8Eez40gIIXj66adRXV2NvXv3iiapfNNNN+GLL76A2WxGXFwcHnvsMezatQubNm3Cq6++ioSEBOzdu1eUtUgIglnAZryx/uGRCb7uE6TUvQ9obGwclrKmEELQ1dWFoqIiFBUV4fTp07j88sthNBqxYsWKWZ3E6Imyr69PdCld4OzonhA+AW63m09PDwwMDEtPj5WKp2ljf3SYsyyLsrIyBAcHiy5GAwz9rPX09GDZsmXDfn5oit9sNvPPMCIiYtzxx5ngbXErdqlgJBzH4bHHHkNHRwf27Nkj+s+/xIT4PnW/IJh8+WNhYnPwi5/PudS9FOj9SH9/Pz755BMUFBTg+PHjWLFiBYxGI9auXTutFyeVlFWpVKJLqwJnzWGysrIEP0V5p6e9O9CpyAw9UfrDy52OkUVHR/sli1BTUwOXyzWpbj19hrSLPzAwkD/tzzS1TUsuvrK4nQ4cx+G3v/0tBgYG8PLLL4teupCYFJ+/kJYbgsiXNwoT6PUvfzGTQP9nABavZrwwQshvGIbJB3APhrruLwLwPCHkwjPNeD8AyD1zyeMA8ggh3YJ8iJHrlQL9uYHH48GRI0dQUFCAzz//HIsWLUJ+fj6uvfbaCWd/qZxtdHS06A1/NNg4nU5RDFpGisywLAu3243MzEyfzUePB+1FWLRokehjZBzHzVgzn6rL0WfIcdy0yyQdHR2806K/veRZlsV9990HpVKJv/71r6I3X0pMiTkV6BmG+T8MncgjAHRiqHu+AMB7ABIANAPYSAjpPjNe9wKAazA0XncbIeT7M9fZBuC3Zy77R0LIHkE+wFhrlgL9uQfHcSgvL0dBQQE++ugjqFQqrF+/HkajcVhJgKZO/THORBvftFqt6NoAwJC9bVtbGxYsWACr1Sra6B7gX6U9+tyDg4MFGZkcWSahCoehoaFjnoxbW1vR0dGB7Oxsv6fHPR4P7r33XoSHh+PPf/6zFOTPXUQJ9J9fnyfItUJf/VISzJEQF0IIWltbUVBQgKKiIlitVlx11VUICQnBO++8g0OHDone6ezvxre6ujoMDAwMUxgcb3QvPDxc0FRuT08PqqqqkJmZKfqcusfjQUlJCSIjI32SvfFWOLRarbyBjMFggEql4rUJsrKy/J4ed7vduPPOO5GUlIQnnnhCCvLnNr4P9BFB5J8bcif/g1MgbM9XUqCX8C89PT345S9/icOHDyMyMhIXXnghjEYjLr30UlG6jKnqmj+yCNQJTaFQTDix4D26Z7FY+NE9GrBmCq1LZ2dniz7RQBXnFi5cKJouAlU4NJvNGBwchEKh4Ec2xc7geONyubB9+3bk5OTg4Ycf9utaJKaEFOj9jNSaep7x2GOPgWVZ1NfXAwC++OILFBQU4KGHHsLSpUthNBpx9dVX+6QxjZYK/HWaLS0tRXh4OBISEiZ8uY8c3RsYGIDZbEZZWdmMatLAUMq6vb0dubm5otelqTGO2JsrrVYLjUYDp9MJtVqN8PBwtLS0oLKyEnq9nhc7EvN073A4cOutt2LNmjW4//77pSAvAWDoREo4zt/LOGeRTvTnGd999x0uuOCCUS84juPwww8/YN++fTh8+DDCwsL4un5UVNSsX4j+1I13Op0oKSlBQkLCrGWEXS4Xn+KfyugeIQQNDQ3o7e0dNcImBrQfwB/iR1QfQKFQIDU1lf8Z4jiOz5h0d3cLInY0FQYHB3HzzTfDaDTinnvukYL8+YPPv1E54Try2focQa4V8ea/5tyJfs4H+gceeAD79+9HQEAAkpOTsWfPHr6B6qmnnsKrr74KuVyO559/HuvWrfPzaoWB1rELCgpw4MABOJ1OrFu3DkajEUuWLJlWPdN7Pt9fga68vBxpaWmC+3lPNrpH5XQ5jpv2cxMCf+rW04ZQnU43qT6Adxc/y7IIDw9HRETElDzip0p/fz+2bNmCLVu24Pbbb5eC/PmFFOj9zJwP9J988gmuuOIKKBQKPPjggwCAZ555BidPnsRNN92EY8eOoa2tDVdddRVOnTrl9yYjoSGEwGw2Y//+/SgqKkJjYyPWrFkDo9GIiy66aMLO6anWxH0FdYATo1RAR/e6urp4m1OPx4OQkBC/fHaLxYKamhq/iNGwLDusTDId3G43LBYLzGYz+vr6oNfrERERMaumSJvNhs2bN2P79u3YunXrjK4h4VdECfSfXpMtyLUMbx+dc4F+zreq/uhHP+KD2cqVK3H69GkAQGFhIbZs2QKVSoVFixYhJSUFx44d8+dSfQLDMDAYDNi2bRsKCgpw9OhRXHHFFXj77bdx8cUX46677sKBAwcwODg47O+53W6cOHECwcHBWLJkieiBrrOzEzU1NcjJyRHlNMswDIKCgpCcnIzly5eDEAKNRoPBwUEcO3YMtbW1sNlsmGRjLAidnZ2oq6tDbm6u6EHe4/GguLgYCxYsmHaQBwClUomoqChkZmZi5cqViI6Ohs1mw3fffYcTJ06gpaUFDodjytfr7u7Gj3/8Y9x9990+D/KHDh1CWloaUlJS8PTTT/v0XhICQwDCEkF+zUXmVTPea6+9hs2bNwMYaq5aufKsf3FcXBxaW1v9tTTR0Gg0uP7663H99dfD4/Hg6NGjKCwsxFNPPYX4+HisX78eaWlp2LVrF/73f/9XdBEeAGhqaoLFYvGLxSztB/Dubvd4PLBYLGhpaeFPqb5qRDt9+jQ6Ozv98tnp2GRCQoIgnf0MwyA0NBShoaG8n4HZbEZFRQU8Hg+vezBeit9kMmHTpk3YtWsXbrjhhlmvZyJYlsXPf/5zHD58GHFxcVixYgU2bNiApUuX+vS+EhJiMCcC/VVXXYWOjo5RX//jH//Iu0b98Y9/hEKhwM033wwAY57M5lvdT6FQYPXq1Vi9ejUIITh58iReeOEFPPTQQ8jLy8MHH3wAo9GIpKQkUZ4NIQSnTp2C2+1GTk6O6DVxOjq4ePHiYUp7CoUCkZGRiIyMBCGEnzWvq6uDWq3m6/qzaVIkhKCxsRE2m82n7nfj4XQ6UVxcjOTkZJ/5BWg0GiQkJCAhIWHU5onqHuj1eqhUKnR0dGDjxo14/PHHkZ+f75P1eHPs2DGkpKQgKSkJALBlyxYUFhZKgf48QkQ/+vOOORHoP/300wl//4033sCBAwfw2Wef8QErLi4OLS1nXQJPnz6NmJgYn67zXIZhGNTW1uL777/H8ePHoVKpUFhYiAceeABmsxlXXHEFjEYjcnNzfRKAvZX2/KHXTxvfJrNa9T6lAmdnzcvKykAI4Uf3tFrtlD8D3eB4PB5kZWWJvsGh43sjNzi+ZOTmiXbxb9u2DX19fbDZbHj00UdFCfLAUIYvPj6e//+4uDh8++23otxbYvYQAnBSoB+XOV+jP3ToEJ555hkUFRUNc1XbsGED3nnnHTidTjQ0NKCmpgYXXnihH1fqf5xOJw4fPoxFixYhJiYGd911Fw4dOoTPPvsMubm5ePHFF7Fq1SpesMfpdApyX9oPEB4ejpSUFNGDvNlsRmVlJXJycqatMqjVapGYmIgLLriAHz2sq6vDN998g+rqanR3d4ObYL6X4zhUVFSAYZhJzWl8wcDAAIqLi5Geni66XwCF6h6kpqbib3/7G+RyOa699lq89dZbuPDCC0Wpl0sZPom5zJw40U/EPffcA6fTiauvvhrAUEPeiy++iIyMDGzatAlLly6FQqHgXzDTYe/evdi9ezcqKytx7NgxXHDBUKNmY2Mj0tPTkZaWNuye5zqbNm0a8+t6vZ4fbXK5XPjyyy9RUFCARx55BIsXL0Z+fj7WrVs3I913eppMTk6GwWCY7UeYNm1tbWhtbUVubu6slQUDAgIQExODmJgYsCwLq9WKzs5OVFdXQ6fT8ZK8VHCHWtyGhIQgMTFRgE8zPXp7e1FRUeGX8b2xqK2txS233MJvKIGhsbqTJ0/6/N5Shu98Z+420gnBnB+v8yWVlZWQyWS444478N///d/DAr3RaER5ebmfV+hbOI7DiRMnUFBQgI8//hh6vR7XXnstjEYjYmNjJz0R0UDjDzEYYOj7ZLVafa7dTghBX18fL8krl8sRFhYGk8mEmJgYvzQ8Us3+rKysYZkuf1FVVYWf/vSn2LNnD/LyhDEnmQ4ejweLFy/GZ599htjYWKxYsQJvv/02MjIyRF/LHMTnqZHsEC35aI0w36vYou/m3HjdnD/R+5L09HR/L8GvyGQy5OXlIS8vD48//jgaGhpQWFiIO++8EwMDA7jmmmuQn58/ZkrabDajtrYW2dnZogca76a/7Oxsn6fLGYZBcHAwgoODkZycDJvNhtLSUigUCrS2tsLhcEzYfS40FosFtbW1yMnJEV2zfyzKy8uxY8cOvPnmm8jKyvLLGhQKBV544QWsW7cOLMti27ZtUpCXmDNIJ3oBWLt27agTfUZGBhYvXozg4GD84Q9/wGWXXebnVYqLxWLBgQMHUFRUhNraWqxevRr5+fm4+OKL8T//8z8ICQnB5s2bRTHi8YbWxNVqtV/6AUY2vtHuc5PJ5PPRPQDo6upCY2MjcnJyRH/2Y3HixAncddddePfdd+f9xnkOI8qJ/sPLhJmQiDvwvXSin29MZXRvJNHR0WhubkZ4eDh++OEH/Md//AcqKip8YjRzrhIeHo6tW7di69atcDgc+PTTT/H+++9jx44dCAsLw69//Wu43W5Rgw01xomIiJiRGMxsGUu33rv73FtD3nt0z2AwCPKc2tvb0draiuXLl4tuzDMW3377LX71q1/hgw8+QGpqqr+XI3EeQ84I5kiMjRToJ2Gy0b2xUKlU/Ex1Xl4ekpOTcerUKf7EP99Qq9W45pprUFhYiA0bNmDLli04cOAAnn/+eURHRyM/Px/r16+HwWDw2Qmb2rwKYYwzE3p6elBZWYmsrCxotdox/4xMJuNH9wghvIZ8SUkJAPBBX6PRTPs5tbS0wGQyYfny5eeEzPORI0fw4IMPoqCgwC+NiBIS8wkp0PsAk8nEp17r6+tRU1PDC3HMV44ePYqUlBT85je/AcMwvEhPdXU1CgoK8F//9V9gGIav63u7pc2WwcFBlJaWim7zSqH9CDk5OVOWtGUYBlqtlh/fc7lc/HXsdjvCwsJ4gZnJegyo+54/RIjG4vPPP8ejjz6K/fv3+6URUWIuQiSb2gmQavSzYN++ffjFL34Bk8mEkJAQ5OTk4OOPP8YHH3yARx99FAqFAnK5HI899hiuu+66aV17vNE9YG667hFC0NHRgaKiIhQVFaG9vZ0X6cnLy5vxKZR29mdkZPildNLR0YHm5mZBa+Isy6K7uxsmkwk2mw1BQUH86J63bC4hBLW1tXA6nX6Z0R+Ljz/+GE8++ST279/vl8yKhF/weY0+K1hDDlyUJsi1Fn5aPOdq9FKgP0cZb3Rvvrju9fX14dChQygqKsKJEydw0UUXwWg0Ys2aNVPuFKcOcP4aIWtpaUFXVxeys7N9pltPCEFvby8/uqdUKnlJ3qamJgDwi/veWBQVFeHZZ5/F/v37/aKZIOE3pEDvZ6TU/TnKeB3I47kUhaJmAAAR1klEQVTuUYGRuUJQUBA2btyIjRs3wu124+uvv0ZBQQF2796N5ORk5Ofn45prrhnXo56epIUQwpkuhBA0NDSgr68Py5cv9+lJmmEY6PV66PV6pKSkwG63o6urC8eOHQPDMIiJiUFfXx+CgoL8Guzff/99vPzyy/jwww/9psAnMbeRtO7HRwr05xnz0XVPqVTiiiuuwBVXXAGO41BaWoqCggL8+Mc/hkajwfr162E0GhEfHw+GYVBUVIS4uDi/OMDRGX2WZZGVlSV6cFWpVOjp6UFCQgLi4uJgsVjQ1NSE/v5+hISE8KN7YqXxCSF4++238eabb+LgwYN+EUYSkkceeQQRERHYuXMnAOB3v/sdIiMjce+99/p5ZfMbSet+YqRA70dmMro33zW5ZTIZcnJykJOTg9///vdobm5GYWEh7rnnHvT09CAkJAQcx+Ef//iH6EGe4zicPHkSKpXKL8Y8LMuipKQEBoOBN2iJiopCVFQUOI7jXfdqamqg0Wj4FL+vMh6EEOzZswcFBQU4ePDgOSGzO1u2b9+OG2+8ETt37gTHcXjnnXdw7Ngxfy9LQmJCpEDvR2Yyuidpcp+FYRgsXLgQ9957L+666y5s3boVPT090Gg0WL16NS699FIYjUZccsklPp8bZ1kWpaWlCA0N9cu4mNvtRklJCWJjYxEdHT3q92UyGcLCwhAWFgZCCO+6V1JSAoZhhrnuCQEhBC+99BIOHz6M/fv3T3na4FwnMTER4eHhOHHiBDo7O7F8+XK/THJIjEaaox8f/7fhSkwLyXVvbH7+858jNzcXH374Id5//3189913uO6661BYWIhLL70U27dvx759+9DX1yf4van73oIFC/wS5F0uF06cOIGEhIQxg/xIGIaBTqfDokWLsGLFCixbtgxKpRI1NTX45ptvcOrUKVit1jGzR1OBEILnnnsOX375Jfbt2+ezIL93715kZGRAJpPh+++/H/Z7Tz31FFJSUpCWloaPP/5Y0Pvu2LEDr7/+Ovbs2YNt27YJem2JGUIICCfMr7mI1HV/jjLe6B4wlNp/7bXXoFAo8Oyzz+Laa6+d8X12796NV155he+CfvLJJ7F+/XpBPoOY0IazsWBZFt999x0KCgpw+PBhGAwG5OfnIz8/H5GRkbNKsTudTpSUlCAxMRELFiyY8XVmisPhQElJCVJSUgQ5WU51dG88CCF45plnUFlZibfeesunjZD+mkxxuVxYtmwZ3G43ampq5tzEiw/weQ1rmS6QFOSkCHKtlH+Vz7mueynQz3N2794NnU6H+++/399LEQVCCGpqalBQUIADBw7A4/HgmmuugdFonPYYGhXiobr1YkPvv2TJkhlZBE/GeKN7BoNhzBFHjuPw+OOPo62tDa+//rpoPRIjvSaeeuopAMBDDz0EAFi3bh12794t6GTKnXfeiZCQEDz99NOCXXMOI0qg37csWZBrpX5TMecCvVSjl5hXMAyDxYsX4ze/+Q0eeOABmEwmFBUVYffu3WhpacHatWthNBpx4YUXTnhS6+vrQ3l5ud+EeKhufmZm5riZjNky1uieyWRCRUUFWJZFeHg49Ho9v8n53e9+h76+Przxxht+PeX6ejKF4zh888032Lt3r2DXlJglRBqvmwipRi+BF154AVlZWdi2bRusVqu/lyMaDMNgwYIF2LFjB4qKivD1119j9erV+Pvf/45Vq1bh7rvvxocffgi73T7s73V3d6OiogJZWVl+CfI2mw3l5eXIysryWZAfi8DAQCQkJCAvLw/Lly+HVqvFu+++i+zsbFx11VWoq6vD3/72N0GD/FVXXYXMzMxRvwoLC8f9O76cTDl58iRSUlJw5ZVXSkY8EucN0ol+HjDRGN9dd92FRx55BAzD4JFHHsF9992H1157zQ+r9D86nQ433HADbrjhBng8Hhw5cgSFhYV44oknkJiYiPz8fLAsi3/84x949913/eLl3t3djVOnTiE7O9uvnexKpRJRUVG48847UV5eDpfLhcjISKxatQqpqal48sknBQmE59pkytKlS1FfXy/ItSSEg0A60U+EFOjnAVN9Wd5+++0wGo0+Xs35gUKhwNq1a7F27Vrew/7xxx/HV199hYyMDLzyyiswGo1ITEwUbV7eZDKhvr4ey5cv590R/Ynb7cadd96JpKQkPPHEE5DJZCCE4OTJk4iIiPDbujZs2ICf/OQn+PWvf422tjZpMmU+INnUTogU6Oc57e3t/EjWvn37kJmZ6ecVnXvIZDJ8/fXX6OvrQ21tLWw2GwoLC/GrX/0KVqsVV155Ja677jpkZ2f7THGuo6MDLS0tyM3NPSe85F0uF7Zv347s7Gw+IwQMpcgzMjJEWYP3ZEp+fj4/mZKRkYFNmzZh6dKlUCgUgpcTJCTON6Su+3nOLbfcguLiYjAMg8TERLz00ktTmsWeb7z++uu46aabRp2ke3p68NFHH6GgoAAnT57ExRdfjOuuuw6XXnqpYKNlra2t6Ojo8Kk5znRwOBzYunUrVq9ejfvvv39eKTNKzAif/4BkatRk7+JEQa61tKR6znXdS4FeQnAOHTqEnTt3gmVZ7NixA7t27fL3kkTB5XLh888/R0FBAY4cOYL09HQYjUb86Ec/mnHTXlNTE7q7u5GVlXVOnEoHBwdx8803Iz8/H7/4xS+kIC8xFXz+Q5KhUZP3UhIFuVZmmRToJSQmhGVZLF68GIcPH0ZcXBxWrFiB//u//8PSpUv9vTRR4TgOP/zwAwoKCvDJJ58gNDQU+fn5MBqNiIqKmjRAEkJQX1+PgYEBZGZmnhNe8v39/diyZQu2bNmC22+/XQryElNFCvR+xv95QIk5xbFjx5CSkoKkpCQAwJYtW1BYWDjvAr1MJsOKFSuwYsUK/OEPf0BdXR0KCwuxfft2OBwOXqRnyZIlo4K4twPesmXLzomAarPZsHnzZmzfvh1bt27193IkJIZDAI7z9yLOXfx/TJCYU7S2tvLOacD8sNGdDIZhkJKSgvvuuw9ffPEFDhw4gIULF+KPf/wjLrnkEjz00EM4cuQIPB4PPB4P/vKXv4AQgvT09HMiyFutVvznf/4n7r77binIS5yzcJwwv+YiUqCXEJT5bqM7FSIiInDbbbdh3759+Oabb3DllVfinXfewcqVK3HJJZegoqICcXFx58RzM5vNuPHGG3H//fdjy5Yt/l6OhITEDJBS9xKCItnoTo/AwEBs2LABV199NTZu3IhFixYhICAA69atQ1xcHPLz83HttdciIiJC9MDf0dGBTZs24bHHHkN+fr6o95aQmA4EgKSXMz5SoJcQlBUrVqCmpgYNDQ2IjY3FO++8g7ffftvfyzrnuf/++3HDDTdg+/btAMALzxQUFOCmm26CQqHAtddei/z8fCQnJ/s86Le2tmLz5s145plncPXVV/v0XhISs0aq0U+I1HUvITgffvghfvnLX4JlWWzbtg2/+93vBL1+YmIigoKCIJfLoVAoRnmRn4+43e5xhXAIIWhvb0dhYSGKiorQ2dnJi/Tk5uYK3pHf1NSEn/zkJ3j22WexZs0aQa8tMS/xeSpqqVpN/ndhoiDXuuDU3Ou6lwK9xHlHYmIivv/+e7/KrPqT3t5efPTRRygqKkJJSQlWrVoFo9GI1atXz1oat7a2FrfccgtefPFFQW1dJeY1Pg/06Wo1+Xt8oiDXurB27gV6KXUvIXGeERwcjM2bN2Pz5s1wuVz46quvUFBQgIcffhiLFy+G0WjEunXrpu1RX1VVhZ/+9KfYs2cP8vLyfLR6CQkfIKXuJ0Q60UucdyxatAihoaFgGAZ33HEHfvazn/l7SecEHMehuLgYBQUFOHToEIKCgniRntjY2Anr+uXl5dixYwfefPNNZGVlibhqiXmA70/0KjV5PS5RkGutrJ97J3op0Eucd7S1tSEmJgZdXV24+uqr8de//hWrV6/297LOKQghaGxs5Ov6/f39uOaaa5Cfn4+MjIxhdf0TJ07grrvuwrvvvov09HSfruuBBx7A/v37ERAQgOTkZOzZs4fPPDz11FN49dVXIZfL8fzzz2PdunU+XYuEaIgS6F+LSRTkWhc3SoFeQuKcYvfu3dDpdLj//vv9vZRzGovFgoMHD6KwsBC1tbX4/9u7v5Co0jCO4993nV0HiiWpdIdcVkPXRUO8cXeKLcI/oTgosVDOGEMIXQRe5UVz0UVdBONeLrpYUGBXC/1jlojSiqmLQN0LhQy0WmVXnLUNC0qyf5y9iIZ2t6YxZ+Y4x98HhDkzcuYRhIfned/3OVu3bsXn8+Fyuejs7OTMmTMpeX78h/T391NTU4PL5eLgwYMAdHV1cfv2bfx+P0NDQ8zMzFBXV8fExMSymO8vS5b2RP9Nrts68UVRSu71/R/OS/QamCNZZX5+nsePH8df9/f369G6SVi7di3BYJCzZ88yODhIY2Mjp0+fpq2tjUgkkpEkD7Bjx474E/i8Xi/T09MARCIRWltbyc3Npbi4mJKSEoaGhjISk4jTaTOeZJXZ2Vl27twJwMuXLwkEAjQ0NNgcVXZxu900NTXR1NSEZVm2TeA7efIku3fvBl6f2/d6vfHPNDpZFkWb8RJSRS9JGx4eprKykoWFBebn56moqODWrVsZjWHjxo2Mjo4yOjrK2NhYSs7ot7e3k5+f/6/OwNzcHPX19ZSWllJfX8/Dhw+X/D3LUTqSfF1dHZs2bfrfTyQSif/O0aNHcblctLW1ARqdLEtjoVn3iaiil6RVV1fT3NzMoUOHePr0KXv27HFE23zv3r10dHQQDAbj74XDYWprawmFQoTDYcLhMF1dXTZGmT2uXLmS8PO+vj4uXLjA1atX48lco5NlSVTRJ6TNeLIoz58/p7q6Grfbzc2bNx2zWWpqagqfzxfvUJSVlRGNRvF4PMRiMbZv3874+LjNUWa/S5cuceDAAa5fv8769evj74+NjREIBOKb8Wpra7lz545j/r9WuLS3Zso+dVu964pScq+av5y3GU8VvSzK3NwcT5484cWLFywsLLBq1Sq7Q0qL2dlZPB4PAB6Ph/v379sckTN0dHTw7Nmz+Px8r9dLb28vFRUV7Nq1i/LyclwuFz09PUrysigfKFpXNFX0sijNzc20trYyOTlJLBaju7vb7pBS4r8V/Zo1a3j06FH887y8PMeu04ukWdor+q8/dVs/532VknvV/z2hil5WrlOnTuFyuQgEArx69YotW7Zw7do1ampq7A4t5QoKCojFYvHWfX5+vt0hiYh8FO26l6QFg0HOnTsHQE5ODoODg45M8vC6c9HX1we83jzW0tJic0Qi8l6Wdt0nokQvK57f72fz5s2Mj49TWFjIiRMnCIVCDAwMUFpaysDAAKFQ6KPv/67je4cPH2bDhg1UVVVRVVXFxYsXU/GniKxYSvTvpzV6kTS7ceMGq1evJhgMxvcAaHSvrCDpX6N3ua2fPk/NGn3jQ63Ri8gibdu2jampKbvDEHGsNwNz5N3UuhexSXd3N5WVlbS3t2tHv8hSaI0+ISV6ERvs37+fe/fuMTIygsfjobOz0+6QRMSh1LoXsUFBQUH89b59+/D5fDZGI5Ld1LpPTBW9iA1isVj89fnz5x3xzAAR26h1n5AqepE08/v9RKNRHjx4QGFhIUeOHCEajTIyMoIxhqKiIo4dO2Z3mCLiUDpeJyIi6ZT243Uln7itH3NTc7zuhwUdrxMREVlWtEafmNboRUREHEwVvYiIZDdLFX0iquhFRCSrvWndZ2rXvTGmwRgzboy5a4z5+AdhZIgSvYiISJKMMTlAD9AIlAN+Y0y5vVElpta9iIhkvQy27r8F7lqW9TuAMeYXoAW4nbEIFulDiT7txyJERESWYpJnl9uYWJei27mNMb+9dX3csqzjb11vAP5863oa+C5F350WquhFRCSrWZbVkMGve1cBvKxnzmiNXkREJHnTwJdvXRcCMzbFkhQlehERkeQNA6XGmGJjzGdAK/CrzTElpNa9iIhIkizLemmM6QAuAznAScuyxmwOK6EPzboXERGRLKbWvYiIiIMp0YuIiDiYEr2IiIiDKdGLiIg4mBK9iIiIgynRi4iIOJgSvYiIiIP9A69t2xAUWl98AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 648x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatter_plot_3d(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate derivatives (vectorized version)\n",
    "dx = lorenz_forced_odes_vectorized(t[:-1], x.T, uf, sigma, beta, rho).T\n",
    "assert dx.shape == (5000, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Identify system dynamics using sparse regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (i) Using SINDy recursive least-squares method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "lamb = 0.025  # sparsification parameter lambda"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_u = np.hstack([x, u.reshape(-1,1)])\n",
    "assert x_u.shape == (5000, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "poly_order = 2\n",
    "theta = polynomial_features(x_u, order=poly_order)\n",
    "assert theta.shape == (5000, 15), theta.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Estimate sparse dynamic model\n",
    "xi = sparsify_dynamics_lstsq(theta, dx, lamb, n)\n",
    "assert xi.shape == (15, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0.        ,   0.        ,   0.        ],\n",
       "       [-10.        ,  28.        ,   0.        ],\n",
       "       [ 10.        ,  -1.        ,   0.        ],\n",
       "       [  0.        ,   0.        ,  -2.66666667],\n",
       "       [  1.        ,   0.        ,   0.        ],\n",
       "       [  0.        ,   0.        ,   0.        ],\n",
       "       [  0.        ,   0.        ,   1.        ],\n",
       "       [  0.        ,  -1.        ,   0.        ],\n",
       "       [  0.        ,   0.        ,   0.        ],\n",
       "       [  0.        ,   0.        ,   0.        ],\n",
       "       [  0.        ,   0.        ,   0.        ],\n",
       "       [  0.        ,   0.        ,   0.        ],\n",
       "       [  0.        ,   0.        ,   0.        ],\n",
       "       [  0.        ,   0.        ,   0.        ],\n",
       "       [  0.        ,   0.        ,   0.        ]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Coefficients found by sparse regression\n",
    "xi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y1</th>\n",
       "      <th>y2</th>\n",
       "      <th>y3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y1</th>\n",
       "      <td>-10.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y2</th>\n",
       "      <td>10.0</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y3</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-2.667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>u</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y1**2</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y1*y2</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y1*y3</th>\n",
       "      <td>0.0</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y1*u</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y2**2</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y2*y3</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y2*u</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y3**2</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y3*u</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>u**2</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         y1    y2     y3\n",
       "1       0.0   0.0  0.000\n",
       "y1    -10.0  28.0  0.000\n",
       "y2     10.0  -1.0  0.000\n",
       "y3      0.0   0.0 -2.667\n",
       "u       1.0   0.0  0.000\n",
       "y1**2   0.0   0.0  0.000\n",
       "y1*y2   0.0   0.0  1.000\n",
       "y1*y3   0.0  -1.0  0.000\n",
       "y1*u    0.0   0.0  0.000\n",
       "y2**2   0.0   0.0  0.000\n",
       "y2*y3   0.0   0.0  0.000\n",
       "y2*u    0.0   0.0  0.000\n",
       "y3**2   0.0   0.0  0.000\n",
       "y3*u    0.0   0.0  0.000\n",
       "u**2    0.0   0.0  0.000"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Display coefficients with labels\n",
    "var_names = ['y1', 'y2', 'y3', 'u']\n",
    "coef_labels = polynomial_feature_labels(x_u.shape[1], poly_order, \n",
    "                                        names=var_names)\n",
    "assert len(coef_labels) == 15\n",
    "pd.DataFrame(xi, columns=var_names[:3], index=coef_labels).round(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### B. Using L1-regularized feature selection in Scikit-Learn\n",
    "\n",
    "See: https://scikit-learn.org/stable/modules/feature_selection.html#l1-based-feature-selection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((5000, 15), (5000, 3))"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly_order = 2\n",
    "poly = PolynomialFeatures(poly_order)\n",
    "theta = poly.fit_transform(x_u)\n",
    "assert theta.shape == (5000, 15), theta.shape\n",
    "X, y = theta, dx\n",
    "X.shape, y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Set L1 penalty weight\n",
    "alpha = 0.5\n",
    "\n",
    "# Specify how many features to use\n",
    "max_features = 8\n",
    "\n",
    "# Find sparse model\n",
    "estimator = Lasso(normalize=True, alpha=alpha)\n",
    "selector = SelectFromModel(estimator, threshold=-np.inf, \n",
    "                           max_features=max_features)\n",
    "selector.fit(X, y)\n",
    "\n",
    "X_transform = selector.transform(X)\n",
    "n_features = selector.transform(X).shape[1]\n",
    "n_features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0.   ,   0.   ,   0.   ],\n",
       "       [-10.   ,  28.   ,  -0.   ],\n",
       "       [ 10.   ,  -1.   ,   0.   ],\n",
       "       [ -0.   ,   0.   ,  -2.667],\n",
       "       [  1.   ,   0.   ,   0.   ],\n",
       "       [  0.   ,  -0.   ,   1.   ],\n",
       "       [  0.   ,  -1.   ,  -0.   ],\n",
       "       [  0.   ,   0.   ,   0.   ]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fit sparse model\n",
    "estimator = LinearRegression()\n",
    "estimator.fit(X_transform, y)\n",
    "estimator.coef_.T.round(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y1</th>\n",
       "      <th>y2</th>\n",
       "      <th>y3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y1</th>\n",
       "      <td>-10.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>-0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y2</th>\n",
       "      <td>10.0</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y3</th>\n",
       "      <td>-0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-2.667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>u</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y1*y2</th>\n",
       "      <td>0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>1.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y1*y3</th>\n",
       "      <td>0.0</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>-0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y2**2</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         y1    y2     y3\n",
       "1       0.0   0.0  0.000\n",
       "y1    -10.0  28.0 -0.000\n",
       "y2     10.0  -1.0  0.000\n",
       "y3     -0.0   0.0 -2.667\n",
       "u       1.0   0.0  0.000\n",
       "y1*y2   0.0  -0.0  1.000\n",
       "y1*y3   0.0  -1.0 -0.000\n",
       "y2**2   0.0   0.0  0.000"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Display coefficients with labels\n",
    "selected_features = selector.get_support()\n",
    "np.array(coef_labels)[selected_features]\n",
    "pd.DataFrame(estimator.coef_.T, columns=var_names[:3], \n",
    "             index=np.array(coef_labels)[selected_features]).round(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### C. Using L1-regularized feature selection in Scikit-Learn with cross-validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Set L1 penalty\n",
    "alpha = 0.5\n",
    "\n",
    "# Specify how many features to use\n",
    "max_features = 8\n",
    "\n",
    "estimator = MultiTaskLassoCV(normalize=True, cv=5, alphas=[alpha]*4)\n",
    "\n",
    "# Set minimum threshold\n",
    "selector = SelectFromModel(estimator, threshold=-np.inf, \n",
    "                           max_features=max_features)\n",
    "selector.fit(X, y)\n",
    "\n",
    "X_transform = selector.transform(X)\n",
    "n_features = selector.transform(X).shape[1]\n",
    "n_features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0.   ,   0.   ,   0.   ],\n",
       "       [-10.   ,  28.   ,  -0.   ],\n",
       "       [ 10.   ,  -1.   ,   0.   ],\n",
       "       [ -0.   ,   0.   ,  -2.667],\n",
       "       [  1.   ,   0.   ,   0.   ],\n",
       "       [  0.   ,  -0.   ,   1.   ],\n",
       "       [  0.   ,  -1.   ,  -0.   ],\n",
       "       [  0.   ,   0.   ,   0.   ]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "estimator = LinearRegression()\n",
    "estimator.fit(X_transform, y)\n",
    "estimator.coef_.T.round(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y1</th>\n",
       "      <th>y2</th>\n",
       "      <th>y3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y1</th>\n",
       "      <td>-10.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>-0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y2</th>\n",
       "      <td>10.0</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y3</th>\n",
       "      <td>-0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-2.667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>u</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y1*y2</th>\n",
       "      <td>0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>1.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y1*y3</th>\n",
       "      <td>0.0</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>-0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y2**2</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         y1    y2     y3\n",
       "1       0.0   0.0  0.000\n",
       "y1    -10.0  28.0 -0.000\n",
       "y2     10.0  -1.0  0.000\n",
       "y3     -0.0   0.0 -2.667\n",
       "u       1.0   0.0  0.000\n",
       "y1*y2   0.0  -0.0  1.000\n",
       "y1*y3   0.0  -1.0 -0.000\n",
       "y2**2   0.0   0.0  0.000"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Display coefficients with labels\n",
    "selected_features = selector.get_support()\n",
    "np.array(coef_labels)[selected_features]\n",
    "pd.DataFrame(estimator.coef_.T, columns=var_names[:3], \n",
    "             index=np.array(coef_labels)[selected_features]).round(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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