1장_머신 러닝과 선형회귀.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "4317c2b0",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "from mpl_toolkits import mplot3d\n",
    "import matplotlib.font_manager as mfm\n",
    "\n",
    "np.set_printoptions(precision=4, linewidth=150)\n",
    "\n",
    "mpl.style.use('bmh')\n",
    "mpl.style.use('seaborn-whitegrid')\n",
    "style = plt.style.library['bmh']\n",
    "\n",
    "style_colors = [ c['color'] for c in style['axes.prop_cycle'] ]\n",
    "g_color = False\n",
    "file_print = False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "67f33f8c",
   "metadata": {},
   "outputs": [],
   "source": [
    "D1 = np.array([[1.0, 1.2, 3, 4, 5, 6],\n",
    "              [1.5, 3, 2.3, 5.3, 3.8, 5.5]])\n",
    "D2 = np.array([[-0.6, 1.0, 1.2, 3, 4, 5, 6],\n",
    "              [2.9, 1.5, 3, 2.3, 5.3, 3.8, 5.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "02ba92fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(1, 2, sharex=True, sharey = True)\n",
    "fig.set_size_inches((15, 6))\n",
    "\n",
    "ax1.plot(D1[0], D1[1], 'ko', markersize = 10)\n",
    "ax1.set_xlim([-1,7])\n",
    "ax1.set_ylim([1,6])\n",
    "ax1.set_title(\"D1\", fontsize = 18)\n",
    "\n",
    "ax2.plot(D2[0], D2[1], 'ko', markersize = 10)\n",
    "ax2.set_xlim([-1,7])\n",
    "ax2.set_ylim([1,6])\n",
    "ax2.set_title(\"D2\", fontsize = 18)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "ec2cb78b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def machine_learning(D):\n",
    "    N = D.shape[1]\n",
    "    X = np.c_[np.ones(N), D[0]]\n",
    "    y = D[1]\n",
    "    \n",
    "    w = np.linalg.solve(np.dot(X.T, X), np.dot(X.T, y))\n",
    "    return w\n",
    "\n",
    "def more_clever(D):\n",
    "    first, last = D[:,0], D[:,-1]\n",
    "    w1 = (last[1] - first[1]) / (last[0] - first[0])\n",
    "    w0 = -w1 * first[0] + first[1]\n",
    "    return (w0, w1)\n",
    "\n",
    "def f(x, w):\n",
    "    return w[1] * x + w[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "2c7a2272",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.3995 0.6437]\n"
     ]
    }
   ],
   "source": [
    "# D1에 대해서 w[1]*x + w[0]에서 w[0], w[1]을 구합니다. \n",
    "w_ml_d1 = machine_learning(D1)\n",
    "w_mc_d1 = more_clever(D1)\n",
    "\n",
    "# D2에 대해서 w[1]*x + w[0]에서 w[0], w[1]을 구합니다. \n",
    "w_ml_d2 = machine_learning(D2)\n",
    "w_mc_d2 = more_clever(D2)\n",
    "\n",
    "print(w_ml_d1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "5f37e5bc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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xsTEHDx5k37593L17l/v37+uK338/R/j8d4/r7/Y1adOm/WyoyX/Xe/jwIVqt9ot/Lvny5ZNCJr5r//79GBoa6oZK/Uqjd/fuXd3jGnLkyIG/vz9FixaNr6hC/BKpkVIj/0tqpPgVT548YcyYMSxbtgytVou5uTkDBw5k0KBBumGc+iBFN3u/eoZQHxkZffmP9FtnFaKioujSpQvnzp2jXLlyVKhQgY4dO1K2bNlPzpZ9PHDGZYz7z46D/956HzP07duX4sWLf3GZ/549jY9tKYrCoEGD2LFjB6VKlaJEiRK0atWKMmXK0KFDh8/W+drEEwn1mXw8u2xiYvLZe6ampj+1T5FynDt3jkaNGhEdHc2pU6coVqzYL22rfv36PH/+HBsbG/z8/MiePXs8phWJJTnWR5AaCVIj/0tqpPhZYWFhFC1alDdv3mBoaIiTk5Nusid9k6KbPfEvPz8/Tp8+zcSJEz+ZVez58+efLPfxL/D9+/c/e9bNsGHDKFmyJC1atEjQrB+/OFpYWFCxYsVP3gsICODdu3efDJ+Jj22dPXuWHTt24OzsTN++fXXLxMTE8PbtW3LmzPkrv9Iv+7j/e/fuffbe/fv3EzmNSEpu3bqFra0toaGhtGnTRjeU7Gf4+/vTokULwsLCqFmzpm42TyGSOqmRUiOFAIiMjMTIyAhDQ0NSpUpF165duX37NpMnT/5keLi+kWmIBG/fvgXg999//+T1VatWAf93Vqxo0aKkT58eHx8foqKidMudP38eHx+fz8blJ4SiRYuSKVMmVq9erRtCAxAaGkq/fv0YNmxYnKd0j+u2vvb5bNy4kYiICN3no5YMGTJQokQJduzY8cl9FQ8fPuTw4cMqJhP67MmTJ9SpU4eXL19St25dVqxY8dNn1pctW4a9vT1hYWG0bdsWPz8/afREsiE1UmqkSNm0Wi2enp4UKlSItWvX6l6fMmUKPj4+et3ogVzZE/x787iRkRGDBw+mbdu2GBkZceDAAY4ePYqxsbHuIG9iYsLQoUMZMmQIDg4ONGzYkLCwMFatWkX+/PkT/IwlgLGxMaNGjaJfv340bdqU5s2bY2pqipeXF0+ePGHGjBlfHabzs9sqUaIElpaWTJ48mSdPnmBlZcWpU6fw8/PD1NT0kyKoliFDhuDo6Ejz5s1p3bo1UVFRrF69+rN7JUTKFBQUhJubG56enoSGhpIqVSpMTEx4/fo1ZcuWxdvb+4tDnL5HURTGjh3L2LFjgX+vXkycOFH1m9GFiE9SI6VGiuTrf+ujpaUl7dq1Y+DAgeTLl4/du3czZMgQLl26BMD69etxdHQEfn7ocWKTZk9QsGBB5s6dy/z585k5cyapUqWiQIECrFixgrVr13L69Gmio6MxNjamUaNGWFpa4uHhgZubG1ZWVlSvXp2BAwdiYWGRKHnr1q3L8uXLWbRoEQsXLsTAwIACBQqwaNGiH57xLy7bypgxI4sXL2bGjBksXLgQExMT8ubNy8yZMwkICGDVqlUEBwf/0qQWv6pEiRIsXbqUWbNmMXv2bNKmTYujoyNBQUHs2rVLtVxCff7+/jRv3pzo6Gjd5A+hoaHAv/cp9e/fH0tLyx/ebnR0NE5OTrorggsWLKBHjx7xml0IfSA1UmqkSJ6+VB9DQkJYunQpy5cvp3DhwromL0eOHIwfP17X6CUlGiWJn9Y4d+4cpUqVUjuGEKp6+fIlmTJl+uz1Hj16EBgYyMGDBxM/lFBdUFAQNjY23xw+ZmFhQUBAAPnz54/zdkNCQmjRogW7du3C3NycDRs2YG9vHx+Rv0mO9z9GPi8h/iU1UvyvuNRHgDRp0jBy5Eh69eqFubl5IqX7OV875ieN649CiG9q2bIlXbp0+eS14OBgTp069dmU3yLlcHNz++5U7tHR0cyaNSvO23z27BnVqlVj165dZMyYkQMHDiRKoyeEED9LaqT4X3GpjwYGBjRv3hxXV1e9b/S+RZo9IZKBhg0bcvToUQYOHMjGjRtZunQpbdq0QavV0qtXL7XjCZV4enrGqdlbvXp1nLYXGBhIhQoVOH/+PPnz5+fEiROUK1cuPqIKIUSCkRop/ldc6qNWq8XLyyuREiUcuWdPiGSgb9++ZMyYkY0bN7Jv3z5MTU0pWbIkc+fO1ftZokTC+XhvXnwsd/ToURo2bMibN28oW7YsO3bs+OKwKCGE0DdSI8X/CgkJidNyca2j+kyaPSGSAQMDAxwdHZPkjcMi4VhaWsapoH1vgpZNmzbRtm1bIiMjsbe3Z/369Yk22YQQQvwqqZHiI0VR8PLyQqPRxGk21p+ZwEzfyDBOIYRIpqpUqfLdZYyNjb/5BWjOnDm0aNGCyMhIevTogY+PjzR6QgghkqSePXvSqlWrODV636uPSYU0e0IIkQydOnWKAwcOfHc5Y2Nj+vfv/9nrWq2WAQMG0K9fPxRFYfLkySxcuDDOz+gSQggh9EFsbKzu/9u2bUu2bNmYMGHCdydd+Vp9TGqkagshRDLz4cMHmjVrRkREBLVq1eLYsWPExMR8cjO6sbExxsbGeHt7f/bYhQ8fPtC+fXu8vLwwMjJi+fLlyeLsphBCiJTj3r17jB49msjISDZs2AD8O+Ll7t27uvs2//c5e/Dt+pgUyZU9IYRIZszMzFi7di1t27bFz8+Py5cv0717d6ysrDAwMMDKyoru3bsTEBCAra3tJ+u+fv2a2rVr4+XlhZWVFTt37pRGTwghRJLx6tUrBgwYQKFChVi9ejVbtmzh0aNHuvdNTU0BsLW1JSAgIM71MamSh6oLIUQyoSgKGo3mp9e/d+8etra2BAYGkj17dvz8/PTqGVRyvP8x8nkJIVKS8PBw5syZw5QpU3j//j3w77DN8ePHkzdvXpXTJZyIiAg2bdqEtbW1PFRdCCGSq7CwMGrVqsX27dt/av0LFy5QoUIFAgMDKVq0KCdPntSrRk8IIYT4mg8fPlCkSBGGDx/O+/fvqVOnDufPn8fT0zNZN3q7du2iaNGi3xyBI82eECLBBQUF4ezs/MkwCWdnZ4KCgtSOlixER0fTokUL9u/fT79+/YiMjPyh9Xft2kXVqlV59uwZ1atX58iRI+TIkSOB0gohhPgvqZE/R1EU3ayaZmZm1K9fn5IlS7J792527dpFiRIlVE6YcJ49e4aDgwP16tXjzp07FC1a9KvLSrMnhEhQ/v7+2NjYsHTpUkJCQlAUhZCQEJYuXYqNjQ3+/v5qR0zStFotnTt3xt/fn4wZM+Ln56e7HyEu/vnnHxo0aEBoaCht2rTB39+ftGnTJlxgIYQQOlIjf86xY8eoXLkyPj4+utemT5/OmTNnqF27torJEpZWq8Xd3Z3ChQuzfv16zM3NmTp1KufPn//qOtLsiSShUKFCDB06VO0Y4gcFBQXRvHlzwsPDP5npCv69GhUeHk7z5s3l7OVPUhSFQYMG4enpSapUqfDz86NQoUJxXnf8+PF06tSJmJgYhg4dyurVq3+oURRC6AepkUmT1Mgfd+3aNRo3bkzlypU5fvw4s2fP1r1nYWGBgUHybW0uX75M5cqV6dmzJ+/evcPW1parV68yePBgjI2Nv7pe8v1EhBCqc3Nz+6yA/a/o6GhmzZqVSImSl+nTpzNz5kyMjY3x8fGhTJkycVovJiaG7t27M3r0aAwMDJg/fz6TJ09O1kVSCCH0jdTIuHv8+DFdu3blzz//ZOvWraRKlYrRo0fj6+urdrQEFxYWxpAhQyhRogQnTpwga9asbNy4EV9f3zjdjyiVXQiRYDw9PeNUyFavXp1IiZKPp0+fMm7cOABWrlxJnTp14rReaGgojRo1YunSpZibm+Pj40OvXr0SMqoQQogvkBoZN4cOHeL3339n2bJlaDQaevTowe3btxk7dixWVlZqx0tQfn5+FC1alGnTpqHVaunVqxeBgYG0aNEizrNvy0PVhRAJJjQ0NF6XE/8nW7Zs7Nu3j4sXL+Lg4BCndZ4/f079+vU5d+4cGTNmZPv27ZQvXz6BkwohhPgSqZFf999HCZUpU4YMGTJQsWJFJkyYQMGCBVVOl/CePHlCv3798PLyAqBYsWJ4eHhQrly5H96WXNlLRmrUqMG4cePw8vKibt262NjY0KxZMwICAnj58iV9+/alRIkSVKlShVmzZqHVaj9Zf+/evbRu3RobGxtKly5Njx49CAwM/GSZQoUKMXv2bHr06EHRokWxs7MjJiYGgAMHDtC6dWuKFStGmTJlcHFx4e7du3HKfujQIdq1a0eJEiWoVKkS/fv3/+QBmF/yvf117dqVcuXK6fJ99OjRIwoVKsT8+fPjvK3v/e7iyywtLeN1OfHvcI6PypUrh5OTU5zWu3HjBhUqVODcuXPkz5+f48ePS6MnUhSpkVIj9Y3UyM/FxsayevVqypQpw7t374B/78W7cuUKGzduTPaNXmxsLAsWLMDa2hovLy8sLCxwc3Pj7NmzP9XogTR7yc6+ffuYM2cOzZs3p3fv3ty5cwcXFxc6deqEgYEBQ4cOpWDBgri7u7N161bdemvWrKFXr15ER0czYMAAOnbsSEBAAA4ODgQEBHyyj5UrV/LhwwdGjhxJy5YtMTIywsfHh549e2Jubs6gQYPo2LEjFy5coGXLlt8tZr6+vjg5OfHu3TtcXFxo3749x48fp2PHjrqHYv6vuOzP3t6et2/fcvz48U/W9fPz070f121963cXX9euXbtv3jQMYGxs/M3nw4j/c/nyZfLly8fGjRt/aL3jx49TsWJF7t69S5kyZTh+/DgFChRIoJRC6C+pkVIj9YnUyP+jKAr+/v6ULFmS9u3bc+7cOZYtW6Z7PyXMEn3p0iUqVqxI7969ef/+PQ0aNODatWsMGDDg1/4tKUnc2bNn1Y6gN6pXr64UKlRICQwM1L02depUpWDBgkq/fv10r4WFhSl//PGHMmDAAEVRFOX169dKsWLFlObNmyuRkZG65R4+fKh7/aOCBQsqpUqVUt69e6d7LSQkRClZsqTSv3//T/K8ePFCKVOmjOLs7PzVzLGxsUqlSpUUe3t7JSIiQvf6sWPHlIIFCyqenp66/Q4ZMuSH9hcaGqoUK1ZMGTZs2CfLNW7cWGnRosUPZ//S7y6+7fbt24qFhYUCfPU/CwsL5fbt22pH1Xt3795VsmXLpgBKs2bNFK1WG6f1fHx8FDMzMwVQGjRooISGhiZw0oQjx/sfI5/Xp6RGSo3UN1Ij/3X69GmlWrVqut85Z86cyj///KPExMSoHS1RhIaGKq6uroqhoaECKNmzZ1c2bdoU5zr/0deO+Sn+yp5Go/nqf4sXL9Ytt3jx4m8u+1+lSpX66nLdu3fXLXfu3Llvbudn5MqV65Op1z/O0vPfZ45YWFiQIUMGXr58CcCJEyeIiIigU6dOmJiY6JbLkSMHDRs2JCAggBcvXuheL1as2Cc3xB47dozQ0FBq1arF69evdf8ZGhpSvnx5jh49+tWhHFeuXOHly5e0bNkSMzMz3esVK1bEy8uLRo0afbZOXPeXKlUqatasyb59+3Q3QN+9e5dr167pzlj+aPb//d3Ft+XPnx9vb28sLCw+O3tpbGyMhYUF3t7e5M+fX6WEScPLly+pW7cuT58+5a+//sLT0zNOx4v58+fTrFkzPnz4gJOTE5s3byZVqlSJkFgkB8mtPoLUSKmR+kVqJIwaNYqyZcty8OBB0qVLx4wZM7h58yYdOnTA0NBQ7XgJbseOHRQpUoQZM2agKAp9+vTh2rVrNG3aNN6Oe3J9PZnJkCHDJz9//IeSPn36z15XFAVAN+4/X758n23v4wHmyZMnZM6c+YvbevDgAQD9+/f/aq7Xr1/r1v+vx48fA5A7d+7P3rOxsfnitn5kfw0aNGDHjh2cOHGCqlWr4ufnh6GhIXZ2dj+V/X9/d/F9tra2BAQEMGvWLFavXk1oaCiWlpY4OjrSv3//ZF3E4kNISAh2dnbcvHmTYsWKsXXr1k++9H2JVqtl6NChTJ8+HYAJEyYwfPjweCscQiRVUiM/3Z/USPWl9BpZpUoVzMzM6NOnD0OHDiVdunRqR0oUjx8/pk+fPrqHwpcsWRIPDw9Kly4d7/tK8c3ex4P593Tv3v2Ts47fcu7cuTgtV6pUqTjvP66+Nqb3Z7/kfcz33zNO/3um5eNN7OPHjydHjhxf3E6aNGm++PrHdX/k+V4/sr/KlSuTLl06/P39qVq1Kv7+/lSoUEFX8H80e0o4y5QQ8ufPz/z58z+54V98X2RkJE2bNuXs2bPky5ePnTt3fvXf0n/X6dixI+vXr8fIyIhly5bRvn37REoskpPkVh9BauT/7k9qpH5IKTUyJCSEGTNmEBwczIIFC4B/r6rfv3//iyc7kqOPE7CMHDmSkJAQLC0tGT9+PL17906we1xTfLMnIHv27ADcuXOHwoULf/LenTt3AMiaNet310+fPj0VK1b85L1Tp06h1Wo/GfryX9myZQPg/v37VKpU6ZP3hg0bRsmSJWnRosVP78/Y2Jh69eqxc+dObt68ya1bt+jatWu8ZBciod24cYNTp06ROXNmdu/e/c1/hwBv376lcePGHDp0iNSpU7Np06ZPhqcJIX6c1EipkeLXREVFsXjxYsaNG8fLly/RaDS4urqSN29eNBpNimn0zp8/j5OTE2fPngWgcePGzJ07l5w5cyboflP8PXvi37H/pqamrFixgqioKN3rz549Y/v27djY2Hw29OVL6y9duvSTh4M+f/4cZ2dnZsyY8dWzpkWLFiV9+vT4+Ph8su/z58/j4+NDeHj4L+/P3t6eN2/eMHPmTMzMzD758vsr2YVIaDY2Nhw6dIidO3d+dyjPgwcPqFy5MocOHSJbtmwcPnxYGj0h4oHUSKmR4udotVrWr1+PtbU1Li4uvHz5kooVK3L48GHd/bIpQWhoKAMGDKBMmTKcPXuWHDlysGXLFjZv3pzgjR7IlT0BpEuXjgEDBjB58mQcHBywt7cnLCyMdevWodVqGTly5DfXT58+vW79Vq1a0bBhQ2JiYli7di2RkZEMGTLkq+uamJgwdOhQhgwZgoODAw0bNiQsLIxVq1aRP3/+z85Y/sz+SpYsSfbs2Tlw4AD169f/ZIKKX8kuREIJCgrSNXclSpT47vKXLl3Czs6OJ0+eUKRIEfz9/cmVK1dCxxQiRZAaKTVS/LioqCiqVKnC6dOnAShcuDCTJ0+mUaNGKeoEwdatW+nduzePHj3CwMCAfv36MW7cOFKnTp1oGaTZEwB07NiRzJkzs3z5cmbOnIm5uTlly5ald+/en8xc9q31s2TJwooVK5g1axZmZmb88ccfTJ8+nVKlSn1z3UaNGmFpaYmHhwdubm5YWVlRvXp1Bg4ciIWFxS/vT6PRYG9vj7u7Ow0aNIjX7ELENw8PD3r37h3ne+327t1L06ZNCQkJoWrVqmzZsiXF3OAuRGKRGik1UvwYExMTrK2tefToEWPGjKFTp04p6rmLDx8+xMXFRfe8ztKlS+Ph4UHJkiUTPYtGSYg7oBPRuXPn5GAjhEgWfHx8aNGiBVqtlkWLFtGjR49vLr969Wo6d+5MTEwMrVq1YuXKlZiamiZS2sQnx/sfI5+XECKx3Lt3j1GjRtG2bVvq1asHwKtXrzA3N//qSYnkKCYmhnnz5jFq1CjCwsJInTo1EydOxNnZOcEnMPraMV8vW+zmzZtz+fLlz16vW7cuc+fOVSGREEIkrAMHDuDg4IBWq2Xs2LHfbPQURWHSpEm64WOurq5MnTr1h2bsE0IIIX5VcHAwEydOZOHChURFRXHjxg1ds/ete1mTozNnzuDk5MSFCxcAaNasGXPmzNFNdKQWvWv2FEUhKCiIWrVqUadOnU/eU/vDEkKIhHDhwgUaNWpEVFQUvXr1YtSoUV9dNiYmhl69eukeZD1nzhxcXFwSMa0QQoiULiwsjNmzZzNt2jTev3+PRqOhXbt2jB8/Xu1oie79+/eMHDmS+fPnoygKuXLlYsGCBV8cFq0GvWv2Hj16RHh4ODVr1qRRo0ZqxxFCiAQVFBSEra0tISEhtGzZkjlz5nz15vWwsDBatWqFr68vZmZmrF27liZNmiRyYiGEECnZmTNnaNSoEU+fPgWgXr16TJ48meLFi6sbLJEpisLmzZtxcXHhyZMnGBoa0r9/f8aMGfPJREdq07tm7/bt2wDfnWZcCCGSg1evXhEVFUXNmjVZtWrVV8f0P3/+nAYNGnD27FnSp0/P9u3bP3vulRBCCJHQChUqRHR0NKVKlWLatGnUqFFD7UiJ7v79+7i4uLB9+3YAypUrh4eHB8WKFVM52ef07gaPW7duAf/X7H3pGTJCCJFclC1bluPHj7N58+avTq5y8+ZNKlasyNmzZ8mbNy/Hjx+XRk8IIUSiOHr0KE2aNNF9J7eysuLEiROcPn06xTV6MTExuLm5UaRIEbZv346VlRULFy7k2LFjetnogZ42e6lSpWLy5MmUKFGCEiVKUKtWLXx9fdWOJoQQ8eLDhw/s379f93PhwoW/+sydEydOULFiRe7cuUOpUqU4fvx4nKZ6F0IIIX7F1atXadiwIVWqVGHLli0sWLBA997vv/+e4iYFO336NGXKlMHV1ZXw8HBatmxJYGAgPXv2TPCZNn+F3v0p3b59m7CwMEJCQpg2bRqTJk0iVapUDBgwgC1btqgdTwghfklsbCxt27alVq1arFq16pvLbt26lRo1avDq1StsbW05ePAgWbNmTaSkQgghUqJHjx7RpUsXbGxs2L59O6lSpeLvv//+7uOAkqt3797Ru3dvypcvz8WLF8mTJw9+fn5s2LCBbNmyqR3vu/Tunr2WLVui1Wpp27at7rX69evToEEDpk+fjr29vV53z0II8TWKouDs7IyPjw9p0qT55s3sCxYsoE+fPmi1Wrp27crChQsxNjZOvLBCCCFSnHnz5jF48GA+fPiAkZERPXv2ZNSoUWTJkkXtaIlOURS8vb3p27cvT58+xdDQkIEDBzJ69Gi9moDle/Tuyp6Dg8MnjR6AmZkZjRo1Ijg4WDeBixBCJDV///03ixcvxszMjO3bt2NjY/PZMlqtlqFDh9K7d2+0Wi3jxo1j8eLF0ugJIYRIcDly5ODDhw+0bNmS69evM3/+/BTZ6N29e5f69evTsmVLnj59Svny5Tl//jxTp05NUo0e6OGVva9Jnz49IBO2CCGSpnnz5jF+/HgMDQ3ZsGEDVapU+WyZyMhIOnfuzNq1azEyMmLJkiV07Ngx8cMKIYRI9mJjY/H09OTevXv8/fffADRu3JiAgAD+/PNPldOpIzo6mlmzZjFmzBgiIiJIkyYNU6dOpVu3bkn2HkW9Sv38+XPq16/P/PnzP3vv7t27wL9nHIQQIinZuHEjffv2BWDx4sU0bNjws2Xevn2Lra0ta9euxdLSkh07dkijJ4QQIt4pioKvry/FixenY8eOjB8/nqCgIAA0Gk2KbfROnDhBqVKlGDJkCBERETg4OBAYGIiTk1OSbfRAz5q9LFmyEBISgpeXF6GhobrXnz59io+PD+XKlSNTpkwqJhRCiB+XP39+MmbMyJQpU+jcufNn7z98+JAqVapw4MABsmbNyuHDh6lbt64KSYUQQiRnp06donr16jRo0IArV66QK1cuVqxYQd68edWOppo3b97Qo0cPKlWqxOXLl8mXLx87d+5k7dq1yWJSNL0bxjl69Gh69epF69atadGiBWFhYaxZswYjIyPdJWYhhEhKSpUqxdWrV8mYMeNn7wUEBGBnZ8fjx4+xtrbG39+f3Llzq5BSCCFEchUTE4ODgwPe3t7Av7dHjRw5kp49e2JmZqZyOnUoisKGDRvo168fz58/x8jIiEGDBjFy5EgsLCzUjhdv9OrKHkCtWrVYsGAB5ubmzJgxgxUrVlC8eHHWrVune9C6EELouxs3brB+/Xrdz5kyZUKj0XyyzP79+6lSpQqPHz+mSpUqHD16VBo9IYQQ8c7IyAiNRoO5uTnDhg3jzp079O/fP8U2ekFBQdSrVw8HBweeP39O5cqVuXjxIpMmTUpWjR7o4ZU9+Lfhq1WrltoxhBDipzx58oS6dety//59TE1NadKkyWfLrFmzhk6dOhEdHU2LFi1YtWpVii26Qggh4tf79++ZPn06derU0U0INnPmTGbNmkX27NlVTqeeqKgoZsyYwfjx4/nw4QPp0qVj2rRpdO7cOUnfl/ctetnsCSFEUvXmzRtdo1e+fHnq1KnzyfuKojB16lSGDRsGQP/+/ZkxY0ayLTJCCCEST1RUFO7u7owfP57g4GD27NnDiRMn0Gg0KX6Sw6NHj+Lk5MS1a9cAaNeuHW5ubmTOnFnlZAlLmj0hhIgn4eHh2Nvbc+XKFaytrdmxY8cnz+OJjY3FxcWFRYsWodFocHNzo3///iomFkIIkRxotVo2bNjAyJEjuXPnDgCVKlVi2rRpn91CkNK8fv2aIUOGsHTpUgB+//13Fi1alGJGEUqzJ4QQ8SAmJoZWrVpx7NgxcuTIwa5du8iQIYPu/fDwcBwcHNi2bRumpqasXr2aFi1aqJhYCCFEcnD9+nXatWvH+fPnAbC2tmbKlCnY29un6EZPURTWrFnDgAEDePnyJcbGxgwdOpThw4enqNsmpNkTQoh4MGDAAHbs2EH69OnZvXs3OXPm1L338uVL7O3tOXXqFOnSpWPr1q1ffKi6EEII8aMyZ85MUFAQv/32G+PGjaNDhw4YGaXsr/i3b9+mZ8+e7N27F4CqVavi7u6OtbW1yskSn9wkIoQQ8aBbt24UKFAAX1/fT4rJ7du3qVixIqdOnSJ37twcO3ZMGj0hhBA/7c6dO/Tp04fIyEgAMmTIwM6dO7l16xZdunRJ0Y1eZGQkEyZMoGjRouzdu5f06dOzbNkyDh48mCIbPZAre0IIES/+/PNPrl279kmRPXXqFA0aNCA4OJgSJUrg6+tLtmzZVEwphBAiqXr58iUTJkxg0aJFREdHky9fPvr16wdA+fLl1Q2nBw4fPoyTkxOBgYEAtG/fnhkzZpApUyaVk6lLruwJIcRPWr16te6Gb+CTRm/79u1Ur16d4OBg6taty6FDh6TRE0II8cPCwsKYMGEC+fPnZ+7cucTExNC+ffsvPtYnJXr16hWdO3fmr7/+IjAwkIIFC7J//35WrlyZ4hs9kCt7QgjxU/z8/OjUqROxsbHY2NhQtmxZ3Xvu7u706tULrVZLp06d8PDwwNjYWMW0QgghkqINGzbQr18/nj17BoCtrS1TpkzBxsZG5WTqUxSF1atXM3DgQIKDgzExMWH48OEMHToUU1NTtePpDWn2hBDiB504cYLmzZsTGxvLkCFDdI2eoiiMGDGCyZMnAzBmzBhGjx6domdDE0II8fOio6N59uwZZcuWZerUqVSrVk3tSHrh5s2b9OjRgwMHDgBQrVo13N3dKVSokMrJ9I80e0II8QOuXr1K/fr1iYiIoFOnTrrGLioqii5duuDp6YmhoSEeHh506dJF5bRCCCGSkkOHDnHt2jV69uwJQJs2bUifPj22trZy4pB/J2CZMmUKkyZNIioqiowZM+Lm5oajo6N8Pl8hzZ4QQsTRgwcPqFu3Lm/evKFhw4YsXrwYjUbDu3fvaN68OXv37iVVqlR4eXlha2urdlwhhBBJxOXLlxk2bBi+vr6YmJhgZ2dH7ty5MTAwwM7OTu14euHAgQP06NGDmzdvAtC5c2emTZv2yTNtxeek2RNCiDhQFIV27drx+PFjKleuzPr16zEyMuLx48fY2dkREBBAlixZ8PX1pVSpUmrHFUIIkQQ8ePCAv//+m5UrV6IoCpaWlgwaNEgamP8IDg7G1dWVlStXAlC4cGE8PDyoWrWqysmSBpmNUwgh4kCj0bBkyRIaNGjAtm3bMDc358qVK5QvX56AgAAKFSrEiRMnpNETQgjxXbGxsQwePJiCBQvyzz//YGhoSO/evQkKCmL06NFYWlqqHVF1iqKwYsUKChUqxMqVKzE1NWX8+PFcvHhRGr0fIFf2hBDiGxRF0d0HUKhQIbZv3w7AwYMHady4Me/evaNixYps27ZNzsQKIYSIE0NDQ65du0ZkZCStWrVi4sSJ5M+fX+1YeuP69ev06NGDw4cPA1CrVi0WLlxIgQIFVE6W9MiVPSGE+AqtVkuHDh2YO3fuJ6+vW7eOunXr8u7dO5o2bcrevXul0RNCCPFVsbGxLF++nPPnz+temzlzJmfPnmX9+vXS6P1/Hz58YPTo0RQrVozDhw+TOXNmPD092b17tzR6P0maPSGE+AJFURg4cCCrV69mxIgRPHnyBEVRmD59Om3atCEqKoo+ffqwceNGzM3N1Y4rhBBCDymKwvbt27GxsaFLly64urqiKAoABQsWlKH//7Fv3z7+/PNPxo8fT3R0NN26deP69eu0bdtWZtr8BTKMUwghvmDq1KnMnj0bY2NjNm/eTJYsWejTpw/z588HwM3Njf79+0sBEkII8UUnTpxgyJAhHDlyBIA8efLII3m+4MWLFwwcOBBPT08AihQpgoeHB5UrV1Y5WfIgzZ4QQvyP5cuXM2zYMDQaDZ6enlSqVInmzZuzZcsWTExMWLVqFa1atVI7phBCCD308OFD+vXrh4+PDwAZMmRg1KhR9OjRA1NTU5XT6Q+tVsvy5csZPHgwb968wczMjFGjRuHq6oqJiYna8ZINafaEEOI/tm3bRrdu3QCYN28eNWrUoGbNmpw4cYK0adOydetWmQVMCCHEVxkZGbFz504sLCwYMGAArq6upEmTRu1YeuXq1av06NGDo0ePAlCnTh0WLlwo9y4mAGn2hBDi/4uKiqJfv35otVpGjRqFra0tFStW5NatW+TKlQt/f3+KFCmidkwhhBB65N27dyxZsoR+/fphZGREtmzZWL9+PaVLlyZbtmxqx9MrERERTJgwgWnTphETE0OWLFmYPXs2rVq1ktsiEog0e0II8f+ZmJiwd+9eVq9eja2tLRUqVODFixcUL14cX19ffvvtN7UjCiGE0BORkZG4u7szfvx4Xr16RZo0aXQjQ+zt7VVOp392795Nz549uXPnDgBOTk5MnjyZdOnSqZwseZNmTwiR4oWHh2NhYQFAvnz5KF26NNWrVyc8PJw6derg7e1N6tSpVU4phBBCH2i1WtatW8fIkSO5d+8eAFWqVKFYsWLqBtNTz549Y8CAAaxbtw6AokWL4uHhQcWKFVVOljLIoxeEECnaxyt3U6dORVEUFi9eTMOGDQkPD6dDhw7s2LFDGj0hhBAAHDx4kFKlStGuXTvu3bvHH3/8wbZt2zh06BBly5ZVO55e0Wq1eHh4ULhwYdatW4e5uTlTp07l/Pnz0uglIrmyJ4RIsUJCQrCzs+PWrVts2LCBt2/fMmXKFABGjRrF2LFj5R4CIYQQOjdv3uTixYvkyJGD8ePH4+joiKGhodqx9M7ly5dxcnLixIkTANSrV4+FCxeSN29elZOlPNLsCSFSpMjISJo0acK5c+fIly8fv//+O1OmTMHQ0JBFixbp7rsQQgiRcgUFBXHhwgWaN28OQOfOnYmNjaVjx46Ym5urnE7/hIeHM27cONzc3IiJiSFr1qzMnTuX5s2by8lTlcgwTiFEihMbG4ujoyP79u0jc+bMZMuWDS8vLywsLNi6das0ekIIkcK9ePECFxcXChcuTIcOHXj27Bnw72MVevbsKY3eF/j7+/PHH38wdepUYmNjcXZ2JjAwkBYtWkijpyK5sieESFEURaFPnz54eXmROnVq0qZNy7Fjx8icOTM7duygTJkyakcUQgihktDQUGbOnMn06dMJDQ1Fo9HQsmVLtWPptadPn9KvXz82btwIgI2NDR4eHpQvX17lZAKk2RNCpDDBwcFs374dExMTzM3NuXnzJgUKFGDnzp3ky5dP7XhCCCFU8HEykbFjx/L8+XMA6tevz+TJk/nzzz9VTqefYmNj8fDwYNiwYbx//x4LCwvGjh1L3759MTY2Vjue+P9kGKcQIkXJlCkTM2fOxNjYmBcvXlC+fHmOHz8ujZ4QQqRgGo0GLy8vnj9/Trly5Th48CA7duyQRu8rLl68SKVKlejVqxfv37+nfv36XLt2DVdXV2n09Iw0e0KIFOHjQ1w3btxI27ZtCQsLo3Hjxuzbt4+MGTOqnE4IIURiO3jwIIGBgcC/zZ6bmxve3t6cOHGCv/76S+V0+iksLIxBgwZRunRpTp06xW+//Ya3tzfbt28nd+7cascTXyDNnhAi2du/fz/W1tbUqVOHVq1aERUVRa9evfD29tY9TF0IIUTKEBAQgJ2dHdWrV8fV1VX3eokSJWjWrJlMJvIVO3bs4I8//mDGjBlotVpcXFy4fv26fGZ6Tu7ZE0Ika+fPn6dx48ZERUWxZ88eAKZNm4arq6sUJyGESEEePHjAqFGjWL16NYqikDp1asqXL49Wq8XAQK5/fM3jx4/p27cvmzZtAv5tij08PGRCsyRCmj0hRLJ1+/ZtbG1tCQkJAf6dMnvVqlU4ODionEwIIURiefPmDRMnTmT+/PlERkZibGyMs7MzI0aMIFOmTGrH01uxsbEsXLiQESNGEBISQqpUqRg/fjwuLi4YGUkLkVTIn5QQIll6+vQptWrV4sWLFwBYWVmxZcsWqlevrnIyIYQQien9+/fMmzePqKgoHBwcmDBhgkzK9R0XLlyge/funD17FoCGDRsyb948cuXKpXIy8aPkmrUQItl5+/YtNWvW5P79+wD89ttvHDt2TBo9IYRIAWJiYti4cSNarRaA3Llzs3DhQs6dO8fatWul0fuG0NBQBgwYQOnSpTl79iw5cuRg8+bNbN26VRq9JEqaPSFEsnPkyBFu3rwJgLW1NadPn6Zo0aIqpxJCCJGQFEVh69at2NjY0KpVK9avX697r0uXLpQsWVLFdPpv69atFClShFmzZgHQr18/rl27RuPGjdUNJn6JDOMUQiQr/v7+ODg4EBsbS8WKFfHz8yNNmjRqxxJCCJGAjh07xpAhQzh27BgAefPmJXXq1CqnShoePnxInz592LJlCwClSpVi8eLF0hwnE3JlTwiRLCiKQv/+/bG3tycsLIx27dpx4MABafSEECIZu379Ok2aNKFy5cocO3aMjBkzMmfOHK5fv469vb3a8fRaTEwMs2fPpkiRImzZsgVLS0vmzJnDqVOnpNFLRuTKnhAiyVMUhapVq3L06FEAhg8fzoQJE+TRCkIIkczt2rWLLVu2YGFhwYABAxg0aBBWVlZqx9J7Z8+excnJifPnzwPQtGlT5syZQ44cOVROJuKbNHtCiCQtOjqaKlWqcOrUKQCcnZ2ZOHGiyqmEEEIkhLdv33Lp0iX++usvAHr27Mnz58/p27cvWbNmVTmd/gsJCWHUqFHMmzcPrVZLrly5mD9/vlwFTcZkGKcQIskKCQmhVKlSukavb9++LFiwQOVUQggh4ltkZCSzZs0if/78NGrUiFevXgFgamrK5MmTpdH7DkVR2Lx5M9bW1syZMweNRoOrqytXr16VRi+Zkyt7Qogk6enTp1SpUoWgoCAAevfuzezZs9UNJYQQIl7Fxsaydu1aRo0apXucTtWqVXn79i0ZMmRQOV3S8ODBA3r37s327dsBKFu2LB4eHhQvXlzdYCJRyJU9IUSSc/36dUqWLKlr9Lp06cK8efNUTiWEECK+KIrCzp07KVmyJO3bt+f+/fsULVoUX19fDh48SP78+dWOqPdiYmJwc3OjSJEibN++HSsrK+bPn8/x48el0UtB5MqeECJJOXr0KA0bNuTNmzeYmZlhb2/P4sWL1Y4lhBAino0ZM4aAgABy5szJuHHjcHR0xNDQUO1YScLp06dxcnLi4sWLALRo0YLZs2fz22+/qRtMJDpp9oQQSYa3tzft2rUjMjISe3t7Fi5cSJYsWTAwkEEKQgiR1N2+fRtjY2Ny586NRqNhxowZnDx5kt69e2NmZqZ2vCTh3bt3jBgxgoULF6IoCnny5GHBggXY2dmpHU2oRL4hCSGShNmzZ9OiRQsiIyNxcnLCx8eHHDlyYGxsrHY0IYQQv+D58+f07t0ba2trBg8erHu9cuXKuLq6SqMXB4qi4OXlhbW1NQsWLMDAwIAhQ4Zw9epVafRSOLmyJ4TQa1qtFldXV2bNmqV7LXfu3BgZyeFLCCGSspCQENzc3JgxYwZhYWEYGBiQOnVqYmNjZbjmD7h37x69evXCz88PgPLly+Ph4YGNjY3KyYQ+kG9LQgi99eHDB9q3b4+XlxcajQZFUciZMyeOjo5qRxNCCPGToqKiWLJkCePGjePFixcA2NvbM3nyZP744w+V0yUd0dHRzJo1izFjxhAREUGaNGmYOnUq3bp1k9sbhI40e0IIvfT69WsaNWrE0aNHMTY2Jjo6mgwZMrB7925y5MihdjwhhBA/6f79+/Tt25fY2FgqVKjA1KlTqVKlitqxkpQTJ07g5OTE5cuXAWjdujWzZs2S5w2Kz0izJ4TQO/fu3cPW1pbAwEAsLS0JDQ3FwsICX19fChcurHY8IYQQP+jUqVOULVsWjUZDgQIFGD9+PIULF6Zx48ZoNBq14yUZb9++ZdiwYXh4eKAoCnnz5mXRokXUrVtX7WhCT8k1XiGEXrlw4QIVKlQgMDCQ3377jdDQUIyMjPDx8aFcuXJqxxNCCPEDLl26RL169Shfvjxbt27VvT5s2DCaNGkijV4cKYrC+vXrKVy4MO7u7hgaGjJs2DCuXLkijZ74Jr1u9gIDAylatKg8LFmIFGLXrl1UrVqVZ8+eUb16dfbu3UuxYsVYuXKlFDMhhEhC7t27h6OjIyVKlGDXrl1YWVnx6tUrtWMlSXfu3MHW1hYHBweeP39OpUqVuHjxIpMmTcLCwkLteELP6e0wzpiYGIYNG0Z0dLTaUYQQiWDFihV069aN2NhYHBwcWLFiBaamppw5c0YeryCEEElEcHAwkyZNYsGCBURFRWFsbEyvXr0YMWIEGTNmVDtekhIdHY2bmxtjx47lw4cPpE2blmnTptGlSxeZgEXEmd42ex4eHty6dUvtGEKIBKYoCuPHj+fvv/8GoF27duTJkwcTExMAafSEECIJWbp0KbNmzUKj0dCuXTvGjRtH3rx51Y6V5Bw/fhwnJyeuXLkCQNu2bXFzcyNLliwqJxNJjV6eFrhx4waLFi3C2dlZ7ShCiAQUExND9+7d+fvvv9FoNAwfPpwdO3YwYcIEVq9erXY8IYQQ3xETE8PVq1d1P7u4uNCmTRvOnz/P6tWrpdH7QW/evMHJyYlKlSpx5coVfv/9d3bv3o2np6c0euKn6F2z93H4ZsWKFWnYsKHacYQQCSQ0NJSGDRuydOlSzMzMcHd3559//uHt27c0atSINm3aqB1RCCHEVyiKwpYtW/jzzz+pVq0a79+/ByBVqlSsWbOG4sWLqxswiVEUhbVr11K4cGEWL16MsbExI0eOJCAggNq1a6sdTyRhetfsLVmyhPv37zNu3Di1owghEsizZ8/466+/8Pf3J0OGDPj4+DBz5kyePHlClSpVWLduHUZGejvKXAghUrSjR49SqVIlmjRpQmBgIFZWVty9e1ftWEnW7du3qVu3Lm3btuXFixdUqVKFixcvMn78eMzNzdWOJ5I4vWr2bt26xYIFCxgyZIg8FFKIZOrGjRtUqFCB8+fPky9fPvbs2cPff//NjRs3sLGxYdu2bVLchBBCD127do1GjRpRpUoVTpw4QaZMmZg7dy7Xr1+nWLFiasdLcqKiopg4cSJFixZlz549pEuXjmXLlnHw4EGKFCmidjyRTOjNqfPY2FiGDRtGqVKlaNmypdpxhBAJ4NixYzRs2JDXr19TpkwZduzYwejRozlz5gx58+Zl586dpE2bVu2YQggh/oeiKLRr144LFy6QKlUqBg4ciKurK6lTp1Y7WpJ0+PBhevTowfXr1wFwdHRkxowZZM6cWeVkIrnRm2Zv2bJlBAYGsnbtWl6/fg2gG/8dERHB69evSZs2rUw1K0QS5ePjQ5s2bYiMjKRBgwasX7+eVKlSMX78eB4+fMjs2bPJli2b2jGFEEL8f2/fviUqKorMmTOj0WiYPHkyW7duZfTo0TIC6ye9evWKwYMHs3z5cgAKFCiAu7s7NWrUUDmZSK40iqIoaoeAf89onD59+pvL7Nu3jxw5cnzy2rlz5yhVqlRCRhNC/KJ58+bRt29fFEXBycmJefPmYWRkhEajUTuaSELkeP9j5PMSP+vDhw/Mnz+fSZMm0ahRI1asWKF2pCRPURRWr17NwIEDCQ4OxsTEhGHDhjF06FDMzMzUjieSga8d8/Xmyt6QIUN0V/I+Cg4OZtCgQTRq1IjGjRuTKVMmldIJIX6GVqtlyJAhzJgxA4CJEycybNgwJk+ezIsXL5g5c6ZcrRdCCD0RGxvLmjVrGDVqFA8ePADg4cOHxMTEyKRZv+DmzZv07NmT/fv3A1CtWjXc3d0pVKiQyslESqA3/3KLFi362WuPHj0CIGfOnFSsWDGxIwkhfkFkZCQdO3Zk/fr1GBkZsWzZMtq3b8/SpUsZMWIEGo2GVq1aUaFCBbWjCiFEiqYoCv7+/gwdOpTLly8DYGNjw9SpU6lbt66MwvhJkZGRTJ06lYkTJxIVFUWGDBmYOXMmjo6O8pmKRKM3zZ4QIvl4+/YtjRs35tChQ6ROnZpNmzZRu3ZtNm/ejJOTEwALFiyQRk8IIfTA7du3adCgAYqikCtXLiZMmEDbtm1l5MUvOHjwID169ODGjRsAdOrUiWnTppExY0aVk4mURpo9IUS8evDgAXZ2dly9epVs2bLh5+dH8eLFOXToEA4ODmi1WsaMGUPPnj3VjiqEECnWgwcPyJkzJxqNhgIFCtCnTx9y5cqFs7Oz3EP2C4KDg3F1dWXlypUAFC5cGHd3d/766y+Vk4mUSq+bvRw5cujOiAgh9N+lS5ews7PjyZMnFClSBH9/f3LlysWlS5do2LAhkZGRODs7M3r0aLWjCiFEivTs2TPGjh3LkiVL8PPzo06dOgDMnj1b3WBJnKIorFy5EldXV169eoWpqSkjR45k0KBBmJqaqh1PpGByfV4IES/27NlDlSpVePLkCVWrVuXo0aPkypULAFdXV96/f0+LFi2YO3dukrtXISgoCGdnZ6ysrDAwMMDKygpnZ2eCgoLUjiaEEHHy/v17Ro8eTf78+XF3d0dRFM6fP692rGQhMDCQ6tWr06lTJ169ekXNmjW5fPkyI0eOTBGNntRIPackcWfPnlU7ghAp3sqVKxUjIyMFUFq1aqV8+PDhk/dfvXqlDBw48LPXkwI/Pz/FwsJCMTY2VgDdf8bGxoqFhYXi5+endsQUQ473P0Y+L6EoihIZGanMnTtXyZQpk+741ahRI+XatWtqR0vyIiIilFGjRunqQ6ZMmRRPT09Fq9WqHS3RSI3UH1875suVPSHET1MUhYkTJ9KhQwdiYmIYNGgQa9euxdTUlIiICJT//xjP9OnTM2PGjCR3hjMoKIjmzZsTHh5OdHT0J+9FR0cTHh5O8+bN5eylEEJvzZo1iz59+vDy5UsqVqzI0aNH2bJlC9bW1mpHS9L27duHjY0N48ePJzo6mm7duhEYGEjbtm2T3OiVnyU1MmmQZk8I8VNiYmLo0aMHI0eORKPRMHfuXKZNm4aBgQEfPnygfv369OjRg9jYWLWj/jQ3N7fPCtj/io6OZtasWYmUSAghvu/58+e6/+/RowdVqlRhy5YtHD16lEqVKqmYLOl78eIFjo6O1KpVi1u3blGkSBGOHDnC4sWLSZ8+vdrxEpXUyKRBmj0hxA8LCwujcePGLF68GDMzMzZt2oSLiwvw70N527Vrx4EDB9i2bdsnXzqSGk9PzzgVstWrVydSIiGE+LoLFy5Qp04dSpUqRXh4OABp0qTh8OHDNGrUKMVccUoIWq2WZcuWUbhwYTw9PTEzM2PixIlcuHCBypUrqx1PFVIjkwa9no1TCKF/Xrx4QYMGDThz5gzp06dn+/btVKxYEfh3WGevXr3YtGkTadKkYdeuXfz2228qJ/55oaGh8bqcEEIkhLt37zJy5EjWrl0LgJWVFZcuXZJnmcaTa9eu0aNHD44cOQJAnTp1WLhwIfnz51c5mbqkRiYNcmVPCBFnt27dokKFCpw5c4a8efNy/PhxXaMHMGbMGDw8PDA1NWXbtm3Y2NiomPbXWVpaxutyQggRn4KDg+nXrx+FChVi7dq1mJiYMGDAAO7cuSONXjyIiIhg5MiRFC9enCNHjpAlSxbWrl3Lzp07U3yjB1Ijkwpp9oQQcXLy5EkqVKjAnTt3KFWqFMePH6dQoUK69xcuXMi4ceMwMDBgw4YNVK1aVcW08aNdu3YYGxt/cxljY2McHR0TKZEQQvwfOzs75syZQ0xMDO3bt+fmzZu4ubmRIUMGtaMleXv27OHPP/9k4sSJREdH4+TkxPXr13FwcJDhsP+f1MikQZo9IcR3bd26lerVq/Pq1StsbW05ePAgWbNm1b0fHR3N8uXLAVi8eDGNGjVSK2q8GjhwYJwKWf/+/RMpkRAiJYuOjiYkJET385AhQ7C1teXChQusXLmS3Llzq5gueXj27Blt2rShTp06BAUFUbRoUY4dO4a7uzvp0qVTO55ekRqZNEizJ4T4pgULFtC0aVM+fPhA165d2bZt22dDMoyNjdm/fz9r1qyhS5cuKiWNf/nz58fb2xsLC4vPCpqxsTEWFhZ4e3vLcB4hRIJSFIVNmzZRtGhRhg0bpnu9adOm+Pn5UaxYMRXTJQ9arZbFixdjbW3NunXrMDc3Z8qUKZw/f/6T2xXE/5EamTRIsyeE+CKtVsvQoUPp3bs3Wq2WsWPHsnjxYoyM/m9ep/v376PVaoF/JwRo06aNWnETjK2tLQEBAXTv3h0rKysMDAywsrKie/fuBAQEYGtrq3ZEIUQydvjwYSpWrEjz5s25efMm+/fvJyoqCkCGE8aTy5cvU6VKFZycnHj79i316tXjypUrDBky5LtXrlI6qZH6T6N8fOpxEnXu3DlKlSqldgwhkpXIyEg6d+7M2rVrMTIyYsmSJXTs2PGTZW7evEmlSpWoV68ey5cvl4IoEpwc73+MfF5J25UrVxg2bBg7duwAIHPmzPz9999069ZNjrfxJDw8nHHjxuHm5kZMTAxZs2Zlzpw5tGjRQhppkeR87Zgvj14QQnzi7du3NG3alAMHDmBpaYm3tzd169b9ZJknT55Qp04dgoODefnyJUn8nJEQQuiVu3fvUqxYMbRaLZaWlri6ujJgwABSp06tdrRkw9/fH2dnZ+7du4dGo6Fnz55MmjSJtGnTqh1NiHglzZ4QQufhw4fY2dlx5coVsmbNip+fHyVKlPhkmTdv3lCvXj3u379P2bJl8fb2xsTERKXEQgiRPISGhuruh86bNy+tWrUiQ4YMjBw5kixZsqicLvl4+vQp/fv3Z8OGDQDY2Njg4eFB+fLlVU4mRMKQe/aEEAAEBARQoUIFrly5grW1NSdPnvys0YuIiKBhw4ZcvnyZwoUL4+vrK8/PEUKIXxAREcH06dPJlSuX7qHdAGvWrGHevHnS6MUTrVbLokWLKFy4MBs2bMDCwoLp06dz9uxZafREsibNnhCC/fv3U6VKFR4/fkyVKlU4evToZ1N4x8TE0KpVK44ePUr27NnZtWsXGTNmVCmxEEIkbbGxsaxYsYKCBQsyePBg3rx5w+bNm3Xvyz1j8ScgIIBKlSrh7OzM+/fvqV+/PlevXsXV1VXufxTJnjR7QqRwa9asoV69erx//54WLVqwe/du0qdP/9lyYWFhBAcHky5dOnbv3k2uXLlUSCuEEEmboij4+vpSvHhxOnfuzKNHjyhWrBj+/v64ubmpHS9ZCQsLY/DgwZQsWZKTJ0/y22+/4e3tzfbt28mTJ4/a8YRIFHLPnhAplKIoTJ06VffMpn79+uHm5oaBwZfPAaVJk4Y9e/YQFBREkSJFEjOqEEIkG/PmzaNv374A5MmThwkTJuDg4PDVY6/4Ob6+vvTq1Yv79++j0WhwcXFhwoQJWFlZqR1NiET1Q0eWJ0+ecPnyZd1ztYQQSVNsbCy9evVi2LBhaDQaZs6cyaxZs774ZWPfvn3ExsYCkCpVKmxsbBI7rhDJltTVlOHDhw+6/2/Tpg358uVj5syZBAYG0rZtW2n04tHjx49p3rw5DRo04P79+5QoUYJTp04xd+5cafREivRDV/ZatGjB69evsbCwoFSpUpQrV45y5crxxx9/yNhyIZKI8PBwHBwc2LZtG6ampqxevZoWLVp8cVlPT08cHR1p0aIFGzZskH/nQsQzqavJ29OnTxkzZgwHDhzgypUrmJiYkDFjRm7evImhoaHa8ZKV2NhYFi5cyIgRIwgJCSFVqlSMHz8eFxcXjIxkIJtIuX7ob//kyZPZuHEj586d4/Dhwxw+fBiNRoOlpSWlSpWifPnylCtXDmtr64TKK4T4BS9fvsTe3p5Tp06RLl06tm7dSpUqVb64rL+/P506dQKgXLly8sVTiAQgdTV5ev/+PdOmTWPWrFmEh4djYGDAkSNHqFmzJoA0evHswoULdO/enbNnzwJgb2/P/Pnz5d5yIQCN8pNPQ7516xanT5/m9OnTnDt3juDgYN2XQSsrK2rUqIGjo2OC39vztafFCyE+dfv2bWxtbbl9+za5c+fG39//q18gT506RY0aNQgPD2fw4MFMnTo1kdMK8bnkfryP77qa3D8vfRQZGYm7uzsTJkwgODgYgMaNGzNp0iRp2BNAaGgoo0ePZs6cOWi1WrJnz878+fNp3Lix2tGESHRfO+b/dLP3v4KCgtixYwdLlizByMiIDx8+YGhoSPfu3XU3IicEKWZCfN+pU6do0KABwcHBlChRAl9fX7Jly/bFZa9fv07lypV5/fo1HTt2ZPny5XJVT+iFlHa8/9W6mtI+L31Qo0YNDhw4AEClSpWYNm0aFStWVDlV8rRt2zZ69+7Nw4cPMTAwoE+fPowbN47UqVOrHU0IVXztmB9vg5jz589P3759yZYtG+/evSN79uxs2rSJRYsW8eHDB4YMGRJfuxJC/IBt27bRunVrIiIiqFevHhs3bvxqMXz06BF16tTh9evXNGjQgCVLlkijJ4RKpK4mDTExMbp7wjp16sTz58+ZMmUKDRo0kONnAnj06BF9+vTRPZOwVKlSeHh4yIkNIb7ih6d/ioyMJCoq6qvvt2zZksOHD2NnZ8eyZctYsGAB3t7enDp16peCCiF+3KJFi2jSpAkRERF07tyZbdu2ffOsZ+rUqcmfPz+VKlViw4YNclO7EIlA6mrSdP78eWrXrs3w4cN1r7Vt25aAgADs7e2l0YtnsbGxzJkzB2trazZv3oylpSVz5szh1KlT0ugJ8Q0/1Oxt3ryZ0qVLU6pUKZydndm3bx8xMTGfLRcWFqb7/5o1azJz5kxWrFjx62mFEHGiKArDhw/H2dkZrVbLmDFjWLp0KcbGxt9cL02aNOzcuZMdO3ZgYWGRSGmFSLmkriY9d+7coU2bNpQqVYq9e/eyevVq3aMVDAwMZPKVBHDu3DnKli1Lv379CA0NpWnTply/fp0+ffrI5y3Ed/zQaXt3d3ccHR0JCgri8OHDHDhwACsrKypVqkTRokWxtLTk5MmTnz0vpkqVKsyfPz9egwshviwqKoouXbrg6emJoaEhHh4edOnS5avLR0dHs3DhQpydnTE2NsbMzAwzM7NETCxEyiV1Nel4+fIl48ePx93dnejoaExMTHBxcWH48OFyzEwgISEhjBo1innz5qHVasmVKxfz58/H3t5e7WhCJBk/1OylSZOGwYMHA/D69Wt8fHzYvn07fn5++Pn5AWBmZoa7uzsAK1euJHPmzNja2mJpaRnP0YUQ/+vdu3c0a9aMffv2kSpVKry8vLC1tf3q8lqtls6dO+Pp6cmFCxf4559/Ei+sEELqahLx6NEjihQpQkhICBqNhg4dOjB27Fhy586tdrRkSVEUtmzZgouLC48fP8bQ0JCBAwcyZswY+XsvxA/6oWavSZMmjBs3jqFDh5I+fXq6du1K165defz4Mbdv3yYiIoJSpUqRKVMmABYuXEhoaCjPnz8nR44cCfILCCH+9fjxY+zs7AgICCBLliz4+vp+8z4GRVEYNGgQnp6epEqVil69eiViWiEESF3VZ1qtVndFNUeOHFSuXBmNRsOUKVP4888/VU6XfD148AAXFxe2bdsGQJkyZfDw8KBEiRIqJxMiafrhRy8cO3aM5cuXY21tjaur6zeXPXz4MGvXriVXrlwMGDAgQYY5yNTSQsDVq1extbXl4cOHFCpUCH9/f/LmzfvNdaZNm8aQIUMwNjZmx44d1KlTJ5HSCvFzkuvxPqHqanL9vBKaoij4+PgwYsQIPD09KV26NAARERGYm5urnC75iomJYe7cuYwePZqwsDBSp07N5MmT6dGjh9yXJ0QcxPtz9oKCgsifP/8vB/tVUsxESnfw4EEaN27Mu3fvqFSpElu3biVDhgzfXGfFihV07twZjUbDmjVrcHBwSKS0Qvy85H68j++6mtw/r4Rw6NAhBg8ezOnTpwHo2LGjTISTCM6cOUP37t25ePEiAM2aNWPu3Ln89ttv6gYTIgn52jH/hx+98JE+NHpCpHTr1q2jbt26unv19uzZ891G78CBA3Tr1g2AOXPmSKMnhJ6QuqqegIAA6tevT7Vq1Th9+jRZsmRh4cKFLF68WO1oydq7d+9wcXGhXLlyXLx4kdy5c7Njxw68vb2l0RMinshDtIRIghRFYcaMGbqJHfr27Yubm1uchrqUKVOGmjVrUqZMGVxcXBI6qhBC6LWVK1fSqVMnFEXB0tKSQYMGMWDAAJkIJAEpisKmTZvo27cvT5480U3AMnr0aFKlSqV2PCGSFWn2hEhiYmNj6du3LwsWLABg5syZ9O/fP87rW1pasmPHDnlguhAixVIURffQ89q1a2NlZUWHDh0YMWIEmTNnVjld8nbv3j169+6Nr68vAOXLl8fDwwMbGxuVkwmRPP30ME4hROKLiIigefPmLFiwABMTE9avXx+nRu9jcY2MjATA2NhY90VHCCFSioiICKZOnUrlypV1D6//7bffePjwIXPmzJFGLwFFR0czffp0/vjjD3x9fUmTJg0LFy7k2LFj0ugJkYDk1L4QSURwcDANGzbkxIkTpE2blq1bt1K1atXvrvfixQvq1KnDrVu3dLObCSFEShITE8OqVasYPXo0jx8/BsDf31/3cO7UqVOrGS/ZO3nyJE5OTgQEBADQqlUrZs2aRbZs2VROJkTyJ1f2hEgC7ty5Q8WKFTlx4gS5cuXi2LFjcWr0QkJCsLOz49atWxQrVoyhQ4cmQlohhNAPiqKwbds2ihUrRpcuXXj8+DElSpRg9+7dukZPJJy3b9/i7OxMxYoVCQgIIG/evPj5+bF+/Xpp9IRIJHJlTwg9d+bMGRo0aMCLFy8oVqwYfn5+cZqlLDIykqZNm3Lu3Dny5cvHzp07SZMmTSIkFkII/dCqVSu8vLwAyJMnDxMmTMDBwUH3sHSRMBRFYePGjfTr149nz55hZGTEoEGDGDlyJBYWFmrHEyJFkaOdEHrM19eXatWq8eLFC2rXrs3hw4fj1OhptVo6dOjA3r17yZw5M7t37yZr1qyJkFgIIfRHzZo1yZgxI3PmzCEwMJC2bdtKo5fA7ty5g52dHa1bt+bZs2dUqlSJCxcuMGnSJGn0hFCBHPGE0FNLliyhYcOGhIeH06FDB3x9fbGysorTuvPnz2fDhg2kTp2anTt3yvO7hBDJ3pMnT+jevTvjx4/Xvda5c2eCgoLo06cPpqamKqZL/qKjo5kyZQp//PEHO3fuJG3atCxevJjDhw9TtGhRteMJkWLJME4h9IyiKIwePZoJEyYAMHr0aMaMGfNDs2d269aNY8eO0aNHD0qUKJFQUYUQQnXv3r1j2rRpzJo1i4iICNKmTcuAAQNIlSoVxsbGGBsbqx0x2Tt27BhOTk5cvXoVgLZt2+Lm5kaWLFlUTiaEkGZPCD0SFRVFt27dWLVqFYaGhixatIhu3brFef2Pz44yNzdnw4YNCZhUCCHUFRkZycKFC5k4cSKvXr0CoFmzZkycOFEezJ1I3rx5w9ChQ1m8eDEA+fPnZ+HChdSpU0flZEKIj6TZE0JPvH//nubNm7Nnzx4sLCzw8vLCzs4uzuv7+Pjg6enJmjVrMDc3T8CkQgihrmfPnlG+fHnu378PQJUqVZg2bRrly5dXOVnKoCgK69ato3///rx48QJjY2OGDBnC8OHDpf4IoWek2RNCDzx58gQ7OzsuXbpE5syZ8fX1pXTp0nFe/8CBAzg4OBAVFcWGDRvo2LFjwoUVQgiVZcmShTx58mBpacnkyZNp0KDBDw11Fz/v9u3bODs7s2fPHuDfRtvDwwNra2uVkwkhvkQmaBFCZVevXqV8+fJcunSJAgUKcOLEiR9q9C5cuECjRo2Iioqid+/edOjQIQHTCiFE4jt79iy1a9fmypUrAGg0GjZs2MClS5ewt7eXRi8RREVFMXHiRIoWLcqePXtIly4dy5Yt4+DBg9LoCaHHpNkTQkWHDh2icuXKPHz4kAoVKnD8+HHy5csX5/WDgoKwtbUlJCSEVq1aMWfOHPnSI4RINm7fvk2rVq0oU6YMe/fuZeLEibr3smTJgqGhoYrpUo4jR45QvHhxRo4cSWRkJI6OjgQGBtK5c2d5lIUQek7+hQqhko0bN1KnTh3evn1L48aN2bdvHxkzZozz+s+ePaNOnTo8f/6cWrVqsXLlSim6Qohk4cWLF/Tu3Rtra2s2btyIqakpgwcPZuHChWpHS1Fev35Nt27dqFq1KtevX6dAgQLs3buXVatWkTlzZrXjCSHiQO7ZEyKRKYrCrFmzGDhwIAC9evVizpw5P3yGetKkSdy5c4fSpUvj4+Mjz5ASQiQLW7ZswdHRkdDQUDQaDR07dmTcuHHkzJlT7WgphqIoeHp6MnDgQF6+fImJiQlDhw5l2LBhmJmZqR1PCPEDpNkTIhHFxsYycOBA5syZA8C0adNwdXX9qaGX06dP153tTp06dXxHFUIIVRQvXpyoqCgaNGjA5MmT5YHciezmzZv07NmT/fv3A/DXX3/h7u5O4cKFVU4mhPgZ0uwJkUgiIiJwdHRk06ZNmJiY8M8//+Dg4PBD24iNjSU2NhYTExNMTU2ZPn16AqUVQoiEpygK3t7eeHl5sX79egwMDMiTJw+BgYHkzZtX7XgpSmRkJFOnTmXixIlERUWRIUMG3NzcaN++vdwLLkQSppc3+Jw4cQIHBwdKlChBlSpVmDhxImFhYWrHEuKnvXr1itq1a7Np0ybSpEnDrl27frjRUxSFnj170rBhQ0JDQxMoqRBCJI4DBw5Qrlw5WrZsiZeXF1u2bNG9J41e4jp06BDFihXj77//Jioqio4dOxIYGEiHDh2k0RMiidO7Zu/kyZN07tyZ6OhoXF1dadSoERs2bKBr165otVq14wnxw+7evUulSpU4duwYOXPm5OjRo1SrVu2HtzN69GiWLFnCoUOHuH79evwHFUKIRHDp0iVsbW2pUaMGZ86cIWvWrHh4eNCwYUO1o6U4wcHBdOrUiWrVqnHjxg0KFSrEgQMHWLFixQ9NGCaE0F961+xNmzaNbNmy4enpSdu2bXF1dWXIkCGcP3+eI0eOqB1PxEFQUBDOzs5YWVlhYGCAlZUVzs7OBAUFqR0t0Z07d44KFSpw48YNbGxsOHHixE/dfzJv3jwmTJiAoaEhGzdupEyZMgmQVgghEla/fv0oUaIEO3fuJHXq1EyYMIHbt2/TvXt3jIxSxp0l+lAjFUVh5cqVFC5cmH/++QdTU1PGjh3LpUuXfupkpBBCf+lVsxcZGUm6dOlo2bLlJ7M9lS1bFoAbN26oFU3Ekb+/PzY2NixdupSQkBAURSEkJISlS5diY2ODv7+/2hETjb+/P3/99RfPnz+nZs2aHDlyhOzZs//wdtavX0/fvn0BWLJkCfb29vEdVQghEkWuXLkwMjKiT58+BAUFMWLECFKlSqV2rESjDzUyMDCQGjVq0LFjR169ekWNGjUICAhg9OjRMquzEMmQXp1GMzU1ZdmyZZ+9/nHI2m+//ZbYkcQPCAoKonnz5oSHh3/2XnR0NNHR0TRv3pyAgADy58+vQsLEs2zZMpycnIiNjaVdu3YsW7YMExOTH97Onj17aN++PYqiMHXqVDp16pQAaYUQIv6Fh4czd+5c3ZUrAGdnZxo3bky+fPlUTpf41K6RHz58YPLkyUyZMoWoqCgyZcrEzJkzadu2rdyXJ0QypldX9v7X48eP8fHxYeLEiRQsWJDatWurHUl8g5ubG9HR0d9cJjo6mlmzZiVSosSnKAp///03Xbt2JTY2luHDh7Nq1aqfavTg36YxOjqaAQMGMGjQoHhOK4QQ8S8mJoalS5dSoEABhg0bxogRI3j//j0AZmZmKbLRA3Vr5P79+7GxsWHcuHFERUXRpUsXAgMDadeunTR6QiRzGkVRFLVDfMnbt28pV64cAObm5nh4eOh+/q9z585RqlSpxI4nvsDKyoqQkJA4Lffu3btESJS4oqOjcXJyYsWKFRgYGLBgwQJ69Ojxy9tcuXIlnTt3xsBAr8/NCJHg5Hj/YxL781IUhW3btjFs2DDdiJySJUsydepUatWqlWg59JUaNfLly5cMHDiQ1atXA2BtbY2HhwdVqlSJl+0LIfTH1475evvtUaPRMGvWLKZOnUr+/Pnp1KkTO3fuVDuW+Ia4Pg4gOT42ICQkBHt7e1asWIG5uTlbtmz56Ubv+fPnfPjwAQBjY2O6du0qjZ4QQq8FBwdTuXJlGjduzPXr18mXLx/r1q3jzJkz0uj9f4lZI7VaLcuWLaNw4cKsXr0aMzMzJk6cyMWLF6XREyKF0dtvkGnSpMHOzo7GjRuzZs0afvvtN6ZMmaJ2LPENlpaW8bpcUvH06VP++usvdu3aRaZMmThw4MBPT6Ly5s0batWqRb169ZLl1U8hRNLxI7NGZsiQgejoaDJmzMjcuXO5fv06rVu3lhNV/5FYNfLatWtUq1aNrl278vr1a2rXrs3ly5cZPnz4T99SIIRIupLEUdjMzIxq1arx9OlTXr9+rXYc8RXt2rXD2Nj4m8sYGxvj6OiYSIkS3vXr16lQoQIXLlzg999/5/jx418cbhwX4eHh2Nvbc+XKFV68eEFMTEw8pxVCiLj53qyRq1evpnv37ty+fRv4dzTO2rVrCQoKwsXFRZqKL0joGhkREcHIkSMpXrw4R44cIXPmzKxdu5Zdu3bx+++//9Q2hRBJn141e0FBQdSoUYM1a9Z89l5YWBgajUYKiB4bOHBgnApZ//79EylRwjp69CiVKlXi/v37lC9fnuPHj/90QY2JiaF169YcO3aMHDlysGvXLjJkyBDPiYUQ4vv+O2vk/04oEh0dTXh4OO3bt2fJkiWMHj1a997vv/+OlZVVYsdNMhKyRu7duxcbGxsmTpxIdHQ03bt3JzAwEAcHB5mARYgUTq+avdy5cxMSEsL69euJiorSvf748WN2795NmTJlkt0QwOQkf/78eHt7Y2Fh8VlBMzY2xsLCAm9v72Tx2AVvb29q1arFmzdvaNiwIfv27SNTpkw/tS1FUejWrRvbt28nffr07N69m5w5c8ZzYiGEiJu4zBoJ/x7zx4wZk/CBkomEqJHPnz+nbdu21K5dm9u3b1O0aFGOHTuGh4cH6dKli+9fQQiRBOlVs2dkZMTIkSO5efMmjo6OrFmzhvnz59O8eXM0Gg2jRo1SO6L4DltbWwICAujevfsn93l0796dgIAAbG1t1Y74y2bPnk3Lli2JjIykZ8+e+Pj4YGFh8dPbGzp0KP/88w8WFhb4+flhbW0dj2mFEOLHeHp6xqnZe/nyJQULFkyERMlHfNVIrVbL4sWLKVy4MGvXrsXc3JwpU6Zw/vx5KlasmMC/hRAiKdHLRy/4+fmxdOlSbt68iYWFBeXLl6d///7kzZv3s2VlKm6RWLRaLa6urrpnIE2ZMoXBgwf/0hCZ2NhYWrVqxdatW9m+fTv16tWLr7hCJDtyvP8xP/t5GRgYEJevBgYGBsTGxv5MNPELrly5gpOTE8ePHwegXr16LFiwIMU+v1AI8a+vHfONVMjyXXZ2dtjZ2akdQwidDx8+0L59e7y8vDA2NmbFihW0bdv2l7draGjIhg0bOHPmDOXLl4+HpEII8WvMzc0JDw//7nJyW0XiCg8PZ/z48cyYMYOYmBiyZs3KnDlzaNGihdyXJ4T4Kr0aximEPvo4dbWXlxdWVlb4+/v/cqN38uRJwsLCgH8bPmn0hBBqu3XrFi1btoxTo5fcZlbWd/7+/hQtWpQpU6YQGxtLz549uX79Oi1btpRGTwjxTdLsCfEN9+/fp3Llyhw9epTs2bNz5MgRatas+UvbPHHiBDVq1KBWrVrJ8gHzQoik5dmzZzg7O1OkSBG8vLwwNTXFyOjbA3+S08zK+uzp06e0bt0aOzs77t69i42NDcePH2fhwoWkTZtW7XhCiCRAmj0hvuLChQuUL1+e69evU7RoUU6ePImNjc0vbfPq1avUr1+fiIgIihQpQqpUqeIprRBC/Ljp06fz+++/s2jRIrRaLV26dOH27dts27YtRcysrK+0Wi2LFi2icOHCbNiwAQsLC6ZPn87Zs2dlJIgQ4odIsyfEF+zatYuqVavy7NkzqlevzpEjR8iRI8cvbfPBgwfUq1dP97gGDw8PGX4jhFDVhw8fCAsLo2HDhgQEBLB06VJy5MiRImZW1lcBAQFUqlQJZ2dn3r9/T/369bl69Squrq7ffU6fEEL8L72coEUINf3zzz907dqV2NhY2rRpw/LlyzE1Nf2lbQYHB1O3bl0ePXpE5cqVWb9+/XeHSQkhRHzSarV4eXmh1WpxcHAAYMCAAVSvXp3KlSt/tnz+/PmZP38+8+fPT+yoKVJYWBhjx45l5syZxMbGki1bNubNm0fTpk3lxKAQ4qfJlT0h/j9FURg3bhydOnUiNjaWoUOHsnr16l9u9MLCwmjQoAGBgYH8+eefbN++HXNz83hKLYQQ37dv3z7Kli1L69at6du3LyEhIQCkSpXqi42eSFx+fn788ccfTJ8+Ha1WS69evbh+/TrNmjWTRk8I8Uvk0oIQQHR0ND179mTZsmUYGBgwb948nJ2d42XbJiYmFChQgOfPn7Nz5065qV4IkWguXrzI0KFD2bVrFwDZsmVjzJgxcsJJTzx58oS+ffvi7e0NQPHixfHw8KBs2bIqJxNCJBfS7IkULzQ0lJYtW+Lv74+5uTnr1q2jUaNG8bZ9Y2NjVq5cyYsXL8iaNWu8bVcIIb6nRIkSAFhZWTFkyBD69euHhYWFyqlEbGws7u7uDBs2jJCQECwsLBg/fjx9+vSRIf5CiHglRxSRoj179owGDRpw7tw5MmbMyPbt2+NlpjNFUVi8eDEODg66yQ2k0RNCJDZjY2N69erFiBEjyJgxo9pxBP9ebe3evTtnzpwBwN7envnz55MrVy6VkwkhkiO5Z0+kWDdu3KBChQqcO3eO/Pnzc/z48Xib0nrq1Kn06NGDunXrotVq42WbQgjxo27cuMGsWbOk0dMDoaGhDBw4kNKlS3PmzBmyZ8+Oj48PW7dulUZPCJFgpNkTKdKxY8eoWLEi9+7do0yZMhw/fpwCBQrEy7aXLVvGsGHD0Gg09O/fHwMD+WcmhFBH3rx51Y4ggO3bt1OkSBFmzpyJoij07duX69ev06RJE5mARQiRoORbqEhxfHx8qFmzJq9fv6ZBgwYcOHCAzJkzx8u2t2zZQvfu3QGYP38+LVu2jJftCiGESHoePXpE06ZNadiwIQ8fPqRkyZKcPn2a2bNnkzp1arXjCSFSAGn2RIoyd+5cmjdvTmRkJE5OTmzevJlUqVLFy7YPHz5M69at0Wq1jB49Ot5m8xRCCJG0xMbGMnfuXKytrdm8eTOWlpbMnj2bU6dOUapUKbXjCSFSEJmgRaQIWq2WIUOGMGPGDAAmTpyoG2oZH27fvk3Dhg11TeSYMWPiZbtCCCGSlnPnzuHk5MS5c+cAaNy4MfPmzSNHjhwqJxNCpETS7IlkLzIyko4dO7J+/XqMjIxYvnw5jo6O8bqPPHny0KJFC968ecOCBQvkHgwhhEhhQkJCGDVqFPPmzUOr1ZIzZ07mz59Pw4YN1Y4mhEjBpNkTydrbt29p3Lgxhw4dInXq1Pj4+FCrVq1434+RkRGLFy8mJiYGQ0PDeN++EEII/bVlyxZcXFx49OgRhoaGDBgwgLFjx2Jpaal2NCFECif37Ilk68GDB1SqVIlDhw7x22+/ceTIkXht9N6/f0/Pnj158+YNABqNBmNj43jbvhBCCP328OFDGjduTJMmTXj06JHusQpubm7S6Akh9IJc2RPJ0sWLF7Gzs+Pp06cUKVIEf3//eH2OUWRkJE2aNGH//v08efKErVu3xtu2hRBC6LeYmBjmzZvHqFGjCAsLI3Xq1EyaNImePXvK6A4hhF6RZk8kO3v27KFZs2aEhITw119/sXnzZtKlSxdv24+NjcXR0ZH9+/eTJUsWZs2aFW/bFkIIod/OnDmDk5MTFy5cAKB58+bMnj2b7Nmzq5xMCCE+J8M4RbKyatUq7OzsCAkJoXXr1uzatSteGz1FUejTpw9eXl5YWVmxc+dO8uXLF2/bF0IIoZ/ev39Pnz59KFeuHBcuXCBXrlxs374dLy8vafSEEHpLmj2RLCiKwsSJE+nQoQMxMTG4urqyZs0aTE1N43U/48aNY+HChZiamrJt2zaKFy8er9sXQgihXxRFwdvbG2tra+bNm4eBgQGDBg3i2rVrNGjQQO14QgjxTTKMUyR5MTEx9OrVi8WLF6PRaJgzZw4uLi7xvp89e/YwZswYDAwMWLduHX/99Ve870MIIYT+uHfvHr1798bX1xeAcuXK4eHhQbFixVROJoQQcSPNnkjSwsLCaNWqFb6+vpiZmbF27VqaNGmSIPuqWbMmffr0oWjRogm2DyGEEOqLjo5m9uzZjBkzhvDwcNKkScPkyZPp3r27TMAihEhSpNkTSdaLFy+oX78+Z8+eJX369Gzbto1KlSrF+34URUGj0WBgYMCcOXPifftCCCH0x8mTJ3FyciIgIACAVq1aMWvWLLJly6ZyMiGE+HFyz55Ikm7dukWFChU4e/YsefPm5fjx4wnS6J0/f56aNWvy8uXLeN+2EEII/fH27VucnZ2pWLEiAQEB5MmTBz8/P9avXy+NnhAiyZJmTyQ5J0+epEKFCty5c4dSpUpx4sQJChUqFO/7uXXrFvXq1ePAgQNMnz493rcvhBBCfYqisGHDBqytrVm0aBGGhoYMHTqUq1evYmtrq3Y8IYT4JTKMUyQpW7ZswcHBgQ8fPmBnZ8eGDRuwtLSM9/08ffqUOnXq8PLlS+rUqcOECRPifR9CCCHUdefOHXr16sXOnTsBqFixIh4eHhQtWlTlZEIIET/kyp5IMhYsWEDTpk358OED3bp1Y+vWrQnS6L19+5Z69epx7949ypYty6ZNmzAxMYn3/QghhFBHdHQ0U6ZMoWjRouzcuZO0adOyePFijhw5Io2eECJZkSt7Qu9ptVqGDRvGtGnTABg/fjwjRoxAo9HE+74iIiJo1KgRAQEBFCpUCF9f3wRpKIUQQqjj+PHjODk5ceXKFQDatm2Lm5sbWbJkUTmZEELEP2n2hF6LjIykU6dOrFu3DiMjI5YsWULHjh0TbH///PMPhw8fJnv27OzatYuMGTMm2L6EEEIknjdv3jB06FAWL14MQP78+Vm0aBG1a9dWOZkQQiQcafaE3nr79i1NmzblwIEDWFpasmnTJurUqZOg++zRowcvX76kadOm5M6dO0H3JYQQIuEpisK6devo378/L168wNjYmMGDBzNixAjMzc3VjieEEAlKmj2hlx4+fIidnR1XrlwhW7Zs+Pn5Ubx48QTb34cPHzAzM0Oj0TB69OgE248QQojEExQURM+ePdmzZw8AlStXxsPDgyJFiqicTAghEodM0CL0zuXLl6lQoQJXrlzB2tqaEydOJGijN2fOHMqWLcvTp08TbB/xISgoCGdnZ6ysrDAwMMDKygpnZ2eCgoLUjiaEEHolKiqKSZMmUbRoUfbs2UO6dOlYunQphw4dkkYvGZL6KMTXSbMn9Mr+/fupXLkyjx8/pkqVKhw7dixBh1OuXbuWfv36cfnyZY4cOZJg+/lV/v7+2NjYsHTpUkJCQlAUhZCQEJYuXYqNjQ3+/v5qRxRCCL1w5MgRSpQowYgRI/jw4QOOjo4EBgbSpUsXDAzka09yI/VRiG+To57QG2vWrKFevXq8f/+eli1bsnv3btKlS5dg+9u1axcdOnQAYPr06bRs2TLB9vUrgoKCaN68OeHh4URHR3/yXnR0NOHh4TRv3lzOYAohUrTXr1/TrVs3qlatyrVr1yhQoAB79+5l1apVZM6cWe14IgFIfRTi+6TZE6pTFIUpU6bQrl07oqOjGTBgAOvWrcPMzCzB9nnq1CmaNm1KTEwMrq6uuLq6Jti+fpWbm9tnRex/RUdHM2vWrERKJIQQ+kNRFDw9PSlcuDBLly7FxMSE0aNHExAQQM2aNdWOJxKQ1Echvk+aPaGq2NhYevXqxbBhw9BoNMyaNQs3N7cEHWoTGBhI/fr1CQ8Pp3379kydOjXB9hUfPD0941TMVq9enUiJhBBCP9y6dYvatWvj6OjIy5cv+euvv7h06RJjx45N0BOGQj9IfRTi+2Q2TqGa8PBwHBwc2LZtG6ampnh6etK8efME3+/GjRt59eoV9evXZ+nSpXp/D0doaGi8LieEEEldZGQk06ZNY+LEiURGRpIhQwZmzJhBhw4d0Gg0ascTiUTqoxDfJ82eUMWLFy+wt7fn9OnTpEuXjm3btlG5cuVE2feoUaPIkSMHrVu3xtjYOFH2+SssLS0JCQmJ03JCCJHcHTp0iB49ehAYGAhAx44dmT59OhkzZlQ5mUhsUh+F+D79vqQhkqXbt29TsWJFTp8+Te7cuTl+/HiCN3rh4eG8evUKAI1GQ+fOnbGwsEjQfcaXdu3afbcpNTY2xtHRMZESCSFE4nv16hWdO3emWrVqBAYGUqhQIQ4cOMCKFSuk0UuhpD4K8X3S7IlEderUKSpUqEBQUBAlSpTg5MmTFC5cOEH3GR0dTcuWLalUqRIPHjxI0H0lhIEDB8apmPXv3z+REgkhROJRFIWVK1dSuHBhVqxYgYmJCWPHjuXSpUtUq1ZN7XhCRVIfhfg+afZEotm2bRvVq1cnODiYevXqcejQIbJmzZqg+9RqtXTr1g1fX1+Cg4MJDw9P0P0lhPz58+Pt7Y2FhcVnRc3Y2BgLCwu8vb3Jnz+/SgmFECJh3Lhxgxo1atCxY0eCg4OpUaMGly9fZvTo0ZiamqodT6hM6qMQ3yfNnkgU7u7uNGnShIiICDp37sy2bdtInTp1gu93yJAhrFy5EgsLC/z8/BL8KmJCsbW1JSAggO7du2NlZYWBgQFWVlZ0796dgIAAbG1t1Y4ohBDx5sOHD4wZMwYbGxsOHjxIxowZWbVqFXv37qVgwYJqxxN6ROqjEN+mURRFUTvErzh37hylSpVSO4b4CkVRGDFiBJMnTwbg77//5u+//06U2dJmzJjBoEGDMDIywtfXlzp16iT4PoUQCUeO9z8mqX5e+/fvp0ePHty6dQuALl26MHXqVDJkyKByMiGE0F9fO+bLbJwiwURFRdGlSxc8PT0xNDTEw8ODLl26JMq+V65cyaBBg3T/L42eEELot5cvX+Lq6sqqVasAsLa2xt3dnapVq6qcTAghki5p9kSCePfuHc2aNWPfvn2kSpUKb29v6tWrl2j7/zgl95w5c2jTpk2i7VcIIcSPURSFFStWMGjQIF6/fo2pqSmjRo1i0KBBmJiYqB1PCCGSNGn2RLx79OgRdnZ2XL58mSxZsuDn50fJkiUTNcPkyZOxs7OjSpUqibpfIYQQcXf9+nV69OjB4cOHAahduzYLFy7k999/VzmZEEIkDzJBi4hXV65coUKFCly+fJlChQpx8uTJRGv0rl+/zrNnz3Q/S6MnhBD6KSIiglGjRlGsWDEOHz5M5syZWbNmDbt27ZJGTwgh4pFc2RPx5sCBAzRp0oR3795RqVIltm3bRvr06RNl3/fv36dWrVqYmZlx8OBBcubMmSj7FUII8WP27t1Lz549uX37NgDdu3dnypQppEuXTuVkQgiR/MiVPREv1q1bR926dXX36u3duzfRGr2XL19Sp04dnjx5Qo4cOciUKVOi7FcIIUTcvXjxgnbt2lG7dm1u377NH3/8wdGjR/Hw8JBGTwghEoheNntHjhyhTZs2FCtWjBIlStCxY0cuXryodizxBYqiMG3aNNq0aUN0dDR9+/Zl48aNmJmZJcr+Q0NDqV+/Pjdv3sTGxoatW7cm2r6FEEJ8n1arZcmSJRQqVIg1a9Zgbm7O5MmTOX/+PJUqVVI7nhBCJGt61+ydPn2abt26ERISQv/+/enVqxcPHjygXbt2BAQEqB1P/EdsbCwuLi4MGTIEgJkzZzJ79mwMDBLnr1VUVBRNmzblzJkz5M2bl507d5I2bdpE2bcQQojvu3r1KlWrVqV79+68ffuWunXrcuXKFYYOHSozbQohRCLQu3v2Jk2aRLZs2di4cSPm5uYANG7cGDs7O2bNmsWKFStUTijg35vr27Rpw5YtWzAxMWH16tW0bNky0fav1Wrp0KEDe/bsIXPmzOzatYts2bIl2v6FEEJ8XXh4OBMmTGD69OnExMSQNWtWZs+eTcuWLdFoNGrHE0KIFEOvmr13794RGBhIp06ddI0eQMaMGSlTpgzHjh1TMZ34KDg4mIYNG3LixAnSpk3L1q1bE/2htxqNhkKFCpE6dWr8/f0pUKBAou5fCCHEl+3atYuePXty9+5dNBoNPXv2ZNKkSTLyQgghVKBXzZ6lpSU7d+78pNH76M2bNxgaGqqQSvzXnTt3qFevHrdu3SJXrlz4+/tTpEiRRM+h0WgYM2YM3bt357fffkv0/QshhPjU06dP6d+/Pxs2bADgzz//xMPDgwoVKqicTAghUi69umfP0NCQPHnykCVLlk9eDwwM5Pz585QoUUKlZALgzJkzVKhQgVu3blG8eHFOnDiR6I3exo0befjwoe5nafSEEEJdWq0Wd3d3rK2t2bBhA+bm5kydOpVz585JoyeEECrTqyt7XxIWFqabAKR79+4qp0m5fH19admyJeHh4dSpUwdvb29Sp06dqBk2b96Mg4MD2bNnJyAgQIYECSGEygICAnBycuLkyZMA2NnZsWDBAvLkyaNuMCGEEICeXdn7XxEREfTs2ZPAwEC6d+9O2bJl1Y6UIi1evJiGDRsSHh5Ohw4d2LFjR6I3eocOHcLBwQGtVkvnzp2l0RNCCBWFhYUxePBgSpYsycmTJ8mWLRteXl7s2LFDGj0hhNAjetvsvX//ns6dO3Pq1CmaNWtG//791Y6U4iiKwsiRI3FyckKr1TJ69GhWrFiBsbFxoua4ePEiDRs2JDIyEmdnZ/7+++9E3b8QQoj/4+fnxx9//MH06dPRarX07t2b69ev07x5c5lpUwgh9IxeDuN89eoVXbp04fr167Rq1YqxY8dKAUlkUVFRdOvWjVWrVmFoaIi7uztdu3ZN9BwfJ4R5//49LVq0YO7cufJ3QQghVPDkyRP69euHl5cXAMWLF8fDw0NG3QghhB7Tu2YvNDRU1+h17NiRYcOGqR0pxXn//j3NmjVj7969WFhY4OXlhZ2dXaLnCAkJoU6dOjx//pyaNWuyevVqmZFVCCESWWxsLO7u7gwfPpz3799jYWHB+PHj6dOnD0ZGevc1QgghxH/o3VF63LhxXL9+nfbt20ujp4InT55gZ2fHpUuXyJw5M76+vpQuXVqVLJaWlnTr1g0vLy82b96MqampKjmEECKlunjxIt27d+fMmTMA2NvbM3/+fHLlyqVyMiGEEHGhV81eUFAQW7duJXXq1FhbW7N169bPlmnUqJEKyVKGa9euUa9ePR4+fEiBAgXYuXMn+fLlUy2PRqNhyJAh9O/fHxMTE9VyCCFEShMaGsqYMWOYPXs2sbGxZM+enXnz5tG4cWMZSi+EEEmIXjV7p0+fBv4dvve1q3rS7CWMQ4cO0bhxY96+fUuFChXYtm0bGTNmTPQcsbGxDBo0CBcXF/LmzQsgjZ4QQiSi7du307t3bx48eICBgQF9+/Zl/PjxiT4LsxBCiF+nV82eg4MDDg4OasdIcTZs2ED79u2JioqicePGrF27FnNz80TPoSgKvXr1wsPDA39/f65cuSL36AkhRCJ59OgRffv2xcfHB4CSJUvi4eGh2lB+IYQQv05vH70gEp6iKMycOZPWrVsTFRWFi4sL3t7eqjR6AGPGjMHDwwNTU1M8PDyk0RNCiEQQGxvL3Llzsba2xsfHB0tLS2bNmsWpU6ek0RNCiCROr67sicQTGxvLwIEDmTNnDgAzZsxgwIABqt2LMX/+fMaNG4eBgQEbNmygatWqquQQQoiU5Ny5czg5OXHu3DkAGjduzNy5c8mZM6fKyYQQQsQHafZSoIiICBwdHdm0aRMmJiasXLmS1q1bq5Zn48aN9OnTB4DFixfLfZlCCJHAQkJCGD16NHPnzkWr1ZIjRw7mz58vx18hhEhmpNlLYV69ekWjRo04duwYadKkYcuWLVSrVk21PHfu3KFdu3YoisKkSZPo0qWLalmEECIl2LJlCy4uLjx69AgDAwP69+/P2LFjZQIWIYRIhqTZS0Hu3r2Lra0tN27cIGfOnPj7+/PHH3+omilfvny4ublx9+5dhg4dqmoWIYRIzh4+fIiLi4vusUalS5fGw8ODkiVLqpxMCCFEQpFmL4U4d+4c9evX5/nz59jY2ODn50f27NnVjgWAi4uL2hGEECLZiomJYd68eYwaNYqwsDBSp07NxIkTcXZ2lomwhBAimZPZOFMAf39//vrrL54/f07NmjU5fPiwqo3ekydPqFatGjdu3FAtgxBCpARnz56lbNmyDBgwgLCwMJo1a8b169dxcXGRRk8IIVIAafaSuWXLlmFvb09YWBjt2rXDz8+PNGnSqJbn7du31KtXj0OHDjFw4EDVcgghREpQrlw5Lly4QK5cudi+fTve3t56M6pDCCFEwpNmL5lSFIW///6brl27Ehsby/Dhw1m1ahUmJiaqZYqIiMDe3p7Lly9TuHBhVq5cqVoWIYRICTQaDYMGDeLatWs0aNBA7ThCCCESmdyzlwxFR0fj5OTEihUrMDAwYMGCBfTo0UPVTDExMbT6f+3df1TV9eHH8RfID0FkilH5I2dTak2nx0QWzJUSMkHCn8mcimip5Y95yBPq1s42z8pZ87BStjklzR8zfyQW4QUtpjJ/NtOcBmlYKp1JzevgAkoX/Xz/2JG+Dk0rve8P9z4f/+HnnnNfR5EXr/v53M9NS9Pf//53dezYUUVFRWrXrp3RTADg7Q4cOKBevXqZjgEAMISx52VcLpceffRRFRUVKSQkROvWrdMjjzxiNJNlWZoyZYry8/PVtm1bbd26VZ07dzaaCQB8AUMPAHwbY8+L/Otf/9LgwYN18OBBRUZG6s0331RMTIzpWNqxY4defvllhYSEqKCgQN/73vdMRwIAAAC8HmPPS5SWliopKUknT55Ut27d5HA41K1bN9OxJEn9+/fX0qVL1aFDB8XGxpqOAwAAAPgExp4XKCkp0ZAhQ3Tu3Dn94Ac/UH5+viIjI03HUn19vYKDgyVJjz/+uOE0AAAAgG/hbpzN3IYNGzRw4ECdO3dOqampKi4utsXQczgcuvfee/XPf/7TdBQAAADAJzH2mrHs7GylpaWpvr5eTz75pDZt2qTQ0FDTsbR3716NHDlSJ0+e1MaNG03HAQAAAHwSY68ZunTpkjIzM/XUU0/JsizNnz9fOTk5atGiheloKi0t1eDBg1VXV6eMjAz9+te/Nh0JAAAA8Em8Z6+ZuXDhgtLT07VhwwYFBgZq+fLlGjNmjOlYkqTTp08rMTFRTqdTKSkpWrp0qfz8/EzHAgAAAHwSY68ZcTqdGjp0qEpKShQeHq68vDzFx8ebjiVJOnv2rH784x+roqJCP/zhD7Vu3ToFBPDtBQAAAJjCb+PNxMcff6ykpCSVlZWpY8eOcjgc+v73v286VqNt27aptLRUPXr0UH5+vi3eOwgAAAD4Mt6z1wwcPHhQsbGxKisrU48ePbR3715jQ6+8vFxTp05VeHi4/P39FR4erqlTp6pv375av369CgsL1bZtWyPZAAAw5Vr9WF5ebjoaAB/G2LO5oqIiPfjggzpz5owGDBigkpISderUyUgWh8Ohnj17atmyZXK5XLIsSy6XS8uWLVPPnj0VFhamjh07GskGAIAp1+tHh8NhOiIAH8XYs7Hly5dr8ODBqqmp0ejRo+VwONSmTRsjWcrLyzVy5EjV1dXJ7XZfccztdquurk4jR47kFUwAgE+hHwHYGWPPhizL0rx58zRx4kRdvHhRc+bM0erVqxUcHGws08KFC5uU2P9yu93Kzs72UCIAAMyjHwHYGWPPZtxutyZNmqRf/epX8vf3V05OjubPny9/f7P/VKtXr76hMlu1apWHEgEAYB79CMDOuBunjdTU1GjUqFFyOBwKCQnR2rVrNWTIENOxJP032818HAAA3oB+BGBnnNmziTNnzuihhx6Sw+HQbbfdpuLiYtsMPUkKCwu7qY8DAMAb0I8A7IyxZwMffPCBYmNj9e6776pr167avXu3HnjgAdOxrjB27Fi1aNHiSx8TGBiocePGeSgRAADmjR07VoGBgV/6GPoRgCmMPcN27dqluLg4ffzxx+rbt692796tqKgo07GamDVr1nVvEBMYGKjMzEwPJQIAwLxZs2bd0NijHwGYwNgzaNOmTUpISJDT6VRKSor+9re/6fbbbzcd6wqffvqp3n//fXXt2lUbN25UaGhok1ILDAxUaGioNm7cqK5duxpKCgCA59GPAOyMsWfISy+9pJEjR+rChQuaMmWK8vLy1KpVK9OxruByuZScnKx+/frpnXfeUVJSkg4fPqzJkycrPDxc/v7+Cg8P1+TJk3X48GElJSWZjgwAgMfRjwDsys+yLMt0iG/iwIED6tOnj+kYN+zSpUvKysrSwoULJUnPPfec5syZIz8/P8PJrlRfX6+UlBS99dZb+s53vqNdu3bpzjvvNB0LgA9rbj/vTePvCwB8x7V+5vPRCx504cIFZWRkaN26dQoICFBubq7S09NNx2ri4sWLSk9P11tvvaXbb79dW7duZegBAAAAzQxjz0POnTunoUOHaufOnWrdunXj+/XsxrIszZw5U+vXr1fr1q1VWFjI+wwAAACAZoix5wGnTp3SoEGDVFpaqg4dOmjLli3q1auX6VhX9dvf/lY5OTkKCgrS66+/rt69e5uOBAAAAOBr4AYtt9h7772nBx54QKWlperevbv27t1r26EnSZ07d1ZQUJD++te/asCAAabjAAAAAPiaOLN3C23btk0jRoyQy+VS//79lZeXpzZt2piO9aXGjx+vhx9+WJ06dTIdBQAAAMA3wJm9W2TlypVKTk6Wy+XST37yExUWFtp26O3YsUMHDx5s/JqhBwAAADR/jL2bzLIsPfvssxo/frwaGhr09NNPa82aNQoODjYd7aoOHjyoRx55RA899JDKyspMxwEAAABwk3AZ503U0NCgadOm6S9/+Yv8/Pz04osvasaMGaZjXVN5ebmSkpLkcrmUlpame+65x3QkAAAAADcJY+8mqa2tVVpamgoKCtSyZUutWbNGw4cPNx3rms6cOaPExERVVlYqISFBr7zyivz9OdELAAAAeAvG3k1QWVmplJQU/eMf/1BERITy8/MVFxdnOtY1VVVVadCgQTpx4oSio6O1adMm215mCgAAAODrYex9Q8eOHVNSUpJOnDihu+++Ww6HQ/fee6/pWNdkWZaGDRum9957T/fcc4+2bNmi1q1bm44FAAAA4Cbjur1vYM+ePYqLi9OJEyfUp08f7dmzx9ZDT5L8/Pz0xBNPqEuXLioqKlJkZKTpSAAAAABuAcbe17R582bFx8fr7NmzSk5O1vbt23XHHXeYjnVDRo0apbKyMnXp0sV0FAAAAAC3CGPva8jJydHw4cN14cIFTZo0Sa+//rrCwsJMx/pSCxYs0L59+xq/5j16AAAAgHdj7H0Fly5d0uzZszV9+nRZlqV58+ZpyZIlCgiw91sfFy1apDlz5igxMVFOp9N0HAAAAAAeYO+VYiP19fWaMGGC1q5dq4CAAC1dulQZGRmmY13Xq6++qpkzZ0qS/vCHPygiIsJwIgAAAACewNi7Af/5z380bNgwbd++XWFhYXrttdeUmJhoOtZ1bdu2Tenp6bIsS7/73e80YcIE05EAAAAAeAhj7zpOnz6t5ORkHTlyRO3bt1dBQYF69+5tOtZ1vfPOOxo2bJjcbrcyMzOVlZVlOhIAAAAAD7L9e/aeeeYZjRs3zshzHz58WLGxsTpy5Ijuu+8+7dmzp1kMvdraWqWmpqq2tlZjx47V73//e/n5+ZmOBQAAAMCDbD32NmzYoA0bNhh57uLiYv3oRz/SJ598ogcffFC7du3St7/9bSNZvqpWrVppyZIlGj58uF5++WX5+9v6nxkAAADALWDLFXDx4kUtXrxYv/zlL408/5o1azRo0CBVV1dr1KhRKioqUtu2bY1k+bpSU1P12muvKTAw0HQUAAAAAAbYbuzV19dr2LBhWrRokYYMGeLRDyq3LEvz58/X2LFj5Xa79dRTT2nt2rVq2bKlxzJ8XXV1dUpJSdHOnTtNRwEAAABgA7a7QUt9fb1qamqUnZ2t5ORkxcfHe+R5GxoaNGPGDP35z3+Wn5+fsrOzGz+ywO7cbrfS0tJUUFCg48eP6+jRo7b/7D8AAAAAt5btFkFYWJi2bt3q0bFSW1ur0aNHKz8/X8HBwVqzZo1GjBjhsef/JizL0uTJk/Xmm28qIiJCmzdvZugBAAAAsN/Y8/f39+gNRT777DOlpKRo//79atu2rd544w3169fPY8//Tc2ZM0crVqxQaGiotmzZovvuu890JAAAAAA24GdZlmU6xJeJj49Xx44dtWrVqqseP3DggIcTAQBM6dOnj+kIzQb9CAC+5Wodabsze18VxQ8AQFP0IwDAdnfjBAAAAAB8c4w9AAAAAPBCjD0DTp8+renTpysmJkYxMTHKysqS0+k0HcsnlJSU6Kc//al69eql3r17KyMjQ4cOHTIdy+eUlZWpR48eWrRokekoPsHpdOqZZ55RXFyc7r//fo0bN47ve9gWHWkG/WgP9KPneXtHMvY87Ny5cxo/frwOHTqkxx9/XBMmTFBxcbEmTJigzz//3HQ8r7Z//35NmjRJLpdLmZmZmjZtmk6dOqWxY8fq8OHDpuP5jIaGBs2dO1dut9t0FJ9QU1OjMWPGyOFwaPTo0Zo5c6YqKys1fvx4HTt2zHQ84Ap0pBn0oz3Qj57nCx3Z7G/Q0tysWLFCZ86cUX5+vrp27SpJ6tWrlyZMmKDNmzdr1KhRhhN6r+eee07t27fX+vXrFRISIkkaOnSokpOTlZ2dreXLlxtO6BuWLFmi48ePm47hM5YuXaqPPvpIq1atUt++fSVJycnJSkhI0LJly/T8888bTgh8gY40g360B/rR83yhI21/Zq+4uPiaH7vQHBUUFCgmJqaxxCQpLi5Od999twoKCgwm825VVVUqKyvToEGDGotMkm677Tb17dtXBw8eNJjOd3zwwQf605/+pKlTp5qO4hMsy1JeXp769+/fWGKSFBkZqaysLEVHRxtMBzRFR3oe/WgP9KPn+UpH2n7seZOqqiqdPn1a3bt3b3Kse/fuOnLkiIFUviEsLEyFhYXKyMhocuzcuXNq0aKF50P5mMuXp8TFxSk1NdV0HJ9QUVGhyspKxcXFSfpvsdXW1kqSxowZw1kS2AodaQb9aB79aIavdCRjz4MqKyslSXfccUeTY5GRkaqpqZHL5fJ0LJ/QokULdenSpcnffVlZmd5991317t3bUDLfsXTpUp08eVLz5s0zHcVnnDx5UpLUrl07LViwQNHR0br//vs1cOBAFRcXG04HXImONIN+NI9+NMNXOpKx50GXXy34/5dJXBYcHCxJqqur82gmX1ZbW6vZs2dLkiZPnmw4jXc7fvy4cnJyNHv2bN15552m4/iM6upqSdKLL76oHTt26Be/+IUWLFigli1batq0adq9e7fhhMAX6Ej7oB89h340x1c6khu0eNClS5eu+xh/f/a3J5w/f15PPvmkysrKNGXKFMXExJiO5LUuXryouXPnqk+fPl5zSURzcfnuhdXV1SoqKtK3vvUtSVJ8fLwGDhyohQsXNl6+AphGR9oD/eg59KNZvtKR/NT0oFatWkmS6uvrmxy7/GeXH4Nbp7q6WhMnTtS+ffs0YsQIZWZmmo7k1XJzc1VWVqZZs2bJ6XTK6XQ2vpp2/vx5OZ3OG/olD19daGioJCkxMbGxxCQpPDxc8fHxOnr0aOPZFMA0OtI8+tGz6EezfKUjObPnQR06dJAkffbZZ02OffrppwoPD2/8xsOtcfbsWT322GMqLS1VWlqafvOb38jPz890LK9WUlIit9utRx99tMmx3Nxc5ebm6u2331anTp0MpPNul9+DExER0eRYRESELMtSXV0dv0DDFuhIs+hHz6MfzfKVjmTseVB4eLg6deqko0ePNjn2/vvvq0ePHgZS+Y6amprGIsvIyNDcuXNNR/IJs2fPbnyl8rJ///vfevrppzVkyBANHTpUkZGRhtJ5t6ioKAUFBenDDz9scqyiokLBwcFXLTnABDrSHPrRDPrRLF/pSMaehyUmJmrlypUqLy9v/Byh3bt366OPPtJjjz1mOJ13mzdvnkpLS5Wenk6RedDVfkGrqKiQJN11111ecT28XYWGhio+Pl5vv/22jh8/rqioKEnS6dOnVVxcrISEBG6rDluhI82gH82gH83ylY70syzLMh3ClzidTqWkpKhFixaaOHGi6uvrtWzZMnXu3FmvvvqqgoKCTEf0SuXl5UpOTlbr1q3185///Kr/eYcMGWIgmW+qqKjQww8/rOnTp2vGjBmm43i1ioqKxkuE0tPTFRgYqJUrV+r8+fPatGmT7rrrLsMJgS/QkZ5HP9oL/ehZvtCRnNnzsIiICK1evVrz58/XSy+9pJYtWyohIUFZWVmU2C20f/9+SZLL5brmq5aUGbxRp06dtH79er3wwgvKzc2VZVmKjo5WVlaWV5QYvAsd6Xn0I3yZL3QkZ/YAAAAAwAvx0QsAAAAA4IUYewAAAADghRh7AAAAAOCFGHsAAAAA4IUYewAAAADghRh7AAAAAOCFGHsAAAAA4IUYewAAAADghRh7AAAAAOCFGHsAAAAA4IUYewAAAADghRh7AAAAAOCFGHsAAAAA4IUYewAAAADghQJMBwBwfdu3b9crr7yizz//XBcvXtTcuXPVq1cvvfDCCzp06JAkadiwYRo5cqTZoAAAeBgdCVybn2VZlukQAK4tLy9PJSUlevbZZxUSEqIVK1YoJydHI0aMUM+ePZWQkKBp06appKREe/fuVZs2bUxHBgDAI+hI4MtxGSdgY5WVlSosLNTzzz+vkJAQSVK3bt1UXV2tU6dOKTk5WSdOnNDOnTvVuXNnhYWFGU4MAIBn0JHA9XEZJ2Bjb7zxhiZNmqSAgC/+q3744YeSpMGDB0uSvvvd7yo/P1/t27e/4nEAAHgzOhK4Pi7jBGzMsiz5+fld8WdPPPGEtm/frl27dqldu3aGkgEAYBYdCVwfl3ECNva/JeZ2u7V//35FRUVRYgAAn0ZHAtfH2AOakUOHDqm2tlaxsbFNjnGSHgDgy+hIoCnGHmBjZ8+e1cmTJxu/3rVrlyQpJibmisetX79eW7du9Wg2AABMoiOB62PsATZVVVWllJQUDRo0SFVVVbIsS4WFhZKkqKioxsfV1NQoPz9fAwYMMBUVAACPoiOBG8PYA2zqk08+kdPpVGpqqsLDw/XHP/5R/fr1U0BAgI4dOyZJcjqdyszM1MyZMxUUFGQ4MQAAnkFHAjeGu3ECNrZ48WLt27dPDQ0N6t+/v6ZMmaLi4mItXrxYQUFBCgoK0s9+9jNFR0ebjgoAgEfRkcD1MfYAAAAAwAtxGScAAAAAeCHGHgAAAAB4IcYeAAAAAHghxh4AAAAAeCHGHgAAAAB4IcYeAAAAAHghxh4AAAAAeCHGHgAAAAB4IcYeAAAAAHghxh4AAAAAeCHGHgAAAAB4of8Dhb3giqBYevkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1080x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-1, 7, 100)\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, sharex=True, sharey=True)\n",
    "fig.set_size_inches((15,6))\n",
    "\n",
    "ax1.xaxis.set_tick_params(labelsize=18)\n",
    "ax1.yaxis.set_tick_params(labelsize=18)\n",
    "ax1.set_xlabel('$x$', fontsize=25)\n",
    "ax1.set_ylabel('$y$', fontsize=25)\n",
    "ax1.grid(False)\n",
    "\n",
    "ax2.xaxis.set_tick_params(labelsize=18)\n",
    "ax2.yaxis.set_tick_params(labelsize=18)\n",
    "ax2.set_xlabel('$x$', fontsize=25)\n",
    "ax2.set_ylabel('$y$', fontsize=25)\n",
    "ax2.grid(False)\n",
    "\n",
    "ax1.plot(D1[0], D1[1], 'ko', markersize=10)\n",
    "ax1.plot(x, f(x, w_ml_d1), c='k', lw=2, label='machine learning')\n",
    "ax1.plot(x, f(x, w_mc_d1), '--', c='k', lw=2, label='more clever')\n",
    "ax1.set_xlim([-1,7])\n",
    "ax1.set_ylim([1,6])\n",
    "ax1.legend(fontsize=18)\n",
    "\n",
    "ax2.plot(D2[0], D2[1], 'ko', markersize=10)\n",
    "ax2.plot(x, f(x, w_ml_d2), c='k', lw=2, label='machine learning')\n",
    "ax2.plot(x, f(x, w_mc_d2), '--', c='k', lw=2, label='more clever')\n",
    "ax2.set_xlim([-1,7])\n",
    "ax2.set_ylim([1,6])\n",
    "ax2.legend(fontsize=18)\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33f6e0d7",
   "metadata": {},
   "source": [
    "* 머신 러닝은 입력과 출력이 있을 때 숨어있는 입력과 출력의 관계를 찾는 과정"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "30704213",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_iters = 150\n",
    "alpha = 0.02\n",
    "\n",
    "np.random.seed(2)\n",
    "w = np.random.randn(2)\n",
    "N = D1.shape[1] \n",
    "\n",
    "ws, L = [], []\n",
    "\n",
    "# 1열에 1, 2열에 데이터의 x좌표를 가지는 행렬을 만듭니다.\n",
    "# X: (N,2), y: (N,)\n",
    "X = np.c_[np.ones(N), D1[0]]\n",
    "y = D1[1]\n",
    "\n",
    "# 여기서 우리의 경험 E를 반복하면서 태스크 T를 개선해 나간다.\n",
    "for i in range(num_iters) :\n",
    "    # grad L\n",
    "    c = (1/N) * np.dot(X.T, np.dot(X, w) - y) \n",
    "    # 안전장치 grad L을 이용해서 w를 수정한다.\n",
    "    w -= alpha * c \n",
    "    # w가 변화되는 과정을 저장해둔다.\n",
    "    ws.append(w)\n",
    "    \n",
    "    # 손실을 계산한다.\n",
    "    L.append( ((np.dot(X, w) - y)**2).sum()/(2*N) )\n",
    "\n",
    "x = np.linspace(-1, 7, 100)\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2)\n",
    "fig.set_size_inches((15,6))\n",
    "\n",
    "ax1.xaxis.set_tick_params(labelsize=18)\n",
    "ax1.yaxis.set_tick_params(labelsize=18)\n",
    "ax1.set_xlabel('$x$', fontsize=25)\n",
    "ax1.set_ylabel('$y$', fontsize=25)\n",
    "ax1.grid(False)\n",
    "    \n",
    "ax2.xaxis.set_tick_params(labelsize=18)\n",
    "ax2.yaxis.set_tick_params(labelsize=18)\n",
    "ax2.set_xlabel('$x$', fontsize=25)\n",
    "ax2.set_ylabel('$y$', fontsize=25)\n",
    "ax2.grid(False)\n",
    "    \n",
    "ax1.plot(D1[0], D1[1], 'ko', markersize=8)\n",
    "ax1.plot(x, f(x, w), c='k', lw=2, label='machine learning')\n",
    "ax1.set_xlim([-1,7])\n",
    "ax1.set_ylim([1,6])\n",
    "ax1.legend(fontsize=18)\n",
    "\n",
    "ax2.plot(L[:50], '--', c='k', label='loss')\n",
    "ax2.legend(fontsize=18)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "74d51ecf",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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