{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "

Practical Work 2 : Comparing one-step explicit schemes

\n", "
\n", "\n", "*Authored in 2025 for educational purpose by S. Cardonna, Q. Richard, V. Lleras & P. Azerad. If you identify any issues or have suggestions for improvement, feel free to contact me.* \n", " \n", "**Introduction** \n", "For this second practical work, we first remind some classical one-step schemes. We then implement them and compare them, especially with convergence tests, as it has been done in the previous practical work.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "

Part 1 - Main explicit one-step schemes

\n", "
\n", "\n", "**Euler scheme**\n", "$$\n", "y_1 = y_0 + h \\, f(t_0, y_0)\n", "$$\n", "\n", "**Midpoint scheme**\n", "\n", "$$\n", "u = y_0 + \\frac{h}{2} \\, f(t_0, y_0)\n", "$$\n", "\n", "$$\n", "y_1 = y_0 + h \\, f\\left(t_0 + \\frac{h}{2}, u\\right)\n", "$$\n", "\n", "**Heun scheme**\n", "\n", "$$\n", "u_2 = y_0 + \\frac{h}{3} \\, f(t_0, y_0)\n", "$$\n", "\n", "$$\n", "u_3 = y_0 + \\frac{2h}{3} \\, f\\left(t_0 + \\frac{h}{3}, u_2\\right)\n", "$$\n", "\n", "$$\n", "y_1 = y_0 + h \\left(\\frac{1}{4} f(t_0, y_0) + \\frac{3}{4} f\\left(t_0 + \\frac{2h}{3}, u_3\\right)\\right)\n", "$$\n", "\n", "**Runge-Kutta 4 scheme**\n", "\n", "$$\n", "u_2 = y_0 + \\frac{h}{2} \\, f(t_0, y_0)\n", "$$\n", "\n", "$$\n", "u_3 = y_0 + \\frac{h}{2} \\, f\\left(t_0 + \\frac{h}{2}, u_2\\right)\n", "$$\n", "\n", "$$\n", "u_4 = y_0 + h \\, f\\left(t_0 + \\frac{h}{2}, u_3\\right)\n", "$$\n", "\n", "$$\n", "y_1 = y_0 + h \\left(\\frac{1}{6} f(t_0, y_0) + \\frac{2}{6} f\\left(t_0 + \\frac{h}{2}, u_2\\right) + \\frac{2}{6} f\\left(t_0 + \\frac{h}{2}, u_3\\right) + \\frac{1}{6} f(t_0 + h, u_4)\\right)\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "

Part 2 - Numerical comparison of various schemes

\n", "
\n", "\n", "Let us now use the code we wrote the previous time, and add midpoint, Heun and RK4 schemes. This will be useful to check during convergence test which test is the most efficient for solving this kind of equations." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA1kAAAIoCAYAAACbCCHjAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/NK7nSAAAACXBIWXMAAA9hAAAPYQGoP6dpAAEAAElEQVR4nOzdd1iT5/oH8G8SQggk7DBkqYCyp3uvarXWWm2109X22GH3tKfz13NOh60dtrXb9rS2dban0y3iXixlKAIudtgECBnP74+Ql7wkYSib+3NdXJB35XmzyP0+93M/AsYYAyGEEEIIIYSQTiHs6QYQQgghhBBCSH9CQRYhhBBCCCGEdCIKsgghhBBCCCGkE1GQRQghhBBCCCGdiIIsQgghhBBCCOlEFGQRQgghhBBCSCeiIIsQQgghhBBCOhEFWYQQQgghhBDSiSjIIoQQQgghhJBOREEWIYRYMHjwYCxbtqxLjr1s2TIMHjy4S45tjVarxXPPPQc/Pz8IhULMnz+/W+/fmq58nIllCQkJEAgESEhI6JLjf/vttxAIBLh48WKXHL+lKVOmICIiolvuq7d55513EBISAr1ezy0TCAR47bXXeqQ9A+X9fD2v8RdeeAGjR4/u/EaRXoeCLNJv5eTkYOXKlRg6dCjs7Ozg6OiI8ePH48MPP0R9fX1PN4+QbvXNN99gzZo1uO222/Ddd9/hySef7OkmEUKuQ3V1Nd5++208//zzEArp61xf8cQTTyA1NRW//fZbTzeFdDGbnm4AIV3hzz//xO233w6JRIIlS5YgIiICjY2NOHToEJ599lmkp6fjiy++6OlmkgHqyy+/5F157g779u2Dj48P3n///W6937acO3eOviB2s0mTJqG+vh62trY93RRyHb755htotVrceeedPd0U0gFeXl645ZZb8O6772LevHk93RzShSjIIv1OXl4e7rjjDgQEBGDfvn3w9vbm1j3yyCO4cOEC/vzzzx5s4fVraGiAra0tfTnto8RicbffZ0lJCZydnbv9fi1hjKGhoQFSqRQSiaSnmzNgmH5u2NnZ9XRzyHXasGED5s2bR89lH7Ro0SLcfvvtyM3NxdChQ3u6OaSL0Dc00u+88847qK2txddff80LsIyCgoLw+OOPc7e1Wi3eeOMNBAYGQiKRYPDgwXjxxRehVqt5+w0ePBhz587FoUOHMGrUKNjZ2WHo0KH473//y21z6tQpCAQCfPfdd2b3u3PnTggEAvzxxx/csvz8fKxYsQKenp6QSCQIDw/HN998w9vPOH7i559/xksvvQQfHx/Y29ujuroaALBlyxaEhYXBzs4OERER+OWXXyyO+dHr9fjggw8QHh4OOzs7eHp6YuXKlaioqOjweRpVVlbiySefxODBgyGRSODr64slS5ZAqVRy26jVarz66qsICgqCRCKBn58fnnvuObPH15KDBw/i9ttvh7+/P7fvk08+aZbuuWzZMshkMuTn52P+/PmQyWRQKBR45plnoNPpeNu+++67GDduHNzc3CCVShEfH4+tW7e22o7c3FwIBAKLvUBHjhyBQCDATz/9BACoqanBE088wT0mHh4euOGGG5CUlMRrb8vn5+eff0Z8fDzkcjkcHR0RGRmJDz/8sM3HSKVS4emnn4afnx8kEgmGDx+Od999F4wxAMDFixchEAiwf/9+pKenQyAQtDoeZ+7cuVb/6Y8dOxYjRozgbm/YsAHTpk2Dh4cHJBIJwsLCsH79erP9jK+pnTt3YsSIEZBKpfj888+5dS3HcOTm5uL222+Hq6sr7O3tMWbMGLMLI9bGRFgab5SdnY2FCxfCy8sLdnZ28PX1xR133IGqqiqL52lkHOuTkZGBqVOnwt7eHj4+PnjnnXeuuS3GY6alpWHy5Mmwt7dHUFAQ9xo8cOAARo8eDalUiuHDh2PPnj1m7brezw1rY7KOHz+OOXPmwMXFBQ4ODoiKiuK9BtPS0rBs2TIuBdvLywsrVqxAWVlZq4+jNUVFRVi+fDl8fX0hkUjg7e2NW265xexx/PvvvzF58mTuvTFy5Ej8+OOPZsdr63kC2v95JBAIsGrVKu7zVSqVYuzYsThz5gwA4PPPP0dQUBDs7OwwZcoUi2Nzjh8/jhtvvBFOTk6wt7fH5MmTcfjwYd427fm8sCQvLw9paWmYMWNGq9sZJScnY/bs2XB0dIRMJsP06dNx7Ngxs+2Mr0upVApfX1/861//woYNG65rjF173s8AcOnSJcybNw8ODg7w8PDAk08+yf3fbGv8YHsfx65+jf/999+YOHEiHBwcIJfLcdNNNyE9Pd1sO+Pz9r///a9dxyV9E/VkkX7n999/x9ChQzFu3Lh2bX///ffju+++w2233Yann34ax48fx5tvvonMzEz88ssvvG0vXLiA2267Dffddx+WLl2Kb775BsuWLUN8fDzCw8MxYsQIDB06FJs3b8bSpUt5+27atAkuLi6YNWsWAKC4uBhjxozh/pkrFAr8/fffuO+++1BdXY0nnniCt/8bb7wBW1tbPPPMM1Cr1bC1tcWff/6JxYsXIzIyEm+++SYqKipw3333wcfHx+w8V65ciW+//RbLly/HY489hry8PHz88cdITk7G4cOHeb0rbZ0nANTW1mLixInIzMzEihUrEBcXB6VSid9++w1Xr16Fu7s79Ho95s2bh0OHDuEf//gHQkNDcebMGbz//vs4f/48fv3111afmy1btqCurg4PPfQQ3NzccOLECaxbtw5Xr17Fli1beNvqdDrMmjULo0ePxrvvvos9e/bgvffeQ2BgIB566CFuuw8//BDz5s3D3XffjcbGRvz888+4/fbb8ccff+Cmm26y2I6hQ4di/Pjx2Lhxo9lYpo0bN0Iul+OWW24BADz44IPYunUrVq1ahbCwMJSVleHQoUPIzMxEXFycxePv3r0bd955J6ZPn463334bAJCZmYnDhw/zLgi0xBjDvHnzsH//ftx3332IiYnBzp078eyzzyI/Px/vv/8+FAoFvv/+e/z73/9GbW0t3nzzTQBAaGioxWMuXrwYS5YswcmTJzFy5Ehu+aVLl3Ds2DGsWbOGW7Z+/XqEh4dj3rx5sLGxwe+//46HH34Yer0ejzzyCO+4586dw5133omVK1figQcewPDhwy3ef3FxMcaNG4e6ujo89thjcHNzw3fffYd58+Zh69atuPXWW60+HpY0NjZi1qxZUKvVePTRR+Hl5YX8/Hz88ccfqKyshJOTU6v7V1RU4MYbb8SCBQuwaNEibN26Fc8//zwiIyMxe/bsDrXF9Jhz587FHXfcgdtvvx3r16/HHXfcgY0bN+KJJ57Agw8+iLvuuosbQ3flyhXI5XLu8bnezw1Ldu/ejblz58Lb2xuPP/44vLy8kJmZiT/++IN7De7evRu5ublYvnw5vLy8uLTr9PR0HDt2DAKBoEOPw8KFC5Geno5HH30UgwcPRklJCXbv3o3Lly9zFyG+/fZbrFixAuHh4Vi9ejWcnZ2RnJyMHTt24K677uI9pm09Tx39PDp48CB+++037rX85ptvYu7cuXjuuefw6aef4uGHH0ZFRQXeeecdrFixAvv27eP23bdvH2bPno34+Hi8+uqrEAqF3EWJgwcPYtSoUQCu7fMCMFzcAdDqNkbp6emYOHEiHB0d8dxzz0EsFuPzzz/HlClTuKAeMATvU6dOhUAgwOrVq+Hg4ICvvvrqunqb2/t+VqlUmDZtGgoLC7nX348//oj9+/e3637a8zh29Wv8+++/x9KlSzFr1iy8/fbbqKurw/r16zFhwgQkJyfzLqw5OTkhMDAQhw8fpvGx/RkjpB+pqqpiANgtt9zSru1TUlIYAHb//ffzlj/zzDMMANu3bx+3LCAggAFgiYmJ3LKSkhImkUjY008/zS1bvXo1E4vFrLy8nFumVquZs7MzW7FiBbfsvvvuY97e3kypVPLu+4477mBOTk6srq6OMcbY/v37GQA2dOhQbplRZGQk8/X1ZTU1NdyyhIQEBoAFBARwyw4ePMgAsI0bN/L237Fjh9ny9p7nK6+8wgCw7du3s5b0ej1jjLHvv/+eCYVCdvDgQd76zz77jAFghw8fNtvXVMvzZYyxN998kwkEAnbp0iVu2dKlSxkA9n//93+8bWNjY1l8fHyrx2xsbGQRERFs2rRpvOUBAQFs6dKl3O3PP/+cAWCZmZm8fd3d3XnbOTk5sUceeaTV81q6dCnv+Xn88ceZo6Mj02q1re7X0q+//soAsH/961+85bfddhsTCATswoUL3LLJkyez8PDwNo9ZVVVl9lwzxtg777xj9rhben5mzZrFhg4dyltmfE3t2LHDbPuWj/MTTzzBAPBeMzU1NWzIkCFs8ODBTKfTMcYY27BhAwPA8vLyeMczvl/279/PGGMsOTmZAWBbtmxp89xbmjx5MgPA/vvf/3LL1Go18/LyYgsXLuSWtbctpsf88ccfuWVZWVkMABMKhezYsWPc8p07dzIAbMOGDdyyzvjcaNkurVbLhgwZwgICAlhFRQVvW+N7mTHLz/dPP/1k9nlh7fEwVVFRwQCwNWvWWN2msrKSyeVyNnr0aFZfX2+1Xe19njryeQSASSQS3jkYPwO8vLxYdXU1t3z16tW889Xr9Sw4OJjNmjXL7PEbMmQIu+GGG7hl7fm8sOSll15iAHif/aZtf/XVV7nb8+fPZ7a2tiwnJ4dbVlBQwORyOZs0aRK37NFHH2UCgYAlJydzy8rKypirq2ubz6fRtb6f33vvPQaA/frrr9x29fX1LCQkxOw9ZElbj2NXv8ZramqYs7Mze+CBB3j7FhUVMScnJ7PljDE2c+ZMFhoa2up5kb6N0gVJv2JMoTNe9W3LX3/9BQB46qmneMuffvppADBLaQgLC8PEiRO52wqFAsOHD0dubi63bPHixdBoNNi+fTu3bNeuXaisrMTixYsBGHogtm3bhptvvhmMMSiVSu5n1qxZqKqqMktzWLp0KaRSKXe7oKAAZ86cwZIlSyCTybjlkydPRmRkJG/fLVu2wMnJCTfccAPvvuLj4yGTycyuFrbnPLdt24bo6GiLPQvGq31btmxBaGgoQkJCePc7bdo0AGjzKqXp+apUKiiVSowbNw6MMSQnJ5tt/+CDD/JuT5w4kdfmlsesqKhAVVUVJk6c2GZ6zqJFi2BnZ4eNGzdyy3bu3AmlUol77rmHW+bs7Izjx4+joKCg1eOZcnZ2hkqlwu7du9u9D2B4/YpEIjz22GO85U8//TQYY/j77787dDwAcHR0xOzZs7F582Yu5RAw9MSOGTMG/v7+3DLTx7KqqgpKpRKTJ09Gbm6uWSrekCFDuF7cts5p1KhRmDBhArdMJpPhH//4By5evIiMjIwOnY+xp2rnzp2oq6vr0L7G+zZ9fm1tbTFq1Ciz11VHj3nHHXdwt4cPHw5nZ2eEhobySjsb/zbeV2d8bliSnJyMvLw8PPHEE2bj9kyv3Jsep6GhAUqlEmPGjAGANt8/LUmlUtja2iIhIcEsZdlo9+7dqKmpwQsvvGA27qhlj0J7nqeOfh5Nnz6d1/tgfD4WLlzI+x/T8nlKSUlBdnY27rrrLpSVlXH3o1KpMH36dCQmJnKFb67l8wIAysrKYGNjw/vst0Sn02HXrl2YP38+Lw3Y29sbd911Fw4dOsT939yxYwfGjh2LmJgYbjtXV1fcfffdHWqbqfa+n3fs2AEfHx9eIQg7Ozs88MAD7bqfth7Hrn6N7969G5WVlbjzzjt5ry2RSITRo0db/F/n4uLCS60n/Q8FWaRfcXR0BGDIz26PS5cuQSgUIigoiLfcy8sLzs7OuHTpEm+56RdMIxcXF96XhOjoaISEhGDTpk3csk2bNsHd3Z37Z15aWorKykp88cUXUCgUvJ/ly5cDMBQqMDVkyBCztgMwa7ulZdnZ2aiqqoKHh4fZ/dXW1prdV3vOMycnp825abKzs5Genm52n8OGDbN4ji1dvnwZy5Ytg6urKzfOavLkyQBg9iXezs4OCoWi1TYDwB9//IExY8bAzs4Orq6uUCgUWL9+fZvjc5ydnXHzzTfzxoJs3LgRPj4+3PMKGMYEnj17Fn5+fhg1ahRee+21Nr+QP/zwwxg2bBhmz54NX19frFixAjt27Gh1H8DwGhg0aJDZRQVjKmDL1297LV68GFeuXMHRo0cBGJ7r06dPcxcJjA4fPowZM2bAwcEBzs7OUCgUePHFFwGYPz8tX7+tnZOlVMJrPachQ4bgqaeewldffQV3d3fMmjULn3zySZvPt5Gvr6/ZF3pLr6uOsHRMJycn+Pn5mS0DwN1XZ3xuWJKTkwMAbb6fy8vL8fjjj8PT0xNSqRQKhYI7fnsfTyOJRIK3334bf//9Nzw9PTFp0iS88847KCoq6nC7gPY9Tx39PGr5OWh8Ptp6nrKzswEYAtyW9/XVV19BrVZzj9e1fF50RGlpKerq6qy+p/R6Pa5cuQLA8N5qz/+TqqoqFBUVcT/l5eVW77+97+dLly4hMDDQ7Dm01B5L2nocu/o1bnzOp02bZvac79q1y+L/OsZYh1NsSd9CY7JIv+Lo6IhBgwbh7NmzHdqvvR90IpHI4nLTK/6A4Uvqv//9byiVSsjlcvz222+48847YWNjeMsZr2Lec889ZmO3jKKioni327oa3Rq9Xg8PDw9eL4yplsFJe8+zPfcbGRmJtWvXWlzf8suKKZ1OhxtuuAHl5eV4/vnnERISAgcHB+Tn52PZsmVmJdCttdnUwYMHMW/ePEyaNAmffvopvL29IRaLsWHDBosD6VtasmQJtmzZgiNHjiAyMhK//fYbHn74YV6Vx0WLFmHixIn45ZdfsGvXLqxZswZvv/02tm/fbnUMj4eHB1JSUrBz5078/fff+Pvvv7FhwwYsWbLEYhGVrnbzzTfD3t4emzdvxrhx47B582YIhULcfvvt3DY5OTmYPn06QkJCsHbtWvj5+cHW1hZ//fUX3n//fbPn53pev5ZYe8+2LHQCAO+99x6WLVuG//3vf9i1axcee+wxvPnmmzh27Bh8fX1bvZ/2vBc60pbWjtnWfXX350ZLixYtwpEjR/Dss88iJiYGMpkMer0eN9544zVNSfDEE0/g5ptvxq+//oqdO3fi5Zdfxptvvol9+/YhNja2Q8dqz/PU0c+j632e1qxZw+sVMmXsgbqWzwsAcHNzg1arRU1NTbszNzrL448/zvtcmjx5cpdNbN1e1/o4WjrOtbzGjeu+//57eHl5ma03/u83VVFRAXd393a3jfQ9FGSRfmfu3Ln44osvcPToUYwdO7bVbQMCAqDX65Gdnc0rBFBcXIzKykoEBARcUxsWL16M119/Hdu2bYOnpyeqq6t56UEKhQJyuRw6na7d1aEstR0wFKloqeWywMBA7NmzB+PHj++0L12BgYFtBrOBgYFITU3F9OnTO3zF7syZMzh//jy+++47LFmyhFve0ZQ6U9u2bYOdnR127tzJG8y9YcOGdu1/4403QqFQYOPGjRg9ejTq6upw7733mm3n7e2Nhx9+GA8//DBKSkoQFxeHf//7363+s7e1tcXNN9+Mm2++GXq9Hg8//DA+//xzvPzyy1av5gYEBGDPnj1mX7SysrK49dfCwcEBc+fOxZYtW7B27Vps2rQJEydOxKBBg7htfv/9d6jVavz222+8K/7tHahuTUBAAM6dO2e2vOU5ubi4ADBUuDRlracrMjISkZGReOmll3DkyBGMHz8en332Gf71r39dV3uvpS3XqjM+NywJDAwEAJw9e9bqcSsqKrB37168/vrreOWVV7jlxiv413PfTz/9NJ5++mlkZ2cjJiYG7733Hn744Qdeu9rbo9HWfV3r51FH7wcwXPRrz/N0LZ8XISEhAAxVBlsG1qYUCgXs7e2tvqeEQiEXXAYEBLTr/8lzzz3HS800vv4tae/7OSAgABkZGWa9O5baY01rj2NXv8aNx/fw8Gj3ezMvLw/R0dHt2pb0TZQuSPqd5557Dg4ODrj//vtRXFxstj4nJ4cr2TpnzhwAwAcffMDbxnil01q1ubaEhoYiMjISmzZtwqZNm+Dt7Y1JkyZx60UiERYuXIht27ZZDFRKS0vbvI9BgwYhIiIC//3vf1FbW8stP3DgAFdm2GjRokXQ6XR44403zI6j1WrNvhy2x8KFC5GammpWgRFovqK7aNEi5Ofn48svvzTbpr6+HiqVyurxjVeLTa9EM8baVda8tWMKBAJeD8PFixfbrHJoZGNjgzvvvBObN2/Gt99+i8jISN4XHJ1OZ5ZS4uHhgUGDBrVasr5leWChUMgdt7X95syZA51Oh48//pi3/P3334dAILjm6neA4UJBQUEBvvrqK6SmppqlClp6fqqqqtodsFozZ84cnDhxgktVBAzj8b744gsMHjwYYWFhAJq/1CQmJnLb6XQ6s0nGq6urodVqecsiIyMhFArbNY1Ae7S3LderMz43LImLi8OQIUPwwQcfmH0WGJ9fS883YP7Z2V51dXVoaGjgLQsMDIRcLueel5kzZ0Iul+PNN98027ajverA9X0edUR8fDwCAwPx7rvv8j6bjYzP07V+XgDgLiCeOnWq1e1EIhFmzpyJ//3vf7wS7MXFxfjxxx8xYcIELs1+1qxZOHr0KFJSUrjtysvLzTIgwsLCMGPGDO4nPj7e6v239/08a9Ys5Ofn47fffuO2a2hosPhctdSex7GrX+OzZs2Co6Mj/vOf/0Cj0Zitb/nerKqqQk5OTrurIJO+iXqySL8TGBiIH3/8EYsXL0ZoaCiWLFmCiIgINDY24siRI9iyZQs3L090dDSWLl2KL774ApWVlZg8eTJOnDiB7777DvPnz8fUqVOvuR2LFy/GK6+8Ajs7O9x3331mEwe/9dZb2L9/P0aPHo0HHngAYWFhKC8vR1JSEvbs2dNqnrvRf/7zH9xyyy0YP348li9fjoqKCnz88ceIiIjg/XOfPHkyVq5ciTfffBMpKSmYOXMmxGIxsrOzsWXLFnz44Ye47bbbOnR+zz77LLZu3Yrbb78dK1asQHx8PMrLy/Hbb7/hs88+Q3R0NO69915s3rwZDz74IPbv34/x48dDp9MhKysLmzdv5uZNsiQkJASBgYF45plnkJ+fD0dHR2zbtu26xsLcdNNNWLt2LW688UbcddddKCkpwSeffIKgoCCkpaW16xhLlizBRx99hP3793Pl1o1qamrg6+uL2267DdHR0ZDJZNizZw9OnjyJ9957z+ox77//fpSXl2PatGnw9fXFpUuXsG7dOsTExFgttQ4Y0vqmTp2Kf/7zn7h48SKio6Oxa9cu/O9//8MTTzzBffm/FnPmzIFcLsczzzzDfbk3NXPmTK73beXKlaitrcWXX34JDw8PFBYWXvP9vvDCC/jpp58we/ZsPPbYY3B1dcV3332HvLw8bNu2jXsfhYeHY8yYMVi9ejXKy8vh6uqKn3/+2Syg2rdvH1atWoXbb78dw4YNg1arxffff2/xnK5Ve9vSGTrjc6MloVCI9evX4+abb0ZMTAyWL18Ob29vZGVlIT09HTt37oSjoyM3bkqj0cDHxwe7du1CXl7eNZ3H+fPnMX36dCxatAhhYWGwsbHBL7/8guLiYq7X39HREe+//z7uv/9+jBw5EnfddRdcXFyQmpqKurq6DqfSXs/nUUcIhUJ89dVXmD17NsLDw7F8+XL4+PggPz8f+/fvh6OjI37//fdr/rwADNNKREREYM+ePVixYkWr2/7rX//C7t27MWHCBDz88MOwsbHB559/DrVazZtL7LnnnsMPP/yAG264AY8++ihXwt3f3x/l5eXX1PvX3vfzypUr8fHHH+POO+/E448/Dm9vb2zcuJEreNLafbfncezq17ijoyPWr1+Pe++9F3FxcbjjjjugUChw+fJl/Pnnnxg/fjzvYtiePXvAGOOm/iD9VLfVMSSkm50/f5498MADbPDgwczW1pbJ5XI2fvx4tm7dOtbQ0MBtp9Fo2Ouvv86GDBnCxGIx8/PzY6tXr+Ztw5ihNO1NN91kdj+TJ09mkydPNluenZ3NADAA7NChQxbbWFxczB555BHm5+fHxGIx8/LyYtOnT2dffPEFt42x3LK1EtQ///wzCwkJYRKJhEVERLDffvuNLVy4kIWEhJht+8UXX7D4+HgmlUqZXC5nkZGR7LnnnmMFBQXXdJ5lZWVs1apVzMfHh9na2jJfX1+2dOlSXnnpxsZG9vbbb7Pw8HAmkUiYi4sLi4+PZ6+//jqrqqqyeE5GGRkZbMaMGUwmkzF3d3f2wAMPsNTUVLOy1kuXLmUODg5m+7/66qus5cfc119/zYKDg5lEImEhISFsw4YNFrdrWYrYVHh4OBMKhezq1au85Wq1mj377LMsOjqayeVy5uDgwKKjo9mnn37K265lCfetW7eymTNnMg8PD2Zra8v8/f3ZypUrWWFhYauPD2OG0sFPPvkkGzRoEBOLxSw4OJitWbOGV5aYsfaXcDd19913MwBsxowZFtf/9ttvLCoqitnZ2bHBgwezt99+m33zzTdm5Z6tvaaM61o+zjk5Oey2225jzs7OzM7Ojo0aNYr98ccfZvvm5OSwGTNmMIlEwjw9PdmLL77Idu/ezSv5nJuby1asWMECAwOZnZ0dc3V1ZVOnTmV79uxp8/ytPWYtn7/2tqW1Y1p7jACYlaa+3s8NS6XlGWPs0KFD7IYbbuBeu1FRUWzdunXc+qtXr7Jbb72VOTs7MycnJ3b77bezgoICs5Lh7SnhrlQq2SOPPMJCQkKYg4MDc3JyYqNHj2abN2822/a3335j48aNY1KplDk6OrJRo0axn376iVvfkeepvZ9Hlh73vLw8i2XnrT3WycnJbMGCBczNzY1JJBIWEBDAFi1axPbu3csYa//nhTVr165lMpnMrOx4y+eDMcaSkpLYrFmzmEwmY/b29mzq1KnsyJEjZsdMTk5mEydOZBKJhPn6+rI333yTffTRRwwAKyoqarNN1/N+zs3NZTfddBOTSqVMoVCwp59+mm3bto0B4E1t0FJHHseufo3v37+fzZo1izk5OTE7OzsWGBjIli1bxk6dOsXbbvHixWzChAmtPJKkPxAwdg197oSQXi0mJgYKheK6xi8R62JjY+Hq6oq9e/f2dFMIIQNUVVUVhg4dinfeeQf33Xdfl93PE088gc8//xy1tbXtKjDUmT744AM8+eSTuHr1Knx8fLr1vrtKUVERhgwZgp9//pl6svo5GpNFSB+m0WjMUpISEhKQmpqKKVOm9Eyj+rlTp04hJSWFV4yDEEK6m5OTE5577jmsWbPmmqo7WlJfX8+7XVZWhu+//x4TJkzo8gCr5X03NDTg888/R3BwcL8JsABD4BgZGUkB1gBAPVmE9GEXL17EjBkzcM8992DQoEHIysrCZ599BicnJ5w9exZubm493cR+4+zZszh9+jTee+89KJVK5Obmmk2QSgghfVlMTAymTJmC0NBQFBcX4+uvv0ZBQQH27t3LK97UFWbPng1/f3/ExMSgqqoKP/zwA9LT07Fx40bcddddXXrfhHQFKnxBSB/m4uKC+Ph4fPXVVygtLYWDgwNuuukmvPXWWxRgdbKtW7fi//7v/zB8+HD89NNPFGARQvqdOXPmYOvWrfjiiy8gEAgQFxeHr7/+ussDLMBQoe+rr77Cxo0bodPpEBYWhp9//tmssikhfQX1ZBFCCCGEEEJIJ6IxWYQQQgghhBDSiSjIIoQQQgghhJBORGOy2qDX61FQUAC5XH5NE/ERQgghhBBC+gfGGGpqajBo0CBuQm1LKMhqQ0FBAfz8/Hq6GYQQQgghhJBe4sqVK/D19bW6noKsNsjlcgCGB9LR0bGHW0MIIb2PRqPBrl27MHPmTIjF4p5uDiGEENJlqqur4efnx8UI1lCQ1QZjiqCjoyMFWYQQYoFGo4G9vT0cHR0pyCKEEDIgtDWMiApfEEIIIYQQQkgnoiCLEEIIIYQQQjoRBVmEEEIIIYQQ0okoyCKEEEIIIYSQTkRBFiGEEEIIIYR0IgqyCCGEEEIIIaQTUZBFCCGEEEIIIZ2IgixCCCGEEEII6UT9PsiqrKzEiBEjEBMTg4iICHz55Zc93SRCCCGEEEJIP2bT0w3oanK5HImJibC3t4dKpUJERAQWLFgANze3nm4aIYQQQgghpB/q9z1ZIpEI9vb2AAC1Wg3GGBhjPdwqQgghhBBCSH/V64OsxMRE3HzzzRg0aBAEAgF+/fVXs20++eQTDB48GHZ2dhg9ejROnDjBW19ZWYno6Gj4+vri2Wefhbu7eze1nhBCCCGEEDLQ9PogS6VSITo6Gp988onF9Zs2bcJTTz2FV199FUlJSYiOjsasWbNQUlLCbePs7IzU1FTk5eXhxx9/RHFxcXc1nxBCCCGEEDLA9PoxWbNnz8bs2bOtrl+7di0eeOABLF++HADw2Wef4c8//8Q333yDF154gbetp6cnoqOjcfDgQdx2220Wj6dWq6FWq7nb1dXVAACNRgONRnO9p0MIIf2O8bORPiMJIYR0Jp2e4dSlCpTUqOEhl2BEgAtEQkGPtqm9/+t6fZDVmsbGRpw+fRqrV6/mlgmFQsyYMQNHjx4FABQXF8Pe3h5yuRxVVVVITEzEQw89ZPWYb775Jl5//XWz5bt27eLGdhFCCDG3e/funm4CIYSQfiK1TIDtF4WobGwOqpxtGRYM1iParefqK9TV1bVruz4dZCmVSuh0Onh6evKWe3p6IisrCwBw6dIl/OMf/+AKXjz66KOIjIy0eszVq1fjqaee4m5XV1fDz88PM2fOhKOjY9ecCCGE9GEajQa7d+/GDTfcALFY3NPNIYQQ0sftTC/GhqOpaBlKVTUKsOG8COvuiMascE+L+3Y1Y5ZbW/p0kNUeo0aNQkpKSru3l0gkkEgkZsvFYjF9eSCEkFbQ5yQhhJDrpdMz/Pvvc2YBFgAwAAIA//77HGZH+fRI6mB7/8/16SDL3d0dIpHIrJBFcXExvLy8eqhVhBBCCCGEDBw6PUO9Rof6Rh0aNIafeo0ODRq9xeX1Gh0aGnVo0OpR39i8TK3RoaiqAYVVDVbviwEorGrAibxyjA3svfPe9ukgy9bWFvHx8di7dy/mz58PANDr9di7dy9WrVrVs40jhBBCCCGkhzDGoNExLnipNw18Gk0DIV2LQEjfIhDSmQRC+uZjNRoDIz0adfpuP7+SGuuBWG/Q64Os2tpaXLhwgbudl5eHlJQUuLq6wt/fH0899RSWLl2KESNGYNSoUfjggw+gUqm4aoOEEEIIIYT0FowxqLX6FsGNvjngMQls2u4R0psFQqaBkk7f/QUi7MRCSMUiSMUi2DX9SG2Nt4WG203LuPViEaRN665W1OHj/Tlt3o+H3K4bzuba9fog69SpU5g6dSp321iUYunSpfj222+xePFilJaW4pVXXkFRURFiYmKwY8cOs2IYhBBCCCEDjU7PcCKvHCU1DfCQ22HUENceL4HdW+n1rEWw0jIQ0rUIhCz1COnbTI1r0OrAujn2EQrABTYSm+agRyoWQWIMimxbBEZiEaS2whaBkDFoag6WTIMmiY0QAsH1vb50eoZtSfkoqmqwOC5LAMDLyfBa7s16fZA1ZcoUsDZeiatWraL0QEIIIYQQEzvOFuL13zN441u8nezw6s1huDHCuwdb1jFand5kzI6el6rGC2Ya9RYCIQvLraTGNWq7P+VNLBKYBzG2ItjZCFsEQs1Bj3kgxO8hMu8pEsJWdP3BT3cRCQV49eYwPPRDEgQAL9AynsGrN4f1+osFvT7IIoQQQgghHbPjbCEe+iHJrCegqKoBD/2QhPX3xF1XoMUYQ6NOj4ZGfYsxOyaBT6O+xW1+6pul1DhL44E0uu5PeZPYWEprE7YIhFoPekwDHn7KXHNQJBYJu/3c+oIbI7yx/p44s4sEXn3oIgEFWYQQQggh/YhOz/DabxlWS2ADwPPbzqCouoHrGeJS41oZ39MyDa67h/sIBGgKbCyP72lOg2sR+LQyHsg0ADL2HtnZiCDs5b0kA8GNEd64Icyrz6a7UpBFCCGEENILMMZQ16hDrVqLmgYtatVa1Bp/q7WobdA0/a1DrVrDratp0ELV2LxtVZ0GmjYioKp6DV77LaNT2i0SCng9NOZFDYQWAqEWgY/F8UD8HqHOGO9D+haRUNCry7S3hoIsQgghhJDroNbqUNughUqtQ41J8NMcHJkEQybLebcbtKht1HZrQYQYPycMVch444GMxQv4gZB5j5AxZU5KKW+EWERBFiGEEEIGHJ2ecb0/KrUWNaa9Ri2CpJbBUI2af7uz5wgSCQWQSWyaf+xsrN+2a/4tl9jAQWKD7OIaPPZzSpv38/yNoX22l4CQ3o6CLEIIIYT0Ccb5hSym0nE9SM2pdMbAyRhMcbfVWqgadZ3ePntbUeuBUItgqPm2GA4SEfe3nfj60uKGecrx5t9Zfb4ENiF9GQVZhBBCCOlSWp2+OZXObJyReW+RaTBkOj5JpdZC28nVFsQigUkgJIZM0hQo2YmbAiORYXlTcCSzaw6Q5E3Bk/F2bxmQ319KYBPSl1GQRQghhLRioE7maizC0DKVrrVxRYZgSAOVWse73aDp3HQ6gQBwsOX3EsntbAzLTG+3CIaMAZHcJMVOYiPq1Lb1Fv2hBDYhfRkFWYQQQogVfXEy10at3mIqXU1TYQbTVLqWPUWm45NUam2nl+iW2Ah5wU/LYIjrLeIFQ+KmwKm5R8leTCW226Ovl8AmpC+jIIsQQgixoKsnczWlNxZhsJBKZ5Y61yIYqjVJpatRa9Go7dxeI6EATcGQuCn4EUFmJ+YFQ6apdNaKNThIbGBrQ1XoultfLoFNSF9GQRYhhBDSgk7P8Prv1idzFQB4/fcMTAxWoF6j68C4Ik3T2CSTOY8auqYIg1QsMgt+HCQWblurXNdJRRgIIWQgoiCLEELIgMQYg6pRh6p6DarqNKhu0Bj+rtcg7WolL0XQbF8AhVUNCH91Z6e2yUYosDiWiB8MmafPtQyQHGxFsKG5iwghpMdQkEUIIaTP0ukZquv5AVJVvQbV9drmvxuMy1r8btBC10mDjkyDHK63qI30OUsFGiQ21GtECCH9AQVZhBBCelSDRofqBtMgyCRAqm8RPDVoUFWvNQRW9RrUqLXXff+2IiEcpWI4SW2afouh0epxOKeszX2/WToCU4Z7UBEGQgghPBRkEUIIuS6MMTTogILKetRp61v0KPF7jiwFT+pOKNTgYCviAiRHqRiOdoa/nbhlNiZ/89dZ6j3S6RkmvL2vzclcJ1OARQghxAIKsgghhFhMu7OUctcycGpOu7MBThy85vsXCMALjHhBkZ2YF0Dxgic7Q++TuJPHH9FkroQQQq4HBVmEENJPqLU6k14irUkPkqGwg3nA1Llpd2KRAE5SW7MAyVpvErfOXgyZrU2v6xGiyVwJIYRcKwqyCCGklzBWuzMbh2Tag2Ql5a6z0u7sbUUWe5As9S452Rv+ltoAxw7swy1zZ8PW1rYTHonegyZzJYQQci0oyCKEkE6k0zPUtCPlztJ4pep6DbTXWe3OmHZnGhCZ9ig5tki5c7Tj9y5dS9qdRqOBrQj9tioeTeZKCCGkoyjIIoR0OZ2e9amegOa0O61JD5KGm0/JfIxS83adl3ZnMg7JSsqdpfFKcknvS7sjhBBCOqTyClDXSoVXezfA2a/72nMNKMgihHSpHWcLzca0eHfxmBbGGOqMk8xaSK0z9hpZKxHeoOm8tDt+D5Ll3iUne34gZSemuZIIIYQMUJVXgI/jAa3a+jY2EmDV6V4daFGQRQjpMjvOFuKhH5LMSmAXVTXgoR+SsP6eOKuBlmnaXVspdy3HK3VW2p1cYsONOzIvCW7a08QPnuR2YtjadG61O0IIIWRAqCtrPcACDOvryijIIoQMPDo9w2u/ZVicY8i47OktqdiTWYyaBq1ZIFXT0Llpd62VB285fxKl3RFCCCHkelCQRQhpE2PM0EtUp0FFXSMq6zWorGtEpfF2XdPteg0q6jSoqmtEaY0aqkZdq8dVqXXYejq/1W3sbUVmAZKjpZS7lgUdpDaQikWUdkcIIYT0Jez6MlF6CwqyCBlAjCXCK7nAyCRoUhmDpMYWwZShd0l3nel31syN8sbooW5mVe6MARSl3RFCCCH9jLoGqLgEVFy0/NMPUJBFSB9V36hDZX0jKlQaVNbzg6aqeg0qVC17nDSoqm+ERnftwZJULIKLvRhO9rZwsRfD2V4MZ3tbOEvFcLG3hZO94bezvRiXylR4Zktam8e8e3QAlccmhBBC+hOdFqjObw6aKlsEVK1VDuwnKMgipIeptbqmniNDQGQMhiqagibTtLyq+ub0vOuZeNbWRmgIkqS2TYFSiyBJ2hQ8mQRNhqp3onbfR5y/C97bdR5FVQ0Wx2UJAHg5Gcq5E0IIIaSPqa+w0AvVFExVXQH0bYytlroCLoObfgKa/9bUAz/d0aVN7w4UZBHSSTQ6Papa9BxxaXlNQVOVhTFMdW2MW2qNjVBgEgyJ4SRt0cNkJWjqjhLhIqEAr94chod+SIIA4AVaxnt+9eawXj1fFiGEEDJgaRsNwZKldL7KS0BDVev7i2wBZ3+TQKrpxznAEFTZOVneryCls86gR1GQRUgLOj1Ddb2lAg+Ggg4VdRqzwg9Vddc3Ca1QAC7tzjRAcrYSNDlJxXBxsIWDbe8u7HBjhDfW3xNnNk+WVxfPk0UIIYSQNjAGqJQmgdNFfm9UdT7A2siakXk2BU2DzX/k3oDwGsZV27sZ5sFqa54s+9491ICCLNJv6fUMNWqtebqdqrmgQ6WFoKm6QXNdhW2cpC3HKpkGTYbgyEnanIbnbG/br8uF3xjhjRvCvHAirxwlNQ3wkBtSBKkHixBCCOlimnqg8rLllL6Ki4BG1fr+NlLLKX0ugw29VLYOnd9mZz/DRMOtjduyd+vVc2QBFGSRPsBYEa9CxR+TxEvLq+cvMwZN11MQzzgRrWkwZAyarBV+cJSKKXiwQCQUUHELQgghpLPp9UBtsfWUvprCNg4gABwHWUjna/pb5gH0RMaMs1+vD6LaQkEW6TaMMTRo9BbmVTIPmkwLP1xvRTx7W5HZmCSnpjFMzYUf+EGTk1QMsYhKhxNCCCGkh5mWO29Zpa/iEqBrJa0OAGzlFnqihjQFVH6G1DvS6SjI6iN0etar0q3UWh1/nqUWQRO/wENz4YfGTqiIx41JMu1hMiv8YPjt2MGKeIQQQggh3Uqv45c7b5nSV6dsfX+BCHDytZzS5zIEkLr0TG/UAEdBVh+w42yhWeEA704qHKDR6bneogqToIk/Ga154Yd6zfVXxDNLtzMbq9RU+MHB8FtqS8ESIYQQQvqg+grLk+9WXjKMmWqz3LmL9ZQ+J19AJO7S5pOOoyCrl9txthAP/ZBkNs9QUVUDHvohCevvicONEd7Q6RlXPpxLt1NZqIJXz+9hqu2MinjGgg4t51lyaB6r5GwSUPX2iniEEEIIIR1iWu7cLKXvYtvlzoViy+XOjb1T1sqdk16LgqxeTKdneP33DIsTuRqXPfJjMuzFqahRX3vPkkAAONq1KOhgYTJa0wIPTvbifl0RjxBCCCGEw5ih2h0XOOWZ9ExdAqqvtl3u3MHDSkrf4KZy55Sx059QkNWLncgr56UIWqLTM16AZakinqWgybTHiSriEUIIIWTA0zRYKHd+sbl3qrG29f1t7Kyn9LkEdE25c9JrUZDVi5XUtB5gGb04JwQL4nypIh4hhBBCiDWm5c4tpfS1We4cgHyQ5XQ+l8GGiXlpOARpQkFWL+Yht2vXdpE+znCXUflNQgghhAxw6toWAdQlfm+Uto0L2LYyK+OiBgNOfoC4fd/NCKEgqxcbNcQV3k52KKpqsDguSwDAy8lQzp0QQgghpN/T64DqAuspfarS1vcXCE3KnQ82SelrmjfK3pV6o0inoCCrFxMJBXj15jA89EMSBAAv0DK+/V+9OYzGUxFCCCGk/6ivtJ7SV3kF0Gta39/O2XpKn5MflTsn3YKCrF7uxghvrL8nzmyeLK9OmieLEEIIIaRb6TTN5c4tpfU1VLa+v1AMOPtZTulzDgCkzl3XdkLaiYKsPuDGCG/cEOaFE3nlKKlpgIfckCJIPViEEEII6XUYA+rKTUqdX+Sn9FW1p9y5wkKFvqYfx0FU7pz0ehRk9REioQBjA916uhmEEEII6QsqrxjmdbLG3s3QG3StTMudW0rra0+5c7MAKqA5sJLIrr1thPQCFGQRQgghhPQnlVeAj+MBrdr6NjYSYNVp64EWY83lzi2l9NUUtN0Oubf1lD6ZJyCkaWdI/0VBFiGEEEJIf1JX1nqABRjWV18F1DWWq/RVXAK09a0fw1ju3FJKn7MfIJZe96kQ0ldRkEUIIYQQMhB9c2Pr6wVCwNG3OY2v5Y+9G5U7J8QKCrIIIYQQQvqyhiqgLKfp5wJw9WT797Vzsp7S5+QH2Nh2SZMJ6e8oyCKEEEII6e009UB5niGIKm8KpoxBVVsT8Fqz9A9gyMTObSchBAAFWYQQQgghvYNOC1Rdbg6euEAqxzCvFJj1fR08ALcgwC0QENsDJz5v+/4k8k5rOiGEj4IsQgghhJDuwhhQU8jviTL+rrgI6DXW95U4NgdSbkHNf7sGAnaOzdsVpLQvyCKEdBkKsgghhBBCOltdOb9HikvxywU0Kuv7iSRNQZRJIOXa9LeDOxWaIKSPoCCLEEIIIeRaNKqA8twWqX1Nv+vLre8nEBkq9hmDJ9OAytHn+uePsnczzIPV1jxZ9m7Xdz+EEKsoyCKEEEIIsUbbaJg3ihdENf3d1oS88kEmAZRJIOUc0LVV+5z9DBMN15VZ38bezfpExISQ60ZBFiGEEEIGNr0eqM7nB1DG9L6KSwDTWd9X6sIfH2VM73MdCkhk3XcOLTn7URBFSA+iIIsQQggh/R9jgEppMjbKNKDKBbQN1vcV2zcXmOACqqagyt61+86BENJnUJBFCCGEkP6jobopkMoxT+9TV1nfT2gDuAxpkdrX9FvuTQUnCCEdQkEWIYQQQvoWrbp5Yl6uel9TAYra4lZ2FABOfoDbUPMeKSd/QERfiwghnYM+TQghhBDS++h1QOVlk14pk4Cqsq2JeRXmY6TcggDXIYBY2m2nQAgZuCjIIoQQQkjPYMzQ88QrgW4sOJEH6Bqt72srbzEprzGoCgTsnLrvHAghxAIKsgghhBDSteorDJPw8gpONKX4NdZa308kMVTpazk5r1uQobeKxkkRQnopCrIIIYQQcv0a6wxBU7nJhLzGYKq1+ZoEQsDZnx9AuTaNmXLyBYSi7jsHQgjpJBRkEUIIIaR9dBrDOCleel/T7+qrre8r9+YHUMYflwDARtI97SeE9DlHC47irRNv4YVRL2DsoLE93Zx2oyCLEEIIIc30eqCmgB9AlV0w9FBVXAT0Wuv72jkBbsEmQdTQ5sBKIu+2UyCE9A+MMXyY9CFyq3LxYdKHGOM9BoI+kiZMQRYhhBAy0DAG1JWbjI3K4Ree0NZb39dGanmMlGvTxLx95AsQIaT3O1JwBOll6QCA9LJ0HCk4gvE+43u4Ve1DQRYhhBDSX6lrLYyRavrdUGl9P6EN4DLYfIyUcWJeobC7zoAQMoBo9BqcrziPM6VnkFqSil2XdnHrBBBgXfI6jBs0rk/0ZlGQRQghhPRlWrUhjY83l1TT37VFre/r6Gu5DLqzPyASd0vzCSEDV5GqCGmlaUgrTcMZ5Rmkl6VDrVNb3JaB9aneLAqyCCGEkN5OrwOqrjYHUOUmAVXlZYDpre9r786fQ4orODEEsLXvvnMghAxodZo6ZJRlIE2ZhjOlZ5BWmoaS+hKz7eS2ckS6RSK7MhvKeiWYycTjQoGwz/RmUZBFCCGE9AaMAarSFnNJNY2RKs8FrFzdBQDYyvgBlGtgc+EJqUv3nQMhhADQMz0uVl809FCVnkGaMg3ZFdnQMR1vO5FAhGEuwxCliEKUIgqR7pEIcAzA0YKjeHDPgxaP21d6syjIIoQQQiypvNL6/E72boCzX8eP21DVFEC1nJw3B2issb6fyNYwNsq1ZdGJQEDmSQUnCCE9prKh0tBDpTzDpf7VWPg887D3QLQiGpHukYhSRCHMLQxSGylvG8YY1iWvgwACXi+WUV8Zm0VBFiGEENJS5RXg43jDeCdrbCTAqtOWAy1NPVCe16J6X1OKn6q0lTsWtJiY1ySgcvKjiXkJIT1Oo9fgfPl5pCmbx1Jdqr5ktp2dyA5hbmG8XiovB692Hb9IVWQxwAIMY7OKVEXQ6DWwFdle9/l0FQqyCCGEkJbqyloPsADD+qI0oDSrRY9ULlB1BbDyBQGAoeeJC6JMUvxcBgNiu848E0IIuWaMGQIa04AqoyzDYnGKwY6DDQGVuyGoCnIJgljY8QI6tiJb/Dz3Z5Q3lFvdxtXOtVcHWAAFWYQQQsi1+/ku6+skToC76RipwObAiibmJYT0QnWaOqSXpXMBVVppGkrrzXvfHW0dEamIRLR7NKIUUYhwj4CTxKnT2uHl4NWuXq/ejIIsQgghRKs2FJdQZgPK88CVE+3bT2QLuAWbj5FyCzKM2erF4wUIIQObnulxseoiUktTuYAquzIb+hbVSm0ENgh2CebS/qLcoxDgGNCrx0P1BhRkEUIIGRgYM6QBKs83/WQbfsqyDfNMtVYG3ZoVuwCf2E5vKiGEdLaKhgoumEorTcNZ5VnUaMyLU3jae/LS/kLdQs2KU5C2UZBFCCGkf9FpmopONPVKKS80B1YNldb3kzgaeqDchwESGXDyq7bvi67kEkJ6IY1Og3MV5wwBVdO8VJdrLpttZyeyQ7h7OBdQRbpHwtPBswda3P9QkEUIIaRvqitvTu8ry27umarIA/RaKzsJDNUA3YcZ0vzcgw1/uwfzy6AXpLQvyCKEkB5mLE6Rqkzl5qXKKMtAo77RbNshTkMQ6R6JaIVhLFWQcxBshBQOdAV6VAkhhPReOi1Qeak5mFKeN1TwU55vfQ4rsUNTANUURBl7qNwCATGlvRBC+i5jcYrU0lRuol9lvdJsOyeJEzcfVbR7NMLdwzu1OAVpHQVZhBBCel59ZXPwxAVU2YZiFHqN9f0cffm9Ue7Bhh4qx0HXl8pn72aYB6utebLs3a79PgghpA16pkdeVR6X9pdWmoYLlRcsFqcY5jqMS/uLUkTBX+5PxSl6EAVZhBBCuodeB1ReNgmmTMZLqUqs72cjbSqF3jKYCgJsHbqmrc5+homGW+sts3ezPBExIYRco/KGcq53ylicolZTa7adl4MXL6AKdQ2FnQ3NsdebDIgg69Zbb0VCQgKmT5+OrVu39nRzCCGkf1PX8Cv3GXulynIACxNYcuSDDMFUy/FSjj6AUNh97Tdy9qMgihDSZYzFKVJLU7l5qa7UXDHbTmojRbhbODcvVaQiEh72Hj3QYtIRAyLIevzxx7FixQp89913Pd0UQgjpH/R6oPoqoMyGsCQLUVf2QLTxS0MvVU2h9f1EkqbxUU3BFDdeKpgm6CWE9FuMMRSoCnCm9Aw3L1VmWabF4hRDnYY2j6VSRCPQOZCKU/RBA+IZmzJlChISEnq6GYQQ0vc0qprS+7L5Y6XKLgDaegCACMAQADAddy3zNOmNMknzc/IDhKIeOBFCCOk+Ko0K6cp0Lu0vrTQNZQ3m6cfOEmcuoIpSRCHCPQKOto490GLS2Xp9kJWYmIg1a9bg9OnTKCwsxC+//IL58+fztvnkk0+wZs0aFBUVITo6GuvWrcOoUaN6psGEENLXMAZUF/Ar9xmDquqr1vcTigG3QOhdg3ChUoCho26EjWeIoWdK6txtzSeEkJ6kZ3rkVuY2B1TKNORU5lgsTjHcdTg3H1W0Ihp+cj8qTtFP9fogS6VSITo6GitWrMCCBQvM1m/atAlPPfUUPvvsM4wePRoffPABZs2ahXPnzsHDg/JVCSGEo6k3jIvieqOMc0zlAI3mA6s59u4tyqE3/e0cAIhsoNNokPnXXxgSNQcQi7vvfAghpAeU1ZfhjPIMF1ClK9MtFqfwdvDmBVQhriFUnGIA6fVB1uzZszF79myr69euXYsHHngAy5cvBwB89tln+PPPP/HNN9/ghRde6PD9qdVqqNXNA7Orq6sBABqNBhpNK2WECSGkN2AMqC2GoCwbgrILQNkFCMouQFCWDVRdgQDM8m5CG8BlMJhbMJhbEJiboXofcw0C7F0t35eeAfrmz0b6jCSE9DeNukacqziHs2VncUZ5BmfLzuJqrXkPv9RGinDXcES4RyDSLRIR7hFQSBX8jRh9TvYH7X0Oe32Q1ZrGxkacPn0aq1ev5pYJhULMmDEDR48evaZjvvnmm3j99dfNlu/atQv29vbX3FZCCOlMQr0GDupiyNSFkDcUQtZQCJna8Fusr7e6X6PIAbV23qiReKPWbhBqJV6otRsElUQBJmj6l9AAIB9AvhL8gVat271793WdEyGE9CTGGCr1lbiiu4Ir2iu4qruKAl0BdNCZbesh9ICvjS/8RH7ws/GDQqiAqFEEFAD1BfU4iZM9cAakO9TV1bVruz4dZCmVSuh0Onh6evKWe3p6Iisri7s9Y8YMpKamQqVSwdfXF1u2bMHYsWMtHnP16tV46qmnuNvV1dXw8/PDzJkz4ehIAxEJId2IMaBOaeiFauqNEiizISjPASovQdAi35/bTSAEnAP4vVLuwWCuQRDYu0EuEKAz6/hpNBrs3r0bN9xwA8SULkgI6SNUGhXSy9JxpuwMzirP4kzZGZQ3lJtt5yxxRoRbBKLcoxDhFoFwt3DIbaka6kBlzHJrS58Ostprz5497d5WIpFAIpGYLReLxfTlgRDSNbSNQMXF5gl6TYtPNFRa30/iZDJWKpibrFfgOgSwkaC7h1LT5yQhpLfS6XXIrcrl5qNKLU1FTmUOWIsUahuhDUJcQrhqf1HuUfCV+1JxCsJp7/+5Ph1kubu7QyQSobi4mLe8uLgYXl5ePdQqQgixoq7cpHKfSfGJ8jyAmaejGAgAZ//mOaVMJ+uVeQD0j58QQszwilOUpuFs2VmoNCqz7QY5DOICqkj3SIS6hUIiMr/YTkhH9ekgy9bWFvHx8di7dy9X1l2v12Pv3r1YtWpVzzaOEDIw6bSGXqmybH4pdOV5oN48DYVjK+P1RnHBlOtQQCzttuYTQkhf06hrRFZ5FhdQpSnTkF+bb7ad1EaKSPdI3rxU7lL3HmgxGQh6fZBVW1uLCxcucLfz8vKQkpICV1dX+Pv746mnnsLSpUsxYsQIjBo1Ch988AFUKhVXbZAQQrpEfQWgvGAeTJXnAvpWKg85+ZmUQg9qnqRX7k29UoQQ0gbGGPJr87lg6kzpGWSWZ0LT4nNXAAECnQN5AVWgUyBENBk66Sa9Psg6deoUpk6dyt02FqVYunQpvv32WyxevBilpaV45ZVXUFRUhJiYGOzYscOsGAYhhHSYXgdUXjIEU8rzTQFVU1ClKrW+n9i+KYAKbg6i3IIBt0DA1qH72k8IIX1cbWMtzpadNYylKj2DNGWaxeIUrnauvICKilOQniZgjFmeNIUAMFQQcXJyQlVVFVUXJKS/aqhuCqAu8ItPlOUAOrX1/eSD+IGU8W/5IEAo7L729zCNRoO//voLc+bMocIXhJBrptPrkFOVwwVTaaVpVotThLqGcoUpIhWR8JVRcQrSPdobG/T6nixCCOkUej1QdcWkN8okza+2yPp+NnaGXikuta9pvJRbECChq6SEEHKtlPVKXkB1VnkWdVrzOYh8ZD5cMBWliEKIawgVpyC9HgVZhJD+RV3bVAI922S81AXDMq31SXoh8zIrhQ73YMMYqgHUK0UIIV2hUdeIzPJMrjjFGeUZi8Up7G3sDcUpFJFcYEXFKUhfREEWIaTrVF4B6sqsr7d3A5z9On5cxoDq/OYeKdPiE9Xm/7Q5IlvANZCf2ucWbOiZsnPqeDsIIYSYYYzhau1VXkCVWZ4JrV7L285YnMKY9heliMJQp6FUnIL0CxRkEUK6RuUV4ON4QNvKmCYbCbDqtPVAq7EOKM9p7o3iik9cACzMd8JxUDQFTy3GSzkHAPTPmxBCOlVNYw3OKs/y5qWqUFeYbedq58oFU8biFDJbWQ+0mJCuR0EWIaRr1JW1HmABhvV1SkBoY2FeqWzDGCpYqc0jtDHMIcUrhd40Xkrq0umnQwghxFCc4kLlBV5AlVuVa1acQiwUc8UpjFX/fGQ+VJyCDBgUZBFCetY3cwALA505UhfAfXjz5LzG8VIuAYCIKtkRQkhXUtYreZP8pivTrRenMEn7C3ENga3ItgdaTEjvQEEWIaRz1ZUbeqEu7G3f9to6QCACXAY390QZe6XcggEHty5tLiGE9HdHC47irRNv4YVRL2DsoLFWt1Pr1Mgsy+RN9FugKjDbzkHsgAj3CC6ginSPhJuUPqsJMUVBFiGk4/R6oPqqIb2v9Hzz3FJtTdJryaL/AsNmAzZ0xZMQQjobYwwfJn2I3KpcfJj0IcZ4j4FAIDAUp6i5ilRlKjfRb1ZFlsXiFEEuQc1jqdyjMMRpCBWnIKQNFGQRQqzTqg0T8irPGXqnSs81T9SraSXFz8kPkHsBV0+2fR/OARRgEUJIFzlScATpZekAgPSydPzz0D9R1ViFM6VnrBenUEQhWhGNKPcohLuHw0Hs0N3NJqTPoyCLEALUV5j0SJkEVJWXAKa3vI9Q3FRwIhhQDDdJ8QsCJDKgIAX4YnK3ngYhhBBD79WVmitILknGe6fe4637Pfd37m+xUIxQt1BEuRuCqkhFJAY5DKLiFIR0AgqyCBkorjXFT+IEKIY1FZ8wCaicAwARfYQQQkhPa9Q1IqMsA6mlqUguSUZKSQrKGqzPUbho2CLMD5qP4a7DqTgFIV2EviER0t9ca4qfo29TMGXyoxhumHPqWq5q2rsZ5sFqa54sexosTQghHVHRUIGUkhSklKYgpSQFZ5Vn0ahv5G1jI7CBWCRGg7aBV15dKBAivSwdL415iXqsCOlCFGQR0ldZSvFTngcqLl57il9ncvYzTDRcZ/1qKuzdrE9ETAghBIwx5FXnGYKqkhQklyTjYvVFs+1c7VwRrYhGrEcsYj1iUamuxKP7HjXbTs/0SC9Lx5GCIxjvM74bzoCQgYmCLEJ6M4spftmGoKovpPg5+1EQRQghHdCgbUB6WTqSS5KRWpKKlNIUVKorzbYb6jQUsR6xiPGIQaxHLPzl/lzPFGMMd/55JwQQmE0SDBgqBq5LXodxg8ZRbxYhXYSCLEJ6g5YpfsrzhjS/a0nxcx8GyDyuLcWPEEJIt1LWK5t7qUqTkVGWYVZGXSKSIMI9guulilZEw0niZPWYGr0GRaoiiwEWADAwFKmKoNFraEwWIV2EgixCuhMvxc/kp8MpfsGGiXo7O8WPEEJIl9EzPXIqcwy9VE1FKq7UXDHbzl3qbuilUhh6qUJcQyAWidt9P7YiW/w892eUN5Rb3cbVzpUCLNJrla77GBAJoXj4YfN1n34K6PRQPLqqB1rWfhRkEdLZTFP8uMIT15DiZyw8QVX8CCGkT6rT1OGs8qyh4l9pClJLU1HTWMPbxjjZb6yiOfXPR+Zz3Wl8Xg5e8HLwuq5jENJjREIoP1oHALxAq/TTT6H8aB3cHzMfb9jb0Dc3Qq4Vl+Jn0iPV4RS/4KagilL8CCGkrytWFSO5NJlL/8sqz4KO6XjbSG2kiHKP4gKqKEUU5LbyHmoxIb2TMbAyBlrOt96Kis2bUbb+M7g/9qjFHq7ehoIsQtpSX8Evhd7RFD9jjxSl+BFCSL+h0+uQXZmN5JJkrkhFgarAbDtPe09egYphLsNgI6SvX4S0hul0kI0bB9XRo1B+tI4LtvpKgAVQkEWIgV4PVOe3mFuqIyl+LeaWohQ/QgjpV1QaFVJLU7leqjRlGlQaFW8boUCI4S7DuYAq1iOWUvYIaSddbS1Uhw6jNiEBtYmJ0JW3GFMotDxGq7eib4FkYLGU4mccO9VWih9XeIJS/AghpD9jjKFQVdjcS1WaivMV56Fvkb3gIHZAtCK6OfXPPQr2YvseajUhfU/j5cuGoCohAaqTpwCNhlsnlMsh9vKCOjsbArEYTKNB6aef9plAi4Is0j+Zpfg19Uq1meIXyO+RohQ/Qgjp9zR6Dc6Xn+eCqpTSFJTUlZht5yPzMQRUTUUqgpyDIBKKeqDFhPRNTKtFfXIyahISULs/AY25ubz1toMHQzZlCmRTpqDu5EkoP/mESxE0Fr0A0CcCLQqySN/VMsXPdMJelfk/R46lFD/3YYDLYErxI4SQAaC6sRqpJalcQHVWeRb12nreNjYCG4S6hSJaEc2NqfKw9+ihFhPSd+kqK1F78JChx+rgQeirq5tX2tjAPj6+KbCaDMmQIQCaqgiaBFiAeTGM3h5o0TdK0vvxUvyaeqSuKcWvqTw6pfgRQsiAwRjD1ZqrSC5t6qUqSUFOZY7ZRL1yWzk3L1WMRwwi3CMgtZH2UKsJ6bsYY2jMzTUEVfsTUJecDOiaq2yKnJ0hmzwJsilT4DB+PESOjuYH0ektFrngbuusZCX1IhRkkd7DmOJnLIV+LSl+7sMMvVSU4kcIIQOSRqdBRnkGUkpSuKCqrKHMbLsAxwCulyrWIxZDnIZAKBD2QIsJ6ftYYyPqTp1CzX7D+CrNFf4k25LgYENv1dQpkEZHQyBqPc22tYmGe3sPlhEFWaR7cSl+pnNLdTTFz6TwBKX4EULIgFbZUImU0uaA6qzyLBr1jbxtxEIxwt3CEeMRY/hRxMBN6tZDLSakf9CWlaH2QKKhaMXhw9CrmqttCsRi2I8eDdnUKZBNngJbX5+ea2gPoW+npGto1UB5Lr9HSnkeUF4AWpS85TGm+Bl7pCjFjxBCSBPGGC5WX+R6qZJLknGx+qLZdi4SFy6givWIRZhbGCQiSfc3mJB+hDEG9blzXBpgfVoawJrTbkXu7pBNmQz5lClwGDsWQgeHHmxtz6Mgi1yf+kqTHimTAhQVF4EWs9xzuBQ/kx4pxTDD5L0SmvWeEEKIgVqnRroyneulSilNQaW60my7oU5DuR6qWI9YBDgGQEAX5gi5bvqGBtQdP46a/ftRm3AA2qIi3nq7sLCmNMCpsAsPg0BIKbdGFGSRtjEGVF01n1eq9FwbKX6O/FLoXIpfACASd1/7CSGE9AnKeiVX9S+5NBkZZRnQ6rW8bSQiCSLcI7iAKloRDWc7555pMCH9kKa4GLUJBwxpgEePgjU0cOsEdnZwGDcOsimTIZs8GWJPzx5sae9GQRZpZpbid74pza+tFD8fftEJ498yT0rxI4QQYpGe6ZFbmYvk0mQu/e9KzRWz7dyl7lwwFesRi1DXUIjpQh0hnYbp9WhIT0ft/gTUJOyHOiOTt97G25tLA7QfPRpCO7seamnfQkFWb1d5Bagzr4rEsXcDnP06dkzTFD/TwhMdTfFzDzb8UIofIYSQNtRr63FWeZYbS5VamoqaxhreNgIIEOQSxE32G+MRA1+ZL6X+EdLJ9CoVao8cMYyvOpAInVLZvFIggDQ6mqsGKBk2jN6D14CCrN6s8grwcbyhh8kaGwmw6rR5oMVL8TMWnriWFL+mwhOU4kcIIaQDSupKuLFUySXJOFd+DlrGT/2T2kgR5R6FaA9DL1WUIgqOthbmzCGEXLfGq/mGoCohAXXHj4NpNNw6oYMDHCZMMARWkybCxo2qb14vCrJ6s7qy1gMswLA+/xRQkNTcI9XuFD9jr5Rxwl5K8SOEENJxOr0OFyovcL1UKSUpKFAVmG3nae/JTfYb4xGD4S7DYSOkryKEdAWm06E+NRW1+/ejNiEB6uwLvPViPz/Ipk6BfOpU2MfHQ2Br2zMN7afok60/2LLM8nKhDeAayC+FTil+hBBCrpNKo0JaaRrXS5WmTIOqxYU9oUCI4S7DeVX/vGXePdRiQgYGXXU1VIcOoSYhAaoDidBVVTWvFIlgHxfHpQHaDhlCaYBdiIKs/kDsAHiEms8tRSl+hBBCrhNjDIWqQi6gSilNwfmK89AzPW87B7EDohXRXFAVpYiCg3hgz5NDSHdQ5+UZqgHu34+606cBXfP4eqGTE2QTJxoCqwnjIXJ27rmGDjAUZPUHy/8EBsX2dCsIIYT0A1q9FucqzvEm/C2pMx/L6yPz4fVSBTkHQSQU9UCLCRlYmEaDutNJXBpg46VLvPW2gYGQT50C2ZQpkMbEQGBDX/d7Aj3q/QJ19RJCCLk21Y3VSCtN48ZSnVGeQb22nreNjcAGIa4h3FiqWI9YeNh79FCLCRl4tBUVUCUmGtIADx6Cvra2eaVYDIeRIw29VVMmw9bfv+caSjgUZBFCCCEDBGMMV2uuIqW0uZcqpzIHDIy3ndxWzvVQxXjEIMI9AlIbaQ+1mpCBhzEGdXY2avcbqgHWp6QYKkc3Ebm6QjZ5MmRTpsBh/HiIZJSa29tQkEUIIYT0UxqdBhnlGUgpSeHS/8oazOde9Jf7cz1UMYoYDHUeCqFA2AMtJmTg0qvVqDtxggusNAX8Cp2S0FBuUmC7yEgIhPQe7c0oyOrN7N0M82C1NU+WPc1lQAghBKhsqERqaSrXS5Velg61jv8/RCwUI8wtjOulilZEw13q3kMtJmRg05SUNKcBHjkKVlfHrRNIJHAYMwayqVMgmzwZYm+qztmXUJDVmzn7GSYarjO/6sixdzOfiJgQQki/xxjDxeqLhl6qpvS/vKo8s+2cJc68Xqpw93BIRJIeaDEhhDGGhowMrreq4exZ3nobDw+uxLrDmDEQSilNt6+iIKu3c/ajIIoQQgjUOjXSlelcQJVakooKdYXZdkOchnABVYxHDAY7Dqa5cAjpQfq6OqiOHTMEVgcOQFvCr9ZpFxXFpQFKQkPp/dpPUJBFCCGE9EJl9WW8XqqMsgxo9BreNhKRBOFu4Yj1iEWsRyyiFdFwtnPumQYTQjiaggLUHjiAmv37UXfsOFhjI7dOYG8P2fhxhh6rSZNgo1D0YEtJV6EgixBCCOlheqZHbmUuF1CllKTgcs1ls+3c7Ny4sVSxHrEIdQ2FmCadJ6THMZ0O9WlphkmBExKgPneOt17s4wPZ1KmQTZkC+1EjIbS17aGWku5CQRYhhBDSzeq19TirPMtV/EstTUV1YzVvGwEECHQO5HqpYhQx8JX7UioRIb2ErrYWqkOHUZuQgNrEROjKy5tXCoWQxsZyaYC2QUH03h1gKMgihBBCulhJXQnXQ5VSkoKs8ixomZa3jdRGikj3SK6XKkoRBUdbxx5qMSHEksbLl1GbkGBIAzx1GtA0p/AK5XLIJk6AbOpUOEyYABsXlx5sKelpFGQRQgghbThacBRvnXgLL4x6AWMHjW11W51ehwuVFwxBVakhqMqvzTfbzsPeo7mXyiMGw1yGQSyk1D9CehOm1aIuKYlLA2zMzeWttx0yxDC2asoU2MfFQiCm9zAxoCCLEEIIaQVjDB8mfYjcqlx8mPQhxniP4aX9qDQqpJWmcQFVWmkaajW1vGMIBUIMcxmGGEUMF1h5OXhR+hAhvZCushK1Bw8Z0gAPHoS+2iSV18YG9iNGNKcBDh7cY+0kvRsFWYQQQkgrjhQcQXpZOgAgvSwdf+T8AZFQxAVV5yrOQc/0vH0cxA6Ico/ieqmiFFFwEDv0RPMJIW1gjKExNxe1+/ejJiEB9UnJgL75PS1ycYFs0iTD3FXjx0Mkl/dcY0mfQUEWIYQQYoVWp8Wak2sggAAMDADw4uEXzbYb5DCIG0sV6xGLIOcgiISi7m4uIaSd9I2NqDt5kksD1Fy5wlsvGTaMSwOURkdBIKL3M+kYCrIIIYSQJg3aBpxRnkFScRKSS5JxqvgU1Dq12XYB8gBM9J2IGI8YxChi4Ong2QOtJYR0hLasDLUHElG7fz9Uhw9DX1fHrROIxbAfMwayqVMgnzwZYh+fnmso6RcoyCKEEDJgVTZUIrkkGUklSUgqSUJGWQa0em2r+wgFQshsZXhu5HM0poqQXowxBnVWlqEaYEICGtLOAIxx60UKd8ibeqscxoyB0IFSensjxhgYYxAKhT3dlA6hIIsQQsiAwBhDfm1+c1BVnITcqlyz7TykHojzjIOTrRM2nd9ktl7P9EgvS8eRgiMY7zO+O5pOCGknfUMDVMeOGYpWJByAtqiIt94uPJxLA7QLD4Ogj31x7w90Oh3Kyspgb28PmUwGADh37hw2b96M0tJSlJaWQqlU8n5/9dVXuPfee3u45R1DQRYhhJB+SafXIbsym0v9SypOQkl9idl2gU6BiPWMRZxHHOI84zDIYRAA4M4/7+SNxTIlgADrktdh3KBx1JtFSA/TFBejdn8CahMSoDp2DKyhgVsnkErhMG4cZFMmQzZpMsSeHj3Y0v5JpVJxAVFAQAAUCgUAIDk5GZ9++qlZwFRRUQHGGL777jssWbIEAJCTk4NXXnnF6n2UlpZ2y7l0JgqyCCGE9AvG8VTGnqrUklSzUuo2QhuEu4UjziOOq/znYmc+YWijrhFFqiKLARYAMDAUqYqg0WtgK7LtkvMhhFjG9Ho0nD3LpQGqMzJ56228vSGf2jR31ahRENrZ9UxD+yC9Xo/y8nJeYBQfHw9/f38AwKFDh/DGG2/w1tfX13P7f/vtt1i6dCkAoKioCF999ZXF+xEIBKg2KY0fFBSEBx54AO7u7lAoFGa/PT373rhXCrIIIYT0ScbxVMagKr0s3Ww8lUwsQ7RHNBdURbhHQGojbfPYtiJb/Dz3Z5Q3lFvdxtXOlQIsQrqJrlYF1dEjhjTAA4nQKZXNKwUCSKOjIZs6FbIpUyAZFkw9zE0aGhp4vUjGv2fNmoWQkBAAwK5du/DEE09AqVSirKwMej1/SooNGzZg2bJlAICamhrs2rXL7H5sbW25HiyjsLAwvPHGGxYDJ1dXV9jYNIchw4YNwxdffNHJZ9+zKMgihBDS6zHGUKAqQFKxoUBFcnEycqpyzLZTSBWI84zjUv+CnYOvuZS6l4MXvBy8rrfphJBr1Hj1KpcGWHfiBJhGw60TOjjAYeLEpjTASbBxde3BlnYPvV6Pqqoqi2OWlEol7r77bsTGxgIAfvnlFyxZsgS1tbUWj7VhwwYuyNLr9cjM5PcGOjs7c0GRo6MjtzwmJgbffvutWeAkk8nMAtuAgAC89NJLnfkQ9CkUZBFCCOl1dHodLlRewOni01xPVUmd+XiqoU5DEesRi3jPeMR6xMJH5kNXsAnpo5hWi/rU1KaiFQlQZ1/grRf7+zenAcbHQ2Db93uSa2pqkJeXx/Uytex1evLJJzFu3DgAwM8//4y7777b6rHCw8O5IMve3p4LsGxsbMx6knx9fbn9Ro0ahb1793Lr3N3dIRaLLd6Ht7c3lw5IWkdBFiGEkB7XoG3AWeVZJJck43TJacvjqQQ2CHMPM/RSecRZHU9FCOk7dNXVUB06hJqEBKgOJEJXVdW8UiSCfVwclwZoO2Rwn7iIUlhYiNOnT1tM0ystLcW///1vTJ8+HQDw+++/txo4zZ49mwuy3N3dAQByudysJ0mhUCAsLIzbb/z48cjOzuZ6olp73FxdXTFt2rTOOHVigoIsQggh3a6yoRIppSlcKXVL46kcxA6IUcQg1iMWcZ5x7R5PRQjp3dS5eVxvVd3p04BOx60TOjlBNmmSIQ1wwgSInJx6pI1arRaMMa5HJzs7G3v27LFaYvzzzz/H3LlzAQAJCQm46667rB774sWL3N+enp7w8PCwWOxBoVBgzJgx3LZTp05FfX097NpRyEMmkyEoKOgaz550hg4FWRqNBitXrsTLL7+MIUOGdFWbCCGE9COm46mMpdRbG08V62Eopz7MZdg1j6cihPQerLERdUlJ3PiqxkuXeOttgwINkwJPnQppdDQENp3bB8AYg0qlglKphLu7Ozc3U3JyMjZt2mQWMJWWlqKyshK//PIL5s+fDwA4deoUHn74Yav3UWQyH5efnx/i4+O5QKll8BQfH89tO336dBQXF7frPMRisdU0PtL7dOhVLBaLsW3bNrz88std1R5CCCF9nHE8lbFARVJJEorrzL9EDHEawhWoiPWIha/Mt0+kAhFC2qatqIAqMRE1+xOgOnQIetMCDGIxHEaNapoUeDJs/fw6dGydTofy8nIuMAoLC+NS6Q4dOoT169ebBU4NTXNnbd++HbfeeisAwwS4b7/9ttX7UZpUMAwODsatt95qNXAaOnQot+2ECRNw6tSpDp0T6X86fKlg/vz5+PXXX/Hkk092RXsIIYT0MWqdGnnaPHyd/jVSlalILUlFjaaGt42NwAZhbmFcQBXjEQNXu/5fDYyQgYIxBvX5bC4NsD4lBWDN88yJ3NwgmzwZsimT4TBuPEQyB25dfX29WQre5MmTueIMO3bswH/+8x+ul6m8vBzM5NimgVN+fj5+/PFHi220s7ODSqXibkdERODxxx+3OjeTq0nFwhEjRmD79u2d8liRgaHDQVZwcDD+7//+D4cPH0Z8fDwcHBx46x977LFOaxwhhJDep0pdhZSSFJwuOY3k4mSkl6VDo9cAqc3b2NvYI8YjhuupovFUhPQ/erUadSdOoHb/ftQkJEBbUMhbr/X3R1VwEK56eSFPJMKixYsxKDAQALBlyxY8++yzKC0tRV1dndmxt23bxgVZ1dXVOHjwoNk2Li4ucHd35/WAx8fH49133+WNazIGTg4ODrxtIyIi8MEHH3TGQ0GIGQEzvRTQDq2NxRIIBMjNzb3uRvUm1dXVcHJyQlVVFW+eAEIIGQgYYyhUFXIFKpJLknGh8oLZdjKBDGP9xiLeKx5xHnEIdgmGjZBqKxHS1zU2NvKKPVTk5kKYnAzHc+fhWVQEscnEtXobGyRWVSKhphYHVLUo1vKL2WzduhULFy4EYAiyFi1axK0Ti8W8nqTVq1djxowZAICrV6/i6NGjvMDJ1dWVxieRHtHe2KDD/wHz8vKuq2GEEEJ6L+N4KmOBirbGU8V6xCLKLQqpB1Jx04Sb6EsPIX1AWVkZsrOzrVbK+7//+z/ExcUBAL75+muse/JJTJHJMNlBhkgpv0da4+gIxezZkE2ZjJ0FBXj4nnsAAI6OjghsUSnPx8eH22/q1Kk4evQoF1S1Vmbc19cXt99+exc9GoR0jeu6zGjsBKOByoQQ0jepderm+amKT7c6nirWIxaxnrGI9YjljafSaDRIE6R1d9MJISby8vJw8uRJq4HTZ599xs23tGXLFjz00ENWj7XszjsRXFmJ2v37MW7HTkwe3JzFpAeQby/FVU8vVAUHYcb998M7KgoAMFulQn5+Ptzd3WHbxkTBxklvCTHFGENhYSEyMzN5Py+++CLXs9lXXFOQ9d///hdr1qxBdnY2AGDYsGF49tlnce+993Zq4wghhHQu43gq0/mpNHoNbxvjeCpjKfUI9wjYi+17qMWEDAyMMdTW1kIikXABSlpaGnbt2mUWMBl/b9++HVOnTgUA7Nq1Cw8++CB3vEfc3OEKhs1lZQAMBSGMIjIy8c/AIOxydeF6moY4OCCkrg7+xSVweettXNUYPhfEAAT29pCNH2+oBjh5EsKtBEcODg5mY/UJsUSn00Gj0XBzfh07dgxPPPEEsrKyUGU6IXWTG2+8sf8HWWvXrsXLL7+MVatWYfz48QAM5TIffPBBKJVKqjpICCG9SEFtAa+UuqXxVO5Sd14p9WEuw2g8FSHXSafToaysDEqlEv7+/tzcTIcPH8bmzZvN5mVSKpVQq9XYu3cvpk2bBsDwxfPZZ5+1eh8lJSXc34GBgZg0aRIXNE0oKUV0RgZuW3gbtAtuRWxsLACg9NNP4bZrFx5/4gm8OH4cahMOoHb/fqiPn+AdW+zrC9nUqZBNmQz7kSMhbKNnihBL1Go1srOzkZmZiYyMDK5n6ty5c3jrrbfwxBNPAAAkEgmOHz8OABCJRAgMDERoaCj3Y4w5+pIO/xddt24d1q9fjyVLlnDL5s2bh/DwcLz22msUZBFCSA/RMz2yK7IN46lKDEUqilRFZtsNdhyMOM84Q2DlEQdfOc1PRUhb6urqeD1JI0eO5Ep8//333/jiiy94QVNFRQU3rGLPnj2YPn06ACAjIwMfffSR1fsxnZspIiICd999N29ck+nf/v7+3LYzZswwu9Jf+umnwEfr4B4dBcWsWSj54AOUffY5JCEhqNi4EcqPP27eWCiENC7WMCnwlCmwDQykzwXSbjU1NcjKyoKjoyOGDx8OAEhJScGIESOg0+ks7nPu3Dnu79DQUGzevBmhoaEIDg6GRCLplnZ3pQ4HWYWFhVxOr6lx48ahsLDQwh6EEEK6glqnRroynUv9SylJsTieKtQt1JD619RTRfNTkYFOr9ejoqLCLAVv7ty58Pb2BgBs2rQJa9as4da1LDO+e/duLqjJz8/Hr7/+avG+XFxcUF9fz90eMWIEVq9ebTYnk2mZcaNx48ZZ/M7VXoqHH4auugbKj9ZBue5jbt4qdVYWAEDo6AjZhAmQTZ0ChwkTYOPics33RQYGtVqN48eP88ZLZWRk4OrVqwCAVatWYd26dQAMFcl1Oh0cHR0RFhbG65kKDQ3F4MGDuePa2dn1u+ImHQ6ygoKCsHnzZrz44ou85Zs2bUJwcHCnNYwQQghflboKqaWpOF18GsklyTirPGtxPFW0IhqxnobxVJHukTSeivR7arXaYvpdaWkpHnjgAa7H58svv8Q///lPlJWVQW9Setxo165dXJBVU1OD06dP89bb2tpywZBQKOSWT5gwAZ9++qnZhLZubm6wseF/1YqNjeVS97oCYwwNGRmo3bsPNfv2cQGVMcCyHTrUMLZqymTYx8ZCQBVBSQuMMVy5coULonx9fXHbbbcBAGprazF58mSL+3l6evJ6oJycnFBYWAhPT88B2Sva4SDr9ddfx+LFi5GYmMjlRx4+fBh79+7F5s2bO72BhBAyUBXWFnJpf6eLT1scT+Vm58al/sV6xmK4y3AaT0X6PJVKhYKCAquV8l5++WUEBQUBMIwVf/rpp60ea+LEiVyQJRQKUVpayq1zcnLi9STJ5XJu3cyZM/HHH3/wAieZTGbxy2JISAhCQkI66/Q7jGk0qDt5EjVNgZXWNLNIIDAEWCIRoNPBce5NUDz8cI+1lfQ+Go0Ga9as4YKqrKwsqFQqbv3s2bO5IMvNzQ0jRoyAQqFAaGgor4fKxUJPqJeXV7edR2/T4f/ECxcuxIkTJ7B27Vquazw0NBQnTpzo0iszhBDSn+mZ3jA/VXEyTpecbnM8lbHyn5/cb0BeISR9T0FBATIzM61Wyvv4448RFhYGAPjkk0/w/PPPWz3W3XffzQVZzs7OAAAbGxuuLLhp+p2xZwoAbrnlFowcORIKhQJubm6tlhn39/fnjXnqbXS1tVAdPIiaPXtRm5gIfU1zqrBAKoVswgQwMNTu3gP3xx6F4uGHUfrpp1B+ZEjlokBr4Kivr8e5c+d4KX4+Pj744IMPABjeO++88w6vqp+NjQ2Cg4MRGhqKCRMm8I538uTJ7mx+n9WhIEuj0WDlypV4+eWX8cMPP3RVmwghpN8zHU+VXJKM5JJk1DTyx1OJBCKEuoZyPVUxHjFwk7r1UIsJMZ8fMzMzE8ePH7eaqrd161bExMQAADZu3IjnnnvO6rEvX77MBVnu7u6QyWRmxR6MvwMDA7n9Fi9ejFtvvRXOzs5tXnDo63MzaYqLUbtvH2r27oPq+HFA05wuLHJzg3zaVMimTYPD2LEo++YbKD9axwVYQHNgRYFW/9TQ0MCVRAcM742TJ0/i4sWL3HvXKDg4mAuyBAIBnnjiCYjFYq53KjAwkCaXv04dCrLEYjG2bduGl19+uavaQwgh/ZJxPFVSsSGoOqM8YzaeSmojRbQimguqaDwV6WparRbl5eVwdnbmenWOHTtmcW4m49+HDx/GiBEjAAB//PFHq4FTUVFzb2xAQABCQ0OtBk5RTRPaAsDy5cuxYsWKdp1Df56biTGGxgsXULN3L2r27kPDmTO89bZDhkA+fRpk06ZDGh0FgUjUvFKn5wVYRtxtnfmYNNL7McZQVFRkNllvZmYmXF1dcfbsWW7bnJwc5OXlATAUYDFN7YuIiOAd97XXXuvO0xgQOpwuOH/+fPz6669Uqp0QQlpRpCriClQklSThQsUFMPCvJBrHUxkr/9F4KnI9GGOoq6vjgqHQ0FAu+Ni5cye2bt1qFjAZy4yfOHECI0eOBGAYZ/3qq69avR/TEuOhoaG48cYbzQIm42/TL3KLFi3CokWL2nUuAzkFlul0qE9K4sZXaS5fbl4pEEAaHQ3Z9GmQT58OydChVo+jeHSV9XXUg9Xr6fV6XLp0CVevXsXEiRO55RMmTMCRI0cs7lNWVgatVssVW3n77bchEokQGhoKDw+PAf2+6gkd/m8eHByM//u//8Phw4cRHx9vdvXoscce67TGEUJIX6BneuRU5iCpOIlL/ytUmU9pMdhxMGI9YhHrEYt4z3gaT0VapdfrUV5ezguMpk+fDicnJwDA5s2b8fXXX/N6mxoaGrj9jx8/jlGjRgEAzp49i6+++sri/QgEAlRUVHC34+Li8MADD1gtMW46xmnu3LmYO3duV5z+gKKvr4fq8GHU7N2H2oQE6EyeD4GtLRzGjoVsxnTIp0yBjULRgy0lXSE7Oxupqam8Xqlz586hvr4eUqkUtbW1XDVLX19fCIVCDB06lOuVMvZQhYSE8KpZGudmIz1DwFomabZhyJAh1g8mECA3N/e6G9WbVFdXw8nJCVVVVXB0dOzp5hBCeoFGXSPSy9K5nqrWxlMZS6nHeMTAXdp3x4K0RqPR4K+//sKcOXMoh78VDQ0NZmOWSktLcc8993DjhL744gt88MEHKC0tRXl5uVmZ8WPHjmH06NEArFfVM5YZ/+mnn7gr4CdPnsTOnTstTmrr6uoKkWmaGekW2rIy1CYkGMZXHT4MplZz64ROTpBPmQzZ9OmQjR8PYT9NhxxIVCoVsrKykJmZiezsbLz22mvcRbZbb73V4jxrtra2GD58OPbt28d9RpSWlkIul/PGXpHu1d7YoEM9WYwxJCQkwMPDA1Kp9LobSQghfUF1YzVSSlIMqX/FSTirPItGfSNvG248VVMp9Sj3KBpP1Y/p9XpUVVVZLTH+7LPPcqWL16xZg9dff51XEtnU2LFjuS9QKpUKmZmZvPXOzs4W52aaNWsW3NzczNL0LJUZHzlyJJcOSHpO48WLhjTAvXtRn5zMzV0FAGIfn6Y0wBmwj4+DwIZSh/uynTt3YufOncjIyEBmZiYum6Z9AvjHP/4BHx8fAIYJqvPz880m7B0yZIjZPGsK6snsMzocZAUHByM9Pb1PTTx86623IiEhAdOnT8fWrVt7ujmEkF6uSFXEpf5ZG0/laueKOI84rkjFMNdhEAupF6cvq6iowOXLl62WGF+7di18fX0BAK+++ir+9a9/WT3WbbfdxgVZNjY2XIAlFovN0vBM0+4XLFiA6OhorrfJzc3Nau9geHg4wsPDO+v0SRdgej0azpzhAqvGnBzeervw8ObxVcOGUfpwH8EYQ35+PjIzM7kgKjMzE1u3buWCoN27d+P999/n7efh4cEFUKa91P/85z/xz3/+s1vPoS+orq7GkSNHkJiYiHvuuYerPtpXdCjIEgqFCA4ORllZWZ8Ksh5//HGsWLEC3333XU83hRDSyxjHUxkLVCQVJ1kcTxXgGMDNTRXnGQd/uT99IeoDcnNzkZ6ebjVw+umnn7g0+Pfeew///ve/rR7rySef5IIsY8+TXC63WPDB9Grzvffei5tvvhkKhQKOjo6tvm4CAgIQEBDQGadOeoi+sRF1x44Z5q/avx9ak8mPYWMDh1GjDIHVtGkQm4xvI72PVquFQCDg0mk3btyIDz/8EFlZWaipqTHbPjMzk3vvz5w5E3q9ntcz5eZGU3C0prS0FAcPHsTBgweRmJiIlJQULhhVKBT9O8gCgLfeegvPPvss1q9fb1b+sbeaMmUKEhISeroZhJBewDieylhKPbkkGdWN1bxtRAIRQlxDuAIV/Xk8VV+g0WggEom4VLmkpCQcO3bMaonxhIQE7kLgt99+izfeeMPqsYuKirggy9vbG56enlYr5ZlOTPuPf/wDK1eubNe4iL4+NxNpm66qCrUHDhjGVx08CH1dHbdO6OAA2eRJkE2bDtmkiRDR+O5ep6GhAefPn+d6pIy9U+fPn8eBAwcwZswYAEBNTQ03Ea9IJEJQUJBZ4QmjmTNnYubMmT1yPn2FRqPheuqPHz/OPc6mAgMDMXHiRN4UD31Fh4OsJUuWoK6uDtHR0bC1tTUbm1VeXt6h4yUmJmLNmjU4ffo0CgsL8csvv2D+/Pm8bT755BOsWbMGRUVFiI6Oxrp167iKSYQQ0pr2jqeKUkRxvVQ0nqrrMMagUqmgVCrh4+PD/YPdu3cvdu/ebXFC28rKSmRlZWH48OEAgF9//bXVwKmkpIQLsgIDAzFixAirlfKGDRvG7ffII4/gkUceadd50LhkosnP58qs1508Ceh03DobT0/Ipk2FfNp02I8eBWHTHGSkZ1VXVyMzMxNDhw7lepw2bNiA+++/36zIjFFmZib35f/GG2/E1q1bERoaiqCgIG5uOdI2xhiys7O5XqqDBw9i7ty5+OijjwAAUVFRkEgkCA4OxsSJEzFp0iRMnDiRG7fWF3U4yDLODt1ZVCoVoqOjsWLFCixYsMBs/aZNm/DUU0/hs88+w+jRo/HBBx9g1qxZOHfuHDw8PAAAMTEx0Gq1Zvvu2rULgwYN6tT2EkJ6tyJVEZJLkrnKf9kV2VbHU3HzU7kOp/FU10in06G0tBRXrlxBYmIixo8fz/XubN26Fb/88otZmp6xzHhmZiZ35TcxMRFvv/221ftRKpVckBUTE4MFCxZYDZyM2wHA0qVLsXTp0q46fTKAMMagzszkAit1iwIlkuBgbnyVXXg4BCZFSkj3qq6uRlJSEm+8VGZmJgoKCgAA33//Pe655x4AhpLoer0ezs7OZiXRQ0NDeem7gwcPxuDBg3vilPoknU6HTz/9lAusiouLeesPHTrE/S2VSlFSUtKvKnl3OMjq7H9Ws2fPxuzZs62uX7t2LR544AEsX74cAPDZZ5/hzz//xDfffIMXXngBAJCSktJp7VGr1VCblFGtrjakEWk0Gmg0mk67H0LI9dMzPfKq8pBcmozk0mSklKZYHE/lL/dHjCIGMYoYxCpizcdT6QCNjt7fAFBfX88FQ8bAaP78+Vxxhq+//hobN27ktikvL4fpTCBpaWlc4JSamooff/zR4v3Y2dmhrKyM+1wdPXo0Hn30UV61PNMfV1dXbtubb74ZN998c6vnQZ/XpDMwjQb1p09DtT8Bqv37oS00+XwRCmEXGwvZtGlwmDoFYj8/bpVWp+P1bJHOp9frcfnyZWRlZSErKwsTJkzAiBEjAAD79+83y4oy8vb2Rl1dHe+z5/Lly/D09LQ4XlKn00FHz2WbNBoNkpKSkJ+fz+s0effdd7nKihKJBCNHjsSECRMwceJEjBkzhvdZLZVK+8Rnd3vbeE31QXNycrBhwwbk5OTgww8/hIeHB/7++2/4+/t3aqWjxsZGnD59GqtXr+aWCYVCzJgxA0ePHu20+zH15ptv4vXXXzdbvmvXLtjbU/oQIT1Jy7Qo0BXgkvYSLmov4rLuMupZPW8bAQTwFnljsM1gBIgC4G/jD7lQDpQDKAfSz6UjHek9cwLdTK/XQ6VSobq6GtXV1aiqqkJNTQ2qqqowZ84c7jPtl19+wV9//YXq6mreRSaj2tpa+DV9gUxISOBdfTSSyWRwdHTE3r17ufkSZTIZli1bBicnJ8jlcjg5OcHR0RFOTk6QSCRQKpX466+/uGO0nDizpqYGNTU1yMvL67THhJC2CNRqOJw7B1lGBhyysiCqb57gWS8Wo25YMGrDw1EbEgK9sTLkmTOGH9JlysvLsXfvXly5cgVXr15Ffn4+7/PqjjvuwB133AEAKC4uhqenJ/z8/ODr68v7kclkAMD77CEdp1arcf78eaSnpyMjIwPnzp2DWq2GTCaDra0tN4Z26tSp0Gq1CAsLQ3BwMJdiqdFocPDgwZ48hWtWZzLmsjUdDrIOHDiA2bNnY/z48UhMTMS///1veHh4IDU1FV9//XWnlkhXKpXQ6XTw9PTkLff09ERWVla7jzNjxgykpqZCpVLB19cXW7ZswdixYy1uu3r1ajz11FPc7erqavj5+WHmzJn9qguTkL6gprEGaco0Q09VSTLSy9LNxlPZiewQ6R6JWEUsYj1iEeEWAQdx/5y4U61W83qZWv688cYbcHFxAWAoCbx27VqrV2CfeeYZrlJTUlISSk0qoInFYq58uEKhwKRJkxAaGgoA8Pf3xy233MJbL5fLkZCQgBtuuIFXbnzOnDld9VAQ0qm0paWG3qp9+1B34gRgcqVa5OoC+8lTIJs2FdIxYyCkSWC7RF1dHc6dO4fMzEyud2r27NlcJlNWVhZWrFjB20csFiM4OBihoaG45ZZbeJ85xv1I53v88cfx1VdfmfXouLq6Yvz48Rg/fjz3v6g//h8wZrm1pcNB1gsvvIB//etfeOqppyCXy7nl06ZNw8cff9zRw3WLPXv2tHtbiUQCiURitlwsFludq4QQ0rajBUfx1om38MKoFzB2kOWLHMbxVMbKf+crzlscTxXrEctV/uvr46kKCwtx8eJFqyXGv/vuO67s7zPPPMMNErbkscce48aqymQyLsBycnIyG78kl8u5z7Tly5dj9uzZ3PrWyozHxsYiNjaWt8z4j5Y+J0lfwRhDY04OavbsRc2+fWhIS+Ottw0IgGzGdMinT4c0OhqCphLe5PpptVpugt3i4mIsX74cmZmZuHTpEi/1GDBMkfCPf/wDABASEoIlS5YgJCSEGzM1dOhQs8l6SecoKSnhyqkfPHgQu3fvhqurKwBw6duDBg3CpEmTuJ/Q0FDehOn9VXv/z3X4lXnmzBmLOfYeHh5QKpUdPVyr3N3dIRKJzAbKFRcXc5M8EkJ6P8YYPkz6ELlVufgw6UOM8R4DBobcylwklTSXUs+vzTfb11/uzxWoiPOIQ4BjQK+fnyo9PR1nz561WmJ8z549XDD01ltvtRo4FRYWckGW8TPRWolxZ2dnbr9Vq1bh/vvvh7u7e5sVsGgwNxkImE6H+uTkpsIVe6G5dJm3XhodDdn06ZBPnwbboUN7/edMb8YYQ2FhoVnhiczMTMydOxdfffUVAMDZ2Rk7d+7kKvu5u7vz5pUyLektFotpvtMuVFxcjD179iAxMRGJiYlmGWOHDx/mxsI+9NBDWLFiBYYMGULvk1Z0OMhydnZGYWEhN6+IUXJycqeXWbS1tUV8fDz27t3LDWDU6/XYu3cvVq1a1an3RQjpOkcKjiC9zDAOKr0sHff8dQ8u1VxClbqKt51QIESIawiv8l9PzE/FGENtbS0cHBy4q3IHDx7E8ePHLZYYVyqVyMjIgHfTxKJffvklPvzwQ6vHLykp4YIsf39/DBkyxGrgZHpB6YUXXsA///nPdl0pNF5xJGQg09fXQ3XkCGr27kNtQgJ0JtPMCGxtYT92DOTTpkM2dQrETe9J0n46nQ55eXmor69HZGQkAENas5eXFyorKy3uk5GRwf0tkUjw3//+F35+fggNDeVN4k26DmMM58+fh6urK/eY//HHH7j//vt520VERHC9VOPGjeOW9+Wy6t2pw0HWHXfcgeeffx5btmyBQCCAXq/H4cOH8cwzz2DJkiUdbkBtbS0uXLjA3c7Ly0NKSgpcXV3h7++Pp556CkuXLsWIESMwatQofPDBB1CpVJRrS0gvp9KokFqSilPFp7AxcyNvXZrSkJojtZEiyj0KsZ6G9L9oRXSXjKfS6XQoKytDaWkpQkJCIGpK/fnf//6Hffv2WQya1Go1CgoKuMBp+/btrU5hoVQquW3DwsIwadIks9Lixt+mJYGffvppPP300+06D0rFI6Rt2vJy1O5PQM2+fVAdPgzW0Fy4QujkBNnkSZBPmw6HCRMgkvXP8Ztd4ezZs7yJejMzM7liB5MnT0ZCQgIAQ+Dk6OiI6upqBAYG8sqht5ywFwDuvvvuHjibgUWn0+HMmTNcKfXExESUlJRg3bp1XKfFpEmTMHLkSC6oGj9+PJdFQa5Nh4Os//znP3jkkUfg5+cHnU6HsLAw6HQ63HXXXXjppZc63IBTp05h6tSp3G1j0YmlS5fi22+/xeLFi1FaWopXXnkFRUVFiImJwY4dO8yKYRBCelZZfRk3P1VSSRKyyrOgZ5YndwSA50c+j8Uhi69pPFVdXR0vKJo+fToXgHzzzTf4/fffeesrKiq4XP/8/Hxu/ryEhIRWU/VKS0u5wGn06NG4++67Lc7LpFAoMHToUG6/f/zjH9w4AkJI12u8dMmQBrh3L+qTkwGTiWXFgwZxaYD28fEQ0MUKq2pqapCVlYWMjAxoNBpez8bMmTNRWGg+RYZEIjEbF5WYmAgvLy+LY9xJ97l8+TIefvhhHDp0CFVV/MwRiUTCK3gUHByMEydOdHcT+zUBaznKsJ2uXLmCM2fOoLa2FrGxsQgODu7stvUK1dXVcHJyQlVVFVUXJKQJYwz5tflIKklCUnESThefxsXqi2bbDXIYBJVGherGal4BC6FAiFDXUPx0009gjKG8vNxs/NKyZcu4sUTvvvsufv75Z259y/KpV69e5dIXnn76aaxdu9Ziu11dXXHo0CGuUt5ff/2FQ4cOWUzTc3d35+aGIq3TaDT466+/MGfOHOptI92C6fVoOHu2KbDag8YLObz1krBQyKcbCldIhg+ncSNW/PDDDzh16hTXO3X16lVuna+vL65cucLdXrBgAQoLC3m9UqGhoRg8eDCXHUB6Rl1dHY4dO4aDBw/C29ubu8inUqng7OwMrVYLmUyG8ePHcz1VI0aM4CaOJx3T3tjgmkuy+Pn5cfOmEEL6Nz3T40LlBSQVNwVVJadRUlditl2QcxCi3aIRZBcEb503Mkoy8IXqC4vHSy9Lh99EPxQeLeQGPZuaM2cOfH19ARiKP5w+fZq33tbWlutNajBJB1qwYAGCgoLMAiY3Nzezq61z5szpl+VlCemP9I2NqDt+HDV79qJ23z5oTa7Cw8YGDqNGQjZtOuTTpkLc1Fs9kDHGcOXKFV7RicrKSmzatInb5vPPPzeb987T0xOhoaEICwuDXq/nxoBu3769W9tPrKuqqsLhw4e51L9Tp05xVV5HjhzJBVkODg749ttvMXz4cMTExPTJSoz19fXYtWsXxo0b1+fG7PW9R5sQ0uU0Og3Sy9KRVJKEE/knkFqailpdLW8bARPAvtoet466FaN9RiPWIxbPPfYcXv+ieTLvoa8MhXSwFAKhhavIDJBMl0B/2BBgOTk58QIj0072ZcuWYdq0abz1MpnM4tVp4xwdhJC+T1dVhdrERNTs3QfVwYPQq1TcOqG9PRyaxlfJJk+CaIBmm+h0Ol5P0htvvIHffvsNmZmZUJk8XgAgEAjw7bffQiqVAgAWL16M0aNH83qmjPMbkd6jtraWm0QZMBSkMO11BAzFKCZNmsQbggP0zTFv1dXV+Ouvv7Bt2zb89ddfqKurw/r16/Hggw/2dNM6hIIsQgagvLw85Obmcql5RWVFyG3IRaGoEFWyKgh9hVDr1Lx9dA061F+oh+q8CnXn61CXWwfWyLDl8hauV9vYbW5jYwN3T3fYe9oD1grhCQDvYd7Yd3UfvBXerZYZj4yM5CpXEUL6N01BAVdmve7kKUCr5dbZeHhANm0q5NOnw370aAjbmJ6gP6mvr+cm6zUtPnHx4kVUVFRwn6E5OTk4deoUAMNn8bBhw3hBlCmq1Nw7Xbp0iVekorKyEoWFhdyFxXHjxiE5ORmTJk3CxIkTMWnSJAwePLhPp8WqVCps3rwZ27Ztw+7du9HY2Mit8/f375Pnds1jsgYKGpNFeivjW9f4wXPy5Emkp6ebVcoz/p2WlgZ7e3sAwL0r78X/Tv0PDsMcYD/MHtIAKQQi/geYi8QFsR6xKDhZgP3f74djgyMUbuZFH+6//36uApGxZK+TkxMEAgGKVEUobyiHNa52rvByoDnv+joak0WuB2MM6qwsLrBSZ2Ty1kuCgwxpgNOnwS4iAoJ+PtlpZWUlMjMzMWrUKK6H6vHHH8e6devMJus1Sk9PR1hYGADg6NGjKCoqQmhoKAIDA+k92Uf8/vvv2Lx5MxITE3H58mWz9Tk5OVyBpcbGxjbnP+wLTM+jvLwcnp6e0DZdVBk2bBgWLlyIBQsWID4+vlcFWV0+JosQ0rm0Wi3Kysrg4eHBfZjs2LEDJ06cMCsvbvxdXl7OFWdYv349NmzYYPHYYncxNp3ZhEu6S0gqSULeuDwEjAvgbSPVSOHDfBAkDcK9U+5FpE+kYZqGKXoIn2/flxrTyXABwMvBi4IoQogZptGg7vRpw/xVe/dCU1DQvFIohDQuFvKmwMo2IMD6gfow48UvY4+UsXeqqKgIAJCdnY2goCAAhkl6GWNwdXU1KzwRGhoKf39/7rhjx47tkfMh7aPT6ZCWloaDBw9i+fLlkMvlAIBDhw7hhx9+AACIRCLEx8fzyqmbzn3YlwOsvLw8bN++Hdu3b4dAIODGBLq6umLlypXw9PTEggULEBYW1qsCq2txTUFWQ0MD0tLSUFJSYjZgfd68eZ3SMEL6MsYYVCoVlEollEol7yrMDz/8gAMHDlgMmABDCV1j7vXWrVvx9ddfW72f0tJSLsiKi4tDYWEh3BXukPpKofXUokpehSKbIlSzaqzN4lfcC3IOQpxHHOI84xDvGW81GGrPxLeEENIWXa0KqkOHULNvL2oPJEJvUlJaYGcHh/HjIZ82DbKpU2DTTybT1uv1uHjxIhdILVmyhJuI/KOPPsIbb7xhcT8fHx+UlpZyQdZDDz2ElStXQqFQ9PkvngNNY2MjTp8+zaX+HTp0CNXV1QCA4cOHY9asWQCA+fPnQyKRYNKkSRgzZgxvDFZfl5GRwQVWycnJ3HKhUIjS0lKuoMXHH3/cU03sEh0Osnbs2IElS5ZAqVSarRMIBNDpdJ3SMEJ6E51Oh4qKCi4gUiqVmD9/PvfP7v3338eOHTt4gZNpxbvq6mrualVCQoLVwEkgEKCsrIz7cJ0yZQqEQqHVEuM+Pj7Q6DXIKMuAwxQHBIUGIbk0GVVqk/kwGGAjsEGYWxjiPOMQ5xGHWI9YONs5d82DRQghTTQlJYaJgffuQd3RY2BNFdAAQOTiAtnUqZBPnwaHceMgbCrG0JedOXMGv/76KxdUZWVl8f4XREZGcl+qw8PDERQUxPVGGSftDQkJMUtBcnd379bzIJ3j119/xV133YX6+nrecrlcjgkTJvBKqI8dO7Zf9kI+8sgj+PTTT7nbQqEQU6ZMwYIFCzB//vw+VzGwIzocZD366KO4/fbb8corr9CEwKTPamho4MYrmQZOjz32GBc4vfTSS9i+fTtKS0tRXl5u1mtrmoubkZGBXbt2md2PRCKBQqHgBVnz58/H4MGDLQZOrq6uvCpR99xzD+655x7eMes0dUgtTcUfJX8gKSsJaaVpaNA18LaR2kgR5R7F9VJFukfCXmx//Q8cIYS0gjGGxtxc1OzZi5p9e9GQmsZbLw7wh3z6DMinT4M0JgaCPja/Um1tLbKysnhl0VevXo1Ro0YBAJKSkvDKK6/w9rG1tcXw4cMRGhoKJycnbvnixYuxePHibm0/6XyVlZW8cur3338/7rvvPgBAUFAQ6uvr4e7uzitSER0d3e/mFtPpdDh69Ci2b9+OVatWcePHxowZgy+//BI33HADFi5ciHnz5g2YiwYdDrKKi4vx1FNPUYBFeg29Xo/KykqzMUulpaUoKyvDmjVruMDpwQcfxA8//GBW1tZo+fLlXOBUUlKCzEz+AGxnZ2eu6EN9fT237ZIlSzBhwgRewKRQKODg4GCW2jF37lzMnTu33edX0VDBTfqbVJyEzPJM6Bi/x9hJ4oRYj1jEe8QjzjMOoW6hEAtpsDMhpOsxnQ71KSnc+KrGS5d46+2io5rHVwUG9ol0N9P5oY4dO4bXXnsNmZmZFgsS3HDDDVyQNWLECCxdupTXOzVkyJB+94V6IKuvr8eff/7JBVVpaWm8giRDhw7lgqywsDBkZGQgJCSkT7zuO0qj0SAhIQHbt2/HL7/8guLiYgCAl5cXnnvuOQDAbbfdhnnz5vEuMAwUHQ6ybrvtNiQkJCAwMLAr2kMIAMNYo4KCArMKecZepZ9++on7wFq8eDG2bt1q9Vgvv/wy9+Y2jpUCALFYbNaTpDFJZXn00Udxxx13cAGTm5ub1SpNEydOxMSJEzvl3AtqC3C6+DQXWOVW5Zpt4+XghTgPQy9VnEcchjoPhVBAY6cIId1D39AA1ZEjqNm7F7X7E6Arb64iKhCLYT92jGH+qqlTIfb06MGWWscYQ35+Pq8curEAxX/+8x888MADAAxFiXbu3Mnt5+HhwSs6YTovUXh4OL799tvuPhXShS5duoTy8nLExsYCMIyxWrRoES+wGjZsGNdLNXnyZG65UCg0K5vfHxQVFeGFF17Ab7/9hoqKCm65k5MT5s2bh9GjR3PLpFIpNy/bQNPhIOvjjz/G7bffjoMHDyIyMtLsS+djjz3WaY0j/UtGRgZycnKsBk6HDx/m9Ti1Nrv8Z599xlWyM5YPl8vlFlPwTD8IX3rpJTz33HNwd3eHo6Njq1eWumNeJsYYcqtycbr4NBdYFamKzLYb6jSUG08V7xmPQbJBXd42Qggxpa2oMIyv2rcXqsNHwEzGmQgdHSGbPNkwvmrCRIhkDj3YUj6tVovc3FxIpVJuTr+TJ09i+vTpqKmpsbiPaRZDVFQUvvzySy6ocu0nRTmIOcYYzp07x/VSHTx4EJcvX8a4ceNw+PBhAIZAYvHixbwUQC+v/l1Ft6amBpcvX0Z4eDgAw5yYmzdvRn19PTw8PDB//nwsWLAAU6dO7dOVDztbh4Osn376Cbt27YKdnR0SEhJ4X1IFAgEFWf2cVquFjU3zyyYhIQEZGRkWS4xXVFTg4sWLXMrFq6++2mqPU2VlJTfTvLe3Nzw9Pc3mZDL+Nm3DmjVr8OGHH0IikbTZfuM/2J6i0WuQVZaFpJIknC4+jeSSZFSqK3nbiAQihLqGGoKqpsDKxc6lZxpMCBnQGi9f5tIA65KSAJOxqTaDvLk0QPsRIyDo4fmYNBqNWY9UZmYmzp8/j8bGRjz//PN46623ABj+F9TU1MDGxoZXfML4ExISwh3X0dER999/f0+dFukmK1euxC+//ILS0lLechsbG9jY2PBSSH/66aeeaGK3Ki8vx++//45t27Zh165dCAoKwtmzZwEA9vb2+PjjjxEUFITx48dTOqwVHQ6y/vnPf+L111/HCy+8QKWd+zhj6lx5eTlvjo0tW7bg9OnTFgOn2tpaqNVq7rn/5JNP2gycjFf9QkNDMWLECKuBk2l38scff9zuUp7GghK9Ub22HmmlaUgqTsLpktNIK01DvZZfZchOZIcoRRQXUEUroqlIBSGkRzC9Hg3p6YY0wL17oc6+wFsvCQ2FfNo0yGdMh6SHxplUVVVxgZSPjw9mzpwJACgsLER0dLTFfaRSKa/Cm6enJzIyMhAYGEhX3geQxsZGnDp1ComJiTh79iy+//577jVszLCxs7PD2LFjufS/MWPGcFOl9HdFRUX45ZdfsH37duzfv59XMbyxsRGVlZVcFtGKFSt6qJV9h4BZmz7cCldXV5w8eXLAjMlq76zOvYFOp0N5eTnXizR+/Hhu3SeffIIjR46YFYYwBkwajYYLnBYtWoQtW7ZYvZ+ysjIucHr//fdx6NAhqyXGLaWU9mdV6ipDgYqm8VQZZRnQMi1vG0dbR25+qjjPOIS5hkEsGjiPEel/NBoN/vrrL8yZM2dAvd/7C31jI+qOn0DN3j2o3bcf2pKS5pUiEexHjoR8+nTIp02F2MenW9umVqvx9ddf83qoCkwmLl64cCF3oY8xhoCAAPj5+Zn1TAUEBNCF4QFIpVLh2LFjXPrfsWPHeCX1c3JyuCp4J0+ehEajQXx8fLsyY/qjpUuX4r///S93OyoqCgsXLsSCBQsQHh7eL4t3XIv2xgYd7slaunQpNm3ahBdffPG6Gkg6zvQKAgC89tpr2Lt3L29ckzFmFgqFaGxs5LpwExMTsXnzZovHtbW15fU4zZkzB4MGDbIYOCkUCl4bnnzySTz55JNdc8J9QJGqyDCWqimwulB5wWwbT3tPQyn1psp/gc6BVKSCENKjdNXVqE08iJq9e6BKPAi9ScVVob09HCZOhHzGdMgmTYKoC6uC6fV6XL58mZfe5+/vz5VBt7GxwVNPPQW1Ws3bz9vbG6GhoYiPj+eWCQQCi9X/yMBRUVEBBwcHrnfy5Zdfxvvvv8/bRqFQcL1UppkwI0eO7Na29qSsrCxs27YN27dvx5dffom4uDgAhosW586dw4IFC7BgwQJuMmxybTocZOl0OrzzzjvYuXMnoqKizK5arl27ttMaR/hKS0shl8u5wCkrKwuHDh0y287FxQUKhQK1tbVcVb277roLo0aNMkvTM5YZN7Vs2bIuP5e+iDGGvKo8nC45zZVTL1AVmG03xGlIc+U/zzgMchhEV38IIT1OU1hoGF+1by9UJ04C2uZedpHCvXl81ejREHbylXzGGPc5yBjD8uXLkZaWhnPnzqGuro63bUxMDBdkiUQi3H///bC3t+eNlzK92EcGrqKiIhw8eJDrqTpz5gz27NmDadOmAQAmTZqErVu3YtKkSdzP8OHDB9z/ZMYYUlJSsH37dmzbto1X2GX79u1ckDVv3jzMmzevp5rZ73Q4yDpz5gxXxtI4AM5ooL1ou5uHhwfq6uq4Ky+PPPIIFi5cyAuc3NzceEUhjG655Zbubm6fp9VrkVWexfVUJZcko0JdwdtGJBAhxDWE66mK9YyFqx1VniKE9DzGGNTnzjWNr9qHhowM3nrboEAusLKLjISgE9LpVCoVzp07Z1Z8wt3dHQcPHgRg+K5w/PhxZGVlATBMpzFs2DAuiGo5rqq943PJwJCZmYn33nsPiYmJyM7ONluflpbGBVnz5s3D/Pnzu7mFvUtOTg5uuOEG5OXlccvEYjFmzJiBBQsW0PfDLtThIGv//v1d0Q7SDi0ncuuseZmIQb22HmdKz3A9VamlqWZFKiQiiaFIRdOYqmhFNBzEA2NALCGk92NaLepOnUbNPkNgpcnPb14pEEAaF2coXDF9GmwHD77m+ykvL0d+fj5vqospU6bgwIEDFreXy+W83qx//etfEIlECAsLw9ChQy1eHCQDG2MMWVlZSExMREhICDf/VENDA77++msAhoA9KiqK66WaOHEiPD09uWMMtHF4Wq0WBw4cQGVlJRYuXAgA8Pf3R1VVFaRSKWbPno2FCxfipptuGpCTA3c3+lQjA1aVugrJJclc5b+Msgxo9fwiFXJbeXORCo84hLuFU5EKQkivolepUHvoMGr37UVNwgHoq6q4dQKJBA7jx0M+fRpkU6bApmlewfYqLCxEeno6r/BEZmYmiouL4erqCqVSyQVOMpkMAODu7s71SoWFhXF/mzJ+ASTESKvVIjU1lUv/O3jwIJRKJQDDMAZjkBUVFYXVq1dj/PjxGD9+/IBPHW1oaMCePXuwfft2/O9//+MqRi9YsAACgQBisRi7du1CaGgo7O2pcnF36nCQNXXq1FbTAvft23ddDSKkqxSpirgCFaeLT1ssUuFh78EVqIjzjEOQcxAVqSCE9Dra0lLU7N+Pmr17UXf0GFhjI7dO5OwM2dSphomBx42DsI0vVjqdDhcvXkRmZiby8vLw6KOPcuuWLl2K3bt3W9zPwcEBNTU1XHWtdevWYcOGDVAoFJ1whqS/M+3ZVKlU8PHxQZXJBQLAUHp/zJgxGDFiBLdMJBLhP//5T7e2tTf6+++/8d133+HPP/9EbW0tt9zd3R033HADVCoVd+HDtEAM6T4dDrJiYmJ4tzUaDVJSUnD27FksXbq0s9pFyHVhjCGvOo8rUJFUkoT82nyz7QY7DuYKVMR5xMFH5kNjCwkhvZI6Nxc1ewzzV9WnpQEmM7CI/f25+auksbEQtDI56IEDB5Dw/+zdd1yV5f/H8ddhT3EgKoobUZwIboYiiHscMr+l5aiszOybZTvNxre+ZWVm2jK1X0O/xdFcqYCD4V7kQFTEkQNFZe9z7t8fxB1H0ESFw/g8Hw8ede7rvu9zHRQ8n3Nd1/vatk0dlUpISDBK73vkkUfU0YHOnTtz9uxZozh0T09P2rdvr76BK9aqVav7+4JFjZKZmcnOnTvVUSpbW1t+//13oKhgd3NzQ1EUfH191el/3t7eso/ZX27cuEGdOnXU8LMNGzawcuVKAJo2bcqYMWMIDQ3F19dXpt9WEeX+U7g5CrPYW2+9ZVRJC1GZCg2FJFxPKAqpuFIUUnE997rROWYaMzzqeeDdyBvvRt54uXjRwLZ8U2eEEKKyKHo9OXF/FO1fFbmF/DNnjNptOncu2r9qYCBWbduqHxBlZGSUmt73448/qkXRypUrWbx4sfG9bGzw8PCgQ4cOZGVlqUXWvHnz+Pjjjyv8tYqaafPmzYSHhxMVFcX+/fuNNre1sbEhLy9P3ZNq06ZNNGrUSC0iRFF64m+//UZYWBhbt24lIiJCnTY5YcIEbG1tCQ0NpUePHrVu/Vl1cN9K3QkTJtCzZ0/mzZt3v24pxC3lFuZyOOWwmvwXdzWO7ELjGGArMys6N+ysxql3bdgVByuHW9xRCCFMz5CbS9aOnUXBFVu3ob927e9GS0vse/cumgbYvz+WjRqphdWKFSv47rvviI+P588//yx134SEBHXK0MCBA8nNzTVaM9WiRYsy39zKyL64U5cuXWL37t1GaX4LFixg/fr16uPmzZsbxamXHKVydXWtzO5WWefOnUOn06HT6YiJiVH3PwWIiYlRi6xevXrRq1cvU3VT3IH7VmTt3LkTGxub+3U7IYyk5aVx6MohNfnv6LWjpUMqLB3p5tKtKE69kTcdG3TEylymGQghqrbCGzfI3LadzC2RZMbEouT8nWpq5uiIxseH5BbNOajRcCQxkfgvviB++nS2bt2qpvtduHDBaO1U48aNjab4lXwDGxoaKsET4p4oikJSUpLRHlWnThWtcz579izNmzcHiv6uubq6qsl/LVq0MGW3q7zDhw/TpUsXo2M9e/ZEq9UyZswY2rVrZ6KeibtR7iJLq9UaPVYUhUuXLrFv3z7efPPN+9YxUbslZyWrARUHrhzg1I1TKChG5zS0baiupfJu5E3bum0xN5NpBkKIqi///Hl1/6rs/fvBYFDbLJo0wTEwkNiCfB775BPS9u0t8x7x8fFqkTVkyBDq1q2rrpeqV69epbwOUfssW7aMN954gwsXjNc5azQaunbtypUrV9Qia/LkyUyePNkU3azSFEUhLi4OnU6HhYWFuvl2p06daNmyJS1atFALKzc3NxP3VtytchdZN+fqm5mZ4eHhwdtvv82gQYPuW8dE7aEoCmfSz6gBFQeSD/BnZunpLi3qtFDj1L1dvGnm2EymsgghqgVFUcg9cpTUzZu4vnETZufPG7Ufz8tjS0YGQ+e+xeBp09BoNFj89htpWVlYWFjg7u5uFIfeoUMH2rdvr17v6emJp6dnZb8sUUMVFhZy6NAhdaTqlVdeUaem2dracuHCBSwsLOjRo4c69a9v3761Pk79dgwGA7t371anAp4+fRqABg0a8Nprr2FhYYFGoyE+Pl5mhtUQ5S6yli5dWhH9ELVIoaGQhBsJRsl/twqpKB6p6t6oO862zibqsRBClE9qairxhw9zcfNmOmRkYnnwIIXJyQCYAYWKwr7sbLZkZrIlM5OLhQXY2dnR1dpa/fBowIABxMfH06ZNGywtZX8+UXHy8vLYu3evOvUvNjbWKMysR48eapE1aNAgtmzZQq9evWTfpTv0wQcf8Pnnn3Px4kX1mI2NDYMHD0ar1WIoMZItBVbNcU9rsjIzM43+YgDqfhlCFMvT53H46mF16l/c1TiyCrKMzrEys6KTcyc1Tr1bw24SUiGEqBYuXbpEWFhY0T5TR49S9/RpvAv1+Nnb4/lXmEQhoLGzw9ClM+9s3sy1li1p4e9Hd09Pxv81MuXm5maUEFanTh35N1VUiMzMTDIzM2ncuDEAcXFx+Pn5GZ3j5OSkxqkPGzZMPV6vXj0GDBhQqf2tTvLy8oiMjCQwMFAtmDIyMrh48SKOjo4MHz4crVbLkCFDsLe3N3FvRUUqd5GVlJTE9OnT2bZtG7m5uerx4k3lSsZzitopPT+dQ1cOqaNUR1KOUGAoMDrHwdKBbi7diooql+50dO6Itbm1iXoshBClXf18IZib0eCpp9TNeou/HrWxwbN9Bxo+O53LR46w4803CXRw5Ek7Oyzt/n7jlG5mRn63bng9ORW73r3RWFnxE5LaJyrX9evXiYmJUUeqDhw4wJQpU/j6668B8PLyonXr1nTv3l0NqejcubPEqd+hrKwsNm7ciE6nY926daSnp7N27VqGDx8OwJQpU+jbty9BQUFqZL2o+cpdZE2YMAFFUfjuu+9oVCI+VtReV7Ovqql/B5IPcOLGiVIhFc62zn+vp2rkjXtddwmpEEJUWRcvXuQ3nY7+ly7x9ttvs/CvqX4ATzVogItzQ7KzskgKfQCbo0d5s1FjtV3fpAlOg4JxHjIEmy5d0Mj+NcIE9Ho9M2bMICoqiiNHjpRqL14TBGBpaUliYmJldq/ay8jI4LfffkOn07Fx40ZySqSCurq6kpaWpj5u06YNbdq0MUU3hQmVu8iKi4tj//79eHh4VER/RBWnKArnMs5xIPnv5L/zGedLndfcsblR8p+bo5sU5EKIKiEzM5Pjx4+X2rB32LBh6sa79vb2TNu2lacaNGCGc0M0Clxp6MwUK2vcsov25MvetbvohhoNtl5eOA4MxCEwEOtWrUz10kQtpCgKp0+fJjo6mmvXrvHCCy8AYG5uTmRkJAkJCQC0b99eDanw8/NTEwDFnTMYDOqU3osXL/LII4+oba1bt0ar1RIaGkrPnj1lc2BR/iKrR48enD9/XoqsWkJv0HPixom/49STD3At95rRORo0eNT3UEequrt0p6FdQxP1WAghiqSkpJCZmUnLli2Bok+eO3XqxLlz58o8v2RUspOTE59//DGeefkQHc3Tp09DoR7+2vRcY22Nfd++RYVV//5YOEswj6gcBoOB+Ph4depfVFSUGqhgb2/Pc889h4VF0du7uXPnYmlpia+vLy4uLqbsdrV1/vx5Vq1aRVhYGE2aNGHFihUAeHh4MGbMGDp16kRoaChdunSRD5OFkXIXWd9++y1PPfUUFy5coFOnTqUSj27eRE1UL3n6PI6kHCkaqbqyn7grcWQWZBqdY2lmSWfnzmpB1c2lG45WjibqsRCiNlMUhQsXLnDs2DF1RKr4/1NSUhg6dCjr168HwNHRkaysotAdFxcXozh0T09POnbsiD4tjczt28kIjyAoJsZoY2AAzMxo+tl8HPr1w0yS1UQl0Ov1Rmujxo4di06nMzrH0tJSjVPPzs5WA1PGjRtXqX2tKU6ePIlOpyMsLIy9e//ep87e3p68vDx1XdXNfw5ClFTuIuvq1askJiYabS6n0Wgk+KKaysjPKAqp+Gt/qsMph0uFVNhb2heFVLgUJf91cu4kIRVCiEpVWFjI6dOniY+Pp7CwkNDQULWtY8eOpKenl3ldRkaG0eMtW7bQtGlTGjRooB4rSL5CRmQEmT/9xIk9e6GwUG2zcG2CRUMXcuPi0FhaohQUkHfyJHWCg+/zKxSiSG5urlGc+o4dOzh58qSaBNi9e3c2btxInz591Ol/PXv2lDj1+2TChAn8+OOP6mONRkO/fv0IDQ1lzJgxElwh7li5i6wpU6bg5eXFzz//LMEX1VBKToo67e/AlaKQCoNiHMPfwKaBGlDR3aU77eq1k5AKIUSlWrVqFYcOHVJHp06cOEF+fj5QNE2nuMjSaDR06dKFlJQUo1GpDh064OHhUSoiuXi2RV5SEhkREWRERJAb94fROdbubXEICsIxKIjMbdtJ+fxznGc8S8Np07i6aBEpCz4HoOG0aRX9bRC1xJEjR1ixYgVRUVHs3r1b/bteLCYmhgceeACA5557jpdeekn2TrtHBoOBvXv3otPpeO2113BycgKgc+fOWFhYEBgYiFarZdSoUWqBK0R5lLvIOnv2LGvWrKFt27YV0R9xHymKwvmM82pAxYHkA5zLKL0Wwc3RTQ2o6N6oO80dm0vxLISoUGlpaRw/flyd2pednc3ChQvV9nfeeYeDBw8aXWNra0v79u3p0qWLOnsCICoq6h9/ZymKQu6Ro2phlX9Tkpptt244Bg3EMSgIq7/WcF1dtMiowIK/CysptMTdunbtGjExMXTp0oVWf4WkHDp0iPfee089p3HjxkYhFZ06dVLbHBxkD8m7pdfriY6ORqfTsWrVKv7880+g6MOX8ePHAzB16lSeeOIJ6tevb8quihqg3EVWYGAgcXFxUmSZwM6LO/lgzwe80vMV+rj2KdWuN+g5mXpSHak6eOUgV3OuGp2jQYN7PXejosrFThbDCiEq3n//+1/Cw8OJj49XF+oXs7KyYv78+eqC/TFjxtC9e3ej0anmzZuXmdh1qwJLKSwke98+MiIiyYiMpPDSpb8bLSyw79ULx+AgHAIDsSwrFEBvMCqwiqmP9YbS1whxkwsXLhAdHa1O/zt69CgAH374IbNmzQIgICCARx99VC2s2rZtKx923kdnzpzhvffe47fffuPq1b/fFzk4ODB8+HA1HAeKNlsW4n4od5E1YsQInn/+eQ4fPkznzp1LDVePHDnyvnVO/E1RFD478Bmn007z2YHP6N2kNwWGgqKQir+S/+KuxJFRYLz+wMLMgk4NOqnT/7q5dKOOVR0TvQohRE1kMBhITk7m999/5+TJk+oUv3PnznH27Fm1MNq3bx+RkZHqda6urkbhE4WFhWqR9eabb95dX3JzyYqNJSM8gsytW9GX2KtGY2eHg58fjkFBOAT4Y17n9r8LGz47/dZtMoIl/sGpU6cYPHhwmftPeXp6Go1Iubm5sXz58srsXo2WnZ3NlStX1OLJwsKCb7/9FoD69eszatQotFotQUFB2NjYmLCnoibTKIqi/PNpf7td7n9NDL5IT0/HycmJtLQ0Na3HFGIvxPJUxFPq47ZObTmXcY58g/G8bTsLO7q5dFPj1Ds7d8bGQn6BCCHuXUFBAadOnaJ9+/bqp+wzZ87kyy+/NNqIs6QzZ87QokULADZv3syFCxfUoqp4DcS90qelkbltGxkREWTGxBolAprXrYtDYCCOQUHY9+2DmbyhEveRwWDg2LFj6iiVh4cHc+fOBSAvLw8nJycKCgrw8vLCz88Pf39/fH19adhQtjm539LS0li3bh06nY7ff/8dPz8/Nm3apLZ/8MEH+Pj4EBAQIOvZxD2509qg3CNZBoNMj6hsiqLw/p73jY6dSjsFQH2b+n/vT9WoOx71PLAwK/cfqxBCqLKyskhISDCKRY+Pj+fUqVMUFhZy8eJFmjRpAoC1tTU5OTlYWFjQrl07NXSi+L+urq7qfQcNGnTf+liQnExGZCSZERFklZEI6PhXcIVd9+5oLOR3org/FEVh3759alEVExPD9evX1fZOnTqpRZa1tTXbtm3D09PTpB/S1mRXr17lt99+Q6fTERERQUHB3+nISUlJFBQUqAXVK6+8YqpuilpK/uWpBnZc3MHZ9LOljr/V5y207lqZty2EuCvXr19XC6ixY8eqI0uzZ8/mk08+KfMaBwcHzp8/rxZZ06ZNY8KECSQkJDBixIgK/YQ473SJRMA/bk4EdMfhr+AKG09P+b0o7ovc3FxOnTqlBk9oNBoefPBBzpw5o55jb29P37598fPzIyAgwOj63r17V2Z3a52HH36YiIgI9XGHDh3QarWEhobSrVs3+T0gTOqOiqwFCxYwdepUbGxsWLBgwW3PnTFjxn3pmCiiKAqfH/wcM42ZUdS6mcaMX078gtZda8LeCSGqi+PHjxMeHm40OnXlyhW1vX379vj6+gJFb1ScnZ2NRqSKv5o1a2b0xsXNzU2dRni/FSUCHikKrrhVImBwEI4DB6qJgELci4yMDHbs2EFUVBTR0dHs3r0bW1tbrl27pm4IPHLkSJKSktSQCi8vL5l+VsESExPVRMCwsDD1Q54xY8Zw/fp1tFotWq2WDh06mLinQvztjtZktWrVin379tGgQQM1brTMm2k0nD59+r520NRMvSbr5rVYN/sy6Ev6Ne1XiT0SQlRFer2epKQko+l9L774Ih07dgRg0aJFPPPMM6Wuc3Nzw9PTkzlz5tCnT1FqqcFguO3625sVFBSwYcMGhg4des9vNtVEwPCIokTAy5f/brS0LEoEDArCIXBA2YmAQtyFr776im+//ZYDBw6UWhbRuHFjdu3apa4tFBVPURSOHj2KTqcjLCyMP0qMXC9atIinn35aPU9Gq0Rlu69rspKSksr8f1GxikexNGhQKF0La9Dw+cHP6evaV37JCFEL7d69m08//ZT4+HgSEhLIy8szag8ICFCLLB8fH0aNGmU0OtW+ffsy99wpT4F1Pxhycv5OBNy27Z4SAYW4nT///FONU3/33Xdp0KABAJcuXWLfvn1A0QfLxaNU/v7+tGnTRv6NrUQHDx5k3LhxnDx5Uj1mbm7OgAEDCA0NZcyYMepx+XMRVVm512Tl5ubeMu7y0qVL6hCuuHcFhgIuZ10us8ACUFC4nHWZAkMBVuZWldw7IURFysjIMBqVKp7m9+677zJu3DigKE1r5cqV6jU2NjZ4eHioRVT37t3Vtp49e7J69erKfhm3pE9NJXP79qJEwOgYlNxctc28Xj0cAgf8lQjYFzNraxP2VFRXiqJw6tQpoz2qSn5QPHjwYEaNGgXAuHHj8PDwwM/Pj2bNmpmqy7WOXq8nNjaWwsJCAgMDAWjRogVJSUlYW1szaNAgtFotI0eOlM2BRbVT7iKre/fu/PTTT3Tr1s3oeFhYGE899ZTRJm/i3liZW7Fi+Aqu516/5Tn1bepLgSVENaUoClevXsXMzAxnZ2cAdu3axdixY/nzzz/LvObIkSNqkeXl5cVHH32krpdq0aKFum6kKipITlaDK7L37IUSW35YurqqwRWSCCjuhsFgoKCgAOu/ivIff/yRRx55xOgcMzMzvLy88Pf3N1r+UPwzJCpefn4+W7duRafTsXr1aq5cuUKfPn3YsWMHULSP1aZNm+jRoweOjo4m7q0Qd6/c/4r179+f3r17M3fuXF5++WWysrJ45pln+N///sd7771XEX2s1RrbN6axfWNTd0MIcQ8UReH8+fNGI1LF/3/9+nXmzp3L7NmzAWjYsKFaYDVu3NgodMLT05MuXbqo923YsCEvvviiSV7Tnco7fVpdX1VWIqBjcFHUunWHDjL1R5RLQUEBBw8eNIpTnzNnDs899xwAffr0wcrKip49e6pT//r06SNx6iayYcMGVqxYwdq1a0lNTVWP16tXDw8PD/R6vfohUfGolhDVWbmLrEWLFjFs2DAef/xx1q1bx6VLl3BwcGDPnj1qxKkQQtRGBQUFJCYmEh8fT+PGjdUgiePHj+Pp6VnmNRqNxmgGQMuWLdmxYwft27enXr16ldLv+0lNBAwvGrHKLxmGpNEUJQIGBeEYNBArCRIQ5ZSamsrnn39OVFQUO3bsIDs726h9586dapHVunVrUlNTsbW1NUVXa73MzEyjNZ/ffPONOmW5UaNGjBkzBq1WS//+/SWdUdRId5QueDODwcCzzz7L4sWLsbCwYO3atYSEhFRE/0zO1OmCQoiqKTc3F51OZzQqderUKXUzzEcffZTly5cDRcVX3bp1admypdHIVIcOHfDw8MDOzs6UL+We5Wdns23xYjplZJK1dSuFycl/N1paYt+7N44DB+I4MBCLhg1N11FRraSlpbFjxw4MBgPDhg0DIDs7m7p166o/Z/Xr18fX11cdqerWrZu8YTehlJQU1qxZg06nIzw8nCNHjuDu7g7A2rVr2bp1K1qtlj59+lTpqc1C3M59TRcsKTExkYcffpjLly+zadMmtm/fzsiRI3nuued477335JebEKLGuHHjhlH4RIsWLXj22WfV9gkTJnDz51R2dna0b9/eaL2HpaUl6enpNepNRclEwIytW3FLT6c4E9DMzg57f/+/EwFlXYW4A1evXiU6OloNqjh06BAGgwFvb2+1yLKzs+Pll1+mSZMm+Pv74+npWelpmMLYhQsXWL16NTqdju3bt6MvsdYyIiJCLbJGjBjBiBEjTNVNISpduUeyHB0dGTZsGF9++SV169YFYMeOHTz66KM4Ojpy8ODBiuinychIlhC1h8FgYMaMGeq6qcsl92gC+vXrR0xMjPp43LhxODk5GY1Mubm51dg3ffrUVDK2bSMjIoKsmFijRMBCe3vqhwyizqBB2PfpI4mAolyCg4OJiIgodbx169YMGDCAb775RtbsVUFbt24ttX6qW7duaLVaQkND6SBrLUUNVGEjWYsWLSqV1tO3b18OHjzIv//973J3VAghKoNer+fMmTNGI1PFa6dWrVoFFCWPrVmzhvPnz6vXNW3aVC2gfHx8jO5ZMj69piq4fJmMiEgyIstOBHQMDsK2f3+2Xr5M++HDZTaDKJOiKJw8eZKoqCiio6M5evQoe/fuVd+AN/xrGmnHjh3VqX9+fn40bdrUlN0Wf1EUhWPHjqHT6WjUqBFTp04FoFevXjg4ONC5c2e0Wi1arZbWrVubuLdCVA13tSarNpGRLCGql/z8fC5fvkzz5s3VY4MGDSI6OprcEiMvxRo3bsylS5fUx0uWLMHCwkLdrLc2/tznJSYWFVYREeQePmzUZt2uXVFwRXAQ1u3bo9FoKCgoYMOGDQwdOlSKLKE6ceIEmzdvVtP/kkuu1QOOHj2qBsKcOXMGR0dHdXNgYXqKorB//350Oh06nY6EhASgqBA+cuSIel5aWhpOTk6m6qYQla7CRrKKHTt2jHPnzpGfn68e02g0Mt9WCFEpMjMzOX78eKlY9MTERFxdXTl37px6bkFBAbm5uVhbW+Ph4VEqfKKkxx57rLJfiskpBoNxImCJDVvRaLD18vo7EbBE8SpEsYKCAvbv30+nTp3URLlly5bx/vvvq+dYWVnRq1cvdZSqZcuWalvJ/xem99Zbb7F06VKj36NWVlbq5sAGg0GdFi0FlhBlK3eRdfr0acaMGcPhw4fRaDTqou/iIf+SCx6FEOJepaSkEB8fz/nz53n44YfV4yEhIermlTdLT08nNzcXGxsbABYsWICtrS2tWrWqUeET90IpKCB7796izYEjt5SdCBgUhGPgAEkEFKVkZ2eze/duNaRi586dZGdns379eoYOHQrAwIED2b9/vzr9r0ePHurPpKg6CgoKiImJoX///up7uaSkJM6dO4e9vT1Dhw5Fq9UydOjQWjmyL8TdKneR9dxzz9GqVSsiIyNp1aoVe/bs4dq1a7zwwgvMmzevIvoohKgldu/eza5du4zWTBXvIWVmZsaYMWPUPW86dOjAqVOnjDbqLf5/V1dXo8XWnTt3NsnrqWoM2dlkxsaSGRFBxrbtGNLS1DYzOzvsA4oTAQMwL7G/jRDF9uzZw/PPP8/evXvVGPVi9evXN9rzbeDAgQwcOLCyuyjuQE5ODuHh4YSFhbFmzRpSU1M5cOAAXl5eAMyYMQOtVsugQYNknzEh7lK5i6ydO3eyZcsWnJ2dMTMzw8zMDF9fX95//31mzJhR49IFhRD3T2FhIadPnzYqor799lt1Hc+iRYv4/vvvS13XokULOnToQFpamvoP/uLFi/n2228rtf/VkT41lYytfyUCxhonAprXr49D4AAcg4IkEVAYKY5Tj4qKwtfXlwceeAAoShguHkF2dXU1CqmQOPWqLTMzk/Xr1xMWFsaGDRvIyspS21xcXDh79qxaZHl7e+Pt7W2qrgpRI5S7yNLr9Tj+teeJs7MzFy9exMPDgxYtWqiLIoUQolhYWBgrV64kPj6eEydOGK3jBHjllVfUdVEBAQFkZmaW2qzX3t6+1H0lYOHWCi5d+isRMJLsvTclAjZtqgZX2Hp5oZHpkwI4f/68GlARFRXF8ePH1bbLly+rRVb79u1Zvnw5/fr1o3Xr1hLPXcUpiqL+Ge3Zs4d//etfapubm5uaCNivXz+ZSi3EfVbuIqtTp07ExcXRqlUrevXqxYcffoiVlRVff/21xHYKUcukpaWVikQ/duwY4eHh6u+Do0eP8ssvv6jX2Nra0r59e7WIKjnHf8qUKUyZMqXSX0dNkJeYqAZX5JZI/gKw9vBQgyuKEwFF7aUoCqmpqdSrVw8oGuFo1apVqTXVnTp1wt/fnyFDhqjHNBoNjz76aKX2V5TPpUuX1M2Bu3XrxkcffQSAv78/vXv3pn///mi1Wnx8fOR3gRAVqNxF1htvvKEOMb/99tsMHz4cPz8/GjRoUCv2jBGitlEUheTkZJycnNSpekuXLuWNN97g4sWLZV5z7NgxtcgaOnQoDg4OalHVvHlzmVJ0HygGA7mHDxcFV0RESiKguCW9Xs+RI0eMRqpat27Nzp07AXBwcKBnz57o9Xr8/Pzw9/enX79+EqdejZw5c0aNWt+xY4caSpaQkMCHH36IRqPBwsJC/TMXQlS8chdZISEh6v+3bduW48ePc/36derVqyefiAhRjRkMBs6ePVtqVCo+Pp7U1FQ2bdrEoEGDALC2tlYLLFdX11KR6CXn8vv4+JTaxFfcHaNEwIhICq9cUds0lpbY9SlOBAzEwtnZhD0VVcFXX33F2rVriY2NJTU11agtOzubvLw8rP9ahxcdHS3TxaqpkSNHsnbtWqNjvXv3RqvVMmbMGHlvJoSJ3PU+WSXVr1//ftxGCFEJ8vPzOXXqFPHx8XTv3p1WrVoB8H//939MmjSpzGs0Gg3nz59XHw8aNIidO3fSoUMH2SOlghmys8mMiSEjIoLMbdsxpKerbWZ2djj0D8Bh4EBJBKzFiuPU9+zZw0svvaS+qY6IiGD9+vVA0WhVv3791JCKHj16qAUWIAVWNaAoCgcPHmTdunW8/vrr6p9ZixYtMDMzw9/fn9DQUEaPHk2zZs1M3FshxB0XWXe6TuK77767684IIe6vK1eusHnzZqPRqVOnTlFYWAgUpfk9/fTTQNGCdisrK9q1a1dqZKpdu3ZGMb7Ozs44y0hJhSm8cYPMrdvIiIwkKyYGJS9PbTOvXx/HgYE4BgVh16cPZlZWJuypMIW0tDRiY2PVqX/79u1T49S1Wi3u7u4ATJ48mb59++Lv70/Xrl2xsLgvn6uKSmQwGNi5c6c6FfDMmTNA0fqq/v37A0XhQbNnz6ah7GcnRJVyx79xly1bRosWLfDy8lLn+gohTO/69etGU/tCQkLUab0JCQk88sgjpa4pXiNVnBQKRdP6srKy5I2YiaiJgBERZO/bZ5wI2KyZur5KEgFrt48//phZs2aV+ne4adOmBAQEGIVXDB06VN0YWFQvJ06cYP78+axatYrLly+rx21tbRkyZIhR4mrTpk1N0UUhxD+443dTTz/9ND///DNJSUlMnjyZCRMmyDRBIUzgwoULvPvuu+rI1JUS63KgaNPe4iLL09MTf39/o1EpT09PmjZtWmqevkwXqlyKopCfmFi0vio8gtyjR43ardu3x3HgQByDg7D28JB1FbXIuXPnjEIqFi5cSFBQEADu7u4oioK7u7s69c/f35+WLVvK35FqLDc3l/T0dFxcXICi0crFixcDUKdOHUaMGEFoaCghISHY2dmZsqtCiDukUcoxLJWXl4dOp+O7775jx44dDBs2jMcee4xBgwbV2F/u6enpODk5kZaWZhQ1LURF0Ov1JCUllQqfGDlyJK+//joAFy9eLPXJZfPmzdUiKiQkhMGDB5ui++IfKAYDuX/8QUZkJBnhEeT/NfUHKEoE7N7970RANzeT9bO8CgoK2LBhA0OHDpX9y+5CSkoKq1atIioqiujoaM6ePWvU/uabb/L2228DReuv0tLSaNKkiSm6Ku6jzMxMNmzYgE6nY/369Tz44IMsWbIEKPoQZtasWQQFBREYGIiVTAsWosq409qgXPOCrK2teeihh3jooYc4e/Ysy5YtY9q0aRQWFnL06FEcZNG1EHckNzeXjIwMdQ799evX6d+/PydOnCCvxPqbYiXfUDVp0oQ333wTd3d3OnToQPv27eVnrwpTCgrI2rOnKLgickvpRMC+ff5OBJTI7BpPr9dz+PBhLC0t6dixI1D0wcnUqVPVc8zNzfHx8VFHqXx9fdU2Ozs7Gcmoxm7cuMGaNWvQ6XRs2rTJ6Pf9gQMH1M2DNRoN8+bNM2FPhRD36q4XX5iZmaHRaFAUpdQGhkKIIunp6Rw/ftxozVR8fDynT58mNDSU//3vfwDUrVuXxMRE8vLysLGxwcPDA09PT3V0qmvXruo9NRqN+qm2qJoM2dlkRseQEVlGIqC9PQ4B/jgGBWHv7y+JgDVcfn4++/fvV6f+xcbGkpaWxiOPPML3338PFG36O3ToULy9vdUNY+WDk5opICCAw4cPq4/btGlDaGgooaGhsjmwEDVMuYqsktMFY2JiGD58OAsXLmTw4MGyuaiotRRF4erVq8THx1NYWMjAgQOBok+sXVxcyhyZAowi0c3MzPj9999p1qwZLVq0kPVR1ZCaCBgRQVZsrHEiYIMGOAYG4hgchF3v3pIIWAsUFhYyZMgQYmNjycnJMWpzdHQ0mlZpZmamRq2LmuHs2bOsWrWKDRs28Ntvv6nprCNGjACKUiBDQ0Pp1KmTFFZC1FB3XGRNmzaNFStW4ObmxpQpU/j5558lwlnUSuHh4Rw5csRodOr69esAdO/enf379wNFU37c3d1JSUkxGpUq/mrcuLHRff39/Sv9tYh7U3Dx4t+JgPv3GycCurn9nQjYrZskAtZQqampapx6ZmYmX3zxBQAWFhZcuXKFnJwcnJ2d1al//v7+dOnSRVI8a6CEhATCwsLQ6XTqvwNQ9G/GyJEjAZg7dy7vvfeeqboohKhEdxx8YWZmRvPmzfHy8rrtpy46ne6+da4qkOCL2qegoIDExER1al9eXh5z585V2z08PDhx4oTRNRqNhpYtW+Lj46NOAYSitVc2NjaV1ndRsRRFIf/UKTW4osxEwKCgokTAdu1qzSfUtSn4Ijk5mejoaDWkIi4uTo1Tt7KyIi0tTf2Zj4mJoUGDBrRv377W/F2ojaKionj66ac5duyYeszMzAw/Pz+0Wi0PPvhgqQ/VhBDV130Pvnj00UflHwlRY82fP5/o6Gji4+M5efKkulkvFMXnvvXWW+rf/yFDhtC5c2ej0al27dqVuRhdCqzqT00E/CtqPb9k8ptGg613cSJgEFbNmpmuo6JCnD9/HrcSSY9Tp05lzZo1RucUx6n7+/sb7V9VMrBC1AwGg4Hdu3djbW1N9+7dAWjUqBHHjh3D0tKSgQMHotVqGTVqlBrHLoSoncq1GbEQ1dGNGzeMItHj4+NJTk5m37596jnh4eFs2LBBfWxvb0/79u3VIqqgoECN0J0/f35lvwRRyZT8fLL27CUjIrwoEfDqVbVNY2mJfd++OAQNlETAGkZRFI4fP240UnXu3DnOnDlDixYtAOjfvz9nzpxRiyo/Pz8ZpajhCgsLiYqKQqfTsWrVKi5evMgDDzzAL7/8AhTNbtDpdAwYMIC6deuatrNCiCpDJoWLGkFRFJKTk43e7MyaNYv/+7//Izk5ucxrUlJS1HWFkydPJigoSB2datasmYS51DJqImBEBJnbtmHIyFDbihIBA3AMDsLezx9zB3sT9lTcb9u3b2fBggVER0dztURBDUVrqw4fPqwWWf/+9795/vnnTdFNUck2bNhAWFgYv/32G9euXVOP16lTh3r16hmdO2bMmMrunhCiipMiS1Qrer2eM2fOlBqZio+PJy0tjdTUVJycnICiNMziAqtZs2algiccHR3V+z7wwAMmeT3CtApv3CBzy9aiRMAdO4wTAZ2dixIBgwZKImANkZ+fz759+4iKimLIkCHq1ggpKSnqemIbGxt69+6tjlT17t0be/u/i2qZNl9z5efnG236+9Zbb7F3714AGjRowOjRo9FqtQwcOBBra2tTdVMIUU1IkSWqpPz8fE6ePEl8fDzDhg1T429nzJjBokWLyrzGzMyM06dP4+XlBcAzzzzDhAkTaN++vYSWCJVRIuC+fWAwqG1qImBwELZdu0oiYDWXlZXFrl271D2qdu3aRW5uLlAU1lFcZAUEBPD+++/j5+eHj4+PvIGuRW7cuMG6desICwtj69atnD17Vp3y9/jjj9OzZ09CQ0Px8/OTREghRLnIbwxhcqdPnyYmJsZoVCoxMVHd5Hr//v3qAuN27dphbW2Nh4eHOiJVPMXP3d3d6M2Rh4eHSV6PqFrURMC/gitySySAAVh36IBj0EAcg4KxbucuIxXVmMFgUKf5xsfH06VLF6MQGwBnZ2f8/f3p1KmT0bFXXnmlUvsqTOfKlSusXr0anU5HZGSk0d+R8PBwxo4dCxSFnAghxN2SIktUipSUFKMiasaMGbRq1Qooiv2fNWtWqWvq1KlDhw4djDbzffLJJ5k+fbps1ituSzEYyImLK1pfFRFpnAhoZoZd9+5FwRWSCFitXbp0iejoaDWoomfPnnzzzTdAUeKfjY0NdevWJSAgQJ3+5+HhIYV0Lfbrr78ybtw4DCVGsDt27EhoaCharZYuXbqYsHdCiJpEiixRIfbu3cu3336rFlUpKSlG7X379lWLrO7duxMQEFBqw15XV9dSb4YkEl3cyp0kAjoGB+EwYIAkAlZTiqLwww8/sH37dqKiojh58qRRe05Ojvr/FhYWJCYm0rBhQymqaqmTJ08SFhZG+/btGT16NAB9+vRBURR8fHwIDQ1lzJgxMutBCFEhpMgS5VZYWMjp06eJj4/n2LFjaiH19ttvM2TIEAD+/PNPvv76a6PrWrZsqRZQbdq0UY8HBgYSGBhYqa9B1AyGrKy/EwG3bzdOBHRw+DsR0NdPEgGrGUVRiI+P59SpU4wcORIoCp14//33iY+PVx936dJFHaW6eV8q2aeodlEUhT/++AOdTodOp+PIkSMADBo0SC2ymjZtysWLFyV2XwhR4Wp8kZWamkpQUBCFhYUUFhby3HPP8cQTT5i6W9VCTk4Oer0eBwcHAHbs2MHUqVM5efIk+fn5pc6Pi4tTiywfHx9ef/11tajy8PAwSugS4m4ZJQLGxqKU+Lto3tAZx8CBRYmAvXpJImA1UlhYSFxcnNEeVSkpKdja2pKamqqmvk2ZMoWrV6/i7+9Pv379ZF8igaIovPHGG6xcuZLExET1uIWFBYGBgTz44ING50uBJYSoDDW+yHJ0dCQqKgo7OzuysrLo1KkTWq2WBjJdSJWWlma0Xqp4dCopKYmPPvqIF154AQAHBweOHj0KgK2tbalI9J49e6r3dHNz49133zXJ6xE1T8GFC2RERpIRHkH2/v3GiYDNmxclAgYFYdutKxrZ36zamT17NvPnzyejxEgk/B2nnpKSgqurKwAvvviiKbooqpDCwkIOHTqEj48PUDSiuXv3bhITE7GxsSEkJAStVsvw4cOpX7++iXsrhKitanyRZW5ujp2dHVC0b5KiKCiKYuJeVb7izXrj4+Nxdnamc+fOABw8eFBN7itLUlKS+v8eHh5s2LCBDh060Lx5c9msV1QYRVHIO3lSDa4olQjo2UEtrKzdJRGwOsjMzDSKU//xxx9p2rQpUPShTUZGBnXq1MHX1xd/f381Tt1KRiMFRf9+b9myxWhz4AsXLtCkSRMAXn75ZZ588kmGDBmizr4QQghTMnmRFRUVxUcffcT+/fu5dOkSq1atUudOF/viiy/46KOPuHz5Ml27duXzzz83GjX5J6mpqQQEBHDy5Ek++ugjnJ2d7/OrqFpyc3PZsmWL0Xqp+Ph4UlNTAXj66afVvabc3d0BcHV1NYpDL/4quabB2tpanQ4oxP1WMhEwIyKCgrPn/m40M8PO2xvHoIE4DAzCqllT03VU3JG0tDS1oIqKimL//v3qtgwA0dHR/Otf/wLgkUceYfDgwXTp0kWSQ4UqKyuLTZs2ERYWxrp160hPT1fb6tevT3x8vFpkBQcHm6qbQghRJpMXWVlZWXTt2pUpU6ag1WpLta9cuZKZM2fy5Zdf0qtXL+bPn09ISAgJCQlqAdCtW7dSe6EAbN68GVdXV+rWrUtcXBzJyclotVoeeOABGjVqVOGvrSLl5+dz6tQptYBq2bIlEyZMAIqKrGHDhpW6RqPR0Lp1a+rVq6cec3BwID09HUdHx0rru6g9rn6+EMzNaDhtWum2RYtQ8guw8/YuKqy2RKK/+ncKpcbKyjgRUKb9VGnXr1/n6tWr6rS+DRs28PDDDxud4+bmRkBAAH5+fkYhFc2aNaOZROmLm4SFhTFx4kT1cZMmTRgzZgyhoaH4+/vL5sBCiCpNo1ShuXMajabUSFavXr3o0aMHCxcuBIo2m3Rzc+PZZ5+9q80jp02bRmBgIA888ECZ7Xl5eUb7MqWnp+Pm5kZKSgp16tQp9/PdTwkJCbzxxhscP36cxMREo8IyODiY9evXGz12dnamffv26le7du2wtbU1RddFLXX9y6+4/sUX1H/mGeo/9SQAhuxsrsyeQ+amTWisrIyCK8wcHLDz98chMBA7336YSVhKlaQoCmfOnCE6OpqYmBiio6NJTExk7ty5vPrqqwBcuHCBQYMGqQEVfn5+tGjRwsQ9F1XR1atXWbt2LatXryY4OJhnn30WgBs3buDr68vw4cMZM2YMPXv2lGnqQgiTS09Px9nZmbS0tNvWBlW6yMrPz8fOzo5ff/3VqPCaOHEiqamp/Pbbb/94z+TkZOzs7HB0dCQtLY1+/frx888/q2uSbvbWW28xd+7cUsd/+ukndW2XqVy6dImnn35afWxjY4ObmxvNmjXDw8ODwYMHm7B3QpStfkQkzuHhZHh6olEM2CWcwKxEcEWhoyOZnp5kduxIdpvWIJ9OV1lpaWl8++23HDt2jGvXrhm1aTQahgwZwtSpU03UO1GdpKSksGvXLnbu3El8fLy6ObCHhwf//e9/Tdw7IYS4tezsbB5++OF/LLKq9LuZlJQU9Hp9qal9jRo14vjx43d0j7NnzzJ16lQ18OLZZ5+9ZYEF8OqrrzJz5kz1cfFI1qBBg0w+kqXX68nJyVFHppo2bSoL/kWVVXD5MlmRW8hKTSVHo8GxRHiFmZMTdbRjsA8ciE2XzpIIWMUUFhbyxx9/EB0djZ2dnbrtRX5+Pk899RQ5OTlYWlri7e2Nr68vffr0IScnhzFjxmBpaWni3ouqTFEUQkJC2LZtm9FxLy8vxowZw+jRo2nfvr1pOieEEHeg5PrQ26nSRdb90LNnTw4dOnTH51tbW2NtbV3quKWlpcnfPFhaWvL888+btA9C3E7e6aSi9VXh4eQePmzcqNGAooCFBe127ZQPCKqQvLw89u7dq4ZUxMbGkpmZCYCnpyfT/lpTZ2lpyaJFi2jRogW9evVSR/cLCgrYsGFDlfg9KaoORVE4evQo27ZtY/r06erx+vXro9Fo6Nu3L6GhoYwZM4aWLVuarqNCCFEOd/rvXJUuspydnTE3Nyc5OdnoeHJysmwmKEQVoCgKuceOkREeTkZEBPmn/t4IFI0GW+/uOAYFUXA5mRvLlqGxtEQpKCBl8eIywzBE5cjPzzeKRvf29lb3wCvm5OSkxqkriqIWxZMmTarMropqRlEU9u3bR1hYGDqdjpMnTwIQEhKiptm+//77LFy4UE0GFEKImqhKF1lWVlZ4e3sTGRmprskyGAxERkYafSomhKg8il5PzoEDf41YRVBw8eLfjZaW2PfuXbSH1cBALJydubpoETeWLcN5xrM0nDaNq4sWkbLgcwAptCrJ9evXiYmJUUeqTp06xZUrV9R0tp49e3L16lX8/f3VPao6d+4scerijh07doyvvvqKVatWcf78efW4tbU1gwYNIjc3Vz3Wrl07U3RRCCEqlcmLrMzMTE6dOqU+TkpK4tChQ9SvX5/mzZszc+ZMJk6ciI+PDz179mT+/PlkZWUxefJkE/ZaiNrFkJ9P9q5dZIRHkBEZif76dbVNY2uLg58fjsHBOAT4Y15i7WJxQVVcYMHfhZUUWhVr+/bt/O9//yM6OprDN0/dBI4cOUK3bt0A+Pzzz1myZIlM4RR3LD8/n9zcXHWt8okTJ1iwYAEA9vb2DBs2jNDQUIYMGSJbhAghaiWTF1n79u1jwIAB6uPi0ImJEyeybNkyxo0bx9WrV5k9ezaXL1+mW7dubNy4sdrvcyVEVWfIyiIzOoaM8HAyt2/H8NcaHSgKrnDs3x/HQcHY9+uHmY1N2TfRG4wKrGLqY72hjItEeSiKQlJSElFRUYwYMYIGDRoARUVW8abjAB06dMDPz08dqWrevLnaZi9R+eIOZGdns2nTJnQ6HWvXrmXGjBm8/fbbAAwaNIgpU6YwatQogoODZbsQIUStV6Ui3Kui9PR0nJyc/jGmUYiaQJ+aSsbWbWSEh5MVG4tSYs84i4YNcQwOwjEoCLsePdBIwIFJGAwG4uPj1al/0dHRXLhwASjavLV4U/d9+/bxww8/4O/vj6+vr7p5e0UoDr4YOnSoBF/UMOnp6axbtw6dTsfvv/9Odna22ta/f3+2bt1qwt4JIUTlu9PawOQjWUII0ypITi5aXxURQfaevaDXq22WzZvjGBxEneBgbLp0kah1E9u6dStjx44ttUeVpaUlPXv2NAqz8PHxwcfHp7K7KGoQg8GAh4cHly9fVo+1aNECrVZLaGgovXv3NmHvhBCiapMiS4haKP/MGTW4IicuzqjN2sMDx+BgHIODsW7nLut0Kllubq4apx4dHc3o0aN56qmnAGjVqhXXrl3Dzs6OPn36qEEVvXr1kulZ4p5cuHCB1atXExsby48//ohGo8HMzIyQkBB27dpFaGgooaGheHl5ye8EIYS4A1JkCVELKIpC3vHjRcEV4eHk/RWrXMzWy6soETA4CKsSa3VExSsoKGDr1q1ER0cTFRXF7t27ySsxTdPW1lYtslq0aMGePXvo1q2bTMsT9+z06dPodDrCwsLYtWuXevyFF17A29sbgMWLF0sBL4QQd0GKLCFqKMVgIOfQITI2F+1hVfDnn383Wlhg37MnjoOCcQgMxLIC1+sIY9euXePSpUt06tQJgMLCQkaMGEF+fr56TqNGjdRRqpLBQBqNhh49elR6n0XNsnHjRl555RXibhrF7tu3L1qtlmbNmqnHpMASQoi7I0WWEDWIkp9P1p69RZsDb4lEfzVFbdPY2GDv2486wcE49O+PuZOTCXtae1y8eNEopKI4Ov3gwYNA0ZtYrVaLlZWVWli1bdtWpmSJ+0JRFPbv30/dunVp27YtULQHZVxcHObm5vTv3x+tVsvo0aNxdXU1cW+FEKLmkCJLiGrOkJNDZsxfUetbt2HIyFDbzBwdcRjQH8egIBx8fTGzszNdR2uZV199lV9++YXExMRSbYWFheTn56tBFT///HNld0/UYHq9nh07dqDT6dDpdJw7d47nnnuO+fPnA+Dv78/SpUsZPnw4zs7Opu2sEELUUFJkCVEN6dPSyNy2jYyICDKjY1Byc9U2c2dnHAcOxDE4GPuePdCUSJwT95fBYODYsWNERUWxd+9elixZgtlfCYx//vkniYmJmJmZ0a1bN3WUytfXl4YNG5q456KmMRgMREZGEhYWxurVq0lOTlbb7O3tKblbi4WFBZMmTTJBL4UQovaQIkuIaqLgyhUyt2whY3M4WXv2QGGh2mbZrFlRcMWgYGy7dkVjbm7CntZcBQUFHDx4UA2piImJ4fr162r7zJkz6dy5MwDPPvss48ePp2/fvrLHnqgQBoNBLeoBJk+erO6ZVrduXUaOHIlWq2XQoEGytkoIISqZFFlCVGH558+riYA5hw5BiU+jrd3d/4paD8K6fXtZw1MBcnNzMTMzU6f1vfPOO7zzzjtG59jZ2dG3b1/8/f2pV6+eerxnz56V2ldRO2RkZLB+/Xp0Oh179+7l5MmTWFhYYGZmxhNPPMGlS5fQarUMGDBAEiiFEMKEpMgSogpRFIW8EyeLgisiIsg7ftyo3aZrF+oEB+MYFIRVy5am6WQNlpGRwY4dO9SQit27d/Prr78yYsQIAHx9falbty5+fn7q9D8vLy95Mysq1LVr11izZg06nY7NmzcbJVHu2LEDf39/AObMmWOqLgohhLiJFFlCmJhiMJD7xx+k/1VYFZw993ejuTl2PXsUTQUMCsKyUSPTdbSGOnPmDAsWLCAqKoqDBw9iMBiM2vfu3asWWQMHDuTatWtGU7SEqEjffPMNTz/9NHq9Xj3m7u6ubg5cvJ+VEEKIqkWKLCFMQCkoIHvvXjIiIsgIj6Dw6lW1TWNlhb2vb1Ei4ID+WJSYgibuzZ9//kl0dDRNmjShf//+AOTn5/Ppp5+q57Rq1UodpfLz81NjrwHMZa2bqEBJSUnodDp69+5Nv379AOjWrRt6vZ6uXbui1WoJDQ3F09NTpgcLIUQVJ0WWEJXEkJtLVmxs0RqrrVsxpKWpbWYODjgEBOAYHIyDny9m9vYm7GnNoCgKp06dUkMqoqKiSEpKAmDs2LFqkeXu7s7MmTPx8fHBz8/PaCNWISpafHw8YWFh6HQ6de+0yZMnq0WWj48PiYmJtG7d2pTdFEIIUU5SZAlRgfQZGWRu2160h1V0NEpOjtpmXr8+jgMDcQwOxq53b8wkav2+KSwspHXr1pw/f97ouJmZGV5eXmoCIIBGo+Hjjz+u7C6KWqygoIC5c+cSFhbG8RLrLs3MzAgICCAgIEA9ptFopMASQohqSIosIe6zwpQUMrZsISM8gqxdu6CgQG2zcG2iBlfYdu8uUev3oDhOvXiUKi8vj02bNgFF+wC5urqSnJxMz5491al/EqcuTMFgMHDy5Ek8PDwAsLS0VAssS0tLgoODCQ0NZeTIkbI5sBBC1BBSZAlxH+T/eYGMiKLgipz9B4yi1q3atMExOAjH4GBsZC3FPdm1axfh4eFERUWxY8cOsrOz1TZzc3MyMzNxcHAA4Oeff6Zx48ayP5AwiYKCArZv365uDpyRkUFKSgo2NjZAURKgwWBg2LBhODk5mbi3Qggh7jcpsoS4C4qikJ+YSEZ4OOnh4eQdizdqt+ncuSgRMDgIa5nqc1fS09PZtWsXwcHBamE6f/58Vq5cqZ5Tr149NU7dz8/PqKBq1apVpfdZ1G65ubmEh4cTFhbGmjVruHHjhtrm5OTEsWPH6N69OwD/+te/TNVNIYQQlUCKLCHukKIo5B4+rG4OnH/mzN+NZmbY+fj8FbU+EEtXV5P1s7q6evUqMTEx6vS/Q4cOYTAYOH78uDrNavjw4QBqYdWxY0eJUxdVxvz583n11VfVxw0bNmT06NFotVoCAwPVTa2FEELUfFJkCXEbSmEh2fv2F20OHBlJ4eXLapvG0hL7vn1xHBSMw4ABWNSvb8KeVl86nY433niD+Pj4Um2tW7fm0qVLapE1YcIEJkyYUNldFMLI9evX1c2BH330UR544AEAxowZwxdffIFWq0Wr1eLr6yux/0IIUUtJkSXETQx5eWTt2EFGeASZW7agT01V28zs7LAP8KdOcDD2/v6Y/7X+R9xecZx68SjV448/jp+fHwDW1tZqgdWxY0ejPaqaNm1qym4Lobp8+TKrV68mLCyMrVu3qpsDW1tbq0WWh4cH586dk3WXQgghpMgSAkCfmUnm9u1kRESQtT0KQ8lAhbp1cRgYiGNQEPZ9+2JmbW3CnlYPBoOBI0eOqEVVdHQ0l0uMAjZr1kwtsvz8/Fi1ahW+vr6SrCaqnLy8PIKDg4mJiUEpEWjTpUsXdXPgkqTAEkIIAVJkiVqs8Pp1Mouj1nfsQCkZtd648V/BFcHYeXdHYyE/KrdTUFBAWlqaWiTFx8fTtWtXo3Osra3p2bMnfn5+jBw5Uj1ep04dRo8eXZndFeKWjh8/zsGDB3nooYeAor+3eXl5KIpCz549CQ0NZcyYMbi7u5u4p0IIIaoyeecoapWCixfJiIgkIzyc7P37wWBQ26xatsQxOBjHQcHYdOokn0jfRk5ODrt371ZHqnbu3Mno0aP58ccfAejQoQMtW7bEw8NDDano0aOHGl8tRFWhKAqHDh1Cp9MRFhZGfHw8lpaWDBkyhLp16wKwaNEiXFxccHNzM21nhRBCVBtSZIkaL+/0aTI2F+1hlXvkiFGbjacnjoOKNge2atNGCqvbUBSFN998k23btrFnzx4KSoz8ARwp8b01MzPj9OnT8v0UVdbhw4dZvnw5Op2OpKQk9bilpSUDBw4kJSVFLbK8vb1N1EshhBDVlRRZosZRFIXco8eKEgEjIshPTPy7UaPB1rs7dYKDcRgYhFUzCVYoy9WrV4mOjubs2bM8//zzQNFakw0bNnDw4EEAXF1djUIqPD09je4hBZaoSgoLCyksLFRHU6Oiovj4448BsLW1ZfDgwYSGhjJs2DC1uBJCCCHulhRZokZQ9Hqy9+8nIyKCjIgICi9e+rvR0hL7Pr2L1lgFBmIh4QqlnD9/3iikojjtz9LSkqeeekrd5HfWrFnk5eXh7+9Pq1atpJASVVpeXh4RERHq5sDvvfceTz75JACjR49mx44dhIaGEhISgr29vYl7K4QQoiaRIktUW4b8fLJ37iwqrCK3oL9+XW3T2Nri4O+PY1AQDv0DMHd0NGFPq5bihLTiAmnq1Kl88803pc7r1KkT/v7+ZGZmqkVWcRiAEFVVZmYmGzduJCwsjPXr15ORkaG2bd68WS2ymjZtqq4hFEIIIe43KbJEtWLIyiIzOpqMzeFkbt+OIStLbTNzcsJxwAAcBwUXRa1LyAJQFKd++PBhdZQqKiqKHTt20Lp1awA8PT0xNzene/fu6vS/fv360aBBAxP3XIjyyc7OxtXV1aiwcnV1VaPWfX19Tdg7IYQQtYkUWaLKK7xxg8yt28gIDycrNhYlP19ts3BxwTFoYFHUuo8PGktLE/a06khKSuLXX38lKiqKmJgYUktsqAywfft2tciaMmUKjz/+OA6ysbKoRpKTk1m9ejUJCQl88sknANjZ2dGrVy9Onz5NaGgoWq2Wnj17YmZmZuLeCiGEqG2kyBJVUkFyctE0wPAIsvfuBb1ebbNs0Zw6wUWJgDZduqCp5W+gsrOz2b17N82bN6dNmzYAxMXF8dJLL6nnODg40K9fP3WkqkePHmpbnTp1Kr3PQtyNc+fOodPp0Ol0RpsDz5o1iyZNmgDwyy+/4OTkJOsFhRBCmJQUWaLKyEtKUoMrcuP+MGqzbt8ex+CizYGt3d1r9RuotLQ0YmNj1al/e/fupaCggDlz5vDWW28B4Ovry6hRowgICMDf35+uXbtiIRsqi2pKp9Px/vvvs2/fPqPjPXr0QKvVYlliBFuSAYUQQlQF8q5LmIyiKOTFx/81YhVO3slTfzdqNNh6eRUlAgYHYSWbgHLp0iWGDRtGXFwchhKbKEPRIn5ra2v1sbOzM6tXr67kHgpx7xRF4fDhwzRq1IhGjRoBkJWVxb59+9BoNPj5+aHVahkzZgzNmzc3cW+FEEKIskmRJSqVoteTc+gQGeFFhVXBhQt/N1pYYN+rF47BQTgEBmLp4mK6jprQuXPn1Dj1Ro0a8c477wDg4uJCYmIiBoOBtm3bqlP//P39admyZa0e3RPVm8FgYM+ePepUwMTERD788ENmzZoFwPDhw/nqq68YNWqUWngJIYQQVZkUWaLCKfn5ZO3eU7Q58JYt6FNS1DaNjQ0Ofr44BgfjEBCAuZOTCXtqGgkJCWpRFRUVxblz59S21q1bq0WWubk5a9euxd3dXV1/IkR1pdfriYqKQqfTsWrVKi6U+MDFxsaGGzduqI/r1avH1KlTTdFNIYQQ4q5IkSUqhCE7m8zoGDIiIsjctg1DiUhlszp1cBzQH4egIBx8fTH7aw+m2kCv15OUlETbtm3VYw888ABHjhxRH5ubm+Pt7a2OUimKoo5S+fv7V3qfhbhfSv5dzs3NZdiwYeTk5ADg6OjI8OHD0Wq1DBkyRDYHFkIIUa1JkSXuG31aGhlbt5IREUFWdAxKXp7aZt7QGceBA3EMCsa+Zw80VlYm7Gnlyc/PZ//+/eooVWxsLHl5eaSlpWH11/dg0KBBNGjQQC2qevfuLXHqosbIyspi48aN6HQ6zp49S0xMDAD29vaMHz8evV5PaGgoAwcOxEb2thNCCFFDSJEl7knBlStkRkYW7WG1Zy8UFqptls2a4RgcjGNwMLbdutaqqPWff/6Zb775hl27dqmf1BdzdHTk1KlTeHp6AvDxxx+bootCVJjU1FTWrVuHTqdj48aNRj8DJ06coF27dgB88803puqiEEIIUaGkyBLlln/unBpckRMXB3/tVQNg3a5dUSLgoGCsPTxqfBhDamqqGqf+7LPP0rRpUwDOnz/P1q1bgaKkPz8/P3WkqkuXLhKnLmqsefPm8dprr1FQUKAea9Wqlbo5cMmpskIIIURNJe/0xD9SFIW8EyfI2BxORkQEeQkJRu22XbviOKhoc2CrFi1M1MvKkZycrO5PFRUVxR9//KFuiNq5c2fGjx8PwKhRo3BycsLf35/27dvX+GJT1E5//vknq1aton///uqxtm3bUlBQgKenp1pYde3aVX4GhKgEer3e6AMOIUT5WVpaYm5ufs/3kSJLlEkxGMiJiysasYqIoKBE4h3m5tj17FE0FXDgQCxraKSyoijo9Xp11Gnt2rWMHDmy1Hnu7u74+/vTunVr9ZiHhwceHh6V1lchKsupU6fQ6XSEhYWxZ88eAF599VV69eoFQEhICPHx8bRv396U3RSiVlEUhcuXL5OammrqrghRI9StW5fGjRvf0weEUmQJlVJQQNaePUWJgBGRFF69qrZprK2x9/Utmgo4oD/mdeuarJ8VRVEUjh8/bjRS9eSTT/L6668D4OPjg0ajoXPnzvj7++Pn54efn5/EqYsaLzMzk3nz5qHT6Th8+LB6XKPR0K9fP6MPFGxtbaXAEqKSFRdYLi4u2NnZycixEHdJURSys7O5cuUKwD29x5Miq5Yz5OSQFRtbNGK1bRuGtDS1zczBAYf+/XEMCsLBzxezGhipnJ2dzTfffENUVBTR0dFcLVFYAmoSGhT9oF2/fp26NbDAFKIkRVG4cOECzZo1A8Da2poFCxZw48YNzM3NCQwMRKvVMmrUKJo0aUJBQQEbNmwwca+FqJ30er1aYDVo0MDU3RGi2rP9a2uhK1eu4OLictdTB6XIqoX06elkbt9OxuZwMmNiUEokf5k3aIBjYCCOg4Kx69ULsxoUtZ6fn8++fftIS0tjyJAhQNG829dff52srCygaBPU3r17qyNVvXv3NrqHFFiiptLr9cTExBAWFsaqVaswNzcnKSkJjUaDpaUlc+fOpU6dOowYMYL69euburtCiL8Ur8Gys7MzcU+EqDmKf54KCgqkyBK3V5iSQkbklqKo9d27ocTCWEtXVxyDg4qi1r280NyHxX5VQVZWFrt27VKn/u3atYvc3Fw8PDyMiqx///vf2Nvb4+/vj4+PD9bW1ibuuRCVIz8/ny1btqDT6Vi9erXRSK6DgwNnz56lZcuWADz77LMm6qUQ4k7IFEEh7p/78fMkRVYNlv/nn2pwRc6BA0ZR61Zt2xQFVwQFYePpWeN+OT/88MP88ssvFJbYtwuK4tQ7duxIQUEBlpaWALz77rum6KIQJvfyyy8zf/589XG9evUYNWoUWq2W4OBg2RxYCCGEuEtSZNUgiqKQf+oU6eHhZIRHkBcfb9Ru06VLUXBFUBDWrVuZqJf3z+XLl9WQir179xITE6MmAdrb21NYWEizZs0ICAhQ96mSOHVRG6WlpbF+/Xp0Oh3PP/88/fr1A2DEiBGsWLGCMWPGoNVqCQgIUD98EEKIqkCj0bBq1SpGjx5t6q4IUS5SZFVxVz9fCOZmNJw2rXTbokUohXocA/zJiIggY3M4+WfP/n2CmRl2PXr8VVgNxLKap+BduHCByMhINaTixIkTRu0HDx6kR48eQFGk9Ouvv06LFi2kqBK10tWrV1mzZg06nY6IiAjy8/MBaNasmVpk9e/fnwsXLmBmZmbKrgohaqmrV68ye/Zs1q9fT3JyMvXq1aNr167Mnj1b/T1VVeh0Or788kv279/P9evXOXjwIN26dSvXPeLi4vjggw+IiYkhJSWFli1b8tRTT/Hcc8+V6z6LFy9m8eLFnDlzBoCOHTsye/ZsdSnErZw6dYpnnnmGnTt3YmFhQa9evfj+++9p2LDhHT93bGwsAQEBdOrUiUOHDpWr37WNFFlVnbkZKQs+B1ALLaWwkEtvziZt1SrM7O25tmiRerrG0hL7fv1wDA7GIXAAFvXqmaTb96o4Tr1p06bUqVMHgGXLlvHGG2+o52g0Grp06aKGVLRr105tK7lnlRC1SUpKCmPHjiUqKgqDwaAe9/DwIDQ0lHHjxqnHpLgSQphSaGgo+fn5LF++nNatW5OcnExkZCTXrl0zdddKycrKwtfXlwcffJAnnnjiru6xf/9+XFxc+OGHH3Bzc2PHjh1MnToVc3Nzpk+ffsf3adasGR988AHu7u4oisLy5csZNWoUBw8epGPHjre8burUqaSlpbF9+3bs7OzYuXMnSomlJP8kNTWVRx99lIEDB5KcnHzH19VWUmRVccWFVcqCz8k/nYTG0pL0DRtQ8vIAMGRlYWZnh0P/AByDg7H388fcofpFrev1euLi4tSQiujoaFJSUvjf//7H2LFjARgwYICa/Ofv70+/fv0k7U/UeqdPn+bEiRMMHjwYgPr163Pq1CkMBgNeXl6Ehoai1Wrp0KGDiXsqhBB/S01NJTo6mm3bthEQEABAixYt6Nmz522vO3z4MM899xw7d+7Ezs6O0NBQPvnkExwcHACYNGkSqampeHl5sXDhQvLy8nj44YdZsGABVn8lJhsMBv773//y9ddfc/nyZdq1a8ebb77JAw88cMvnfeSRRwDU0aO7MWXKFKPHrVu3ZufOneh0unIVWSNGjDB6/N5777F48WJ27dp12yLLzMyMkJAQvLy8AIz2OLwTTz31FA8//DDm5uasXr26XNfWRlJkVQMNp00jP+kM6WvXqsc0NjbUGT4Mx6Ag7Pv0wayaJuIdO3aMF198kdjYWNLT043abGxsuHjxovq4b9++7Ny5s7K7KESVoigKx44dQ6fTERYWRlxcHM7Ozly6dAkLCwvMzMxYvnw5rVq1olWr6r/2Ughx94q3JymLubm5UbjN7c41MzNT9w661bn25dxL08HBAQcHB1avXk3v3r3vKNk3KyuLkJAQ+vTpw969e7ly5QqPP/4406dPZ9myZep5kZGR2NjYsG3bNs6cOcPkyZNp0KAB7733HgDvv/8+P/zwA19++SXu7u5ERUUxYcIEGjZsqBZ8lSUtLe2etsXQ6/X88ssvZGVl0adPn9ueO2rUKLWY7N69e7meZ+nSpZw+fZoffvhBAsPulCJuKy0tTQGUtLQ0k/ZDn5urHPNoX/TVsZNiKCgwaX/KKzMzUwkPD1fefPNNZeXKlerxs2fPKoACKHXq1FGGDh2qfPDBB8qOHTuUvLw8E/ZYiKrljz/+UF599VWlXbt26s8MoJibmytBQUHKpUuXTNa3/Px8ZfXq1Up+fr7J+iBEbZWTk6McO3ZMycnJKdVW8nfFzV9Dhw41OtfOzu6W5wYEBBid6+zsXOqcu/Hrr78q9erVU2xsbJS+ffsqr776qhIXF1fqNaxatUpRFEX5+uuvlXr16imZmZlq+/r16xUzMzPl8uXLiqIoysSJE5X69esrWVlZ6jmLFy9WHBwcFL1er+Tm5ip2dnbKjh07jJ7nscceUx566KF/7HNSUpICKAcPHryr11xSbGysYmFhoWzatKnc1/7xxx+Kvb29Ym5urjg5OSnr16+/7fmRkZGKnZ2d8tFHHylNmjRRoqKi1LZff/1VcXBwuOW1J06cUFxcXJSEhARFURRlzpw5SteuXcvd5+rkdj9Xd1obyEhWNXFtyRKgaM2VUlBAytdflxmGUVXcuHGDmJgYdfrfgQMH1Dj1ESNG8OCDDwLQvHlzvv76a3r06EHnzp3vesM3IWoavV4PoP5M/Pzzz7z//vsAWFtbM2jQILRaLSNGjKBBgwYm66cQQtyt0NBQhg0bRnR0NLt27eL333/nww8/5Ntvv2XSpEmlzo+Pj6dr165Go2b9+vXDYDCQkJBAo0aNAOjatavR5sx9+vQhMzOT8+fPk5mZSXZ2NsHBwUb3zs/PV6fRVYYjR44watQo5syZw6BBg8p9vYeHB4cOHSItLY1ff/2ViRMnsn37djw9Pcs8/5VXXuGZZ57hxRdfpGPHjowYMYL/+7//Y8SIERw+fBhfX98yr9Pr9Tz88MPMnTvXaO27+GdSZFUDVxctImXB5zjPeJaG06apj4EqU2hlZ2cb7Y7drFkzsrOzjc5xc3MjICBAXTtS7G4XkApR0+Tn57N161Z1c+AlS5YwfPhwAMaOHUtiYiJarZahQ4fi6Oho4t4KIaq6zMzMW7bd/KHmlStXbnnuzSE597Iu6WY2NjYEBwcTHBzMm2++yeOPP86cOXPKLLLuh+Lvyfr162natKlR251MWbwfjh07xsCBA5k6dapRoFd5WFlZ0bZtWwC8vb3Zu3cvn332GV999VWZ5//xxx88//zzAAwZMoQlS5YwduxYFi5cyLJly/jwww/LvC4jI4N9+/Zx8OBBdd2YwWBAURQsLCzYvHkzgYGBd/Uaajopsqq4mwssMA7DKPm4siiKwpkzZ9SAiqioKKytrTl8+DAAlpaW9OjRg8uXL6shFX5+frRo0aJS+ylEdZCTk8OmTZvQ6XSsXbuW1NRUtW3dunVqkeXl5cXKlStN1EshRHVUnnVSFXVueXl6et4yVKFDhw4sW7aMrKwstQ+xsbGYmZkZhTjExcWRk5OjriPbtWsXDg4OuLm5Ub9+faytrTl37lylr78COHr0KIGBgUycOFFdI3Y/GAwG8v4KRStL06ZNiYqK4qGHHgKKRhEzMzOZPHkyXbp0UUPGblanTh31/V2xRYsWsWXLFn799VdZ+3sbUmRVdXqDUYFVTH2sN5RxUcVYuXIla9asISoqij///NOozdzcnLS0NJycnADYtGlTpX0iJER1denSJdq2bWs06uvi4qJuDjxgwAAT9k4IISrOtWvXGDt2LFOmTKFLly44Ojqyb98+PvzwQ0aNGlXmNePHj2fOnDlMnDiRt956i6tXr/Lss8/yyCOPqFMFoWhWwGOPPcYbb7zBmTNnmDNnDtOnT8fMzAxHR0defPFFnn/+eQwGA76+vqSlpREbG0udOnWYOHFimc99/fp1zp07pwZyJSQkANC4cWMaN258R6/5yJEjBAYGEhISwsyZM7l8+TJQ9B6qPHtVvfrqqwwZMoTmzZuTkZHBTz/9xLZt29i0adMtr3nppZeYNm0ajRs3Zty4caSlpakJjcePHyc2NrbMKYNmZmZ06tTJ6JiLiws2NjaljoubVMxysZqjqgRfVKaCggJl3759yvz585XCwkL1+KOPPqoucLW0tFT69u2rvPzyy8r69euVGzdumK7DQlQDKSkpynfffaf897//NTreoUMHpXnz5sq///1vJSoqyuhnrrqQ4AshTOd2C/SrstzcXOWVV15Runfvrjg5OSl2dnaKh4eH8sYbbyjZ2dnqeZQIvlCUosCHAQMGKDY2Nkr9+vWVJ554QsnIyFDbJ06cqIwaNUqZPXu20qBBA8XBwUF54oknlNzcXPUcg8GgzJ8/X/Hw8FAsLS2Vhg0bKiEhIcr27dtv2d+lS5eWGQoyZ84co+e+OSSkpDlz5pR5jxYtWqjnFAdrbN269Zb3mTJlitKiRQvFyspKadiwoTJw4EBl8+bNtzy/2C+//KJ4e3srdnZ2iouLizJ58mTl/PnzyuOPP640aNBAOXHixD/eo/h1SPDFP9cGGkUpxy5ktVB6ejpOTk6kpaWpm+LWNHl5eezdu1cNqdixYwcZGRkARjuab9y4kd27d+Pv70+vXr2MFpUKIUq7ePEiq1evRqfTsW3bNvR6Pfb29ly9elWdxnL58mUaNWqERqMxcW/vXkFBARs2bGDo0KFYWlqaujtC1Cq5ubkkJSXRqlUro0j22qp4nyxT7OMUEBDAgAEDeOutt+76Hlu3bkWr1XL69Gnq1at3/zonyuV2P1d3WhvIdMFabsmSJTzzzDOl5vE6OTnh6+urJpwBDB48uFRohRCitBUrVvD555+zY8cOo+PdunVDq9WSn5+vFll3Os1ECCFE1ZWWlkZiYiLr16+/p/ts2LCB1157TQqsGkCKrFrg+vXrxMTEqCEVb775prqYvmXLluTl5eHi4qKGVPj7+9OpUyeJUxfiDiiKQnx8PM2bN8fBwQEoSt4qLrD69OmDVqtlzJgxtGnTxpRdFUIIUUGcnJxKrVe/Gx999NF96I2oCqTIqoEyMjL4/fff1el/N6fCbN26VS2y+vXrR0JCAu7u7tV6upIQlUlRFA4cOIBOpyMsLIyEhAR+/PFHHn74YQDGjRuHo6Mjo0ePLhURLIQQouIsW7bM1F0QApAiq9pTFIWkpCRyc3PVDeiuXLnCuHHjjM5r3769OkrVv39/9biNjY1sLifEHdDr9ezcuROdTodOp+Ps2bNqm5WVldG+Ma1ateKZZ54xQS+FEEIIURVIkVXNGAwG4uPjjfaounDhAlqtlrCwMABat27NoEGD6NChA/7+/vj6+uLi4mLingtRvV26dAk/Pz/1sZ2dHUOHDlU3By7evkAIIYQQQoqsaiQ2NpZRo0Zx7do1o+OWlpYUFhaqjzUazW33ShBC3Fpubi7h4eGEhYWRn5/PTz/9BECzZs0ICQnBxcUFrVbLoEGDJGFTCCGEEGWSIqsaad26NdeuXcPOzo4+ffqo0/969uwpb/aEuAcZGRls2LABnU7Hhg0byMzMBMDCwoJFixZRt25doGgbAyGEEEKIfyJFVjXSpEkT9u/fT+fOnWUvGiHuk9mzZ/Phhx8abWPg5uaGVqtFq9Xi6Ohowt4JIYQQojqSIqua6d69u6m7IES1dfnyZVatWoVWq6VRo0YANGrUiLy8PNq2bUtoaCihoaH4+PhI2qYQQggh7pqZqTsghBAV6cyZM3z66af4+vri6urKtGnTWLVqldr+r3/9iz/++IMTJ07wwQcf0KNHDymwhBCimti2bRsajYbU1NQKuf+1a9dwcXExSpC9lTNnzqDRaDh06FCF9KU22LhxI926dcNgMJi6K/dMiiwhRI1z/fp1/vOf/+Dt7U2rVq2YOXMmsbGxKIpCr169aNCggXpugwYN6Ny5sxRWQohaT29Q2Jl4jd8OXWBn4jX0BqVCn2/SpEloNJpSX4MHD67Q5y2P9957j1GjRtGyZUtTd6VS5ebm8swzz9CgQQMcHBwIDQ0lOTn5tteU9Wep0WjUDZbPnDnDY489RqtWrbC1taVNmzbMmTOH/Px89R6DBw/G0tKSH3/8sUJfX2WQ6YJCiGpPURSuX79uVDzNnj0bvV6PmZkZ/v7+hIaGMnr0aJo1a2bCngohRNW08cgl5q49xqW0XPVYEycb5ozwZHCnJhX2vIMHD2bp0qVGx6ytrSvs+cqSn5+PlZVVqePZ2dksWbKkViY2P//886xfv55ffvkFJycnpk+fjlarJTY29pbXXLp0yejx77//zmOPPUZoaCgAx48fx2Aw8NVXX9G2bVuOHDnCE088QVZWFvPmzVOvmzRpEgsWLOCRRx6pmBdXSWQkSwhRLRkMBnbs2MGLL75ImzZtGDlypNpWv359XnnlFb799lsuX77M1q1bmT59uhRYQghRho1HLvH0DweMCiyAy2m5PP3DATYeuXSLK++dtbU1jRs3NvqqV68eUPb0u9TUVDQaDdu2bbvlPWNiYvDz88PW1hY3NzdmzJhBVlaW2t6yZUveeecdHn30UerUqcPUqVPLvM+GDRuwtramd+/e6rEbN24wfvx4GjZsiK2tLe7u7qWKxJK2b99Oz549sba2pkmTJrzyyitG2+7079+f6dOnM336dJycnHB2dubNN99EUf4eRczLy+PFF1+kadOm2Nvb06tXr9u+/nuVlpbGkiVL+OSTTwgMDMTb25ulS5eyY8cOdu3adcvrbv5z/O233xgwYACtW7cG/i6oBw0aROvWrRk5ciQvvvgiOp3O6D4jRoxg3759JCYmVthrrAwykiWEqDYKCgqIiooiLCyM1atXG31qduXKFdLS0tRNgd99911TdVMIIUxKURRyCvR3dK7eoDBnzVHKmhioABrgrTXH6NfWGXOz20+rtrU0N/nU68TERAYPHsy7777Ld999x9WrV9UipmQxNG/ePGbPns2cOXNuea/o6Gi8vb2Njr355pscO3aM33//HWdnZ06dOkVOTk6Z11+4cIGhQ4cyadIkvv/+e44fP84TTzyBjY0Nb731lnre8uXLeeyxx9izZw/79u1j6tSpNG/enCeeeAKA6dOnc+zYMVasWIGrqyurVq1i8ODBHD58GHd39zKfe8iQIURHR9/ytbVo0YKjR4+W2bZ//34KCgoICgpSj7Vv357mzZuzc+dOo6LzVpKTk1m/fj3Lly+/7XlpaWnUr1/f6Fjz5s1p1KgR0dHRtGnT5h+fq6qSIksIUW1MmjRJ3RwYoE6dOowYMQKtVktISAj29vYm7J0QQlQNOQV6PGffnyluCnA5PZfOb23+x3OPvR2CnVX53lquW7cOBwcHo2OvvfYar732WrnuU+z9999n/Pjx/Pvf/wbA3d2dBQsWEBAQwOLFi7GxsQEgMDCQF1544bb3Onv2LK6urkbHzp07h5eXFz4+PgC3Xau1aNEi3NzcWLhwIRqNhvbt23Px4kVefvllZs+ejZlZ0YQyNzc3Pv30UzQaDR4eHhw+fJhPP/2UJ554gnPnzrF06VLOnTun9uXFF19k48aNLF26lP/85z9lPve33357y+IPuO1WQJcvX8bKykrdI7JYo0aNuHz58i2vK2n58uU4Ojqi1Wpvec6pU6f4/PPPjaYKFnN1deXs2bN39FxVlRRZQogqJzMzk99//52wsDDee+899ZOswYMHs3nzZkaPHo1WqyUwMLDS5+4LIYS4fwYMGMDixYuNjt08slEecXFx/PHHH0bBCYqiYDAYSEpKokOHDgBqkXQ7OTk5alFW7OmnnyY0NJQDBw4waNAgRo8eTd++fcu8Pj4+nj59+hiN7vXr14/MzEz+/PNPmjdvDkDv3r2NzunTpw8ff/wxer2ew4cPo9fradeundG98/LyjNYh36xp06b/+Poq0nfffcf48eNLff+KXbhwgcGDBzN27Fh1xK4kW1tbsrOzK7qbFUqKLCFElXDjxg3Wrl1LWFgYmzZtUjcH9vb2ZtasWQCMGzeOhx56CAsL+dUlhBC3YmtpzrG3Q+7o3D1J15m0dO8/nrdscg96trp98WNraX5Hz1mSvb09bdu2LbOteKSn5PqkgoKC294vMzOTJ598khkzZpRqKy5qip/3nzg7O3Pjxg2jY0OGDOHs2bNs2LCB8PBwBg4cyDPPPFPmaMz9kJmZibm5Ofv378fc3Pj7e/MI4M39vNvpgo0bNyY/P5/U1FSj0azk5GQaN278j32Ojo4mISGBlStXltl+8eJFBgwYQN++ffn666/LPOf69es0bNjwH5+rKpN3KkIIkzpz5gxPPvkkW7ZsMVoM3KZNG0JDQ42ifMtKfxJCCGFMo9Hc8bQ9P/eGNHGy4XJabpnrsjRAYycb/Nwb/uOarPut+E32pUuX8PLyAvjHPai6d+/OsWPHblm4lYeXlxc//PBDmf2aOHEiEydOxM/Pj1mzZpVZZHXo0IGwsDAURVFHqmJjY3F0dDQKYtq9e7fRdbt27cLd3R1zc3O8vLzQ6/VcuXIFPz+/O+77vUwX9Pb2xtLSksjISDUZMCEhgXPnztGnT59/fO4lS5bg7e1N165dS7VduHCBAQMGqGEaxYV0Sbm5uSQmJqp/5tWVFFlCiEp19uxZLl68qP6idnFxITo6msLCQjp37oxWq0Wr1creVUIIUQnMzTTMGeHJ0z8cQANGhVbxb+A5IzwrrMDKy8srtc7HwsICZ2dnbG1t6d27Nx988AGtWrXiypUrvPHGG7e938svv0zv3r2ZPn06jz/+OPb29hw7dozw8HAWLlxYrr6FhITw6quvcuPGDTXxcPbs2Xh7e9OxY0fy8vJYt26dOgXxZtOmTWP+/Pk8++yzTJ8+nYSEBObMmcPMmTONiotz584xc+ZMnnzySQ4cOMDnn3/Oxx9/DEC7du0YP348jz76KB9//DFeXl5cvXqVyMhIunTpwrBhw8p87nuZLujk5MRjjz3GzJkzqV+/PnXq1OHZZ5+lT58+RqEX7du35/3332fMmDHqsfT0dH755Re1/yVduHCB/v3706JFC+bNm8fVq1fVtpIjZLt27cLa2vqOCrqqTIosIUSFS0hIQKfTERYWxv79++nUqROHDx8GwM7Ojh9++IFOnTqVmnMuhBCi4g3u1ITFE7qX2iercSXsk7Vx40aaNDG+v4eHB8ePHweK1vY89thjeHt74+HhwYcffsigQYNueb8uXbqwfft2Xn/9dfz8/FAUhTZt2jBu3Lhy961z5850796d//3vfzz55JNA0YyKV199lTNnzmBra4ufnx8rVqwo8/qmTZuyYcMGZs2aRdeuXalfvz6PPfZYqULx0UcfJScnh549e2Jubs5zzz1nFCu/dOlS3n33XV544QUuXLiAs7MzvXv3Zvjw4eV+TXfq008/xczMjNDQUPLy8ggJCWHRokVG5yQkJJCWlmZ0bMWKFSiKwkMPPVTqnuHh4Zw6dYpTp06V2lKl5JTQn3/+mfHjx2NnZ3cfX1Hl0yglX5UoJT09HScnJ9LS0qhTp46puyNEtXH48GF++eUXwsLCOHbsmHpco9Hg5+fH+vXrbzufXFQfBQUFbNiwgaFDh952CooQ4v7Lzc0lKSmJVq1a3TJk4E7pDQp7kq5zJSMXF0cberaqX+lTBKua9evXM2vWLI4cOVLm1LZ71b9/f7p168b8+fPv+72ro5SUFDw8PNi3bx+tWrUyWT9u93N1p7WBjGQJIe4Lg8GARqNRp/jNmzeP77//Hiia+jFw4EC0Wi2jRo2iUaNGpuyqEEKIMpibaejT5taJdbXRsGHDOHnyJBcuXMDNzc3U3anxzpw5w6JFi0xaYN0vUmQJIe5aYWEh0dHR6HQ6Vq1axdq1a9WFquPGjSM9PR2tVsuIESNK7bchhBBCVAfFe26Jiufj43NH8frVQa0oslq2bEmdOnUwMzOjXr16bN261dRdEqLaysvLIzIyEp1Ox2+//UZKSoratnr1arXIGjp0KEOHDjVVN4UQQogqb9u2babugqggtaLIAtixY4es/xDiHh09epS+ffuSnp6uHmvQoAGjRo0iNDSUgQMHmrB3QgghhBBVQ60psoQQ5ZOamsq6desoLCxk0qRJQFGUrIWFBU2aNFGj1v39/WVzYCGEEEKIEu5/TEo5RUVFMWLECFxdXdFoNKxevbrUOV988QUtW7bExsaGXr16sWfPnnI9h0ajISAggB49evDjjz/ep54LUfNcuXKFr7/+msGDB9OwYUMeeeQR5syZo0arWlpasmfPHv78808WLlxIYGCgFFhCCCGEEDcx+bujrKwsunbtypQpU9BqtaXaV65cycyZM/nyyy/p1asX8+fPJyQkhISEBFxcXADo1q0bhYWFpa7dvHkzrq6uxMTE0LRpUy5dukRQUBCdO3emS5cuFf7ahKguvv/+e5YsWUJMTAwGg0E97unpqe6RURxh2qZNG1N1UwghhBCiWjB5kTVkyBCGDBlyy/ZPPvmEJ554gsmTJwPw5Zdfsn79er777jteeeUVAA4dOnTb5yje9bpJkyYMHTqUAwcO3LLIysvLIy8vT31cvPakoKCAgoKCO35dQlRlJ0+epHXr1pibmwOwe/duoqKiAPD29mb06NGMGjWK9u3bq9fI339xK8V/N+TviBCVr6CgAEVRMBgMRh+SCSHunsFgQFEUCgoK1PdKxe703zqTF1m3k5+fz/79+3n11VfVY2ZmZgQFBbFz5847ukdWVhYGgwFHR0cyMzPZsmULDz744C3Pf//995k7d26p45s3b672O0+L2ktRFM6ePcvOnTvZtWsXZ8+e5d1336VTp04AtG7dmilTptC7d291hPj06dOcPn3alN0W1Ux4eLipuyBErWNhYUHjxo3JzMwkPz/f1N0RokbIz88nJyeHqKioUrPlsrOz7+geVbrISklJQa/Xl9q4tFGjRhw/fvyO7pGcnMyYMWMA0Ov1PPHEE/To0eOW57/66qvMnDlTfZyeno6bmxuDBg267a7OQlQ1BoOBffv2sWrVKn777TdOnTqltllYWODo6CgR6+K+KCgoIDw8nODgYCwtLU3dHSFqldzcXM6fP4+Dg4M6rbumCgwMpGvXrnz66ae3PKd169Y899xzPPfcc/fteSdPnkxqaiqrVq26b/csacmSJfzvf/9j06ZN/3ju3Llz+e233zhw4ECF9KU2+PLLL9mwYQNr1qy55Tm5ubnY2tri7+9f6ueqZMLy7VTpIut+aN26NXFxcXd8vrW1NdbW1qWOW1paypsHUa3s27cPX19f9bG1tTUhISGEhoYyfPhw6tevb8LeiZpIfk8KUfn0ej0ajQYzMzPMzO4yzyz1PGRfu3W7XQOo63Z3976NSZMmsXz5cp588km+/PJLo7ZnnnmGRYsWMXHiRJYtWwaATqfD0tLyH19n8ffjflmwYAGKopTrnhqNhlWrVjF69Ojbnpebm8ucOXP45Zdf7uj+Go0G4L6+PlPIzc3lqaeeYv/+/cTHxzN8+PAyw+9uduLECWbNmkVsbCz5+fl06dKFd955hwEDBqjnFH+PSvr555/517/+BcDjjz/Oe++9R2xsLH5+fmU+j5mZGRqNpsx/1+7037kqXWQ5Oztjbm5OcnKy0fHk5GQaN25sol4JUbXk5eWxZcsWdDod9erV48MPPwSK1lZ5enrSuXNnQkNDGTJkiOwVJ4QQwljqeVjoDYV5tz7Hwhqm76+QQsvNzY0VK1bw6aefYmtrCxS9Af/pp59o3ry50bmm+nDQycmpwu7966+/UqdOHfr161dhz1EV6fV6bG1tmTFjBmFhYXd83fDhw3F3d2fLli3Y2toyf/58hg8fTmJiolFtsHTpUgYPHqw+rlu3rvr/VlZWPPzwwyxYsOCWRdb9UKXLYCsrK7y9vYmMjFSPGQwGIiMj6dOnjwl7JoRpZWVlodPpmDBhAi4uLgwdOpRvv/2W7777Tp07rNFoOHLk791qJwAAMehJREFUCCtWrGDs2LFSYAkhhCgt+9rtCywoar/dSNc96N69O25ubuh0OvWYTqejefPmeHl5GZ3bv39//v3vf6uPr1y5wogRI7C1taVVq1ZlbtOj0WhYvHgxQ4YMwdbWltatW/Prr78anXP48GECAwOxtbWlQYMGTJ06lczMTLV90qRJRiNS/fv3Z8aMGbz00kvUr1+fxo0b89Zbb6ntLVu2BGDMmDFoNBr1cVlWrFjBiBEjjI5t27aNnj17Ym9vT926denXrx9nz54t83qDwcDbb79Ns2bNsLa2plu3bmzcuFFtP3PmDBqNhhUrVtC3b19sbGzo1KkT27dvN7rPkSNH1A9jGzVqxCOPPEJKSsot+32v7O3tWbx4MU888cQdD5ykpKRw8uRJXnnlFbp06YK7uzsffPAB2dnZHDlyxOjcunXr0rhxY/Xr5il/I0aMYM2aNeTk5Ny313QzkxdZmZmZHDp0SE0ITEpK4tChQ5w7dw6AmTNn8s0337B8+XLi4+N5+umnycrKUtMGhahtXnjhBRo2bEhoaCg//vgj6enpNG7cmKeffpqVK1caDZOXNWQuhBCihlMUyM+6s6/CO3yTWZjzz/f6a0/F8poyZQpLly5VH3/33Xd39D5v0qRJnD9/nq1bt/Lrr7+yaNEirly5Uuq8N998k9DQUOLi4hg/fjz/+te/iI+PB4o+tAwJCaFevXrs3buXX375hYiICKZPn37b516+fDn29vbs3r2bDz/8kLffflsN/9m7dy9QNJpy6dIl9XFZYmJi8PHxUR8XFhYyevRoAgIC+OOPP9i5cydTp0695b/nn332GR9//DHz5s3jjz/+ICQkhJEjR3Ly5Emj82bNmsULL7zAwYMH6dOnDyNGjODataLCOTU1lcDAQLy8vNi3bx8bN24kOTn5tkFx586dw8HB4bZf//nPf277PSyvBg0a4OHhwffff09WVhaFhYV89dVXuLi44O3tbXTuM888g7OzMz179uS7775T9/ss5uPjQ2FhIbt3776vfSzJ5NMF9+3bZzSPsjh0ongO7rhx47h69SqzZ8/m8uXLaoV+cxiGEDXR1atXWbNmDePHj1c/hbG2tiYnJ4eWLVui1WoJDQ2ld+/e1X5+thBCiPukIBv+43p/7/nd4H8+57WLYGVf7ltPmDCBV199VR2tiY2NZcWKFWzbtu2W15w4cYLff/+dPXv2qIFmS5YsoUOHDqXOHTt2LI8//jgA77zzDuHh4Xz++ecsWrSIn376idzcXL7//nvs7Yv6vnDhQkaMGMF///vfW77f7NKlC3PmzAHA3d2dhQsXEhkZSXBwMA0bNgT+Hk25ldTUVNLS0nB1/fvPKj09nbS0NIYPH67uS1nWayo2b948Xn75ZXW90X//+1+2bt3K/Pnz+eKLL9Tzpk+fTmhoKACLFy9m48aNLFmyhJdeeomFCxfi5eVlVBR99913uLm5ceLECdq1a1fqeV1dXf9xC6X7Pb1To9EQERHB6NGjcXR0xMzMDBcXFzZu3Ei9evXU895++20CAwOxs7Nj8+bNTJs2jczMTGbMmKGeY2dnh5OT0y1HCO8HkxdZ/fv3L1Vd3mz69On/+ImCEDXFn3/+yerVqwkLCyMqKgqDwYCLi4s6neCpp55i7NixdOvWTUaqhBBCVHsNGzZk2LBhLFu2DEVRGDZsGM7Ozre9Jj4+HgsLC6MRjPbt2xutvSl28xKTPn36qAVCfHw8Xbt2VQssgH79+mEwGEhISLhtkVVSkyZNyhxFu53iqWolp7LVr1+fSZMmERISQnBwMEFBQTz44IM0adKk1PXp6elcvHix1Hqufv36lQp9K/k9sLCwwMfHRx3Ni4uLY+vWrWUuK0hMTCyzyLKwsKBt27bleLX3TlEUnnnmGVxcXIiOjsbW1pZvv/2WESNGsHfvXvV79Oabb6rXeHl5kZWVxUcffWRUZAHY2trecRz73TB5kSWEKJpXvnz5csLCwkoNXXfv3t2omGrevHmpxcBCCCGEytKuaFTpTlz+485GqaZshMZdbn+O5d3vJzplyhT1A/WSIzBV1c0JcxqNptybQTdo0ACNRsONGzeMji9dupQZM2awceNGVq5cyRtvvEF4eDi9e/e+536XJTMzUx25u1lZxR0UTRf09PS87X1fe+01XnvttfvSR4AtW7awbt06bty4oW6rtGjRIsLDw1m+fDmvvPJKmdf16tWLd955h7y8PKME8evXr6ujjhVBiiwhTEBRFLKzs9VPzq5fv85LL70EFP2i7tu3L6GhoYwZM+a2C2aFEEKIUjSaO5+2Z2F75+fdxVTAOzV48GDy8/PRaDSEhIT84/nt27ensLCQ/fv3q9MFExISSE1NLXXurl27ePTRR40eF4dqdOjQgWXLlpGVlaX+mxwbG4uZmRkeHh53/XosLS3R6/W3PcfKygpPT0+OHTvGoEGDjNq8vLzw8vLi1VdfpU+fPvz000+liqw6derg6upKbGwsAQEB6vHY2Fh69uxpdO6uXbvw9/cHUL9vxUVt9+7dCQsLo2XLllhY3FlpYIrpgsWjTjcvjzAzM7ttgXvo0CHq1atnVGAlJiaSm5tbKlzlfpIiS4hKoigK+/btIywsDJ1OR7du3fjf//4HFP1jMWXKFHx8fBg9evQtPzkSQgghaiJzc3N1+pq5ufk/nu/h4cHgwYN58sknWbx4MRYWFvz73/9WY+BL+uWXX/Dx8cHX15cff/yRPXv2sGTJEgDGjx/PnDlzmDhxIm+99RZXr17l2Wef5ZFHHrmn9f8tW7YkMjKSfv36YW1tbbRmqKSQkBBiYmLU1MSkpCS+/vprRo4ciaurKwkJCZw8edKoSCxp1qxZzJkzhzZt2tCtWzeWLl3KoUOHSiUtfvHFF7i7u9OhQwc+/fRTbty4wZQpU4CikIhvvvmGhx56SE1MPHXqFCtWrODbb78t88/jfkwXPHbsGPn5+Vy/fp2MjAy1aOvWrRsAe/bs4dFHHyUyMpKmTZvSp08f6tWrx8SJE5k9eza2trZ88803JCUlMWzYMADWrl1LcnIyvXv3xsbGhvDwcP7zn//w4osvGj13dHQ0rVu3Vte9VQQpsoSoQHq9ntjYWHQ6HTqdjvPnz6tt169fp7CwUP3UqPgXvhBCCFFp7BoU7YP1T/tk2TWo8K4UTwG7U0uXLuXxxx8nICCARo0a8e677xqtxyk2d+5cVqxYwbRp02jSpAk///yzOtXNzs6OTZs28dxzz9GjRw/s7OwIDQ3lk08+uafX8vHHH6sJ2U2bNuXMmTNlnvfYY4/h4+NDWloaTk5O2NnZcfz4cZYvX861a9do0qQJzzzzDE8++WSZ18+YMYO0tDReeOEFrly5gqenJ2vWrMHd3d3ovA8++IAPPviAQ4cO0bZtW9asWaOueyseDXv55ZcZNGgQeXl5tGjRgsGDB1doqNbQoUONgieKR5WKsxqys7NJSEigoKAAKNo/d+PGjbz++usEBgZSUFBAx44d+e233+jatStQNIL4xRdf8Pzzz6MoCm3btuWTTz7hiSeeMHrun3/+udSx+02j/FPqRC2Xnp6Ok5MTaWlp5f7hF2Lw4MFs2rRJfWxvb8+wYcPQarUMHToUR0dHE/ZOiPujoKCADRs2MHTo0FLrFIQQFSs3N5ekpCRatWpVai+gO5Z6/vb7YNk1qJCNiCuDRqNh1apVRvtcVTVjx46le/fuvPrqq/f93mfOnKFVq1YcPHhQHSGq7Y4ePUpgYCAnTpy45UbTt/u5utPaQEayhLgPcnJy2LRpE6tWrWLBggXqD23//v3Zs2cPI0eORKvVEhwcXOZUBiGEEMJk6rpV2yKqJvjoo49Yu3atqbtRa1y6dInvv//+lgXW/SJFlhB3KT09nfXr16PT6diwYYO6IDMkJISHH34YgGeffZYXXnhBPt0XQgghRJlatmzJs88+a+pu1BpBQUGV8jxSZAlRTseOHeOll14iPDyc/Px89Xjz5s3RarVGe2eU3HdDCCGEEJWrtq+KadmyZa3/HpiKFFlC/IMLFy6QmppKx44dgaKFuevXrweK0o1CQ0PRarWl9rMSQgghhBC1kxRZQpTh9OnTaiLgzp07CQkJYePGjQA0a9aMr7/+mn79+tGhQwcprIQQQgghhBEpsoT4y7Fjx9Q9rG7eYC83Nxe9Xq/uFVHRsZ9CCCGEEKL6kiJL1FqKohiNQj377LNs2bIFKNoIsX///mi1WkaPHo2rq6upuimEEEIIIaoZKbJEraLX69m5cydhYWH89ttv7Nixg8aNGwPw0EMPYWtrS2hoKCNGjFA36RNCCCGEEKI8pMgSNV5BQQHbtm0jLCyM1atXk5ycrLatXr2ap556CoDHH3+cxx9/3FTdFEIIIYQQNYSZqTsgREWKiYnBxcWFQYMG8dVXX5GcnIyTkxOPPPIIq1atYuLEiabuohBCCCGqsMjISDp06IBer//Hc5ctW0bdunUrvlM12JdffsmIESNM3Y17JkWWqDEyMjJYuXIl69atU495enqSmZmJi4sLU6dOZePGjVy5coXvv/+e0aNHY2tra8IeCyGEELXXpEmTGD16dKnj27ZtQ6PRkJqaWul9KstLL73EG2+8oYZf1QZxcXE89NBDuLm5YWtrS4cOHfjss8/+8boTJ04watQonJ2dqVOnDr6+vmzdulVtX7ZsGRqNpsyvK1euADBlyhQOHDhAdHR0hb2+yiDTBUW1du3aNdauXYtOp2Pz5s3k5eXRp08fhg8fDkD9+vXZv38/HTt2rFW/HIUQQoi7sfPiTj7Y8wGv9HyFPq59TN0dk4uJiSExMZHQ0FBTd6VS7d+/HxcXF3744Qfc3NzYsWMHU6dOxdzcnOnTp9/yuuHDh+Pu7s6WLVuwtbVl/vz5DB8+nMTERBo3bsy4ceMYPHiw0TWTJk0iNzcXFxcXAKysrHj44YdZsGABfn5+Ffo6K5KMZIlqaenSpQQHB9OoUSMmT57M2rVrycvLw93dnf79+2MwGNRzu3TpIgWWEEII8Q8UReGzA59xOu00nx34DEVRTN0lVUxMDH5+ftja2uLm5saMGTPIyspS2zUaDatXrza6pm7duixbtgyAM2fOoNFo0Ol0DBgwADs7O7p27crOnTtv+7wrVqwgODgYGxsb9VhcXBwDBgzA0dGROnXq4O3tzb59+255j8WLF9OmTRusrKzw8PDg//7v/4zaNRoNixcvZsiQIdja2tK6dWt+/fVXo3POnz/Pgw8+SN26dalfvz6jRo3izJkzt+37vZgyZQqfffYZAQEBtG7dmgkTJjB58mR0Ot0tr0lJSeHkyZO88sordOnSBXd3dz744AOys7M5cuQIALa2tjRu3Fj9Mjc3Z8uWLTz22GNG9xoxYgRr1qwhJyenwl5jRZMiS1QLf/75p9HjtWvXEhERgV6vp0uXLsydO5fDhw+TkJDAf/7zH8zM5K+2EEKI2klRFLILssv9tfXcVo5eOwrA0WtH2Xpua7mur6iiLDExkcGDBxMaGsoff/zBypUriYmJue2Iyq28/vrrvPjiixw6dIh27drx0EMPUVhYeMvzo6Oj8fHxMTo2fvx4mjVrxt69e9m/fz+vvPIKlpaWZV6/atUqnnvuOV544QWOHDnCk08+yeTJk42m0AG8+eabhIaGEhcXx/jx4/nXv/5FfHw8UBTgFRISgqOjI9HR0cTGxuLg4MDgwYPJz8+/Zd8dHBxu+1Uc/HWn0tLSqF+//i3bGzRogIeHB99//z1ZWVkUFhby1Vdf4eLigre3d5nXfP/999jZ2fHAAw8YHffx8aGwsJDdu3eXq49ViUwXFFVWfHw8Op2OsLAwDh48yMmTJ2nbti0ATz75JL1790ar1arHhBBCCAE5hTn0+qnXPd/nuW3Plev83Q/vxs7SrlzXrFu3DgcHB6NjNwdMvP/++4wfP55///vfALi7u7NgwQICAgJYvHix0SjTP3nxxRcZNmwYAHPnzqVjx46cOnWK9u3bl3n+2bNnS+2Vee7cOWbNmqVe4+7ufsvnmzdvHpMmTWLatGkAzJw5k127djFv3jwGDBignjd27Fg14fidd94hPDyczz//nEWLFrFy5UoMBgPffvutur/n0qVLqVu3Ltu2bWPQoEFlPvehQ4du+72oU6fObdtL2rFjBytXrmT9+vW3PEej0RAREcHo0aNxdHTEzMwMFxcXNm7cSL169cq8ZsmSJTz88MOl1sjb2dnh5OTE2bNn77iPVY0UWaLKUBSFgwcPqoXV8ePH1TYzMzN2796tFlQhISGEhISYqqtCCCGEuA8GDBjA4sWLjY7t3r2bCRMmqI/j4uL4448/+PHHH9VjiqJgMBhISkqiQ4cOd/x8Xbp0Uf+/SZMmAFy5cuWWRVZOTk6pIm7mzJk8/vjj/N///R9BQUGMHTuWNm3alHl9fHw8U6dONTrWr1+/UiESffr0KfW4uEiKi4vj1KlTODo6Gp2Tm5tLYmLiLV4p9+1D6CNHjjBq1CjmzJlzy4IOiv5MnnnmGVxcXIiOjsbW1pZvv/2WESNGsHfvXvX7XWznzp3Ex8eXmj5ZzNbWluzs7PvyGkxBiixRZWzYsEENrACwtLQkKCiI0NBQRo4cScOGDU3YOyGEEKJ6sLWwZffDdz7NSlEUJm+aTMKNBAzK32uazTRmeNTzYGnIUnUE5Z+et7zs7e1LFQM3LxHIzMzkySefZMaMGaWub968OVA0inLzdMWCgoJS55ec1lf8mkqu476Zs7MzN27cMDr21ltv8fDDD7N+/Xp+//135syZw4oVKxgzZswt73MvMjMz8fb2Nioyi93uvdHNI4Q3mzBhAl9++eVtzzl27BgDBw5k6tSpvPHGG7c9d8uWLaxbt44bN26oo2SLFi0iPDyc5cuX88orrxid/+2339KtW7dbTiW8fv16tX7vJ0WWqHQFBQVERUURFhaGh4cHzz1XNB1hwIABNGzYEH9/f7RaLcOGDcPJycnEvRVCCCGqF41GU65pe7EXYom/Hl/quEExEH89nkNXD9Gvab/72cVy6d69O8eOHbvtyEzDhg25dOmS+vjkyZP3ZRTEy8uLY8eOlTrerl072rVrx/PPP89DDz3E0qVLyyyyOnToQGxsrNG+nLGxsXh6ehqdt2vXLh599FGjx15eXkDR61+5ciUuLi7lmuJ3r9MFjx49SmBgIBMnTuS99977x+cr/n7fvC7ezMysVCGbmZnJ//73P95///0y75WYmEhubq76PaiOpMgSlSI3N5fw8HB0Oh1r1qzh+vXrAHTs2FEtsuzs7Lh48SIWFvLXUgghhKgMiqLw+cHP0aBBoXRwhQYNnx/8nL6ufe9oNKsivPzyy/Tu3Zvp06fz+OOPY29vz7FjxwgPD2fhwoUABAYGsnDhQvr06YNer+fll1++ZRhFeYSEhLB8+XL1cU5ODrNmzeKBBx6gVatW/Pnnn+zdu/eWEe+zZs3iwQcfxMvLi6CgIHXbmYiICKPzfvnlF3x8fPD19eXHH39kz549LFmyBCgK2vjoo48YNWoUb7/9Ns2aNePs2bPodDpeeuklmjVrVuZz38t0wSNHjhAYGEhISAgzZ87k8uXLAJibm6ujS3v27OHRRx8lMjKSpk2b0qdPH+rVq8fEiROZPXs2tra2fPPNNyQlJanr4IqtXLmSwsJCo2mhJUVHR9O6detbTsOsDiSCTVS4p59+moYNGzJy5EiWLVumDv8+8cQTzJs3z2h4XwosIYQQovIUGAq4nHW5zAILQEHhctZlCgylp95Vli5durB9+3ZOnDiBn58fXl5ezJ492yiQ4uOPP8bNzQ0/Pz8efvhhXnzxRezsyhfCUZbx48dz9OhREhISgKIi49q1azz66KO0a9eOBx98kCFDhjB37twyrx89ejSfffYZ8+bNo2PHjnz11VcsXbqU/v37G503d+5cVqxYQZcuXfj+++/5+eef1dEuOzs7oqKiaN68OVqtlg4dOvDYY4+Rm5tbrpGt8vj111+5evUqP/zwA02aNFG/evTooZ6TnZ1NQkKCOi3T2dmZjRs3kpmZSWBgID4+PsTExPDbb7/RtWtXo/svWbIErVZL3bp1y3z+n3/+mSeeeKJCXltl0ShVaROEKig9PR0nJyfS0tIq7C9yTXLjxg02bdrEuHHj1E+8Jk6cyPfff0/Tpk3RarWEhobi6+sre1cJUUMUFBSwYcMGhg4del8+ORZC3Lnc3FySkpJo1apVuVL2SrqcdZnruddv2V7fpj6N7RvfbRervVmzZpGens5XX31VIffXaDSsWrWK0aNHV8j9q5viaYonTpww2bKR2/1c3WltIMMG4p5dvnyZ3377jbCwMLZu3UphYSHt2rWje/fuQNEvp2nTptGjRw/Zv0oIIYSoYhrbN67VRdQ/ef3111m0aBEGg0Hex1SCS5cu8f3331f7dflSZIm7cvnyZVasWEFYWBixsbFGU/46d+5slMTTqVMnU3RRCCGEEOKe1a1bl9dee83U3ag1goKCTN2F+0KKLHHHCgoK1KlAR48e5fnnn1fbevbsiVarRavV3nZTPiGEEEII8TdZuVMzSZElbklRFOLi4tDpdOh0OoKDg/n0008B8Pf3Z/jw4QQHBzNmzBjc3NxM3FshhBBCCCGqBimyhBGDwcDu3bvVwur06dNqW25uLp988gkajQZLS0vWrl1rwp4KIYQQQghRNUmRJYz06dOHPXv2qI9tbGwYPHgwoaGhDB8+3GR7ZAghhBBCCFFdSJFVS+Xl5REREcHvv//O/Pnz1f2pevbsSXx8PCNGjECr1TJ48GDs7e1N3FshhBBCCCGqDymyapGsrCx+//13dDod69atIyMjA4CxY8cSEBAAwFtvvcW8efOwtrY2ZVeFEEIIIYSotqTIqgUOHDjAO++8w8aNG8nNzVWPu7q6otVqadSokXqsQYMGpuiiEEIIIYQQNYbsqFYDXblyhbNnz6qP9Xo9q1evJjc3l9atWzNr1ix27tzJ+fPn+fzzz2nfvr0JeyuEEEIIYRqRkZF06NABvV7/j+cuW7aMunXrVnynarAvv/ySESNGmLoblUKKrBri3LlzfPbZZwQEBNCkSRPefvtttc3Hx4cPPviAQ4cOcerUKT788EN69+4tu5YLIYQQwmQmTZqERqNRU4tbtWrFSy+9ZDTrBkCj0bB69Wr1cUFBAQ899BBNmzblyJEjRufm5eXRrVs3NBoNhw4d+v/27jwoqittA/hzu8PSyCYiQQZw11ETkMWghRiJKOigIIiDkrBFKm6JE2Zwi8tgmJosZlRAkVIGxHEhMSKMo44IgyxRQTGkEEoiJTETNkENyhJB+vvDj670dLOoDd3g86u6pX3vWd5zsbVfz7mne4xh/fr12LJlC8RisSqGNCA0NDTAw8MDFhYW0NHRgZWVFdauXYvGxsZu65WXl8PLywumpqYwNDTEzJkz8Z///Ed2PSkpSfbz/N+jrq4OABAaGoqioiLk5ub26Rg1AZcLDmDl5eWyrdYLCwvlrv3000+y3wuCgA0bNvR3eERERDQA3I2JBcQiDF+9WvHavn3Akw4Mf39tn/Tt4eGBxMREtLW14dq1awgKCoIgCPj000+Vlm9uboavry++//575OXlYfTo0XLX169fDwsLCxQXF/fYd15eHioqKuDr66uSsQwUIpEIXl5eiIqKwvDhw3Hr1i2sWbMG9+7dw9GjR7us5+npifHjxyMrKwsSiQS7d++Gp6cnKioqYG5ujt///vfw8PCQqxMcHIzW1laYmZkBALS1tbF8+XJER0fDxcWlT8epbpzKGMAWLVqETZs2obCwEIIgwMXFBbt27UJlZSXOnTun7vCIiIhoIBCLUB8d8zSh+pW7+/ahPjoGEPfdx0UdHR2Ym5vDysoK3t7ecHNzQ0ZGhtKyDx48wNy5c1FVVaU0wTp79izOnz+PnTt39qrv48ePY+7cudDV1ZWdKy4uhqurKwwMDGBoaAgHBwdcvXq1yzbi4uIwduxYaGtrY+LEiTh8+LDcdUEQEBcXh/nz50MikWDMmDE4ceKEXJkff/wRS5cuhbGxMUxMTODl5YXKyspejeF5DB06FKtWrYKjoyNGjhyJOXPmYPXq1d3OLtXX1+P777/Hxo0bYWNjg/Hjx+OTTz5Bc3OzbDZRIpHA3NxcdojFYmRlZeHdd9+Va2vhwoVIT09HS0tLn41REzDJGkAuXLggN4Xu7++PefPmYf/+/aiurkZOTg7+8Ic/YOTIkWqMkoiIiNRJKpWio7m518ew4GAMW7US9dExqNuzBx3Nzajbswf10TEYtmolhgUH96odqVT6QnGXlJTgm2++gba2tsK1mpoa2U7IFy9ehLm5udz12tpahIWF4fDhw9DT0+tVf7m5uXB0dJQ7FxAQAEtLSxQWFuLatWvYuHEjtLS0lNZPTU3FunXr8Mc//hElJSV47733EBISIreEDgC2bt0KX19fFBcXIyAgAP7+/igrKwPwdOmju7s7DAwMkJubi/z8fOjr68PDwwOPHz/uMnZ9ff1uj5UrV/bqHgBAVVUVTp48Kbu/ygwbNgwTJ05EcnIympqa0N7ejvj4eJiZmcHBwUFpneTkZOjp6WHJkiVy5x0dHdHe3o4rV670OsaBiMsFBxAnJyfk5ORg3rx5AJ5ut05ERET0a9KWFty0V/7BtycNcfvRELe/y9fdmVh0DUIvE5xOp0+fhr6+Ptrb2/HLL79AJBIhNjZWody6deswZswYZGRkKCRRUqkUwcHBWLlyJRwdHXs9C/TDDz/AwsJC7tydO3cQEREh2xRs/PjxXdbfuXMngoODsfr/l1mGh4fj8uXL2LlzJ1xdXWXl/Pz8sGLFCgDAxx9/jIyMDMTExGDfvn1ISUlBR0cHDh48CEEQAACJiYkwNjZGdna27DPf/+rpeTNDQ8PuBw9g2bJlSEtLQ0tLCxYuXIiDBw92WVYQBFy4cAHe3t4wMDCASCSCmZkZzp07h6FDhyqtk5CQgOXLl0Mikcid19PTg5GRkdwmbYMRZ7IGEAMDA8yePVvdYRARERGphKurK7799ltcuXIFQUFBCAkJUfqMlKenJ8rLyxEfH69wLSYmBg8fPsSmTZueqe+Wlha5pYLA00RpxYoVcHNzwyeffIKKioou65eVlcHZ2VnunLOzs2yWqtOMGTMUXneWKS4uxq1bt2BgYCCbhTIxMUFra2u3fY8bN67bo/MZqO7s2rULRUVFSEtLQ0VFBcLDw7ssK5VKsWbNGpiZmSE3NxcFBQXw9vbGwoULUV1drVD+0qVLKCsrU1gq2EkikaC5ubnHGAcyzmQNMMqm0ImIiIg6CRIJJhZde+Z69QcOoCFuPwQtLUjb2jBs1UqYhoU9U7/PasiQIRg3bhwA4O9//ztsbW2RkJCg8OH8nXfewaJFixAaGgqpVCqXEGRlZeHSpUvQ0dGRq+Po6IiAgAAcOnRIad+mpqa4f/++3Lk///nPWL58Of71r3/h7Nmz2L59O44fP47Fixc/89h649GjR3BwcMCRI0cUrg0fPrzLevr6+t22+/bbb2P//u5nIDufnfrtb38LExMTuLi4YOvWrRgxYoRC2aysLJw+fRr379+XzZLt27cPGRkZOHToEDZu3ChX/uDBg5g6dWqXSwnv3bvX7fgGAyZZRERERIOIIAjPvGzv7r59aIjbD9MP3sfw1atlm14IWlpKdx3sCyKRCJs3b0Z4eLjSZWZBQUEQiUQICQlBR0cH/vSnPwEAoqOjERUVJStXVVUFd3d3pKSkwMnJqcv+7OzsUFpaqnB+woQJmDBhAj788EMsW7YMiYmJSpOsSZMmIT8/H0FBQbJz+fn5mDx5sly5y5cvIzAwUO61nZ0dAMDe3h4pKSkwMzPr1RK/TqpYLvhrHR0dAJ5uga9M56zT/379j0gkktXt9OjRI3z55Zf461//qrStiooKtLa2yu7BYMUki4iIiOgl1plQdSZYAGS/1kfHyL3ua35+foiIiMDevXtlSdSvvfPOOxCJRAgKCoJUKkVERASsra3lynTO8owdOxaWlpZd9uXu7i43y9XS0oKIiAgsWbIEo0ePxn//+18UFhZ2ucV7REQEli5dCjs7O7i5ueGf//wnTp48iQsXLsiV++qrr+Do6IiZM2fiyJEjKCgoQEJCAoCnG218/vnn8PLywo4dO2BpaYkffvgBJ0+exPr167uMv3P273mcOXMGtbW1mDZtGvT19XHjxg1ERETA2dkZo0aNAgAUFBQgMDAQmZmZ+M1vfoMZM2Zg6NChCAoKwrZt2yCRSHDgwAHcvn0bv/vd7+TaT0lJQXt7O95++22l/efm5mLMmDEYO3bsc49hIOAzWUREREQvsycdcglWp+GrV8P0g/eBJx1dVFS9V155BWvXrsVnn32GpqYmpWUCAgJw+PBhbNq0qcvv0+qNgIAA3LhxAzdv3gQAiMViNDQ0IDAwEBMmTMDSpUsxf/58REZGKq3v7e2NPXv2YOfOnZgyZQri4+ORmJio8Px8ZGQkjh8/DhsbGyQnJ+PYsWOy2S49PT3k5OTA2toaPj4+mDRpEt599120trY+82xUb3UmSDNnzsSkSZPw4YcfYtGiRTh9+rSsTHNzM27evIm2tjYAT5dWnjt3Do8ePcJbb70FR0dH5OXlIS0tDba2tnLtJyQkwMfHB8bGxkr7P3bsGMKeYRnqQCVIX3S/zUGusbERRkZG+Pnnn/vsDzsR0UDW1taGM2fOYMGCBV1udUxEfaO1tRW3b9/G6NGjFTZxoJ5FRESgsbFR6YYaqiAIAlJTU+Ht7d0n7Q80N27cwFtvvYXy8nIYGRmpO5wudfe+6m1uwJksIiIiInopffTRRxg5cqTCc0XUN6qrq5GcnKzRCZaq8JksIiIiInopGRsbY/PmzeoO46Xh5uam7hD6DZMsIiIiIqI+wKdyXl5cLkhERERERKRCTLKIiIiIBjjOmBCpjireT0yyiIiIiAaozh09O78sloheXOf76UV2zOUzWUREREQDlFgshrGxMerq6gA8/d4lQRDUHBXRwCSVStHc3Iy6ujoYGxtDLBY/d1tMsoiIiIgGMHNzcwCQJVpE9GKMjY1l76vnxSSLiIiIaAATBAEjRoyAmZkZ2tra1B0O0YCmpaX1QjNYnZhkEREREQ0CYrFYJR8OiejFceMLIiIiIiIiFWKSRUREREREpEJMsoiIiIiIiFSIz2T1oPPLyBobG9UcCRGRZmpra0NzczMaGxtf6DtFiIiINF1nTtDTFxYzyerBw4cPAQBWVlZqjoSIiIiIiDTBw4cPYWRk1OV1QdpTGvaS6+joQFVVFQwMDPrsy/2mTZuGwsLCPml7MBns92kgj0+TY9eU2NQVR3/029jYCCsrK/z4448wNDTs076I+oqm/F1Biviz6dlgv0eaND6pVIqHDx/CwsICIlHXT15xJqsHIpEIlpaWfdqHWCzmB5NeGOz3aSCPT5Nj15TY1BVHf/ZraGioEfea6Hloyt8VpIg/m54N9nukaePrbgarEze+0ABr1qxRdwgDwmC/TwN5fJocu6bEpq44NGX8RJqO7xXNxZ9Nzwb7PRqI4+NyQSIieiGNjY0wMjLCzz//rFH/00hERKQunMkiIqIXoqOjg+3bt0NHR0fdoRAREWkEzmQRERERERGpEGeyiIiIiIiIVIhJFhERERERkQoxySIiIiIiIlIhJllEREREREQqxCSLiIiIiIhIhZhkERFRv1q8eDGGDh2KJUuWqDsUIiKiPsEki4iI+tW6deuQnJys7jCIiIj6DJMsIiLqV7Nnz4aBgYG6wyAiIuozTLKIiEgmJycHCxcuhIWFBQRBwKlTpxTK7N27F6NGjYKuri6cnJxQUFDQ/4ESERFpMCZZREQk09TUBFtbW+zdu1fp9ZSUFISHh2P79u0oKiqCra0t3N3dUVdXJyszdepUvPbaawpHVVVVfw2DiIhIrQSpVCpVdxBERKR5BEFAamoqvL29ZeecnJwwbdo0xMbGAgA6OjpgZWWF999/Hxs3bux129nZ2YiNjcWJEydUHTYREZHacSaLiIh65fHjx7h27Rrc3Nxk50QiEdzc3HDp0iU1RkZERKRZmGQREVGv1NfX48mTJ3j11Vflzr/66quoqanpdTtubm7w8/PDmTNnYGlpyQSNiIgGnVfUHQAREb1cLly4oO4QiIiI+hRnsoiIqFdMTU0hFotRW1srd762thbm5uZqioqIiEjzMMkiIqJe0dbWhoODAzIzM2XnOjo6kJmZiRkzZqgxMiIiIs3C5YJERCTz6NEj3Lp1S/b69u3b+Pbbb2FiYgJra2uEh4cjKCgIjo6OeOONN7B79240NTUhJCREjVETERFpFm7hTkREMtnZ2XB1dVU4HxQUhKSkJABAbGwsPv/8c9TU1GDq1KmIjo6Gk5NTP0dKRESkuZhkERERERERqRCfySIiIiIiIlIhJllEREREREQqxCSLiIiIiIhIhZhkERERERERqRCTLCIiIiIiIhVikkVERERERKRCTLKIiIiIiIhUiEkWERERERGRCjHJIiIi6qXg4GB4e3v3eT+zZs3C0aNHZa8FQcCpU6e6LF9aWgpLS0s0NTX1eWxERNQzJllERKRWd+/exapVq2BtbQ0dHR2Ym5vD3d0d+fn5sjI9JRn9Zc+ePUhKSurTPtLT01FbWwt/f/9e15k8eTKmT5+Ov/3tb30YGRER9RaTLCIiUitfX19cv34dhw4dQnl5OdLT0zF79mw0NDSoOzQFRkZGMDY27tM+oqOjERISApHo2f6JDgkJQVxcHNrb2/soMiIi6i0mWUREpDYPHjxAbm4uPv30U7i6umLkyJF44403sGnTJixatAgAMGrUKADA4sWLIQiC7DUApKWlwd7eHrq6uhgzZgwiIyPlkgxBEBAXF4f58+dDIpFgzJgxOHHiRLcxnThxAq+//jokEgmGDRsGNzc32TK8Xy8XrKyshCAICsfs2bNlbeXl5cHFxQUSiQRWVlb44IMPul3Sd/fuXWRlZWHhwoUK1+rr67F48WLo6elh/PjxSE9Pl7s+d+5c3Lt3DxcvXux2fERE1PeYZBERkdro6+tDX18fp06dwi+//KK0TGFhIQAgMTER1dXVste5ubkIDAzEunXrUFpaivj4eCQlJeEvf/mLXP2tW7fC19cXxcXFCAgIgL+/P8rKypT2VV1djWXLliE0NBRlZWXIzs6Gj48PpFKpQlkrKytUV1fLjuvXr2PYsGGYNWsWAKCiogIeHh7w9fXFd999h5SUFOTl5WHt2rVd3o+8vDzo6elh0qRJCtciIyOxdOlSfPfdd1iwYAECAgJw79492XVtbW1MnToVubm5XbZPRET9Q5Aq+5eDiIion3z99dcICwtDS0sL7O3t8eabb8Lf3x82NjayMoIgIDU1VW7TCTc3N8yZMwebNm2SnfvHP/6B9evXo6qqSlZv5cqViIuLk5WZPn067O3tsW/fPoVYioqK4ODggMrKSowcOVLhenBwMB48eKDwfFhraytmz56N4cOHIy0tDSKRCCtWrIBYLEZ8fLysXF5eHt588000NTVBV1dXof3du3cjJiYGFRUVcucFQcCWLVvw8ccfAwCampqgr6+Ps2fPwsPDQ1bOx8cHRkZGSExMVGibiIj6D2eyiIhIrXx9fVFVVYX09HR4eHggOzsb9vb2PW4wUVxcjB07dshmw/T19REWFobq6mo0NzfLys2YMUOu3owZM7qcybK1tcWcOXPw+uuvw8/PDwcOHMD9+/d7HENoaCgePnyIo0ePyp6lKi4uRlJSklx87u7u6OjowO3bt5W209LSojT5AiCXdA4ZMgSGhoaoq6uTKyORSOTGTkRE6vGKugMgIiLS1dXF3LlzMXfuXGzduhUrVqzA9u3bERwc3GWdR48eITIyEj4+Pkrbex5isRgZGRn45ptvcP78ecTExOCjjz7ClStXMHr0aKV1oqKi8O9//xsFBQUwMDCQi++9997DBx98oFDH2tpaaVumpqZdJnVaWlpyrwVBQEdHh9y5e/fuYezYsd2OkYiI+h5nsoiISONMnjxZboMILS0tPHnyRK6Mvb09bt68iXHjxikcv96Z7/Lly3L1Ll++rPSZp06CIMDZ2RmRkZG4fv06tLW1kZqaqrTs119/jR07duDLL79USG7s7e1RWlqqND5tbW2l7dnZ2aGmpqZXs2fKlJSUwM7O7rnqEhGR6nAmi4iI1KahoQF+fn4IDQ2FjY0NDAwMcPXqVXz22Wfw8vKSlRs1ahQyMzPh7OwMHR0dDB06FNu2bYOnpyesra2xZMkSiEQiFBcXo6SkBFFRUbK6X331FRwdHTFz5kwcOXIEBQUFSEhIUBrPlStXkJmZiXnz5sHMzAxXrlzB3bt3lSZlJSUlCAwMxIYNGzBlyhTU1NQAeLoBhYmJCTZs2IDp06dj7dq1WLFiBYYMGYLS0lJkZGQgNjZWaf92dnYwNTVFfn4+PD09n+leVlZW4qeffoKbm9sz1SMiItXjTBYREamNvr4+nJycsGvXLsyaNQuvvfYatm7dirCwMLlE5IsvvkBGRgasrKxkMzXu7u44ffo0zp8/j2nTpmH69OnYtWuXwoYVkZGROH78OGxsbJCcnIxjx45h8uTJSuMxNDRETk4OFixYgAkTJmDLli344osvMH/+fIWyV69eRXNzM6KiojBixAjZ0bl80cbGBhcvXkR5eTlcXFxgZ2eHbdu2wcLCosv7IRaLERISgiNHjjzzvTx27BjmzZundMMOIiLqX9xdkIiIBi1luxJqupqaGkyZMgVFRUW9TpgeP36M8ePH4+jRo3B2du7jCImIqCecySIiItIg5ubmSEhIwJ07d3pd586dO9i8eTMTLCIiDcFnsoiIiDTMs868dW6oQUREmoFJFhERDVpcEU9EROrA5YJEREREREQqxCSLiIiIiIhIhZhkERERERERqRCTLCIiIiIiIhVikkVERERERKRCTLKIiIiIiIhUiEkWERERERGRCjHJIiIiIiIiUiEmWURERERERCr0f7fDv48Y2ptJAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "*** ERRORS FOR h = 0.03125 ***\n", "Euler: 1.11426e+02\n", "Midpoint: 1.21982e+00\n", "Heun: 9.52017e-03\n", "RK4: 5.94392e-05\n" ] } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "def euler_method(f, t0, y0, t_final, h):\n", " t_vals = np.arange(t0, t_final + h, h)\n", " num_vals = np.zeros(len(t_vals))\n", " num_vals[0] = y0\n", " for j in range(len(t_vals) - 1):\n", " num_vals[j + 1] = num_vals[j] + h * f(t_vals[j], num_vals[j])\n", " return t_vals, num_vals\n", "\n", "def midpoint_method(f, t0, y0, t_final, h):\n", " t_vals = np.arange(t0, t_final + h, h)\n", " num_vals = np.zeros(len(t_vals))\n", " num_vals[0] = y0\n", " for j in range(len(t_vals) - 1):\n", " u = num_vals[j] + (h / 2) * f(t_vals[j], num_vals[j])\n", " num_vals[j + 1] = num_vals[j] + h * f(t_vals[j] + h / 2, u)\n", " return t_vals, num_vals\n", "\n", "def heun_method(f, t0, y0, t_final, h):\n", " t_vals = np.arange(t0, t_final + h, h)\n", " num_vals = np.zeros(len(t_vals))\n", " num_vals[0] = y0\n", " for j in range(len(t_vals) - 1):\n", " u2 = num_vals[j] + (h / 3) * f(t_vals[j], num_vals[j])\n", " u3 = num_vals[j] + (2 * h / 3) * f(t_vals[j] + h / 3, u2)\n", " num_vals[j + 1] = num_vals[j] + h * (1 / 4 * f(t_vals[j], num_vals[j]) + 3 / 4 * f(t_vals[j] + 2 * h / 3, u3))\n", " return t_vals, num_vals\n", "\n", "def rk4_method(f, t0, y0, t_final, h):\n", " t_vals = np.arange(t0, t_final + h, h)\n", " num_vals = np.zeros(len(t_vals))\n", " num_vals[0] = y0\n", " for j in range(len(t_vals) - 1):\n", " k1 = f(t_vals[j], num_vals[j])\n", " k2 = f(t_vals[j] + h / 2, num_vals[j] + h / 2 * k1)\n", " k3 = f(t_vals[j] + h / 2, num_vals[j] + h / 2 * k2)\n", " k4 = f(t_vals[j] + h, num_vals[j] + h * k3)\n", " num_vals[j + 1] = num_vals[j] + h * (k1 + 2 * k2 + 2 * k3 + k4) / 6\n", " return t_vals, num_vals\n", "\n", "# Parameters\n", "t0 = 0\n", "t_final = 7\n", "y0 = 1\n", "h = 5e-1\n", "\n", "# Define the ODE y' = y\n", "f = lambda t, y: y\n", "\n", "# Exact solution\n", "def exact_solution(t):\n", " return np.exp(t)\n", "\n", "# Compute numerical solutions\n", "t_vals = np.arange(t0, t_final + h, h)\n", "t_vals, euler_vals = euler_method(f, t0, y0, t_final, h)\n", "t_vals, midpoint_vals = midpoint_method(f, t0, y0, t_final, h)\n", "t_vals, heun_vals = heun_method(f, t0, y0, t_final, h)\n", "t_vals, rk4_vals = rk4_method(f, t0, y0, t_final, h)\n", "\n", "\n", "# Plot numerical solutions and exact solution\n", "plt.figure(figsize=(10, 6))\n", "plt.plot(t_vals, exact_solution(t_vals), '--', label=\"Exact solution\", color=\"black\", linewidth=2)\n", "plt.plot(t_vals, euler_vals, 'o-', label=\"Euler\", color=\"red\")\n", "plt.plot(t_vals, midpoint_vals, 'x-', label=\"Midpoint\", color=\"green\")\n", "plt.plot(t_vals, heun_vals, '^-', label=\"Heun\", color=\"blue\")\n", "plt.plot(t_vals, rk4_vals, 's-', label=\"RK4\", color=\"magenta\")\n", "\n", "plt.xlabel(\"Time (t)\")\n", "plt.ylabel(\"y(t)\")\n", "plt.title(\"Comparison of various numerical solutions with exact solution\")\n", "plt.legend()\n", "plt.grid()\n", "plt.show()\n", "\n", "# Error analysis\n", "h_values = [h, h/2, h/4, h/8, h/16]\n", "errors_euler, errors_midpoint, errors_heun, errors_rk4 = [], [], [], []\n", "\n", "for h_val in h_values:\n", " t_vals = np.arange(t0, t_final + h_val, h_val)\n", " exact_vals = exact_solution(t_vals)\n", " \n", " _, euler_vals = euler_method(f, t0, y0, t_final, h_val)\n", " _, midpoint_vals = midpoint_method(f, t0, y0, t_final, h_val)\n", " _, heun_vals = heun_method(f, t0, y0, t_final, h_val)\n", " _, rk4_vals = rk4_method(f, t0, y0, t_final, h_val)\n", " \n", " errors_euler.append(np.max(np.abs(euler_vals - exact_vals)))\n", " errors_midpoint.append(np.max(np.abs(midpoint_vals - exact_vals)))\n", " errors_heun.append(np.max(np.abs(heun_vals - exact_vals)))\n", " errors_rk4.append(np.max(np.abs(rk4_vals - exact_vals)))\n", "\n", "# Plot errors\n", "plt.figure(figsize=(10, 6))\n", "plt.loglog(h_values, [h**1 for h in h_values], 'k--', label='Slope 1, 2, 3 & 4')\n", "plt.loglog(h_values, [h**2 for h in h_values], 'k--')\n", "plt.loglog(h_values, [h**3 for h in h_values], 'k--')\n", "plt.loglog(h_values, [h**4 for h in h_values], 'k--')\n", "\n", "slope_euler = np.polyfit(np.log(h_values), np.log(errors_euler), 1)\n", "slope_midpoint = np.polyfit(np.log(h_values), np.log(errors_midpoint), 1)\n", "slope_heun = np.polyfit(np.log(h_values), np.log(errors_heun), 1)\n", "slope_rk4 = np.polyfit(np.log(h_values), np.log(errors_rk4), 1)\n", "\n", "plt.loglog(h_values, errors_euler, 'o-', label='Euler (slope = {:.2f})'.format(slope_euler[0]))\n", "plt.loglog(h_values, errors_midpoint, 's-', label='Midpoint (slope = {:.2f})'.format(slope_midpoint[0]))\n", "plt.loglog(h_values, errors_heun, '^-', label=\"Heun (slope = {:.2f})\".format(slope_heun[0]))\n", "plt.loglog(h_values, errors_rk4, 'x-', label='RK4 (slope = {:.2f})'.format(slope_rk4[0]))\n", "plt.xlabel(\"Step size (h)\")\n", "plt.ylabel(\"Maximum error\")\n", "plt.title(\"Convergence analysis of various numerical schemes (log-log scale)\")\n", "plt.legend()\n", "plt.grid()\n", "plt.show()\n", "\n", "# Print errors for the smallest step size\n", "print(f\"*** ERRORS FOR h = {h_values[-1]} ***\")\n", "print(f\"Euler: {errors_euler[-1]:.5e}\")\n", "print(f\"Midpoint: {errors_midpoint[-1]:.5e}\")\n", "print(f\"Heun: {errors_heun[-1]:.5e}\")\n", "print(f\"RK4: {errors_rk4[-1]:.5e}\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Thanks to our convergence analysis, we can numerically verify that Euler's method is of order 1, the Midpoint scheme is of order 2, Heun's method is of order 3, and the Runge-Kutta method is of order 4 (the theoretical proofs being studied in tutorial classes)." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.16" } }, "nbformat": 4, "nbformat_minor": 2 }