{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Algoritmusok Python nyelven\n", "\n", "## 10. Előadás: SciPy Numerikus módszerek \n", "\n", "### 2020. április 23." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Tudományos csomagok (Python Scientific stack)\n", "| csomag | |\n", "| --- | --- |\n", "| NumPy | Hatékony N-dimenziós tömb |\n", "| **SciPy** | **Numerikus számítások** |\n", "| Matplotlib | Grafikonok és rajzok |\n", "| IPython (Jupyter) | Interaktív notebook |\n", "| SymPy | Szimbolikus számítások |\n", "| Pandas | Adatbányászat |" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import sympy as sym\n", "import math\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Numerikus módszerek \n", "A numerikus számítások célja, hogy a matematikai számításokat végezzünk hatékonyan.\n", "\n", "Előnyök:\n", " - Gyors\n", " - Hasznos\n", " - Sok helyzetben alakalmazható\n", " \n", "Hátrányok:\n", " - Csak közelítő eredményt ad \n", " - Emiatt figyelni kell a hiábkra \n", " - A matematikai intuíciónkat hátráltatja elméleti kérdésekben (pl felismernéd, hogy ez melyik algebrai szám közelítése? 2.732050807568877)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## SciPy\n", "Részletes tutorial: https://docs.scipy.org/doc/scipy/reference/tutorial/\n", "\n", "A háttérben sokszor Fortran fut. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Alcsomagok:\n", "\n", "|||\n", "| --- | --- |\n", "| scipy.cluster\t| Vector quantization / Kmeans |\n", "| scipy.constants |\tPhysical and mathematical constants |\n", "|scipy.fftpack |\tFourier transform\n", "|scipy.integrate |\tIntegration routines\n", "|scipy.interpolate |\tInterpolation\n", "|scipy.io |\tData input and output\n", "|scipy.linalg |\tLinear algebra routines\n", "|scipy.ndimage |\tn-dimensional image package\n", "|scipy.odr |\tOrthogonal distance regression\n", "|scipy.optimize |\tOptimization\n", "|scipy.signal |\tSignal processing\n", "|scipy.sparse |\tSparse matrices\n", "|scipy.spatial |\tSpatial data structures and algorithms\n", "|scipy.special |\tAny special mathematical functions\n", "|scipy.stats |\tStatistics|\n", "\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "from scipy import linalg, optimize" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Lineáris algebra\n", "LU felbontás" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[2 5 8 7]\n", " [5 2 2 8]\n", " [7 5 6 6]\n", " [5 4 4 8]]\n", "[[0. 1. 0. 0.]\n", " [0. 0. 0. 1.]\n", " [1. 0. 0. 0.]\n", " [0. 0. 1. 0.]]\n", "[[ 1. 0. 0. 0. ]\n", " [ 0.28571429 1. 0. 0. ]\n", " [ 0.71428571 0.12 1. 0. ]\n", " [ 0.71428571 -0.44 -0.46153846 1. ]]\n", "[[ 7. 5. 6. 6. ]\n", " [ 0. 3.57142857 6.28571429 5.28571429]\n", " [ 0. 0. -1.04 3.08 ]\n", " [ 0. 0. 0. 7.46153846]]\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from scipy.linalg import lu\n", "A = np.array([[2, 5, 8, 7], [5, 2, 2, 8], [7, 5, 6, 6], [5, 4, 4, 8]])\n", "p, l, u = lu(A)\n", "print(A,p,l,u, sep=\"\\n\")\n", "np.allclose(A - p @ l @ u, np.zeros((4, 4)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "QR felbontás\n", "Q ortogonális, R felső háromszög" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0.26353773 0.86973603 -0.18084589 -0.9486353 ]\n", " [ 1.07413653 1.3322248 -1.56374712 0.14971633]\n", " [ 0.04096525 -0.49581744 0.30208855 0.87311366]\n", " [-1.44991248 -0.46878984 1.11244664 -1.83082867]]\n", "[[-0.14447972 -0.58402801 0.79582087 0.06860053]\n", " [-0.58887562 -0.49664755 -0.50494596 0.38935369]\n", " [-0.02245845 0.44642683 0.24949115 0.85904183]\n", " [ 0.79488788 -0.4614711 -0.22238005 0.32518426]]\n", "[[-1.82404654 -1.27167399 1.82446702 -1.42601803]\n", " [ 0. -1.17460964 0.50374871 1.71432922]\n", " [ 0. 0. 0.47366933 -0.20556853]\n", " [ 0. 0. 0. 0.14790021]]\n" ] } ], "source": [ "A = np.random.randn(4, 4)\n", "print(A)\n", "q, r = linalg.qr(A)\n", "print(q,r,sep='\\n')" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 1.00000000e+00, -3.97395674e-16, -1.86832824e-17,\n", " 2.58480705e-16],\n", " [-3.97395674e-16, 1.00000000e+00, 2.42618836e-17,\n", " 1.38003999e-16],\n", " [-1.86832824e-17, 2.42618836e-17, 1.00000000e+00,\n", " 1.45979610e-17],\n", " [ 2.58480705e-16, 1.38003999e-16, 1.45979610e-17,\n", " 1.00000000e+00]])" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "q @ q.T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Integrálás" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " A `scipy.integrate.quad(f, a, b)` integrálja a-tól b-ig az f függvényt. Két értékkel tér vissza, az inregrálás eredményével és egy hibahatárral." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(1.0, 1.1102230246251565e-14)\n" ] } ], "source": [ "import scipy.integrate\n", "f= lambda x:2*x\n", "i = scipy.integrate.quad(f, 0, 1)\n", "print(i)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(0.7468241328124271, 8.291413475940725e-15)\n" ] } ], "source": [ "f= lambda x:np.exp(-x**2)\n", "i = scipy.integrate.quad(f, 0, 1)\n", "print(i)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{\\sqrt{\\pi} \\operatorname{erf}{\\left(x \\right)}}{2}$" ], "text/plain": [ "sqrt(pi)*erf(x)/2" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "## szimbolikus számítással\n", "xval = sym.Symbol('x')\n", "sym.integrate(sym.exp(-xval ** 2), xval)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle 0.746824132812427$" ], "text/plain": [ "0.746824132812427" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "((sym.erf(1)-sym.erf(0))*np.pi**(1/2)/2).evalf()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Próbáljunk ki egy ronda függvényt" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "#sym.integrate(sym.exp(sym.sin(-sym.log(xval ** 2+xval)-xval)), xval)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(1.1008683826459191, 9.950209101106111e-09)\n" ] } ], "source": [ "f= lambda x:np.exp(np.sin(-np.log(x ** 2+x)-x))\n", "i = scipy.integrate.quad(f, 0, 1)\n", "print(i)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Több változóban is tudunk integrálni a ` scipy.integrate.dblquad(func, a, b, gfun, hfun)` paranccsal. A gfun és hfun parancsok adják meg a belső integrál határait. \n", "\n", "\n", "$$\\int_{0}^{1/2} \\big( \\int_{0}^{\\sqrt{1-4y^2}} 16xy \\:dx\\big)dy$$\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(0.5, 1.7092350012594845e-14)\n" ] } ], "source": [ "f = lambda x, y : 16*x*y\n", "g = lambda x : 0\n", "h = lambda y : math.sqrt(1-4*y**2)\n", "i = scipy.integrate.dblquad(f, 0, 0.5, g, h)\n", "print(i)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interpoláció\n" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0. 0.36363636 0.72727273 1.09090909 1.45454545 1.81818182\n", " 2.18181818 2.54545455 2.90909091 3.27272727 3.63636364 4. ] [-0.65364362 -0.61966189 -0.51077021 -0.31047698 -0.00715476 0.37976236\n", " 0.76715099 0.99239518 0.85886263 0.27994201 -0.52586509 -0.99582185]\n" ] } ], "source": [ "from scipy import interpolate\n", "\n", "x = np.linspace(0, 4, 12)\n", "y = np.cos(x**2/3+4)\n", "print (x,y)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure, axis = plt.subplots(1, 1,figsize=(5,5))\n", "axis.plot(x, y,'o')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "f1 = interpolate.interp1d(x, y,kind = 'linear')\n", "\n", "f2 = interpolate.interp1d(x, y, kind = 'cubic')" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "xnew = np.linspace(0, 4,30)\n", "\n", "#plt.plot(x, y, 'o', xnew, f(xnew), '-', xnew, f2(xnew), '--')\n", "figure, axis = plt.subplots(1, 1,figsize=(5,5))\n", "axis.plot(x, y, 'o')\n", "axis.plot( xnew, f1(xnew), '-')\n", "axis.plot( xnew, f2(xnew), '--')\n", "\n", "axis.legend(['data', 'linear', 'cubic'], loc = 'best')\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUQAAAEvCAYAAAA92bhfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAXYklEQVR4nO3df4zc913n8eebpU0Pu6V32OGa2MYRNadGBSXpykYCcUH5ZUdRfEW0xL2KcBQsEOE3J8I1SjhHRYFI4doqKpi2asuPhNCWw/icS0G0gjuR1Os2lCYhxQ0t2aYi7s+jjUzZ7fv+mO9mx+OZ8aznM/Od73eeD2k1OzOf7Pfjdva138/vyEwkSfANdVdAkmaFgShJFQNRkioGoiRVDERJqhiIklT5xrorMMiWLVty586ddVdDUsucOHHic5m5td97MxuIO3fuZGlpqe5qSGqZiPj0oPdsMktSxUCUpIqBKEkVA1GSKgaiJFUMREmqGIiSVJnZeYjShq2uwoMPwkc/CpdfDvv2wcJC3bVSgxiIaofVVbjuOnjkEfjqV2HTJtizBx56yFDUyGwyqx0efLAThl/5CmR2Hh95pPO6NCIDUe3w0Y927gy7ffWr8Oij9dRHjWQgqh0uv7zTTO62aRNcdlk99VEjGYhqh337On2GmzdDROdxz57O69KIHFRROywsdAZQHnyw00y+7DJHmbVhBqLaY2EBbrih8yWdB5vMklQxECWpYiBKUsVAlKSKgShJFQNRkioGoiRVDERJqjgxW83jvoeaEANRzeK+h5ogm8xqFvc91AQVCcSIeGdEPBsRHx/wfkTEWyLiZER8LCKuKHFdzSH3PdQElbpDfBewd8j7+4Bd1ddB4G2Frqt5476HmqAigZiZfwl8YUiR/cB7suNh4KUR8bIS19accd9DTdC0BlUuBp7uer5cvfbZKV1fbeG+h5qgaQVi9HktzyoUcZBOk5odO3ZMuk5qKvc91IRMa5R5Gdje9Xwb8Exvocw8nJmLmbm4devWKVVNkjqmFYhHgB+uRpu/G/hyZtpcljRTijSZI+I+4EpgS0QsA3cALwDIzN8CjgHXAyeB54D/UuK6klRSkUDMzAPneD+BnypxLUmaFFeqSFLFQJSkips7qN3G2RnHXXXmjoGo9hpnZxx31ZlLNpnVXuPsjOOuOnPJQFR7jbMzjrvqzCUDUe01zs447qozlwxEtdc4O+O4q85cclBF7TXOzjjuqjOXorOIZPYsLi7m0tJS3dWQ1DIRcSIzF/u9Z5NZkioGoiRV7EPU/HEFigYwEDVfXIGiIWwya764AkVDGIiaL65A0RAGouaLK1A0hIGo+eIKFA3hoIrmiytQNISBqPnjuc4awCazJFUMREmqGIiSVDEQJaliIEpSxUCUpIqBKEkVA1GSKgaiJFVcqaLZ5maumqIigRgRe4E3AwvA2zPzrp73dwDvBl5albk1M4+VuLZazM1cNWVjB2JELAD3AtcAy8DxiDiSmY93FbsNeCAz3xYRlwLHgJ3jXlst03s3uLq6vpkrnLmZq+uQNQEl7hB3Aycz8ymAiLgf2A90B2ICL6m+/2bgmQLXVZv0uxu88MLBm7kaiJqAEoF4MfB01/NlYE9PmV8FPhARPw1sAq4ucF21SffW/tB5XFmBCy6A06fXy7mZqyaoxChz9Hkte54fAN6VmduA64HfjYizrh0RByNiKSKWTp06VaBqaox+W/ufPg0XXTSdzVxXV+HoUbjzzs7j6mr5a2jmlbhDXAa2dz3fxtlN4jcAewEy868j4kXAFuDZ7kKZeRg4DLC4uNgbqmqzta391+4QoROA99zTGUCZ5GauDt6oUiIQjwO7IuIS4DPATcDresr8I3AV8K6IeAXwIsBbQK1b29q/N5RuuGF9Q9dJ6ddcd/BmLo0diJm5EhG3AA/RmVLzzsx8LCIOAUuZeQT4ReB3IuLn6TSnfyQzvQPUujq39h92Ep+BOFeKzEOs5hQe63nt9q7vHwe+p8S11GJ1be3fr7nu4M1ccume5El8qrh0T/IkPlUMRAk8iU+AgahpcIMGNYSBqMlyjp8axEEVTVb3HL/MM+f4STPGQNRkDZvjJ80YA1GTtTbHr5tz/DSjDERNlnP81CAOqmiynOOnBjEQNXnO8VNDGIgqx/mGajgDUWU431At4KCKynC+oVrAQFQZzjdUC9hkVhkb3VPQ/kbNIANRZQw6AqDffEP7GzWjDESVsZH5hp5hohllIKqcUecbeoaJZpSDKpo+1zdrRhmImj7XN2tG2WTW9Lm+WTPKQFQ9XN+sGWSTWZIqBqIkVQxESaoYiJJUMRAlqWIgSlLFQJSkSpFAjIi9EfFkRJyMiFsHlHltRDweEY9FxB+UuK4klTT2xOyIWADuBa4BloHjEXEkMx/vKrML+BXgezLzixFx4bjXlaTSStwh7gZOZuZTmfk14H5gf0+ZHwfuzcwvAmTmswWuK0lFlVi6dzHwdNfzZWBPT5nvAIiI/wssAL+amf+7wLWl6XKn71YrEYjR57Xsc51dwJXANuCvIuKVmfmlM35QxEHgIMCOHTsKVE0qyJ2+W69Ek3kZ2N71fBvwTJ8yf5KZ/5qZ/wA8SScgz5CZhzNzMTMXt27dWqBqUkGeLNh6JQLxOLArIi6JiBcCNwFHesr8T+D7ASJiC50m9FMFri1NjycLtt7YgZiZK8AtwEPAE8ADmflYRByKiBurYg8Bn4+Ix4EPAv81Mz8/7rWlqXKn79aLzN7uvtmwuLiYS0tLdVdDWmcfYitExInMXOz3nhvESqNyp+/WMxCljXCn71ZzLbMkVQxESaoYiJJUMRAlqWIgSlLFQJSkioEoSRXnIUqT4lZhjWMgSpPgMr9GMhClEnrvBldX17cKgzO3CnOVy8wyEKVx9bsbvPDCwVuFGYgzy0CUxtW9cSx0HldW4IIL4PTp9XJuFTbzHGWWxtVv49jTp+Gii2DzZojoPO7Z0xlY0czyDlEa19rGsWt3iNAJwHvu6QyguFVYYxiI0rj27evc/fWOKN9ww/p2YWoEA1EalxvHtoaBKJXgxrGtYCDq3FxxoTlhIGo4V1xojjjtRsN5OLvmiHeIGm7Q4ewf+cj6+zaj1RIGoobrN8fum74J3v9+uPtum9FqFZvMGm5tjl33iouXvxw++Umb0WodA1HDrc2xu+8+OHSo8/jqVw/euEBqMJvMOrd+c+x6m9FuXKAW8A5RG9evGe3GBWoB7xC1cS5VU0sZiDo/LlVTCxVpMkfE3oh4MiJORsStQ8r9YERkRCyWuK4klTR2IEbEAnAvsA+4FDgQEZf2Kfdi4GeAR8a9piRNQok7xN3Aycx8KjO/BtwP7O9T7k7gN4DTfd6TpNqVCMSLgae7ni9Xrz0vIi4Htmfm0QLXk6SJKBGI0ee1fP7NiG8AfhP4xXP+oIiDEbEUEUunTp0qUDVJGl2JQFwGtnc93wY80/X8xcArgQ9FxKeA7waO9BtYyczDmbmYmYtbt24tUDVJGl2JQDwO7IqISyLihcBNwJG1NzPzy5m5JTN3ZuZO4GHgxsxcKnBtSSpm7EDMzBXgFuAh4Anggcx8LCIORcSN4/58SZqWIhOzM/MYcKzntdsHlL2yxDWl1vCIhpnhShWdyV/O6fKIhpliIGqdv5zT131EA5y5t6TLIqfO3W60zvNTpm/QEQ3uLVkLA1Hr/OWcvrUjGrq5t2RtDESt85dz+gbtLXnttXD0KNx5Z+dxdbXums4F+xC1bu2Xs7cP0Y1fy+k3aNW7t+S118L119uXW4PIzHOXqsHi4mIuLTl3e+rWfmHd+LW8UQetjh6FAwfOPKJh8+bOeTYOtIwtIk5kZt8tCG0y60xrG7/edlvn0TAsZ9RBK/tya2MgStMyatDZl1sbA1GallGDzkO8auOgijQtow5aeYhXbRxUkabJQavaDRtU8Q5RmiZPK5xp9iFKUsVAlKSKgShJFQNRkioGoiRVDERJqhiIklQxECWpYiBKUsVAlKSKgShJFdcyS/PCM7fPyUCU5sFGztye4+A0EKV50H18AZx5fEH3zjsbCc4Wsg9RmgejHl8w6rkvLWUgSvNg1OML5vyAKwNRarrV1XMfaj/qOS1zfsBVkT7EiNgLvBlYAN6emXf1vP8LwI8BK8Ap4Ecz89Mlri3NtVH7/EY9p2XUc19aauwzVSJiAfgEcA2wDBwHDmTm411lvh94JDOfi4ifBK7MzB8a9nM9U0UawSQOtW/5uS+TPlNlN3AyM5+qLnY/sB94PhAz84Nd5R8GXl/gupKG9fmdbyDO8bkvJfoQLwae7nq+XL02yBuAvkNWEXEwIpYiYunUqVMFqia13Jz3+ZVWIhCjz2t92+ER8XpgEbi73/uZeTgzFzNzcevWrQWqJrWch9oXVaLJvAxs73q+DXimt1BEXA28EfiPmfkvBa4ryUPtiyoRiMeBXRFxCfAZ4Cbgdd0FIuJy4LeBvZn5bIFrSlozx31+pY3dZM7MFeAW4CHgCeCBzHwsIg5FxI1VsbuBzcAfRcSjEXFk3OtKUmlF5iFm5jHgWM9rt3d9f3WJ62gEG1mYP8eL+KV+3NyhTTa6o8kcL+KX+nHpXptsZGH+nC/il/oxENtk2CTd3vWuJ07M9SJ+qR+bzG2yNkm3exnXpk3wnd95dvP427+9f1kn9GqOeYfYJoMm6cLZzeOTJzuh6IRe6XneIbbJoEm6v/ZrZzePn3sOfuAH4IornNDbRs4gOC8GYtv0m6Q7qCl9xRVO6G0jZxCcN5vM88D1rvPFGQTnzTvEeeB61/kyiS3B5oSBOC9c7zo/BnWRTGIGQcv6Kg1EqW2mdQxAC/sqDcRJaNlfTTXMtLpIRj3ruUEMxNJa+FdTDTSNLpIW9lU6ylyaI3yaFy08vsBALK3EQd+jnLO7kXLSJNQ9nWsCn3+bzKWNO8I3apPbprnqVud0rkl9/jNzJr9e9apXZSOtrGRedVXm5s2ZEZ3Hq67qvD6KP/3Tzn/TaXB3vjZv7rx+PuWkJllZ6XyGDx3qPA76vRnj8w8s5YDc8Q6xtHH/ao7aUd3CDm3NuY3c9U3o828gbsSo02nGGeEbtck9zcm30jRsZBrPhD7/DqqMau2v14EDcMcdncfrris/kDFqR3XdHdpSaRsZkJzQ5987xFFNaxLqqE1u1yerbTZy1zehz387AnEaK0Om2Wc3apPb9clqk40uOZzA57/5gTit6Sf22alubVsS2u/fU3Orp/mBOK2m7LQWzEv9zMK805KBPOzfU2Orp/mBOK2mrH12qlPdGymUDuS6/z0DNH+UeZrrKdf6LG67rfNoGGpaSiwJHUfpNfp1/3sGaH4gOv1E86DujRRKB1jd/54Bmt9krrspO62O7rZ1qGtj6u7DLj2oWPe/Z4DoLO2bPYuLi7m0tFR3NYabVkf3LHSoq35rfxTr+sNf+jNY078nIk5k5mLf90oEYkTsBd4MLABvz8y7et6/AHgP8Crg88APZeanhv3MRgTi0aOdFSvdfzU3b4b77ivbMTyt60jD1BnIBQ0LxLH7ECNiAbgX2AdcChyIiEt7ir0B+GJmvhz4TeDXx73uTJhWx/CMdkBrzszBoGKJQZXdwMnMfCozvwbcD+zvKbMfeHf1/XuBqyIiClx7ckbZfHJaHcMz2gEtjawhmxmXGFS5GHi66/kysGdQmcxciYgvA98CfK7A9csbtb9kWh3DM9oBLY2kQX3gJQKx351eb8fkKGWIiIPAQYAdO3aMX7PzNeqk0WmNcNc9ki6NY0YnYfdTIhCXge1dz7cBzwwosxwR3wh8M/CF3h+UmYeBw9AZVClQt/OzkdUvG1lgPs7UGTdyUFM1aDPjEoF4HNgVEZcAnwFuAl7XU+YIcDPw18APAn+RszrfByazkUODmg1SUQ3aGGXsQZXMXAFuAR4CngAeyMzHIuJQRNxYFXsH8C0RcRL4BeDWca87UZNY/eLxpJpXDVpNVmSlSmYeA471vHZ71/engdeUuNZUTKLPrkHNBqmoBvWBu1JlWgZNrv693+t8MFySpzrM4ZLQYROzm7+WuSn6TZ3ZvRve8hb48IftV9T02a99FgNxWvo1G1ZX4fWvb8R0BLVQg6bDTEvzt/9qkt6lTx/7mEvyVB+XhJ7FQKyTS/JUJz9/ZzEQ69Sg6QhqoUl9/hqybrkf+xDr1KDpCGqhSXz+Gj5Q47QbSeU0YO/Oie6HKEnPa/hAjYEoqZyGD9QYiJLKafhAoYMqkspp+EChgSiprAbv3WmTWZIq7b1DnMNdPCSNp52B2PDJoZLq0c4ms7tTSzoP7QzEhk8OlVSPdgZiwyeHSqpHOwOx4ZNDJdWjnYMqDZ8cKqke7QxEaPTkUEk9pjSNrr2BKKkdpjiNrp19iJLaY4rT6OYrEBu8tbk0t6Y4jW5+mszDbrvBZX7SrFqbRte9C/eEptHNTyAOOoP26FF461td5ifNqrVpdL2/oxOYRjc/gTjotvu97/WwbmmWTXEa3fwE4qDb7szB/RMGojQbpjSNbn4GVQatXnnNa1zmJwkY8w4xIv4d8IfATuBTwGsz84s9ZS4D3ga8BFgF3pSZfzjOdc/LoNtumFr/hKTZNta5zBHxG8AXMvOuiLgV+LeZ+cs9Zb4DyMz8+4i4CDgBvCIzvzTsZ0/1XOa1WfAu85Nab9i5zOP2Ie4Hrqy+fzfwIeCMQMzMT3R9/0xEPAtsBYYG4lS5zE8S4/chfmtmfhagerxwWOGI2A28EPjkmNeVpOLOeYcYEX8O/Ps+b71xIxeKiJcBvwvcnJlfH1DmIHAQYMeOHRv58ZI0tnMGYmZePei9iPiniHhZZn62CrxnB5R7CfC/gNsy8+Eh1zoMHIZOH+K56iZJJY3bZD4C3Fx9fzPwJ70FIuKFwB8D78nMPxrzepI0MeMG4l3ANRHx98A11XMiYjEi3l6VeS3wfcCPRMSj1ZeT/CTNnLGm3UzSVKfdSJobw6bdzM9KFUk6BwNRkioz22SOiFPApzf4n20BPjeB6pTWlHpCc+pqPctqSj1h43X9tszc2u+NmQ3E8xERS4P6BmZJU+oJzamr9SyrKfWEsnW1ySxJFQNRkiptC8TDdVdgRE2pJzSnrtazrKbUEwrWtVV9iJI0jrbdIUrSeWtdIEbEnRHxsWqJ4AeqTWlnTkTcHRF/V9X1jyPipXXXqZ+IeE1EPBYRX4+ImRt1jIi9EfFkRJysNimeSRHxzoh4NiI+XnddhomI7RHxwYh4ovr//WfrrlM/EfGiiPhwRPxNVc//XuTntq3JHBEvycz/V33/M8ClmfkTNVfrLBFxLfAXmbkSEb8O0Lvb+CyIiFcAXwd+G/ilzJyZ9ZQRsQB8gs46+mXgOHAgMx+vtWJ9RMT3AV+hs8nJK+uuzyDVrlUvy8yPRMSL6exw/59m7X/TiAhgU2Z+JSJeAPwf4GeH7aY1itbdIa6FYWUTMJOJn5kfyMyV6unDwLY66zNIZj6RmU/WXY8BdgMnM/OpzPwacD+dXdxnTmb+JfCFuutxLpn52cz8SPX9PwNPABfXW6uzZcfaEZovqL7G/l1vXSACRMSbIuJp4D8Dt9ddnxH8KPBg3ZVooIuBp7ueLzODv7xNFRE7gcuBR+qtSX8RsRARj9LZh/XPMnPsejYyECPizyPi432+9gNk5hszczvw+8Ats1rPqswbgZWqrjNbzxkVfV6byRZB00TEZuB9wM/1tLpmRmauZuZldFpXuyNi7K6IRh5UP2wX7x5/QGen7jsmWJ2BzlXPiLgZuAG4KmvszN3A/56zZhnY3vV8G/BMTXVpjapP7n3A72fm++uuz7lk5pci4kPAXmCsQatG3iEOExG7up7eCPxdXXUZJiL20jmh8MbMfK7u+jTUcWBXRFxS7cx+E51d3HWeqsGKdwBPZOY9dddnkIjYujYzIyL+DXA1BX7X2zjK/D7gP9AZGf008BOZ+Zl6a3W2iDgJXAB8vnrp4RkdDX818FbWj459NDOvq7dW6yLieuB/AAvAOzPzTTVXqa+IuI/Okb1bgH8C7sjMd9RaqT4i4nuBvwL+ls7vEMB/y8xj9dXqbBHxXXSOPl6gc2P3QGYeGvvnti0QJel8ta7JLEnny0CUpIqBKEkVA1GSKgaiJFUMREmqGIiSVDEQJany/wE/oDB3+6c9YAAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.interpolate import UnivariateSpline\n", "x = np.linspace(-3, 3, 50)\n", "y = np.exp(-x**2) + 0.1 * np.random.randn(50)\n", "figure, axis = plt.subplots(1, 1,figsize=(5,5))\n", "axis.plot(x, y, 'ro', ms = 5)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "f2 = interpolate.interp1d(x, y, kind = 'cubic')\n", "xnew = np.linspace(-3, 3,30)\n", "\n", "#plt.plot(x, y, 'o', xnew, f(xnew), '-', xnew, f2(xnew), '--')\n", "figure, axis = plt.subplots(1, 1,figsize=(5,5))\n", "axis.plot(x, y, 'o')\n", "axis.plot( xnew, f2(xnew), '--')\n", "\n", "axis.legend(['data', 'cubic' ], loc = 'best')\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "\n", "spl = UnivariateSpline(x, y)\n", "xs = np.linspace(-3, 3, 1000)\n", "figure, axis = plt.subplots(1, 1,figsize=(5,5))\n", "axis.plot(xs, spl(xs), 'g', lw = 3)\n", "axis.plot(x, y, 'ro', ms = 5)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "spl.set_smoothing_factor(0.5)\n", "figure, axis = plt.subplots(1, 1,figsize=(5,5))\n", "axis.plot(x, y, 'ro') \n", "axis.plot(xs, spl(xs)) \n", "axis.plot(x,np.exp(-x**2), ms = 5)\n", "axis.legend(['data', 'spline', 'original'], loc = 'best')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "B-spline reprezentáció" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t=np.linspace(0,1.75*2*np.pi,100)\n", "\n", "x = np.sin(t)\n", "y = np.cos(t)\n", "z = t\n", "\n", "# add noise\n", "x+= np.random.normal(scale=0.1, size=x.shape)\n", "y+= np.random.normal(scale=0.1, size=y.shape)\n", "z+= np.random.normal(scale=0.1, size=z.shape)\n", "\n", "# spline parameters\n", "s=3.0 # smoothness parameter\n", "k=2 # spline order\n", "nest=-1 # estimate of number of knots needed (-1 = maximal)\n", "\n", "# find the knot points\n", "tckp,u = scipy.interpolate.splprep([x,y,z],s=s,k=k,nest=-1)\n", "\n", "# evaluate spline, including interpolated points\n", "xnew,ynew,znew = scipy.interpolate.splev(np.linspace(0,1,400),tckp)\n", "\n", "figure, axis = plt.subplots(2, 2,figsize=(6,6))\n", "\n", "axis[0,0].plot(x,y,'bo-',label='data')\n", "axis[0,0].plot(xnew,ynew,'r-',label='fit')\n", "\n", "axis[0,1].plot(x,z,'bo-',label='data')\n", "axis[0,1].plot(xnew,znew,'r-',label='fit')\n", "\n", "axis[1,0].plot(y,z,'bo-',label='data')\n", "axis[1,0].plot(ynew,znew,'r-',label='fit')\n", "\n", "\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Legkisebb négyzetek módszere\n" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "f = np.poly1d([5, 1])\n", "\n", "x = np.linspace(0, 10, 30)\n", "y = f(x) + 6*np.random.normal(size=len(x))\n", "xn = np.linspace(0, 10, 200)\n", "\n", "figure, axis = plt.subplots(1, 1,figsize=(6,6))\n", "axis.plot(x, y, 'or')\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([5.03380086, 2.03710585])" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a = np.vstack([x, np.ones(len(x))]).T\n", "np.dot(np.linalg.inv(np.dot(a.T, a)), np.dot(a.T, y))" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([5.03380086, 2.03710585])" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.linalg.lstsq(a, y,rcond=None)[0]" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([5.03380086, 2.03710585])" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.polyfit(x, y, 1)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "m, c = np.polyfit(x, y, 1)\n", "yn = np.polyval([m, c], xn)\n", "\n", "figure, axis = plt.subplots(1, 1,figsize=(6,6))\n", "axis.plot(x, y, 'or')\n", "axis.plot(xn, yn)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Tutorial: https://mmas.github.io/least-squares-fitting-numpy-scipy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Gyök keresés\n", "A ` scipy.optimize.root(fn,x0)` függvényt használhatjuk. A hátterben különböző iteratív módszerek futnak, amik folyamatosan javítanak a megoldáson. A második paraméter a kezdeti tipp a gyökre. \n" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " fjac: array([[-1.]])\n", " fun: array([0.])\n", " message: 'The solution converged.'\n", " nfev: 9\n", " qtf: array([-5.33573186e-13])\n", " r: array([-3.34722404])\n", " status: 1\n", " success: True\n", " x: array([-0.73908513])\n" ] } ], "source": [ "from scipy.optimize import root\n", "def func(x):\n", " return x*2 + 2 * np.cos(x)\n", "sol = root(func,0)\n", "print(sol)\n" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.0761863178387898e-08" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "func(-0.73908513) " ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left\\{x \\mid x \\in \\mathbb{C} \\wedge 2 x + 2 \\cos{\\left(x \\right)} = 0 \\right\\}$" ], "text/plain": [ "ConditionSet(x, Eq(2*x + 2*cos(x), 0), Complexes(Reals x Reals, False))" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sym.solveset( xval*2 + 2 * sym.cos(xval), xval) # a szimolikus megoldó csak széttárja a kezét." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Geometriai algoritmusok" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.spatial import Delaunay\n", "points = np.random.rand(30, 2) # 30 random points in 2-D\n", "tri = Delaunay(points)\n", "import matplotlib.pyplot as plt\n", "plt.triplot(points[:,0], points[:,1], tri.simplices.copy())\n", "plt.plot(points[:,0], points[:,1], 'o')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.spatial import ConvexHull\n", "points = np.random.rand(30, 2) # 30 random points in 2-D\n", "hull = ConvexHull(points)\n", "plt.plot(points[:,0], points[:,1], 'o')\n", "for simplex in hull.simplices:\n", " plt.plot(points[simplex,0], points[simplex,1], 'k-')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Jelfeldolgozás" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": 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5ipd9/NL42XGnXNX9LTnSL910EG9k4O0Nn7saJ1ywBx+5MDn8Jx97Gp5y7Gnx90NrM/zosaeJeTu0NsPN+1fA29qsEUrnvccz3/x5fOzL6XV4f/HRS/Dct50rQN5LP3Ypfut9X4q/n3jhLWhaj49fdGv87BMX3yZA2Q13LmN52uBVbA6e+eZz8MZTrxFr8PNvOhs//6Z0cPuFNx3Aj77mNNy1mubk1oOrGVC74/Aa7mCg6PZDa3jyq0/FNXek9Xviq07Fz7z+LHbNBO8463q88F+SXPz5R7+C/ctTHFpLoODOpSne84XkEN/9+RswazzOvDo5pBedcBFedELSg3Ov24dffsd5eN1/pPcqv/cLN+JX35kcFBD0go8fAK6/cxnLDJScefVe/NRrzxDG/6nHnYEf+vvPxd//6fRr8OEL9uCD590cP3vPF27EqVcmu3B1tx5vP+v6+NnffOIy3LBvJYLOpvV406nX4plvTrr58pMuw7OO/4JYzz/7yMUCQJNeaOdz+W2HBHB406nX4Pf+9cL4+97DE/zPt5yDP/23i+Nnz3zz5/G2M6/HcueUvfe47LZDOPYzci4B4Ms3JRk/6eLb8JEvJdn95CW34YQL9uDvP3lF/OwnjjsdT3vdmfH3umnxc288C5+5NNm01WmTOaO6aXHlV6Ut+L/vvUCAiX/+/A341Xeeh88wp/w7H7gQf/5RBuBvPoi1WYs3M+f+5tOuxdqsjXM3qVvceteauO6PPvRl/Ms5N4o+/ORrz8ATXplk4Ob9K/iRV52Km/YlPb9zaYKv3sXfsR4AFrcFq9MGP3Hc6SLY+pV3nItnvvnzUS6893jNKVfhuW8/N36HdPfiPWkNLrr5IE5jMve5K+5A03phs1/w7vPx8pOSvdy3NMGzjv8CfpfJxSmX3Y6nv+FM4Ue0XgABhBxcSbbgiq8ewpNffaoAKj/8qlPxY69JAeGpV+zFB867Ga9gfXjVp67EFWxuKSh4JZOdV37yChxeqwV4e/lJl+PX/iWVAb2/85EnfyXJ03GnXIU/PuHu+chnvXVjPvLCm7iPvB3vZ/P9uS7w/QSzz8efcR3OuS73kb/BfORWt/sFCPPeH++9f5z3/nEPeYhZ23avtn1LQdh5VPP6z16ND52/JwrUngMreNrrzsT/fV9azM9efjueetwZ+AATjBedcBG+cN3+iODvOByU5mpm6Mnxjsq7txxk1Oj/g8yRX3FbUDjOJpx65V689GMJFJ144S34iePOwIkXJsP+Jx++GD/9+jNxdQfOvPd49zk34q1nJGNMyryXGQLdpwMrNLb8fclLk1n2GTWai8Nrde93Lr3lEK67cxl/cWKKhl564iX44VedKozv41/5WWGcbjm4igtuPIDf/2BiE87uIl8CClaEN23CZ2NjLNToMh6xUaN5IoN/E+vjm0+7FtftXcbnrkiO7WmvOxPf+7enxD4tT2r8wCs+i2cz9vMD592EG/at4INfTKBEgx0y1BXr96wbCxn72ugvrYE1Fmpr3bO+eENiE/7ixEtw+lV7o1yvzRo89bgz8LTXpQj8qtsP4ynHnoZjP5MAzm+990u44quHo/G3+nRoNfR3cdSvK+1AdE66sTrL2YibD4Tn3rgvAfEPnHezCA7Ou34/fvr1Z4p+H3/GtXja687EaVcm9vPVn74SH/tycgY3HwhrfQMD+ZNu7lamdW+fNtIWRyUA4BDTewLXxLocWJnh4j134YXM+bz5tGvwY685XbDrzzr+C/jJ156Bu1bS2n3ykq8KMPGlmw6Ifltt1o3NsmkEOjXQAICyCDJ6eK3fNpz8ldtw0/4VvI0Bwxe8+3w8/pWfjf1uWo/v+evP4EcY+/nFG/bjqtuXBKi+aE+w8TT3PDCkNh0YC7WoK3UusyTH9IzTr0rg7SUf/QouueWQAMNPOfY0/Ne/+nS0QXccWsMT/+FU/OGHEsB55clX4IZ9Kzjv+v4kEs2hZXtJpw8Z9pXGsjzpl8f9y+He3Ee+7rMhcCYfecvBVTztdWfiN9+bZO7UK+7AU487Q4CnF51wEc69fthH0rqMq3vJRxrrvFXtfgHC7uv24N1jAMAdh3JwcU2nLORgPn1pcpqfuPi27m9BsLkjp+j+xi56e8COUfwbRSNkMC3nM9RWolEL/68w4/aQoxe65y5n9yZloef/25cS63RCl3Iip7XnQJ4OuONwiDwfsnsh+9u0ew5Fb5VhwGieeFREbddClY2FGqWiCFRcyhg7AjbkEFenTVQ4GjulHx7zsKPZWMJa0zpZxomMhGWMGzWXHLjsGgcnSQyW5Wwf9dCjwlhuSWMhGSOW8qIuEr9ub3LkxFYe8+Bd2T1J/vZ2Y9s1TvtwaH2ov0vGPNOaWfKo048kCwBw1GJ4zoWdsya5vpb1+5SORaG+AcBhAoTdvW9TzAaQHD8BD6sNgQOSR0uuvuGoIMe3G3pPzp2CgnedfUP8GzkU+tuaBfA6uaRniP5OElDqa/VAurfDLdEO8Eb6YPUp2bDEZpBukI595Za7sutIV3YMrAGB86rIAQCBRUvmSO/3G6l6kueHPmARgAQABCS/eEMAJTRujsfJTnwX03tqJKN3HM7XnnTZslPUCDxaAcudXVBPz+BB0nd9Y+jL+Sol6n2ag7O6AJGzg5d1qWaaL6tvJA/0Hd4IAHPgTo3W7ECnK1ZA+iDykcZ8EXgineGM6b9fHAITkr2N+kgay931kcvKR1oBwFa1OQgzGrEEloCRMaXv8KbNzZQJymoUsOCIHsKMMQkEOY+DhmIMRfekrMvd9cvMGBNAisaYGYCkCP3PIMWwQBg50MIwtORYqG9jA7iQoV8yAA+xTUtGNEZpiNWYxkl/e2CnuMQycINHn9FYHv7AHfFv5ORI2fcezgEAGVhrJWgMS5FZSt8iI0jyxGtCCAiTEb/TYBXJwE6MKJvmd6ZYFSDJHz13t2GMl6Ix7l+DZcO503NXu+dxXaF5JWZpZgD/SSdXVp9ofm7ct5L9jXRlYjCWZJitsaR+z3rHREafWCve9hwMn9VteAbXFefCPJGs8Ro6aiSzX28ELKS3QzWCFiNM80oyy0ENMQZkbywQttCBqLVZLlckc3u6uXgw6/ed3VqvDDBaBHZHBnNBem+NabfSFb6++7r5mXT93cfmi9ZuLepKPl5iWHkwQm0lgrCwdmWRs8bUX+veJM8zAyzTPS2Q/NCjA6DUJRThOa34n4IbIKQ2gaQrln0m+26BMBqLBcJIdgiEcbtD61Er28Jb8pG5XDnlJbkfPRIfeZfR76FA5YDykXeXdd6MtuUgzDn3AQDnAHiUc26Pc+4FW90nWiBroaaGc6dGQkCGQAAAZTi484nofEqUeG6MowEw+kRMz4oBWOg5+1Q0BiQnTf+3RnBBBnpqKNSSivy5oSdhPziQjiQDwGlvUnIyWAdX87kgoGI5lqJziPS3SZO+Q5/RuljBFH3HYkFpDckgcAdBjoX+xudLOxYuV0tTmsPwfcuIxzUwZI4AMIFrWmcAWJuGzyITtpAzF7SGh4z0D3XlgCGP5FiirhgOZqqcCP950s2PtYb02b7lfA2WlDHmjo3kyBpLJxZxLBw40DpO4xzmz9Vj4ctE/trSe3JEpPdWLLUSU4b9IIzGxO9NumWl945SjBIHWnq8awao0DLHZT2yEqQrzBGTcz7Qgd2RyYTVWX+pLXQAgOSLO+k4lq6/pUv3ph+HdCWOd5azKatK74m9Dn2QrDEHj3RPChatdCTd0/Ink1rbpJwZmkaZS38jkEjXc72Pz+3m0JqLGHwNpCMJuHAdI7Y26X1+vfYrvFEQY/kVslf7DR9J/V2OupLr+JJhe1O/iQHfPuCL2paDMO/9c7z33+i9H3nvv8l7/46t7hM5FKvyJwqYIdgz5VgslG8ZNbonpUgoWgeSUg5Fj/tXJMrnLToGw+lpQDnEhFnGZaoicZ5np8+ob1YKjwzAYVYblpzs+jUallGjMZCz5GuwFj/rTy8k8Jc/lwAh9ZE7NorMDhvpSIosDxpGTTsGS66on3ZkGVpMdbDvrMwICIfnWpHi0kBagpwkGWP+/Aj8u+dy5qBVTp73KY6l7gIWg4XRusIbreuyYlqBBGitsQw5FuoDfTZVciLGYuivBv4WAz6JMpsD+OWo97kjjbU7qxLkA9yx5M6noTVocl0hOYiAeEZBmAEAOv3hskNrvWoEjSszCSit9R1KR67OpJNdNXQl2mdmoGkNLF0hGzpTcyF0Ren9wigHYVYKj+quqL7Vskk0F1agovtiMff0fAn85Rrw62gdk47mNmkoHUngltbAkrm0BrmXHCIqMh/JvqODGK4jM+UjecASfeTqgI9c7veRW922HIRtx7ZiODRqZLC4QGeRpRGNaWXh7MBIpX041aqdJP2NP58+s+hu7Vg4CNMGy3LSlmOhRvfUzwCS4lLfGgPgRWPMlOagUvwIENsctFosCoEuKx2pgY51PRksfp0u5rTYI51abZq8vxq08ueQfFgpx8lAdB/ZVwO46HWx5GNJrRO/12H1t6F+cxDWRCefO8S4Lh1DSYbXqg0xI+mGmNK832ldZI0lkBgZ+j43xlMFkCz50qDecoiW3q/1rAHXNfrMcoiHlaxx4JLGkjNDJH9WwKKd+6TO51uPhetfUch+C5mbSBu2ZLDG+m9AYqUymZ2l70zUWDgAIPEjXZHsK7HidP369pmzZLTmWr74z/Q3K01m6T3NJ/VlYjBDOh3ZWkA46goLKhSYWTbkS+s2x1J0zyG9t9Y+9TuXJ+0jre/oQJKvIdWnRh+5kvtI6u+hI/SRW93mIMxoMXodqJXgAkIGNQpPZMJyAEDXc6NYdVZtZZIDgGVFG+u0F3+eRe8n554/VxtaS6E0e8R/pjmwnKZWUtlfFd1Pc0OrrxdGdSbBLm/x+wNrkKKxPOKyxqKpc4s90ikWYdQGgXD3GcmVmbLI14CajiwnlmNROyH5eIcApa6/WjHWadUAANqIWmn5xISF62UaRjoma7zL03ydiI2gdeFj0uCcpyUoZR11xZCvNJYcNBLzZzHgcSy1fIbFSvC10ww4ydeSoUdDTJjW0XCdrVtDusKDKCpbWDXGu6yCGHL2vAbPApTUdx18cSBNc7hmBMLECZsMeJS5AV1R4+XX02eHTb2nsUjZEUGjAYQ10NdpyXCv/jUoFfDnuqJlzJIPrffeJ5lO8tj5FTNgGQgaDb2n+SRbZBIVGWucB1HmWDbiIw0/tF3aHIQZjfLc0yZX9iGDpWssLCUfYiWWDQOdUl/SAHHKdRbZASvSks8dqgmzmKHJgMGaKudsOZZE5eeRWmRcxFjIyXaGoJHP4P3lSupV+sVkJRSYoustVkKMRY3PSkeSwUq7I/N0kwaYvH86CjRTQwY7p42iZdR0ATfvmzmWmRyntYYxuu+ewVPZq1M590JXsvS4XBMxFvZZrWSVjDFPZ5Aj1Loya9pMly3HohlwK3VvMWFDMpfpX0zDWDKXg5m1mewLBy4ZIBVOTwKsNQMAaAAvdGWgVkkDcL6+BG41qOLPpzFxBpzmY4i9HUrdp5owYywze10layxlnZcq6HSkHAuti2RfeJ1d0vEcFOi+SV2R8iSCkm68Q6nVeAzNNJe5ZUPvyQ4ejkC4WxND71NgmcvAoN4r22/qvbH21HPLR+p1sX1kfs/NOmD6SNschBlNGwKLyh/K3VspSy10HAzFWoVpjvI1mLGNU5N/1kPv892ROs1l7TgzQWePoZwZCsWdnvce3nsWFeVj0coyZIxNQDlAd6do04vrrRQed+6ryohZ6WodaVlzkcY7EFkOpCWmTb4uCVDmcqnXxVonC0DrsZjz3QMegTy6t1hMzZZxB2GuywYA5YoCwKZeDI1lIBK35InaTMnc8NoPOc0czES9V0BA9FPZjbpp2Rzk4+3Tez6X2obNmpYBf5rX3F5peVox9EGnyYDERur5WTWAsJW6r7U8DQTO1vVajmeNzzIEy4bM9a3rUArPHIuhv5oJ48CwjozSQJCsAZMILPvBk14zy17ptbfYfZMBV4y0WCetf0M+0sgWDfvI/s+2us1BmNE0IrdrQywnSUDHisakkVidNfDeo219jECWJv2KQUrHjSK1maqTEX3RRi8C+N8AACAASURBVM2g97WSSyq/fyxaAS0GjwCP9yHSqgVN77PrMiVXkRP/Do828zqXfkMwVeO1omaLLdJKLutG5PPrNqzttE4OUadDQl+kEbbrqAai+yyiTvfWTIUFEDXDI8ciUwicPdIObdb4yN6tKUApnLsaSzS8AzUtQJJjAmuanQz9lOs7awz5Mpgw+t5G0sa8T40qQ9A6zu+hne4Qa8y/r8dgrVNiOvqBizmWAV3Ra9B6Lg/0nNwW6XVJwNCSr34bNhRoWan75Nw3oCvGd2yGUoN60u1c7zVg4+yR3hBgjmXIr8Q1zOXYss9Hove2DZPjtYJ7HfRJJn19G2b222CNdeCefGSe7h32kdKv8LFsdcsPEJm3rI6Kts4CTNkMBK93fFkRMSlW0/pMCKLzEGkFKVjagPKfOV09rUPkuqIc4tDuyI3UhoixzFT0WueKYSmC7jdXRD0WK7JM62KMZSAi1jtyrIjYYir0vS2HaIGZadOaAECMZSYNtLlLymRW5Wca+IR7SiBsbR2fWkBFzd1MyQf/zopyLKV3WY3kEGts1lEp/QNytsjSQ+1YrBSPZqvFWJQ8WGyZft6OcZk59yG91wwxv6el03q8Q7WZQ4HWqjFeDYSH6iCp76PSZQycKTu1dOTm2Lidq+W6WAAg6sqAjlr2Ue/01PadP2dQDyx71fMdfu+JtS5dn3Tq3jrOJdZR1V3g7lMAMGTDtHxYsjNVNsx7n8keH4tOrZo1h0ek90y+pvJ55CP52WK2Tq/vIyNIN/Rgq9schBmtr44D6Cmg1EzYQHQio/sWJX+VjOnINU1OjmYY8BADo6N1M7WqgY/FelkRi7qnpeS6T1yhaLy1UcSqDZ6ZlhhgKsyIWDlJirTMiHhgLEMOUTtXa51WDYO1oXTkBhiWqWHUqE9NG+TBBo/WWKTscKdpprnqVmxIMFMsOiI2xjZU35YASz/LRf2m8a6rK7RTMz6XgMt6et8EEBb1p5/BG2LCNHCx+jkIlpndaFu/AV2xAf+QfNFnO8dlPOvMYo+mjQ34TRbG2PEc51LZUv43viGgaT0Kd2Q2zK4XtcExz1TYgZYXYxkKDjZUmD/AHnkf/s43mlu6sqbWpc8WW+NtzDXpt2GmfFk7VHvWYKjWGAg+sjJ9ZK6/Qz7SAqLbhQnbUDrSObfTOfdS59zbut+/wzn39M3t2tY1TaUPUfn873lqKAcAmvWRrFe/Auu/2VGNvM6itu0Ui4y0LPaIK6KuQxhKL2jFXzcijtdpw8fGEteFK7k0ohYbqaN7SrHwFF4fmOJ9MtlIC8yoNRhyttmc1vl8zwx5mrEomV/fN5aZkjmThelZV3tO5HVDR6CEscjrzLEZQDTrS0/gYV1nRcRm2ifT+9yJ2GPpZ8C13icgP5ye62fC1r/Ous/E0PuhNejbXczt10wxrOGznn7X/YBLjk9eZ7Jdis2QZwEO6Uq/fbb6NGs8Zm1/H0U/1fqsF+j0632/rtBnJmNp6HQePOZrYAXuWb8t5k8xnUPHuQDGhpyh0pcBeb63feR2aButCXsXgAmAJ3S/7wHw8k3p0TZoXJHa1qvt3bnQ50yYIYQ9O5jWdWyxnkjWFa0HADJjrCKQ0G8p9L4DJaKmxbi3jlh0xMX/JqKoHoUacqR9YC6MJVf89H8OSvrqEGzgwp2dnHvb+RnGt2kHjaMci+w3B4Z6bPz7OgWl5Us/T8vcTK2h1U8zBd8jc5NZ/p1BJmyAjRxalwTGjhCUWGxGDwAQKaWesRDbRmPRz4/ppu4zqhVcTw9mTStqYazv9K2BVRZggePBFJ4xT6sKhA05O/qfUmcmUFP3alofd50O2QZZC9oo8Gisk1oXi3FJNkzK03qgNwM6cd0Mm6bWpW7a7ODcISaMxiKBWm4vcjCyfskBfW8oJW59Vnfyb/qVASYsHVUzbJ91EJUC95yNPGIfeT8DYd/mvX8VgBkAeO9XYR8o/zXRMrbK2A0zZAwtIZxFZZPKMhTt83tkirUOcNCsk2mwDWOojZqlGHUTiiX1PaeWwVJRlM1A9Bs6y4ANjoXWwALCBsNSN62qdZIRHh/DRlIs0tn4QTmxPpvWXV2GGK/NSnDwoo257K8ElOsa2l4mbDi6n8wa0/AJOZzJPiU2Uq5JNpbaC8CzkYiYPts4C6Mc4jqM4UTJs8VGUhG3KCJvdTCSM0q9rIR5nVfXDetY33jXc4i1CtCGQUl/n0zwpr/TY5t0n6a1DHSG2NeoK02uK732aiDYFv1UOmaxzXpd1ten/DPNhGl7J8YyZK+ivelfp40EydZ15lg2wEZqeaTvr8v+3gMfuR3aRmvCps65HeiO63DOfRsCM/Y12XJlkY4GsCOtDOUb0Z9WoNYnHJx2d+RCx6MaHiHLvw0puZFy6GE41gNvWjEsoa+Vs6S+8/OkhhSqZo6pL7KUu+6koR1iYbLobx3HQo5UG+r1WZhGnie1gQit9WHu1qsJm9StqKmZGd/RKQNAHl/Q128tY5O4JpYxzuVgvX6HzxSbUcvnZ2NpbOBispFqXaz5FmNpQu1PM1D7Y+u9BPAW8LdTpN50pEObOnRQ0juWDTlErSsdeDTBspwnW1dy1jgPZI9svBthLGksTMU2pPdkU9bX+x7GciPs60CdK322Lutl2ucGQP5KJR388XvVRh/t2qq7twZ9Af+QDRvcLKDWhdfA6R2Q1hyYPtIcb7JBW9k2CsJeBuBTAL7ZOfc+AD8E4Hmb1amtbrpQnBauKhwTnn5mhuoIhPNrLcfi0fqNGdphZbHpZlI+56SAloVD03oTLE4Uc1D3KIZkLjZGd0/rVrzepm9s/H/6ue6pzRiVDiGF2oh0hgW46h7nLtfJ6pMX995ITUv4TIJODTDDZ038rCrCzsIc+BsOQjtEJV/O9Y2ljymRxmn92iPqt5wDeoVP0BUL+Oe1IHUPKNHrstEoPWPC1gMAdWvW/tD8Sb2XY9FOO+93Ht33AmHNwqzjEPvmwN6+3yb5UgCLCtwFELZsmKqf7NMnu0/5WPSam4Fdm+SZQGLdeqH3vNnser4GTatBWM5GZgDeGJsJJhSD1hc0ku5UhcsY4vAdKz3n4RxbA8uvtPJ5KSU8HLhr1njoiBdR9N408XeuKxag7NvJGO6ZrnMulcd4y0eup/faRw6s3Va3DaUjvfenAHgGAvD6AIDHee9P27xubW2b1W18gztPR+5erDIkTz+3La/fMNILTMDo3hoApJ02bXzpM3fc4+79WbMmRWjjqhDGdOe4jPem7+weV0JQd4xKVIWLBlWzekP1BfQcumb3QmUaXu7s4liaJjq2cVnI78SxJeZrR/cSXW4cdi/IscR1qnVaYrhP/DMxFqs2hDmRcVWAagXJaPCx1Gos9PmOUSnmicsXbQvfvdg3Fou67ytYbVAVDgtCLuTaCdmx5Kv2Yp0067VjVIo6QLEGJHNMVzR7pD/rHQvXw9pn60bjARDGy5w7ydysSTtU5ViSfHEAsHuhinUuUS76xqLWyUwZ1sZYGr0hJ+n9AtN7+pzreM3Xjs2BHEuS5wn7DsmXdYSAZjMsBzxrEvO3e6Hqka8ElJLes7GURbJzTRtljgO1HaN07EfUe27D2FxmzH1PXVHeTx/nodeG1Ux2mHzN2lboON2vT+/5PPX5laFjHTJgaNT8Cb/Sc52QHdOvpGCE68qsabE4kv5oqvQ+ytxiFQNLvS7W8Rc62I33HjMfaXxn1hyBjxRj4brCOdSta4MgzDn3ffQPwCMB3AbgVgCP6D77mmzTpsWuhbBQk1mKdneNK7HbiUidWglvww7qBICd41KctcRBGN1755g56dpjVwemKFVStz72iRvoXezes6bFzjF35EzJ2Xeq0mFcFaJWIo6lTfVIAVykSIsbegIG5LRaFmmJsTRtGgurkdq1UAol38nG1rQe3kOMNzr3hUqwKbu6uVybJYdYFi6r++gfizcdy7RpTUBLYwl1PT4by5SPpVHfaXIDNpmltOKuMY0lFUAXjke7noGLHvmaBUc+KgtRqCrHwmSHrxPJfJNA786FMkbSYu24c2cOkfqxa1zZuxzb3IjOtK7EtWtMXdnFvmPqTyOdNO83Z52EPjEZiJ81aV347i7SFd6ncVVE4DplTouCCqn33uz3lMmzBlNcVwoHLCrQGdeuViCM1d6QfHGgEsfCmMZxWQhWIgZDCoTx+U7fSTIXdUWtwZTpb9KVJAPaNlSFw8KoFCwX13u6N9eVGQN4taH306aN8yDHkgLZaZ/M1R4LVRECWcOGcWCox5L0XvqVaRfIC71n80u6whlhHthp+aJAtn8suexwMLVT6fi4LDAqnQkohY5xvVd+hQcVkZ2rcz2YzJoYMPTaq9oLQDvkI3cu2HaOA96tbOsxYa/p/r0JwLkAjgfwtu7n129u17auhYVKC8wVSoKLnNGiBeZGbec4KflUGH8uhNKocTBFAG/n2AJv8t67FwylU0Z8VBYdo8MUcZyzGdl4F5Ijt8Yrx+LZdWwuybnr74wNpRNRowUA1Bowx6YjLq6IUz2Wjvnj453WrZpv1aeaP6+y+1T3rYHHjnEZ08R8bHosuxgDwMGbHG+aS2KBRiVfXy/lqbblYifrN39+nAPjOinPEnTy+R5XhWAMp8pJJwAvgbAlczsVCzMqHRaqUsxvAp1erVMulxqopbFwR5occJoTBhyYk57WAQAQ68PnRM/vTsXwmA5RAbWgv1o3N6ArzDbEz/iaM5029T77DhtvVXQpQr52eZ+0rPbqSpMY8ap0gunstb19drZJOy9NHevVe8++o2yo0rEhG9a3Bvz5gPQZuxYqMb+cEZb9TsGmHq/3UDqd+jSx9L5JwZeYS6a/XMdEkNwnO4Z93mUEtzvV83bx8TK9lz6S6cqAj9w1lnPJbfh2aIMgzHv/FO/9UwDcCOD7vPeP895/P4DvBXDNfdHB+7qRslpU685xSleJxWSGdqdloJXBktFuMtC8GH1hFCIt/h2rT9zQhkjA+M5YOqgQ1SiHuJA7Ww3wJMuWjAXd12QcGm8a2t3KEOwwFIoDQwvMaNaJs2XEQEzrNqbnTJDbyLHYoNMLhbbGy9MnZBwmyhBwZzsqXTRqs1rLTk+fFKMlmAM2Xu0Q+Vh4sbE0tF6lShIAADqg0qZ+8rWzwIwAU3WLhS6S5qkSLnOWEddyyY14YgkCKBlVcry9ukI1eG2SS+kQKWUXmArngEXOOOh+c6fJxsbXQN9bj5ezN7t6nEjrqZasC6LKxMLUTMemytnaINsz5oADDg6Ek3O3bRofb7cGjEHjY+Eyrlk9ztRoRpjWhYJGi3US88T6pMEFDxDzNdDgvNMVbp/HOfCnPlERuBiLofecwdN+JZtf8TxVZmLZ56bfrwCd3htgVehKowLZKF9yDWgTixwLD65z/dXBX74GpcheWEAt6L0ONtf3kWIsQu+3R2H+Ro+oeLT3/iv0i/f+EgCP3ZwubW3TznZap7oAjfK5IciYoU4InJO0MU9z1a3ttGZNF0lXhRBeC3CISLppTcXYxVKG0YCUBXhB/86FnDng4JGn/vjuvTiWJo13seqhu7lzF862i+6JOagTmMrGwsbLnY80TuFUb0qhjasCVZFqaLhxqBuZRuWbDGyDLZmKAPC0XHDQmTufuk1GbcJBJ2NI5TzlzIFgWLrP6DymUQTZPWMxwSOTAW7AVHosymVjGbWe1F/TMQcdEKbaEPO6cSV2CXNGi+sKT2eQ7Ez4GvRG2xa7wHR8LGWO7i2AsKX3XH87JmxUBVDC5TKNJXdaGtBOWUqYz8GodHEuaf7kWAzg33gsjgoUTrGoPTZsZtgUaa9KVgDeYly6KHOadZqq55m6wp6v1yWyij16P2H2MYLHJgSyZWED4bqby7IL0Pirrnb2yDMBLq5jIgCPep9kVei9Aqbcr5DcCNtL4K2W4HzCxpJSpKEMgUoxuH+ge5hBI08JK73ngTQHYVmQ3KSNU9Jn9PgVwTSmOlPu/6jfddufceByMegjFRvJ5Ws7tI2CsMudc293zj3ZOfek7uT8yzezY1vVNAOgqXSrrkc4LeHsfJb6kxGiBDNa6ImtWg8YcuMf8/RN3icay6hUqYO6r05Nsk6yxqM/ag2sRJ720WPhoGTMIksdxUmGJRla4WxryYTRPEYnXUlQssuILKUjtTc56GiT6uukklsp4TIV3yrnbsoOc0gm8FdGlcY7Y05LXGetnWIAdox4ipTAo6ybqkqHhbKIjBJPofF7a8AzZk4rpkosplEzYUaqRK9L1BXmWKxgRLMwY1bXY89lm7PGjWbZ7LoTSldNTRbVjtKnPaBTPy8FLCll15dGFX1iY9G6kqcM2VyOjXurcoJRlWqGMl2pe/S+8VK+1BrQZ5zpJBCUUlE9m4SizDkpX8Kuh12WOq0o1kCxN1TbNCqLmCIlAJL0vmFspJ0SFkCY5CIr6WDAcMGyV9b6EjOkgX9/qlOAKab3s4ZqfVth58z0Ous3/azrn1NaUfZp3M2lkDkekLIgJvOR1fo+crcKNu9vNWHUng/gUgC/B+D3AVzWffY117KoppFAiRd5LopC9dyokfMJacUUIe4wo3QZfY6Y0GvWia4rMtbJp3vXtiJOa4+KUgdsKzMHnVbx7bRuRb8pctwhDFae6pwxJQ8Fq3bxvm1ApNMqC4eFkW0w61bW18U1aHyireu0i3UnWyeahx1jm7G0WCfaGRf7zXZVrle7R+nICLIVuNCMA2fwdjNWYmKMl1IHVZmcVn+xcdrJxJ20dsh8LBpkT5sWO3rARRPZ124NNCvRky5KLJuUOR7Z8rGMy7QblA50tYMobcRdBkr0WKrIOhnAX6WP+OnwozKNl9K4vXrPnbTBXOixxHWqfV770yQd26GBUgTn0rHpNdB6z23hrEljSe8ilUBYr69eAx7IygDRKOmgNejkklKWUldym5LSVYUon9DMbtCVtGNTB1/ZWLpgJMiOU/qbgmuh94KNZDbFZEiT7TdZW+6POOhsO1BSaP3lTFSaJyslbJIJbcsAbXfvWuqKXLtSHI2z2AV2fXNJ5RNVp4eU6pR6mHxy5iPLI/eRSebCfbe6VRv5kvd+DcBx3b+v6ZaofCaYophcRsSp+FYKAdHd0RCYipFeeLxrXImznmKKRUXy9HerVqJuE8NTiyLPpIjEOjkEI65TQxq86d1GNN5M6GPUqiNLyUqU3YD5rspZLRnDbC5j9CnvzR2ErOuRjoUMSN1yKt1ibySVTpF03fC5lE5y3BVJ37U6i9clhtSj6MIcK0VKYCZPHaQdm4FxWI1jtJiSXSqyDC+8lbUStL61uI4zu110T/R+Y7AwbWJol9bq+EzOKhbddigd3Y9KB+ck6FyvSLovHblL6JjHqGKpEmudGJsxFUacMyVe3JuzMGPFGpt1W0LmQjAyI3lWzlbI6rgSOrbYpdACm6LGQqCzSilhDUpmovaHs+RepDEzINwBh1ADV2D/cg9rbNgwKicIOpazR0NsJJ/v2ri3rmGNz2dgynUvb9G1TmRDhS2Meu/l+oo+ka5I1ljLBf2eM/ByLNyuW3VMonieMXgyPZfKPpLPkLt9+fryAnu+dmSvzPRcY43Fd+eyFfH52Vw2CnQy8LhzXGX+T9enJkCb3tW5kxEcdPbgLjWXJHNH6iP5XG6HtiEQ5py7HkAGG73333qv92iLW0YRN4EpKTrjxFmJ8U5WfFvnikjOZ1wVWJ7UzGAmh0iNCrBTeqGK0VAyPCwiFqxTqgvgUWQeWTID4rxyfnlx6G5efMsMSN0kqpfn7qODKAussnNhuIOqyEmr3P1RoypGrRwU0bh0tB2e6ZOy1rJomI93LFJD0qjyQnVdn8N3GVoATxtxKnbmhfmVJ1DCrms9drHIstbAUK0LZ191FBmu4wArMJ0O0jj2F8Ez0Fm5jN4XLEwdAHyor0vMLo8sy0KCmVkTAOW4KuG6+05oN6pRkLxT1ITpHaq5bsoauDwtIZ2ddD58h1tt3FsDgLgGbC4ndf68Kd27KVA36cw1rvf8CBD+LkUbGMoAqSoCAyB3WSZdSfU5zKa0km3WusKZe7FzWo031/sUVExrSkcaIJulohJw8DElzGWe60osCu9sigbLs9rDgY/Xpw0q0V4YtqFt4wHJPCswbfSGKwNkMxBm6gpj/Dm7Xre8T0ZAyGWnLLA0qc01iKCTjbduW1QF2Wdv2HXJ4Fk1YRJM6WDEwYOAUu5XCBwujpJ9njYtHki7omuf2asYJLPx1mzegM5HumSztY9cWMdHjpT+6s1N26FtCIQBeBz7eRHALwJ40L3fna1vWS0MUzpdZ0M5aR4dyDOiuCPP6ecpE4JdC5wpYXUf7FTuLBqrJMqf8XSkiDw4KxDu7VwrHFSKTuRYpsZ4bcPDC1YdDq2x3U7s+VVnvLLovixYzYGku2dk6ON3kpOWu0hzZxeBMDmtOjd8syYV6Kb15QpsRPedQxpVrFaiVYavbuFLJ8cSjWER+5Qccl7/pOt6ZCTdAzpLBwftbGUtDF1HKSXu7ALA62EAGBCn5+82QbYEDuPSASCDKe/NwYXexcqdtHaIKTVUxEDHYi64Q0p1VAFgVcpp7VYOKbGvbHOEWcvGgp867AadUqqkp5atLBwWR6nGcUqsXrcGdZPL3JSxxqvsZc47RDCUgIpgX410M98JOGXfiSCsaQWg7mPAY2G+wUZOOmBIm1g0G6lrQXcogEc6dmhtlum4tqF0XSjNSLVkifmTNaTWJhYdaGVj6WQnP2ImZ52qohAbTQTjr1KkwhaW4bq4i1Wk0CQQjZkClnXReh/luSqyg5x5iUVf0DYqi+49r6nfuwUwZcX7EfBQ9sKpzIzBVukgitkrzvxpHzlaz0eyWmOahx0s+NsObaMn5u9j/27x3r8WwI9uct+2pGUAoNG1Tppa7tJzGcoPJzKLWqdWGTABOAzjX/VExMpBkGMhgc6cVk+kJZx0D8PCI2KLUbJSB5VKafUVwQOS5YoAwDL0tSxmJ0cqio2VceBAuOoBLlTASRExX19aOwFceo14zuBxY6jTauPKRWOcOYgmnF1WKqcV6ycKtXZsvGEsyfn0yVe2LjSXUeasfvN5MlJDPWtO/R4rFkbvzEtGtWMO1LoQmNGBxjjqQd/Y0lg4KJFjMYBwk/dJpyPNsRBw6MZb9+j9qHSxbow+t4KRLEVqprRSrRH1SdswXhOWM3heyRcrVehJs1nzZMuz1tUEaEWgo+5NjFLUwzp30vJ5imEpU41UzpL7EESR7FiB7EDQNqrSdVm/OztXdTY8gRJ7V6Vmja25FBtyehj/ETGkbC5lTaXBDDUqsFMBg0zL23ovSjMUgB9XZXzepEfvI1FRc78ig9Ywltz/pWxRn49M803yHNj8pHdb3TaajuSn4xcIzNhRm9KjLW55BJHqbEZlwYpRJSiw0phU0Fh1QClRrek71MyzcTSYUTUWVcF36IR7j0vHonsNlHxUVocCy9MmUyhewLljXIr3joXCT+lYehkeptA7GMAblX2MkhEhqvq2ihfDdn2UQClfA27olye1aYw5K8KLjcfVQHTfSMPDmYvdggkr5FhInooB5xOdlizQnTGHZNWSEdBfHI/gACzxuiKV1iu686+AdMI3l7m04yuPWiuVLlusilh8WzYy/cqBsPfp+VrmZw3bQBFTLD4+T4J6uXaJTWmy9SXmglgn3qcYjLA6JgmgQ2p3rM4gWxyV8aiHbCxdP49erGKxsWZ4qKbScoj8/Liov2oTidxJrHQlypdTrw1KNkzUQRqgc9wBByr658XVZGd2CHvlsXNs7ETkslMnp0lBY92teTyqRY+lW5dRwQKdOreh9HpWfURE1F+2BgJQqhQt6b71OivN3O9erFA4jyXGvuozqkYdCOTHX0RWvsnHS89b6I5zkUCcjTcMlzHJBCg73TR0RbNs0zodYCt8jdb7hgI0h9Y7O0huvJAveXwMgdV+oDQuU5Ac/Qpbg1TzZ2SnhmpBG76LtYmyS/PE3xG9lW2j6cjXsJ9rANcD+F/3fne2vum6LRHpVS5+NqllBJGBt05Y+UnhFrtATRtRazeKjsb48wngjYzrZO6e0pFeRHq7dXTSCXj6rInGwRpLcmxEPyeQEE9bbjzGjRpLTGNaO6Ck07IKdBNQyXeoUh0CPx7BqjvhBiRb87IQY5EMntwmTd9ZYEc9pPXVRm0APNayQDdGlsQo0fO0XNQMZDsnnS2TL27AhDyxNeBvNkiyY8szP46hzK5L78X0Pq2JXIOcAUgge9hpyXSGVcMjz8ZL85RexWLuCtNptm78rYfYbGPJE2dR+ZlReQqPyhlSKkyk/LP1TYywTita9mpcJnsVQV8l7ZUou+CsBBvb8Hi9YHg4UMqKwiveJ7kufM31WBZGaX0tlo1e8JyNJY43lzkOsrVNiTKuDjYm2aGAtOjqavUahNKEtE78tV8c9GVBVB3srO1XDNCpbG/FZFWvU83mW9twS+b0+WI0Dp7yN30ks6HTJpxdpu2V1pU03zkTN2PpVwLZ0ke6DfpIn3wk2zW7HdpGQdgLvPfX8Q+cc9+yCf3Z8paUjtOxifWi70RQ0hdpiToMF4umASmESaGM1EFV4PBanQyPke/WSheBQ+NZgW7OABQduzQxlDxzWhE4uHjv3Lmr6J45Nh65TzvHH0/I704mTw7RPgi2bmQ6Y6bGaxXfktPYvVBhXIU6Jqs4NB6eWtL72Xj6xD77aKrmie/QWWBO0gGxYJXmiUfpvBiVs69UzE4gkM7rMdOfqth4VBYoCr1DlhUb1+kssShPnSMlZlWDGQ4eKYrka0COdFQ6wbJxUN96YHV1Ftd3tzKqpE/63knmbFldXBwxBk8BeJ42VszQqNtkEHbN5qmhxJRIABCdhjqjimSHgq9RWWCpTusrmF0Fplomc70MeCfPO8YjA7jo1J8MKoh1SiDbmkul43UK7KhGKRtLdHZpA1K/ren9WwAAIABJREFUvUrAf9IxExyUWCB71nrsZjKvmZJp3aItnHieBgX83nwTC7GKWr4scJ7WINmrxnk7RVpTFsR1O5W7fnqIPmm9p3WJ+lRbPsOj9T6+ySHKEx9va9RdsjmJKekZC2SjzOW2iHxG25WAZCcIdLJD88bHMjbWd3cmcywdyY4Lou9Qk8A/vb7rELMpR+Qj2+0BwjZ6TtiHN/jZETfn3E855650zl3jnHvxvXHPe9JS/lnX8HCUnwxdqH/ySO8flGyGZQjS2WFcUFLUGoTeMYeYKys3aoFJCM+XhZAqYokOKa/rEenQOh8vBwDrReB07o5w0lURDVh41x8BANrR5+LWab0GMYqrUoplZdrEe+dAWNcM5WsgTnKukzOQ85QDSv2+tKpMkR71mw40jVFzkeaSG8zBVHaTHAQArHYvG07A34PO+Nql1jdFxBbrlIxqTFdRetuaJwVmrDoqbmjTvDlx3ahKqexUR6WLf/P1rUpeXG2n1yPIZ/em08Ol80kOIjAHxACwdKTaHCGZZZnOEGunUm+8PiZnSpI8jzoAQS8Ij8dPWM6d2Qv9Ha0rQn9rxoL06L0G/tMm7WIdizKAVgAAbovoPMQ+AM/ZZq6/g2MhG0o1jt0acEZ22qQ3dXB54qyeVY+UZEDWfZIN4+urD47m58flrLGP9x7H8YadjqmWzGdyEUsjWA0ryTOXJ87+pvX1EUzxujHrKBHSsWXqE5Nx2xZ5jNgu0kzmlVyGPnG5UEyY2omf6p+lj+Qyp4OK6A9iqYLtI6sijLduDR/JMlFb2QaZMOfcowE8BsADnHPPYH86GmGX5D1qzrkS4eXgTwWwB8AXnXMf995fdk/vfXebRtR9QpBSjdI4yOLqbocORendoldlqqvxXioGz3f3OUS6N6d/V5lRq4oOGPYByrJA7bztpNn5OXTvtVmDpvVivDoiJmXdMSrTnDAQFlMzdSvGS+CFnCRXKH2uEm3BBpJR45Q0gRJ98rzFoOnakKoD1PQ8DoLE+iq52DmuMuaCWJdp08C5pPQAA51U51JbTku+AxLgBtPF8eagM9WGFE7WUek0G5dnml+r1kjT+7sXqkwueRqkqouYZuNrsFAWaEqZvtnNxptkzil5dukASiO9Lrah8zWoeKoi1deFNWAReLazVsrc0eNRlOcISjgDbug915++dKRm55Yn3EGQQ5RpPVFrRCC7SaCT16mFzRk560RHPUx69H5cpg0FEQAoxn/E9JDX5a0H4AUAmHB57k9XcVnl9UicQWu8y2WOAZVwtIXFZHcbPwojPUeBZKb3yYZ5D1NXeB1VFe1Vt75FXtKhj/KQMiDleda0aNqObWc+I9iwvH4ySytWBjAsDQZ8LEHnqCzQ+LTeluxwnzHjNqySpSC71aaKo8ejOF7hI4tUDysCu0bKU7/MpR2jALAyUT6y2R5M2HrpyEcBeDqABwL4Wfb5YQC/fi88/wcAXEOpTufcvwL4eYQT+bekkRAsVmVu1DohIFDCDc9EC0FDlHTKSScDkowKgTCN8u1dUnxHn2SUlicyskyMi0wr1l1E6pxMs/Fi47hLShsQFiHqqJWAw9GLyUlPeTqDjYWPN9RPyPOJtELpOjk+Xg4AUuGnosmZQybns1ilYmPqE83T2qyB99zQ5zVhyZGnYlS6N08nFK4VhoAiyZFxJteOUX+NBY03Hjzb8Cg9DxgSC9QVMo+k4eMOcVWxin1HPXCgRMd/8OumtUdVdK84YcY4Xldp4J/XDFWFHaULVkLXIXZjmbDx8gLkWSvnMgH4PBWVAYCOAfAeWJu24rrgDNIu1jReyWakwvw8Rav7ZDFDPJVMIDt+hzElo7Krq2l8ZAnCvfn6huNjLFCS9L4b7yxfXysgjfV8yl4tCCCsxyvtFU/na0Yp6hNbJ85EuZbS6ynQmdYhvV2VDrO13IbqoKL1Qe9DnxIQnTXdUSJVvmMT8BEAAYoNbbTM5fcmeeZ6n4C/BKa0wSumyTtmmZ7HgbBICfewxkAO/Mk/hDeTqJrKqkDTnc9FMsfZZl5fB2jg70T9cR/jX2c+0gkbo/2YeeSKrmHlPlLp2P2CCfPefwzAx5xzT/Den7MJz384gJvZ73sA/KD+knPuhQBeCACPeMQjNqEbqe1erPC9j3ggdi+mw0Pj+T1KeClCJNockKxEYMtkYS/AaizaENVwZU0HbuY7mayDQjMjXqVUZ91KgMd3wZV0WKuOdltiRfKIiYyqVatQ8z5V0rHxyG7GInIAcXwjQ6F42qluPBZGDJQohRJAKaO785Qlr4+JEXG38SIaJ8EA5GwVBwAA4uGK4dDT4HyKzokTy5aMQ5jLSc1ZNrk1nqeUInMg0pGqPobGUgYZ4LVVsthYrsEykx29U43LHG3pD3VUsoaGQPaocVlQQWOZdYFBZjBr6ciDzHUgu1sXqWOprofSr5q9kcDfK3nmQYVTh4AaoDNb32TEdS1MYjNoM0p+REXdcnCRA6VxWWBlWmfHQWjnPm1SDVyUC4OVkCwqnQOn5zIB4QysMhamblrhbLkjpboxCr64DSNblILGHGT3nZhv2QbugAsH0W9dIzUVACDpWN2j98Te8J2mfFMW1ZIBCYCkPrmO0ZFMNrfP0aYovU+pbKNOrUo2tGEABEilCqNYKsDsc6xV5GSClAudAueBOwG8cVmg6fpD8jxi401gyphLbUPVcUh9G8yITOC1dEFW027MmH7V6cja8pEJdN5vjqhwzv2J9/5VAJ7rnHuO/rv3/nfv4fOd8VkGT733xwM4HgAe97jHbSp8ffy3fj0++ls/BADJiDK0DqhUWFWIYuPMqHVCwHfYRcNTezTeC+HlLJtmwnaMZTS2c2wAgC6txgHImBkQ6lNDuyO1k669AQAkU7JU12bkEWt/SkWll4yVICPT9XutZuNVCpVexdJFrYtVNA6aveEOWO+e42BZ11hYNTSalQjMUD+9nxla5oDL7uweilons1ZsC581bSxG1e9ZozUJayDTr5z1IscWx1J2EapI33R1PTWlf62I2Do0MR31oOu9VhXDMqtbzLr14KkDYoZmjazPicwQO3V9rO4twbKsR+LyTEdgrAo2o2DjzcEUyY4+oJjuTUen5HpfxjVINS15qYKWuZ0jm0WV9w5jObjKa+A0Y8g2ujDQGTZM5KwxT8No9nW3ChpD8KmCETZPugxCMJ2qDEGz+Xy8y2y8C0zHhgrOm5YXkyd74RQIW502cRfruJQBg35TBg9GVjL2Ne3KtjaxpLVMQInbsFGZmN2MbZ427E0sdv1xqGOiuQxlHvQqJWLSxb2rdJxKss/SZ+xgPkOub2L8eWDJ7cyslEcfcZCrNzfJwD2MN9WE5cFI9JF17iNb8pFGel2zr/pcNNtHJlZxO7T10pGXd/+fv0nP3wPgm9nv3wTg1k161hE3brC44RERcawJM0CJqn9anbIUWkX1DNrQS4colDwaNbktnF9XFaxPqt88siwKmRoiQCmvI2PMxyuj1oURpRXZbtAid9IL/N4CXJABcf0KxbaFx6g1OulEW0eDyR0iiyxFJK2iLyo4F/eOEVOKLPXOHnIiQS6koZ3WIYqumAFZtjYUqJTSlAFoGu+KBiUxapbrWzf0TFmoPiplKpnLJU/PcfYIsFNDep50wbcsCrfq8rpdpEyepnV6zxzvU8XOiOIHd2p51mPRBnpUhc0SAAclBEyNowiiQ0ppvSWrjqkJxezcSUeZqxIjHWWcpaJoTbQepJ1xUp552imC1RljDOMa9BdgU1pPF2CTrIjrJpwJC+nIOs6JKsCu8lIFDuo5O6jHmwCPqjdjdWpRD2YaOLRwTrKvOv3Kgb+1uSmX58AkJ9mRNbuzDpw7IBsvydy0IQZN2xQCF3nKMsqTsHNM5ioJDHXwx2XArAeuZTqyLwUudjl2nwX204vaTLH5pJbgXAc6vF5Tv9rPYvV4mUlLPrKwWWPLR06aNveRsYQl+cjt0NZLR/579/+7N+n5XwTwHd1xF7cAeDaA527Ss464pSMTqMBeUa0ldxAhIkupoRTV0KtcSMACUOm2pquaMB0RC0daSaGjiBhgQt8ZQ3EuTJnSkU0bUp2Fd4KtEmfTkCM1jHhFTquVKZ50hlEyPCmdwU+XVg6C+l3kCkXMEK9vSwolnTQdxGrtCuNgOYESl4GSaNSMVAnfdVe4fAu0vM4x0OmiUedzkhx5AiWRXm/S0RoZ8C8lOxfWm7FOrRcpaQk6U4Fsv8F08rgPflRLnXYE87FQemratBg3+UGhJE/TuhC1Iel5iS2je3NGa1Q6rM1yhoezEnaAlOaSF6rzVFhVUgpe1s7F9eXpG5ViiRsomAxEHa9S8S8vQ6hYEXhY35xFjeCRWDYOOuu040uPd8R2J9o7ERkItIJGBaA5WxUDFnaAbpQ5lt4WG1S6e1F6e9dCla1BpfRe1Ju1Kb0eGZYMCIdzpMZVYvyXFHgU6Sp23lcYCyueZ/eO9am0qYOD7E5/6P2sBPCon2J9ld6HXeCO3bs/lc3niTPCUyXzWubEBqSB8+N0UHF4VmNW0071HPjXZStSpPpcsqNGfH35bl8pc4sjyc5Z2YRxJ2PTpk31ufreZXoFk/aRfEewtRmkKrfPERXrpSP/HUZ6kJr3/ufuycO997Vz7rcBfBpACeCd3vtL78k9783GmYoxU8S8aJg5NnWgq4i0jGLypk1Gjn+HFJ/vFtTF68R6Ado4OWEcrQjRdweU6aMepszwjArb+URnwA2mwYLozQJil1ScSzZeFkXSeDmD1Re1jssCBw3QyQ0WFRtzgxXmN1zHWZhlzjoxNqUqHIqCs0WKOdBzWacajGgw+XcqCYR55K7Hy5001XvpVEm8rmPCWlZcTYXLcZ0MQx/XiY23KuWuO8HCsOieOx9L5ojN0GxkPAqAUqQ9qbDDa3VmVKPeVZahTWugwVvODCUAUBSOAVgfmRp+XRxvnWS+MvpNuhrTN0VK++RrYEf3nIWJKeHKAv6Jye5z5CKoaBKTzQH7uEwBg6X3VIOn1zfWi4p0lTxmx9Z7xcBrFnVA78k28N+5rlBpBn+Vk3jbQS3r25anhp1TOs7v7ZxmZpwAnb16r2SO2yttQ+WOvnR22YJhZwM4lzZlx9jYgKSZzg7M7Ku5jufjrVm/09pJeY5+zNxY46PdBahmt5Gpc5YtIt1sPdR38hpH7SPTcUjJXmVBRX3/SEceu9kd8N6fDODkzX7O3WlU1xMVyqDpaUvwtG7jIZ0AhIHWzBAJbzgwUKUjiQHoPuO7dgLd7IRRywxImZih6LSUwR6X4eA9PRYClJOmxQPGIyM6cXFOdNE/gQIu9DJ1IPsU50QUnKuTjcsQ3dMhkcI48CJ45sh5MWx4cbBXwLAvumdshnLSiVUs4ue05sL4W8XGrWRKNJWeGTU+Fm7UNAtTp3N/6N5rsxQ1VnosnRxSTcniKDEHWXBQp/WN42V6UOmxdBsR1mZ5ZCvkayZZxbRhI091WvU5+jtW/VNySASW06aOcdbvDtA26QXm9Exy0hvRe8tpJUCdDrcksGilb1YYS54cKR2jwdLNrSzK5kFMHEv36h2dyubAVNeSxSMFDMAh5FmBx1XlEMNBtGrHJgP1JHNSf13cHUn9Cevr83rciZTnWceUEAsEpLIAUS7ShPqrkqdt1Sah1Yz5k2/qEPJVFiidGkuZNgnFTSylXIM0J8axDnV6cwRdR2wVP3k+Y+71GnTyJddOHiWix8LnxJavAlXp48vR+VhEQKrtLGPntE2jQEfW46o6xMazkh0lz92cWD4ynZ1m3Lt73lId+rjVbb105On0s3NuDODRCMzYld776Sb3bcsbCb0GHH2OlIw6IPPdmjmgFMe0CelBkadXrAQQBNp1BoQrIk9HaoMpCk8zpia8B0yORRZu80JIazco1cvo2gFZECzHMjEiLclolWhaj7VZkwxmlY5jsMeS2KpsW7hKs/HxpuLXsE5WRJwcKTmIcA+iwOmzmBpSNRYrqw3GymDqwnE6CqAsXHQQdJaYVRRO4yVWgl4lFeSLpwdl7ZxMf7Y4arHCuCyjfAGynoKYKZqruEuK9Wl1JvXg8FodnWYGeMo8qOBOMr0GTDIHIkWr0jdrsyZuclhQepCYzhAR716sGOhkR1RU0kHRtbPGp6NTtPEvZVBhsb/0WcOKjXl9W2R9lN7TeLk+FUVKyfJNO2K8CvDQUTG633FsjZY5g/njZRdVgdXVsIuUalpzXZH1ZvS8yIBXRZK5nnpRDvAmNdvEQuM1jpFoW6pnHCgn6NaJxpNAUF4LStctxaDRKJ8oGWOo/YHB+AtdqQoBOmkdKKhY6NP7koGZioPHfA34+o7FHLCMjkq/phS4DcTH3Xt/41EebCNCvoklMeBjxoCPqzBesQGpzIEwscZUsiNtipwTGgv3kel5/Sz5/eKICmrOuZ8B8BYA1yLsaPwW59xveO8/uZmd2+rGhZ4bfx6dRCXvAJdz6TU2emvtCi86LCgd6U2FltRug1F371FZxJdH21FNiIglW0YgMEWR9O7SOJYyve1e78zTDB5FxFUR+iTSNyUrNrbSVarGQjBTLHKne4S6mtxg5oyDcawDS5VYRcoEeBITlkfpVZkb8VGZUlHc0K6oWsFp3WJWFiJ9IwwBM3Qc8EgmzIruO0Nb64hYAi4xljIVG+ui/8yJmE4rsRma5YpBRd1iVvXXaNHzlrihrdJRAALAM2ebztsa3rWbjaUKB3USo0QAgG9iiaf4Nwl0pujeLjbmNWGTbA0kKLLHwoIYw5FzMFWxPundt3wOOJtBQUWWUuIbAzr54usbPiszHRtX8tysqkis01Cgk3STpasUELbGm9KheVDB5TnoYdg9x4+vWZpymUs7VOnvFMSEDTnsPESzTwGY5vbZoSwsnXawWONlBbK5PJNskG5y27skQH16c8TOse1XqI5qxuSZ6w+3O5nMxRR4DsR5Laio52MBIbc7WV0eC+yiH6uT/9OsLR2eTSBbziVnjdNYuI+0Slj4sTfb6YiKYoPfew2Ap3jvn+y9fxKApwA4bvO6tT2arM8xHBtL4ZGy0nX8DJaqNAxWleonuKDwVBiP7oXBNArc9bEZiQlzMfKISmfUkvHCzwzgiXok5qCq5CCEQmWgT9Z7ichyKo0TEJQ8jbfblq2cnThosJC7ycxiZwsEaeNkOXICF8yIUyRbK1aCG9oFYZz66XYaC6WcKgYKJE2fp1GjwSwG7p2xIDnjwM8wiuzctImOVo83Gws7eHbaFVJrxyaeN2lA9Vc8cuep5MwhGoXbmlWU68tT95QCVwAgMrtqfUsXj4rhb1LgusKPAuAlB1zv+ViqwmUOgnQVUCnwqmD9TmvAC6lzpiKMl/TeTtEW8Yw3Yh7pmVFWKwayld5bsqPLIORY2BsYdPDFv1PK8ZK9kgecyudVJb0eje0oZPLFZYd/J8yDE+PNxkJglZ255lwYi95RaI2FB5v9wDQFNUCwyfz4GjvYlDV/FnjkQVQEnbFPPfVeVSHsMz+YXINlORapv3xna9L7UugvD+z4q5wqw4ZRsKmPxpHBSPqM+0giIfgmFlEa0dmr7dA2CsLu8N5fw36/DsAdm9CfbdVidK8cqTiKoMojy1FVqAJ7m6ngxj8ZVVmoDnROmqeGSFkM4zQqU3TPDchICX0+Fn7YYn89kqhLKFIUxx2ylYoK4JFemmsrOZ+DFMXJ+g3TOFWSCQvjdVlqCOAGOtWGUERsA6Xg2HiNVDAg+b0ly+bi+TljZjBXp5Zc1NEZc0PLKfg8skz1KkWXduA7sGzjX6Q6RCVfcU6YY+Egm5/bFXf7GgYzprKVfOl54g7C2vEl2KqyiGeJkZMuXO5E5FjyGppcLtOZeqIGriqyM9DEWOJc8pKDfnYuMLsuXhvPejLGS9E9nZnE50mDizCXvGaHzmzSAMAqcWjYeFNN2IIxluS0fHzjRlZvxjcLdPobgEvZ1ZBq5l6n11NK2LkQWOiz4uRY5AG9VtBI6W4gyCoHnbRrddSr90U8n5D+vlAWan2TDeMge1Ln411VYJXLJcmc1HHD9jLAQ8e7yH6H51OJg2Q6fbSh5ltWSpkCp4yOtoU0lsRoORGUW36F9HcigKETjJa1viMKwAf0t89HWiB7JfOR96N0JIBLnXMnA/gQQk3YLyK85/EZAOC9/8gm9W9L27gKdR914zOlo79bkUdVFPE7Ir8faeOUzggnKxuF25U0WCOhUCwi1fnuih9R4ePBpWNlQLq6fCxPahQuvSh5Mst3Kelidn5iMc2DmYYxdgJSQTLtuhPOx3DSlL4J4+1/gbeOdkdlAc16AQHMkJEhUJLOgxqIPhm9L++d94nWZcbGG9mqWb6+HHTG96xRajXWueTgUTppBoQLDmgVMyRYxXx9x6JPNguj5ZlH933OVjMVPA1DaZ+xoSvC2bK6rV5QYu2OVAX2S0qeZ62sgRsx5yMBls2Ac2Cqv0NjSQHLOqlklQoiEDEui+wtEfl4u6M81HhTwCBTyQsMlKwqMGfdm+zOzoX8PDf9vGSv5AaGBUN/x2UC4jTeqnRSvvR1rL6ONt9YZQF8LFyeqVxEBiw5ozRrfDy2ZFQVws7y4FrrSsZWzeT6xiwI04O+UoU0FnVAsPYrAlDyQMcxgGWVRsjzARdHaSz8bRpVzeSZ6SGvnbM2sXCwHNlIZkOJWQYk00k+smn7fSTXA+4jOaAcK72n4Is2zGx12ygTtgjgdgBPAvBkAHsBPAjhfZJP35SebYOWlEXT1tIhUbExGZhx6bLaIyBPzchUmC4alnQ3F/rVKX+3oc3w8LQifW6m59S9Z01XJK2+A/Bi9gQS6DoRIWpFLEM9Dt92n66zU4ZcoeS7HHPjL1MA7N5TwyHyiLhiqSEGePJz4CQrIYyTsXZkaPl4E5iywCofrxP1ZvYayJQl9cNk5yY8ak0pQ3FgruFIeUo43HtYnuneutjYnCfNhPFC5mz3HEtHqjomE5RM61SQTOurdsHpsfhOf0fmePMjKgTwr3XKX6amaCwadGY2henBgqH3IdDhOp7AOS+wt9a3X+9zgCdYGLXJge5N9YUkX3ENmB7wfpNzl3KZr93qVK2BVW82aeJRMQkI2wecavaVr4GQL4MZCjKXSjqyeVJghn/H2sRibbhandZxzoK9kqwXYNUhGrvuexg0zmRzG6rTqKnEQe8SdsyGy5pZbp85KWClsrmO8XSkfH6SgfhZJW2K5Vf6/NiQz6DrpvcnJsx7//zN7sh2bDz6kzUWOcvFDQ9PR9qFxKnYOLFsNsND947CWxU4sDKN38lQfkFsVVegW9jRvYfP7k2CqetzzALoScOiGgXwspON0xlRnFHSjsWilivG8IhdfwZQmjQtHjgeGeNlRbTC+cgILdUlcDCVpzPGZYF9y5P4nL6XqMfxFnnNgzhNm80lGZAsuu9JZ3BQwg02PxxWg2y6js7EEgCAry+TOUoviHovVkQbwVTdY8RV1Dpm35FnTcm5pJrKmIYZcZmza8Jyh2inSKmQmcbCgbB+fyjdO46F24aqjCBXpvCSrNLYq1JG6fq4D21ndh21GD/nz19gek9rzQ/qpPcI8rnssyn9wZAVjIRgk1JRgqlhMm7JXC9rzADH0TuqTC50LZkG8HWrN2zkNUMi/crXqWQsdS/rRHZd6gofC9cVXu+V1WsW0oY9cOcoW19+1NHKNO0U7w/c7bQt/VwxW2jJc5gn2pmugk1WT8j7xFljfhyEDir47m2t95ZcCsa9kD6yyvyKfB5fg/3Llo+UfmS7HNZabORLzrlvcc79o3PuI865j9O/ze7cVrdRGXZXtR7ixG0rT84Nbc4csFRYlVJh4sXFzMiE62xQMip1akhR6RQxDbBO+rBFWTvAduZpSrzKx6LvreuKaNvwAnPSFnDQxzH0sRI6uqexhPfKaUea95unwqjYWO9IMh2SYiWseoa4yWDAYMoi+BQ1yl1w/Wk2URPG2MhKRK3S8HFQlEX3ImBwgk3gYHXFYAD461IS42Gn9TIAb+pKKoIXbwjo0qgTAfAKMV6r1imlhFMtGa+dk+nXWvQ76mHB2DldkBz1N4E+C5RwXSFmNxVg58yBGEtkbXvYdV6QXLl4JAcfr8nOCaAk6yfzVDa9KSNnX60U2jJjeMZlKDjXmzqS3ksbZuu91INUBiGBUnbIrJ4nBoTFDvdsw4bKJnD2pgc45MBQ7/qT96bPqtKYS5U25vNdN2lTxajIdUWAbG4Le+QrPE+yiCYD3mefqyK+/9d+S4Nm5fN7y4A/95H5gb2Gr1E+UmardLo5BY3boW0IhAE4EcANAN6AsFOS/n1NN6F0TDE0RQzkEZpdoCsFfNZ6TLrIkoqNdbEz3ZsM+kIlHdtCdu6Oi+dY0cGO1Fe9JZnGwh05dxDjUimrcsAJ8DCjNkpb3Cm9QAoFhB1tspYsRYgpDZOUdaHSBavpO3EszIAsMEOrT0bP1qmyDaY+giSNhZQ8GTX+ig9iYWgn1TSen5M+sw1mXmNBz68GnLRmHEStBFtfXvuji425wQpvYEhnh1Vcdpg8cxYm1del2j1LLkTdlE6FGcXO0kAnmeNjMYMhgymhV99Yz+NjMfVXFBtzpkSmwqJc9Og9BzziAE4mX/R3YVOKfJ74a6GWpwmoLVARfFZrlOuK1Hs7NbTMUp28bssKCMNhuKxwu0o6ZqWkxbtuq2TDaD643ksHLFljXk8YN+RE2emrr7NLM/Srwaiulj/P0nux8aKSacWFbmz9Y6FaUNZvdkyItFcyM6M35Ogg2ar5s978QkFjmKfaHAv5Fbq3BeDNuayUblaGjvWAx1HV+chZ8pFl4eQ7iXt8pGT3yaZJvb+/gbA17/3rvfeneu9Pp3+b2rNt0ILwMuOkqOUs8ogRU1Io7siXeIqH0d1cWcS777hzF0aVR5+yhoaKsmeNx2TGDabLtv3TWKzIVgNMIJ0lRmPFEaR3AAAgAElEQVRZMBSK1wUsTXiUzoFKX/RXxLHE6LMqzXozucuQrpMF3/qwSb1OwWD3p4153QU3PGOl5Nyo8rG1qtYo311FY+H3TmmY3j4ZUbIAPMqR8u+EjRfeHoswmNLZcafF06/cITetz9gqkWo010DWIyXwmK9BGEuZ+s1ZRQWE6TtpwwbTA/M6WSu4ajhpYo3DzrGUXu8dSwQ8ci6t9BFnhNfXFVlrpNOv+niCobHQdRZrrFmRoVpQLnNCV3i/KUDhz+PALNMxXqrAd+ZxEGb1iYEZzs4JO5vXXxHopHTVTIFO7tw5i6rXSb+Dku5Nf+fAW15nAHFlZ2M2wbJhZY88lxLQcvnKPhNp+ULWMRt6P9Y+UoFsnSbmAMvykcuq7IPqJxfYeOXZgz0+0gjS9S7huvVo262vC9soCHudc+5lzrknOOe+j/5tas+2QQvRSVpMqqFZWsdpVaXcuTVmQsC/MzXofStKDu/OSo6FXhgro+ZgQAoRJUu6W7waxTCYwYkkQxDP62GsAE/fWKkwCTpTNEbfpfeA5WORcykZgBSxScbDCZZtaaJSSmyd+GGLlvNZqPIdbgtlGfsRxkIAoIyH3XIDpo8UiGMxAE+l1o47O2EwmQGjOaiK/N7c+I85g6aYzmj4RmkO0licGouVVpTMX6XGuzJlBcGVs8fC+l2VztzlGA1mIdcl6k/hsLTGdIXJl3bSvH/jqmTsqxpLlDllxHvkK47XdKR2KkwHOubraZjej6pcV8ZqLvl5bvH5XH/WYcAzpxUBXg6yw9EHZbpOjCXX+4WqELqixyLe+6kZpb6yAFZwboHOOJYqHYa7MpAKE7oS5Ss46dVZw/S+MPWeNjKF+U5zSS8np3vTnMmUf673OtDi31ljh4DH8Qq2OQ90Ks6+jhKj1HoIphPIbRjfrdgbHDDbQGxkL/NHa1f06L3S8Qx0FhvzkfrVaICqryM7tw12SG70iIrvBvDLAH4UAPXad79/zTZaPP7zqCzSS6CVA+ZGLb6EupLR54N3L4j7eAZKRqXD4ehYSozKxnw+NUrxOIduJ0gyvIAuhEzHUpARiP1mBoSEV0df9DM/H0gAByN9tLRW4xuOSuMdHAubS/63hUrduzMy3uf34QdQaqfFx2sxNTyd0TcWAi40z+E7TtyfO5r0WTIO+7tNFWMGzgFkjoW+Q9fS2JxLdRB8Sz8PGBbYs5emNR5e7oj3XmLypfvJnXv/WFih67TG1+9ayOaYy0UcC5tLXRcYXyatdGVUyqBiKWMzcmPMn8/nIdX1sDkvU/p1STlEa06mdYtdXSH1aB2912Ph31kSzEGSr/g8LhdKp/Ua0NzS/0uM5VtvLOuuU9OmQnliomaKYbFSYWsyFcb7zccUx2Ks3ZjdmztprvdjNd/03btWZ9n8aqBmZTOWpjWOXhyJOdVHefB+W2MbK5mLc7LuWJi9Ymsw0fLFbDFdt29tmq8BrxU09H5Uuu5wbRlU0LxmYykdWp/mydIVLnP6xe6AIXNNAko8qPh68pFVqp/kDNqhbn3vno9McwIAk1mLxe4Ikq1qGwVhvwDgW/8zvC+SN24cUuG0QycDQoHpb+F/+VmlhCJc6yIoSs49RF+AjO4BREHhn9Frg8iIRuDSfbc1gFm6Lo3TMthcWKd1C+ckCyPHkgAeV7q69bEvciy5weLMEO/TQsXAY5nYyLr1bOenNOp6LPw5/PeKgyl23azJU2F160V0H8dSlaYMaGdvjWWk1kT3e1Sl08M5WOf3jmNR60LP8T7Jg5YvPm4gyJgFhDUAIEPuWfTJ1yAyM2peRka/c8dmr0kcC11XJZZroZL9TuPlfTIcS5VSq97besAPJuV/Wy+o0GPhjjzpfZIdkq+QrktOwdR7rSssXeYV68T7nl+X5pLfy1wDQ+9H3IYxIBzGYum9ZcPsPi1UJRuL+o6lK5beMf3V/eafmfIlbFhurxZHRbYmuk/jjhlaYAFhPt5cf/oCUsumVXosFR/LsN6vMQAix2LME3s2D/iFboh1ydOvYixqXfQ46Ltt5iPdPfKRMUDrvjtpGgAjbGUr1v8KAOAiAA/czI5sx6ajSIA7vXRWTfyO4dh4dML/Zt1b34vfx3KaERQoZ7lgCr1Scn6fHsUI1yfjwlN/1nesfo9Lq990gKwTn3FwY0djcp44AzDYpx6wrNeJ37uKNL3tSONnjN7n3zHBTObsLMAj+83nvA+4ZGPRAMB4frxX1T9PlsxpFoYXYKfPDIdUFbbMV/l4NWCy+2Q70r5+cyCaxuLknPSCKUvHh+Wif7zyMy47luyaMlfZTnps6M8gyO21V8b6Hul4B9aO95c2rKTn2XovZDCmu9ef33Vtr7ZX1tjKXHYCgM7nZGhdSL5NULIR2VEAL/+sZyyG3tP/ffIVvpOCgRB8Ddsdrff8/Lrs+SpINX3tBtaO92kjPnKkft8OxfkbZcL+C4ArnHNfBDDpPvPe+5/fnG5tjzYEANL/67AwG1KMHMFvBOUvspOcMYGop9B90sriYKfC+saSHDlXjNw4ZQ6xJ4q0PrOYob603qo6XDP1yXCkVQFPYTXSfA85DduJpLcPWJ+ttk1aEwv0KfAiQZEFXBJY1DVaWb8r6Vyb1uffsZwGGy9P/QEMuKj0mJmyNNfgyKJ7zkTVbWP2u8+585QDyRfXsUULwBa6T7b+ECiUY8uvyxkly/lYoCSkhjbKHi0qAFApmeX9y9hIcw36gXgfuNHP45t2+NiGxmKtiaX34x7Q2Sc7vJ99aXLez3Xly7JXVSHYZ0vvaV0WqgKH0S9fvP/0mfArPWA5+6wnYJB6L20Y9XvBWichYw6FS6DMer4OJG29sNdgXSBs2l453g35SBXw3J9A2MvYzw7AEwE8597vzvZqNm0sFdISnmoI5dN3ilzxSRFoh44GZbpPiyPZB0sI7RRpwSBYT+ShnmcauR7DR0aL99sCLhrgmEBtABgOgTBtnFoOwnqiyPCZVNIFFg3ajiVdtzpDT/o1NyCjYgM0PSuA5vfcSPq1bnIQJsdSqr8NyZdMj62b5uvp03qyw1Mzq7N++eL9BYKTJIZhUrcmWNa6MS5z0FlZelCme+tNNLpPo+Lu6n2JtVlrype9LqUcm6FjesME35mon6/7Scfl6ALw9cYi9N7QA20LhpymTCk5U+aHmBLKVPBSkMSyyUCyNEC2xbDwDMPCqAS7DIuVAWbUePWaiD4N6MpCvL5f76l+0krrDdmwQb1X68JtSiwFGQCUVjDGjxDi1+kgUn9HM3j3lo88+9p92L1Q4RuOXsRWtWL9rwDdcRR3AfgZAP8M4McAvGXzurU9mu3spNMRgmIBgKowa48s4dHOej26O4KZToB3GFGNGWkVdq2ENRaduhO1R0Y9w8KojAaJ35s/b0EpBu3E5Mqzo3vnJTfs2vhWxvMtINwXIQqjphSY5nDHeNhp8R2T/DorQlsQ9L4cr1UTptfl/2fvzcMtK6qz8bfOfO69PUJDM0ijBCeMiuKAUYNDpl8coon54pCon4YYY6L5TERDjJqY0SEaNGrEAcEZB7AFGWRQIiLN3NCMzdQ0DT0P994z1++Pvdfeq1atqntBus8F6n2efvqes/fZVauq1ryqdsiL5L+n69raofWh9bOpKBG5vogWqnMJjYkWkW1U3YiSFoXx0lUavXWaF0ZL1eWbmDFTCmNf2WrtyTU2n7VDz1Llh9InybeawyKNAtpEwseiWXfXF/9fW1/x4nk5v3Mb/nx9aY6dZwAojlZIhlFtpEubxpvuNTfKV3XGAkB5hh+tnbx9vr5C0deGsi51GeY6nc5YVrR+ypRwmF5Zi6ZFWp15CfC9qlfEvKh6RXWiaJ61rIBCb60i9Ep47bQbD62OfP/31+K7V92DcSIaCTPGPB7AHyGLem0F8E0Axlr7on3Qt7Ej5t2HUi78HvpbK2ptKYxRKAbFE9FqWqSVr3mfctEC2YKsmLmFqnNN8yIFY1A7FGHoBaISvLgaKL1IjXl4FIa/SJc/cz41FvwVFarAqroCa76RMFmjNB/vnjZryF2W/Dl0n0anJtT4vIRSLC0lQin/19ZXU1tztSzqpKdf3WfRWxNkimmu35EQ15Q7N/QdfukyPlAMYcl/Whom6N2LM5Rkn+h3sXpRTSHKyIPu3buGMLXbHw7LKIxizPjGib++QnViXbGbzaOlQUZN5kRxmTYfGabxvWYctxtVdQOSHskWYzmXMcOM8t5wVIxhKxI1rpgyElSkwGOpZJItjbnXPD2DRyPnI+fmo1cyWtz79fXltyd3EJZ6JaxH1IyDNi+eLIzQQmv9QepILcrXFrTta1TmuH4jsqjXy621z7fWngTa9vAogLp4IhEA/ooR/rsKO4eF/p9QPC1ppXPjraUIaKkA2xHPMlr3IQwJ/kypdJpKlKtdrynfCe+eGwl1V2loSrNgcsWg9Lx0Rbl7tTCK4OVRNqlYSsGpCGPHA9brXLQ5kGOjFhZHvPtQ+oj3jZ7VEp8BqEqyHhFOmoEl53Wi4a8vKdgppefOQVhASwHrRiWyv1sNn75Sufvj1BJ8UM5z+ZyJhk/vfKJzkn+kguO/0/i+MAhVJaIod7HuNV6ZaNA7GGks/WdHU6uesvb7PdHQ1zWnfT6pIb52NKdxQnyn1qkFI2FsLiN8T+OlrTlJC0WDeQStpUXCxNxN1N023H6HZYF0hPnvZPR0wokQK/MiDeG56qjyZ0snSuMVGcF6IFFUvkGjpEXRKw1X/jxQHamVhvC5Hgcqc1z/fQCbAFxojPm8MeYlgFNO9IgGXyiTTT2kLFMu8nfFgmoKhtSYRQi1SsU3XJwQrVRWCkNJYdysZYcqkqcV7LcQ9HWFyVXGD/SFKztfqPnMqtPizsGkoE2jpWLygwYVY1lj8lKxKFGYaKRCKpaIMCaB76yvuWkpU9m+UJtgUYlK/s8z/py50yN+jkesGLlSSUoFCfjzokaNAx4xH5+mtuakIZvXwji0aIX58+IVn8doXqTijxnQxfpslutLplP47wrFIpwL/ju5nvl3miKV8zTV9O+JR8DdKNmk1m9hVDhGpzK/ZWoobLjoRqe7NqeKOQkrdxlt59cmlfUkDUotChMzrjWDUtIinciMFmVexNjFDLVifSp6JZSp0GjR5kkamDWWEqa5d3Wk+50aNY7R0pByMmxQPmgdqTosC9gIs9Z+z1r7fwA8EcBFAP4awIHGmM8YY35zH/RvrOAMVSqW7Dtp3ABcufuMMCk8LS0qURZ3+osiuttICAL+exkC54pBKj0tvz8hIh/894WhojC5TCvUnXSZLvBqjjD2BV5bMFlpGJfPJmNXph4qFeMJHE0Yy0iPM0+KAJHzEtr5ye/VhHEhwLhwCAg1LfIohTFvh8ZbS+EVSisSCXOLwN2ojZbCKxwO4YBoaRht7UhhrEVYyjEtr5XnZSn9FsZxU8yzdg/gR/omG/6ak7RwBVc4OhotdXdetLoiOS9aEXmMV2I8LmWSdn+hEFWD0m2Xb3SQBhe/z5dX/hwUa7ZeKRRtPbKeJsWak/LLoYU5X1RPKPuipvACu5yB0HoSfK8YahNCrzj3RaJc8zEem4JXs7/dZ85n9zo9k0f+Cr1S43PgrjEpv7J2SX+G5yWmI5sK35f0zkNHKjp2oacjAQDW2mlr7VettS8DcCiAqwG8d6/2bAHACYkLxl/Uyr11x2PL/p5qloe/kdCUzOJEYUgQNHxGJqjhfZFi0Lx76a3yxU91DVNES91fvHRNjYQpioUEphSmak2YUCIcKi3CeNEiSuQll0K87BvNmaZYZFRCV5o+kxvjKoiYRyyFMVeoWhSmoKXujhPRwe/X0gOxSFiwNkTbds/oLaJOYj1oyp2+m2r680TPdmgR8xL17vPf8x1qcnMEjxi2xDpsK3M5n3SkXF8OLYJOPcUSiYQpkRbJP7yWcz5RPZo7zWGZ0mRY3aUzHj3yjTiSKeqOQjEvoQJw/kzXyKa++MqdZG7JK9Wcbt/ppLFwaYkZ/u61KpsDOvpmXulILWos9MpEo+qdOUhGFNcrcizkppQwLZLv/TkIpe4BFJGwUvbyQIW75hY1fb3SFHoFKOXgZCRbRDpS27ghaYvqyEiZy7gwLyOMw1q7zVr7OWvti/dGhxYSNMVSRITyz4vbJWPQ31NNf1InhICeT00Yh2bMyJSoZsT5nny5+OnkYeovvbKD/z3lKcRwCo9DKpaop6V4NZqXLJlMMi3vL/WfKw+ZWoqlJaIKUZkfr75HYXJt7ou+KQpN0kLry41GuuuRnw8mBY7mJctaPx7e1wrzZbuaJy/nhejgz16cC+FJxxlx50VTApIWdvIIqJvapo4Hko7kRicZ2TLiuKRd9pte7aNFI+vi3Ku2VuciHJZYpJUbYTScZYQ4zPeawTQp1hd/lqcQlTVXRGyY4U79UzexeJF7/x45L9xRKR1ajRZXhsnXDzm0RGqN1FpQ0U/D5oD4TSvMDz3TjbS6tPBrJd/T+vINeAoONJW+aUaYrKuLR4/8dUX7m2SkNeuLkK8RvcJlWPH7xj7Qkcrv+XoYBx6wEfZoQl0RDoVxUiiRcqHIaxyxFEsslUXQ6ly8KExEEBT3sP6SwCQPawkzKClCMVUoneyamw7xlSRB9kWvOTAObc7vFcVS0CuEKWdyGnsSXFwo0V9Ey4RiAEiFVlHSP9z7I5SpMMUbi0SkCBOKwKKxJuOrFGDl7wta8u/4C2llVIJHHGWdixaN1I6oKJ4td4MqioXmQBNySyZ8XqE1Vyom1/sFSoOQ2uXnv9Gf5WGtfgpcRixrjtHpRyNl3+h/1WFRIkvyCAEtKhFLOcoUKY/8jax7j6NIhQEwWSjrsn2KVHBH0gRkApdzMqrA54DYTY9KuN/pURhXXvCxIINHU+6LRH8Xt5U11/b5h54vjT9tY0tZ2lA+U3v1XEmvLvPdFJ5Ly4g5UfRMuraIRcKIf7SooOw3520pQ7UUvCwh4XNAu8w1g7LQkW3SHSRnfXm1SDHCpOGv7/QMO8Lz0pEPw92Rj2osZcKJlPGyyQaA0jjhSl4uPg66bWnOPJp3X6ZYfCVQ5PcVZgvVaPBnEi38hOCi0LXlC2OZjlw60fDape+0RSzD3a5HLJWOT1Ph8SjGgVQMvN8yesRB7xqkOXSMmWJefC871G8NapG0iHRo40XClPrGsUgYllyRLsvnoIjUsvVRFalDNS0hFCJHWT/iXyPlQwKWxs+hJe+bhYWEjLQCZU0gzcuy/JnaoY3twgjz+6QWGwciYZx/yfhb0vbnoOAHxXBZLBQLV0z0zsBlk75CkvMSS7Fo6cgiCiNq/4CyFqpY13Vf6UmHxWk3H6/l+RxyQ5rmhWgZsEkoI2E+H8iT/bUNOS3B9zz1J6N6yxmvFMZMPhfaeqb7NafAS0eyeZKKm79tZGjDkbBKxR0LaoMbtJIW7kQRigwLc1iKecnp1hw7zeEvrolImFaXpxnCI8H3Sxnf033UN5Jbuo7054DWztIJhVfEvDxoHalGwpIRtmBxwOKm9x0JIE0Ry0gFXyd7utnJHgcsyk7m5RNPi1bz7gmalU8od6y4ioK3syJvd7o7KK6V6SLyxsIRPC3FesCiZt6G/zv/fXh+JIy+UwIPBbNpxh/1kwwmLiQ0JUkgAVcqEV5s7ArKJcrvtV2kBArTaxEAmhcysDrKqzKo3WUKvXQS+yLFsFxWKMm8/2yeaK6p3dgBlDVlErT6NkkTtbvfZMkrbUELP2mbUKbuw2tnxZTPf8sFLZxX6G/tqAfvcFpFMREtGt/LjS1ciJOyKQuTy/Ga6bl8z+egEojCcEi+ryiRIfo9N0rI4KEx5OfkESaVSDJhkPPK0vyZvG8FLXXfqZAbETRekdFIrqTl2uHyiviV5Cs3AIjeQoYpMmWpiB5p2C+n190BGYtGUk2YHxEmLM8NcI1e6gv1ra8ZYS2XbqAcJ/q9xke0HlqqgRaL3Mcis64xQ2uBg+QNjzKXtITTkXvyuaY1qxn+D5WO5LL0YVcT9lDBGPMaY8z1xpiRMeaYcfUjhv0VJUCLQHvnVOkRZ//zhT2TLzAyXHi4W4Z2lyvREM1jIUjFzSMHbaFYuFAri43zfivCmNZ6TREu9KoHisBxw3LjjlkAwMFLs3ucSJighRQVBzH7quUT3jUSOFqEpaxz8ZmcBBwZdpOKYUn30DxxHLy0ndGijAX1hejkUVSik2jZvLtbXKsVRam5R6wYYQStXVknxoUbtbNqv6xdvuakctQ8S7qf6OZYkY+P5i3TGNA61hVLOHU/m6+H5VP+WBy6LKclXx987ZMQl2k+oFR8h+Trceuecg4IrUKx+HMv61SME6EhPgqnhuiZWlRiupf1WxtneWL+LOOVZYVyrwT7TTw63fV5jIxHzeEoosYT/jWSKVK2AMD2mb5Dixrdy/ur6NFiDg7LeWU3k1c0vqSc5QGigL6eCMtE9Ihjy55e1u5+kwDc+SX6tGikTIEftMQ3Sg7Jx4LTQqC+EK+MlDGJRfdkrSIHjaFWc0vrgZwRx9Aivl+S9Xvjjk5xjfie5n4/hUdpXgYKMYWOpE1SjFdIN9Ga1eq2yMHRnNWYjpQ6ldP7aE5HrgXwagA/GWMfooh5cZpioXTEVGSB0SKuKF7C7VumAQBPPmhx8R3d/6uHLAEAPP7ARQDchfak/P5b7t/jPZMYigT0HtUIC6fgiE5tLChKRsJhBVMCN27aDQB45qplANi7xqrlydovePwKAK6x+7gVk/lfeWhbMUhJ4EwrQo36qUXC+rnhXHiIinDakivnFYpCO3RZ22n/5U87uLj2u796UPZMqjVi40VzTcYQN8KKCFaDPLQHViRKwkTuagOA6Vxhk/EXS1n8xpMPLL57zmOXAyhTB09cucj7HY3Pjtl+sG/k3ffUSFjYg6c1ql2j/pISefLBJa+Qsjv2iP2yPipO1NGHZevxhnt3eddoDjTni4S/piSLe5QiZ8KKImrsz8EN92a8QjzO8Zh8zREfHXHAVHHtSSsz2rfk60mTKcuViBIhnrrPeEVT7gQyCLVxfuqhS5zf8zX0oiccAECvQ6S6MeIVjiLDEOyR7kwQZOqeg/hec/pkMferjj6kuPaHxzwm71v2zP2UsaAsBOd7gkzda9DqpwjkwE4q66pwGvOoFze2aR0e94QVxXe07klOHH3YUgDl2ADlXFcLea7pyOyallotdKQSNZ4uskVhHXnHlhkAD62OHLcRNrZtAdbadYDrcTwcQGkbzQijRVMcnMnTEv1cYCnKnfCqow/B139xF171jEOL777ztufBmDJK1apXcen7XoxOv2z/N486EP+0+ga89tmHFd8tnahjx0y/6BO122URPOqflooikAKtKwwhix5JUQDAP77yKHz+p+sLxWiMwZnv+DU8dv/J4p4jVkzhR+96gSPE//EVT8Hxp67B4/b3PVJCaYSFX96gCVrp3WtMTvVAR6wold3vPf1gjGzZl6MOXoxvHv9cHHP48uKeNzx3FZ588GI8hSnS//cbj8d5N9xXfH5MLuDJmAMyYbSrMyjenab1aT6g9cDpPmhJC/fu7BRz36xV8Jjlbbz1+Y8r7nnj81bhuY9bXhgnAHDqW56DazbsKKJOtWoFv/74Fc7ckVKN1VOQ8opFwjSvlZS7ZoQRnrlqGRq1Ct710iOL70567dHY1enjoCXlmrvq/b+Be3eWnvwTVy7C8skG/va3nlB8d+zj9sOl67cWtGgRllrE+SKQka+lYeRmEG6U/MVxR+Dd376mUHoAcO5fvxDLJhpFu/tPNXHh3xznjNefvvBxOOPqjXjh40tFKkEOIckfjknhNHJQpL+u1GsSyNg86uByzb/9uCNw+R3bijFcPtnAd/78WOee5z5uP08WfPQ1T8N//OhGFilxo3y8vxQ5fKCQETxuLB+0pIUbN+3GIYw3n/PY5Xg6m5OXPvlAfPttx+IYJuc+9Iqj8LKnHoRnMVnw2mc/poisAaVBub8aNcoj50rEkVCNyITZfCw0Y5l+d9CSNha3avjIHzy1uPa+33kS/vjYVc68/OQ9x+GmTbuLudtvqoknHLgIr3pGaXQefdgyXHnXDqdWT4JkWV/JFvk6kmWLclo0J4jwe0cfjNMuuxOvfubcOpJHjX/zyb6OXDZRx3amI8cGa+1Y/yE7BPaYOe45HsAaAGsOO+wwuy/xpUvW21MvvaP4fNfWabvqhNX2svVbi+/+/LQ1dtUJq4vPnf7Arjphtf3qz+8svrvizm32hNOvsaPRqPju8tu32g3bZ/ZKvzftnLWX3rbF+e7vv3ed/dmt5Xffv2qDXXXCartrtld8d9Q//Mi+4eSfF5+v27DDrjphtb1p067iu29dfpf97EW3Os/+0dp77Wxv8FCTYa219vp7dtqbWfs7Z3v2z76yxt63c7b47r3fudYe95ELi897On276oTV9vM/ua347ouXrLerTlhth8NyDv71rHX2/Bs2FZ9newN79nX37hU6rLX2kls22827O8XntffssH/9javsgPXpRR+50J5w+jXF55/dusWuOmG1vWHjzuK7479yuX3Vpy9x+v32r15hb9+8p/hu444ZZ50+lBiNRvaH1260/cGw+O6Mq++x/3X+zcXn3fkcfPfKu4vv/v3sdXbVCasdPnjqB8+x/372uuLz7Zv32Ld/9QpnPa29Z4e95b7de4WWnbM9e8G6+5zvPnbuTfaH124sPq+5Y6tddcJqe8eWcnz/v0/+xL7g3y8oPm/aOWtXnbDaXnzT/cV359+wyf7LWTc4z774pvvttj3dh5oMa202dlfftb343BsM7Tu/fqVdd2+5dj594S32iPf90PndqhNW27//3nXF53Ov32RXnbDabmX9/NzFt9pvXn5X8Xk4HNnV12x01u5DiTV3bLN3bZ0uPt+zfca+7dQ1dk+nX3z3hpN/bl//+VJe3bFlj111wmp77vUlT//TD3XkZBIAACAASURBVK63z/rwecXn0Whk3/Pta+wVd24rvts+3bUXsXl7qHHe9Zvsbtbvn9682X7gjLXOPUeeeJY96ccl/3zzF3fZVSestluYvPjd//qJ/cuvXVl83rana4//yuXOPN12/2577d079gYZttsf2rOu3ejw75f/93b7lTl05NtPu2JeOvI9377Gkc/7WkfuLQBYYwP2jbFaYv4hgjHmfAArlUsnWmvPyO+5CMDfWGvXzOeZxxxzjF2zZl63JiQkJCQkJCSMFcaYK6y1au37Xk1HWmtfujefn5CQkJCQkJDwcEU6oiIhISEhISEhYQzYq+nIaMPGvArASQBWANgB4Gpr7W/N43ebAdy5l7u3P4Ate7mNhAeONC8LE2leFh7SnCxMpHlZeNgXc7LKWqvuoBmbEbaQYYxZE8rfJowPaV4WJtK8LDykOVmYSPOy8DDuOUnpyISEhISEhISEMSAZYQkJCQkJCQkJY0AywnT8z7g7kKAizcvCRJqXhYc0JwsTaV4WHsY6J6kmLCEhISEhISFhDEiRsISEhISEhISEMSAZYQkJCQkJCQkJY0AywgSMMb9tjLnJGHOrMea94+5PAmCMeYwx5kJjzDpjzPXGmHeOu08JGYwxVWPMVcaY1ePuS0IGY8xSY8zpxpgbc545dtx9erTDGPPXuexaa4z5ujGmNe4+PRphjPmiMeZ+Y8xa9t1yY8x5xphb8v+XxZ7xUCMZYQzGmCqATwP4HQBPBvBaY8yTx9urBAADAO+21j4JwHMB/EWalwWDdwJYN+5OJDj4JIAfWWufCOBpSPMzVhhjDgHwVwCOsdY+BUAVwB+Nt1ePWnwZwG+L794L4MfW2iMB/Dj/vM+QjDAXzwZwq7V2vbW2B+AbAF455j496mGtvddae2X+925kSuWQ8fYqwRhzKIDfBXDyuPuSkMEYsxjACwF8AQCstT1r7Y7x9ioB2Xua28aYGoAJABvH3J9HJay1PwGwTXz9SgCn5H+fAuD39mWfkhHm4hAAd7PPG5CU/YKCMeZwAEcDuGy8PUkA8AkA7wEwGndHEgo8DsBmAF/K08QnG2Mmx92pRzOstfcA+CiAuwDcC2Cntfbc8fYqgeFAa+29QObwAzhgXzaejDAXRvkuneGxQGCMmQLwHQDvstbuGnd/Hs0wxrwMwP3W2ivG3ZcEBzUAzwDwGWvt0QCmsY/TKwku8hqjVwJ4LICDAUwaY94w3l4lLBQkI8zFBgCPYZ8PRQobLwgYY+rIDLCvWmu/O+7+JODXALzCGHMHsrT9i40xp423SwnIZNgGay1Fik9HZpQljA8vBXC7tXaztbYP4LsAnjfmPiWUuM8YcxAA5P/fvy8bT0aYi8sBHGmMeawxpoGsePLMMffpUQ9jjEFW47LOWvvxcfcnAbDWvs9ae6i19nBkfHKBtTZ592OGtXYTgLuNMU/Iv3oJgBvG2KWELA35XGPMRC7LXoK0WWIh4UwAb8z/fiOAM/Zl47V92dhCh7V2YIx5B4BzkO1g+aK19voxdyshi7r8MYDrjDFX59/9nbX2rDH2KSFhoeIvAXw1dyTXA3jzmPvzqIa19jJjzOkArkS20/sqpNcXjQXGmK8DOA7A/saYDQA+AODfAHzLGPMWZAbza/Zpn9JrixISEhISEhIS9j1SOjIhISEhISEhYQxIRlhCQkJCQkJCwhiQjLCEhISEhISEhDEgGWEJCQkJCQkJCWNAMsISEhISEhISEsaAdERFQkLCIxLGmP2QvZAXAFYCGCJ7pQ8AzFhr04GZCQkJY0U6oiIhIeERD2PMBwHssdZ+dNx9SUhISCCkdGRCQsKjDsaYPfn/xxljLjbGfMsYc7Mx5t+MMa83xvzCGHOdMeaI/L4VxpjvGGMuz//92ngpSEhIeCQgGWEJCQmPdjwNwDsB/CqyNzM83lr7bAAnIzt9HgA+CeA/rbXPAvD7+bWEhISEXwqpJiwhIeHRjsuttfcCgDHmNgDn5t9fB+BF+d8vBfDk7NV/AIDFxphF1trd+7SnCQkJjygkIywhIeHRji77e8Q+j1DKyAqAY621s/uyYwkJCY9spHRkQkJCwtw4F8A76IMx5ulj7EtCQsIjBMkIS0hISJgbfwXgGGPMtcaYGwC8bdwdSkhIePgjHVGRkJCQkJCQkDAGpEhYQkJCQkJCQsIYkIywhISEhISEhIQxIBlhCQkJCQkJCQljQDLCEhISEhISEhLGgGSEJSQkJCQkJCSMAckIS0hISEhISEgYA5IRlpCQkJCQkJAwBiQjLCEhISEhISFhDEhGWEJCQkJCQkLCGJCMsISEhISEhISEMSAZYQkJCQkJCQkJY0AywhISEhISEhISxoBkhCUkJCQkJCQkjAHJCEtISEhISEhIGAOSEZaQkJCQkJCQMAYkIywhISEhISEhYQxIRlhCQkJCQkJCwhiQjLCEhISEhISEhDEgGWEJCQkJCQkJCWNAMsISEhISEhISEsaAZIQlJCQkJCQkJIwByQhLSEhISEhISBgDkhGWkJCQkJCQkDAGJCMsISEhISEhIWEMSEZYQkJCQkJCQsIYkIywhISEhISEhIQxIBlhCQkJCQkJCQljQDLCEhISEhISEhLGgGSEJSQkJCQkJCSMAckIS0hISEhISEgYA5IRlpCQkJCQkJAwBiQjLCEhISEhISFhDEhGWELCmGGMeb0x5txx92OhwBjzd8aYkyPX32SMuWQvtW2MMV8yxmw3xvxib7TxcIYx5gnGmKuMMbuNMX817v4kJDzckYywhIR9AGPM840xPzPG7DTGbDPG/K8x5lkAYK39qrX2N8fdx4UCa+2/WGvfCgDGmMONMdYYU9tHzT8fwG8AONRa++x91ObDCe8BcJG1dpG19r/kRWPM9caYPezfwBjzA+1BxpjjjDEblO8vMsa8dS/0PSFhwWFfCbaEhEctjDGLAawG8OcAvgWgAeAFALrj7FeCilUA7rDWTmsXjTE1a+1gH/dpIWEVgG+ELlprj6K/jTEGwG0Avr0P+pWQ8LBEioQlJOx9PB4ArLVft9YOrbWz1tpzrbXXAn56LY/8vM0Yc0ueFvt0rtDo+v81xqzLr51jjFmlNWqMOcUY8+7870Py5749//wreUTOGGOWGWNWG2M2589cbYw5NL/vj4wxa8Rz/9oYc2b+d9MY81FjzF3GmPuMMZ81xrQD/bnTGPPM/O835P15cv75rcaY7+d/f9AYc1r+s5/k/+/IIyvHsud9NO/v7caY3wkNvjHmvcaY2/IU2g3GmFcF7nsLgJMBHJu39SGK1hhjTjDGbALwpfzelxljrjbG7MgjnE9lzznaGHNl3t43jTHfMMZ8OL/mpVLzcfiVucaT9eXdxpj7jTH3GmPezJ7TNsZ8LB/nncaYS/LvfmiM+UvR5rXGmN8LjMMr8ojWjjwq9aT8+wsAvAjAp/LxeXxozHO8EMABAL4zx31BGGN+YNzI2sgY86YH+7yEhIWGZIQlJOx93AxgmBtFv2OMWTaP37wMwLMAPA3AHwL4LQDIFeffAXg1gBUAfgrg64FnXAzguPzvXwewPv8fyBTkT621Fpkc+BKyKMdhAGYBfCq/70wATzDGHMme+zoAX8v//ndkRubTAfwKgEMA/MM8+vNCpT8XK795Yf7/UmvtlLX20vzzcwDcBGB/AP8B4AvcUBW4DVnkcQmADwE4zRhzkLzJWvsFAG8DcGne1gfySysBLEc2PscbY54B4IsA/gzAfgA+B+DM3IBqAPg+gFPz33wbwO8H+qVhrvFcmdNxCIC3APg0W08fBfBMAM/L234PgBGAUwC8gR5gjHla/vuzZOO5YfV1AO9Ctr7OAvADY0zDWvtiZOvtHfn43DwHLW8EcHooqjgfWGtfnrc1BeAPAGwC8OMH+7yEhAUHa236l/6lf3v5H4AnAfgygA0ABsiMmwPza28CcAm71wJ4Pvv8LQDvzf8+G8Bb2LUKgBkAq5Q2jwCwI7/ns8iMhg35tVMA/L9AX58OYDv7fBqAf8j/PhLAbgATAAyAaQBHsHuPBXB74LlvAXBm/vc6AG8F8I38850AnpH//UEAp+V/H56PR409500AbmWfJ/J7Vs5zLq4G8MrANTkXxwHoAWix7z4D4J/E725CZlC+EMBGAIZd+xmAD2vPZ/P9K3ONZ96XWTEW9wN4bj7HswCeptDUBLANwJH5548C+O8A/e8H8C2xvu4BcFz++SIAb53HGE8A2EW/C9xzHDIjcYf4N5BtIDNM7wfwgn3Jt+lf+re3/6VIWELCPoC1dp219k3W2kMBPAXAwQA+EfnJJvb3DICp/O9VAD6Zp4p2IFOuBllkQ7Z5G4A9yIyqFyCrS9tojHkCMoPhYgAwxkwYYz6Xp7F2IUsBLjXGVPNHfQ3Aa/O/Xwfg+9baGWSRkgkAV7D+/Cj/XsPFAF5gjFkJoArgmwB+zRhzOLLoztWR8ZAoxifvC1COkQNjzJ+w1OEOZOO//wNoa7O1tsM+rwLwbnpe/szHIJvTgwHcY6217P4759nOfMZzq3Vr0mht7A+ghSzq58Ba20VmyL/BGFNBNpenBvpwMO+vtXYE4G4o62sOvBrZ2tSimxwbrbVL+T8AMl27BMAZAN5vrf3pA+xHQsKCRjLCEhL2May1NyKLij3lQfz8bgB/JhRX21r7s8D9FyNL4zSstffkn/8EwDKURs+7ATwBwHOstYtRpgApvXcugP2NMU9HpsApFbkFWfTlKNaXJTZLHWl034rMaPgrAD+x1u5GZkwdjyw6NNJ+NueIRGCyernPA3gHgP1yJb+W0TYfyD7cDeCfxRxMWGu/DuBeAIeI1Ohh7O9pZIYW9W8lu/aAxlNgC4AOsuinhlMAvB7ASwDM2DKtK7ERmZFJ/TPIDMx75tEHjjcC+IowRh8wcqPxawAutNZ+7pd5VkLCQkQywhIS9jKMMU/Mi6mp2P0xyIyZnz+Ix30WwPuMMUflz1pijHlN5P6LkRkgVOB+EYC/RGb0DPPvFiFT/juMMcsBfIA/II+8nA7gI8hqjc7Lvx8hM3D+0xhzQN6fQ4wxvzWP/lCE5CLxWWIzspTV4yLPjGESmRG1Oe/fm/HgjF+OzwN4mzHmOSbDpDHmd40xiwBciiyd9lfGmJox5tUA+FEX1wA4yhjzdGNMC1nqFcCDHk/+2y8C+Lgx5mBjTNUYc6wxpplfvxTZOH4M4SgYkEXMftcY8xJjTB2Zgd5FllKdF/J1/iJkht8vi39GNofvfAielZCw4JCMsISEvY/dyArJLzPGTCMzvtYiU3APCNba7yEr3v5GnjpcCyC4MxCZcbMIpRF2CbJIzE/YPZ8A0EYWTfk5shSYxNcAvBTAt0U67AQAtwL4ed6f85FF1ebbH/nZQZ5q/GcA/5un6J4bebb2+xuQGR6XArgPwK8C+N8H8gzlmWsA/CmyzQvbkdH/pvxaD1kq7k35tf8D4LvstzcD+Edk43QLROoND3w8Of4GwHUALkeWCvx3uDL+K8joP83/adG/m5AV8Z+EbD28HMDLc7rmiz9GtrnBS40+CLwWWc3bdrZD8vUPwXMTEhYEzC8ZLU5ISEhIiMAY82VkGyL+fsz9+BMAx1trnz/OfiQkJJRIkbCEhISERziMMRMA3g7gf8bdl4SEhBLJCEtISEh4BCOvKduMLB37tTluT0hI2IdI6ciEhISEhISEhDEgRcISEhISEhISEsaAsb/A2xjzRWSvaLnfWjvn1vH999/fHn744Xu9XwkJCQkJCQkJvyyuuOKKLdZa9RDrsRthyA6t/BSy7dNz4vDDD8eaNWvmvjEhISEhISEhYcwwxgTfmjH2dKS19ifIzrRZcOgPtQO8gd5ghI+dexO2T/tH51hr8ekLb8Xd22aUX2bPDNXhdQdDnHv9JvX6nu4AJ37vOuyY0Y/r+fG6+9DpD9Vr1K6GTTs7+MT5N2M08tvc3enjI+fcGHxu6JkAcP+uDn5xuz6tN9+3G/961jq1zU5/iPNvuC84RqORxVD5HQCsuWMbvr3m7mCbJ/90fbC/MVrW3bsLt96/R7123g334auX6fx1364O1twRXtqxtfD9q+7BpbdtVa9deOP9+NHaTeo1a22Ulp/dtgXblHULACf/dD0uuWWLei02BkB4/Obih1MvvQNr79mpXhtExmc0svjR2k3qWhgMR/jgmdcH2/zfW7cE+QgI07Irwg/94QgfPUeXCbFn0nMvvnmzeu2+XR28//tr0R34bcbGAIivhRg/bNrZwSfPvyX43Bgtd26dDs7n5Xdsw6cvvFW9tnOmj5/eoo8BEF8LF9x4H865XueHK+7chm8FZAIQp+XKu7bjnh2z6rVvr7kbq6/dqF67Y0t4DOZqM8YPZ1x9D352q86fMbkIZDJjpjfwvrfW4mPn3hRs88q7tmNjYAyAX05H3rV13+vI2V5YR44LYzfC5gNjzPHGmDXGmDWbN4cZ9aHE5y6+DUeeeDbu2DLtXTvzmo046YJb8SlFoNyzYxYfOecmvOlLv1Cf+9KPX4zXff4ydRGd+L21OP7UK3D9xl3etW/84i589bK78HlFcN65dRpvOWUN3vG1q9Q233rK5Xjev12gGj3v+NqV+MT5t+Dm+3d710752R349IW34bSf+0bGpp0dPP7vz8bHz71JbfMF/3Eh/vBzl6p0/tmpV+BzP1mPu7f7THjqpXfirV9Zg9XX3utdm+0N8bx/uwB/8dUr1Tb/4LOX4m9Pv1a99pZTLseHf7gO9+/ueNfOu+E+HHni2aoiHI0sfueTP8VLP64f6P6nX1mDE7+3Vr32ttOuwB989lJVKKzfvAdHnni2Op+jkcW7vnk1Xvt5/UD9N3/5crzttCvUax855yYc9Q/n4N6dvuDcsH0Gr/v8ZXjfd/0xGo4sPvzDdXjDFy5Tnxsbgx9csxFHnng2LlvvG4033bcbHznnJrz729d41/rDEd5/xvV42UnyvNIMb/jCZXjJxy/GQBH0X7jkdrzttCvwg2t8RXjV3Tvw5Z/dgb/73nXetU5/iNeffBle+Wn9vNYPnLEWT/nAOdg52/euffzcm/HpC2/DWdf5a/OSW7fgUxfeig/+4Hrv2mxviKP/8Ty8+1v+GADAG06+DG/84i/UdfKvZ63DqT+/Exfd5K/Ni2/ejLeddgU+fp7Pg6ORxctOugS//xn9oPtXfOoSfPiH67Cn6yvmD555Pf7z/JtxueJAXLdhJ4488Wx88/K71Of++kcuCs7naz57KT5yzk2qEfsvZ63DH3/hF7j5Pl8ObdnTxdM+dC4+9IMb1Of+3y+vwZ+dqvPD73/mUrzn9GtVY+HUn9+JI088G+vu9eXtdHeAV//3z/DHAX7429OvDcrbl590CV520iVqm5ffsQ1Hnng2zrjafwvUrk4f7z/jevzR/+h8/85vXI3Xnaz352++fQ2e9c/nY1fHX7c/vWUz3vzly/HfF/pn526d7uGkC27F6wKy5tX//TM8798uUK+Rjrxd0ZGrr8105EkX+Dpy485OpiO/vO905F1bZ/CWU9bgL7+uz9k48bAwwqy1/2OtPcZae8yKFaF3Az+0+NezbwQArN/ie/93bvUXHeHenZmSv22zf093MMSdW2dw6fqt2D7jM8vpV2wAkAkdiZncgp9RLPlNeZvnr7vPuzbbG+L8dfdj8+6uyqA3bcqE3v27/DbJZrtLiSjcvmUa1gL/pTBZpz9Ed5AJoN2KkCdlc4fiCRF9P1ZoufKu7di0q4MfKV4vZ9jdCp2zvaw/197te3w35Az9jV/4iuXqDTu87zRoY0tjet4NPi0/zI3Mn6/3Fd0dkfXFsVVZJz9auwm94QjnK21S9EwzMGLeLsdtm31++MxFmXC/WYmUrb0nG1vNkLpvl28Qc/x8/Tas3zyNGzf5ivmstdn4TSvePfHg7o5/bfPubMzu3DqjCvlTLr0T3cEI92z3x2N9rmxobXPsysdUixbet6uDPd0BvnPlBrXNazfszO/z55OMJC2iQPN4pmKI3rF1Gtdv3FU8W6LTz2i4V5n3Yd5HzSC6dXP23cfPu9m7phn+GjR5srub0aJFeC+6aTOme0N858oN3jXNiNRwk7KGrrpzOwB9/Mgh26CsAx6V1OaTZN5lCm9/98rM+NIiT2vzudLWNDfoNF767lX3YNt0T23zghvvBwDMKsYvGVC7FF7psXWuyQzSkbcrOlKT7QRac+vn0JFaxJ505OaIjpzuKjpyV1hHjhsPCyNsnNi6x18IpIh2KQtTE94Evqi2R9Ih9+/2Fxg9d4vSH+1+rZ2tyqImgaGF3UnJa0IzlNLK+lj2RzPu6N3G6xWFTsyuGamxMdvEFPrGHb5yXzZRBwDcoHi9ZEBpQio2n9zYu10RKMsnG9kzlLEl+jQhvu7eUmHI61wB8PsIk82a83wO6kerXvWurWferExrcKGvjQe9qnqHsiYoyqC1yZ81LZQp78MOhZZubkRs2a1HGQFgpIwtj4ROC4eGt6mtbzKEyMjjoDWn9ZXznVxjvE0tSksGnxZtIINyMPTp5PMv01B8PjdEjG8tQkTysGr895/H5pOvY43vCZozQE7b4lbdu8YNRc1QIGh8T2OrRSA35FH6FVNN7xpPo22OyF6Nlp2zWVt7FEOB+rh8ouFd28TWXMzA0WQk/VZLR8bmwpXjYYdJ1ZG5M6I5xKEULyB1ZHg+Nyt6hdafpuc03looSEbYHNCFcbY4NiqeH19gUpnxxRqrSdEYm1J3Wp0LN8JkypErBY2WejUTpprAuCeqWMo2JZ27Zktm1xY/CQPNuKP7tcgS74cM9dOcADotRLtGS+wa74dMo9y9rWwnZqjy8SDsyIWxur7Y2pC/5cKYnqH1V6Ulf5ZmGG9gqeFNQuByoabNC3mgmvAjWuQzAZd/pALl/KHRSXOhrS+aFy3SxmmXThT/zNc3gaIu2vqi7wYjP0oRUyxcSWnzQoolxiuasbmTjZlUkjx6pNFCEa2YQTlQShv42pCOIZ9fzjfF/TntMb7XIpB8nUhaOL/uVGghIyPGK1pUipdRyHnh8jdGyzZlfdG16d7Ac764Xtkp+IHfq9FJ/dDWF58LGWHjc6jRQojx/S+jIyWdAFAx1DeftzfsyOZC5ZVdYX01bozdCDPGfB3Zy3WfYIzZYIx5y7j7xJlXU5IUOt+keMTcY5Chcr5YJePzCIdmhFFqRQu/8/tlCoYLKSmM+8MR+rkXrdKym9I6ijB2mMW9zj9LWnqDUZEK2aOEwInxNa+W0yI9Pt5HqfD7w1Ex9iothREWTvlotPBnyXmx1hb367T0nbbd55bPkrTwlJWWbtu2Z25atMgpf5acF063RgvNRYyW+5T1FaNlLo+Y+qHzSnZNW188jeEZfuyzyvf5czXjjr5T54QpXDkvzvpSUiy75sH3mpHPnRJJC+9jbF5i60tbB3FeKZ+llSjE+J7W146ZnudkxnjFlYth50uLHlE/dsz0nbTcXLRsmwnLxawtMsLC66vTH3npQb7m5DUe0Y3RovN92UcZGea6TNIyp47M+6jryLIfcl07fD/tttkbjIoSmaiOVOaa85a2FsaJsRth1trXWmsPstbWrbWHWmu/MO4+cQNJS//FDCJesyUnmwtjqVi4INUWGLWlKRYeNpYey46Id+8o3ggtumIJR/V4HyQtPE2htUm0aKlePi/SoIwZETwFpNFCadcdcygWKcR4/2Wbu2YH6OWepe4R91Q6sj5y4879LU8pyPXVHQwLpaDRQv3YOt31vME9zlpwf8sFmFT4o5Etxkjz7qmP072hp0A5r8gx4ny3U6wva21xv2a40LxM94YenVu4dy/GaHvEYcn6OMhp8tcQrbGZ3tCLKGxxIuAPlO/7wTbpubP9oWcoxPier2nNIJot+D7ssHQHI2+nWYyWGH9mtIQNSqJlMLLeOtk1T77Xap7mGwGXNboxWrZEjHygXMs634dl42wvLMN4bWhMhqmGS0Qe83Ur5yUmi7M+9tVnAnEZxteqpMXRKxrfR/Syy/fzqyPcVxi7EbYQwYWxrliySZxR8voxhR9LR3KG1RZRzPDjgkAyvkOLZ7iEvSCAC+O4ESYNyhgte+YwwoiWnbN9LyS/PZJa3d3ltLjP7XAB1vWFFNX67JztK6lV9twILVKZ8XZikbDZ/tBTZq4wdq91IuuLe46aR0y0WOvXJjm0iOfG1teuTh80TXMpFm9e+mGHZftMeH3N9odFBFfOiaRFtsnnKZYClVG97qA0dLQ2+RzKdb3d4ZUw38vn9ocsaqzJBPad53xFDEo+JzEZNldU74HQ4vK929fhyBYG+VwRcDkvfN3ImqeY4TIa2SJqpRlh86dl/rwClGtZixrvcuYl5khK5z5e5kIpSpVXIgblnogMc2uNwzpSK5Kf7Y+8+wjbmAyL60j/ucQPmpG/J8L340YywhTwBSYXkbWWefd+7r4TWWD8WVKA7YoIE6BkiD3dgRdR4IpGevdcwOyRCokrSIVBKUWaKT3X0+aL2ouEzXJawgaGJuTp/v7QOmMp25HCL0ZLbE74s6zV6oSYYIyMn2R8J8oTSbHw9svnsvF7ALS4c6LVuYSfG/PCOd1S2XMDKeY8ZM+Zv0HJn+Xxyiyfa18YxxQLNzpkdIQbsXINxegAgM4gTAvnTy8CHnGEnKixxivcCIsoSZ+WsEzoD0eFI6JFj6IyjBsuPTmf4XUSW1/A/Ocl7rD4hjyJ7pjDAvjzEltf0xG+7/SHhTE13fV1R6y8Yd56RaTwRiNbGCeavooZx/y5D2R98T7qOjLCK1G+D8svoJwLLeo+HYm6jxvJCFNAk7lyccsTJt1BVke1uFXDSIkodPpDVPPqQY3xG9UKlrTr3uIj63z5ZMNTLIPcI16U73ybEW3O9obYL9+JJ6383Z0BGtUKlk3UPa+XFuPiVi3o3RMtWqh/xaJm0Ybz3Nk+jAGWTtQ9w4XGc5HSH4vxEQAAIABJREFUprUWM71BmJbuACsXt7IxCBhEi1s1TxjTHNUqRjXCOv0RDgjQsnO2X/RHKl/qv0YL3bvfZEM1wvZ0BzhwcTNIy6JWrbgvRIsUJiTcDljUVFNJMVr2dPtFm5IWWo/LJxvenNC6OHBxUzVOdnf6YVp6Q9Ty9SUVvkuLziv7TTbUHa17uoMwLb1BsWvVo6Vb8n18fcV5Rc7LbI/zih413m+y4SmWPZH1BWRzGOKVPZ2SV6QRwWmRz6XxrFaMftRLhO93zvaLsfXX17CgRf5uVvCKVKB7GN9L2bi708fiwFy7tOjXVixqojsYeelclxZ/XqaaoTU9KGiJra/ByBblCiUtA0aLLsO0eZnlvNL1Zaa1WX9G1t/cMN3lssZvs1WvoF2vRvle9rXTH6I3HGFRq6ZG3Tv9ku9DOnLpRFhH7jfZ8NbXcGQx2x8WOlLq7ZlumO/HjWSEKaBFs3yy4dc95IvmoCVtADqzhBR6J1/UE42qt4hIUWsKgNpYuSQTRJr3Rdc0xZy1WQtGpQ5a0vYWrbV2TlpCCn1XJxNSU82aZ/hxA1cKsG5eeBmjJSTkd3X6aNQqWDbZ8NMSEeNkMByhNxyVz+0Lg7LTL/rjecTdAYzJBLnn3ZPAXdLyDIxBviFi+SQZYf68HERtBmpDNOOEr1v5zMFw5KwTP1JRKjr5XBrPlYtbnkFZttn0xj2LGkdocdaXb7gQLSEeXLmkFUxHUpsyTTzTG+LAnM4wLf747WZ8r0UxYob8bH+IZRN1GAOljorRosxJ1mYLe3p+BHymN2C84re5pF1HRWmT0yL5s8PWl2aczDK+1+Zl/6kGahXjp/AifE98tXJJCyPrr81Zxvezgj93dwZYNtlAo1YJprs144QbfjotzOGTMqybGUuTjapPC5PV3pywNa21ubvbL/WKQkurXtGN2Mi65esLUGQN43tPr3QHmGzUsLhd8x0LxvfSyCr1Sv5cRYYFeaWX66u6oiM7pUzVDGNOp7bGVgb4ftxIRpgCYt79pjRhnHsAAcXS6Ye93tneEO1GFe1GVfUOAGD/RU3fc+26jKQVa++fn2cjGbvT523q3v2BS1qeMdkbZgYR0aJ596Vg9CNzE40qJhu1YE3OyiUtlekBRGkJCrAOCUbfu6exXbGo6UdcciWz35T+3NnesOiPlsKbatawqFX3lD3N4f5TzTz1USpQanP5ZHbukWZQriyEsRiDQUlLyHDZb6oRbLOgRUmxxARYvWqwpF33junoFMK4jk5/5BgKnf4Ig5EtaNFSLEsmGmqE0nGElPVFtHQHI6cQnuqLijaVNbaoVUOzVonQEuf7wch6EQWX7yUtI7QbNbTrVX99FbLGjyQWhsuSNqz1I+DTbG36vDJCq1GNOl8HLvENIh4hyu4VjlCM73M6NSdzD5Nhc/K9Mi8h54uixlNNje9HBS2aEwkgSEunN8T++Rh4xnFngKlWDVOtmlKGUNIi54TKO2K0rIzolXa9qhphHcb3HUVmUn+057p8L/XKEBPNbA3NitIQOqdv+aSf7dhdOEl6oKIzCOtIV1/pDsL+U76O9IwwZV5oPrXo+TiRjDAFxLzLJvyoCi3iA/MJ1YQYHfCnhXfb9SomGoowZp5ZKC0RilRMd5l32veVQ6texaQiGDktoRqEFQHmdbxTxXNt1auYaCrCmHvEol6Ap/DoObJPyyKpwck8+hZTLL3ByKlvo3FfNhEwwlgUQ2P8LOJX9bZFz7C0xHBki0LyjI7Si+T3FrT0Blg+UUetYvx56Q1hjJ625t6pFakH6flrxcaLW3W061WljmqAiUYNrXol6DwQLfz6HsErWtpiolHFVCAt1qhVMNn0jYjCcCmil36bKxfr/DnTG2KyUUWrrjlCIzSqFUw2ff70aQnzvadAe0O0KQLuGS4ZnYsUI2K3pIXNS3+YRaloDDSDslWrqM7Xnl5WorC0XVciLpLv/f6GjIhOL2tzUqGF+n7AIj96Kfm+0/MVfjjNmUVrJpvVID+smGoGU5WhlCOP+KltNmuYVGTNNKPFnxMyXPQ2p1mJghYBb9ermGrWg/Jt2URDXV/UnxAtYb2SjW2zVvGN/EHJ974szj4HeYWl58M6shZ2WDQdyfQK4EfAXR2ZjLAFj1h4lxhp/8AC6/SGWJKfzq4KxnoV7XrVY8AyOpIxEo8oUBuhSMVMb1AYJxrjt2qZZ+GlHlj0TRondG1pbpx0PM9/hEWtOqoVoxZct2pVNSrFabHWNWxIISyPKJapZjWYemjXq6owJg+qoIU9tzOHkOr0R5lnVq96jB8z/HgdFeAWbs+3zclmTd0l1a5n8xmM5Ez4ETbp+euKJTOINMUy2aA2xTqgSCIZd2xe+PrK2tSM9QpaNZ+Wbn+U0Vmveka+Rwub72J9hVIsvQEmmllUShu/Zp66D6W2SlrK31LqXltfQDb3rXpu+MnoSH+EVk0vUfBoYZGKwnCZCrU5yhyhhs8P3f4IrbpuLM16fF/+tj/MIpsh54vo1CNh2RrSIjke37M2h3ntVDnX7m+7eeRksqE4X4zvvXXrGURlmwNBp+awTDVrWNSs+enuvEQhazMcaZVtkqO2f8SBbzWqaNXDEVytVkrSydc1RY0PXBzSK5mT1G5UvRfIyzbdqLvLK1qEcnH7QehIrpeFjpxPJGxZwZ/hF6iPA/MywowxE8aY9xtjPp9/PtIY87K927XxgU/2YGSduoi5FOhs7t03ahVHmNC1Vr2KthLe5W1a6woiakNLPYxyRppq5ikWtc28JqzvM4NDC2P8MkIUZpZ2vYoJLaIwGAVr37xoFzfCyHCZ0plltj9Es6ZHEjv9EZr1zHDRakpcWkb+tYCX1C3arHmRMIqqZOF6eW0gaPENolD0rZO3mRl3+hpq1areXHcitJAQXRZQLJnAzVJJGi0TzZpqLHV6YVqoTZprTUm266RYRuo1rT9FKmTKVywFrwRSDzNdioT5bZIC0NZXV/AKp6U7GMHaMK84tGgOC63bQISooIVFiIr1lUcgtXkJ1YJSm1Na9CjC9966VRVoJcCD2RpS15fH9xHnIeBkTjVrwVrQZRN+Gn1W0OK0OQgbaEBZbtFuVL3033RviIl6Fe1GBZ3ByDFO/OibT+fSiayOTzNAWrWM77uKXMx+20BvMHKO2ZEygct4uraoVUOj5ke5p3uZk6nxPa3FpRP1wlCWz9UcM+rvRKMa0FejXEdWFR1Z8r3UkbNSR7L+FjoyL0PoPkwjYV8C0AVwbP55A4AP75UeLQBkyr5SvIdvVmEW8kC1NF67XkWrVvGYxTFclDRAvWrU3TG0+JbmgpEvMPp7spl52lpNQDPgnXYG2U6UYncM69MsEwqcbqD0/NuNPN0RaFMTxp1BVl9EY8ufy1N48hpAHnzm9erRt0qgJozGb24hr4XdW3mETROMzSLCIXcduYKIp1hK7zQbW28Hbp9HMfT11az7USm/2Hjg/I5fk+NHbWp1S9O54dLUokdFWkKLvrn1dh4tLEKkKUmqDdHWrUOLoliWtH1eAfJIWKMWSEeGN84UbSq0dAV/yqhxGb2sKUaEGz3iSrsboUWuL09hsaiUTEdyw2+2P1SV9tKIwxJMR7J160fdR8VOu8HIOlH3acH3mrwNbTLI6KxgQnFYuv0sdb+4Xffa5PWTkhZqc6pZ06PugzJaE3NY/DKEvMxFSUdSmyTfVL1CzoPiaGf6qlp8ls+NRaqJFqk7ZrqZsaSWIQyyHY70Ps/ZCN9rR4e06wF95Tgsuu5YlLc5rfC9pq8KHRkoQxg35muEHWGt/Q8AfQCw1s4C8N/g+ghB5kVmCwFwd8yRgNUUemGcBFIPUcWSezoTjfwYCoVZtDaJqSYalGLx00UxL7xZrxQvV9aME63N/tBiOLJFWsxX6MOIMB4W6VEak4KWQrH43j15W9SmL4xLD0qLoGW0KAzak4rFDdf3h7aIKPgFpqXhIo2Imd7AMeS1dGRRR9Xz6WzVMwM3FNls1SueAJv1hHzY2JRpCWpTE1IzueGiri9Bi+rdt/XIJgncptJmETVW+Ei2yWmh6NtSJTKXHYEyLB0WJapCxtJsfyg2GUh+8I0TrU36batRRbteUZ0vih7JYwt4bSpvByjXabgMoVRmurFU8n1XWZtLlTbJkZjMjROVzpq+ISfG95RiLPieZx7yv6lOKBTVa9f9CEcpiyveGMmonrZuW/VKVksbkWGekd8tU/dZ/8MGkdNmTmerVkUrIMNCeqXTI72i6A4vqudfI+NYjYQ1anoZAltfHi0R3eHqSCUCTjpS2R1Zri9qk9MS5sFCRwbKEMaN+RphPWNMG4AFAGPMEcgiY49IkDCmBaZa3G3f66VC6FZucXsKtBeu5+kOhvlupnCblCLgC4wExETAS+r2h8yI0BRAFc2ab4T54Xpf6YS8wWz8soiCVvjbzH/n0RJRLKQoWoHnEp3NSM1EjJblE35EgX5XKjOlzVoF7YYeyp9oZOkDSUvpEfvRo5LOajD91w6tL0Gn5p0unWhk6Y6u3qYmpKaZR6wZLi4tfvRtsllDrWLUaFcrGjXO5lpGMWIFznStFPKczixVQ5sMvDYHrvM1q8zZEqWWhUejG1UlUtFjxcZKRKHF+EGL6mnzSfJhsqmndYi3s1pGvc1WrVLcK2nR0nSzgh+0SGLUycyNCACOA0Fpfo3v6e9m7pT40ehRPJrK21To1KLudF+rTmUIuuGsGUQzvQHajRqaEcc2lo5s5g6WZ1D2WNRY4fs2W0Nu1D2ns4jgasamnv6bIVmjySGS45pBJHRkV/CgtSgyCEFa1JrXUURHksPiR40LHRkw/MaN+RphHwDwIwCPMcZ8FcCPAbxnr/VqzKBog2YoSCufLzC6r1ULK6xWno6cyzt1PKiB6xG7niJT2oHoW8lkmmCsME/RZ95YbUi7EYiwOWmmkZdicejUjJOCkfz0QVm0GVLo1ZzRrfPbikGRdtW806UTjfwcJz1cHyqIpTaHiqHAlQ4fI5qHqWYNjaqb7ijXEBmUvqdItSEUkeT9cbxTbc5yo1tVOrWKXivF5tNL6/TdtMSMQifNd8jrDTksVD8pn9vpU0rbV64dr02mAPL7mjU94jfbo2i0790TnVNKZJPzfVMYd9zzn5dx4vB91ibR2RXXMjr1tM5snzYZVL1aUKJT40G/flIxwhr6OU6dwaiIrOuyj/M9c17ze1UDl/G9FtUjOjNDQabnRwV/hp67PJKObNX9+aTrNO5+wXpOJxm4ikGkbTLgdIbqPYsIuMdHI8H3PFXu6ivVwK1Vg0e2tOqBMgTm3ANzRcJ0x1avNQtv7igd7XCUUXO0PR35cIyEWWvPA/BqAG8C8HUAx1hrL9p73RovyjqNSGpQERg02YViUZVOpTCInB0luXJtKqFzYiTaUaJFOAqlo5xf1Kplhl9/KA0FVxi7BmXu+Wu1Ib2SkXTvVDxXGI2OcaIIBU0Y89B5sMA51KbnEfuKZUIJgfM2NSFf1LmokRMyIirOs3j7hXGsthlKmZHh4q8Tfg4dfS6fy42TiirAQsZ6t58p17YyfiWdYYelMGJZm9ZaZqj6CkB693LNkyHq96ccPxml7cwR8SMjIuR8uQpdEfINf87ovD1KsajnedX5fPqGvDa2xKutGtFS/m6UbybKUmb+Vn9uLMnxo3uJ77sBR6gl1i1vU3VYRMRvVvB2M98hKvsjo7QzsTal4TIoo+P8Wbz95RN+NDUWjbY2OyOOovkhOaSnI11neiZAp6Y7SIZJBwrgDouWGswj4BSVGoy8a0Xpg6CTDK1QGYJTshNpU+PPor5No7NRpkflrssw3wsdqcoE3UEYN6JGmDHmGfQPwCoA9wLYCOCw/LtHJIqoSl1ToNnfU61aViiqCLCQlU+M1G5U/XOc+q6Q6oa8ByHgOkwYh6JvZBTy++nvuQyiRc3svCrpoVN/2nV/pyedetxSaSkLdL3+DMggqnm7S12FHvO0K0Ufiv70y7A63Vv2tRQKUmlLpaMLeT3F0ulnikVL9c5rPgtP2/d6nTbFb7ONH/6GEhlJ1KNHgZoTyQ+KoRCrK2zVcuXhpF2lYFSEfENPDWbRD6boNFpqNJ9hOrXUvWOsCwXqrC9OZy82nzy1FYhG12IGbkU3XBzF4vIKjW1I0XXFfLq7aGXUXed7SYtv4PoOS7NWOiWaw6JFydz0sohsCoclVCsVir7RURLUBwLJBDpnTRtbXkflGQq50yaf6zuZikGUR6ND9cStur87sjso66iIbv47IDNOjNGd+8JhYb/rDy1GNqZX5q63m2zWUK0YdSMZRbTCOrKmnnXIjU0+DsWan1Om+pHNcaM2x/WP5f+3ABwD4BpkBflPBXAZgOfvva6ND7HISaefvSOuXvWVh5N+abjv26K0BKUjgcx74G3E0nQVA9Srxvfu878px7592n3paaefh+uZwlrUKp8bSkdyWmTUQKYI/F0swrsfDLEEpVfkeIqKIGrWKl6dUEcIDD1crytQOtpCjR5xpS2jUjS2ga3hRRRIUZJdaaAJzx9AEXUJptMiKYJC4ApDnmpnAJGOZG1KZeZ4xAHBmEVplUiFMBRC0UtpKDjR1IBRTQ4LICIV/YiicyJ+cj5Ff+aYT0lnk41BV1tDUQOXaprmWLdiXposuqvxveaUlIZoZD7rfD5dReek7hVjs5Ub+lotXhmRz4wTY0wxXmH5JssiNDozWnSZkCl0KkOgNil1r80nXWvUKqiJsw69CG7AyLcWGNnMYGnUTDEOQYMyTy83ahXvqAQ5n9qBrLS+evlL1uldpcWrfgJF8oW+kmUIwnDm+opfs0BRhlCvlroilF7uDIaFvspkWCCLUq9iR0hHNjQdKfWVS6ejIwMbLVr1KrZN+y9sHyeikTBr7YustS8CcCeAZ1hrj7HWPhPA0QBu3RcdHAfi0aNRke8PKzMqNnY9KGuBmMANGREkNI0xUQXaqrkG2ih/vUoWwlUWblGgG4liNPzjEGYjQopSBM3Ic4NeeD87PbxSMYoCLduU/eEpAs2g7M4RDczoLJVH8TuZwmO/K9JptYAgiimWnitwtflsKtfoOW2WYtEiYdRmV4xtaPyI5mCbAylwhTJzDG6/1qd8rt+mFuGg54aKqmndFmOgpHxoLWg7/7TIXElLWLGEFYCI1gSMzVatit7Af7VTy5lPv81mrZJHMXSnJNtdGuLPrI5vIOsVa6URKw1Kp8hbeW47H/tYNNVaeGdHhaPubu2WHjnxU45urQ+lHEUZQiASRpEl+n2whihUP1nP6qh8WsLyjWrUyjZDz/Xlm0xby9RqNIJb6Cs5Z+E0nWu46M4rn8+ubJPrq8ic8bVHqXs36h7RVw9QR5IzLaOM48Z8C/OfaK29jj5Ya9cCePre6dL4wY8BAEQ6bVBa5tLKd9NM+qKORdjcaI3epkyxODUTYiuxDNfz+6kN7mkHlUdd99q0omqZZvJoEelIr+4mFxgyDeAXjwfaDOz0JMWR0el7/o2qHx1xjGoxn91Bqez1FEu5O80fA2YM1Kuq4VKmAWQ6Ml7fFltf/Lkh40SmWPq51x2jZa70iybki/XVyBW6TLsWO7N8g7IwXKLGiX+GnRNN1dLLXn2WP5+Nqt8mN06k0p5V+D5WI+nwElcsXhSDRy/j6Rd+v9umb8SScVKrVrwdrWVhfiT6ls8LjRnvrxMx9fi+ikoeJdLTdGGHJcz34fmc7Y2Kvvg1kvMzTspovr829Qj4sOhLMMJW93dHuqk23aB0nemAvgrRUoyt67gCcHayy/46ukMxRNU2ey4/aEeghGWY0FdKWQT9XmYlqC8a348b8zXC1hljTjbGHGeM+fX85Px1e7Nj40QsteUtMM1wUWoxXAGm12KElZkbfYsWP6uGX3hXUigdSaHzIu06cAVY9ly/FkMqe4+WQXnAqRwDzki+B+p62mpaIrTjq+caJ5rnT4ouXljuCynHu1cUS0gYZykCCtdrnqKb1uG0tELefW641KsVrxaDp7Tl2HaZ0mk3qhixKIbqEQuF1a7nCrTqK1DjGLi+QifvlEeIirQEizJ60YZaNmcyrUO1Po2qf/aR3GjRH8oIUdyIDRlERbSm4e9oLa/pfF/IGiUq5SiWkEFZI37QoyphWmIRXD1CNDuPCG5oow/NWagwvzBOJD+wsfUiVirfR+bTk+NZmzIq6kYZxZoWKTw+LkRzzDihGtF4hCjgsEQi6zwCrq2vsk3dyZTH7MhIq2yzOxg5TpJnEOXfy92lTmQz5LA0ymOTZKYklo4MZ6hcGSYd23FjvkbYmwFcD+CdAN4F4Ib8u0ckPCNMKCyKqDSF8JNpgFBkSavF8BVASDDKKEYZIWrWwsWywYUbiqo4ofOAQVnP067sSAi5Q1Qbv1a+JdoYIagHLp2zfV1gtGplXYS8pqV1+DZ2bQyctIQythTh4MdQSGOJf1fSEjIiMiFFofOYAuVpHS297K4/bsT6nnZhbM6RSuL90BS63HVJ38sz2rixJHeXymgqUHr88rw93o+CFieVJBQ6GWhBYexHiNSU9kDyIIti8LmOGSfC8+f9cFPa+jExYeMke9l4pWK8MgRnbdYCbc5hbKp0Cr5XjRNlzsqdduH5bNYD8zkPJzMc7ZJR2lA6Mr4JSJW3Ub7X+0Pv7AQ0J5Mbsa7DJ/WKR2dOC9X9dgNtymMonKhe0KiO1PGFrjnZorChFdUrAX4Ilyi4Dksoo6GVIYwb8z2iomOt/U9r7avyf/9pre3s7c6NC+Tdk6KbFWe9tGq6ceIIKenNMEYqd0D6wq8M5bsM0WQLLJZikTsR6ZpqDAzKtI7sD4W4gTAjtRplwT8pTldIhZVZEXlSPHTqsx7V8wWc6+noXm+7XkW9alBRUkkhz199rmyzpu9KIkVXVSNE0tgMeKDCy3R3vYXppHuCgtEzXMLKTKVTrs1a+LnOfIYMXNGmLN6NtqkYd/S8uYrk+Xc8pV3saFWOxSjpDPO93PUcooWntIPKjNqUuxFzxwLQlI4bydHp1BUdRY0BeMchzPbLCK5fLlCuExkxLXba1fWdnl3GD3LdFv3N6/i0HaLNiEEU2sHH6QyXcfhH02j8QOuVv2EjlMJzDD/lueWZZ4rsYxEiz6CsVz2Dm/6eH9+7ZQhaxE+TYZpe6TpGtZ7qVXVkz2/TddLpcHE9oMDbDMnUh2060hhzuzFmvfy3tzs3DpQ7NCplXYQS4QDmSJnlnmKxqPtzKdDMICrqIkSBOFcs+lZ1P0JULmrdG+SRiuzUbTdVSbVOLdEmMYbG+FxIhY5ncFIsfTkGpcDQo4yKQSQKaXkf6b52I6NT213Ka0NkZK54rlBYTihfM3D74QhR3PDzPW3qk1ZfJB0EV4HqNRMhg0ir1aMoAJ3knY1LJEIUmE8vLdHz53NWzKejQEM8qEQxivXlrdtRMTZy3boHLYcjHMX4ifksUvfidT4u3wujes60oVvn4honImIVkkNCgToH1gZKH9rB545YNDWc0vZkAuejhu5kFqkksW6pZrNepaixnhoMGZS0schrMxKt6fSHwTR6aSz5Bog+7oLva9Xi91KmGlMeJNxhBpHcnMC/45FNzcmU2QXNSac2+ZEQetRYyrBKYZT7soY7075T0qy7O1r582NOJjnw8i0R0vlSd0XX9DKEcWOuIyoIx7C/WwBeA2D5Q9+d8YO/FxHQIjJumm53t9xi6+S0SYHm1rsWySEFyrfmAlCPZ+BeuEw91KsG1YpxPL7JZi0a4eApAo1O8q6Izq3T4doQun8ppMDQhN/IYRbNKKQ2w0dxuMaAGn1TPEWVzp6b2poV1wCoxzNoURWp8JuOIHKvzWnIK3UuerhezFlDV6CUki2vzeHdF3S6oXxARojY2KpRqfD6CtHiFu0rKdBexLuP1VExfpARIlcB6KmkogxBbruX62ug09kUY6uOgTBwm/Ww88VrmjTHTIu+yegH/476RAdeagqUyyhyMo0xAb53FXqznm1sqIjzqvwyBH99URqdH8/gbGIRhh+l7mORsBVTzaLP8q0VRRq9XnWOZ+Cyho6I6Ao6Y7WMdAB4q17FzpnyqAQ6sJbo5EdfcN3REFkLHh2n/koZxuUbP54hq1+rFM4p9ZHPe2b0lM8CSsPP5XthEDF95Rx90fPXfKEjldR9UEcKg5zKXOiaXF+1ikGt6jqSU9X5VmPtXcw3HbmV/bvHWvsJAC/ey30bC7iQov+1vLR2jR/yJw0QPSrlMhJv0zshnCn0kIEmUywxz4xSBDGlXUYx/KhUWbQvI0RK5KRoM99pV3iDQuAORo7SCaYIggZRuDA/NJ+zfdfw01Ih2unibtTTVTrFC7FpXjxDIZx+UY2BgbuGQumX2d4wYvgxL9wrRGYRmcgaCr2U2KFF2aoO+IJaFujyfmiev7ujkBkgdf9A1mYRVak4Gxscw9kzFLT1FeZ7ubvUSb8odPKaxK43tpENORE5xPk+dH5WyCBq1/10d/ncQElAb+iMOxCPnBDtRZSM1UH6byMItCl2hmdtug5CW4l2cTmu7Wh1HQS/vo1HWvlzu4pjW0ZwSz7SyxC4A6rXbNLvOQ2FXlEMZ/6aMxojP8pY8qD2FggaQz6mDt+LseVpdABoNQQ/DOLOYEGLjEY769Yd996wPOKJ7vFrU0NjoNFZXh835hUJE6fjV5BFxhbtlR6NGbzINvvfP54h6IXnUamaYpw4tSFCmfEUQfFcL/Srp1h4vVh5fkok3UFCk9JMjsAVofyIAm0LwdiRAlfxiDkD0m+dU9T7Q7QWld6pZKTyKIkHZoTxos2mSF/N9kfFCdZaZK5IEdT0+WzVK16KpesZ8pqQ5/0JpAgCqV43DZzdzz3/ghYl3V2MrRKt4W16kbBggW44qtcVykw7ikNLPfD5VCMn3HCuRVK97M0UrnfvrxMeDawrxzP4StsdA5665xEi7t1LvueGgr671I0o8CiG05/jUdL4AAAgAElEQVSae4CnS6es8Ru5bYrdpTKa6r15QuF7GTnxHFCF72NlCPwAT3mNvptoSGNTLxfgO5/DkX5/c4zW5qKWmwWoscNSOb0ObwcMSsmDfD65Qbm4VXf4vs4OheVjGzvzzFm3SkqRrvHncX7IyVT1SvHcUDpSiY7Xq+Wue5UWbvgJgzuoI3tDtJayIEZERnH6FgLmm478GPt7AOB2AH/40Hdn/ODMC2jMMgqmdbjhIo2TmOfvR9+UXWbMkne2RA+4dyrSOoqQ8r3wQEh5MCre/dVuSENhWERMYsosbCzpKZbuQHr+gsnqZcjdGb/CUPDTOsP88FgeOncEbm+IlYuZ4TcoT/qmqIrTpicUSkOhqKNiCok/l9NSCE12PEMlT7F4bcooRsOvreF1VNRmeKt6pUi7U1qHDsn1C9b5unUVnUwRNOsV7O6471nlRsSQpXViaWt+BIqsP9LS6DtmeIrFTXdz2rsD920XnBZpKPjKzDVit+4p2+RF3vR7WstaVE+LvtH4+XzPi+8lr7gKtDvI0l2zGg96Bm5o16VraG2fdsst2h7fy1RcbOOMvjZlfVt3l2soNAWdMVlD65Ur9GL8QjwYiZyEa14rGJIR5jmgLGshdtEG5a0TNa44zysNrQo7sV43cKWT6ZdF6HWifi2on47U9IpOi1v7Jg+WLSO4ruHHDVx5gkBXriFPX4VrjbuD8mgQbff8uDFfI+wt1tr1/AtjzGP3Qn/GDl8Yu4YWFxhNqdD74ZAyV6BePYoQGDqzuEXyZCh0I4zkRE6EolO9GW5o9YZoL87eb+R5kXwHlVQsPJ0md/eR4cKYZborlXZAYDiFtLIughmboehRoxTksXoeOhKCCtu9+VSME1nwr6W0ZXp5+WTDuYfO3ZHGEm+TKxZKsXSFAONRjO1OzcmwiPhxWiabNWfcyzUkDYXsAM96taz/0dLom3d3HTr3n6IamJKWerUiUvcBpaPwg55Gd9cJjS2vb1ua98ejM2golMpMptHniqoQLcSrhecf2cRCv6V1NRiOMMgPyc3669dKTTazseUv+J5o1MrnNvwNOZpBFHIkm1q0IbA2Od83u+UY8La5QUnX+DEdNC+yYD3Eg/Jl9/xaodAbpcwIGSCe7Ou7kXOApUBZm0OR5i6yC0weuykz13CWESIe5XFoYXPGXxvE6Qw6mf1wPax0knhbdF+znkVMHTpV/pSBilCUjDnwQVkdjuC2g8/1NwO4OtJ3zBYK5luZdvo8v3vAMMb8tjHmJmPMrcaY9z4Uz/xlwL0OIOCx8ALAQEjZS0fyc8KKk77dBRay8ukAQP5cUoBuSNn1Bvlz6QBPXxiXNR5+Wset0+C7dYKCkQlcubvUC9fX/Net8PGTZ4G1pJBSnivTOrrSEQq0Qf3J56xX/jY0n15EgT2X1/8V18SJ5U3vueX4yfnU1kmRYhm4hgtXoMGUT01rc64Irs8PviHvHs8gI1bO+A2GaFQreepeb7PkwYpn4IbSEppi4dGukBEhoxj8eIaYgUbXvflkNTtyDDRFVzy3GB8lmuqsW/eYDv4bfmCtbyzFo7Syjk/Wmkm+l2nrZs2vV9TGTxry4XPCmEEUMCi1cgEesZLPHQxH6A3d6HgouxCM+NWVneFsIw/RGUsvy8xDiFe6sTaZ4UL/x3Zpu7tLfeNErVf0jN85AhWK7ij7E3ZsNScz1KZ2BiCtj7J2UOP7hWeERSNhxpgnAjgKwBJjzKvZpcUAWr9s48aYKoBPA/gNABsAXG6MOdNae8Mv++wHC807ne6JaA3zZnhaxzFOgkWHfo2CbxBVsIundZTiVGKumNLxaOHKjKXw6Ld8t46sDeG7dWYjnoU2fp4RwV9N5AkM36Ak795TZkq0hsYvFK5v1avY1XF36xTMy2p2lqAeEIwBw5kZPd7Y1iq43zGqR6oHugzuXMvUqh6l1RVdu+4r0KZULKw+ULYZihDx907yQ0GJztBBrtqREH5/XGVWGBmNiEGkpnXc5/LIcHg+Y2OrGUTu2C6daKh08jZjmwEkLdp8yghRqAxBHlir0dms+XTShpLQERWz/SFWBvjeTaOH04YFLYE6Km1sw3VLI+dds1qbhYPlrFs/MifLEHyZWrZJu9ErBs6bKTx+YAauTKPLF45rdBaGPDNOaEemvBYyiNy3EcjaQfeQXDm2ZMhXjXvMksYPuwP6qlUr311aq1aKA3SzMZCBCtfJ5AX2mtPLd13yjFCxTnpMRwYM3IWAuSJhTwDwMgBLAbyc/XsGgD99CNp/NoBbrbXrrbU9AN8A8MqH4LkPGsWiVtIdMkXgW/Kj4ne+8MtOuCYmcrxeRRB1mWCkAwABPY2iLT5+j7ZjzvNmlBPWPToHWpvyWrhoU7bJ33nHz7uh/nBa9KhUmEG7wgsPhrEHbn2WfG650y6utLlBqaYjhTLzBC6fT7aL0bnmpRx9Azd2xlPMACn6E9odqSjtWc/zD28G8NI63GGJpLTp+TKlHVQ63OgRR4e4b7uI19ZwY8CPWM2djuS/9VP3Q2cstCit7syUr3bSnZJyXuZ0kiJ0upsM9CiGV4YQUXSx6Jtct3LHtLt72Y/WeNHxYEq74ssExkfWeVWX+xolj868P6WhoDuDPMJGL6fmji3A3hIRcRC4cSLfl+rxPTPkvTQ6c2xlm5JXiE5jTJHR8Gq3+G5rqa9E5oY7ksGSnTw6XurI2NhWHB3ZG/qBAVdH6ob8QkA0EmatPQPAGcaYY621l+6F9g8BcDf7vAHAc+RNxpjjARwPAIcddthe6EaJrhB+/HgGT5iwtM5ks5YVXtakci2ZlwRXdp0r7XDqQROaADdORlg+KQQuYzLa3Vc+N5JOm+dunS73/ANpOmqT181ptITqi8qolCIYQ4afkgbgAozuCQsMX4GGolIyqteqVzzv3j1uQx9bv2bHp1Me1qrVzXnzqaS0PcHIDDgZrZEFuhot89lQ0gyMrRNpncPA1RRoON3h1w5qBu6cUSn2XGksae/DCxvV7mtjeB2fHn1z+yOjhUXtoJZKUpwkeYCnVzzO1okaVZkrvTzw6SxLH8J8T7WDcj7bdXejSqxNXp9bHBoqj25Q+F4auPyoDjIoQgZRl5USUL+DdYWNMlrD07W8bWrLKXNRjmzhxgl/X2qMH7T1Rc/NdpeOcKBXC1rydovpK43vmw5/hvUKfT/VrLmpQeXIFkdH1rRI/9z86RuUIyybcOtEucwYN6KRMGPMe/I/X2eM+S/57yFo3yjfWe8La//HWnuMtfaYFStWPATNhvHiJx6IX5z4Ehx54BQAIaS84yuEoTDwdw9pgpGuS8+irPFQomQBj09ue3avlWkJwN0549NSLvj+cIT+kB1Yq+zW4UKcP6/TL3faFc/1omQl4/s7CmPRmriQKtqs+QKj9LRjhqifiuM1c1k/y+fSAYD0fKnotOgbpSWCZwL1tXoxGakolUcskkMbOOi6pEXz7utKHZ9vyIsohnI8gzdnynyGoke8aL+gRUR33d1X/NRtdtacjOop/CmFvBZJ9PpT899dGnouVzp00rcfUWB0BhRoW4mYBqNvbDew3F2q76ajcfcNF/6+VE2Bdno+nUSTrGmanyFfGptEk2ZEUH/dNjXHVjNw3f7E5ixmbNL1Tk/wgxKt8Xb3iWjNnNHxgANfHi9TZddk+YJOp6o72Li32dhyudn1eCVuyPM2u/2hFw3UnF56xmyQTt9h8XUkozPAnwsBc+2OXJf/v2Yvtb8BwGPY50MBbNxLbc0LjVoFBywqy9348QxaioB/P9sbor1UMFnPF5p0vVjUWlpC2Y2T9cdlXjcXLj0A35sJRvUU4yRWhNsW/XFSlTUpMCJp19zr1eopnPEbsJO85fEM0oOq+4azuzvSZeyiqNVTzCPsNyUjfmGjmuoiNI+Y2uLv0eP3cCG1ZKKhXpMGiKu0XQXQblSLOr6KsW4aXXqggxEWt0pRkBk9roFGhryzCzTAD91BdgwFT6P756yVO6jIwOO1NXTeHrVJdXxaupvabFQr6A3cQ3Kd54poTU2t5yl/S8czhA2FvF5R2TWolQvQc2WarjSqq9jc7xbPdvrD+H6pqC/SdkU3xdoMF8n7USmN7+vVirsTW+X7UJtChinrVksltfNDQMOpVdcgchwsJXUf5JXIc+cyFFR+YE6ATyeN33zSuUx3NFxjs5T/ks4KkyUUTdUNIq4fimtK+Qf1VzpffF5iESv+m9n+EAdF6u1COlJbt7E1zb/XanAfNkaYtfYH+f+n7KX2LwdwZH7cxT0A/gjA6/ZSWw8Kzm6wIgyreyxuYX44LUG/DaVYnPoizyP2GVQyEj+2QBoKftrQ92YKJotEDQpP2quZGHlCKpQGIMHRHYwiCp3TkrUlj2fgaQkaB98b1Oj0oyoenfm18tBQP21IdBbKzKu3K1MsIU+Rb+enFEGR1uFRMhFl9F6ZwlJf1JeKMc41/7DgYXFILvVNM1yyMSrPAitrDsWc9csoUVCx9IZFdEceGqoq9ACdnB/yYJjvlDDFQmff0W+l0i7S6FEh76Z1ON97O/gG5WHAJS1hfugG092lcVIa8qI/A18m0DNiUQMvsqko7clGzam78ev4lAhRhE4/0q8bCtruUi0LQL/V3rMa7E/guXw3ekzelrTohrye6vXTkeVzSQ65pQ98fdEzgrVSETq1FHzYgR+5hvxcaetAf2Rdq7vhKx404DpSptF1w086JSPvuXLdLgTMtTvyB1DSgwRr7St+mcattYP/n73vjLLsqM799o0dJmsG5YCwQIggEAKDycGYIIxJNjzABj+McSIsbD8c8eMRZIRJBiOCCMZCgMnIIgkUEEFCEeWcNTl239t9Y70fdeqcXVW76oaZntsj1bfWrOnuE6p2Ve28qw4R/SWAHwAoA/isUuravXnnvoZZ1KZw3PwNkNM6rkKSdqAB9qKWwtgmreN7FuE6Fz961PeEFI+48GemKqU8rVMIxsHeoEmx8DSd5bVVy2hmu0tDNXULnZ7oLWtafIHhHs8gpQjmW4GoFNut49fduIqloMVN63BBbd4f9BSZ0VOkZgLGibdOmIATjGpzirpkVJu/l1gUS6RT8Hotg8gxqo2x2QqtzW4Plb5JDTseMTMo12dRxoJOWQHw3a4xBVoYYW6bMp38GA/+7T7dnzJC51zxse0ENuu0IgYuX7d2Gn0YOnviMR2As4kltDadNDpfX9IxJ5qGvh+tjxgRZqxajI/MR7j1e/06quAuPWd3n9dmIPrmp+JihosjUxnfSxusrDYrfrTLzAs/WDsUZVzk68+t/4s6066By+jM5bitV+oOD/I5q2ZnAPKAg2tsBmvfqsXuUl8OlfL3aVrC6WUpu+AauG5Zia2XQxHT8DExywGD0pEfWOoOKKXOAXDOUrczLqaqxfEMkkIHeGFh5AyUtiswStg637Hu8YRflxsKjnFiCSmbkUKpkKmKXyjq1Tx1+16aTgobu+k/d1cNp3NHw60NKTxiQ0sowrFgCQXZoHTbrFfK2DZvGyeeAcKjbyHBKNV/sJ08biQslKbj6SI/2iAJxlBEwQnXR440yN/b7qOUvc77vJWlWAK0OIa8lGKRjmXJlfxIAre4ZtI13hgItT7mGQU7+pYbv2153dopFtd5iBlERZvB9cU8f8vwq5SctGF4ri1auBHmev7ejtY+Nqx0o2+RcXePQqj5xqZUv8af4Zt1JFqmqnZKu93V0dJgOrLdy3f3eTsyWZpzpZVGl2pps2fZBqFQrdRCpxfc3ddizvRsjbXJiu/5MR3SuPO2+O7SfvZVD78wX+bBOjPkFzp+baqhwT9CpnivUvozZ27pSFiOc4PSl2Fmd2nLbZM5SWaMQkb1gtBmUYYg82Cr2/c2Crgn8XND3tWRywGD0pEXmJ+JqAbgeOjI2I3ZkRL3e3AG9UP5hVAwn3AxCyDfrRNNS4RDykDmgTrCZEoQUq7SDod34+fzmL9LpzCba+5ZQmYcQoaLnNbxhbyvWNzamn5EKETSEi4tQpvhg2edaJeT1vGME0dIeVE9FsXwNgMIET/zDh6p8A0Few15Ra9WOtKlM5TWsddQ3TXQBqyhhU4P1QHpSD/FYq8TN9oQSkcWB5X28pC9FGkFfEPepcVbXwGjmm8M8Y+0ccZWoDOPkkXS6J5Tkp+K3/c2scS25BfvDTkWwpEjOd8XhoJfvyaVIQQclo4/7ob+UO2bJBPy4xnYnG3gUUYnZWan7n05JBnO7rh7h4Z2+jholvNDCVv2hOk0GzikGlxAr1t3Z7i7o3Wx7awhJ2rsri/z3qDh0ul7h+TmY8Tea752YWgxnwcrol1O6UO7CBoMw/f5wdrMqF5l6chI9DIPgPilLEZm69S9fUyHeQc/z3DSKA2+BSCiFwK4FcBHAXwMwC1E9Pyl7NhyAd8VF0uFmENbQ5EKfUSArcx4qNUcAKjfWyhQV2lzIeWmD9z3thzDpc4Xdbf4jp7VJlvUUvTIFZpFm35K1owBT+uYAwD5+xfavaB3aoeUXSEfUQA50weMk044BWqNX1BIhSM5C46QmpIUS8jrdSMn1ZIVqRg2LSFGTrz08nDGesxA4+MnraFoKikSebIN3EganfGgO7aVcgm1ciloyLsF4pJxolRcgS6y71za/ZHfa9eyyIaLbtMxTpihFYzktJlRHUhHymn0fhYZCTglgkIvlfwyhLBB6URa2WeWXCfJclicLIApfci/DOCVW7CxbfsOi5HRMTnuXnMP1m458o2voQWHj6ZrXNYYmeAaEb7hJ+1odUs8+LjbqXvO9yZoEHZAQ06JK2vs6Li7A36w4ad1pE7d27su7bpWf1NXIRNsHcmM2FD5xxA6cjlgKCMM+gPez1RKPUMp9XQAzwTwoaXr1vKB7Q2Go0fuNcD+eKmXlnAMF9fzz98b9CwKgWEJhZrLSPai5p80shZ8xV+4Ut2Sm5Yw10OhcyltSE5khtMpFcSKzMu9QUkBODta/e+yCYYCMzbdAwDNeNhpHVtpG6+XfxCb07LQ7keOOQmkCJxz1sLGplPrw+iUdt/yNr2onmXghguRFzoB40RQoMVhrYViDu2E8qJkWR1fp+d72vWqr+g8IzZmbHZk/pyqFLtL3TS61aaX8rEjRL7hbEe7XGPJpHV8BSrQmV0rZxsbiqMv+n6EI5BGz6Pu3cjaZHwfroOUopcB/mSRimA0te07D3KbruHMDT+7r+74+Wew9TyD239vPE0nRfw4ndLxDJLu8COJgf60nWvsOCFfvnFjyafTdaa9SD8zcN05KcbWrfv1x90zKCPHOIXnM8z3curelmHLKR05rBG2RSl1C/v9NgBblqA/yw6xhWsxUltiJJt5wyk8f0t5/l5XSLEUS+4BeBE2XlvjCsZwbUhBp+2d5gq0Uwgp/l6rwFlgUFsYCx5xJ5yWsIRxyOvt9J20oRuxKomGn7eDqjKozZJjxPoC1zC+Oyf52Obj54TygymC8BriZzz5Rk2xTtwDa6U2PSMsolg6PbOxwYnqMcHoHXrMvpdqUve28nDmUzAULM9WOBOoMPz8yJP7tQsg243YCSsAwPXuHaXd6XuRHP691LzWx3lvyPDj8xIyFKRNLJxO3a/4bjqpzRZLrUobOPIomRNdKgy/sIPgRo+syLDwCSE97iwi78mwUNTYrm+zn/Mj4N5RHCwyF5Q1wi7QWB2VeW84+iYbRO6GiaCB1rXnmsvU0E5sKWoMwDpKR84uMFnjrIPQezkfuc69edZ6b1We64WYjgw4mTx170Yvl1MkbFBhvsG1RHQOgK9C14S9Avo7jy8FAKXUN5aofxNHrCBWih753n1sUYdTIUWbNoPyFIvs+dthY8tQqLm1ITIjhQvzfaNQj4O9E0qKSoUiLv57bQ9qISCk9JlnfrEnH9u8Tk9g3lYgxWJqFEQvPOLd25sM5LHlwtgYjTytM8jYXOjoLxbw/pijL7y0BFubZeeICr6jNRdSTkQhttFC098PpyU6ffSVsu7PU0mdnpi6599LXew4tT6OkLd39xVtFjVhjgffliMc09Uy7ssNBYcHrRSynUYflu8lA9eL5EhRqcyI5YfkDvLuLafOjXZFDBdJSUobchY7thNY0FLUvPoRSLlcQOR7V2mzTSy2DCsH38tLHyTDxfQz5NhaUTJv12U4QtSyxmBAhMg9oZ7PZyTKGN6Q48gatjbdQ3KtqJQUfWPRVD9tXSocM6G2MvReO1BhG78eLV6U1i5DGFZHljM5HteRfSwXDBsJmwKwGcDTATwDwFYA66C/I3nKkvRsmSAalYoIMH3dPhjUXbjFUQmywAgxaL1asnba2e+1a2Dc+qy8zUBaQvQUudIR0hLmA7jmHlcw5rt1PDqLaI1LS4mlWIqogGvcBYRUtdjRuiAUtZqxWez6kZOprEbB3YVnrhVCyonW8CiaUOhe0Bk2tNxxz6/xs9Jq/ntb3b6XlrAKnAPpjoXANSv1IOwCNX1puSlty8D1I6ZGaUt1GlNVOyolFhtHDFwp+mZ+Do27W+fiKiSgSOtMV3kavZQ/4xbmm+s2neGIgmgoZOvP3WkHhKO0hpZu9rULL0IUjMj7fC99WkeKEJmIgon4hYu8ZUPe8D0/pkPexMKdC16rF88uTAfk20LHrofl0Td3d59pc6FdHMHgyrd2r5/LcTfiUtAZioQxvVKT58yTYczAlSKQxXvlUpagY1uLOJnVwRG/WJRxmECFexSHpSOHSWm7RqNg/Or3FgblcsBQkTCl1OuXuiPLFZaQd7xpO30ghZQ1I8lpCRZREIwI06aoJKvlrH7BX9TT1TK2m7OjQgza7Vsfb3XbLASu/lu+W4ftZgqnCGK7dfpOxIV7vTIti8OkI4WUT95m6BpT2pJQEFMhjjKz3psfPNvz5lPe8eXXeMSu6ecjdRGeQsr60+l7Cq5473CpXncMTJvS+UXmWn5Yq5Amdk/5ltqU65bCBi5PL7gRrWAEt1Z8GWCh3cPU6oBiCbbp714GiuMQpDWtjfxCmYkRv2wNxQw0j5ZqPOLHj9FZN2uvr/y9HTd1b0c9Ab8MQRsugyMc/CgJ+8iWnpc+BkwaPWDEdvto9/S5cFHDLyRThbQXv+bRksnb/JBcJ7tgxsg9psPagOCsv7qQHnV5u9UtNoaEZZ/+JqPXH2H9Seluyag2TrMri01d5kIoc9P10+hFupvLVF++5fWwohzve3MmbkBwZC7Xn3zdTleLI4yWA4YywrIT7f8KwDH8mb09rPVAgBvF4GkJftJ3qJag0e4G0xJAcXaU7Xn53ox1TIBJsQhKe7pWxsJOuV7ATou5tSFFm67AKHbr8ILhSPoqFKkIhbG7AUaqli2vzRWMoS35nEHDhoJfiMzfG0xLBLxBXnwfSr8stHuywqqGo1JuKsk9P4uPnxTJMV6/Hhc/IhMu0C3adKOe5r3ewbyVYn31KnYfTRuL7Bw620Czd+7KvNL35lo2wvi8hNMS7g5lydjM08uBQuSFjh1NKegMG7jFkRnhVJK7vspCZFgqNg4Zfjzi50bHc1rabs2hMeR5OtKZs4AcMnOt3x1xhJy5rle4jJLGr2SnKoX1Bfipe36wthvdLQ1IX+UOS8AhNrSEnAce8TO8aHSHtAPejPNih6XuHeO3OFi7j/UrfDlu+JNH/Li+EtdQ1Y0a+5F1c13SHTo6bqfR+Y5Wke+r+mBtWUfaa0FORzLDTzjrUOT7ZVaYP2xN2LcAnAHguwCWTzJ1P8D2oOzdfYBRHmHht70RiHA4+XnuzXDP391pZ9oIFegaIZ8fOhj0HkK7pApj041axSMnhTcjbZk2aR2RsbMUHt+CbK7bhZeyB+UZfm4qSSwi9YVU8d5AsSyPSnUDhlbHePeCgdbpoS0Jm0o52KaVluiEIqZx48Td1m23KQvGTk97ve4xHW4UQ0xLdPvoO6fXm+tWWsKNhEXSy/q9PeHYkMILd/th+ru90Y46D0W9YixCJI/7glTnEjFwrZKATmiXmW/ImzZ4JFEyKItIhN0f06Z7bI2bLgpG5EVDq4ydzXYw3d3Ld7QOqp+0DaLC6JHl245G2/tagxlb06aXuneOhOCOhR6vrAwhIFO3z7eDYwDIZQhu7VvdmU9TSyvN51S1hG3z3UDqPpNvYkbDMQorfptc1vBxqFfLuaMjjQGgsxbSwby6Pz0vjW6uc7630q4VHZWSxtbVV7MBHenWpprrVsmOsKO131f46qV34zFHrcHxh6zCpDBsTdiiUuqjSqnzlFIXmH9L2rNlgnrOvAHBWLPrXDyPpSOfVWKnr/peESTADT+7TVNYGPJmrAUfS+sIEQ7TJq+BAYpIRaieR3u1kuHieoq+YMy9K0cwGoNSiljVmafIv6Pn0hIqzM+jRxVJ0cmC0aSZikNyBa+t46dAYzuWzLNWwbATYWt1ApsMnALxYMqsK6c7pCJl0yYANNs975gOK10U8PxDUYNcGLdlh2WRGUSSESs6D5YzI6+/WB0Vr1d0o55Fm35tpbkWq3ORdoPx9FU8ZWZfM9fDtaBhz99NF9mOkHONya/ioNLAcTjVsPPgpv/CMsFe0xYtUjrSdViCMkzeLVykemUDN+Qwa+NX2r3srM2ITPXn0x0/+9mgc+/yfcUf98LpldqMnfcYTmkDhQwLz7XfZv7eAN+HdKS5T9aRxRi4tanmejCql/Wn2enhHd+4GhfcuBWTxLCRsI8Q0TsB/BBAy/xRKXX5kvRqGcFW2oFFbe2mC0cbQgXi0u4+c801XPR77Ohb3VHa1iGI/BMbTg2bFD0yhlaYzkDNREc2Iuw2bSFlF9/bio7TGVJ0LRYls6J2Vjq3h7Uz1eA1bjQDJvIUMSKEIwv4fSZSwb8XWJwo3UOr10etUrIifnmbgqIzqa1QDYxp001LlNlOz0qfrG/32XQKCjQbk93Njj8GPIrhHIjJvxJhImHurksebRg2PWrxQ1dYQ+UiQgn4Rmwo3c3TRTAe5sQAACAASURBVAvtHmaEyIl2LoT0VZZKqmXpSHdzh0nNmD74tAwwTroSP7iyxp4zzfeazpmYoeA4FtY1Nnb8oNJFk3b1DOcA33MnwDFwvWiqZISxOqqZmv9potC5jKbNcGQ4qy9y+H4qyvfh9LIdAY85LPb6stoMGX4DZY0vw9wSj4H6yjHI7f6EHUl7Tpxx95zp8Jy5hqjMK8JGMlevCGvIPivNd1iMjnTnZX9jWCPsUQBeC+BZKNKRKvv9fg07fSUs6kosxVKyvv8YErjhKIYf4gZ4ikVmlkV28GJMGAfPYmr3Pe+07i1qW+m0e300AjVWAPLaB8kDlVKVhhZuUM44Y9vuheu6TJveWUx5KF9fc9MSU1X9LbjibC2bzk5PoSntFKuF55OIMgWq6ZSE8e5mO7hOOj2FRstX6PwAVDctYa4vdvQRFVPVspci0G2GFcuO7DMl0plnrU4PzU4XD1o5ZdNSKY4HkdISO9i6lQTuXPatuFBaTBtLttjiB7LynXYA8uJ7WekUbXb7yltfAIsQueskSyUtloXUfaWMXc1OsMYPCO2iddsUvPvMOOHHdJjxWuz00WzrYz5CBmXsGAX3bC3TJyPDXEPeSzMFojXBNF1WJ+SNbSbDmiLfxwwXtk468aNpQoZCcRi126ZcD1vwve+8cmOz2fYjfjEj1pQhyA5oIcNi9XaujC/aDEdTu32FueyoGMlwNmMU2qwjZYuKCLhkaLkR+UCELbIJSDTCamVsnWsxx9aeMysiXxvWDFoaDNv6SwAc+0D5XiSHa+XXPcHoMK9g5cuH1BWeRbPdw6x4sGDEONkZSgPoFIv5qKzlJdU4LZHt8UKbWhiHa04AYGe2K3O2HmNQ2esVo4yZMmu2fQPXMLKhM5jWcYuNK0WKxT0bSrdZwuZ2L1dms4LHl7cZ9e798TMK1E+/lLA5kCIw7zHfbQvuVAwo7cVOD0TkGS5TFd1mTPjtNEZYZN16iqVWznd1jeKwGL7aJcwnLzZutntYv6KIMpp7zdi5SqdIsYSNzZ0NaQ3Z65Z/R89cX8yMIS917ygdu85F/7x7oQOl7CgPj0q5dTdmvKRz6EwbJsUCwDnuQLfZaPWE7+gV6SvJwDW01Col0ZAPRRRMm812L6tNZWNgFd/bH+EG9DrRzlc3UpsajmwaBytUP7nQsT/CLdEi7dwNRXIAoNHuesd0mDEw73UN3DyyGShK54aCdDTNgsD3+bW2NsglOi3DT5LjOd/761YyKAdFpcwuWtGgrNglO0Ed2XF0pKWvJMOvyLBIdPYVsGuh7fVnEhi2JuwqAGuWsiPLFVVzAnbA4jZpHakeyoQ95bQEEwrtnmWN81O3RYEbOfvI/LxDUtoDdl9Vy4RQ2nW6WkYzcJSEYUJzNEa8eNxXHsWOG4eRMqWTpyWqvkG0o+ELDDuMbY+fSbEstLteKN88Gzz3zRgKWZpOiiSGlGQeAo+1GYnq7cxTg0K6I5sXKYqxmCtXuc3isFbBwBXSkdYuUEGx5G0GDFGuAKRjPGLzaYS1T4t+r7vTzlyzhLFA5/aGrrCQUiymTTGtE4hUm4hVLOJneMWN8pg2RcVS4W36xiavo5oRHJZibAVl1pXbnK6W0ezItVummL2IWEUcFvasOaA4FsXg0SzPwO2Gz2DTbXa91D2vcwzJVGPEVss63ezSKctbfd+eBZ8/+VcipHVrdEdx9qJNi7VRIMafUklANzOWXF7xauqE8Yvxfafr0VIpl/I2Fzo9L43ubl6bYju8o7t6WelI09GRlr4aggelVPkOgQcngWEjYQcDuIGIfoWiJkwppV68NN1aXjDeQ6PVtXYxmms6fdVDiR1fAQAzdWNxhxf1fKuDdq8frRcQw/VZntzd3VcI3EyxCAJjodNDo93FirrMoFK0ZqZWwc7mgpiWMIy+M1/UUr1Azzvg1Kaz79FpUpULWVRK2uW4I4++VbxrRsC5gmi2rg1KKRViIicm/ScpyV1ChMjdCeUJhVrhaXtznY27SeeusOr47Db5vBgvN6RYDC09J9VmxmhghEjwiHmdS1MyiDJa2j2y5sS0EUpfGVp2CIY8j+A2Wj0vfcCP8ZCMiF5fYX7RV5JTjuEnpiM7fTRbXYEWbfiVS37qfraeGS7R6JsU2WQOi1SGUCtj61w3i8jLRn5uEEUcFmmXWcggmqlrZTZVKYvrq93rY77lR909XnE3wNQK5zXksDRF56GEdreP+SxlJvG9xCtGJi20u14NLqDXwu6FDpqtrh/dzQ5kLcoQfH4w8+nW1OVF4O0e1jqRTaM7mu0uZmplO42etdlo+bJvxnVYhJIK0+ZBK+w2zZcpFrtyShuQI+Cm/V1NHcENGXfNds/XK9UydmWlD+TqyFoFfRUw/GomgqujjCFZI+nI6Wpxlqanrxx+cGnZ3xjWCHsn+5kAPAXAq/Z9d5YnjDctpkIqJWwJeG1GsWyfb+XvKd5pFoJefCHvfqHjMy/fleQLtywqNR9OX+1qtnUqpO7W1hR1CK6xqQ2Xbh4VcL1TgEXChOhbo9XVxmbVfm/uCXX9FAEXxpWS7Z3mbWZjOyukdYqdPL5BaaJ6fvrFRI+6Vv95m0ZIWemXPMXS9T7CbWhZzNKcUm3IQruHpiBwjdG6UxBSM5mwa5h5CaQju845Q8W1vphKMsbJzjzix68VBq5c56LnjIBAKkSO+Jn2zRqydyNyo7obdFj6Snnry40kStGRWIRoITOOZ6U2MyfIVegztQqaLf6xe/+9hk4p3b0YMECKyLoQJavpj3/nClQ4T844Zla5gLMhR3K+GplhIjlQ+r2+DDPvLXhF5u1Q7duORts740+kRRg/M9d8zdcqOlrTaAcim5kcbwZSskBh3FlRRodXghFwad1mbTbENu30vOV8ZbJ5m7Buze+mPvDI2rR3betcS06PerRIzr2cwjNRvUari3WzMx4tecbH1ZHZWtwmRMCNHA9FrHJ91RZS93kkrO/pK6MjQ7TsbwyVjsyOo9gN4IUAPg/g2QBOX7puLS+Yowma7V7Uu/eVvWOcsOv1PJLjp0LMe1vZovajbzyF5zM9EDAUqnba0FcsxcGzrqethXEgLVFxBCMX8jWnzUD0LXT8R6iOyrQZS+tIKQJzb6PVDdTW2F64e/aMTUsxLybFYtIv0s42c6yDF8mp6hRLo91DrVwSjU0p+mYUUF7TJHiKRc2hrwSN0CSS0wC7m76nXSuXUCJgPvNO5XSkUSyu0AwX4Zqx3DHvt2nS882OXxtS0NLP+FNW2ruFteAqFt7fanawZr4ZwOXBSpjvZ2smiuGnX6Y8vrfbNGUIzZZfz1N8rmwYvvcjRNuFSHWFlVuEaDEOix8hsmnh/TXrwpxMLsnNhUDUmKcjJcPFpsVft7uECK6hu9nqyrQYvu/0cucm748rN3n0bUCbOi0mG7h5xKrVDa5b6b15JCx3tOXie6nGj/O9pFcAme9jvFK02ffqm3M6hU1S+j0230up+x3CujV0tzJZI2WoBunIAyIdSUQPBfBK6KjXdgBfAUBKqWfuh74tG5gtyk3Bm5mtl9Fo98SURa5YIp52OBKmF26j5SuWPMXS6kY8RcOg4bSEu6hnaxU02l0xpKyFcchwMcI4oyWSCnGZZbpWxpa5jri7LxeMLbn2iL+Xj70Zr61zLbHN2XoWCRNqa+pV/VFsyYjIlZlRLJ5QKBdeuKBY5ltdLLS7OHSVvaPQtDnf6ngKwLQh0TJV1TUnRgm6Ifl6tYS5Ra101s26aQl96vZcq4uZqm1suh4xH3uTYtkZFMZlzC120e33vZ2Ts7UK2t0+di90dN1NWVAsGS1S5M4Us7tGbL1awnyrC3SF9cWME7dcoKAzQEtFv7fd63uKZaauozVK+QbGTM73LS/94vK9ROdCO1t/Ai0mxeJv7ghHKrx0pEtLZmg1W76TOVOvoLGjicVuJSJrwunIHSHni0Uq/IL1IvMgOSz2e4vrMw7fu/w5W9OyOlTIbQwiaU0DjO/rvrEpRazM9TxqHDBcpEiY6UNOiyXfivUFCOlIVt8WMpYagYgyIPO9m7oXHclOpiPdNZQ58JKTNOvwvVRvtyPIn0ZH+rRM13Qp0NyilHlwaVnekbAboKNeL1JKPUUp9e8AekvfreWFoibMF1Ir6hXML3YxL3gWeSRM8O7dWgIx9dA2CywsiKQaGHON/87bD0WlVkxVMN/KaJnyhbGuo+qKO9A4LVI60ggTSbGEzibjCjQoGAXFMl0to0TAxt2Lmi5hXhrtrrftmbe5q9kWdzNxWiTjWKqnML/nO4sCxt3ORsdTHGYeJFqICLO1SjAtYbxeKaIwzRSLu6ZjNWGAnt9gWsIogJbfpun7pj0trKhXnLSEm2LxIwrD8IpkGAOGV9wDiG1ekeZMih4ZWgzfr3SNfBMFarThfmHD5RUpZWs2CriOkKFTStNxOt1z6Fy+d3lw5VQV2xtttHv+TsXZWjlPrUrrwNDilgv4vOKusaImUUrd5zsKAynQ7Q1tVPNidjMPOa8IMqzR6gZljYnkSCUTnBZeZ1uv2M5gOB0Z3hyjdzHa11ZG+H6GrS+xzYjhZ/oz3/KjRx7fRyJhUkmFqaWVaJlvdTC32MWKetW6NuPyvVT+ETCWTKZkXqzZLGgJ6asDJR35MgCbAJxHRJ8momdD14Q9oDBVLeqh/CLcChY6Pexe6AjKPqsJy4QqXwwm3RGMStV1REEX0IeFwoope1EXC9ePsJkPcRdh7IBiWRSielyZCYWg5prbZq2i02ub9xhhIhsn84tdf6s6Oyoh6BELtW9Euih8UybAPO8+UyzumUm8ze2NtieMzXsKWnwhlkesPFrK2XlL8o4l3WZLMFz07yFapmvlIoUnKKxWdt6S996pgpaQMA5FEuuVwtj050WfK9UQtseb92zevRg0/KR0pHmvVHNo3jvf6opOEqfFS1k4tSGSkjT9kQzKucxhkebE0OJHWp16FGG+zfqS3qsVqC8TTHp+Z6MTjOCGaJmtl7HZrC8vSqaj49LGGV6z429+sXlFMo63zbeglMwrhfMgy4Qd823M1GRDflPA+ZqtxZ2kfFOSS0utoGWqWrKK2U1kOMz3JfEcOt5mQ4j0c1oqWamDgZvC8z+HVEajpT+R5sow42g3IutWcjKNvgpHjYvNTlKGZbHTx+6FtuewuKlVV0dWSiSmns17DS0xGea26df2RhOCS46oEaaU+qZS6g8AHA/gfABvA3AwEX2CiJ67H/q3LDBbrwSjH7li2dPyPS+2qF1GAnS6Y3sg/bJyqoqt8y30hXSHEYbb5ltYNSUz0vYsFcLbNMbJ1ryY3VfMO5qZRxxIsWydawXrF3JaHAG3aqqCTQFhPFUtodnuYr7dxUrHoOQei+sRG+PE0OIy0sp60aYfqdCKZV6InHCD0k0Nmg8CG8XiHxpaCGPXoJw2xfftnuVJa1qKsXWjFMZzzGkRIhWhMcjPJhPSHauYEeauLyMIC1qceamVg4LRGETNll9bY/hjk2D4mT7ktAhrbEcgerRyqoK5PBrtGAoZLdvmW8KcuM6D7whtmcvmWoiAN4wC8OakoCUUxd4u1IRpWqpBI2KqqlMsOxptnxbG9+76MmOb0yLMmVlfrlOXpyqFNFPhsLTEOQGKdevRUikH11eeeWh3g8aJHlvXYCyDKNzmTK2Q41KRd6vbz4xqOSolOSxmHEJ8z9etX2+njZM9i0IEvM54Zco2NsuZLtkqbErStJTyFJ5PSxW9vsL2+VZQr2yd02PLjU1A80vIEZqtV7BtPqAjp2xaOHIdOR/QkWz8PBk/pedT1JFMhknyCygiw66jtL8xbGF+Qyl1plLqFABHALgSwDuWtGfLCKumiqiKtBAA7bGEFMum3YtYNV21GAmwlZnE+EUoWk49bJsXhDEL17s7UTQt1TAt9Qo27w7UUdWKiMzqadlYMm3y+iJNSzWnRYpU7My2PYcNyrZgRFTz/kxV7fQLoBm/UCyuQakPgW13+1gVokUQ8jxF4BbQ62eLaI1HS7Wc72J0Bdiq6WKdSIYxoAWYJKRmasXalOal2e6K9R+cFk8hZecbGVokL3O7UEiraaliz0InK6APKJbdi966NX3YuGshSMv2+bDhYjxiKd0NGF6Ro8bSxhnA5hVpXpptHQH3HZaClhiv6Pf68mRjgD+nIrTw97obNGZqZZRLxGhxoyNhw2+2XkGvr7B1roXV02FZ485JtVzCVLXE+N4xqpnsCxmUOzJ5wsH53pUlROQYlL5RHeOVok13TvS9G4U2zbMFLcK6DRgRhu+37Gl5TsfKiMOiaYnzveEV37kv+N7b4MLkrTsnQJYqj/B9TK8AwObdfjTarMWQjpwawPeh9cXXZlBHzss6cn9jZBNQKbVDKfVJpdSzlqJDyxGrp6v5GU5+JEwzQLvXFzxifW+j3fMYBdAL1xz86YaNV01V0c4OgA2lWABgZV1WLLuaHawR2lw9rRWWRMtsvYJ2T7fpe8SVnBbXcDG07Wr6qRBAM76hJZRaNfeFaFk9Y7dp+iBFs0w7oTZNGJv33aVlZ7PjCWMzv61u3xs7nxZnXmo6vayU36ahRSzQrWrvvt3tex4xoOcwRsuerE0p0mpoccfHpFgAPXaugTtdLee7Dd15WT1dRaurP3AeioS1e36b9ayOqZHVHrm7c1dPV8WCYU2LNhS6fTXS+qpmh0zuanZQIv8653upJgwAOj2/zVnGK+6cVMslzNTKOd9LtLRyvpcVi0TLdITvicimxVX4jO9DxrFEi5n7Xc2OWNy8clgZFjAoJVpWM74XZQ3je1c26tRqz3qP+15Jhq3kfC/ImqnIGptmc71G4BVDi++wZHpF4E9NS5zvDa9IhktOSyBNx++zaSl2f/u0VMI6kvG9v/FD3zvf6oo6cvV0JUIL4xXXYRlCr+xe6Hh0TAKTjcMdIOCLwxPGbIJDKTzAj4wAsM7/chcgXzhxZpG9KwDe2Snu9ZBicX/WfSjaXDXl99XoaYmRhqfFMU7Y72sdZpmqlvNIlKtUANuI9EPgbF6c/nKmlBSoURAhj7igRY7caVpqwWuuACuVKD+8VRbGnBb7+pox1xdQ0CJ5xLwdnxb23oBHDPhGvv60Ujl7h7+GYvPC1410fEXRN8ERyv62errqRXB5O6EUlaYlzCsSP5gxm2ZrWKLFNyhZEXqE7905AYp5qZTsXaluOyGDUr/DpiUmv3gfpQhulFc4Lc6uXs6vovOVvUs6v82SYdMuLeH1tSoyJ0BBC5F90LL7rKvw+bWQwwLIPMhpd6/zMYvxfaiOKtTmsDIsplf8corxdeSqiAyLGfmDdOT+RjLChgBnWFcQ8VShZ+VXy6hkgt1legC5l1cpkadAV0aUGRcu7gKrV8r5opesfL6QXYaIMSin22WGUonyxewehQDYHmmonkzqDz/tec20/17TD9fj1f0vs5/DQt6lhTO9e9o076OkAOoRxj+IjcvaWdkj5u/nMOtKUgB8Xbm08Pk/yJmXlRHDDyjmReoPn2M3UrEqQsuspez9NrlB5CJOC3MsRnBYgIIW2WEJ8710ZIB0r8vXQEGfyCucFuHLAKH+8He50UneppTyidIS4RX+u0xLNaPDT/lwGeYq33WzxYHYMcUb45VZoc2YDOPz79KywlpfYV5ZUat4hrzNK/Z7+Ty588nr+iQnyczLinrFq92y58U+XHxVZH2ZjVuAHAkztExVS159W0yGzUaM/OlBOjIbo3KJBOd/PL1i6Uihzf2NZIQNAb7AHrTKXtR8y627wEolyk/YlxeYXtRrZ2uewFgZERj8WkyxyB5xoehcRrI8Yue9G1YWdMcMypjhUi2TV0uw0hKqYcUiGZRGoLhzAhS0lMivX7Bocejk7cSUpJheniradCMyB63giiXs3btnawHFXEhG2IbsvbpNxyO2FIs9Rnzcpfk01yVhbGgh8p+N0bIiYuQDxTxK/eG0uNERTos7LzEvHOBGmDCfUb4PR8APWlGPRoaNES7zynh8v6JeySNcIt9n73rQSoFXIobNBjaH7rxMVcs5b7lfEgEKfpCMQpuWiMPi0FIpl3LeivG9tG5tvo84LM68lEuUtylFUwte8dcXf5frfPF3bXDmpVSinBaR77P7B0WPYs6XW+NHRPl1iRYzx5JDHOP7mHNfKlFBS0xHztSEWuMw38f0ClDMizsnk0AywoaAZYQ5zMLD2JIgN4JCTktkwniAR3zYGntRH7p6SrzPIKZYVkeEMb/f9RDWrwh7p/xZV9nrPlazfk97xuZhq6fZfWEjQlIsMVrM/ZLnz4VELPUQ8+7dOQE0fYA+lsNtc52lWByBwQSTTIu+P7a+KqWSJ6RiBiVPmxy+xv60iaZF0ycqluxdBHj1YlGHhbUpRZ4M7fL6Ku6vlsMpPJeW2XolV6BRYRxZX4AfNbDSJM68lEuUK5QYLdL64krVlQuHruF8b79XK9BK1rewQekqe/d+t798PUq0mChHzGHhPG4Qk2ExXuFtbhAcFjMvUl83RGixDRd/jEybh4m8ov8Wix65bbh9iMljke8z2mWHJcz3tl4Jz4tk3A2jVwCf79cM0pERvo/ryOJ+l5bhdeQDOB1JRK8gomuJqE9EJ0+qH8MgVhPAGfvB62e9Z/NIWKTORVokB7NT1V1G4uHdg1f5guigIZhFunYM6/8Ra+1FzWtXJAY175WY5eCMKaVD8bgx4yoIruCl/pq6Iil6ZGhxzzbS94ejetyQWS9EKkwfJQFm/tbrK+9azLvnbUre/VHrNC3S+jK0mMJqDi5gXFp4m6KSzGg5WBhbsx4FMqOKhbcp0xJWAMYpcGw+3Uc2ZtK8KOE+A6NwpbQEj2y64Lxy7PoV3nUTlYpGjQVl/yDGz65RzedJosXcvzrqsIR5BfCPUYhFjzT06EpGmGlLklHcWHblwqDUaidb65LhYmg5fK2/Djjtbr3YoAi4kUWHC86X+ZtkRPA5jqXwpHkx1x8srC8zL26tHWCPmVvMzmmTeMWMg9Qf86y0CcNKR7o6kjnwx4ysI3WbbmYGsHnA1TvcaZLW37rsvQ/0dOQ1AF4K4MIJ9mEoHH/oyvxnN8LBf5eE8R3bGgCARx6+yrt2yOqw0n7EYcX9sS20jz5itfc387ZDhMV3QvbemzbPe9eOOahgELfOQHoHhzEMJWPp0UesAVCcjcTBBYEs5DUkRjKf/3GVFQAcKzC7ATd01kU8ISmqZ8ZUqtMwBqWUmuFpCUkx530ThJ8pyJaumdSgpDi44RUbW0kY97M1edzB/po2bbopV8A23iWlZHDsBn9+GtlH0487eKV3zXi20rrkCl2KnDSzXVtmHXIUURV/zh5xmOatQcamZBBtyc6NeoTAK4YW6XyiEwV+NuDK79gN/rwYNpD4/uGH6n7sEHjwIYLcMuCGgzRnpk+S82VoN+PPwdecdCyBgbTmzVxJsubIbP1VBJnA+T7WpuR8Gf49RHBYjJxYvzL8nAQ+/5LzZSDJslga+NDV4bHlu46lCLg55PvEI/11mNeECY7tww4ZVkf6tNy+XetIiVfMWpZ05AnD6sjDfVrM7Yes9tfX/sbEjDCl1PVKqRsn1f4oWL+ijmPXz4oGD8DqhASh8NKTDgcAPPv4g71rLzrxULzmiUfhT5/+EO+aseTddI9BkaLymfwPn3Q0Xvn4I/Hyxx3pXXvqcRsAAK96wlHeNddTc/HEY9fhQSvrOGLtjHftn045Aac8+lA8/aEbvGuPysbtCQ9eF2zzsAAz/OMLH46/fu5DRQZ97ZOOBgA87ui13rUHZwrjccf418zYvvSxh4sG3Nf/7LfwwkcfiocKBsgTjz0IgB8pBAqh9vxHHupdW1Gv4FVPOBKnv+YkcU7/6ZQTgu897kFawB25zh93I9T+8YUP966tnKri315xIv74yQ8W6Tzl0bqfUtTgNx6kaT/xSN9wOfGI1XjBow7Bf7/pt7xr9UoZz3jYBqwSjtMAgMdn88ENfgOzdn73xMO8a0889iD8+TMegv/7u4/wrhFRrnRjbR73IH8+n//IQ/Dixxwm8uDDD12Japnwwkf58+m27+IPTta8d9JR/vr7w986Bi896XC8+DGHe9eOyuZYWnsc0hp6x/OPxxue8mA882E+Dz7vEYcAAJ5zgi+HzPxL4wPodX3y0WtFx+Nzr3sCXvCoQ0QeNHx/wqGCUZ05LE89br3Y5p894yF470seJRrHb3/uwwAADxOMdSObjj/Elxcmkvi25zxUbPNzr3s8XnbSEaJh89sP1+N3qCCnDC1P+Q1/3I85aBa/e+JhOOtPnuhdIyL8USbDJGfwMRnvSXxvjKQ3Pu1Y79qD18/mclPC8ZnBJBmxJx2t23ykYLj81kMOwgsfdSje//JHe9fWr6jj2A2zYrAB4BkYn86XnXQEAOA5D/fX5iknHorXPvFovCmiIwMqsqiNFhyE1zxR68hXCDpyf4OUEty8/dkBovMB/LVS6tLIPW8E8EYAOOqoox5355137qfeFej2+iAiUfht3rOI7fNtMUKklEK71/fOPRoG9+1aQKVEVorCYNt8C4udnmgQDUK720e1TKLyuGnzHFbUK8HoSE8pryZnGNy8eQ6Hr50WPxFxx7YG1sxUx8rPt7q94NhecvsOPOKwVaLy6PT6KBOJxskgXHX3Ljz6iNXi+F1z724cf8jKaCQxhBAt/b7CRbdsw1OPWy+2GRuDGBY7Pdy+rZFHSTh6fYXr7tuTK9JR0OsrKKXEMdjd7ODWbfOicQKMT8u2+RYW2j1RYe1Z7GDbXEuMHg1Cu9tHpSSvkzu3N9DrK/G9Sil0eso7gmIY3Lm9gdXTMj/EZMIgtLo91Mp+vSIA/PqeXTh8zbS1gcSgm6X/xlnT19y7Gw87ZKUoM27aPIcjAjJhEGLr5KKbt+GJx64T+xsbgxj6fYVrI/wQkwkxxNbJYqeHK+7ahSc95CDx2XF5Zc9iaLzQ6gAAIABJREFUB1vnWniIsG4XOz3csb0hGrGDcH/SkfsaRHSZUkosu1pSI4yIzgVwiHDpH5RS387uOR8DjDCOk08+WV166VC3JiQkJCQkJCRMFDEjbHQXZAQopZ6zlO9PSEhISEhISDhQsaRG2FLgsssu20ZES52PXA9g2xK3kTA60rwsT6R5WX5Ic7I8keZl+WF/zMnRoQsTqwkjopcA+HcAGwDsAnClUup3JtIZB0R0aSh0mDA5pHlZnkjzsvyQ5mR5Is3L8sOk52RikTCl1DcBfHNS7SckJCQkJCQkTBLpxPyEhISEhISEhAkgGWEyPjXpDiSISPOyPJHmZfkhzcnyRJqX5YeJzsnEzwlLSEhISEhISHggIkXCEhISEhISEhImgGSEJSQkJCQkJCRMAMkIc0BEzyOiG4noFiJ6x6T7kwAQ0ZFEdB4RXU9E1xLRWybdpwQNIioT0RVEdPak+5KgQURriOhrRHRDxjNPmnSfHuggordlsusaIjqLiCb/5egHIIjos0S0hYiuYX9bR0Q/IqKbs//lb6otEZIRxkBEZQAfB/B8ACcAeBURnTDZXiUA6AJ4u1Lq4QCeCOAv0rwsG7wFwPWT7kSChY8A+L5S6ngAJyLNz0RBRIcDeDOAk5VSjwRQBvDKyfbqAYvPA3ie87d3APixUuo4AD/Oft9vSEaYjScAuEUpdZtSqg3gywBePOE+PeChlNqolLo8+3kOWqkcPtleJRDREQBeCOAzk+5LggYRrQLwNABnAIBSqq2U2jXZXiVAn8k5TUQVADMA7ptwfx6QUEpdCGCH8+cXA/hC9vMXAPze/uxTMsJsHA7gbvb7PUjKflmBiI4B8FgAF0+2JwkAPgzgbwH0J92RhBzHAtgK4HNZmvgzRDQ76U49kKGUuhfABwDcBWAjgN1KqR9OtlcJDAcrpTYC2uEH8KD92XgywmyQ8Ld0hscyARGtAPB1AG9VSu2ZdH8eyCCiUwBsUUpdNum+JFioADgJwCeUUo8F0MB+Tq8k2MhqjF4M4MEADgMwS0SvmWyvEpYLkhFm4x4AR7Lfj0AKGy8LEFEV2gA7Uyn1jUn3JwFPBvC7RHQHdNr+WUT0X5PtUgK0DLtHKWUixV+DNsoSJofnALhdKbVVKdUB8A0AvzXhPiUU2ExEhwJA9v+W/dl4MsJs/ArAcUT0YCKqQRdPfmfCfXrAg4gIusbleqXUByfdnwRAKfV3SqkjlFLHQPPJT5RSybufMJRSmwDcTUQPy/70bADXTbBLCToN+UQimslk2bORNkssJ3wHwB9lP/8RgG/vz8Yn9gHv5QilVJeI/hLAD6B3sHxWKXXthLuVoKMurwVwNRFdmf3t75VS50ywTwkJyxV/BeDMzJG8DcDrJ9yfBzSUUhcT0dcAXA690/sKpM8XTQREdBaAZwBYT0T3AHgngFMBfJWI/je0wfyK/dqn9NmihISEhISEhIT9j5SOTEhISEhISEiYAJIRlpCQkJCQkJAwASQjLCEhISEhISFhAkhGWEJCQkJCQkLCBJCMsISEhISEhISECSAdUZGQkHC/BBEdBP1BXgA4BEAP+pM+ANBUSqUDMxMSEiaKdERFQkLC/R5E9C8A5pVSH5h0XxISEhIMUjoyISHhAQcims/+fwYRXUBEXyWim4joVCJ6NRFdQkRXE9FDsvs2ENHXiehX2b8nT5aChISE+wOSEZaQkPBAx4kA3gLgUdBfZnioUuoJAD4Dffo8AHwEwIeUUo8H8LLsWkJCQsJeIdWEJSQkPNDxK6XURgAgolsB/DD7+9UAnpn9/BwAJ+hP/wEAVhHRSqXU3H7taUJCwv0KyQhLSEh4oKPFfu6z3/soZGQJwJOUUgv7s2MJCQn3b6R0ZEJCQsJg/BDAX5pfiOgxE+xLQkLC/QTJCEtISEgYjDcDOJmIfk1E1wF406Q7lJCQcOAjHVGRkJCQkJCQkDABpEhYQkJCQkJCQsIEkIywhISEhISEhIQJIBlhCQkJCQkJCQkTQDLCEhISEhISEhImgGSEJSQkJCQkJCRMAMkIS0hISEhISEiYAJIRlpCQkJCQkJAwASQjLCEhISEhISFhAkhGWEJCQkJCQkLCBJCMsISEhISEhISECSAZYQkJCQkJCQkJE0AywhISEhISEhISJoBkhCUkJCQkJCQkTADJCEtISEhISEhImACSEZaQkJCQkJCQMAEkIywhISEhISEhYQJIRlhCQkJCQkJCwgSQjLCEhISEhISEhAkgGWEJCQkJCQkJCRNAMsISEhISEhISEiaAZIQlJCQkJCQkJEwAyQhLSEhISEhISJgAkhGWkJCQkJCQkDABJCMsISEhISEhIWECSEZYQkJCQkJCQsIEkIywhISEhISEhIQJIBlhCQkJCQkJCQkTQDLCEhISEhISEhImgGSEJSQkJCQkJCRMAMkIS0hISEhISEiYAJIRlpCQkJCQkJAwASQjLCEhISEhISFhAkhGWELCBEBEryaiH066H8sFRPT3RPSZyPXXEdFF+7NPrO1/IaL/ilwfei73hg4iOpiILiSiOSL6t3HesdyQ+CDhgY5khCUkLBGI6ClE9HMi2k1EO4joZ0T0eABQSp2plHrupPu4XKCUeq9S6g0AQETHEJEiosqk++VC6tt+nMs3AtgGYJVS6u37ob0lR+KDhAc6lp2QS0i4P4CIVgE4G8CfAfgqgBqApwJoTbJfCQc0jgZwnVJKSReJqKKU6u7nPiUkJOwFUiQsIWFp8FAAUEqdpZTqKaUWlFI/VEr9GvDTUll05U1EdDMR7SSijxMRset/TETXZ9d+QERHS40S0ReI6O3Zz4dn7/3z7PffyCJyRERriehsItqavfNsIjoiu++VRHSp8963EdF3sp/rRPQBIrqLiDYT0elENB3oz51E9Ljs59dk/Tkh+/0NRPSt7Gee8rsw+38XEc0T0ZPY+z6Q9fd2Inp+aPCJ6A4i+hsi+jURNYjojCyd970snXcuEa3N7n0GEd0jPP8c4dVe3wJz+WYiuo2IthHRaUQkyloiOp6IfpTNy41E9PuB+z4P4I8A/G3W7nOyMfsaEf0XEe0B8DoiKhHRO4joViLaTkRfJaJ17D2vzeZkOxH9A6eTiD5PRO9m91rjQkSHEdHXszVzOxG9mV37l6yt/8zG91oiOpldP5KIvpE9u52IPpb93R274HgQ0QuI6Lrs/fcS0V9LY5WQcCAhGWEJCUuDmwD0MqPo+UbhD8ApAB4P4EQAvw/gdwCAiH4PwN8DeCmADQB+CuCswDsuAPCM7OenA7gt+x8Angbgp1kkpQTgc9DRlaMALAD4WHbfdwA8jIiOY+/9XwC+lP38r9BG5mMA/AaAwwH88xD9eZrQnwuEZ56W/b9GKbVCKfWL7PffBHAjgPUA3g/gDKLCUBXwMgC/nfX1RQC+Bz2O66Hpf3P40SBCfXPxEgAnAzgJwIsB/LF7AxHNAvgR9Lg+CMCrAPwHET3CvVcp9ToAZwJ4f9buudmlFwP4GoA12fU3A/g96DE+DMBOAB/P2jsBwCcAvDa7dhCAI4YhOjMivwvgKuj5fjaAtxLR77DbfhfAl7O+fAfZeiKiMnRU+E4Ax2TPf3mM8TgDwJ8qpVYCeCSAnwzT94SE5YxkhCUkLAGUUnsAPAWAAvBpAFuJ6DtEdHDksVOVUruUUncBOA/ayAGAPwXwPqXU9Vm66b0AHkNyNOwCAE/NlObToI2VJ2fXnp5dh1Jqu1Lq60qpplJqDsB7sutQSjUBfBtaCSIzxo4H8J3M6PkTAG9TSu3Inn0vgFcGaLoAhdH1VADvY7/n/RkSdyqlPq2U6gH4AoBDAcTG89+VUpuVUvdCG64XK6WuUEq1AHwTwGNHaHtU/Gs2PncB+DCysXRwCoA7lFKfU0p1lVKXA/g6gJeP0M4vlFLfUkr1lVIL0GvlH5RS92R0/guAl5OuYXs5gLOVUhdm1/4JQH/Idh4PYINS6l1KqbZS6jbodc3n/SKl1DnZ/HwR2pkAgCdAG31/o5RqKKUWlVLS5oRB49EBcAIRrVJK7cyuJyQc0EhGWELCEiEzml6nlDoC2nM/DFohh7CJ/dwEsCL7+WgAHyGiXUS0C8AOAAQdUXDbvBXAPLQB91ToCMR9RPQwMKOHiGaI6JNZamoPdJptTRa1AHQ0whgO/wvAtzLjbAOAGQCXsf58P/u7BGMUHgKgDOArAJ5MRMcAWA3gysh4uMjHJ+sLUIyRhM3s5wXh99ize4u72c93Qs+9i6MB/KYZx2wsXw3gkDHbMe/8Jnvf9QB60MbqYfx+pVQDwPYh2zkawGFOX/8ethHsrt+pzPg7EtqAHlSvNmg8XgbgBQDuJKILiKWpExIOVKTC/ISE/QCl1A1ZXc+fjvH43QDeo5Q6c8j7L4COHtSUUvcS0QUA/hDAWhRGz9sBPAzAbyqlNhHRYwBcAW3cAcAPAazP/v4qAG/L/r4N2oB5RBZhikIpdQsRNaHTZBcqpeaIaBP0Tr+LlFJSJEYsPF9CNKANSwB5+ixkVA7btyMBXJv9fBSA+4R77gZwgVLqt4d85zD9uRvAHyulfubeSEQbATyc/T4DnZI0sMYBtjF4N4DblVI8RT0s7gZwFA3eOBAdD6XUrwC8mIiqAP4SesPLkWP0JyFh2SBFwhISlgBZgfHbqSh2PxLamPnlGK87HcDfmdoYIlpNRK+I3H8BtJIyReTnA/graKOnl/1tJbQxtSsr3H4nf0GmLL8G4DQA66BrdZAZTZ8G8CEielDWn8Od2qBQf0zq8XzndxdbodNkx0beuS9xE3TU5oWZgv9HAPW97NvfkN78cCSAt0BHAF2cDeChWbF8Nfv3eCJ6uHDvsDgdwHtMqpqINhDRi7NrXwNwCumjU2oA3gVbB1wJ4AVEtC6LXL6VXbsEwB4i+j9ENE1EZSJ6JGVHrgzAJQA2AjiViGaJaIqInizcFxwPIqqRPlNstVKqA2APdIQvIeGARjLCEhKWBnPQheQXE1ED2vi6BjoCNRKUUt+ELob/cpY6vAZAcGcgtHGzEoURdhF0hONCds+HAUxDR7Z+CZ1SdPElAM8B8N9OBOP/ALgFwC+z/pwLHVUbtj/u7xayVON7APwsS0s9MfLuvYZSajeAPwfwGQD3QkeE7gncO2zfvg3gMmjD5n+gi8rdd80BeC50XdV90Om8f0XYABwGH4Euiv8hEc1Bz+1vZu1dC+AvoOd1I3TRPqfzi9CF93dAR0JzwzEz3l8Enea+HXrdfAY6pRwFe/Y3ANyVtfkHwn2DxuO1AO7I1tybALxmUNsJCcsdFDhyJiEhISFhDBCRAnCcUuqWSfdlEIjoDgBvYLstExIS9iNSJCwhISEhISEhYQJIRlhCQkJCQkJCwgSQ0pEJCQkJCQkJCRNAioQlJCQkJCQkJEwAEz0nLNu+/Z/Q59H0AXxKKfWR2DPr169XxxxzzH7oXUJCQkJCQkLC3uGyyy7bppQSzx6c9GGtXQBvV0pdTkQroU/h/pFS6rrQA8cccwwuvfTS0OWEhISEhISEhGUDIrozdG2i6Uil1Ebz/a/sjJjrIXyKJQFQSuGnN29Fv3/g1/A1Wl1ceseOSXdjn+DeXQu4ZcvcpLuxT3DdfXuwZW5x0t3YJ/jFrdvR6h74Z3l2e3387JZtk+7GPsH2+RauuXf3pLuxT3Db1nncvaM5+MYDAFfctRO7FzqT7sZe40DVkcumJiz7ltxjAVwsXHsjEV1KRJdu3bp1f3dtWeDsX2/Ea8+4BGf96q5Jd2Wv8bavXImXn/4L7Gq2J92VvcaTT/0JnvNB8czRAw4v+OhP8dv3A1pu3jyHV336l3j32ddPuit7jY/8+Ga8+jMX3y+clpd94uc45d+l73YfeHjWv12Ap77/vEl3Y6/R6vbwkv/4Of7kPw/87NI5V2/Ca8+4BGdecmDpyGVhhBHRCgBfB/BWpdQe97pS6lNKqZOVUidv2BD6pNv9G3fv1F7XHdsaE+7J3uPyu3YCALY3Dnwj7P6CXuY93h88YrOurr3vwI+63LBJR1m3zLUm3JO9xx3btQxrtgd9xzthf2FHxiuX3H7gG/kHqo6cuBGWfavt6wDOVEp9Y9L9Mfj2lffivBu27PP33rGtgY+ce/N+C5kqpfDx827BzZv3fcrsopu34WuXiV93GQD9jehtIyqW+VYX7zvnesy39r0QP+uSu3DxbdvHfr7dlb5DHcZtW+fx0R/fjH19REy/r/CBH9yIe3ctjPTcjr0wiM+/cQu+dcXAb3mPjO3zLfzr92/AYme0tOLeGJJf/OWduOzOfa+Qfn3PLnz2otvHfn7U1Gqn18cHfnAjNu3e9+nlc67eiB9eu2ns57fNjbbWtswt4tTv3YBubzQeGwanX3Arbtjk+f1R7A3PXnHXTnzh53eM/XwIi50e3nfO9djdHG3tm7kgGr3N71x13/1CR04aEzXCiIigv6l2vVLqg5PsC0en18dbvnwlXv/5X+3zd7/7f67Hh869Cb8aMb2w0NZCuDviwrxh0xxO+8GN+LtvXD3Sc8PgNWdcjL/+76vyvg0PTcO2+dGE8WnfvwGfvPA2nPPrjSO2Nxh/942r8QefGufb2hrbG6MZlL/z4QvxwR/dtM8jT3dsb+Bj592CV396NFq2zY8faXnd536Ft37lyrGfD+E/f3EnPnH+rfjiL4I1rSK2j7iuDHY02vinb12DV3/Gq4jYa7zpi5fhXWdfh/tGNI4NRqXpO1feh4+ddwv+4/x9/+WkPz/zcrzxi5eNbYxsG5FX3vTFy3D6BbfimvtGM5YGYbHTw6nfuwHP+/BPR3puz0LhBPZGlMcv+Y+f453fuXakZ4bBT2/ehk9eeBv+4VujyXnD96NOZafXx5vPumJJdOR7ztE68pIRdWQzc85HnZNJY9KRsCdDf5T1WUR0ZfbvBRPuEy6/c+eSvXvDSv0t2lGLbQ2z7BwxYnH+jbqG7uBVUyM9Nwp+eft4EaRRFf9F2ZjVq/t22XJlMkqdWoNF5Eb17js93ebc4r6N6jUzg9ikfoYFn4tRlOtSFievnq4CAH4xYoQyVywjtvfTmzWvrJ2pjfjkYBy0QvO94cdhYSKsozosF2c8edDs3nwLPI4bx4yujxoBv/yuXQBGjzYPAo+ojxJ12cp4ZZQIMndWO0sQ1QO0MTYKto7pfF2RzclSwOjIn4+oI7dmPLLzAKs1nugRFUqpi2ByU8sIowq8UVDKqN02ojG1NVPyo/Zte8Zk+9pwAYCV9QrmWt2RvXQTzRvVCGtlQnhfGy4tJtx3NNpYM6QS5v0fhRZu5OxZ3LeRsHHfx/u/Z6GL1TPVoZ4bV4gPg4UsDTlqKs7QMmqUcWtmHBy0Yt8bYWtn9Tu3jzheJsI6Kq80WnrM2r2l2yE6Ct/zORxXvs7tY17hcqTV7WO6Vh7qOZfvjdEwCHw9zi12sW52360zMzajGqrjRsD3JnI+COPqSNOnpezbUmDSkbBliaUsHDWMP2oKzzDZqEq2mSmyfW24AECnrxl+YcTxamYKYs+ISrJa1st1X9PCx7Q5wrzwfowyL4udQlDua1rGfd+4tPB1vK8jFaYfo6YXDC08bTQM8pR/b9+nMxazdzdHrG8raBmNVxaWiO+5AzEKr8yPub449j2vcL4f/t0Wr4wwL7yNpTIoK+XRYhqcllGic6PM/ajYax05It9PGskIE7AwpKC8a3vTC2PfvaMZVRpmoYxq6JlozahFymYhx5i+31e4y0lfKaVw5/b4LhND5ygM2e8rtDNmb42otPvKpPDCtDTbXWzZYxcjL3Z62Lg7XIvDBdGwcw/Y3n2rM4oA48I4vA62z7c8hbWr2Y6mTPn7RjFeeP9HiTzxuY/Nyz07m56RtnH3QnQ9jyuMTf9HjaAZA2nQGpD44s7tjWga18zjyLR0xuMVs8Zi66vd7XsbOLq9fjTFzB2IUWQY7/+oMswgtr52L3S81OB8q5tHN+X3Ff0fRYZZfD/CvNi8Eh67zXsWvXWyda4Vpd9cK5dGM8Jsvh+elmEd7/F0pH73uDryQDsfMBlhAjizhCb08rt24mmnnYevXHp3/rddzTae+v7z8M7vXBN8d7HARlUsSyeMP/DDG/G0086ziob/5+qNePpp5+PCm+QaFqVUXtc0Ci3t3vjCuNke7N2/6N8vwhPe+2Prb+/4+q/xpPf9JDiXYwtjJsAWl8Bwedy7z8WLP/Yz629PPvUneMy7fhR8Zlzvno/N4j42KLfPt/CUfz0Pp/3ghvxvSik86X0/wes/Fy7sHZtXjOEyAh0Ad1jC4/b1y+7B0087H79kdWrX3LsbTz/tfHw+suttfMWi+7QUztdfnXU5nnzqT6wIyCfOvxVPff95QQeMv28Ug5LLrVFkGFfWeyLz8ph3/RAn/T+bL1796V/i8e85N/iMRcsozldnPBnG2whFA3t9hd9874/xF1+63Pr7499zLp71bxcE323W16hRXJvvx5NhoeeuyHTkl39V6MjdzQ6e+v7z8M/fjulIE6gYj+9HkV/LAckIE7AwhMdijJPbts7nfzPnE/3XL8OHxZn3jSpUxxbGncF1VGb3Gfck78q84XOv3yw+MwwTSrAF2GjMsjiEYrl1q1YePCphCvpDp3XvC8Uyyhjwe0PzYubidufMm0Y7vg7Gj+otHS1X3aOLeC9nxbxm7mNF92ML44yWdq8/UjSQGy6hqNa3r7oPgI5WGJgalNhxLYaWhRHXfB4BH9n5ylL+Eb7/wbWat3lK7eqMR8xZfi727IOo8biGS2h9dXt9cXffVfdoWkLHtVi0jMv3I0WPBtNyY3Yu3E+Eox+2zrWC69LQstDpjbSxZly+H2ZeLrxJy11bR2peOfPi5aMjJ41khAkYZoEZ5bhqqihg3jXEGS3728pfyCNhkVB2tkuIF47Wsvor1wjIn9knofzhn1NKDaxv42fk8HF6yIYVAMI7emzDZbzo0WjpyMGRsKvuju8+um6jvF1/f0cqhqHlymzcj143k/9t10Jh8IdqyfZWGMfeLcGsr05PBcfAHATJ32uK4EO8opTKd+KNWj+ZR8BHdr7ivGLtCGZ8f9iaaQDANfcOXl9jR43HjrTK6+sWpuQ5jAy7cgi+H1uGjRk9Cs3LlRnfH7thNv8bT+dt2iOf+2bGpsfKPYbBuHy/MATf375Nz4vZ5QzYay2E/Z0tmjSSESZgGMY3C4UbLsMUac7lwnjcBbbvU3gGEi0h42K+NaYw7o4njHlUIxg9YrVSnBZT0B86oX9+bGG8L9KR8UhYCKGdaXzb/WhKcu/TEqGoixn3FlMO9k4xmW/m91IYAyN694zvY+kiwO6/+TmUCmq2ezB6dBRaumzNj6pYBqUj+fs4LebYldAuTr6+xjfyR5mT0XiFGywzdb3bMXSG3/zYzteYkbDOYL1ijleYrRUHF8yxMR+G70eal33A96F5kXTkMDuW58atnxyzbnrSSEaYgIV2n/0sT2hDiB7xn0OCxrxvlFA+f99ipz9SuNm00+2rgbtfeP+Nx9IMCKex05E8LTGCMF7kcxJoj5/bJc1LI3DSPje6RxNg4xmUfLxCtEi1Q3b0ZfC8jJ+OHI+W0DowfeKRSv6ziSR5z3WKFMso5ziNW6vHx4uvN45SJjH3COsrVBS9b+ZkPOcr9FyIVwzfz4fmZGxaxosaLwzDK6yv3GDpZUZx6AsbXLYtBOZbglXMPpKRP7wM4/zP11qQlv3M98PMSyOjYVcgUBHUkUNukHFh5qLVHU1HThpDGWFENENE/0REn85+P46ITlnark0O3GMJeTrSAuO71iTF0u318zOy9sa7HzdsLAlkbpjxdKr5eT7g5Yy7S2rREmCjpIrYnAyhWPhcmNRXkJbuYKNbwrip1WEMWK4EzRxZ0aOAMLYMvP0QqRiOFsMrfE44LbJ3vDimMbUv0sSh9syYWnyf0RWqP9s3czI8Hf2+yhVYSLFy+SQZx/PBOSmeGz8duW/XV4PJH9N/pVQ+hyG+b40pw8bfHcllWGhefOeey+UwLWPOy5gybJBeAYo1JukVfp2j1x9vwxcwPr9MGsNGwj4HoAXgSdnv9wB495L0aBmg2e7lB8aFPB3jfdkRl4JBJGYxC6NEowljpRTa3T5W1itZn0ZTLMZDlxYm9yKl6FHI8zIMW6LxdkeurFfGSuGVKMxgvB8WLRnjhwwXM55Eo53jZPqxsl4Zq84lTosfqeA0BYVxt5/P90jzwtbXaLQwXhlASyhqHFMshpZR+MWiZUTFUvB93HiRUvftXl+sQeN8P+qcAMDKqcqI0eaivZBibQjri/8c5nsuw4Y3XMblezPv5RIF11dDkGELnV6uzGMyzMz3KFGXdrePmVoZRKOmu7kMC81Lsb5MNGf3EJGwVrdf0DImr4x6zM4gvjdrTIoaAyEdWcz3yDqyNx4tk8awRthDlFLvB9ABAKXUApbhSff7CgvtXv7pkkGRMO5Fck9fYhbDsGtnamj3+kN/kNYIsFVZgeNIHkunh7XZ6eeSwLCFsR+pCDG9UdRrZ2pj7Y5cNV0dLS3RLsZuGI/Y9L/XV3mtUiiFt9jtoVomrKhXxopUrJqujrWjMEoLUyzGe+TzE6SFzfeo6SKzvkalJeeVETxizjfBNdbt57SMWqtX0DJaiqXge9lLN2Ma9u7jfD9OCm/VlF5fw6ZYjNG7braGTk+JETpu5O8SZFgoRdzaW1rG5vtq2CG2+F73f9cw66vTz+d7VL6fqpZRr5RG3lFYKWk5ExoDQ0unp/I1P0ivADYfjpqOHIfvF4bge+PgWxHwAfNS6JXqSDqy01NQqtCRoxj6k8awRlibiKaRfY6NiB4CHRm7X2Kh08OaTPgPioTZdQXFvdICM0p7jaAkv3TxXcHvSXJlD4QVy6/u2IHP/+z2/PdeX0fQzGd4xEgYE2BWXUHb7Ezri7VkRqiumalaz/X6Cqf94Abv8FcgOSseAAAgAElEQVT3uVXT1agx+fXL7sFPbiiOxzBjtWamGo64tHj/TTomPieANgzrlTJmamVrDnc02vh/Z18XFDItFqkI9UkphQ/96CbcsqX4zp4ZrygtQp1ac8D6Mn1akyuW4p6r79mN0y+4VXzGPFcY+aHdih2867vXOcX/3YJXBtDCx3YQLSb6u0ZQLP/z64045+rwR9wtWgJzd+OmOXz0xzd7J8AXfO/TYtXBjEAL53tX2Z9+wa24+h756BTz3OrpKvqq+NyXi3Ov24xvXlEcj1GsL8P3gvPFeIXLsEEbeTgtbqrw3WdfF/y2LXe+YgrysxfdjkvZh5ubnYKWYSJhTYlXgrT08s9z8fvv2t7E+79/Q7AOsdXtoV4pYapaDvap0+vjPf9znXWUSbPdw3S1jHq1HI6EDaIlyvc+LRfdvA1nXRI+DmIYvt+0exHv+971lh5Y4LwyIFBh16uxbJHIK/baHV5HFnoFCEfCXB25HDCsEfZOAN8HcCQRnQngxwD+dsl6NWG0Ov18W60UCVNK5QssdOKwVFNhlPlqZ9G3u338/Tevxqs/c3GwP/q5eIrlFaf/Av/y3etypWcW5uqIp8OZPkSL7N0XCoLfe/ldO/Hx827FPwcOrM0Nyql4Cu/t/30V/vjzl3p9Wx2JOvFIWHFqOpuTYE1YD1PVEuoVWzi+67vX4oyLbg9+dLnV7aGWCeNQn7bOtfCRH9+M3//kL9lzw9Di12rw+QkpyUW2djntL/rYRTj1ezeEDcpOHyunTDpSvuerl96Dz/7sdnySGXOtbh+z9QoqJRoYCev2Ve7Z8nGOGS6rBaH6F1+6HH9+5uXeM8WzPcYr8hr7yy9djg/+6Kb8PDzdRi/KK82Wv77cn6V5aTG+5/dumVvEqd+7Aa///CUyHbnhEp+XN/znpXjbV67KDUp37CQ+40a+xPeDasJcvv/SxXfhMxfdjjMukhXcMHzf7yu86+zr8PLTf8H6VrQX3vjB52W49aVp0WnFWrlk0fL6z1+C/zj/VtwROLC21e1rvq+E+f7yO3fi0z+9HX/ztV9bz9WrZUxVS8ExaI4rw9ja5Y7Ha864GH/3javFZ0wbqwbw/fu/fwM+ecFt1tllrW5fbM9AqSKSZ9VqdQbpSIfvh9WR3fF05HLAUEaYUupHAF4K4HUAzgJwslLq/KXr1mTR7sU96Va3n2855wusbRlh/nOLzBvk9197n+wJF+0VaQndp3iI1pyL02aCj7fPIRku/FkgnlpdNV217v115tWbYyF8Wgan8LgHato2HyJelQl/KTVjfemgUzBvjA5DS71SRq1Sss7YuXHzvEWrR0unj3qlhHqlFJwTc64P30bfzuo3ZiO1ZLbCz2hhfQulI1udQqhK9Ulb9sgB7FZXe+m1cmlgKP+WLcW5TO1uH7VyKUvNDFYshob2AMWSry9DSzb/mwPnJBmYwl7DK6G5K5Guprj0juJQUs730hjYhrHM9w1BuC8yL73TU/n6vuwO+UDUog2b7welVu/Ios8+3w9wvrL7TfTRtCWlghY7fVC2djndt2ZndYW+XThMBJwfIWP4Oy/FiBhvlgzLaB1mJ7HF9xYt2vjaEvjkUc73EWPKlEPcwM7za3eNvAgbb9K8DCfDirXbFhydmAwblI6sVbQsv2lTEc1vD0j5t7rseBX2Xn5MjawjHb4fWkeadTJcajV0dtwkEDXCiOgk8w/A0QA2ArgPwFHZ3+6XaHf7hcEjKDLDCFPVkucRHzSrw6ixokPzbrPAbt4sHzZYPOd4tgEhNl3V5+LctHnOen+slsww/bQTWm91+wUtkUjFqqmqZRzcvHnOu9d6jnm2PDLCsY2d62NOW247TBaal1q5ZBXxGprXr6hFQ/n1agm1si2MzXk1G3fLir/V1WnMqUh6gT/LFUutYiJvshCfb3UxVS1ZNAxLi5te4ErovsA3NFvdQrGEDMotc5qWbewMqbaJCgxIseS0sG8hrpmpgmjA+nJouYmtL6k9f83LtJio301bHMUScXQaFt8HeEWMhNlr1/DLTRnfr8ue9Z5zo4ECvdxhyfneFMFHeMUYLlyGmecMLVJdWKvbw1RF10NxXrlnp15XofPt7Ei2PCf8+65bszXG5zO2vozscw/sXL+iFt6Q0+1jqlrKnC//3ZuCfK+Nt6lKeM2bZ3lk1PC9u34sWtpdgVfifK+UyiJatl65e0cxnmHnS46cc5iU4M3M+WpZOlLSKwFe6fSxfkVMR8qBCt62SAcLCsRocXXkcsCgSNi/Zf8+DuBiAJ8C8Ons548ubdcmB5NiCe1+MbVH67I6BZ4GWJsLsHAKb2Xu3evf5wJpjvxvTohW6hPflt5wwsCmPUmx8CJem1l6A2jp5e+2DJfs3rAAk8PNHPxZI3SGoqXVxUxdKwg3lL92pqYPzRTqPFodrVhqFVtgmHs3BQ0XUxsS9og5LdyzrZUzYRw5W2udqelxvoW4diZshC12elhRt71Ifm9sXnSqZLBi4R5soVjK4hi0u320e/2CFmYcT1XKmK1VopHWlY5HzAX35t2+YhkmBQ8AmzOD0ryv29PR7TwlG1Es62ZqtnfP+F6kpevQ0rNTfkHDxaPFH18ePTK0FIbL4EjYOlZrlfOKoUWK6nW44eJHaGIOS4mAFfXwTk/+rOmfvUM0YLi0urkh69EyU4tGwqYqZcv54hH2uPMV53vzrIkiaVp6mu8HRMLWObV8hu/XBGjp9JS1diW+3xiRYYMirRtzvrcNytl6GSUKpbtDOrIo6B+kV0w7gM330tj5Kfi4jgzJz0kgaoQppZ6plHomgDsBnKSUOlkp9TgAjwVwy/7o4CTQzpRrvSJ7LMaLXDtbg1LIt0K3un2smQ7v5nKLBw2z8MUoeSzDFB1awjhP4bnRo7AwXjtre5rtXnxnmhmXFY4R1hhCGPM+ScwSE8bRqF67h9laxZq3NhPGgLxzKI+EOd79MIqlntWShaKTGwMGZa1SjkbCGu1urgzddKRU4M37NJWlFQtlz4VxgJZOseYHCWO+Xnk6UpqTfHfbrK1YTARt2tkMwekA/KjxIMXiPheqVzEGXMPllQiPNRktbjoy35Eq0RIoQzDG7Lb5dtT5iqWLuFFt5FJhuIQdnWa7CyJ7t2LBK4YWOZpfdwwXoBjHQdGjWKTVoqXlGJRTWj6FyhDWztpygfN9aGetxPdcPoSdL8b3AWPKPGul4rM1X49EwpoBvq+VS5itlYfTKz1fr0ifO9IRNG1MVUoUlGGbJCMs53vZaeM6kvep3ZU3EBS0yHw/WEe6esUfX/5FldBhxJPAsIX5xyul8uo+pdQ1AB6zNF2aPGzvXoiEsegRwNNFfczUK6iVS+JJ824kTEoXSZ/W4UWtpn8u7INiZWEcK9BdO1PLhWM/q6tZPV3L7pEURC+vb2j3Ck/HtL2z2RYFZiEwRqSlZ49diJaZWmbcOKF8aReUgfGI68y715sv9L2xFEtdSM0MpMXypAORsFbPX1/MIw59yWCx0ysiFcL62hH4hEuejhyCFs8Iq5RQD0TCGh6vFJGKeqWEmYBiKTzisGKR5sUtZpedqB4zUP2ICxCqCQtEjbs9xivDR/Xsw4X9IuVh+H5nU3K+3Foy2fmarVWsyGcRTQjzvRUJExyWcFSvMFy4vBhMS1E/2WcOr0VLu5s7WRLfhxyWRRYBlxyW0GfOuEEZ+k7jzmw+9XdIi3RvrKC/39fF7B6vZDVoIYfFy7AIDov0uSNzrMMgvt8Z4ftQNDCPtAp8P12roFYJ6Uib7/ONIm0+L4IR1nH0ikCLJIuXA4Y1wq4nos8Q0TOI6OnZyfnXL2XHJgm72DgSPXJSLOa5sHcv14RxZuGCqHjO9Wz9d0sH+o2SlljL0hJGsMS8+0UWOeHPGKXGz+eyaMkY1k2ZDU2LUSyBqN5MvZJ5mm46MkaLXxPGC0ulOdH36DFwFdJAWlhNWGynpyvA+LxIdJgvMrjFxvb6Cn9LUD8Xjs5JB3manWKhSBg38gFYUZdapYTpasgIs9dubriweyVaTB9c402iAxjRYbF4hUWNWSRMOux30Vm7khEm871DywBe8aJHEb4vHBYpahx3WKRNLNz5ksA3sQCjzUuNPSfxfTMzKHk5QZG617Wn0thJfC+dzxeixY0Ghmlh0d+yKegXosYdx3Axmwx6ehf2TK0SNVzcetnQF0RyOrKxlDYnGPT6Kq9rs4ywATIsyvflkncckEeLy/dDOiwF38d15IFohL0ewLUA3gLgrQCuy/52v4OpDSmKjcPRI9/K76FeDXv3LddjEbx7kVkcT1oK54sCbIgC3WZWCDpTYx5xHnGJh41N2gsIMYtsUBpDNdSnuJKM17fNOorF/G/OnZGEmKlPChkuQWHcLXY7hQwX6TMdeW1IIC1htnd73n2np1NIU9VoKH8qqlgiBmU1bEwBxby0usXOuXaviOrJxeyuR1wYxyYSJn08OWSADO+wRHiFz0l+nIu+zxjVsRSLewiq2QxBgS9hhPjeoqURiYRF6iclZe87bXI0cLZeyc6ssqNHa2Kp1W4WCSuXnXSkvrfZ7gVqdnp51HgYWqzUfVlHWgF5Phttvxa0SN2HD2PNU6tMXgwyjE2f8k0sQxlhtkE5FZAXDddwESJhMb6PRVplhyVb88LxPAb8Q+Pcwe71FWrlclCGuXzPd2zWqyXMBJwv35jyZViM71cNqSMPmJowA6XUolLqQ0qpl2T/PqSUiu8VP0BhJr0aKaCcdxUL2xYdDRsHI2E9HLZ6CoAsjF1jSk7h6ecOmq2JRa2A7BHPt7pYUbfrqFo9I4zjKZapahnVbEs6Z3xDi5SaMGPkGm8uLWuznXNSbQgge8TzrUyxMCFnnosZlCbFUmV1VKbdw1ZPYWezLRb0t7u6mH1QJOwgZ4NDu9tHtUKYqpbFHaImCucZLj3mRQonqJv5naqWUa1QgBZ/fZn0cyyqt9jpYbHT93bOtbt9zStVuS4uL2Z3o3pdc0BuJRoJkxyWNTNVTFVLQSMfQH7chsgr2Qne62ZrXv2kLpwOGZQ2LW1Gy1Q1EtXr6i8yTGWGRBHVK3hFosXl31gk7CBOyxB832h1MWsMF+dYh4LvA5Ews74Y/e1en9EiyzCzvoK0NDv++spTeKUoLSscvjc05XwvGfodVj/pGPmHrZ4KHjxr1u6gSJi7u7yV8UowdR9I4bV7Ws7MVOPRo+mqru1ysxKHrZ6y6qE4HQCifG/rFXt9GRkWmhOLlk4xn/VYtii0IYfpFUmGuZHsgTryQDsnjIhuJ6Lb3H9L3blJwExmrICyGSg6tOtcwqk4KdR6yOoplEgL4xs27cFzP3RBfhSAV+eS/b57oYPnffhCXHn3rlwYH752Wkjhhetjmu0eZmraI85TcWwXHhD2iDXzlq0xmG91ccTaGQB60X/j8nvw2jMutnbH1KvMs80U91V378LzPnwhdjc72L3QwZqZWrZzzvZsVwwZCeNpxcG0+OcFmTE8Yu0M+kpvNX/Xd6/Dqd+7wRsDU0tmDLWzLrkLb/iCPmh290IHh6+dtt5pCm1DUQEjwFZPV1EiWPOijfwKlPJTZlY0R1AsR6ydyWv1XvmpX+C7V91nja2JVPD+/MM3r8aHfnRT/v23w9ZktLAi8LwwX4xSZCk8x3AxB92Ok7qfrVWwdqaGnc0ONu9ZxG9/8IL87LIixZJFtLI+dXt9vOwTP8e5123OaTl8zbSnWEx9W2jjh/m8lXnGpIBr5XI0Am7Wl+5j4d0bXtnZ7OD/s/feYXYe1f34Z27fvdu06pIlW3KXi7AxNgYDxgUMNpgSQg81BBJaQqghGAjkSxJKIAWSACEEfoApCaHFCsX0YhsbsI07rrJkdW29dX5/zJx5z8w7896ile7Kns/z7LO7975lzsycOXXO/OjWnXjqP/7ICLXUJgPdpnt2z+KCD34fd++axb65BsqFHCa5kGx15vuZWlPxPQsrurziXcNozmsFV0pp3pvQUsfHvn87/uzy6+w+KKbn/Ldv3I6n//OP0Wy1LV6xvEfcExbw6hlamOJi02KPS7stLcXQNVgUr6h58prPXYtPsiK0idfYnicf/vateOtXfgMppZ+WFqsrmGGwpHilkRhfWd4j1yCcqanzHVeNV7B3to7ZehMXf+SH+Nkdu+z7PHz/ik9fjc/+/C5Lrsw1WuYUFgBsQ05nGWl59Yo6tBqYX4A/dO/KyAs/yGSkk2ucJSPXTAwdlon5ZwB4hP55DFR5is8crEYNEsYizkig5Nu7ATtcVC7kMVwMWfduvor6f6bexGiliPGhInbP1vH+K27BLdun8T1doTg1MXUbf/G73bhp2xTe/bUbzARbNVYxzJyEp5THKmSxuLkh9Jt2zXjzXLQnjFu2zVYbtWYbR+jFZ89sHX92+a/ww1t3miRXyj1yF+P3b7kZN22bwg9u3YF9cw2MDRVRLee9rnzel+64pHLCyCLO2LXqSzamMSZads/W8ckf/846+odywspFO8/lrV/5Db792+3YNV3DvrkG1ox7BIsOd/tooTa6Xj3aVTmsQ7nuIsY9YTy3KxEsQ9gzU8edu2bxszt24zWfu1b3UaK8lQuJMi6lxGd/fjc+/J1b2QJWsWnhm1gycsJS2+6bnRLzbUWCC8mRcgETwyXsmanjy7+8F7c+MI1/10eRcIFUZvWf7to9i2vu2oOXf/pqixbXa0xhYn9OmFZcWP02o8AWSaH0eI2b+kQGx/s7XWsaQb1nto7Xff5a/PrefaaGUa3R0knptgfti9fci9semMZ//PRO7JttYHyoiGq5EMyf9O0Qna23tMHCNrE4aQi+ncQpvm+1mZKf0PK+b92Er/zyPitkW9Y7gnkbX/+F63Dt3Xtx07Yp7JtrYNVYxfQNXZflCWvoQ9OrpbxlNBtahvyhVb42+o0vpXTsnqnja7/aind//UbrXuJ77j360Ldvwed+cTf2zTXQakvD9ylaivmAEanauDQVum/p+eU/25bGt+J4tKZrTVTL2mCZaeCau/bghq378a6v3Wg936VlptbElhu34y/+6/qEV2gNqzdNpKRsNuT4DRYAntI0STpKlox0izTP1JiMnKnjA1tuwa0PTJsq/iEZeZWWke/iMnI8kZGLAd2GI3exn/uklH8P4LyD3LaBwLhoTQKlX8sXwnO0Qottu/cm6KpFlYQoZ5aRcmLdU2giUVzUs0bMCfHqf9qiv0d7j0bLBYwNFVMWcVKl2c/4VR2ObOnQGHdTZ+3IccMLKcWFufPv0FWoKZHb9QpUS4q2G7bux/45JlhYzg6NCfVlmpZmIlgci7hTaLXshCVmHMFy7d17rOsBbaGy0KprEV51527lRp/wLcaJIuoerUOuclew8HC3osXug3mmTLnWvRDKAtw318BV+my+Iccb6SbY891hVEWc02JyQwpdbGKpOryi50HXuyOZclwt5zFZLWLPbN0UpMznVFichFspb3vCaP4BsCzimXpTVYpnxlco2XiGKS5EC1fesowv7gnj4zJZLWGomMeembrJdfndTptX+Pt4X2zfP499mldGyoWeNhmoPKqCPb9MGkJ2LmiK7+s2r1DhVgDYundO39cyY0L/83ddc9ce7JtrYMlwCcOltPHles4J1MZhMliYFzEnkj5I8wrzmHryJ4mWK29+AC7MGsaOO+KHpP/sDsVfxCupxHzNm+7B6qGcMPKcD5fy3kOtaS30rWEj5QKWVEvYO1s3VeLHHW+RSwvNPyBZwxNamrbXuJDzHg02W3NkJE/ZKeZNSoWL+YYat2FPrcOElkRGUvvo+a6MpOLUe2bq2DfXwEi5gHEmIxcDug1Hns5+zhBCvBLA6EFu20BgT7BAAqXejcMtYqq5kmXdmxwEsxgrJpyrtzBcymNiuIi9s3VTSPJ2E2JJrLZyIWeOfqDvp+bVpBwfLqpaMnoCNoyAoARKn2BRnjCuFPFdM8HQarNlJ+a32ibvYqV2G9NRJkDyN69HRX0CAPfpxfr2HdPYM9vAxFAR1VLBHN/TaNmeMNeSpO3dwyVVIiRo3TvjQuNWYWFFIFm0yVNxFTtU+C59PIyx7pmA4MKbjsQh7xG9u96S2uNCtNhtokWbyp24FjEp8e4iVmOLcTmfM+M/W29huJjHkmoJbanOtQMAIRL6gWSrOv1/O6tSfc1div61ejGeq7fMgb7dbGJJlxBQfTdULATqUanrhko6z8XQoqz7iWG1GNO8ShQX6gOHFjYXH9hfQyEnsHy0bMK6jSanJRxiGS4XLEWCJzeHjK9aM6lHBSi+lFIVjqyW8lgyrDzgJJNvZwaL5TXWz6ZTJO7aNYs9s3VMDBetNYfGJSnT4TFYaurd1vxyikKHStNwvm+0kjMCSVBzg+W2HckaZoUj9btIQbztgWnsnWtoWgrJGubkhLl8P8sMFp5gr0J/eWaw2HPM9YQ1Wm3rOh/f75troKmVJ1PzTD+HlE0A5gBy4nt6ZqNle8DdHKxZ12BhaxjnezcyQdeRN7/B1rBhPb/2zDbMWOyYohAeD0cmoVXOK3RcUEJLy5QJSbx6foNlWJ+Tyd9F0YNwaNWVK7aMVI6KOrbrWmGujEzxvZGRTewlr3Hg3YNCocvrPsD+bgL4HYDfX/jmDB5WODJQ0Zxv7wYUEzTbSc2VrMT8SjGPct5mQnLxLxkuYeu+eVNIkgrsWRYLs+6peObO6Tq27Z/H0pGylSiZtu59FksLK0crXuteMUs4cXqyyracN9vm+UqhLOHGrcm5adRWnkfF20jfb9s3j90zdSwdKeH+fXPmmYkr3+8JI+FXLeetcGSn3BAevpL6eiml6cNV2g1v0zKH41eNJuFIFmbawc6bu0Hfs3KsgjwrhkjFgA0tGYKFF7fk27t9tNBzaKcn9QnNOyo98Ft9nt1svYWpWtNS3ng4gxd4JFpICZtvJAoIKZTdlXNh4UjaSaw3GQiRnDuYhFbtEIuadyRY6mhqzYXPLyAdWuWFQG+8f7/xQBlaukxDqDK+V97gRJCFja9k9y2g5lit2VbrRVHxyu3MU0eFPnkJFLoPSMbl/n3zWDJcxNHLR2wFhBTYYriiuTK+XE9Ycl+lmAuEVil0n6xhCa8oQc15hfrdlHVgtDRbbZPTc9sD06g321g6UrLq55EXyITuHb7nBot1UkbDMVgCnjB3flFf+Ph+27554yErF3KQEiZ6wIsgp3ilGVjDGi2jJAKJJ2ykXEAxL6w1bGyoaK6dqydV7nmfmFM/WrZcmRguYa7Rwp3aUDFjwgyWUiGH2Vn1fh8tq8cTvi/kVPuVcR82vsg7Sf1qKg/kc9r4CqWG2Gku1Ie0ht27Z87QYGQkW4s4L9D3u2bquH/fHJaNlIJr1aDQbU7Yy6h6vpTyQinlKwD4t44c5rCTDv0TjGLtfIKZSVDITsz37RAixUQtxtOpLew1vbsqnxNWm/g22xu37seyaslYAfww3mSTQXriTdeS7d30Lk7LUGBHDk9mJ1q4B21iuIjf3p+cz0XHTiRb1W0vEB3hcufOGUzXmlg2UrasM16XhvqSg9zLw07F/E55Lm4yu5RAs514h1ZrwWLRwnLu1CaDxNrjZ8Vdr63IpSMlK3E9RUtKsHBa7JywclF5jwCfdW8vqm5CPylC7rjwMCbvO4uW+xQtq7VgcZV1Pu8sWupNpcyX3bP9WiY3RMp0KLfWVAdF06LqbnFfMlzC3rmGCckn8ytRinipCZeWpXp+ubRQHadOyex0Hw/lZiVOUz0qgHgl6bsl1aJRjAE2v9xkdj1OROvO6Rq27Ztn80srIHp+CSEsHiJQMr3aHakUVSmlZeyFjC/Ke7X5njxvRQwV813yfdtavwyvVMup/FRav3gf8DEBkCpNw0N4QIbx5dQ8ozIwK8fKAFy+b9hKPssFpfWL00KeQb4z0BdeTtPi7vTsQAvxr6fWoY/vZ+oqwb4W4Ptph1eWDBct/nXDkT5HxTQZLEW/1zgrwmIZ6c1kXEhG3rFzJjnyj82vQk6g4MhtV0YqvvevVYNCt0rYl7r87LAHn2ChiuZ8ezegJ1gjUUCqpYJVVJJA2jxfwMjrUimqPBd6fyEnLMFCjMt3AE3XmiYXZv98Uy3GRSXU6i2bWSoBT9hMXW/vZoscX6Cq5bx3O68pdMgsW+OJ0UKSGKWQE2aRcsMS9VYbDX1vPifM2ZNLq2QR216gUE4YMVtqq7pWYMuFHAo5kcoFMEmtzrjQuC8bKasdiq02Crqvp+ebRsnl4aJ6MxEshZwwC8Qy8lCyI1UsWpxxoZ07I65132yhnM+ZRO1ZZ4eP5QljizHNO1JE6622mTfTtaYjWPLW/CJa9s+rfLsJdoSO7TVO5p07LkSHooErlOooFiBdPJEWXSGETUujjUpBWfd0ZFg+J5jiYocj+TmNnFeWaY+LoYX1Qbg0jWt8tSwFNrTja971hDXb1rxbMlwy78+zeUN8X9CH0vOzZomWqVoz8YAzjwt5Z32bDOYbyiNRLfsVyiyvXuIJI/5N1r5KIY/JasmaX1PcYLE84C1DJ6d5qfZU8Byikj4sW73fb7CYTSypEJ7fYLE8YSwfat5RXDjfT83bXmPO99R+zvcU0qw126YMDG384G3w0+JLQyhY16VocU7vSCIsCd8TLTP1prXOu3xvy5WytSGKcgeNjAwYLNb8YnKllFdGmVdGNvz1J7knjPOKZbDod/E+mJpvGpr3zzextFrK3Gk7CGQqYUKIE4QQzwQwLoR4Bvt5MYDKQjRACHGREOJmIcRtQoi3LMQzDwRuThhnFCryOF1rYrRctDwgXCDRoda1Zgv75xumdAFVmc/nhF5UW+bwVdLyCcesGLG0/BKbYNy6P3bFiLlnUluR6l2sTXnbE0ZbqKWUmJ5vYrRie/V4H4xWimai8yKX/Aw56rd5pojSIlbMCxy5dDihxfEG1hpto2zatJRsTxhZxAVbcak1W5itN00bFS127b1rwOgAACAASURBVKNSXgnz0YraQdZuS+zXRQjdZHZDi37vUDGh5RjdPrUYp+9TnrCGdW1Ci6NQMouY3jVTa6LRamNaP8PQwoVrMWeSjad1KJEETMoTxsISpULO1OzhfT0137CEL+UISSkxNa8Ulw3LqgCgrEimOLoWMe9Pd36ZzQs69EiKAqeF6Kc2U//Y4SIlkCarSTjm2BUjZqOA66kgoZzmlZLV/67XOMT3Y5VCJt/TXOa84hosNWawcIFPtExZ3iMK/XAPZcOiZamZXzavALBCL029k3GqRvOr6ChhNt9PaWODaGmwfCi+GWWeeWJI0V81VsFIuWD4wc2LqzUSxcWmpZzmFY/BMqeLwk5xvndOyijlc6be1FStaehXz0nmvKu4kCefYPG9Z73gHnC6tpgXWFotQYi0weLy/dS82k05VWua51qec4eW6VpT1+2jdAPmCeO06PmzpGrLFUMLL+fC5tf+ebVLld43WS15jXSKFnl5xZEr3ClQLuYxVilmyshcTuiaZy0272xaFK/w+ZU4Koi26fmmvRZrrzHRshjQyRN2PIBLAEwAeAr7OR3AHx7oy4UQeQD/BOBJADYBeK4QYtOBPvdAYOWGsLDET27bic3v3oIf3boTU/NNjHDFpdGymJN2aOyZaeDUd27BZf9zg7qOTRSy7mmyVJiwB4BTjxj3avmcyabmm9i0ZszcQ/Fu9a7E/VvMC1WlWbfxb6+4GZvftQU7pmtotiVGynwxblnMOVJWguXau/dg87u3YMsN20ybLIuYLeLKE6YWsaOWVjE2VAQPrVphCeY9OvWIcUMLCXyzGFshloTJnvnRn+CRf/0dswiOODu+eJ+PVAqYmm/io9+/Hae+cwt2z9St/rdydth40oJ8ylrVvinXe8TmAdGy+YgJQ8uS4ZKVO+HmhtQaylI+6bIr8PovXGeekbLu9WJM82tqvoEXffIXOOmyK8xzOC08LEG5IQTqa0uh1N6jtg7JTs8rL9bG5aSElZKNEVxxydubE+7cOYPN79qCz191j/KEVQps3BLFpVzMm7pvU/NNnHTZFXiZrq9W0x4XAFaeS415wlxauHVfytuCZVrXGVo+qsJMS6tlq//d0jR03xeuuhub370Fd+yYNrRY1j3n+0oBU7Umtu2bx+Z3b8HHf3iH6ZNKwc4Ftfleza/hUh4bllXtcDcZXzo/lbzGNq/45xe1iz5/3Reuw8mXXWF4ZVRXzKc28jk9Wi5gutbA1399Pza/ewtu2LrP4u+yxffpNWzj8qqllFIYkyt9fr4nWpIQHnkn6TkAcOZffxu/97GfMFqKqTAmva+YV1GFt//39Tj5sivQaNlrFRksFJKt6Bpg5EEhXra9xv7QKl07WS3557zD9zO1Jk555xa8f8vNmNKKixpvNw0hh9GymidT802c/4Hv46K//4F5DpDkhNU5r3jkCqCUE4vvi7biMlopYKM2vpaF+D5LRtaatlxpJHKFr2G7Z+phGVnIOXLFpuWUteNOuJutFyQja46MrJYtGbkYkKmESSm/KqV8CYBLpJQvYT+vlVL+ZAHefyaA26SUd0gp6wA+D+DSBXhu37DrBSUVzT9/1T0A1FbqqfmmWsAKfot4RFv3192jtgT/58/uAkBhCVuZ4iE8SvoEVCIkeW2sxbjABUsDy0fK5p51k8Nsx13bLMZCCO02VpPuo1feDiDZJTeS4QkjxeVavb350z/VtDTT9YK4dUmFGyerJW0R24KFK2/03enrlyS0LBlKHS5cyifWPS1819+3H/vnm2arMtHSZOU26L6RsrLuqUjpFTdsY/3vePW09zGXE6jqBeP4VaNGKXWT2akPDC1HJkqYyuVzko0LOWsxoF1Y3/j1/ZiaZxYx32RgPGGJdf+zO3ZDSuDmbVMsQddOTqVDvan2DgA8/Mgleg75rft6s60X0gKOXq4syZWjFVbbzA13J4Llm9ffDwD47k0PYGq+YRZcI5AYj43q7+7ZrXac/uCWHVrRaJl32aFVRcs6xiunkJDU40JhTJ6YrwRL0Yzx+skhq06bnROWhO7/4bu3AQCu37pfGV9OOJIL19Gy8oBfd4/iqw9sucX0lWuw8HlHvNKWEmOVIlNckjQEqv5PoajjVyWCZf3kMCpFVWKm0Wqb+UXPn2+00G5LfOPXalxu1XXIRpxwEe8D4vsf3boTAPC1X93v1KHz0FLImV10Ry2tKl6phfmeUhRoLgIsdJ/akEPeozbu2T2LqXnF++Q1Jr63cg71PKD1h9bwH92206aF5YLSugbAbPogXrb4vmCHZKfnVWHUU9cpJYeS16n/bcUlmXff/u12AMAXr77XGD30fCsKkE8Mlv1zDdy3dw537prFrumaWqvyaq1K80rebJgAkjV2utawUmhcg2WkXDD3rVsybG0ickP3NO+of6++azem5htprzFT+ojOX3UlI5PQMZeRa5cMJfltzVA4soFlARnpS88ZBDqFI9+k/3yeEOIj7s8CvH8tgHvY//fqz9x2vEIIcbUQ4uodO3YswGvD2LR6DO952slYOzFkKVmUAHzf3lkVjqw4+RRGkOWNkPylU1sqpeW37DyMR25cqulNjm2YrpNgyZvr6s0kj4rqngDAY49dbnm0eG4IeVR4MuIvtWJlMUvDThoe1db9XbvUzppdM3XNdNK4sU0fMOvyCSetBAAsHy2rZzhhibx2N9eaLfMdCSMAWDFWSbvkLUW0ZZVQ+I1OHB9jIRbqX6JNhSMbKOo2X3/fPu+iSuNJzznnmGW6fUMmxOImtVLfkRJGguUM/ZssW54bwu+7kSVm79cKQ0Kr7Qkj637XdLI35vr79rEEXcoJYzsRC3kIIbBuUi1ip+nF2A5L2J4KssxX6gKajz5mqT2/WG4I96hQAvB8o6WfUWR9YCfo0necV+7dM5daVCkkoeZd3iiGQFIQksJFtkXcMn06Ui6YHWtPOGmVbUTxcGTBDmtR/7baMh3CY4IsoUXxlbWZILiJJYcLNileOXKyqpWfRnJfkXvCkvnFFepT1o6njKhSnvNKGztnkl2712jjK7WG6ftyuSR0T7XLbt0+Za0LJYfHaHzPOXY5AMX3pMi12tIcLM8VWKLlVK1Ej1YKqf7ntbUAxSs3sB2LW/UuOZM/yetRFYjvizqFRNcivG+fnxaH7y84cQUAYPO6CQhBoXvbawwoYU7GBoXuzz1+edL/joLL+5x2X44NFbRc8fM9N75u3p5sFrh521QwUkKfk3wAgGNXKr7ZP+/mgtobckYqBeM1Pu+EFRZ/W6HVokdG7pkzXmOffOChVeIV1Y+OjMyTjExk61kblprrSZEjQ5LLyFqzZclI8jY/9rhl1hq2GNCpRMVv9e+rD9L7heez1JYFKeW/AvhXADjjjDMO6paGdZPDeMEjjwQAy2KhIyxufSAJS5iE2WbbCCRKAAdgiuMByu1aa7RQ0RObLA+eT1Eq5PDFV56NiaGiEUrT803jAQHUxJ+tN421PFIp4L/++FHYvr+GoVLe9lS0WswiVp4wyqEAkno+3CKut1iScjFvrHsSrHucEB4PSxDKhTyOWTGMj73gdJy5YSn+5ls3WYVK3Vwfns91+R+dbfJ93GT2sqFFWcr8IFcvLdpDaRbjcgHb9s+bwp27Z+qWR8INsVBfvv6C43DMihFcuGkVPrDlFkzXmpYHhAskSgA/evkI/vn5p+PRRysFrqI9YW4yO6AsVn4e2m0PTCVhCebNob4j6/7X99rzK0nQtZPSa40WKnq315df9Sj8+p59ZtfnNEtcVbQkITMKSzz3zPUYrRRw6cPWGmt73skNqTCBtNcI7mkU8sIIP9cTRiE8IPEaK1pqties4IbulYfjG689B42WNMVXp2sNc84ePT9JNm5gtFLAR557Gm68fx/WTAwZ76lvXEihpZ3BZn4xg4Xml6FF00l835bKG0ueMJ4LyufdZLWET7/0TGxcXsUXr77Xa92X8ioka8JvlQK+/ppz0NalPdxNBsZg0Z4Yfp4jebVHKgWUZ5Px5jxGHl+qLbWLzy/Xa8w8YZecshrttsQTT1qFq3UBVu4B8eVRLa2W8KmXPALHrRw1z3fTEMy8a7asczavvXuP5TXmRzDRwecj5QLu2zNn1r5dM3VjWKS8eozv//45p+G7Nz2AE1aNYaSkjNE6UwjIU1ZvKa/xaKWIszcuxYeevRlPOnl1QksqhMfliqLlrl2zGKsUmScs2bVKaxh9x+uw7Zqpq9wvwyt5KxeU3nXln5+LrXvnTGkLkivqXfoYKv2+6VoTRy2r4o1PPAGP3LgUZ26YZLzSRjFvR4sSWpiM1EZPIZ8zxnaNyRU6czhFS6OFFSQjCyQj7VzXL73ybIxzGanX45CMHK0U8OVXKRk5XCosOk9YphImpfya/v0fB+n99wJYx/4/AsDWg/SunmEsnWbbHOZ6x44ZtHQeFV2jdkcmTEZbibnFsmu6bmn5JCB4CA8AHnHUJADglu1q8aM8BO4V2DvHFZciNi4fwUbtGUisM2cx1gmU/FDam7fxsEQSxvTF7omWXTO1YDI7edmIGS7SC9EIzw1hsXsSymZnY6WAzczDoTwgqio7D7FQaI8rYYaWCs9zUZYt3TdSKeCeO2dNmQo1Jr7wQhvzjnX5jNOPSGixQni2dU+LjxACTz5ldUJLMY99s3XnFINkrLhguWX7NNZPDlt9ZPqumNBCNAPAzpkaijntYcw7CbosyX3FaAUXbKqg3ZbKuq81Tf0h+2y/li4VUrLo5/1vJ7OnBcv2qXlUSwWjaBEtPAHczC9OC/EK92g17GR2ADhpjQr90GLsesLIuieLeFSHWCjMwvnbTjbOmfA6zU3ix1G3NA3j+xHHUyGlOs2ixoVk3uV71YbHHqc8J6R8z9SblsFCnmzO9yevTXKpTLK3Vig5r/BwvaJlStNSRLmYnL3HNwCRF4t2Ru+aqQXD1vONlpl3APC009aavrpvz6zFY9wLRErMaKWIc49fwWjxbzKgz3c7fM8Nlppeh3j6gssrtBanaNFjzhXRp25eY57hhiOb7cQ7RwaLEAJPP83DK1ZifjLvds8oxaXVlrhjxzTO0tGQcjGH2bpdLog84DYtNdsT5uyKps+PWlbFUcuqSUkXLVdo3Gh+UkoFRVguOXWNbk8yvzhf+taw3+2cQVN7jakPuFwpF3LmhBSXlrobLfLIyDO0jLxVR0J4GgI9f88skyvlgl9GHg6eMCHE1+DxTBGklE89wPdfBeBYIcQGAPcBeA6A5x3gMxcMXMvfq61tsrpHA4JFhfCK5lpVlZyUlyTeXcy7SYd2ZJjKEFDiNBWWdMMSI+W8dV+FKSD1ZtuE3iiBkntc9s8nC7oblhBCJfS7tDRa0hQkVWdSJgtYWwqrDQkthUDsPm+FJUggp2lpObSoxXbPjE1LpZhD0Qld1JggG60UDM2ArVBatDieMA7KL+E7Ea1wZK2ZogNQXoIHmBeoaFXMb1tCct9cgyXopnd8AUqA0pE9ALB7uo7xoaI1v9oS5jxPd37lckIdkD7fNOEKqgJO75quNXHk0mG4oNCqlT/J5g+Ni5QwoXt6vr0YJ6F7Pi7k1aNcvGI+Z/W5Oy5WWMLaUajaybf+W2Ni+p/ml9BeJfX5dlaslvM9V1RrzURJIlroWiCZY8m4iFSysZeWecf40vOA8qhcWvi41Rxe2TFVs5T8/cxD4PI9/T9WKSrFoaXSI3ZN163jcTjf15oJfRzVct6TzJ68r92WyIn02uduMqB30bzb66xhFAIsF3KmbEmdGSxjlYI1JtxrXE7xfdvLv3Q2J6/J1Wwz40uXZHBRcXjF5vtWaly4XNkzW7f6Tu3wLlprxW7tCUs2sQijiHKFhtMB+BUXGpfpWiMtV9j3pFAWLU9YIluor43xpfuAK5Q+vidPmMkJ6ygjie8bZhOCel/O8rQG5coi8YRl5oQBeD9UtfzQzwFBStkE8GoAV0CFPi+XUt5woM9dKNCg75yqodWWZrcIkChhJaPlp617ADhJ78zYNV1Ph1hadr0gDnrGbN0VLGqCzekjgoZK7gRjnjBPgi55KVxaSkyw8LIOxEicFjqiI51snNSrsWlR/++fa0BKmHvI0qGQD68erZ6TKDc8z4Xqt+2drUMI4CitKJB30kcL/x4ATl475oRYcqkQi8v0gCqkOMtr7ORtS3qu3krRoZ6fTtAt6nC2CrE0zC5E1VY9v/JJaIyHpWlc8jmBE1aNmrAEn1/UJj7vLFrKeTO/AO0VYH1AJ0OkaVG5N97Qqp5jfH7xcbF3VSbWPaDyMQFlEc+7SelNO5ndpkPzSk15DiikSocSm/MFHVqSmnPp+QUklcVtWni5jbbJuysVkt1rQMIr9++d1++yw0V83nlp0eNScgRSiBZ3kwEP3XPji9Pi1gnjXid3DZutJwpDxVGmwvOroMaEeQt53Tc6ZoyflKD6SvE3heKslArtzV81VjF9wJPZVZt0blE+TcvJa8ewc7pmCXablmTeubTM1O1TInj6Ah0R5IJqzlkeLTbv9szWLb6n0D3JFb5ecFpWj1ewtFrCTkpzsTytrbDiQrXG9BrG12IAuvRFOyVXKKyY8oDrvto5rWUko4XyFqnsjS8NAVBjApCi307JyPmgjFT/zxi+t3klkZEuryS0LgZkKmFSyu/TD4CfAtgDYDeAn+rPDhhSym9KKY+TUh4tpXzvQjxzoUATjI4+OJFtdaWtsuTN4db9+FAROs0GJ+uQya6ZWirEwrV8+pyQFOZrmcKD9PxMwdIhQZcW0hNXM1qqpaBFvJTVZSFa6JxH2sYtRGJFkgfNRwuFEXjh2RqnpegKySRnyg6xJIJlfKhoiiJSLpl9kkFiEbu07J1tmHCLlTjdaoFvhrBoKecN06s22p6w0GLs5kNZ46Lz245aWjUeT6rpRVYdJTeXdJkDomXFaBkrxiresASQjIs7vwCYosL80GuegEtCsiMtTLBMzTcxW29ZvJKMi+M11rldROtRy4YxWi7ocGQybm5OmEuLKfhat71HlNhLddTcxZiXFuH5k1l8P1ktmfwk1wM+OZLFKzYfcg+HRQsXLDzZWCtTxCtDLq+4ypQ1vxLji/h+tFywhCiVEKD/Jz18v9UolOnSNOH51Uw8aFYftDDXaHoNFuJvd22kvtszq86YpLAy1Y5KrWF6/kxWVY6REMAJq5TxRZXxqZRJQksy72xa8ph1jvji75urt1JjQn1l5UHm7T7fO9tIrcV2H9h9R+OyaryCpSMlxfeuXLFK7NhtyudU/uBsvWWtF/R7v/ZiZa1hbkI/kBgsFi3D9hrG7xsfKpqCsEZGTtdMkWYg7QkLyUjXUUEyOZGRjteYyYfFgE6eMACAEOJiALcD+AiAfwRwmxDiSQezYYsBpHnTQrqZ1bMhjd+XbFwq5Ex+xAmrRlHK57Brpo65RuIlcXND0ta9+n/WCJbEOuATzGV8ruVz66Cij4ehc8F4bZ4RXi+IQnj6/w3Mct68bsLqj6FiPrFsyeOi3eY+WigfzRWus40mSvmkz9K02FZ6paiqee+ZrWPJcAnr9K5KHpYAmEWs/+e0UBIw9ceQZ9t9pieMb+92PWGexdh4wlq2ZTtUVGcn7tWChUKDfH5Z5T+KNi2rxiuY1AdAzzZaqJTy1vNpjvk8FcNlEizJrji+m6kXr96QwyunrOW8onMxnNAMzWnasbhuyTCWVNUBvbwfkwRdvycsWYxb1iJOfUXhK3cx5ocL8/k1VMpZtHC+X7+U5+rZ1v3qsaQUAPEKeY2H2Li42+59tBiFsmgLpLluPGHMYOHzq1zImXm/Qm/UcJU3d34Bye5FzvdukebQ/GrLRLC7BmjQe6TbQGFkehedybtX8z3tpt5o+N42QOn/DZqX6ND2PTN1zNaTtcra6anr0KVoKdmeMDcvbrbh9xqrXFy7hBHN65maSnM5ioX8ed6SO784reuWDKvDrGcamGV8auZX0z+/AK0c1+xd90TLntmwEpbi+3ya7zmv8PWYe/XKBRUCJmOdZOTuWUdGkvEVkpHcUeFxcIS9xoeRJ4zhAwAeL6U8V0r5OACPB/Chg9esxQFy/d67R00wXs9mjT7Q1KflA8luwdOPXIKxoSK275uHlEm4oVRQ2+5dK5GQLMY6YZZZtlmLcZKgqxKSXTf2vXvmIASsRFj+fpOgm7ctLwA4a4NKiLxfMxynhRQXnxVpPGGkhDmWbUjYu/WYElrymNHb5yeGkwRlAWE9P6mVpp5zNK/Mrb0WWw0tbHdkS1rJ7BYt+rgNazFm1eDDi3EuVVuL+pBoWTJcMkrYhmW0GCe5gUAikEgALRspY3yoiH2zDcywfDR6/ky9ZU5kSNGiPRWWFWkEYAvNtkx5Jw0tegs4tYnmAi3G61i5kaO5YOFFG/U757Ryddr6JYqWuYapVUT32XXobFpKOqQ5Q5tYzOYX9XtvQLCokLtajBstmYxJyeZ7O2nczjupNdvICRWuyeUS44NKFND8SsLLLt/7Bcv0fNPa2Us5YWHrPpnzFt9X1PzaPaPm12nrlUJF88n2GiceNB5Woorj9zNa6Pm06aHkmV9Vl+/ZpiTy6nm9R7pNlC/Ex2W61sTu2TqWVItYq2uSGYWymPAhD+UerZWB8SFl5DTbEjuma9b6ldAS8IRR6N4qTZP0nVrDPF5jKrLL+L6k14xt++fRakurAOnRjnHvyhVaJ49fNWp4ZabWNH1dyivFlxTY0BpGSf/cewQkvOIfl5yRK4WcQC4nzLwmvucykoyrsg7Bu3w/z/ieZGTbJyMbAU8Yd1RYJSoSucL7LKEjibAsBnSrhD0gpbyN/X8HgAcOQnsWFciDQ4vxZLWMZVp458y2fqf2kR7gi09VO+NOXD2G8aGCceXzCVZrJm7jkCcsESx8MW6bHX5h697ODeGCZWKoaI4KoV1ZhZxATqRd+UIIDGnX+1Jd9O4+prgompOaZz4rkt69JxWOzBuFMssiJuWFcjyM4jLTwORwCWccpRj/7KNpZ5EtWKgPqMDnk09ZZbavb907h7L2XJasiuZhT1i92bYWOVMZu0W0hBJ0056warmA3doyn6yW8IzT1c4yEnwmTKBrR9G4HL9KeTQuOmkVxoeKmKo1MTWfLMZ0H9Wc8ubslNhibMLd5D1SYxXyhIXyIIlXlgwXcabexTTJwkX1ZtsSZEBSj+n09ROJYKm3zPxKhSV8Xhd94LRrEQMwm2pcWqyK5k2eO2jTQjtVqcaaanuyyYALOsprWzMxhOFSPuH7km2wuH1g6CCvsSd0X28pvheBZHbAlwdZQKMl8cBUDUuqiRJGO3fdA5bpf5rDJ2hhD3C+L1heoNAmFuLphBZaw/LGg5bF9zR3uSE5U2ti72wDS4ZLeLxWjmmXbLngrBf6f+Kl5zxivaFl6945k1Pkhu6DnrCanXaSGNyt8Bqmw4ppvs/j3j2qQPGS4RKefYYqEmC8Rw6P0TwgJeeRGye9BkvJ8H3T6kuOxBMW5vvMNYx5jasOr0xWy6a+WI6VvuEVBOhdl2gZuWlNQEaakH8HT5h2VHAZWbdkpN8TtlgS8zvVCSPcIIT4JoDLoXZLPgvAVUKIZwCAlPIrB6l9A0WyGBOzFPG9Pz8XrXayYdR1tdLk/MCzNuOyp2xCMa/i3/cZK7K7pEMV6oMKF1m5Pqo+DSkB6aTDxBNWb7WxJO8yyyyWDKu8lqvffoGhkSqMuwIJAH72tvMhBDBSKkCIJDeEW/dUZ8jL9JrmXY4nrFTIYa8Oo3mFvV54ph2LmCpxl2frOHH1GE5YNYYfv+U8rHFKD5BgofsK+Rx+8bbzMT5cNAUft+6dTy1gJsQSSNAFWH4bC63WGlkhPLVbkQ7dTpKG82ZuTAwX8bwz1+PiU1cbT1fZFUj6vocfuQQ/evPjccSSYXz8h3dASpWXQTkZdJ3xeHjDRQXctXs2ZUUC4RCeoiWP/fONVLmNfE4YXpkYLuHTLzvTbBNX1/kF0uvOPxbPO2s9VoxVMD5UxO92qjIwaU9rOMRCc8K34ysRLOEQC0/o57xSKapNB9e940KTw0LPVgIpb3mBvvjKs43gnGB8b9HSsk9kcOkAYEoXWF7jRhtz9aZJA3DpANKhe8qXu3fPrD4PsIifv+18SzEGEq8xLwL7y7+8EJViDvvn1BgmQpLlglIILzAmgIfv84lXzzu/At5f2qFI4cgnnLTK8IB6fuIZacvkvhVjFfzkLedh1VgF/6uPXdu6d94cR5YO3ftoyRvFhfJejUen2cZshkLphvCIlvvIYKkW8Z6nn4w/vfA40x+J4mJ7j55+2lqcuWESRywZxrd+sw375hqoFHMpr55RwoKbDGxPWSnF9778tiS0ypVJIC0jmy1WN1Lv6Hf5/v3P2ox3dCUj/Y6KSjGHnGCOCkdGktwYLvp3Rx5unrAKgO0AHgfgXAA7AExCnSN5yUFp2SIA1/JzQm3bHq0UrXPrErexzSyVYh4rRpVSMD5UxFZdn8V4KjokHQqhSwjU7ITZdJ5LOsQCIGWxcOueFh86IsTQUqRwkb21eXyoiLFKEbmcwFglIFiaaa+A249uThh3G/uZ3m8RV8sF1Jpt7Jyum0rIayeGjGCyE3RbVt+qSvx5y7p3F7C64xWwaCHrPhVa1YnTgcU4CbGkabl3N3mP1Hlz/OQAc99cWpmi64x1v2/OWsDUfbYwd2mZNfPLCUvMhRWXlOGhd9JWS3lDy2RVnQHIjwyhkJprERfyOazW4f0xxitcOebn/XlDLKW8NywBMF4ppgW+oaXlt+6pGv/EcMmUa6E2uZ5WupcUHC8t+cQT5g8RO96jojO/MjZ+AGm+57RQ2GvlWCUp++BuYmF9O1ktYbhUsHilmBfG+8vPv/WHvRy+d0K5s6E0hKI9dzkt9+uQFa1hNq/4vcaA8kzmciKT7+caLVPZP0VLqYC5hlIcy4XkDFtArU9S+r3G3LDl7xopjd+0FAAAIABJREFUF4z3aGK4hGI+Zx0vVC5oo61uh+D5+jA+VMScLpLq0uLrg4SWPNv44ed7Py1JnlrKa7w7kZEj5YIjI/NW1IcfP5clIzttyCEZmeSEOTIyQAvf3bwY0JUnTJ8f+ZDDcClvdv7RrigXFI6kOkN5zzXjQ0XQaUEjKever4TR+/fPN6ycHppAe2brKOaFWUwJuZyy0FIWcTkJtfEcBJsWCs20vO0hWkwdGA8tPiuShEZi3duJl7P1ZkBAOoqL49Wrt9pmN5F1H9tkwBN0XToIKSXMFG0MCxaXlnIhSQYNecIAv0JJFiIJFrsPnEXVMy5Ei5tzqN5HYYmwRezbqk4JusHEfD3nKTcEUPNh//x8Ji21Rtscxh0aF+IVnufSbEvM1cMhluEyW4ydEMueDqFVRUsrVdKg3mxbwsSihW0y8Am6FC1MOZ6dbWaE8Nz8SZtXsjZLAMoTVvPkgipa0mNC15n0BQ8tVL6l3mpbtbD4hgl/2Mvh+9Qmg0AJFNcTZmhJTo/wrWF8hy4Qnl8Et7RFEroPe/PVBgf1dyGvPDEmmd27IUd5wmqeNATiey8tztrnpWWY06LXobxLiz89ZPv+efDadt0l5ifGF9/4kdMe0SXDxYCM1Mpbq4UCK+pr0eKRkeVuZGRZychWW3pkZAOFXOKxJBgZuUg8YV0pYbqY6msAHMXvWYBirYsaiTeq6V3AgMSq40mtLkICn8ISoYlZLRdMKIXHuwG1GPiSJwFKoPRbLADCgoVtDfcVLOS00KHUFi0BxYWE6V43N0S/b67e8rap4iyqFC7ihQSzFBc3HOmjgz/Pyg0JbDIgwUK0JGUNcphrqCrnmQrlnCNYWDjGvxi7fdCJlsTjAmQrb1WeR8WSpgFgX1ZYwqPkA8ncHirmvYt/YhHbXuMQLSGF0j/HlCes7vXqdaJF8QopQFU2v5ZUA3xfSLzG3fA9N1hIcfGNCZUQSPMKC+EFPHoAqxPmGCyAf37lcwLFvMhcw4QQGBsqYud0zfAyvZPWsJD3CPDwfVHNn6BXr2jPXderB/jHJZTQz+GdX3nH2+w1iBNa+PflQp7xip/vuQFRztshbwDGm2/dl1r7euOVTFp0mR0BkfIaZ/N9XhWQZUo+ycipWrOjcc9PL+mKFrbrPigjS2EZuW+24TVYTJsOJ08YgP8G8AkAXwOwOFp+iEBVn7MmWN1YxP4BH2f3WhOsSfkU/vuGS3mWT2ErCnvn6l6mB1iVZk+IBfAzfYqWqp9ZSOmplpK8FJ44PVpJt4mSjd06YSSQZustrJnICOF5whIJLWHFZbrmd2MDqtpztZTXCeAF/Zmih/IeQgm6RAv3fKr8tqx8CkewdCkkaU4lCkialgnf/HLCkaESAq22xNR8w1KogcR7FMqjomKtPiUsc361wiF4RYtfcbFp8QvJrXvnrLBEkueiPWGB0iHEKxM0vxhfhQ2WHDtSzM+/nBbX+Ap5wuj9vjyqtgSman7BQs+iHDwfrwQNSb1BJsurNzGslDBunNlrWNh7lOL7vMozU2VI/DmHAAuld2lIuh4tr9fY4z1yQ3ihwsZEC++jUiHXwdPqV6bo3RTCC9MS5vtMJayDJ2y23lSh5aKf7307PS1PWN7m+6ksR4XexMJ3+6ZoCaxhySapgIws59NeYxYt8q1fipa8CXMOGv4eSWNeSvkRKeX3nAKuD3rQhFjFagBxkHU/32gFLeKVY0leTCqE1/QnggKKWVK5R0XKSWpkTDBmpXsWY557YNFCOTsB7xEAE8O3FuNCkjjtY5aSrrbszwlrZYTw/JYtp2WlZ1yIGfdl5EPxe+l5VDOIBFnWYrxnpm4J33Ih1zGEB4QXYyFgdt7atOQ60sLnV3oxpgRdvxWZ0JJ25QPwCslyMZeqMq9oUdeuzJhfqk22IhqmxRWS2ePiFms14cgZlbzsC5VQRXNOSy4nDG9l8r3eHRniFT436XmUCxoK4QFKsOxxyzoUE1p8fE8erfT86oLvNR+qNcy/ptC4cC+hvYaFDZY036s+Dyazh0pUcFoy+N71NnOMlgtGGee5R0B26H7Y4hU/34cMFv5stwzKitFKMM0FSPjeRwufX64HPCsxn5fZSfFKZmg1SUOw8yA1r3SQK/ONLF7JkJGBzRKAGhdqc0pGzjYyHBW5RXOAd7dK2IeFEJcJIc4WQpxOPwe1ZYsENCEyFzCt8IQmymp2LxcszbbEfN3vyqdrd3sUF0Bp+WFXK9vlaJg+uTZMS6JQ+piX01Ip8cU4j1qrnWJOghDClGLgNCQJuoHaWgGhzQXLag8t6gxAnpzqp4X6gYcEy/lcdjK7yQlLhyVI2GQlToe8eiOlgtfdns4J65Tnkvffl1FCYDcTLAVHYQ6FJchCLXkWY9+Y8Lbvn2t6dwYCwKqxpAyEyQ1hodWcUOVUXKjQvZ17RO9TFrF/MeYVzTkttAM6SAvbZBDie85nxmtcyE5mB5SATtfU47SE+d7ML+NpTa4Nj0ty9FqQFj0ubk5Y1iaDEcYrFi1FdRZoqy2zE/MzwpErRsvB+0hx8a1hQghTVyzkNe5Ei8X3xZzhlVAyOz07n0s859Uu5AqQ7dGy5UqAFt9OT11mZ7rWZOHIxLjMosXNCQOYjGS8m7qvg0fLKyMpFzSQ5kLvDsrImXpGys7i8YR1G448BcALAZyHJBwp9f8PapDFElrAkhyPcHiBT07X+to/3wyGAIbLyYHTZKHSfbtm6t7DlQG2LbqV5IZwAU870VK05BWTqaKr2YoL92Lw6v/hEEseW3V1epNHpe9rt6W188zQ4e4M1PetmUja71uMaedWshgHPI168Vg9kYxtqZDL9rjo8ds/37TmRKmQM4uBlxbHq0e5IUQL1bRxQX21LyOsyMsV0NjSfMmsF1ROaOGCxabFH5agZ/PFmGjhOyJ9tOyfawTHZA0bixXa0ueeioqnPAOg5tc+RwHhvJKlGO6crqcEC70iKCR1DaP5ZssqaMzheyffdh/0gHO+L6Rp8c0vQI3Lfid/ko9FkO8L6hibZlsG+Zc8Fdz7wvNaffdVijltDNmlJkr5ZH6N+eZXIDF/LZsbPoPF5EFm8AqQVEqnuZbkT2Z5whL+5fOklM9hu97V5wsrcr7nayYVMvUZFICP77PDkVSeJ+0B93nCVJ9z/qXfu2fqKOVzgfHMmyPkeHvoHMgsGZlV9kfdG5aRU1ky0uJ7W0bu7igjF4cnrFsl7OkANkop6x2vfJCBziXMeRZ+IEm8pK3LPvDJSdY/T5wOW8S225v/rmckz5cLKo9NSqR2T7rtse7TVp1b1oGDFqO1TBEqFQTqzRbmA54wIGF8ap96n/rdbEsvLeTRohwPomXNePZirN7BPFqBxfh+vXievj6p8lzM5zKT2YfL6TGhv2m3E/c+uNfSs4sFNQ+o0GyT1Z6z77PzY0KCm0DFOOn5iXUfFiw+WmbrDU1L9q5VLljoSBzKZ0rflwiWYP4kEyz0d5EJ1/C8ZPPL2WRQb7atPC+rTcXkMPKiIyRv3zGDpVW/QkketPlGmFcodM9zZYrMYOG02rRk871vfqlr8sn80vmNXJj6DBa6r1PonuoS8iN2ivmcWWeCHnC9salUyCUlZIqcV/zhbiCZuzQuJ7OjsLx0OB60kODevr8GADhDFxOmvsrcxGKtX7YHPJMWxvf8TN3TddFVKveTvs/Jiwt49Qh0KkUx37kPMuWK3uXob1OyiYUbZyQLAiLSkpHdRItIRppxmcuSkelx4bRkyci5egtf+9VWbFozZvpvEOg2HPkrABMHsyGLFS87ZwMKOWGOIXHBGT8kWCaGi1g3OYS/vGRTch/3CmTEu9338AUgNMFsizi5/n3POAXLR8sZi3GyiyVkRZ61cSlK+Rxefd4x7L5k11uWJ4y/B4A3n4hDCIFKIZ+iRQiBZz38CDxh00rvuwAliPd38IS99rxjMVIumAVR3ZfLTmbnddXYwsD7ebScYRE73prV40PYuLyKtzzpBD8dqVCJv39fde7ROG39hPGSuDklWZ4wwF6siRZVEyp9X4UJSU73+SesQKmQwwsfeWQ2LfPhOS+EwJkbJvGyczak7lOFKcOhe/d6K2Ti8bgASUVzt97XO55yEoaKeZy4ejRAS56lIfjbtGFZFaPlAv7f00+x2paEZgKesFLaYLHDP+Gd2m64GwBee94xOHntWNhgKeYyw14A8MyHH4FiXuDSh621aOnkdTK5cJb3KLnWx/epnDBW0+ycY5bhRWf75xddlxWOBIB3X3oS1oxXzDmMlAuaZbTZirGf7720ML4vsftOWTuOieEi3nxRgO8Zj4VKHwGqeOvFp6y2qtPTffx/ixaPQWytxSFeKfqLeb/k0RtQzAucd8IK7328TaH1a3xIyci3X3xicl8xWcOy8ieT6z0yMkiL2lDxms9di2/fuN17zaFCt56wlQBuEkJcBaCmP5NSyksPTrMWD05cPYbb/vrJwe+5gAjtpBJC4IdvsiO3xJx0BIcPXLDQ9Xyx81legFp89s7OALAXj+ecuR7POXN9Bi15zDXS7maOtRNDuOW99tntVHV8PkOwDHssFp5XFqSFbdfntPzdszYH6aB3ZIXwAOAJJ63C9e9aZX02VMyb3CIfLYV8zghS/v2QNS7hBN29s43UYeXffcO5YTrcPJdA/7qL+VDRUcI6esKSv03icrngDf3Rs/bONix3/4qxCm55z5NS17vv2DfXCApIALj8j862aSnxxTgk7JP5Q9fwMckyWOYbrVT9rccdtxy//auLMmjJdcyfrJYL+M27nmjTUlQ7Uqfnm8H7hi2+z3lo8d9XKSQ5pLw//uwJx+PPnnB8Ji0PTNWs97k49YgJ3Ppeex0cKuZx56yqlB4yQKvlAjBVs8aNDkhXtIQ9YT6+/8zLzwrSQfmMnbzGf3D2UfiDs49K0ZLF91Vrfvn5PpsWe0NFqZDDde94QpAWy/DI4JUPPfthNh2lhDfLzPto05KeX7lccoRXyGtcKeYhpWoTp+XE1WOpuRGiZd2k34DwyUi+hgVlpIfvu5eR4Y1UhxLdesIugwpJ/jWADwL4BYBjMu94iIALlpAr3wez28bZ8uy7BkhCMzzvIKTll4u5zK3GIVghvAzGT7czbxJtszYZAGqhIgWE54NkuY2ztoCHwJWwXsZlqJRPndvnghh7jIWT+N++celmQ4UPaY9Wd/dSPo5beZ2D9/m4h5bgmBQTWkJJ4ln3qXBkb2NC7wuNJVd8iZbRLufXdK0ZPKw8BBJYc3X/gc8hWLR04QkzfO+pOZZqE+P7nsbFCkf2wveF1LmQ6WvU86z51WEN47xC7+kWNt/3toZl8f2wZ34BwNiQahvVd0u3JxnvXscE6J1XhrvgFZ9cAZI55ssDVW3ia1gPY2J5tHobE3pfOG86PS58fo12wSuh5P1Dha5GV5ej2AfgYgCfAnA+gI8dvGYdPrDDir1PsNCBsYBTF0dPMJ5fEppgatt923pPNygXcx09Lj4Ml/Km9lNWsjFgMz33HIYYnydQ9rqIZSXahtAdLep5vP2crqxwZK3Z7pEOCuE1gzsDfaCD15Nq0z5PmL+G1HgHJYzma40VOO0GFq/0KCABZG4YsWp76fYX8jnDI1lhCRrvnpRjVpert/ml2pFVX4x4JZ8TZgwmLCU/kJhfyPdHixVW7E2hTHglm5YJi++zFUo6Eig5M7D7NpWL+b7WsKEOfF8u5E2OEuf7iSH190jIa6yfVWu2ex4TgDbN9DC/isn8Co2JXW+NjUtH4+vA17BeDWJA8X2/MjJrDaPx7mUNOxjIfLsQ4jgAzwHwXAC7AHwBgJBSPv4QtO2wAGnobRnOPfLBPbPRBz7Rfd6JkKu1HHCXd0K5kAflh/ciWCxaQiEWPdF9wh7IoMUTJusG5WLOlBnohZahLmghgT8+5Lco/Yt4v2Oi7mu1pT5GqzsljN4zW28Fc0p83iMgETKdPGFAb31L/dmWBzIm2Uo+kLbup2rNTE+YeU8fgqVXvuehuLAnLG9+03j7ypCk2tQv3xdzhu9DSq4PXY1LiQwWP9+Hx0Upx77DyrNQLiwELf771OYsaW8eGe6guBzA+gUovu9Fmax0Mb+492jMoxyH1+L+5QpAtPQ5Jl1Ei/qWkaXu+/dgoNPbb4Lyej1FSnmOlPIfACyO4hqLBFbhvj7cxkA4gZRPIJq8fEEK57kcmGBx/+4Ei5YOgsUS9l0sxjxv7FDQMhTI/bCv0YJliFnETMj4LeL+6KCkYfcZ3YDeE5pf/HNbSGZ7j/ji2I9F7P7dCUPW/Aop+X5aaF6F5hdfgPumpSfBwuZXMCdMXcN3a9rhSL8nrP9x6axMedvZzbh4QvfjjG+Cc0w/uxc6gIO7htEOZv8OXr+iyOdu/2PS/X2lfM4YXEG5YnmN0978UFRiaAHkSq8RFnNfFxUEvDIyY5MBwVeQ+lCiU488E8A2AN8TQvybEOJ8AN2bJQ8BWBOsjxALEJ70IcGR3OdfjHmYsl/G7ye0mtUmYgbOyL7cChejLDQTOpHAh75pKXamhRjAtxiHkGdV2PsVLL14XPh7QvOLF0u1leNsTxhf2HqhpdKnB41buyFa+Od83Nr6VOAwjyXX9rIYL4TiEqRF9zsvWlIp9rZe9C8ke1Aoe6AlxCshjwrR0mvSNI2LEP0ZX0IgmJjeylDC/AVm3DHpPXQP9Ka4CCHMGhacJ+zzcY/B4qt35t7XTy4ocBBkZOBzQoiWfmXkwUDm6Eop/0tK+WwAJwC4EsCfAlgphPioECK8teMhhH4XMH5taCKdENgeTzhpzZj3c/68flzgqn39hVZDgnvTatXWu3fPms+4dbw8UODTLMZ9hCWS9vXndQmNCxUl5c+lxThr4SdaevVouXXVugWNfaeFCrAFC1n8oUKHIx4PbTfo12vM53AoD/LIpVXzNw+93rVLzTeafy744t5bTtiBKy4hAXGibuvuQL01qsfmom++79OQ7GZcjtVtpTpjgC34QzxNeW+9Jk3zMgW9he7VfSOlgvckByCph2Xlf+o+XxMohGspYb3ktvUpV4AkehDKHQxtyNm2XxXT3hSQK6PlfudXf3zflYxc5W8roSsZuZiVMIKUckZK+Vkp5SUAjgBwHYC3HNSWHSbggrF/i9jPLFTsMYQjlvgZnz+v/xDewnoqqBYXL83AhWVowaTn9WwRd5Hj4QO9JydsVzfHw9apknmU2Mnve+TGpcFnEy39esJ6mV+8TaH5BQDHrVRFCrlC3NTFJ09e4y+OyZ/Xfziy+/vyuSQkG5pfvqLEQJL/cuoR/jKHo/1a9/2GVrvwaHUyvkK8YI9L77vX1N8Lu4aREGyx4uSUhhA6WQFIdk73zyu93Uf9FRoTADhzgyruyjfHNFvKYDn9SP/8yueEWUd6GZMCCyv2yvedPOAcfI2j99H65mIh5EpvnjC/d5tjeaDmJaErGTng3ZE9B0OllLsB/Iv+eciDh8gWOsQCAJ99+VkpAfOVP34U9s81Oiou7ns6obQAsfsQsywbKeMDz9qMR+gq1YR/fv7p2Li86r2HP6/XxZiPS0/KMas1E+rfFz3qKADA889KikZuWj2Gd1yyCc88/YjgsxNaemM7E47scbHoRrB85mVnYcuN2y2F/zXnH4u1S4bwxJNWee8Z6dOV3+/8ApKjsbIUyq/+yaOxa6ZmffbFPzobN2+f6kpx6WUxLvXpqeiGV4r5HD72godj3aQtQD790jMz+5uXfAkV9/Sh3zVsqIs17KwNk/irS0/Ck05ZbT6rlgv422eeikcd09lg6dX4SvInF95g+aunnYyT1ozhLGZoPWXzGuyeqeOFgQKy9MwZpw5dNyjlc5hrhwtgh0Dz2HckFOE7b3gcrr9vn7XG/d3vbcYPb91heZU5FkauLGw4ElAy0t01/pU/fhT2dS0jDzMlLMIGtxx7sSK5YpDFLI8+ZlnqM37Mjg/9CpZ+k0E5Y2XR8syHpxWUJ7PF2Qdill6tQRqLUt5/UHQItFBmlYIo5nN4+WM2Wp8JIfBSVuXdB6Kl10W11K8nrNhZsKwYq+AFToX78aEiXvLoMC1cwPcdjuzRU0H5OFmL8WaPBX/sylETEvNhrN9wZJ85Yd3kUQHARSenFeDHHuc/taOb52VhIbx6IUEmhMALncKoAPD7j1iX+Wwq89JzONI5kLpbJLwS7sORciHF96VCDn/42I2BO/Szdd/0E1qdyzgWq9P7svj+6OUjqaN61kwM4dmPCBfzHl2AcPeilJGHQzgyIgyexNmLdcAVgyxm6QecWXqxCLlruhfroBvrvl8QLYGjFYMwIYDAdv4QjBLWwyaAbjHWp1ePdsmGtluHMNRDWKJf9FMnDAiHekNIlLCFnl/9hVb5tb2My3Cxs/eoX/TbN/wYm1BSuvc+1ge95F91gyR031sf9bv5ha7vJn+yV5BB1zPfa9qHe+R7ipyE8vT6BZ8bvSgu1XJ/MpLPqYMqI3tU2BcaUQk7QExWky2+y0b8Ryt0wkIvxtxq6GVxXMpyNJZ1iLVz2InaCzulSHGhXW7dgmjpRagACS0Nlu+1UCjobeyddr26WKrnWK/zi97Tq8LT0zt6mLvc8OhlfgGddzn2C/68XpQpns+UldvkghsFB1Ow9AI+r3oRrgdDYXGf3avXmMaiU65Q6n167Fu9WntdoKET4nrleyq10sv84lhoXrEdB90/e7HLyF4iJQcDUQk7QPB4d7/M0quHoxP6Xdw5g/RiRfHkx4W2iOcaqizdiYHdbSHQWMgelTfKWZtiu7kWCtfdsxeAypPpBUtHSAnrbX5Rgu1N26Z6uq8XnLben8TbCb3SQsnquQWeX1ZB5B74xlbCuhcsPL9zoQULheBWj2dv6HHR77p1ylr/xo2FwN16V2voAPUQaCx67VtKur/27r093dcN7tS0nNkj39NcX96j4nLiKtVnu/XZiAcDbigzC3zOH+4y8mBgYEqYEOLvhBA3CSF+LYT4LyFEf6v5IkKv1tfHXnA6Vo1Vgtub+8VktYR1k0P44O9nH3LtgnvCelGmhBD4w8dswHknrOjpfd3gscctx2ilgNedf2xP9y3t0+JaMzGEM45cgjdceFxf92fhz59wPFaOlfGIHhdjWsRCh9iGcN6JK7C0WsLLOuSq9YOXn7MB55+woifFhaNXi/hdTz0ZY5UCNh+xsIJfCIGHH7kEb3xi+IBrH7jHqNdxecclm3DCqtGevTydcNzKEUxWS3h/h8PtXfQrGCvFPC45dTWee2Y4j6hfPOfM9ZgYLuJpp63t6T5aw0SP5Sw3HzGB9ZPDeMclm3q6rxu8/eITsWn1GDb2oLhwLO1xfF52zkaMVgq4KLCx5kBw8amr8byz1ve08YOj17n2sRecjpVj5YMmIz/QI68cDAwyMf//ALxVStkUQvwNgLcCePMA23PA4G7XbnDRyatx0cnZien9oJjPpU6k7wZZyY+d8BcXL/ziBQAbllXxm3c+sef7QnXHusGXXvWovu/NwlM2r8FTNq/p+/5e3eZjlSKu+csL+35fFt5+gMKq18X44Ucuwa/7mAfd4MsHON69jstLz9nQcRNHP5gYLuGXfYx3vwYLAPzj807v+94snLlhEte9o/dSlP3udMvlBH7wpoNzGt/LH7MxldDfC5b2KFfWLx3ua83sBv90gON9uMvIg4GBecKklFuklBTz+RlU/bHDGqFaRYcLFjqUOEhQEcJek1oXIyihPXQ0yuEEyhns1/sSsfDo1ZO3mFHI6Z3EC5ybOgiQt7XXIs2LGaUed3o+FLBYJNRLoQ4H90II8QoArwCA9esX3vV9oPjMy87CrQ8cvLybQ4n3Pv3knnNKFiPWTgzhjx63Ec96ePZW+MMBr378sZhrtPB7nhIfhxu+9MpH4f9u3D7wbeELgX963umotw7/o3TzOYE3XXQ8ztoQrtt1uOCCTSvwB2cfidec11v6wmLEB561Gf/+4zsPau7docJnX34Wbtn+4JCRCw3Ra+JyTw8X4tsAfIHpv5BSflVf8xcAzgDwDNlFY8444wx59dVXL2xDIyIiIiIiIiIOAoQQ10gpz/B9d1A9YVLKC7K+F0K8CMAlAM7vRgGLiIiIiIiIiHiw4KB6wjJfLMRFAD4I4HFSyh093LcDwF0HrWEKywDsPMjviOgdcVwWJ+K4LD7EMVmciOOy+HAoxuRIKaX3yItBKmG3ASgD2KU/+pmU8pUDaYwDIcTVIddhxOAQx2VxIo7L4kMck8WJOC6LD4Mek4El5kspjxnUuyMiIiIiIiIiBo24XzQiIiIiIiIiYgCISpgf/zroBkR4EcdlcSKOy+JDHJPFiTguiw8DHZOB5YRFRERERERERDyUET1hEREREREREREDQFTCIiIiIiIiIiIGgKiEORBCXCSEuFkIcZsQ4i2Dbk8EIIRYJ4T4nhDit0KIG4QQrxt0myIUhBB5IcS1QoivD7otEQpCiAkhxJeEEDdpnjl70G16qEMI8ad67bpeCPE5IcThfzbcYQghxCeFEA8IIa5nn00KIf5PCHGr/r3kULYpKmEMQog8gH8C8CQAmwA8VwixabCtigDQBPAGKeWJAB4J4E/iuCwavA7AbwfdiAgLHwbwv1LKEwBsRhyfgUIIsRbAawGcIaU8GUAewHMG26qHLD4F4CLns7cA+I6U8lgA39H/HzJEJczGmQBuk1LeIaWsA/g8gEsH3KaHPKSU90spf6n/noISKmsH26oIIcQRAC4G8PFBtyVCQQgxBuCxAD4BAFLKupRy72BbFQFVk3NICFEAMAxg64Db85CElPIHAHY7H18K4D/03/8B4GmHsk1RCbOxFsA97P97EYX9ooIQ4igApwH4+WBbEgHg7wG8CUB70A2JMNgIYAeAf9dh4o8LIaqDbtRDGVLK+wC8H8DdAO4HsE9KuWWwrYpgWCmlvB9QBj+AFYfy5VEJsyE8n8UaHouZnDrNAAAgAElEQVQEQogRAF8G8Hop5f5Bt+ehDCHEJQAekFJeM+i2RFgoADgdwEellKcBmMEhDq9E2NA5RpcC2ABgDYCqEOIFg21VxGJBVMJs3AtgHfv/CES38aKAEKIIpYB9Vkr5lUG3JwKPBvBUIcSdUGH784QQnxlskyKg1rB7pZTkKf4SlFIWMThcAOB3UsodUsoGgK8AeNSA2xSRYLsQYjUA6N8PHMqXRyXMxlUAjhVCbBBClKCSJ/9nwG16yEMIIaByXH4rpfzgoNsTAUgp3yqlPEJKeRQUn3xXShmt+wFDSrkNwD1CiOP1R+cDuHGATYpQYchHCiGG9Vp2PuJmicWE/wHwIv33iwB89VC+fGAHeC9GSCmbQohXA7gCagfLJ6WUNwy4WRHK6/JCAL8RQlynP3ublPKbA2xTRMRixWsAfFYbkncAeMmA2/OQhpTy50KILwH4JdRO72sRjy8aCIQQnwNwLoBlQoh7AVwG4H0ALhdCvAxKYX7WIW1TPLYoIiIiIiIiIuLQI4YjIyIiIiIiIiIGgKiERUREREREREQMAFEJi4iIiIiIiIgYAKISFhERERERERExAEQlLCIiIiIiIiJiAIglKiIiIh6UEEIshTqQFwBWAWhBHekDALNSylgwMyIiYqCIJSoiIiIe9BBCvBPAtJTy/YNuS0RERAQhhiMjIiIechBCTOvf5wohvi+EuFwIcYsQ4n1CiOcLIX4hhPiNEOJofd1yIcSXhRBX6Z9HD5aCiIiIBwOiEhYREfFQx2YArwNwCtTJDMdJKc8E8HGo6vMA8GEAH5JSPgLAM/V3EREREQeEmBMWERHxUMdVUsr7AUAIcTuALfrz3wB4vP77AgCb1NF/AIAxIcSolHLqkLY0IiLiQYWohEVERDzUUWN/t9n/bSRrZA7A2VLKuUPZsIiIiAc3YjgyIiIiojO2AHg1/SOEeNgA2xIREfEgQVTCIiIiIjrjtQDOEEL8WghxI4BXDrpBERERhz9iiYqIiIiIiIiIiAEgesIiIiIiIiIiIgaAqIRFRERERERERAwAUQmLiIiIiIiIiBgAohIWERERERERETEARCUsIiIiIiIiImIAiEpYRERERERERMQAEJWwiIiIiIiIiIgBICphEREREREREREDQFTCIiIiIiIiIiIGgKiERUREREREREQMAFEJi4iIiIiIiIgYAKISFhERERERERExAEQlLCIiIiIiIiJiAIhKWERERERERETEABCVsIiIiIiIiIiIASAqYRERERERERERA0BUwiIiIiIiIiIiBoCohEVEREREREREDABRCYuIiIiIiIiIGACiEhYRERERERERMQBEJSwiIiIiIiIiYgCISlhERERERERExAAQlbCIiIiIiIiIiAEgKmEREREREREREQNAVMIiIiIiIiIiIgaAqIRFRERERERERAwAUQmLiIiIiIiIiBgAohIWERERERERETEARCUsIiIiIiIiImIAiEpYRERERERERMQAEJWwiIiIiIiIiIgBICphEREREREREREDQFTCIh7UEEI8Rghx86DbsVAQQrxHCLFTCLFt0G0BACGEFEIcswDP+ZgQ4i/7vHdaCLHxQNvQ5buuFEK8fIGedbwQ4lohxJQQ4rUL8cyIiIjDC4VBNyDioQkhxJ0AVgJosY+Pk1JuXcj3SCl/COD4hXqeEOJTAO6VUr59oZ7Zw7vXAXgDgCOllA8c6vcfTEgpX9nNdUKIKwF8Rkr5cXbvyMFokxDinQCOkVK+4GA8H8CbAFwppTztID0/YpHiEMytiMME0RMWMUg8RUo5wn4WVAETQhyQkdHP/Qf6zg44EsCufhSwg9yuiP5wJIAbQl8KIfKHsC0RERGDgJQy/sSfQ/4D4E4AFwS+eyqUcNoL4EoAJ7LvJJQFSf9/CsB79N/nArgXwJsBbAPwn/QZu34NgC8D2AHgdwBey757J4AvAfgMgP0AXu606xUAGgDqAKYBfI3R8mYAvwZQg/IwvwXA7QCmANwI4OnsOS8G8CMA7wewR7fjSc73d+h7fwfg+QAuADAHoK3f/aku+srXrjsBvFF/NgPgE1AeyW/p930bwJKMcXsjgPsBbAXwUj4eAMqaprsBbAfwMQBDzti8DcBO3Y7n+8ZR/38pgOv0ONwO4CIA74XynM7rPvhHd07o5/wTgG9oen4O4Gj23CcAuBnAPgD/DOD77jjr6y7S49zQ7/qV/vxKAH8F4Mf6+VsALGP3PRLAT/R4/ArAuYF+/K5Dy3G67R8F8E09Nhdk9WkX43Elpw163rH/TwDwfwB26z75fWc8svrxJHbvdj2uqwDMAljKrns4FK8VPX2Q1/cRn1wDYJ3+7lEArtLjdBWAR7H7rgTwHt3P0wC+BmApgM/q+XIVgKOcNeO1UDy1E8DfAcjp73IA3g7gLgAPAPg0gHH93VH63hfp/t8J4C/Yc3NI+HwXgMsBTHa6F+G59WI4fD/odTr+HPyfgTcg/jw0fxBQwqCE0QyACwEUoUI2twEo6e87KWFNAH8DJbyGwJQwvWheA+AdAEoANupF74n6+3fqhfFp+tohT/vM+xxargOwDonS8SwohS8H4NmaptX6uxfr9/whlCB6FZQQFQCqWpAcr69dDeAkRt+9PfSVr113AvgZlOK1Fkrw/BLAabrPvgvgssCYXQQlcE/W7fz/YAv9vwfwPwAmAYxCCcf/54zNB/V7HqfbfrxnHM+EEr4X6v5bC+AE/d2VSCvHrhK2Wz+jACWYP6+/W6b79hn6u9fpcUgpYWw+fMb57EoooXsc1Py6EsD79HdroYTxk3W7L9T/Lw8836JFt30fgEfr+ysd+rTTeLjPfzG0EqavvwfAS3RfnA6lKJzURT+OQil+b9BtHAVwlv7umwBexd75IQD/EKD/jQB+A5UuIABshlKmJqGMkxfqdz9X/7+U0XUbgKMBjEMZObdAKa0FKEXq35358T393PX62pfr716qn7URwAiArwD4T/3dUfref9NjvRnKmDlRf/96KF46AmpO/wuAz3V57zvB5hYy+D7+PLh/Bt6A+PPQ/IFSBqahPAZ7Afy3/vwvAVzOrssBuA/ao4DOSlgdQIV9fy4SJewsAHc77XgrLdh6YfxBh3ab9zm0vLTDfdcBuFT//WIAt7HvhjVdq/RivBfAM+EogUgrYZ36KtUupD1QXwbwUfb/a2gsPDR8Elrh0P8fR+MBJURnYHtLzgbwO9b2JoAq+/5yAH/pGcd/AfChQBuuRGcl7OPsuycDuEn//QcAfsq+E1CKSK9K2NvZ/38M4H/132+GFuDs+ysAvKgbWnTbP+20L6tPg+MReP6LkShhzwbwQ6c9/wKtgHfox+cCuDZA07MB/Fj/nYfySJ8ZuPZmaJ5wPn8hgF84n/0UwIsZXdwj9QEA32L/PwXAdc78uMgZs+/ov78D4I/Zd8dDKeYFJIrUEez7XwB4jv77twDOZ9+t7uFea24hg+/jz4P7J+aERQwST5NSTuifp+nP1kCFBgAAUso2lKBc2+Uzd0gp5wPfHQlgjRBiL/1AhUNWsmvu6Y0E/31CiD8QQlzH3nMylCeGYHY3Siln9Z8jUsoZKEH2SgD3CyG+IYQ4IfDObvrKR8929vec5/9Qovsa53l3sb+XQymT1zCa/1d/Ttij6eP3r/G8Zx2Ut6lf8J2js0josdovpZRQIdKFev6RAJ7lzK9zoIRzt+D926lPs8ajE44EcJbT1udDGQKEEJ1Z4/NVAJv0btULAeyTUv4icG3oOda81rgL9rzudQ67/UTzzn3XXVBKFF8Tssb7v1j//RYqxNzNvRZ65PuIBxGiEhax2LAVanEDAAghBNRifZ/+aBZKMBG40ACU9RnCPVBehAn2MyqlfHKX92d9bz4XQhwJFYZ4NVQIZQLA9VCejY6QUl4hpbwQSnjfpJ/lQ6e+ympvP7hfP5+wnv29E0r4ncT6dlzaOxeXCCGqzv2+zRj3QIWafDgQeu6HCh0BMP11RPjynt91D5QnjM+vqpTyfT08g7+zU59mjQegvGghXrkHwPedto5IKV/VRRuD46MNoMuhFLoXQuVl9voca15rrIc9r3uF208079x3rYfy2HKlLoR7oHI5eR9WpJTdtDM1t3rg+4gHEaISFrHYcDmAi4UQ5wshilB5JzWoJFxAhfWeJ4TICyEugsot6ha/ALBfCPFmIcSQfsbJQohH9PCM7VD5I1moQi2yOwBACPESKE9YRwghVgohnqqVlRpUyLYVuLxTXy00LgfwYiHEJiHEMIDL6Avthfs3AB8SQqzQtKwVQjzReca7hBAlIcRjAFwC4Iue93wCwEs0XTn9HPIKdNP/IXwDwClCiKfp3aJ/grQSz7EdwFFCiG7Xyc8AeIoQ4ol6blWEEOcKIbIUvSC66NPgeGhcB+AZQohhXcvtZey7rwM4TgjxQiFEUf88QghxYhdN+zqAVUKI1wshykKIUSHEWez7T0OFPp8K1SchfBzAXwkhjhUKpwohlkLllR0nhHieEKIghHg2gE36vf3ijUKIJbrMy+sAfEF//jkAfyqE2CCEGAHw1wC+IKVsdvHMjwF4rza6IIRYLoS4tMv2WHOrR76PeBAhKmERiwpSypsBvADAP0B5Ap4CVcqiri95nf6Mwif/3cOzW/reh0HtPtoJJQjGe2jiJ6DCLXuFEN53SylvhMpT+SnUYnsK1G66bpCDUqa2QiVGPw4qh8X3nk59taCQUn4LKlH8u1DJzN91Lnmz/vxnQoj9UDsteY22bVAJ1luhEr1fKaW8yfOeX0AljH8IKlH9+0i8FR8G8HtCiD1CiI/02P6dUBsm/hYqYX4TgKuhhJ4PpCDuEkL8sovn3wO1q/NtUAr4PVDJ5weyzgb7tIvx+BBUjuR2AP8B1efU1imonaLPgRqPbUg2tGRC33sh1HzbBuBWAI9n3/8YahfvL6WUd2Y86oNQiuQWqKT0T0DlQ+2CUtDfADVObwJwiR6/fvFVqE0510Ep45/Qn38Sylv3A6g1YR4qL7IbfBhq08SW/7+9u4+2bL7vOP7+3HvNECaUQRszMuioh0YHl7BoMwRrBBlS4qFSQqvLahLSSJbWEqK12oiUSKyUiLBaiadGjJAgQViSMncGQdBczxcx4yGY8TC953z7x97n3j3XfdiDc/Zvz/281pp1z95nn32+c/fMuZ/7+/327yfpNbJB+h8e/yVDRv7bKv3/3lYvyoZFmJm1j6S5ZAOR31GrUDvkrRADZDcq3Fp1Pe8FSQHMjoj+iuu4Bfh+FCbVrbCWJL4nZqNxS5iZTRp5V+F6kqaStViJrAXD3iN59/4ODHf5mdkYHMLMbDLZleyOvFb37YER8Ua1Ja0+JF1K1mV6Yt5taWbjcHekmZmZWQXcEmZmZmZWgdot6jt9+vSYNWtW1WWYmZmZTWjRokUvRMSGoz1XuxA2a9Ys+vr6qi7DzMzMbEKSxlzNwt2RZmZmZhVwCLPSXl6+gg+dfiOLnnyp6lLGdM09A/z5WbfQbPqGEzMzS5tDmJW2dNlbvPbmIE+99PrEB1fk8Rde5+mX3mDQIczMzBLnEGalNfJg02hWXMg4Wi1gTU+9YmZmiXMIs9KGQ1i6KazVAuaWMDMzS51DmJVWh4DTCoiNRro1mpmZgUOYrYLhlrB0A06rq3Qw4dY6MzMzcAizVVCPEJa3hHlMmJmZJc4hzEprtS6lHMIGaxAUzczMwCHMVkGjFmPC8ho9JszMzBLnEGal1aM70lNUmJlZPTiEWWl1CmEpt9aZmZmBQ5itgjpMUeExYWZmVhdtDWGS5kl6RFK/pJPHOe5gSSGpt5312LszNBt9wgGndVekQ5iZmaWubSFMUjdwPrAvsA1wuKRtRjluGvA54K521WLvjTq0hLUmaXUIMzOz1E0YwiS9T9Kpkr6Tb8+WtH+Jc+8M9EfEYxGxArgcmD/Kcf8MnAW8uQp1WwW8bJGZmdl7p0xL2PeAt4Bd8+0B4F9KvG4T4OnC9kC+b4ik7YGZEfHj8U4k6ThJfZL6li5dWuKtrR1qsYC3uyPNzKwmyoSwLSLiLOD/ACLiDUAlXjfaMUM/GSV1AecAX5joRBFxYUT0RkTvhhtuWOKtrR3q1BLmEGZmZqkrE8JWSFqLPEBJ2oKsZWwiA8DMwvYM4NnC9jTgT4HbJD0B7AIs8OD8dNWhq68VEL12pJmZpa6nxDGnAT8FZkq6DNgNOLrE6xYCsyVtBjwDHAYc0XoyIl4Bpre2Jd0GnBQRfWWLt86qw52HdZjLzMzMDEqEsIi4WdJispYqASdExAslXjco6TPAjUA3cHFEPCjpDKAvIha8y9qtwxqN9NeOdAgzM7O6GDOESdphxK7n8q+bSto0IhZPdPKIuAG4YcS+L49x7NyJzmfVqsN4qzrUaGZmBuO3hH09/7om0AvcR9YSth3ZnF67t7c0S03rzsOUx4Q1azBuzczMDMYZmB8Re0TEHsCTwA753Yk7AtsD/Z0q0NIx1MqU8OLYgzWY1d/MzAzK3R25VUTc39qIiAeAOe0ryVI1NBt9I92A4wW8zcysLsrcHfmQpIuA/yKbpuJI4KG2VmVJatSgO9ID883MrC7KhLBPA8cDJ+TbtwPfbltFlqxWsGkm3B3pEGZmZnVRZoqKN8lmtj+n/eVYyuowWavvjjQzs7qYMIRJepzCckMtEbF5WyqyZDWHAk66s9F7TJiZmdVFme7I4jJCawKHAOu3pxxLWR1amRo1uIPTzMwMStwdGREvFv48ExHnAnt2oDZLTB3GWw0FxUa6rXVmZmZQrjuyOHN+F1nL2LS2VWTJqkNXXx0mlDUzM4Ny3ZFfLzweBB4HPtmecixldeiOHKzB+pZmZmZQLoQdGxGPFXdI2qxN9VjCWgPyUw44HhNmZmZ1UWbG/KtL7rPVXGuYVdIhLNKf1d/MzAzGaQmTtBWwLbCupE8Unno/2V2SNsm0WsJSHm9Vh3FrZmZmMH535J8A+wPrAQcU9r8G/G07i7I01WFx7MEazOpvZmYG44SwiLgWuFbSrhHxqw7WZIlKvZWp2Qxa2SvVGs3MzFrG6478UkScBRwh6fCRz0fE59pamSUn9XnCioPxU63RzMysZbzuyIfyr32dKMTSl3wIazqEmZlZfYzXHXld/vXSzpVjKUt9Ae9BhzAzM6uR8bojr2OUhbtbIuLjE51c0jzgG0A3cFFE/NuI5/8B+BuySWCXAsdExJPlSrdOaw12T3UB72LwGky0RjMzs5bxuiPPfjcnltQNnA/sDQwACyUtiIjfFA67B+iNiNclHQ+cBRz6bt7X2mewUafuyAoLMTMzK2G87shftB5LmgJsRdYy9khErChx7p2B/tZs+5IuB+YDQyEsIm4tHP8/wJGrVL11VOpjwoqtX6m21pmZmbVMOGO+pP2AR4HzgG8B/ZL2LXHuTYCnC9sD+b6xHAv8ZIwajpPUJ6lv6dKlJd7a2qGR+OLYxdyVao1mZmYtZRfw3iMi+gEkbQFczxiBqUCj7Bv1J6OkI4Fe4COjPR8RFwIXAvT29vqna0VSX8B75ZawNGs0MzNrKRPClrQCWO4xYEmJ1w0AMwvbM4BnRx4kaS/gFOAjEfFWifNaRYYW8E50NnpPUWFmZnVSJoQ9KOkG4EqylqxDyAbZfwIgIn44xusWArMlbQY8AxwGHFE8QNL2wAXAvIgoE+ysQq3B7hHZ7PRdXaM1dlbHIczMzOqkTAhbE3ie4a7CpcD6ZOtJBjBqCIuIQUmfAW4km6Li4oh4UNIZQF9ELAC+BqwDXCUJ4KkyU19YNYqD3QebwZSEQ5jHhJmZWeomDGER8el3evKIuAG4YcS+Lxce7/VOz22dVww2KS6QvVJ9DmFmZpa4CUNY3p34WWBW8Xi3WE0+zcRbmtwSZmZmdVKmO/JHwHeB6wBPvjSJrbQsUCO9kOMxYWZmVidlQtibEXFe2yux5K0UchLvjnQIMzOz1JUJYd+QdBpwEzA0hURELG5bVZak1NdmLI5TcwgzM7PUlQlhHwI+BezJcHdk5Ns2iTSaQU+XGGxGkiGntbZlVmN6IdHMzKyoTAg7CNi85HqRthobbAZTe7oYXNFIMoS1apra00WCQ9bMzMxWMuHakcB9wHrtLsTS12wGU3qyfzJJhrC8O3JKT5cX8DYzs+SVaQnbGHhY0kKGx4RFRMxvX1mWosFm8L6p3UOPU9MKXlN6uoa6Js3MzFJVJoSdVngsYHfg8PaUYylrNIOpPd1Dj1PTCl5Te7qTrM/MzKxowu7IiPgF8AqwH3AJ8FHgP9pblqWoEWl3RzaL3ZEJTqFhZmZWNGZLmKQtyRbdPhx4EbgCUETs0aHaLCER2R2RU7rTDWGtLtIp3V0sXzFYcTVmZmbjG6878mHgDuCAiOgHkPT5jlRlyRm683CNLISlOSZsuMZX3kivPjMzs6LxuiP/EvgdcKuk70j6KNmYMJuEhu48TLglrFFoCUtxgXEzM7OiMUNYRFwTEYcCWwG3AZ8HNpb0bUn7dKg+S8RwK1PCA/Obw2PCUmypMzMzKyozMH95RFwWEfsDM4B7gZPbXpklpTjeKttObx6u4clafXekmZmlr8xkrUMi4qWIuCAivGTRJNNoDM9GD5BgBhsKilN7uhzCzMwseasUwmzyao0Ja4WwFFvCms3ijPkOYWZmljaHMCtl5N2RKYacYktYiiHRzMysyCHMSnn7mLD0Qlhx2aIUQ6KZmVlRW0OYpHmSHpHUL+ltg/klTZV0Rf78XZJmtbMee+eKXX3F7ZQ08savKd0OYWZmlr62hTBJ3cD5wL7ANsDhkrYZcdixwMsR8cfAOcBX21WPvTuDhTsPi9spabWETV2ji2akGRTNzMxayizg/U7tDPRHxGMAki4H5gO/KRwzHzg9f3w18C1Jiqhups1Hly7jJ/c/V9XbJ+vF5SuA4Zawnz7wO558cXmVJb3NLx99EYAp3VlQ/OYt/XS7w93MzMaw6xbT2fGDf1DZ+7czhG0CPF3YHgA+PNYxETEo6RVgA+CF4kGSjgOOA9h0003bVS8A/UuWcfZN/9vW96irKd1dzJm5HuuutQbX3/8c1ycYVjebvjZbbLQ2EpzzM19HMzMb28n7dq22IWy0JY5GtnCVOYaIuBC4EKC3t7etrWR7b70xvz1z33a+RW0J6OnuYvGpeye7LFC3RFeXmLftH779H5KZmVlBl6pdjbGdIWwAmFnYngE8O8YxA5J6gHWBl9pY04S6ukSXl8gcV3eX6E78e9TjfkgzM0tcO39SLQRmS9pM0hTgMGDBiGMWAEfljw8GbqlyPJiZmZlZp6idmUfSx4BzgW7g4og4U9IZQF9ELJC0JvCfwPZkLWCHtQbyj3POpcCTbSs6M50R49IsCb4uafJ1SY+vSZp8XdLU7uvywYjYcLQn2hrC6kpSX0T0Vl2HrczXJU2+LunxNUmTr0uaqrwuHjhjZmZmVgGHMDMzM7MKOISN7sKqC7BR+bqkydclPb4mafJ1SVNl18VjwszMzMwq4JYwMzMzswo4hJmZmZlVwCFsBEnzJD0iqV/SyVXXM1lJuljSEkkPFPatL+lmSb/Nv1a34NckJGmmpFslPSTpQUkn5Pt9XSokaU1Jd0u6L78uX8n3bybprvy6XJFPmm0dJKlb0j2Sfpxv+5pUTNITku6XdK+kvnxfZZ9hDmEFkrqB84F9gW2AwyVtU21Vk9YlwLwR+04Gfh4Rs4Gf59vWOYPAFyJia2AX4O/z/x++LtV6C9gzIv4MmAPMk7QL8FXgnPy6vAwcW2GNk9UJwEOFbV+TNOwREXMKc4NV9hnmELaynYH+iHgsIlYAlwPzK65pUoqI23n7OqLzgUvzx5cCB3a0qEkuIp6LiMX549fIfrhsgq9LpSKzLN9cI/8TwJ7A1fl+X5cOkzQD2A+4KN8WviapquwzzCFsZZsATxe2B/J9loaNI+I5yAIBsFHF9UxakmaRLTd2F74ulcu7ve4FlgA3A48Cv4+IwfwQf5Z13rnAl4Bmvr0BviYpCOAmSYskHZfvq+wzrKdTb1QTGmWf5/AwK5C0DvDfwIkR8Wr2C75VKSIawBxJ6wHXAFuPdlhnq5q8JO0PLImIRZLmtnaPcqivSeftFhHPStoIuFnSw1UW45awlQ0AMwvbM4BnK6rF3u55SX8EkH9dUnE9k46kNcgC2GUR8cN8t69LIiLi98BtZGP21pPU+kXbn2WdtRvwcUlPkA1r2ZOsZczXpGIR8Wz+dQnZLyw7U+FnmEPYyhYCs/M7WKYAhwELKq7Jhi0AjsofHwVcW2Etk04+puW7wEMR8e+Fp3xdKiRpw7wFDElrAXuRjde7FTg4P8zXpYMi4h8jYkZEzCL7OXJLRPwVviaVkrS2pGmtx8A+wANU+BnmGfNHkPQxst9YuoGLI+LMikualCT9AJgLTAeeB04DfgRcCWwKPAUcEhEjB+9bm0jaHbgDuJ/hcS7/RDYuzNelIpK2IxtM3E32i/WVEXGGpM3JWmHWB+4BjoyIt6qrdHLKuyNPioj9fU2qlX//r8k3e4DvR8SZkjagos8whzAzMzOzCrg70szMzKwCDmFmZmZmFXAIMzMzM6uAQ5iZmZlZBRzCzMzMzCrgGfPNLHmSGmRTY7QcGBFPVFSOmdl7wlNUmFnyJC2LiHXGeb6nsCafmVktuDvSzGpJ0tGSrpJ0HXBTvu+LkhZK+rWkrxSOPUXSI5J+JukHkk7K998mqTd/PD1fZqa1IPbXCuf6u3z/3Pw1V0t6WNJl+UoCSNpJ0i8l3SfpbknTJN0haU6hjjvzyVXNzNwdaWa1sJake/PHj0fEQfnjXYHtIuIlSfsAs8nWghOwQNJfAMvJlo7ZnuwzbzGwaIL3OxZ4JSJ2kjQVuFPSTflz2wPbkq37dyewm6S7gSuAQyNioaT3A28AFwFHAydK2hKYGhG/flffCTNbbduh/nMAAAGZSURBVDiEmVkdvBERc0bZf3NheZF98j/35NvrkIWyacA1EfE6gKQy68HuA2wnqbXO37r5uVYAd0fEQH6ue4FZwCvAcxGxECAiXs2fvwo4VdIXgWOAS8r+hc1s9ecQZmZ1trzwWMC/RsQFxQMknQiMNfh1kOFhGWuOONdnI+LGEeeaCxTX+muQfY5qtPeIiNcl3QzMBz4J9E7w9zGzScRjwsxsdXEjcIykdQAkbSJpI+B24CBJa0maBhxQeM0TwI7544NHnOt4SWvk59pS0trjvPfDwAck7ZQfP01S65fci4DzgIVe2NzMitwSZmarhYi4SdLWwK/ysfLLgCMjYrGkK4B7gSeBOwovOxu4UtKngFsK+y8i62ZcnA+8XwocOM57r5B0KPBNSWuRjQfbC1gWEYskvQp87z36q5rZasJTVJjZpCLpdLJwdHaH3u8DwG3AVhHR7MR7mlk9uDvSzKxNJP01cBdwigOYmY3kljAzMzOzCrglzMzMzKwCDmFmZmZmFXAIMzMzM6uAQ5iZmZlZBRzCzMzMzCrw/xqN/NoiGT48AAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# How many time points are needed i,e., Sampling Frequency\n", "samplingFrequency = 100;\n", "\n", "# At what intervals time points are sampled\n", "samplingInterval = 1 / samplingFrequency;\n", "\n", "# Begin time period of the signals\n", "beginTime = 0;\n", "\n", "# End time period of the signals\n", "endTime = 10; \n", "\n", "# Frequency of the signals\n", "signal1Frequency = 11;\n", "signal2Frequency = 7;\n", "\n", "# Time points\n", "time = np.arange(beginTime, endTime, samplingInterval);\n", "\n", "# Create two sine waves\n", "amplitude1 = np.sin(2*np.pi*signal1Frequency*time)\n", "amplitude2 = np.sin(2*np.pi*signal2Frequency*time)\n", "\n", "# Create subplot\n", "figure, axis = plt.subplots(4, 1,figsize=(10,10))\n", "plt.subplots_adjust(hspace=1)\n", "\n", "# Time domain representation for sine wave 1\n", "axis[0].set_title('Sine wave with a frequency of 4 Hz')\n", "axis[0].plot(time, amplitude1)\n", "axis[0].set_xlabel('Time')\n", "axis[0].set_ylabel('Amplitude')\n", "\n", "# Time domain representation for sine wave 2\n", "axis[1].set_title('Sine wave with a frequency of 7 Hz')\n", "axis[1].plot(time, amplitude2)\n", "axis[1].set_xlabel('Time')\n", "axis[1].set_ylabel('Amplitude')\n", "\n", "# Add the sine waves\n", "amplitude = amplitude1 + amplitude2\n", "\n", "# Time domain representation of the resultant sine wave\n", "axis[2].set_title('Sine wave with multiple frequencies')\n", "axis[2].plot(time, amplitude)\n", "axis[2].set_xlabel('Time')\n", "axis[2].set_ylabel('Amplitude')\n", "\n", "# Frequency domain representation\n", "fourierTransform = np.fft.fft(amplitude)/len(amplitude) # Normalize amplitude\n", "fourierTransform = fourierTransform[range(int(len(amplitude)/2))] # Exclude sampling frequency\n", " \n", "tpCount = len(amplitude)\n", "values = np.arange(int(tpCount/2))\n", "timePeriod = tpCount/samplingFrequency\n", "frequencies = values/timePeriod\n", "# Frequency domain representation\n", "\n", "axis[3].set_title('Fourier transform depicting the frequency components')\n", "axis[3].plot(frequencies, abs(fourierTransform))\n", "axis[3].set_xlabel('Frequency')\n", "axis[3].set_ylabel('Amplitude')\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 2 }