{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from matplotlib import animation\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from matplotlib.animation import PillowWriter\n", "from matplotlib import cm\n", "from skimage import color\n", "from skimage import io\n", "import numba\n", "from numba import jit" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Laplaces Equation:\n", "\n", "$$\\nabla^2 V=0$$\n", "\n", "everywhere in the square. We are in 2D, so this means\n", "\n", "$$\\frac{\\partial^2 V}{\\partial x^2}+\\frac{\\partial^2 V}{\\partial y^2}=0$$\n", "\n", "This equation can be discretely approximated as\n", "\n", "$$\\frac{V(x_{i+1}, y_j) - 2V(x_i, y_j) + V(x_{i-1}, y_j)}{(\\Delta x)^2} + \\frac{V(x_i, y_{j+1}) - 2V(x_i, y_j) + V(x_i, y_{j-1})}{(\\Delta y)^2} = 0 $$\n", "\n", "Noting that $ \\Delta x = \\Delta y$ in our array, we can solve for $V(x_i, y_j)$ yielding\n", "\n", "$$V(x_i, y_j) = \\frac{1}{4}(V(x_{i+1}, y_{j}) + V(x_{i-1}, y_{j}) + V(x_{i}, y_{j+1}) + V(x_{i}, y_{j-1}))$$\n", "\n", "So the idea is that if repeatedly set\n", "\n", "$$V(x_i, y_j) \\to \\frac{1}{4}(V(x_{i+1}, y_{j}) + V(x_{i-1}, y_{j}) + V(x_{i}, y_{j+1}) + V(x_{i}, y_{j-1}))$$\n", "\n", "$V$ will eventually converge to the true solution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Part 1: Boundaries Only" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define the boundary conditions" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "edge = np.linspace(-1, 1, 300)\n", "upper_y = np.cos(np.pi * edge / 2)\n", "lower_y = edge**4\n", "upper_x = 1/(np.e**-1 - np.e) * (np.exp(edge)-np.e)\n", "lower_x = 0.5 * (edge**2-edge)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Get a meshgrid" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "xv, yv = np.meshgrid(edge, edge)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define function to solve for the potential" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "@numba.jit(\"f8[:,:](f8[:,:], i8)\", nopython=True, nogil=True)\n", "def compute_potential(potential, n_iter):\n", " length = len(potential[0])\n", " for n in range(n_iter):\n", " for i in range(1, length-1):\n", " for j in range(1, length-1):\n", " potential[j][i] = 1/4 * (potential[j+1][i] + potential[j-1][i] + potential[j][i+1] + potential[j][i-1])\n", " return potential" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Solve for potential" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "potential = np.zeros((300,300))\n", "potential[0,:]= lower_y\n", "potential[-1,:]= upper_y\n", "potential[:,0]= lower_x\n", "potential[:,-1]= upper_x\n", "potential = compute_potential(potential, n_iter=10000)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1, figsize=(8,6))\n", "clr_plot = ax.contourf(xv, yv, potential, 30)\n", "ax.set_xlabel('x/a')\n", "ax.set_ylabel('y/a')\n", "fig.colorbar(clr_plot, label='$V/V_0$')\n", "ax.set_title('Potential in square')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# With a Block of Fixed Potential" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define a block which is set at a constant potential of $V=1$" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def potential_block(x, y):\n", " return np.select([(x>0.5)*(x<0.7)*(y>0.5)*(y<0.7),\n", " (x<=0.5)+(x>=0.7)+(y<=0.5)+(y>=0.7)],\n", " [1.,\n", " 0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Show the location of the fixed potential" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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ipptjtpcU1rd7P61PW2BvAjZJejfwCeC6unWb5XI7IobNYeDSpvlLgNFOhW3vAH5e0rxe60JCMiKGz05gkaTLJc0GbqAx3tYbJP2danwtJF0FzAaeq1O3VV+X25IuAP4MuAw4BPya7RfalDsE/Ah4HTgxdipdt35ExBjbJyTdCjwIzALusr1f0i3V+juBfw7cJOk14BXg16sbOW3rlvbX72+SG4CHbG+snjfaAHy0Q9nlto/1UT8iAgDbW4AtLcvubJr+JPDJunVL+r3cXgPcU03fA7x/kutHREyofkNyge0jANXf+R3KGdgm6RFJ68dRH0nrqyfndx0/+UqfzY6IqKfr5bakbwIXtln1sR72s8z2qKT5wHZJT1R3nGqrnpMaATh39oLiLfuIiEHpGpK2r+u0TtKzkhbaPiJpIXC0wzZGq79HJW2i8dT7DqBW/YiIqdLv5fZm4OZq+mbggdYCkuZImjs2DVwP7KtbPyJiKvUbkhuBFZKeAlZU80i6SNLY3aMFwLckPQp8F/i67a2l+hER00VfjwDZfg54b5vlo8DqavogcEUv9SMipov0uImIKEhIRkQUJCQjIgoSkhERBQnJiIiChGREREFCMiKiICEZEVGQkIyIKEhIRkQUJCQjIgoSkhERBQnJiIiChGREREFCMiKiICEZEUNH0kpJT0o6UA1H3br+70n6jqRXJf1Oy7pDkvZK2i1pV7d99TvudkTEpJI0C7idxmgGh4Gdkjbbfqyp2PPAv6PzMNXLbR+rs7+cSUbEsFkKHLB90PZx4H5gTXMB20dt7wRe63dnfZ1JSroA+DPgMuAQ8Gu2X2gp8/aqzJifAz5u+48l/T7wr4H/V637PdtbiIgZ5YxXXuPsfc/ULT6v5TJ4pBpSeszFwNNN84eBq3tojoFtkgz8acu2T9Pv5fYG4CHbG6vfBTYAHz2lNfaTwJXwxmnyM8CmpiJ/ZPu/9NmOiJg5jtleUlivNsvcw/aX2R6VNB/YLukJ2zs6Fe73cnsNcE81fQ+dr//HvBf4vu2/7nO/EfHmdRi4tGn+EmC0buVqoEJsH6Vxwra0VL7fkFxg+0i1wyPA/C7lbwDua1l2q6Q9ku6SdH6f7YmImW8nsEjS5ZJm08iVzXUqSpojae7YNHA9sK9Up+vltqRvAhe2WfWxOo1q2s5s4J8B/7Fp8R3AJ2icKn8C+APgNzvUXw+sBzhr1txedh0RM4jtE5JuBR4EZgF32d4v6ZZq/Z2SLgR2AX8LOCnpt4HFwDxgkyRo5N+9treW9tc1JG1f12mdpGclLbR9RNJC4GhhU6uA79l+tmnbb0xL+jzwtUI7RoARgHNnL+jl94eImGGqG7xbWpbd2TT9f2lchrd6Cbiil331e7m9Gbi5mr4ZeKBQdh0tl9pVsI5ZS5fT3oiIydZvSG4EVkh6isaDnRsBJF0k6Y2Ul3ROtf4rLfU/VT35vgdYDnykz/ZERAxUX48A2X6Oxh3r1uWjwOqm+Z8Ab21T7sZ+9h8RMdHS4yYioiAhGRFRkJCMiChISEZEFCQkIyIKEpIREQUJyYiIgoRkRERBQjIioiAhGRFRkJCMiChISEZEFCQkIyIKEpIREQUJyYiIgoRkRERBQjIioiAhGRFRkJCMiCjoKyQl/QtJ+yWdlLSkUG6lpCclHZC0oWn5BZK2S3qq+nt+P+2JiDeHTpnStF6SPlOt3yPpqrp1W/V7JrkP+BVgR6cCkmYBt9MYd3sxsE7S4mr1BuAh24uAh6r5iIiOumTKmFXAouqzHrijh7qn6CskbT9u+8kuxZYCB2wftH0cuB9YU61bA9xTTd8DvL+f9kTEm0IpU8asAb7ohoeB8yQtrFn3FH0NKVvTxcDTTfOHgaur6QW2jwDYPiJpfqeNSFpP418EgFe3PvPZfRPR2GliHnBsqhsxgWby8c3kYwN4+3gqvfTa0Qe3PvPZeTWLnyVpV9P8iO2RpvlSppTKXFyz7im6hqSkbwIXtln1MdsPdKsPqM0y16h3aoXG/0gjVZt22e74G+iwy/ENr5l8bNA4vvHUs71ykM1ot4uaZXrOo64hafu6bmW6OAxc2jR/CTBaTT8raWF1FrkQONrnviJi5itlSrcys2vUPcVkPAK0E1gk6XJJs4EbgM3Vus3AzdX0zUCdM9OIeHMrZcqYzcBN1V3ua4AXq5/26tQ9Rb+PAK2VdBh4J/B1SQ9Wyy+StAXA9gngVuBB4HHgS7b3V5vYCKyQ9BSwopqvY6R7kaGW4xteM/nYYBocX6dMkXSLpFuqYluAg8AB4PPAb5XqlvYnu+efByMi3jTS4yYioiAhGRFRMBQh2W/3x+mubvdMSYck7ZW0e7yPYkyWfrqNDYMax3etpBer72q3pI9PRTvHQ9Jdko5Kavss8rB/dz2zPe0/wDtoPMT658CSDmVmAd8Hfo7Gbf5HgcVT3faax/cpYEM1vQH4ZIdyh4B5U93eGsfT9bsAVgPfoPHc2jXAX051uwd8fNcCX5vqto7z+N4NXAXs67B+aL+78XyG4kzS/Xd/nO5mWvfMfrqNDYNh/v9aV7Z3AM8Xigzzd9ezoQjJmjp1QxoGp3TPBDp1zzSwTdIjVTfN6arOdzHM31fdtr9T0qOSviHpFyanaZNimL+7nk1G3+1apkv3x4lSOr4eNrPM9mjVx327pCeqf/Wnm366jQ2DOm3/HvA22y9LWg18lcYbaWaCYf7uejZtQtIT2/1xypWOT1Kt7pm2R6u/RyVtonHZNx1Dsp9uY8Oga9ttv9Q0vUXS5yTNsz0TXn4xzN9dz2bS5XbP3Y2mka7dMyXNkTR3bBq4nsb7PKejfrqNDYOuxyfpQkmqppfS+G/tuUlv6cQY5u+ud1N956jOB1hL41+vV4FngQer5RcBW5rKrQb+isadx49Ndbt7OL630njp8FPV3wtaj4/GndRHq8/+6X587b4L4BbglmpaNF5++n1gLx2eWpiunxrHd2v1PT0KPAy8a6rb3MOx3QccAV6r/rv74Ez67nr9pFtiRETBTLrcjogYuIRkRERBQjIioiAhGRFRkJCMiChISEZEFCQkIyIK/j+8qO9tTpqDFgAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(5,4))\n", "plt.contourf(xv, yv, potential_block(xv,yv))\n", "plt.colorbar()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Obtain the fixed potential, and the places where the potential is fixed" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "fixed = potential_block(xv,yv)\n", "fixed_bool = fixed!=0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Modify the compute potential function so it doesn't set the modify the points at the fixed potential during the training procedure" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "@numba.jit(\"f8[:,:](f8[:,:], b1[:,:], i8)\", nopython=True, nogil=True)\n", "def compute_potential(potential, fixed_bool, n_iter):\n", " length = len(potential[0])\n", " for n in range(n_iter):\n", " for i in range(1, length-1):\n", " for j in range(1, length-1):\n", " if not(fixed_bool[j][i]):\n", " potential[j][i] = 1/4 * (potential[j+1][i] + potential[j-1][i] + potential[j][i+1] + potential[j][i-1])\n", " return potential" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Solve for the potential" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "potential = np.zeros((300,300))\n", "potential[0,:]= lower_y\n", "potential[-1,:]= upper_y\n", "potential[:,0]= lower_x\n", "potential[:,-1]= upper_x\n", "potential[fixed_bool] = fixed[fixed_bool]\n", "potential = compute_potential(potential, fixed_bool, n_iter=10000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1, figsize=(8,6))\n", "clr_plot = ax.contourf(xv, yv, potential, 30)\n", "ax.set_xlabel('x/a')\n", "ax.set_ylabel('y/a')\n", "fig.colorbar(clr_plot, label='$V/V_0$')\n", "ax.set_title('Potential in square')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# For an Image" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Load image" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ ":1: FutureWarning: Non RGB image conversion is now deprecated. For RGBA images, please use rgb2gray(rgba2rgb(rgb)) instead. In version 0.19, a ValueError will be raised if input image last dimension length is not 3.\n", " img = color.rgb2gray(io.imread('../../output/accordion.png'))\n" ] } ], "source": [ "img = color.rgb2gray(io.imread('../../output/accordion.png'))\n", "img = np.flip(img, axis=0)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(4,4))\n", "plt.contourf(img)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Solve for potential" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "potential = np.zeros((300,300))\n", "HV_bool = img<0.05\n", "LV_bool = img>0.95\n", "fixed_bool = HV_bool + LV_bool\n", "fixed = img\n", "potential[fixed_bool] = fixed[fixed_bool]\n", "potential[0,:]= lower_y\n", "potential[-1,:]= upper_y\n", "potential[:,0]= lower_x\n", "potential[:,-1]= upper_x\n", "potential = compute_potential(potential, fixed_bool, n_iter=10000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot potential" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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A0gVBH16CLvpY/wD8hEFheqy8KEhJOHSRmnQI+YQB5E1AhHavAeQVB5DPe1AT40UwGUosTIkcxr8mRgRAfiEAfmIAxhcEU6VrJsKK5BcsFaslCiKXTm4jh7dgbGEALQmIEOU1gDziAMK9BzUxXgSIEwrgbzinJB5yGnsXsSIAwoQATFQMQLIg6PIS9DkVsWsWQhEGy8VqiYIA+vIWTFEYQH9eA2hPRoSNN+gc3oOaGC8C5BUKNoYwxGORIgAgXASAvxCAvGIAhhEEi0ARBstDEQWkr5zoEgshYYQYBhcG0FtIoSbUewDhAgHCRAK4jV1OsbAopBp+kxgRAGFCAEYSA5BFEEyhemFMzYImRRgsBisnCmTffnRn/MpEOVZPzOUtiD2nSxiAI5wArV4D8BcH0C4QfMUBhAsESBcJNV0GchFFQ06j3yRWBEB/QgD8xQDk8Q5APkEwRBVDH3wqHdYPSUUcTJeVEwUhhExPDPUWDCUMIHxmAqR5DcA/rAB+4gD6EwhgN1axQsEk1sDmEBN9GncfUgRATagQgJHFAGQTBEPiMwPBx1vgWwK5eA2mSxEFFSEhBJcAyOFFgLzCoOu8ZK8BDCIOIE0gQJhIgP6Egg9jG/RQcggAiBMBECYEYDwxAP6CIJeXYOjCRSHCoC8OsYk7U9aqX2FWUhSEhBByLKkc6i2A6QgD6PAaQHZxAPkFAqSLBGg3fkMJhrHIZfhNYkUAhAsB6EkMwCiCYAx8cwtiFk0qTIOVFAU5CPUWxAgD57V7EgbQHk6AFq8BdOYbgJ84AH/vAcQJBMgjEkxCjOZUBEQfhr6NFBEA/QsB6EcMQH5BMFYuQYgwAIo4WDCKKDBInYUQS0wZ5D6EAQzjNYBwcQDhAgHSRAKkCwUXQxvjoUk1/jUxIqCmVzEAowqCPgipbBgyG6F4DRaLlRUFOUIIubwFrdfuSRjAAF4DyCYOIFwgQLwXoabNuPUlGBaJXMbfZEghANMQAxAmCKYy48CX4jVYHFZWFLjo21uQM79gdl6cMOg6F/y8BpBXHMAwAqEmRijUdBnEZRANfRh9kxQBAHEiACKEAAQvZLTsgiCmdkHxGkyfIgo8yeUtaKMvYQD9eQ0gUBxAVu8BxAmEmpRwQxcpBjWnoOjbsPuSKgBqBhUC0KsYgH5DBuFGO0x0xAoDKF6DqbLSoiC1kFEXMWGEPoRB17k+52cTB9Cb9wDmDUaqSKjJKRZ8mIohjyWXAIB4EVAzhFcA4moPhAqCqXgJTOr7Sqw4KEyLlRYFLlwhhFBvQRuLKAygO6QA+cUBxAkESPMimLQZuaEFwxTIafSbpIoAGM4rAMOIAZimIDDJUQq5MD5FFPRMm2AYSxhAfDgB/LwGECEOYDCBsH65BKFQ42sgF0E89GnsXYwqAiBKCEB8VcKpC4LQEIJJEQaLz8qLgtAQQoy3IFelww39SJhd0HW+bxvZxQEEeQ8gXiCsX64noWBjDIM7JXIYf5MxhAAMKwYg3kCPZZxjwwmFabDyosBFzCyEIcMIkB4O6Drfpw3oWRxAlECAOJEAbuPVl1hYNnIb/5okEQCjCAFISyQcK2SQ4i2oGVMcHNY17jlywvAXXgKKKIggpvRxH2EEyCMMIN1rAOHiAPoTCJBPJKx3o8MorYpo6MvoN0kWAZAkBGA8MQDj5xDkEAZQPAeLRhEFLeT2FkxVGPi0UbcD+cQBBHoPIFoggN3IpAoFkxhjObaQGMrAd5FFANSMKARgGmIglwHOJQxg4/2lCITpMqooEJHzgZcDa8CVqnp5Y//PAj9UvdwMfCVwiqreJyKfAh4AjgCHVfXxnRc8ajdSMVMTcyyU1KRvYQDpXgPftiBOHECkQIBgkQD9C4UupmKUhyKr8a9JFAGQZynjHPUGxvYO2MgpDGrKAobTZTRRICJrwCuA84A9wPUicrWqfrQ+RlVfBrysOv7pwE+r6n1GM09V1XsH7LYXfSUdpgqDWRt+XgMYRxxApECAJC+CSZvhGlIwLCq9GH6TDCIApiMEIK/R7eMpvA9hUJgmY3oKzgVuUdVbAUTk9cBFwEcdxz8TeN1AfVunLYQQ6y2IDSOAnzCAPDkCPiIjpD3zBjqoQIAkkWDiY/CWWTj0bvCbZBIAkEcEQN4KhLkNbZ9u+SIMVoMxRcEZwG3G6z3AE2wHishO4HzgMmOzAm8XEQX+t6rudpx7CXAJwPZNx8GD++C4+RXqclc3TPEIpAoDGN5rULcH3W1CuPcAEgQC2I1LJqHQJJfhzCkuBjfmMWQUADVTFAKwuMa1/m0vav8L3YwpCmy/Vted/unAuxuhgyep6u0i8gjgOhH5mKq+a67BmVjYDXDillOiim3HegtSwghDCgMYXxzAgAKhxmWEehILoSyEIY+hB+Nfk0sEwOIJgSGT94o48MqJOxF4DfAoZrb2N1T1D439a8ANwGdV9bsH63gHY4qCPcBZxuszgdsdx15MI3SgqrdX/98tIm9mFo6YEwVTZihhAHm8BiHt1W2CX7uQRyBAgkioaTNaExEMk6dHw1+TUwBAfwsTDWE4x8rmN3/bqyQQfHLigJ8APqqqTxeRU4CPi8hrVfWhav8LgJuBSRVU6G95rm6uB84RkbNFZCszw39186BKbT0ZeIuxbZeIHF//DXwn8JHUDsk+9y9r0153idq1vW437+Z97Uaka/+Wfe0GbvMB9VptzOemsfmA/w97bb//jahuN+SmsWn/pvV/oWw6KBv+ZWX/mt+/ZWXE99/H55ryPXNhft+H8A5MZXrf4e3z/5aY9Zy4ysjXOXEmChwvIgIcB9wHHAYQkTOB7wKuHK7LfozmKVDVwyJyGXAtM/fLVap6k4hcWu2/ojr0GcDbVXWvcfqpwJtnY81m4E9V9W3eF3fkFfRFl0cg1WMA+cIJs7Zm/+f2HIS2XRPrQVg/32JAkr0JXSyzMOiZ7ELObHuBvQEmUxECXSyxMPDJifs9Zg+6twPHAz+oqvUN7LeBn6u2T4pR6xSo6jXANY1tVzRevxp4dWPbrcDX99y9IPqoW2CSUxjAdMSBb/s1qQJhvR2H4eldLBTW6dP4Q38CAMZzlS+KGBibQ7rGnYdOTG3mZBG5wXi920ho98mJ+7fAB4B/A3wZs9y3vwO+HbhbVW8UkaekdjI3paJhg7ZZCDEVDmtSvQWQTxhA/+LAt22zfd9r1DRv+ikiYb3NFkNVBEM4fRv+DddaQhFQU8TAKNzbUhTPJyfuR4HLVVWBW0Tkk8BXAE8CvkdELgS2AyeIyGtU9Yfzdj+OIgoy0uUtGFIYAN7ioC/Xf6j3IOYaJn2IhA3tBxq4ZRURQxp6Zx+WWABAEQELwHpOHPBZZjlxz2oc8xngacDficipwGOBW1X1F4BfAKg8BS+aiiCAVRYFLXkFfXkLfMglDKAfr8Gs3dn/Q4iDmhwiAfILhdbrT8B4Ljp9Gv+aIgIKoXjmxL0UeLWIfJhZuOHnp1iBt8nqioKeSPUW+B4TIgzA32sA/YuDkGs0rxVyPRsuIzOkWCjMM4Txh/EFQDH+y0NXTlw1bf47O9p4J/DOHroXTREFEaR6C3IKAyCr1wCGmVGQSyCEXtdFm1EqgiEPQxn+mpIMWCiEU0SBg5Syxz4zEXIJA+jHawDDzShIEQjN64Ze24dYY7bsYmJoI9/GGAKgGP/CMrLaoiChXkGXtyDXFMXcwgD6Fweza1Bdw/8c81qh17Ndu2asudJTMprLQqkHsPiUZZOnzWqLgpHxNfghwgD8wgkQFlKA9ITBMQRCsw8mS1xYZeEpxn85KAJg8SiioIXUlRNzhRFCjoN+vQYQb6xzCYTQ6/r0p0kRDP1TXP7LRxEBi08RBQn4JByOKQwgzGsAYeIA4rwHs+sd+zvGAPchEkxiDdaqi4mxs/trivEfjiIElosiCgZeB8FFH8IAwrwGcEwcwDDeg9k1j/0da1T7Fgm+TMUorgrF+I/HlMXAYV3jrvQyxytJEQUddIUQcnkLIEwYAL15Ddavk+g9gPHqEdiMxZRvYoV2pmT8cwi/RfYold/RclNEwUDkFgahx0K6OIDhwguz6x77O8dNtM2wlBvdNBjT+A/p5em61lRFQ/mdLD9FFGSg79LHbYQKA4gXBzCO92B23Y2vc980Q4xRuTGGM5Un/UUJ70xlWm1N+c6vDkUUQGdeQeoshJo+vAX18eAfTqjJIQ5geIEwu/7G10PeNKdi4Ap2FsXwh5DbaxZCH4JgbJFTcFNEQSZ8vQUhwgDCDH2M1wCOiQNYTIEw68PG1+Wms/wso/H3IWUl0VByC4Lyu5w+RRRMnKG8BjUp3gOYhkCY9cO+vdyUFo9VNf5dDCkOUlmEPhZmFFHgiU8IIbe3oCbGA5BLHMD4AgHyPbFMOcErt/FbpBvx2IY/V0hojNj75gP9fNa53ssifQ8LRRSMxhDCoD4P4sUB5BUIoeKgJqcXoY2xjVNOxhAZUx2/ofJAXNfpWyz0JQxSmFp/Cn4UUVCTqYhRyEyEoYRBfS6kiQMYN/+gZiqFilaNqRp8k6kmgQ7xnc0pDFL7VwTB4lJEQQC+sxD6nKKYatzr81PaqDEFAgxb/8CkFCpaPaZq/H3py/M1BY/B2NcvpFFEwcjELrGc4jUw26hJbQvSvAi5BELNIgmFIQzcVN97F4tu/H1IKfDVByn9KIJg8SmiIJA+vAUpwgDyGPSpCgTIIxKg3wJFUzdeUy7ONNbYNb9nMeT6bkI+cTCWtyD0mkd3HO2nI8AhXeOeh47vrf1lpogCkxEXR4oVBpDHa9Bsr8mYiYq5vQg+TN3I98kyvfcchj+0/dTvaA5xMLQwmJIgKKRRREGPhOYWpAoDyPOU39Z+zRTqIMBwImFKjCGSFoG+BYAvuXNlphJWcFEEwXJRREEEucoe20gRBpA/DOBznZhr5ZjmCMshElKMWci5izg2LqYiALrINdtmKGEQep0iCJaPIgp6JmYmQqowqOnbe2C7Vsz1cgkE6Medm8pUDFhbP8YeIxdDjl1zNo1J6vcS0mp1xAiDKcxEMCmCYDEoomCi5BIGkM/1H3O9MQXCen88DEvojXoqhj4XYwuGIcazzejHnjv0SqNTCiWECI4iCBaHIgqaeCYbhoQQYusW5BQGJrZEQuhHLExNILiYmpFPMWA1Q4qqKZJjDEOuETvLJkQchAqDvrwFRRAsL0UUDESKMAB6EQdNXGKhyRiFk4YUCEPSp+Gytb1MY2cyhAAI6UPIOG8+oL0KgzFZZkEgIucDLwfWgCtV9fLG/p8Ffqh6uRn4SuAUYBfwx8BpwFFgt6q+fKh+d1FEwYLQl9cghhxTFlPyHVIrKY7F1AwXLM7YNeljLHN60EJn2aSuDZIDX6Hh6yVYckGwBrwCOA/YA1wvIler6kfrY1T1ZcDLquOfDvy0qt4nItuAn1HV94vI8cCNInKdee6YrJYoOJL3Sxo6CyG1/PGUhEGT2LyF3As2wTQMXU6j5evBqQkZy0XxJow5nikiOEYc+AiDqXsLfATB0W3ji+QEzgVuUdVbAUTk9cBFgMuwPxN4HYCq3gHcUf39gIjcDJzRcu6gjCoKPNwvTwHeAnyy2vQmVf0Vn3OnSg5hAMOEE1IINfZ9rslQk9vYDfm0mtJGSqimZiihMNUxbWvTZ3xDxEFuYTC1WQiwMILgZBG5wXi9W1V3V3+fAdxm7NsDPMHWiIjsBM4HLrPsewzwjcD7cnQ4B6OJAh/3S8Xfqep3R567tCyaOIBhvQc2puC+t9GH0XK1n1p0yoWvaBjqM+h7TF3X6hrfLfs0qzAYGh9xMYWwwWHdxL0P7Upt5l5Vfbxjn+3DcX25nw68W1Xv29CAyHHAG4EXqur98d3My5ieglD3S65zuwkodxxTyCjnKopDiIP6Gm34XH9M78GUiDFYIee0jVVfYzq24EoRATkTbH1Kjvt6DXyEwdTCCCsQNqjZA5xlvD4TuN1x7MVUoYMaEdnCTBC8VlXf1EsPIxlTFPi6X54oIh9kNuAvUtWbAs5FRC4BLgHYzjjrGgyBabhTBIKPAEi9fsxaDYssEGINVup5XeO0yGMK440r+AmvHF6DKXkMcoQglkQQAFwPnCMiZwOfZWb4n9U8SEROBJ4M/LCxTYA/AG5W1d8aprv+jCkKfNwv7wceraoPisiFwF8A53ieO9s4iwHtBjhx05dM5huZ01vQJNaw575+mzhICREsgjHr02DZPl/bWIeM0yKMKQwvBLraSxUHvuGENqbiLejyEiyRIEBVD4vIZcC1zPLarlLVm0Tk0mr/FdWhzwDerqp7jdOfBDwb+LCIfKDa9ouqes0wvW9nTFHQ6X4x4yyqeo2IvFJETvY5dxHoUxj0zaa9BwFa++8zWyI1f2AKxizV4MQKAdf+NoHg6wKvGVsgDDG2EB8i8xUHKcIgh7dg7GTDZRIENZURv6ax7YrG61cDr25s+3vsD7aTYExR0Ol+EZHTgLtUVUXkXGAT8DngC13nDkmfCyRNjVoM2F7bBIJvzkOO5MLcSz77XqPPtlzGqvk5mGPfNuahoZshS2RPZWy7jo8RB30Lg7G9BVNILizkYTRR4Ol++X7gP4rIYWA/cLGqKmA9d5Q3ksgieQuahsi23/VefGss5J55MGQWug+pT66uz8DmuXGNea7QTZNQL0RuQtoOGd/mdzpWdKUKgzFJ8TIso5dgmRm1TkGX+0VVfw/4Pd9zF5VFEAZdgqB5XIrXAIZd4XEIcrixfT6D5nepTYwtiwDrSww099nEwZDCYKreguIlWC5Wq6LhhJmyMPAVBL6EVGZcZHHQt7EKabuvpM+xCBUgqWKrPi5EGIB9TGNm36yfO6HZCD60egl2TMuLV5ixaewODMpaf29X9u3vre0xiTVKXeeFxnM37zuy/m/KhPZzbe+h7ILAdp7PeC/S+PrSNr4QPsausXVdw9XXtvcwds2HXBRBsJisliiYOLmfyFNJ7Y+PMIiZPjk14xUrWHIaq9TrmUxNgPUxvpBf8A4lDNqWsl5reTbZfMC9ry3s0JZPUEIHy0cJH0yMqYQRchkln/cTu9DTmFPnUgxmX8bK99ohYz1WaKHP8YU8gteVNxOSZ5ASSpgyY3sJjhzdxH0Hl7dYXZ8UUTBBxhYGuY2SrzCA+GqMfU6dy/XEPISxMttpmwkCYWPd99TEHGM85PiabfnmGbhwCYOUpMMhiPISlLDB5CmioLBOn0+ovkIn1/LQPkbm8M61QVzkvm77ocNHKWPtGjffdRdyMvb4+iYgxngFpjxNsbCclJyCjORMNpxafsGQxOYahNK3IAh5H3183j5t5h5nM/7f/Jebscc3pv2Y/IJQ2vIKhsAZOihegoWgiIIJM6QwGOJaodcYew2HWEJFTd8emi6GEmG5mNL4tpEr8dCVdNiWcJgLV5JhSTBcXooomDhTNNbQvuZBzmstksEKfXKt//WN7zWmPs4xYmBsYT31Mc1N8RIsPkUULABjP0k2qQXBUMIApi0OhnxyPbprW69JqFMc55g+TWmMbX1fJG9BYbUoomCFySE2Ym+gsU9xUzJaYxgr2999XHcK4xzbh9gxbn6XY7/XvvSZ0zJGXkGol2Dz9mn8jgsbKaJgQehjmmAMrhvlkF4DGNdoDW2swD6+fQsDGGecU645he91ahgh1FswNCWfYLkpomCByDmHPYauG2SKMJi6OKivEysGcgsCn32uvsTQ9zjnGN8pfa99hcFUqkb2RvESLBylTsGCkVrYqO+kwqO7tiWVj419b+YNN0edg2absaQKuT7yB6Yyzos0vvVxQyUuhtQ0CClktPmA/zLIIcsll+WRl4ciCmwcN+3ymLE39SFnGcSSo5pj09j4GK8+noKHNFixC/ukjLVtzGxjPXZugou+v9t9FDVahmJGQ3gJjugm7j8YoGoK6xRRsKCEGs8hBUGKtwDyl3kewygN7SFIHfNcDDnWfYVkus7rY5xtwiB1XYS1/e0LHcUQlE9QpiEuJCWnICO6M/MvsIOQdeBDSTXKU1jUaSzGChkM5T0am9T8gSG/233ULrAlHI45NTEkdFByCaZPEQULTtvNcejiLU1SbsCraqzGEGOLNNZjeAeGwpZ0uLCJiMVLsLAUUdBk4vkENnLf1HPfPJddGPQ5u2AoFmGspzTGY3sLFpHiJVgMiihYEpo3ntiQQV8GagqGrw+mOLtgmcY6x3TDRRoPX29B3zULbDMPSn2C1aCIgkwMnU9gI+UGOsSNM+YGPeUn2CkKgpS2pzbWUx7f0PaH8BaMkVdgzSewhA5sXoIdxXMwScrsg4I3XVP7fG9yoRncuWcj5GAoV3bKFL/YqYpTGOupCwLzOrnFVB8zEQoFX4qnwGQB8wly0HYDPbJry/q/LkKOXWSPQZ+CwBxD1zj6HJPC2GO9KIIglNzeAp8Qgs8aCLmnLa4KInK+iHxcRG4RkRc7jnmKiHxARG4Skb8NOXcsiqcgA1MIHcTiuoGmGpv6/Jwu0jGfYvs0VH2O9VTqF/iwqGIgZIx9v8OL4BlY5dCBiKwBrwDOA/YA14vI1ar6UeOYhwGvBM5X1c+IyCN8zx2TIgpqVtBLYLs55X7yXAaD1Zex6mOsc43z0AJsKEEQOuZDravh068xhUJJMpzjXOAWVb0VQEReD1wEmIb9WcCbVPUzAKp6d8C5o1HCB4ksqpdgCEHg0/bUwwh9GKu+3P5tbU85yXMIQRA75n2Ew+r329WuT42CZghhzCJGNhbcS3CyiNxg/LvE2HcGcJvxek+1zeRfAQ8XkXeKyI0i8pyAc0ejeApWjBgx4L0wS8dNzPUkG8pQT7F9CYI2Vm2spxyWsbXVl+dgSt4Cn4WQfEMHY3HkqPDggeTv7b2q+njHPtsCFM1B2Qx8E/A0YAfwDyLyXs9zR6OIAogOHSyalyDESMXceGwZ07brNW+sUwsj5OhLc6zbbvipY+0SCFMe60URA7a2XcIgNLegSepiSYvAAnkJutgDnGW8PhO43XLMvaq6F9grIu8Cvt7z3NEo4YMVwWakbDfPwzvXst2EXG3Zrj0V13YOY+UjCOqxyTHWbW25Qgkh5B7r1NkbbTkafQoCn+sMUbtg6NLHsfkES17B8HrgHBE5W0S2AhcDVzeOeQvwr0Vks4jsBJ4A3Ox57mgUT8EKeAl8jVRf1G03b2bNp66x6xfkfnpNHWcfb4DtnK5xhvHGuo/pnKFCoOsz8B3r5rjmCtk0PQZd3oJJLKc8odDBEKjqYRG5DLgWWAOuUtWbROTSav8VqnqziLwN+BBwFLhSVT8CYDt3lDdioYiCCBZFEKQaqVih4Lqp+hisRTRWsHGs+xhn1zG2sbaJsFwGK4UxBEFfoZnm9df2Hlof37GnKG4+oBze3p9ICFkV0WSJQgcAqOo1wDWNbVc0Xr8MeJnPuVNhtUXBEk9D7BIErhtMLnd2TfOm2ofBqm/AQ7vFfXI0+hznZju2sW4b5yEFWG5BkDtHw6etELd9qjDoSjyceq7BkocOlppRcwq6qjqJyA+JyIeqf+8Rka839n1KRD5cVYu6Yag+L4KXoPnUat5cXLHnnLkEPu02t5l9XMSZBT7jHJJHcGinbPjnQ9s1zX62vY8uYsYtpyBoi+f39R32aT81l8Env6CPXIJmNcPmzAOvfAKP0IHNS3Dc9vETXgvzjOYp8Kzq9Engyar6eRG5ANjNLFmj5qmqeu9QfV5EQWBiMxguYmOUrtKrNg9B25NsnwV3+gwV+AggE99xdh1nG29bmMbcNqTHIGV1wya5ZsrYjg8xuLbxhTwer1CPQc1QeQU+oYPiJVhsxgwfdFZ1UtX3GMe/l9nUjTwEhg6mLgjawgW+YiDHTaXZRtNoNW+oTbGQKgyamO3lnmoYK7py3rzNtsyx7hJhfRgw2zGh5BQDsUmdNW1CwZU8a9KHsDXDBlMPIbRRvATTZUxRYKvq9ATHsQDPB/7aeK3A20VEgf+tqrttJ1VVqC4B2L7puKQOTxVfQ2W7gfgYqK6kpbYqanX7sQYr9Sl2CEHgIwa6xjkkMcw13q6x7mOcoT2Xo09B0EdybFdbvsmzORI6m+Pq6y3wwacwURCRoYPCdBlTFHhXdRKRpzITBd9mbH6Sqt5eLTJxnYh8TFXfNdfgTCzsBjhxyymz9pfISxBrqFxGKiZr2XZO03DFGCyTUGGQm3qcc4wxxI2z69yusW6KsJweA5gXYjkEQYgYGOJpuc0zkDsMNhZd+QQldLAajCkKvKo6icjXAVcCF6jq5+rtqnp79f/dIvJmZuGIOVGQyqILAh9D1cf0pbrNFINlMtbNdegxdi1j27YErtm2Od6HdopThNmEQcoY504mNEkRAzGhmrYliV3ioA9hYIot01uQK4SQvGRyZG2CIUIHqsL+A/0XslpGxhQF61WdgM8yq+r0LPMAEXkU8Cbg2ar6z8b2XcAmVX2g+vs7gV/xumqAl2DRBEEuQ5Vys2gar1SDNQa++RlDjrGvWGiKMZsI60sYxBBT36GPBNm2NlzJnNBv4iy4hcGiUEIHi8doosCnIhTwy8CXAK8UEYDD1QIVpwJvrrZtBv5UVd+WtX8LIAh8jFXzBmczUslPDI62FtFgxYRjfMYY8o6zrU1zvG1jPaVxhnyzOPrOureFvsw+DSkMavpOMuwrdFASDKfPqMWLuipCqeqPAT9mOe9WZgtLhLHJryzDVAVBl8Fqe3INEQOxyUibD7jbTzVYQ2ATW3U/bH+nCK4cCV+u8W6OtU2ENd3PQwuD1Fkc3rUbIkJjIYmc0B0Cy5lj0OYtSJmWGPx9LAmGS8tqVzS0MHVBEOodaN4UbUYqV0Zysx3TaKUarD6NVWjeQJcY6HOMXW22jbWPCBtSGPQ1iyNXbkxoIuf6eQ1BC/mm2vpMAbWNjfldNL8vub1WJcFweSiiYAFoEwS+xqqrcplJ7A1jPlxw7O/aaKUYrD7q9+cMxQwxxiYbBdaxv9vG2lcY9EVM4ibknS0Tim/SLHTPqMkhDHLnFgTPOphwgmEhnSIKDKbmJQhJJnR5B3wMVa6nhmY7NqOVarDMm2GuyoQhY1v31STXGLeJiGaooNmm71ibBq7pnenbM5NrWmeXEMgtuGzXbSbNwnBTQNf74MgrGEIodVFCB4tLEQUVMYKgj4puzba7nqZixUAfsW6/GPfGY9sMVh9PsrnyMlKEQMwYu85pjiOYQmv+mDYR1pcw6Hta55AJnM2+DD0FNHZRKt/QwZAJhidssyjdwugUUUCYIOh7sZ4Qo+VjsLrEgI+Bat4oNu23J2y6cgpiDZbrSRYIvqmm5A2kiq2uMfZadKaiOfZ+YYNj+7tEWJ8eg5gQzaz/8TNmfAWYzRNju9YizahJ9U5ZKQmGS08RBZ4MsXKfb7ggVAz4CgFf49R2nGm0Ug1W25Ms+AuDHEmaoWIgdYxd2M6vx7w7RNMtwtqEQVR/PUM0EJfAufH4qC62nhsyo8blNcg508O8R9i+tzYBNbaXoLBYrLwo8PESDCEITJo30K4ff6wYcBkon5tBzaaDG29CZps2gRBisLqeZOGYMAB3Lf6+xICPV6BNBISMcxNz3Jtj3hRjG8WWa/u8MFhvw8jlCHmq7Stn49hx3l2JxjXDA/ySZmHea2CKhBjB1ZaT0exbG0N5CUroYLFYaVHQJQiGFAOuG6ivd8BXDNiMVIpxsp1bGyybQGjPKTi2z2Wwqq1z1zTFAbjnvsfkDIR6BaLFVttNd//Gfjfbao65bbzbxtoUYTXN6aEhSZ5d32fIP7UzZ26BPY/g2N+pU0DNv33HtXgJ/NGjwuFS5jiKlRYFbeQQBDGu7ZzegTYxYP3RR041WqcyXGbbPsYK/A2W62nWNhXMJKaOQ6oYcN5YY8bZdU5jzNvG2x46CPMaQHfYJlQQxE7t7CPB0NW2a7ptlzjIVYfj6K5trePZ1ncbxUtQcLGyoqDNS5DTQ9B182xLJrTdOFPEgO9845AngA1q3GzPIRBcru4Qg7URuzAIiVeH5AtECYEM49xkfdwbY+4a7+ZY+4iwtrCNSTNsEyMGfL0CfeYV1KRM/6yPDa3DYcOcadDlQYy9P0BcXYIpewkKaaysKHDhIwh8C4eYhUra2knxDuQQA20/8Kb6b6481jzXZazMftieZn0N1rHt9ulph3a6v9KDegUCb6Q+Gdvm2JttzY25Zbx9x9rcNr+6uePJ1CNUM5WpnT60VeY0+xNah2O2f35WDdhrDvjOPgoRBE1yhQ2Kl2B5WElR4PISdAmC0CpiXcf7zizo+rF7iYEOIeA7jch1XG2wQo2V2edQcTAjrFBLyiyCXEIgdsqW7bz9B7bMj7nDe2ATB/PJnVW/W3INanFgqxvRd52HnNM7XfhM+wT/qbYb94eLA+gWWKkzj5ykhhQLC8dKioJQcpQUdbkIUxMJ6+0+YqBLCMSWIX3wwDarRyHEWJnvwUccNPeF0LdXwFdwpZZ9bY67OeYbBJkhxsyx9h3nY9tsAixtWmFKnYccAsCn3a5pttA+1da+v10c2Mg9FblPkVtKGi8uRRRUdLn4XbT9iH2OD/mhd4UKfMRAlxAIce/df3D7XBsPHti24TpND4LNexAqDsBuuOrjakIy1XMLAfATXbHu1PsPbp8bd3PMN4y3Y6xDRdixbW7vjE+hob6EQMosGpPQabbgV4fDvn9eHLQRO102Oik2IyV0sBisnCiwhQ5CBYGvEOhD9YeEClxioEsInLRtn7PfNfcd3Dl3XpehMvsUKw7A7iFo3oRNQmLSub0CvqLLZ8xrmmNvjvtQ4uAYftUGfT6XUCEQZMgsOS4uXNM9m30JrcNRYxe4/mGw1EJascmxxUuwERE5H3g5M3fZlap6ueO4bwbeC/ygqv55te2ngR8DFPgw8KOqOgnVtHKiwJcYQdAlFnwz4HOGClxiwDQqNoN08ta9jncB9z60a+4c01A1PQjebm5ozaCHeYEA/mEEX6MzhBAIHfOa5tg3x308cbCRkGmEPuIMOkRASOzb51hDONim2ML8tE9wiwPo9h40jzPxGbeYYlq5BYGLZfMSiMga8ArgPGAPcL2IXK2qH7Uc92vAtca2M4CfAr5KVfeLyBuAi4FXD9T9VlZLFGyar9lv8xLYBEFXToANn+VeXao+NVQQKgaaBumUrQ9Y+27DNFRdT7Fm37rEAbiTEmG+5oEv3gYnsxhoCgGbCAgZd5MhxUGNj0hI8dJAWq0H32lz1iI3Ds9CWw0OcNfhgG7vQfM4Z38jvS45BYGLEC9BiHdsgpwL3KKqtwKIyOuBi4CPNo77SeCNwDc3tm8GdojIIWAncHu/3fVntUSBB76CwCUGfNd994kHdoYKOvIGQsRA0xiduuWL1vfR5J6Hjl9vI+Qp1uxnSFJiTdODEEOMEIC0UEyX+PIdd9g49jV9i4Oa0CTPkNBAaGGt1DnztvO76m9AWJEu8PMehJDd6xIgCFbZS1BxBnCb8XoP8ATzgMoj8Azg32CIAlX9rIj8BvAZYD/wdlV9e+899mSlRUFbjfwaX0EQu7pbaqigK2/AJgZMQ2IaJdMgnRZgnGy4vAdd4sB8Tz41D0yaCWI1MeWFc3oFQoRAzLjHiANzrLvyO3J4Z2qC8gMiij6lrNDnqgMB7d9FCPdohYQOatpEWJ+ia+7QDLNpevcSHJXO3BEPThaRG4zXu1V1d/W37WbTHNjfBn5eVY+IHDtcRB7OzKtwNvAF4P+IyA+r6mtSO5yDlRYFXbSVyq3pSwyAv3egK1TQ5hmwGaRT1u4/tq26S93Z8Vh416ET19usjdS9D+1av/59B3du6FOIOADHTRmcT25OAp44fZKo2nIzXOIL3ELAHPtQzHFvCjIzz6PVawDe+R0mzbn9XV6c0LBA6hNr83Orv3NtbXkXiwJnuAvacw8gLHTQJFkMQNCYhwqCBfcS3Kuqj3fs2wOcZbw+k/kQwOOB11eC4GTgQhE5DGwBPqmq9wCIyJuAbwWKKBiTLi9BjCDoVQxAq3cgVAzAMcPUFAO1EDh1bSuwtfr7CHcdeWjDe7nnyAmctuWL3HnoxPW2anHgCiu0iQOwJyU237PTtRuIr6FJCRG4PDFgFwOnGY+Ks/GfUY/9aWv7Nwi0euxNUVZTj3tUSAGc+R01rqx8G6FJgqEiIDTjve34pkgFu0Cwfg891v8At0Aw8Z1eaxI8U6NHQbDkXA+cIyJnA59llij4LPMAVT27/ltEXg28VVX/QkSeAHyLiOxkFj54GmB6JEZlZUVBG12CwMc70IcYgHbvgG+owE8MzFNvtwkEsBuoEHFgvpe2G7PLYLhWReuKOfve7GJDBD5eAd+xnzETBjavQlOU+YZxvPM7oDWE40Umb0DOp9P6+9ds1/d76BJS0C0QYN7TAulCoHntDfSwHkeTHNNvp4qqHhaRy5jNKlgDrlLVm0Tk0mr/FS3nvk9E/hx4P3AY+Cdgt+v4oRHV/otWTIUTd5yuT/zS5wV5CUIW1oH4giK5Egl9QgWuJ1SbQdp1+qcB2HvHo+f23XXkofWn1nuOnADMhMH6fuPvex46fv3vOqwAx8RBjXlzrrG5emF+HQZf2lzOodMJ+xYDLmpRdueRHXNjX49715g3x9ocZ9vY9rEUbYgQiBUBLiPU/O6Z+H4Pm+NkHSNLbNuV/5KLmOmbMbkaMZ+J+Xm8/omvurHFRR/Ntkefpaf/4guS2vj0pT/bS9+mTvEUNAiZYhi7wM5Q3oHwUMExajFge10LhNk5x9zddTgBNnoN6r7URqqZbwBuz4H5XmHjjTklqczWtknKLIIQMQDdY2+ycezBHH9o99Y0czxC6kpAS/KdJ7mMTq4nUNvxze8huL1YEJEH4xGKiSUmobYmpyBoYxm8BMvOyosC20pkttexS+/6LFkaUp54SO+Ai12nf3qDcbrryEMbjFxbrgHMhxTM99B2U26+/xqXJ6FJ103Mp8hQn2IAwsbebNM3nADtM0PAL4QDaa7mEG8NhAkBnyJQTZrfQ3B/F33KeoNf7kGNy6DbxEJw2CazGID239KCJxeuPCsnCnyWRoY4QZDLO5BrmmFM7kCXUbJhCoPaOJnCoO6L6TWAdnEA9psyzLt2YxOdUgzN0GKgeaxNlNnG3vQauDw1XfkdYBcINV1hHB+PTooQcIkA30JQtimdtpobZp+6BJS3OKhxTJ/LnbdhMrQgKF6CxWDlRIFJm5fARWxpYghfyTDVOwDx4YIumk+sbcYJmPMa1P01DVVNm0AA+43HFgNuO76J7xNnbjEAcUIsVhhAePInuEM4EBfGCY1Fx1aD7CoG1Zy10fw++oa5QhNk50IvNiMeMs8+YBZObOItFEGwCIjIs4DvAY4wq6fwl6r6Ot/zV1oUuOhauxzyC4K+vAOQXxCY59kSEJvGqe6P6TWA+ZBCTfOGDG6BUBPqsmy7SYVWHQyZWlgTO+YuamFg9sMmDCA8vwO6Qzgp5PLYgF0EuApCmUIV7AIhVRxAu/cAWnIzEqbbNvEJ9XSJuxWderiIPFlVL65fiMgrgCIKQnDNNuhVEGT2DsBw4QIXpmFqxrmbXoO6v7aQQo3NewDtBr0pGHyfUHyePH3EAAw33m35BXWfcuR3QHcIJ4TQJ8rQz6YpAmIKQsXmwPiGXryqJyYSkvORKgiKl2BSbBOR72JWhvlMIKgk1kqJAjUWRHKtgmgjhyAYou4ADC8IXGGE+tpNA1X30eY1MN8T+AmEJikioCZEDMB43oEmzTBC3beu/I4ulznMi62cyWSuzyyHxwY2fi4u2kJdKeIA2r0HMJ+T0WbMbYKhr4TPmhRBUOgfEfkKVf2Ysek/Ad8HfC0zYXBZSHteoqBSHV8NrH/TVfVXQi60CLQlF84d28OaBV0LGPl4B6C/cIGLWGEAOMUB+AmEJk3B4JuJ7hOPbnsCjZ1imEpXbkfdT9/ET+gO30D7HP8uQkI3Zv9qcnhsZsyLhZBptZAuDqBdIDTJUVwotjS0jdgaERA3S8Qb7b8WxIS4RkTeCbxEVT+jqvtIKJncKQpE5ApmSzs+FbgS+H7gH2Mv2Gj7fODlzCpCXamqlzf2S7X/QmAf8COq+n6fc33pSjC0eQmiBMGAyYQwnCAw220aJ8BqoIAgcQBugdAkRQSs9z1ADMB4gsBFlzAAd+InzIsDmBdbOV3CsUmDseGbZq2HZpIm+E2rNfueo+4GtK+/kEJoMmjfgqCQla8Afhz4WxF5C/Cr9boKMfh4Cr5VVb9ORD6kqv9NRH4TeFPsBWtEZA14BXAes8UlrheRq1XVXI/6AuCc6t8TgN8HnuB5rpOu1RBtXgLbQiUpgqDvZEIY3kDZYtw2AwUbvQbgFgfQLhBq2oSCz9Q0nwS1NjEA4wkC33EPDeHEhG98CAndmP2rSc3laFbpbBaC8pk9YxMHNs9KmzgAt/egxmXM28RCSlEv32TCVEHQq5dgxVDVh4DfFZFXMQsVvE9EXgO8TFX95uUa+IiC+s63T0QeCXyO2ZKPqZwL3KKqtwKIyOuZLSdpGvaLgD/WWS3m94rIw0TkdOAxHucmY1vgqDb+fQmC2GRCmMYTq2tGAsyvuNj0GsC8OIB2gVDjOyfdxDVdLVUMwPAeAls56hBhABtDCmAXB5D/hu767HzFAMTlzvhOq62vHZqTARvrQEC3OAC/Ylw5qnm6rt9FySGYJqp6APgNEfl94AXA+0Xkf6vqb4S04yMK3ioiDwNexmwBBwVeFdhfG2cwS4Ko2cPMG9B1zBme53biuxSyLWyw3kakIOij9gBMw33dlmMA8eIA5g2FSyTY6Jqzbpu61pawNgUxYLt+2zRRyJfbkYKvEDD7uH5uzxUi63Zd4QSznzEhBXBP9wS/ZZ5z0YcYKF6CcRCRxzALJTwWeBTwAPA/gDyiQEROV9U7VPWl1aY3ishbge2q2n539cOWBdIs3+U6xufcWQMilwCXAGzfajcgNnFQewnawgY2kZAqCHLVHoA0A2XeKFOL68C8MID5ZYDbxAHMCwToNvRduOawh+QN1KQKAptxSm3TJ+kT7F4DGCZ0Y17PxFcMQJoY7sozqK8dOq3WRxyA23tQk1Mk5K7+2aTkEQyPiHyI2dTDzwAfA24G/i+zEPvHQ9tr8xRcJSIPB94JvA34e1U9COSqYLEHOMt4fSZwu+cxWz3OBUBVd1MtS3nCrjO0bSpi24wDW9igZm7aoYcgSF3ICPpLJmwap713PDpaGJjtmf00DRXQKQ6gWyD44hIC5rXXj/XwDkA/gqDenqvaJMwLA3AnfUJ/oZtm2yYpiZ2QV8T65mQ0PSvNfIy2fIOaNu+ByZBFhEJCBT6CoHgJeuEZwK2aacljpyhQ1QtEZDvwlOqivyEin2EmEN6mqp9JvPb1wDkicjbwWeBi4FmNY64GLqtyBp4AfFFV7xCRezzObaVt1kGbl+DYMbP/UwTBFMMFOY1TjSsRDuLEAdgNu00otAkAk6mJgeYxfQkD6E76XG/DQyC0ERq+GTqXI1UYQPdMDh9xAP4CoU+KIFgYHgHcmqux1pwCVT0gIl/ObP7j5ysjfAHweyJymqqeG3thVT0sIpcB1zKbVniVqt4kIpdW+68ArmE2HfEWZlMSf7Tt3Jh++Kx50PQS2PIImuQQBEPPLugyULmFAXTnG8BG42ATCOvnBoYSXJXupiQIUkgRBuAWB5Aetmleo8kY4Zu6DZcwAIKqdILdawD+4gCGFwg5S4YXBuG5wCtF5OMce2i/M7Yxn0TD04B/FJF/Aq4Cfl9VXykiroog3qjqNcwMv7ntCuNvBX7C99wU6tCBj5egSdNL4CsIQlY2hH6rE/oaqL6EAdApDsBfILhoK3nrKwZgeEGQMu4mTWEA7Qmf0C4OYogN3/QpBtrIVaUzdX0P6E8gxM4oyFFBtJDMb6vqx0TkK5g9tL9aRE4E/h8zkfBuVfVeSEN8whBVEaHvZPak/njgz4A/qKcELgon7DpDv/ncWcXH2kNQ/+8SBV1eglRBELJ2AYwrCIa4ZjMZEeaFQRumQfOteW8rgzuVcc5xfdt1m+NsG+Mu0eUrEnw8OLbPakxB0DVm5niZ49Qck2aYxZaU2Vb3IbRypK9QSJ1WGOIdaBMEv/dNf3qjqj4+qTMWtj3qLD3jRS9MauOTL3hRL33LjYjcykwA/Lc6rC8iO5gVHLwAeGLI+/Aqc6yqKiJ3AncCh4GTmM1GuE5Vfy7wPYzHpsrwNwRBMomCIHbtAhjPUKU+ucZ4DaBbIIQsfuOqiT9FQVC3kSOJDuxhG5dXxiUOQsM1TcYO37TRVvcBwqZ4dtV+sHkNarpCC02GqCGQSxD0iRyFTfs3dR+4HDQrGv53Vb2XmSc92JveOWoi8lMiciPw68C7ga9V1f8IfBPw70IvOEWSvQQWQgXBaVu+6C0Idp3+6fV/Mey949Hr/1JIbaOt/y5DcNrafq8FbtpwtXHq2tbJCoLUtnzeg2tcT1m7P2qlQReu9myfS+7vfijN65j9Mfs6F/YwBNOpW744l4Nhm7Fx8ta9TiN60rZ9k4jdL4IgWDVU9SFV/V3gK5nN2PtHEfkVEYkqKuLjKTgZ+D5V3fDrUNWjIvLdMRddZHzDBhAmCGCc6YY5qNtMmbZotlNj8xrUhHgPmsfbmJonxqfNHDUMwC+XA+LzOboExVDhm1hSpnjGVox0hRR88g76YAqCpNDOYBUNVfWXW/bdHHKxRcLlJbDRVpwoVBBMIZkwpf2hQgomKZ6DKSUTxrQfW6THxFVYCtyCK4fnYMjwTSq+C35BWClpmJ+hAO0hhZrQ0EIMsWKgeAmGp/eKhstOV4JhG7aaBDW24kSrIAjM6/QhDKBbHITQJgbqfsQy1FjX1+pLGIA91yCVEDEA06wUWeOz4FdIKekUcQD5BEKKZ6AIgmEZsqLhUhKTXNhWl8AnbACLIwjaDG6XITWv15cwMPsRKw6WRRCY18wlDGB+XENDNS7aPDqLWCmyiU9RqBivAbSHFExSBEKOEEGIIIithFmYY5iKhqtMa0lji5egK2xgEwRTEgO+xtU8rsuw9i0MzD749t9H1AwtCJp99xVeqXR5ZLpCNb7iIDaXo+5jCn0ItJBZCZBfGID/0tVD5wEUQTAOqvqJnO2tzJwNH9ruc21eAmgPG8A0BcFdRx6Kftquz207f6h5+fWsAXMczW2uWQXNaw0hCMxxs41d1/7U65vEzP6oqWcKdP1rY2xBkFM0uGYlQPvMBLBXhzxl6wNOwzlF9/wU+9Q3InK+iHxcRG4RkRdb9l8kIh8SkQ+IyA0i8m3GvoeJyJ+LyMdE5GYReeKwvXez0p6CZj6BDWuCocVLABvDBmYeQYggGEoM5OSuIw85b/CpmfK2J7M2Qp+0pz7e9bk+7yu3S7zNY5DClMI3sd/PPkIJYF+VMofXoE9CBcEyeAlEZI1ZzP48ZtMArxeRq1X1o8Zh7wCurur8fB3wBmaJgAAvZ1aO+Pur6sDDTSXpYCU9BT55Ba2hA+xeArDnEcDGpwObIMgx97rrhpjiGehiKl6DIdsccrx928rtMvfxsoS210Zq7Y1Ycnhamu8t1GMAbq+Bi7Gf0FdREFScC9yiqreq6kPA64GLzANU9UEjzr8LUAAROQH4duAPquMeUtUvDNXxLlZKFKjHu7V5BtoWPqppCxuYSYUuQZBK202ty6DceWRH0L82uoRBarGjXOIg9WnURxD0QR/CwGdcU8WBbwgnhlxCaJGFwdDiYIxrTowzgNuM13uqbRsQkWeIyMeAvwKeV23+UuAe4A9F5J9E5EoRGd/lU7FSoqANm60LCR3AvJfA/HGPIQjaxICvkY85d+pegz7d0316Y8xrdNHXLIhQcdB3Pkfu95mjvRzCwEbXU/ZQRjr2OoN6CY7C5gNp/4CTq1yA+t8lxhVsMee57H9VfbOqfgXwvcBLq82bgccxW1zwG4G9wFxOwlisdE4BtOcTmPiEDmD+B2PmEUBeQdDlHbCRe8553Z4tqawr1yB1dkLdTug5seTyDnR9Bj7FmEJyDXzxmfFRk+u6U5z+mWOKZ9eS4DGzEsCdY1DjO3UxloUQBPm4t2UhoT3AWcbrM4HbXQ2p6rtE5MtE5OTq3D2q+r5q958zIVGwsp6COsnQRqjdbC5CUnsJmnkEQwgC25NqiFfgniMnWP914Wq/7ck5x/oLvuPYtwALCc90EXJsbo/MkGsKTFEQxGJ7Lzbh5LteAtjDCD704dpPaXNBBUEX1wPniMjZVaLgxcDV5gEi8uXVCsOIyOOArcDnVPVO4DYReWx16NMAM0FxVFbeU2DSmU/QETqw/WjqsEGuJ6sQ70CXUQmpX2871lbq1uU5GNNrMOQyzyY5vDJmGy4PQtvYxhDiMYhtP4UhBEHsTI763BrX+hIuj0GTkDoGTXJ5DVY8d8CKqh4WkcuAa4E14CpVvUlELq32X8FswcDniMghYD/wg0bi4U8Cr60Exa3Ajw7+JhysnCjItlwy86ED2OglcNWHj7kphoYKXAYpRAh0YbbVfK82cdDm8k4VBmA3ZkMLgtzhGVvbIaGanMstp9J3Qm2T1OqcuZeqNvvUtvTynZawQZMQYQBxUxdziIEl9RIAoKpzSxNXYqD++9eAX3Oc+wHAFZoYlZUTBTa8kwwtdK1fniNsEGKYbEYpVAiYNyXfJKj6GiniIKcwmLoY8PW8uK61aMJgKEEQWp2zr8qcoWtM9E2I1yCXZ2CZBcEyU0SBB64kw5q2cqJDCYIYMeDzROI6xiUWUsVBLmGQQqoIM+kjRGNe1zdMk2NcY5lygag+EjZrusJavt4CV9JhKF1eg5xhgiIIFpeVFgW+Mw98MH9QdehgdsOe3WxyCYIUMeAjAnxpttUUCW3ioMuQjWXAcuVr9BGiaRMHfQqDWG/B1DwDvu30Iahsyy7n6LdvCKFJyREotLGSoiDnzAOTZm2CFLoEga8Y8BUCXU8iXe+rvo6POHB5DZrCoGYIgZDDO5BTDLja9k3uHNNjMIQg6LM41JDCoI+lqcemeAkWm5UUBUMTejMJFQShYiDGFWk7xyYUXPkIPuJgLEPm45GBtHyNEC9NWx5HlzjwEQahhHgLhqjO2UaIgQ2dzTHEyp+LThEEi89KiQJdyxcu6IvmTSNEDLgMT454pE+7TZFg8x64xIEpDKCfJEQbbeNt9q9JmxhIDdN0hWbM63eFZ2wGLmYRIB+DNkYxLoif8dE23XOKuRmFwhCslCjoEzN5p3kTj72RuASBjxjwEQIx8UhwPw3cZVn1DfzEgY/XIPcNuUsQjJWv4WrbVxz05TFw0XepbhtDVObsQ6Aus7cg1EuQK9RqQxQ8CoMWLBRRUOE7BdHGfQd3bpiBcOehE72nl5mYNwsfQRAiBmIFgE9btptB3Y8YcTCEMAgVBCliIMRT03ajbJsqes+RE4KFQY5yvlOe+hkz7dM3cTN2yeUiCApTp4iCRO4/uN1aq+DYDWlWp6DrBmwTBL5iIEUI5Ji7bF6neXMIEQc2r0Ef0xZTQjRm/12khGu6QjLNPrjGEPoTBjnIVYyrxje3w0coTC1xcxnp00tQSGNlRUE9HTHUC3n4wJb1WgUPHthmrWroovl00Zbg5iMIbManTQiklDz1ndvsEgi20ELTsIV4DWJuxiEJnCFioK+cjWbbrsROX88LDBOWaSOnGMg128O3tkZqOKFL+K9fN6PoH4LiJVguVk4UtE1HdLHpoGwoYGTjvoM7W/bud063M2neKHzFgOvmECICXP1vK8zUvEaoQGgTBy6vQawwSBEEi5qzEZKvMQQ56kCECAHb5+YzswPy52h0hQ36nM46NYqXYNqsnCjIxf4DW9YXRWqGEOzGYHZTsd1McoqBNiHQLlzCz2kKBh+B4CsOXE+8zae1rtiurwCDdDGQ68ktJWcjJJxgMsa0TxiuMmfbsT4JnF3Cqm38XOGqrt87TN9LEEoRBNOniIIQ9q9tWCkRNoYQagNaG0TzB13foO88sjFWObsxpIkBlxAIFQH3HzyWbdm1poOtfVMkuASCrziwhRS6vAbQnd0dIwZy3Zhjy8t25Wy0eQ2awmD9vAG9BbGCoM9pn662uopvdYW0IDw8GMqUBEEJHSwfRRREUOcVuLwF9c3/lK0P2OP+npnsG0RFBiFgGv0uuo61iQbz2l0CoUsctOUbuLwGkFb4yUcMdN2QY/I2QsSCj6iCdmGVM0+ji5hS3UPM9OhK4AT3LBmfRNi5fkXMJor5/k2Z4iVYDIoocLD5wGya4qb9mzi642hrXkHtLagN6Unb9kUn9cV4BWxCIEQAwOw9mHQlUDbbb4qELoHQFAdwzNB1iQPXjbmNVM9AjryNUHKEY2zhhKGEQY5pn33N9PCp0Nk1hbZLHEDeqcWLLAgKi8MookBETgL+DHgM8Cng36vq5xvHnAX8MXAacBTYraovr/a9BPgPwD3V4b9YrW3dim7q7tva/o4ZCVUIoektyCkM+hACTaPfRdfxTdHQFnqo+9omDmDe0LnEQUxSlo/ByZXAGZO7YWJL7gwNx3QlcXbVg4jFJ1SQIgbGmOlh8x7YxMGMjTkboVVIc+cQ2L6rZUGkQhtjeQpeDLxDVS8XkRdXr3++ccxh4GdU9f0icjxwo4hcp6ofrfb/L1X9jQH77MQlDCBeHKQKAR8RsP/Altb9OyzLRLvaN0WCSyDYvAc+oQWbOIA4gRDrFcidwNlGW66G2RdfQQXz4YSmMDCJ9RaECgJfMdAlBHI8Qbvqa0D7TI/mjIWUhcpyeAd87jW2708MIfkEJXSwOIwlCi4CnlL9/UfAO2mIAlW9A7ij+vsBEbkZOAP4KInELpm8HkJoeAtMTGFwwrYDG56SQ8WBy9jYhECbCOgy/jHnNQWDef0QgRASWmjeqGOTzVKFgI8ICA3f1MTkanSJAx9hkOItGFoM9OFGb5vx0VZjo8ZHoIZ6P0LeZ+yDR/EaFJqMJQpOrYw+qnqHiDyi7WAReQzwjcD7jM2XichzgBuYeRQ+7zj3EuASgK27Hh7V2TqvYAOOMALM5xiY4iCGEG+AjwA4HCgSmsLHdh1TJIQIhFTvQY3rSSR0CmHfCZxdxORquMSBTxjGJQxiCvLUxCZ2mn1tkrM6Z5O2hM6aru9dqEDNMbU1Rz7LEMJgDC+BHJ3lhRXC6U0UiMjfMMsHaPJLge0cB7wReKGq1nOrfh94KaDV/78JPM92vqruBnYD7Dr5rPYKRA3qZEMTW8KhKQyA9VACMBdOgO7pfqEhAZcQCDX+LmztNIWC2YcQgeAbXrB5D8B9s24SU+kxxFNjIzSPw5bc2fbdaXpbXGPV5jXoEgZgrwExhBjoqzqnT1sxlTpN6nH2zYEYUgjY2iweg0JNb6JAVb/DtU9E7hKR0ysvwenA3Y7jtjATBK9V1TcZbd9lHPMq4K35em6nzVsAG8sfN70GNfVNP9WoRImA/Wte13TSqM/QvJYpEkIEgm94oXkzdIkEH3J7A0KNf0g7roTOUHEQKwyguxpfbGXIPmZ5xHjkuhI7wR6iqWkrLuViTBFQKLQxVvjgauC5wOXV/29pHiAiAvwBcLOq/lZj3+l1+AF4BvCR1A7ZvAIuNngLGsIA2OA1AKwCIZRgIeAhAjYdnM+tcJZztrVnCAWzHzkFgivpLtfNMsYbkCOJ04YtsTMmFGMTB6bXoBlOsMfD3RU4a/oWA33P8uhqx1VrA9pFQgpjiYDiLSjUjCUKLgfeICLPBz4D/ACAiDwSuFJVLwSeBDwb+LCIfKA6r556+Osi8g3MwgefAn7c98JmkqFr6qE5LdEUC6a3wCUMgLkExLb4e5MuYxIqAmyGv4224+cEg3nNDAIhdAZDTdf6DK7zTFJEQGwip087MaEYmziwhRRqr4Erz6DqlbO/qdPt+pjlEZPf4Qrn+VbsNAkxrFPzAvQhDMqsg8VjFFGgqp8DnmbZfjtwYfX33wNWC6Wqz+61gy20CgOY8xpAe/y9i5wiYNN+j0INDcyQSbPtDSIhg0BwTXO03ei7hEIXsSKgj0ROk5RcjTZx4AopuKZ7+tKnVyBFyIXgaqctybOmbf2PQmERKRUNPWgLLcwlHjbEAeRL+AsRAj4CoJmda3uPzXa8REJmDwK0F0tKJcUTkO2zdbQX42nxFQdtIQVfUpIGQ4WAz2ceG6LzSfIEP6FQ4+PB8m0rhNDrmpQwQmGlRIEGeNLbKhs2kw5r4+jz5OxNS06AyxvgEgK+U3PajjNDKCYukdCnQDDpKsds4mswkkRAakIntApKM5l1/fCGpyWHOAB/gRAyjTBECHSJgFwJnm1t+YhR3/DDULjqWhTyIiLnAy8H1piFvS9v7P8hjtXfeRD4j6r6QWP/GrMp9Z9V1e8eptfdrJQoSKHpLaiNY6c4gCyGIkQIuIy7Y9VcJ6YoMtu0jQP0KxCgOxEvhugcjvUG/D5b1+dnTexstmkZK9s45RIH4F7Mq42QmQNTSvA0aSvKVRPitfJZbbRPbEXCusjlLejKJ7AtWb0oVAb9FcB5wB7gehG52qi4C/BJ4Mmq+nkRuYDZ1PgnGPtfANwMhNdt75EiCgKw1i2wTFW0GsQAYvICbELAJQJ8PAK2883kS9s5XQIhNAcB2kWCjR2BxzdJmdYZmtTZdk7XWNmEVA5xAPMCIZRcdR/6qNLZhavdLq+Vy2OVGubKJSruO7izeA3yci5wi6reCiAir2dWqXddFKjqe4zj3wucWb8QkTOB7wJ+FfjPQ3TYl5UVBT7LmdtCCC5hAMzXMSDOUMy1kSAE2gSAeazL4MOx92s73jyny4PgFEstoRafwkkmWZI4bf2y0PXZhiZ2xuZrNL0HseIA2stxm0+PPgl1MfkBobU5THLmd3QlB/t4FCAsvGXDNwnShxCvQcktAOBkEbnBeL27KoYHs5L7txn79rDRC9Dk+cBfG69/G/g5YHJLX66sKEjBlXjoelIOpc2YxAgBn7CB7RibUGgTCF0hhs7wArS6ztfb7ukpMUUExMzs6GrDOxzTIQ5gY5VNmK+02VUXAtKmC+b2BgR9B9o+V0e+T5cY7Zo+WhO62qgvoVVSTabgNeg9dHA0PFxq4V5Vfbxjn+1mYHULi8hTmYmCb6tefzdwt6reKCJPSe5lZooo6MCVcGh7OjbJYSSa12r2q+24eaEQFsY4vF28Db/vcT75B9AhEiAucbNJZHGn9X2Bwi2E4HCMx3RYX+9BjUsk+BKTGzBKgmeAYGgLbYG/UDDJ5WGwVbpsYwrCYMHZA5xlvD4TuL15kIh8HXAlcEE1FR9mNXi+R0QuBLYDJ4jIa1T1h3vusxcrKQp8QgcmbTMRusRBDCGJgl1eAVMMbNnnJwwO7ZQN58UIhJjwwvq+rpyMHBn+FvoSAb5PLG05G23hmByhhZrQUtw+xHgDUkt2x4TtvBKEO6Ya5xAK0L40eRuh4qCNrhCCWT57BbkeOEdEzgY+C1wMPMs8QEQeBbwJeLaq/nO9XVV/AfiF6pinAC+aiiCAFRUFLtrqEbQJg/rcmhCB4PNUGSoGml4BUwxs3tf+lH1459qG402BUFeDbBMIKeEFaBcIJjEJnF1tzh0XMcWzSwC01YboSuxsehBaczUCQws1IUl0TVJnB8SW7M6Rt9PWTkh4q8ubAOkeBZ/Po166vY2xvAWLPOugRlUPi8hlwLXMpiRepao3icil1f4rgF8GvgR45axqP4dbwhGTYeVEQaiXwKRLGNSkuo9DZg24xIBLCHSJAhNTINi8B+b1XQbMdox5XPPYtri6SS5D4Lpuk9Bpnim1IVzCqjlmQd4Dj9BCjW8SXRdJ0z0j6nRAvrBddHgrQiRAWCl0X4Hg4zXoEgYl4dBNVXL/msa2K4y/fwz4sY423gm8s4fuRbNaoiDD/cJm4HLQ9oQZIgbgmCCwiYG1vbObzaa9x24mR3fNbjJHdm1ZP+7wzrUNf5viwLxmlziYHTPfZx+BAO6bfGwip6/RiPEGhEwLdWEz/mY7od4Dn9AChE/9jGEMERAi0H3F6dAioUsgdHkOurwGfXgMypoHi8tqiYKMuAxc6LkufJ9Mu7wDbWKgprktpzgw34vLVe4SCM1zNvQ5YyKn7bpNUoWAT6KnLXfDFZbJEloAq0BY77NH7NuF1+yAzOt3pHro2rw2wTNDajoqm7atkbLeRCMPpIltQbEmPuGEQgGKKMhChqkvQGiCoX+ooE0QmLjEweGdaxvayykOmu/PVheiSWpSZ2weR9v5PkKgLdGzLbkzhziA8HLcWad+RuYFxIiA1N9j9kqeNZ4CoS9x0CYMhsovWIZ8gmWniIKRCXVT+yQRmsLAVxCYbNp7kKO7trG299Cc16Buv/7bVxxAd8Kh6/gmqU+ELoYQAu6cjmMGo5ncmUMcQGARKZOQKaCJZZ8hPMEz9HNzYQtzQXolTwgTCF3eAx9xECMMXJS8gtWiiIIGbTMQcl6jjRRjkyoIakxhAO0hBbM/LnFgvi/ffIK2gkqpxIZwUoWATRS0hWhyiQPoLiIF/UwB9UkKzSUEYoRDl9EPyYVJEgiB3oP9B7ZECQMXpXZBAYoo6J2QJxXfWLTPzIK1vYeixIBJLQzq9o7s2rLhOjnFwezYY3+3TQ3ti5xeG2j/bDa0bYxtjU0c2EIzvuLAPCYkia6JTTRErfmQKSwQ5z1Q6/fRpCvhsz6m2Y+QEEOoOAj1GriEQckvKLRRRIGFGG9BrEvb/cTTLgbA3+ikUAuLptegvqYt36Duay0MoF0cQHcuQR/em/jkwnAxYH4mTbFmjm2TWhy46kV01YnwyenwnQYK+QWA2S8bvkIgNLnTtc8V9uqz1LevOIjxGoQKA5e3YNFCCKJ+yb2FeYoocNBX3Bq6n2KadMWlc4UM2mh6DWA+pFD3xeU1ALs4gO5cgq7PwyYaYj7DPkWa6zNpS/Cs//cJKcz6SbVv/v10ucnX+5N5ZkeTuPCZ73Hdn5OL0Focs2OwHmMe14c4yCEMCgUbKyUKdNP8DbBP498kVAzANARBjek1qK/n6zUAuziAcIFgI7en5li7eTw2IZ+JmeBpCoP62mZoJrWIlHlsTW6vTM7pnrbjY4R0k7ZKntBd6rt3cZAoDGzkCCOElDouMw8Wg5USBTb6FgkxRgfsTzdtCWt9CwKTZkjBlmtQv67/Brs4ALf3APImG/rmI+QUaJA+88OWiBhaRMqnRsT6++hZKMfMFsid09HM4TBJKdbVmziweA1c4QSbMAjxFpSEw9Vm5UVBX/hlt6cbH8ibQxCCbYYCtHsNgLknspo274FJH8mGseKs+br5WaTO/LDVishVYdI8riZ3pU7bNZqkCAHIF8aBfJU8Y8SBbd2PWK+BrzAoSYeFJkUUNDi8Pe1JKacYgDBBMISXoEnbDAVTCNjEAXR7D2raREIMXUlIU/ks2oRB3c+msMo9DbSJ2VasQEud6QFpYsD2+fRR5rtLHPh4DVLCCTlZtGTDQhxFFGQitxiAYYxQbdBTjJjP1MWaUHGwfl5HtriLkAxk38+hua0PMWAb0zZhAP1NA20SIwSGmOnRfB3yuZj7hxQHPl4DZziho6hUireghBBWlyIKMhCbNwB+T6TNbTlc1HBMENR/5xIGTWLEAbgFwoa2M0w7ihUD0K+nxiUMIL1GBPiVlJ6d79ff1Jocx9oZZwZO7jVA2rwCXfu9wgkNYeAbRigU2iiiwEJICCFnIiGE5w/kEATmtpweA2BDQleIOID5MfIRCT50TVHzEQMwTOjGJzxjS+jMMQ302PlJb2HuWvZr5M2vyfE99hlvmzjI5TXwCid4CIMmU8ktOGXt/kGvV/CjiIIE+ppZ4NrWpyAw96XeUE1c4qApAsz3ahMI0L2gkO+xLlzT1vr6HHzxFQbgNw3UZ5ZHSsJh7lkeMHwIJ6bMd0hIIcVrECoMYr0FOUMIZTri4rBSokBl9uPLkb0eU3MAxhUEbWLAdlzszbVZzwDmp4G1eQja9rmIEQHmtXz22WZ5DJXcGZLQ2TUN1GeWR1/lpKcaSrMRKsZCQgo2r0FoOCGEpjAoBY0KLlZKFNTkEgY2UsMFrm0mfQoC2zm5xIFvSKG5ryZEJLTRNb5doYKaoWd7+CZ0tk0DbZvlMfQMD7Nfc+cO6DlrI0clz66QQowwyBFGaOITQliUGQhyNP5BYdVZSVEAacIg9LxY74CNoQSB7fwUcdDmNQA/70CMSPAZ07Zjcxue5mcRkwxnEwbQ7TWA9lkeXUa8KRpikzzbbtZTEQPN9l3f364Qjq/XoC3PwJXomRpGKN6Cgo2VFQWQ32PgW3c9JpENxqlDYJKSb2C7sQJOcQDdRj/E4Me007cgqLf1LQwgfZYH9CMCwD+XA8b7TZjXacs1gDCvgU+egbmvM7+gUEhkpUVBDCkL5sDwT0KpXgJbe7mEAbjFAcTlFvjSJij6CBXk/hxChEG9DbpneaTO8PB12YYIARi/SJdJ7JLiocLApE0YbCBDGMGkr3oFZebBdFl5UeDyFoRMS/R9gprKDINUUoVB3YZJWz36XLkFPp6FMQRB7Hi2TQF1iYAuodVnHDYkqRP6/yz6mn7rU33SRxg0cww2XL8tv6CFrhBCKXtc6HeNVAcicpKIXCci/1L9/3DHcZ8SkQ+LyAdE5IbQ8+cY8N36rNK2iIIgF7b3trb3kNc6Dpv3HZn7F3OMz7VTvTShMz5Sab6HtifyXOGXNrrG37bP9lls2nswiyAwhWfI52Oj2Sezz+Z7Mv827wvmw4T5YGI+jLi2t7I/v2etsDqMIgqAFwPvUNVzgHdUr108VVW/QVUfH3l+J7kXgfF52lp0QZB6QwX3e/QVByYhAsD3WqmCoG0lPtc5objElYmPUc4hEnyFWNv+PsRAW/uQ/ptpCoP6GuZ7NP/esk/X7xEpwqAubgTHSiHbqFdTLBR8GEsUXAT8UfX3HwHfO9T5+deKb6/NDvMCYNEFQc5rtr3X+gbbxyqQXWIgRx5HTL9jhYGraJSJj+G3GXbff77t2nB5B3LgI2BzfI/NzyHEa+AjDIJp8Rbs71kknFoKFS00Y4mCU1X1DoDq/0c4jlPg7SJyo4hcEnE+InKJiNwgIjcc2TubX2sTBj7egqiFYJZYEOS6dvOGaiOXOOhTDECezyG2DR9hANMJHbhEX07vQMhY5voN5RQGtm25vQUPHtj4vu8/mPnJaUkRkfNF5OMicouIzHmrReQrROQfROSgiLzI2H6WiPw/EblZRG4SkRcM2/N2eks0FJG/AU6z7PqlgGaepKq3i8gjgOtE5GOq+q6QfqjqbmA3wPYzz8qaRZWygpuNMWoQ5CLHaov1+W3vybzRhrjnuwTFFMRAs73U5EPwT+BMneERGrJxMYYYsJ2X63vcVia5mYDYXPYa/BMP+yR1BkKzxPEyzDwQkTXgFcB5wB7gehG5WlU/ahx2H/BTzHuyDwM/o6rvF5HjgRtF5LrGuaPRmyhQ1e9w7RORu0TkdFW9Q0ROB+52tHF79f/dIvJm4FzgXYDX+W2EzC7oi9RpVlMRBCa5l2JuI1dYYWqCwGw3h5Fsm/ZZ07fnoG9RVpPrs8gx9l1lkq1TRyth0DVV0TVFccNMhJbllcvqicmcC9yiqrcCiMjrmYW11w27qt4N3C0i32WeWHm3a0/3AyJyM3CGee6YjBU+uBp4bvX3c4G3NA8QkV2VikJEdgHfCXzE9/wYcqpwn7DBkV1bgpPRFoVcIYW+GWp2Qco1QmlL4BwSn5yQXJ9zH59F7mRaWzjBTD5s0hVGGIt7H9o1dheG4uQ69Fz9M0PYZwC3Ga/3VNuCEJHHAN8IvC+ppxkZq07B5cAbROT5wGeAHwAQkUcCV6rqhcCpwJtFpO7nn6rq29rO70IbEqjLWxDiTQgp3VrfHFKWeZ2il6BJrqetuq3cTKkoVNe1Uqoemvh4DWLxFR05xd4Qn0OulUNdyzHX//uGEdq2tdFWyGjZSh7LEc3h/bq3MettwyUs24LC0yJyHPBG4IWqOpmYyiiiQFU/BzzNsv124MLq71uBrw85fyq4kopg2NUOp0AuF3izzGzO9kIZa5ZHLmEA8bkZtvND+pOTqQuzJmaege+Y++YRxIQQCknsAc4yXp8J3O57sohsYSYIXquqb8rctyRWrqLh0R1HN2TsxuYWxNSBXzVBUJMreavGN+fAdW4Kizb+PmPVZ1ihrxDQmNNvc+TL1MIgxFtQM1bCYWED1wPniMjZwGeBi4Fn+ZwoM/f3HwA3q+pv9dfFOMbKKRiVtnXJY35sG6qUObwEzaTCVREEJjnjvs0x9HnyWnRBEDt+Yyzx3EdOSP3+p/A5pNCcstjML3Bhe3hJSZbuu17BMqOqh4HLgGuBm4E3qOpNInKpiFwKICKnicge4D8D/0VE9ojICcCTgGcD/6aq1vsBEblwpLcyx8p5CmwMORNhEesQ5Can56A59avtuBimOO65QwmpDCE6pvY55FpO3BZKaHoLxvAMlDUQulHVa4BrGtuuMP6+k1lYocnfY89JmAQr6SmAdm9BDlxeghimdkPMRV9eA999XUx53Mf0GJiegFUUBCa5PBehSXG2WQhmWNTF2CWPl6FGwbKzWqLAU5uZqjwku7erlvsqhgy6yPn+msZq0ZIJQxlSGAwpAmqmECrwJeWzcFU+TGFDdcOyQFIhgBI+qMgZQrD9sIsgcJM7ETGVRRr32FBCfa7PcUOySGPfJ+Yyyyah0xALhVBWy1MAG9YdDw0hhMb1UuoQrCJTMAhT6EMoOWdijOERgMXyCrhI9dwMsR5FodDFyomC3PgskxzDot8gYxkzw3wVx9w0SmOJ12Ua95T3Erv+xNjl2ttorntQmD4rKQpc3gLTLReb7Vur/WWvVjgEQ4mDVX1KrRnTM7Do425jjJUZc9BcLbGwmpScAg/a8g0O7RS27MtSUhOY1k1iKvSZc7BM452remQfLNM4+xDyWdhqbNjyCZaN03pcyEGOlnBMLKslCjYZHoJtup6ha1Y59E04PLxdNlQ1rKuSbbhc4A065caZo5b90AvmhGKOz6IXIuqLqQmDZR1nH9o+i3pc6t9tHTpIXcK6UEhltURBIEd2zM8Htm0bi9yL2pjtLYJAWMb6AzkYSxgs+7jG0BSy5uuY32+ZeVDom9UTBTuOrM/bdXkLbPRZ9TDkZjrUUsuLIBBijF8xXPkpY+qHSxA0vQSrEDooTJfVEwUepAgAWxghlaGEQNf1pygOfIXBqhmuvvIwVm0cwe/35/vbaLbVFjZwLYg0f5zXYaNTqhkuBqspChzeAhttIYQ6r6BONtxwTPXj77opt91kxxYDTaYqDroM4Coasppc4mBVxjD2NxcVCrAIAZuXYJFWRDy1TEFceFZTFDjoSjjs8iCYS6DW3gLXk+wiiYEmUxcHhXlKqMXN0L+3phiI8RIsklAoLBYrJQrEmH3Ql7fAFARHdm1hbe8h75vr1MVAk6mKg0IaZmb8sn62Y/zWrMbf2NaVS7AoYYLCYrNSosCHVG/B+nGNG4Dr5rpoQsDGMhuPZcIVSnCJ1mX8TMf2Crj2mYLA9BIsq0egzxoFhTRWThRs3n7o2PKhPXoLgA2hhGUw/m0Ur8HiYIYSViVEAMMJgq5aA839ZbZBYUqsnCjwIcZbYEs6NHMManxnJkTXQR+5ilfxGiwGRQzkxff32ikYFsBLcPLWvWN3odAjKykKcngLamGwcZtdGMAxY913xTJb+0MLheI1KEyFvgVByO/Zd7aB9VzHuixTzjMYdTGko1ruP5Gs5IJIPoQslLTxRzr7kR/aKRvjhDvXRithWl976Osve8ikMF2O7NrS6/cv5PfkOrYpCHzrErgIXQq+ULCxUqJA5Njsg83bDRW549iTtGsFRRtu9X7sxz33wzcM9BgiYehrF2FQGJqpiIH6eBtdgmCM0MFx26ezZkZhPFYyfBCDmUdgCyPMbz+2YFJ9A2gWOAL3TWMIl38ztNEXJc+gMBR9CYJQEd12fGhiYUyIwHy4KRRCWClPAcAOw0MQ6i3wies1PQZNr0EzrOCi6VHo88l+CM9B8RgU+mZRBUGIl2CqyYddlBLHi8PKiQIYVhjM9s3fCHzFwYZ2ehYJRRgUFpVlEQTz++P2bWDHuDOSCovFSoqCvugSBm3iIGauch8CoW+vQREGhdwsqiCwsWiegFO2PjB2FwqZWSlRsGaUOe7DW2Db5ysOII9AyEURBoVFYBEEgfOcwNkGiyYYXCxLNUMROV9EPi4it4jIiy37RUR+p9r/IRF5nO+5Y7JSoiCGVGFg2z87pv2GMAVxUIRBYRXJLQhivQQhCYZlOuKwiMga8ArgAuCrgGeKyFc1DrsAOKf6dwnw+wHnjsbKiQJz2o2Pt6CNHMJg6uKgCIPCVOnj+zOUIEitSVAYnXOBW1T1VlV9CHg9cFHjmIuAP9YZ7wUeJiKne547GisnCpqkhBEgXBgsojgowqAwNZZNECxLaGCFOAO4zXi9p9rmc4zPuaOxknUKjtt+kAcPhNV+N0sgm2sjNGkunGRbJ8G2uNLs2Fn7dX0DG201D9owl3SOIfX8Nkodg8LYDJFDENR+h6cxtrzxhgefFk7Y5rEUbINTxyxr3ECOHp1bDTSCk0XkBuP1blXdXV/Ccnzzpuw6xufc0RjFUyAiJ4nIdSLyL9X/D7cc81gR+YDx734ReWG17yUi8llj34WhfUgNI7jyC8DvB+zyGsyO7/YIxE5pTKF4DApTIPd3pY/v9Zhhg1K4KBv3qurjjX+7jX17gLOM12cCtzfOdx3jc+5ojBU+eDHwDlU9B3hH9XoDqvpxVf0GVf0G4JuAfcCbjUP+V71fVa/xueia+CXj+IQRIFwYuMSBDZ+QAkRUR0sMJ4y1fkOhMBVy/wZK6GAhuR44R0TOFpGtwMXA1Y1jrgaeU81C+Bbgi6p6h+e5ozGWKLgI+KPq7z8Cvrfj+KcBn1DVT6de2HSLubwFc7QIAxO/5ML5bW03hSl6DfoSBsVbUOhikb0EheVBVQ8DlwHXAjcDb1DVm0TkUhG5tDrsGuBW4BbgVcB/ajt34LfgZKycglMrxYSq3iEij+g4/mLgdY1tl4nIc4AbgJ9R1c/bThSRS5hNB2H7qce3XmTH9kPsr5ZU3rC8coO2/IJmDoEtfyAkz2B2fHeuAbBhyWYfUvIE+soxKPkFhSmTJKY9QwdTXg7Zl1GXTR6IykN9TWPbFcbfCvyE77lToTdPgYj8jYh8xPIvaOpF5V75HuD/GJt/H/gy4BuAO4DfdJ2vqrvrmNDWE2eP5C5vQZOY/AJI8xjk8BqEMEWPQaFgYxm9BDlCB6VGQSEnvXkKVPU7XPtE5C4ROb3yEpwO3N3S1AXA+1X1LqPt9b9F5FXAW0P7d8K2A9x/cGaZzdkIprdgjh1HYP/sRmJ6CyCfx8B17LFzJLvHYGoUb0FhigzhJbCx6DkHZTGkxWKsnIKrgedWfz8XeEvLsc+kETqohETNM4CP+Fx0bZOfonbORmjQlngI8R4D17HHzsnrMSjegkIhnaFyCRY5vLAsJY6XmbFEweXAeSLyL8B51WtE5JEish5nEZGd1f43Nc7/dRH5sIh8CHgq8NO+Fz5p2771v3OEEUKn/yyjMOiDknRYMBk7dDC138cycOra1rG7ULAwSqKhqn6O2YyC5vbbgQuN1/uAL7Ec9+w++hUTRmjSFUaA6YYSYpMH+yxsVCgsKyEPCIXCUKxkmWOXt6BJX2EEGNZjsKgUb0FhGVjm32hh+VhJUdCkjzCCjzDIhc+6Cd5tRbpJi3u1sChMYdZBoTBVVmrtg81GRcOTtu3jvoM7rcflCCP4kCuM4MOiz0goFMaiCN4F5OhRZF9Jaoxh5TwFJ2/du/63bxjBZBXCCMVbUCisNvV07cLqsXKioI3UEsiQL4zQhzBYRBdnySsoFAqF4VhJUeDyFrTRmnTYUu3QhyGLk/gKg/LUXygsH67S7YVCzUqKgibJtQsaLEsYIYYiJgqFQmFxWSlRsEWOPdGb3oI2YsMIXaSGEYagGPhCoVBYLVZKFACcsvWB9b/HTDq0ERJGWLXcgkKhYMcslpZCPeOqsNqsnCiIIVfSYZNF8BYUCoVpYZuybGIu1FYohLKSomAob0GT4i0oFAqFwpRZSVHgSx9TFJtM3QtQ8goKheHo8gJE0VJgzVmYrWfKYkjTZaVEwWYj0dDHW+Dd7gDegpiZCGNRhEQhN2t7/X9jXSza4l1lteHCkKxUmWOAU7d8kbsOnQjMhME9Dx0PzITBvQ/tAjaWQD5h24H16l59lT92lTZOxWcVxUKh0M7mfUeK0F00jh6FB8Mf8Aor5inok9wzEWzkDjWUvIJCoX9cwjynByBkBkJMASNznZj64amwnKykKDh1yxfX/w5NOuyrbkGTKYYFCoUxyRlCyM3Qi40NMQOhrH+wmqyUKDCLF02NFC9AERCFQhhTzisYOtnQJLRWQR1+LSwPKyUKTHy8BT60rolgkCuEsAjkvOFO+emwMDxjfR/GFhF9JhsONQPhtJIxuRCsnCg4zRADXcSsibCBHkIIU5/CWCisKm0hhGXIK+iiTuAuLDYrJwpMXN6CZWLsBZIKhdzk8haM/fSfSqlsWOiDlRQFXd6C0CqHsSGEJsULsJESOihMiSFFhM3gJ3sVAqZJF9IQkZNE5DoR+Zfq/4c7jrtKRO4WkY80tr9MRD4mIh8SkTeLyMMG6TgrJgo2WxINY70F3iGEFpY5r6BQ6JOpegvGDiHEYuYVmMmG5gwEc1pioZMXA+9Q1XOAd1SvbbwaON+y/Trga1T164B/Bn6hj07aWClRYBLiLUgiMa+gUCjYGcOTNLa3oOuYZl5BWwghJa+g1Cro5CLgj6q//wj4XttBqvou4D7L9rer6uHq5XuBM3voo5WVEwWnrN0/t+3UDoEQU/p4Vcl10yyhg8JQLJK3YFFCCHeWpMNTVfUOgOr/RyS09Tzgr7P0yoOVK3NsctqWL859ec3SxzZ8yh5v3n6ol+zeNo7smIYbslAYkrW9hziyK/23FlLKeGpljzcf2JiPtGn/pkFDk/c8dPz0ErWPHOXoA8l9OllEbjBe71bV3fULEfkb4DTLeb+UemHjGr8EHAZem6vNLlZSFJyydj/3HDlhwzZzTYQacz2EXBzdpr1kBfclCMbI0C5egkIIuYRBTrbsU2cZ8c0H1DoraG3//DTkpsF3HdfGpoPiTHI+fGDLenL0/gNb1pOmHzywbT1v6v6D272Xkl8y7lXVx7t2qup3uPaJyF0icrqq3iEipwN3h15cRJ4LfDfwNFUdrGTmSoUPtjCvnn3rFixqCGHIBZEWfYpXYXHJISRDvr8L/V1PCCGUZENvrgaeW/39XOAtISeLyPnAzwPfo6qDGp+VEgUmttyC9X1Tc4X1xND12n0oXoJCLFMTBrlyC3ymJ6YkHMZSkg1buRw4T0T+BTiveo2IPFJErqkPEpHXAf8APFZE9ojI86tdvwccD1wnIh8QkSuG6vjKhQ9OW9vPnQ7fm28IwcwrKOSjCIJCKlMLJbSFEUKwhRFy4RNC8OWuQyc6E7fvPLJjZUodq+rngKdZtt8OXGi8fqbj/C/vr3ftrKynAI55C0JKHzfJUa9gqqyMO7WwVKSKy6G+97lnInR5CzYQGEIoD0Grw0qJgi0ye7s+anVVQghToXgJCjmZkjDoM4wQcoxvzYKuBZJseQVltcTlYRRRICI/ICI3ichREXFmd4rI+SLycRG5RURebGz3KiEZQ1vNgkVNNrSRM58g1UtQBEGhDxZdGPjQ9XyT6i0IXUrZRnOmV2HajOUp+AjwfcC7XAeIyBrwCuAC4KuAZ4rIV1W7fUtIznHq2lbgmLcgRwihZkfLugdjkHKzGSocUARBoU8WRRjYyJV0aJKScGgLIbQlG5YCRovJKKJAVW9W1Y93HHYucIuq3qqqDwGvZ1Y6EjxLSC4jvSyUkkDJJShMnbW9h5LEwRDf8dxhBJPWmQiGtyA1hFBTllBebKacU3AGcJvxek+1DfKWkOwk2zoIE6HricX3JljCBoVFYghhMJUwQlDSYQe+IYSSV7Ac9DYlsa0EpKr6FHKw+bmCfzUicglwSfXy4HGP/MxH2o6fICcD947diQAWrb9Q+jwEi9ZfWLw+L1p/AR7bR6P3633Xvv3gn56c2MyijWUWehMFbSUgPdkDnGW8PhO4vfrbu4RkVat6N4CI3NBWtnKKLFqfF62/UPo8BIvWX1i8Pi9af2HW5z7aVVXbcsQFD6YcPrgeOEdEzhaRrcDFzEpHQmIJyUKhUCgUCvOMNSXxGSKyB3gi8Fcicm21fb0EZLWW9GXAtcDNwBtU9aaqCWsJyUKhUCgUCvGMUuZYVd8MvNmyvVkC8hrgGstx1hKSHuzuPmRyLFqfF62/UPo8BIvWX1i8Pi9af2Ex+7zUyIArMhYKhUKhUJgwU84pKBQKhUKhMCBLJwqmXELZ0Y/O64nIY6vlM+t/94vIC6t9LxGRzxr7Lpy7yAh9ro77lIh8uOrXDaHnD91nETlLRP6fiNxcfYdeYOwbZJxd30tjv4jI71T7PyQij/M9ty88+vxDVV8/JCLvEZGvN/ZZvyMj9/cpIvJF47P+Zd9zR+zzzxr9/YiIHBGRk6p9Y4zxVSJyt4hYp4BP8XtcqFDVpfoHfCWzua/vBB7vOGYN+ATwpcBW4IPAV1X7fh14cfX3i4Ff67m/Qder+n4n8Ojq9UuAFw08xl59Bj4FnJz6nofqM3A68Ljq7+OBfza+F72Pc9v30jjmQuCvmdXx+Bbgfb7njtjnbwUeXv19Qd3ntu/IyP19CvDWmHPH6nPj+KcD/3esMa6u+e3A44CPOPZP6ntc/h37t3SeAl28Esqh13sa8AlV/XSfneogdYzGKFPdeU1VvUNV31/9/QCzWS9nNI/rkbbvZc1FwB/rjPcCD5NZrQ6fc0fps6q+R1U/X718L7OaI2ORMk6THeMGzwReN0C/nKjqu4D7Wg6Z2ve4ULF0osCTyZRQjrjexcz/4C+rXHBXDeGKx7/PCrxdRG6UWWXJ0PNzEnRNEXkM8I3A+4zNfY9z2/ey6xifc/sg9LrPZ/aEWOP6jvSFb3+fKCIfFJG/FpGvDjw3N97XFZGdwPnAG43NQ4+xD1P7HhcqRpmSmIpMpISyL239DWxnK/A9wC8Ym38feCmz/r8U+E3geXE93XCtHH1+kqreLiKPAK4TkY9VTxC9kHGcj2N2U32hqt5fbe5lnJuXtmxrfi9dxwz6nTbwvq6IPJWZKPg2Y/Og3xH8+vt+ZuG5B6vckb8AzvE8tw9Crvt04N2qaj6lDz3GPkzte1yoWEhRoBMpoexLW39FJOR6FwDvV9W7jLbX/xaRVwFvTe1vrj7rrO4Eqnq3iLyZmWvwXfQwxrn6LCJbmAmC16rqm4y2exnnBm3fy65jtnqc2wc+fUZEvg64ErhAZ3VGgNbvyGj9NYQgqnqNiLxSRE72ObcnQq4750kcYYx9mNr3uFCxquGDKZVQDrneXKywMnA1zwCGWPCps88isktEjq//Br7T6NsYZap9+izAHwA3q+pvNfYNMc5t38uaq4HnVNnb3wJ8sQqH+JzbB53XFZFHAW8Cnq2q/2xsb/uOjNnf06rvAiJyLrP75Od8zh2rz1VfTwSejPHdHmmMfZja97hQM3amY+5/zG7Ye4CDwF3AtdX2RwLXGMddyCy7/BPMwg719i8B3gH8S/X/ST3313o9S393Mrsxndg4/0+ADwMfYvbjOX2AMe7sM7Ps4Q9W/24ac4wD+vxtzFyVHwI+UP27cMhxtn0vgUuBS6u/BXhFtf/DGDNsXN/pAca2q89XAp83xvSGru/IyP29rOrPB5klRn7r1Me4ev0jwOsb5401xq8D7gAOMbsfP3/q3+Pyb/avVDQsFAqFQqEArG74oFAoFAqFQoMiCgqFQqFQKABFFBQKhUKhUKgooqBQKBQKhQJQREGhUCgUCoWKIgoKhQVDRN4mIqX0a6FQyE4RBYXCAiEiO5jVWPjs2H0pFArLRxEFhcIEEZFvrhZf2l5VpbtJRL6G2bK+76yO+WURuV5EPiIiu+sqfIVCoRBLKV5UKEwUEfnvwHZgB7BHVf+niPwO8Beq+n9F5CStFr4RkT8B3qCqfzlilwuFwoJTREGhMFGq2u/XAweYldo9IiI3Ak9U1YdE5N8BP8esBPZJwO+q6uXj9bhQKCw6C7lKYqGwIpwEHAdsAbaLyKnAbZUg2A68klnN+NtE5CXMvAqFQqEQTREFhcJ02Q38f8DZwK8BNwNvq/bVAuBeETkO+H7gzwfvYaFQWCqKKCgUJoiIPAc4rKp/KiJrwHuYLfn8tQCq+gUReRWzFeY+xSzMUCgUCkmUnIJCYQEQkW3Au1X18WP3pVAoLC9FFBQKhUKhUABKnYJCoVAoFAoVRRQUCoVCoVAAiigoFAqFQqFQUURBoVAoFAoFoIiCQqFQKBQKFUUUFAqFQqFQAIooKBQKhUKhUPH/A/QhWjy1fQH8AAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1, figsize=(8,6))\n", "clr_plot = ax.contourf(xv, yv, potential, 30)\n", "ax.set_xlabel('x/a')\n", "ax.set_ylabel('y/a')\n", "fig.colorbar(clr_plot, label='$V/V_0$')\n", "ax.set_title('Potential in square')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Can look at electric field magnitude too!" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "Ex, Ey = np.gradient(-potential)\n", "E_mag = np.sqrt(Ex**2 + Ey**2)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1, figsize=(8,6))\n", "clr_plot = ax.contourf(xv, yv, E_mag, 50)\n", "ax.set_xlabel('x/a')\n", "ax.set_ylabel('y/a')\n", "fig.colorbar(clr_plot, label='$V/V_0$')\n", "ax.set_title('Electric Field Magnitude')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "def init():\n", " # Plot the surface.\n", " ax.plot_surface(xv, yv, potential, cmap=cm.coolwarm,\n", " linewidth=0, antialiased=False)\n", " ax.set_xlabel('$x/a$')\n", " ax.set_ylabel('$y/a$')\n", " return fig,\n", "\n", "def animate(i):\n", " ax.view_init(elev=30, azim=2*i)\n", " return fig," ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "ax = Axes3D(fig)\n", "ani = animation.FuncAnimation(fig, animate, init_func=init,\n", " frames=180, interval=50)\n", "ani.save('rotate_azimuth_angle_3d_surf.gif',writer='pillow',fps=20)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 4 }