{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from scipy.sparse.linalg import eigsh\n", "from scipy.sparse.linalg import eigs\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", "plt.style.use(['science', 'notebook'])\n", "from scipy import sparse" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Create a meshgrid of $x$ and $y$ coordinates" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [], "source": [ "N = 150\n", "X, Y = np.meshgrid(np.linspace(0,1,N, dtype=float),\n", " np.linspace(0,1,N, dtype=float))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our equation is\n", "\n", "$$\\left[-\\frac{1}{2}(D \\oplus D) + m\\Delta x^2 V \\right] \\psi = \\left(m \\Delta x^2 E\\right) \\psi$$\n", "\n", "where $D$ has -2 on the main diagonal and 1 on the two neighbouring diagonals, $\\psi$ is a vector. Firstly, we define our potential in units of $m \\Delta x^2$; in other words `get_potential` actually returns $m\\Delta x^2 V$" ] }, { "cell_type": "code", "execution_count": 100, "metadata": {}, "outputs": [], "source": [ "def get_potential(x,y):\n", " return 0*x\n", "def get_potential(x, y):\n", " return np.exp(-(x-0.3)**2/(2*0.1**2))*np.exp(-(y-0.3)**2/(2*0.1**2))\n", "V = get_potential(X,Y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we construct\n", "\n", "$$- \\frac{1}{2} D \\oplus D + m\\Delta x^2 V $$\n", "\n", "Let $T=- \\frac{1}{2} D \\oplus D$ and $U = 2m\\Delta x^2 V$" ] }, { "cell_type": "code", "execution_count": 102, "metadata": {}, "outputs": [], "source": [ "diag = np.ones([N])\n", "diags = np.array([diag, -2*diag, diag])\n", "D = sparse.spdiags(diags, np.array([-1,0,1]), N, N)\n", "T = -1/2 * sparse.kronsum(D,D)\n", "U = sparse.diags(V.reshape(N**2), (0))\n", "H = T+U" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Get eigenvectors and eigenvalues" ] }, { "cell_type": "code", "execution_count": 103, "metadata": {}, "outputs": [], "source": [ "eigenvalues, eigenvectors = eigsh(H, k=10, which='SM')" ] }, { "cell_type": "code", "execution_count": 104, "metadata": {}, "outputs": [], "source": [ "def get_e(n):\n", " return eigenvectors.T[n].reshape((N,N))" ] }, { "cell_type": "code", "execution_count": 109, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 109, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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teZ7H1NQUTj31VFl9j4yMIBqNypbrDw8PY8WKFbJUoclkEvF4nMn1axQ57mWuLrcCuC+PnfVZAH1E3Ldco7IU3NxarRYqlQo+n080SeW4THymTqfD9PS0yGjlW4G73W4Eg0EWB1cEdlUqCMdx0Gg0UKvVUKlUUKlU1MWTHYBcrI9SXq9aX2jhF6+U9tU8F0btUupnlM+w5Xvs4s98vCrnsRgrNyHNzc3weDy0b2BulWq1WnNyUWa/PsdxePfddzE5OclUlAVgxq3GKNVgldK2msawHGrpXJY71bqn5ODvEq/aihm2UtpkU837ab59Zwtc1Go1mpubkU6nEYtlVKHk+2mxWKBUKuFyuZBKpUTfW6EhJPvzIyMjzMDlgbkla5BaWC2R/qvlFir13EsdXJjhzKVUr0CtEFhthP5Y8RynZP9ZoVDA6/UWbEP+jsfj4Hm+aC5U4d/hcBgulwuJREJW+3wCLY7jsHLlSvqYVquFUqmEx+OhYQFA5toTr8/09LTouLAvICNaGhkZoXuezEU5BzNuNUY13ZIL4cZczL6Fg0o6naZunWIDTywWQzKZRCgUKqoGJX8nk0n4fD5ZoQBErj89PS1rICTSfo/HI9k+HA4jGAziyJEjku+R5zMZ848dOwa1Wi0acAtdk0QigT179sgavCORCPbu3StyZQsfPxt/TT+jUlZkPktGYFLvAV7Zs0dSHETUoGQ/q1h7omSdmpoq2if5O5FIIBqN5mQFEgqksv/P3oZwOp0YGBgQ5V9VKBQwGo2w2+2iRN8cx8FkMiEWi9H7LVv+L1zFTU5OQqVSoa+vjxm4P8OMWwUhgw75W85gKfybzCizN5uLzT5TqRQmJiYKthEe83g8UCgUsgZm8vfAwEDR9yB838lkMm9MV6GBfP/+/aLZaKH+peT6+Qz222+/XXDgEf5NjOCBAwcKthH+HY1GMTk5KVuuH4/H4XA4ZKk80+k0EokElEql5GBJ2hkMBslzBjJqyaamJlntXS4XPB4P1q5dK+ua7N27F5s2bYLBYMhpE+2Tl5hYim3btkm2OX78ONRqNU3KXIxoNIo9e/Zgy5Ytsl7/3XffRXt7O9ra2mS1z4bnebS3t+P9998Hz2eqYhAjpNPpoNFo4HA4kEwmRdevqakJfr8fDocDHR0dIoMm/JsYXo/HA6vVylJ1gRm3ipJMJmWXICn0dzgcRiqVyivBzzcwk7I0cvsX/i/VnuM41NXViWarhdo7nU5EIhHZcv2DBw+iv78fer1esv3s7CwcDgdOO+00We/xzTffxGmnnYa6ujrJz4xI6s8880zJtkBpcn2n04mRkRFs3LhRVt9erxc9PT2ywgxmZ2cRj8dlKV+BjJq1qalJ1jWJxWIIhUKyzgPISPD1en1e5WtU8Hc5+2hk9eZZqUX9aHk5JyuB0BVYLgqFAqeddhpef/11+P1+NDY2UiNlNpvh9Xrh9XphNptF9zVxUZKAfXI8X//vvPMOzjzzTBYHB2bcKoparcZFF100rz4OHTqE1tZWtLe3S7aNx+NwuVyy5fqDg4PgOE62XP/48ePo6OiQlQ2BbIrLlesrFAqYTCY62y+GRqMpWa5fLffrXwJL9dqVYoAqYaxKhRgqIJNogExKifeBqKynp6ep+5g8r76+XtQ+e+UmfD+RSITVgwNTS9Ycwpt2qcH2/2qXat5ThfoWqiTHenIfT8gsjVbOiq/SVNoYEnejUOXIcZlQAJPJhGg0SpWS5HVbW1sBICflmtC48XxGQTkxMYFQKPQXraJkxq3GKGXQL9VAVLP9Uh30gaW7UimVUj6jUj/PWvj8S/kcF2PlRl4XAFQqFVpbW5FMJhGNRum58DyPhoYGKJVKKiQhj5FVWDqdhtfrFb3f7PeuUCgwPj7+Fx0mwNySNUipX9JaodRzWarvc7lDVgXpdFpSAEX+j0QitP3cZ5WblWQ+eFZqEX7zZEEBkt/vRyQSKXi+wr8TiQQSiQSOHj0qS1zl8/mQTCYxNTVV9DoU+1ulUuGUU06hxzQaDTQajSgVFzG6Wq0WiUQi7yqtra0NU1NTVBgm3J8Tfk8ikQg9d4vF8hfnomTGrcao9ux6sQuKCgeEVColS64fj8dFcn2pwSSZTMLr9SKZTEoOyn6/H7FYLO+gle/vaDQqO7t+JBJBKBQSKU6LnUsoFMLx48fpvkyx9kSJ+dZbb8m6JrFYjIqdpAZlAslULyXiicfjOHToUE4+1I3IJCX2WmXcGBIEzIA5kMkFKnxt4eslEgn6XgudLxngiVHQ6/Wy3mMgEIDVaqW5OQsJsIr1NTU1hffff1/0+iTlls1mg06no589CREgCbKF4QMcx6GpqQnT09P0MxK6JUk70s/bb7+NLVu2oLm5uSZW2AsFM24VhOM42Gw2APJmddkDCs/zCAQCNKZGaoZIDMQHH3xQ8DWEfxPjQKoISD0nkUjgnXfeyTnHfOdODEmhigP5jOTevXsLJlkW/i2U68tRYsZiMSrXlxqAYrEYFeZI9UsGj2QyKXIXCQdN4XOI3JvMyov1SwbQ5uZmmEwm+lihcyflV9avXy/rmuzbtw8bNmyQdS5TU1NwuVyyVZ4vv/wytm7dKlJLZmclqRSnn356wceOHDkCo9GInp48G3xZhEIhzM7OylabTk1NobGxEU1NTXJPVQTP89BqtTh69CgCgQBd5XIcR7OVzM7OisRbZJV28uRJ+Hw+UaJlpVIJjUZDQ29I0mqhcROu6uLxOMbHx9Hd3f0XY+CYcaswMzMzAKQHSeH/wuM8z4tufAAFKwSQNnV1dbJez263I5VK0bIdUs/Zt28f1q9fn5O5P99zbDYbPB4PNmzYAI7jYDKbEAqGCrZ/4403sGnTJlnJje12OyYnJ3HGGWfI+gxKydxP5PrFBk0hXq8X3d3dskMBwuGwrMEWyMj1GxoaZJ13IpGAWq2WleUfAFWbCjNhFEL4OclloQZMYUhAokkLjgdUrtJDBITfr2q0zwfHcVi7di3sdjt8Pp9oMmAymeDz+RAMBtHQ0EDHAlJ6KJFIwOl00oki+Yy6u7sxNDSEQCAguheExo1MyAYHB9HY2CiqlrGcYcatwmzevHlez08mkzCbzeju7pZsm06nceLECVltgcxsNZFIlCzXlzMgqtVqnLv1XNExg9mIeCT/wFPKl6vWvohyXbWMyrgkCcQ1mWzM3I/kriD/868vjkikFMgqP5lMwuPxUONDVnYAMD09DZ1OR+8zhUIBq9Wat26jSqWC2WxGMBgUucoLTZ4dDgfsdjtWrVpV89dqvvxl7TAuAYR+czmU0rbUvktpv6pvLitEXJP5AQCNvjruKSmqZYCW+4BQCYId1fvM1YnK9LMYKzcCx2Xi1sLhMM1VSYyPRqOBXq8XpYMjj5EMJSSDEXlcqVSivr6epm3LPmdhP6FQCB6PR9T/coUZtxpE7k1Xzpetmje00KgJ/y9k4Grly1Ur51FNqjVhytc+XeKoMtUx91OMBnfxx1f9lbxUWtWEbCuQ3JXJZBLJZBKJREKkbuQ4Dq2trUgkEojH4wDmvs/Nzc1QKpUIBoOia0vKaBH3JXk9ILO6Ix4cr9crMmr5RCbJZBLf//734XZLXNQlDHNL1hjluOvkzirL2UeRM9BpdVqRUcsm32OlnkupK85qtK0FyHUg+7Jy1KZkwCXxVFJiolAohFgsBpfLJUsYlU6nYbPZoFQqwfM8LMhkwJFySU515K7Epjoywd0rpvM/J5vwnxPcGDIpXdF89hocePYtyfNOJpOIRCJ48803JYVbQEaQcfDgQZEbMd9zgFxXoPBvkkKO5zMZSfR6PcLhMA1hIBiNRgQCgRw1pEKhQFNTEz0ufD3i1rTb7TAYDKKK3sLzJf384he/wHXXXYeGhgZ5F3uJwYxbDVLNlYScvrPVmNkDaPYXWysjnkmj12J2xk6fQ7Lrk9Ijwv6y//b5fDRhcbF25O9oNEoVf1J9E7m+XMVpMBikCXql+k4kEojFYti9e7esvhOJBPbv3y/6nLLbZfPyyy8XFfqQv6PRKAYGBvImZSZ/k98k9GJ4eFhW3+l0Gh6Ph+YglSdxKc70CrGBy7dqCxvEf6eUgC4KdHV1SZ53KBTC8PAwNTbCNvmec+DAAaxZswZWq7WgYIv8nw+e5zE+Po6BgQHR50iSX9tsNphMJtFKzGAwIB6PI51OQ6PRUMOkVqtprFswGMxxPXZ3d2N0dDRHGJR9zqlUalknWGbGrcIMDQ1RWTxQXEKf72+/3w+FQiHaHC7WBwAa6yT1OuS8hIGh+doBc6u2t956q+jA9qErLi26aiPENcDRo0fp8+LxOCYmJopm1yf/k5gut9stOdCS8xYGIJOZar6+icGSqzgNhUJoaWmhCYiLnbfP58P09DRVkEr1vX//fqxdu5YOoPnakt+lKkjfeOMNbN68mYYZFGNychIejwennXaarL6dTidOOeUUaDQaHP6QFjPtQPtM8edIuSClCBdISRrVAebTu6C3FVdQclwmz6OcRNLAnNq0lPym2bS1tSEUCmFiYkKUWkulUqG5uRkOhyMn+XRHRwdGRkYQiURE96xOp6P13kwmkyjsRavVwmq1wuPxiFyb5LtB2jHjxigJtVpdUs0n4f/AnAKqra1N1nP27NmDDRs2FM3cT/6fnp5GMBjEunXrZM0+X3vtNZx11llFkxuXsr9/4UcuourJt956Cxs2bJAlZXc4HBgdHZUt1/d4POjs7JTlbnG5XAgGg7IVp6Ojo6ivr5fVdzKZLHkAVavV1OBLUWiVsNAIJ0WauHR7uYaNrN6UKfHxQoatmgiNwnzo7OzE5OQk/H4/zf7P8zxMJhMCgQAikYio+rZSqYTJZEIwGBTtpZFz6ejowMTEhCi4HMgkG6+rq8Pk5KQoAFz4WeWrEbecWL7vbJEQVtotB5/PB5VKhZaWFlntFQoFzGazrBkYKZ1Rqez6iSYtYlp5AxqQf+9NDqUOKqW2X2w38HIg+5rPJwRAnZhLqjy9AuiamHssaJrbXytEVAegTVt09VYpY1UOpCip0+kUpcQyGAxIJBJ0NUZQKpWoq6uD0+mk+5pA5j0YjUbU1dXB5/OJSugQ92V3dzdGRkYQCoXoc8hrLveVG1NL1hjlDORyB9BS2pZzLqVQ6rnUEqVc71qhlGtdzc+lVHdk93h5rxPNLS03LyplDIlxMZvN1N1OtgSIQSL5JoWudYVCgc7OTsTjcZEwiLgoDQYDxsbG6GuQ38RIjo6OIpXKLIHJ+0in08vauLGVW41Ra4N+sXOJlRHO5OvWwjJeXkaJarSvJQNUSRJNmQ9H7SyvwGcp14Vc66EztECFx0pecBpB6e3C/H0UEO/wPJ9X0FRov1q4+pHaP8/3v0qlEmX7aWtrw+TkZI7hbGlpwcTEBK2RSMYEvV4PrVYLt9uds1Wg0WhgNpths9loNW9hv52dnRgbG4PRaKSpupb7yo0ZtxqjnNXVYqzcEk3aeSd9X24GKHtAI3FNZCAVPpbv71QqhXA4TF1PxQZMkvDZ4XCIjjdsyOwdxrSZvapkW+ZDSv46CZvNRgfXYgO01+tFNBrF4OCgrIE8nU7jyJEj0CnPLnp95isiKZVImxav/eppAPnT3PE8jzfeeKOo0If8HYvFMDg4SNWm5eynu91u9PX10ddXqVR0ry0UCokMksVigcvlgsvlAsdxdBWnUqlgMBhEib5J/42NjZidncXExAQaGhpEK8K6ujoYjUY4HA56DzDjxqhJsmeVQkFKvkGRzFITiYQoALTYAJpKpeDxePImcW6APAFGPiJtWkR/I5brFxtAhXJ9OTPmYDCIEydO5GTXLzQjj0aj2L17t6yBPJlM4uDBg3kfJwgHtnQ6jddee03WAEoMSqEBVPg3cWmNjY3Rx9Z94jwA+VfUW//PRwEAwy8eKDoAZx8jeU0LPc5xmUTL9fX1IJFaPgugF4dtlYUxNPd3Oau2qA7YsWNH3smR2+3G4OAgzjnnHFl9lZILNR88n0kqfvjwYbrnRoyVVqvF7OwsLBYLPa5QKKDVahEIBKirEshcd7KCs9lsiMfjIqOoVCphNBrhcrlgMBhExlyn00GtVmN6ehodHR3MuDFK47333qN1lEpxW5C/iVx/fHy8aDshUrNP8n8qlUI6nabBqFKzzXg8jsnJSWokhO2M2vzGzSPIJ0xcSvUecRsiLBEmiC5WHYDjMhJ8i8Ui+T45jkMkEqFyfamZtd/vx/j4OE4//XRZ1+TgwYPo7e2lm/f5zoXgcrkwPDyMs88uvqIhlJLw2W63Y2pqClu2zGXlSMSlXcV928+QlMmPj4/D7/dj9erVck4bx44dw4oVKzBcpM30CsDik9Vd2ShTmVg3IZVc9c+3L6vVip6eHpw8eRJarVY0gWhqaoLT6RSFxgBz7kThMZ7nUVdXB5vNhsnJSdTX14tWaQ0NDYjH46JK3GTMMBqNUKlUOHDgAOrq6phxY8inp6cnpxyKHJcF+Xt8fBzJZBKrV6+WbAtkgnjPP/98WcmNp6en4XA4ZJcy2b17N0499dSc2SpRSWYjNGzZx7MNnF6vL0mu7/f70dXVJeu8R0dHYbVa0djYKNmWzF7lzsgVCgVNg1RLFPpMFoqjFxlRfgRY9RjdqMXK93KNefY+lxSlti9EY2MjxsfHEQwGRZMYk8mESCSCYDBIhR9ARllpsVjg9XpzXJccx8FoNMLtdtP4OHK8vr4edrsd4+Nzihzy3Pr6ehw6dAjpdBoOhwNtbW3zfl+1CFNLVhir1YqGhgbU19ejvr6eFji0WCyoq6uD2WyGyWSCyWSC0WiEwWCAwWCAXq+nxQpJwKharaYDqVKphEKhEJW/AaorQCml70KGrdDjpQwU5Qwqy20/rxihFaVZNc/KylpBnudlh4PIpZhLcjHi3CoJiYV1OBwAxKsqhUIhqgkJZAycXq/H9PS0qNgwx2WKlqrValrXjXxnSakc0k86nRYZxiuvvBLBYBB33XXXAr7zhYUZtxqj2oNtqYawWoZz3RUXVKVfYHkYrFLQyHBHlkq519CXJyZ/esU8T6YKLNbKTWh40ul0TvZ/hUIBpVIJr9crctsrlUq0trYiHA7TdHiE+vp6uvcpPFeO42gtwenpafoYMOex+Kd/+qd5v6dapbZ8K4ySV2KltC/1y1moffZAKrVqE7ZTzE08S3qf1TKyywF/HaAtUfEvLPq5lHFklSbk+FwX+OhGLYwvTor2rH0+H2KxmGQqOvJ3IpGg6eKk9s/z9ZNOp2EwGET7xi0tLZiamsr5DpPjwhRdPM/DbDbD7XbD4/HQFG3EkGm1WiQSCSSTSdE+GzGW0WgU8XicZkUh2Unmk06s1mHGrQapBTdjISoRAlAqlVqJFVI/ptNpUTBtobakfTgcllRi8nxGrh+Px0WZ3Yu9RiwWg81mg9frpceyn0eOBYNBBINBuFZpEdWVbtwA4ODBg3nPJxqNIplMIhAIyB64K4k+MicMKaaSzDZshHx7vEJVKRFLkc9Gam+bfG8Siblkc8LHpMRQhNHRURq7BmQyj1itVrhcLoRCIZFwq7GxETMzM6KE1ABopn+SRFz4Wt3d3Th27Bi8Xi+sViv9fBQKBbq6umimkoaGhmWvlASYcasqchWSwv8TiURJcv10Og232w2tViv5Gl6vF5FIhAaOSp1PLBbDxMQEZmdn6WO9ECfT9dRnqiPLxWeZU82pNq/Avt9LS/CTySRisRjeeOMNWdeShDBkfwZA/nindDotW3EajUZx8uTJnITP+Z5Lzpu4i6TERel0GpFIhO6PSAmRhKmbyqH3b7Yi8c5ETr92ux2RSERUrbnY+5y5oCFHpUgoxyVZqK9SyDZwZ555puhxh8OBsbExbNq0SVZ/NpsNq1evzklsLBey8jpw4AA0Gg01LEqlEmq1Gk6nE42NjfQ+VSqVUKlU8Hg8MJvNIreo0WhEPB5HLBYT7aUplUro9XoEg0FRrCRxazY0NMDlcsHj8UCj0cz7/ql1mHGrMG+//XZORdx8A0ShgZQE/pJqu1KDSzKZxPj4OFQqlWRb4pog5e3zvX72bDN7P6DSezu9vb2S7zMQCGBkZASbNm2SNcs+ePAgenp60NzcnLetEI/Hg2PHjmHr1q2yznffvn3o7e1FU1OTZFsSCiCU6xdjz5496O3tlRUKYLPZoD6vR1a/xciXw5RMrOrr5fmbiTHKt99WLQqt2oRku8GFVGoPrRQMBgP6+vpw4sQJ6PV6AHP3JQkFEMJxmSwm09PT1B1Kzrm9vR2BQACzs7M0FADIrNJaWlpgt9tFYwLPZ2LqrFYrnE4nFaktZ5hxqzBnnXWW6CYs9QtEYoxOPfVUWe1ff/11nH766TSlTjFIbJTcUiYkuz4Z5E5uFls2uXttxZBjJEgOPDnlWoDMrJf8SLHQA1ylkcqhmP0ZZbvram3vTeiS9FmAZkduG3srYAqW1m+hkAC5VMoYGo1G6HQ6mv2f9G00GhGLxeDz+USrMZ1OB4vFAo/HkxOwrVKpEI/H4fOJAwhVKhXa29tp9QHhdoRCocDKlSvx4osvyq6EsVRZ3uvSRYBI9gutFKQo9Tml7KPNd88tu/RIuSzkDP8vFVdj/slHJSYkclksl6QQf4FqQ4uxciOvq9VqoVKpRNW0AdBYy+xQAL1eD7VaTbcTCGRlFw6H6X4geU9arRYajQbj4+OikjdAZt+upaUFAwMDeOGFF6r4bhcXZtxqjPkaoEqyEOfi65bn5yz1PGrlGlaLYi5Jl0TsutTkopRrd/hDC6susreW1r7UFV4hKm0MSayb3+8XSf6BzPeOFCsm/5OyN6Q9Oa5QKNDW1oZEIkG3MkhfCoUC3d3dOZUEOI7D6aefDovFgnBYon7QEoa5JWuQUgaXhVy5CVnIFUA5q9m/BOZT1kUo7BG6JoWCHbL/m31ceEwf0VZ8tVUtRjdqEf7Nu+B5HuFwGKFQCIcPH877vshv8pNMJvHuu+/S75CUGCvf42azGStWrKD3Z3Nzsygwm3h7WlpaRCEK5DUbGxupSra1tZUeJwVup6enqbCMPFZXVwetVovp6Wk0NzfTx1KpFAwGAz75yU8u3AewwDDjVmNUe2Cej+Est9hoPoSDK6HQQJFIJJBOpxGLxWQNJIlEAqFQCF6vt6jSlOczSZbj8ThsNpusQSsSicBut8uSyUciEYTDYRw9elTWeYfDYZrwWarvNbgw73WVWrUV4vnnn8+5N0gMFlBYvBPr24GVo7mrwXJcktn7bZXCXwfU+TN/G41Gel/H43G6nywl9nK73ejp6ZFUyRb6n+d5fPDBB1Q5S9o0NDTAbrcjFArBYDCA53kqCpmcnEQgEBAlTTabzfB6vfR+Fb5WZ2cnxsfHEY/HqWAFAK0+4HA46L51KpViaklGaYRCIVHMlNQglf0/ySEnV64fj8cxPj4OjUYja7ANBoN0tip1XoFAAMePH4dKpULrlz6MaiUPfO655+jfhdSN6XQab775piyVZzQapTFjxdoStWkikcDMzEzevrL/J0ZWuK+a3Z4MGkStlq2MK9Q3qaZMBqBCbfkz2/Nex1INm3CCcfHFF9PXGhsbQyQSwfr16yX7eP6fS3vNYkitAEt1SeaDZOyYmZlBMplEZ2enrOcRRWO5OUXT6TROOeUU7N+/X1RNm9wjLpeL3jc8z9PXcTqdaGpqEhkyo9FIBSlCd6bJZIJer4fT6YTRaBQ9x2KxIJFI0CKoy71QKcCMW8UZGxuD2+0uaVaXb2AuRa4vjIsq9loKhQLhcFj2bHVwcBCtra2wWq2o0NZFXnru+iTW7YkWXLX6fD588MEHOP/882X1d+DAAXR1deWVuefre2BgAJs3b5bV9759+9DV1YXmZmktOgnOXblypay+x8bG0NjYKBkK4ELlK02PnqHHqndrRzVZbSrlni8FjUaDlStX4sSJE3QFCMwFbQtDAch3oaWlBbOzs1AoFCJD1tXVheHhYQSDQVq7jeM4KlaZmprK2cuzWq2IRqMYHR2FyWRixo1RGqeccsq8MjbMzMzAbrfLluu7XC50d3fDYpH247hcLgQCAdmz1bGxMVgsloyvX3C8UvttwpVDMXdsOa7axRi8FpNy3ZH53MNyeelvtBUbQQq5JB3NmXCA+a7ahK5JQin3ldBIzAetVksLlCYSCeoiNRgMSCaT8Hg8ouwher2ehgKQdFxkn02n08Hr9UKn04m8L6SsjcfjyUnFpdfrwXEcHA5HzVW2qDTL2+m6BClV9FFNQYmwfSX326rNchaUzK6pvjqx1IlB9v6YrYYrqIxuXMS6QBCHAszOzoq2AUgoQPYKjtQlnJ6eFn02CoWC7tkJXZA8z1PPAqkFJ3xeT08Pfv/739PakcsVZtyWAcv5BiXUyntcbMOpTFXeJUmM0/CW0gb+5Dwn/kOrgcE1mZ+x+SdbKYlSVmI8z1MXXyqVQiqVonu1JEdlLBZDNBqlIiKixgwGgwgEAggEAtSYENe/TqeDy+Wir0P2cUlKPeHkkuM4UegAOabVatHc3IxUKkVXgsK+gMxWR3aariuvvBKTk5P4xS9+UcnLWlMs73XpEqSc1VU1++Z5HmOna6mYRI5LcqpD/P+K6cJt5ajiFtug1AJCt1M27oZcl1s5cHwm5yJRkEonfO4r+7WG5BX5rijENfnqq69SI0VWSVKCLwB46aWXAJSulBSKkcj+K8fNFRQVQqpyC/O5kr7a2towNjZGM5uQ72ddXR3sdjvGxsaokIS8pjCZMskGRIxiX18fPve5z1XwCtcWzLjVGNV0SwLVXwFlGzYgIwsvZuAA4Oi5WrQ8O513kCEZGIqVJxEeC4fDsNlstFZWsfaxWAyRSAQDAwOSylQA8Pv9GBoawtjYmGR7kjh59+7dRfsUtt+3b1/ePglnobpxSaOjo3SmPzk5KTlwl0O2YWt2zLm98012KqGSFHL22WfDZrPB7/dj3bp1sozT888/j0suuaTs951OpzEwMICJiQno9XpqgBobGzE9PY1gMIi6ukw6FRKYPTExgUgkIgoRqK+vh8PhgNfrFZ2fw+HAf/7nf9L75/zzz8fVV1+NU089FUajEeFwGH6/n75uKpWCVquFwWBANBrFHXfcgcceewxerxebNm3CfffdhwsuuCDnPdx33334xS9+AZvNhv7+ftx55524/PLLc97vww8/jAcffBAjIyNYuXIlvvGNb+ArX/kKfdzv9+Mf//Ef8dxzz+H48eNIpVI45ZRT8K1vfQuf+tSnRH3ddddd+O53v5vzGp/85Cfxxz/+seA1Z8atwjgcDvj9mWm01Gyw0EAulOtLtQ8EAjh69GhOCZZ87ZPJJOLxOF577TVZA3kqlYLD4cB6dMl67/kMG4EYOHMACJjztxkeHs47wCSTSSSTyYLlSbL/T6fT1G2U/bjQXSNUkZpMpqKDHDkWDofR1NRE63IVa+/3+zE+Po7TTz+96PmSn3379qG/v5+qJbPbHzlfB1sbYPXOXTN3g6yPRpKgKZPN46yzzsLIyAhisRjWrVtXsH0hMUkt77cRDl1ej+6H3VAqlbKy/FdqQtjX14f9+/cjFJorM06+t16vF1qtlk5WtVotFAoFHA4H2tvb6XmoVCrodDrMzs7SgG1inEwmE775zW9CoVDgiSeewG233YYXX3wRSqUSzc3NmJ2dhVqtpsaNiFauv/56PPvss7j//vuxatUq/OxnP8OOHTuwZ88eUdWEO+64Aw888ADuvvtunHHGGXjiiSdwxRVXYNeuXfjYxz5G2z388MPYuXMnbr31Vmzfvh0vvfQSbrjhBvA8j69+9asAMjl0//mf/xlf+MIXcMcdd0ChUOA3v/kNPv3pT+Ohhx7C1772tZzrt3v3bpHCs6Gh+M3PjFuFEaa6KSTHzz6W/X8sFqPVdaUG8mg0ivb2dtFgm92eHAsGgxgaGsKWLVtkDeTvvfceVqxYgaAMMUkxwyaXs88+O+/xQCCAQ4cOyS5PQq5JW5v0SOv3++FyuWj8kxSTk5OwWq2yQgFIQUgiFJBCoVBApVIVVbFVer8tm5ObteD+S377gDk3GXMx8rkjF1KsRHJNlqN+nK97XKFQoLOzE8PDwznCkPr6eszOzlLjRs7ParXCbrfnZDHp6OjAxMQEDAYDnn76adjtdvzHf/wHDAYDPB4PTjvtNFx11VX49a9/jUsvvRRKpRIrVqzAxMQE/H4/NW7vvfcefv3rX+ORRx7BF77wBQDAhRdeiA0bNuDOO+/EM888AwCYnZ3FAw88gFtuuQU33XQTAGDbtm0YGhrCLbfcQo1bMpnEbbfdhmuvvRZ33303bTc9PY077rgDX/rSl6BWq9Hb24uTJ0/CYDDQ67Bjxw5MTEzgvvvuy2vczjnnnJIUnsy4VZjOzk460yoHp9OJUCgkW64/OjqKuro6NDZKa8FJ4KacCgKAeFMayLiMdFFZT81LIfdkPpm2ELbntjCQ1Zuclcp8xSRymWkHWu3S7QDxqrF9pnjbUl35lboHhQVKY7EYzT5CXJVut1sUt2o0GpFKpeD1ekUhRkajEXq9Hm63Gy+99BLWrl2Lnp4eOJ1O1NXVQaFQYP369XjxxRfx0Y9+FEAmYbJOp8Pw8DCSySSUSiWeeeYZqNVqXHXVVbRvlUqFq6++Gvfeey9isRi0Wi2ef/55xONxXHPNNaL3c8011+CLX/wiRkZG0Nvbiz179sDhcOS0u/baa/Hoo49i9+7d2LZtW8Ex6Mwzz8Rrr71WkWvN1JI1SK0oAwEgdon0iqaUVVuxtExDZ1ROpl1L17BaVMolmY9qTCjyrdrylbQplamO3HtwRsb8crEmTWq1mrochSpGi8UChUJB60GS48T9JhSZ8DwPjUYDvV6PEydOoLu7WyQ+6enpQVdXF06cOEH7IZ6jlStX4ujRo9BoNBgYGEBvb69oBQUAGzZsQDwex9DQEABgYGAAWq0Wq1evzmkHAEeOHKHtAOSU7MpuV4jXX3+9oDu8q6sLSqUSPT09+Pa3v41IJFK0L7ZyqzHKcZXIHchLFZ8sNAl14ceqpSAtte9y2leCwx/S1vxMdL77bZUuhTTTXngFF4lEkEgkqMiimOiIqBOF8WT5hExS/eSrqO1wOGhbILOyS6VScLvd9FxJ+3g8jmAwKDJiBoMBgUAAJpNJ1LdWq4XZbIbf70cikYBGo6Hf/6amJgwNDWHfvn3YvHlz3qK0xKCS83C73bBarTnfrXztgNxCt9nt8vGv//qv2Lt3Lx577DHR8dWrV+Pee+/F5s2bwXEc/vd//xc//vGPcfDgwaIle5hxqzHKMUDVMm5yjMRMO2AMSTYrSvsMECriKa3mDHu++y7FBrbshM9SA2EqlaKDV3YbRbqjYvttmnjhfa6gCTBdvh6un71CZ+HZ5+q466ySR46R3tLLz8hZfUl5DWbaMyImISEjgBtPR+SmPyEUCknubQOZayClHi3WRzqdxujoqGi7oa6uDi6XK6eEjcVioSVvhIasra2NnoPw3MjjdrudZisRPiZMvkw+w0suuQSvvPKK6DEh2eNEIddsvnbCc5PLq6++iq9//eu49tpr8dnPflb0WLaL8+KLL0ZnZyduvPFGvPjii9i+fXvePplxqzHmY4CKzRqBzMwvnU4jEonImm3G4/GqbPbnm1GTfbfjx4/nnAcJlv3ggw9kzZR9Ph+CwaAo+XQhdWgqlUIkEsHrr78ueT1Ie2FsFCHfwMbzvCjhs5Q4KBwOY2RkhCbTFT5uRAUUOyVAMsnnO1fiSSykei2F+dxf8xUxtbe345RTTpFsl0wm8corr+CMM84o+7XS6TS0Wi3GxsZEuSCbmpowMTGBYDAInU5HDVx7ezsmJiYQi8XocaJ6tNlsCIfD9DOpq6tDMBhEKBSiQhGe52l4gcFggNvthsVioa+bSqXQ398Ps9mMQ4cO5Zyvx5NRCZEVV0NDg8hdWqwdkFmhCbUHZMWWT+G4b98+XHbZZfjIRz6Cf/u3f5N1Pf/2b/8WN954I/bt28eM20IxMTEhKkdRqvsilUqJ5PpSz0mn09S1AeQfZIXHk8kk9u7dK2sGGolEQJwL+VxGcmbWpSIc2Ml5EEk/yZ8pde6JRAL19fVobGyUnGGTMjNSClLy/3vvvYfOzk6alFn4eDZutxuDg4M455xzZL33PXv2YP369XkTJw9k913F/TYAsFgsBRWkx0rsa6Q3//H2mYVRSpL8lNks9J7bihUrYLfbRaWYlEol1Go1gsEgFVnw/FyKLpfLJRJfCBMjk8nHmjVrMD4+jo6ODoyNjdH8kRMTE1i9ejWNk5uamhIZN6VSiQ0bNuAPf/gDwuGwaN/tyJEj0Gg0dI9tw4YNiMViGB4eFu27kT00Mkkge2sDAwMi45bdjnD48GHs2LEDmzZtwu9//3tRQmk5FPsMmXGrMBaLBUqlUnKWXuj/YDCI4eFhbNmyJefxfM85dOgQOjo6aPHCYgSDQbz77rv48Ic/LOu9nNxcvUKUhfZD4p89Bev3irPTh8NhTE9Po6tLXrzd9PQ0zGYzzchQDDJTJmVm5LZfKrWwJgpcsmIKxKAJKCbtyaeUnO9+m9ea6z4sRiVCT+RSyCVXKhyXKUSane+RTNxmZ2dFUneVSgW1Wk3LMQnbW61Wuhr7yEc+gnvvvRc2m41WFxgaGsLRo0dx0003ZVb+RiOi0Sii0YzcOZ1OQ6FQ4LLLLsN3vvMdPPXUU7juuusAZCbATz75JC655BJotZk74dJLL4VGo8Hjjz+O73znO/QcH3vsMZx66qno7c3MYLZu3YqmpiY8/vjjohXVY489hoaGBlFlj8HBQVx88cVYtWoVdu3aJapBJ8Xjjz8OAEUnjsy4VZi6ujrZUvt8kJsuW71UCGHcnBSlujyVKekaW7XIQs/Iq83AeeWpSE+uAtSJ/I9lh2XU+ediwABAffXpwCKWwKm0V0C4emu1Zwy43PukUsYNyLwmSXYcjUbp6kuj0VCDJdyDI2MJ2VIg59HQ0EBzVl5xxRV49NFH8Xd/93fYuXMnQqEQfvWrX6GpqQlXXXWVqL7kpz/9aVx//fU499xzoVQqsWnTJlx11VW48cYbkUgk0Nvbi5///OcYGRmhBgTIlN75xje+gXvuuQdmsxlbtmzBk08+iZdffhlPP/00badWq/H9738fN9xwAzo6OrB9+3a8/PLLeOSRR/DTn/6U7u/Nzs7i4osvRjwex3e/+90cFeXmzZupYd28eTM+97nPob+/HxzH4YUXXsBPf/pTXHrppdi2bVvBa82MG6MsquGSLEY1FYrV7LtSCMUkclyShVZsQuSkRcvmf64uTbVZyCU5H8a7yy/TQwgZAXxjI/A/C2fAiYEhrje3200HcJ7P5Ij0er3w+/20EgCQMSyBQAA+nw/19fXU2JpMJni9XgQCAfzgBz+gq6p0Oo2zzjoLn/3sZ6HVapFIJDKiJIWC7rmr1Wqa7ePRRx/Fbbfdhttvvx1erxcbN27Ec889R71HhLvvvhsmkwk/+clPaPqt3/72t/jEJz4haveVr3wFHMfhwQcfxP3334/u7m489NBDuOGGG2ibI0eO0BXsxz/+8ZxrRdJ2AUB/fz8eeughzMzMIJVKoa+vD3feeSe+9a1vFb3ezLjVGOUISqqllqw22a5JqWDuarDcVnmAPMNWLpp4ZQK4F2q/TUi+vbehoSHJ/fFkMolUKiUSNMndQyfH0uk0WlvnkmRyHAez2UwLkQIZL4xWq0U8HqdCDXJcpVJRZSPpU6FQwGg0IhgMoqmpCf/4j/+IWCwGn8+H7u5uHDlyhLrogUyc2K5du7BlyxZ87nOfoy5QvV6PH/3oR/jRj35U9PoplUrcfvvtuP322yWv9c6dO7Fz586Cj1900UWyx6InnnhCVrtsmHGrMapp3IDSVinFktkuJOUYILmDT7aCVOp5iUQCwWCQznqLPScYDCIWi9GNfKm+o9EoJicnRbFPmcdPl/2+SzVshVZvQRPyipqATLaLSiglawFhNpBCqfFIkVCS4i67jZz99GQyicOHD6O5uZlm/jEYDFStS1yRCoWCxqcR1SPpq1C1gO7ubgwNDSEUCkGtVtNVmkqlAs/z8Pv9VGTC8zx0Oh3OOeccPPDAA9i3bx/OOuushbvgCwgzbgtINQZbEthJ6kJJ9Z1KpWQPtsD6vO8j2yUZMs4/1k3IW2+9JTofEitWTEEqPJZOpzEzM4PDhw8DQMEBh3zZk8kk3n77bVkDVygUQiKRgMPhkBzcEokEkskkXC6XbEGRcDAjg22ycpc2L4UMHPfAJTjrSY/oHF/9l9x2hcQkcl2SXqv4/2Iu7/FueX3KZe3atZJtotEoxsfHZQua8pFKpbB+/XoMDAyI8pI2NjZifHwckUiEqoFJVYDJyUkkEplNU7Iv19zcDLvdjmRy7q7QarVQq9WYnZ1FS0uL6B5qb2+n7j9gzii2tLRg+/btOO2008p+T7UOM24V5uTJkxgcHCxoNIDiA1z2YCtHyh6JRODxeAq2IT+khhUZbIsNuFP/byMqPI7kJZ9qsv6b29Dxv3PGIxaL4dChQzjrrLNkGaAPPvgAjY2N6OjoqLiC9MCBA+js7BS5mApBQgFIVQA57bu6ukShAAPnaUX7bZ76wkrHSrsjlSnIFjYtFYSuyWKJA4RUypXf0NCAuro6UZYO4ookBU7J/arX66HVauk+GxkbzGYz7HY7pqamaNwakHEZWiwWOBwO6rokEySy4vP5fLR9KpVCS0uLrKoISxVm3CpMT08PVqxYUdRwFCMYDOLgwYM5tZQK8f7776OhoUFWouVoNIo9e/bIGmynZL165SH7bqS2FZCRRJeiIJV7rQmluoFLoZb2OIsxvaL0DCLzoZz9tkqv2kqhUnuzFosF0WiUijyAjGEi+28kgTIAaDQaKBQKUR1Dglqtht/vp/tmZA8vkUggEAiIclaq1WqYTKa8cW7LmaURrLOEIEGZpHSJUqmkPna5cv1SKKV9JQQlC62SXMospFilGiKS7HRfL/2N/JCEYi7JQvkeqymEKcRbH5V+T5WcoJBQAJ7nRYl/1Wo1rFYrwuGwKPs/CcAWVt8GgNbWVpq5hxzneZ6u8qanp0XnrlQq0d2dmR2QYrTMuDFKYr4DWrUFJaWyEGKSShvM5aiAXAikKl4P92V+L3UxiUO6FF8Ocu4p4R5xKpWiRXaJESKPK5VKqFQq+P1+xGIx+h0mCSDC4bBIMLJixQqk02lRkVOOy1TxjsfjouLIHMdBrVYjGo0imUzSY6R/IOPtIeexnGFuyRqkVGMlt30phrBYhv7FoFoGfCkZQk9u8vaq8+bHtDjtCaKfz7UKjmago0Qf9ljP3OpNrpikmi5JoYAJyBUqpdNpJBIJvPzyy5JCLCD/VgTP82hubhbthxFXpDDZscFgQDAYhNfrpc9TKpV0/41k0uE4jlblnp6epsHR5DV7enpw/PhxBINBkauTGEXh/t5yhRm3GqOabsmlxK7ParH93zKRuiSrfigUKjgACY/HYjEEg8EcSX2+58ZiMSSTSUxMTMhSkAaDQUxPT4vyAxY7j1AoRBPTFuuf9P3BBx9QCbjlpm2yKgFMdpaWuqoY9tZcwcr7778PjuOQUH9EVh/EEDW6KnNO1SRkBM7esKGoeCscDuPw4cPYunWrpNq10PcxHo9j79690Ol0NCsJEXOEQiHR3hmppq3T6ehxUi1AmIqLCEba2towPT2NZDJJ22s0Guh0OjidTpoHlbB69Wr86U9/QjQapf0sR5hxqzDxeByBQGakKTToFRvg4vE4ksmkKKN9sef5/X5EIhGaM67YaxJXCXFLFOrfc+/5QB6Phb21MsUlpSBpoPbs2UOPJRIJHDhwAIB0jFEoFEIkEkEgECjajuM4GqDr8/kkBy3yQ2KIpM6DKOBaWlok2wKZrA09PT0wm83gOA6TVb7OcojqgL/60IcAAIeerUx/Cx28LQVx1xWCiC9INpFyUCqVOPXUU7F//35RbbXGxkZ6vwJzISDEYAmNnk6ng0KhEJXJAQCr1YrZ2Vk4HA50dXXR77RKpYLZbIbD4aB5G8n9tn37djz++OM4fvx4weKgSx1m3CqM0+nE4OBg0QG12LF0Oo10Ok2l/dlts/8nN7JQtFLoeel0Gna7nWbLL3QuvvTC55TMlz2C5I2Lx+N44403ZCtIP/jgA1gsFllxSaFQCPv378+pHFyIQCCA1tZWtLVJZwr2eDxwu91YsaJI+XEBZDAioQByjNuktEi2IvzrzVqgAq5qRVq6zULgqQfqPdLtgMq5xA0GA+rr6+F0OkWJt/V6PUKhEN1T43keBoMBOp0OwWAQzc3N9Lve0NAAl8sFh8OBuro6em5arRbJZBKzs7M5gpRkMgmv10uD0YGMsb366quXrWEDmHGrOCtWrMhxA5RCLBbDm2++KTu4MpVKQa/X0zxsxUgmkxgcHERHh7yU6ouZmaRvePFeuxjVdOEUG0QXcr+NuCabHbniC6GYpBxhRjFm2oGuidzj1Q4BeOujWpwnkWOyUp+7wWBAPB5HKBSicn2lUgmDwQCHw0EragNzBotUABe6IqPRKHVf83wmI0lDQwOcTidSqVSOkMTv94uCuYUuzOUKU0vWGOWoH6upliyHkV7xz2JQisimlij3fKqpYHzzY/LdcaUYomwxSa1Sye8XkesLQwGIgauvrxdVYiexnWSrgrRVKBRobW2Fz+dDMpkUeWA6OjqQTqepS54YOa1WS71CAP4i4tyWt+legpRq3EoZDOX2nU8pKSUTJ+QzZiO9QO+IvOcXotYMeLXZ9VktpOYFC+WSjOoqo54NmjKJl2sFoWsyHA4DKCwiIlsFUiKiYvvd9fWZ5TcxNpFIhBo4ns9UBQgEAjlCjxUrVmB0dJQKq4CMC5tkHonH4/S7TbL9T0xM0Bg50k9vby8OHz6Mqampv4g4N2bcljilGMNyVoWlUGyVJsfACffd/HWZAf7jj8dqbnVVKfIpPpPJ5J8Dc7U4tg5YObo455ZPNVmIqQ554QALZdjI6rF7XF77kBF45513Cu5Dp9NpRKNRHDt2rKT9c+EPSaBtMploxh2TyYTZ2VmRvN9kMsHj8cDnyyiFicHS6/Xw+/1oaGigr2EwGKBSqTA+Pi4KJwCA9vZ2WhGAfO9J8dORkRHU1dUx48ZYWKptgKqFHPdjOSu4iYkJJJNJpNNpjI2NyZop+3w+hMPhoqED5FgymUQsFsPBgwdlzcBDoRD8fj+Gh4fzGidhWxLM++KLL+ZtA4hThaXTaRw8ePDPYoOPlXahlghyQhuEjHfLN7LZLlHyf8us9HMvuuiigo/5fD4MDAxg69at8k4kD4lEAu+++y78fj8aGxsBzAmIgsEgVWKSXJNut1tUHV6tVoPjOExNZWYRwvuHCFJI5n8go6B0OBxwuVx0BUf6X7duHe68886i73k5wIxbhQkGg6JccHLdFtkD4nvvvSfrucSdQjad5bwOCUbN11b1i8sqooorxEhvaeEEJJ6MGBYgd1YsNBAKhYJK9XU6neSMOh6Pw+v10nygxdpyHIcTJ06gqakJTU1NkrN3v9+PoaEhmvA5X3shb731FjZs2ACLxYJdj8wdzycmWSiXJOG0w8BhgcYpn5hkPsKP+WapGektvDIspyirEOGKqFw4jsP69euxd+9eRCIR2l99fT1CoRBNo0XatrS0wG63iyT8Op1OJEZRKpXgOA5tbW0YHBxEMBgUFTM1GAwIh8NwOByisaCxsRHNzc149NFHceutt6KhQUb12yUIM24VJpVK0ZQ6QG58VDGpPlm1zczM0LIYxQZyjuMwOTkJhUKBzs5OSfcIALz++us477zzCrZ99ReZ9xEwA03O3PeXT7I/1gPoI7ltK8Fpp51GFWOnnHKKrOdEo1GYTCb09PRItg2HwxgdHZUl7QcyM2iDwSBK7FyISCQChUJBKy8vNeytc9L9hDqzZyZ3FSVFJcUkcrwGUgbuP/9Oi2sfyq+YrJQnheSPdDqdIjciqagdDAbpd9FoNEKn09HSV4S2tjYMDQ0hEAhQQyasARcIBESrtPr6erjdbiokIf13d3ejqalJtDpcbjDjVmEsFguMRpm1NPKQTqdx9OhR2bFRbrcbHMfRzWo5aLXakmaicsUkchnvLrwfks94lkqpIptaY9dntYiVHy+8bFiIKgBy490qdZ9oNBpYLBb4fD4qxVcqldBoNHA4HNRgARkDF4vF4HQ6RfFparUaPp9PlFaLlLzJriBAFJQjIyNUQQlkJuGbN2+mabuWIywUoMYoRy1ZyT26UlVxY9KLI0aFWWiXZCWolpiklFCT6SLzxWJ7gZUOBairq6OxagQSCuDz+URVubVaLQKBAE28TI43NjaKtiI4LpMwmdQZFIYIaLVaqFQqumcNsFAARhlUaoZXCT9/PoSxL4tJsdUbIWTMrGIu/fdkTYlsaulcqo2rUV6OSDmrrFLFJAvNyMhI3n1qUhD42LFjBfeq8x3P/p+kxiL7Z6FQiLoiidEj+2/Ce2zFihWYmJigQdvk+VarVZSKi+czMXTT09OYmJjISZjc2tqKqakpJBIJFgrAWHhKNTpEZbcYLNSqrRxDPB8DJKWATCQSNBapWNtgMIhkMkkrL0sNholE4s/Jnucy3CxGJYBCnLk/cz7VyExSDuUkCCi29xaNRvPucROREskJWU4oQCgUwpEjR+heLQnQdjqdsFqt1GhZLBbMzs7C7/dT46PT6Wi1AGER0vr6erhcLthsNqhUqpx7PhQKoa6ujp5TU1MTbDYbBgYGkEqlln2GkuX97pYoUqsr4cAorB2Vb7DNHkSBjIqP9C1s9+6X2nOUkpXebxNSaPWWve926NAhpNNp7N+/X5YilAxS4+PjOW3zPTeVSuH555+njwEoOEglk0l4PB4MDw9LDmipVArRaBQnTpyQpcRMJBLwer2Vvcg1SCl5HRcCMoFYv3593sddLhcikQhWrVpV9mskk0mEw2HY7XYYDAZqNIkrkhgyovR1uVy0qCmQyT+ZSCRyqgJwHIdIJAK1Wk2rDBCB2dDQEFVmkvZarRY8n8lRyVZujJLwer04cuQIAHmui0LHXnnllaJ9AOIVzeTkpKwZJM/z+OCDD/K2AzJTaDmpnBZyr23FihVwOBzo7u6WZSRGRkag0+nQ0dEh2T4Wi+Gdd97BhRdemNM2H4cOHUJrayva26WXGx6PB8eOHcO5554r632+9dZbWLNmDWxF2sy051exVhO5rslKIuXmzLdqi2vk7e1NrwC0eYSRhRSTlXLjr1q1CjMzM6LioiTOLZFIAJi7P5ubm+F0OkWrKxIKkF2Vu7OzEydPnqRqbCBj4KxWK9xuN1VcEmXlmjVr8OSTT8Lv9+NLX/rSvN9XrcKMW4UhSYzlGJpCx1977TWcd955NI6lUHsgs08Qi8VkZ/d+4YUXcO655+Z1SbxUiQtQBVpbW8FxnOyE1BqNBlqtVpbMmWRKr5VZ7Bs3tCyIUnK4r3LJqac6gLYiFrmWUm6VQ6X2WBUKBerq6uD1emEwGABkvst1dXVwOBwIBoNQq9XgeR4mkwnBYJAaJvKd7+jowMmTJ2m4C8/zIgVmIpGgY4NarYbZbKa1CsnrmUwmbNy4Ec899xyCweCyDQdgxq3CaLVaGqNWLiQ2Sq5PfDHVlfNFSlgSKj+qgvFnhlbnP16OgSs3x2Sti0mA4uc435WbcEXV2NgIl8tF3YhKpRIqlQpOpxNNTU30+2mxWBAOh+HxeKBQKMDzPHU/ejweWoeO53nodDpEo1GRK57jOFq0NLsUjtFoxD333LNsDRvAQgGWPJVUPcoduBZa/v+na/UlG+RaMuDlUomSQ4UMG2G4r7T+khWeDpcjJjlZ/tYXZTbLCVAsh2e5bsnsPXGC0WiEWq0WJULmOI4GXAuPqVQqeDwekYJSpVLBYDBgejqjjJmZmcGtt96Kyy+/HJ/+9Kdx9913Y3Jyrhog8XhMTMzVE0qlUtBqtYhGo7j55pvR3t4OvV6PrVu34vXXX895L+l0Gvfccw9WrlwJnU6HjRs34ve//33e9/3www9j3bp10Gq16O/vx7/8y7+IHvf7/fje976H8847D42NjbBarTjvvPPwxz/+MW9/u3fvxnnnnQe9Xo+2tjZ885vfpAmni8FWbjVIqauraq3cqikmETLenZvhpNKKvOVAqYZgaDWgTki3k7OCW8h9t0oHb6uS0kaZiEr27NmTs8edTCaRSCTw2muvFd0nz34MEE8+165dSw2lwWCA1+tFIBCARqOh+2/CSgHEFdna2gqbzSZKxWUwGBAKhRCLxXDddddBpVLhlltuQUNDA+677z5cd911+PWvf02VngBEab9InNv111+PZ599Fvfffz9WrVqFn/3sZ9ixYwf27NmDTZs20XO/44478MADD+Duu+/GGWecgSeeeAJXXHEFdu3ahY99bC4P6sMPP4ydO3fi1ltvxfbt2/HSSy/hhhtuAM/z+OpXvwoAGB8fxz//8z/jC1/4Au644w4oFAr85je/wac//Wk89NBD+NrXvkb7e//993HxxRdjx44d2LVrF0ZGRnDzzTdjamoKTz75ZPHPvfhHzlgMSjFAlVy51TpyB5ZUKkVz8Ek9JxaLIZVKwel0yuo/HA7D6XQikUhIioKi0Sii0SiOHz8uS1xE8oRWAqkVWzbDfcX3zQoxJa/uLaWWQhvysX79+py9bbfbDbvdTqu159s7L7R/TvB6vThw4ABNYkxCCzweD02kTFZv4XAYfr+fpugyGo00T6RwFdne3o7f/OY3mJycxFNPPYWGhgZ0dXVBp9Phy1/+Mp566ilceeWV9Bx6e3tx7NgxuN1uJJNJTE5O4te//jUeeeQRfOELXwAAXHjhhdiwYQPuvPNOPPPMMwCA2dlZPPDAA7jllltw0003AQC2bduGoaEh3HLLLdS4JZNJ3Hbbbbj22mtx991303bT09O444478KUvfQlqtRq9vb04efIk3XcEgB07dmBiYgL33XefyLh95zvfQWdnJ5566imaxk6j0eC6667Dt7/9bWzZsqXgZ8mMWxUoNkAWOp79mN/vF8WuFGofCAQQiURykjUXek46ncbo6Kioii8AjH/7VEAtrZSc7AQa3BW/ZLIgcn2pgSWZTEKhUMBut+dtLzzG85lQgJGREVl9JxIJmjNSjlAImMvoXqw9x3Hwer2Yy1mxPKi0mKQSLknCbEtuxYD/vr01RzEZDoepK7BcjEYj+vr6MDg4SPfKOI5DQ0ODyBVJRGQulwstLS30O2o0GhGJRP4cB5n5biuVSuzbtw/9/f1oa2tDLJY57xUrVmDjxo145ZVXcPnll9Nz0Gg0MBqNGBgYgNFoxIEDB6BWq3HVVVfRNiqVCldffTXuvfdexGIxaLVaPP/884jH47jmmmtE7+maa67BF7/4RYyMjKC3txd79uyBw+HIaXfttdfi0Ucfxe7du7Ft27aC6QnPPPNMvPbaa/T/RCKB5557Dt/85jdF+VmvvPJKfPnLX8bTTz/NjNtC4vV68cYbbwDInxhZzmwvlUrh2LFjokTLhZ4TjUZpYuFCryF8Ds/zdNWRb4a5WMipCXbJJZdQF0sxjh07Bo1GIysuKRaL4c0338RZZ50l6zwPHTqElpYWWbk/idtJbnzUwZt7K6KULHXVRhhdWXzvydWYCYCeXpFJoiyXaohJvFbA6q18v/moVChAW1sbhoeH4fF4aIkbk8lEM6CQAG0gk7mfeBOAuVRcfr+fqoGBjIvvoosugtvtpm5LIOMCJWpIYeA3MXCjo6PQarXo7e3NMdobNmxAPB7H0NAQNmzYgIGBAWi1WqxevTqnHQAcOXIEvb29GBgYAAC6ws3Xbtu2bQWvz+uvvy5SfQ8PDyMajeb0p9Pp0NfXR0OuCsGMW4WxWCzYsWPHvL4Mr7zyCs4880yqpirGxMQEfD5fzg1QCJvNhr6+vpy+x8o604UhZAQskO+CrQVjPV+yxSRy99vKNWwEKQNXKU6uyl9JYiGSJRejmqpOjuNgNBoRDAYBzHl4rFYrwuEwleWTUIBwOJzjiuzo6KDFSTmOQzAYRGNjI/R6vShswGKxIBgMQqFQYGZmRjTBXb9+PXw+H5xOJ/r7+3POk5TAIZl13G43rFZrzvcqXzsAOUncs9vl41//9V+xd+9ePPbYY/RYof5In8X6A5hasuIs9Eqo1qT9lcQtKDOV/M9PLt6JCFgOhrNSyNlvKydFViEq6ZIkCFWThVzylVq5EZqbmxEMBkWrMiAT9E+CuQHQDCUkoxDP89Dr9dDpdKIEy0DGQAKZ/THhmKDX6+lrkfehUCjQ2tpKq3Tne79y3n++dkDp35FXX30VX//613Httdfis5/9rKz+5Ix5bOVWg1TTYBXqOzsMwNUIGLL0DYudjb7Sg4yw36WEsyk3S8nJVYAxVJn+K7F6O7kqcw8Jz6nWxSQEsloi90U4HEYikYDP55Pc0y50PJ1Oo7GxETzPQ6vV5ghEiJiE7KkB4v03Ev/G85mYtnQ6DZvNBpPJBJ/PR92WJCbO5/PBbM5Y65UrV+L48eO02C85x9WrV9NwAiEeTyY3GllxNTQ0wOPx5Hz/8rUDMisuYQYfssLKVxR13759uOyyy/CRj3wE//Zv/yZ6rNiKz+PxUHdnIZhxq0FKVUuWOjjX6mAuZ99NLkxtWh1cjfLbVsrYLjTvvPOOaD86mUwilUrRPSW5e+fC48FgUJQ3lBg3r9cLi8VCRSPRaFS0Jw5kVnoul0uUf5K4N7u7uzE8PExfp6enB8PDwxgaGqJ7vTqdDgqFAuPj4zRxcyqVQm9vL958802Ew2HRvtuRI0eg0WjoHtuGDRsQi8UwPDws2ncje16kiDAxNgMDAyLjlt2OcPjwYezYsQObNm3C73//+5yivn19fdBqtfS6E6LRKE6ePIkrrrii6OfIjFuFqdRgWYoBKqVtsfPLdstMdAFdE/nbLgZCl4uU0pTjOKqALKZOJQPXkSNHZM3CfT4fgsEgpqenJc8jmUwiFovRoNhi7b2/+WtwBcQkUvtt1XDXSa3eTMHKv2YxqvEeC3HRRReJ/p+amoLL5cLpp59edp/hcBhvv/02dUEqFAoolUoEg0EqDgEymftDoRACgQDq6uro/htJxQXMTWg7Oztx5pln4t///d8xNTVFV4Qejwfvvfcevv71r4tUmFarFV6vF+l0Gul0Gh/+8Ifx6KOP4qmnnsJ1110HIPN9ePLJJ3HJJZfQ87r00kuh0Wjw+OOP4zvf+Q4918ceewynnnoqenszvuetW7eiqakJjz/+OLZv3y5q19DQgPPPP58eGxwcxMUXX4xVq1Zh165dIjEMQaPR4NJLL8Vvf/tb3HXXXTRj0+9+9zvEYjFcdtllRa85M24VJplMwuFwlCX/Fw6K4+PjNM9cseeFQiFEIhG8//77slwmsVgMhw4doul8eJ7HgT9twxqJ97XYLkkgkxxaqCAFCmfXJ0rSfDNpYR9kNkwytRf7ATLyZIvFgsbGRsnzCAQCGBkZwaZNmyRn+s8/CqqUrERmksVEaIjCBdTztjagd0R8bLx7cSZT2SEBhRIozwe1Wo1TTjkFhw4dEmUrIam4COR+8Hg8ogGfiE7I6o+4Nz/2sY/hf/7nf3DjjTfi2muvxcmTJ/HDH/4Qzc3N2LZtG1VKzs7O4rLLLsPf/u3foqWlBalUCuvWrcNVV12FG2+8EYlEAr29vfj5z3+OkZERPP744/S1W1pa8I1vfAP33HMPzGYztmzZgieffBIvv/wynn76adF7/P73v48bbrgBHR0d2L59O15++WU88sgj+OlPf0qrfs/OzuLiiy9GPB7Hd7/73RzV4+bNm6lhveuuu7B161ZceeWV+NrXvobR0VHcfPPN+MxnPoMzzjij6DVnxq3CJJNJjI2NlSz/Fx4HQOstkQ3gQs8lxrChoUEyDIC4R3p6ekSJWw/8aUEvUVGyXZPuhkxcXciYuenlJDg+ceIElEol+vqkc0vF43GMjY1h5cqVss7Pbrejrq5OVv5QUhCymvn7FnJF85dAPlFJpfZ6rVYr1Go1nE4njXXT6/UwGAwIBAKi/TdS140gzD8pFIKYTCY8+OCD+NnPfoYf/vCH4DgOGzduxK233gqlUkldnEBmTNFoNHC73ejs7IRSqcSjjz6K2267Dbfffju8Xi9NqJwdP3b33XfDZDLhJz/5CWw2G/r7+/Hb3/4Wn/jEJ0TtvvKVr4DjODz44IO4//770d3djYceegg33HADbXPkyBGMjWX02R//+MdzrtPIyAj9Pm7atAnPP/88vv3tb+Ov//qvYbFY8LnPfQ4/+MEPJK83M24VRqfT4cwzz5xXHw6HAz09PXRDuBgzMzNIJpPo7JS3tFKpVLBYLEUH3FL2VRaS//mcAR9/vLIz6nKo1T3LSjO6ErD4co/7LPmPA4WN7XzEJMvJgKvValrbjXhO6uvrEQgEEAgE6CTVZDIhHo/TnJLEmLW0tMBut8NkMtFj69atw+23345UKoX169djdHQU9fX14HkeExMTCAaDaGtrw7Fjx+D1eqFUKvHyyy/j8ssvx9lnn40f/ehH+NGPflT0vJVKJW6//Xbcfvvtku9x586d2LlzZ8HHL7roopK+QxdccAH27Nkjuz2BhQLUIKXMEpdzKMB8qKbadCEpt0r1YlOo2vVCMrqyMv1UUqXLcRzdVyNSfrJa8/v91JUOgHoHhHFxdXV10Gq1CIfD1OXIcZn8k8lkEoFAgD6fBHuTVRJ5H/39/bBarXjwwQeX9djBVm41yEKHAkglla2F/bZSKHUgWqpf8IVY0Ux2Ap2T+R/rPw4cz40BXnSERo38zXPF9/OyqwQMDw+LRESxWEx2jtB8xwFg9erV4PlM2RpS1424rkmtN+F+PQkFcDqdVH3I85kEyy6XCx6Ph36fSYmsyclJ6PV6ashItW+73S4y0kajEb/85S+XtVqYGbcapZqhALVOJUMCpCjHEPJ8Jh+l1AAXjUaRSqVEQbT5fv79oRXoWSZiEiGFxCT5qFRmkmKrNaH61+Irfq1JEVsA1Ehk5wglykc5e90OhwPHjh2jn7nRaITX64XX66WJkw0GAxKJhCgejRg9p9NJV3oKhQJ6vR5Op5OKzshxq9UKl8uFuro6Oja0tLRgdnYWs7OzNK9jKpWSte2xlGHGrQappFsy3wwykUggHo8LHtdKJkxeTIioBMiUwACKz5RJNQCXyyVrhp1MJvHqq68WNUDkuUBmn/PIkSOS4iCez+TxfPfdd4sOfIB0nspsFnsfKt++m9xzsrXJf52Tq4BWu/y2OonM03LDW97+p9OoYnJsbAyhUEh2jtB8WCwWHDx4UJSBBMiUoQmHw/SeaGpqQjAYRCgUoinyzGYzotGoKCMJx3Fob2/H1NQUNcQ8z6O5uRlutxs+n49WIOA4DlqtFqFQSCRYq5Xq89WCGbcKU0rMVKHHQ6EQDh8+TGeGxZ6XSqWQSqXw0ksvFR2QyUCaTqdx4MAB+v+RVz5W8btAmN+Q/7OdXjM4/35DRuRVhQJiA0OyLnR1dRU1QByXCdB95513cM4558hSth4+fBiNjY3o6JDOPeX1enH06FFs3bq1aLs3nwMG11TmGlWDYq7JWqGSxr4aEz2Oy+R03Lt3L+LxODUsJEEyCc1RKBRQqVTw+Xx09cVxHFpaWjA2NoZgMEgNmdlshkqlgtvtFhkyEuCdvQJsa2vD1NQUgsEgM26M8jAajZKDKlDYrTEwMIDu7m7RzV1o0HW73ZiamhLFUuXrk/DWW29hw4YNVIp85BXxuWcrJUvdbyuUuLdSg/cTj/bhpjuKKyZJmqR86X6yITFx+YJIK8F8XMazLQvnni2XDQPAQFYWpGwxSa2l3Sq0evPUA/We3OOVEpTo9XoaCkDEIlqtFnV1dTRXJMdlYi/1ej1sNht9fZK9w263o6mpifap1WoRi8VE8W/CfTZhaSatVgur1YrDhw9DrVYz48YoDaVSiZ6ennn1oVarYTabaTLUYmg0GnAcRwMk5VCtPTqpjPTEwMmp/FxqEcz5sNSUlWM9+QfhalJo9UbESPNZOc13v62c157oAur88tpW8v4gmUn8fj/t22q10sw3JJmA0WhEKpUSxakBmQz5Ho9HFAPb0NAgKo/DcRzUajUaGxsxOzsrcluaTCZMT0/TifNyhoUC1CCliERKvUGrcUMP98kvtTIolQplgSnneiw3AU+5FBNklCImKcRi7ysKKeU+4XmeprhKpVI0xRuhoaGBptIifatUKoTDYVpwFMjEtKXTaUSjcxuJpPQMiX8DMhPqtrY2+npk/KivrwfHcZicnBSNKR/5yEcwNDSEn//852Vfj6UAW7nVKNVUSwrbS4UBSDEsnQSk4POkVm9ChKISOSwVA/Sj72oR//OiezkpJQtRipiEYG8tLCqppgHcvXs3eJ6nhsRms8kOAcgVDYHmpiRuQ6fTiWQyCbVaDYVCAYPBgNnZWSiVSvA8D5VKBZVKBZfLRVWOHJep3m2z2UT7byQh8uTkJE1dpVAooFAoqGCFuFd1Oh1UKpUst/1Shhm3GqSacVr5+i40y7a3Am22kk5lUcg30KTTaaoIJSqzQkpJnudF5UyKCX4ikQgtMSIlGopEIojFYhgaGio4GAKb8r6n7Lgrwtj8PN7zopBrcrKztIlHrWBry72/yb5bwAxs3LiRrnySyST6+vqKio3y7XETpqamcPToUXovkj1er9dLC49qtVqk02mEw3O1ppRKJXQ6HU3FRYyeWq3GzMwMFZIQUqkUIpEIdVsCmZI3J06cQCwWo9sXPM/j+uuvr9CVrE2Ycasw5RimfANkPB5HLBaTHGxDoRCSySSttyQ1s0wkEnA4HAIl1dzSq9S0W+Wu2oTPL7Z6yzdjj+iBF154oagilPw/NTUlOl5oEEqn0xgYGJClloxEItTVJEeJSQwtOSbME7pc9jz6jwOOP6fazCcmqZbhq7bb8r5fNeH///cxGt82H9FRc3MznE4n7Pa5G1qhUCCZTNIMJEAmFGB0dBSRSITui9XV1dHkyuTeJvFvXq8Xer2e3ktdXV0YHBwUGTGtVksN5IoVmbATEjy+nGHGrQq8/vrrSKfTBY2ScCUB5Low0uk0/H4/zVBQTF2ZSqUQi8Vw7NgxyaBS4qv3+XyIRqN47bdnLck7YNu2bXmND2F4eBjJZBL9/dLpM5LJJF555RWcd955sl778OHDqK+vl5XLk4gE1q5dK6vvpYjPMhfuUQ6FxCQLtd+Wb/VGiAs0WpWYiKxevRozMzMIh8PUIFmtVrjdbhqMrVQqodVqaZ5JQnt7O0ZHRxGNRqnbsqmpCV6vF8FgkLZVqVSoq6uD3+9Ha2srfb5Wq6WJl/v6+lgoAKM8zjzzTMkVQLHZ+/79+9HT0yMr87zH48Hx48dx7rnnyjq3d955B6tWrUJjYyNe+21p70vIfFdtwn5K2XsDgH+8xygZDlAKS2V/rhaY7AQ08cU+i4WlUqEAKpUKSqWSVqomQhKigCQTYNKOrPJIKADHcbDb7TQVF8dlEiz7/X6RK1On0yGRSGByclKUv9JqtWJ2dhbj4+N/EcaNqSWrgMFggF6vh06ng1arhUajgUajofnfSC65Ql+YUtWSfymDs7sK+99LyTW4mPttxciOGStWw61SLKSSspLfLyLzd7vnfLUkDZYwgwjJTkLSvAEZz41Op4Pb7RYpJU0mE3XBk+P5XKgcl0mwPDw8jJ6engU1bl6vF++++y6Gh4epwQ2HwxgZGYHHU524FrZyq1FK+UKVKiiR097eKtmkYgz3FY7bKqaUK8RSMVg/+u5cBeagaa5gZiExSa2zFEUlQK5rUhjMTVz4APLuaxfbD88+1tLSAp7nYbFYaCJjns8EXWu1WkSjUUQiEerRaW1txejoKBVGEaXkzMwM3fYAMi5HtVoNl8tF93eBzP7bsWPHaKUAsv8WjUYxNTWF2dlZdHV1Vf36Op1O/OQnP8Gvf/1rrFq1Ctdffz2uvvpqTE5O4oILLsAnPvEJPPzww0gmk7TadiVgxq0GKWVwnk+cVrlhAJVySTLE+zpLhewJh88CNDkr566slfi2iB4YGBigsWdkZVXKlgN53O12i2LdGhsbYbPZaFVupVIJo9GI2dlZ6HQ66orUarXw+Xw0vk2hUKClpQVTU1OIx+PUaLW0tMDlcsHtdlMDQbKaTExMwGw2U/fqpZdeilAohLvuugv/9m//VvXr+Nxzz8Fms+FPf/oTRkZG8J//+Z+YnJzETTfdhFtuuQVDQ0P0GlYSZtxqkGq6JbNvoEoE21aCsR6gZ0xe24geotIg2bNln8+HZDKJiYkJyVl1KpVCOp3OKWeS3Y78eL1eBAIBOByOoiEGJMwgEongzTffLDDD31HS9VlqSKXdKjczyUIav/POO6+kyu754HkeHo8H7777Lr1ntFotzVRCYtQ0Gg0UCgUikQg1TGSvzel00r5Iu+npaZhMJrr6UygUcLvdtFApMLfac7vd1FVJAr3/6Z/+aV7XRi5msxmf/OQn0d/fj/7+flxyySW455578PTTT8Pn81V0tSaEGbcqEAwGC6olpQZPns/ERzmdTlHm/kI/sVisaK2p7NcLBAIYHh7GxMQEgLmEvvvOAladlH5vYz3y0xZVk7GxsYKz5kgkgnQ6DZ8vk7ZeTmkSEhck9RONRmE0GtHU1CQ5Ww+FQhgZGcFpp52W9/GDry30VWMUwtYGcHnmiN/6hRbXXzT/PTej0Yienh4MDQ1RGT5RPfp8PjpJbWxsxNjYGF0tchwHs9lMa78JxS0qlQqhUIjGupFVnbBSN8dxaG5uhsfjgd/vh8lkooHjJDC82sRiMYyNjeFjH/sYgMz38e///u/xzDPP4JFHHsF1111Xlddlxq0KDAwM0DgoOW6L7HbxeJzGoWU/nm+gBpBTa6rQawSDQdTX1+P5x04HlrBY6tX/Ob+gYnJkZASxWAzr1q2T7CedTmNkZET2rNztdsNisaCtTVodQfIIkpl5OVSqtt2xrEvBc5n4tHLJtxd6clX1g/4Xy2VZCZdZV1cXhoaGEAqFYLVaaVYSEqsGgCZNDofD1GUJZEIBxsfHqWHiuEzJm+HhYVHIkMlkgs/nE1XqBoC6ujp4PB762gspJuns7MR///d/48UXX8Qll1yCZDKJuro6fOYzn8Hvf//7qp0LM25V4Nxzz52Xwuq9995Dc3MzDbgsRiAQgNvtll1rymazZfz3RU5vIcUkQgq5JoUDacAMmAMLe17VJmia+7vSYpJsoyaEVNGej5GTSyWVkguBpx7oHcmcd6VCAUgfgUCArpoUCgWamprgdDpFe2VarRZ2u52u7nQ6HZRKJZxOJ7q6umhMnMVigdfrpXXieD6TiHlmZkYU+K1UKmG1WmGz2dDQ0LCgxu28887Dhg1zpSNUKhV9T48//rho37GSsFCAGqTUPbeFYint+9R6eIRQKSlFudf9uHQMe0ntihE2VKbm22KKSQpl6KnEvST8TpPK2qRvo9FI99qIISWpuITFTYnrnIQCkP03jUYjCgUQ5qkUvr5Go0FDQwNOnjxJ9/QWCovFQstskfMBMmFT8/FsFIOt3JY45QhKan3g/0uhmkrJUg3W8X75gh45CMUkw32AMSR+fLKzsq9XLSL6jCtaqVQiHA6XtYfO85nA7FNOOQVAZkCPRqNUPclxmdRewWBQVAGgtbUV4+Pj0Gq1VClJArGFghEStC0MD1AoFOjo6KCuTOGe3ssvvzzvslxLAWbcapCFMEDCMIBaykYvVzUZKZLmr9qrWTmxTjzPIxqNIp1O09yB4sGw9oLZSi0oW04M4nxYrFUdSYllNpsl98sLPTY6Oorh4WH6f1NTEyYnJ2mxXJIg2W63U9k+yQlJKmcTA9fa2orp6Wl6DMjsa504cUKUnqu+vh6Tk5M0wTKQMXp/9Vd/he9973v47//+b3ziE5+o6rUjK9GXXnoJr7/+Og1pIIIaqR+FQgG1Wo1YLIYzzjijJKPMjFsNUu1QANK+lDCAxXZJ5htIDx8+nNeokM34fEal0M9rr70mawZO2hw5ckRSIMTzmQTYBw8ezDPgyTNuM+1As6O0azUfN2OlKqYvRRrcGddko0t8fNe+C/Hly06gu7u82AViqN5++23RSk6r1dK8kBzH0Wz/4XAYWq2Wuh2TyaRo/8xkymzSElUkaadWq0XpucheWywWo4HiJDSAPK/aEOO2d+9e/OQnP0FLSwui0SgUCgUSiQR1u5L6d8Ifns8kHSeq0J/+9Kf42te+Jjt1GDNuVWBsbIzWgJIaJPPFSvl8Pni9XlEWg0IDbyqVQjQaxeuvvy7LRZJOp/9cvn5l3nNfLDFJKRBRyQv/dSau+tLJHMMxOzuLeDyO7u5uWQrVN998M28+0Hw/AwMDqKurkzWD9Pl8GBgYyJuUee8Lue0rISapxP5ZuYQN+QO57a3ywkxGV1ZGGVopiGu1Eu5jtVqNtWvX4oMPPqDfeZVKhXQ6DY/HQ1XQpCqAUB1tMBgQCASoEIMQi8XoIE8MJqn/Jnw+UVqSlH+pVAp6vR6XXXbZ/N+YBKQ01G233YbbbrutIn3KFZ4w41YFhPEo+UqcSA2gyWQSBoMBzc3Nkm1jsRgOHz6MLVu2yBqcDx8+jObmZhzdu8gXKYs6P+D/876yXNdkWgF0dHTkHI9EIgiHw7IST5PBQm7Mj/BzrARCpeR8qZRhK2X1lr2iViXnXwA3H/NxSY71AN3j83v9+X7mPM/TzP1+v59WBSB7bcJYNbPZDL/fLwonIq5IYfmk9vZ2TExMIBAI4L777sMbb7wBjuNw+umnY+fOnVi9ejUVkpBKAe3t7aKVTzQaxR133IHHHnsMXq8XmzZtwn333YcLLrhAdP7pdBr33XcffvGLX8Bms6G/vx933nknLr/88pz3+vDDD+PBBx/EyMgIVq5ciW984xvYuXMnTZig0Wjwd3/3dzhw4ACcTieGh4dxwQUX4NVXX6WvRa73XXfdhe9973s5r/HJT34Sf/zjH4tec2bcqkBvb++8lvxutxtGoxEtLdJT+Wg0SuNb5MBxHP7r56tK+uQX2yW53Lj3Hi1qPetWNd2Tk9LVgiqC8L6dEKRQzE70vJAoFArEYjFRDsmmpiY4HA7o9XrqYlSpVLDb7TSBsslkgkqlgtfrhcVioUZLrVbjpptugslkws033wyr1YqHHnoI3/72t/Hss88CmFNkRiIRzMzMoK6ujq4Ur7/+ejz77LO4//77sWrVKvzsZz/Djh07sGfPHmzatIme9x133IEHHngAd999N8444ww88cQTuOKKK7Br1y4anA1kDNvOnTtx6623Yvv27XjppZdwww03gOd5fPWrX6Xj4okTJ3Do0CG0tLSgqakJ0WgUXq+Xvk8CMXK7d+8WrdjkVBFnxq1GqZY/fCFDBxaLWn+Pmrg8V9dMu/w+B9cA+kj551SIkd5MvFcpSKXdWgiKTcgmuoobuOx9t4g+956Suz9LtgLIqkyhUMBkMsHpdNLAbaPRCK/XS7OSABk3JqnVSAZ7kvTY7/fTPd0XX3wRdrsdP/7xj9HY2Iimpib09/fj4x//OH7xi1/g8ssvp14ko9FI82MqlUq89957+PWvf41HHnkEX/jCFwAAF154ITZs2IA777wTzzzzDABgdnYWDzzwAG655RbcdNNNAIBt27ZhaGgIt9xyCzVuyWQSt912G6699lrcfffdtN309DTuuOMOfOlLX4JarUY6ncZzzz2H/fv345vf/CbefPNNuFwufPjDH8anP/1pXH/99Tlu/3POOafkNF3MuNUgpQzO81VWLoZSUhsDYhJhXsQ1KRzgs/cDiykmq0WphnMph10MrpHXTvi5VCNX6UjvXMUEOcjxNEx05QpHinH06FEcPXpUtK8NSG8xkDaJRAKbN28GkMkhqdfrEYvFRAbO4/HQFR0AtLW1YXx8XBTwXVdXR/OqApnCyOvWrYPJZKJGtLOzExs2bMDbb7+NT37yk/QcAKCnpwdvv/02rFYrnnnmGajValx11VX0/ahUKlx99dW49957EYvFoNVq8fzzzyMej+Oaa64RXZNrrrkGX/ziFzEyMoLe3l7s2bMHDocjp921116LRx99FLt378a2bdvoqvHss8/G7t27sWnTJni9XjQ0NOCee+6habm2bNkyr+8PM241SjXVkklV/kFoKYhJCiGcSafTaaRSKSQSCVlCHiAj/pAS/xAlZjqdxvT0tKxQgFgshqGhoay+Ts85f089YAqW997lGqFyKWf1RpB7T42uLK//bEpxoc+0A+0zxdsETZnPpb+/Hx0dHXmNlxQ8z2NwcBAnTpygxxoaGjAxMUHVgkqlEhqNBna7nbrcNBoNDAYDDe4GMsanoaGBJu4+efIkzjnnHKxYsQITExNIpVJQq9Xo6enBm2++iVQqhWAwCI1GA57nodfrcfjwYYyMjOC9995Db28vDRMgbNiwAfF4HENDQ9iwYQMGBgag1WqxevXqnHZARjnc29uLgYEBAMCpp55asN22bdsAZNySkUgELS0tMBgMsFqtePXVVxEIBLBz50786Ec/wv3330+vcVdXF2ZnZ9HZ2Ymrr74ad911V96adUKYcatRiBJSasAlqsxAICDLRSIMEpVDre63EcXk888/D2DOSAkHHLvdLkvMA2TygWYfy5fHMxwO04DZYjN1okoj5yYUFy13mh2AQ1rLU3FGegFDWLpdOfzsubX44c7yq7+TwZmsrpRKJQwGA50sAZn7zWg0iuqv6fV6RKNRuN1ueqy+vh5OpxMejwc+nw8mkwlmsxkqlQputxsrVqygFbp1Oh0cDgdaW1vpffipT30Kv/zlL/HBBx+gvj7Xh0yMKymo6na7aXyaVDsAOX0K25GabXfccQeeeuopbNy4EePj4zCZTHjiiSewZcsWPP744/ibv/kb7N69G6tXr8Y999xDBXP/+7//ix//+Mc4ePAgXnghj+RYADNuVeD999+H3++XZWzy+e4JQ0NDkgMukPF1v/fee7IGZ5KQeSkw1iNdI+zwO5fhm7dFRO97fHwcgUBAlM+uGM899xy2bt0qy/AMDAzAbDbLinny+/3w+/1Ysyb/0qqYUlLuflu1V22E+azehEiJSSqVKFouhVZv+eLd5oNCocCaNWvw7rvv0lyKarUaSqUSLpeLiknIio5MhEh8msfjoSsVkpCbVL0g6HQ6RKNROtEFQBN3u1wu6HQ6cByHdDqN7u5utLa25h0Psj1BxCjKaQcUd92TfbPvfve7uPjii/H+++/jV7/6FWZmZvD5z38e8Xgcvb29cLvd0Gg0+MQnPoFt27ahv78fVqsVF198MTo7O3HjjTfixRdfxPbt2wu/VsFHGGXT19cnkvHmm90XK8Ny4sQJqFQqWZnqk8kkXnnlFXzoQx+SdW7EdbCcINdyKXD977SQZ3KXFu6G6lTiHumtbLt8yHFPVgK9Xg+lUolgMEjzLGq1WkQiEZpVhKTYcrlcNHuJsJSNVpvZrFYoFKivr4fJZEIgEBAdczqdCAQCVFVpsVgQiUSosjqdTkOtVqOxsfHPpa/EeDyZMuRkxdXQ0ECrkAsNV752QGaFRgLJyf/CxwFg3bp1tGrHwYMHoVKp8Nhjj+HQoUP44IMP8Ktf/Qq7du3Crl27kEgkkEwm8eyzz+KjH/0orrrqKtx4443Yt29fUeO2dEaFJYTJZEJdXR3MZjNMJhOMRiMMBgP0ej10Oh10Oh1NeKpWq6FSqWiqmUrHUWXz0/e3yG47LV2UYMFxSyuAAdSukEOVXJrVtwH5BqRUUUml9tuqSSXES8QdSVKyke95U1MT9fQQib9SqRQV5DWbzVAqlaJSWEajEStXrsTo6Ch9DbVajaamJoyNjaGvr4++RnNzMy2llUqloFAosGHDBoyMjCAcFvtyjxw5Ao1GQ/fYNmzYgFgshuHh4Zx2AGjOTOIpyZ5AZ7cj12JmZgaHDx9GOBxGNBqFTqfDRRddhK9+9atobm7Grl27EAqF8Nprr+H+++/H2rVrAYgXBsVgxq0GKUUkMh+1pFApKddo1BqLoZicj+Hk83wfy5XOV9olKeUCrlXms2ojFHMDE/exzWbDzMwMpqenMTU1hcnJSUxMTGB8fBxjY2MYHR3FyMgITp48ieHhYQwPD2NwcBCDg4N/zgoEGgogzOxvMBig0+mQTCZF+7OJRAKxWEyUaEBY65HneWzfvh3Hjx+n6eB4nkcoFMKxY8dwzjnn0HYqlQo6nQ4jIyNIJpNQKpW47LLLkEgk8NRTT9H3mkwm8eSTT+KSSy6hq8RLL70UGo0Gjz/+uOi6PPbYYzj11FPR25v5ALZu3Yqmpqa87RoaGnD++efT9/K///u/uPzyy7Fx40a8++67ePvtt3H66adj8+bNqK+vR0dHB13Zbd26Ff/wD/9APVmkf/L+CsHckjVKra485HJirfj/cgOCy3EZlbPyLbSvUIm+S0Vqv210JeBsqvpp5GWkF7B68z8mdE1GdbWVkLscskvgzMzMyJL95/s5efIkrblI9sFCoRBNqWUymRAOh+kxkpVkamoKGo2GPs9oNGJmZoa6MT/zmc/g8ccfx9e//nV86Utfgk6nwy9/+Us0NTXhoosuoqK0mZkZfOxjH8MXv/hFfOITn4BCocCmTZuoiy+RSKC3txc///nPMTIyIjJQLS0t+MY3voF77rkHZrMZW7ZswZNPPomXX34ZTz/9NG2nVqvx/e9/HzfccAM6Ojqwfft2vPzyy3jkkUfw05/+FBqNhgqxnnjiCTQ2NuIf/uEf8NhjjyGZTGLlypUIhUL41re+hdtvvx0mkwmbN2/G5z73OfT394PjOLzwwgv46U9/iksvvZQqLwvBjFsNUs2VW0pZnVgkQrZRI5BVRiWzXhDFpM1mEwlySLzQ+Hgm51K+/J3ZAp7jx4/ntMn3XJ/PB7fbDafTKSkSSiaTiEajeOONNwTHL8GJtcDaE1gS6CPlrY67JuZv3OSsyCqxapPLDxzn4qlLSldM8nwmQ8jx48fp99VqtSIQCNC9eZIF3+l0orm5GTzP01AAUmoHyAgyhPtsRqMRP/jBD/CrX/0KP/jBD8BxHLZu3Yqbb74Za9aswejoKKxWK4DMvWw2m/Hkk0/Sem6PPvoobrvtNtx+++3wer3YuHEjnnvuOWzZIt6+uPvuu2EymfCTn/yEpt/67W9/m1NV4Ctf+Qo4jsODDz6I+++/H93d3XjooYdwww03AJjLNXnhhRfiC1/4Anbt2kWfS2rcfeMb36AZl/r7+/HQQw9hZmYGqVQKfX19uPPOO/Gtb31L8rpzeQbGpb1kqAGCwaAocTIgv0wKz/Ow2WxIp9NUvgsUHqDT6TSGhobQ19dXcJAVPvefjp6JlaOZ88x2SwqzNpD9tnyKsTp/7rHxEhOmJ9RAn9iFT3NLCnE1ilduRG1HVgjmQGYl8/er3waQMfaRSATxeJxmW5f6GRwcxJo1a3LygOb7mZqagk6nQ0tLi6RIKBwOY3BwUJT388b/rkdSBayYnntPxC1Jrn/2yi27KsDoyvwxcfkylKiSuceA/O5RIP9+YLZxy7dyI6scoahEmA9y1clcpSTJH5q950bUkkLDlS+I2+rNNW6FQgHyVZ7P9161WbaLvHdTMHN9ywkH4PlMdYj333+fSvfr6+vh8Xjg9XrR1dWFVCqF2dlZGAwGmi2frGRsNhuam5uRTqeRTCbR0tKCwcFBNDQ0oL6+HqOjo1i7di2OHz8Og8GAzs5OHD9+HKeeeiqOHz8OhUKBFStWwGazYcOGDfjDH/6AG2+8EQcOHMBpp51W8vupBGRMyucJmad3hD6ZrdyqwPHjx2lm7lJ+gMwAGQqFwPM8nE6nrOcQSO41ue0rxXAfoE5ItysXoWuyczK/nFyYB29iYgJerzcnmLQQQ0ND6O3tlaW69Hg8svN+khm53LyfcqiU+ILjCxs4KSY7K1N1G5jf+1nIVVsl6O7uFoUCECGZy+Wiq6v6+npMTU2JUnapVCo4nU7aRqFQQKPRwOPxwGw20/7NZjN8Ph9N40Xi5EKhEBWsAJnMJ+vWraMGZjFYCIUzM25V4PTTT5/XjXPy5EkkEgn098tL8z4yMkIzgJfDfMQkw9LRCkWfm716qwQLsS9WDjuf0CKpFh/LFpOUkk+yFqlWSMBCkR3f5q/LeCoqUb1BrVZDq9XSwG0y+UkkEjQLiUKhQENDA2ZnZ6kRJOEBHo8HBoMBHMfRenAkMByYc1kS40ieS8IDNBoNOC6TXKCtrQ0bN26c/5uqYZhxq0Hmo4Asxld+owWUmdIo/cfn3998DJuwj/kauKUirS93pUSoJcm8nNWbxVf+vttSW5XJgagWU6kUvF4vVSM2NTXR2o0AaCUAp9OJ+vp6ukdHkisT8ZNQdQlkxg3SJ1m9cRwHtVqN5uZmzM7Ogud52cU+K/WeOY7Dr371K0xOTsJgMNAg9FIqccfjcWzfvl20UpWCGbcapFTjRtqXsmIpNujUYnxbIQIF7vVSJwdLXZ1aiwgnHZUuczO6MmM8F5p9+/YVFRwV+jGZTOjt7QXHcdDpdAgEAtQ1p9Vqadot8j3mOA7xeFyUV9JiscDlcolS6LW1tWF0dJQe4zgOK1aswPHjx2ksHc/zsFgscDgcNP/kQhu3p59+Gm+//TbdUyS13Yr9EE2BUqlEOBzGu+++i40bN8oe65hxq1FqfbCtxKpN2JfU6i07JKCS7i85XxThQJUvKTOQO9CRgFmSlBnIZBFejNi8SmIKZtx0hVZvcj+bWlqJCimWemvlypVl7aW/9957NNcpkNlbE6bPslgsCAQCCIVCNJFxc3MzbDYbNYIkufLMzAzUajV4nqcrtenpaZjNZvA8T5WQk5OTqKurE+3dES3AQmX1IerIP/zhDxXrU+4knhm3GqTUPSO5K72UUrrUzFLl4MGD1KhEo1HE43G8/fbbshSk6XQar732Gv2/0HOEK+Th4WHJQY2cC0nKTIxbISa6Cqsba9UQVINac0mSfTcA+L+HO/GHj5SmmOR5Hv39/di/fz90Oh0N5CahAMCcwILkgOR5HjqdTiT7J3ttQCZhOjkGgK5uiEuT4ziYzWYEg0EqRAGANWvW4De/+c2CrdzIuZCVWL7HpI6Vu4fOjFsVmJ2dpbOyUkIAhDP+ZDKJAwcO5B2Qs1cI6XQab775puTrAR/POddyxCSVXLUJ+8yWvJfCz05uxT0XTIDjOLhcLgQCAaxatapoDk/y88Ybb9BiiMVm3xzH4ciRIzAYDFi5cqXkOfn9fhw+fBjnnXceAODRcfHj2WISZxPQZiv/GtQi89l3K8RiGfr5iEoMBgNaW1tpdW1Sm83pdCIej1OjZTKZ4HJllo1kr83v99NKARzHoa2tDcPDw9TAAUB7eztOnjwpUkyTkIFIJELzOlqtVuzbtw/vvfdeyVsZ82Ex8r8y41YFkslkTuJkOTFU5EZzu92IRCLo6uoCIF0Qce/evdi4cWPBwRnI3Fy//S/pcy93vy2hnn84wOhK0Bi8ciDy/Hg8jng8jsbGRolnZCD7INWYzZKJST6l5HJASliyVMQ+2RRyTc7n/bS2tsJms9E0W2q1mk7GyL1rsVgwMzPnfydjh8PhQGNjIxWl6HQ6eL1eNDY20hVdXV0d/H4/VWIqFApYLBZ4PB7qRuc4Djt27MCbb76JV199VTLLx1KGGbcqsGLFCrS1tZX9fFIHTE4sFZAxXAaDgfraq8noSsC4SFVziqXiyh50qiUoKWWmW6lZ8VJ0SQo9ArY2oHu8cNu/JPR6PcLhMP2Ok3skGMxE5SsUCjQ3N9OMHGTFY7FY4PP5RCKUdDoNh8OR0zfJY0kMqNFopOEBZMJ78cUXL2vDBrDEyVVhvoNauWrJYnzlN3ObbdVMvzVfShnIyQCaLdAoZ8+y2sw3DKBckgswfS1HCVnoORNdxZ+30Ia+1Z57LBKJ0DyQwWAQgUAAfr8fPp8PXq8XHo8HbrcbLpcLTqcTDocDkUgmfQyp4UaKjwKZUjDCbQyyb0bEHzyfKVCaSqWoUQQyQdtkP46syogSk2xFkGMKhYJuZ6RSKZqvcjF57bXXaMotwjvvvJNTpaBc2MqtRqlFteRSXEHUGoWUkouVCJlRGKFrUigqefvtt0tWSwYCAVqyRa1WIxaL0Vg0tVqNuro6eL1ekXgpFouJStyQ4G5S543sv01OTopWgh0dHRgdHUUqlaKv39HRgRMnTiAYDC5oKEA+0uk0FAoFbrnlFvT29uK+++5DV1cXXnvtNVx11VV46623aJLp+cCMWw1SLbVkNtlikqUQ31YsgwfZyyB7ntFoVLaIx+12U9lysZ9AIECLPkrFO5EB7OjRowA2lfV+pzoKZ+GvdYKmTNhA70hGqbtYFLpnmpz5jxcjpgV+Et9RkmKS53l88MEHmJ6ept/txsZGOJ1Oet8Q4xYMBlFfXw+FQkHbkHtMo9FApVLBZrPRlZfZbAbHcZidnaUBzmazGQqFAjabjaZ+02q14DgOx44do7FjiwVxrf7hD3/AxRdfjEsvvRT/9//+X/zud7/DH//4x4oYNoAZt5olnU7TchVyfsigW0hdmVJ2zisMYCFXbeUKS3b+0Yi/tT5Lr8GePXtkzazT6TRGRkYKin6AOVFPLBYTFZss9EPiijiOg16fu1wrt4ZbrWJvze/CqyTl3IPFwivsf47MKOW8uyYAr7X081i1ahX27t0rkvmTVFxAZsBXKBTw+XzUSJHgbmEhU4VCQcMHiIFSKBQIh8M09o08FovFoFKp6H0NZIyo1WpdVONGaGtrw+23346HHnoIt9xyCy677DJ0dHRUrH9m3KrAyZMnRfndCkn4i8VUAZmQgmKuDjIDSiaTOHr0aFFFJlDhFBE1yvbt2zE9PY3Z2VlRMuVivPDCCzjjjDOoHLsYR48ehV6vlxUKEAgE4HK5cM/e/ppQSh5bl3usEmnYKoXUflu1+itmmLNrugGlKyaJwnHFihWYmJigwi+LxUKrUJO0VHq9nu5D8TyPhoYG+P1+hEIhmhuyra0N4+PjVG1JRCh2u51OpBQKBVpaWjA1NUWNJc/zWLNmDf7u7/6OFhhdTH784x/j1VdfxRtvvIHZ2Vlcfvnl+OQnP4lXXnkFFsv840eYcasC7e3tsFqtJfnlhT82mw12u1324Pzqq6/izDPPzLtCIPzrSIXe3AIhd/WWT1RSjkCkFLdupfdDC+23TVVoEpvPqBGO/zk393yNXL4ySIWodCqufAgNW1JVePVWCsJ9t1LheZ7K/LNXXm63m353zWazSAFJ2jgcDrS3t4PnM5n+9Xo9gsEgnTCTY8I0XCQInFQZATL7e2eddRb+4z/+A3a7Ha2txRMLVAOyCv3+97+PP/7xjwAyyvCXXnoJOp0O4+PjFSnFw9SSVUCv18NisaCurg5msxkmkwlGoxEGgwF6vZ66JDQaDdRqNS19IVx5VUtQUkgpmW+GSqg1IUmxc61FFkspCcwZLznt5LYthD3POEkCn5Wp3MdKoZR7sJwVYL5zrzQ8nylaStK3kUmYSqWCz+ej/zc3NyOVSlEjyHEcjEYjPB4P9e4YDAbwPE+fRwK+SVJm8nok/RYJDOc4Du3t7bjgggsWzTVJ3ufZZ5+Nt956Cy6XC6FQCENDQ+jp6amYa5Kt3JYBUsaQVAMQMp8yNwvF6MpMMVIpVp0UF8YESltdLUQoALCwOSXLNVSDaypbLX2hmY9r096aP4Yz34rt+PHjBVO65ftttVqh1WpptnuXy4Xm5mZwHAer1YrZ2VkqaCIuSq/XS0vckDpvQjWl0WjE7OwsNVJKpRJarRYzMzNQqVTgeZ7GwNrtc37XVCqFU045BU1NiyvR/dd//Vfs3LkTqVQKLS0teOaZZ/Af//EfNJvKfGHGrQYpZ+VWrZVera3a5LBQxqpcgibpxMLzcUnOdwU2HwNXirBkqmOu6nal99uqSUwL3DJ1Oh5ceVTWNgPP8zh69Ch6enpEx0KhEDguU9Otvr5eVL5GpVIhHo/TNhzHobGxEXa7nUr8Se03l8uVU78t+1h7ezsmJyepUK0WBCXd3d34n//5H0xOTiIcDuPLX/5yRftnxq0GKSeIW4rlmjA5m+t/p8X/b+0sQqEQhoeHJYU75Mt+5MgRkby/WN5Psi8q1TadTiORKJ6TrJLxbfM1akIquYIjIQFAefttE12Fs/QLIX3rI/L6VaZyQxSKVQQAMqs4ICMqkStZT6fTiEajmJiYgNFoFMWskfvQbDbD7XYjHA7TNlarVRQKQFZxDoeDqi6bmprgdDrh9/tRV5c5uZaWFppf1Wg0UmHK5OQkRkZGFj0UQAjP8+jsrM4mLDNuVSC7DlMxdwWQq570+XyIRqOYnJyUFQaQSCRw8uRJKgXO/kkpzyx6vqXuYYWMC5eCa3oFsGI697hwEMp2sSYSCaTTaVF+z2JK0unpaVgsFqo+K/ZD1G4dHR2SbUOhEP7fCytqQilZDpV2Uco1OssRopQkxUY1Gg3N+E/chyqVCoFAAPX19eA4DhqNBgaDQdSG3FfCEBWNRkNdmKSdVquF2+2mJXFIqMHMzAz0ej0NIF9squllYcatCkxPT2NkZKRstSRJ/OvxeGS1B0DLzhd6vBymOspXhy0GZE+ro6MDMzMz6O+Xt5QZHBzEihUrZKUkcjgc0Gq1ojIihZBatRWiUirJSjC45s+rlJPyn1PINVnNJMqVVGDmW73NRylJaG9vp/GUROzh9/sRiUTofpxGo4HD4aAT08bGRtqGBGSTBMxkJadUKmEwGESrPKVSSYubkhAXhUKBtWvX4sknn8SKFUsgY8M8YcatCqxcuZJm9C8Hp9OJkZER2XJYm82Gzs5OyRLstZxTstJUaw+yVIhSstpikqHVmd+aePF25XJyVWkGrlIspb04KbRaLfR6Pc0zSVZTfr8fFosFHMfBYDBQtSMAqqR2u93UxWg0GqHRaGjSBo7jYDKZchIym81mhMNhUe23lpYWHD169M9Zc5Y3LBSgRqmmoGQ+dakWg1LTgtWyoKQa154YtmqTrUgtRra0vtj7nq8Bq0bcnJSrvtAeNtlrJVL+RCKBeDxOtyBItWySwk2pVEKtVsPtziiMOI5Da2srEokEzVBEVnQej4e+jsViQTKZFOWebGlpQTKZRCwWo16blpYWxONxGv8GAJs3b8bY2Bimp/P4+5cRbOVWBeY7uJb6/GLt84UBCCn0Ja4l11ghpDb/a518YpKlcN3ngy4KRHWLfRblQVyTEX1m//DTL2txQ2pXjkgp37ZAXV0dlf5zHAe32w2dTkdXWG63m8r3dTod3X8jySAsFgsVoAj31aanp6HRaMDzPHVtTk5OQqlU0r09jUaD8fG5mkMqlQpf//rXl71rkq3capBy1JLF2i8HpaTU6k24Mvh/b3SX5ZYsNOuOxWKIRqOIRCJIJBKIxWKySp3c+Hz144gWatVGKGX1Nl/krOiqme1EavUW1wDbtm3DX/3VX+Hiiy/Gjh07cOmll2LHjh245JJLcPHFF2P79u246KKLEIvFaDVtIJME2e/PbOIRST8RQpHHSSgAkNlDE8alkVVfMBjEXXfdhQsuuADnnHMOfvCDH9DKAcRlSRJECEveqNVqRKNR3HzzzWhvb4der8fWrVvx+uuv57zPdDqNe+65BytXroROp8PGjRvx+9//Pu81efjhh7Fu3TpotVr09/fjX/7lX3La/Pd//zf+z//5P1i7di0UCgUuuuiigtd49+7dOO+886DX69HW1oZvfvOb1K0rBVu51Si1sme01IjoM/tObrcbb7zxhiy1aTqdxssvvwxAuuo5UWA6HA7JtiO9HfOqLC7FQhs2wslVQMusdDt3gzieL59rcqnvqcnJR0qEHIcPH6YGymq1wm630xWWyWSCy+VCJBKhVQFMJhMN0uZ5HmazGXa7HS6XCwaDgRonALjttttgNpvxwAMP4NZbb8UDDzwAi8VC1ZLd3d04cuQIAoEAjXO7/vrr8eyzz+L+++/HqlWr8LOf/Qw7duzAnj17RKn/7rjjDjzwwAO4++67ccYZZ+CJJ57AFVdcgV27duFjH/sYbffwww9j586duPXWW7F9+3a89NJLuOGGG8DzPL761a/Sdn/84x9x6NAhnHvuuSJ3aTbvv/8+nTTs2rULIyMjuPnmmzE1NYUnn3xS+rORbMEoGY/HIysOqtAPmbG98847stpHo1EcOHAAHMeJwgwyYQCfKPn8K+EaG+7LPdY3PP9+5RDXZNxAGzZskKU2feWVV/ChD32IFoksxvHjx6FWq+XFOB2owJvJw+jKjHvvL51qrNqy3aauRoCrwDzTYrGIZP1KpRJWq5Wm1OK4TC5I4h3gOA5arRY8z4vCigDA6/VCrVbjT3/6EyYnJ/HLX/4Szc3N6O3thV6vx86dO/HSSy/hU5/6FN3jI6n+jhw5Ap7nYbPZ8Otf/xqPPPIIvvCFLwAALrzwQmzYsAF33nknnnnmGQCZ5O0PPPAAbrnlFtx0000AMqvVoaEh3HLLLdS4JZNJ3Hbbbbj22mtx991303bT09O444478KUvfYkmjH744Ydp0vcPfehDBa/Zd77zHXR2duKpp56iz9VoNLjuuuvw7W9/G1u2bCl6zZlxqyJKpTLH904+1GK/Q6EQJiYm0NfXV7Qt6ffQoUPo6+uD1WrNaXP3B0DP2JxSstpiknxGLfuxco1cvpi3QvtuKpWKSqelEJYEqQZEKSm89vn22xzN0plLaoWJrkz5l2IUks5Xat+tEvL8cl4TKE/92tzcjJGRTAZzshLzeDyIRCKoq6uDUqmETqeDw+Gg4QLNzc04efIkYrEYjEYjrfPm8XjoCqu3txfxeBwulwutra3YsmUL3n77bXzqU58SFUBVKpXQ6/Xo6OjA/v37oVarcdVVV9HzU6lUuPrqq3HvvfciFotBq9Xi+eefRzwexzXXXCN6L9dccw2++MUvYmRkBL29vdizZw8cDkdOu2uvvRaPPvoodu/ejW3btgGYG5uKkUgk8Nxzz+Gb3/wmNWwAcOWVV+LLX/4ynn76aWbcFoP6+npJWX4xvF4vZmZm0NgoL7qa5JSTs/IQUskExCO98pPjDvdlMkP0VrhSgTATRq0w3Jc/CL1caikdmhwDl+2ajOrkrTql3JULKbyplBFVKBSiitskADsUCtEkyTqdDqFQiLoiVSoVNBoNfD4fGhoaqADF7/djdHQUO3bsAJDxVJDip2vWrMGzzz4Lq9UKl8slmvD29fXh05/+NBobG9Hb2wuDQRwftGHDBsTjcQwNDWHDhg0YGBiAVqvF6tWrc9oBwJEjR9Db24uBgQEAwKmnnlqwHTFuchgeHkY0Gs3pT6fToa+vD0eOHJHsgxm3GqQctWS+PbqL3tUCJS5Iyhk0RsosDTXSW3kDR2B7lrXPTHv1C5xWm7/ercUvVhZP80YSJwOgcWyhUIiqG7VarcgIkTpsJMWWSqVCMpmk4QJAppJ3MBiEyWSiHpzW1laabScYDFIRClFZclwm2fL69euxZ88ebNy4Mef9kKTF5LXcbjdVbEq1AzIT+2Lt5FKoP9KnnP6YWrIGKVUtCSzeYF6uYSv3+XJi3iJ64Jvq88s7oQrxkQPFJaq2NvH/jmbpPmtp1UaQIwhZChUoSiE7GYLb7YbX64Xf70cwGKQFSOPxOFXdDgwMIJVKURd4IBCgqzUiDiFxbTqdDmq1mqbZIis+EufG8zx11QWDc64KUuCTHON5nhpVUvgYyGRKaW1tzZtfMnscIUZRTjugcjGmxfqTO9axlVsNUk4oQCES88xrWMwlM1/DJuxnPiu4fO7VlBLU/SP1k0qlRGVCyGwbyM37SVKiCWXbwvbkN3BWTlJeAtm3+UummGuyWi7JYjXbmpzFnyv8HjQ5MwYuoge0MeD0008v+tx0Oo1IJAKPx0NTZun1enovAZmVmMPhoOpLvV5PK3ADma2HxsZGmmKLZCUJBAKIx+M09R4AuFwuut9MsqDMzs7S9HKpVArt7e2ioHACOUZWXA0NDSLRS7F2QMbQt7e303ZkhVVqGZtiKz6Px0PdncVgxm2RIUYsOxEyUUECc8pHYaCocDBNJpPw+Xy5AzfXDSC/mCSfQShl0KiUYRP2J0deXgpHj8ovSeLxeKBSqWTl8VQoFJJJlmHLnAOZXMxXyFOLqzaCnL03IXL33SqFrQ1QS6T5dDZJG7h8yIkh5XkefX19eOedd6DRaKh70OVy0RWYyWSC2+2mmUtIKq7Z2VmqmiRVAgKBAOrq6tDd3Y2ZmRlEIhFayRuYS8dHxgiOyxQonZqaonGcXV1dOHToEMLhsGjf7ciRI9BoNHSPbcOGDYjFYhgeHhbtu5E9r1NOOYW2A4CBgQGRcctuJ5e+vj5otVq6l0eIRqM4efIkrrjiCsk+mHGrAna7HQMDA7Kl/wByBtBUKoW33npL1uAcDocxPT0Np9NJ3RgAAGX3Yl2CqlJsIBKKSrZu3Sqrv1deeQXr16+XJchJp9NQqVTSoQA2WS8NQJ5LcqmTLSwpl1JXbdnu32IQBWs1REk6nQ5Wq5VOQonqkZSvATKrtUAgQNNnkQlUPB6HXq+nAdlkBXjOOefgkUcegcfjgVqtRktLC+x2O95//318/vOfRzAYRFNTE3g+U/JmenoaY2NjSKfTOPvss/Ff//VfeOqpp3DdddcByMj5n3zySVxyySU0Pu7SSy+FRqPB448/ju985zv0/Tz22GM49dRT0dubmeVu3boVTU1NePzxx7F9+3ZRu4aGBpx/fmnbBBqNBpdeeil++9vf4q677qIr2t/97neIxWK47LLLJPtgxq0KNDQ04IwzzpBlmIQGjRAMBnHw4EFccMEFsl5v//796OnpQXNz1ih5qEJvKIuJrow7phr9lrIC+Esh36ptoVc/Ukx0ARZfac9ZPQQEyhcVS1KKYZOD0DUZNgCGcObv08a1ONwt/YUgVQCAzGqOVNwmHhphVQAiJmlubsbo6Cjdn1MqlXTVt2PHDjz//PP43ve+h7/927/FkSNH8NBDD6GtrQ1XXnklIpEIotEo7HY7PvWpT+Gaa67BlVdeCYvFgr6+Plx11VW48cYbkUgk0Nvbi5///OcYGRnB448/Ts+5paUF3/jGN3DPPffAbDZjy5YtePLJJ/Hyyy/j6aefpu3UajW+//3v44YbbkBHRwe2b9+Ol19+GY888gh++tOfiipujI2NYd++fQBAhTS/+93vAABnnXUWenp6AAB33XUXtm7diiuvvBJf+9rXMDo6iptvvhmf+cxncMYZZ0heb2bcqoBarYbRaCz7+ZVQS5aqlHQ0A1avdLtqZ5Qo18Dl2xu84D0tXt9YWSss57P50GEtClV3Wc77bbY2oE3mirWQcZ5pr0y+0PkYNk89UJ+7HTVvOI5DfX09HA4Hraat0+kQDodp4LZarUYikUAikaDub61Wi0AgQCevdXV1sNls0Gg0+Pd//3fcdddd+PGPfwye53H66afjBz/4AQwGA5RKpcgVCQBtbW0YHx8Hz/N49NFHcdttt+H222+H1+vFxo0b8dxzz+XEj919990wmUz4yU9+ApvNhv7+fvz2t7/FJz4hThDxla98BRzH4cEHH8T999+P7u5uPPTQQ7jhhhtE7V555RUaOE4gbsZHH30Un//85wEAmzZtwvPPP49vf/vb+Ou//mtYLBZ87nOfww9+8AN51zuPcIFpqOcJyU1YLuFwGPv27cOFF14oq/2BAwfQ1dWFlpYWeuyid7XgucyeD4mzIvs+/rpcCXYx4yY0GsS45Vu5yY1zA3IrIANz+xdC45ZvZu+1Zn4LXZP21rnzNAWBsZ5Mcls5xu2VV17B1q1bZbklT5w4AaVSSQPs8/GRA1r6/hJq8WAtNG5ttlyXZLbrbqqjcGHYfMYhX8mbUj6XZJ7pbr46bPn2miL6XOOWbcx5wdxAF81VHhYybo2u/C7JfGInfSTXuEntuQkh+6TEwGXfg3X+jAuTrNzcDcC/jb6SNwQAyLiyu7u7kUwmkUqlMDk5Cb1ej9bWVrhcLsRiMRrAHY/HYbVaMTU1BaPRiBUrVsButyMUCqGhoQF+vx/Nzc1Ip9OYmprC2rVr4fF46Gu5XC6sX78eHo+H5kYNBAI4/fTTMT4+jk2bNmHTpk04++yzZaWwWoLQO4yt3KpAJeSwpaol87UXKiUrkZlkofIAVsI92TOWGSjlUolQCuEeKjB/pepSpJTVWzXPoRKUsoIrluotFoth//79aGtrA8dxUKlUiEQitM4aqc1GpPk6nQ5arZZWy84WoPA8TwUkQhVkS0sLXC4X/H4/HYM6Ojpw7NgxKlRRKBTo7OzEsWPHkEgkRNk/lhvMuNUgFTGOf+5CzgArR9Cw0Alu52PghKKSw4cPSwp6EokEDh06RCcJUm0BYHR0NG/YAACg+ZPzffsAlmf5m4AZMAcyf0d1mdUPWb2VMhkphL218nuR5kB+D4Jw343EmOVDo9Ggs7MTdrudlr0hxoqoJ5ubm2Gz2aj3wGg0wu12IxwOU6NktVppIVMyRgSDQZjNZtpGqVTCbrfTBM3EeI2Pj1ODqFKpcO+99y5rwwYw41YVEokEjQ0p5ycejyORSODkyZOy2vv9fiSTSdjtdkGc1TmLeg0WgmzVZL59t/r6ekkxj9/vp+U8pNqOjIxAqVSit7e3YJsfFkiYvJz324RUY/W2WIY+3+ot+3PsmAJOS2rxfldhq9rV1YXJyUlEIhFwXCYpMgnyJjkfyX4bAFqvbXZ2llbgbmxspAaPxMu1tbVhZmaGpvtTKBQwGAzw+/30fgZAS9wAoFUBljvMuFWBYDCIY8eOiXK6laKcJJkKyCYz+SnUj9frhdFopGlyOI4DCqQ1KmeAXayyJBNd8kQuxfissw+vbSq+70YytAtjhQqhUqmoqi0fxcQk2RRbMS/HVRuQmXzwZTgmfBZpNWaxIO354KkHVEW20EkS5UL77ETMUV9fD4/HQw1LU1MTZmZmqPEiZW9IKABZiUWjUWi1WmrwfD4f6uvr6XPUajU1msBcgmZhgvWOjg4cP34cwWCQGTdG+dTX18uOscpHLBaDw+FAf3+/rPZutxsNDQ00eLIUpeRyjrGKa0oTU+Qj317chiIBqedlCTqWatXp+VJs9ZbtmgwbMsZrKUJck0nVXKxqPlKpFLRarWh1Rv4ne2tKpRJqtRoOhwN1dXXUXTk2NkbjvEiiAZcro7rheR51dXVwOBzUwBFVptvtpqpMouA+evQo0uk0M26MxaGQQKSU9pUSk9jaMuqzxWKmHWifKfx4oYBu8p5TSkCnlUgj8efM6rI47TTJJinlX6aYpFrIWZFVa9VGyK44EdHnfi8KGTayAiMJlGdmZkR5Jb1eLzVwpNRNNBqlOST1er2ophupAEAgSsupqSkAoIITpVIJm81GxwedTodUKoVVq1Yx48Yoj+effx79/f2iNDT5KGTA0uk0/lpQ4VaSs88W/Xvun38vlwFWysAJWYwaX3LIdgf76wor8ZaLS9LWNie4yEa4epsv1TZscjl69GjRvXESq6ZSqRAOh9HQ0ACFQgGNRgOn0wmLxQKO49DU1ITp6WkqNtHr9YhGowgEAnRlRgQoJOejSqVCOp2mqfuAjOpSmJaP4zg0NDTgmWeewUc/+lF8+MMfXuQrVl2YcasCP/rRj/DVr35VFHdWCvNVSxba08geYKVckpXO8MBYHAbXAIq0dDsgE0JRSeTkbCw2CasVwwUUXr2FDZn38Ld1Z2AXf6LgXno6nQbHcXA6nYjFYtSNSFZ1ZLVGajPGYjGaqkun02F2dhYGgwE8z8NiscBms8HtdtNUWStWrMDg4KBor76jowNjY2PUPdnT0wOr1Yr77rsPn/3sZyuizK5VWMmbKlBXV4dgMEgzcpf6Q/zrCw0Jjq5FisnE81W1JuQLQK4W5+6dfx+VWrWdXDX3UwojvZVPii2HUlN3EWrJ+CVVmQTIBoMBOp0OGo0GKpVKJOwgqy+9Xk/3zchqLRgMUrWz2WxGKpUSGUCz2UwVj0RcRvbVgMwenkqlwuxsJgM5MYIcx8HhcFBDZrFYcMsttyxrwwawlVtVMJvNCARyfS6lhAMgq0KuXM7dW54aLZvlsGqLaTOZVM5+B3jnbOn28yV7dVRITFLtkIBSDVo+iIGrRDHZQqu3SromFwqpau8nThReuRFj0tLSArfbTYO5has1YZ5JYqgsFgt4nkdTUxN8Ph/i8Thd0VmtVlrRAshI/lOpFEKhEHVPqlQqeL1eWtstnU6XnKV/KcKMWwW4/PLLsX//fiSTSSSTSfj9fjz11FO46aab8NGPfhSf//zn82b/L/bzTDSKy7Jyt5XDclLryd17y953K1RXrRrkE5PINWbOpsKptuQw1jN/dWg2I72ZOK5qk881KbUqczSXl8FfWDw1e0JSauhJtrDk7LOlZ1GJRAJutxuNjY2YmpqiYSVms5kWOiXjgFKpRCSSeQESD0dScHEcB6vVSuNcgcyKrr6+ngaEk35aWlrgcDiQTqeZWpIhn3/6p39CMpmkMVA//OEPoVQqceONN9JUOsVkwvl4//33yz6fhFp6gC2237YUV221KiSpBCGjtNEb66ne64//uXJS93j5fRRbvREsvuqGBMipCO61ZiYoxe6lfOpj8n3bNGXAz0ZfkPTMpNNpNDY2UrEIz/NQKpVQKpVwOp1obGykRml8fJxmLiGhBMJCpw0NDZidnaUGTqPRwGw204rcHMfBbDbD7XZjfHwcqVRq0bY+FpLl/w4XgL1792JgYIAmRj148CAA4Oabb0Zvby/+5m/+puQsJeFwAZmZBJVwSdYyM+2LG5owXwqt4ortG0pRTcMmZLx7fgZOilLUvaXGZ8oxbELI51TqhCmpymSzl/LMpNNpzMzMwGAwIBwOIxKJiFZT4XCYhgIYjUa6elMoFLSwqVDiny37r6+vh9/vh9frFe21TUxMoKGhga3cGPIQptHRarWor6///9o77/AoqvWPf7dvek9IJQmhaICAqMBFgUAUUARp4lUQBalXuaAioAKCIIiAAiolomLBfik/uICUIC30HkJJJZCebEjZ3WTL+f2xd4Yts7uz2QSSzfk8zzyQ2TO7M7Oz53ve97znfaFUKtG6dWtERETA09PToQwlAoEABQU8Y98bmOZotXFhLCJ1UqD7SeBkI2YkMw8muV/u4PslbAzOCJw1642r/E1DBoqU+ztWFcAYax4B43NWuRmqOTBWaFlZGWd1APO/q6qqIBaLIRaLUVZWxkZXM5lLGFHy9PRETU0Nqqur2f7B398fpaWl7HuJxWLU1NRALBazVqBUKkV+fj4b0MIkXa6srGyQROFNHSpuDcDQoUORlJTElrrx8PDAoUOHMGTIEDa1Ex83BdcPwhlsBTQ4m9bqQVIWwF0WhasjYoJKGtuivR3B3emr5YYtqKThP/N+CxvDrSjLkkkNBZ+oSUesNkctNi4qvS1LCXnUWM7lMpanUqHkHLCap8+Ty+Vwd3dnU3IxbkSZTAZ3d3fU1Bh80Uxdt+LiYjaHJCNuTJ5JAAgNDUVeXh50Oh0kEgmEQiE8PDzYtW4CgQC9evVCfn4+tmzZgkWLFjl/c5owVNwagMWLF2Pjxo3snJtGo4Fer8eZM2cQERGBJUuWOGy5MRkLHMFapCTfgIZyf+uLbps79yOopL6ZSerjkrwTbjvfYWPDLFlwNNikNNBSKDyr79WR00gMg5eGoCGEjYFr3tNawdXEuEeQL6rhnSQdMIgVsyibEAJfX19UV1ezSwEYgVOpVHBzc2OXDJWVlbE5Ub29vSESiVBZWQk3NzcQQhAWFgaFQsFWF2C8S8xyAVeGilsD8PHHH5tUhz106BDee+897N+/v97vyZS2cITc1oZowqaUmYRJuuxsfTZzrFlvTZmGWgLQlDKY3Al3XOC4kiBbE4r60pDCxmArsEdllHM7oAzYf2k/r0EsAHZNnIeHB7uESCQSsevTmPI1wcHByMrKYt2LjFCVl5ezbkY3NzfU1NSYLBeQSqUoLi5GSIjB1ysQCDBv3ryGv0FNDCpuDcB///tfbNmyhV0KUFZWhvz8fPTr1w8AsHz5cocDSvR6PRAW1uDnaq2DbYjOwFb1APPXmOrgDY2xa9K4w2zMxdxM554XaUgW7Mh8m6NWW1MSNob6CJwtAsqsW29NLdG3uShrJIb5vaSkJN7R0VqtFllZWfD29kZVVRXUajW7PEAoFLJr1sRiMTw8PNhgM2YpADM/xwiet7c3iouL2akNiUQCvV6PykrDD4NWBaDwpnXr1hg4cCDrliwtLcXatWsxdepUiMVixMbGOuyWZLIOOIKxS/J+rm+7HXHv/3zTPDHHRNyu/+fytd6YebfQgoYpiGmOwMrcfEN/B01R2BjuhBuCKvhiy3pz1vPgyEBNL+T/zAK2rTdG2DQS4ObNmw4NZJVKJWuhlZaWIux/A9ugoCDcuXPHpEq3SqViq20LhUIEBASguLiYtd7c3d1RW1trMm8fGBiI27dvsyVv6FIACi/Cw8NZq02n08Hd3R1VVVWQy+XQarVQKpWQyWSOW24B/CcfrJUXUcvtZ4FwxmozFjZnjndG5Piib8Rkc3qh7ffnspgdsdqasrAxFIU0XKCJSGc5T8rHalP4GQYyjYm5wHG5VHu36YKTt9N5D2aZLCV5eXkQiUSse5JZCsBYb0yeyaKiIkilUhBC4OXlhZKSEpSVlbHWYkhICHJyctg8k0xg27Vr1+gibgp/UlNTMXv2bDasl3ElLFu2DGKxGPPmzWMXZTqyOYKA2I8IbMi0T86KGtf71SeikMt6s+aapDQ+jgicLeutPgFACj/rrzFWFR+4hNWcGg/bnwUYEhk7MqBlUm8ZB5cAhvVpVVVVJkEhzCJtJgpSKBSitLQUnp6e7No3gUCAO3fusOLp5eWFjIwMxMfHU3FzZfLy8jBz5kzs22fIJpCUlITPP/8cUVFRdo9Vq9WYN28efvzxR1RUVKBLly744osv0Lt3b7aNXC7H/v37eVV35oIQgoMpKeiXmMj/GAF/l06Fr2E5QH2stoLQxonUY1yGfMvbOErE7YZPtGs+18S4IhvSJVkcbBlh2NJQ+DmXmqyxYb5vRkR97gJHLx51eEAbGBgIsVgMT09Pdo5MJBJBKBSiuLiYzQ8ZHByMu3fvora2lu1j/P39UVFRwWYzYaKuRSIRa/WFhYXh3LlzuH37tsvnl2yR4qZUKtGvXz/IZDJs3rwZAoEAH3zwARITE3Hp0iV4eNgYlgGYMGECdu3ahU8//RSxsbFYunQpEhMT0aNHD7i7u0Or1cLNzQ29e/eGTqfD9OnT0b59e4eDShzhfmUmaYw5K67PcETgygLsz5vU/q9eaUPPu1mbbzNG5WbpKrvrwy8vYnH9qiY9UBrCenMUW1abPYxTgDHwWRLDzOVa46Unn0WB2LG1NRqNBhkZGWzOSJVKxdZ1YxItA2AXaRsnRA4MDER5eblJbsrw8HBkZ2ezrshOnTpBo9Fg8eLF2LJli0Pn1txokeKWnJyMrKwsXL9+HXFxcQCAzp07o23bttiwYQPeeustq8devHgRW7ZswTfffIPXXnsNANCpUyd07doVWq0W7777LkQiESZOnIiZM2ciNDQUbdu2ZUtPOLJdvXq1XtfHZT1wuSQdtdruh7AZf1ZogSHVlsrM+HVXGmpo2cKaC7Yx5t3szbfVl+YobAyOCpythM/2hKs+wmYsaFwDI2O3o0fNvUARc4wFTis2eDSYdkQAXLt2zeG5dqVSyQaUlJWVsUWPg4KCcOvWLXYNm0QiQV1dHbtIm0nNVVVVxSaF8PT0hEQigUKhYDOgEEKwZs0ax29aM6NFituOHTvQo0cPVtgAICYmBr169cL27dttituOHTsgkUgwevRodp+vry+effZZfPvtt5BKpRAKhZDJZLh79y6kUil8fX3ZyV9HNr75JUMLGt9yu5/CZvyZfC04W+VTGmveLbie62BtJQdmghWas7AxFIXUv6SNI3NkjsBlpdmDETpHXcN6oSFy0XgO3TxLCdem1+shlUqRm5sLgUDAzq0xa+EYy0woFMLHxwdlZWWsmEmlUkilUpSUlLD9iJubG6qqqtgISkII/P0bYSFgE6NFFitNS0tDx44dLfbHx8fbtZbS0tIQExPDprwBDKOrffv2QavVYvr06Zg7dy5KSkrw/fff48svv8Tx48eRn5+PwsJCFBcXo7S0FOXl5aioqEBlZSWqq6vZUhdMnkpHI5qIwLFJeEd+5A9C2Bris80tvlpZw1pY5p0vk2XD2GI2P4eWBl/vgHmABt/5NS6rjXFBm1MfYTPGmruU+Tx3pWmmFb0QeDy8A8LCwhASEoLg4GAEBgbCz88PPj4+8PLygoeHB9zc3CCTySCRSNg6bkzwiL+/PxQKBTtNwRQxZVJ1lZWVYcWKFXjppZfQtWtXvPfee6iurjbJH8lESpaUlECr1bLCqFarMWvWLISGhsLNzQ09e/bE4cOHLa5Pr9dj6dKliI6OhlwuR0JCAv7880/Oe5GcnIwOHTpAJpOhffv2WL9+PWe7bdu2oWvXrpDL5WjdujUWL15ssfzpww8/5BT/559/3tbXxNIiLbfy8nL4+Vn+KpgHydFjQ0NDkZycjKeeegpffPEFnnzySTz77LMYN24cBg8eXO/zLCy0Et/PA3suSb6UBt6/NE9i7b3OwfwcuBLuGuNRw7/4ZUPNu/GZbzOHT0kXV7DajCn357cGzjzEnrHeAku5l01UefG3yKu8GsYSZH5X5p9rbf5NLwQOHTzEWmwAOPNMckVKBwQEWASXMBlHiooMPt9p06ZBLpdj+vTpCAoKwpdffonp06fjl19+YTOXMHks1Wo1u9QAsIwd+PLLLzFgwACkpqaiS5cu7DXMmzcPK1aswJIlS9CtWzf88ssvGDVqFHbu3IlnnnmGbZecnIzJkydj7ty5SEpKwoEDBzBt2jQQQjB16lS23d69ezFixAhMmDABq1atwvnz5/Hee++hqqoKn3zyicU9PHr0qMlAn6/V2SLFDQBnqD2fIA7mYTHft3jxYgDAe++9Bx8fH1y4cAF5eXlYunQpevfujWHDhtUvS0ms/bLKjbV425kyLA0NH4GzhbFrsiGtN1vzbfWx2sr9G3+d1oOAr8Bx4WxeUGctNi7UcsvBDWPBMXNvbirDvjF9nnM4sAQwBJfcvHmTLV/DuCOZ6Mk//vgD+fn52L17N1QqFSQSCZYvX47Ro0dj9+7d6N69O8rK7q2TCQkJwa1btxAWFsYZO9CnTx/Ex8dj/vz52LFjBwCguLgYK1aswJw5c/DOO+8AABITE5GRkYE5c+aw4qbVavH+++9j7NixWLJkCdsuPz8f8+bNw+uvvw6JxDAZOWfOHDzxxBPYuHEj2666uhqLFy/GzJkz0aqVaWmS7t2712vReYsUNz8/P5SXW/7SFAoFp0VnjL+/P27dskz/npCQgL///hujRo1CbGwsvvrqK7Rr1w7/+Mc/EB4ejpiYGIcDSpis4Laoz3wbnx97UxI2Bj4CZ269mVdKbiispZuyNbhozEKczQE+AmfNevNTmKZQ4/MMN4aoGUME1q13RuCYDCjeMnecSzMUIGYGrnwGt9XV1WxnX1xcjMDAQBBCEBISguPHjyM+Ph7R0dG4du0am6OyY8eOOHDgALp3747i4mJ4e3uzAShpaWkAgO3bt1vEDojFYrz44otYtmwZamtrIZPJsHfvXtTV1WHMmDEm1zdmzBiMHz8e2dnZiImJQWpqKkpKSizajR07Ft9++y2OHj2KxMRE5OXl4cKFC6ywGbdbsGABdu/ezYqts7TIObf4+Hj2Szbm6tWrdtd+xMfHIzs72yTYQyAQQCKRQCKR4Omnn0b79u0REhLCpsZhLD29Xg+tVou6ujqo1WoolUrWP15RUYHy8nKUlpaiuLgYhYWFnAJsDePRrXEHez/TcN0PnBVdrbhxIhu53KmO0hjJfpsafK7RfP7NPEqxsUXLEcxzlpo/B8aWPeOOFIvFbFkbT09PeHt7w9fXF/7+/ggMDERwcDBatWqF8PBwtGvXziThMVPEVCqVIi8vDxER97IpBAcHs3UkMzIy2Dk7JruJQCDAyJEjkZ+fj127dlnEDgCG/q2urg4ZGRkADDEGMpnMJPiOaQeAjVFg+lPzWAa+7Zhz4Yp5iIyMhEgkQuvWrTF79mx2OYQ9WqTlNmTIELzzzjvIyspC7P/cfjk5OTh27BiWLVtm99gFCxbg999/x7hx4wAYTPIvvvgCIpGIzTFZUVEBNzc37NixA507d8b06dMdiphyJEMJY7nxcd80V6vNEazNvRkLvTPzbsHF9ufbzF2S9qy2liBsDNYKgNrDkQjK+ymAdVLTSErGamOETi80BJt0fbgTKmst3ZN8MpcwC7zz8/PZgqRVVVVwd3dni5hKJBJ4enrCzc0Nd+/eZY8pLy+HSqWCj48PRCIR5HI56urqrMYdAGAH1uXl5fD19bXoj7jaAbB4T77tmH3GA/q4uDgsW7YMXbt2hUAgwF9//YXPPvsM586dw759+7i+ChNapLhNnDgRn3/+Obs2jTHZQ0NDMXnyZLZdbm4u2rRpg/nz52P+/PkADEIWGxuL8ePHY9KkSfDx8YFcLgchBMePH8cjjzwCAFi1ahVu3ryJlStXNtp1tCq07ZKsj9XWHIStNNCxunNcrklnrDdmTZb5fFt9rbeWJGwM9gTOmvVmLlpcyzxqPOoXPGJtjpRP0Iq5wBmjF957NlJSUjiTNdgb6Hp5eUEikcDd3d3EaySTydjAM2ZdG5Mw2fjYyspKhISEQKfTQSaTITAwkI24NMY87oArxsBaO+YzbWGrnfl7mrs4n3rqKURERGDGjBnYv38/kpKSbH5WixQ3Y8vIuAS8ucVECIFOpzPJrv3LL78gODgY0dHROH/+PBQKBZtPctOmTfj555+h1Wpx8eJF1NTU4OWXX4aPjw8bNWTsT+eVpcTGF8gnn6Qx9kazFb73L82TUO+cwDDpw6xR5WXIfMFlMTEj6/rgc9cQfm4892csalzzSiq3plEENt9OBaXGKkNkDXsCxxWBKFfbHrTZyvnIhcrNfnYb5vOY35q1gB9jF6X5nBtz/NCBz6K8ptJhL41Go0F2djZ8fHxQXV0NtVrN5pdk1rExC7nVajWbZYkQQ0JmZu1bSEgIRCKR1dgBJlqcsbiMlyIYnydXO8BgmTGLzpm/rbUzp6Kiwm4k5D//+U/MmDEDp0+fpuLGRXJyMm7dumWSoSQ7O9siQ0l0dLTFaGL27NkICjJNT56bm4vo6Gikp6dj0KBBrFsyNzcXjzzyCHx8fODv7293dMblrkw5dAiJfftavRbz9W1cP3yuFEfmVPjafr0pYk/gjGGsN53onuVVH9ckV5Qc12fxpbGstsJW9tuYwyV+1qpNcC3bsJbFwxaOCJy0znZdPkeEzZn1h0xUJJfIGQ+ctGLTDDuyWsOxZWVlllHRgM2Br16vh0KhgK+vL0QiEYqKihATE4Ps7GyEhISgsrIStbW1EAgEuHXrFmJiYkwsOE9PTygUCnh5eUEkEiE+Ph5bt26FUqk0mXe7evUqpFIp2y/Gx8ejtrYWmZmZJvNuzNwYE6PAzK2lpaWZiJutdj179mTb5eTkQKlU8s53yWdA0CIDSuxlKLGFubABhnpuwcHBiImJwaxZszBz5ky88MILAIC3334br732Glq1asUu4vT394evry+8vb3h6ekJd3d3yGQy1gIE7gWfWFvIbd7pmM+3mYtcU5qEb0hsibK9a7ZnOQqI6SatuydsfF2StjrR+giQLYpCDALVkO9b2MrwvszmKHzcg46sw9QLud2EfIVN5dZwC+trZdwCb7zPeN6NeV7iWseYJHO4e/euSTKH2tpaNpEDYJijl0gkCAoKYmu+EULQo0cPXL16FQUFBRAKhSgpKcGdO3dw5coVDBw4EIQQNvhCIBAgJCQEhYWFEIvFGDJkCDQaDX7//fd756rV4tdff8XTTz8Nmcyg4AMHDoRUKsVPP/1kcp0//vgjOnbsiJiYGABAz549ERgYyNnO398fvXr1AgBERUUhISGBs51EIsGgQYNs3nPmuO7du9tsB7RQyy0tLQ1Dhw612B8fH2/yZfMlPT0dxcXF+PXXX/Gf//wHWq0WGo0GWq2WLUGxdetWtnQ8H8sNAOtiYGA6VqHeuXVD5jRHq80YvhaccaemFfN3wQqI4Z5zWWzmnRvfebdqT37t+NDQlQ7MMXYhM5/VUHXbGJTu1l235u5JRuCYARwfYeMSooaCeV9jV7exBccsGdAL7/2/1+M9UKV23FddV2d4aENCQtC3b19s27YN06ZNwwsvvAChUIiffvoJwcHBePnll5Gbm4vCwkKoVCqMHDkS//rXv+Dn54ewsDB06dIFo0ePxowZM6DRaBATE4N169YhOzvbRHiCg4Mxc+ZMLF26FF5eXnjkkUfw66+/4uDBgyaGgEQiwUcffYRp06YhPDwcSUlJOHjwIL755husXbuWrSwOAB9//DEGDx6MyZMn45///CfOnz+PxYsX49///rfJGreuXbvilVdeQfv27SEQCLBv3z6sXbsWAwcORCKPaiktUtycyVBijlarxZQpUxAQEIDU1FQEBgZCJBLh+vXreOWVV3Dq1CmnaidlZ2ebdKpMR8tgbLFxpX9i/rbWcTR3YbMH17wN45rUC227uojA0M78ngOGwYU9QW3s1FsFoY5VkW5IikLuzUE5s7jeGEcEjkEtt28dWkvH1dCYz+Uaiykjaow7V0CAc+fO1Suxg16vh1wuh7e3N5YuXYqffvoJK1euhEAgQKdOnfDmm2/C09OTHSyr1Wo2tVWHDh3w8ccfIz8/H99++y3ef/99fPDBB6ioqEBCQgL27NnDBsUxLFmyBJ6enli9ejUKCwvRvn17/Pbbb3juuedM2k2ZMgUCgQArV67Ep59+iqioKHzxxReYNm2aSbtnnnkGf/zxBxYuXIjvvvsOISEheO+99/D++++btGvfvj2++OILFBQUQKfTscF97777Lq/vQ8CRlaMeSYWaF1KpFG+//TaWLl1qsv/999/HJ598Aq2Wf7TBlClTsGnTJmzYsAFhYWFsNe6CggKsXLkSU6dOhVarRVJSEmvFcT2w1h7m6upqJPbuA+BeJ8t0aH4KQ0fNCJxWbOhw+Yob1/wIlzXDFXxhLSDDkc6Wyy3INbrm2sclSFydnHm5GaajE+kM13DXxzSLuzHGwsa4JhmIwHD/teJ758f8yyxDMBY34/tvbLVx3W+uTty4nXFFaq773RiCx/Vdmd+vwFLuZ4rPPuPvmLlXXKJk/JlCvWFwxvW9M/uM38NW5QG+98z8mrnui05k+n5a8b2/BcT0WnNv5zmc3EGv16OkpIRdFxsbG4vbt28jPDwchYWF0Gg0eOihh3D9+nW0atUKeXl58PHxQUREBMrLy/H0009j4cKFePPNN/lddPOC/YZapOXmTIYSY+bOnYuNGzdi8+bNqK2txWeffcZW4yaEoKamBnv37oVYLEbHjh0RHBzM2y1pElxiNvfDhTWXi7XIshqPxomMLLGckrSKeQVtZzHPbsHAVZaEGRAwEZVasWXHZcsdybyXNaxZbc64Ix25tw+C0kBDZ+/nmPPDAlsWnPFaN8Y9ybW+01FrjWuwxCd3KBMRaQ6zT6i/Z60J9fe8Acw5M9lDbFlq5vt0Oh1qamrY6iP5+ffCXP39/XH79m2oVCoIBAK2kkBNTQ0EAgG0Wi2CgoJcVdhMaJHi5kyGEoYlS5Zg2bJlWLNmDcaOHQsAeP3119nXtVotZDIZrl+/7pRb8u7du1bFjetHfb8zkpivi3MkmbD5sQ3h3rImcPZgRMzczcuIYn0Ezpz6ChuT+f5BuSAdhTlfR0TOPPpS6W7d0jIWOHOxAAxCxWeph7H1WJ8k2IDloMj8nI2Fz1jwmGP8vH2wc/d/HbbeAENxUqVSCY1Gw4qgWCyGVCplBY8QAi8vL9TU1KC6uho6na5eeRqbIy3jKs1wJkMJAKxZswYffPABlixZwo6AUlJS8OOPP0Kr1bKbn58fBg0aBEIIxo4di/j4eM5RGWA935xer4dg4GCLHx+frCS2rDZnYDqv+nYI1igNNPrROzH65xI4xnrzqDG8bmy9Affm4LjuJ9e9N7fyjDvmhpxrc6bC9IOGOXc+Fce5sBVyzwgcE14v0tm/78xcq6PLFRyBeX6M17cB954XJrDEeH9fG0t9bFFbW4vCwkKEhoYiOzsbOp0OIpEIIpGIXZ9LCIFIJIKbmxvu3LkDNzc3pwbbzYkWKW7OZCj55ZdfMGPGDAwcOBD9+vXD1KlTsX79erRr1w5jxoxBVFQU65o8ceIEhg0bBj8/P3Tu3BkhISEOr3XT6/Vs52rPejDuYBtD2O5nR1uf0b8xtgTOHOOOxxh74t2YVltzFjVzmFD/+qTcAqx/b+YWHFfVdmOY+dH7ZQHbmqc0TsDg4e6OGzdvOpzkQa/XQ61WQy6XQyQSQaFQsEsFwsLCWMFjUnOJRCKoVCoqbq6MMxlK9uzZA0II9uzZgz179rD7b9y4gQMHDuDQoUPsvnnz5qF3795o164dO4Ky99AyYmuywNPL3yKYAXC8FEh9ha0s4MG5xBR+hk7C3iJ0RzGee2Mi2bjmNOukph2rPauNK/uJWs5/frPa07A1FxekIzgqcsauSlsCx2AscOb5Hfli/Juqr2eC67uzl02ooqKC/xy80ebh4QGpVAqZTIaamhr4+BhS8nh4eEAkErGR4YQQREZG4uDBgxbJkl2VFhktuXr1arz11lucGUqWL1/OZiixx4ABAxAdHY3r16+jtLQUhYWFbLSkVqtFbW0tmxJn7NixGDFiBO+kycZbZWUlRg64F3bL/Eg8q7mtNq75Bq4fFleHa7zPOHWVtR8sn33W4Donrn3GI2BG5LgCALj2cZ23+b1SupuKm/n7cIkbERgsQ64Fu8aLjI0taHv329i64xsF2ZSiJa21s7bP3LLmEymrFVuvgM5ct1Z8T/S4nkeupTTOPsvm8E2LZ9yuRun4uje9Xo/y8nLcuHEDUqkUKpUKhBC0b98emZmZUKlUCAkJQU1NDeLi4jB//nwcOHAAubm5vLJ8NENadrSkvQwlfMRty5YtOHfuHH7++WcMHz4c3t7eSElJYV2SYrEYAwcOxMyZM/H00087db6nT59m/8/8GBzJKVkndSyRbFOuO8acG98abVwjfnPristVxIW51VbjYbuwKN/gnoZc0N2cMPYkOBIEZK06ADPPZW2tGWCZrs4W1uq1WXtGzNejmrez95u9ePGiiWcHAC/3pE6ng1wuh7u7O2pqakwymzCR4VKpFAKBAMOHD2eTTYwYMYLfjWimtEhxczZDiUKhwMyZM7F8+XI20SchBLdu3TIJKNHpdDh58iQUCgWCg4Px8MMPOxz2SwhhsxKYw2W16UT1Twpc42HYnBn52yrg2JAwHSOfTtGaSwvgXmjLhXHHxPzfVvotvsJ218f2+quWQo2H4X7aG7QwrkbGMjMXOXMrUazlF0BiTXi49vN5Rmy9pzX+0bMnsnNyeOWcNd4YIczOzkZQUBDu3LnDLtr29PREVVUVNBoN275Dhw71DmJpTrRIcXM2Q8msWbPQrl07vPrqq+y+uro6TJo0ycRyy8rKQlVVFf7++2889thjvJInm28ikYgtz85ltZkLmzm2Es0a42wE5YOCr8iZC5x5eiR7x0rrTNs5K2yNnb2kucLcF76WuUZi+C7MBwjG1rhEYxrF6CyOipYjBAcHm34Wn8ohAJvyz8fHB0KhEEVFRazbMSgoCPn5+Wy+Si8vLwQEBDTeRTQRWpy4MQ8Dl7+ZY/7RgiNHjuD777/HuXPnTN7Dzc0NR48eNWk7bdo0xMbGWqSfcRS9Xm93VFhfYWuuomYOM/K35Sa0JnByteE15p5yBSJYcwdzzQnZs5ypsNmHuUdEYD8YR6i/9/xbEzlmLZyxV6IxKrI7i4e7O/5v504T8XJk7VtISAiEQiEUCgXc3NxAiKHkjUgkYi06Gi3ZTDFeu2YO88U6k6Fk8uTJmDBhAiIiIlBRUQHg3qjpo48+Yh8yrVaLCxcuIDMzE5cvX0ZQUBBeeuklh1JvMVttbS3QoRMA03kfW5Fg9oRNLTdsruYSs+WCZF43LnvDiBHjkrQV5GLujrQndOZQUasfxs+yPaGzt87MGGYxdWNaYvXhucGDUVlVZSFc9tDr9ewURnBwMEpKSgxLif6XqaSiogJ6vZ6KW3NlzZo1GDBgAFs6gREQZnHj1KlT0b59+3pnKElPT0d6ejrWr19v8dqpU6fQr18/9OzZEyKRCO7u7hCLxQgKCkJISAjc3d15rW0z3xhXqfEP0fgHaW618RE2V8bW4l8Gc4EDTAXOmqXMR9jMrTfjOZ/7EeJv3rEbw7f0EZMfs6lRJ733HdiykM2L4dq679YSJDxIlEqlw4NgZimRXq+Hn58fioqKoFKpIJcbfvCRkZG4ceMGFbfmyrBhw7B582ZkZmZiypQpEIvF7HqPH374ARs2bMD777+PpUuX1itDSUpKisW+GTNmQKfTYe3atYiLi0NERAQAYO3atbh48SIWLVpU7+thH2wewsb839qP3tVFzRzGSrMWKWoscLYsN8AgUMZtjbFmsTVmJgxjGsO1zEcEze9DfdKeOYN5MJAtLwTXoOR+BD7Vl1YhIThw8KBDg2DGwgsLC4NAIIC7uzsqKirg6+sLQggCAwMxZ84chxLDN2dccp1bSUkJli1bhpCQEDzzzDM4ffo0NmzYgDNnzmD48OFYtWoV+vbtCzc3NyxevBgCgQDz5s1DVVUVLl26BE9PQ2w2V4YSLvr27QutVou4uDhUVFSw0ZJ5eXmora2Fm5sbJBIJVqxYwWv0xTVhPGKwIbrTPGqP6biNRc5c3JhOlmv0ytUhOLJ2ypn1QfVZ5+boPuP7wtwrLjEyPta4IKkx5vfAWofKfCbf+8jnO7A2MHmQHXR9LBzGmub7/fF9HmydC1cCBL7HPkjqs+4NMEy/FBUVIT8/H2q1Gm5ublAqlejSpQs2bdqERYsW4fbt22w2ExfDtde5BQUFYcWKFUhKSsKmTZtQVlaGhIQEbNmyBUlJSfD398fBgwcxefJkjBw5ElqtFmKxGP3790d5eTkrblwZSoxJT0/H/PnzcezYMej1emRnZ2PgwIEYNmwYm34rNTUVU6ZMgVQqxUMPPVSvRdxarZYzFJ3B2rqd+2U5AIaF0A0B3yi5+mBc2oZLqADb1hvj7rP2uqMZY7hgXKqODBCasgViDnN99gSlvstZuLD122nKeLi74/qNGw6n5CKEQKlUQiAQwNvbGyUlJRCLxRAIBAgLC0NsbCyys7NdVdxYXE7c1Go1Ll++jE2bNiE9PR2tW7eGTqfDoEGD8MILLwAAa6JnZGSgffv2rPX2wQcfIDExEZcuXYKHhweio6OtRlCeOXMG/fr1Q9++ffH777/Dx8cHN2/eRHV1NQYPHgwAEIvFOHDgAAYMGMAeZ+uhtPbwGlJw+XDOA1mLkmzIDu9+FXsE+AddOLIonQtr8zH2Oj9rLsn63G+udYoUA8bzoI7QnISeD5WVlQ6n5BIIBPDx8YFcLkdBQQECAgJQWmoouaHT6fDwww/jsccee8BX1vi4zM+KCZndunUrpk+fDpFIhNGjR2Pq1KlQqVT4+eefsXDhQsyaNQvu7u7YuHEjsrKyTFJwde7cGW3btsWGDRtsZinR6/UYN24c+vfvj61bt7L7P/vsM1y4cAErVqyATqeDWq1GbW0t/P39odPpsGHDBgQEBNi11LgeWhIaZrhOG1aFszCBKM2hg7AXNOPIyN+Re+doZ2s++GiK4edNGXtZY8xpTpYZHx579NF6uyc1Gg3u3LkDPz8/lJSUQKFQQKfTQShsGQ+hy8y5aTQaSCQSjBw5Eunp6fjll1/QqVMn9vWCggJs3rwZOTk5mDJlCt5++22o1WocO3bM5H369DFUvf7777+tftbBgwfRv39/HD58GE8++SS733gdCbOI+5VXXsGRI0cgkUggk8kcCu015sSJE+jfrx/na3znvYzXA9miOYhbfXL3mfMgouT43ltHvoMH9X05c7+au2AVFRcDsL3ImvHGZGZmwtfXl01gbG85UG1tLQoKChAeHs5mIKnPEiK9Xg+VSoU2bdogIyMDYrEY2dnZOHLkCLZs2fKA72Cj4XpzbkwWj2effRZTpkxBp06dUFdXB7FYDL1ej9DQUMyZMwdff/01ysvLkZaWhiFDhli8D58UXMxibbVajR49euDs2bPw8/PDqFGjsHDhQkgkEmi1Wnh4eECpVLKl34ODg9mFlXxDe01ckzyxtnanKXYSjY2tkX9Tvh985tKq1JYjeo1Gg6NHj+LJJ5/kXZTy1q1bqKysRMeOHe99vp1n8dy5c4iJieFdSbq6uhp5eXlo27atzfc3/l0UFxdDIpFY/Qzz35BOp0NFRQW8vb1ZUeBbhUMoFJrUV7QVjajRaHBWIoFEIuE1Zy6VSlFQUACtVmvTlci8JpfL2bRZwcHBDnl4LDw+xFDOKzMzE15eXmy1gJaAy4ibQqFAQUEBRo4cCS8vQxyzVHrPd1VXVwepVIpXX30VWq0W5eXlbF5IY/ik4GKq3I4ePRpvvPEGli1bhjNnzmDOnDnYsGEDPDw82CUI1dXVGDBgAEQiEWbNmoVOnTo59HAymy1xa8qdtCtz8tQpSKVShIWF8erg9Xo9rl69iri4OIjFYt6iwHRy5m2uWOm8BQIBTp48CalUyquD1+v10Gq1KCoqAgCT97G26XQ6XLt2DXK53KFnOD8/n9cxQqEQ/v7+KCgoQFBQkNXfivn+O3fuQCAQIDIyktfvjBCCkydPonPnzqwo2vOulJSUICMjAz169ODthbl48SK8vb0RHR3Nq314eDhSU1PZAbEz1NYaQlRjY2OxadMmVsBdnWYvbnq9HkKhEDt27MD8+fMxYMAAtG7dGu3atUN0dDQSEhIglUpZoWPyPgL1T8HFCM2YMWPYNWx9+/aFTqfDnDlzkJqaiocffhh6vR5SqRTXr183Edr6cPPmTaeOt0W1ymABVFRU4Pr16+jevTv7mj2LMiMjAzKZDKGhobysz/p08EqlEhUVFQgJCeHtoqmuroZQKIRMJnOog2fmI/h08KV6PXQ6HUpLS3l17kKhEGKxGAUFBfDw8OB1jJeXF8rKyiCRSNiIN3sdvEKhQHl5OeLi4ngPpK5cuYKgoCB2jZS9Dr6urg7Hjh3DY489xnpN7HH79m2UlpaaWIh2n83qavb54oOnpydOnDiBhx56yOp5Mb9x5juOjIxETk6OzcTmxs8PY+VlZGSwa8jsPWNubm7IzMxEXV0dhEIhr9+KVCrF6dOn4eXlxet3Ym+TyWSoqKjAhQsXeN//5kyzFzemM3r22WchEAhw4MAB/PnnnwAMVphMJkN4eDi6du2KXr16oXPnzgDgVAouJunoU089ZbK/W7duAIBt27ahpqYGWq0WgYGB+M9//gOZTIbo6GhEREQ49FAybe7evYsDBw/y9tszx8jlcgsRMW972KyDP3jwoMnr9kbwhBCUlJTwHsGLRCIUFxfzHvW7u7ujuLgYMpmM9wi+vLwclZWVaNOmjc12xtvly5cRGhpqUTHdGlqtFocPH0b37t15u3oKCgpQWFhYrw4+PDycV3tfX1/cvn2bLWRpDePvuFWrVrhz5w5CQkJ4P5deXl7IyMhAYGAgr2dSp9OhrKwM169fN3kmbX2eXq/HtWvXUFhYyKsDZ445cuQIRCKR1TaAqetRp9Ph+PHjEIlENgcnxv/Py8tDVVUV7whGZlF1QECAzc9htqCgIFy/fh1+fn7w9PS0O3Cy9zvV6/V47LHHcPDgQZw9e5btr1yVZi9uDIGBgXjllVfwyiuvADCk0jpx4gSuXLmC27dvY9u2bVi/fj3UajUSEhLg5+eHc+fOWbwPnxRc8fHxACwtv507dwIANm7ciK1bt0IsFqOurg6rV6+GVCrFsGHD0KdPH4ceSmaTSqXQaDQ2BcH8vXJycuDj44PAwEBe7QHDfGLPnj3Z+k/2Ovjy8nJkZmY6FFrMWLIxMTG8jykqKkJgYCC7BtEebm5uKCoqsjtQMe7w/Pz8oFAoLDpreyPy3Nxcu6NrZtNoNCgrK0NGRgYEAn7BAmq1GhkZGSgpKXFo1H7s2DGLDt68Xpjx96vX63Hs2DEIhUJez6VOp0NBQQFUKhWvuSSBQABPT0/cvXsXAQEBvEQBMFS59/X1haenJ6/zUiqVSEtLw2OPPWbV2jV/prOzs1FdXW0ShGbvuTl9+jRCQ0N5W5VqtRonTpxA586d2ZRYfD7n9u3baN26tc3foT2EQiGbd3LEiBEuL2yAC4kbcC9VFQA8/PDDrEjV1tYiPT0d+fn5uHXrFi5duoS6ujqcOXMGTzzxBBsgwjcF16BBgyCTybBnzx52TRtgyMgNAPv372eXF8THx2Pjxo28fzTWKCsrQ05ODlq3bs37mPLycojFYl4dPPOvu7s7VCqVzVGvcSep1WpRVVWFsrIy3h1vbW0tazXzdano9XpcuXIFcrmcV3tmKcbhw4fZa7O2mXfwXFaotU5Vq9Xi9u3b7MiaT+crlUqhVCrh4eHBSxQY6yUkJIS3a7K8vBz5+flISEiwO6BhSE9Ph0wms5p4nOu5OXbsGNq0aQMfH34VbmtqanDmzBnExMTwDknXaDRQKBS8B0MeHh7w8fFBeXk5mwrPHpGRkTh69Chqamrg4WE/n5lAIEBcXBzS09PZTPz2kMvlCAsLQ1ZWlt0BNENoaChyc3ORm5vLe76OC6FQCIlEAp1O5/QcXnPBpcRNIBCw7iEmnNbb2xv+/v7o0qULunTpAgCoqqrCO++8g759++LOnTvYvn07BAJDCq7IyEhMnjyZfU+uFFwBAQGYO3cuPvroI3h7e6Nfv344c+YMFi5ciKSkJFy/fh1XrlxhI7H++OMPHDp0CJGRkejWrRuvjtx8X11dHSorK3Hp0iXeI/e6ujro9XrcuXPHblvm/hFCcP78eV5uE+YHrdfrkZWVxXmMtc67trYWWq2W/dve5zHXYz4nZGtjBCEoKMhuW8DQWR86dAg9e/aETMZv5XplZSWuXLmCRx55hPdzKpPJoFQq0aZNG97HFP8v9DwoKIhXezc3N2RkZLCfx4ewsDBcuXIFMTExvKwEgUCA8PBw3Llzh7e4eXh4wNPTE0VFRbwtnrCwMGRmZrJ5EvkQHR2NPXv2YNSoUbyiRsViMXx9ffHNN9/gzTfftNlW/7+5VrlcjjNnzuDy5csYMWKESaFi86LFTOWQ2tpaLFy4EOPGjUNISAhnG+O/tVotKioq8O233+K1114DYBB7nU4HhUKBw4cPIy8vD4BBCLt27QqZTGb1PHJychAdHQ21Wo158+bhxx9/REVFBbp06YJPPvkEvXv3trjWTz75BBs2bEBhYSHat2+P+fPnc1bxTk5OxsqVK5GdnY3o6GjMnDkTU6ZMsWi3bds2LFy4kB0YTJw4EXPnzrVw7R89ehTvvvsuzp8/Dx8fH7z00ktYsmQJb3F2KXFjuHHjBpYuXYqrV6/C3d0dsbGxGDBgAJuhxMvLC15eXvjtt98wYsQIPP/88wAMD8fvv/9u4vpirADzaMVXX30VO3fuxKeffoqlS5dCLBajbdu20Ov1+OqrryAWiyGRSFBVVYVTp07By8sL3bp1Q7t27XjNG5m3YR5ma6HBXO9ZXl6OkpISPPzww3bFhunMbty4AYlE4pDL8NSpU4iLi7NrITLo9XqkpKQgNjaW91yVm5sbbty4YVHM0RYBAQFQKpW8XUACgQC+vr5QKBRo1aoVr2O8vLxQV1cHlUrF+0cXFBSEs2fPslYjH4KDg5Gfn89bEIRCIfz8/HD27Fn06tWL1zHe3t64du0aZDIZHn30Ubvt9Xo9AgIC8MYbb2DJkiXw8PBgO1GmkzbvvLVaLTIzMzFnzhzMnTvXahvz7dSpU/j888/xxBNP2BQQ82O2bNlicV7GbY1FRSAQICsrC2vXrgUAkzbG12O8ljU8PBz5+flYvHgxG/TD/Mu0Md/UajUWLVqEhIQESCQSznbMezCbh4cHTpw4gX/84x/w8PCAXq/H999/D7FYjLFjx0IsFmPnzp04fvw4Fi9eDA8PD0j+t1zB+P2ZPmTChAnYtWsXPv30U8TGxuLLL7/EgAEDkJqayhoBADBv3jysWLECS5YsQbdu3fDLL79g1KhR2LlzJ5555hm2XXJyMiZPnoy5c+ciKSkJBw4cwLRp00AIwdSpU9l2e/fuxYgRIzBhwgSsWrUK58+fx3vvvYeqqip88sknbLtLly7hqaeewoABA7Bz505kZ2dj1qxZuHPnDn799Vdez7PLLOJmUKlUGDNmDC5cuIDHH38carUa169fh0KhwOOPP47vv/8ePj4+UCqVSEhIgEwmM0m/pVQq2fRb1qipqUHXrl2h0Wjw4YcfIioqCqdPn8aCBQswZMgQk5s/YsQIDBkyBKNGjXLquvR6Pbt4nG+HePfuXaSnp6NHjx68P4eZJOfrNgGAtLQ0+Pj48HYBAUBqairi4+Ph7e3Nq71Op0NKSgoSExN5C2JZWRkOHz6MYcOG8T6vs2fP4sqVKxg3bhzvY5jlH8OGDbPa4RqPyDUaDT7++GMMGTIEMTExJq9b66jVajU+/vhjzJgxA0KhkJcoMAOr7t27m3TiXO2ZfWKxGOXl5eyAytb16PV6iMViBAQEQK1Wsxa4eSfN1XlfvnwZHTp0gJ+fn812zGu1tbX4+eefMXHiRHapjS0xEIvFuHTpEnbs2IGlS5dCKpVyvrfxsRKJBGvXrkVlZSWWLl3K+Z7MeRq7IZ9++mn861//wtChQ3k9L0qlEgMGDMCuXbt4P//p6en4v//7P7z77rsAgNWrV+Ott94yybCUnZ2Ntm3bYvny5TYzLF28eBFdunTBN998w1qDWq0W8fHxaN++PXbs2AHA4C2IjIzEnDlzsHDhQvb4/v37o6SkBJcuXWKPDQsLw6BBg7B582a23fjx47Fjxw4UFBSwkatdu3aFt7e3SZKMRYsWYfHixbh16xY7qBw2bBiuXLmCq1evssd+//33GDduHM6ePWvLU+J6i7gZBAIBUlNTcfLkSURGRgIAMjIycPHiRWzatAnPPfccDh06hOTk5Hqn3zp27Bhu3ryJvXv34umnnwYAJCYmory8HCtWrIBSqYS7uyGTsLe3NyorK52+LiaMvK6ujrebSSaTIS8vzyFxq6urw9GjRx0St+zsbOTm5mLKlCkWI3auzlej0eCPP/7A0aNH0bt3b84Ol2vfl19+icGDByMwMNDu5+h0OtTW1mLLli3Y+b/KxlxtzN9HLBbjxo0bWLt2rdXzMP87NDQUNTU1mDFjBtsJWuuoma2qqgrLly9HRESEyTFcHarx6P3kyZNo3749u4+r0zZeNrBv3z50794d4eHhJp2ztY67pKQEL774Io4cOcKKiLVzYjr5Xbt2YdWqVThw4ADvZ+bTTz+Fl5cXp9vKGtHR0XjxxRfRrl07Xu31ej3i4+MxYsQI3gvaP/74Y1RVVTk0t71161Ze83QM7u7uOHLkCO/2APDQQw/hoYceYv/esWMHevTowfZdABATE4NevXph+/btNvuvHTt2QCKRYPTo0ew+sViMF198EcuWLUNtbS1kMhn27t2Luro6jBkzxuT4MWPGYPz48cjOzkZMTAxSU1NRUlJi0W7s2LH49ttvcfToUSQmJiIvLw8XLlzAxo0bLdotWLAAu3fvxmuvvQaNRoM9e/bgrbfeMlnO8cILL2DixInYvn07r2kAlxM3uVyOuLg4Vtj0ej3i4uIQFxeH3r17Y/bs2Vi7dq1TDwcTdWQ+6vL19TXJcgDci9orLCy06nKx5ms33z777DMMHz4cAQEBnGLA1flu3LgRf//9t80O2nhUDxgssc2bN3OKB9fn+Pn5QaVS4d133zUZBVvr4EUiEXQ6HVQqFXbt2mXxmrUOWKvV4tixY+jUqZNFR84seTDfDh06hIiICMTHx9sduTOfP2DAAKxZswZhYWEmbax18oWFhejSpQu7to4PKSkp2Lx5M7777jte7QHgt99+g1AoxMiRI3kfExgYiMcffxxRUVG8j9m7dy8efvhh3hbywIED0bdvX97vDwCzZs1yqD0Am2WnuBAKhZg4caJDx/j7+3Mmd7CFI8LWUKSlpXFainwyLKWlpSEmJoYdgBsfW1dXh4yMDMTHxyMtLQ0ymcykj2TaAYbI8piYGLbws/nyFuN2iYmJVtsx53L16lUAQGZmJtRqtUU7uVyONm3asO3s4XLiBhjyQ27btg1Dhw416WyCgoLw+eef47nnnsO1a9fYuTZj+DwcSUlJaNu2LWbPno1169YhKioKp06dwurVqzFlyhSTh/3GjRtITU1FcnKyRSduy61i3Mkzr5eVlSE1NRWRkZFWO2mm+jezeXl5ITIyEqGhoRafwyVAgCEa9KuvvrIqGObWQk5ODgYPHsy5btAaf/31F3766ScTN4Y9/vzzTyiVSowdO5b3MZGRkWjbti37Q+PDnj170LlzZ96dVkREBG7evOlQQtrExEQkJibybg+AnTN2BEeEkMF4ET8fRCLRA+ngWzLl5eWcc9x8MizZOpZ5nfnX19fXYhqEqx0Ai/fk247Zx6edv78/737GJcVNr9fjn//8J4YPH45HHnkErVu3RlRUFCIiIhAWFsYGZ9T34ZDL5Th69ChGjBhh0mm+/vrr+OKLL0za7t+/v2EuCsBHH32ExMREPPHEE7yP8fDwwNChQxEWFsb7mO3bt6Nbt268s6p06NABp06d4v3+gGGegnHp8oUrQsseXAMYe/Ts2dPhY/gG01AoDQXX3DtHDAVnGz7HOtLO2vnwbWf8nnzb2cOlxI2JYlq3bh26dOmCrKwstrK2SqVCZWUl/Pz8cP78eXZOwhw+N0+tVmP06NEoLi7GDz/8wFpuixYtglgsxrp16xrj8jBv3jyHjzGOVOLLoEGDHGovEol4h6hTKBTncSbDkr+/P27dusV5LPM6869CobAQOa52gMHiMo7mZc6Pq505FRUVvNopFAreXhiXEjfmC3j99dfx73//G/7+/rh58yYKCgqgUChQXV2NwsJC9OvXD9999129H45Nmzbh0KFDyMjIYNcq9e7dGz4+Ppg0aRKmTJmChISEhr9ACoVCAdg5MXP4ZljaunWrSeAbc6xUKjVJQFFbW4vMzEyTeTdmzov5HEZs0tLSTMTNVjtj70hOTg6USiXbrk2bNpDJZBbXp1arkZWVxT/ynGNBb7Onrq6O6PV6q6+rVCqSmJhIevXqZfFanz59SO/evW2+/+TJk4mfn5/F/gsXLhAA5Oeff3b8pCkUCoUnn332GRGJRCQzM5Pdl52dTcRiMVmxYoXNY8+fP08AkO+++47dp9FoSIcOHcjgwYPZfUVFRUQqlZIPP/zQ5Pj+/fuTjh07sn/X1dWRwMBA8uqrr5q0mzBhAvH39ye1tbXsvoSEBNK3b1+Tdh999BGRSCSkoKCA3Td06FDStm1botFo2H0//PADAUDOnDlj6/LuJaYgLihuxuj1epONwZmHY8GCBQQAuXnzpsn+DRs2EADk8OHDDXsRFAqFYkR1dTVp06YN6dixI9m2bRvZvn076dy5M4mJiSFVVVVsu5ycHCISicjChQtNjh89ejTx9fUlycnJZP/+/WTEiBFEJpORs2fPmrSbPXs2kclkZOXKlSQlJYVMmTKFCAQCsmPHDpN269atIwKBgLz//vskJSWFzJs3jwgEAvLFF1+YtNu1axcRCARk0qRJJCUlhaxatYrIZDLyzjvvmLQ7f/48kcvlZNiwYWT//v3k66+/Jn5+fmTkyJH2bk3LETdrOPNwZGdnEy8vL9K2bVvy3XffkYMHD5Lly5cTLy8v0q1bN6LT6R7EJVEolBZEbm4uGT58OPHy8iKenp5k6NChJDs726RNdnY2AUAWLFhgsl+pVJKZM2eSkJAQIpPJyOOPP05SUlIsPkOr1ZKPPvqIREVFEalUSjp16kR+//13zvNZv349adu2LZFKpSQuLo58+eWXnO3+/PNP0rlzZyKVSklkZCRZuHAh0Wq1Fu3+/vtv0qNHDyKTyUhwcDD597//TWpqauzdlns5Y4mLZShxhJMnT+Kll15CTk4Om17ryJEjJtGIOTk5iImJwYIFC/Dhhx+y+8+fP48XX3wRGRkZ0Ov1kMvlGDp0KNatW0cj5ygUCuXB4LoZShxBpVKxlbJ1Oh3++usvixRS0dHRnBGUK1asQFFREdavX8/mZtu+fTvmzJlDxY1CoVAeMC3acmOqeAPA119/jYkTJ7IZrW3BNzcbhUKhUO4rrOXGP6WCC+JIRgljbOVm27t3L2praxvqFCkUCoVSD1q0uNUXPrnZKBRK45KXl4eRI0fCx8cH3t7eGD58OOfiZC5u3bqFcePGISoqCu7u7mjXrh0++OAD1NTUNPJZW3L79m28+eab6NmzJ9zd3SEQCJCTk8PrWLVajVmzZiE0NBRubm7o2bMnW6C3pUPFrR7wzc1GoTQ1nBEEwFB6ZdSoUQgMDISbmxvat2+P1atXN+IZc6NUKtGvXz9cu3YNmzdvxg8//ICbN28iMTHRrkDV1NQgKSkJhw8fxkcffYRdu3bh9ddfx8qVKzF+/Pj7dAX3yMjIwG+//QY/Pz88+eSTDh07YcIEJCcnY9GiRdi5cydCQ0MxYMAAXLhwoXFOtjlBWuhSAHOSk5MJAItQWi6SkpJIjx49LPb/9ddfdJ2bi3Hr1i0yYsQI4u3tTby8vMiwYcNIbm6uw+/z8ccfEwCciQPuFzU1NSQuLo7Ex8eTrVu3km3btpGOHTuS2NhYUl1dbff406dPEy8vL/Lcc8+RrVu3koMHD5INGzaQlStX3oezN+Xzzz8nQqHQZK1pVlYWEYlEds9n7969BADZu3evyf7Zs2cTkUjEJ9y8QTFeOuRIP8Qkjfjmm2/YfRqNhrRr144899xzjXGqzQFWy6jlVg+sZaY2z7nWUqmvdXDmzBlMmjQJHTp0gLu7O6KiovDyyy8jOzv7Ppy1Jc5YB8ZkZWVhyZIlDlURbwyYGobbtm3D888/j6FDh2LHjh3Izc3Fhg0bbB6r1+sxbtw49O/fHzt27MDzzz+PxMRETJo0yWZ5qMbCXskqWzhSsup+QOf+GwcqbvUgPj4e2dnZUCqVJvvNc7PxxRlXUVPzuTsjCL/88gvS0tIwffp07N69G8uWLcO5c+fw6KOPIi8v7z5dwT2cEQNjpk6dipdfftmk2OSDwBlBOHToEK5evfpAhIyLtLQ0i3pfgOG3aa/el3HJqqtXr6K6uhoHDx7kLFnVlKFz/7ah4lYPhgwZAo1GY1L3TavV4tdff8XTTz/Nu1I24Lx10NR87s4IwuzZs3Hs2DFMmzYNffr0wUsvvYQ9e/ZAoVAgOTn5Pl3BPZwRA4YtW7bg3LlzWLp0aWOdJm+cEYSjR48CMAymevToAYlEguDgYEyfPh0qlapRztcWztQzY0pWMZW6vby80L9/fwwePNiiZFVThs7926ZFL+IGgD/++AMAcPbsWQDA7t27ERQUhKCgIPTp0we5ublo06YN5s+fz1YC7tKlC0aPHo0ZM2ZAo9EgJiYG69atQ3Z2Nn766SeHPp8Rg+vXr7OdaOfOndG2bVts2LDB5kj54sWL2LJli8l6uz59+iA+Ph7z589/IOvtnKlwzlU2p3Xr1ggKCsKdO3ca5Xxt4Uy1Y8Dgpp45cyaWL1/eJFzVzghCfn4+AGD06NF44403sGzZMpw5cwbz589HXl4etm7d2ijnbIvmVrKqoSE86621VFq8uJmXT5g2bRoAg0gcOnQIhBDodDo2PRfDt99+i/fffx8ffPABKioqkJCQgD179uCRRx5x6POdEQNbPvdly5ahtrbWISuyIXBWEMxJT09HcXHxA3HpOSMGADBr1iy0a9cOr776aiOcXf2ob2fIPP9jxozBokWLAAB9+/aFTqfDnDlzeJVaaUicqWfmKiWr+NZla6m0eLcksYwWBSEEhw4dAnAv/ZZxXkkAcHNzw6pVq1BYWAi1Wo2TJ0+ib9++Dn++M66ipuhzd1YQjNFqtZgyZQqCgoIwYcKEhjpFh6ivGBw5cgTff/891q1bZ7dC8f3CGUEICAgAADz11FMm+5lq6vfbDe5MPbPLly/Dz8+PFTaGxx9/HIBhQNUcaOi5f1ejxYvbg8YZMWiqPveGcpW88cYbOH78OH788ccHkq/TGTGYPHkyJkyYgIiICFRUVKCiogJarRY6nQ4VFRUPJJLN2QKXgOV3y3yv9Y34qy9DhgzBiRMnkJWVxe7LycnBsWPHMGTIEJvHtmrVCgqFwmLwd/LkSQBAeHh4w59wI9CQc/+uCBW3JkB9xaAp+tydEQRj5s6di40bN+Kbb75hrYP7jTNikJ6ejvXr18PPz4/djh07hhMnTsDPz8/peZ2qqipcvnwZGo2G9zHOCMKgQYMgk8mwZ88ek/179+4FADz66KMOnL3zTJw4EdHR0Rg6dCi2b9+OHTt2YOjQoYiMjMTkyZPZdrm5uRCLxawrFQBeffVVeHl54ZlnnsHmzZuRkpKCTz/9FO+88w66deuGXr163ddrAQxz/3/88YfJ3P8ff/yBv//+2+p1GM/9f/311zhw4ABefPFFZGdnY+HChff9GpocHC45yn0kODiYTJo0yWL/1KlTSWBgoM1jX3jhBdKuXTuL/b/++isBQK5cudJg58kXZyqcMyxevJgAIGvWrGno03MIZwrapqSkWGwJCQmkY8eOJCUlheTl5Tl1bhs2bCA+Pj6ci6/1ej3R6XTsxuBsgcsPP/yQiEQiMnfuXLJv3z6ydOlSIpfLybhx45y6lvriTD2ztLQ0MmrUKBIREUHkcjlp27Ytefvtt0l5efn9uwAjYEhYb7H16dOHEOJ8XbYWBC1W2lRwRgwWLlxIJBKJRUaFBQsWEKlUStRqdYOeKx+cEQRCCFm9ejUBQJYsWdKYp8kLZ8XAnD59+jRIhpKqqioybdo0Mnz4cEII4Sz0aA1nBEGv15OVK1eSNm3aEIlEQqKiosi8efNIXV2ds5dEoTQUVNyaCs6Iwfnz5wkA8t1337H7NBoN6dChAxk8eHCjnbMtnBGEn3/+mQgEAjJw4ECSmppqsqWlpT2Iy3FKDMyxJ24qlYqoVCqi1+vZfRqNhuTk5JCCggJ2/40bN0hiYiL56quvCCHEpD0hhKSmppI///yT/Pzzz2TXrl2ktLTUgSumUJo1VNyaCs5aB6NHjya+vr4kOTmZ7N+/n4wYMYLIZDJy9uzZ+30pLPUVhHHjxtl1z7gq165dI15eXiQ4OJgcPXqU3X/58mUiEAhIbGwsu+/gwYMkIiKCZGVlmbxHaWkp+eyzz8j48ePJ5MmTSa9evYibmxs5f/78/boMCuVBQ8WtKeGMdUB97s0fxvI6f/48EYlErEXGsHbtWvLkk08SQgyW3PLly0l8fDwh5J5Lsry8nIwfP548+uij7LOzb98+EhwcTGpra+/TlVAoDxxWy1r8Iu6mQFRUFP7880+bbZj1duYw6+1WrVrVWKdHaWSYiFdvb29ERkbi5MmTmDp1KgDg7t27yMrKQufOnQEApaWlOHv2LJKSkgAAIpEIhBCsX78e27Ztw+XLlxEWFgalUomUlBQEBQVBKpWaVJ2nUFoC9GmnUJoIfn5+aNeuHc6cOcPuUyqVuH37Nv7xj38AMCypOHfuHJ599lm2TWZmJtauXYvx48cjLCwMAKDRaFBQUID27dvf34ugUJoIVNwolCaCh4cHunXrhsLCQhQWFgIwLMQ/e/YsmxkkIyMDZWVl6N+/P3vcpUuXUFRUZJL2TKVS4caNG+jUqRMA7rWUFIorQ8WNQmkiSKVSPProo6ioqGDTWaWlpcHPzw9BQUGorq7G4cOH8eijj7IuRo1Gg9OnTyM4OBiPPfYYtFotAIM788qVK2xqNypulJYGFTcKpQmRkJAAvV6Pixcvoq6uDv/973/Z+beamhocP37cJJuIQCCAUChEVVUVRCIRxGIxCCHYvHkzRCIREhMTH9SlUCgPFCpuFEoTwsfHB7GxsUhNTUVmZib+/vtvNml0WVkZLl26hGeeeYZtLxaLMWDAAHh7e2PBggVISUnB77//jt27d0OhUODAgQMPpN4ahfKgoeJGoTQh3N3d0bVrV+zbtw8rVqzA7NmzARhKzhw9ehTBwcGIiYkxiZzt3bs31qxZgwsXLmDTpk3Izc3F0qVLMWTIEJw+fdqh/JMUiqsg4Agvp5XuKJQHhE6nw+eff45Zs2ahR48eOH78OACDS/Kll15CVFQU1q5d+4DPkkJpsrCTy9Ryo1CaECKRCLGxsfDw8EBycjK7X6fTQaFQYNiwYZzHkf8V1WUK6xJC2BI7FEpLhFpuFMoD5ttvv0VhYSHmzp2LU6dO4c0338SECRMwadKkB31qFEpzg7XcaIYSCuUBU1xcjE8//RS//vorBAIB3n77bYwZM8aiHc0yQqHwh1puFAqFQnEV6JwbhUKhUFwXKm4UCoVCcTmouFEoFArF5aDiRqFQKBSXg4obhUKhUFwOKm4UCoVCcTmouFEoFArF5aDiRqFQKBSXg4obhUKhUFwOKm4UCoVCcTmouFEoFArF5aDiRqFQKBSXg4obhUKhUFwOKm4UCoVCcTmouFEoFArF5aDiRqFQKBSXg4obhUKhUFwOKm4UCoVCcTmouFEoFArF5aDiRqFQKBSXg4obhUKhUFwOKm4UCoVCcTmouFEoFArF5aDiRqFQKBSXg4obhUKhUFwOKm4UCoVCcTmouFEoFArF5aDiRqFQKBSXg4obhUKhUFwOKm4UCoVCcTmouFEoFArF5aDiRqFQKBSXg4obhUKhUFwOKm4UCoVCcTmouFEoFArF5aDiRqFQKBSXg4obhUKhUFwOKm4UCoVCcTmouFEoFArF5aDiRqFQKBSXg4obhUKhUFwOKm4UCoVCcTmouFEoFArF5aDiRqFQKBSXg4obhUKhUFwOKm4UCoVCcTmouFEoFArF5RBz7BPc97OgUCgUCqUBoZYbhUKhUFwOKm4UCoVCcTmouFEoFArF5fh/n/ccpSVI24kAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "my_cmap = plt.get_cmap('cool')\n", "def init():\n", " # Plot the surface.\n", " ax.plot_surface(X, Y, get_e(3)**2, cmap=my_cmap,\n", " linewidth=0, antialiased=False)\n", " ax.set_xlabel('$x/a$')\n", " ax.set_ylabel('$y/a$')\n", " ax.set_zlabel('$\\propto|\\psi|^2$')\n", " return fig,\n", "\n", "def animate(i):\n", " ax.view_init(elev=10, azim=4*i)\n", " return fig,\n", "\n", "fig = plt.figure()\n", "ax = Axes3D(fig)\n", "ani = animation.FuncAnimation(fig, animate, init_func=init,\n", " frames=90, interval=50)\n", "ani.save('rotate_azimuth_angle_3d_surf.gif',writer='pillow',fps=20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**For infinite square well only**: Note that $E_{n_x, n_y} = \\alpha ( n_x^2 + n_y^2 ) $. First energy at $n_x=1$ and $n_y=1$. This means we can find $\\alpha = \\text{half the lowest eigenvalue}$ and we can plot $E/\\alpha$ which should be distributed like $n_x^2 + n_y^2$ for different combinations of $n_x$ and $n_y$." ] }, { "cell_type": "code", "execution_count": 113, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 113, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "alpha = eigenvalues[0]/2\n", "E_div_alpha = eigenvalues/alpha\n", "_ = np.arange(0, len(eigenvalues), 1)\n", "plt.scatter(_, E_div_alpha)\n", "#[plt.axhline(nx**2 + ny**2,color='r') for nx in range(1,5) for ny in range(1,5)]" ] }, { "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": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }