From 097753e4084fafad470307444b0912535e06d6fc Mon Sep 17 00:00:00 2001 From: Alexander Goscinski Date: Tue, 27 Feb 2024 11:10:39 +0100 Subject: [PATCH 1/2] add notebook 01-BasisExpansion --- notebooks/01-BasisExpansion.ipynb | 819 ++++++++++++++++++++++++++++++ 1 file changed, 819 insertions(+) create mode 100644 notebooks/01-BasisExpansion.ipynb diff --git a/notebooks/01-BasisExpansion.ipynb b/notebooks/01-BasisExpansion.ipynb new file mode 100644 index 0000000..001e220 --- /dev/null +++ b/notebooks/01-BasisExpansion.ipynb @@ -0,0 +1,819 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "806ce41b", + "metadata": {}, + "outputs": [], + "source": [ + "from typing import Callable\n", + "import numpy as np\n", + "import scipy\n", + "from scipy.special import legendre\n", + "import matplotlib.pyplot as plt\n", + "from ipywidgets import interactive, IntSlider, Layout" + ] + }, + { + "cell_type": "markdown", + "id": "28cea43a-4a4f-4577-8ccf-92ad1dec3afb", + "metadata": {}, + "source": [ + "## Basis functions" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "4eeb5603", + "metadata": {}, + "outputs": [], + "source": [ + "a = -np.pi\n", + "b = np.pi\n", + "r_grid = np.linspace(a, b, 300) # radial grid defined on the interval [a, b]" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "19d9032d", + "metadata": {}, + "outputs": [], + "source": [ + "nb_basis_functions = 6 # for plotting the legendre polynomials in this section" + ] + }, + { + "cell_type": "markdown", + "id": "ba3796df", + "metadata": {}, + "source": [ + "### Legendre polynomials" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "c98f65b8", + "metadata": { + "hide_input": false + }, + "outputs": [], + "source": [ + "def legendre_polynomial(\n", + " n: int, a: float, b: float\n", + ") -> Callable[[np.ndarray], np.ndarray]:\n", + " \"\"\"\n", + " Returns a function that copmutes the Legendre polynomials realigned\n", + " to the range [a, b].\n", + "\n", + " :param n: Specifies which basis function to compute.\n", + " :param a: The start of the interval to which the basis functions are realigned.\n", + " :param b: The end of the interval to which the basis functions are realigned.\n", + "\n", + " References\n", + " ----------\n", + " https://en.wikipedia.org/wiki/Legendre_polynomials\n", + " \"\"\"\n", + " legendre_n = legendre(n)\n", + " # normalization retrieved from https://math.stackexchange.com/a/4425578\n", + " norm = np.sqrt(1 / (2 * n + 1))\n", + " return lambda r: legendre_n(2 * (r - a) / (b - a) - 1) / np.sqrt(b - a) / norm" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "90b75a9e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for n in range(nb_basis_functions):\n", + " plt.plot(\n", + " r_grid, legendre_polynomial(n, a, b)(r_grid), label=\"$b_{\" + str(n) + \"}(r)$\"\n", + " )\n", + "plt.title(\"Legendre polynomials $P_n$\")\n", + "plt.xlabel(\"$r$\")\n", + "plt.ylabel(\"$b_n(r)$\")\n", + "plt.legend()\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "id": "bd716680", + "metadata": {}, + "source": [ + "### Fourier series" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "f53c7098", + "metadata": { + "lines_to_next_cell": 1 + }, + "outputs": [], + "source": [ + "def fourier_series(n: int, a: float, b: float) -> Callable[[np.ndarray], np.ndarray]:\n", + " \"\"\"\n", + " Returns a function that copmutes the Fourier basis realigned to the range [a, b].\n", + "\n", + " :param n: Specifies which basis function to compute.\n", + " :param a: The start of the interval to which the basis functions are realigned.\n", + " :param b: The end of the interval to which the basis functions are realigned.\n", + "\n", + " References\n", + " ----------\n", + " https://en.wikipedia.org/wiki/Fourier_series#Sine-cosine_form\n", + " \"\"\"\n", + " if n == 0:\n", + " return lambda r: np.ones_like(r) / np.sqrt((b - a))\n", + " elif n % 2 == 1:\n", + " n = n + 1\n", + " return lambda r: np.cos(2 * np.pi * (n // 2) * (r - a) / (b - a)) / np.sqrt(\n", + " (b - a) / 2\n", + " )\n", + " else:\n", + " return lambda r: np.sin(2 * np.pi * (n // 2) * (r - a) / (b - a)) / np.sqrt(\n", + " (b - a) / 2\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "64dcc2a1", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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aupTU889Dmzcyf7NwYGm1s/3rasq3N9NcbfE/b0zSUjw1g0mL8yiYmBbweO0Ndax56zVKf/gOl92G1mBk2olLWXjOBSSkBj6OwhGM3QzVG6BmC9RuxV2xl6aNzWxqSafMlIpNpyXbaePyCBpGivg6CMIlvt7/wj/5+H8f4dR02aljGlqZ3llP/rx2TNlO6UlTJow9CaadJ/2riU6jou5gO6tfK6WxorfB0B2NTsX8M0Yzc0kRak10epH2t+7nk/JP+K76O3Y07UCk76+LgNDva90ZkzKGE4pO4MSiE5mZNTPku21RFPn+zVf44a1X+3y9eMZszrj59xgTk0I6b6xh31tK/X33Yd2wYcDjBK2W9KuvJvOG61EZjSO0uuHjcnpY+7+DbF9VhdfT7XMpwOEf04KJqRx/8UTSchMGHLN82xY+ePSv2DstvV4zJiVz3h/vI2f02BCsXiHuaKuA3e9D6SdQ/j14XYheaNqZRPX+ZNYVF9Bh9HlpRZEMt5Or3v4spEsI5v6tGEZBEM6sNFEUaS0vY+0rz7Fr6yYAxte1ML6hlYyFqWSNPYjgsXedYEiBaefDwusha0JI1zJURK/Ipk/LWfu/g4giaA1qphyTz7i52WQUJKLRqOhosVO1p5Udq6v9hlPO6GRO+/l0ElKjI3zR6erkgwMf8O7+d9nRvKPHa+PTxjM1YyqT0icxLnUc2aZs0g3pJOuSEQQBr+jF4XHQaG2krrOOKksVO5t2sr1pO/ta9+EW3f6xipOLOX/8+Zw97mzSDKHZbX/z6nLWvfsmADNPPo15Z56HPiGBvd9/w9cv/Re3w0Hu2PFcePeDaI7AwqaiKNL25pvU33c/osuFYDCQcu45pJx+OoapUxGMRtz19VjXraP1jTewbdgIgH78eAr/9U90JSWRfQMB0FLbyUdPbKO9wQZA/vhUph6XT8GENExJOlwOD40VHezbUM/uNbV43SIarYpjL5rAlKPz+xyzavcO3rzvj3g9HnLHTeD4y68hu2QMNaV7+PrF/9JUUYbelMBP7vgzOWPGjeTbVYhW3E7Y+xFsegEOfEl3i9ypGkX1Kh0d9XbWjC3AYtRh0Ok59vxLmHDSKRiSQr9xUwyjMDFS6fpbPvmQL559AoDZZXXktXeSdMpS8m86D9WBlbDzHbB0a5Y77mQ4+lcw+riwrWkwvB4vX720hz1rpHVNWJjD0eeNx5Tc981XFEX2rq3j2zf24bC6MaXoOPvm2aTnD7xrDSet9lZe3v0yr+x5hQ6nZLRpBA3HFh7LSaNO4qj8o8g2ZQ95/A5nB99Vf8eXlV+yumo1na5OALQqLeeOO5drp187rFDb/vU/8L+HpabIJ139c2afemaP1xvLD/HGvf8Pu6WDqccvZdkNNx9R+hBRFGn420O0PPccAIknnEDunXegze/bGBBFEcsXX1B7zz14GptQJSUx6umnMM6aNYKrDo7qva189OR2nDY3Cal6Trh0IiXTM/s93txsY9VLe6jc3QrAvNNLWHDm6B6fi47mJl66/Ras7W2Mm7+IM371+x5GtcNq5Z0H76Z6zy5Sc/K4/MF/oDOawvcmFaIblw02vQjfPQrm6q7ni4+BSadjF8dRcdv9uBubWD+hiCajjoS0dC6+9yFSsnP6HXa4KIZRmBjJOkarX36O9e+9hUFv4Jht+9HZHSSedBKF//wHgkqAsm9g7VOSRS5b4mNPgqV3Q97MsK7tcESvyGfP7mTfhgYElcDxF09gyjH5Ad102xutfPTEdlpqOjEmaTnn13NG3DjqdHXy3+3/5aXdL2FzS7vskuQSfjLhJ5wx5gwyjBkhn9PqsvLxoY95s/RNdjbvBECj0nDuuHO5fub1QRtglpZmlv/+l9g7zMw788ccf9lP+zyubNtm3v7LXYiil7Nu/X+MX3jUsN9LLCCKIvUPPEDrCy8CkPXrX5Pxs+sC+oy6Ghqo/tXN2LZsQWUyUfTfZzDNnh3uJQdNzf423v/nFtxOL3njUjjt+ukYEwf3CopekfUfHmL9h2UAzFlWzOJzpZCYKIq8/cBdlG3dRNaoEi6+72G0BkOvMeydFl74/S/paGpk6vFLOPUXvw7pe1OIATwu2PAcfPMwWHx9TBNzYPZl0k/6GOx7Sym/4gq87e3UTh7HZp2IRqfnkvsfJqt4dFiXpxhGYWIkDSOP28VLf7iFpspyxk+cyoR3VyI6naScey55f/lz1wW95SCseQw2LgevJHBmxoVwyv2QOHTvRjB8u2IfWz+vRKUWWHbtNMbMzgrqfHuni/89upmmSguJaXrO/8M8ElLCH1bzil7eO/Ae/9j0D5psTQBMTp/MdTOu46Sik1CrRkakvLF+I09sfYK1tWsBMGlM3DDzBi6dcilalTagMT5+7BF2rf6S7NFjueT+h1Fr+j/v29deYO07b5CUmcXVjzyBVt/7RhdvNP/3vzQ89DAIArn33E3aBRcEdb7XaqXyhl9gXbsWdWoqJa+/hq64OEyrDZ7mGgtv/20jTruHUVPTOe366Wi0wX1+t6+qYvVrpQAc85PxzFxSxL71a3jv4T+j1mi44qHHSM8v6Pf8qj07eePu2xFFLxfe8yCFk6YO6z0pxBAHV8HHf4DG3dL/U4rgmFtg1mWgla4vrupqDl10EZ7GJpg5nc+NIk6bjeMvv4Z5Pzo37EtUCjzGAWqNlmXX3wyCwL69O9H/6XZQq2l/5x1aX3yx68D0MXDG3+Gm9TD9J9Jz216Hf8+XYrthtnt3fVfD1s8rAVhy1eSgjSIAQ4KWs2+eTWqOCUurg4+e2I7b5Qn1UntQbi7n6pVXc8d3d9Bka6IoqYhHT3yU13/0OicXnzxiRhHA3Jy5PHPKMzy37DlmZM7A6rby941/5/z3zmdT/aZBz28oO8iub74C4OTrbhrQKAJYeO4FJGVm0dHUyLr/vRWS9xDNdHzxhWQUATm33x60UQRInqInn8AwfTqetjYqf349no6BkwtGCnuni4+e2I7T7iFvXAqn/jx4owhg+gmFLDpnDADfrdhH2bY6Vi1/BoB5Z/54QKMIoHDSVKafdAoAq196FmXPfQTQ2QRvXgUvnC0ZRcZ06X70y00w/1q/UeS126n65a/wNDahnzCBqhOOwmmzkTt2PHNOPyuy76EPFMMoiskdN4FJR0m6oa3l+8i57fcA1D/4N6wbN/Y8OH00nPcMXPeVlN5vb4P3fgnLz4T2asJBU5XFv8NceNZoJszPHfJYhkQtZ/xiBnqThoYyM2vePhCqZfbA4/Xwws4XOO+989jUsAmTxsRv5v6Gd89+lyWjlkRUczMvdx4vnv4i9x51L+mGdA62H+SqlVfxyMZHcHqc/Z63+uXnQBSZdPTx5I4dP+g8Wr2B4y+7BoBNH73bZ5ZRvOCqrqbm9v8HQNoll5B+xeVDHktlNFL0+GNo8vNwlpVRd9ddEb/5i6LIF8/vwtxoIynDwGnXT0erG7pRP2dZMZOPzkMU4aPH38TcWE9iegYLzwnMmDzqgkvR6g3U7tvLvnXfD3kdCjHA7g/g8UWS5lVQw4Kfw698BtFhGdN1992Hfdcu1GlppD5wPzu+WQXAcZdejWoEN6GBohhGUc7i8y9GEFQc2LAWx1GLSP7Rj8Djoea2P+CxdPY+oWCOZBydcj9oTZIW6cmjYc+HIV2X2+nh02d24HF5KZ6WwdxTS4Y9ZmqOiaVXTwFg21dVlG1rGvaY3WmyNfGzz37GQxsewuFxsChvEe+e/S5XTbsKnTo6MrRUgopzx5/Le+e8x9ljz0ZE5Lkdz3Hxhxezv3V/r+PrDx2gfNtmVGo1R18Y+E1/wsKjyCgchdNmY+unH4XyLUQNosdD9W9/h9dsxjBzBjm3/2HYY2qysih85BHQaDB/9DHtb0XW47bzmxrKtjej1qgC1hQNhCAIHHfRBDKLErC3/wDAvB/9uE9dUV8kpKYx90fnALDu3RURNxwVwoDTCu/eCK9fCp2NkDUZrvsSTv8bGHtn15o/+4z2t94GlYqCR/7Oxu++xutxUzR1BkVTZ0TgDQyOYhhFOen5hUw65ngANn30P3Lvvgttfj6uqioaHnyw75PUGjjql3D9t5IQ29YKr10CH/1OSqEMAes+OERrnRVTio4lV02WBOEhoGR6JjNOKgTgq5f24LC6QjLu+rr1/OT9n7Cubh1GjZE7F9/JUyc/NWIFF4MlRZ/C/cfcz6MnPEqaPo3S1lIu+egSVh5a2eO4TR++C8CERceQmhO4x05QqVh4jhR63fjhu7gc9kHOiD1aXngR2+bNqBITKfj73xG0gem1BsM4axbZt9wMQP1fH8RVVzfIGeGhvdHKdyv2AbDonDFkFYUmxVmjVTNuVjuitx0EIyrdtKDOn33qmWi0OuoP7pMKjCrED80H4JmlsOUlEFRwzK/h519D/qw+D3c3N1N3190AZFxzDcLUKexc/QUAR/3kkhFadPAohlEMMPf0swEo/eE77G4XeX99AASBtjffxLp+ff8nZoyFaz6HxTdJ/1/3FLx4jhQXHgYN5Wa2fFYBwAmXTBz2LvVwFp87ltQcE1azk+/fGV5ITRRFlu9czrWfXkuTrYlxqeN47YzX+MmEn8REqvqS4iW8ffbbLMpbhM1t43erf8ff1v8Nl9dFR0sTe75fDcDcM84JeuyJRx1HSnYOtg4ze7//JsQrjyzOigoa//EPALJv+z26wsKQjp9+9dUYZ87Ea7FQd/c9I+4ZEUWRr18txe30UjAxlZknFYV0/L1rPgFAo5/Nug+qsLQGbjibklOYfNyJAGz84N2Qrkshguz5EJ46ARp2QkI2XPGelAWt6T9RpuFvf8PT0oJ+4kQyf3kTO776DI/LRfbosRREsThfMYxigJwx48gbNxGvx832Lz8lYcECUn8i7fbr7r0X0TWAV0Wjg2V/hotfA10SlH8HT50IdduHtBbRK/L1K3sRRRg/P4fRM4MXWw+GRqvmxMsmArDrmxpqD7QPaRyX18U9a+7h4Q0P4xW9nDX2LF4+/WXGpI4J5XLDTqYxkyeXPsm1068F4MVdL3Lj5zey8dP38Xo8FEyaEpC26HBUajUzlkpl97d9sXKQo2OLuj//GdFux7RwIannnx/y8QW1mrz77wOtFsuqVVi+/DLkcwzE/g0NVO5qQa1RccIlk0LmsQVorCijdt9eVGo1+ROPxu3w8N2K3mHcgZh7+jm+df6AuakxZGtTiACiCN/9E167FBxmGLUYfr4aRh874Gmda9fR/r/3QBCk74pGzdbPPgZg1rIzonpjqhhGMcKsU38EwLbPVyJ6vWTf+mvUaWk49u2n5aWXBx9g4mlw7edSFlt7Bfx3ma8aaXDs+aGOhvIOtAY1R58fvgq3+ePTmHy0FOb69o1SRG9wO3Kz08wNn9/AW/veQkDg9/N/z/1H349JG5uF59QqNTfPuZlHT3gUo8bImpo1fPeppG+ZefLpQx536vFLUKnV1O7bS2NFWYhWG1ksX39N59erQaMh9+67wnYB1o8fT8bVVwNSSM3rDE2YejBcTg/fvSUZKnNPKyY1J7Sf6e1fSN6isfMWcuIVcxAE2L+xgco9LQGPkVFYROGUaSCK7PZlTCrEIB43fHgrfHYHIErC6ivfh+SBJQii2039/fcBkHrRhRinT6d862bMjfUYEpOYdPTxI7D4oaMYRjHChEXHoE9IoKO5kardO1CnppL9m1sBaHrySTztAXhVsifBtV9IFbJdnfDyBbAjcPGo0+5mzbtSaGv+6aPDXmto0dlj0RrUNJR3sHdd4DqOJlsTV628irW1azFqjPzzpH9y+ZTLo3qHEihLipfw/KnPM7EzG0MnuDQi4vj+KxsPRkJqGmPnLgS6boixjOhyUf9XSXuXfvnl6EeHt2hcxs9+hiYrC1dlJS3Ll4d1Lpmtn1fQ2eYgKd3A7FNGhXRsl9PBrm+kDdOMk5aRWZjEtBOkMOT3b+0PaoMy9filAOz8+nNFhB2LuGySNnXDs4AAy/4Cpz8M6sG1em1vv41j337UKSlk33ILgL+kyORjT0Cri472T/2hGEYxgkarZcKiYwDY9c0qAFLOPRf9+PF429tp+s9TgQ1kSodLV8DUc6WCkCuukSpoB8C2L6uwmZ0kZxn9AulwYkrWMe+0EgDW/u8gHpd30HNqLbVctfIq9rXuI9OYyfJTl3NC0QnhXegIMyVjChe7TwLgYJ6Fn311vb969lCQa8/s+X41Xk9460eFm7Z33sF56BDqtDQyf3FD2OdTJyaQdau0QWl++pnANijDwGp2sukTSd+36NwxQ6pXNBCHNm/A0dlJUkYWxTOk6t7zzyhBZ1DTVGmhdH19wGNNWHQ0Wr2B1toaakr3hHSdCmHG0QEv/wT2fQIaI1z4Iiy+EQLYXHqtVhr/9S8AMn9xA+qUFJw2K/vXS1mOU449KaxLDwWKYRRDTD7mBAD2rf0Ot9OJoFaT/bvfAtD60ku46gO8aGn0cN5/Yf51gAgf/w6+//eAp9gtLjZ/Wg5INYvUmpH56Mw4qZCEVD2WVgc7vx24HlO5uZwrVl5Bubmc/IR8lp+6nMkZk0dknSOJy+mgeuNm6T9Tc2l3tHPtJ9eypWHLkMYbNX0WhqRkbOZ2KncOTXsWDXgdDpoeexyAzOt/jjoMjSj7IuWsM9GPH4fXbKb52efCOtemT8pxOTxkFycxfl7o+0rJIvyJRx2LoJK+48ZEHXNOlap8r33vIB734BsUAJ3ByIRFRwOw+5uR1WApDANbG7x4rlTqRZcEl78Nk88c9DSZlpdextPYhLaoiLSLLwakPo5up4O0vIKYaDKsGEYxROGkqSRlZOGwdnJws5SNlnDssRjnzUV0Oml++pnAB1Op4fSH4FjJsOLTPw5oHG3+vAKn3UNGYSLj54av0d/haLRq5p1eAsCGj6WbQl9UmCu4euXV1HXWMTplNMtPW86o5NCGGaKFsq2bcDnsJGVm8cil/2VO9hwsLgs/++xnbKjbEPR4ao2GCb6eaXKWWyzS9tpruOvr0eTlkXrRRSM2r6BWk3WzlL7f8sILuJubwzJPZ7uDHaulzcHCs8eEPDTstNs4uEm6rsiFZWVmnFSEKVlHR7OdvT8EHtae6Btn37o1eL2x7Y08IrC1SVWsq9aDIRWu/B8UB95P0WPppOXZZwHIuulGBF+z4d3frgKkMFosSBoUwyiGEFQqJh4lZQLsWytVlRUEgaybpHT8tjfeCNxrJJ0MJ/0JjpMqavdnHNk7XWxfVQXAgh+NDmkGTCBMPiqP5EwDNrOTXd/W9Hq9xlLDtZ9eS6OtkXGp43hu2XPkJgy9Cne0s++H7wCpSGOiLpEnlj7hT+e/8Ysb2d4YvNdn4mLpBrZ/3fd43KGpHTWSeJ1Omv8rXZAzb7gelX5kNQyJS5ZgmD4d0WajZfkLYZlj08pyPC4vuWNSKJqcHvLxD2xch9vpIDU3j+zRY3u8ptWpmbNM8hptXFmGxxOY12jUtBnoExKwtrdRs2d3yNesEEIcFil8VrsFTJlw1YdQMDeoIVpfeQVPWxu6khKSzzgDALvFQsWOrUBvgztaUQyjGGP8gsWApAWQb2CmhQv9XqOW554PbkBBgBP/X0/jaGNPEen2VVW47B4yChIZPWPoQt+hotao/BflzZ9V9HDl13XWcc0n11DbWUtJcglPn/I0GcaMEV/jSOF2uTiwcR0A4xdKmjOT1sS/l/ybhbkLsbqtXP/59ZS2lgY1buGUqSSkpmHvtFCxY1vI1x1u2t95F3dDA5rcXFLPOWfE5xcEgczrfw74bg5mc0jHt3e6/JuCBT8aHZZdd+mabwHJSO5r/CnH5mNM1mFuslO6NrANmFqjZdy8RdL4674L3WIVQovLBq9eBFXrJE/RFf+D3OAKe3rtdlqefx6QNieCRgPAoc3r8Xo8ZBYVk5Y3cL+9aEExjGKMvHETMaWk4rB2UrlrB+C7KP/sZwC0rVjRd6uQgZCNo2N+Lf3/g1tg13sAuBwetn4pNYmde1rxiHuLZCYtysOUoqOzzcHetZIrv93Rzs8/+zlVlioKEwt55pRnyDSOvOE2klRs34LTZiUxLZ388RP9z+vVev550j+ZkTUDs9PMzz79GWXtZQGPq1Kp/dlpsuEVK4huN83PSGHkjJ9e7XffjzSJJ54oaY0sFlpfeSWkY+/8phq3y0tmUSKFk3u3XRgubqeT8m2Sbk3efB2OVqdm1hKpkOTWLyoDzjQb7wvT7lv7PaI3ME+TwgjiccEbV/TUFAVpFAG0v/8+npYWNPl5fm8R4Bddj5u/KGRLDjeKYRRjCCqVfwcmf+AAEo45Bt2YMXgtFtrfHkL/JkGAJXfBnCtA9MJb18Ch1ZSuq8PR6SY508DYOdmhehtBo9aqmLVU0gxt+awCm8vGL7/8JQfbD5JtyuaZZc+QkzBy2qdIcWDjWgDGzl/sF8fKmLQmHl/yOBPTJtJsb+b6z6+nyRZ4lfMxcxcAcHDTuphKr+746itclZWoU1P9hU8jgaBSkeHboLS+/ApiiOoaedxetn0lhbJnLSkKi7eoatd2XA47iWnpvcJo3ZlyTD4anYrmagvVpW0BjV08fTZagxFLSzMNZQdDtGKFkCCK8P4tsO9TKfvs0jeCDp9Jw4i0viCFkNMvu9zvLXI7nRzaIjU8Hze/b4M7GlEMoxhEtrwPbPjBfwMTVCrSr7gCkHpEiUNJuxYE+NGjUgaCx4n4yiVs+0wqJDf9hEJUEfIWyUw9Jh+tXk1rnZV73/o7mxs2k6RN4smlT1KQGBsu2uEgiiKHNksXmbFz5vd5TIo+hf+c/B+KkoqotlTzyy9+idVlDWj8UdNnotHp6WhqpCmGij22+gqcpl5wASqjMaJrSV62DHVWJu7GRsyffRaSMfdvqMfa7iQhRce4MGSiARzYJHkJx8xZMKDhZUjQMnmxVNxv6xeVAY2t0ekonj4TkCQAClHEqr929T37yfNBCa270/nd9zj27UdlMpH6k65K8xU7t0oGd0bmgAZ3tKEYRjFI0dQZaHR6LC3NNFWW+59POfss1CkpuKqq6BhqiwKVGn78DBQfQ7WlhJYGDxqdislHRb7Zqs6oYdIiSVTt2pqIVqXlHyf9g/FpwbfDiEWaK8vpaG5Eo9VROHV6v8dlGDN4fMnjpOpT2dG8g9tW34YngIwgrU7PqGlSt+tYCafZS0uxrl0LajVpF49cJlp/CDodaRdK62gNpCL9IIiiyObPJQNk+omFYSmTIYqi/+89Zm7fBnd3Zvj6spVtb6KtPjCje/TseQAc3KIYRlHDphfg679Kj894BCaeOuSh5OKmKeed16NMRveNXCxko8kohlEMotHpKPLdGMt8bkoAldHoT1MeVhVerQEufJFt7gsAmJS8Fr0mOjKVKouljKvi1mncO+MB5ucOfiGPFw76dttF02YMWjm2JKWEf530L3QqHauqVvHQhocCmkPWGcnlIKKd1pclLU/SkiVo8yJvvAOkXXgBaLXYNm/GtmPohTcBqve20lxlQaNTMfXY8HhFmyvL6WiSDO5R02YOenxqjoni6RkgwjZftupgjJ4lGUa1+/ZiNYe3CKZCABxaLYXQAI77Hcy7eshDOfbvp/Obb0AQSL/8sh6vlW2V7k8lM4MPz0USxTCKUUpmzgGkmjbdSbvkEumivGEjtu07hjy+2WrkkEUS4E3nBXjn5xBh4eTa2rU8tP9+qlL2okJFxsHoLxQWSg75dtvy7nswZmXP4q/HSTvCl3e/zNv73h70nJJZ0ueqbn8pDmuQIv4RxtPeTvt7UpJA2mWXRng1XWiyskhetgyQCq8Oh61fSobH5MV5GBIGb8UwFMq3bwGgcMo0tHpDQOfM9HmNdn9fi8M6+KYpKSOTrFElIIp+kbdChGg5JImtRQ9M/wmc+MfhDecrT5G0dAm6UV2149rq62irq0WlVlM0dcaw5hhpFMMoRpEt8Oo9O3HZ7f7ntTnZJJ8muURbX3t1yONvX1UFIhSNVpGuq4fd78E3fx/eoodBhbmCW1fdikf0YJgpue93fVuD23VkFI1z2m3U7JXqwMi770A4ufhkbpx1IwD3/XDfoNWxkzOzScsrQPR6qdgZ3Wn7bW+9jWizoZ8wAdP86PIcpvsMNfNHH+FuCbz5ancsrQ7Kt0vieTl8FQ5kQ6V4+qyAzymclEZ6fgJuh4fd39cGdE6Jz6A/fDOnMILYzfDqxWBrhfw5cNa/Amrz0R8ei4X2Dz4A8GtcZeS/c/7EyehNsdW8WzGMYpS0vHySs3LwuN1U7upZ0C/tAikEZv54ZfCp+4Db2XWxm3H6NPjRI9ILX/0ZSj8d3sKHgNVl5Vdf/gqz08z0zOn8/vwbSUzXY+90sX9Dw4ivJxJU7d6B1+MhJTuH1Jzgilf+fMbPObn4ZNxeN7d8dQt1nQNXLi6eMQuA8m1bhrja8CN6PP6U+LTLLo06/YJh5kwM06YhOp20vfHmkMbYs6YWUYT88amk5oTnxuJ2uajcLXmW5d5ogSAIAtN9zWV3f18bUBZj8bRZAFTs2BpTWY9xg9cref4bd0NiLlz0MmiHl6xg/vAjRJsN3ZgxGOf13LD5w2gz5gxrjkigGEYxiiAIlMyULmSyK1zGOHcuupISRKuVjk9WBj32wa2NOKxuktINFE/NkFL45/0UEOGta6H5QAjeQWCIosjd39/NgfYDZBmz+MeJ/8CoMzDtOElvsf3rgfunxQsV26XKsYFoQA5HEATuP/p+JqRNoNnezK+/+jVOT/+p5MXTZ/vmjN6Qh3XtWlxVVaiSk0k5M/A+TiOFIAj+8F7bW28FbQiIXpHd30sFHScfHT7tVG3pbtwOB6aUVDJHlQR17vh52ai1KlpqOmko7xj0+PxJk1FrtVhammmtPTK+t1HFt4/A3o9ArYeLXoHk/GEP2eYrDZN63nk9Nidej4dKn8dZln3EEophFMPIcdvKw0IegiCQct6PAWhbEXxNoz1rJI/CxMW5XQUdT30QCheAox1evwycgWWjDJdX9rzCx2UfoxE0PHz8w2SZsgCYfFQ+gkqgocxMa110a2FCgVxSfyiGEUg1jv550j9J1iWzo3kHD294uN9ji6bOQFCpaK2tob0hiBYzI0jbu+8CkHzG6RFP0e+P5GXLUCUk4KqsxLZx4+AndKO6tBVzkx2dQR3W+mHypqp4xuygvW56k5axs6XvYyDhNK1OT/4EqamzbOgrjBAHV0kef5B6ZBYOXwzt2LcP+9ZtoNGQcvZZPV6rP7Qfp82GPiGBrJLRw55rpFEMoximaIqUmdZYUYbN0nPHlnL22aBWY9u8GceBwD08HS12KndLmohJi7rtVDU6uOAFSMyBhl2w8rbhv4FB2NKwhYfXSzfwW+fdypycrp2HKVlH8VSpX5RsyMUrVnM7jeWHAIYlYixILOCBYx8A4NU9r7LyUN/eRL3JRN44qar24UZ3NOCxWOj4VKoRlHruuRFeTf+ojEaSfHq/tnfeCercXd9Jhsb4BblodeqQr01muAa3XMZj37o6XM7B9X6jfJ/fip2KYTRimGtgxTVS4d5Zl0kRgBAgb7oTTzgeTWbPjgOVOyV5R+Hk6ahU4fv8hgvFMIphElLTyCgcBaJI1WE6I212NonHSQ372t4ePBtJZu/aOvDpGlKyDtuJJ+fBj58GBKkGxvYVw30L/dLuaOe3X/8Wt+hmWckyLpt8Wa9jJvoMt71r6/B641ezIF9kMouKSUgdXjuI4wqP49rp1wJw1/d3caj9UJ/HFU6RMhKrdg89szFcdKxciWi3oxszBsP0/us5RQNy37aOj1fitQbmZbV3uji4uRGAKWEMo7nsduoPSgVc5U1WsBRMSCMpw4DT7vGveSBG+Qo9Vu7cjjeA2loKw8TjhhU/BWsT5EyHMx4elthaRnQ6/Rmhqeed1+t1Wfc6aoB6a9GMYhjFOIW+C5p88+xOqi+c1v7u/xBdg6fUiqLInjXSTnXS4n4uyGOOh+N+Kz1+/xYp9TPEyLqiems9o5JGcc9R9/Tp5h89IxO9SUNnm4PqPa0hX0e0IF9kQpXyeuOsG5mfOx+r28pvv/5tn3qjosnRaxjJYbSUc8+JOtH14RjnzkVbVITXaqXj888DOqd0XT0et5eMwkSyRiUNfsIQqSndg9fjISkzi5TsoVXUFlSC/1oRSDgtd+wEtAYjdksHTRXlgx6vMExWPwQVa0CfDBcsH7bYWqbjq1V4WlvRZGWReOyxPV7zuN1U75bqdxUO0eCONIphFOPIFnlfIY/E449HnZGBp7kZy9dfDzpW3UEz7Q02NHo1Y+dk9X/g8X+AUYvB2SHtRtyh6Qkl8/a+t/m84nM0Kg1/O+5vJGgT+jxOrVUx3tciYc/awFKGY5HqPb6LzOSpIRlP/r2mG9IpbS3ln5v+2euY/ImTEVQq2hvqMTcN7gkYKZwVFdg2bASVipSzzhr8hAgjCAIp55wNBB5OkzcnU47OC6vhV7VbDncE3zC0O5MW54IgFaM0N9kGPFalVpM/YRLQ9blWCBMVP8Dqv0mPf/R/kBG6lhyy6DrlnHP8fdFk6g/ux+WwY0hKlmpXxSCKYRTjyBZ5U2V5L52RoNX6bx7t738w6Fh7fFkw42ZnoTNo+j9QrYHzngFDKtRsgi/uGdri++Bg+0EeXP8gAL+a/SumZg5sDExcLKWuH9zciNPuDtk6ogW7xeJv+1IwKTSGEUCmMZN7j7oXgOW7lrOmZk2P13VGEzm+3kbR5DVqf/d/ACQcdRTanNhoGpxy9jkAWH9Yi6umZsBjW+s6aazoQKUSGD8/vO+vcpf0dx2uYZScYaRwohTi3fPD4Hq/gklTAKjas2tY8yoMgL0d3rpO0hXNuAimnz/4OQHibm6m89vvAEjpQ+MnXy8KJ03p1eg6VojNVSv4MSWnkJYv1RORCwB2J/lHZwBgWbVqwJpGbpeHfRulmkCTAumLllII5zwuPV7z75DUN3J6nNy2+jZsbhsL8xZy5dQrBz0npySZ1BwTbqeXA5vir6ZR9d5dIIqk5eUPW190OMcXHc+FEy8E4E/f/ok2e1uP12Wj+3D9WqQQvV7a5TCaT7sTC+gKCzAtWACi6Ndl9Mc+X12uwsnpGBN1YVuTy+mgbv9eAIqmDM8wApjo62G4f0P9oKUJCn0Gfs2enUo9o3Dx4W+gvQJSi6UstBDS8emn4PFgmDoV/ZjeGWfVeyWDN5QbuZFGMYzigIKJUgpszd7eOzDDlCnoiosRHQ4sX/XfWLZiZwsuu4fEND3541IDm3jSGbDg59Lj924C69Aq/Mr8Y9M/2NOyh1R9Kn855i+ohME/noIgSK58YG8Au9VYQw43hOsi85t5v2F0ymgabA3cvebuHjcqOXRXHSU7e9uWLbhqalAlJpK0dEmklxMUsiEnVwnuC1EU2b9BKo8wfn74UvRBCnd43G5MKamk5g6/ns3omVmoNAKtdVaaqwcun5E7fiIqtQZLa0vUloOIaba+DtvfBEHt8+wnh3R484cfAZB8+um9XhNFkZrSPQAUTJwS0nlHEsUwigPyfYZRdR8eI0EQSD5D+gCbP/q43zHkC/K4udldtYsC4eR7IXMiWOrho98FseqerKlZwwu7pJ479x19H9mmwG8MExZIhlH1vjY62x1DXkM0UhVmw8ioMfLgsQ+iUWn4ouIL3tnfpYPJGy9pQVpqqrB3WsIyfzCYP5bKCyQtOQmVIbCeXtFC0slLEbRanPsP4Ni3r89jmqostNZZUWtUjJk5gMYvBNTuk7xF+RMmh0THpDdqpGKwdF1L+kOr05MzVupzqOiMQkxrmeQtAjj+NihaENLhXfX1WH01ueTWU91pqanC3mFGo9WRPXpMSOceSRTDKA6QLfP6A/tw95F9Jlv2lm+/xdPeu7O1y+nh0PZmAMbNDVLXoDXAuU9Iu5MdK2Dnu8GdD3S6Ornr+7sAuHDihZxQdEJQ5yelG8gZnQwiAaUMxwpup5P6A1I6dWEY3dKTMybzq9m/AuCv6/5KpbkSkMK0Kb72I3X7S8M2fyCIXi8dn3wCQNKpvS/I0Y46KYmEY44BwLzykz6PkQ2K4ukZ6IwDaPxCQO0+aVefN35iyMYcN0/azOzb2BBwOE0xjEKI1wvv3iglxRQtgmN/E/IpOlauBFHEOGcO2vzenkZZzpE7bgJqTXiaHo8EimEUB6TlFWBMSsbtctJwaH+v1/XjxqGfMAFcrj5Thit2NON2eEhKN5BdMoT04IK5cMyvpccf3gqW4IyTRzY8Qm1nLQWJBdw699bg5wd/deD9G+NHZ9RQdgCvRwp3pATZHy1Yrpx6JQtyF2Bz27hrzV14RS+Av9BjrU+PEilsmzfjbmhAlZhIwtFHR3QtQyX51GUAmFeu7GU4iKLIvvXSZ1fOtAwntT5DN5SGUcn0TDRaFeZGG40VA7cIkeeNtMEdV2z4L5R/C1oTnPuklCQTYto/6j+MBl1hdzmKEasohlEcIAiC/4PYlwAbuj7Icny4O7IxMW5u9tDd6sffBjnTwNoMH9wCAYoqf6j9gTdK3wDg3qPuxaQdWrNMubxAzf74CafJsfq88RPDXq9HJai456h7MGqMrK9bz4rSFb65pXCaHHqJFF1htCWodOETJYeTxJNOksJpB3qH0+oPmelosaPVqymenhHWdXQ0N2FpbkIQVOSOGR+ycXUGDcXTpQrI+wZp7iwb3E2VFbjs9pCt4YiltRw+k7zuLL0b0kPfhsNZVSW1AFGpSF52Sp/H1JRK959Y1heBYhjFDf6d/YG+9QvJp58GQOcPP+BubvY/73J4KNveBHS5woeERiftUlRa2PMBbHtj0FM6XZ3c9V1XCG1B3tDj4ckZRrJL4iucJhsj8t823BQmFXLznJsB+PuGv1NrqSVv/ARpLftLI5ZB1COM1oeuIVZQJyWR4CuG13FYOG3feimMNnpmZlhbgECX9y9zVDHaEGu1xs+TPbcDZ6clpmeQmJ6BKHr91bcVhogowvu/AlcnjDoK5l8XlmlkjappwQI0Wb01cPZOi785cO64CWFZw0ihGEZxgvxBrD/Qt2taN2oUhmnTwOvF/EnXRbl8RzNup5fkTMPwq+zmTpc8RwAf/w46Bs4S+7+N/0dNZ82wQmjdGecLp8VL2n6XQHbSiM158aSLmZ09G6vbyj1r7iGreDRqrRZ7h5m2+sgU0bRt2oS7sRFVUhKJRx0VkTWEir7CaaJX9H9mRySMJhvcIQyjyRRPy0CrV2NpcVB/yDzgsV2bOSWcNiw2LZeaxGoMcPa/IUy1g8wfS4aRvMk+HFkPmZKTiyk5JSxrGCkUwyhOyBkjZXm0N9RjNfcWWENXFoGlm85o/8Zu2WihCNcc82vImyUVGPu4/0az62rX8fre1wG456h7hhxC644/nLavDas5tNW4R5qOliY6mhsRBBU5Y0MX7hgMlaDi3qPuRa/W813Nd3xQ/hHZvkKPkQqnyWLlpCVLEGI0jCaTeNJJCDodzoMH/eG0hvIOOtudaPVqiianh30NXYZR6A1ujU5NyQwpnLZ/kHCavJlTdEbDoL0KPvmT9PikO0Ja3bo7zqoqHLt3g1pN0skn93lMnc/ADWV4NlIohlGcYEhIJC2vAJCy0/oiaYlU+6Vz3Xo8ZjMuh4fyoWaj9YdaA2f9U8pS2/UulPbOwLG77f4stAsmXMDCvIUhmTo500h2cRKiCAc3x7bXSL55ZY4qRmcITX+jQClJKeHGWTcC8Lf1fyOlpKjHmkaSntloy0Z8/lCjTkz0Z6d1rJR0Uwe3SqHf4mkZqLXhvSR7PR5/6CpcIVp5g3JoW+OA4bTcsXKYNrL6tZhFFKV+lc4OKFwAi24I21SWL74AwDR3Lpq0vgvN+g2jEdzIhQvFMIoj5A9kXT+Gka6kBN24seB2Y/l6NZW7W3C7vCRlGMgsSgzdQvJmwuJfSI8//A04etbAeWrbU1RZqsgx5XDrvOGH0Lozdq5P4xDj4bS6MGQNBcPlUy5nWsY0OpwdfOuV+vBFwjCybdkaN2E0GX847VOpWvyhLZJhNHpWZtjnbqwow+10oDclkJ5fEJY5iiano9aoMDfZaanpv9hj7thxIAh0NDXS2Ra/TaDDxo63YP9noNbD2Y+BKnzatI7PJcNooMKq8n1HNnhjGcUwiiO6DKP+XdNJS5YC0PHFFxzaJomuR8/MDH3W0wm3Q8ooaK+EVQ/4nz7YdpDndj4HwO0Lbu+3QexQGTtbMoxq9rVj7+xd0ylWkHf1ORFyS2tUGu49+l40goavPFJBt8byg7icI5vxJ1drTzzuuJgPo8kkHn88qNU49x+gYfN+WuusqNQCxdPCbxjJxm3uuAlh62OlM2gonCx5FQ5t7T8RQmc0kVHg80Yq4bTgsLfDJ/9PenzsbyArfMaIu7XVX9Qx8aS+DSNLawuWlmYEQUX2mPCE80aSmDeMHnvsMUpKSjAYDCxcuJB169YFdN5rr72GIAicE0M9lwYjx2ep1x3Y168LO2nJSQBYVn9DmWwYzQjDBVmXAD96RHr8w+NQswVRFLnvh/twe92cUHgCJ406KeTTpmQZSc9PQPSKVOxsHvyEKEQURRoOHQC6tGORYHzaeC6fejmdBg8Og4jX46Hh0MERXUPHl18BkHjSiSM6bzhRp6RgmjcPgNKPJW9cwcQ09GEu6gj4+6OF2xMpV+4+tLVpwOMUndEQ+fJ+qdtAxjg45pawTmVZ9TV4vegnTUJX2LeXUfYWpRcUjnjoPxzEtGH0+uuvc+utt3LXXXexadMmZs6cybJly2hoGDiMUlZWxm9/+1uO9aXOxgvZJaMRVCqs7W10NPd9QTJMm4YmO5tWTQ52iwu9SUPe+NTwLGj8yTD1x1KH5/dv5r1977ChfgNGjZHbF94etto8Jb5aKrLhF2u0N9Rj77Sg1mjILBoV0bVcP+N6chNzqU+xAV0Vk0cCZ1kZzgMHQKMhMc6+q0k+Q6+8TPJqjpkV3hYgMjVhzEjrTsmMTBAkYbmltf86RbLOaSAvt8JhVG+C9c9Ij8/4O2j0YZ2u4wspWUfWqPZFvV9fFPthNIDwb1HCyCOPPMJ1113H1VdfDcCTTz7Jhx9+yLPPPssf/vCHPs/xeDxceuml3HPPPXzzzTe0tbWN4Ir7RhRFbC7P8AcSNGQUFdNUfojyvbsZm9y3SM5wwok0bZAuVgWT03B4vODxDn/+vlhyP8YDX9Bev42H10ohtWum/oxUXTZWpzssU+ZNSYNPyinf2YzF5kSlji37v7JUunmlF5Xg8AoQpt9TYOi4dc7veXHb3YyqN7F3xwamnHLmiMxs9ukaDHPn4jCYIvx7CC3qY47DoXucNpVkEOVOTg3b90HG0WmhtaYKgNRRY8M7n0FFVnEyjWVm9m5qYPKxfTeqTS32ZTzu30un3Rm28F7c4PWgf/8W1KIX99TzcRYeE9bvhddmo/Pb7wDQHn9Cv5+Zap/BnV4Sus+VUasOe2Hb/ohZw8jpdLJx40Zuv/12/3MqlYqlS5eyZs2afs+79957yc7O5pprruGbb74ZcA6Hw4HD0aWpMJsHrssxVGwuD1Pu7Lt/UrCc2GJgGvDA8s/4/v2+y/LPqU/mzEzJsv/HrkpuuLMiJHP3x0Xqn6DPe5s2rx3BnsUDr2XzAKF5v30hiHCDYACbh9P/9AUV2jAZfWHiqJYfmAt81aTjzhB9LoaHyJjEHMBJ6e6tTLlzJRD+C9aD37zNDOD/rLm8FxW/h9DyYIHU2sTi6WDe31eFfb4iWxXnAG2aZOY81P81MlQssGs4Hi2vvrOXFZ9t7/MYlejhZ4IGrFaO/n9v0KbrezOnIHGF+hPu1W7FLJpYsvEkGjeG93uxsHYnd9vt1BvTOO3lMhDKex8kilxbsRsjcNNnTTSsDs2adt27DJMuMiZKzJrnTU1NeDwecnJ6ppnn5ORQV9d3YcFvv/2W//73vzz99NMBzfHAAw+QkpLi/ykqKhr2usNNg04SH2c7+g8nVqaPw2rKRfC60XSG1ygCeFM3mreTpKy3q5vUQHgr+4oCHNRKHrixrvDOFQ6yHJJgtUE3MuGVwRGosZ4BQLIdTAkbwj5jkrOTqS1lAKzNje32Av1RnSPpjJJa+27jE2oyfZ+rRv3IfK72+76Do9wqdP1k7XsFNY06KfSdO8A1SwGyaOW3GqmjwN/cF9JIatjnPKp2BwBr8qZCP96bZLcZo9eBBxVNuvC2sxkpYtZjFCwdHR1cfvnlPP3002RmBiY2vv3227n11q50crPZHBbjyKhVs+ve0NRoaSofz5t/+pqxQis77z65T9f09i8q2fC/Q6S27eM/822k3Ry++jAer4erP72Mva3w4w4Lv3at44afpeMtnB+2OQHKtzXx5TO7OCEpkX/fOT9iLtlgEUWR5254EQfw+M1nkjU6cuLrw3nyppWI7TYmpq7miV//imRdctjmsnzwPs0fedGOH89Xf78kbPNECpfDwyt/+A6vBxbUfcPO5TcjaMPbjfyzx3ewfw1cdvpiHjlrZGpCvX3/etobbLx97mzGzOm75dB3L1ezbeV7/HqWgWOvjP1aVeFC9971aHbY8OTP4f9d8SD/L4zp+SDVEKs68S94gZ/dfhU3L+y73ty+Nd/w+eOQN2YsO+7pu7nsUDBqI7epjVnDKDMzE7VaTX19fY/n6+vryc3t3Yn8wIEDlJWVceaZXfoIr1cKsWg0Gvbu3cvYsT3TDPV6PXp9eIVtIDWBDZXLsGD0GDRaHU6bFUdLA+n5hb2Oqd7ZAkBW83Yc39Vj+t1vQzJ3X6wofZe9rXtI0iZxc/4iaHoDw2e3wXVfhbXuxrjpWXytUWFptmNvdpCRH8I6TWGkvaEOR6cFlVpDwZixaLTR8xUdM2EGB9avRddsZ/mup7ltQf+VzYdLy+rVACQvOSli7vRwUranDa8HDM5WTE0HYetmTGGu09RSfgiAgnHjR+x3OmZWFps/raB2VyvTFvWtMyocN55tQEtlWVz+rUNC5TrY8SYgoP7RI5gM4b8v2bZtw9vagioxkfRFCxD6uRa1lksZtHnjJsTN3y9mQ2k6nY65c+fyha8iJ0iGzhdffMHixYt7HT9p0iS2b9/Oli1b/D9nnXUWJ554Ilu2bImJMFkgqDUaskaPAfou9Gi3uKg7ILUMyWjejmPPHlyHGZehwuw0889N/wTghlk3kH7Kn0GfDLVbYdMLYZlTRqtXUzhJ0ivEUnaaXL8oc1QxmjB7EIIlp0TyXqWbdby25zUOtocndV90Oun06f+STgp9SYdooHyHVEoiL7kTAej44suwzuey22nxNfjMLhkT1rm6UzxNCq1U7GpB9PYdT8vyraex/BCiN7b0gCOC1wsf/156PPsyyJ89ItNavpY2JwlHHTWgN7OrsGPsV7yWiVnDCODWW2/l6aefZvny5ezevZsbbriBzs5Of5baFVdc4RdnGwwGpk2b1uMnNTWVpKQkpk2bhi5OisdB1we0r67VlbtbEEVIz08gbaLkTeocRIQ+VJ7Y8gStjlbGpIzhokkXQWK2VPgR4It7wdoSlnll5J5NsWgYRbJ+UX9k+wzuUdY03KKbh9Y/FJZ5rJs24e3sRJ2ZKTU+jjNEUfQbRqPnSXVhLGH6Dso0VhwCUSQhNY2E1JETOOeOTUFnUGO3uGgo7zsZJD2/ELVWi8tuo61h4MbTRyRbX4WazaBLgiV3jti08mcy8fjj+j1G9HppKJM2SLlReM0aKjFtGF144YU8/PDD3HnnncyaNYstW7awcuVKvyC7oqKC2trIdASPJNnFXTuwwyn3FT0snppB4rHSB96yOvQX5YNtB3ltz2sA3Db/NrQq345jwXWQNQlsLfDVX0I+b3dKpku71fpD5pipgl0vF3aMIm2RTHaJFGrWt3vQixq+rf6W1VWrQz6P/4J8zDFxmb7dWmelo8WOWqNi9OnzQavFVVGBs7yPjJ8QIRfmHElvEYBaraLQ1xi3vJ+Cqyq1msyiEgAay0a2gGjUYzfD53dLj4//vbS5HAHcLS3Yt0uZhAnH9F9DrK2hDpfdhlqrJb0gPqIuEOOGEcBNN91EeXk5DoeDtWvXsrCbQGzVqlU8//zz/Z77/PPP8+6774Z/kSNMVvFowOea7lYBW/SKVOySvDSjpqaTeJz0ge/8/ntEV+gMB1EUeXD9g7hFNycUncBRBd20E2otnPY36fGG/0L9zpDNeziJaQapCrYoecqiHVEUo9pjlJiegTEpGdHr5eKMswB4aP1DuLyhNTo7v/kWgIRjjwnpuNGC7C0qmJCKIT0Z05w5AFh87zscNJRJBnf26JFv11A81RdOG6ASfXaJdM1qKOu9mTui+ebv0NkA6WNh4fUjNm3nt9+CKKKfNAltTv/GmLz5ziwqRqWOvQzg/oh5w0ihNxmFoxBUKuyWjh4VsJuqLNjMTjR6NXnjUjFMm4Y6PR2vxYJ18+aQzb+qchXf13yPVqXl9/N+3/uAMcfD5LOkitif/ilk8/bFqCnSblU2CKMZc2MDdksHKrWGzFElkV5OLwRB8N9Yj9XOJt2QTpm5zO8ZDAWu+nocpaUgCCTESdPYw5ENo1E+/U2izwAMV0gb8Ic7RtpjBNImDKC+zIzN4uzzmC6dkeIx8tN8QGqnBHDqA6AZObmHHEVIPK7/MBp0efjkzXi8oBhGcYhGp/Nno3UPp8mu7MKJaag1KgSVioRjpCJznatDExJxeVw8vOFhAK6YcgVFyf24V0++B1RaOPAl7P88JHP3xSjfbrVyZ3O//eOihfpDPuF1UfQJr2XkG6u5qppfzv4lIGnJWuyhMTxl48AwYzqatPgr9ue0u6nd3wZ0CZMTfO1OOteuxesIfZNej9tNU0UZ0BUOHUkS0wxkFCSACJX9bFDkdTUoobQuPv0TeJwwbimMP2XEphU9Hv/3UI4q9EeD7/6iGEYKMUH3cJpMhV9flO5/LtQ6o9f3vk5FRwUZhgyum3Fd/wemj4EFP5Mef3oHeEPQEqUP8saloNGq6Gx30lLTGZY5QoXcODYS4Y5AkQ2jhkMHOXfcuUxKn0SHq4PHNj8WkvHlcJL8uYw3qva04vWIpGQZSc02AaCfMAFNdjai3Y51Q+iLZ7ZUV+Jxu9EZTaRk5wx+QhiQNyj96YyyRhWDIGBpacZqbh/JpUUnh1bD3o9ApYFlf+m3uGI4sG/fjqe9HVVSEsZZswY8tlExjBRiieySngJsh81N3UGppYl8kQIkj5Eg4CgtxdVPxfBAMTvNPLntSQBunH0jCdqEgU847rdgSIWGXbD5xWHN3R8arZqCiZLnob+LcrQg/61kvUU0IhttjRVlCEjCeoC39r3Fwbbh7fZFt5vO778HusJL8YYcRpO9RSCFKBP84bTQ64y6h9EiJWaXdUaV/aTt64wm0nLzAGg80nVG3m4Sg3k/hazwNvw9HHmTnHD00Qia/usS2S0WOpqkauqKYaQQE3R5jKSLYtVu6YKUmmMiOdPoP06TloZxxgwALMMMpz2z/RnaHe2MSRnDuePOHfwEUzoc7ysS+OWfwdF3Ou9wkTUOFTujW2fUVCllJUWjvkgmLTcfrd6A2+mgtaaaebnzOLHoRDyih0c3PTqssW3btuHt6ECdkhK3afqy13ZUN8MIINEXTrN8G3qdkd8TGQF9kUzuuBS0BjW2DhcNFX1/z7N82bQNR7rOaMdbUq03XVLX9XEEke8D8meyP+R7S3JWNoaE2CigGyiKYRSnyIZRa10tLru9Wxitdy+bBDk77bvvhzxfjaWGl3e9DMCtc29FowqwAur8a6WwWmcDfPePIc8/EKOmSO+59kAbTnt0dmh3WDsxN0q9oqLZMBJUKv9nS77h3jL3FtSCmq8qv2JT/aYhjy2n6SccfTRCHGW4yLTVW7G0OlBrVBSMT+3xWsLixaBS4dx/AFdNTUjn9XuMIhiiVatVFE2WNyh9e279Xu4jWWfksks13gCOuQUSAmtfFSrcra3Yd0qZwoNlhcZrGA0UwyhuSUhNw5SSCqJIQ8WhHmn6vY71Zf90/vADomdoWp9/bf4XTq+T+bnzOa4wCH2IRgdL75Eef/9vaK8e0vwDkZJtJDnTgNctUlPaFvLxQ0FTheQtSszIxJiYFOHVDIxc6LHedwMbkzKGc8dLHsK/b/z7kEXuXWn6A+9UY5XK3a2AT/em62n4qVNSMM6cCYDl29CF07oX4Iukxwi6MkT7K52R5U/ZP4INo/VPQ3sFJOXDol+M+PTWH36Q0vTHj0ebPXDNpHgVXoNiGMU18ge2fNteaaeqVZF/2E4VwDh9OqrERLzt7dh3Bd/pe1fzLj44+AEAv5n7m+Abtk4+E0YdBW4bfHl/0PMPhiAIfq/RQLVUIkmjL2soK4q9RTJyBlGjrzYOwC9m/gKjxsi2xm18XhF8lqG7paVrp3p0fKbpywaB7Dk5nHDojNob6nHarFFRgE9+3/UHzX16buXCtC3VVbicoc/Oi3qsLbDaV03+pD+CzjTiS+j8fg1AQKUyFI+RQkwi7xArd5YCkN/HThVA0Ggw+QpjyuLXQBFFkUc2PALAaaNPY2rm1OAXKghwis8g2voq1O8KfoxBKIryekZNFb5CaTFhGPlCHhVdlZqzTFlcOfVKAB7d+GjQRR/9O9WJEwfdqcYiHo+X6lLJYyT38DucxGN8htHatUP23B5OY2UZABkFo1APIKQdCZIzfZ5br0jNvrZeryekpWNMTkEUvTR3+2wdMXzzd7C3Q/ZUmHnxiE8viqL/+p9wVO9+o93xuN00V1UAXQZtPKEYRnGMbMk3V5UBUDip750qdH0RgjWMvq3+lrV1a9GqtNw85+ahLRSgcK5U9BExLF6jwolpCCqB9kYb5mZbyMcfLrKREQseo/SCQhAEbOZ2Otta/c9fNfUq0g3pVHRUsKJ0RVBjdq7x7VT7aAAdDzQcMuOyezAkaMkq6jtUapg6FVVSEl6zGfuu0GwO5PpFmaOKQzLecJHbg1Ttbu31miAIXeUgjjQBdmsZrHtKenzyvaAaeY2dq6ICV3U1aLWY5s0b8NjWmio8LhdagzFiJSDCiWIYxTGyYWTrqEUUxX53qgAJiyXXqW3TJry2wAwHr+jln5v/CcDFky6mILFgeAs+6Q4QVLD3Q6hcN7yxDkNn1JBTIt2Qqvb0vihHElEU/R6jWDCMtHoDqTm5QFcmHUCCNoEbZt4AwJNbn8TitAQ8ZueaH6QxBtmpxipyGK1wkmSg94WgVmNauADo+n0Ml6ZKaVefWRQdhlGRb3NWuacfnZEs7D/SUva/+otUzHH08TBuSUSWIG9OTDNnokoYuNSKP4w2qiQu+xnG3ztS8JOeX4hKowXRhdZgIbOfnSqAbnQJmrw8RJcL64aNAY3/afmn7GnZQ4I2gWunXzv8BWdNgFmXSo8/vxtCXKla9phFm2FkbmzAabOhUmtI81Usj3bkpp/NlT1DHudNOI/i5GJa7C28uCuw2lTOykpcVVWg0WCaOzfUS40KZOF1f/oimYRFPs/tmqFniHanOcpKQBROTAMBWmo66WzvrSPye7krj6BQWv0u2PaG9Pjke0a0mGN35KzkQDR+8Sy8BsUwimtUajWmZGlnn5ZpRdXPThV8ReYWyxflNYOO7fa6/dWOr5x6JWmGELVvOOEPoNZD+Xew/4vQjOmj0FfosXpva1S1B2ny60AKI64DCRQ5NNN4mBZEq9Jy0+ybAFi+azlt9rZBx5I/b8YAdqqxiNPmpr5MKq5aOHng70nC4kUA2DZtHnZ7ELfLRUtNFRA9HiNDYlcosa8NSkbhKEDyREbTdzSsfPVnQIQpZ0P+7IgsQfR46Fy7FggsnB3PwmtQDKO4R1BlAaA1tA16rD9tPwCd0XsH3qPMXEaaPo0rplwxrDX2IKUQFvhaiXxxt1QFNkTkjpHag1jNTlpqo6c9SGN5GQCZMXSRkW+0fe3sTyk+hUnpk+h0dfLsjmcHHcv6gy+MFqf6ourSVkSv1AYkOcM44LG6MWOk9iAOB7ZhNnZuralC9HrRmxJITO9dvyxSFPmMw6o+0vbTCwoRBKkBtrW9bYRXFgGqNsKeDyQJwYl/jNgy7Dt34jWbUSUlBVRcVTGMFGIWl8OD3ZYMgNfVOOjx8m7VsWcP7ub+09odHgdPbH0CgGunXzt4649gOeZWqepr3XbY+XbIhlVrVeT5yhVEUzitKYZS9WXkUFpTVQXiYcarSlD5G8y+uudVGq39f/ZEr7dLX+T7/MUbgYbRQPbcSr8HOXV6qHRVUi8OvoRGGCn064x6e261Oj2pvtYgTUdCZtqXvmKOMy8e8dYf3ZE/a6aFCwZsAwJg6zD7jdZoEfWHGsUwimNq97eBIF2E2hsHL5yoychAP2kSMLD48429b1DXWUeOKYcLJ10YkrX2ICEDjv6V9PirP4MnuNTvgZDDadFkGDX6M4dKIrqOYEjNzUOt0eCy2zA39TZ8ji04lplZM7F77Dy17al+x3GUluJpbUVlMvlb08QbVXsGrl90OCY5pP3D8ATYfsMoSsJoMnnjUlBrVXS2OWirt/Z6XV5vU7zrjA5+DQdXgUobkdYf3elK0x9cX9TsE/QnZ2WjMwzsAY1VFMMojqnc04pKLbnQ22prcTudg57TpTPqO5zW6erkme3PAHDDzBvQq/UhWu1hLPoFJGRBy0HY8nLIhpUz82pKW/F6QhemGypup5PWWslojSWPkVqjId0nFJc1Ut0RBMFfvmHFvhVUW/o2zOWdqnH+PAStNjyLjSCdbQ5a66wgQP6E1IDOkb+D9h078JjNQ55b9kRmRJlhpNGqyRubAvRdBTujqEtnFLeIInx5n/R43tWQFrm/kddm84dtAwlny38XWQ8WjyiGURxTtacFhEQ0eiOi6PULMQciYZFU6NG6bn2fr7+06yVa7C0UJxdz9rizQ7reHugT4ZhfS49XPwzuwY26QMgsSkJv0uC0e2goD0/T2mBorq5E9HoxJCWTkBaYRyFakG+4/YU85ufOZ1HeItxeN09seaLPYzp/iO/6RXJRx6yiJAwJgRl+2pwcdGPGgNeLdd3Qy1ZEW6p+d+QNSl+eW79+rSqODaPSlVC1HjRGOPa3EV2KbcsWRJcLTU4OupKSQY9v8hV2VAwjhZjDZnHSVGlBEAQyfR9guVLpQBjnzgW1GldlZa9mlu2OdpbvXA7ATbNuCrxR7FCZ91NIzIH2StjyUkiGVKmEqAqnddcXRZMOJBDk0N9AO/tfzZZCou8ffJ+DbT2L9olOJ9b1G4A4Noz2Sp+xQL1FMgmLhqczctqsmBvrgeg0jAp838GafW2I3p46o65QWkV8ZqZ5vV1FbBddD0mRLZAoZ6OZFiwI6BokG6zR+LkKFYphFKfIJffT8xPILpErYA9uGKkTEzFMldp6dB62W31p90t0uDoYnzaeU0pOCe2C+0Jr7OY1+ju4Q9M/qWu3Gvn2II1RVpk4GALRgkzPms6JRSfiFb08tuWxHq/ZduxAtNlQp6ejHz8+rGuNFNW+psWFE4IrZ2GSBdi+m1awyN6ihLR0jEnJQxojnGSPSkKrV+Owummq7lkINDU3H5Va0q919KFfi3l2/w/qd4A+GY76VaRX448OJPiKiw5GcxR7IkOFYhjFKfIFuWB8areY/eCGEXR9Qaxruwyjdkc7L+2SvDY3zLwBlTBCH525V0FSHpirYHNgBQMHQ86KqTtoxu0KTU+qodLiM1YzC2PvIiNfGFuqq/C4ezcFlZHrGn1a/in7Wvf5n5fDRKYFC+Kyeq6l1U57ow1BwJ8NGShySwbngQMDZoj2R7QKr2VUahV541IBqPFdq2Qk/ZpURb8p3sJpXi+selB6vPhGMEU2fO61WrFt3w7g75c5ENb2NmwdZhAEqTVQnBJ/VyMFQBIXA+RPSPPHggON2ZsW+HRG3XarL+1+CYvLwvi08SwZNYIl67VGKX0fJK+Ryz7sIVOyjZiSdXjcXhrKhi5uDQXN1ZUApBdGtvP5UEjOykZrMOL1uGmrq+n3uAlpEzi5+GRAahUi02UYzQ/vQiOEHEbLGpWE3hhc2FmTloZ+wgQAf7gxGJqj3DACKPCFF6v29lHocRD9Wsyy+z1o3A36FFh4faRXg3XTZnC50OTnoS0c3NCRN9cp2Tlo9YZwLy9iKIZRHGKzOGmulgoY5o9P9V8c2+rrcDkHD0eZ5swGjQZXTQ3OqurIeYtk5lwBSfnQUQObXhj2cIIgkO/bwVcftlsdSZx2G+bGBgAyCmLPMBIEgcwAM4iunyndBD4r/4z9rfslfdEmXybMgsBc+LFGley1nTi0qvCm+ZLBaF3fdyLEQES7xwi6fi+1+9vw9qMziqvWIF4vfO3zFi26AYypEV0OdG1OEuYHpy+KZ+E1KIZRXNJdX2RK1mFKScWQmASiSEv14JlpqoQEjL7qp9a1ayPnLZLRGuC430iPv30kJF4j2TCSf1eRQP5bmFJSo1IHEgh+nZFPK9UfstdIROQ/2/4j6YvsdtTp6ejGjh2BlY48ssdIMYz6JqsoEa1B0hk1V/XUGfnD/wHoImOGPe9Dwy5JW7Qo8t4i6IoKBBJGgy6daqZiGCnEGt31RSDt7DOCyEyDri9K25pvI+stkpl9OSQXQkctbHx+2MPJWUJ1B9rxuCNTz6g5DtJegynG9/MZPwfgk7JPqPp6JSDd/GMtGy8QzE02OprtCCrBX7MnWEzzJZ2Ro7QUd2vgGZTW9japMnG37300olKrunlue74/v36tqhKvN7I6wJDQXVu06AYwhqi35DDwWDqx7dgBSDq/QJBDadFWGyvUKIZRHNJdXyQjhzwCdU3Luo/WNd9gcXZEzlsko9Ef5jWyDWu49LwEDIla3C5vxOoZyfqijBjUF8lkBGEYTUyfyJJRSxARqVj9MRDH+iLfdzC7OAmdYWhlLTQZGX5vmm3jxoDPkw3ulOwctIbo1oEUjPc1dj4spJ2SnYNGp8ftctJeXxeBlYWYPR9Aw06ft+iGSK8GANvmTeDxoC0oQFdYMOjxoijGxWYuEBTDKM44XF8k4+9aHajHaM4c0GgwNFvIaYuwt0hm1mWQMgos9bBh8OakA9FdZ1SzLzL1jPwXmYLYvcjIn6v2+vqAKqtfP/N61B6RjP1NQPzqi6qHqS+SkQ3HYMJpzVU+gzsGdGsFE1MBKaTdXWekUqn9WU8xXwG7u7Zo4fVR4S2C4MNo1vY27JYOBEEV1xlpoBhGccfh+iKZrmqygRlGKqORtrFZAJzUmBVZb5GMRgfH+arEfvsoOHv3WQqGSOuMWqpi32OUkJqG3pSAKHppHSAzTWZS+iQu8MzF4AJ7og7duHEjsMqRR/YYBVu/6HASfDqjzmAMIznTMQYMo8yiJHQGNU6bm6bKjsNekwXYMa4z2vNBV92iKPEWAXT6yrEEWr9INlBTc3PR6sLUCipKUAyjOONwfZGMHPJob6jH5RhcvNzuaGd1tlQA8ZS2wsh7i2RmXQKpxdDZMGytkZwuXLu/fcT7prmcDtoapBBBLLulhW71TFp8N+TBOLdDMoa2Frg4ZD4UtrVFCnOzDUuLA5VKIHeI+iIZWYDt2L0n4L5p8t8hFjxGKlW3DNG9bT1ei4tmsl4vfP036fHCn0e8bpGMx9KJfedOIHB90ZESRgPFMIo7+tIXAZiSUzAmpwScmfbS7pfYWiB1tU/ZPbgnYMRQa+FYX12j7/85rGrY6fmJ6E0aXA4PjZWWwU8IIa011SCKGJKSpb9LDCN7JuQQzmAk7CgDYMcogae2PRWuZUWM2v3tAGT6qjsPB01WltS/ShSxbghMZ9QSQx4j6LpW1exv6/G8vP5AejxGLXs/hPrtoEuSGmNHCbYtW8DrRVtQgDYvL6BzZM9dRgwWow0WxTCKI+wWV5/6Ihk5xXKwHZjZaealXS9RWiAgqlS4a2pw1daGfL1DZubFvrpGtbDllSEPo1IJ/VbfDTdd+qKimM/Kkj0TgXiMRJcLq6+T965igY8PfUxZe1k4lzfiyDf4/HGhMXiDSdt3WDuxtEqe3lgJ0eb7voO1+3v2TZM9ka011bGZmSaK3bRF0eMtArBulIqGmubNDfgcf/PYIsVjpBBDyBfktFxTD32RjPyBHkxn9Pqe17G4LBRlj8c4ZTJAwLvVEUGjh6N9PYa+/T/w9N+OYjAiJcBujgN9kUx6EIaRvz9aaipjZ56AV/TGndeo1qdZk43u4RKMAFv2BiekpaM3JYRk/nCTOSoRjU6Fw+qmpbbT/3xKdg5qrRa3yxmbPdNKV0LddtAlSu0/ogib73punBuYYSRlpPlqYymhNIVYovaA5MLvry9TIK5pm9vGi7uknmTXTL8G01yploq8w4ga5lwJpkxoK4cdK4Y8jKwzqtnf3qv6bjiJp3i932NUO/jO3rZpEwDGeXO5frYkRP3o0EdUdgQWhot2bB1OWuukpID8UBlGPo+RfdcuPJaBQ77+EhAxlDWkVqvIHSN512q7hdNUKjVpeVIaeXOA+rWoQRRh9cPS4wXXRZW3yOt0Ytu2DejqyTcY1vY2HJ2dIAj+v0k8oxhGcYR8UcnvR/CZni+LZPs3jN4qfYtWRyuFiYWcWnIqRp+rNZg6KiOCztS1C/vmEUnkOAQyC6Xqu05b7+q74aTrBhb7hlFydjZqrRaPy4W5oWHAY60bJcPINGcuUzOncnT+0XhED8/veH4EVhp+ZH1Rmq9OVijQ5uaiLSoCr9dvWPZHrOmLZPwhbd/vT8Z/zQpQvxY1lH0D1RtAY4gqbRGAfcdORIdDqjo/enRA58ibaam+VO9oRLyhGEZxgsvpodFXqLA/F768s2+rr8XjdvUew+PiuZ3PAfDT6T9Fo9Jg8rlaHfv2B1V9d0SYfy0YUqBpr1Rufwio1CryxqYCI5e273a5/E1X4yGUplKp/Tew5ur+w7Si1+s3sGVtw7XTrwXgnf3v0GiNwXDJYYRaXyQTqM4oVg3uvHG9PUYQwwLsb/4u/Tv7ckjMjuxaDsOvL5o7J2B9YyxlOoYCxTCKE+oPmfF6RRJS9SRl9F3tNiEtHZ3RiOj10lbXW0z9/sH3abA2kGXM4uyxZwOgSU9HN2YMADafaDZqMCTDAqnNBKsfltzXQ0AOpx3eliBctNVWI3q96E0JJKRFj4t9OASSmeY8eBBPezuCwYBhsqRdm5szl1lZs3B5Xf4Qbiwj39hDpS+S8RtG6wY2jGTPSqx5jHJHp6BSCVhaHZibu6raywLs5gAyaaOGqo1wcBWoNF1ayCgiWH0RdEUZ0vJjJ0Q7HBTDKE6o7bZT7W8XIAhCv+E0j9fDf7f/F4Arp16JTt3lLpW9RlElwJZZdANoE6BuG+z7bEhDyALs2v3tPbJiwoW/AF9h7GekyXRlpvV/A5PDaMaZMxG0UphJEASum3EdAK/vfZ12R3u/50c7TrvbX/ahr6zQ4SAbRradO/Fa+y5s6nY6aW+oB2LPE6nVq8kclQR0hSOh2+cqljxG3z4i/Tv9AkiNLs+d6PX6s0Jl/WggyL//dMUwUoglAt2p9uea/qz8Myo6KkjRp/CTCT/p8Zoc9og6ATZIosZ5V0uPvxma1yirOAmNToW909UjKyZcdE/VjxcCyUzrcuH33KkeW3AsE9ImYHVbeXXPq+FbZJipP2hG9IokpRtISg9tjzJdYQGa/Dxwu/03tsNpra1GFL3oExIwpaSGdP6RQA4/dq9nlJaXD4KAvcOM1RwDRnPDbqnSNQIcc0ukV9MLx759eM1mVCYThsmTAj5Pvl/E0zVrIBTDKA7werzUHZSq4g5qGPm1IF03MFEUeXr70wBcNvkyTFpTj3OMvp2FfeeufnerEeWoX4JaD5VroezboE/vnhUzEjoj2asSa+GOgcgo6Ppcif0YpzbZYzR3To/nBUHwa41e2v0SVlcUfsYCQL6h540PT8FOeYcv/x4Pp3srkFj0RMrXrtpu30Gt3kBypqTRiQkB9rf/J/07+UzImhjZtfSBdYO0OTHOmoWgCay5sctux9woJVXEe480GcUwigOaqiy4HB50Rg3p+QPXLulq39DlMVpdtZrS1lJMGhMXT7q41znagnw0OTngdvvTPKOKpFyYc7n0ePVDQxrCf1E+EP5daTy6pVPzChAEFU6blU5fgcHuuOrqcFVXg0qFceasXq+fUnwKo5JG0e5oZ0Xp0MsvRJKucHZqWMY3+QxK6+a+DaNYF8jKAuzWOis2S1dDYtnojvpwWmsZbPd9duXq/FGGnPxw+OZkIFpqq6VzkpIxJiWHZV3RhmIYxQFyTD5vrCRgHIj0/K5QmiiKiKLIU9ulAnsXTrqQFH3v3a4gCNGtMwI4+mZJ7Hjoa6gKPuTnz4o50BbihfVE9HpprZUy0tLz46ceiEarJTU3F+i75ozVd0E2TJ6MOrG38a5Wqbl6mhQSXb5rOU6Ps9cx0YzH5aXuUGBe26FinC3dzGxbtyG6exc1bY5xT6QxUUdaruSt7q4zSi/o7eWOSr77J4geGLsE8mdHejW9ELu1lRmSvugI8RaBYhjFBV36osFd+Km5eajUalx2G5bWZjbUb2Bb4zZ0Kh1XTLmi3/OM0awzAknkOP0C6fF3jwZ9ek5JMoJKwNLiwNI6eJPdodLR3ITb6UCl1pCSnRu2eSLBQDqj/sJo3Tlr7FlkG7NpsDbw/oGhlV+IFA0VHXhcXgyJWv/NPdTox49DlZSEaLVi37u31+ux7jGCruK03dP2YyJlv6MONr8kPT72N5FdSz+4qqpwNzSAVotx5oyAz4vH0P9gKIZRjCOKIjVyxesAdqpqjYaUHKlpYEtVlb8dw4/H/5hMY2a/5/n1DVu2Irp610CKCo6+Wfp39wfQtC+oU3UGDZmFiUB4w2nyzUs2UOMJf8p+H5lpssfINKf/FGGdWseVU68E4Nkdz+KJof5Y/s3J2P6zQoeLoFJhnDULANumngJsr9dDqy/kEcs3sPw+Cj0G03ImYqx5DDwOKFoIxUdFejV9InuLjFOmoDIaAz7PXzQ0jkL/g6EYRjFOe4MNm9mJSiOQXZwU0DnyB3znvvX8UPsDakHNVdOuGvAc/fhxqFJSEG027Lt3D3fZ4SF7Ekw4DRDh+38FfXruWDmcFkbDSL55xeFFpr9msh6zGUdpKdClk+mP8yecT4o+hYqOCj4rH1r5hUjgL+wY4jT9wzHNkUI01k09Q9rtDfV4XC40Oj3JWVlhXUM4kb3eTRUduBySYSx/V8yNDbjs4fPmDhlrC2x4Vnp87G8gSoXvsrffGETjWFBCaQoxiKyJySlJRqMNzAMhf8A37FoNwKmjT6UgcWC9i6BSYZrtuyhHq84IurxGW1+V3NtBkOczjOrC6jGShdfxoy+S6RL29zSMbFu2gCiiLR6FZpCbtklr4tLJlwLwzPZn+s1wiyZEr+j/zIRLXyRj9HncbJs29/jdtNZIBndaXj4qVex6IpMzjCSm6fF6ReoOSb9TU3KKX/Qrbyyiig3/BacFcqbB+FMivZp+sQ1BX9TDE5kfu57IYFEMoxinxi+8Tg34HHlnb66Vql9fPfXqgM7rqmcUxYZR8WLJne1xwtongzpVNoyaqiw47b3FraGgtTZ+4/Vyc8nOtlYc3co6+AWfA4TRunPJpEswaozsbd3Lmpo1oV9oiGmu6cRhdaPRq8kqSgzrXMYZ00GjwV1fj7umxv+8fPNKy80P6/wjgT9DtA8BdtSF01x2WCvJETjqV1HrLXI3NeEsKwO6vI6BYG5slDyRWl1MeyKDRTGMYpxghNcysms62aLhqPyjmJgeWL0NuYS8beNGxCE2bR0RZK/R+mfBbg74tMQ0A4npekSvSH1Z4OcFg7+0fhx2qDYkJPoLC8q94KAr7GMK0IWfok/hvPHnAfh790Uz8ncwd3QyKnV4L6kqo9HfTsXaTWckZzqmxYEnMn8gAXa0GUbbXoPOBkguhGk/jvRq+kWuOq8fPx51amrA58m/71j3RAaLYhjFMJ3tDtobbCB0eTsCQZUu7WoTHBouG9u7blF/GKdORTAY8LS14Tx0KOj1jhgTToPMCeBoh43PB3Wq7HkLRzjNabNi8dX4iUeNEXQZfLIuwet0Yt+2HQDjnMBrp1w+5XLUgpofan9gV/Ou0C80hNQdHJkwmoy847d1q2fU6jNEU+PBYySHtA+24/FIG7BAWs6MOF4vfP9v6fHiX4BaG9n1DIBtky8rNFh9kWwYxaGHeyBi3jB67LHHKCkpwWAwsHDhQtatW9fvsU8//TTHHnssaWlppKWlsXTp0gGPj3bkm3dGfiJ6U+BfynerPsCql0JF47x5AZ8n6HQYp00DfLqRaEWlktzaAD88Dm5HwKfmhVGA3eLTgZhSUjEkhjfkEilkw0gO7dh37EB0OlFnZKArKQl4nPzEfE4pkfQaz+98PtTLDCl+w2hMeCpeH46sM7J2q4Ate+jiIZSWnpeA3qTB7fTS5Os9d/jnKioo/Ria94E+Beb0X+okGrBu8fVHC2JzAvFZjDYQYtowev3117n11lu566672LRpEzNnzmTZsmU0NDT0efyqVau4+OKL+eqrr1izZg1FRUWccsopVFdH0ZctCGqGEEazu+28sucV2hMlwyjYHZhRFmD3068paphxASTlQUctbH8z4NNyu+1WvSFuKNt6BFxkZFG5HNrpStOfE3Qau6x9+7TsU2osNYMcHRk62x2Ym+wgQM7okakKLHuMHKWleDo6cDudmJsaAV9vsRhHUAn+Fj2y0SmHCFvraqMnjP/dP6V/5/8U9IFlBEcCr92OfZeUSSxfvwOlq0da/F6z+iKmDaNHHnmE6667jquvvpopU6bw5JNPYjKZePbZZ/s8/uWXX+YXv/gFs2bNYtKkSTzzzDN4vV6++OKLEV55aPBnwgQRRnvvwHu02Ftwp0oepmCLpslfLNvmLUGdN+Jo9LDoBunxd/+Q3N4BkFGQiNagxmX30FxtCemS5N91POhA+uPwUJq/sGOQO1WAyRmTWZS3CI/o4cVdL4ZukSFEvnFn5CeiMwbWe2q4aLKy0BYVgShi27KVtvpaEEX0pgSMySPjtQo3hxtGKVk5qNRq3E4HHS3NkVyaROU6qPwB1DpYeH2kVzMg9p07weVCnZWJtiC4a49fExnHm7m+iFnDyOl0snHjRpYuXep/TqVSsXTpUtasCSyTxWq14nK5SE9P7/N1h8OB2Wzu8RMtuJ0ev5s5N0AXvsfr4YVdLwAwZZyUshmsa9o4ayYAzgMH8LS1BXXuiDP3atAnQ1MplK4M6BRV991qiMNpcigtnj1Gad08Rl6v1x9yHax+UX/IXqO39r1FuyP6uqvLn5HcIDYnoaC7zqi7vigWm8f2RXfPLYBKrfYXpo2KcNp3/5D+nXGB1KsxirH5vPumWbOC+nzYLRZsHdI9Lz0Ok0UGImYNo6amJjweDzk5OT2ez8nJoa4usPo1t912G/n5+T2Mq+488MADpKSk+H+KiqJHgNZQ3oHXK2JK0ZGUYQjonFWVqyg3l5OsS+bYGacCXSGPQNGkp6MrLgaIzoay3TEkw7yfSo+DaBMSLp3RkRCvT83JRVCpcNlttG7fhqetDUGvxzBp0pDGW5y/mIlpE7G5bby+9/UQr3b4dOmLRra5pl9ntGkzbXJGWhyE0WSyi5MQBHq06JHfn1yzKWI07Yc9H0qPZS1jFGP1bU6Ms4ILo7XWSb/nxLR0tIbA7jHxQswaRsPlr3/9K6+99hrvvPMOhn7+6Lfffjvt7e3+n8rK6EkVlS/IuWMCa0EgiiLP7pRCjBdOvJC8wjEAtNXWBB2zjxmdEUjhNLUOKtdCeWCexK4K2G0hW4bX6/HfwOLZMFJrtKRkS5uVhjXfA2CYNg1BpxvSeIIg+NuEvLL7FRyewIX04cbt8tBQ0QFE0GO0dWu3NjPxYxjpDBoyfC166g5KXouoEWCv+TcgwoRTISuwUieRQhRFv+whWH2RvGlOjSODO1Bi1jDKzMxErVZTX1/f4/n6+npycwd2bT788MP89a9/5dNPP2XGjP6b6en1epKTk3v8RAvdDaNA2Nyw2d8s9pLJl5CclY1KrcHtctLR0hTU3DGjMwLJzT3jQunxmn8HdEo4Gsp2NDXidjlRazQkZ2eHZMxoRb6BNe7aAXSFX4fKqaNPJTchl2Z7c1Q1l22ssOB1ixiTtCRnBt57KhToxo5FlZyMaLPRcvAAAOlxdgPLOyyk3SXsj6BhZGmELa9Ij2PAW+SqrMTT3Iyg1WKYOiWoc/21seLI4A6UmDWMdDodc+fO7SGcloXUixcv7ve8v/3tb9x3332sXLmSefMCL40eTYiiGLRhJBfKO3PsmWQaM1Gp1aTmSAZka01w4TTj7FmAFEoT3eGpEB1SFt8k/bvnQ2g+MOjh4WgoK+uLUnPjv1Caf2dfVQHgb3w6VLQqLZdPvhyA5TuX4xWjIyvJry8K0GsbSgSVyv89bKuXpAPxtrP364x8rUG6PEYRzFBc95TULLZgbtQ2i+2OrC8yTJ2KSq8P6ty2OKqNFSwxaxgB3HrrrTz99NMsX76c3bt3c8MNN9DZ2cnVV0uCzSuuuILbb7/df/yDDz7IHXfcwbPPPktJSQl1dXXU1dVhsYQ2+yjcmJts2DpcqDQCWaMGr4dzsP0gqypXIdAVloDuQtngdmD6ceNQJSYiWq3+5qBRTfYkGHcyIAbcJiTUDWW7eqTFbxhNRt7Zt9s6AUn0OVzOm3AeSdokysxlfFX51bDHCwX+zckIh9FkTLPn4FYJWB02ANJy40sgK2/6Gis6cDs9fsOovaEej9s18gtydsL6p6XHUdz+ozuy3CHYMBp08xjFmcEdCDFtGF144YU8/PDD3HnnncyaNYstW7awcuVKvyC7oqKCWl8/MIAnnngCp9PJ+eefT15env/n4YcfjtRbGBLyTjWrKCmgxrHLdy4H4ISiExidMtr//FBj9oJK5fcCxITOCGDxjdK/m1+SumEPQqgbyso90uI5VV/G3zNNr0VbWDho49hASNAmcMHECwB4fsfzwx5vuIiiSO0IF3Y8HOOc2Vh1UtkNQ1Jy3BUNTcowYErW4fWINFR0kJCahtZgRBS9tAWYYBNSNr8MtlZIGw2Tzxz5+YdAl75oVlDniaIYV0VDgyWmDSOAm266ifLychwOB2vXrmXhwoX+11atWsXzzz/v/39ZWRmiKPb6ufvuu0d+4cNAFiMGslNttDb6dRk/nfbTHq/5szyGELP3h9O2bA363Igw5gSp+7XLGlCbkO4NZV0Oz7Cn79p9HQGGkc/4s+m06ELgLZK5dPKlaFVatjRuYWtjZD935iY7NrMTlVogqzgyxf2M06bRaZTCI6npmRFZQzgRBKErnHagHUEQhnXNGhYed5dGcfGNEAPhcI/FgmPfPiD4cLatw4zDKnl8U3ID744QL8S8YXQkEsxO9dU9r+LyupiVNYtZ2bN6vOb3GNUFH7OXv2i2WPEYCUKX12jdU+B2Dnh4YpqBxDSpoWxD+fDrV7UeQbuvxLQM1AiIgoBn/JiQjZtlyuK00acBRLzgoxxGyxoVmNc2HKhMJhwF0k0rSRO9fbqGQ+7onvWM5FD0iBtGu9+DtnIwZcCsS0d27iFi37YNvF60BQVog0z4kDdySZlZaHXBaZPiAcUwijGcdjct1YEVdrS5bbxR+gYAV029qtfrw4nZG2fOBEHAVVWFq58WLFHHtPMhMVdqE7Lz7UEPl1s81B8anmHkdjrpaJYy/1KPhN2XKJLgkAxPe3ZoPRlXTJF6Un1e/nlE24REWl8kY89IA8DUaYvoOsJF90KPoihGxmMkivD9v6TH868DnWnk5h4Gw9EXHclhNFAMo5ijvsyMKEJSuoGE1IEt+fcPvE+7o53CxEJOKDqh1+v+mL3XS3tDfe8BBkCdmIh+wgQgyhvKdkejgwXXSY/X/Fu64A1AzmG71aEit2zQGY2YUlKHNVYs4Ni/nwSrVObAogqtQHVi+kQW5i3EI3p4ZfcrIR07GEa6cWx/WDSSt0pfFyObkyDJGpWISiNg63BhbrJ1azkzgoZR5Vqo2QRqfdf1IwYYqr4IjmzhNSiGUczRlSI8cE0lr+j1hxsum3IZ6j5i4oIg+HcEw9IZxUI9I5l5PwWtCeq2w6HVAx7qbw1yyIw4iBE1EPHYsmEgbFu2kOCQPJBDCdMOhuw1emvfW3S6OkM+/mA47W6aq4JrxxMuOnyZf7qDh/A6Bw4PxyIarZrsUZKGq+5Ae2SKPK55TPp35oWQEBtaLtHrxbZV0uGZhpKRdgSn6oNiGMUcgQqvv63+ljJzGYnaRM4Zd06/xw2nzL78hYsZjxGAKR1mXSI9li94/ZA1KhGVWsBmdtLRPPRCj21HWKE02+ZuhlEYas4cU3AMJcklWFwW3tn3TsjHHwy/1zZjcK9tOHFYO7F1SgaaqdOGY/fuiK0lnOT4G8qa/YaRtb3NLw4OK61lsOcD6fGiX4R/vhDhPHAAb0cHgsnk9+wHQzy2mQkGxTCKIUSvSP2hwAo7ys1izxt/HgnahH6P6970M1jk2LV9x47Y2q0u+gUgwL5PoHFvv4dptGoyi3y71UNDD6f5hddHyEWmu8dI7g8XSlSCisunSAUfX9r9Eh7v8LMGg6F7YcdIIn9nDYIKjVeMrQ1KEMjhytqD7ehNJhJSJV3ViBR6XPsUiF4YexJkTw7/fCHCry+aMQNBownqXFEU/R45xWOkEPW01ltxWN1otCp/H6G+2Nuyl7W1a1ELai6ZfMmAYw7HNa0tKkKdkYHocmHfuTPo8yNGxliYeLr0+IfHBzw0VxZgHxy6AFvefR0JFxl3ayvOQ4f84utw7ezPHHsmKfoUqi3VI17w0a8virDwWv7OJienAvhDJ/GGbIC2VFtw2twjF06zm2GTtMFk0Y3hnSvEDEdf1NnWisthRxBU/u4IRxqKYRRDyBfk7JJk1Or+/3Sytmhp8VLyEwe+GQ8ny0MQhNjUGQEc5WsTsvU16Oy/V1yOT8s1HAF2a71UZPRI8BjJN+eE4pKunX0YhLJGjZELJkgFH2Xv6EggeW194ewo8RilFxYBMVRTLEgSUvUkZRgQRSmMKX+Pwi7A3vwiODsgcyKMWxLeuUKMXEZlKPoieSOXnJWFOk7LQAyGYhjFEIH0R2uyNfHRoY8A/OGGgZDbCFhaW3Dag0/5NcVaPSOZUYshfza47bD+v/0eJtdRaaq04HYGH7JxOexY/Kn6R4BhJO9UZ80K+87+4kkXo1Fp2Nywme2N28Myx+G0NXTz2hb0H6IekbX4QrQZk6aCSoWrpiZ2SmcEiT8R4uAICbC9nq72QYtuiIn2HzLu1lacZWWAFEoLliNdeA2KYRRT+LUNA7jwX9vzGi6vi5lZM5mZNXhXc0NiIsZkabwh6YxmSnPYtm0L+tyIIghdzWXXPw2uvsXVSRkGjMk6vF6Rxsrge+rJDT71CQkYkwbOJIwHZJ2LcfYsv36tJUw3sCxTFqePlkKiI1XwUfYWZRUnoRrAazsSyDewjOIS9OPHA/EfThsxw2jPB9BWAcZ0mHlR+OYJA/bt0iZBN3o06tTUoM8/0jSRfaEYRjGCvdNFa50V6NK99DrGbeeNvVJBx0C8RTLDudAYpk4FtRp3fT2uSPQvGg5TzobkQuhshO1v9HmIIAj+3/dQwmndM9LiPVVfdLux+S7KPTxGYQx5yJ/zT8s/pdZSO8jRw6fOZxjJNa4iRQ+BbF5+1wYlTgXYcnmS+kPmbuH/mmGV0RiQNT7t4fxrQGsMzxxhQg6pDsVbBEdeFm1fKIZRjFBfJl2QU7KMGJN0fR7z4cEPaXW0kp+Qz5JRgcfEh6MzUplM6Cf6Cj1ujTGvkVoLi66XHq95rN+Cj/JutX4ImWlHklvaUVqKaLWiSkxEP25cVzG+MO7sJ6VPYmGuVPDx1T2vhm0eGfkzkFMSWe+frcOMo1MStafm5Ha16IlTj1FGQSJqjQqH1Q1CKoKgwmW30dk6eEPooKneCJU/gEoL868N/fhhRvbeG2YOzTDyX7MUj5FCtFPv36n2fUEWRdEfTrhk8iVoVIGnaHZ5jIaW/irvTGLyojznCtAlQuMeONh3dlOO32MUfGbakVRBVv77G2fMQFCpSM/v8kSGbWdPl9doRekKrC5r2OZxOT00V0vGSH/fw5FC1hclZWSh1RswzpI8RvYdOxFdwbX3iQXUGhVZvkKPTZWdpGTnAGEKp8neounnQ1JsZWWJotjltZ0xuJSi1/leL211crJI/De87g/FMIoR6gdx4X9f8z0H2g9g0pj48fgfBzV2+jBj9saZs4AYNYwMKV1NIX94ss9DsouTEVQCnW0OLK3BFXo8knoOyR5Deaeakp2DoFLhdjiwtDSHbd5jC4+lJLmEDlcH7+wPX8HHxooORK9IQoqOxLTINtbsMril3nu6khJUKSmIdjv2vaWRXFrY8GeIHhZOCyntVbDT9xmKoYKOMs6yMrzt7Qh6PYaJwRd2tLS24HY6UKnVpGTlhGGFsYFiGMUAoihSX+Zz4fezU5W9RT8e/2OSdElBjd89lDaUnb2sb7DvjNHd6sKf4y/42Hyg18tavdqfgRSs1+hIckvLLnzZg6jWaP11UMIplO1R8HFX+Ao+dt+cRFov1npYbSxBpery3MapzkgOX0o6ozCFadc9BaIHSo6FvKGFoiKJXQ6jTZ2KoA0+1V7+XKVk56BS924jdaSgGEYxQHuDDUenG7VGRWYfhR33t+7nu5rvEBAGLejYFym5eSAIODo7sXUEHy7SlRR37VZLY3C3mjEWxp8iPV7bt9dITtsPpgK2s5sGQi6LEK94zGacBw8CXYYyDE/YHwxywccqSxWrKleFZQ6/vijCYTToljnUzRMph9Ni0nMbALLWr7nKQnK23MoohJXVHRbY+Lz0OAa9RdDltR2q8PpIr3gtoxhGMYAsvM4skgSIh/PS7pcAWDJqCUVJRUGPr9XpSc7MAoaWQSSoVBinTwdi+KK86Abp3y2vgL238ePPignCYyTH6g1JyRgS+69UHg/IugZtYSGa9HT/86m5YQp5HEb3go/y9yHU+D1GERZeQ7fMofwug9sf0o5Tj1Fimh6Tr3SGoE4FQvy52vqq9N1PHwMTTg3duCOIX+c3TOH1kRD6HwjFMIoB/JV2+9AXtdhbeP/A+0BwKfqHM9ydvT+cFmuZaTJjToCsyeC0wObeN1ZZ29VY0YHH7Q1oSL8OJDcvZMuMVmQXfndvEXRdYNvqw59Kf+HEC1ELajbUb2BPy56Qjt3Z7sDS6kAQpBpGkUQUxT6zHY0zZ4Ag4KqsxN0cPk1XpBAEwe+tc3RKG432hjo8bvfwB/d64YcnpMcLbwBV7N0avXY79r1S78chp+ofQaH/gYi9v/4RyEAu/LdK38LpdTIlYwqzs4Mv/y4znJR9iAM3viD4tEZI4bTDdCop2UYMCVo8bi9NARZ6PBKF14fvVFN9RuFINPzMScjh5OKTAXhl9yshHVvenKTnJ6IzBNeUM9R0trXistt69bJSJyWhGzsGiOHv4SDI4bS2RgGNTo/X46G9oX74A+/7FFoO+JIxgpcjRAP2XbvB7UadmYkmf2jXnFalhhGgGEZRj9vloalKuhEfbhi5vC5e2/saAJdNvmxYgtBhp+z7QmnOsjI8bW1DXkdEmXEhGNOkird7P+7xkiAI3bJiAtMZ+QWycb77EkWxR6p+d2SDu72+Fm+YRNHduXSylGH44cEPabGHrsbNYOUyRpKBeln56xnFad80OYzZUGbxe2LlDciwkLWFc64AfWyGvW3bupXLGMK9wOv10H4E9XUcCMUwinKaKi14PSLGJC1JGYYer31R8QUN1gbSDeksK1k2rHmGG0pTp6aiKykBuvQmMYfOBHOvkh73IcKWK2DXB1gB+0iJ17uqqvC0toJWi37y5B6vJWVmoVJr8LjdWEYgvDMzayZTM6bi9DpZUboiZONGpfC6jzoz8V4BO6s4CUEAS6uDxAw543GYhlGDr4aZoIL514VglZGhv3B2oHQ0NeFxu1FrNCT5NKdHKophFOUMlCIshwsumHgBOnXf1bADRb7IttXVInoD09AcTtdFOYZ3q/OvBUENZd9AXU8DL0fu13QoMAF22xFS9dpfv2jSJFT6nvV9VCo1KTkhuoEFgCAIfq/R63tex+UdfvkIr1ekobwDiA7h9UDV1P1NnXfsQAyF9ibK0Bk0pOdLHh2NXhL5tw7XY7TuP9K/E0+HtOLhjRVB/K1Ahim8TsnORaU6clP1QTGMop7+WhDsbN7J5obNaFQafzbOcEjOknb2bpeTDl83+GCRC/vFtL4hpVDqoQa9Cj7mFCeDAB3NdjrbHQMO47Basba3AfHvlu7uwu8LOeQx7BtYgJxaciqZxkwabA18Xv75sMdrre3E5fCg1atJy0sIwQqHuR5f5mhfnyvd2LGoEhMRrVYc+/aN9NJGBDmk7fXIza+HUQrC1gpbJTkCC68f7tIihrupCVdNDQgChmnThjRG2xES+g8ExTCKcur60TbI3qJlJcvIMg3f7RmKnb3fY7Rt25C9TlGBnLq//U3o7DISdUYNGfnSjbF+EK+R7C0yJqegN0X+ZhpO5ExEWYB/OPINPCRakADQqrUhTd2X/9bZJcmoVJFvBDyQqF8q9BjjpTMGQQ5p2ywmYJifq80vgcsK2VOh5JhQLC8iyMVV9ePGoh5iaZCBQrRHGophFMVYzU46mu0gSBdlmSZbEx8fksTBl066NGTz+TPThnihMUyYgGAw4DWbcZaVh2xdI07hfMifAx4HbHiux0ty2v5gDWXlXWy864u8Tif23buB/j1GqTnD+1wNhZ9M/AlalZZtjdvY3jg8zVs06YsC6WUV/wJsOTNNkg+YmxpxO53BD+T1SJWuQcpIjXA18+HgD2cPMU0fjqws2sFQDKMoRi7smJabgN7YlSK8onQFLq+LGZkzmJ41PWTz+WvO1A3NNS1otRimTgVifLcqCF2Vb9c/De6ui26gDWW7dl/xfZFx7NmD6HSiTk1FO2pUn8fIrvm2EdAYyWQaMzlt9GkAvLzn5WGNVRdFhR07Wppxu5yo1GqSs7L7PCbeBdhpuSZ0BjUetwGt3giiOLQ6WaUrpQxUYxpM/0noFzqCdIWzhya8hiOr4fVgKIZRFCNnP3Xfqbo8Lt7Y+wbAkNp/DEQoGjP6L8pbt4RiSZFjytmQmAuWetj1rv9puY5KQ5kZj6f/cKG8qz9ihNczpvebIiwb3O0NdSOSsi8jfz8+KfuERmvjkMZw2t201HYC0eExkj2RKdm5/faykr0GMV06YwAElVToURAEjMm+iv1D8Ub6U/SvlDJSYxTR48G+TfKK9hfOHgypHlQdEP/XrEBQDKMoRvYYdd+pflb+GY22RjKNmZxSfEpI5/O3b6gbepXi7jqjmEajkzLUAH54HHzNddNyTOiMGtwuLy3Vnf2efqR4jLoax/Z/QU7KzEStkVL2O5qGJuwfClMzpjI7ezZur5s3St8Y0hgN5R0gQmK6noQU/eAnhJm2AD5XmrQ0dMVSdlXMls4YBDmkrdKkAUPwRtbvgkOrfSn614Z6eSOK8+BBvJ2dCCYT+nHjhjRGe2M9Xo8HjVZHUnpGiFcYeyiGUZQiekUaynoLr+WwwAUTL0CrDr578kB0FeOrw+sZ2s5eThV17C3Fa7WGbG0RYd7VoNZDzWaoXAf4dqslUksI2XDti7bDup/HK34X/gApwiqVmpRsn7B/BHVG0OU1emPvGzg9wetQurJCe7fjiQSBhju6MkRjfIPSD/I10eWUvotBf67kFP1JP4LU4PtLRhP+zcnUqQj9eBEHo+t6lYcQg+1QQo3yG4hSWuusOO0eNDqVPxNqe+N2tjVuQ6vS8pMJoY+JJ6VnotHq8HrcmJuGFnrQ5uaiyckBjwf7zp0hXuEIk5AJM3y/57VP+J/2C7D7KfRo77Rg65D1YfHbJ83d2oqrvALoqnzeH5HQGYHUWDnHlEOLvcWfsBAM/j6FYyIfRoPuNYwGzhzqCmnHsNZvAGQvutMmZWAFlbJvbYGtr0uPYzhFX6a/djzBMFBtrCMRxTCKUuS2E9nFyajU0p9J9hadNvo0Mo2ZIZ9TUKm6pewPvTZI3ITTQGooCbDrPWivArp2q/15jOSbf0JqGjpj7GoXBsPuC9PoSkpQp6YOeKy/fUP9yBpGWpWWiyZdBMDLu19G9IVEA0EUxa4Cq1EgvIbAe1nJoU3btm1BvedYwZikIznLiKAeQiht84vgtkHOdCg+KkwrHDnk6+xwMtIU4XVPFMMoSjlcX9RobeSTsk+A0IuuuxMaAbbPjR8P6cK506DkWBA9sP4ZoOtv0lpnxd7Zu7LykbL7CmanKns4RqL69eGcP/589Go9u1t2s7lhc8DnWVodWM1OVCqBrFFJYVxhYHg9HtrrJYHsoKG0iRMQ9Hq87e04y8pGYHUjT+7oZARVKgCW1hZcdvvgJ3ncsO5p6XGMp+gDeK1WHKWlABhnzhryOEdKlf5AUQyjKOXwppVvlr6J2+tmVtYspmZMDdu8Xa1BQpCZtmVLfOxW5YKPG54Dp9W/WwVoKO/tNTpSdl9ymCaQnWpaCIT9QyXVkMqPxvwICK7go/wdzChMRKOLfIsEc1MjXo8btVZLUsbAHmNBp8MwZQrQ1UMr3sgZnYygMqLSSN/FgHRGpR9DeyUY02H6+WFeYfix7dgBXi+a3Fy0OX2XbwiEIyVZJFAUwygKcTk8tFRbAEnP4vQ4/Sn6ch+ocNGVmTZ0w8gwdSqo1bgbG3HX1YVqaZFjwqmQWgz2Ntgu/R1kr1FfFbCPhN2XKIr+jKdAaqek+kJp7fUjm7IvI3tZv6z4klpLYMZZf+14IkWbL7ydmhOYQDbudUY+rZ+gksJpAXkj1/pE13OvAq0xTCsbOfyNY4cRRvO4XZgbGgCluKOMYhhFIQ3lZkQRElL1JKbp+aTsE5rtzWQbs1lSvCSsc6eFQCSrMhrRT5wAxElWjEoNC34mPV77HxBFvxi3L8PoSNh9OcvK8La3S54J3996IOSUfa/HTccQhf3DYULaBBbkLsAjenht72sBneP32kaJ8LolSE+kMc4z0zILE1FrVIj4KmEPtpmr2yE1hxbUMP+aEVhh+AmF8Lq9oR5R9KLVG0hISw/V0mIaxTCKQrqH0URR5OXdkuj6wkkXolWFNkX/cPzF+Brr8QyjO3fcVd+dfRloE6BBqn8ip2/XHzL3Che2BSiQjWXknaphyhQEnW7Q46VefL5mshHQGUGXt3VF6QpsbtuAx3o8XhoqOoAo8hgF6YmUv4P2vXvxBqK/iTHUGhVZoxJRBeoxklP0p5wlNYuOA2wh8Bi1dmse21+R1iMNxTCKQroLr7c2bmVn8050Kh3nTwh/TDwhLR2t3oDo9dLeUD/kceIqMw3AmAqzLpYer/0PmUXSbtXe6aK9sesma+swY++UwqCpcZyqP5Sdalcz2ZHXGQEcX3g8BYkFmJ1mPjz44YDHtlR34nF50Zs0pGZHR2ZhsJ5ITV4e6qxMcLux79oVzqVFjJzRKf7MtAEzaa0tsM1X5DMOUvQBXPX1uOvrQa32t2IaCkdKX8dgUAyjKKR77ZRXdr8CwOljTifdEH43pyAI/hv6sFL2fboT+86diK7emVsxyYKfS//u/Qi1uZzMIqmGSvdwmrz7SkzPQKs3jPgSRwr/TnVm4C0IUmWP0QgXeZRRq9RcPEkybgdL3Zf1RdklyQiq6NhF+z2RAXY/FwShK20/HjJE+yCnW2bagJ+rTcvBbYe8mVC0cGQWF2Zk7Zh+wgRUpqEb74FUUz/SGLJh5HK5qKysZO/evbS0tIRyTUc0llY7nW0OBJWAmGHns/LPALhkUvhS9A+nq5ns0G9gupJiVMnJiA4Hdl86acyTNQHGLgFEWP8MuaO7wmkyR0KHaq/djn3PHgAMQTSt7PIYRcYwAjh3/LkYNUb2t+1nbd3afo+LtvpFHrfL78EN5rMVd57bw8gpSfZ7jGzmdhzWPtr0eNywTiq1wcLrYz5FX0Y2jIYTRoNuobQ4vmYFS1CGUUdHB0888QTHH388ycnJlJSUMHnyZLKysiguLua6665j/fr14VrrEYF8QU7PT+Dt8hW4RTdzsucwOWPyiK0hNQS1jASVyl8NOa7SheXU/U0vklMkaWtk7wJ0q2EUx7sv+67d4HajzshAWxD4+wxFL77hkqxL5qyxZwH4tXt9UXdYuYxIM1SBrHzTjNfMtKQMA6aURBCk7gB9XrP2fgjmKjBlwtQfj/AKw4d96/D1RdAtRKsYRn4CNoweeeQRSkpKeO6551i6dCnvvvsuW7ZsobS0lDVr1nDXXXfhdrs55ZRTOPXUU9m3b1841x23yIZRVnECK0pXAOFP0T+ctBCk7EOcFXqUGbsE0seCo50c65cANFVacDulFPRAKxPHMv7+aDNmBCXW9Av7h9GLLxTI36evK7+m0lzZ63V7p4u2eqnPX7QYRq3de1kF8Ts3TJsGKhXu2lpc9Q3hWl7EEATB5zVKBfoJ/8sp+vOuBm18hLdFtxubr+XScDLS3E4nHc1SY2cllNZFwIbR+vXrWb16NevWreOOO+5g2bJlTJ8+nXHjxrFgwQJ++tOf8txzz1FXV8c555zDN998E851xy2y8Lo+sYwWews5phxOGnXSiK4hFEUeIU7d+CqVVDEXSNr1OMYkLV6vSGOlJLjuyhyKX+G1v3ZKkBfkpIxM1FrtsHrxhYLRKaM5Ov9oRERe3ftqr9flop3JWUaMiYNn3I0EXTqQwPRFMurEBH/HddmgjTdyRiejknVGh3uMardB+Xeg0sC8n4784sKEY/9+RJsNVWIiujFjhjxOW30tiCI6owljcnQ0So4GAjaMXn31VaZOnYrH4+Hdd9+lo6Ojz+P0ej3XX389P/1p/HwIRwqvx+u/KH9qew+AiyZdhEalGdF1yDsHc1MjbmfwHcll5IrIzkOH8LT33XA1Jpl1CeiSEJpLycmWfj/1h9oRRfHI8BgN0YUvqFR+AXYkdUbQVfDxnX3vYHVZe7wWbfoi6JY5NIRdvT9tP542KN3IGd2lM+r1ufKn6J8NyfHznZS/g4bp0wIq9tkf3TMdlVT9LoL+jarVai6++GIaGyO344tXmms6cTu9qPWw0bkGvVrP+eNHvmy9MTlFan4qirQ3DL1ytSYtDe2oUQDYtu8I1fIijz5JqmsE5HokAW/9ITM2cztOm3STTYlTj5G7uRlXdTUIAgafhiwY/j975x0eR3nt/89s31Xv1ZZc5V6xjTHd9GIgIaa3EBNyA+kJJJdAyvXl/pKQ4JAKAadRAiExEEpCqAY3XGRbstwlWb337Tvz+2N2diVbZbU7s7ty9vM8eli0szOvpdXsec/5nu8JdDzGODA6u+hsSlJL6Pf08+qxV4c8F7DLiJMyGkQmkD0tS9qDyCsJBkbt9fXBJwY6YN9L8uPTpEVfIVDOHkdX6HB0J4TXwxJWqLls2TKqq6vVXst/PMpOtS+9HQSJq6ZeRbolPerrEARBlWGyMEj8ebql8ZevAwTyet4A5N+d8rNKycrBaDLHcHHaoexUTdOmok8Z/2BV5QYcibO6GugEXaB1/7mDzyFKIiCPOmk57rfLmBI/pYVIBLKBknZlJVIEpq3xislqGJKJDNgw7P49+FxQuBiKl8VugRoQ7EiLLDD6T3DpD4ewAqP777+f73znO9TVnSpcTBA+yk71kFGeAK7cuGNBoIMoAi8jOI3nNWVNg5mXkms8Akj0dTppqT4BQEbB6ZktgshvyAEriJbYdaYpXDPtGpKMSVT3VLOtcRsAve0OnAMedAaB7OLkGK9QxuN2BQWyhePTGAGYpk5Fl5SEZLfjOnpU7eXFBYUzSgDwOO04+nrB54FPnpafPI1a9AF8/f24jx0HIhNew3+GS384hBUY3XDDDXzyySfMnTuXW2+9ld/97nfs2rULdwR6lATQclzW4TQnVbMsfxllmWUxW0sgY6RSZ5pz775RDfUmJCvuxaRzkmmU0/eNh2uA0zstPbgjLRyC5qGxzRgBJJuSuXb6tQA8e1Bu3Q90hU5KQW+MD//bnmZZIGu2JWFNGX95T9DrsSyQy56n69y0gunZIMgZzO7mRjj4D+htgKQcmHtdjFenLs79+0GSMBYVYcjKiuhcXWGK+k93wvrLr66uZtOmTXzjG9/A4XDw6KOPsnz5clJSUlgQoafCfyouh5cuf4twS0ott8yKbov+yWSoVPIwz5qFYDTi6+7Gc7plGKeeD9ll5Btks8P2utPbWl8SRZx+rVi4O1Ul4O5pjW3LvoKSlf2w/kNqe2vjU3g9aEZauALZgAP26Za59ZM3JQ2dv2W/o6FhUIv+Z8FwepW11RgcC+BxOunv7ABOb9+1cAir3amkpISSkhLWrFkT+F5fXx/l5eXsO007H7SmtaYXJOg1d5CZnsp5k86L6XrSVfIy0plMmOfMxrl3H469+zD5xdinBYIAKz5P3ok3OOC4mL4OWaiefpruvtzHjyP29yNYrZhnzAjrHCmZcsu+z+Oht72N9Lx8lVc5PkpSSzin6Bw2N2zmhYMvMK1mNRCfwutIdCBB64zTMzDKLExCZ8xE9NbRvG8X87u2nnYt+gqK/YlFJWNHS3IK1uTx6wVPZ0LOGJ04cWLU51NSUjjnnHP44he/CEBDQ2TalFD55S9/SWlpKRaLhRUrVrBjx45Rj3/ppZeYNWsWFouF+fPn88Ybb0RlnWPR7C+jtSTXxKRF/2QULUN/ZwceV2STuQO71dMxaF54I3nJsuDT7fDrQE7TjFGgRXjuHARDeO/PIS37EerX1EIxfHzl8Ku01ck2JHlxJLxWY5aVkl1wHzuObwSrlYmMTieQmi0H2a2H5Qwuc6+DlNgG3mojSVJQ5xdpR1rC8XpEQg6Mli1bxuc///lRR3709PTw1FNPMW/ePF5++WVVFjgaf/nLX/ja177GI488wu7du1m4cCGXXnopra3DO7xu2bKFm266ibvvvps9e/Zw7bXXcu2111JREftW8sOH5MCzK62RT82IvW29NTkFS7JSs49MKHvaCrABTElkrFiNgU6QPAiCQFqMsyBaEc7g2OFQKxupFisLV1KaWoq1OwPRK2FJNpKaHT8OyWp4YxmysjAWF4MkyRqV05Dc0kkA9PT4A7/TrEUfwNPQiK+jA4xGLHPmRHSugAVEoox2CiEHRgcOHCApKYmLL76Y/Px8rrzyStatW8f999/PrbfeypIlS8jNzeWZZ57hRz/6EV/60pe0XDcgjylZt24dd911F3PmzOE3v/kNNpuNZ555ZtjjN2zYwGWXXcY3v/lNZs+ezQ9/+EOWLFnCL37xC83XOhqSJNFeK+uLysomk2aOj92q2qNBXFVViKehQF+3fB1pghxcW5LSMBiNMV6RNqjVIqyWsF8tdIKOm2ffTG6/3NmUV5oSV2Z3as3fO93nphXPkh2gnR4PUuFSKD4jxitSH6e/FGopK0Nnjkw7FY8z0nwekXd2bcHlie3nRMiBUVZWFj/96U9pamriF7/4BTNmzKC9vT0wE+2WW25h165dbN26lSuuuEKzBSu43W527drFRRddFPieTqfjoosuYuvWrcO+ZuvWrUOOB7j00ktHPN7lctHb2zvkSwuOnqjF4DLjE7x8euVVmlwjHALDZBsjK3kYi4vRZ2QgeTy4qqrUWFp8kVGCNUme6m0gPkZIqI1ot+M6fBiIXPQZ9JyJfcu+wpppaygamAaAKyt+XNrdTgcDXZ0AZORHpl2zLlIyt6dhSRuYMn8yICDho7vs9lgvRxPCdZ0fju44HHi9vWIvB59y8vNvvoHH54nZOsYtFLBarVx//fVcf330HZkH097ejs/nIy8vb8j38/LyOHjw4LCvaW5uHvb45ubh3Z0fffRRvv/976uz4FGobWzEaRzAl+ykLDc8UasWqJUxEgQB64IF9H/wAY69+yIuxcQj+qw0qAefNwUcXWDNiPWSVMVZWQmiiCE3F2N+ZKVCJWMU67Egg0kyJlHinAXANt97fJrYNj8oKMGjNSUVS3JkvkqDM0aSJMVVVkwNUlv/jU6XhCj2U2Ofxun1FyjjCHNO4XDE4/ii93duJ42ZCFkujPrYZd7jw6gjTvn2t79NT09P4EsrQ8uLVp7F/Y9fys3fOFuT84dLuoofYMHd6umZxvfq5Q8Zt1CEe9uzMV6N+qh5Q1Y0Rj2tLXHRsg/g6HOj65N1Re+63qCmpya2C/KjGKyqsas3z5kjW2d0deEZPDrjdGH7b7EZ9ADUHznNrEEAye3GeeAAEHlHmstux97TDcSP63WHo4P2WnkY96xZJTFdiyqB0YEDB3j00Uf59a9/zYcffkhXV5capx2V7Oxs9Ho9LS0tQ77f0tJC/gg72vz8/HEdbzabSU1NHfKlFSa9ieKs+HJMDmSMVDDjswRGg5yeafy+djnrKOgzafn4PRDj4wNfLQIdaSqk8FMyszAYTYg+H71twzdKRBvFdd6V0ovb4OD5g8/HeEUyau7qdSYT5tmzgdNwblrDLqjfQbrZBUDHidMv8HMeOozkcqFLS8NUWhrRuZTNrjU1DbMtSYXVRc7LR14mu0+2c1k4d2ZM16JKYLRmzRpsNhsDAwM8/fTTrF69mmnTpqlx6hExmUwsXbqUd955J/A9URR55513WLly5bCvWbly5ZDjAd5+++0Rj/9PR9lJ2Hu6cdntYxw9Olb/wFFPXR3ezs6I1xZPSJJEl3/EhaDLoKU7HQ7Fhw2EWgQyRhEKr0Fu2Vc69+JFgK0YOxZMTQdg09FN9Lv7Y7giGbVbqoN+RqfZBmX7kwDkFmYC0NvRfNo57Q92nY+0DBpvwmuP6OHv+14jzZUNQG5pbH2VVAmM8vPz+fKXv8w3vvEN/vCHP7B7924O+4WaWvK1r32Np556ij/84Q9UVVXxhS98gYGBAe666y4Abr/9dr797W8Hjv/yl7/MW2+9xWOPPcbBgwf53ve+x86dO7nvvvs0X+tExGxLwpaWDkReTtOnpmKaKneNnG435f6uDrwuF4KgQ9Cl0uKZEXTePQ3wtLTgbW4GnQ7rvLmqnFOtIcVqoWSM5s2eztS0qdi9djYd3RTbRTEoYxTGjLThOC070/paoEK2hyk+6wIAvM4O+rtcsVyV6jj3qSe8Vkq08TIK5J3ad9C12wBIy7NitsW2s1eVwGj16tVs3LhxyPf0er0apx6VG264gZ/85Cc8/PDDLFq0iPLyct56662AwPrEiRM0NQU7X8466yyee+45nnzySRYuXMhf//pXNm3axLx58zRf60RFTc8ZZbfqPM0CI2VsSlJGDoKgp8VThlS9GZpj74+lBsqHqHnGDHRJ6qTd0wPDZGMfGEmiJDvPA/lT07h51s0APHfwOURJjOXSghojtTJGfq3faWWdsev3IHqgeBk5i84HQBK7aT7eHctVqY5ao0Bg0PDYONEXPXfwOXL7ZF1RfhyYq6oSGO3cuZPvfe97TJkyhbVr17J+/Xpee+01NU49Jvfddx+1tbW4XC62b9/OihUrAs+9//77/P73vx9y/Gc+8xkOHTqEy+WioqIiKtYCE5mgzihyl2LlD/p00zcoQWNWcRE6vYBDTKPPlwvbfxPjlamDmjtVBbVm8alBd6sdl92LwagjsyiJq6ddTYoxhbq+Oj5q+Chm63IO9MuT4oGMfHX0h0OsM/xC3gmN1w07n5Yfr7iX1JxcEHSAj7oDo09rmEj4urtx19QAYPHLEiJh8Py9WHOg4wB7WveQPzAFiI85hREFRp2dnbS3t/P6669TW1vLvn37+OpXv0pubu4pWp4EE5NAa7UKH2CBNP7+/UhibHfiaqKUOzILi8gulluqmz0zYf9LMNARy6Wpgpo7VYV4cr9W9EU5JSno9TpsRlvAff7Zqth1GAYykekZmKw2Vc4pCMLppTM68Ar0t0BKAcy5Bp1eT1J6LgBNR2tjvDj1cPjdyo0lkzFkRG5E0OW3gYiHjNFzVc+BJFA4IEst4mFOYViBUUVFBQsWLCAnJ4e8vDwmT57MI488gk6nY+XKlaxbt47HH39c5aUmiAVqfoCZZ85EsFgQ+/oCu5/Tge5Bu6+8qXIauMW0CrxO2P37GK4sciSvF0dlJaBOR5qCckPubWvF5/Wqdt5wUAKjwTvVG2fdiIDAlsYtHO8+HpN1BQSyKutAApnb08HoUcnKnnE3+H1vMgv996yGBny+02MDFtycRN784Ozvx+nPRKarlIkMlw5HB29Uv0GaMwedx4jeqCOrODK/LjUIKzD67Gc/S3Z2Nh999BGVlZV8//vf59VXX+WMM86ISqt+gugRHN8QuUuxYDBgmSuLd0+Lm7KfYEt1QeDDtUVYIj/5ydMQQwfXSHEdPYpkt6NLSsKsYqdpckZmsGW/PbYt+4rwevDg2OKUYs6fdD4g6x9igdr6IoXTZnZh/U5o2Al6Eyy9M/DtnBJ5ZprX00lnw0CMFqcuwY60yAOjrmb5fZWUkYnJYo34fJHw8pGX8YgelrIKgJxJctY21oS1gsrKSn71q1+xcuVKZs2axV133cXu3buZO3cu999/v9prTBBDlB2Fs68XZ3/k7cvBm3J5xOeKByRRpKdF9jBKLygkf6ocGLV1mvHZCqC3Aaqio7fTgoB/0fz5CCo2VAg6XeC9FUudkcfto6Nefl+fnMK/ZfYtALx67FV63dqMAxqNLo0Espb580EQ8NTX4+2YwKVeJVs073pIzgl8W8mwSWI3LdXxM94lXCRJwrlPLqWpKryOsb7II3r4y6G/ALDEHxjFQxkNwgyMzjjjDLq7u4d8TxAE1q9fz6uvvqrGuhLECSaLlaQM2RtE2WlEgvU0M3rs6+zA63Gj0+tJy8kjNduKJdmI6JVom/pf8kETuHU/sFPVYIxLsEwbu5lpbSf6EEUJW6qJ5IyhQzmX5y9nevp0HF4Hm45sivra1PYwUtCnpGCa5rfOmKiZ294mqPy7/HjF54c8pQSSkq8rUCadyHhOnMDX3Y1gMmEpK4v4fPEivH7nxDu02lvJsmRh6ZR1UxMuMFqzZg3f/e53eemll7j33nv5yle+coqLdF9fH2lpsW+1S6Auqgqw/Tse16HDiA5HxOeLNcqHV1puHjq9HkEQAn/cLUmrQWeEum3QuCeWywwbpdyipvBaIZAxiqEAO6AvmpJ6immeIAjcPFtu3X/+4PP4ouhmLknSII2R+h9gSklGCXwnHLs2guiFySuhcNGQpwKBkdhDc3V39NemMsom0jJ7NoIp8iHVWmUix8tzVXKJ+jPTbqCzXi55xkNHGowjMJo7dy47d+7kS1/6Erfccgs7duxg6tSp3HXXXWzYsIGf/vSn3HXXXfzsZz/Tcr0JYoBaw2QBDPn5GHJywOcLzP2ZyCg3mcG7r4DOqBGYe538zQmYNfL19eE+JguP1WzVVwjq1+IjMBqOK6dcSaoplfr+ejY3bI7auhx9vbgG5A+LNA0EshPa6NHrgp3PyI9PyhYBpGRmozeaAJHOxmZc9omr8YOgvYlFpc2JVpnI8aC06BsEAxdaL0cUJawpRlKyLDFb02BCDoweffRR3nzzTZqammhqauLNN9/k4Ycfxul08pvf/IZvfetbHD58mB/84AdarjdBDEhXcWaaIAiDBspO0DT+IIaz1lcMylqqe2DFvfI3K16G/viYCxYqzv37QZIwFhVhyM5W/fzx4GXUUiNrUPJGMJWzGW18esangei27it/aylZORhN5jGOHj/K36Bz336kOBnkGzKVf4eBNkgtgllXnfK0oNMFfJ8ksSsgrp+oBAc4R17OliQpuJmLYcZIyRZdUnoJriY5DMmbkhbxqBO1CEtjlJeXx6WXXsoDDzzA888/T1VVFX19fXz44Yd88YtfVHuNCWKM2uMbLBN5t3oSgVb9QTcZZc5Pb7sTR9p8KF4GPjfs3DjsOeKV4A1Z/WwRBH9mPW0tMWnZH+hx0d/pAgFyS0aezXTDrBvQCTq2NW3jWPexqKwtsKsv0Kad2jx9OoLVijgwgPt4bOwIwkKSYNuv5cfLgi36J6Ns5ia6zkh0uXAePAioExg5+npx2eVMZKxa9TudnbxZ/SYgNzgEukLjpIwGKjlfA1itVlasWMHnP39qajPBxCaws29uVGUwY1DfcBpkjIbp8DDbjGTky4Z8LdW9wazRzqdlp94JgpLC10J4DZCckYXBbJY7+1pbxn6ByigfmJkFSZgshhGPK0ou4oJJ8gwuZaerNcOVaNVEMBiw+kchTai/w7od0FQOejMsuXPEw4I6o+4JnTFyVVWBx4M+MxNjUeR+VlpnIkPh5cMv4xbdzMuax4KcBWOWs2NB7A0DEsQ9isbBZR8IjCiIBOu8uaDT4W1qwtM6scpLgxFFHz0twzvIKn/kzdU9MOca2Zm3vwUObIr2MsNCkqSg6FMDfRHIZdXBQXe0Gc8NWWndf+34a/S4tG8Bj8aQzwk5okdp0V/wGUjKGvGwQMu+P2OkxoYuFjgGjeNRo8ykdSZyLDyihxcOvQDAzbNvxt7rpq/DKWdtT8eMUYLTF6PJTEqW7BOiRjlNl5SEefp0YGIPlO1rb8fn9aI3GEjJzhnyXF5AZ9Qrp/vPuFt+YoLMT/M0NODr7ASjEcucOZpdR81ZfONF0RflTx27k/aMvDOYkTFDbt0/uknjlaFpR5qCZaKNBulpkEeAQDALOwLK+0oSu3H2e+htn5gdsMGsrTqbE60zkWPx7ol3Ay36l5ZeGhjenJFnw2wdOWsbbRKBUYKQUHYYau3sTwf33a5Aq34+Ot1Q80MlC9Fa04skSnDGXXL6v2EX1H0S9bWOl0AnzKxZ6MzapdzTVdavhYooSrTU9AGhaRsEQeCWWXLWSOvWfUmSAoJ0LT/AlJK268gRxIEJ4BC98xmQfFByNuSPPkg1PVBK60WSfBNWZ6Sm8BqGbxaJJoEW/bLPYNKbBrnOx0+2CBKBUYIQUVLTan2AnQ7zmrpH6e7IKkzCYNLhdvroarZDUjbMv15+cgJkjbQ0dhxM8H0V3YxRZ+MAXpcPo0VPRkFSSK+5YuoVpJnTaOhv4IP6DzRb20B3Fx6XE0HQkZ6Xr9l1jHm5GAoKQBRxVFRqdh1V8Dhl7yIYtkX/ZJLSMzBarICEJPZMyMDI296Op74eBEF2K1eB4D1LuxLtSFR1VLG7dTcGwcDamWsBAs7kI3WFxopEYJQgJNJVLnkouhVnRcXEaxf2M9ruS6fXkVsySGcEwRv6gU3QG/up8qOhpbHjYNT0yBoPgRtyaSo6XWjaDavBGpXWfeVvLDU3F71h+K4rtZgwfkYVfwV7B6RNgrIrxjx8sH5N8k3Mln0lW2SePg19yshdk6EyxDQ0BhmjP1f9GYCLSy8mx5aDNM6sbTRJBEYJQkJtMz7ztGnobDZEux3X0ei0QKtN9xg6kIADtnJTLlgIk8+SHXsVg7o4RHS7cR2oArQxdhxMRqG8c+3raMfjdml6rcGE2wlzY9mN6AU9O5p3cLjrsBZLG7bTUSsCJe14dsCWpGCWddnnQB+aFiVYTuuira4Pn0fUaoWaEDR2VCdra+/pxuN0IAg60jTMRA5Hu6M90KJ/2+zbAOhuteN2eDEYdWQVhZa1jRaJwChBSKQPMuNTo8ND0OuDfkbxfFMehbGEjIHA6Pig3aqSNdq5US4PxCGuqiokjwd9ejrGyZM1vZY1JRWzLQkkiZ4ozkxrDgRG40vhFyQXcOHkCwHtWve7ozjLKljS3hu/nVsntkLzfjBYYcntIb9MCSx1ul55dmF9n1Yr1ATV9UX+TGRKdg4Go7aZyJN56dBLeEQPC3IWMD9HLgsqm5OckhR0+vgKReJrNQnilvS8fARBh8flZKC7S5VzTpg0/jCIPh89rc3AyBkjxQG7s7Eft9NvYDjrKkgtBnu77IYdhyi6L8tCdVqER0MQhKiPBnHZPXQ1hT+bSWndf/3463Q7u9VcGhDdWVaWOXPAYMDX1o63KXbDfEcl0KK/FmyZIb9M+fkZDPIH8ETSGUk+X6BjVxHJR0o0Oh2Hw+1z85dDfwGC2SIYlLWNszIaJAKjBCGiNxhJzZFb0tUa4aDsVp0TUIDd29aK6PNhMJpIyRx+XEZSupnkDDOSBG21/t2q3gDLPyc/3v4buUwQZ6i9Ux0LNUfOhEKrX9eQmm3Bljr+oZxLcpcwK3MWTp+Tvx39m9rLi4qHkYLOasUycyYQpxuU7jqo+of8eIwW/ZNRAgCvpxOYWIGR6+gxRLsdnc2Gefo0Vc4Zq1b9t2reosPZQa4tl9UlqwPfD3akxZfwGhKBUYJxkK6yUFbJGLmOHsXXPwHahQcRaNXPy0fQjfxndIrOCGDJHXJZoHmfXCaIMwLCa5V2qmOh9siZsRhrPtpYCILAzbNuBuCFgy/gFdUbZyKJIj0t/kxklD7A4np24c6n5Rb9KedC3vj8tJT7ldvejSR5AoL7iYBjbzkgN6kIev3oB4dIdxS1awqSJPHnA7Lo+qZZN2HUySU8r9tHR30/EH+t+gDx46h0miBJEl6vF98E7bQajazSqbTV19Hd2YHTqYI+JiUF3cKFeFtb6amowLZoIXq9HoPBEDfDBEci1HJHXmkax3a30Xx80E3ZlimXBXb/Qc4alZyl5VLHhbezE09dHQDWBeq0CI9FtFv2m1UYQXDF1Cv42a6f0TTQxPt173NRyUWqrK2vsx2vx41Oryc1J1eVc46FZcECeO75+MsYue2w6/fy43Fmi8CvX0tKwjUwgCR209tuxNHnxpoy/ixhtAl2haq3OQmU0gqjFxjtbt1NVWcVZr2Z62dcH/h+24k+RFHClmoiOSM2o0lGIxEYqYjb7aapqQm73R7rpWhC5uwFLJk0FYPZTHV1tSrn9H7pfiSnk0adgN5/TpvNRkFBASZT/N7AQhXI5k31Z4z8YwkCAd+Kz8uBUdU/5HJB+iRN1xsqyg3ZNHUq+tTo7OSiORZEkqSAGD4/ghS+WW/m+pnX89T+p3i26lnVAiMl4E7LzUenUqZgLJQPX+eBA0huN0K8/N3tfwkcXZA+GWZeNu6Xy/q1IpqPHsaW4sBplzO3pfOHL33HE06Vy9mSKNLtb26IZsZIsbW4aupVpFvSA98fvDmJx01wIjBSCVEUqa6uRq/XU1hYiMlkistfeCS4HXZ62loxGI2q6R+86el429rQJSVjLCzA7XbT1tZGdXU1M2bMQDdKmSqWhOoHkjM5BUEnYO9109/lIiXTIj+RN1cuD1R/CJ/8Di7+vtZLDonBs5mihdJWPdDdhdthx2S1aXat3nYHzgEPeoOO7EnJEZ1rbdlanql4hp0tOznUeYiyzLKI1xdN4bWCqbQUXVoaYk8PzkOHsc6fF7Vrj4gkwfbfyo+X3wO68ILEjPxCmo8expo0IAdG1fEfGPn6+gIWJmr5iPV3deJ1uxB0OlJz8lQ551g09Dfwzol3ALh19q1DnlPKmqGM44kFicBIJdxuN6IoMmnSJGw27W7sscSg12Hv7ECQJMxmsyqBny81FXdHB4LHjdliwWq1YjQaqa2txe12Y7FYVFi5+gQEsoWjB4hGk57s4mTaTvTRUt0bDIxALg9Ufyhnjs57AEyxf98oQnhFdxINLEnJWFPTcPT20NXUSN7U6Zpdq9mfLcqelIzeEFnQnZ+Uz0UlF/HPmn/y3MHn+P5ZkQe33c2K8Dp6gZEgCFgXLGBg82Yc+/bGR2BU8xG0VoLRBotvHfv4EUgPtOzLH8QTQWfk3L8fJAljcTGGrJEH5Y6HYCYyD70hOh/7Lxx8AVESObPgTKZnDP2bVv4O41FfBAnxterEa4ZDDfQGI4IgIEkSolcdwanOagVBQPJ6kTwe+Xtx/jP0eT30trYCoXUOKe2ozSfflGdeBuklcrlg/4uqr3O8SKIYk4wRDNIZaVxOUzqTIimjDWZw636XM3Ibi2DnUHRHNsSddYbSor/wRrBmhH0aZePicfk702r65NmFcYwW+qLuKDte2z12Xj4i25GcnC3q73Iy0O1C0AmB6QDxRnx/AiWIKwRBCOw2vF6POufU6dCZ5SyK5JgYE7C7W5qRJBGjxUpS+tg37YDO6PhJ7cI6vVwmALlsEOPWfXd1NWJ/P4LFgtnfwh0tMlQeOTMSgVEgU9W5IS/KWcTszNm4fK7AB0EkdMVABwLBDGFcWGd01cChN+THy8eeizYays+xv7MZvVGH2+GluzW+NaCK47UWwuvh5jpqwavHXqXP3cfklMmcU3zOkOeUbFFWURJGc3R0dOMlERglGBd6oyzM9HnUCYwAdDYrAOIEEa0P1oGEUk5UMkZtdX34vCeNJVh8KxiToPWAXFaLIYERBPPmIkQp3a6glI7U8sgaDq/bR3udui3CgiAEskaRtu6LPh89Lf7AKIqdQwBW/5BSd20t3i51DFzDZvtvQRJh2oWQOyuiUynvK3tPN9nFcqt4PPsZSZIUzNqqWM6OpjeWKIkB0fXNs29GJwwNM5rjXF8EicAowTjR+63kfR63aucUrP7AaIJkjMZ7k0nPtWG2GfB5RDoa+oc+aU2HRTfJjxWxaYyItrHjYKLhft1W148oSlhTTUO1XhFy2ZTLyLRk0mJv4d0T74Z9nlBMQ7VCn56OqbQU8GtcYoWzF3b/SX585hcjPp3ZloQ1Vf4ATs2UZ/E1x3Fg5Kmrw9fVhWAyYZkVWVA4mK5G+Z6VWVCs2jlH4uOGj6nprSHZmMy106895fkWv3VJfpzqiyARGCUYxIMPPshVV1016jHKjB3vSRmjjo4OcnNzqampGfX1N954I4899tiQ7+n8YnXR4UAS43/Q43gDI0EnBLJGw+5WlXLBoTegUx0bhHCItrHjYKLhfh3ohFG5RVhp3Ydge3I4hGoaqhWBuWnlMdQZ7fkTuPsguwymrx77+BBQ/k7NVjkjHc8CbOVv0DJ7tmq2CaLPR7diGhqFTKTyN3DdjOtIMg4dDuvziLSd8GdtExmjBBOB8vJyFo6RLQhmjIYGRuvXr+eaa66h1L/rHImHHnqI9evX09MTvDkJJpPs7ipJSK7oTVgPl2BgFPpNRindnCLABsiZCdNWA5Lcuh8DRLsd12F5WrxaLcLjQdGCOPv7cPRps6PXshNm7cy1GAQDu1t3c6DjQFjniGa5YziUKe5K5jDqiL6g6PrML4BKwWtQryWXCDsaBvC449OAN6AvUrGMJmcivVHJRB7vPs7HjR8jIHDTrJtOeb6tXpYTWJKNpOVYNV1LJCQCowQBysvLWTBGN9JgjZEyjdtut/P0009z9913j/par9fLvHnzmDZtGn/+858D3xcEIVhOmwA6o3C8ZpTxEyPqGxRn391/Alf/8MdoiLOyEkQRQ14exvz8qF/faLGQnCm3JmuVNVJGgajVkTaYvKQ8Lim9BIA/HfhTWOcI1QJCK5RMoWPfvthkbg++Dt0n5C60BTeodtqMgE9WK7Y0E5Io0XaiT7Xzq4kWHWmdTfWALLzWOhOpZIsumHQBk1JONa0NmqvGp7GjQiIwSgBAc3MzLS0t+Hw+zj33XGw2G8uWLWP/SXoDvX9chyRJ+Pwt+2+88QZms5kzzzwzcFxNTQ2CIPDiiy9yzjnnYDabefXVVwG4+uqreeGFF4acVzdBdEZuh52BLrn1N2McLdVKKa2n1YGzfxjh+vSLIHMauHpg7/OqrHU8BMto0c8WKSiZEi0csAe6XfR3uhAEyClJUf38ALfPuR2At6rfomWgZdyv7wzoQGKUMSqbiWA2I/b24q6pjf4Ctv1K/u8Zn1XV0ysg7G9uDJa0T+4QjQNEpxPnwYOAyh1pjdExDe1x9fDqMfkef+uc4b2nlIx5PA6OHUwiMNIQSZKwu70x+ZLG2fpdXl4OwOOPP86jjz7Kzp07SU5O5qabhqZDBUE4RYC9efNmli5dOuS4vf4P2h//+Mc8/PDDVFZWsnq1rBlYvnw5O3bswDWobBbQGdnjOzBS2qmtqWlYkkN3TrYkG0nLlYO/IQNlFXQ6eUwIwI4nIco7dkcMjB1PJkPlIcWDUTJ1mYXJmCzadNzNzZ7LktwleCUvLxx6YewXnESsS2mC0Yhl7lwgBn5GDbvlgco6Iyxbp+qpB+vXgkOd409n5DxQBV4v+pxsDCpqgaL1vnr5yMs4fU7KMso4I++MYY9RZkbmq2SXoRUJ52sNcXh8zHn4nzG59oEfXIrNFPqvt7y8HIvFwqZNmyj0/1GuX7+eVatW0d7ezrZt2/j617+OKIrcd+/nueHaawI6o9ra2sBrBp8vKSmJl1566RTdUWFhIW63m+bmZkpKSoBgxkhyu0Al80gtiOQmkz8ljZ5WB83VPZTMG8bRdtHN8M4Pof0wHH9XziJFiXjIGCkeK0oHjZo0q+xfNBK3z7md3a27efHQi6ybvw6bMbTMh8ftoq+9DYhdKQ3kTIVj924c+/aSft210buwki2a9ylILVD11IP1a+l5sm9OPLbsD25+ULPMFI3AyCt6ef6gnOm+ZfYtw65/cNY2tzS+A6NExigBIAcya9euHRLgZGTI5oWiKPK1r32Nd999lz179vCLX/+Gzq6uQGeaw+E4ZXTH3r17WbNmzbBibKs/CBo8bFcwGAJdGGIcC7DDEV4rKLvV1pFuyuaU4PiDKLbue5qb8ba2gl4fyBjEAi3dr4OO19rekM+fdD7FycX0unt57dhrIb9O8W+yJCVjTYndh0agMy2aGaPeRqj8u/z4zC+ofnqjxUJyRqb82NSHIEB/l4uB7vi6z2ihL4LBmkjtAqN3TrxD80AzmZZMrph6xbDHKJsTLbO2ahHfq5vgWI16Dvzg0phdezyUl5fz+c8PdZndtm0bRUVFHD16lLlz51JUJP9hXXLJxXzw0cfcWCR7YmRnZ9N1kilceXk5Dz744LDX6uyUNTo5OTlDvq+z2vC53YhO57jWHk0iuckE0/i9SKKEoBtmV7h8ndyZc+Rf0H4UsrWbG6agdMKYZ84MlDRjQcagkockSartmkWfSGutvyOtVFttg16n59Y5t/J/O/6PP1X9ic+UfeYUg7vhGLyrj6UoVckYug4dRnQ4AplcTdnxFIhemHwWFC7W5BIZBUX0d3XS39lCZmESHQ0DtFT3MnVxztgvjhJaBEYel5O+Dn8mUiONkSRJ/LHyjwB8ZuZnMOvNwx4XEF7HeRkNEhkjTREEAZvJEJOv8dxc7XY7R44cwecLtrCKosiGDRu48847aWxsDARFAMXFxTS3tOD1a4wWL17MgQPBFuXe3l5qampYvHj4m1xFRQXFxcVkZw9tHVUcsKW4DozCF8hmFSejN+pw2UcZS5A1DWb6g+kdT4a7zHHh8OvLYqkvAr9/j6DD43Rg7+lW7bwdjQN43SImi56MfO0Dv+umX0eKMYXa3lo+rA/NzTwQcMewjAZgKCjAkJMDPp/cqag1bjvs2ig/Xvlfml0mUKZtaggKsONIZ+RpacXb1AQ6HdZ56mVtu/2aSC0zkeVt5exr34dJZ+LGWTeOeNxEEV5DIjBKAOzbtw+9Xs/GjRv55JNPOHToEGvXrsXhcPDAAw+ccrxOJ2ejfF65Zf/SSy+lsrIykDXau3cver2e+f4xAyezefNmLrnkklPPa43vwEiSpEBgFM7MIb1eR+5kuSNqVI2DIsIuf1Z2AtYYx549ANhGCGSjhcFoJNWfRVRTZ6T8rPOmpA6fpVMZm9EWMHwMtXW/s1FuqY6V8FpBEAQsgXJaFPyM9j4vD1HOKIWy4UswapAxRIA9hnVGDHDsG5S1TUoa4+jQiUYmUskWXTXtKrKtw/sk+XwirbWyRUIiY5RgQlBeXs7MmTN55JFHuO6661i6dClGo5EtW7aQkpJCYWEhDQ3BD6rGpiby83JBkv2M5s+fz5IlS3jxRXlC/N69eykrKztFdwTgdDrZtGkT69ad2nkiWCwgCEg+H1IcCrAdfb24BgYASM8PTyCaO2UUB2yFqRfIzr/uftjz55GPUwHR5cLpz/ZZFy3S9FqhoIXOSBlBEM2d6s2zb0Yv6NnRvIODnQfHPD7WHWmDUUo5muuMRBG2/Vp+vOJeeaiyRgy2ggiUtGv7EMXYDm5WcGrU/BCO59p4qOut450T7wBw2+zbRjyuo74fn0fEbDOQnhu7cn2oJAKjBNx7771UVFSwdu1a6uvr6e/v5/nnnycrS+6cWr58ORUVFTQ0NNDf389bb73F6gvl1nufVxZgP/zww2zYsEHuWrvvPioqKoa91saNG1m+fPkQzyMFQadDZ1G609SbxaYWyk0mJTsHo2n4OvpYKOaCwzpgKwgCnOk3fNz+a/BpFyQ6Kw8geTzos7IwTjrVkC3apGvQst+ktAhPi15glJ+UzyUloRs+Ku+tzBiX0mCo0aOmHHsHOo6AKQUW3aLppTIGldLS820YzXq8Lh+djQOaXjdU7Eo5W3XhtbYB95+q/oSExKqiVUzPGFkPGXSdT4tK1jZSEoFRgjExGAw89thjXHDBBSxatIivf/3r5ObmAsGZaVdeeSX33HPPkMzScBiNRp544okRn1fEv/EZGEV+k1F2q2OOJVhwI9iyZCfgg6F3N40XpYxmXbwoLpxoM1Ru2Xf0uelplb2xoj208rY58g76jeo3aLW3jnicvbcHZ79cZgg3E6km1nlzQafD29yMp2X8RpUhs/WX8n+X3A4WbX83abn5IAi4HQ6cfT3BET3HY68zktxunPvljaR1ibrl7M6Am7r6w2N7XD1sOroJgDvm3DHqsRPFv0ghERglCIk1a9Zw+PBhjh49yj333HOKySPAV77yFSaNkXX43Oc+R1lZ2YjPBwTYp2lglJxhDo4lqB1lLIHJBss+Jz/++OcwTsPOUFGE17Y4KKOB+u7Xyg05szAJs82oyjlDZX7OfBbnLsYrennh4MiGj4FMZFYORvOp5edoo0tKwjxjBqBhOa3lABx/D4RBxqYaYjCZSM2WN3NdzY3k+weYxkNg5Dx4EMnlQp+ejmmMWZPjRctS2kuHX8LhdTAzYyZnFpxaARhMcIBz/AuvIREYJQgTJTDynjRMNlIEJWPk9eIbiI80t0KwIy38m4wgCMGumLHEn8vWgd4MjX5XYJWRJAl7uZIxiq3wWkERyXY3N6kyryu4U43NDVkZE/Li4RdxeId3dY/1jLThUEo6Tq3Kadv82aJZV0FGiTbXOInAaJCmxkBZtflY7AOjYNZ2sapZW0dfL07/QObgIF118Pg8PF8lGzreMfeOUddt73XT2+4EIaixjHcSgVGCsDAMGiarJjqjEcEfdCnT3uMFtYzSlA/pltF0RgDJObDIP5Jlyy8iuuZweBoa8bW1g8EQU2PHwaTm5KLTG/B63PR1tkd8vqZjsU3hXzDpAoqSi+hx9Yxo+NgVJx1pgwkYPZZrkDHqa4Z9cqMGZ92v/vlHIDgapCFQVu1pc2DvjW122r6nHFB/c6IE3MlZ2RiHaYSJhLdq3qLV0UqONYfLSy8f9VjlPpdZkITZOjGsExOBUYKwCJbSPKpP4hb8AmznIG+kWCOJYsCdONIPsMFGj2Oy8j75v4fegPYjEV33ZJSdqmXOHHQq3zjDRafXk5aXDwQD0XDxeQe3CMcmY6TX6bl1tuxm/qcDf0KUTv1bCQivNR7yOR4CnWmVlep3iG7/LfjcMOlMmLRc3XOPwuBZfGabkcxCuS0+luU0SZJw7N4NgG3xIlXPrdX7SpIk/lD5B0DuvjTqRy9RB4XXEyNbBInAKEGY6PR6BJ389vGpfOPUWeSOL2fV2G3O0aKvsx2vx41ObyA1Jzeic+VMTgmMJejvGmMsQfYMmHk5IAXFqioR9C9apOp5IyXYQRRZYNRe528RTjKQnhe7FuHrZlxHsjGZmt4aPmr46JTnuzQUyIaLaepUdMnJSA4HriMqBuSuPtj5tPw4itkigIzCYCkNgsFyLMtp3sZGeRyPwYBl3jxVz61VR9r25u0c6jqE1WDlMzM/M+bxsS5nh0MiMEoQFoIgYAjojNRNRStGj66qKiTfKJ1bUUT5kE7Ly0enj8xvxWQxkFmUDITovqt8gOx9HgYiLy8pBB2vF6l2TjUI6owi60xTbsgFU9Ni2nGXZEzi0zM+DRDYaSuIoi9gTRBPpTRBp8O6QDZoVdXocfefwNkDmdM0NXQcjmDGSNavFUyLvQBbKaNZZs9WffyK0tmp9vtKMXS8Zto1pJlHD3YGj+OZKMJrSARGCSJgcDlNTQSzGQQB0W7HdfSYqucOF7W7OwLltOMhlNNKzoLCJeB1wie/U+X6ot2O89AhIH6E1wpqZYwC+qIo+heNxC2zbwkYPla2B0dt9LW34/N40BsMAdfveMGyQOWBsj4vbPuV/Pis+0AX3Y+f1Jw8BJ0Or9tFf1dnIIPRWtuHz6OuHCBUBttlqI0WGaPj3cfZ3LAZASFgRzEaHQ3+cTxWQ1TG8ajFhA2MOjs7ueWWW0hNTSU9PZ27776b/v7+UY+///77KSsrw2q1MnnyZL70pS/R0xP7roSJil4jAbYgCAEBtnLjiDVq32Tyx6MzEgT5gwTk+Wme4bubxoNjfwX4fBgKCjDm50d8PjUJuF9HEBhJkkTzsW4gPlL4BckFXD5FFqlurNwY+H5gxEx+YWDUTrygugP2gU3QUwe2bFh4kzrnHAd6g4H0Qfq1tFwrlmQjPq9IW90o1hkaotU4HkkU6fLPSVOzVf+PB+Rs0YWTL2Ry6uQxj1eycXmlKRPC2FFhwgZGt9xyC5WVlbz99tv84x//4MMPP+See+4Z8fjGxkYaGxv5yU9+QkVFBb///e956623uPvuu6O46tMLrUppAIJJDrriLTAKZ3jscChT3ltrehF9IexWZ18DaZPB3gF7R/bECZXATjXGg2OHQwmMelqbw9av9Xe5GOhxI+gEckvjQ/R559w7AXi79m3q+uoA6AyUO+JHeK2gBEbu48fxdXdHdjJJgi0/lx8vvweM6paNQiU9UKZtRBCEmPoZiQMDmmVt+zo78Lpd6PR6UnPyVDlnh6Mj0Fl5x9zRDR0VlKxtwfR0VdYQLSZkYFRVVcVbb73F7373O1asWMHZZ5/NE088wQsvvEBj4/C7zHnz5vHyyy9z9dVXM23aNC688ELWr1/Pa6+9hjcO53JNBLQqpUEwMFJ8dmJNMGOkzgdYRr4Ns82A1yPSXj9ypjOA3hCcPr71F/KcqQiIl8Gxw5GcmYXRbEH0+ehpbQ7rHIqgNmdSMkZTfGRiyjLLWFW0ClESAzqNeBReKxgyMwOGg/ZINyjVH0LTXjBYg8alMUDRGSmO0AUx9DPSMmurvK/ScvPRG9Rpkf/Lob/gFt3Mz57PopxFIb2mScnaxkE5ezxMyMBo69atpKenc8YZZwS+d9FFF6HT6di+fXvI5+np6SE1NRXDCG8cl8tFb2/vkK8EQQKBkdeLqHbLvj8w8tSewNvRoeq5x4vP66GnVR6NoFYpTdAJgaGmTUdDvCkvvhXMadBxFA6/Ffa1JUkKCq/jMDASBCFgdtjZUB/WOZritBPmrrl3AbDp6CY6nZ2qB9xqY126BADH7ggDoy3+MUCLb4WkrAhXFT7pBcGMEQTfH03HepA0cpcfCUe5dl2hamsiHV5HwL399rm3h9TM0NfppL/TJd/r4iRrGyoTMjBqbm4OzOpSMBgMZGZm0twc2g6zvb2dH/7wh6OW3x599FHS0tICX2ONu5joPPjgg1x11VUhH6/T6dH5BZSt/t9JTU3NqK+58cYbeeyxx8Y8t6DTYSqVHXGVD/FY0dPagiSKGM0WkjIyVTtvwXTlptwd2gvMKXCG/MHK1vANH93VNfh6ehDMZiyjjGeJJZn+DEpnY3iBUXMcCa8Hszx/OXOy5uD0OXnh4AuaD/mMFNsSOTCy+712wqLlABx9Wx7/oWQ9Y8TJ+rXckhR0egF7r5u+DmdU12IPlLPV35yo/b7adHQTXa4uipKLuGjyRSG9RvkbzC5OxmSZGMaOCnEVGD344IOy8HaUr4MHI/e26e3t5corr2TOnDl873vfG/G4b3/72/T09AS+6urqIr52PFNeXs7CcUx3FgQhIMD+3//9X6655hpKx5j189BDD7F+/fqQRO/mWbOB2OuMlKxFRmGRqm3fhdPD2K2u+DzojFD7MdTvCuu6AWPH+fMCmbl4I5LAyOPyBcqT8ZYxEgSBu+bJwe1fKp+nt70NCP574w2rPzBy7t+PGO78QiVbNPtqyJyq0srCQyml9bQ0IYo+DCY9OZNTgKAeJhpIohhwFdciaxvQRKrwvvKK3oDNxB1z78CgCy3ICeiL4mxzEgpxFRh9/etfp6qqatSvqVOnkp+fT2vr0GnVXq+Xzs5O8seo1fb19XHZZZeRkpLC3//+d4zGkV07zWYzqampQ75OZ8rLy1ngb9ENFb3RiN3h4A9//OOYQnav18u8efOYNm0af/7zn8c8t2W2HBgpXh+xQvlwVvvDK7ckVd6t9vhnCYVCaiHMv15+vPWJsK4bGBwbh2U0hcyi8AOj1ppeJFEiOcNMSmZ8OHoP5qLJF1GUXITYOQCShDkpCWtKfN5bTKWl6DMz5QnwFZVjv+Bkehth/0vy47O+pO7iwiAlOxu9wYDP66XPH5TGQoDtrq5G7OlBsFiwzFI/a9uloqj/7dq3aehvIMOcwbXTrw35dRNVXwRxFhjl5OQwa9asUb9MJhMrV66ku7ubXbuCO+Z3330XURRZsWLFiOfv7e3lkksuwWQy8eqrr2KJkzEI8UBzczMtLS34fD7OPfdcbDYby5YtY//+/aO+zmA08u77H2AymTjzzOCE5ZqaGgRB4MUXX+Scc87BbDbz6quvAnD11Vfzwgtjd1ZZ5siBkXP/fqRwd6sqoGSMlA9rtRi8W20OtZwGwTEhB16BzupxX1fRNsSbseNglCC0q6F+3NqPeNUXKRh0Bu6YewdpA/KmLD2/MKYGlKMhCALWJXIA7dgTRjlt+29A9MDks6D4jLGP1xidTj9oZtpJDthRDIwCXaHz5wesSdRisCYyPcLASJIkNlbI9hI3zb4JqyG0bkK300uHP2tbMC09ojXEgrgKjEJl9uzZXHbZZaxbt44dO3bw8ccfc99993HjjTdS6Ld9b2hoYNasWezYsQMIBkUDAwM8/fTT9Pb20tzcTHNzM744cVeOJeX+LMLjjz/Oo48+ys6dO0lOTuamm0b3G9GbTGzbuZOF8+cP+f5ev/fJj3/8Yx5++GEqKytZvXo1AMuXL2fHjh24XKOPwzAWFaFPT5d3q1VVYf7LIqezUS6hZhaqrzFT2lgbx5PGz58H01aDJI5ba+Tr7sZ15CgQn8JrhfSCQhAEnAP9OPrG1/QwEUYQXDv9WnJdclDsTIvv27BtsV9ntGucgZGzF3b6PZuiPP5jNNIHzUyDYKmno74ftzM6HcoBfZEGf4PdzU1IkojRYiU5IzKh+9amrVR1VmE1WLmpLHTvqZbjvUgSpGRZSM4wR7SGWBDff5Gj8OyzzzJr1ixWr17NFVdcwdlnn82TTz4ZeN7j8XDo0CHsdjsAu3fvZvv27ezfv5/p06dTUFAQ+NJMOyRJ4B6Izdc4d9nl5eVYLBY2bdrEqlWrmDNnDuvXr6eyspL29nauu+46MjIyuP7664e8zmA0Ut/QQG5uzinnS0pK4qWXXuLiiy9m+vTppKXJN6DCwkLcbveYQnlBEAI3DnukXTFhIklSsJSmcsYIgjflkDvTFM7+qvzfPX+G/tbRjx2E8nM0TZ2KIVM9IbnaGE1mUrPlBovOhtD/PiVJmhCBkdVgZYF+OgCVvuNR74gaD7ZAZ9ru8a1z9x/B1QtZM2DmZRqtbvwEndXlclNSupmULAuSFKLhqgooXX5aOF4HMtyFxRFnIp+peAaAT8/4NOmW9JBf1+jPgE9EfRHAxJKKDyIzM5PnnntuxOdLS0uH/BGff/750b/5eOzwvzFqw/1OI5iSQj68vLyctWvXBjJuABkZGQCIosiXv/xlPvvZz/KHPwyd9aQ3mnA6XZiNRnw+L3q9/Jbau3cva9asGVaMbfXPBFKC1tGwLl5M/3vvyROo77oz5H+PWth7unENDIAgBISbaqLcOLqaBnAOeLAkhZhWLz0bis6Ahp1yuWL1wyG9zL5rJwC2pUvDWm80ySwqprethc7GeopnhzZgs6vJjmvAi96oI3tSssYrjIwsh4VW4KiukR3NO1hRMLIMIJZY5sxBMJvxdXfjrq7GPDUEAbXPA9t+LT+OwfiP0QjM4hvkrJ4/NY2+DifNx3qYNEvbDYO3qwt3tVwC16Kc3eHfSGRFuJGr7Khke9N29II+pPEfg2meoMaOCvHzbk0QU8rLy1l00h/ptm3bKCoqIjc3l/PPP5+UlJRTXqfT6cjKyqKntxefO2j0WF5ezvnnnz/stTo7OwFZUzYWNr++wb5nT0x21Uq2KC03D4MGHVzWFFNg8vu4TOYEIZg12vE7uWwRAo6dsi5P8aeJZxSXccUdOhQaj3YD8sgVvSF+b2+SJNHbJGdMe5I8AR1HPCKYTFj9pXJHqG37+1+C3npIyoUFN2q4uvETyBg1BwOjQOY2Cp1pir7INGUKBv/mU02CGe7ISv/Ke/LyKZdTmBz6plD0iTRXy/ejRMYowakYbXLmJlbXDhG73c6RI0eGaK1EUWTDhg3ceeedY75+4YL5vPjXv+L1uDFZrfT29lJTU8PiEernFRUVFBcXk52dPea5LX5xoq+9HXdNDeYpU0L+d6mBkpbOivAmMxoF09LobrHTdKyb0gVj/0wClF0B2WXQfgh2PgNnf2XUw0WHA8eBAwDYzoi9EHYslNJl1zg605r8gVG871TtPd04B/pBEOhPFvm48WMOdR6iLDM+faWsS5Zg37kT+67dpJ9UTj8FUYSPfiY/XvlfYIyvJhdFkNzT2oLP60VvMAQ6p5qP9yD6RHR67YJq+yf+rK1Gf4NK6TmS0n9dbx1v174NELCXCJX2+n68Lh8mq4HMgtCrFvFE/G6pTgcEQS5nxeJrHLXlffv2odfr2bhxI5988gmHDh1i7dq1OBwOHnjggTFff/FFF3HoyFHa/RYKe/fuRa/XM/8kQbbC5s2bueSSS0Jam85sDk753hWeb08kKLsvLUc2FEwPc7eq0wWDoW2/As/oLf+OffvB48GQl4exKD4NBQcT8DIah/u1kjEqjPPASPnwSsvNY/XUiwH4feXvY7ii0RmsMxqTg/+A9sOyS/sZ8TeLMjkjC4PZjCSKge6trKJkTFYDHqcvtBE9EWD338dsZ6hfzpYkaZDGKPzN3B8O/AFREjm76GxmZswc12uV+1j+1LQJNTh2MInAKAHl5eXMnDmTRx55hOuuu46lS5diNBrZsmXLsOWzk1m4aBHz587h5b/9DZADo7KysmHtEJxOJ5s2bWLdunUhr0/Rw9h3xi4w0tKAT2lnbanpxesZZ4fkvOshtRj6W2Dv86MeGtQXLYnb9vDBKMFoT2sL3hDm8Q0ZQTA1Pn2BFDoGZSLvnHcnAG9Wv0ljf4wyzGOgaGHctbV429tHPlCS4KOfyo+XrwNL/P0ehEF6wa4m+feg0wnhN0KMA9Fux+nP2lqXqp8x6u/swONyotPrSc8vCOscHY4ONh3dBMBn53123K9vnsDGjgqJwCgB9957LxUVFaxdu5b6+nr6+/t5/vnnycoKrdXTYDTxtfu+yG+e+h2iKHLfffdRUVEx7LEbN25k+fLlQzyPxsK2TL6B2GORMVIhLT0WablWrClGRK9EW23f+F5sMMniVoCPN4A4cmDl8LdbWyeA8BogKT0Dk9WGJImB2Vaj0XikG5AHx8b7CILg+2oSc7PmsqJgBT7JF7dZI31aGuYZM4AxBsoefx8a98jDYs/8QnQWFwaK/qajPtjxWDgjHQi+j7TAsXcveL3y4Ngi9Zs5FOF1Wl5B2MNjn616FpfPxfzs+ZyRN77gTZKkYDk7ERglON256KKL+MxnPsMbb7xBcXExW7duDTynNxm56IILuOWGtWNaHxiNRp54YnyOzdbFi0Gnw1NXh6elJaz1h4PH5aS3TS4PapkxEgQhkDUKS/y55HawZkBXtWz6OAyS1xsQfU4EfRHIP5dMZZhsCDqjwA3Z/wEXz5yciVw3X86g/u3I32h3jJKRiSHKeBDHaH5Gm/1zEJfeAUnj0MtFmaxiOTAaXKZVdGlNx7o1a/QI6IuWLtUkaxvURIZ3v+p39/PCIdl897PzPjvuNfZ1OBnocaPTCeROib9sYagkAqMEIfHvf/+btrY27HY79fX1rFy5MvCcTqdHp9dzz113UjjGSJbPfe5zlI1zcKk+ORmz3zbfvnPn+BcfJoozriUlFVuqtruf/Ei6YkxJsOJe+fFHPxvWw8p58BCi3Y4uJQXz9OmRLDWqBBywQ+hMa/SXQOJdXwTBnb2SuViev5wF2Qtw+Vz88cAfY7m0EVF0RvaRHLDrd0LNZtAZgu7scYrSTNHRcCLwvdySFPRGHY4+D90tY1uJhIOW+iIYlIkMcyP3l0N/oc/dx5S0KVww6YJxv165f2VPTsFo0oe1hnggERgliBh5mKzsv+P1aDO6Q8lyRFOAHelNZjwoAuzmYz1IYhi71eX3yJ2Izfvg2LunPO3Y7W/TX7IYQT9xblhK4DCWyaOj301X0wAQ/FnGK26Hnf4OOSukfEALgsC6BXLW6C8H/0KPK3rjKUIlMFC28gCiw3HqAZv92qIFN0C6dl2cajD4faVkh/QGHfn+LIcW5TTJ7ZZLaWjYkRZBq77D6wgE5Z+b/zn0uvHfJyby4NjBJAKjBKpgMMoePz6NZprZ/ELFaAqwoyG8VsiZlILBqMM54KErnN2qLROW3ik/VlqlB6H83GwaCD61JCPEUpoimM3It2FNVt9vSk2UcoctLR1LctCE8rzi85iZMRO7185zB0c2r40VxqIiDLm54PXiOHmGYmsVHHodEGDVV2KxvHGRUVCIoNPhdjjo7+oIfD8wosdfllUT54EDSE4n+vR0TNOmqX5+ICKX/r8d+Rudzk6Kkou4fMrlYV1fmfkY75uTsUgERglUQTE/1Cxj5E/juw4fxtfdrck1Tkar4bHDoTfoyC2Vd6tN4d6UV35RLmPUbIa6HYFvS5IUTOFPAGPHwQRa9htHHybbOIH0RUFn4qG7ekEQAlqjZ6uexe7RppwTLvJAWUVndNIG5aPH5f/OvhpyxtfeHQv0BmNgZlq0BNiKDMCqkb7IZR9goEs2zx3vZs7tcwfGf3x23mcx6sY/2NbZ76GjwZ+1nYCDYweTCIwSqIKSMfK6x26rDuv82dmY/ONFojU3LZoZIxjkZxRuu3BaMSz0uwx/8KPAt901Nfg6OhBMJiwjeEvFK0N29p0dIx7X5P8gmwj6otE6HS8uuZjS1FJ6XD28eOjFaC9tTJQSkP2TT4Lf7KqRna4Bzvla9BcVJopAeXCZNm9KKoJOoL/TRW/HMOXCCAhmbbXSF8n3q+SMTMy28RkrvnLsFVrtreRac7l2+rVhXV/ZnGTk27ClxnfWdiwSgVECVdCb5B2Gz+PWrKMj2LavvQBbEsWA4DcaGSOAohnyeICGI13h/wzP/hoIOjj6NjTIIlnFlM+yYD46DcaaaIneYAx4znTUnxj2GLfTS1udbMpXOCEyRiPrQPQ6fcA75g8H/oDL54rq2sbCtnwZAPY95UhK2XzLEyD5YOoFUKj+tHitGE6/ZrIYyJkse7ep6WckiWLA5kC5j6lNR5jWIl7Ry9P7nwZkl2uTPrx7ROPhbgAKZ6o/5iTaJAKjBKqgNxgRBAFJkvB5vZpcQ/HfcURBZ9Tb3obX40anN5CWk6f59UDuTNP5d6t9HaO7WI9I1jSYv1Z+/OFPgEE71SUTw7/oZLKKJwNDSx6DaanuRRIlkjPNpGTG1/iJ4eg8qSPtZK6adhUFSQW0O9r5+5G/R3NpY2KePh19ejqSw4GjohL6WmDPn+Unz/l6bBc3TkZ6XxX6M7dq6oxcR44i9vQg2GxYZs9W7byDCVd4/Wb1mzT0N5BpyeTTMz8d9vUbjnQBUDQBNidjkQiMEqiC3JnmF2Br3ZlWWYlo11Z/oWQnMguL0EWpi8to1pNbKu9WG/y7r7A45+uAIIthm/dr3iKsNVmTlA+w2mGfnyhjQAB8Xg/dLU3AyPP3jDpjYD7VxoqNeERtytPhIOh0wcztJ5/IpqJeJxQvh9KzY7y68RFs2T8pMPJ/sDepqDOy75RLj7ZFCxHCNF4ci+AokNAzRqIk8tT+pwC4bc5tWA3WsK7tHPAERqkUzkwP6xzxRCIwSqAaBn85zatRZ5qxqAhDfr7cFbNvnybXUGivkz+ElV1ltFDS0I2Hu8I/Sc5MmHsdAJ7X1+M5cQIEQTbKnIBkDeNSPJiJMjgWoLu5CUkUMVmtJGeO7Cx/3fTryLJk0TjQyOvHX4/iCsfGtmw5APZtH8vDiwHOf2Bc8xnjASWAcPT2YO8Nls0U4XBXsx17rzr3MkWsbtXQXHWsTORw/Lv231T3VJNiSuHGshvDvnbTsR6QID3PRlKaOezzxAuJwCiBagQF2NoERoIgRG1umnKTUbIV0UJJQ0eUMQI49xsAOD5+HwBzWRn6EObexSOBkkfDiVO0Vz6vSMvxXmBiZIw6BnljjdaZZDFYuGPuHQA8vf9pfKOMeok2AZ3Rrl1IbgcUnQHTVsd4VePHaLGQmpMLDNUZWZKNZBbK4uUmf/t5JEiSpLldxuBMZKgaI0mSAtmiW2bfQrIpeYxXjIyykZsIGr9QSARGCVRDr3HLPgTLQVo7YLfXyaW0aGeM8qfJE6n7Op30tkfQFZM3F2Zfjb1V/p1MlDEgw5FRUIQg6HANDDDQPTST1naiD69HxJJkJKPAFqMVhk5nfeimoWvL1pJqSqWmt4a3a9/WemkhY545E11qCpLbh7PLCOc/OOGyRQpBAfZQnywlyG46ErkA21NXh7e1FYxGrAsXRHy+4ehqbPBnIm0kZ4Q243Jzw2YOdh7EZrBxy6xbIrq+spErOg3KaJAIjBIM4sEHH+Sqq64K67UdHR2UTJ1GXX09XvfInWk33ngjjz32WNhrDAiw9+5FCmHiejhIohgYFRDtwMhkMZBbImd2IvZSOfebDCiB0ezo/jvUxGAyBSaFd9QN7UxTfkYF09M08YZRm5NHgYxGkjGJ2+bcBsCv9/46brJGgk6Hzf8eHXBMgekXxXhF4aO07J+sMyqYoZ4AW8kWWefORWfRpjmg3a+JzJo0OaS/A0mS+O2+3wJwQ9kNpFvSw762y+GlvU4efl04Y+J3pEEiMEowiPLychYuXBjWa9evX8+aNWuYPGkSkigijtCZ9tBDD7F+/Xp6esLbiZmnT0eflobkcOCsrAzrHGPR296K1+VCbzAEWsWjibLraohEZwR4TcW4e2Xdl83xQaTLiinK0M/Bs60gGBhNlBR+QCBbHJoO5JbZt5BqSuV4z3H+WfNPLZcWOgMdJJmPAWB3TJqw2SKAzCJF2D/0faVkjNrr+nA7IuuyVexFtGrTB+jwayKzJ5WEdPyWxi3sa9uHWW/m9rm3R3TtpqPdSBKk5lhJzpj4+iJIBEYJBlFeXs6CBeNP9drtdp5++mk+97nPjTozzev1Mm/ePKZNm8af//znsNYo6HQBAePAjk/GODo8lDJaRmFx1DrSBhMQYEeYMVJM+MzpHgzH/gad1ZEuLWYEW6uDH2CiTwzs6IsmgHeKKPqC2rWi0DJ4KaYUbp8jf3D9Zt9v4iNrtPUJbFlyhsBx8ASSRvYc0SBrhFJacoaF1GwLkhTmYOdB2LfLLvRalrOVe1Z2CBluSZL4ZfkvATlblG3Njujayn3qdCmjQSIwSuCnubmZlpYWfD4f5557LjabjWXLlrH/5JlIw/DGG29gNps588wzA6NBjh09iiAIvPjii5xzzjmYzWZeffVVAK6++mpeeOGFsNeatMLfFbN9e9jnGA3lwzfaZTSFAr/OqLfdSV9nmH5GgH2H/4Y8I1c24Pvop2otMeoM5znTeqIPj9OH2WYguzh84Wi06GlpxutxYzCaSM/PD/l1t8y+hTRzGtU91bxZ86aGKwwBeyfseApzmhedzYI4MICzqiq2a4oAJXPX19GG2zHUAkTZoESSufU0NOCprwe9HquGcwoVK4usEDJGmxs2s799Pxa9JWALEQkBfdEEydqGQiIwSgDI2SKAxx9/nEcffZSdO3eSnJzMTTfdNOZrN2/ezFK/9kfpTCvfI5/vxz/+MQ8//DCVlZWsXi13rixfvpwdO3bgcoXn6mtbsQIA++7dQfddFVECo1B2X1ow2H03krb9AX9glHTFrfI3yp+H7uHdo+OdwRkjRb8WcNqdkY6gi/9yjmIBkVk8Cd04Jpcnm5K5Y47cofbbvb/FK8YwQ7P1l+DuRyhcgG3FSgDsGmVuo4E1OQVbWjpwataoWClpH4rgb9CfLbLMm4s+eXxjOkLF43bR3dwMjF1KG5wtumnWTRFni9xOL20n/PqiCZC1DZVEYKQhkiRh99hj8jXekRLl5eVYLBY2bdrEqlWrmDNnDuvXr6eyspK6ujrOP/985syZw4IFC3jppZeGvLa2tpbCQlmLYzDJNea9+/aSlJTESy+9xMUXX8z06dNJS5MFjYWFhbjdbpr9f8zjxTxjxiD33YqwzjEaHYOEjLEiqDPqDuv13vZ23EePgSBgu/xmmHIeiB748MfqLTKKZBTKnWnO/j7sPd1A8ANrIpTRIBgYhaoDGczNs28m3ZxOTW8Nb1bHKGtk74TtsmCX8x7Atszftr9jxygvin+UoLv9JJ1RUZn8vmo70YcrTJ2RktVOWr4ighWOTmdDPZIkYhkU5I3E+3Xvc6DjAFaDlTvn3RnxtZuP9SCJEilZlgnhOh8q2lhwJgDA4XWw4jnt/iBGY/vN27EZQ29fLi8vZ+3atYEAByAjQ74xiKLI448/zqJFi2hubmbp0qVcccUVJCXJOyCHw4HF322hlNIqKipYs2YNpf7Br4OxWmV3VXuY7tWCTodt+XL6/vUv7Nu3Y1ui3sR4uSPNrwOJUcYI5CzInn+dCDuNH9AXlZWhT0+HC/4bqj+APc/Cqq/Io0MmEEaTmbS8PLqbm+ior8OSkkajX/uhfIDFOwEdSBiBUZIxiTvm3sGG3Rv47b7fcvmUyzHoonz73vZrcPdB3nyYdSU23wHA72fk8yHEQI+nBtmTS6ir3Ef7iZoh30/OsJCWa6Wn1UHjkW6mLBhfdkWSpEDWVslya0Egwz2pZNSONEmS+NXeXwFw86ybybRkRnzthtNQXwSJjFECP+Xl5SxatGjI97Zt20ZRURElJSWB5/Lz88nOzqazszNwXHZ2Nl1d8ge43ijPTKuoquKcc84Z9lrKa3NycsJer82vM1JS1WrR0xbsSEvPK1D13OOhcHo6gkDYOqPADdlvxsfkFTDjEllr9MH/U3OpUWOw0WNrTR9elw9LkpGsQm1KFGoz3s6hk7lp1k2km9Op7a3ljeo31Fza2Di6YPtv5MfnfQsEAcvsWeiSkxH7+3FWHYzuelQke1IpEMzoDUYJuhsOjn+D4qmrw9vUBEYjtiXauc53hOjS/+6JdwO+RXfOvVOVawfL2RNjcxIqiYyRhlgNVrbfrI1AOJRrh4rdbufIkSP4fMGOF1EU2bBhA3feeeeQY3ft2oXP52PSpGC78eLFiwNdZoIgYHe5qKtvYP7cOcNer6KiguLiYrKzw69vJ515JgCOPXsQ3W7VpsYrIsbMGHWkKZisss6otbaPxiPdlK0IXawLQd1H0uCd6gXfgSP/gn0vwtlfg9xZai5Zc7KKJnFs53Y66k7g8ylltImhL/J5PXQ1NQChCWSHI8mYxJ1z7+Tx3Y/z272/5YopV0Qva/Txz8HVC3nzYJbsdSbo9ViXLmHggw+xf/IJ1nlzo7MWlVEC1eECo+KZGRzY3Eh9GJnbAX8ZzbpgATqbduajoZRoRUnkl3tlbdGtc26NyLdIwePy0Voju84nMkYJQkYQBGxGW0y+xmN2t2/fPvR6PRs3buSTTz7h0KFDrF27FofDwQMPPBA4rrOzk9tvv50nn3xyyOsvvfRSKisrA1mjqsNH0Ov1zJoxY9jrbd68mUsuuSSMn2gQ09Sp6HOykVwuHH7huBooXU/hfnipSbhdMd72dtzH/PqipYMGxxYuhtlXAxK8/78qrjQ6KL+TjoZgiXGilNG6GhsQfT5MVhspWeFvCG6adRMZ5gxO9J3gH8f/oeIKR6G/NZgtuuC/QRf82Eha7u8Q/WTiCrCz/VrCga5OHH29Q55T3l8d9f04+8dnKKu06StdtFoRiiby7dq3OdJ1hGRjcsD+IVKaj/cgihLJmWZSsk4ffREkAqMEyGW0mTNn8sgjj3DdddexdOlSjEYjW7ZsIcU/X8vlcnHttdfy4IMPctZZZw15/fz581myZAkvvvgiAFWHDjFtyhSMulPfXk6nk02bNrFu3bqI1iwIAknKMEsVy2mhpqWjgbILaxynAFsRw5pnzZL1RYM5/zuAAAdegaa9Ea8xmgSGydadoNmvL5ook7wH7+ojcei2GW2BFuvf7v0tHlEb9/chbP4peOxQtBTKLh+6HkWAvXMnki8OPJbCwGS1kZabB5yaNbKlmsgokEu1DUdC36BIkhQQXts0FF67nQ56WluAke9ZPtHHr8t/DcBtc24jzZymyrXrleaHGRkTwnV+PCQCowTce++9VFRUsHbtWurr6+nv7+f5558nK0ueuSNJEnfeeScXXnght91227DnePjhh9mwYQOiKPLFL36R9998Hc8wJo8bN25k+fLlnOkvhUVCoG1fRT+j9jjoSFMo8OuMetoc9HeFrjMa2LoNCO7mh5A3B+ZfLz9+b2JljTKLJyEIOhx9vXhcfVhTjGQWTAx9USTC65O5oewGMi2Z1PfX8+rRVyM+36j01MPOp+XHF373FJdry5w5ss6otxfngYnrZ6RkI08WYMOgtv1x6Izc1TV429oQTCasixepsMLhUWbv2dLSsaUOH/D8q/ZfHOs5RoophVvn3Kratev9P4/i2RMjazseEoFRgjH5+OOP+ctf/sKmTZtYtGgRixYtOsX48corr+See+6hoaEh0JnmG2ZmmtFo5IknnlBlXUqK2rF3L6IzfCNEBUkUA14moToTa4nZaiCnJBWAuqrQb8oDW7cCkLTqrOEPOO9BEPRw+C2omzglEKPJTHqB3DUp+topmjlxdqpKJkKNEq3NaOPueXcD8gw1pzfy9/6IfPAj8Lmh5GyYev4pTwsGQ2CDorzvJiI5k0sBaD8xjAB7lvzBXz+OzK19h19ftGgROrN2YzKCmcjh71de0cuvyuVOtDvm3EGqKVWV6zoHPLTVymXH4rLIu9vijURglGBMzj77bERRpLy8PPA1f/78U477yle+wqRJk9Ab5M40SZLwnTTo9XOf+xxlZWWqrMtYUoIhLw/J48Gxe3fE5+tpbcHrdqE3GsflTKwlk5Sb8sHOMY6UcdfVyU67BsNQfdFgsqfDIr9x53v/o8Yyo4byASb52iaMvggi70g7mRtm3UB+Uj4t9hb+cugvqpzzFDqOwR7/6J7Vp2aLFJJWykaPA1u3aLOOKJA1igC7aEYGCNDVNIC9NzRDWUV4bdNYXxTMcA//vnrt2GvU9NaQZk7jltm3qHbdxsPyfLSMfNtpMx9tMInAKIHqCIIQyBoNNzNNzeso3Wlq7FbbTsizxLKKJo/LmVhLJs2Wd2N1B7tCMu0c2CL/HKyLFqJLGqXMdO63QGeE4+9D9WY1lhoVMgvlnbHoa2PSBEnhe5xOulv9zsST1QmMzHoz/7XwvwD43f7f0efuU+W8Q3j//2R7h+kXw+SRS99JZ8mBkWPXblUyt7EgZ1BgdPLfmSXZSFaRPHKm/tDYGxRJFLEr5Wx/0KgVQZf+U99XLp8r4HK9bv46kk3qjc1RNmrFs06/bBEkAqMEGqE4YHvd4Y39CBWlXDTwceS71bZaOTDKKZkS8bnUIn9qGgajDkevm87GgTGPD5TRxrohZ5TAUnnMBO+th3E6pccKwSB7X+noIC1HuxZoNeloqANJGlUHEg5XT7uaKWlT6HZ184fKP6h2XgBaDsB+v8P9hQ+NeqhpyhQ5c+t2q5K5jQUZhUXo9AbcDjt9HW2nPK9kbkMpaTsPVOHr7kaXlIR1mMy6moxWon3h4Au02FvIs+Vx46wbVb1unaIvmjUxNifjJREYJdCEQMZIg1lmg1ECAGdVFd6u8GcaQXwGRnqjjkL/cMa6qtF3q/JOVQmMRtAXDeacb4DBAie2wpG3I11qVLD3yl2SPk8Hvgky1X0sHUi4GHQG7l98PwB/PPBHOhwd6p383f8BJJi9BgoXjXqoIAiDymkTU2ekNxjJLCwChtcZTZojZ0bqqzrHzNwObJE3abYVKxCMRpVXGsQ50E9/RzsAWcWThjzX5+7jqf1PAfDFRV/ErFev3NXX6aS7xY4gnH7+RQqJwCiBJkQrMDLk5GCeORMkKRAUhEs8BkYQTFfXj9EV46yqwtfT49+pzhv7xKkFsNxvm/DvR0CM/3brlloAE5Lko6uxfqzD4wI1hdcnc9Hki5ibNReH1xH4IIyYE9vg0Osg6MbMFiko5TSllDsRyfbr19qG6UwrnJ6O3qCjv8tFd8voo4yUwCjprBA2JxHQXlsDQEp2DpakoWWyjRUb6XH1MDVtKldPu1rV6yr3odzSVMw27QK/WJIIjBJoQrCU5kYURU2vpdyA+reEX05z2e0BP5CcklI1lqUak+b4jR6PdOPzjvyzVAJD2/Lloe9Uz/4aWNKg9QDsfSHitWrJQLeL7mY7gkE2SBzuAyweUVt4PRhBEPjyki8D8OKhF2nsb4zshJIE//qu/HjxbZATWqOEza/1cx44EHHmNlYov5+OYQTYBpOegulyGfTEgZEzt6LDgWPXLkD7wKi19jgAuaVTh3y/3dHOn6tk0fyXFn9JdXd0RWd1upbRIBEYJdAIvcEQGKmheTlN0Rlt2RKSQHk4FP+S5MwsrCnqtLSqRVZhMtYUI16Xj5bq3hGPU3br4xJ82jLhnK/Lj99bDx5HJEvVlDq/4DMpTW7ZnyiBkfLeyhpGIKsGKwtXsiJ/BR7RExDbhs3Bf0D9DjBY4fxvh/wyY24u5hnT5cytyvMLo4UijB/OywiCjRD1o5S07Tt3IXk8GAoKME0pVXuJQxgpw/3bvb/F4XWwIHsBF06+UNVrSpJEfZWiLzo9hdeQCIwSaIjRHB0Btu2MMxCMRryNTbhrasI6R7yW0QAEnUBxmSL+HP6mLLpc2AM71XF2wiz/PKRNgt6G4OiHOET5t+dOkX9H7f7fWTxj7+mmv6sTBEHTTKSSNXrt2Gsc6jwU3kl8Hvj39+THZ90nl1rHgW2C64yUYbIdDfXD6teUwKjh8MiZ22AZbaXmHlutNf6MUUkwY1TXW8dfD/8VgK8s/Yrqa+j0WxYYjDryp8bXBlJNEoFRAs0IlNNc2gZGOqsVq9+zZyDMclo8B0YAxcpudQQ/I8eePUguF4acHEzTpo3v5EaLPAMLYPPPwB6aZ1I0GbxTnbJIHn47ETJGyodXRn4hJkvog53Hy/yc+VxWehkSEj/Z+ZPwMqe7/wgdR8GWBWd9adwvDwiwIyhpx5LUnFyMFiuiz0t386klyexiOXPrcfloqe4Z9hzKvz151SpN1+rzegOt+jmDSmk/3/NzvJKXVYWrWJa/TPXrKn+DBdPTMBjjw9JECxKBUQLNMPgzRh6NM0YQrOeH27Yf74GRslttqenD5Th1Nzvw8cdABDvVBWvlyemuHtj8WERr1YLORv9O1aSjbIU8xb2/s+OUoZ/xhhIY5ZykA9GCLy/5MkadkW1N2/i48ePxvdjVL/sWAZz3AFjGnw2wLVsOBgOeujrcJ06M+/WxRhCEQDmtdZhs5NDM7ak6Km9bG65Dh+ThzRr7F3U11uPzeDBZraTl5AJQ3lrOWzVvISDw1aVf1eS6JyrlzsfJc7M0OX+8kAiMEmiGcZAAO1ztT6gogZF9+3Ykz/gGa4qij7a6GiB+A6OUTAvpeTYkURpW49D/oWzSmHT2OeFdQKeHi74vP97xJHSdKkCNJUoZrXBGOtbUZNLyZGfykfQg8UKg3BGFwKg4pZibZ90MwGM7H8MrjsPOYOsvYaAVMqbA0rvCur4+OQnb4sUA9G+eOKahg8ktlbOtrdXHhn1eadsfToCtlBAts2djyNBWmNw6aCMn6HRIksSPd/4YgGunX0tZpjrTBQbjdftoONINwOQ5icAoQYKw0Bv9o0FE8ZTRIGpjmTMbfXo64sAAjpPmuI1Fd3MzXpcLg9FERn6hRiuMnMlz5ZtybeVQvxpPS0tgp5p0dgQp/OmrYcq58mysd38YyVJVp87/QaRkzpTRIG1xrjOKZmAEsG7BOtLMaRztPsqmo5tCe1FfC2z5ufx49XfBYAr7+knnyoH5wIcTMzDKmzJGYOR//7XV9uIcGHpPU7LVI84oVJFghlt+X/2z5p/sa9uH1WDlvsX3aXLNhsPd+DwiyRlmMgomhrlquCQCowQBHnzwQa666qqwXtvR0UFubi41g8TP8miQoQLsG2+8kcceU79UI+h0wbb9ce5W25VRIJNKAp108UiJP319onKoydyA/99rWTA/sp2qIMDFPwQE2fU4TgbMelw+GvwDPJUUfvZkObMXzzojj9NJV1MDEL3AKM2cxr0L7gXgF3t+gd0zuucOAO/+ANz9ULgE5lwX0fWTzz0XkGeFiRprC7VA+T211hwfNsudnGEhI9+GJA31FZNEkX6lnK2xvkhZH8gZI5fPxeO7Hwfgrnl3kWvL1eSagTLavKwJM7w5XBKBUYIA5eXlLFy4MKzXrl+/nmuuuYbS0tIh3zeY5d2nojN66KGHWL9+PT09w4sXIyH5PPmm3P/BB+N6XbzrixQKZ6ZjMOoY6HbR0RAcD9K/+SMAksMtow25yCJY5B82+daDoLEHVSg0HOrC5xVJyZI/lCDoNdXmN7mLR9pOVIMkkZSeQVJ69Dxfbii7gUkpk+hwdrCxcuPoBzeWw55n5ceX/R/oIvtIMM+ciSE3F8npxL5zZ0TnigXK5sjZ30df+6mjQSAYnA/O3DorD+Brb0eXlIRtyRJN1yhJEm2DMpHPVT1HQ38DubZc7phzh2bXVf69Jad5GQ0SgVGCQZSXl7NgwYJxv85ut/P0009z9913n/JcQGfkcuP1epk3bx7Tpk3jz3/+c8TrPZmks88GQcB1oApPS2vIr2udIIGRwagPTJRXdm+S1xvshDlXhcAI5HKKKRkadgbnZcWQ2gr/DXnQTlUppXXU1SL64tOxu7VGfl9FK1ukYNQbA+Lb31f8npaBluEPlCR469uABPOuh8krIr62IAgknXM2MDHLaQajMeBQ3lIzfDmtZJ4/MKroQBLlrFL/h/JmLOmssxBM4ZciQ2GgqxNHXy+CTocuJ4Un9z0JyGaONqM2Ja6eNjs9rQ50OuG0NnZUSARGCQBobm6mpaUFn8/Hueeei81mY9myZewPQa/zxhtvYDabOfPM4ATumpoaBEFg02v/4JobbyK/dAqvvvoqAFdffTUvvKC+y7IhKwuLf2jjwEeh35SVjFFunAdGMGi36g8WHOXliH196NPTscwLYQxIKKTkwzlfkx//+3vgHnt4rVZIkhTcqc4L7lTT8wowWa14PW55SGsc0ur/YI1GR9rJXDT5IhbnLsbpcwbKLKdwYBOc2CKbOV78fdWunXyOP3M7YQXY/nJa9fFhny+cno7RrMfR66atrg+A/g8/BIJZay1RHK8zC4t56sDT9Hv6mZ05W/XRH4M5USlr/PKnpWGyquukHY8kAiMNkSQJ0W6Pydd4u8DKy8sBePzxx3n00UfZuXMnycnJ3HTTTWO+dvPmzSz1+wgp7N27F4CfbdjA1+67j/ffeJ3zzz8PgOXLl7Njxw5cGmgQFI1D/wcfhnS8s78/kDJXZiXFMyXzZPFn87Ee3A5vsBtt1SoENfVRZ34R0kugrxE+ely9846TrmY7fR1O9AZdIFsGsqZM6SBqOX40VssblWC5Y5y+UiogCAIPLHsAAYF/HP8He1r3DD3A44B/PSw/XvVlSCtW7dpJZ60EvR738eO46xtUO2+0CAqwh39f6Y26QNaktqIDb2cnzn3yBjLpHO0DozZ/JtJSkM1Lh+WM7jeXfROdoN3HebBN//R1ux7M6R/6xRDJ4eDQkqVjH6gBZbt3IdhCT6uWl5djsVjYtGkThYVyZ9b69etZtWoV7e3tXHbZZXi9XrxeL1/+8pdZt25d4LW1tbWB1ww+X1JSEi+99BJJOvB5PCT5De4KCwtxu900NzdTUqLumITk886l/Re/YODjj5E8njFnhikixtScXCzJyaMeGw+k5dhIy7XS0+qg7mAngj8zploZTcFogUt+CC/eLncsLbkN0tWdDh8KSmasaGY6RtPQwC9v6nTqqypoOX6EeedfFPW1jYbo8wWmtOeWxiYTOTd7Lp+a8SlePvIyj25/lOevfB69zv8z3PoL6DkBqUVyYKQi+tRUrIsW4di1i4GPNmO68UZVz681gZb9muEzRgCl87Op3ttObUUHM337QZIwz56NMU8b4fNglNL/Lg7hk3ysnrxaEzNHBZ9HpP6QLDQ/3f2LFBIZowSAHMisXbt2SICT4e9w8vl8fPjhh5SXl7N9+3b+93//l46OoPDQ4XBgsViGnG/v3r2sWbOG0tLSQX5GcobIapUDJLs9hI6ZcWKZOxd9ZibiwAD23XvGPL7l+BFA/pCdKCjdaTU7G3AdqAL8+iq1mb0GSs4GrzM4KiLKKIHR5Hmn3pCV31k8Zow6G+vxetwYLVbS88Y3WkNNvrTkS6QYU6jqrOLlIy/L3+xtkh3OAS76HpjU16UknyMH6v0TUGeUUzoFBIH+zg7sPd3DHqMECC01vXS8vw0IZqu1RslE7uM4Zr2Zby77pqbXazzajdctYks1kV0c/5tHNZiwGaPOzk7uv/9+XnvtNXQ6HZ/+9KfZsGEDySHs+iVJ4oorruCtt97i73//O9dee60maxSsVsp279Lk3KFcezyUl5fz+c9/fsj3tm3bRlFREXl5eYHvuVwuJEkaUqrLzs6m66SJ2uXl5Tz44IOA3wF7oD8QGHV2yvXqnJycca0xFASdjuRzzqHnlVfo//ADklYsH/X45mNyYJQ/babqa9GKyfOy2PdePbUVHRQA1rlzMWRpsJMTBLjsUfjtuVDxMiz7HJRo79Gi4HZ4aTraDQSDwcHkTZ0ByKUF0eeLK6uFwe3UQoSdXpGQacnki4u/yP/t+D+e2PMEl5ZeStq/vweeASheBvM/o8l1k845m7bHH2dg2zZEtxudxoJkNTFZrGQUFNHVWE9r9TFKF52a9U/OMJM9KZn2un5OHOgkj+joizxOJ13+cSWdqW7unn8vRclFml6zdn+wjHa6t+krTNiM0S233EJlZSVvv/02//jHP/jwww+55557Qnrt448/HpVfsCAI6Gy2mHyN599nt9s5cuQIvkHdPaIosmHDBu68804Auru7WbhwIcXFxXzzm98kOzs7cOzixYs5cOBA4P97e3upqalhsd8FVxkm6/FriioqKiguLh5yDjUZT9u+EhhNpIxR0Qy5bd/h0tGfXEzyeedpd7GCBbD0Tvnx61+XB41GifqDXYg+ibQcK+l5p2Y1MvIHCbDr42sERbSNHUfjhrIbmJ4+nW5XN7/48L9h3wuAAJf9Pzn41QDL7NkYcnKQ7Hbs27drcg0tUX5vLSMYPUIwWG+zTUWXloY1jI7e8dJSfRQkiQGzl6ysAu6aG55LeahIkkT1PlmDOWWB+hvZeGVCBkZVVVW89dZb/O53v2PFihWcffbZPPHEE7zwwgs0Np46/G8w5eXlPPbYYzzzzDNRWm38s2/fPvR6PRs3buSTTz7h0KFDrF27FofDwQMPPABAeno6e/fupbq6mueee46WlmAL8KWXXkplZWUga7R37170ej3z/R1iysw0r9uN6POxefNmLrnkEs3+PUmrVoFOh/vosVHFn/beHnrb5H/HRAqMDCY9xWVpALRnzSd59YXaXnD1w/Jg0dYDsP032l5rELUV7cDQbrTBCDodeVPis5zW5u9Ii4fAyKAz8OByOXv7YsMHHDIa5WC3WDv9o6DTkXyh/L7se+cdza6jFQEB9ig6o5L58sauM2MOtrPORjBoX4A5UCEHme3pbh5Y9gAWg2WMV0RGZ+MAve1y84MyDuU/gQkZGG3dupX09HTOOOOMwPcuuugidDod20fZndjtdm6++WZ++ctfkp+fP+Z1XC4Xvb29Q75OR8rLy5k5cyaPPPII1113HUuXLsVoNLJlyxZSUlKGHJuXl8fChQvZPKgVd/78+SxZsoQXX3wRkAOjsrKygO5Irzeg94ug+3p72LRp0xDxttro09KwKjOb3n9/xOOUD9OMgkIsSROrdl5glYPQ9oKlWObM0fZitky4+Afy4/cehR7tO41EUaJ6nz8wmj9ymTDXH9A2x1FgJIliINMQD4ERwIqCFVycNAVRgEdzc5Eu/K7m10zxB+z9776HFAdGoeMhKMAeOWOUNyUVo+jAa7ThWHC+5muSJIktu98CIHlyAedP0v6ayt9g8ewMjOb4KVVrzYQMjJqbm8nNHar+NxgMt7ZJUAAARtRJREFUZGZm0tzcPOLrvvrVr3LWWWdxzTXXhHSdRx99lLS0tMDXpEmTIlp3vHLvvfdSUVHB2rVrqa+vp7+/n+eff54sv26lpaWFvj7Zr6Onp4cPP/yQsrKhQwoffvhhNmzYgCiK3HfffVRUVAx5XimnbXzmGZYvXz7E80gLUgK71X+PeExLoIw2Q9O1aEHG8Y9AEumzFNDfFYXRCwtvhklnytqUf35b88u1HO/B0efBZDVQNHNkQzkl09caR4FRV3MjroEBDEZT/FhA9NTzzaO7sIoiu0x6NjWGZmcRCbYVKxBsNrytrTgrKzW/nprkTpED2u7mJlz24X28vPV1ZLbJbfotxlLN1/Re3XvQJG/Orz3n9qjIQar3yoHRlAXayB7ilbgKjB588EEEQRj16+DBg2Gd+9VXX+Xdd9/l8ccfD/k13/72t+np6Ql81dXFp5Gc1tTW1nLOOeewcOFCzjnnHO6///5AmUzhyiuv5J577qGhYfhsgtEsZ490wBNPPKH1kkm5aDUA9h2f4OvuHvaY5uOK8HpiBUaSKOL54G3SeuW2XeXmpSk6HVz5GAh6OPAKHBk54FSD43uDZTS9YeTbVL4SGNUex+cdxzR5DWk6cgiA3CnT0EehvBISbz1IgbOfL5AOwGO7HqPTeeqEeDXRmc0k+7sl+959V9NrqY01JZWUbFlTM1I5re/f75DTJvu11RzsHbd33HgY8Azwk82PkuKQM+8L52vQhXryNXtctNbIgVhpIjCKHV//+tepqqoa9Wvq1Knk5+fT2jp05IPX66Wzs3PEEtm7777LsWPHSE9Px2AwYPDfsD796U9z/vnnD/sas9lMamrqkK//RJYvX055eTl79+5l3759p3SvKXzlK18ZMaumBEY3Xf/pU7JNWmAqKcE8Ywb4fCOKsAMZowkWGDn37cPX3k5ur7xJqN47/Ewn1cmfB2d+QX78xjfA49TkMpIkcbxc/jdNXTS64FN2wLbh83jiRoDddPQwAAUz4qTT8fC/oOo1EPTcetmvKMsoo8fVw2M71R/mfDKBcto7EyswAsj3Z5Kb/b/Pk+l75x2yOg+g10n0tjvpaOjXbC1P7HkCsbEbgPTCIsy2JM2upVDjL6PllqaSlGbW/HrxRFwFRjk5OcyaNWvUL5PJxMqVK+nu7mbXrmAr/LvvvosoiqxYMfy8nwcffJB9+/ZRXl4e+AL42c9+xsaNYwxaTBAxigDb5/VGbWefcrFs+tf371OzG/2dHfR3dSIIOvJi4EwcCX3+D5mSGXKnVuPhblz2KHWLnf8gpBRAVzV89DNNLtHZNEBvmwO9QTem066g08Wdn1HzUTljlD9d+w3AmHgc8Kbf5+bML2AsWMjDKx9GQODVY6+yvUnbjrHk884DvR7X4cO46+s1vZbaFMycBUDj4VOrFN72dhy7d6MX3RTPkHWYx/dos0HZ37af56qeI7tHvocWRslaRNEXTVn4n5UtgjgLjEJl9uzZXHbZZaxbt44dO3bw8ccfc99993HjjTcGDAobGhqYNWsWO3bsACA/P5958+YN+QKYPHkyU6bE/4ysiY5Op8NgUtr2tck0nEzKRXJg1L/5I0SHY8hzSpt+VvEkjBZtOzvURilL5K9eQUa+DVGUAkaImmNOkb2NAD76KbSGV9oejeryoODTZBm7FBVPgZHH7QrM3iuIh8Do/UehqwZSCuWgFliQs4Abym4A4IfbfojLp51GTZ+eHpg23z/ButMKZsi/v6YjB08pk/W9+y5IEpZ585i2Qs6SHy9Xv6TtET18b+v3kJCY65avkz9d+8DI4/JRXyU3ePyn6YtgggZGAM8++yyzZs1i9erVXHHFFZx99tk8+eSTgec9Hg+HDh3SxF05QXgE/YyiExiZZ8/GWFiI5HQGJtArBB2vJ1YZzV1Tg/vYMTAYSD7vXKYslEtNUdEZKcy5FmZeBj43vPJFENWdbq+UBqcuDM03JRgYHVF1HeHQWn0c0efDlpZOao724yFGpWE3bPHr+a76qRzU+vnSki+RY82htreWp/Y9pekyFDuJvnff0/Q6apM3ZRo6vZ6B7q7APEUFxYIg5aLVTFmQjaAT6Gjop6fNMdypwuaPlX/kcNdh0k3ppPglYdEIjOoOdOLziqRmW8gs1L5sF29M2MAoMzOT5557jr6+Pnp6enjmmWeGuF6XlpYiSdKI+iGQtQxauV4nOBUlM+NxRqGLCtlgM9kvwu57e2g5Leh4PbECI+WGbFt2BvrUVKYskndztRUd+DxRaokWBLjqZ2BOhYadqnob9XU6aa3tAyF0wacSGLXVVuPzRs+AcjiCZbSZsXUJ9rrhlftAEmHe9VB2+ZCnU0wpAW+jpyue5lj3yG3pkZKy2t8IsXMn3pMc8uMZo9lCTolcTWg8EsyM+vr7sW/ZCshZaUuykcIZsq+Yoo1Tg7reOn6999cAfGX653H19aHTG8gp0d4C4uhuWcM7ZWHOf4zb9WAmbGCUYOJhDBg9OjXt4BhMoJz23ntIfm2TJEkB35uJFhj1vin7mKT6DTLzSlKxpZnwuHzUVWnbZTSE1EJ5yCzAOz+EzpGN8MaDIvgsmJqGLTW0MRLpeQVYUlLxeb2jGvJFA6UjLeZltI9+Bq2VsjHn5f9v2EMuLrmYc4vPxSt6+e7H38UraqP9M02ahHn2bPD56Hv7bU2uoRUFM2SdkfJ7BRjYvBnJ48FUWoppmqxPVJoEqlUKjCRJ4gfbfoDL52JFwQrmeuQBzjklUzCMMRg7UrxuX+DvcPrSGGc9Y0QiMEoQNQwmM4IgIPpEfJ7o7OxtS5agT0/H19ODfedOAHrbWnD29aLTG8gumTj6MveJEzgrKkCnI8UfGAk6gelL5JvXkV0to71cfZbcAVPOBa8DXv0SqBDsHhu0Uw0VQRAo9OtBGg+pr3kaD4GOtFgGRq1V8OGP5ceX/wiShs+8CYLAd8/8LinGFPa37+f3lb/XbEmpl8sZq94339TsGlqgvK+aBgmwlexzykWrA9kU5f3adLwHe6874uu+fORltjVtw6w38/CZDwcz3FEoo52o7MTj8pGcaSZvyn9mJ3YiMEoQNQRBCHSnRUtnJBgMgXJa7xvyTVnpMonG7ktNet/6JwC2FcuHDI2dfoY85Le6vB2vW129z6gIAlz9czBYoWYz7P5DRKcb6HbRcKQbgGlLxzeXSdnZDy55RBt7T7c8YkYQyJ8eo0yk6JNLaKIHyq6AeZ8e9fD8pHweWC6P/flV+a840qWNTiv18ssAsG/fgbcjSo0CKqC8r1prjuH1eBDtdvrek7VSKRdfHDguJdNCbkkKSHB8T+uw5wqV+r56fvyJHNjev/h+JqdODlgGFEQhMDrq32BNX5L7H1lGg0RglCDKKH5GykDZaJB2xRUA9P3zn0huN42HqwAoKpsdtTWogbLbVnbfCvlTUknOMONx+aitjPKHTuYUWO0fL/Gv70JP+C3ZR3e1ggT5U9NIzbKO67WF/tbqpmFaq6NFk19flFlYHBWfmWHZ9itZ92VO9Rtyjv3BtmbaGs4rPg+P6OGhjx/CI6qfzTVNmoRl3jwQRfr+9S/Vz68VaXn5WFPT5DJt9VH63nsPyeHAOGkSlpOGxk7zl50OfxJ+5laURB76+CHsXjtL85Zy25zbEH0+eXgs2pf+PW4f1fvle8j0pXmaXiueSQRGCaJKUIAdnYwRyKMJ9NnZ+Hp66N+yJVBuKSzTeMaYiriqq3FVVYFeP2SnCv5ymv+mfHRnZLvVsFhxLxQvA1cvbPoChDkX68hO+QNlxrLx6xpksbOOvo42+jqj2KE3iKYjMS6jtVTKei+AS/5H1oGFgCAIPLLyEVJNqRzoOMDT+5/WZHmBctobE6ecJgjCoLb9Q/S+/gYAqVdccUo2ZYY/c9t0tIe+zvDub89WPcuull1YDVZ+uOqH6AQdbSdq8LpcmKxWMgqLIvjXjE3t/g68Lp+cAStNGfsFpymJwChBVDEpGSO3EzFKgyUFvZ7Uy+RUfsdrrwV8ZgrLZkXl+mrQ95Ysuk5auRJDxqmzw5RyWs3+djyuKJbTAHR6uO63YLRB9Yew7ZfjPkVvu4OW6l4EAaYtGX9gZLJYyZ5cAsQua6RkjGLieO1xwsvrwOeSrRSW3D6ul+fYcvjOiu8A8Nu9v+Vgp/o/w9TLLgXk7jRPawwC+DAp9JfTGg7sp98/PDv1yitOOS4l00LhjHQgGOSPh+M9x9mwewMA3zjjG0xKkX2LGg4ekNcxczY6nbaDXI/ukn8v05f+55bRIBEYJRjEgw8+yFVXXRXWazs6OsjNzaWmpmbU42657TZ+u/H3IEU3a6TcyOq3bUGSRFJzcknJnDjGZcou++QymkJuSQqp2Ra8bpGa/THImGRNCxo/vvMDaN4/rpcrHyRFZRlhjx8oDDgVV4X1+kgQRV9ABxITx+t3fyh3oSXlwJpfhFRCO5krplzB6smr8Upe/vuj/1bd+NFYVIR14UKQJPr+OXHKaQH9WmUFeDyYZ8zAMnP44HfGMnmDcmSc5TSv6OW/N8s/81WFq/jMzM8Enms4JAdGRbPmhrP8kPG4fNT67x3Tz/jP7EZTSARGCQKUl5ezcOHCsF67fv16rrnmGkpLS0c97qGHHuLxX/6K3r4+PE51zdBGw7poEcaiIjoN8gdG4cyJoy9yHT2K68gRMBoDw3FPRhCEQNZovDdl1VhyB5RdKRs/vrxuXLPUjnwi71SVckQ4KB8c9VUHwj5HuLTV1uB22DFZbeSUlEb34sffh62/kB+v+QUkj0+4riAIAg+d+RCZlkwOdx3mpzt/qt4a/aReMfG60/KnTUcQdAw4BnAa9KReeeWIx05bkoNOJ9Be109n00DI13hq/1NUdFSQYkrh+2d9P5CtkSSJxoOVABTN0rb0X7O/Ha9HNnXMmfyfW0aDRGCUYBDl5eUsOElQGAp2u52nn36au+++e9TjvF4v8+bNY+qUKby86RXcUcwYCYJA6hVX0JUkl/IKJ5Dwuuf11wFIPuss9GlpIx43w7/LO1HZicsRg0nzggBrfg5JudBWBf/+Xkgv62wcoKOhH51eYOri8D7UIRgYtVYfw+2IruN9Q1WFvIYy7csdQ7B3wt/9g33P+CyUXRbR6bKt2fzPqv8B4LmDz/HeCXXdqlMuuwwEAcfu3XgaGlQ9t1aYrDay/NqeriTLsGU0BWuyiUn++X6hblB2Nu/kN3tlk9TvrPgOeUnBzUFvWwv9XZ3o9AbNhdeHtjcDcln+P7mMBonAKIGf5uZmWlpa8Pl8nHvuudhsNpYtW8b+/WOXRN544w3MZjNnnnlm4Hs1NTUIgsCLL77IOeecg9ls5tVXXwXgqquuYtPrr+NxRc/oESDp8svosvkDo8kTw79I8vno2fQKAGnXrBn12KyiZDLybfi8IkfD0DioQlI2XPsr+fH2X8PRsedjKWW0yXMysSSFb5+Qmp1DWm4ekiTSeCi65bT6Kv+ufva86F1UkuAfX4G+RsiaAZesV+W05xSfw+1zZI3Sd7d8l+aBZlXOC2DMy8PmH/TdvWmTaufVmhyjfN/oKS3GNGnSqMfOGJS5Hev+1uXs4oEPH0CURNZMW8NVU4dKGZT3Vd7UaYGOXi0Y6HFxwj9vcdaZ+ZpdZ6KQCIwSAHK2CODxxx/n0UcfZefOnSQnJ3PTTTeN+drNmzezdOnSId/bu3cvAD/+8Y95+OGHqaysZLV/NMCZK1dSvm8fTocTbxTb9rsNAj69DqPXh6ki+uWWcBjYtg1vUxO61FSSVw9fRlMQBIFZZxUAcHBrUzSWNzwzLoZl6+THf78X+kb+YJVEiUPb5OcVfUYkFPsDk3p/+SEaSJIUuF5xNAOj3X+AA6+AzgCfehJMNtVO/ZUlX2FO1hx6XD18e/O38ak4Dy/9U9cB0PP3TUhRasCIlNTqEwB0poxtwzBlYTYGo46eNgetNX0jHqe05rc6WilNLeW/V/z3Kcc0BMpo2uqLDm1vRpIgf2oqGfn/ebPRTiYRGGmIJEl4XL6YfI03E1NeXo7FYmHTpk2sWrWKOXPmsH79eiorK2lvlwV5drudkpISvvGNbwx5bW1tLYWFhaecLykpiZdeeomLL76Y6dOnk+YvAxUVFeF2e2htb8PtjF7Jo/6AXO7I7HfQ8/LfonbdSOj5298BSLvqSnTmsUXJZSvyEXQCzcd7x6VxUJ1Lfgi5c2GgFV66C3zDe+PUH+yir9OJ2WYIjFWIhKDOKHqBUWdjPY7eHgxGE/nTpkfnok374I1vyY8v/C4ULVH19Ea9kR+d+yNsBhs7W3by5P4nx35RiKRcfDG65GQ89fXYP9mp2nm1wnnoMMkH5I7D7r4e7L09ox5vshiY4n8vj7ZB+dOBP/Fh/YeYdCZ+ct5PsBlPDWzrKuWM/aQ588Nd/phIksTBrfLmZNbKAs2uM5EwxHoBpzNet8iTX/4gJte+Z8N5GM2hax3Ky8tZu3btkAAnw98WrrTVr1+/fki5TMHhcGCxDE3z7t27lzVr1gwrxrZarYHXuR0OktJDXmZE1B+QbzJZDjeO2nJcR45gnhG/s9J8vb30/VseP5B23adCek1SmpmSeVnU7Gvn4JYmzvp0lD6oT8ZohbV/hCfPhxNb4J3vy946J3Hg40YAZi7Lw2CKXJtTPFsOjJqPHsLjdmE0hdfhNh6UgDt/xkz0hig4qTt74KU7gq35Z31Jk8uUpJbw0JkP8Z2PvsNv9v6GZXnLOCP/jIjPq7NaSb38crpfeomev/2NpBXLVVitdnS//FfMXh+peiO9Pg8NVZXMWHHWqK+ZvaqAI5+0cHhHM2d9evop9+J9bft4fNfjADyw/AHKMk/tZOxtb6W7pQlBp9M0Y9Ra20dX0wB6oy7QwPGfTiJjlACQA6NFixYN+d62bdsoKioiNzeXI0eOcPDgQS4fpl08OzubrpOmZpeXl3P++ecPe63OTnnYaVZmJm6nE0nSPp3u83pp8OtOJs2Vd1/df/2r5teNhN433kByueT24Hmh3xhnK+W07c34fDEsVWRPD+qNtjwBVa8NedrZ7+H4Xnno5uyzQzMjHIv0/EKSM7Pweb00HoyOzuhEhVw2njw3vI7OcSFJ8Or98tDetElw7a9Bp91t/OppV7Nm2hpESeQbH3yDVrs6/kNp/nJa77/+ha8/hpnNMRBdLnpfkbWRStam7sDYusvimRmkZltwO30BbyCFHlcP3/rwW3glL5eUXDKkNX8wSrYof+oMzDb1yqQno2S1pi7KwWxN5EogkTHSFINJxz0bzovZtUPFbrdz5MgRfL6gjkAURTZs2MCdd94JwDe+8Q1+/OMfs2XLllNev3jxYv785z8H/r+3t5eamhoWL1487PUqKiooLi4mJycH0efD45RdXbWk5fhRPE4HluQUSm64ifr3PqRn0yvkfP3r6EyhTXGPNt1KGe1TnxpXl0jJ/CysKUYcvW5OVHYyZUEM/ZrmrIGV98nt5Jv+C3LnyJ5HyLoG0SuRMzmFnEnqtAcLgkDJ/EVUfvAOtRXllCxYpMp5R0ISxWBgNF/bawFygHngFdAZ4TO/B1um5pf87xX/TVVnFUe6jvC197/Gxks3YtRHlhmzLlqEacoU3NXV9L31JunXX6/SatWl7+1/4+vpwVBQwJQLL6Jy/27qKveN+TpBJzDn7EK2bTrOgY8aA5sVn+jjWx9+i4b+BoqSi/jeWd8b8W9beV9Nmjf+TuFQ8Xp8ge45ZY0JEhkjTREEAaNZH5Ov8XyQ7tu3D71ez8aNG/nkk084dOgQa9euxeFw8MADD/DKK68wc+ZMZo5ganbppZdSWVkZyBrt3bsXvV7P/PnD18U3b97MJZdcgskiB0PuKPgZ1e7bA8DkuQtIPuccDHl58ogQf6kq3nAdPYpz3z4wGEhbc/W4XqvX6yhbIXeWVPlLVTHlou/B5JXyyJAXbwe3HUmSAmU0tW/ISoByYn+5qucdjtaa4zj7+zBZrZq3U3P0Hfj3I/Ljyx6F4sjLWqFgM9rYcP4GUkwp7G3by//75P9FfE5BEAJZI2UDEI8oWeX0T32KSfMWgiDQXldLf1fnmK+dtbLAr/froaOxH4Cf7/k5Wxq3YNFb2HCB/DMdDkmSgvqiudoFRtV723HZvSRnmCkqO9VR/z+VRGCUgPLycmbOnMkjjzzCddddx9KlSzEajWzZsoWUlBS2bdvGCy+8QGlpKd/4xjd46qmn+MEPfhB4/fz581myZAkvvvgiIAdGZWVlp+iOAJxOJ5s2bWLdunWYrHJ6OBqeMzX+wKhk4WIEvZ70T8uanXgtp3X5f5bJ552HIStr3K9XutNq93cw0BO9zr9h0Rvh+o2yK3NLBbzyX7TW9NLZKOsaZi5XV9cweZ5c0mqpPoajr1fVc59MrT/4Kp4zH71BwwR853H462dBEmHxrbDsc9pdaxgmpU7i/875PwD+cugv/P1I5MFM2pprQKfDsXu3bGAaZ7hPnMC+bRsIAumfug5bahp5U2TNnrLRGo2kNDOl8+W/3aqPmnir5i2eqXgGgB+s+sGwuiKFrqZG+jra0OkNmg67rvhA9pKatbIAne4/27toMInAKAH33nsvFRUVrF27lvr6evr7+3n++efJ8n8gP/roo9TV1VFTU8NPfvIT1q1bx8MPPzzkHA8//DAbNmxAFEXuu+8+Kioqhr3Wxo0bWb58OWeeeSYmm5wx8jidiD7t5nu57AM0HZFnP5UukLt30j71aRAEBrZsxV1Xp9m1w8HX3x/omsu48cawzpFVmEz+1FREUaJycxxkjVIL4DN/kEtAlX/nwEuy8/G0JTmYbeoKlpMzMskqngySFFLZIxKUckeJlmU0Vx88fzM4u+VhvVf+NKyRH5FybvG5/Nei/wLgB1t/wCfNn0R0PmNeLil+C4rOP/15jKOjT7f/bzBp1SqMRbLBY+lCWR4QSmAEMMevnavcWs/3Nn8fgLvm3cXlU4Yf7aNQs3cXAMWz52jmX9RW10fjkW50OoG552g7nHaikQiMEqjClVdeyT333EPDGG62RqORJ554AgCD0YTBaESSJE3LaScq9yGJIhmFxaTmyO7QpuIiklauBKDruec1u3Y49Pzt74gDA5imTiXp7FVhn2fBhbIRXcUH9fg8ceAXU7oKrvopDjGVQ8dl6watbshKoFJdvluT84Mc0Nf7Ha81C4x8HnjxDtlJPDkf1v4JDNp32o3EvQvu5bLSy/BKXr76/lep7a2N6HyZt98GQM+rr+Lr7lZhheogOp10v/QSwBD9k7Kxqt1fHpIH0+S5WVjTDHgdEoUtZawqXMWXF395zNdVl8uBUeki7cql+9+rB+TNSXJG7N5T8UgiMEowLu68805+8pOfDPvcV77yFSaN4Qr7uc99jrKyYArZZJPNxFx27TpTavfKH46lC4aKwTP8N+XuF1/E1zeyEVs0kUSRTr+QPfO2WyOy5p+2WL7hOfo8YU371oQlt1OR9Qg+zOQaj1JgOqzJZaYslj9Qqst3auaufqJyLz6Ph9ScXDKLRn/fh4Ukwetfh2PvgMEKNz0nZ95iiCAI/HDVD5mfPZ8eVw/3vXMfPa7RfX1Gw3rGGZhnz0ZyOunyByLxQM+rr+Lr7MRQWDBkPmHBzDKMFiv2nm5aa6vHPI/dO0BF3kcALGu9jB+d+yP0Y4yM8bhd1Pv1RVMWqutPpeDod3N4h3xPUDZQCYIkAqMEMUVpQ3Xb7Zp8gEmSxPHdsolc6Uk3meRzz8U0bRriwADdL8WH1qj//Q/wnDiBLjWVtGuuiehcOr2O+ecXA1D+Tl1Ux6+MhNfjY3+9HBgvsr2C8PwN0K6+vqR4znyMZgsDXZ20Vh9T/fwAx3fLpaSpS5ZpM1vq48dld2sEuP5pKFo61iuigsVg4ecX/pz8pHxqemv40rtfwukNb+6hIAhk3iZvULqefQ7JM7wRaDSRRJHOjb8HIPP22xEGacf0BiOT/V1i1btHLyV6RA/f+PAbfJj6Cl6dm9TeXHqqx55hWH+gAq/HTXJWNlmTSsL/h4zCgY8a8XlFcktSyJuSqsk1JjKJwChBTDFarAiCgM/rxet2q37+1prj9HW0YTCbT2l7FXQ6Mu+8A4DOP/0pLm7KnX/6IyCn73UqeJfMObsQg0lHR30/jYe7Iz5fpBze0YKjz0Nyhomp01zg6IQ/fQp61R1hYjAaA636x8f4AAsHSZI4vkcOuKcuXqb6+dn7QnAI7+X/D2aNPNE9FmRbs/nl6l+SYkxhd+tuvvnBN/GK4Q0uTr3yCvSZmXibmwOGprGk/4MPcFdXo0tOHtZGYNpSedbb0Z3bRzyHKIk8/PHDfNzwMYJFpGS5XDouf/vEmNev9r+vpixaqknA7fOJAdH1gguK/+MHxg5HIjBKEFN0Ol2gO02LctqxndsAuYw2nAty2po16LOy8DY10fvPf6l+/fHgPHwY+9ZtoNORecvNqpzTkmRk1ply+WXvu7EVmUuSxN535DUsuGAy+lv+AlnToecE/PnT4OhW9XpTl8iOysf3qB8YtdVW09/RLgfcardTV70mez4BnPlFWPF5dc+vEjMzZvLE6icw6828X/8+P9j6g7CykjqzmYwbbwCg849/UnuZ40bJFqXfsBZ9cvIpz09dsgwEgZbjR+jrbD/leUmS+H87/h//OP4P9IKen5z3Ey64chGCACcqO+lo6B/x2pIkcfQT+Z6lScANHN/TRn+XC2uKkelLE07Xw5EIjBLEHHOSX2c0MPINI1yO7dwBwLQzTh1lAv6bsj8I6XzmmZiWmzqf2QhAyurVgS4YNVhwoVxOq97XTndL9GbTnUzdgU46GwcwmvXMObsAkrLg1pchOQ9aK+XgyKlee72iM2o+epj+zg7VzgtwbJecLZg8byEGNQ1Cj73nb8v3waJbhh2jEk8szVvKj8/9MTpBx9+P/p0f7/xxWH9D6TfeCEYjjj17sO8OreNLCxwVldh37ACDIVDiO5mk9AwKZsjl4OO7dpzy/G/2/obnDj4HwP+c/T+cN+k80nKsTF0sN36MljVqOX6Uvo42jGYLJQuHN8iNBEmS2P1PWTA/79wi9MZECDAciZ9KgpijBEYelwuviuWs3vZWWmuOIQg6eZc3Ahk33YRgseA8cAD79pHT41rirquj5zV5ZEbWOnU9ajLyk2Q/FQl2vVWj6rnHw+5/yTfkOasKgy36GaVw29/BmgENO+HZ6+X2dBVIzsikYOYsAA5vP9WxPRIOb5UFtTOWjz4za1zUboEXbgGfG2avgat/rum4D7W4YPIFfG/l9wB5MOpPd/103MGRMTeX9GtlTV37r3+t9hJDpvMZ2Wco9YrLMebnj3hcoJzmz+4oPLXvKX61Vx6D8+3l3+aqqVcFnlt88WQADn/SQn/X8JqsIzvk9+mURUs1mfNXW9FBe10/RrOeBRckRNcjEf9/dQlOe/R6Q2AkiJpZo0P+D6/CstnYUtNGPM6QkUH6p2TDx/Zf/DImWaOOJ58En4+ks8/GukB9p9szrpwCwKHtLfS0RT9r1HCoi4ZD3ej0AgtWFw99Mm8u3LYJLGlQtx2eXQsudd4HZWeeA8DhbZtVOR9AR0Md7XW16PQGpo+QiRw31R/KGTPPAEy7ED79O9BPnIlN1824ju+e+V0Afl/5ex7f/fi4/46y7rkH9HoGNm/GsU9b/6nhcB09Su+bsr9W1l13jXrsjOWy1ceJir0BE9Hf7P0NP9/zcwC+tPhL3Dx7aDk8b0oqhTPSEX0Se/41fNbo6I6tAEwfY0htOEiSxM43agCYd14RluQoDDyeoCQCowRxgSVJruU7VQyMDn78AQCzVo09ry7rnnUIJhP2nTuxb92q2hpCwX3iBN1/3wRA9n99QZNr5JWmMnluFpIYvDlGC0mS2PEPubV5zqpCUrOGmYtXuEjOHJlT4cQW+NN14Og69bhxMvNM2Qeq4VCVauW0w9vkgLtkwSIsw2hQxs3Rd+DZz4DHDtMvghufi6lXUbisLVvLd1Z8B4BnKp7hJzt/Mq7gyDRpEmlXyRmWtid+ockaR6PtF78ESSLl4ouwzB7dbTqzsJic0qmIPh+Ht33Er8p/xS/LfwnAl5d8mXUL1g37ujOuLAWgYnMDfZ1Ds0ZtJ2robKxHpzcwdbH6/kU1+ztoqe5Fb9Sx6KLJqp//dCIRGCWIC8z+wMjjdKrSndbZ2EBr9TF0en3gw3E0jPn5pN8gC0BbN2yIataobcPPwesl6eyzsS3RxrcEYNlVpQAc2tYcmN0UDeqqOmWHXYPA0stHaT8uWioHR5Y0qN8Bv78K+iLzX0rJypbLaZLE4e0fR3QukIO8Q1vk7NPMM8+O+HxUvQbP3wReJ8y8DG54FozaDlTWkptm3cS3l38bgD8e+CPf/fi74+pWy/6vL4DBwMDmzQxsP1W/oxXOqir63noLBIHs++4P6TWz/Ruut996ll/vlct/X136VT43f+RSeHFZBkUz0xG9EjtfH+qDdODDdwGYuuQMzH5/N7UQRYltm2TbioUXFmNLjc/B2fFCIjBKEBfoDYaAp5Ea3WlKtqhk/qJRy2iDyb5nHYLVinPvPvkmGQWcBw7Q+/rrAOR+7auaXit/ShrTFucgSbDt79p4+5yMKEpsefkoAPPPLSY5Y4zxBsVnwF1vyoLslgrYeBl0jm2kNxqzzjoXgMr334noPCCLYzvqT6A3GiMvo21/Ev5yG/hcMOsq2dXaqM34h2hy8+yb+Z9V/4Ne0PPKsVf46vtfDdnnyFRSQsbazwDQ+thjUdmgSJJEy//7EQCpl1+OpWz4YdknM3WF//df343Noedby77FZ+d9dtTXCILAimumAVC1pSnQoSaKPqo+eh+AOedeGMa/YnSO7Gims3EAs83A4ku08UY6nUgERgniBkuKbDTmsttl198wkUSRAx/KH4KhlNEUDDk5ZH3ubgBaf/IYokvb4auSJNHyv48CkHrllVjmzNH0egBnXjsNQSdQs7+DuoNjTwiPlINbm+hokG/IShlhTPLmysFR+mR5eOrvVsvC5DCZffb56A0GWmuO0RKh2WPFe28Dsug67DKaKMLbj8Cb3wQkWHqXPEfOcPrs4q+Zfg0/O/9nmHQm3q97n7v/eTdt9raQXpv9hS8g2Gw49+2j9x//0HahQP/772Pftg3BZCLna18L6TU9rh6+Vf4wzRlOBAT+y/gpbpszfBfbyRRMS2Oqf4Py8V+PIEkSJ/bvZaCrE0tyClNUbtN3O71s8W+EFl8yGUtSQls0FonAKEGABx98kKuuumrsA4eho6OD3NxcampqRj3uxhtv5LHHHhv2ObMtCUGnw+f1RNSdVrNvDz2tLZiTkpgxThFj1mc/iyEvD09DAx1PPx32GkKh9/U3sO/ciWCxkPv10G7IkZKeZ2PeebIVwOYXDuPzajdDzTngCaTvz7iidHw35Kxp8Nl/QcEisHfAH9ZA+XNhrcOaksq0ZbJYVglswsHjdgUykfMuuDi8kzh74S+3yq7WABd+F6762YQSWofKBZMv4LcX/5ZUUyr72vdx0+s3caDjwJivM+TkkH3PPQC0/OhH+Pq1K/uKTict//d/AGTecQem4rFtMo52HeWm129iR/MOakvlsr97Tw2iGPog7LM+NR2dQaCuqouafe2B92XZWediMKobuOx6sxZ7j5vUbAsLVyc60UIhERglCFBeXs7ChQvDeu369eu55pprKC0tHfW4hx56iPXr19PTc+p8JZ1OhzX5/7d353FRluvjxz8zw76LgiyKICqJ+4orLpBbaZ40rTyFy7fMtJNZli1qnXPM49HvqWOa+DuZ/jplpuWaZZpLmguiNoQouCAiIAKy78PM8/1jiDRhBERn0Ov9evmHw/M8c80tzlxzP9d93c4AlJfUf1PZmD3GlSUdQsPqvDO12t4ez9fnAnA9cjVll+7sNk5N9Pn5ZCxZAkCzF6Zj7eNzV56nOiGjA7B3tiYnvRjtj7fvxFtfR7dcpKRARxNvx6qtSerExds4cxT8GBh0sHUGfP8GVNR9Jq/T4HAAzv68H11Z/bavOHf0Z8qKi3DxaI5ffZo6Zp6D/wyFhJ2gsYWxkRD6GtzHnYd7evVk/SPr8Xfx51rxNSK+j+DbxNvPArlPnYJ1Kz/0mVlkLl9+1+LLioxEdzkZK09Pmk5//rbH703ey6TvJnGl4Ao+jj68O/lj7BydyM/MICmm9hsWu3rY0zXMWAC9//OTVcv0Ow0dVr8XUoPrqYVV/8cHPNEWK2vT+7QJI0mMRBWtVkvneiwVLy4uZs2aNUybNs3kcRUVFXTs2JHAwEA+r9wo9Y8cXN2Mx5aXUXC9dlPvN8rPyqhqutY5fGSdzwdwGTUKxwEDUMrLSV+wsFa7aNfVtcX/oCIzE5tWrXC/zdLghmbrYE3/cW0AiP42iey0hu84npKQw5mf0wAYPCkIjVU932psHGD8Ogg1JqtERcKaYXWuO/Lr3BVXz+aUFRVx+kDdt51QFIWT324BoHPYcFR16S+kKBDzlTEpun4eXHxh6vfQ9ak6x9EYtXJpxRePfEF/n/6U6kt589CbzD88n2JdzW0j1DY2eL1jXP6f89/PKT55ssHjKk1I4PoaY9+i5u+8XW2X69+U6ctYcnwJs/fPpriimN5evdnw6AaCvTrSYbBxk9mY3d/V6fl7PuKPSzM78jOiMej1+D7UgeYBgfV/QX9g0BvY99lZDHoF/87N8O/crMGufb+TxEgAkJ6ezrVr19Dr9YSGhuLg4ECvXr2IjY297bnfffcdtra29OnzezFqUlISKpWKjRs3MnDgQGxtbdm+fTsAo0ePZsOGDdVey8rGBms746qcs4f21/l1RG/fjKIYaNmhM01b1G/aWKVS4fXuQlT29hRHR5O9dm29rlOTgn37yduyBVQqvBe/j9r23i/NbhfiRauOTdFXGPhx3Rn0+oZL/kqLdOxdZ7xl0mGgDz5t3O7sgmo1DH0Hnt5obAR5VQurQ437idWyFk2t1tDj0T8BcPLbLRj0tb/tAXA55hSZyUlY29rR+eE6JNwlOcZO1lueh/ICaDUAnv/JYjaEvVdcbFxYEbaCGV1moELF1gtbeXLnkyZvrTkNHIDr44+DopD21lsYihougTeUlpL22lzQ6XAKC8P54ZpvjV7IucDTO5/m87PGL3N/bv9nIh+OpIldEwA6h48ClYrEU9FkXq59wm5to2HAhNboy4w9m1p2GnIHr+hWp35IJuNyATb2Vgx6Kkj2RKsDSYwEYJwtAvjwww9ZvHgxJ06cwMnJiaeeuv232kOHDtGjx81v9DExMQAsXbqUBQsWEBcXR1iY8ZtV7969OX78OGU1FDc7OBtvp8Uf+ZnCnNoXCBfmZBO77wcA+jw+sdbnVcemRQuav2Vcdpzx4b8pqUWCWBu61FTS3jRe1z0i4q4uzzdFpVIx5M8PYetgRWZyAUc3N8wqNUVROPBFPIU5Zbh62NOvcmaqQbQbDi/8DC16Q1k+bJkO6ydAXkqtTu84OBw7ZxfyMq5V9SKqregd3wDQKWx41e1ekxQF4nfCx/0gbjOoNDDkHXh2Gzh51Om57xdWaite7Poia4avwdPek0t5l3h659P86+S/aly11nzeG1h5eaG7nMzVBQsbbJVaxj+XUnb+PJpmzfD+63vVJg3l+nJWx6xm4rcTOZdzDnc7d1aGreSN3m9grf69Dsjdx5egytYNxzZ/Vac4si4fAaUE1C7EH7OnKK9hFnyknc/l+I5EAAZOaItTk8bXF8ucJDG6ixRFQVdaapY/dX0D0Wq12NnZsXXrVvr3709wcDCLFi0iLi6OrKws/P396dy5M127dmXIkJu/2Vy+fBmfP9TIaLVaHB0d2bRpEw8//DBt2rTB1dW4bN7Hx4fy8nLS09OrjcXazh6NtTV6XXmd3miit32NXqfDp137BtnY0238eOM3SZ2OlFkvUZFZ91t7NzKUlJAy+xUMeXnYdeqEx11enn87jm62DH3G2MguZu8Vzp+4s55BAKd+uMzFU5moNSrCpwZjY9fARcWuLWDKdxC2ADQ2cH43rOwDRz66be2Rta0d3UeMBuDwV5/XusD/kvYkyad/Ra2xoseox25/Qk4SfPkkbHgaCtLAPRCm7YFBc+/LIuu66uXVi01jNjHcfzh6Rc/a02sZt30ch1IO3fK+pXFxwfd/l4FGQ/7OneR8/sUdP3/uN9+Qs95YyO/z/iKsmja95Zjo9GjG7xjPCu0Kyg3lDPAdwDdjviG0RWi11wyp/CJ2LuowmclJtYqjrLiI41s3AeDmPYjSQj27VsdSoavbbOYfFeaU8sMnp1EUCOrjRVCfmrc2EdWT/6V3UUVZGcsjxpvluf/y/7/G2q72hcdarZYJEybclOA0aWKcKjZU1tgcOXIEp2ruw5eUlGD3h+eKiYlhzJgx1RZj21du/1FcXH2NgUqlqto/LXbvLrqPHI27j+ni3czkJLS7jf2A+o5/qkGmjVUqFd7vL6IsMZHyixe58uJM/NZ+arIWoSZKRQWpr75GaWwsaldXfD/4AHVDbj5aT627edB9uB+nfkhm77qzOLjY4NuuSb2udf7ENY5tq/yWOrEdXgG16x9VZxprGPiqsffPtpmQEg2734HoTyD8PWOxdg3//j0eeYyYPd+Re+0q2l076Dn6cZNPZdDrOfDZJwB0G/EoLh6eNR9clAU/f2CMo6IU1NbQ7yVjgbVNwzbsa+zc7dxZNmgZjwQ8wt+P/Z3kgmRe3PsiIV4hzOk5h+Cmv7eucOjRA89XXyXjn//k2vvvY+XVHBcTt75MKTp6lKvvvgdAs1mzcAq9OdFJyE5ghXYFB64cAKCpXVNe7/U6IwNGmnxP8fDzp11If85FHWbvmlVMXLj4tnVox7duorSwAHefFjz22tNsXvYL6Yn57PssnvApwajVdX8PKyup4NsVMRTnlePu40jok+3kFlo9yIyRAIyJUdeuXW967NixY/j6+uLpaeLDAGjWrBk5OTdv36DVahk8eHC1x2dnG2+PeXjUfEvBytoG3/YdMej17Fr5gcmaEMVgYM9/VmDQ62nbux/+XRru9pTG2ZmWH69E4+pKaWwsV56fjr6wbrUOik5H2rw3Kdy3D5WNDS0/XlmrZcH3SshjgQR0aYa+wsB3H/9K2oXcOl8j8ZdMfvz0DCjQaZAvHUPvwevzCIKpP8CYFcaGkDlJsCkCIgfArxtBf2vHZRt7BwY8FQHA0W82kHut+lnL30Tv2Ex26hXsnV3oM+7J6g8qSIcf34MPO8PRFcakKCAUZhyB8IWSFJkwxG8IW8duJSI4Amu1NVHpUUz8diIv73uZXzJ+qZpBcp8yGbcJE4z1Rq++RsG+utcfFkUd58qMF0Gnw3nEiJu234m7HsfrB1/niR1PcODKAdQqNRODJrL9T9sZ1XpUrZKLQc9Mw8rWltT4OE7/ZLrAP/3COaJ3bAZg4NOTcfdxZvjzHVGpVZyPvsb+z85iMNRt1r+0SMf2f2u5nlqEg6sNj87q0vAztg8IlWKOHTMbqfz8fFxdXcnLy8PFxeWmn5WWlnLp0iUCAgKqZk8URaHiLjcJrImVrW2tvykUFxfj7OzMkiVLeO211wDjLFH37t159NFH+fvf/05AQADu7u6o1Wpmz57NpEmTqs5ftmwZn3/+eVWdUn5+Pm5ubkRFRdGr163NytasWcO7777LlStXqo3nt7H0cHNlw1uvUFZcRN/xT9HviUnVHv/zhs+I2rIRazt7pvxrFc5NG371RUlcHMlTpmLIz8e2XTtarvoYa9/bf/jrc3NJnfs6RYcOgZUVvh/8q97fdu+mCp2eHctjSDufi8ZaTfjkYNr0MJ0Qg/F3/Nd9KZWN6iAoxIuwiPao6vFt946UFcLhf8PRlcaNWAFc/aD7s9B5AjT5vduvYjCwYeEbpJ07S/PWbXjyr0ur7R2TcvY0G//6ForBwPAXXr65d5HBYNzTLfoT47Yev2174d3VWCjeJvy+XoZ/N6QWprL81HK+u/T76q7OzTozvt14wluF46S2J/WVVyjY8yNoNHjNn4/bxAm1ep/L27aNq+/MR9HpcBwUSouPPqJMrWd/8n6+jP8Sbaa26tgR/iN4seuLBLgG1Pk1RO/YzMHPP8Xazp6n/vpPPFrdeo2y4iLWv/0q2WkpBPUL5dGXX6/62fkT19jz6RkUg4J/p6aET+2Arf3tk5vca8V8vzrW2N3a0YrHZnfDo2UtauEeIKY+v/9IEqM6qGti1FgcO3aM0NBQ2rZty7p163BxceHtt98mNjaWEydO4OzsTGpqKr6+vly9epXw8HC+/PLLqqX9sbGxdO/enYyMDJo0acKhQ4cYOnQoBQUF1Y7F5MmT0Wg0rKmhgeKNY3kx6jC7Pv4AgCGTp9N95Oiq4xRFQbt7J/s+jQRg5Mw5d6Wd/m9KYk9zZcYM9FlZqF1c8Jz7Gm6PP45Kc2tvEEVRKNx/gPS//Y2Kq1dR2drSYvm/cRpU+07c95quXM/u/5wmKda42Wr7ft70GRtY475KBdmlHPwyoer44P7eDHo6CLXGjBPRJTnGZOVYJBRn/f54q/7GvcgCh0DzjuRfz+K/816mtCCfwJ4hPPKXuTf1vEq/cI7NS96jJD+P9gOHMHLmHFS6YrgSZSyqjt8JBVd/v37LEOj3F3joEUmI7lBibiKfnfmM7Re3ozMY68Bs1DYMajmIQd4D6Pj/DlC+09gQ0XnYMJrPe6PGPmAV169z7R9LyN+xw3idIQM5P/tR9lz9iUOphyipMPZLs1JbMdx/OJM7TOYh94fqHbtBr+frRfO5Evcrzk09mLDgfdy8vKt+Xl5SzNfvL+DquXgcm7gTsWzlLcX8F09lsGftGfQ6Ay7N7Ah9KohWHW6tgzI+n4EzP6dxZMtFdKV6HFxsGPNyV5r6NsDmxvcZSYzukvs1MYqMjGTFihUsWLCAOXPmkJuby+jRo1mxYgVNqylMnDt3Lh06dGDy5MlVj4WEhDB16lSmT5/OihUriIyM5PTp07ecW1paipeXF7t27bppef8fj7lxLH/e8F+ithiLsNv1GUCXh0cB8OveXSQcOQgYV6H1n1i7lvx3QpeWRspfXqa08rVZt/LD7fFxOPTojsa9KYb8PEp+jSVvxw5KK1ey2bRqhc+//hf7Dh3uenx3yqA3ELU9kVO7k0EBK1sN7Xo3x79jU1w87FEMkJNeRNKvWVw4kYHBoKC2UtF3bCBdwlpaTj2DrgTitkLMl3DpIHDD25yjB3h3Iancl60/JqHXG/Dw8SJk1Ahc3ZuQGBtL9N6fqCjX4enpwsShHthcOwXX4kC54ZaujTN0fBx6/Q9433mxv7hZVkkWm89vZmfiThLzEqseVykKz2hdGbU7B7VBwWBtRcXg3lgP6odDYFsqlAp0ly5TceQ46j0/oy6vwKCCvYPd+CSkAOWG31FfJ1/GBI5hQtAEmtk3zExzaWEh6+e/Rk5aCjb29vQd9xQtgjuRnXqFI5u+IC/jGnaOTjyx4H08/VtXe42My/l8vzqWwmzjHQdPfxeCQrxo7u+Cjb2G4rxyrl7MJf5oOnmZxuTOu40rw/+nI45usgKtOpIY3SX3a2J0O0VFRRgMBpydnSksLGTQoEFERkbedJts586dzJ07l9OnT6M2UXS4atUqtmzZwu7du2s85o9jqSgKRzatJ2rzVyjKzf12VGo1/cY/TcifJtSt6d4dUCoqyP7sv2RFRmLIz6/xOJWtLe7PPkPT6S+gcWpcdSZp53M4/PUFMi4XmDzON6gJAye2pamPBX9DzUuFM9vg4j64fBhuaCyYUuzCtivBlBpuvZXm75jNaN94bDQ3JEPOPtAmDNqPgdaDwEo+hO42RVGIz45n9+XdRF2NIu56HAbFQEC6wjN7DXRMNv0RdsEL1gzXcNFHhQoVbZu0ZYDvAIb5DyPYPfiuJPMF2Vns/Pc/SY2/tU+Tk3tTHnv1bbzamN6stry0guM7LhF7IAWDvubXaOtoRe9HA+gY6mve2VoLJ4nRXfKgJkaJiYn86U/G5nh6vZ7nnnuOl19++ZbjPvzwQ8aNG0fLljU3Vvzkk08YOHAgQUFBNR5T01hmJCUStfkrMi4nUlFWhl/HLnQZ9gg+7eo/9X0nDEVF5H27k6KfD1ESF4ehoBC1oyM2Af44Dx6My6hRWJkoMLd0iqKQkpDDxZMZpCfmU5hTilqjwtHNFt92TWjbsznNA0y/wVicijJI00LGGcg4C1nnKMq5jjbJQEKWPRWKGhfbCrp6FdLO3xV1k5bGzWy9u0CLXsZ2AcKsCsoL0GZoScxLJDH3IrqY0wRGX6XF5SLcs3UoahX5zhqS/B243LsFqi7BtHTxo33T9nTx6IKzzb2pvTHo9cT8+D3njx0m68plXDw8CejWk15jxmFT2cS2Norzy4k/epWUhByupxai1xmwdbDC3ceJwG4etO7mIUXWtSCJ0V3yoCZG95qMpRBCiIZUl8RI5t2EEEIIISpJYiSEEEIIUUkSIyGEEEKISpIYCSGEEEJUapSJUXZ2NpMmTcLFxQU3NzemTZtGYWHhbc87evQoQ4cOxdHRERcXF0JDQykpKbkHEQshhBCiMWiUidGkSZOIi4tjz549fPvttxw8eJDnn3/e5DlHjx5lxIgRDBs2jOPHjxMdHc2sWbNM9typD1nkd+dkDIUQQphLo1uuf/bsWYKDg4mOjqZnz54A7Nq1i1GjRpGSknLT7vA36tOnDw8//DB/+9vf6v3cppb76fV6zp07h6enZ7XdokXtXb9+nYyMDNq1a4emmu02hBBCiLqoy3L9RtcV6ujRo7i5uVUlRQDh4eGo1WqioqKqGhHeKCMjg6ioKCZNmkS/fv24ePEiDz30EIsWLWLAgAENEpdGo8HNzY2MjAwAHBwcLGd7hEZCURSKi4vJyMjAzc1NkiIhhBD3XKNLjNLT0/H0vHnXbysrK9zd3UlPT6/2nMRE4z477777LsuWLaNr16589tlnhIWFcfr0adq2bVvteWVlZZSVlVX9Pd/E9g8AXl5eAFXJkagfNze3qrEUQggh7iWLSYzmzZvHkiVLTB5z9uzZel3bYDDurzV9+nSmTJkCQLdu3di7dy+ffvopixcvrva8xYsX895779X6eVQqFd7e3nh6eqLT6eoV64PO2tpaZoqEEEKYjcUkRq+++upNu7VXp3Xr1nh5ed0yI1NRUUF2dnaNswze3t4ABAcH3/R4+/btSU5OrvH53nzzTebMmVP19/z8fJP7gP1Go9HIh7sQQgjRCFlMYuTh4YFHLTbc7Nu3L7m5uZw8eZIePXoAsG/fPgwGAyEhIdWe4+/vj4+PDwkJCTc9fu7cOUaOHFnjc9na2mJrK7tnCyGEEA+KRrdcv3379owYMYLnnnuO48ePc/jwYWbNmsWTTz5ZtSItNTWVhx56iOPHjwPGW1xz585l+fLlfP3111y4cIH58+cTHx/PtGnTzPlyhBBCCGFBLGbGqC6++OILZs2aRVhYGGq1mnHjxrF8+fKqn+t0OhISEiguLq56bPbs2ZSWlvLKK6+QnZ1Nly5d2LNnD4GBgeZ4CUIIIYSwQI2uj5E55eXl4ebmxpUrV27bB0EIIYQQluG3GuHc3FxcXV1NHtsoZ4zMpaCgAKBWBdhCCCGEsCwFBQW3TYxkxqgODAYDaWlpODs7m615429Zr8xaVU/GxzQZn5rJ2Jgm42OajI9p5h4fRVEoKCjAx8fntluByYxRHajValq0aGHuMABwcXGR/3wmyPiYJuNTMxkb02R8TJPxMc2c43O7maLfNLpVaUIIIYQQd4skRkIIIYQQlSQxamRsbW1ZuHChNJ6sgYyPaTI+NZOxMU3GxzQZH9Ma0/hI8bUQQgghRCWZMRJCCCGEqCSJkRBCCCFEJUmMhBBCCCEqSWIkhBBCCFFJEqNGbMyYMfj5+WFnZ4e3tzfPPPMMaWlp5g7LIiQlJTFt2jQCAgKwt7cnMDCQhQsXUl5ebu7QLMaiRYvo168fDg4OuLm5mTscs1u5ciX+/v7Y2dkREhLC8ePHzR2SRTh48CCjR4/Gx8cHlUrF1q1bzR2SxVi8eDG9evXC2dkZT09Pxo4dS0JCgrnDshirVq2ic+fOVU0d+/bty/fff2/usG5LEqNGbMiQIWzcuJGEhAS++eYbLl68yPjx480dlkWIj4/HYDCwevVq4uLi+OCDD4iMjOStt94yd2gWo7y8nCeeeIIZM2aYOxSz++qrr5gzZw4LFy7k1KlTdOnSheHDh5ORkWHu0MyuqKiILl26sHLlSnOHYnF++uknZs6cybFjx9izZw86nY5hw4ZRVFRk7tAsQosWLfjHP/7ByZMnOXHiBEOHDuWxxx4jLi7O3KGZJMv17yPbt29n7NixlJWVYW1tbe5wLM7SpUtZtWoViYmJ5g7Foqxbt47Zs2eTm5tr7lDMJiQkhF69erFixQrAuC9iy5Yteemll5g3b56Zo7McKpWKLVu2MHbsWHOHYpEyMzPx9PTkp59+IjQ01NzhWCR3d3eWLl3KtGnTzB1KjWTG6D6RnZ3NF198Qb9+/SQpqkFeXh7u7u7mDkNYmPLyck6ePEl4eHjVY2q1mvDwcI4ePWrGyERjk5eXByDvM9XQ6/Vs2LCBoqIi+vbta+5wTJLEqJF74403cHR0pGnTpiQnJ7Nt2zZzh2SRLly4wEcffcT06dPNHYqwMFlZWej1epo3b37T482bNyc9Pd1MUYnGxmAwMHv2bPr370/Hjh3NHY7FiI2NxcnJCVtbW1544QW2bNlCcHCwucMySRIjCzNv3jxUKpXJP/Hx8VXHz507l19++YXdu3ej0Wh49tlnuZ/vjtZ1fABSU1MZMWIETzzxBM8995yZIr836jM+Qog7N3PmTE6fPs2GDRvMHYpFCQoKQqvVEhUVxYwZM4iIiODMmTPmDsskqTGyMJmZmVy/ft3kMa1bt8bGxuaWx1NSUmjZsiVHjhyx+KnK+qrr+KSlpTF48GD69OnDunXrUKvv7+8C9fn9edBrjMrLy3FwcODrr7++qXYmIiKC3NxcmYW9gdQYVW/WrFls27aNgwcPEhAQYO5wLFp4eDiBgYGsXr3a3KHUyMrcAYibeXh44OHhUa9zDQYDAGVlZQ0ZkkWpy/ikpqYyZMgQevTowdq1a+/7pAju7PfnQWVjY0OPHj3Yu3dv1Qe+wWBg7969zJo1y7zBCYumKAovvfQSW7Zs4cCBA5IU1YLBYLD4zyhJjBqpqKgooqOjGTBgAE2aNOHixYvMnz+fwMDA+3a2qC5SU1MZPHgwrVq1YtmyZWRmZlb9zMvLy4yRWY7k5GSys7NJTk5Gr9ej1WoBaNOmDU5OTuYN7h6bM2cOERER9OzZk969e/Phhx9SVFTElClTzB2a2RUWFnLhwoWqv1+6dAmtVou7uzt+fn5mjMz8Zs6cyfr169m2bRvOzs5VNWmurq7Y29ubOTrze/PNNxk5ciR+fn4UFBSwfv16Dhw4wA8//GDu0ExTRKP066+/KkOGDFHc3d0VW1tbxd/fX3nhhReUlJQUc4dmEdauXasA1f4RRhEREdWOz/79+80dmll89NFHip+fn2JjY6P07t1bOXbsmLlDsgj79++v9vckIiLC3KGZXU3vMWvXrjV3aBZh6tSpSqtWrRQbGxvFw8NDCQsLU3bv3m3usG5LaoyEEEIIISrd/0UXQgghhBC1JImREEIIIUQlSYyEEEIIISpJYiSEEEIIUUkSIyGEEEKISpIYCSGEEEJUksRICCGEEKKSJEZCCCGEEJUkMRJCCCGEqCSJkRBCVKOiosLcIQghzEASIyHEAy8pKQmVSsXGjRsZOHAgtra2bN++3dxhCSHMwMrcAQghhLnFxMQAsHTpUt5//30CAgLw8PAwc1RCCHOQxEgI8cDTarU4OjqyadMm/P39zR2OEMKM5FaaEOKBFxMTw5gxYyQpEkJIYiSEEFqtlsGDB5s7DCGEBZDESAjxQMvPzycpKYlu3bqZOxQhhAWQxEgI8UCLiYlBo9HQqVMnc4cihLAAkhgJIR5oMTExBAUFYWdnZ+5QhBAWQKUoimLuIIQQQgghLIHMGAkhhBBCVJLESAghhBCikiRGQgghhBCVJDESQgghhKgkiZEQQgghRCVJjIQQQgghKkliJIQQQghRSRIjIYQQQohKkhgJIYQQQlSSxEgIIYQQopIkRkIIIYQQlSQxEkIIIYSo9H9UhPDoZIYYUwAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for n in range(nb_basis_functions):\n", + " plt.plot(r_grid, fourier_series(n, a, b)(r_grid), label=f\"$b_{n}(r)$\")\n", + "\n", + "plt.title(\"Fourier series\")\n", + "plt.xlabel(\"$r$\")\n", + "plt.ylabel(\"$b_n(r)$\")\n", + "plt.legend()\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "id": "f3ac9094", + "metadata": {}, + "source": [ + "### Schauder basis" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "44e01baf", + "metadata": { + "lines_to_next_cell": 1 + }, + "outputs": [], + "source": [ + "def schauder(\n", + " n: int, nb_basis_functions: int, a: float, b: float\n", + ") -> Callable[[np.ndarray], np.ndarray]:\n", + " \"\"\"\n", + " This is a subset of functions used in the construction of the\n", + " Franklin system which is a Schauder basis of $L_p$ for\n", + " $1 < p < \\\\infty$ and in particular an ONB of L_2([0,1])\n", + " The Franklin system itself can be obtained by Gram-Schmidt\n", + " orthogonalization of the Faber-Schauder basis on C[0,1]\n", + "\n", + " :param n: Specifies which basis function to compute.\n", + " :param nb_basis_functions: The maximum number of basis,\n", + " i.e. the dimension of the basis.\n", + " :param a: The start of the interval to which the basis functions are realigned.\n", + " :param b: The end of the interval to which the basis functions are realigned.\n", + " \"\"\"\n", + "\n", + " def fpeak0(x):\n", + " # peaked function on [-1,1]\n", + " return -2 * np.abs(x) + 2\n", + "\n", + " def fpeak1(x):\n", + " # scale f0 to [0,1]\n", + " return fpeak0(2 * x - 1)\n", + "\n", + " def fpeak(x, a, b):\n", + " # peak function on [a,b]\n", + " return np.where(x > a, np.where(x < b, fpeak1((x - a) / (b - a)), 0), 0)\n", + "\n", + " bounds = np.linspace(a, b, nb_basis_functions + 1)\n", + " return lambda r: fpeak(r, bounds[n], bounds[n + 1]) * np.sqrt(\n", + " 0.75 * nb_basis_functions / (b - a)\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "dd0cd40e", + "metadata": { + "lines_to_end_of_cell_marker": 0, + "lines_to_next_cell": 1 + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for n in range(nb_basis_functions):\n", + " plt.plot(r_grid, schauder(n, nb_basis_functions, a, b)(r_grid), label=f\"$b_{n}(r)$\")\n", + "\n", + "plt.title(\"Schauder-like functions\")\n", + "plt.xlabel(\"$r$\")\n", + "plt.ylabel(\"$b_n(r)$\")\n", + "plt.legend()\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "id": "dacd1a7a", + "metadata": {}, + "source": [ + "## Target functions" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "9aabb922", + "metadata": {}, + "outputs": [], + "source": [ + "def normalize_function(\n", + " f: Callable[[np.ndarray], np.ndarray], a: float, b: float\n", + ") -> Callable[[np.ndarray], np.ndarray]:\n", + " \"\"\"\n", + " Normalizes a function on the interval [a, b]\n", + "\n", + " :param f: The function that should be normalized.\n", + " :param a: Beginning of the interval to integrate.\n", + " :param b: End of the interval to integrate.\n", + " \"\"\"\n", + " norm = np.sqrt(scipy.integrate.quad(lambda r: f(r) ** 2, a, b)[0])\n", + " return lambda r: f(r) / norm\n", + "\n", + "\n", + "def gaussian(r_i: float, sigma: float = 0.3) -> Callable[[np.ndarray], np.ndarray]:\n", + " \"\"\"\n", + " Returns a Gaussian function for a set of parameters\n", + "\n", + " .. math:\n", + "\n", + " exp(-0.5*(r-r_i)/σ^2)/(σ*sqrt(2π))\n", + "\n", + " :param r_i: The center of Gaussian function.\n", + " :param sigma: The sigma of the Gaussian function.\n", + " \"\"\"\n", + " return lambda r: np.exp(-0.5 * ((r - r_i) / sigma) ** 2) / (\n", + " sigma * np.sqrt(2 * np.pi)\n", + " )" + ] + }, + { + "cell_type": "markdown", + "id": "effce22c", + "metadata": {}, + "source": [ + "### Gaussian probality density function centered at the origin" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "0a06c796", + "metadata": {}, + "outputs": [], + "source": [ + "def gaussian_origin(sigma: float = 0.3) -> Callable[[np.ndarray], np.ndarray]:\n", + " \"\"\"\n", + " Returns a function that computes a Gaussian function centered at the origin.\n", + "\n", + " :param sigma: The sigma of the Gaussian function.\n", + " \"\"\"\n", + " gaussian_f = gaussian(0, sigma)\n", + " return lambda r: gaussian_f(r)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "56476f48", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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33nor7r//foSEhCAzMxNfffUVBg0a1OAvKm9vb3Tr1g0bNmxAp06dEBwcjO7du6N79+5Yvnw5Bg8ejB49emD69Olo3749cnJysHfvXpw/fx6HDx+uc98NqTc1NRVjx47F4MGD8cgjj6CgoMA+p5Gz8V7VNeQ9iouLw4YNG5CcnIy+ffvCz88P48aNq3XfcXFx+Pbbb7F06VJERkaiXbt2DZoqITY2Fi+//DJSUlKQkZGBCRMmwN/fH2fPnsWmTZvwl7/8Bc8880yt27/88sv2+Z8ef/xx6HQ6vPvuu6ioqGj0vDRhYWF46qmn8Oabb2L8+PEYNWoUDh8+jG+++QatWrVqFjN9kxt5/HouIg85deqUMHPmTKFDhw6C0WgUvL29hS5duggzZswQ0tPTHdY9f/68cM899wiBgYGCyWQS7rvvPuHixYtOL2fevn270L17d0Gv1wudO3cWPvrooxqXkKelpQl33323EBkZKej1eiEyMlJ44IEHhD/++MO+zrvvvisMHTpUaNmypWAwGITY2Fjh73//u1BcXGxfx9kl5D/++KPQv39/wdvbW4iMjBSeffZZYdu2bU4vrXV2iXptl8E7s3r1aqFPnz6CwWAQgoKChNtvv13YsWOHwzo7d+4UEhMTBZPJJBiNRiE2NlZ4+OGHhZ9//tnhmL6+vjX2f+N5EwRB2LNnjxAXFyfo9foa5//06dPC1KlThfDwcKFFixZCVFSUcNdddwmfffZZjXN24MABp6+pPvUKgiB8/vnnQteuXQWDwSB069ZN+OKLL+p97ur7HpWVlQlTpkwRAgMD63V5+vHjx4WhQ4cK3t7eDpdXi+fxxikLnH1+xNc2ePBgwdfXV/D19RW6dOkizJo1Szhx4sRNX9uhQ4eExMREwc/PT/Dx8RGGDx8u7Nmzx+lxnb0HzmqqqqoS5s2bJ4SHhwve3t7CHXfcIfz+++9Cy5YthRkzZtjXq+0S8qZ+zkm9eO8qIiKSnaKiIgQFBeHll1/G888/L3U5pFAck0NERJK6evVqjWXimLhhw4Z5thhSFY7JISIiSW3YsAFr167FmDFj4Ofnhx9++AGffPIJRo4cedN5o4jqwpBDRESS6tmzJ3Q6HZYsWYKSkhL7YOSXX35Z6tJI4Tgmh4iIiFSJY3KIiIhIlRhyiIiISJWa7Zgcm82Gixcvwt/fn5NNERERKYQgCCgtLUVkZKT9hse1abYh5+LFi426zwoRERFJLysryz5zfW2abcgRp83Pyspq1P1WiIiIyPNKSkoQHR1d6+1vqmu2IUfsogoICGDIISIiUpj6DDXhwGMiIiJSJYYcIiIiUiVZhJzdu3dj3LhxiIyMhEajwebNm+u97Y8//gidTofevXu7rT4iIiJSHlmEHLPZjF69emH58uUN2q6oqAhTp07FiBEj3FQZERERKZUsBh6PHj0ao0ePbvB2M2bMwJQpU+Dl5dWg1h8iIiJSP1m05DTGmjVrcObMGSxYsEDqUoiIiEiGZNGS01AnT57E3Llz8b///Q86Xf1eQkVFBSoqKuw/l5SUuKs8IiIikgHFteRYrVZMmTIFixYtQqdOneq9XWpqKkwmk/3B2Y6JiIjUTSMIgiB1EdVpNBps2rQJEyZMcPp8UVERgoKC4OXlZV9ms9kgCAK8vLywfft23HHHHTW2c9aSEx0djeLiYk4GSEREpBAlJSUwmUz1+v5WXHdVQEAAjh496rDsnXfewXfffYfPPvsM7dq1c7qdwWCAwWDwRIlEREQkA7IIOWVlZTh16pT957NnzyI9PR3BwcFo06YNUlJScOHCBfz73/+GVqtF9+7dHbYPDQ2F0WissZyIiIiaL1mEnJ9//hnDhw+3/5ycnAwASEpKwtq1a3Hp0iVkZmZKVR4REREpkOzG5HhKQ/r0iEhZSkpKUF5ejuDg4HpfgUlEyqDqMTlERHXZsGEDPv74YwiCgFatWuHll19GVFSU1GURkQQUdwk5EVFtvvzyS3z00Uf2qy3z8/Mxf/58FBQUSF0aEUmAIYeIVCE3Nxfvv/8+AODBBx/EBx98gMjISIflRNS8MOQQkSps3rwZVqsVPXv2xOTJk2EymTBnzhwAwA8//IDs7GyJKyQiT2PIISLFKy0txfbt2wEA9913HzQaDQCgffv2iIuLgyAIvIkvUTPEkENEirdt2zZUVFSgffv26NWrl8NzEydOBADs2LEDZrNZivKISCIMOUSkeHv27AEAjBkzxt6KI+rRowdat24Ni8WCgwcPSlEeEUmEIYeIFC0/Px8nT56ERqNB//79azyv0WgwYMAAAMC+ffs8XR4RSYghh4gU7aeffgIAdOnSBSaTyek68fHxAK7Nrl5ZWemx2ohIWgw5RKRoYuuM2FrjTKdOnRAcHIyrV6/iyJEjniqNiCTGkENEilVeXo6jR48CuN5a44xGo7E/v3//fo/URkTSY8ghIsU6fvw4rFYrQkNDERkZWee6vXv3BgAcO3bMA5URkRww5BCRYomB5ZZbbrnpuuI6586dQ2lpqVvrIiJ5YMghIsUSQ063bt1uuq7JZLLfqPP33393a11EJA8MOUSkSFVVVThx4gSA+rXkVF+PXVZEzQNDDhEp0qlTp2CxWBAQEIDWrVvXaxsx5Pz222/uLI2IZIIhh4gUqXpX1Y2zHNdGDDmnTp1CRUWF22ojInlgyCEiRTp58iSAa5MA1ldoaCgCAwNRVVWFjIwMN1VGRHLBkENEinT69GkAQIcOHeq9jUajsa8vbk9E6sWQQ0SKYzabkZ2dDQBo3759g7YV1z916pTL6yIieWHIISLFOXPmDIBr3U/+/v4N2jY2NtZhH0SkXgw5RKQ4YleTGFgaQuyuOnfuHKqqqlxaFxHJC0MOESlOU0JOSEgI/Pz8UFVVhczMTFeXRkQywpBDRIrTlJCj0Wjs43I4+JhI3RhyiEhRKioqcP78eQANH3QsEsMRBx8TqRtDDhEpSlZWFgRBgMlkQnBwcKP20a5dOwBgdxWRyjHkEJGiiMEkOjq60fsQt2XIIVI3hhwiUpSsrCwAQJs2bRq9j+joaGg0GpSUlKC4uNhVpRGRzDDkEJGinDt3DgDQtm3bRu/DYDAgLCwMAFtziNSMIYeIFMUV3VXVt2fIIVIvhhwiUozy8nLk5uYCaFp3FXC9JYghh0i9GHKISDHOnz8PQRAQEBAAk8nUpH2xJYdI/RhyiEgxxEDS1Fac6vtgyCFSL4YcIlIMV1xZJeIVVkTqx5BDRIpx4cIFAEDr1q2bvC+DwYCQkBAAwMWLF5u8PyKSH4YcIlIMMeRERUW5ZH+RkZEO+yUidWHIISJFsNlsuHTpEoDr4aSpxLDEkEOkTgw5RKQI+fn5qKyshE6nQ2hoqEv2KYYldlcRqZMsQs7u3bsxbtw4REZGQqPRYPPmzXWu/8UXX+DOO+9ESEgIAgICMGDAAGzbts0zxRKRJMQgEhERAa3WNb+62JJDpG6yCDlmsxm9evXC8uXL67X+7t27ceedd+Lrr7/GwYMHMXz4cIwbNw6//PKLmyslIqmIQcRVXVXV93Xp0iUIguCy/RKRPOikLgAARo8ejdGjR9d7/WXLljn8vHjxYmzZsgX//e9/0adPHxdXR0Ry4I6QExoaCp1OB4vFgvz8fPvVVkSkDrJoyWkqm82G0tJSBAcHS10KEbmJ2F3lqiurAMDLy8t+o052WRGpjypCzhtvvIGysjJMmjSp1nUqKipQUlLi8CAi5RBDjitbcoDroYmDj4nUR/EhZ926dVi0aBE2btxY5xUXqampMJlM9kdT72BMRJ5TVVWF7OxsAK5tyam+P7bkEKmPokPO+vXr8eijj2Ljxo1ISEioc92UlBQUFxfbH+L08EQkf7m5uRAEAXq9HkFBQS7dd/XBx0SkLrIYeNwYn3zyCR555BGsX78eY8eOven6BoMBBoPBA5URkavl5OQAAMLCwqDRaFy67/DwcACwtxQRkXrIIuSUlZXh1KlT9p/Pnj2L9PR0BAcHo02bNkhJScGFCxfw73//G8C1LqqkpCT84x//QHx8vP2Xk7e3N0wmkySvgYjcRww5YiBxJXHgcU5ODgRBcHmIIiLpyKK76ueff0afPn3sl38nJyejT58+mD9/PoBrzciZmZn29d977z1UVVVh1qxZiIiIsD+eeuopSeonIveq3pLjaiEhIdBoNLBYLCgsLHT5/olIOrJoyRk2bFidE3GtXbvW4eddu3a5tyAikhWxtdYdIUen0yEkJAS5ubnIzs7mVBREKiKLlhwiorq4syUHuHarCIDjcojUhiGHiGTP3SGHg4+J1Ikhh4hkrby83D55J0MOETUEQw4RyZoYPPz8/ODr6+uWYzDkEKkTQw4RyZq7u6qq75shh0hdGHKISNY8EXLEgceFhYWoqKhw23GIyLMYcohI1nJzcwG4N+RU7woTj0dEyseQQ0SyJnYhuWO24+pCQkIAMOQQqQlDDhHJmie6qwAgNDQUAEMOkZow5BCRbAmCwJBDRI3GkENEslVWVoarV68CuB5C3IUhh0h9GHKISLbE8ThBQUHQ6/VuPZY4JicvL8+txyEiz2HIISLZ8lRXFcCQQ6RGDDlEJFueDDlid9Xly5dRVVXl9uMRkfsx5BCRbHky5AQGBqJFixYQBAGXL192+/GIyP0YcohItsSQ4+45cgBAo9FwrhwilWHIISLZ8mRLDsArrIjUhiGHiGTJk3PkiDj4mEhdGHKISJYKCwtRVVUFrVaLVq1aeeSYbMkhUheGHCKSJbE1JTg4GF5eXh45JltyiNSFIYeIZCk/Px/A9eDhCWzJIVIXhhwikiWxNUWKkJOXlwdBEDx2XCJyD4YcIpIlsSXHU+NxAKBly5bQaDSorKxEUVGRx45LRO7BkENEsiS25Hgy5Oh0OgQHBzscn4iUiyGHiGRJiu4qgONyiNSEIYeIZEmKgcfVj8eWHCLlY8ghItmpqqqyj4nxZHcVwJYcIjVhyCEi2bl8+TIEQYBer0dAQIBHj837VxGpB0MOEcmO2FUkXu3kSWzJIVIPhhwikh2pBh0DjnPlEJGyMeQQkexINegYuB5yzGYzrly54vHjE5HrMOQQkexIMUeOyGg0wt/fHwC7rIiUjiGHiGRHypYc4NpYIODaAGgiUi6GHCKSHSlbcqoflyGHSNkYcohIdqQceAxcDzkcfEykbAw5RCQr5eXlMJvNANiSQ0RNw5BDRLIitp74+vrCx8dHkhrEkCOODSIiZWLIISJZEYOFVK04wPWBxww5RMomi5Cze/dujBs3DpGRkdBoNNi8efNNt9m1axduvfVWGAwGdOjQAWvXrnV7nUTkflIPOgaujwVidxWRsski5JjNZvTq1QvLly+v1/pnz57F2LFjMXz4cKSnp+Ovf/0rHn30UWzbts3NlRKRu0k96Bi43pJz5coVTghIpGA6qQsAgNGjR2P06NH1Xn/lypVo164d3nzzTQBA165d8cMPP+Ctt95CYmKiu8okIg+Qeo4c4NqEgL6+vjCbzbh8+bJkY4OIqGlk0ZLTUHv37kVCQoLDssTEROzdu1eiiojIVeTQXVX9+ByXQ6Rcigw52dnZCAsLc1gWFhaGkpISXL161ek2FRUVKCkpcXgQkfzIYeBx9eMz5BAplyJDTmOkpqbCZDLZH9HR0VKXREQ3EARBFmNyAM6VQ6QGigw54eHhyMnJcViWk5ODgIAAeHt7O90mJSUFxcXF9kdWVpYnSiWiBigrK4PFYgFwffCvVDjrMZHyyWLgcUMNGDAAX3/9tcOyHTt2YMCAAbVuYzAYYDAY3F0aETWB2DVkMpmg1+slrYU36SRSPlm05JSVlSE9PR3p6ekArl0inp6ejszMTADXWmGmTp1qX3/GjBk4c+YMnn32WRw/fhzvvPMONm7ciKefflqK8onIRcSQI3UrDsAxOURqIIuQ8/PPP6NPnz7o06cPACA5ORl9+vTB/PnzAQCXLl2yBx4AaNeuHb766ivs2LEDvXr1wptvvon333+fl48TKZzYasKQQ0SuIIvuqmHDhkEQhFqfdzab8bBhw/DLL7+4sSoi8jQ5hhyz2Yzy8nIYjUaJKyKihpJFSw4REXA95Eh9+TgAeHt72ycBZGsOkTIx5BCRbMipJQfgjTqJlI4hh4hkQ24hh3PlECkbQw4RyYZcZjsWcfAxkbIx5BCRLFRUVMBsNgMAgoODJa7mGoYcImVjyCEiWRC7hIxGo2zu+s2QQ6RsDDlEJAvVJwLUaDQSV3MNBx4TKRtDDhHJgtwGHQMceEykdAw5RCQLcpojRyTWUlpaioqKComrIaKGYsghIlmQY0uOj4+PfaZjdlkRKQ9DDhHJghxDjkaj4d3IiRSMIYeIZEFuc+SIOC6HSLkYcohIFsQQIZc5ckQMOUTKxZBDRJKzWq0oLCwEIK/uKoCXkRMpGUMOEUmusLAQgiDAy8sLgYGBUpfjgGNyiJSLIYeIJCcGiKCgIGi18vq1xJBDpFzy+m1CRM2SHK+sEvHWDkTKxZBDRJKT40SAIrGmoqIiVFVVSVwNETUEQw4RSU7OLTkBAQHQ6XQQBME+OJqIlIEhh4gkJ+eWHI1GY7+sneNyiJSFIYeIJFf9DuRyxMvIiZSJIYeIJCfXiQBFnBCQSJkYcohIUoIgyLq7CuBl5ERKxZBDRJIqKyuDxWIBIP+WHHZXESkLQw4RSUpsHfH394der5e4GufYkkOkTAw5RCQpuXdVARx4TKRUDDlEJCk5z5EjEgNYQUEBBEGQuBoiqi+GHCKSlBJCTlBQEDQaDaqqqlBSUiJ1OURUTww5RCQpsQtIzt1VOp3Ofnd0dlkRKQdDDhFJSgktOQAHHxMpEUMOEUlKaSGHLTlEysGQQ0SSUkrI4azHRMrDkENEkrFYLCgtLQUg/5DD7ioi5WHIISLJiIHBYDDA19dX4mrqxlmPiZSHIYeIJFO9q0qj0UhcTd3YkkOkPAw5RCQZpYzHATjwmEiJGHKISDJKuKWDSAw55eXluHLlisTVEFF9MOQQkWTEVhEltOQYjUb7uCF2WREpA0MOEUlGDAvBwcESV1I/HHxMpCyyCTnLly9HTEwMjEYj4uPjsX///jrXX7ZsGTp37gxvb29ER0fj6aefRnl5uYeqJSJXUFJ3FcDBx0RKI4uQs2HDBiQnJ2PBggU4dOgQevXqhcTEROTm5jpdf926dZg7dy4WLFiA33//Hf/617+wYcMGPPfccx6unIiaQkkDjwEOPiZSGlmEnKVLl2L69OmYNm0aunXrhpUrV8LHxwerV692uv6ePXswaNAgTJkyBTExMRg5ciQeeOCBm7b+EJF82Gw2FBQUAGBLDhG5h+Qhx2Kx4ODBg0hISLAv02q1SEhIwN69e51uM3DgQBw8eNAeas6cOYOvv/4aY8aMqfU4FRUVKCkpcXgQkXSKiopgs9mg1Wrtd/iWO97agUhZdFIXkJ+fD6vVirCwMIflYWFhOH78uNNtpkyZgvz8fAwePBiCIKCqqgozZsyos7sqNTUVixYtcmntRNR4YpdPcHAwtFrJ/96qF4YcImVRxm+WG+zatQuLFy/GO++8g0OHDuGLL77AV199hZdeeqnWbVJSUlBcXGx/ZGVlebBiIrqR0sbjAByTQ6Q0krfktGrVCl5eXsjJyXFYnpOTg/DwcKfbzJs3Dw899BAeffRRAECPHj1gNpvxl7/8Bc8//7zTvwoNBgMMBoPrXwARNYqS5sgRibWWlJTAYrFAr9dLXBER1UXylhy9Xo+4uDikpaXZl9lsNqSlpWHAgAFOt7ly5UqNIOPl5QUAEATBfcUSkcuIg46VFHL8/PzswUasn4jkS/KQAwDJyclYtWoVPvjgA/z++++YOXMmzGYzpk2bBgCYOnUqUlJS7OuPGzcOK1aswPr163H27Fns2LED8+bNw7hx4+xhh4jkTWzJUcqVVQCg0WjYZUWkIJJ3VwHA5MmTkZeXh/nz5yM7Oxu9e/fG1q1b7YORMzMzHVpuXnjhBWg0Grzwwgu4cOECQkJCMG7cOLzyyitSvQQiaiAljskBroWyS5cusSWHSAFkEXIAYPbs2Zg9e7bT53bt2uXws06nw4IFC7BgwQIPVEZE7qDUkMOWHCLlkEV3FRE1L4IgKHLgMcD7VxEpCUMOEXmc2WyGxWIBoLyQI95MlHPlEMkfQw4ReZzYCuLv76+4y7A5ISCRcjDkEJHHKe3u49Xx/lVEysGQQ0Qep9RBx8D1YFZQUACbzSZxNURUF4YcIvI4JbfkBAYGQqvVwmazoaioSOpyiKgODDlE5HFKvbIKALRarX3wMa+wIpI3hhwi8jgld1cBnCuHSCkYcojI49QScjj4mEjeGHKIyOOUPCYH4GXkRErBkENEHmWxWFBaWgpAuS05DDlEytCke1dVVlYiOzsbV65cQUhIiH0wHhFRbcRgYDQa4ePjI3E1jcMxOUTK0OCWnNLSUqxYsQK33347AgICEBMTg65duyIkJARt27bF9OnTceDAAXfUSkQqUP3KKo1GI3E1jcMxOUTK0KCQs3TpUsTExGDNmjVISEjA5s2bkZ6ejj/++AN79+7FggULUFVVhZEjR2LUqFE4efKku+omIoVS+qBjwDHkCIIgcTVEVJsGdVcdOHAAu3fvxi233OL0+X79+uGRRx7BypUrsWbNGvzvf/9Dx44dXVIoEamDkufIEYld8xaLBWVlZfD395e4IiJypkEh55NPPgEAWK1W/Pe//8WIESOc/uM2GAyYMWOGayokIlUpKCgAoNwrqwBAr9cjICAAJSUluHz5MkMOkUw16uoqLy8vPPDAA8jLy3N1PUSkcmpoyQGuhzQOPiaSr0ZfQt63b1+cPXvWlbUQUTOg9DlyRLzCikj+Gh1ynnjiCTz33HPIyspyZT1EpHJiKFD6lBO8wopI/ho9T87kyZMBALfccgvGjx+PYcOGoU+fPujRowf0er3LCiQi9bBarSgsLASg/JYcTghIJH+NDjlnz57F4cOHkZ6ejsOHDyM1NRUZGRnQ6XTo3Lkzjhw54so6iUgFCgsLIQgCvLy8EBgYKHU5TcKWHCL5a3TIadu2Ldq2bYvx48fbl5WWliI9PZ0Bh4icEgNBcHCwYicCFHHgMZH8Nem2Djfy9/fHkCFDMGTIEFfulohUQg0TAYrYkkMkfw0aeJyZmdmgnV+4cKFB6xORuqnlyirgesgxm80oLy+XuBoicqZBIadv37547LHH6rw3VXFxMVatWoXu3bvj888/b3KBRKQeapkjBwB8fHzg7e0NgK05RHLVoO6qsWPHws/PD3feeSeMRiPi4uIQGRkJo9GIwsJC/Pbbbzh27BhuvfVWLFmyBGPGjHFX3USkQGrqrgKuvY7z58/j8uXLiIqKkrocIrpBg0LORx99hKysLLz00ksICQlBREQE8vPzcfXqVbRq1QoPPvggEhMT0b17d3fVS0QKpraQ06pVK5w/f56Dj4lkqkEhJzIyEunp6UhMTMTVq1exePFihIaGuqs2IlIZNY3JATj4mEjuGjQm529/+xvGjRuHIUOGQKPR4OOPP8aBAwdw9epVd9VHRCohCIKqxuQAvLUDkdw1KOQ88cQT+PnnnzFq1CgIgoDly5djwIABCAgIQNeuXXH//ffj1VdfxTfffOOueolIocrKylBZWQlA+bd0EHHWYyJ5a/A8OT179kTPnj2xdu1a7N27F76+vjhy5AjS09ORnp6OLVu24JVXXkFpaak76iUihcrLywMAmEwmtGjRQuJqXIPdVUTy1ujJAE+ePGn///j4eMTHx9t/FgShaVURkeqIXTpqGY8DcNZjIrlr9F3I66L06dqJyPXEIBASEiJxJa4jtuQUFxejqqpK4mqI6EZuCTlERDcSu6vUFHICAgKg0+kgCAIKCgqkLoeIbsCQQ0QeIYYcNXVXaTQajsshkjGGHCLyCDV2VwEcfEwkZww5ROQRamzJATj4mEjOGHKIyO1sNpu9pYMtOUTkKbIJOcuXL0dMTAyMRiPi4+Oxf//+OtcvKirCrFmzEBERAYPBgE6dOuHrr7/2ULVE1BBFRUWwWq3QarUICgqSuhyX4qzHRPLV6HlyXGnDhg1ITk7GypUrER8fj2XLliExMREnTpxwem8si8WCO++8E6Ghofjss88QFRWFc+fOITAw0PPFE9FNiV1VwcHB8PLykrga12JLDpF8ySLkLF26FNOnT8e0adMAACtXrsRXX32F1atXY+7cuTXWX716NQoKCrBnzx77zKkxMTGeLJmIGkCNl4+LeGsHIvmSvLvKYrHg4MGDSEhIsC/TarVISEjA3r17nW7zn//8BwMGDMCsWbMQFhaG7t27Y/HixbBarbUep6KiAiUlJQ4PIvIMtV5ZBTiGHM72TiQvkoec/Px8WK1WhIWFOSwPCwtDdna2023OnDmDzz77DFarFV9//TXmzZuHN998Ey+//HKtx0lNTYXJZLI/oqOjXfo6iKh2ar2yCgACAwOh0WhgtVpRXFwsdTlEVI3kIacxbDYbQkND8d577yEuLg6TJ0/G888/j5UrV9a6TUpKCoqLi+2PrKwsD1ZM1Lyp8b5VIp1OZx9MLYY5IpIHycfktGrVCl5eXsjJyXFYnpOTg/DwcKfbREREoEWLFg4DGLt27Yrs7GxYLBbo9foa2xgMBhgMBtcWT0T1ouYxOcC132MFBQXIz89Hx44dpS6HiP4/yVty9Ho94uLikJaWZl9ms9mQlpaGAQMGON1m0KBBOHXqFGw2m33ZH3/8gYiICKcBh4ikpfaQI14FmpubK3ElRFSd5CEHAJKTk7Fq1Sp88MEH+P333zFz5kyYzWb71VZTp05FSkqKff2ZM2eioKAATz31FP744w989dVXWLx4MWbNmiXVSyCiWlRWVqKoqAiAOrurgOvhjd1VRPIieXcVAEyePBl5eXmYP38+srOz0bt3b2zdutU+GDkzMxNa7fU8Fh0djW3btuHpp59Gz549ERUVhaeeegpz5syR6iUQUS3ES6v1ej0CAgIkrsY9GHKI5EkWIQcAZs+ejdmzZzt9bteuXTWWDRgwAPv27XNzVUTUVNUHHWs0GomrcQ+xu4ohh0heZNFdRUTqpebLx0ViSw7H5BDJC0MOEbmV2gcdA9dbcoqLi2GxWCSuhohEDDlE5FZqnu1Y5OvrC6PRCIBdVkRywpBDRG7VHLqrNBoNx+UQyRBDDhG5lZpnO66O43KI5Ichh4jcSmzZEFs61IoTAhLJD0MOEbnN1atXYTabATSflhx2VxHJB0MOEbmN2FXl6+sLb29viatxL7bkEMkPQw4RuY144121d1UBnBCQSI4YcojIbcRWjeYQcsTuqvz8fIebBxORdBhyiMhtxJYc8T50ahYcHAytVgur1YrCwkKpyyEiMOQQkRs1p5YcrVZrH1zNcTlE8sCQQ0Ru05xacgCOyyGSG4YcInKb5tSSA3BCQCK5YcghIrcoLy9HcXExgObTksO5cojkhSGHiNxC/KL39fWFr6+vxNV4BkMOkbww5BCRWzSnOXJEHJNDJC8MOUTkFs1tPA7AWY+J5IYhh4jcorldWQVcvz/XlStX7PfsIiLpMOQQkVs0x5Yco9GIgIAAAGzNIZIDhhwicovm2JIDXH+9DDlE0mPIISK3aI4tOcD1kJOdnS1xJUTEkENELtcc58gRhYeHA7jekkVE0mHIISKXE1txmtMcOSK25BDJB0MOEblccx2PA1xvyWHIIZIeQw4RuVxzHY8DOHZXCYIgcTVEzRtDDhG5XHNuyWnVqhW0Wi0sFgsKCwulLoeoWWPIISKXa84tOTqdzj4pILusiKTFkENELieGnObYkgPwCisiuWDIISKXa44356yOg4+J5IEhh4hcqry8HCUlJQAYchhyiKTFkENELtWc58gRMeQQyQNDDhG51KVLlwBc/6JvjjghIJE8MOQQkUuJISciIkLiSqQjBryCggJYLBaJqyFqvhhyiMilxJATGRkpcSXS8ff3h7e3NwBeYUUkJYYcInKpixcvAmjeIUej0XBcDpEMMOQQkUuxu+oazpVDJD2GHCJymaqqKvvVVQw5bMkhkpqsQs7y5csRExMDo9GI+Ph47N+/v17brV+/HhqNBhMmTHBvgURUJ/GmlEajEYGBgVKXIyleYUUkPdmEnA0bNiA5ORkLFizAoUOH0KtXLyQmJtr/KqxNRkYGnnnmGQwZMsRDlRJRbap3VWk0GomrkRa7q4ikJ5uQs3TpUkyfPh3Tpk1Dt27dsHLlSvj4+GD16tW1bmO1WvHggw9i0aJFaN++vQerJSJnOB7nuurdVYIgSFwNUfMki5BjsVhw8OBBJCQk2JdptVokJCRg7969tW734osvIjQ0FH/+859veoyKigqUlJQ4PIjItXj5+HUhISHQaDQOt7kgIs+SRcjJz8+H1WqtccfisLCwWvuzf/jhB/zrX//CqlWr6nWM1NRUmEwm+yM6OrrJdRORI/HycbbkAHq9Hi1btgRwPfwRkWfJIuQ0VGlpKR566CGsWrUKrVq1qtc2KSkpKC4utj+ysrLcXCVR88PuKkfieRDDHxF5lk7qAgCgVatW8PLyqjFALycnx+n9b06fPo2MjAyMGzfOvsxmswEAdDodTpw4gdjYWIdtDAYDDAaDG6onIuDaGDnx3zBDzjVRUVE4evQoLly4IHUpRM2SLFpy9Ho94uLikJaWZl9ms9mQlpaGAQMG1Fi/S5cuOHr0KNLT0+2P8ePHY/jw4UhPT2dXFJEE8vLyYLVaHbppmruoqCgAYMghkogsWnIAIDk5GUlJSbjtttvQr18/LFu2DGazGdOmTQMATJ06FVFRUUhNTYXRaET37t0dthfn5LhxORF5RvW7jzf3y8dFDDlE0pJNyJk8eTLy8vIwf/58ZGdno3fv3ti6dat9MHJmZia0Wlk0PBGRExyPU5MYci5evAhBEBj+iDxMNiEHAGbPno3Zs2c7fW7Xrl11brt27VrXF0RE9cYbc9YUFhYGnU4Hi8WCvLw8hIaGSl0SUbPCphEicgm25NTk5eVlv3iCV1gReR5DDhG5BEOOc2KX1fnz5yWuhKj5Ycghoiaz2Wyc7bgW1cflEJFnMeQQUZNdvnwZVVVV0Ol09Z6gs7lgSw6RdBhyiKjJxEukw8LCeBXkDXgZOZF0+NuIiJpMbKXgRJw1tW7dGsC1yRItFovE1RA1Lww5RNRk4r3gxC90ui4gIAC+vr4QBIHjcog8jCGHiJpMbMlhyKlJo9Fw8DGRRBhyiKjJGHLqxsHHRNJgyCGiJrly5QoKCgoAMOTUhoOPiaTBkENETSJ+cQcFBcHX11fiauSJIYdIGgw5RNQk7Kq6ueohRxAEiashaj4YcoioSRhybk6cBbqsrAylpaUSV0PUfDDkEFGTiJePi60VVJPBYLDPBM3Bx0Sew5BDRE2SmZkJAGjbtq3ElchbmzZtAFw/X0Tkfgw5RNRoFovFPveL+CVOzjHkEHkeQw4RNZo4kNbX1xdBQUFSlyNrDDlEnseQQ0SNdu7cOQDXuqo0Go3E1cib2J0nnjMicj+GHCJqNLFVgl1VNyeeo6KiIl5hReQhDDlE1GgcdFx/RqMRoaGhANiaQ+QpDDlE1GhsyWkYMQxyXA6RZzDkEFGjVFRUIDs7GwBbcupLDINsySHyDIYcImqUrKwsCIKAgIAAmEwmqctRBLbkEHkWQw4RNcrZs2cBADExMdIWoiBiyDl79izvYUXkAQw5RNQoYshp3769xJUoR5s2baDT6WA2m5GXlyd1OUSqx5BDRI0ihpx27dpJXIly6HQ6+41MxfNHRO7DkENEDSYIAkNOI4nniyGHyP0YcoiowfLy8mA2m6HT6RAdHS11OYoidu8x5BC5H0MOETWY+AUdHR0NnU4ncTXKwpYcIs9hyCGiBmNXVeOJ5+zSpUu4evWqxNUQqRtDDhE1GENO4wUEBCA4OBgAkJGRIW0xRCrHkENEDXbq1CkAvHy8sWJjYwFcP49E5B4MOUTUICUlJcjNzQUAdOjQQeJqlKljx44AGHKI3I0hh4gaRPxijoqKgo+Pj8TVKJMYDk+ePClxJUTqxpBDRA0ihhy24jSe2F11/vx5lJeXS1wNkXox5BBRg4itD2KXCzVccHAwWrZsCUEQcPr0aanLIVIthhwiahC25LiGeP44LofIfRhyiKjeioqKkJ+fD41GY+9yocbh4GMi95NVyFm+fDliYmJgNBoRHx+P/fv317ruqlWrMGTIEAQFBSEoKAgJCQl1rk9ETffHH38AAFq3bg2j0ShxNcomtuScOHFC4kqI1Es2IWfDhg1ITk7GggULcOjQIfTq1QuJiYn2S1VvtGvXLjzwwAPYuXMn9u7di+joaIwcORIXLlzwcOVEzcfx48cBAF26dJG4EuXr3LkzgGszHxcXF0tcDZE6ySbkLF26FNOnT8e0adPQrVs3rFy5Ej4+Pli9erXT9T/++GM8/vjj6N27N7p06YL3338fNpsNaWlpHq6cqPlgyHEdPz8/tG7dGgBbc4jcRRYhx2Kx4ODBg0hISLAv02q1SEhIwN69e+u1jytXrqCystI+XfqNKioqUFJS4vAgovqzWq327iqGHNcQz6MYHonItWQRcvLz82G1WhEWFuawPCwsDNnZ2fXax5w5cxAZGekQlKpLTU2FyWSyP6Kjo5tcN1FzkpGRgYqKCvj6+vLfj4t07doVAEMOkbvIIuQ01auvvor169dj06ZNtQ6GTElJQXFxsf2RlZXl4SqJlE38Iu7cuTM0Go3E1aiD2JLzxx9/wGq1SlwNkfropC4AAFq1agUvLy/k5OQ4LM/JyUF4eHid277xxht49dVX8e2336Jnz561rmcwGGAwGFxSL1FzxPE4rhcdHQ1fX1+YzWacO3eONzwlcjFZtOTo9XrExcU5DBoWBxEPGDCg1u2WLFmCl156CVu3bsVtt93miVKJmiVBEHDs2DEA17tYqOk0Go09NIrnl4hcRxYhBwCSk5OxatUqfPDBB/j9998xc+ZMmM1mTJs2DQAwdepUpKSk2Nd/7bXXMG/ePKxevRoxMTHIzs5GdnY2ysrKpHoJRKqVm5uLvLw8eHl5sSXHxbp37w4AOHr0qMSVEKmPLLqrAGDy5MnIy8vD/PnzkZ2djd69e2Pr1q32wciZmZnQaq9nshUrVsBiseDee+912M+CBQuwcOFCT5ZOpHq//vorAKBTp06cBNDFevToAeDaORYEgeOdiFxINiEHAGbPno3Zs2c7fW7Xrl0OP2dkZLi/ICICcL2VQWx1INeJjY2F0WhEaWkpzp07h5iYGKlLIlIN2XRXEZF8iSFHbHUg19HpdPZxTuyyInIthhwiqlNubi5yc3Oh1Wo56NhNxBYysVuQiFyDIYeI6nT48GEA1+6azfE47iFOf3HkyBHYbDaJqyFSD4YcIqrToUOHAAC33nqrxJWoV8eOHeHr64uysjKcPHlS6nKIVIMhh4hqZbPZkJ6eDoAhx528vLzQq1cvAMAvv/wicTVE6sGQQ0S1OnnyJMrKyuDr64uOHTtKXY6qiSFSbDkjoqZjyCGiWolfuL1794aXl5fE1aibGHJOnDgBs9kscTVE6sCQQ0S1OnjwIACgT58+EleifiEhIWjdujVsNhu7rIhchCGHiJwqKCjAiRMnAAB9+/aVuJrmQTzPP/30k8SVEKkDQw4RObV//34AQOfOnREcHCxxNc2DeEPiAwcOoKqqSuJqiJSPIYeInNq3bx8AoH///hJX0nx07twZJpMJZrOZEwMSuQBDDhHVcOXKFfskgPHx8RJX03xotVr069cPALusiFyBIYeIahC7S6KiotC6dWupy2lWxC6rPXv2cPZjoiZiyCGiGr7//nsAwJAhQ6DRaCSupnnp06cP/Pz8UFBQwC4roiZiyCEiByUlJfb5cW6//XaJq2l+dDodBg0aBOB62CSixmHIISIHP/zwA6xWK2JjY9lVJRExXP7444+orKyUuBoi5WLIISIHO3fuBMBWHCndcsstaNmyJcxmMw4cOCB1OUSKxZBDRHbnzp3D8ePHodVqGXIkpNVqMXz4cADAtm3bJK6GSLkYcojITvxCjY+P5wSAEhs5ciSAa3clz8nJkbgaImViyCEiAIDFYsF3330HABg1apTE1VBERAR69+4NQRCwfft2qcshUiSGHCICcG0sjtlsRmhoKG/IKRNi2Ny2bRssFovE1RApD0MOEUEQBGzatAkAMG7cOM6NIxPx8fEICQlBcXGxvZWNiOqPIYeIsH//fly4cAG+vr5ITEyUuhz6/3Q6HSZMmAAA2LRpE2dAJmoghhyiZk4QBHz66acAgNGjR8Pb21viiqi6kSNHws/PDxcvXsSePXukLodIURhyiJq5/fv348SJEzAYDBg/frzU5dANjEaj/X356KOPYLVaJa6ISDkYcoiaMZvNhg8//BAAMH78eAQFBUlcETlz9913w9/fHxcuXODYHKIGYMghasa+/fZbnDt3Dr6+vpg4caLU5VAtfHx8MGnSJADXWnOuXr0qcUVEysCQQ9RMlZSUYO3atQCA+++/H35+ftIWRHUaM2YMIiIiUFBQgE8++UTqcogUgSGHqJlas2YNSktLERMTg3HjxkldDt2EXq/HY489BgDYsmULzpw5I3FFRPLHkEPUDO3duxfffvstNBoNHn/8cXh5eUldEtVDXFwcBg8eDJvNhjfeeIMTBBLdBEMOUTOTn5+Pt99+GwDwpz/9CV27dpW4ImqImTNnIigoCFlZWfjXv/4ldTlEssaQQ9SMlJeX46WXXkJpaSliY2Px4IMPSl0SNVBAQACefvppAMDXX3/Nu5QT1YEhh6iZqKqqwptvvokzZ87AZDLhueeeg06nk7osaoQ+ffrYA+qKFStw6NAhiSsikieGHKJmwGq1YunSpdi3bx90Oh2ee+45hIaGSl0WNcHkyZMxdOhQWK1WvPLKKzh8+LDUJRHJDkMOkcpdvXoVL730Ev73v//ZA063bt2kLouaSKPR4Omnn0a/fv1gsViwcOFC7N69W+qyiGSFIYdIxTIyMvC3v/0NBw8ehF6vR0pKCvr27St1WeQiOp0Oc+fOxcCBA1FVVYXXX38dq1evRlVVldSlEcmCRhAEQeoipFBSUgKTyYTi4mIEBARIXQ6RS1ksFnzxxRfYuHEjKisrERwcjBdeeAEdO3aUujRyA5vNhrVr12LTpk0AgJiYGDz++OO8co5UqSHf3ww5DDmkIhaLBd999x02btyIvLw8AEDfvn3x1FNPwWQySVwdudtPP/2Ef/zjHygtLQUADBw4EPfeey86dOgAjUYjcXVErqHYkLN8+XK8/vrryM7ORq9evfD222+jX79+ta7/6aefYt68ecjIyEDHjh3x2muvYcyYMfU6FkMOqUVVVRWOHTuGffv24fvvv7d/wQUHB+PRRx/F4MGD+QXXjBQXF+ODDz7At99+C/HXe0xMDBISEjBkyBAEBwdLXCFR0ygy5GzYsAFTp07FypUrER8fj2XLluHTTz/FiRMnnF4FsmfPHgwdOhSpqam46667sG7dOrz22ms4dOgQunfvftPjMeSQEgmCgKKiIpw7dw4nT57EyZMnceTIEZjNZvs6oaGhuPvuuzFq1Cjo9XoJqyUpZWVlYePGjfjxxx9RWVlpXx4VFYWePXuiS5cuaNOmDaKjo2EwGCSslKhhFBly4uPj0bdvX/zzn/8EcK2POTo6Gk888QTmzp1bY/3JkyfDbDbjyy+/tC/r378/evfujZUrV970eO4KOZWVlSgsLKzXus5OfW1vR0PepobsV+rt67tfT27v6XNlsVhQWVmJiooKVFZWwmKxoKKiAmVlZSgpKbE/CgoKkJ2djYqKihr7MZlM6NevHwYOHIhbb70VWi2vKaBrysrKsHv3bqSlpeHkyZM1Pp8ajQZBQUEICgpCcHAwAgMDERQUBG9vbxgMBhiNRof/enl5QavV2h83/qzVap22HDakNbG+27OFUv5atGiBoKAgl+6zId/fspgJzGKx4ODBg0hJSbEv02q1SEhIwN69e51us3fvXiQnJzssS0xMxObNm52uX1FR4fDlUFJS0vTCnThz5gyeeeYZt+ybCLj2iz08PBwdOnRAx44d0aVLF3Tu3JnBhpzy8/PDmDFjMGbMGJSWluLYsWM4evQozpw5g8zMTHuALigowOnTp6Uul1SmS5cueP311yU7vixCTn5+PqxWK8LCwhyWh4WF4fjx4063yc7Odrp+dna20/VTU1OxaNEi1xRcB41GU2sXgaf+umnIfqXevrZ1PXmu6rt9Q/bRkO1btGgBvV5f4+Hv74+AgAD7fwMDAxEREYGQkBDOVEyN4u/vj/79+6N///72ZcXFxcjLy0NhYSEKCgpQWFiI4uJiXL16FRUVFSgvL0d5ebn9/202m8PDarXWWHYjd7TEyqQTgm5C6t9VzeY3ZUpKikPLT0lJCaKjo11+nE6dOuHzzz93+X6JiNzBZDLxyjtSLVmEnFatWsHLyws5OTkOy3NychAeHu50m/Dw8AatbzAYOLiOiIioGZFFJ75er0dcXBzS0tLsy2w2G9LS0jBgwACn2wwYMMBhfQDYsWNHresTERFR8yKLlhwASE5ORlJSEm677Tb069cPy5Ytg9lsxrRp0wAAU6dORVRUFFJTUwEATz31FG6//Xa8+eabGDt2LNavX4+ff/4Z7733npQvg4iIiGRCNiFn8uTJyMvLw/z585GdnY3evXtj69at9sHFmZmZDlePDBw4EOvWrcMLL7yA5557Dh07dsTmzZvrNUcOERERqZ9s5snxNE4GSEREpDwN+f6WxZgcIiIiIldjyCEiIiJVYsghIiIiVWLIISIiIlViyCEiIiJVYsghIiIiVWLIISIiIlViyCEiIiJVYsghIiIiVZLNbR08TZzouaSkROJKiIiIqL7E7+363LCh2Yac0tJSAEB0dLTElRAREVFDlZaWwmQy1blOs713lc1mw8WLF+Hv7w+NRiNJDSUlJYiOjkZWVhbvn+UEz0/deH5qx3NTN56fuvH81E3q8yMIAkpLSxEZGelw425nmm1LjlarRevWraUuAwAQEBDAf0h14PmpG89P7Xhu6sbzUzeen7pJeX5u1oIj4sBjIiIiUiWGHCIiIlIlhhwJGQwGLFiwAAaDQepSZInnp248P7Xjuakbz0/deH7qpqTz02wHHhMREZG6sSWHiIiIVIkhh4iIiFSJIYeIiIhUiSGHiIiIVIkhRybGjx+PNm3awGg0IiIiAg899BAuXrwodVmykJGRgT//+c9o164dvL29ERsbiwULFsBisUhdmmy88sorGDhwIHx8fBAYGCh1OZJbvnw5YmJiYDQaER8fj/3790tdkizs3r0b48aNQ2RkJDQaDTZv3ix1SbKRmpqKvn37wt/fH6GhoZgwYQJOnDghdVmysWLFCvTs2dM+AeCAAQPwzTffSF3WTTHkyMTw4cOxceNGnDhxAp9//jlOnz6Ne++9V+qyZOH48eOw2Wx49913cezYMbz11ltYuXIlnnvuOalLkw2LxYL77rsPM2fOlLoUyW3YsAHJyclYsGABDh06hF69eiExMRG5ublSlyY5s9mMXr16Yfny5VKXIjvff/89Zs2ahX379mHHjh2orKzEyJEjYTabpS5NFlq3bo1XX30VBw8exM8//4w77rgDd999N44dOyZ1aXUTSJa2bNkiaDQawWKxSF2KLC1ZskRo166d1GXIzpo1awSTySR1GZLq16+fMGvWLPvPVqtViIyMFFJTUyWsSn4ACJs2bZK6DNnKzc0VAAjff/+91KXIVlBQkPD+++9LXUad2JIjQwUFBfj4448xcOBAtGjRQupyZKm4uBjBwcFSl0EyY7FYcPDgQSQkJNiXabVaJCQkYO/evRJWRkpTXFwMAPw944TVasX69ethNpsxYMAAqcupE0OOjMyZMwe+vr5o2bIlMjMzsWXLFqlLkqVTp07h7bffxmOPPSZ1KSQz+fn5sFqtCAsLc1geFhaG7OxsiaoipbHZbPjrX/+KQYMGoXv37lKXIxtHjx6Fn58fDAYDZsyYgU2bNqFbt25Sl1Unhhw3mjt3LjQaTZ2P48eP29f/+9//jl9++QXbt2+Hl5cXpk6dCkHFE1I39PwAwIULFzBq1Cjcd999mD59ukSVe0Zjzg8RNd2sWbPw66+/Yv369VKXIiudO3dGeno6fvrpJ8ycORNJSUn47bffpC6rTrytgxvl5eXh8uXLda7Tvn176PX6GsvPnz+P6Oho7NmzR/bNgY3V0PNz8eJFDBs2DP3798fatWuh1ao7ozfm87N27Vr89a9/RVFRkZurkyeLxQIfHx989tlnmDBhgn15UlISioqK2DpajUajwaZNmxzOEwGzZ8/Gli1bsHv3brRr107qcmQtISEBsbGxePfdd6UupVY6qQtQs5CQEISEhDRqW5vNBgCoqKhwZUmy0pDzc+HCBQwfPhxxcXFYs2aN6gMO0LTPT3Ol1+sRFxeHtLQ0+5e3zWZDWloaZs+eLW1xJGuCIOCJJ57Apk2bsGvXLgacerDZbLL/jmLIkYGffvoJBw4cwODBgxEUFITTp09j3rx5iI2NVW0rTkNcuHABw4YNQ9u2bfHGG28gLy/P/lx4eLiElclHZmYmCgoKkJmZCavVivT0dABAhw4d4OfnJ21xHpacnIykpCTcdttt6NevH5YtWwaz2Yxp06ZJXZrkysrKcOrUKfvPZ8+eRXp6OoKDg9GmTRsJK5PerFmzsG7dOmzZsgX+/v72MVwmkwne3t4SVye9lJQUjB49Gm3atEFpaSnWrVuHXbt2Ydu2bVKXVjdpL+4iQRCEI0eOCMOHDxeCg4MFg8EgxMTECDNmzBDOnz8vdWmysGbNGgGA0wddk5SU5PT87Ny5U+rSJPH2228Lbdq0EfR6vdCvXz9h3759UpckCzt37nT6OUlKSpK6NMnV9jtmzZo1UpcmC4888ojQtm1bQa/XCyEhIcKIESOE7du3S13WTXFMDhEREamS+gc2EBERUbPEkENERESqxJBDREREqsSQQ0RERKrEkENERESqxJBDREREqsSQQ0RERKrEkENERESqxJBDREREqsSQQ0SqV1VVJXUJRCQBhhwiUpWMjAxoNBps3LgRQ4YMgcFgwH/+8x+pyyIiCfAu5ESkKocPHwYAvP7661i8eDHatWuHkJAQiasiIikw5BCRqqSnp8PX1xeffvopYmJipC6HiCTE7ioiUpXDhw9j/PjxDDhExJBDROqSnp6OYcOGSV0GEckAQw4RqUZJSQkyMjLQp08fqUshIhlgyCEi1Th8+DC8vLzQo0cPqUshIhlgyCEi1Th8+DA6d+4Mo9EodSlEJAMaQRAEqYsgIiIicjW25BAREZEqMeQQERGRKjHkEBERkSox5BAREZEqMeQQERGRKjHkEBERkSox5BAREZEqMeQQERGRKjHkEBERkSox5BAREZEqMeQQERGRKjHkEBERkSr9P4/HDwuwgHPGAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# We limit our function on a grid to the range [0, 6]\n", + "gaussian_origin_f = gaussian_origin()\n", + "gaussian_origin_f = normalize_function(gaussian_origin_f, a, b)\n", + "plt.plot(r_grid, gaussian_origin_f(r_grid), color=\"k\", alpha=0.7)\n", + "plt.title(\"Gaussian centered at the origin\")\n", + "plt.xlabel(\"$r$\")\n", + "plt.ylabel(\"$f(r)$\")\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "id": "3edd5caa", + "metadata": {}, + "source": [ + "### Gaussian probablity density function centered at the boundary" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "6b31d63f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def gaussian_boundary(\n", + " a: float, b: float, sigma: float = 0.3\n", + ") -> Callable[[np.ndarray], np.ndarray]:\n", + " \"\"\"\n", + " Returns a function that computes a Gaussian function centered\n", + " at the end of the interval [a, b].\n", + "\n", + " :param a: The start of the interval.\n", + " :param b: The end of the interval.\n", + " :param sigma: The sigma of the Gaussian function.\n", + " \"\"\"\n", + " gaussian_f = gaussian(b, sigma)\n", + " return lambda r: gaussian_f(r)\n", + "\n", + "\n", + "gaussian_boundary_f = gaussian_boundary(a, b)\n", + "gaussian_boundary_f = normalize_function(gaussian_boundary_f, a, b)\n", + "plt.plot(r_grid, gaussian_boundary_f(r_grid), color=\"k\", alpha=0.7)\n", + "plt.title(\"Gaussian centered at the boundary\")\n", + "plt.xlabel(\"$r$\")\n", + "plt.ylabel(\"$f(r)$\")\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "id": "9cfdf23c", + "metadata": {}, + "source": [ + "### Sawtooth function" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "df831ddd-4658-4a56-966b-fc129502cf1a", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def sawtooth(a: float, b: float):\n", + " \"\"\"\n", + " Returns a function that computes the sawtooth function realigned\n", + " to the interval [a, b].\n", + "\n", + " :param a: The start of the interval.\n", + " :param b: The end of the interval.\n", + " \"\"\"\n", + " return lambda r: (r % 1) * np.sqrt(3) / np.sqrt(b - a)\n", + "\n", + "\n", + "sawtooth_f = sawtooth(a, b)\n", + "plt.plot(r_grid, sawtooth_f(r_grid), color=\"k\", alpha=0.7)\n", + "plt.title(\"Sawtooth $t$ mod $1$\")\n", + "plt.xlabel(\"$r$\")\n", + "plt.ylabel(\"$f(r)$\")\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "id": "a65e3858", + "metadata": {}, + "source": [ + "## Basis expansion and reconstruction\n", + "\n", + "The basis expansion coefficients for an orthonormal basis can be expressed as\n", + "$$ c_n = \\int_\\mathbb{R}\\mathrm{d}r\\,b_n(r)f(r)$$\n", + "\n", + "For an orthonormal complete basis $\\{b_n\\}_n$ we can than reconstruct the target function $f$ in the limit of the number of basis functions\n", + "$$ \\sum_n c_n b_n(r) =_{n \\rightarrow\\infty} f(r)$$" + ] + }, + { + "cell_type": "markdown", + "id": "d9bec282", + "metadata": {}, + "source": [ + "### Approximation error of the basis reconstruction\n", + "\n", + "Looking at the function gives use already an idea about how suitable a basis is to reconstruct a function. Now we more rigorous quantify this intuition by computing the approximation error on the interval $[-π,π]$. \n", + "$$ \\ell(\\{b_n\\}_{n=0}^M, f) = \\int_{-π}^{π}\\mathrm{d}r\\,(\\sum_n^M c_n b_n(r) - f(r))^2$$ \n", + "An compare the results for different type of basis funcitons $\\{b_n\\}_n^M$ and target functions $f$ with respect to the total number of basis functions $M+1$. In principle we can use any other loss function (for example L1 norm). For the sake of this exercise, the differences between loss functions is not relevant and we only chose the mean squared error as it is widely used." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "f20b7369", + "metadata": {}, + "outputs": [], + "source": [ + "NB_GRID_POINTS = 500\n", + "INTEGRATION_GRID = np.linspace(a, b, NB_GRID_POINTS)\n", + "GRID_DX = (b - a) / NB_GRID_POINTS\n", + "\n", + "\n", + "def basis_function_expansion(\n", + " basis_f: Callable[[np.ndarray], np.ndarray],\n", + " target_f: Callable[[np.ndarray], np.ndarray],\n", + " a: float,\n", + " b: float,\n", + ") -> float:\n", + " \"\"\"\n", + " Expands a basis function on a target function on the interval [a, b]\n", + " and returns the basis expansion coefficient.\n", + "\n", + " :param basis_f: Basis function.\n", + " :param target_f: Target function.\n", + " :param a: Beginning of the interval to integrate on\n", + " :param b: End of the interval to integrate on.\n", + " \"\"\"\n", + "\n", + " norm_target = np.sqrt(\n", + " scipy.integrate.simpson(\n", + " target_f(INTEGRATION_GRID) ** 2, x=INTEGRATION_GRID, dx=GRID_DX\n", + " )\n", + " )\n", + " norm_basis = np.sqrt(\n", + " scipy.integrate.simpson(\n", + " basis_f(INTEGRATION_GRID) ** 2, x=INTEGRATION_GRID, dx=GRID_DX\n", + " )\n", + " )\n", + " return scipy.integrate.simpson(\n", + " basis_f(INTEGRATION_GRID)\n", + " * target_f(INTEGRATION_GRID)\n", + " / (norm_basis * norm_target),\n", + " x=INTEGRATION_GRID,\n", + " dx=GRID_DX,\n", + " )\n", + "\n", + "\n", + "def basis_reconstruction(\n", + " basis: Callable[[int], Callable[[np.ndarray], np.ndarray]],\n", + " target_f: Callable[[np.ndarray], np.ndarray],\n", + " nb_basis_functions: int,\n", + " a: float,\n", + " b: float,\n", + ") -> Callable[[np.ndarray], np.ndarray]:\n", + " \"\"\"\n", + " Expand function on basis on the interval [a, b]\n", + "\n", + " Expands a basis on a target function on the interval [a, b]\n", + " and returns the basis reconstruction in form of a lambda\n", + " function that multiplies the basis functions with the basis\n", + " expansion coefficients.\n", + "\n", + " :param basis_f: Basis function.\n", + " :param target_f: Target function.\n", + " :param nb_basis_functions: Number of basis functions to use for reconstruction.\n", + " :param a: Beginning of the interval to integrate on\n", + " :param b: End of the interval to integrate on.\n", + " \"\"\"\n", + " expansion_coeffs = np.zeros(nb_basis_functions)\n", + " for n in range(nb_basis_functions):\n", + " expansion_coeffs[n] = basis_function_expansion(basis(n), target_f, a, b)\n", + "\n", + " return lambda r: np.sum(\n", + " [\n", + " expansion_coeffs[n] * basis(n)(r) # TODO add norm here\n", + " for n in range(nb_basis_functions)\n", + " ],\n", + " axis=0,\n", + " )\n", + "\n", + "\n", + "def squared_error(\n", + " f_1: Callable[[np.ndarray], np.ndarray],\n", + " f_2: Callable[[np.ndarray], np.ndarray],\n", + " a: float,\n", + " b: float,\n", + ") -> float:\n", + " \"\"\"\n", + " Computes the squared error between the two functions integrated\n", + " on the interval [a, b].\n", + "\n", + " .. math:\n", + "\n", + " \\\\int_a^b\\\\mathrm{d}r\\\\, (f_1(r) - f_2(r))^2\n", + "\n", + " :param f_1: First function\n", + " :param f_2: Second function.\n", + " :param a: beginning of the interval to integrate\n", + " :param b: end of the interval to integrate\n", + " \"\"\"\n", + " return scipy.integrate.simpson(\n", + " (f_1(INTEGRATION_GRID) - f_2(INTEGRATION_GRID)) ** 2,\n", + " x=INTEGRATION_GRID,\n", + " dx=GRID_DX,\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "636ffad0", + "metadata": { + "lines_to_next_cell": 1 + }, + "outputs": [], + "source": [ + "nbs_basis_functions = np.arange(1, 26)\n", + "\n", + "basis_function_options = [\"Legendre\", \"Fourier\", \"Schauder\"]\n", + "target_function_options = [\"Gaussian at origin\", \"Gaussian at boundary\", \"Sawtooth\"]\n", + "\n", + "basis_reconstructions = {}\n", + "basis_expansion_error = {}\n", + "basis_f_eval_on_grid = {}\n", + "target_f_eval_on_grid = {}\n", + "for basis in basis_function_options:\n", + " if basis == \"Legendre\":\n", + " basis_f = legendre_polynomial\n", + " elif basis == \"Schauder\":\n", + " basis_f = lambda n, a, b: schauder(n, max(nbs_basis_functions) + 1, a, b)\n", + " elif basis == \"Fourier\":\n", + " basis_f = fourier_series\n", + " else:\n", + " raise ValueError(f\"basis {basis!r} not known.\")\n", + "\n", + " basis_reconstructions[basis] = {}\n", + " basis_expansion_error[basis] = {}\n", + " basis_f_eval_on_grid[basis] = {}\n", + " target_f_eval_on_grid[basis] = {}\n", + " for target in target_function_options:\n", + " if target == \"Gaussian at origin\":\n", + " target_f = gaussian_origin_f\n", + " elif target == \"Gaussian at boundary\":\n", + " target_f = gaussian_boundary_f\n", + " elif target == \"Sawtooth\":\n", + " target_f = sawtooth_f\n", + " else:\n", + " raise ValueError(f\"target function {target_f} is not supported.\")\n", + "\n", + " basis_reconstructions[basis][target] = {}\n", + " basis_expansion_error[basis][target] = {}\n", + " basis_f_eval_on_grid[basis][target] = {}\n", + " target_f_eval_on_grid[basis][target] = target_f(r_grid)\n", + "\n", + " for nb_basis_functions in nbs_basis_functions:\n", + " basis_reconstructions_f = basis_reconstruction(\n", + " lambda n: basis_f(n, a, b), target_f, nb_basis_functions, a, b\n", + " )\n", + "\n", + " basis_expansion_error[basis][target][nb_basis_functions] = squared_error(\n", + " basis_reconstructions_f, target_f, a, b\n", + " )\n", + " basis_reconstructions[basis][target][nb_basis_functions] = (\n", + " basis_reconstructions_f(r_grid)\n", + " )\n", + " basis_f_eval_on_grid[basis][target][nb_basis_functions - 1] = basis_f(\n", + " nb_basis_functions - 1, a, b\n", + " )(r_grid)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "b4ceea97-8ccf-4365-8618-0bbd00aa1f54", + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "8674b0a15bfa40d898c89a3013c70757", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "interactive(children=(IntSlider(value=1, description='nb basis functions', layout=Layout(width='400px'), max=2…" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def basis_reconstruction_exercise(nb_basis_functions, basis, target):\n", + " global nbs_basis_functions, r_grid, a, b\n", + " global legendre_polynomial, schauder, fourier_series\n", + " global gaussian_origin_f, gaussian_boundary_f, sawtooth_f\n", + " global basis_expansion_error, basis_reconstruction\n", + " global target_f_eval_on_grid, basis_f_eval_on_grid\n", + "\n", + " if target == \"Gaussian at origin\":\n", + " target_f = gaussian_origin_f\n", + " elif target == \"Gaussian at boundary\":\n", + " target_f = gaussian_boundary_f\n", + " elif target == \"Sawtooth\":\n", + " target_f = sawtooth_f\n", + " else:\n", + " raise ValueError(f\"Target function {target_f} is not supported.\")\n", + "\n", + " fig = plt.figure(figsize=(13, 8))\n", + " gs = fig.add_gridspec(2, 2)\n", + " ax1 = fig.add_subplot(gs[0, 0])\n", + " ax2 = fig.add_subplot(gs[0, 1])\n", + " ax3 = fig.add_subplot(gs[1, :])\n", + "\n", + " fig.suptitle(\"Target function reconstruction by basis expansion\")\n", + "\n", + " for n in range(nb_basis_functions):\n", + " ax1.plot(\n", + " r_grid,\n", + " basis_f_eval_on_grid[basis][target][n],\n", + " label=\"$b_{\" + str(n) + \"}(r)$\",\n", + " )\n", + "\n", + " ax1.set_title(f\"{basis} basis functions\")\n", + " ax1.set_xlabel(\"$r$\")\n", + " ax1.set_ylabel(\"$b_n(r)$\")\n", + " if basis == \"Legendre\":\n", + " ax1.set_ylim(-1.0, 1.0)\n", + " elif basis == \"Schauder\":\n", + " ax1.set_ylim(-0.05, 3.5)\n", + " elif basis == \"Fourier\":\n", + " ax1.set_ylim(-0.75, 0.75)\n", + "\n", + " ax1.legend(ncol=4)\n", + "\n", + " ax2.plot(\n", + " r_grid,\n", + " basis_reconstructions[basis][target][nb_basis_functions],\n", + " label=\"$\\\\sum_{n=0}^{\" + str(nb_basis_functions - 1) + \"}c_nb_n(r)$\",\n", + " )\n", + " ax2.plot(\n", + " r_grid,\n", + " target_f_eval_on_grid[basis][target],\n", + " alpha=0.7,\n", + " color=\"k\",\n", + " label=\"$f(r)$\",\n", + " )\n", + " ax2.set_title(f\"{basis} basis reconstruction of {target}\")\n", + " ax2.set_xlabel(\"$r$\")\n", + " ax2.set_ylabel(\"$f(r)$\")\n", + " if target == \"Gaussian at origin\":\n", + " ax2.set_ylim(-0.2, 1.5)\n", + " elif target == \"Gaussian at boundary\":\n", + " ax2.set_ylim(-0.2, 2.0)\n", + " elif target == \"Sawtooth\":\n", + " ax2.set_ylim(-0.05, 1.0)\n", + " ax2.legend()\n", + "\n", + " selected_error = basis_expansion_error[basis][target]\n", + " for basis_expansion_error_values in basis_expansion_error.values():\n", + " ax3.plot(\n", + " nbs_basis_functions, basis_expansion_error_values[target].values(), lw=2\n", + " )\n", + " ax3.plot(\n", + " nbs_basis_functions, selected_error.values(), color=\"yellow\", alpha=0.2, lw=10\n", + " )\n", + " ax3.scatter(\n", + " [nb_basis_functions], [selected_error[nb_basis_functions]], color=\"red\", s=50\n", + " )\n", + " ax3.set_title(f\"Reconstruction error of {target} using {basis} basis\")\n", + " ax3.set_xticks(nbs_basis_functions[::2])\n", + " ax3.set_xlabel(\"number of basis functions\")\n", + " ax3.set_ylabel(\n", + " \"Error $\\\\int_{-π}^{π} \\\\mathrm{d}r\\\\, (f(r)-\\\\sum_n^{n_{basis}} c_n b_n(r))^2$\"\n", + " )\n", + " ax3.set_ylim(-0.05, 1.05)\n", + " plt.show()\n", + "\n", + "\n", + "interactive_plot = interactive(\n", + " basis_reconstruction_exercise,\n", + " nb_basis_functions=IntSlider(\n", + " min=min(nbs_basis_functions),\n", + " max=max(nbs_basis_functions),\n", + " description=\"nb basis functions\",\n", + " style={\"description_width\": \"initial\", \"width\": \"800px\"},\n", + " layout=Layout(width=\"400px\"),\n", + " ),\n", + " basis=basis_function_options,\n", + " target=target_function_options,\n", + ")\n", + "interactive_plot" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "66425911-44d5-46a9-b676-bd0ecee74f1e", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "hide_input": false, + "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": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} From 294b6518a3741e1a13a44dbf9330300b1337ee6d Mon Sep 17 00:00:00 2001 From: Alexander Goscinski Date: Tue, 27 Feb 2024 11:10:56 +0100 Subject: [PATCH 2/2] add tox.ini with envs lint, format, run-notebooks --- tox.ini | 33 +++++++++++++++++++++++++++++++++ 1 file changed, 33 insertions(+) create mode 100644 tox.ini diff --git a/tox.ini b/tox.ini new file mode 100644 index 0000000..868e74a --- /dev/null +++ b/tox.ini @@ -0,0 +1,33 @@ +[tox] +lint_folders = + "{toxinidir}/notebooks" + +[testenv] + +[testenv:run-notebooks] +deps = + numpy + scipy + matplotlib + ipywidgets + jupyter +commands = + jupyter execute {toxinidir}/notebooks/01-BasisExpansion.ipynb + +[testenv:format] +# formats project source code files +skip_install = true +deps = + black[jupyter] +commands = + black {[tox]lint_folders} + +[testenv:lint] +skip_install = true +deps = + flake8-nb +commands = + flake8_nb {[tox]lint_folders} + +[flake8_nb] +max_line_length = 88