diff --git "a/Chapitre 3 - Espace vectoriel/3.1. D\303\251finition d'un espace vectoriel.ipynb" "b/Chapitre 3 - Espace vectoriel/3.1. D\303\251finition d'un espace vectoriel.ipynb" index d42c205..cee7d92 100644 --- "a/Chapitre 3 - Espace vectoriel/3.1. D\303\251finition d'un espace vectoriel.ipynb" +++ "b/Chapitre 3 - Espace vectoriel/3.1. D\303\251finition d'un espace vectoriel.ipynb" @@ -1,1020 +1,2315 @@ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Concept(s)-clé(s) et théorie\n", "\n", - "Soit $V$ un ensemble non-vide muni d'une opération binaire $+$ et d'une action sur les nombres réels $\\cdot$, c'est-à-dire que pour tout $u,v\\in V$, il existe un unique élément $u+v\\in V$ et pour tout $u\\in V$, $\\lambda\\in \\mathbb{R}$, il existe un unique élément $\\lambda\\cdot u\\in V$. On dira que $V$ est un $\\mathbb{R}$-espace vectoriel si les huit axiomes suivants sont satisfaits, pour tous $u,v,w\\in V$ et $\\lambda, \\mu\\in \\mathbb{R}$.\n", + "Soit $ V $ un ensemble non-vide muni d'une opération binaire $+$ et d'une action sur les nombres réels $\\cdot$, c'est-à-dire que pour tout $u,v\\in V$, il existe un unique élément $u+v\\in V$ et pour tout $u\\in V$, $\\lambda\\in \\mathbb{R}$, il existe un unique élément $\\lambda\\cdot u\\in V$. On dira que $V$ est un $\\mathbb{R}$-espace vectoriel si les huit axiomes suivants sont satisfaits, pour tous $u,v,w\\in V$ et $\\lambda, \\mu\\in \\mathbb{R}$.\n", "\n", "\n", "1. $u+ v=v+ u$\n", "2. $(u+ v) + w = u + (v+ w)$\n", "3. $\\lambda\\cdot( u + v)= \\lambda \\cdot u + \\lambda \\cdot v$\n", "4. $(\\lambda + \\mu)\\cdot v=\\lambda \\dot v + \\mu\\cdot v$\n", "5. $\\lambda \\cdot (\\mu\\cdot v)=(\\lambda \\mu)\\cdot v$\n", "6. $1\\cdot u=u$\n", "7. Il existe un élément neutre pour la loi $+$, i.e. un élément $e\\in V$ tel que $e+ u=u$ pour tout $u\\in V$.\n", "8. Pour tout $u\\in V$, il existe un unique inverse par rapport à la loi $+$, i.e. un élément $u' \\in V$ tel que $u+ u'=e$. \n", "\n", "Remarques: \n", "1. On écrit $\\lambda v$ au lieu de $\\lambda \\cdot v$. \n", "2. Les éléments de $V$ sont appelés des vecteurs (même si on ne les écrit pas $\\overrightarrow v$) et les éléments de $\\mathbb{R}$ des scalaires.\n", "\n" ] }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "import AL_Fct as al\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import plotly\n", + "import plotly.graph_objs as go\n", + "import pandas as pd\n", + "import random\n", + "from IPython.core.magic import register_cell_magic\n", + "from IPython.display import HTML, display" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "linkText": "Export to plot.ly", + "plotlyServerURL": "https://plot.ly", + "showLink": false + }, + "data": [ + { + "line": { + "color": "teal", + "width": 3 + }, + "mode": "lines", + "name": "Vecteur u", + "type": "scatter", + "uid": "6970a911-e01a-4ea5-9fc2-a2f14994e97a", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#what they seee\n", + "u=[[1],[1]]\n", + "v=[[2],[4]]\n", + "lam=2\n", + "mu=2\n", + "o=[[0],[0]]\n", + "\n", + "#Initial settings, change to np.array\n", + "u=np.array(u)\n", + "v=np.array(v)\n", + "data = []\n", + "t = np.linspace(-5, 5, 51)\n", + "s = np.linspace(0, 1, 10)\n", + "peak = go.Scatter(x=u[0], y=u[1], marker=dict(symbol=6, size=12, color='teal'), showlegend=False)\n", + "peak2 = go.Scatter(x=v[0], y=v[1], marker=dict(symbol=6, size=12, color='slateblue'), showlegend=False)\n", + "vector = go.Scatter(x=o[0] + s * u[0], y=o[1] + s * u[1], mode='lines',\n", + "line=dict(width=3, color='teal'), name='Vecteur u')\n", + "vector2 = go.Scatter(x=o[0] + s * v[0], y=o[1] + s * v[1], mode='lines',\n", + "line=dict(width=3, color='slateblue'), name='Vecteur v')\n", + "zero = go.Scatter(x=t*0, y=t*0, name='Origine', marker=dict(symbol=6, size=12, color='black'),\n", + " showlegend=False)\n", + "data.append(vector)\n", + "data.append(vector2)\n", + "data.append(zero)\n", + "data.append(peak)\n", + "data.append(peak2)\n", + "\n", + "#axiom 1 and 2(similar)\n", + "trace1= go.Scatter(x=u[0] + s * v[0], y=u[1] + s * v[1], mode='lines',\n", + "line=dict(width=1, color='slateblue', dash='dash'), name='\"v\"')\n", + "trace2= go.Scatter(x=v[0] + s * u[0], y=v[1] + s * u[1], mode='lines',\n", + "line=dict(width=1, color='teal', dash='dash'), name='\"u\"')\n", + "w=u+v\n", + "sumUV=go.Scatter(x=o[0] + s *w[0], y=o[1] + s * w[1], mode='lines',\n", + "line=dict(width=1, color='orangered', dash='dash'), name='u+v')\n", + "peakUV = go.Scatter(x=w[0], y=w[1], marker=dict(symbol=6, size=12, color='orangered'), showlegend=False)\n", + "\n", + "data.append(trace1)\n", + "data.append(trace2)\n", + "\n", + "data.append(sumUV)\n", + "data.append(peakUV)\n", + "\n", + "fig = go.FigureWidget(data=data)\n", + "plotly.offline.iplot(fig)\n", + "\n" + ] + }, { "cell_type": "markdown", "metadata": {}, 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EGGQ5AjNIUQYxEZgGEIOMQGAGKcogJgLTAGKAEQjMACUZRkRgGsJ0PgqB6bwgw3gITEOYzkchMJ0X5DQeAlNZDAJTCTDIcgRmkKIMYiIwDSAGGYHADFKUQUwEpgHEACMQmAFKMoyIwDSE6XwUAtN5QYbxEJiGMJ2PQmA6L8hpPASmshgEphJgkOUIzCBFGcREYBpADDICgRmkKIOYCEwDiAFGIDADlGQYEYFpCNP5KASm84IM4yEwDWE6H4XAdF6Q03gITGUxCEwlwCDLEZhBijKIicA0gBhkBAIzSFEGMRGYBhADjEBgBijJMCIC0xCm81EITOcFGcZDYBrCdD4Kgem8IKfxEJjKYhCYSoBBliMwgxRlEBOBaQAxyAgEZpCiDGIiMA0gBhiBwAxQkmFEBKYhTOejEJjOCzKMh8A0hOl8FALTeUFO4yEwlcUgMJUAgyxHYAYpyiAmAtMAYpARCMwgRRnERGAaQAwwAoEZoCTDiAhMQ5jORyEwnRdkGA+BaQjT+SgEpvOCnMZDYCqLQWAqAQZZjsAMUpRBTASmAcQgIxCYQYoyiInANIAYYAQCM0BJhhERmIYwnY9CYDovyDAeAtMQpvNRbROYZ86KPPPsmPzPn1ntvBnf8RCYyn4QmEqAQZYjMIMUZRATgWkAMcgIBGaQogxiIjANIAYYgcAMUJJhRASmIUznoxCYzgsyjIfANITpfFRbBOaZMyI/eXYsk5fSEfk///dVzpvxHQ+BqewHgakEGGQ5AjNIUQYxEZgGEIOMQGAGKcogJgLTAGKAEQjMACUZRkRgGsJ0PgqB6bwgw3gITEOYzkc1XWCePj0Ql+fO52Vs2IDA1J6WCEwlQQSmEmCQ5QjMIEUZxERgGkAMMgKBGaQog5gITAOIAUYgMAOUZBgRgWkI0/koBKbzggzjITANYTof1VSBeeqUyE+ey6+4PD8rLjduFPnoA93s1523rHHejO94CExlPwhMJcAgyxGYQYoyiInANIAYZAQCM0hRBjERmAYQA4xAYAYoyTAiAtMQpvNRCEznBRnGQ2AawnQ+qmkC8+SpjjzzbCe7XfzChRz+piQuH8zF5bp1+dd2bkNgak5NBKaGnoggMJUAgyxHYAYpyiAmAtMAYpARCMwgRRnERGAaQAwwAoEZoCTDiAhMQ5jORyEwnRdkGA+BaQjT+aimCMwTJwfi8uLFHPrmTfkVlw8+2JV1axcWgcDUnZgITB0/BKaSX5TlCMwoTelzIjD1DKNMQGBGaUqfE4GpZxhhAgIzQkt2GRGYdiy9T0Jgem/ILh8C046l90nRBebxEwNxeelSTnvL5p48+EAvu+py7VUutERg6s5MBKaOHwJTyS/KcgRmlKb0ORGYeoZRJiAwozSlz4nA1DOMMAGBGaElu4wITDuW3ichML03ZJcPgWnH0vukqALz+PF0m3iSl2NyaXJWXG7pyUeTuHygK2uWuUMcgak7MxGYOn4ITCW/KMsRmFGa0udEYOoZRpmAwIzSlD4nAlPPMMIEBGaEluwyIjDtWHqfhMD03pBdPgSmHUvvk6IJzGPHOvKT53JxOTkrLrduHYjLiYnhiCMwh+N0ta0QmDp+CEwlvyjLEZhRmtLnRGDqGUaZgMCM0pQ+JwJTzzDCBARmhJbsMiIw7Vh6n4TA9N6QXT4Eph1L75OiCMyjSVzOXnE5NZVT3bZtIC5Xrx6NNAJzNF6Lt0Zg6vghMJX8oixHYEZpSp8TgalnGGUCAjNKU/qcCEw9wwgTEJgRWrLLiMC0Y+l9EgLTe0N2+RCYdiy9T/IuMN8/OnjG5fR0TvO6JC4fzG8VHx8vRhiBWYxbfxUCU8cPgankF2U5AjNKU/qcCEw9wygTEJhRmtLnRGDqGUaYgMCM0JJdRgSmHUvvkxCY3huyy4fAtGPpfZJXgfne+wNxeflyTvH66/IrLtNbxcdX6cgiMHX8EJg6fghMJb8oyxGYUZrS50Rg6hlGmYDAjNKUPicCU88wwgQEZoSW7DIiMO1Yep+EwPTekF0+BKYdS++TvAnMI+8NxOXMTE7vhutn3yr+QFdWKcVlvw8Epu7MRGDq+CEwlfyiLEdgRmlKnxOBqWcYZQICM0pT+pwITD3DCBMQmBFassuIwLRj6X0SAtN7Q3b5EJh2LL1P8iIwjxzJn3H5k2fHpNvNqW2/YSAuV660JYnA1PFEYOr4ITCV/KIsR2BGaUqfE4GpZxhlAgIzSlP6nAhMPcMIExCYEVqyy4jAtGPpfRIC03tDdvkQmHYsvU+qW2C+Oysu01vF58Tl9sHLeVasKIcgAlPHFYGp44fAVPKLshyBGaUpfU4Epp5hlAkIzChN6XMiMPUMI0xAYEZoyS4jAtOOpfdJCEzvDdnlQ2DasfQ+qS6BefjdwVvFe72c0o4kLmdfzjM2Vi45BKaOLwJTxw+BqeQXZTkCM0pT+pwITD3DKBMQmFGa0udEYOoZRpiAwIzQkl1GBKYdS++TEJjeG7LLh8C0Y+l9UtUC89DhwTMu+2xu3DF7xeWDXel0qiGGwNRxRmDq+CEwlfyiLEdgRmlKnxOBqWcYZQICM0pT+pwITD3DCBMQmBFassuIwLRj6X0SAtN7Q3b5EJh2LL1PqkpgvnMoF5fPPDe4tHLnjbNvFX+gOnHZ7wOBqTszEZg6fghMJb8oyxGYUZrS50Rg6hlGmYDAjNKUPicCU88wwgQEZoSW7DIiMO1Yep+EwPTekF0+BKYdS++TyhaYb7+Ti8tnfzoQl7t2Dl7OUxcfBKaOPAJTxw+BqeQXZTkCM0pT+pwITD3DKBMQmFGa0udEYOoZRpiAwIzQkl1GBKYdS++TEJjeG7LLh8C0Y+l9UlkC8+2382dcPvf8QFzu3pWLywc/Mvua8RrhIDB18BGYOn4ITCW/KMsRmFGa0udEYOoZRpmAwIzSlD4nAlPPMMIEBGaEluwyIjDtWHqfhMD03pBdPgSmHUvvk6wF5luZuByTnz4/eJjlTbtzcfnAh+sXl/0+EJi6MxOBqeOHwFTyi7IcgRmlKX1OBKaeYZQJCMwoTelzIjD1DCNMQGBGaMkuIwLTjqX3SQhM7w3Z5UNg2rH0PslKYL75Vi4un39hobhMbxX/yP1+xCUC0+aMRGAqOR4+flE5geURCCAwI7RkkxGBacMxwhQEZoSWbDIiMG04ep+CwPTekG0+BKYtT8/TEJie27HNhsC05el5mlZgvvFmLi5f+NlAXN58U3o5T1c+fH/P7aFzBaauGgSmjh9XYCr5RVmOwIzSlD4nAlPPMMoEBGaUpvQ5EZh6hhEmIDAjtGSXEYFpx9L7JASm94bs8iEw7Vh6n1RUYL7+Rno5z5i88POBuLzl5lxc3v8hv+Ky3wcCU3dmIjB1/BCYSn5RliMwozSlz4nA1DOMMgGBGaUpfU4Epp5hhAkIzAgt2WVEYNqx9D4Jgem9Ibt8CEw7lt4njSowX3s9F5c/e3EgLvfckovLD33Qv7hEYNqckQhMJUduIVcCDLIcgRmkKIOYCEwDiEFGIDCDFGUQE4FpADHACARmgJIMIyIwDWE6H4XAdF6QYTwEpiFM56OGFZhJXKZbxX8+T1zeuie9nKcrH/pAHHGJwLQ5IRGYSo4ITCXAIMsRmEGKMoiJwDSAGGQEAjNIUQYxEZgGEAOMQGAGKMkwIgLTEKbzUQhM5wUZxkNgGsJ0Pmo5gfnqa7m4fPGlwRWXe2/NxeUH74snLhGYNickAlPJEYGpBBhkOQIzSFEGMRGYBhCDjEBgBinKICYC0wBigBEIzAAlGUZEYBrCdD4Kgem8IMN4CExDmM5HXU1gHnw1F5cv7VsoLtOt4h8ILC4RmDYnJAJTyRGBqQQYZDkCM0hRBjERmAYQg4xAYAYpyiAmAtMAYoARCMwAJRlGRGAawnQ+CoHpvCDDeAhMQ5jORy0WmAcO5uJy3/6BuLxtb/6My/vujXvF5eIaeImP7sRshcD87vd/IF/5+rcXkPrcbz0qX/i9x7KvnTx9Vj7/+J/KC/tezf7+nW8+Lh+7/+657eevf/TTD8lXv/hZmZgYz76PwNSdgFFWIzCjNKXPicDUM4wyAYEZpSl9TgSmnmGECQjMCC3ZZURg2rH0PgmB6b0hu3wITDuW3if1BebLr+Ticv/LA3F5+225uLz3nuaIy34fCEzdmdkagfn0sy8uEI99bJcuTckf/clfy0MP3Cef+fWH5bU3D8uXn/wreeLx35G9t+yUHz+/X77x50/Jt578A9myaYN84y+eypb25ScCU3cCRlmNwIzSlD4nAlPPMMoEBGaUpvQ5EZh6hhEmIDAjtGSXEYFpx9L7JASm94bs8iEw7Vh6n3T03Qn5//5heoG4vOP2XFzec3fzxCUC0+aMbL3ATMLyj//sb+WJP/zdTFAuFppJWO7ZvSOTm+mzWGgiMG1ORO9TEJjeG7LLh8C0Y+l9EgLTe0N2+RCYdiw9T0Jgem7HPhsC056p14kITK/N2OdCYNoz9TTxzFmRl/blz7d8483BFZd33pGLy7vvaq64RGDanImtEZjzbyGff/v4YiGZsPavsvz8b//mgqsz0/cWX6GJwLQ5Eb1PQWB6b8guHwLTjqX3SQhM7w3Z5UNg2rH0PAmB6bkd+2wITHumXiciML02Y58LgWnP1MPEVw505MV9nUxeTk4OEt11Z/5W8bvvbL64RGDanImtEJjzUfWfd/nYbzySXVWZBOZTf/f3C24vXyww07b9Z2IuFpjTM12bJpjimsCKTkfSP1a7vfb8w9V1ISWGWzHWkVQzXZcI2clounZSRAUxVo51pNsV6Wb/JOfTVAKdTkdS171eTy536bqpPfePa+XYmMx0e5L+j0+zCaxcMSYzM3Td7Jbzo1u1Ykwu03Ujqj7yvshzz/fkuRd68vahwT+nt2wW+ciHOvLRD6+QvXva90/wdI7zKU6gdQIzoUov5XnjnSPZcyy1V2AePTXvPyEU74GVzgmsW7My+x9EFy7NOE9KPC2BDWtXyvTlnlyaomstS+/rN65bJZNTMzI5zX+I8t6VNt/G9avk0uSMTNG1FqXr9atWjkm6in76cldOnZt2nZVwegJbNq6Ss+cvZ7KDT7MJbNs4LifPTWX/IYpPswls2zQuJ85MZRcT8IlHYGZG5OcvdeTnL0l2xeX8HtNzLT9wj2RvFF89LnLdptVy7MyktO2/QaW7B/gUJ9B6gckzMIufPG1ayS3k7WmbW8jb0zW3kLena24hb0fX3ELejp77R8kt5O3pm1vI29M1t5DH7PrQ4XR7eH6b+IkTg2dbbr+hl71JPP1Kf57/6b+FvG2ymreQ687xxgvM9FKe//q9/y7/6tFPysTEuPRvIf/C7z+W3RbOW8h1J1BbViMw29K0ZFfvTE335MLk5fYcdEuPFIHZnuIRmO3oGoHZjp4RmO3qOR0tArM9nSMw43R98WK6yjJ/Ic/BVwfScnxccml597VfyoPAjNO1p6SNF5gJdnqm5bf/5ntz3L/2pc/NvVU8fbEvNV/Y92q2zXe++fjcMy/T39Mt5/2XAD366YcWPC+Tl/h4Op3Ly4LALI+tt8kITG+NlJcHgVkeW2+TEZjeGiknDwKzHK5ep3IFptdm7HMhMO2Zep2IwPTazCDXa6/nV1umF/KcOz/4+i0396+27MqmjcsfBwJzeUZscSWBVgjMMotHYJZJ189sBKafLspOgsAsm7Cf+QhMP12UnQSBWTZhH/MRmD56qCoFArMq0vXvB4FZfwdVJUBgVkV6tP2cOjV7i/j+jrz99uBqyyQq772nm11xmQTmKB8E5ii02LZPAIGpPBcQmEqAQZYjMIMUZRATgWkAMcgIBGaQogxiIjANIAYYgcAMUJJhRASmIUznoxCYzgsyjIfANIRpMGrfy/mVlumKy+l578a7+678FvEkLtMt40U+CMwi1FiDwFSeAwhMJcAgyxGYQYoyiInANIAYZAQCM0hRBjERmAYQA4xAYAYoyS10FDYAACAASURBVDAiAtMQpvNRCEznBRnGQ2Aawiw46r33+7eIdyT9uf+51gt5iuwKgVmEGmsQmMpzAIGpBBhkOQIzSFEGMRGYBhCDjEBgBinKICYC0wBigBEIzAAlGUZEYBrCdD4Kgem8IMN4CExDmCOMSldX9p9rma667H+GfSHPCLua2xSBWYQaaxCYynMAgakEGGQ5AjNIUQYxEZgGEIOMQGAGKcogJgLTAGKAEQjMACUZRkRgGsJ0PgqB6bwgw3gITEOYQ4xKz7N8cX9+m/ipU4MFo76QZ4hdXbEJArMINdYgMJXnAAJTCTDIcgRmkKIMYiIwDSAGGYHADFKUQUwEpgHEACMQmAFKMoyIwDSE6XwUAtN5QYbxEJiGMK8yKr05vP9cy/RG8f5H80KeIqkRmEWosQaBqTwHEJhKgEGWIzCDFGUQE4FpADHICARmkKIMYiIwDSAGGIHADFCSYUQEpiFM56MQmM4LMoyHwDSEuWjUwVdn3yS+b0wuXhx80+KFPEVSIzCLUGMNAlN5DiAwlQCDLEdgBinKICYC0wBikBEIzCBFGcREYBpADDACgRmgJMOICExDmM5HITCdF2QYD4FpCFNETpzoyIv7cnF56HB5L+QpkhqBWYQaaxCYynMAgakEGGQ5AjNIUQYxEZgGEIOMQGAGKcogJgLTAGKAEQjMACUZRkRgGsJ0PgqB6bwgw3gITD3MXk/kpdnnWiZxOTOTzyzzhTxFUiMwi1BjDQJTeQ4gMJUAgyxHYAYpyiAmAtMAYpARCMwgRRnERGAaQAwwAoEZoCTDiAhMQ5jORyEwnRdkGA+BWRzmu0fyKy3Tr6PHBldbVvFCniKpEZhFqLEGgak8BxCYSoBBliMwgxRlEBOBaQAxyAgEZpCiDGIiMA0gBhiBwAxQkmFEBKYhTOejEJjOCzKMh8AcDebkZP5CnnSb+CsH6nshz2ip860RmEWosQaBqTwHEJhKgEGWIzCDFGUQE4FpADHICARmkKIMYiIwDSAGGIHADFCSYUQEpiFM56MQmM4LMoyHwBwO5htv9q+2HJMzZwdr6nohz3CpF26FwCxCjTUITOU5gMBUAgyyHIEZpCiDmAhMA4hBRiAwgxRlEBOBaQAxwAgEZoCSDCMiMA1hOh+FwHRekGE8BObVYSZRma62TLeIJ4HZ/2y/oSf33pP/Sn+O8kFgRmnKV04EprIPBKYSYJDlCMwgRRnERGAaQAwyAoEZpCiDmAhMA4gBRiAwA5RkGBGBaQjT+SgEpvOCDOMhMK+EmW4Nz98kPibplvH08fZCniKnAAKzCDXWIDCV5wACUwkwyHIEZpCiDGIiMA0gBhmBwAxSlEFMBKYBxAAjEJgBSjKMiMA0hOl8FALTeUGG8RCYOcz0Ep7+C3nSy3n6H68v5ClyCiAwi1BjDQJTeQ4gMJUAgyxHYAYpyiAmAtMAYpARCMwgRRnERGAaQAwwAoEZoCTDiAhMQ5jORyEwnRdkGK/NAnNmJt0inl9p+dL+jvRm7wbftFHk3nu62S3iSWA25YPAbEqT1R4HAlPJG4GpBBhkOQIzSFEGMRGYBhCDjEBgBinKICYC0wBigBEIzAAlGUZEYBrCdD4Kgem8IMN4bRSY7xzqyL79+W3iJ04MrraM9EKeIqcAArMINdYgMJXnAAJTCTDIcgRmkKIMYiIwDSAGGYHADFKUQUwEpgHEACMQmAFKMoyIwDSE6XwUAtN5QYbx2iAwL1wUef2Nztyvo0fjv5CnyCmAwCxCjTUITOU5gMBUAgyyHIEZpCiDmAhMA4hBRiAwgxRlEBOBaQAxwAgEZoCSDCMiMA1hOh+FwHRekGG8pgrMI+8NhOVrr3dkamoAbf16kdtv68m9d3clXXXZlg8Csy1N2x4nAlPJE4GpBBhkOQIzSFEGMRGYBhCDjEBgBinKICYC0wBigBEIzAAlGUZEYBrCdD4Kgem8IMN4TRGYU9MLr7J8993BVZYJ1+5dPdmzpye33tKTW/f0ZOVKQ4hBRiEwgxTlLCYCU1kIAlMJMMhyBGaQogxiIjANIAYZgcAMUpRBTASmAcQAIxCYAUoyjIjANITpfBQC03lBhvEiC8xjxwdXWb76WkcuXhyAWbtWMlGZ/bqlJ9df354rLa92eiAwDX9wWjQKgaksG4GpBBhkOQIzSFEGMRGYBhCDjEBgBinKICYC0wBigBEIzAAlGUZEYBrCdD4Kgem8IMN4kQRmekt4/1mW6bbwt99ZeJXlzp2DKyzT1ZbjqwxBNWAUArMBJdZwCAhMJXQEphJgkOUIzCBFGcREYBpADDICgRmkKIOYCEwDiAFGIDADlGQYEYFpCNP5KASm84IM43kXmKdOJ2k5lonLgwc7cu784ODHx/NnWaYrLJOw3H4DV1le69RAYBr+4LRoFAJTWTYCUwkwyHIEZpCiDGIiMA0gBhmBwAxSlEFMBKYBxAAjEJgBSjKMiMA0hOl8FALTeUGG8TwKzLfezm8NT7eFv/Hmwqsst2/vyW23Dp5nuXq1IYyGj0JgNrzgkg4PgakEi8BUAgyyHIEZpCiDmAhMA4hBRiAwgxRlEBOBaQAxwAgEZoCSDCMiMA1hOh+FwHRekGE8DwIzXVWZ3Rr+ekdeOTgmZ84MDnDFmMgdd8w+y3JPT3Zs5yrLovUjMIuSa/c6BKayfwSmEmCQ5QjMIEUZxERgGkAMMgKBGaQog5gITAOIAUYgMAOUZBgRgWkI0/koBKbzggzj1SUwD7+bX2V54GBH0vMs53+u29aT228fPM9yYsLwgFs8CoHZ4vIVh47AVMBLSxGYSoBBliMwgxRlEBOBaQAxyAgEZpCiDGIiMA0gBhiBwAxQkmFEBKYhTOejEJjOCzKMV5XAnJzMr7I8+FpHDhzoyMlTC6VlepZl/3mWN97IVZaGFc+NQmCWQbX5MxGYyo4RmEqAQZYjMIMUZRATgWkAMcgIBGaQogxiIjANIAYYgcAMUJJhRASmIUznoxCYzgsyjFemwHz/aP+28PxKy/mfzZvSreHduedZrl1jeFCMWpIAApMTowgBBGYRavPWIDCVAIMsR2AGKcogJgLTAGKQEQjMIEUZxERgGkAMMAKBGaAkw4gITEOYzkchMJ0XZBjPUmDOzORXWSZZmX4dO75QWt66pyd3pFvD9/Rk106usjSscahRCMyhMLHRIgIITOUpgcBUAgyyHIEZpCiDmAhMA4hBRiAwgxRlEBOBaQAxwAgEZoCSDCMiMA1hOh+FwHRekGE8rcA8cTJ/W3i6LfyVgx3pdgfh1q8XufP27tzzLNetMwzOqJEJIDBHRsYCEUFgKk8DBKYSYJDlCMwgRRnERGAaQAwyAoEZpCiDmAhMA4gBRiAwA5RkGBGBaQjT+SgEpvOCDOMVEZj9qyyTsHz//YVXWd60uyd33tGT2/b2ZPcurrI0rEo9CoGpRtjKAQhMZe0ITCXAIMsRmEGKMoiJwDSAGGQEAjNIUQYxEZgGEAOMQGAGKMkwIgLTEKbzUQhM5wUZxhtGYJ49K3Lg4Fh2hWW6NXx6ehAgvSE8Cct0peWtt/Zkw3rDcIwyJYDANMXZmmEITGXVCEwlwCDLEZhBijKIicA0gBhkBAIzSFEGMRGYBhADjEBgBijJMCIC0xCm81EITOcFGca7msB86+2OvHIgF5bvHll4lWV6S/idt+fPs7z5Jq6yNKyj1FEIzFLxNnY4AlNZLQJTCTDIcgRmkKIMYiIwDSAGGYHADFKUQUwEpgHEACMQmAFKMoyIwDSE6XwUAtN5QYbx+gLz3Pne7BWWY5m4nJwc7GTVKslkZbrS8vbburJxg2EARlVGAIFZGepG7QiBqawTgakEGGQ5AjNIUQYxEZgGEIOMQGAGKcogJgLTAGKAEQjMACUZRkRgGsJ0PgqB6bwgg3gXLoi8c7gjp0+skud+NiPvHFp4leUN1+dXWCZpmd4azic+AQRm/A7rOAIEppI6AlMJMMhyBGaQogxiIjANIAYZgcAMUpRBTASmAcQAIxCYAUoyjIjANITpfBQC03lBI8abmRE5dLiTScr8d5GTJxcKy04nvTG8J3fMPs9y8+YRd8Lm7gkgMN1X5DIgAlNZCwJTCTDIcgRmkKIMYiIwDSAGGYHADFKUQUwEpgHEACMQmAFKMoyIwDSE6XwUAtN5QcvEe+/9jhw61JF3Dkv2++JnWKblK1ZI9pbwO/eukJ27Lsttt3VjHzTplyWAwFwWERssQQCBqTwtEJhKgEGWIzCDFGUQE4FpADHICARmkKIMYiIwDSAGGIHADFCSYUQEpiFM56MQmM4Lmhfv9On8VvBMWM5eYTn/LeH9Tbdv78nunT3ZtUuy33fsyG8LH+Yt5HFokPRaBBCYnB9FCCAwi1CbtwaBqQQYZDkCM0hRBjERmAYQg4xAYAYpyiAmAtMAYoARCMwAJRlGRGAawnQ+CoHps6BLl+bdCp5dYdmRc+euzLp5k8iuXb3sCstdO/PfV65c+pgQmD67LiMVArMMqs2ficBUdozAVAIMshyBGaQog5gITAOIQUYgMIMUZRATgWkAMcAIBGaAkgwjIjANYTofhcCsv6BeL5eV+a3g6XeRY8cXPrcypZyYyG8F74vKJC7Xrxs+PwJzeFbRt0RgRm+wnvwITCV3BKYSYJDlCMwgRRnERGAaQAwyAoEZpCiDmAhMA4gBRiAwA5RkGBGBaQjT+SgEZvUFHT2WS8r+7eBJXi7+pBftLJSVItu26t4QjsCsvuu69ojArIt87P0iMJX9ITCVAIMsR2AGKcogJgLTAGKQEQjMIEUZxERgGkAMMAKBGaAkw4gITEOYzkchMMst6OzZK59bOTl55T6vvy7d/j17O/jOnuzcqZOVSx0VArPcrj1NR2B6aiNOFgSmsisEphJgkOUIzCBFGcREYBpADDICgRmkKIOYCEwDiAFGIDADlGQYEYFpCNP5KASmXUFTU1c+t/LMmSvnb9xw5XMrx8ftclxtEgKzfMZe9oDA9NJErBwITGVfCEwlwCDLEZhBijKIicA0gBhkBAIzSFEGMRGYBhADjEBgBijJMCIC0xCm81EIzOIFHX63/9xKyZ5f+f7RK28FT2Jy8XMrk8Cs44PArIN6PftEYNbDPfpeEZjKBhGYSoBBliMwgxRlEBOBaQAxyAgEZpCiDGIiMA0gBhiBwAxQkmFEBKYhTOejEJjDFXTiREfeOTTvCsvDHel2r1ybbv3evbM3+2ZwkXRruJcPAtNLE+XnQGCWz7iJe0BgKltFYCoBBlmOwAxSlEFMBKYBxCAjEJhBijKIicA0gBhgBAIzQEmGERGYhjCdj0JgXlnQ+fNXPrfy4sUrt0sv1ek/t7L/ZvD08h2vHwSm12bscyEw7Zm2YSICU9kyAlMJMMhyBGaQogxiIjANIAYZgcAMUpRBTASmAcQAIxCYAUoyjIjANITpfFTbBeblywuvqkxXWZ46daWFXL/uyudWTkw4L3dRPARmrL40aRGYGnrtXYvAVHaPwFQCDLIcgRmkKIOYCEwDiEFGIDCDFGUQE4FpADHACARmgJIMIyIwDWE6H9UWgZlu9z5xsiMnTuS/v/d+/tzKI+9dKStXrrzyuZWbNzkvcoh4CMwhIDVkEwRmQ4qs+DAQmErgCEwlwCDLEZhBijKIicA0gBhkBAIzSFEGMRGYBhADjEBgBijJMCIC0xCm81FNEpjpLeDpWZUnTi6Ulelrp05fvYgdO/rPrZTs+ZXbt/t5bqXl6YPAtKTpexYC03c/XtMhMJXNIDCVAIMsR2AGKcogJgLTAGKQEQjMIEUZxERgGkAMMAKBGaAkw4gITEOYzkdFE5jnL+SS8uScpJwVlic6cu78tWGnqyi3bu3J1i09ue46kf5zK1escF6SUTwEphHIAGMQmAFKchgRgaksBYGpBBhkOQIzSFEGMRGYBhCDjEBgBinKICYC0wBigBEIzAAlGUZEYBrCdD7Ko8A8faZ/JeXglu/sqsoTHZmcvDrQsTHJ5OTWrbO/b+kLy/z39P02fxCY7Wkfgdmeri2PFIGppInAVAIMshyBGaQog5gITAOIQUYgMIMUZRATgWkAMcAIBGaAkgwjIjANYTofVYfA7PUW3+K98O8zM1eHNj6+SFLOycqebN7sHHbN8RCYNRdQ4e4RmBXCbtCuEJjKMhGYSoBBliMwgxRlEBOBaQAxyAgEZpCiDGIiMA0gBhiBwAxQkmFEBKYhTOejyhKY09NXex6lyMkl3vI9H9PatYslZbrtO//a+vXOgTqOh8B0XI5xNASmMdCWjENgKotGYCoBBlmOwAxSlEFMBKYBxCAjEJhBijKIicA0gBhgBAIzQEmGERGYhjCdj9IIzAsXRU4ueGnO4HmUZ89d+8A3bcxv696SbvledKv3xGrn0ILGQ2AGLa5AbARmAWgsEQSm8iRAYCoBBlmOwAxSlEFMBKYBxCAjEJhBijKIicA0gBhgBAIzQEmGERGYhjCdj1pOYJ45e/XnUV66dPWD63Su/TzKtrw4x1P9CExPbZSbBYFZLt+mTkdgKptFYCoBBlmOwAxSlEFMBKYBxCAjEJhBijKIicA0gBhgBAIzQEmGERGYhjCdj0oC85XXJ+Xo8UXPpZx9ac7ly1c/gFWrrvY8SsmurOTjiwAC01cfZaZBYJZJt7mzEZjKbhGYSoBBliMwgxRlEBOBaQAxyAgEZpCiDGIiMA0gBhiBwAxQkmFEBKYhzBpGpSsjz1/oyPnzMvurI+cviJzL/j779QuDP18r4po1V39pzoYNNRwcuyxMAIFZGF24hQjMcJW5CIzAVNaAwFQCDLIcgRmkKIOYCEwDiEFGIDCDFGUQE4FpADHACARmgJIMIyIwDWEajEovxEkCck4+JgmZ/T3/WiYm533/Wm/xXirOxg35FZPpmZSLn0e5ZsLgABjhggAC00UNlYRAYFaCuXE7QWAqK0VgKgEGWY7ADFKUQUwEpgHEICMQmEGKMoiJwDSAGGAEAjNASYYREZiGMJcY1e0uFpLXvmJyamq0POnW7nXrerJunci6tSLr+3/O/j779fTndT3Zu2tCTp6blJkut3yPRjne1gjMeJ0VTYzALEqu3esQmMr+EZhKgEGWIzCDFGUQE4FpADHICARmkKIMYiIwDSAGGIHADFCSYUQE5ugw0xu5l7o9u3+V5PwrJtO2o3zGxpJsvFI+rl87+/V5sjJJyfHx4acv9xKf4SexpXcCCEzvDdnlQ2DasWzTJASmsm0EphJgkOUIzCBFGcREYBpADDICgRmkKIOYCEwDiAFGIDADlGQYEYEpkq56XOr27ExILvF8yXRV5SiftUk+LroaMl0tmUTl3BWT2d97kp5DWdYHgVkWWX9zEZj+OikrEQKzLLLNnovAHKLf737/B/KVr3872/LRTz8kX/3iZ2ViIv/PhgjMIQA2YBMEZgNKHPIQEJhDgmrAZgjMBpQ45CEgMIcEFXwzBGbwAkeMH01gTl8WmZ4SSc+KnJruZL/3f02lP2ff60j259lfc3+eGnw9e/nN7PMl03ajfFavvrqQTBJy/ezt3P1buzudUaaXty0Cszy23iYjML01Ul4eBGZ5bJs8GYG5TLs/fn6/fOPPn5JvPfkHsmXTBvnGXzyVrfjC7z2GwGzyT8aiY0NgtqdsBGZ7ukZgtqdrBGY7ukZgtqPn/lFaCsx0ZWIuFnOJmP15VjYOZOJAOs7/3nwZea01vRIe37hyxdK3Z2e3ci/xfMmVK2OeIwjMmL0VSY3ALEIt5hoEZsze6k6NwFymgSQs9+zeIZ/59YezLRcLTa7ArPsUrmb/CMxqOHvYCwLTQwvVZEBgVsPZw14QmB5aKD8DArN8xmXsIcnD9Gtm9vfs7zP517rdzuzvi77fFUn/bnbyzIxcnOwOffXiwisbO9m6JC1HfSN2EQ5JHqYX16Rf46t6c3/O/y6yajx9r5f/ed6v/O+97Pvpz+nZkX1BObG6SJJ4axCY8TormhiBWZRcvHUIzHideUiMwLxGC5cuTckf/clfy0MP3DcnMF9787B8+cm/kice/x3Ze8tOeffEiE+49tA6GUYmsGHNKun1enLu0uWR17IgFoFN61bJ9HRPLkzRdazmRk+7ef24TE7NyMWpmdEXsyIUgSSrL16akUvTdB2quBHDJoG5dcNqmZzuyvEzk9nqdNVbduHb/N9nr4TrXxF3rd+vWLt41oK/dxbsa8m5S+W5xsxhMvaPc4EEnBOAC0XgAkk4XxgulogL1ucSsdjagYS82voRay5l8/QCmqXkYpKFy319sZC82pq0Dz7FCNyweSL7meYt5MX4RVqVZPXRU5PSLeOS5UggWpB1x5Y18t6pi9n/n27TJ4lbPsUJIDCvwa4vMB/7jUfkY/ffnW25WGAWR89KCEAAAhCAAASqIjD/Kq90tVUmZLLfe7mYmRkImrnvL/H19D+gh902lz692f309ze7n2vub96aobIt3Md8UVQVX/YDgaIEVqwQSXJvxZjI2Ir89xVjnbk/97+WbbNo2/yKxE52ZeLqdIXi7K/V6Wtzf86/nn1t9grGwbadbF3UW6uLMmcdBCAAAQhAICIBBOYQAvNaV2C27b8YRDzJLTKnh5j3r8KwmMcMvwTo2m831smyrlv2X32tGVrPS31MTolMTqbfe9mfp7I/p6/lf8+/t3CbwdcG26Rn0c2fM+rbd62PjXnVEkg/3/0XkGR/Truf/drcn/tfS99KX5zdbv66pb7Wmf3iMPPnz11y1uxLUhbMmve1K7LOP5b5uTuzAjCTfJ05IbiUHFxKBGbCcAlBmEnFJb8+2H6+eLz6jM4V8rE/u+iZwT/Di5KLt46u43VWNDFdFyUXb11bu/bycrR4Z0yeGIG5THM8AzPqqW2bm2dg2vL0PI1nYHpuxzYbz8AszjNdodh/a+7U7NtxkzBc8mtX+/rsW3fzdZ25F2YUT3XtlUmsXP1XL7/6a5lfC7aZvRIsX9ObWzvynHlr05Vm/QzLzRl8f7DvpfKXxdPjXJ6B6bGV8jJZvsSnvJRMtiDAMzAtKMaYwTMwY/RkkZJnYFpQbN8MBOYynfMW8vb9UCx1xAjM9pwHCMz2dN0mgZmuPjx/XuT8hY5cuJC/XTeXjZ3s9+zvywrIwbZlvvAiu+0zu81z4Usr5n+9/4y5/i2i6YUY/T9nz6Pr30o6+/Xt28bl0iTPwGz6TzcCs+kNLzw+BGZ7+kZgtqdrBGZ7ukZgtqdryyNFYA5B87vf/4F85evfzrZ89NMPyVe/+FmZmBjP/s5byIcA2IBNEJgNKHHIQ0BgDgmqAZtFF5hJRCYhmYnJ7FdHzqevnRc5l/6cCcv86xeN3zeXrvTrvzU3icb+c+X6kjF7W+6SX58VjQskY3r77mBGGacWbyEvg6q/mQhMf52UmQiBWSZdX7MRmL76KDMNArNMur5mIzB99RElDQJT2RQCUwkwyHIEZpCiDGIiMA0gBhnhTWCm5zVeTUgmCXlunpBMcnLU53euXSuybl1P1q298grFheIxycnBFY1LicpoL7xAYAb5oVTGRGAqAQZbjsAMVpgiLgJTAS/YUgRmsMIUcRGYCngtXorAVJaPwFQCDLIcgRmkKIOYCEwDiEFGlC0wL8/MuzJykXycf8Vk/2rJy5dHA7d69UBIrlsnsj7JyXWSCcpMVKY/Z3/P/9zmh4YjMEc7t6JujcCM2lyx3AjMYtwirkJgRmytWGYEZjFuEVchMCO2Vn9mBKayAwSmEmCQ5QjMIEUZxERgGkAMMqKIwFzq9uy5W7gX3c59aXI0EOmqxvnCMReQPVl/FSEZ7SrI0WjYbo3AtOXpdRoC02sz5eRCYJbD1eNUBKbHVsrJhMAsh6vHqQhMj634z4TAVHaEwFQCDLIcgRmkKIOYCEwDiEFGJIF58vSMHD/ZveL27P4LbxY/X3KUQ0tXPC4lJPMrJK+8YjJdUcmnHAIIzHK4epuKwPTWSLl5EJjl8vU0HYHpqY1ysyAwy+XraToC01MbcbIgMJVdITCVAIMsR2AGKcogJgLTAKKzESdOduTECZHs95MiJ07kv5882ZHp6dHCrplY+vbsuasl593CnZ45yccHAQSmjx7KToHALJuwr/kITF99lJkGgVkmXV+zEZi++igzDQKzTLrNnY3AVHaLwFQCDLIcgRmkKIOYCEwDiBWPSM+OvJqkTLLyWp/08pr+MyKHuVoyvX2bTzwCCMx4nRVJjMAsQi3uGgRm3O5GTY7AHJVY3O0RmHG7GzU5AnNUYmyfCCAwlecBAlMJMMhyBGaQogxiIjANIJYw4tKlRZJy7orKjpw5c+0dbtggsnVLT7Zu7cnWLf0/i+y9aZWMrZiRi1MzJSRmpCcCCExPbZSXBYFZHluPkxGYHlspJxMCsxyuHqciMD22Uk4mBGY5XJs+FYGpbBiBqQQYZDkCM0hRBjERmAYQC444d26xpBzc8n3h4rWHbkmCMsnJvqScJytXrVp6bZGX+BQ8NJbVTACBWXMBFe0egVkRaCe7QWA6KaKCGAjMCiA72QUC00kRFcRAYFYAuYG7QGAqS0VgKgEGWY7ADFKUQUwEpgHEa4w4eerK51GenH0u5dQ1nkeZ3ridXUW5hKRM8jK9MGfUDwJzVGJxt0dgxu1ulOQIzFFoxd8WgRm/w2GPAIE5LKn42yEw43c47BEgMIclxXbzCSAwlecDAlMJMMhyBGaQogxiIjB1EGdmrv08yl7v6vMnJga3dy+UlT3ZuFGXa6nVCEx7pl4nIjC9NmObC4Fpy9P7NASm94bs8iEw7Vh6n4TA9N6QXT4Eph3LNk1CYCrbRmAqAQZZjsAMUpRBTATm8hAnJ6/+PMrTp6+9fv36xZIyPZsy/1rVb+1GYC7fdVO2QGA2pclrHwcCsx09948SgdmevhGY7ekagdmerhGY7ena8kgRmEqaCEwlwCDLEZhBijKIicDMIZ4/p8RKqgAAIABJREFUf5XnUZ7sZN+71mfz5qs/jzK99dvLB4HppYnycyAwy2fsYQ8ITA8tVJcBgVkd67r3hMCsu4Hq9o/ArI513XtCYNbdQMz9IzCVvSEwlQCDLEdgBinKIGbbBOaJkx05dFjkyJH0bMrBS3Mmp64Oc8WKK59HuWXeS3PGxgyKqGAEArMCyE52gcB0UkTJMRCYJQN2Nh6B6ayQEuMgMEuE62w0AtNZISXGQWCWCLfBoxGYynIRmEqAQZYjMIMUZRCzyQLz7FmRQ4eTsBz8uniVt3uvXn21l+b0ZNMmA9AORiAwHZRQUQQEZkWga94NArPmAirePQKzYuA17g6BWSP8ineNwKwYeI27Q2DWCD/wrhGYyvIQmEqAQZYjMIMUZRCzKQLz0qVFsvJQR86cvRLQunUiu3b2sl/Zi3Nmn0eZvt70DwKz6Q0Pjg+B2Y6uEZjt6Ll/lAjM9vSNwGxP1wjM9nSNwGxP15ZHisBU0kRgKgEGWY7ADFKUQcyIAvPyjMihQx05PHdlpcjxE50raIyvEtm1K5eV/V+bNxtACzoCgRm0uAKxEZgFoAVcgsAMWJoiMgJTAS/YUgRmsMIUcRGYCnjBliIwgxXmJC4CU1kEAlMJMMhyBGaQogxiRhCYh9/t3wKeX2X53ntXysqEIpOUs8Jy906R66/vGRBqzggEZnO6XO5IEJjLEWrG9xGYzehx2KNAYA5LKv52CMz4HQ57BAjMYUnF3w6BGb/DOo4AgamkjsBUAgyyHIEZpCiDmN4E5tFj+Ut20hWW/WdX9pbwkDdc35eVg1vCDXA0egQCs9H1Ljg4BGY7ukZgtqPn/lEiMNvTNwKzPV0jMNvTNQKzPV1bHikCU0kTgakEGGQ5AjNIUQYx6xSYp07Nysp5L9mZWuJt4Fs2p1vAF94OvmqVwcG3bAQCsz2FIzDb0TUCsx09IzDb1XM6WgRmezpHYLanawRme7q2PFIEppImAlMJMMhyBGaQogxiViUwz5+f95Kd2asrz1+48gD6L9nZPe/ZlWvXGhwoIwSB2Z6TAIHZjq4RmO3oGYHZrp4RmO3qG4HZnr4RmO3p2vJIEZhKmghMJcAgyxGYQYoyiFmGwJycXPRG8MMdOX36yrDj44Pbv/vPrty8yeCgGLEkAQRme04MBGY7ukZgtqNnBGa7ekZgtqtvBGZ7+kZgtqdryyNFYCppIjCVAIMsR2AGKcogplZgdruLZaXIsWNXvmSn05knK7OX7Yhcfx0v2TGocOgRCMyhUYXfEIEZvsKhDgCBORSmxmzEMzAbU+WyB8It5MsiaswGCMzGVLnsgSAwl0XEBksQQGAqTwsEphJgkOUIzCBFGcQcVWAeea8z+4KdXFy+e2TpN4JvvyE9t3Lw7MqdNyIrDepSjUBgqvCFWozADFVX4bAIzMLoQi5EYIasrVBoBGYhbCEXITBD1lYoNAKzELbWL0JgKk8BBKYSYJDlCMwgRRnEvJbAPH78ypfszMxcudMtW2ZFZSYs87eDr1ppEI4RpgQQmKY4XQ9DYLquxywcAtMMZYhBCMwQNZmERGCaYAwxBIEZoiaTkAhME4ytG4LAVFaOwFQCDLIcgRmkKIOYfYH57tHL2RWV2a9DHTl8uCOXJq/cwfr1i24F39kTXrJjUEQFIxCYFUB2sgsEppMiSo6BwCwZsLPxCExnhZQYB4FZIlxnoxGYzgopMQ4Cs0S4DR6NwFSWi8BUAgyyHIEZpChFzLPnRA4cGJPX3xiT194QOXv2ymGr00t25r0NPF1duYmX7Cio17sUgVkv/yr3jsCsknZ9+0Jg1se+jj0jMOugXs8+EZj1cK9jrwjMOqjXs08EZj3co+8VgalsEIGpBBhkOQIzSFEjxnz7nY68ciD/tfjZldlLdmZl5e7ZZ1dex0t2RiTse3MEpu9+LNMhMC1p+p2FwPTbTRnJEJhlUPU5E4Hps5cyUiEwy6DqcyYC02cv3lMhMJUNITCVAIMsR2AGKWqZmJcuSS4sD47JgYMduXhx4YI9t/TkQ/eNyd5be7J12+VmHDRHcVUCCMz2nBwIzHZ0jcBsR8/9o0RgtqdvBGZ7ukZgtqdrBGZ7urY8UgSmkiYCUwkwyHIEZpCiloiZrqzsX2WZrric/1m3TuTO23tyxx3d7PfxcZFR30IelwzJEZjtOQcQmO3oGoHZjp4RmO3qOR0tArM9nSMw29M1ArM9XVseKQJTSROBqQQYZDkCM0hRInL5cv8qy468+uqYnD6zMPvuXT25846e3HF7/obwxR8EZpyutUkRmFqCcdYjMON0pUmKwNTQi7eWKzDjdVY0MQKzKLl46xCY8TormhiBWZRcu9chMJX9IzCVAIMsR2D6Lurosfwqy3Rb+OtvdKQ3z0uuXSNy294kLbuZtFzuDeEITN9dW6ZDYFrS9D0Lgem7H6t0CEwrkjHmIDBj9GSREoFpQTHGDARmjJ4sUiIwLSi2bwYCU9k5AlMJMMhyBKa/ovrC8tXXOnLs+MJbw2+8sSd33JZfZXnLzVdeZXmto0Fg+uu6rEQIzLLI+puLwPTXSRmJEJhlUPU7E4HptxvrZAhMa6J+5yEw/XZjnQyBaU20HfMQmMqeEZhKgEGWIzDrL+rkqfwqy4Ov5ldZTk0NMk1MiNy6pzf3PMuNG4rnRWAWZxdtJQIzWmPF8yIwi7OLtBKBGaktfVYEpp5hlAkIzChN6XMiMPUMo0xAYEZpyldOBKayDwSmEmCQ5QjMeop67fXBbeGH3114leWO7b3sbeHpeZbpd6sPAtOKpP85CEz/HVklRGBakfQ9B4Hpux/rdAhMa6J+5yEw/XZjnQyBaU3U7zwEpt9uPCdDYCrbQWAqAQZZjsCspqiz50QOHBiTV1/vyOuvd+Tc+cF+V68WufWWntx2W36l5ZYtdtJy/tEhMKvp2sNeEJgeWqgmAwKzGs517wWBWXcD1e4fgVkt7zr3hsCsk361+0ZgVsu7zr0hMOukH3ffCExldwhMJcAgyxGY5RX19juDqyzffGvhVZbbb+jJnj358yzTlZZVfBCYVVD2sQ8Epo8eqkiBwKyCcv37QGDW30GVCRCYVdKud18IzHr5V7l3BGaVtOvdFwKzXv5R947AVDaHwFQCDLIcgWlX1KVLkj3L8rU38mdZnjw5kJbjqyQTltnzLO/oyfXXVSMt5x8dAtOua++TEJjeG7LLh8C0Y+l5EgLTczv22RCY9ky9TkRgem3GPhcC056p14kITK/N+M6FwFT2g8BUAgyyHIGpK+rdIx1JbwtPwjI913JmZjDv+ut72a3he/fmt4avXKnbl3Y1AlNLMM56BGacrrRJEZhagjHWIzBj9GSVEoFpRdL/HASm/46sEiIwrUj6n4PA9N+Rx4QITGUrCEwlwCDLEZijFXX5ssiBg7mwTL/ee39wlWUSlOkKyz239OT223py447qr7K81tEgMEfrOvLWCMzI7Y2WHYE5Gq+oWyMwozZXLDcCsxi3iKsQmBFbK5YZgVmMW8RVCMyIrdWfGYGp7ACBqQQYZDkCc/mijh7Lr67sS8uLFwdrrtuWP8syics7bu/JxOrl59W1BQKzLvLV7xeBWT3zuvaIwKyLfLX7RWBWy7vuvSEw626guv0jMKtjXfeeEJh1N1Dd/hGY1bFu0p4QmMo2EZhKgEGWIzCXLmr+beHvHBpcZblihWRXWCZhuXdPT3bv9nWV5bVOOwRmkB9Kg5gITAOIQUYgMIMUpYyJwFQCDLYcgRmsMEVcBKYCXrClCMxghSniIjAV8Fq8FIGpLB+BqQQYZDkCMy/q1GmR118fm7vK8vSZQYFbt+bCMj3P8ra9PVm3Lki5i2IiMGP2ViQ1ArMItZhrEJgxexs1NQJzVGKxt0dgxu5vlPQIzFFoxd4WgRm7v1HSIzBHocW2fQIITOW5gMBUAgyyvM0C8623B7eFp9vDe7MXU3Y6+bMs+8+zvOXmOFdZXuu0Q2AG+aE0iInANIAYZAQCM0hRypgITCXAYMsRmMEKU8RFYCrgBVuKwAxWmCIuAlMBr8VLEZjK8hGYSoBBlrdNYL79Tkde2teRl1/pyLHjg1vDt2zJr7DsP89y08YgBY4QE4E5AqzgmyIwgxc4QnwE5giwAm+KwAxcXoHoCMwC0IIuQWAGLa5AbARmAWhBlyAwgxZXc2wEprIABKYSYJDlbRCY586LvLRvLBOX6WU8/U//Csv+70EqKxwTgVkYXbiFCMxwlRUOjMAsjC7UQgRmqLrUYRGYaoRhBiAww1SlDorAVCMMMwCBGaYqV0ERmMo6EJhKgEGWN1lgHjjYkZf2pysux6T/5vAdO3py3z09ufeenlx/XTNuDR/2VENgDksq/nYIzPgdDnsECMxhScXeDoEZu79R0yMwRyUWd3sEZtzuRk2OwByVWNztEZhxu6szOQJTSR+BqQQYZHnTBObx4/kt4i/u78jhw/nVlqvHJROW997TlbvubJe0nH8aIjCD/FAaxERgGkAMMgKBGaQoZUwEphJgsOUIzGCFKeIiMBXwgi1FYAYrTBEXgamA1+KlCExl+QhMJcAgy5sgMLvddIt4fqVluuIy/T190st3kri8756ubGzgMy1HPcUQmKMSi7s9AjNud6MmR2COSizm9gjMmL0VTY3ALEou3joEZrzOiiZGYBYlF28dAjNeZx4SIzCVLSAwlQCDLI8sMA8dzq+2TL+On8ivttywQTJhmcTlnlvae7XlUqcfAjPID6VBTASmAcQgIxCYQYpSxkRgKgEGW47ADFaYIi4CUwEv2FIEZrDCFHERmAp4LV6KwFSWj8BUAgyyPJrAvHBx8EKeg68OXshz5x351Zb33t2ViYkg8CuOicCsGHiNu0Ng1gi/4l0jMCsGXtPuEJg1ga9ptwjMmsDXsFsEZg3Qa9olArMm8DXsFoFZA/QG7BKBqSwRgakEGGR5FIGZ3h7+4uxt4ufP53Cv2zYrLe/pyc4budpyuVMOgbkcoeZ8H4HZnC6XOxIE5nKEmvF9BGYzehz2KBCYw5KKvx0CM36Hwx4BAnNYUvG3Q2DG77COI0BgKqkjMJUAgyz3LDBPnuy/Rbwjb7+TX205Npa/kKd/m3hncBFmEOL1xURg1se+6j0jMKsmXt/+EJj1sa9yzwjMKmnXvy8EZv0dVJUAgVkV6fr3g8Csv4OqEiAwqyLdrP0gMJV9IjCVAIMs9ygws+da7h/Lnm15+XIOctfOwdWW27ZytWWR0wuBWYRazDUIzJi9FUmNwCxCLd4aBGa8zjSJEZgaerHWIjBj9aVJi8DU0Iu1FoEZqy8vaRGYyiYQmEqAQZZ7EZjvHpl9Ic/+jhw9ml9WuWZNutqyK/fe3ZM7bkdaak8pBKaWYJz1CMw4XWmTIjC1BGOsR2DG6MkqJQLTiqT/OQhM/x1ZJURgWpH0PweB6b8jjwkRmMpWEJhKgEGW1ykwJyfzF/KkZ1u+cmBwL/ite9It4umKy66sXx8EZICYCMwAJRlFRGAagQwwBoEZoCSDiAhMA4iBRiAwA5WljIrAVAIMtByBGagsZVQEphJgS5cjMJXFIzCVAIMsr0NgvvHm7NWW+8bkzNkc1OZNs1db3tOTm2/iassyTh8EZhlUfc5EYPrspYxUCMwyqPqbicD010mZiRCYZdL1NRuB6auPMtMgMMuk62s2AtNXH1HSIDCVTSEwlQCDLK9KYJ4+k19tmZ5r+eZbg6st774rv9IyvZhnfFUQaEFjIjCDFlcgNgKzALSgSxCYQYsbMTYCc0RgwTdHYAYvcIT4CMwRYAXfFIEZvMAR4iMwR4DFpnMEEJjKkwGBqQQYZHnZAnP/y4MX8kxN5VBuuKGXPdcy3Sa+fTtXW1Z1qiAwqyJd/34QmPV3UFUCBGZVpOvdDwKzXv5V7x2BWTXx+vaHwKyPfdV7RmBWTby+/SEw62Mfec8ITGV7CEwlwCDLyxCY77/fyZ5r+dL+jrz3Xn615cqVMvdcy3vuRlrWcXogMOugXs8+EZj1cK9jrwjMOqhXv08EZvXM69wjArNO+tXuG4FZLe8694bArJN+tftGYFbLuyl7Q2Aqm0RgKgEGWW4lMKen0y3i6dmWY7Lv5cEt4jftTreI57+2bEZc1nlaIDDrpF/tvhGY1fKuc28IzDrpV7dvBGZ1rD3sCYHpoYVqMiAwq+HsYS8ITA8tVJMBgVkN56btBYGpbBSBqQQYZLlWYL719uCFPKdO5we9bl3+Qp50i/jeW5GWXk4FBKaXJsrPgcAsn7GXPSAwvTRRbg4EZrl8vU1HYHprpLw8CMzy2HqbjMD01kh5eRCY5bFt8uRWCMzvfv8H8pWvf3tBj5/7rUflC7/3WPa1k6fPyucf/1N5Yd+r2d+/883H5WP33z23/fz1j376IfnqFz8rExPj2fcRmE3+8RgcWxGBefbc4IU8r78xuNry9r39qy27snZtO/hFOkoEZqS2dFkRmDp+kVYjMCO1VTwrArM4u4grEZgRWyuWGYFZjFvEVQjMiK0Vy4zALMat7ataIzCffvbFBeKxX/ylS1PyR3/y1/LQA/fJZ379YXntzcPy5Sf/Sp54/Hdk7y075cfP75dv/PlT8q0n/0C2bNog3/iLp7KlffmJwGzHj9AoAvOVg4OrLS9dyvls3TK4RXz3Lq629HzWIDA9t2ObDYFpy9PzNASm53bssiEw7VhGmITAjNCSTUYEpg3HCFMQmBFassmIwLTh2LYprReYSVj+8Z/9rTzxh7+bCcrFQjMJyz27d2RyM30WC00EZjt+ZJYTmMeO5S/jSc+3PPzu4GrL/LmW+W3iK1a0g1X0o0RgRm9w+PwIzOFZRd8SgRm9weHyIzCH49SUrRCYTWly+eNAYC7PqClbIDCb0uTyx4HAXJ4RW1xJoDUCc/4t5PNvH18sJBOi/lWWn//t31xwdWb63uIrNBGY7fixWkpgzszMvpBn/1gmLnuzF1bu2NGbfZN4T66/jqsto50hCMxojRXPi8Aszi7aSgRmtMaK5UVgFuMWdRUCM2pzo+dGYI7OLOoKBGbU5kbPjcAcnRkrRFohMOcX3X/e5WO/8Uh2VWUSmE/93d8vuL18scBM2/afiblYYB4/M8l51AICa1evlJ705OLkjLz9jsjPXurIz1/syPET+cGvXi3ywXt78oH7RO65C2kZ+ZRYv2alTF/uyeT0TOTDIPsQBNavXSXT0126HoJV9E02rF0lk1NdmbrMz3X0Lq+Vf9XKMUn/wXH6clfOXJhu8qFybCKyaf24nL9wWS53u/BoOIH0HxxPn5+Wbpd/x2541bJ1w7icPDctvf6VIU0/4BYf39YNq+Xkucm5i4DagmLbxtVtOdRSjjO0wEzy8d/8uyeXBLP4ZTvzN0ov5XnjnSPZcyy1V2BOTvMvTaWcmc6GXrrYkWde6Mqzz/dk/yuDf3m6/daOfPhDHfnwBzuyZbOz0MQpRGDlivxq2hn+JbkQv0iLVq3oZD1TdaTWimVdtbIjMzN0XYxenFVjnY6krru9XvYfovg0m8D4yo5Mz/Ra9z9+m93q0kc3vnIs+w8T/FQ3v/3xVWPZf1ym6+Z3ne6aaKNLScfNpziB0AKz6GHPF5g8A7MoxXasO3NW5Jlnx+SZ58bkzJn8mDdsELnvnq6k51vuuYX/99q0M4FbyJvW6NWPh1vI29M1t5C3o2tuIW9Hz/2j5Bby9vTNLeTt6ZpbyNvTNbeQt6dryyNtvMBML+X5r9/77/KvHv2kTEyMS/8W8i/8/mPZbeG8hdzydGrOrNNncnH5k2fH5Ny5/LjuuUvkrru6cu/dXZmYaM6xciQLCSAw23NGIDDb0zUCsx1dIzDb0TMCs109p6NFYLancwRme7pGYLana8sjbbzATLDSMy2//Tffm+P2tS99bu6t4umLfan5wr5Xs22+883H5555mf6ertjsvwRo8a3pvMTH8nSsf9bp05JJy/Tr/Pk8z9139eThXxrLnm157uLl+kOSoFQCCMxS8boajsB0VUepYRCYpeJ1MxyB6aaKSoJwBWYlmF3sBIHpooZKQiAwK8HsYicITBc1hAvRCoFZZisIzDLpVjf71KmO/OTZ9GtMLlzI95uE5YMPdOXOO3rZSwHSM7UQmNV1UteeEJh1ka9+vwjM6pnXtUcEZl3kq90vArNa3nXvDYFZdwPV7R+BWR3ruveEwKy7ger2j8CsjnWT9oTAVLaJwFQCrHn5yZO5uEy3i1+4mIe59+5cXN5x++D5lgjMmouqcPcIzAph17wrBGbNBVS4ewRmhbBr3BUCs0b4NewagVkD9Jp2icCsCXwNu0Vg1gC9pl0iMGsCH3y3CExlgQhMJcCalp9I4vKZXFxevDQrLu/pyUcf6Mrtt135Yh4EZk1F1bBbBGYN0GvaJQKzJvA17BaBWQP0GnaJwKwBeo27RGDWCL/iXSMwKwZe4+4QmDXCr3jXCMyKgTdkdwhMZZEITCXAipcfP5GkZX6r+KVZcXnfvbm4vG3v1d8ojsCsuKgad4fArBF+xbtGYFYMvMbdITBrhF/hrhGYFcJ2sCsEpoMSKoqAwKwItIPdIDAdlFBRBARmRaAbthsEprJQBKYSYEXLjx0fiMvJyXynH7gvF5d7b726uOzHQ2BWVJSD3SAwHZRQUQQEZkWgHewGgemghAoiIDArgOxoFwhMR2WUHAWBWTJgR+MRmI7KKDkKArNkwA0dj8BUFovAVAIsefnRYwNxOTWV7+yDH8jF5a17lheXCMySC3I4HoHpsJSSIiEwSwLrcCwC02EpJURCYJYA1fFIBKbjcoyjITCNgToeh8B0XI5xNASmMdCWjENgKotGYCoBlrT86NHBW8Wnp/OdfOgD+ct5RhGXCMySCnI8FoHpuBzjaAhMY6COxyEwHZdjGA2BaQgzwCgEZoCSjCIiMI1ABhiDwAxQklFEBKYRyJaNQWAqC0dgKgEaL3///YG4vHw5H37/B3NxueeW4a+4XByLW8iNi3I8DoHpuBzjaAhMY6COxyEwHZdjGA2BaQgzwCgEZoCSjCIiMI1ABhiDwAxQklFEBKYRyJaNQWAqC0dgKgEaLX9vVlw+88yYXJ6ZFZcfym8Vv+Xm4uKyHw+BaVRUgDEIzAAlGUVEYBqBDDAGgRmgJIOICEwDiIFGIDADlaWMisBUAgy0HIEZqCxlVASmEmBLlyMwlcUjMJUAlcuPvJdfcfnMs2MyMysuP3x/Li5vvkkvLhGYyoICLkdgBiytYGQEZkFwAZchMAOWViAyArMAtMBLEJiByxsxOgJzRGCBN0dgBi5vxOgIzBGBsXlGAIGpPBEQmEqABZe/e2Twcp5uNx/ykQ935aMP9OSm3XbiEoFZsKDAyxCYgcsbMToCc0RggTdHYAYub4ToCMwRYDVgUwRmA0oc8hAQmEOCasBmCMwGlDjkISAwhwTFZgsIIDCVJwQCUwlwxOWH3x2Iy96sp3wgicsHe7J7l724RGCOWFADNkdgNqDEIQ8BgTkkqAZshsBsQIlDHAICcwhIDdoEgdmgMpc5FARme7pGYLanawRme7q2PFIEppImAlMJcMjlhw8PXs7TX/LgR7ry4APliksE5pAFNWgzBGaDylzmUBCY7ekagdmOrhGY7ei5f5QIzPb0jcBsT9cIzPZ0jcBsT9eWR4rAVNJEYCoBLrP8UBKXz3TkmefG5rZMz7dM4nLXzvKuuFwci5f4lNuzp+kITE9tlJsFgVkuX0/TEZie2igvCwKzPLYeJyMwPbZSTiYEZjlcPU5FYHpspZxMCMxyuDZ9KgJT2TACUwnwKsvfOZRfcfnsrLjsdCR7MU8SlztvrE5c9uMhMMvp2eNUBKbHVsrJhMAsh6vHqQhMj63YZ0Jg2jP1PBGB6bkd22wITFuenqchMD23Y5sNgWnLsy3TEJjKphGYSoCLlr/9Ti4un/tpfsXl2JjIgw/kL+e5cUf14hKBadtvhGkIzAgt2WREYNpwjDAFgRmhJX1GBKaeYaQJCMxIbemyIjB1/CKtRmBGakuXFYGp49fW1QhMZfMITCXA2eVvvZ3E5Zj89PlO9pUVSVw+mIvLHdvrE5cITJt+I01BYEZqS5cVganjF2k1AjNSW8WzIjCLs4u4EoEZsbVimRGYxbhFXIXAjNhascwIzGLc2r4Kgak8AxCYOoBvvpXeKj4mP31hVlyuyG8VT+JyuwNxicDU9RtxNQIzYmvFMiMwi3GLuAqBGbG10TMjMEdnFnkFAjNye6NlR2COxivy1gjMyO2Nlh2BORovts4JIDCVZwICsxjAN97MxeXzP8vF5cqVA3F5ww31X3G5+Kh4BmaxniOuQmBGbK1YZgRmMW4RVyEwI7Y2emYE5ujMIq9AYEZub7TsCMzReEXeGoEZub3RsiMwR+PF1ghMk3MAgTkaxiQu063iL8yKy1WrBi/nueF6f+Kyf3QIzNF6jrw1AjNye6NlR2COxivy1gjMyO0Nnx2BOTyrJmyJwGxCi8MdAwJzOE5N2AqB2YQWhzsGBOZwnNhqIQGuwFSeEQjM4QC+/kYuLn/28/yKy/Hxgbi8/jq/4hKBOVy/TdoKgdmkNq99LAjM9nSNwGxH1wjMdvTcP0oEZnv6RmC2p2sEZnu6RmC2p2vLI0VgKmkiMK8N8LXXc3H58xdzcbl69eCt4tdt8y8uEZjKH5CAyxGYAUsrGBmBWRBcwGUIzIClFYiMwCwALfASBGbg8kaMjsAcEVjgzRGYgcsbMToCc0RgbJ4RQGAqTwQE5tIAX30tF5cvvpSLy4m+uHywJ9u2xhGXCEzlD0jA5QjMgKUVjIzALAgu4DIEZsDSCkRGYBaAFngJAjNweSNGR2COCCzw5gjMwOWNGB2BOSIwNkdgWpwDCMyFFA++mr+c58V9s+JyYvBynq0BxSUC0+KnJNYMBGasvjRpEZgaerHWIjBj9VU0LQKzKLmY6xCYMXsrkhqBWYRe5O9IAAAgAElEQVRazDUIzJi9FUmNwCxCjTVcgak8BxCYOcADSVw+MyYv7c/F5Zo1A3G5ZUu8Ky4Xnxa8xEf5gxJoOQIzUFnKqAhMJcBAyxGYgcpSREVgKuAFXIrADFhawcgIzILgAi5DYAYsrWBkBGZBcC1fhsBUngBtF5gHDua3iu+bFZdr1w5ezrNlc3xx2T89EJjKH5RAyxGYgcpSRkVgKgEGWo7ADFSWIioCUwEv4FIEZsDSCkZGYBYEF3AZAjNgaQUjIzALgmv5MgSm8gRoq8B85UAuLve/nF9xuW5dX1x2ZfMmJVSHyxGYDkspKRICsySwDsciMB2WUlIkBGZJYJ2NRWA6K6TkOAjMkgE7Go/AdFRGyVEQmCUDdjQegemojEBREJjKstomMNNbxX/4ozF5+ZVcXK5P4vLBrjz4QFc2bVTCdLwcgem4HONoCExjoI7HITAdl2McDYFpDNTpOASm02JKioXALAmsw7EITIellBQJgVkSWIdjEZgOSwkQCYGpLKktAvPCBZF/+Mcx+eenxzJiG9ZLJi0/+kBXNjZYXPZPDwSm8gcl0HIEZqCylFERmEqAgZYjMAOVpYiKwFTAC7gUgRmwtIKREZgFwQVchsAMWFrByAjMguBavgyBqTwB2iAwf/pCR37wj2Ny9Fh+1eXHf6krv/xQVzZsUMILtByBGagsZVQEphJgoOUIzEBlKaMiMJUAgyxHYAYpyigmAtMIZIAxCMwAJRlFRGAagQwwBoEZoCSHERGYylKaLDCPvJeLy5+9mIvL22/rycMf78qte5rzcp5h60dgDksq/nYIzPgdDnsECMxhScXfDoEZv8NhjgCBOQyl5myDwGxOl8sdCQJzOULN+T4CszldLnckCMzlCPH9pQggMJXnRVMFZhKX//BPYzI5md8u/vCvdOWhX+gqacVdjsCM292oyRGYoxKLuz0CM253oyZHYI5KLOb2CMyYvRVNjcAsSi7eOgRmvM6KJkZgFiUXbx0CM15nHhIjMJUtNE1gHjjYyZ51+eZb+VWXD36kKw//Sk+2bmnfVZfzTw0EpvIHJdByBGagspRREZhKgIGWIzADlaWIisBUwAu4FIEZsLSCkRGYBcEFXIbADFhawcgIzILgWr4Mgak8AZoiMM+ezV/S86Mf5y/p2b0rv138nrvbLS77pwcCU/mDEmg5AjNQWcqoCEwlwEDLEZiBylJERWAq4AVcisAMWFrByAjMguACLkNgBiytYGQEZkFwLV+GwFSeAE0QmM88NyY/+MeOnDjZkRUrRD75cDeTl+nPfHICCMz2nAkIzPZ0jcBsT9cIzHZ0jcBsR8/9o0RgtqdvBGZ7ukZgtqdrBGZ7urY8UgSmkmZkgXnocH67+L79+e3i997Tk098vCs7d3LV5eLTAoGp/EEJtByBGagsZVQEphJgoOUIzEBlKaIiMBXwAi5FYAYsrWBkBGZBcAGXITADllYwMgKzILiWL0NgKk+AiAJzZia/XfyffjgmU1MiW7f25BO/0pMHPtzel/QsdxogMJcj1JzvIzCb0+VyR4LAXI5Qc76PwGxOl9c6EgRmO3ruHyUCsz19IzDb0zUCsz1dIzDb07XlkSIwlTSjCcx9L3ckvWH8nUP5VZe/9IvpJT1dWb9OCaLhyxGYDS943uEhMNvTNQKzPV0jMNvRNQKzHT0jMNvVczpaBGZ7OkdgtqdrBGZ7urY8UgSmkmYUgXnyVBKXHfnJs/lLevbemr+k57a93C4+zCmAwByGUjO2QWA2o8dhjgKBOQylZmyDwGxGj8sdBQJzOULN+j5XYDarz2sdDQKzPV0jMNvTNQKzPV1bHikCU0kzgsD8lx+PyT/+sCOnTnVkYkLkkU905Zcf4nbxUapHYI5CK/a2CMzY/Y2SHoE5Cq3Y2yIwY/c3bHoE5rCkmrEdArMZPQ5zFAjMYSg1YxsEZjN6HOYoEJjDUGKbxQQQmMpzwrPAfOvt/Hbxlw/kt4t/5P5edrv4ddu46nLU2hGYoxKLuz0CM253oyZHYI5KLO72CMy43Y2SHIE5Cq342yIw43c47BEgMIclFX87BGb8Doc9AgTmsKTYbj4BBKbyfPAoMNOLedJLev756TG5fFlkx/aefPLhrtx3L+KyaN0IzKLk4q1DYMbrrGhiBGZRcvHWITDjdVYkMQKzCLW4axCYcbsbNTkCc1RicbdHYMbtbtTkCMxRibF9IoDAVJ4H3gTmz1/qyD/985gcOpxfdZluF0/Puly1SnmgLV+OwGzPCYDAbE/XCMz2dI3AbEfXCMx29Nw/SgRme/pGYLanawRme7pGYLana8sjRWAqaXoRmMeOd+QH/9SR536av6Tnrjvzqy537+KqS2XF2XIEpgXFGDMQmDF6skiJwLSgGGMGAjNGT9qUCEwtwVjrEZix+tKkRWBq6MVai8CM1ZcmLQJTQ6+9axGYyu49CMwfPp3fLn76jMjGDSKPfLIrH32Al/Qoq12wHIFpSdP3LASm734s0yEwLWn6noXA9N2PVToEphXJGHMQmDF6skiJwLSgGGMGAjNGTxYpEZgWFNs3A4Gp7LxOgfn6Gx35x38ekwMH89vFf/Fj3ewlPUli8rElgMC05el5GgLTczu22RCYtjw9T0Ngem7HLhsC045lhEkIzAgt2WREYNpwjDAFgRmhJZuMCEwbjm2bgsBUNl6HwLx4UeQf/mlMnv7RmMzMiNy0u5c96/KO27ldXFnnVZcjMMsi628uAtNfJ2UlQmCWRdbfXASmv07KSITALIOq35kITL/dWCdDYFoT9TsPgem3G+tkCExrou2Yh8BU9ly1wHz+hU52u/i7RzqyYoXIr32qK7/yy9wurqxx2eUIzGURNWYDBGZjqlz2QBCYyyJqzAYIzMZUec0DQWC2o+f+USIw29M3ArM9XSMw29M1ArM9XVseKQJTSbMqgfne+/nbxX/6Qn67+Afv68knP9GVG67nqktlhUMtR2AOhakRGyEwG1HjUAeBwBwKUyM2QmA2osZlDwKBuSyiRm2AwGxUndc8GARme7pGYLanawRme7q2PFIEppJmFQIzPefyhz8ak7NnRbZt7cmvPtKVD34AcamsbqTlCMyRcIXeGIEZur6RwiMwR8IVemMEZuj6hg6PwBwaVSM2RGA2osahDgKBORSmRmyEwGxEjUMdBAJzKExstIgAAlN5SpQpMA+82pH0hvGDr+ZXXT788a584le6snq1MjTLRyaAwBwZWdgFCMyw1Y0cHIE5MrKwCxCYYasbKTgCcyRc4TdGYIavcOgDQGAOjSr8hgjM8BUOfQAIzKFRseE8AghM5elQhsA8e06y28XTVZe9nshte3vyqU925eabuOpSWVfh5QjMwujCLURghquscGAEZmF04RYiMMNVVigwArMQtrCLEJhhqxs5OAJzZGRhFyAww1Y3cnAE5sjIWCAiCEzlaWAtMJ/9aXq7eEeOvNeRNRMiv/arXfmFj/KSHmVN6uUITDXCMAMQmGGqUgdFYKoRhhmAwAxTlSooAlOFL9xiBGa4ygoHRmAWRhduIQIzXGWFAyMwC6Nr9UIEprJ+K4F5+N387eIv/Cy/XfyBj3TlkU90ZfMmZUCWmxBAYJpgDDEEgRmiJpOQCEwTjCGGIDBD1KQOicBUIww1AIEZqi5VWASmCl+oxQjMUHWpwiIwVfhauxiBqaxeKzC7XZH0kp6n/2VMzp0T2bGjJ7/2SFfuupPbxZXVmC5HYJridD0Mgem6HtNwCExTnK6HITBd12MWDoFphjLEIARmiJpMQiIwTTCGGILADFGTSUgEpgnG1g1BYCor1wjMl1/pZM+5fO31/KrL9HbxTz7clU7+Vz6OCCAwHZVRchQEZsmAHY1HYDoqo+QoCMySATsZj8B0UkRFMRCYFYF2sBsEpoMSKoqAwKwItIPdIDAdlBAwAgJTWVoRgXnqtGS3iz/9o7Fs73ff1cvk5Y7tXHWprKO05QjM0tC6G4zAdFdJaYEQmKWhdTcYgemuklICITBLwep2KALTbTXmwRCY5kjdDkRguq3GPBgC0xxpKwYiMJU1jyown3l2TH74Lx15//2ObNwo8ulPzciH70dcKmsofTkCs3TEbnaAwHRTRelBEJilI3azAwSmmypKDYLALBWvu+EITHeVlBYIgVkaWneDEZjuKiktEAKzNLSNHozAVNY7rMB8+51OdsXlz17M7w9/6Be68qlPdmXNGmUAlldCAIFZCWYXO0FguqihkhAIzEowu9gJAtNFDaWHQGCWjtjVDhCYruooNQwCs1S8roYjMF3VUWoYBGapeBs7HIGprHY5gTk9nd8unp51eeGCyM039eTXPtWVW/dw1aUSfaXLEZiV4q51ZwjMWvFXunMEZqW4a90ZArNW/JXtHIFZGWoXO0JguqihkhAIzEowu9gJAtNFDZWEQGBWgrlxO0FgKiu9lsDct7+TvV389Tc6snKlZOLy47/UVe6R5XUQQGDWQb2efSIw6+Fex14RmHVQr2efCMx6uFe9VwRm1cTr3R8Cs17+Ve4dgVkl7Xr3hcCsl3+Ve0dgVkm7OftCYCq7XEpgHj+RbhfvyI9+nL+k54MfyK+63LqFqy6VuGtbjsCsDX3lO0ZgVo68th0iMGtDX/mOEZiVI69lhwjMWrDXtlMEZm3oK98xArNy5LXtEIFZG/rKd4zArBx5I3bYKIF58vRZ+fJ//Ev5D//2X8veW3bOFXTp0pT80Z/8tXzvvz2dfe1rX/qcfObXH577flr3+cf/VF7Y92r2te9883H52P13z33/u9//gXzl69/O/v7opx+Sr37xszIxMZ79fbHA/PEz6e3iHTl6rCPbtvXk05/qyn33Ii6j/7QgMKM3OHx+BObwrKJvicCM3uDw+RGYw7OKvCUCM3J7o2dHYI7OLOoKBGbU5kbPjcAcnVnUFQjMqM3Vm7sRAnO+oNy5fZv856//+wUC8xt/8VRG+Qu/95j0ZeUXfv+xTFL21z70wH2Z1HztzcPy5Sf/Sp54/HeyGT9+fr9848+fkm89+QeyZdMGmT9rvsB8662O/PBfxuTFl/KX9Dz88a786iNdWbGi3oLZuw0BBKYNxwhTEJgRWrLJiMC04RhhCgIzQkv6jAhMPcNIExCYkdrSZUVg6vhFWo3AjNSWLisCU8evrasbITD75S11BeZSX5svIZOw/OM/+1t54g9/NxOUi4Vm2nbP7h1zV2wuFpqvHbqYvaAnPevy4kWR2/bmV13u2sVVl036oUJgNqnNax8LArM9XSMw29M1ArMdXSMw29Fz/ygRmO3pG4HZnq4RmO3pGoHZnq4tj7TxAnPxFZUJXrol/OlnX8xuBf/Zy68tuMIyfb8vOD//27+Z3XrevzozfW/xvK/9pyl5862OrFkjmbj82Ed5SY/lCeplFgLTSxPl50Bgls/Yyx4QmF6aKD8HArN8xh72gMD00EJ1GRCY1bGue08IzLobqG7/CMzqWNe9JwRm3Q3E3H8rBOb8KyyXEphP/d3fL3iu5WKB+dhvPDL3TMzFAvN/+z8uy623dOR/fHSFbNwQ8yQgNQQgAAEIQAACEIAABCAAAQhAAAIQgAAEvBJwLTAXv3xnMcTFL9tZ6nbxsq/A/PunL8mdd3C7uNcT3CoXV2BakfQ/hysw/XdklZArMK1I+p/DFZj+O7JIyBWYFhTjzOAKzDhdaZNyBaaWYJz1XIEZpyttUq7A1BJs53rXAnPUSup4Bubit5CPmpntYxBAYMboySIlAtOCYowZCMwYPVmkRGBaUPQ/A4HpvyPLhAhMS5q+ZyEwffdjmQ6BaUnT9ywEpu9+vKZrvMBM4Kt4C7nXgsllQwCBacMxwhQEZoSWbDIiMG04RpiCwIzQkj4jAlPPMNIEBGaktnRZEZg6fpFWIzAjtaXLisDU8Wvr6kYIzKVuNX/00w/NPddy8fe/9qXPzb1VPBWfrtz8/ON/Ki/sezU7Dxbfmp5e+vOVr387+978uenvXIHZjh8dBGY7ek5HicBsT9cIzPZ0jcBsR9cIzHb03D9KBGZ7+kZgtqdrBGZ7ukZgtqdryyNthMC0BDLqLATmqMRibo/AjNlbkdQIzCLUYq5BYMbsrUhqBGYRavHWIDDjdaZJjMDU0Iu1FoEZqy9NWgSmhl6stQjMWH15SYvAVDaBwFQCDLIcgRmkKIOYCEwDiEFGIDCDFGUQE4FpADHACARmgJIMIyIwDWE6H4XAdF6QYTwEpiFM56MQmM4LchoPgaksBoGpBBhkOQIzSFEGMRGYBhCDjEBgBinKICYC0wBigBEIzAAlGUZEYBrCdD4Kgem8IMN4CExDmM5HITCdF+Q0HgJTWQwCUwkwyHIEZpCiDGIiMA0gBhmBwAxSlEFMBKYBxAAjEJgBSjKMiMA0hOl8FALTeUGG8RCYhjCdj0JgOi/IaTwEprIYBKYSYJDlCMwgRRnERGAaQAwyAoEZpCiDmAhMA4gBRiAwA5RkGBGBaQjT+SgEpvOCDOMhMA1hOh+FwHRekNN4CExlMQhMJcAgyxGYQYoyiInANIAYZAQCM0hRBjERmAYQA4xAYAYoyTAiAtMQpvNRCEznBRnGQ2AawnQ+CoHpvCCn8RCYymIQmEqAQZYjMIMUZRATgWkAMcgIBGaQogxiIjANIAYYgcAMUJJhRASmIUznoxCYzgsyjIfANITpfBQC03lBTuMhMJXFIDCVAIMsR2AGKcogJgLTAGKQEQjMIEUZxERgGkAMMAKBGaAkw4gITEOYzkchMJ0XZBgPgWkI0/koBKbzgpzGQ2Aqi0FgKgEGWY7ADFKUQUwEpgHEICMQmEGKMoiJwDSAGGAEAjNASYYREZiGMJ2PQmA6L8gwHgLTEKbzUQhM5wU5jYfAdFoMsSAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAERBCZnAQQgAAEIQAACEIAABCAAAQhAAAIQgAAEIOCWAALTbTUEgwAEIAABCEAAAhCAAAQgAAEIQAACEIAABBCYnAMQgAAEIAABCEAAAhCAAAQgAAEIQAACEICAWwIITGU1r715WP74z/5WnvjD35UtmzbMTbt0aUr+6E/+Wr73357Ovva1L31OPvPrDyv3xnIPBE6ePiuff/xP5YV9r2ZxPvdbj8oXfu8xD9HIUAKB9DP+v37pP8nh947Lzu3b5D9//d/L3lt2lrAnRnoh8I2/eEp+/Nx++daTf7Dgn+te8pFDRyD1++2/+d7cEP7/s46nl9X8e5eXJsrNsbjntLfvfPNx+dj9d5e7Y6bXSqDfewrx1S9+ViYmxmvNw87LIfDj5/fLv/l3T2bDP3TPbfx7WDmYa586/39b4UlqryNcAARmwcrmS6yl/gGb/gdS+iSx1d/2C7//GP+CVZC3l2X9f4F66IH7MiG9+O9ecpLDhkD6f7BffvKv5InHfwdpaYPU/ZS+3OJfnN1XVShg+mf2t/6v/0f+l//pf8jkdP9fop/48u/y/58LEfWziH/v8tNFmUnSv1P/l//7/5XP//ZvZhIrCY8vP/GX/MfFMqHXPHu+tH700w8hMGvuo6zdp5/lb/z5U0jLsgA7mbvYi+BJnBQTKAYCU1nWUldgph/EL//Hv5T/8G//9Zz0mP8v1spdsrxGAkv9Q5ZuayykxF33/4X5sd94BLFRImdPo7/7/R/IG+8ckYd/8YP/f3t3rCpHGYYBOPcQCIFYpPDWvAkhlhYSexu9AC1FbAykPJVNELFJKYkYwUrSySxMWCdzMMnMv/O9+z2ps/98//Nyzpl9d2bWSXSlYAbO4kOogbgXXNp51wWxix3Km99igQwYZzrPfvjR/dPKNz//osAcYHz0kmu/w4+eyfHHCCwvDnEeNsb5mldVYG5Md63AXLtqa3pj7I/uRuwiL5+yfPTF16dblj5++OCtsrrImMbYKLB8VMC0nE/+N6IWfvn57+hnvz1XYBbOas/RlB97ah63lvOu4+yPPrI7JY5OYOzxzy8S8F5qrPWRqy9vKZ5m8YiuIxMZe+zp5/rHJzenK+enf2uP4xs7gdWTBRSYG9O7rcBc/iD6o7sRutDL55PlaaRnvz73B7ZQNnuOsvzZnj8hvH/vrmee7gldYK3ptqXvvn/65qoOtzEVCOVCI7iC/kLQgw+zdi7mvGsweoHlXblTIISBI8x3RczPmfczPRD74KWX52Hzh4vTXVC+Q+LgcAYcfsr7y6++vfPqr79P3zHgWeQDkK94SQXmIty1T4Dm/7L2TDRXYF7PT8f5g6OXu5qvvPvn9ev/XHGp1MrM/12y/v3ln299IqjYyst7+YUt5zuYT5jmq6qXu/MczKy83yXr8x1N///FH6/cjpgV8+q0rsC8ghDfcwvOv94TLPC/3/Y73d0wgWH+z8jLAnP67wrr68t52tGyO1FWX2fOI3elwNyo6xmYGwHDXu4qj7DANoy79jyetROsDYfw0qICiuqiwew4lvJyR8wCS3kGZoEQLjiC8vKC2IUOpdAqFMbOo9z2/mp6Lvl8Be7Oh7TcQQJr76XcDXNQGKGHVWBuDG7tF+60pG/D3Ahb9OXLT4mcRBcNaqexzkuOacnPHn9zZ/4G+p0OYZmCAgrMgqHsOJIT5R0xCy3lvKtQGANHcdv4QNziSyswiwe0Ybzl+ynPp96AWfyl892un3/6yelLUl2BWTywguMpMD8wlLUv+Dh/2PD8i/iHn25OR/Bshw+ELviy5WMGPGS6YEg7jbT8OZb1TrDFl1FgFg9ow3hrf7un5dySuAG1yEuddxUJYvAYtz3qyd/nwfAFlldgFghh4AjLv8/eOw/EPnjp5aO8ZH1wIGGHV2CGBWZcAgQIECBAgAABAgQIECBAgAABAp0EFJid0rZXAgQIECBAgAABAgQIECBAgAABAmECCsywwIxLgAABAgQIECBAgAABAgQIECBAoJOAArNT2vZKgAABAgQIECBAgAABAgQIECBAIExAgRkWmHEJECBAgAABAgQIECBAgAABAgQIdBJQYHZK214JECBAgAABAgQIECBAgAABAgQIhAkoMMMCMy4BAgQIECBAgAABAgQIECBAgACBTgIKzE5p2ysBAgQIECBAgAABAgQIECBAgACBMAEFZlhgxiVAgAABAgQIECBAgAABAgQIECDQSUCB2SlteyVAgAABAgQIECBAgAABAgQIECAQJqDADAvMuAQIECBAgAABAgQIECBAgAABAgQ6CSgwO6VtrwQIECBAgAABAgQIECBAgAABAgTCBBSYYYEZlwABAgQIECBAgAABAgQIECBAgEAnAQVmp7TtlQABAgQIECBAgAABAgQIECBAgECYgAIzLDDjEiBAgAABAgQIECBAgAABAgQIEOgkoMDslLa9EiBAgAABAgQIECBAgAABAgQIEAgTUGCGBWZcAgQIECBAgAABAgQIECBAgAABAp0EFJid0rZXAgQIECBAgAABAgQIECBAgAABAmECCsywwIxLgAABAgQIECBAgAABAgQIECBAoJOAArNT2vZKgAABAgQIECBAgAABAgQIECBAIExAgRkWmHEJECBAgAABAgQIECBAgAABAgQIdBJQYHZK214JECBAgAABAgQIECBAgAABAgQIhAkoMMMCMy4BAgQIECBAgAABAgQIECBAgACBTgIKzE5p2ysBAgQIECBAgAABAgQIECBAgACBMAEFZlhgxiVAgAABAgQIECBAgAABAgQIECDQSUCB2SlteyVAgAABAgQIECBAgAABAgQIECAQJqDADAvMuAQIECBAgAABAgQIECBAgAABAgQ6CSgwO6VtrwQIECBAgAABAgQIECBAgAABAgTCBBSYYYEZlwABAgQIECBAgAABAgQIECBAgEAnAQVmp7TtlQABAgQIECBAgAABAgQIECBAgECYgAIzLDDjEiBAgAABAgQIECBAgAABAgQIEOgkoMDslLa9EiBAgAABAgQIECBAgAABAgQIEAgTUGCGBWZcAgQIECBAgAABAgQIECBAgAABAp0EFJid0rZXAgQIECBAgAABAgQIECBAgAABAmECCsywwIxLgAABAgQIECBAgAABAgQIECBAoJOAArNT2vZKgAABAgQIECBAgAABAgQIECBAIExAgRkWmHEJECBAgAABAgQIECBAgAABAgQIdBJQYHZK214JECBAgAABAgQIECBAgAABAgQIhAkoMMMCMy4BAgQIECBAgAABAgQIECBAgACBTgIKzE5p2ysBAgQIECBAgAABAgQIECBAgACBMAEFZlhgxiVAgAABAgQIECBAgAABAgQIECDQSUCB2SlteyVAgAABAgQIECBAgAABAgQIECAQJqDADAvMuAQIECBAgAABAgQIECBAgAABAgQ6CSgwO6VtrwQIECBAgAABAgQIECBAgAABAgTCBBSYYYEZlwABAgQIECBAgAABAgQIECBAgEAnAQVmp7TtlQABAgQIECBAgAABAgQIECBAgECYgAIzLDDjEiBAgAABAgQIECBAgAABAgQIEOgkoMDslLa9EiBAgAABAgQIECBAgAABAgQIEAgTUGCGBWZcAgQIECBAgAABAgQIECBAgAABAp0EFJid0rZXAgQIECBAgAABAgQIECBAgAABAmECCsywwIxLgAABAgQIECBAgAABAgQIECBAoJOAArNT2vZKgAABAgQIECBAgAABAgQIECBAIExAgRkWmHEJECBAgAABAgQIECBAgAABAgQIdBJQYHZK214JECBAgAABAgQIECBAgAABAgQIhAkoMMMCMy4BAgQIECBAgAABAgQIECBAgACBTgIKzE5p2ysBAgQIECBAgAABAgQIECBAgACBMAEFZlhgxiVAgAABAgQIECBAgAABAgQIECDQSUCB2SlteyVAgAABAgQIECBAgAABAgQIECAQJqDADAvMuAQIECBAgAABAgQIECBAgAABAgQ6CSgwO6VtrwQIECBAgAABAljrlU8AAADNSURBVAQIECBAgAABAgTCBBSYYYEZlwABAgQIECBAgAABAgQIECBAgEAnAQVmp7TtlQABAgQIECBAgAABAgQIECBAgECYgAIzLDDjEiBAgAABAgQIECBAgAABAgQIEOgkoMDslLa9EiBAgAABAgQIECBAgAABAgQIEAgTUGCGBWZcAgQIECBAgAABAgQIECBAgAABAp0EFJid0rZXAgQIECBAgAABAgQIECBAgAABAmECCsywwIxLgAABAgQIECBAgAABAgQIECBAoJPAv+0mx7ZmwggpAAAAAElFTkSuQmCC", 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