{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Alcove art in olive wood\n", "$\\newcommand{\\K}{\\mathbb{K}}$\n", "\n", "\n", "Sage Days 107
\n", "Orsay, Wednesday 20th of February 2020\n", "\n", "[Nicolas M. Thiéry](http://Nicolas.Thiery.name)
\n", "LRI, Université Paris Saclay\n", "\n", "
\n", "View the (live) slides online:\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "notes" } }, "source": [ "## Abstract\n", "\n", "I made the above piece of art in 2015 as a gift for a friend working on crystals and root\n", "systems. It represents an alcove walk in the root system of affine type $\\tilde A_2$.\n", "\n", "It is about 10 cm high and laser cut in a 3mm slice of wood.\n", "The wood comes from an old olive tree in my grand parents' garden in\n", "Provence that had died of frost in the harsh winter of 1955. \n", "\n", "\n", "In this presentation I briefly explain the math behind, describe the process to reproduce it, and propose a project to improve the process." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## The maths behind\n", "### Root systems\n", "A *root system* encodes a well-behaved arrangement of reflections:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 5 graphics primitives" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "L = RootSystem([\"G\",2]).ambient_space()\n", "L.plot(fundamental_weights=false, roots=false)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "These reflections generate a group: the *Coxeter group*. Here it's a dihedral group.\n", "\n", "Let's draw all the reflection hyperplanes for this group:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 17 graphics primitives" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "L.plot(alcoves=true, fundamental_weights=false, roots=false)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- The hyperplanes cut the space into alcoves\n", "- The alcoves are in bijection with the elements of the group" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### A 3D example: the symmetric group $S_4$ (type $A_4$)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "L = RootSystem([\"A\",3]).ambient_space()\n", "L.plot(fundamental_weights=false, alcoves=true)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Affine root systems\n", "Now what happens with these three affine reflections?" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 6 graphics primitives" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "L = RootSystem([\"A\",2,1]).ambient_space()\n", "L.plot(fundamental_weights=false, alcoves=false, fundamental_chamber=false, roots=false)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 148 graphics primitives" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "L.plot(fundamental_chamber=false, roots=false, fundamental_weights=false)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Alcoves walks\n", "- Alcove: an element `w` of the group\n", "- Alcove path: an expression of `w` in terms of the generators" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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ctk3nilk6kzmNPEm2b8+YokWZzdWVgCjQ+1BW8WpLZ/GSZ/Ok8BZ1cSHvrDgk7rBVq6TJtjebN29WH6JChVrQ1VXh99/bWyvJ/PgjYwGWK15cvdbVq1fbWytpbNokbsudvweIG9Wq3ByOSVBQEHPlyhU/bh587bUoNmuWefeKHKeQt4UEjRkDPH6MIYoCABg3bhyKFSumXXDgASDooHXnXvkOMMZo1wHA+vUASUz+9D7QoAHQs6cUuY5Ahw4d0LJlSwBAYOBYeHk9Qr9+0XbWSi6xvXtjZo4cuPXwIQCgUaNG6NGjh521kkfHjkDz5sC9ftNAEli3zt4qSaNAgQKYOHFi/L8Gwt8/C8aOfQIXF7uqZTXuMoXVqVMHT548kSkyTUJDQzERwFcAfgLwRZMmwLlz2gXfH239uZEPgINTgdxdNKtRDUCfHHfxZ3h3NC2UDTXOZ9I7LFVc8O67Y7BnjwKgJSIj26NcuVPw8PCwt2LSiIuLQ3B4uPpvz7t34XL+vB01kosLgG9KX0b9fb9gq2dXlIitBkh4/ByFevU+g7v7LBgMXwP4GZ07j0KePLlt1n7hwoVx5swZKbJcSFKKJADFixfHo0ePZInLkJwAKgPwA/BcltAfAeTScP4OACvlqBKLLDiKRvBGBOrjJMSj9SqRA0ADALvtrYhuuALoDeA3eyuiE1vwLnriL0TB296q6MB2AF8D8IdEC2MWxYoVw8P4r0CtSDXytpzJIzgYiI5GEAl3AG9kz47NmzcjT5482uSGHwRCNgKMS/YHIxAZ/2Z1zQV4VUp5rns+oMBAIEsRbToA+P57YPNmYNRbJ9Fx50Bs+XgzSgzuqFmuI3DixAkMGjQQwDWIF1de5M4NZMtmZ8VkEhkJvHiBlwBKAMgCYO4PP+Ctt96ys2JyOP7bNQxaXBnfdjyJQnvWiLWbSZPsrZYUwsPD0alTJ4SEvABwDa6u+ZAlC5A/v+10kDmTz5wbr4fiNyN//z1JgM0APQtZx7xI2GDd11q/dihc09zcyBkzSMWo8FT+d3jPvSyjQ+V479iTuLg4VqlSJUngWp8+6QTYZEZMgWvduiUJsClbtmyKAJvMSFxkLKt4+rFJzgtUjAq5YMErEuQgGDZsWJLAtXXr4jeZHa+ui1lkPiNvMJA+PuQbb5BGY7oBNlKxkZE3BU2WKZMQNHnrn6uMgxv3tckcWf3SY+HChSkC19IMsMmsjBsnAtfu3aOiKHzrrbfUa56ZSTIzpsfC9w/QBUaeW31N/CI2lqxcmXzzzczrghLPtWvXUgSuKYq4tMqVHarKptlkPiO/bJl4rSYKepo5c2aKABvp2MjI//uvuLxNm5L+/sDrQxiG7HxyIUC3tvXm2bNnzJMnjzpWx48fV/+WIsAms3L7dorAtfPnz9M13tU3R44cDAjIxGN48znzuATz04rJcu+YYlf+/ts+ikkiceDaxIkT1d+fPy8+VubPt59u1pK5jHxICFmwIPm//yX5dfIAm/Xr18tv2wZGPr1Ehi/uBPOZSz4eKm9u0nnHY/DgweoYffjhh0n+liLAJrPSpUuqgWsDBgxQr71vJg79H1T9AHMihE98UyaY47vvivw1kZG2V0wC27ZtSxK4FpEsFWr//iJ11tOndlLQSjKXkR85UoROp5J0PXGATalSpRgp+0azgZH//nuR3ymtlOQHeojqIld+P6VL+3ri6+tLNze3dAPXTAE2//5rBwVlsG9fmoFriQNsXFxcePr0aTsoqI1L62/QFQZ+335/6geYigFMmWJTvWQQExPDihUrphu4FhQkkuB+/rkdFNRA5jHyphto6tRU/6woClu2bKkO0rRp0+S2r7ORDwwUof2DBqV9TFy0gde9avBijoZiwyuToCgKW7RokeHYKIr4iqlQId3aMI5JXJxItt6wYZqfIj/88IPaBw0bNtRnWVEnFKPCFnnOsHyWO4wJT2dwRo1KcyLmyCQem0aNGqU5Nj/8ICZily7ZWEENZB4j/+67InQ6nRm6ObNFq9HZyPfrZ16Z0LPfi9nikUGZJ0Tekq+sS5fEQzRnjg0VlIGphuOptL+yzJktOiqbxx4XX1kTM/iKDA1NdUnVkUn+lXXmzJk0j42JEZOQzJTmIHMYeQs2ddJb99WEjkb+3DmxqbNggXnHHy/ahY/civNloOMnu7Jmv2TgQPFVExhoAwVlYEpI1qdPhocmT1iWfN3XEYkOjWYZ93tsnf+0eV+QJueIo0f1V04Clu6XmBKWbdxoA+Uk4PhG3kL3rOSphxN7cGhCJyOvKKJQRpUq5rtn+e+/zSh4cv+bjp+21hrPJ1Pq4X79bKCgDIYMET6gjx+bdXhaHhyOyox39tMNcbz6zy3zTjAYyFq1yDp1HL4QavLUwuZ6PrVpQ5YunTlSDzu+kZ8/P0WRkIxIzRdbMzoZ+bVrMyj5lwb7Go5jJLz44Mg9abrIRksMQ6aJr0kcuWYmmamIyOPzT5gdYRzy+gHLTjx8WNzYy5fropcMtMQwXLsmXH6/+05HBSXh2Eb+6VPhs9S/v0Wn6VIOUAcjHxkpPM46dLD83LDH4QxwLcKjJbpJ0UUPtEQjx8aKrxuHjq9Jp9xfRiSPqnRU+pQ7xHwuzxh854XlJ/foIWpZyqi3rANao5EzSzlAxzbyn3+eZuHujEhe2Ds8PFybLjoY+SlThMPQzZvWnX+43woS4IUFjlfY25zC3Rnx338OHl+TVuSaGbx48YL58+dX+8gRC3uf+v0KAfKnnlbeX/7+omLU2LFyFZNA8sLdW7ZssViGqbB3797y9ZOJ4xp5k5vFDz9YLaJjx47qII4bN06bPpKN/P374v4fNcp6GcY4I32z1eXVrD40xBi0KaQopP868swwMvyORlEKGzZsqPb93LlzrZblsPE16UWumcnSpUvVPvLx8aHBoHEMJaIYFTbIfok1vK5ru7cmTiQ9PMhbZq7n24hp06apfd+qVSur3VmXLBHv+ZMnJSsoEcc08ooifJQ0Okz7+fnRw8ODAOjp6cnbt29br1NsWIKR39+WNMSQUUHiv1bQq5fwNAsNtV4lkvT95TgJ8NBHv1gv5PkZclejhOs70IE0xMZfn+UJtVavXq0+QJUqVWKshoQfDhtfk1HkmhkYDAbWrFlT7atly5ZJVFAbqwYeIUDum6NxUyQigixenOzUSY5iEnj48CG9vb0JgG5ubrx8+bLVsgwGER5Rr57j7jFLTTUsjU2bgC5dgG3bgLZtNYkaM2YMZs2aBQDo0qULNmzYYL2wI92Ah1uA6lOAS+MBGsXv3bICWXIBHrnFfxP/fyq/u3wzF977oBDGTKuAvn2154g/UuYj1Ci0GdlH5IRr2Z6Az2zzTowKFNdx+zcIOxNPtW+AqzMBJb7KlasX4JEr7WtM9P/Riic+7PsFrt19iisPge3bt6NNmzaarm/0aGDxYuDGDaB4cU2i5BAUBJQvD3z4IbBokSZRBw8eRNOmTQEABQsWxM2bN5Erl5aCBtqJCIpAxSJhqFfYHxse1dcu8K+/RGWzPXuAFi20y9PIhx9+iJUrRdGHwYMHY+HChZrkHTgANGsG/Pkn8MEHEhSUjOMZ+ehooEoVoFIlYPt2zeLCwsJQoUIFBAYGAgD27t2L5s2bWy/QEAn4/QScH6lZN5b7DC51f9IsJ+jYERS40QQunvG/aLoTKNo67ROMMcCNBcDlqYAhoXoRclQAas0FqACH3tWs1/EHhdBgjPb6AmFhwqa2agWslFSQRRP9+4v6jH5+QL58msV17doV69evBwCMHDkSs2eb+ZLWiW/ePIBZh+vj6v4glGlaUrtAEmjSBAgNBc6fB9ylFqSziOPHj6Nhw4YAgLx588LPzw958+bVLLdrV+DYMTERyZ5dszipOF6N17lzgQcPgB9+kCIuZ86cmD59uvrvoUOHwmAwWC/Q3RsoPxjw0P5wuwSf1iwDVFAwcnyCgQeAc8MAJXnRE4iH7eE/wLZqwIXRCQY+S07AZw7Q1hco1hYo1g7IXkazanXKyJk/5MwJfPcdsGqVeJDsyvnzwLJlwOTJUgw8AMyePRuenmIA58+fDz8/PylyrcH/yAPMPlwPIxqekGPgAcDFBZg/H7hyBfj5ZzkyrUBRFAwZMkT995QpU6QYeACYPRt4/hyYOVOKOKk4lpF//Bj49lvgiy/ETF4SvXv3Ru3atQEAvr6+WLZsmTaB7p5As52Ai5s2OeUHaTsfAG7+CAQdSvq7sGviayMxoVeB/e8AhzoAL2/F/9IFKNsPeNcPqDwccIuvseriAjTfLZahNJClylBN5yemTx+gVi1gyBAgvna77SGFApUrA599Jk1sqVKlMGrUKACiNuyIESOkybaU0T0fII9rKL7aUEeu4Nq1gY8/Br7+WlR1swMrV67E6dNiYlW1alUMGDBAmuxSpYCRI4Wxv3dPmlgpONZyTZ8+Yh3ezw/ILbdo7rFjx9CoUSMAQL58+eDn56e9VOCFr4CrM6w7N29toPUpwEXDe/blXWB7dcAQkfJvWXIL4+3iCvhOBvwWJ+whAEDBN4Fa84C8PmnLv7EAODsk7b+ngzHra3DrcB1w87Lq/NQ4ckR89S9fLm4Vm/P330D37sCuXWLtSCIRERGoWLGiWiN5586daN06nSU3HTi08CLe+rIm/hhwBB8uaSy/gSdPgAoVxOAtWCBffjqEh4ejYsWKCAgIAADs2bMHLSTvD7x8CVSsCDRsCKxbJ1W0JhxnJn/qFLBiBTBtmnQDDwANGzZEr169AADPnz/H5MmTtQutPhHIWdm6c2vP12bgSeDkp6kbeACICwEOvwf8Ux64uSDBwHuXBBr/DbQ4kL6BB4AKg4EC1j3sbnV+kGrgAaBxY6BHD+Crr4Dw8IyPl0pUFDBqFNChg3QDDwDZsmXDzETf+sOGDUNcXCpLbjphjDViyBhP1M12Gf9b1FCfRgoXFjP5H38USzc2ZPr06aqB79Spk3QDD4i1+JkzxXbNwYPSxVuNY8zkFUW8/qKigHPnADeNyyBp8ODBA1SsWBFRUVFwc3PDpUuXUKVKFW1Cn50AdjcSm5Xm8lpPoNFqbe36LQVOW7Bk4OYNVBkLVB4JuFuwDBPmB+yoARijzT6FBZvCpcU+sewjmfv3xUrekCFAoq0W/Zk6VfxcvQqUK6dLEyTRsGFDnDhxAoBYn//yyy91aSs5v3x0CP3/fBPHf7mM+p9W06+hmBigWjWgdGngv/90uUeSc+fOHVSuXBmxsbHw8PDA1atXUbZsWV3aUhSgUSNhys6e1c2UWYRjzORXrwZOnhSbMzr2SokSJTB27FgAgNFoxPDhw6H5HZe/PlBxmPnHu7gD1SZoazPC3zLvntd6Ae/eAKp/bZmBB4Cc5YEa08w+nABcqk/U7eEtWRIYM0bsy9++rUsTKXnwQLxRhg3TzcADgIuLC+bPn6/+e+LEiXj27Jlu7ZkI8Q/F+JWV8WGZI/oaeADw9BSDt3s38O+/+rYVz8iRIxEbGwtAfCHpZeABwNVVmLGLF4Fff9WtGYuw/0zexgtZkZGRqFy5Mu7fvw8A+Pfff9GuXTttQg1RwI6aQLiZXhFehYCa3wFl+li+ZEMC+1sDT3abf06TjUCJzpa1kxjFCOxuDDw/Yd7xWXIB1ScBFQYBrlmsbzcNIiPFbL52bRFSoTv/+x+wdy9w86Zw9dGZPn36YMWKFQCAgQMHYvHixbq2N6LOASw9Wwc3ToejWJ0iurYFQNzDrVsDd+8Cly8Lw68T+/btU5dmChcujJs3byJHjhy6tWeid2/hAa7D9qLF2H8mP3Om8D2ykW+wt7d3Ej/kYcOGqW95q3HPCtT7DYCZs9foQODkJ8B/dYGnRy1r685vlhl4ADg3wqLllhS4ugH1fwNc038Y1dlCXKhw49xeA3i80/p208DbG5g1C9i8WcTX6MrRo+JL87vvbGLgAbF+nD3e2XrJkiXw9fXVra0bO+5gwdlGGNfqjG0MPCC+8ubOFUZexw1Yg8GAoUMTPLymT59uEwMv2hJLNlOm2KS5dHGbNGnSJLu1fu8e0KuX8D3q0sVmzVapUgX79u3D/fv3ERwcjNy5c6sBElaTrSQQEww8P5n2MbUXCD/7sGvi31EBwmiH3QRlaqjHAAAgAElEQVTy1RVRpekR+RA41DEhEtVc4kIA92xAwSaWnZcYrwJiqSlwb5qHuFSfAmQvBby4KH4R8wy4twp4fhrIWwfwzG99+8moWlUY+M2bRWySqx7TFUUB3nsPKFpUhNzaYP0YAHLkyAFXV1fs3bsXJHH9+nV89NFHcNGh/T6N/RAT44JVpyvC3cuGQUoFCwLPngkj37evLhFES5cuxfLlywEAderUwaJFi3Tpw9TIkUPcLjNnAt26Afnl3foWY9/lGjuGiZ0/fx61a9cGSeTMmRM3b95EoUKFtAk1RIjZ68s7Kf9WoDHQ8pAY+cADwjUx5FLC392yAlXGAJVHiRdBckjgYHvgsZVRwO7ZgPY3Ae+i1p0PAIoB2NUACD6T8k/ZK8C1/WWxPPP8jLi+Z4kil1zcgYpfAtW+FikQJHD2LPDGGyKzwMCBUkQm5fffhW/3kSNiN82GREdHo0qVKrh79y4AYOPGjejcWcOSWyrsmHIabSe+gfUjj+O92Q2kyjaL4GARyty5swgwkyo6GBUqVMDz588BAEePHtU+kbMQU/B+5crCM9xe2G+55sAB4Ws0c6Zd4oB9fHzwySefABCpDyZM0LgZCghDWi+13RaXeJfJ+FlEoabAO+eAN5YAnvFRk8YowHcS8G8lwH+tMOqJuf2r9QYeEC+gS19bfz4AuLoD9ZeDLinX2V3rzE9Yf89XB2h1BGi4GvCOTzZDA3D9B+CfCsCtn8U6v0Zq1xaTQF3ia8LCgLFjRc4VGxt4APDy8sKcOXPUf48YMQLR0RqW3JIRFxmHYd/mQ9Pc59FlpoT8NNaQN6/wWPrtN/HGlsjkyZNVA9+rVy+bG3gA8PIC5swRa/MSMrRYjX1m8kajeEKzZhVrnrp8a2dMYGAgKlSogLCwMLi4uODs2bPw8cnAd9wMeGogXG4lijgt+ylQ75fUD459AfhOAW4uEobQRIHG4sWQtxYQ8RDY8hoAjaGe2UoDHVP5yrCQ47+0Q4NsCXcti7aDS9M0PCUMEcDVWcC1WUn3BXLXFNdX6C1NugQGismg9PiasWOFwBs3gBIlJAo2H5Jo2bIl9u3bB0CsKZu8w7Qyr/NBjNjcGOfW3kLNbhWlyLQKgwHw8QFy5QIOH5ayJHb16lXUqFEDRqMR3t7euHHjBorbKbMdKXKyPX4MXLoEeHjYXgf7WNdffxU+RvPn283AA0ChQoXwzTffABAP1JAhQ7S7VALYHjAT956+Jv6RJWf6LogeeYDac0XemCLvJPz+6RFgZx0R8PRwC6w28G7eiHmZDUZ/V4Tk0p5U7dmzZ+gw9ijO3xP/VuAOl1pz0j7BPRtQYzLQ/jpQsnvC70MuAnubisye0UFW61OokA7xNbduiY3BMWPsZuAB4VI5b948uMY/I9OmTcPjx481y3167RkmbX4d/ascta+BB0SysnnzxGRv7VrN4khi2LBhMBrFl+LYsWPtZuAB8c6aN0942ejsJJU2tsxrTNLhyqnExMSwfPnyak7vtWvXapIXHS2qwfV+7xaVsyPIpxZWE3i4jdxaISG3+yqQJ/qT/zUkNxYj97Ykj38sintcmkRem0veXk7e30gG7CWfnyXDbpHRz0ijyOMecu8Fg1wK8HCZjzRdG0l+/vnnBMDCucFt06qRAbstExB4iNzuk/T6DmrLNR4dTZYrR7ZqJalUYMeOZIkSIhe6AzBw4ED1/uwt4bn5rMpB5sYLBl19ql05WXTqJPLOa+zzf/75R+2rkiVLMtJBqs1oKHKnGdsbeQcsjJj8xojQcKPNmiXqOl+5okEhQwx5dQ75d05hBC9M0CBMcPCDn0mAvstOWC3j4sWLdHV1JQBmz56djx8/tk6Q0UD6/UKuLxD/EvvEap1MbN0qKvRs3apR0O7dQtBff2nWSRZPnz5l7ty51Xv0pIYyRBfWXqcrDJzbycLC3Hpz65aoIDVpktUiYmJiWK5cOWkTNpmYylVbWOpYCrY18g5a4lxRFLZu3Vq9OSZPnmyVnIAAMkcO8ssvJSkW84J8dlrK9NQQY+A1r9fpm60ejXGWl7BRFIXNmjVT+2j69OmadWLYHfLUYDLymWZRikK+/baY0VtYjzmBuDiyalWycWOHqx4+f/58te/r169vVbk6xaiwae5zrORxi7ER1lfr0o2xY0VNTH9/q06fPXu22kdNmjSxuqSfXsyfT7q4kOfP27Zd2xr5Nm3I0qXJqCibNmsOV69epZubGwEwa9asvH//vsUy+vYl8+Ylnz/XQUEJnJ9/kAR4eMAfFp+7ceNG9QEqU6YMo7SOoWIk1+UVM/mNRaUY1StXxFfUrFlWCli0SDyFZ89q1kU2sbGxrFy5sjoGK1eutFjG+pHHCJA7pp7WQUMJhIWRhQuTPXpYfOqTJ0+YM2dOAqCLiwvPndNYtlAHYmPJypXJt96y7RzCdkZ+2zbxGbxxo82atJQhQ4aoD1GvXr0sOvf0aWEfFi/WSTlJHCvelY9dizI8INzsc6Kioli6dGm1bzZt2qRdkfsbk67LB+zVLpPkF1+Ir6mAAAtPfPaMzJOH/ET70pFe7Ny5Ux2DokWLMjzcgjF8EcVS7vfZrqADV5wmyeXLhZ04dMii0z799FO1b/r166ePbhLYuVNc3rp1tmvTNkY+JoasWJFs3tzhPoMTExwczHz58qk3y5EjR8w6T1HIRo3IatXEF78j8+DwXUbCi/sbjTf7nO+++07tkxYtWmj/DFaM5LaaSY38riZS7o3nz8XXVN++Fp44eLB4Ozx5olkHPXn33XfVsZgwwfy9mm9b7ac7Ynljh4Zi9rbAaCTr1CFr1TK7MvbZs2fp4uJCAMyZMycDAwN1VlIb7duTr71G2mpP2DZG/ocfRGX7S5ds0pwWfvzxR/Uhql27No1m3Ghr1oi38549NlBQAvsaf80oePL+wTsZHvvo0SNmy5aNAOjq6spLMsYw+Sxe8mx+8WLxVXXmjJknXL4s1nlmz5bSvp7cvHmTWbJkIQB6enry7t27GZ7z8PRjZkM4R9Ter7t+Ujh2TDxQv/6a4aGKorBx48bqM/v999/bQEFt3LhBZslCTptmm/b0N/KBgcJ36PPPdW9KBnFxcaxevbp60/z222/pHh8RITy/One2kYISeBn4ko9di/FYsfcyPPajjz5S+2LgwIHaG09tFi95Nh8XJ76qGjUyQ5yiCN/L8uXFF2cmYOTIkeqYvP/++xke/2GZwyzgEsSQey9soJ0k/vc/smBBMjQ03cP++usvtS/Kly/PmEwzhqS3N/nwof5t6W/k+/cXvkNPHcgnNwP27t2r3jiFChViaDo32sSJwvPrtoN/BSfnyOcrSYDn5uxL85iTJ0+q/ZAnTx4+e6bdCybNWbzk2fyePWIyuGZNBgdu2SLJ99J2hISEsGDBgurYHDiQtjvk8V98CZA/f3jQhhpK4MEDYQVHjUrzkIiICJYsWVLth3///deGCmojJIQsUID84AP929LXyJ8/L76b58/XtRk96NKli3rzjBkzJtVj/P1JLy/h+ZXZUIwKL2VvwOteNWiIMaT4u9FoZL169dQ+WLBggYxG057FS57Nk2bE15gi195+26H3ilJj2bJl6tjUrFmTBkMqYxhnZN1svnw967VUx9jhmTJFrGvcvJnqnydPnqz2wTvvvONwLpMZ8csvYn5x7Ji+7ehn5BVF+ApVrix8hzIZt2/fpqenJwHQw8ODfn5+KY7p3l14fIWF2UFBCVz5/RQJ8GCvJSn+9ueff6oPUJUqVRgrYwwzmsVLns2b4msmTkzjgJkzJUSu2QeDwcBatWqpY7R06dIUx/wx4DAB8uCCC3bQUAKRkWTJkuS776b40/3795k1a1YCoLu7O69evWoHBbVhMJA+PuQbb5i9x2wV+hn5devEa2rnTt2a0Jtx48apD1HHjh2T/O3QIXF5v/9uJ+UkcahsHz5zyccXd4LV34WHh7No0aLqte/atUt7Q+bM4nWYzacZXyM9cs32HD58WB2j/Pnz88WLhDX38IBwFnENYLfiR+2ooQT+/ls8aP/9l+TXPXv2VK996NChdlJOOyY7smKFfm3oY+QjI4WPUCpv4MxEeHg4ixQpot5Mu3eLPC22egPbgifnHzMM2XnAJ+FBGT9+vHrN78oaQ3Nn8ZJn82nG1/TtS+bLRwYHp3peZqF79+7qWA0bNkz9/biG++mFSN47bHlQn0OhKOSbb5JVqqgrAkeOHFGvOV++fAzO9GNIFimi34qAPkZ+6tR019IyEytWrFBvqKpVqzIuLo7LltlmLc1W7G89nbFw561/rvLu3bvqMlWWLFl4U8YYWjKL12E2nyK+JrNErpmBv78/vby81GWL69ev8/Z+f3oiil832W9v9eRw7pwYrwULaDQaWbt2bfWZ/Omnn+ytnWZMe3tffaWPfPlG/uFDsSs+cqR00fbAaDSybt26ifxwF7FgQeHh9aoQ9SKK99zL8FT+d/j++++r1zoqHc8Gi7B0Fi95Np8kvsaQiSLXzGTixInqmLVt25Zdih5nMdfHfBn40t6qyaNfPzJPHv62YIF6rTVq1Eh1wzkz8s03+nnpyS8a8uGHwK5dorJ9rgxqlmYSTpw4gQYNRHk0d3dvuLvfhZ9fQdgxTbV0TozdjPozO6MtgB0AChYsCD8/P+TUWryaCrCjlsgfbykFmgAtD0opJHH8ONCwIbCv/19o9nNPUSC2RQvNch2ByMhIVKxYEQ8fPgTQFMB+rBp4FL0W276ilW4EBSGkbFmUio1FaGwsAGDfvn1o1qyZnRWTQ0QEUKkSULcusGGDXNlSjXzMvB/hOWwQ/L9ehuedPpEl1iEYN24c/vtvZ/y/HqBIkSxqMYdXgdiYGKx+9gwlAFQHsOSbb9C3Y0ftgsP3AY9GWX9+iZ+AbHW16wGg95e58N3RN4FKFRG4bJuoTPaK8N9/f2HcuA8AnAXwEnnzdkLWrJ72VksaiqIg/MkTGElUApAje3YcPHjQ3mpJZc3OPOg1vjQWfnkTg6cXB7xTqfVsBVKN/NMuA1Bg089ogd3Yh5ayxDogtQGcs7cS0qkKYB2ALgCuQFLZsLEQbw1rOQlAUlm/JyiICGRHK+zGXZSRI9RhIID3AUwG0AfC2L9auAKoiVfxyRMQQCvsxnvYgM/P9gNq1ZIiV6qRj4wglAYN4Rodiesrz4rSXq8AAQEBeO+99xATEw3ABcBEFCkyAq6uUfZWTR5xcYgLCkIwADcA7UuXw9q1q+Hm5qZN7uOvgTANVYxzdwUKa69rGhAAdOkCfFtxBXJfPQ6sXAlUqKBZriOgKAo+/uhDXL52FsBdALmQP78HPF+diTw8SMwLCEAvEhUgnsJNmzahZMmS9lZNCooi6hTHxgKrVgFuVStJm8nL33g9JQJs+Arsepvo0aOHutnTt+8weniIjZJXhng3NaVyZdaq7qNe65IlKYOkLMYQQwbsIR9sTvmzNr7y1YZCqf/9yX7SKGdztFu3eDe1wHj33vbtpch1BP744w91zCqXr8TXX1deCffeJMyYQbq5cfyAAeq1dujQwd5aSWPFCmE2D+qQfUIfF8o+fV4JH2Qy9YCTr74SLk9WFrBxPBIFriW+3ty5kwbYSMdU/m9LGf3aYCoBJ69AoJ6J8PBwFilQIEngmi0CbGxKQACZPTs5ZEiK2BUpgXp2JjxcTEC6ddNHvj5G/vFjMSiZOBKNFO6TiUPHTTPbsDAxKN2721lBGaQSuNatW8KXy9Chw9I+Vys2MPKmwLW6dRPNbDN5yo3EjE8Uld0h0deJ3gE2NuXjj5NMGhN/uVSpUoVxmdwVdtw4MWm8d08f+fqlNZgxQ9RzzYQ5JUz8+uuvafrk/v67VQVsHI9UAtf8/f3p6Snygri5ufPatWv6tG0DI29KAnX8eLI/ZOLkeSbu3LlDz/jc8lnc3ZPkV9I7wMZmmJZ/f/xR/VXy5HkLFy60o4LauH2b9PQkv/5avzb0M/LR0WSZMmTr1pkuwx9JhoaGJknnun///iR/NxpFWgMfHzFbzJSY0rmmErg2adIk9drffruNPu3rbOQzTOeaCdNgJ+a9zp3VMRqdSuCangE2NkFRyAYNyOrVUwSunThxQn4abDvQpQtZrBj5Use4NX1TDW/aJN7CmSjPs4lRo0ZlWJjBVMDml19srJwsTIUZQkJS/CkiIoJFipRQ+2Dbtm3y29fZyI8YkUFhhqCgTFXQJjH79u1LqHmQL1+qNQ9evsx8BW2SsGqVeMD2ph75nLigzaBBg2ysnHb27ROXt2qVvu3oa+QVhWzRIlNV3SEtK7H2wQdp2knHxvSGWrYszUPWrFmjPkRlylSQX3VHRyNvdom1TFSa0oTBYGCNKlXUsfk1nTJ5q1enaycdF9MbqkuXNA9JXprS19fXhgpqIy6OrFGDbNhQ/4UO/StD+fqKh2jOHN2bkkWHDh3UB2j8+PQLXmfKVD2mtaZatdJda1IUhfXrN1L74ocffpCrh45Gvn17slQpM4olm4rMN2uWaZYVlyxZoo5J7Zo1061DbCoyn8qKh2PzzTdisTqDtaZvv/1W7QspReZtxE8/iZfv6dP6t6W/kSfJQYPInDlFvVcH57///lNvmqJFizI8PDzDc0x7lzdu2EBBGZh2jQ8fzvDQM2fO0MXFhQCYPXsuBsocQ52M/I4d4vLWrTPzhG3bxAkbN0rVQw+Cg4OZL3du9R49cuRIhuecOSP2mBPtXTo29+6ZvWscFRXFUqVKqf2xefNmGyiojeBg4SzUp49t2rONkX/2jMyTR2SSc2BiY2NZJdFn8J9//mnWeZGZKb7GlGDdAv/Pvn0/UfukX7/+8nTRwcjHxpKVKgkPSYsmdW3akKVLk1FR0nTRg6FDhqhj0dOCMTR5IT5/rqNyslAj18zz/9ywYUOiZcUyjI6O1llBbQwZIjzMHz+2TXu2MfIkuWCBmE6cO2ezJi1lQaI0pvXr10/3Mzg5mSa+ZuxYiyO5njx5Qm/vHARAFxcXnj9/Xo4uOhj5efPE6qDFKl67Jlx+v/tOmi6yuXr1Kt3d3AiAWT09ef+++QVBTPFEDl8I6+BBiyO5FEVhs2bN1Gd3xowZOiqojatXRcVJW6poOyMfGyuquzSRVwxCJk+fPmXuRJ/BJ0+etOj8TBFfc/t2BkVP02bWrFlq3zRq9KactU/JRv7pU+EROWCAlQKGDSOzZSMfPZKij0wURWHrli3VMZg0aZLFMhy+pG2qkWvmcfHiRbq6usYvK2bnY1tNky1AUYRHedmywsPcVtjOyJPkrl3iLf333zZt1hwGDhyoPkAfffSRVTLOnxezSIeNr+ncWXgsRERYfGp0dDRLlSqn9tHfMsZQspH//HPhERkUZKWAFy/I/PnJ3r2l6COTf//9V+37EkWKMMKqMRQG5u23HXKelU7kmnl89tlnah/1sdWCtwX8+6+4PFtvG9jWyJNkhw6iAnuGbg+249KlS+osIFu2bHykYSbnsPE1e/aIO2zNGqtFbN26VX2IihV7jZFax1Cikb94UbxgNTsALVki+snCLzk9iYmJYYUyZdS+/+uvv6yWtWWLuLx//pGooAwyjFzLmKCgoCRf46dOnZKooDZiYoQneYsWtn/B2t7I+/kJV5QpU2zedGooisLmzZurN8Z3GtdkHTK+Ji5OlLtr1EjTHaYoClu0eFvtq6lTp2rTa1v1+Hqujcjr88kDHUjfqeStZaT/OjJgN/nsFBl6g4wKJA2pf+MqivCArFhRQjiGwSAcmOvVc5g0jnPmzFH7vHGDBpqWyhSFbNWKLFfOwUJXMoxcM4958+apfdVAY1/J5PvvxSTEHq78tjfyJDlqFJk1K2nBxpFebNq0Sb0pSpcuzSgJ3hWm+JqLFyUoKIPFi8Wm95kzmkVduXKFrq5i88/Ly5sPHjywXljQMfJEP/LuX+bXfV3jKVITb61A7niD3NuKD9a8zyV9+/PY1ozdCc1i/34x3TXTu0pPAgMDmTM+4MfFxYVnz57VLPPyZbE2P3u2BAVlcOOG2PTOMHItY2JjY1mpUiX1mV6ldzipGQQGCg9yewXl2sfIh4aKMNFevezSvImoqCiWSfQZvGHDBilyHSq+5vlz4TvXt680kYMHf5HgxtdTQkXziEfkKhfrin0n/lmXl1Qkzb7ff58sWlTkgbUj/T79VO3rT6SOIZkjB/nkiTSR1mN25Jp57NixI9GyYjG+1DMxjBnE1yCnvdLr2MfIk+Svv4rZ0tGjdlNh+vTp6s3QrFkzqZ9227c7SHzNl1+KpzkgQJrI58+fM1euvGrfHTt2TLvQS5O0G/ltNbTrYeLuXRFxOWGCPJkWcu7cOTUQLYe3N59ItMjPn5N585KffCJNpHWYItfWr5cqtl27dur9+bWeKR4z4Nw58RFtz0SZ9jPyRiNZuzZZp45d1j4fP37M7Nmzq3kvLuqwtmL3+JorV8R3+axZ0kUvXrxYfYh8fN6wKKYgVRQjuauJNiP/aLucizMxfrww9OnkLtILRVH4ZqOElBKzdVhbWbRIGCAJK0DWYXXkWsbcuHGD7u7u8cuKXrynV7L2dFAU4TFepYp9U0rYz8iT5JEj4i2+fLnNm+7Tp4/6AH2u0y6pXeNrEu+w6eCUGxcXx0qVqql9+Pvvv2sXGnqT/MvLOgO/v6329pMTHi6WbNLIQqonf//9t9q35UuXlp8cjsLwVK1KNm5sp2VFqyPXzGPEiBFqH3bTq+xSOqxdK8ybvYtX2dfIk2SPHmShQmKd3kacOnVKHfzcuXPzqY7+jnaLr9m6VdxhW7bo1sSePXvUfsyfvzDDZJQhujrHcgO/2p0Mva697dT480/RjwcO6CM/FSIjI1myaFG1b//R0d9x925xeRq8Mq1Dc+RaxoSEhLBAotKIB/UooJoGkZHCU9wRytDa38j7+wtPmzFjbNKcyKxYXx34efPm6dqeXeJrYmLEDL5VK92naB06dFL7csyYsdoFGg3kfw0sM/Jnh2tvN019jGT9+mTNmjarDjNlyhS1T9+2QWbFjh3JEiWsipGzHs2Ra+bx888/q335+uuvJ6nupidTpghP8UTFuuyG/Y08SU6aJMLtbdAjK1euVAe9UqVKjLVBDoKlS20cXzN7tliLv3xZ96Zu3bpFd3cPAqC7uwdv3bqlXWjINeEqaZaRdyEvTkrTh14KJ0+KAVy6VL824nnw4AG9vbwIgG6urrxigxwEfn7i8bMiU4J1mCLX5s7VvSmDwcDXX39dfeZ//vln3du8f1/MW0eP1r0ps3AMIx8RIaYSHTvq2szLly9ZrFgxdcB32iibmMEgJoI2ia958kR403zxhc4NJTBmzFi1Tzt2lFSG6MoMy2bzW8qSDzbr9+Xy0Ufik+zFC33kx/O/nj3VvvzSpmNoo9CVxJFrNkrydPDgQbVPCxQowBCdK/z06mXzFeh0cQwjT4pFQUAsEurE119/rQ52exvnBbZZfM0nnwjfOBvmlA0LC2P+/IXVvt2zZ492ocY4EeyUrl98vpT+9Xtbki90+IJ59EhsrgwbJl92PEePHlX7MF+uXAwODtatreSYMlD37KlzQxs2iAdhu2RPqAzo1q2b2rcjRozQrR2TL0k6xbpsjuMYeUUR2/xVq+rib3T37l16xX8GZ8mShTfsUOFD9/ias2eFT9zixTo1kDa///57omWwaoyTMYYvfMk1WdI28k8OkMEXyN1Nk23EupGnB5PRkl90330n3KWuXZMrl6TRaGSdRMsKP9qhwsfy5WbXkrGOqCgR9NRWB0+oDLh37576/Lu7u/P6dfkb9Sav8Nq1HSYjBklHMvJkgpFatEi66K5du9rkTZ4eusbXmF6S1arZxSnXaDTSx+cNtY8Xy3rR+E5N3cAf7ppwjKKQ/uvJzaVSRsDeWCS+CmQQFSUCH3QwUsuXL1f7rlqlSnJekhZiNIqwlVq1dDJSppekDgbWHBJ/ybdr1066fNNL0oxiXTbFsYw8KZYbJMcAHzhwwKZrcukxYYJO8TWm5S4ZSyVWcuzYMbWfc+XKy+cyloyMseR2n6TG+y8vMvxuymPjIknfaeTabEmP/7eqSHYmg40bRT9v2yZHHsnQ0FAWypdP7nKXlRw9qtNyg2m5a7iOnlAZkHxPbrvEJaPQULEOr/tylxU4npE3bRwOHixFnMFgYM2aNdWB/eWXX6TItRZd4mtMG9edOkkUah09e/5P7evBg+VsHBqeXmDsH+4JRvtiBmHqEQ/Jox+mnP0f7EiGafT+kZryUjBm9Gi1zzrr7HxgDr16idRSUjcObbRxnRGrVq3SxbvOZhvXVuB4Rp6U6gKY2E/Wx8fHZn6y6WGKr9m/X5JAkwuqDPdFjTx48IBeXt7x6SLcpLgALllCDm/7ffysvBoZZ2bCqafHyZ11kxr6NR7k3dXaFJKWvF64oHrEh997uLvz9u3bmmVq5cEDkfV31ChJAk+csJkLakYoisKGDRtKjZOxuQuqhTimkTdl2NcYzPPixYskEW+HDh2SqKT1mOJratSQEF9jCiYbKyEQSRJTp05V+7x581aagnlMle179yb58j4ZZ2HEjmIkb68gNxZJMPTbfazWR8UUzBMYqElMpw4d1L76yoHG0BTMc/OmRkFGo/AdtmEwWUacPn060bJiLgZpDMiySzCZBTimkSelhOUPHz7crrkr0sMUX7NkiUZBPXoI3zcZKQUkERkZyWLFXlP7fuvWrVbLGjpUUmX72HDywnhyRx3tM3kyISy/f3+rRezevVvto8L588tJCyEJaWH5f/xh87QQ5pA4d9Vnn31mtRy7pYWwAMc18ooiilFaWfX2+vXrds9ClxG9e2tcpjx82G4J3jIicYKtUqXKMdqKMTQleJs+XZJS1+aJGf1lSRnj5s8X3mBWJNiKi4tj1YoV5SZ4k4wpwdZ//1kpwLQB1bVrxsfamORZaC9cuGCxDLsneDMTxzXyZGDVTPUAACAASURBVEKq3JkzLT61bdu26gP0zTff6KCcdjTF1xiNwtfNTqmaM0JRFDZq9KY6BrOsSHcsNVVzbKjwn18FcpUrGS3Beys2lqxc2apUuYsWLVL75g0fH+2pmnUgcapcq/Yn7Ziq2RxmzJihjkHTpk0tXla0e6pmM3FsI0+KohfZs1tU9GL79u3q4BUvXtzulWHSw+r4GlPRFRkFO3Ti/PnzatELb+8cFhW92LZNctGVy98m3YC9MF6O3J07haLr1pl9yvPnz5k3Vy71HpVSdEUnTEUvFiyw8MQ7d+xedCUjoqOjWbZsWXUcLKkM9+yZ8PS2e9EVM3B8I2/aefv4Y7MOj42NZcVEn8GrV0tYf9URU3xNmzYWnGQqn/g/CaX3dKZfv/7qWPTta94TERNDVqhANm8u6TM4NlQERiU28mtzyJnNk6J83WuvmV2+7ovBg9U++cDOJTDNwaryde+9RxYrRjrwBIskN2/enGhZsZTZNZ4dqnxiBji+kScTClGfPp3hoXPnzlUHrWHDhg5TrT09LI6vGTVK+LhpKaJtIwIDA5ktW04CohD1GTOKic+ZIzwUL12SpETyWbzs2fyNG8IVZerUjFW5fJlurq7i68bLiw8fPpSjg45YXIjalKhp5Uo91ZKCoihs0aKFajO+/fbbDM9xuELoGZA5jHxcnAjXb9gw3aldUFAQcyX6DD5txkvBEVAUMWs1K77m5k1hUKZMsYluMpgzZ446JvXrN0r3xRsYKDwTBw6U1Hhqs3g9ZvMjR4oXbzpGW1EUtmreXO2LqWa8FByF778388VrMAjf4AYNHHs3MhG+vr50jX/xZsuWLd0Xr6ngWvny0mLhdCdzGHlShOsDZDrLLwMGDFAfoI/NXN5xFC5dMjO+pkMH4dsmqbK9LYiJiWGZMhXUsVmzZk2ax/bvLzwTpRXrSmsWL3s2HxJCFihAfvBBmods2bJF7YPXihVjZKYaQ2HYMlxCW7JEPKenTtlMNxkMGjRIHZsPP/wwzeO2bBGXp8Er2OZkHiNPkp07k8WLp7rOd+HCBfVtnD17dgZYsFHrKGQYX/Pff+IO+/tvm+olg23btqkPUZEiJRiRSuTI+fNiVW7+fEmNpjeL12M2/8svaW6GR0dHs1ypUmofrLNgo9ZR+PdfcXmbNqVxQJLItczFs2fPmCdPHnV8Tpw4keKY6Gjh0f3225nmI4VkZjPyt2+L+OFkLpGKorBp06bqAM20wuXSEUg3viY2Vviyvflm5rrDEvH2223UMZqULAZcUcSlVa4ssZZERrN42bN5g4H08SHfeCOFW+usWbPUa3+rceNMsVeUHEUh33mHLFMmjdAVaZFr9mHhwoXqGNWrVy+FW+vMmWIt3gbFuqSSuYw8SX71FenlJcL541m/fr06OGXLlrUq8MZRSDO+ZsECqwNvHIVr167RzU0EqHl6ZqV/ojH8+28xS5RWrMucWbwes/lDh8SFJApuCggIYA5vb3Xz+XwmHsOrV4XL74wZyf4gPXLN9sTFxbFKlSqqLfnjjz/UvwUEiPfXl1/aUUEryXxG3lTCpnt3kiKEvlSiz+DNmzfbWUFtpBpfY3LK7dfPnqpJYciQoYlSTfQgKbYXXntNeCJKw9xZvOzZPEl260YWKaKmmuj78cfqNfd/JcYwlQm71Mg1+7Fr165Ey4pFGB5f4advX5sXXJNG5jPypJglAeShQ5w2bZo6KC1btsyUn8HJSRFfM2iQ8GHTmAzLEQgODmbu3PnVMTt8+DCnThUOQ9KKdVkyi9djNn/vnvja/OornjlzRg0Iy5U9u+ZkWI6Aaem9T5/4X0iPXLMvHRIljRs3bhxPn7ZbwTUpZE4jbzSSb7zBmGrV1M9gNzc3+vr62lszaajxNad8hdvNnDn2VkkaS5YsUR+iSpV8mDWrkSNHSmzA0lm8HrP5b76hkiULGyaqZfCDhNTEjsJPPwm7fvqo7Mg1++Pn58csWbIQAD08PFm7dpS9Cq5JwYUkkQmJPXgQHk2b4gsAiwAMHjwYCxcutLda0rh5E6hWjRhZaCW+854G+PoCHh72VksKRqMRNWrUwtWrlwAAWbMOwuPHC5E7t4t24XFhwJbSQGyw5ee65wA63gU882nXIyICYwoXxqyXLwEAFcuWxaWrV+HxyowhUKsW8NmzafjsyUS4XLgAVK9ub7WkMWbMGMyaNQtADwBrsH17LNq0yZxjJ9XI16pVC48ePZIlLl1evnyJbJGR8ADwFMD+n35Cnhw5bNK2rVg0HDgeVAmD2p9Dts614RkejFjvXDB4eQOurvZWTxNnzpzBvHlz4/91HXnyeCFLliya5Q5pGYFx7SKsPn/uLm/M2JFdsx4GgwHBwcHICqASgAL582PevHma5doTEoiMdkdIhAdyecfA72AkOq4ajO05uiJu3jDQ09PeKkojMjIcn33WBopyAcBpeHl9gJw5bWdfihUrhnPnzkmRJdXIFypUCEFBQbLEmU1uAC9s3qrt2IOmaIrDcIcRAKDABaHIpf6EIHe6/x+C3HiKAriA1wFImC1LpwWAfVIk7RoLtNIwoTx6E2g8WYoqKASgKAA5j6o8COASaiAQhcy6f0z/H4acUOAGAHCFEWdQG8HIi5aSxs7x+A3AbgCnANyxacsFCxZEYGCgFFnuUqTEU6xYMZni0sUtPByuUVEIAhADoFXevJg9ezY8X5HZxNat+bB+fQFMa7oerffNSPI3VxB5EII8CLFIpn/d1jjy5dyMD9QZf39/jB8/HgBREnG4gjtwgxvG5fDG6qxZNcn+/UQMShR4iZxeKecuBXMocHcDjAoQGJbyS+hljAuWHcmGggW9NOkQFdUJkeE/IBQuCEct1MINAMDkSZNQrlw5TbJlMG5pfWw+XFaTDAVu6ICtGNd+H07vrIvnbdriWffukjS0LwZDHEaPHoOgoCcArgHIBy+vIsiZ02gzHaTaUntuCFiNKc/8jBls0yYhwGbixIn21kwKpjzzQ4cyIcDGw0PsdGn5qVzZ3pdGRVH41ltvqWN2qGWrpDr26mVhukML2FxabLBuKKiL+BcvRLLUxJfTrNlZ9Vrr1q3rEHnja9fWfitlySJyLcXGkhw3TngTOWjeeEuZOXNmQuDaW29xwQIlU+SNT4vMZ+STVYy6du2aWgEqa9akATaZFVPFqODg+F+YKkC5u2t7Mn/80Z6XRTJl4FrsqlUp9SxYkFy/Xn7jOhr5f/4RRZCSX8rPPxtYtWrVVANs7IXJA9naH1fXZIFr4eEiLsABK0BZSkBAAHPkyEFAVIw6f/58pqkAlRaZz8j/84+4wxIFPQ0bNkx9iHr06GFH5bRz6pS4vJ9+SvaH7t1FBIq1T2b16nb3AUseuLZlyxby4MG0de7aVW5sgA5G/vlzkZMsrUvYsSNpLdfEATb2It4D2epbKWdO8t13kwldsUL88eBBu1yTLPr27auO1YABA9Tf79olLm/tWjsqZyWZy8ibUuG1aJHklfrixQvmz58QYHPo0CE7Kmk9ikLWry8ytaYobO/vLyrtFCli3ZO5d69drikxiQPXWrVqJQLXLl5MX+/8+ck1a+RMoSQb+Y0byUKF0lf/+HFxbMeOHdVrHzdunJT2tXDsmHW3UaFC4oPy5s1kAo1Gsm5d8vXXU7l5MwenT59OCFzLlStF4JopAWwqufUcmsxl5E1JrVMJelq6dKn6EPn4+NCQCW+0lSvFg7RvXxoHTJwoFkMtXZ/v0sWWl5EqDx8+pHeiwLXLly+LP9y7Z941dOpkUQnIVJFk5IOCxIeVOWpfvSrO8fPzo4eHBwHQ09OTt2/f1nYtEkjvCyS1Hzc3sfSeZuDa8ePiwJ9/tul1yEBRFDZs2FC1IXPnzk1xjJ+fePwmT7aDghrIPEb+yZN0y9MYDAbWTBRduGzZMhsrqA1TYfv33kvnoIgIkWq5ShXLnkwHyO39wQcfqGMzePDghD+8eGH+teTJQ/7xh/Wzeo1GXlHE53qBAuar/OhRwvmjR49W+6CLA7x4fX0t2+apWlVsl4SEpCP0ww9FB714YbPrkMHq1avVsalYsSJj00iFOno0mTUref++jRXUQOYx8p9+mmGhyf3796sDVbBgQYaGhtpQQW1MmCBWY+7cyeDANWvEE1e+vPlPZ65cohqJnUrZHD9+XB2XvHnz8nniLE9Go0gMYsmUsn37dCswpYkGI//kifggskRNIOmnfWhoKAsVKqT2xb40P9n0JS6OXLRIJNwy9zpKlRL/zXDu9PChcA0bPtwm1yKDiIgIFi9eXB2X7du3p3lsaKhYsurZ04YKaiRzGHlTyfiFCzM89P3331cHa9SoUTZQTjt374rPYLOWahWFbNSILFdOfDum92QmN54VK5Lp3MB6YDQaWbduXXVMFi1alPKgnDktt565conNPkuw0sivXWuZQTT9uLun/Oj47bff1L6oUaMG42y8Gb57t5iRp3ebJP9xdSUrVSJr1TJzuX3aNHHx16/rfj0ymDhxojombdu2zfD4X38V/XLkiA2Uk4DjG3lFIZs0EUsUZjwQd+/epaenJwEwS5YsvJlih8jx6NpV7Kea7XRx5ox4Mtu1S//pnD9f5EhN/hS3aSPyf9uAFStWqA9Q1apVUzdqJUpYbkFNP5YsRVlh5H19Lf/QMP3ky5dSntFoZO3atdU++SmFG5U++PmRHTum1PGDDxIq9qX106aN+K/Z/gyRkWLq366drtckA39/f3p5eREA3d3ded2MF5PRKGINatdOURvGIXF8I792rbjDdu0y+5QJEyaoD9G7KXy9HIsDB8TlWew+bUpwnXxaZvqpWzfhDjx9WhRBTz7NHDZM17XTsLAwFilSRB2LPXv2pH5g9erWWVF3dzMqSyfCCiN/86ZYRrNGvbJlU5d59OhRtU/y5cvHYDUgQj5hYeSYMSn36uvWTfD8URRRvyC1ayhXTixPxJdvMJ/164UAG385Wkr37t3VsRhuwRLTkSPi8n77TUflJOHYRj4iQvgsdehg0Wnh4eEsWrSoOng7pZUbkovBQNasSdarZ8WMICCAzJGD7NFDbK4mfzpNT7AJRRFF0IsXT3pc/vzk0qW6uL199dVX6hh07Ngx7QMbN7bcgtaoId6QlmDlcs2xY2KpwlIVa9VKW2bPnj3VvhkyZIhl12EGRiO5fLmor5NYp8KFxSpX8vvt/PmEICfTj4uLmOknK8RmHopCNm2aKCzW8Th06JA6Bvnz5+cLCyc8PXuKF6Cjb/05tpGfPFmsO/v5WXzqn3/+qQ5g5cqV09wttydLl4qHKZWaweYxa5Yw8P37J30606k2z5cvhSuml1fSc2rWJPfvt1KRlNy+fVt1GfTw8KBfemPYvr1layA//WRdYJeGjVejUazFFixovqrNm6ct7/79+8yaNStNLqVXTb6WEjh6lKxTJ6kuHh6icmZ8sapUGTAg6Tl9+ojzrM4WcuGCeHOk4o5obwwGA318fFQbsXTpUotl3L8vPG1Gj9ZBQYk4rpHX2INGo5H169dXB3HBggWSFdTGixfC0yw9e5whpvLxLVsmLNtky2ae54m/f+rO3u+/LyUHSZcuXdS+HzNmTPoH/+9/GVpMxcVFJPPRsrQhwU8+NJQcNYp0dVUyNPKdO6cva/LkyWoftW7dWnNVswcPROqf5Hp06UKa45YfFCQKySN+qal9e/Hhpyn4Z8AAsUnuYBWxli1bpvZ9zZo1rY6rmTRJvAitmIfaDMc18r16af4WOnnypDqQuXPn5tOnTyUqqI3hw823x+myZYt4KlesEH6Yln4WHDokEqAltgqenuT48RbsBCdl7969ar8XLlyYYelNH0ly4EDzpsZa/f0lBUNdukS6wJihump5vDSIiIhgyZIl1b76999/rdInIkJ89Hp7J22/enXLA53PnRNDb0optGaNVSolEBQkjPxnn2kUJI+QkBAWLFhQ7fcDli77JSIiQvgNpLcaaW8c08ibdjV+/VWzqN69e6uDOXDgQAnKaef6dbFn+O23EoQpCtmqldghs9YP3mAQDtDJ1yKKFiX//NOiDYO4uDhWr15d7fPly5dnfNK4calbyfLlRfHy+H9H+9TXlt7gRD9h5I/0slqEopDNG0erKn78cdqxaUOHZixv7dq1al+VL1+eMRaMoSk4q2TJlCtaP/5ofaqiuDiyWjXhqSslIdfcuWLZ5sIFCcK0M3LkSLXPu0pIqvbXX6LfLfANsSmOZ+Ql+yc9evSI2bJloymr3CVLvDF0om1b4WEmrbD95ctibX72bG1yQkJEzHpy//v69cmTJ80S8eOPP6oPUJ06dcxLrTtzZtL2cuYUNW1jYsjYWEaWqpTwt5Urrb8+xUgGXySN1m8yb9qUoErpIpGMihL7igsWiFi9xJdhzlq2oihs0qSJ2mfff/+9WXqcOyc8ixO35+ZGDhmibUWLFAWrXVyEp64UYmOFo33TpnZP43jjxo3/4+68w6OoujB+0iAJJECA0HtvivReBaRJx4L0Dkr9UFQ6CkhRioCADSkiCAgoIKD0Ir1I7z0JJQ3Sd97vj5u52ZTN7uzeOzPr73nyPMru3nvm3pkzM/eec16u35o1a1bcFrA0qSgsdsDBKG/dMZ+T//57dsYKzDSYMWMGv4iaNWvm8tqnK2zfzg5v40bBDX/wAYu2CQlxva1r11iZwbSPpr17p87TT8Pz58+RO3duPtaHDx92rL/jx5mH8vBgT+5pK0/u3MltiM1diG0eG0BsLFCyYAwfjk2bUn/+9CmruuHpyf4cLch46tQpXhgrMDAQoZlU3gwNZcnfaWP3W7ZkMguu8uwZi8zt18/1tlKxYwczVEYJaQ20a9eOn58TJkwQ1u6pUw7na+qOuZy8pJzh2NhYlChRgk/u5s2bhbbvKAkJLKJMygONenX27y+uzZ07mdCItTfJlg2YMSPD15CRI0fyMX73XY1LIrdvs51DGyS0tEr8mjhR44GIYebMFBOa1o+zOYcPHwI3bmhre8CAAXzsBg4cmO7z+HhWny9tcnDp0qz6tqjzSX1WcLUWXIYIf4XVxs6dO/kYFypUCC8EPyz072+38oohmMvJS6z+s2nTJj7BJUuWRKwBJ5r0pcmvv4ZwCZuEBJY5q4Zd8LWKEuxRNtm7XLx4EV5eXiAi+Pv7434mDtsprl5FkierppXgrb8K0cOHQLYs8SACPD0sOHdObPshISEIDAwEEcHDwwOnT58GwIZ327b0pYoCA9nqnMhyROqq3+zZ4tpMhdDNKG0kJCSgQoUK3AesdmXZzwYhIewGaV1/zwyYx8lfv85ikaZMkdK8oiho1qwZn+SZM2dK6ccWugQZyJSwefKERcGkzZhp1gzKuXNo2bIlH9tp06aJ7TsZZcxY3m9iZ31ViHr3TOKHPHSwnFz2uXPn8jFs2LAhLl5U0KpV6uH28GDLNSJW5axR9++TBdfkISysTBsLFizgY1u3bl1pS7Zz5rAbZQbV0A3DPE6+QwcWiySxIv/58+fh6ekJIkK2bNnwMJP1ZdEMHswehqWHC+/Zw7zBunVy2j9/nmX5WHkexdMTi4mQmwhFixZFTEyMnL4jIhAbaFXn14XQNy2oal1EQE7/OMiKxI2Pj0eZMmVAlBNEX8HTM3WYZoMG8nRGt25lfWzZIqd9jpAEEW08efIEOXPm5E7+uMTS2zZ0jQzFHE5e1daS5ZisGDp0KJ/s3r17S+8PSEn8mz9fl+6YwIbMG6aisDCTEiVSOfvnRDjdp4/cNPYVK1I2YcvLVyFSFKButVh+mAsWyOsrMREYNuwciJ6kcu5FirBQSVlOIy6Ore23aKGTY1q+nB1Y2tIbktD7ms9AodRQjHfyiYks9kgnlVw97+pASgmP8uV1LOFx44bUpS9ObCwOtGmD6LRROBUqWKk8CyYpiTl3tS/JKkSqWhcRUKFEjLQ5/PvvjOq0vUTTpnuly82p1TFUsS7puFS0SRvWb+/Zs2fHo0ePpPYHsGu+ZUsdlr4cxHgnv2iR+M1CO1ivz9WpU0dqSKVajG/HDmldZMxHH0mXsFE3CwsQ4Ye0jp6I5cVfvSq+Yyvx79hAeSpE0dFAwdwpT/Ey7ls3b2YsRuLhsRZEheHn54d7UueQbRZ+8IG0LjLG6fKrjqMoCpo2bWrIPtzFi+zG+cUXunVpE2Od/NOnLOZowABdu9Vjpx0wuKx2VBQrOShRwiZd2N8//7DEKWtv5ePDEqwy1YzTTmKX7il7AqPlqBBNmGB1v2ol9hE+Opol+qYtY1y9OksRcSkcVQP9+7PIW2uxLt3QLKSgDaMj6kaMALJnlxSOqgFjnfz774tL4NGIdcxswYIFES3hRFMFcmQ8zDrEDz8wz3HwoPCmbSbwWCxsjaNgwdTeKziYlU4QtYZ+5w4LpSRioZWCVYhu3wZ8vRPYfcozUdgcWiyszFCBAqmHJ18+lgeorl6kTSw7JEGGSNWeyUisSxc0SaJpI21uzKa0mWs68Pw5KzHRt6/uXafCOCd/4YKYVHwXkJX9BrAIMX9/YOxYoc1qw2JhNWerVRO69qkoCho0aMDHLsNU/OjoFOFaa2/22msaJIbsMGkSbze+pdjXpW6dErnJ/xsrZjnv6FEm1mE9HFmysJW1jOrwWZeIqF69umMlIhxEVZGsVMngVPyJEx0UN9aGWbLclyxh83zihCHdAzDKySsKizEqU8YwcWkgdR0LX19fIXUsVFTResGrFNo5fJidZQKKvaloKqp1+zZ7LU+76PzWW04oUaThxQtW5kBtU5AKkbpcTATkDYx1eQ4fPGDnQ9oh6NAh8xK1ThV7cxBVD96WWJduvHgBFCoEdOkirEkz1atSi73Vq2dcSKUxTv6339gZtm2bId1bI7oiHcCe2HQI/HCcd99lyyUCJGycLo+7bx+LqLD2cr6+7GnclfRytSYuEWKKua5ClJQEvFouZbN1xQrn24qJYUt2aUsAV6zoeMVC67LN+fLlQ6SQOWR14jt2dLkpMaghTH//LaQ5s1WeVVNX1q41pn/9nbwqdNGqlSmyBUTWlgbYqkitWkBV+SHcjnP/PvM048a53JS10MUbb7yh7TU4KYnJYeXJk9rrFS7MrgBnzgdFQWx1K/1aF1WIVLUuIuC1CrFOzaGisKiq4sVTH2auXCyYTOvyiCYBFgeYPJktE2mtryMNRQHq1mWSji6uHVlrSOTKlQtPTVJIplMndpobUVtPfyf/xRdsLV5EyTxBrFixgp8YrqjEAGxTjcjxCoS6MW0ai3S5ds3pJoRJ1oWHMxFxb+/UXrB+fefq2544wduI83NehSg8nC3PqOY4s3Vw9izLi7A+LC8vFmPgrL/RJKVoh7t3WWStgHuFWNS04qVLnW7CYrGgdu3a/FpeIDNzTSM3b7Ib66RJ+vetr5N//JjFFI0YoWu39hCh9wiwvcYCBYDu3QUbKIKYGKdE0a0RLj595QqrTGjtET08WDiCxrizpN59eRuWQc4VCBozOkXS762u2p4ow8JY6Yq0pX2aNxdTx8RhUXQ7vP02i6y1J9ZlCH36sHAUJwvim13X+eOPnRRFdxF9nXzfvi5NokxcVW4HWCSYry9w544EA0Xwyy/M8/z5p+afHjp0iI9P7ty58VzkHP7xB6vBbO0dAwLYW5+jKYOPHyM+a3bm5D20l/q8cgXw9mRFyHy9Exy+EBMS2ApRjhypzS9Vim09iVqRjIqKQoECBfgc7N69W3MbBw4w2wTu34rl0SP2EOiIpFYaoqOjUbBgQT4+O2VlXLuAmrry1lv69qufk1dfx5Ys0a1Lrbz11lv8JBkzRluCzc2bLBLMoFLnjqEoTE6oYkVNG5QWiwXVq1fnY7PUhVdqm4jwlrNmpSzb1GuiycO2aRHPu3T0lXr7dlauwtrc7Nm13Zu0sHLlSj4HlSpVQqKG9eukJBa9WqOG9EoCrjFzJlvG07gUOGHCBD427du3l2Sc6/z4o/NLgc6ij5NXFBZDVKWKOfWxkrl79y58fX1BRPD29sYVDQk2nTuzSDCDRIsc5/RptiSycKHDP/n+++/5BfTKK6+4tGdhF1vrHq+/br+4SlwcYgqVSvmNg/JbqloXEVA4T4zdORS4yqQJi8WCWrVq8bn4WkMW07ffMjuPHJFnnxBiY4GSJTUFZty+fRtZs2YFEcHHxwfXXNh3ko3FAtSsyW64egVm6OPk165lZ5hW6XgDmDRpEr+I2rRp49Bv/v6bHd6aNZKNE8XAgQ5L2ERGRiJfvnx8TP4WFOZml7NngcaNM97BzCwHXw3PJUJM/uJ2VYgSEoByxVIk/TILcwsPZ+XQ0+4X16unX7LL0aNHNUePREayCFqJ1RHEogrpOhie27VrVz4m//vf/yQb5zpHjrgenqsF+U7+xQsWO9Spk/SuRPDixQsULlyYnzR//PFHpt9PTGSRX3XrmiIi1DFCQ5m00PDhdr/64Ycf8rHo3LmzDsZZocYiFiuW2qsGBbFc/IzeChUF8Y1eT/muHRWir76yCu6pEZvhHKqRn3nzpjbDlchPV3jvvff4nLzvgAzRuHEsgla0WJc0FIVpFpQtazdZcu/evXwsgoODEWF49qFj9OjBbrx6mCvfyU+axGKHbt6U3pUo1q5dy0+ccuXKZbpLv3Qpu+AlVywWz9y5bEkkk2zA69evp1K2v2nUHNrKKqpUCchoA/LCBSR5eAFEiM+Szab4eFgYkMMvji23kCXD6E1ZOVyu8ODBA/j7+0MNZf03k2Wsa9dY5KwksS55nD/Pzs9582x+JSkpCa+++iq/Vr/99lsdDXQNNXVFjxcPuU7+zh12RXz8sdRuRKMoCurXr89Pnq9sJNioBYj69NHZQBGoEjbNmtl8FO3QoQMfg08kFJHSjIb6AMqw4fzzpB69MmxuyKAU5aW+vVMvkGZWjcEM0VOfffYZn5sWLVrYTEpr355FzsoS65LKsGHsjVMtfpeGZcuWeJlyJgAAIABJREFU8TGoVq2a3L0iCUyfzm7AsgsYynXy3buzwHFTBuVmzsmTJ3mVxRw5ciAsgwSbkSNZNIUOOgRy+P135rk2b0730a5du/gFVKBAASlVOp0ms0pf6rn29CnisuVK+fzYsVRNnD3LBLmJgOxZ4/mG6YsXrK6ar2/q5kXWVRNBTEwMihcvzudoSwa6fTt3MtvXrzfAQBGopcgHDkz3UXh4OPLkycOP/6CESquyiYlhK5Ht2sntR56TV4UdVq6U1oVs+vbty0+iwYMHp/rs0iW2DzhrlkHGiUBRgDfeYNEMVjF/iYmJqFixIj/2lWacQ1s1e/PnZ4HgFgurIZD877FVU1SIFAVoUi+O/+SLL9i/rV7NIqSsmwsOZhtkZnxI3LBhA5+jUqVKIc5qDhMSmEBXo0ZutFeUEQsXstCl06dT/fPo0aP5sb+ld+C5QDZsYOeZzLB+OU5eDcqtVcvkQbmZ8/jxY2TPnh1EBA8PD5w5cwYAu2hatUrnG92TDO5WixYt4hdQrVq1hJa4FY4t9Y0aNYD9+xFTqlLKvyWrEKlqXURAqUIxOHSIbZxb/1yS1olQFEVB48aN+Vx9YSVDZMM3uh8Z3K0uX74Mb29vqNVj7+qdQioQRWGHVqGCPHlQOU5eFVs2fVCufb744gt+ETVu3BiKomS2yuGeWK07PX36FLly5eLHfFQnsWWXsaWj16xZytN8UAHEPolG8fwxGX3M/2SpFsrgzJkzqTRMHz9+jCdPgJw5M1zlcE/SrDu1bt2an5+TJ0821jYBnDnDbsiySu2Id/IRESzW7L33hDdtBHFxcShVqhQ/qdat+xVlyrCaJG79GmyN1Q7y+++/z4+1Z8+eRlumnb/+SqeIrXh58f8+2PhT/pGXp5LKuZcvb4AWrwAGDx7M56xfv3729ivdk+Qd5D+sJP0KFy6Ml7JVznVi0CB2Y37yRHzb4p382LEsNujBA+FNG8WWLVv4iRUQkB8eHjFCik6ZiqVLYSFCyeTN5mzZsuGBu85hYiIrn5E7d7rH9FjKiuJ0K9U/58zJnqJMVs/KYcLCwpAjR47kc7QQPDwSM4s8dE+uXUO8tzeK8uMk/Pzzz0ZbJYywMFbRY+hQ8W17AAAJIu6Pvyhr+5b0eOg0Cun/qahmDQcADR06lE6cOJ78L9FUoMBL8vT0NNQukSQlJlJcWBj1I6LlRLRg2DDq37+/0Wa5RlQU0fLlROvXE1ks/J9X0XvUi1aRpydR585EQ4YQ5cploJ0CWLNmDX355Xgi6kJEqyhvXm/KksXHaLOEoSgKZQkNpTBFofJE5OfrS4cOHSIPDw+jTRPGmjVEE74MomVfvqSWg0sQ+fuLaVjkHSO8YTsoRKhOx9Otc/63/lLKEv+X/qYQIY4IJYhwwfhBFv73jFhI5UmqZrQpEv6ugagYiF6AaLbQ88JMf68ZP9DS/q5RafhQPKbRBODUKWF+WeiTfExEAnlVqUjxBYrRjaV7iP4jd9moqCjq2LEjRUZGEBGRh0cXKlBgOXl4WOz80n0olJRE+0JD6Ssi+pSImteqRbuXLPnPPCk9v/+SRnacTh3ImzZSFhqycj4FVC5utFnCGDOmA+3fv5XY7E2i4ODm5ONz22izhOEB0JDQUPrcYqHyROTl6Ul//vknBQUFGW2aMN4cXZLOXvWjq5sukV/VcuZ8kgeQaYKNuzJq1Cj+JNGixVsgMnXFZOfo3h1K/vyoWKQIP9bffvvNaKuEMaLqPngQSx7KSx44UG6A0SYJ488//+Rzli9fcRQtapGeYKM7yTV6+7Zpw4910KBBRlslDJmJa+KdvI0EG3fl0qVLPCbXz88Pd+/eNbP2iXNYJa79+uuv/CIqWbJkqgQbd+XiluvwokQE+THRjVxZA2AhD1xe6+5B5EBCQkKqxLWffvpJlwQbXbFS23j8+DECAgJAlDp3xZ2Rnbgm3skDLMHG29vN00FZskmrVq34BTRlyhQAKSqGIhTwDCdN4pqiKGjSpAk/5lnuPocWBS1zn0Ap7zsoXow9yQcHB+N61oo4G9gQisW942AXLlzI56p27dqwWCxQFFalWWaCja6k0c2bPTtlz6FRo0baxORNiOzENTlOHvgPFHYBfv/9d34yFSlSJFVM7qxZptMjdw41cc0q6ens2bOpEmweufEcbpv4D4iA3z4+hhIlSnAnf3LmLoAIh0f9YrSJTpM2ce2YVX0e2Qk2upGBAnZcXBxKly7Nj3u92xbngS6Ja/KcvFuXaATi4+NRtmxZfiKtW7cu1edxcUyZrmVLN06KyiRxbciQIfzY+/bta4BxrhMfHY/SPrfxetBJKBYllZMHgGP538R9r6KIeeqeCTXDhw/nc9SrV/pKmzITbHSjUydWuD9NXeetW7fyYy9WrBhi3LLMpt1Cm0KQ5+QBNy62DsybN4+fRA0aNMjwlVAVIdq2zQADRZBJ4lrqBBvCcTecwznt9sGLEnFhE5ODS+vkb+++jnjywd6mU4000ynOnz/P37ayZcuGhxnUzJeZYKMLe/awCywDuS5FUdCiRQt+fk6fPt0AA13DgZL5QpDr5JOSmGxSnTpu9bgbGhqKwMBAvrlzMiM1CbBDev11VpbdjoCN+bh6le2bfPaZza989dVX/CKqW7euW619hlwIQwBF4v0q+/i/pXXyAPB3rQ/xkvzw8Ng9I8x0CkVR0KxZMz43n2eifvXll8yRnDuno4EiSEwEKlcG6te36Tv+/fdfeHl5gYjg7++P+24jfaVJ/Mpl5Dp5IEUAdfVq6V2JYuDAgfwC6t+/f6bfvXCBXURz5+pknCjatQOKF89UTSIhIQHly5fnY7HGbURsgQHl9iOXx3M8vZaiB5uRk4+8H4lQz3w4VMxdBFCBzZs38zkpXrw4YjPRsY2PB8qVA5o2davnLBajTGRXPPeDDz7gY9GjRw+djHMdjTK2LiHfyQOsOmChQsbppWng9OnTXCwkICAAISEhdn8zfDhbV3Pgq+Zgxw52hm3Y4MBXd/CLqFChQnjhBnN4avUleJAFi7ruS/XvGTl5ADjQ5zuACOeWHNLTTKeIi4tDyZIl+Zxs3LjR7m/++INN96ZNOhgogmfP2H6eA3tBz549Q1BQEB+PI25Q+TY2lkWYv/GGPjdefZz8zZus3vfEibp05yyKoqBRo0b8hJkzZ45Dv1MFbAa4Q35NQgIrt9i4scNnWNu2bfmYTLKKcjAjikVBg8CzqJT1GhJjUwt923LylkQLLvpXx0X/6rAkmrh2PoBZs2bxuWjatKnDS2itWwMlSjAHY3pGjGCReapclx0WL17Mx6RmzZrm1j8AMHMmWym9dEmf/vRx8gATdvD1ZeKZJmX9+vX8ZCldujTiNSyWLVrEQtYElpyQw/z5bH1JQxLJlStXUok03DGDyKkN1o08AiJg96z0+yi2nDwAnF18CCDCwX7f62GmUzx69IiL2Hh6euKchoX2y5eZY5kxQ6KBIrh4kcUmWwmg2CMxMRGVK1fm1+6PP/4o0UDXePgQyJYNGDVKvz71c/LR0UyqrVs33brUQkxMDIoWLcpPlK1bt2r6fWIiUKkS0KCBidc+1aDcNFKGjjBmzBg+Nt27d5dgnOu8fPISRbweoEP+jIVOMnPyAHCo6DsI9cyHyPuRMs10mj59+vA5GDJkiObfjx7NHEwGgTjmQFFYTHKpUpqz5ffs2cPHJn/+/Igyqa50795Anjz6Zsvr5+QBJr9GBOzbZ/+7OjNt2jR+krRs2dKpSJJdLL8Gv5g1v2boUBZTl4EouT3Cw8ORN29ePkb79++XYKBrTG26Fz4Uj+t7Mn7TsOfkHxy9h5fkh721P5JpplMcP36cj33OnDkzFJa3R3g4czAZhNSbg23b2AXkZM2kjh078jEaP368YONc5/hxdnhLl+rbr75O3mIBatcGqlY1lTLy/fv34e/vDyKCl5cXLrqQxvrmm0DRooDpBGvOnWPLNF995XQTy5cv5xfRa6+9hiQTzeG9Yw/hRy/xYa29Nr9jz8kDwN4mUxBHWXBnz3UJVjqHoiioW7cuH/v58+c73dayZczR/POPQANFEB8PlC7NYpKdfBW+ceMGsmTJAiJClixZcPPmTcFGOo+isEjyV17R3/Xp6+QB4NgxdpYtX65717bo0aMHv4BGjBjhUlvXrzMR6Klmyq9RFBZDV66cS8VMkpKSULVqVT5WK1asEGika7xT7BDyeYZmutTiiJN/+eQlHngVwbH8HWSY6RRr1qzhY16+fHkkuDSHwKuvsmctU+1PzpnD1uJdlFwbP348H6tOnToJMs51Vq9mbu/vv/XvW38nDwA9e7J0+vBwQ7q35vDhw/ykCAoKwrNnz+z/yA4ffgj4+QH3zJJfs3EjO8O2b3e5qf379/Pxyps3LyIiIgQY6BoHF58DEfB93wOZfs8RJw8Ah0asA4hwatYukWY6xYsXL1CoUCE+5jsEiNDu3ctOh1WrXLdPCCEhQEAA8P77LjcVFRWF/Pnz8/Has2ePAANdIzoaKFgQ6NLFmP6NcfIPHrAdoDFjDOlexWKxoEaNGvyEWLx4sZB2IyOBfPmAd94R0pxrxMaypKc2bYQ12a1bNz5mY8eOFdauM1gSLajufxHV/S/aDX901MkrFgVnAxvgWtZK6cIw9WbixIl8rNu2bSus3a5dmeOJjhbWpPP07w8EBbH4eAH88MMPfMwqV66MxERj53DCBBZBfuuWMf0b4+QB4PPPWUzXlSuGmSDzZPiO5dfgkNH5NTNmCB/n27dvw9fXF0QEb29vXL16VVjbWvm+7wE2zkvshxM66uQB4OLqU7CQB/Z1+1qEmU5x584daeN8+zZzPJ9+KqxJ5zh1isUeL1okrElZD2/OcPs2ixz/5BPDTDDQyUt4wtSC7Nc6iwWoXp39Gbb2qQblSnhjsn7CbGeQDFHk/Ujk8wzFO8Ucu5NqcfIAcKBsfzz3yIVn1566YqbTdO/eXeobk9FPmFAUFnNcqRKLQRbIkSNH+Njlzp1byDKsM3TrxiLHjXxjMs7JA8CvvwpbK9aKHhs0h1h+Db43Kr+mVy8WMydh70PGWrFWPqy1F370EveOORb4rdXJh10IQSQFYF8V19eKtaLH3oe6Vty1q/CmHWMd2/vA7t1SmhcZUOEM+/axw/vpJ927ToWxTl5RgCZNXI760IqeoVbvvMPW5yP1zq9Ro5iWLZPWxerVq4VFfWjl2u478KF4TG261+HfaHXyALC37Rwkkheub3Yt6kMLaaOYlkuMRFu1ip0me/dK6yJjXr4EihQBOsiLYhIZGq0VM0UxGevkAeDsWZfjt7WiZ9LEvXss0ubDD6V2kxo1H+HVV6UG5YqM39bKm/mPoajXfbx84nhCgjNOPj46Hrd8yuBU0Ou6SQVa5yNUrVpVaj6CxWJQ/PaUKUzx6brcfATrJMcWLVroVi5bzUewEusyDOOdPAAMGeJ0JqZWjEh/1ul8TkF9PNMhszhtJuYTHWSIds08CSJg3YjDmn7njJMHgH8mbAWIcOyTLZp+5wwRERG6Zxb/8w87Xb75RnpXDB2ffFwtV+IM4eEsQrxnT+ldOYQ5nHxYmNM1VbRgVCEjHd5MU1AXWnWsEWRdU2WoZBmixNhEVMx6HQ0Cz2p+snbWySsWBSdyt8Qd71KIi9RWU0UrY8eO5WOpZ40gtaaKLqkrOq9hulJ40BnGjGHxDhkIrhmCOZw8wJZrPD3Z8o0kjCxJqu4x7ZKdX/PppyxkQsdqn65UR9TKoq774EEWnFqtvU6rs04eAK5vuYhE8sLe1o5XR9SKkdU+1UCs0aMld3TwoO7RCM6WEHeGK1dYxHImYl26Yx4nr9Y5b9JEShlHo8UFJEaLpXDrFnPwEyZI6sA2M2fO5GOrpc65Fp5ee4ZcHs8xoJxzSxiuOHkA2PfqCERRdoSec6zOuVas6/ZPNEB7QU2puHxZUgcGxhU7IwbkDG3asMhwM9XtN4+TB1IUi379VXjTZpAJU/M+vpaVX9O1q2EKXLGxsZoVi7TyfpV9CKQIhFxwbu/GVSf//OZzPPXIjQNl+jn1+8zYvn07HzujFLhiY5mwSOvWkjr4/nt2fR/WtpciCi2yns6wfTs7PAmnvkuYy8kDQNu2drVHtWImwd/+/ZmK1FPR+TVqQRIDtXS1aI9q5cKma/CiRMxpu9fpNlx18gCw763FsJAHLq7MXHtUC2bS0t20iZ1Gf/whuGET1PoIDQ1FYGAgiAgeHh44JVDhJyGBRYJLWohwCfM5+atX2TvjZ58JaU5RFLRo0YJfQNOnTxfSrrMIrMWUQlISi4GrW9fQM0xRFDRv3pyP9QxBMkSKRUHzXKdQxucW4qOd3zQT4eQTYxNxLWtlnAuoJyykcv78+XzM6tWrp1uYX0YoCtCsGVC2LKv+KwyTVO2bN28eH+sGDRoIG2sdthSdxnxOHgDGjgX8/YVsT2/dupVParFixRAj8A3BWQRVVU3hm2/Y49fx44IadJ4LFy7A09MTRIRs2bLhoQAZot8+PgYiYNtE14qgi3DyAHBq9h6ACIffX+tSOwAQFhaGHDly8HP0xAlxbwjOcv48c1jz5glq8No109Tfjo+PR9myZfl4r1u3zuU2w8JYBLgTYl26YE4nHxEhJNA0Li4OpUuX5hO6fv16QQa6Rnw8UKaMS/oIKahyP717izBNCMOGDeNj3stFGaK4yDiU8r6DVrlPuPzkLMrJA8DRAp3w0KswXoS6tnY+ZMgQPlZ9+vRx2S5RqCJioaECGjOZks7vv//Ox7xIkSJ46aJdgwezCHAd0nycwpxOHmCiIkTA0Yz1Oh1h9uzZfDIbNWpk6GtwWray/BpscTW/ZvRopmz/6JEQu0Tw9OlT5MqVi4/9MRfS/r5ovRdelIiLW1zPJBPp5O/uvYk4yoK9jSc73cbZs2f5W0/27NnxyERzqMoBDxrkYkOqJqaAJ2ZRKIqCN954g5+fU6ZMcbotAxL2NWNeJ5+UxGQCa9VyKtwqJCQEAQEBfJPlzJkzEox0Hhc0i1O4fJntX8ycKdQ2ESxcuJBfRLVr13YqJ+HxuVBkpyiMeFVM5q5IJw8Ae+uMRwz54sGRu5p/qygKmjRpwsdo1qxZQmwSyYIFLBrM6UsnMRGoWNGU6vaXLl3iOQl+fn6458RegVp6q3x5XUtvaca8Th4A9u9nTwErV2r+af/+/fkFNMjlxxE5XLzI1ua/cDa/pnVroGRJcwXlJpOQkICKFSvyOVjlhAxR3zIHkNvjKZ7fEpOGKdrJRz2MQohnfhwu8pbm327cuJGPTalSpRDn9J1eHgkJQIUKQKNGTvroRYvYXUJgFItIRo0axefgHSeiftQiugYUYNWEuZ08AHTvrrkg88mTJ3niQ44cOZxStteLESPYastjrfk1f/zBzrDNm6XYJYJdu3bxi6hgwYKI1jCHx3+8CCJgydviareIdvIAcHDAjwARzi7KXHrQmtjYWBQvXpyPzW+//SbMHtHs3MlOM83bWU+fsljhAQOk2CWC58+fI0+ePHweDh486PBvY2JYpLdAsS5pmN/J37mjSVpFURTUr1+fT9w8YSECcnj+HMidG+jbV8OP4uNZjFuzZqZ7DU5L+/bt+Vx86qAMkWJRUC/gHKr4XhUqvyfDyVsSLfg3W01c8nsNSfGOlXH8/PPP+Zg0b97cVHtFGdGuHVCsmMbUleHDgcBAFjNsYpYuXcrnolq1ag4vK372GVspNVAUzWHM7+QBYOJElq7vQN33n3/+mU9a2bJlpRcjEsHixeyt1uHouS+/ZLs9589LtUsE165dg4+PD4gIWbNmxS0HZIjWvn8YRMBfc08LtUWGkweA88uOAEQ40Ptbu9998OABsmXLxuv8XBAWRyuPq1dZBKTDKSYXLrB1SIk1YkSRlJSEV155hfuM7777zu5vTCJR7TDu4eRfvGDp+p07Z/q1ly9fonDhwnzC/hCetieHxESgcmWgXj0HHsxDQ1ls27BhutgmgnHjxvE56WJHsv5F6AsU9nqITgWcj6qyhSwnDwCHivdAmEcwIu5mruDUs2dPPhbDhw8Xbocs/vc/lrpiN1lcUYDmzVmMsBs8YAHA33//zeckODgYkXaqY/bsySK8danYKQD3cPIAsGYNWxz86y+bX5kyZQqfrNbSCnDIYQ/Lr8Fae/k1gwZJqosgj8jISAQHB/O52ZuJDNGkRnuRheJwc6/2iBV7yHTyj47fxwvyx94a/7P5nWPHjvExyJUrF5660RxGRADBwYDdsk+//cZO5G3bdLFLFF26dOFz82Emde6PHmWHJ1GsSzju4+QVhT3qVqmSYRnHu3fvws/PD0RM2f6ytFJ68ujUCShcOJP6YmfOsHWdhQt1tUsE3333Hb+IXnnllQzVju4cug9fisHHdfdKsUGmkweAvc2nI558cGtn+oVai8WC2rVr8zFYtGiRFBtk8u23zMHZLOAaF8eivVq1Mv1eUVpu3bqFrFmzgojg4+ODa9eupfuOxcIiuqtW1VlFy0Xcx8kDbNGaCFi6NN1Hb7/9Nr+ARo0aZYBxrnPzJlOQmjQpgw8VhcWyVaxo7qBcG1gsFlSrVo3P0TcZyBB1L3IYBTwfI+qhHLUu2U4+5lkM7nsVwz/B7dJ99tNPP/Fjr1ixIhKl1ZuWR1ISUK0aULOmjdSVWbPYWvwl7bX+zcAnn3zC5+jNN99M9/nKlcz96CDWJRT3cvIA0KcPC0d5/pz/04EDB/jk5MmTB8+tPnM3xo9nwUR3065WbNjAzrA//zTELhEcPHiQz1Pu3LlTzdOBRWdBBPw4wPEwNq3IdvIAcGT0eoAIJz7byf8tOjoaBQoU4Me+S7pyjDwOHGCnYTpRtcePWSzwiBGG2CWCtPP0p9W1Fh3NIrl1FFwThvs5+UeP2Mk0ciQAx54Q3YmoKCB/fuAt6/yamBgWw9a+vVFmCSOjN66k+CS85ncJNbP9C0uiPDEJPZy8YlFwJkcj3MhSAQkv2RuXvSdEd+Ott9g5mkoeuW/fdA9f7oitN65PPmEPXzoKrgnD/Zw8kPJaePGiQ2u97saPLL8GB9T8munTWQxbBuuE7kZGeycreh1ga73L5IaE6uHkAeDKujOwkAf2dV6Qbq33um5q7vK4e5c5vPHjk//h+HF2wi5ZYqhdIsho7+TmTRbBbYBYlxDc08nHxQGlSiGxWTPktcpYyyxqw52wWNi652uvAUl37rPYtXHjjDZLGNZRUM0bv4m8HmF4r4S8ZRoVvZw8AOwvPwjhHjnxbst2DkVtuBuTJ7P9oxvXFaZjYCMgwh2xjoLKmTMn2rWLM0pwTQju6eQBKJs343ci5HAw/trdOHIkOVSr5nIWu6aTsr0evHz5EkWKFEm+kMrBh47jwQn5FRj1dPJPLoXhBPmhcvL5mS9fPrvx1+7Ey5csEmzua6vthja7Iyn5DNlBtAmrV7tXtJA1HgBAgqhRowaFhISIai5ToqOjqWlUFE0moteJ6PzWrVSoUCFd+taLTzpdpPX36tKyngco16h+RpsjlG3bttCUKTOIaC0RNabg4ETy8fGR2mdISAhZLBby9PSkAgUKSO0rKSmJQkNDiYjIj4gaBAfTrh07pPapN3+ufEwlFo6m47nfoIpbviDy8zPaJGGEhYVRmza1CVhHRAspe/ZtlCNHoG7958+fn06ePCmmMZF3jEKFCvHXHNl/WYlwgwjbk///byL2RPEf+bOQB2rQcVSjk/iB3jPaHAl/k0EUCKIQEK0Sfn6Y4a+a1X+PM37Ahf9Nosk4RPVwnirDixKNNkfw39HkudsAogcgyibsvHDkr1ChQsL8sts+yQ+Pjqb/RUXRK0R0hYheKVOGTq1eTd7e3rr0L5sftwZR36nFaWvTL6ntgY/o8oaLFF+srNFmCeHx43vUpVMZik9MIKJ+RPQd5cnTgbJmPSW1Xz2f5CslJNDSJ0+oLBFZiMiDiK5u3kxlihaV2q9e3H2chcp3qUgzm++mkTta0/3RX9LTHqOMNksIiqJQnz516eLF40RUnIguU/bs31COHHN1s8G0T/K68egRkC0blJEjUb16dX73W5pBkpQ7ooZRvv02UmqatkufYOOuvNWtG5+zkSNGo1o1oEYNp7RhNKHbmryiAA0bAhUr4tPx4/mxtm3r/iGwKmoF8KgoAP36AUFBwLNnRpslhJUrV/I5q1SpEj7+2IKsWd0zfBKAm2689unDdE2fP8ehQ4f4hKRNsHFXxo9nwvY8IUpNhNq5M9PfuQOpEtdy5kR4eLjtBBvB6Obk17OEKPz5J6KjoxEcXJAf859unMymos4X1/J5/BgICHDrRCiVtAlRu3fvdutEKMAdnbwak2v11P7OO+/wSXHXkgYqN26w0LTJk63+UVGAxo2ZTI8bljRQSUpKwmtVqvC5WrZsGf8swwQbweji5GNimGi1VeLaqlUpew5ly1ZEglvPIQvtTafK+cUXPHfFnbFOXOvQoQP/959+Ym5n3z4DjXMS93LyigLUqQO88kqqCkH37t1LlWBzyU1rZwBAx44sNC2dgPyZM6yG/IIFhtglgm+//ZZfQK9WqpQqcS1dgo0EdHHy06alS1yzWCyoUaMOP/aFblhgTmXFCubs0hUpS85dQYsWblecTOXmzZs8cS1LliypEtcsFqB2beDVV92rOBngbk5+dXJM7t9/p/vIOsGmVatWplfbyYjdu9nh/fyzjS8MHgzkzAk8eaKrXSKIiIhAcFAQn6N9GTwS8QSbG3JskO7k791j62wZJK79888//NgDAnLiiVvOIauj/t57Nr6wZQs7gbdu1dUuUXTu3JnPUUaJa8eOscOzegF1C9zHyUdHAwULAjaSnlIn2BB+//13nQ10jcREoFIloH79TB6EwsKYYMjQobraJoL/jR3L56arDfEXNcGmY0c5Nkh38u++m2niWs+evfgYDB3qPqIvKmPHsuTrBw9sfEFQ8gsCAAAgAElEQVRR2JN86dLsyd6N+Ouvv/jcZJa41qsX2w50F8EQwJ2c/IQJrIBEJvJx69at4xNVpkwZt5D+U1ElAE+etPNFVfrv3Dld7BLBtWvX4OPtDSJCVh8f3M4kTGHtWva0tGePeDukOvnDh5nh39qWAHz48CF8fVm8tYeHJ867gXyjytWrTNP0s8/sfPHff91G+k8lMTERVaz2ir7//nub33340L2k/wB3cfK3b7MFWztC0IqioEGDBnyyzC7irfLsGYtA69fPgS/HxwPlygFNm7rN2mf7tm35nEyYMCHT7yoKe5upXFl8KRRpTt5iYTGg1arZXbCdMWMGH4vGjZu5zbJiu3YsktchMe/332fRNiYX8VaxFvOuXr26XTHvzz9nN7wrV3Qy0EXcw8l368ZimKKj7X711KlT8PDwABEhMDAQoaGhOhjoGh98wK6Jx48d/MH27eypcdMmqXaJYOfOnSlZfPny4YUDVZ5OnmRvNYsXi7VFmpP/4Qc2HwftF1mLjY1FkSIl+Jhs3rxZrC0S2LGDHd6GDQ7+QH1q6d9fql0ieP78OXLnzs3n4/Dhw3Z/ExvLbnht2uhgoADM7+T37WNn2E8/OfyT/v3780kbOHCgRONcR327nT1b4w/btAFKlGBnnElJSEhAhTJl+FysWrXK4d/KyK+R4uQjI4F8+ZIz1xxj48aNfEyKFi2JWFPPIVC+PIvg1fTS8fXXDq4/GsvIkSP5XLzzzjsO/27jRuaW/vhDonGCMLeTT0piMUu1a2tKhwwJCUFAQEDy2qcHTp8+LdFI53Fpn+rKFfbOOGOGFNtEsGDBAn4B1alZ0+5rsDVqfs0HH4izR4qT/+ijNJlr9lEUBY0aNeVjM3PmTHH2CGb+fLYFdOaMxh86FElgLBcvXoSXlxeICH5+frh3757Dv1UUtmJarpz5U1fM7eSXLWO3y2PHNP90zpw5/CJq2LChKdc+t251MeJszBi2C/TwoVC7RPDkyRPkTL7REhH++ecfzW3Mni02v0a4k1cz16ZM0fzTc+fOwcPDE0QEX99sePRIfqllrTx5wiJ2Bw92soE9e9gJvm6dULtEoCgKWrVqxc/PqVOnam7j3Dl2A/zqKwkGCsS8Tj48nAXl9url1M/j4+NRxmqpYP369YINdI24OPYE71LuSHg4i+fq3VukaUIYNnQoH/veTs6h6Pwa4U6+Y0egSJEMMtccY8gQqzHq3UeMTQIZOpRF7IaFudBIhw4ujZEsfv/9d6sls6J46fQcChgjyZjXyQt4St22bVuqiYxxKDRAH9Sn1H//dbEh9W3HiSdlWZw/fx6eyZvf2f38XHpKFZlfI9TJ281cs8+TJ08QEJCTn6PHjx933S5BqE+pX37pYkPXrzv9tiOLtA+Av/zyi9NthYW5+LajA+Z08up68+efu9RM2leyadOmCTLQNYSuNzu5byELRVHQtFEjYevNIvNrhDl5gevN1vsWNWvWMcWyovV6s5BUEyf2LWQyd+5coUu58+ezPWbN+xY6YU4n36YNi1ESEHXgyuaKLIRHjqgRSBqiV2SxadMmfgGVKFJESOSI0xFIaRDm5AVGjiQkJKBMmQp8zFavXu1ym66iRo5s3y6owVS1s40lJCQEgYGBQoMynI5A0gnzOfk//mBn2MaNwpocMWIEv4jeffddYe06g6wYcHTrxso+OJBLIIvY2FiUsCotsUlgHL+aS+BKfo0QJy8hBtw6lyBfvkIO5RLIQloMuIZcApkMGDCAj/WAAQOEtbtzJzu8X38V1qQwzOXkExKkZHM6k/AgA5nZnLh9m5V9sJMVLJOZM2fyMW7WuLHQpQcRvlWIkxdxt8mANm3a8bGbOHGi0La1IC2b0zor2KBlxdOnT6dKlAwRPIdt22rICtYRczn5r76SVpdlyZIl/CKqUaOGpphtUfz8s7y6LABS6vsYIGHz8OFDZPP1BRHB08NDSl0WV1dJXHbyotaNMuDq1avw9vYBK3Prm2l9H1lIr8ui1vf57jtJHdhGURQ0bNiQ+4C5c+cK78Ph+j46Yx4nr1ZYHDJESvNpixD98MMPUvqxhewKiwCAFy+AQoWArl0ldpIxvXulVFgcJqlKpqv7nS45eR0qLI4d+z8+hl266C9DpEuFRTuVOmXxyy+/8LGVWbzQbqVOAzCPk1drpUsMOHW0nKgMpkyRWyudo9bc37tXckcpWNdKzxkQILVWuiv5NS45eZcz1+wTERGBXLny8rHMqOa+LHSrlX7/PvOCGdRrl8XLly9RtGhRPq7btm2T1pdac79nT2ldaMYcTv7MGfYePn++9K46derEJ/ujjz6S3h/AIsf8/OSqHnEUBahbN516lrzuFNSpWZOP6QIdlKuczUFy2smrmWstW0oPn1ixYgUfy0qVXk2lniUL3VWPMlDPksnUqVP5mOohKKSqZx09KrUbhzHeyav6peXL61IE4ubNm8iSJUvy2mcW3JD+aM0ix2Trl6ZC1cH95hvpXa1evZpfQBXKlNFFv9TZagJOO3nR9RUyISkpCVWqvMbHdPny5dL71F2/VNXBffNN6V1ZS4N6eXnpIg2alARUrZqBDq5BGO/kf/2VnWE7d+rW5ccff8wvoo5SF8lTlO113gJgpQ4kL7BGR0ejYHAwH8udOs6hM/k1Tjl5GZXS7HDgwAE+prly5UW41Dlkkbfd9N4C+OUXdmH8+afUbt59910+liNHjpTalzX797PDW7lSty5tYqyTj4lhMUft2unabVRUFAoUKMAnf/fu3VL6sVhYxFiNGgbc0R89ArJnB0aPltbFhAkT+Bi2b9tWWj8Z4Ux+jVNOXkbNYwfo1u0tPrajR8uTIfr0U6bHo3swj6IADRsCFStKiCdmHDp0iI9h7ty58fz5cyn92KJ7d4dlMKRirJP/7DO2Nnf1qu5d//jjj1Zrn5WQKOFE++47G8r2ejFzJovpunxZeNO3b99GVh8W8ufj7Y1rOq2vWqM1v0azk5eWuWafu3fvIksW3+RlBm9ckSBDdOsWi7i1I9Ylj9On2fguWiS8aYvFgurVq/NrfMmSJcL7sMedO+wG+sknunedCuOc/IMHbJd97FhDurdYLKhptWH49ddfC20/MpJFivXoIbRZbcTGAiVLAq1bC2+6q5Wy/f8Mm0Nt+TWanLzUzDXHmDRpktWGoXgZoi5dWMStgQm2wMCBQK5cwNOnQpv9/vvv+dhVqVJFykOcI0yaxG6kN28a0j0AI538e++xWKOICMNMOHLkCD8RgoKC8EzgK/m4cewedv++sCadY9Mm4RI2+/bt4+MWHBSECAPnUEt+jSYnLz1zzT4vXrxA/vyF+VhvF1ZMhkXYErGIW0MJDQUCA4Hhw4U1GRkZiXz58vFx++uvv4S1rRU1daVzZ8NMMMjJHz3KzrAVKwzp3pr33nuPnwwfCNpcu3aNrUKZouilogDNmgkrKZiUlIRXK1XiY/btt98KMNI1rPNrNmzYgCJFiiAwMDDdn5rS7uHhkeHnBQsWZBKFumSuOcbatWv5WJcqVU5I9FJSEouwrVvXJAW15s5lme6CsqQ/+ugjPmadjfSuyaxZw9ydUfca/Z28xcJii157Taeg3Mx58OAB/P39eYjVvy4XeAfat2cRYqapYXH+vKDi4MCyZcv4BVTtlVd0ieO2h5pfM24c8Prrr3P7nPmrW7cuMHmyTplr9lEUBXXq1Of2fSVAhuibb5jTMU35+vh4oEwZoHlzl+86169f5yHSWbNmxU0j10mSURSgXj2gShVjVv70d/IrV7Iz7MAB3bu2xfTp0/lF1KJFC5eSJf78kx2eyYSogGHDWNmI0FCnmwgPD0eenCkiFwdMNIdqfs1HH811yclPHTNGx8w1xzhx4gS3L3v2HAhzISv8+XMgd26gj9mEqH7/nV04v/3mUjMdOnTgY/Xxxx8LMs51Tpxgh7d0qf596+vko6JYTFH37rp2a4+YmBgUK1aMnxxbtmxxqp2EBBYR1qiRSV6DrXn6lG1wDRrkdBOjR43iY/SW7oHVmaPm17Rp8wLBVrH7Wv5y5syJ8M6ddc5cc4w+ffpyOwcNcl6GaNQoFllrOklZRQHeeIMFCjhZG2j37t18jAoUKIAok81h377sBqtzJKfOTv7jj1lM0Z07unbrCBs2bOAnSOnSpRHnxIm2cCGLCBOgQyCHBQuclrC5cuUKvJPFV3yzZMFdk6j8WKPm1wwc6NzT/NR+/QzKXLPP48eP4eeXPXlPwRNnz57V3MalSyyi1kWxLnlcusQyi2fN0vzTxMREVLLaK1pphiykNDx+zG6wOuZkAdDTyd+8ydY5J03SrUstKIqCxo0b85NktsZysqqy/cCBkgwUQUICUKGCU68abaxkFCdPnizHPhdR82vKl9f+NJ8zZ06EV6liUOaaY3zxxRfc3oYNm2heVlQflAWIdclj5EinXjW+/vprPja1atUypJS4I8yapVuFDI5+Tr5zZxaxYGhQbuacOXMGnp6eICIEBATg8ePHDv922DAWCebCkrc+qBI2GzY4/JM//viDX0CF8+d3WtleD9T8mo4dtT3NT+3QweDMNfvExcWhWLFS3OZfNcgQqYJrmzdLNFAETmwaPH36FLly5eLjctQslcEyIC4OKFUKaNVKvyVdfZz8X3+xM2ztWl26c4XBgwfzk6Vfv34O/UYNXpk3T7JxomjfHihWzKHwn/j4eJQrleJYfv75Z/n2ucjAgUDOnC+QN69jT/M5c+RAeJ48BmeuOcaWLVtSbriFiyPGoTkEypYVEryiD0uXagr/ef/99/mY9DRTjV8b/PYbO7zff9enP/lOPjGRxQ7Vq+cWZ1hYWBhy5MiRvPbpgZN2ZIjUMPSyZQUp2+uBGsg/fbrdr3755Zf8Aqpfp470Mq0iUPNr6tVz7Gl+av36Jslcs4+iKGjaNCVM9DMHZIjmzRMahi4fDYH8//77L7yS94r8/f3xwExqHTZQFOD111nUqB4+Q76TX7KE3bZOnJDelShSObb69TN1bJs3C08o1QcHUnLDwsKQI3t2h294ZmLePMDD4wWCgjJ/ms8ZGIhwb2+Hbnhm4cKFC/D0TN4E982WqWNTb3jDhulooAj+/ptdWGvW2PyKoiho0aKFphueWbhwga3NS1AhTIdcJ6+ur/XtK7Ub0cTHx6NcuXJ2lyjU0jBvvKGzgSJwoLjO4EGDUpau3G4O2dtV6dKZP81PLVfO4aUrMzF8eMoSRY8etpcoJJWG0YfOnTMtrmO9dFW8uGNLV2Zi+HB2AxasJ54OuU5e3SnXsIFpFrZv32619lk4w81GtcijDjoEcvj2W5ubjWfOnOFlAAL8/TVtQpsFll/zAjlyZPw0nzN7doSTGTPX7PPs2TPkyBGU6WajKri2cKEBBorg5k1W3WvixHQfxcXFoVQp5zahzYKaujJggNx+5Dn5ixfZ+8gXX0jrQjZt2rSxGTaolmsfNcoY24SQlMRKONasmSpsUFEUNG7QwOlwUrOg5tcEBWX8ND81b16TZq45hnXYYLVqqcMGFYUdWsWKugiuyeOTTzLMrbEOJ23SRHs4qVlYtEh+bo0cJ68oTA+zVClpyvZ6cOXKFXh7eyevffqmSgDq04cJL+mdvSacgwfZ0/yPP/J/sk4MK1WsmFOJYWaB5de8QPbsqZ/mc/r5sad4JxLDzEJiYiLKlcs4AWj9ejatu3YZaKAIoqPTZck/fvwY2ZP3ijw9nUsMMwuJiUClSiy/Q9Z9So6T37ZNSB0KMzB69Gh+Eb2dLEOko4SqPliJ0MbExKB44ZTyts6WeDATo0YBWbKkfpqf6uvrUokHs2Cdyp83bwFER0fzEg/t2xttnSBUEdr9+wEA/fr148c8eLDzJR7Mwu7d7PB++UVO++KdfHw8U7Z//XW3fQ22Jjw8HHny5OEn1f79B1CnDovwMkEBRjHcvcuLcn322Wf8WFs0a+a2r8HWPH8OBAW9gIcHU7Ly9PBAeECAG2SuOUb79tZFuT7hxdoMEOuSg1q5tmpVnDh2jO8V5cjhWrE2M/Hmm+zGLCPPULyTnzOHrcVfuCC8aaOwLq9bqFAlECXh77+NtkowkydDyZIFJZOXp7w8PYWUXTYLLL/mOxQOLoyvidwoc80+169fh7c3K6/r5VUQfn4WjBtntFWCOXoUChFqWBUSFFF22Sxcv85uzFOnim/bAwBIEDH/3qKsNavQsw796MGHi0Q1azgWi4XeffddunHjOhEReXgEUoEC18nDw8Ngy8RhSUqiF6Gh1ICI9hDR592704cffWS0WcKwWIjeeVuhHvdmUsGgOPJav44oIMBos4SxYMFC+umn2URUkYiOUXCwP/n4eBttljAAUImQEDqmKORHRJV8fOjgoUPk4/3fOcYFC4hW/JydNq+NoTJtyhL5+4tpWOQdI6paYyhEqETnQYT/8N9rGUZruPvfkOQDrEiEB8YPsvC/vdQYIMK7tNpoUyT8hYLoFRAlgWiMsHPCTH9ZrP57rfEDLvwvlPIikCLwP5oNnDolzC+LfZJ/8JyyVC5DUfVa053PVotq1nASEhKoa9eu9PDhAyIi8vAoT/nz7ydPz//Ok3yOxETaHxZGW4moPxG916YNrZo+3WizhBEX70EVu1Wk7yO7UD2fE3Tpl39JyZ3XaLOE8fnng2nTpuVEtIiIelKePI0oa9ZnRpslDAA0NDSUJlosRETk7+1NYfv2UTY/P4MtE8egz4rS+l056crmi5S/fhlzPskDyDTBxl2ZNWsWf4KoVKkRiBRs2mS0VYJ59VUoRCibHJpGRDjyH5rDGTNY4tqN3bdYgs2ECUabJAzrxDV//6Lw8LCgXDmjrRJMcvXU1lWr8vNzkknLljuDWj1VRuKaeCdvI8HGXXn06FGqmNxz5865R11uLWzZwm7MrVtj8eLF/CKqWbOmaetya+HhQyBbNqvENTXB5vZtI80SgqIoaNSoEZ+zOXPmoGtXNp2ZlH1xL6x0EK6myV25Y0IBIq2oiWsVKshJXBPv5AGm30qUKsHGXenTpw+/gIYMGQLADRR2tGCxsPpC3t5AZCQSExNRuXJlfsw//gfmsHfvNIlraoKNySQMnWH9+vV8rkqXLo34+HjExrKXlcDA/8RzVjpFszFjUvYcuptMStQZ1MS1nTvltC/HyQPAW2+ZUitTC8ePH+cnU86cOVPF5I4axZ4OHz400EARTJzIzrBPPuH/tGfPHn7cZtTK1MI//7DDS5e4pibY7NtniF0iSKtNvHXrVv7ZrFns8PSWmhOOKrlmlbgWHh6OvHnz8uM2k6C8VvRIXJPn5O/eZa/EJlK914KiKKhbty4/kebPn5/q8+fP2dNh797G2CeE6GgWnBsUlO6Rr2PHjvzYzaR6rwWLBahd20bimvrhq6+6bVbb9OnT+Ry1bNkyXeJa/vwsZeXJE4MMFMHQoUCOHECapKfly5fzY3/ttdeQ5KZzqEfimjwnDwCTJzNd1xs3pHYjgzVr1vCTqHz58kjIYLHsm2/Y09I//xhgoAjatmUHkIEm3I0bN5AlC0uwyZIlC27evGmAga6xahU7vL17bXzh2DH2hWXL9DRLCPfv34e/vz+ICF5eXriYgWjonj3s8Jo2NcBAEZw7x9ROvvwy3UdJSUmoarUJu2LFCgMMdI3795mkg+zENblO/uVLpuvasaPUbkTz4sULFCpUiJ9AO20slqkCNnXquGEFhwsXmAeoUsXmV8aPH8/HoFOnTjoa5zrR0UDBgkCXLna+2LMnkDcvEB6ui12i6NGjB5+bESNG2PxerVpsmo8d09E4ESgKuztlIrm2f/9+PgZ58+ZFRESEzka6Ro8eTNIhMlJuP3KdPMB0XYnYY4WbMHHiRH7ytG3bNtPvqgI2q1frZJwoypZlm1nXr9v8SlRUFPLnz8/H4q+//tLRQNeYMIFtPt66ZeeLDx6wzZUxY3SxSwRHjhzhcxIUFIRnz57Z/O79++xhuFgx/ewTwqZN7MKyI7nWrVs3PhZjx47VyTjXOXyYHd6338rvS76TVxSgfn2gcmVWV9Pk3LlzB76+viAieHt74+rVq3Z/06ULe2qMjtbBQBGsXs3OMAeiS3744Qd+EVWpUgWJbjCHt28zB//ppw7+4PPPWXTRlSsyzRKCxWJBzZo1+ZwsXrzY7m/69mXT7cBXzUFsLFCiBNC6td2v3r59m1+vPj4+Dl2vRmOxADVqsEhzPbYS5Dt5ADh5kj01usFZ1r17d81PBrfcKb/GYmGxdVmzOhTob7FYUKNGDT4mS5Ys0cFI1+jaVeNNNzYWKF4caNNGql0i+PHHH/lcVK5c2aGbbmIiW/v193eL56yUzLXLlx36uvWbd7t27SQb5zo//MBuugcP6tOfPk4eAPr1Y1EcmbxaGo0ra3yffsr8punza0aMYGeYBsUu6+WB3LlzZ7o8YDT79rHDW7VK4w83bmQ/3L5dil0iSLt8tkfDEuiSJezwTC/Vq2aujR7t8E/S7qHt2LFDooGuERXFop6SpSl0QT8n//gxEBAAfPCBbl1qIe1u/fLlyzX9Xt3oM3V+zZMnLKYuf37NP3333Xcd2ugzkqQkFhFZp44TSUDqRl+5cqbVy7PeCO/oRDBDsWJsff7+ffG2CUPNXNO4Eb569Wq70XBmYPx4Jt1gJTInHf2cPADMns2cjAnrlFvH3VatWtWpuFvT59c0aeL0JrgjIXtGs2yZiyGtasieCeuUpw1pveFEWLIaMVqrlgQDRWAzc80+9vJazMCNGyyiPI1ctHT0dfJxcUz3tUULU8UcRkREpMqg258sM6YVU+fXHD3KLqDatZ1uYtq0aZkm3xhJeDh7AOzVy8WGhgzJMPnGaDp16sTHfrwLCYbqfX73boHGiSDTzDXHSJuh/sRkWWAdO7KIchnqT5mhr5MHUophWaVgG83YsWOF1cIwbX5N0aLsKfXBA6ebiImJQdGiRflYbdu2TaCBrjF6tKAyE2FhLI3eRNqh1mUm8ufP71KZCRdW7ORiN3PNMaxrTQ0dOlSMbQJQdVx//ln/vvV38orCnuRLl2ZP9gZzRUJVu169nFpWlMfixcJ23TIqiGU0ly+zYIwZMwQ1OH9+qoJYRiKjYJy6926aAnvqhlbXri43lVHVWKNJTAQqVWKR5Ea8/Orv5AG2Ju/lxdboDaZt27b8Apo4caKQNp0IEJCH4Pg5RVHQsGFDPmZz5swRYKRrtG7NwqqFlX5OSADKlwcaNzZ8WVFG6WeNUbTyERyaNnPmTD5mTZs2NXxZ8euv2TPDyZPG9G+MkwdYlE1AAIu6MYgdO3bwk6FQoUJ48eKFsLZNk1+jZsI4sZlli9OnT3ORioCAAISEhAhrWyt//MEOb+NGwQ3v2MEa/vVXwQ07zrNnzxAUFMTPUZEiLmo+nICHZ9fQnLlmn9jYWJQsWZKP20bhJ4fjPHvGIsf79TPMBAOdvMFHn5CQgPLly/MTYY1ghQVT5NdIzGkfOHAgH7sBAwYIb98R4uNZxGPTppIeuNu2ZZMYEyOhcfuMGDGCj3GPHj2Et1+uHHvClFkB0S6aM9ccY/PmzXzsSpQogViDXllM8CxroJMHDH2PmT9/Pj8J6tWrJ+WVTs2vsVN+Qx5qdSoJZTJDQ0MRGBgIIoKHhwdOCRQedpQvv2T3MGnLrlevstexzz6T1IFtLl68CC8vLxAR/P39cV9CcLsDNerksnevk5lr9lEUBc2bN+fX+AxhGzaOY5ZVaWOdvEE7EmFhYciRIwc/AU6cOCGlH+v8Gt33J3ftkl5ndt68eXwMGzRooOvaZ2goi3SUHkAxdizbz3AhKkkriqKgRYsWfGynT58urS+12rTumsXWJVwlyVdduHABnp6eICJky5YND3VU+DFTfImxTh5IKXqtY2zRkCFD+AXUp08fqX1lUhJbLjooRsTHx6Ns2bJ8LNetWyetr7QMGsQiHaWHQkdEsFLE770nuaMUtm7dyse0WLFiiJG4XKTqxuTKpbNUoE5iDMOGDeNj2cvlJArHMVOkuPFOHtA1S+Ds2bP87p49e3Y8evRIep+659fMmMHOMK5cLY/ff/+dX0RFihTBSx3m8MwZtsqnW1Lj8uVsPI8eld5VXFwcSpcuzcd0/fr10vtUFSB1EwATlrlmn6dPnyJXrlx8PI/pUFg/Lo49wZsl59McTl6nfF9FUdCkSRM+4bNmzZLan4qu+TUxMbqqOCuKgjfeeIOP6ZQpUyT3xyIby5fXscRMUhJQtSrb45A8prNnz+Zj2ahRI12WwNJouctHWOaaYyxcuJCPae3atYWEoWaG2aq3mMPJA7pU7tm4cSOf7FKlSiFOx8Uy3fJrunZlj2Vr10ruKIVLly7xhDI/Pz/cu3dPWl8bNshVtrfJ/v2s45UrpXUREhKCgIAAvpl9RsdkrG3b2OE5UMLdNYRnrtknISEBFStW5Nf+KgkbvSpmrMNoHicvuQZnbGwsihcvzif6t99+k9KPLXTJr7l2jd1JypWT1IFtRo0axcf2nXfekdJHTAyLBjWsZHj37kCBAuxclUD//v35GA4aNEhKH5nx6qvM0UtNEhWeueYYu3bt4mNbsGBBREtS+DFjRXXzOHkgpZr+gQPCm/7888/5JDdv3tyQLLidO9nhbdggqYMqVVgHFy5I6sA2z58/R+7cufkYH5SgiDB9OtskNEz8584dwNdXyuL1yZMneYJZYGAgQkNDhfdhj1u32DNCmTKSOlAz13QP5WG0b9+en5+fCky+UjGrNpK5nLyqi/Xaa0LLOD548ADZsmXj9SwuGOAEVaTl16hB+QYq4yxdupRfRNWqVRO69vngAYtkNFzGc+JEtudx86awJhVFQf369fnYzZs3T1jbWnn7bXYaCSiRkxrpmWv2uXbtGnx8fEBEyJo1K27ZFQB2HDOrnJrLyQPAkSPCFW579uzJL6Dhw4cLa9cZpOTXWCwsBs7Hx1Ch2WQL9fMAABTQSURBVKSkJLzyyit8rL/77jthbb/3Hotk1CDWJYcXL4BChYDOnYU1+fPPP/MxK1u2rKFF32Jj2ctK9uyC95ilZ645xrhx4/hYd+nSRVi7P//stFSDdMzn5AGgRw8gOFjIVv+xY8f4pObKlQtPnz4VYKBrCM+vGT+enWF6qxFkwN9//83HO1++fIgUMIfqfX/FCgEGimDNGmbQX3+53NTLly9RpEgRPmZ/GJYencLcuezwhg0T1KBumWv2iYyMRHBwMB/vvS6WNgZY5HfhwiwS3IyY08nfv8+84LhxLjVjsVhQu3ZtPqGLFi0SZKBrCM2viYxkrwa5c+uczWKbLl268DH/8MMPXWrLYgFq1hS+gucaigLUq8f2QFx8N58yZQofq9bSQ1scp0ABFgYoZGtAt8w1x/juu+/4mL/yyitOqcBZM3kyiwB3QqxLF8zp5AFg2jS2/OBC9aSffvqJT2bFihUdUrbXixUrBOXXvPEGa8hEAh63bt1C1qxZQUTw8fHBNRfm8Mcfpe3Fu8aJE8ywJUucbuLu3bvw8/MDEcHb2xuXL18WaKBrqGVlGjVysSE1c23BAhFmCcFisaBatWrcN3zjQoXWu3fZ8pYLYl3SMa+Tj4lhakbt2zv18+joaBQoUIBP5K5duwQb6BpC8mvOnmVXYtWqQm0TwSeffMLH/s0333Sqjago9kTpoliXPPr0YW9Qz5879fO3336bj9EoHbKTtVK3Lju9Dh1ysgE1c61CBdOJox88eJCPfe7cufHc6Tlkkd+SomqFYF4nDwDr1zud+SLCycjG5fya0qXZU5LAKAFRiLjJfvwxe0oSINYlh0eP2A7lyJGaf2rtZPLkyeO0k5HJw4dsr7RIEScbMCxzzTFcvckeOMAO74cfxNsmEnM7eUVh74sanwTSLhdcv35dopGu4XR+jbqOISnxSASuLJfdvMnWOSdNkmigCGbNYovXFy86/BORywWyGTiQnWYLF2r8oeGZa/ZxZbksKYntE9WoYZqtMJuY28kDTq3pidz4k41T+TUWC3uC9PU1vo5pJriy8d2pE4tYECjWJYe4OKBUKaBlS4fjv0Vv/MkkMZGVmfHz01gu2/DMNcdwduP722/ZzU+gWJc0zO/kAfY44eDuvIwQPtlMmsSeWh3Orxk2jJ1hc+dKtUsEzoSw/vWX7uV3XOO33xze/JYRwicbtQinw0Uj1cy1//1Pql0icCaENTKSRXhLEOuSgns4+dBQVlXRTuBuYmKitGQcmWjKrwkNZcsDBQtKt0sUWpLREhNZZGK9euYo0+oQigI0b87qAdh53JWVjCObEiXYC7VD9QNNk7nmGFqT0caNY/cwCWJdUnAPJw8A8+axXaDz521+xTqtvnr16tJLiorE4fyahg3ZF93gCVBFS1mJJUvY4UkS65LHhQvs/Mzk7UpmWr1s1IjR6tXtfNF0mWv20VJW4to1tgo1bZqOBrqI+zj5+HigbFmbtS/SFsg65HTclzE4lF9z6BC7gOrV09U2EThSIO7ZMxaR2LevAQaKYPhw9sYZEpLhx2+++abUAlmyef11dvrt2GHjC6bMXHMM6wJxOXLksFkgrn17FtltkLa7U7iPkwcyrWKnR6lb2djNrylShD0tGin97iSOlHoeMYLtJ7vh4TGePmU1hAYMSPfRn3/+yY9dZqlbmTx7xlYKg4NtfMG0mWuOYa/Us1pFVgexLqG4l5MHMqxHradohWz69rWRX7NwITvDDKgzLopff/2VX0QlS5ZMJdpy8SJzIF98YaCBIli0iC1enz7N/ymtaMVPP/1koIGuMXYsOw3TaYurehBvvWWIXSLITLQlIYFFcjdq5EZ7Rcm4n5NXlWVmzgTA1tNatWrFLyDZ8nOyefw4g/ya+HgWw5Ytm/nqmGrAlvyiorAIxFKlTB0R6hiJiUClSmzvJNkb6C0/JxOLhdUay5IljSSzmrkmUdlND2zJLy5cqJOymwTcz8kDTKA6WSPSCCFp2aTLr+nZ0+02s2yRkZC6Kj2ns1iXPHbtYgf0yy948uQJcubMyc9RPYSkZbNuHTu8Tp2S/8FtMtfsk5GQ+pMnLIJ74ECjrXMO93Tyz58DefIgqWdPlClThk/IunXrjLZMCKnya+7cZY8QJUsabZYwhgwZwuesZ8/+KF2abeq522twprz5JlC0KEYOHMiPtZfDgebmp0IF5ugvX4YbZa45xtatW/mcFS1aFIMGJSIwUFBFTgNwTycPAN98gytECEqejAYNGhgi6ScLNb/mRumWbhpTaJuwsDCrp9tq8PR8ZoRioVyuX0e4lxfqJp+f2bJlw8OHD422ShiXLrHTsm/RPW6WuWYfRVHQsmXL5PMzB4jOwUCxLpfxAAASRI0aNSgkJERUc5ny8uVLKh8RQSOIaDgRHV69mipUqKBL33oAEE1td5ROhBSnkZX2UJ6fvjLaJKGsWvUTzZ8/m4i+IKIeFByclXx8fIw2SxhJSUn0JDSUFCIKIKLauXPT7l27jDZLKBOGPaOW/0yj+4GVqcL2L4n8/Iw2SRi3bt2ibt2aE9EUIlpFgYEnKSAgu27958+fn06ePCmkLW8hrSQTEhJCDx8+FNmkTTyIaCEReRJRBBElvfeeLv3qhQcRnaRtdIkq0pmL+2h8daMtEk0MEYUTURMimkBhYeOMNUcCRYnoHhFFE1HrZ8+Iqv+3JrEIDaRgekJJUVepegNfo80RjIWIHhJRSSKaT1FRVSkqKtJgm5zDbZ/ku718SV9FRFADIjpMRM1q1qQ9S5eSh4eHLv3LZueK+9T6mw70Q7HJ1PPpfLq4+Rol5c5ntFlCiIoKp44dy1Bk5DMi+oSIplBwcDPy8blttGnCKJSURF+FhlIDYus1Pp6e9ODPPyk4KMho04TwPNKLynaqREOCN9Jn19+mre+upcJj3zHaLGGMHv0mHTiwjYiqEdEJypFjImXPvlK3/kU+ybvnmnxyTG5St24oUaIE3yTZvHmz0ZYJIeFlAspnuYEmOU9DefIUCArKMMHGXRk5ciSfs27deqF4cVNXpHWO5BrS/Xv14sc60F3DMzLAOnHteN42uOtdArHhsfZ/6Abs3LkzVeJar14JCApiyWDuiHs6+fHjWdz43bvYuHGjzQQbd2V+p33wpCSc/eUK+4evv06XYOOuXLp0CV5eXqkS13791U66vLuhqsH89FO6BJvT/4E5TJu4dnP7FSSQN/a2nGGsYQJISEhAhQoVuE9ZtWoVQkKAgADggw+Mts453M/J37jBYnKTk54URUHTpk3TJdi4K2GXniAHRWBIxX0p/5hBgo07kjZxberUqcn/DjRpApQvbzqVOO2ouo61a3M1iTlz5mSYYOOO2Epc21ttDKIpGx6fcu8IIuvEtTp16vDEtTlz2I3t338NNtAJ3M/Jd+zIarhYJT2dO3cuXYKNuzKk4n7koAiEXUpTO3/3bp5g465YJ64VLVo0VeLa2bOsLM/8+QYaKAK1+LpV0lN8fHyqfI717lb8xAo1cW3LltT/HnEnHE888uBgSffNBUibuPbPP//wz+Ljmdpmixbu95zlXk5edXQ//5zuo6FDh/LJ6dOnjwHGuc659VfgSUn4quO+jL/QoQMrgeeGWb1pHd0vGdysBg92WBvGnEREsDrqPXum+2jbtm2pbnAx7lTGMBnV0dlKXNvfYxlAhAvfumdW77Bhw/gc9e7dO93nW7dmfIMzO+7j5NUli/r1MzzD0t6Fjx8/boCRzqNYFDTNeQrls9xAwksbaxbXr7OlquRlDndi7ty5fG4aNmyY4ZJFWBirizJ0qAEGimDsWFZu48GDdB+lTrAhTHOnguTJqEsWthLXkuKTcMX3VVzIVhuWRPeqz3P+/Hm+GmArcU1dqipd2r1qLLmPk1c3H0+etPmV+fPn84uobt26brX2uXHcUbb5OM3Ozemjj9imsxtV2gwNDUVgYCDffDx16pTN7371FVu2OXdORwNFcOUKK5z3+ec2v3Lx4kW+6ezv74/77iItBPDNx/ffz/x7Z+bvA4hwaMgqfQwTgKIoaNasGfcdM2bY3kBWN51nz9bRQBdxDyf/7BkLI+zfP9OvJSQkoHz58nyy1qxZo5OBrhEbHovi3vfQJq8Dbx9RUUC+fIAb1cwfaFW/ZYCdUNCEBLYBa0Mbxry0bQsUL56qBHZGjBgxgo9FD3cRCQW79BwNIzxSqCseeRZE9GP3qJm/efNmPiclSpRArJ05/OADdsNzF90D93Dy6qjaUNyxxjrGtVChQnjhBkWTPm+xF96UgCvbHVTy/v57tjjoBupXp0+f5oo7gYGBCHFgDnfsYIe3caMOBopg+3Zm8K+/2v1qWgWzw4cP62Cga5w6xV6iv/7ase/fP3gbsZQVe+ubX/0qNjYWJUuW5POxKQNBorSoz5z9+ulgoADM7+T//Ze9H82Z4/BP2rVrxydt4sSJEo1znQcnHiEbRWNM9b2O/8hiYWKb1avzMD0zoigKGjZsyOdibib6p2lx8MHYeBISgHLlWAyog68eS5Ys4WNSo0YNU9eXVxSgQQO2HaZFymBvgwmIpay4t9/cOrYzZ87kc9GsWTOHl3gXL2Y3PneoG2huJ68oLGapdGm2te8gV69e5YLJvr6+uH37tjwbXaRnyYPI6xGG8Dsale0PH2ZPj99/L8cwAfzyyy/8AipTpgziNcyhA0vc5kDdRDh71uGfJCYmonLlynxsfvjhB3n2uYhaO373bm2/exH6Ao88C+FIoS5yDBPAw4cPUwnMnz9/3uHfJiYClSvbjAMxFeZ28lu2sDNs61bNPx07dqxV6nw3Cca5zrFvL4AIWP7efucaePddtj4fGSnWMAG8fPkSRYsW5XOwbds2zW2MGcO1YcyJGg40ZIjmn+7Zs4ePTb58+RBpyjlkKSkdOjj3+4NDVgNEOPPVXqF2iaJ37958DoY6EdK1Z4/NiG5TYV4nn0o5Q/utMiIiAnnz5uWTuG+fjdhzg7AkWlA72wW86nsFSfFOKtvfu8cibT78UKxxApg6dSof+1atWjkV6RQezsLOTau1MWQIc/JhYU79vFOnTnyM/t/evcVEdYRxAB+Rm1wMl4CU5aVpUgXiZVUSIOlLX5rGPqAGraumxpA0jaltjBZpvWAIIUYbS6ymESWbBk1Mmr5hiUXlljVISpUYyoabBSKQigiLXYXd8+/DlEltqLLnzOw5PX6/d78zzpz9zi7n+2ZKS0slD8648nJesdvbq+/fBwMauhLy0RO7Rv89rkh7e7uY+6SkJPyhszmjqIifl2Ll1hXrJvmTJ/91Bl7oampqxEKuW7cOgYB1brTvP24FY0DTNwYPjTxxAoiK0v9JVGBoaAjLli0DYwxLly5Fd3e37lgLNJBaw3yL7pkzukP09/cjOjoajDFER0ejr69P4gCNmf/+YPTZc7+2HWAMza7v5AxMAk3TkJ+fL3JDdXW17ljzu6wcPy5vfLJZM8mPjvJqmv37DYUJBAJwOp1iMS9cuCBpgMb4Rn14I2IUxVke48GePuVdsHp/UyvgcrnEnH/2wonkoVtgKxjzSdxsp6ysTMxVUVGRpAEat2MHkJHBK3aNan3rIzxakorJgcfGg0lQV1cn5jw7OxuzBtfw8GFrn2FuzSS/dy+QmsrPcjWopaVFLGhaWhomJyclDNCYLwtvIZb9icFWSc0wV6/yr7vXr8uJZ0BbW5uY79TUVDyWsIb/2NTRGiRumzk9PY2MjAwxZz+H+oZTgdZW/t+T9T547NeHmGYJaHJ+LiegAT6fD5mZmWK+GxoaDMf8e+dzbN8uYYAKWC/Jd3Tw2qRz56SF3LZtm1jUAwcOSIurx0DzEGKYH0ffuSUvqKbxHSpzckKrc5MsGAxiw4YNYq7Pnz8vLXZxMZCZCfjM7q/x+3lt56ZN0kK63W4xZ7m5uZgzdQ2B9euBjRvl/nK69V4VZlkk+ut/kxdUhyNHjoi5/kDiIQZuN38wtrRICymNtZK8pgGFhbw2SeKN/uDBA8TGxoIxhsjISPT09EiLHaqtDg8cEQ8xMy65Sauzkz8cz56VGzcEtbW14gO0evVqqclqcJD/JP7K7P6aykpe2ynxHgoGg8jLyxNz9+1iu44UuHSJJyvZPVr+ST9+j3wTd9Lelxs4BIODg4iJiQFjDFFRUfB6vdJiB4NAXh7gdPI/MVqJtZL8lSv8DmtslB762LFj4kO0SeK3sFDc/LoTjAF1nyjqVC0pAZKTgUeP1MR/iampKaxYsULM8Y0bN6Rf4+hRICYGGDCrv2ZkhNd0Kvg16PF4xNylpKRgwoRjiKamgPR0Xpmrwu0vfgQYw53yejUXeIXi4mIxxwcPHpQe3+Ph6eviRemhDbFOkp+Z4bVImzcrCj+DrKwsscjXrl1Tcp3/Muefw5rYHhQkdEELKuqeGBsDli8H9u1TE/8lSktLxdxu2bJFyTVmZgCHA9hqVn/N7t28plPRe51du3aJOfzUhGOIDh0C4uIAVfumaUENvyS/i4Got/Hct/jGOBmamprE3Kanp+PJkxCbDxdp507+oFQUXhfrJPmqKl6L1L/I/Vt0uHz5sljolStXGn6rHgp3CS+ZvOPWXxK6KKdP89K+MJbj9fb2vlAK2K90Dfm3pdu3lV1iYffu8QsrrNAaGRlBXFycKD29H8ZjiIaHeSWu6h2QvT90IcAi0PyhvPc1rxIIBLB27Vrx2a+pqVF2reFh/qC00m4q1knyPp/y6hBN01BYWIj4+HhUVlaG9TzYZ1PPUF8ehj3unz8H6uvD2ms9NjaGPXv2gDGGsrIypdfSNN4AHfZyyvkLK/6Da0VFBRhjcLlcGFlgX3qVGhqAcJxl0lHxU1gP/Z6dncWpU6eQmJgIp9OpvF+msdFaTehLAIC9RrxeL0tISGAOh8PsodhOR0cHW7VqFUtMTDR7KP9bfr+f3b17lxUUFJg9FNsZHx9nExMTLCcnx+yhhNVrl+QJIeR1EmH2AAghhKhDSZ4QQmyMkjwhhNgYJXlCCLExSvKEEGJjlOQJIcTGKMkTQoiNUZInhBAboyRPCCE2RkmeEEJsjJI8IYTYGCV5QgixMUryhBBiY5TkCSHExijJE0KIjVGSJ4QQG6MkTwghNvYXUTEBIacpJJwAAAAASUVORK5CYII=\n", "text/plain": [ "Graphics object consisting of 158 graphics primitives" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "L = RootSystem([\"A\",2,1]).ambient_space()\n", "w1 = [0,1,2,0,2,1,2,1]\n", "L.plot(alcove_walk=w1, fundamental_chamber=False, labels=False)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Why care?\n", "\n", "- Root systems are the work horse in the study of Lie groups and algebras, Weyl and Coxeter groups, crystals, ...\n", "- Many questions reduce to geometric or combinatorial considerations on the underlying root system" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Steps to reproduce the alcove art" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Prepare the base picture with SageMath" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Draw an alcove path of type $\\tilde A_2$:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "L = RootSystem([\"A\",2,1]).ambient_space()\n", "w1 = [0,1,2,0,2,1,2,1,0,2,0,2,1,2,1,2,0,2,0,1,2,1,0,1]\n", "p = L.plot(alcove_walk=w1, bounding_box=[[-4.5,4.5],[-2.5,6]], fundamental_chamber=False, labels=False)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 298 graphics primitives" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Customize the arrow sizes:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "for x in p:\n", " if isinstance(x, sage.plot.arrow.Arrow):\n", " x._options['arrowsize'] = 3" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 298 graphics primitives" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Export as SVG:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "ename": "NameError", "evalue": "name 'p' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msave\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"alcoves.svg\"\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m#, transparent=True, frame=False)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;31mNameError\u001b[0m: name 'p' is not defined" ] } ], "source": [ "p.save(\"alcoves.svg\") #, transparent=True, frame=False)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### How to make it fit on a piece of wood?\n", "Input:\n", "\n", " \n", " \n", " \n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Output:\n", "\n", " \n", " \n", " \n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### General procedure\n", "- Manually draw the mask of the area to be carved\n", "- Currently: use inkscape and its arithmetic on surfaces" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Postprocess the base picture\n", "\n", "Open `alcoves.svg` in inkscape:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "!inkscape alcoves.svg" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "The picture contains an outer frame made of a path with four nodes,\n", "and a background made of a filled path with four nodes. We need to\n", "remove them.\n", "\n", "- Select all (Ctrl+A)\n", "- Ungroup (Shift+Ctrl+G)\n", "- Shift-click in the middle of the picture to keep only the outer\n", " frame selected\n", "- Delete the outer frame (Delete)\n", "\n", "- Select all (Ctrl+A)\n", "- Ungroup (Shift+Ctrl+G)\n", "- Ungroup (Shift+Ctrl+G)\n", "- Unselect all by clicking well outside of the picture\n", "- Select the white background by clicking close to the picture\n", "- Delete (Delete)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Combine all the picture as a single surface, without contours:\n", "\n", "- Select all, then ungroup\n", "- Path -> Object to path (Shift+Ctrl+C)\n", "- Path -> Combine (Ctrl-K)\n", "- Path -> Stroke to Path (Ctrl+Alt+C)\n", "- Fill-and-stroke tab (Shift+Ctrl+F)\n", "- Stroke paint -> No paint\n", "- Fill -> Flat color" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Save as alcoves-flat.svg (Shift+Ctrl+S)\n", "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Prepare blueprint\n", "\n", "- Scan the pieces of wood (e.g. on an A4 format sheet) and save in `alcoves-wood.jpg`\n", " \n", "- Create `alcoves-print.svg` with three layers: `BluePrint`, `Calibrate`, `Cut`\n", "- Insert `alcoves-wood.jpg` in BluePrint\n", "- Draw two little crosses to calibrate (top left, bottom left) in the layer Calibrate
\n", " Variant: import [calibrate.svg](calibrate.svg) as layer\n", "- Copy paste the content of `alcoves-flat.svg` in the layer Cut" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Cut the base picture to the shape of the wood piece\n", "\n", "#### Manually draw the mask of the area to be carved\n", "\n", "- Display the layer `BluePrint`\n", "- Create a new layer `Mask`\n", "- Manually draw the mask in this layer\n", "- Filled, No contour, 50% opacity\n", "- Hide the layer `BluePrint`" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "#### Add the frontier of the mask to the alcoves\n", "\n", "- Copy the mask (Ctrl+C)\n", "- Hide layer `Mask`\n", "- Paste in Place (Ctrl+Alt+V) in layer `Cut`\n", "- No fill, stroke ~2 mm\n", "- Stroke to path (Ctrl+Alt+C)\n", "- Fill, no stroke\n", "- Select alcoves and frontier (Ctrl+A)\n", "- Union (Ctrl-+)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "#### Intersect with the mask\n", "\n", "- Show layer `Mask`\n", "- Sélectionner the mask and the alcoves\n", "- Intersect Ctrl-*\n", "- Move to the above layer (Shift+PgUp) why?\n", "- Suppress layer `Mask`" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "#### Extract the contour\n", "\n", "- Opacity: 100%\n", "- Strok to path\n", "- No fill, Stroke: 0.1 px, red" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "#### Remove the outside path\n", "\n", "- Path -> Break Apart (Shift+Ctrl+K)\n", "- Select the outside path (zooming in if needed)\n", "- Delete\n", "- Select all (Ctrl+A)\n", "- Union (Ctrl+*)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "#### Check\n", "\n", "- Show the layer `BluePrint`\n", " " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Laser print\n", "\n", "- Print `alcoves-print.svg` file with its three layers on A4 paper (be careful to stick to 100% zoom!)\n", "\n", "- Put the sheet on the laser cutter, with its lower left corner on the\n", " upper limit of the 12 mark.\n", "\n", "- Hide the layers except for `Cut`\n", "\n", "- Export `alcoves-print.svg` to eps (Save a copy -> eps -> ...)\n", "\n", "- Launch a dry run (laser pointer on, bay open, no blower) and check that the laser draws the alignment crosses at the correct locations. The instructions below use the Linux cups-epilog driver for our Fablab's [Epilog Mini laser cutter 24''](https://nthiery.github.io/FabLab/machines/laser_cutter/):" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "!sudo ifconfig eth0 129.175.5.208/16\n", "!export DEVICE_URI=\"epilog://129.175.5.206/Legend/rp=100/rs=20/vp=100/vs=20/vf=500/rm=grey\"\n", "!../cups-epilog/epilog 123 nthiery alcoves < 2015-12-16-alcoves1.eps" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Put the wood on the sheet, with a bit of two-sided tape to prevent\n", " the air blower from moving the wood\n", "- Launch a full run:" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "!../cups-epilog/epilog 123 nthiery alcoves < 2015-12-16-alcoves1.eps" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Projects\n", "### More artwork based on root systems!\n", "See the 2D and 3D pictures in the [Sage documentation](https://doc.sagemath.org/html/en/reference/combinat/sage/combinat/root_system/plot.html) for inspiration" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Automatize the production of this (and similar) artwork!\n", "- Input: Sage's picture + mask\n", "- Output: cut line for the laser printer as svg" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Why automatize?\n", "- Easier and quicker to reproduce and reuse\n", "- Clearer description of the process\n", "- Easier to show the intermediate steps to better explain the process" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Suggestion:\n", "- Python's 2D computational geometry library [shapely](https://shapely.readthedocs.io/en/latest/)\n", "- See e.g. the following [course worksheets](https://gitlab.u-psud.fr/Info122/Info122/tree/master/Semaine1)" ] } ], "metadata": { "celltoolbar": "Diaporama", "kernelspec": { "display_name": "SageMath 9.0", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" }, "rise": { "auto_select": "first", "autolaunch": true, "scroll": true, "start_slideshow_at": "selected", "transition": "none" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }