{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Power broadening\n", "\n", "Power broadening and saturation are simple effects that can replicated using the rate equations. This example shows how this works." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pylcp" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Two levels with a single laser\n", "\n", "This is the simplest case to consider. We will plot up the scattering rate $R_{sc} = \\sum_l R_{ge,l}(N_e-N_g)$, where $R_{ge, l}$ is the pumping rate due to laser $l$. We can compare to the standard analytical expression for a two-level system\n", "\n", "$$\n", " R_{sc} = \\frac{1}{2}\\frac{s}{1+s+4 \\Delta^2/\\Gamma^2},\n", "$$\n", "\n", "which is shown in the plots as the black dashed lines.\n", "\n", "We start by generating the Hamiltonian. Here, we use an $F=0\\rightarrow F'=1$ transition as our model system, but we will consider coupling only two of these four states together using a circularly-polarized laser beam propogating along $\\hat{z}$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "Hg, Bgq = pylcp.hamiltonians.singleF(F=0, muB=0)\n", "He, Beq = pylcp.hamiltonians.singleF(F=1, muB=1)\n", "\n", "dijq = pylcp.hamiltonians.dqij_two_bare_hyperfine(0, 1)\n", "\n", "ham = pylcp.hamiltonian(Hg, He, Bgq, Beq, dijq)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Add in a constant, small magnetic field to establish a quantization axis along the $\\hat{x}$ axis:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "magField = lambda R: np.array([1e-5, 0.0, 0.0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We next run through a loop of both detuning and intensity, remaking the single laser every time. Note that it is $\\sigma^-$ polarized relative to *both* its $k$ vector and the quantization axis." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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fZjwzAmeXv/Cf3EVsPpSOxyofaiobGHdHP4d7IyU4BlGQBaGVHM4rYc2nO/go4884O7ni5uZO7IODHG4LQFmWKXrmGbauWEkfrZZXunTF09+fHh9/hEv//v/3fprwcNzCw/F59BGKnnmWp9LSmFN0lsKfNvHYbbcTsGwZTp07KfhMbkynngZmPDcCFzctVedrKak8zellh6ivbSL63iDUGrE0TWhZ4jdKEFrBnrWFZHyWz7urnsRb34U5U15lxpOjHK4YA1T++9/sWrmK+wsLONTQQKfQUAKXff+/ivEvqdzc6LbgPSbOns13PXuSZjKx9uRJip97DtlqbeP0N8fo68qtz4bTJdBIadVZPsx4gdSV6aR/uJemBsd6LoL9E2fIgtCCZFlmW+optqWdQKtxJmXEA4QFjWLK/KH4dtcrHe+G1R85SsHrb/B0cTGP+fgwatJEun/4ISpX1199nKRW0/m5Z9F07sR/XnsNd5Wami1bqPj8C3wefqiN0rcMV93Fzl5aVw1OGme+zH2FuoYaGuqaSZoTgou7k9IRhXZCnCELQguRZZmfvj9G2tINvLrsQUy1FxgZNp7pzw53yGJsq6+n+Omn+L6slK5OGmb26Yv/v/71m8X4l7xmzqRLfALFTU3cUXCG0++8Q92ePa2YunVoXTQkzg4mZVois+Jfo7G5jvOnTKx8Zze1pkal4wnthDhDFoQWYLPJbFh6mOxVm1iY/hzx4ffQq093kueGovN0zG5P5//xD+qPHuMuD0+mGYz4v/EGGh+fG/oekiTR9e9/o3bvHvzLSnm5uIi3nnqagJUrUOscq+GGWqMi5v5BuLg5sX9jEQcLtnF+XyG2Zhsp88Mc9ucs2A9xhiwIN8lmtZH75UF2rz/Joow/MWXkw9wa/wemPTnUYV+kLRs3cmTJ19xVcIYGWabHgw+iGzf2d30vtdFItzff5KWufuyoreWHgwc4/9rrLZy4bahUEuPv7EdYbA+8DV1Zt/e/fJv+KSve2ompvE7peIKDE2fIgnATrFYbOZ8dIH/zUfSunjx7yyIGBAeSOCcEZwfd9F5ubub8P//JG2WlhLi64jV4MJ2eePymvqdbeDiBc+bw1ptvYrJZqV6xAq8//gGXgQNbKHXbkSSJUdN64+SsRqN+h/fTnkaWrdisDzH1yTCMvm5KRxQclDhDFoTfydpsI+uT/aSnZvHK9/dTXVPBoPA+JM8LddhiDFC9ahU79u1na20ts3186fr6a0ha7U1/X59ZjzIieAhj3Nw5UldH6dvvtEBaZUiSxPDEAJLvHcvjKe/S3z8cS2UDP7y5i6rztUrHExyUKMiC8DtYm2xkfrKf9LRMPsv5G/dMfJ4hI/qR+FgwTs6O0Sryamz19ZQteJ+y5mae9PGl+y23XHN5042SNBp8n3iSkuYm/lhYwIl166jJy2uR762UsJgepDwwmsAug9h8OJ2vM97lh7d2UnmuRuloggMSBVkQbpC1yUbGJ/s4truYZT+/z33RfyYxMYGER4egcXLcYgxQ+c03VJeUEKXXM6NTJ3znzW3R76+bGEmfUaNIMRhYWFFO6ZtvIctyix6jrQ2J7MaEu/ozpOcoDhftYnH626x4axcXSkRRFm6MKMiCcAMunhnvI2/jTjQqJ16Y8SmJSfFMfmQIaifH/nOyVlVR+vEn/LHgDFtqavC8+26c/Pxa9BiSJNHpqaeY5e1DttnM/p07MWdltegxlDB4vD8pD49ifvJbnDi3j/+u+5RV7+wWZ8rCDXHsVxBBaEPWZhuZn+4nPT2Tt1fOp7T6LP2H+RP38OB20Uax/NNPSS06iwxEdOqEdys18HALC6NX/GTe9/enq5OG0nfeQW5qapVjtaWgMX6kPBzB3OR/MWpAPJaqOla8La4pC9fP8V9FBKENWK02sj87QEZ6Jl/mvsL9MX9h1MShxD44CLXa8f+MmisqOL/kaxaUl/O4jy+dHn4Yjadnqx3P94knGKHTc66pmYNHj1G9enWrHastDRzdlZSHIvAydCZ95xK+znj3YlEuFUVZ+G2O/0oiCK3MZrWR8/kBTuwuJXv3v7kv+s8kJE4m9oH2UYwBKr/7jrr6emYYPZjYsyde9/yxVY/nHBiIcdpU1tdYWFBexoWvFjv8teTLBo7uysQ/DGDC4KkcLtrJ1xnvsvLtXWKdsvCb2seriSC0EptNZu3iQ2zI3kKztYm5SW+SkBhP3EPtY5gawNbQwIWl/0YGHvb2xvsPd99Qe8zfy/v++5lh9GBrbS1HDxygZvPmVj9mWwka40fygxHMS3qTg4Xbydq8nFXv7sZSWa90NMGOtY9XFEFoBbJNZv3Sw2Sl/siCtKc5U3qYXoN9mdyOijGAKW0N286e5a6CM6DV4nHHHW1yXOfevek6MZIpBiPfVFZyYfHiNjluWxk0zp/kByKYn/wWw/tGU3HexKp386mpblA6mmCn2s+riiC0IFmW2fSfo2Sv3MBHmS9yx7jHiZw0gfhHBjv8bOpfkmWZC4sX81XlBW4xGvGYOrVVrx1fyWvmTB7w8uJ2Dw9qNm6i4cSJNjt2Wxg8oRvx94zA2cmVJeteZ1nWF6x6N586s9iQQvj/tZ9XFkFoIbIss2XFCfZtKGLTwVRuHTWbxLgpJMwKRqN17HXGV6rdsoWj+/ezrbaWGUYPvGbe06bHdx89mp5BQfhqNOytq+PC4iVtevy2EBrdg5FTAkkZ8RAb9q9gRc43rF6QT0Nds9LRBDsjCrIgXGFnxhmyl22huqaCO8c/SXLcrSQ9FuLQHbiupeKrr6i32XjSx5euEyNx7t27TY8vSRJe987kWEMDjxcXUb5yJc2VlW2aoS0Mi+9F/J2jmZv0Jlm7lrJl68+s+WAPTQ1WpaMJdkQUZEH4hT1rC8lYuoUFaU+zvyAPn+56kuaEoHXg3tTX0nDiBBfWb6C3szN3eHriNXOmIjkMSUmM6NYNb7WG7PJyqv7zH0VytLYRyQHETh/NM9MW0rvrEAqOlpG+aC/NTaIoCxeJgiwIlxzaXEz64q28v+YZIvpPJjFyBinzQnFxd1I6WquoXLqUpVWVvHz+HM59++I+erQiOVTOznjddRf3eHmyuPIClUv/jdzc/oZzJUlizK19GBsfhizL/POH2WRmZZD16QGsVpvS8QQ70P7e9gvC73BiVyk/fn2Y3Sc3MqTnKG6PeZiU+aG4GW5+lyN7ZKuvp2p1KsuqqvhL5y543vNHJElSLI/nnXcQt2gR7ioVTaWlWDZuQj9pomJ5WoskSUy4qz9NDVZmlDzGp9kvoXVywdlVQ9TMgUgq5X4GgvJEQRY6vMKDF0j9eAelF4qZMHgqrnonpj4Zht7LRelorcacnc320lKagdE+PhgTEhTNo/H2xjs6mvGZmZxobES/fHm7LMgAKpVE1L0DaWqw0tBcz2fZL9HVsydaNw3jbuur6BsjQVmiIAsd2rmT1axauIOP0/+Kh7svDyS8wJTH2/8m81X/XU6NzcZDXt4YExNQubsrHQmP6beSv3o1fyg4w4Z16+haVobG11fpWK1CrVYR99Agmhqa6erZE72rJ/m5p3F20zAyOVDpeIJCxDVkocOqKLKwasFOPs94BZC4O+pJkuaG4O2vUzpaq2osKKBm61Ym6HTc5uGB5/TpSkcCLi6B6t+rF4FaZ3Krq6letUrpSK1K46QmYVYwQUP6c8F8nleW3U/Wd3nsWVuodDRBIaIgCx2SqbyO1QvyOXbmIJZ6E48k/I0pc8PpEmBUOlqrq1r+A8uqq3m7rBRtn964hIQoHQkASa3GY9pUbjUaWV5dRdV/l7eb/tbXonXRkDw3lN79AhnZL5YP0p4lffFWjuSVKB1NUIBDF2RJkpIlScqTJKlSkqQcSZIGXcdjgiVJapQk6ce2yCjYn1pTI6vey+fYycMEdA7i8ZS3SHl0ON0HeCkdrdXJzc1Ur1jB8uoqBrm44HHrdLu6Zmm85VYmGwxMcNfRcOoUdTt3Kh2p1bnonEiZF8r06AcY3DOCz7JfInfxIU7vK1c6mtDGHLYgS5KUCPwAfA1EAOXARkmSrrmjuiRJGuArwNwWGQX701DXzOoF+fyQu5jPsl+iydrIxD8OJDCsfV6rvJJl0yYOFBRwtqmJiR6eGKekKB3pf9F286fT2DHM9PLCYrNR9d/lSkdqEzpPZ6bMD+Ou2LncOeFJkCH9470UH69SOprQhhy2IAMvActlWV4oy/IR4D4uPp+Hf+UxLwBaYE3rxxPsTXOTlfQP97Jm7X9Zt3cZsxNeZ/z0gQSNueZ7uHanavlyjjc2cruHB95RUWi87G9UwHjrrRypr2fK6VNUZmZitViUjtQmPDq7MWXeUHp27U3+yU18vOYvrH5/F+VnO8bzFxy0IEuSFAAMA1Zcvk2W5XpgPZB4jccMAV4E5gOiNU4HY7PayP7sAKcOlpC9+1tmxb9GzPRRDI3rqXS0NtNcUYFl/QYSDQbm+fjiMf1WpSNdlT46mgGdOuGmUvFTeTmmNelKR2ozvj30JMwOZkjASGrqTSzJ+herF+wWeyl3EA5ZkIHLr6Inr7i9AOh25Z1/MVT9sSzLa2/0YJIkHbjaB9C2jX+F30WWZTb8+wg7fzqAVuPCizM+JyZ5HKNv6Vg/PlNGJhuqqvisogJN5864jxmjdKSrUjk745GSwjSDkVSTCVNqqtKR2pR/P0+SZoXzaPwrnC47wsr1X7F6QT61JrFDVHvnqAW5y6XPV15gsQBX2zvuOcAdeL41Qwn2aevqk+Ss/pl//PAoRRUn6B3amYl/GGBXk5nagik1lRXV1TirJAxJiUhq+90sw5iSTILBgLdGTe2OHTSVdKxZx4GhviTcP5zHEt4gvM8kqkvrSPtgD4317a+lqPD/OGpjkMvTDw1X3G4Ezv3yBkmSBgN/AibKsvy7xn1kWb7q7O1LZ8lBv+d7Cm1j74+F5Hy/jQ/TnydlxIMMHxlO7EODUakd9b3o79NYUEDprl1sqrHwYufOGJOTlY70q1yGDKFH7948X3Cxj7hpzRq8H3xQ4VRtK2isH7XmEWxddZLlmz+kx7F+OLtpSJoTglrTsX5/OwpH/amevfS51xW39/zF1y6bD7gCayVJMkuSZAb+AIy79O+xrZpUUMyxHefZ9P0x/rt5IWODkkmOuo2E2cE4tbM9ja+Hac0attXWMtTVDf8B/XHu31/pSL9KkiSMSUlsra3hieIiqlPTlI6kiPDJPQme2I1hfaNY9vMH5OTksHbxIWRb+16f3VE56hnykUsfU4DlAJIkuQORwF+vuO+LwBtX3PZPwB+4GyhqzaCCMs4evsCaT3eCTcXMSS/g1clI8tz2u3PTr5FlmerUNKL0esa5u2NMSnaI4XpDUhL933+fjRYLxQcO4Hf0KC79+ikdq01JksTYGX2pszRRW/9nvlz7CnpXD9z0WsbM6OMQP0fh+jlkQZZlWZYk6TXgS0mSNgEbgZeB6ku3xQLfAnfLspwJlP7y8ZIkmQAvWZZPtHF0oQ2UFZpJXbibTzP+Ru8ug0kZN5Mp88PQeTorHU0RDYcOUXT0KFlmE3/w9MKQdNWFCHbHOTCALsHBjDpXQpbZTL+0Nbg82bEKMoCkkoiaOZA688VJXT4GP/asK8TNqO1QqwQ6AkcdskaW5SVcXHM8D/gZcAFGy7JcBdiABqBJuYSCEkzldaQuyGdx9j9pbG4gNvx2kh4LwbOL8psnKKU6NY10k4kdtXW4hoWh7fb/LUSwW4bkJJINBk43NmJKS2v3rTSvRa1REf/oEMaPmYhapeHLta+StXQ7h0WLzXbFYQsygCzLn8uyPESWZR9ZllNkWS64dHuuLMt+11riJMvyfbIst8+93TqwOnMjqxfks257KmfLj/No/MskzR5Kl8D235/6WmSrFdOaNaSZTCQZDBiSk5SOdEMMCQnEGYz8qXNnmoqLqdu9W+lIitG6XJzQ5d3ViNHNmw8zXiD9s52cOVChdDShhTh0QRaEy5oarKQt3EtFiYkRfaOZk/QvEh4Ip9cQH6WjKap2+w6OnS2ksKmR8QYDhsmTlY50Q5w6dcItYiTrLGaWV1VhSuuYk7suczNoSZkXwp0xj9HFoyefZP4PaYt2c/60SeloQjTfF1QAACAASURBVAsQBVlweFarjaxP95O5djUL0p5GpVITfcdQBo7uOC0xr8W0Jo3uTlq+7tETz/Hj7LJV5m8xJiXjLKn4svIC1WvSkZs69pUoo68bKXPDuDfueYJ7jcHWKLNm4R6qSmuVjibcJFGQBYcmyzIblh4hJ3st3258h6kjHyY4shvhk8VkF7mpCVNWNltqawjQajEmOdZw9WX62BgiPDyotlo5XHqemq3blI6kuE49DSTPDmNi8DTKTMWs3LiYVNHNy+GJgiw4tG2pp9iSs4/Psl/inonPERMfydjb+4nlIEBN3lYOlZbyp5ISVFotuomTlI70u6j1eozjxxOt0/OjxYI5K1PpSHahR5A3k2YOxFXrzpbD6axY97Xo5uXgHHLZkyAA7N9YxPY1pzC6eTM/+W2GjQwj+v4gVCpRjAFMmRlkms3E6PUYJoxHrXPcmeaGyXE8lZ2Nm0qFOTuHLn/9K5JTx1tTfqX+I7sQVz2c+qY3eGfVfIxu3rjqnEh4LBh1B+tG1x6In5jgkE7ml5Hx5XbeWTWfC5bzDBkyhIRZwWicOl4XrquRm5ow5eSSZTYzWa/HMDle6Ug3RTdxInpXVzbUWDhZVkZN3lalI9mNsJgeRE+N4JHJr1LfWEvBwQv8+PXhDrtEzJGJM2TB4ZQcryLt4118lPkXunj2onu3HiTNCemQXbiupSYvj6bqau7x8mSY0QNdZKTSkW6KWqfDffw4Ni1dyt66eoKzMtGNE11v4f9186qpbuTErgEcKtzB2XIP3D2cGTW1Y+1o5ujEGbLgUC6U1LDmw718lf06bs567ol7kpR5oei9XJSOZldMGZnU2mzc4eGJMXKCQw9XX2aIm0ycXk+W2YwpO6fDz7b+JUklEX3fQPz6elBVU8aHGX8iZ9lW9q2/srW/YM/EGbLgMGqqGkh9P5+G2mbGBSUT6BdE0uwwvP11SkezK3JjI6bcXG4/c5rXu/qREOdYa4+vRTdxIsONHpiLizlUWkq3vDx048YpHctuaJzUJMwaQn1NE1U15XyY/jzO2vdwM2rpHdZJ6XjCdRAFWXAIDXXNpL6/hxXrvsJb78fQPhOIe3Aw/v2utv11x1aTl8fB0lIsNhvBRqPDD1dfpta5Y5gwngWmavydnDBlZoqCfAVnNyeS54bQUPsAdY0WSivPkvP5QVzna/Hr66F0POE3iCFrwe5Zm2xkfLSP9B9/4Md9P9DDtx9jZ/SlT7h41381pswsssxm4vR6jA4+u/pKhsnxhLq4UtJ8cdKaGLb+/+k8XUieF8qdUXMJ7DKI/BM/k7ZwNxXFFqWjCb9BFGTBrsk2mbWLD5KTm83yzR8ya/KrxEwfScik7kpHs0tyYyPm3FzcVCqSDUb0DtYq87foIiORnZ15oLCQQ6Wl1OTlKR3JLnn76UiYFQySjZzd3/JNzrukLsjHUtmgdDThV4iCLNi1zT8c59iOUoxu3jwQ8z9EJY4TM0d/RU1eHjaTiYe9vQn18EDfToarL1Pr3DFOGE+sXk+m2YwpQzQJuRa/vh5MfiiYh+Nf5mjxbpav+5K0D/JpqBONQ+yVKMiC3crPLSBn+VYydi7B3zuQqKhJTLpnIJJo/HFNpuxsPqmoYFlVFe7jxqJybz/D1Zfp4yYTq9eTYzFjzhXD1r+m99BOxN8znNkJb3CwcBvFp8vJWLQXa5NN6WjCVYiCLNilY9vPk/n1Dj5Mfx6NWotPdx3xjwxBrRG/stciNzdjyV3LalM13Z2cMMTFKR2pVegiJzDMYCROr6e+upraHTuUjmTXgid2I2b6SJ5IeReNWsu2LTvJXXwQ2SYah9gb8eom2J2zRypZ89lOPsr4EwO7D2fapJkkzQlB6yoWBfya2h07OHL+PBesVoa1o9nVV1LrdBjHjmWejy9qLo4KCL8uYmogAyK6UlRxgndXP8na9I38/MNxpWMJVxAFWbAr5WctZCzaS0N9AwO7D+cPMfNJmReKu9FZ6Wh2z5ydzcH6euJ0eoxjRqPW65WO1Gr0sbHsr6/jroIzF4etbWII9tdIksTEPw5gzIQIbhs7l48yXyR3eR75uQVKRxN+QZxyCHbDfKGe1AW7ydmxnIj+cUwd/QDJc8Pw7NL+roO2NNlmw5yTS4rRSLLBgCE2VulIrUo/aSL93Nw409jIyaJiuu3ejVt4uNKx7Jpao2Lyw4OptzRRXVNBxs6v8TX642bU0m94F6XjCYgzZMFO1FuaSF2Qz/drP+GnQ2nYZCuxDw2mS6BR6WgOoS4/nzPFRXxaUYGk0aCb5JhbLV4vtYcHnhERROp05JjNmMWw9XXRumhIfCyYaVH3cPeEp6lrsLDm010UHr6gdDQBUZAFO9DcaGXNh3tZve4/5B3JYnb868TfF05AsI/S0RyGOSubTLOZYw0NuI0Yjsaz/Xcw08fGEq83UGW1YsrJEbsbXSd3ozMp88JwN7qSk/8dn2a8RNrC3ZQVmpWO1uGJgiwoyma1kfXZAUpOVFFUcYLHEt4g9vbhDBrnr3Q0hyHLMuacHHLMZmL1+nY/XH2ZPiqKCXo9T3fqRHNxCfX79ysdyWF4dHYj6bEQkkffS7Otka+y/0HqgnxM5XVKR+vQREEWFCPLMhu+O8r6nE1U1ZRxx7jHiUoZzfCkAKWjOZT6/QcoPHOG4w2NjNHp0EdHKx2pTWh8fXENH8rq6mpWVVeLYesb1DnAQNKjQ3lk8ssUlZ9g855cVi/Ip87cqHS0DksUZEEx29ecZu3qzSzK/BNny4/TK9iHCXf2Q5JE448bYc7OppNGw/JevfAaNgyNr6/SkdqMITYWJ0liWXUVpuxsMWx9g3oN8SHhgWE8nvIOoQHjKS26QNrCvTQ1WJWO1iGJgiwoYv/GIrK/28rCNc+TNPx+YiZNJvbBQajU4lfyRlwerv6ppobOGg2G2BilI7UpfUwM43XuHKqvp/jESRqOHlU6ksMZOLorkbcFIyPz1sq5ZK5dTeYn+7FaxVKytiZe/YQ2dzK/jI3fHmF/wVZG9Z9MyqTbSZwdgpNWrXQ0h9N4/DjFx4/zeHERVuQOM1x9mVPXrniHhhHh7s7mmhrM2TlKR3JI4ZN7EhLZnTvHP8m3G98hNzuX9V8fFiMObUysQxbaVPHxKtI+2kVJRQHjgpJx93AmeV4oLjonpaM5JFN2Nj9aLES4ueEdHIKTf8ebDGeIjeGf+fm4SRLmnBx8585ROpLDkSSJsbf3o9bciKX+eT7P/Tt+3oG4GbWMmtZH6XgdhjhDFtpMRZGF1A928XnW38nZ/S3ObhqS54ag93JROprDMufkkmMxE63Xo4/pWMPVl+mjo3FXqVhhqqb00CEaT59WOpJDUqkkou8LIi46nmdvWYTOxcj2jFPsWVuodLQOQxRkoU2YKupY/d5ulmS9haWumnuiniVhVjDe/jqlozmsxoICGg4fZorByCRdxy3I2l69cO7Xj3STifUWC+bcXKUjOSyNk5qEWUPoN6A356sKeWP5I2Qs2cbR7eeUjtYhiIIstLo6SyOpC/Zw/PRRCsuP8Wj8KyTNCsevr4fS0RyaOScXs9VKgl5Pp/79cA7suMvF9DExRF/aktGUI64j3wxnNyeS54bSO6AP/f1CWZTxIms+2UnBwQqlo7V7oiALraqpwUraB3s5dvQYfl4BPDNtIQn3DycwtOMszWkt5pwcXjxXwg/V1R2mGci16GNjiNLp2VJTQ8XufJrOiTO6m+Hu4cyUx8O4K3Y+PoaufJX7Ohkf7+f8aZPS0do1UZCFVmNttpH58T4y167m7VXzqGuwEDGlj+jC1QKazpdSsWsXP9fUME7n3mGHqy9z7tcPv8BAPvDvhhNgzl2rdCSH59HZjZQ5YdwX9ycSh82kucFK6vv5VJ6rUTpauyUKstAqZJvM2sWHyM7O4duN7/Bw3MsMj+3PsIReSkdrF8xrc/m5pob+zi749wrAecAApSMpSpIk9DHRjHBz42xTk+ja1UI6BxhImT2U7r592HI4g2+y32X1e/lYKhuUjtYuiYIstDhZlvnpv8c4nFfEsp8/4N6oPxEdH8m420UXrpZizsnBisxtHh7oY2LE/ytgiInhXHMTtxecoXLbNpoviB2MWkKPQd5E3TuQwT1HcahwO/9d+wWp7+dTX9OkdLR2R6xDFlrcrqwz/LxmHzoXD5679SMCB3ch5r4gVCpRNFpCc2Ultdu2M1lvAOjww9WXuQQH09O/Gz2LisizWOi1bh0e06crHatd6DeiC/GW4TQ2/4O3V87DU+eL1kVDyuOhoqFPCxJnyEKLOrCpiIxvtvKvHx7jSNEu/AN9iH90CGon8avWUizrfuRnk4lXzp+7uMFCaIjSkeyCpFKhj44mWq8n22zGJIatW1TIpO7E3jaSOYn/pJ9fKOdOVpP5sWix2ZLEq6TQYo7vLCXti20sTH+OYX2jiAgfR/LcELQuYiCmJZlzcsg0m/BWa9BFRyGpxJ/xZfrYGOL1Bga4OFOzJQ+rWezx25JGpgQSlTIaT10nvtv0LjlZOaz96hCyTbTYbAnilVJoEYUHL5DzxQFWbfmE3l2GcEfMLJLnheCq1yodrV2xWixU//QT6ywWvureo8Mvd7qS27BhBHbqRM8qLbbGRizr12NMTlY6VrshSRIT7upPfU0TQwpG8Xnu33HRuuHi7sS42/uKuQw3SRRk4aadO1XN6g930djQxC2jZ2Mw6pgyPwyDt6vS0dody/oNnKypoYtGQ39fX9yGD1c6kl2RNBdHDT757DOONTTwj+wcUZBbmEolEXv/IBrrmqltsLAo40VcnXW46JwYIfYyvymiIAs3paLIwur3dvFFxqt4G7pw6/hHSZkXipefu9LR2iVzdjZ9nZ1Z1rMX+uhoJI34E76SISaGId8s5cPyCl7cuBFbbS0qNzelY7UraicV8Y8OobGuGWcnF4xu3mxPO4WLu4bgid2VjuewxMUn4Xczldex6r3dLMl+iwuW88QP/yPxjwymS4BR6Wjtkq2uDtPGjbxdVkqDLKPvYHsfXy+3UaMY5O2Ns0pid2Ullp9+UjpSu6R10ZA0N4QJERd/D79c+yrpX23jyFbRJe33EgVZ+F1qqhtY9e5uNuxI5+T5g8xOeI3kR4bRI8hb6WjtluWnn9hTWUmG2YybTof76NFKR7JLKq0W/cSJTDUYLzUJEb2tW4urTkvyvFC8OhnRuxhZmP48aZ9s59TecqWjOSRRkIUbVl/TROqCfMpLqgjvM4n5SW+R+MAI+oR3Ujpau2bOziHbbCZap0M/cSIqrZgwdy362Bhm+/iQYjRiWb8eW2Oj0pHaLb2XC1MfH8rdcfPx8wpgUfqLpH24i6IjlUpHcziiIAs3pLG+mbQP9rAq5zsWpj+HSlIRc/dQgsb6KR2tXZMbGzGvW0euxUyMTo9ezK7+Vbpx45BcXHinrIyD5eXUbtmidKR2zaOzG1PmDeW+uOeI6B8Hsoo1H+7l/CmxGcWNEAVZuG7NTVbSF+1jTc5K0rZ/xR3jniB8ci+GxvZUOlq7V5OXh1xTw0f+3Qjz9EQ3bqzSkeyaytUV3bhx1NisZIomIW3Ct4eelHnhjBuSSLmpmKVr32HVezupKLIoHc1hiIIsXBer1UbWpwfYtXUv3/+0gFnxrxIzbQwRUwOVjtYhmLKz2VNXh4dajWH8ODFr+DroY2OJ0evJtZixrF2H3NysdKR2z6+PB5MfHYKH3oeCsqN8lfUvVr27m6rSWqWjOQRRkIXfZLPJrP3qEMd2FdPZozsvTP+UmOQJjBebRbQJubkZy9p1vHiuhCMNDWK4+jrpJkYyzGCkymrlVGkptdu3Kx2pQ+g5yJvkR4YxO+E1zpQeZmn2Ala/m4/5Qr3S0eyeKMjCr5JtMuuXHiY77Ude/s+91DXWMHTMQKLuGYgkNotoE7Xbt3Pk3DkuWK2MMBrRRUYqHckhqHU6jGPGkB4QSA+tFlNWltKROow+4Z1IemgEcxL/SQ/f/pgv1LP6vXxqTWJy3a8RBVm4psvbKGav2shHmS8yNeJh+gZ3I/bBQajU4lenrZiyssi6NLvaOHYsar1e6UgOQx8Xh5MksayqCnNOLrLVqnSkDmPgaD8S7h3JsD6TOFS4gx9ylrD6vd1i28ZfIdr8CNe0dfVJdmSf4OPMvzAt4hESY6eQMCsYjZPYbq2tyFYr5pxchrm5YlTp0MfFKR3JoeijJqFxcuKtslLCXV3x37ET95EjlI7VYYRM6k5Tg5WyJUV8vf6fOKm1qDUqpjwehtZVlJ8rif8R4ap2ZJxmS+pRtBpnnpzyHv0H9SFxTghOzqIYt6XaHTsxl5UR7uqGRqtFP2mi0pEcitpoxGP0aKLOniXbYiY8K0sU5DY2LL4XTQ1Wmq3/5L3Up3B2ckXtpCJ5bqh4PbmCQ487SpKULElSniRJlZIk5UiSNOga94u/9PWSS/dNlySpX1vndRT5uQVkfLOFV79/gKKKk/TpH0jKvFCcxTvaNmfOymJJ5QVeLz2P+6gI1EbRlvRGGeJiidXryTKbMeVki2FrBURMCST21rE8lvA6XvrOlByvJn3RXpobxc/ilxy2IEuSlAj8AHwNRADlwEZJkq7WoaIHsBoYB8QA/kCGJEmi1dEV9m84y5rFeSxIe5qR/WIZFDSYlPmhuOiclI7W4cg2G6acbLLMZia46zCI4erfRRcVxSiDnqd9O9FcWkbd7t1KR+pwJEli3Iy+xE2dQJ+uwazfv4L0zDQyP9mPtdmmdDy74cinPC8By2VZXgggSdJ9QAnw8KWv/V+yLH/8y39LkvQysAwIAvLbIKtDOLS5mPX/PsJXa18lLHA8t8c9xJTHQ3E3OisdrUOq27WLE0XFlDQ1EWEwoI+KUjqSQ9J4euIZMYphP/1EYVMTXlnZuA0bpnSsDkdSSUy4ewDNTTaOF/fm46y/oFE5oVJLxD08GLWYKOqYBVmSpABgGPDm5dtkWa6XJGk9kMgVBfkqDJc+i2arlxzZeo6ML3ajVbtwb9SL+Pv7MfWJoeg8XZSO1mGZsrKptlq518sLz1GjUHt4KB3JYeknx5GWncXC8nJWZmXR+YXnkVSiALQ1lUoiauZArM02mm1NfJ7zdzQaLSq1itgHgjr86g2HLMjA5V6NJ6+4vYCLw9fXJEnSaOBvwJeyLJ+5noNJknTgGl/qfT2Pt3fHdpwn9eOtvJf6NHFhdzEmNIapTwzF4OOqdLQOS7bZMGdnE+LqSoirK/o40QzkZuijoxmj0/NcSQmnzp7FP38PbkPDlI7VIanUKmLuH4S1WUZGxlvfhRO7SslVS0TfF4SqA/c3cNS3I10ufa664nYL4Hm1B0iS9JwkSXXAz8ABYF7rxXMcJ3aVsnrRNj5Ie47uPn2JCJ7ElCfC8OgsWjMqqW7PHk4XFvJQYSGySoU+Rux9fDM0Xl54REQQ6a4j22zGnJWpdKQOTa1RMfmhwcTFxeKt78Kynz8gM3UtPy45hGyTlY6nGEctyJc32zRccbsRuNbu2B8BIcA0wBvYKUmSz/UcTJblQVf7AE78jux242R+GdmfHWD5zx/S2bMH98U/x7QnwvHq6q50tA7PlJFBltmMp1qN+4gRaDyv+j5TuAGGyXHc7uGBv9YJU2YWsk1MJlKS2klF/CND6DbAkz5dg/k4889krvqRH7853GGLsqMOWZ+99LkXsPMXt/f8xdf+F1mWq4Fq4Oila82lwBx++3pzu3Qyv4xVC7cjySqmjZqF0ahn6hND8fbXKR2tw5NtNsyZWWSYTTzm44MhPl7pSO2CPjqacJ0ObDYazp2jbvdu3MLDlY7VoWm0ahJmByPbZGw2K4sy/4ST5k0kCSLvHtDh2vM6akE+culjCrAcQJIkdyAS+Ot1PL4OaAA65LKnU3vLWfXhdhamPceQnqNJHH03KfND8e0uWjLag7qdOykvKcFsszFGb0AfK4arW4LGxwe3kSN4dXUq7ioVz6VniIJsB5wuFWWbTcbVWYe3visHfy4BSSLyrv4dqig75JC1LMsy8BpwtyRJD0mS1B/4kotnwF9KkhQrSVKFJEmTASRJelaSpPGSJPlJkhQGfHvpW32tyBNQ0Ol95az6YBsfpr2A0d2HuJG3kzwvlE49rxz9F5RiysjAQ60mMyAQzzFjxHB1CzLExzPU1ZUMswlTdpZoEmIntC4akuaEEDUxGq3GmY8yXiRrxXo2fHukQw1fO2RBBpBleQkX1xzP4+JELRdgtCzLVYCNi2fATZIkOQN9gM+5eM13NSADY2VZPqREdqWc2ltOxkf7yNn1PXpXTx5K+DPTHh9G516iGNsLubkZU1Y275SVUWW1iuHqFqaPiWGUwUBJUxPHi4qo3bHztx8ktInLRdmvjxdDe0eyMP15Mn/oWEXZUYesAZBl+XMuFtorb88Fftmx6+E2C2WnTu0pY+XC7dTX1xIbdidaFw1TnxhG5wBRjO1J7fbtHC0u5vuqSuZ07Yo+WjQDaUkaT088x4xhxvlzFDY2YcpIF72t7YjWRUPy3BAunjPBB+nP4eq8EFmmQwxfO3RBFq7PxQlc21iY9jwBnYO4LXI2yfND6RIg+iLbG1N6BhlmE7F6PZ5jxoje1a3AEB/PU5s2AWDOzqHLn/+MpBEvhfZC66oheW4oIOFj8MNL34X9m84iyzIT2/lEL4cdshauz4ldpaz6YBsfpD2Ph7svt054hJT5YaIY2yG5qQlz9sXe1ZP1BgwJYri6Neijo5CcnPj7+XMcKSmhZutWpSMJV9C6akieF8KYMaOxWpv5x/JHyVjxI+uWHMLWjoevRUFux45uP0fWZwfYfmwdXrrOPJT0Z255UgxT26uavDys1dV80q07Izw80Ine1a1CbTDgPnYsNpmLk7syMpSOJFyF1kVD0twQegzwJSb0Dj5Mf570lWvJ/fIgNmv7XEMuxmnaqcN5JaR9so0KcymjByQQOTSZqY8PFbOp7ZgpPYNttTX0dNJinDAetU6sCW8thoR44tek8bdz55mXnUPXv/4VSdshV0HatcsTvSRJQq1S81Hmi/gYvkC2yUTfH9TuNqRoX89GAODgz8Ws+iiP91Y/zbaj2bjqtdzyVLgoxnbM1tCAKSeHv5w7R2FTk5hd3cp0Eycx3MOTetnG6fJyLJs3Kx1JuIbLRTk5YSrP3rIIg5sX+7ecJvvTA1ib2teZsijI7czeH8+y6uPNvJf6FAGdg7gzZg5TnwjDp5to+mHPLBs3sqesjEZZJtzLC31kpNKR2jW1zh1jZCTpAYH01Goxpa1ROpLwK5yc1STODmZoxCDqGmt4+T/3kpaaTvpH+2hubD9rycWQdTuyK+sMW1ac4EzZEYK6DeeuuDlMe3Ionl1Eb2p7Z0pNY43ZRILegDEqCpW7+Jm1NkNSIuWZmXxcUc7Dubl0rakR/+92TKNVEz9rCKpPJP5Y+hxf5L5Ms7URa7OVhFnBaF0cv5zd9DOQJMkTMMuy3NwCeYTfQZZltqedIuPbLRRVnCAkYCyjwiKZ8ngYHp3Erk32zmo2Y1m/nsl6PT5qDYbkJKUjdQi6CRNwMRj44fQphrq64b/uR4zi/96uaZzUTH5kCGonFRq1E1/mvkJgl8FYF8gkzQ3B2dWxi3JLDFmXc3EHJUEBsiyzeflx0pZu4t3VT1BaXYjB15VpTw0VxdhBmHNyKa2tZYCzC706dUI3ZozSkToElbMzhrhYkgwG0kzVVKelKh1JuA5qjYrYBwaRODWWv96xGJ2Lkfyde1n1zm7qLI1Kx7spLVGQ2+8qbTtns8msX3qEtP+s593VTxAVMoPbJj/ALU8NxeDtqnQ84TqZ0lJ5p6yUJZUX0MdPRnJyUjpSh2FMTiZRbyDLbKZy4yaaL1xQOpJwHVRqFVEzBxI2qTe1DWYWpD3NsvQlrHhzF5bKBqXj/W6OfX7fgVmtNtZ+eZBjO0qRbVamjHyIpOhbSZkXiqteLN9wFE2lpVRs3kKuxcLynr0wJokh07bkNnw4/bp14wtZxslmw5SZiddddykdS7gOkuriblBOWjXzat/igzXPUt9YS3PT/Ux5fChGX8c7KRGzrB1Qc6OVzI/2kbYqi8xdS+nu249pCbcx9YkwUYwdjDkjg/VmE320zgT26oVrWJjSkToUSa3GkJhIgFbLjro6MdvawUiSxJjpfUj+4wSemPIuh8/uoKSolBVv7qSi2KJ0vBsmCrKDaahrJvX9PaxavYrPsl+iu08fug/0JHleKM5uYqjT0VSnrUGvUnO/lxeGxEQklfiTbGuGpCTMNiuPni2kbPt2Gs8WKR1JuAGSJDEiKYCU+8YyP/lt3Jz1rN2WyvJ/befcqWql492QlhqyniBJksuNPECW5Q63F/HNqjU1kvp+Pms3ZrJ0w5s8EvcyMfGTiHtwMGon8ULuaBpPn6Zm715Gu7khSZKYXa0Ql0FBdOvbj+CSEnItFgLWrMHnkQ6/QZzDCY3ugdZVQ+YXu/jpYCr/h737jo6qWvs4/t3pySSZSe+V3lvoHQGl96YoNsCCoojtXnvXq4iIoiKKKAqCdBDpTXpHIJRQ0ntmJj2TzH7/CNzl5UWlJDmZZH/WmjVrDTPn/LI082Sfs/ezT8bvw2J5icGPtyaskbfW8W5IRRXkR688boSgfG8tVZBvgjmrkNWzjpGdkkukfyOeHPghvQd3pec9DbCrYe3jagvT6jUsM5n4o6iI97p1w6V+fa0j1UpCCDwHDmDg0SOsMZsYvXoVPpMmIoSar2prGncOxsnFAWH/IV/9+gqzV76IxfI6AyfFULeNv9bx/lFFFOTXubp5pVIpspLyWPXJERZv+pKC4lzGdJ1K9yEt6TSirvrSsFHSasW0ciUrzSbGGAxqdKwx/aBB9J35CY4ISs7HUfTHSVybNdU6lnIL6rbxZ+RTHXB0fJc1e76j1FLGb1//QVF+A5p2C9E63t+qiIL8HyllQQUcB7o7fwAAIABJREFUR7mO5PNGVs8+zILfZnAh7Q8e7/8+7YdE0+auCFWMbVjhoUPEXbjA2eJienvq0Q8erHWkWs0pPBz/tm0ZdOgQmaWleK1YoQqyDQtr7M3IZ9rhMtuZPHMB32/5gJzc+ykwt6ftgMhq+91ZEdc6U4UQnwshWlTAsZQ/uXg8k1WfHGX9vp9JzbnEtCEzGTa5CzH9qu//UMqNMa5YQYLFwliDAd/OnXEMCNA6Uq2nHzqEvQUFPJgQj2nNGmSJbTeZqO0Co/UMm94avY873u7+zFg5ldXfb2PHorPVdk/lihghvwxMBCYLIQ4CXwCLpJSFFXDsWuvUrmTWfXMQS2kJ3ZsMpWfzoQx8pA3Rrfy0jqbcJmthIbnrf6OzTkdnnQ790KFaR1IAz379aPfW2xhTkjmRlkbwjh149O6tdSzlNvgEuzPy+RicXR1w32Rg5qqnsbf7lEJzCb0fbIyDo73WEf/HbY+QpZSfSCmbAt2AWGA2kCKE+FQI0ex2j1/bSCnZv+Yiy77YyYyVT7E7dh06d1dGPNNeFeMaInfTJg5kZPBWWip2Oh0eve/QOpIC2Ht44NW7N4M89awwmTCuWKF1JKUCeHi7MGx6a0YPuo+JfV/HxyOQ2ANJrPrkKEX5Fq3j/Y8Km54rpfxdSjkBCKZ81NwdOCqE2C2EuO9ml0XVRtYyK9sWnmHVgq18tOIJWkR2ZliPBxg2vTUh9b20jqdUENPyFSw3mzDY2+PR7y7sXG2vo1BNpR82lOF6PUGODuRt30FpTo7WkZQK4OruxJCnWtGrTw8Qgo9WPsHS1T+y7MPD5GYXaR3vvyp8vYyU0iSl/FRK2RzoApwBPgeShRCfCCEaV/Q5a4KSolLWzTnBqV3JHL/0O3e2vod7Bz3OyOdj1F7GNYglNZXM339nQ24uQzz1GNTl6mpF17EjDUJDedDbB2tJiercVYM4Opdv39ikcwj39nieXw8t4IfVn7P0vQNkJuZqHQ+o5E5dUso9UsoH+N9R8wkhxC4hRKfKPLctyTcVs2LGEZav/IWEjLPc2foeRg0cz/Bn26hNImoY06rVnCgsoImLC9HR0bi2bq11pApRYClAyuo5UeZmCAcHPAcNYnNuLtOSkzGpy9Y1ir29HT3vbciQe3vxzNBPOXphB0djD7Dsw8PEn8rSOl7VtM6UUpqllJ9JKVsCnSi/19yxKs5d3WWn5LP0vYP8tOprft71KWXWMqJb+jHkqZa46FQrzJpESolpxQrauen4OjQM/ZAhNt8q01Jm4Y09b9Dh+w6MXTuWBHOC1pFum37oEFq5urIzP4/kY8coOntW60hKBRJC0H5wNMMmd+X5UV9QP7glZy4dZ8mMPZz6PVnTbFX2bSCECAOQUu6TUj4spfyoqs5dXSWfy2HZfw7x3dqP+f30Wp4ZOovB4/pw56SmODhVr9l/yu0rPHqUy2fOMDszA3sh0A8donWk22IqNjF502S+XfYt5986z8n0k9yz7h6Oph/VOtptcalfn+Dmzemk07E214xp2XKtIymVoEnXEIZMaYODsz37zm7g4+VTWT13H/tWX9Dsak9V/nm+VQjxP9OEhRA6IUSdKsxQrWQm5lFcUErD0DZMGzaLYQ/3oOvo+tjZqTXGNZFx6VKWm0wkWyy4tWuHU1iY1pFuWUJuAuPXjee3Rb+RMCcB/2H+WIutnF5wmgdWP8D6i+u1jnhb9COGM0pvIKO0FNPKlVjVmuQaKbKZL8OmteKBAc/Ru+UY3JzcSTlv0mydclUWZDfAeM1rEUCt/fOzec8wWtwRRvM6HRn1ZBda3GG7X9DK3yvLyyNn7Tp+MRkZoTdgGDVS60i3LCUvhfHrxvPHvj/IWJVB1AtR9L6zN46OjhSnFnPmnTM8vfppVset1jrqLdMPHEh3Hx+m+flTlpND3pYtWkdSKol/hCejno+hb9fB+IZ60u+RZthrtD9AVZ71CHDnn1+QUp4CanUV6jyiLqNejKFO6+rf+Fy5deZ16zicnY2LnR0xAQF49OmjdaRbNu+PeWQVZKFrqKPum3WZNnAac/vMZd7AeTSb3gzXKFfiP43n40MfY7FWr3WeN8per8fzrjvZkZfHRxnpGJcs1TqSUok8fV0Z/mwbBj3RAmfXitpz6eZVZUF+C/haCPHfoiyEuIP/P2quVYSdwCfYXesYSiUzLv2FNq6ufB8WjmHwYOxcbHNZfm5JLivPrSTu1ThK0kp4ttuzPNryUYQQxATG8MOAHwi7JwxDJwPp+elsibfdkaVh5EiinJxYZDSSvnOn2ie5hnPROeLupe3vZZUVZCnlHmAq8IMQIkEIcQj4Faj1k7uUmq3ozBmSDx9mhdmEt4MDhtGjtI50y1bFrSLjcAayTOIb5svYhmP/59+j9FHcVfcuvHt5U2osZVHsIo2S3j7XmBjq1KtHMxcX1pvNmJYt0zqSUsNV6YVyKeVioB7wOOX7IfeQUs6uygyKUtWMS39hpdnE9rx8XJo1w6VBA60j3RIpJYvPLCZrcxbevbwZXm84rg7/f538uIbjKDWXcu5f59gbt5ezOba5bEgIgWHUSEbqDRwqLMS4bBmyrEzrWEoNVpXLnuwApJRGKeUqKeVMKeXuqjq/omjBWlyMceVKfjGZGGHQYxhpu5O59qXuIy4rDgR4dfZiTIMx131fc9/mNItshntTd3J25LA4dnEVJ604+qFD6eflxTtBQZSmppL/++9aR1JqsKocIW8TQoQCCCH0QohpQoiHhdpHUKnBcjds5FBqKoVWK519fPEc0F/rSLdsUewi7BzsiJwWSbe63QjzvP58TCEE4xqOw/sOb7K3ZLPq/CpyS6pHa8Kb5eDri2evXhwuKOD7nGyMS5ZoHUmpwaqyIDejfBcoASwFHgReAj6swgyKUqWMixfT2MWFOaGhePXvj727bU7gS8lLYfP5zcS9EUdZYRnjGo772/ffFXUXQc2D8OrqRX5+PqviVlVR0opnGDUSD3t7Ps/MJGPTZixp6VpHUmqoqizIx4APgDmAP9AG6AzcXYUZFKXKFJ09S/K+ffxRVER9ZxebXnu85OwSsvdkY+dsR4RfBJ2DO//t+10dXBlebzj+Q8qX8y2KXWSzva51nTvTOCqKus7OrDca1ShZqTRVWZAfpbx/dWNguJSyGCgEbHP9h6L8A+OiRfxiMvJ9TjbOjRvh2rKl1pFuSZm1jGXnlpG9JRvvXt6MaTAGe7t/bu06psEYKIVzz5/jzNkzHEw7WAVpK56wt8cwZgzjDF6sM5sx/vwz0mKb66uV6q1CCrIQIlAI8YEQYuWV5/rXvkdKeVpK2UlK2U1KGXfl5QDgh4rIoCjVSVlePjnLV/Cz0chYgxfed9+NrU6X+CPrD9Kz0sEK3q29GVr3xraMDPMMo2NYR9ybuWM+bGZ7wvZKTlp5DCNH0Nfbm09DQihNTyd3y1atIyk10G0XZCFEAHAUmA4MuvJ8XAhxz3Xe6yuEaCOEGA7/LdJP3G4GRaluzKtXsTMzAwch6BQQgOeAAVpHumU7E3dir7On7pt1aR3SGoOL4YY/2yOsBx4tPMg9lsvOpJ2VmLJyOfj44N2vH6mlpfxsNJLz009aR1JqoIoYIb8KeAITgXCgB7ADmCeEaCSEuFsIsV4IkQukAfsBdRNGqbGklOT8+BP1nZx5OzAIrxHDsXO13X2tdyTuIH1lOsWpxXQN6XpTn+0a2hX3Ju44eDgQlxNHYm5iJaWsfF7jxuEoBB+kp5Py++8Ux8X984cU5SZUREHuAcyVUs6TUiZKKXdIKfsCe4D5lDcA6QKcpLwQfww8UwHnVZRqqfDQIZJPn8YKtHR1xTBm7D9+prrKKMjgZMpJMtZmYO9qT7fQbjf1+TCPMOoG1yV8SjjCTtj0KNm1VUuimjWjg86NFSYTOYtsd321Uj1VREGOAA5c5/V3gLaUj5ZDpZQdpJRjpZTTpZQzK+C8ilIt5fz4E9/lZDMnKxNdp444R0dpHemW7UraRd7pPFxCXAgPDidaH33Tx+gW0o28k3mkLk1lR+KOSkhZNYQQeI0bxziDF0tMRozLlmEtKNA6llKDVERBNlO+teK1/rjyPFNKWas3kFBqD0t6Opm//cYyk4lxBi8M4/5+vW51tzNpJ3nH83Bv7k7X0K63NDGtW2g3HAwO5OzIYX/yfgpLCyshadXQDxxAZ39/vg4NQ+bnY1plu1tMKtVPRRTkZGCaEOJTIcREIUQHIYQ7kH/l37Mr4ByKYhNyfvqJtdlZRDg60SwyEo+ePbWOdMssZRZ2J+8mYEQAPn18bvpy9VWt/FvhHeGNnaMdxjgjB1Kvd0HNNtjpdHgNG4arnR3LTUayv//eZtdXK9VPRRTk7YAf5RtGfAn8TvmWiscBCYwSQvQUQtz41ExFsUHWoiKMixZTz9mZ6f5+eN1zN8JBu71Vb9eR9CMY042UpJeg0+toG9j2lo7jaO9I55DOeLTwoOBMgU1ftgbwHn8P9kLwXno6Z0+fJn/XLq0jKTXEbRdkKeU0KaUPEAWMoPze8XrACRDAFGATkCWEOC+EWCyEePZ2z6so1Y1p1SpSMtKp5+RMa28fvEbZ7jaLUH652rjHSNamLNoGtr3uzk43qmtIVwLHBuJzlw87E3fa9KjSKTKSwDvuYJhez/c52WTP/07rSEoNUWGduqSUl6WUy6WUL0spB0opg4FgYADwCrDiyvlGAe9V1HkVpTqQUpK9YAGvp6bxs8mIfugQ7A22fVFoR+IOco/l4tHC46aXO12rS0gX7JzsMO4yEp8SzwXThQpKqQ3vCRMYb/BildlMyo4dFJ87p3UkpQao1NaZUspUKeWvUsq3pZQjpJTRgA/QpzLPqyhVLf/33Zw9dZoDhQUM9dTjfe99Wke6LYm5iZxLPkfhhULcm5RP6Lodfm5+NPJuhGm/idzjuTZ/2dqtfTvqNGvGj+EReNjZkb3ge60jKTVAVfayBkBKmSOl3FLV51WUypT93Xf8kJPNML2eoF69bHqpE5Qvd5JSEjQ+iLrBdQnzuP5WizejW2i3/3btsvWCLITAe8IE6jg5sSbXTObKlZTm5GgdS7FxVV6QFaWmKY6LI3/nTpq7uHKvwQvv+ydoHem27U3Zi52LHd7dvekS0qVCjtklpAvuTd3JP5XPkbQjNr38CcBz4AAcfH1ZkJ3DhsxMjIsWaR1JsXGqICvKbcqe/x0ZpaUM8vSkTrNmuHXooHWk22KVVg6mHeT8S+cpSiiiQ1DF/DxNfJtgCDEQMjGE0rJSjqYfrZDjasXOyQnvu8dxn7cX3+Vkk7VwIdbiYq1jKTbMpguyEGKQEGKvECJHCLFRCNHkL97XXgixTAgR/6f3NqvqvErNY0lPJ2PZMkZdvsTJ4iK877vPZnd1uupszlkykjMoNZbiFuxGa//WFXJcRztH2gS2waOpB2V5ZTa9Hvkqr7Fj6efjS0ZpKfviEzCtXKl1JMWG2WxBFkIMAJZR3iu7A5AJ7BBCBF/n7eMo39TiTqAb5eujtwkhvKsorlJDZX/3HauysghxcKRFeASegwZqHem27U/ZT35sPm713WgS0AR3J/cKO3a7wHYY9xhJ+iaJ/an7K+y4WnHw8cF3xHDmhITSzMWFrHnzkGVlWsdSbJTNFmTgNeAXKeVnUsozwAOU/zyTrn2jlPIpKeV7V7Z7PAE8AngDN7axq6JcR5nJRNaPPzEvO5uJPj74PPAAdk5OWse6bQdSD2AttOLZ0vOWm4H8lXaB7dA11JF/Np8/0v6gwGL7vaB9HnqIBm5unCsu5uy5c+Ru2KB1JMVG2WRBFkJEATHA8quvSSmLgG2Ur3v+J5lXnj0qPJxSa+T8tIjC/HyG6/X0CA7GYOONQADKrGUcSjuET28fvHt50y6wXYUev6F3Q3yCfbB3syfvch6H0w9X6PG14BQWhme/fuzIz2d2ZiaZX8216cYninZssiBTvsMUwLXdBeKB0Bv4fOcrz0du5GRCiJPXewB1biyuUtNYCwvJ+u478q1WHvbxwXf8eOzddVrHum2x2bFkpWSRsigFB+FAK/9WFXp8ezt72gS0wfsOb6yl1hpx2RrAZ+LD3OPlxc78fM4eO0b+rt+1jqTYIFstyIFXnq/dRSoP8Pq7Dwoh7IG3gANSStteDKloxrhsGbsSE5kQHw/OznjdO17rSBVif+p+8k/lU5JaQlPfprg5Xm8jt9vTNrAtfv390NXTcSDF9id2Abg0bEhIr56M0Ov5NjubrLlztY6k2CBb7Xx/9ZKz5zWv64HUf/jsXMr7bt9w6yEp5V/N3j4JNL7R4yg1gywtJfubb/k6O4t7vbzwGj0aB6+//TvQZuxP3U/e6Tx0jW59M4l/0i6oHdZiK5dnXkZMF+SW5OLhZPt3j3wnTuShzVsollYK9u+n8OhRXFu21DqWYkNsdYSceOU58prXI/70b/+PEOIDymdcD5ZSnqycaEpNZ1q1mkPnz3OuuJhhPj74PHC/1pEqhMVq4WDqQfJj89E11NEuqGLvH19V36s+Xp5eWLIt5F/M53Ca7d9HBnCLiSGsXTvchB3b8/LImDNH60iKjbHVgnzmymPI1ReEEDqgB/DL9T4ghJgOTAPGSSnVfmnKLZEWC5lz5uBiJ3g5IICAIUNwDL7eSjvbczLzJEVlRUT/OxqPCA9a+lXO6M5O2BETEFM+2zo2v8bcRwbwnTwJs9XKsynJxG/eQuHx41pHUmyITRZkWT6F8R3gHiHERCFEA+BbwAR8K4ToK4TIEkLcBSCEeBR4H5gKbBVC6K88bH8WjlKlTKtWkXTxApGOTvQ1eOH76CNaR6owB1IPUJRUBBJaBLTAxcGl0s7VNrAtukY6CuIKakSDkKt03brRICaG3u7ufJOdTcbs2VpHUmyITRZkACnlAsrXHD8J/A64AJ2klEbAChQDliuNQj6j/GedTflEsKuPNRpEV2xU+ej4C15KSWWJyYR+yBCcwsO1jlVh9qfuJ2NVBrnHcit8udO12gW2wzPGk/AnwonNjsVUbKrU81UVIQR+Ux5nso8vS0xGErdspfDYMa1jKTbCZgsygJRynpSymZTSV0o5WEoZf+X1TVLKYCnlZillspTSTkoprvPoqfXPoNgO08qVHDh3jtPFRQzz8alRo2NLmYUjaUfK7x9X4oSuq+oa6uLr7kveyTyKUos4mHawUs9XlXRdu9KgbQwLwyMw2NuTMfszrSMpNsKmC7KiVBVZUkLmnC/4LDOTh7x9CBo+DKew29+SsLo4kXkCc6IZaZV4hnnSwq9FpZ5PCEFMQAy5R3Ix7TNxMLXmFOTyUfIU6jk7szbXzKWtWyk8atsbaShVQxVkRbkBxhUrKElM5C4PD8b4+uL7SM0ZHUP5/WPhKAgcHUgr/1Y42Vd+C9D/ttGMza9R95EBdF264NqiBXsLCvgmO0uNkpUbogqyovwDa3ExmXO+4HRxMSMMBoJGDMcp9EYawtmOA2kHcPR1xKurFzGBMVVyzraBbdE1KJ/YFZtec+4jQ/ko2XfKFB7x9mGpycTFbVspOFCz/uhQKp4qyIryD3IW/siO8+eZkpRIib09PpNr1ui4pKyEI2lHOPvcWUqySir9/vFVUfooAgICCH0oFClljbpsDaDr0pl6HTow0MOTb7OzSf/wI9XjWvlbqiAryt8oM5tJ/+ILZmSkM8XXl4B77sYpNETrWBXqROYJzAlmrMVWPPw8aOZbNVuFCyFoG9gWz3aeyFLJgbSaNYIUQuD/zDSe8vPjSV8/Co8dI3fTJq1jKdWYKsiK8jey5n7NusRESqRkWFBwjbt3DOX3j69252oZ0LJK7h9f1TawLbmHc4n/NL7G3UcGcGvThpA+fTCWlTE3K4uMGR8jS0u1jqVUU6ogK8pfsKSlkb1gAW3d3HgvKBj/iQ/j4O2tdawKdyD1AKXmUtybuNM2oGouV18VExiDWz238vvIabHkFOVU6fmrgv/TT+Hh4MD8nGwOnDqFcfnyf/6QUiupgqwofyFz9mfsy8kGoFloKN4TJmicqOIVlxVzLOMYAcMC8O7uXWX3j6+K8owiMCAQJz8nCi8UcijtUJWevyo416tHyIgRPOLjw4yMdDJmfYq1sFDrWEo1pAqyolxHcVwcST//zDPJySSUlOD3+GPYuVX8VoRaO5FxAnOymYy1GbjYu1TZ/eOrhBC0DWiLoZMBa7G1Rl62BvB7Ygpj/fxJKy0lNjGR7O8WaB1JqYZUQVaUa0gpSXv3PeZlZdLC1ZX2jRpiGDlS61iV4kDqAfJO5FF0uYiW/i1xtHes8gwxgTH4DfDDo4VHjZvYdZVjUBABE+5jZWQU9ZydyfrqKyzp6VrHUqoZVZAV5Rp527cTv20bP+Tk8KyfP/7TpyMcq75QVYUDaQeqrF3mX2kX2A5ZKrn8yWXOpJ0huyhbkxyVzXfSJNy8vfnFZGRRcjIZH8/UOpJSzaiCrCh/IktKSH/3PXwcHPglIpJG3brh0bu31rEqRXFZMUdTj5J/5sr+x5W8ocRfifCMwN/Dn5KMEgriCmrkfWQAe70ev6emUtfJmZmZGVxeupTCEye0jqVUI6ogK8qfZP+wkD2nT7PGbCLMxYWAF19ECKF1rEpxPOM4JbKEyOmR6EP1NPFpokkOIQQxgTE1to3mnxlGjqRdixZ01+mYnZlB2ltvq2Yhyn+pgqwoV5RmZpL22We8lZ5GsZQYxozGpUF9rWNVmgOpByhJK8HRy5FW/q00uX981dW+1gVnatb+yNcSDg4E/OtFnvbz43KJBfPRo5jXqF1glXKqICvKFekzZ7IkKQkHBCNCw/B78kmtI1WqfSn7SP05FfMhs2b3j69qG9gWj+YeRDwdwXnjeTILMzXNU5l0HTpQp18/5l7ZLSztg/9gzc/XOJVSHaiCrChAweEjGJcsZZnJyIv+/gQ88QQOXl5ax6o0+ZZ8jqUeI/90Pu5N3OkQ1EHTPOEe4YR4hVCUVERxcjF7U/Zqmqey+T/3HMLRkSlJifx6IU7tBqUAqiArCtJiIfW11wD4PjyCji1a4DVurLahKtnB1IPkXsjF3t0en1AfGvs01jSPEIKOwR0xHzSTvSObPcl7NM1T2ZzCwvB++CHuNnjxbno6Cd9+S1FsrNaxFI2pgqzUetkLFrD76FGeTk7GUQgCX3+txi5zumpPyh6Ek8B/kD/tA9tjb2evdSQ6BHXAvYk7+Sfz2Zuyt8ZPdvKdPJnejRvTwsWVWelppL76GtJq1TqWoiFVkJVazZKURNKsT3k9LZVu7joMo0bi1rq11rEq3d7kvbiEueDVzYuOwR21jgNA+6D2uNVzozitmOSUZC6aLmodqVLZubgQ+PLLvOjvT6SjE4XHjmH8eYnWsRQNqYKs1FpSSlLfepv5yckY7O0ZGRGJ/zPPaB2r0qXlp3E27SxnnzuLtcSq+f3jq7xdvGkc2JiQB0PAvnwUX9O5d+1CvSGDGeflxYnCQlI++ojSzJo7oU35e6ogK7VW7oaN5G3dSpG08kpAIAEvPI+9waB1rEq3L3UfBWcKcHB3IMw7jDCPMK0j/VfHoI4YOhiwc7Rjb3LNnth1lf8LLyB0Ot5MT+PH+HjS3nlH60iKRlRBVmql0pwcUl5/ncSSEp7w9aN5167ohwzROlaV2JO8h7xTeega6+gQ1KFaNT7pENSBoqQizv3rHPtT92OxWrSOVOkc/f3xn/Y0rwYE8mlmBqdXrsK8caPWsRQNqIKs1Eppb73NogsXeDo5GZydCXrj9WpVmCqLlJK9KXuxZFnKlzsFV4/L1Ve1DmiNR4gH1mIrOQk5/JH5h9aRqoTX2LHEdOrEGIMX76enkfr6G5Tm1Ly9oZW/pwqyUuuYN27k9IoVzMhI59XAAAKmPY1TZKTWsarE1aYb4VPC8WjsQfvA9lpH+h8uDi60DmyNrrGOvJN5teaytbC3J+jtt5gSHMwL/gGUZWaS9ra6dF3bqIKs1CqlOTmkvvY6b6SlMsbgRdtOnfEaP17rWFVmb8pe8k7lYTpgoqF3Q7xcql/zkw7BHdC30SPLZK2Y2HWVc1QUIdOmEeTgwHvpacQuX07upk1ax1KqkCrISq2S9tbblGVl8bSvH1OCgwl6+y2EvfZrcKvKnuQ9GH83Ysm0VJvlTtfqGNQRfXs9vnf6cjzjOHkleVpHqjLe992LW6tWOAnBq6mpJL/6mrp0XYuogqzUGqbVqzm5fDnzsrJo6OJCyLRpOEdFaR2ryljKLBxIPUDeyTx0TXTVZrnTtRp6N0TvrCd1SSp5F/I4mHZQ60hVRtjbE/TOO0wJCial1MKPcedJfeWVGt8kRSmnCrJSK5QkJpL42us8n5JCkZS4tm6N9333ah2rSh1OP4wx3oi0SvQReloHVM8GKPZ29rQPbI+10Ir5qJldSbu0jlSlnKOjCH3mGT4ICuZIYSHmDRsxLlENQ2oDVZCVGk+WlpL87HN8fvkSAng0IoLgDz6oVZeqAbYnbsfJ34mo56JoF9wOZ3tnrSP9pS4hXfBo7kHusVy2J26vdSNE7wn30bZXL94PCsZktZLw9jsUX6jZncsUVZCVWiDzyy/JPXyYo4WFvB8UROjrr+MUGqJ1rColpWR7wnaKLhXhHOhMj9AeWkf6W11Du+Le2J2S1BISUxI5m3NW60hVStjZEfTuu9gbDLyTlsbMhASSp09HlpRoHU2pRKogKzVaweHDXP50NmVS8nVYOE1GjUQ/cIDWsarcJfMlLiRf4OJ/LmK1WOke1l3rSH/L19WXFsEtaPBRAxw8HdieuF3rSFXOMcCfoLff4hk/P1aYTWw5cID0mZ9oHUupRKogKzVWaVYWiU89zcvJSXyelYVjWBgBL7+sdSxNbE/YTu7xXHT1dTQObkygLlDrSP+oe1h3pFViOmBie0LtK8gAHnfcQYPx43k9IJAXU1KInzuX3C1btI6lVBJVkJUaSZZquAyGAAAgAElEQVSVkfzss3x3JpazxcVM8vcn5D8fYO/urnU0TWxP3E7u0Vw8WnhU+9HxVd1DuyNLJUlfJ3Es+RiZhbVz04WAF56nf6uWfB4airu9PcnPv0BJQoLWsZRKoAqyUiNlfvY5R7duY3ZmJh8HhxD94ou4tmypdSxNmIpNHEk/gnsTdzxae9A91DYKcn2v+oSFhuEU5ETeqTx2Ju7UOpIm7FxdCZ01i6be3uwryOfzSxdJnDoVa3Gx1tGUCqYKslLj5O3cSeacOdRxcuK7sHBaDxmC1721pxvXtXYl7aK0tBTvHt4EhgTS1Lep1pFuiBCC7qHd8WzpSe6xXHYk7tA6kmaco6MJfutNIhydWJiTw2/7D5D21ttax1IqmCrISo1SEh9PwjPTeTklmXiLhWYNGxL01pu1YuOIv7I9cTupi1PJ/DWTbqHdsBO282vfPbQ7hs4GDJ0M7E7eTUlZ7Z1l7Nm/P40eeID3g4L5V2oKfyxcSI5an1yj2M5vpqL8g7K8PBIee4wZcec5W1xMsLs7IZ98UmvvGwNYrBZ2Ju4k92gurnVdq/1yp2u1C2qHPkiPS7gLuaZcDqQe0DqSpgKee5ZenTryiLcPGWWlpL7xJgWHDmkdS6kgqiArNYIsKyN5+rMsPXSYVWYzn4aEEPnOO7g0qK91NE0dTT9K5uVMygrK0NfTV9v+1X/F2d6ZDkEdSF2UStamrFq5/OnPhJMToZ98wgP169PSxZUtOdnET3kCS1KS1tGUCqAKslIjZMz8hLxt2wCYFRxCo8en1Mr1xtfanrAdS6YFQ2cD7YPb4+bopnWkm9Y9tDvuzd3Lu3Yl1L6uXddyDAwk9NNZlDo48HlmJrPOnSXh8SlY8/O1jqbcJlWQFZtnWrmSU59/zra8PAbr9XQaMAC/qU9qHUtzUko2Xt6IR3MPgsYF2cxyp2t1C+2Ge2N3ipOKuRR/iVNZp7SOpDm3Vq0If+stPg0J5WejkRX795P0/PPIsjKtoym3QRVkxabl797NuRde5PGkRA4XFuBcr255n2o79b/28czjXLp8iaRvkhAIeof31jrSLfFz8yMmLAbfAb5YC6z8evFXrSNVC4ZhQ2kyaRKzQkL4Licb08ZNpL37Xq2/gmDL1LeWYrOKYmO5OOUJnk6IJ9LJiWfqNyD088+xd9dpHa1aWH9xPab9JqwWK20D2+Ln5qd1pFvWL6of/oP9cQlzYf2l9VilVetI1YL/9Gfoelc/FoZHYAViv/2W7G/nax1LuUWqICs2yZKSQsKkyVzOycFVCN6Niibiqy9xCgvTOlq1UGYt47dLv2HaZ0LfXs+dkXdqHem29Inog0AQ90Yc8ZfiOZp+VOtI1YKwtydkxkfomjVjc14u9yXEc/qddzCtXat1NOUWqIKs2JzSnBwSJk1i/6VLRDk58UlYOFEzP8a1WTOto1Ubh9MPk5yUjCXbgr6Znj4RfbSOdFt8XH3oENQB5yBnzPvN6rL1n9jpdIR9MYeBDRvRw92dx5ISiXvuefL37NE6mnKTVEFWbEpZXh4JkyYzf/8BpqUkY7JaCXzlFTx69tQ6WrWy/uJ6HL0dafBhAzqFd8LLxUvrSLetX1Q/9O31mPaZ2HB5A6XWUq0jVRsOvr6Efz2XF+vVJ8jBkXlpqSQ8PoWCI0e0jqbcBFWQFZthLSwk8ZFHWbxrF59lZfJ1aBh1pjyO19gxWkerVixWCxsubSDzt0yklPSL7Kd1pArRK7wXhqYGEJCemV7rm4Rcyzkqiogv5vCf6GgmeftgzM3l4qTJFJ0+rXU05QapgqzYBFlSQuLUqZgOHOBno5EvQ8No+9BD+D2pljdda3/KflLjUslYk4GzszO9wntpHalC6J31dA3vSt036uLg7sD6S+u1jlTtuLVqRfTnn+Hs7MyHGem8dPYMlx58iOILF7WOptwAVZCVak+WlJD49DT2b9iIBH4ID6fTuHEE/OvFWt2j+q/8evHX8slcbfV0C++Gh5OH1pEqzF1Rd1GaW0rS/CQ2XNqApcyidaRqx71zZ0I+nsFzgUGcLS7mzdjTXJ4wQRVlG6AKslKtWUtKSHxyKr+uWslDCfGcKSrCs1+/8g0j1Frj/6ekrIRNlzdh3GdE315Pv6iacbn6qp5hPdF56sg9kkvGuQx2J+/WOlK15NG7Nw0+eJ+5YeEcKChkw4ULXJ5wH8UXLmgdTfkb6htNqbasxcUkTpnC2jVreDY5mRnBIXQcMICQD95H2NtrHa9a2pqwlTxLHmGTw/Bp5EO30G5aR6pQbo5udA/vjr6dHuMeIyvjVmodqdrSDx5Mo3fe5seIcHq5u5OQnMLFe++j+Nw5raMpf8GmC7IQYpAQYq8QIkcIsVEI0eRv3hsuhJgvhCgTQrxalTmVm2ctKCDxscfJ276DNWYzM4NDuHPoEEJnfoxwctI6XrW15OwSCs4V4BLmQu/I3jbZu/qfDKozCENXA6YDJrZc2kJmYabWkaotr1GjqPvuuwg7O15JTeGVkye5eN8EimJjtY6mXIfNFmQhxABgGfA90AHIBHYIIYKv815f4Azgig3/zLVFmdFI/IMPsfa338gpK+M/wcH0GT6ckBkzVDH+G/HmeHbH7ebyjMuU5pYyqv4orSNVii4hXYhoGEG9N+tRJspYeV6Nkv+OYcQIgt59hw9DQjlZVMiLp04SN/5eCg4e1Dqacg1bLk6vAb9IKT+TUp4BHqD855l07RullJlABymlWh9TzVnS0rh8773M37aVf6emkFJaimf//oR89CHC0VHreNXa0rNLMe4x4lbfjUZ1GtHKv5XWkSqFg50DI+qNQEpJ1sYslp5dqlpp/gPD0KE0/uhDvomMIsli4WB6GvEPPUzu1q1aR1P+xCYLshAiCogBll99TUpZBGwDrrvnnpTyWJWEU25Z8cWLXBo7jll79zInK4v5YeF0njCB4P98gHBw0DpetVZSVsLyc8vJ2ZaDdw9vRtYfWaNnoA+vNxwHJwfSlqURdz6OvSl7tY5U7ekHDaLx558xv05d2rnp+D07m9OPPoZxxQqtoylX2GRBBiKuPF87ZTAeCK3iLEoFKDh4kMtjx2FJTsYewcLwcDo8NZXA115VE7huwJb4LeQU5eDbzxff1r4MqjNI60iVKlAXSPfo7hg6Gcjels3Ss0u1jmQTPHr1ImLe19i5u7M+18yESxc5Pv1ZMj77TO0SVQ3YakEOvPJsvOb1PKDCewQKIU5e7wHUqehz1Uam1auJnXA/z8ae5pKlhId9fGj96qv4T51ao0d5FWnJ2SWUZJSg76jnrjp3oXfWax2p0o2qPwrvHt4YdxnZfGGzmtx1g3Tt2hGx4DvebNyETm46xly+xO4PPyTlhRewlpRoHa9Ws9WCfPU3z/Oa1/VAahVnUW6RlJKMzz7j2NPTuC8ujkKrlSA3HSEzPsL7vvu0jmczLpkusSduD3GvxlGaU3Mnc12rc0hnIhpEEP2vaKz2VlacV5deb5RL48ZEL17Ev9q351EfX4qtEtPKVSQ8+BClOTlax6u1bLUgJ155jrzm9Yg//VuFkVI2ud4DiKvoc9UW1vx8kqY+RfInsxgff5l2bm7MatKUBgsW4Nm/v9bxbMrVyVy6BjoaRTeihV8LrSNViauTuxx9HTEdMKnJXTfJKSyMyJ9+ZEKfPjRzdeXrrCy+2biRS6NGU3TmjNbxaiVbLchnrjyGXH1BCKEDegC/aJRJuUEl8fFcGjuOk2vW4GRnx+yQUP7dvj3RPy/GrXXNnBlcWfJK8vjlzC9kb8nGq4dXjZ/Mda1h9YZhhx3J85OJOx3HlvgtWkeyKfYGA+HzvkY/ZAjd3d35Jiebfx08yNnRYzCvV73Cq5pNFmRZPvvgHeAeIcREIUQD4FvABHwrhOgrhMgSQtylaVDl/8nbuZPzI0fx7u7fuT8hnkKrlZa9ehH50484hYdrHc/mLD6zGHOhGUNnA0ExQQyuM1jrSFUqUBdI33p98e7lTca6DL4+8bWanHSThJMTQe+9S6cXX+TnyEiSLCW8dfkySU89TfpHM5ClapvLqmKTBRlASrmA8jXHTwK/Ay5AJymlEbACxYDqPF9NyNJS0j+eyfEHHmTyyZPsLyhgUUQEoZMmEvbVl9gbDFpHtDlFpUUsOLmAsvwy/Ab4Ma7xuBq1kcSNeqjZQ/j08SH3SC5HYo+oJVC3QAiB76SJNPv6a75q3ISpvr4UWa1snTWL+PsfwJKWrnXEWsFmCzKAlHKelLKZlNJXSjlYShl/5fVNUspgKeXm63xGSClfr/q0tZclLY3L999P1pdfklNWRqSTEwvq1aflJ5/gP326WtZ0i1aeX0n8kXguvnsRJzsnxjcar3UkTTT2aUy3ht2Iej4KR29H5p2Yp3Ukm+XerRv1li4hqFFDzhQXMykxgU9/+424oUPJ2/W71vFqPJsuyEr1l7tlK3FDh/HpbxuYmZFBtLMzr3XoQIMlS9APuG4PF+UGlFpL+fbkt2SszcCnjw/D6w3Hx9VH61iaebjZw7hGuZIfm8/vZ37nRMYJrSPZLKeICCIXLaLr6NEsiohkba6ZySeOE/vQQ6R/+CFSLY2qNKogK5XCWlBAyquvcXjSRB4+fpx1uWaG6vV4DhpE1NIluDSor3VEm7b+0nrOnzhPUXwRvt19ub/p/VpH0lRMQAzN/Zpj3G0kc0Mm8/5Qo+TbYafTEfzB+3R4/z0W1atPV507rkD8V3O5OHYsxXFqgUllUAVZqXCFx49zcfgIjIsX8256OvWdnVlcvwEd3n+P4A/ex06n0zqiTbNKK/NOzEM4CYLvC2Zgw4GEuIdoHUtTQggebvowvv19yd6azYbTG7hgVHv/3g4hBF6jRtFg6RIeaN0aATyQEM8b27YRO3QY2T8sRFrVMrOKpAqyUmGsxcWkf/ghJ0aN5p39+8krK+M/QcG83KMHDVYsx2vUqFq1JKeybI7fTGxCLE5+Tujb6nmw6YNaR6oWuod1p2mTpuga6sjems0Xx7/QOlKN4NKgAVG/LMXr7nHMDgnhfHEJo8+eZdtLLxF//wOUxMdrHbHGUAVZqRAFR45wcegwls38hMEX4kgrLcUqBAGTJxO56Ceco6O1jlgjWMoszDw0k+T5yWSuz6RnWE/qetXVOla1YCfseKjZQwSNDcKrmxe/XvxV3UuuIHZubgS9+iqt587l6+bNGWUwcL6kmIL9+zk3eAjZCxao0XIFUAVZuS1lZjOpb7zB5bvvYffJk7ySmspL/gHM7NiBZj8uxH/a02oP4wq06MwiTh88TcG5Avz7+jO19VStI1Ur/SL70axBM6RVYtxt5MODH6p1yRXIo2dP6q5ZzSOjRzPIU8+hggKGnz7N5lde4fK4uymKjdU6ok1TBVm5JVJKTGvWcr5ffxZ88QW78nJp4+rK2uhoRj3xBNErVuAWE6N1zBrFVGxizpE5pC5KxX+4P6Obj6aOQe1v8mf2dvZMbzsdrJD8fTJ7ju9hc/z/W/2o3AYHHx9CZn1CyMcziAkOZqyXgYcTEnhl4wb+GDqMtPc/wJqfr3VMm6QKsnLTis+dI/7BB9n95JNMOHqEL7KycBV2ONetS5NFiwh44XnsXF21jlnjfHX8K8wlZnzu9CG0VyiPtXxM60jVUoegDtzR/A58evuQ+nMqHx/6GEuZ6hFUkYQQePbrR911a5l0z3hWRUWRV2alqLSUlHnzON9/AKa1a9XViZukCrJyw8pMJlLfepsLQ4dh2r2HyYkJtHN1Y0X9Btz1738TvXyZ6kVdSRLMCfxw/Afyz+Rj6GDg4RYP1+p1x/9kWptpBAwIoDCukLOxZ1l8ZrHWkWokB29vQj76kDbfzueDdu3wcXDgo4wMHjx4kJ1TnuDyvfdSdOqU1jFthirIyj+SJSVkL/iec33vZP5nn/FWchKOQrAqMorpw4bRcN1afCdPUveKK9FHhz4ibX0aGWsyCNQFcm/je7WOVK3VMdRhdPPR1H27Li4hLsw5NoecIrWtYGVx79qF6NWr8Hn0EaYFB9Pa1ZW74y/z2rp1xA0fQfJLL2FJS9M6ZrWnCrLyl6SUmNetI27AQNa89BKjjx9jXnYWd7h74BgeTp0vviDsqy9xCgvTOmqNtvHyRn499CsZ6zIIGhvEk62exMXBRetY1d5jLR9D76XHdMDE5c2XeXf/u1pHqtHsXFzwnzqVJuvW8uyoUayIjCLU0Qk7YN8PCzndpy/pH8+kLDdX66jVlirIyv8jpSRvxw4ujRxF7NSnsCQksDUvjxF6AysaN2HwKy8TvWY1Hr16qnXFlcxYZOStvW+RujgVn14+dGrTiQHRquXojfBx9eHxlo/j5OtEyk8prDy4Um3PWAWcIiIIm/M57ebP54E2bQCYnZXJwNjTLPzwP5zv3Yesed9gLSzUOGn1I9RN91snhDjZuHHjxidPntQ6SoWQUlKwbx8Zn8zi7L59zMnKZF9BAeuj6+Do4IDXmNH4PvYYDr6+WketNV7Y+QJrL6zFYrTg5unG8hHLifCM0DqWzSizlnH/+vtZ/9l6iuKLaPNSG1YOXYneWa91tFpBWiwYf/mF9E9ns/HSJWZkZtDY2YX/BAdj7+eL78RJGMaMxs7ZWeuoFaZJkyacOnXqlJSyyc1+Vo2QlfIR8c5dXB5/L/H3P8DsTZsYcfkSBnsHlkRE4t23D9GrVxP4yiuqGFehbQnbWHFwBUnzk3DQOzC13VRVjG+SvZ09r3d+ndDhoQh7QWpqKh8c+EDrWLWGcHTEa+xY6m34jTEvvsiqK1s7Sil5+cQfrPz3vznfuw/Z332HtaBA67iac9A6gKIdWVZG7pYtZH35FWcPH2a5ycQTvr501ukYrNcT2bMnfk8+gWuzZlpHrXVMxSbe2P0GSfOTcAl2oYVfi1q7veLtitZH80T7J/jY4WOkVbL8j+XcGXkn3UK7aR2t1rDT6fCb8jhed4/Db+7XZC5cSCMXZ/6VmkJwViaPXbpE1y++xPv++/EaNxZ7T0+tI2tCjZBrIWtRETmLFnOh/wC2TZrM1I0bGHn5EkXSSrGUtO7enZjFiwif+5UqxhqwSisv7XqJsxvOUpJWQsjIEN7o/Ab2dmrf6Ft1X+P7aOrTlOzN2STMSeClnS+Rmp+qdaxax8Hbm4Dnn6P+xo088vgUfmvQkCGeeuJKiinLyWHLO+9wpnsP0t59D0tystZxq5waIdcilrR0jIsXkf3TIk6npNDAxYW9BfkEOTiyPiqasF498X3kEdxat9Y6aq32zR/fsC1xGwVxBYQ9EsYT7Z5QHbluk4OdA292fpPR6aPJ2ZXDmaVneEb/DPPvnI+jvaPW8WodxwB/Al9+CZ9Jkwj49ltyFi+mpKCA19JSyU9J5v6ZyQxdsAD/fv3wvu9eXFq0qBUTSNWkrttgC5O6pJQUHj1Kzg8Lyfj1V37NyeH7nGxyrVZWREbh5uCAR58++EyciGvTm56DoFSwvSl7eWjFQ5SVlOFocKRrSFdm3zEbO6EuZlWE5eeW88KKF4h7I47wJ8N5ePDD/Kv9v7SOVeuV5uSQvWAB2Qt/ZEdKMt9kZxPo4MC7QcEUWa0YWrTAe/w9eNx1V7WfAHY7k7pUQb4N1bkgl+XlYV69mpxFi8k+fRqdnR2vp6ZyrqSYewxe9PXzw3fECLzvn4BTeLjWcRUgNT+VUStHceyDYzgFOhEzMYbFAxerGcEV7LXdr/HDph9wDnbGztGO97q+p5aSVRPW/HyMvywj+7vvyEtIwFEI+l28QFMXF+4xeBETFIRhxAi8Ro/CKTJS67jXpQqyRqpbQZZSUnjkKMZlv5Czdh27MjJYbDJyqqiIjdF1sEqJW0gIXnePwzByJA5eXlpHVq4osBTw4G8PsvXbrZgPmmn4SkMWDl1IY5/GWkercYrLirnv1/s4fvE4qUtSqfNgHeYPnE9T36ZaR1OukKWl5G7eQs7335O4dy8/m4z8bDTS0tWVGcEhSCnRdeyIYcRwPPr0wc6l+jTKuZ2CrO4h1wCW1FRMq1djWrac3Lg4nO3smJaUxPmSYsYYDLwTGIRnu3Z4jR+Pxx29EA7qP3t1Yimz8PS2pzl04hBZG7Oo83IdXun2iirGlcTZ3pkZPWYwyjSKRGMi5784z6NOj7JgwAKi9FFax1MA4eCA55198byzLwGnTxO1cCETV68hLS8PgAcTEwhansLwLVto6++PfuAA9EOG4NqypU3fa1Yj5Nug5Qi5LDeX3I2bMK1aReaePWzONbPCZCLfamVRRCTZpaX4eHvjNWwYhjGjcY6OrvKMyj+zSmt584/Ytdg521GaW8r4mPH8u8O/tY5W4+1J3sPkNZM5/955XKNdaT25NT/0/4EAXYDW0ZTrKDObMa1ajXHxIi6cOs1Kk4nlZhM+9vb8FB6BFXCJjEA/aDD6QQNxitBmzb66ZK2Rqi7I1oIC8rZvx7xuHcZt2zEXFmKwt2fgpYt429szxFNPP08P/Dp3xjB8BB59elerSznK/5JS8sGBD/hq7VfEfxpPvbfq0b9Jf97v+r5a4lRF1l1YxzNrn8G034T3Hd7U86rH/Lvmq/v21difb82Z1q7jkslEpJMT/05JIdFSwmBPPX08PPBv0QLP/v3x7HcXjkFBVZZPFWSNVEVBLsvLI2/bdnI3bMC8YweHs7P5NdfMb7m53OnhwUsBgeRbyzBERqEfNAj9sKE4hYZWWh6lYkgp+fjwx3yx8QsuvHuBoLFB3DniTj6/43Oc7NWuWVVp4emFvLf/PQriCihOLqbL0C7M6T0HLxc1x6K6s+bnY/5tA6aVK8nYu5fNZjOrzWaOFBaypU75UkF7IfBt1QqPvn3xuLNvpX8/qoKskcoqyJb0dPK2biN3y2Zyd+/hoMlIiKMjOjt7xl2+RF8PT/p7eNAoIADP/v3QDx5s8/dOapMyaxlv73ubxacWc+7Fc/j29aXr2K58c+c36Bx1WserlWYdnsWnv37KxQ8u4j/Yn3Yj2vFV36/wd/PXOppygywpKZjWrMG8ajUZsbF42tuzzGTk7bQ0Oul09HH3oJe7Oz5Nm+LRqxced/TCuVGjCv/eVAVZIxVVkKXVStGp0+Rt30be9h0UHT/OueJi5mdnsz0/D087e14KCKCTToeduzsevXvjOaA/ug4dEI6qqYEtsVgt/HvXv1l9bDUOng5Ysi00rdOUr/p+hbeLt9bxbt3V7xEb/aPw6u2DeZvncfHDi/jc4UPLMS2Z23cuYR5qe1FbU3T2LOZff8W8bh1JcXFsys1jY14uj/v40sjFhdUmEz3d3QmJCMe9e3fcu3dH1749dq6ut31uVZA1crsFufCPk+T89CN5O3aQmJzC9vw8dubn825gECkWC9vy8+jl7kF9Pz88e/fGo28fdJ06YeekLmnaInOJmed2PMdvG38j4bME6rxWh3aN2/FZ78/wdLKx3r1lFkg8AOc3wfnNkHIUPIKh7h3lj+ge4Gpbl3yllHx+7HNmbZpFUWIRnq088XP1Y1avWWpJlI2SUlIcG4t5wwZyN2ykJC6OZIuFd9PT2J2fTx1nZyZ4eTPA0xPh7Ixb+3Z49uuPYdjQWz6nWvZko0pTUzD9sox30tJYZjLRUedGT5079kLQNDqaDnfcgUevnrjFxKiRsI27YLzA1K1TObL2CCk/pRA2OYzuzbszs+dM3BzdtI53c+K2wMopYE7i+2Ml/PiHhR2Xy6jvk8f2+5Nw2L8ABwcnnHpMg27Pgb1tfM0IIXi85eO4O7rz4cEPMR8xk3ggkXtz7+X1Hq8zuM5grSMqN0kIgUujRrg0aoT/1KkUX7iA3+bNfL15CzlHjrAvPx83u/IueA+cP8dXRUXYe+pvqyDfDtv4TamhdB07Ihwdmejjw/SAAPStWpVfPunRHecGDdQ94RpiW8I2Xtj5Amazmeyt2UQ9F8Xg7oN5r+t7tjWBq8wCW98mc8MMlp6y8EiMExYrjGvqyBcDXLlotOLpLPj+WAkvb83jx8S36XRxJ4yYC3rbmWg4ockEPJw8eLXoVXJ25BD7ZizPmp7ldJfTPBPzDA526mvTVjlHR+McHY3vxImEZmQQtWMnedu3k7drF28GBuEgBO7du2uWT/2fpSE7nQ7fKVMICg5C16WL6pxVw5SUlTD7yGzm7plLzo4cfAf4Ev1yNI+3fJzJLSbbVn/qnMvwy0Ns27WHe5YVMqi+A//X3p3HyVHWiR//PFXVd/fcM5nJJJkkE3IaSAAJEC7lDHe4BQRExdX9Cairi+iq6OrqegGeuCIrl4Lch+ByIyGcIReBhNxhMvfZd1dXPb8/qmcy5OIIpHuS7/v1el5V/fTT3c/0VNe3nqOqXCwuPfMomHQMNM2lqXs1rH6cT4cfxzTaOPn2FF9b9xRXtc/FnP87mHpisf+K9+yMfc5gbGwsX419lZV3rmTjtRu5pfIWVnSv4IeH/ZAxsZFzgCG2z6qtpeLMM6g48wx0LsfYRYtIPP0MkcPmFq1OMoa8C0rt0pmidKzqXcVV/7yKRc8uouXGFsoOKKP5omZ+fNSP+eS4Txa7eu9P+wq4+TRuf6GFLz+S4Q8nBznz8Olw9k1Qv53bc2YG4OGvseaZv/KLhVmumxfEMhSc+DM46PO7v/67YHNiM1c+dSXLNy3HCBv0L+yn/tB6rj70ak6fdLr0YoltyKSuIpGALLZmuzY3v34zv1n8GzoXdNL6l1YaP9PIfkftxy+P+uXIu41iyyKcm+eTifeStDUpG8Z/4iKY99/g38kpWlrDkr/Aw18jnkhyyf1prj8hSOOZ/wlzr9h99f8QpPNpfrDwB9z3+n1s+OUGtK0Zc9kY5h00j6vnXC1X9hLvIJO6hCgBL7e9zA9f+CFLX1qKr9pHbFaM6PQoF825iCsPuJKQteunVOxWGxZi33wWF9/ZQV3E4Np5YTjlOtj/ond/rVIw63xoPIDozfOZVrOGw29K8gkTCnQAACAASURBVITzbSbkknDUN0fMKVIhK8SPDv8Rh485nO/Hvs+6+9ex5vtreODyB3ih9QW+NOtLnD/tfHyGTLwUu0YCshC7qC3ZxrWLruW+RffRdkcbieUJxn5xLBMOmMAP5v6AuY3FG5P6wNY8Rebm8zjvjh76s5obTo3AWTfCjPnv731qp6A++yj/aZ1KxPcmh9+UZJH/v6jLJeG4/xwxQRlg3oR5zK6bzbdrv83TM5/GX+Onr7WPa1Zcw30H3cdVB13FnIY5xa6mGMEkIAvxAfVkevjjsj9yx5t3kBpIsfrbqyk/qJwpP57CubPP5Yr9rxiZ10Re+SjceRG/XjhAzoG/f7qS0IW3wuTjP9j7VYyDSx/lm9ZpHDZuObVhRX7Br7DstDeubIycyW31kXr+cOwfuGf8PVy76Fpa1raw6YZN9O7byxtnvsERM47giv2vYEbN++6tFELGkHeFjCHvnbrT3dz+5u3csuwWNj+7Ge1qqo6sItedY/bk2Xz74G+P3AtJrHiA+G2foS+VoyGmcMwwgU/fARM/hFNBkt1w63wG1i9mzh+T3Do/xAEnXgynXg8j8GYavZlerlt0HXe8dgcd93bQt7CPyT+ejFVmccy4Y/jcvp9jRrUE5r2NTOoqEgnIe5dN8U38+fU/c++qe+lY0EHng50ov6L+3HomHjiRL+73ReZPmj9y79S09G/0/+Uy5t0a59CxJj87uRYuvAvGHfzhfUa6D249k1sfeZ4rHs3y0KdCHDLvPJj/ezBH5hjsss5l/OLVX/DC6hewYhbdj3WTH8hTfWw1c6fM5dIZl3LI6ENkRvZeQiZ1CfERcVyHBZsX8LdVf+Op1U+R68vhr/UTXxyn7sw6xh46ls/P/DznTT2PoDVCb3WpNTz3Szoe+C4n3pbiY3UmPzl5FFx8LzQe8OF+VqgCLrqPC81zCFrPcOpf06yq+RuVyU4452bv+RFmZu1M/nT8n3h+5vNct+g6Xpv+Gp0PdbLqG6voOKSD5899nin1Uzh78tmc0nwKMX+s2FUWJUpayLtAWsh7rrfjb/PQ2oe49617WbtqLT1P9dD3fB9VR1ZRf2491cFqLph2AedNPW9k72AdGx7+Kiy6mT+8mmNFp8svTh+NcckD2z/H+MOSS8Jfz+ftxU8ypsxgTY9L85QZcMGd3pjzCOVql6c2PsWNy2/k1TdfpW9BH7Wn1JJ6K4WTdqjbv455E+dxavOp7D9q/5F1cRjxnkiXdZFIQN6zdKe7eWLjEzy09iFe2fAKbtbFDJm8dfVblB1YRtWRVUyeOpmLZ1zMqc2nEjADxa7yrkn3wl2X8vQT/4eh4PBxJqpqAlxwF9Ts89F/vp2B+/+VzOK/Me03CS6c6eP7J49Fnf9XGHPgR//5HyGtNa+0v8Kflv+J51qeY2DRAO13t+OmXSoOr6DmuBrG1I3hpIknccL4E5hcOVm6tPcQEpCLRALyyNeSaOGpjU/x+MbHefXtVxlYPkD/wn7iS+LUnVFHzfE1GNrgE02f4JzJ53Dw6IP3jFbNhoXouz/HjU+v5RuPZbhlfoiTjj4MzrsdIjW7rx6uC0/9kLcf/m9Ouj3F9FqD/zk1RvTE78IhXx5RM7B3ZH3/eu5adRf3rb6Pzcs30/dcH/Xn1WN32yRXJik7sIyJYydy9LijOXrc0cysmTly5yEICcjFIgF55MnkMyxqX8Rzm5/juZbnWN26mvjSOJGpEdyMy6bfbaLi4ArKDy5n8vjJnDzxZE5rPm3PuRqTk4dnfwrP/jf/8mCSx9fm+dvZYWYfcxac/nvwFWkcfNEtxO++gi89lODqw/xMqzW9WzjOvwFi9cWp04cs62R5bMNjPLTmIRa2LiS5LknH/R0kXk8QagpRf0494X3CVAQqOGT0IRzWeBiHjj6UmtBuPEASu0wCcpFIQC59KTvF8q7lvNL+Ci+1vcSSjiXkdZ740jidD3WSXpsm1Byi4fwGQk0hRoVHcWzTsZzSfArTqqbtWd2ILYvg719nzbKXaK4yWLgpz8fqA8RO+BbM/UrxW6Mbnoe7PwcDLXznqQzlAcVXPlGPcdw1MPvCEXlq1I50pbt4ZN0j/H3t31nSsoTEsgTBpiBm0GTtj9YSmxkjOjNKZEqE5rpmDqo/iI/Xf5z96/anNlxb7OqLnZCAXCQSkEuLq102Dmzk9e7XWda1jNc6XmNlz0qSm5Ik30ySfCNJemOayT+eTGZThlxnjuj0KJNGTxrqLpxRPWPPCsIAiU544hp6n7+F7z6d4dalOZZ+McqYpolw5p9gzIc8k3pXpHrgwct549n7+NTdaaJ+xa/mBZm9/wFw4k9h7EHFruGHri3ZxpMbn+SJjU/w6uZXGVg9QGJZgvjSOIHRAcZ+YSz9r/Rjhk3CzWHGVo9lVt0s9q3Zl4/VfIwpVVNG/nyGPYgE5CKRgFw8OSfHuv51rOxdyZs9b7KqZxUrulfQ291Lel2a9Lo0vhoflYdVsvFXG1GWIjItQmRqhIrGCuY0zOGwxsOY2zh3z72VXrILXrwBXryBZ1Z2c9bf0pwwyeInxwQYPfdT3lWygmXFruW2tIZX/xf779/k1wv6eG6Tw93nhNFao2acDod9FUbPKnYtPxKJXIIXW1/kny3/ZMHmBbTGW1GGouOBDgZeHiDbmiXQGGDitybiZlycpEO4Pszk6slMqZrC1KqpTK6czOTKySPzKnF7AAnIRSIB+aOXtJOs71/PuoF1rO9fz5q+NazuW83GgY1kOjNkNmXIbMxQ9ckq7F6btf+5luC4IKEJIcr2LyM6PUrEF2Hfmn05qMHr9ptePX3PvhFA73pY+FvyL/+ZO5bEOaLJJGDBW90ucw+YCfN+7I3Plrr+FnjsO7D8LvKuZs4fk5w4yeLyOX5q9z3Gu2vUhCNH1PWw3w+tNW/H3+altpd4qe0lFnUsoqWrhcyGDJGpEQYWDdByUws6rwmND1FzYg2xmTGyrVl8NT5GlY2iuaKZSRWTmFA+gfFl45lQPoGaUM2e1wtUQiQgF4kE5F3napfOVCctiZahtCm+aSh1JjvJdeTItmbJteVQPkX1MdW0/KmF/pf7veA7LkTNvBqsCgvlKiZUT2BG9Qz2q92P2XWzmVQxac+ftZpLwooHYPFtxFc+y81LbH62MEt1SPE/p4SYPb4KPnE1fPyzI++KWOsXwCP/zrKli/nJghwPrLS56rAAVx8egMrxsN/5MOtTI/r85feqLdnG4s7FLOlYwvKu5bzR/QbxzjjpdWkCDQECDQHe+uZb5Lq8C9hEJkdovLSRbHsWN+3ir/cTi8YYGxvLuLJxjImNYUx0DI3RRhqjjTREG6T7exdJQC4SCcg7Z7s23eluOlOddKQ6aE+1055qpyPVQWuylbZkG+2pdnKZHIbfIL0+TXJlklxHjlxnjrpT6wg0BFj1zVUE6gME6gOEp4SpnFuJm3PxBXxMqpjElKopTKmcwrTqaUyrmkbUHy32n757JLtg1T9g1SO4q57gmdUDfLzRZGm7w/eezvKNuQGOnjEKdciXvEAcqix2jT8414E3H4J//oJ1Kxaxsd/lyPEWVz6aYb9RBmdN9xFrngNTToDJ86Bu2h7bch4u7+ZZ07eGFd0rWNm7kpU9Xuob6CPbkiWfyFM2q4yep3voeqSLXGcOq8xizOfHEJkWofPhTvw1fvy1XrLKLaqD1TREGqiP1DMqMopR4VHUheuGUm2olrAvXOw/vWRJQC6SvS0gu9olnovTm+mlL9tHb6aX3mwvPZkeejI9dKe76c50e8t0N73ZXpy0g91jk+/NY/faRKZEsKosNv1qE3aPTa47h7/az6QfTKJ3QS/JN5P4a/0ERgWITItglVkEzSBNZU1MKJ/AhPIJQ91w48rG7dldz1tL98LGF2D9c96M5M2v8ermPDe+luPBVXkCJtxzbph9R5lQPQnm/Is3O9k3wu7DvDNaw7pnYMH16NVP8JflNjctzvHC2w5nTfdx02khHFdjVjbB+MOg6VAvVU3cKwI0eF3d7al21vatZXXfatb2r2Vd/zrWD6ynK96F3WljlVsoS9F2Zxt2l02uK4dVbjHhGxPo/HsniWUJfFU+fFU+Kg6vwF/jJ7Mxg1VuYZVZRAIRakI1VIeqqQ5WUx2qpipYRVWwispgJVXBKioCFUPJN9J6ZXaBBOQiGWkBWWtNxsmQtJPEc3ESuQQJ20vxXJx4Lk5/tp+B3MBQimfj9Of6h/Jd7U0kyXXncBIO+YE84eYwviofm2/eTH4gT74/jxk2Gf9v4+l4oIPep3uxKix8lT5qTqwh3Bym/8V+rCrL+9FX+KgKV9EYbWR0dDRjYmO8LrXYOMbGxjIqMmrPuBjHe6U1DLRA50poWwatS6B1MdmONbyy2eGZDQ6vdzrcOj/Eg6vyvLrZ4ZQpPg4YX4maeSbMusC70tWeHoD6W2DpX2Hx7bSsW8UbXS7HTLS47ME0r7Y6HNlkcUSTybETLSIVNdCw35ZUO80L0pa/2H/FbtWf7WdTfBMbBzYODQu1JFrYnNhMW6oNV7vkOnJk3s5gd9vYvTaVR1RiRk3W/mAt+b48bs4ltm+Mpq800fN0D6m3UlhlFmbMpHxOOb4KH+kNaayYhRk1MYIGUX+Ucn855YFyygJllPkLqbAe88WI+b0U9UeJ+qLE/DEivghhKzyihpz22oCslDoF+BYwBXgFuFJrvd3oqJQ6GPgJsB+wDPi21vqZXfz8jyQg265NNp8l42TI5DNknSyZfIZ0Pk06nybjFNbt9FBeKp/ylnaKVD5F0k6Ssr1lMp/0lnYSx3VwMy5u2sVJO+BCcGyQ9Po06bVpnJSDk3QoP6ScYGOQ9T9fj5Pw8qwyi+bvNtP5cCc9T/dgRb2j5ZqTa4jsE6HrH11YMS/PqrQINnoXmYj5Y9SF6hgV2dL11RBpGEr1kfq9rwvMzkB8sxdU+jZ4E7F61kHPWuh6i/6BAd7oclja7tJUbnD8JIv9b0iQsuHIJpMjmizO+5iFWd64pZt2whHFu7BHMWkNbUu9+ziveoTk+kUs2OTw7IY8z25wuO2MEPGc5ppnshzQYDKr3mS/UQajyvxeUK6e5I1FV07wluWNUNYIwfI9/6BmGNu16Ux10pps3TKklGwfGmrqTHXSnenGTtm4WRdfhY/UmhTpdWnyA3mcuEP1sdWYZSbrfriOfCKPk3AITw4z8ZsT6Xyok/jSOGbExAyb1JxYg3+Un96nejHCBmbYxFfpIzQ+hJN00FpjBk2UpQhbYSK+iBegfYV1K0LIFyJshQn7woSs0FAKW+98HLSCXjK9ZcAMELSC+A3/hz7Bba8MyEqpk4D7gCuBx4HvAccBM7XWm7cquz/wHPBz4GbgS8C/AIdqrV/bhTrsUkB+q/ctvvr0V8k62aGgm3WyONrbGN2Mi7Y1btYFA/zVfrJtWXIdOdysi5tziU6PYkZMOh/uRGe9sla5Rd3pdXQ/2U3fP/u80yMyDo2faSQyNcKKL6zACBmYIZNgU5Cmy5voe6GP+JI4Ztj7sZQf7AXkgUUD3g8oanoBuNzCVCblgXIqA5VD3VOVwcqhrqvBbqyaUA01oZqRexek98OxvVsLZvq8ruV0rzfGm+qGVJd3LnCi3UvxNi8PWNHpsKLTZU2Py9pel58cG2Rpu8PRN6fYp8pgRp3BBTN9nD7VR9rWhMprvS7Ywe7YUR/7yIJGMpunbSBDa1+G1v407QMZuhI5upM5uhNZBjI2Wdslm3fJ5V1MQxHwGQQtk7DfpDrqpzoaoDrip64sSENZkPryIA3lQaoiH/6OcEi8rdCtv8Dr2u98k46ky71v5FnU6rC43eGEZotrPhHkCw+mSdrQXKmYWGnwqZlbulb9oZh3lbBoPUTrIDoKItUQroFwNYSrvHH5YIW39IX2+ADuuA692V46U510pbu2DFFluunNeMNXg0NZvZleMnYGN+diBk2y7d7ETCfp4KQcYrNjmGGT1ttbcVMuTsrBV+NjzGfH0HZXG92PdKMdjfIrxl0+jsjkCGt/uBYjaGAGTQKjA9SfW098aZzUWymMgIERMIjtF8NX6yO+JI7h9/LMsEmgIYCbddF5jQoolKkwlEHADBCwAgTMACErxNmTz+biGRd/4O9ob7394veAu7XWvwFQSn0GaAUuKzw33NXAUq31fxTKfhU4HrgCuGT3VHdbrnZZP7Ce9rvb6VvY5wXfnEvTV5rw1/lZeeVKlF9hBAwikyOM+/I44q/FGXhtYGhDC44JYkZNdNbbyPzlfnzV3k4lOjVKoD4wtAH7qn0on2LGn2bgM3zv6BqKnR4jdk6MqC/6zi6lw8uoCFQMdTeVB8qJ+WMjqwtZa8hnwclCPldYDqbMlmRnIJ8GezClIJcCO+ktc0nIJSAb37LM9ENmAG2ncDRYhmJNj8umAZeulKYzqblgXx8dSc2/P56hLaFpjbscPcHif04N8euXcqzucWmuNJhU5X2nh4wxSV4dw18xGmqnel2so2cRapjlteA+4E5fa03GdulP2/Qkc/SmvODaFc/SmcjSGc/SPpChfSBDa3+GgVQWJ9mLE+9Gu3mCY2aQWrWQ9JqXcVL9uNkklUdejK9uAq3/ewVKmSjLh6+2iZqTvkpq1UKyb6/AiJRjRqoINu2HFavGtbMEQyHqy4LUlwWpKwtQFwtSGwtQG/MCeGXET1XYT0XER9RvYRjv42+O1cPMs7wEkOqhrnUJX2hdDJsXQ8cK6F4D2uH8mT7vgKjX5YFVeS7c18cDK/OceWeaUdEEo2Nt/OvH/Vw6289vX86RczS1YYOasOKYiSa2C5k8lAXAMH0QKPNa1oGYtx6Igj8K/oiXfGHwh8EX8QK4L+z1alghsAJenhUAK+gtzYDXrW4GvMdF7ro1DXPoQPu9SOfT9GX6hoa9+rJ9DOQGtgyNZQdITNsyZBbPxUnYCYLnBqk/qx7X9nrzjKCBMhUN5zd4PXwZF+X3tgllKLSjsXtt3JxLeFIYX7WP7ke7vYZL1sVX5WP8v42n6x9ddNzXAS5gwJjLxlBxcAVLv7YUI2ww6XuTiOfiH+E3uHMjMiArpSYABwI/G8zTWmeUUk8DJzEsICulfMDpeF3bg2W1UuofwIW7qcrbFcT7cVUeWUn5QeVe8PUbmDETZSpm3ORdNSpo+AmaAYKmn/FnNhA6J0Co8Dhseuuhr/kJmQEiZpCwWVifHiRiBogYXrmoGSg8DhBUprdf1y7owhJdeOx6QUy7kM5DqgN025a895JcB7QzbH1Y3juWw/Pzw/Lyw5KzZd2xC4/twvrw/EKeY4OT27J0bQDyriabB0NByKdoGXAZyGrSeUjbmoMaTfoymqfWO6RsTcqGydUGx0y0+P0rOZa0OcRzEM9p/nhKkNaE5sw70/RnNP1ZzTkzfNwyP8RPFmR5tdWhNqyojRjMn2ZREYRTJlvURw3qo4rxFQYaxfVnjycXHU0u1kQmNo7e6DhaYhNIxJrJWlHyrovtaGzHJb9Bk1v7NrbjYuddco5LxnbJ5h2ytksm75DOuWRsh1QuTzLrkMjmSebyJDJ5BjI2ubyDzqZw0gNoJ4+/ZhyZt1eQ3bjMC76JHsrmnImvZhybrj0X5QtgxWoJjJlOcMwMlC+Ir2YcgXA5ZjCKVTkaZfmpOeXr4DrofA5lersVIxRD+UPk+zvItryJr7IBIxhh0y/OxghGWR+rJjBmOtXHfYnMhqXY3ZswIhWY4XL8teNRgQi4DoZlEQ1YlAV9RAMWkYBJJGAR9puEfCYhv0nQ56WAZRCwTPyW4SVT4TMNLHMK/oqpWFXnY5kKP3kiyY00DqxhUmIjwcRGAgMbcBJvc9rH2khMstjU79KW0NRHvR1/IqdZ1e3SmXLoSmmObQ7zj9Ve8NZ4Qfnf5ya56rAePnt/mtaEpiwAMb/i1ycG2djvcvcbeSI+RdgH+9WbHDja5KUWh0xeE7IUIR9MrTFwXG87C5iKgAU+A69HQZlg+gvJtyUZw5eWtzSswvqwx4ZZWA6um957Dj5Wg3nGVo9N79KqaqvnhtaVt66GlVEGoUJqeMfzfrBGga8BIsPzVeFg08uztUPSyZJ0bRJOhqSTIzkrQ9LNkXKyW1JTltQJGdJujrSTI+VkSDs5Zv6ombSTJe1kybg2GSdL/an11J5Si3Y0OqdRlve/HXfFOLTj9RYHi9hrPCIDMtBUWK7dKn8jcPBWeY2AuYOyNUqpoNY68+FX8d3Zre38pq0DJ+t1TfvSLgFXM6oPomh6Blx8WqM0+E1oiBl0p1z6Ml4MdbWmMWYQ8sHKLteLqxoClmJSlUFr3KU9qXE1ZDQ0VBpUBuHFFgetwdUQtBQHjDbZ0Oeyrs/FLeRPrzUYHTP4x+o8edd7j4ClOK7ZYlW3w5K2LWUPGG0wudrkL8ts0nmN44LPhEtm+Vne4fDE2jyOBseFI8dbHNRoct0LWXrSGkeDAn7wySCvbHa4ZYmNozV5F07ax+KUKT6+/n8ZNg245F3Iu3D3OSGe3+Twnaez2A7YrubCmX6+PMfPGXekWNzmkHMg58Cay6MsfNth3m0p3MLv7PKD/Fw3L8iX/p7htVaHYGFH+MRFYdoSmj8vsQn7IOxTRAo9mGUBRXOVQdSvKAsoQj5Fc6XizrNClAcV5QEoDypsbfKjk+vo0xF63Bg9OsqTqpxuXUb7PiGed8vocKK0ZWvoYizZniRuNukFM9fFqqhCqQS59nvQ2gHHQQXCBOonkWtfg92zGe3YaCdPaOL+GMEo8VceQOdz6HwOM1JB2UFnkFj6fyTfXIDOpXFzKaqOuQx//WQ2/fJsUAojXEagcRp187+Fk+jBSfVhRqvwj2rGjFVj+EOMveKv+EIR6suCjCoLUF8epO7Q+VRHvK7o8pCPoG8wAM4l73rd11nbJZ6x6UlOpTt5Kl3xLO1xr9Xd2pdh3L/dg5PoJR/v8g6mADeTINu6EifRi5seoPKTn8NfP4lNvzwb5QtgBCIERk+ldv7VJJY+Rmr1ixj+EMoKEJt9Ir66CfQ//1eU5UdZfsxwBZFph5Pr3EC+pwVME2VY+OomYEWryG5eCcpAGSbKqsRXvS9OJoGbSaCUotpIMiaUo64sTY3dSl16gLoDB5hqJKk2UlSpAdp1gmOnJLH/wyKeg/6MJlTYXi6e5aMtoYlnNfGcxjIg60DLgEvShpStMQ04cLTJDa/keK3NGTowXPIvURa1Opx4e4ps3vutf/FAH789KcRJt8V58W0Hv+ntE174XIS2hOYz96exDPAZipMnW1x9eIDvPpXhtTbXyzfh2uOD2C5c83QWy2Do8y+d7efWpTmWd7iYysv/0sf9+E3FDa/kMA0wFTRXGZw+1ceT6/Ks6nYxlJd/8mSLWEBxzxs2hlIYCuqjiqPGWyxuc9jQ56KUdyA8p9GkIqh4ar2DobzffnlQceBok7W9LpvjLgqv7JQak4ogvLV5y+trLDi81qQ94dKR1F4MB8aUGZQHFau6HcDL85uKpgqDvoymN62H4n0srLACBhuSkFEK21DYpiISMcm2xYnzJuy/u6LAO43UgDx4+5e+rfITwNYnW+6sLEAF0LazD1NK7WiQuHlnr3s3lvJzRDrD//t7mj8vsVF4G8zD54eZUm0w53fezkEBc8aYPHx+mF++kOOPi+yhDfGW+SEOHmNy/K0pwNtoZ9R5ZW9fZvP7V7e873UnBDm+2eSzD2QwCxvn+AqD+88L88S6PL9/JVfY8BX/cYSf0TGDny30gp6hoDbiBeTXO1xuWmx7P0gDKoI+JlebPL42T9LWGAqifsUls6A7pVnWseXHO7vBi4rxnNf4NpW3swAImDAqqrAMhWV4nwfw8UaTqTUGZmGHowo7h68c7O00fIb3dwD86OgAtuO9Z8BURPxw1HiTnm/ECFjeTsxQCkcrbj8rQsbWZPJeK7nLP5p8ueLrc1tI5b0Wsh0Zxa35fek0F5PMt9OadIlnXZ4bcyFxW7HukT/Qn3Xpz2iyYw8mdPLVdN77X6RWPT+49dDwmetQVoDNf/p/KKPQcphwALWnX0X/gr+QXPkcqtBCqT39m1jRarofvR4ML4j4GyYTqJ9EZtPrZNYtAtNCmT4CoydjBKM4yV4vEPmCGCHvcom+uolE/WEvaPmD+GuaUL4AY79yJ8oXJBqwvG7hiJ+qKfOpi53ndRlHA9SXh2gojPVWRwOY76e7+F1orRlIe2PT3vh0ms54lo6Dm+iMn0FnIktvMkdPKkdfymbc1+7BzSZxM0m0dgHw1zeDYaLtDNrOoHwB0C5uJlE4MLExw2VeQO5YS3L5k2g3D45D+aHnYkWr6Pm/33pl3TxmpJL6C/6b1Ipn6FtwO2hNq+vQcvTnic48hk2/+zluJgGuixEqY+yXbyW+6CF6Hvv90HY74ZgLGT37cNJ3XUXUjVMWVJSFAzQddzG+jhX8dOGLRP2K/Rv9VDSMI1Zdh9m6nIUtOb58cJCQBdHKGgJuEuVkmDvOIv2tMnTh4HSwzfbn04Mkc5B1NLYD1SFF2Ke4/gQv2OZdhlr0R0+0mFqjsV3vIDniV2Tzmv3qvRZ43oWqkFfWZ3i/o7wLdt470M67ms1xd+hg2m96ZVf3uCzY5OAUDtQPG2diGXD3G3ncQtmZdQZHjbd4dkOeB1bmCw0I+OmxQQKW4ppnsmgNjtZMrzW56bQQ979pc/NSe6ixcN0JQeaOM7novvRQ3j7VBg+fH+Yvy22ufzE39L7XnxDktKk+jr0lhe1439fYMsVLn49yyxKb7z/rfZ4Grj0+wKf383PS7+P0ZzVae/uaNZfHAFiYL95pgiNyUpdS6hjgMeBArfWrw/J/DZystR4/LG8S8BZwltb67mH5/4Y36zqgtc6/y+ftMCBPnz498EEnda1/4xXG33E0rlZe6xbQKDTehj/Y4vUeK7QyvMlegB58jfK6i1zX21m5g683LFxX42q9TDxQoQAAC1tJREFU5X2V5b2Hk8dFbSlr+nFdF9d1Cxu4Qpt+tGHh2lkclJenDLQvhOs4OHkHDTgYYPrRpp98LoOjwcXAxUAHorh5B9vOoVE4GGgriLaC5DIpXO0FRgcDwpXYeYd8No2DSR7vs7QvQjaVwHa9z7K1iY7Wks875NIp8pjYmDi+KE6wnGwiTs7R2JjktIUbG0XWgUwyQU77yCoLxxdDh6twEr1oxy78k8GMVoPr4qQHhsZpjULrzM0m0U5+qEvNCHizwrWdHcpTpokyfWjXKbynsd2JS0qBqRSGoTCVwjS2JEMpfKa37jMNTMM7QPFbBlYhz+uK9ZbDu2hDw7twLYNIwOvqDQcsYkGvy7cs5C2Dg0dBJSzvuCSyeQbSXnf7QNomkc2Tynld8emcQ9oupJzjtc7zzlAr3Xa8lMu72K7GzrtDQwCO6yXbcXG1Ju9uyXMKv5vBgLM9eviwjtbe/9q0cHPpoXwNmMEoOp/bko/2Dpz8IZxkL9pxGPzlW2V1uLkMbnrAK6cdgoEAoVAQI96Gz83gJ49POYTLKrCcNEaqBx8OPpXH7/cTCIZQqW5MJ4elHCxcAtEYpmOjMn1YysXCwbJ8+IMBVGYAw8lhKhcTF18ogqEdVDaBhYOhNKZpYvkDqFwS5dqYaExcTH8QQ2lULompvD2XaRhYlg/tZDHcPAba2xtYfgylMfIZVOHwwjQUhmmBY2Nor6xCY5iW1+Bwcl5rGa91a5gmqjC8ZQzuFQ3DK1voaRksq5RC6cE9nB5qlBiF/53XoBncszJUzlCwcOxlHPLZn37g7XZvnNT1dmE5Hnh1WH7TsOcGteBt8eO3ym8CWt8tGAPs6IstBOrp717d7audOIt/XrD6Xcsp3nsLZWfzfXb6Lmr46o5LDr7/4JSurTeg4QFo67qod5TbcQV29LrB3oLt1Uehtn3dsOcGH3s/RDXUw7DlNcPz1LDP9FrUw9ff8R6DeVDorlPecBgMBViGrRuK7QZpsS3LNKgI+6kIF/dcYdfVOIUADQwF66EDZu0F7m2W6KFWmdaF9e3lFz7HaxsNf84ry9DnFMoVygy30+eGyuh3PB7+um1Lb/vczl43vGGn2fKbdQFnJ20+zU4+ZIc1285z77Fduc3nbce4quKdgjlSA/LKQjoNuBtAKRUBjgK+M7yg1jqtlHqsUPbnhbIGMG/wtcUSCVgcvo/c21SIUmYYCgPFCOhUECPcCDp3ZQvtHY79CLhAKfV5pdQU4CagH7hJKXWcUqpbKXVC4SU/AQ5VSv1HoQv7OqAG+FUx6i+EEEJsbUQGZACt9c145xxfDiwAgngX+ujD6ynJAnah7JPAfOBU4GVgGnCk1vrd+4uFEEKI3WCkdlkDoLW+EbhxO/mPA6O3ynsQeHA3VU0IIYR4X0ZsC1kIIYTYk0hAFkIIIUqABGQhhBCiBEhAFkIIIUqABGQhhBCiBEhAFkIIIUqABGQhhBCiBEhAFkIIIUrAiLzbU6lQSg0EAoFYc/Mu3YVRCCHEHmLNmjVks9m41rrs/b5WAvIuUEq1AWFgU7Hr8iEaPLpYU9RalCb5bnZMvpsdk+9m+/bU72UskNJa17/fF0pAFu8weO/nD3Ivzz2dfDc7Jt/Njsl3s33yvWxLxpCFEEKIEiABWQghhCgBEpCFEEKIEiABWQghhCgBEpCFEEKIEiCzrIUQQogSIC1kIYQQogRIQBZCCCFKgARkIYQQogRIQBZCCCFKgARkIYQQogRIQBZCCCFKgARkIYQQogRIQBbvSin1RaWUVkp9t9h1KTblOU8p9bRSqksp1aKU+rNSqrrYdSsWpdQpSqkXlFK9SqnHlFJy9x5AKXWCUupRpVSrUqpTKXWvUqqp2PUqJUqpeYV9y03FrkspkIAsdqqwA/khkCh2XUrIpcAfgQOAC4EjgLuLWqMiUUqdBNwD3AIcDHQBzyqlRhe1YqXhYuB+4DDgJKAJeEwp5StqrUqEUqoc+APQW+y6lAq5UpfYIaWUAh4DVgHzgP/VWl9T3FqVHqXUpcCNQLPWem2x67M7KaVeBtZorc8rPA4CrcB1WuvvFbNupUYp9UngCeBorfWTxa5PsSmlbgQagBCwXmv9mSJXqeikhSx25jJgP+B7Ra5HqesqLGNFrcVuppSaABwI3DuYp7XOAE/jtQjFO+2V28n2KKVOAM4HvlbsupQSCchiu5RS44CfAl/QWncUuz4lbi6QBt4sdkV2s8Hx0K17BTYCY3ZzXUaCuYAGFhe7IsWklCrD66q+Wmv9RrHrU0okIIsd+SNwr9b6nmJXpJQppcYA/wr8WmudLXZ9drP6wrJvq/wEULmb61LSlFJR4FvAXVrrDcWuT5H9HO8g7tpiV6TUSEDeyyilzi3MatxZ+i4wFbi82PXdnd7jd3PksPLlwEPASuD7Rat48Qx2wZZtlV8OtO3mupSswiSuu4E8cGWRq1NUSqnjgHOAS7RMYNqGTOoS21BKvQWMBzLDsiOADeS01jIG5k1e+gfQCMzVWrcXuUq7nVJqKvAGcJbW+u5h+Q8ClVrrw4pWuRKhlDKA24Bj8baTlUWuUlEppR4DPoE3xDMohNeVnwFmaK03FqNupcAqdgVESTqGbbeNZ/CO8q/f/dUpLUopE/grXi/CoXtjMC5YWUinUTjtSykVAY4CvlO8apWU64FTgU/u7cG44GK8ADzcbUAL8A1g826vUQmRgCy2sb0xLqWUDfRordcUoUoloxCM/4wXdE4Fugpd1wCZvWkcWWutlVI/Am5SSv0TeBb4AdAP7PUXelBK/RfweeBTwJvDtpOc1jq941fuubTW2wRcpVQaGNjb9y0gY8hCvF/nABfgjZM+gzehaTBdVcR6FYXW+ma80+MuBxYAQbxeg60neu1VlFKH4G0Pfrzeg+HbyW+LWDVRwmQMWQghhCgB0kIWQgghSoAEZCGEEKIESEAWQgghSoAEZCGEEKIESEAWQgghSoAEZCGEEKIESEAWQgghSoAEZCGEEKIESEAWQgghSoAEZCGEEKIESEAWQgghSoAEZCHETimlFiultFLqD++x/BVKqbhSKlp4/N3C63eUqj/av0CIkUFuvyiE2CGl1CxgP2AAOFcpdcV7uHXgZcDtWuvEVvm/w7tD1tbiu15TIUY+CchCiJ25BMgA3wJ+BZwO/GVHhZVSc4HpwKe38/SLWus7PoI6CrFHkC5rIcR2KaV8ePd+fhS4FcgBF7/Lyy4DXtFaL/qIqyfEHkcCshBiR04CaoC7tNZ9wGPAsUqp0dsrrJSqAM4Gbth9VRRizyEBWQixI5cASeC+wuNb8fYZF+6g/KeBPDvp0hZC7JgEZCHENpRStcCJwN1a62Qh+368yV2X7OBllwG3DisvhHgfJCALIbbnAsAH3DKYUZhd/TdgmlLq48MLK6UOAT4GvKdTo4QQ25KALITYnkuAFuDJrfJvLiy3ntx1Gd4s6sUfcb2E2GNJQBZCvINSajbeuce3aa3drZ7+J7AO+JRSyl8oXw6cg0zmEmKXSEAWQmztksLylq2f0FrrQn4VcHIh+0LABuQcYyF2gQRkIcSQwrnH5wOvaa2X76DYYKC+pLAcnMyV+oirJ8QeTa7UJYQY7mS8c4/fUEp9ayfleoB5Sqk5wL7s+FQoIcR7JAFZCDHcvoXl4YX0bn4MLNRaL/voqiTE3kF5Q0JCCPH+KaW+jheQnyt2XYQY6SQgCyGEECVAJnUJIYQQJUACshBCCFECJCALIYQQJUACshBCCFECJCALIYQQJUACshBCCFECJCALIYQQJUACshBCCFECJCALIYQQJUACshBCCFECJCALIYQQJUACshBCCFECJCALIYQQJUACshBCCFECJCALIYQQJUACshBCCFEC/j+sDsx9k5p5SgAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Make two independent axes: dets/betas:\n", "dets = np.arange(-5.0, 5.1, 0.1)\n", "intensities = np.logspace(-2, 2, 5)\n", "\n", "fig, ax = plt.subplots(nrows=1, ncols=1)\n", "for intensity in intensities:\n", " Rijl = np.zeros(dets.shape)\n", " Neq = np.zeros(dets.shape + (4,))\n", " for ii, det in enumerate(dets):\n", " laserBeams = pylcp.laserBeams(\n", " [{'kvec':np.array([1., 0, 0.]),\n", " 's':intensity, 'pol':-1, 'delta':det}]\n", " )\n", " \n", " rateeq = pylcp.rateeq(laserBeams, magField, ham)\n", " \n", " Neq[ii] = rateeq.equilibrium_populations(\n", " np.array([0., 0., 0.]),\n", " np.array([0., 0., 0.]),\n", " 0.\n", " )\n", " \n", " Rijl[ii] = np.sum(rateeq.Rijl['g->e'], axis=2)[0][0]\n", "\n", " ax.plot(dets, Rijl*(Neq[:, 0]-Neq[:, 1]))\n", " ax.plot(dets, intensity/2/(1+intensity+4*dets**2), 'k--', linewidth=0.5)\n", "\n", "ax.set_xlabel('$\\Delta/\\Gamma$')\n", "ax.set_ylabel('$R_{sc}/\\Gamma$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Coupling three states together\n", "\n", "Instead of just considering a single laser coupling the $m_F=0$ and $m_F'=-1$, we can add in a second laser and consider coupling $m_F=0$ to $m_F'=+1$ as well. We add this coupling laser by adding a counter propogating laser with the same circular polarization *relative to its $k$ vector*. Relative to the quanitization axis, this laser has $\\sigma^+$ light.\n", "\n", "We then compare to the modified analytic formula\n", "\n", "$$\n", " R_{sc} = \\frac{1}{2}\\frac{s}{1+3 s/2+4 \\Delta^2/\\Gamma^2},\n", "$$\n", "\n", "which is shown in the plot as black dashed lines." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Make two independent axes: dets/betas:\n", "fig, ax = plt.subplots(nrows=1, ncols=1)\n", "for intensity in intensities:\n", " Rijl = np.zeros(dets.shape + (2,))\n", " Neq = np.zeros(dets.shape + (4,))\n", " for ii, det in enumerate(dets):\n", " laserBeams = pylcp.laserBeams(\n", " [{'kvec':np.array([1., 0, 0.]),\n", " 's':intensity, 'pol':-1, 'delta':det},\n", " {'kvec':np.array([-1., 0, 0.]),\n", " 's':intensity, 'pol':-1, 'delta':det}]\n", " )\n", " \n", " rateeq = pylcp.rateeq(laserBeams, magField, ham)\n", " \n", " Neq[ii] = rateeq.equilibrium_populations(\n", " np.array([0., 0., 0.]),\n", " np.array([0., 0., 0.]),\n", " 0.\n", " )\n", " \n", " Rijl[ii] = np.sum(rateeq.Rijl['g->e'], axis=2)[:, 0]\n", "\n", " ax.plot(dets, Rijl[:, 0]*(Neq[:, 0]-Neq[:, 1]))\n", " ax.plot(dets, intensity/2/(1+3*intensity/2+4*dets**2), 'k--', linewidth=0.5)\n", "\n", "ax.set_xlabel('$\\Delta/\\Gamma$')\n", "ax.set_ylabel('$R_{ge}/\\Gamma$');" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 4 }