{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Some imports\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy.special\n", "from prettytable import PrettyTable" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Hamiltonian of the Cooper box is given by\n", "$$\n", "H = E_C \\sum_N (N-N_g)^2 |N \\rangle \\langle N |\n", "- \n", "\\frac{1}{2}E_0 \\sum_N\n", "\\big[\n", "|N+1\\rangle \\langle N| + |N-1\\rangle \\langle N|\n", "\\big]\n", "$$\n", "For simplicity, we set $E_C = 1$ and measure all energies relative to $E_C$. The following function calculates the eigenvalues of the Hamiltonian with $E_0 = 0$.\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "####################################################\n", "# Return the energy eigenvalues of the unperturbed #\n", "# Hamiltonian (the diagonal part) #\n", "####################################################\n", "def E0(N, Ng):\n", " return (N-Ng)**2\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we plot the eigenvalues for different values of $N_g$. We plot three curves, corresponding to N=-1,0,1" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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aUwb3Np2DW8Tog09ZnLtY7a52vXPuHdMpAAAA+Nrei9d1urxOz9yToRAHp3z+\nhtEHn9KvWz/d3+9+rT+/Xg1tDaZzAAAAIOmVnQXqGRuuJ0almE7BbWD0wecsG7JM9e312pS/yXQK\nAABA0Dt1qVZ7LlZp6d39FR4aYjoHt4HRB5+T2yNXY3uP1Zqza9TW2WY6BwAAIKi9sqtAseGhmjs2\nzXQKbhOjDz5p6ZClqmiu0CeFn5hOAQAACFol1xu15dQVzRvXT90inKZzcJsYffBJ45PHKychR6tO\nr5LLdpnOAQAACEordxUq1OHQ0gnpplPQBYw++CTLsrRkyBIV1xXry7IvTecAAAAEncr6Vm08ckkz\n7khRz24RpnPQBYw++Kwp/aYoJSZFq06vkm3bpnMAAACCyup9RWrvdGn5xAzTKegiRh98VqgjVItz\nF+tk5UkduXbEdA4AAEDQaGjt0Jr9JXoot7cykmJM56CLGH3waY9nPq748HitOr3KdAoAAEDQePdg\nqepaOrRi0gDTKXADRh98WmRopObmzNXu8t3Kv5FvOgcAACDgtXW49MaeIo3LSNCI1O6mc+AGjD74\nvKcHPa3I0EitPr3adAoAAEDA++h4ua7WtehnnPIFDEYffF5ceJxmDJyhLUVbdKXhiukcAACAgOVy\n2Xp1V6Fy+nTTpKwk0zlwE0Yf/MKi3EWSpLfPvm24BAAAIHBtP1+hixUN+tmkDFmWZToHbsLog1/o\nHd1bj2Q8ovcvvK+alhrTOQAAAAHplZ0F6hsfqalD+5hOgRsx+uA3luQuUXNHs97Ne9d0CgAAQMD5\nqrhaR0puaPnEDIWGMBMCCb+b8BuZ8Zma1HeS3j33rpo7mk3nAAAABJRXdhQoITpMT41ONZ0CN2P0\nwa8sHbJUN1pv6MMLH5pOAQAACBh5V+u1/XyFFo1PV2RYiOkcuBmjD35lVK9RGpE0Qm+ffVsdrg7T\nOQAAAAHh1V0FinSGaOH4fqZT4AGMPvidpUOWqryhXJ8Xf246BQAAwO+V1zRr8/HLmjMmVfHRYaZz\n4AGMPvidSamTlBGXoTdPvynbtk3nAAAA+LU3dhfJlrTs7v6mU+AhjD74HYfl0OLcxcq7kae9l/ea\nzgEAAPBbNU1teu+rUk0bnqy+8VGmc+AhjD74pUczHlXPqJ5adXqV6RQAAAC/9fb+EjW1dWrFpAzT\nKfAgRh/8kjPEqYWDF+qrq1/pVOUp0zkAAAB+p7mtU6v3FWtydpIG9e5mOgcexOiD35qZNVOxYbF6\n88ybplMC0bIFAAAgAElEQVQAAAD8zqYjZapubNPPJg0wnQIPY/TBb0U7ozUne462lWxTcW2x6RwA\nAAC/0dHp0srdhRqZ1l1j+ieYzoGHMfrg1+bmzJXT4dTqM6tNpwAAAPiNT09fVVl1s342aYAsyzKd\nAw9j9MGv9YjsoemZ07W5YLMqmypN5wAAAPg827b1yo4CDUiK1pScXqZz4AWMPvi9xbmL1Wl3au25\ntaZTAAAAfN7uC1U6e6VOK+4ZIIeDU75gwOiD30vtlqop/aZoQ94G1bfVm84BAADwaa/sLFCvbuF6\nfGSy6RR4CaMPAWHJkCVqaG/QxvyNplMAAAB81slLNdpXcF3L7u6v8NAQ0znwEkYfAkJuYq7G9hmr\ntWfXqq2zzXQOAACAT3plZ4FiI0L19Jg00ynwIkYfAsbSIUtV2Vypjws+Np0CAADgc4qqGrXl9FXN\nH9dPsRFO0znwIkYfAsb4PuOVk5Cj1WdWq9PVaToHAADAp6zcVShniENLJqSbToGXMfoQMCzL0tIh\nS1VcV6ztpdtN5wAAAPiMa3Utev/oJc0Y1Vc9YyNM58DLGH0IKFP6TVG/bv302qnXZNu26RwAAACf\n8NquQnW6bP2XSQNMp8AARh8CSogjRD8d+lOdrz6v3eW7TecAAAAYV93YpncOlurx4clKS4wynQMD\nGH0IOFMzpio5OlmvnnyV0z4AABD0Vu0pUktHp34+mVO+YMXoQ8BxOpxaOmSpTlae1KGrh0znAAAA\nGFPb3K639hXr4SG9ldkz1nQODGH0ISBNHzhdSZFJWnlypekUAAAAY97eV6z61g79YnKm6RQYxOhD\nQAoPCdfi3MU6dPWQjlccN50DAADgdY2tHXpjb5HuG9RTuclxpnNgEKMPAWtm1kzFh8dz2gcAAILS\nuoOlqmlq1y/u5ZQv2DH6ELCinFFaMHiBdpfv1tnrZ03nAAAAeE1Le6dW7i7UhMxEjUqLN50Dwxh9\nCGhzBs1RrDNWr518zXQKAACA12w4XKbK+lY9O3mg6RT4AEYfAlpsWKzm5szVttJtunjjoukcAAAA\nj2vrcOmVHQUa3S9e4zISTOfABzD6EPDm58xXZGikXj/9uukUAAAAj/vTsXJdrm3RL+7NlGVZpnPg\nAxh9CHjdI7prdvZsbSnaotK6UtM5AAAAHtPR6dLLOy5qSEo3/SQryXQOfASjD0FhUe4ihVqheuP0\nG6ZTAAAAPOaTU1dUfL1Jz04eyCkf/orRh6DQI7KHZmTN0OaLm3Wl4YrpHAAAALdzuWz9+xcXldUr\nRg8M7mU6Bz6E0YegsSR3iWRJb55503QKAACA2209e00XKhr0i8mZcjg45cP/wuhD0OgT00fTBkzT\n+/nvq6q5ynQOAACA29i2rX//8oLSE6P06LBk0znwMYw+BJVlQ5apw+7QW2feMp0CAADgNjvyK3W6\nvE4//0mmQjjlw7f4zOizLKu7ZVmbLMs6b1nWOcuyxptuQuBJ65amh/s/rPV561XTUmM6BwAAoMts\n+y/P8qV0j9T0kSmmc+CDfGb0Sfq9pM9s2x4kabikc4Z7EKCWD12u5o5mrT231nQKAABAlx0orNaR\nkhv62aQMhYX60rf38BU+8afCsqxuku6R9IYk2bbdZts2xzDwiAHdB+j+tPu17tw61bfVm84BAADo\nkn//8oKSYsM1a3Sq6RT4KJ8YfZIyJFVKetOyrGOWZb1uWVb0tz/JsqxnLMs6bFnW4crKSu9XImAs\nH7Zc9e31eu/8e6ZTAAAAbtuRkhvae/G6npmYoQhniOkc+ChfGX2hkkZJ+qNt2yMlNUr6r9/+JNu2\nV9q2Pdq27dFJSUnebkQAGZw4WBNTJurts2+rqb3JdA4AAMBteenLi4qPcmru2DTTKfBhvjL6Lkm6\nZNv2wa//fpP+MgIBj3lm2DOqaa3RpvxNplMAAABu2enyWn1xvkLL7u6v6PBQ0znwYT4x+mzbviqp\nzLKs7K9/6T5JZw0mIQiM6DlCY3qP0eozq9Xa2Wo6BwAA4Ja8vOOiYsNDtWB8uukU+DifGH1fe07S\nO5ZlnZQ0QtL/MNyDIPDMsGdU2VypP134k+kUAACAm3bhWr22nL6qRXelKy7SaToHPs5nRp9t28e/\nfl5vmG3b023bvmG6CYFvTO8xGp40XKtOr1K7q910DgAAwE15eUeBIkJDtPTu/qZT4Ad8ZvQBJliW\npWeGPaPLjZf1SeEnpnMAAAB+VMn1Rm0+cVnzx6UpITrMdA78AKMPQW9iykTlJOTo9VOvq9PVaToH\nAADgB72ys0AhDkvLJ2aYToGfYPQh6FmWpeXDlqukrkRbS7aazgEAAPhel2uatenIJc0enaqe3SJM\n58BPMPoASfel3aeMuAytPLlSLttlOgcAAOA7rdxVKNuWVkzilA83j9EHSHJYDi0ftlwXay5qR9kO\n0zkAAAB/p7K+Ve8eKtWTo1LUNz7KdA78CKMP+NpD6Q8pNTZVK0+ulG3bpnMAAAD+k9f3FKq906X/\n8pNM0ynwM4w+4GuhjlAtG7JMZ66f0b7L+0znAAAA/NWNxjat3V+iR4clq3+PaNM58DOMPuBvTBsw\nTb2iemnlyZWmUwAAAP7qzX3Famzr1C8mc8qHW8foA/6GM8SppUOW6mjFUR2+eth0DgAAgOpb2rV6\nb5EezO2l7N6xpnPghxh9wLc8OfBJJUYkctoHAAB8wpoDJapr6dCzkweaToGfYvQB3xIRGqFFuYu0\n/8p+naw8aToHAAAEsaa2Dr2+u0iTspI0tG+c6Rz4KUYf8B2eyn5KceFxeu3ka6ZTAABAEHv3UJmq\nG9v03L08y4fbx+gDvkO0M1rzc+Zrx6UdyqvOM50DAACCUGtHp1buKtC4jASNTk8wnQM/xugDvsfc\nnLmKccbwbB8AADBi4+FLulbXqufu5Vk+dA2jD/ge3cK66elBT2tryVbl38g3nQMAAIJIa0enXvry\nokalddddAxJN58DPMfqAH7Aod5FinDF65cQrplMAAEAQ2fBVma7UtuiFKVmyLMt0Dvwcow/4AXHh\ncZqXM0//UfIfPNsHAAC8oqW9Uy99WaDR/eJ1d2YP0zkIAIw+4EcsGLxAsc5Y/fHEH02nAACAILD+\nqzJdreOUD+7D6AN+RFx4nOYPnq/tpdt1vvq86RwAABDAWto79fKOixqTnsCzfHAbRh9wE+YPnq9Y\nZ6xePv6y6RQAABDA3j1Uqmt1rfrllIGc8sFtGH3ATegW1k0Lchfoy7Ivdfb6WdM5AAAgAP3llK9A\nY/sn6K4BPMsH92H0ATdpfs58xYbF6o/HebYPAAC43zsHS1VZ36oXpmSZTkGAYfQBNyk2LFaLBi/S\njks7dKbqjOkcAAAQQJrbOvXHHQUan5GocRk8ywf3YvQBt2BezjzFhcfp5RM82wcAANznnYMlqmrg\nlA+ewegDbkFMWIwWDV6kXZd26VTlKdM5AAAgADS1deiVnQWakJmoMf0TTOcgADH6gFs0N2euuod3\n57QPAAC4xdoDJapqaNML93PKB89g9AG3KNoZrUW5i7SnfI9OVJ4wnQMAAPxYU1uHXt1ZqIkDe2h0\nOqd88AxGH3Ab5g6aq/jweN7kCQAAuuTt/SW63timX3LKBw9i9AG3IcoZpcVDFmvv5b06XnHcdA4A\nAPBDja0dWrmrUPdkJemOfvGmcxDAGH3AbZqTPUcJEQl6+TjP9gEAgFv31v5iVTe26YX7B5pOQYBj\n9AG3KcoZpSW5S7T/yn4dqzhmOgcAAPiRhq9P+X6SnaSRaZzywbMYfUAXPJX9lBIiEvTS8ZdMpwAA\nAD/y1r5i1TS18ywfvILRB3RBlDNKS4cs1cErB3Xk2hHTOQAAwA/Ut7Rr5a5C3Tuop0akdjedgyDA\n6AO66Knsp5QYkcizfQAA4Kas3lus2uZ2/ZJn+eAljD6giyJDI7Vs6DIdunpIX139ynQOAADwYXUt\n7Xptd6Huz+mpYX055YN3MPoAN5iVNUtJkUmc9gEAgB/05p5i1bV08CwfvIrRB7hBRGiElg1dpsPX\nDuvQlUOmcwAAgA+qbW7X63sKNWVwLw1JiTOdgyDC6APcZGbWTPWM7KmXjr8k27ZN5wAAAB+zak+R\n6ls6eJYPXsfoA9wkPCRcy4Yu09GKozp49aDpHAAA4ENqm9q1ak+RHsztpdxkTvngXYw+wI1mZM1Q\nz6ieevn4y5z2AQCAv3pjT6HqW3mWD2Yw+gA3Cg8J1/Khy3Ws4pj2X9lvOgcAAPiAmqY2rdpbrIeH\n9FZOn26mcxCEGH2Amz058En1ju7NaR8AAJAkvb67SA2tHfrfeJYPhjD6ADcLCwnT8qHLdaLyhPZd\n3mc6BwAAGHSjsU1v7i3S1KF9NKg3p3wwg9EHeMATmU+oT3QfTvsAAAhyr+0uVFN7J6d8MIrRB3iA\nM8Sp5cOW62TVSe0p32M6BwAAGFDd2Ka39hVr6tA+yuoVazoHQYzRB3jI9AHTlRydzGkfAABBauWu\nr0/57uOUD2Yx+gAPcYY4tWL4Cp2+flq7y3ebzgEAAF50vaFVb+8v1rThyRrIKR8MY/QBHvTYgMfU\nN6Yvp30AAASZlbsK1dLeqec55YMPYPQBHuR0OPXMsGd05voZ7by003QOAADwgqqGVr29v0SPj0jR\ngKQY0zkAow/wtMcGPKbU2FRO+wAACBKv7ixQa0ennrs303QKIInRB3hcqCNUK4at0Lnqc/qy7EvT\nOQAAwIMq6lu05kCJpo9MUQanfPARjD7AC6ZmTFW/bv30xxN/5LQPAIAA9urOQrV32nr+Xp7lg+9g\n9AFe8M1p3/nq89pWus10DgAA8ICrtS1ae6BET4xMUXqPaNM5wF8x+gAveaT/I8qIy9Afjv1BHa4O\n0zkAAMDNXvzigly2zb188DmMPsBLQhwhem7kcyqqLdKfC/9sOgcAALhRcVWjNnxVpqfHpCk1Icp0\nDvCfMPoAL7ov7T4NSRyil4+/rLbONtM5AADATf5tW76cIQ49yxs74YMYfYAXWZal50c9ryuNV7Qx\nf6PpHAAA4AbnrtRp84nLWjIhXT1jI0znAH+H0Qd42bg+4zSm9xitPLlSTe1NpnMAAEAX/ebzPMWG\nh2rFPQNMpwDfidEHeNk3p33VLdVae26t6RwAANAFR0qqtf18hVZMGqC4KKfpHOA7MfoAA4YnDdfk\n1MlafXq1altrTecAAIDbYNu2/vmzPPWICdeSCemmc4DvxegDDHlu5HNqaG/QG6ffMJ0CAABuw64L\nVTpYVK3n78tUVFio6RzgezH6AEMGxg/U1IypWndunSqaKkznAACAW+By2fqXz8+rb3yk5tyZZjoH\n+EGMPsCgn4/4uTpdnVp5cqXpFAAAcAs+O3NVp8vr9ML9WQoL5Vtq+Db+hAIGpcamakbWDL2f/77K\n6spM5wAAgJvQ0enSb7bmKatXjKaPTDGdA/woRh9g2IphKxTqCNVLJ14ynQIAAG7CB0fLVVjZqF89\nkK0Qh2U6B/hRjD7AsKSoJM3NmatPCz9V/o180zkAAOAHtLR36nfb8jU8tbseGNzLdA5wUxh9gA9Y\nOmSpYpwx+sOxP5hOAQAAP2DdwVJdrm3Rrx/MlmVxygf/wOgDfEBceJyWDFmiHWU7dLziuOkcAADw\nHRpaO/TSlxc1ITNREzJ7mM4BbhqjD/AR83LmKSEiQS8ee1G2bZvOAQAA37JqT5GuN7bpHx/INp0C\n3BJGH+AjopxRembYM/rq6lfaf3m/6RwAAPA3bjS26bVdhXpgcC+NTIs3nQPcEkYf4ENmZc1ScnSy\nfn/s95z2AQDgQ17ZWaCGtg7944Oc8sH/MPoAHxIWEqafj/i5zl4/q22l20znAAAASVdrW7R6X7Ge\nGJmirF6xpnOAW8boA3zMoxmPKiMuQ3849gd1uDpM5wAAEPRe/OKCXLatF+7PMp0C3BZGH+BjQhwh\nem7kcyqqLdLHBR+bzgEAIKgVVzVqw1dlenpMmlITokznALeF0Qf4oPvS7tOQxCH644k/qq2zzXQO\nAABB69+25csZ4tCz92aaTgFuG6MP8EGWZen5Uc/rSuMVbczfaDoHAICgdO5KnTafuKwlE9LVMzbC\ndA5w2xh9gI8a12ecxvQeo5UnV6qpvcl0DgAAQec3n+cpNjxUK+4ZYDoF6BJGH+Cjvjntq26p1pqz\na0znAAAQVA4XV2v7+QqtmDRAcVFO0zlAlzD6AB82PGm4JqdO1uozq1XbWms6BwCAoGDbtv758zz1\niAnXkgnppnOALmP0AT7uuZHPqbG9UW+cfsN0CgAAQWHXhSodKqrW8/dlKios1HQO0GWMPsDHDYwf\nqKkZU7Xu3DpVNFWYzgEAIKC5XLb+5fPz6hsfqTl3ppnOAdyC0Qf4gZ+P+Lk6XZ169cSrplMAAAho\nW05f1enyOr1wf5bCQvlWGYGBP8mAH0iNTdWMrBn64MIHKqsrM50DAEBA6uh06bf/kaesXjGaPjLF\ndA7gNow+wE+sGLZCoY5QvXTiJdMpAAAEpA+OlquwslG/eiBbIQ7LdA7gNow+wE8kRSVpbs5cfVr4\nqfJv5JvOAQAgoLS0d+p32/I1PLW7Hhjcy3QO4FaMPsCPLB2yVDHOGP3h6B9MpwAAEFDeOViqy7Ut\n+vWD2bIsTvkQWBh9gB+JC4/TkiFLtOPSDh2vOG46BwCAgNDQ2qGXv7yoCZmJmpDZw3QO4HaMPsDP\nzMuZp4SIBL147EXZtm06BwAAv7dqT5GuN7bpf39wkOkUwCMYfYCfiXJG6Zlhz+irq19p/+X9pnMA\nAPBrNxrb9NquQj0wuJdGpHY3nQN4BKMP8EOzsmYpOTpZvzv6O7lsl+kcAAD81ss7LqqhrUP/+GC2\n6RTAYxh9gB8KCwnTsyOf1bnqc/q06FPTOQAA+KWy6ia9ta9EM0f1VVavWNM5gMcw+gA/NTVjqnIS\ncvTi0RfV2tlqOgcAAL/zL5/nyeGQfvUAp3wIbIw+wE85LId+NfpXutJ4RevOrTOdAwCAXzl5qUab\nT1zWT+/OUO+4CNM5gEcx+gA/NrbPWE1MmajXTr6mmpYa0zkAAPgF27b1/3xyTonRYVoxKcN0DuBx\njD7Az/3DHf+gxo5GvXryVdMpAAD4hW3nKnSwqFq/vH+gYiOcpnMAj2P0AX4uMz5TT2Q+offy3lNZ\nXZnpHAAAfFpHp0v/35ZzyugRrTlj0kznAF7B6AMCwC9G/EJOh1O/O/o70ykAAPi0974qU0Flo/6P\nhwfJGcK3wggO/EkHAkBSVJIW5S7S1pKtOlF5wnQOAAA+qaG1Q7/blq870+P1wOBepnMAr+nS6LMs\na6hlWa9ZltXdXUEAbs+S3CVKjEjUbw//VrZtm84BAMDnrNxZoKqGNv3TIzmyLMt0DuA1XT3p+7Wk\ncNu2/+61gZZlRVqWdZdlWWFd/BoAbkKUM0q/GPkLHas4pi9KvzCdAwCAT7lW16LXdhfp0WF9NDIt\n3nQO4FVdHX0TJK38rg/Ytt0s6f+S9N+6+DUA3KQnMp9QRlyG/u3ov6nd1W46BwAAn/GvW/PV4XLp\n1w8OMp0CeF1XR18fScU/8PHXJT3axa8B4CaFOkL1D3f8g0rqSrQpf5PpHAAAfELe1XptPFKmhePT\nlZYYZToH8Lqujr4qSak/8PEjkrjxEvCie/reozt736lXTryihrYG0zkAABj3/245p5jwUD13b6bp\nFMCIro6+nZKW/sDHLUk80wd4kWVZ+tXoX6m6pVqrTq8ynQMAgFF7L1ZpR16lnr03U92j+LYUwamr\no+83khZblvX893x8gqSCLn4NALcoNzFXj/R/RG+ffVtXG6+azgEAwAiXy9b/+PScUrpHauH4dNM5\ngDFdGn22bR+XtFzSby3L2mVZ1izLsjIsy+ppWdYsSf9T0lp3hAK4Nc+Pel4u26V/P/bvplMAADDi\nT8fLdeZynX79ULYinCGmcwBjunw5u23bqyXdIylU0npJFyRd+fqvD0v6fVe/BoBblxKTonk587S5\nYLPyqvNM5wAA4FUt7Z36zed5GpoSp8eGJZvOAYzq8uiTJNu299u2fZekLElPS1omaYxt24/ats17\n4wFDfjr0p4oNi9W/HvlX0ykAAHjVm3uLdbm2Rf/0SI4cDi5iR3D70dFnWdY/WZZ1Uxea2LZ90bbt\nDbZtr7Zt+3DX8wB0RVx4nFYMW6F9l/dpX/k+0zkAAHhFdWObXv7you4b1FPjBySazgGMu5mTvv9b\n0lN/+wuWZUV6JgeAu80ZNEcpMSn67ZHfqtPVaToHAACPe3H7BTW2dei/PsxF7IB0+z/e+WvLsiq+\n6wOWZfW2LCu6C00A3CgsJEy/HPVL5d/I18eFH5vOAQDAo4qrGrX2QIlm35mmgb1iTecAPqErz/R9\n31n5Ckk1XfjnAnCzB9Mf1NAeQ/WHY39Qc0ez6RwAADzmnz8/r7BQh16YMtB0CuAz3PIiFy/+cwHc\nhm8ubK9oqtDas9yiAgAITEdKbujTU1f1zD0Z6hkbYToH8BmMMyBI3NHrDk1Onaw3Tr+h683XTecA\nAOBWtv2Xi9iTYsO1fGKG6RzApzD6gCDywh0vqKWjRa+ceMV0CgAAbvX5mas6UnJD/zAlS9HhoaZz\nAJ9ys6PP9mgFAK/oH9dfM7NmalP+JhXXFpvOAQDALdo7Xfqfn+VpYM8Yzbqjr+kcwOfc7Oj775Zl\nHbYs64+WZS2VlObJKACe87PhP1NYSJh+d/R3plMAAHCLdQdLVVTVqP/2yCCFhvCDbMC33cz/Fdsl\n1Usapb+8mfM1SYslybKsnZZlvWhZ1jLLskZblhXusVIAbtEjsoeWDlmq7aXbdfTaUdM5AAB0SV1L\nu36//YLGZyRqcnZP0zmAT/rR0Wfb9hTbtntIypQ0R9JvJe2UVCdpoqRnJa2UdFBSg6RfeqwWgFss\nzF2onpE99dsjv5Vt89PbAAD/9cqOAlU3tumfHsmRZVmmcwCfdNPn37ZtF9q2vcG27V/btn2vbdvx\nkgZJmi/p95L2SmqWFOeZVADuEhkaqWdHPquTlSe1tWSr6RwAAG7L5ZpmvbGnSNNHJGtoX74Fxf/P\n3n1HV1VgfR//nvQCJLQQeu+9CAiCgCiKglhQbGPHgoIUAUU6iCBFUMQ6NkQUsYCgYAFBUHrvEJBQ\nQichjbTz/nF9nveZotLCvsn5fdZiOWvG5frOzMpdd+eeu7f8mYt66Nl13Z2u685wXbeP67qt8Q18\ndfjj8U8R8V+dK3emauGqTF47mczsTOscERGR8zZh4U5coF+H6tYpIn7tb4c+x3FecRyntXMOn5e7\nPltd1/3o0uSJSG4JDAikT+M+xJ+J59Mdn1rniIiInJcthxL5Yt0BHmxRgTKFI6xzRPzauXzS9xSw\nCDjiOM47juN0dBwnJJe7ROQyaFmqJc1LNueNjW+QlJFknSMiInJOXNdlzPztRIUH82TbKtY5In7v\nXIa+UsATwBp839+bCxx3HGem4zh3Oo5TMDcDRST3OI5D3yZ9STqbxDsb37HOEREROSc/7zzGL7uP\n83S7qkSFB1vniPi9c9needR13bdc170BiAHuAxYAHYFPgKOO43zzx9mG4rmbKyKXWo0iNehUuRMf\nb/uYg8kHrXNERET+UnaOy0vfbqd80Qjua17eOkckTzivRS6u6yb9sbilK1Ac6ALMBJrhu9936I/b\nfb0cx9FPoUge8XTDpwlwApi0ZpJ1ioiIyF+auWo/2xPOMOD6GoQE6RC7yLm44J8U13XPuq47x3Xd\nB4ESwDXAG0BFYBIQ5zjOmkuTKSK5KTYylofqPsSCfQtYnbDaOkdEROS/SkzNZPyCHTSrWIQb6sRa\n54jkGZfk1yOu6+a4rrvIdd2nXdctBzQFxgLhl+KfLyK574HaD1AysiRjV40lOyfbOkdEROQ/TP5x\nF4lpmQzpVEuH2EXOw7mcbGjtOE65c/0HOo5TD6jluu7zruvWuqg6EblswoPC6dO4D9tPbufL3V9a\n54iIiPyL3UfP8OGv++jWtBy1S+kQu8j5OJdP+hbxb8fWHccZ4DjOiT/5+28B3rvILhEx0KFCBxrF\nNOLVda/qhIOIiPgN13UZ8c02wkMC6XttNesckTznXIa+//bZeRgQfYlbRMSY4zgMaDqAU+mneHPD\nm9Y5IiIiACzacZQlO4/R65qqFC0Qap0jkudo5ZGI/ItaRWtxa9VbmbFtBnsT91rniIiIx2Vk5TDy\nm21UKh7JP66sYJ0jkidp6BOR//BUw6cICwrj5VUvW6eIiIjHfbB8H3uPpzD4plo60SBygfSTIyL/\noVh4MR6v/zhLDy5l6YGl1jkiIuJRx5PPMuXHXbStXpy21WOsc0TyLA19IvJf3V3jbsoXKs+4VePI\nzMm0zhEREQ+asHAHaZnZvHCTFsKLXIxzHfrcXK0QEb8THBhM/yv6sy9pHzO3z7TOERERj9l8MJGZ\nq+J5oEUFKhcvYJ0jkqed69A3zHGc7P/5AwwB+L//3r//ZyKS97Uq3YqWpVsybf00TqaftM4RERGP\ncF2XEXO3UiQihKevqWqdI5LnnevQ55znHxHJBxzHoX+T/qRmpfLautesc0RExCPmbTrMyn0n6deh\nOlHhwdY5Inne3w59rusGXMCfwMsRLyK5r1J0Je6qcRef7/yc7Se3W+eIiEg+l5aRzZj526lVshB3\nNClrnSOSL2iRi4j8rcfrP05UaBRjV47FdfUVXxERyT1vLYnj4Ok0hnaqRWCAHiATuRQ09InI34oK\njeLphk+z+shqvv/9e+scERHJpw6dTmPaz7u5sV5JmlUqap0jkm9o6BORc3Jb1duoVrgaE1ZPID0r\n3TpHRETyoZe+3Y7rwnM31LBOEclXNPSJyDkJDAhkwBUDOJRyiA+2fGCdIyIi+cyqfSeZs+EQj7Wu\nRJnCEdY5IvmKhj4ROWdNSzbl2vLX8u7md0lISbDOERGRfCInx2X43C3EFgrj8TaVrXNE8h0NfSJy\nXjjcdfIAACAASURBVPo07kN2TjavrH3FOkVERPKJz9ccYPPBJJ7rWIOIkCDrHJF8R0OfiJyXMgXL\ncH/t+5kXN4/1R9db54iISB53Jj2TcQu207h8YTrXL2WdI5IvaegTkfP2SN1HiAmPYezKseS4OdY5\nIiKSh722aDfHkzMY2qkWjqMTDSK5QUOfiJy3iOAInmn8DJtPbGbunrnWOSIikkftPZ7CP3/ZS9fG\nZahXJto6RyTf0tAnIhfkxko3Uq9YPV5Z+wopmSnWOSIikgeNnreNkMAAnr2+unWKSL6moU9ELkiA\nE8CApgM4nnactze+bZ0jIiJ5zJKdx/hh2xGevqYqMQXDrHNE8jUNfSJyweoVr0fnyp35cOuHxCfF\nW+eIiEgekZmdw8hvtlK+aAQPtqxgnSOS72noE5GL0qtRL4ICghi/erx1ioiI5BEf//Y7u44m88KN\ntQgNCrTOEcn3NPSJyEWJiYihe73u/BT/E78e+tU6R0RE/NzJlAwmfr+TVlWL0b5mjHWOiCdo6BOR\ni3ZfrfsoXaA041aNIysnyzpHRET82KTvd5KSkc3gm3SiQeRy0dAnIhctNDCUZ5s8y+7Tu5m1c5Z1\njoiI+KntCUl8vOJ37mtenmolClrniHiGhj4RuSTalWtHs9hmvLbuNU6nn7bOERERP+O6LsPnbKVQ\neDDPtK9qnSPiKX419DmOE+g4zjrHcb6xbhGR8+M4Dv2b9ic5M5nXN7xunSMiIn5mwZYj/Bp3gj7X\nViM6IsQ6R8RT/GroA3oB26wjLlh2JqQnWVeImKlWuBpdq3Xlsx2fsevULuscERHxE+mZ2Yyev5Vq\nJQpwd9Ny1jkinuM3Q5/jOGWAG4F3rFsuSHYWvHMNfDvAukTEVI8GPYgIjmDsqrG4rmudIyIifuDd\nX/YSfzKNoZ1qExToN28/RTzDn37qXgH6Azl/9jc4jtPdcZzVjuOsPnbs2OUrOxeBQVD5GtgwA35f\nbl0jYqZwWGGeavAUKw6vYMG+BdY5IiJiLP5kKq/+tIvra8fSskox6xwRT/KLoc9xnJuAo67rrvmr\nv8913bdc123ium6T4sWLX6a689C6H0SVhXl9fY96injUndXvpGaRmoxbNY7kjGTrHBERMTTim60E\nOA5DOtWyThHxLL8Y+oCWQGfHcfYBM4F2juNMt026ACGRcMNYOLoVVrxhXSNiJjAgkBeav8DxtONa\n6iIi4mE/bjvC91uP0POaqpSKDrfOEfEsvxj6XNd9znXdMq7rVgC6AT+5rnuvcdaFqd4RqnaAxS9B\n4kHrGhEz9YrX47ZqtzFj2wx2nNxhnSMiIpdZWkY2Q+dsoWpMAR5qWdE6R8TT/GLoy1ccx/dpX04W\nLHjeukbEVK+GvSgYUpDRK0aT4/7p13VFRCQfen3xbg6cSmPEzXUICdJbThFLfvcT6LruYtd1b7Lu\nuChFKkKrvrD1K9j9o3WNiJnosGj6NO7DuqPrmLNnjnWOiIhcJnHHknnz5zhuaViaKysXtc4R8Ty/\nG/ryjRY9oUhlmP8sZJ21rhExc3OVm6lfvD4TV08k8WyidY6IiOQy13UZOmcLoUEBPNexhnWOiKCh\nL/cEh0HHl+HkHlg2xbpGxEyAE8Dg5oNJzEhkylr9LIiI5HfzNyWwdNdx+nWoTkzBMOscEUFDX+6q\ncg3U6gJLx8OpfdY1ImaqF6nO3TXuZtbOWWw+vtk6R0REckny2SxGfLOF2qUKcW/z8tY5IvIHDX25\nrcOL4ATC/P7gutY1ImZ6NOhBsfBijPxtJNk52dY5IiKSCyb/sJOjZ84yqksdAgMc6xwR+YOGvtwW\nVRraPge7FsCO+dY1ImYKhBSgX5N+bD2xlVk7Z1nniIjIJbY9IYl/LttHtyvK0rBcYescEfk/NPRd\nDs0eh+I14duBkJFiXSNi5oaKN9AsthlT1k7heNpx6xwREblEXNdl8FebKRQWRP8OWt4i4m809F0O\ngcFw00RI3A9LxlvXiJhxHIfnmz9PWnYak9ZMss4REZFLZPbag6zad4qBN9SgcGSIdY6I/BsNfZdL\n+RZQ/y5Y/ioc22ldI2KmUlQlHqj9AHP2zGF1wmrrHBERuUiJqZmMmb+NRuWi6dq4rHWOiPwXGvou\np2tHQEgEzO+npS7iaY/WfZSSkSUZvWI0mTmZ1jkiInIRXl64nVOpGYzsUocALW8R8Usa+i6nAjHQ\nbjDs/Rk2z7auETETERzBwKYD2X16NzO2zbDOERGRC7TxwGk+XrGf+1tUoHapKOscEfkTGvoutyYP\nQckGsGAQpCdZ14iYaVu2La3LtGbq+qkkpCRY54iIyHnKznF54avNFCsQSu9rq1nniMhf0NB3uQUE\n+pa6JB+BxWOsa0TMOI7DwKYDyXFzeHnVy9Y5IiJynj5ZuZ+NBxJ54caaFAoLts4Rkb+goc9C6cbQ\n+AFY8SYkbLKuETFTtmBZHqn7CAt/X8jyg8utc0RE5BwdTz7Lywt2cGWlonSuX8o6R0T+hoY+K9cM\ngfBomNcXcnKsa0TMPFjnQcoXKs+LK18kIzvDOkdERM7BS99uJzUji5FdauM4Wt4i4u809FmJKOLb\n5hm/AjZokYV4V2hgKM83fZ7fk37nvc3vWeeIiMjfWLXvJJ+vOcAjrSpRJaagdY6InAMNfZbq3w1l\nm8P3QyD1pHWNiJkWpVtwXfnreHvT2xw4c8A6R0RE/kRWdg6Dv9pM6ehwnm5XxTpHRM6Rhj5LAQFw\n4wRIOw0/jrCuETH17BXPEuAEMGblGFzdsRQR8UvvL9/H9oQzDOlUi4iQIOscETlHGvqsxdaBZo/D\nmvfhwBrrGhEzsZGx9GjQgyUHlrAofpF1joiI/JuExHQmfb+TdjViuK5WCescETkPGvr8QZuBUKAE\nzOsNOdnWNSJm7q55N1WiqzB25VhSM1Otc0RE5P8YNW8rWTkuwzppeYtIXqOhzx+EFYLrX4TDG2D1\nP61rRMwEBwTzQvMXOJRyiLc3vW2dIyIif/hl13G+2XiYHm2rUK5ohHWOiJwnDX3+ovatUKkN/DgS\nko9a14iYaVyiMZ0rd+b9Le8TlxhnnSMi4nlns7IZ8vVmKhSNoHvrStY5InIBNPT5C8eBjuMhMxUW\nDrauETHVu3FvwoPCefG3F7XURUTE2NtL4og7nsKIm+sQFhxonSMiF0BDnz8pVhVa9oSNM2HfL9Y1\nImaKhRejZ8OerEhYwXf7vrPOERHxrPiTqbz602461o2ldbXi1jkicoE09PmbVv0gqhzM6wfZmdY1\nIma6VutKraK1eHnVyyRnJFvniIh40vC5WwgMcBh8Uy3rFBG5CBr6/E1IBNwwFo5tg9+mWdeImAkM\nCGRw88EcTzvO1PVTrXNERDzn+61H+GHbUZ5pX5WSUeHWOSJ28sEHMRr6/FGNjlDtBlj8EiQesK4R\nMVOnWB26VuvKjO0z2H5yu3WOiIhnpGZkMXzuFqqVKMCDLSta54jYyc6Cf14PP4+zLrkoGvr81Q1j\nARfm9QUtshAP69moJ9Gh0QxbPoysnCzrHBERT5j0/U4OnEpjVJe6BAfq7aJ42Io34OBqKFrFuuSi\n6KfYXxUuD+1egJ3fwZYvrGtEzESFRvFcs+fYcmILH2/72DpHRCTf23jgNO/+spd7mpWjacUi1jki\ndk7uhZ9GQbXrofYt1jUXRUOfP2v2OJRqBPP7Q+pJ6xoRMx3Kd6BNmTa8tu414s/EW+eIiORbmdk5\nDJi9ieIFQxlwQw3rHBE7rgvf9IaAQLhxgu+8Wh6moc+fBQRC5ymQfhoWvmBdI2LGcRwGNR9EYEAg\nI38dqdt9IiK55O2lcWw7nMTIm+tQKCzYOkfEzoaZELcI2g+DqDLWNRdNQ5+/i60LLXvB+o9hzyLr\nGhEzsZGxPNPoGX49/Ctz4+Za54iI5Dt7j6fwyg+76Fg3lutqx1rniNhJPgYLnoMyTaHJw9Y1l4SG\nvrygdX/fl0fn9oKMVOsaETN3VL+DBsUbMG7VOE6knbDOERHJN3JyXAbO3khYUADDOte2zhGx9d1A\nOJsMnV+FgPwxLuWP/xb5XXAYdJoMp3+HxS9a14iYCXACGNZiGCmZKYxdNdY6R0Qk3/hsdTwr9p7k\n+Y41iSkYZp0jYmfnQtj8ObTuBzH553utGvryigpXQeMH4NepcGi9dY2ImcrRleletzvf7v2WJQeW\nWOeIiOR5R5PSGT1/G80rFeHOK8pa54jYOXvGt7yleA24qrd1zSWloS8vaT8cImNgzlOQnWldI2Lm\n4boPUzmqMiN/G0lKZop1johInjZ0zhbOZuUw5tZ6OHl8Q6HIRflpFCQd9D3WGRRqXXNJaejLS8Kj\n4cbxkLDJ94mfiEeFBIYwrMUwjqQc4dV1r1rniIjkWd9tTuDbzQk8074qFYtFWueI2IlfBSvehKaP\nQtmm1jWXnIa+vKZmJ6hxEyweAyf2WNeImGkQ04BuNboxY9sMNhzbYJ0jIpLnJKVnMuTrzdQsWYhH\nW1WyzhGxk5UBc56GQqXgmiHWNblCQ19e1HE8BIb4tnnqXpl4WK9GvYiJiGHY8mFk6pFnEZHzMvbb\n7RxPPsvY2+oSHKi3hOJhy16BY9vgxokQWtC6JlfoJzwvKlQSrh0B+5bCuunWNSJmIoMjGdx8MLtP\n7+bdze9a54iI5Bkr957k4xX7efiqitQrE22dI2Ln2A5Y8jLUuQ2qX29dk2s09OVVje6H8i1h4SA4\nc8S6RsTM1WWv5oYKN/DWxreIOx1nnSMi4vfSM7MZ+MVGyhYJp/e11axzROzk5MCcnhAcAde/ZF2T\nqzT05VUBAb7bfZnp8G1/6xoRUwOaDiAiOIJhvw4jx82xzhER8WtTF+0m7lgKL95Sl4iQIOscETtr\n/gnxv0GHF6FAjHVNrtLQl5cVqwpX94etX8H2edY1ImaKhhfl2SbPsu7oOmbtmGWdIyLit7YnJDFt\n8R5ua1SGVlWLW+eI2Ek8CN8Pg4pXQ4O7rWtynYa+vK5lL4ipDfP6QnqidY2Imc6VO9O8ZHMmrZ1E\nQkqCdY6IiN/JznEZMHsTUeHBvHBjTescETuu63vvnJMFnV4BD9yn1NCX1wUG+w5IJh+BH4Zb14iY\ncRyHIc2HkJ2TzegVo3G12VZE5F98sHwfG+JPM6RTLQpHhljniNjZ+hXs/BbaPg9FvHGuRENfflCm\nMTR7Ala/C/t/s64RMVO2UFl6NOjB4vjFfP/799Y5IiJ+I/5kKuMX7qBt9eJ0rl/KOkfETtopmN8f\nStaH5k9a11w2Gvryi3aDILqc77Bk1lnrGhEz99a6l5pFavLiihdJPKtHnkVEXNdl0FebARh1S10c\nDzzKJvKnFg6G1BO+J+UCvbPISENffhESCTdNguM7YekE6xoRM0EBQQxvMZzTZ08zcc1E6xwREXNf\nrz/Ekp3H6N+hOqWjw61zROzE/QzrPoIWT/s+6fMQDX35SZX2UK8bLJ0IR7Za14iYqVm0JvfXvp8v\ndn3BisMrrHNERMycSD7L8LlbaFgumvuurGCdI2InMw3m9oLCFaHNQOuay05DX37T4UUIK+R7zDMn\n27pGxMwT9Z+gbMGyDP91OOlZ6dY5IiImRs3bRvLZLMbeVo/AAD3WKR62+CU4tRc6T4Fg733iraEv\nv4ksCtePhYOrYdU71jUiZsKCwhh25TDiz8QzbcM06xwRkctu8Y6jfLnuIE+0qUK1EgWtc0TsHN4A\ny1+FhvdBxdbWNSY09OVHdW/3Per5w3A4HW9dI2Kmacmm3Fr1Vj7Y8gHbTmyzzhERuWxSzmYx6MvN\nVC4eSY+2la1zROxkZ/megIsoCteNtK4xo6EvP3Ic31IXgHl9fAcoRTyqT+M+RIdGM3T5ULJysqxz\nREQuiwkLd3LwdBpjb6tHaFCgdY6Ind9e933S13EchBe2rjGjoS+/ii4H1wyGXQth82zrGhEzUaFR\nPNfsObad3Mb0rdOtc0REct36+NO8t3wv9zYvR5MKRaxzROycjINFL0L1jlCri3WNKQ19+VnT7lC6\nMXw7AFJPWteImLmu/HW0KduGqeunEn9GjzyLSP6VmZ3DwNkbKVEwjP7X17DOEbHjujD3GQgIgo7j\nfU/CeZiGvvwsINB3eDL9NCwYZF0jYsZxHAY1G0RgQCAjfh2Bq0eeRSSfemtJHNsTzjCySx0KhQVb\n54jY2fAJ7P0Zrh0GUaWta8xp6MvvStSGq3rDhhmw+0frGhEzsZGx9G7Um98O/8bXe762zhERueT2\nHEtm8o+7uLFuSa6tVcI6R8RO8lH47jko2xwaP2Rd4xc09HlBq35QtKrvIGV6knWNiJmu1bvSKKYR\n41aN40jKEescEZFLJjvH5dlZGwgLCmBo51rWOSJ2XNe3yDAz1XeTL0DjDmjo84bgMOgyDZIOwkI9\n5ineFeAEMKLlCDKzMxn26zA95iki+cY7S+NYu/80w2+uTUzBMOscETubPodtc6Ht81C8unWN39DQ\n5xVlr4CWvWDth7Dre+saETPlC5XnmcbP8MvBX/hy95fWOSIiF23XkTNM+H4nHWqXoEsDfXdJPCzp\nMMzvB2WugBY9rWv8ioY+L2nzHMTU8h2oTDtlXSNi5q4ad9E0tinjVo3jUPIh6xwRkQuWlZ1D31kb\nKBAaxOhb6uJ4fEOheJjr+r7KlHUWurzhW2go/0tDn5cEhfoe80w55jvjIOJR//OYp+u6DFk2hBw3\nxzpJROSCTFu8h40HEhnVpQ7FCoRa54jYWTcddi2A9kOhWBXrGr+joc9rSjXwLXbZ+Cls+8a6RsRM\n6QKl6XdFP1YkrODTHZ9a54iInLcthxKZ/OMuOtUvRce6Ja1zROycjvdt6yx/FTR9zLrGL2no86LW\n/SC2HnzzDKScsK4RMXN71dtpWaolk9ZMYn/SfuscEZFzlpGVQ9/PNlA4MoQRnWtb54jYcV2Y8xS4\nOdBlqrZ1/gn9r+JFgcFwy5uQngjzevt+WEQ8yHEchrUYRpATxOBlg8nOybZOEhE5J1N+3MX2hDO8\ndGtdCkeGWOeI2Fn9LsQthg6joHAF6xq/paHPq0rU8i122fo1bJ5tXSNiJjYyloHNBrL26Fqmb5tu\nnSMi8rfWx59m2s97uL1xGa6pqSPs4mEn42DhYKjcDho/aF3j1zT0eVmLnlC6iW+17Rkdqhbv6lSp\nE23LtmXK2inEnY6zzhER+VPpmdn0/Ww9MQVDGdJJR9jFw3Jy4KseEBAEnV8Fba79Sxr6vCwwCG55\nAzLTfCtu9ZineJTjOAy5cggRwREM+mUQWTlZ1kkiIv/VhIU72HMshbG31aNQWLB1joidFdNg/3K4\n/iWIKmNd4/c09HldsapwzVDY+S1s+MS6RsRMsfBiDGo+iM0nNvPe5vesc0RE/sOqfSd555e93NOs\nHK2rFbfOEbFzbCf8OAKq3QAN7rauyRM09Ak0exzKt/Td7ks8YF0jYub6CtfToUIHXt/wOjtO7rDO\nERH5X6kZWfSbtYEyhcN5vmNN6xwRO9lZ8NXjEBwOnSbrsc5zpKFPfKttb54KOdkw52k95imeNqjZ\nIKJCohj0yyAyszOtc0REABj77XZ+P5HKy7fXJzI0yDpHxM7yyXBwDXQcDwW1yOhcaegTnyIV4boR\nsOcnWKNH28S7CocVZuiVQ9lxagdvbnzTOkdEhGW7j/PBr7/zYMsKNK9U1DpHxM6RLbBoDNS6Gerc\nZl2Tp2jok/+vycNQqS0seAFO7rWuETHTtlxbOlfuzDub3mHL8S3WOSLiYWfSM+n/+UYqFYukf4ca\n1jkidrIy4MvHITwabpyoxzrPk4Y++f8cB25+DQIC4eunfKtwRTxqQNMBFA0vyvO/PM/Z7LPWOSLi\nUaPnbeNwYhrj76hPeEigdY6InaXjIWEj3PQKRBazrslzNPTJv4oqA9ePgd9/gZV6tE28q1BIIUa0\nGEFcYhxT1021zhERD1q04ygzV8XTvXVlGpUrbJ0jYufQOlgyHurdCTVvsq7JkzT0yX9qcA9Uux5+\nGA7Hd1vXiJhpWbolt1e7nfe3vM/6o+utc0TEQxJTMxk4eyPVShSg97VVrXNE7GSdhS+fgAIxcMNY\n65o8S0Of/CfH8a3ADQr1rcTNybYuEjHTr0k/ShUoxaBfBpGamWqdIyIeMWzuFk4kZzChawNCg/RY\np3jYohfh2Dbo/CqE6xPvC6WhT/67grFw4wQ4sAqWT7GuETETGRzJyJYj2X9mP5PXTrbOEREPWLAl\ngS/XHaRH2yrULRNlnSNiJ36l731oo39A1Wuta/I0DX3y5+rcBjU7+37DcmSrdY2ImStir+Cemvcw\nY/sMVh5eaZ0jIvnYieSzDPpyE7VLFeKpdlWsc0TsZKT6tnUWKg3XjbauyfM09Mmfcxy4aRKEFvI9\n5qlD1eJhvRr1onyh8gxeNpiUzBTrHBHJh1zXZfDXm0lMy2TCHfUJDtTbNPGwH0fAyT1w81QIK2Rd\nk+fp1UT+WmQx3+B3eAMsnWBdI2ImPCicUS1HkZCawMurXrbOEZF8aO7Gw8zflEDva6tRI1ZvcsXD\n9i6FFdOgaXeodLV1Tb6goU/+Xq3OUPcOWPIyHNIGQ/GuBjENuL/2/czeNZtfDv5inSMi+cjRM+kM\n+XozDcpG071VJescETtnz8DXT0KRStB+mHVNvqGhT85Nx3EQUQy+esK3OlfEo3o06EHlqMoMXT6U\npIwk6xwRyQdc1+X5LzaRlpHNhDvqE6THOsXLFg6G0/HQZRqERFrX5Bt6VZFzE17Ytyr36FZY/JJ1\njYiZ0MBQRrcazYm0E4xdqXtBInLxZq89yA/bjvJsh+pULl7AOkfEzu4fYM17cGUPKNfcuiZf0dAn\n567addDwPlj2CsSvsq4RMVO7aG0erfcoc/bM4af9P1nniEgeduh0GsPnbKFpxSI81LKidY6InbTT\n8PXTUKw6tBtsXZPvaOiT89PhRd/q3K8e963SFfGo7nW7U6NIDYb/OpxT6aesc0QkD3JdlwGzN5Lt\nuoy/vT4BAY51koid756D5CNwyzQIDrOuyXc09Mn5CSsEN78GJ3bD9/otjHhXcGAwo68azZmMMwxd\nPhTXda2TRCSPeX/5PpbuOs5zHWtSrmiEdY6InS1fwoYZcFVvKN3YuiZf0tAn569SG2jxNKx6B7bP\nt64RMVOtcDV6N+7NovhFzNo5yzpHRPKQbYeTGDN/O+1rxnBvs3LWOSJ2TsfD3F6+Ya/NQOuafEtD\nn1yYdkMgth583QOSDlvXiJi5p+Y9tCzVknGrxrHn9B7rHBHJA9Iysun5yTqiIoIZe1s9HEePdYpH\n5WTDF919f73tHQgMti7KtzT0yYUJCoHb/wlZ6fDlY5CTY10kYiLACWDUVaOIDI6k/5L+nM3WSRMR\n+Wuj529l19FkJt5Rn6IFQq1zROwsnQj7l0PH8b67fJJrNPTJhStWFa5/Cfb+DL++al0jYqZYeDFG\nthzJzlM7eWXNK9Y5IuLHFm5JYPpv++neuhKtqha3zhGxE78KFo+BOrdD/W7WNfmehj65OI3+ATU7\nw48j4dA66xoRM63LtOaemvcwfdt0lh5Yap0jIn7oSFI6A2ZvpE7pQvS7rrp1joid9CSY/TBElYab\nJoIecc51Gvrk4jgOdJoMBWLg84fhbLJ1kYiZ3o17U7VwVV5Y9gLH045b54iIH8nJcenz2XrSM3OY\n3K0hIUF6CyYeNr8fJMbDre9AWJR1jSfoFUcuXkQRuPUtOBkH32nrknhXaGAo41qNIyUzhReWvUCO\nq++6iojP20vjWLb7BEM71aJy8QLWOSJ2NnwKGz+FqwdAuWbWNZ6hoU8ujQpXQas+sO4j360VEY+q\nUrgK/Zr0Y9nBZczYNsM6R0T8wMYDp3l5wQ5uqBPLnVeUtc4RsXNyL8zrC2WbQ6t+1jWeoqFPLp02\nz/lurMzt5bu5IuJRd1a/kzZl2jBxzUR2nNxhnSMihlLOZtFr5nqKFwxlzK11dZ5BvCs7C754FJwA\nuO1tCAyyLvIUDX1y6QQG+26s5GT/ccYh27pIxITjOIxoOYLo0GgGLBlAWlaadZKIGBkxdyv7TqQw\n6c4GREeEWOeI2Pl5LBxY5VvcEl3OusZzNPTJpVWkku/Wyu/L4JeJ1jUiZgqHFWbUVaPYk7iHCasn\nWOeIiIF5Gw/z6ep4nmxTmeaVilrniNjZtwyWjof6d0Pd261rPElDn1x69bv5bq4sGuO7wSLiUS1K\nteCB2g/w6Y5P+Wn/T9Y5InIZHTydxnNfbKR+2WieaV/NOkfETtop+KI7RJeHjuOsazxLQ59ceo7j\n++g+qrTvBkt6knWRiJmeDXtSs0hNhiwfwpGUI9Y5InIZZOe49J65nuwclyndGhAcqLdb4lGuC9/0\nhuQEuO1dCC1oXeRZehWS3BEW5bu9khjvu8Ui4lHBgcGMbT2WjOwMBi0bpDMOIh7w+qLdrNx3kpFd\n6lC+aKR1joid9R/7trq3HQRlGlvXeJqGPsk95Zr5brBs/BQ2fmZdI2KmYlRFBlwxgBWHV/DBlg+s\nc0QkF63df4pXftxF5/qluKVhaescETvHd8P8/lChFbTsZV3jeRr6JHe16ue7xfJNH99tFhGPurXq\nrVxb/lqmrJ3CluNbrHNEJBecSc+k18x1lIwKY9QtdXSeQbwrK8P3FZ/AYLjlTQgItC7yPA19krsC\ng3y3WJwA322W7CzrIhETjuMw9MqhFA0vyoClA0jNTLVOEpFLbMjXWzh4Ko3J3RpQKCzYOkfEzqLR\ncHg9dH7Vt+NBzGnok9wXXc632OXAKt+NFhGPigqNYkyrMexP2s9LK1+yzhGRS+jLdQf4ct1Bel1T\njcbli1jniNiJWwzLJkPjB6BWZ+sa+YOGPrk86t7uu82ydDz8vty6RsTMFbFX8EjdR/hy95cs2LfA\nOkdELoH9J1IZ/NUWmpQvTI+2la1zROyknIAvH4eiVaDDi9Y18n9o6JPLp+M4342W2Y/6braIuc/W\nfwAAIABJREFUeNQTDZ6gbrG6DP91OIeTD1vniMhFyMrOoden63AceKVbA4J0nkG8ynVhztOQchxu\nfxdCtLnWn+iVSS6f0IK+Gy3JCb6bLa5rXSRiIjggmLGtxpKdk83ApQPJzsm2ThKRCzTlx12s23+a\n0bfUpUzhCOscETtr3oMd86D9MChZ37pG/o2GPrm8yjT23WrZ8qXvdouIR5UtVJYXmr/A2qNreWfT\nO9Y5InIBVsSd4LVFu7m9cRk61y9lnSNi5+h2+O55qNwOmj9pXSP/hYY+ufxa9vLdbJnf33fDRcSj\nbqp0EzdUvIFpG6ax/uh66xwROQ+JqZn0/nQ9ZYtEMKxzbescETuZ6TD7EQiJgC7TIEDjhT/S/yty\n+QUE+m62BAb7brhkZVgXiZhwHIfBzQcTGxnLwKUDSc5Itk4SkXPgui7Pf7mJo2fOMrlbQwqEBlkn\nidj5cTgc2QQ3vw4FY61r5E9o6BMbUaV9t1sOr/fdchHxqIIhBXmp1UscTjnM6BX6WRDJC2atOcC8\nTYfpc101GpSNts4RsbPrB/jtdWjaHapfb10jf0FDn9ip1dl3w2XZZN9NFxGPahDTgMfrP843cd8w\nd89c6xwR+Qtxx5IZNmcLV1YqymOtdZ5BPCz5GHz1BMTUgmtHWNfI39DQJ7Y6vAjFqvrOOJw5Yl0j\nYubRuo/SKKYRo34bxd7EvdY5IvJfpGdm02PGOoIDA5h4Z30CAxzrJBEbOdnwxSOQnujbzB4cbl0k\nf0NDn9gKiYSu78PZM77v92VnWReJmAgKCGJs67GEBobSZ3EfUjNTrZNE5N8Mm7OFbYeTmHRnfUpG\n6U2ueNjP43xPaXV8GUrUsq6Rc6ChT+yVqA03TYJ9S/X9PvG02MhYXmr1EntO72HUb6NwdctSxG/M\nWh3PzFXx9GhbmXY1SljniNjZ/QP8PBbq3w2N/mFdI+dIQ5/4hwZ3+V44fpkIO76zrhEx06J0Cx6v\n/zhz4+Yye9ds6xwRAbYnJDH46800r1SE3u2rWeeI2Ek84PtKTkxNuHECOHrEOa/Q0Cf+44ZxEFsX\nvnwMTv1uXSNi5rF6j3FlySsZs2IM205ss84R8bQz6Zk8MX0tBcOCmXJXQ4IC9dZJPCorA2Y9CNkZ\ncMeHvrt8kmfolUv8R3C470XEzYFZ90PWWesiEROBAYG81PolosOi6bO4D0kZSdZJIp7kui4DZ29i\n/8lUXrurITEFw6yTROz8MBQOrPSd3CpW1bpGzpOGPvEvRSpBl9fh0DpYMMi6RsRMkbAijL96PAkp\nCQz+ZbC+3ydi4IPl+5i36TD9rqtOs0pFrXNE7Gz9+o97fI9BnVuta+QCaOgT/1OzE1z5FKx6GzZ9\nbl0jYqZhTEN6N+7NT/E/8eHWD61zRDxl7f5TjJ6/jfY1Y3isdSXrHBE7J/bAVz2gdBO4bpR1jVwg\nDX3in9oPg7LNYU5POLbDukbEzH217qN9ufZMWjOJtUfWWueIeMKplAye+ngtJQqFMaFrAwJ0j0+8\nKjMNPvsHBAb5TmwFhVgXyQXS0Cf+KTAYur7n+57fZ/+AjBTrIhETjuMwouUIShUoxbM/P8uJtBPW\nSSL5Wk6OyzOfrud4cgbT7mlMVESwdZKInfn94MhmuPVtiC5rXSMXQUOf+K9CpeC2d3yf9H3TG/Sd\nJvGogiEFmdhmIqfPnmbA0gFk52RbJ4nkW1MX7ebnnccY0qkWdctEWeeI2Fk33fen9bNQ9VrrGrlI\nGvrEv1VuC22eg42fwpr3rWtEzNQoUoNBzQex4vAK3tj4hnWOSL60bPdxJv2wky4NSnFPs3LWOSJ2\nEjbBvL5QsbXvfZjkeRr6xP+1fhYqXwPf9vdt9RTxqFuq3MLNlW/mzQ1v8svBX6xzRPKVhMR0es1c\nR6XiBRh9S10cHZ0Wr0pP9H21JiwabnsXAgKti+QS0NAn/i8gwPcseWRx+Ox+SDtlXSRiwnEcBjUf\nRJXCVXhu6XMkpCRYJ4nkC5nZOTz9yVpSM7J5495GRIYGWSeJ2HBd+PopOPW7b7dCgRjrIrlENPRJ\n3hBZ1Lc1KukgfPWkvt8nnhUeFM7EqyeSmZNJ35/7kpmdaZ0kkueNX7CDVftOMebWulSJKWidI2Jn\nxRuwbQ60HwrlW1jXyCWkoU/yjrJNffdhdsyH5VOsa0TMVIiqwPAWw9l4bCMT10y0zhHJ0xZuSeDN\nJXHc27wcNzcobZ0jYid+JSx8AarfCC16WtfIJaahT/KWZo9Dzc7ww3D4fbl1jYiZDhU6cE/Ne5i+\nbToL9y20zhHJk/afSKXvrA3UKxPF4JtqWeeI2Ek5AbMegEKlocvroO+05jsa+iRvcRy4eSoUrgCz\nHoTko9ZFImb6Nu5LvWL1GLJ8CPsS91nniOQp6ZnZPPHxGhxg6t2NCA3SsgrxqJxs+OIRSDkOd3wI\n4dHWRZILNPRJ3hNWyPeilH4aZj/se7ES8aDgwGDGXz2eoIAg+vzch7SsNOskkTxj+NytbDmUxMQ7\nGlC2SIR1joidJeNhz09ww1go1cC6RnKJhj7Jm2LrwI0TYO8SWDzGukbETMkCJXmp1UvsPrWbF1e8\naJ0jkid8sfYAn6zczxNtKtO+VgnrHBE7exb53kfV6waNH7CukVykoU/yrob3+v4seRl2fW9dI2Lm\nqtJX0b1ed77a/RVf7vrSOkfEr+08coZBX26mWcUi9L22mnWOiJ2kQzD7ESheA26aqO/x5XMa+iRv\n6zgeStSBLx6F0/HWNSJmnqj/BM1KNmP0itHsOLnDOkfELyWfzeLx6WuIDA3i1bsaEhSot0HiUdmZ\nvt0ImWm+r8yERFoXSS7Tq53kbcHhvher7CyYdT9kZVgXiZgIDAhkbKuxRIVE0WdxH85knLFOEvEr\nruvy3Beb2Hc8hVfvakhMoTDrJBE7PwyD+N+g8xQork+8vUBDn+R9RStDl6lwcI3vvoyIRxUNL8rL\nV7/MweSDDFk2BNd1rZNE/MZHv/3O3A2H6Htdda6sXNQ6R8TOtrnw62twxaNQ93brGrlMNPRJ/lDr\nZmj+JKx8EzZ/YV0jYqZRiUY80+gZftj/A9O3TbfOEfEL6+NPM/KbrbSrEcMTV1e2zhGxczIOvnoS\nSjWCDqOta+Qy0tAn+Uf74VCmKcx5Go7pO03iXffXvp92ZdsxcfVE1h5Za50jYupkSgY9Pl5LTMEw\nJt5Rn4AALasQj8pIhc/+AU4A3PEBBIVaF8llpKFP8o+gEOj6vu97fp90g7RT1kUiJhzHYeRVIyld\nsDS9F/fmcPJh6yQRE5nZOTz58RqOJZ9l2r2NiI4IsU4SseG68HUPSNgMt70D0eWsi+Qy09An+UtU\nabhzum+T5+cP+Ra8iHhQoZBCTGk7hbPZZ+m1qJcOt4snjZi7ld/iTjLutnrUKxNtnSNiZ+kE2PIF\ntB8GVa+1rhEDGvok/ynX3He4fc9P8MNQ6xoRM5WiKzGu9Ti2n9yuxS7iOTNW7Oej337nsdaV6NKw\ntHWOiJ0d38JPo6DuHdCyl3WNGNHQJ/lT4/uhaXffdqr1n1jXiJhpXaY1PRv15Lt93/Hu5netc0Qu\ni5V7TzLk6820qV6c/tfXsM4RsXN0O8x+FEo18J1n0AF2z9LQJ/lXhxehQiuY2wsOrLauETHzcJ2H\nuaHiDUxZO4XF8Yutc0Ry1YFTqTwxfQ3likYwuVtDArW4Rbwq9aRvx0FwONz5se+v4lka+iT/Cgz2\nHW4vGAsz74EkLbMQb3Ich+EthlOjSA0GLh3IntN7rJNEckVqRhbdP1xDRnYOb/+jCVHhwdZJIjay\ns+DzByHpIHT72LfzQDxNQ5/kbxFF4K5P4OwZ+PQeyEy3LhIxER4UzpR2UwgLDKPnTz1JPJtonSRy\nSbmuy7OzNrItIYkpdzWkcvEC1kkidha+AHGL4aZJULapdY34AQ19kv+VqA23vgkH1/ge9dQyC/Go\n2MhYJrWdxKGUQzz787Nk5Wi7reQfUxftZt6mwwy8vgZtq8dY54jYWTcdVkyDZk9Aw3uta8RPaOgT\nb6jZCdo8Dxtn+pa7iHhUw5iGDG4+mF8P/8rENROtc0Quie+3HmH8wp3c0rA03VtXss4RsRO/Er7p\nDZXawHWjrGvEjwRZB4hcNq2fhaNb4PshULwmVG1vXSRi4taqt7Lz1E4+2voR1QpXo0uVLtZJIhds\n55EzPDNzHfXKRDHm1ro42k4oXpV40LfDoFBpuP09CNTbfPn/9EmfeEdAAHSZBjG1fYfbj++yLhIx\n069JP5qVbMaIX0ew/uh66xyRC3IqJYNHPlhNRGgQb93XhLDgQOskERuZaTDzbt9f75rp22kg8n9o\n6BNvCYmEu2b4fvv1yV2QrmUW4k1BAUGMbz2eEhEl6L24N0dSjlgniZyXrOwcnvpkLQmJ6bx5X2Ni\no8Ksk0RsuC7MeRoOb4Db3oYY3aaU/6ShT7wnuhzc8RGc2gufPww52dZFIiaiw6J5td2rpGam0mtR\nL9KztN1W8o5R87axbPcJRt9Sh0blClvniNhZNhk2zYJ2L0D1G6xrxE9p6BNvqtASbhgHu7+HH4db\n14iYqVK4CmNajWHLiS0M+3UYrrbbSh7w2ap43l++j4daVqRrk7LWOSJ2di6EH4ZB7VuhVV/rGvFj\nGvrEu654GJo85PsN2cbPrGtEzLQr146nGjzFvLh5vL/lfesckb+05veTDPpqE62qFuP5jnqMTTzs\n2E6Y/TDE1oWbp4KWGMlf0NAn3nb9WCjf0vcs/MG11jUiZrrX68515a9j0ppJLD2w1DpH5L86dDqN\nxz5aS+nocF69qyFBgXobIx6Vdgo+6QZBodBtBoREWBeJn9OrpXhbUAjc8SFExvjWHJ9JsC4SMeE4\nDiNbjqR6keoMWDKAvYl7rZNE/kV6ZjaPfbSG9Mxs3rm/CdERIdZJIjZysn07CU7v9+0oiNYjzvL3\n/GLocxynrOM4ixzH2eY4zhbHcXpZN4mHRBbzbfRMPw2f3gdZZ62LRExEBEcwue1kggOD6flTT5Iy\nkqyTRABwXZf+n29k86FEJndrQJWYgtZJIna+HwJ7foQbx0P5K61rJI/wi6EPyAL6uq5bE2gO9HAc\np5Zxk3hJbF245Q04sBK+6eNbfyziQaUKlGJim4kcOHOA/kv6k63ttuIH3vg5jjkbDtHvuupcU7OE\ndY6InfWfwK+vQdPu0PgB6xrJQ/xi6HNd97Drumv/+NdngG1Aadsq8ZxaN8PVA2D9dFjxhnWNiJnG\nJRrzfPPnWXZwGZPXTrbOEY/7afsRxi3YTqf6pXiyTWXrHBE7B9bA3F5QoRV0eNG6RvKYIOuAf+c4\nTgWgIbDCtkQ86eqBcGQLLBgExWtA5bbWRSImulbryo6TO3hvy3tULVyVTpU7WSeJB+0+eoZen6yn\ndqlCjLutHo62E4pXJR2GmXdDwVjfLoLAYOsiyWP84pO+/+E4TgFgNvCM67r/8WUSx3G6O46z2nGc\n1ceOHbv8gZL/BQTALW9C8eow6wE4sce6SMTMgKYDuCL2CoYtH8bm45utc8RjElMzefTDNYQGB/DW\nfU0IDwm0ThKxkZkOn94DZ8/AXZ9ARBHrIsmD/GbocxwnGN/A97Hrul/8t7/Hdd23XNdt4rpuk+LF\ni1/eQPGO0AK+9ceO4/utWrqWWYg3BQcEM+HqCRSPKE6vn3pxLFW/bJPLIys7h6dnruPAqVTeuLcx\npaLDrZNEbLiu75HOg2vg1jehRG3rIsmj/GLoc3zPa7wLbHNdd6J1jwhFKkLXD+D4Lpj9CGRnWReJ\nmCgcVpjJbSdzJvMMvRb1Ii0rzTpJPGD0/G0s2XmMkTfXoUkFfaohHrZsMmycCW2eh5p6zF4unF8M\nfUBL4D6gneM46//409E6Sjyu0tXQ8WXYtQC+fVYbPcWzqhepzkutXmLz8c0MWDJAGz0lV737y17e\nW7aPh1pWpFvTctY5InY2fQ4/DIXat0LrZ61rJI/zi6HPdd1fXNd1XNet57pugz/+zLfuEuGKh6Hl\nM7D6n7DsFesaETPtyrVjQNMBLIpfxNhVY3H1SxDJBd9uOsyoeVu5vnYsg26saZ0jYmffMvjqCSjf\nErpM8+0cELkIfre9U8TvXDMUEg/AD8OgUBmo19W6SMTEPTXv4XDyYT7Y+gGlC5Tm/tr3WydJPrLm\n95P0+nQ9DctG80q3BgQGaFOneNSxHTDzLihcAe6cDsFh1kWSD2joE/k7AQHQ5XU4k+D7rVvBWKjY\nyrpKxESfJn04nHKY8avHUyKyBNdXuN46SfKBuGPJPPLBakpHh/PO/VcQFqxNneJRZxJg+u0QGAr3\nfK5NnXLJ6LNikXMRFArdpkPRyjDzHji6zbpIxESAE8CLrV6kUUwjnl/6PGuOrLFOkjzuePJZHnhv\nFQGOw/sPXkGRyBDrJBEbZ5Nhxh2QegLu+QwKl7cuknxEQ5/IuQovDPfM8j1m8XFX36FUEQ8KDQxl\nSrsplC5Qmp4/9SQuMc46SfKo1IwsHn5/FUfPpPPO/U0oXzTSOknERnYWfP4gJGyCru9DqYbWRZLP\naOgTOR/R5eDuzyD1JMzo6juUKuJBUaFRTGs/jaCAIJ784UmOpx23TpI8JjvHpecn69l0MJEp3RrS\nsFxh6yQRG64L8/rAroVw40Sodp11keRDGvpEzlepBnDHh3BkK3x2P2RnWheJmChTsAyvX/M6J9NP\n0uPHHqRmplonSR7hui7D5mzhh21HGNa5NtfVjrVOErGzdAKs/QBa9YUmD1rXSD6loU/kQlRtDzdN\ngj0/wje9dcNPPKt2sdq83Ppltp/czrNLniUrJ8s6SfKAt5bE8dFvv/NY60r848oK1jkidjZ8Cj+N\nhLp3QLvB1jWSj2noE7lQje/3HUtd9xEsGW9dI2Lm6rJXM6jZIJYcWMKYFWN0w0/+0pwNhxjz7XZu\nqleSAdfXsM4RsRP3M3zdAyq0gpungqMzJZJ7dLJB5GK0HeS74bdoFESVgQZ3WReJmLij+h0cSj7E\nu5vfpWSBkjxS9xHrJPFDv8WdoN9nG2hasQjju9YnQLf4xKuObIVP74WiVXy3+IK0tVZyl4Y+kYvh\nONBpCiQdgjlP+W74VW5rXSViomejnhxKOcTktZMpGVmSGyvdaJ0kfmT30TN0/3A1ZYuE89Z9jXWL\nT7wr6RB8fDuERPq2godHWxeJB+jxTpGLFRQCd34ExarDp/dBwmbrIhETAU4Ao1qOokmJJryw7AVW\nHl5pnSR+4mhSOvf/cxUhQYG8/2BToiP0qYZ4VHoSfHwHpCf6toFHl7UuEo/Q0CdyKYRF+X5bF1rQ\nd8Mv8aB1kYiJkMAQXmn7CuULlueZRc+w+9Ru6yQxlnI2i4c+WMWp1Azee+AKyhaJsE4SsZGdCZ/9\nA45uhTs+gJL1rIvEQzT0iVwqUaV9g9/ZM77BLz3RukjERFRoFK+3f53QoFCe+PEJjqYetU4SI1nZ\nOfSYsZath5KYencj6paJsk4SseG6MLcXxC2CzlOgSnvrIvEYDX0il1JsHbjzQzi+w/fbvKwM6yIR\nE6UKlOL1a14n8WwiPX7sQUpminWSXGau6zL4680s3nGMUV3q0rZGjHWSiJ2fx8L6j+HqgdDwXusa\n8SANfSKXWuV20PlViFsMc3vqhp94Vs2iNZnYZiK7Tu2i7+K+ZOZkWifJZTR10W4+WRlPj7aVubtZ\nOescETvrpsPiMdDgHmgz0LpGPEpDn0huaHA3tHkeNnzie6EX8airSl/F4OaDWXZoGaN+G6Ubfh7x\n5boDjF+4ky4NStHvuurWOSJ2dv/oe6yzUlvoNFm3+MSMTjaI5Jar+0NivO+Rjqgy0Ogf1kUiJm6r\ndhuHUg7x1sa3KBlZksfrP26dJLlo+e7j9P98I1dWKsq42+vj6E2ueFXCJvjsfiheA+74EAKDrYvE\nwzT0ieQWx4GbJvnu8cx9BgqWgqr64rZ401MNnuJw8mGmrp9KyciS3FzlZuskyQXbE5J47KM1VCwW\nyRv3NSYkSA8UiUclHvAtdQsr5FvyFlbIukg8Tq/GIrkpMNi3lrlELZh1PxzeYF0kYsJxHIa3GE6z\nks0YtnwYvx761TpJLrGExHQefG8VEaGBvPdgU6LC9amGeFTaaZh+O2Sk+Aa+QqWsi0Q09InkutCC\ncPcsCC/sO8h66nfrIhETwYHBTGoziYrRFem9uDfbT263TpJLJDEtkwffX0VSWib/fOAKSkeHWyeJ\n2MhMh0/vhRO74c6PoERt6yIRQEOfyOVRqKTvt31Z6fBhZ0g6bF0kYqJgSEFev+Z1CgQX4LHvHyMu\nMc46SS5SakYWD72/it1HzzDt3sbULqVbfOJR2Znw+YOwbyncPBUqtbEuEvlfGvpELpeYmnDvF5By\nHD7qAiknrItETMRGxvLOde8A8OjCRzmYfNC4SC5UemY2j364mnX7TzGlW0NaVytunSRiIycbvnoC\ndsyHjuOh/p3WRSL/QkOfyOVUpjHcNRNO7YPpt0B6onWRiIkKURV469q3SP9/7N13XJZl+8fxD3sP\nEQRZgqIgiOJW3Gnu3JorU7My29mwaXvYU2rTMlNzZFqKuWe5twLiABGV4WAjyLzH74/Lp57n+bUs\nvM8b7uP9evnKSLi/xriu4zrP4zh15UzZMoXs0mzVkcQtqtIbeGT5Cfal5jFrRAv6RddXHUkINYxG\nWP8knFwFPWdCu/tVJxLi/5GiTwhTC+0Co5bAtdNaj1/lDdWJhFAi3Cucz3t9Tn55Pg9sfYCC8gLV\nkcRfpDcYeXpVAtvPXOP1wVGMaB2oOpIQahiNsPUlOL4YukyHLk+pTiTEb5KiTwgVmvSG4fMh8zCs\nGAe6CtWJhFCiuU9zPun5CZklmTy47UGKK4tVRxJ/wmg08lLcSdbGX+bZvuFM6BiiOpIQ6ux6Dw58\nAu0ehDteVp1GiN8lRZ8QqkQNhUGfQNpP8P1krQFcCAvU1q8tH3b/kHMF53h4x8OUVpWqjiR+h9Fo\n5K0NZ/j2cAYP92jEtO5hqiMJoc7+T+DndyBmHPR9VzufVwgzJUWfECq1HAf9ZsHZ9RA3DQwG1YmE\nUKJrYFfe7fouCTkJPPHTE1TqK1VHEr9h7o5zfLX3AhNjQ3i6d7jqOEKoc2wRbH0RIgfDXR+BtdxS\nC/MmX6FCqNb+5paQkyth43StP0AIC9QnpA+vdnyVA1cO8MyuZ6gyyOq3OflqTxpztp9jROtAXhkY\niZWsaghLlbgK1j0BYXfCsK/AxlZ1IiH+lBR9QpiDrk9D5yfh6New7WUp/ITFGtp4KDPazWBnxk5e\n3vcyBqOsfpuD5YfSeXPDGfpH+/HusGisraXgExbq7AZY8yA06KQdvm5rrzqREH+JPJoQwlz0nAkV\nJbD/Y3Bwh27Pqk4khBLjmo6jtKqUj058hLOtMy93eFlWlRRaG5/Fi3En6R7uw5y7W2JrI8+LhYU6\n/xOsmgj+MTB2Bdg5qU4kxF8mRZ8Q5sLKSuvvq7wBP70F9q7QcZrqVEIoMSV6CiVVJXyd9DUudi48\n1fopKfwU2HrqKk+tTKBdiBfzxrfG3lYKPmGh0g/BirFQtzGM+x4c3FQnEuKWSNEnhDmxtoZBH0Nl\nCWx5HuxdoPW9qlMJYXJWVlY80eoJSqtKWXRqES52LkxtMVV1LIuy91wujyw/QbMADxZMbIujnY3q\nSEKocTkelo0Et/owIQ6cvVQnEuKWSdEnhLmxsYXhC2DFGFj3uFb4RY9QnUoIk7OysuL59s9Tqivl\n0/hPcbFz4Z7Ie1THsgjHLuVz/zdHaejjwuJJbXF1kNsFYaFykmHpMHB0hwlrwbWe6kRC/C3yU1wI\nc2RrD6OWwLIRWsO4vQuE91OdSgiTs7ay5rXY1yjTlTHryCycbZ0Z3mS46li1WlJWERMXHsHPw5El\n97XH01kGVQgLlX8BvhkMVjZawecZpDqREH+bbM4XwlzZO8OYFeDXHFbeC2k/q04khBK21ra82+Vd\nOgV04rUDr7HpwibVkWqt1OxiJnx9GHdHO5ZOaY+Pm4PqSEKocf2yVvDpyrWCr24j1YmE+Eek6BPC\nnDm6w/gftIvNt2Mh47DqREIoYW9jz+zus2nl24oX9rzAzxk/q45U66TnlTLuq0NYW1mxdEp7Ajxl\nMqGwUDdytYKvNF+7BvtGqk4kxD8mRZ8Q5s7ZC+6JAzdfWDoCriSqTiSEEk62TnxyxyeEe4Uz/efp\nHLxyUHWkWuNqUTnjFhykQmdg2ZT2hHq7qI4khBplhbBkKBSmw9jvIKC16kRCVAsp+oSoCdx8te0l\nDm7axSgnRXUiIZRwtXdlXq95BLsH89jOx4jPjlcdqcbLK6lg3FcHKbhRxeJJ7Qj3k1H0wkJV3oDl\noyD7DNy9DEI6qU4kRLWRok+ImsIzWCv8rKy1bScFF1UnEkIJT0dP5veej4+TD9O2T+Ns/lnVkWqs\norIqJnx9mKzCMhbc24YWQZ6qIwmhRlU5fDsGMo/AiAXQuJfqREJUKyn6hKhJvMPgnjVQVaoVftev\nqE4khBLeTt7M7z0fF3sXHtz2IGlFaaoj1TillTomLzpCyrVi5o1vTfuGdVVHEkINfRV8Pwku7ILB\nn0HkYNWJhKh2UvQJUdP4NYPxq7VG88V3aRPGhLBA/q7+zL9zPlZYMWXLFCn8bsGNCq3gO5FewEej\nW9I9XM4eExZKXwU/3AfJG6H/vyBmjOpEQtwWUvQJURMFtoZx30PxFVjYHwozVCcSQokQjxDm956P\n3qhn0uZJnCs4pzqS2bterm3pPHKxgNl3x9Avur7qSEKooauAlRPg9Fro8za0u191IiFuGyn6hKip\nGnTUpnqW5muFX/4F1YmEUKJxncYs7LsQWytbJm+ZzJm8M6ojma2i0iru+eoQCRmFfDKmJYNjAlRH\nEkKNqjJYMfbXFb6OD6tOJMRtJUWfEDVZUFu4dy1UFmuFX26q6kRCKNHQoyEL+y7E0dbFmCmLAAAg\nAElEQVSR+7bex8mck6ojmZ38G5WMmX+QM1e0Hj5Z4RMW699TOlN3wKCPZYVPWAQp+oSo6fxbwr3r\nQF8Ji/pDtkwyFJYp2D2YRX0X4W7vzv3b7udE9gnVkcxGTnEFY748yPmcEr6c0Jpekb6qIwmhRkWx\ndubtxb0wdB60mqA6kRAmIUWfELWBXzRM3KD9ftEAuJqkNo8QigS4BrCo7yK8nbx5cNuDHLl6RHUk\n5a4WlXP3lwdIzy9l4cS2MrRFWK5/H7yecQiGL4AWo1UnEsJkpOgToraoFwETN4KNPSweCJdllUNY\nJj8XPxb2WYi/iz/Ttk9j/+X9qiMpk1VYxt1fHuBaUTmLJ7cjNsxbdSQh1CjN1446uhwPo76BZsNU\nJxLCpKToE6I28Q6DSRvB3g0WD4YMWeUQlsnH2YcFfRYQ7B7MozseZXfmbtWRTC4jv5S7vzhA/o1K\nlkxpT7tQL9WRhFDj30ccZZ+B0cug6UDViYQwOSn6hKhtvEK1ws/ZC5YMgUuWu8ohLFtdp7os6L2A\nsDphPP7T4+y4tEN1JJNJyylh1BcHKKnQsXxKB1oF11EdSQg1iq9qbQ9552HsCmjSR3UiIZSQok+I\n2sgzCCZtAnd/WDoc0napTiSEEp6OnszvPZ/IupFM3zWdzRc2q4502527VszdXx6kUmdg+ZQORAd6\nqI4khBpFWb+eZTtuFTS6Q3UiIZSRok+I2sq9vjbcpU7IzdHU21UnEkIJd3t3vrzzS1r4tOC5Pc+x\n7vw61ZFumzNXrjP6y4MArHigA5H+7ooTCaFIwSVY2A9u5MA9ayC0i+pEQiglRZ8QtZlrPbh3PXg3\nhm/HQPIm1YmEUMLFzoXPe31OW9+2vLj3RVafW606UrU7mVnEmPkHsbOx5rsHOtDY1011JCHUyDuv\nbeksL4QJcRDcXnUiIZSTok+I2s6lrnaOn28z+G48nF6rOpEQSjjbOfNJz0+IDYhl5v6ZrDi7QnWk\nanM8vYCxXx3Exd6WlQ92pKGPq+pIQqiRk6IVfJU3tGtfQGvViYQwC1L0CWEJnOrAhLXaxW/VJEhc\npTqREEo42jryUY+P6B7UnbcOvcU3p75RHekfO3whn3u+OoSXiz0rp3YkuK6z6khCqHHttFbwGXRa\ne0P9FqoTCWE2pOgTwlI4usP41dAgFlbfDyeWqU4khBL2NvZ82O1D7mxwJ+8ffZ+vTn6lOtLftj81\nl3u/PoyvhyMrH+xIgKeT6khCqHElQSv4rKy1M2t9I1UnEsKsSNEnhCVxcIWxK6Fhd1g7DY4uVJ1I\nCCXsbOyY1XUW/UP7M/f4XD6P/xyj0ag61i3ZlZLDpEVHCPZy5rsHOuLr7qg6khBqZB3TzuGzc9aO\nLPJpojqREGbHVnUAIYSJ2TvDmBWwcgKsfwL0ldD+QdWphDA5W2tb3u78NnbWdnyW8BmVhkoea/kY\nVlZWqqP9qe2nrzFt2XHC6rmydEp7vFzsVUcSQo30Q7BshNbGcO86qNNAdSIhzJIUfUJYIjtHuHsp\nfD8JNj0Lugro9JjqVEKYnI21Da93eh17G3u+OvkVFfoKnmnzjFkXfptOXuHRb08Q5e/ON5Pb4+Fs\npzqSEGpc3AvLRoGbn1bweQSoTiSE2ZKiTwhLZWsPIxfB6gdg28ta4dftGdWphDA5aytrXu7wMg42\nDiw5vYRKfSUvtH8Bayvz64BYG5/FUysTiAnyZOGktrg7SsEnLNT5n7SjiDyD4d4ftcJPCPG7pOgT\nwpLZ2MHwr8DWAX56UzvT6M43wNr8bnaFuJ2srKx4tu2z2NnYsTBpISVVJbwR+wZ2NuZTVH1z4CIz\nfzxF+1AvFtzbFhcHuYQLC3VqjfbA0rsJ3BMHrj6qEwlh9uSKIYSls7aBwZ+Bowcc+ASuX4ah87RC\nUAgLYmVlxZOtnsTd3p25x+eSW5bL7O6zcbNXe8i5wWBk1pZk5u06T6+mvnw8piVO9jZKMwmhzIHP\nYMsLENQexnwLzl6qEwlRI8jjfCGEtrLX911tle/UalgyDMoKVKcSwuSsrKyYEj2Ftzu/zbGrx5i4\neSLXblxTlqdSZ+CplfHM23Wece2DmTe+lRR8wjIZDLD5BdjyPDQdCBPipOAT4hZI0SeE0FhZacNc\nhi+AjEPwdT8oylSdSggl7mp0F5/2+pSskizGbxpPakGqyTNcL69i0qLDxMVf5pk+4bw5pBm2NnLZ\nFhaoqhx+mAwHP4X2U2HkYrCTMymFuBVy9RBC/LfoEXDPam2b51e94GqS6kRCKBHrH8uivovQG/RM\n2DyBo1ePmuy1rxaVM2reAQ6l5fPhqBY83CPMrCeKCnHblBXA0mFaH9+db2i7UqxltVuIWyVFnxDi\n/wvtCpM3AVawsB+k7VKdSAglIrwiWNp/Kd5O3jyw7QG2XNxy218z5Voxwz7bR0Z+KQsntWVYq8Db\n/ppCmKWiTG3XScZhbRdKp8e0XSlCiFsmRZ8Q4rf5RsGUbeAeAEuHQ+Iq1YmEUMLf1Z8l/ZYQ7R3N\nM7ueYcnpJbfttQ6m5THi8/1UGYysnNqRLo1lKqGwUFeTtN0m17O03SfRI1QnEqJGk6JPCPH7PAJh\n8mYI7gCrp8DeOWA0qk4lhMl5OHjwZe8v6dWgF7OOzGLWkVkYjIZqfY31iZeZsOAwPm4OrJkWS5S/\nR7V+fCFqjLRd2i4TrLRrUGhX1YmEqPGk6BNC/DEnTxj/AzQbDttnwqZnwaBXnUoIk3OwceD9ru8z\nruk4lpxewrO7n6VCX1EtH3vB3gs8+u0JWgR58MNDsQTWca6WjytEjZO4Sttd4h6g7TbxjVKdSIha\nQc7pE0L8OVsHGPYVuPvD/o+1IS/Dv5LpacLi2Fjb8Fzb56jvUp9/Hf0XuWW5zO0xFw+Hv7cqZzAY\neWvjGRbsvUC/Zn7MvjsGRzsZUiEskNEI++ZqDxdDusDdS7WHjkKIaiErfUKIv8baGnq/qU1OO7sB\nvhkCpfmqUwlhclZWVtwbdS+zus4iISeBiZsncvXG1Vv+OBU6PY+uOMGCvReYGBvCJ2NbScEnLJNB\nr+0i2T4TooZpu0uk4BOiWknRJ4S4NR0egpGL4PIJWNAbCi6pTiSEEv1C+/FFry+4duMa4zaMIzk/\n+S+/b1FpFRMWHGZD4hVe6B/BzLsisbGWqYTCAlWVwcoJcPhL6PiINqXT1kF1KiFqHSn6hBC3LmoI\nTIiDGzmw4E64kqA6kRBKtKvfjkX9FoEVTNw8kUNXDv3p+1wuLGPkF/s5nl7A3NExPNC1kZzBJyxT\naT58M1jbPdL3XejzlrarRAhR7eQ7Swjx9zSIhfu2go09LOwPqTtUJxJCiSZ1mrCs/zL8XPyYun0q\nG9I2/O6fPXPlOkM/28eVonIWT27H4JgAEyYVwowUXNJ2i1yO13aPdHhIdSIhajUp+oQQf59PONy3\nDeqEwvJREL9cdSIhlPBz8WNxv8W0rNeSGXtm8HXS1xj/53iT/am5jJp3ACusWDW1I7GNvBWlFUKx\nKwnaLpEbOdqukaghqhMJUetJ0SeE+Gfc68OkjRDSGeIegt3vy1l+wiK527szr9c8+oX0Y/ax2bxz\n+B30N483WRufxb0LD+Pv6cSah2OJ8HNXnFYIRVK3a7tDbOy13SINYlUnEsIiyJEN1ai8So+DrbX0\nZgjL4+gOY1fBj4/CzjehKAv6/wts5EeMsCz2Nva82/VdfF18WXRqEdml2YTxAP/acoEODb344p42\neDjZqY4phBonlsG6x8CnKYxbpT00FEKYhNyRVROd3sCUxUfxdXfkraHNZOy2sDy29jB0nnaW394P\n4XqWdpaf4987v0yImsrayprpbabj7ViPfx17n62l5+jd/Gk+HtUOB1u5NggLZDDArndh13vQsDuM\nWqI9LBRCmIxs76wm1lZWtAmpww/HM7n7iwNcKSpTHUkI07Oygl4zYeBsOL8T5t8BOX99jL0QtUV2\ncTnr9zaiLHMc9s7XSLV9k7MFSapjCWF65UWwYqxW8MWM13aFSMEnhMlJ0VdNrK2teKJXE768pzXn\nc25w18d7OXxBDq4WFqrNZLh3nXaxn98Tzm5UnUgIk4nPKGTQx/tIyrrO7IH38N1dy3CwsWfS5kms\nPrdadTwhTCcnRbsGpG6Dfu/D4E+0XSFCCJOToq+a9Y7yI+7hWNwd7Rg7/yBLDlz8fxPchLAIDWLh\ngV3g3RhWjIGf3tG2+AhRi608msGoLw5ga2PFDw/FclcLf8K9wlkxcAVt/doyc/9M3jz4JlX6KtVR\nhbi9kjdpuz3KCmDCj9D+AW03iBBCCSn6boOwem7EPdKJbk18eHntKZ77IZHyKr3qWEKYnkcATNoE\nMeO0fo7vxkH5ddWphKh2VXoDM9cm8ez3ibQL8WLdI52J9P91C5uHgwef9fyMSc0m8V3yd0zZOoXc\nslyFiYW4TQwG+Pk9+HY01G0ED+6CkE6qUwlh8axq6ipUmzZtjEePHlUd4w8ZDEbmbE/ho52ptAjy\n5IvxrfHzcFQdSwjTMxrh8HzYPEO7CRi9XFsBFKIWyC2pYNqy4xy+kM8DXRvybJ9wbG1+/5nqpgub\neGXfK7g7uDOn+xyifaJNmFaI26j8unZ0z9n10GKM1t9t56Q6lRC1mpWV1TGj0djmz/6crPTdRtbW\nVjzVO5x541uTeq2YgR/v5ehF6fMTFsjKStvac++PUJqvbflJ3qQ6lRD/WGJmIXd9vJfEzELmjo7h\nhf5N/7DgA+gX2o+l/ZdiZ23HxM0TWXNujYnSCnEb5abCVz21n+1934Uhn0vBJ4QZkaLPBPo28yPu\n4U64OtgwZv5Blh26pDqSEGqEdIYHfgavhtrWn12zpM9P1Fg/HMtkxLwDWFtZ8f3UWAbHBPzl9w33\nC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InyUx1LCNPTVcDe2bDnA7Bzhj5vQcw4GXOu2E/J2by0JomswjLGtg/mub4ReDhZ3kXd\nlPQGPSuSVzD3+FwAHo55mHFNx2FrLUOPlEo/pB3DkHMWooZC3/fATY4lEZYnpSCF1w68RmJOIh3r\nd+TlDi8T5B6kOpYyUvSJWxKfUciMHxI5e7WYPlG+vDaoGX4eMvJcWKCcZG3VL/0AhHSBgXPAO0x1\nKouTU1zBG+tP82PCZcLqufLOsGjahnipjmVRrpRc4a1Db7ErcxdNvZryauyrRNaNVB3L8pQXwfbX\n4OjX4B4AAz6A8L6qUwlhcuW6cr5M/JKFSQtxs3fjmbbPMLDhQIvf9SFFn7hlVXoDC/ZeYPa2FOxs\nrHmubzjj2jeQ8efC8hgMcHwxbJsJunLo9gzEPg629qqT1XpGo5FVRzN5a+MZyir1PNwjjKndG+Jg\na6M6mkUyGo1svbSVdw69Q0FFAfc0vYdpMdMsZkCCcqd/hI3PwI1saD8VerwIDq6qUwlhcoeuHOL1\nA6+TXpzOoEaDeLrN09RxlHkUIEWf+Acu5d3gxTVJ7E3NpVWwJ+8Ob04TXzfVsYQwveKr2qHup+Og\nXqQ2LCGonepUtVZaTgkvrDnJwbR82oV48fawaMLqyQ2uOSiqKGLO8Tl8n/I9/i7+vNzxZToHdFYd\nq/YqyoJNz8LZ9eAbDYPmQkBr1amEMLnC8kI+OPYBcalxBLkF8UrHV+hQv4PqWGZFij7xjxiNRtac\nyOKN9acpqdAxtVsjHu4RhqOdPG0XFih5E2x4Gq5nQdv7oOcr4Cgj7atLpc7AF7vO8/FPqTjaWvNC\n/6aMahMkuwzM0LFrx3jtwGtcKLpAv9B+PNv2WbydvFXHqj0Mem0b5/bXwKCDHs9Dh2lyyLqwOEaj\nkY0XNjLryCyKKoqYGDWRqS2m4mgrrUf/S4o+US3yb1Ty5obTrD6eRai3C28PjaZjo7qqYwlhehXF\nsPMtODQP3Pyg/7+g6UDVqWq8Y5fymfHDSc5llzCgeX1m3hVJPTe5qJuzSn0lC04uYP7J+TjZOvF0\nm6cZEjbE4vtq/rFrp7R+4swj0LAHDPwQvBqqTiWEyWUWZ/LmwTfZd3kf0d7RzOw4k3CvcNWxzJYU\nfaJa7T2XywtrTpKeX8qoNoG80L8pns7S3yQsUOYx7cbs2kmIGAj93wd3f9WpapfBeVAAACAASURB\nVJzr5VXM2nyWZYfSqe/uyBtDmtGzqUwirEnSCtN47cBrHM8+Tlu/trzS4RVCPEJUx6p5qsq0Ixj2\nzdV2EPR5B5qPksnBwuLoDDqWnl7Kp/GfYm1lzWOtHmN0+GhsrGWX2R+Rok9Uu7JKPR/tPMeXu9Pw\ndLLjyTubMLptELY2cj6QsDD6KjjwKfz8DljbQdfp2pAFOzko/M/oDUZ+OJ7Jv7Ykk1tSwcTYUKb3\nboKLgxwHUBMZjAZWn1vNh0c/pEJfwYSoCdzX7D5c7aUX808ZjXDmR21gVMEFaDEWer8JLrKbRlie\nA5cP8MHRD0guSKZ7YHde7PAifi5yhNhfIUWfuG1OX77OzB+TOHKxgEY+LjzXN4I7I31la4+wPPlp\nsPl5SNkM7oHQ82WIHiUHJf8Go9HIrpQc3t10lrNXi2kR5Mnrg6JoEeSpOpqoBjmlOXxw7AM2pG2g\njkMdpraYysgmI7GTXrTfln4Itr4EmYfBJwL6vguNeqhOJYTJJecnM/v4bPZl7cPfxZ/pbaZzZ4M7\n5Z7yFkjRJ24ro9HIttPXeHfzWdJybtAuxIvn+0fQMljG5woLdGE3bH0ZrsSDXzTc+To0ukN1KrOR\nlFXEO5vOsC81j2AvZ57tG86A6PpyUa+FTuWd4sOjH3L46mGC3YJ5ovUT9AruJZ/rf8tNhR2vwpl1\n4OoHPV6AmHFgIyvdwrJcvXGVT+M/ZW3qWlztXXmw+YOMjhiNg42D6mg1jhR9wiR0egMrjmQwZ3sK\nuSWVDGhen2f7hNOgrovqaEKYlsEAp1bDjtegMB0a9dSKP79mqpMpk1lQygdbU1hzIos6znY81rMx\n49o3wN5WVkJrM6PRyJ6sPcw+NpvUwlRa+LRgepvptKzXUnU0dUpyYNd7cGwh2DpCp8eh48NgL9dK\nYVmKK4tZmLSQJaeXoDfqGRsxlvub34+Hg0zE/ruk6BMmVVKh48vdaczfnYbOYGB8hwY8ekdjvFxk\n2IuwMLoKODxfG8xQXgQxY7UDlT0CVCczmaKyKj77KZWF+y8CMLlTKA91b4SHk2z1syQ6g44fz//I\nJyc+Iacsh57BPXm81eOEeoSqjmY6laVw8FPYOxeqSqH1ROg+A1zrqU4mhElV6atYlbKKeQnzKKgo\noH9ofx5t+SiBboGqo9V4UvQJJbKvlzN7ewrfHcnAxd6WaT3CmNQpRM73E5anrAD2fACHvgAra+2s\nrc5P1Orz/Sp0epYcuMQnP6VSVFbFsJaBPNW7CQGeMuDGkpVWlfLN6W9YmLSQCn0FI5qM4KEWD1HX\nqRYPLDHoIX45/PQWFF/RJv32nAk+TVQnE8KkjEYj29O3M+fYHNKL02nr15bpracT5R2lOlqtIUWf\nUOrctWLe3XSWHWez8fdwZHrvcIa0DMBGDlsWlqbgEux8E06uBOe60O05aD0JbGvPKrjBYGT9ySu8\nv+UsGflldGnszYx+EUT5194CV9y63LJc5iXM4/uU73GwcWBys8ncE3kPznbOqqNVH6MRUrfDtlcg\n+zQEtIHeb0CDWNXJhDC5E9kn+ODoByTkJNDIoxFPtXmKLgFdpMe3mknRJ8zCgfN5vLPpDImZRTSt\n784L/SPo0thHdSwhTO/yCe1G8MJu7cDlnjMhcnCNP4vrYFoe72w8Q0JmERF+brzQvyldm8j3uPh9\nF4ouMOfYHHZm7KSeUz0ebvkwgxsNrvlncV2Oh20va9/jdUKh10yIHFLjv8eFuFUXiy4y5/gcdqTv\nwMfJh0daPsKgRoOwtZaBRbeDFH3CbPx7FWDW5rNkFmirAM/3a0qkv7vqaEKY1v+uAgS2hTvfgAYd\nVSe7ZeeuFfPe5rNsP5NN/Zur+UNlNV/cguPXjvPBsQ9IzEkkzDOMJ1s/WTNXAQrTtdX8xO/AyUtb\nzW8zuVat5gvxV+SV5fF5wue/rOZPajaJCZETatdqvhmSok+YnX/3+3y8M5Xr5Vq/z/TeTfCXfh9h\naX6r36fXq+DdWHWyP/W/fbsP9WjE5E6h0rcr/haj0ci2S9uYc3wOGcUZtPNrx1NtniKqbg3o9/l/\nfbsPQecna3XfrhC/pUxXxjenvuHrpK9/6dud2mIq3k7eqqNZBCn6hNkqKq3is5+1yX5WwOTOoUzt\nJpP9hAWqvAEHP6sRk/1KKnTM353G/D1pVOllQq+oXlX6KlamrOSLhC9+mez3WKvHCHA1w6m3ugo4\n8hXsmvUfE3pfAA+ZQigsy78n9H564lOyy7Itc0KvGZCiT5i9/zzDy83BlnEdGjC5Uwj13B1VRxPC\ntP7zDC9rW2g5Hjo+Al7qL5x5JRUs2n+Rbw5coqisigHR9Xm2r5zFKW6P4spivk76WjvDy6Cnf8P+\nTIqaRFidMNXRtALv6EI4+DmUXL15Fudr4BetOpkQJlWuKycuNY7FpxaTWZJJc5/mTG89nVa+rVRH\ns0hS9Ika49TlIj77+TybTl7B1tqa4a0DuL9LQxr6uKqOJoRp5Z2HvR9Cwndg1EPUUOj0BNRvbvIo\n6XmlzN+TxsqjGVTqDdzZ1JdpPcKICfI0eRZhea7euMriU4v54dwPlOnK6BbYjcnNJqu5qSy+qhV6\nR7+GiuvQsLu2jbNhd9NnEUKhoooiVpxdwfKzy8kvz6e5d3MmR0/mjqA7al4vbi0iRZ+ocS7m3mD+\nnjRWHcukSm+gb5QfD3ZrJDeZwvJcv6Jt+zy6ECqLodEdWvEX2vW2TwJMyirii91pbEi8jI21FUNb\nBvBA10aE1ZOHMML0CssL+Tb5W5afWU5hRSExPjFMajaJ7kHdsbayvr0vnpsK+z+ChG/BoNOm7XZ6\nHPxb3t7XFcLMXL1xlW9Of8P3Kd9Tpiujc0BnJjebTBvfNlLsmQEp+kSNlVNcwaL9F1hy4BLXy3V0\naOjF1G6N6NbER364CMtSVqitLhz8HG5kazebnR6HpoOgGsfbG41GDpzP4/Nd59lzLhdXB1vGtQ9m\ncudQfGW7tTADZboy1pxbwzenvyGrJIuGHg2ZGDWRgQ0HYmdTzf3gmcdg32w4sx5s7KHlOG27dd1G\n1fs6Qpi584Xn+TrpazambcSIkb6hfZkUNYlwr3DV0cR/kKJP1HglFTq+PZTOgr0XuHq9nKb13Zna\nrSEDoutja3Obn/AKYU6qyrXVhv0fQX6ads5f7KPQYizY/f2iTG8wsjnpKl/sPk9iZhHerg5M7hzC\nuPYNZLCSMEs6g44tF7ewMGkhyQXJ1HOux4TICYxoMgIXu3/QZ2o0QuoO2DcHLu7RJnC2nQLtp5rl\nYCUhbqfj146zMGkhP2f+jJOtE8MaD2NC5AT8Xf1VRxO/QYo+UWtU6gysjc/ii91ppGaXEFjHifu7\nNGRUmyCc7GVMvLAgBj2cWafdmF4+AS71oMNUaHMfOP31bdDlVXp+OJ7J/N1pXMwrJaSuMw90bcSw\nVgFy9IKoEYxGI/su72Nh0kIOXz2Mm70bo8NHM7bp2FsbE6/Xwak1sG8uXDsJbv7Q8WFofS84uN2+\nv4AQZsZgNLArYxdfJ31NfE48ng6ejI0Yy5iIMXg6SpuNOZOiT9Q6BoORHWezmbfrPMcuFVDH2Y57\nY0O4t2MIdWRsvLAkRqO2GrF3DpzfAfZu0GYidJgG7r//JLaorIqlBy+xcN9FcksqaB7owdRujegT\n5SeHqosa62TOSRaeWsj2S9uxs7ZjcNhgJkZNJNg9+PffqbIUTiyB/Z9AUTp4h2tbp6NHyqHqwqJU\n6avYcGEDi5IWcb7oPP4u/kyImsDQsKFyqHoNIUWfqNWOXMxn3s/n2XE2Gyc7G+5uG8SULqEE1pEf\nUMLCXEnUVilOrQYrG2h+N3R6DHx+7bm4WlTO1/susPxQOiUVOro28WFqt4Z0bFhX+mRFrXGx6CKL\nTi3ix/M/ojfq6RXci8nRk//7oPfSfDj8pXagelk+BLXXhiQ16QvW0jYgLMeNqht8n/I9S04v4Vrp\nNZrUacLkZpPpHdIbO2vZ3l+TSNEnLELy1WK+2H2eH+MvYwQGtfDnwW4NifBzVx1NCNMquKitWpxY\nArpyCB9AZtQDzE2uQ1x8FnqDkYHNte+PKH8P1WmFuG1ySnNYemYpK5NXUlJVQvv67ZkcchcdU/dh\ndWIJVJVCk37Q+QkI7qA6rhAmlVeWx7Izy1iRvILiymLa+rVlcrPJdPLvJA8Baygp+oRFySosY8Ge\nC6w4kk5ppZ7WDeowsnUgA5rXx81RnlgJy1FacJWLG2cTnLoUV2MJZ4wNSAscSkz/KQQEBKmOJ4TJ\nFJfmsWr/WyzN2kkOekKqdAx2bcSg2OepF9xJdTwhTEZn0LH/8n7iUuP4KeMn9AY9PYN7MrnZZKJ9\nolXHE/+QFH3CIhWWVvLdkQxWHcskNbsEJzsb+kX7MbJ1EO1DvbCWviVRCxmNRo5dKmDl0Qw2JF7h\nRqWepl5WzPCPp1PxZmyvJYC1HYT3g5b3aOf+2diqji3E7XElAU4sg5MroayASvcANoV1ZLV1Kcfz\nkrC2sibWP5ahYUPpHtQdexvp4RO104WiC8SlxrHu/DpyynLwcvRiQMMBjGwyklCPUNXxRDWRok9Y\nNKPRyImMQlYdzWR9wmWKK3QEeTkxsnUQw1sHEuDppDqiEP/Y1aJyfjieyQ/HMknLvYGzvQ0Dousz\nqm0QbRrU+XWrztUkiF8Gid9BaR64+kGL0dByPHg3VvuXEKI63MjTirwTy7QpnDYO0HQgxIyDht1/\nOdcy/Xo6calxrD2/luzSbDwcPBgQOoChjYcS4RWh9K8gRHUoqSxhy8UtrEldQ0JOAjZWNnQJ6MKQ\nxkPoGtC1+s+1FMpJ0SfETWWVeracusrKoxnsP5+HlRV0auTNyDaB9InykxH1okap0OnZfjqbVccy\n2J2Sg8EI7UK9GNk6kP7R9XFx+IMVPF0lnNsCJ5bCuW1g1GuDLGLGQdRQcJReWFGD6HXa9NoTSyF5\nExiqwL+l9vUcPQKc6vz+uxr0HLxykLjUOHak76DKUEWEVwRDwoYwIHSAjKgXNYrBaODYtWOsObeG\nbZe2Ua4vp6FHQ4aGDWVgo4G3doyJqHGk6BPiN2Tkl/L9sUy+P5ZJVmEZbo62DGrhz8g2QbQI9JAm\nZmG2krKK+P5YJnHxWRSWVlHfw5HhrQIZ0TqQEO+/cSh18VVt5e/EMshNBjtniBys3TA36CSTDIX5\nyj2nFXoJK6DkKjh7a1NrW44D36g/f///UVRRxMYLG4lLjeN03mlsrW3pEdSDIWFDiPWPxdZatkIL\n83S55DJrz69lbepaskqycLVzpV9oP4aEDSHaO1ruaSyEFH1C/AGDwcjBtDxWHctkU9IVyqsMNPF1\nZWTrIIa0DMDHzUF1RCHIv1FJ3IksVh3L5MyV69jbWtM70peRbYLoHOZdPWfrGY2QeRTil0LSaqi4\nDp4NtK2fLcaApwx/EWag/Lp2iPqJpZB5WDuepHFv7eu0ce9qO1svOT+ZuNQ4NqRtoKCiAB8nH+5q\ndBdDwoZID5QwC+W6cnak7yAuNY5DVw5hxEj7+u0ZEjaEnsE9cbKV9hVLI0WfEH/R9fIq1idcYdWx\nDE6kF2JrbUX38HqMahNIj4h62NnIiocwHZ3ewO5zOaw6msn2M9eo0huJDvBgVJtABrUIwMP5NvZj\nVJbC2fXasQ8XdgNW0LCbNvwlYgDYyc2EMCGDAS7t0wq902tBV6Ydot5yvLay5+Z72166Sl/F7szd\nrEldw96sveiNemJ8YhgSNoQ+IX1wtXe9ba8txP8yGo0k5SYRlxrHpgubKK4qJsA1gMFhgxncaDD+\nrv6qIwqFpOgT4m9IzS5m1dFMVp/IIqe4Am9XewZE1+eOpr60D/WS/j9xW1TqDBy5mM+OM9msT7xM\ndnEFXi72DG0ZwMg2gWrOnSy4CPHfQvxyKEoHBw+IHKRNAG3YHez/xpZSIf6MQQ+ZRyBls7byXHgJ\nHNyh2XCt2AtoDSbespZTmsP6tPXEpcaRVpSGk60TPYJ60COoB7EBsbjbSy+sqH4Go4Ez+WfYnbGb\nrZe2klqYiqONI3c2uJMhYUNo49cGayt5KC2k6BPiH9HpDexK0VZbfk7JprzKgLO9DZ3CvOkZUY8e\nEfXwdXdUHVPUYDnFFfycnM3Os9nsOZdLSYUOe1trujb2ZkTrIO6IqIe9rRlc0A0GuLhHm/6ZvEnb\n/mnjAKFdoHEfaNIb6oSoTilqsrICSN0BKVsgdZv279a2ENJZ6zGNGAj2zqpTYjQaScxNJC41ju2X\ntlNYUYiNlQ2tfFvRNaArXYO6EuoeKn1U4m8rrSrlwJUD7M7cze7M3eSW5WKFFTH1YhjUaBB9Qvrg\nZu+mOqYwM1L0CVFNyqv0HDifx86z2g16VmEZAM0C3LkjwpeeEfWIDvCQMwDFHzIajZy6fJ2dZ7PZ\ncTabhIxCAHzdHX75OooNq4uzvRkPjdBVQvoBOLdVW4nJS9Xe7hMBTfpAk74Q2E7OABR/zGiEnGRt\nkmzKFkg/qE2Sda6r9ec16aOdJenooTrp79Ib9JzMPcnuzN3sytxFSkEKAIGugXQL6kbXwK608W0j\nZwCKP5VRnPFLkXfk6hGqDFW42bkRGxBLt8BudArohJejl+qYwoxJ0SfEbWA0Gkm+VqwVgGeyOZ5e\ngMEI3q4O9Aj3oWfTenRu7IPrH43NFxajtFLH3nO5/HRzRe/a9QqsrCAmyJM7wutxR9N6RNZ3r7kr\nA3nntZv2lM1a75VBB46eENZLKwDDeoKz3KwIoKocLu2FlJsPDAovaW/3i765YtwXAlr9cp5eTXOl\n5Ap7svawK3MXh64cokJfgbOtMx39O9ItsBtdArvI2HwBQJWhivjsePZkal8vaUVpAIR6hNItUHtg\nEFMvBjtrOU9P/DVS9AlhAgU3KtmVksOOs9nsSs7merkOOxsr2ofW5Y6IetwRUe/vjdMXNVZGfukv\nq8IH0vKo1Blwc7ClSxNv7ojwpXu4D96utXA6bPl1SPvpZhG4BUpzwcpaOwewSR/txr5eU5P3YwmF\nrl+5uSq8BdJ+hqobYOuk9YQ26a19TXgEKA5Z/cp0ZRy5eoRdGbvYlbmLa6XXAIiqG/XLTX3Tuk2l\nH8uCFJQXsDdrL7szd7Pv8j6KK4uxtbalrW9bugZ2pWtgV4Ldg1XHFDWUFH1CmJhOb+DYpYJfbvjP\nZZcA0NDH5Zc+wLYhXjINtJbR6Q0cTy9kx9lr7DzzH593b5dfCv82IV7m0Z9nKgYDXD6hreikbIar\nidrbPYJ/3QYa0hnspC+2VjEY4MqJX1d/ryRob/cI+rXwD+1iUVNgjUYjKQUpv2wDTcxJxIgRbyfv\nX272O9bviLOd+p5FUX2MRiPnCs9pn/eMXSTmJmIwGqjrWJeugV3pFtiNDv4dcLGTh8Lin5OiTwjF\n0vNK2Xn2GjuTczh4Po9KvQFXB1tigjxpEeRBi0BPYoI8qScDYWqUnOIKEjMLScgoJD6ziPj0Aq6X\n67C1tqJ9Qy/uiPDljoh6hMoK76+uX7654rNVWw2sKtVWfAJa3fzVWvvlESQrgTVJaT5cPg5ZxyHr\nmDZ1szRPW+ENbHezwO8D9SLl83pTfnk++7L2aSs+WfsorirGztqOyLqRRHtH08y7GdHe0QS5BdXc\nbd8WqKSyhNN5pzmZe5Kk3CQScxLJLssGILJuJN0Cu9EtsJus8IrbQoo+IczIjQode1Nz2Z2SQ0Jm\nIWevFKMzaN979T0caRHoSYubxWB0gAdujrKX3xzcqNCRlFVEQmYhCRlFxGcU/jLIx8baiia+bsQE\nedC1sQ+dG3vL5+2vqCqHi3shdTtkHYUriaCv0P6bS71fC8CAVuDfUnoCzUVVGVw9qRV3//6Vn3bz\nP1qBTzj4t4JGPbSeTvm8/alferuy9pCQncCZ/DOU6bSfL+727v9VBEZ5R0lPoJmo0leRUphCUk7S\nL0VeWlEaRrRrerBbMFHeUXSo34EuAV3wcfZRnFjUdlL0CWHGyqv0nLp8nYSMwpsFRSEX80oB7YF4\nmI/rzSLQk5hAT8L93Cxre6ACOr2B5GvFJGQU/fJ5SblWzM3anCAvp19WZ1sEeRLl727ekzZrCl0l\nZJ+CzKO/rhjlpsDNGyi8Gv1HIdhaG/wh20JvL4Mecs/dLO6Oav+8dkob1APg5v/rCm1gG6gfA45y\nVt0/pTPoOF94nqTcX4uJc4XnMBgNAPi7+P9SBDbzbkZk3UjZFnqbGY1G0ovTf/l8nMw9ydm8s1Qa\nKgHwcvT67+K8bhSejp6KUwtLI0WfEDVMwY1KErOKiE//tRDMu6FdWOxtrWnm764VgUGetAj0pEFd\nZ9n+8zcZjUYy8suIv/n/OSGjkKTLRZRXaTdXdZzttKL7ZpHXPNCDurVx+Iq5Ki/i/9q71+C4zvqO\n49+/dZd8kRPHF8l2ArZLQqEDCcOldHqjlMAwoRTChBcUKEyGFqaX4UWhzLQd3hTKTDu9t0AZoKWU\ncmvTabikXAaGTmhCxokTkpCQIbEkG9v4JlmSdfv3xVlJK1myN7a0uzr6fmZ29uicZ9d/+dmzq98+\nzzmHoYNVo0r3wfBQsW1DK+x4z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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(15,15))\n", "ax = fig.add_subplot(1,1,1)\n", "R = np.arange(-2,2,0.1)\n", "ax.plot(R,E0(-1,R))\n", "ax.plot(R,E0(0,R))\n", "ax.plot(R,E0(1,R))\n", "ax.set_ylabel(\"E/$E_C$\",fontsize=20)\n", "ax.set_xlabel(\"$N_g$\", fontsize=20)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now study the behaviour for non-zero values of $E_0$. To do this, we approximate the Hamiltonian by the Hamiltonian on a finite subspace. This is a hermitian matrix for which we can find the eigenvalues using standard methods. More specifically, we introduce the parameter prec and restrict the Hamiltonian to the subspace of dimension $2*prec + 1$ spanned by the vectors $|n\\rangle$ with $-prec \\leq n \\leq prec$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#######################################################\n", "# Return a finite part of the Hamiltonian #\n", "# prec = precision #\n", "# E0 = energy of Josephson junction #\n", "# Ec = characteristic energy of capacitors #\n", "# Ng = gate voltage #\n", "#######################################################\n", "def hamiltonian(Ec,E0,Ng,prec=10):\n", " H0 = Ec * np.diag((np.arange(-prec, prec+1)-Ng)**2, 0)\n", " V = -0.5*E0 * np.diag(np.ones(2*prec),1) -0.5*E0 * np.diag(np.ones(2*prec),-1)\n", " return H0 + V" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#######################################################\n", "# Return an approximation of the n-th energy #\n", "# E0 = energy of Josephson junction #\n", "# Ec = characteristic energy of capacitors #\n", "# Ng = gate voltage #\n", "#######################################################\n", "def solve(Ec,E0,Ng,n, prec=10):\n", " H = hamiltonian(Ec, E0, Ng, prec)\n", " E, v = np.linalg.eig(H)\n", " s = np.argsort(E)\n", " return E[s[n]], v[:,s[n]], H\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we again plot the first few eigenvalues" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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14tRS6pDq/DwKV69afmJvu8iZMxDBII/TUccYlQr0XA5qwtoRFu2C+/bCt3kz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\nWpiq28EEkbW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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#########################################\n", "# Plot the n-th eigenvalue depending on #\n", "# the array R with Ng-values #\n", "#########################################\n", "def plot(axis, E0, R,n, prec=10):\n", " y = []\n", " for r in R:\n", " E,_,_ = solve(1, E0, r, n, prec=prec)\n", " y.append(E)\n", " axis.plot(R,y)\n", "\n", "\n", "\n", "fig = plt.figure(figsize=(15,15))\n", "ax = fig.add_subplot(1,1,1)\n", "E0 = 0.1\n", "prec = 5\n", "plot(ax, E0=E0, R=R, n=0, prec=prec)\n", "plot(ax, E0=E0, R=R, n=1, prec=prec)\n", "plot(ax, E0=E0, R=R, n=2, prec=prec)\n", "plot(ax, E0=E0, R=R, n=3, prec=prec)\n", "ax.set_ylabel(\"E/$E_C$\",fontsize=20)\n", "ax.set_xlabel(\"$N_g$\", fontsize=20)\n", "\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Hamiltonian: \n", " 30.25 -0.05 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 \n", " -0.05 20.25 -0.05 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 \n", " 0.0 -0.05 12.25 -0.05 0.0 0.0 0.0 0.0 0.0 0.0 0.0 \n", " 0.0 0.0 -0.05 6.25 -0.05 0.0 0.0 0.0 0.0 0.0 0.0 \n", " 0.0 0.0 0.0 -0.05 2.25 -0.05 0.0 0.0 0.0 0.0 0.0 \n", " 0.0 0.0 0.0 0.0 -0.05 0.25 -0.05 0.0 0.0 0.0 0.0 \n", " 0.0 0.0 0.0 0.0 0.0 -0.05 0.25 -0.05 0.0 0.0 0.0 \n", " 0.0 0.0 0.0 0.0 0.0 0.0 -0.05 2.25 -0.05 0.0 0.0 \n", " 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.05 6.25 -0.05 0.0 \n", " 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.05 12.25 -0.05 \n", " 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.05 20.25 \n" ] } ], "source": [ "#####################################################\n", "# Now plot the eigenstates in the N-representation #\n", "# at the point Ng #\n", "#####################################################\n", "Ng = 0.5\n", "fig = plt.figure(figsize=(25,5))\n", "vectors = 2\n", "for i in range(vectors):\n", " ax = fig.add_subplot(1,vectors+1,i+1)\n", " E,v,H = solve(1, E0=E0, Ng=Ng, n = i, prec=prec)\n", " v = v / np.linalg.norm(v)\n", " ax.bar(range(-prec,prec+1), v)\n", " ax.set_ylim(-1, 1)\n", " ax.set_xticks(range(-prec,prec+1))\n", " ax.set_title(\"Eigenstate for energy level \"+str(i))\n", "\n", "\n", "plt.show()\n", "# And print the Hamiltonian used\n", "p = PrettyTable()\n", "for row in H:\n", " p.add_row(row)\n", "\n", "print(\"Hamiltonian: \\n\", p.get_string(header=False, border=False))\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.2" } }, "nbformat": 4, "nbformat_minor": 2 }