{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Quantum Linear Systems Problem" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The quantum linear system problem (QLSP) is a quantum variant of the linear system problem $Ax=b$. Given access to an invertible matrix $A$ and a normalized quantum state $|b\\rangle$, QLSP asks for a construction of the solution quantum state\n", "$$ |x\\rangle := A^{-1}|b\\rangle / ||A^{-1}|b\\rangle ||_2 $$\n", "with bounded error.\n", "\n", "Suppose the condition number of the coefficient matrix is $\\kappa := ||A||_2 / ||A^{-1}||_2$ and $A \\in \\mathbb{C}^{N \\times N}$. There are near-optimal quantum algorithms for solving QLSP with bounded error $\\epsilon$ and complexity $\\tilde{O}(\\kappa \\log(1/\\epsilon) \\text{ polylog}(N))$. In this example, we will deploy a much simpler construction of the solution to QLSP (sacrificing total complexity for pedagogy)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The equivalent problem in function approximation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The immediate idea for solving QLSP is approximately implementing the map $A \\mapsto A^{-1}$. Hence, in light of QSP, the implementation boilds down to a scalar function $f(x) = x^{-1}$. Without loss of generality, we assume the matrix is normalized so that $||A||_2 \\leq 1$. Then, the condition number implies that the eigenvalues of $A$ lie in the interval $D_\\kappa := [-1,-\\kappa]\\cup[\\kappa, 1]$. We seek to find an odd polynomial approximation to $f(x)$ on the interval $D_\\kappa$ so as to exclude the singularity of $f(x)$ at $x=0$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Setup" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the sake of this demonstration, we set $\\kappa = 10$. To improve the numerical stability of our methods, we scale down the target function by a factor of $1/(2\\kappa) = 1/20$ so that\n", "$$ f(x) = \\frac{1}{2\\kappa x}, \\quad \\max_{x\\in D_\\kappa} |f(x)| = \\frac{1}{2}. $$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "kappa = 10\n", "targ = lambda x: 1/(2*kappa*x)\n", "deg = 151\n", "parity = deg % 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Polynomial approximation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To numerically find the best polynomial approximating $f(x)$ on the interval $D_\\kappa$, we use a subroutine which solves the problem using convex optimization. We first set the parameters of the subroutine." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "opts = {\n", " 'intervals': [1/kappa, 1],\n", " 'objnorm': np.inf,\n", " 'epsil': 0.01,\n", " 'npts': 500,\n", " 'fscale': 1,\n", " 'isplot': True,\n", " 'method': 'cvxpy'\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then, simply calling our subroutine yields the coefficients of the approximation polynomial in the Chebyshev basis. Since the solver outputs all coefficients, we post-select those of odd order due to the parity constraint." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "norm error = 1.2780815006330215e-07\n", "max of solution = 0.909880628720708\n" ] }, { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from qsppack.utils import cvx_poly_coef\n", "\n", "coef_full = cvx_poly_coef(targ, deg, opts)\n", "coef = coef_full[parity::2]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Above we see that both the $\\ell_\\infty$-error from the optimization scheme and the maximum value of the solution are outputted by `cvx_poly_coef`. The former verifies suitable convergence, the latter verifies that our polynomial satisfies the constraints. Additionally, since `isplot=True`, plots of the polynomial approximation and its error are shown." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solving the phase factors for QLSP" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will now initialize the parameters of the solver for finding phase factors using Newton's method." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "opts.update({\n", " 'maxiter': 100,\n", " 'criteria': 1e-12,\n", " 'useReal': True,\n", " 'targetPre': True,\n", " 'method': 'Newton'\n", "})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once these parameters are intialized, we can run the solver." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "iter err \n", " 1 +1.9077e-01\n", " 2 +2.6351e-02\n", " 3 +1.1432e-03\n", " 4 +2.6715e-06\n", " 5 +1.4836e-11\n", "Stop criteria satisfied.\n", " 4 +2.6715e-06\n", " 5 +1.4836e-11\n", "Stop criteria satisfied.\n" ] } ], "source": [ "from qsppack.solver import solve\n", "phi_proc, out = solve(coef, parity, opts)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Verifying the solution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We verify the solved phase factors by computing the residual error in terms of the $\\ell_\\infty$ norm." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The residual error is\n", "5.384581669432009e-15\n" ] }, { "data": { "image/png": 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hhBCPcSSEOnbsiFq1auHOO+/EqFGj0LRpU+F2iqJgxowZePXVVzF48GA8++yzuOqqq+LqcDohJYQcZLJrY4TU7cntHxbEFXnhGmOWPiGEEK9xJITuu+8+XHbZZQiFQqbbBQIBDBkyBEOGDMG9996LjRs3OupkdcUyfV4iI0ym+rRsu2bHsqpATeMNIYSQVMRRjNAVV1wRFUF33XWX1D75+fkYNGiQk+bSFreCpfVo3GniP01jhNT7Bwy2B4BDZRX4YNFm7NxfYr+ThBBCSAKIO2vskUcewc0332z4Oa1AxljF98hUjXbiPfp2xXbMXb0TALBo056qY0nGBckusfHw57/j5mm/4vwXf3TQS8YIEUK8Z9f+EmwtPJTsbpAkErcQev/99/Hiiy9izJgxGtdKUVERbr/9dnTp0iXeJtIWOYuQfSm0evt+XDTpJ1SEFYx+dX70fdkFWMUxQrHbRYK01+w4YLuPhBCSCHpN+AZ9H/oW+0vKk90VkiTiFkKnn346PvvsM7zzzjsYNWoUSkpKMHHiRHTo0AGPP/44LrnkEjf6WT2x0DBS64gpQHFpBZ785g8sL9hnq/myCl0QkmQ1aeESG4IoISfxS4QQkijCqsGsQFVrjaQXjoKl9QwaNAjffvstBg8ejCZNmmD//v0444wz8PDDD6Nz585uNJGWyFaWfurbVXjh+zV48ptVWP/wadLH1wshsxghzXa6pTie+Golvvt9e8x2TuKXCCEkUYQVOSs4qd64IoQWLVqEO+64AwcOVLpAjj/+eLz33nuWWWXpjmUdIQklEQ4DS/7c66j9sgpdOUUHMUI/r9uF//64Qdy3JI8sXyzdip/X7ca/TjsCIa4BQgjRwYc1ArjgGrvoootw7LHHYvny5Zg8eTJmz56NpUuX4swzz0RJCbOF4qFCsqCio4VXEWsRMhMuRpWlzXooI+S85Jo3F2LynHX4cNGfws9nr9qBm6Yuwt6DpQnuWXIoLQ/jj21FdFkScphkP6wRfxC3EPrkk08wfvx4rFq1CqNHj8aAAQPw3XffYf78+Rg+fDj279/vRj+rJZZ1hCTT50WC6Z35m3DDW7+gtNxYJek/k150VbWhmaXFL2PM9iKxIL/klZ/x4eICPPrlygT3KDlc/trPOPk/s/CBgTAkJN3QPtT5ZMAiCSduIbRq1SrcddddqFGjRvS9nj174vvvv8fq1asxZMiQeJtwzEMPPYRjjz0WderUQZMmTXDmmWdi5crUmfTkCiqKLS+3Tf8N//ttC95ZsMlw35gYIVPlIrYCiXaJHCdVnra2pEmQ5JzVuwAArxu4MglJN6QSUki1J24h1KxZM+H7nTt3xuzZs7Fnzx7h54ng+++/x/XXX4958+bh66+/Rnl5OU4++eRoLFOysXoCKdVndYmOoSgai9A1byzEPR8vi74uLC4z3DcmRsi0naq/1QLntbnrY7aNDC6yY4yiKPj71EW4ffpvmvdFmWheIKqBVJ3h0E9IJdRBBHApWNqItm3bYvbs2V42YcoXX3yhef3qq6+iSZMmWLhwIU444YQk9cpdFGh/zF8s2yq9rx2LkCK5HVT9kbUIbSk8hI8WFwAA7jnjSORkhg63mZhRKs10ECHkMMmOYyT+wFMhBBhbjJJBYWEhAKBBgwbCz0tKSjQB3vv22avLYxc3PEeKopgKE7NJXm9xMs0ak1yZHqgSQLLfTy2YvHCnWQkqLxaM9TUp4rIkxGuYPk8Ah66xbt264YMPPpDefsuWLRg7diwefvhhJ825gqIouOWWW3D88cejW7duwm0eeugh1K1bN/qvVatWnvYppqChA8KKcz93Wbk+a8ysHfOCiqJtZURNaXlYI0S8eECrqLAQQu436Ws43hNSSYXHD2EkNXAkhM477zxceumlaN26NcaNG4cvv/wSO3bsiFomiouLsXTpUkyaNAkjR45EmzZtsHDhQpxxxhmudt4ON9xwA3777Te8/fbbhtuMGzcOhYWF0X+bNhkHGsfLmh37ceK/Z8Z9nLCimAohszgbvUVINn3eysIS6Y7VsLJ6+350uvNz3PdJVUyTug9uxQg9/vUfKC6tMPw87WKEON4TAkAX+xj/cylJURy5xu6++26MGTMGTz75JCZNmoRHHnkEgUAAgUAAmZmZKC2trMuiKAoGDhyIqVOn4qyzznK143a48cYb8fHHH2PWrFlo2bKl4XbZ2dnIzs5OSJ+e/W61K8dRFOcTm94iZVZPR7PEhsWAIWsReua7VQCAL5dtUx1bvM/O/SVoWCvLsRtrwYbdGNixsfCzYNwpA4SQVET9EClTt41UTxzHCOXl5eGRRx7BhAkT8NNPP+HHH39EQUEBiouL0ahRI3Tp0gWDBg0yFR5eoygKbrzxRnzwwQeYOXMm2rVrl7S+6HHLBhFWFMcm3dJy7X7/nL7EcFtNsLSFrUc5LJSsuiU6B0bWrd4TvsFZx7TAE+f1ND+oYVvGZzzdYoRYLyXxfLBoM37fUoTbR3Txxf22pbAY9WtmRRMT0hWv4xNJahB3sHRmZiaOP/54HH/88W70x1Wuv/56vPXWW/joo49Qp04dbN1amVFVt25dTd2jVCasS5+3g1mMkl442AkqjOfJyixG6P1f/nQshMxW2KBrjHjNzdN+BQAM6NAIJ3QSWybt8OQ3fyAYCGDs0I629/196z4Mf3I2OjSpjW9uOTHuvqQyaus2M8jSF0+cAm+++SYOHjzoxaFtMXHiRBQWFmLQoEHIy8uL/ps2bVqyu+aaSShsUFBRBjMhpLcaGNUREvcpHiHk0WBkcr6rowwqLq3Awg27Obj7jN0H4l/OZe/BUjz5zSo88fUfKDpkXCfMiE9+rSxVsXo7q/6rxxsWV0xfPBFCr732GvLy8nDhhRfik08+QXl5uRfNWBJJLdf/Gz16dFL6E2Hn/hK8/4s7yxzoCyrqKS4zDhK2k7VmVU1aTTxixqvByMw1Vh3XY73itfk4e+KPmDxnXcxntAjZp7i0ApdO/hlvzIuvKrcbQl9dCLXcIiPSav90RyOE+MNIWzwRQt988w3++OMP9OvXDw8++CDy8vJwzTXXJLW4op/YsMs9a1mlRcj486e/XWX4WamNAdGOLz2e8cQzIWRmEaqGrrEf11YupzHlp41J7kn14I156zHrjx2468OlcR3Hjdtbfbs6EVZulO2oLrCOEAE8EkIA0LRpU4wdOxY//vgjvv76a8ydOxeDBg1C69atMX78+GhxQxIfYYuCimaYLcgaY0FRhH8KkRUzIgHilWvMTOpUQx0URXQ+02m83150CCf/53u88kOsZcwO+w+5Y9V2+ltVo75dnRyNQqgK9VBF11j64pkQKi0txfvvv49zzjkHgwcPRseOHfHee+/hww8/xMaNG3HSSSd51bTvcXPiNVp9XgYzIaSPEdI+OXkXI6QZjOI4T9MXbta8NrP6VOdg6VTKhPlh1U70eeAbfLtim/XGkjz97Sr8sW0/7v/fcgDAG/M2oO+D32L19iJbx3HLauj21XByeZ2406orTJ8ngEdC6PLLL0ezZs3w9NNP45RTTsG6deswffp0/PWvf8UxxxyDSZMmYfny5V40nRK4Oe0qigKnD3h2Jkk7S2zEM55o+uTwOD+v243/e/dXzXvrdx7AxJlrcLA09sm+OsYIRRC5Td2wSrhNaXkYF7/yE7YXleDK/y5w5XgAUFKmPQF3fbgUW/cdwr8+sOficksru3HutfF69o8ns5hzumDnAY9UXzxZa6xTp05YvHgxWrduLfw8FAp5WrU5nYjHNWbHFKzeUnaJDSvEdYSku2TI+l0HYt677fDK9rv2l+DO07tqPjOyCG3YdQDvLNiEywe0Q6PazgttfvxrAQ6UlOPCPuLfg5ekwuB+xwdL8JbDWKb9JeWolRXSWGxm/L4dl782H/eM7GooYOy6Qdyqcu6G90V9SZ1YMWgRqkL9oEB9mL54YhEaN26coQiKUL9+fS+aTgncDM4Nh527P+wszWEnWDoeX7sbfvrsDOPb+peNe2LeM7ocZ0/8Ec/NWIObpi523BdFUTD27UUY9/4SbCksdnwcx+0L+5TwbpjiVAT9tnkvuo3/Msb6N/btRQCAez5Z7pqAcc8i5MYx4kv5LudaElGYPk8Aly1Cc+fOtdymf//+bjaZkrjpibFaa8xqX1nsrT4veVDBidhbXIrbp/+Gv/RsId03PdkZxtVyRdYfI2G6c38JgKoMLCeoU5WLDpUjr67jQznCb6LHTZ6fsQaAeaFNtwSMm5Xg4z+G6m8HmkZfUT6d4aKrBHBZCI0aNcr080AggLVr17rZZNqjKM7N7WYCKragomL4WWyfnA8o//5yJRZt3Iup8zfh0XOOcnSMnExji5BICFnFCMXzpKh++k5GKJI4a8z8+3yzfBs++a0AE87shjo5mV51TZqKsII73l+CXm3r47zeraLvy4gco23sCiTXLEIuHMNO7Zuf1u7C6/M2YPzpXdEkNwcALUJqFAohApeF0Lp18aWopgvuZo05twjZiS+wU1AxnuyL9Ttj43vsYrZ+kmiBVbfcJyLUFqFkJKeJbg2ry3PV65XByi3q1cBtw7tE39+46yDu/ngp/nZCe/Rr39DNbpry+dItmLZgE6Yt2KQRQnK45RpzKWvM5WBpq9/++S/NAwAcKCnHa5f3AcD0eTUVmhghCqF0xZNgaQAoLCzEF198gYKCAjRv3hwjRoxAbm6uV82lLfEsumq2/EI8MUJGD5z/nbse36zYhpcu6Y0aWWKxoumSw3EpM2Q8aYUE5h+RReixL1c6a1xHeZInHTsT74L1u/HIF79HX+/ar10OYuzURVi8aS9mrtyB9Q+f5lofrdhzULyMhIw2eftncfyRXfHrloh1Y8kT9TFkf/vrVA8YrCxdBRddJYBHwdJz585Ffn4+nnrqKfz88894+umn0a5dO6kYonTATQuEojiPA7EzR9uLERJvMP7jZZi9aifeNFmmwI3ByOwQsjFCz85YHXc/AKBcXackCZrITkHFc174EfPXVwWTZ2Zoz0sygr3NiOt3ZNc1FkdbWrdy/GiyxiSFVZmqZhgtQlVoRCVPS9riiUXo73//OyZOnIjzzjsv+t67776LsWPHYsGC+GuEpDquu8acWoQcusbiXWJjf0llLR/h5KLe1+F5MmteLIQkj6sotl0k6kknGbEZYteY3HXPDJk/J63eXoQVW4pw+lF5MedlzuqdyAgGcFy+hy60BLoa4/nN2nmIkDoe1OJaUgiptktG+vyz363CJ79uwbS/9UW9mlkJb98ITWVpWoTSFk8sQqtXr8bZZ5+tee+ss87CmjVrvGgurQkrzn3bdiZmzVNtnDFCZpOK9xah2PdCErPc+S/+iGFPfC8syKhG7/ooj2OBTDfcKCLRI3vULJ0Q0h9q2BOzcOPbizBj5XbN+4XFZRg16Sec/9K8amN9iEdzue1+0WSNSR5PfR2ScU0e++oPrNxWhEmz/RVHqrk2jBFKWzwRQt27d8fEiRM177344os48sgjvWgurYlnYLXzu9cWfLaIEYqjT+64DoyPIooRknna/2ndbqzZcQD/+3WL4Ta/bd6Lo+79Cv+duz76nlpslts44T+v242j7v0K0+bHt2hqPPOulUUowpLN+zSvC1UxPde+udBR214XgrQrbOKxCKkvuxtfy0ntG7UILy6riL8TFpSUi9vwW1Vr9UMbLULpiydC6IUXXsB//vMf5Ofn48QTT0S7du3w+OOP44UXXvCiuZTDTddYXCu9O1x93nqJDTnXmeg8uGIRMvlMnD6vfa/okDg4FwBKTAbyW975FftLyjH+42XR99SBqXYsd9dNWYj9JeX45/Ql0vuIELYoeFMU1C0rhGIPX9XANyu2m2xpzEUv/2S5jeHPKI60euNDxhEjpDof7lg87d9TagFS5NICskbcPv03dL7zC6zdsd/TdtxAmz6fxI6QpOJJjFDXrl3x+++/46effopmjR133HHIzEx+TZLqRjwD67QF8sucqJuxXmKjcikLJ1gd20mcjpqIRUgj1lSHW16wD6c+Pdtw/937S3GwtBw1s2J/OiIBqHWNWT8Nh8MKdh4oEVqunCC6P3YUlSAcVhBUtXHWxNhEBn2wtNGl+c83f+C0o5qhQ5M6h9uU71+hQUaYTBFLNyu0W7flfF8Xls8zPJ50jJDq3ttXbCz03WDq/Mpx5eXZa/HQWdpaYH5b8kX9k4y4xnbuL8HEmWtwcd82aNeoVpJ6RhKJZ6vPz5kzB2+++SamTJmCN998Ez/88INXTaUcbmaNJSrl006cw6pt+9FrwjeWxxSdBeuV7S0PK5U1pj6O2iI0eY55DMN/vvkD3e/5Styu7vWfe4ujgeGAnGvsxqmL0OeBb7FtnzMhqUd0rYpKyjHmdW3Swm+bC2O208cImTHymTnRv/XX8JCBK6bwYBl63Cc+lzIksixTPKLLjjVV7nhVf+87VI7bp/+GOat3mu6jbteOizYeROfMb1YXkZvx9Kd/wCs/rNNYdlMVvwlPv+KJEHrsscdw0UUXoVGjRjjttNPQuHFjXHzxxfj3v//tRXNpTaIGFnUzVj+uDxf96Vk/ZAK8zWKYImOz+km6sLgsWshRZrozfApXvb1kcyEGPPwdLnx5nvV+Kj79zTgGyQlGTX77u7XLKsOGVUodd6Jvc/iTs4T7/Lp5r/Tx3cZ2HaE42nIS3Gx+vKpjPPXtH5g6fxNGTbJ2JQKJrWuVjErqdlEHSEfGlq37DgGoXHQ5lVm9vQjHPfgt3vhxfbK74ns8cY098cQTmDFjBjp37hx97+KLL8agQYNw6623etFkSuFujFDilZDTOkJSzVjsWl6hINvqrjU5RsTlpO7jWz9txFs/bcQP/xyMpQX7jHbV9TPWRaduduSzsRbQZGTrxHt//LR2F3q2rme6fpugVc2r9bsOxtUHIxJZqTu+YGl3f6Pq423aba+20z5dfFC8rmYzRPF4fjNQqEXqg5/9jl5tqhYDb1onJwk9co87PliK7UUluOujZbikX9uk9KGkvMLm2JEcPLEIZWZmomXLlpr3mjdvjqws/9SPSCbu1hFy71jm7cgHFcaTfaFuR3SaysMKFEXBrD92RBdFVfPHtiIsLYh180QIBgJYvb0Iv27aG/PZGz9uwIotckLISX2eZJTwl7kURv1+8LPfcf5L83Dru7+53iYQf7xMPD8j+8HSztHE17lSEqHqbztWOyA2PsjLW1LUNauM00SjH6vGvr04+rff+mqXZC8Z8vvWfeh85xe4JwVcjJ4IoVtvvRXnnHMOZs+ejXXr1mHWrFm44IILcNttt6GgoCD6j8RPomKENK4xq/R53Q/QzlitSTUWfF4RVvDR4gJcOvlnDHvi+5h2T/7PLDz42e+CPSN9CWDYE7OiazCp0dfDMe9nbO+srkSiYjPUyNwfRv2KZBp9/Ku936rs17TOLjT/XG3J+OTXAk08lpPjybZl9zhuZyapm7cbVK+3Sno5fogsTYmyCG3YdQDfLN9muZ3+WqrPp9+sV6nGk1+vAgC8pion4lccucY6dOiA//3vf+jSpYvw87FjxwIAvvzyS837n3/+OW688UYAlT+Sigrv61n4EVeDpT2aXPVjmJ2AT32XRCZyURsxiNK8w2F8fXiA26vLOJKpUWIW/3ugRP5+FE0gVpOKl5Wlv1i6FS3r10C3FnV1fTLe5+yJc1FaHo7ZxwjZicGtJ9GwApgsG6fhxrcXYUS3Zph4cS/T40Uwuvf2HCjFV8u34tTueaiTU5XlqtYbimLPoqQV9+7GCNm1COktIN4KIc8ObcmJ/54JAPjvFX1wYqfGhtvp71W1EOLaY/GRzOtvF0cWoQ0bNqCwsNL90L9//5iK0eFw2PJfuoogwD91hOwcV5s+b88FVB5WsPtA1QKe8XS5IqwY+ilkLC5GogywV2hOdApk4pucoD53Ipb+WYhr3lyI05+xl5m5cMMeLPmz0HBhUqfICiFrC5o94fj50q1YtHFPXMcb8/oC/HP6Etz2ntYd+NHiKquY3QnSjlvZ7vFCskrxMPpr4+VcL44RSqz7eOEG4/sBED20udp8WlPthVDTpk2xcWPl4Dlv3jzs2mVd84N4Q1JcYw6Cpf/2Ruwac1aWMdHTs5mYkMmICZqMdFbLZ6hxctq/WLrV/k4A/j51kenna3xSuC5SO0o6Rswq1kwwKaonUtGVvMakkrVaBxndewsOT5yfq67VsoLC6PuAfTGjTdGO3yqobj4zaG8I1zfvZRyJOEZIzKGyCqzbeQBH3/cVnvzmD9f6YDUX6y3qGteYyX7lFWH8tHaXYWmIVGL9zgO4dPLP+HGNu/O4m54Pr3EkhEaMGIFrr70Wt99+OwKBAHbuNK9hQbS4eXskLH3eRh0h0efqVc3l24x9zyzzqkzC4mL2xHeoTH6SEsYIWTQvk7IuYvaq1Ph9jT0s2JwU+RMhsvBp3hJcS7O21QLNztPqRl3Wm+2HD9XmMomDhRYFD9W/RW1MS2y/9DFEiXSNyWaNvfHjenS56wsMfXwm9h0qx5PfrHKtD1bXWf/9g5pYMOP9PvmtAOe/NA8n/2eWb2v1yPbrxrcXYdYfOzSlPtINRzFCTz75JAKBAJ5//nkAwMiRI1G/fn306tVL869t27Zu9pUI8Gog0w8gmuq4Fk261SXRYczEikz9oi+XWQdQyuD0vOsrOruBX8bhOasrnyjlhZCFm0TweVhREDqsgOw+cTq1fuh3s+8aU/fBXAm9OW8D7vxwKe46vSuuPL6d5fHUQqekPIycTG2qcjAAqG0W+nPg5YOUMFha8Ku+66NlnvXF6h7Rt5kRkrMIbdxVWbZg4+6D2H2gFA1rZzvtYtLZUnjImwOnjkHImUWoVq1aeOmll7Bz504oioLbb78do0aNwoEDB/D000/j3HPPRfv27dGwYUOcfPLJbvc55UnFGCF15L9ljJCHM3NxmbH76oHPVljuv6PInYrNom8o8wSW2gs7yvXdW4uQ8/P33IzVjvbTtxlWKgXtPR8vw/u/bAZQGcdltKyM1jVm3tadHy4FANz/v+WG2xhljZVIWDT138VLa4ZonEv07W811up/jyHJ7EB10oWMJTqR/OfrP/CqRYV8NV7F8pjFY/qNuAoqZmVlYfTo0bjsssvQqVMnAJWB0itWrMCCBQuwYMEC/PLLL650tHqRektsrNtZVWXVqkWrTLanv12Fm4d1tPwBir5acak/Vq9WBN2Qmf+vn/ILzjy6BU7tnudeXyyuyNI/C9GhSW3X2rNC7DaMLdxnJYTEMULAb5v34vkZa4R1pMx4adZaW9tHiBVCCr5YtjX6cHBGj+Y45v6vAQArJwzXFJA7VFaBpX8WGh4r3v6oD3eovAJ1oV3PsdIiohZiibMI2YkRShZ6sSNrrVWft2QUSjViw64DeOrbSteiujikGW7NRhVhRSPMU0cGuVBZevLkyZrXwWAQRx55JI488khcdtll8R6eWJAIIaQfLNxYD0xmUU3RBG8ns8tLxHWErL/4V8u34avl27D+4dNc64vVLXD6Mz+gf/uGrrVnhciSUx5WkBnSCyHzjouyvMKKgjOenSPY2jtiMijDwHrV8gvqsguvz92AH9fuwpMX9ERuTiYunvSTJtDajRIK6ntPfTxh4K6+DEaMEEpsjFCisepBTPq8QYzQk9/8gS17D+Hhs7tXln7RLM3hH3lXpKocLmvtc+MyPf7VSrw6Zz0+ufH4lFyo1rNFV4kxqVBZWt1Huym3Mq6RokPWGVpCi5BPhJDYNZbwbkBRFNzyzq+W2811OSPEDJFFUJTt58QiZHVvyV4DO8tKiCxCmoBm1aEe+GwFvvt9O577rtINt0CXvu2G8UDdHfV5FcXP6b+lbLxT4cEyfPf7trjWJou3oOL+knJc9PI8vDFvQxx9MP/crOaZ+sHmyW9WYdqCTVh2eAke9Xnzk0XI7VINsjzz3WrsLynHY1+tjL7nAx0sDYVQEkih+wOAKNPEfHuZJxGnsQmHSv0hhEY+U7lC9Q+rduKU/8zCwg17Emr2377vEE57ejYe/XJlzGeLBcuHuIHsUhFii1DsZBF31liC0LdZoSgxS1Xo2XNQXPvJjQKo6iULylTntbTcekLW/5aNfobnv/QjrnhtASbbiDXRIxrn3v55I75dIZewMGn2Wsxdswt3HY6bAirP3+dLtuDPvXJrrFkJ3pgq+KoZUXRuSg6fYztCaM+BUnz8a0FCUu21SS2SFiE3ZyRVk6k0z1EIESHaSU/7mRvB0mHF+olBdBS/WIT+3FuM+/+3HFe/sQArtxXh7IlzE2oReuSLlVhWsA8TZ2qLmVaEFZz5nPeuI7N7QGS1EVuELO4jizpC8WBnkBZZhDRVzW10yQ3rwartVXWj1OdVdE1iKsTrzqmRhe33rUUA7C+voiZiXdFfsyv/G1tTTMQBwZIpH/36J66d8gsGPPyd1DEqwgrOnjgXt0xbLPxcf87UoiByajS1qwKR41btY1Uo9ZLJP2Hs24vwyBfGS/+4hSYwP4GuMfFxtQfec6AUQx+fiWe+XYU9B0ptx/h5CYVQEvBqtWev0D/NWwZLS/z+rpvyi7W7RvBDPlha4du6HYkMBRVNEoC3y3ioMRtkRRNymROLkDB9XqJzLqO/316ZvS4qFAB7mYBWNYLsohaTkX4cKqvA5B/WaRIcotvYjBEK2SzYqD5XkbhZJ9fs/V824+XZsdaoH1ZZu3jfXbAp+ve6nQewcMMevL/oTxwoKcfeg6WYNHstthdVpozru6aOXVyxZR/mrtmpOWeRkdsoTguorDs1+Yd1UQvQ0j8r3WkfL/Z+fU1tqQa5fbyajfTHfeWHdViz4wAe//oPHH3/1+g94RvfFKR0VQj99ttv2Lt3r5uHrJakggxSa7WYOcxi8JQVKht0hepijiN4b0thMT5b4qxCsxfkN64KDDT62hnBQMJK9ydKI5q1I3JpiSwP0jFCNop5eoG+6y/OWqsRGXb6tFvlMguHlehE4HRCUJ/DiLXn2e9W477/Lcfgx2bGuD1kXWMR9GuZWfVTfZ0jGVhG5+fndbsxabY4k08m7k3EgvW7catqeZSczKopbu2OAxg7dTEmfLoCV7++0LRvES6b/LOuEOfh76T6nqXl2mMMe+J73Pe/5Xji6/grZBcWl+HndbttPPxVbbdiyz6pPTx7MNcdVvTA4FkNI5u4KoSOPvpovP/++24ekvgAuzFCXpbtf/1H54GTXtCwVlUhNaNvHQoGUCs77gRNKRKlE8wmENlgaatFciNP2urDWU1cgYDcg4ad0+SkkroR6nXjzn5hLgY+OgOPfvE7ut79hdQSB/oJUR3MHDlP81RWDSvXmLVFqOoAD32+Al3u+gK/mKznJqrebTQenPfij5jwqXXtLzus1VnB1F9vzY79mPXHDgBVcXRWl66yZlTs+xUmFqHIfa2/nnbuuT+2FWHxpr34y7M/4LwXf8QHEsViAXeC8eNBHWCuF+GZgqfBeILx3cRVIeRfl4W/SDHPmG1zuls6yI3A0kRidP9nhoKmq4SXlFfY9pcbpeonqmCjmdgVWYQKi8tQeFDrFiorlxMYRnVz4iEcVrBx10Hc+eESbNgV60LS9sPqWLHvGQWgRoRQWUUYizbuxY6iEjw/cw3CCnDhy/MsLYf6vpSp3ohcE40Y0e1v96FGfd+++H2l9ebhz4xjXUTrud2qW8DWS/S/QfW9o3dLjv9oqWXQewDi86kem4xihJxaLyvCCk7+zyyc+dwcrD9sNVfHahWXVuCej5dh7urYpXectOldjJD2tcjNavUwlCgS85hKUprYarQW27skYHxWsFXI94efMAFzi5BZrMUp/5mF9bsOYvZtg6XbNboGXlrj1Jg1I7r+pz/zAwDg9/uHR5eBsIpnikwwdixCslSEFVz8yk/YuPsgZv2xE7NMzr113Szx56L9ig6Vo6wijO0GFc6DgUD0eEWHylAnR1sgMcb6UK62CB0+X2brrcVhETLqg9FnkV0/iSPg2i76r66Y3Dv/lbAuB3U1g0TtGLl4nf4Ut+6LdRcpSlVR0ncWbMJrc9fjtbnrY+qR+UUI/bm3OEZkZoRiG0rUeGUFg6WTQCqsyqupVWLbIuTWZOWPpwVZjL52ZihgahGKPPXNXGm8KGtMUUuD7bw0NavbNJ1sTa7/5j1VcWGyMULq7+5WHaGwomDj7sq+RP433NaiTaPimkZPu4XFZdhqEBuhrmPT98FvBX2x7ocopsWor1YiLzMUO0VExoOS8gr8tnmv5vxoLEIeDHNWRUvtZjNaEtDuF3X3adLn5YRw5PWMldvxxdKqOMc1O/bjb28swJLNlRXIRRbK+et3o9eEb/DR4j+xX5Uoob83nQy9bs9Hm/ccxICHv8NXy7VlEkRjoF+WJ6EQSgKp4BpTDzh2f2xuuWd8YjWVxmjCzAgGhU/WeszK+8ueUq+esHYfKNXEt5hNOGaVdq+fsgiv/LAOQGyQqdFxPHGN2TiQE9cYYLxA8KGyCkMhpBZPBwQ1s8ysMZFrr3VP6bcxf125f9UXFt23kcnr2jd/wRnPzsGrqnUI1b99tytLHygpx09rd0dfFx2KdWvFWIQ0n9m/eYI6IRQ5hMY1ZuOBrbwijMtfnY9r3lwY/T1d/foCfLlsG0Y+W2k13SQQ5gdLK7D7QCn+PnUxWtavEX2/oFBbT8kPFpZ3FmwWvi+0LvpkkKcQIkLUY0ZMZWmrpzKX7u1kZAjFgyhFHKgcAPRmYZFoMps4Nu8pxhxVTIDRqfGq3P8Jj87QvDZNnzfpw8ptRdEFRWUtQl65xmRxYgENIIASgwyrkvIwvpEsKhjTloRFSNMffbC0SQxNhEPlVf0WPcVHJq/vfq+0YE4+LGwBbyfiSyf/rCmkePErP8duZOLGdzLnql2VgPgcG1k1ROdW/fvcf7i6vt4iaVV1X23l+21zoeYzJ+ff7Qdzo2w1kXWRFiGSMthNuU3GZOUHjPqbGQrEPA2JRFPIZEQ64d8zMGrST3giWsJe3JZX52y/rm6R2SWW7YNljJDAIuTW17Mz/lrdzvcZrBRvZhH6VbL6dyQG6FBZBc56fg563PeV4baR02l0/sNhJUakvv3zxpjtDqosUSJxbia2Za13Tu7ThbrlSvTn8NdNe2NqkykCEWOHALR9jbofVZdWNkZI33pBYTE+/W1LzNhg7f6t+vy6Kb9oiqo6KdgZjw76x7u/4urXtQUyRe5WRVGEMUJGD4+JhsHSSSA1XGNVxKbcyu8bD7LWjc+WbEGLejWsN/QYowEsIxSMyQYqr1CQnaErQCfhPnv6u9WonZOBXzbuFX6eqAUgzQZr2UnOyjVWEQ5j5srtePSLqmVErCYz2W9vJ8PVqs2IZUSPURX0kvKwtPu4uKwCWRlBfLDoT8NrHiFyTKOssbCixLT7+o8b8PbPGzHsiKZ4/LweqJmVgWKVEBKJVf17f+4tRnlFGBmhoOb+M7McyywHIkskiPgvgorqoqw6O+iDpSM6Q31PjHt/CS7s01rYLz3qY13w0jxhm1b3hv5+fOSL33HtoPYxx5ehsLgsGqMoInJuRZRXhPHeQpEbLHb7sCK2Lu7Y54/q0rQIESHxBEu7ZZWQCZZeVlCI66b8IhwEE43R184QZI1FzqmmAJ2kQH7ws9818TpqEhVgbhqUKjnJy6w1NvrV+Zr3rATM7gOl2CexoK8915j0phqMqkgfKquQtk5ERMlBiTX2wmEF5RVhzYOLehKrrIkT225ZhYLPl27FM4cXilVfF5HrQpQuHqnvpT6+2Vd0SwjtOVCKAQ9/h/s+EVvl1L8HN4Klhe5HAxRoY2AURW4/q+B8s5+N3Qchs2U/SsvDGP7kbFw/5RdxP2w8TFSEFWQIMmdvm5640gpmUAglgVRYYkP9NKcfQGav2qHf3BNkrLxrd5jXgPEDGYKsscgAqQ6OlQmotiJRFiEjvbV4017pCcfJ6vOuucZcjBEywmjh1ZKysHQcXcSqJGPBKjpUjn4Pf6d5wtdUiFcU0+8dKcSoFj8iwSK6xyIuKa1oMO6rW/VjXp69FgWFhwwXh7Vai82KYCCgmfDDggcY9ftqFAV4+PPfddtZt2kZnO9iZtzaHfsNP/tl4x6s3FaET5dskW5LUcQej4qw2DXmF1wVQjNmzMCpp57q5iGJD9D/8OapMjcS2a6IFNCUwqyxyGSiLiroRpaN1QKQbmF0bca9v8Q1ISSyRrgVf2ZkURPhtFCsvoBkhJJy+fXyDpZWWrdkzunnS7dgh0F9IqBykjK7PVrVrwlAe11EgkWU6ROxvKhFg6lrzCUhtHmP+Sr0atF2oMT+MibBgFbkRP7U34ci64iiKJikCiQX7SfCToxQhLKKML5dsQ3bBDWIzDALVlYHN4sEsVksWsy2Ji42PxRidjVG6MQTT3TzcNWWFJi7TbPGEoVMu6KFGf1GZigQ4yYoqwjj1017Y1aPj5fEFVQ0iIcKigvQibDKGBEJJbc8f0YFDUU4PaVGFqFDZWHpY0bW9pLZXrSNeqyZNn8jnvrGeP2rlvVrYEthMf6pcleIroHIIhQNbNe5xowmObdcY3stKkOr+2p0PcwIBAKaY/y0bhe++307vlmhjQsrr1BwuE5olNjijrExWiKcVO7/79z1psuVhMOKMAbR7GFEvU7b4Mdm4uMbBqBh7aolhYx+52UiIRRWDO+FsAIk21hE11gSSAUrhppkpbHLTKiy2TfJpLKytN41puAvz83BF8uqCqu5cZ4T5hoz6GtQUggpimJpERJNlslZdNWpa8zYIiR7zEhskFRsicU293yy3DR+qmZWCDdNXYxlBVXpz4s27sWMlbGTvlHbGouQohiKXbtCyGgSLS41jwdTW6+cCCF9HaFnvluNyXPWxfRfFFQusohZXaOiQ2WWvx/R56LsP80+koJ0466D+GDRZoTDiqbQ4p97i/HsjNWW/QDEFsNwWDEp+ZH8zDEKISJEPfAkyt2iJ9XS543IDAVj/OPCbBwXznOiCpSZBYbLiLGwYu0aE02WTtKDnXLdlIX4YulWRxahQAAoLDazCMkdNBIs7fS3YCceMaxAI4IiXK4LWBf1JXLvamNyKkWfCLvX0ejrWwWRq/tjxx1aRcCxO0u023aLLKnRr843FNBVx4098DaL41aEFfy+dR9enbNOM0bor8M/p/+Gm6f9igmfroj5TofKwti0+yBmr9qBnftLhOJq7ppdMSUMgEohZuQqTdb8oobp80kg1ZbYSNRCnnqS1a7bhIIBBBRdHSHBj98N4Zco8XjRy+LU31AgICXGysNhS9eYKI7EzbRrKz5bshWfLdmKsUM6ONq/xKSOkOxl2nK4ArXMdRUXdpQnrCjIlPBRiGq/VBW/1LrGjK5Xic3ruHq7OKi32EoIqfrqRAjpLUJGiO5l0fAVWXPPiIUb9sTUS9Ij6o6+zpeejbsPYviTswFUxiJe1r8tgNh+/3g4YH7ynHXIb1xL89mhsgoMVBVW/XHckJh2jDIlK2tYifuWKCu2GbQIJYFUcI1VKAqu+u8CPPrF767FZdgl1VafNyIjGLv6vOgpyI0BIVHiced+8aQSDMp9jyWbC7Fup3nGn2iyTEYlWifntDIwWbxfSbnYIpQlqLz7v98qFyyVS7u22cmY/RVkCPqgR1GA93/R1o+J1jDS1REyCoq2K2hPeXKW8H2jWk3RfqljhEyEkFHGpr6ytEw7EWTXB7SLE1ft2RPnRv+eNn9TVGyZWebu/HCp5rVeSNp56CoPK3hu5mrhZ36w/LsqhMLhMA4eNF/AkKQGP6/bjW9WbMPzM9ckzTKTjCeFJ8/v6foxRZWlRa4xN85zsp+uMoJBKZ//NW8ujP7dpE62cBtx6nbiVbnTU2p0LQ6VVQhFfnZm7HC86/Dk4zRGyE7XwwqQKVnC4ZZ3ftW8FlmEwiYWIbeyxqxcY2rhLFq7LYJRVfet+w4Zin41//5yJT5fsgXz11dl1Mace5d+mk6Eg3rZjuVb9uHsiXNRsLfYlotSv0SGnZ/iD6t2GpY68UOMUFyusUOHDmHq1Kn49NNPMWfOHGzfvh2KoiA7Oxtdu3bFkCFDMGrUKPTo0cOt/lYLUsAgpKummpwbNRkWoeyMoHSciyzCxQZFmRUuTA4VSfa3B4MBKZ//XlUcRF69GsIsLtEk6kXdKKu539HSDAHja/G8QaZgdkYIRdC6OA5FY4Ss2xR1024FbRmLkIjINd9XrOq/ohi6wMpccnFaucZkRUMwCMDgUHfpLCMipv+yGdN1VjKvAvvdOuzKrUW2LHMx1fFtzAub9hgbSFI2Rqi4uBiPPvoonnrqKRQWFqJLly4YOnQomjRpgpycHOzevRtr167Fyy+/jMcffxz9+/fHo48+in79+rnd/9QkBZRQVkbVgJishfGSYYkKBgOuuy4rn6S0g8YnvxbEbOeG+Er205WsiKyRFbJcXLK0InZmMlrXKx6s6jc5vQ3tXs8cgUXo0OGJSmbCEk28drpQIRkjJNz3cEPqRVHNLEJuPWhYWZZk17IyW+fPTqkFNfqvWGQRxyN/XHfO3bVTFhquhyfiq+XahYLtWKbMYsL84BpzJIQ6duyIWrVq4c4778SoUaPQtGlT4XaKomDGjBl49dVXMXjwYDz77LO46qqr4uowSQxqM+ghCz+8VyTjBxIMBA4Hs7trEQrrgqUjSxKoceP7Jts1FgrKBUvXyKwSQv88pTMumvRTzDaJCoyOzIE/rNop/NxpwTe7ltTsjFghFLF4GGVfqRG6xgz6fl7vlnhnwWbdtuIVwmWIPLQUqISQAmOLUKJ+27LWBpl1/uzi1XOcWw+IdkSQCDsB7yUmc0iyxyzAoRC67777cNlllyEUCpluFwgEMGTIEAwZMgT33nsvNm40r3WQLqRC1pj6yVBmnSMviPfJp3/7hggFA5htMMGJCAXhusUuMxRAOGx9UDcGhESml4sIBQLCgmp6amZVjR0dmtTGEXm5WLFFm7r97QrxYqZuE0kxV8ctqXF6Su1ez+yM2PG0uKyyCrXMpCObwg0AOfrqf4gES8dnESqQtggl5j6VFVxuLG8Ti79dY/FiFaiuxtwilKIxQldccYXtffLz85Gfn++kOZIE1O6CpAmhOH8fwUDA9rpulRYhdwkF5frhRkzUzdN+td7IQ0LBgFScknrSzwwFhed8l6O6L/aJtJ2VEQQEXhCjdayssCvkRa4xoHISkRFCom2MeiASQn/uLRYujClDRNior5miGFuyEmYRcsE15hSvvqJfsmnteArMtk1W6IUa1hFKAqmQPq8ew62qt3pFMqoIhzyIEapfMwul5dZrAPnBRBwvoWBAyo2jzpDywi1hh4joF7mm4sFuEKhInACVk4iMu1EUL2P0GxKl6n++dKtgSzki4lcd96UoiucxQlYk0zUWVhQEAu5bcKb85A/Pih3Xmtm2fogRSos6Qs8//zzatWuHnJwc9OrVC7Nnz05qf1JAB2kGUDsm0Hg4vkMjwz44QYFi+1yHojFC7nH1CflSC6r6YUCIl+Vb9kk94eXmZEb/rlsj02RL74lcmiwXhZDVSu8ijIRYcVmFlHAQuUWNfkJuT/yR/hUdqsoGVGAczJw4i5Cka8yDp1NFcWchZT1bbS6s6hV25oVDJg9HyXbnAzaF0Lfffiv8289MmzYNN910E/71r39h0aJFGDhwIEaMGMF4JQvUw0eiXGP6wTnesVJR7Fvf3M4au6RvG9TJyZRyjVUHi9Dq7fvx/R87LLeLWApuPFy12ctv3rpBTdPPI1YDkZXEKWHF/vU0EmKHysJSwsHO2mzrLYpZ2iXyXffpLEJG1bXHvb/E1fYN+yU5yXoRI6Qo9h/EUgm3XGN/n7rYhd7Eh61f/ooVKzBlyhS89dZbWLHCeKVbP/HEE0/gyiuvxFVXXYUjjjgCTz75JFq1aoWJEycmrU9241aSgTrbxKpWh1vo4zTdcI3ZPdNuxwhFLrXMHJusxW2TQcnhCcqNJ+aereqZfm4VAByxWrhqEQrbtwjpa/hE+lNcWiH11CwSQkaxRUbxSEZYZc5F6gKpLUJhxb3CiU6RCdwHDtcRchmvLEJ2mH6tdyVrzDLB9JjNIRt3H8QTX610o0uOkb78s2bNQrdu3fDcc8/h+eefR/fu3TFrlrjsuV8oLS3FwoULcfLJJ2veP/nkkzF37lyDvbzH/zJIa41JlEVI/1TmhoHEruh00SgAoGoglBkQX5u73t3GfUxk4oxcc6cp6gDQpqG5xSfTYpaLiAI3hVCFoti2COmXYalfs9JlWFxW4Xi9KxFnH9MSY4d2tNU3q2OXVIRRVhHWxIKYrTVmxNAuTXDPyK629jFDOmvMA8FSVFKe1PUSa2WF0KtNAzSqLa7cHi92XGNW284RLNSaSKR/+evWrcOGDRtQXFyMgwcPYsOGDVi3zlk2RaLYuXMnKioqYuocNW3aFFu3xgYGlpSUYN++fZp/6Yp6YkqYa0w3GMWbHaEozixCXjzFyRwzkQuKJpuIpcANl4TVXKO2CF0xoF3M583r1gDgbrB0RVixff/qz0W9GlkAKp+mZUSVzP2T37gWHj+vB1rWr4kXLj4GY4d2xK2ndBZu2799w6pjW1h2SsvDMQUyw6pg6b8e3cKyb0ClizS/cW2pbWWQryztzeOpH+L+nBbJtMKtYGkg9iEg0Uj/8i+77DLUqFEDl19+OS6//HLk5OTgsssu87JvrqG3CiiKIrQUPPTQQ6hbt270X6tWrTzqjyeHdRX1zzdRBRX1E4Ebg4jdcx0KBlw12dmxCKUTkQnSjdMicilecGzVb1ftcmqSG/t0XHF4wp63dnfMZ05RlKrU7btO74rMUADtdat5q3nxkl4ay9Wj5xyFOjmVSb37S8rkYoQk3FDqNoZ3y8MtJ3USitH8xrXwyNlHRV/LuEH264TQa3PXY9IPawHIx18pipKUSdGpRSjJ87cpkTHHaW0oK+zMC1YWITetsU6w1XpFRQVuvPFGXH/99agQlL/3G40aNUIoFIqx/mzfvl1YDXvcuHEoLCyM/tu0aVOiuuo7tK6xxKTPxwZLu/E0ZTwIHNO6XmwfPIoR8vOAKeKq42MtJ24SEUJuuCTq1YzNOqurek+9kGgoEEANXZp6RVjBTdMWxd0P/TEj4qVnq7pYeu8phpYXADjlyGYIqSas7IxgNJuusLjMtUB60aQoujfvGHEEmterEX0tU8dItCTKtn2VhZlkJzoFXhU3NMdpm8mewE05/JWsXMNOMbPyPH3h0ZrXVnGmTiuau4Wt1i+88EIEAgEEg0FceOGFXvXJNbKystCrVy98/fXXmve//vpr9O/fP2b77Oxs5Obmav55QSpUlvaDa+yndfE/oZvNsyd1bRbznmzxQ1ki46sbg7t+Anebk7o2xTm9WmLq1X01k7IXRFKAq2KErPc5rXue8P0GNbPw8qW90aVZneh72aqBVT35B4MB1MrWlk8LhxV8tsR5DR0R6hihYCCA7IyQZbFCtSUkEAgg97AQ2ldc7lr1XdGiqiJrZSgU0NTUkhFCZmvHZWcE8dZVx1keQ1G8s2CYYcdiqw40T/YELoNXwtIsJV7vZrayCHnlvpPF/1cxTm655RZMmjQJkydPxooVK3DzzTdj48aNuOaaa5LXKf/rII01JmGuMZfPi1UdIdHYV1mN2r0+RESVG+KqQa2suI9hxomdGuOxc3ugb37DhLkn7JyX2tni+q9hpVLEndCpcfQ99ZO6erIKBYDa2TqLkE6FndRVvHaiHdRZYxEBZDXBqyesAIDcw66xfYfKXFuhW3RdRSIgYkWI/C9TJNNMCGVlBNGrbX3LYyiA4+rW8WBHfKktLKJlUfxClWvMK4uQ8T2hv8+sXLvJsAKqqfZC6Pzzz8eTTz6J++67Dz179sSsWbPw2WefoU2bNsnumq9Rzw2JKoHudsCiVR0h0UehoLs61U76vBUNa3srhNSDUShBk1Fk/lEkKgnVyDKfdNQTulr8qAflYDCAmllaQaUPrRnYUVvY0wnqgoqR82plPdBahKCyCGljhFrUq4Fze7V01C+xEIrdLtLniEAwqgekxkoIyQgcRVEMJ8UxA+Xctf8+5yjrjXTYsQjpXZh+JfKVvLK2vP/Ln4af2RVfyfaSuLbExp49e6AoCho0aODWIV3juuuuw3XXXZfsbkRJhbhZtUUoUQskepHCavYDM7YIudePSPtuBEs39NgipD7/ibII2XGN1coWC6GIiFJ3WSOEVH8HAwHUztG5xnSNu/F0+ufeYmwvKjnc/mFRYXFctfgMBgLR6tv7DpVHhdDfh3bEJf3a4LfNe/Huws3C45ghEmOiB5BMXZ/lXGNlhp9lZQTjPq9Nc3Oktju3dyvUyArhhrfk477s9E19HZPt0jEj0rNkBJ8nOwvMLnHL2RdffBHt2rVDo0aN0LhxY7Rt2xYvvPCCG32rtqTCLaK2ZLpllrfCi1RTc4uQnJsgHiLjgTuuMW/qgURQT4huxmlkZQTxxHk9hJ/ZOS/62J4IkdtGfe20rjG1pSuATk216dn6+86NQfyPbfs1bQLW51TdzwCA3BqV31cdLH1i58Zx1YURB0sLYoR0ViwZ19j+ErMYoUoRe/fp5jWCzKy47ZvIp9Xbda/ZeQhTiyZZ19j718XGpHpNwGPXmBm2RW+SJ8W4ztD999+Pa6+9FsXFxfjrX/+Ks846CyUlJbj++utx//33u9VHkgTUwdKJWgvG7aBsBRZCSPBZIGCe4dWukXEKtFkbbli76guyo9xEPV66+UR3dKt6mrXFtG0etghJHKemKli8hSqjSYkKoapt1enatVSusFAggFtP6YK/9GweLdynr/fjtlswci6tJmdNjFAgEBVzZRVhVbxRfNdF1AdhjFBIG9ck4xrbc7DU8LPId7GyoFTG9cVu07tNfQxSxYBZYddSY+eSq89hjoW7NoKby7fI4pZFyMnuaWMRWrNmDR544AGcf/75WL9+Pd577z28++67WL9+PS644AI88MADWL16tZt9rTakxhIbVX8nag2sTXsOSm8r+8Rh5hozdseI98nOCGomYCNeu/zY6N9VdYQsd7NE79JxG/WE6LYYMLpedgRiTZVFSL1bRLSrf1eZGVV/56oWdQ0GA6hbIxNPXXA0hnSpDIrWB0u7PYhHzqvVV9XHCEX2m71qJ/7cWwwgfredaHfRe1XxJYeX+ZBImNi131gIZUeFlfl9pSixouSCY1vhvWv72xo37VpBbLnGVCIrRzJGyIs6Ypf2M49zjTRpdS6OalnX9HMnwevJsELFg+PeTp8+HXXq1MGkSZOQk1Plu83OzsbLL7+M3NxcvPvuu650kiQebYxQYoTQhl3uCyEzk6tMgK6asKJYTmY5mUE0rlPluohsbhUI/sVNAy3bN8qa8gK3xYDR9bIzP6gtO+qJRRG8lxWqelJXW6PU3YiM7/r72+0MFlk3o1p8BiCegOLNqBLVvRHdm/uKK91ckUzFnftLLI9ttk324ZRzq/uqshq8dpvmEg8fejJtXkNbwdKqY+dIlrTwoiRAjawQ7ji1i8kWh92bFufCqiyHk/Xi7I4fyTYNOPpVvf766/joo4/QsmVLvP/++3j99dc1/9577z20atUKH330Ed544w23+5zyJPuiy6CNEUqMa2zCmd2kt5X6nTlYYiMA4/T5irC4IrmakG6JjkDUImS+X83MDEuhU8dji5A6O1C2PsqADlXLMKifUPWB3YYWIRtrjdVUBUurDxeO1uupek/tGonE2uj7Efk71jXmjQg0+ooRd6smuy0QEGYaxts3UUyL+t5sWb8GmuXmRBeybXw4HilS98mMHSYWoYhrSHRffXXzCdG/FcQ+bKi/8kfXD7DsB2D/PNnZXp0+L1tQ0ZPK8gpw9QntDcs9RJqMWBONyKsrF4Rul0cdZO8lC0cj6+jRoxEIBKAoiuEyG5HP58+fj0suuSSuTlY3UsAzppmYEmEQOqNHc5x5dAvcNG2x1PYyLpXKQdX+yTbaI6xYC7BQUC+EKv+32s8qNgkwDhZ2C3UsmGxasPq7XjuoPV7/cQMA4PrBHVARVvDczNW4/8xuhm4TOzFClhYhdTaPqv9ai1CsENK7xkLBAD4bOxBz1+zEU9+sQpFJELAMZlacfw7vgjOPbq7pD1B5P4jckxGx5NS9ni1YdV5930256jg0r1cjKlgiS5JslLDW7iwytghFBIPeMnJur5bo1LSqEKaixNbLUn/XHocFmhW2XWOS57N2dobmOsnG/mQEA3js3B74x7u/2uqXGZG71ugBKdLNvQeNs/kA4M7Tu+LDxQXR160b1MSgzo2jv2UnlFaEcV7vVli5tQiv/ODvNUkBhxahn3/+GSNGjEDfvn0xf/78mH8///wz+vXrh+HDh+Pnn392u88kAXitfZrq1nyyW49D9gnLbCvRE7o6NsPu8YDKyUw9NkaOZfXEGQoGLAdvr11jaiEka/LXFgEM4PIBbZHfuBbO7d0SY07Ixy93noROTeuYuMbE74tM6zUNAlOrgqWr9lFXllZPFOp+RJ7s9fdBRjCArs1zcdXAfFfMt5E2Refg2kHtkXd40VdNBexAQHgOIscY0N5ZrSPR70xvJVNbberXrBQlny+1rrxt6ho7bInSi0LRQ1aj2tmaxXHtWFMiGYH2g6Wtt89vXAvvXdtPK4RsLB1yTq+WmqrU8RJWVS4XEXExFhYbC6EuzerEZCFmZQQxdmjHuPoWXUInRYKmHV2V3r17Y9iwYVi2bBny8/PRq1cvzb/8/HwsWbIEw4YNQ69evdzuc8qT7OJR+SaLP0ZwZZkvEz654XjNa7umY9nN7Rx22BFN0LJ+DdN9rPpZKYTU9WAi/TDfT2bV+0S6xmSFaW5OJk47Kg8nd22KprnZGD/ySHz3f4NQ57AVJhgVAeL9o0/iuvtNNICqLWLqGDZRHSH1xKYJllZtYzSJqdt2o6RDRNB0zcs1Ldaouf4B8eQcEUtmJQnMELnGAgIrWYSOTa1T1msdFqhmtYaMssb0LtHIK7W7R38axg7pYNjOlKv6AvAmff75UcegS7NczfigtgiZ1fmKrLXl5tgfuTWtjmgW6C4a58OKookb+tepR2DUca1t9a1r88rlqcyKbPoJx/L03HPPRUVFBUaPHo2DB6vMpsXFxbjiiisQDodx/vnnu9LJ6kYyXWM9W9XDd/83yHI7dxY8NUEfB2DzTpR1DZhahHSvJ112rOVxZQSNph6MZNZY0G+uMckn12AAeO6iY/DSpb1Nz41RFpqhQBIJIZVFSK1PRLequvaVkWvMKA5KPYm6kSgQ+S7BYABvXHkc+uaLi86qv7ORRUjdNydP2yKLhPowekFw+lHNLY/5iEQsSJVrTNt+zNkVlELQPyDccnJn9MtvCD2DOzeOJiroXXC92tQ37Z/MuYy6JVXvqcX0rNsGC4Vubk5G9OHTzbE/8gBgdEyZ20M0zofDCmplZ+DCPq0wskdzjB7QFg/8tTsu7NNKeIxBnbVlDW4Y3CH6myssNo4bU5PsTGrHI2uLFi1w33334R//+Afatm2LE088EYFAALNmzcKOHTvw2GOPoUWLFm72lbiA7P22rGCfp/2ItX7YNGUbbF4jMxR9Aqoszla14YuX9MK9Hy9DQaF54KeZZUYmRkg9OFYtsWEhoILiiU9NrSxvhVBpuX3XmOyyKEZP3EYDoOh8qdPn1ZaaiFVBPaSrxajapaZxjRm4T9Rd0gdSO0F/Xa0Cx4HKX4PoPtQvzGoXoUVI9dvTX8/MUBBd83KxfIvxeCCzBl40WFp3/FiLkHZZEsCgArxAw6p/d3bXupK5j6PXw0BM18gMoV5N7bm4sE8rjB95pPTvyQ5K1CIk7nv/DpWirFZWCAcMarSJhFCL+pWu2ofO0grce844EiO65eHT37Zg2oJNAIA7Tu2CnMwQZq7cEd2uvup+2HPAPD7JL8Q1st5yyy2oW7cuJkyYgOnTpwMA2rRpgxdffBFXXXWVKx0k7mL2c+/Vpj4WbtiTlH7Yfbg1mkz0KfHqrfQTixOjl9XcEwwENOby6GAl4xqzOAmyVhqnqAs2OgmWNt3OwjWmvxQiUag214cFwfzq69m1eS5GHdcazevV0FpaBEULS3UuHfWkGa9F6MYhHWKsIEbnTC0WAwFxynVIE0ck34/GdbKxo6gEw45oYrqd6Lyrs+5ENJSoeB5Nn7ewCIl+L6LzJXpPLfL01j4rC7dMunfEGqfeUl2vKhgMaIp+ApXjlFoE2Rnm6mRnmAbqG32n0f3bolndnKg7660xffHUt6vQsn6NmABo0SEeOVts4cvOCOGETo01oicrFLuGnPoBY69JfJKfiPsR88orr8SVV16JXbt2AQAaNow1WRItybQCmk3IiYxr0/dDJphYPUEZfY+YH3ZA+Gfltg5Cwq0m/oyQ1iIUcTdZxSBUusasxZKXnHdslelbOlhask920+dF2xvF7kSuo/p6ZgSDeOCv3QFo04f1/c0OxQohJ27ht8f0xYUvz9O8d0nfNvi/kzvHbCtjBTOKGdOn2Mvy3f+diF37S9FWUBldfd5EYrxuDeOK5oEAUL+WdcXzqvR584eRqppQVe/Jjksai5CuHatlgmTOZWS+V2+arRNceve1/vvZseK1bVQLS/4sNPw8cp/qHzJaNaiJK49vF33do1U9TB5dWeT1h9U7sXbHgZhjqGlZv6Zpv9TnNisjhDOPbo7xHy+NxhiqRejQLk2wwsSaGCG5jjEX1hqL0LBhQ4qgFCBi8RH9HhPpp9UPbjJByJrXEkJIgd7sL/cd4wqWDmizbiIDsGWMkIRrzEvyG9XSPFFLW4QkRxAj873R6VRfx/vP7Ial956i+VxtqGnbsFbMPup+hUysC6KAafXUcHTreuIOqjihU2P0ax879hkGYxt8Z71rzCxrLLKNLHVyMoUiKLZvAouQwfIoQKW7tl4Na9dYdjRYWs5So75OInEmtgipXWPadtTCWZR9KfPTEwVg679Pbd3CwPHYE60EedXH2s7bGUYipyX/8L3RWVXKwAh91lzNrAzMvm1I9D31fXvDkA5SJQ862FhHzgtSqw52NSHZWWOAtihYhHh61S+/IS44VhxMJ0J/Dqz0iX5SkPmxK7pK0HoRZDTOmPbFpqApC1daG2SsPVauMS/iDKLompZdTFJWPBtZ3yKD6j1nHKnbvor6NTNjJq+womDq1X1xzYntcWm/trHH1UykEP4NGAgh1Y3x/KhjNE/XIozOgFE1YUPXmM5tJ7KKuR3IDWh/B6I2c00sQq0b1Dw8GZrfL9H0ed05OSIvV9cXUYyQSAjFtnGF6jrFxAipvqTIwiVzG0ctQqr3QrrvU1N3nw7prHVF2hljjQolRohmjdl4qNR/EhFb/72iD648vh0mq5YHMkJ9biMWPrXbWn29cjJDpvPCe9f0w99OzMfVJ+RbtuslFEJpimiQjscgdPuILji2rTgbRkicFiFD15hJjJDs1zMPlra2CKn7FrUIWQVLB6zFXe3sDDx5fk/NEh5uof9esvVOZF1jRqIzsv+gzk2wTGf1MaMirKBvfkPcPqJLVMyoA5s1tXFsWoTCKk9ZXt0auMtixXQjRA8bgPG9qy/EKRIl6rfcWgxZbXmwKlugp3WDSjeKlTUzcp7V98FVx7fDVQO1IjPysfoUiQ6tv44L7hyG9o2rrAr68U19b9QTLF4s83AajREyuZ/UmY1Tr+6LofqYLINm7jztiOjffdo2wIr7hqNhbfPfeXSNPd37ZmONfrmSyHlp1aAm7jq9q9Raiup7JGKFU8cvVoS196VZlfrebRtg3IgjvH3Ik4BCKAkkOVMQgHjAi8dSFQjY+16xrjHz7fU/JqO29A/J2gFVroNmW8m4uNREliexTp/X1h8y4syjW+C83i0tt7OLvnuyFiFZM7x6su2vciOpJxX1hKu2yoium8htoH7HrDaOGlFlYLu/T6PtjSYAo+5oMsJg8BsViGwAONHGyuxmiIStmZu05eEMI6sYv4gQUruobh3eOeY+i1xW9bkTXX/9W3qLof7cqy1CAzrEprjLuHhF50b/nvoe7pvfMEb0nty1mfDYPXXuoxpZIcvfVuQ3EGsRMt7nkbOPwrAjqixNToyK6vs0cl3V94jeUmm3uGUyoBBKAn64LUSDdDzrOcoUBFSjHyDsWoSMttcH3WpihFxQoNb91L4uC8ea+o2OK7sqgOw6YHbQfy/5GCH7FqGHVWm5xtl/wKjjWuOIvFwM6RKb6SRKazeyOqn7qN9GbxFq07AmBnZ0R1SoM4o0/ZEJlg6KXWNqylRP3k9d0BP3n9nN0p1iheh6mt0LEZeY0Xd65sKjMeWq44TfRSRCIy4WdUq+KPXdKtnCLH2+WW4OZt82GHNuHwI7RNxg6iPrz5dVra97/3Kk8H11Nl3EumL1YGqUPm82RjWvVwOTLutddQwHUUzqB7bIWGQk0AH5ZUiSiac9HDJkCC6++GIsX77cy2aIDaZf2w+AwZNwnBLNjs7Qb2oVayJbi0XR/a2NEdJtazBzmg2yltltun0jFiHr9Hl5N1NfQTG5CHec2gXNHSyiGPNUKSlwZMVlM1Wf1AJBfxseczg4+exjWuKBv3bH538fKDSbi55kjYJLzc6rXgh9Nnag6bIJAzs2iv6GIhgd3cg1ZnQPBfUWIV2/3x7TV/O6TJXtVq9mFi7p2wYNaloHLuuxSpIzE0IZgolQzfBuzTQWmEh17fN7t9Ls88R5PdCpaW08eFZlpp/6e+w9GFuUT38K9edKf47VQqhHq3po1aAm6qlihcISXkaxRUj7um+7yt9mxGWox2iZnIxgAI+fW3kO7v9L5eLT6q8w6rjWmH5tP7x+RZ+qPhvGCJl9Cy1OvKvqsVi0cr3eIiS7DEky8bRC28yZMwEAU6dOxYUXXsiV6A+TzCqaHRpXZgWIbs54umV3X/0EKlOoMJ727Oyj3ywrFERxuLIgmVUshL6f0lljgYBpUKqavvkN8foVfdCuUS0MfHRG9P2XL+2NIV2aYH9JBZ7+dpXUsSKI7smrjm+HSRYLJspWN25UOxvTr+2PWtkhTcCvvt1XL++DeWt3xVSr1aNfKNVpH2PiK6RuErnvXFcQiwIY34f6Yonqft8zsmtMZpooWNrJ78LKKmDmJo1YBIwe+mOSHIKV1bX1nHVMS5x1TEvNdhF2ChbsjRk/LGIIK8IKZt06GBt2H4hWmVYfQybwPHI91IfW31t1a2ZiyT0n2578Q8EAzu7VEmf3qjoH6nYipSDUGMUI2ZlfjB4GzVB/Z9FDimyMkNmSJInGU6kWDodRVFSEjz/+GHl5eV42lVIk0zWWk1V5yd1W6QHYdY2Zv9YTYxGSSZ9XzGOEDMcA3aHV50qm3pGaiGvMMmssGMDNJ3Uy3UbNCZ0ao5XuqfOkrk0rF810kIYv2uVOiSBhOxNvrzb10aVZrrDgZIS6NTJxypHNLGOURAO40eU0O/f6BSll3MMy33nYEU1xZk9xZX2j/uiDpdUBvyHBZFImqI3j5CHL0iJkEjgfif8wXPjThYe+XQdihZCZGBFREVbQWuf2VB9DpnZUVAipBghR2YQ6OZnSMXYRRHE0Vhb6bi3qVm6n+iL1a2ZieDdxHJIIJzWz1PelOqkiYjnsr1sQWC+E+uY3wN+HdsQH1w2w3bZXxG0Ruuuuu3D//fcbfl6rVi2ceuqpOPXUU+NtirhAZBISmbvjGbTsBkvrsZ81JnvkgOCvSiR1kGnpfj36H325DdvzMa3rY8Y/BmHwYzOl9xGhT+mVwem1cxJ3pR5InTyRAuK4EaNjqe8dvfWjYK92uRWZ72O1RX7jWpo4DD1Gt5C+RpBa7IvEbQNBIUMnpajicY1F7ncvin0e27Y+5q/fg7OOjhWUmmB4ibZFFkR1n2UW142eW1VzHZrUwZc3nYBGteOzbogSJYy+1hc3DcSc1btwSb82MZ/N/9ewmOrdZjgJltZmjVUJvnnjhmLrvkMxJRGydLFy9Wpk2XroSwRxmwUeeeQR3HzzzYafb9y4Md4mqh12xoxHJRY0tNd2ZeMii1A89fwCAXsxRvqB0zpGSJc1JtGWPkZINu5F3xdNoTaLQSbGNXZ4pBFNNlcMaBfzXjuDond2Ag6NYlPMcDqRycY1qVGLRaeru4t2MwyWNumifmVuJ9/HbuC/VLC0zjUmsnqcdUxLXHBsKzxz4dGqvkh12RYyrjEv2n3jyuPwzS0nYLAgWF5bcFG8v7pekDjgGqafx24fsQhp6dysjmWquxWiByyjMbFLs1xceXw7oQiVFUGXHRZRtw2PrXxuhbo9tWusfq2sGBEEeJPc4TZx9/D999/Hiy++iDFjxmieyIqKinD77bejS5cu8TaR1nT0qOKmOFjaOZWuMRvb67a12jcm0Fky20G9m74N2YnTyCL0N0ERMP3gFbEIifrbvJ58ULNsFhfgbFVyp9feiXhWuwHsxPpYYXRPmIlsfd0UmQndSrRbiSmZJTYCAeuigpmhIB4++yiM7FG1Qrx6khIFsoqwugLmwdKV7WlFnFSzluRkhtChibjSsboNI2E5b9zQ6N+iLEO7FiEvEdV169YiVlSIcCJC7znjSPzwz8EYdVysVckKdTxVDYtCmoA31kK3iVsInX766fjss8/wzjvvYNSoUSgpKcHEiRPRoUMHPP7447jkkkvc6Ge1wo4Lyuwmkin/b0S2YJBMpGtMv6nVj8Vp37S7SVqEdNupRaN6wBcFN+tbMLMIGdGnXWxhSjsLrhpVNDbD6Pzecar5g4yslc2oLZlsHVmczGWv6irpSi3BYvW5xQZGD8j6wo9OltNQbyc7uVvFiZjFE2YJrBKyQf/xoP6eRsJTPUmLgqHVt64dQe7FvC56eOnSLBdvjTkOM/8xyPX2AoGA5ZpiRqjd/TkSD2hpIYQAYNCgQfj222/xySefoEmTJrjhhhvQv39/LF26FC+++KIbTaQtdsqlW6H2tbtvEbJ3BLtZY7LWHP1G2jpCuo8lrUrZBhYh0TnUtxGZZOzM0RNHHRPznp3Kq6I1kawwus2uPqE9TjAp1hfvIOeqRcjBoTo1rYOhAteLGTGB/of/HzeiCzJDgWgKuOH+Br+TmPX0dBYiub5VbVgmqTIja7UZYdc1ZrY2mVscKrOnoEViL+DQIuTFEklG7uz+7RtZrhGXaJmhrhMk44rTfzUntYu8xhUhtGjRItxxxx04cOAAioqKMGDAALz33nvo3Nm+/5FocVNMP3F+z+jf7gdLB+xZhPSTicXODRymWppljRmht75os8bUxcRijxdp467Tu6JBrSyMH1lZQE2Y5WQwHqgHl7OOboH6NTPx7EWx4sgIo4Duo1rWNdzH7Nw0Mjn38d6eMiX9ZTEbYEd0a4ZOTWujd5tYa5u9dGPjifBvJ7bHivuG45jW9U2P0aut+HNz15hc/9T3qqww7NOuAR4+qzvevaaf8HMza2SGIGvMbLV6tygpr4rtkvmaVkJH9Pl/zu9hGLPnNk4SHCIk2uAiK7AjSGfrJpG4hdBFF12EY489FsuXL8fkyZMxe/ZsLF26FGeeeSZKSkrc6GNaY2oRiuMX4EUdIS8rSwcDAax6YAR6tKqHc3q1lBr8FGgn6pg4I4ODPHZuD81r9ROx2u2UaXIOrzy+HRbeOQydDq/mbOfHrxYy5/RuiV/uOimmBL8ZIjP7yB7N8epo4wUVzSxyZnEATi0606/tjxcuPsbdVadNujLx4l748qYTXEkSMCv9IPOEfM4xLfHo2Ufhm1tO1Lyv3jUYCGhcPrJWiL+dkI+2DWviFptZORf0aW24VqBZjFDEKqoW+s0cFPS0i7pygEwKuJXBR3SMvx7dUpge74XwsMpGNSPRden0laOtaBRnIHkiiFsIffLJJxg/fjxWrVqF0aNHY8CAAfjuu+8wf/58DB8+HPv373ejn2lLPMtemOGFayye/WUKKmaGgvjo+gF47Nwe0mnXZgskGh2hU9M6msqw6tRYK9eYuj3133bMwWqxFQ6bD3SiPohihC4+rrVpZovZRGu2srgoCFWGXm3qY3g3d2uLWfVEZrFTGeLNggkGAzjv2FYxIjCkKTTpzCLUsHY2Zt46GGOHdoyrj2pkXGPqmkZ3nnYEjsjLxf1ndnOtD3rUcSpm1p7I8ixmK6ADQNfm4sDkRFkvnLizIyTaImSnJAhQac1/a0xsEU0/Efc0u2rVKtx1112oUaPKxN2zZ098//33WL16NYYMsbeeC9FiNkHFc/+LzN3xWYTsucbsth0b32ONfhCz0z/1E+Idpx6BXm3q44nzemgmJ6FVTbIvgLE4Ug+KVhaXd67phx6t6uE9lVtDNKgeKC03PY7ZuRl6eJHG7Iwgpl/bD91bVLnYypKcbaPGaU0iu/dtp6a1cdpR7heI1QdLJ7MCvRqz4HvRZ83q5uDzvw/EJX3tZyTJorZKXDuoveF2z1x4NF66pBfuOUO8xleEI5rl4u0xfWN+06J7yncWoQRHCTn5zauLLPpnxKgibiHUrJm4imXnzp0xe/Zs7NmzJ94m0hqz30c8P0iR+TqewNdAnPvbzhqT/DWpd4sZMEwmTvVHTXJzMP3a/jjrmJaaAUu4cK3B97AzR6uvuZXFpWerevjo+gHorXJraAueVfaxfWNzF5TZ6e+b3xDTr+2H2f8cjF5tGuCTG4+PfpbstGM1Jx1e2dtu6X47960CBYFAAM/ZiNmS7ofqdvKHBKqkUe1sXHRca1x5fLuYcxv5DahFvZNaTHYpV8WpXD+4g+F2tbIzcPKRzaSSDfq1b4h8XUyQ6HfrhfBwkn2ZLC7v3xZ1cjJw0XGtk90V1/B0rbG2bdti9uzZXjZRbTiyeS6WFeyLed+rp8IrBrTD8oJ9+N9vW6LvxSWE4vSNWX3PlvWdBdVqssZccDOGLISQ0dewU8reaTZLBLVYm3v7EGwvKkEbi8wgq2vfSxBkDNiPF/CSPu0a4LOxA9HC5r0S/yTkzm/UbA22ZFuHHjy81tXfh3XEnFU7ce2UXwCoY4SqtnVSx8ou6nR4Nwr2RYSc/ncgzjaLuzlXSXR/muTmYNFdJ9mqYO13PP8mRhYjokXtblBjahGKYwDOyQzh2YuO0cZ/xCNk4nxOapZrHmCpD/6UnX7NssbMjmEoXAJqIWScNaZHdDQZbeQkGFntrmhYO1tY7VWP08FUv8BisunaPNd21pJf5jWNRUgfkJ3YrhiSm5OJHqrA/ci9pr5NEyHavBLgeleff2S+Mcm4N+IRQdUma6xbt2744IMPpLffsmULxo4di4cffthJc2mB0djhVjGqMQPbWffB5jHzG1dZGSoLKjrv6wiThQJvPaUz6uhqk8jEgyhQtFljJttOv1abOixjwbGVeefwx+8kGNlJ4KXT+8zNOkDJIl4DhlvzvplLyU9WCLUFRvQwkAjKPRLg+jIdotv7hsOuONEaaMkgFQoW+h1HQui8887DpZdeitatW2PcuHH48ssvsWPHjujkVFxcjKVLl2LSpEkYOXIk2rRpg4ULF+KMM85wtfPVCwcZLTbu/7N7tbTugY0fVINaWeilqpdSmT4v3x81Ywa2M3VPiLrV2yDVV41+9Xn991MPcnrXj5H+UB/BKmtMjVPXXrwWIVmcilg/xQg5xVaMkIdfVy1g9e3k1XWv3lK8aB8AIhahxN4HokrRbjDhzG44pnU9PH+4qKkooeG4/IZYfPdJePy8HjGfJYPU00H+GzMcCaG7774bf/zxBy688EJMmjQJI0aMQLNmzZCZmYkaNWqgdu3a6NGjB66++mrs27cPU6dOxZw5c9C1a1e3+1/tcUkHSTmurLZQp0AGdVligUC8zjF73D1S7l7Sps/LH1/CM2Yra6xf+4a4+3Rtn2UGMCcFB51koDi9cn6KEXKK3YKKMfu71A+1IS8iLF6/og/uPeNI9GpT32AvY566oCeyQkG8fGlvl3pYifYBwH7ldDdw+76LXNeW9Wvi/esG4NTueZr39dSrmZX0uK0I/uhFauM4WDovLw+PPPIIJkyYgHnz5mHevHkoKChAcXExGjVqhC5dumDQoEFo2dLaEkFMXGMWk1ooGJBcOdm6D1bzpzrzKBjQiquAZBsAMEO3do7Vw6RIYOnL+AcDYiuOxjVmI8Xf6AlX3Rdx1pj4eIFAAFcc3w6fL92C+esrMynNYnfe+Vs/rN91AEdbVCkW0bNVPXTNy7VlheovKBwnQ3WwCMU7n4nWhnOCOsg4clpP6NTYdIkTM/7SswVO657nelCr1h2WnGk4UfednSSHZNHNIL6UyBN31lhmZiYGDhyIgQMHutGftMVoODEbZiLuqAqTbWz1QaK6s/pvrUVIbkLp1LR2TNl69VDzzS0nYNgTs3T9sj5udkYIxWXaM6HoSkvbWWvMaABU90UUH2F1DtXj9/EdGuHJ83uic7PYFbb7tGvgeILNCAXx6djjpZ9YHzm7O846xtkDi1cuikTi1KX7/a2D8NPa3TjrGHdiRbRCyJ3z6kVmT0YoiFO7N8Peg2XRdPNE64Uym0X9nJICOggndW2KJ87rgSObp4Yg8uM5jVsIde/eHcceeyx69+6NY489Fj169EBWlrN1odIZoznLai7LyQyhrMK8WB4g99xmtY16oA4FdUJIMm/MapsOTeqged0cFBQeku4XAORkBmOEkL49O2veyPxWRbElgy0W8BzRrRkWbtiDNg1rIhAI4EyPAi7tmO3PP9Z5PRCvglYTid06QhHaNKxlWZbADupgab9bIp4f1UvzOtELabptETLKWq2T436FmbeuOg73fLIMOZkh/La5MO7jBQIBxw8ypBJXhNDXX3+N//73v5UHzMhA9+7d0bt3b/Tp0wdDhw5FmzbeVRitLhgJBPPK0gEc1bIu5qzeZX18F5RQbMl/7WuZNmS2cTLEVS4DUGbZ3oV9WuPfX65En7YNzNPnDQZa9eHU5+PjGwZg14FSDLJwY1w+oB3yG9fC0a3su7z8SLrFCHmJ+n7yuQ6KIVUtQpMu7Y2V24qEa4oBlWU7/thWhPN6my/RYYf+HRrhq5tPxN0fLXVFCJH4idtueskll6C0tBTjx4/HlClTMGHCBNSvXx8vvfQSxowZg/z8fJx22mlYv369C92tvjgdi68fVJnKabYe1OEWrPtgsY16oI5xjcF5GqfVICrz8JdjsEK2ukfBYADXnNgeb4/pi1cvN16A1KxPRnWJmubmYHDnJpaTaigYwJAuTVHfZvVjt3j83B4Y3NlZzImaLofdeX9NcApxJHX5bBefgH2igzT3jt8tQnoS3Vu3LELDujbF9YM7GP5uG9bOxrvX9Me5LgqhCKl2jd3Cj986bovQP//5T9x777245pprou/deuut+Pzzz3Hddddh/PjxeOmllzBgwAD88ssvaNq0abxNVktEP8Of7hhqvk+g8uni07HHo7i0Aue88KPptlZYxUpkaISQrs/SFqHYjfRmdf34UFgca+nRIyqhr0AvXCqFSOTpz2wcMowRUn1rjYXMsof+4OxeLXF2r5Zoe/uncR3n/ev6Y+2OAzjSYLFKr7j5pE44qWtTw0UyneDH1Q3aNnLP5ZYIEm4RqgaxaQkKcyISuLLoaocOsWu9jBgxAmPGjMHs2bPx3XffoWHDhpgwYUK8zaUVTXNzLIOlAeDI5nUtq+nKjPUXWqwdowmWFsYIWeNkztlzoNRym2xBKruiKLrMNjuxIAaoDqF1FfpwNvWQmlkZ6NaibsK/dygYQI9W9VxZViGCX+oIAcDiu0/CT3cMjcmK9D+pHSOUDJwUS60OJLrmlAxxjyb5+fmYMWOG8LMBAwbg008/RU5ODm644QZ8+ml8T6HVGcMJxWSMLi6tCg52Y0I6pnV99FSVz9eToXeNQWchchgjZPW72H1QQggZLKqotwjJImO2Vk+gaaaDqhV+qsxbr2YWmlosN0OqhxC6rH9bAMCwI+glSTZxC6Frr70Wjz/+OKZMmRLz2bJly1BcXAygcjX6goKCeJtLO8ysGL9s3Fu1ncVYLiuU9CXm1ahrGumXA6is0WPdhsyko3eV7ZUQQnecegQA4G8n5Gv7peujWTtqZCpLJ2JxSeI9lw9oCwA4s2fz5HYkhUn0Q/6zFx0NALj/L0cmtmEX6do8F7+OPxkvX9rLemPiKXHHCN1www1YunQpLrnkErz44os499xzkZeXh+XLl+OJJ57A8ccfDwAoKipCjRr+KRPvN5ymz0ewEhiyU7ZRNoa+WrFoUUgp15gD7SBKi9fTs1U9/H7/cORkhvDirLXCBmPaNhu8DT4b0T0P//5yJY5t20DzfdM18LE60KZhLfx+/3Che5XIkei7//SjmmPYEU2FsYGphN0FgqsDfhwpXSmS8MILL2DYsGF48MEH8fe//z36fp8+fTBx4kQAwJw5c4SxRKQS4/T5KoIBoFHtbGwvKonZzso4Iet5M0qH1le4FhdUlMlMs0avKR44s7vEXuKAaTVurD5fOzsDP44bimAA2Fesqt/kx183kSbVJ9Rkk4y4D14z4hauVYs655xzcM4552Dbtm3YvHkzmjRpglatWmk+Hz58uFvNVTuMLUJVH7w9pi/GTl0k3s5CYsgGCstahELBgC5rKiAXgyPKGjMZRNc9dGpc8U/qtHpba42ZfBb53gGVASHVQhZOObIpvly2DUMtCkASLSl2mQnxHX40nrteNrNp06bCFPlevegHdYJZjItmO5fCVYzSUvUxQcGAThwF3FnYFYDO0hTfF6tfsyrmSd8/MwEm4+oKpXCw9OPn9cSpK7ZhCIUQcQEfzm2ESEOnuE8wmkdjY3HEW1otzio7UTcyCJYO6dbVCgQCmjbjqSytH0TdemJQFKB+zSoffMDG3S7Th1rZGRh1XGuc26tlymX61M7OwF96tkCdlEvTJn4kXVPBiTyRpIT/O7lTcjsiwP2FVIgjZIWKgyx7W9x/ZjeUvb8Es/7YoXlfZBHSWERM+qYmkYYTBQrq1qgSdnbWGpPlgb/KxS+R1Obo1vWwaONeXHCs+xWGCUkHxo88Ev8c3sWXsV20CPkEIxeQ2gJk5sqxzBqTVCDN69XA61f0iXlfnyoeCgZM6woZ90MUI6R7LddVKerXUlmEdJ81q2tsxenUtDYAcaFGkn68PaYv/nfj8QlfUiRVoD2IyOBHEQTQIuQbDCWEIE1dhHXWWHy2GL0QcuoaE/XTy5Wrm9SpEjt6sXhJvzZYs+OAcO2tSZceiye//QN/O6G9Z30jqUNOZgjdWtRNdjf8C5UQSWEohPyCRB0h07HGY59TjEUooLUIBRCQdI0lzjmmKJUFIu8940goioIauoVpszNCeOgssWurdcOaeOK8ngnoJSGpD3UQSWUohHyCTB0hwNiy41ZBRSP0QigYBELBKrdRIKDtw0NndcePa3bh41911cQlOuJ2emWklD0hhBCihwEQPkctfMwEglsxQkbECKFAAPp1L9VbHNeugTA7QNQNP9aVIITI48eFNAmRhULIJ8SbDWa1XbwuqdissUCMRUim/o9M+rxbhnYOzYQkBv7WSCpDIeQTZOoIKVAMBVOiLEJ1ciq9qUO6NBHECKmzyMTiK7ExQhyeCUkEXGuPpDIUQj7B2CIkW2Aoro8tiQihb245Ec+POgYX920TmzWmaU8cPC20COnG0PN6V9Zq6d2mfpy9JoQQQsyptkJo/fr1uPLKK9GuXTvUqFED7du3x/jx41FaWprsrgkxDJbWp88bWoRc7pCOiPWnaW4OTu2eV7nWmMYCpLUIGa+dZt3WzSd1wqujj8Wrlx8bV58JIYmBBiGSylTbrLHff/8d4XAYL774Ijp06IClS5dizJgxOHDgAB577LFkdy8G6crSRktsWB0gTqEkWsJD6xrTr4smHhxlLFyZoSAGS6yBdfUJ+Xhp1lqMOq615baEEO+gDiKpTLUVQsOHD9esdp+fn4+VK1di4sSJ/hRC8e5vqYOMLE5yLetXnwe0mWT69PlgIIAK6cdEZ8PoP4d3wRk9mqNLszouHpUQQkg6UW1dYyIKCwvRoEEDw89LSkqwb98+zb9ko9EpiplrrOqDyaN7Y9gRWotKvMHSIouTVggFdFlj8m06NauHggF0a1EXGfo8fkJIYuFTB0lh0mYGWbNmDZ555hlcc801hts89NBDqFu3bvRfq1YJXGBRYq2xytfWu7dpWEtwnPjIFIgNfW0hNZauOkJItcHLZXII8ZqUE0L33HPPYeuD8b8FCxZo9ikoKMDw4cNx7rnn4qqrrjI89rhx41BYWBj9t2nTJq+/ThS59Hmz/d1fWV2NaPFRvbssqI8ZkhRDngVacmwmJCEwWJqkMikXI3TDDTfgggsuMN2mbdu20b8LCgowePBg9OvXDy+99JLpftnZ2cjOznajm7aJt6Ci3jijH5fiXXQ1SyCE9AHU2mDpAAJJViIcmwlJDK9d3gd/e2MBJvy1W7K7QohtUk4INWrUCI0aNZLa9s8//8TgwYPRq1cvvPrqqwgG/WsAkwlmVhTjyV2Tui48fnzIWIT0MUKy0KxOSGpzfMdG+O2eU0zd5YT4lZQTQrIUFBRg0KBBaN26NR577DHs2LEj+lmzZs2S2DMxshYhIxN0KBjAyB7NUVhchnaNasVUVY43ZEdkEdIPemoxFww4L6hICEk9KIJIqlJthdBXX32F1atXY/Xq1WjZsqXms1RaekG/xIaZ9eSZC482Pk6cNqHsjFDMe2YDnx+GxFS6zoQQQpKDf31FcTJ69GgoiiL850eMg6W9DYKWRWgR0vdNJdKCgYC0+PLqKzXNzfHoyIQQQqoL1VYIpRpu19xxW1yIYoRya2Qa72DDJNSkjrsB6lOuOg6DOzfG4+f1cPW4hBBCqh/V1jWWasSb1aVHL5jiDUgWWYSObJ6LKwa0Q/N6sZYXmYKKL13SC58u2YLrBneIq296BnRohAEd5ALqCSGEpDcUQimEosjHvbhvEYqNEQoEArh7ZFfh9vq1x0ScfGQznHyk/wLXCSGEpA90jfkEtfWkRb0a+PKmE4TbORU48cYWiSxCbrdBCCGEJBoKIZ+gDiweP7IrOhstJKoSG3ayVePVKKIYIUv8kDpGCCGEmEAh5EOM4oUUaGN9vrpZbDUCYl1o8WbLyViECCGEkFSDs5sPaJqb7ShrrK1gcVUjambFFw4mYxGqk1PVRlZGMO7aRYQQQojXMFjaB3x8w/H4cNGfltspijb3S3aF97fH9EWNrNhgZzvICaFMvHXVcQgFA4eDq8vjapMQQgjxGgqhJHP2MS3RNDdHu06XyfZqi5CZDlJv1699Q8PtZG02OZlyQqq/Km3d5YoAhBBCiOvQNZZkIjYeeTdSlcJxu/aQGQ1qZdnehzqIEEKI36EQ8glOV243wu0V3evXtC+ECCGEEL9DIZRCKLCxxIbLNX0cWYQEii6RVixCCCHECgohH2Ia+5O4bmioGWewNSGEEOJHKISSTCQ2SMpSYmeJDZcVkxNLDm0/hBBC/A6FUJKpCpaW3T7xnNGjeRJaJYQQQryHQsgnaNPnjSpLK/IxQi5JptycDDx1QU9H+zIciBBCiN+hEPIJ0hahBLvGMkNBxwHOrCxNCCHE71AI+YSAREXFjGAw4a4xLihPCCGkOsPK0j7BzOjytxPzsXJrEQZ0aCStTKQFjIXRJq7FWgXHpo2IEEKIn6AQSgHGjTgi+rfrFhqafAghhKQxdI35hIDB33qkLTQuCZx4DsNgaUIIIX6HQsgvSKoGWWHiVtaY2/WICCGEED9BIeQT1DIoaCKKUkmY0CBECCHE71AI+QS19gkFTYSQpKVHWjB5GCzNdcUIIYT4HQohn6CuuWO61lgKWYQIIYQQv0Mh5ENCZq6xBPYj3vZoDyKEEOJ3KIR8glr7BE1cY67XEUrYgSqht4wQQoifoBDyCbLB0rLEVQjRJSh6CCGE+B0KIZ8gGyxt9pkXJF9OEUIIId5BIeQT1MHSZlonQ1IIuSVg4soaY5QQIYQQn0Mh5BfUMUImPqVQKHUsQqKv4QOPHSGEEBKFQsgnyMYISVuE3Fpig8KFEEJINYZCyIeYxQHJBlJTvxBCCCHWUAj5BHUVZjdihKTbtfjcrTXLou0xbIgQQoiPoBDyCRrXmFnWmGyMkA98WhQ9hBBC/A6FkE8ISAZLZwQTe8l8oKcIIYQQz6AQ8gmaOkJmWWOSrrEaWSGp7ax0TnxLbNAkRAghxN9QCPkE2UVXZWOEHjrrKHRqWhv/Ob9HvF1zDF1jhBBC/E5GsjtAKnG7snS7RrXw1c0nWm7XLDcHRYf2G37eNDdbqj1CCCEkFaFFyIe4UUdIlhcu6YX+7Rvi7TF9Ne+/87d+6N++ISZfdqzjY9MgRAghxO/QIuRDzOKh3V5rrH3j2nhLJ4IAoE+7BsL344XiiBBCiJ+gRcgnqOsImQVLJzprLB4CDBIihBDic1JnVq3mqBc3NV1rLMGrzxNCCCHVGQohn6Cu12NWUDEjwYuuxkPq9JQQQki6QiHkE8Iai5DxdrQIEUIIIe5BIeQTwiqLkJnYcTtrzEsYIkQIIcTvUAj5hOoYI8RgaUIIIX6HQsgnaGKEqknWmAiKI0IIIX4itWfVFKZhrSwAwMldmwIAFMjFCI3o3gwAKz4TQgghbsCCikni2/87Eau270fvNvUByMcIndY9D03+loNOTWt73UVCCCGk2kMhlCTq1czCsW0bRF+rXWNm7qNAIIA+7RoYfu435o0bitLyME7494xkd4UQQgiJgULIJ1SolVA1olndnGR3gRBCCDGEMUI+QammQogQQgjxMxRCPoE6iBBCCEk8FEI+IZwmSojJ84QQQvwEhZBPSBMdRAghhPgKCiGfkC4WIUIIIcRPpIUQKikpQc+ePREIBLB48eJkd4cQQgghPiEthNBtt92G5s2bJ7sbptAiRAghhCSeai+EPv/8c3z11Vd47LHHkt0VU8LUQYQQQkjCqdYFFbdt24YxY8bgww8/RM2aNZPdHVNoESKEEEIST7UVQoqiYPTo0bjmmmvQu3dvrF+/3nKfkpISlJSURF/v27fPwx5qoQ4ihBBCEk/KucbuueceBAIB038LFizAM888g3379mHcuHHSx37ooYdQt27d6L9WrVp5+E20pEtlaZNl1AghhJCEk3IWoRtuuAEXXHCB6TZt27bFhAkTMG/ePGRnZ2s+6927N0aNGoX//ve/MfuNGzcOt9xyS/T1vn37EiaG0kQHEUIIIb4i5YRQo0aN0KhRI8vtnn76aUyYMCH6uqCgAKeccgqmTZuG4447TrhPdnZ2jHBKFNV10VVCCCHEz6ScEJKldevWmte1a9cGALRv3x4tW7ZMRpdMYdYYIYQQknhSLkao2kKLECGEEJJw0kYItW3bFoqioGfPnsnuipC++Q2T3QVCCCEk7ai2rrFUo3+HRphy1XHIb1wr2V0hhBBC0gYKIR8xoIN1EHjqw/x5Qggh/iFtXGOEEEIIIXoohAghhBCStlAIkQTD7DhCCCH+gUKIEEIIIWkLhRAhhBBC0hYKIZJQsjJ4yxFCCPEPnJVIQrj/L0civ1Et3HHqEcnuCiGEEBIloChc28GIffv2oW7duigsLERubm6yu0MIIYQQCezM37QIEUIIISRtoRAihBBCSNpCIUQIIYSQtIVCiBBCCCFpC4UQIYQQQtIWCiFCCCGEpC0UQoQQQghJWyiECCGEEJK2UAgRQgghJG2hECKEEEJI2kIhRAghhJC0hUKIEEIIIWkLhRAhhBBC0hYKIUIIIYSkLRnJ7oCfURQFALBv374k94QQQgghskTm7cg8bgaFkAlFRUUAgFatWiW5J4QQQgixS1FREerWrWu6TUCRkUtpSjgcRkFBAerUqYNAIJDs7viSffv2oVWrVti0aRNyc3OT3Z20h9fDX/B6+A9eE3/h1fVQFAVFRUVo3rw5gkHzKCBahEwIBoNo2bJlsruREuTm5nJQ8RG8Hv6C18N/8Jr4Cy+uh5UlKAKDpQkhhBCStlAIEUIIISRtoRAicZGdnY3x48cjOzs72V0h4PXwG7we/oPXxF/44XowWJoQQgghaQstQoQQQghJWyiECCGEEJK2UAgRQgghJG2hECKWPP/882jXrh1ycnLQq1cvzJ4923Db999/HyeddBIaN26M3Nxc9OvXD19++WUCe1v9sXM91MyZMwcZGRno2bOntx1MM+xej5KSEvzrX/9CmzZtkJ2djfbt22Py5MkJ6m31x+71mDJlCnr06IGaNWsiLy8Pl19+OXbt2pWg3lZvZs2ahZEjR6J58+YIBAL48MMPLff5/vvv0atXL+Tk5CA/Px8vvPCC5/2kECKmTJs2DTfddBP+9a9/YdGiRRg4cCBGjBiBjRs3CrefNWsWTjrpJHz22WdYuHAhBg8ejJEjR2LRokUJ7nn1xO71iFBYWIhLL70UQ4cOTVBP0wMn1+O8887Dt99+i1deeQUrV67E22+/jS5duiSw19UXu9fjhx9+wKWXXoorr7wSy5Ytw7vvvov58+fjqquuSnDPqycHDhxAjx498Oyzz0ptv27dOpx66qkYOHAgFi1ahDvuuANjx47F9OnTve2oQogJffr0Ua655hrNe126dFFuv/126WN07dpVuffee93uWlri9Hqcf/75yp133qmMHz9e6dGjh4c9TC/sXo/PP/9cqVu3rrJr165EdC/tsHs9/v3vfyv5+fma955++mmlZcuWnvUxXQGgfPDBB6bb3HbbbUqXLl007/3tb39T+vbt62HPFIUWIWJIaWkpFi5ciJNPPlnz/sknn4y5c+dKHSMcDqOoqAgNGjTwootphdPr8eqrr2LNmjUYP368111MK5xcj48//hi9e/fGo48+ihYtWqBTp074xz/+geLi4kR0uVrj5Hr0798fmzdvxmeffQZFUbBt2za89957OO200xLRZaLjxx9/jLl+p5xyChYsWICysjLP2uVaY8SQnTt3oqKiAk2bNtW837RpU2zdulXqGI8//jgOHDiA8847z4suphVOrseqVatw++23Y/bs2cjI4M/dTZxcj7Vr1+KHH35ATk4OPvjgA+zcuRPXXXcddu/ezTihOHFyPfr3748pU6bg/PPPx6FDh1BeXo4zzjgDzzzzTCK6THRs3bpVeP3Ky8uxc+dO5OXledIuLULEkkAgoHmtKErMeyLefvtt3HPPPZg2bRqaNGniVffSDtnrUVFRgYsuugj33nsvOnXqlKjupR12fh/hcBiBQABTpkxBnz59cOqpp+KJJ57Aa6+9RquQS9i5HsuXL8fYsWNx9913Y+HChfjiiy+wbt06XHPNNYnoKhEgun6i992Ej4jEkEaNGiEUCsU8TW3fvj1GteuZNm0arrzySrz77rsYNmyYl91MG+xej6KiIixYsACLFi3CDTfcAKByIlYUBRkZGfjqq68wZMiQhPS9OuLk95GXl4cWLVpoVsU+4ogjoCgKNm/ejI4dO3ra5+qMk+vx0EMPYcCAAbj11lsBAEcddRRq1aqFgQMHYsKECZ5ZIIiYZs2aCa9fRkYGGjZs6Fm7tAgRQ7KystCrVy98/fXXmve//vpr9O/f33C/t99+G6NHj8Zbb71FX7uL2L0eubm5WLJkCRYvXhz9d80116Bz585YvHgxjjvuuER1vVri5PcxYMAAFBQUYP/+/dH3/vjjDwSDQbRs2dLT/lZ3nFyPgwcPIhjUToOhUAhAlSWCJI5+/frFXL+vvvoKvXv3RmZmpncNexqKTVKeqVOnKpmZmcorr7yiLF++XLnpppuUWrVqKevXr1cURVFuv/125ZJLLolu/9ZbbykZGRnKc889p2zZsiX6b+/evcn6CtUKu9dDD7PG3MXu9SgqKlJatmypnHPOOcqyZcuU77//XunYsaNy1VVXJesrVCvsXo9XX31VycjIUJ5//nllzZo1yg8//KD07t1b6dOnT7K+QrWiqKhIWbRokbJo0SIFgPLEE08oixYtUjZs2KAoSuz1WLt2rVKzZk3l5ptvVpYvX6688sorSmZmpvLee+952k8KIWLJc889p7Rp00bJyspSjjnmGOX777+PfnbZZZcpJ554YvT1iSeeqACI+XfZZZclvuPVFDvXQw+FkPvYvR4rVqxQhg0bptSoUUNp2bKlcssttygHDx5McK+rL3avx9NPP6107dpVqVGjhpKXl6eMGjVK2bx5c4J7XT2ZMWOG6Xwguh4zZ85Ujj76aCUrK0tp27atMnHiRM/7ydXnCSGEEJK2MEaIEEIIIWkLhRAhhBBC0hYKIUIIIYSkLRRChBBCCElbKIQIIYQQkrZQCBFCCCEkbaEQIoQQQkjaQiFECCGEkLSFQogQQgghaQuFECGEEELSFgohQgghhKQtFEKEkLRhy5YtqF27Ni644ALN+//73/+QmZmJf/3rX0nqGSEkWVAIEULShry8PNx222145513sHDhQgDAzJkzce655+Laa6/FAw88kOQeEkISDVefJ4SkFQcPHkTHjh1xxBFH4KGHHsLQoUNxzjnn4JVXXkEgEEh29wghCYZCiBCSdrz66qu44oorUKtWLZx22ml46623EAqFkt0tQkgSoGuMEJJ2dOrUCQAQCATw2muvUQQRksZQCBFC0orFixfj9NNPx4ABA7B//35Mnjw52V0ihCQRusYIIWnDypUrccIJJ6BXr1746KOPcO6552LOnDlYvXo16tatm+zuEUKSAC1ChJC0YP369Rg2bBg6d+6M6dOnIzMzEw8//DD27NmDBx98MNndI4QkCVqECCHVni1btmDgwIGoW7cuZsyYgdzc3OhnV199NV5//XX8/vvvaNu2bfI6SQhJChRChBBCCElb6BojhBBCSNpCIUQIIYSQtIVCiBBCCCFpC4UQIYQQQtIWCiFCCCGEpC0UQoQQQghJWyiECCGEEJK2UAgRQgghJG2hECKEEEJI2kIhRAghhJC0hUKIEEIIIWkLhRAhhBBC0pb/B0Xc6DRwLBIAAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from qsppack.utils import chebyshev_to_func, get_entry\n", "import matplotlib.pyplot as plt\n", "\n", "xlist = np.linspace(1/kappa, 1, 1000)\n", "func = lambda x: chebyshev_to_func(x, coef, parity, True)\n", "targ_value = targ(xlist)\n", "func_value = func(xlist)\n", "QSP_value = get_entry(xlist, phi_proc, out)\n", "err = np.linalg.norm(QSP_value - func_value, np.inf)\n", "print('The residual error is')\n", "print(err)\n", "\n", "plt.plot(xlist, QSP_value - func_value)\n", "plt.xlabel('$x$', fontsize=12)\n", "plt.ylabel('$g(x,\\\\Phi^*)-f_\\\\mathrm{poly}(x)$', fontsize=12)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the residual error above attains almost machine precision." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Additional plots\n", "\n", "We would like to approximate the inverse function $f(x) = \\frac{1}{2\\kappa x}$ by an odd polynomial $p(x)$ on the interval $[\\kappa^{-1}, 1]$, and represent this polynomial using QSP. For $\\kappa=10$, the following example shows one such odd polynomial of degree $d=101$ that is bounded by $1$ on $[-1,1]$. \n", "\n", "The QSP error is close to machine precision. The phase factors are symmetric with respect to the center of the interval after removing a factor of $\\pi/4$ on both ends and decay rapidly from the center." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Condition number κ: 10\n", "Degree of the approximating polynomial: 101\n", "Parity: 1 (odd polynomial)\n", "norm error = 1.927251413680331e-05\n", "max of solution = 0.758781110079824\n", "Number of odd coefficients: 51\n" ] } ], "source": [ "# Recalculate with higher degree for high-precision example\n", "kappa_high = 10\n", "deg_high = 101\n", "parity_high = deg_high % 2\n", "\n", "# Define target function for matrix inversion\n", "targ_high = lambda x: 1/(2*kappa_high*x)\n", "\n", "print(f\"Condition number κ: {kappa_high}\")\n", "print(f\"Degree of the approximating polynomial: {deg_high}\")\n", "print(f\"Parity: {parity_high} (odd polynomial)\")\n", "\n", "# Set up optimization options for higher degree polynomial\n", "opts_high = {\n", " 'intervals': [1/kappa_high, 1],\n", " 'objnorm': np.inf,\n", " 'epsil': 0.1, # Following MATLAB code\n", " 'npts': 500,\n", " 'fscale': 1,\n", " 'isplot': False, # Disable plotting during computation\n", " 'method': 'cvxpy'\n", "}\n", "\n", "# Find best approximation polynomial using convex optimization\n", "coef_full_high = cvx_poly_coef(targ_high, deg_high, opts_high)\n", "\n", "# Extract odd coefficients only (due to odd parity)\n", "coef_high = coef_full_high[parity_high::2]\n", "\n", "print(f\"Number of odd coefficients: {len(coef_high)}\")" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "iter err \n", " 1 +1.1196e-01\n", " 2 +5.8736e-03\n", " 3 +2.3323e-05\n", " 4 +3.8406e-10\n", "Stop criteria satisfied.\n", "Converged in 5 iterations\n" ] } ], "source": [ "# Set up solver options - use Newton method for reliable convergence\n", "solver_opts_high = {\n", " 'maxiter': 100,\n", " 'criteria': 1e-12,\n", " 'useReal': True,\n", " 'targetPre': True,\n", " 'method': 'Newton'\n", "}\n", "\n", "# Solve for phase factors\n", "phi_proc_high, out_high = solve(coef_high, parity_high, solver_opts_high)\n", "\n", "print(f\"Converged in {out_high['iter']} iterations\")" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The QSP vs polynomial error is: 4.163336342344337e-15\n", "The QSP vs target error is: 2.1213282169696424e-05\n" ] } ], "source": [ "# Evaluate the functions for comparison\n", "xlist_high = np.linspace(1/kappa_high, 1, 1000)\n", "targ_value_high = targ_high(xlist_high)\n", "func_value_high = chebyshev_to_func(xlist_high, coef_high, parity_high, True)\n", "QSP_value_high = get_entry(xlist_high, phi_proc_high, out_high)\n", "\n", "# Calculate errors\n", "poly_error_high = np.linalg.norm(QSP_value_high - func_value_high, np.inf)\n", "qsp_error_high = np.linalg.norm(QSP_value_high - targ_value_high, np.inf)\n", "\n", "print('The QSP vs polynomial error is:', poly_error_high)\n", "print('The QSP vs target error is:', qsp_error_high)\n", "\n", "# Prepare phase factors with pi/4 removed from both ends\n", "phi_shift_high = phi_proc_high.copy()\n", "phi_shift_high[0] = phi_shift_high[0] - np.pi/4\n", "phi_shift_high[-1] = phi_shift_high[-1] - np.pi/4\n", "\n", "# Create extended x-list from 0 to 1 for QSP plotting (as in MATLAB code)\n", "xlist_extend = np.linspace(0, 1, 1000)\n", "QSP_value_extend = get_entry(xlist_extend, phi_proc_high, out_high)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Figure saved as 'qsp_inversion.png'\n" ] } ], "source": [ "# Generate the three-subplot figure matching the MATLAB version\n", "fig, axes = plt.subplots(1, 3, figsize=(15, 4))\n", "\n", "# Left subplot: target function on original interval and QSP on extended interval\n", "axes[0].plot(xlist_high, targ_value_high, 'r-', linewidth=2.5, label='Target')\n", "axes[0].plot(xlist_extend, QSP_value_extend, 'b--', linewidth=1.5, label='QSP')\n", "axes[0].set_xlabel('$x$', fontsize=12)\n", "axes[0].set_ylabel('$f(x)$', fontsize=12)\n", "axes[0].set_ylim([0, 1])\n", "axes[0].legend(loc='best')\n", "axes[0].grid(True)\n", "axes[0].set_title('Target vs QSP')\n", "\n", "# Middle subplot: error between QSP and polynomial approximation\n", "axes[1].plot(xlist_high, QSP_value_high - func_value_high, 'k-', linewidth=1.5)\n", "axes[1].set_xlabel('$x$', fontsize=12)\n", "axes[1].set_ylabel('QSP error', fontsize=12)\n", "axes[1].grid(True)\n", "axes[1].set_title('QSP vs Polynomial Error')\n", "\n", "# Right subplot: phase factors (after removing pi/4 factor) on log scale\n", "axes[2].semilogy(range(1, len(phi_shift_high)+1), np.abs(phi_shift_high), 'bo-', markersize=4, linewidth=1)\n", "axes[2].set_xlabel('Index $j$', fontsize=12)\n", "axes[2].set_ylabel('$|\\\\psi_j|$', fontsize=12)\n", "axes[2].grid(True)\n", "axes[2].axis('tight')\n", "axes[2].set_title('Phase Factor Decay')\n", "\n", "plt.tight_layout()\n", "plt.savefig('qsp_inversion.png', dpi=300, bbox_inches='tight')\n", "plt.show()\n", "\n", "print(f\"Figure saved as 'qsp_inversion.png'\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above figure shows the QSP representation of $f(x)=\\frac{1}{2\\kappa x}$ using an odd polynomial of degree $101$:\n", "\n", "- **Left panel**: The target function on the interval $[\\kappa^{-1}, 1]$ and the QSP representation extended to $[0, 1]$, showing perfect agreement on the target interval\n", "- **Middle panel**: Error between the QSP representation and the polynomial approximation, demonstrating machine precision accuracy\n", "- **Right panel**: Phase factors after removing a factor of $\\pi/4$ on both ends, plotted on log scale, showing the characteristic symmetric decay behavior\n", "\n", "The QSP error is close to machine precision. The phase factors exhibit symmetric decay behavior away from the center, which can be explained using the infinite quantum signal processing (iQSP) framework. This example is related to the quantum linear system problem." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Reference" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1. Gilyén, A., Su, Y., Low, G. H., & Wiebe, N. (2019, June). Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics. In *Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing* (pp. 193-204).\n", "2. Dong, Y., Meng, X., Whaley, K. B., & Lin, L. (2021). Efficient phase-factor evaluation in quantum signal processing. *Physical Review A*, 103(4), 042419." ] } ], "metadata": { "kernelspec": { "display_name": "regular", "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": "3.13.5" } }, "nbformat": 4, "nbformat_minor": 2 }