{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Uniform Singular Value Amplification" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this example, We introduce the implementation of uniform singular value amplification." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What is uniform singular value amplification?\n", "Uniform singular value amplification uniformly amplifies the singular values of a matrix represented as a projected unitary. Suppose that we have access to a unitary $U$, its inverse $U^\\dagger$, and the controlled reflection operators $(2\\Pi - I)$, $(2\\tilde{\\Pi}-I)$. We are interested in $A := \\tilde{\\Pi}U\\Pi$, which has a singular value decomposition $A=W\\Sigma V$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The equivalent problem in function approximation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The goal of uniform singular value amplification is to implement the singular value transformation of $A$ for function $f(x)$. Here, $f(x)$ is a linear function $\\lambda x$ over some interval and zero outside the interval.\n", "\n", "For numerical demonstration, we consider the target function\n", "$$ f(x)=x/a, \\quad x\\in[0,a],\\quad a=0.2. $$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "a = 0.2\n", "targ = lambda x: x / a" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To numerically find the best odd polynomial approximating $f(x)$, we use a subroutine which solves the interpolation problem formulated as a convex optimization problem. For this example, we will look for a degree-101 polynomial. We also specify a parameter `delta` to serve as a buffer, i.e., we use the polynomial approximation from $[0,a-\\delta]$. Next, we set the parameters for our subroutine. To improve the numerical stability of our method, we scale the target function by a factor of 0.9." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "deg = 101\n", "delta = 0.01\n", "opts = {\n", " 'intervals': [0, a], # Change to [-1, 1] for QSP operations\n", " 'objnorm': np.inf,\n", " 'epsil': 0.01,\n", " 'npts': 500,\n", " 'fscale': 0.9,\n", " 'isplot': True,\n", " 'method': 'cvxpy'\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With these parameters set, we can now call our convex optimization subroutine from the `optimization` submodule. The optimization routine will output all Chebyshev coefficients, so we postselect those with the desired parity." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/jameslarsen/miniconda3/envs/qspy/lib/python3.13/site-packages/cvxpy/problems/problem.py:1504: UserWarning: Solution may be inaccurate. Try another solver, adjusting the solver settings, or solve with verbose=True for more information.\n", " warnings.warn(\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "norm error = 6.226057844394006e-06\n", "max of solution = 0.9899984954139619\n" ] }, { "data": { "image/png": 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", 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LUc8++6zvY3LCe++9h/b2dlRWVlo3DpWFDbuu2h8c2fHyxhtv4ODBg1LG1ZdspShZjg0TNhMnTkR5eTkAseWoeDyeIWa8hodVzdcAmgmbUaNG9fsSjzzySHzyySc5/6aoqAiVlZUZ/3Ti4MGDlmWZ7QC6+uqrEY1GtVk/qhDHhmVstm3bpk0PmFzCRrecDXsKmzhxIkpLSzN+p1M5ipWiWL6GceGFFyISieDdd99V2hFkZajZs2dbWTS2LQ0NDWhoaJA2tmxkO6/Hjx+P6dOnI51O44UXXpA1tAyylaJkOzYjR45ETU0NALHCxp7nAcixUYY5c+b0C6Jt3rzZ6vIaRJhbM378eEvV26mpqcGXv/xlAHpM/S7EsRk3bhzC4TC6uroyVr9Vlb1792LLli0wDANz5szJ+B0TNqtXr1ZeDAD5L1bnnnsuysrK8Mknnyi/BlYux6a6uhqnnXYaALXLUX3zNUCPa8audSoFcoHsjg0ApWZHmaaZUYpijs2ePXusGV1+4rewsZehAH7CRrXgMKCZsLnpppvw5ptvYuHChfjoo4/w1FNP4dFHH7VCtEEkVxnKDtv+pUuXKmP5ZsPe6yKfYxONRq0LuMpP1Qy2avQxxxxjBVUZxx13HCKRCPbt26dFGTSfsCkpKcGFF14IQO1ylGmalmPTV9gAmbOjVCWbsAHULUflOq/Z8fLiiy9Kb7jZ0NBghfjHjx+PESNGoLS0FKZp5nX9RWEXNixnI7KXDU9h097ebolEcmw88qlPfQrPPfccli5dimnTpuHHP/4xHnzwQVx++eWyhyaMQoTN7NmzrfWjVL5Yt7S0WBeWfI4NoNeU71xlKKDnKXvGjBkA9ChHDWQvs3LUH//4R2XLhHv27EFbWxvC4bDVq8TO5z//eRiGgX/9619SbmgDsWfPHmzfvh2hUMhaFJahorCxP7D0dWw+9alPoba2Fi0tLdYDgCxYyWn06NEoKiqCYRhSp3zLdmy8ZGzY8TdixAgMHz7cy7CEoJWwAYDzzz8f7733Hrq6urBx40ari21QKUTYGIaBU045BYD8tU/ywS5+Q4cO7Zff6ItOAeJ8wgbQK0A8kLA555xzUF5ejp07dyq7PcytmThxImKxWL/f19bWWueLiiHi1atXA+hZ46pvJlBFYcOa8xmGgdGjR2f8LhQKKdOF2F6GYsic8i1b2HhxbFQODgMaCpvBRiHCBugJVgNQOpNSSL6GoYuwOXToEN577z0AsG6WfdElQHzo0CHrYstuoH0pLi621vZStRyVK19jR+VyVK4yFKCmsOnbnK8v9pyNzJyZfUYUQzXHRpdSlMrBYYCEjdIcOHAA9fX1MAxjwIDWyJEjAagtbArJ1zB06WXz+uuvA+i5idbW1mZ9DRM2a9eulZ4zyAd7Chs3bhwqKipyvk71clQhwuYLX/gCgJ6pyPa29ipQiLDZtm2blMBrNgY6r8866ywUFRVh27Zt1jEmg2zCRpZjY5qmNdvVnrHRxbFROTgMkLBRGubWTJw40Wr6lougOTa6ZGwGKkMBPdtSXV2NeDyOd955x6+hOabQp7Czzz4bFRUV2L17t+VWqQQTNn2netsZO3YsTjjhBJimieeee86voQ1IV1eX1bYhm7Cpra1FZWUl0um0MqKfOTa5hE1ZWRlOP/10AHLLUUy8MJcGgLQp362trZawqK2t9bUUFYlEAHjL2JBjQ7im0DIUoIewceLYsNBnU1MTDh06JHRcXihE2BiGoUU5qtCLVXFxsSU8mVhViXwzouyw9a9YpkUF1q5di0Qigdra2gxngWEYhnLlqFzBYTsqTPvOV4ry27FhLmFlZSVKS0t9FTbM3Xfr2MTjceuBk4QN4Rg3wqahoQGJRELouNzCboKFCJvS0lJrm1R5Mu1La2urtdp1PmED6BEgdvIU5seF2A3xeNy6gQ0kbNhxKDLX4BR7GcowjKyvUU3YDOTYAL0ictWqVZ473rohnU7nDQ/v37/f13ExYcPK16wU1dDQIKy8y4QNu666FTabN29GOp3GkCFDLJGkGiRsFMaJsBk+fDjC4TBM01TuZsNgT3aFlKIA9QPEq1evRiqVwvjx4zFu3Li8rw2SYwOoK2y2bt2KdDqNioqKAS+6fvQOcUq+fA1DNWFTiGNTV1eHSCQC0zSlOLD79u1Dd3c3wuFwhgAbMmSINfPMT9fGHhwGYE2ZTqfTwr4fXsLGnq/JJb5lQ8JGUUzTdCRsQqGQpf5VLUc5cWwA9XM2hZShGKwfydatW5W6kTJaWlqsG1QhgUBVhY09XzPQRdf+lKwCpmlqLWzyndeGYVjNKxsbG30Zlx3m4o0dO9bKmLBxyQgQ9xU2sVjM+n5EnVO8hY2qZSiAhI2y7N+/H4cOHUIoFMo59bYvKudsurq6rBtIUBwbJ8JmyJAhlmBQsRzFZquMHj0aQ4YMGfD1qgqbQvM1QO9TsipCc9u2bThw4ABisRiOO+64nK+zCxvZy3Tka87XFxWETbbckowp332FDSD+nGLChvUaclt6I2FDuIa5NZMmTUJJSUlBf6OysNmzZw+Anrb8fZcdyIXKU767urosgVKIsAHULkc5vVipKmwKmerNYI5NR0eHlNxHX5hbM2vWLBQXF+d83WGHHYZwOIy2tjbrvJJFvuZ8fWHnfd9px36QbUYUQwXHBhBfGuXl2KjenA8gYaMsTNhMmzat4L9hB6xqfTmAzHxNoXVZlUtRa9asQXd3N2prazFlypSC/oYFiEnYiMOJsKmoqLAayqng2hRShgJ6yhZM9MsuRw3UnM8OcwJVc2xkTPmW4diw792LsEkkEpYrSsKGcMz7778PoLB8DUNlx8ZpvgbodWz27t2rxBO1HdaY7zOf+UzBQo05NmvWrEEqlRI2Njc4FTYsz6WqsMnXw4ZhGIZSOZtChQ2gTs7GSQsH1UtRsh0bkcKmq6sLXV1dALwJm61btyKRSKCsrGzA0qNMSNgoipPgMEPl7sNOZ0QBQHV1tfWUt23bNhHDcg1bPNFJ582jjz4aZWVlaG1tlX5D6osXx0Z2zoNx8OBBa3X7QoQNoE7OpqWlxWp2OHv27AFfr4qwYY5NITc5mcKmkFKUn46NveswQ+SyCs3Nzdb/Z5/Z0dHh+NzVYUYUQMJGSZzOiGIEzbEB1M3ZsIsPuxgVQiQSwac+9SkAapWj2tvbrQt/ocKGOR2JREJKZiIbzCKvq6sbsFM3Q5Up3++88w5M08S4ceOs8zgfqggbJ44Ne0jx+3hJJpPWg0g+x+bQoUNoaWkRPp50Op1V2IhcVoF951VVVSgvLwfQc59xusSLDvkagISNkuzZswfNzc0Ih8MFZQUYKgsbN44NoG7Oht0I2cWoUFQMELObY01NDYYNG1bQ3xQXF1v9P1QpRznJ1zBUETbs8wsV/qoIm0Ka8zFkOTa7du1CKpVCUVFRVtFYUVFhHfd+lKMOHjyIVCqVUQoFxJaimLAZMmRIxmQUp+UoHWZEASRslIS5NZMnT0ZRUVHBf2cPD6tSHmB4dWxUEzbs4uPEsQGA6dOnA1Bre9xerFQLEDvJ1zBUETasKVuhwpKJt127dqG1tVXYuAai0KnegDxhw0pM48ePRyiU/Zbn55Rvlq8ZNmwYotGo9XO/hE00GrW+B7fCRtXFLxkkbBTETRkK6A10JhIJ5dZXcuvYqF6KcurYqBRWZQRF2DjpYcNQZX+w87W6urqg11dXV1vfP9tuGbhxbPwuReXL1zD8nPKdLTgMiM3Y2IWNYRiWa+NE2KRSKcshJMeGcIxbYVNUVGRdGFUqR6VSKWs8QXBsksmkdSNyK2xkOwR2giJs3JSiVAkPs9BzocIGkF+OctKcD5A33TvfjCiGDMemr7Bh14ZDhw5xX+/PLmyAnrX4AGdN+rZv346uri4UFRXl/S5VgISNgrgVNoCaOZv9+/cjlUohHA5brlKhsIzNjh07lFnck92EDMMouHTAYDfShoYGZcqFQRA2qVTKcvUGQykKkC9sGhoa0N3dXVBzPkB+KSrfzVgFx6a6utoqEfF2EPsKGzeODQsOH3HEEQiHw1zHxxsSNophmqZ1o3HSnI+horBhT3WjRo1yfEKMGjUKxcXFSKVS1swG2bAb+bBhwxxvDxM2yWQyYwqmLDo7O62p9E6FjUq9bHbs2IF4PI6ioiKMHz++4L9TTdjo5Ng4ac4HyBM2TkpRMh2bcDhsXR94n1M8hI0u+RqAhI1y7Nq1Cy0tLYhEIgV3tLWjYvdhFhx2mq8Behb3nDRpEgB1cjZu8zVAz2wiNt1Sdq4D6MlnpNPpjMxGoajk2LCcyeTJkx2JTVUyNjqWopxM9QZ6b6qdnZ2Ix+OihtUPJ6Wo7du3C3dScwkbQFzOhqewUT1fA5CwUQ7Wcfjwww8v6CmoLyo26XN6AeyLalO+vQgbQJ1cB5B5sXLacEslYeMmXwP07ovGxkappU4vpajNmzdL6WTtpDkf0NNDhR1jfgWI4/G4tZ5WIcKmpaVFuKOUrYcNQ1QvGx4ZGxI2hGu85GsANUtRXhwbQL0AMbvouBU2qrgEgLeLFRM27EItEzdTvYEeh4TdbJlrIgM3pahx48ahuLgY3d3dvi4HwHD6wBIKhVBVVQXAv3LUJ598AtM0UVpaaonYbJSUlFilVdHlqEIcG9VKUaZpatOcDyBhoxxBFDZeHRvVhI2brsN2VHVsnBIExyYcDlsuicz94aYUFQ6HLSEnoxzl1LEB/M/Z2MtQAzmSfgWIdSxF7dq1C21tbYhEIpaDrjIkbBSDqWKvwiYoGRtAvV42XktRQXNsGhsbHbdm542bHjYM2QHizs5Oa4FCp7PsZOZs3Dyw+L2sQiH5GoYfU767u7stEauTY8POr8MOOyyjqaCqkLBRDOa0jBs3ztXfB9GxYU8I27ZtU2KKdFAyNslkElu2bAHgbqaDyOmpTmhvb7eOMS/CRtY2sDJUJBKxguWFIlPYOGnOx/DbsWHuSyHCxg/HhgmWaDRqfRd2/MrYOBU2bAanU+EtCxI2isHUvNsDiD0FtLa2or29ndu43GKapmfHZvz48QiHw+js7FRCsLldToEh+0bKaGpqskKn2Z4eByIUCglduK9Q2NPksGHDHJVyGLKFpr0M5TTALUvYOG3Ox5BViso31Zvhh2PDnPSampqsyzv45dg4DQ+ze0mhi8vKhoSNQnR1dVkHkFthU1FRYR20KoiAxsZG66nArbCJRqOWg6VCzoaXYyNb2LAbalVVFSKRiKv3UCFn4zZfw5BdinITHGawjI3fZdr6+npHzfkYKpei/HBs8uVrADEZm66uLqvU6daxaWtrAwDHjqIsSNgoBLvRhMNha/aAUwzDUKocxdyaYcOGobi42PX7qJSz4ZWxkV2K8nJDZajQpM9LvgaQvz/cTPVm2Ker+wlzawptzsfQpRQlquRdqLDheT6xMpJhGKisrARAwobwEfYEP2zYMMeWtB2VAsRe8zUMVXrZeFkniqGKY8ND2Kjg2LCsRyHlhmzILg26mRHFYE/g8Xjceir3Azf5GsBfYdPe3m4dl4UcG2PHjoVhGOjo6BB2PA8kbNix2Nra6njl7Vyw77qystIqf5GwIXzDa76GoaJj47YMxVBlyvfBgwdhmqardaIYsh0CBo/jTQVhwy7cbrdDdsbGi8CsqKjwvekdAFf5GsBfYcPcmiFDhlgCMB9FRUXWdUpUOWogYVNVVWXNOuJ1PPbN1wDOMzYkbAjXsBtNvkZShaBS92Fejo0qpSh2samurnadS2H7t6WlReo0aZ6OjcwmfWw7ss0yKQTZQtNLKcre9E6GsHF6XvuZsXFShmKIDhDn6zoM9JSLeOds2HdtPz+cOjYUHiZcYy9FeSGIjo0qpSiv+Rqg5+LO1jOSWY4KmmOjq7DxUooC/A/kAu6a8wH+OjZOZkQxRAeIB3JsAP7nVDbHhkpRhG8EsRTFy7FhC2E2Njb6HpS0w0PYhEIhax/LFDZBydjwEjYNDQ1Ip9PcxlUoXveDDGHj9ryWIWxUcmwKETa8WyiQsCGkwqsUpVJ4mJdjU1ZWZokB9p4y8NrDhiE71wEEz7FxKwzYvkilUtYMEj/xUooC9HRsVC1FqeTYiMzYkLAhfCOIpShejg3Qe+PS3bGx/32QHBsZXaGTySRaWloAuHdsioqKUFFRAUCO0NStFGVvzuc2Y9Pc3Cx8RXIvpSgRjk1bW5slEGSXoig8TPgG7/BwfX09EomE53G5paOjwxIhXh0boPfCz27IMuAlbFRwbHgKm66uLuvi5yf2m3khM19yITNno1spym1zPiBTfIp2x7yUonbs2MG9LMmCw6WlpXkFgooZGwoPE67hlbEZPny4NWNH5mwVVjIqKytz3XDQjgrChlcpSgXHhsfxVlZWZl3sZJSjmHCuqKjwtDifCsJGl1KU2+Z8QE8XcXa8iHRe4/G49X04eahiDpR9sUpeFFKGAihjwwMSNgrBqxQVCoWsjrAyy1H2fI2XhoMMFYQNb8dG91IUIDdn4zU4zJAlNDs6OqzGero4Nm6b8zH8GK/dPXRyM45EItZNn7cDWaiwoYyNd0jYKASvUhSgRoCYZ74G8L8dezZ4Z2xklaISiYSVTfEqpGUKG689bBiy9oeXlb0Zshwbp8Fhhh/ncWtrK4CeG7jTflNsP/BeRNipsKGMjXtI2ChCIpHgujS8Ck36eM2IYpBjww/7TcVLNgVQw7Hx6jrJyjzZy1BuXU3dHBs/hQ0LhTuBlcpkOTb2UhSPQH4+x6arq2vAz0ilUparSMKGcAS7wBmG4fnpE1BjZhRvx0a2sEmlUparxitjI7vbrb1ZoFtkdh/mXYrye394nREF6OvYiByvF2EjyrEZqOswwx7I5zGGfMKGfU4+7GOg8DDhCHaBGzp0qOcbDaCGsAmaY8PWiQL4BLwB+Qsv8nAHqRTlHh45J1nCxmvGRqRj46V0ItuxKSsrs0pFPM6pgYTNQDkb9j2EQiEUFxd7Ho8fkLBRBF7BYYYKwiZoGRse60Qx7MJGRv8XXsFhQI1SlK7hYa8zooDM3jB+4LY5H0P1UhQTQ7KEDcDvnOrq6kI8HgeQKWwikYh1DStU2JSXl3OZBOIHWgmbO++8E4ZhZPwr5CDRAZ7BYUCN8HDQHBte+Rqgdz/bQ7x+EhTHRveMjW6lKC/N+Ri6CBtZ4WGA35RvdkwYhtHvuyg0QKxbcBgAvD12SuDoo4/G3//+d+u/eZRtVIDnjQaQHx5OJpPWiRyUjA2vHjZAjxVcVlaG9vZ21NfXc+nz4wRybDLRuRTFjp2uri50dXUJLRccOnTIWpHeaXM+hh9CTLXwsGmarhwbr8cj+46rqqoQCmX6GCUlJWhpaXHk2OiCVo4N0GOhjRw50vrH4+lZBUSVovbt2yel1LFv3z6k02lEIhEuQgDovfg3NTUJb8eeDZ6Ojf19ZORseApp1jMpCBmbzs5O7k/q+eBRiqqsrLRKBKLLUcxdLC0tddycj+GHY+PlZizCsWlsbLS6wBdyPeT1sJAtX8MotJeNbl2HAQ2FzZYtWzB69GhMnDgRl156KbZt25b39fF4HC0tLRn/VIR3KYo9FSQSCe4dNAuB2dWjR4/u96TgFvvNy88F/xi8hY3MALEIx6ahocF3wcmrFFVeXo6ioiIA/ro2PEpRoVAIlZWVAMSfF+z6yT7PDaqXokQ4NsytGTp0qHWc5UMlYUOOjWA+/elP48knn8Tf/vY3PPbYY9i3bx9OOumkvDfuRYsWoaqqyvrnNvAmGt6lqFgsZr2XjHIU73wN0NOOnZ1cMgLE7IbHy4FSoY0/D2HDerCYpum7iOZVijIMQ4qDxms/+JWzYcLGjWBgDMbp3k7KUAC/jE2+8yPIGRuthM25556LL37xi5g+fTrOPPNM/OUvfwEAPPHEEzn/ZsGCBWhubrb+sUS/avAuRQFyA8S8Z0QxZOZs2EUmCI4NTyEdiUSs9/G7HMWrFAXICRDzKEUB/gsbL46NH9O9VZsV5VTY8M7YkGOjEWVlZZg+fTq2bNmS8zVFRUWorKzM+KcivEtRgNwAMRM2PB0bQK6wEZWx0d2xAeQ06evu7raeNnkIGxn7g0cpCtBL2NhLUaLyf0zYqNLHxq2woVKUO7QWNvF4HBs3brScCZ0R6djILEUFybEJUsaGd+lTxswo9sRvGAaXWWV+CxvTNLUrRTHBwEPYpFIp7r1iGOx9VSlFFdp1mKGSsKHwsGD+7//9v1i5ciU+/vhj/POf/8SXvvQltLS0YN68ebKH5hneNxpArrAJomPDc7o3IK93CiDOsZEhbKqqqri0ffA7Y9PZ2Wk1TxtMpaiSkhJrRpWo8aoaHnaasamvr/fkahUibChjI5ldu3bhq1/9KqZOnYqLL74YsVgMb775JsaPHy97aJ5IpVLWRZpnKUpmxkaUYyOr+7B9nSjdp3t3d3dbFyudhQ3PfA3gv9Bkx1M0GvX8NKxTeNgwDOE5m6CEh5PJpKd9mk/YsPBwEEtRWjXoe/rpp2UPQQhNTU1Ip9MA+N1oAHmOjWmaQmZFAfIcm0OHDnFbJ4ohe0Vp+w3GKzIdG17njN+lKLtr5rVVvU6ODdAjRg8cOCBc2OiasSkqKkJVVRWam5tx4MAB1+KdMjaENNiTW2VlpeumV9mQFR4+ePCgZbG77U6aC1nCht3shg4dimg0yuU9Za9PNHToUG49hmQ06eM11ZshU9h4RaeMDSB+yjePjI1MYQPweVggYUNIQ0S+BpDn2DC3ZsSIEQU1o3KCLGHDO18D9Do2zc3NVpt6PxBxvAWhFOW3sOG5H3RzbAZTKSqZTFrHlBNhw+N4pPAwIQ0RM6KAXmHT1tYmbPZBNtgNh2deiMGEjd8ZG94zooBMx8TPxna8g8OA3FIUb2Hjl4Omo2PDI2MDiM3KdXd3Ww8KXsPDPKajt7a2Wu/j5FgV7dhQgz5CKCJ62AA9JzU7Sf0MEOc7mbzCLgyySlE8hU0oFLLErIxut7o7NrwzNuz8a2pqstb1EYnOwoZXKUqEsGFuDeBtrah0Om2V1L3AhEMkEnFUxvZ6TpmmSaUoQh6iHBtATjlKpLCRnbHhWYoC9G4KZ4d9L21tbQM+AfKCt2NTXV1tOWh+CM3BXIoSmbFhN+Li4mJEIs7nx9hLLjycbnY+MIekULwKm66uLsu5ImFD+I6ojA0gJ0DM+4Zjxy5s/Fy1nPdyCgwZTfpElKIqKiqsPJVfrg3vjI3dQfNDaIpwbESv7s0rPCwyY+MlXwMA4XAYxcXFAPjkbNwKG68PPUw0hkKhrKKEhA0hFFGlKCC4jk0ikeDaZ2IgRJSi7O8nw7HhKaQNw/C9HMW7FAX4m7MRIWzsTf9EoFMpyksOiOfMKFmODbsOV1VVZZ39WGiDPgoPE66gUlThlJaWWnVqPwPEooRNUBwbwP+cjQhn0M/eQjwFpv0mLsq1MU2Te3hYRCmKh7Dh2cuGOSKyhE2u63AhDfq6u7utvBk5NoQj/HBsghIeNgxDSs5GxHRvQE6TPlGlT7+FDe9SFOCvg8ZTYIbDYctFEZWzaW9vt8q/KpeieJROeE759urYeC1F5boOF1KKsgs7cmwIRwQtYyNS2AByAsSiS1FBcGz8btInwrHRVdgA4gPEzK0JhUKOb9J9Ub0UxdOxcSts7DMm3eQJeQqbWCzGtXmsaEjYKEDQSlEiw8OA/8ImnU5zXyeKIcOxCUIpyp4lEZGxEb0/TNPk/kAjWtjYg8Nel4BQXdio4Niw15um6ar9ADsOcl2HnQgbncpQAAkb6dgvcBQeLgy/m/QdOnTIWsuL9z6S4dgEoRTF9n04HPac97Dj1/7o6OiwpuLq5th4LUMBvTfbrq4udHV1eX4/O0FxbJjwAAaeuZSNQjM2+cLDTNiRsCEc0draimQyCUCsY9PQ0OBb237RwsbvJn3sRs1znSiG3+Hhrq4u60Kms2PD9v2QIUM8uwd2/HLQ2Ph5rOzN8EvY8BCSFRUV1n7jPV4vC2AyRDg2dqFSCNFo1PqO3Ig/Jv55lKJ0ytcAJGykw25oJSUljg/8Qhg2bJjVpMqv7EPQMjai8jX296yvr/elLw/7zsLhMKqqqri+NxM2+/fv5/q+2RAx1RvwrxRld814CTOdHJtQKCQsQOxlAUyGCtO9DcOw+um4ETaFZmy6u7uRSqWyvoZKUYQrRJahgJ4LCAt1+lGOSiQS1slAwmZg2H5PJBIZreBFYZ9JxNPpAOSUonjnuPwSNiJyTn5mbHggasp3UEpRAHwRNvnen4QN4QqRwWGGnzkbew+NoAkb3lO9gZ6LC7uI+jkTR8TxZp+eyjJJohAtbA4ePCh0G3QUNjwdG0DclO+ghIcB/4RNrpwNCRvCFSKnejP8FDbsZCovL3e1Tksh+B0eFrWcAsPPnI2IdaIY7PtJpVLC942IHjZA775IpVJC110Scd7rlLEBxM2M4pGxUaFBHyBW2IRCIWsZlFw5GwoPE64QXYoC5AgbUW4N4H94WGQpCvB3yreoqd5AT68Ltt9Fl6NEZWxisZjlSIjcH+TYiBM2PDM2QXZsgIEDxBQeJlzhRymK3Tj9EAJ+CJsgZWzs76vbitLZ8KtJn8heSX7kbEjYqJ2xUSE8DKgjbMixIRzhh2Mj+oJnZ6AphjwIUsYGCI5jA/gXIBZVigL8ETY6lqJ4h4dVztjoHh42TZOEDSEPPzI2bFqvqMXx7AzU7ZIH7Kbc1tbmqiOnU0RnbILk2PglbESVogB/9gc5NmpnbFToYwO4FzadnZ3WtTGfsBmoSR8JG8IVfpSi/HRs/ChFVVVVWVOV/QgQU8amcPwWNiIEtB/7Q6SwEfUAo0t4mEfGRnfHhl2HQ6FQXlEykGND4WHCFX6UomQ4NiKFjb25nOhyVDqdtsRnEBwbEjYDo3spyr5cA090yNgkEglrDbHBHB62X4fz9aui8DAhBD9KUUFzbAD/cjYi14liyJjuLboUJbr7sO4ZGxEC0y44RDzE6NDHxt7kcjCHhwu9DlPGhhCCH6UoPx0b0St7M/wSNuzmNmTIEMRiMSGf4Ve3WyAYjo1pmlpnbEzTFLIf7AuCiniIEdV5WISwKS4u9tRHizkU7e3tnpc6kdHHxqmwoYwNwY2Ojg7rgPVjVlRzc7PwjrB+OzaiMzai8zVAMB0bkcKmvb3dWjhWR8emvb3dKhXx3g8i3VkdSlG8bsTs75PJpOeynsqODRtT0BwbR5L2ySef5D6AmTNn4phjjuH+vjrAbmTRaFTogcMObtM00dbWxu3ClA2/hI1fTfpET/UGem+kTU1NSCQS3FcQZ3R2dloXSFGOjR99bOwrY7u5WQyE6PAwG38sFuM+/iFDhmDnzp3chU0ikbBufrzCw+wa0dLSglQqhXA47Pk9eUz1BjIzJW1tbVaHXqeYpqm0sAlqeNiRsPnGN77BbeE80zRhGAbuuOOOQSts7MFh3gsS2ikuLkYsFkN3dzeampoCIWz8KkWJnuoN9HxXoVAI6XQaBw8exMiRI4V8DvuuIpEIt5tTX5gAbG5uRjwed31DyIe9DCXivOm74jrvz7CXoXi/tyjHhld2xY79GtHU1MTFveIlbCKRCIqKihCPx9He3u56bPF43CplyRA2AzmaQQ0POxI2ixcv5j6AmTNncn9PXfAjOMwYMmQIDhw4gKamJowbN07Y5wRN2PhRigqHw6iurkZDQwPq6+uFCRv7OlGihPSQIUMQiUSQTCZRX1+Puro67p8hOsfF9nVXVxfa29u5P62KXK9LlLBhZSj2kMQD5lS3tbWhsbFRKWED9NzM4/G4pwCxPbviZx8bHo4Nc/iBgDs28+bNEzWOQYkfwWFGVVUVDhw4IDxAHNTwsEhhw96/oaFBu6ZwfTEMAzU1NdizZw8OHDigpbApKytDcXExurq60NDQwP2iLnKFddGODW+3d+jQoWhra+M2Xh7N+Rjl5eU4dOiQpynfTNhEo1FXYWa/MjbZwsOdnZ2W26SbsKHwsET86GHD8GPKd1dXl3UCBi08LDJjA/jTFM4vh1B0+Fa0QDMMQ+j+EDl+0Y4N7xIm7ynfPJrzMXhM+faSrwHkOjb27RaRZRMJCRuJ+FmK8mPKN3tvwzCE5ngA/8LDfmRs7O+vu2MD9B5r7GbIGz9cQZHiTOdSlAjHBuAnbHiXogA9hU2ha/blEzbMqSotLeUS7PYT9xP9bSQSCWzatAn19fVobm5GVVUVRowYgalTpwqb4REE/CxF+eHYsPeurKxEKCRWMwetFOVnG3/Rxxu7+ZGwyY6OpSjRwoZ3KYqnY8OjFKWzY6NbcBjwIGzq6+uxZMkS/OUvf8GaNWusNtZ2iouLccIJJ+C8887DvHnzhN8cdMPPUpQfjo0fK3szgiZs/HBsRDoFdtjNT9SxJrLrMEPk/tCxFCUqY8O7FMUzY8PDsfHSnA+Q26BP1+Aw4ELYbNmyBbfffjuee+45q3HR8OHDMWvWLFRXV6OyshLNzc1obGzEhx9+iJUrV2LlypX44Q9/iIsvvhh33303Jk+ezH1DdMTvWVGAP46N6OAwkJmxSafTQhwi+zpRfmVsglCK8suxEbkdVIrKRJdSlIiMTZAdm3wN+gaNsPnud7+LRx99FKlUCqeddhouu+wyzJ07FxMnTsz5N9u2bcM//vEPPPXUU1i2bBmeeeYZfOtb38LDDz/sefC64/esKECsY+PXVG+g94KYTqfR2tpqbR9PGhsbkUqlAIh31XRdeDEbQcjY+BEe1rEUxTs8rHLGRtfwsGmaXEtROgobR4+5jz/+OK699lp88sknePnll3HllVfmFTUAMGnSJFx11VX43//9X+zYsQPXXHMNfvvb33oadFAI2qwoP4VNcXGxdVKKKkexm1pVVZWwdaIY5NgUjh/ChokOEceWjqWowZixsa8X5RYZwqajo8NacoRHeDjwwmbbtm148MEHMXr0aFcfNmbMGDz00EPYunWrq78PGkEND/shbADxORu/pnoDwXJsRAsbPwQauzHaO+7ygkpRvaicseHp2Lhpzge4EzZs34fD4QGDv0ENDzsSNn07on788ceuPlRUZ1Wd6O7utg4cCg+7Q7Sw8WuqN5Dp2HhdTTgX5NgUDtsG3sLGvrK3yFJUR0cHEokEt/cV2aAPUDNjo+t0b7sIHajDeL4GfYOmFNWX2bNn4+233+Y1lkEFe2oLhUJC8iF9CVp4GBDfpM+vGVFAr7Dp7u4W4hKIvqHaETkrKp1O+3KcsRsjb3HW3t5uCQ4RAtMuPHh+/6IzNiqWonQNDzv5TMrYZKGpqQlz587Fiy++OOBr//nPf3r5qMDBylDV1dXCe74AwQsPA/6VovwQNqWlpdaFSETOpqOjw2rJoHODvtbWVqTTaQB6OjbsgUbEyt5Az+KN7EbE8yFGl1lR1KCvV6QUUv4iYZOFv//974hGo7jwwgtzLpD5/vvv46KLLsKcOXO8fFTg8DM4DAQzYyO6+7CfGRvAn5k40WhUeM1cZCmKbUdJSYl10ReBqIyN3TUTuRApoIewsY+VRwlWNceGZx+bQr8fN8ImmUz2K10OmvBwX04++WSsWrUKdXV1uPrqq/HjH//Y+t3WrVtx+eWXY+bMmXj++ecxatQoz4MNEn72sAF6n6Lj8bjjngiFEjTHxq9MCkNkUzj78SbqhsoQKWz8WmTVLmx4Zp78OKZ0EjZsP6ZSKc8iMpFIWK6kauFhr8IGgNU3biCciCm7+Onr2gya8HA2pk6ditWrV+O4447DnXfeiauuugrf/va3cdRRR2Hp0qWoqanBgw8+iI8++ojHeDNYtGgRDMPAjTfeyP29RePnjCggM0gmqhzl102HIVrYsO/JjwwUIHbKt58izV7GYWUjXvh1jLFtME3T0xN7X/zo/ixC2IgKD5eUlKCoqAiA9/HaBUjQSlFA4eUoJzOx7O+fS9gMOseGUVtbi+XLl2PYsGFYsmQJ/uu//gtDhw7Ffffdh23btuF73/uedfDy4l//+hceffRRHHPMMVzf1y/8LkWFQiHrZBclbGQ5NqLCw6KeUnOh6/pEfbGLAi83hWz4JdBKSkqs7BtP58mP/cBb2JimKSw8DPCb8s3EV1FREZc1ClUID0ejUeuBNFsOJhtOSlGGYeTM2QxqYdPW1oZ77rkH06ZNs540TdPEiSeeiOuuu05IHbytrQ2XX345HnvsMd/cAd74XYoCxOZsnHS75IXojA27mAfBsfFrnSig5ymQ3Vh4l6P8cmwMwxCSs9GxFNXZ2Wl14BYh8nkFiHnmawA1HBvDMBwHiJ0IG/vrSNj8m0WLFmHChAm4/fbb0dnZiZtuugmffPIJvvSlL2H58uU4/fTTrQsqT66//nqcd955OPPMMwd8bTweR0tLS8Y/FfC7FAWIFTadnZ1W+CwoGRvmbAXJsfFD2BiGISxn42e5U8TMKB1LUWwfGoYhJG/Ba8o3z+Z89vfh4di4bdAHOJ8Z5VbY9O1lM2jDw7fddhtaWlpw9dVXY8uWLbjvvvswZswYLFu2DDfccANWr16NOXPmYPv27ZyGCzz99NN4++23sWjRooJev2jRIlRVVVn/xo4dy20sXvC7FAWInfLNbjjhcNi3E0G0sAmiY+NnpgvQW9iI6GWjYynK7oSIaE3By7Hh2ZwP6L2hJxKJgoO7ffHq2ADuhU2hn5lrIcxBGx7+6le/io0bN+I3v/kNxowZk/G7Bx54AD/72c+wZcsWzJ49G2vXrvU0UADYuXMnbrjhBvzud78ruMS1YMECNDc3W/927tzpeRw8CJpjYy9DiZ51wxCZsTFN03fHxo/p3n7N8BIlbPzcDipF9SA6a8Y7Y8O7FAW4d214CBvmqIgID9tfF6RSlKPVvfvy+9//Pu/v58+fj7q6Onz961/Haaed5vkit3btWhw4cACzZs2yfpZKpfDqq6/iF7/4BeLxOMLhcMbfFBUVcQ8u8yBojo3f+Rqg9+bQ2dmJzs5OT3ZvX7q6uqyF5PxybNh3J6JcSo6Nc6gU1YPI4DCgbsYmGo0iFotZy9+4OeZkOjYkbARyySWXoLa2Fl/4whc8v9cZZ5yB9957L+NnV155JY444gjccsst/USNygQtPCxD2FRUVCAcDiOVSqGxsZGrsGHiT1SuIBt+NLbz27HhLaKpFDUwujk2qmZsgB7Xxr6un1O8NugD5AibVCpl/TcJmxyceuqpeOONNzy/T0VFBaZNm5bxs7KyMgwbNqzfz1UmmUxaF2g/hU3QHBvDMDB06FA0NDTg0KFDrledz4b9Yu7Hkhfss+yfzRM/p3sD4pZVkNWPhxdUiuoPr1IU74wN0HNTb2xslFqKEp2xyRYetv9/HYWNoyv2hx9+6PqDjjzySC7vEwTsJ7BfT9CAWMfG75W9GaICxH7na+yf1dLSwn2Fbz+newPBKEXxztiYpqllKUpUcz6GqqUowNuUb9M0pQgbpxmbbOFhtr2hUEjo0iWicCRspk2bhssvvxzvv/++qw9bv349Lr30UkyfPt3V32djxYoVePDBB7m9nx+wi9uQIUMQifhimgHwx7Hxu6+QqACx3835gN79w7uxnX1lbxI2hcO7FNXW1mbltnQsRYnO2PAqRfF2bAB34WG7ENGtFGWfEeXXZBCeOBI2P/rRj/D8889jxowZOO6443Dffffhrbfe6rd4FiMej+PNN9/EokWLMH36dMyaNQt//etfcfvtt3MZvK7ImBEFBC9jA4hzbPye6g30XMCY0OUpCNra2qxzVOfwcCqVskS5juFhdowWFRVxzYP1hZ2D7e3tlpDygl8ZG16ODc/SiZf1ouzlHB362GQTNjqWoQCHGZs77rgD1157Le655x48+eST+MEPfgDDMBCNRjFhwgQMHToUFRUVaGlpwaFDh7Bjxw4kk0mYpomqqirccMMNWLBggdWIbLAiY0YU0HuTDpKwEdV9WEYpijW2O3ToEFpaWvq1UHCLXzdUOyLCw/bjVkfHxl6GEvkUbBfjzc3NnsXsYM7YeClFMWETi8U8TWyR0aBvUAkbAKipqcFDDz2Ee++9F8uWLcOf//xnvPHGG9i8eXO/144cORKnnHIKzjvvPFxyySVa1upEIGNGFNB7AQlKeBgIlmMDIEPY8MIeHPbLVhYRHmY3vvLyci5rAQ0E74yNX+XASCSC8vJytLW1oampSXlho3LGxkspike+BpDToE/nrsOAQ2EzZcoUXH/99bjxxhtRUlKCefPmYd68eQB6moodOHAAzc3NqKqqQk1NzaB3ZnLBSlF+OzZ+hIdlZWyC4NjYP4+nIPA7OAyI2Q6/jzHepSg/V4uvqqqyhI1X/AoPx+NxT/2oVAsPyxI2PBr0DSrHZuvWrXj33Xet/77rrrvw2c9+FieeeCJGjBhBQqZAZDk27ILa2tqKdDrNdRqzbMdGVHhYhmNj/3we+B0cBoKxHSLCw/b3FcmQIUOwe/duLsJGdHjYfvNsbW31LGxEZGzcODY8etgA8sPDOuLozlZSUpKx8XfddRceffRR7oMKOrLCw/ZZN7xnq8gWNuTY5EaGkCbHpj8iHIVc8HRnRZeiQqFQzoUYnSCqj439vZ0guxQ1mB0bR8Jm8uTJeP3114VkNAYTssLDxcXF1vISvPdh0MLD5Nh4IwjChnfGRoSjkAudhA3Q6wx4WUlbZCkqyBmbIIaHHQmbyy+/HLt378aUKVNw1VVXAei5SZPQcYasUhQgJmdjmiY5NpwQKWxkdLluaWlBOp3m8p6yhA2vhol+l6IAPue56IwNoK6w0c2xMU3TsWMz6MPDP/jBD9DU1ISHH34YixcvhmEY+POf/4zq6mqMHTsWM2fOtP7NmDEDEydOFDVurZFVigJ6bjj79+/nKkZZZgegBn1eCVp42DRNtLe3c7nZyGoymE6n0dnZ6fkGRaWo3HgVNslk0rrxqxYe9tpiwYmw6e7utq7Fg7kU5UjYGIaBhQsX4vbbb8cbb7yBs846y+pfs2HDBixfvhzLly+3ppRWVlbimGOOwcyZM3HsscfiG9/4hoht0A4ZT9AMEY4Ne69YLOb7lH52k2tqakIqleK2EGoQS1F+Hm+s2WAymURLSwuXm43fjg3rusoyaV6FjZ83C17neSqVssSGSEHmVdjYy4WqhIdlODZ2cTKYw8Ou+vkXFxfjjDPOAADMnTsXv/3tb5FKpbBhwwasX78e77zzjvW/r732Gl577TUYhkHC5t8wt8Tvsg0gpkmfvQzld/tt+3fIo2cHI0ilKBmOjYhmg34LG8MwUF5ejtbWVrS2tmLkyJGe3k9Hx8YuGESeC+zm7zY8zG7EsVgMsViM27h0m+7NxIlhGAV/D0HM2HhaqOiVV16xWsCHw2FMnz4d06dPxxVXXGG9ZteuXZbIIXp6NcTjcQD+3zQBMU36ZOVrACAajaKiogKtra04dOgQN2ETRMfGT2ED8G82KCsEzYSNV3QUNmzfxWIxa+KBCHg5Nry/W10dm9LS0oIfMvMtgjkohc3cuXMHfE1dXR3q6upw/vnne/mowGC/QPpxgeuLiFKUrJW9GdXV1Zaw4UE6nZaeseEpPGWF1Xlvi4wmkDx72ehYivIjOAyoL2zcODYy+ti4yfVkK0XpHh7m16GNKAh2gSwrK+OWB3GCiBW+Za3szeAdIG5vb7dmwfjt2PBeikDGyt4M3tsiQ9jw7GWjs2Mjesy8hA3vG7GupSivwkZ3x4aEjc/IcgIYIsPDMh0bgN+Ubyb6IpGI72Fo3qWo1tZWpFIpAHJKUYDewoZnLxsd+9j4db3yKmxETaXXtRTlVtiwBzrdw8MkbHxGtrAR6djIEja8m/TZ8zV+h6F5iwH7jDW/VvZm8NyWRCJhXWz9FGgiSlE6OjaqCxtRbhgbV3d3NxKJhKO/lZ2xKRR2XUin0+ju7gZAjg3hENnChhybgZE1I8r+mbyawvmVkcgGT2FjLzP6WR7UvRTV1taGZDLp+n38ul55nRUlOmMDOBddujg29vGxvydhQzhCtrAR4dioEB62j8MrMvcR+8xUKpVR83aLXxmJbIgQNlVVVb5m03g5NvYGcn7cLOziz8vYdQsP8/5uY7EYotEoAOc5GxkN+tx8ZjQatRZEZtccCg/beOutt/Dqq6/yfMvAIVvYiHRsZIeHRZSi/IY1hbOPwwsyHRueIpoJG79zQrwyNvaboh8iMxqNWmLBy7muS3hYZJnP7dh0cWwMw8jI2XR3d1slKRI2AK644gqcfvrpPN8ycMgWNqIb9MkgSKUo1tgO4CtsdHds2L71WzzzKkWxv49Go0L7wdjhca4P9owN4H7KN29hE4/HByxPuxE29td3dHRk7AMKD/8bHrmAICNb2Ngb9PHaV7KFjcjwsAx4CgIVymo8S1F+CxtepSgZmQUe7iwJG/dTvnkLGwBWc9dcuO2dY2/Sx7YzGo1y7eLsJ5Sx8RnZN032ud3d3QVZm4UgW9gEybGxfy45Nr3IFja8HBs/98NgFDYihKPbKd+8G/QBA5ej3OZ67KUo3YPDAAkb35F906yoqLAyHDp3hLUjKjxMjo03RJSiZPXiGazCxq+MFq+1ooJYiopEIla4dyBh47UU1dnZqX1wGCBh4zuyS1GhUIhrziaVSlnbpIJjw6O8Jlt8BsWxEREeplJU4fB0bFQPD/tRipIVHjYMo+AAMQ9hQ44N4RjZwgbge8OxX/BlORzsZpdIJFxfGO0E0bGhUpQ7Brtjo1spShXHJp1OcytFAb3lqIFaQLj9THt4WPeuwwAJG99RQdjwnPLN3qOkpMS32R59KS0ttUJuPHI2QXRsZJeivDppss4bytjoJWxEuAxuwsN2Z4VHx2/Rjk228DA5NkTBqCBseDo2soPDQI9VyzNALHsfiXDUZDo2pml6dtL8XI7Ajr0U5UWc6VqK8rtBX3d3t6tOyX5kbJwcw/askJ/ChsLDPZCw8RnZN02Ar2MjOzjM4LlNQSpFyXRsSkpKrC7BXrdFVlaIfW/JZHLAqbb50NGxMU3TN2FsL524EcGqTfdmAqOoqIhLp2w/MzYUHiYco4Kw4RkeVsGxAfiu6ROkUpRMx4Zns0FZwsZ+ceexNIFOwiYej1sLP4o+F4qKiqyZP05nRiWTSeuGrppjwyNfA/gnbOwZGxI2REEkk0nrgFfBsQlKKQrgl4UAyLHhCa+ymsgMRT5CoZD1xO7l2NKxFGU//kSP2zAM1zkb0ctVuAkP8wwOA86FDY8GfRQeJgrCfmGU8QTNCLJjw2OxQnZhJcfGO7o7NgAfN1BHx4bts/Lycl8WHnUrbOzLVYjolOtmXLIcG8rY9BDh+WZHH3201l+GaNiFori4WGqrap6OjeyVvRm8Z68AwRA2sh0bHttimqZUYVNRUYG9e/d62gYZNwuvDzB+HzteHRtRx4Ybx4a3sGHCw4+MDSs/6nwv5yps/vSnP/F8u8Ahu8TBEDHdW3Z4mJcYYGJPpvjktS2pVMq6wOrs2NhnypBjUzj2bIhpmlbH8ULx2+3z6tiIGqeX8LBuGZvOzk4rJK+zsKFSlI/IDqUygjbdG+Dn2KggPnmXbwC9hY19O2RcbHkcWzKFTTqddjWjy++JDkwEqCZsdAwP82jQR8KGKAgVZkQBYhwb2cKGt2Mjcx/xFjaxWExa80QeIpptR2lpqS9Zj77wWFZBxs3CHv50us4R4P/1io3X6awo0cFyL6UoHj1sADkN+ig8TBSEKsKGHJvcqLCP2Gd3d3d76p2i0rboNlXajq6lqHA4bN0Q3fSGkSVsVMvY6BIeNk2T1or6NyRsfESFGw0gpkGfbGHD27GRWYrSuXdKX3gKG1kXWh6Ojax94SYfwtAlPOxXKUr1jI2XZRxI2BCuUUXYsJt2a2srUqmUp/dSJTwcJMcmHA5bFxUvN1MVtiUIjo3XYyudTkvr5uomH8Kg8HAPbFzxeLzg5R5kCBv7ApleGvRR52HCESrcaIBMN8Krw6FKKYqXY6NCeBgIhiAA+GyHrHWiGF5LUfYbtU6OjS6lKL8yNkDhY5PRoI99ZiQSQTQadfT+QVsEk8t070QigU2bNqG+vh7Nzc2oqqrCiBEjMHXqVMdfcJBRRdgUFRWhuLgYXV1daGpqcu22JBIJ60SXLWx4OTYqhIfZ5+/Zs8dTDkp2cz6g93vkER6W7di4FWds/KFQiFuYtFB4ODaqz4oSLXxjsRjC4TBSqRTa2toKeuiR4dh4CSwHrRTlWtjU19djyZIl+Mtf/oI1a9ZkDTkWFxfjhBNOwHnnnYd58+ZhxIgRngarO6oIG6BHiOzbt8/TDcf+t7IdDh45CPvfy94e9vk8HBsV1iXT2Xny6tjYbxROe8l4RceMjdtZUaKOD8MwUF5ejubm5oJFl8xSlBdhc+jQIaTTaQB6z4pyLGy2bNmC22+/Hc899xy6u7sBAMOHD8esWbNQXV2NyspKNDc3o7GxER9++CFWrlyJlStX4oc//CEuvvhi3H333Zg8eTL3DdEBlYRNVVUV9u3b5ylAzILDFRUViES49np0jP3m46YZGUMlxwbgk7FRwbHRWdh4dQNljp8yNnxgwqZQgairsLHndAaNsPnud7+LRx99FKlUCqeddhouu+wyzJ07FxMnTsz5N9u2bcM//vEPPPXUU1i2bBmeeeYZfOtb38LDDz/sefC6oZKw4bGsgir5GqD3opZKpdDZ2en6gqKKY8NTEAQlPKzrrCiZGSHK2PDB6dhk9LHxkuvpO86SkhIpPaN44Sg8/Pjjj+Paa6/FJ598gpdffhlXXnllXlEDAJMmTcJVV12F//3f/8WOHTtwzTXX4Le//a2rwT7yyCM45phjUFlZicrKSsyePRsvvPCCq/eSgSo3TYDPlG+VhE1ZWZnl0njJ2ZBjwxf7dpim6eo9ZDs2XktRMoWZThkbVfvYAM6nfOvm2PQdp875GsChsNm2bRsefPBBjB492tWHjRkzBg899BC2bt3q6u/r6upw77334q233sJbb72F008/HRdddBE++OADV+/nN6rcNAE+TfpUEjahUCgwU6Ttnx8UxyadTjvOTjBkCxudS1E6OTaqLqkAOP8edQ0PMwaVsBk5ciSXD3X7PhdccAE+97nP4fDDD8fhhx+Oe+65B+Xl5XjzzTe5jEs0qtw0AT6OjSrN+Rg8OsSq0KAPCEY2BchcBsGtiJY93ZtXKUo3x4Ya9PXi9HvUzbGJRCIZOUmd8zWAxz42H3/8Ma9xOCaVSuHpp59Ge3s7Zs+enfN18XgcLS0tGf9koZKwYTduHqUo2c35GDxmRqmyj3iWomRui2EYnrdFtkDzusSFjo5NOp32fdyqrhVlf+9Cv0eZfWzc5nrsfzeoHJu+zJ49G2+//TavsRTEe++9h/LychQVFeGaa67Bc889h6OOOirn6xctWoSqqirr39ixY30cbS+sBwIg/6YJBC88DPBxbFTJQQXFsQG8b4vs7bBf5N0cWzrOirLfwMmxcR8eliFs3H6m/e8GtbBpamrC3Llz8eKLLw742n/+859ePspi6tSpWL9+Pd58801ce+21mDdvHjZs2JDz9QsWLEBzc7P1b+fOnVzG4RQZF4p88HRsVBE2Xh2beDxuPZHL3kdBcWzsn+9V2Mi62EYiEetp1o2wkVmKcuvYsH0ViUSsm6po3AgbNgsSoPCw15lY5Nj8m7///e+IRqO48MILsXjx4qyvef/993HRRRdhzpw5Xj7KIhaLYfLkyTj++OOxaNEizJgxAw899FDO1xcVFVmzqNg/GbALRSwWQ1FRkZQx2CHHpj/2G6/uLgcg3+lg6O7YAN6OLRUcG7fCprKy0remgnZhU+gMOvt2DfbwMJWievEkbE4++WSsWrUKdXV1uPrqq/HjH//Y+t3WrVtx+eWXY+bMmXj++ecxatQoz4PNhmmarurefqPK0zODh2OjWnjYq2PDRF55ebn0Hg5Bcmy8zsBTQdh4ObZUyNi4Le/4eewwEZBOpwu+prNxRqNRoQ+MTkp66XTaEiC6Chvdw8Oe28VOnToVq1evxvnnn48777wT27dvRyQSwZIlS5BIJDBy5Ejceuut+Pa3v+15sP/xH/+Bc889F2PHjkVrayuefvpprFixoqBSmGxUuckweDo2qoSHeTk2svM1gHdhk0qlrKdGnR0b0zSlz4oCvB1bKsyKcuvY+Pmd22+m7e3tBZXA/CpTOnFsvKyynQv2XXR3dyOdTiMU6u9JeM3YBMmx4dIHv7a2FsuXL8eMGTOwZMkSAMCIESNwyy234Nprr+VWo92/fz+uuOIK7N27F1VVVTjmmGPw4osv4qyzzuLy/iJRVdhQxqYXlfoMeV080n4D1lnYxONxJJNJAGo4NrqVotw6NjKuV5FIBLFYDN3d3ejo6MCwYcMG/Bu/RK8Tx8Y+q4u3sAF6zols7+vVsQlSeNizsGlra8NDDz2E+++/H42NjTAMA6Zp4sQTT8R1113H1R58/PHHub2X36gmbOzlAbdrK6kmbHg5NirsIzaGrq4udHd3IxaLOfp79h2okOnyImzs+1LmxdaLaJbpOPHI2PhJWVkZuru7CxZifolGJ98jEzbFxcVZnRU32IVNV1dXVvFC4eFePH3rixYtwoQJE3D77bejs7MTN910Ez755BN86UtfwvLly3H66afj4MGDvMaqNSqVOYBeMZJIJDKsUyeoJmx4OTYq7CP7DcWNUFNhOQUGD2FTVlbG7SbhBh7hYZmzonTI2ADOx+uXsHEyLt7BYaDHzWK5v1w5GwoP9+LpSnHbbbehpaUFV199NbZs2YL77rsPY8aMwbJly3DDDTdg9erVmDNnDrZv385puPqiUpkD6Dlw2Y3CTbmjq6vLOsFUETZBcmwikYh1YfQiCFTYFh7CRvaFVtfwMPveEokEuru7C/47WcLYrbARfXw4cWx4N+djDBQg5pmx0T087EnYfPWrX8XGjRvxm9/8BmPGjMn43QMPPICf/exn2LJlC2bPno21a9d6GqjuqHTTBHo6wnqZGcX+xt5ZVjZeHRvVXDUvgkAlx8bLrCgVZkTZP99LeFhmxgZw5trIul45XS/Kr+/WSXhYhGMDFC5sKGPjUdj8/ve/x2GHHZbz9/Pnz8fSpUvR2NiI0047zctHaY9qwgbwNuWb/U1VVZXUEoEdr46Naq4aD6dDhW3xsh0qzIgC3B9bpmlKdZ1isRii0SgAZzkbmRkboPBlFfzO2MgqRQG9wiZXdIAyNr0IvyNdcskl+Nvf/paxwNZgREVh42XKt2r5GoAcGzsqOTY8BJrs7XB7bHV2diKdTme8h9+4ydnIFjaqZWzchId1c2xI2Djk1FNPxRtvvOHHRymLisKGl2OjCuTY9BIUx0YVYeP22LLfCGXlFtzMjNItPOxXH5uuri6kUqm8r/XqnOSChE3hOBI2H374oesPOvLII7m8j66oKGy8ODaquRtA5lN1oS3Z7ai2TUEQBEAwtsNtxkaFWV1eHBvVw8N+97EBBh6bbMeGwsMOhc20adNw+eWX4/3333f1YevXr8ell16K6dOnu/p7nVFZ2LhxbFS54dhh3206nXY1hT1Ijo1KxxsTim4Ep+6zolQ4T9w4NrqEh/36fouKiixhOtD3KFvYUHjYobD50Y9+hOeffx4zZszAcccdh/vuuw9vvfUWEolE1tfH43G8+eabWLRoEaZPn45Zs2bhr3/9K26//XYug9cJlW40jCDMVrFTVlZmNRr00vtFlX0UBKcD6N0O+zIPhaLKdngtRcm8UVDGxjuGYRQcIJYlbCg83IujRO8dd9yBa6+9Fvfccw+efPJJ/OAHP4BhGIhGo5gwYQKGDh2KiooKtLS04NChQ9ixYweSySRM00RVVRVuuOEGLFiwACNGjBC1Pcqi2k0T8ObYqBROZRiGYR1/LS0tqK2tdfT3KjXoA4Lj2JSWliIUCiGdTqOlpcWRza2KsCHHxh/czory40ZcXl6OlpaWAb9HGX1sUqmU1afIq7AxDIN7PshvHE9VqqmpwUMPPYR7770Xy5Ytw5///Ge88cYb2Lx5c7/Xjhw5EqeccgrOO+88XHLJJdzWjNIRlW40jKA5NgAsYUOOjTr7h/U6ampqQktLC0aNGlXw36oy3dtrxkbm+N04NrqFh/34fgsdmwzHxv4zrxmb8vJyV0vsqITrOdglJSWYN28e5s2bBwCor6/HgQMH0NzcjKqqKtTU1AxKZyYbpmkqF0wFgpexAXouxLt373YsBlTcR0GZ7g0gQ9g4QZXjzL52VyKRsHrDDIQKpSinjk08Hkc8HgdA4WE7hX6PMoQNjxXF2Xh1Dw4DnFb3BnpW8yYhk522tjYrNKmKGwB4m+6t0nRiO26frDs6OqxpnKpsk5cVvlXbP/YAsRNUETb2z29tbUV1dXVBf6fC+N26IID6woYcm8zPjMVirmffjR49GgAwduxYlyNUB2Fd8+LxuPRVhVWBXcwjkYhS5Tgv071VuGBnw63LwV4fCoWUeWJxKwbsf6PK/nEr0lQ5zqLRKIqLi9HV1eVI2KhQSnPq2LB9VFpa6ntjVVVnRQF6ODZesjFHHHEEXnjhBUyZMsX1e6iCsMYKo0aNwvz587Fp0yZRH6EN9uyGSrVLHo6N7BtOX9w6Nvap3qrso6A06APcb4sq070Bd8eWCuN3shwAIDdE78Sxsc+y8+P7LXS9KFEN+tj7iRI2AHDOOefkXSZJF4QJm7vvvhuvvPIKjjrqKJx66qlYunSpo9Vlg4RqoVQGOTa9qJavAYKXsQH0LUXZx+BkG1QYv5MFHAE1hE0hs6LsD2RDhw4VNSQLlad7i5qJpSvChM13vvMdrF+/Hm+88QYmTZqEb37zmxgzZgx+8IMfZJ1BFWRUFTbswtXW1oZkMunob1W7cTJ4ODaq4FYM2J9kVdket9uiQimH4aaXjQrjD6pjc+jQIQA9360fJbOgl6KChPAe3yeeeCIWL16MPXv24Oabb8bDDz+MI488EmeccQZeeOEF0R+vBKoLG0DvJ2k7Xh0blfYRG0t7e/uA69PYkRn+zIWb/WJfGVuF7dC1FOXUsZHpXjoRNo2NjQBQcN7JKzqEh0nY9ODL4iXvvvsubrvtNixcuBBDhgzBzTffjLq6OnzhC1/AzTff7McQpKLiTRPoSdCzk89pzka1DAfDq2OjUimq70ycQmGvjcViygT43fRMsi84qJKw0a0UFXTHxi9hU6hjI6NBHzk2mQgTNp2dnfjtb3+LE088Ecceeyzef/99/OY3v8GuXbuwaNEiPPHEE/jTn/6EX//616KGoAyqChvA3Q0nnU5bFx4Vbjh2guTYFBUVWcJEt5tpX9zsF7uYU2Gmmq6lKJ0yNkwMdHZ2Ip1O530tEzZ+5GsA5+FhytjIQ1hhcuTIkQiHw7jiiiuwePHijNW9GSeffDKGDRsmagjKoOJNkzFkyBDs3bvXkWNjP7FVunkC7h0bFcPDQM8xU19f70gQqHi8eRE2MlfGtuPFsdFxVpSM48cuYDs6OvJ+b7IcGxVLUeTYZCJM2Nx///247LLL8n7RQ4YMwccffyxqCMqg6k0TcDflm12sw+GwUn15APeOjYrhYcCdsAmaY6PKdnjJ2JBjUxj2+8VAwsbvjI3K4WHK2GQi7DHoqquuoi/536j4BM1wM+XbPiNKlZ4vjCA6NoAzQaDi8RYEYeOlFKWjYyPjXAiFQgU36fPbsSkk/5NKpazlKHjf/8ixKRyujs3pp59e8GtfeeUVnh+tNKq6AYA3x0aVG46dIDo2gN6CAHDXRVmFfIodXcPD7IbMwtjhcDjv62UH6cvKytDR0VGwsPErY1OIY2Nfs4lKUfLgKmzGjx/P8+0Cg4pP0Aw3jo0KF+tckGOjZo8hN0sqqHacOXVsuru7kUgkAKgxKwrocRsGug6pIGzq6+u1dGzsjQV5l+kpPFw4XIXN4sWLeb5dYFBZ2HhxbFTcHrsQME2z4FKZ6o6NG0Gg0ra42S+qCRunotn+OpmlqKKiIoRCIaTTabS1tQ14XMgW+YWWolTM2NizLrwD7+TYFI4vUw3a29sLru8GEZWFDXNsglKKYmNKp9MZtvBAqLqPgubYpFKpgveLCjOK7DgtRbHxFxcX+76YpB3DMBwthKmCYwOom7EppBQlwjmh8HDhCBU2S5YswaRJk1BZWYnKykpMmjRpULo6qt40AXd9bFQWNmVlZZYb4EQMyL6Y58JNNkVFx8Y+ZdupMFDlOHNailIpI+Sk8Z3sc6HQ9aJkZWw6OztzdgIXNSMKIMfGCcKEza9+9Stcc801uOiii/DMM8/gmWeewYUXXojrrrsOv/zlL0V9rJKoLGyClrExDMNVzkbVfRQUx8YwDMfbotpx5taxUcFxKtSxSaVS1mtkC5t8Isw0TWl9bIDcY5MtbChj04Mwf/Shhx7C/fffj+uuu8762ec//3lMmTIFP//5z3H99deL+milME1T2Zsm4C5jo+KN005FRQVaWloKvgGlUinrJqSaY+NlVpRqx1tlZSWampoKFtEqOR6A+4yNCuMv1LGxH2eyjp9CQ7osmO2XsCkuLkZVVRWam5uxY8cOTJ8+Peu4ALHCJpFI9JvdRo5NJsIcm+3bt+Ozn/1sv5+fc8452LFjh6iPVQ67banajQYInmMDuC8Z2P9WFYLi2ADOt0W144yNv6Ojo6BFSVUSZoU6Nuw6YF/Ow28KCQ8zt8a+3p1oDMPA1KlTAQCbNm3K+ho/hA0Aq1dO388lYdODMGEzatQo/Otf/+r38zVr1qC2tlbUxyoHu4iHQiEl1rvpS9BmRQHOSwbsdbFYLBCdlFXdP7oLG6eLkqpUiirUsZGdrwEKG6s9X+Nnk1AmbDZv3pz19yIFhl1o9i1HkWOTibBS1Lx583Ddddehvr4ep556KgBgxYoVuPPOO/Gd73xH1Mcqh70MpVqXXiDTsdF1Gm5fnDo2qk71BoLToA/QX9gUFRUhFouhu7sbra2t1rmTC5XG79Sx0UXY+FWGYhx++OEA5Dg2kUgEkUgEyWSShM0ACBM2t99+O5LJJG6++WZ0d3fDNE0UFRXhpptuwh133CHqY5VD5XwN0CtskskkOjo6CnKVVLpgZ8OtY6NavgYIzpIKgHtho4LjwaioqMDBgwcLEs0qlaKcZmxUEDb5ZkX53cOGIbMUBfSUo9ra2nIKGwoP9yCsFBUOh3HPPfegsbER77zzDt555x00NjZi4cKFA7b0DhKq3mQYZWVl1v4oNGejurAhx0bN/eN06rqK2+FENKskzILq2Pg11ZthFzamafb7vR/CBqBS1EAIb9C3evVqrFixAq+++ipWr14t+uOUQ+WbJtATiHOas1HxhmPHrWOj4j6yi7R0Oj3g61OplHVDUG17nHZRVsnxYDgRzSqNP6gZG78dmylTpsAwDDQ1NaG+vr7f70U7J7mEDYWHMxFWivrkk09w8cUX4+23385oAnfsscfi2WefHTTrSql802RUVVXh0KFDBd9wVJ11w3Dr2KhcijJNE+3t7QN+5/YnctX2j+4ZG8CdY6PC+HVybJzMivJb2JSUlGDcuHHYsWMHNm/ejJqamozf++XY9O3eTY5NJsIcm29/+9tIp9N477330NjYiMbGRrz33nswDAPXXHONqI9VDh2EjdNlFVS6YGcjSI6NvR1/IdvDXhONRqVN182FE2FjmqaSx5mTXjYqlaKC5tjIytgA+QPEMkpRyWQSyWRS6OfqhjBhs2LFCjzyyCM4+uijrZ8dffTR+MUvfoGVK1eK+ljlUPmmyXCyrIL9hqPqNgXJsbF37C1k/6i8b5wIm87OTqv0ppKw0bUU5dSxkXn8qJyxAfIHiGUIG7t7Q45ND8KETU1NTdadW1paimHDhon6WOXQQdg4cWzi8bj1dKDCBTsbQXJsAGeCQOUyoZPwsF04qPQUqmt4WEfHJt+sKFmlKKAwYSNKYGQTNvbvSbU+XLIQJmxuueUW3HLLLRk3y6amJvzHf/wHbr75ZlEfqxyq3zQBZ46N/YajwgU7G04dGxWmuObDibDRwbFxcpyVl5dbi2eqgJNjS6VSmk4ZG9VLUfma9Ml0bIqLi5XslSYDR+HhKVOm4Prrr8eNN9444Gv/+Mc/4u2330ZdXR2mTp0KwzDw4YcfIhKJoKOjA88995z12ldeecXxwHVBB2HjxLFhF+vS0lJlp+07dWxUsN/z4cTpUNmxcSPQVNsOJxkblUpROvaxUTE8DPQKm61btyKZTFoZOECusKEyVC+OhM3WrVvx7rvvWv9911134bOf/SxOPPHEfq+dMGECJkyYkPGzbIuGBR0dhI0bx0aFi3UuyLFR83hzsh0qiQI7upaidHJsnMyKkpGxqaurQ0lJCTo7O/Hxxx9jypQp1u9kChuVSraycSRs2M5k3HXXXdixY0dWYbN48WLvo+vDokWL8Oyzz+LDDz9ESUkJTjrpJPzkJz+xFLSKqH7TBJw5Nio7AoygOTZBydjYt2Og5TtUFdC6lqJ0zNgkEgkkEglEo9GM3ycSCeu7leHYhEIhTJkyBe+++y42bdqUIWxk9LEhx6Y/jorXkydPxuuvv+5oJWierFy5Etdffz3efPNNvPzyy0gmkzj77LMHPFllElTHRuXtsd98snUH7Yvq+yhojk22tW76opIosFNoKcq+jSpsg06OjX1Zl2wBYvsD2EDrdYkiV4BYhmNDzfn648ixufzyy3HrrbdiypQpuOCCCwAABw8eRHNzsy8nwosvvpjx34sXL0ZNTQ3Wrl2Lz3zmM8I/3w2q3zQBdxkbFS7WuWBjS6fTBa1/pcLFPB9ByKYAPTdXwzBgmiZaWlryXohVKuPYKdQNtAsIFbbBPtMonU5nDWSn02klHOZYLIZwOGx10e47FlaGqqqqkpbzyxUgpoyNGjgSNj/4wQ/Q1NSEhx9+GIsXL4ZhGPjzn/+M6upqjB07FjNnzrT+zZgxAxMnThQ1bgC9N6R8dmQ8Hkc8Hrf+28maOzxQvcwBBC9jU1ZWZt1AW1tbBxQ2qotPN6UoFbeF9eRpbm5Gc3Mzamtrc75W1eOs0FIUEzaqNEq0i6uOjo6sYqutrc1yOGUeP4ZhoKysDC0tLVndeJnBYYZKjg1lbPrjqBRlGAYWLlyI+vp6vPzyyzBNE+PHj8fMmTOxf/9+LF++HHfffTe++MUvYvLkyRg6dChOPfVU3HDDDViyZAnXgZumifnz5+Pkk0/GtGnTcr5u0aJFqKqqsv6NHTuW6zgGGqPKNxpG0BwbwzAKfrJOJBLWhYEcG/EUui2qbkehx5Vq47c/zecq3bMHm0gkIv3pP1+AWAVhk6v7MDk2auCqQURxcTHOOOMMAMDcuXOxdu1atLW14Z133sETTzyBm266CaeddhoikQhee+01PPzww7jqqqu4Dvw73/kO3n33XSxdujTv6xYsWGA9ITY3N2Pnzp1cx5GPeDyORCIBQG1hEzTHBij8ydp+g1J1m4Li2ACFb4vqs6IGOq5UK6WFQiHLucyVs7GXZGX3Q8kXdpbZw4bBHJt9+/ZZx3IymUR3dzcAfxv0kbDpj6dFMF955RVrDn84HMb06dMxffp0XHHFFdZrdu3ahfXr1+Odd97xNlIb3/3ud7F8+XK8+uqrqKury/vaoqIiaVaw/eKtygUuG8yxaWtr69eXoS8qz7qxU+iTNft9aWlpv9kXqhBEx2YgEa3qdrDxt7W15cyqsN8Dao2/vLwc7e3tAzo2KjiX+YSNzKnejKqqKtTW1mL//v3YvHkzjj/++IwZwxQelosnYTN37twBX1NXV4e6ujqcf/75Xj4KQE9p57vf/S6ee+45rFixQniGxyt2EaBS99S+2C9kLS0teZ+EVL3h9KVQx0aHDFSQHBuWq9m7d2/e16l6nNnH09bWlvN7VnH8Azk2KgSHGfmWVVChFAX0uDb79+/Hpk2bcPzxx/uytAE5NoWh7t02C9dffz1+97vf4amnnkJFRQX27duHffv29VvCXRVUv8kwotGo9YQxUM5G5enEdpw6NipczHMRJMdm3LhxADBgSVjV7bCvtp5PNKtWigJ6xxIUx0a2sOmbs7Hna0SV8ph4ofBwfrQSNo888giam5sxd+5cjBo1yvr3hz/8QfbQsqKLsAEKz9moesPpSxAdm0IyUKqXCll4/5NPPsn7OhWFAZAZTM93bKlYinKSsZGN6hkboP/MKD8EBjk2heGoFPXkk09yH8DMmTNxzDHHFPTaQpqtqYROwmbIkCHYu3dvwY6NShfsbDh1bFTeR2469qq6PUzY6OrYAD1jamxszHtsqTh+nRybQmZFyczYAP2FjegZUQBlbArFkbD5xje+wc1iYxfoO+64o2Bhoxs6lDkYg92xUXkfsbEN1HCQNTQD1N0/rBQ1kGOjouPBKOTYUtFxCopjo0opigmbLVu2WOcmQI6NCjgSNiLWf5o5cyb391QFHdwARqG9bHQRNkFybEpLSxEKhazOsLmEjf2Gper2MMdm9+7dSKVSOTvHqnycFXJsqSjMCnVsVDh2dBA2EydORCQSQUdHB3bv3i1d2FDGphdHwmbevHmixhFIdLhpMgp1bFTPcDCC5Niwjr1NTU1oaWnBqFGjsr6O7RtVut1mY9SoUQiHw0gmk9i/fz9Gjx6d9XU6CBtybMSRb1aUKhmbaDSKSZMmYfPmzdi0aZMvJSFybApDq/Cwbqj0BDQQTh0b1bep0EZquojPQmZG6bBvwuEwxowZAyB3Oco0TSUdD0YholnF8Q+0EKaKwqavY2OapjIZGyAzZyPbsSFh0wsJG4HoctMECnNsUqmUdfKqdMHORqFTpHXJQRWyPbq4aQMFiNlCjYBajgejkFKUio5TvvIOoNa5kGusra2tSKVSAOQ7NoAawobCw/0hYSMQnYRNIY6N/UlPpQt2Ngp1bA4ePAhAjYt5PoLi2AADT/lm28EWQ1QNXcPDOjk2uWZFMbemuLhYiRu5fZVvcmzUgYSNQHQSNoU4NuxiHYlElM1wMAp1bD766CMAwGGHHSZ8TF5wImxUF50DNemziwLZaxZlQ/c+NjpM9841VpavUaEMBWQ6NrL72FB4uBcSNgLRSdgU4tjYb5wq3nDsFHLzSSQS+PjjjwEAU6ZM8WVcbnFSilL9eBuoFKWiKLCjaylKJ8cml7BRZUYUg3Uf3rFjh+X++iFskskkkskkAHJsskHCRiC63GgAZ46NShfrXBQiBLZv345kMonS0tKcs3NUIYiOzUClKFW3w8m+UKkUlc+xMU1TSWHTd1aUasKmpqYGVVVVME0T7777LgB/hA0AxONxAJSxyQYJG4HoJGwKcWx0CacCmY5Nro7VmzdvBtDj1qi8SCkwuBwb1YVNXV0dAGDjxo05X6Oi65TPseno6LBCuSoJG9UdG8MwrHLUunXrAIgVNvYIACtHkWPTH7Wv5pqjy40GcObY6LA9bIz2jqB9YcKG2ckqEyTHhgmb/fv3W0+ddlR0O+zMmTMHhmFg06ZNWVcpT6fTSgqbfI4NO+9DoZASge1c4WHVMjZAb86moaEBgFhhEw6HEY1GAfQIG9M0KWOTBRI2AlFp+uRA2B2bXA6HLjdOoLdbL5A7Z6OjsMknPHVx1IYNG2Y9Xe7atavf71U/zoYOHYoZM2YAAF599dV+v7ffjFUSZ/kcG3vPLRXyc7o4NkCvsGGIdk7sAeJEImG1RiDHphcSNoLo7u62rEIdHA4mvpLJpPUE0BfVbzh27Ksw53I5tmzZAkD94DAQrOnehmHkLUfpcJzNnTsXALBixYp+v2PCIRQKKXWzyefYqPYQZh+r/UFLRWHT98FItHNiFzb2a7VKx5psSNgIwu4SqHyBZpSXl1sOR66cjQ43HDsDzYzS0bEJQoM+IH8vGxXLOH059dRTAQArV67s9ztVZw/aHZu+rqxKwWGgV9iYppkxtVmV5RTs9HVs/BQ2rMxuGAZisZjQz9UJEjaCYBeKsrKynAv9qYRhGAPmbHQTNvnEQEdHh+UW6CBs2L4JgmMD5O9lo8Nx9pnPfAaGYWDjxo3Yv39/xu+YMFOpDAXkFguAusIGyJwZpdJyCowpU6ZkCFgZjk1JSYlSIlo2JGwEoVNwmDHQzCgdbjh28jk2rDFfdXU1hg0b5uu43DB8+HAAPQ4Hm73SFx0dG12FTXV1NaZPnw6gv2uj6vjtYqFvzkY1YRMOh60ZQPbSmYqlqJKSEkuoA/4Jm87OTgoO54CEjSB0FDYDOTa6bVO+jI19qrcOHHPMMaisrERjYyPefvvtrK/RybHJV4pSVRj0heVscgkb1RybcDhs3RT75mxUEzZA9plRKgobILMcJcuxIXohYSMI3UQAEDzHJt+aPiw4rEMZCuhZxuL0008HALz88stZX6OTY1NIKUo1YdCXXAFilTNCuWZGqShssoWdVczYAJnXERkZGxI2mZCwEYSOwiZoGZtCHBtdhA0AnH322QCAl156KevvdXRsdC1FAcApp5wCANiwYQMOHDhg/Vzl8eeaGaWDsInH49b/VyljA5BjoxokbASho7AZTI6NjsLmrLPOAgCsWrWq3xN3KpWyLvo67B8mbJqbm/sJT5UdDzvDhw+3cjb2fjYqO04DOTYqXa/6Chvm1tgnOqiCXdj42ceGMjbZIWEjCB2FDTk2anPYYYdh4sSJSCQS/XId9huVDsdceXm59dTd17XR6TjLNu1bZWGmo2PDyi32GVGqLYFCjo1aqHV0BAgdhc1gcWwaGxut9ueTJ0/2fVxuMQwjZzmKbWM0Gs1YT0ZlcgWIdTrOsuVsVB5/LsdGtQZ9QG7HRrUyFNCzfthpp52Gk08+Wfj4SNgMDAkbQah4oRiIQmdFqXjBzkYux4YFh0ePHq1kuSAfrBzVN0Cso5DOFSBWWRj05TOf+QwA4P3337fEssqlKJ0cm76zolSdEQX0dJl+5ZVX8OqrrwrvJ0Ph4YEhYSMIHW80+Rwb0zS1CqcCuR0bHctQjNNPPx2hUAgbN27MEAQ6iQFGtgCxaZrKNrjLxogRI3D00UcD6M3ZqFyK0nlWlMrChuFHkzxybAaGhI0gdBQ2+Rybrq4uqzGcihfsbORybHQWNkOHDsUJJ5wAINO10c1NA7KXouxrA+myLSxnw8pRKotMnRwbHYWNH1B4eGBI2AhCxVkGA5HPsbG7Hjo8SQPBdGyA7OUo3dw0IHspim1HKBTS5mLdt1GfyqUonR0blTM2fkKOzcCQsBFE0BwbdrEuKytTbkZCLgZybHTpOtwXFiB++eWXkU6nAQTHsbGXoXRZ+4Y5Nu+++y4OHjyodCkqm2PT1dWF7u5uAGoKm76zosixoYzNQOhxh9IQHYVNIY6NihfrXGRzbEzT1K7rcF8+/elPo6KiAgcPHsS6desA6O3Y7Nq1yyo/6Xic1dTU4MgjjwQAvPbaa0pvQzbHxv4go5LLRKWo7JBjMzAkbASho7BhT2ttbW1IJpMZv1P5Yp0L+yKY7Ma5b98+tLW1IRQKYdKkSTKH55poNIrTTjsNQG85SkfHZsyYMTAMA/F4HPX19QD0PM6AzGnfKoefszk2TNhUVFQgHA5LGVc2dJoV5SeUsRkYEjaC0FnYAP3LNzpuDxtrOp22LFtWhpo4cSJisZi0sXmlbz8bHR2baDSKkSNHAugtR6mcT8mHPUCssjjL5tio2pqCMjbZIcdmYEjYCCCZTFo3UhUvbrmIxWLWCdI3Z6PyxToXpaWlVh6IXbx1Dw4zWID49ddfR3t7u5aODdA/QKzjcQZk5mxU3hf5HBvVhQ05Nj2QsBkYEjYC0K29vZ1cORsdbziGYWSUowD9g8OMKVOmYPz48UgkEnj11Ve1dGyA/r1sdDzOAGDkyJGYOnUqTNO0yp4quk75MjYkbPSAwsMDQ8JGAPb29rqVO3LNjNL1htN3ZpTuwWGGYRiWa/PSSy9pu3/6zoxSeUbRQLCcDYPdmFWCCRudHJuOjg6k02mrFEXChhybgSBhIwBdbzJAsBwboP/MqKCUooDMad86ZqCA4JSigExho2pbBCYWdHBs7OHhlpYWywmjjA2FhwciInsAQUTnp84gOzapVAofffQRgGAImzPOOAOGYeCDDz6wnmZ12z99HRtdjzOgN2cDqDt+XUtRrAxVWlqqzSKvomDuTFdXlyWeybHJRL1HigCg88U5yI7Njh07kEgkUFRUZN1Qdaa6uhrHH388AGDPnj0A9HNsgpKxAYBRo0ZZglnV8dvFAnNAdBI2g70MBVDGphBI2AhA54tzLsdG11KH3bFhZajJkycrWSZwAytHMXQ75lgpau/evUgkEtpO92Yw10bV8bNxJZNJq9uwqsu/MGHT1dVlrZw+2MtQAGVsCiEYV3fF0FnYBNmxCUpw2A4LEDN02z81NTWIRqNIp9PYs2ePtscZ48wzzwQAqz+PatgDzSxArHofGwDYvXs3AHJsAMrYFAIJGwHofHEOcsYmSMFhxuzZszNuAKo9dQ9EKBTKKEfpepwxvvSlL+HRRx/FQw89JHsoWbHP1GQ5G1VLUXYXgpUqSdj0CpvOzk50dXUBIMemLyRsBKCznR5kxyaIwiYWi1nLKwD67R8gM0Csc/Ae6BFq3/zmN5Xuk9S3P4yqwsYwDMuJ2LVrFwASNkCvsEmn01ZOioRNJiRsBKCrCAAGh2Oj8k3HDawcFY1GtZwxEiTHRgf6zoxSVdgAvSKMOTaUsekVNnZI2GRCwkYAOj91BtWxqa+vx44dOwAEy7EBgM997nNWSccwDNnDcYy9l42ux5lO6OLYAP2FDTk26PfwEg6HEY1GJY1GTbQTNq+++iouuOACjB49GoZh4L//+79lD6kfOl+cB3JsdMtwsH2wfv16mKaJyspK1NTUSB4VXyZPnowVK1bgL3/5i+yhuMJeitK5jKsLOjs2JGx6yp32jvYUHO6PdsKmvb0dM2bMwC9+8QvZQ8mJzsImm2Oj66KeQK8QY31eDj/8cC1djYE45ZRTcMQRR8gehiuClLHRAbtjk0gkrJk1KgsbdlyQsOnBXo6iMlR/tOs8fO655+Lcc8+VPYy8BEHYNDc3wzRNGIaR0aVUt23qO96glaGCACtFbdq0yfqZbseZTtgdG7szq6Ib23e9LcrY9FBcXGxN0ydh0x/tHBsd0NlOZ09t9ic5+6KeuoVT+16sgxYcDgLMsWFTV0OhEF2sBWJ3bNjNsbS0FJGIes+5fcss5Nj0QI5NftQ7kjkTj8cRj8et/2Ynskh0dmzKy8sRCoWQTqfR3NyM0tJSrbeHHBv1qaqqQnl5eUYZKojlQlXI5tioWIYC+js2JGx6sAsbytj0J/COzaJFi1BVVWX982ONIJ2FgGEY1kWO5Wx03p6+jg0JG/UwDMMqRwF6Hmc6YXdsdBM2VIrqgRyb/ARe2CxYsADNzc3WP5auF4nuAUh7zgbQW9j0HTOVotTE/sChYwlXJ3R1bMLhsJI5IBmQsMlP4EtRRUVFvudCdBYCAPo5NrougAn02LSstFZbW6vsBXywQ46Nf+jq2AwdOpRKlP+GhE1+tBM2bW1t+Oijj6z//vjjj7F+/XpUV1dnXBxlkUwmrRCkrhfoIDk2hmGgoqICzc3N5NYojN2x0fE40wmdHBt7foTyNb2QsMmPdsLmrbfeylgbZ/78+QCAefPmYcmSJZJG1QsTAYC+lnqQMjZAj9PU3NxM+RqFIWHjHzo7NkQPFB7Oj3bCZu7cudbCXyrCREAsFsvoDqkTQXJsgN5xk7BRFypF+YdOjo1d2JBj0ws5NvkJfHjYb3QXAUDwHJuRI0cCAKZNmyZ5JEQuyLHxD10dGxI2vZCwyY92jo3q6C4CgOA5Ng899BD+8Y9/4JxzzpE9FCIHdXV11v/X9TjTBbtjo/rEABI22SFhkx8SNpzRfao3kNuxUfXiNxDTpk0jt0ZxSkpKMGLECNTX12ubTdMFXR0bytj0Qhmb/FApijO6uxtAf8eGPdXpvE2E+rByFB1nYtEpY0OzorJDjk1+SNhwRud1ohhBy9gQenD00UcDgBJtG4KMro4NCZteSNjkh4QNZ4IgAoKWsSH04P7778f//M//4MILL5Q9lEDDHrri8TgOHjwIgISNbpCwyQ9lbDgTBBFAjg0hg+HDh5Oo8QG7WDhw4AAAPYQNZWx6oYxNfsix4UwQRAA5NgQRXIqKihAOhwHA6gmmg7Ahx6YXcmzyQ8KGM0EQAewi19railQqFYhtIgiiB8Mw+q2arbKwCYV6blPDhw+XPBp1IGGTHypFcSZI072BHtdG9+neBEFkUl5ebs12LC4uVrZLeiwWw09/+lN0dHSQsLFBwiY/JGw4EwR3IxaLoaSkBJ2dndi3bx9SqRQAvbeJIIhe7I6N6g8s3//+92UPQTlI2OSHSlGcCcJ0b6A3Z7Nz507rZ33ta4Ig9MR+fVK1DEXkhsLD+SFhw5kgODZA78Vu165dAHouhKzWTRCE3tgfUkjY6Ac5NvmhOxVngiJs+jo2um8PQRC9kGOjNyRs8kPChjNBETZ9HRvdt4cgiF5I2OgNCZv8kLDhTBBmRQHk2BBEkKFSlN6QsMkPCRvOBM2xYcJG9ZkTBEEUDjk2esOEaUlJidVskeiFpntzJJFIIB6PAwjerCjdhRpBEL2QY6M3Y8eOxU033YSxY8fKHoqSkLDhCHNrAP2FALvYBaW0RhBEL/YHL3Jj9cMwDNx///2yh6EsVIriCBM2RUVFiEajkkfjDebYMEjYEERwIMeGCDIkbDgSlHwN0P9iF4RtIgiiB8rYEEGGhA1HgiRsyLEhiOBCjg0RZEjYcCRIeZS+FzuqwxNEcCDHhggyJGw4EpR1ogBybAgiyJBjQwQZEjYcCVIpijI2BBFcyLEhggwJG44ESdiQY0MQwYUcGyLIkLDhSJCETd/VvIOwTQRB9MAeXIqLizPa8xNEEKAGfRwJkrAxDANVVVVobGwEEIxtIgiih7Fjx+JHP/oRxowZA8MwZA+HILhCwoYjQRI2AEjYEESAufvuu2UPgSCEQKUojrDp3kGYFQVk5mxoujdBEAShAyRsOBJEx4YRlG0iCIIggg0JG44ETdgwxyYWiyEWi8kdDEEQBEEUAAkbjgRN2DDHJijbQxAEQQQfEjYcCZqwYY5NULaHIAiCCD4kbDgSNGFDjg1BEAShGyRsOBI0YcMcG5oRRRAEQegCCRuOBG2694gRIwAA1dXVkkdCEARBEIVBDfo40d3dje7ubgDBcWwuuugi3HjjjfjqV78qeygEQRAEURAkbDjBylBAcIRNZWUlHnjgAdnDIAiCIIiCoVIUJ5iwKS4uRiRCepEgCIIgZEDChhNBCw4TBEEQhI6QsOEECRuCIAiCkA8JG04wYROUGVEEQRAEoSNaCptf/epXmDhxIoqLizFr1iy89tprsodkTfUmx4YgCIIg5KGdsPnDH/6AG2+8EbfddhvWrVuHU045Beeeey4++eQTqeOiUhRBEARByEc7YXP//ffjqquuwtVXX40jjzwSDz74IMaOHYtHHnlE6rhI2BAEQRCEfLQSNt3d3Vi7di3OPvvsjJ+fffbZWLVqlaRR9UDChiAIgiDko1XDlYaGBqRSKdTW1mb8vLa2Fvv27cv6N/F4HPF43PrvlpYWIWMjYUMQBEEQ8tHKsWEYhpHx36Zp9vsZY9GiRaiqqrL+jR07VsiYTNNEcXExzYoiCIIgCIloJWyGDx+OcDjcz505cOBAPxeHsWDBAjQ3N1v/du7cKWRs9957Lzo7O/HjH/9YyPsTBEEQBDEwWgmbWCyGWbNm4eWXX874+csvv4yTTjop698UFRWhsrIy459IcjlHBEEQBEGIR6uMDQDMnz8fV1xxBY4//njMnj0bjz76KD755BNcc801sodGEARBEIRktBM2X/nKV3Dw4EHcfffd2Lt3L6ZNm4a//vWvGD9+vOyhEQRBEAQhGcM0TVP2IPykpaUFVVVVaG5uFl6WIgiCIAiCD4Xev7XK2BAEQRAEQeSDhA1BEARBEIGBhA1BEARBEIGBhA1BEARBEIGBhA1BEARBEIGBhA1BEARBEIGBhA1BEARBEIGBhA1BEARBEIGBhA1BEARBEIGBhA1BEARBEIFBu7WivMJWkGhpaZE8EoIgCIIgCoXdtwdaCWrQCZvW1lYAwNixYyWPhCAIgiAIp7S2tqKqqirn7wfdIpjpdBp79uxBRUUFDMPg9r4tLS0YO3Ysdu7cGdjFNYO+jUHfPiD420jbpz9B30baPveYponW1laMHj0aoVDuJM2gc2xCoRDq6uqEvX9lZWUgD1Y7Qd/GoG8fEPxtpO3Tn6BvI22fO/I5NQwKDxMEQRAEERhI2BAEQRAEERhI2HCiqKgId9xxB4qKimQPRRhB38agbx8Q/G2k7dOfoG8jbZ94Bl14mCAIgiCI4EKODUEQBEEQgYGEDUEQBEEQgYGEDUEQBEEQgYGEzb/51a9+hYkTJ6K4uBizZs3Ca6+9lvf1K1euxKxZs1BcXIxJkybh17/+db/XPPPMMzjqqKNQVFSEo446Cs8995znz/UC72187LHHcMopp2Do0KEYOnQozjzzTKxZsybjNXfeeScMw8j4N3LkSO7bBvDfviVLlvQbu2EY6Orq8vS5XuC9jXPnzs26jeedd571GlX34d69e3HZZZdh6tSpCIVCuPHGG7O+TqXzkPf2qXYOAvy3UbXzkPf26XwOPvvsszjrrLMwYsQIVFZWYvbs2fjb3/7W73W+n4MmYT799NNmNBo1H3vsMXPDhg3mDTfcYJaVlZk7duzI+vpt27aZpaWl5g033GBu2LDBfOyxx8xoNGr+6U9/sl6zatUqMxwOmwsXLjQ3btxoLly40IxEIuabb77p+nNV28bLLrvM/OUvf2muW7fO3Lhxo3nllVeaVVVV5q5du6zX3HHHHebRRx9t7t271/p34MABLbZv8eLFZmVlZcbY9+7d6+lzVdvGgwcPZmzb+++/b4bDYXPx4sXWa1Tdhx9//LH5ve99z3ziiSfMmTNnmjfccEO/16h0HorYPpXOQVHbqNJ5KGL7dD4Hb7jhBvMnP/mJuWbNGnPz5s3mggULzGg0ar799tvWa2ScgyRsTNM84YQTzGuuuSbjZ0cccYR56623Zn39zTffbB5xxBEZP/v2t79tnnjiidZ/X3LJJeY555yT8ZrPfvaz5qWXXur6c70gYhv7kkwmzYqKCvOJJ56wfnbHHXeYM2bMcD/wAhGxfYsXLzarqqq4fq4X/NiHDzzwgFlRUWG2tbVZP1N1H9o59dRTs940VDoPRWxfX2Seg6YpZhtVOg/92Ie6noOMo446yrzrrrus/5ZxDg76UlR3dzfWrl2Ls88+O+PnZ599NlatWpX1b1avXt3v9Z/97Gfx1ltvIZFI5H0Ne083n+sWUdvYl46ODiQSCVRXV2f8fMuWLRg9ejQmTpyISy+9FNu2bfOwNf0RuX1tbW0YP3486urqcP7552PdunWePtctfu3Dxx9/HJdeeinKysoyfq7iPiwEVc5Dvz5H1jkIiN1GFc5Dvz5H53MwnU6jtbU14/iTcQ4OemHT0NCAVCqF2trajJ/X1tZi3759Wf9m3759WV+fTCbR0NCQ9zXsPd18rltEbWNfbr31VowZMwZnnnmm9bNPf/rTePLJJ/G3v/0Njz32GPbt24eTTjoJBw8e9LhVvYjaviOOOAJLlizB8uXLsXTpUhQXF2POnDnYsmWL6891ix/7cM2aNXj//fdx9dVXZ/xc1X1YCKqch359jqxzEBC3jaqch358ju7n4H333Yf29nZccskl1s9knIODbhHMXPRd6ds0zbyrf2d7fd+fF/KeTj/XCyK2kfHTn/4US5cuxYoVK1BcXGz9/Nxzz7X+//Tp0zF79mwcdthheOKJJzB//nxX2+FkvF6278QTT8SJJ55o/X7OnDk47rjj8PDDD+PnP/+568/1gsh9+Pjjj2PatGk44YQTMn6u8j7k9Z5+7UORn6PCOQjw30bVzkORn6PzObh06VLceeed+J//+R/U1NQ4fk+e3+ugd2yGDx+OcDjcTxkeOHCgn4JkjBw5MuvrI5EIhg0blvc17D3dfK5bRG0j42c/+xkWLlyIl156Ccccc0zesZSVlWH69OnW0xYPRG8fIxQK4VOf+pQ19iDtw46ODjz99NP9nhSzoco+LARVzkPRnyP7HAT8+y5lnYeiP0fnc/APf/gDrrrqKixbtizDLQTknIODXtjEYjHMmjULL7/8csbPX375ZZx00klZ/2b27Nn9Xv/SSy/h+OOPRzQazfsa9p5uPtctorYRAP7f//t/+PGPf4wXX3wRxx9//IBjicfj2LhxI0aNGuViS7IjcvvsmKaJ9evXW2MPyj4EgGXLliEej+NrX/vagGNRZR8WgirnocjPUeEcBPz7LmWdh6I/R9dzcOnSpfjGN76Bp556KmOKOkPKOegqchww2FSzxx9/3NywYYN54403mmVlZeb27dtN0zTNW2+91bziiius17NptDfddJO5YcMG8/HHH+83jfaNN94ww+Gwee+995obN24077333pxT3HJ9rurb+JOf/MSMxWLmn/70p4xpiK2trdZrvv/975srVqwwt23bZr755pvm+eefb1ZUVHDfRhHbd+edd5ovvviiuXXrVnPdunXmlVdeaUYiEfOf//xnwZ+r+jYyTj75ZPMrX/lK1s9VdR+apmmuW7fOXLdunTlr1izzsssuM9etW2d+8MEH1u9VOg9FbJ9K56CobVTpPBSxfQwdz8GnnnrKjEQi5i9/+cuM46+pqcl6jYxzkITNv/nlL39pjh8/3ozFYuZxxx1nrly50vrdvHnzzFNPPTXj9StWrDCPPfZYMxaLmRMmTDAfeeSRfu/5xz/+0Zw6daoZjUbNI444wnzmmWccfS5veG/j+PHjTQD9/t1xxx3Wa77yla+Yo0aNMqPRqDl69Gjz4osvznpSq7h9N954ozlu3DgzFouZI0aMMM8++2xz1apVjj6XNyKO002bNpkAzJdeeinrZ6q8D7Mdf+PHj894jUrnIe/tU+0cFLGNqp2HIo5RXc/BU089Nev2zZs3L+M9/T4HaXVvgiAIgiACw6DP2BAEQRAEERxI2BAEQRAEERhI2BAEQRAEERhI2BAEQRAEERhI2BAEQRAEERhI2BAEQRAEERhI2BAEQRAEERhI2BAEQRAEERhI2BAEQRAEERhI2BAEQRAEERhI2BAEQRAEERhI2BAEQRAEERhI2BAEoS2XXXYZDMPAPffc0+93r7/+OoqLi1FTU4OtW7dKGB1BEDKg1b0JgtCWjz76CEceeSQqKiqwfft2VFZWAgA2bdqEk046CV1dXVixYgU+9alPSR4pQRB+QY4NQRDaMnnyZFx55ZVobGzEQw89BADYv38/zj33XDQ3N2PZsmUkaghikEGODUEQWrNr1y5MmTIFxcXF+OCDD3DRRRfhrbfewmOPPYarr75a9vAIgvAZcmwIgtCauro6XHvttWhqasKMGTPw1ltv4Y477iBRQxCDFHJsCILQnl27dmHcuHEwTRPf+MY3sHjxYtlDIghCEuTYEAShNaZpYv78+WDPaJFIRPKICIKQCQkbgiC0Zv78+fjjH/+ICy64ADU1NViyZAm2bNkie1gEQUiChA1BENpy//3348EHH8SnP/1p/OEPf8Att9yCZDKJ22+/XfbQCIKQBGVsCILQkmXLluHSSy/FYYcdhlWrVmHEiBHo7OzEpEmTsH//fqxfvx7HHHOM7GESBOEz5NgQBKEdK1euxNe//nUMHz4cL774IkaMGAEAKCkpwa233grTNHHbbbdJHiVBEDIgx4YgCK3YsGED5syZg+7ubvzjH//ACSeckPH7rq4uTJ48Gbt378aqVaswe/ZsSSMlCEIGJGwIgiAIgggMVIoiCIIgCCIwkLAhCIIgCCIwkLAhCIIgCCIwkLAhCIIgCCIwkLAhCIIgCCIwkLAhCIIgCCIwkLAhCIIgCCIwkLAhCIIgCCIwkLAhCIIgCCIwkLAhCIIgCCIwkLAhCIIgCCIwkLAhCIIgCCIwkLAhCIIgCCIw/H//yF9TA7/jjAAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from qsppack.utils import cvx_poly_coef\n", "coef_full = cvx_poly_coef(targ, deg, opts)\n", "parity = deg % 2\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 for phase factors" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we have a suitable polynomial approximation for our desired function, we can use the Newton method to solve for phase factors. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "iter err \n", " 1 +7.6677e-01\n", " 2 +2.2044e-01\n", " 3 +4.8863e-02\n", " 4 +5.9244e-03\n", " 5 +1.6429e-04\n", " 6 +1.7844e-07\n", "Stop criteria satisfied.\n" ] } ], "source": [ "opts.update({\n", " 'maxiter': 100,\n", " 'criteria': 1e-12,\n", " 'useReal': True,\n", " 'targetPre': True,\n", " 'method': 'Newton'\n", "})\n", "\n", "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": [ "Finally, we verify the phase factors by computing and plotting the residual error." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The residual error is\n", "3.405054016525355e-13\n" ] }, { "data": { "image/png": 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", "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", "xlist1 = np.linspace(0, a - delta, 500)\n", "xlist2 = np.linspace(a + delta, 1, 500)\n", "xlist = np.concatenate((xlist1, xlist2))\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": [ "## 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": "qspy", "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": "3.13.2" } }, "nbformat": 4, "nbformat_minor": 2 }