{ "cells": [ { "cell_type": "markdown", "metadata": { "nbsphinx": "hidden" }, "source": [ "# Spectral Estimation of Random Signals\n", "\n", "*This jupyter notebook is part of a [collection of notebooks](../index.ipynb) on various topics of Digital Signal Processing. Please direct questions and suggestions to [Sascha.Spors@uni-rostock.de](mailto:Sascha.Spors@uni-rostock.de).*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction\n", "\n", "In the preceding sections various statistical measures have been introduced to characterize random processes and signals. For instance, the probability density function (PDF) $p_x(\\theta)$, the mean value $\\mu_x$, the auto-correlation function (ACF) $\\varphi_{xx}[\\kappa]$ and its Fourier transformation, the power spectral density (PSD) $\\Phi_{xx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$. For many random processes whose internal structure is known, these measures can be derived in closed-form. However, for practical random signals measures of interest have to be estimated from a limited number of samples. These estimated quantities can e.g. be used to fit a parametric model of the random process or as parameters in algorithms." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Problem Statement\n", "\n", "The estimation of the spectral properties of a random signal is of special interest for spectral analysis. The discrete Fourier transform (DFT) of a random signal is also random. It is not very well suited to gain insights into the average spectral structure of a random signal. We aim at estimating the PSD $\\hat{\\Phi}_{xx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ of a wide-sense stationary (WSS) and ergodic process from a limited number of samples. This is known as [*spectral (density) estimation*](https://en.wikipedia.org/wiki/Spectral_density_estimation). Many techniques have been developed for this purpose. They can be classified into\n", "\n", "1. non-parametric and\n", "2. parametric\n", "\n", "techniques. Non-parametric techniques estimate the PSD of the random signal without assuming any particular structure for the generating random process. In contrary, parametric techniques assume that the generating random process can be modeled by a few parameters. Their aim is to estimate these parameters in order to characterize the spectral properties of the random signal." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Evaluation\n", "\n", "Various measures have been introduced in order to evaluate the performance of a particular estimation technique. The estimate $\\hat{\\Phi}_{xx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ can be regarded as a random signal itself. The performance of an estimator is therefore evaluated in a statistical sense. For the PSD, the following metrics are of interest\n", "\n", "#### Bias\n", "\n", "The [bias of an estimator](https://en.wikipedia.org/wiki/Estimator#Bias) \n", "\n", "\\begin{equation}\n", "b_{\\hat{\\Phi}_{xx}} \n", "= E\\{ \\hat{\\Phi}_{xx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) - \\Phi_{xx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})\\}\n", "= E\\{ \\hat{\\Phi}_{xx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) \\} - \\Phi_{xx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})\n", "\\end{equation}\n", "\n", "quantifies the difference between the estimated $\\hat{\\Phi}_{xx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ and the true $\\Phi_{xx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$. An estimator is \n", "* biased if $b_{\\hat{\\Phi}_{xx}} \\neq 0$ and \n", "* bias-free if $b_{\\hat{\\Phi}_{xx}} = 0$.\n", "\n", "#### Variance\n", "\n", "The [variance of an estimator](https://en.wikipedia.org/wiki/Estimator#Variance)\n", "\n", "\\begin{equation}\n", "\\sigma^2_{\\hat{\\Phi}_{xx}} = E \\left\\{ \\left(\\hat{\\Phi}_{xx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) - E\\{ \\hat{\\Phi}_{xx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})\\} \\right)^2 \\right\\}\n", "\\end{equation}\n", "\n", "quantifies its quadratic deviation from its mean value $E\\{ \\hat{\\Phi}_{xx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})\\}$.\n", "\n", "#### Consistency\n", "\n", "A [consistent estimator](https://en.wikipedia.org/wiki/Estimator#Consistency) is an estimator for which the following conditions hold for a large number $N$ of samples:\n", "\n", "1. the estimator is unbiased\n", " $$ \\lim_{N \\to \\infty} b_{\\hat{\\Phi}_{xx}} = 0 $$\n", "\n", "2. its variance converges towards zero\n", " $$ \\lim_{N \\to \\infty} \\sigma^2_{\\hat{\\Phi}_{xx}} = 0 $$\n", " \n", "3. it converges in probability to the true $\\Phi_{xx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$\n", " $$ \\lim_{N \\to \\infty} \\Pr \\left\\{ | \\hat{\\Phi}_{xx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) - \\Phi_{xx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})| > \\alpha \\right\\} = 0$$\n", " where $\\alpha > 0$ denotes a (small) constant.\n", "\n", "The last condition ensures that a consistent estimator does not generate outliers. Consistency is a desired property of an estimator. It ensures that if the number of samples $N$ increases towards infinity, the resulting estimates converges towards the true PSD." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Example - Discrete Fourier transform of sample functions\n", "\n", "The following example computes and plots the magnitude of the discrete Fourier transform (DFT) $|X_n[\\mu]|$ of an ensemble of random signals $x_n[k]$. In the plot, each color denotes one sample function and $\\Omega[\\mu] = \\frac{2 \\pi}{N} \\mu$ where $N$ denotes the length of the sample function. The magnitude spectra are plotted as continuous signals for ease of illustration." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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IoLU+r7UutNYl8GvAayY9V2v9q1rrV2mtX7W0tDS9QwuCcOXY+NJpRoAdibFHfLmVbrEar07teEmR4Cmv/n4SeToUM0k/R6cJKgxRUTSML6vmhe6Fq3a2Ijc1ZQBBw911JIZOM8o9ukArpyzOZM6ZIFyvTLP7UgG/DnxBa/3vRm4/OvKwbwU+N60zCYIwJWyhv9NsALvXlI2OwphmhJkWKe2gDew1EmMoZuJ+RhkbUeaE4VCUVe/paoqyrMT1Ll5TptMUPdjLKTNnFKdMEK5fpumUfS3wncA3bBt/8bNKqYeVUg8BXw/8wBTPJAjCNLDxpVuJsnLySIxe1uNg4yAw3WL/OI+JvIjQDXcfiTEiyhIbXzphiArDYdF/LcrOX7Wz5VmBF5gf1WHDI08KymKnsNJpehGnTESZIFzveNO6kNb6k4CacJeMwBCEG50iN/FlqwlUw2P7Ox7Wy3rcNnsbcR5P3SkL3dCIsr3iSwVoSHoZfhVfjjpl+f44Zd5ITRlAGhdEreG/qXVRQFGg4927QGunTOJLQbhukYn+giDsP0Vqui+jCBzH1pRNdsrafpvj88d5ZvOZqR0vKRICN9hTlGVJQbNaddTPKZPUxJdBMBJfVjVlV9MpG68pg51Lyav5ZOVehf7ilAnCdY+IMkEQ9h8bX6rAR4WBHYkx2Slr+k1OzJ2YqlOWFAmRa+LLvXZftuZN92jSz9BJggoDVBRRptucst7V6xA3c8qsU9aonLJtoiw1Rfx7dV+udM1jRJQJwvWLiDJBEPafIkOXoIIQJwh3XbPUz/u0/BbH546zGq+ymWxO5XijTtnoINlR8rQgbHp4gUNc1ZQFoRGZ8bScMivKtjtlVpSVuwyxLUrNWq9yyiS+FITrFRFlgiDsP7VTFpgaLO3v2n3Z8lscnz8OTK/Yv64p80LiCWIRzER/L3CJWj5JL6NMJnRf7lNNWT3R39aUJYNxYVWJMrIMne8cmbHWSynt2LckE6dMEK5XRJQJgrD/lJkVZbZbUbs7RFle5iRFQtNvcnzOiLJpRZhxERO6IZEb7e6UJQV+6BI2vbr7UkUhKhyJLyunLNmaKDpfCKNOWbibUzay87KcUOxf1ZOBxJeCcD0jokwQhH1H56NOWYAu3R3xZTWjrOW1uKl9E5EbTd0pC9xgz5oyL3AIm/5wJEYVX1YT/Uff01Vyy7bvvoTd40sAHe8Ugyu28zLwnL3jy7KArbNXemRBEF4gIsoEQdh/UiNWVBihggCt3R2F/tU0/5bfwlEOt8/dztMb0xFlSZHUTtnuw2NL/KByyjLKdCS+rArsswH15B8ryu77yElWnuvWrxPnMZ300nZjaq0p8lFRZrsvtxX6lyOibJJTVomyY/ONvZ2yR/4I/sMroDe9bQqCIAwRUSYIwr6jE+PeqCAyhf6ls2MkRjczwqUVtAA4Pn+cpzYvHl/GvYw/ffdDDDqTY8dLoRJlgRvsuZDcC1zClk/cy9FJarovg3AoirIBzB4z3/cuUOQl937oaR7/9Ln6dX7+vp/n7R99+yWdq7D1X1V86XoOjqv2dsomDJCt4subFxp715RtPgtFAsuPXtL5BEG4uogoEwRh36kK4euastLZ4ZSNxpcAJ+ZOcK53bmz10iRWnu1w8qEVLpy+NPdpElX3ZeRFEyf6F0VJWWj80Kmdsnqif7St0H/hVvN993wtquLesObr1NYpTndOX9K58lqUGYdMKWVWLe0o9B+pKZuwammlmxD5DoutYO/4MrWf9eoTl3Q+QRCuLiLKBEHYd7QthFdhw9RgFeyoKRuNL4G62P9iQ2Qr4VKkL7yAPSmS4ZqlCU5ZtYzcC1yipkeeluRpbkZ8hKGZpp/nxv2bu8U8qXuhPlvcHYqmkxsX2Eq3yMvJi8VHKWzUWMWXYOrKti8lvxSn7GA7JPLcvePLxMasq09e9GyCIFx9RJQJgrDvVEJBhZGpwSrUju7EXm6dMn8YX8LFx2JUwiV/geuDirIgL/M9J/rniXltL3AJmz4AWeGaNUuBGShbxolxysIZaCxaUWaeN+qUrQ7WANhKty5+NivqqoXkAEHk7hweO9Z9OckpS1maCQl9Z29RVtW6rU5vcK8gCENElAmCsO8MnbIIFYTGKdsuymxM2fTNfsxbZm7Bc7yLjsWohEv+AudvVSJsr92XmV1G7gcOYct0QGZOiBOZOBbse8xi8CNoHx6PL61TprUm00b4bMQbFz3b0KEb/qgOG95Fui93d8pCzyHeS7xW8eWKxJeCcC0QUSYIwr5TizI7PLbM9e4jMaxT5jket83edtEOzEqM5S8wvtwuyrIyoyjHhUtuRZkXDp2y3Gua+DKyoiyOjVPmNaB9aCy+HFhR1st6aGUE1Xq8ftGz1fGlNx5f7qgpy0a7LyfXlC3NhISXGl+uPwPFxeNVQRCuLiLKBEHYd8ZEWeCjc73nSIyK43PHLx5f1qJsdwfozx4+y3f/xqcn3jcmyrxw7LaK0ZqysGmdMq9p4kvrlJU9G/35kRFlvQv12ZJehi71mBBbGVxclOXbui+hEmV7OWXbzl6UrPXT2ikrSk1e7CLMUivKyhw2Tl30fIIgXF1ElAmCsO9UNU/K921NWbljJEYv6+E5HoET1Lcdnz/Oc93ndl19BKM1Zbs7QJ8+ucbHH18mmyBGqgn+lVM2elvFaHwZVU6Z36xHYgDovq0R8xo2vrxQC0WtIRnkrCVr9Wte6K2xG3/4+B/yyMojdU3aaHwZRN6uC8kBym3DY9d6KVpT15TBHlP9066phwMp9heEa4CIMkEQ9p16JIbvm5qyvDROmdb1Y7pZl5bfQilV33Zi7gSlLjm1tbtrU4myYo9aqY4VMb1kZyRXTfAfFWXbp/qPFfq3hk6ZE5qJ/gC6v80py/rk/eE4j7ibjTlly/3JTpnWmn/z6X/Dex56z0ihv1vfHzRc0kGOHvnsRgv9tztly3Zw7FI7ILSvs6soS7pw0yvN9yLKBGHqiCgTBGHfqWqelO+bheR5aUTFiCPVz/r1jLKK2+duB/buwLyUmrJOnNmvO0XZpThlY/GlXXWUey1bUxaZ91iJMq8BrUMAFN1hMX/cGxdlVRfmdvp5n6RIeODCA7VDt30khtaQJUMROuaUbRuJUQ2ONTVllVO2i4BNuzD/EojmRZQJwjVARJkgCPtOHV/a3ZfAjg7MXtarOy8rbpu7DUc5e4qyS+m+rMRYd4JTVtWPVSMxYKdTVseXoYvjOvi+IvMbZiF5NRKjb+uxfFvoD+SdoSgbdDPW4jX73iPWd+m+XLNibSPZ4NyW2QQwVlMWVfsvh8Kq3ijgOOhtw2NXuua+g+2R+HK3zyrtQdCGg3dKB6YgXANElAmCsC8UZcHJzZPAUDRUNWUAulSUcb+OH3t5b6zIH4x7tRAusNxf3v06tSh7YfFlNcE/8iIiLxq7raLuvrS1XWFoui/H40sbVfq2pgwoesNZZLEVZbr0KLN5NpPNiWddjYd7J59ePQmMO2WVUzdaV6bTFBwHp9nc1Skzhf57xJdlYSLlcAYO3CGzygThGiCiTBCEfeFDT32Ib/3jbzXzuEYK/WtnqVD8zf/3PH/6Sw8CNr7cJsoAFqKFXQUMQF7VlO0RX25V8eVFnLLADcZuq6iiQj8woibw7UiMcCS+jK0o86KhU9YfWUTezVjpr6GLFrpospVOdspGRdnp9efMS26LL4GxDkydZsaFjKIJTllCM3Bphd6O+DItUrLS1qNVnZdB24iyzpnhiAxBEKaCiDJBEPaFB5cfJNc5m+kmOjMCwoiyKr5UbCwnbC6bCLOX7XTKAObCOdaT3cdHXE58OdEpK+1IDCckcq1TNmkkhho6VoGvyfxWvcsToBzYER9+A5oHQDkUo4X+vZTVwRo6b6OLFt188kT/KuJ85dIrObN5BthZUwbbRVmKCgKcKJrolB1smzOOOmWrg1W+7UPfxjs/8U7zwGpwbNAyogxgTdwyQZgmIsoEQdgXHlt7DIA4jyfXlJWKNC5qF2o3UbYQLuw5/f5ia5a01nWhf3dCoX8VVYbesNB/h1OWFniBW3eGBm5p48tgKDIHI06Z40JridwKtajt2/hyvXbKevku8eXAOGWvv/X19K3AGq8ps8JqVJRlmRG8Ubij+7IaHAvUNWWbcZd3/OU7OLl1kic3bEF/5YpV8SXA6pP0s/5Yp6cgCPuHiDJBEK46eZnzxIYpFE+KhHLEKatrygoTC2axEVO7xZfz0fylOWW7xJdJXpIVRlTsVeg/2n05ySnzR2aF+W5O5jVMfFm9n2o+mN8wX1uHKOIE5SiaswGDbsZGMhRlcdGl1DvPvBavMRPM8Nqjr8UrfVAax93plFWfG4w4ZWG0Y07ZSjfhYNsIRxNf5vzyF36MR9ce5e4Dd3Oud86IrmrvZdCGAycAGCw/xhv+4A28/WNvrx08QRD2DxFlgiBcdU5unqyFTZzHkI/El7UoU6SJJs9KiqKkl/does0dr7UQmpqy3dyai8WXVT0ZTBZlYyMxdpvonxinrCJQua0pi1C2pqyODW2zAO1D5EmC5zs02j5xL2Mz3UDnRpRpSjqVEBphLV7jQHSAO+bvoKGaaHf8fVWF/smO+NJHNaKdc8o6Q6fMdxXRTb/P41v3866veRdvvP2N9PM+nawzHl/6DZi7hTMrj7CVbvGps5/i2z/87Xxu5XMTPmFBEK4WIsoEQbjqPLr+aP19XMRoW1i+vdDfbl+i0zOu0W41ZYUujHCYQCXGil1E2ehssknx5aThsZO6L0dFma8ySjegdLxhfFntnKycsvZhiiTD9R2ils+gm5KWsXHKcvM+N5KdsexavMZitIjruBwOj5Kp8bP4oQtqZ02ZUzllIzVlWVGy3s/qmrLffvw/4s89yBuO/E+85Y63cLhlukTP9c6NxJdt8/XACc7Y7tkfec2P4ODwXX/2XfzB438wJpCfvNDlO/7TpyYKXkEQLg8RZYIgXHWqejIwrlMtyoIAx9aUFaVDlpkara3e+DLyURaiBYBd68rqmrJddl+OibI9nLKLzSkbjS8DUvtcU2emgmAYX9ZO2RJ5VuD5DlHbp98xz6niS5gsylYHqxxoHABgyT9EqpK6zgxAOYogdHeMxFD+zu7LVTujbGkm5Pnu8/zJyd8jXXstr57/xwAcaR4BrCiruy9nzNcDd3K2dx6A173kdXzgmz7Aq4+8mh//ux/nFz/7i/U1/ure+3nbqf+HZ87uPrZEEIRLQ0SZIAhXnUfXHmXG/uUe57GpKVOA69bxZVY06sd3ekYQTKwpC+cBdq0ryy8SX3YuEl8mRYLv+DjK2XOi/5hTpo17lVpRqcKQMrHPGXXKShfXM4X+6aAArYxLVlqnbILQrJwygAX/AIWT88CFB8Yes30peVXov737cqU7nFF2rmcG0ebdL6nnlB1pTRJl9s/gwB2cJcVTHkvNJeajed79unfz6iOv5i9O/cXw83vyE7zZ/RTlhS/seC+CIFweIsoEQbiqaK15bO0xvnzpywHrOuUFylW1qwSQjIiybt90KW6f6A+mpgzYdVbZxWrKKqcs9JxdRVk1CsN3fBRqp1OWFCY2tPh2jEaSmGuqKESnCbiB6bwEaB8m1wGeUxC1fCghKCLKos1sMAfsdMryMmcj2eBAZJyytjND4eR85vxnxh5nRNnOQv/t3ZejK5ZWBivmsflMLcoONg7iKGdyfHnwDs54HofDeRxl/qpwHZeb2zfTzcxj46xgec00AGTd3WfJCYJwaUxNlCmlblFK3aOU+rxS6hGl1Pfb2xeVUh9TSj1hvy5M60yCIFx9LvQvsJ6s84qlVwCmPkvnJcp2EFZOWaqHAqwSZW2/veP15iPrlMWTnbJ6IXlaTGwGqJyym+Ybk0diFEk9NFYpReRFE5yyop7mD+AVJqpMeua1nSBEJ6nZe1nRWqLQPq5T0Gj7ADSyNjpvcaBh3tN2UVa9x8opK3NNGPo7RVnkjRX6l1k1p6xBGQ8F5XAZ+agoa9eizHM8lhpLnO+fHzpl/tApO+e53OSOvCeMm9m1j33g9AZBaa6X93cfWyIIwqUxTacsB35Qa3038FrgHUqpu4F3An+ptb4T+Ev7e0EQXqQ8tm7qyV659ErAFvqqZX8hAAAgAElEQVQXJcpOk6+csrQcirJB34iHveLLWsCc/hT8/a/X91dOmdZQFjtF2ZYVL0dmo11ryqrYEkxtWZyPO2VmJMbQKfNyIyKTvu0qDUPKNAM/Gj6pfZhch3gqJapGUuRNdNFiqTUP2tkhyqqxE4uNxfq9NcMGj60/VgshME5ZFk+a6B8OGw4Yjy9XB6t4ysPVrbGF5EdaR2x82TOCzLF/LczdwhnP5+g2A3ImmKGf9ynKgnufWaWJuUYRi1MmCFfK1ESZ1vqs1vp++30H+AJwDPgW4L32Ye8F3jKtMwmCcPV5dM10Xn7ZwS8zUWAeU+YlyjWipprrlanZ+jl9W5w+Kb5s+2085dUuUvKn/5Hue/91fX8xssdxUoTZiTOUgsOz4URRFudxPQoDTBfmbsNjK/xspyjTaTYs8gczEgMfj8TEl0Azn4Uy4mA7QpWtHaKsWrFUxZd5VjLbnKHUJQ8uPzg8Y8OdMBLDdF/qJEGX5nNY7iS0Q49G4LIyWGGxsUjoeWMLyWtRlnSG0SWQo7nguhxNxj+LSjj38z6fenqVYy0j8MrB5A0FgiBcOtekpkwpdRvwFcC9wGGt9Vl71zng8C7PebtS6j6l1H3Ly9LlIwjXK4+uPcotM7fQDtpDgTPqlFXxJUMBMLB1UC1vp1OmlGI+mq8FzOpfPM6ZT/pQDmvJqnqvSR2YW3FOO/CYbfiX5JRNEmU74su0B1oT9218GYboLEf7DU6u2HlfjQUKHeASE9n4sp0fJPRcZiIPyuaOOrmqy7KKL/OsZL41Ryt1eOThe+rH+ZMK/YMA1bB7OK2QWumm9eDYlcEKBxsHCX13bCH5keYRzvfPo5OOGRxrudC/QKngaH98aGwVMa8Ntnjg9AbH52yzQyKiTBCulKmLMqVUG/hD4J9rrcf+L9amIGTihEit9a9qrV+ltX7V0tLSFE4qCMIL4bG1x7hr8S4AIi9ikA9MTZlvhFMdX6qhAKsExqT4EkyEWYmydLWPLhSkXbTWFFlJ2DIDVSfNKuvEOTORRzv06CX5jrqzpEj2FGW61Kb7cqTQX2cJnk5IeqPxZc5zHc3X/du/5vxWDEqRqyZe2a9rypr5vFkOHrgUeXNHndyk+DIMfP7pA/O84l2/PzxjNKHQ3/dxQjvI1kaYy524HhxbizLP2RFfJkXCero17LwEznTN3s2jm+ehGArAln3M/c+eI8lLbmqaz9MRUSYIV8xURZlSyscIst/RWn/Q3nxeKXXU3n8UuDDNMwmCcPXoZT1Od07zsoWXAVbg5Am61Ci7DFs5Dvg+mR4RZYlxnCbFl2BE2Xq8DlqTbeVGlCVblLkRBGHTiJ5Jq5Y6ccYRnXDnvR/j2z7/Mc789M9w5offyXM/8ANkZ87sEGWRG42Jsty6SqM1ZTpJ8XVK0h/u9IwHKWftTvKq67EgxC17+JFLqUoa2RwN36UVehR5Y2JNme/4zPhmnEg15+yWpE2jM2w+CBoeRV4O6+mqif5RtfLJiDLjlE0SZePxJcC5dMvsvbSc7ZkA42iWwObp+vbKKbvv9FmUgqXQfAbuhO0EgiBcHt60LqTMJt9fB76gtf53I3d9CPhu4Gfs1z+e1pkEQbh6/MrHn+JcbGZVjTplST6gLBRqRNQ4QUCGEWCOo4iTgkbUqEcvbGchWuCpjafQW8vkA8fM+xpskAdGUERN86Ns0lLyTpzzhkfv4a5Pf5i7gM6pJu7sLPm5czT/wVeSLCRjYjBwg3FRZhemj9aU6TgmiNK6puzJzZTDWUEQtSCFno1Jcx3gFR2UUqR+nyibodF0aQUeOm+xHo//G3R1sMpitFgvPi+yEtd38FPwCyjyDNfz6/2XaZzT8INhTVnDdEoOnbKErzlxgKIs6vVNoefuqCkDOJd3uLv5kvr2WpTlBaw8CYvHgaEoe/jsOe468rK6+9LLRZQJwpUyTafsa4HvBL5BKfVZ++uNGDH2BqXUE8Dr7e8FQXiR8ZGHz3LPM58F4GWLximL3IhB3odSobzhvwFVGJKqBp6T4jdciqScOA6jooovs6cfBm0Ei+6s1k5R7ZRNii+TjNlsQNFs881v/hkaH/sEd9zzVzizsyRPPTk2pwwqITkUZVlaibLhj8syTfBVTtLPePdfP8mjayleCbcdMQX6Ve1aoT3cwsR6sdcjyFo0A49W6KGLJpvJxlicOjo4FoaiLLDLx3s9U4MWNIxArIr9qzVL9V7RJCHNSzYHZsXSRrJBoQtbU7YzvgQ4V8Rj8eXZ3lkWwwUirWHt6fr26s/piZUVvur2RUiNPRhkw+5QQRBeGNPsvvyk1lpprb9ca/1K++sjWutVrfXrtNZ3aq1fr7Veu/irCYJwvdGJczr6NPPhPIebpl8n9EKSfIAuQfnjoiwjInBT/NClSPWu9WRgRNlmskn61HBqvN5arTsvA+uUFRPjy5xWkaCbLTLXoxPnKKUIT5wgffKpsTllMMkps/FlOB5fBm7O8uqAn/0vj3Hk4BxOqXED47hVoiwvPbxskyxL6HtbBFlk40sXXbTIdc5mr8N9HzlJUZTGzbIrlsBEp57vEAxMRNjtmkaAIDLvN4vNbLbaKauWow8GrPZ2Do6dFF8uRot4jsc5nY51X57tnuVo66j5zci4i7ZtBsj1gNceP1DPN4sKEWWCcKXIRH9BEK4KW4OM1HmWly2+rI7fIjciyWN0qcZEmRME5EQETowfehTp7vVkYOLLQhd0Tj1e36a7ayNO2d7xZaNIUc1xwRTecYLkqad2rylLOvDMJ+rXHIsvk4TALRj0Ml56uM1r7zqCzsENG/U1yqJEa4WnYtY3n2Hg9QjykEZg40u7//LR+5/j3g89zfmnN1mNV4eDY0tNmWtc38WzoqzXNY0BoY0vk0EOuW028H1UNOy+rOraqhllUImy8e5LRzkcbh7mHPlw7yXGKbtp5pgZiDtSL1aLZyfhNbcvgh0PEpW9iX92giBcOiLKBEG4KnTiBIJz3DH3svo2030ZU5bsiC8zFRE4A/zQRWdq+Jf9YOdk+GqAbPe5Z+vbys56HVcOa8rGnTKtNZ04o5ElqJZ5/areKzhxgmJ9HX9rsGN4bFIkcN9/ht/6FrKOiR9HF5IbUVbi5ZrFxWdxGw3KQuOFzfoa1VlclbG+/jSJ1yPMfBq+SzN0a1G2/LwRPINuxtpg6JRVLqDnO7g9U7fVr0SZ7TZNehk6NQ0AY05ZHI8Mjg1YiY1TttRY2tF9CXYshkMdX2qtOds7a6LNoGUGy1qanjn3wVnNYiuo48umFlEmCFeKiDJBEK6YOCvIvfMoJ+emxvH69nq8RKlQvl/fbkRZSKD6BJGLyhwzo+yZT8DPnYC1Z8ZevxJlyfmV+jbd29hZU7YtvoyzkqzQBFmM2zaCo3bKTtwBwNL5eLJTtvok6JK8Z0TTqFNWpimBr3FQPFe+HxUG6AL8Or4s6rN5pKxtnSL2ewSFR9N3aIceujDn2TxnRM3mZpe0TOvBsdXzXc9B9a0oszVlzVlz3v5WSlmJMj9A2ZEYOo4n7r080Dhgasq2idcjjYOcc906vtxINhjkA25q3WRuS4bRZKkVugw5Mm9vyIwYa+s+giBcGSLKBEG4YrbiDCc03XoHg6EoqwSO3i7KqvhS9fBDF5W5Jr48fS+UOZz/3NjrL0RmJW6xOozRdHeDwjo+VXxZbIsvq72XQRrjW6esXlB+xwkADp9Px2rKQs8KyfWTAGQ9s+dyvKYsIbBvp8g2KTzXNCC4Ie3QoxuPOmUp650zxF4PB0XTcWiOxJe9ZXPm9U3jyNWDY63AdB2NSs37GPSNKIvaPkoZUabT4VgOpzHqlBmxdrAdstxfpuk1afrNHfElwJFwgQueS2Ej5LrzsnXUDJQdccoeem4TXYQstO1rpD1KHEKVkScDBEF44YgoEwThiunEOW50Bl16hHq4lCPyIgZFjC6GQ2MBnDAgd0ICuvihi5N7Jr5ctoX8uzhlrKe4tvNQ97dq4VM5Zdk2p2zLCjAvGeDPGBeoii+9I0dQzSY3rZREI+uRqtlqlSjLB8YBGu2+1HFMpeOCvMlaYSLXUnu0Qpdekg+dMpWy3jtH7Bth09TKOmVNnNIlXzf1d1sdc3/tlFnB6ZTD+WRJzwg3x1FEM4ERZdkwvhw6ZaambDbyiHyX1cEqBxsHzfvzHOJt4vVIMEuuFKuOOcvZrhVl7UqUDcXwvc+sosuQZpRBnkKZMwjMmftbk5fGC4JwaYgoEwThiunEOU54jjI9xFY8FEYmvkwpdzhlNr7UHfzQxS18M2rhghVl6ztFmVNqvG5JcMgUo5f9DkU9PHZvp8yNjShTahhfKqXwj9/OzSvsmOif65x88zkAcruXs4ovdVmatUauvXbe4EJmCum1DoxTluR1g4Dru6z1V4g9I7oaWtEMXSgazMWH6hEfvY65TjXNvxKcKh8RZf2hOGrOBns4ZQOWO8lwmn+8UouyyJ/glNn1VucwrzXmlIXjTtmDz24QOi0yPaijy6Rhtqz0O9I8LwhXgogyQRCumK1BhnIH6LzNancoIiIvIimzHTVlBKFxylQP19d4RUDTjWDlCXP/Nqes5bdY6nk4pSI4ZgSA7ndqN8oPXZSjdtSUVVGlige4rWYtmCqc47dy84oejy/dajenea1sYN5PNdG/KqzPHevSFU3OpmYfr8YbEWXWKWvPsR6v4TXNj9ughFbgAQ6HBreac7iKgf3cqviyrinL4vps6WBY29WaDehvJkOnbLT70jployuWqgaCiYX+rukaPWdHgZzpnaHhNYxDGbTGasrWeimh26SbdWuxltkRKHFXnDJBuBJElAmCcMV04hxUhi591vsjosyNyHVhui/DoRtVhg1QDr4zQDsJfhnSTAZQZuCGY8NKwbhat/eMcAhuvRkAPejVzpjrO3i+s6P7shPn+EWOynOcVquu96q57WYWetDsj7t7ALEd65En5v1U8WW17HuAuT3Mmzyfm0L6svBoR0aUVTPT3JlF1rOt2s0Lco3rKCLf4UB8MxrNwVtmSPvmvVT1c7VTNirK+kNx1JwN6HfSke5L3whfpSiTmOVuwtKMEWnViiWgnlM2OrT2iDLv+VxhotqzXdN5qZQyYzLS4XU3+hmR06SX9urOy8LOM0u6OztnBUG4dESUCYJwxXTiDOVkoH3WeuNOGWAL/YduVFVQHqg+2jGio2lHT3D862DzOSiysWvcsmWcqvDEneY1B/2hG+U7eMEkUZbRsNP5nWZrh1NW3HYMgNbzQ4enOnNaibI4w/EUjmt+XJZWlHUdU9Q+Uy5wOjWiTGuHVmAWn1c7M725A6zlMWHLvH/PRq7t0GO+f5i01aW9EFIMYC6cw3eMo1g5ZSodirKqvg2gYePL6jwqCFBKoRoN9MB0Xy61TdNCJ+0MRZnvojVkxVCUzRUFUVlyLjPx6NneWdN5CXYkxlCUbQ4yGl7LOGU2vmTWbAXI+iLKBOFKEFEmCMIVsxVnoDKafmNclLkRaG3iy2DolBWedb1Un0IZcRNtbgIKXvrfgS5g4/TYNY5sGhERvPRLACjjfj3Ly/UdXN+hSLfXlOU0ciNqnFardrEq8luNmGg+t1rfVkWZsWOn5qfF+DJy60xt6ZiSgluC29lU5hq6dGlHZmtA7ZTNLrGuNI0goEDjWq3ZDDxm+wfptlaJmh46dsZWLFUC00mGQqyIh983ZwPKXJPY2NOxjRROGJL2B3STnKWZ4eDYJVv3FXrmx/5ohKmyHkfygnOpEVX1jDIYjsTQGq01G4OMlt+il/Xq+NKdNU5Z3h9O/hcE4fIRUSYIwhXTiXOUkzETjIuy0AtxrXk1Kspy60YFakCu7ET4jXVYvB0OGdG1vdh/aT1nq6VxDt8OgI4Hw7ERnoPnuxOdsmZhRcuEmrLk4AyxD9Gzy/Vt1R7MZO4mcEPytNixjBxgS6ck3oBjwTFSOxdXl2YGWS/Nya3o8RYOs+46zOASK3DsmduBy8xgjtXoLFHbx0l8DoTDFUuVU8aoKBsYAau15nTfOGT9rWH3JYCKImLbybl9Rpn5M6lE2chnlfY4XBScj9eI85i1eI2b2iNOmS4gT4izkjQvaQdGlJW21sybN45jORBRJghXgogyQRCumEqUNf1oh1PmWUOmGtcAkFvhEzh9cmX+Yg8212Hp5UaYwY5i/4X1jJVZhTNrYjhdaAob3e0WX27FOYuOEWGTaspSnfP8AfBPn69vq5yyZOYIhG3ytBxfRm6vuUlK6g1YVEtknok6y0LRquaUWfGlFo6y6TjM5iV9pcG6eQdwcLXLhfBZwpaPo10OeEv1dap6OTUYdj6Wsbn2359c5+c+/iQAg+5wzRKAE0XEPSPklmZClgdGcA5ryuwy81FRlnQ5kuecGyyPd17CcPVS2mXTrnuaC2bRaPqJ3TCwYAScjrcQBOGFI6JMEIQrZqMfgypoB80dNWW+1UCjc8oKW0zv6wEZRnQEmxtw6OXQPgx+c4com9nIODev0KF5HV0oiniAcky9l+c75BPiywNqKMpaoVfPKQNIioTnDircU2eGZ66cspnDEM6QpXrHMnKADR2TuH3cNGChMVufqR165KUmtuKv15pBK8VcmjJQmtKODFkszI/fC+GzuOv3m9vUUJTV8eWgi/J9CtcU8AN89tl1eo6Jc/u9fOzzVVFE2jeO2tK2vZcAoW+dstHxIWmHI6ViebDCsx2zymooyuz6q7TLhu1EnY+MUOsOjChrzCzQ1REqFqdMEK4EEWWCIFwxmzZiawcNNgYZRWlneLkhXh1fjjhlyggIXw9ItHHK/MI3okwpWLhtLL7UZUm0mbM8B12MW1QWUMQxrnWpXN8dRn6WrThjXo07ZZ1RUZYbUaaW1yi61rErzP1JewmCGfJc4fmjNWXm+ls6IfH6FLHmWNtEg7owBfwA/YF5nY4VdPNxj9iB0oq1ucx8RuuN8yQP/QoACxwcfkbVexl0cNptisAFKwgffn7LuG7AoGcduZGasrwSZTa+VKi6q3NifJl0OaI8NJqHlh8CGMaXdvUSSZfNfsarY4+Df3OMo1sn6CXGGXPDNl2aOKk4ZYJwJYgoEwThitmyBeizYROtYcOOxYi8XeJLK8o8PSDG/sVeRrB0l3nA4vExpyxfXsEp4MKcYiPbAs81TlmS4FrnZ7fuyzlta8qaTWYi45RV4yCMU2Yemz71lDlz3zhLSXMBwjZZrvDD8WXkAF0Vk7k5WVJya9MIniTLalFWOWWbpXl/B+ItBkqTD8wH0oo1PS8l8xJWg6qTc76+Ti0wu0aUlYEPtsngc89vEiszd3bQHxdlqhFRDGIcBYutgJXBCgvRQt3VOTG+THscccyfzwMXHsBRDktN69rVTlmPjUHG8czBORvwLY/8H9z7V7ezmr0E/CZ9p4mbDbs0BUG4fESUCYJwxWylRlTMRWbURTWrbLeasgwjELwyJsaMYXDLBhw04y5qp6y0A1yfN9P1V2bNsmwn8NGlIk9SPOv87BZfzmpTB1XFl6WGgY3ukiLhuQPGaUueNDVaYdcUxseNeQhnyHNnfBn5iCgr3IIszrmtYcTUhc4KLSvKBnGOUrCemYjv0GCVvtKk/QytNWG/ZM0zn9PZwMSSrWK2vk7VWaq6mzgzbXTg46Q56/2YZ1Z6oCDxwC4cGHHKIsok5kA7xHXU2OBYGHHKxuLLLkfcFlGiUX/3AIeah2oRN6wp67DZz2hqRfO4w6de8iG2VuZ4/+ovcM8HTtFjBj8fbhwQBOHyEVEmCMIV07Xx5ULTRF3VVP/QC/FrUdaoH5/j4RQpTlnQ08ZJKhs3U6YFa+97H3ruVshj6J4DIHv6MQAuzCs2kg1UEFAWiiLJhk7ZxO7LnJmy6r5s1S5WVeyfFAkX5oEgIHnSOGVhx1wzjeYgaJOV3nj3pRVlfSem9DRZUnBHY86cr7PMTGSukSQFru+wYYvhj/YuGHerhKSf4/UKLjjmwzkVmdeMitbwM0pLHFehux3cVhtCnyCH+5815zvYDukpGCRGVFaF/iqKULGZUQawOlitx2HASE3ZWHzZ4Yjf5use1vzg+we8NB2O5qjjy7TH5sCIstkDEZ899pfc+t9+kC9p38Pn//Ysy/ndBLk4ZYJwJYgoEwThiullxilbbFyaU5aXLm4RUxaKnnXKsubNdD/+cc7/xE/SeczWJtkIMztl1i+tzMJ6vI4KQxNfZhmurfdyd4kvW2UKrosKglowVXVlSZGgHYV/+60kT1mnbMsU/ceua7ovCw8/2Blf9r0Y5SmyuOCobQ5Y7VyonbI0yfF8l/XYirJklcwxrt3ysx1UoVk1eoqnIrvKKR1+RkVWmtlrvR7OzAyEIUEGDz5vOkVf//JDbOiCOLWirHLKogiVja9Yqor8Yff4sh3OcmzLCLsTvfbwviq+TLps9BKaWjE/bwR27Kzz1Qc/BAo2shNExbBTVBCEy+eiokwp9ZJL/DV7sdcSBOHGQ2tN364COtgyUddqb1JN2dApy0oXL4/RpaKfb1KqnCw8Qr5i6rm2/m58MXl2+iROWJAE1ikLI3SJmSHmD+PL0eGxWms6cU6zSHFaLZRSduckdQdmameYhSfuIK2css3nh/cFM+RlgBfujC+zIMYJHMpSg41I1zvLtRuXpEZUrcVrzLgRPjDrGrF55gkzpFU5xll6KnJI3RgnHe4HzfMSz3coOx2cdgsVhgQ5PHz2AsfmG3zJsTm6SjNIzdmGTlmIm6UszYRorVkeLE+OL/Px+JKgzbGeeY2bu8NO2dGRGB07E2123gi1TtYnbLgcuKlNJ72FRimiTBCuBO8SHvNeQANqj8do4DeB37oKZxIE4UVELy3QyvxlfbDVArqs9yY5ZcPhsVnh4BUxulD0BqsUTkLmH6BYN25V97/eR/HNPq7dgZmdPUfQLPAdn/VkHSeM0LFLkRe40eT4Ms5K8lLTzBKclhER7Wg8voyLGIUiuuNOuh/5M8pej3DjNMxAnMempkwHeP7wx181EiMLE3w79T+PCwpX0+ms0LJRZ5YWNH2HjWSDxcD8m3XJXweOcPZJI8oOuGc4X5Z0HYfE61EMhp9rkZr4s+x2cdtt3Cgi2NQ8sbzMlx47ytHZiJ7SJIWH9gOUYz4HFUX4VpRtpVtkZcbBaKdTFmfj3ZcEbZa2zPs8NNpEOTISo7dpR2LMt+E56BUxBC2Onpjj8588TDTTRxCEF85FRZnW+uuncRBBEF6cdOIMpYxTNBOaqfmVUxa6IZ7dsVg5OQBZoXDzGI1PL9mkdBIyd4l8eQ2UQqcpndWjzFfx5flVwnbJQjjPZrKJCkPKgU+RaVwrmLzAoSw0ZalxHEUnNmcK8wSnZWLVysXqjDhloRsS3nECgOSpp2isn8adOUJSJBTeDCUevjviwNmRGHkwIPKMo5QlOdozK5h6pWkUyK2oWo/XmbdO1SF/GXg555/ewm243Oae4kxR0HUcCm9A0htZAZWXeJ6NL9szuI0mQQ5nOxu87cvnODof0XfMv5fzxrBrM3UDgiJjqRXsmFEGozVlo05ZD8I2cxvmz21uLRne54XgeJB0ibvmM23NRjS8Bt08Ab/JkRNzfO4TPr38JrNr1BsKcEEQLp1LiS8XL+HX/MVeRxCEG5OtQQ62ViryIhZafu2UuY5LZIekjomyDLwipiSkX2ZoJyajSbG+QXDbbfgveQlbJwNYfwatNdlaF38uZD5aGNaUaY8i17jW+akK/qsOzC3rhgXpAKdpnbJwPL5MioTQCwnvuMP8/pH7oUgIlEdSJOSOqa3ynOFy9DJJ0I5D6RY0m3Z5eVzgugo/h9Md4/YVmYkf15I1FpqHKXA55pki/TwriQ5E3KHOMKfNubUfE/eG1ymy0sxgyzKcdhsvahJkoJyYLz02x01zDXp2VlnWHBbm95WLi2ap4dQrlsZryqruS+uUaQ1ph5KIaMuIscbySMG+UnYpeY+8b87XmPFp+216ZVo7ZQBn05ejZYCsILxgLqXQ/wxwH/CZPX49tF8HFATh+mbUKYvciMVWWDtlAI1yvBAdjChz8xitQnqOA15OlpYUa2u4i4vMfdOb6J3skz33DMXaGjor8ZdmWQgXzEiMMEBrl7xgpKbMiLNqvlfllPlJPHTKqvhyVJQ5IcEtt4Dvk37hIfs+ApIiIXNMPZU/Isp0nFB6PijF3Ix53Swt8FxFkMMTG4/TDj3r4hmnbLGxyJq3xDHnDMoxn0f7UIM7nOeZcUytneMPdooy+xPanWnjWadMuQlfdmyO+aZPFpjXSqPhv4u7NgBZCpgoyiJ/W6F/NgBdknWNwCs8hXtuuKAdMHVlaZfCzlhrzAS0/BbdMoOgxcyBCC/IOJvdRdLdQBCEF8aliLIvaK2Pa61v3+0XsHrRVxEE4YakE487ZYtNn/V+itaauJfRKMZHNgCkmcYrBmgCeo5CeQVZXFCsr+EtLjD7pjeBhs4TGdnTjwLgH15iLpwzTpkfoEuXonDGhsfCcBJ+5ZR5STysKaviy5GRGIEboHyf8LZb61llgReNO2Uqrs+uk4TcN6+zOGPuzxIjwOZo8Pj647RClzIvWMtXWYvXWIwWueAc4ijLRG3zOcwdbnCHOkPDM/VmnjcuyvKsxFF21VK7jd9oE+Qw1yo40A5RStGeNTFhGs0N/zxKK7qe7HDyPS5Kq2Ghf+ccgRWFdXyZmuL8vGMXpb/iH5CfP4/Oh1Gqccq6EJdoBWHDo+236eoc/CZKKZoHMs6md9HvrE36z0QQhEvgUkTZV1+lxwiCcAOyNcEpW+umPP3ZZX7znX9LMzOCqBJlWmuypDTdl9qn5zg4AaRJQb6+gTu/QHjiBOHxY2yeapA98SAA/rFjLEQLdU2ZLtW4KNsWX1ZOmRP3cZrG0Qo9B89Rw/gyT4g8E0GGd95JcuosoIj8FkmekGOe5zMUZWWakNvI9NC8EUNpolGey7xq8bypDiIAACAASURBVPj643jtR+nlZ3l08wvcvXg3b33pWzmvDnGovEDUMp/D0oGCBdXFd030GDkDkn5uujkxosytRFmrTWCdsqVZXZ9lbtHGp+FQlG2V5nPonO6jN31minlmg1nonIdf+FKcx/+UwHWGTllqR5LYerLmq18FRUF2briknbCNTrq4WQmhg3IU7aBNlwIC60IecuiWh1g/u77Hfy2CIOzFRUWZ1joGUEo9rJT6HaXUDyul/pFS6mal1I+OPkYQhC8+tkacstANWWz5rPVT1s/1KbKSZm4Gl1airMhLyhIzp0y79JXCjTyyJKdYX8ddNCJl7htfR7wW0Pvk3wDgv+R25sN5NtNNCHzKwsw7G070N0Ipr+NLu6h7MKidMqUU7cgbiy8D18Sq4Z13kq12KaKbCLzQxJfKCI5xpywltbni/KyJN7MMHN9hloiTWyfZmnsPbunyZUfu5n1veh/H2sc4w0EWilUaLXPOo42zADj+YQCaXg80pHZnZpGVuBiB6c60ybyAIIP59rBA//BiE8qM1B9OJFq3TtnWsqkPO+reglLKbkjI4NzDhJ4zrClLTP1YttEHpWh+5Vea3z///PAPOWhRxB2apcJpGJew7bfpoSEwbuHszSaGPX9qpIVUEITL4nKGx/5D4NeAAfA24HPAG/fjUIIgvHjoxBmojMAJcB2XxVZInJV0No0oCAtT71TVlKW2LsnLY1J8SqXwGxHZIIeiwFs0eyRnv/XbAdj8+IM4fol7+DYWogVKXZL7DrqAQru1U+ba+HJ7TZnu93Bbw0n5rWAoyqruS4DwpS+1tx0lcm18iXGiPD2cv6WThNQ1EeBC2zhUWeqgfI8F1eKlCy/lpvyfEBQHuHnumBFEwLN6CQdNFOaETY+FzIz7yL1jALSVmUNRdTjmWYFTWrev3WY5VbgaZoJhvd5N8xEq75F4w/e3nitK5bKxbt7jIexi8c5Z+4CThL6zI77M1np4hw4R3Hqr+f2YKJuhjP9/9t48yLLsru/8nLvft7+XW2XW0tXd6m6pW0ICJAtGMJZs5GBxmMUGzMCMIOyxDQO2B8cw2EMwHpgYHHZ4MA6CLQxmCQbbYzMYDB4PRiOJGQRjIaGttXRXL7VXbi/ffrdzz/xxzrv3ZVVmdlWBNjifiIqufHnfvefelPJ96/v9nd9vSkMJ/IYWZU2/wVQAvhau/Yt9PLHg4Fbt5FkslgfjvkWZUupQKfUupdQ/VUq9A3gT8Pz9vl8I8TNCiF0hxEdWXvv7QogbQog/MH+syLNYPscYLwpcNyc0bRDWmlp8jY+0KPPNkO2lU5YZB8uVCamJ2vxmgzw1rlBfizL/0mM0zimUVPhNCZ1tuiamy1yFKkqk8nEdLcLujS8LfFXo3Ysroqwdecf6lFWi7Ak9dzOdtwndkEQm5GVk7qHuv6XSlNT85hy09b1lhRZlcenxb/7Cv+ER/+04Jbgr45leLnRd1+tfn/Kl3/gk/vCTzFVI5pwDoKd0jLisK5N5iVPqdTrtNrcTfZ+NlWBiuxvj5jNSt76/g1wwb2yhjBE2UGbEkhkfxfAlQs9diS+NU7Y/xt/exj93DoQ4LsrCFiqb0FDQ2n2JG//d99ByI2bCqeLLqNNny3+O4d5K41mLxfJA3LcoE0I8ufq1Uuo54PMe4Fo/C3z5Ca//sFLqDebPbzzA+SwWy2cBkyQn8CWxq+OrvhFlU9NewS21yFqKsjwxTplMqtgtiHyKXKEQuP26vUPn8/SuQb9ZQHuHfqjPlboKmStKfFxTz3ZSfLlmZksua8pAF/uf5JTd8GKEW5IeuYRuSCYzCqXvxaMetF1mKakLKJdW1MRxBHnh6iHpptt/K/RwSqpoFeBlqe9rp32dp958DrH/SV4SOzR5grd4fZ4odYF8JcqKEkfWczuvzfR9lXnt2m33ItxiRuLU97eXwbR1vn6Gsi7yB2D4so4vl6IsNTVle4f4OzuIIMDb2ronvhTZjEYpaOy+xPTd76YpfKaOQPlaEDbbfbb9jzGZNCrhbbFYHowHiS9/UghxVQjxXiHETwohfg74iBCi8YrvBJRS7wHsthyL5Y8Zk6TA84rKKRsYUbaM4YS6yykzNVOeI8k3XgdAFOv3SDeonDKA9ptfg3AUQUs7ZT3T+iFxJNLs6vTQQqjafZktd1/mbJimr6tOWTP0jvUpW9aU/dC/+E3CbkGym1ROWVGYejVZizKVpCSuwhcNHMfBj1zywkUEHqVpLNuKPFylqkhVKcULWQ+FgKOr+kR7n+Sac5Gy6PITg/+MNanbV6RGlBVZLcrcVourU30v2azuIbbdjfCyCZmoR1jtZjBtnsdxFIXIaeam3mwpyqa3absZaV7Hl0pBsXuAv7MN6E0V+fXr1TkJWpRpQYAgGN6iHI/pzSRKCBau/rk245CefwUQ3HlxdSSAxWK5Xx4kvnybUuoS8I3Av0NHlzHwB0KIj/8h1vCdQogPmXizf9pBQoi/JoR4nxDifXt7e3+Iy1kslj9KxkmO5xbVLsalKMuW3elVn1KA8MygbuOi+EKSJzoWrEVZWNWUAXgXnuSRL9tn7fVA2K6csoVTUGKaxpqdkcvaMpnX8WXllK2IslbkHRtIHrkRslSo4UuE3YL0+kHllOXGdfNlLTJ0TVlJuOxhFrnkhY8IAlSiRVnTd3EQuvkrkMmSVHnMgg0YXdPF9ePr3PAvaYEYNImk3u2YzOpCf1GkiChiIuH6Qq8lW6yKshg/n1A4EbIoyWWpRVnrPK1GwSIYE2b63svDG1x914DkyOOic3AsvpSJg8pzvO2lKNshu7nqlLXICi26A7Nbc3Bbr2NqNj20Qo/YvwGU3LpiG8haLA/DgzhlACilriqlfk0p9YNKqb+klHoSeONDXv/HgceBNwC3gH98xnV/Sin1RqXUGzc2Nh7ychaL5Y+aSVLguDmRuyLKFJQmplSiR1GXVpEt40uvRCZ6p14j1u+VbnjMKWPwKPEgx9s0dVehdsrmTk7paIfGVfocfjVzsi70HwhTk7USX7bDuqZs6ZTdPFqwXd4m7ObI4YjOQs++XNanebIWGWWaknqKhqt3HfqhS176uqHtMr40LTOW3V8X5jyzeFs7ZfufBOBO+AizTLeVCJkihI4vS1nqcVF5itNq8dEbYzJzv0VS17d1Io8w14JxMck4mGakbsC0uUMjmjL3J3iJfrbptdvMbkdMrsVc4E5d6J9Oyed6vf6O3hTgnz9PcfsOKjd908IWC1MbGORalHVu6WcydfR7Q88hdQSt8IDbV2wDWYvlYbifMUvvv4/zvOdhLq6UuqOUkkqpEr2z8089zHksFstnjkmS4zi1U9aJPGJHgFSEDY9StMlWG8ea+DJwoUiNKGtoF6aIOvzFf/5+juZmh+HgUf3ftnZwYi8mcAJmIqM0w8C9Up+jdsrqmrIeZvfiGfFl6Ia8sD/jothDmHZf67cWevdlVgIlbl6LsiJJyb2SlhkyHoQuWRnpeZyZXnfTiDJpxiAtjHu3aJ43ouw5AA6jR4xT1kIIRRi7JLO8qotzsgVuq8VHboxITUxYLGpRJoQgzrQom48z9iYpjhOQhT1895CFPwEjuOSB7vGdDH121J1jTlm+0M9/KcqCCxegLMnvmF5lQZNFqR9O6JcI36dx24gyUa9lLpoMope5/cKYUq4MPLdYLPfF/ThlrzHx4ml/Pgysv+JZTkAIsb3y5dei22xYLJbPIZazL5dOmRCCc5GOI9cv6ohvHtXuVxVf+iATHT22zGzKfb/NB64e8ck7JqLrG1HWOV+duxf1mFKLMrfUhe91R//l7MucrqoL5Ze0Qo9ZJpGlIi307MsX96ZcErvsdrQbtHZzqvuUpRLfyRHZSqF/mpL7krYRZX4AuYoRYVQ5ZQ3jkC3L3efGKcta52F8A/Y+BsJl0jTxpWkrETUcklmONIJJpHOcVosP3xjR6eh7UGlCUdaF9LFxruajjL1pQhstsFy1y9yfUMyBfEEx0s86GQZsl3fqPmXZlDzVNWn+dl1TBpBfNxFm0GJuRFn78jn8Ry4R3tRNYqeiboExd1qs+8+Rp5KDG/WGBIvFcn9493HMq+/jGPlKBwghfgl4K7AuhLgO/I/AW4UQbwAU8BLw1+/jWhaL5bOISZLTE3nllAFs+j4g2bjU5sYnhsxj3V/MEQ5ZInFcgRu4lYi5fqRFxjzWH/yHM/06jQFc/CJ4pB4a0g/7jEVSx5emXYXrOSDqQv9JUtBWJr68S5QBTNOcrNS7L1/cn/FGsc/NcJ1z7ZTejTHpxdTMtJRV2wjQNWW5L+mZ9hy+DwsV4YQhSInKcyIjyjKMU2ZEWdG6AGUBL7wbBo8RhRGzbKHHGAFRrDdILN0+kS5wjFP2lm0tbIMcZvmsag/SSHVUOB9n7IUFPYwrWVxnEXfI9iTl6BZFYoTiwmFrco2ktRJfLgKcZgOnberklqLsRi3KFlJfr/PEI6i2Q/aR3wfQDWQNqdvikvcsALeujNi41MZisdw/9yPKfgD4r5VS2SseeQZKqW864eWf/sOc02KxfGYpZMksk3TIKqcMYM330KJM110lUZ9UpsReTL4oCCIPNwgojdj5X/6vK/xlQja2dXf71YHm/JX/cOyavajHWN2qRZnU5xBC4HkORV6ilGKSFLSEFnfHWmKYoeRHJgZcxpd9MeXj4hKDi03a13cpVUmWFviurNpGgCn09wvWYlNjFSgyFSNi7TaVaVY5Zbk6Hl/K7kV9kpsfgFd/Fc3QY57KSpSFoWI+L6r4UiymlOtNXtif8V++VrfUCIrjoixOtGM1PkrYa0jWSxc/n6CSQ/Kej1KQ7N6mWNSFfb3d26ThilM2d3U7DNPo1t/aAsepRVnYYpr2cWVK85knySIX3vlOnFIwVfW/yXOvxZr8EH7kMtqrY1aLxXJ/3E98eQ14rxDi8uqLQojPE0L8zKdiURaL5XODZb+vkrRqiQHQM6Jk42IbVEkaDEgKHZ9liSSIXUQYki9SKENaLVPT1NPC43B6+r8Be2GPEYu6pqyoBZMbOMhMssh1PNmUJ8eXAIdzHa+FbsgLezMGzowj1WS8fYnm9UNQiizN8byyGkWklELkGbkH6w0tyny/JC9jRKhFmcpSQqHvPzUu0jK+FL1LZhUK1p+kueyZtnTKQnnMKSOZMhY6Cn7VBd1vLChgshKn+kVCWWYc7i/Ym6ScUy7t5A5luqCM9f3Pd3cpEgdvU1eaBHuTlZYYU/KpwNupq0nqXmWmLUbQZJr28LMJ0atfTXD5UZAlG0cwU/UQ9dxvEZczoqZPOrO9yiyWB+V+Zl9+Hzpq/I9CiK8SQnyNEOJdwD8H3vWpXZ7FYvlsZjlfslDHnbK2ESXNXogvJ2ShdspA15T5kYcIApJZAmXIj71Db+BWcYdW6HE4P12UDaIBh3K84pTVRfie71LkZbWuWKbgOIioXttSlA2NU+bgszeaEKsFR7TZWz+PN09ZG0OWFngedXyZ5wilyD3BVstMHnAluYpwjFOm0pTQFL8npRZXy/jS6V+sb2T9SZqBR1qUFKbxbhTmxwr9xXzGvtL3+dQjRlAZpwxAlSVCSmSZcjRM2JskDApBO9tDpSmiYa5/OKJYuASXLxNs9SgOoSnN4PB0SjEpq3qyJf75HbIqvmyzKLr4+YTwsccIHtW1fjuHiklZ/6xk0CEgJ2q4JPMci8XyYNxvS4z3AP8n8GvATwDfr5T6QqXUz3/KVmaxWD7rGZv5kkWZHqspayhBgcLxHYLikDzorzhlBUGknTI3LwjcmAtdLZTKqMWgGXA4O12UbTe3GbNSU5avijLHiDK9rihPcZrNKpYDHV/6Cl7432/TXWwwWUBXmVFDfperPb0D8dKeIk8LfB8dXypV7a7MPNhsmhovXyIJUMbtKpOEYOmUyWV8aURiow1N09Jn40maoY4UF6b5a+Rn5KmsNkOI+ZibucNON2JtYHZ75jDNjXNnWlbIMmU2ypjuJ3gK2nKIWiQsR2LOD6cUiYu3tU30xKMkQ5/NQjeTLWdT5ELib+8ce87B+fPkN27qL8IWC9XFEwkiCAgevQzAI/uKWVGPfSoDXUMWRnUTXIvFcv/cT0uMHwM+DEyB1wDvBP7m/Xbyt1gsf3wZLwpAUlIec8oiCXOhGC1yovyQwu+TSCPKFpIg9nDCALeQhE4TNRoiSokMYvr3IcoyD2QVX66IssChyCRjI2rCPDlWTwbaKTtXOKRXcy6MnuJopugKI3LiPs/HWjRd3EcX+gcCULrzvdmYkLt1zzTfNcI01PVzKsuWpfYsjFO2jC8bgQvLujITXwLMzDinyNPPaGbmhjpFxrVU8Nrz3crtCwqYGudOGZGYq5xsmiOH+uuOGCGyHL+lxehslGhRtrlB9NrXkc88LidXUUqRH+pzLdthLPHPX6C4cweVZSQiInE6+L4ZadXv4zZ8Lh6qSiDqG9DCMQpV1QTXYrHcP/fjlH0QeLVS6nuVUp9QSv0XwHuB3717HqbFYvmTxSTJwTGu1IpT5hWKhQOH05QoO6DwBixy3U9MO2UeIgjxpKThtpFHR7gypfRj1poBB2fUlJ1rniP3QFVO2bD6nuu7yJX4MsiSY/VkoEVZr9RipZn22J+U9NDCwm0OuFZ4yPUel3YVRVZWrTbIprUo86CzbIlhRJn0jChLUzz0+efyeHwZ+S6sPQ69SxC2tUgD5soMRff0M6pEWZlzLXN53fkuItDCLShqIbQUZaXIKRcSfyJRQNudQZoRxyGu7zA/KlASvI0Noi/4IgBeM3qZtCjJhzrG9Xfuji/PV73KhndG5F6bsFG7X8F6zM5hHaUCOJHefBAEOamNLy2WB+YVd18qpX7yhNf+sRDiA8BvAK/6VCzMYrF89jNJCoQZCL7qlDlpyVwohtM5UTYEJ2A2TWHLFPpHLioI8IuSlt9BHg5xZYp0egyaAR+7dfrsxO3mNrlL3acsq0XZ3fGll54tytpZn/1JyeVGChKC9hq711Pko+e5ePWIm1mJH3qwANIpZaJFVOZBJzSizMmAgMKvRVlp+ozNTNf8xapT9vYfgGRUrQVgUobmGWqBMxsuh7nnzL2Q113oIoRAhCFBkdU1ZUaUuR44UrGRgeh4+DMPd1zQClo02gGzqcMaWpSFr3sDAJePbpMWJeUoB6ITasrqthgHN8Yox6PRqd2vYC1g85Mcc8oc09LEdVKSmas3RqxExxaL5WzuJ768dNIf9OzLb1t5rfOpX67FYvlsYpzk4GhhsOqUlYlkIRTDyZw4NU1GD3Q0t2yJkTkegSzphB3kkRZlhfC1UzbLUErde0FgPV6n9L26piw7qL63jC+XTpmbLO6JL5sroqyV9rkzkjze0iIu7qyzP01Rj17i/D7IrMQLzL9d0zHKDBzPPOgGxhVy9WuF1zD3nla7J2dGnC1yiecIfNeBzg5svgaAhjn3rHDA8YmE3lU5XXHKZn7E687ra4koJCzEPU6Zbx79+cIhWosQcYSTGVHWDZgnWvR56xt4/T5Oy2HtaESazMmngCPwNjePPSf/Qi3Kxs9e0c+rv+KU9VzaM8gntYD2GkaUiQWqVOTJK7awtFgsK9xPn7KfQzd3PemfO8vXFfCzgC38t1j+BKGdMlO/tdISo5gXzB0YzWb0kkMAZkcZUpYUeUkQuyyEi19AP+ohbx/iSkmBy6AZkBW6/9nSSVrFdVx6nY2VmrIxFBl4gdl9mTJemPFKyRxnfXDs/YHn0FdmiHba59bREZd6KYyg3d+gKK+SXrpIR4LMFH5kKsSyKSo1I4s8H9+MPfKFFpvSNR33s5RCaTE2NU7ZPJPEwcoAUEPdyLaAoFGJsjq+LGj0OqyZliFOGNGQCQfZ8UL/uOlSZuAj6G43EdcjvKyk5beImy5HUhfge2ZusDjXJrx9RD4fI+YuXr9VDYxfsuxVll2/TvryAXhP0W3UUaXRpES3Duv3mM0PjpgCTZJZThDfz8eMxWKB+4sv3/bpWIjFYvncY5LkhIEWHrFp61DkkiIrmUeK8WROlOoP7WQkK+fEjzwmpaQjYT3qUhwOccuIohD0m7p26nCanSjKAAadrdopI4d0DN46bhVfFjgCWCzuiS8BetLUlGVdJrMRO5sJCJd+fw24ynT7Em0ESgq8yIjNdEqZGkvKr903X+g6sMLR31NpSiHMVAGz63KRSWL/XlHWMLsv55mEoEWE7s5fi7KM8+c3quNFFBGX3j1OWavtMzYp7ualNuqDHkGhaPpNGnHOLfSmBG9Tn6u8uIN6fkS+dx0xc/HXe/esTfg+3rkt8hs3kLsL2IGOUw8aD0yU2V6JmkPTJsRVE2CLdG6L/S2WB+F+W2JYLBbLPYwXBY1QC62lU7aYaPdG+YLxbE6YzkDlpEeyHkYeeYxKfdxW2EYOh3hOSZ5J1owoO1iOWjqBje4OpePjIBFCVTVanmkeO0lyWqFHOZvhNI/Hl8ksJ1SCeZzi4NIoQjbcGcR9NjtaWB2ub1MY0efFRoilE9KZdsWcoD5nYERZLvRxy/hSAdPMiLJcVkX9qxxzyvwGXjnG9RzmY9P0tix49JGt6ngnDImlc09NWW8QVMdcerSLDD2CHFp+i0awIBVtCMNKoBaPP6Hf//736G7+m9pNPJpn/PL7r1fRcbBznvT551FT/bNou3VUHDR0a9zenbpzf9wy8WU5qp61xWK5f6wos1gsD80kzWlE+gN8WeifTPUHsdvwmM7niFKhyiH5SBf5AwSxy8gM1d4JO8jhIb4HeSIZGFE2PKOB7Fb3PKXj4Yhl53sjylaax7YjX4uyxnGnbLSnRdR+Rzs8HRnQE1NoDNhs63s4KiNurel1+EtRlk2YTMzw86hVnc9HvyZNIwyVpXrUkwPTbDW+vNf1q3ZfZrqrv8hnhE2PZTmdUxY89VgtykQUEUmnaomx7Ju2sd6kRJGiuHC+Te4JggJdU+ZOQDiUWxeqovv8NZ+vT/iR92tRdk7Xk/3y+2/w3f/qg1zZ0/fkX7hA+uzHyH0dfzbZr9bilHMWPY+1/br+rx2HTFSMV2rbzooyi+XBsKLMYrE8NJOkIFrGl56OLxcTLRSCps9kvoBSoNQQOXGqpqjaKdPHnQtaFIdDfF+Qp5K1pnbczmyL0dqmcLVTBqyIMh1fjpOCbiBQaXqPUzY2ouxOUwuHThnSkBPjlOlrj2aKG+umOH65USCdMhtrsRLF9aDtpSjLTSSq0hSZSZQjqjFUSS6J/Xt/3S4L/afL+ZfZnKi57HJWIlA886p6V6QT3l3or0XPer/FQsAoAM9zyAOH0DhlsdD3KdfraQLlxdfixRL5kSugRLXzcneiHbGP3tTPc7kDMwtauGKOu9qTLJ+RrYdsH5QsCv1MW5HHhBhf6sjaxpcWy4NhRZnFYnloxoucMNBuVeia+NI4Zc12wGy+QJVQckQ5dY/Hl2ZmYt9pIIdD/MgjTyWDlqkpe4UGsoXrITAf+kaUuYGj+5QtMtYdva67a8qWTtn1eA+Ai0EDJxlC3CfyXTqRx3CquG0iQddzQTiQTphPdVQXNesaLK+cISgrUVamGUVRgluLsnlWVAJsFdcRxL7LfDn/MptWokwoSeKFrHdrUSmiiLAQ98SX64MWHw4Kbq/pa2QeeCU0RURD3QGgWDtfn6e7TdAvyK8ZR2xHf2/fxJTP3tQu4lKUJVEPx03qcVMA2Zxis8nOYd3Mthl6TFSDQGpHzTplFsuDYUWZxWJ5aCZJQehr4bFsibGML1vdgPligSoFpRjCzKtG7wSxyxgtAJoEyMND/NgnzyQNzyFwnfsQZT5CHRdlnnGjZouCgWlqe3dLjNH+giIQjJ0pqTvnnBfCQosygM1OxMGk5NaaFplq7zYELcimzKda0LVbtSgTMsF3UgqjP1SSUGQlwhPM0gKlFIu81I1jT6AZeswyXVNGXjtlqiwoouNrF1GIX6hqIPly92XUiPjwmiC9pN3K1Oi/pgpoFHp+Zd6qNwyEvkfSCzDz0vHOaxdtKco+epcomzXWcdysGsyOLECmcK5DlMP05sv6eoHHhAZBcYQXOHbUksXygFhRZrFYHppxUuB7plu9qSlbTDKEI+h3QxbzuY4vxQiB4PC2dpqCyGOijCgrXORoRNDQIkEW6hXnX55rnkO6HmopylItIjwjfOaLgh5GlN3llI33FsiGSypTpuERfVwjynSx+2Y7ZG9asD/QgkjdeBnCNqRT5jMthnqdtfqE+QLf0TMrRRiishRZlDiuQy4VaVGyyIoTC/0BmqHLLJVG+M2ImkZRlQW0WseOdcIIP1f3OGXCD/jLb7rEV75Wx5CJp9VWs/SIFi/pZRrRCRB6Lge9bvW1f+kxYFWUjVBK1U5Z0MHxc+2UKQXm+t62fg7zF54HtPM3Fw28fELU9ElsfGmxPBBWlFkslodmnOR43nGnbDHNiVo+/VaIm+sPeeVq0XR408RlkcvUOGXsH4JSBC39/iwpXlGUtYIWpRtAmetocWX3JcBomrLpnx5firZPUqRM/CPivNRiY+mUtUN2Jwnpcqfiyy9owZSOmU/1faz31+sTFgmBm5ElWpSVaYbMS5yla5cWzLOTd1+Cdpdmpk8Z2YyopZ0yp8wJOu1jx4ooxMtLEpmQl3ktyoKA7/2KV/MNb9KOV+KaCQLSQ+xdxZEZmV+fK/QcrvbO6ev4Je5AbybYn2R4jmA4z7k5SvC3z9H9i19H7jVwghJQkM8h0+I6vKDfl77wYnXuPA2Z/R9jvGJunTKL5QGxosxisTwUaSHJihLPzH6sasomGXHLZ70VEiotGpSnHabDm1MQ4IcuUzMJoLija56Cjnam8lSy1tJd/c9CuQGUGUTde+JLmSvWHS1M3BVRVmSS2VGK1/HBKZgGE8TcbBaIdSS52YnYHadE6PXIK5+EUMeXyVyLssExp2yO7xbGKQt0n7Jc4np6LdO0YJHLM+JLyhpRigAAIABJREFUV8eXQROyGWGzFmXN/vFBKU4Y4S53dOZzVL4UZf6x4+auFspx4SAP9gmyMamIq++HvsPz0Q5uKPGbEryQslTsT1PeeFmL04/eGCFcl60f+EF85VINbMhm+g/Q2Noh8aF8+Zp+VqMRa+/apRiCn06rmrJP3J7wzo/fOfH+LRZLjRVlFovloViOMnLcgsiNqnYLyTQnbvtsdyNCs8OSQDsr4/2EINItH+aOGbt0+zYAYU+LpzyV9BtnO2UAygl0XVPYqQv9jfDxgIGj1ydWasrG+4m5VogQOdNgTJGU5Co45pSlRUmkjCh78XlKtwnplCyZkrnQierojzzB9wrytMAJQlSaIPN6kPk0LVic5ZSFno4v/SaUOVGkn6NX5kQrESPoQn/HNKSdZJPKKXOC4Nhxc+OUOfMpxTghyMYkZb3RIPRcrrFF99EF7UcUCMFokVOUii99YgMh6rqyZc80LzbrTydVfNlq9Lk1AK7dpEwSrn3Hf0MwzhBeiS/n1e7L//nXn+V7/vWHTrx/i8VSY0WZxWJ5KJajjISTH5t7uZjmxK2Ac92IuFyKBkUR6LgyiFzGSU5uvi5uGVHW1/FanspXjC8BlOsjZHrcKTNCyFPQN+OfVp2y0b4u1G8OIhAFU18Xrk/lOjR0TdlGWzt+fqnvyc3mpEMX0gkynZH59dxLfQMLfF/q+DKK9O7LvMQ3rt3RXIudkzr6g4kvl04ZEJpmvL7McFrHo1cnCnHSHJSuK1sW+gv/uFM2M5sc1PAmxcIhyCckaf3rPvQcrqpNtt4wZuPN+j6X9WQX+jGPrTcrUXZwoJ9ZsKx1y2ZVfNmK+twaCPyrd7jx3X+Hxfvfz9W3fR5hp8DLpyTTnHlW8HsvHHIwyyhkeeIzsFgsGivKLBbLQ7F0yhB5FV1CHV/udGPCcikaAtJIC6Ag9jiYZeS+Fl25iS/DNS10dK+ygGlakBZnDLR2fESZM4vakCwL/Y0oQ9BR9xb6L3uUdTYicHLSSIuLqdxYccq0SInSNooSVy5I9nTdWZkuyF3ohCuxYp7ge+Wx+FLmJb4ZobRnen+dNPsSloX+pqYM+IMb+nn4MsVt3VVTFkbmezDNp8dqylaZCv16ObxFkbgE+YTFrH6WoedwTZndmEYM7hlRttEKeWany7OmV9lSlEWdZRPdaeWUNaMBNwcQ7o2YvvOdbH3f/8Dha57ADUq8ZEwyz/md5/fJZIlSZ7c5sVgsVpRZLJaHZCnKlMirxrFSlqTzgqgdEAcuXbMz0w0CFpGuKwsil+EsW3HKbgEQmvmLeVL3KhueUSiunABX5twO4hWnzMSXClrSzI9ciS9HewuCyKXdDRGiIG/oYyZyfaUlhhaYvfE5ks4Yv90kuZVAOkHkCbkHnWBFlBUJga/Ik2V8mVJkJeF9irJG4DFfxpfAr3zA7GQsUpy7dl+KUD+XINe9wcosAyHgrmHiY1Ovp0a7FAuXyM1ZzHJK41QJIci9FnOvq+vlgH3TrHejHfLa8x1ujhKGs4zhoY58mz3zHFdqyvyoy+0tvab17/h2Bt/8zaiwo0XZ/IiyULzn2b1qXUvhZ7FYTsaKMovF8lCMExORkVVO2bJHWWx2EA5MquYEIbNQD7MOIu2UycDUlN25g9NsEprdl0unDM6ef6mEhysLbvnBSk2Z/pXW9lzcdAFCHKspG+0t6GzEtCMfRA5NCSgmx5yyEBR0x5tMe3vEzzxNcnMK6QQnT8k8aAcrDla+wA8UebX7MqUoSkIz13IpRE6rKWuZPmXKOGVJocWrU+b3iDIn0s8oKGqnTARBVc+3ZCLMrtfRPkXiEMcCVN3YF7RbthdehqYesbRvxOO6ccpA15WNR/r1jnEySSdVfEnQ4GOv7fJbf+/Psv5d3wWAiLq4gcKd6UkCv/uJPdZb+n8f+2dMabBYLFaUWSyWh2RiRJkku6dxbNzWomoQ6H5ZbhAyDfWHtB953JlMyE3TWZUkuIMBfqRFS54W9Buv3NVf4eGWObdc557dl0+GY9ToEKfROCZYxvsLuhsxG60Q4RS045BmnDEtN/SGAbRI2nRdwjxm1LlN9MwzJDdHlIXEkxmF5+CIlV+dRYIfCIq8hCiqxixFdztl/r0d/QEaoUup4Nl9/Ty+6rVa8Dlljtu+2ymrRdksn6GyvI4u3/2P4IP/Qt+nGZJejvcpEq/6eSyL9gFC3+WXLn4//Pn/FdA1ZZ4j6MY+z+zoZ/HRmyNmoxSJomOczNX4Er9JI25z9ZH6OYuogxOUuFP98x4eJXzdF5w/9iwsFsvJWFFmsVgeimV8KVV2rHEs1E5Zb9mWIowYB3oeYhC73Jockq9oFHfQr2qwli0x4GxRVuLiFQW3hIRsArKo4stvTf4l8g9+5djcy7JUlSi7tNbg0Y2AC90OrXDGlHM6BkRHe0/45vrtm0RPPw2yJB35BDJD3hUVki8IQjNiyW/o+LIoiSLjlL1CfNkyjto//W294eEb37BGEApceW986URmE8JdThnZHN7zD+Hffw8kY4YYUTY5okg8mj3z81kVZZ7DrrMOnZ1qnWutAMcR9BoB53sxH705ZjHNmQtod5airI4vCZo0/WY1ixPAbXRxwxLfCLeoFPylL7wA1JsJLBbLyVhRZrFYHorxIkcIyMrkWONYgKitRVnbNTVMQczQ2wV0fLk3Gx4TZV6vj+s5CEfomjIzlPw0UaaUQuLgy5zbpnM/6RjvuX+n1+ZuUE5GOGpevWd6mFBKRWdd1785jiT0QtrBWMeXK1xQLlJIDpo3iZ55BoDk0CeUBSpc2ekoc1CyEpQyaCKzjLJQeIFLM3ArUXZW81iAF8faVYzVgrd9WYOL19+Jc0qhfywdptkUled65+XV94LMtGP4n/4ZR+j7LidD5AIa6/o888lxUZYW9W7I/WlaxYwAT+90+MjNEfksZ+4oOl0jytJpHV/6DVp+q5owoF/q4fq1KHu0E/PkVpvYd6uI1GKxnIwVZRaL5aEYJwWt0CMpVkTZZFlTpp2mlhkKnjshQ38pylz2F0eUjkC5Wqi4gwFCCPzQJU8lvdjHEaeLslIqQODJgltS16bxuz+O++vfCcB/2voWytYjOMUQnvuPQN0Oo7th5kPKlMANaLn7TPMeSqnq/GupYBgdsSjn+Bcv4jRjkqGPLyVutLLTMdfipBZlMdIMIfd8h1bkVTVlp7bEMO995vJ2dc5z3ZQ4OcQ9oSUGQEdFx52yF94FbgCPfAnqvT/KkdKCKN/Xu1Jb57Sgmo9WRZlLmq+KsuyYKHtmp8OL+zOyWUHiQBTF+hrL+NKLwXHuccqCZg83LPEK/Wxeu67dvo12aAv9LZZXwIoyi8XyUEySgk7kk8q07uY/zUBQjQpqGFGWEDD1hzz6+etcePWAw4Uu+sd0onf7ush+KcocR9BvnN7VXxqHx89zbuW6MJ73/EPUo18EQBxElPF5vfPyV74dZvsr7TBqURa5ES1nF6n8qh5OlYp4JrkTDUnLFCEE4eOXtFNWljhBLVzItSAMTFQpvVjXlqE3HTRDrxKWp8WXz+x0edPlPt/9VZ+vX8jmyIkp9r9796Up9O+oyNSUZbqb/wvvgotvhj/zfSSLQzKnpHQdcrNzMjq3jhc4x50y3znWcmR/mlY92pbr0mMuCwrf1OWZwexks6qVRjtoH3PKwkYX11eVU/Yqs2tzvRXY+NJieQU+baJMCPEzQohdIcRHVl4bCCF+UwjxnPlv/6xzWCyWzx7GSU470k5Z7MXIoyPmB1Oiho/j6A/xGP2hn6gAJRRf8m2X2XmixzjTDo4TahHgDY6LMoB+M+DwlN160ggfp8w5WIz0VZ78Cl7+c/8MiaLhOpSLBOeRN+hI799+J8PdGY4raPW1sFk6ZW11E4CJETBHu3OcQnErOCIptIiYXbhIOvKJshIRrYiyQgs9P9LiUnoRRaEdN893aId1RntafHmhF/Hzb+lwYdPM08ymlFMtaJz23fGlvnabqOroL1wXbn8YHv3T8MgXM72khakKPMxjxt/coNEJ7qkpW8aXSikO7nLKXnteF/v7hUKF5qPCDE0nm1d91e5xykL4gbUn9O5RlbF17f+G2x9mvRWyP7G7Ly2Ws/h0OmU/C3z5Xa99L/BbSqkngN8yX1ssls8BJklOJ/JJZELohtz83r/L8L0fqFwygEhpgTUzI35SI3KmuRFlxnVy+7qbfhDVomzQDDicn/whXqyIMpFLDr7+Z+Abfp7bM0UBxI5DOZvh9Lfg7f8Tv3j7t/n19/974oFXCcalw9cuX9ZrOtRr231Zu1S3wzGZTFFK8bHWOVQpWB8p3LCeIbl0yvzYiDI3RK6IsuaKKDstvpz/3u/x0td/PZPffBcgIJ9TTrXIcZont8Rol0HllDlqASh47K36Pt74rQAoV5HPTN+29XXidnB896Xnkub6WY8XBZksWW/V0ey5TsRWHBAgcMzOWMJWPWbJ9FVr+S1d36YUB4sDfvgj/y3/77kxAnDIyPZuw098Cd86/nEbX1osr8CnTZQppd4DHN718lcDP2f+/nPA13y61mOxWP5wTJKCVuRWNWX5zZskiSJu16JMFDoSHOf6Qz0x9V/zYoLAqWqkVuPLzOzqXDtj1FLllKkCX8KtzVeBF3BnnFAICIVDOZ/rbv5v/hv8/tpFokWfqzxPUiTIUlKUBaHj0Sqv6vsZ6rXtvjxGeIJDL0Wh+OkP/zS/GFUGP160IsqMUxbE+j4KN6Q0v1Zd3z0uyk5xyvLbuoP/3o/+KMrTTpScTkCIY7tHoS70b5a+rinLc0Qx1e08dnT8OTunNyYIUlBmjub6Oo3O3aKsdsr2pvreV+NLIQRvauvrl30j1szQdB1f1k6ZVJJnD57lm3/jm7k2vcLU1+dxPIfk8a+BV30Zn3/0mwzndtSSxXIWn+masi2l1C3z99vA1mkHCiH+mhDifUKI9+3t7Z12mMVi+TQxTnJaISgUkRshJxMyFVRF/kA1m3FktlomRcI8K5BiRui0zowvz5p/uawpc8oCv4BbM/1rZHeSkguFL9BOWbMJQvB8ENJN1rjpvswP/u4Pkppu/2FZEokxrlsyNfHl7ksTOttNpNRO0I984Ed4fuuTJKbn2vm1R+uFLJ2yhr4P6QSUjhalq/GlIyBwT/51Kw/1v1WzF19kdE2LnnI6w2m17mkKuxSxzdLX7lSWIbIjuPwl4OprTQsdfQqz89XtthFBoOPLyfE+ZZUoM6+vxpcAj+FTovA2zIilqqZsXtWUtXzt5n3bf/g2UpnyI3/6p0jlNqknaLoFaSJg+w2ExQSllB21ZLGcwWdalFUovfVJnfH9n1JKvVEp9caNjY3TDrNYLJ8mJklBI9If6pEXUY7HZF6DMKqFxFKUHaZ1ZHgwzRDOgobXRgT3OmVLUbbWDBjOM2R576+F1fgyKOD2VPf4ujNO9K7OvEQtFjiNBrnM2Z3l+GXM686t86tXfpVfePYXAAhLiRDQbismhymlLNm/NuHcox2K0Rfyjos/xjt2foHpc3+fQU+LiW575ffPsqYs1qKlEH4lytyV+LIRePcIrCXyaAi+T/ia17D/ARe1mFBOJvcU+UNd6N8oXab5lHIxRZSLKroEPX4JVur1zO/LuBOwmNajlkLPqeLLZQH+3aKsM5HccRXd9l1O2Wp8Geh1nm+d5xe/8hd5487rKWWTaeQQqZRkVkDcw6GkxYJd2xbDYjmVz7QouyOE2AYw/939DK/HYrHcB0opJklBHOoP9Uj4yNmcwm8SivpDV+U6itxLTHxZJAznGcJd0PY7VeG6O9A1ZXcX+isFRyfUla0W+vdEo3bKximOKyiSehj5S+OXaCb6/F+x1uNLz38pP/oHPwpAKPVxrY7DdJhweGtOkZdcfLyH77oU6Qbv+cSUN1waEJk6/OX8SaB2yppaLEl85IpT1jK7MqNT6skAiuEQr99n429+F/lYcfS+G5SzKe4JomwptGLp6pqy2QjhKF3kb1gW3bvrl/Q6Ns8B0OwEx0YtrcaXS1G2Gl/KvCTfS7jhlXRNzRxh2/Qpq+PLt+y8hb/1BX+Ln/+Kn2entUPouYSiyzwGv5iTznOI9IimLjO7A9NiOYPPtCj7VeAd5u/vAP7tZ3AtFovlPplnki/l/TRd7RQ1Eii8Bkq4BHJRHVfFl5mJL2XCwSxDuHO6YUcLHN+vXCE/9I7FlwDDk0TZSnx5zl+rRNmdSYLjOxSmV5jTbHLl6ArdRCuqXvkiP/SlP8SFlu4wHxb63K1+yPQwYfdlvQFh63KHjVbIh64f8aHrI97+9BbRlhYmS2EEVE6ZCJr4oUuxEl+6vlN16z9t5yWAHB7h9vu03vpWou2A/XffojgcnuyU+T64LpF0SGWKWkx0ndnGU9Uxy/YUbkc7ZN6Gvve4c3zUUui5x0SZ6wh6cV0PuPvymLJQvPb1G3zF67Sw0/Hl5Fh82Yt6/NXX/dVj80C/+Y3PMIlK3GxCMssh0n3SOmJu519aLGfw6WyJ8UvAe4GnhBDXhRB/BfgHwNuFEM8BX2a+tlgsn+XMdl/gZ4N/xOXRuwCIk5LMxFj+sg8DtVNWoIVMWqQcTrVT1o96OEGI1+tV0Z5vdl8qpVgzXf0PTvgQX3XKtrw+t2c6vtwdp3h3ibLnj56nm2qB0kk/Sjfs8k/e9k+43LnMY0IX7bfXGszGGbevjAhiT8/H7ET8zpUDAP7c01vEO9oZEvHq7ksjQL0IP3SRfrRSU+bepygb4vb7CCHYeOsWxbhg8fu/j9O+V5SBFoVhoX91yzRBdOsRUVDHl35Di6ZlfNm4a/7lap+y/UnGWjOodqYC3Hxe95L7jq9/hldtGsFVxZfzKr48iQudDaYxuPMjiqyk8HR7ja6Y2fmXFssZnDwh91OAUuqbTvnWn/10rcFisfzRMLpzjU2gWeqh09G8IDcF3/58WB2n8gIESKEFViITDo1TttHo418aoGTdwNQPXVC6ZmzplJ1UGL5aU7bh9bk1+xBlqdidJARhrxZljQZXjq5wIXuKTjzGO/okAE8NnuLXvvbX4Hd0jNna7II64qUP77P5SBvhCDZNlPfYepPHN1qIzQ7nv3ad5ld+Zb2QpSjzY/zIRTou7gk1ZWfFl3I4JHy1drqaT20Qb99kcUueGF+C7lUWFub5yhIxOH/s+9N8SuRGuGaX6FKUNXv6fiYHOnINPYdcKmSp7hmxBHDr+RH9c41qmLl+U0uPc5J5FV+exCAe8EIE7nwIXUjp4gEbXmLjS4vlDD7T8aXFYvkcZHKg40Jf6Z5e0UKSGVHmTfar41RRIFyg1EIlKRL2ZwuEm7DW6LL19/4uF3/qJ6vjq6HkST2U/KSu/qvx5Zrb4Sg94uZ4RC4VYehSmAJ2p9nkyugKg9kO64MMjl4GWdQnWgxBuLQ3dby2mORsPqJdoaUoe/vTW9rJC9t0nnBxe736/YUZ8eRFBJFHgU/pGqcsuM/48vAQz/RpE0GLjTdh1n6KKIsigkqUCcTgkWPfn+ZTmn6z2hSwFGXttYhmN+DGJ4yQNkIxK0r2pinrK/VkZam4dWXE9qt6x85NsFyTquLLk1iL1phG4E30ztKk1MfuRKkVZRbLGVhRZrFYHpjkSIsyUY4A8Oc5ua/FjDO8XR2nColwBSgjymTC7lTHYr1Qx5bCqX8N+aZJaZ4W9Br6PcOTRNmKU7bm6Ot+bO8aAHHsVV31yzjg5vA2/rTJ+nYIZaGF2ZLFEOIerUFUvbT5iI7aNtv6tbc/bTr1hG3dOHUVU+iPH+tNCrlCNfR6XK8WZac1jlVFgRyPq92nBE2a63M2/vbfpvs1X33ie5wwxM/1/anSQbSPD0KZZTNaQatqNLsUZUIILj494NrHDylLRejp554Wkv1Jeqxx7OHNKdmiYOdV3eMXD1aE4hnx5SAaMI0E/mJkrqFdtXNBauNLi+UMPm3xpcVi+eNDMdEbpYt8DAL8eVbVlDl7N6rjVC4RrsOg0SRDt8TYm2tR1g2795x3OUMynRd0Nxq0Q+9Ep6yOLwsGThtKeHb/OSCkGfscGVF2szykO9tEIFi7vAbXgcMXYO1xfaLFIcT946LsshZlf/7126SF5PMvLQVT615RVixAuOD6+JGrB363tbvkBfXuy9Max8rxGJRaEWUNyOas/42/fuLxoJ0yL5egFJTogeQrnOaUAVx8esDH33ubvasTQs/siM1L9qfZsZ2XN5/TP6N7nbIVIXZWfBkNmMbgm4HtSR4Agg1/bp0yi+UMrFNmsVgenKkWZVmqi/r9WUrut/DIUbv3OmXnOlqwJUXC4ULHZ52gc89p20YcLeueBq2TG8iuOmU7/jqxF/PBvfcB0Gr6VUL5crHL+kzvtFx/0jR9PXi+PtFiCPEAP3CJmj5x26fV1+Lk8Y0W3/Plr8ZdFr+Hbd04dZU8AV/XbgXLaQQtfV/aKdPC57T4Ug71s3D7RvwELS30Snni8aCdsmB8gFuCUOCcIMrafrtyytz1WpRdeErHpNeePaycsv1pSiZLNlqromxEqx/SXos4Rrgyi/OM+LIbdpnHDp5pZJsuCog6rDkLu/vSYjkD65RZLJYHxk903dgim0IU4M4S8qBN6EmK3V2UUgghUFIiPIedbpOrpUciE0YpEJ/slHU2tMAZ7esC+tO6+tc1ZTlOLvnC7S/kI3feD7yFdtNHlroT9fPZDdbn5wlil/aFbT2O6OBKfaLFEFq63cNgp0ncDk5t8lrNfVylWICnhcuyx5qK2zhJjhCCVqgj2NPiy6Uo85ZOmW/cp3x+XACtIMIA7+pLxIU+p/D9Y9+f5lMuti7S/eq/gLexjtuqxVOjE7B+scW1jx0SXtD3fX2on/Wy0F8pxa3njzj/VP/eZ7EqxM6ILx3h4HTatVM2KyDq0XPmHM4yclninzLhwGL5k4z9f4XFYnlgGpkp4C70h64zXZDHfaJIoNKUcqLFiypKhOuw042g9EmLlHGm64w64b1OWRh7RE2f8Z4WCmvN4NRCfyFAqBKVpXzR9hdxVNyg154Rhh4KgRIun1xcZTt9lPULbV27NngMDu8SZbEWRF/5HZ/Hn/mvXn36TQdtvfOwWFnPilPmRx55IlFxC6fMUWVJ0zhlcXDyv38LM2Jp2Ty3Ej3Z7NRliMUdVJqx4y83Bxx3ypY1ZcEjj9D/pns3vV96esDtF0b4ZgTljaPjomy0t2A+zth5onfPe4/VlJ0RXwK43R6uTBAC0pluINtG35cdtWSxnIwVZRaL5YFQStGWuuZoWR0kpnNm8SadnhYfxa6ON5UsEZ7DuW5MWfqM0zlJqT+Yu8G9ThlAZz1iZERZvxGcWOhf5CWu7yCAMk354p0vBqDdfxEv0L/WVKvLldELdKebrF0wYmLt8eNO2bwWZWHsVTVtJ7J0rlYjzGKxIsq0U1aGDRyZIY+OaAYe5zoRl9dOFjByqJ/jaqG/vsYpomx2gDN+gdJts924CJxeU3YaF18zoJSK/LZ+xteHWlivm9YXt55f1pOd8PM5VlN2+jUAwv4aAgj8kmSuRy01S/3sbLG/xXIyVpRZLJYH4nCWscYRid9n4QgcBMkkJ/XarJ/X4qMSZUWJ8Fx2ehEon93pBOFqEXCSUwbQ3YgZL+NLU1OmR+PWyLzE9RxwXVSW8UTvCdyyg4ifw/ONKGt2GO0tcAqP9aUoGzwOo2va7ZK57k7fGNzfjYfmHGndHJf8eHwJkLsxTllQ7O7iOIL/579/G9/4posnnrKqKVu22XglUfbuf4AQOcrvcS5YA0D4KwPglWKWz6oh4Sex/XgPz3dYXNXXuGHiy2VN2c3nR4RNj8G5E0TXaqR6hvADiPt6kkDoysopi6R2UPdssb/FciJWlFkslgfi9uGIrpgz6z1BKgShE3A018Jg83EtFPLKKVMIz2W7G6NKn4PZDOHMCZwY3/FPPH9nI2ZymCJlyVozIJMl07Q4dozMpXbKwhCVZrr2KXmCmfMxXCPK8jimN9N1U+urTpkqYfgSLLQjtHTKXpFldJcap+za/wcvvBv6uk9YtXNU+bhlXglTz3VOH0Y+HOI0GvXoptWasrvZfw7e9zM4W09SFpJNT4tJ5dfu3qJYIJWshoSfhOs77DzZZ/KyFkjXhwtcR9BvGKfsuSO2H+8hnBPW/ADxZau/RQn4ZNWoJT/X19y3TpnFciJWlFkslgficPcmAOXGa0iEIHY8jgrtoGw9vQNAsbsHLONLl+2udsqGixnCXdDyT3bJADrrMapUTA8TBmbU0t01SEVR4vkOThCg0hRZKuajx8gYs5drMZQEAeuz8yBgsG1cnYFphXF4RdeTwf2LstX4cu8T8L99A3S24at+GKidsiRzcMqcYm/vFU8pj4Z1dAm16Ll7lyfAb34/eDHi0T+FSlI2ff2+KUl1yHLu5VlOGei6ssVBSqcU3DhaMDAjlmajlNHegp27W2Es8WMQzvG1nsJac51ZBF6ZkM4LiLq4qa4ntDswLZaTsaLMYrE8EGPTzT/ceS2JEETCYeT0aTgL4vUOTru9UlMGwnPZ6kSgPCbZAuEuTmyHsaS73IG5t2DQ1G7a3aJsGV+KMKTMUr2jb/oqAJ4bfwKAue+wPj9PbyvGW7akWPYnO7iie5QBxKcIkLtZirK9j8MvfB04PnzLL0NLt5yoRNmi1KLMPIOzKA7vFmXGfcrucspefA984jfgP/87OO0+KklY9/S6j8o66pzmWsydVVMGuq4M4JHcYbTIqyL/Fz+od9VuP3FyvR9C1GLMP9spW4vWmEXg5lOSaQ5xD1Es6AWlrSmzWE7BijKLxfJALIbaKWte0KIsVIJJsEUv1o6Nt7m5IsoUwvMIPAdfRCRFAu6cXnTKhz61KBvvn+6UyUIdiy/vjBNU0WUzusjHxs8CMPEEm4tLbFxcEYCNgXbGHsYpW4qR3/geSEbwLf8aBo/W3zbTCLKFxHVUFeGQxIqkAAAgAElEQVSehRwOcQcr118Knbtryj70L/U63/ztiDBC5fUkg0NZt+lYDiNvBye301jS324QdQIum8Hm662Aq88e8Nv/6pNsPdph89IZ7w+a2i3zwtOPoW4g62RjkrmOLwEutwrbQNZiOQUryiwWywORj+8A4HZ3SLyQTuIxj9YZtHWPBW9zQ4sypbQoMzVPkReCyBHugrUz3KlmN8T1HEZ7C9aaJ8+/lLnE8x1E4KPSlN2JFoT/f3tvHmfHVd55f8+pqrsvvS/aZUmWLS/yIrxhE2ziYIjBZIAAQ1hDIAS/eUlIMgQyeTNkmCXvOyETPgx5GSAYBggQlmFxgLA4sVmMjW1ZeJEsWTLW0nv3vX33W1Vn/jh1t+7b0pVb3X0lne/nU586depU3dPVt/v+7vM853l2DzyPJzNalGWtMNFSqhFPVqNvm04gWxdlnQb614SKgtd+FkZ3t5x2mlZuWo6su3BPhjc728hRBg3hV10gyib3w/Cl4ESQES2Get2gYLvfWHjQqaVMCMHozh42uxZCwUZX8k8f3UfvSJzb79yNPFkOsVBCb0vlcwuolVqyihmqJQ/P0b/zTdGKEWUGwxKY5LEGg+H0yAViIz5I2Q4xNDsIQtLXrz/InaEhCg88CL6H8kVdlMWcCDlVRcoqPW0Sx9YQUpAaiJCd1LFOAD8+OMVMvsLTkzmensxz7XGXHcMJZCiMKpcZz+oP+eevu4GHn/wZANnQKBIa6TBq9G+DIz86fUtZcgS2vQj2vAUu+JVFp2vuSwA7ZHfkvvRmZ7F62rkvm0SZUjB5AC5/NQAirFd7Roo66/+Um6kP7TSmDGDDRb0cfmCC3RWLdftyJPqjvPz3ryASb78AozHH+CldlwB90T7yEegpzEESyrKHGLoo+RPGfWkwtMVYygwGw2lhF6coiwiE4hQtm97MKAD9I0GtxaEh3MlJlFtG+SBsLcoSoRjIKljFJdNh1EgNRslMFYmFLFIRm689cpz/8k9P8oMnJ8lXPDK5CtOlqnZfVrX7EuDmLdeB0GLFc7YAtLeUZY9C9rh2w51iLnUsB97wFbj4ZW1P19yXAHbEOWWgv18u4xcKrTFlTpuYstw4lDMwsBMAEVjK/Pkg51d1tjG0Q0sZwOZdeqXsrcUQImxxx7uvJJYKneIqtMXwFCsvAXrDvbr+ZT7IaedrS+NouGQsZQbDEhhLmcFg6BilFNHKNPlIP2GgLCXx/AhONUdyOCjEPTiEqlbxZqe1pSxIbpqOxBDlAghvycSxNdIDUY4f0B/mX37nDRQqHlsH46QiDp6v+Ks/+CEHp/K8KBTCL1cYz5YZSIToi6a5JKZTVFhyE05cLhYatWD/Yw/pOCd5Zr6bNrsv7WhIC1Pf15UE2tCoe9kkyqQFdrR19eWkXrjA4IV6SLgmyrTbctydqQ/tNKYMINUT5pjlkfIl216+sV7z85QkR05am7NGzIlRjjmEc9qSV/K1UBxyyswWqqbUksHQBiPKDAZDx2RLLj3+HNWItrKUhCRUXkdi/lns1CZAW8oA3LETLe7LdCSGyOoP804sZdWyR3G+yo7hVoFhScFANMSxfIHjBZ9RVWYiW2IoqS11V8UvoAhIHIY2phbnCOu7QO9PPAKpdc/5WSzECTUEhhOPgOfhzcxgDwy0Hb+oGHmNULw1T9nUAb2vWcoC96UXWMrGKtP1oTVLWawD96IQgm/1uBRdn0+sO7W7s85L/gp899TjAD8ZJxTMqezqBRz9QfLg6VyFkXRkyWsNhvMR8zXFYDB0zFimRL/IomI6DURZSYS3jmTuKDKlhZY9pM+542PafRkUzO6LNlxqnVjKgHpm/4WEhKAvFeapuQpuqcTEfJnhlLb0XBZuZM8f3NDGYlSzlFULnceTdYC0ZL2agJPQ8z9ZXFm9GHnfgoUGoVhrTNnkfu1iTepEuDLSaimbdGdxA5GUr+aJWJElE/MuRIQtKqJR97IjYn2QGOpoqEynsGtFyV39Gj1S/06NC9NgWIwRZQaDoWNOZIoMiAxWUn8ohwsDgEMi9yxWUguguqVsYhzliXoZoP54wxqTPkmgP2hLGVCvgbkQz/W5YnMveSXJzOUZz5Z0LjRgi2jce2BjG1EWSUMssF6dQVEGuv4lgJPSAvRkaTHcdu5L0Csbm0XZ1H4YuLC+2nGhpawsfSYLOn7tVHUvFxK2aykxTkOUnQZ2Oo3j6p+lXALsKKmgKLkptWQwLMaIMoPB0DHjc3n6mCfcq602iZwO8m+xlA1qS1l1fByUQIS1KBuIN1nKTiXKBiIglraUeVWfoZ4oowMpivkiU7kyQ4Eok7MZXUqJNkH+NWrWsjMtyoIVmKG0ft2TW8oWFCOv32ShpewADO6sH9YtZVltKataMFYYA3RM2clKLC0kbFtIQX2V65km3DuA7epFGKWg/mXCFCU3GJbEiDKDwdAxc1NjWEIR7x3BVz7p3AhClYm7s/UAdBkOY6XTVE/ofGY1S1m8Kc7pZBn9AWzHItETXtJS5ro+liO5dOsgtu/iK+ruS292GsuvIm1Bz8gSsVW1ckud5ijrkFqwv1MTZSdZgenNzIAQWKkFz6I5pqyUgdyYtpQFiEjNUqaTxroWjOUDUVbNdZQOo0bYlvTFw1jt6lyeAaJ9gwgUIUfpouTRnnpRcuO+NBgWY0SZwWDomMKs/vC3ksOUvTIDhfVEqkexYq2WFntoaJEoC1sNF9mpLGWga2Bm24gy5Sv8IKN/KhUnjl48UAv096ZnkMqlbzSOtdTqvhWylNXSYtiREFZf30kTyHpzs1ipVD1lSOMm8YalbDII8m+ylIlwq6XMtWE8r591vpo/PVHmSAYSK2MlA0j0DQPgWC6loP6lXckQD1nGUmYwtMGIMoPB0DGVIJs/8SFK1RL9+fXEy88uIcq0606EtIgIB2V5bGETs0+9OrCWq2whnqtdk5YtEOEwjlflnS/cxvXb9IpQb3aGqJ9ndNtJalqusPvSDsmWclPtcGdnF7suoVWUTQXpMJosZbJmKcvlwLaJhRIN9+VpxpSNpqOLVreeSVL9enWrRVlbyiI9UMowkAybouQGQxtMSgyDwdAxaj4QZYkhpifnCXsxEoWjWOHW73f20BD5n/4UaFh2opYO3k+F26SpaEN6IEohU6Fa8XBCjcSsbjUo5+RYOl7NdfmTW3cgLD3GnZ7h+tAP2PLKVy9988GL9D45fOof+jRwwvpfqmXLRrmpJfBm57AWrryE1piyyf1ghaF3S/10zX3pZ7OIUIiR2EjdfZmv5E8rpuzDr7uy47HPhd6eYco2WH5Bx5StT8PkkwwmwkwZS5nBsAhjKTMYDB0ji1O6ER9g8pfafZbKHUMuWLxnDw2Bp92KCy1lp4onq1EvTL7AhVm3lDmyHsemKg2rizc9TbQvge1YLMnQxfCWb8POX+9oLp1Sd1+GrFNayrwlLWWJRkzZ5H7o366TygbUf+ZqFek4jMQbomy+On9a7suIYxE52XNaJn0RXWpJunktyqKBpSwRNqsvDYY2GFFmMBg6Ild2SbqzeMKBSA8zxwr4eKTmT2A5fsvYWq4yABEKajVaet9JPBnomDJYvALTq9bcl7Iu+FS58QHvzsxg9fWf+gU2Xw/WmXUW1N2XtsQeHMSdnkZ57bPfezMzixPHQiNPmVLafTl4YcvpmqVMj22IMqUU+Wr+tNyXK01/pJ9cFKzKDPm5CiqsRdlgwjaB/gZDG4woMxgMHTGWKTFAhnK4H4Qgc6zMbHQcu+xh2a3xQbW0GEA9JUbE1mLidC1lC1dg1ixltiPrJZz8sn59v1LBn5/H7j+zqyo7pZanzApJnKEh8H3c6elF45RSuHNz2EvFlKF0wfTZZ+qZ/GsIKesJeaUTYjg2zHRpmmwli6/803JfrjQ94R7yEUG4MIHn+uT8fkCxLuozV6hScf1T3sNgOJ/oClEmhDgihNgnhHhECPHgWs/HYDAsZixTYkBk8OM68WruhMt0/Bii5CNlq9XDGWpkfBdhLa5qqy87tZSF4zahqL3IfVmLKbMcWY9XU1UtyrwZXQeyI0vZClC3lDmyKYnu4hWYfj4P1SpWTxtRVrN0ndgLqEWWMmhYy0QoxEhc54x7OvM0wGm5L1caS1qU4w7h3AkAshUtlkfD+nc6nTfWMoOhma4QZQE3K6WuUErtWeuJGAyGxYxldYklKzFEIVuhOq+YCx9FKLBEvmWs3SLKAvelfXruSyEEqYHIohWYXrU5pkxbymruy5ooWytLWSjIU2a1iLLFcWVti5HXbxKIsuMP6f0CSxmACBLIilCI4bherHBw7iDQXaIMwE1EiWe0KMsU9ErPoZD+fZm0GAZDK90kygwGQxczFpRYctLDTBzRQf555xkApCiAV62PbS7CXRdl1um5L0G7MLNTpZa+miiz7SZLWSDK3OmapWxtRFmiL4KUgmgi1Jko62snyoJ0IccfBiF1oP8CZHixpezgbCDKush9CUAiRmJ2AikFmby2mm6O6d/X48ezazkzg6Hr6BZRpoDvCiF+LoR4+1pPxmAwLObEXJEBkcVODjN2OANCURLPAmCFfCg0YqdEKIQVJHMVMW0Ziztxfnf37/LiLS/u+DW1KCvi+6re5zatvqwF+vt1S5mew6Ii36vElsv6+a3/eD2xVAi7X8fenUyUtY8pC0TVsYehZzM4kUVDmi1lIzEtyg5lDgF0VaA/gEinCFdckv1hsvPakrgurAvI33twao1nZzB0F90iym5USl0FvAR4lxDiBQsHCCHeLoR4UAjx4ORJSpcYDIaVITs7RQgXEkOMH85iDbjEKto6Zjk+5Fs/YO1YUEA7oeO7hBC864p3sa1nW8evmRqI4nuK3GzDWtay+rLuvtQxZXVLWf/axJQJIUj2BWLUtrH6+3EnF4syd+Yk7staOars0ZZM/s3IQIwKxyHmxEiFUhya06Ks29yXVlqvME2mbTJzwXuilOXG7YP8+OBUi+A2GM53ukKUKaWOBfsJ4KvANW3GfEwptUcptWewaWWXwWBYHUoZnThWxQaZOJJFDJeJlfUHqgwpyDd9WVIK29G5tkTIec6vmarlKmtyYbbPU9awlAnHQSa6Q5joBLKLv0R2FFMGLZn8m2kO9AcYiY8wFeSQ6zb3ZaRXC+R43Cc74+rO0hw37RhgtlDlMePCNBjqrLkoE0LEhRDJWhv4NeAXazsrg8GwEJXTFp/Z0gCVkoc/mCMeaCXLaXVfknkWOxSIMue5i7L0wOIEsvWYspaUGI2YMqu/v6OKAauBMzhEtY2lzJudBdtuLx6bRdlSlrIm9yVQjyuD7rOURfr0l2jbzlEuepRUCkoZbtiuxdq9B43nw2CoseaiDBgG7hNC7AV+BnxLKfXtNZ6TwWBoolT1CJW0JWZ8VgfqVwazpEr6X4gM+a2WsqMP4ES1eFqOKEv0RbBsybGnZut9bVNiVBopMdoGz68ROqt/G0vZ3CxWb0978dhiKWsvykQ90F8/21pcGUDMOXVd0dUk0a9Xhwq0azljbYPiHEPJCBeNJLnvKRNXZjDUWHNRppR6Wim1O9guUUp9cK3nZDAYWhkP0mEAjI1ZhKI2pXiGVDVIARGSC0TZgzgpCVIuy5UopeDymzdw4P5xjjyqP7zbZ/QPYspmZrDXKEdZO+yhIbzpaVS12tLvzs5i9y6xGKFZVLXJUQaNQH8ZWMpqaTEiVgRHPncRvBIkg6LkqqJLQWXZAqUMADduH+DBI7MUK+2rHhgM5xtrLsoMBkP3cyJIHKuEZPxoheGtKUp+iWRZIuNxHczfHOh/9AHSN+xi6z9+qf0Kw9Pg2pdfQP/6BD/4zBMUspWWjP71PGW1mLLp6TXLUdYOe3AQlFqU1d+bWaLuJTQsZYkRiLTP6VZLiUFghay5L7stngygb3CjbhSOAZBRG6A0B8CNOwaoeD4PHJlZq+kZDF2FEWUGg+GUjGVKDJKhFBpl5lie4S0pSm6JZFkgUymIDzZEmVuGE3sRm59HZNeuZb+25UhufesuykWXez77JG5gVbEW5ClTSnVe93KVWCpX2ZLFyAEsB6zQklYyWGwpq7kvuy2eDLQo84FqdopYOkTGHa5byq7d2k/IktxnUmMYDIARZQaDoQN+dmSGAZFhWu5GKRjemqLslUmUBVYyCfF+KAQfrCceBa8CG553xl6/f32C61+xjcN7p9j/s3GkJRBS1EWZX66gCgVUqdRdlrKaKFuQxkeLsjbFyGukN8D6pYub1JPHOq2B/t2WowwgHkpQiIA7N0d6MEqm0g9FbSmLhiyu3tzLvSauzGAAjCgzGAyn4If7J/jc/b/kolSZCe8iQIuyolskVlJYdUtZIDyOPqD3Z1CUAey+ZSPrd/aSnSxiOfpfV20RgSqXcetpJrpJlOmVh82WMuV5eJnMyd26v/NDeOGfLnl6YUqMWkxZN1rKhBAUYzYqO096IEq2lK67L0G7MJ84kTUllwwGjCgzGAwnYWK+xB99cS8XjSTZ4OQYL20hNRglmghR9spES0q7L2MDkA/ipo4+AOmNkBo9o3MRUvCiN11MKGpj10SZlAjHQVXKeEHcltVNlrL+fmQ8Tu5f/rXe52WzoFT7YuQ1oj1gh5Y8vTAlRtgK0xfp68qYMoBKzEHM50kNRsmXo7jFQv3cjdt1Sa4fHzLWMoPBiDKDwdAW31e854t7yZVdPvy6KxG5ScayQ4xs1SkxSm6JaNEL3JeDUM7oeLKjD8CGpV1vyyHZF+G2d1zKnpdurfeJcBhVqdSz+dtrlM2/HcKyGHjn75K75x5y/6qFWa1o+nLqc9ZTYjSlG3nLJW/h9gtuX8ZsVw4vGcXKFUkHyYAzpR6o6iR3l65Pk446JjWGwYARZQaDYQk+ft/T3PvUFP/+9l3s6JXkyhEKpTDDNVHmlQgXPWQ6BfGgAPn4LyDz7Bl3XTaz8aI+Lr95Q/1YhMP45fKa171cir43vpHQli2Mf/A/4VcqTdn8TxJTdgrEAksZwJsvfTO/uvlXlzfZFUIlEwyMlSh/4e8BePbQVmY+9UlUpYIlBc/f3s99B6dQypRcMpzfGFFmMBgWse9ohv/3O/v5tV3DvP7aTZCfZLyqVwMOb9FpGsqVIuGSi5VsEmX7g7zPKyjKFiLCIVS5YSlbjgVqJRChEMPvfz+VZ55h5lN31WPflpMqpB7oH1raxdlN2C+8gYm0wn/kXwAYn9rI+H/7MHNf/jIAN24f5ESmxKHJ/FpO02BYc4woMxgMLdz71CRvvesB+uNh/usrL9dZ53OTjFcuxLIUAxt13JLMafeTlQrclwAH/kmncxjdvWrzlaEwKrCUiVgMGY2u2mt3SuKmG0n86ouY+uhHKT/xJLBE3csOaVjKuitR7FJc/Jtv44/fZrPvw28gFFJELosRuXArM5/+DMr3uWmHFvX3PWVKLhnOb4woMxgMgC6l9IFvPM4bPvEz0lGHT731efTGA0tMfoLx6oUMjNhYdhBkX9DB2jKV1oH+AGP7YORysMOrNm8RDuNXyrgzs13numxm+L3vBd9n+uMfB8Dqee7uSxk5uyxl6xPr2ZDYwM/G7ifVZ5H1Rui7/UYqhw+Tv/deNvbF2Dmc5H/ee5hsqXrqGxoM5yhGlBkMBp4cy/KKj/yIT/7oMG+6fjPfuPNGLhpJ1c972Qkmq9sY2Zqs99k5ncJAW8oGGjdbRdclaGGiyhW86emuWnm5kNCGDfT/zu+gKhVENLosi14t0F+eJaIM4NrRa3lw7EFS/SEy3gipPVuxh4aYuesuAP7zKy9jLFviL/73Y2s8U4Nh7TCizGA4j3lyLMsff2kvL/vwfUzlKvz9W57Hf7jjUqIhqzFIKWb2PoxLmOHtOh+W53uEi9qiIZNJXQ6oVnNxhVZeLoWOKSt3Xd3LdvS/7bdx1q9f9grRWnkpllHsfbW5dvRa5qvzVFMV5r1BVCVH7+tfT/7HP6F04ABXberlzpu385WHj/HNR4+v9XQNhjXBiDKD4TxDKcU9+yd4wyfu57a/uZdvPnqC112zie+8+yZu3jm0+ILHvsLxA3pl4/B2bYkqe2XiOqQMK50GIRrWso3XrMaPUUeGdEqMbreUgXY7bvy7jzL6wQ8u6z7Ohg3IeJzQps1naGYrz/NGtAX1RGgMH4fcdIGe33w1IhJh5tOfBuDOW7ZzxcYe3v/VXzCWKa3ldA2GNcFe6wkYDIaVRynFI8/Ocfe+E9y9b4xjc0WGU2H+5Lad/NtrNtETW8INlpvE++Z7eaT8VwxtSpDs126zklciFiRgt5KBSzM2AMrXiWNXEREO48/M4M7OYndRNv+lCO/YwXIj7pzRUXb+/MEzMp/VYiA6wPae7eyf/wXbuIXMTJVUby/pO+5g7qtf45Hh32DT5cN86DVX8NL/fi9/9KW9fPqt1yClWOupGwyrhhFlBsM5SqHicv/hGe49MMV3HtNCzLEEN+0Y5I9fvJOXXjZKyD6JsVwp+NYf8ovZ68lV0tzyG9v1Skxg/8x+EoEhQ6aC2LNdd2hRJlb3Q1SEw7hTU+C6XW8pO9+5dvRavj35fbZxC9mg0lLfG9/AvvvGOfxYhomjRd544zr+/GW7+NOv7OOTPzrM2266YG0nbTCsIkaUGQznCPOlKvuOZvj5M7Pcd3CKh345S9VThGzJ87f18we3Xsitu4ZJRzuMQ3rsq1Qe+y4/L32a9Tt72XhxQ/Dc9fhdXOhGQRaRsZju/JU/XoGf6tTIcAhvSmeD76Zs/obFXDNyDZ97/HMI4ZKZ1x8/ld71PL39FUQqc+QzPTzz2Ayvfd5Gvv/EBP/xW09waDLHv7vtoqWtuQbDOYQRZQbDWYZSihOZEk9N5Dg4kePx41n2Hp3j0GSOWkL0S9aleOuNW7lx+wB7Nve1Bu53Qm4S7v4j9lrvoFh2uP4V2+qnDswe4EfHfsSro5dgJY8g5NqGpopQwxnYbYljDa3sGdmDkAIVniWbi6CU4l8+vx9hO1zxs7/hkZv+nMfvO87Wywf429ddwYf++QCf/NERvvvYOO976cX8m6vW1621BsO5iBFlBkOXUvV8js8VOTiRqwuwpyZyHJrIkSu79XEDiTBXbExzx+517N7Yw+Ub0s/dqlCcY+qxL/PZRz/GdsIcm7mZC64cqJdWArjrsbuI2lG2WcO4qZnl/pjLpjlXl7GUdTepUIpdfbuYi8yQKaY49NAkz+yb5oZXbiP9yzTrZh7i8L495GbLJHrDvP/Xd/EbV27g/V/bx3u+tJcvPvgsv33jVl5w4SAR5zS/aBgMZwFGlBkMa0Sh4nJ8rsjR2SLH5oocmy1yfK7RHsuW8JtKAQ6nwuwYSvKqqzewfSjBjqEE24cS9CeWGTaeOQYH/5mpx7/K3889yhcTMUqW5PnFV3NZRXHtyxsxPWP5Me5++m5ec9FrkP96uBHkv4aIcJOl7CwI9D/fuWb0Gp6KjDOQ2cK9XzjA4KYku2/ZSGbujQx98G95+ro9PPmTE+x56RYAdq1L8eXfvYF/eOBZ/r/v7uftn/k5ibDNiy4e4qWXjfKCHYOnbwk2GLoUI8oMhjOEUor5skumUGWuUGUqX2Zyvs2W0/tmaxeALQUj6Qjre6Jct62fDT1RNvTG2BaIr45jwU5FOQfP/hQO/gB16Hs8kXmabyXifDGVopJKcPvIDbxi6zv4yf1T/HJ0H07/8yju3UvxkUf43MWT+Pj81sW/hZv9E12MfI0R4SZL2TKKfBtWh2tHr+WByOdwVRgvV+X2O3cjLUn6ZS8j+dcfYoAJnvhxhKtv24wIVl5KKfi3127i1Xs28JND09y97wTfeWyM//3IcRxLcMXGHq67oJ/rLujnqk29RqQZzlqMKDMYmvB8Rb7ikiu55MrBVnLJFKvMFavM5St6X6gyV6i1K/q4WMVrNm01kQzbDCbDDCbDXLIuVW+vS0dZ3xtlfU+U4VQE60wv/y/MwOSTcOJROP4wHH+Y4vRT/DwS4p54gnuSScYTo0gEL73g13nH5e9gfXQj3/v7x7GFzf0DX+Fb7/kOu7//DPg+4T0hfu1tt7IhuYFD81nCg9tOPYcVRgaWMplOnzVlh85nrhy6knzkwwDsvmUDg5u0tVXOPEHP7Tcz/J1v8diut3B0/2zL4hIAx5K84MJBXnDhIH/5iku5/+kZ7j04yU+fnuF/3HOID//gIJYU7BhKcMm6NJeuT3HJujQ7h5OkY2dPol3D+YsRZYazDqUUFc+nVPEpVj29VRbsqx6lpnbz+Xy5SXA1Ca9c2aVQ8U75+rGQRU/UoScWoifmcNFIinTMoSfq0BsLkY7pfV/cYSgZYSARXrlv7l4V5k9A5mhjm/slTB2Ayf2owhSTlsXecIiHk708kkryRHIjLoqoHeWGdTdw58YXctP6m+iP9nNk3xT/8IX7yU6VuGpPhOs+VyV6/DBTL76aqi245VsP4u+OwwvBz2SRqS5wXwaB/t1c99LQIGpH6R+Z46n8Z3nHrX8FpQx8531k9n6WZF4wML2BEEUe//6TbLz4hiXv41iSG3cMcGNQzHy+VOXBZ2Z58MgMjx3P8i8HJvnyQ0fr4weTYbYPaqvz1oE4G/tibOiNsrEvRiJsPgoN3YF5JxoWoZTC8xVubfP8YK+oen5wzqfq6XHVpvOu7+N6irLrU/F8Kq7eyq5Xb9f6y8HW6PMaxwvG1falQGQtZZE6GVHHIuJI4mGbRLD1xUNsCv4pJ8I28bBNMtJoJ4J2OqpFVzrmELZX2DWiFFTykJ+EwjTkp6AwpY/zU5A9rsVX9pgWZMoHIC8ERxybw/FeDqT6eXL9evarPmY8nVAsbIW5pP9i3jR0JVcPX801o9cQtrSgyc2W+fZn9nHooUl6+h1u6t2L89/+J/boKF+6cyP/mH6cpJPgzslBLv3EF5ndcBHe/DxWKr2yz6IDau5Lk6Ps7OF5PVv46Pp7+ct77uTI5D4OS9Tcga0AABTNSURBVJ/ZzRvps2L82aESw8d+zNO8gOLf/irR614Dl78GIid3lScjDjfvHGqpSjGRLfHY8SxPTczz1HiOg5M5vvbwMeYXhA70xBwt0Hq1UNvQG2M4FWEwGWYosGqbhQWG1eCsFGW5sst9T02hUCgFtY9npZRuKwha+nwwpn4+6GfR9bTcU6nGB3/zucZx62sC+ErhK/CUqosbX4HvK3yl8JQK2tpVpmp9zWP82n3aX6+Ca5d+DT2vukhaJKga4kkLq6Dt+4HIOn3BczoIASFLErIlYdsibOt2o0/vExG7ZVzIlsRCFlHHIhqyiDi6Hau1a+dq7abjiCNXZym9UuBVtKiq5IJ90C7ntFWgtpWzrcelOSjMagHmLi4xUxKCsXCcE8kBxhK9jK3bygl7B0epcqSSYbKarY91ZIXtqU38St9F7OzbyaUDl7KrbxeO1XDhlAtVDjw2xuFHpjiybwrl+VykHmXkKx9H2pLe172OwT/8Q95pV/j+N17FRGGCkb/8MIn//AXGPvCXoJQuRr7G1NyXZ0M2f4Pm5sGr+P/H7uWe6b1sETa3bHwhm0avYt/kPj5y7Q94/+d/wrPrX8T/yl7O87/3p+z83l9gXfZq2PNWGLms4wTFQ6kIQ6kIN1/UEGpKKWbyFY7O6kU2z84WODpb4Ohskacmcvxw/wSlqr/oXqlIIwShZgHvizukYyF6Yw49UW057wks5bGQZdJ3GE6bs1KUHZ7K81ufuH+tp3FGEAKkEFhCIARYUiCFQAod3GoJgZT6WI8RwRiC/gVjZDAmaNtSEnEEthTYlqzvHanvY1sSx9Jtp3a+NtYK2rI2RvfV2rV7OMHY5nvUxZWlxVSz2LKDOa44SoHvgleCUgU8VwsmtwRuGdxisC9BtRT0lxYcN42rFhvH1VIb4RUcq1O7QAEIJfEiaTKRJDORBDOJXmb6hpl2wsxYFrMCplSVMTfHWHmW2UpNdPnANJSnGZSDjCZGuX7kSramt7IltYXNqc1sSW/Bka0xNJWSy9GDs4wfmuXZfeMcP1JEKQiLMiOZJ9j4+FdIJAS973onva/5TezBQQB6ifORF32E+47dx42bfgX1oWv55W+/jeJDD+li5GtMLY7MWMrOHi7acgsPfPcDOFe/GW5+PziR+rnZ62d56qevJZ4/zPj4jfzFxhxjfb/g4mN3c8WhLzMqI/SmN9M7cBG9I7tJDl1GpH8H4WhfR/9XhBD0J8L0J8Ls3rh4YYhSiqlchfFsSS/KyerFORPB8US2zN6jc0zOl08a7hCy5KKwhp6oQzLikIjYJJss8fV9sCUj2lLvWKY89fmGaLYGnS1cfNkV6q6v/wAhQFD70qT/GBt9gtqfp+4T9S9X9X3QVzvfen0woj62cc+F19evC85rYaRFlFwgmGTQVxNWyxYnSmn3VX1beLygn6XON43xXfA9vVde0G4+dsH3FxwHY+rH7fraHbsnec1ARHnVpn2tXWk6v/BcsPery3u2Naww2BH9wWGHwY6CHcYLJyg6UfJOhIITpmCHKVg2BcsmLyU5IcgKn3nlMa9csn6Feb9C1i0y7xbIVuaZK8/RsN82EAh6I730RfoYiY8wGh9t2Y/ERxiKDuFUffx8Hj+Xw8vn8fN5SjM55o7NkZkokpmtks1LMtU486Kn/uaN5ccYmH6UwalH6YuXiFy4g/Ttt5N68Ys7Cpb3Mhkm/vpD9L/1LYQ2r21R7Oy3v8Oxd7+bgd/7PQZ///9a07kYzgzz3/sev3j/37D/+b9PvmCjhM/0wDM8mr6PY6mD5ENzsOBfp1CKCJKotIjIEBErTMSOELFjhEMJHCdGyInhyBCO5eBIh5AVart3pINjOYTkgv4F1ylfUigr8hVFruSTLytyJY/5oiJb9JkveWTyPpmSx1zBJVNoxLF2QsSRJMJ2w+ofsok6ssVbEGv2CIQsYgs8CdGQHlPzNoQsSdhpeCZqfcaqt7IIIX6ulNpzynFnoyjbsyWtHvzzWgBokz+xpR2ca253dE61dK3I/Ws+1VMKpCXON1931iJA2iAtvRdW0F5wbIfBCuk+KxRszW0HpIOSDq5lU7VsqtKiKi1caVGRkjKCspSUBJSBshSUhaCEoCyU7kNRwqesvGDzKSuXklel7JcpukUK1QL5ap6CW6BYLVCpFLF8sDywfbA9Wo5r7TAWKRkjJWKkiJJUYZIqRFyFSKgQCT9EXDlEPZuoJwl7ErvqQ7mCKpfxyyXcUpVKVVB2LUpVSaUqKfs2VStGJZSmFOmlFO6lHOnFtWMtTzriZkkxR184T3/aY2A4RGLDIOFt2wht346VSKzJO+BMMf/DH3L0nb/H8L//M/pe//q1no7hDKA8j0O3vQQRieD83vt4Nt/PwZ9PkJstA+AkBJERH1KTeJGjVOWzVHiGkjtBsZyl5JYoCkVJCIpCUBWCSrCvWg5VKakIQQWoAlV83DZfjs40trSxhY0lLaSwsNB7gYVAArqNkqhg85UAZeH7EqUEvi/xfYHng7dgjxKAQCmJVq2y3qf3svV8U58lLGwhsaTEkhZ2fa/btrSwLQsn6HOsWr++xpYSq369DM4JZL1d6695WoL7WwJLyOCeos29tCHDlhIpZP1+uk8gm19TSKRE31dIpBQI9BiBtriIJjXfLERb+pcY00xH92nqH4wNdiTKzkr3JaA/sGvUf3DR2q6fE4vHnexc23GahlZrc4+FX91onFO1eygBQgangj8MIVvbwV7VzwV/OEKiUPhC4gfz9JXAR5vcfUXQFvhC4Pv65fQYHYtWG6sQTeMb1yt0TJqHvm89Dg50HBxKG8lQ9bi3pTblKz3O94I+X7+Or1C+h+974Hko30d5Hn7F1XvPRXkuvufpve+hPA/lFcDPBW0PfB/le+ggPB+p0Ju/xF6BaNMf8yHlK2xfYPsCJ9g3CyvbB+kpLA+k7yOXiLvzhcSXDr508GQI33LaHnvSwZchPCtM2Q5TsCJ4oRieE8N1onh2FM8K41oRqqEIbnhp61XY9onFFL0JSSLlkOgN07uhh94LBulZn8Y5x3M21WPKTDb/cwZhWQy95z0cf9/7qPzBWxhet47tt7+M6q/fykw1xcQz80wcyTJ7SIAaAq5CAH1Jh2R/lFjSIRJRxMIVIlaeqMwSFTNE/Qmi7gnC7hhOeQJRmtOxnMU5fOVRFVClIeAqAi3khND9ToSqEwv2ETw7gmeHqdohPDuMZzl40sKVNq608ILNlRauEHjCwhMCN9g8IfBAtwEXhYfC9V085em97+Eqvdd9VTzl4Su/Zav1uX5w7HtBf2OMorWt/7O34gVb5WS/ID/YDGecrrCUCSFuA/47YAEfV0r9l5ON3xWLqs/tuACxYOqi+WcJmmLB8ZLjYdH9QH9on6voH00EgjH4hlV3BTf3s2BMQ4TW+tv16etk8FoNsasIRCmiqV9fp4REIfV1C45VIF49IUFa+FKipERJK9ia2kIf16xvqskSp6SFEHpft8xJGyUdlLTwhd5UsPnCQiEDMaw3hQzEbiCMlcDzBUrV33GnhR2WhMI2oaiNE7YIRSyciE0oYhFNhIgkHCIJh2iw1+0Q4biNdZ7HnVSOHuXwK1/Fls9/nvAFW9d6OoYziF8oMP/975P5+jfI/+hH+stXOk3kwgsJ79yJ3LaTUnoDeStFvhpmfrbC/EyJYq5KMVuhmKviL7VwSYATsnAilv6bCwkcx8exPUKWiyWr2KKKJSpYVLApY6kiliphqSK2l8fy81h+TrfdLNIvIL0S0isg8JDCQ3+FrrX11916Oziv27UPLavhCbCbPAJWuNG2w0FfKOh3Orymud8J/u/ZeFL/f/WEhS+DTQj9v1BawZfN4Dj4H6wCUan/Twb/iyEQhIqq7wUr94PN86l4XrDYzMP1FVXP0wvNan1N4/VCN79p0ZvXsrjNC4Sl56v6l/5aW9XFaLOhwNeL4VANI4RSbRYFBsfUFvs1zuv+4JraYr8mcdG6gLDpvii++eZ/d3a4L4UQFnAAuBU4CjwAvE4p9fhS12we3Kbe+8r/RKtlqt2HYTvLVfvj1s/S5d3r5H2djBXNxrmOr1lkxWuy4Olf81IWvfMLKQVCisBAGcT82RLLEkhLYNkSacmgLZraei8tqfuDYys4bzsSOySxHAvbkVjBsR0cLzrnaPFlhy3kmU4aazCcY7iTk8x//weUnniC8v79lA4cQBUKLWOsvj7swUFkMoEVTyDiCfx4mmo0TTWUpGInqVhRqsrB9SVVT1D1BK4ncF1B1UVvVfA8heeBX9uvuGVIIYVCiOBrn/CDth8IuUDcBcegEKrW9gMjg9/oU17wtTc4D8FeBZ8WalF7cZ/+ocXC68VS1zTiq6nvg8+zutcnWOhVOxYCUWvLwFMka+5GAbL5mtq2+HztfrXXEk33p+X1ZNO9gnbwukLKprELx0s9rj5fCbKpLYT+kl8bC017wdW/cflZ4768BjiolHoaQAjxD8AdwJKiLByLsPWqS9Djm06INs2l/MFt9Iloc4MltVpwg6XOt339U5xvd6/WvlPdq+mPgYV/GEGfFC1ja+/N2oD6H1TL9U19Uo+tXyeaFzs0xus3eDC3+h9K670X9i0SS6J2LIK/B1EXUUK0iioR9Ekr6BdiyfsZDIazD3twkN7XvqZ+rHyf6tGjehsbxx0f0/vJSfxcDndyEu/IYfycXgijymUc4Lnm9VcIfGkH4QgL97pdtxoJ2WRtr1n6n3u75V7Sov4lvOaJEEJ7FABEwwOhEIC9uK/mnaj3Nd2rHj7TdK9mD8hJ+2peFf3Pvx6CQ7OzasH/4LoHpaWzdS8av4PWYavtJahZzlZOoXeDKFsPPNt0fBS4duEgIcTbgbcHh+WXvOOyX6zC3M5nBoCptZ7EOY55xiuLeb4rj3nGK495xivPajzjjpapd4Mo6wil1MeAjwEIIR7sxAxoeO6YZ7zymGe8spjnu/KYZ7zymGe88nTTM+6GCOFjwMam4w1Bn8FgMBgMBsN5QzeIsgeAHUKIrUKIEPBa4OtrPCeDwWAwGAyGVWXN3ZdKKVcIcSfwHXRKjE8qpR47xWUfW/mZnfeYZ7zymGe8spjnu/KYZ7zymGe88nTNM17zlBgGg8FgMBgMhu5wXxoMBoPBYDCc9xhRZjAYDAaDwdAFdLUoE0LcJoTYL4Q4KIR4b5vzYSHEF4Lz9wshtqz+LM9eOni+bxZCTAohHgm2t63FPM9mhBCfFEJMCCHa5tUTmr8NfgePCiGuWu05nu108IxfKITINL2P/3y153g2I4TYKIT4oRDicSHEY0KI/7vNGPM+XgYdPmPzPl4GQoiIEOJnQoi9wTP+D23GrLmm6FpRFpRf+gjwEmAX8DohxK4Fw34bmFVKbQc+BPzX1Z3l2UuHzxfgC0qpK4Lt46s6yXODTwG3neT8S4AdwfZ24KOrMKdzjU9x8mcMcG/T+/gDqzCncwkXeI9SahdwHfCuNv8rzPt4eXTyjMG8j5dDGbhFKbUbuAK4TQhx3YIxa64pulaU0VR+SSlVAWrll5q5A7graP8j8CJRq9ljOBWdPF/DMlFK/Sswc5IhdwCfVpqfAj1CiNHVmd25QQfP2LAMlFInlFIPBe154Al0JZZmzPt4GXT4jA3LIHhv5oLDWsWthSsd11xTdLMoa1d+aeGbtD5GKeUCGaB/VWZ39tPJ8wV4ZeCO+EchxMY25w3Lo9Pfg2F5XB+4Lf5JCHHJWk/mbCVw51wJ3L/glHkfnyFO8ozBvI+XhRDCEkI8AkwA/6yUWvJ9vFaaoptFmWHt+QawRSl1OfDPNL5BGAxnEw8BmwO3xYeBr63xfM5KhBAJ4MvAu5VS2bWez7nIKZ6xeR8vE6WUp5S6Al056BohxKVrPaeFdLMo66T8Un2MEMIG0sD0qszu7OeUz1cpNa2UKgeHHweuXqW5nU+YMmMrjFIqW3NbKKXuBhwhxMAaT+usQgjhoMXCZ5VSX2kzxLyPl8mpnrF5H585lFJzwA9ZHIu65pqim0VZJ+WXvg68KWi/CviBMtlwO+WUz3dBTMjL0XEOhjPL14E3BqvXrgMySqkTaz2pcwkhxEgtLkQIcQ36/5758tYhwbP7BPCEUuqvlxhm3sfLoJNnbN7Hy0MIMSiE6AnaUeBW4MkFw9ZcU6x5maWlWKr8khDiA8CDSqmvo9/EnxFCHEQH+r527WZ8dtHh8/19IcTL0SuDZoA3r9mEz1KEEJ8HXggMCCGOAv8POsAUpdTfAXcDLwUOAgXgLWsz07OXDp7xq4B3CiFcoAi81nx5Oy2eD7wB2BfE4wC8D9gE5n18hujkGZv38fIYBe4KMg9I4ItKqW92m6YwZZYMBoPBYDAYuoBudl8aDAaDwWAwnDcYUWYwGAwGg8HQBRhRZjAYDAaDwdAFGFFmMBgMBoPB0AUYUWYwGAwGg8HQBRhRZjAYDAaDwdAFGFFmMBgMBoPB0AUYUWYwGM55hBBbhBB3CyH2CyEOCCH+tKm/2JSwc6nro0KIR4QQFVPaxmAwrBRGlBkMhnMaIYRE1xT8O6XUTuAyYI8Q4u3BkENBkeIlUUoVgzHHV3a2BoPhfMaIMoPBcK7zYuBIUEYFpVQZuBP4o3aDhRD3CCEuCtr9QohfrNpMDQbDeY0RZQaD4VznYmBvc0dQLDsFhNqM3w4cCNqXA/tWdHYGg8EQYESZwWA41/GARHOHEEIAMcBd0L8ZOKaU8oOuy4FHV2OSBoPBYESZwWA417kHeGkgxGrcCjwE+AvG7qZVhF2NEWUGg2GVMKLMYDCc0yil9gIPAx8AEEIMA38NvK/N8CuASDBuB3AHxn1pMBhWCSPKDAbDOY0Q4r3AHuDPhBC3AB8FNgP/o83w3YAUQuwF/hx4HHjTas3VYDCc3wil1FrPwWAwGNYEIcQW4JtKqUuD46eAq5RS80uMPwLsUUpNrdYcDQbD+YOxlBkMhvMZD0gHiWGTgGonyGrJYwGHxXFoBoPBcEYwljKDwWAwGAyGLsBYygwGg8FgMBi6ACPKDAaDwWAwGLoAI8oMBoPBYDAYugAjygwGg8FgMBi6ACPKDAaDwWAwGLoAI8oMBoPBYDAYugAjygwGg8FgMBi6gP8DUshlPlOjqz8AAAAASUVORK5CYII=\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy.signal as sig\n", "\n", "N = 256 # number of samples\n", "M = 5 # number of sample functions\n", "\n", "# generate random signal\n", "np.random.seed(1)\n", "x = np.random.normal(size=(M, N))\n", "h = sig.firwin2(N, [0, .4, .42, .65, .67, 1], [0, 0, 1, 1, 0, 0])\n", "x = [np.convolve(xi, h, mode='same') for xi in x]\n", "\n", "# DFT of signal\n", "X = np.fft.rfft(x, axis=1)\n", "Om = np.linspace(0, np.pi, X.shape[1])\n", "\n", "# plot signal and its spectrum\n", "plt.figure(figsize=(10,4))\n", "plt.plot(Om, np.abs(X.T))\n", "plt.title('Magnitude spectrum')\n", "plt.xlabel(r'$\\Omega[\\mu]$')\n", "plt.ylabel(r'$|X[\\mu]|$')\n", "plt.axis([0, np.pi, 0, 30]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise**\n", "\n", "* Increase the number `N` of samples. What changes? What does not change with respect to the evaluation criteria introduced above?\n", "* Is the DFT of a single sample function a consistent estimator for the spectral properties of a random process?\n", "\n", "Solution: Increasing the number of samples does only lead to an increase in the number of discrete frequencies $\\mu$. The amplitude of the fluctuations (variance) of the spectra within $1.3 < \\Omega < 2$ is not decreased when increasing the number of samples. The DFT of a single sample function is hence not a consistent estimator since at least the second condition is violated." ] }, { "cell_type": "markdown", "metadata": { "nbsphinx": "hidden" }, "source": [ "**Copyright**\n", "\n", "This notebook is provided as [Open Educational Resource](https://en.wikipedia.org/wiki/Open_educational_resources). Feel free to use the notebook for your own purposes. The text is licensed under [Creative Commons Attribution 4.0](https://creativecommons.org/licenses/by/4.0/), the code of the IPython examples under the [MIT license](https://opensource.org/licenses/MIT). Please attribute the work as follows: *Sascha Spors, Digital Signal Processing - Lecture notes featuring computational examples, 2016-2018*." ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 1 }