{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Lecture 5: Data Analysis with QInfer (1.5 hours) #" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### ABSTRACT ###\n", "\n", "We will now introduce Bayesian parameter estimation and the sequential Monte Carlo algorithm as implemented by [**QInfer**](http://qinfer.org). The intent is not to have a deep understanding of the general problem of parameter estimation at the end of this, but to get a flavor of how to use what you have learned in the previous lectures to utilize a mature, but specialized Python package. Part of the goal will be for you to see analogies to these examples in the statistical problems you might be facing in your own research, and to have a new Pythonic solution. (Also, at the end you should be excited and eager to use Bayesian inference for all your statistical needs!) \n", "\n", "In this Lecture you will learn how to:\n", "- estimate the bias of a classical coin,\n", "- use QInfer to perform:\n", " - **quantum state tomography**,\n", " - **phase estimation**,\n", " - **randomized benchmarking**,\n", "- specify **custom models** to use with QInfer.\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Preamble ###\n", "\n", "Here we import all the necessary modules as well as make the code compatible with Python 2.7:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from __future__ import division, print_function\n", "\n", "import qinfer as qi\n", "import numpy as np\n", "import scipy as sp\n", "import matplotlib.pyplot as plt\n", "\n", "%matplotlib inline\n", "# Use nice plotting defaults if available.\n", "try: plt.style.use('ggplot')\n", "except: pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Starting simple: estimating the bias of a coin\n", "\n", "Suppose we have a coin that we do not know the bias $p$ of. We will guess what $p$ is by flipping the coin many times. \n", "\n", "If we knew the bias, we could determine the exact distribution of the number of \"Heads\" we would see. If we label the number of flips $N$ and the number of heads $n$, then the distribution of $n$ is a [Binomial distribution](https://en.wikipedia.org/wiki/Binomial_distribution):\n", "$$\n", "\\operatorname{Pr}(n|p) = \\binom{N}{n} p^n (1-p)^{N-n}.\n", "$$\n", "\n", "Now suppose we have flipped the coin and $n$ heads did actually occur in $N$ flips. What is the distribution of $p|n$? The answer is given by [Bayes' rule](https://en.wikipedia.org/wiki/Bayes%27_theorem):\n", "$$\n", "\\operatorname{Pr}(n|p) = \\frac{\\operatorname{Pr}(n|p)\\operatorname{Pr}(p)}{\\operatorname{Pr}(n)},\n", "$$\n", "where $\\operatorname{Pr}(n|p)$ is called the likelihood function, $\\operatorname{Pr}(p)$ the prior, $\\operatorname{Pr}(p|n)$ the posterior and $\\operatorname{Pr}(n)$ is called the evidence. The likelihood function we have determined above. The prior is the input to the problem and the evidence can be determined by normalization of probability.\n", "\n", "The input, the prior, can be anything. A typical choice for generic problems is the uniform prior $\\operatorname{Pr}(p) = 1/V$, where $V$ is the volume of the parameter space, in this case $V = 1$ since the bias can be between 0 and 1. For the uniform prior, the posterior is\n", "$$\n", "\\operatorname{Pr}(p|n) = \\frac{p^n (1-p)^{N-n}}{B(n+1,N-n+1)},\n", "$$\n", "where $B$ is the Beta function. (See a derivation of a slightly more general form [here](https://en.wikipedia.org/wiki/Conjugate_prior#Example))." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Flipping coins" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Suppose we flip our coin 10 times. What does $\\operatorname{Pr}(n|p)$ look like?" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAABOYAAAHgCAYAAAABnWKQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAAAAYMD/A8RZzmZwFW+TAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Create a variable for the number of flips (go ahead and change this if you want).\n", "N = 10\n", "# This creates an array containing [0, 1, ..., N].\n", "n = np.arange(0, N + 1)\n", "\n", "# This sets up the figure as an matrix of subfigures with 1 row and 3 columns.\n", "fig, axarr = plt.subplots(1, 3, figsize=(15, 5))\n", "# This is the probability mass function (pmf) of the binomial distribution for p = 0.\n", "dist = sp.stats.binom.pmf(n, N, 0)\n", "# On the first (0 indexed!) subplot, make a bar plot with x-axis given by the array n and y-axis given by the pmf.\n", "axarr[0].bar(n, dist)\n", "\n", "# The rest is just annotation and repeating for different biases.\n", "axarr[0].set_xlabel(\"$n$\")\n", "axarr[0].set_ylabel(\"$\\operatorname{Pr}(n|p)$\")\n", "axarr[0].set_title(\"$p=0$\")\n", "\n", "dist = sp.stats.binom.pmf(n, N, 0.1)\n", "axarr[1].bar(n, dist)\n", "axarr[1].set_xlabel(\"$n$\")\n", "axarr[1].set_title(\"$p = 0.1$\")\n", "\n", "dist = sp.stats.binom.pmf(n, N, 0.5)\n", "axarr[2].bar(n, dist)\n", "axarr[2].set_xlabel(\"$n$\")\n", "axarr[2].set_title(\"$p = 0.5$\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In reality, we often have data, in this case $n$, so we are interested not in $\\operatorname{Pr}(n|p)$ but in $\\operatorname{Pr}(p|n)$. We still use $\\operatorname{Pr}(n|p)$ in Bayes' rule but think of it as a function of $p$ for fixed data $n$. Below we plot what that looks like." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAABOgAAAHfCAYAAADqeOdbAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ " # This creates an array with 100 values between 0 and 1.\n", "p = np.linspace(0, 1, 100)\n", "\n", "fig, axarr = plt.subplots(1, 3, figsize=(15, 5))\n", "likelihood = sp.stats.binom.pmf(0, N, p)\n", "axarr[0].plot(p, likelihood, linewidth=3)\n", "axarr[0].set_xlabel(\"$p$\")\n", "axarr[0].set_ylabel(\"$\\operatorname{Pr}(n|p)$\")\n", "axarr[0].set_title(\"$n = 0$\")\n", "\n", "likelihood = sp.stats.binom.pmf(1, N, p)\n", "axarr[1].plot(p, likelihood, linewidth=3)\n", "axarr[1].set_xlabel(\"$p$\")\n", "axarr[1].set_title(\"$n = 1$\")\n", "\n", "likelihood = sp.stats.binom.pmf(5, N, p)\n", "axarr[2].plot(p, likelihood, linewidth=3)\n", "axarr[2].set_xlabel(\"$p$\")\n", "axarr[2].set_title(\"$n = 5$\")" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "Bayes' rule states:\n", "$$\n", "\\operatorname{Pr}(p|n) = \\frac{\\operatorname{Pr}(n|p)\\operatorname{Pr}(p)}{\\operatorname{Pr}(n)} = \\frac{p^n (1-p)^{N-n}}{B(n+1,N-n+1)},\n", "$$\n", "For the uniform prior $\\operatorname{Pr}(p) = 1$. Since this is just proportional to $\\operatorname{Pr}(p|n)$ we should expect the posterior to look the same.\n", "\n", "(Note that $\\operatorname{Pr}(p|n)$ is not strictly a probability, but a density, or measure, and can be greater than 1 for any particular value of $p$ since only questions about the probability over intervals return non-zero answers.)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAABOQAAAHfCAYAAADwRAfVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Rather than write it out many times, we define a function to compute the posterior which compresses further code.\n", "def posterior(p, n, N):\n", " return p ** n * (1 - p) ** (N - n) / sp.special.beta(n + 1, N - n + 1)\n", "\n", "# Note that notebooks have access to the variables defined in previous run cells, so we do not need to redefine N and p.\n", "fig, axarr = plt.subplots(1, 3, figsize=(15, 5))\n", "axarr[0].plot(p, posterior(p, 0, N), linewidth=3)\n", "axarr[0].set_xlabel(\"$p$\")\n", "axarr[0].set_ylabel(\"$\\operatorname{Pr}(p|n)$\")\n", "axarr[0].set_title(\"$n = 0$\")\n", "\n", "axarr[1].plot(p, posterior(p, 1, N), linewidth=3)\n", "axarr[1].set_xlabel(\"$p$\")\n", "axarr[1].set_title(\"$n = 1$\")\n", "\n", "axarr[2].plot(p, posterior(p, 5, N), linewidth=3)\n", "axarr[2].set_xlabel(\"$p$\")\n", "axarr[2].set_title(\"$n = 5$\")" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "# Enter: QInfer\n", "\n", "For more complicated models, such an analytic solution is not obtainable and we must turn to numerical algorithms. The algorithm we use is called [sequential Monte Carlo or the particle filter](https://en.wikipedia.org/wiki/Particle_filter). We begin by drawing $k$ samples $\\{p_i\\}$ from the prior and approximating it as\n", "$$\n", "\\operatorname{Pr}(p) = \\frac{1}{k}\\sum_{i=1}^k \\delta(p-p_i).\n", "$$\n", "The samples are called particles. Each particle is associated a weight $w_i$ which is conventionally set to be $1/k$ initially. The weights are updated via Bayes rule as follows:\n", "$$\n", "w_i(n) \\mapsto \\Pr(n|p_i)/k.\n", "$$\n", "The set of weights $\\{w_i(n)\\}$ are not normalized so we make one final assignment\n", "$$\n", "w_i(n) \\mapsto \\frac{w_i(n)}{\\sum_j w_j(n)}.\n", "$$\n", "Then the posterior is approximated by\n", "$$\n", "\\operatorname{Pr}(p|n) = \\sum_{i=1}^k w_i(n) \\delta(p-p_i).\n", "$$\n", "\n", "That's it; that's the basics!\n", "\n", "QInfer is numerical algorithm to approximate Bayesian inference. Beyond flipping coins, we treat Bayesian inference as the problem of inferring a set of parameters $\\boldsymbol{x} \\in \\mathbb R^n$ from data conditioned on an experiment. That is, we want to know what $\\Pr(\\boldsymbol{x}|d,e)$ is. Data are generated from a distribution given by a physical model that is known: $\\Pr(d|\\boldsymbol{x},e)$. In order to compute this, we also need a prior $\\Pr(\\boldsymbol{x})$.\n", "\n", "QInfer mirrors these objects with the following classes\n", "* **qinfer.Distribution** Represents drawing samples from a prior distribution.\n", "* **qinfer.Model** Represents evaluation of the likelihood function.\n", "* **qinfer.SMCUpdater** Represents Bayesian updating via the particle filtering algorithm.\n", "\n", "QInfer implements many commonly used distributions and models used in quantum information science, including\n", "* quantum state tomography\n", "* phase estimation\n", "* randomized benchmarking\n", "\n", "We'll jump right in and learn how to use QInfer to solve problems in these domains." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Quantum state tomography\n", "\n", "To define the model, we start with a basis for traceless Hermitian operators\n", "$\\{B_j\\}_{j=1}^{d^2-1}$. In the case of a qubit, this could be the basis of\n", "Pauli matrices, for example. Then, any state $\\rho$ can be written\n", "$$\n", " \\rho = \\frac{I}{d}+\\sum_{j=1}^{d^2-1} \\theta_j B_j,\n", "$$\n", "for some vector of parameters $\\vec\\theta$. These parameters must be constrained such that $\\rho\\geq0$. Defining a basis turns the quantum problem into an effectively classical one.\n", "\n", "QInfer's TomographyModel abstracts many of the implementation\n", "details of this problem, exposing tomographic models and estimates in terms\n", "of QuTip objects, which you will learn about next lecture. For now, the added functionality provided by QuTip will be hidden.\n", "\n", "Tomography support in QInfer requires one of the bases mentioned above in\n", "order to parameterize the state. Many common choices of basis are included as\n", "TomographyBasis objects, such as the [Pauli](https://en.wikipedia.org/wiki/Pauli_matrices) or [Gell-Mann](https://en.wikipedia.org/wiki/Gell-Mann_matrices) bases.\n", "\n", "Let us look at an example for a single qubit. Take the Pauli basis:\n", "$$\n", " \\{\\sigma_x/\\sqrt{2}, \\sigma_y/\\sqrt{2}, \\sigma_z/\\sqrt{2}\\}.\n", "$$\n", "As written above, any state can now be describe by 3 real numbers $(x,y,z)$, often called the Bloch vector, as follows:\n", "$$\n", " \\rho = 1/\\sqrt{2}\\left(\\frac{I}{\\sqrt{2}} + x\\sigma_x +y\\sigma_y + z\\sigma_z\\right).\n", "$$\n", "\n", "Many of the most commonly used priors are already implemented as a Distribution. Here we will focus on the GinibreDistribution because is most closely resembles the \"flat\" prior." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "basis = qi.tomography.pauli_basis(1)\n", "prior = qi.tomography.distributions.GinibreDistribution(basis)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In doing simulations, we need to select a \"true\" state. We can use our prior distribution to select an unbiased \"random\" state for us." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "true_state = prior.sample()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a qubit is point in a 3 dimensional space, for visualization purposes, it is more convenient to consider a *rebit*; a qubit constrained to the $X$-$Z$ plane. The Tomography module implements the visualization of distributions through the methods plot_rebit_prior and plot_rebit_posterior. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\cgranade\\Anaconda2\\lib\\site-packages\\matplotlib\\__init__.py:898: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter.\n", " warnings.warn(self.msg_depr % (key, alt_key))\n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZYAAAGDCAYAAAAI4za+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAAPYQAAD2EBqD+naQAAIABJREFUeJzsvXec1HT+P/7MJJnJtN1ll60CAkoRRReFE4UTRIpIuY/1\nFAsWlM5x1KU3d1mkKOWWBYED9Tjr158o4klR7kBF0aOcNFFQ6rIsbJmdlmTy+yOTTDKTTFl2BZY8\nH497nMymvPNO8nrl/Xo9X88XIQiCAAMGDBgwYKCWYLrcAzBgwIABA/ULhmMxYMCAAQO1CsOxGDBg\nwICBWoXhWK5A7Nix43IP4YqEMS/6MOZGG8a86KMu58ZwLFcgdu7cebmHcEXCmBd9GHOjDWNe9FGX\nc2M4FgMGDBgwUKswHIsBAwYMGKhVGI7FgAEDBgzUKgzHcgUiMzPzcg/hioQxL/ow5kYbxrzooy7n\nhjAq7w0YMGDAQG2CutwDqO+4ePEiOI5LaJ+kpCRUVlbW0YiuXhjzog9jbrRhzIs+ajI3FEWhQYMG\nsber6aAMxAeO48CybEL7CIKQ8D7XAox50YcxN9ow5kUfdTk3Ro7FgAEDBgzUKgzHYsCAAQMGahWG\nYzFgwIABA7UKw7EYMGDAgIFaheFYDBgwYMBAraJes8IOHjyIDRs24JdffkF5eTnGjx+P9u3bR93n\nxx9/xBtvvIGTJ0+iYcOGePDBB9G1a9ffZ8AGDBgwUA9Qr1csPp8PTZs2xaBBg+La/ty5cygsLETb\ntm0xf/589O7dGytWrMC+ffvqeKQGDBgwUH9Qr1csubm5yM3NjXv7zz//HJmZmXjqqacAADk5OTh0\n6BA2btyIW2+9ta6GacCAAQP1CvV6xZIofvrpJ7Rt21b1W25uLo4cOXKZRmTAgAEDVx8Mx6JAeXk5\nkpOTVb8lJyfD7XYb1bsGDBgwECfqdSjMgIGrHT6fD6WlpSgpKYHb7QbHceA4DjzPg2VZ8DwPjuPg\ndDrh9XpBURQoigJJkqBpGiRJIiUlBRkZGUhLSwNJkpf7kgxcAzAciwIpKSmoqKhQ/VZRUQGbzQaa\npnX327FjR0Sbz8zMTDz77LNISkpCogLSNE0jNTU1oX2uBdSnefF6vTh79ixOnz6Ns2fP4uzZszhz\n5gzOnj2LCxcuyNuZzWZkZmYiOzsbDodDdhwURYGmaTAMA5IkQVEUCIIAx3Hw+XyyA2JZFnv27MHZ\ns2dRWlqKQCAAADCZTMjMzERWVhays7NV/5+RkQGKqh+moT49M7WNmswNQRAAgLVr16KkpET1t06d\nOqFz584ADMeiQsuWLbFnzx7Vb3v37kXLli2j7te5c2d5QsNRWVmZcBgtNTVVZVwMiLga54XjOBw5\ncgT79+/H3r17ceLECRAEAYZhkJGRgczMTGRkZCA7Oxu33XYbMjMz0aBBA/kFjheJzg3HcTh//jxK\nSkpQUlKCo0eP4quvvkJJSQnOnz8PlmVBURRatmyJW2+9FbfeeisaNWqU8LguN67GZ+b3Qk3mhqZp\npKen49lnn426Xb12LNJXoYSSkhIcP34cDocDDRs2xPr163HhwgWMGDECANCjRw/861//wltvvYVu\n3bph//79+OabbzBp0qTLdQkGriJITmTfvn3Yt28fTpw4AYqi0KJFC9x6660YMmQIGjdufEUYZ4qi\nkJWVhaysLN1tWJbF4cOHsX//fhQVFeHkyZP1wtkYqHvU60ZfBw4cwKxZsyJ+79KlC4YNG4aioiKU\nlpZixowZqn3WrVuHkydPIi0tDY888gjuueeeGo+htLTUWLHUEq6keREEAYcPH8aePXtkJ0KSJFq1\naoW2bdvi1ltv/V2dyO81NyzLqpxnuLO54447ojqr3xtX0jNzpeFSViyxUK8dy5UAw7HUHi73vPh8\nPnz99df4/PPPcfz4cbRu3Rq333777+5EtHA550ZyNvv378euXbtw7tw53HHHHejZsyduvvnma3Ze\nrnQYjuUqhuFYag+XY14uXLiArVu3Ytu2bXC73bjrrrvQo0cP3HDDDb/rOGLhSnpmeJ7HDz/8gM8/\n/xw//vgjrr/+evTs2RN33303LBbL7zqWK2lerjTUpWOp1zkWAwZqgp9//hmbN2/GV199BYfDgfvu\nuw/5+fkGuyhOkCSJDh06oEOHDgCAX375BZs3b8batWthtVpx33334b777jPmsx7DWLHUMYwVS+2h\nruYlEAhg9+7d8hd28+bN0bNnT9zVoQPsPAt4qgGbHZzVAeEKrQO50p4ZgudBuV0Rc3fhwgV88cUX\n2Lp1K6qqqnD33XejV69eaN68eZ2M40qblysJRijsKobhWGoPtT0v5eXleO+997BlyxZ06NAB999/\nv5wTIHge5KG98BXNBfw+wGyBZdgk8K1vuyKdy+/5zOg5DeXf45k7v9+Pb775Bp988gnOnTuHRx99\nFL169arVGhrjXdKH4ViuYhiOpfZQW/Oyb98+vPnmmygrK8Njjz2G7t27RxgzuqoC3rxBomGUYLaA\nmbcKrCMZNUUso1xT1PYzozfOeJxGTeauoqIC77//Pj7//HPceeedGDBgQK2wy4x3SR9GjsWAgUuE\nt7oaGz94Hx9+vAEtW7bC0JdeQvMWLfR38FSrDSMg/ttTDdTQsUhG2XuFrIJiOQ+tcVJeN0DRYEZM\nAUwk2C0b4Cuaq3Yairkjc+8E3b0fEAiA4DgQPK95rcnJyXjhhRfw/PPPY+fOnZg9ezYA4Mknn8Td\nd99t1MpcZTAci4F6jePHj+OtN97Awd3fok+gEsUZSbCW/wSLvwq8jpEDAFjtgNkS8dUNq73GY6Hc\nrpCxBgC/L9Io/06I6jx0xmktXIXAr0fhW14Y2megWFwMTzUIqwOU2wVCCIAZXwDu6AGQDTPhXTJH\n05FqOTaQpKxkcebMGaxfvx5LlixBr1698MgjjyApKel3nScDNYPhWAzUO/A8j23btuGdd95BUlIS\nnnv4QeSd3QeCDYp5x2HQOZsDlmGTQiEfCwPL0DzR+OkgZpgrgVWQ6lgOp/il73HXWvgsmvOAu0p7\nnG5XyKlI+6xbBmbUdBCMPcJRWWcshmfWXzQdKWd1xFy9ZWdnY+zYsWBZFv/6178watQoZGRkYODA\ngbj55psv6foN1C0Mx2Kg3kBgWWx47x3887330K1rV8wvLESDhg1BnzsNL+tXbxwjrCWQJPjWt4GZ\nt0rczhrdoMcT5iKstrhWQcpjkW1yQXXoDO+6ZbUbPtNzcpUXIbiqtMdpsWjuQzicEEymkBMO/i5c\nKFVtL4XFCFclaJ6Hf8dmTcfmd6rvCU3T6Nu3L/r27YuffvpJbh0+atQotGvXruZzYKDOYPRjMXDV\nQxAEbNu8GQMe/D+UvLEcaxrweOHIV0gv+Q0Ez4fCWkrEEdYSSBKsIxlseg5YR3LIQfA86KoK0OdO\ng3ZVyKuLcMPqK5oLyuOS9wmUlYqhI2ksFgaWYZMiVkHKY9Hd+8EnORXFcWm3SzUGzutJbNJ05kRw\nVYHdskFznAJt0Z7HpAZAtcYqhyDk7cncO0UHuWQOPNOGwzN5MKh2HUHm3hnaPrgqCp9bJVq0aIE5\nc+agsLAQ7733HoYNG4ajR48mdu0G6hzGisXAVY3du3djyZIlaNe6FZbnmOEU0sQ/KMMuNQhr6UFv\nZYKcJlHDXJTbBe/8ySDb5IIZNQ0IBAATCTRuGrnyUK4mKFr7uFUV8OaPlceAEVNAtGwb9ypGc06G\nTAS7ZQP4PbsAQB4nkd0IrLMBAGjOI2tziIYkbJXDfrkJlmF58BUVgu7eL5RrCV6DGEabJp8PZgtg\nNgNnToDd/BH4A3t0V2eZmZkoKCjAsWPHsGjRIlitVowePRo5OTlxXb+BuoXhWAxclThy5AgWLlyI\nzMxMLFq0CNkBP7xTdqk3Chp2wZGsG9ZKlP6rm5soWBFhWMn2nUCYGdDnToMwm0G2yQW/Z1fIkAJg\nCooBm1N9EgVxgEhJjR2W8vvgXZafEAlAK9QHwgR+eSEAhMYZpAlLc6I3j1qOiurcA4FWbcHMWwXC\nVantIKVqBwsDyzPD4V+/UnQoQVKAMhemda+aNWuGpUuX4n//+x+mTZuGZs2aYfjw4WjQoEFc82Cg\nbmA4FgNXFU6dOoVFixaB53lMmTIFTZo0Ef9QVRE1fyGFtZQ5lRrRf3VyE4LPqzKsZIfOoDreC8/k\nwREMKtUXukY4TmmkheoqWAaOCIXDggZYqK6KGEOiVOjwOSF4PnJFMi4fhCCIztFqh2AyAe5IJxwt\nJxVwJIMWoHl/iPQsMGPngEhNB7t7hzw3qtVMkHEW7V7dcsstWL16NXbu3IkRI0bgrrvuwgsvvBD3\nXBioXRiOxcBVgQsXLmDevHk4evQo/vrXv6JNmzaqv9ck3FUj+q8eDdlmVxlWwsyEnIp07CCDit+z\nK+r4lEaa4Fiwmz5QhM9MYL/cBLrrA+qdLpEKHX5eeKoBuxPCsZ/gmT9Z5Ry573Zohqm0nLcE3mqD\nZfAE+Fa8Ero/L40Fu2s7uA/fEldGo6aBk3bw+8TrDV5XvPeqU6dOuPvuu7Fp0yYMHDgQjz/+OPr1\n6xe1A6yB2ofhWAxc0fD7/SguLsa3336LyZMnRzgUCbJRnL8GhN8H+LyAzQlec+sgalAEGc2BKQ0r\nfe60DoMqCcyY2XLeQm9lJB2L4HlQnXuE8hPB8wkWJuTgLAyY4ZNrlDPSOy8cyaCrKiIJCYqVBLdj\nM8yNmkLweWOGEUmPG+zX2zQcZG/RmUiORILZApCkTG6gykrip2oTBB544AH07NkTGzduxIABAzBo\n0CD06tXrkufHQHwwHIuBKxb79+/Hyy+/jAEDBmDkyJFIS0uLKUEhHPsp/tBWDYogBZJEoFVbMafi\nqQZsDnA2DYOqc2zBVSHnQ+JJtOs5TM5qU4WdrBlZqHQnyAyLBT3HGwiILK92HdWhPo25lvIiRHUl\n+N07we/eqTocfU/Q2JstIpkBkIkEaNQUvMUmHq8G94qiKDz33HPo2bMnlixZgk8++QSzZs0yVJV/\nB5AzZ86cebkHUZ/hdrsRUH6JxQGr1QqPp5aNxFUEv9+PRYsWYevWrViwYAHatWsHgiBizgvtqQbh\nqgLVoTOoTt0hVFWA/fR9mLvej4CZidheoGjQzVqA/+FrgOdlWi2f3QQwaTPxCZ4HeXgfvIUTwW3Z\nAO7LTaCbt4SQlqHaR/PYA0eA27Ud5v97CoHsxhBM8TG4CEEAcfQAvPPywG3eAO6LT0E3bwk+uwl4\nRzICZgZ2Z1KtPzNkIADui0/F8UswW0B17AqyeSv4Vi4IGXqeB//D16q5lnXF5k4AlfsHcLt3ah6L\n+/4rWF4YDVOTZqDatgf9wKPgGzUDb7HKc1qTewWI7xLHcejcuTOuu+465OXlwW63o0U0OZ9rBDWx\nMyRJwm6PHXI1RCjrGIYIZWKQVilPPfUU+vXrp/pbtHkheB7kwT0RciPcdztAP/YcuNRMXV0syuOK\nqwgSSExgka6uAuF1Q6i4CCK5gZhw97jFENCTQ+JmcMVzzrp4ZiIEJ4PEAe67HaDv6wvvwmkAwvTA\nshuDdaZAIEnVuKU6FhUJYfB4EMkNxDnZ8jHobn3gXTRddW2RCgQBCN747pXWvPh8Prz66qs4derU\nNb96MUQoDdR7sB4PlixaiOPHfsHK+YVIua4JBKilTTweFwizVdOYUG4XvAnIjSjDNnoJZ00kkpep\nroJQdk40lmGgH3sBdFVFfDTnOhDEjAfhyXzC5gR4FuYmzQGrHWT7TgDHyYWP4XOrHLeyNoZIToVQ\ncVFVMwOzRXROimuLxQSrCSwWC/Ly8rB3714MHToUAwcOxAMPPBB7RwMJwai8N3DZsX/PHjz96MO4\n8buteI04D8e8CSAP7YWJY0XDkjcI3ilD4Br3HMhDe0FXV0VWZusYXy25EbJNLgiKBn3+jGZ1d1Qk\nUsVvtYt5g7DtyfadIJz+Vb4u78RBIA/t1R9HDZUDagOS4+VSMxE4/hM8kwaHKufv6ga63581lQEo\njyti3PyeXfAumQOB9UPwecEf2CP+IRgmZLd8rLo22l2lqWZAu10R49RSQ4iG2267DW+88Qb27duH\nkSNHXrMRgrqCkWOpYxg5Fn1IuZRtn/8LhXYvcu1m8Q/BeL3lnp7wFk6MiONTN90G78tjxFxDsxYQ\n0jJgAjTzAXSfPwNuF7jNHwEISYv4Vs4P5SuCx9CK1RM8D7q6CmTFBZBCALzVJuY34on1kyRIigTd\nsSuoP9wDwe2CqXEzmP/8ArzzJkVcl+WPPWCqvAhSCEAg6YTyC3X9zNDVVfDNnaAe855doLv1Bbdl\ng3pjngfVpRe4pFTtPNMXnyJw+lcwf5kBqsv9oO99AOy2jeJ2imsjKy6A2xx5bPqPPcE7QirHylwO\nt/kj1T212u2680JR1DWde6nLHIsRCjNwWaDMpUwe+CS8U4aoNwjqRmmzknj5v2PJtoTLjWhKi+jU\nrugVUErV5NHyMgTPw3R4PzzKfYfmAY4kCGdPaRdZnjkh5i3CQj6xBDEJnofn1G+gqyrrroWyXjiO\nYXTZWtK4rfnLIZw5KVKMt3wsh7+Eh54Gm5EjOu8nh4B+6Gn1tVl0jm1Rr96i1bgAsfMB0url1Vdf\nxaZNm6753EttwAiFGfhdIQgCioqKUFxcjKKiIjFBrxfqkf4X/rtyZSDJtiiML1NQDKbwddkwS04H\nZotYK6GXrwiDnrAk6XVrilPG3Hd5IQifVyXOqLwuomEWmHH5INvkqgQsAW1BTHk1dXAPXOOeU4TV\n9sDEJUYYiQk90UpJK01HWFN0jDS8y/LhXTBVU3VAT+xToC2RYpgDR0AIH0e0HFSckHIvgwYNwpAh\nQ7Bz587YOxnQheFYDPxu8Hg8GD16NGiaxrJly9AwJUVMYHMsLEMnRhgQdtd2sZ4h/HcpFg/EZ6CU\nlezZjeLPV4R1QmTGvQxmxBS5E6IeCJ4HodfTJMCD3fKxpsH0v7MK3iWzQXXoDLJNblTDKK2mUFYS\n2SOlqBBUeVliuaMYUDlnaczDJoGz2HQdesx9YxR0cowNyMgBM2o6mDGzxeLKjBxwFpt6w1rMQd12\n221Yu3Yt/vnPf2Lt2rUwSLM1g0E3rmMYdGMRZ86cwdixYzF48GB06dIlgsrKTH9N1KAK8KGQyYE9\nYPLmgbDZAY6DyZkE7txZ+CSJkWC4KxGWkCaFVucYEl1W6onii6MninR8gqLhXTI7kiI8ajq8C6aE\nepM4kiG4KiMYUszEuSJ7Sqeqna6qALu+GOY+j4nNtMLAjJ0DNGpaq50pE6Vm18a+BM+D8rlVxaFs\nWEFqtHvaID29Ru+SIAhYvHgxzp49i9mzZ8NsNid8jCsddUk3NhxLHcNwLMD333+PwsJCzJs3D82b\nNwcQWZuhWecg1Ux06wM0zICz1S24WFpaY+MmIV4jF9NJaNWu6DkjCwPLc38BHE74FPIs1kmvwDNz\nlKoWBCYSRGpDeGaO0nVk9LnTwMXzAAgdBzYNSG0INr1uZeTDFYd5xgbS49akUespSUdTmI5wGtEq\n/DXu6aW+S5s2bcL69evx2muvIS0t7dIm6wqDUcdi4KrFu+++i82bN2P16tXqfuVhcXHpa906exmE\n6ioQdieE8guge/wJsNqiqhQniniPIYXQ6PNn4q8jCV5XRE+TjGz4314V+k0QQGQ3BkwmkO07gWrX\nUV0LMmSCLLOvSTCw2oELpWC3fhypfvzSeLkIs7YRXrColNAh23cCdVc3eCWhSWVNCxBJhBhfAFNa\nOlBZDqHapdmDJV7xydp4LrTQu3dvNG3aFIMHD8asWbOMlshxwnAsBuoEHMchPz8fFEWhuLgYZBxa\nWvyBPQBJQjh7St2Kd8hEEA0zEuqSGE+flXi2EUgSgs0Zv06V4rqUPU2ss5aK1+f3gT+4VxSuDBpB\n88MD4ZkxUm08i18RHRAQqmoP5nYkQgLdMFOuBVE1D7PbQXXuUSuilOHzpXQOzLh8FUGB7tpbk3Fn\nLVgBeN0Q6FBPGrJNLnDudIRyMqDuwVIbxaGJ9twJx0033YSVK1di9OjR+POf/4w+ffrEve+1CsOx\nGKh1VFRU4K9//Sv69OmDhx9+WHMbPXowSCqy4K54HphR0+E5fjSuLolx9Z9PoBdLLEl+peEirHZY\nxhdE5IG4lDRdurCgx1SjaN2qdoEkwaWkyR0aAYDu0R+E3Qk4k8FnNa51ynHE6iHAq8etcx0qGnXQ\necTsKCk5jhqITyrBeT21Ur2fmpqK1atXY8aMGTh04AAmvDQIJp+n7ujdVzkMx2KgVnH06FFMmjQJ\nkydPRrt27XS306vNIPTk0QN83F0S4wmfJNKLJVodiaaDGjIRTN48wFUJmEgIFgYCYdIP1egYTyIl\nVZSD0RljgKIhtM4FM38NhF+OwLt4tsp4CpcgfaKJ8NWDyaQed/i/g9cBggiNP+g8dGnfih4sQM36\n7CjBlpVqUsYT6bYpgaZpzJ0zB28tKMRLPbpi3s2NYLfZLllmpj7CoBsbqDVs27YN06dPx9KlS6M6\nFQma9GA96qjJFH9tQjx1DQnWPuhRmcPrVcg2uSDMFhAmEjCRYLdsgG/+ZFVNCqCWIAFp0qTjgiBi\njlEgSYAPaFCO50acUwuxpFCUfycsVlEfLIhw2jS7/TNYBk+ITg+XnAcZKXUT3oNFuj6pTYF1zt9g\nzS9GoFXsVauEQLVOkW0CNS5KUG4XHv9tD55qlIpB3/+ME+WVcc/1tQRjxWKgVvDOO+9g586dWLNm\nDRgmUqI+Xmh+oT4zXDRO8YZA4gmfXGKIRUZYrYsYulKsHIKhH7CsLDpJWO0IlJ2DV5lfGF8Aa+Eq\nlXIv4XbFN8YYeYhobKxoYSLNvw+eAABib5WDe0H1eUw1bp6xqbpo+t9+PUSjDo6fyG4kF1aq7nN4\nDxboKBiErcai5VBMdkft3Oewue6Y5kSO1Yzx+3/FjJsaoV0dC4JebTDoxnWMa4FuvG7dOhw8eBAF\nBQUwRemNES8InheFBisvQnBViTUeB/eKXRITyLFEq1VJpJ5F2l7LeClp08y4l9V5A0CuSRGqKsRc\niMLhcN/tUNeuhIVn4h1jNFl9LqgQrEXXpdwuzf2sBSvAOpKj/l3we2PSvaXxczs2g+7aW2TCNcwC\nl5KKAEXHRftW0rdlOjZJAY2uB2tzxqQjJ9mscH+3U3MOASSc1A+f6wt+DiP2HseM4lVo0/HuqPte\naTDqWK5i1HfHsnLlSpw8eRKzZs0CIcXSawAtww1ANDwsC8JkAuH3IWC1xcXw4hkbSK9b3Jc0AR43\nYLFCMJvBBb+I461nMXEsqPIyCOdLgorFJhAmE5DUAJzVBtPh/WKb3r6PwzNzZMT+1jl/g/+j9aJx\nDTK3uGOHQXf4I4RzZ+SQGf3YcxF1J/GMkeB5UEf2w7ssP8J46jkHZt4qwF0dqdEGsbhS4HkQ6Vna\nfy8ojrs+xsSxMB3ep3aqQ/NANG8p34dwqMgQZgvYr7aCbJipLlAdmgf+ptyo18c6kpGamqpZ+wQg\nrvoYrbGFO3vPUyPw0uLlGDN2LNq3bx/XvFwJMOpYDFyRWLJkCVwuV4RTSZTeSfA8yBO/iJXVAR4o\np0CaLeAbNxe/uH+NzupRGX7CBPbDN0F17gG+VVuYft0fllifADI9G3x6dly1D2IoZh88YasN9rsd\ncs2F0PIWUBAguCp1wy7UXd3U7K7B4+B/f63YqlcKmdmdEeePZ4wCScJ6x12AFussWphMjzTQMAu4\nUAoiisBkvCA9bniLwvI/ywvBjJoOkmM1Cx0jyRATwH21LfIY0vXqXB9hdcBz6jdQkjhnamaowLSq\nIm7yhnJslNsFpGfBOnclBJ4HaBqU1YEVK9th2LBhGD58ODp27Bj3/NRXGMl7AwlDEATMnz8fHMdh\n0qRJEU5F2UMlZq8RAJTXDZw7De+S2fAumg7v4lnAudOgfG5dIUgpWSob/hkj4V04TdTaatcR3I7N\noKo1+nkUvwKTyQTK547rWsXzRzYQo7v3k8dCBrdht2yI1AAbmgfB54VPKhqUjrFigbiCCf6b++83\nIFg27n4iEeNkrJoilYSkEKxE0DloanhJmmWLZyFwoaxGGl8q6Bn+AK+Z9Na838WvhOZKeQylcwy/\nPrsT5KG9YeKciucwQfJG+HPtmfQShNO/gmfEVZfT6cSKFStQXFyMf//73/HPTz2F4VgMJIyFCxeC\nYRiMGTMmIvwVyxGEg+B5EJw/snZl3TJRHyqGAdA1/F176+4rXCgVjx0PdA1jQD0Wf7Ag8nwJrDMW\ngxk7B8zIqeB2boFw9pRYEKhzDDL3TlDtOsIzebBKoZi+eL5GTgYIGUL/269HOrugc5Bl7QtWwDpz\nKZiR00J5H78PvvmTQTRrEVVgMibCDL8o5pkPIqkBmFHTgfAwsd58h0fsoznHYZNA8Hz05zAO4Uo1\nY64S3I7NYcdTi33abDYsX74ca9euxX/+85/456gewgiFGUgIS5cuhclkwsiRkbkEAAlVSkvGTyBJ\n7X18PsAWg9UTzRDZojC/fHE6Fj32mERSkI4X3Ia6obUoCqnYnt+3G8yo6RHsKOkYdP8nAHc1mBFT\nQhTlokIwo6bBu2ROjeokVHU6HKeSkQlXfmYdyaCDQph0936iNpsjCQjwICrLITiSwKVmysdNJNmt\nZPlJ+mkq1tywPBBJDSJXWBHhuczQ71IOibFphqai1kMFn8N4il4jQnIDRwAcF7qPfh+E8yXyapHg\neSRxfqyYMRUvTZkGC0niD3dfXQn92oLhWAzEjZUrV8LlciEvL09/ozhpvCaOBVVdJRqU9CyQ7TuJ\n+QblPjZHbANgtekbIpKK1NF6Zrho0G1xVm5Hoz9bGFiGToRAEKHz6BT+EUraq4WB5aVxYL/cBDL3\nTggXy0KhMiVFOXisGhX0hfWbl7XLCoohkBpNrBxJMP9pAAR3NbhjhyKT5cMmAXanmiIdh8OT61Dm\n/A0AAc+0YRFf/Ur2mpCUEnnPBo8HTKTKefCMSJrQzb3FeA5jNU/TLKBVKgNIxyMIOZ8jOSKT34fF\ndgojXim7NedkAAAgAElEQVTEX6dOR7urKKFfWzAci4G4sG7dOpw6dQozZ86Myv6Kp1LaxLEwHdgD\nj9KYDh4HQKyPkGoaBIoE7a6CEPwihcBDIGlVHUagrDTSEA2dCC4lDeSFUnDf7VDoaIly/OY/DYj7\n6z+iC6LNAZhMoLv1EfMsGTkAYQL332/AjJoGIi1D06AJPA/mL9NB2ByAzQH22+2gu/YGkZYRqRO2\nbpkYJoIg/5aINhaAuB289GWurBOxzlisXnVJzm2UvgpANFCeanimDQczZram04WnGpQAeIvmghkx\nJXTPKBqEMxn+D98MkRwkqrTXDVB02CpP1CUTfF7A4Yz5HEYlRsQKyUkfGEGxz3BHZA9wWJxBYvgr\n8zB5+gzccsstUeeovsFwLAZi4u2338ahQ4dQUFAQk1Ic60sQAKjqqpBTAeRktnX2Mghd7geRngV2\n13aQbpdKjJIZMUVVx0K7q+CZPxlkm1y1CGPjpghQNCirDfyBPZEhqIeeBqqrAFskC0vvmqQuiFq0\nVs7qANW5B7xL5oBsk6vp6JCUAsKUCv/br4O+pxe4D94AB+gaW8LugP+j9aExW+0Jse3ilUJRGkRZ\nup/16ybcI36L4fAIngcqy4MhOVbf2bmDhtxkku8ZM+5lbQc3fw2EY0dCagOKVZ5Kl2x8AWzzVkGo\ndontjGkLCK87eO9jhPL0GHNZjcBMegVg/WC3fyaLfVIaobckgcfKggK8MGUmZs2ahdatW+vOU32D\nkbw3EBVbt27F119/jfz8/LjrVPTkT2ToJdVLz0KoLIf/7VWgbmgdkdD3LstXscEkg8Xv2QXvgqki\no2zBFMBVJe5DkrAMCZMYGTxBDINpUHujIVoXRKUzpR97DsQtt8NaqEx454Jt0FAsOuzcQ3R+ZgvI\n3DtBZGRrJpGFAC86xOB5eMaWENtOHtP8NbDOXwPrtEUwNblB/ruUmCaqK2WnIgleyrTpsDHBREb+\nFoN6TLldEFxVgNkiSsA8P1qbZRY05CqZGL2wot8XKWGzbhno7v3VumTzJ0PweuCZPRqe8c/DM+F5\nCD/+APa9v8ecP/F+52ky5oi0DCC1IegBgyNDb2Hz0yArB0VFRZg6dSrOnj0bda7qE4wViwFdHD16\nFGvWrMHq1atrpaJeht7XYHZjsFs/Ab9nl5hAjpJ8VRqsiOOYTCBZPwI/Hwb31TYwE+aCIEmx58eW\nDeBXiPUnRAIJcb2VGABZqkWqlQCCSW5B+xiUzw3L+ALg3Gn431+rscLJAxpmgikols+jJ5ppLVwF\nvzNKjYuiX4oUSgq0aivnJ5i8eSJLKy1dDslJxl01pkFjINBmdZ5ozBwQgiDqnemtADzVMg2b++83\ngMMphtQCvCzQCYStsAAxbJiepb3C8Xljr/KCvwnnSyIckJQniRbKE0gSRM71EWFUfs8uCA89HVEg\nGm2FmOYgUVhYiDFjxlyy5NHVAsOxGNBEeXk5Jk2ahGXLltX6i8DZnbAMnhBKWAebUwm0GaAoMONe\n1s1VKNlgksEKb3Ll/2AdzI+/CE/xPMDvA921NzxhUis1SYiHx+T1tLaiJbkFkgRrc8Kcxod6keix\ntpShOr2Yf+VFMW+jAV1nVLACniBLS/B6QAAqY61sUkY4ksQVjM0B9tP3QobWkQSh9Aw8C6dGT+Zb\n7XLPGPPjg+CZPkIznMg6kiMdN2PTbq2gwxSUV3mK3xC+yvaLNG+5NbSrEjSg2emSIBDx3Oit0lQf\nHu5qEBYGQiAAyuMCZ3XgxhtvxKBBgzBp0iQsWrToklQqrgYYjsVABDiOw9ixYzFlyhRkZmbGvV+8\nOYAARQNtcsUGUJIRCYampAp1rVwFM3xyKEegMFiq/IrNLiZ6+z8RMgh6Eu2XKByoK70fR5Jb8LgT\nY23prPIEV1UwPKghs6FL/RbPTfd/QsxJSFL2iuPze3aBP7BHpDwvmApmzGxReDLI3GPGvQzf6tdi\nXqfyS144dyb2fRAgr/QEwqS5SuQBTYcjBAT1imqw2ElTBbMFcCTp9rkBQp0utfNl+pL9AkkGlSJ+\n1mSrdevWDUeOHMGKFSswZEjtd/e8kmA4FgMRyM/PR9++fZGbGyrqi+U0EmmcBYjOxZ+cCiSHjChd\nVSG3tQ19NU8HkZIKwe6ANSMLlW6xi6TSYMm5iGeGg9uyQaYqy0ZGr09InNIk8rVzomaZ4POKeZoo\nVeUAVH3sld0fAWg6CrJ9JxBmRjO0xNkcsAzNC+UWZNqzqDGmCT1mGEWJ57LaZHKEZvhLolUDkXMY\n5qz1VgDKL3kiSvI+2vOjxdzSC0sy81aBqHZBKL8A7ueDoNp1BL9vt+qaEOAjC3KDThFBdpreMxir\ndidWn5/BgwdjzJgx2LZtG7p166Z7nKsdhmMxoMI777wDs9mMBx98UP4tHqeRSOMsXYQZaulLniko\nButIhpOxAkHHIpAkiKYtwEycC8KkyJ8c3AvLkAkQLBY53KZpNONsFiVdO7tjs9iXXsFSs85aqlM8\nSaqS4VpzFh6TJzt0BtXxXngmD9YNoRHNWiryE8GY/4E9oHUcpJSAlpUJgobV/8E6mB8eKBaJaoW/\nkhsA9iQEys7Jq0Kp14ocvpT6qYQl/nXDf8ECQr08RKLPjx5VmHUkizUl50vAbXwPQptcMV9jdwJJ\nKeI8Siw1JaSVE2VWrYDZLRvgXTBFfgZjIlYLA4LA3Llz8fzzz6NJkya48cYbYx/zKoShblzHuJrU\njXfv3i3rHSl71EeTZZdeNvrc6UtWwo11HuW8iKymi6raErFjowmw2gCrDXyDdFDVVeJLbU8CIEDw\numPKvUsgeB60qwKeyYPlKvjwFQbVubvacA/NA+xOED5vqMJcZ86UysWEmQk5FcX21sLX4XemyNvr\nyeg3SE/XfGboi+eBc6cjEtBMfjEIhoFnktY5RUKASlnZLkrUw+0CLFbAbEbg2BGVQkC0a1XOqZZa\n86U8P9GUsU0+DwIWq+p+az1nZPtOMD/+IuCqFD9SNn8kiowGSQf0k0PicizxvCsAcPbsWYwcORKr\nVq1CcvLl6eNiqBsbqHOcPn0ar7zyClavXq1yKgDik2mphcZZvNUW+YWtsbLQKuqT+5sc2CN+1aem\na4bbEDTS4dCS3Tcd3h+Sm9HI0/C7d4J+7AVtpth57XwCUe0CoQgTSV/d5pKTmqEluCphBgHWpqY1\nhxtmzutRs9MkQ0rRmkYfNjtYqzaTSTCZVOE4KKrK4feJDvWuruC+/lJO8MeTwyIIQr8osYbPT6wQ\nWmqTZhHGM67VYrAuxrduGayzloKNU3gz3vqhrKwsTJkyBWPGjMHKlSsj37mrHIZjMQCPx4OxY8di\n3rx5cDo16jvieOkvtTe51CmQ27ElxJBqmAkuJS1iZaErt/GX6aA6dIZgYcAnoMAr9QzxKqXxh+WB\n27FFFLOUdL205oCmtQ2lHnPJ5wF5aG9koynGGndoKfx8BM/D8/3X8C7LDzbE6g/a4ZT7xejdl3BH\nRTB2BKqrgJPHVe0LTGnpIScOgO7aWx4bv3snmHEvR30+xFVKNYjUdOB8CQSekzW9VDmkGjw/NQnB\nRlx3+GrRr6YlC4HAJdPStfbPzc1Fnz59kJ+fj+nTp8d1/KsFhmO5xiEIAiZOnIihQ4eiWbNmmtvE\n89In8kJpQWkgZM2wYAghEG4gdFZQRFIDoFFT3QZSWpB6uXjCFZKDIR4pP8N+uUmzop5nbJrHFUyk\ntk4ZYVJUj/+kWgVYhkyEr3ge6O791KuMGMaScrtkpxIp8ijWrcRTf0N53UDFBQAKKqzPE6qKlxC2\neouWw5JXl3t341jPZ9DsX++AadEa3H+/EXvmKPIw0ei6uvczAdFT1f1ROGj63GkdEkZAXt0lgnh6\n6Eh46KGHcPDgQbz77rt47LHHEjrPlQzDsVzjKCoqwq233op77rlHd5t4nYbe13RcMiSJGAg96q3D\nCTZOmRZ5bFKDMK1zC4Kc1Ka79wOSUmDNL4ZwoVSU9PhyEygQqv7rMqqrNHXKpMJPwu9TfWnzu3eC\nfuBRkYHkcCZmLINzF8shEcEkOVVWAsJEwv+BotHYsEkgmjSHUHFRRVCwDBwB5DRRz3fY6o3fswug\nKLllMcHYIZhM4nksDDxFc+Ee9TIWfHUa89t3BbFkqpyXUTrLaHRdomkLbSkWqx1k+06q7pzsl58m\n1tNeb0VOkjH7z2h2LvW4E1KAzsvLw5AhQ3DDDTfgjjvuiH/cVzAMSZdrGHv37sXBgwfxwgsvxNxW\nchpcaiYgAFRZScxeIQk1/YqjP4aEaPIq4eeX+2m4q2CuKlc10qLcrmDXSULz3JJUO79nF7xLXwZB\nm+GZMgTeuRPgXTAV/G6xlzrtqohs0BWss/EumAp220YAAH1fXxAZ2SDbd9KsHmc3/BMC6w8pCsQx\nF6q5i1KvE9GoasYIUO06gsy9U3ZA4DjNvjgIiGwusn0nMexFm2GdtVS8juD8U517yM9H4Lef4Z3w\nPLxThkA4cwIwmXDR2gBnq/wotzYQ51saa1hjLb1+Pjh5XPMZ4q02UHd1E+tVTCZACMD88EAELFbt\nudKA5vM0NA9o1DSqenP4nLL/KIbpwJ6w530PTFx08g5Jkli4cCEKCwvhdsfXgO5KBzlz5syZl3sQ\n9RlutxsBqSlUnLBarfB4PHU0IhE+nw9jxozBwoULYbNph3PCIbOS5k4At/kjcF98CrpZCwhpGaH+\nJIptaVcFUF0FqmNXCO5qCKd+Bf/D17D8sQdMlRdBCgEIJA2YTBAoGnSzFuB/+Brg+ZBGVnYT+djy\nvJhMQGpDWO7pCfqPPUD3egh8dmMIFKU5VqH0LEw0De/CaaFx33I7TIwFBGECaDPIljeL9Q7yufPA\nN2oG8729Qd3XL9gx0gsq907xWs6eEk/E86Da3gHvy2MhlJ2DuVkLmFyVIGgzyHYdReXebn1AgACE\nAOD1wtTyFhDJqeC++FQ8XxCmRk1hapMLwmIBefPt4kpAOR7FXCghUDTMN7QSJVL8PlgGDAbVsSuo\nTt0h+H0gb78bJtYP39wJIYPN8+D/9wMsT7wotv3leVEcc8sG9cF5HvQ994PIyAbhTIbvbwXgtn8G\n7j+fw/zQM6AfHgiq1/+Bz24isruqq1TnoTrdBy4AfGhticMX/LBYaNxGV4Nq0gzc7p2gej+CgDmk\n7EBWXAC3+aOIMVAdu4L7+gtx3D98DXPX+yGQNOjqSoDnQOX+AeymD8B+sA7cfz4H1awlkJoOxu6I\n/S6ZTBDSMmDuej+oLr1A9X4YfHYT8BZGc74lhF+rZcBgtVPkefA/fAPLXV0RsFhF+ZvqKpAVF1TP\nPgBYLBZkZmbizTffxL333ht9vLWEmtgZkiRht8deDRqhsGsUr732GgYOHIjUVI0qbx3EkygleB6U\n1w3h2BF4NNRn+T271Aq0iqR0eLhNbuQkhRVsVvkcpsP71aywYZNUISmlrDqRkQ3/+2vlcZNtcoFz\np0OSKmYLLKOmgZkwV/y6b5gJPjkVAYqGYHWA/FWj4VPwWiTZELkLpCSBHxyT+alhCPz4Q0R4SbDb\nI/IS5gefltV8ydw7QySG9CwIJlL3y1nqee8pK5WVC+RzDZ4AmEgQlRf18whAMJeg3dsGJAnh5K/w\nLZ+nvvfBvvOqvE9YSJPd8jE8T4zEl1+cAwB8ecKNR//0DMj3VoirApMpZuGoTJ5QjptlQf4ayQyU\nGnH5lhfCOmspuKQk1SXrhWYTyYvoXaveilE4XwLaYhVXclFqwbp06YKNGzfim2++QceOHeMfxxUI\nIxR2DWLv3r04efIkHnjgAc2/q1uyKsI7MdoES6sEnDyuoz7bT63f5PeB27FZDiVJiVo2PQec1SEK\nJSrCCp7vv5YNQ7S2swTPQzh2BN4ls+FdNB2e6YqwD8R8SUTIZ8kcMbdBEPB/sA7Ekf/pn0u6lqDi\nLbvlY+1jFs0F9Noumyg5B8OMnSP2e6mqUOUtvAumwrtwGoTSswBNR72nFGMFOB6+iHYEr4DwVAOS\ngKQSksGWQok2p2ZIyP/BOpElFuXeywgLafIH9qCcDaDCywEAyr0cKkgb6K4PgNv+Gbzjn1eFtqSw\nlBR2Y8bOgXXmYnA/H1KNmzCZtO9L3z/L/xbOl4AtK5V3Syg0Gw/Cw7dS7kkJ6XmPs2X3tGnTsHDh\nwqs+JGY4lmsMPp8PBQUFmDVrlubfo758MfIgshHWM0KCIBtiQK/X+15dgy7L5sdwcJTbpe/YAP0v\ny3NnVLmTaOcikhvAmr8c3H+/EVcuuvkNt/bvPq/KecDrBThON9cTF21brx3BuTOiivLgcRFOg0jN\nADOhAESzFghQtNjUrHAVrDOXgBk5DURSspjg1zOaYXmf8HwFcXsnfHlGnWP44kgpfF9sFOctzMBK\nHSepzt3hXTIH3oXT4Jn5F5ANM8UPg6ATFPQUjklR9UAy6AF3yHDH+iBJFOHXym7/TFyFKec4yCiE\nxRKXY3Y6nRgxYgQKCwtrNKYrBUYo7BpDrBBYtHBXTNqxZNh0aj6I7MZgt3+mYlrpsZiiOg8lE8hq\nEyVIeB7w+2GuqoDAsbqODYBKjkQ5vohwS/Bcmgy0inKwH7wBqkNnMTcTTY9Ma39lQjeobSZ43Bpt\neSdAMFuiMosInofn1G8gzGbd65Io3NbZ4rGFygpRAidYXU44UwCbUwwLAfAWjAf8PrlGRZNSPESk\nW4cXZvKtbxMZYmdOoLxRK2zdfFI13m0nPPjTXffDJtHKwxhvpMcdqikK/t23bpm4qqNoWQJGc16r\nXaB79AfVoTPYLzfB+szw0N9rSE3Wg9xdNHitIAjwlRWwzlgsMgcJQm4GJtAW7XfCzKhDgagfITHD\nsVxDkEJgEydO1N8oyssnaEmbh1E/dY3Q0DxwdqdYuyCJAgpCVOehZ6h5JsQEorr2hnD2VFh/9jyQ\n7TuF6mGC+xLZjcUeJ44kTQ0tWXBR2p6xg7U5YBlfAMLnFVdiJAVBCIhGWSlSmJ6lecyAxw3Li2Ph\ne32hwlmMB/vZB+J5ZOdsA5WWIeZLZi0DfF4IHAv2sw9AN2uhe7ukFaZLT41XcV387p0QutwPECax\nIVoQvnXLRKVpjWdAdS8R7JNiF6vxQZuBQ/vgVebSpLyBzwv2y02o/HNLXHBzqjGXuVm4UrNhIymA\n5yJXPnorL9YPNqUhAEmUc2Io76MQ5TQ/PFB8Njr3AJ2WDk9QX6421CHCIeVmSP64/MEV6NAZ5oee\ngRAIgB4wWP7wivgoe2Y4/G+/rqrnkTBt2jQ8//zzWLduXdzkmisJhlZYHeNK0Qrz+Xx45plnsHz5\n8qgJ+1haR9HqUqRe9r4Vr4gV4D36y+J/bPBrOB59LKndL3niF5VBB8OAu66ZuKrKGyQmt0FoanJZ\nZy0NJdIVmlqAKIvO7dgsrniCFf4BloXv5TGql5645XZwFptan8tsgeX50eC++VLV+4MpKBb7p0hV\n6wqRSCZvnqhwHGw2xv18ENQNN4k5nWB1vKg6IApdhjvkaJTX8PslSsH0B5HcAELFRZUDlObF/85q\ndd8SAEx+MdgMUZPLXFUOT96Lkcd0JIEzkah0pEHwVINwJCPw609AQGFCTARMzVsBAkAGOPx/B87j\n7cNVEeN+opUTf2pEgbc5xRUkSQWvkQDBcwgcO6w4rgD7ri1gHntO9QwSECCcPhEx39b8Ygglp4HG\nTeFsdL1KX05Pay3eglo96GmghW9Duyrk1Y2k26anq7Z9+3Zs3boVs2fPvqSx6cHQCrtEfPbZZ/j4\n449RXl6Opk2b4rnnntNVFT1w4IBm/mHlypWXTSyuNhAvC0wKd6kNbxY4xhZT5Zj0uMF+vS1UFCgI\n8H/yDugnh8gvmZJ9E03tFgBQXaU6FzN8svi79EUrMZq0vm4DAc2VFV1VoV3hP0Hso0LYHYDNAf8/\nV4Ju1gIUH4gMDa55TZb7kI1uIACwfviVhlxCdRVAEKqmUZx03nmrxHmT5puiYZ29DILbBSKpgXZr\nZyX0FKFfWQOBY2V1YkkpQLA5Qr9JUFSXEzyPQFmpauXDH9wLqmNX0UkdPQBi6HR8IWRi/ZfHEBA0\nTMi+n+X/9HLaVPt/Hq7Chz+bAFToXBgFEwE8eVMy7rWUw3J3N1Ulv7doLqg+j4JsdD18KxYoVoPj\nwH61FdyHb4F5ZQ08p34DXVUpfwQFWrUN9QGyOcDZ4leHiIZ4WGUCSULwecWcGkSHzYx7WbutAq7u\nkFi9dyxfffUV3nzzTbz00ku48cYbsXHjRuTn52Px4sVICqMiKrF48WJYraEiq6vZqcQVAgtCTp5C\niNCqIpq2iE439lSrmkFJoB96WvOFi1bRr3QA0rm8fysQt5VCGiYTAEI7vGGza7/oeqE+twveRdPF\nr/rZy0Jy9OFyJtL2gqDQ9FJIqCipyMGxEA0z9av7g1LtVLuO6vkeMgGEzRlb0kQvvEPTmvRt0ueN\n7OuicOaU2wXv/Mkg2+RGNlCTQn/zx+OBhW/h5oZNMGv7SZR7OK2RxYSe0wGAFCuFmd2uRxPSC4Zg\nNJ8L7sO3gAefkvNGMFvA7toO7sO3QLbvBOH0r3Ap9d/GFwDVVZo0denaE6mY10JMpYng/QrJ72jr\nwUm4WkNi9Z4VtnHjRnTv3h1dunTBddddhxdffBEWiwVffPFF1P2SkpKQnJws/+9qRSwWmAQlxZiq\nrgrlCgDZgRCsLzqzJQZrTIvGLH3pSRRjyu0Cfe40CHeV7rmkVRX75SYIEJlmelX4Eee02vRpt8Fz\nCBUXQ8fQuSYiuzHMTw7WpBLT3furx5KSBiK7se7cECZT5HGKX4Fw/mxMSqxm1fj4AhCCAKqsRNwm\nNTNE357wPLjtn4EZNR3WmUtgnfu62pgFHa/MWFs0XczHuCpV47byPjT/4p9Y2rMROmTXrsH7Q+Mk\nLO3fAs1SaJBOp/hceN0wl58HUV0JZtR0mTrOffiWGLYLBOCZPkJ0NhYG5ocHRjzDhM+ryQqj3a5a\noSHHQ2eW7hfdvb8mPT2coXa1ssTq9YqF4zj88ssv6qZVBIG2bdviyJEjUfedMGECWJZF48aN8eij\nj6JVq1Z1Pdw6QVFREZ5++umoIbDwEBczdo62Uff5oiY/o7HG9MJogVZtRW0ljoVw+leZDcSMy9c9\nl7TSoa+/AWBZEDnXw5q/XByfzSFLzGuec3yBZhJVTtybLSDSMsDbnaC8bhAIRCaJh+aBdSSLhluL\n8pqSKuZcFCsw1pGs3+RK5zgShTlWwyu+9W1wLPg7OFclYHdCOPaTuvgzbLUZYuX1B0FRoAjIGlda\nzDKyfScQGdlgxswWcyEUDYH1g2rSHEnvFGH8I4PwVVkylu06Cy5Q85QtZSIw8q7rcGdjJ6ykeByC\n50Ge+AXCudORGmZQFKkmpahWZ4LWSlOPBq9DQ06oSR3iKyCWn12dtgpaDDUpJPbDDz/g9ttvj3s8\nlxP12rFUVVUhEAhErDiSk5Nx+vRpzX1SUlLw4osv4oYbbgDLsti6dStmzpyJuXPnomnTpr/DqGsP\n58+fxw8//IDRo0dH3S7ihSB0wkuOJFhnLQ3qa5nAbt8EqlN3eXWQaGiLP/EL6MwcCOdLQKRngd2x\nRcFG2qBJb1VWasd66TVf9PmTwcxfE1LRNZng/2BdqL1xkL1mOnlcNmZiWGi6nGxnbcHVkB7FOPh3\nuKtBIdSmV5dRpxPOItKzwUx/DQjwES1/lRBIEtbrmuDChQugqyo0jaS1oFiVjFeG8MT+Kt3gDZIu\nlPMu9yqZPkLlqJB9HZCRA7pzKujTv+DelIa4qW9zzPryBE5X+qPeFy3kJJkxo8t1yGIAkCHnRLld\ngM8bcirSNUmy9gf3iuy7slLwjZtDkBrPCYicU5MOzTxajcmlVOLrHEcgSQg2Z0IMtfHjx2Ps2LFY\nt24dCILQ3OZKQr12LDVBTk4OcnJCHetatmyJkpISfPLJJxgxYoTmPjt27MDOneq8QmZmJp599lkk\nJSUhUeIdTdMJSa3ooaCgAFOmTEFaWlrU7arPn1U94Fp0YWZcPoRfj8L7t4JQMn1YHqib24H2VCNQ\n7YLJ7gCdlg5KgzWiPAeZeyfo/k9AqLiolkBRSHJIX9XWl5cDbpfYw4MwAb/9Ajo9C3RmDixJ0V/6\n8OsCAPh9MHmqYW/RBgDAeT0gnxmOwCMDYbKJ4/eXloBXGDN5PGYLbHNXwnyxFDBb4PtgXeQ8DZ0I\n4WIpvPMmheZpxBRY77hLrI5HunxetqwUgWoXCIcTzPDJobmVVlHfbgfZMFNFpVYfKwTpmdG7Zriq\nZAp2eP2Qqr9KWJ932B0QTv0GZsQUuVWvr2guHAv+DrrNrfCfP4fAxTLQlReRU3oGC+5tizf3ncem\nY/EXHT7QsgGeapMCx0d/h/mBR2HPylbdw4DOSoNwJIEZOVVmgzkW/B3W65qI82uzAiOmwLssX55T\nWK0R88wMnwyToheODLMFlCMJzgTeQ49Hu7ZG6zha42OGT4Y1I0tswR2G1NRU/OEPf8D333+Pnj17\nxj2maKiJnZGc2tq1a1FSUqL6W6dOndC5c2cA9dyxOJ1OmEwmVFSomScVFRVISdHuJKiFG2+8EYcP\nH9b9e+fOneUJDUdlZeVloRufOHECx48fR+vWrXWPJdM2KUr1Qsgy6LOXQSi/IBoYkgqFVwAxmV5U\nqKb16iQgAYC2WFVJS7irNavjJbYVIMqBIMDD/8k7ahqu2YLAsDy4W+dGVZ6lae2CwYDFqqKgUhwP\n8AEEeB7eKhdoV6Vu2CRw+jd4F4oyLPzunQDHqaTxifRseKYNU8/TsnwgTE8tgsI8vgDWwlWAuwpC\nuUgTpvs+Bu8rk6MeS4L0zEjzHH7NgqsK5ocHwrNvd6RKQNi/Vcyy40dD90kRguJclfBYHaD5ALwF\n40G2yYX50efATBqIZ8fPx7clNMrcsZ/7NBuNZ9s2gGXNQlD39YHgdaPqt2Ohla7FqrvSEFyV8C6Y\nKsLbPdAAACAASURBVP/EuSpVzzrRsm0oRKjoQxO+auQQqjFR0uR5jsfFUlESJp7EPmG2aoY7vWYr\nPBrvINEysk9OpdsDuLWFIQcOHIgXX3wRt99+O0xRxDHjxaXQjZ999tmo29Xr5D1FUWjevDn2798v\n/yYIAv73v/8llDM5fvx4Qo7oSsCiRYswZswY3b8rE43+f6yISIBT7TqC3bUdQtk5eKaPELn3GoZW\nxXbSSUACGknLKLIv0hgsA0dAqK4C3bW3RqKzUHWecIl88tBe+N9+PWZiXyvZCps9ZMyUMFtANMwS\n8z92MZShSnIvmQOYiOgEB+hIi8yfDIEABEXxIkFSMY+lOc9asiJbNsgUbCK7kfx3MvdOEBnZ2tdq\nMkU4f+6/38D8+CAQgYCoXh1UOaC79xOrzX1eVJOWuJwKIBZLVntZUO3vhnfJHHimDVclvTmbA0Lw\nGlTX9MLoiILWcJKIkrwg0baVZBHlb3zr28DMXwOqy/3wLp4Nz8xR8OQNAnnil7gT+8pwJ1NQDOvc\n10E0baHbYkJrLNHgdDrRrVs3fPTRR1G3uxJQr1csANCnTx8UFRWhefPmMt3Y5/Oha9euAID169fj\nwoULcpjr008/RUZGBho1aiTnWH788UdMnTo1ylmuLBw8eBAEQaB169a626g6NoaHP0gS/g/WqUIk\nupIl4fFendh0RNJST/Yl6zqxoJBjg+KO/aNX6AfrYVTkg3H5IcMtrSgEQZSUUbzAeslW69yVMtss\nvIrd/84qUQblxbGwTF0EorI8VJFvtuhKd8RTWQ53SHGA7t4PQrV2aCVapbhAkiCatQQzanpE4SAd\npGBL9UNSQab//bWaSgnhelyytpsq3yKqHEgrNlOrW/Dfi4m1ifhvGYdu//5cN+nNN24OKiNLQdCw\nizmVYD0OKVW6u6thFoBA2Tl4w8gLsYogBZIE+ECEIyV83oRaH0vOgrA6IlelcYwjFp555hk8/fTT\n6NOnD8xmc42PU9eo947l7rvvRlVVFd599125QHLKlClyDUt5eTnKysrk7TmOwxtvvIGLFy/CbDbj\n+uuvx7Rp09CmTZvLdQkJY9GiRZgxY0b0jfQK6wqKwTVIB/3kEBCuSkUyXUumZaIosAepOrufaMAt\n1ohiL0CdtNQ83uAJCFRVwrdouvwb1b0fTGkZUXWWIhyEYjWkzNcwBcUQSEVMOUqy1ZSaDmRdB+uc\nvwF+f0QVO7drO6i774O3eJ7acDRqGrONM2FhtK/HwogSMsMmAYIAdqu2PlcsQUqOsYHkWPUYFCs1\nycmbGzUNKR9oOOBwPS5tbTcxHCqUlYL98lN4nxyFT/d4o44vHJ/+VI6OHe4FczgUWVB+OAgkKXYG\nVXQHJWxOMYzEimzC8Fwd2SZXJXIZF8NL63mIpuoc5Xi6Hy2FqyBI56pBvQzDMHjkkUewfv36mOGo\ny4l671gAoFevXujVq5fm34YNG6b6d//+/dG/f//fY1h1gm+//RY5OTlo1KhR9A2j6CZJX11KZk34\nqkawO0TNrmB/9IgCP52vM95qCzHL7E4wE+eCICkIPAf243cAmob15SKxkVbwa5to1gKWIRPgK35F\nvXoI6iwhp0kY+8ck53Po7v3Er2mSEsNXOnOgdIygaPjfDq5MhubBlJ6l0tYC1AlvACoDxsVo4ywE\nApqrISEQCK3sXBXyF7mqULFx05iGKJ5W0lIVuOrag+eQxhFBH9dbOfr9IBo1BdWpOzykBT+XXYwY\nU8dGTrx0Zw5W7jqNb06qJV6Olnng69oWjPLHOFZmrCM5yIKLnquLxxEA0H4n9JhksfTF9D5aKi/K\nAp81XcU88sgjGDBgAB599NG4mm5dDlwTjuVagSAIWLp0KRYvXiz/plcJHFOpGJF1KfzBvaC69gbX\nMCsk0RL+5QvofiVqN+jKQ6BlW5h8HtCPPSe+sIIQYssAwJ5dENp3gq1gBQJhOkv8vt2wFqxQ9z1n\nbLDMWAwTIMb9TSTYLzaC6twDhOIlVsrXRDjGYJLat7xQlAAJNy5RwnOCIzm6vAdFg/vvN6qkP/vl\nJtBtcsVDh9W9KKnQvCV2MWLM6m8JdieYaYtAmEgI7mqw28SQmWVYHkzOZLG+KKeJqN7r8+qutISq\nCiApGYGbb8f/flPnf2gTgVG5yWhfdQxJx0oxOseKb9NTsGRvharm5Uc/g843tEbg50Oaz6Iu9Ay4\nsmtrPI4A2nVYQnC1F+09CQfB87pUdMFVFfM9iQUKwEsDHsea1xZhzF9G1VgloC5hOJZ6hM2bN+P2\n22+XKYSxtL3i+apN5MtXBY2vRO3wgKILoYI1paVXJgQCss6S8jxCIKDZOdH/9TaRuWUWhSOJpBTQ\n589AsDtVtSWajlHx1SsEAhHGhUhNr9mXLEQDRnXuERqvhrGSpHUS1bWKdc+V2wnHf1LnACRnqsf2\na9U2Ug4mqChMP/Yc3NYUbDwcYhldl2TBjPZJSPv47yC++zd8ZguSRk1Dpx1voVXfZzHr+yqcrhTn\nb+PRCtw5Oh/2qlJdEUdN6HacDO4bpyOQHDHR5AYw89eI+m5RmGTRxkZ53WILhMETIDdeszCwDJkA\nNrz1c7yrKcVYyUN70eVf/8Dfv/oRp499j+y/Tq8VIc3ahOFY6gl4nsfq1auxZs0a+bdYlcDxCufF\nbNkahxw5wfNRZVqUToVyu4CcJnKzJ8m4MXpy+CYTvBqdE5lR08Rt/ZJw5HR4Zo+OMLa6jjEQQLju\nFuGqhODzIeDzarcGiOcrG4CpSXNYp78KWKwQzGZwFluE4Y/VflkL8baPpl0VoWNL2ymdqQbbj5m3\nCtAhBphtTnjZAA6Xip0P+7ZKxROpLthemyCuGoPHIRzJsP6xOxp7yzC/QwP84xiNT39x4dA5N6pN\nZpjTc5AItFfeE0E0agqmoBiUIwleszUqLT0eRxxv22ITx0I4dgS+5YWhwlq7AwLPg0hN0xYATUC2\nX7q/BOvHsBuysOzgr5heg1VPXaNe042vJfy///f/cP/996tjrjE6LdYWNPWqFMliE8eCvlgKkLSu\nXhagpv/i3OmI2Lm3qBDmhwdGnCeqY1D+m6Lk//YVzQXlc4OuqgBhsWiPiyTl65AcrGBPgveVSeA2\n/BNEdmNYZy2DdeZSWAtWxPXVKF2jJ+9FeKYOg2fKEAjHforYTq/bodTGWYu+GtN5K86vRx+XnakO\n249jbGKfmH//CwBA39cX1tnLECi/gIPHS2ClTZhzVxqebeOEddGkkFMJzqngqhSp2QunIuW3g3ju\nJifm9GwGK23C4VJ3wlXl8spu1lIwY+eAGTkV3I4tCBz/CVxqJqzXNYnpiGurqyTB86DKy+QVnUhF\nnwLP3AmA1wOBpKK+J8rjaLYGB1Tv9J2pTpzy+nGqoqrW3+lLhbFiqQfgOA7vvvsu/vGPf6j/UAeN\njbQQLWQmfnnvg6eoULsRlUKmRfW1rdc+WEMOX6+boKojpNkCwpkc6nvf/wkIvxwGt3MrqK69tcfV\nqCn4sJWE8gtZlfvIahRXKCKeFQUA/WZXZ06I4cCwL2vO6xEdBkVHvefS+ZlR07S3I0kxZBNk+6n+\nZneKBbXBRL1yNclPeQ0/+2gU3ZeFhu7zMJVVQhgyQTNsJl/3umVwFK5C2xQGRf/XChsPlaFdtg2W\nBD93SY87FLYLgt+3W3xOEKN3iMY8k21yQXAs6HOnE2JuUW6Xroo14XCCtdiAGKHl8BUU2b4TzA8P\nhBAIADZ7SEQ1eI7RN2Zj6bFzeK2W3+lLheFY6gE2b96Mnj17RvDaYyXo407yxgG9kJloyEJfcECQ\nWeZIAhgG7K7toJIbgHY4AZ8XzKjpovHR1eGKlMPXvM6XxoeMo8Qi+/BN0H3/DKHkVLDyfx6YUdPg\nXTInQiaeyGkCVuFUYsXh4563MEMmMbIitMD0PgqkL/owh8SWlcqV41FDdMHz67UaJrIbA24XzH0e\ng3BvH7CbPxL1uMblQzgm5mSYUdMi6z2sNjzSwgbHod3gvtsBU9feIGx2semWpxoEY4V//Up1rxq/\nD4K3GoQzGQ3MwEO3NISJNAFCgjL8l7IyD5tnSUfNM2WoKjQmi6VGe1c81fo6e0kN5O2jhdWUHx5y\n3ZAy1xUmonpTeiouBpJR6uOQEl8U9neB4VjqAd599128+uqrEb/HWknEE1uWUGMnpFcvM3YOEHCC\nvKG1+BUeplzL/XwoUodr+GTNHIbWdSIQAG2xgL6nVygXsGcXzH0fh3fdMlH7SrEyUta7AAAzdg5I\nnld1nYx3rqIijOKs15ND01mGt09W5KcC1a4w5y06SSK7EVhnyKhJ51dtF6xd4exO4PC+UAgySIKg\n+z8BIjklJOlD0RGGnFq9APYnXoL/ux2avWWQmRMzv2AzBWAixMaRCT1vCazMw4/LW22qeaZ79Id3\n8WyV0/QVzY1PushqB/vhm/Jzq+qiGjx3zOdF8b5o1g0pRVSDz/pj//kK77z/PgYPHhz92L8jDMdy\nlePo0aNo2LChruRM9JWEdkhGDi9JLx8jts5VG9Y8EDnXAzQd90uvKqLMagTB5wHhJnSVa9ntn8E6\naykQCECw2WHNyBK1lGJcp5ycVr6UgLzigd8XWhFFURTgdmyGuVFTQAhEJrprmDBVOgztgkNFxbnC\nWRJmBv63X5cdgrJzJe2qEJWXNWp3BLMlaiiPP7gXlqETgUAAVLULfoXCtESCsM5aCsEbqnkhnMkR\ncxY4dgRgGO36nuJXYJ29LC6yQyAQSPijJx7qPKCfqA+0agtm/hoQfh/g9Wivfvy+mEWXEtuP27EZ\nTN48CBfLQk4q3o8RpZPUCQejugpseo78Tt/XsycGDBiAF198sVY0xGoDhmO5yvHmm2/imWeeSXzH\nKLIi5K8/q14+66ylGoa1UA4jxfPSa9aKDJ4AIqWBTkw6CXSX+0VpmSeHgHUkw8lYQVS5on7JSsbD\nv2OzpiFDsN+IFApiv9wUud1zfwH38yExDDF5cGh1Ez5XicqqQ726UiobaB033FlSnXuA37db0X0w\nZLSY4ZNhmfYq8NvPkZ0/FfdGtbpTtg2QaNkKhWlpPEIgoJKa8Su+ykNzOxH/P3tvHiZFda+Pv9VV\n1V3Vy8wwMAy7gLJIgo5ejES4ylUILhGjRo1GxS2CyEV/Ccu44comGmNCBJQQiX69IYmauGEEDUbc\nEqOICbiiyD7AMEvvtZzfH6equpZzqnsQvJo7n+fJE+mprqqu5Xy29/O+iCqe+R7P4CUAY+/uioY9\nK+5DMa5pGCSYOw0/dwnMbZ8hbz3T7FmdNkqeCjjOhUWHb+sECbqG/PxZHQ5GPE6SF/T4MjFRFDFq\n1Ci88sorOOmkk7j7/jKt07F8jS2bzeLjjz/G8OHDO/5lngZITAm8fFxZ3Q4IUTFnRZbSSJY9SFZi\nrrWlje0GtT/iFPoPov2OeAIQIqW/+2hK9EQK2PZZab4AoKWKLt2g3vkAyP69gK4D8QSkZKq0QMf5\npZYDKRH6mQ38WYYQTzG/50CUlTiKv33Icy3zv5wLde5S5BiqhMrC5YBhes7RPn6u8SpmtuiWVra/\nY1PNsFid0b0XtHgScrd65zcFynwTpzolSYBS7ID1WyvUNWFd01BHz9tvOu2U/5i9Jwt0YGxcX7o2\nnFKbc2+bdhxQMOJxkpqG2JRG6OvWeOa5dCU4JHvhhRfi5ptv7nQsnfbF7U9/+hO+973vHdB3eeUD\nwkq/eQ1Jl5xvuZeeCwkuFDgvcknR0X6B7QZ1YOGcZsnnRmOIXdPolCz8PGFiRER+4Y1QGhc4wl0k\n3Ybi75Z7+ys/voP+Zqv0Q/I5doRumhDfX++AE8KGEeVsO5BNe+ZW9HiS6rA37fD1JGYhcuTRMCXZ\n+b74/rvemRZGZsFDOJHNpbkKeewECpSo6gJiMRMH7ombYdoqKbmpZuwejdv5KAuXU1SUXSaVoqWM\nyr5XKxZBvX0RyNgJ0NY+x3XMlfZMPN9NpmgPI5eFoCZAIhGqb59LQ4hSfRMecwBiivOZowN0+yKQ\nPTs9/TkAtL9UycwSAxTgLl2GBSAOkaVhQI5GIRHiy0IbgSFHOc8HANTV1SEajWL79u3o3bs3/7y+\nJOt0LF9TI4Tgqaeewq9//esD+75/sltNQE+kKPLF9/Jpa1chNqWx1NQNWfy5xlssEglnHgQabQwX\nn/iNV9HReoHtBrXHigU6rGf9d2HxfCjTZnvRR/b5WXK12lP/45Q17BfW0//p2dfhiLL7IH7UGOIJ\nYOfWIE+VRTRYTHm1V/xOQezeC0bfgYh06RrQuSksWQB17lIUqymDgl3C8Wc28vcv83GhVQX6WUKy\nGiTTDumM8yB2q/eUz2K8gdOefQPSyvYzw5RYdiHGUCxAmbMEAoe8kezZifyiOZRwNKayeylDhpft\nmUR0DZEPNiBvwdil40YHASB/X4f8xvXUeWfa2eXRS68FyWWCfUDASytkX5vqLlBmzQe61jERg7Zz\ndAdurNJluX6LM28kySVZbOcZo8wIWpc6z/cvueQSPProo5g1axZzn1+mdTqWr6m98847+MY3vgFF\nUcpvzDDeZDfrpZZGj4MwYLBFW54HlDhACKK9+4Oc+QMQ0yzPuMvLkKSopxYtnX0xot+/DDjrogCN\nSSSRLD+vUiw4jWz/oiRZpSdH833ChYhNngn9tZcYJJqNtGfRsg8oMlBjP77DOZ7HigWgbT8E67yZ\ndf0Vi6BMm02H8MLKPpZjQS7DLi1NngX9tRdL/ZEpNyA2Yy70Pz8R+D3qrfcjd/t1zAUqt+Etz7Wi\nrAwlFugAkmqIV6BKIMTjHIVIBGT/Pv69ssugc5dyQREsIk8AkNtbLTBDDDnLqTNBEK6Snof63l0e\nreuB4m+XAQB1RO+84Vw3Jmz70msdOQkoChBPeQAB/oxQt66ToGsl+LLrd6pzl3J1WJx5I05/j+zd\nDUlRPeXn4447Dvfddx+KxeL/OqV+p2P5mtojjzyC66677oC/H4oKc6ORlATVt5hxOY3oRoyC9O0x\nKCy9x+OQylmgwZqwSheZdqi3L0Lx8YcBXYfYrT6gr27TmMhd6zzOSTxuNKLfuxikvRXK9DlOHRxV\nXZwatRCJgBTykLNpICJAvXEhSCYNbfWfkF/QCPWuBxD9/mWlYzrXgi666N2fXdKw5nBYET8xdMjp\nVkrcSExvpmHJ+8I0StBoZtkn7pRMoCYgj50QLC0tWeClrbGypegPfhToZ5HmPewFqq2For6sAbxy\nA3v2PdGHHl3Sl/f3EwoFaGueCi9xckp39ud+Is+A5s5PXI6Eh56yS0UcGQX11vvp81IsALKM6AVX\nOg7AP3NF0q1OSUw+6dTAwCk7K2kEeh0GFNllYLJzK0TjM3bmYl+bMB0kX/lZEAScdtppWLVqFc46\n6yz8b1qnY/kaWnNzM9rb29G/f//Q7UIbyxW+1HJ7KwquaDSMLr4c9NYvguSHL0f6DUSu8WruviVF\n9TQ2yfYtpSjcKn9IZ5wPLU6jW3GL7xhWecSmw5evuA4kn4dAiEfT3Ub9kL27IfTsi9iMuSgsvJG9\neEyaDgB0cbcQZSSXdTTvldk/YzaxkawCEimYTbsQm3YLBAglwbBUNVAoQNDSkDWN9gCSKU4Z0Etb\nQ/IZgCC4La9PphWRu/W/KYNxNgMJ8Mw6yelWEFF0BleN9W967olgGIHeBdGLHsp/IVkNkm7z6Nk4\n5ckK508CgZD79/BE42qsrIsnbWwYUOcsBtGKVC4iy5m5+vEdyP90Nn2mRoyC0KM3SDYDGXDeI55W\njTLtFhDftLz7dxbuvoH97ljXhgsmWLsK8iVTnAzOfr/POeccTJkypdOxdFrHbeXKlbjgggtCtyk7\nC1DpS+13QLzoMJuhKKcK0FE8lmN1zmJ+Wch68WznFG1tRn5xUIdDnfcgdFGE3N7KKUHR8khhMT2e\nuWOLt/luMfwaG9cDgkA5tQyD6tHrGnI3+0oaS++hi9PYCVSmN570wkxNIyirvGIRFRAjBBBFkGIB\neVtrJspgZp44FZFB3yhfBozGICgJKiTF6pMxmYmfhjisAdA0YF8T0CJBrKpBJFUF89OPkGPo3QNw\nKE+EiAjtrVc8i5/25ycRmz6HzoWYBggxQYqF0oCkXQaVo8FzclH8eJ4f33PoXnB5iy/JtLuo7xk9\nwucfp1D2mm4A4NEf8l5jS3H03ImQR5xAtYKECLQnHylx1zGGRh3HL0SY52eXBVnAF0/pGIBy3Wxa\nXjUMaH9+AtL4czx9Lfv9Tg09Gn379sWmTZtw5JFH4n/LOh3L18xM08Rf/vIXXH311aHblZsFqHSo\nLOCAeNFhJFKCroY0JwXDgGBozAwBhULFESx/DicNVHUpr9NRLAC6wRaJum42pONG06jw9PMgZDNA\nW0vpe/595nMUpmyaECKid5ss5zx0HeaOjyBUVZcEzOxz8DMzr1gEpXFBcHH009ZcPQMwdJiJFLNP\nZoM1iEvTBgClMLnVVX6cNB2kmA/QthRWLIIycx7I7u0orvwV5DGngRAC+T9OgP7ZJ6XeRe/+MD/3\nzkLFZsyl6ol5b3lVHNZQEntLt9PnYfH84PPjew6N9W8CkkTh6vk8iGlAmTmP3n9L3yZ6wZVILlyO\nfFSFQMySwJwgQHv5eTrMGKI/5DAl9+oDdcGvYO74HLlbp3kcrfbWOsRuuQ+CxBEEi0SAdBv0v6/z\n6u+seRryyWeEwpYNX0maiBTpJl80ydPXcgNP5EwbJv7wh/j1b36DefPmBfb7ZVmnY/ma2euvv45v\nf/vbEDtADeGYKzqqdKjM/7JpLz+P2KTpcHos1stXfHwF04l5pviTKZBPPwrCZmFlCJU6O6B8xsX4\nuzhiFEWg3fYLEEPninUJiSpoa1dBGnMayL4mFB66l5a1ps9hH1OSnfJYYBtejTymQH91DaJnnF+2\nxCUOa4CgxiHEk47oFuIJICJCrulCeb0yaafHFJvSCHPIUcx7qyWrISr7IBTykE8+A0J9b+RumRLM\nwm68h31tZBmaq8nt3MfJM50ehLpweRAWvvBGGtTU9fKUV431b0Iee2aAJcFfXmUt+tIxI53mu3Tc\n6MAwrJbqgmRdHXLNzSAQoXWpg6SoQC4D+aJJ4fpDvuFRZfoctqNtXABBklB8fAVDansGdSBjz4Sx\ncX0AqSiPm8BkN3afT2A2x5r7sftaLFqgYVNuwLatW1EoFBCLxZj7PtTW6Vi+ZvbCCy/goosuKr9h\nBaWuSvVY3H0NIRIB8jkKUzYMQI6C6Jq3gQ3Q42qap8+hTJ8TXHDsDGHMadDVOCKJlEvvQwSJsVFv\neiIVFFK6egYdgkRwIRKPGw1p5EnI3TTZtRjOYjbfkUgiesYFQDzhKX0xG9I+p+reRhzWACSSiE2e\nhcKSBZ5Fj5gmjfgz4czMDikig6dK2rcbyGUZi3JQPM1jmXZ2E9x972wpAcbzw6NtUabdQgOEcsJv\n/qBHjXug3E4W6yuB+iN4c1+T03wXDh9KS6n5HFcUrSP6Q4HhUQ58WlATIHt3sYdG4wn6O2SZIfrF\nZs+u2FxMCKye54nfGoXXX38dY8aM6fi+D4J1OpavkRFC8OGHH2Lw4MFlt7WH74RCvtQUjsaY0VFY\nk18wDEj5LARiwtz+GfI2pt4ehOt1GFeGVYhEvOU43stZXQu9Ww9avnPPdFj7YTU3TUkGhjUE5nDs\noTEPdUomDUhSEPm1ZAHU237uhdtOngXS3gJks4Cpe87FQRPdRXtBJJEENOpUPfQl8STUu5fB3NME\nZDIQqmtoyaZQAFLV0OJWFkcItBcZ/YFJJdp6HimismAZXVw4aC/kMhB8nG929shtgruuOcllEbvi\nehSW/8wTgcM0ISSr2cckhNLmxDmwcEY2KTYcD9K6v1QOtLNYSQqUiPyOQYgnS0COHVsCjMTEIhA9\nIPM7P17mqReda+gfGlXvWERh6RER6DegQyqUPHPeVZ1O5fOy7lNPGInFTzzV6Vg6rbzZTqViMSRX\nZMqDBYc1+QFA3LoZpGkHUF3LHNRSpt2C4tpVwYjsmsbgtD1PBzxhvWS6xo1cBTWJ3PbPIbe3OYuk\nKcl0iLC6Fixzos9sBmjayXwBSVsLRS5V1wJWScNpmk+eGchoaAOaQOvWg0Kg21spBNtfGpoxF2hu\nQv5XP/MsmMI3j6X6KRb9iRs95VD29+mPaP9BwPcu5i4cyGWg19Y7FCr2Ng4cWpQgt7dQmLGmQX/7\nNcgjRlOAgWt/zMb3pJnQnvs9jcBnzYMQVTzXhlcSFOp6AGocWizO7FUYFhVJWSLOFYvoAGCZ2Sjn\n/ra3MgdVK9Jj4Zkv49fWPB18xifNoMEBi29u0kwUf7vMIvlshGGrWH4BlUemVssFVzLvxcChR+LT\nT+8HIaTD4mkHwzody9fIXnjhBXznO9+paNuOSNTy4KQgAAp5L82826xegL3wqnOXghTzXAEu5iJ2\nTSMgRCDv3wuyfUupju2OXBMpiO+/i/SB0tarCS7kFLqG/M/vhHrHIkZGczcdLHRnNJdeS52hdVw9\nnkT03IleoaligQ7l2U7F3t+KRbRcE09R51LT1WnIe5gGFKs8kqKLJi/6d+9DX7cG8unngezfB23t\nc5COGVm6zlZD3hnu4zbBcyDpdgh9+kMeMKg0Z0MIco0/Ci8JXnEdIIpAuh2SacIc/E1vs3ztKkgQ\nnJkkY+jRNNvkEHES0zxgjRt7Hx1RVSxHp29sehfRH04KyDJDkiCdcAr0114sgRdq62CaJuSLJkF2\nsX93lFfOv72HBw8U4l4EgqAOqy/5zW9+E//617/wzW9+s+LrcLCs07F8jexvf/sbJk+eXNnGZZr3\nXP4poFTfJiiVr3ilAKsXYLz1Ksg5l1A6b8v8fQ5j07uQzjg/iA6aeQVTPMqOXGEYHWK7ZS0SkZjC\nZDHWXn4esYlTQVqa2Qtcug3qnCWU5FJRYWYzMPfstlA6opVp6cHvusp+XpZfwYHSmpIMMrQhfEtU\nAQAAIABJREFUtERSDr1nSjIw5Cg6U5HNwEaUBbKApfdQKYI1TyM2eWap9GQ3wf/wMOT/Oh1E10qO\njTMA6ZQE5yym5T1Fgbm/2VOK8uiX2N+zVB3taXMtWQ1ZK7Kfq3gIL5h/Uf6CSqlhdPrq/GUUaaYo\nMHM5oLXZeYbE40YjevYlgKEj+v3LQAydottamqmccJ/DoMVToccI0z8KbO/iwXOu6VuvQj7/SiZL\nwWmjT8CaJx/HMf37fiERvwOxTsfyNbE9e/agpqYGsiyX3xgo+7LxqEbU2xeBjDsLSKQoI64V6fNZ\nX/l8YTzkme6Kxp3hyxApYuSyoU7SbSyKDSmZAup6AHU9SouhGgcxDEQPH4Li/1tKF35WeaeqBsWV\nyzzlMaFLN0iFrLNogDUAZ103JhWLa0EJUOMzFs9y6D0xl6WU7z7xssD1Mk1KcTJgENRb76dlMht6\nO2psoJlsn49gSQ14nMTG9SCSDK2mW2CIFsUQRmxfQ96dtbEcp/+esq4hC6gRPedSkGwGue2fQ7DL\nUBzj0unPWQzoBop/fBTymNNQcHPGqXGQ1v3I3eaCH0+aDu31taVn5ZpGCEc28Kl9GBUER6U0pgTp\nbng8eLLs6T1FdA1Syz6M6FaN+95+G9r/W0IlFw5EmO4ArdOxfE3sxRdfxNixYyvevuycCk9T3SYJ\ntCI2T6QPa1ArWQ1Eo7TmziCLdFsoEsd9DiFSxOAMrglRJTBIF06xYS1GNaXt5fZWp8/BkurVt3wM\necxplhKlCG3tc5DHnE6jUmvRYCHUiByllP4uKLJ9jVnZVrnFMxTN5Kf/KJNd6k8+CrL1U0QvmgwY\nGqITLqILpWuXfgfNE+lizSUBoP2WkMDG40QHDHayWJbjlLPtoUJrfuQi2bGlvNoj6/q5rVgA2bmN\nvgsTpzoDkM40/vS7GPNH93jnjxa70HkVVhDKofV4PHju+xb5YIPDo9Z11+do6jsR3dethnzY4R0W\npjtQ63QsXxN76aWXsHDhwtBtuGSBWRoBEdOElEuHU5PbJIH2HErfgZC6uyL9eNKhTJF/OJlqpRwo\nysV1Drz+i/3SsGR6i799KBiJhVJssFX/AhPOCYtWnpiIvL8hSMeiqij8/A5nXzyEGgBInMhdcDMV\nJFMQNI3Z61LnLyuhyHi1+USKNtQlCept90P7x2vBa+kbppTGnwPz80+8k9sW67JQ1wOCVnAWcw9v\nVk0tSCLp3JdAOfWK64FkCsU/PBzqjCotCwmGQYdTK8h+yjXyuYtquXdhxaKgblBIVsg6R4FD6yIo\nnAoCjwamqiY0e6X7Kf3+sd1SeG7RffjRfb88IGG6A7VOx/I1sFwuh2KxiOpq/kPBfVmHDEfEpwjJ\npSZnkASSZDUt+TAEmfwkgX7eonKOxi+TC1mmDgygsxDxFAyUSmrxeQ/C3PG51YyPQE5VA6IEqZgD\ndMMpISAaY7744rAGh4okrNSkWZ9HW5uZssnqHYsCC5sfoeamPectWtpjSwBdZ1K+A1YvI9sOccvH\nJfoa3yIsGAbIZz5qj8kzEekzAOqdDwBaESSRhKHEIQ8c7AQCfkZi+7cp02YD2z4D8UHDnUh97hJn\ngWbS5iz/GS3XuOc6LCkCO7tgfo+z+EvZNEi6vfIeygGIhDGze9+7QDLtXkcphkzaM86RREQ27Yxo\nbe9DREJROduL9H0sl71admK3Klz/7mf4ESEV95wOhnU6lq+BrVu3Dv/5n/8Zug1fdrU8NbmQSYO0\nNLNJAjnmF1kin35UcWPS8/26HlDnPQhiGEAsBtPPfzRjLiJd60ByWTqHs/kDiN3qSw3UEaMgfftk\npwwljhhFiSF9KDBn0NA36xBWauKJk5GWZqcU53dS/vshDmsIDki66dcBPuX7xvVAVAmCGtzEnKz7\nvuRuKLPmgbS3ee6B6fqNXIVDW9umEllcLm0O3YdfaI2ItbR0lm2vfPHPZdgotMmzOsTIIChxRFub\nrWNUAYSA5LLOvTPKvQu5LPT1b5aYoFNV5Sl2XLxnyLSzaV0GDIIQi4Ps2FLaVzQG9Ya7oXG2Z6pu\ncn5/QhKBSASZeAqxMvDtg2mdjuVrYKtXr8bUqVPDNwqL1Dif2yzGgpqEuHd3gCSQRzURqAezJurL\noLZY2VWk30DPIikOawCadpQiaysa1197ydnGPwVuQ5+jP7jK0/cIGzTklUh45QsYOmI/uQuktRnI\npClxYzQGo+/AknNxRaBCz75QGhdQaK1LkVA+cXzpfvjvDyE0c7GULFn3jznFbv1diKnQew8oadno\nGqRMu5VRJvmllogIgLBLk/7FnFtC8gUTlkNysrhUFWfxZwQyasI76yPJlLVYECBYZd1KUHTmnt0o\n3Huz03vzQLGtAIP/LswCuveCfNEk6EocYiEP8skH0F9d44EY61s3I3re5cB3LwjwnqH/IDati5oI\nlK9ohpTmbh9mrN9/ynkX4MV3/4XT+g0M/e7BtE7H8hU30zSxbds29OvXL3zDMBRYmcizUt4w2wJR\nMmeinld+kLJpaOtWe4ch1z6H6Pd+6NmPPOFCIJvxNIYd6hB7aJFR8jLeehX47g8gdOnqEBxCkjp0\njoJhwNy3h7m4Cr37g3ywITD8KHXvAc0SfyKt+ykVPgDStBOEmNBfetYTBQvde9IBSM6wIREEkJA5\nFgDc+2sPnQqGAamQA/l4E3JLXdPtP7kruAD/980QunUHaWmGPHYC9E82ufRI2oC+/StaxImbRt8t\ntGaLVzUu4JaFQudJQDnB8j+dzc2M/c+ylKyCoRsOPUu53lvYu2A7Rkiyk0U6z2E0Riny9+z2gjUA\np1fGA9NI+4J9OG3NU0Hm53JyyIzfDzWBk1vacfe99+K0M88M/e7BtE7H8hW3jRs3Yvjw4WW3Y77k\n0+cAkYhH3MqeBIYQCZRxyvEoOVYp3QUvutK14KT6xKkUAWbtR2w4HmT/PifjcPceHE32kGOTdCvy\nP7+T0tp0qQEMvUPnaNPLBCSJ+/YHtCIKIcOPUj4L0rQj0DeJXjwZ5OQzKL2OJKP4h4cBXXfUC+Ux\np9Hot1s9oMShr11F/+7Xa4mWqHnC0H/2Qij06I38Uh+C6d6boc5fVprTiMdhfr7ZK7I2cSoICLRn\nV0IaNRZGLO65RrxFGEBpv7EYSEyBnG0HMu20h0NMdllo0DcgMkqqZhklRn/W6X6WU7W1SG981xUE\ndUD2gdHvyT8wD8qseWyGCDdztm//JJ/hB2+M4MDYuB7y5dNCVTR5wmx+oEfPZDX27NnzpU7hdzqW\nr7i98847OPbYY51/82YdWAqN5NOPvGWkaxoRvWwazD27kJ95RcX9kICx6C5CEF3+8xZiCrspPu/B\nslQfyrTZELrWldBkLLZli1XWXUpjQmavngEzprJfVMt5BiSJ715OF0zW4lSgnwlagdv0z/90Nr3m\nV14P6LozVyKdcHJg1kUafw70Pz8BpNuRX/4zz99ss+978p5fQ0+3eRYsu0mu3riQfb6ZNhR79C3N\nFDEkBNS5S8BiAnYf3x+QCIbhIM6YevSTZwKShPw9N5d2FI0h6ueW8zkObl+oHNrJ/bx+EdkHSyKa\ny20WiQDgCKpZTAms4I0bHMS8g6rl0HRhf+/Tpw+2b9+OPn368K/TQbRI+U067X/T3nvvPRx11FEA\nXA9W41XI3zQZ+VlX0YjUoM1S+8HV6noBhhnseyyeD+haYJit8MA8qr9eodkvAqIxAICx6V2gey+o\n85dBmbsEyvyHPC+l/7zJvib2AtHeWopOq7uwewfJFPSarlAWLIMyZwmi51wKY8dWKNNugfKTO6HO\n/hmMrZ86dOy2IzHWv2lFybOh3vYLKP99M/TXX4LY2sy+nvZiBNr4V6bfBeUnd1KpYxul5LZojMoJ\nN+0A8hx233y+dM1/9TM6lAlAOnxocCbigXmIdK1D9Ac/KhFBcu4XEUWovftBq+vl1VC3M0tF5Zxv\nwkHzCcUCvYY/vgPK9DkQG46nkXaxwNVlt78rN+2AnG51nkMpm3aePfc9cM5/yd10Yt0+p5hCSSN5\nrMhZi5rFdU/8vyPM7DkjREuDvp5jX9PIlH0IvBOWRHTgXq1YhOjZl0B7+XlLVOyGwP6dJj7j+kn7\ndiPS73AoC5cz3x/b3NeVdZ5hfz/66KOxYcOG0Ot0MK0zY/mK286dO9GjRw8AlfF/OXYAzfxKMe5O\ndrRwOVUJtKDBWjxJZXV9FjhvDo0HSbdDrM46tOXsyC8OIkS80+qjx9FMKKqg+NuHuP0XltQsOelU\n5vW0nae+brWnbKfccDcHpTQTxf95kJI03vJT9u/TNe81t0snvPJMWwtIPHng98uWt33z5WBWd/UM\nGHEqEa2tWw3phJMrYhi2LZS81P2Mhcx7uLVldDVJy2WcbEIwDG5kzyrrui04ZxSHevO9FN1n09uz\nZB9811iPJyGHSETbmR1glQLb9nPFyzpK8QKg/Lsb8vfhw4fjmWeewemnn87e90G2TsfyFbZCoYBo\nNFqqi3bEKXyBZn6lVjHEmCUr62eKvfRaaGuegnz+5YCjcBmUky3+/tdUTtY3GOd2MoZNGllu1iAa\no6grxvUkyWoYQ49GtE9/5G6c5OxDqO7CZiTu0ctZnLSnVyJ25fWlPoxF0qg9s9J3HtZ1SrBp5km6\nnQ5rVni/QhvfZ5xXmr+JJ6EnUhYVzDw2t1gZhuGwIKeS0hNJpgLMA0ywxFU/BsllIRs7QRKp0tBv\nzss1V+4ZtOeM5EIe+emXe/6mTL+L7dBYcPKqGm7Ag2wGEkC3BZCfO8OzXVmY+IEOcpYBckBNYMiQ\nOtx7773s/R4C63QsX2F7//33MXTo0NIHHXAK3LotQ7a2ErSJ3zr0YjBkZeUJFwaYYo2N6xG1IKdE\nFCH0OizQ4DXWv0mH/HyLktO/sUoKyLQDrN9qD75ZCC9n7sB1PQU5CjndShcIX3nGPSjn0Nlcei2Q\nqqILlOVo9E82QZ2zGEQrekWpgFKk3bc/lLuXg7TuZxNkrnkK8jmXuFiCI9BeXgVp1NjA/Sq0tULe\nv6e03ZOPOHLEnswySfVgiChCtB1+CE/bgUTPem29c90r6b8BgJTP0vPr2h3qHYuoXj1ANd6f+z0F\nNuzfB6lbD+g1tTCT1UyOssID8+j9N0wgl0Eul/ZyhTHeIW3tKuZMipP9uiHJccYzxdgWvfqVzS4o\nl92ZHhBAhwc5Xdcy7O+yKELX9S+tgd/pWL7CtmHDBqe/AlTA/+WyMNgk6QC0mGsdyJ5Y500Mg/Z7\n3L9l4lSY+5og2Op/kuyNpIGAIy3b0PSpDiISQbT3YSAWnFY6ZiSMDW/Rl3zcBHrs1hZozz8OafQ4\nCP0GeheiXBb6O294Hd7aVYj2H1RScrQRVdEYtJpu9DxtUSrfNZcNEwUW+iyeACQJZO9u5N0lqmsa\nIfTq51Dz2GWV4r/+UZqFsI6vr1sNecAgbmbpLLK8hnaMPwDKHUSMKhQ+O2BQif8rkQrlAhMMA+TT\nDwOSCULPvtBfeDyIIJzSCDK0gfkMisMaQDb79hVCWImYUnLA9nPiL6n6giaPkmVMBWndD/nE8ZDH\nnE4h8dZgcmgQmEgFyUknToUQT1EwiU7VWt2lwkrGAiL9BkKdfR8QU0Gi0RIAAEDv3r2/tAa+QIgb\nu9lpB9v27NkDTdPKb+iy2tpaNDc3Y+bMmbj++uvRq1eJil4wDNqs4zxY5TQfOqoJwbNoe4tHo4N+\nGIM6fxmKjD4LnafIenoyiAgg27YEshb7Bbadhr5utQuKa0WsllKk3N6KvFtC1joPXklBbm+F9tgS\nuj9L7RFqHKRpR0nIzF6Y33kD8iVTQFxsAFTi+L+8ZbxrZkFftyYgccy7Fp7zadqB/E1BKQTlJ3dC\nqK1D7vbrgr/NKl05EsXZNPsaTLsFQn0vL0TXdX3MmAqxtRkklwFpafZQ6ceungH99ZcCEbsfkOEJ\nDCbNpMOL6TYHFk16HwbRed6oZLB97+z9yOlWkJ1baaZlQ3ejVIGR7N3NDC5svSD/71amzwnMkfif\nh3LvEPeezF3ikYUQDAPipvWOExNHjEL07EtA2lshdO0Os6W5lFFZQaB9Dbnvz52/RPH3vw7q6VTA\nZOG5H4zvPPbYY6ipqXH6LPY60xGTZRl1deXF0zozlq+w7dy5Ez179vR8FjZv8kXgiB11LmW5j1jf\n8UXO6o0Lkb/npuCGVtZDRBFk8DcRre/llHiKjz8MafQ4RzCqEtZYj1gSMQMRsHrr/SXJZVicYtW1\niH73B0Cx6KnrQ03AUOKef9vyxP5zIPkMUMaxcCP/uh4grfu5jWI7ilbvXg742IWN9W/S7Qjh6s8L\n2QyEzR86Q5PiiFFU+0an8z7F3y+nXF92eS+RgpxNg7gCEn/kbu7civz8WaVn6/+7DcL7G5Bb4nLY\nk2YCwxpgSnJ5TSCtWFZB0599CLzmOoOw0pZulvbt9gZZ1j3xlKpEKjjnNimbdjjcxIbjIR0zshQI\nWO+WU5b1OTDCkYIgTTsDbBL+jIkVHFZSmj7qqKO+tAb+QXcsu3btclBMnXbgFmjcV2DlHq4Dahjy\nLIT7iMVlxDp2OXJBwTAgfPieQwFuLzzG1s2Q+/QHKeQhxNSAfLAbSssSS9LfecN7Hi7deJtTzE+3\nrw892jMw5+HdKjcdH2LM8uakGSCZdgg1XUPBB+KwBpibPyjxkLkX5o3r6aClewrevY+YUsq6QNkK\nchvegnrHIpjbPkPk2BMQURRvqWbSTAhdujr9G5sGBclqRFv2ouBbDAXDRH7JAu/ztvRuqHOXolhd\ny9UEcnjSEikIPBJPay4kgE5UOFQ11vNQCb+dHk9SaemmHYHZIoHBpA0gfKLfleU4xuuXCgK35yVk\n0ogocUQ+eC8oOV7Xo6xDHTJkyJfWwD8ojiWfz+Ovf/0r/vGPf6Curg67d+/GiBEjcNJJJ0FRlINx\niP9zFmjcMywQjfv0zAEEGoaV9kXKmsXhVDGXke/YYsPxgKIwWQHsnhGLQ0l/5w1IJ5xcQmrZUTAs\nKhc3VUY+C0iylxJm8XwvJQxAX2brJa+Ubt/5qmFAAAn+DhcBYVg26JbppeUgwWHVlcaeyWnq07/L\nYycEtV5WLIJy3WxIY06FXtMVRIiwIbos1ctiAcjn6OI/Z3Fwyn3p3VCmzYZ0zEhannTre7AyoxCq\nHyFZzSejJISeIwQQRWVQm8yCoZRYANwOgpKQ+hCH18yiZb+tm+l5mgYEUQwNsiJd64Lsz76sQYgp\nVDdFiHSYMojdL6VgEr98NACKpGtphiSKTFLZsj0d0DLWl9XA/0KOZfv27fjzn/+M5uZmnHjiiZg1\naxYikQhM08Rbb72FX/ziF+jatSvGjx+P3r17H6xz/j9h/sa939hlrUZI514KacBgDwdXJXDESswf\n8fFU+2QgtNnrZAV3e1kB5MuneZqNLEfILBNYUTBxacMAYDaE6R+8bUUPKog3dxGiVukp5UyeBXnC\nhdCe+p/A7ALP7NKMaHzmXE9lxhzk77+D2dS30WhCgj3jIlTXQu/Wwzkmq+EbSXOyLEWln2U47AKm\n4WQVnmsSZ0CmfQzTzjGs+RmepIBQ1wPItCPXeBXNUJv3UGRcWwugFaGtXQUJAojdX3IttHbAoM5/\niDIhFPIghg7sawKamxx+N56QllOGDVEtFdRk4L6rt97foXeL1Yg3lDikRBUQEaDecDdINlMKVGw4\n/infZZfQTJPpqNwOGPjyGvgddiymaeJvf/sbXnnlFdTV1eHUU0/1NJcBIBKJ4Fvf+ha+9a1vYceO\nHXjhhRewd+9enHjiiRgxYgQikc6B/3L23nvv4frrr+f+nV3Wmu/VGreiefvh6giqzG9MRzZjLkX7\n6OVV+9zHZmYFltoeUOJCElhlHE7NnRTznpKD3N5a0jCxj2FTwnRxlZh8qCBB1wLHFEeMYs40MDOi\nJQtoRmRlcpWWGv0LjWA5OD+ljHrbL6D8+A4gEqELJiuyTXA4pVz1eWKawUzg6p9Ae/PlkoPhleGs\nrMK9aFIYrheySyQJsckzA6AAiKJD9xL4+6XXoviHh2nU7iqN5W79bwpasGhgjA1vlRZl//Og61R+\nwc0zN3km9L+vK20rsKlXHIblkCCM9e4Vn3yESRoZNrzp75fa9Pqed2zyzFKgYrFJMM9LlmEOGe6C\npgseB2wf96ijjsKGDRu+Oo6ltbUVq1evxscff4wRI0Zg2rRpiMViZb/Xq1cvXHbZZcjn83jllVew\nYMECDBkyBGPHjkVVVdUXOvl/Z2M17j3Gk1N1Kxba5YsFy2CWYW4tZ0xHtvBGui9JLqva5z62kG5j\nR4OaBnHLu76yxgwUli50XlahW31lkSGPTj6RhPZWqTck9OwDLdUFRBRhWguvPxOTRv6Xt/RmESNy\nMyIX6imsHMJqwtoLDbdvE4shv2iOc27Bsk8jDCXOBGmYQ4Z76vOlhr0GyFFob74M/bk/IHZNI7S/\nv8IEZ2hrnqYLcLd6z/AkEUWYQ47yLmwvPg1pwkUBZU3B6mnZPGnqrffTPpcgQHv5eUjHjPQKztlZ\npGlCbDjeaagLug6SSEEcMQryqedAkKKAogCShOJvl3mfRx8rtv7J+6XjJlIAMSFERPr/IVP+PDZi\n461XIZ9/Zfjw5i33IaLGuQg5rraOK1Bhzty42KOd4M4+L8sBf9kN/Iody9NPP43jjjsO3//+90O3\n4zXvFUXBuHHjMG7cOGzatAlPPfUULr744o6f8f8Bs2ugoXXQsOaf23wLW4dYjN0W1p8hqKh85MjH\n8jTsfSSETlnjjkUgTTspQOCtddwXq5LrQwwD+pOPQrf+rSxYFogivWgnBbkbJjFr2jlWRjRrHgQl\nDrHheAc2i0QqkD0ACEXocRc2iyfNj1CLFHIwY2ooQsgv+uY07OcvAxEjkEedAvnYEwBFRaTPYdDe\nWAtl5jwIokj7R2ueomWZKfQ83NBjx0GqCaDfQCDTDpviRBdFCBZ4RGze48lE9ScfBfn0I8hjJ0Co\n7gL51HNolH/yGZDHTqClXHvOJlkVnP2YMRfSqFO8ZdWJUyF953sQ+g6A/uSjpefRKoGKDcdD7FaP\n3O3XheqzOM+BZs2UmCbkdCtACJQZc2mZyi0GJsuewMA9vClfNg3Yu7v0zPgQcqHvmF26ZczceILD\nCnqoRxxxBD755BMcaqvYsYQ5gY4274888kgceeSRB3bG/wesvb0dqVSIShz4zT/90w89E+CeHssX\nsbD+DJfXi31cro4HqwGs6/TFSiQhJFKQJBlCt+5Q714Okg3COEOPcfUMaM8/TjcoM1xqw1HlXVvZ\nL2ua3XgWRBHa269BHnsmXYSnz/HMwdgLV6TfQG4T1h6K88Oc7d9p+gIDM1mN2n4DSjMJ3AWGA3HV\nNZDPP/c6uYlTIQ49ms4aEQKoKtXLuXSqM7kPlIe4A5bIWMu+EivApx94Mi1j07uQjhsNo60FkVgU\n+utrrbklE9FzJ0Lf8gldhIkZILQUCnkPVNxd8pRHjAb59CPHwdvZrrsUywNr2DNIupqEuMXiUztm\nJFtC2gc68d8DseF4SAOOQO7WaYFqgo2QA8CHnvfsC2XuktBnIOz77vdQURQUi0Ucauts3n8Fbdeu\nXaivrw/dhlXWMmMqRMMMQERhRVoHOgwJhPdnIqYB9fafg+xtKtGOjPyvQOMw7NztSNv9YthN/uLj\nK4Iv9eRZMI882on2WGUlVnPUrfte7nqE6q0rbBgvSachDRgMoboLlPkPsbXlH5gHdfZ9TEoPsnMr\n8vfewoU5V2SMBUYcMYoilyrIFN2Ls9CjN0gxD6gJaIzrxc2O5i8DAQBdA9m+xRupT5wKY8cW6kRN\nk2YD+5ogVXeB9vdXgpP21zSCDBmOSDODFZuHPDMNkOY9JQc/aSZIsoqW5bJpKNNmUwoVrj5LGkiV\nIPpcPrU5iwGBZjNuNgT3PZDHnknfDY6zj1i8bdA1ZjZO2aVry972L9JDPdjW2bz/CtrOnTvRvXv3\nstv5y1pye2tQ0Gnp3YFJ7QNxLmGiToFZk8kzYWzfAmngYBpZVXDuQPDFsOWEmS/1kgVQ5y4B8jkg\nWQ3zM/ZMgv8YzEiPZzmO3vrVM6Bv/jDoTBuOd5A7JFlFy37797JFoeIJJqWHM4RXLD8Ux7uPrAUm\neu5EFB9fwWRlRj7HX5x9oIjgwTTP79M/2QTp8KFAuhVobwNisVIfyv5dVkOemCbIDm+mpN56v5dt\noFgCdpA4g5CThzyzJJaFZDWUGXMpu8JHG0tzNfb1jnOifLt/bHF6CV27s4dQM2nkbLJJ/yyMfQ+s\nOS9mINK6H5GmndAslgO770VMs8PMGB3poR5qwpXO5v1X0NxU+R0yXsM6WU1fClGCVMwBunFAlC4s\nZ0DFpHwLh9Vw7Oh8DA8ZxY0q02mQtv0QJJmpQ+FEzQdKX+PXW7chv126IvLZR6XShu1Mt35KiTQv\nuBKapeBIdmwpRaD2YiZJgEmCOiUrFkGZOc/7G13w1koZE1gLDLJp2rPS9UDfRD7zAvbimkh6CTl9\nx/L/PnHEKEjfHuNlNbjhbva9I4SZKbmHVf3XgTVpb+uf+IlGCQj0tasgn3ouyO7tEKprS4Ok7uvN\nk0mOWmubxenlQTy6hlCJuyTqCwYcsIquobjyVxwwxFOUxsgCFth9rzAkYViQUUkPtaamBi0tLeja\ntSt3my9qB715z7PO5n3ltnPnTgwaNKjjX+Q1rNNtyP90tvXinwwPDLMCDqLQSDms4XggVPyuFyPa\n3lKCuIb8Lu5MQqYNaGn2sP266W3KZQDuqNNhMv7vmxGRpKBC5JK7oVw3G6Krsc10uhYdPTdLyLrE\npULgreVgzP4FJmoYQDTmQFZzrgxQnnBhUP6YmBBSNSj+v6UwNq5nPif+AVbWjBHJpJn3TuhWz+6p\n8WDAFrmlh73aI4X8EP1MjtL5j1V/gHTMSCASoQ5k6k3soCsSAXr2pQ49l4FQ1wNmexu05kFKAAAg\nAElEQVR0S4ZZMA2mGqhy3WxIJ51Ky2n+e+iiJHKyzdHjoK9bDfX2RSB7dnrYugGUtHl8+/BcGsOg\nsteffliC0lfwDvutvr4eu3fvxuGHH17R9gdiB6V531HrbN6H265duzB69OgOf49ZY7WiIoAzXFhm\nqpwVKQv9B9GXOJ6AoLIpNITuPQFCQgWYwszR57jyegqx5ER7dGOOHKwchb75A0iHH4noGefTOngh\nCz3GhuP6X87AVHyXbiBNOylCjbVI+QYTWWwD8tgzKbxXTbCpaGyNlpiC2PQ5EAhxtOKdEox1vA6J\ns5lm6Rr6M0BiBuWPr7geJJUJn8fxBxWMzFJb8xRzEl6v6Ur7Cr77pq1dxZivYVPYuwEEBAIQU6mj\niCmIXnAVir99CHKqmu6HG5y0U746S0YBahxGTbeynF5CdS2QrIKxeL4HAs3iFLOfI/mwwwFdc+Di\n7vOAuz3AAL7Y7yIkOVha7CAtU319PZqamira9kDtoHOF7d27Fxs3bkQ0GsXgwYNRW1u+6dRpXquk\nec8yTwkkm4Egyyg+9qA3KuKUGVgLFDdSnjabvowW3JOFTjPbWh06eHnsBKq8l6oOYPd5JmXTyNvf\n/+4FEBKpUk8lqqD42NIStp+l+WEN2knfHgNt7XOlRemaRsiHHc5EZLFeTiKKIIU88vfeAmX6Xc4A\nJNOR+R0ni23AA6yYDsBFRXP9rRDqekK985dAsgrmlk9KjX93CcaGMXckI5RkSvffuABCqsqhItHW\nPAUhkUJ+wQ3e67H8Z1QYzDbWc+LPkBmLt7FxPeSzLmT2DcgXoLBX5y517hUzSBgynCqLWj0Yni4M\n+vYPIK5499Bzr2MxQEBlnGKAJ3thohVtXSCeXo0NIuBkXtwMh5GVd+/eHbt37w55WL64HVTH8tJL\nL+GRRx6BJElob2+HIAg4/vjjcdlll6GmpuZgHurf2tLpNJLJA0Ny+EtJjrgU4HnxnSiLEAgxlc1p\nxStzmYbz34WFN1KtbtuZxRTA0EH2NkE64zyI9b29hI6TZwEuNBfXrGP7J8+Ve1dAME3Ip3yXzjnY\nUbwkBfi2jPVv0gExezDOagTzEFncDMBeXCzHzHVkj6/wqFuWZRtYeg/UOx8Azp0IEMDcvd0ZxFSm\nzwn2jWyCRha81TLeYqLHk5DGn0NRZ/O9kFnCgU6TFhelOsOR+TNk7eXng9nJ5FlAbR00N1WP+zz7\nDggMUJqS7IAs5KYdbObonVshGp9B6D+IWybUhx6NmJYvZUAAlOtmU1XOqi4l2DSDNJX3Gx2S0LYW\nIJ9HpL5XKKeY3+gg6fDSb44nYaiJ8mhF+13kZF68DIeVldfX1+Nvf/sb9zcfDDuojuWTTz7BQw89\nBEmSkM/nsXHjRvz1r3/FzTffjDvuuKMze/mSza92Z7/4+usvMcSTGHVaXrTmTtuLBTrTkUiBNO30\n1H7V236O3G0+7P6SBVDnPYhiVZfwk+dAZsnWzQFBK8gypFFjnczCY8VCsH5dDpHlM0ONU9i2Ff3a\njk6Zdgt1zHU9UPztsoC6ZUVsA7kMcnNnQJl2i7fEwYHR2jBmXjM9rMTHJFZcsYhPYKjr9L85UTSP\n76ocKimia4h8sAHaujVBGPmUGzwUJGGDwIUH5lG4L+e6kmQ14nV9sV9WPOfEgk3zzHMPM2lAEFB8\n8pFSBjxpJsRhDV4y1pAqgGAYiHzwnpdfrhJYuXUdKlbkDOnLfe1KYbW1tZAkuktFUXDsscfi2GOP\nxfvvv4/f/e53mDw5KJ7TaQdulTSg/YpyphxD9LDDPTruvCiL37N5unQAaw6CbPssUPsl+5q82ZGN\nqqpA+Mw+tkfkq0cf5G6azFwYbVmAso4wGgMIG5Glzl/GPBcxl4X2+kuQTz/PiciN9W+WyAFffAYA\nFZkSWDNDBFzuLSdb8JcpuVrxVdxaethioqtJoK2FnZkwCQwrKBOBjUIyQ7ROBMOA1LIPuQfms2Hk\nvucw9BksFijRZJkIvqNsEzyqnaiucRmf/SzfPDTdgUpXeK4DOJmX20Km8Lt3745du3ZVdC0O1A6q\nYyGEYM2aNRg7dqzn86FDh+Ltt98+mIf6t7VsWxuUiFC26V2pqJcnMpoxF0Kmne6vTJ3Webl69XOm\nwQWVpd0+i5aAThwf3Kcap0g0xsCbYCGneM7RLhlIIM53eegvUsyDiLX8aXtf/Zrk2eJXXGGuXMaB\ngooNx5d4xnr0RvF3ywGAqeHi5uYShzUwZ0gcAILPkVQamfrPk3dfJQL+sKcsc2eUJMMEshlIYDBW\nc8x+9jQ7KGjeA9lS/hRz2RKfneVMwwIPnqyAsf5NOvSpqKHSC5WY+xm0n/G8u7dlSznzRNOSFl+Z\nHQB1rYP22kvQn/19sBJwgNIVrOwwNPMKmcJXVRWFQoH9vYNkB9WxnH322bjvvvvw4osvYtSoUWho\naECfPn1QKBQO+UDOv4MJhoG9b/wVtZveptKoIVDCMD4oWwCruG615+9CIe9MEYdFeTynpQ89GnBp\ntwtKAtAKlICPpSERERE9+xLuwJteZj5DzGW9cF0e+ss678AcjELFoKL9BgDfuxiIJ6HFgxP+/v0E\nzPWSOj2fKJUeln84GQIxQXZs87Ic+7i5SuWz2RCquwDRKCBEHCftdyTGpnchnXF+QCseYLAWlysb\nqQkgyxn2nDzL2YefaZd3b+znj5cpS9l0iQLFp1WPup6l+xiJsAOPKY0QqroEZjPcsgLicaMhjT0L\nZNd2ByItnXE+5MunwYgqzvnlcmkIUTUUTh/4nROnOuUtcVgDBEmGvHcnX0SsqgbSqLGB0ioZ1hDM\nRr6AdEVHMi9DjbsIQa0B3lFjv7QpfPG222677WDtLBKJ4IQTToAkSXjppZewcuVKrFq1Cs888wy+\n8Y1voKqq6v/cUGQ2m4XprvGHmJxpx4bbp6O9UMCILknAMGC8/TqiY06FGfVyromtzdBX/8m7A8OA\nNPw/kL/rJ9DXrkL01HMA06QvHwDpxPHQX34eJJtB9PTvw/jn24Bh0AVmyg0wevYDIhHImXYU5s0s\nPfyu8zAUFWZUAVHiED7ZBORz0N96FaS9LbBP+T/HgWQz0F9+PnieJ41HhIB7HDOqBH4j87wnzYTZ\nsy+IDdONRDznV5g7HfrzT0Bftwbi4G+AdOsBU45CHjAIxtuvM3+/34gkM7fXe/aDKUchfLwJhV/O\ngb5uDfS3XkX09O8DWhHioGHQXXMOZNd26K+9BPnkM0DyOWh/fBTRU8+B8c+3QbZvAUQRypQbIJ18\nBqTTzoXRtZ5e70QKZlSBQAjVNZ83E/rqP0H/y3OQBwwC6dodaiKBrKZzf1cEgPY/DwJaEbELfwRp\n5BhII8dA6H84jFiQz4/7DJx8OoSPNzLPwVG2bG2G2KM3Cg/e4/v+G5DHnw3tmZWInnoO9DfWInr2\nJcjff0dgu9joUxDRNRBRpvuNREC6dkd0zKmQThoP6Zhvg3z+MQoPLrSu+zpIg46EUN+L3g/r/Iov\nPhM4v7K/859vI3bhj0CyGUpQ+eBC6KufAmneg+j3LqZBguv6Ckkfqs61D/2V1ZBOGg/T6t/xniWz\nRx9ImTS9doRmbu5/O9ehAhMMA+IHG5BfeCP0davpM3nupTCHHAVitSr++Mc/4qKLLkIul6ton7aJ\noohEorwTPCSa92PGjMGYMWPQ1taGjRs3YtOmTXj99dexcuVK1NbWYtSoUZ3DkSzLZZDNF5CUXNEV\nL00ux25cdKGI1r8JseF4CDW17OZzz76AJEGw6uGVpOt2xuQp8cCu/VYBqsUTxhmQs6Po0OP4fqOD\n/nKzHa9dBZlBHVOulu2BZccUylybTYNEIs6Mjr8sR5E8WUoPYnFDCYSwWY6nzeYPrLbup8OBuu6V\nd05WAbJM+waWeco0MSWQherrViPapz8y+/dAUlQucSVz2POaRhgxNp8bl8WhUCjfI1ATgE/u2Sl1\nAZDGnwP9z0/QLNdgK1mSnduQXzTHk8F6EI8te9l9srlLOtbD4CIfzQCSz2HbnrvU4U+DEAHZupm7\nD1a/hwV4CMgNT5rp0Lx0dAiSp9Vky2cAgCRJFQe8B2KHxLHYVlVVhZEjR2LkyJEAKIx206ZN2L59\n+6E8bMCef/55PP3002hpaUH//v1x+eWX44gjjuBu/69//Qu/+c1vsG3bNnTr1g1nn302xowZc+hP\nVE1AFyVIgqu5zUmTK2qsFwsO5bZ81oUw9+52nIDTfJ48E2TXtpJeeTRGJ8PLpesuODBQojwRunZ3\nEFJiw/FseV1LAEkgJpt+3DoO6zdKx4x09m+bG4nlPz+PuZwWEUWLufaTQBlE//s6z7Q5AEQ+eA9F\nq7xj/xZxxChEv3sBt+6uJ4LiV85gpyQh+oOrqIOEAP3TDyF2q0d+/ixPTywg/DRxKqDrpet7zMiA\nVowbYSQYRql0NmBQoLTGpL6PJyhCjvUMlAsGrPsmW0zC0hnnUZbh5j1ARETxtw9BGj0O8iVTqAOP\nssk8bUExrlMo5NmQ8Wz2wKDkgeOLHmSexzkSAr22nrIrNO3gl2hFkd4PBppOcwMc0q3Buaqld3th\n8h0ZgqwgMBRFEVoFIJoDtUPqWPyWTCZx3HHH4bjjjvvSjvnaa6/hkUcewdVXX40jjjgCzz77LObM\nmYP777+fWZZramrC/PnzMX78eFx33XXYsGEDli5ditra2lCp4INhejwJ4Tvfg/jsH+gHZajdPf0E\ne5DMj06xKLcFKYr8vFkBqVuhZx/kbrja81AXH19RXvOE03dwZ0jy2DMBSYZwZIM13Ejp4M19e7wC\nSJNnQhgwyBGZcqSF7cbtnMUg+/ZA6FqH4spfBX4j1ETlC6PLOTIjO1eWZ7/MIGAy3MpjTuM3xKu6\n0FmdIUdBvesBWo60aDwAUIcwe6rnGuivvVRayIY1IJKqYsKD7fPjUb67iSsrYRhwb2cPtArJFNQ7\nH0Dx98tLA5yXXguiFytCYek1XaljbG8p9dhsx71uNeTDDodW18szMCgOa4A8bgKEeBLEMEqaNtkM\n1fBx69mwtFkmTgWSlNvL0Y4nJqLnXwHEk0xADI8RGH37Q7D2a2u2+PtA5pCjaBP9yUfY5J59+jsZ\nYZgeD3fosQKaF6ZV0MeRJAm6DSc/BPaFHMvDDz+MbDZ7QN+Nx+O47LLLvsjhK7Jnn30WY8eOxUkn\nnQQA+NGPfoS3334bf/nLX3DWWWcFtn/hhRdQX1/vlOp69eqF999/H88+++whdyxEFFGs74PkDydB\nOWVMWWp3d2lAMAxI48+BPOZ0QFUpFLFQoIyztfW0+VgMDhyqdz4QeKiNt15F9LwruNEtwGsOngJt\n7Sr2lLm1oEnZtEcACUXKs6XOWQL5P0bRgTHfbySiDOg6iit/BemYkTA2vOVaBGZxFRNjM+aWjsVy\njiFlEOe/3UJmLkiw2HA8hK7dQbLpoLzu5FnQ4vQ4piQDkuyh8VCm38Vgay5FqPb1I3t2sc/PBsJw\nZJrtBahSaKu7rBlEtzUi+v3LQfbucpxiJWg1U5IhceZm3ASlToC0cDnI5g9K/RbbUUgShEgEucar\nPPcW/QayS2F3LYb+zhtBQMDkmdD/+kKA9yyMEViIxWkPRZJL18S5jlQGHGoc0e9eAEJIiW+sWz30\nmq4wJTng3MURoxA9dyJgGCByFOKwBv7QYxmaF55VQp8viuJX17F8GY7hi5iu69i8eTPOPvts5zNB\nEDB8+HB8+OGHzO989NFHGD58uOezhoYGrFix4pCeq206Iaiuqw+nKudZpp0tSGS9iMyH1/6fvw+w\nZxeIrjHruvaAm4cqf0ojyODhkCBASFUFKULs6N+iIQ/okOza5tEhcR9XjychJ1Mldl4n44oA3XtZ\n6DEGQm7+svBhvXIDoPbLTFyfuyJYm/FWHDGKyty2t9Khwr79PcfxD6pyHYJdtrQyER56T6jrAeXH\nd0Co6xEemVYKbbW2Y2dA86HOXer9HBa6raYWJJHko9U4PFt+glIiioBhosAQ7FJv/wWKj68I3tvZ\n97H3nU2zOfFcEr8s2WwW2srh+LKCMv+x7KDKoTe6phHCwMEelgG3c3dKlz6mZP2T95nSDOVoXnhW\nCX2+nbGEqtR+Afu3FkZpb2+HaZqorvY+MNXV1WhpaWF+p6Wlhbl9Nps9pDVJ2zRNgyyX59Lym5RN\nU+qQMacFIjl93WqAmFBvXAhlxlyIDcfTh/XK66G98RcaGUZjdPuYgtjEqQ5kVsqlPcexB9yCGvfz\nqTzukOEQRIm/oFk05Pmf34n8T2cj//M7IB03OqBDIhWykNtbITftgJxNA1VdHOBB/p6bre/eSZvd\nnAWU5DPQktXQ6npZYkls9uLgb3+6hPxSk852NhmmPOFCCNW1UKbeBGX6HEDXabnH0EF0DXos7vQ2\n5KYdkHJp2vyfvwzqbT8vOQS3RUsKh37qGM/5TbkBRI0D3bqDqPHg+btr+rbj9B0nEPn6KGsC17GQ\n9xzH2PQuiK5B69bDy9fVeBXyN01GftZVEN9/t0RQyvidgUWS5wR1nUnpAlve2P/bFJXvuP2ZqMvc\n90tOt0IwaN5MOc1S7GMJgpfeaPF8isLksH/LY89kZlnS4UMtEMdsqHcthjL/IZjDGiD/cDKUuUug\nzH+owzpKtrPkPfuyLP/79Fg6rbwZhgGxAw+QY/YD7FscnCjJ1m23IqvoZdNABEDqOwCwCB7Jjq1B\nOm9fdCtl06UBN7cVC0A2AzFkEE+IqYCPhlwc1gChuhaCKEGZPscZGCSbPyxN8kdjiF15PWLTbimB\nDFxRnNRBaWSbflzQCkDPPp4BUCJGIA8YBNkX5TnstKYJ8vknpejaLtkADrsxwCZGJP0HQXtmpWeC\n3/NbLD17Qde46D1nkbD4rQQrMnVr3pfrH/gXdcfB8kSz4glvBJxIQTAMB0UoEMKWWZ6/jElQalTX\nBuZguNkjR4iLWNfUPwyrf/YRpMMOrywTdT0PYb0oen0YIAy7j+N+B8KIOnkksKZJ55bGnOY8P5WK\nuh2o2c37aDR6UPdr2yF3LJs3b8bAgQMBUPXJL1M9MpVKIRKJoLW11fN5a2srlxSzpqaGuX08Hudm\nEuvWrcOrr3qjqvr6elx22WWoqqrq0HBoMpmEJEkd5lXL5dKeco07SgqUBRbPR/KeX0Pt3a/0/e2f\nI82g85aSVUi5ziWzdxdMDgomoqhAIYfCmqcQu+J6FGwadutFNJt2IJKs9vQpAjX9iVMh9OxbQkfZ\n5/yrn0GZOa+0yPboA7lbd8SqqqHnk8DUm0p9jJgC5doboXbvgZSieq6Tns8h9/57ILu2e8qFyrU3\nQhlxAiTf9vZ3tH17YOZzQDSGLEdjXayqRrKujl5LzvCq9O2TkZ9vgyhmQ0gkgVQVlJ59nGMX2lpB\npjQi/8B8B72nXHsjlJ69kWScH1DHjUD11CjI9/waZjaNSDwJuWsd+zemRqHYvDdAWW9fRwAoanmY\nchRoawEpFqE9/VsYG9dDvXEhO9PZ/hmEVBUSC5eD5DKIxJOIpKpRfO8fpXsVjUGZehOiw/8DuPZG\n5H851/PMkOa9gV6Zcu2NULt1B7p1d36bkEiBaBoimXYgpgap923EJOPZ4N0v+x3R8zkUDjsC6i0/\nDei9+OmN/O+LHldLzyanlxLp2RfJhcshd62j5/OP1wPXR/2PbzPv24FaLBZDLBbr8Dpjl84efvjh\nAEPyqFGjHLmPQ+5Ynn76aQwYMAATJkzARx99hG3btuGUU0451IcFQOuIAwcOxHvvvYcRI0YAoLQz\n//znP3HaaacxvzN48GCsX7/e89m7776LwYMHc48zevRorn5KW1tbh1LOfD6PfD6P5ubm8hu7TIiq\nnnKNk3JzygJ6us1zDPv7/ug2H1WRc20nx1S2PsqkGTANA4iplCp9woV0lsM0SlnQxvWUit16uZhO\nb8UiqHcFAQV2/Tz/09kAAGX2fdAEAcUdW2lEPegbgbmUXNOuQLRH+wC5QEki/8u5gK+p7RZWshcp\nHq2MkEw510pu5xBOptudLMUzwT93KdqyOSCbc6Jnfd2akhO1msHubfwRbZe6Ov4zoybp/wDkrH0w\nTUlAOLIhUJtvb09D3LoZaNpRum7RGGLX3wb5u+cDENiwcUFAfsENtJ/RlToneX+zV4+kWKD/XrAM\nOOwI5jNDA4rZEJIlbqw2+zeoSQhRlQ6OujOOabfQeafW/VRUTJI8maj7WsqFPFN2WE+3Yf+ePcF9\nT5oJ+awfgrTs89Eb0fclv2eP5/44z6bG1rQvpmpARBG5bI6Kw7muD23ui8h/+hFIIhUKEXdoeCrI\ndjKZDAghHV5nZFlGXV1d2f76IXcsqVQKbW1tePzxx3Huuedi5cqVX5pjAYAzzjgDDzzwAAYOHOjA\njQuFgjOX8thjj6G5uRlTp9Jyxrhx4/DnP/8Zjz76KE4++WS89957eOONN3DDDTd8Kecry/IBoTU8\nYkKa5qJ24cwJ+MpElTT8AIoGk0aNhf6qa+Gr6wFi6BCKeZCYBRbItAeZhgGQTDtfcAqg/7ZeYFYp\nQ2w4HvKEC0FampGf3+gtXQwZjoh/LoXF1cRhDvZzpTGFlXgzCy4KEr6Gh8LtYdjmbvY6vYVozBlu\n49LtpEYFrnU54/G0seSnUcgHSpjYv9cLErH1Yja9i9jl11H6n6k3QdD1kixDGKCAgDbC/aZrToNc\nWbCsMnqjn99JnRQISCEHrapXgB6fyafnkh2GmoCcbefOmOgvP0+RYYbh0AUB7DIonS0SIVR1CX/H\nXNeHmdG7ZqsCx2HNPXEGK3VdP6BebqV2yOtS27dvx8UXX4zW1lY89dRTOPXUUw/1IT12wgkn4JJL\nLsHvfvc7zJw5E1u2bMFNN93kzLC0tLRg3759zvbdu3dHY2Mj3nvvPcyYMQPPPvssrrnmmkMONbbt\ni8AAnYZdl24oVtdC604bd6ENXtb3OQ0/m/Lb2PYpomdfQrOhRArmlo+Rv/165G6egvyMK2gNvmdf\ndsMzl6WNypnzINT3Zm9joaj8TXX9k/dpoz+bCeqXPzAPUqY9qGHiByCoiVIvwX9cF1eanG6l+/I5\nIXZDvRG6Wppg54ECSC7D+b3ewVNxWAOU6XdB+fEdUKbPoYu41Wy2QRooFhxCTEGNI79zO+T9ez2N\n5zBzHJS/4c76LsMZ8xrR0R9cBWXGXCCZQn7+LOR/Ohu5myZDfP9dRHSNKjxyrr3AacgLNbXOMfxN\nd+f8mL0LI1Qi230t3b9BHjeBLshKnMsILSSrIJ90Gsx9TSj+8VGYn39Cr0uW/QzKluR0uXfMDbhg\nXmPreWadu1DIs4/NeCZ0XXeY6A+FHfKM5bzzzgMAXHHFFXjssccQi8XKfOPg2/jx4zF+/Hjm36ZM\nmRL4bNiwYViwYMGhPi2mhQ0uVUKT77dKMxGeeSlFKLGl8darIJ98AHnsmRDUBPK/+pkXQixJgCAE\nWWetOrc93Fd8/nHGTIQ1A+Ihk4wDho7IwKHI3To1XEWvTCZiqHFIdfVQb7ib1spX/wmQZUS/fxmQ\naUfUuvak3VpQfHVxY/2bEA4f4prhEaCtXQUJgqMjwhtexd/XlZ8BcaHmPFG0jZqzfiNzVmjiVDrD\nMXoshF6HAbLMvdfMSNxquBf9DM9uZ2xvz8s28zkgnyuBLNz7nruUDt8y7rmuJiG17WcKqJFMO90P\nD5ARMj0vdO0OjQfT5dHWWCAMKZvmAlFIug35e26mWZQ1OEtLsWluGZfJnO0zD+AiTPHVnq1yGycT\nt0XRPBB+y7EcqlmWg+pYXnzxxUCZa+jQoc5/X3TRRdi4cePBPOS/nUmSxCSGq3SKmmVhrKhhzorH\n/GpTihjr34Ty4zvoXMfIMcj//M7SkJ1N7BeNIXbNLEQvvRbmvj2lmjQh3LkU+/ju4U852w7kc7S8\nwUEKQY6Glv2YIksz5gCZduRuudb7G+t6QBwxiklfLx97QmkWwTJjw1vc2QjBMCCNHldWS0MwDIoI\nq6rxaNx7tGKsRZTXn3IWOev/uc9ImQXQ81wkUyBW1uVcB5GDIKuqgSDx4easey506wEhl4YgSdDe\necPzNwd5FVMQmz4HAiGBCXpDjTNRWySmINqjF4o6J4Pjcbklkk7ZjskIffWMUtO+WCg5gGymBIMO\nlEG9AXWYXIQjLGahA5nPMwsJyUP1WaJoHp2br1PG8uCDD+Loo49Gt27duNsMGzbsYB7y384kSWI2\n+yudou5IVlOOGl1Ot4KIYmCRswfNAAAREfKZFzgDkWwU2gIoC5bB6DuQ0rPs3ObMcniYAKKxgNgW\nsw5+BQN6fOm10N58OTQjYF1DSqrIJpF0KP9hOQOLaoS0t7Ij3UwaUUEAtCLV7oinHMdRTksjtN6/\n/k2QfAZCPAkBhKKwIHDKP6bn/7kcUyELIPO5mDEXkW8cA/WuxfS3JRKITZ5VKknayL99exCpq+dA\nh5PMe+44wRlzIY0eV3p+rGwG3XtBuftXIJ9+VJrkj1r0+n0HgmzdHAA7kEQSelRFrKoaGU6Duiwc\nW004gZCbBgnxhBekYGW1QiQCyFFm1gVRhJxuhaHEIeUyFFlnZ/MMNgCbkifs/Px/I1aZmyuK5s7c\nDePr41gAOpT42WefwTAMHH744aFOptOCVlVVhc2bNwf/UEGZp6NZDddZLVxOX2LOIudQilgPc6SS\nEoklFUtESm8iDmtgQ5L3NdEFnDG57Jzjcgt67FrstWdW0gW44XjqvLRisOzHuoa8Rr5JHYgy7RYI\nyWqQdBuKf3qMZmnT72IvnNEYzH+940VOWZxSpiSHammE8pZtXA8kUh7Ho0yfw5/VcM9s+J4R24gc\nY5edojH2uSy8Eertv3AyNWX6HAg1tWzk37ylnMVVCl34CgtvhLJwObNsK7e3MvoH86He+UsnMPCD\nHb5omZjJCH31DOhrn6M7sM//5ecRmziVCt5dMoU6Qvu6iCIIISj+5gFAkiB9+x7JaYIAACAASURB\nVGTk7Pkl13vFCwCE/oOo/HKh4AAE3LNVLHE2liiav4x4qEc/Drpjufnmm9GvXz/ouo7t27fj6KOP\nxpVXXtnpYCq0+vp67Ny5M/iHSojlQsS/mI1CXo25yKBGdy1yNrGl/TBH2veXzo3He8RgLI5ecBV7\nYXLX+XnnGIsBNbWUeNM1mW1sXA8SjQGiHFQ+VBMlpT87+lTZksGIiBSN9Iu7EJs+B9C1kijXy88H\nBxwnzQBpb2GwHqxBtPdhIMViUKLXTZrJCxwIoXxVhuEiiTyTygfcdj+KTzziIYm0FzmnVBONUUE2\nn+lKHKJ/AYwq0GNxKifMqtW7B2NNA0i3OfBv28SG4wGDslyrdyyi/ZFcFtqap6kOiV3mSbeBtO73\nDuMWC5SWqK5X5WzV9v/8n1dI2BhWJuZR3MsDByN61g8BWQbJtEM+6dRS7/CcS2D0HUglFTJpkJZm\n6NbfmBxx7gpABUEirGpC2Ln7RdFYvbxDLbx40B3LpEmTcOKJJwKgMxl//etfsWDBAsyaNavTuVRg\nPD3qiqaoedQmjOYdAL6z4kmwVtVAnbMEKOSAeLJUF3ZFv2xJ3Vme8xT6D4I6/0GgrZUNL82mIVu/\nhweXJlU1EAyDEgD+1xklgMD0OSCffuSdO7CyNkON0wFFd8P75nuZw3QkGkUkWQV13kMOjNS/wNhl\nPUQiVH8m4+1bOKwHtk56NChZbH/OkyoQevaFnqyGsG83m2X3mkbI51+JiCjCNAxEBw5B8fEVpQib\nkQUC1qJpLYDOb3I5YF6t3rFIBIAXem0DCnI3u36vS4ZAVhPOYigTQPvTY5DHngn55DPoDMna5wLN\nedsBC7EY+5x4qo4VEjaWM9bibVrnn7eJMX3HdX5jNuN9vkMm7ysNEiuhzi+XiX0Zar4H1bGoqor+\n/fs7/1YUBd/5zndw7LHH4oknnsDVV199MA/3b2mxWAzFYjHwOe9hAUrkf9yZFUbzDgihDLdq4YH9\niBJyN00OLNiB6DdVRaPVlmZA15yGvDsKU6bdAv/C5BwnGnVeWnHEqGB2YDkPTzR3TSPky6dBMIwg\no66b/t7eD6xZjK2fQrcbxlZ9HjEFxd/8kg7nuUoq/gXGLuvR0tBdgeYpj9beLVlsf86TKnAyTTUB\neeyEIMvu4vlQ5y9D4rABaG5uhpxphzzmdMgnjvcOGTIWJNaiKRiG08fx6sjPKpEigsKupbFnepid\n5XETvGqQdkR+3f/P3peHSVFe67/VVdVd1d0zwwwwLLIblnBBxgiiYa4aLxiNkUTjlhhE3FhENMoy\nbij7ACZxIQKiRKPx6k3MZhKvgXjldyGJCTGgVwUJGlHZt5npbbqW7/fHV3t9X3XPCEbMnOfxebCn\nu/Y653znvOd951K6Ek9ywQzyk2fDUJLuak7XQHa/D23jesQvm+RD8tkoQ5LLMIZ16XbaYm1FXJaV\n6AUDNG81z9JtKZNANAoEwFuJZTIZVFRUhD4/lnZMA8sZZ5yBDRs2YMKECb7Pu3TpEiJ27LC2Wyld\ncqYT5jTv7O2xgpWBcGMwMXkWij9/iptBGb0H0Gb/ng+AbAbFX/6nq9GylDbkfVmYaUJ7+TdMxA3J\ntDj78ar2CXoRZkKl3FTB4LGSKuRxGXUZEE2v4/fW59X5K7hcaV7zOhfH0ZbBesByGsbmTZAvv85S\nqbTuRaoixPDM3F7OM6eTbWGvAssoDTEBBFbANuIKJAiOZIHx9lZIYy9CrEcfV+QtVcle6VbVwOhc\n6y/9CTFfkEeRDh6qjY/B3LXTST70jevpqs+L2psyB/GrpoBkmgHD8KtwWs11sViAmM8he3AvZEVt\nN4glSrKiFIw/GHyYJdQpcxzdlmA1IVi2Da7o2osU3bdvH7p16xb5LHxcO6aBZcKECbjvvvuwatUq\nXHLJJaitrQVAG0VHjhw5lrv6TJsgCCCElKS0Di6XfdKpez6gsw+mAfncCyGP+5o7C+ExXmZjDBlB\nnVymBSTTBKhJNsusR1ejZG3X61BjMSbiRujWA8Ufr3Z2IdaNpi9XPotYVTWKcZXbA7Bf8LIhmjw2\n36OH/b/jWMi5pCog9OpHKWlyOSDFWflxjlEwdOTvvtnnJDB4OMR8zrrOlVzQQP6jXRDialm9OJ4x\nyy/WikjM54Cu3emz1XwEyGVp38QTnLmghmQ6LL07tQHi0Dq/aJsVJFs9yQebAn+piySbMhuQJDpT\nYiVSxs63IfY52U9i2h4QS4myU9SqwP57MPiYCTWUPJhSeAK+nBWdkGtxNF1sGppyjnvfvn2Obz5e\ndkwDSyqVwvz58/H000/j1ltvRU1NDaqrq3H06NHQKqbD+NapUyccOXKkNEEcJ/Mll18HoiSBPR8E\nEEp3QCiTfpuIIqUayTRFaoOU0vP2ZXHeLEySneaz4xSmzgHiihNweIJh6DeQeyy6Gl2i8P2NN4uh\na77fRZVJmOUkxYAkxyG0tjLRUdofX2awG89h6454kFh0RToTravv9/eDMs3I3D3VobWJOv/Ikg+v\n/NJ8BIXFs8J9EysoRPfXGmgZVJJ9fFytKxuhzJgbVgNNBEpHvFWfJDvly/iV14Nc8A0XJMAqGUY5\n3DIRl+1hHA7OM4VWhNPucAZrvSbmcyVXdN77AcAJLqVWpyfcigWgfZYbbrgB3/zmN7Ft2zbouo4h\nQ4Zw2YQ7LGw9evTA/v37SwcWXnYqy4ix1PtKZDPBoTghoYDIcaj3PQjtr38oSzkwKotjZmFT5yD+\nrcmUnjyRRMw0nKl2oWt3V77Xcw5sOnaP8ywXopmqCG9n5iII1TWUyTaZRqyQBY4e5s4csMxtUDdB\n/9ufaL/pwF4f/JOMHEOz/2KB3kdNY64IvUgsZ0U6fwXI/j0OlFX71X/67q/OU0QsUTrhAiU8pUmn\nb2IhmYwtr1KEmn0uqQqf8qihJBHb9rp/9WDLDKQr3ESDEAhdugOy26TX1r+A+GWT2Ku7iqqw5PFf\nNsJ4eyviX7+KGyhsnXlvgHB0Y4L7UFJu/zImovj8E/QelFlyClqbVka8YMehoXEkwUeOgRBXmDLM\ntu3fvx8jRozA8bTjNiGTTqcdRuEOa5t1794d+/bt87EWsCyqgRhZLuJM4Ht1z6VR9X6CwSmzIXTr\nSZFQzUchVNWwIcwRxszCVi6FMmMuiK4hNmgYhLe3Ojh/5Y5lzHMghSwt1TVaFBoJqs8hEDNccikB\n0RS8TjhdCfLudv8QngfV5Js5WL4WMMzIDFZPpiHVjwM5sDdEyGls3gRy8QQnqAiGXhqJZf0OX/82\nhOrOIE1HHCir9/6SdJV/6j9AycNzbEQQqBLm4QOu3PQZX3I0crz3AITQMuW48RDs50mK095ZMg1i\nwcXlliYUVrIHUFHZCVL92BDKzR5+Nba8Cu3kIWHUHqvf9+QKmkzoOkguww0UrMFPE2y5ZfPQfpeu\n3w6IFutEMCCUtaIpV9ETiCAyTbC3YZoQR9VDOuNLyN85ObIEuHfvXowbNw7H08oOLC+//DJGjhzp\nkDd+HGtqasJf//pXnHvuuR97W59FswNLKYssPbWx1u7NpphoplXLoM5fgeKPV1NM/uJVIGLbtByi\nyAIdtJQVVMS60RB4PQXrHMxdO9HqzHaMh5SuAKmoalPN2ZlyVtOQjxzgTOHf42MdABhCZIwX2GGc\nzjSxHV08DrJ7F4R0JYihh9kEpviRWM75iyKIWonCgtvC1yZV4UoEpyvC6DmPc3Suv5XJkw/edc/f\nSSZOcml4YPW8xo6H0KUbpLPPD2nUU66yce614M0hpStAYmJYiXRlI5Q5S/yUL9170UAkSRAqqkBa\n8+x+X2sr8vNvpcO3rJJcLAZ94zp/o18UPfo4nl5fzz7Ie+HEgWfBGxDKbqK34Z3kJY3Es6LzPUs9\neiF+xfVuULGPmfH879+//7iXwsoevezZsyeefPJJrFy5Ejt27GjXzrZv344VK1bgqaeeQq9evdq1\njX8Fs0th5RiPLZXJsMthNQbgdwC8pvb+PaHldrlsugD4UrmxmLPMt/crj70IxZ8/xWESTjvsru5s\nx3zk75uBwtIGSKPqIdaNdtl/M80ljzNSGdMraWuakMeO91PpFxksypbZ9yd0L2Ythvnuduu4b0Zh\naQOQaYHSsJSyGt98N4Q+AyDVj/X/zprwFkyTuU3y3g6HsRgf/INZNpHHXuS//mrKup6Bc1q1DIIk\nIXHdrUA84aNxJwf3hq/BkyuoNLb3WvDueboCglakkO/A9RZEyZWufnghffaaDqPwvbnQNm+EUNEJ\nyu0LKPNz3Wh3m1Y2b2x51UGKKbfNh7rwEUpTVGyFdOoZPllscuSQk4ho61+gz6JpAIbGPDb7WQi+\nAyVZtcF5J6c2QCBgSiLbSaNXnlhX2HLUWkU17YnyVkQey2azSKc5fuAYWdkrliFDhmDIkCE4cuQI\n1q9fj5/97Gc4/fTTUV9fH8nrXywWsXHjRrz66qsYOHAgrrrqKlRXVx+Tg/+sWo8ePcpasURZm1mN\nvdkUD28fi5W93GYZMwuz4dDxhJ9c0jSjSSqtQMglY2xYCrLng1Djn3uc+Sxfa8UraSuKEJLpNpUZ\nWfdCMPRwD2ztAxTt9L25Dkxb6NnXT8po92gumeDbppSuhKEHtsmhqxEqO0Fd8ijtQalJENOEYJps\nlFaxCP2Pr9AA3bnWJd+MGvbzXAvePS8+vcpXXvRxbwU0S0AInTVqWApy5JB/lmridECWIY0Z68vm\nvUJq9iySEIv5NGVQtLVVKHsAk1U6eGyMd4An/saD96uNjwHNR0AMHSSfc1dGnmcU4At2HasqxfG0\nNvdYqqurcdlll8EwDPz5z3/Ggw8+iO7du+O8887zQdj27duHl156Cfv27UN9fT1mz57dPi33f0Er\ntxRWykrBIb0WnMkIlRKspnZ8/LdAmo+2GeJoH485eDiFW1p1cO3VDXTYbeJ06H9/G4nbF0LQihA6\ndwXiDMJCayYGqQrKV5Wu8JFkAqDOU02GnUjUcaopaNYKKaiMaUvaJm6cRSeref0QztS4zzlY+47v\n+5DvmL29MpLxB07Pvrz3t6KmBi3b/s//Pe5AnuQGiDgl9dQ2b6RaNwg40lQF5LHjaZASBPe+c7Yt\n1PaAcvsCCAnVEfdyaFxsipOdb7sT96IEefw3XaaAqQ0u2MLbv6gfR3V4gj26J1c4lEVAeP5KuelO\nZ5XOy+iFVJqNJLN6Qe6xUULMUMnJehYpNZGlQmkJhQWNiCIIgMLiWVAalkKA4EfLebj6eKU13ntd\n1tDmJ2Ttbt6LoogzzzwTZ555Jj788EP8+te/RnNzM4YPH46tW7eisrIS5513Hvr06VN6Yx3mM1VV\n0ZrPu7XyNsAb22usmQwH3ZOqCDPLloA42rK+gtbqMP3qajJMWz95NqQ5jRTZBCB2zvkoPNLIrJPb\nTkIwDJB/BGhbvMcTTwC63qZVhd1od2rw9hS+qiJe0xVk7EXOakGsG82s4RtKMtTf0Dauo6inwwcg\nd+kGo6oGhhznshsIPXpBaVzjItyYU/AcZxHIWJkJAqvxba+ULNVFx5HOXOT0sYLXmbntG29H8adP\nALoOeex4OtBpSQPYFCfa+l8xaGnmQFm2lqsf4/SqDu4J3VNxaB1ATApWSaZgDB7uy+bV2u4eGWMO\nTb5hQKiqZgedTjU+XjwiihRxZX1XrBsNsn+PS6ZqXSPpwssjy87i0DqQI4fcQOlFyxUZXH2epKgc\nyn1elaKlpeW4l8EAQCBlEseU07zP5/N44403MGzYMCSTfEqFf6Xm/YEDB9qkeQ8AlUkVF59/Hh7r\nLiOmFdsNbzxWFm85inzDDb6XSR47njadM83QXvkt5Kum+BAyLI1070yGu3FKm66tf4HOIxzYawlL\nxdyyUyEHKEmInWqQh0CRRgyeJmXGPZQ0cmoDYn0G+I7Z/g5LyMoZOMtngIRKg5IkQU9V0MHA3bv8\n2SxojT1+5Q0OXNhQaNC0nbAycxG0V34LaWS93+lMbYA55BQQIebXUreDkw39tRrCPqc+tQHCgEHQ\ng1PaAGpqasL67FZwiHWupbT7chyk+Sht+gdMuW0+Ct+bC3XhSpCYQMt1hDCvoTJjLgr33wVxVD3i\nX/82SD4HoaoaxeceA3Qd0qj60PyUMWQEdYaMa2mvRFkrST+qTfGtFOyeD2tf9vWpqalxdN3pNd0S\n0m3R//YnxK+8wb8KCRxXCF337KMwNm8KE0tGPGe2yS1N/OswYy6ETtXI3x0WIFQWr4Je0y38XLTB\nN/z5z3/Gn/70J8yYMcN3bco1W/O+lJW9YrGb95IkYezYsRg4cGDoO6qq4vTTT+duY/v27Vi3bh0A\n4Lzzzit31/9yph06gL4HP8J7iRqcnFa4ZRxe5tLeYS6WCYbhk2dl6nAHuJmkXCakkY5iK785Xt0Z\n0lnnuTMr8QRtGKcqUFg00/lMmdYAYUhdhPJftZPtC4Ucky4GAlz9dfDFzBx00+DhiAVFrhIKpPpx\nFliCIuPkliZ/lmkakM+/BIVlbs9DHFoHQY5DOrgPJF0Ryq6994k3BR9FB8/LWHVRBCqqEG85CuTz\n/D5SnIpc2c+YNzP3XWcrixeUFMxD+6G/9DPEvzER8llfhlDbA9pf/teHsNJe+S3kvidH09IwVpKl\nKIuY3GQR5U5aij3Fr/654b/pSpU10+QZkA09I5NnW/eZ02vKNiNumiCmEVqJRV0HIV3B5+qzQBbt\nJacEgNdff/0TkVnvaN5/Cs3MZjA8ncAbTTkaWAD6IOWykAkseCh9qQve8tSsxYh17hoWEbI+J/lc\nWeJfviFJTfPJszKb5auXQV28CkSU6PI/H9ZIpxsPN8fFkWMgxEQUVgVq548/QJuqns8Kj1DHyiXb\nVFPuy5Vtocig2UsgiCK9Hut/BWP1Mrqi6fs5EDsL5gyc2XKzeu8BkGq7c4cuAYSDXSwGQYpHB+Rp\nd0AfMsLpu/iMFzwzzZAB7j0komj1ZuCTDQAA89ABthDVpFsoj1UANci9zokEIMnQlSSkzl0pw/Th\ng9Be/o2lOXJOuAmuaSBpEajsVLI/5awgDc13b3yURa0FCFHSvTx4uRADEgqE6i6AolJJajkBQ4hx\ny0ihpMHzzENjqzySpiMoLLiNCcEmYsR1sEqHx2o+LWivv/46LrnkkpLf+7jWZqUXu3k/c+ZMKIqC\nBx98EE8//XQIHrtv3z786Ec/woMPPghVVTF79mxceumlHUGlDIul0jilSye83uSBCcapQp0NJc03\nXA80H4XSsJRCa4fWAft3I99wA4XdPjgP0qh6SBde5nxeuGsKCnOuh7htKxN662RmDddD+8kPQf7v\nNZA9HzjyrIgn+BlaSzO0H6+CuG0r5SSzmX49pr3yIhLTGnxQyfg3JkbAfI3wZ/ksiGmGYcgTp4PY\nsGDAVf8r5JBfMhuF++9ywQYrG0F270LhrimUU425bxfdREQRWrICxU5dUOx2EooVjMHQAKxWW/8C\npdK3PpPHXhTSamFBUgXDgNzSBIGYUGYtduG0gOuwyryH3vstFXJoXX4nBFmG0KM31HkroM5fAXX+\nDyDUdkf8iuvDczic61z88WpoP16F2FtbQs+bfP4lcChn7PN8cgVVVwSgJSsiYfDe4yd7wgAHY/Mm\nINMMksuCNB1hQ5k9UtT5j3Y5UN6YrlFKlYYbkL97KvJ3Tob597dRfMZ6bgEmdJ87f1UoUFZqxjVy\nxMtYEOyI6xBUHPVCjX3IL845l7KyqKKOgXU07z+FJnfuis/Pmod3J15DP+BxSa2mQ4vxr30LSKZR\n/Mna0AutLviBywxrf85ZOrOGJJXZi31kkULnWnaGls04hIFq42MwOeUj01P+EZQURYdxYb4B522/\nQAQu1b1XG90zd+DMDPC4puygFQUxDjipqPKiF5EjDq2DPG48IEvuNSgju+aV5QA4NPGOwyrjHnrv\nt7pwJU0+TAOCKIEcPuAHA/TsFw6WkuxcZ1tF00bf8USr1DvvZ54naS04/xtFueM7fg7yjGRaIABs\nPfpA+Srj60U0QN+4PnJ1ykMMMp+RAOCDXqOmsHhZAIINlKGZchyQX9lsNrL3fSztmFC69OrVC9de\ne63TvJ8yZcondgKfRZMUFWToqRA/fwriC5chlqrgc0nZdCG2EwpOVUcNTUXxE9kvQ0x0Xl5jy6sQ\nR9Uztc619b+i8NGiRbkSUT4yrUl3cdtWCJJMVzJBB3HtLSAg7gsdgI6GtdHDL1eszwDaiI+YTWGi\nmwKloXImqx1HsXwtyLvvoPDgfDq8OfYi2pC14NNRJSCePLG6cCXI/t3Qd27zCWOBBQrhZdeGAems\n89yej9UniF89PVzWs8xGymmvvIj4NyYCzQaFHnufj+B+eIJcyVRZqoje42feG8+zZj/nDm1/j150\nUNBTvnIUN02TQpu/cpn/PeI4/uB1YDlzLZkGhoyA3Pdk+tu4gsLimSWTFNvaMg7g/U2b5tM89uab\nb+Lf/u3fyt7Xx7FjLvQV1bzvsPKNiCL6fm4gtrcU8LluvSiShPXC2lxSnuzLN4cQZ7/oghyHnGuh\njWyr94JUhftd+2XINAf0LmIAR+tcHnuRf8YiWQEk2YJCthO1J+d9Ylu1PYCEClJsderpSPqho1Ev\nl5dFlknvYWf+gEuiaBM7xkSQhAL521Md9BWzxs5YMRBRBAzTmUi374M8djwN0AwhL564E0XeWQ5R\nkiDUdIFcdSYgx6nY1W9/AmnMWKq0KcvQkyrdBi+7lkRHkMs5B4stN8opxfoMcHoo+nvvQDr585Tk\nMZmGOHKM30nHEyCFHIO52YJiZ5pQDFCqaK/8FvE+J4NY5+/t67iBY66FQGzyPGvjnfsXHIS0ryVT\ncXPybIh1o0NDj6XKSbE+A6DO/T5FDYoxENHjOon1X0xEYtZil1/MKxcdxXrhsbKBN/Y+22CfVOMe\nOI4klB328e2UU07BG2+8gc997nPRU+u2FVtp6QewuKZmQ3t1A9ux/uFliF26+Ykmp93hvBh2toiY\nCOOtLb6JbHHkGEj1Y/1OcuJ06wVqADQNcqYpOpOynKjrfC8KZZ1B/ZgKRQWswBKV7Xkzf8c5zVlC\nS0DWtLPDf5VQIJ16BorPPhYaxCxZY/dwRTlQVEKzX19gUFRAlhCr7elR1tRB5DgEYoLAlRVAPOFz\niPa/fZDaidOpIuMrL7p6JdPvgjBoOPs5mTwL5PBBdokqnwUYsNggxbs4cozVlPeiAWcBsPoe1vMm\nVHUGUdOexEMEqapGbPsbIJVVDqWKr9RXyKFw3wxnP97AZLy9FdLZ5wOmDkAAZJlSzXuBBYw5IiGh\nsIcerUl7r3RzlONnUt3bDfkvX0KF1QIrMGX5WiDTQtnBTRPy0LqyVhXlrIzbK+4FfHKNe6ANcywd\n1j5rzxyLjS/fsWMHnnnmGdx7770ArMZuLgM0HwEUFcWfPhHKGH1U7EIMhdnXOuUAb508hO6yf9/4\nGIgYg1BsdSg/zMMH/VnYzEWIde0GaEX6HUWltCCGTvXWy6AW586iRMAmy8Xdy/t3U66sgCnL1kIQ\nRVoejMVAjh6G0KnGH1Ts7y5eBa1rz5LHqlslvdD8yqlnhIKBlyXZ/re6eDWKVbSZajsNQZIdh8ib\nk6A0JAQwTR8FjDNzkc84k+5QVSCfY99vz/591zBwztx5jcWraTM90+JMnAf1WpSZi1B4aD7U+Sv8\nMgj2NuavoPMyljkzQq0FCLFY4JlqgDmYZt1StsXK7NMw1BSEd/7PuQ/iyDGIf/UK5O+bETo3deFK\nEEFwHD9vMDPy3lvS2m2ZySll9r6C5Tv06ktX/1HHU8Y+J0yYgKeeesr5/+M5x9JmVFiHfXI2YMAA\nvPvuu87/E1FEsaIKWvfeIGoS0pgwQaF55BD0mm7Q0lUOYZ3x1hYU7r8bpOWoi47iEU3qGp2yv2sq\nRc7ccSOQbYHa+BjUBT+A2rgGyLYgP/s65Gddi/z8W2F++A8gnkD+3pthbN7kkj+KIuRsMxO9FEWS\naSOjyiW5DH7fKel5LZ4AZBmkkEfxv9b6dU487L3Odz1lEd6x2uUdLwGhtv5XiF88IYwAs8kfA//2\nEgTa9XOhk2cKnMvJZdDVqc1j5tmWQ0zapTuIrgH5vNPH8p3DlNl+JJ3Xgqs03nEU8sgvnuVH3XmI\nLsW60RA6d6W0Ja2t7GfuqN+5GZs3OcmR/Uw51/GRRojFAmVwuHMy8vfchPwdN0JsOuy7D8bmTS71\njtfsWZ3anihW1UCr7hIt/8Bl5Da5XGxB0seyLVC+K3xvLgoPzgN59x33HYhaPUfYJ9m4BzpKYZ9q\nEy0hJ9M0EYu5OYDdv5D7D2L2Ohx9jUCjT4h7ygc8rqdYjN1PsKatlZmLQkyu+sZ1iPfqS51HMg1S\nyPnLHVaW6ZVg5TUhAXCX+kBwElsFERCme/eU9IL9DInAKe2JdaMhf/VyqHcso30LDmUK61jtSXsi\nir5raGx5FeT8S/jOyPvveAJIVYape5KMXleoISxCqO6M4k9+6H7GaA4bQ0ZAas1BGjMW+qb1bh+r\npiu01/4Aqf8g9sMX7NXwjkNRuOdqz+7YbAvKzEXsbei6//f2ueQ4szzFMOUJC7KuvfBcWMulrdxZ\nPBnpbidRye4SgAygDX0TNcUu31mDsVq6KpJoMmo/n2TjHugILJ9669+/P95991187nOfC/8x24LC\n/XeFPw/AGr2iT5FEk1Mb+NTbpuHPPi3SPACQTj0D+Tv9jLN+kspGqPMehlbdNaRXEuyTRDXK9UI6\nHHSmzIb+h5dD31cbH2M29+3Vh75xHa33e1FSUxsQv3o6SD4LKZ+JhH/ax8mUbC6BREM8AYgiErcv\nDHNxTbsD5qBhTqOfeZ+uvQVCtx4gTUdpE1uWIf/7eUyHaSch4uDhiPfqC2QzgKJC+8tGiL0HcJ1s\nsFejbfhvpiwyDJMb+ILlVh48mNUvcYY8WdtmPaMM2Ljx1hYo190KoQ0IPdwBIwAAIABJREFUKlbi\nEgJdXH0TzAN7gMrqktDftvREymEm4CHUDCUZuZ9PsnEPdPRYjrt9nB4LADz//POIxWK4+OKLQ9+T\nsy3Ah/8IsaqWkh+WM010MDBVQTPnXIbCV3v3AwyTXcO1aOiDfQOhR28UGucwa9CF++92PlJuXwDh\npH5c/iTnnHj9kcWrIKUrkZk5qeS+7O/bPRLvufN4p9xt0ZVZyR6RdZxi3WhIZ5zj8oElFCRuvhso\nFkOQbFs6NzFlNmJ9BwJgc3Gp8x5G8fknXcnebifRfpam0Z5X81G/suG0BiRGnI6szi4ZMnnHGKtI\n1u+kfMZZ7Wp/fJmucDyzQ/FvTfEHR8vRxfr0B5qbQj0OsW40laI+chBC51rnObX3w5JSDm87zAPH\nBJRMbUBy1BiXhLKEMa/TxOkQ+g0EjhzyVQYgSXRqXxAAUXKQi0FaJSHXAtJ0lK6GveAQjgJpkJfP\n+X5QrTJwvaRchvne2qjKm+5bgLnz5qPG0x/5VHCFddg/x0477TSsWrUqFFh4DL+RrKqwaLtbCyGp\nXMAluWOhz2AazL6BOn8FO8Py1u5tWHQuw0Qg+SxiqW9mM+x9yXEoMxf6IKyscoS4bavLNpyu5Pcu\n7PMrQbOPOKX1l8d/M1SS9OrAC0oKRIxB7j8QcqrCgnhnIVgIsKAGCjm4zy0PEWIRcyZRmH8rLUUG\nSyWPNEJc8iiEVKUPPeQLoqFVIC2vmBENX+8qTSq2QuzZxz87dONMGIoKk1HSFHIZwEMFZJvx1haQ\n/btRuP9uqAtXQrIcsqEkIRECZFsg6zpIPA4jrvhgviQeh55IwiRmCNIsnXkuyKAw95rkQRKWMu4c\n0bwVyHsqA2LdaLpK93LbWQSh9rXnDrpueZUyG3MUSO2J/KhVEBMRyem9kD0fIH//3dj313dRu/8D\nGDU1nwiRbUdg+ZRbv379sGvXLhBCIHj0z7kvQeNjlHQwyiKcNxFFCP0H0YBRyFsOvQXItrAdMYcr\nyZmatyGdr7yI+BXXlTzfqMliRRTZ9e7KKuTvneG+pAFSTPt6aXb566EF7BKWt1xlnZ+QzVDZXs81\nFQzDpbMnBEIyBZJpdleNVqAgl0zwrZqEBKNcwRKTSlWw5y9G1VOSQpYDaT4K8fBBGL0HAPD3qXhC\nVEKmBfFMM5BMQ0+muasXwTAQy7Wg+Mf/CbEdxPsPpgigQOZtqEnEWLxkV98Efec22m/RdTon9dof\nIJ7UD3l7hWddl1iX7iiu+4UPZYghIyDmc9D++HKYeWHAIF/ZV8plkH3nAGRFDZXAWP0IbmNc9z/j\nTL68lY1QZsyFqGsQ+g1kvpv2jBmzj2JJc2vpqvYNQPLeaUHAO5kCBiXjbSKr/LjWEVhOABs2bBje\nfPNNDBs2zP2Ql6EU2HMJXoty3oJh0EHB1gLNwLOUckWo7cl8cEmxEHYeU+Y4gk8Og+ypZ4AEETpg\nv+C8pj4RhHAzdvJsFJ//kf8lXb0snI3rGuKXXgNyYC+dY2g+yuwZ+OaC4gmQo4chHtwXorO3hy+l\nUfX+WSA7UDCEnnjJgD1XIY6qR/ySqwGO0qG6eDWf5iSbgQCrpETgMgLXjYbQtbt1L2Ju4ItbvGN2\n2W/ybGBoHTO4SLkMkM3A2LzJB28X60bDfH8HWld6AoKVeYv5HLR1v4D8lcugLniEcq5lWqDvfJvO\nT3nnYabMgf6H3zOvi3zOBXSfnt4ZyWdDxwIA8iUTytKgd2Qd7Gf8qAQxngC6duc/41NmuwOmETRB\nrY8soWwTvFV8QuEnB3s+gGj8g65c2jiRHzXntm7fUYzr1snXqzne1hFYTgAbN24cfve73/kDy8eQ\nIfVJpOYyQCLhOH2pkKOlioCzJFXV4SbmjbMAIQbj4D46+HdgLyAI0HduA2QZgkD1w+VzLgCJK9AT\n/lVElAPwvljO9zaug3TOBb7hO6GmC5PqBjn3BYrpGgRDt6jSY3Ta++IJKP78KTfrTaZBYjEqUGUp\nGxJihvpWLD61kEO8ZS4dYAyWJHmMxZ1qoC59HObuXcjfezMFR7AcT7FAS5XB4Oql1MlnASlOz0uS\nIVRWufNOduCTZUh1ox3whTdwsWZakM/SIc/A88bLvO2kwOv87YFR+cxzkb97qv83q5bSbD5EtcIg\nIW0+AnTqDHHkGFrSZJQ/S1HL855xoWt3tnN+4TmntIlMC5Dy09p79Ynos0mYx2eLuIEQ7uqCt6oo\nC1mWqnDeDaG2B73vW17FX45kMHlA97L9w7GwjsByAtgXvvAFPPDAA77PeKsOCDGqoxEBa6SDli1h\nev1pd0A4qU84W7b4qoR+g+gcS/PR0EAcybb4+jbEciRCdWeQdCUMxrFwCRMXrQRE2eGwsr9nkwV6\nX0gehFWIxRzsf2z768h74cgTp4O05kOOTzrjHBS8olxTZkMe/026TTvTY/Gpea3YCqGqBnqX7nwG\n5KBDEUWQA3vdYMGD9npKlWxKnfGW2uc7bgJgBxOLQ45K+a6imvNBfft8FvAMa3rRUfrf33RWeDbJ\nplBRxc7Mba16zzkYW16lA6H3fJ/9myCGyCmnEt9nJNMCobITpDPPDZUKnfJnKaYErZX9jC9aSROu\nRSsps7J9be3r9LVvIX/fzVRBdMY9ECBQup3KKhR/9pRviFMa93UUvnu37/j0dBVMSfahM0OrZUb5\ntRxkmZTLuBIacGUa9vz5D+gkS5BV9ROVKe4ILCeAiaKI2tpa7N69Gz170pp9aEbFEl0qzL6W+/AB\nfIoKANSp8178XBb5u6c6DLHe7NJp4jMcSWRNl9tw/BCFFYvc+RX7ewxHrq3/FRJT57jlGOslLT7/\nJOSrplhlocawEwkcL3P1sYrSf0ij6oF0pY/OXlv3S35ZKsUO6IaaZPCFzYG2eSPkkfUOjFvf+TaX\ntRcAdCUJUdf8jslaVcY0jXm+DodcsRXI5yOHQnnCVqbWCnXxKpi73kPhwfn8PpVVvmQmPmp45YN4\nAkKXbm6WTwiEzl1h6gb0Xz1Dv+NZmcUvvQZO494+R2/5kzd7IscRbzoCFDiQ+tZWkE4iIEoorFjE\nrgbY5dxMiz8J8QbvRxpDWkLB8qzD8JzLgmgatF8/55YorfKrOXg4xHwupEsTXIEBCL1LdjD83y9e\niAu+FIfy9YuPu7y51zoCywli5513HtatW4eJEyc6n3nRIXJLkwtBBXwPnw1H5CKEvI7H1hAJOktd\ns7bZyCxbkKYjTPLByAyJl8HHYu7qZfFq95iS4e8bb21B/OqbfI1cfec2yOdcACHTTNForODVdMRf\nUoqom+t/+xOkVDq0CtB3bosMAF4TDAOx7W9A3+gZUuzSDURRIWYzrmSztW3j4D5LprYGJJUOzdTQ\nUuYaoFgEJEp+ae7eBSJJ/Pq+fX1TaajzHgI5uJ+WBje8COmML0G3uNmYK0m7x0NMB0bNm4VyGvgs\ntBhL2fPqmyhgoX6sfxUytQHyxRMos3IrZYWAJFEG5YgVCa/fUPzxarpqCiQVznVJ0vvGRWZZKpNe\nyh3n+gSDN0dLyGb1ZgE4vMETkgQJhIrbBUqjdlnRK/rGepeMt7bg9/k0lj/wILQ0X1L+eFhHYDlB\n7KyzzsKMGTN8gcVnvOW/pkF8vzRCyJkEj4nhGv71t0H79XPudxllC6FzLYw+J7cJzVKSWLNIG5rE\noqbxUvj7nBIExyG5So30/5V7vsfOXjvVwOw9gDpLRunG/h5iMZfokVE6IfGE01C2uaeCw5VAgBjT\nDsrWnAGrLKPcMhdE09glNcvMQweA/bsdp0aRSRFoN8tBmocO+OdgpjYAg4ZBzOcgeog0g88IKRZo\nZcqzKgXgaJEgkYDeqTOIKCKmaz4uL90qUwmm4aAOydHDgKGDxBVA19zAbe1P37Qe0pixKHhhuVPm\nAKLsgBH0nW9DOnkIDdQJ1ZGdtoOazZdm95OUGfeAFFvDz/iNs6Crbg+QBXMmoggyZATkg3sig7c4\ncgwFr9w23zdfJigpyJkmZmKnzlsBcmifU3rzcbN5VsbB59upTAweHnqXjEm3ovjwo6is/GSDCtAR\nWE4YS6VSEAQBmUwG6TRjFcBb/gcpWnjCVqJIWWN1DUgG2GkDdW6hSzd3G7Y2hUUhY7YBzeJk3lZT\n1Csk5RyXIKB1+Z1Qlq+F0NIMLUDhr+/chpihUeivYUCo6uSyAACAEGMHo3gCwjtvOL2XIKuuN8jJ\n46/0U71bx0i0IrROXWjpaNfO6OnqqLo/43Nun8YyKZcBWgtuULLKhMxVxJQ5QG1P2ji2iEl9jm0l\nZUYoSb1iiawxS54z7kFhMRXLgpKk6pL2tbQDQkUV8lZAE0eOoSsRw4CQTFOW5cB1YAb0VUvpEOt3\n7/EwLi9gXnctXYVEIY/8/XeFHLI4cgzUex8EaWkCdM2CTg+ClkyHS8UWzNnpO/Ekm2MxiKPqIZ3x\nJf+MizVfZh7aD6GQYwftg3v9s2WeFbT3njJLtnZlIrBC/O3GP+LfzzqL+fwcb+sILCeQnX322diw\nYQO+ev75IYQIr5kfpGjhOp5e/WAkKKmi03S0LU6n2x0erU6d2yU0xDLbAYhHDgFNh3109olJtzgN\nTWRbIFZW+Sj8HS6qu6a6L/Hk2f6hQ4aejLb+BcQ/N9SXIXv11L1svZBlkKaj/mG2idNpScZGIRVy\ngCT7qG5CNfAoFF8b+jSO5bN+EkQrq/WJXxECoWt3FH/6BOSrpkBX09xs2+baEutGA4rC5E8zlCTE\n1gIHlfaCEyglw3CDirV9OyA4WfepZ/jKf+q8h8PXoYT6JzPwBK57zEJwBR2ysXkT8q9v9rM2fP3b\nkAA2oKTxMZhW8sDU+Jk8C1CTiF86Cfl7poVXJEseRf6OG7krymCy5us5WahFpWEpBFnmJigkXeVD\nU/7u97/HjBlhdudPwjoCywlkY8eOxbKlS/G1fj2Y2bGvpm1NeCOXcZrNjiiSZyo8JInqCUReTRGh\ntifUpY9DU5JtXpkEjTm74lWczGZBdH9DE2oKcueuvuApjxuPwoMRehsAEIuF9GQQTwD5cOZobN4E\ncskE6N17Q8pnIF8+CUI8QP3ilC4ehmbP/bz3TjjwAL6ZAZZ0sZCqACS5fVKzaoqipixn5E0YjC2v\n0mAweRa0Zx+zrrkOee8HgKIyBbogCG5WH+BPkyfNoFPw299wHKsXXu4gp+xAmWmODgiMrLv4/JMh\nYANPBtsZYi1D7tl+ZvhBytN7SiT4K8tcxrlHPgGyqmqQpsNO+Tb+tW9xfp/lrygZyZqRUJnIN6H/\nwLLGDEzTxEcffYTevXvjn2EdgeUEsh49euDAnj3I/WAxRK1IPwxkaZpH9pennS7Vj7NKV4yZBYbY\nlBvAGiD17BupX8EyXyBJV4C8t4M9u5KsoNPpH+1iOlpJUf1IOJPtLATPnAElTwyUuG6cBaIX2Zlj\nXIF0aB8NeDXd6L9ZGb5puuqSK1korLm+l50lXeyc/6zFtE9TKH8FqCfTEC00mB1MIMu0vJNphpCu\nhLZ5IwDQVZ2XJHTyTPosOAJdc+jkOm+ifOljEPM5n3ha0dqu7SDt4U6So+fADF42GwMjIBibNyF+\nydW+EqwZBcsFImHZttnPjMxjIrZ7T9feQme5RJn9vQBgwE7S1IUr3X7ezIUg2Qz795LkuybOirJH\nb2YZWW5pQoGBfFMXrSwLMLJ161aMGDEC/yzrCCwnmI0aNhR/3bIBp9d4HqRAlsale1m0EkSKDgp2\nZs1EvliIsMJDC8pWrQtCV1m0+97AWErT24uEizcdZpeRDMNXCoKahDrvYWtAUgBSaej/91p48v7G\nWSDFVmg/+aE719NnAAdBZDkvXo8kXQHCminySBc757/8Tnr+AdLMKCOi6F/leQXXKjs54ljKrEWM\nVd39dMVx1pchdO8FUsgh/o2JIM1Hudl2sKFvZ+3qopUgBCC73/cj24LqkpNng1RVQ5m5iA4SzloM\n/e9v0ca7JWhFCnk/W3eckjU6iURChbnnA6dcymRcnjIbAgBRKyJWyCN7cC8kRXUQXUFlTahJKDff\nA6FbD2jWAC+zpCwnnITLJ8KVrnS/b5rQXv5N2PHfOAvF559E/BsTkX99s7uinNoAnacFw4Pi7/0o\nUNql5LHBbfzud7/DeeedV/bzdKytI7CcYPaVC76CJ373K39gCS6FeQ+l1WyOMtuxRyJfGLVsnoWC\nXJQ4EoPqP/JYTZMtu/zr5+iLe/VN0H7/a8iXT6KrD0V1yoTyyHoUn38yzDd1zlfo3AroXI+yfC2X\npjw41+IDHahJ5kxRqeG9tphNiY9khY+pVjAMyBOmUW62Qp79LOzfg8KKRT42Z2afwwKAkEOHfH+z\np83RSkk2tY3rA8FrOe1Xfe1btLSTTEN45/8CszEzob3yojtYeO2tfj36Iu2taV17Ukj9/t3Q178Q\nAm+oi1dZ4A9raHflUloG/OP/+HjGzMHDucOPyqJVjnM2Bw/3oQX1FE0SErMWA/t3h8AC5mBKfino\nmhP0fI4/maJl1osnlN+bjOD+ckralimLVwFJV8abEILXXnsNs2bNatPzdCytI7CcYDbo1C9gV01P\n5GISkqbOXgp/DLoXwGJA9opNebcRVCws5QyDjrSM8gXLBMNA/qNdkFuaXdJASYb+tz/5aFkQiyH+\n9W+DjL3InUi3JtZ9eiqZFjbf1Flf9s8kZFu4Il+8UmNi8myQbIbZzOfem1SFK/iVthmQc9HCUBFm\nlxu58GORQre9tC6sPkdi6hwUn38S0HUniLtl0vn+87cGBO3toZAHiYmAKEIs5MIw29X3uzNRxVa0\nrn3Ave6e58KhoI/HQ/0yceQYAEB+8SzfObauXu7ftnX9iSizhx+T7nBobPsbIVSYMWQEYp27Oqg2\n5xw8CZZ3ot7Y8qpLurn+V84+yuUAY4NxaMnSZ4x3Z9OmTRg9erRPHPCTto7AcoIZEUV8/aoJ+G22\nBd/+6gXMzCeKZLJcKzljEk9QXH5Q/bAEjUnUUB3P7HJaJviyDx4OqX5cgMp9FrQ/vuyWYCy545CV\nGM505npYQYklRmbPImRbQAzD1agJNPOZsgQzF4G8t8Np7IeILcssO9rmXSWyUYCzIfToDSQUyOde\nCHnseJrpb94E+fLrfEEUmuYLvsqMeyB0rnXLXp7zDwYFcvSwuxq6czl/Bez9f3tGiiFgFURjUWjv\n2XQFUs62edff8/xxecaWr6W8ehGrTR8HX/MRdwX19lb+c+ixIKjFGDw8lNBIEGC8vjny3fnxj3+M\ne++9N3Jfx9s6AssJaBeOH49Jkybh8muu9VHp21aqT1GO+baRy0KIxWjd3s7EpjbAPLTfP2g3azFi\nnbv6Mu1ggDLe3grpwsvb1KyOIhUMYvcNJQl5wCDKdBuxbXpcYWVAbf0LvrkepjPglRoP7AFiMbSy\niClnzLV0WcL3RiDEyYSj5hTKpjv3HJ9viLGqGiRdCTOhwtz+BhNCLRg6tMpqEDuIZlvoXItHTE7+\nj6+yHaw3KNgT5Pa1YWiz+FbA1v8LPXpDWbbWAYj4BksDaCzIMvJzp5cngeBJEiLfDca9tfVTIMdL\nrraJKKJYUQUhmXaQhXJgH0zKfrAlufUhI5x7AQCkxHu9Z88eCIKA7t27B5+KT9Q6AssJaIqiYNiw\nYXjttddw2mmnMb9Tbp8C4DOnBmWN5aumOA47OGgnDq0D9u92SwU8GLT1MuiiWFr0y7bAy+6ltJBA\nKS28L1+5UOiYzdeUzTiU7vK48Yh//SqgogpGkq9NznVkHFirkErTATlrm74V0P7dnh5UaQhtSeMR\nQDbS4MRDsqn3PuhwrNmlHZaYnFDbg92L6dEbyuJVEOQ4pU/xlKz0nW8zp92d0o5Nu/LsGkj149wV\nGoMDy9jyKtQFP6DyDrxV2Y0z/dv2ZPaR7wbj3toszsz5lalz+JLQjH3wCCWZGi6MhKLUe/3MM8/g\nqquuYv7tk7SOwHKC2re//W18//vf5waWcq1cTe5IZwgOiWMABs17GUpSgntedh6lhU3YF1mWC5yz\nXUcXR45B/IrrIGqtfhjw1AaIAwY5dB62McuEFsJISLF7U8QwXPRX8Dp4nVk7e1Be45Ux7cDGXXG1\nNNFymKVrwkUXLmMDGogkU40TIeYjuRTrRkPs0g36Jj9PmlFVg3jfk0HOPt8/DwMg3qsfSGsBQoIz\nd6OmgKajzlCo0H+gJU5XANIVMNUU5AGDkbh0IsyEWnLFYOu0IBbzBUBxVD2Eqk6BFRPt6QldezgJ\nWLkWyej9MRMKTdPw5z//GbfddlvZx3O8rCOwnKDWt29fZDIZHD58GDU1jHmUMo37oDc+Fq1PH8zs\nIjJtwUOCGXT65QQ2r6NkBTB94zpIhPg5pSL6EsFzNjZvAjnnKy5Dsn0dPKqA3m1xy4SbN0EcVc8W\nEPv1cxCH1kHQtRAE2Xt+7elBBY2IIoR+A5nU+pEAAlspUY2GUpOcH9AgKJbK6If/AEwDJFWBxO0L\noa/7BSUDTVeBZFsAXXen3OMWx1pAJtuZyr9zsgXtHY/4V68AueBSaC8868J0UxWIWXM8+t/+BLFL\nN+TnTnd+E0tXAJXVSPTu79O85z1v5uDhvgFQZcZcCDVdYO7fDWIFMDu42MOgyoy5wEl9yr4vUdcU\nra0fO6F46aWX8OUvf5lZHv+krSOwnMB25ZVX4tlnn8W0adPavxHeg958xCnbsCyUFfNkg5VUZOAo\nJcoEuI48ff8PYTQdCR1vOdQeJc+ZB4O2VAGjShIxXUP8yhscaC1JJKAueRRk9y4nEwcQpp/xXIcg\na0JbByZDlm3xz4R4zp3ZwL76JjoX4u0rlZCwdpi1sy3Arp1+wMENt0P68iWuRogXOWczAOcyFMnn\n2YedODCRZxYLgEMIac3xxAcPQ/7OKczfkOl3QRg03K9bwkqkFq92VrB28KAzV420BHbtrWi1afKt\n60USCoy26pvwrukxANz89Kc/xUMPPdS24zlO1hFYTmD70pe+hDVr1mDKlCmIWcJWJVXmgsbjqsq0\nQMpnuA1jljNklkdisdBApL5xnVvq4DDpBksARBShntQHLboRPl4eXQevjMA65xg7MDooMc62uPDU\nwcMRMwzn3JmDioHB0KBeO0hod+Ub4xzFkWMcZgGhz8lQl60Fmo5QBdFsC+SzLwBJKM55CSCU3NMW\ng7NXC5azc2DAuhZmaF7z3ZAmif63PyF+5fUglkInkslwgkIIxKF19HuWjLRN+mmzAPiGZZMVTlmW\ntZotrFgUqVtify8q2XBKYLOXQJBkIEmTh2CJtBzjITa1ZBr4GICbHTt2oLa29p/CZMyyjsByApso\nijjrrLPwyiuv4D/OPrusXknQ9GSaL3V7+aTI+m6w7yIwXowgJYq31IFiCSZd3vEGXkyhpmvkNkIw\nTjUZ2gYBQWLKHEdrJIgSExT28ZSLWBPKLBUKqQqgNU8b00IM2s+f8jezy7TgdbKhuQ7vWTyBxNQ5\nEDp1hvbsYz6YsLJ8Lch7O/zBMrBa8JaU1Dvv5672bHPuu5f1d1oDMKQuVFaTRtWH2IEBa6XDCvB2\nEC0H+FAGGagDDklXhXn24gkaqDwDiW2xUqi0tmrd2/bUU0/h6quvbtcxHQ/rCCwnuF155ZVoaGjA\nl0edFllSikJ+CRyp23g5cyoeI6JIg4kQg2DqkJuPAKZ/Mj2YVWrrf9WmnoJPayPTDMhxaH/5Xy5a\nh4vCYZyzo2ve0gSSzbgosa99CyCmo/Xhs4gM2Ms2G285ynZoqQrfnIaXf8t2qvrGdZD7nlw+3Bjh\nPotQ28N11vbzsXKpo5Ap9B9I6VUkGYKmQdu4Ltxv8qwWvAGVx7vmcIOBB+5oDIE74i1H3fO3v2fP\nyLy1hZlw2EGUu+r0/IY742WtuPWN6yCdeoYfHOIdfp06x5VAbqe1BbFZjuVyObz33nsYNmzYMdne\nsbCOwHKCW+fOnZFMJrFr5w7URmTEUasZW+pW37gO8jkXQP6PryJ+xfUwsy1oXfAd5m+4WPwP3gVp\nzYM0HQk5SAChspWPc0orll8CIAAEASSbgdh/EPRXXvQhjmzBKeYwo4XCybN6EF/7Foq/fAby+G9C\n7NXfjxJjrQDLYDkQDAPmoQPMACoYhnN8TOdrOdX2UL4gSwf05LEXAYU8lNlLaGkv0+zMpDgKmV88\nN+xMg5P03mPwBFTt1/8V7kFMbaBlNfvalFmuJAzWafv3iWnshMNONqTWXGj1rUydA2ga5ExTpLKl\nLeIV79WPzWY9fwXIwX3QXnkREgSQIZTgsc2l5+NgP//5z3HJJZd84vuNso7A8hmwCRMm4MlfvIBZ\nHAdXqkFORBHm4OFUCjXgXBxtE2+JhxOohH4DKdwUAlMVUZ23AhAQcsQOqWAECaOX0kWQZDrhnmmm\ntXpRhPyVy4BsixNUTEmmP+QMvIHAUSF0xMWs62W8tQXy2IsQ0lVnNPFLsRwIhgE50wRSyAHdToLS\nsNRx7Ojdjw4O2vvwlHJ8kgVduoGo7ciSUxVhaPbE6dD/spGSbE6cDqQruQqZkfQqDI60oJQyALfE\nFeeIYwVXIDzBuq7dqegcx3Hb/Rbh83VMtF4wMWCtGIgohvSL7OtB9u9B4XtzAQDG65t9+ixtKT1H\nWXt6pIQQ/OY3v8EPf/jDdu3zeFlHYPkM2GmnnYYHvv995KZPR/LpcEmJR/3uzRYpLTqL/v2eUNYq\nETilGy/Tq2DqIHZdnfVyHthD2V8ZSo0kngAQPZXso3QJOEjh86eAVHeGFjEDA3jEwe6e6tuWcPIQ\nyCPHAKYBddEqqmPjaRyzrhkQXTMPzsv4jnvLq5Q8kDHDwpYsuANCG52WYBps2WPrnrY+uYKuYnhD\nnekqKq8rSiDxBMyEGi3HcM4FIdVLLyChFOqJNUfiDE5aYmWlzA4aMgHyDdeXTAxCFjX86rk2Xn2W\nNm2fY+XOkwXt5ZdfxmmnnYZEItHmfR5P6wgsnwETBAHTbroJD6za9kh2AAAgAElEQVRbj/mspmA5\npJS8XoGXb8n+TS7Ldn5T50CoqqGiRpyX03hrC+JXTXb7G6IIElegJ5Kcl6sBsV79mDrhXgepLloJ\nrVO1/7owkE1McTBLuKv4/JOQTj2DWcKzVzSsJj4vA+YNGHr7BbrqUsvYMyxCVQ1DsoBCYu0VZjnG\nLSvZ99QulXrVCz33i2SaaZYeTyBx3a0QO1Wz9drLkGMo1bT23nvpwsuorszhAxSuveG/IdWPc3pm\nZWX1ZbJIs4EdHKofz7UJ6rPwtl+ulQO7D5ppmlizZg3WrFnT5v0db+sILJ8R++IXv4jHH38c7zdn\n0bOnv6RUTrlG4E182w1Y7wqIuDQXwWawuuAHMHMZNp29PSeRroIoyS6/l+Uc5GwLQ+K3MQJ15HGQ\nrf6/M1cLUxto4GOtpg7uiy4JWTT8XloWez9cR8dzboQ48yK0DHmKqxeTqoAgSexj3PMBROMfzCxW\nL+RDQAtbcMuRt42J0F75rZt9WzQsTK2SANdX6+MP0Ml21nGVIccARDetvY5V//nTIO/tgDx2PIRO\nNZC/NZlywOVagOajLvzZ0sxhZvVl9r6YJd3eAyi3WroKxNBA8jm/ZPbUOY4+S8nSXrnWDjmFX/zi\nFxg7diwqKtqHUDue1hFYPkP2ne98Bw888ACWLVvm+7xUtijlMpQyfcpstK7ylKgm3QIkU1AXrnTq\n5vakuJyuYDsZXYfQuz+Enr2pTkY+DygKIEqQh33BHW6zAhRyWUgADCXJl/hV1OjyRDzhCm9ZxswA\nVzZS1BdrW4Lg9Di8/Q3ERAidu0G972GQfBbab38CecI0wDABXQPZ/b5bQgyWL3j9gh69fQJPRIiB\nqCkIJ/UBdMM9JsYxsrJYwTCQ/+sfXTp46zgwYDBD3nYm9J3bHK4uPVUBU5JdcsNcFkI8zPWFYiul\nSzkGzpRZ7vQ4Vvf6G0BCcWQKgiVFAFyWCF4yZevoUOEwJbwCs4clH1oAZfpdKHxvLsS60T4NGNT2\nhK6EIettHWj0WRulLorFIv7zP/8TTz/9dPv2d5ztMxtYMpkM1q5di7/+9a+IxWIYPXo0rrnmGiiK\nwv3NI488gg0bNvg+q6urwx133HG8D/eY2LBhw1AoFLBjxw4MHDjQ97dIiGM+SzmiLviGX/jK4m5S\nFq8KTZ2jshNngjhFm6iGAfGDdyG0FoAjhlOnR+8BzExRnfcw8jyJ31iMvQJa/4IrK1smDJiYJlfn\nQj7nAogjx4ThplNmQ/9/v6MZ8ox7QN59x6J7ucctmdjH7HH83GE4T1Cxr4VmwVxtvRPu+TKyWCmX\n8WuM2A5y/gqGvO39UOetgHTyEHrOAwbBDAxoyi1NPq4v+94SQ2PotbCdKa9XJhVyIO+9E6LfQb+B\n3P6SOu/hyFIochkfoamz767dkVzyKEzDAGQ5pKOj3L6A/Yy0FnzwZZ+wljXHciwYxL3WVqmLp59+\nGpdffvmnrrdi22c2sDz00ENoamrC3Llzoes6HnnkETz66KOYMWNG5O/q6upw0003gVgU4LIsfxKH\ne8zstttuw9KlS7Fy5cryf2RnS/mcvxQEcLMmLcmetPc5kP27/TQfE6dDqu0OGGZoNUEOsgEGQroC\nxf96HNB1N+il0hCqqiFXVEG2BL3k3v19Knrc1YIkg6QqfNrqpKoaUv04aK+8iPjFE5Cfd4vfia1a\n5jgxAYLrFEsM5JXjfOyVlS35jGKAHj5dCZJpcgkaWfeDV0bhqEeiNQ9AAHSdWWrhkViSfA7o3puu\n+iw6liADtGAY7JLVrMWAVeoMSTNbqw6eJDbv2XA0czzONaoJHlrFCgI3ORL6DQQOHwgDTTxsxsdy\nHqUtgSqTyeCll17CM88887H3e7zsMxlYPvroI2zduhWNjY3o378/AGDSpElobGzE1VdfjU6dOnF/\nK8vyp4YWoT3Wr18/1NTU4LXXXsMXvvCFsn5jOxLtlRfLHlYs2YzVWtmQ40UrQYrFsKPgveRqymG2\n9cmx3jbfgX8inoAccLZM5zhlDpWzfelnlDDSnrA+eghC35MR73MykG2O7ud4OcXKYCKOok+XchkI\n2WYa5AJ9FYce/r6H/EJmrPvBK6NwSogk04zCQwtoOSlV4Tser8iUuuRRoKWZMhOYBkBMkI/eR952\ntPEEEpNnIza0DqYkc1FwQv+BiFVUghRyELrUuhB2z/UlhSxfEpv3bIhUBdNGFALRTfBgAGYSfs5c\nBIEQIHMUJJeF8eF7oTLY8ZpVKTdQrVmzBtdddx3Ef8LMTLn2mQws77zzDlKplBNUAOCUU06BIAjY\nsWMHRo0axf3tm2++iRtuuAGpVArDhg3DlVdeiXS6nXXTf5LdcsstmDVrFp544omymE7tICH3PRnQ\nNKiLV1M8fwksfeSLwJkHQGtriHgQAA1qDL0OJDjzDwxQQfDYzMHDaVM8n6UN96YjQK4F0lcug9C7\nP8SThwAQqMPc/QFIPIFYdefofo5nuru9TMTMUuC9D7L3W1ldMovVk2ko0++C9v9eoo16QiB07gr9\n3XciS2qtT66A2vgYF42H7r1BMs3Qt74KsUs3CFU1CM32rF4GdfFqFKtqmE7dHr7kUrTY52kRW7Ik\nsbVXXgyX4G6cRftqFqLQsagmOEOnxmZbIMUCkKqgVDYB4kzvalFZ+ljkfT3eA5OHDh3Ca6+9hltv\nvfWYbvdY22cysBw9ehRVVX5nF4vFkE6ncfToUe7v6urqMHr0aNTW1mLfvn145plnsGTJEixcuPBT\nQUVdrtXW1uLf/u3fsGHDBpxzzjll/cYJEh/DfC+WmuSUGcKqkkgokOrHwvjAnx1qr7yIeP9BzJIb\nevdz5kB4L7CYzzkQYl9JbspsyP9+Hsy3t4ZKdaR7T+acjd3P8XKKGVteBWSZBi/TLNuZsBxw8edP\nhcETFjkhEcWSnG3x4aeBmEZoGNI4uA/KLXMhpCpAdB3ar5/zzeWQAgVPhLP8Rqc8p977IPLzbqEz\nLUynnQOqaphOnY+0m+tTI7WDsaEmXYScEIO24UVIY8bCtGV6c7TpDsMAYtZKxmsR5Jskn4U6bwWK\nzz/hSFdL9eOsnlcN5Jam8GyKFxUYkTS0dw6lrfbQQw/h5ptv/tT7oxMqsDzzzDP45S9/Gfmd73//\n++3e/he/+EXn371790afPn1w880348033/xU8fCUY1OmTMGNN96Is846CzHvcNcxslDpJNAYFUeO\nCZM6ehxlsIwGTYP+wDzogf2QSyY434215v2iTRFEgIJhQDA0xL96JUi2xc8gsGoZ1MWrmJxU6qKV\nMIbW0T6CdWykNe/r5/iyXDUVHsosZQwHbGzehPilk0quFnlZsdnSFAYSWOcDkfYJC96BQcA3l8Qt\n/xVb6TxJsRVCpxpO6Y8irVjT+Nzhy4pKOqtiGkCXbs5AaZgpugHm4OGUSUFJQjIM2t+JJ6D9YQP0\n3/zET0/EIt8881w/+ea0BsiXX+fIH5eChwtV1VAa10QmDe2ZQ2mrffjhh9i9ezdOP/30Y7K942kn\nVGC56KKLSmbg3bp1Q6dOndDU1OT73DRNZDKZyP5K0Gpra1FRUYG9e/dGBpaNGzdi06ZNvs+6deuG\na665BpWVlQ4QoFyTZfljiXcBQE1NDS688EL8/ve/xxVXXPGxthU0vZAPwVuVaQ3QNq53ywxWXyS5\n5FFAa0UsmYbcuSskRfVsqavzr/xHu0IT8vLY8RBMAqWYh1zbHWpFJTRNK/v48l74bVALhDc8WChA\n7dINidpuAIDMu+8ARw5ZXxCccxMunYj04PYlG/l8humgxWQSqkc4Si/koR06ADObQSyVRqyiCsW3\ntzjXXRw5BvFvTIRACAwekKC1APmkbhDjcZDpd6GwYhFlTBg3HkKqgrIuJ0tMm6cqLN17M7yquvom\noNiKwn0zwtf67a3c4UskFBQtVuVk46Oo6dUX+Y92uewK1vG3PtKI9P0/RExR0PrGZhT/8Hun3Cef\nfhaErj3Q+sgSpO//oXPt9IoxkO//IcxcBpATyN1xY2ibqeVrkezVt7z7UlXtuy8syx7cy7z+sUIe\nqig69zD8DpRvd9xxB+bNm/exfYNt7fEz9krpiSeewL59+3x/GzNmDOrr6wGcYIGloqKirGGgQYMG\nIZvN4r333nP6LG+88QYIISEYbpQdOnQILS0tqK6ujvxefX29c0GD1tzcXJYz9FpNTQ0OHz7cpt+w\n7LLLLsOECRNw9tlnIx6Pl/x+uTViuaUpBG8tWKUTr4SssXkTzEsmOBxg+Vwe8Kj5+fYdV5GYtZjC\nk1UVpOmIX+Rp2h3AqDE+NUCesY7PB0+1M3VWY7vpCFoP7UNuSB0AQPzofXclYDtNSYKZUNt1jwTD\ngKzrTJ2TQlxF3tqmXVppDWTvuhW8HRr6e28Ginz5AXL0CFr37YE5tA5k0HCoy9bCfHe7n1zz9oWc\nAckXINaNBjmwB62PP+AEM/XeB0FamgBdo5Bl79Cpd6UEgCQU5rbtoIJ4wrmWcgsbOKFnmiEUi9D/\n8PswFHxqA8ShddAzzf77oaYBNY34vo+Y2zRbmkP3T4irzLKr977wTE5wgBIAMjMnfezy2LZt21Ao\nFNCzZ89j4huA9vkZWZbRtWtXXHPNNZHfO/Y1kk+BnXTSSairq8Pq1avx97//Hdu2bcPatWsxZswY\n34rl1ltvxV/+8hcAQKFQwNNPP40dO3bgwIEDeOONN7B8+XL07NkTI0aM+GedyscyRVHwzW9+E6tX\nry75XadG3HA9CndNQWHO9RC3baX8TUGLmCj3WVuH57ItNJjkc25WbG279ZEl0A4dCB2z3NIEef9u\nyJkm91ij6GksR2dYOjROjd6SubWn/aV8BlIuwywvxa+4Hshl/fssYYJhQM62QHx7C/INNyB/3wwU\nHpwH6ezzoSx7PORsJCYXVSPN1kFp6L2lPFt+gHk+q5dByrbQ7euaW560t/vduxHrczLUxjVQ562A\nOvcB6H/7E5U5GDfeCSoATRby824BdA2FhxdCOvNcd0Lfc63J3o+Qn3UtCjMnOYqYyqJVUO97yNm2\nfS9CipVes5+hfA7yOReEy5crGyGPHc9/zhIJ9jYZ8x/eEq2yeBWUxjXcIOA8e0cOIt50GEI+A3Xe\nCogjx7jXf1oDis8/6SQCyox7IIgi5Gxz2c8NQKstS5Yswe233172b/7ZdkKtWNpiM2bMwOOPP44F\nCxY4A5KTJk3yfWfPnj3I5XIAaHP//fffx4YNG5DL5VBdXY0RI0bgiiuugCSduJfp4osvxo033ojt\n27dj8ODB3O+1qUbMmxHxlj3aOIns2z+nrGPmMjQTRXSzlD/x3gvqkjXUUWx/A0JVNaVD37/HNxAK\ngAYnAuZxkL0fUp32MjNQ+1iZMxwrG6E2PhY5ie7dtxO8A9fIkR9YuBJk74fs8+E02FFsBfnoHyCG\nTldEug557EWQz/oyhFQlu++QroRy8910loUxTAm7uVxsRevyO+lzVNuTOuSrpkC+ZEIIeBE1JChr\nWgRZZgU0znMWU1QmMo4Eg41l5UB+g0OtPgCI3b9JJCBoRchnfRny+d8AKeRCpKLlrlx+9KMf4Utf\n+hJ69epV8rufFjtxPWYJS6VSJYchn3vuOeff8Xgcd93F0Oc4wU0QBCxYsAC33XYbfvSjH/GDZBu4\nirgOoFPnSGhs2bxanPmQWNJ1HpHKjbzjS1chtv0NCJaDF4fWIX7ZJH/ZzNoX1BQNLDz6l8A+7eDL\nAjVI2RbkH1lCOdBY17j5CAqLZ/mcjtBnQHTwZlwj460tgCBwz0cwDP7MiyC4SLD773aHNGcu5M/C\n3H83xLrRYcc9eZaftNHzHEU57sjZqHicrxRaWc110PGaLtBrezJJT9trUi4DbeM6xC+9Jiye9ghN\nFMz3doRYoFkSFKUa+++//z7+53/+51NHi1/KPpOlsA7zW/fu3XHxxRdj1apV/C9FlSECxisZmJJM\n1QC79gyx8JYstXn2b8+H+Mo60+6A3Nlt9kcqN3KOT8znaLDxaJlrmzciMWV2aF8QYoBOKUzC5SWG\n02Sco/bjVYi9tQVkzwf0e3YwCF5jRYUy/S4oM2ljvfWRJSCiSI/Du++pDYCagrJ8LVDbk3lsZrEV\nicmz/J9Png0jSTV0is+u4ZTMXvCtiMS60TSoJFPh/UyeDe2VFwHQBj2qqqHMXgLltvlQbr4bQqca\n/wBkG0qiduAJPkOakoJpgQeC90pL8lfFkqLC6D0AOKkP0KUW6NkHRu8BJVeYzBKrbboG6dQzQA6w\nG/ZMSv0nV1D+M+/3rOeGZ6ZpYu7cuZg/f/5xQXYeT/vMrlg6zG+XXnppZEmsrVxFIb1762XkNf5L\nldq8++fNh0iK6jb/S5D2MTNjOxh5sn3950+D1I12RKqQTMM8tB+F2de6zep5Dzv9meKza7hOM3iO\n9gyHMoOWzbT1L4SVFm+cheJPn3DFqGzizWwLjCEjoDY+BjQfAclQNUhjZaNLURJPhCWln1wB5d4H\nfXBpPVVh6e1Yx6brtAR4YC+lpfcMAApduoX40sSRY6Au+AGQz4EYOqAkEb/0GuBrV4EUC9BeeM43\n7KjOe7jdJVGeEVGE0bUHpMoqCgywBm21ZDQkmyK91NCzwFs9lzOPIsRiKNjKnkzEWyIUcMShdRA6\n19JZIJtlukSwtUtgffv2jfzep9E6Asu/iJUqibWVVM/3YqbpxHLkcFiJUhtr/1HzIVGULUxtesAJ\nRsGJeVukCulKCBrtCfia1a9vhjrvYeipCkj142C8vpntNIPnaPVBtPUvUCLLP7wMpF2eMqG2hxtU\nrOthDw8KClX+hKEhb5fJLHMoSnJZFBjyyoKuQ+tcBVLlQklFz7EZW15FEYA0qj7MGtCpM+JX3uCT\n5zU2bwI55yvQXvltWK9m8mxKRwOUXRJtr9kqkaXml0oGhrbwiTHKVrbKJI95AUAIOi+Nqkf+3pst\ncbzxiH/1CsqQwHlWT9QSmG0dgeVfyLwlsenTp4f+Xi5XUfDFVGYuKq2mVwYteFtI/exAFJXRs6hP\nnGAEOBPpqOwE89ABFGZfy+2DkIP7ICoq9EDwM5SkE2CFhApx5Bg3UFgrI2PLq5AvuiJUk1dum++D\nZ9v7EtIVMA/tp01vXl/Gon1nXtMUw5GXojPxar+z6HhMgz1Fb1G6kEAz3izzOTrWFCiRvTc1TfnZ\nDI1Jl8/iE7P/7us1WtfSJQu9hwaJHr1BJBna/77kESqLAakUCkvmeJib53ODHnBil8BsOzGPusPa\nbZdeeim2bt2K7du3t3sbISisl5jRtkAN2Xbqwfr4xymREFEEAZBfPAva+l9BHnsRlOl3QZDjkFpz\nzO/bqyL58klAr36U/j+XgVBshTi0jt8HEQSnf2P3AHQ1TdkGrJ5K/s4bIZ15rgM51Tb8N83o4wla\nRgrW5JOcvlZFFVqX30nLJ7U9uL0vYprMfgnxqn5axrr+Np1JqCfG6rfFRC4qixQLzL5alLUJ3t4W\n4wWGXNbZH9nzIf95LaPX6L2WxpZXUXh4IYiSpKvllibIp30RxZ8/hcJ370HhofkgRw47Mt4huPQj\nSyDlM77dncglMNs6Viz/YsYribUpewy+vBwUl6CkfH0Xw+Z7OpYlkjxPJrkBwufrQtu3A4Ogppn6\n7frObczpcu2VF0Oa68HsWBxaByGhIP61q4ArrgeJx2HEFXrOmgbB0J3rJNaNBinkGaWUOSCG4ZxT\n8adPcIkuJZKB/rc/hfjV5KF1ocvkW+HlMkAiEYLcep+BIKcWSSiIpcMEkYgnIMQVX0mnnGfpuFGg\n8KDmCcXdXwQrNZWKju41hsq2HPJK6DqVzl611O2FlVgNneglMNs6Asu/oAVLYm0m0Au8vLxas13O\n8W5THzIC5BhxJ9nHwpZJbmQqLXrLVsWN60LIHWXGPdB3bqOljNa8w4oc/8Y10JUARNUKsGLdaMjj\nvwly5FCYLWDwcApb1opAqsJh6ZXHXoTCQwsgDq3zBAYRQs9eIIj5z8nWorHKLfbKQE+mIdWPC9Dq\nzwE0DXKmienQzV07A9P81uwPwGQ49nJqmcRk6sEXn10DqX4chH4D6QomSlUzcO18Fiw5tcN4IBTi\nmfuJYqUut9cYFEbjklda8GIhXQGSaYksB38WSmC2dQSWf1HzosSG9ezepuwx+PIab2+FdOHlUBsf\nAylY5QQh5iCrytlmey1KJtnrpJjB05NVOr8xTei//SnEL3yRyg8f3A+YBsjhA4hlmkG8UFVLU146\n9Qwgl0WIUv6RJVT90KJdQTyBxKzFFGFVbKXXzqtOCDrgaHSuhWSdU1AmmZimK2nscYKxQh5EkkCa\njwJ7PwRECWI84YPWRmqVEA7DsbdpDRFkCCXoJHs+8CHKjNc306wcJFJV0z3R8qV427KaDgYGKV2J\nQlylv7f25xNS61Tjk912N2T9V45FMT3Y51VZDVR3DktDeFZDn4USmG0dgeVf1OyS2He+8x38ePmS\nko7Za7ysThdFRyJW3r/7uGSkrGMJyiS7BJamk7kznao3q4RFr96zN9R7vgeoKZhNh0M09FJtd4pM\nAg1q8W9MRP7emyOb/r59Lr+TlqNEie1YJQmx7W8A/T7Hlkme1gDBMxBoZ86KJMF4fbMfsTVxOuTO\nXUCEWPQ0fwTLQPB+2c39wnfvCX/XNNx/l9gOe2UxB0ZgVdjW1XQwCMmduyKfy7OToXMugN6lO3ve\nqi3097wgGYuFWL2Fz9cxV0M7d+7Eyy+/jCeeeIK9jxPMTuz1Vod9LOvevTuuvfZaNCz/Hoj8/9s7\n8+goqrT/f6u3dHf2lZhACJCA+ALmHUBEkG0CjM4AiqPOb5QBUYyDAREMO7LvKiKLbCKgg4ijqIOg\nsg+IyKsDyMi+RANIMPvSe3X9/qju6q7uqu5O6M7G8zmHc+ibW9W3blXfp+6zeiSp9BPU5hnIBkAc\nVOasx+JxTkajlQ88qyXOMsnQhAmunaa35sA4fbRgFIbNKr3gOQMChfTqL8A4fTSMU54Hykt5g76j\nr3nzSjBu5+CUSpfe3JfR3+M7OVO1vOG9utIRxMlB89hwCWPvIi9jLwDYzSbJMgCwsbD+Yw1vGJe5\nJ9CF1yhAVravQiE/Dx7n4ZRKcG07QDd/DXSzVkA3ewXYgqt8ZgS350I6Z5q3wRuQdggw/vCtYP+R\nywMmDoisgM1TRSrxfe7HQKmQcEyZDCSleOUbkwoAraiowOTJk7F48eJGrwJzQjuWO5z+/fvjwrlz\n2FIeh+G//iRrsPSF5Fte3gLvN9Ln8/gAQ2cwYA0zvdpMRskgTPdFg7FZYZz2d2+V1IK10kbdxGRo\nJ8wFk5zqfZzHjgYWMx+Y53bdzoqSknr7FyYJEeru3+lMFyNpeO/zkCB8At1FMCwLVFVK9zUZoPrf\n+2E7sgfqYaN9Gqb9Ga19GfeFYmhAQFU1GZYFc+E0jB6Zo21H9kDdKpNXQxqrwWjCJEsZS+18nalW\ntBMXgFFpAK0WnNEAldkAqz5S0p09YBWpP7Vq3gKRKjhQxxSWZTFhwgRMmTIFd911l9/+jQUSLARG\n5+Zi3Nix+HbQM+jbOavGHluSaqalU6FdulHY9jMarUuoOPvUwObCsKxXDZiwvAVQxCc6vJx04DQa\ncBaLtErKbPKZvl07Ya70wuzuuqsJ48squ1235ePNroUUEFVrtJ09yVfGlAmo9DK8OxdnN+ETiB1C\nZTLwaWEmzOWrLu793FUeIEwnCEhnNL+cYdrX3zwXU2ctGAx5ilcbGqvBOoVJAFU1+WfGO3O0dvJi\ncFcuuOwQbtkIPEsZe2GzQtWlJ0xLvL2zmBZ6yec5EBWp5/fJPu+LNwglIpxz5s82tGjRIgwYMAC/\n+93vvK+nEUOChQDDMFi0ZAlGjhyJlLZ3o7XbjyMg5HT31ZX8Dy0iGupbNySDAQOxuTAsC3VVOTiG\ngXbsq6407bdueLl4KjLaSy/G+nDXrqaqAlx5qTj7L8PI6MkdC4Gbrtz9utnvv3F5bdntAMeBY20w\nzRsPAFAvfkf2TVYywPPsKX4np9VDaTb5NPY654a7egEmz4VYrYbq/r7gqspdKj9HXXm/qXgk7of7\nYupZC8a5+9Qu3QhUVwZWVVOuWqMuHKZFkyQWeulSxqLnRKGAaeObkseqq8qlK3P6yCKtzOomFEQD\nB5dLdQAebe6C2Bltr46IBKJiBXvLxx9/DJZl8fjjj8vPUyOFBAsBANDpdHj99dcxbtw4bNiwAVFR\nUTU4WN7Dx/nWJlm2NoDkhM4fqNFDVcHc1UJ6AZq82Nsl1s2V1BoRDTUHmOaOF43XenC3xHGTwDRP\nh3bBGuldnFsEtvs1acfOEP7P/XYTnM0qqfLjlEpYIqPB6COgMlZB/cQzUOvEZZ55d+RXwXgsSk5U\nhiqXUHGbB92cleAM1UIZXyahmSi1PMOyUJkM3kJJTj3ptpg6XaUlPb8CfSmRe2Zs0jtOJiZO/j44\n51MqY4DDqYD7tUC61IFc3EtqOlS9/yAuiOanLIPUrkYu2v57E4ddu3Zh3bp1gc1XI6NpWIqIoJCS\nkoJJkyZhwoQJYGtgWJeLqme1esGYapw+mi9s1bUnlFndAo68lzTebl4JRhcuvYhUVYBJaemzWJNk\nFPrAoVCkZ0I3723o5q6Gbs4qsAVXYc+/CFtcM8mocvfzKLO6QZs3H7opS8BExUA7803opiwBtDrY\njuyRNDY78TToClmYLbxrrOm1aTAuyAPHwOeCL5oHowGcoYqP/h/N5+8SDNWOgmO4lu9dH0bGUC2k\njwFk6+Uw1VUBO2ZIPzOTgfBISeM/Fx7hP7pf1qlA6VXqwHmNcs8uwMnOTUBZJBz3RSra/ufXZ2Ph\n/Pl44403oAxCDrWGCO1YCBGdO3dG//79sXjxYkydOjWgY+Tcj+X017r5b4NTqQOz47gtnM5AREan\nB2xWaGcsg/Vf28Q7IIUSUKv9ZrO1t+3gygAcHgX7L5e91GSLyY0AACAASURBVGrKVm1hO7gb6pZt\nJO1AwnUv3QjuygXx2+3wXFj/7wjYMyd51ZRHeeqAa9M4cVO1iAM9ZfKFRUZDEaaF5v/lCLschc0K\nVVkx74CgCQO02oBVOpYje1y2JLnIdZUKKLoF6473oOqZDSalpRBcKbVbk3pmWPh3IpBD0oX5by+C\nAwf28jm+DIAjHkh0P8Ij3bJEK8GF8UZ/ubnhIqL9B1E6hZyHEDaxdrzyw2Us2fAOoqODGCjcwCDB\nQnjxxBNPYPbs2fjkk08wdOjQgI7xmabeHYsZnNUCa0xCYINx/ECV92RBlT2IV2m4x2o8Ow4AXxck\n7G8vggvTgpXwQPLy4smZCMu3+wGbDZq/PCcTOf0q76Xlww7EKZUAa/d+u3UzAJs3r+SFmK/xBKKe\n0WihLi0SRbYru/RAWM5ECMGZTqeE998Ge+YktIs3CDsVxfkfxV5YL0wUJ810fI+sodppS9KHe9t+\nnI4QDkFqO7JXSFrpfm2SAtVjbmuSZdvzXnimrYFKDeuRPVAmNJOMB1IZqmByy2btnAM5L0KR6tZH\nEKWwq3F4DcJiBsdxmPbfX/BsZioy2v8PrNKHNglIsBCSTJs2DTk5OWjdujWysrxzTwVEDaKr5XD+\nQBmVGgBcQgXgF/B33uTrcwDgNGGwhXl7/0junNYugXbiQnCF1+ULNtlZXoXib7z+Iq8tZsBkBBPB\nG39rUptGWLhfmATrt/uhatUWtiN7RWlgbFfPQ79gLew3fpEuSRwRLe2FtWYJdDOXwyhXBsDj2txt\nSdolvMcfU10FrqzE5YkGuLzQHG/r7tmFpdx0FfGJ/A7BbecWaJZrKUFliYwWAnWj9DqgS0+Xo4Ew\n34t8ZjPmKkpl3aYDCaJ0CjmV2SAI4XXnfka72Ej8YfaS265P09AhwUJIolKp8MYbb+C5557DypUr\n0axZsxqfo6bFw6Rw/kDVRb+CKymS3wH5MhrLeSCp1L4LNimUYOITZeupAy77g6SrrzPYTRMGrqwE\nyqJC3vjrIwOvszaNvV1H3mW3qJBPnXJwN586JjLaOxp/eC44lpUvsexjDmCzQjdnJS8EtHrvwlly\nuyeVGpaIaKilasI4vdCc1+9QIak80sYo78ny9uyrQWyT9AI/WaSCU2l1ojxhojG6ZzP2nDdDNWz/\nd0QyR5u6sjygFEjO+jFM+ywceXgYrnC78ObiRWAdMTVNGRIshCzR0dFYuHAhxo0bh7Vr19bMUww1\nLx7m6zycPhIoK5VXEd26IZ9HSm7xCONtDO7Bjcp7sngXU30EoI8AGxktq8IBIOmxBrUaqu59Ybt8\nzi0+5XNBNSVnF2HCtMJHpdEgfssGwP74PXTz13jv2javhH7hOt9CXGYOuMpymOa/grC/TwYrkQ3a\n+XJgO7KHVwtyHJj4RNgtZmgqywAZbz8mLhGWj/gMvcouPcBotEB1hej7fXqXBVDtUXrntwjasTME\nFZwtsofPnbNkNmNHPJFoh7ZgDTilo3BaDRNo/njmDNZ/sB0bNmyATav1+ntThAQL4ZOMjAzk5eXh\nxRdfxJo1axAeHrgaC6hZ8S5f2PQRUOl03uqJnImS0fwAXAZurQ5heQtcmZYdWQA4Y7XgLgyAD84r\nLfZyMVW06yi4/4pUOLHx3gWjHK6+ln9ugqp7P6gmLYL18w+E72Cqq8A5BJDoOp55CVAwgoCUTUEj\nt6hZzD6FOC8gvDMTO2vde2aDFjkItGwDld0u3iXlvALLtwe9SiqzZ0/xarv/HAV78js+Vc79fWGc\nmuO9M/S1k/AV5e68x3JzodMLOw3zzRtgfeycPV9+hEBemfLTAGqk4j179izmz5+PNWvWQHuHCBWA\nBAsRAL/73e8wZswYjB49GmvWrIFOpwv42EAz0/rrxymV0N3dEcaEZq6a5zo9LB+s847mf+1dcFfO\ni1O3jxwH7eTFYBQKICoWNp0eSosrAJE9+R3U/QdDMkPxgrUiAeJU4XAy9TW4qkrX273ebbFxqMSY\n+ERY3dO56CPAmQwwTn5epNKRNKw7/3ksaopwl22CcXjkqYoLwYTp+HGq1bC35dVrMJvBVZWLbTEW\nM5iqCqgBURwNLI4KoWsWe9ioXuOdE77/xiVQHd5+rFYPVXoGVJ0fAKPRCmWOvdLeKJV+F2ifGZkl\nFnhllx7gyktd9XQcgsguUwvI67nT6n2XnwbA6vRuakoFrId2Q9Uj20vFe+nSJcycORNvv/02YmJi\nvJ75pgwJFiIg7rvvPlgsFuTm5mL16tUICwvze0ygmWID7afS6kQ1z6Wi+ZX3ZIGpljBUb3wT2rEz\nYHxrLp/2nVEI+m/hbdXXG7SECkc3Z6W0Sis8AsYlU7zVY1nd+KwBKhVUPbOFHYA2bz7MXiqhRXzK\nfdECNwmcWiMZAOrM4ivnAcfEJYCx2WBrng5VdSVMC17xVouVl8I0dzz/vYFUCHVPd2MRe/s5SxO7\nZ7l2L+XLRMeCi4rxb4PzoXayxTXzOl7z6DAYZ78kr17zlyfMhxByHqM4f1qs/hw9GfZ2HUXPan5+\nPqZMmYJVq1YhPj4edxokWIiA6dmzJ6xWK8aMGYOVK1dCo9H47B9olcBaVxOUeGNVZw8Wp6p34lwI\nLWZwvxZAyeYLgsu9YJPsG7R7u1PV4shQLFbN5cHy8WZp9ZgjLxkAqJ941q9A4+x26bfsu71Tr6u0\nOsBglPeAG/sqUF4CZVIyrBHRsnYFWMze8ycXt+KeiddjpyFkXNBoRMeyJ78TbE1WfSQYD/Udq9WL\ndhBCRmbnbtGtJILKWCVUJWUM1YBCwdejCdD+4fe585PaxnUMr0a0O/pfu3YNeXl5WL58OZKSkrzO\ncSdAkfdEjejbty8ee+wxvPTSS7BYLL47+zJy1qafB1IR0ExEpCvvlzvOhVATBjCMZIS5bER1uDgt\nP1deCtNbc8GV/CZkKNaOnwPtmOlgYuIkc6Jxt34VB3I6gjitiSm8Y4LUePXhQh9nwKn61g0++lsX\nAVtcM4ADVMWFMF7/hY92l3V9ZmE7cQyM1QJVcSEUaW2gXboRurmroB0zHbb/O+KdN82BU4Ulmpec\nV1yZmz12GgqbFerS34Dr+eDKyxDmtK24z6mjr3vWAZsuglfBuaW9txf/5rMkguL8abBaPey/3YTl\n481gomOl51LKZbw2z52fY65du4aXX34Zb7zxBlJSaphzrwlBOxaixgwcOBAMw+DFF1/EihUr5I2S\ngRo5axnvIuWWy7E2Pu+XxE7CeuhLPiLe8WYuVcRKzgDOSaTlt+79l2Ohc2Uo1s1aLuu6DEBS3ePP\nLVtOZYPwSFdwn6ONSWst/f0RUVB16Qnj1BfE50jP9Js3jT17CqrsQdBOXMjvsOISYfv5MtR9HoK6\n10D+2lqkywdiOu1bjtQscnY2f1myfZVEcKqmLDabz7T9AWUt8PXc+XhW8/PzkZeXh9dffx0tWrSQ\nP8cdAMNxXKAFOIla8Ntvv8FqrVmMbVxcHEpKSkI0ouBx8OBBbNmyBatWrZI06DsXRM8FU87G4q+f\n1LyoK8thmvycSFWi6toTthPHXAb0hGa8Abu02GWw1oTVqkyy+tYNmKa9IHwW0sxERAGGar488PV8\nmN95U3QtTKtMIfOv1MLKsCxUZgNfSMxsAvSRQkyJ5zUC4Mc/9lVxDIkmjE8vc/Wil5pL0aIVjPMm\neJ1Dt2g97L9c8Zp7e7uOUJoMkgGQou/2uFfyY50BxCX4jDdyn1v3kszMXS1gjYyBqrhQNPdOdHNX\nwTjjRfE9yR4EJjoWyuhYmDQ6Qei5P2fKLj2g6t4PoqwFEs+d532SelbPqyMwedo0LF++vNHsVGqz\nzqjVaiQmJvrtRzsWotb06dMHarUaOTk5WL16NSIixF4xgcax3Fa8i4dqwrn4aZ7KAWe18OdyeDn5\n2hEEWlNd6o3VK81M3gLoFq0HZzKIr8XhdCAHd/Vizdxq7ax3m6Pmimc6fk1quvQ5DNX8rs+ZN00X\nDlt4JOwqNew+AiCZqGhox88Bc1dzWCNdpZJ9paH3m8HAPX2P+07QGfiYnhmQDczdjqNLTYPRsXi6\nZxx2Ci1ERkO3cB04szGg507qWf3vL9cxY/r0WgcSN0XIxkLcFj169MCYMWPwwgsvoKKiwuvvUqVY\npQi0nxcSGW3ZMyfBqdTCuewqtc+ytJ7lbJXnTslm5/W0w6j7D/YuCbx0KjiGqdG1+CzB6ytrr2eb\no+aKJTIa1uQWQGoa1E88w8fGSJ0jLIz3cpqaA8vHW8DdvA5V4XVoKh0ZiuW+W6mC9d9fgVOppSP1\nPfozzVLAOGqayOGcW3W2xJyuXgQ4irWJ7TWTwdnt0M1eCWWXHm7tEpmzjdUioWV641WYFk6E/Zcr\nshmspXB/Vk/kF2DmnDl4++23Sai4oZw1a9as+h5EU8ZgMMDu7pYZADqdDkajMUQjCj6pqalo3bo1\nJk6ciO7du9c4Qj9QpOaFU6mhbpUJ9j/fAizrStl/V5rYa0mhAKdUQ8EBMFZDwQCcUs0v6AsnuhYx\nlgX7n2+h6fMH2DW87UhINV9eAgUD2JObQ9P3Iah6DwQTpoVtz+figbIsVL0Hwh7ue4fihGFZKMuL\nZc9ji4qTvEbowsF+d0j+uhUK2DVa2MMjobTboExJA/vf/7j6D88Fk5QK08KJwoJrXrcUtn07YTuw\nC+pWmbAnN4e6dSbY/xwTHWc9sAuax4bDFhkrmmfJ+zE8F9avdsDywTqoW2WCi08S3xv3exSfBKXd\nJj0X93YFk54BVfYgqHoNhLrvw7B+tQPWzSthO/w1NI/9Deqhw6Ea+AjYu9L42Ce3Z0Zpt0OZmAzz\nuqUu1WnHLlBm3sPPD8tCYayGkrWCU6qlx+jGwYMH8dZbb2HVqlWIi4sL6F43JGqzziiVyoCCpEkV\nRgSFrKwsLF26FBMmTMD48ePRrVu3Ovlef2o0kbFWoYTl402Azeaq6KdS+XRPlTOc2+6+F5w/F+UA\ncJ6fU6llzyN3jQCENlVElMiW4KXaAwNEx7rSwyuV4DgOsJoBi9lnehWktHRLeulKcsk9Okzy+wQX\nYKkElX7cyIX0PVJzwTBCVVI1BxjdbTkWM2xH9kLzl1HgDNVQAV47Fps+gr/nHvY4URGu4bmwnTjG\nB0nK2Fo4jsO6detw7tw5bNiw4Y6KqA8UUoURQSMtLQ0bN27Epk2b8I9//COo52ZYFsbrv0gWkpJT\no3mquYwzc6Hq8xBU9/fhXVZnjQXnzD/mjptg8Kmigg8X5QATbTrPb937ubdLr4xbrvMa3dvU8Ym8\nO3JpEZTnTnqp9mAxw7b3XxDyvHMc/9npgu0rOFSldqmOXpvuSrKpDxe5FqO0GNZ/rIHi/GlemDEM\nTK9NE6dHCdiNfLJ4Lobn8u7NMkk1neWSLdvWA6VFwLV8qEuLYK4oF/pwSiUQFeNSY0oU4TJvXgl1\nn4ck3dEBwGQy4ZVXXgHHcXjjjTdIqMhAOxYiqISHh2PVqlVYtmwZpk+fjpkzZ0KtVt/WOZ0CospP\nZL4nUu6rDBhRXXTngi7nnuov4WCgjgeyDgKO87tHpfOeUB5GcT/zY/zhW5hWzod27AxXVL5jrE6X\nXPbMSa8cWJzT7ditboj73xmNFpyxGrrZK2H5eBMfo+P0ntLqvV2Lh+fyCStbtrlNN/JO4uzOh76E\nqmd/2aSa6uxBQgZod6M/N3oymLtdyTWt+kiXa7ecMHW2e7ijFxYWYvz48Xj22WfRr18/v/flToYE\nCxF0FAoFJkyYgJ07d+K5557DsmXL/OqgfXlm1ToyX0ooeKQncS60uvlvu7zI3AWDxwLmHvmtrioP\nqH6Ir9QhjFtUu5BN1+EKHagDg8pQ5UqZ72PnISUcbGF6wKNuiCBgn8/zSPA5GeonnnWlpJeq8eIs\nQ+BMuZK3AIzZ5FC/qfiaOQHs5uwqNayxiXxGAWM1NP8vB5xCAVVxIa9u0+nFsT8cJxQWcx+PabU4\nuab7iwBjs0oLPn2ElwA8efIk5s+fj4ULFyIjIyOg+3InQ4KFCBl/+tOfkJ6ejpycHMydOxd33323\nZD+/ucJqmKZcQOqNWeLN3OlFZouMFZI3OoWbe/Ciy6NojvQ4ZVCZDIBKDW3uNEChhHXv58IuwvLx\nZokd06SAVWkMy4IxVLquRyb9ijNbgKdwcH+TF+VNc2b5FSX4FC/SAbkWV1d6B3YGiHtSTVHsiERO\nL0ajBfdrQUDPiXBelpUuZWwyICxvgXAPduzYgZ07d2L9+vV3XDLJ2kKChQgpHTp0wNtvv42XX34Z\nTz/9NAYOHOjVx++OpJYqFamIdi5MK/kWzWr1ssKN9Yi6F8VBKFVQmQ18ckwJGJYFd/WCayegcaWY\nh7GaX7idJX8dxnEkpdSo0JW74d8rg7BnevzVi/gknG4Gbveqh0LeNIkEn16LtFwRsIRmsGn1UFeV\nw+gZN+JnvqQIJKcXw7JQJ1hq9JxwSiWY9Ey3evcOx4QzJ6FbtAFmAIsXLIDVasXatWuhUtFyGSg0\nU0TISUhIwDvvvIMZM2bg3LlzGDt2LBiGcXXwsyOpbSVKKfuHZ0p4pwBRmk2wHtkjKvlrPbgL6pZt\neAO5Y7GVDN77+2QwEkWyAMei+LaUuuhVYWF2LyjlVIOJVIMRkbyA8ijf61xwVX98HLqZy8GV/AYw\nCtiuXuDT49us4MpLvdLjc78WwPT6DN87LpmU9O5F1bzUUY7dFhsdB8X50+CUyhrPlyQB7Fg5pRJs\ndJykOo/V6uXPXV3pHQAKoPy3Qoxd+Ar69++PJ554IrBxEgIkWIg6QaPRYNGiRdi8eTPGjBmDJUuW\nQK93/OD97EicAiLitXdhq6qoUWS+p/1DrqysbtE6yZK/cEvHw+j0UGcPdqnC4EjTr9bwpZPDI73H\nJVcWOSJSSG7pVLOp+w8GEx4JcByUBVdgWjrVtTC7R/a7ReQr78mCMqGZK1W8Y+G2xcRDaTR45QET\n3Hbdrl3KVuUpzN0Ldsmpo4RMyw6Bpx07w2u+YPEuKibMr5ydLcAdq8JkhPWbvWLX6IO7oW7dVsg8\n7IXEua9a7JieNxl5U6ehc+fO0scRPiHBQtQZDMNgxIgRyMzMxPDhwzFx4kR07do1oB0Jp1RCl5p2\n+znUZGu/s5Kup7oFa/mxsyzsxb9BER7hOw7CcwcgtyhGxcKuUvPJLZduBHflgrhy5fBcQYVkemuu\npDoJunCfC7fkvDrVYu7XLmOrUqS1hu7VZUCYDlCqvOJGZFPMO+bYuvdf0Az5a0B2D192Nps+IjAn\nAIdq0VOFpx46TNYW5z5HdrMJ/7hRhgNhcVi24i3c1by55DGEf0iwEHVOjx490KFDB8ybNw+7du3C\nxIkToQ8wV5jwVmuzglEowJlNvFpGq4fSaPCf70tuobeYJBdAzmwC4FBpLZ0K7cQFwvGB1GyXE5pW\nvSs+Bazdpb5xnsfpXWW3y6qT7Hd3gsot4M993DBUQ8UBSEnjbSpmE5iwAMruwrXIi4pZ/X0ylPdk\nScekeC7abio+7k9P+N1tMCwLdVU5LDKqSJsuIjAngFrY4py74VtjZmPanDnoPegP2PTc82Bu00X+\nToeyG4cYX9mNY2JioJBIG6FQKGqcBqaxYjAYUFpairi4OL8ljxmGAWcy8otZmA5cRSkf78cATEwc\nYDSAM5kcn+PFah8nHMcLjLJix7EMf6xKDa7ophA/yH8hwCQm855kNhu4okI+1bqW/24mJh5cabH3\nOBOa8RH97t/J2QE7BygYgFGIx+U4t9d5YuOFflxpEcDxw+MYBRSw82PjID3uhGb8OYX5iRcWXa9r\n95wnlpU+Z2wCuJIi6fmRmWNG45ovye909IVCwc+D+z2NctVW8XlvJL7X+V3Qh6PMZJFVm9rtdrz3\n3nvYt28f5syZg/T0dMl+TZFQZjcmwRJifAmWxpIen2g4sFDAzAJ65Z3x4nG7xMfHo7jYW/gDQEFB\nAWbMmIFevXphxIgRki95TRlKm08QBACg2srBYLNDr2P8dyYkuZN3KXXFnSWiCaKRU2y0Yfe5YnAM\n/XQDwiNNf0FBAUaOHAmWZbFp0yYSKiGCdiwE0Uiwg8HXF0twNL8cf+6YiEj69fqH41WGtEupW+i1\nhyAaCdU24PDVMpSZbKgwyxfMItxgFLh48SLtUuoYeuchiEZCqZFFpUOgHLxShqc6JQhv5IQ0t4qL\nsWLFCsyZMwdpaWn1PZw7BtqxEA2SDz/8EM2bN8f169freygNAg4K7L/s8uDZd6kUlVZy6PRHTEwM\n3nrrLRIqdQztWIiQsH37dowfP174HBYWhpSUFPTu3Rvjxo1DQkKCz+MZhhHnE7vDqbJxOHClTPhc\nbLCiymJHpKru5qh5AJHoDMPgo48+wv33318HI/JPWFgYKisr63sYdxwkWIiQwTAM8vLy0KJFC5jN\nZhw/fhxbtmzBgQMHsG/fPp/V9x5//HE88sgj0Gg0dTjihkuFmUWZ0SZqO5Jfhif+Jw51FYq2YsUK\n0eePPvoIhw8fxooVK0RjyMzMrJPxEA0XEixESOnbty86duwIAPjLX/6CmJgYrF+/Hl999RWGDBni\n1d9oNEKn04FhmKAKFed5GyWMAgeveAey7b1YiofaxiGijn7Fjz76qOjzDz/8gMOHD+ORRx4J6HiT\nyUSlfO8QyMZC1Ck9evQAx3EoKCjA9u3b0bx5cxw7dgxTpkzBvffeiy5dugCQt7Fs2rQJ/fr1Q+vW\nrdG5c2dMmzYNFRUVoj5//vOfkZ2djdOnT2Po0KHIyMjA4sWL6+waA8HKKVBpZQL6Z7Iz2H+p1Osc\nN6ssqDDba3Ceuvu5Hzx4EM2bN8fu3bsxf/58dO7cGW3btoXFYsGCBQvQpk0br2O2bNmC5s2bo6io\nSNT+9ddfY8iQIcjMzET79u0xcuRIXL58ua4uhagFtGMh6pT8/HwAQGxsrNA2depUxMfH4+WXX4bR\naAQgbWN5/fXXsWzZMvTu3Rt/+9vfcOXKFWzevBmnTp3CZ599BqVbPqiSkhIMGzYMgwcPxp///Ge/\nNp26RsVw4BgGbx4pwLnfDD77snYOJpu099fYzy9Ao/ItMKLClJjStyXuqqutjRtLly6FXq/H6NGj\nYTQaoVQqZW1nUvd869atmDhxIgYMGIBp06bBYDBg06ZNePTRR7Fnzx40a9asLi6DqCEkWJoYjN3u\nqmmh04PVRcAeaEGlEFBRUYGSkhLBxvLmm29Cr9cjOzsbhw4dAsDnLNq+fbtPY31JSQlWrVqFvn37\n4r333hPaW7dujRkzZuDjjz8WFWT67bffsHjxYvz1r38N3cXdBgw4RKk4THiwBXafL8H7J26iNpYS\nq52D1SIf05J1VwTGP9gC0RrwSRrrGI7j8Omnn9aq+mJFRQVmz56NZ599FrNnzxbahw4dit69e2PV\nqlWYM2dOMIdLBAkSLE0Ixm6H8vIZPr26ycinaM+ZCNyTBbuy7m81x3F48sknXeNjGLRo0QKrVq0S\n3jQZhsFf//pXvx5ghw8fhtVqxXPPPSdqf+qpp7B48WLs27dPJFg0Gk2jqPwXrrRjyN2x+F1qJGbv\nu+ploK8tCgbI6ZaKXunRfMLKevJMfvLJJ2td0nf//v0wGAwYMmSIKFmiRqNBx44dcfTo0WANkwgy\nJFiaECpDFUwr5vFCBQDMJpjfXgjt4o2wR8pU0AshDMNgwYIFaNWqFVQqFRISEpCRkeHVr0WLFn7P\nde3aNQD8DsUdtVqNtLQ0L1tMcnJyo6lRrlZwaBOjworBmVh59Dq+K6jwf5APkiLUmJndCsl6JVRM\n/QZQBnJv5bh69So4jsPgwYO9/sYwTINTbxIuGscvjwgMkwEweujrrVbAUAXUg2ABgKysLMErTI5Q\neAo1Ng8wjuMQpQJe7pGK765FY8XRa7DZa77N6NcmBiO7pCBKzdWZG7IvanJvWY+EkRzHgWEYrFmz\nBtHR3s8vuaI3XEiwNCW0Ov6fc8cCACo1oJevoNdYcAbnXb58WfQWbLVaUVBQgAcffLC+hhZUdEoO\nD7aMwN1JbTF7bz5uVJj9HwQgTMkgr3caOjYLh1Zhrw9zSsDExMTAYrHAYrGIhINzV+qkZcuWAIDE\nxETcd999dTpG4vYgd+MmhE0fyZdsdVTdg1qNsJw8sPoI3wc2Ah588EGo1Wq88847ovatW7eisrIS\n2dnZ9TSy4KMEh7v0CszMTg/4mMc7JaFrSgS0ioaTO0zObtayZUtwHIdjx44JbZWVldixY4eoX79+\n/aDT6bB8+XKv3QwAKpLXgKEdSxOCUyjAtu3I146vruJrwesj6sVwDyAgVUyg6pq4uDjk5uZi2bJl\neOqpp9C/f39cvnwZW7ZsQVZWFoYOHXq7w21QMAyDkzeqAu7/3S8V+GO7OOjrzwHQC7l7m52djaSk\nJLz00kvIyckBAHzwwQdITk7GrVu3hH6xsbGYO3cu8vLy8NBDD2Hw4MGIjY1FQUEB9u7diz59+mD6\n9Ol1ci1EzWiyguWTTz7BiRMnkJ+fD5VKhXfffTeg4z788EPs378f1dXVaNeuHUaNGoXk5OQQjzZ4\ncEolrBHRQET92FTcCSTXV03ygY0fPx7x8fHYtGkT5syZg5iYGAwbNgyTJk0SxbA0BSqtHL68IF1S\nV4qLxUZHyeIQDkoCX/dP7m8ajQYbN27E9OnTsXTpUjRr1gw5OTlQKBT48ccfRX2ffPJJpKamYvXq\n1Vi9ejWsViuSk5PRvXv3Jvcy0ZRosjXvP/roI4SHh6OoqAgHDhwISLB8+umn+Oyzz5Cbm4vExERs\n27YNBQUFWLZsWa09jKjmPVEbSszAM/88V6Nj8nql4cG08AZhtG8oJCQkeEXyEzyhrHnfZG0sjz/+\nOB5++OEapcvevXs3HnvsMXTu3BlpaWnIzc1FSUkJjh8/HsKREoQYhmFw8ldvNZiCAV7snorX/piB\nWJ33i87Oc0UwUv0vogHQZAVLTbl16xbKyspErrF6xSAb6wAAD4dJREFUvR6ZmZm4cOFCPY6MuNMw\n2IBd58VqsGYRGqwc0g79WkWhbawabw3OxP1pUaI+524ZEKT4SoK4LUiwOCgr42tdePrLR0dHC38j\niLrAxAIXi1wu47/PiMXrf8xA8wgFn2OM49PBjOuRigkPtoBawdsyOAAXigxUx4aodxqV8X7r1q34\n7LPPfPZZtmwZUlJS6mhEBBFcGIbBmVvVAACtSoG83mnokKSTjE3RKTj0TItAu0Q+5uV6hRk7zxUj\nK1mPMHplJOqRRiVYBg0ahD59+vjsU9tspzExMQCA8vJy4f/Oz+np6T6PPXLkCL755huvcYwYMQJR\nUVGyxlSFgn79hBgjC+w8V4w2cTpM69cSsWEMFD4SfSnAoZmOwZKH2+CDU4XYda4YRhsQRkHpAHhB\nHRcXV9/DaJCo1eoaz41zN7xp0yYUFhaK/tajRw/07NkTQCMTLJGRkYiMjAzJuZOSkhATE4PTp08L\nEb8GgwEXL17EwIEDfR7bs2dPYUI9qaio8OkVRhDumFjg3uRwDGqfgHClHYFmj4xQ2vG3rCTc3yIa\nNyotiE3QkHcY+Fga8ryU5na8wkaMGOGzX6MSLDWhqKgIVVVVKCoqgt1uF+qAJCcnC/mLxo0bh6ee\negpdu3YFADz88MP45JNPkJycjKSkJGzbtg3x8fHC3wkilDAMg4RwDYbeEw9NLSLowxQcOiSGwcYo\nYbGzUJOphagnmqxg2b59u1DvAwAmTZoEAJg5cybuueceAMCvv/4Kg8GVtHHIkCEwm81Yv349qqur\n0b59e0ydOrXRZMklGjccx4G1WqBR1H6nwYCDmrOBUTANOl8Y0bRpsgGSDQUKkCSI+oMCJOWhAEmC\nIAii0UA6nnrEbrdLGvAVCgXs9oaTpbahQPMiD82NNBTTUz+QYKlH5AIvSUUmDc2LPDQ30pDnZf1A\nqjCCIAgiqJBgIQiCIIIKCRaCIAgiqJBgIQiCIIIKCRaCIAgiqJBXWIipTdQ+wzBQq9UhGE3jhuZF\nHpobaWhe5KnN3AS6nlHkPUEQBBFUSBXWANm0aVN9D6FBQvMiD82NNDQv8oRybkiwNEA86xwQPDQv\n8tDcSEPzIk8o54YEC0EQBBFUSLAQBEEQQYUEC0EQBBFUSLA0QHr06FHfQ2iQ0LzIQ3MjDc2LPKGc\nG3I3JgiCIIIK7VgIgiCIoEKChSAIgggqJFgIgiCIoEKChSAIgggqlISyAfDJJ5/gxIkTyM/Ph0ql\nwrvvvhvQcR9++CH279+P6upqtGvXDqNGjUJycnKIR1t3VFVVYePGjfjhhx+gUCjQrVs3jBgxAlqt\nVvaY1atX49ChQ6K2rKwsTJkyJdTDDSlffvkl/vWvf6GsrAzp6el45plnkJGRIdv/p59+wpYtW3Dt\n2jUkJCTg0UcfRZ8+fepuwHVETeblzJkzmD17tlf7unXrEB0dHeqh1hlnz57F559/jitXrqCsrAx5\neXno0qWLz2OC/byQYGkAsCyL7t27IzMzEwcOHAjomE8//RRffvklcnNzkZiYiG3btmH+/PlYtmxZ\nrTIqN0TeeustlJeX49VXX4XNZsPq1auxbt06jB071udxWVlZePHFF+F0eGzs2W2PHj2K9957D88/\n/zwyMjLwxRdfYP78+Vi+fDmioqK8+t+6dQuLFi3CwIED8dJLL+HHH3/E2rVrERcXh06dOtXDFYSG\nms6Lk+XLl0On0wmfm5JQAQCz2Yz09HT069cPr732mt/+oXheSBXWAHj88cfx8MMPIy0tLeBjdu/e\njcceewydO3dGWloacnNzUVJSguPHj4dwpHXH9evXcerUKbzwwgto06YN2rVrh2eeeQZHjx5FWVmZ\nz2PVajWioqIQHR2N6Oho6PX6Ohp1aPjiiy+QnZ2N3r17IzU1FaNGjUJYWJjsS8jXX3+NZs2a4emn\nn0ZKSgr+8Ic/oFu3bvjiiy/qeOShpabz4sT92WhqQgXgX6yefPJJdO3aNaD+oXheSLA0Qm7duoWy\nsjJ07NhRaNPr9cjMzMSFCxfqcWTB48KFCwgPD0erVq2Etk6dOoFhGFy8eNHnsT/99BNGjRqFcePG\nYcOGDaiqqgr1cEOGzWbDlStXRPeaYRh07NhR9l5fvHhR1B/gF5um8mwAtZsXJxMnTkROTg7mzZuH\n8+fPh3qoDZ5QPC9NQ2dyh+F8Y/d824qOjvb7Nt9YKCsr87o+hUKBiIgIn9eYlZWFbt26ISkpCYWF\nhdi6dSsWLlyIefPmgWGYUA876FRWVsJut0ve6xs3bkgeIzV30dHRMBgMsFqtjV41CNRuXmJiYjBq\n1Ci0adMGVqsV+/btw6xZs7Bw4UKkp6fXwagbJqF4XkiwhIitW7fis88+89ln2bJlSElJqaMRNQwC\nnZfa8sADDwj/b9GiBdLS0jBmzBj89NNP6NChQ63PSzR+UlJSRL+3tm3borCwEDt37kRubm49jqzp\nQYIlRAwaNMivV0WzZs1qde6YmBgAQHl5ufB/5+eG/uYV6LzExMSgvLxc1G6321FVVSW6Zn8kJSUh\nMjISN2/ebJSCJTIyEgqFwmsuPO+9O1JzV15eDr1e3yR2K0Dt5kWKjIyMO14dFornhQRLiIiMjERk\nZGRIzp2UlISYmBicPn0aLVu2BAAYDAZcvHgRAwcODMl3BotA56Vt27aorq7G1atXBTvL6dOnwXEc\nMjMzA/6+4uJiVFZWIjY2ttZjrk9UKhVat26N06dPCy6jHMfhv//9Lx566CHJY9q2bYuTJ0+K2k6d\nOoW2bduGfLx1RW3mRYr8/PwaCaKmSCieF+WsWbNm3ea4iNukqKgIt27dwqVLl3D+/Hn87//+L8rK\nyqDVagXX4XHjxiE+Ph6pqakA+Lf3Tz/9FKmpqbDZbNi4cSNsNhtGjhwJhaLx+2RERUXh0qVL+Oab\nb5Ceno5bt25h/fr1yMrKQu/evYV+7vNiMpmwbds26HQ62O12XLlyBWvWrIFer8ewYcMa7bzodDps\n374d8fHxUKvV2LZtG37++We88MILCAsLw9atW3Ho0CHcd999AIDk5GTs2LED1dXVSEhIwNGjR7Fz\n506MHDmy1rvkhkhN52XXrl0oLy+HQqFAaWkpduzYgW+//RYjR45EUlJSPV9N8DCZTLh27RrKysqw\nd+9eZGRkQKPRwGazQa/X18nzQjuWBsD27dtFQX2TJk0CAMycORP33HMPAODXX3+FwWAQ+gwZMgRm\nsxnr169HdXU12rdvj6lTpzaZGBYAGDt2LN555x3MnTtXCJB85plnRH3c50WhUODnn3/GoUOHYDAY\nEBsbi3vvvRdPPvlko56XBx54AJWVldi+fbsQCDht2jQhVqOsrAzFxcVC/6SkJEyePBmbN2/G7t27\nER8fj7///e9NKoYFqPm82Gw2bNmyBaWlpdBoNGjZsiVmzJgh/MaaCleuXBEFgm7ZsgUA0Lt3b4we\nPbpOnhdKm08QBEEElcapGyAIgiAaLCRYCIIgiKBCgoUgCIIIKiRYCIIgiKBCgoUgCIIIKiRYCIIg\niKBCgoUgCIIIKiRYCIIgiKBCgoUgCIIIKiRYCIIgiKBCgoUg6ohz585h//79ftvqg/fff98rdbqv\ndoLwBQkWgqgj9uzZI6R499VWH3Tt2hV79uwJuJ0gfEGChSDqgNLSUqhUKiHzrlxbfdGuXTtcunQJ\ndrs9oHaC8AUJFoKoA/bu3Yvs7Gy/bfVJly5dcPz48YDbCUIOEiwEEWJYlsWVK1dElS+l2uqbBx98\nEIcPHw64nSDkIMFCECHm+PHjQrU+X23BZNOmTTU+JiwsDImJibh+/XpA7QQhBwkWgggx33zzDXr2\n7Om3LZi4VxutCQMGDMBXX30VcDtBSEGChSBCyLVr15CcnAy1Wu2zraGQkpKCkpISmEymgNoJQgoS\nLAQRQr7++msMGDDAb1tDolevXvj3v/8dcDtBeKKq7wEQRFPFaDSioqICSUlJPts8qa6uxnvvvYdj\nx47BaDSK/vb888/j97//fa3HxLIsduzYAYZhUFJSgjZt2qBfv36iPl26dMHixYu9hJ9cO0F4QoKF\nIELE6dOn0bFjR79t7hiNRsyaNQudOnXCnDlzkJ+fj7Vr12LevHmIjIxEQkLCbY1p2bJlyMrKQnZ2\nNmw2G0aNGoVOnTqJzqtQKJCYmIibN28iOTnZbztBeEKqMIIIER06dMCpU6f8trnz/vvvo02bNhg2\nbBjS0tLQq1cvpKWlobi4+LaFysGDB1FcXCzEzqhUKqhUKpw5c0bUz263o7Cw0Et4yLUThCckWAgi\nROj1ekRFRaGwsNBnm5OqqiocOHAAQ4cOFbXbbDawLHvb4/nyyy/Ro0cP4bPJZEJlZSU0Go2o3/ff\nfy+ZZkaunSA8IcFCECFEyk1XznX33LlziIuLE9lfTCYTrl+/jjZt2tzWOCoqKnD16lVkZWUJbWfO\nnAHDMGjbtq2o76FDh9C7d2+vc8i1E4QnZGMhiBCSlpaGwsJCWCwWYWcg1QbwO5PY2FjR8f/+979x\n7733itRg3333Hex2O/Lz85GWlobDhw9jwoQJPt2Xz5w5g/DwcDRv3lx07m7duiEuLk5ou3HjBuLj\n46HVakXHy7UThBS0YyGIENOzZ08cOXLEb9vdd9+NsrIyIeFjUVER9uzZg2effVboc/PmTbRu3Rrd\nu3fH999/j+7du6NXr15+Y2LOnj0LjuNgNpsB8LujS5cuYcSIEaJ+X3/9NQYOHOh1vFw7QUhBOxaC\nCDH33XcflixZInLrlWqLiYnBsGHDsG7dOsTGxqK8vByTJk0S7VachvOCggK0aNECCoUCDzzwgN8x\nnDlzBoMGDcI///lPMAyDiooKzJkzBzExMUIfk8mEoqIipKamio6VaycIOUiwEESIUSqVyMzMxPnz\n59GuXTvZNoAXOL5yiBUUFIBhGJw4cQLt27cHAJw8eVJkO/GkqqoKv/zyC8aNG+dTOBw+fBi9evUK\nuJ0g5CBVGEHUAb///e+9CmZJtfnj1KlTOHHiBPR6PcrKynDs2DG/7r9nz55FXFyc3x0HeYMRwYJ2\nLARRBziN8uXl5YiOjpZt88ef/vSnGn/39evXRW7GUpw9exbt2rWDQqEIqJ0gfEFPC0HUEQMGDMAP\nP/zgty0Y6PV64f+PPPIInn76aZ/9f/jhB8miY3LtBOELhuM4rr4HQRAEQTQdaMdCEARBBBUSLARB\nEERQIcFCEARBBBUSLARBEERQIcFCEARBBBUSLARBEERQIcFCEARBBBUSLARBEERQIcFCEARBBBUS\nLARBEERQIcFCEARBBBUSLARBEERQ+f/7OOs8bmEK9AAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "qi.tomography.plot_rebit_prior(prior, rebit_axes=[1, 3], true_state=true_state, true_size=500)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Brief side note**: Note that this projects the qubit down to a specified pair of axes. To get a better idea of what the GinibreDistribution \"looks like\" we can use the GinibreReditDistribution which does not project down from another axis." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZYAAAGDCAYAAAAI4za+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEAgalP8HIJtyKdXz9skAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "qi.tomography.plot_rebit_prior(\n", " qi.tomography.distributions.GinibreReditDistribution(basis),\n", " rebit_axes=[1, 3]\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the simplest case, we can consider two-outcome measurements represented\n", "by the pair $\\{E,I-E\\}$. The Born rule defines the likelihood function\n", "$$\n", " \\Pr(E|\\rho)=\\operatorname{Tr}(\\rho E).\n", "$$\n", "For multiple measurements, we simply iterate. For many trials of the same\n", "measurement, we can use a *derived model* as discussed below. The actual measurement performed ($E$) is specified as set of experiment parameters, which we will let QInfer automatically choose below." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [], "source": [ "model = qi.tomography.TomographyModel(basis)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The core method in QInfer is the SMCUpdater which performs the Bayesian updates. It is instantiated with a prior and a model. It internally holds a representation of the current distribution as a set of weighted particles, the number of which controls the approximation and must be specified when instantiating.\n", "\n", "Note that the complexity of computing the posterior is roughly linear in the number of particles." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "n_particles = 10000\n", "updater = qi.SMCUpdater(model, n_particles, prior)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For simulations, common randomized measurement choices are already\n", "implemented. For example, RandomPauliHeuristic chooses random\n", "Pauli measurements for qubit tomography." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "hueristic = qi.tomography.RandomPauliHeuristic(updater)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we simulate experiments and update our prior knowledge using QInfer." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "c:\\users\\cgranade\\dropbox\\software-projects\\python-qinfer\\src\\qinfer\\utils.py:268: ApproximationWarning: Numerical error in covariance estimation causing positive semidefinite violation.\n", " warnings.warn('Numerical error in covariance estimation causing positive semidefinite violation.', ApproximationWarning)\n" ] } ], "source": [ "n_measurements = 100\n", "\n", "for idx_meas in range(n_measurements):\n", " expparams = hueristic()\n", " datum = model.simulate_experiment(true_state, expparams)\n", " updater.update(datum, expparams)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we plot the posterior, its mean and a 95% credible ellipse." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAqUAAAGDCAYAAAASxWmEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "qi.tomography.plot_rebit_posterior(updater,\n", " true_state=true_state, rebit_axes=[1, 3],\n", " legend=False, region_est_method='cov'\n", ")\n", "plt.legend(ncol=1, numpoints=1, scatterpoints=1, bbox_to_anchor=(1.9, 0.5), loc='right')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Phase estimation\n", "\n", "Consider the following setup. The qubit begins in the state $|+\\rangle = |0\\rangle + |1\\rangle$ and is subject to the gate $U(t) = \\exp(- j \\omega t \\sigma_z /2)$, where $t$ is time and $\\omega$ is a parameter which controls how strongly the qubit is coupled to some external degrees of freedom. Thinking about the Bloch sphere, the state starts pointing along the positive $x$-axis and rotates in the $x$-$y$ plane. The angle of rotation, which we call the *phase*, is $\\theta = \\omega t$. That is, the state becomes\n", "$$\n", "U(t)|+\\rangle = \\cos(\\omega t /2 ) |+\\rangle - j \\sin(\\omega t /2) |-\\rangle.\n", "$$\n", "Finally, we measure in the basis $\\{|+\\rangle,|-\\rangle\\}$, for which the probability is\n", "$$\n", "\\Pr(+|\\omega,t) = \\cos^2(\\omega t/2).\n", "$$" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA2AAAAHQCAYAAADHxwn4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nlfYmZO4AAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "omega_max = 100\n", "true_omega = 23.3\n", "ts = np.linspace(1, 101,25) / (2 * omega_max)\n", "\n", "ps = np.cos(true_omega * ts / 2) ** 2\n", "\n", "n_counts = 10\n", "counts = np.random.binomial(n_counts, ps)\n", "\n", "plt.figure(figsize = (10,5))\n", "\n", "plt.plot(ts,ps, linewidth = 3, clip_on=False)\n", "\n", "plt.errorbar(ts,counts/n_counts,np.sqrt(ps*(1-ps)/n_counts),\n", " fmt='o',markersize=10, capsize=3, capthick = 3, elinewidth=3, clip_on=False)\n", "\n", "plt.ylim([0,1])\n", "plt.ylabel(\"Probability of '+'\")\n", "plt.xlabel(\"$t$\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The canonical method to estimate the frequency of a sampled signal is via the Fourier transform. This is implemented by the module numpy.fft. " ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The max of the spectrum is 25.46.\n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA28AAAHQCAYAAAA2zFJ1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIiIiCgD/H/MX6DY/Okt7AAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pow_spec = np.abs(np.fft.rfft(counts - np.mean(counts), n=1024)) ** 2\n", "\n", "omega = np.linspace(0, np.pi * omega_max / 2, pow_spec.size)\n", "\n", "plt.figure(figsize=(10, 5))\n", "\n", "plt.plot(omega, pow_spec, linewidth=3, clip_on=False)\n", "\n", "plt.ylabel(\"Power Spectrum\")\n", "plt.xlabel(r\"$\\omega$\")\n", "\n", "ylim = plt.ylim(ymin=0)\n", "plt.vlines(true_omega, *ylim)\n", "plt.ylim(*ylim);\n", "\n", "max_spec = np.argmax(pow_spec) * np.pi * omega_max / 1024\n", "print(\"The max of the spectrum is {:.2f}.\".format(max_spec))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The model for this problem, $\\Pr(+|\\omega,t) = \\cos^2(\\omega t/2)$, is implemented in QInfer through SimplePrecessionModel. Note that this model provides the likelihood function for a single trial. For the multiple trials above, we need to decorate the model with BinomialModel.\n", "\n", "We'll use a uniform prior to specify our initial knowledge. This is implemented by distributions.UniformDistribution and takes as input a range, in this case [0,omega_max]." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [], "source": [ "model = qi.BinomialModel(qi.SimplePrecessionModel())\n", "prior = qi.distributions.UniformDistribution([0, omega_max])\n", "updater = qi.SMCUpdater(model, 10000, prior)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since each data point is a number of counts at a specific evolution time, we update our distribution by iterating over the number of different evolution times chosen." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": true }, "outputs": [], "source": [ "for idx_exp in range(25):\n", " expparams = np.array([(ts[idx_exp], n_counts)], dtype=model.expparams_dtype)\n", " datum = n_counts - counts[idx_exp]\n", " updater.update(datum, expparams)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now the updater represents the posterior distribution. A convenient estimate of $\\omega$ is the mean of this distribution. For distributions of single parameters, plotting the full distribution is also useful. QInfer's plot_posterior_marginal performs a smoothed kernel estimate of the distribution from the current state of the particle filter." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The mean of the distribution is 23.07.\n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0sAAAHQCAYAAABwevHfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nFUsiIiIiIiJeqFgSERERERHx4v8BBhKMWOFpURkAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10, 5))\n", " \n", "updater.plot_posterior_marginal(smoothing=.025, other_plot_args={'linewidth': 3})\n", "\n", "ylim = plt.ylim(ymin=0)\n", "plt.vlines(true_omega, *ylim)\n", "\n", "print(\"The mean of the distribution is {:.2f}.\".format(updater.est_mean()[0]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another useful way to visualize the different in these estimates is to plot the predictive probability curve for all $t$." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA2AAAAHQCAYAAADHxwn4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10, 5))\n", "\n", "plt.plot(ts, ps, linewidth=3, label='True')\n", "\n", "plt.plot(ts,\n", " np.cos(\n", " updater.est_mean() * ts / 2\n", " ) ** 2,\n", " linewidth=3, label=\"Bayes\"\n", ")\n", "\n", "plt.plot(ts,\n", " np.cos(\n", " np.argmax(pow_spec) * np.pi * omega_max / 1024 * ts / 2\n", " ) ** 2,\n", " linewidth=3, label=\"Fourier\"\n", ")\n", "\n", "plt.ylim([0, 1])\n", "plt.ylabel(\"Probability of '+'\")\n", "plt.xlabel(\"$t$\")\n", "\n", "plt.legend(loc=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Randomized Benchmarking\n", "\n", "In recent years, randomized benchmarking (RB) has reached a critical role in\n", "evaluating candidate quantum information processing systems. By\n", "using random sequences of gates drawn from the Clifford group, RB provides\n", "a likelihood function that depends on the fidelity with which each Clifford\n", "group element is implemented, allowing for estimates of that fidelity to\n", "be drawn from experimental data.\n", "\n", "In particular, suppose that each gate is implemented with fidelity $F$, and\n", "consider a fixed initial state and measurement. Then, the survival\n", "probability over sequences of length $m$ is given by [Magesan, Gambetta and Emerson(2011)](https://arxiv.org/abs/1109.6887):\n", "$$\n", " \\Pr(+ | p, A, B; m) = A p^m + B,\n", "$$\n", "where $p = (d F - 1) / (d - 1)$, $d$ is the dimension of the system\n", "under consideration, and where $A$ and $B$ describe the state preparation\n", "and measurement (SPAM) errors. Learning the model $\\boldsymbol{x} = (p, A, B)$\n", "thus provides an estimate of the fidelity of interest $F$.\n", "\n", "The likelihood function for randomized benchmarking is extremely\n", "simple, and requires only scalar arithmetic to compute, making it especially\n", "useful for avoiding the computational overhead typically required to characterize\n", "large quantum systems with classical resources. \n", "\n", "QInfer supports RB experiments through the\n", "RandomizedBenchmarkingModel class. For common priors,\n", "QInfer also provides a simplified interface, simple_est_rb,\n", "that reports the mean and covariance over an RB model given experimental\n", "data. " ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA2IAAAHQCAYAAADDMtnFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "p, A, B = 0.95, 0.5, 0.5\n", "ms = np.linspace(1, 101, 10).astype(int)\n", "\n", "F = A * p ** ms + B\n", "\n", "n_counts = 100\n", "counts = np.random.binomial(n_counts, F)\n", "\n", "plt.figure(figsize=(10, 5))\n", "\n", "plt.plot(ms, F, linewidth=3, clip_on=False)\n", "plt.errorbar(ms, counts / n_counts, np.sqrt(F * (1 - F) / n_counts),\n", " fmt='o', markersize=10,\n", " capsize=3, capthick=3, elinewidth=3, clip_on=False)\n", "\n", "plt.ylabel(\"Probability of '+'\")\n", "plt.xlabel(\"$m$\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The standard method to estimate $p, A$ and $B$ from this data is least squares fitting. This can be achieved by SciPy's method optimize.least_squares." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Least squares solution for (p,A,B) is (0.9504,0.478,0.713).\n" ] } ], "source": [ "def func(x):\n", " p, A, B = x[0], x[1], x[2]\n", " return A * p ** ms + B ** 2 - counts / n_counts\n", "\n", "lstsq = sp.optimize.leastsq(func, np.array([.95, .25, .25]))\n", "\n", "print(\"Least squares solution for (p,A,B) is ({:.4f},{:.3f},{:.3f}).\".format(*lstsq[0]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For some common problems, such as this one, QInfer implements functions which automatically make some choices and perform the updating. For this problem, the function we want is simple_est_rb." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Least squares solution for (p,A,B) is (0.9470,0.489,0.495).\n" ] } ], "source": [ "data = np.column_stack([counts, ms, n_counts * np.ones_like(counts)])\n", "\n", "mean, cov, extra = qi.simple_est_rb(data, return_all=True, n_particles=12000, p_min=0.8)\n", "\n", "print(\"Least squares solution for (p,A,B) is ({:.4f},{:.3f},{:.3f}).\".format(*mean))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we plot the posterior. We cannot do so for the full distribution over $(p,A,B)$, but we can plot the marginal distributions. This is done with the keyword argument idx_param, which defaults to 0, $p$." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0cAAAHQCAYAAABqRhFRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAgieIIAAAAACRJ/w+YRr4j76iA9QAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10, 5))\n", "\n", "extra['updater'].plot_posterior_marginal(smoothing=.01, range_max=1, other_plot_args={'linewidth': 3})\n", "plt.xlim(xmax=1)\n", "plt.vlines(p, *plt.ylim())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Custom Models in QInfer\n", "\n", "Now we will demonstrate how to create a custom Model in QInfer. To this end we return to the coin flipping example." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# We create a model which is abstracted by the Model class, which already implements common methods \n", "# among models and templates what such a class needs to look like\n", "\n", "class CoinFlipsModel(qi.FiniteOutcomeModel):\n", " \n", " # This function is called when an instance of this class is instantiated.\n", " def __init__(self):\n", " # Make sure all the necessary functionality in the Model class is brought over.\n", " super(CoinFlipsModel, self).__init__()\n", " \n", " # The following are functions that are required for the functionality of QInfer.\n", " \n", " @property\n", " def n_modelparams(self):\n", " # The dimension of the parameter space.\n", " return 1 # In this case, it is just the bias p.\n", " \n", " @property\n", " def expparams_dtype(self):\n", " # many models will have complicated experiment design descriptions. Here, it is just the number of flips.\n", " return [('N', int)] # The number of flips is an integer.\n", " \n", " @property\n", " def is_n_outcomes_constant(self):\n", " # We tell QInfer that the number of outcomes\n", " # depends on which experiment we want to perform.\n", " return False\n", " \n", " def n_outcomes(self, expparams):\n", " # The number of outcomes are needed to numerically simulate experiments.\n", " return expparams + 1 # the number of flips + 1\n", " \n", " def are_models_valid(self, modelparams):\n", " # Make sure any boundaries in the parameter space are respected.\n", " # In this case, the modelparams array is a bias, which must be between 0 and 1.\n", " return np.logical_or(modelparams >= 0, modelparams <= 1)[:, 0]\n", " \n", " def likelihood(self, outcomes, modelparams, expparams):\n", " # Finally, we calculate the likelihood function\n", " # Again, call some necessary internal functions.\n", " super(CoinFlipsModel,self).likelihood(outcomes, modelparams, expparams)\n", " \n", " # The tensor storing the values of the likelihood has the following expected shape.\n", " like = np.zeros([outcomes.shape[0], modelparams.shape[0], 1])\n", " \n", " # scipy.stats.binom can vectorize over one of its arguments so we'll have to loop over the other\n", " for idx in range(outcomes.shape[0]):\n", " like[idx] = sp.stats.binom.pmf(outcomes[idx], expparams['N'], modelparams)\n", " \n", " return like" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that is a bit overkill for such a simple problem, but the functionality is there really for the more \"interesting\" models, such as those we encountered above. But we can see that calling model.likelihood gives the correct results." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAABOgAAAHfCAYAAADqeOdbAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "model = CoinFlipsModel() # This instantiates the model we just defined.\n", "\n", "# Recall that model.expparams_dtype was int and we defined N to be an integer above.\n", "expparams = np.array([(N,)], dtype=model.expparams_dtype)\n", "# In the model we asked for outcomes.shape[0], so we have to define it as an object with a shape!\n", "outcome = np.array([0])\n", "\n", "fig, axarr = plt.subplots(1, 3, figsize=(15, 5))\n", "# Note that modelparams are expected to have at least 2D shape;\n", "# indexing by None adds an axis to the (100,) array we defined above for p.\n", "p = np.linspace(0, 1, 100)\n", "axarr[0].plot(p, model.likelihood(outcome, p[:, None], expparams)[0, :, 0], linewidth=3) \n", "axarr[0].set_xlabel(\"$p$\")\n", "axarr[0].set_ylabel(\"$\\operatorname{Pr}(n|p)$\")\n", "axarr[0].set_title(\"$n=0$\")\n", "\n", "outcome = np.array([1])\n", "axarr[1].plot(p, model.likelihood(outcome, p[:, None], expparams)[0, :, 0], linewidth=3)\n", "axarr[1].set_xlabel(\"$p$\")\n", "axarr[1].set_title(\"$n=1$\")\n", "\n", "outcome = np.array([5])\n", "axarr[2].plot(p, model.likelihood(outcome, p[:, None], expparams)[0, :, 0], linewidth=3)\n", "axarr[2].set_xlabel(\"$p$\")\n", "axarr[2].set_title(\"$n=5$\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a side note, we could have also taken a hybrid approach. That is, we could create a model for single coin flip and then decorate that with BinomialModel." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Much of this will be the same as above\n", "\n", "class CoinFlipModel(qi.FiniteOutcomeModel):\n", " \n", " def __init__(self):\n", " super(CoinFlipModel, self).__init__()\n", " \n", " @property\n", " def n_modelparams(self):\n", " return 1\n", " \n", " @property\n", " def expparams_dtype(self):\n", " return []\n", " \n", " @property\n", " def is_n_outcomes_constant(self):\n", " return True\n", " \n", " def n_outcomes(self, expparams):\n", " return 2\n", " \n", " def are_models_valid(self, modelparams):\n", " return np.logical_or(modelparams >= 0, modelparams <= 1)[:, 0]\n", " \n", " def likelihood(self, outcomes, modelparams, expparams):\n", " super(CoinFlipModel,self).likelihood(outcomes, modelparams, expparams)\n", " \n", " pr0 = modelparams[:,np.newaxis]\n", " \n", " return qi.FiniteOutcomeModel.pr0_to_likelihood_array(outcomes, pr0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And, just to verify, let's make sure it gives the same answer." ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAABOgAAAHfCAYAAADqeOdbAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dec_model = qi.BinomialModel(CoinFlipModel())\n", "\n", "# Recall that model.expparams_dtype was int and we defined N to be an integer above.\n", "dec_expparams = np.array([(N,)], dtype=dec_model.expparams_dtype)\n", "\n", "# In the model we asked for outcomes.shape[0], so we have to define it as an object with a shape!\n", "outcome = np.array([N - 0])\n", "\n", "fig, axarr = plt.subplots(1, 3, figsize=(15, 5))\n", "# Note that modelparams are expected to have at least 2D shape;\n", "# indexing by None adds an axis to the (100,) array we defined above for p.\n", "p = np.linspace(0, 1, 100)\n", "axarr[0].plot(p, dec_model.likelihood(outcome, p[:, None], dec_expparams)[0, :, 0], linewidth=3) \n", "axarr[0].set_xlabel(\"$p$\")\n", "axarr[0].set_ylabel(\"$\\operatorname{Pr}(n|p)$\")\n", "axarr[0].set_title(\"$n=0$\")\n", "\n", "outcome = np.array([N-1])\n", "axarr[1].plot(p, dec_model.likelihood(outcome, p[:, None], dec_expparams)[0, :, 0], linewidth=3)\n", "axarr[1].set_xlabel(\"$p$\")\n", "axarr[1].set_title(\"$n=1$\")\n", "\n", "outcome = np.array([N-5])\n", "axarr[2].plot(p, dec_model.likelihood(outcome, p[:, None], dec_expparams)[0, :, 0], linewidth=3)\n", "axarr[2].set_xlabel(\"$p$\")\n", "axarr[2].set_title(\"$n=5$\")" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "As a final check, let's make sure this leads to an approximately correct posterior using QInfer. First, we need a distribution." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# This instantiates the built-in uniform prior over the interval [0, 1].\n", "prior = qi.UniformDistribution([0, 1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The last thing to do is define an SMCUpdater which implements the sequential Monte Carlo algorithm. An SMCUpdater takes a model and prior and then its update function takes data and experiment parameters to produce the posterior distribution. The number of particles used controls the approximation." ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# The number of particles we will use.\n", "n_particles = 10000\n", "\n", "# Instantiates an updater, takes the model and prior we defined above.\n", "updater = qi.SMCUpdater(model, n_particles, prior)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "OK, now we can plug in some data and see how well it does." ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA2QAAAHQCAYAAADOLKmCAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# In the model we asked for outcomes.shape[0], so we have to define it as an object with a shape!\n", "outcome = np.array([5])\n", "\n", "# Call the update function to change the state of the updater, now it stores the posterior.\n", "updater.update(outcome, expparams)\n", "\n", "plt.figure(figsize=(10, 5))\n", "\n", "plt.plot(p, posterior(p, 5, N), label = 'True Posterior', linewidth = 3)\n", "updater.plot_posterior_marginal(smoothing=0.005, other_plot_args={'label': 'QInfer approximation', 'linewidth':3})\n", "\n", "plt.xlabel(\"$p$\")\n", "plt.ylabel(\"$\\operatorname{Pr}(n|p)$\")\n", "\n", "plt.legend()" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [conda root]", "language": "python", "name": "conda-root-py" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }