{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Lecture 8: Random Variables and Their Distributions\n", "\n", "\n", "## Stat 110, Prof. Joe Blitzstein, Harvard University\n", "\n", "----" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Two Basic Types of Random Variables\n", "\n", "There are two basic types of random variables.\n", "\n", "* _Discrete random variables_ are random variables whose values can be enumerated, such as $a_1, a_2, \\dots , a_n$. Here, _discrete_ does not necessarily mean only integers. \n", "\n", "* _Continuous random variables_, on the other hand, can take on values in $\\mathbb{R}$.\n", "\n", "Note that there are other types that might mix the two definitions.\n", "\n", "\n", "### Cumulative distribution function\n", "\n", "Given $X \\le x$ is an event, and a function $F(x) = P(X \\le x)$.\n", "\n", "Then $F$ is known as the __cumulative distribution function__ (CDF) of $X$. In contrast with the probability mass function, the CDF is more general, and is applicable for both discrete and continuous random variables.\n", "\n", "![title](images/L0801.png)\n", "\n", "### Probability mass function\n", "\n", "The __probability mass function__ (PMF) is $P(X=a_j)$, for all $\\text{j}$. A pmf must satisfy the following conditions:\n", "\n", "\\begin{align}\n", " P_j &\\ge 0 \\\\\n", " \\sum_j P_j &= 1\n", "\\end{align}\n", "\n", "![title](images/L0802.png)\n", "\n", "In practice, using a PMF is easier than a CDF, but a PMF is only applicable in the case of __discrete random variables__ only.\n", "\n", "----" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Revisiting the Binomial Distribution $\\operatorname{Bin}(n,p)$\n", "\n", "$X \\sim \\operatorname{Bin}(n, p)$, where\n", "\n", "* $n$ is an integer greater than 0\n", "* $p$ is between 0.0 and 1.0\n", "\n", "Here are a few different ways to explain the Binomial distribution.\n", "\n", "### Explanation with a story\n", "\n", "$X$ is the number of successes in $n$ _independent_ $\\operatorname{Bern}(p)$ trials.\n", "\n", "### Explanation using sum of indicator random variables\n", "\n", "\\begin{align}\n", " &X = X_1 + X_2 + \\dots + X_j \n", " & &\\text{where } X_j =\n", " \\begin{cases}\n", " 1, &\\text{if } j^{\\text{th}} \\text{ trial succeeds} \\\\\n", " 0, &\\text{ otherwise }\n", " \\end{cases} \\\\\n", " & & &\\text{and } X_1, X_2, \\dots , X_j \\text{ are i.i.d } \\operatorname{Bern}(n,p)\n", "\\end{align}\n", "\n", "### Explanation using a probability mass function\n", "\n", "\\begin{align}\n", " P(X=k) = \\binom{n}{k} p^k q^{n-k} \\text{, where } q = 1 - p \\text{ and } k \\in \\{0,1,2, \\dots ,n\\}\n", "\\end{align}\n", "\n", "A probability mass function sums to 1. Note that\n", "\n", "\\begin{align}\n", " \\sum_{k=0}^n \\binom{n}{k} p^k q^{n-k} &= (p + q)^n & &\\text{by the Binomial Theorem} \\\\\n", " &= (p + 1 - p)^n \\\\\n", " &= 1^n \\\\\n", " &= 1\n", "\\end{align}\n", "so the explanation by PMF holds. By the way, it is this relation to the [Binomial Theorem](https://en.wikipedia.org/wiki/Binomial_theorem) that this distribution gets its name.\n", "\n", "----" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sum of Two Binomial Random Variables\n", "\n", "Recall that we left Lecture 7 with this parting thought:\n", " \n", "\\begin{align}\n", " & X \\sim \\operatorname{Bin}(n,p) \\text{, } Y \\sim \\operatorname{Bin}(m,p) \\rightarrow X+Y \\sim \\operatorname{Bin}(n+m, p)\n", "\\end{align}\n", "\n", "Let's see how this is true by using the three explanation approaches we used earlier.\n", "\n", "### Explanation with a story\n", "\n", "$X$ and $Y$ are functions, and since they both have the same sample space $S$ and the same domain. \n", "\n", "$X$ is the number of successes in $n \\operatorname{Bern}(p)$ trials.\n", "\n", "$Y$ is the number of successes in $m \\operatorname{Bern}(p)$ trials.\n", "\n", "$\\therefore X + Y$ is simply the sum of successes in $n+m \\operatorname{Bern}(p)$ trials.\n", "\n", "### Explanation using a sum of indicator random variables\n", "\n", "\\begin{align}\n", " &X = X_1 + X_2 + \\dots + X_n, ~~~~ Y = Y_1 + Y_2 + \\dots + Y_m \\\\\n", " &\\Rightarrow X+Y = \\sum_{i=1}^n X_j + \\sum_{j=1}^m Y_j \\text{, which is } n + m \\text{ i.i.d. } \\operatorname{Bern}(p) \\\\\n", " &\\Rightarrow \\operatorname{Bin}(n + m, p)\n", "\\end{align}\n", "\n", "### Explanation using a probability mass function\n", "\n", "We start with a PMF of the _convolution_ $X+Y=k$\n", "\n", "\\begin{align}\n", " P(X+Y=k) &= \\sum_{j=0}^k P(X+Y=k|X=j)P(X=j) & &\\text{wishful thinking, assume we know } x \\text{ and apply LOTP} \\\\\n", " &= \\sum_{j=0}^k P(Y=k-j|X=j) \\binom{n}{j} p^j q^{n-j} & &\\text{... but since events }Y=k-j \\text{ and } X=j \\text{ are independent}\\\\\n", " &= \\sum_{j=0}^k P(Y=k-j) \\binom{n}{j} p^j q^{n-j} & &P(Y=k-j|X=j) = P(Y=k-j) \\\\\n", " &= \\sum_{j=0}^k \\binom{m}{k-j} p^{k-j} q^{m-k+j}~~~ \\binom{n}{j} p^j q^{n-j} \\\\\n", " &= p^k q^{m+n-k} \\underbrace{\\sum_{j=0}^k \\binom{m}{k-j}\\binom{n}{j}}_{\\text{Vandermonde's Identity}} & &\\text{see Lecture 2, Story Proofs, Ex.3} \\\\\n", " &= \\binom{m+n}{k} p^k q^{m+n-k} ~~~~ \\blacksquare\n", "\\end{align}\n", "\n", "----" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Hypergeometric Distribution\n", "\n", "A common mistake in trying to use the Binomial distribution is forgetting that\n", "\n", "* the trials are independent\n", "* they have the same probability of success\n", "\n", "#### Example: How Many Aces in a 5-card Hand?\n", "\n", "A 5-card hand out of a standard 52-card deck of playing cards, what is the the distribution (PMF or CDF) of the number of aces.\n", "\n", "Let $X = (\\text{# of aces})$.\n", "\n", "Find $P(X=k)$ where $x \\in \\text{\\{0,1,2,3,4\\}}$. At this point, we can conclude that the distribution is __not__ Binomial, _as the trials are not independent_.\n", "\n", "The PMF is given by\n", "\\begin{align}\n", " P(X=k) &= \\frac{\\binom{4}{k}\\binom{48}{5-k}}{\\binom{52}{5}}\n", "\\end{align}\n", "\n", "\n", "#### Example: Sampling White/Black Marbles\n", "\n", "Suppose we have a total of $b$ black and $w$ white marbles. Pick a random sample of $n$ marbles. What is the distribution on the # white marbles?\n", "\n", "\\begin{align}\n", " P(X=k) &= \\frac{\\binom{w}{k}\\binom{b}{n-k}}{\\binom{w+b}{n}}\n", "\\end{align}\n", "\n", "The distribution in the examples above is called the __Hypergeometric distribution__. In the hypergeometric distribution, we sample _without replacement_, and so the trials cannot be independent.\n", "\n", "Note that when the total number of items in our sample is exceedingly large, it becomes highly unlikely that we would choose the same item _more than once_. Therefore, it doesn't matter if you are sampling with replacement or without, suggesting that in this case the hypergeometric behaves as the binomial.\n", "\n", "#### Is the Hypergeometric distribution a valid PMF?\n", "\n", "_Is the hypergeometric non-negative?_\n", "\n", "Yes, obviously.\n", "\n", "_Does the PMF sum to 1?_\n", "\n", "\\begin{align}\n", " P(X=k) &= \\sum_{k=0}^w \\frac{\\binom{w}{k}\\binom{b}{n-k}}{\\binom{w+b}{n}} \\\\\n", " &= \\frac{1}{\\binom{w+b}{n}} \\sum_{k=0}^w \\binom{w}{k}\\binom{b}{n-k} & &\\text{since }\\binom{w+b}{n} \\text{ is constant} \\\\\n", " &= \\frac{1}{\\binom{w+b}{n}} \\binom{w+b}{n} & &\\text{by Vandermonde's Identity } \\\\\n", " &= 1 ~~~~ \\blacksquare\n", "\\end{align}" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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GDRvIbDZTTk4ORUREkE6nIyKi/Px80ul01KxZM0pMTCSLxUKHDx8mV1dXeuONN4iozBY3\nMjKSFAoFvffee7R371568sknCQAX27GxsQSAHnnkEfLw8KCtW7eSt7c3AaDHHnuM4uPjqV+/fgSA\n2wWbTCZq0KAB1a1bl44fP04Wi4XOnj1LOp2Onn/+eV5+er2ezpw5QwBo5MiRVFRUxDspGRkZvAwi\nIyNp//79vFy2bNlCREQTJ04kAFRQUMDTHDt2LCkUCtq0aRMRldnNv/LKK5Lv7VbCwsKoadOm9P33\n39Mnn3xCTZs2JQA0ffp0SbyWLVuSu7s7ff/997xjQ0T02muvEQA6e/Ysubi40KBBgyTXdevWTdJR\n0Wg0/P+XXnpJEte2I1Qeu3btIgA0fvx4iouLox07dtCCBQuobt26pFQqKS4ujoiINm7cSABox44d\nFab38ccfEwDq168f77xVxCuvvMI7wRUdo0aNKjcNlrcjR47QvHnzSKVS0dixY+1EMhGR0WisdH3K\n4MGDq5SnqVOnVvp8AoHgn4cQ8QLBA0RUVBTJ5XKSyWSSUeDQ0FB6+umnqWvXrgSAfvjhByIiWrNm\nDQGgoUOH8jQee+wxUigUfAHgBx98QADo4MGDPA5buPnRRx8REdHUqVPJ09OTcnJyqKSkhObPn0++\nvr7k5eXFF6xt3bqVANAzzzzDRd2GDRuofv36VFJSQt98841EaDNatGhBzZo1IyLiHYOEhASyWCz0\n008/UcOGDUmhUPARwcOHDxMAmjx5Mk8jMTGRFAoFTZw4kYj+6lBoNBo6cOAAEZWJ3hYtWpDZbCYi\nos2bN0vE9Z49ewgAbdu2jaxWK23bto0iIiIkwpdhMpkcitm0tDQCQA0bNuQLQi9dukQ+Pj585HHk\nyJEkk8m48ExLSyO5XE6vvPJKpd+/LWzGgB1NmzalmJgYiaBlMzM9evTg3+mECRPIbDZTrVq1eLlH\nRkZSo0aNJOl37dqV3N3dadu2bZSdnc2fOyMjg5dhdXA0i+Hq6koDBgygQ4cO8XhLlizhQrk89u3b\nR05OTiSTySgkJIRKS0urnZ/b4f333ycA1K1bN9JqtZIZJEe4uLhIfnsCgUBQkygrM7cRCAT3D6Wl\npdBoNBgxYgRatWqFli1bolmzZnzB2e7du7Fnzx5uNz9gwABERERg9erVmD59OvLz83Hw4EEMHTqU\nLwBk26zb2rKGhoYCAG7cuAEA2LVrF7p27YqlS5dizpw5SE1NRe/evfHFF1/YLVibNGkStwvu27cv\nX1j33//+F/Xq1UPHjh15XCLClStX+ALGXbt2oWnTpjh79iyef/55nD17Fm3btsWePXvQqVMnAOD2\n78899xxPp3HjxggJCUFKSgoAQKvVAgCmT5+ODh06AABcXV0hk8m4nTWz701KSuL31ul0MBgMiIyM\nxPHjx9GsWTNs3rwZvXr1kjyjSqWCQqEo14Xg2LFj+XfQoEEDvmATKLP3Z3kBynz/W61WTJgwwWFa\n5VFQUIDnn38eEyZMgI+PD0JCQuzisLLq2LEjGjVqBB8fH+zZswf79+/HzZs38dJLLwEAwsLC8P33\n3yM7Oxs+Pj4AytZXuLu7o1u3bpLn9vPzq1Y+GQkJCVAoFLhw4QKcnJygUqng4+NjZx/v7OwMoGxR\npSPOnz+Pvn37IiwsDBMmTMDw4cOxdu1aDB06tML7nzp1yuEaiFtxd3dHy5Yty30GPz8/7N69G8OG\nDZPUwVuh/68NYc/jiGPHjlXJTSlbvGpLYWGhZL3Gg45Wq0X9+vXvdTYEggcKIeIFggeIvLw8PPLI\nI/jmm28cnmcClW2eI5fL8fHHH6N379749NNPefjUqVP5NRqNBgAkYoKIoFAoeFhaWhpOnjyJDRs2\nYODAgXj77bfRokULh3lQKh03Kzdu3LDzRJGUlISCggL+8k5LS8O5c+fw/PPPo1OnTti+fTuio6Ml\nCyyZEAsICLC7B+s8sAW3DRo04Od8fX0liwyDgoJ4Hti9MzIyMGDAALRt2xbr169Hnz59eJq34uzs\nXK6IL68MAHD/3YyzZ8/C3d2dd5yqitFohE6nQ5s2bcqNw0R8p06dIJfL0aVLF6xbt44vzB0wYAAA\noE2bNvj+++9x8OBB9O7dG0CZiC9vYakt6enpWLlypaTz5oiEhAQ0a9YMjzzySIXpse/V0YLn9PR0\n9OjRA+7u7tiyZQt0Oh1mzpyJmTNnYsiQIRXef/Lkyfj1118rfZ5HH30Uhw4dcnjuxIkT6N27N554\n4gmMHDkSERERmDRpksO4eXl5MJvNDuspY8SIETh37lyleerbt6/dAvFTp05V2nF5kGjTpg3++9//\n3utsCAQPFELECwQPEDk5OWjUqFG555m3EluvMT179kT79u2xYsUKKBQKREdHSwS4k5MTgDK3c4yD\nBw/CYrHweEFBQdBoNNi5c6dkh0X6vyeRf/3rX5IwRwQFBeHKlSsgIi7Kv/zySwDgG+fUrl0bGo0G\nO3bskIzYA2UeNdq0acPv/8cffyAwMBAAkJycjKSkJLz66qsAwEe+bTfk8ff3x65du/j9nZ2d4ePj\nw72q1K5dGzKZDBs3bkTv3r0lHYe9e/eifv36qFOnDg9zdnZGcXGxw2ctrwyAMoHPvAgBgJ+fH/R6\nPXJycvgoeFWwWCyViuwDBw7A2dkZrVu3BgB07doV69atw5YtWxAaGsrdXLKOQFxcXLVF/Nq1a/HG\nG2+gXr166N+/v8M4BQUFuHjxIkaMGFFpem3atIFcLsepU6fQr18/Hl5UVIRnnnkGOTk5iI+P5+L4\n7bffxogRI7BlyxY888wz5aa7bNmycr8vW1in9lbS09Px559/omXLlhgxYgSSk5MxZcoUBAcH886Q\nLadOnQJQ1ikoj61bt0pcMpaHI49UHTp0sNvNtjJsf3s1QUFBAdzc3OzSrOn7CASCcrhXdjwCgaD6\nODs7V2hje/nyZb6w1ZZff/2V2yHv3r1bcm7x4sUEgAYNGkTff/89zZs3j/z9/Umj0dD169eJiGjR\nokXcs0hCQgL9+eeftGfPHvrXv/5FAOjMmTPcJv5Wm3cGs3V+9913KSEhgaZOnco3IVq0aBERlXn7\nAEDR0dG0f/9++vPPP+nIkSN88e3KlSspNzeXNBoNNWzYkPbs2UO//vortWjRgtRqNc9vTEwMAaD4\n+Hh+/2nTphEAysrK4mFhYWEUERFBRERXrlwhuVxO7du3p927d9Off/5JCQkJNG3aNFIoFDRnzhzJ\n8+h0OoqOjpaEMZv4W8vflmeffZY0Gg3/fPXqVZLJZBQVFUXnzp2j4uJi+vnnn6l9+/a0cePGctNR\nqVT09ttvl3u+uLiYAFCLFi142MWLF3k9sL3WaDSSk5MTNWnShIe1adOGGjZsWG76jGPHjpFKpbKr\nV7bs37+fANCCBQsqTY+obN3GrZ53+vbtS0qlkq+NYJhMJqpbty61a9euSgtcb5dt27ZJ6pTVaqUR\nI0aQWq2m3377zS7+Rx99RGq1+rY2xbpTrF+/vkbT69Kli8My37dvn+R3JhAI7gxCxAsEDwgWi8Wh\n60dbMjMzCQB99tlnkvDCwkJydnamli1b2r10mYi3Pfz9/SUvfLPZTOPHj+fuEtnh7e1NixcvJiKq\nVMRbLBZ67bXXSKVSEQByc3Pj97ZdOPr1119zV5bsUKvV9Oabb/IFs8uXL+duLvH/BazLly/naTDR\nuG7dOh72xRdfSLzREJW5UfTy8uKfY2NjycPDQ3JvpVJJL774ot0OnR4eHvTss89Kwqoi4t98800K\nDg6WhH377beS5wFA9erVozNnzpSbjoeHB1947IiUlBQCQKNHj+ZhVquVmjZtSkql0s7FX+fOnQkA\n3+21VatW1Lhx43LTt6Uy7zTz5s0jAHyRcWUsXbqU5HI53bx5k4j+8uizbNkyh/HZoulff/21Sunf\nDp988gnJZDIqLCzkYSaTiZ566iny9vaW1Cur1UrNmjWTeDW612zdupUvIL5+/TpfkL5z504qKioi\nvV5Pv//+u911L774osQdKsNgMFCPHj1oy5YttHbtWsliZ4vFYuclSSAQ1DxCxAsEDxCvvvpqhSOe\nRCTxJsJgI9MrV660i8/OrV+/nrZt20Y7d+506DKPqMzX99q1a2nJkiW0Z88e7lqRiCgnJ4emTZsm\nETmOyMjIoCNHjlB+fj4dOnTIofgyGAy0ZcsWiomJoc2bN0vcMTKuXbtGn3/+OX3xxRf0559/Ss5Z\nrVZatmwZ9xBDVOYpR61WS7Z537JlC73++uuSa0tKSmjHjh0UExNDGzdutCtLxuLFiyW+64nKxMuM\nGTPoypUr5T6/xWKhkpISu/AbN27QvHnzaNq0abRu3TqHcWxJSkqSbHHv6D4zZ86kixcvSsIvXbpE\nhw8ftov/22+/0ahRo/h9x48fb+fT/XYxmUxUVFRUJVeURGXff0BAAH3yySdktVqpqKio0mctKiqy\n62jVJEaj0WEezGaz3b1ZvT5+/Pgdy091sFgs1L17d96B37BhA3377beUmJhIvr6+dOHCBVqwYAF3\ncWrLqFGjHIr4w4cPU+PGjemXX36hSZMm0VdffSU5/+GHH5bboRcIBDWDjOgO7wktEAjuKUSEFi1a\nIC0tDSkpKdwGnhETE4OxY8fi2LFjFS6SvBN88cUXePPNN5GamlrhAsCa4tZFpYL7l6VLl2Lq1Km4\ndu0a96D0oNC9e3f4+vpixYoV9zorAIDDhw8jJiYGS5cuBQDs378fhw8fRkpKCvz8/NC1a1fMmjUL\nmzZt4ouDX331VaSmpuL3339HWFgYnJycMG3aNN5GLFy4EGq1GiNHjsQff/yBmJgYfP311/yeR48e\nxTfffIMffvjh7j+wQPAPQSxsFQgeco4dO4Y//vgDb775pp2AB/7yZHOnF6IZjUYoFAruueXQoUOY\nPXs2Hn300bsi4AEIAf8AMXz4cNSvX79KCz/vJywWC9566y2EhYXd66xwtm7diujoaP7Zy8sL58+f\nh7u7Oxo2bIgVK1bYeWJiHrBGjx6NOXPmwNPTU5JmQkICxowZA6CskxAZGSk537p1axw9elQschUI\n7iBCxAsEDzm//PILAGDYsGEOzzOvNHf6RfvEE0/g1KlTCAkJgVwux4ULF6DRaDBv3rw7el/Bg4lC\noUDnzp3vdTaqzf2Y7wsXLkg893h5eWHVqlU4ffo0Ll26hF9++aXav8NLly5hyZIlSEhIwM6dO7F6\n9WrJeYVCAa1Wi9zcXHh7e9fIcwgEAilCxAsEDzmhoaEYM2ZMuSODkZGR6Nq1q8PNgmqSBQsWYM2a\nNUhPT4erqytGjBiB4cOHw9/f/47eVyD4p5ORkSExSQoICEBCQgIaNGiAgIAA7N+/v1zXmtOnT3do\nzrRkyRKoVCokJSVh9OjRDme53N3dkZ6eLkS8QHCHEDbxAoFAIBA8xDz55JNYsGAB3xfgbtGxY0cs\nXbpUsumaQCCoOcrf3k4gEAgEAsEDj06nQ35+/l2/b0FBgZhpEwjuIMKcRiAQCASCh5hWrVrh9OnT\naN++fZWv+eGHH2AwGBAfH4/mzZvjnXfeqdY9S0pKQEQPnGchgeBBQozECwQCgUDwENOrVy/s2LGj\nWtfExsYiODgYK1euxM8//1zte/7222+Iioqq9nUCgaDqCBEvEAgEAsFDTOPGjeHk5ASz2Vyl+ESE\n4uJi9O7dGzKZDM7OztW+Z1xcHMaPH1/t6wQCQdURIl4gEAgEgoecadOmYfv27VWKm5KSwr1Vpaen\nw8/Pr1r3MhgMCAgIwCOPPFLtfAoEgqojbOIFAoFAIHjICQsLg16vr1LcK1eucF/3SUlJ1fZ7f+7c\nObz88svVzKFAIKguwsWkQCC465hMJrzzzjto3bo1hg4dKjmn1+uhVqsd7i5ry4ULF3D+/HnUqlUL\nbdq0qfHNqrZv345ffvkF8+fPfyh2nMzMzMTp06f/tp1yWloajh8/Dq1WiyeeeKJKu+AeOXIEJpMJ\nTzzxRIXx9u7diy+//BJr1qwp12/57TBz5ky4uLhgwoQJNZbmnYKIsHTpUvTr1w9eXl4Vxn3jjTdQ\nr149YbYiEPxDEeY0AoHgrkJEGDlyJObOnYuSkhIevmfPHrRv3x7u7u7QaDRo0aIFNmzYYHd9eno6\nhg8fjsaNG6Nv376IjIxEVFQUEhMTazSfu3btwldffYXMzMwK4+3duxfu7u4OTRWsVmuN5ul2OXjw\nIMLCwtC/f38eZjAYEBISAg/uoe0sAAAgAElEQVQPD/j6+qJWrVoICQlB48aN0bx5c4SHhyMyMhKX\nL18GABiNRsyYMQP169dH79690bVrVzRr1qxKJhovvvgiFi5cWGm8uLg4/Pzzz5WWeXVZtWoVVqxY\nUaNp3imOHTuGMWPG4NSpU5XGXbVqFTZv3lyj99+/fz+OHj3Kv3eBQHD/IkS8QCC4q6xcuRI//vgj\npk2bhlGjRgEAEhMT8eSTT+Ly5cuYNGkSpkyZgsLCQvTr1w+HDx/m1xqNRvTo0QPLly/HuHHjsG3b\nNsyaNQsnTpzA008/XaO+sIOCggAAeXl5FcZLS0uDXq/HjRs3JOFLlixB7dq1YTAYaixPt8Py5cvR\nuXNnpKenw93dnYer1WoMHjwYvXr1QufOndG2bVs0adIEwcHBKC4uxunTp5GVlYWAgAAAwMSJEzF9\n+nR06NABP//8M5YuXQoiQp8+fZCQkFBhHnJzc6vkapB1emp65sPV1RUFBQU1muadIicnB0BZnivD\narVCLq/Z13jHjh2xfv16NGzYEKtWrarRtAUCQQ1DAoFAcJcoLi4mnU5HrVu3ptLSUh5eVFRECxYs\noOzsbB6Wl5dHXl5eNGbMGB729ddfEwD69ttvJelu3ryZANDnn39eY3mdNWsWAaCkpKRK41osFruw\nDz/8kADQiRMnaixPt0NERAS1adOGmjdvTjqdrtL4+fn5FBISQq6urnTmzBkiIkpISCAA9Nxzz5HV\nauVxb968SU5OTtSnT58K0wwKCqJXXnml0nu/9dZbBIDS0tIqjVsdOnToQI0aNarRNO8U27ZtIwCU\nkJBQaVwfHx/q3bt3jefBZDJRREQEBQQEUElJSY2nLxAIagYxEi8QCO4amzZtQkZGBt544w0olX+t\nq3d2dsZrr70Gb29vHubi4gJnZ2cYjUYe9tNPPyE4OBgvvfSSJN3u3bujVq1aFZp2GI1GifkOAJSW\nlko+FxcX89Fgdl8XFxcAZWZAt8Zn2I6GJiUl4ffff0dxcTH/vH//fqSkpNhdl5OTg+TkZMkzVoXU\n1NQqxz106BCOHDkCHx+fKo1wv/baa7h69SoWLlyIZs2aAQDWrVsHAJgxY4YkjcDAQPTq1Qu7d+8u\nt2yAsrJTKBQAgJs3b+L8+fOwWCx28VgajuzsDQYDkpOTy72PyWRCXFwcjh07ZudK0WKx2K2xSEhI\nwBtvvFFuekSEiRMnIikpSZJvRm5uLq5cuQIqZ1mZxWJBSkqK3ewQEcFkMvHP2dnZSEhI4HWApadQ\nKGA2m5GYmIi0tDSH9ygtLXVYVhaLBcnJyUhPTy83f0VFRfj5558xfPhwBAQEYPXq1fycSqXClClT\nkJaWhi1btji8XiAQ3Afcww6EQCD4h/Hcc8+RRqMhg8FQbpzk5GRavnw5de7cmQDQ3r17iYjIYDCQ\nSqWicePGObyua9eupNVqy023X79+1L59e/5506ZN5OzsTBcuXCAiIqvVSrVr16bJkycTEdH06dMJ\nAKWmptLrr79Orq6upFAoaMyYMZKR9++++45CQkLIZDIREVHdunUJgN0RFBTEr7l58yYNGzaMZDIZ\nASCNRkMvvfQSmc3myoqQTp48WeWRWlvCw8MpNDS0wjhHjx4lANSzZ09JeGRkJIWFhTm85t///jcB\noJMnT5abbmBgIEVHR1PHjh15eTRs2JA2btwoiTdhwgQCQAUFBTzsxo0bNHr0aNJoNASAPDw86IMP\nPpDMCFy6dIlatWrF09bpdLRp0yZ+vnXr1tSqVSv++eTJk+Tl5UVubm6Uk5PjMM+snL/99ltavHgx\nOTk5EQCaNWsWvfjiiySXywkAPf/885K8WCwWmj9/PtWrV48AkEwmox49etD169eJiGjVqlVUu3Zt\nunjxIj333HOkUqkIAD377LNERLR161YCQBMmTCB/f3+eRr9+/ejmzZuSPGq1Who0aJAkbPPmzdSo\nUSNeFiEhIbR161ZJ/t58801ycXHhaQOgsWPHStLR6/Xk5OREI0aMcFg+AoHg3iNEvEAguGsEBgbS\nY489Vu752bNnc/GhUCho4cKF/Nzly5cJAH366acOrx0yZAgBcGjaQkTUq1cvUqlU/HzPnj0JAH35\n5ZdERHTu3DkCQDNnziQiog8++IAAUKdOnQgAPf744xQREUEA6PDhwzzd8ePHEwDeMdm3bx999tln\n1KNHDwJAL730En3zzTe0bds2IiIyGo0UHh5OLi4uNGPGDFq6dCmNHDmSZDIZrVq1qtIy3L59+22J\n+KCgIHriiScqjBMdHU1yuZwSExMl4f7+/nbCnrFgwQICQAcOHCg33cDAQC4oP/30U5o7dy41adKE\n5HK55LpXX32VAFBhYSERlXV2goODeedt1apVXKxnZGQQUVnnrmHDhuTl5UU//vgjrVmzhjp06EC9\nevXi6YaHh1O7du2IiOjUqVPk6+tLarWafv3113Lz/NtvvxEAGjp0KAGgzp07U0BAAK+fAwYM4Hk5\ncuQIEZV1BEePHk0A6LHHHqP//Oc/NHHiRAJAs2fPJiKizz//nACQm5sb1a5dmz744AN69NFHqXbt\n2kT0l4gHQL1796aFCxfSG2+8QSqVilq0aME7i0REarWai38iot27d5NcLqd27dpRTEwMzZs3j5o3\nb04+Pj68g/jdd98RAGrSpAktWbKE0tPTqVWrVg7FemRkJAUHB5dbRgKB4N4iRLxAILgrGI1GAkCj\nR48uN87ly5fpvffeo/bt23PRx2zSk5KSCADNmDHD4bV9+/YltVpdbtpMTKWlpZFerye1Wk0AaPjw\n4UREtGjRIgJAR48eJSKi999/n4upJUuWEBHR77//TgBo2bJlPN3hw4eTXC6XjMYSEa1YsYIA2AnF\n2NhYAsBHR7Ozs+m1114jALRu3bpy87906VJ6++236V//+hcBoH79+tGoUaPoo48+kgg7R1itVlKr\n1TRw4MBy47BncxQnICCAnn76aYfXMVH6+++/l5t2UFAQRUVFSWZgcnNzyc/PT3K/cePGEQD+PC++\n+CIBkIyq9+7dW2Lbz+5vW84Wi0Uyq9GsWTNq3749xcXFkaenJ2k0Gtq+fXu5+SUiOnPmjESwl5aW\nUvfu3Umj0dCePXuIiGjXrl0EgJYuXUpERAcOHODxWWdx3bp1BIB34j755BMu8vV6PRERjRo1iurX\nr09Ef9nEszrH+OGHHwgA7dixg4cplUp64YUX+Gdm+8/s2OPj46l58+bk7+/P89O1a1dydXXlMwNE\nZWtSHNWhESNGkFwul6xfEQgE9w/CJl4gENwVMjIyAEBi934rjzzyCD766CPEx8dj6dKluHr1KiZP\nngwA8PX1BQBkZWU5vDYzMxO1a9cuN+3GjRsDAK5fv44dO3bAaDSiffv2OHPmDADgwIED8PDwQMuW\nLQH8ZZv83HPPYfTo0QAAnU4HoMwempGfnw8PDw87e3Pm5/xWO/ytW7dy943vv/8+6tevj2+//RbT\npk1Dv379ys3/5s2bsXDhQuzduxcAcPToUcTHxyM2NhaFhYXlXgeU2fcbjcYKd95kLiCnTp1qd87P\nz6/ccmfhzJuPI5ycnBAeHg6tVsvDPD09MXDgQGzbto2XtdFohEwmg1KpRFFREX788UdER0fjmWee\n4dcVFxdLvOysXLkSjz/+OLp06cLD5HI5t8EHyry4nD17Fk899RTy8vLQp08fPP300+Xml+UPACIj\nI7FixQoolUq4ubnBx8eH+9qPjIwEULY5EgB8//33AIAFCxbwdRJsbYRtngFg8eLF3APNe++9x9cd\nMBv3Rx99VBJ/2LBh0Gg02LZtG38ms9nM61l2djYOHTqEyZMn4/jx4+jZsyc6dOgAvV6PjRs38vy0\nadMGhYWFqFevHlq3bo0vv/wSROTQtt7b2xtWq7Xc714gENxbhIgXCAR3BSYiHC1ovBWZTIYRI0Yg\nIiICBw4cAFAmgurXr89Fty1GoxEJCQlo165duWk2atQIAHD16lWsW7cOjz32GAYPHozExERYrVb8\n9ttvePLJJ/mCWyYsp02bxtNgCxJtd74sKSlxuDGRs7MzP2/LmTNnkJeXh7p16+Kzzz7DoEGDcPHi\nRXzyyScVLjxdv349cnNzsXbtWv75/PnzSExMrHRTIJYHWxFtS35+PmJjY9GxY0e0bdvW7nyLFi1w\n8eJFhwtwDx8+jLp168Lf37/c+5e3cZeXlxcKCwv5YuLi4mJoNBrIZDLcuHEDBoPBTsy6ubnx7ygn\nJwd//PGHROQ7oqSkBAUFBWjatCmioqKwZs0arF+/vsJr2Hfdu3dv/v16eXlJFqq6u7vD3d2di/jE\nxETUrVsXgYGBPA4T6rYLuQGgTp06/P+QkBDeeWRldWtdUCgUcHd3564yWeeA5e38+fOwWq2YN28e\nHn/8cSQmJmLhwoW4cOGCpAw//vhjxMbGYsiQIUhNTcXkyZPx1FNPOdzTgC0Qrmk3lgKBoGYQv0yB\nQHBX8PHxgVwul4xiM06ePIm4uDhJmEwmg7e3t0T8tGvXDvv37+ej+oytW7eiuLiYj4w6onnz5gDK\nRPTmzZsxevRohIaGoqioCHFxcbh27Rp69uzJ47POhu3MAfN1brsZkVwudyiAmIhnYouhVCqRlZWF\nl19+GVevXkVMTAzq168vuWdFsBHm6vhSZ+L91rwwVqxYgaKiIowbN87h+Xbt2kGv12Pnzp2S8JSU\nFBw6dKjCcgfKhOmtZUREOHjwIJo1a8afqaioiItSlmdbTy4AEBAQgKKiIgB/ebNRq9UV3j8/Px/t\n2rXD0aNHsXr1agQGBmL06NG4fv16uddkZ2cDKKu3DJ1Oh8LCQomQDw4O5hsjabVah/llz3br8zuC\nifhbyyspKQkZGRkIDw+XpMeenf1O5HI5YmNjcfHiRYwdO5afZ3VLqVRi6NChiI2NRUpKCl5++WUc\nPHjQoRea3NxcKJVKPishEAjuL4SIFwgEdwW1Wo2GDRsiPj7e7tzcuXPRo0cPHDx4kIdt2LAB+/fv\nx6BBg3jYyy+/DIvFguHDhyM9PR0AsG/fPowbNw5arRbPPvtsuff38/NDnTp1sHjxYlgsFgwYMIAL\noi+++AJAmatKBht1th1F9vHxgVqtlriLdHJyshNuttfdOhLPRo27deuGWrVqASgTdHFxcfDz88Oh\nQ4fKfQYAaN26NT7//HPeKamM0tJSZGdnQ6vVIjk5GcnJyZLzRISFCxfCxcUFffr0cZjGkCFD4Onp\nicmTJ/OdRK9du4Y+ffqgtLQUY8aMqTAPcrkcly9f5htnWa1WfP7554iLi+OmSkCZMGXlFhQUhNq1\na2PLli28fIkIer0eKSkpyMjIgE6nQ3h4OBYvXizZzOnEiRN8oyIiQn5+Ph555BGo1Wr4+fkhNjYW\n+fn5GD16dLlimgl1Dw8PHsZmG2y//6CgIN4ZaN++PVJTU3HkyBF+ns3aVLYhFoN1aH7//Xcu5NPT\n0/HCCy9ArVZj6NChvKyAv+pZq1atUKtWLQQEBKBbt25c1BcXF2PChAlo164dUlNTMXv2bN6ZUygU\n6N27N4Cy79MWIkJ8fDwaNWpU7kyKQCC4x9wbU3yBQPBPZODAgQTAzvvJ+fPnydfXlwBQ48aNqUGD\nBgSA6tevT6mpqZK4H330ESkUCtJoNFSnTh2SyWSkVqspNja20vuPGTNG4s6PiCg0NJQAUMeOHSVx\nhw0bRq6urnYLVsPCwiSuGocMGUIeHh5299q9e7dk0SMjMzOTGjZsSAAoLCyMunXrxp+3VatWlJeX\nV+lzVIfWrVvbubuMi4vj548fP17pgmOiMpecnp6eJJfLqV69etzl4pQpUyrNQ5MmTQgAOTk5UbNm\nzcjLy4sA0NNPPy1ZUNmxY0eqV68e/8zcfIaHh9OYMWOoZcuW/Bnmzp3L8yWTyfgi2aioKAJALVq0\nICIis9lMAGjkyJGSPE2aNIkA0JYtWxzm+dixYwSA5s+fz8PWrFlDAGjXrl08bNSoUQSASkpK6Ny5\nc6RWq8nT05Oef/55euaZZ7gLyYiICLJarXxha35+vsP7xsfHS1xlNm7cmJRKJcnlclqxYgWPd/Hi\nRQJAH3/8MQ+LjY0luVxOWq2WunTpQp07dyY3NzcCQHPmzKG1a9dyzzjt2rWjli1b8t/StWvXJPk4\nffq03W9FIBDcXyimT58+/U53FAQCgQAoMzFZtWoVgoKC8MQTT/BwX19fDBs2DE5OTtDr9XBxccEr\nr7yCRYsW2S3G7NixI/r06YOCggJotVr06tULq1evRocOHSq9f/369bF69WrExMRwMwd/f39s2rQJ\nK1askNgpu7m5ITIyEm3atJGkkZ+fj+zsbLzwwgsAymztO3fuzBfOMoxGI7Zs2YJPPvlEsqhRq9Vi\n+PDhCAoKQmZmJvLy8tCkSRO8/fbbmDt3Lt9cqqaoU6cOHn30UXTr1g3du3dHnz590KNHD76Q8cqV\nK9i1axdiYmIkpiO30qhRI4wcORImkwlyuRzt27fHkiVLMGLEiErzUFpaiu7du6NOnTowmUwIDQ3F\nRx99hA8//FCyoJKVRefOnQGUfdchISG4dOkSzp07h7Zt22LJkiXIz8+H1WpFt27d0KhRI0RFRSEt\nLQ379++H1WrFuHHjEBMTA41GA7lcDqPRiG7duiE0NJTf67HHHsPly5cRHR3tcFFuQEAAEhIS0KtX\nLzzyyCMAykbgY2NjMWDAAL7GIjU1FXv27MHEiRMRHByMHj16ID8/H8eOHYNGo8H06dPRv39/7Ny5\nEy+++CIyMzNx8uRJTJw4UbL4luHi4oKCggKMGjWKb5LVvXt3LFu2DF27duXxNBoNzpw5g9GjR/MZ\nnbCwMDzzzDNwcnLC9evXoVKp0KNHD3z77bfo168fmjZtijp16vBNxogIUVFRiImJ4Rt7MRYtWoS4\nuDjMnj0bDRo0qPQ7FggEdx8ZUTlziXcQg8GA+fPn49ixY2jYsCGmTJlS4aIoi8WCzZs3Iz4+Hjqd\nDsOGDeONVmFhIWbOnAm5XI7S0lIYjUYolUoUFhbivffeq9BjgkAguLtYLBY0bdoU6enpOHHiBEJC\nQu56HojIzp7caDRWalctEBiNRvz4448YPHiwZJGwwWCo8c7XvSQpKQmtWrVC7dq1cfr0abGwVSC4\nT7nrIj4lJQWPP/44DAYDnn76aRw5cgSZmZmIj493aOOZnZ2NgQMHYv/+/WjTpg0uX76MkpISHDx4\nEOHh4SgpKYGnpyd8fX0RFBQElUoFs9mMevXqYe7cuVzsCwSC+4OzZ8+iQ4cOcHV1xdatWxEREXGv\nsyQQCP7PiRMn0KtXLxQXF+PQoUN8xkEgENx/3PXu9fjx4+Hu7o7z588jNjYWiYmJaNGiBd59912H\n8WfOnIm0tDScPn0ahw8fRlJSEnx8fPDVV18BAHdHNmPGDBw5cgQHDhzA4cOHsXr1aiHgBYL7kGbN\nmmH37t3w8fHBzz//fK+zIxAIbNi0aRN0Oh327NkjBLxAcJ9zV0fi8/Ly4OPjg7Vr16J///48fM2a\nNXj22WeRnZ1t5+/YYrHAarVyu0mLxYJ69eqhb9+++Oqrr1BYWAg3NzcsW7YMKSkpSEpKQt26dfHa\na69VaN/5MEL/98KQnZ2N/Px8GAwG5OfnIzc3F9nZ2dDr9TAajTCZTDCZTCgtLUVRUREMBgOKi4th\nMplgNpvt3NzJZDIoFAoolUo4OTlBpVJBqVRCpVJBpVJBq9XC29sb7u7ucHNzg4eHB1xcXODp6QkP\nDw9oNBpoNBq4uLjAw8PD4aYiDwNmsxl5eXkoLCyEwWBAQUEBL9vi4mKUlJSgsLAQer0eRUVF/DCZ\nTDAajSgpKUFpaSnMZjM/rFYrrFYr96DBzEBYuduWrVqthkqlgqurKzw8PODh4cH9WLP/dTqdw42J\nHhT0ej1ycnJgMBj4UVRUBL1eD71ez8uX/c/KtKSkBEajEaWlpTCZTJI6zjYXcnJygpOTE5ydneHm\n5sYP2/Lz9PSEp6cn/9/Ly+uhqM9GoxE3b95Ebm4ucnJykJ6ezutvSUkJr6tGo5HXaVZX2V/bMpXL\n5VCpVHBycuJlq1aroVQq4ezsDFdXV7i4uPD6y8qSlbePjw8CAgIeahMnIoLJZOJ1ODMzE6mpqcjM\nzERWVhYyMzORn5+PgoICFBYW8vbZbDbz9sC2nNlfV1dX3haz+qrVauHq6gpvb28e5u/v/8CbybCN\nqDIyMpCfn4+ioiIUFxejsLAQRUVFyM/PR05ODm+TWXvL3n8Wi4UfDLlcDqVSCYVCAZVKBY1GA7Va\nzdtXVn9ty1aj0cDd3R3+/v7w9fWFu7s7H2B8WCAilJSUSNpWg8GAzMxMuzLW6/UwGAy8frP2wmg0\nSuqvTCbj5a3VauHs7MzbX/ZOY22Fm5sbdDodvL29uZbw9PSEWq1+qMq5uigrj1JzHDhwAFar1W6n\nvMaNG4OIcO3aNTsRr1Ao+OIfIsK///1v3Lhxg7udS01NBQCMGDECdevWRYsWLbBjxw785z//wdmz\nZ/lGG4zp06djxowZkrATJ04gPDwckyZNwpkzZ+Ds7AxPT094e3tzUcp+uF5eXvyF7u3tzSvUrRt5\n3C5WqxXFxcXQ6/UoKChAUVERCgoKeEOenp6O9PR0pKWlITs7m5/Lzc1FamqqnTu7W5HJZFysMMHi\n4uICZ2dnqNVqXt4ymQwymQxEBIvFwn98rPFjL2/WEcjLy3PoK9sR7KXt4+PDf6De3t688fP09IRO\np4OPjw9cXFy4iGLiydnZucZ/tCaTiTdGrJHKzs5GdnY2b7AKCwuRm5uLgoIC5Ofn84bKYDCgsLAQ\nWVlZVS4DALzBYgJHo9HwDhI75HI5P4Cy3wCrI+np6bxzUFRUxAWrI3eHtjg5OUGn08HPzw86nQ6B\ngYHw9/eHv78/tFotN0/z8vKCr68vPD094erqWmMvfFanmH/1rKws3Lx5k3dAU1NTkZaWxv+mpaUh\nJyeHfxdVgTX+zs7OUCqV/EXMhA6r40DZwEBJSQl/ubMXVUFBQbl+1W1hAsnNzY2XqY+PD7y9vaHV\nauHn5wdfX19e1z08PODl5cVFQE2UKxOERUVFKCwsREFBATIzM5Gbm8s/s2diHXsmGDMyMiR+7x2h\nUCig1WqhVqt5e2HbmWeih32nZrOZv8RZu8HakOLiYhgMBocbR90K+x5tRb63tzf8/f15G+zj4yNp\ns21f+u7u7jXeySIiSac8MzOT183i4mLk5OQgNzeXd3zy8/P5oEp2djZycnJQXFyM/Pz8CstApVLB\n09MTbm5ucHV15R0i1i4A4CKJtcsmk4l/3waDocLnUCqV8Pb2hoeHB3x9feHn54ehQ4ciOjoaSqUS\nSUlJOH36NJydnXnbzL5/Nzc3ODs784XDfxeLxcI74Cz/ubm5/H2XkZGBrKws5OfnIy8vD7m5ubwO\nV9beKRQKuLi48MO208Ped6zu2v6OLBYLF562gwDse68MuVwONzc3+Pr68nedn58fAgIC4Orqygdf\nWNvB2gStVsvrtqura42+6ywWC3JycvhgU3FxMYxGI/R6PbKysvgAICvf3NxcZGRkICUlBdnZ2dV6\nx2u1Wjg5OUnaC9aRZ2XN3mdmsxmpqam8E8berVW5n1qthr+/P2rVqgWdTsf1RFBQEB+0YuXMOres\njdBqtTWuJVj7UFxczOuqXq9HXl4e12tZWVm4ceMG0tPT0bhxY8yePfu273dXRXxOTg5vlG1hG6jY\n7oJ4K5mZmRg1ahS2bt2KOXPmcM8WaWlpAIDBgwdj+fLlcHJyQlpaGho0aICVK1eWu3mJLbYNUUlJ\nCfLy8nD27Fnk5eVBr9dXaQMWVkGdnJyg1Wp575xVWtsXHGscWMPLRCATYpWhUCig0+mg0+ng5uaG\nwMBANGnSBAEBAQgMDISvry+vuB4eHvD29oaXlxfc3d2hVCrvSK/VarXyHnheXh4MBgPy8vKQn5+P\nkpIS3mtn4jcnJ0fSez99+jRycnJQUFBQ6cudNcqsE8KEGpsZYFuuszIHwEdbmKBgeWIvvao0ykzg\nslFuNzc3+Pv7S0YJWCPCwlgDxg7WYNfUy88RpaWlKCgo4I2GXq/nQoK9ENlLMTU1FWfOnEFGRgbf\nOMcRMpmMd6BsX4KsjjNRLJfLIZPJ+AyCyWRCcXExF5dsVKayCUC5XA6dTodatWohMDAQYWFh8Pb2\nRq1ateDj4wOtVsvLmb30WOPs6upaY8LNYrFIOm15eXm8XFkDzdoJvV6PjIwMJCcn4/jx48jLy7Pb\n4Ke8crUVF6wdsRXHLC+sDhuNRhiNRv6iKCwsrLRMgTLhxjrE/v7+aNSoETp06ICgoCAEBQXxzpu/\nvz88PDx4O6ZSqWq83TCbzfx3aFuu7CXHZgNY55l1SM6ePYu9e/eioKCgwjrLcHZ25s/BxJNtW8Hq\nLAA+62W1WvkgBRNu7NDr9VW6L3sXsIEJFxcXBAYGonnz5nB2dubtCKvHrH77+fnBz88P7u7uf6vM\nrVYrF8NsxpWJtOzsbNy4cYMLuuzsbFy9ehUvv/yyw83YKkKlUklGTlk9thXKtuVrsVi4UGYzlvn5\n+RXWX41GA51Ox8syODgY4eHhCAgIQO3ateHv788FMBuYYmV/J2YerVar5F1nNBqRl5eH9PR05OTk\n8E4baxNY3T1+/DgyMjKq/Htlz85mrVibywZ/2PucvUtY+TJhzNpf1jGqrD0CytpeDw8P+Pj4wMPD\nA/7+/mjTpg38/Pz4e822E+Lr68sHKZj2qan212w2S2a2MzIyeHvH3mmss/fnn38iOTmZzw7YbshW\nHgqFggt61illesJ2AI0NaLJyZe2wbRvByrkqnQ+ZTAZ/f38EBgaiXr16f6uM7qqI9/b25r1a223K\n2QYg5e0Kd+DAAQwcOBBarRb79u2TuKYLDw/H/PnzMW7cOL4hRUBAAB599FG+KUllODs7o6SkBHPn\nzrVz+UVEkim63NxcPlEDnEIAACAASURBVMWZlZWF3NxcPoXETFXYCAzrvbMvnYigVColDR0zf2Cj\nhqzxYVP5bCTa3d2d9+R9fHzuu+kjuVzOn8N2y/HboaioiDd8TPizERgmStn0MhsRs/0xsYaMlTkA\nPvrKpvbZND6bfvb29uYjpqyR8vLy4g3XnRTdNY1KpYKPj0+1zMnYC99gMHCTCjYTYVv+bFqUdUBZ\nHWdlzQ7WCLJZLFsTCtsXLfvM6rmPjw/vDN0P5a1QKODl5WU3Q8hmEyqbgWMzDWyk1tbELS8vj4so\ng8EgEYy2M17shWBbh9n0PutYspcqaztYWbLRPNbJuROzWLeLUqnkbYavr2+1ryciLlKLi4slHSo2\nMMLaats23La9YJ1N2zwxUcSEPhNO7GDCkHUK2Cg2a8PZjEBNzc7eLnK5nM/2VAc208feY0zkswEW\nNljD3nm24sXWXNPWZIXB6q6tiY+7uzuf4bZ953l5eUGn08Hf3x9ubm73Tb0F/hK6thuBVcStHrGI\nSDKAx2Z+mUkQq9dsNtB2ppXNvLJZLtbmAn+VLzNRcWQeyAb1WH3VaDQ8nInx+6Ws2W7Bnp6eCAoK\nQpMmTap8LTNRY+811pGx/Wxresm0RHFxcbmmrGxW19bcih3sHWer59ggKut8snbYy8urxtqHu2oT\nf+LECbRq1Qrnzp2TfBnLly/H2LFjUVBQYNeDS05ORtOmTfH0009jxYoVVXbj1blzZ9SrVw/Lli2r\nUvwhQ4YgISEBFy9erPLzCB5+zGYz9Hq9nYgT/LMpKSlBWlra3x5FETxcWCwWGAwGyb4AAoFoLwS3\nMmXKFMTFxVV5J+fyuKtDXeHh4fD398d///tfSfi6devQunVrh1MwsbGx0Gq1WL58uUMBz0ZjbLl5\n8yaOHTtWpc1fGCaTSWwtLbDDZDJVaOYl+GditVrvi5kCwf0FM6sQCGwR7YXgVq5evVrpeo6qcFfn\n+xQKBcaOHYtZs2bB398fjz32GL766its3rwZq1at4vFSUlJQu3ZtyGQynD9/Hj4+Pvjuu++QnZ0N\ng8EAJycnDBs2DK1atcLOnTsxYMAAbNiwAV26dMG5c+cwevRoODs7Y8CAAVXOW2lp6UPhZUJQs1gs\nFoe7Kgr+2Yh6IXCEqBcCR4h6IbiVmtKcd91o791334VMJsP48eNhMpng4+OD+fPnY/DgwQCAffv2\noXPnzlizZg0GDRqE1q1bY9u2bVi8eDE8PDzg6urKFzstWrQIUVFR6N+/P6KjowGUjcyHhoZiy5Yt\n1TKBECPxAkeIxlfgCFEvBI4Q9ULgCFEvBLdSU5rzru/YysjNzUVaWhrq1q0r2b66oKAAL7zwAr79\n9ttqbdZ08eJF/PHHHwgMDET79u2rPXUVFRUFk8mEAwcOVOs6wcNNTk4OzGYzdDrdvc6K4D5C1AuB\nI0S9EDjin1gv2OJ/trj51r1PbA/m+YX9Zf/bLtq9FeYG+9aDeaez9VJn662OLfpli1Pv1SLemtKc\n92z5vCOPDwDg7u6OjRs3Vju90NBQhIaG3nZ+rFar6CkL7CAiYcsosEPUC4EjRL0QOOJBqRdMeNsK\naFthzQ4W59Zw5omPHcyblq1ovnUPFCa8Hf3PjvLy6uiwdbN5q1te23yyDoXt5l627sCZwL/1s21n\nwfavI8xmc7luvWtKc95bH1gCgUAgEAgEgnuK0WjEtWvXHI5u245is8+2u62yc7ZC+E6PctdE2qzT\nYuv73dbPPjtv23Gx7SzY/i0Pf39/eHt7/+28locQ8f9HJpNVaVMnwT+Pe2RxJrjPEfVC4AhRLwSO\nuJ/rhdVqRUpKCnQ63T/KnTLz/X6n9nQwmUy4evUqvLy87DodNaU57//5nbuEUqmE2Wy+19kQ3Gew\nXXYFAltEvRA4QtQLgSPu93pBRDCbzf8oAX83YAtXHX33NaU5hYj/P0LECxxxvze+gnuDqBcCR4h6\nIXDE/V4v5HL5fT1T8CBTntmPEPE1jJOTU4043hc8XCgUCmFmJbBD1AuBI0S9EDhC1It/No46SDWl\nOYWI/z+urq4oLCy819kQ3GeIzp3AEaJeCBwh6oXAEaJe/HORyWQORXxNaU6xsPX/uLu7Q6/X3+ts\nCO4zVCoVSktL/8fevYdHUd7tA79nZ2ZP2WzIkUM4BwTRApUfAoJKFQ+IRWsVfati29e24KlvrUWL\n7aultRWt1kPRekCtLWq14ms9IVVBKoJosaCIAhFEEkJCzpvdze7OzO+PZNbJ7mxIsrOZTbg/15VL\n3N3MPJl8M3PPM888Y3czKMuwLsgM64LMsC6yX11dHV544QXU19ejrKwMc+fOhdvtTvqcoih4/PHH\n8corr8DhcGDBggVYsGBBymEzqUK8VZmTIb5dXl4eGhoaoGmabZP/U/ZhLZAZ1gWZYV2QmWyvi6M9\n9zzxxBO45ppr0NLSEn9tyJAh+Mc//oEpU6bEX6usrMTcuXOxfft2FBUVQVVVrF69Gg888ADWrFkD\nj8eTtOxUId6qzMnhNO2Ki4sRjUbR1NRkd1OIiIiIesXRHuLvuecejB8/Hm+88Qb279+PF154AdFo\nFD/5yU/in9E0DZdeeil27tyJFStW4NChQ6iqqsJdd92FDRs24JZbbjFddqoQb1XmZE98u6KiIgBA\nTU0N8vLybG4NERERUeZZFeL3NdXi3zX74XKImDVkDAa4vBa0LvM2bdoEl8sVf6rusGHDsHXrVvz6\n17+OP3l206ZNWL9+PW6++WZcddVVANpm9bn++uuxevVqrFy5ErfffnvSk3lTzUxkVeZkiG9XXFwM\noG2DjhkzxubWEBEREWWeqqpJ4bM7GltDWLz+Kbx3aC8koe2prlFVwXfHz8DNU+fCIWRm0MeSJUtQ\nUVGBVatW4bXXXsOKFStQVlaGZcuWxYPx/v370djYGP8eQRDg9/sxfPjw+GuJw2CCwSA2bNiA0tJS\niKIIAFizZg0EQcDixYuT2nH++edj48aN+PDDDzsMv9HXl6onHkg/czLEtxs8eDCAtjFPREREREeD\ndEK8qqlYsOZh7G6oRkRV0Gp478nPNgMAfnniPAtamWzHjh147733cNNNN2H58uXxG4jD4TAeeugh\nbNy4EbNmzUr6PkmSUF9fD5/PF38tFovh8ccfx5o1a7Bu3TrU19fjmWeeib//7rvvorS0FKWlpUnL\n01/bs2dPUohP1RNvVeZkiG+nnxXV1dXZ3BIiIiKi3pFOiP9X5R7sbapFRE2eBz8Ui+KJTzfhukmn\nIc+VfNNnulwuF2pra7F8+XLccMMNWLZsGebMmYO1a9cCAKZOnYoXX3wRkiR16BHPz8/vEOCBtgB+\nzTXXxKcCXbBgAb75zW/G329oaIgPgUmUm5sLwHw+eFEUTUO8VZmTIb6d19s2dst4dzIRERFRf5ZO\niH9p70cIxlLPgS87RPzr4B6cO/JrPW1eSuFwGAAwd+5c3HHHHRAEARMnTsTWrVsBtM3PP3/+/C4t\na/z48aitrcWWLVtw991349lnn0UwGMRLL70EAHC73aioqDD93oaGBgBIOjEA2obTmIV4qzInZ6dp\nl5OTA4AhnoiIiI4e+s2bPdGqdD7/vaZpiGboabV6eF62bFn8xtxoNNrjOfl9Ph9OO+00vPTSSzjj\njDPw8ssvY8eOHQCAMWPGoLq62jSQ79u3DwBw/PHHJ72Xaky8VZmTIb6d0+mEy+XqcAMEERERUX+W\nTk/8KUPGIkdypnw/pqmYUjI85fvpqKurw8iRIzuMQ4/FYtA0DZqmoa6uDhdddBFOOeUUzJw5E7Nn\nz8YZZ5wRn10mFUEQcNlllwEA9u7dCwCYPHkygsEgtmzZkvT5devWobi4GCNGjEh6L9WYeKsyJ0N8\nO0EQkJeXxxBPpszOpIlYF2SGdUFmsrUu0gnx546aCKdoPjLb6RAxY9BoDM8tSKd5KTU3N2PUqFEd\npsf0+/1QVRW1tbWIRqNobm6Gz+dDYWEhPB4PNE1DLBaLf/4///kPZsyYgS+++KLDsj/77DMAQFlZ\nGQDgzDPPBAA8+uijHT63adMmvPXWW5g9e7bpNJ2peuKtypwcE2/g8XgQCoXsbgZlGUmSoCgKJIl/\nLvQV1gWZYV2QmWyui3SG03gkGc+e/UNcvOZhtCoxtLSPj8+RnBidV4wHZn/HyqZ2IIpi0snH0KFD\nAQDl5eWYNm0a1qxZ0+kyPB4PPvjgA8ybNw+33XYbBg0ahDfffBN33HEHTj/9dBx77LEAgAkTJuA7\n3/kOVq5ciVAohCuuuAKffPIJli5dClmWsXTp0pRtTDW8x4rMmX3VZKOCggLU1tba3QzKMh6PB8Fg\nEH6/3+6mUBZhXZAZ1gWZyea6UFU1rZOLYwsGYcuCn+PlfR/hX5W74RZlfHPURMwcXJbRJ8GWlJSg\nubm5w2ujR48GAFRVVXVpGePGjcOTTz6JH/7whzj//PPjr8+aNQt//etfO3z24YcfxuDBg3HPPffg\nqaeein//H/7wB0yePNl0+alubAWsyZyClq3Xd2xwxhlnoKWlBe+++67dTaEsUl9fj0gkgoEDB9rd\nFMoirAsyw7ogM9lcF5WVlfB6vRgwYIDdTemW999/H0DbVJK6pqYm/Pa3v8X111+PkpKSLi8rEAjg\n7bffRk1NDb72ta8lzfduVF5ejo8//hh5eXmYNWtWpydAjY2NCAQCpvPLW5E52RNvkJOTg+rqarub\nQVlGlmXOWkRJWBdkhnVBZrK5LmKxWI+H09jJGN51fr8ft99+e7eX5fP5MG9e1x5KVVZWFh8rfyQO\nhwNKitl5rMicvLHVIC8vLz5lEZHO7XbH56Ml0rEuyAzrgsxkc12oqtonQ3xfIElShxtpjazInAzx\nBnl5eWhqarK7GZRl9BuSiIxYF2SGdUFmsrku0pmdhjqX6omtgDWZk781A6/Xi2AwaHcziIiIiHoF\nQ3zmpJonHrAmc/K3ZuD1ehGJRLL2bJmIiIjISulMMUmdO1KITzdzMsQb5OfnAwCnmSQiIqJ+T1VV\naJrGnvgM0R/2ZDYRpBWZk781g4KCtqeK8eZWIiIi6u8URYHD4cjofO5HM0EQUvbGW5E5GeINPB4P\nAPCprURERNTvZetTZPuTVCHeiszJEG/g8/kAtE36T0RERNSf8abWzBNF0XTcuxWZk785g8LCQgBA\nTU2NzS0hIiIiyiyG+MxL1RNvRebkb86guLgYAHD48GGbW0JERESUWbFYjMNpMixViLciczLEG3A4\nDRERER0t2BOfefoMNYk4nMZibrcbALL20chEREREVmGI72jNmjW44oorEIvFTN9XFAWPPvoovvWt\nb+Hb3/42/va3v5kGdKNUPfFWZE5eQzHweDyQZRmNjY12N4WIiIgooxjiv/LSSy/hggsuwHHHHWf6\nfmVlJebOnYvt27ejqKgIqqpi9erVeOCBB7BmzZr4bDOJJEkyPSmwInPyN2cgCAJyc3PR1NRkd1OI\niIiIMopPa22zfv16XHTRRRg7dixee+21pPsENE3DpZdeip07d2LFihU4dOgQqqqqcNddd2HDhg24\n5ZZbUi47VU+8FZmTIT6B2+3mcBpKIghCykcn09GLdUFmWBdkJhvrwsqe+Eh1OZre/SuatzwHpaXe\nkmX2hkAggAsvvBBjxozB+vXrMXjw4KTPbNq0CevXr8eSJUtw1VVXweFwQJZlXH/99Zg5cyZWrlyZ\n8nebKsQD6WdODqdJwBBPZvTLYU6n0+6mUBZhXZAZ1gWZyca6sKInXmlpwMEHL0Hos38BDgkQBECJ\nIu/0q1C8YDmEDA3XWbJkCSoqKrBq1Sq89tprWLFiBcrKyrBs2TLk5eUBAPbv399huIogCPD7/Rg+\nfHj8tUcffRQtLS148cUXUVJSYrquNWvWQBAELF68OOm9888/Hxs3bsSHH36IKVOmJL3PEN+LGOLJ\nTDbufMl+rAsyw7ogM9lYF+mGeE1VcWD56Wit/ASIRTq81/jWnwAIKLnkjjRbaW7Hjh147733cNNN\nN2H58uWQZRnRaBThcBgPPfQQNm7ciFmzZiV9nyRJqK+vh8/nQyQSwV133YUTTzwR9913H95//30U\nFRXhggsuwKWXXgpZlgEA7777LkpLS1FaWpq0PP21PXv2mIb4VGPiAYZ4y+lFQGSU6olrdHRjXZAZ\n1gWZyca6SHc4TfCTNxA5tCcpwAOAFgmi8c0VKPzmUog5A9JppimXy4Xa2losX74cN9xwA5YtW4Y5\nc+Zg7dq1AICpU6fixRdfhCRJHaZ5zM/Pj0/v+Pe//x0HDhzAgQMH8N5772HAgAHYvHkzXnrpJTz3\n3HN4+eWXIQgCGhoaUFRUZNqO3Nzctp83xSw1nf3e082cDPEJGOLJTGeXw+joxbogM6wLMpONdaFp\nGgRB6PH3N295Dlpr6nnOBVFG8JM3kDv1wh6vIxW9B3vu3Lm44447IAgCJk6ciK1btwIAnE4n5s+f\n3+kytm3bBgC48847cfXVV8Pj8aCmpgbf/e538eqrr+L999/HiSeeCLfbjYqKCtNlNDQ0APhq3vdE\nmQzxvLE1AUM8mRFFMet2vmQ/1gWZYV2QmWysi3RDvBbtfCiIBg2aSS+9FfTwvGzZsvjPEI1Gu5Xh\nqqqq4Ha7ccMNN8SniCwuLsby5csBAK+//joAYMyYMaiurjb9/e3btw8AcPzxx5uuI9XDngCGeMtl\n45ky2a+zP0I6erEuyAzrgsxkY12kG+K9x82B4DLvgQYAKDF4xszo8fI7U1dXh5EjR3YYhx6LxaBp\nGjRNQ11dHS666CKccsopmDlzJmbPno0zzjgDV111VfzzHo8H4XAYoVCow7L9fj8AIBJpOwGZPHky\ngsEgtmzZktSOdevWobi4GCNGjDBtZ2e/93QzJ0N8gmz8IyP7sS7IDOuCzLAuyEw21kW6IT73xAUQ\nZJf5m5ITnvGnQi4e1ePld6a5uRmjRo3q0H6/3w9VVVFbW4toNIrm5mb4fD4UFhbC4/FA07QON5lO\nnToVAPDOO+90WPYHH3wAADjhhBMAAGeeeSaAtplsjDZt2oS33noLs2fPTrkdO/u9p1sTHBOfwOFw\nZN0fGREREZHV0g3xDqcHw258E18unwMtGo6PjxdcPjgHHYPBi5+2qqlJRFFMuil36NChAIDy8nJM\nmzYNa9as6XQZZ599NmRZxtKlSzFhwgSUlpbi888/x80334zCwkLMnTsXADBhwgR85zvfwcqVKxEK\nhXDFFVfgk08+wdKlS+Pfn8qReuIZ4omIiIioW9IN8QDgGvY1jL77CwTefw4tO96AQ/Ygd9pF8Bx7\nWtrL7kxJSQmam5s7vDZ69GgAbWPdu6K0tBT33nsvfvzjH2PMmDEYMWIEdu/ejZycHLzwwgtwu93x\nzz788MMYPHgw7rnnHjz11FMAgHHjxuEPf/gDJk+enHIdmbwCwxCfwIqCpsz6uLYCGw+WwyEImF06\nDmMHmD+cgYiIiDLP4XTDP/Ny+Gde3mvrfPDBB5NeO/PMM3HjjTdixoyuj8NfvHgxzjnnHDz22GOo\nqanBtddei8suuyz+wChdTk4Ofv/732Px4sX4+OOPkZeXh1mzZkGSOo/SnYX4dDMnQ3wCVVWP+Ash\ne9S3BvHdN57AJ7UHoWhtN4Is//frmDZoFB75xuXwypl7gAZP7sgM64LMsC7ITLbWRTa2qSv08exG\nfr8ft99+e7eXNWLECPzqV7/q0mfLyspQVlbW7XWYSTdz8sbWBOk++IAyQ9M0XLb2MWw/XIGQEkVE\nVRBRFYSVGDYf3IsfrVuV8fX31R0dZQ7rgsywLshMttYF7wO0T7qZk2k1QTQajT9ml7LHv6v3Y3dD\nNaJq8gMTWtUYNlWVo7yxJmPrT/fR1NQ/sS7IDOuCzLAuKFG6mZMhPgFDfHZaV/EZQp08MEID8HbF\nroytnztfMsO6IDOsCzKTjXWRjdNeHk0Y4i0WDoc73I1M2UHTNHS2m9E0dPp+umKxGO+VoCSsCzLD\nuiAz2VgX2Ti8p7/pbBhVupmTIT5BIBCAz9fJ08fIFieXjoVXSn3jqkMQMGvwmIytPxqNwunM3I2z\n1DexLsgM64LMZGNdCILAp9TbKN3MyRCfIBwOw+Px2N0MSjB94CgMz82HJCSXrNMh4oTiYRiXPzBj\n6+cNz2SGdUFmWBdkJhvrgsNp7JVu5syuasoCwWAQXq/X7mZQAkEQ8MxZP8AxAwbCKzkhAHBAgEeU\nMaloKB49faHdTSQiIupTHA4He+IzrLPhNOlmzuwanGWzaDSKUCgEv99vd1PIRJHHh9fPuw5bDu3D\nu/rDnoaOw6SioXY3jYiIqM8RRRGKkjzrG1knVYi3InMyxBs0NTUBQNJTuih7CIKAaYNG4cSBI+P/\nT0RERN3H4TSZlyrEW5E5OZzGoLm5GQB4Y2sf8MaXO/HGlzvtbgYREVGfxRCfeZqmmd4LYUXmZIg3\naGlpAQDk5OTY3BIiIiKizOKY+MxTVdW0J96KzMnhNAaBQAAAkJuba3NLiIiIiDKLIb5NbW0tXnnl\nFWzbtg0+nw+XX345xoxJnrZaURQ8/vjjeOWVV+BwOLBgwQIsWLCg06G9qYbTWJE52RNvUFdXBwAY\nMGCAzS0hIiIiyize2Ao899xzGD58OP77v/8bq1evxm233YZjjjkGd955Z4fPVVZW4oQTTsAPfvAD\nvPPOO1i/fj0uueQSzJ49G6FQKOXyU00takXmZIg3aGhoAADk5+fb3BIiIiKizDraQ3xtbS0WLlyI\nmTNn4uDBg9i7dy/27duHiRMnYsmSJdiwYQOAtt70Sy+9FDt37sSKFStw6NAhVFVV4a677sKGDRtw\nyy23pFxHqhBvReZkiDfQz6T4sCciIiLq76wcTlN7uAVbPziA7f+pRDAYsWSZmfaXv/wF4XAYK1as\nQFFREQBg6NCheP755+F0OvHHP/4RALBp0yasX78eS5YswVVXXQWHwwFZlnH99ddj5syZWLlyZcrt\nqCgKRFFMet2KzMkx8Qa1tbUA2BNPRERE/Z8VIT4UimLVn/+Nz8vr4BAFCAAURcNJs0binG8eC4cj\nM1NBL1myBBUVFVi1ahVee+01rFixAmVlZVi2bFl82sb9+/ejsbEx/j2CIMDv92P48OEAgI8++giy\nLCeNfy8rK8O0adOwefNmAMCaNWsgCAIWL16c1I7zzz8fGzduxIcffogpU6YkvZ+qJ96KzMkQb1BX\nVwdZlvmwJyIiIur30h1Oo6oaHlqxCYeqAlAUFYh99d6mjV8AAnDu/AkWtDTZjh078N577+Gmm27C\n8uXLIcsyotEowuEwHnroIWzcuBGzZs1K+j5JklBfXw+fzwefz4doNIoDBw5g2LBhHT4nimK8l/zd\nd99FaWkpSktLk5anv7Znzx7TEJ+qJ96KzMnhNAZNTU3w+/18gBB1wDl0yQzrgsywLshMttZFuj3x\ne3YdxuGalrYAnyAaVfDuv/YhFIqm08SUXC4XamtrsXz5ctxwww1obGzESSedhLVr1wIApk6dihdf\nfBGvvPIKXn31Vbzyyit45ZVXsGHDhvjc7JdddhkAYOHChThw4ACAth7y6667DuvXr8fAgQMBtI1f\n14fbJNJnl0n1O07VE29F5mRPvMGhQ4dQXFxsdzMoy4TDYbjdbrubQVmGdUFmWBdkJlvrIt0Qv+0/\nlYhEUvfki6IDuz+rwcTJQ3q8jlTC4TAAYO7cubjjjjsgCAImTpyIrVu3AgCcTifmz5/f6TKmTp2K\n6667Dvfddx+GDRuGgQMHora2FrFY2yWFGTNmAADcbjcqKipMl6HfoJrqoU2pQrwVmZMh3qCuri7l\nmRYdvYLBILxer93NoCzDuiAzrAsyk611ke5wmli08xMADRoUJTNXIfTwvGzZsnhvdjQaRTTavZ7/\ne++9F5dccglWr16NiooKHH/88dizZw8ef/xxnHPOOQCAMWPG4MMPPzQN5Pv27QMAHH/88abL72w4\nTbqZkyHeoLm5mSGekkQikazc+ZK9WBdkhnVBZrK1LtIN8WPHFWHHx1Upe+NVRcOIkZmZLKSurg4j\nR47sMA49FotB0zRomob6+nr86Ec/wqFDh6AoCmRZhizLGDt2LB544IEOy5oxY0a81/3LL7/E+PHj\nceyxx+Lkk08GAEyePBl//vOfsWXLFkyfPr3D965btw7FxcUYMWKEaTtThXgrMifHxBvU19dzZhpK\nEg6HOe0oJWFdkBnWBZnJ1rpwOBzQNK3HQ2omTR4CSTKPkqLkwOgxhSgozMzJS3NzM0aNGtVhTLnf\n74eqqqitrUU0GkVzczN8Ph8KCwvh8XigaVp8qIyZ6upqnH/++QiHw3jkkUfive5nnnkmAODRRx/t\n8PlNmzbhrbfewuzZs1OObU8V4q3InOyJN2hoaGCIpyQ+nw+yLNvdDMoykUiEdUFJWBdkJlvrQhCE\neG+82bjtI5GdIn509Qw89MAmxGIqIq1tPfJOl4ji4hxcuvAEq5scJ4piUpuHDh0KACgvL8e0adOw\nZs2aLi2rsbERTzzxBH7729+iuroad999N2bOnBl/f8KECfjOd76DlStXIhQK4YorrsAnn3yCpUuX\nQpZlLF26NOWyO3vYE0O8hQKBQMobE+joxZudKRXOZEVmWBdkJlvrQpIkxGKxHp9kDB7ix823zMH2\n/xzE7l01kGUREycPwZixhRn9mUtKStDc3NzhtdGjRwMAqqqqurycn//857j77rsRiUQwadIkrFq1\nCnPmzEn63MMPP4zBgwfjnnvuwVNPPQUAGDduHP7whz9g8uTJKZcfi8UgSclx24rMyRDfrrW1Fa2t\nrZwjngC0TRX1f59vw/3b1+Hzphq4RRnnj5qE6yadhiG+AXY3j4iIyBKSJCEajaY13EeWRUyZOhRT\npg61sGWde/DBB5NeO/PMM3HjjTfGx7d3RSwWw3nnnYfvfve7OPvss1NekcjJycHvf/97LF68GB9/\n/DHy8vIwa9YsAwv5EAAAIABJREFU04Cu08fnJ57MWJU5GeLb6Wdt+pygdPTSNA03vfsCXvj8QwRj\nbXe5B9RWPLP7A/xj33a8fO7VGJ3H3nkiIur79J74vmbq1KlJr/n9ftx+++3dWs6dd97Zrc+XlZWh\nrKysS5/VNA0OhyMpxFuVOXljazv98becnYber/4Cqw0BXhfTVDRHWvE//3rOppYRERFZSxTFtOaK\np9RS3WtgVea0pSe+ubkZd911F95//32MHTsWS5YswZAhqR8EEIvFsHr1amzcuBHFxcVYuHAhhg8f\n3uEzH3zwAe655x40NTXhggsuwOWXX256N3AqTU1NAMDhNISVn2xEOGY+z6wGDTvqKlERaEAph9UQ\nEVEfJ4pin+yJ7wtSzUxjVebs9Z74ffv2Yfz48XjwwQdRUlKC119/HePGjcO2bdtMP19dXY1vfOMb\nuOyyy/Cf//wH999/P8aPH48PP/ww/pm77roLU6dOxZdffonc3FwsXrwY8+fP79ZjjvWbIxji6Yum\nWnRWOU6HhMqWhl5rDxERUaZIkpTWXPGUWqqZaazKnL0e4q+55hoUFxfj008/xeOPP46PPvoIU6dO\nxc0332z6+TvvvBONjY3YsWMH3n77bZSXl2PgwIFYsWIFAGDXrl248cYbcccdd2D9+vVYtWoVNm/e\njFdffRVr167tcrvq6+sBAAMGsHf1aDfU1/mUT1E1hkFenuwd7XJzc+1uAhFR2gRB4HCaDOlsjngg\n/czZq8Np6urq8Nprr+H555+Pz40pSRIWLVqEiy++2HTi++XLl+N3v/td/O5ft9vd4clnzz33HEpL\nS3H99dfHbxyYNGkSTj75ZPz1r3/FWWed1aW26Y/vPdpCvKIoiEQiiMViUBQFqqomXcEQBCH+JYpi\nfG5W/b9mN230Zd+bcBI2VO5GMBZJek8AMC5/EIblFli2Pv3hE4qixH8H+pf+uzD+TgRBgMPhgCRJ\n8S9RFPvV78AK+gNMVFXtsH0VRUmqcb2eRVGEJElwOp1H3J6dDQHsrzRNg6IoiEajUFW1Q72a1ahx\nX6F/6fuS/srKutA0DdFoFJFIpMO21hm3s76tnU5nj+b77u9UVe1Qt/p+IPFBR/o2NR7v9P1sOnV7\nzDHHWPFjZITD4chIiO/OaAij/rR/6GyOeKCPhfiNGzdCVdWk+TfHjRsHoG2oTWKI10Mi0LYxbrrp\nJlRWVuKSSy4BAGzYsAGnnXZa0pnOuHHj8MknnyS14dZbb8WvfvWrDq+9/PLLCIfDANpOEoLBYPzx\nvNlKURSEQqH4NEXhcBjRqPk47s7oO309CBq3t04/QBt3fvrBRP93T9brdrvhdDohyzK8Xi9cLldW\n/PGeNGg0zho+AWv270DIMDbeIQjwSk7cNetCqKqKmpqa+AG2J9veSN/+xt+BfiBJDD2qqsZPvPSv\n7l4KFUURHo8HPp8PPp+vW/eP9BZFUdDS0oJAIIBgMNijy736dtQPwnrgMW7TxJOoWCyGaDTa7QOQ\nLMvIyclBTk4OPB5PVm5T4KtgGAgEEAgEEA6Hu/WzJm5LY73q9P2C8b9mIbSrnE5nfH/h9Xrhdruz\nYl9hJvEKTSwWi++fQ6EQQqFQt8Yfy7IMp9Np2mlitn31oNpVLpcLHo8nXrvZul0VRYkf60KhEMLh\ncLe2oyAIkGU56aRHD+3G9SQe7/T9Q09CqdPphMfjgdPpRE5ODlwuV7eX0duMP2dPg7hV6+8OY+1m\nSx2bTS8JoEPmTEevhvj6+nq4XK6kye31nV4gEEj5vVVVVbjiiivw5ptv4r777sNJJ50UX+bEiROT\nPp+bm9vp8ow8Hk+HDdrQ0IDGxsYe3+jhcDggy3JSMNMl7nT1XpbursPj8cS3Z3FxcVafdCRSVRXh\ncBiRSASRSASHDh2K/w664kBdBQBgT8RpGigSw6+xV1bfKacKv6Wlpbj3lAV4etf7WLF9PfYH6uF0\niDhn5PH46dfPwMjcQtTX18PpdMaf5irLctbsNLoiFoshFAohEAigurq6Wwd9Y00bAx2ApJMNvddW\nD8bd4XA4kJOTA5/Ph5KSkqy+2qAH45aWFjQ0NODgwYPd2qZ6r5++TY092J3VcHcDm06v3aKiIrjd\n7qzuudW3bSgUQiQSQXV1dbf2FTqz/bLZVQG9d9YYkPX9RU/ChSiKcLvdkGU562pZ0zS0trYiFAqh\noaEBFRUVPV5WYu3q+wWzTiF9v9CdY58oinC5XHC73fD7/Rg4cGCn83Nni0gkgmAwiEgkgsrKSkQi\nyVd4u0LfR0iSBFmWO5yEGCV2ukWj0ZSdEk6nE4MHD0YsFku6mqb/W19+NtRrKmZXrM1GFPRme4wn\n2oqioLq6Oj6EZujQoX0zxBcWFsbPpI0NP9JlhfXr12PBggXIz8/HO++8g+nTp8ffKygoiH+/UXce\nZ5uTk4OWlha4XC5IkoSioqK0pv0xBhez3idJkuByuTpc/uwLOyMrORwOeL3e+LCo7tq/X4EGYOSQ\nkfEdkL7T0ndgxj9i40HFeHm0s4PppeOm4dJx06BqKgR0PNgXFFg3nMYOkiQhNze32+O6zcJNqmFY\nsizD5XLFT3LSvRydbZqbm+PbTxAEOJ1OOJ3OHj1GOzGcmw1TMdawXrv6wbw/M27bdBivYKUaVgUg\nHoxcLlfS/iKbT3Z6QhAEuN1uuN3utB7/ru9z9X2xXsep9gv6SY1ev/1pv5DIito1nlgaO6DMtq/x\n5MkY+jurXUmSUFVVhWAwiJycHADZHdoTpXuiYdXVBrN26A/RKioqQklJSfx1Y+ZMR68mx9LSUgBA\neXk5jjvuuPjr27dvh9vtxvjx45O+Z+/evZg7dy7mz5+PJ554IumJYqWlpdizZ0/S923fvh2nnHJK\n0uu33norbr311qTXn3zyyXjxpkvv5aHMEvDVpf1M0TQNn1QdgMvjwtgBfBCYIAhH3QmnGU3TUFlZ\nGR8KmC7jsJ++cLm9L9KH8GWSpmk4ePDgUXe/hHH8OCXTNA27du3q8f5Cv2KkX02ymiRJGDp0KCoq\nKuB0OjF8+PA+dcKa6ip7YqeT8T4I45fx6sWRAr3xKr/xSp7x6p7xxLS5uRmjR49OWk4gELAkc/bq\n0XjixIkYPHgwnn/++XiI1zQNzz33HP7f//t/psW5atUq5Obm4rHHHjN9JPDZZ5+N//qv/8KhQ4fi\nT77avXs3tm7dip/97GddblsoFErrkcPUP2mahn9/sRtDhgxmiKc4/Sl8REaapqGlpcXuZlCW6Qv7\nC5/Ph9GjR2Pfvn3YtWtX0o3p+kmE2Q3rZsNYE+83SDVsDUCHq47GfxuvNhivThrvB9PfT7wJ2dhm\n/Z4S4xC6xLYa268zDmVM/K/xC/hq2EziFdSCggLTji+rMmevhniHw4FFixbh9ttvR0FBAWbOnIk/\n/vGPePXVV/Hss8/GP1deXo7Ro0dDEAR89tlnGDBgAO655x7U1taipaUFsixj4cKFOPHEEzFv3jyU\nlpZi/vz5uPPOOxEMBrFo0SIMHz4c5513XpfbFovF2MNISRRFgeDoO5cVqXekegofHd1YF2Smr9SF\nJEkoKyvrMKbeOFta4oQW0Wg0Kbgm9m4nhl2dMTAbQ7Tx38Zx/3pAT5yZzSx8Wy0T9wVYlTl7PbX+\n/Oc/hyRJ+NnPfoZwOIySkhI8+OCDuOiiiwAAb731Fk4//XQ8/fTTuOSSSzB9+nS89dZbePrpp5GX\nlwefz4empiZomoYTTzwRXq8Xb7zxBhYtWoRTTz0VADBnzhzcd9993bp02traysvYlKSv7Hypd6Wa\n+5eObqwLMtOX6sLYO82OzcyxKnP2+m9IlmUsXboU1157LaqrqzF06NAOP8iJJ56Iiy++GLNnzwYA\nXH311bj66qs7XebYsWPxxhtvoKKiAg6Ho0fjESORSNo3n1D/wxBPZvrSQZl6D+uCzLAuKJFVmdO2\n06xUM2P4fD4888wz3V6eIAgYOnRoj9vD4TRkRlVVOASGeOoo1QM86OjGuiAzrAtKZFXmZFW1Y088\nmWFPPJlhzxqZYV2QGdYFJbIqczKdtItGo33qYUnUO1RV5Y2tlIQ9a2SGdUFmWBeUyKrMyapqxz8y\nMqNpGofTUJK+MGUc9T7WBZlhXVAiqzInq8qAf2RERERElGkM8RZTVdXuJhARERFRP2dF5mSIbyeK\nIhRFsbsZlGUEQYCq8eSOOhIEgSf9lIR1QWZYF5TIqszJEN9OkiTEYjG7m0FZxuFwQFO1I3+QjioO\nh4MHZUrCuiAzrAtKZFXmZIhvJ8syotGo3c2gLONwOKCxJ54S8KBMZlgXZIZ1QYmsypwM8e3YE09m\nRFGEwp0vJeDwOzLDuiAzrAtKxJ54i7Ennsy09cRzOA11xJ41MsO6IDOsC0rEnniLeTwehEIhu5tB\nWUaWZfagUBJZlnnljpKwLsgM64ISWZU5GeLb5eTkoKWlxe5mUJbhZVAyI4oiD8qUhHVBZlgXlMiq\nzMkQ387lcqG1tdXuZlCWEQTB7iZQFmJdkBnWBZlhXVAiqzInQ3w7r9eLYDDI8c9ERERElDFWZU6G\n+HZerxeKovDmViIiIiLKGKsyJ0N8O7fbDQAIh8M2t4SIiIiI+iurMidDfLucnBwAQDAYtLklRERE\nRNRfWZU5GeLb+f1+AEBjY6PNLSEiIiKi/sqqzMkQ327gwIEAgEOHDtncEiIiIiLqr6zKnAzx7QoK\nCgAA9fX1NreEiIiIiPorqzInQ3y7/Px8AMDhw4dtbgkRERER9VdWZU6G+HZDhgwBAFRUVNjcEiIi\nIiLqr6zKnAzx7VwuF4qLixniKYkgCFD5EDBKIAgCVFW1uxmUZVgXZIZ1QUZWZU6GeIOSkhIOp6Ek\nTtmJaCRidzMoy7jdbj5XgpKwLsgM64ISWZE5GeINiouLUVVVZXczKMu4PW6EW1vtbgZlGZ/Ph5aW\nFrubQVmGdUFmWBeUyIrMyRBvMHjwYE4xSUk8bjfCoZDdzaAs4/P5EAgE7G4GZRnWBZlhXVAiKzIn\nQ7xBfn4+Ghoa7G4GZRlRkhCNxexuBmUZWZYR4TArSsC6IDOsC0pkReZkiDfIy8tDY2MjNN7ESAaC\n3Q2grCQIrAxKxrogM6wLSmRF5mSIN/D7/YjFYghx6AQRERERZYgVmZMh3iA3NxcA0NzcbHNLiIiI\niKi/siJzMsQb+P1+AEBTU5PNLSEiIiKi/sqKzMkQb+Dz+QCAd5ATERERUcZYkTkZ4g3y8/MBAHV1\ndTa3hIiIiIj6KysyJ0O8QXFxMQCgtrbW5pYQERERUX9lReZkiDfgmHgiIiIiyjSOibeYPj6Js9MQ\nERERUaZYkTkZ4g28Xi8AIBgM2twSIiIiIuqvrMicklWN6Q+cTicEQUA4HLa7KX1OVFWwtXo/wkoU\nxxUMQZHHZ3eTiIiIiLKSFZmTId5AEAT4fD5OMdlNT366Gbf/ew1UTYMAARE1hjnDjsVdsy6ET3bZ\n3TwiIiKirGJF5uRwmgQDBgxAQ0OD3c3oM57Y+S5+veUVNEXCCERb0RwNo1WJ4Z/7d2LBaw9D1VS7\nm2gJh+CAoih2N4NSCO/9ABX3X4jyaweh/H+GoXrVTxCt/TLj63U4WBeUjHVBZlgXlCjdzMkQn8Dj\n8XBMfBe1KjHc/u/XEVKiSe9F1BjKG2uwvmK3DS2zniiJiEaTf06yX+PGv+DL330DLVtfhNJcA6Wh\nEg1v/Qlf/GIiWvdvy+i6ZVlmXVAS1gWZYV1QonQzJ0N8ApfLhdbWVrub0Se8f2hfp++3xCJ4bs+/\ne6cxGSaKIntQslCs8RCqn1gMLRIEjFd9lAjUUBMq778QmqZlbP2SJLEuKAnrgsywLihRupmTIT4B\nQ3zXBWMRCEf4TEu0f2xLh8OBWCxmdzMoQeO/HgeQOqTHmqoRLt+csfWLosi6oCSsCzLDuqBEDPEW\nkySJf2RddHzBEETU1L0KblHG9IGjerFFmeMQBKhq/xjf359EDnwMLdr5nf3RQ5kb0uVwOFgXlIR1\nQWZYF5Qo3czJEJ+Awya6bohvAGYMGg3ZIZq+7xAE/NcxU3u5VZkhOBwZHZZBPSPllwKO1JNsCYID\nYm5JxtbvYF2QCdYFmWFdUKJ0MydDfAJRFHmm3A33n3oJRuYWIkdyxl9zixK8khOPnb4Q+e4cG1tn\nHQECd75ZKO/k70EQ5dQfcDjgnXB6xtYvCKwLSsa6IDOsC0qUbubkPPGUlnyXF2vP/zHW7v8Ef9+z\nFS3RCGYOKcOlx5zIBz5RxjmHjIf/5O+h6Z0n2m5uNRCcHpR872EIUichn4iIqI9iiE+gKAqcTueR\nP0hxskPEvJFfw7yRX7O7KRmjQYMgHOk2XrJDyeX3wVk6AXUv3QY1UAdNU+EqPQ5FFy9HznFzMrpu\nTdPgcPCCJnXEuiAzrAtKlG7mZIhPEIvF4PV67W5Gn/Ru5R4IgoAZg8vsborlVEXlzjdLCYKA/NMX\nY8Bpi6A010AQnRBzBvTKuhVFgSyzp586Yl2QGdYFJUo3czLEJ4hGo/wj66GWWMTuJmSMpjHEZztB\nEKC1BqGipddCvKqyLigZ64LMsC4oUbqZkyE+QSQS4XAaSqKoKkTRfBYeyh6tBz4CADiLe2dqU0VR\nWBeUhHVBZlgXlCjdzMlTwgStra1wu912N4OyjKookCSe81JHsViMdUFJWBdkhnVBidLNnAzxCSKR\nCIfTUBJV09iDQklUXqEhE6wLMsO6oETpZk6G+AQcE09mOJaRzCiKwrqgJKwLMsO6oETpZk5WU4KW\nlhbk5PSPBxSRdTg1GJlhXZAZ1gWZYV1QonQzJ6vJQFVVNDU1YcCA3pnZgoiIiIiOPlZkToZ4g4aG\nBmiahoKCArubQkRERET9lBWZkyHeoKGhAQDYE09EREREGWNF5uRcRwb19fUAgPz8fJtbQtT3tVZ8\ngrp/3IbAtpcBVYG7bDoK5/8C3mNn2900IiIiW1mRORniDRobGwEAeXl5NreEqG8LfrYBFXfNgxYN\nA5oKAAjtXIeK8vdQfMnvMeC0H9ncQiIiIvtYkTk5nMagpaUFADg7DVEaNFXBwRUXQ4sE4wE+/l4k\niJqnr0esocqm1hEREdnPiszJEG8QCAQAAD6fz+aWEPVdwZ3roEZCnX6mceOfe6k1RERE2ceKzMkQ\nb3D48GEAQGFhoc0tIeq7Yof3AaqS8n0tGka0anfvNYiIiCjLWJE5GeINampqAABFRUU2t4So7xIH\nDIHg6OTR4pITcuGI3msQERFRlrEiczLEGwSDQXi9Xj5RjSgNOcedAYip75kXBAf8J1/Riy0iIiLK\nLlZkTqZVg7q6Os4RT0lUVYVD4J9KVwmSjEE/eAKC05v8ntOLgnN/DrlweO83zGKKovCEn5KwLsgM\n64ISWZE5OcWkQW1tLYqLi+1uBmWZ1kgETpfT7mb0Kb7J52Loz17H4ed/idBnGwBocA6ZgMLz/xe5\nUy+0u3mWCIVC8Hg8djejz9E0DZ+X1+GzT6sBDThmfDHKxhRCEAS7m2YJ1gWZYV1QIisyJ0O8QXV1\nNcfDU5LWcBhul9vuZvQ5nrEnYdhNb0JTFUBVIUiy3U2yVEtLC6ej7aaWQASP/GkzDte0IBJpu/n5\n3Xf2Ib/Agx9eNQO5uS7L16mqGpqbWyHLDni9mT8ZZ12QGdYFJbIiczLEG9TU1GDUqFF2N4OyTDjc\niqIiTjvaU9FD5YAgwDlorN1NsVRLSwuf7txNjz3yHqqqmqEqWvy1SERBTXULHnlwM37ys1Ms65FX\nVQ3r3tyNDev3IhZVoKoahpTm4ZvnTcDI0QWWrMMM64LMsC4okRWZkwO0DJqbm5Gbm2t3MyjLxJQY\nRInnuz0VqfoMkYOf2t0My+Xm5kKW+9fVhUz6cn8DqqoCHQK8TlU11NUGsW9vvSXr0jQNf/3zv/HW\nP8sRCkYRjapQFA1f7m/AI3/ajN2f1ViyHjPRaJR1QUlYF5TIiszJEG8QCAQY4slU/xitS1YqLi7u\nN+O4e8Pn5bVQFDXl+9GogvI9hy1Z177P67Dr0xpEo8nPK4hGVTz7zDZoWvLJhFVYF2SGdUFGVmRO\nhvh20WgUwWCQs9MQUUqaqqD+zQfw+Q1l2PU9GXsWDcChv1yLWMNBu5uW9QRBgNDZ6bAAOCwKOZs3\n7Y+PuTcTCkZx4MtGS9ZFRNRdVmVOhvh29fVtl3E5Zo2IzGiqisr7vo3Df7ux7am0mgo13IzG9Y/g\ni19+HdHaL+1uYlYbd2wxOpthTxJFjJ9QYsm6mhrDnb7vcAhoaYlYsi4iou6yKnMyxLdraGgAAPbE\nE5GpwL9fQHDnW9AiwY5vKFEogTpU//U6exrWRwwcmIvRZYWQpOTDjiQ5MGx4HoaU5lmyrsFD/HCI\nqXv1FUVFURFnCiEie1iVOW29Wy8Wi+HRRx/F//3f/8Hv9+MnP/kJZsyY0en3rFy5Etu3b8e9994L\noO3GgF/84hcQBAGxWAytra2QJAnNzc247bbbMGJE1x7v3tTUBADw+/3p/VBE1C/Vr70XWmuL+Zua\nguBHr0NpaYCYw46AVC7/7hSsenIrdu86DEEA9FHpo0cX4LLvTrFsPTNmjcDmTV+Y3kQrCMCgwX4U\nFTPEE5E9rMqctoX4cDiMM844A++//z4uueQSVFVV4aSTTsKDDz6IRYsWJX0+Go3immuuwcMPP4xZ\ns2bFX3e5XHjkkUcwaNAgjBo1CrIsQ1EUDB8+HG531+f2Zk88EXUmVneE4TKSDKW5miG+E06XhO/9\n4EQcrmnB7l010DRgzDFFKCmxdgrX4mIf5s4bjzWvfNbh5lZJcsDlknDpwhMsXR8RUXf0+Z74e++9\nF9u2bcPWrVsxYcIEAMCvf/1r3HzzzVi4cCG83o6PbH/ppZfwt7/9DRMnToSqfjXDgdPZ9vCOpUuX\n4sorr+xxexjiiagzUsEwxGr3p/5ALAox15ox3f1dUXEOBuS3Pb3SbHiNFU4+dTSGDR+AdW/uwZdf\nNECWRUyZOhQnnTwSPp/1D5UiIuqqPh/in376aVx55ZXxAA8AixYtwv/+7//i9ddfx7e+9a0On//W\nt76Fs88+G9deey0+/fSrOacDgQBCoRAURcFNN92E8vJyDB8+HNdffz1KS0u73B790sbRNsWkoiiI\nRCKIxWJQFAWqqiZNvSYIQvxLFEWIogiHwxH/r8Ph6NdTZxUWFmZ0+Zqmxbe//jvQv/TfhfF3IggC\nHA4HJEmKf4mi2K9/Bz2haVp8Oxq3r6IoSTWu17MoipAkCU6nM2l75p95Har2/8d8SI1DhPf4M/p9\nL7ymaVAUBdFoFKqqdqhXsxo17iv0L31fsuvTtrnaJxw/MGPtHTmqAN+78sSMLd/MkCFDLFuWpmmI\nRqOIRCIdtrXOuJ31be10OuHo7A7io5Sqqh3qVt8P6PsJnb5Njcc7fT+bzj72mGOOseLH6FP0+tW3\neywWS9rWQNv+V5ZlyLIMSZKOivq1KnPaEuIbGhqwbds23HbbbR1eLy4uRn5+Pvbu3Zv0PYIgwOv1\nor6+vsPdvAcPtk3ttmjRIowfPx5TpkzBCy+8gKeeego7d+5MOsu59dZb8atf/arDay+++CIaG9um\nG8vLy0MwGIwXVLZSFAWhUAitra1obW1FOBxGNBrt9nL0nb4eBPVQbqQfoI07P/1gov8bAA7UVQAA\nPguJXVqv2+2G0+mELMvwer1wuVxZGUQ9hmFZqqrGt3ckEokfYHuy7Y307W/8HegHEv3L2Ab9xEv/\nUpTU0+mZEUURHo8HPp8PPp8Ponjk31lvUxQFLS0tCAQCCAaDXfsZK9pqEN7PACC+HfWDsB54jNs0\n8SQqFoshGo12CKWFhYUonHIBvO88ieDOdR1vbhUliN4BKLn8fsRiMYTDYXg8nqzcpsBXB9ZAIIBA\nIIBwONytOdMTt6WxXnX6fsH438QQWlERAACIcsMR1+l0OuP7C6/XC7fb3a19RcWXjVA1DcOGZ/4k\nK/GgrNdENBpFKBRCKBRCLBbr8vJkWYbT6TTtNDHbvnpg6iqXywWPx4OcnBzk5ORk5T4YaPtZ9X1v\nKBRCOBzu1nYUBAGyLCed9Oih3biexOOdvn/oybMFnE4nPB4PnE4ncnJy4HJl/1UgTdMQiUQQDofj\n++CePldBz1L6fthYv8Zs0dzcbLrv7QpRFOH3++H1euN/L9laxzpj5kyHLSFePwMx6+H0+XxoaUlx\n8xiA2tpajBkzJv7/1dXVAIArrrgCK1euhCiKqKurw+jRo/GXv/wF11577RHb4/f7O9xkUF9fj8bG\nxm7tIIz0s8rEYKZL3OnqvSzdXYfH44HL5YLP50NxcbHtJx3797f9DOOGjzviZ1VVjQfhSCSCQ4cO\nIRzufFo4I/2EYU/EaRooEsOvsVdW3yl3NfwaT070kx49UPh8vvhOKtt3GkaxWAyhUAiBQADV1dXd\nOugba9oY6AAknWwoioJwTU1bvX/2Wbfa6HA4kJOTA5/Ph5KSki5dbQgEdwEAfOOOXIM9MeTHL6Dh\nzQdRv+YuxGq/hODKgX/mZSic/wuIeYPQ3NyMpqYmHDx4sFvbVO/107epsQe7sxrubmDT6bVbVFQE\nt9ttS8+XEj0EABg3rvOeeP2kIxQKIRKJoLq6ulv7CgDYvy8AweGAouZ32C8nniDr69OvOCTuL3oS\nZERRhNvthizL3arl3qBpGlpbWxEKhdDQ0IAK/SS4BxJrV98vmHUK6VdzunPsE0URLpcLbrcbfr8f\nAwcOhNQHnqQdiUQQDAYRiURQWVmJSKRnU5vq+whJkiDLcoeTEKPETje9J7y7tasf53w+HwYNGpTV\nveOxWAzNzc1oaGiI11V3CIIQ366JdWvcvsZ9cGJHZnf2D8OGDevbN7bq4V2fJ1OnaVpST3ui2tpa\nzJw5M/7/kyZNwsqVK7Fw4cJ4z1dBQQGmT5+Ojz76qEvtyc3NRXNzc7z3rKioCEVFRd39seL0Pxzj\nEBXjgVaEyjo4AAAgAElEQVSSJLhcrg6XP/vCzshKDocDXq836d6Hrtq/X4EGYOSQkfFLdPoflP6H\nZvyDMh5UjJdHu3Iw7c7JSV8hSRJyc3O7fSnPLNykGoYlyzJcLhecfj8kSYL/mGOyIrikQ3CIyD/j\nGuSfcQ00TUv6efx+f492yonh3GyYirGG9drVD+b9mSAIcDqd8fufekKJHoKqqRg0KL/DVRezg64e\njFwuV9L+IpuDTE8IggC32w23253WfNX6PlffF+t1nGq/oJ/U6PXb1/cLnUm3doGOJ5bGDiiz7WsM\nocbQ399q10iSJOTn5/e4hvXa1XObvl3NhhYbt6+x87C7+wdj5kyHLckxJycHAwYMQHl5eYfX9+3b\nh0AggClTUk81FgwGOwQPn8+H73//+0mfC4fDaG1tTXr91ltvxa233pr0+sMPP2zZ9JJ6Lw9lloCv\nLu1niqZpOFxbi6IMj4vvK/SdWHcE2i8f96cDtaZpqN31PnJzvHANPT7t5RmH/fSFy+19kUNwdGvG\nsp7QNA0HDx60dFx8X2AcP07JNE3Drl27MK6HVwj1K0b6VX6ylt6Zmu7JVnc0NzdbkjltOzWbO3cu\nnnvuuQ5nOs888wycTicmT56c8vu8Xm+HS6mapuHQoUMdPvPll19iy5YtOPXUU7vcnubm5qPuplY6\nskgkAqWHw6qo/4pEImjcux3RmuT7d+joFYlETDuP6OgWiUR6NSBS9rMqc9oW4q+66ips2LABixYt\nwpYtW3D77bfjl7/8JRYtWgSPp23qsb179yIUCgFo+4GfeOIJhMNhvP3223j++ecBAP/85z8xcuRI\nrF69GoFAAJs3b8a5556L3NxcfPvb3+5ye0KhUMZ7aajvicVicLB3iRLEYjH2OlKSWCx21A2NpCNj\nXVAiqzKnbSF+1qxZePnll7FmzRpMmzYNy5Ytw09/+lMsX74cQFsP++jRo3HhhRcCADZs2IBf//rX\niEaj2Lt3L1asWAEAOP3003HllVfi4osvRm5uLmbMmAFRFLFmzZpu3fXLM2UyoygKxF4aS1jfGsSn\n9VWoDQd6ZX3Uc4qi9OsxptQziqLw5I6SsC4okVWZ09ZTw3nz5qG8vBxVVVXIz89HTs5Xj8EWBAE3\n3XQT5s6dG//svHnzkpYhiiLuv/9+LFmyBDt27MDgwYMxceLEbo+/ZYgnM70R1ipbGvHzd1fjX5Xl\ncIoiIkoM0waOwu9O+hZG+jkWPxsxxJMZhjUyw7qgRP0ixANtNyYOHTrU9L3f/e53XV7OsGHDMGzY\nsB63g5e7yIyqqhAyGNZqQs045x/3o761BYqmIaK2jb/feLAc8176I9ae92OU+vr3A4T6okzXBfVN\nqqry5I6SsC4okVWZk1XVTtM0/pGRKQGZm1Vlxfb1aIwEoSRMZaVCQyAaxu8//GfG1k3p6T9z7ZCV\n+tMsTGQd1gUZWZU5mVqJbPTcnq2IpnhYj6Jp+Mfn23r8pDwiIiLqvxjiDRiWyIyGzNVFMNb5k+Ui\nagyK1v0nclLmcW9BZngcITOsC0pkRU0wxLcTRbHLj3+mo4cgCBnd+Q7PLej0/YFePyQHb4jKNoIg\nADwoU4JM7y+ob2JdUCKrMidDfDun04lIpPNeUTr6iKIINcVwFytc/bVT4ZHMn8DnEWX86LiTM7Zu\n6rlM1wX1TewMIjOsC0pkVeZkiG8nyzKi0ajdzaAsI4oiNDVzPSgXjjkBZw47Fl6p41RTXsmJGYNH\n43sTTsrYuqnnGOLJDOuCzLAuKJFVmZNzKrZzuVx8XDYlEUURipq5HhSH4MAfT/0vvHXgMzy64x3s\nD9RhsDcP/33cTJw1fAIcAs+zs1FbXfCgTB2JoohYLGZ3MyjLsC4okVWZkyG+ndvtRjgctrsZlGUk\nScr4ZVBBEHD6sPE4fdj4jK6HrCNJElReHqcEkiQxrFES1gUlsipzspuvnSzL/COjJA6HI6PDaRL9\np2Y/3j+0t9fWRz3jcDh4eZySsC7IDOuCElmVOdkT387tdiMUCtndDMoyDocDai9O8VgTCvTauqjn\nHA4HZ5ugJAxrZIZ1QYmsypzdCvGVlZVYu3YtPvjgA1RXV8PlcmHEiBGYNWsWTjvtNDidziMvJEv5\nfD4EAgxQ1BGfskdmWBdkhnVBZlgXlMiqzNml4TTbtm3DBRdcgOHDh+PGG2/Ezp07AQBNTU14/fXX\ncd5552HYsGG45ZZb0NzcnHaj7JCbm4vW1lbOUENEREREGWNV5jxiT/zf//53XHXVVbjyyivxm9/8\nBscee2zSWWVrayv++c9/4rHHHsO4cePw+eefw+12p9Ww3pabmwsACAQCyM/Pt7k1RERERNQfWZU5\njxjiJ02ahD179sDv96f8jMvlwrnnnotzzz0X27dvhyj2vSdM+nw+AAzxRERERJQ5VmXOIw6nGTt2\nbDzAr1279ogD8SdOnAhZNn8CZTbTz4r66nAgIiIiIsp+VmXObk0xuXPnTvz4xz82fa+yshKVlZVp\nNcZO+gZtamqyuSVERERE1F9ZlTm7FeK///3v4+2338Zf/vKXDq/v2LED06dPx8GDB9NqjJ28Xi8A\nIBgM2twSIiJ7BAKtqKsLIhbjdHhERJliVebs1hSTubm5ePbZZ3HaaafhhBNOwHHHHYf169fj/PPP\nxw9+8AN8/etfT6sxdsrJyQEAtLS02NwSIqLetffzOvzjhR2oOtgMURQgCAJmzBqBM88eB0niMwGJ\niKxkVeY84t45EAh0eOz8pEmT8Nvf/hYXXnghVq5ciXPOOQe33XYb7rzzTjgcfXdnzxBPREejPbsP\n49E/bUbFgUYoiopIREFrawwbN+zF449sgdqLTyzuD/Qb1oiIUrEqcx6xJ/6RRx7BL37xC0yaNAkn\nnHACvv71r2Pq1KmYMGECrr32WjzzzDOYP39+Wo3IBvoG5XAaIjpaaJqGv/9tO6LR5OEz0aiKL/bV\nY/euGowbX2JD6/qm0tJSu5tARFnOqsx5xBB/xRVX4JhjjsGHH36IrVu34uWXX8YXX3wBoG1n9fLL\nL6OysjIe8PvizDQAUFBQAACora21uSVERL2j6mAzAs2tKd+PRBRs3vgFQ/wRaJqGXZ/VYMP6z3G4\npgW5uS7MPGUUJk4aDFHsu1eoiSgzrMqcRwzxBQUFmDdvHubNmxd/rba2Nh7qt27dirvvvhu7d+/G\nBx98gClTpqTVILvk5ubC5/P16Rl2KHM4oIDMaH28MlpaInA4On8kfHMnIZ/ar2Y8ux3btlYiEmkb\nelpfF0LV37Zj0zv78MOrpkOS+t6zU8h6mqYlPSyTjk5WZc5u3diqKywsxJw5czBnzpz4a01NTX22\nF15XWFiIuro6u5tBWUZ0OKAqnK2DOnL0g7ooKs7pdCYahwMYUpr6QX8EfLy9qkOA10UiCg4caMQb\na3fj7HPG29Q6yhaiKEJRFEhSj2IX9UNWZE7LrvP5/X54PB6rFmeLgoICHD582O5mUJZxuVxobWVv\nJHXUH+piwAAPRo7KT9kbL4oOzDx5VC+3qm9Z9+aepACvi0VVvPvOPt4cTPB6vbznjjqwInNysJ7B\noEGDUFVVZXczKMu43R6Ew50/qZiOPm63G+Fw2O5mpO3iS78On88JSf7qcCAIgCyLOOuccRg4KNfG\n1mW/wzWdzy4RjagIh6O91BrKVj6fD4FAwO5mUBaxInMyxBsMGjSIY+IpidvtQjjct3tcyXr9JcTn\n5bnx05tm44yzjkFxcQ7y8tw49riB+OFV03HK7DK7m5f1XO4jDY/Q4HRyTPzRLicnh1NYUwdWZM5u\nD86KRqOoqqrCsGHD0NLSgkAggIEDB6bViGwxePBgVFdXQ1XVPj3nPVnL4XBA1fr22GeynsPhgKb1\nj2ESHo+Mb5w+Bt84fYzdTelzpk0fjrfe2GN6b4EgAOOPLeGNrQRRFKGqPI7QV6zInN3+rj179mDk\nyJEAgL///e8499xze7TibDRo0CCoqorq6mq7m0JE1Ov2f9GAA/sb7G5GnzLzlFHw+Zym9xU4XRLO\n+eaxNrSKiLKdFZmT3c0GgwcPBgCGeCI6KgWaW9HUxKFj3eHxyLjupyfj+K8NgiQ54HKJkCQHysYU\n4tr/mYXiEj7BlYiSWZE5OdeRQWFhIQA+8ImIiLrO53Phsu9OQTgcRVNjK7w5Mnw+l93NIqIsZkXm\nZE+8QV5eHoC2Oe+JiIi6w+2W4XJLaKjnMYSIOmdF5mSIN/B6vQDAO8iJiKhHKr5sxM5P9tvdDCLK\nclZkToZ4g5ycHADgAxmIiIiIKGOsyJwcE2+gb1D2xFN/pqkqwp9vgRpsgHPIsZCLRtjdJCIioqOK\nFZmTId6Aw2movwtsfRGH/rwYamsLBEGEFmuFe/Q0DF70V0j5Q+xuHhER0VHBluE0fr8fl1xyCQBg\n1KhROOuss3q88mzjcrkgCAJCoZDdTSGyXMv213DwT5dCaTwELRyAGmqEFg0jtHsj9i+bATXUbHcT\niYiIjgpWZM5uh/jS0lKsWrUKAHDKKafgN7/5TY9Xnm0EQYDH4+GYeOp3NE1D9V//B1rEZGehxqC0\n1KHxnSd6vV1ERERHIysyJ29sTZCTk8PhNGRK0zS7m9BjscP7EGuoSPm+FgmiacPjvdii/qMv1wVl\nDuuCzLAuyCjdzMkQn8Dn8yEQCNjdDMoykighFovZ3YweUyNBwNH5LTBqhCev3SWKYp+uC8oMUerb\n+wvKDFmWWRfUQbqZ84ghXtO0tB4J29d4vV6OiackoigiGo3a3Ywek4tHA5qa+gMOEZ6xM3uvQf1E\nX68LygzRwbqgZJIksS6og3QzZ5dC/PTp07Fz584er6Qv8Xg8DPGURJT69kHZ4fQg79T/hiB7TN8X\nJCfyz76+l1vV9/GgTGb6+v6CMkOWZdYFdZBu5jxiiBcEAdOmTcNJJ52EdevWmX6mtbUVjzzyCMrL\ny3vckGzhdDrR2tpqdzMoyzgcDqhqJz3ZfUDRRbfDM3YGBFfOVy+KTgiyGyULV8A19Hj7GtdH9Ye6\nIOuJrAsyIYoi64I6SDdzdinEr1q1CldffTXOOussPPnkk/H3/j979x0fR33nj/81datWki1ZcsVF\nLtgGg021g20MAewkhJ4jl3AJJblgDkJI+YUjiclBwvcuB0lISE+4IwkhcKQQCB1ssAMYbKpxwQV3\nq9gqqy1Tf39Is2yTLGlnd1ar1/Px8APQLvt5a/zZz7zmM5+ZiUajuPPOOzF16lR8+ctfrojOyZ0y\n5SMKw79fiIoP47/8BMZd/zDCp1yKwKylqD3nekz+zjuo/tC/eF3esCQIwrDvF+Q+oQLGC3If8wVl\nK7RPDOhhT6Io4rbbbsO0adNw9dVXY+vWrVBVFT/4wQ8gSRJuvPFGXHvttaiurh5yIeVCFEVePU4V\nSxBFhOacjdCcs70uhYiIaEQrNHMO6omty5cvx7Jly3D77bcDAP7rv/4L1157beqpU5XAtm2IIm/a\nQ5Wt+51nIEgygrOWeF0KERHRiFRo5hzQ/7lr1y6sXLkSkydPxs6dO3HXXXfhmGOOwWOPPQZN04bc\neDmyLAuCIHhdBpUZG5V1dsbWYrDinV6XMexVVq8gt1TaeEHu4Fl+ylZo5jxqiLcsC01NTVi3bh3u\nu+8+bNq0CV/84hfx0ksvobOzE4sWLcKuXbuGXEC5sW2bIZ7yYr+gfNgvKB/2C8qH/YLSFZo5BzQT\n/9e//hUbNmzApZdeCkmSAACNjY14/vnnMXXqVJx22ml49dVXh1xEOTFNM/U7Ejlsy+IyK8rBfkH5\n2BaXZVIui+MFZSk0cx61N4miiBUrVuQ9UgiHw/jzn/+MSy65BIsXL8bOnTuHXEi5SCaT8Pl8XpdB\nZcY0LR7cUQ4e9FM+psV+QbkMw2C/oAyFZs5BXdiajyRJuPvuuzFlyhQcOXIEU6ZMKfQjPZVIJOD3\n+70ug8qMaZmQ5YK/LlRhTMsqer8w450wu1ohVzdATL/HP5Ut0+R4QbkMw2C/oAyFZs6j9qbt27ej\nsbERoVDfOw9BEHDTTTfBtm1s2rQJ06dPh6IoQy7KS7quD9vaqXhsizPxlKuY/UJv2Ynm396A2DtP\nA5IMWCbC8y9A/T/fBTkypihtkjtsy+Z4QTks7kcoS6GZ86jLaV577TVMmzYNq1atwrZt2/os4vHH\nH8cnPvEJLFu2DKZpDrkgr2maBlVVvS6DygzXMlI+xeoXettuvL/qFHS/+XfYRhJ2shu2nkDXqw9h\n96qTYUYPu94muceyTI4XlMM02S8oU6GZ86i96bLLLsOjjz6K1157DTNnzsT48eNx7rnn4pOf/CQu\nvvhiLFy4EJFIBJ/61Kcwffp0bNmyZVgvR+FMPOVjcgaF8ijWzFrr/90CK9YB2FlP8jMNmJ0tOPLE\n911vk9zDGVfKh9fQULaiz8QDwIIFC/DII4/g/fffx6233oopU6YgHo9DVVWcccYZePDBB7F3717c\nfvvtw/6prfF4HIFAwOsyqAzx1mCUj9v9wrYsRF95CLDzn9G0jSQ6Vv/S1TbJfRwvKB/2C0pXaOYc\n1BUW9fX1uOqqq3D11VcPucFyZlkWOjs7UVNT43UpRDRC2XoCtmX0+x4rwQd1ERENZ25kzgHNxG/Y\nsAGzZ89GIBDA2LFjcdtttw3rde99iUajsG172J9NIKLhS1ADEIP9D+pK3eTSFENEREXhRuYcUIi/\n7rrrIAgC/vu//xuXXXYZbrvtNnzve98bcqPlqr29HQAY4onIM4IgoPbD10NQ8p9iFXwh1K74Somr\nIiIiN7mROY+6nMa2bWzYsAHPPvssFi5cCACYP38+7rjjDnzta18bcsPlqLW1FQAwevRojyshopGs\ndsVXEHvnaSTe3wA72Z36ueALIXT8ckQWftrD6oiIqFBuZM6jzsTbto1kMolx48alfrZ8+XJs2bIl\ndRRRKY4cOQKAIZ6IvCUqPkz46lNouOJH8E1eAKlmHPzTF6Lxmnsx9gv3Q+Bt6oiIhjU3MueAL2xt\nbW3FMcccA0EQUFVVBaDnqtpKugjUOSoaNWqUx5UQ0UgnyAoii65AZNEVXpdCREQucyNzDjjEn3zy\nyRgzZgxOPPFEzJ07FwCwd+9eNDY2Vswtk5wzC7W1tR5XQkTUI/7eSxAkBf4pC7wuhYiIXOJG5jxq\niBdFEQcOHMDGjRuxYcMGbNiwAQ8//DAA4JRTTkFNTQ3mz5+P+fPn4ytf+QrGjBm+jwOPxWIAgFAo\n5HElREQ9zK6W3n9jiCciqhRuZM4BzcQ3NjZi+fLlWL58eepnhw8fxuuvv54K9o888gguv/zyYR3i\nDx06BEVREIlEvC6FiIiIiCqUG5lzUA97Sjdq1CgsW7YMy5YtG3Lj5ebQoUMYM2YMRF40Rmksy4Io\nsE9QJsuyKmYpIbnHskxeeEw5TNNktqAMbmRO9qg0Bw4cQGNjo9dlUJmJJxLwB/xel0FlJpFIFPS4\nbKpM8UQCfj/HC8oUjUYRDoe9LoPKiBuZkyE+TXNzM8aOHet1GVRmEvEEAtwpU5Z4PM6wRjkSCY4X\nlIshnrK5kTkZ4tO0tLSgrq7O6zKozGhaEqrq87oMKjOapkFVVa/LoDKjJZNQfRwvKFM8HueZO8rg\nRuZkiO9l2zaam5uH9YW5VBymZUGS+FWhTJZlQZIkr8ugMmNZFiSR/YIymaYJWR7yZYhUYdzKnEwm\nvTo6OqBpGkM8ERERERWNW5mTIb5Xc3MzAKChocHjSoiIiIioUrmVORnie3V2dgIAqqurPa6EiIiI\niCqVW5mTIb5XR0cHAIZ4IiIiIioetzInQ3wv56ioqqrK40qIiIiIqFK5lTkZ4ns5G7SQx98SERER\nEfXHrczpaYjXdR0//OEPsWzZMlxwwQVYs2ZNv++3bRv33HMPrr322pzX1qxZgwsuuADLli3D3Xff\nDU3TBlWLc2qjpqZmUP8fEREREdFAuZU5PQvx8XgcZ5xxBr7+9a+jqakJlmVhyZIl+NGPfpT3/Zqm\n4corr8TKlSvx1ltvZbx22223YcmSJdB1HdOnT8e///u/45xzzoFpmgOux9mgnIknIiIiomJxK3N6\n9uSBu+66C++++y42btyIGTNmAAC++93v4pvf/CY++9nPIhQKZbz/0UcfxV//+leccMIJGeF88+bN\n+Na3voW7774b1113HQDgpptuwrHHHotHH30U559//oDqiUajUFUViqK49BsSUSUr1dMXxWANBJlP\nhiUiqhRuZU7PQvwDDzyAa665JhXgAeCaa67BzTffjCeeeAIXXXRRxvsvuOACrFixAtdeey02b96c\n+vlDDz2ESZMmZSyxmTFjBs4880zcf//9Aw7xuq6PyABvmiY0TYNhGDBNE5ZlwbbtjPcIgpD6I0kS\nJEmCKIqpf4qiCEEQPPoNim/06NFF/XzbtlPbP5FMwrYsdHR0ZPxdpP+dCIIAURQhy3LqjyRJFf13\nMBS2bcOyLFiWldq+zp/sPu70Z0mSIMsyVFU96vYcNWpUMctPCc48oyTtDIRt2zBNE7quw7Ks1JiR\nPW44fTR9rHD+OGNJpXKzX9i2DV3XoWlaxrZ2pG9nZ1urqgpR5OVu2SzLyui3zjjgjBMOZ5um7++c\ncbaQfpuedUYKp/86290wjJxtDfSMv4qiQFEUyLI8IvqvW5nTkxDf3t6ON998E3fccUfGz+vq6lBb\nW4udO3fm/D+CIMDn8+HIkSMZg+QLL7yApUuX5vylNzU1YePGjTmfs2rVKtx6660ZP3v77beRTCbh\n9/sB9Bwh+Xy+sg71pmkiHo8jmUwimUwikUhA1/VBf44z6DtB0Anl6ZwddPrg5+xMnH8HgL2H9wEA\ntsSP/shxURTh9/tTR6LBYBA+n68sd+6B3n4B9GwLZ3trmpbawQ5l26dztn9XVxdEQUQsFkvtSLJD\nj2VZqQMv589glo4BgHjgAFRVhdnRgXA4DEkqv8fEm6aJ7u5uRKNRxGKxgf2O+3r6IIJbACDVn52d\nsBN40rdp+kGUaZowDAO6rucE/aO1pSgKQqEQQqEQAoFAwdvUsmy8+84hrH1hJzo6EhhdF8IZi6eg\naUZdQd8TZ8cajUYRjUaRSCRSv+u+fVEAgKS09/n/Z29LZxunjxvOuJD+z+wQOpC2HKqqpsaLYDAI\nv99flmMFAAQCwYz/NgwjNT7H43HE43EYhjHgz1MUBaqq5p00ybd9ncA0UD6fD4FAINV3y3W7mqaZ\nGnvj8TgSicSgtqMgCFAUJeegxwnt6e1k7++c8eGoY0IeqqoiEAhAVVWEQiH4fL5Bf0ap2bYNTdOQ\nSCRSY/BQfncAqXDujMPp/Tc9W3R1dQ187M0iSRIikQiCwWDq+1Ku/diRnjkL4UmI7+rqAgDU1tbm\nvBYKhRCPx/v8f9va2jB9+vTUf3d0dGDu3LmD/pzs93Z3dyMY7Bl8u7u7cejQoUENEOmco0onmDmD\nhSN70HVmWQbbRiAQgM/nQzgcRn19vecHHbt39/wOMyfNPOp7LctKBWFN03Do0CEkEokBt+UcMLyn\nqXkDRXb4TZ+VdQblgYbf9IMT56DHCRThcDg1SLkxaGwTYwCAsWPHFvxZ/enoeheapiEWi6G5uXlQ\nO/30Pp0e6ADkHGyYpolES0tPf9+yZVA1iqKIUCiEcDiMMWPGDOhsQzS2FQAQnnn0Plio9LacYNzd\n3Y329nYcOHBgUNvUmfUTRRH19fUIBIL4n1+9ih3b26BpPX20pbkbO95rw7z543DJZcejo6MDLS0t\ng2rH4fTduro6+P3+1N+fqR8CAMycWfwnVw+0LWfbxuNxaJqG5ubmQY0VQM8BgyCKCIbjGeNyvrMC\nzuxsekB2xouBhIvsgxNJkuD3+6EoyqD6cinYto1kMol4PI729nbscw5Mh8AZD9LHhr4mhZyzOYPZ\n90mSBJ/PB7/fj0gkgoaGBsiyZ4sJBswZZzVNw/79+wd90w2HM0bIsgxFUTIOQtJlT7o5M+GDDcbO\nfi4cDqOxsbGsZ8cNw0BXVxfa29tT/WowBEFIbdfsfpu+fdNzRPZE5kDHBwCYOnVqRuYshCffAGcm\n/ciRIxk/t20b7e3tecO9o62tDR/60IdS/z169OiczwF6ZvsHelrT7/cjkUikjooaGhoKehSu88VJ\nX6KSvqOVZRk+ny/j9OdwGIzcJIoigsHgkDvx7t0mbACTx01OnaJzvlDOFy39C5W+U0k/PTqQnelg\nDk6GC0mSEAgEEB7kwUK+cNPXMixFUeDz+aBGIpBlGZEZM8oiuLjBMAwkkkn4e2fVBEGAqqpQVbXf\n8asv6f1XVVWsfm47tr/XCl3PDOiaZuKNDfsxfXod5p04DlVVVWV5FsVN6dt2qEz9ECzbQmNjbcZZ\nl3w7XScY+Xy+nPFiIEGmlAdChRIEAX6/H36/f0j91uGMuc5Y7IwNfY0LzkGNE0YrZVzIxznbXOjZ\nM2fsTZ+Ayrd900Noeugv5xBeKFmWUVtbO+Q+7PRdJ7c52zXf0uL07Zs+eTjYZUDpmbMQniTHUCiE\n2tpabNu2DcuXL0/9fMeOHYhGo1iwYEGf/28sFkM4HE7994QJE/DOO+/kvO/111/H0qVLc36+atUq\nrFq1KufniUTCtQvVnFkeKi4BH5zaL5ZEIoHOzi5EInwIGPDBIDYY0bSgWykSiQSi0WgqxBcqfdmP\nbdtY8/yOnADv0DQTzz2zHSfMH89xZhBEQXRlp9mfRCKBrq5OVFUV9y5ne/d04JWXd6OrI4Gx4yM4\n9fRjUF1d3N+tP+nrxymXc4ZuwoQJQ/r/nTNGzll+cpczmVrIRMFguZU5PTs0W7FiBR588MGMI537\n778fPp8PJ5xwQp//XzAYzFgms2LFCqxbtw579+5N/cy5681pp5024HpisVjJ7jZBw0cikRj0Uieq\nfIZhQCrSzJahW+iO9n86uLUlWpS2qTCJRAJGEccLy7Lxh99txE/uXoeX1+3GO28fwvPPbMf/u+1Z\nrP6bYHIAACAASURBVH9lT9HapcIYhjHizrZT/9zKnJ6F+JUrV2Lt2rW48sor8cILL+Db3/42vvWt\nb2HlypWp2ZItW7agu7sbQM/a95///OeIxWJ47rnn8Ic//AEAcO6556KpqQkrVqzA3/72Nzz00EM4\n66yzMHXq1AHfmQYYuXenof5ZlgVRqtzTkDQ0Pf2iOLOOkixCEPs/a6GqDATlyLKsoi5bWPPcdrz1\nxkHo+gdLgQzDgmFY+PNDb2Pvno6itU1DZ1kWz1JQBrcyp2fp5PTTT8fjjz+ONWvWYPHixfjP//xP\n3HzzzfjOd74DoGcN2KxZs3DJJZcAAP7xj3/grrvugiRJOHjwIO69914APevZn3nmGUyZMgUf+9jH\ncOmll+KUU07BE088MeirwCt5zRgNjW3bEFA5y0DIHT39ojhEUcDcuY3oa/WRJIk46ZSJRWqdClHM\n8cKybDz/3Hboev6ZfsMw8fwz7xWlbSqMbdsVtZyQ3OFG5vR0Ouecc87Btm3b0NbWhkgkkhG6BUHA\nrbfeirPOOgsAcN555+G8887L+zkTJ07EX/7yl9QTsKqrqwddy1Bvn1TOLNvCxpa9aEtEMSVSh+k1\nY7wuiYgG4LyPzMLWLS1IJDLvkCWKAgIBGUvOnOpRZeSVzs4EdK3vpTq2DezcebiEFRHRULmVOT0/\nJ+vcUi2fb37zm4P6rKGE90q1Zt82fOnFB9GlJSAKAnTLwrTqevxk6ScxtbrO6/KIqB919SGs/OIi\n/N8Db2Lvng5IsgjTsDCtaTQu/sTxCFeV/72myV2yLMKy+t/xyzLPJhONJJ6H+HIhCELFXMC4/tAu\nXPnM/yJhZj6AaNPhAzj/bz/Gsxd+CWOCvNvKQAiCABuVd5aGCtPTL4qroaEK116/CJ0dCUSjSUSq\n/QiHGd7LWTHHi3DYhzFjwjhwoCvv67Is4sT544vSNhVGEIQhPc+BKpdbmZOH7b1EUayYL9l/rH80\nJ8ADgA0bMUPDrzat9aCq4asSl1qRC0rUL7SOZgTFOAP8cFHEfvHRj8+GouTutgUBUFQJixZPKVrb\nVBjuRyidW5mTIb5XpYT4Li2BN9v6fuqeZpl4ePvGElY0vAmCULKwRsOHIAgl2ym///ob2L5+fUna\nosL09Iviff70mfW4/NPzEQwp8Plk+HwyFFXCmIYqrLxhEaq4zKoslXK8oOHBrczJ5TS9ZFmGYRhH\nf2OZS5g6JEGEgb47RzLPLD3lJ4oiLA6+lEUURe6UKUfPeFHcyaC5xzVi9pwG7Njehu6ohvoxYYwb\nX9yHS1FhKmWSkNzjVuZkiO9VKSF+tD+EsOJD0sz/uwgATqzn7ekGShRF2Ee5mIxGHu6UKZ9SHdyJ\nooBx4yOQRBE+P3fj5Y7jBWVzK3NyOU2vSgnxoiDiC3OXICDnf4iAX1Jw3fFnlriq4asUM2s0/HAm\nnvLpOegvzXixa8cRbH+vrSRtUWEY4ikbQ7zLFEWBrlfGMpPPzf0Qzp04GwFZgdj74BFFlOCTZHxt\nwbk4uWGytwUOI5IkcfClHOwXlA/7BeUjSVLF3P2O3OFW5uR5uF5+vx+JRMLrMlwhCiLuXvJP2Ni6\nB7/d/DIOxjoxq7YRV8w6DZMjo70ub1jhTpnyYb+gfCRJgsl+QVkY4imbW5mTIb6Xz+dDMpn0ugzX\nCIKA+fWTML9+ktelDGuyLHPwpRzsF5SPLMuw2C8oS6Us1yX3uJU5uZyml6qq0DTN6zJct2bfVqw7\nsN3rMoYtQRC8LoHKEPsF5cN+QfmwX1A2tzInZ+J7BYNBxONxr8twXdI0+rxTDRERERGVlluZkzPx\nvZwNynWuRERERFQsbmVOhvhewWAQACrm4lYiIiIiKj9uZU6G+F5VVVUAgK6uLo8rISIiIqJK5Vbm\nZIjvFQ6HAQDRaNTjSoiIiIioUrmVORnie/n9fgCoyItbiYiIiKg8uJU5GeJ7BQIBAAzxRERERFQ8\nbmVOhvheDPFEREREVGwM8S4LhUIAgO7ubo8rISIiIqJK5Vbm5MOeekUiEQC8Ow2NDIIahCBKXpdB\nREQ04riVORnie3EmnkaS0JyzvC6BiIhoROJMvMuc2/0wxFMls20b6w5sx++3rkdbohvz6ibgilmn\nYXy4xuvSiIiIRgS3MidDfK+amhqIoojm5mavSyEqCs008Jmn78WrzbsRMzQAwCuHduJXm17E/1t4\nES5umu9xhURERJXPrczJC1t7ybKMuro6hnjKy/a6ABd897XH8cqhXakADwCaZSJhGvj/1v0JW44c\n8rC64cmuiJ5BbmO/oHxsm/2CeriVORni04TDYV7YSjlkSYZpGCVpa/aosZhR0+D658YNHb/b8goS\nZv7fQ7MM/PztNa63W8kkSYJpmF6XQWVGkks3XtDwoSgKdF33ugwqI25kTob4NKFQiGviKYesyDDM\n4oc1KxnDmGQXJvr8rn/27q7DEAWhz9dN28Yrzbtcb7eSyYpSkn5Bw4ssl2a8oOFFVVWGeMrgRubk\nmvg0oVAIsVjM6zKozMiSBEMv3sya0dmMlt/fhOir/weIEmCZCJ3wEdR/8i4ooya40kZAVmBYVv/v\nkVRX2hopevoFd8qUSZbkoo4XNDwpigJN01J3JSFyI3NyJj5NVVUVl9NQDllWYBjFCWtmtA27v3Uy\nutb/EbaRhK3FYBtJRF/7C3Z/6yQY7QdcaWdiuBaNwUifrwckBZ+YscCVtkYKWZZhcNkEZWG/oHxU\nVYWmaUd/I40YbmROhvg01dXV6Ojo8LoMKjOKqkAr0ozr4b9/D0ZXC5C9Vt02YXYfQdufv+1KO4Ig\n4NZTPwa/pOS8Jgkiqn0BXNZ0kittjRSqqhatX9DwpaoKNJ1hjTL5/X4kEgmvy6Ay4kbmZIhPE4lE\nGOIph6IoRTs93rH6V4CRzP+iZaBz3X2u3dHgrImz8MPFn0CdP4yw4kOV4odPknHSmEl45KMrUaW6\nvxa/kvX0C4Z4yiQrCmfiKYfP5+NMPGVwI3NyTXya2tpatLe3e10GlRlREGDZ/a8nHyor3tnv67YW\nBywTkNz5qq6YPBfnTpqNjS170KHF0VRTj2OqRrvy2SONIAi8ZRzlEAUR9lGuP6GRRxRFWOwXlMaN\nzMkQnyYcDiMWi8GyLIgiT1JQ8SmjJ0Fv3t7n61KkAYJLAT71maKIJkWG5B+FKgZ4IiKiknMjczKp\npvH7e5YTcN0alUrteTdBUIN5XxOUAGrPvaEo7b796l/wxssPFeWziYiIqH9uZE6G+DThcBgAeK94\nKpnqpVcjeOyZEHyZtx0TfCH4p56M2nNv9KgyGolUnwS/nydoiYiKzY3MydE6zejRPUsLWlpaUF9f\n73E1NBIIooRxN/wJXa/8EUee+AGMtvch14xDzTnXI3LaJyHIuXeTISqWpul1XpdARDQiuJE5GeLT\nOBv0yJEjHldCI4kgSoicdjkip13udSk0Qtmmgejrj6BzzW9gxTvhn7EINcu+4NrDxoiIKJMbmZMh\nPo1zaiMajXpcCY1UW956GoaewJz5H/W6FBohzHgn9t6xDNrBbbCTPWNffMcraH/yh2j8/H2oWnCB\nxxUSEVUeNzIn18SnqaqqAgA+tZU803JgK4607va6DBpBDv3m80ju25QK8ACA3qcHH/zZp6G37fGu\nOCKiCuVG5mSITzNq1CgAQGtrq8eVEBEVn9nViu6Nf+3zgWO2ZaD9mXtKXBURUeVzI3MyxKdxLixo\naWnxuBIiouJL7n0bguzr+w2GhvjWF0pXEBHRCOFG5mSIT6OqKsLhMA4fPux1KURERSf6QrCP8jRi\n0V9VomqIiEYONzInQ3yWcDjMC1spL9u2vS6BytBw7he+yfMhqoE+Xxd8YVQv/mwJK6ocw7lfUPGw\nX1C6QjMnQ3wWVVWhaZrXZVCZkUQRpml6XQaVGXGY9wtBlFB/+Z0Q8gV5WYUyehLC8y8sfWHD3HDv\nF1QckiSxX1CGQjMnbzGZxe/3F/QIXKpMoiTBMAzIMr8y9AGpAvpF5PTLAdtGy/03wtKTEAQRtp5A\n8Ljz0Hj1r/nAsSGohH5B7pNlmf2CMhSaOdmTsjDEUz7OTpkonVgh/SKy8JOoOu0TSOxYDysZhW/8\nXMg1jV6XNWxVSr8gdzkhnsjBEO8yLqehfHh6nPKppGVWgihBr54GUZIg14zyupxhjeMF5cPlNJSt\n0MzJNfFZeKRM+YiCAMvq/y4eNPIIFdYvtv3jJWx5ca3XZQx7oiBWVL8gd4gi+wVlKjRzMsRn4ZEy\n5SOIIu8qQDnYLygfQRTYLyiHyPGCshSaORnis0iSxCNlyiGAO2XKJYC3jKNcHC8oH0Fgv6BMhWZO\nhngiIiIiomGGIT6LZVkQBMHrMqjM2ODsCeVir6B8OF5QPpyFp2yFZk6G+CymaUKSJK/LoDJj2zYP\n7igX+wXlw35BeXA/QtkKzZwM8VkY4ikv24Yo8utCmWz2C8rDtsF+QTk4XlC2QjMn7xOfxbIsfsko\nh8UZFMqi1E1GwNfB8YJyWDaXZVIuLtelbIVmTob4LLquQ1H4mHHKZFs2z9BQBt/E4+AD17lSLtvm\neEG5LMtiv6AMhWZOhvgsDPGUD8/QENATzt7YuB/PP7sdra3d8PtknHLaJHxoyRQEg6rX5VGZsEyO\nF5TLNE32C8rAEO8ywzAY4imHZXOnPNLZto0Hfv863n7zIDSt5+EcWtLE889ux/pX9uCGL52BcJXP\n4yqpHNgVNF50d2vYurkFhmFi0jG1aGis8rqkYYuTQZSt0MzJEJ8lHo/D7/d7XQaVGcs0Icv8uoxk\n725qzgjwDsOw0NWZxJ8ffhuf+pcFHlVH5cSsgPHCsmw8+sgm/OPF9yFKAmD3HMiOG1+Nf7nqJITD\nPGAdLMMwhn2/IHcVmjl5SJglHo8jEAh4XQaVGZNrGUe8F57fkRPgHZZlY9Pbh5BIGCWuispRJax9\n/vujm/HSut0wDAta0oSmmdB1C3v2tOMnd6+DafLJ5oPFu99RtkIzJ0N8Fk3ToKpc20q5eFeBka2t\nLdbv66IkoKszUaJqqNwN5/EikdCx9oWd0PMctFqmjY6OBDa/2+xBZcPfcO4X5L5CMydDfBrbttHd\n3Y1wOOx1KURUZqqOst7dNG2EQpwAoOFv+3ttkKS+44GWNPHmxv0lrIio8riRORni08TjcZimiaoq\nXrhDRJkWLZ4MVc1/KlwQgClTRyHIEE8VwDKPfttU3eByGqJCuJE5GeLTdHZ2AgAikYjHlRBRuZl3\nwjiMn1ANRckcNgUB8PlkXHjJXI8qI3LXpMm1MPsJ6aoqYdaxY0pYEVHlcSNzMsSnaW9vBwDU1NR4\nXAkRlRtJEnHNF07FkmXTEAgokCQBkiTguOPH4oabzkB9PZfhUWWorvbj2NljIMv5I4Isizhh/vgS\nV0VUWdzInLzXUZqOjg4AQHV1tceVEFE5kmUJ55w3Ex8+dwaSSQOKIvW7dphouPrEJ0/Ar37+Cvbt\n7YCum7BtQPVJkGURn7/29D6XlhHRwLiRORni0zinNhjiiag/giCgY99uRDu7MO3EE7wuh8h1qk/G\nv153Ot7fdQRvvr4fmmZiatNoHD9vLGSZAZ6oUG5kTob4NN3d3QCAUCjkcSVEVO72vrMJh9vaGOKp\nYgmCgMlTRmHylFFel0JUcdzInDwPnKatrQ0AUFtb63ElRERE5WHzpmZs4X3hiVzlRubkTHya5uae\nQaqhocHjSoiIiMqDZR39lpNENDhuZE7OxKdpb2+Hz+cr6BG4RERERET9cSNzMsSn6ezs5D3iKQfn\noCg/9gzKZbNfUB62zX5BmdzInAzxaVpbWzFqFC/goUy6rkNV+SROymSYJiSZKxIpk67rUDheUJZk\nMgm/3+91GVRG3MicDPFpDh8+jNGjR3tdBpWZZDLJEE85dF2HojDEU6ZkMgkfxwvKEovFuFSXMriR\nORni03R3d/P2kpTDNAwonHGlLJZpQRJ5v2zKZBomZI4XlIVndCmbG5nTk5GmubkZt912G9avX4+m\npibccsstmDlzZp/vb21txe23346XXnoJU6ZMwS233ILZs2cD6Hni1Y033ghRFKHrOjRNgyRJiEaj\nuPPOOzF16tQB1xWNRjFu3LiCfz+qLLphcAaFclimCYk7ZcpiGDrHC8qhaRqqqqq8LoPKiBuZs+Qz\n8Zs3b8bMmTPx6KOPYtGiRXjvvfdw3HHH4aWXXsr7/u3bt+PYY4/Fn/70JyxcuBB79uzBvHnzsGbN\nGgBAMBjE/fffj3Xr1qGjowO6rqO7uxuTJ08e9FOw2trauCaecuga17hSLt0wOONKOTRdh6IqXpdB\nZSaRSHBNPGVwI3OWfA+0cuVKzJo1C8888wyCwSBs28ZHP/pR3HLLLXj66adz3n/99ddj0qRJWL16\nNcLhMGzbxiWXXIKbb74ZL774ImRZhm3b+OpXv4rPfOYzBdXW3t7OEE85LNuCKAhel0FlRlUVgP2C\nstiWBVHgSlXKZFkWRJH9gj7gRuYsaYhvaWnBs88+i8ceewzBYBBAz2Odr7nmGlx44YVobW1FXV1d\n6v3t7e144okn8OCDDyIcDme8f/ny5di3bx/C4TCSySS6urqwcuVK7NixA5MmTcLXvva1QS2l0XUd\niURixJ3uMk0TmqbBMAyYpgnLsnJuhSUIQuqPJEmQJAmiKKb+KYoihAoOM8W+2Nm27dT213QdsG10\ndHRk/F2k/50IggBRFCHLcuqPJEkV/XcwFLZtw7IsWJaV2r7On+w+7vRnSZIgyzJUVT3q9gyHR9ZY\nAfRsU9M0oes6LMtKjRnZ44bTR9PHCuePM5ZUKjcngmzbTi0TTd/WANDV1QkIAtrbfRnjsqqqDIt5\nWJaV0W+dccAZJxxO303f3znjbCH9dsaMGW78GsOK03+d7W4YRs62BnrGX0VRoCgKZFkeEf3XrcxZ\n0hC/du1aAMCSJUsyfj5t2jQAwK5duzJC/EsvvQTTNLF06dK879+5c2fq/ddffz0WLFiAk046CatX\nr8bDDz+MLVu25Ayoq1atwq233prxs4svvhg//elPAQDV1dXQdR0AoCjle0rUNE3E43Ekk0kkk0kk\nEolU3en2Ht4HANgSz38BnjPoO0HQCeXpnB10+uDn7Eycfx9IW9nt+v1+qKoKRVEQDAbh8/nKcuce\nSDsFallWantrmpbawebb9oPhbP94PA5REBCLxVI7kuzQY1lW6sDL+WOa5qDaO3zkMBRZQUdHB8Lh\nMCSp/C7QNE0T3d3diEajiMViA/sd9/X0QQS3AECqPzs7YSdQpm/T9IMo0zRhGAZ0XT/qfZ0P9z4y\ne8uWnrYURUEoFEIoFEIgECjLbQp8sGONRqOIRqNIJBKp3zX7d8one1s62zh93HDGhfR/ZofQffui\nAABJaT9qzaqqpsaLYDAIv99flmMFAAQCwYz/NgwjNT7H43HE43EYhjHgz1MUBaqq5kya2DZgWyYS\niUTG9nUC00A5D5tx+m65blfTNFNjbzweRyKRGNR2FAQBiqJkHFQ62zK772bv75zxYSj3eldVFYFA\nAKqqIhQKwefzDfozSs22bWiahkQikRqDh3qfeyecO+Nw+qRferbo6uoa8NibTZIkRCIRBIPB1Pel\nXPuxo6OjAwAGvew7W0lDfGdnZ2oQTuf8dyKRyHk/kPtLpr+/paUFAHDdddfhhz/8IQRBQEdHB6ZM\nmYL77rsPN9xww1HrCoVC6O7uTv27rus4cODAoAaIdM5RpRPMnMHCkb1Tc2ZZBttGIBCAz+dDOBxG\nfX193oOO3bt7PnfmpL4vHHbLYNqyLCsVhDVNw6FDh3L+/vvjHDC8p6l5A0V2+E2flXUG5YGG3/SD\nE+egxwkU4XA4NUi5MWjs3drz4IexY8cW/Fn9ObSzBoZhIBaLobm5eVA7/fQ+nR7oAOQcbJimiURL\nS09/7ycY5iOKIkKhEMLhMMaMGTOgsw3R2FYAQLifC+XdEt3S09bMmTNTwbi7uxvt7e04cODAoLap\nM+vnbNP0Gex4LAag50xmdh8ebGBzOH23rq4Ofr8/9feX/jsVm6kf6m2r/0eOO9s2Ho9D0zQ0NzcP\naqwAeg4YBFFEMBzPGJfznRVwZmfTD0Cc8WIg4SL74ESSJPj9fiiKMqi+fDTNB3vGrsbGoT+y3bZt\nJJNJxONxtLe3Y59zEJxlIAdc2X3XGRfyTQo5Z3MGs++TJAk+nw9+vx+RSAQNDQ3D4poUTdMQi8Wg\naRr2798PTdOG9DnOGCHLMhRFyTgISZc96ebMhA82GDv7uXA4jMbGxrKeHTcMA11dXWhvb0/1q8EQ\nBCG1XbP7bfr2Tc8R2ROZAx0fACASiaRqHFZ3p6mrq0t16PQgf+TIEQC5pyGdWfbsdUPp7581axb+\n+Mc/4uKLL05t7Orqapx88sl45513BlSX3+9P7RT8fj+CwWBqtn8onC9O+hKV9B2tLMvw+XwZpz+H\nw2DkJlEUEQwGcw7oBmr3bhM2gMnjJqdO0TlfKOeLlv6FSt+ppJ8eHcjOtJQHQqXi9LvBHizkCzd9\nLcNSFAU+nw9qJAJZlhGZMaPsZ0cGQ9O01C3jBEGAqqpQVRW1tbWD/qzscJ4xbvRuM6ffpoclZ2de\nydK37VCZ+iFYtoXGxtqMsy75drpOMPL5fDnjxUCCzEAPTsqBIAjw+/3w+/399tuj/U7OmOuMxU4/\n7mtccA5qnP5bSeNCtkL7LpB5YJk+AZVv+6aH0PTQX84hvFCyLKO2tnZIYy+AVN91cpuzXfMtLU7f\nvumTh4NdBuSc7Sz0YueSJseJEycCALZt24Z58+alfv76668jFArlzP6kv//UU0/NeL+qqpgzZw58\nPh8uvfTSnLa6u7vzHuGvWrUKq1atyvn5G2+8AaDwDQp8MFNJxSXgg1P7xdTa1oY6PgQMwAeD2GBE\ne08fV9qOOtrVhVEu9Yv0ZT/Zp9ud2xXyovvCiIJYkruDHD7chlGjRtZ4kb5+nPLbsmXLkM9wOWeM\nnLP85C5nUquU9/FPnzguREkPzebOnYtJkybhgQceSP3Msiz8/ve/x6mnnpozADQ1NWH69OkZ77dt\nG7/73e9w0kknwefzwTRN7Nq1K+P/2759O9avX48zzzxzwLW5tT6JKs9gT90T0cgVj8e9LoGIytyw\nXBMvCAKuv/56fP3rX4ff78fChQtxzz334LnnnsOjjz4KoCekv/jii1i0aBFEUcQNN9yAL37xiwiF\nQli6dCl+/vOf4/HHH8fDDz8MAHjqqadw/vnn41e/+hXOPvtsvPXWW7juuuswZswYXHDBBQOurb29\nZ61fTU2N+784ERERERHcy5wlXyR144034u6778Zdd92FD3/4w3jjjTfwwAMPYMWKFQCAJ598EosX\nL8add94JALj22mvxs5/9DPfccw/OPvtsvPzyy/jtb3+LCy+8EABwzjnn4Etf+hI+97nPYdy4cTj3\n3HMxduxYPPXUU6nbUg5E+oWtRERERETF4FbmLPnVlKIo4vOf/zyuvvpqdHV1obq6OmOt7NKlS3HD\nDTekHtwkCAKuvPJKfOYzn0FnZ2fO+0VRxB133IGbbroJW7duRWNj45AuSnVObXAmnoiIiIiKxa3M\n6dktUSRJylu8z+fD97///Zyfi6LY7y9bX1+P+vr6IdfT1dUFACPuYU9EREREVDpuZc7KvefQIHV2\ndqZue0hEREREVAxuZU6G+F6HDx9GTU1NRd9LlQZvqE+po8rGfkH5sF9QPuwXlM2tzMnE2iv7AVRE\nQM8tUEWBXxPKlP4QJiKHZVkQOBFEWSzL4gQhZXArc7JX9dJ1nQ9RoBwcfCmfnoM7hnjKxPGC8rEs\niw/CogxuZU7PLmwtNwzxlI9t2zh+/GQEeJaG0pimCUFkiC9EJR4DmabJgzvKYZomD+4oA0O8ywzD\nGPTj5KnyqaqK48dNzritKZFlWRDAPlGIY+c0eF2C6yzLgsDld5SFZ2gom1uZk6m1F2fiKZ1t2+h4\n4V4c+dsd0Ju3Q1D8qDrlUoy+4JtQ6qd4XR55rGcmnjvlobBtG/HNq9H95t9hAwgfdw4Cxy6riANl\n0zQhSuwXlMk0TS6noQyciXeZpmlQVdXrMqgM2LaNQ7+6Cl3rH4Kd7Hmqmq3H0bnud4hu+Asm3vIi\nfONne1wleYnLJobG6GzB3v86B3rzjt7vlo2OZ38KefRETPzq05BrGr0usSBcNkH5MMRTNrcyJ0eb\nXlxOQ474ljUZAT7FNmHFO3Hol1d6UxiVDdu2uSZ+CPbd9VFo+9+FnYwC6Lntnp2MQj+4DXu/d+6w\nvxWfbds8uKMctm3z4I4yuJU52at68UiZHO1P/Qh2MtbHqzaSe9+C3rKrlCVRmekJmwxrg5HY+Sq0\nfZsAU8990TKgt+xEfOuLpS/MRbZtV+YVu1QQ27YrYrkYucetzMkQ34tHyuTQW3fCmSXMR5B9MNr3\nla6gYU6pnwJlzFSvy3CVbduM8IMU27wadr4A38vWYohvXl3CitzX0y/YMygTQzxlcytzMrWm4ZeM\nAECpn4r+ZlltIwm5dkLpChrmfBPmwjd+jtdlkMcEQQT6u3OLIAEiz4YS0cjgRuZkiE8z3Ndjkjtq\nPnwdBF8f94UXBPgmzYNSd0xpixqGNh85iH997neYft83MPV/bsHFj/0ML+5/z+uyyCOh45f3e/tF\nQVYROn55CSsiIvKOG5mTIT4NQzwBQGDGGag65TIIvlDmC6IE0R9B41W/9qawYWTdge342N9+jMd2\nvY24oUOzDLx8aCc++/T/4N5313ldHnlAHTcLgWOXQlD8Oa8Jsg/+qafAf8wJHlRGRFR6DPEukiQJ\npml6XQaVAUEQ0HDlL9BwxY+gjJ0JCBIEXwiRRVfgmG9vgDpultclljXTsvCF53+PuKHDyrq2IG7q\n+I/1j6E51uVRde4QBAF2P9dNUH7jVv4RwbnnQFD8ENQgBDUAQQkgcOxSjL/hz16XVzBBEGDbWcR3\nUgAAIABJREFUltdlUJkRBAGWxX5BH3Arc/Keir1kWWaIpxRBEBBZdAUii67wupRhZ+2B7UiYRr/v\nefC917Dy+KWlKagIRFGEbTHED5boC2L8DX+C1rwdsbefAgAEZy+D2jjD48rcIYoiLJ7RpSyiKDLE\nUwa3MidDfC9VVZFMJr0ug8pMPB7Hnu3rIcsips76kNflDAt7u4/0u8NKmga2d7QUpW3BFwJKEKIk\nSWJYK4A6ZhqERT0Xhys+n8fVuEeSJIY1ysEz/ZTNrczJEN8rEAggHo97XQaVoa2b16ImUs0QP0CN\nwWpIogj0sc9SRQmTqmqL0nZo9rKifG42WZYZ1gr05hNPAgAWnP8xjytxD8/oUj6yLMMw+j87SSOL\nW5mTIb5XKBRCd3f30d9II4qqqrAM7pQHY/G4Jsj93YVEEHBZ00mutplI6Hjtlb3YurUVsizihPnj\nMHtOAySpOJf9qKrKsEY5VFVlWBui9iNxrH1hFza/ewiCIGDeieNw2unHIBQu/NH0XlNVFZqmeV0G\nlRG3MidDfK9gMFiymfjdXYexq7MNo/0hzB41lvenL2NcNjF4sijhB4s/gc8/9zsksh7uE5AVXH/8\nMowL17jW3p7d7fjFT16CZdnQtJ5gvWVzM6qr/fjCvy1EOOz+cg1JkkqybIeGF0mSYPMMzaBtf68N\nv/nFKzBNC6bZ871qbdmGNc/twLXXL0RDY5XHFRaGy6wom1uZk3en6aUoStGPlHd3HcbHH70Hy/50\nJ/71+d/hwsd+ikUP/Rf+cXBHUdslKrWzJs7CH5dfgzPGTYco9DzD8tjaRty9+J/wb/POdK0dTTPx\ny5++hETCSAV4ANCSJtraYrjv3tdca4uI3KdpJu795XpompkK8ABgGBbicR2//vkrvP0zVRy3Midn\n4nsV+3RXWyKKjz7yY7RrMVi2nbp7x+7oYVzx5G/wwPJrML9+UtHaJyq1+fWTcP+5V8G2bVi23bNO\n3mWvb9iXseNPZ5k29uxuR0tzFPVjwq63TUSFe/P1/f2G9O6Yhh3b2zCtqa6EVREVl1uZkzPxvZwN\nWqwj/l++sxZRPZF3aUbc1PEfrzxWlHaJvLZ7+3rs21mcGfEd77VlzMBnE0UBe3a3F6VtIircvr0d\n/X6HLdPGwQPD+7kSRNncypwM8b18Ph9s2y7aRUn/t30DNKvvgWpj6250aYmitE3kpT07XsXu7euL\n8tmKKvX7ugABitL/e4jIO8GQClHq+7owURIQCCglrIio+NzKnAzxvaqqei6c6ezsLMrnJwy939cl\nQcy5CJCI+nfC/PFQ+wnylmVh+kyehicqVyfMHwexn5s7WJaNY+c0lLAiouJzK3MyxPcaPXo0AODI\nkSNF+fzjRo/v9/WgrGKUL1SUtokq1dRpozBufASynDuUKaqExUunwu/nLB5RuaqvD2P+SeOhKHm+\nw4qEc86dwZl4qjhuZU6G+F61tT0Pnzl8+HBRPv+6eWciIOcfiAKSgs/NOaMoF/4RVTJBEHDV50/F\n7DkNkGURPr8Mn1+GokhYumwazlk+0+sSiegoLrr0eCw7uwl+vwyfT4KqSgiHVZx/4WwsPavJ6/KI\nXOdW5uTdaXpVV1cDADo6Oory+ac3TsUX552Fu15/BrplwrQtCAACsorF46bj2uOWFKVdokrn88n4\n1GcWoLMjgT172iFLIqZMHQXVx+GNaDgQRQFnnTMDS5Y1oaU5ClEUUD8mDFHkM1SoMrmVObmX6xUK\n9SxlKeZTW1cevxTnTJqNX29ai81HDqIxVI0rZp2G0xqm8IFPRAWKVPsxBQHYls0ATzQMybKIUKjn\nCa0M8FTJ3Mqc3NP1KvZMvGN6zRh8d+GFRW2DaKR6d/UaAMCC8z/mcSVENBR79/Tsg2dX+z2uhKh4\n3MqcXITdy7nIoLW1tSTtvXxwB9buf68kbRERERFReXArc3Imvld1dTX8fj8OHDhQkvY6eU94IiIi\nohHHrczJmfhegiBg7NixOHjwoNelUJmRJAmmZXldBpUZURRhsV9QFkmWYZjFeWggDV+KokDX+SwY\n6uFW5mSIT1NbW4v2dj6inTLJsgRD506ZMsmKDIM7ZcqiKgo0TfO6DCozfr8f8Xjc6zKojLiRORni\n00QikaJf2ErDjyTJMCyGeMokSTIM0/S6DCoznHGlfHw+H5LJpNdlUBlxI3MyxKeJRCLo6uryugwq\nM7IswTQY1iiTLEswGeIpi8wQT3kwxFM2NzInQ3ya0aNHo7m52esyqMzIMpdNUC5ZlhnWKIdPVbmc\nhnIEAgEup6EMbmROhvg0jY2NaG5uhm3bXpdCZUQURFjsE5RFEESA/YKyiKIEmxc8UxZJknghPGVw\nI3MyxKdpaGiAaZpoa2vzuhQiIiIiqlBuZE6G+DQNDQ0AgJaWFo8rISIiIqJK5UbmZIhPEw6HAQDR\naNTjSoiIiIioUrmROfnE1jSRSAQA0NnZ6XElRETkFlWVeF0LEZUVNzInQ3wahngiosrTNKPO6xKI\niDIwxLssGAwCALq7uz2uhIiICmVGD6PjxXsR37waYiCCyMJPITjnwxBEriQlIm+5kTkZ4tM4R0V8\n4BMR0fAWe/d57Pv+xwHbgq3FAADRDX+FOn42Jn71KYj+sMcVEtFI5kbm5HREmqqqKgAM8UREw5nR\n2YJ93z8fdjKaCvAAYCej0Ha/gYO/usrD6oiI3MmcnIlPEwgEAACxWOwo7ySvLRw7DbxMjYjy6Vj9\nS8DO/2Ad20iie+MjMDoOQa5uKHFlREQ93MicnIlPI4oi/H4/18SXOePIfpiv/Qn2xr/A6OQ9/Yko\nU+zdZ2FrfT/iXlD8SL6/sYQVERFlciNzciY+SzAYRDze9+BP3rG0OA7+8rPo3vgIICk9PzR1RBb+\nM8Z8+scQZMXbAimvuQvOhyAIXpdBI4joO9p6dxuCGihJLVSeEgkDRw7H4PPLGDUq6HU5NEIVmjkZ\n4rOEw2E+7KlM7f/hRYhvWQNbTwB6IvXzzn/8HpaexNjP/U/R2hZFAYZhQJb5lRkMw7DQ3hGEaVlQ\nAzoCgco60BLYL8pSZOE/I7bpWdjJvsfyQNPpRWtfFEX2izKVTBr4y8Pv4PWN+yBJIizTwqjRQVxw\n8XGY1jS6qG1LksR+QRkKzZzsSVlCoRBDfBlKvP864ltf6AnwWWwtjugrD0K/+D+gjJ5UlPYlSYam\naRx8B8i2bax5fgeefnIbYAOC0BPoTzplAs6/cC5kuTgr+WrHjYVtle5qCUmU2C/KUPjEj0MevQr6\noe2AqWW8JqhBjL7o2xBktWjty7LCflGGDMPCT+5eh+ZDURiGBUPvuW7i0MEofv3zl3Hl507BtKbi\nPVNAVVX2C8pQaObkmvgsiqJA13Wvy6As0Y1/ha1rfb9BFNH9xqNFa18QBFhW/gvlKNczT27Dk3/f\nimTCQDJpIJEwYBgWXlu/F//7m1eL1u7Uk07CtFNOLtrnZxNEkf2iDAmygkk3r0bw2KUQFD9EfwRi\nIALBH0bdJbeh9sP/Vtz2RY4X5eitNw+gtaUbhpH7d6PrFh5+8K2iti9yvKAshWZOHg5mcY6UqbzY\nRhKwzb5ft8z+Q36BBEGAafbdPn0gkdDx7DPvpWa50um6he3b2rB3TzsmTKxxrc13Dx/ET99ejXUH\ndkARJZw/9XhceewijAlWudZGPiL7RdmSwqMx4ct/h976PhLvb4CoBhGYuQSi6i9626Iosl+UoZfW\nvQ9N6/vvpf1IAq0t3airDxWlfUmS2C8oQ6GZkyE+C2fiy1Ng+iK0+8J9rnEVRBn+6cVc48qwNlCb\n322BJAow+njdMEy8vmG/ayH+kZ1v4ksvPAjNMmDaPUtpfv72i7hv88v400f+FTNqincbQYH9ouwp\ndcdAV2pgW1ZJAjwASAzxZSnW3f++XZIExOPF2/8zxFO2QjMnl9Nk4ZesPIWOOxdSeDQg5Omyogy1\ncQYCU08pWvuCIMK2eWf6gdA1A1Y/69JtG67tKA8nunHjCw8ibuqpAA8AmmWgU4vj6mfuK+rfmwCB\n/WIYeHf1Gmx+4cWStcfxojxNmBjp905ZhmFhdF3x7lQjiuwXlKnQzMkQn4VfsvIkiBImfO1pSNWN\nEPwfLJEQ/FVQ6iZj/Jf+5mF1lG78hOqeK1n7oKoSJk+pdaWtB7a9CvTx2C8bwMFYJ15v3etKW0Q0\nvJ2xZBpkOf/YJEki5sxtQDBYvAueibIVmjm5nCaLZVm8crxMqWOmYur3tiP62p8QfeMxCKKE8IIL\nEJr3EQii5HV51Gvc+GrU14dw8EBX3hl5URQw78TxrrT1zuEDSJh9LdwBBADbO1pwYv1EV9ojouFr\n3PgIzvvILDz+6GYYhgUnO6mqhOoaPy667HhvC6QRp9DMybSaxTRN+Hw+r8ugPgiyiqpTP4GqUz9R\n0nZt24Io8sTVQH3mqpPx4x+sRTyupy4kkxURkijiqs+fClV156BrTCAMSRAyltKkEwQBtb7inR63\nYbNfUA6OF+XrjCVTMWXqaLywegf27m6HP6DgtIXH4IT546AoxZ0MsiwLilJZz8qgwhSaORnis/BB\nDMPDK6vvhW0Dpy79TEnasyyGtcGoqQ3gKzefiTc27sfG1/bBMCzMml2PU087BqGwe6erL5t+Ev53\n88swzfxr7AUIOGNck2vtZbPZLygP02KIL2cTJlbj8k+dWPJ2OUlI2QrNnEyrWZLJJL9kw4CWjJW0\nPdu2IUlcsjMYqirh5FMn4uRTi7eUZVZtIy6YOg9/2fkG4kZmkPdLCr5z+sehSsUb5iz2C8rDsiz2\ni2Fg964jsCwbk6eOKkl7pmmyX1CGQjMnQ3yWRCIBv780tyGj4cOyTJ6hGaKn//YXCIKAsz5yflE+\n/z8XXYRp1fW4563VSJg6LMvGhKpafOPkFTh74rFFadPBfkHZBAGwTPaL4SAaLe0zYXimn7IVmjnZ\nm7LEYjEEg8VbQ0vDk2VyLeNQtR85XNTPFwURXzhuCT435wwciHVAESU0BCNFbdNhsl9QlmPnNGDG\nrHqIYt93aKKRSdd1jheUodDMyRCfhSGe8uGyifIniSKMg63QbAuYXpoQD/YL6mXGOtD18h+gHdgK\nuXY8IqdfDrlmrNdlURnhMivKxhDvMk3ToKq8TyzRcPTqP3oe6DN1+kyPK6GRpGv9wzj4i38BIMDW\nuiEofrQ9/A2M+ti/Y/T5N3tdHpWJiRN5q1vKVGjmZIjPwgtbaSQ4efEVkIp4wSfRSJHYtQEHf/Ev\nsLUPLra39QQA4PDfvgu1YVrJb4lL5cO2bby/6wja2xOoqfHjmMmBfp8aSyMLL2x1kWEY0HWdy2mG\n6IT6iRA5OJW9eFzHprfbEY9paGiswrTpdVy/SzREh//23VRoz2ZrMbQ+/E2G+BFq187D+P3/bkAs\nrkMAYNtAIKjgnz89v2R3xKHy5UbmZIhP093dDQAIhULQTRMK164NmG2ZqDq0DbYehzluDqRQjdcl\nUR7PP/Mennx8K0RJgGXaECUBgYCCK685BWPHlWgdeYWoHT8OYjDgdRnksdi7zwG21efreusumPFO\nSAF+v0aSgwe68Iufvgy992F3Dk0z8YufvYx/++IiNI5lnxjJ0jPnUPFpFGkOH+65i0ZtbS2e2LMJ\ne6NHPK5oeOhYex92fHEC9nz3TOy786PY8cXxOPjLq2CV+F7u1L9XXtqNp57YBsOwoCXN1D872hP4\nyd3r0NWV9LrEYWXqggU48eyzvS6DvCYcZTdqA8LR3kMV56nHt8DQzbyvGbqJJx/fWuKKqNykZ86h\n4siSxtmgdXV1OBTrxBee+73HFZW/jjW/QfP/XAuzsxl2Mgor3glbT6Dr5T9g7/fOg231PUNFpWNZ\nNp54bAv0vnYqhoV/rN1V2qKGqdX7tuKfHv8F5v/hdpz58J34zaa1iBulvd80lY/wCR8FxL7P2vom\nzIHoD5ewIioH725qhm3nf822gXffOVTagqjspGfOoWKIT9PZ2QkAiEQi6EzG8e6RA9jR0eJxVeXL\nNnS0/OGmjAu6Uq/pCSR3v4HYu896UBlla2vtRjJp9Pm6YVh48/UDJaxoeFr18iO45tnf4sUD29Ec\n78K2jmZ859XHcd5f70ZHMu51eeSBUR/5GgQ5/4VpghpA3SW3F6XdyVNqMbWJ66rLlWn1keB7WZYN\nu6+UTyNCeuYcKob4NB0dHQCA6upqdOoJKKKMbe3NHldVvuLbXgT6GajsZBSdL9xbuoIqwIQpC9A4\ncY7rn2sNYGfBHUr/Xti/Db/b+gpiWbPucVPHnq7DWPXKIx5VRl5Sx87E+C/9DWJoFAR/FSD7IPjD\nEHwhjPn0jxE6frnrbdqWCex9Cfpbf0Vy79uufz4VbuzYqn5fbxwb4V1qRrj0zDlUvLA1zZEjPWvg\na2tr0bHnPdiwUeMb3neqqQ+EIfdzqrcQVqILOMoYZHbzuoLBmDz91KJ8bl1dCJIkAsi/nEaSBMw6\ndkxR2q4UP3v7BcQNPe9rmmXikZ1v4vbTLkBQcfc5E6HaWkh8ymNZC85agmk/PIDuN/8OvWUnpMgY\nhE88H2IR9h/RjY/g0K+vgaUnAEEATANqQxPGrvwj1MbprrdHQ3P2uTNw/2835lzYCgCKKuHD57r/\nd9XW2o3XN+5HLKZh/PhqHDdvLBSFN+goV+mZc6gY4tNEo1EAQDgcRreehCrKOGnMMR5XVZgT6icV\n7bN9E46H3c9aYEHxIzB9YdHaL5X6sTOgBop3MKJrJtas3oG1L+xCdzSJYFDFaQsnYcmyJvj97nxF\nJUnEmWdNw1NPbMu7Ll6SRHxo8RRX2qpURzsrJwkiDsY6MLW63tV2Z53xIVc/j4pDkGSET/wYDF2H\nnkgWJcDHNj2LAz+5HLaWuXQrufct7P6PhZj83XcgR9w/GJ/WNPqo1+9SprnHNWLJmdPw/DPvwbLt\n1N3AREHA4qVTMfd4957ma1k2/vTQW3ht/V7Ytg3TtKH6JPz5/97GldecwttZlqn0zDlUDPFp4vGe\ngTEQCGC0P4w7Fl4ASSzOyLVs4qwBLXEYKkuLI771RdhaDILsg6UnIFXVITB9kWun8JT6yfA3nQ5t\n/2ZETr8c/qbTIcgq9Obt6Fz7W2gHNqN66TWutJXthNMuLdnyj5nHFe8OJLpm4sc/XIuW5ih0veci\n4O5uDauf24E33ziAf7vxQ/D73ZmFXbJsGo60x7H+pT0ZA70AAZ+5+iTUjhreZ52KrdYXxL7u9j5f\n1y0T1T73bjlpWhae3LMJv9m0DgdinZhcNRpXz1mExeOmF+00/IkfWQGxRLfWbTqtOGed8pl28smw\nrPxnodwWbW1DrDuKQFWT65/dcv+XcwI8AMC2YSW70f70j1F30a2utmnGOqC981TPvfCnnlr02f5j\n55TujOCMWXV9XnzqhnPOm4H5C8bj5X/sRmtrN0bXBXHq6ZNQX+/uhc7PPrUNG17dB8P44EYSWrKn\nv//yZy/jK19fiuoa92+HG+1KwrRsRCI+Lg0agvTMOVSehPj9+/fj1ltvxauvvoqmpiZ885vfxJw5\nfa8DPnToEG699Va8/PLLmDJlCr7xjW9g3rx5qddt28Zjjz2GO++8E52dnbjoootwww03DPoG+h0d\nHZAkCcFgELef/vGidcpYt4b29jhC/3975x0fVbH+/8/Zkm1JNtlUEhJCCwEhBIxfERBBKUoRrlQV\nFLmolIsERa4VscGlCaIiKijKVRCkCAgoSG8iEIFAIEAgBULqJtv78/sjvzM3SzYBYUlE5v167Ss5\nZ8+ZmTPn2WeeZ+aZGU3ALflheRxWeOwmaFr3QHm5FRazAyEhKqg1AXCW5EAWFu+3Z4uZuBaCNACC\nLABFhSY4nW5EtHwYoT0nwlVReEt6hcxmB3JzPRAEICHACZXq1oQanDtbgh3bzuHyZQMUAVLc0yEe\n93VqBLXaf+ESe3dfQFGRCS6n9yo+LpcHZWVWbN96Dr37tfRLXoIg4B8D2+CBrk3xR/olmM0OxMRo\nkdy2AeQBfMj1WoxseR+m/rahWky8SLuIeIT5aRUSl8eNkdu+xqHCiyy/C4YS/FZ4Af0S2mBO50F+\n10+5xjJsupgBs9OONuGxeLBhi1sWimd3u3AOlRsk3eVyQim7deFCFqcDlwI8UMkCEEp0S40Nvc2M\nywEehGn9r/fcxhLYCzJrvsBlh2H/t34z4snjQcnqN1H+y3wIUnllp4nHBWWz+xAz/ntIA8P8kk9V\nbNm/w3J6JyBIoWn7CBQx/tF9vnAZiuAoOA2pSguKS75lchEeoUGfR2/hc7g82LUzu8aVxzwewv69\nF/FIX/+V4eSJK9i0IRNlZVYIAqBWy9G9VyLuvc9/tkVVrhQYkZOjh0wqQYuWEQgMvPEdTq+F0WhH\naYkZGk0AIiJv7apSVW3OG6XOjfiTJ0+iY8eOiI6OxsCBA7Fv3z6kpKRg586d6NSpU7Xrs7Ky0KFD\nB+h0OgwZMgS//fYb2rdvj23btqFbt24AgFdeeQWzZs3C0KFD0a5dO8ydOxfr16/H3r17If0TvUpG\noxFBQUEQBAHnsorRLNG/w+Imox2rV53AmcwiSGUSuF0eNIgJxsAhbRATe+MTG65GkAWgqDgAPyze\ngyuXjSyvFkkReGxIMjQuOwS50i95SZVBOPbHZWxcdwpWqxOCRIDH7UHq/8Wh34BWfslDxOVyY+0P\nGUg/cglSWeUIidvlQYdOjdD30VZ+3XV0289Z2PHreaYYzQB+/eUsDuy9iAkv3g+t1j/1t2/vhWoG\nvIjb5cHB/Tl+M+JFdGFqdH2wKSS3aJTp78o/mrbDV5n7ca68GHaP90o/GlkA3u3wqN/y+uLkXvx2\n5QKsbu8YfIvLgQ0Xj+P+2OYY0CTFL3m5PR78e/8arM3+A0QEh8cNjUwBtTwA3/YchVY6/w37ExE+\nPLYdizJ2e5179q7OeLFdd0j8GLNhcznx7u8/4fuzRyCTSOD2eBCuCsTb9/ZDz3j/6qZCiwGv7F+L\n3ZfPQi6Rwulxo7UuBv/p+Bha6qL9kofHaYMgkaK2juOado69EUrXvoXyrQtATptXutasfcib0Q2N\n3k2H4Ccnz2UoxqUP+sBxORPkdgKCgNI1U6Fq2RUx41f6NTTJbSrDlSWjYTmxBYJcCfK4INWEIvKp\nTyqXC/UjjqLzKPzyOTgunYI0JBru8isIiGmJqFGfIyDKPyM1RYUm1Dac4HJ5kHmqyG9G/KGDufhx\nTQYbOQYAg8GODetOoaTYjL79/ffbMpns+HrJYVy+VAEIAgRUOiX/d188Hh1wl1/bfKPBhlUrjuPc\n2RLIZBK43YTQUCUGDm2Lxn4ORyq4bEBAgNTL5rxRBKrjJSm6du0Kl8uFbdu2QalUgogwYMAAGI1G\nbN9efTnChx9+GGVlZdi5cyfzVoYMGYL8/Hzs378fx48fR9u2bbF06VI8/fTTAIDs7GwkJiZi5cqV\neOyxx667bE8//TR2796NCxcuYM6MHXioZyLa3R3rl+e2Wp2YN2sXDAY7PFet6BIQIMX4iZ38smMm\nEcFQYcO+vRchlUigUsmgUsuhVgdAoZRBoZAhtmGw3ww4u92Fcr0VFosTNpsTDrsbVqsTLpcbKlUA\n2qfG+s0z//rL35F1uthLeQCAXC5Fu9RYDBqS7Jd8LuVXYOGC/T57NgQJ0Lx5OEaP6eCXvAqvGCGV\nSiCVSSCXSSCRCpBKJJBIBEikAgRB8KuiEtny42o4HQ70G/y439O+mh+WfQUAGDTimVue1+W8XMjk\nckRG+8/wrIrD7cKveaex/8p5GB02lNrMaBgYitGtOqNpiH+cfiJCuxXvo8RmqvGaVqHR+GVAml/y\nW5yxF/uunIdOqYE2QIVQhRrhqkAEyhUIkivQKaYZ5H4y1vQ2M0psZpicNlhcTthcTjg8LlicDkSq\ngnB/rH9CNTzkwdAti3G0OBd2t7fDpZTKsaDLEPROaOOXvPR2C7qvm48Sqwnuq3Zu1cgV2Nh3PJqH\n3HzPvNgTLkj/N2pBHk+l0ety/H/jV+KX3bI9ViPOv9AA5PS9bKqgCESDsd/6xeglIuS8mQJHwRng\nKqdVkCuhvqsHYtPW3XQ+Yl4eSzkgkUKQyiudEInUb85IVVwVRbi8cChcJTlwG4v+FwYlSCBRadHo\n3aOQh938nLUrBQZ8PH8fHD4m0IrExAQj7eUuN52X0+nG6pXHIZEIkMmkUCikCAxUQKWWQ6GQIUAh\nRbPm4X6ZTEtEyM0ph9nsgMPugt3uhslkh8XsgNtNiGsUgrtTG950PkClffbBrF0w+rDP5HIpnh/f\nAfGNbnzyaVWKCk34aN4evPxqN4wbPxq//fYbzp49e8Pp1akRX1hYiOjoaGzZsgW9evVi53/88UcM\nGDAAxcXFXove6/V6hIeHY82aNejfvz87//PPP+Phhx9GXl4ePv/8c6xYsQJnzpzxMhZ79OiBsLAw\nrFix4k+V0e12QyqVwmCwwWpxIjIq0C9G6PatZ7Htl7Nwuz3/30CTQCatNNoUChmaNQ/DoKFtr51Q\nLRARKioqUFpaioqKCpjNZlRUVECv16O0tBRGoxF2ux0OhwMOhwNOpxMWiwVmsxlWqxUOhwMulwtu\nt7cyEAQBUqkUMpkMAQEBkMvlkMlkkMvlkMvlUKvV0Ol0CA4ORlBQELRaLTQaDUJCQqDVaqFUKqFU\nKqHRaKDVaiG/gZU2Kips2PJTJswmJ+x2F+x2F1wuD5zOyp1HJYKAf03q7Jce8uPHLqOk2AKNptL5\nkQdIIZdXKiyVSg6lSg61Wl5NLlwuF8rLy2EymWA2m2EwGFjdWq1W2Gw2mEwmGI1GWCwW9nE4HLDb\n7bDZbHA6nXC5XOzj8Xjg8XhY/L+Yp1jvVetWoVBALpcjMDAQWq0WWq0WwcHBCA4OZv9HRkZCq9XW\nafzi+pXfQSqVoc/AITedltFoRFlZGcxmM/tYLBYYjUYYjUZWv+L/Yp3abDbY7XY4nU6iRhq9AAAg\nAElEQVQ4HA4vGRcEgcl2QEAAVCoVgoKC2Kdq/YWEhCAkJIT9HxoaekPyXBtWlxPtV7wHh8cNl8fD\nDEOpIIFUqHTyguUqHBn2mt/ytNvtuHz5MvR6PcrKylBYWMjk12azMVm12+1MpkVZFf9WrVOJRAK5\nXI6AgABWtwqFAjKZDCqVCoGBgdBoNEx+xboU6zssLAzR0dFQKG5s2Py0/goWHt+JYpsJJocdFpcD\ndrcLFpcDNrcTwXIV9g9+2S89/zsvZSGzrAAKqQxKqRyhSjWCA1RQSeVQyeSIVAf5DLMiIjgcDibD\nxcXFKCgoQHFxMUpKSlBcXIyKigoYDAaYTCamn10uF9MHVetZ/BsYGMh0sSivarUagYGB0Ol07FxU\nVFSNnTmuikLYzh+Ex2qAx2qA21QKt7UC5LKD7FZ4bAYom9wLXe/JN11/1uzfUbruHQgyOSTKIEgU\nGkhUwZBqdJBqoyALjoKqZTdI5NVlwePxoKSkBEVFRaioqIDFYoHVaoXJZILFYkFFRQXKysqYThb1\nrdj+ud1u9hGRSCSQyWSQSqWQy+VQKpVQKBRMv4ryW7VulUolgoODERUVhfDwcAQHB0OpVHrpWfK4\nK+uxvAAeuwkSTSgUMTffa+3xEN6Z+gssZicEAZBI/tf5I5VVduR1fbApOnRMuKl8iAg2m81Lt5rN\nZhQXF1erY6PRCLPZzORb1Bd2u91LfivLWVnfarUaKpWK6V+xTRN1RVBQECIjI6HT6ZgtERISAoXi\n5uPxfzuQi53bz8FqdcLp9MDjrlzDXyxnXHwI/pXmnwUGLl4og8dDaNxEB5vNdlPx8EAdG/Fr167F\nY489BovF4lXwEydOIDk5Gb///jtSU1PZ+c2bN6N3797Q6/UICflf78LZs2eRmJiIPXv24K233kLj\nxo2xePFir7yef/55HDt2DAcPHvQ6P23aNLz9dvWYQY/Hg7S0NGRkZEClUiEkJAQ6nY4ZpeIPNzQ0\nlDXoOp2OCZRM5p/IJI/HA6vVCqPRCIPBAIvFAoPBwBR5YWEhCgsLceXKFZSWlrLv9Ho9CgoKYLPV\nPpwqCAIzVkSDRaPRQKVSQaFQQCqVQiqVQhAqFQERwePxwO12w+VyMeUnNt6iI1BeXg7Pde7OKjba\nYWFh7Aeq0+mY8gsJCUFkZCTCwsKg0WiYESUaTyqVyu9GqMPhYMpIVFKlpaUoLS1lCstkMkGv18Ng\nMKCiooIpKrPZDJPJhJKSkuuuAwBMYYkGjlKpZA6S+JFIJOwj4vF44HQ6vZwDi8XCDFaHo/bdQwMC\nAhAZGYmIiAhERkaiQYMGiIqKQlRUFNRqNUJCQhAeHo7Q0FCEh4cjJCQEgYGBfhu9ISLY7XbmQIqK\nX3RACwoKcOXKFfb3ypUrKCsrY+/iehCVv0qlgkwmYw2xaOiIMg5U1qco2w6HgzVUBoOBTTyqDdFA\nCgoKYnUaFhYGnU4HtVqNiIgIhIeHM1nXarUIDQ1lRoA/6lU0CC0WC0wmEwwGA4qLi6HX69mx+Eyi\nYy8ajEVFRSgurn1TOzFuU6FQMH1R1ZkXjR6JRMIcT1EWxboVG3Cr1Qqz2Qy73X7N5xLfY1UjX6fT\nISoqiungsLAwL51dtdEPDg72u5NFRF5OeXFxMZNNq9WKsrIy6PV65vhUVFSwTpXS0lKUlZXBarWi\noqKi1jqQy+UICQlBUFAQAgMDmUMk6gWgstNJrGfxr/i+zWZzrc8hk8mg0+mg1WoRHh6OiIgINGzY\nEBEREVCr1ewTHBzMdLP4/oOCgqBSqaBUKv0iv263mzngYvn1ej1r74qKilBSUoKKigqUl5dDr9cz\nGb6WvpNKpdBoNOxT1ekR2ztRdisn/LuZUyoanlU7AcT3fi0kEgmCgoIQHh7O2rqIiAhER0cjMDCQ\ndb6IukPUCWKdi7Lsz7bO7XajrKyMdTZZrVbY7XYYjUaUlJSwDkCxfvV6PYqKipCXl4fS0tI/1car\n1WoEBAR46QvRkRfrWrQvRL0gOmFi23o9+SkUCkRFRSEmJgaRkZHMnoiNjWWdVmI9i86tqCPUarXf\nbQlRP1itViarRqMR5eXlzF4rKSlBfn4+CgsLkZSUhDlz5txwfnUaE28ymZjhWBUxTOZqA1T8oVy9\nm1XV600mk5eBX/Waaxm0IlU9ZpvNhvLycpw8eRLl5eUwGo3VeqZ9IQpoQEAAU36i4XB1A3e14hWN\nQNEQuxZSqRSRkZGIjIxEUFAQGjRogJYtWyI6OhoNGjRAeHg4E1ytVgudTofQ0FAEBwdDJpPdkl5Y\nj8fDPPDy8nKYzWaUl5ejoqICNpuNee2i8VtWVublvZ84cQJlZWUwGAzXbNxFpSzKkmioiSMDEonE\nSzEDYL0tokEhlkls9K5HKYsGrtjLHRQUhKioKK9eAlGJiOdEBSZ+RIXtr8bPF06nEwaDgSkNo9HI\nDAmxQRQbxYKCAmRkZKCoqAhOp+810IFK5090oKo2gqKMi0axRCKBIAjMkHM4HEw5i+/aarVec2Uh\niUSCyMhIxMTEoEGDBmjTpg10Oh1iYmIQFhYGtVrN6lls9ETlHBgY6DfDze12ezlt5eXlrF5FBS3q\nCaPRiKKiIuTk5ODw4cMoLy+HxVJ9N2Nf9VrVuBD1SFXjWCyLKMN2ux12u501FCaT6bpWa5LJZMwh\njoqKQosWLdCpUyfExsYiNjaWOW9RUVHQarVMj8nl1UeebhaXy8V+h1XrVWzkxNEA0XkWHZKTJ09i\n586dMBgMtcqsiEqlYs8hGk9VdYUoswDYqJfohIgfsZyig3c9+YptgdgxodFo0KBBA7Ru3RoqlYrp\nEVGORfmOiIhAREQEgoNvbjMgj8fDjGHRYRaNtNLSUuTn5zODrrS0FBcuXMCePXvY2tXXi1wu9+o5\nFeW4qqFctX7dbjdzOMURy4qKilrlV6lUIjIyktVlXFwckpOTER0djYYNGyIqKooZwGLHlFj3t2Lk\n0ePxeLV1drsd5eXlKCwsRFlZGXPaRJ0gyu7hw4dRVFR03b9X8dnFUStR54qdP2J7LrYlYv1W7ZgQ\nRybETsFrIZFIoNVqERYWBq1Wi6ioKKSmpiIiIoK1a1WdkPDwcNZJIdo+/tK/LpfLa2S7qKiI6Tux\nTROdvUuXLiEnJ4eNDogbKdWGVCplBr3olIr2RNUOtKodmqKDV7UjU+xUE8t6LedDEARERUWhQYMG\nSEhIuKk6qlMjPjw8nP14q87GLSsrAwCEhYVVux4AysvLodPpfF4fFhbmU+mUlZVVS68mgoODQUSY\nP39+tR87EXkN0en1ejbEWVJSAr1ez3oSxVAVsQdG9N7Fl05EkMlkXopODH8Qew1F5SMO5Ys90cHB\nwcyTDwsL+1NK6ZtvvsFTTz113dffCBKJBIGBgVixYgVGjx59U2lZLBam+ETDX+yBEY1ScXhZ7BGr\n+mMSFZlY5wBY76s4tC8O44vDzzqdjvWYikoqNDSUKa5baXRfzcSJE/Hhhx/e8P1yuZz9NmrDZrNB\nqawMPxIbfLPZzEIqxJGIqvUvDouKDqgo42Jdix9RCYqjWFVDKKo2tOKxKOdhYWHMGbrR+p43bx4m\nTZp0Q/dejVQqRWhoaI2bcZw+fRpJSUk13i8O94s9tVVD3MrLy5kRZTabvQzGqiNeYoNQVYbF4X3R\nsRQbVVF3iHUp9uaJTs71jGJt2LABXbrcfPzstZDJZPjqq68wYcIErzDK64WImJFqtVq9HCqxY0TU\n1VV1eFV9ITqbVcskGkWioS8aTuJHNAxFp0DsxRZ1uDgi4K/R2doYM2YMFi1a5PM7iUTCRnv+DOJo\nsNiOiUa+2MEidtaIbV5V46VquGbVkBURUXarhvgEBwezEe6qbV5oaCgiIyMRFRV105P/amPs2LH4\n9NNP/9Q9om670Z02icirA08c+RVDgkS5FkcDq460iiOv4ihX1bAPsX7FEBVf4YFip54or0qlkp0X\njfE/U9fr1q3Dfffdd0P1cC1kMhmT4djYWJw9e9YrtLo2xBA1sV0THZmqx1VDL0Vbwmq11hjKKo7q\nVg23Ej9iG1fVnhM7UUXnU9TDoaGhftMPdWrEx8dXTuI4c+YM2rVrx86np6cjMDAQiYmJNV5fVUjS\n09OhUChw1113IT4+HidOnKiWV3p6Oh55pPp219OmTcO0adN8lk8QBCgUCoSGhqKgoICdE42N8PDw\nm/aaquJ0Ov0+1OuLm9kN7M8SFRV102mo1WokJCRcs67Fmd23mt69e7MQgEOHDt3y/Lp3v3Xr0ldl\n69at6NevHwDvBj821j+TuatitVpvOvbvemnWzP/rc/vCK961hl41cUQhMpLvhuuLm9GngiD8KUPK\nbDZDo9HccH7Xy7Bhw1BcXAyLxYIDBw7c0rz69Onj9zQlEglr8wCgUaPKDQ+zs7PRpEkTv+fni/Pn\nz6Np06Z1klfv3r3rJJ+AgABER0cjPDwcR48eZaMVt6J99ng8ddbp9GdWALxZ/oxzoVarmezeCHSL\nl6MFAK1WC4vFAoVCcd2holdTpzHxRIQmTZpgyJAhmDlzJoBKYevWrRvkcjm2bdtW7fqWLVuiV69e\nrGfS4/Hg4YcfhsViwd69e7Fhwwb0798fFy5cYC8sPT0d7du3x9q1azFgwIDrLt/1NMqcOw8uFxxf\ncLng+ILLBccXXC44V+MPmajTnnhBEJCWlobJkydDLpejY8eOWLhwIXbv3o0tW7YAqHyQrVu34qGH\nHoJUKsWkSZMwfvx4KJVKdO3aFZ9//jm2bt2KH3/8EQDQq1cvJCUloWfPnnjnnXdgtVrx0ksvoVWr\nVrekl4LD4XA4HA6Hw6lv6nydeCLC0qVLMWXKFJSUlKBFixb4z3/+w3rMxRVpZs6ciSlTpoCI8O23\n3+Kll15CUVERmjVrhunTp2Pw4MEszcLCQkyaNAkrVqyAIAh48sknMX36dDRs+OfWEOWeMscXXC44\nvuBywfEFlwuOL7hccK7GHzJR50a8iLgMz9XbzTocDkydOhVTpkzxmswqXl/bxCyHwwFBEG44zpz/\nyDi+4HLB8QWXC44vuFxwfMHlgnM1t7UR/1eE/8g4vuBywfEFlwuOL7hccHzB5YJzNbddTPxfnbfe\nequ+i8D5C8LlguMLLhccX3C54PiCywXnavwhE7wnnsPhcDgcDofDuc2om4VEORwOh8PhcDgcjt/g\nRjyHw+FwOBwOh3ObwWPiAbhcLixevBhff/01pFIpxowZgyeeeKLOdjzj/PXYt28fPv74Y8hkMrZ9\nuFQqhVQqxfLly2/5Tm6cvxZWqxWTJ09GbGwsXnvtNXbe7XZjyZIlWLp0KQRBwHPPPYfhw4fX6S6G\nnPrDYDBgwoQJ6NChA8aOHQsAOHjwID788EPI5XLY7Xa4XC5IJBIIgoAVK1bwduVvTkFBARYuXIjT\np08jMTER48aN89oF2+l04rPPPsO3334LmUyGcePGYejQoVwu/uZcuHABn376KS5cuIDWrVtj/Pjx\nCA8PBwDs2rULixYtqmZvKJVKLFu2rNZ073ipcbvd6NOnD9LS0tC+fXu0atUKo0ePxoQJE+q7aJx6\nxGazYcWKFSgoKAAAKJVKSKVSdOrUiRvwdxiXL19Gly5dsHDhQhQWFrLzbrcbjz76KCZMmIC2bdui\nTZs2GDNmDDPmOH9vzp8/jw4dOuCbb75BSUkJO+9wOLBixQpcunQJAKBQKCCVStGxY0euO/7mbN++\nHXfddRcz0BcvXoyUlBQmH06nEz179sTLL7+M1NRUtGjRAiNHjsRLL71UzyXn3ErWrVuH1q1bY/36\n9ZBKpZg/fz5SU1NhNpsBABaLBStWrEBhYSEEQWD2RseOHa+dON3hfPXVVySXy+nIkSPs3OrVq0ki\nkdD58+frsWSc+mT79u0EgAoKCuq7KJx6Ztq0aZScnEwJCQk0btw4dn7ZsmUkk8no0KFD7Nz69etJ\nEATKysqqj6Jy6pDx48fTfffdR5GRkTR16lR2fvfu3QSA8vLy6rF0nPqgZ8+eNHbsWLLZbEREdOnS\nJQJAn332GRERffbZZ6RQKOjYsWPsnuXLl5NUKqXc3Nx6KTPn1pOamkqvvPIKOZ1OIiL6448/CACt\nWbOGiIg2b95MAKisrOxPp33H98SvWrUKAwcORPv27dm5/v37IzQ0FGvWrKnHknHqk6KiIgQEBGDX\nrl0YNmwYunXrhrfeegsGg6G+i8apY6ZOnYr09HSEhIR4DXmvWrUKAwYMwD333MPO9enTB5GRkfjh\nhx/qo6icOmTBggXYt28fAgICvOSiqKgIUqkUBw4cYLrjjTfeQHl5eT2WllMX/Pzzz1i4cCEUCgUA\nQK/XAwDCwsIAVOqMYcOGITk5md0zcOBABAYGYu3atXVfYE6d8Pvvv2PGjBmQySoj2EW5EDc0LSoq\ngkajwZYtWzB06FB07doVb7/9NoxG4zXTvuON+L179+KBBx7wOieVStGoUSNcvHixfgrFqXcKCgrg\ncDjw5JNPwu12IykpCQsXLsSQIUPqu2icOkYQBEgkEuj1eq9dpPft24cuXbp4XSuRSJCQkMB1xx2A\nGOdeVlbmJRdXrlyB2+3GsGHD4HQ6kZSUhM8//xwDBw6sx9Jy6pqioiKMHDkSDRo0wMMPPwwiwt69\ne6vpDLlcjri4OK4z7hByc3MxduxYJCYmolOnTgAqdYbZbMZTTz0FAEhKSsKCBQvw5JNPXjO9O3pi\nKxHBZDJBq9VW+06tVsNms9VDqTh/BYqLiyGTybBu3Tr06dMHADB48GA89NBDyMzMRMuWLeu5hJy6\nprS0FFFRUezYZDIhJCSk2nVcd9w52Gw2WCwWL7koLi6GVCrF6tWr0b9/fwDAE088gS5duuD48eNe\nvbCcvydbt27FU089BZlMhs2bN0Oj0cDlcsFms3GdcQezevVqjB49GhEREdi0aRPrmS8uLoZcLsfG\njRvRs2dPAMCAAQPwyCOP4Pz582jatGmNad7RPfGCICA8PJwNbVSlrKyMDYFx7jyeffZZ7N69mxnw\nAPDAAw9AIpHg1KlT9VgyTn3gcDhgMpkQGRnJzoWFhXHdcYdTVlYGAF5G/DPPPINdu3YxAx4AOnfu\nDLlcznXH3xwiwptvvomePXuiR48eOHHiBNq2bQsAkMlk0Gq1XGfcgbhcLkyYMAGDBg3Ck08+ifT0\ndDRr1ox9P2bMGOzdu5cZ8ADQrVs3ALimzrije+IBID4+HmfOnPE6ZzKZkJWVhdTU1HoqFae+SUhI\nQEJCgtc5s9kMj8cD4psc33FYrVYAQGBgIDsXHx+P06dPV7suMzMTU6ZMqdPyceoHX3LRqFEjNGrU\nyOs6i8UCp9PJdcffnGXLluG9997D0qVL8fTTT1f73pfOKC8vR3Z2Nrc3/sYsWLAACxcuxPr169Gv\nX79q3zdt2rRab7sYD38tnXFH98QDlRPR1qxZA7vdzs59//33cLlc6NChQz2WjFOflJaWoqioyOvc\n8uXLIZVKq8U0cv7+qNVqAJXGmEifPn2wbt06r2HwlStXwuFwcN1xh6DRaAB4y0VZWZnXUqRAZZsi\nkUjQtWvXuiwep4755ptv0L9/f58GPFCpM1avXg2n08nOfffddyAi3HvvvXVVTE4d880332DUqFE+\nDXigMpym6jK1QKW9IZfL0blz59oT988COrcvubm5FBQURF27dqUNGzbQjBkzSCaT0RNPPFHfRePU\nI2lpaRQfH087d+6kc+fO0UcffURKpZJGjBhR30Xj1DGnT5+mmTNnklwup/79+9PGjRuJqHL5uODg\nYOrSpQtt2LCBXTN48OB6LjGnLkhPT6d3332XANDjjz9O27dvJyKiyZMnU8OGDWn79u107tw5+uST\nT0itVtPjjz9ezyXm3GqaNm1KHTt2pOeee44GDx5Mffr0oREjRlBmZiYREWVnZ5Narabu3bvTxo0b\n6d133yWpVEojR46s55JzbiXBwcHUvXt3Gj16NA0aNIj69OlDo0aNopycHCIiGjt2LDVu3Jh2795N\nZ8+epXnz5pFCoaDRo0dfM+07PpwmLi4OBw4cwJgxY9CvXz+o1WpMnjwZr7/+en0XjVOPvPHGG8jL\ny2M9Z0qlEiNHjsQHH3xQvwXj1Dm//vorvv/+e7Ru3Rq5ubnYv38/+vTpg5iYGBw8eBBjx45Fv379\noFKpkJaWhjfffLO+i8ypAzZt2oS1a9eiXbt2OH36NI4cOYJu3brh1VdfRU5ODh588EEAlbrjqaee\nwrx58+q5xJxbzaBBg7B161bk5eUhKCgIkZGRyM/Px4kTJ5CUlITGjRsze6Nv377QaDR45ZVXvHaB\n5vz9GDZsGI4cOQKFQoHAwEBERkbi4sWLOHPmDOLj4zFt2jQUFBSwUX61Wo1nn30Ws2fPvmbaAhEP\n0hOxWq1QKBR8+2MOIzc3F4WFhWjevLnPVQU4HKBylRK5XA6pVFrfReH8RcjLy8OVK1fQrFkzhIaG\n1ndxOH8xuL3BuZqcnBwUFRUhMTHR56qJvuBGPIfD4XA4HA6Hc5vBXUAOh8PhcDgcDuc2gxvxHA6H\nw+FwOBzObQY34jkcDofD4XA4nNsMbsRzOBwOh8PhcDi3GdyI53A4HA6Hw+FwbjO4Ec/hcPyGy+VC\nXl4e3G73TaWj1+tvOo3bmfz8/Fvy/CaTiW3nfTtSUlKC8vLy+i7GbYXBYIBer6/vYnA4nFsAN+I5\nnDsIt9uN1NRUbN++nZ3LzMxEs2bNcLOrza5YsQJxcXGIj4/HjBkzbiqtzp074+OPP67x+4KCArz8\n8su3paE/e/bsWjeTc7lcaNKkCbZu3er3vF944QU899xzfk/3VlNSUoIePXogIiICzZo1g8fjqfHa\nHTt2YMKECZg8eTI2bdpUTa6tVivef/99/N///R+6d+/u85qqlJWVYdKkSXA6nX57nrrkpZdewvPP\nP+/3dD0eD958802cP3/e72lzOJzrgxvxHM4dxLFjx3DkyBFER0ezc6tWrYJKpYIgCDecrsFgwPPP\nP4/Y2Fjs2bMHkydPvqlyBgUF4eLFizV+/8UXX2DOnDk4d+4cO/frr79i6tSpN5VvXXDgwAFYLJYa\nv3c6nXA6nbDZbLck/5KSkluS7tU4nU4MHToUV65cuem0pk+fjl9//RWLFi1Cenp6jRvkTJ06FQ8+\n+CCOHDmCQ4cOoV+/fvj3v//NvjeZTOjQoQNmz56N+++/H5GRkejXrx/mzp1bY97Lly/H/Pnzcfjw\n4Zt+jvrAZDLdElkyGo14//338d577/k9bQ6Hc31wI57D+Zvj8XiQlZWFY8eOYdWqVQgJCYHD4cCx\nY8dw7Ngx/Pjjj0hOTsbx48dvuLE/cOAAjEYj1qxZg86dO0OpVN5UmQVBqHUnwzfffBOFhYVo0aIF\nO3f48GF88sknN5VvXeDxeCCTyWr83uVyAUCt19RGbb3KUqm0zkYvbDYbVq5ciV27dt10Wlu2bMGk\nSZPw/PPPIy4ursbrOnTogO3bt2P//v3YvXs3vv76a3z00UesF3327NnIz8/H8ePHMXfuXHz33XeY\nNWsW3n333RrDjMaNG4fCwkLcd999N/0cRHTTI15/FpfLdcOydDVVy6/ValFUVIQlS5b4JW0Oh/Pn\n4UY8h/M35/Dhw2jZsiVSUlLwn//8B+Xl5WjXrh1SUlKQkpKCo0eP4rvvvkPbtm2xevXqGtMxm83Y\nsWMHsrKyqn13+vRpNGzYEE6nE2fPnq3RUDl48CDsdjsAwG63IzMzk3138eJFXL58mX2nVqtBRDh1\n6hQyMjK80rRarSyk4uLFi/j8889x+vRp2O12LFmyBEuWLGH5AMClS5ewZs0a7Nq1Cw6Ho8ZnXL9+\nPWbPng0iwpYtW7Bz504AQEZGBlatWgWDwVDtnvPnz2PdunU4deoUO1dRUYG8vDwAQFZWFpYuXcqO\niQhSqRR5eXn47rvvcODAAa9nEw3OgIAAr3xOnDiBNWvW4OjRo9XqNy8vDx9++CEeeOABBAUFoaio\nyOfzud1ur3SzsrIwePDgWuPkLRYLduzYgTNnznidX7t2LbKzs9nxxYsX8csvv4CIsGzZMqxbtw4A\nsGfPHnzyySc4efJkjXkAlXW8c+fOamErohOalJSEzMzMWsvau3dvdOvWjR3L5XKv0JtVq1ZhzJgx\niI+PZ+dGjRoFg8GAX375xWeaDoeDOVYA8M477yAzMxMGgwHz58/H6tWrazXM3W43tm3bhgkTJiAm\nJgb/+te/vL7PycnBunXrcOLECZbO3r178corrwAAdu/ejU2bNgEAzp07h1WrVqG4uJjdv3r1anzx\nxRew2+347bffkJub65W+0+msJkt6vR7r1q3D1q1bYTabayw7UFn/O3bswMSJE9GwYUOMHj0aQKUc\nG41G5myfPXsWX3zxBdavX4+ff/4ZP/zwA7766itcuHCBpWWxWLBhwwZs3ry51jj94uJipKWlwePx\nICMjA9OnT7+m/HA4dyTE4XD+9jidTiovLyeFQkHr1q0jh8NBDoeDli5dSlqtlqxWK1mtVvJ4PD7v\nX7t2LUVFRREAkkgk9N577xER0R9//EHR0dEkCAIBYJ81a9ZUS8PtdpMgCLRixQoiIpo1axap1Woy\nmUxERNS9e3d67rnniIgoJSWFXn75ZerVqxdL85VXXmFpvf3223TPPfcQEdHXX39NMpmMXSeTySgw\nMJCysrKIiGju3LmkUChIq9WSIAjUpEkTKi8v9/mcw4cPp969e9OECRNYegMGDGD/p6SkkNvtJiIi\nk8lEQ4cOJUEQKCQkhADQxIkTiYho5syZ1KFDBxo0aBABIKVSSX379iUiokcffZQaN25MUqmU1Go1\nAaBevXqR1WolIqLCwkICQNu2bSMiIofDQcOHDycAFBoaSgDoH//4B3tXn332GUmlUgoMDGRl/fXX\nX30+34gRI1g5srOzqWHDhpScnEwWi8Xn9Rs2bKAGDRoQABIEgaZNm8a+0+l09H7Wo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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from matplotlib.ticker import (MultipleLocator, FormatStrFormatter,\n", " AutoMinorLocator)\n", "from scipy.stats import hypergeom\n", "\n", "%matplotlib inline\n", "\n", "plt.xkcd()\n", "_, ax = plt.subplots(figsize=(12,8))\n", "\n", "# seme Hypergeometric parameters\n", "# population and # white marbles are fixed\n", "population_sizes = [200, 200, 200]\n", "w_marbles = [30, 30, 30]\n", "# let sample size n vary\n", "sample_sizes = [30, 60, 90]\n", "params = list(zip(population_sizes, w_marbles, sample_sizes))\n", "\n", "# colorblind-safe, qualitative color scheme\n", "colors = ['#1b9e77', '#d95f02', '#7570b3']\n", "\n", "for i,(N,w,n) in enumerate(params):\n", " rv = hypergeom(N, w, n)\n", " x = np.arange(0, w+1)\n", " pmf_w = rv.pmf(x)\n", " ax.plot(x, pmf_w, 'o', ms=8, color=colors[i], label='n={}'.format(n))\n", " ax.vlines(x, 0, pmf_w, lw=2, color=colors[i], alpha=0.3)\n", "\n", "# legend styling\n", "legend = ax.legend()\n", "for label in legend.get_texts():\n", " label.set_fontsize('large')\n", "for label in legend.get_lines():\n", " label.set_linewidth(1.5)\n", "\n", "# y-axis\n", "ax.set_ylim([0.0, 0.25])\n", "ax.set_ylabel(r'$P(X=k)$')\n", "\n", "# x-axis\n", "ax.set_xlim([0, 25])\n", "ax.set_xlabel('# of white marbles k out of {} in sample size n'.format(w))\n", "\n", "# x-axis tick formatting\n", "majorLocator = MultipleLocator(5)\n", "majorFormatter = FormatStrFormatter('%d')\n", "minorLocator = MultipleLocator(1)\n", "ax.xaxis.set_major_locator(majorLocator)\n", "ax.xaxis.set_major_formatter(majorFormatter)\n", "ax.xaxis.set_minor_locator(minorLocator)\n", "\n", "ax.grid(color='grey', linestyle='-', linewidth=0.3)\n", "\n", "plt.suptitle(r'Hypergeometric PMF: $P(X=k) = \\frac{\\binom{w}{k}\\binom{b}{n-k}}{\\binom{w+b}{n}}$')\n", "plt.title(r'({} white + {} black marbles)'.format(w, N-w))\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "----\n", "\n", "## Appendix A: Independent, Identically Distributed\n", "\n", "A sequence of random variables are independent and identically distributed (i.i.d) if each r.v. has the same probability distribution and all are mutually independent.\n", "\n", "Think of the Binomial distribution where we consider a string of coin flips. The probability $p$ for head's is the *same across all coin flips*, and seeing a head (or tail) in a previous toss *does not affect any of the coin flips that come afterwards*.\n", "\n", "----" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "View [Lecture 8: Random Variables and Their Distributions | Statistics 110](http://bit.ly/2MlKHmi) on YouTube." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 1 }