{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 10: Inequalities and limit theorems\n", " \n", "This Jupyter notebook is the Python equivalent of the R code in section 10.6 R, pp. 447 - 450, [Introduction to Probability, 2nd Edition](https://www.crcpress.com/Introduction-to-Probability-Second-Edition/Blitzstein-Hwang/p/book/9781138369917), Blitzstein & Hwang.\n", "\n", "----" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Jensen's inequality\n", "\n", "Python/NumPy/SciPy make it easy to compare the expectations of $X$ and $g(X)$ for a given choice of $g$, and this allows us to verify some special cases of Jensen's inequality. For example, suppose we simulate 104 times from the $Expo(1)$ distribution:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "np.random.seed(24157817)\n", "\n", "from scipy.stats import expon\n", "\n", "x = expon.rvs(size=10**4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "According to Jensen's inequality, $\\mathbb{E}(log \\, X) \\leq log \\, \\mathbb{E} \\, X$. The former can be approximated by `numpy.mean(numpy.log(x))` and the latter can be approximated by `numpy.log(numpy.mean(x))`, so compute both" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "numpy.mean(numpy.log(x)) = -0.5600958563379892\n", "numpy.log(numpy.mean(x)) = 0.00800014338803644\n" ] } ], "source": [ "meanlog = np.mean(np.log(x))\n", "print('numpy.mean(numpy.log(x)) = {}'.format(meanlog))\n", "\n", "logmean = np.log(np.mean(x))\n", "print('numpy.log(numpy.mean(x)) = {}'.format(logmean))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the $Expo(1)$ distribution, we find that `numpy.mean(numpy.log(x))` is approximately −0.56 (the true value is around −0.577), while `numpy.log(numpy.mean(x))` is approximately 0 (the true value is 0). This indeed suggests $\\mathbb{E}(log \\, X) \\leq log \\, \\mathbb{E} \\, X$. We could also compare `numpy.mean(x**3)` to `numpy.mean(x)**3`, or `numpy.mean(numpy.sqrt(x))` to `numpy.sqrt(numpy.mean(x))` - the possibilities are endless." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Visualization of the law of large numbers\n", "\n", "To plot the running proportion of Heads in a sequence of independent fair coin tosses, we first generate the coin tosses themselves:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "np.random.seed(39088169)\n", "\n", "from scipy.stats import binom\n", "\n", "nsim = 300\n", "p = 1/2\n", "x = binom.rvs(1, p, size=nsim)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we compute $\\bar{X}_n$ for each value of $n$ and store the results in `xbar`:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# divide by sequence from 1 to nsim, inclusive\n", "xbar = np.cumsum(x) / np.arange(1, nsim+1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above line of code performs element-wise division of the two arrays `numpy.cumsum(x)` and `np.arange(1, nsim+1)`. Finally, we plot `xbar` against the number of coin tosses:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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5c6azjXz22WcAbNy4ke+++w6AH374gR9//BGAb7/9lo0bNwLw6aefOtvIBx98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\no8DFwOf3Z2ATtavGe88e797uLk48fA6ANd6SJEl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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.arange(1, nsim+1)\n", "y = xbar\n", "\n", "plt.figure(figsize=(12, 4))\n", "\n", "plt.plot(x, y, '-', label=r'$\\bar{x}$')\n", "plt.hlines(p, 0, nsim, \n", " linestyle='dotted', lw=1.1, alpha=0.5, label=r'$p={}$'.format(p))\n", "\n", "plt.xlim([0.0, nsim])\n", "plt.xlabel(r'$n$: number of coin tosses')\n", "plt.yticks([0.0, 0.5, 1.0])\n", "plt.ylabel(r'$\\bar{x}_{n}$: proportion of H to $n$')\n", "plt.title('Visualizing the Law of Large Numbers')\n", "\n", "plt.legend()\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You should see that the values of `xbar` approach `p`, by the law of large numbers." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Monte Carlo estimate of $\\pi$\n", "\n", "A famous example of Monte Carlo integration is the Monte Carlo estimate of $\\pi$. The unit disk ${(x, y): x^2 +y^2 ≤ 1}$ is inscribed in the square $[−1, 1] \\times [−1, 1]$, which has area 4. If we generate a large number of points that are Uniform on the square, the proportion of points falling inside the disk is approximately equal to the ratio of the disk's area to the square’s area, which is $\\pi/4$. Thus, to estimate $\\pi$ we can take the proportion of points inside the circle and multiply by 4.\n", "\n", "In `matplotlib.pyplot`, to generate Uniform points on the 2D square, we can independently generate the $x$-coordinate and the $y$-coordinate as $Unif(−1, 1)$ r.v.s, using the results of Example 7.1.22:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "np.random.seed(63245986)\n", "\n", "from scipy.stats import uniform\n", "\n", "nsim = 10**6\n", "a = -1\n", "b = 1\n", "\n", "x = uniform.rvs(loc=a, scale=b-a, size=nsim)\n", "y = uniform.rvs(loc=a, scale=b-a, size=nsim)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's try graphing a small portion of those $x$- and $y$-coordinates." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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Oy7oHtkXw+KEuEWPnrAQXfgomJ+9wVyEf5Dx7wAQKFq+SB+sxjzSng0BmVrPh\nP79Zxo9mt+C4FFdmthT3IreawxYz2RAyWe0sDLAV+I3Jul4tVjDrnYtb2Px8NxYLGOxQ0xjHe7M4\nf6gHl++uh7o5A/eKAkuFqkZU7RPjgFny/i+HOttE27nng4B5PuQ+TS6YY5QuZZN+vkE8PZJr0IQ3\nAAgu8mjrgPvHv+l7Gr746yAjJxuGGfSwBYDg8WMToIkku5ZlgZx+BuTU04xL4IUO6KVvgfYfiu/R\nkLUbLIsZH47D/vvkT4J++CaQSEsvJgE5/Qxr35t/Gmyr1C4ycjJgTGFnO9Qgc+78CPjobfaH6ypG\nHp27CWyteKERIF9ZwGcPATfqnYGYtWk89rezcBcjGxJ0SgYA5zbJ4K9W3aWhZNxGcCnL0AnTG+Cg\nYOFIeYHj4EYN4Kefi8wDLy2Kky1N55cXNYsQTK+VFON8vC+LpUIV8kYpbDeuk445f4ORoUdEuFbe\n3Ax3ZTCYS4l5+u5aGeO9WYgn5M2NU6slZc4d7mTcJ50QykOxPmkZ6M4mRJiDG2o3Fgs4O9qpGBKM\nJ1bF5EJBaMbwfy9/sNhUdsipfE7JzviVUrHY+FeNcaCMBcCLb0vkFP5AjvRmFDdZTzaJu2vlUNY7\nB3c3WwDG+5nw0WAuHcgdvnx3w3fduRSphI0vPDaqvGTwFqmlQsVzd/uuQsdbbKNcmxRQruNSxmY2\nLl78B/DZv7xtFEH3It9By7ud1WJFGDX6oluuuajWHWEQAfB2F0RYzyavwe2VbXFP766X8dzJfoVR\nvF6qBXgEt5bZuzDU2Ybxvqy4Nk+NNIFrZ8g7tlvLRYUz4MdTfc4BT8lk7aF45946Oivr+MQpvrCY\nn0/CI3CSXXgIdguxyF9/nbkm7/zI2x2DLZ7XXzcumqZwgWyouG/+aeB468kXjP2iM5PejEgBpwb3\nBy+BnHgS2Nlu2H+lXS5APvEs0NkPulME3v6uf6BlA7CYQTQ4rnoLTj0ttdUFfe/7oNdf9w0czXAL\nC+dg6op0Pd97ETBoPvEsrFNPY2TkJEYAZTFKaO8GH58bpSqeTszhbmoYd4oWrs4XcGNxW2ww9kPo\nTIflkYBnNsqR4QHAT8uUPYtyJgQAiW/khydeu7WCC8f7ldCi5nvCubEuLG9XkbAI7kjtyKZslGuu\nkmqthD+kMPDkQlAMzgVE6C/KAC/XXLFgO2IO8M9xdX4r8EbPb1UCc2rSJtgs13Csv0MJH2yWg3oR\nOsdKhkkzplQLDx9zyN5obhDFIZk3gwNnLAAsdsZ1FJhLKifkWzmWC5XAAIzK03XhuwCJQX1rU5Lo\n5Mx//jBlkSWXMtYyjG479oI9YkNEAAAgAElEQVRH7Vb06xwfaA8ly/iZFQSFnRoGc+nQvPATA+2h\nrkg5zld3KaZWSxjqbMOx/g6sl2piMqLwLevPnh0JZANkklZAte3a/BaO9XdEcnTurpdFhoasABcW\nTpVDEPJ9HuhIYW5zR4RZKOUaE1Qwk4e7Mh5TnJkTlAKXFl30pW9i5KGTmMjnBKeEC/roJE9lIZX+\nvl+g11/3jQT5c+//m9VICDvetND6x9bYYJt+H3T6fXb9RCqS9Bi4jucRcF7679UDB4+AHH8iwDuA\nU2d9tBM++RJoaOAE7tPMpBQCIYDkvcDWikTspMDmkvLbMyPd6C0vYWZhGWP5AYx4vJ23ptekRcrF\n8twcpvryoBYbV9x4NXGEdmM66GTdiTwLCRV2wl3/Mnh7uLGTSVoBct5Yd0bx0C4WKvj2lTl87tyI\nl8ZdUDLRHAq8O7Mp5iA+j1gEuLZQEFlfFz0ROZMQlClrgIMTtIFguJN/VtipKeJ7JvE2eeMQdq9q\njm8A+GGRqjHzrhEWt3aEAN/kwlZoVoYC6msC7beRwHEgjQUOnt50Y7HAXNDzBeHuMZEBh7vSKNec\nAHtWB9uNqnnGHDqrOEwOVgdPB+QETX23ousf6HFPk1Qzy6wguD7PBIZsT92xXHMDaVkfLhfxqPfC\nmUIMMrgxxolBOng++BNHegP8BB3tqYQ3CcUj+PAdRyZpCTefTQj6O5JKPPPWchGdbao4yvJ2VUyG\ni1s7wshhO4yCEGVS1OUIAaUWZhaWMJwBhmYm8dmxCcwm+kOzQOJkF+wXlMUTBCAeKdC2RWqjMczg\nufHDMgniekf4se4PXgI8I0GgXoskPYZdh5x4UhgcAEDOPAvr0U/5fZbTQk89DZx6Gu7114Frr7JF\nP8TACeM2BIwWyXsBoiUoTr8Pd/YD8Uzp3E0M/dk3MOT9lqe8+oayC5uyrA6X+FkUurAav0qYO/+x\nsS6jJ40TkDfLNVwu+bvZmuOKrLAwX6XlnYCfk3kYdnB2tFPICdsE+JwnqTzclcFEvkOZNxwvjdsk\nBc9DEPy4Y31ZDHW2YXqtKMiErmdQ6OEPvgkq7NRC54UBL1xpCncCfgq1zEliUE8oe4SiZO8BNq8c\n6+8IhEVswuYRY70HjXx+e7XEQjI0ftkAF4yjcb8MBeCAGwscTJCpii4pvmTC/GaFLdQ3Vxo+xHwn\nkwgezKUVF71OXJJfAlOqngXglGYx6gTN4a4M+trTmNucM16nrz2NU/mcIsTCyJMs1MH74lAWAmHc\niJpi6PCYu677EAXGcwgaXTyeqFv7q5JcKz+OM8I/f24Ul++tY25jBzsRBbpkkhHfpTxzok+wj/kL\nfHe9DJuUFSOET4YXjvdhei1ouHBDJCsXh6EUhLoYbXPFAjJkJzD8hRdBusyL0IOURg4sdB5pL7Ag\neotmXEOmGf4EGTkJ66c+D/fuVXW2JGjsxTBcx3r0U2zi9QSgZEMhzMCwR06CnnpaaDTQmUnQlXvi\nXgAGHkZIqqny/EzS2tIzDXvWgsB27x5GfvgHgOPgg77HUCdMZl7OHjItTnzB5DH9Y/0d6MokhUy1\nd3vx7Ml+9LWzsKgMWTKagumE6O71cY84LCOYpgz81UcrSNgWjg+0S9la3rPyrqB7SLiBc2VmUxw7\nvVbG+cM9uL0SLGXAhasssMWbhyUJpI2ZtqG4vVpEpe6HLeRwJ+8L7//UWkkQmOVzmPRyTEJ3HPlO\nM7cjYRMj+RQAtg0b07iZKhyyrLnJi7IfOFDGQjqhLnT8Nbc8+dE4bPqlQoWRdwwmorzQzW1WsLhV\nxWAujUeGWDZDOmHhjak1oWxocsOv6+ckMLqWTDEpfh2ZxKNb1TJ50hQPnd3cEcphesZEJmkJfgBH\nR8pWlNN0mGJ2fdkkbq9si52QTADlE8DRfkZaBPxshU+fGcHLHywpxWIAZmT5KY6MkCTzNq7Nb+HC\n8YFAXQnOgpbhxy39+8KPkTXw2YToghDg4hDB8PYaqGFRMC6+90kaOa6mghA2QjAEcr8MGTJyEjj/\nCyrX4Pwv7Prc1qOfAmRvgtb30EyPsQlV6hoENJHUuA3BfgfOyZ+f5c0pruPNCUT1XEQ8a/YOnwTt\n/QrozCQ+02djNtGnTPJyTJ2Dp/wCEBsRznHQ/Bwo19xYOfttKTvgscwm7VjePE704xyjc2NdvkFB\nWOo5D0/Iu/jhrgwqdSreZ4dSvDG1FqipcqwviyszWwAoC/dKBgwFMNSZxpHedoUQDjD9hPXSFiz4\nBHZC/Cw202ZIJlRz7w6g1tjoziSV9mWTFkpe+vSt5RKOOFQJbTw13ovLd/WZ3YfpFuseaa4FpPNd\n9PsZ5kXZDxwoYyGbsmF7g0aOJxd2aoHUHlN6jE2Yqzost1j/1KHUqOh3d72MzXINn3xoQLjhq3XH\nSHrhg1gWYdENAj3zgjOHdVJQ3WWS1s89PIS3pteM4Q/ZsyHH6ChFoAhLwiIY7ExjW7OY+9uTQufA\npWygO44rmNsrpRpWJJeoTgClYMRMObODD/yJfE7RjrcIFC0Eh1KFKAUwpvFLV2Zx8UQ/OtuSsEnZ\nuBMBfJ4H5y7oee38nn/unJoVQudgXBTc66+rxZquvw509ofu8HeLuJoKxnRBqR3GDAops2AvxEz7\nwpfgdg8ZPQKm/sRN8YzqEwAz4VFeUmVuQ4QBJ19bD9sIVUntmcaRwebPZwSAPrXrOgJyurIsF8+N\nXHk4E0BwkUwEQ7VzzLDQxdWipM1NuDa/pQgRuZQt7hb8uYR7EABGAMW8//u762xXfLinDZvlOo4P\ntCOVsEPnXHh955loS4VqYDPhAhjJpbBQqMD15jHOR+LgBGROYObz6asfrgDwF/4Lx/sws6Fmp5Qk\nnRWHUtz2CozJGx6Tp5JDfyb92SSO9GWV9eD0cE7RqTnW32H0HugpmZfvrqOrfygfevEmcKCMharj\nGglnXJFMfykO9bQpClkuhUJY8SsolsSiow/psCH+zr1NHOv39eFfujJrPE4m8siqjyzFhpWl1TMv\nuJtNrpzIcW2+gMFcOhBOMOmOyy56lj3hn2wol8JARxsGc6mAe82h6m8XCxVYDVLOZWIm4E8aIqYp\n8Rw+/9iolBlCAwWdTPfcpb7MLCEspckmRBFvOiZZ6HqYR4fu2QnbwePaq36LCAGV4ub7yVVo5BFQ\n9Ar4cfUq6Pd/j30vtYf3A20dvoSz2EHvXo2Rzt1k6YmSvHTo4t9Eiqfa95qi5gjdYwB4RkFN8QRw\nbkOYMWS6tvXkC+L7UHKkLIM9+4GSOtpIQhtg4+wzo45PkHxoSHxnqqwqcxwI2Ps+uVDAkd4ssqmE\nKF6npxnekXhGckri2dFOJaOpERzXXJ1XDhxyHsNwV0YRNBPHUl+Z8N2ZTZwYaI8kYcqF5mSCsQw5\nzVH/jhcC5H1eKlSNdWO4xkUc24mCKVaeP9QTKsLHdRx0IuRKqYZ8l3pf9PsUlu2gk0xvr5bQ2ds/\n2rjFjXGgjIVixcFrt1YDdeQzSQuPDOWUYi8UZilNBYR5K1RdhOgSqPK55KIvpgEoV7PUy1I7nsfB\nVOxkeq2Ixa0dY1iFgheVUYuXJOzgav7YWJfQXSBQX/jlQhVLhSpuLBI8PNiuxEA3SzV4dDrFzReH\ndd2eskWJa8454F4AWQRLNvRMkrcmiL0kDUq8AqqWwm5SjwKuap1FPzgOLN6J7eKPs5iIa0e4uwPp\nfbK6GPXaJ7WH/1NTJLWdeJPhCdNiq2gwJJL+4i9nb8RI8VT6TogkA+0x/Q2ExyhPgLH9uwzP0Ouv\nA/Vq4B7H5YaEESQBs4gXz7zYzg7g2qblpUFDGAIT+RGcHe1Udq3yqyMXo5rfLLNshYa99LFSrCEk\nSqv3DAAakpddikBJbo62pIXebFIp0jbclcEzJ4LFm6Iw0NGmzSfm7AqZkCl/FnYdl7JN3UQ+F+gj\n32xN5HMYLFYCWROlqqMo9+pVdcNgIplGpds3gwNlLAAqwcWUAtgMXAqRRcAZwX6Rl3rAHSYjIQ0A\nVjo2WHp6uVAVrnjd62GBpdhMGXKk5zYrkcODgqmlyYOxJ5sKLKCVuit4EABR+iNIkS5Fb3saz53M\nMIlTKV+ahzEA5iGRdykWgHxXOlCPoSTxHyyoLG9O0grKRgdf2WjDRG4ZQ6KJFzIuAgv4mYuMVBeD\nq9BsxkRUhoKuV4Cho8DCbShUUpOEtNx+ybMQx03PrxtG6nSvv86UF4VMs58ZEeadE+2p1yArQoZ5\nQ0S6pcFj0KxXZDc8E/e974O+/4r/gazPENP4aHScbNTKhsVC7ghunPhF1CUCJp/7TFlHop9goYur\ncxuK5kAzoIaNASEAob7wHA+VDndlcPFEf+zFfSiXQnsqgam1EnZqLuY2K/j2lVkx/wLBXbgJvH08\ny4xvHKOyK4a70ljcqgi7Oc7mhxcHvHjC54PwcLYswjSizYXZVEJRcNTTVMNSQWc2yhjMpZXMvv3C\ngTMWuJUWJku8G3DBJFkAhIU2gulCZ4Y7hQypunMNXtxFMG2Il6WeXitFiqnIfAObEAzlUoorLpuy\nRe5ze8rGeG+WKbl5l2IlkrdFrO7saKefB+2dl0LVjDgz0o35zTKm10rKC3VquBODuZQSU3WBgKGg\n3wUKZrCIUIgXSpBlo+XiSxyN0yz9rY9FeLZJZ9OehEYwhib6D8XyFuxmJxuWoRBptHiqhhgcB73+\nOtzrr4MMjosdtyk239BNz7eWlPoeA70NAKgs30z8hdQ69TQrQuU4gRRPcvHLRkVIhZdhuMd7Dfc0\nky7K7wcLh0h9PP2M354GnqC4FTSVa2qlyl9I3cEHvWeV9ziTtLAcwuQH2PsarvMSH4HXj7L3zDT3\n9bWnRbaDiSvGYRPmBShVVW8q97Lyc8bN2BrKpYSHlZMCdb0HCn8umdusoKstIUKmYVOMbETwteG5\nh4fERnKxsCNCtzwk88ljfol0OU1ebpue9il/tlqsKPWOugyZdXvFgTIW2tO2Iimsw2Qp2gTo71DL\nWhMA3YGHoe5UuYtQliBmbkBz5bSwxW29VBNeB4tAMGJ1Ep8OXRBotVhRjIV0Qg2ZTHmkHG5kjHsy\n0RTMNSmzb+Edx8WN5P4wN1in8ELwbpnipI1sM+odqTO8ZQVOEwGMp6uaiVnUs3RcHN38AI/n2zD6\n8M82aMnuoS/gcVMO9zNjopHRAkBwBAD/vvOFPlZsXkknlL7wPAa6ABLAXfQ1UedByeD44q+bF+ad\nbfiKkPc37VRH2LMz8i5mJn2vCf/94LhyLqPipYmseeppxkHwRKlC26eNmZEj4xgdGVKkf8Pk4i0C\nsWFohMM9TJExbLNieretkKwuIDj/nR7OIdeWFFVrM0kLS4UKJhe2jd5anqnFK92GVdyUQcGIz6vF\nVTwy1CFJNFMc7c+i7lAvNbWiuPRlbhWXq+YcrcfGupBK2IGsjMmFbWUzcmNR7wM7cCKv1gBixQvr\n5to40me89oZvoFBjZt1ecbCMhVRC7PpNA+qoR1aU49+c4GITf1BcPMFyl3VLEGCZCdfmt9CeTmC8\nN4u76+XQhVWvp8AlQvX4+5DE5H3t1qqQXTUthj3ZBEa7soEXU3c96qQbfQLJJm2jmiP3KABszja5\n/CbyOdxYLAjLF1qedaO8Yw5+X0u1unLsbY2MFVavgrv9CCjGrQLG+zuwXAHoR+/gkdUryFcWYD31\nYmQb4iCKW9AM70DGrnayTZRklv8W3AT1jE0txkqIQH6zJI+B3oao/sX2khiKRt1vwSs93GK6Hhmb\nALVs1WDYUfUDTH2MImsSz8MShrAxI3s75Wqtch0aHoK7u95Y4n6gI4VK3Z8TlTaAzaO6IRHmuTOp\nKJqOlaWkZXDvAM+aMmU4RXkrWF+JP9cBYpPEBajCMN7rF5fT5x45K8PxFGDl3b+MtVJVCGQlPP0b\nub6PfG/4c5KJraWqEzhnW8LGsb4sitU6NpYXpkM70QQOlLHAYVIh5CVhx/uyeHdmAxulungAi4Uq\nbEJwZlitsiinz60WK/jeB0u+t6FQFYMO8FUDuQvdVGiKv7SX760ri6NDqQgPyLKrS4WKYlECQE8m\nheceHgz0mfEi/Jd7ebsaWnWOcTdU1TK+UyeAIDBZhMnFzm+WA94FeQEHWAqWzNpeKlQbehdcr7Tz\n+UM9mF4NMoplJUgASlxPyU+nLoZm3sSpKz+E9YUXgaHHQWcy+5K2GLU47XXhiuuFaNSGRgaHsgCL\nD808hqi2ijoUPISgeQx227/AbyJSEfXF1v3BS0r2xV4R2PmH6DOQkZOsKiYPRdjJhveSzt1k2Spe\nQSqdrKkXrzKqTUbcUz1kN5HvDPB/5FRu7k3Uw3qyRPOxvowotETgi0DJmy55MyXH2gHZ/R8tV6wX\nlOPnPT3ciVvLRT/tmocPKPdmsHPKNWd0pBNESDTL82ndpUoaqI7ptTLG+7Lib3nzB0CZX6/NFwJZ\nWxxyOFaW+aZg8/WxvgyGOtvEPZvZKCtz86sfBotKTnnebNsiqFbK4SSVJnAgjQU9pnVMyoeV3Ucy\nXEqR8+SBZYGO4S5W1tk0EGXeAKAWZNHTHZe8MMfkQh3jvVmxOPIXYmXbDxlwpcHPnh3BYC6tqLZN\nr5WVxVt+OZXwADXvAIZyKaxs13Btfgs3FtU0Kt5mP2W0jGvzWx7jVzWk9GwCmawj7wK6MwlkkjZ6\ns2nBa+CiSRSMo/DsyX587twIXru1EggH8bRSPYany+mOFu6ICdd68oWGufthaEaN8UEpNdKZSUnL\noSYEl2SJY+HSXppi41LiJQi3v1dwSv8uLvhCRSNSEJvqV0hapSkVUQhNtXWoqZHTV+HOfmDUtdiN\n1ye09oTB02E9+ikR7uGqkfw+mfqqZKwce5x9MXUlQCrdrRGqp1ryBZxjfrOMy3fXUaw6OD2cw+fP\nsUJ3a8WKkpHgpxVSrBaryoajXHMx3JXB58756c1yMSj5PVXd/75csW5Q8P/W60u4lAayz2wCHOnL\nApSRBHkfoxb9y/c2sV6qIZtKKJsXk+R2n6Qh41C/XLgllermkAPTjcIi8m8Slhp6lXUp9HnOxNkC\nVAJ6W7YjFzhgFziQxoLuOh/KtQHg6YnqsdxKtS2Cat3BS1dmhTeAk03eCbFYgeAg0SubcchWp73A\n+AZcytV0Jh6/GuvOaIQaNfVJHlwXjvchsehPFopssdfXgY42r1CSfw2+U5dzj+suBS9h7VCq1E6I\nIgouFapiguApjAXLwSeP9UvZJLNK2OPShyu4eKI/cA+O9mWN4jTc2/CZUQczU1MYvX0J+dLsrtzW\nDV3OEW7x+6XUqLefzn/k3xtKQXeKoBIHAQAzIr7/e4Jwp/MSdrPL383uNu454mkq1H3DiC+0nlFE\nP3wTmL7KelpX3fnWF15UftPMgqsUxiIEZHA8kG1h6lOja6kZKxS48663PbZAPvGswldoxgiV2zI8\ncjKyxPxL786KRWaxUMHDg+14dLQbb0ypxd1kT4OpQB5gTj3Wq8zK7n9VT2ZWSDsTzwXPvZ16gSf5\nb77Rkb2yXMROntdt75zybMKFo2R+GJfcljVXAH/BlkMepnT5uAaCDp03YqwKLM3/YcX/APZMdkrb\ne2OrejhQxkLNcQUJRk4bzCQtRfCIQyYJ6uWWZfGjsEGRsAC9jIFurZrgUOZp4K776578stI2KatD\nt4Zli1xW85KrxvnhgYKQNr14ghWckc/FwwzVukrWGuhIBaqz1V2K732whJTNvCFyxTe5aIuehy0b\nJcNdGTwmy8UCIm1SvgcEENa2vmMa686o+emGCZcj0jMQw+UcVbmwWd5BsxDtq8u7JgLMXDdwEAgU\nZj47w649HvvBDYgMn8TRVPAMMP1YLvzkzn4Ak/YCNzDiiFgZDSEtI4NIJFCjnkSMxT1UK8IFU/yU\n2xDDCKVzNwOeJesLL2J45GQ4yVD77IOlImqOKrLEiXy3louKoaDXUDCl9umhhFK1HlBHffmDRbGw\ny0JwsjiSDgI2H/KNjgx9TidgtWIABPgDLoAz+Q7k2pJKu+N4SU2eBcBccyMK8nF8E2gRM1eBp1Tq\nIQlu7Ix7Qlz7hQNlLGyUa/jhnTVFwjeTtHBtPqj4BQDHB7LimDem1kIXZVlK9eRgO2oOk/w01TuS\n44RhamDE+195B26Kw/EBzK/PF/ywl5OrIsrHyDuN1WIlsEizMMNWoJ2sQEuw8ZyzsVjwNRFkjgh/\n5495RWpcqu5I5jfLAZchQdBiplDr1YuiPIUp5ItOUFtAm3DFuccmmDqhQwFCQLdWQOdumnexgNHl\nHLWTVhY/6e/9gGiffzUgkQTaewHcVg8+9jhzae+Bl2C89h5CLFHnCFsQQ7MItGPl4wLaC9ydH0PE\nymgIRWRkGPsUY3GP017TsZFprIay3GHPaKw7Y+QwLW9XlAq6+c40rsxsBWTfdUPBlO43s1FWtFZu\nr5ZwZ7WEZ0/2S4uxmlUWJ2tq0Kub0NeeDq1uKftnyzVX8Jxkg0HWf5D5T7rhIxsPutdhcmEL1z2N\nA5sAn3yoP0BstOAX6XIpzB4BQiRJasbdKtfcAI9Mv8fUey6UQigLD4yO78ukc6CMBUohXDjcmo0q\nEc3idEH1MAIEFly5ZoPutuOQiT5LXnaD6dycJMSLW+msZT6AOXcizLXIF1G5eBLfpXOipaxXcHtF\n7asf2lDbyFyC6o5Dzj/muDa/JQpm6S/sUK5NSKHKfTIJZXElSf05yfXq88V7GPw+c727byZAnv1K\nQ61/FZQx1997Ge71140hBl0SGIgu5QyoEzf1CH9RNRGaQUA0afwcSHsXaCoDZYq0E7Ce+DTwxKeN\nvIS4/ZAXp/0IsUSGcCIWRFNmR1ixrCh9i1giVoZFNrLvbR2e64wYDZdIoulItFZE2LE6fCOSvy+N\njcLhrgw+/9go/uzqvFLrYLviCO4VQVAbxeRRkOvROC7F5XvrjARJg4s/haqdMpHP4bq2ORnKpQMK\nhzIWCxWsFqsiM+q1W8tKoafhzrTIJkt4O/KXP1hEqebgaF8WICz7ixsKeujWtCjrxgPHarGC5e0q\n2lO2kI4HGHmzVK0jm7IFt4sbIXpdoGN9WezUHJHq7lDfqOHhbz2kI9R8pfvq+I9ftcB2iQNlLBDi\nu6zChJni4PFDXQEWMU8VnFwoYKgzbfwdt/r0FCZOGOSEHD6Q/FeLiJdpfrOM716dE5kWfPA8caRX\nMSBkF9pT470KD8ClanEqEYPT7xeCVr2cOipnOJw/3K0QLQF2n3nYRz4Xz4vWDRxTaVc+ER3r7whk\nifCKcAACEsFYmoo1QauSzIC8WwwLMfDFKJZcr0w+dB3Ql39fqQ+wF5h2o1SqpgjCiHLWE59W2q60\nL0Y/wo5Rrr0Lz0mjcwjC5NzNhsaMstCGtDcuqbWRIRTq3eDkS9dloa+LXw70pZl7s9sxohuRQnSr\nwTMa7srgF84MC16WbuDrc0HCy2yS07L1cK5FiJIVZpptKYDXbq3gwnG2ARvv9YnXFGy+SFjmVHEO\nmas00NGmGAu97Wl88qF+sTDr4QebQChA6vyna/OFUMNHz2JbLVaUOZBnSvB7wmtBrBYrStZERXNB\ny4aCfI8AP/ydSVoinMtDErdX1PIExP/xbukTCg6UsdCdSeInj/aKhSqTtIy6Bl1tCSQtIqok6njH\nY89yy1Gx8iizvi0CdGUSqDtUFGhywdxUubakwmA9NdwZSHeUi6Hw0q3HB9oD7F+ZO6FbxJwgOZHv\nxGNjXcL9J0sby23XwyzySwv4HhVuKOnpkbobc3GrgvnNCnOzSZ8P5dKK9CkPq+jcA3nHMtyVwae9\nlNNby0VR5ptDfxtocROIwRVQCGu8sJBlKeGIUCMgjhu+rUOddV13X7MiePt8rQR5WiYgww9FXitO\nP0L5A3HJe3KmQkgthv1MP23Up1ippg2qgprGhbKjpzSgq/CgoBszQHwy53BXRmRBmGLy3IgYyKUx\n1t2m7LoP92Q0wmEaAx2p0JRBGYuFCr59ZQ6fOzcSiLPPbVVw/lAXKnWK2c2Ssa6LHMqUi0npaohc\nz0CGrACpi7wty9lXBIrhwwtL8QW7rz2lnPfWcpERur174lKzOqZNCGziq0bqhoIMAl/mn6ernh3t\nDIjQ8VBHNmljeXbqZugJm8CBMhaStiVCD3yAH+nLKrtViwDnD3cbc1c5eLxtaq2Ez58bNeYAuxTY\nLAeLPC1vVzGYSzdMYdKLmehVGOX2yl4SCjaIZeuZl9/m7sTDvb7bLEwalVKWeiQzn3m8j0N2wb01\nrXI6eiSFS64Vz9srE34cClyV0i/PjnZiebuK4wPtRiLWmZFuQ20ITSLYsoCpK6C332k4Oeq7WyxN\nMZ2A91/xwxFhXIc4JY0vfUu1ZGw71B28WwEnpT3csxCTjxArnh4lTSwvzPWgrkEwfq5mYATOsQ/p\npw2Fm0LOqaQv7kYXQ8uU4LUrPm7EMgi1rAn+7vHCVGN5VtBucm4DN9weLBUqWN72Q6mOS1Gsqov4\nQEcKg7l0bOlonsk1kc/h2vyW8tq8c28zsLGTVRN1b6peQh5gGzDTFtuW+GerxQr62pNoTyeQTdpi\n7uT9kT0WMpfKcSnaU7ZyXq4A2QgupTjtSWHLUtAm8LVH/1stCcCyQu6slDxRvP3BgTIWgGD6TjZp\nBwiCLE2wsefGpcDle+sYyrUJkaTJhW3FktTB42s6C1hGWBVFU8xvrNuvmBaWQqPHCG+vlHB3rSzi\nccYXyDNiBnMpX1+BBI0LWYjEktKONjWvDPE8FcVqXXnhOHj6JW/t3EZJqQEh2u+xvAmgZDeQEV8i\nmG6tAO+/EnuBUXbJb/4pcyM3+G2cOHQwdhyO/RBwUoyemDoJUf2QF5BQ/oBupExfhXv3mgh/BO8B\nDdzXWOmnUvGoOGqVkeqQIdfbF12MI48Ct98J1K54kPBLfDugtt2QvxOapqplFAHAzMBfgzv8HCgh\nGvGaoD2VAAFLu7YAIeF07ZoAACAASURBVDMdFzaRUy/VwkpKDB5BroQOc9VY9T3MpW0c6c0KDsHV\nuQ0/jFCo4vyhLmVTd3q4E6vFVbFWyFV5bU/UryebVDyf85vlhp4VvpyPdWdQ2Gm+nsN6qSY4JXJW\nCF/jWjoLu0RQmKRT0U7ncXz5GL6w6+IkAHNL3V4pCUMjnbBClcI4OMGSM3JlcLnoMOgv0d31HXz3\n/TmcP9yjpPQ0KpXN9R5MnI2RrrTQPdAFmV67xTwuS4UKSjVHMHr5pAGYjSSXAlMeO5eDp1G6ujVD\nCOqui5l79zDcpbmPPf0ACoBeexXWF3/dHOPmHIYmyXemxSn02AZxZaMEckgYYj8Wqr3EuXW4730/\nUD5arhEhX9P6wotwf/CSr2tAKfDR23CnrkgLlRTmaZbMKKcqvvJNdieldMBmCYDinJoK5F5Im7vJ\nQLhfcN/6rsLfoQ34O6GeFuVzFqgcLdyBnXfgEALbskS4c3JhSw1ZeiugrhwbBjmlMYp0DjCjolGa\npo75zTJKVUcqrgc8caRH8ZTeWlbn9uXtaoA8rmc/ML6B7x3mxsOPZrfQlUmiXHMDFSV1uGDe1RuL\nBVw43reripEUjBh5/nAPVosVXF/w+QwtnYVdgmcIcHUx/pkpi4BnOPB66W9NB0tziFA0ZYzVtoTZ\nrW97oiK6xreMMCVIGabF/fZqCXfXy4LoCMDLpiigVK0L6VVZ44DLLpv0HhakmNn8ZlkRkdJDHKJd\nDSYDXTK2J5tEymb3oVKnntuRigZalGKkMA1AZ6lLeg+OY85Zj8k+D8U+7Q5FO7gEckR5ZxOL/kFA\nz9bA4z8PVMu+ZwaAXD7aBDJykuka3Luu1kJwHObh4CJJA0dA2trNu/0oMqOSqsjPH/RQNNNnkwqk\n8rzCftdowW0iA+F+gM7dZGNXAkED4yksTVXPtgGQL83ihdt/gLmf/ArGDo0IUqA+LXES9RNHenFu\nrAs3FrfRlUngkaEcpryUSf0el2uukXSue1OHcinB4eprT4emacqbPy70xM93bqwrkOVwfKBdZI0B\nEKFQfW3QieHc01+q1sVcKvMZLOLPfzYhODfWGdCpANjcPrUWvC9xUazWMblQEKnuFmH1iCqlYjCl\nbxc4cMYCx43FbdRdiusLWwppTz2GZTjcWNwW0qRRoADKGrOVE3MAinTCCo3HX53baGgoADC68AGf\nDQz4LwonTcqW92qxorjJuFEhxwhdypXPzFZ+M4OZgKUNpRNE6Z+vx1DFcyf7MZjrx6Wby3CpC4tS\nXJj7C4w897x6rrEJUNv2d00R8f/d7LLvx+5QLIIREsh07iboK9/0FloCnPvZB7YbZZUfvTHlOsDb\n3w0eJBWDUn6rp1M+94uKSiQsS9UMmP0AJCK8EprFYFi0Ig2viDYCMQiQnldK5qwYq0FKoZ7dZCDs\nhaMS2t+ZSSiKZ8QKFKAKPLcQ49pElKQzkxgZm8Co1F5j3QZvQyTPa8Wqg0eGcvj0J0ZwdW5D1R4w\nCA/xKrLphOXXqYBPALy7Xsax/qxWgbGgFLETaYZaWHZ5u6r8Tq4xYyJQ65hc8FO5Oe9Kh5x9xitp\nyjU3dBACI18hrIaPjuVCVVkfKGUe4K7+oXyMnzfEgTMW9Dxg7hEAoAwOnTC4vF01Zk6MSDm8Oo71\nZ3GsvyOw4M5t7iipkEzjIJw5zWSYU6GGAo9VZZJWwMqWRUR4tU3HpUobhrsyGMyllJeXeV5oQwOp\nESiY5nsUbi0X8Zmzo8zFd+8eRgrTwlCQd5mcl2DiLOyqbWF1HvZxd6jE/Q1ufABq2icocPnPQY//\nxH03GOjcTebxaITHf95o4Jj0I5yNRdXgWJqKHV6JyrowLVoN9S0MCoaBhT2KsBnqkg/KRzebgXDf\nqmO2dXiFqFxjIa+otNKwcI58v01jeLgrw6TVF5aR6RnATnu/2NXrmjNcG0WX3D/SmxEbGl0ozq8e\nC7SnbZFdBgDFSl0YKoSw3b1RElmauy34Krqy6isQTqCWMb9ZxvWFxjwE3xBiwlFLhWqAuHm4JyMK\n65kMjjPDOQAk9LvBXBq3lotIWCQgE20RVh67s7d/NLKxMXGgjIWa44bulGWhIiBoLS8WKrB5lTUv\n9m4TYlToAth35w/1KBYoh+wFkHOaw3Aqn8NEvjPQdjnPN5O0lOprsoQyYBZLkb8/M9Kt1G53KIwG\nUsIiGOxIBdJ79DCDfx9UpUuu5yBPFVwvgRkuJwGE6xiQkZOw92FSNZ7fsDsMM0ji7AqVa1gWcPoZ\nWCbJ6cAP9ze9MgxBjQkDCAFpaw987GoeCfr934Nz50fAR5elgxzQ1dnY4liKmqalejP0xSzq3jTy\nEEVyJKJc8rxtIIp8tHv9dRBtMRWprGHeiz1yVIz1JwTPxAEs2ygA1ux14+pwCCIkP8bjGumu/YGO\nlNBe8T0IrFjSndWS2ORw3Rh5XqWAYigAzGsJ+Jyq6bWSsaTzkd6sCH0QwnRreKi55LnvAbNio45J\ng/y+DH0uPNKbDaQ28uM49+Kt6aCQX397EhP5TkwubImaFRwJyy/lzYmUd9fLikfGNzL2JyPiQBkL\nVccN3SnzGJucfhNUP6TIpmycyncCnn4B11mQ0ZNNYrSLWcWy+BIHH8SX760raYn97UnYFhFMVsDX\nIZDLPmeSlpJJIZe75pDrOsjWuel73mc2MP1MDNlAAvwqbpMLBcVYGPLkVvVr8FrzYTuGKHffvjDT\nI2A6v/XkCwrxTZ5oGxaUisqGoC7guKo6pHS8deppuFcv+fH+BxXrFjwJ6TNiAT15YGPRI7d49Re0\n/kP3SFAX+Ojt4DXmboJ86pearGLZvDdLbp/RQ2TQzthtlgsIUXbvuPYqaBPeC2CfyJTS+AOghoBc\n16jz0Ox196LDAbBNyGa5hlvLReQ700r2AN/oFHbqYsctb2Iu31s3joRjfVnUXSo4C29MrWkuf7++\nAxAMpfLCTEzqf0vyphbwzAlVsVHejC0VKlgrVSPJij3ZJHoySSG1zAv26euOSZpf52asFmv4treZ\ntAhwZrgTg7lUIIuOGzdy2vmZkW5cndsA5iMfb1M4UMaCRcItLC5UpFuVT433Ym7TJ7JMLmx7VdD8\nc6lCHsBWuY6N0hauLwRJfaOepCnARItksME5IKxdWRoUUImYvJ0mQ6A9ZaNcc5S6DjpBaGW7hqvz\nWwbOhjpkHeqRbryBP5hLAaAKYYcrrwG+hZ/wUo10EhGPC3KLOAz7ISccBdP5o8ofNyooZeQhbK2w\nxcRjksukPEB1pVv/4T/cl/BK3Di4ojYoDAbK+rQ2z/ggZy6KeLdCgjz6mEo0jW4RK+z05AsNlRgV\nT0dY1khI2eoAn0CTwcbUlYB2RjNVM/22Ufb/D50HGX4I2FoBNaTpykZHmDrlbkm4psUZWyu+oQAw\nj5BJMyPGdZX7skcdjvnNsjAQChVfd6busmJ5zz08hPnNssIz4It8sRIUX0p4KYp8k8Q9sxxsjkqL\nMIeJMMlDtpc+VL3BDmVEa5mkaCJzh4EQYKNUw3qpBgtAt2c4DOZSuLGo8jDkeR1g8+GzJ/sVBUgK\n36vrUhbO5dkYsgqknvnGN696qGevOFDGwnalbnzwBIw1CvjSnLzi5FKhgsM93uCtOkKjXC/LzHfN\nspXMxYj4NddLNRR26hjMpYxuqbHujC8NCqbsaIIi0Wxw/xer/kRuqusw0JEW/AeX+iEYWTVSPl5+\nwWWG75nhTmH4cJlprv6mC0XpYY9G2HNGwy7OH+Y6DkzOgLIYyTtWQF28YFnAQ+fZYuWR8tDWYfRM\n7DW80kwcXFUblHbK3KhxXVF8y33zTxXJahZqkMbJ6CPAwi1/p50/DszdZMfYSWGINaqR0VBMKWbZ\nauxsK8+WzkyC3n5HXVzRXIlqPwzh3aOPLjOX9tGzoWEWER4Iuc5uSLhh98m9/rp60LHH2bUNxlnU\ndU33uNF7GPWuKgqx2nx4bb6AwVwafe1pPDLE3OaDuZRY7LozyQBPK9dmY7XI5mB9k8Tj/7pnQN7I\ncbXYMIG7Ze16cQwFAuBof1ZRd3TB5vv1Ug3Ta6VAbR8d85tllGsuzh/qEgRIW1LNlDlp8rqheyMA\nf05/bKxL1PHZDxwoYyFMdoCCWWG6xLJe68CEuksxubAlipBwK1Kusig/UK5vYMojXi/XfEEnqMqG\njCBTAY8/6RUpXWoeODIImOsLgKKqxrIftkTcDoAwVrhhoxsm3NIFECBVyvoReunoZrDbjIa4BkYg\nDh4nhUwuKMVTIvUdq7x4uWCSy55AkeImbxBiaZYt30zoJtDXi1/21Su1TAOxULpS2qJ/JpCjZ0Ge\n/tsqWVRru25wmGpkNExdDCNAGp6b/mwblbWOI9yF088A733fvwcfvQ16513g6GMg7V1Nl0DfLUyL\nswX4Cqa2DXL0bGwZbpk0SrdWzOG5Jt8lDl3X5nBvRjD+KRi5nM9fzHPL+AY6r4ljvVTHyzdX0N+e\nDIRVWQ0clZh+a7moCOABEDUiZPRnk7BtEkoijwIFUHfCCzA4lBE7nxpn86Jcv4er9XKPtW0RIQwo\nt5dvvuJmprkUwuig+2QtHChjgUcO9EWVgCkTFnZ2d0+vLxQE6cW2iFKGFVANBuJlNsikH471UoSy\n4by6kHMSj0UIjvRmkE0lUHMc3FwqCtGR/o5gtTbuxpJBvP+Vx+FALiU01flv9LKojbwHMs8iSjBl\nN4jjjt6LCmKcFDIKGNUem1280NYR2AFGqeo1q0zYTF9pWFVNPS0SYIPZTgo3u37PAoaYbHBEkDhN\nqYtR/WvkhQrta5NhrgC3BBCeFppIBlIUo9q8V5gIn1zBNI4xFCDfAr5nyLLYSr2L9urjUy8fTzLj\nmCKWwtXi3k+Hh8LQeHVbKfpKh3wTJCvZ8kX17noZc5s7Qn9B9sjKWCvXQkmLBKx44HqphuXtSoBk\nCbA5Xdas0deYu+tlzKzPcr+dIKfrHmaTYJ88b+rkSa7cyOtEwDu/fBzZJ4bjgTIWMklbquMI9GWT\nWC3VQMGUCR/qz+7qvPLDc7w0S33cUenYd0P0FDJJG+sIxukC1wNwJt+BUs1hCpKrpUAu7rmxLnRl\nkoqxQAF874NFPDbWraqqkaBHZLFQxXd+NKekXwJq/Xb+mS/zHPQemGVX94a47ujd7OLkVDH5bz45\nB0IMhonVZFwEUkC1apFx+gJEu85Ni2KkcWHYDZr6ya9Fjz2ukhh7hoGeEU8jwo00asiIp8Pw8u+z\nPnnhicCzlftdr8G9/roIz4Qu+jE8MMbFtckwl+iDbjRFCETtZzgtjsx1lDdFOZdOvuVwAfKJZ1kI\nqlkuRch7mS/ew+DL3xBteeZnXsSry5bwJiiLHzF7gPvbk4qBIONoXxblmivI2joxXc4+0z2ylMIY\nytVRqVORbWDy4C5vV3F2tNPXgyDAkb4sihVf3l4eMXWX4t2ZDWOGRCZpBaoHc+RzaYVcPtyVxiND\nOaPnxNe1aWVDNI1S1VF2+3JVScelinJhM5BjSxYBEjaJlDg1udcICRIeo6436FVulGNkMpa3q0gl\nbP2nWC/VcenmCvKSBCmlTIr5kaEclrd3xOCuu8H0S7OXgGr/Hw8mN2icCaoZd3SzaOSdUK9Ngfwx\nYHA8kBIZteiKxTOCJ2EkYMYwhuQFYy+eFuO12rvUJ7y+AKzN+X83MGqsRz8FFxBqjrpBBhi4Adde\nBdVqgITukGP00WTExDmOw3r0U6D9hxhHoLipcFHCxluccFojQ6DZfjb0tij3mX/o6YrskmAbT6Oi\njtPbk+g/97Mex6um1E7oziQCVSW5jPHtlW3FY8vBFSFlbRmZmC6HQE0y/iahJD6nO54xIes3ACGe\nA4kH4VJgKNeGTK+FxUIwnE0AY/VMCuBVXpFX6g/nqenGxdxmBUuFqnIcoJe9bnEW9hUWYTnBjVQU\neTrgUqHqZSwkBMmPx57urLBcX1mToREoBcL45b5wB+MssPTFrcjzHh9ox2a5ZibAACjX1KvJ5BwZ\nPLYnkyrlQay/II1IjHK5YrGjltygsclmu3BHx0GjBVlcm8ffF24DK/cAgwu6qfPF7EsjAqDiVdiD\npyWsXZTHxQNbQNLQqBEZGPUaMP0+qKECJRk5CXL6GVDODWhQ0ruZPsZdcBsdR0Z8MmqcRb7ReNQL\nP8n1TnbTT7mdUZ4WxsF4GcLXeviMUjG0WcTl/JCxCUUojqvpEgAbZXUBtQDckeTsj/V3KF4DwN8o\nyWFQPQQKsLlJL+B3dW4DP7jDNA54uIFXsZQzzabXSr5UvifZrBsuuqdkcWsH2VRww2YRoMtgFPFz\ncMgeEVkjRwff1MntlcteU9p0qQkjDpSxEJE5iSO9WaQSNh4ebA8Ui+KwAFw4zkq1yrF7HttnC6cX\nv6cUxapjdKk9PNiO0e4MLt/dCOiD8+vwp2t7Rky55irV0a4ZKpn1ZJOoOy4StoVby9u4u75jvg8A\nNrSBGmZ3LG8zL0MYN0EnMEWRGBUXPpGFbXgkD4GJ0DTZRhkFcXZxYW3jRkyUiBC/tlI4KWLybphv\n36AvgBoSiaoQGSky1aSnJexaPC6uyDgbBKciqzrKniiTAeWRR2NxL5roY2xiqSw41YgoKnuQongn\nESJfrqzg6XE19MyYOJkizRrJ1qmnlYJrezEUgPicH/kaw10ZXDje52c2SBPRkEfqluecJ4704qnx\nXsxusKwxHrOngDL/MOIgq+2zWrQCKdzcUNFTFddLNXz6EwOBmjiKXDSlnoS/ioTGV+PhYb5oW4St\nM9lUgsnfl/yNqWlTF5YBYcJasSL4aqy9FMf6sxjKtWF5dupm5I9j4kAZC92ZJH7qaK8nsFFVCm5w\nBbEog4J/Z1o4AbDyotJTXypURDxfxka5hp87NQwAxoyLsZ423FvfAYWXBuPl+nLXmZ4fzLEuwiqO\n9N8qcmkbA7l0ZM10GVxdMcwo0AlM+aIDdIXsoOTJmhKI/H7ivfKSCBAgTbaGdLtmjYLIIkCyEcMz\nA0JEhMR5TjwJOvuBGiZo0rDhCOtLVAhDb08Yi30vnpYoTgMA0P5DoUaOcdEQC154Bcq494zO3RRZ\nE1HPSzmvKbSje2N0CWxCAqmxpraEcmi4B8pxQd/7PqhBlMtEuA60vVlDMSYHIyr7ZDcIG8tR72u5\n5gY2VUynJYeV7YoogsdF5AC2YAM+/+y0l8btF46aE/MumS+I/tVdKopQ6VUmAWB5uxLq8udwwRZn\nuYYFI5nbqNTVrAjGL+tEri0hCOK8xPXDg2wTaJJ75un85ZoqJMi9zNfmt5TMDdMGd3q1hPOHelqF\npHaDpG0pLFOeb6trI4TBoX4ai7xwhll/FEzzHEQtELJcqIq8WhNkj4BsbNddijen1mOFNcJQqDgo\nVIIa4pSqE1ZPNonHxrqEcFJUZoNMYHLfiigbLE/WluVd1PUXDssCufhldUfdIN0uDprjIdSFiFDU\neXSjAtj/fPpmGO1RZMu97BZjtXPlXsNsCP6ZTOyMWuAb8Ql4qXKAeTFMrnsTyKmnGVtcFpuSSZwz\nmgQ2pYHU2EBbfvCSZBRIz6mtA4H9YpgnRU57DAlphRqVeyT2hmWfyH3cD4Km8dpzNzHy4Y9g24/C\nIZYnWsQW/tWiX3NHLuP8yFCH4ld3wdK4+ZzECkf5951CDQ/cXS8bs9EAoOawYlSNtAzmtyp49mS/\nUHfkRgDRjrc98ni55mKpUFVqEt1cKuL0cCf62pnWxHUptEwBES6R1xouD72kFY0yga9X+4UDZSzI\nkMl6gF9hshEztrBTx2qxgkeGcgCY5LNJJYyjWK2z0AWFqPdOAZGK2Cy2q3GV83yEMYwBVuxKbhtH\nYacuSnNzDHdlMDT9/4C+/SYcqdxw3MlKWSy48p0AC67JErWBdLsG8eswRDHsxXUa7DgD59GMika1\nAHaDhq5nuT17YLHvBsH6C0H+gbFP+2C8+OEMDyGlyo3t5emqPNShhxvke66EyiKMNX4PiOYp2dmG\nunREeFKktMemPUB7CDc1lWK5i3TkyGt7Rl/eqeOF9rcx23kMY08+i5GHBjG/WTZ6UNk8S5RaCRag\nhD/HujOKcWCBpVbeWi6GGgkcO3UX17WiTaapkwJYKlSRa0soRgD3dBzryyKbsjGYS4caEhS+ls4z\nJ/owLtWv4IrCYZu0iXwO1+e3IskIRLsve8WBMhaKVd+NpZP1+AOp1h0RczK5B6/Obwm9bV7Mw1Si\nlYOnIJ4d7YS1BsFyrdYd/PBOsHiICXFKlPIaEmvFipJac2Y4J2o+mCqXZZM2rhv4D9xdx4VEJhcK\noKszeOT9f4d88Z5HUANoIqXK68bI71fcvZyNrU+0/Fiebue6QMKcbtcIcRj2cSoGRk3KUd/tdmfW\nyB0fuGYDFvt+7hDj8g/uB5R+A4FS5bHKUnNBLQ6vcJXu/RC8DJOxJhsbBoIgGZsATSRDeR1Kn/Zg\nRMUJ24T+thmDdJ+fr2z05Yv32LxyJwE8dFJTWPSNLc4Rk0veG0PH2lTMNz6NjAUgONfKKZbcA/v/\nsvfuMXJd553g79zq95vsZj+qm2SLatLiQyIlWVSyBilS8njyMKJIToJMAEMODAQLTHaByX/jSWYW\nmYWR3f1jMcAOFpuJnfF4gUkWUTLO0vaOR+LDdEZj8SGKYndLJEV2k/1+d1d3VT+q7tk/zj3nnud9\nVBUtJO0PsMWuqnvvueeee853vu/3/X4EwEgQjdYvTwH0tDXgpYN7cW18SXEkAHNdkQkACdgG7sX9\ne6w0/9z62htxrK9NmdN7Wuswv74t8ytU1XaXs7BVwt98OIVneloU/m9Zy/yvb00pD/WF/e2YX9+2\nSoAy9sYculvr0Nlch+a6DAY7mzCX2zZKEGUHhNfjJskmEAC9bfWGyqNsB/Y0ivDUnakVIZktK5MB\nwFJ+SxFB8QAs5bedjsij5QIeL08CCAY3bcXHh7+GX7/379mLDYQ77LJz40H6IdAh0I/lpWqVIM5J\n1oKwH7lq8gAExzrLGeMWbynEbYDcImiOI3snAs9AJ0YT5+tjUzEpHQmjKsTi7D0p4ztx/9oFYGOZ\njR0bqDDC0aOAlG4gwPFXrCkU19gzsA2ZjAEQrGQRL6dPyjl/aoe0zOdrxfPoTh8gHPmBjv2oIRRF\n34dHgaGVO9gceBb7OpmSrwzw5uF2OQ2hpyl4mabLPEBElblz4CMEmM+sbaG3rR47JSp2/3KEQD9X\nbrOIO1MryFkA7B1NbNl1lU6OBVgDzu64lN9Gyac43tem6OlwUT8uT8B0hdZEKSqPYFfLPlNngRDy\nSwD+DYAMgD+jlP6J9v3/DuB88GcTgG5KaUfwXQnAR8F3jyilv5bkmiWfIq+VDfJ0wOjMmpLr8gHU\n1WTw6yf7hQSoHj0Ynl7DHUnZa7CzCa9+rjsA2UwKFK08sD6ZXTd5yQFQS7qAApha2xLRBQKgpT6D\nje2SoHiuYQTgmF4t4Mf3F8W5s+2MQOnBwrqoIyYEaMh42NNUi2d6W3EphtJaaQ4hKCGDyZbB0Flw\nMBTGWZgbDtIPbYyGuhpc9laHQUbYe56gNbaWxkVFECxtsYW4lfusEHdhUCcLKWIWbUkSGrbtEMXn\nDmKoKEuDP3hiNn6btXnhMWjXfgBw4ges0SO5EqAcnIDD2UhyvMvK5R5xnSMp0NH1O5I9IpRYXdwY\nSdrjAup6v/mH8C9/F5j5lP24VIL/3tvo/cWv4PW6MUw+fICGnQ38ZP+voJgneJQ3S9s9YqYh9DTF\n7NomxpbcoG4fwJ7GWtRlWPj/1sQaeM0hBw/aKtes9ws1Aq3bcr5opCSUtlAWyWXrUfj5bG6BORIH\n9kiRBtVlOdrbho9n18um2I+yz8xZIIRkAPxbAP8IwASAa4SQv6WUjvDfUEr/mfT7/wHA89IpCpTS\nU2mvm/EImmrV2lfO/mWTk5ZxBc/0tCK/XVQoP/WHPTydcyo4crPhDp7f346toq8QlMhGwcJT44t5\nrG+VlMH2YDGPscU8jvW1Kc7Mo+VNo3ySUqBQ9LGzvo29khS2bKI+V28BBTK0hP71MaD/GZCnTpa9\nQOgLsktcKc6UUHBxB3Tkaixegq4tAFwpsLgD/7231fBxyh1hVKjWwF1E0Bxbz21RVGSOQim85yQ1\n9xH9HZebjzNSBug0zmL5C2xphZGrEoYCgWfcErZTWxQrqhTR+tPlbKQxFwVzqvehyhiDJNwYseeI\nej+yR+Cd+6qK/Ri/A3/yE/Sd+yp6F/4bbnT9AkokA1dg/fC+ZrGDDnP6jOEWlFW66Zgsm/EKsjlp\nXowCvNvM5QDopqe39WOWNraspH4PJM6JG4+WFVVKHiE/O9SJ+/MbGNrXXFX23M8ysnAawH1K6QMA\nIIT8BYDXAYw4fv9PAPyrSi7YXJ/B2SGmJMl36pmAXvOnY0tGiSPAyh+jSmn0Bz2b28LFT+YAwHo+\nl30wsYpzh7tQE3iFBGrujAKYWC4YkQpuPhjLWNLBWgqKmms0rIVHgFcCsanLd+dFHx1somgcv4ln\nFm+hd2sW3pnKJiEjN3zncmxte2yZGyiohkfQjxNSyfLCEkxO5VYwxEYiOO7CQXMcWdapT7T33lfR\n+kGuPbaNmgNklLHy6pSEoeZK0yuJzh2x4FnTCgJDQdiL6fugl7/rjOR8VjgBl6nPWgp0p3Dgqo0x\nKAebYrBkJuQa0blLeHqzf3wMmW0CC7UBAODe/Ab8uQ14hDkO9wJ+hBqP4JmeVvgRSrrW9iN0S5JQ\nQSP4/VOdTRjsbLIqCsdZT2udUt0wHZF2LvkUNx4tKw4QBVvHeHS55FNMrbKNYntXT2+qxjjss3QW\n+gE8lv6eAPCy7YeEkIMAngJwUfq4gRByHUARwJ9QSv+T49jfA/B7AHBg8CnjQVIwek0XNXN+pxTJ\nnnW8zwQV2oCEANBQ42G75Ae85EQQOAFsQN6f38DJ/jbMr28LfgNZhnXb1cjAmupq8ML+9lgWSgCS\nXGubwohGKYu0fyRuUwAAIABJREFUvLj6AfbcfQeTzQfRX3iM7K+8BfS/ADrRWLXJUWAEpDI41jhz\nAbRqFehlboBRMeFaeNIQK+lmowyOWjiicBexbIH6RCv4HXYAwhbpxE6NtjgaqpNaKkFh25wbY9Gs\nwBFLkl6pNp23cS9BeJwcPg3CKZirEClJapU4G9bz6aXFgBB3iuN6sJ6jChiStNiUqPctDlfk/eJX\n4GvcJSR7BP3ZI3gjqF5r2FjA3OIKPi7tgQ9iKOHKfAPFYENkk6iWc/su49wNixtbGJ5ew9z6tjXS\n0NNaj7NDoZCVLLzH6aRtNNWiz1gPiIhunIPiEWDDEp2+cm8BXS31Ch7v0t0FtO3d1x95ownts3QW\nEmBYhf02gL+ilMo9dIBSOkUIOQTgIiHkI0rpp8YJKf1TAH8KAEPHT1J90Y96KASM2CJqje5urQNA\nIwGI3DYDvu7W+gz2tdSj6PtKmkCu/51cKeDNU/34yql+/Gh0NjZfliEhk2R7Yy2Gp3OC/cx9dyxs\nNxSE8XilRn9xAfTiv0evX0Lv+jgAAn/kKkhbl1AYBNLlLV1mlMEB1vyvdQFJMJG5Fh7X5BTb3hit\nB5dF5r4jFkbbRMsdD44VSLKI8LbL54mawM3SSPb/dPgK4zSISa9YQ+qlUqIoRJIFT4THS0XQyU9A\nfuMbaqTq0neAUilR5KWcKhHXMZWey1A3dcigu8yKzbDggJJaWmxK1PsWFymMGpN97Y3o3XgM/51v\n4lipiGdaD2LqF97CktfqZtwNnIPu1noRlpcBgiOBUrD1PoL/5w7Aoa4WHO9ji//44oYy3+9rqZPk\nphlrpAwsvza+FBvtnc1tIUMIjve1KOWWdiMY6GgwFIVLFMZnKbMokfZZOgsTAPZLfw8AmHL89rcB\n/FP5A0rpVPDfB4SQy2B4BsNZkG276Buf8dy/rSKgo6lWYUJsqcsYeIO53BaO9rZhZDqXmIDbRoyk\nW4kywOXR3jY012eczgKn9JT10Qs7Ps4OsVTCjUfLAr0rpyh8GjJPclCkRxhrWO/EFVB5x04IQymX\nSuBBuri8ZdJJ0yyDs+d/nQvIsTPM7eketE5kcSmCREyB8kJd5TBvkoVRn2hFRCYmVK/v7OPYIJVj\njfBzYAGngXf69cj0ijOkngDkmei5WJ6Dd/r1MD1lPbPlPsvI8UfJh1fjXDIhmIielaEJUS38QrVS\ncrLZsDj8/bURogHqM+/NjQO5Mfx0+5D1tx5h3AoAxMLL5zvuMAzubYrEMixtbOMvbzzGfLDp4mX2\njbUepteCzwKHZHq1gLdvTQrnY3g6J3QmuL5OnJUoRWtDLU5kO9DZXG9oYMi/m1/fxue6mzG+XMCm\ng9yv2vZZOgvXABwmhDwFYBLMIfgd/UeEkM8B2APgPemzPQDylNItQkgXgC8A+F+TXvjAnkbsa6mT\n5EQJelpqDUasxloPy9LfbQ01hrMwOrOO7tZ6EAfz0Yv72/FgMe+kX46y/HYpnhecMvQvFxKROdDP\nDnVibCkUiKIIy4I4UlYmlOIpiLA+nIW68dTzwIObMPKWWvmhaFKKSYpkA0KagHI2qg4dp74E3L8G\nDL0EQFv8Io6LLA2LWjAlpkDBElhGmDdWJloOpydwWID4iIQxGR87k8rJMaI23CROg6j0ihFS5wse\nAPglq/6B0S9JnUztObB0RODYVlGIKu6YJM9EH+dRVSpk4GjyKIvtPUzSHh0DVCEGIymWQ0ljFbcD\np5NGVzRpfTHVOghfK+bqaq5Fb1sDjva2AVAFmHwKXLq7gNXCDj6cXHMS6QFsY6VHi0s+xejMGj6e\nXRdz6SvCIZlXohQUSJQOlk2u6uDKmVwDQ7ckfBHVts/MWaCUFgkhvw/gP4OVTn6bUjpMCPljANcp\npX8b/PSfAPgLSpUeOwrg/yKE+GCVMX8iV1FEWU1AmTmxUhBru08pmutqQBCiYD0Ae5vqFF6CBouC\nmE9pIDjCM08M6FL0KYb2NaOzuR4fpBw0/DxNdTXxQBkSEkwB4bRe8qkihMLPee5wl6K6BsDQfCDt\nllDm+G0onP4R5YdRk5RLPyFucvJvvwtcv8D+uH4B/vJM4km+3Nwy1QR+6MhVeF/8erpKiST8BlI4\n3Zb3T0sQBWjPoLgDurGamDgLsABQNcyC/DtxPelv3QkCAPrun4cOw0eXDCCq6I8kESnHokSn7gLD\nVyDehJg0RDnOn/OYhhYWhaOWdJhGUe3L6ZyYqqCk6SJDPyXi3vTj8MIvA7d+FD1OE475RO+bToWd\nAGOiP/OB5v3wFieVOW5hYwfL+SLy2yWMLxWMhZYCBn7ABgpvrPWQt+zY8zslZXM1l9suC9Bo3BuA\n5wfaleqFvvZGvHkqK1IbPJ2S1lHYKmzYQXQp7TPlWaCU/gDAD7TP/qX29/9kOe6/Ang27fUaa72A\nplkVRuJCUvxxZ9vr8YVDXVjc2AJkEIxjPCznQycj4xGlDvbiJ7NKeqIpAL1EDS0C4KmuJtTXqLCO\nQwHa9sq9RUHE0VSbUXTWuXmEYGhfMyZXwgoKEAa+6WtvZJPFJ6PoHTiKN07uN+hE9Rdez1sq5Ye2\nckHLJFVJWJTee1/9YGM51eJXjul9KroxhfPh3IVGCEAl2R3G7uCkkkGAAmO3QM6/5QQxpo26iDNH\nhORlJ8j7jW+AZo8Akx8HB/rwr11A5vU/CNvB8/OaA+pqo94+odNQ4tE/wpQeEzodHI9DFx47nSP9\nGGVXfvm7ApAoa5wAclonMCmd46xS0dIr8n0qv3cATaPGCDsuiKT6pdARB6wOfrUpn+ncmPpBwmoc\n+Zn3gW1+ZBA4wML0UekFHhXgqdfnB9pxf35DSfXaHAUKYGwhL8DpGY+5GVERCtkygeCUrW0UwIeT\nazjU1WI4DPLfDDw5aWAtsu31mF41MWo1HsHq4pwrvZ/KdhWD42bRx3AgRiJTPOc2i0oFw/TqFhY3\ntgwSj81iyfBCKSA4FwDGzggwUAsLKakLfmtDLQo7YbSivaEGQ/uaUVeTCdQwtzA6s46HC3mMaRDQ\nproakc+SdS1GZ9YND7qrpRadzfU42NkkRKwoZeGyMx2b6Pl++PL3/sY30Hcw3W5BlB+mwAJUku8n\nh0+Djn8U/n3iHEgMs2Ol5h07A18S+LFhKWLZIy2Ok10Aihq8AK7jxXeOxVwsXFSa8Eol0LkxZL74\ndeV3lS4CaULyKGmpuI1ltR1FKQ0oheSTtNGmVYGaWqcok2wKBsQF6IxxpBSMh6ZxAtiwOWE6xzhX\nVMTIlut36Kco1SxBX/K20s0IIUItGlNtnE4Y/QksU2N1ZJMYnw9HZ9as8yDAFsynu5oUIKRcYvnh\n5BpO9rcZaYNDnU1Y3NhWnAimIsnfUYLu1jpBgkQA7GutR25zx3A2CJio4IsH9mCwswmX7pq6FxxX\n4eJG4HpGzw+0ixQ6t9m1bbE2cebhupoMBjoa8U9/rjqZ3jivt6x7MNDRiNGZNUPgw/Yw5ZSEy24+\nXsWtiTXheZ4d6kRmhohIwPG+VixuhMIjq5tFfDi5JjTWr40viZJKfdyPTK+Jigd5QB3tbTHKgLgm\nBavWUD//Tzng9fpe9G48KvvlLwcLUElZl/fca/ABEdaWpaqflAk8RVwIOGIhs/WTQiftAzj0AvDw\nAysvQNIcsNIuW4UJqKGJUe4ioDhIjmdqdZI2N0KmPjCHz97eMIyfpI2h8qPkbHR0g3z+y+kjQAag\nMyGoMGZsi7GUAJsTmXbQ+gOb61b9FKvQVyZIo/o+7IIKgQ2eUtJKleAmbBZiSgAe/amEo4PPh0d7\n2/Dj+wtKRQAva7zxeFk5Zk7SUCj5FHU1Gby4v12kKGqCCDEAhYnXA8OSjS3lWfXYDMErhzvFJm8u\nZ18jKFRCpfNHzIgIAAMMyR0ErmzJ08W6MJausjm/vi0kAKplu8pZkN+PR8sFTK5MAmAhJVvEIMr2\nNNViJb9jDVXzB1fyKQo7Pt48paqG6UjXkoTUzW0W4RFYyzV9sAoJfQAc7W2zlgEVfYrCjonELYFg\nsu0QevMTsYjlqIUy7a6+nIVPNu+514DnXmMTYQXlYGksKhSfdLHVz2HkqZvbA8/QnrNNi7kwdrEC\nWKiC/coFaybJqdswC7j1o6CBBHjxV+25dYvgUqKddlGT612ZjSRkko8X6bVMjYTLkUyL9tgsydiO\njARpJYRO/I3lmZHsEQNoKhxSBZRcCv+mBPAyYUSCm5cBxm6BPrhp5UmwlU6niVAZmJIISe601tfe\niLNDXfjrW1OSXgIDIPLoKjcZcO6RUOHxUFeLkZJ981Q/RmfWBA5CTiOUKMXwdA77WuoV3hwXOZ48\n19uyFx9MrIpUBCcD1NWQ+bry8uBeTK1OBal0AhrQUwN8fZvCK4c7/0GQMv3MraHGQ09rvfA82YIc\nhhzlvI9Lq4FbXYZYBwMTJAlzWjxVkNvcwegMm7w50pU/6IxH0FjriYHhEYLmOs9KvCGnNWSZ7XOH\nu6zRkNV80VCtzHgeBk6fA1nsiSwZdJU2AfbQcBIHIu3CF9euakrmpjV9kaPTn6L0zrecu0ZxXNYC\nIB25yhYqSypCtqR9LKitNzeAmz8Md5Ma/XHZUYuInLpoJ8csTIyC7jsQLugUIA3NidqReKdts5io\ngKKxkckAg6dAmtsZGPTT67wFwNxYIue0nLGddjy7+sPpkMrVLHJkQXqn0dACzI2F5dURVOjW9z5F\nhIpOqJoacZiStMZBgfKCf/GT2chjulpqsbixJY7hooLyOXnUVxcTBBi3wcL6loJlODvUicKOH6SW\ntzE6syZ4bAY6GhkezmJcF6KvPaxU41FmvZJNlq9urPVwWdP5KVFOytT1956U6WduhR0fs7mtkMoT\nQV4y+HtmdSvM+xB3HS4BY/eaXzfDSIOBvCh/gKMzawoHw+hMDm+eyho65fLA8ClFT1u94Q0zkhEG\n0Py7T+dFji1DCN48ZQ9t0aCtrQ01glFMeM1PR+y4dDS9VNpkK8MDkuWWK7W0lRbO81SzTGzkKqOr\nDhYY35Hn1o9VJneh+eCDXvoO/LkxseNSnIoYJ03+PRk4CvpX35Ty2SVlt11WdChpHb3ynHxg5oH8\nrYnNiNpNJ9lpy1gF/t+4qJmssVEqAp9eF5LrNBCpihMds563QucrNuWRwCkRkR1+j14G5PxbsTgf\nDjRVqNAfj4C8+jXmWNjAtikiVMZvqxRVEG2fYKBtFYOlply6mmuxnC+KCPBsbhuzObbQ1gRcCnL0\nVk4FOCMGFDjR14LWhlolKsHtaG+r4sBEqUHydHNjrSdksWs0B0TWwhDpa1ufWO6/XNtVzgI3CiDb\nVo/p3JYSOZA7u0SBtYLJjUAAnD/SJYg99N38+GIeg3ubkNvcwftjJuCmRJmsNR983AY6GuEFSmmE\nAE21GWQ1aepjAV7hztSKAsbh53z1c90AmBLmfCCGwvXf0+aulJdap88FjEqEaoOgErWrzEqLakYn\nxM5KDucGSPdU59xcV1MRt98NdS+ChQpxTpomPiR+L1uFzl3SaISTpwFg40kDAJbrvOkhcrFTTsI0\nqFOFAwIHYBUdKxUZk6mlXFOE6NOqd1aA44k1MaYgQJdxjoZwMq5fAFZmAanKgrz6NWsFkh7J8t97\nW8EV6eevJBUZxZzpGs/P1KxgBIAfUPAt5XeceeaSBjJUUgGwk/dx626tVxgiZZNxZtOrDFSfiUg3\n33i0jEfLBYUs70S2Q2mPHsGQlTYBtlZ5hICmlsOy2650FgBgYcPk+c4EXhwfEAsWIqWnOpuESiVH\n4v74/rwgdCpRWIErso1MrymDrsYjONnfJrgafArcmc4hQ0K+8IxH0N1aj2vjS3iwYKpj5reLuPjJ\nnAh3eQQ4FvCglwNyMfKUwSQIzwM2VoGDz4E0tyulZUreOSGXfSXtMiotBMlLtBJjtR2bKKR76nPI\ni6sAgTEHgsDM36v3IsXJ5N9b6LArqkxJuLP1fuMb8K9dkEL6gelsjxU6b+WE/8lAQDymYx08T+Tl\nycBRtkBI0uYYZuymvJ1A6HSVo0mRdvFMxXdQJiZFqEzK5vuKE2VLF9GFx8BP/pKdZ/wj+IDTYSjn\nPqPGibMqZ+ouer7/TRzt+8cY7noRICRybuYpYV7NpqQCYvquEMOkyOmgwzmaoKfVJAMEgI3tokIm\nxc8tt6foU1y+tyBSEwxouY38dhFNdRlBTPUvlhamYpqeyHats6CLMvEFe2KlYH143B4u5vFgMa+E\nq84O7bMCUVymD6miT61sXz6lSgqBo2FtQGadgMSnQGtDTUVoWPmlplyoRwq3UymMKBaHkatsQv3o\nEiMxiqEhLmeRtk42CsmLGeZWjq/ybo5kkyHdY88h9R+v12fea1C7f+wMyLEz5iQqO2lAmJOWfm/b\nbUcR9lSjJJVkj4D0PQ366Q2I1MDBE0oOHKi+85a0bYaYGAirBNCiA+K5zI0F6ZTQGQAQtr0M9U7e\nliSLpzw2dByR7XgRJXCwg0Yyg/J3iRD2z6DKIqqtOhcKvXMJfhnlkE7uDn2cyAyyrohjcMwzS7fw\nSecpFAkn+FettT6DpjpWaihXHZzsbxOpAKN/EfI16E4GACXtYFMu9inFvpYGLG7sKJ9nCEFHo+pE\n8CoJFoFm+wKCcK0p+hRzuS28+rkeo52rC7MziTs/wnaVs9BUl3HmnFwLtm78WJlrfGKlIMJBcQpj\naYwQJlR1ItuBa+NLIfkSZZoQ87kt7PgUe5tqMa2VdRICJc1RcVuyR0AmRkEjwu0kewRk5Coo32Fb\nJv5ypY1jF7DNdYh8tSXMrd9LFLq7HCsX3KZjDbxjZwBpgaeXvmO9jlwRotzLww+BjSWQE+eV52Jr\nr4sBsZrYE7GDDyZx3VEQv6liVCoVC6QmJobmdtNxGTgKyHl8DQ8Rp95ZqdlEvVBScUROp9zBDmoI\nffEKFH3RTXE/OhcK5sZBZ8fSE7BpeCkBstQBxRqWxAr8DI7pzU/i9Qf/N6499xYe5U1ngen1lJQF\nuuhTg8+AW7atHl94mlVaTKwUsF0siZS0R8KFnOtJyLT63HiKmOMZOKassdbD5XsqWPGDiVW0N9Zi\nLhdGxAkBiBQJH51ZVwSsqm27ylngTnJZx0I91gsWYz1/dG18OfE1dEwCv86R7pAw5Mf3F9HZXK+A\nXTIewZ7GWgGAnFrdgicdz0CS4bF88JQrGSzaNnAUVC63ymQYPW2waAEI8+yAXWpaThckEBXi7Y7l\nM9AWpbhdHT/eVfHxpHe2VlVGGUQ3cFRiI6QG2Y5Ns0KmE6bzj2L71eZ4VD1FkyDMniYqpfdhOc5O\nlPomAINsTNltEwIcUKMjleTgk5jJAUEA4sWmPCLBwDoA9fZFoWpZ7v2Qrv3h/FCBTLiRkhu/Az9g\nAXVhSXhVjrg3hOObg5B7AZzuBCYLxErepBuPGtjsYGezmFcXN7bw3sMl8Z18DNuELqOpNiOqJTxC\ncLS3xVjYZbC7fl3fkt6mlOEkwuo+k9RperXw89LJcsyLIiKJMRlnzRXNCju+2O1zLYak1J81HrFq\nTZw/ws5LA7axok/x4/vzWFjfYSR/YCyR8+tqqqSpLoPBTlaONhywUcpgndjFKemkwPuQeMDzv6SE\nbHHsjFIWZZOaZg6HW9rYZkkWsHKAU0bFx7vfBiiqpqiZ+Noa1sAfuRq9k7VoVqCtSwUzJgRZWktk\nLYyTTlDZyFUnLTK3pBgHFrlSFRZ5XyUFtMWNFafWhvQba8RF6hM9OlJOVCmN6TtqcvwVoHswxBa4\nym25VoWlMsTEyFBl0S0LUzAxGsbrKcpKyQCOFJHWNhuDbCSmIfhtz8hVHD3zDdxZjY+6Ht7XbJW/\nzpCwJH56tWBEAXTjmzpO4//i/j3Ggq5vOnVHRU45iHZ4plR1Y61nEDn9vHSyDPMjvMme1noc72vF\nXG7LYEPk9lRnE3raVDloWYRpaF8zplY3BVfCwb2NGFvMGxiFntY6nB3ah9EZVd/jUGeTQLxmPCLy\nWHJojIKpmR3Y06Acu75dwsezOZwd6sTHs6owFBCxOMWAAWUzEOTz48rErAPwOD2yQTrDGecs0sY2\nS4ox0Cft5FTMAREPHx4ld59UTfZXD70DIdYACFI59p2sPoopAC8GZOnchb/3drhgaJUArnJNACF+\nxS9F0iJXAsiziSpFAdoAAGsLAf0x4gW29Lx3hLPzpKMHUea6fmllFrjxfSvzZ5xWBcAcPLqxCozd\nCsdeQhBkInGzCiJ1thSR4uxY+sR/51shYFUGOWrP/HObY/jYezpW/GlqddP4jDNC8sXeFgUAGAZC\nlgEA2Hv6cCGPF/fvUT6fWCmIthQDwiVZ84LrV3ClTB6Z4MJSss3ltoV2kNSbkfeZ1HaVs+ARYsUs\nZAgE09fwtFugazBYzAHgztQK7s9v4GR/m+Dg5uyMKiHInKI7AQDNdTUYnckhv10ShEkZws7PATJv\nnMw69cwB4NHyJj7X3YyZtS3BXc6ZvWT+BiEMZZRCSkj7BAx1dOquOREfPg0qv8wWAJ6V8S9C2th2\nXToxmnriSUPFzHYwUq6VuJUKqxWmt4W/lX8LkibPAKfZNCtI1g2ytPUFoGshhLtP2elSqKmtUY/A\nLJGMtOWs+nOO6usoxwKeBzx7XjirMqGSkffmDk+QzhH9UoYzWC1gqM1sjjBu/jDcyWsOrpK60LQq\nFG2STHpdBtdzIVkVUFkJhbO472NnnKBhuU/o1F1nClQfK9mDg3ij2ZxfG2o9bEoVDfpiz9cJOSow\n0NGIGmlj5zqWGwUri/zys40iAqBTPI8vbuALT3fhK6f6lXlcZpd8sLBulO3XeAT57aIlxVINBN0u\ncxbWt4pGt/W01uF4Xxv+7sFCrPYDL1+5M7WCiwFb1qPlAl49Eg4gU7ehVSmVJAAeLuXFO+4BONHX\niu7WegWF+8bJLF4e3IvHy5POR13Y8fGloz1KCIsPLB3kIi9OdG0BuH0RYucaAQYELEx3wURMsibN\nLL8Wt8iJJUWIHJWApPR8rZ6z5juY4jbrjxd+WTg6LsBUJZUU8nl5nhVQ+00habLpRfzmH4oUgHy8\nNRri2oVHRC/EOfX7hRT1kM1SLpp0F6/IN3MMhiX8H7WzVK7lIyx5DJwqGUwr3oPpT8OyzlIR/o/+\nHVDXoERaeF8lwUH8TEjJOKfD2oIa5dMcXNs4VY6Vngs215Vx6Lqm1eHSuE6i5NbT3qf87sMRpRS/\nV6KeagrUFoXoAwwW3YN7Gq1pBwBorsvg5cE9xrzKyfVGZ3JGSTwAtNRl0FDjKWX4DxbzuDO1giv3\nFqw8C1NrW/jrW5N481S/wibJ53WdZwcADuxhrMB6tBoAtgr5v/8S1T9r0x0ujzDP8PLdBSvZRkOt\nh61ATpogrC7QQz/35zecZBwAQAJkIgHQ116vOCU+gLXNIgCi4B+4xyk3uae1TklJ7GupUyoxbMxh\nSjtkQJtDMVI3OnUX9N0/R6gvUAJp61JexKgJoZLFNe0uPonAkXNSP/UlFtKlAG79CH5Hj5Vgp9KQ\ndOJFRSdpst17UHkSBwZU0i1Bfpt07Y/Mw4tjs2rlCObGwuiS5wmKZKuUcwx6Xc8nAxBORZK+Nnbb\n+rVkLQSLfHPpnW+pN7s0KZ08HSfFz6L801ArzWTYPQaOkI6jMNJJ3CHzMpGpGtc1bVoRBmZBOFrJ\n05vW6zocXNe7o7/vukKsbZ7SWXRHZ+zpZwDY2C4ZgHH5POwzaqSw17dLVtr+//ZwyeoocCtROBUo\n9fUHAIb2hYDL4emcolFRWM8tGweUYbvKWdDNp6wkxeYoEEDxNCmAK/fYYBna16yEr4b2NSs6DTrC\nVcZK2ACQj5YLyJCCwi3eWOvhxiP1GW9slfDqEaY21ljribIeG0VplNledpfH7o9cDR2FoGeS5jXF\n7rlcdHUKRyNO4AgIQurarkrssvWQ7r333SHwCgBt+iToX7sAFLeMsG3cvftyKiBmcRLhYSlSQVKg\n3kVKwhLmj0or+CNXBXkXBQz0ehQGQ2l7gr42ImcfXTLPrIFpw3RO0TyhjhOJGYfViDjFmboYU+C5\nV5njHlFlIp7dO98K79MvAf3PgDx1Unk3bOdJFRmUuU5omN6sFq14ZFoqoROvt0WOwtp25bLp7I66\nHe1tw+hMznACKICmWk+RrdYlrHXzAIE3A1QdIH39AcLKNwCKECEF0N7Vsz/yYgltVzkLjbVm9YEL\n40IBIyTFS1N4aOj+/AaG9jWjs7leyJh6AI71tYqymIGORgGCZAJRNfCwbTgoPgWOB9ziHMWq58Ha\nGmoEa+TbtyYVQo6oQWwzPd/n9NihTbmHXkiVPhALd0SYM7KNEaQyyjUtuxoFOS2z7AHmzlEP6ep4\njCpN/gZ2hBNcaYx3UZOfodwn5WedE7MeqQgqKMrKU/tQokvGb+W0AthCS86/xapgStQoqVUwGAHY\nsxyeBT6m/dvvghIChSQJ1ADTyukcDtYEYERakixEegRGLt+rmmnEY6R7MDEuwJjmpu6CnPltANEp\nllROkMx1ApbeLAu3wrEGFrxCVFviHMu4trgWe57q04mXbBGGnrZ6azo7zjmwGRe30uWp3ziZxYv7\n25VUhMz7Y6xppDoIx13lLDTUekZJCi+D/HgmZ3Ae6CaXzJzIdojUw8VPZsUA88GomhlBBqul5Tmt\n0Zk1PFzMwyPAid42dLfWKYOgu7UehR0fc7ktIwJBAIUERL8H2QtNa5Ee+7EzYUg3k4H30pcrOl9q\nsaekOVDHrsZoD+83L6MgxBn1744I6caBMKuhZUDvXwdmPg3Pee99QI4uRGEQLMp9kU5fwpSAs91p\nojwTowipqsEwA3Nj/Ft7n3Bw5vAV4KNLouY/KuplvbZeBfDq1yLFk0j2CDLZI6DHzghwKOkeNBb7\nJBEOJQKTknQskaUgHtPNO3YGPo/sAAAoc5JW5yIjVHFOq4Fl0LhOXOkEI6rJn73vK6XdMl4hLiKq\nn1e3uFTzkiXeAAAgAElEQVRRX3sjXrGo91KwSrXBziZj0eZVcTxtbHMUXESAUeYDgspZl6eeWCmg\nrkbd+MprQEYHXNLUl7farnIWajOeUZJy7nAXOpvrcbDTxzO9rHRydMYUgGqo9XDcobOQt+SkSpTl\nrz6eXccbJ7NobagRDgWXxuZRAt179AgRTo1O4EGn7iI7NYYa8hSKlIh7qIjWWV9IJAY9MZGnWBhT\n4wUC0198vawvMgeq7WqoLCvM2yMj+CWEuGtCdC7WVdIy8BtaQCVngRw+nex4vX8ldUrbZKhXGiiE\nNhYZYlebE6ctBo6CZjJh2DsTMKdyB8c3uTVI9kjoBFWgZmqrAki60Mc5XOIaEc6LEuFKSDqW1GyL\nceJjs0dAXvvdsGTZywjwp4gEuFIslv5LhWWIKIcl574a8EVIvDEa74gxjnmppAS8pjyCRKnBkyIL\nfdmEsGQrBBg13caW8miqq1F0GX58fx7NdTUYX2KpZttxhzqbxPH6jj/bVo+9zfXobq3DBxOrWNa0\niHxpqpI5frhTwKsw9DWAbU7XkN8poak2g/nJsbuWpqW2XeUsAFAWaN7pcjXBGyezONrbJhbwsUAL\nYnPHF2EfuVTyztSKVeOcW9GnGJ1ZQ3drvfL5yExORBI4axf3BkuU4kSgCSGHu/gL2lsq4vXWg5j6\nhbcwsH9/xfSe4iV37OzS5uidk0ZMxMEgjeITGXFPZOKa8kRqEfwxdBcs6Pqk91gtMJv33GvwgdSl\nZk7nxoGANypKoGEeJIa8OIchMX5AqtYQzowFVBsHSk3b15ViB+KuF+dMkAGNdMwvwR+5ikw1nIUU\nDpvN5GgZ1hZAZVxH7yF4Fi4GbvpCrThFEleL4nRpdOTW58mxQeFdMuAmEDJBNrRYycMUiXGZhl5q\nj1EmGlOC7SqF9CkT6zP5b9w6QoDdSeB2sLNZUDvrBEwv7Jd5FdhTopS1Y3FjCyeyHUaJvEzG9PHs\nuljTqmW7ylnY2C5ierWggFpkzQUe4uGYhImVApYL6mDgDgPXF798byE2xjM6Y4YLfRrKW3OKZ9m6\nW+vQ2Vwv0hdHe9vQI71ovblx9OVH4bWb4X0gOhxnM9fOLm0YWD6fEfKNijgoUYQwLwu4y/r064mc\nMZ8INX5/0tYFpKwpt16rimA277nXlNSDbq6+t/avZTHReRI4lsPFkJe2T6Lapy+QthByHCiVxpAs\n6Vbpghr3bOOcCZINSMfkCqLhK6AJxMWSvGdpHXfX8YKXoBS0cX48sl0GT0eEcFscZknpXxkbJGlU\n0IXHCiDXkGe/975dYjxoD93cgP/+99j4kY6LKxOVKyR0nZ/xpQJeOdyJ+/MbVv4bXXLaxrrIjcsF\n6CmPPU21qMsQtDfWinbkNouCq4eCpSd4VYZVSltLWzQ0tbQ6bziF7S5nYauEv/lwSsk1zeZCli4u\nvmRTCNOt6FMMT6/FKkwCLFKQ3zFTFfKSqIMpxxbzChPX8HQO57qP4lhceJ8LSFjCcXEWtzOttH7c\nlXM0yYEyEGqLmYxwFGIZGeWJUNrFKoQ9EfeQSoAoZkGqCiV0GX2vLyauxY9koxnynkT79LbZFl4r\nKNXzQJ49H0kpHXWdNKY4nRpQ0UpMZukz77nX4M+Ngd5+l31gSbvo9rPiaeBGskeA46+EfCsRbXTh\nDlz4CfX3aprLOgdYMCV0glNHB44soKYQhJOxw9pBNcfhxg/YMZ6nlPrS6U/hv/OtyLEkL8JbRSoW\nap8y0ruXB/dicmVSOAYEwPG+NhztZWsyq6ogApNmW0d8yson9W94KmI2t4BXj3ThpYN7Mb1awMhM\nuNb41CyrVKS0aahrwfj3bOU+6W1XOQsAW+R/OraEoX3NBi0mF196pqc1VuOBAJi3SFnbxEcIgPGI\nVIX8O37ow8W8AbK5Mu9h7xe+jt6xnyjVAVYAH+Ckco7aDSbZmVZjZyPaIueYA3Igcvh0oLbIboYu\nPFbphTXiHts1IkOfjj5hCP4SaCYTeX7bfRjnSjnxO7n2K+z7KMem0l14pe2L2sWr56agq3OxkG4X\npXXacjr+OyHWRTzgxV8Bbv0o3AHHlI6SADCZ1BFLkv6o1PnUzTt2JuRb0bBKyr24IoIO/ET4+4BG\nXUtzKeMbyaKQshqrzcnwr10ICbaA0HnwAfLsefbRncvAp9cj6cl1O9rbio9ncyKk31jrYWKlgFMD\n7UrUobu1TmxAeUVbYcfH2aFOp4SAXiHB2Xy5cf6evvZGA2unKwrLVXdcWpuX1v+8dLICe7RccNIo\nMy+QGojSDAEAplbmEWBwb5OBVeCpCRkkSQB0NNVgOR/v3LU1ZLC6ySIQNlfFpxSTd0fROzOsVAdY\nAXyAXfUxLufq3JlGCNbEWNREZ0wKv/gVFe1fKqm5SQC89C/VLjYqtDx1F/7l/xDmTkvFivLMaRfR\nxFz7ZaY7ohwb23eJIywVti/SkdHHdAyuIpLSOgasaPuNLxNFUR+4fgHCnY8pHY27N+vvoxynKjmf\nzjY6sEpx9xLnhPqX/wMw8wB6mksurZVptnWHzUWHzq8lj13vpS/DH7sFUX7LVS8DALBaQQT2jicA\n9sppCbmkXd7Y8dQAACOSwMGHh7ZLeBCzYdSTKkP7WGp6erWAwo6P5wfahQOgE0TpBFMTKwVJyprE\nq2YlsF3lLHgJu6y7tV4BOXKN8bncFgAiwk2PlkNQYldzLXrbGtDZXI8T2Q50t9ZjeHoN87ltq6Ng\nK6fhjoJoLwF6W+sxvbYFCqAGFP1rD4xFSLycAsBXAojJ6gakX8hI1iT0iUJ3G0AoHbgY5CTlFz4S\nQS2kbrXrOFtsvwfrNThxkIWYpxJYUNpF1PVMKt35x5lTXCrBwlSOZkcqUSk+phPiKpyh8riIkqvv\nYRljKVUU06RDop51tZxP13V1rJI/chUkYmFOfH/zj8J/y1wgGmOnf+0CMH7bdJazyStUSFat2uL9\nps4pGfU9tzigtjHK0xLXxpfEfK+PDZ/CqjrMpaXPHe4yosUua6j1kG1jQoEXP5nF6Mw6fGpiEfRU\nBG/n9CrDOZRTshllu8pZcOJhNJvLbYvwD8A8O06C5BEWmuprb8TJ/jYBeFzY2MHCxg4+nl3H2aFO\nK+83BzLem99IhHXwKUPMfuHpLkysFNBfXEDP7RmAeHaufATe6cYq0NwO0mVGn8raDSahHoZ9klIn\nOh+4fdHYvRjRjKyWN7783TCkCVjpXOPMiDQYWAnJvIxA8Jdjevv9axeAjWWQE+esFQ9RzyTNgpPG\nXBNw4pRNSs0OW5oHiCEEysbjKuLK4splXiTHzgiRKQCK4NKTIl1yPmsuNU3jq4JMsHDKChJLJVE5\n96ju5EMuEMCygG0sWSsrlHM5MBDKfdiiZCNX2Xxz7ExIwDU3FkY8pNJhIHo8DnQ0WtPMAIs8c9Vh\nWyVFYcfH+SMqh8Oeplp0t9QZeLWtHR8Pgio85V6kEkquA6QzB8tAx2rbrnIWklp+W91l3ni8rIBL\nbjxexpfbGwVjlmylAPho4/2mCOp4Ez5HXlMbAm72gkYQpOhAwTQhxWSpguhUhHWhMVIkCScwObfJ\ny70aWlJXMkQKz3CshG4nzlW8S+af+f/PvxYLDp35VGFplH8riJo2N+C/93bVVPtcbVcWlOJOqMeQ\nwJlMQzWtHKOleUhbV7I8vSN6YYgNnfoSMD+u4HnSMC/qO2nvt/7IUPGsNhAxbhwZJFMx5Y2GA2x5\nX20YjchKojLuzxhHkvOtq6Zi4FiweIO1W2tvHAbC2g8aK6d/5zK83/ojZL74dbOfgvMZFRfavfe1\nN+KVfT6uzBH4gCBGZD1N0Nlcr1RSyHT8sirx6MwaRmfWsZLfQW6ziAN7GvBoeTM4S3Q0gFfPnexv\nA2CW/ctARwBB2WXSFSfadpWzIJh+wXb4hR3fjl0grKSSpyB0soyNLVaCOb9uAhwJgbO2tcYjTu9T\nNxfZkmv3QSdGtV2yeyJXwnvvf0/avUfgGBKkImwLjTj2zmXm0acI48bdc5zJk4LOpqe0VaogQU1t\nbNQicah+YlTFWgAGS6N8j3ThMfCTv2S/0+ifyzVnWkgbK1Qq74taYKOopqNMnwQJkufpXdELfcfJ\n9T3oxCj8uTGBeE+S8rDdJ50YBTl2Bl4ZKYGkwEqRu/cywIlzBmhScWo1qWnjfPocEKTw+PsKQOEa\ncYX8o4CZ1agY0lMGdGIU1FVZITmM9N77YUpKcnCNPrVFDP2SIVCmp7gIoiNRdOoujr3zTdD25/Dj\n/b8K3/PAE5a+JAXA5+z2xlohCSDzIABEkDgVfYrHgaPgEeD5AcavELU+ULAS/geL+ZCbJ0hL6EDH\ns0Od+MOlhSnnyVLYrnIWOhpr8YtP7VVCNlOrZonk2EIeDxbCEJAOdTje16YASACGWVjc2IFPganV\nLbH+ZAjBK4dVVUiZtdFWs9vTWoezQ/vSkS0pdc+BORZlnV41xAVE7BTlVERxxwoAtE0QMmUzPA/k\nxDnAQqf7JEyZPP0S6LvfFguw3lb++0S5d8eCYaW/9TKKwxDF0kjvvW/+XYGzEJkW0sdKqaRgJZwL\nXER4Wb6usVPXaMNJjGOSZFE2HD4xhn3Q2+/GqnG6TGEG1MqP9ZC9XEHA75tubjDHxXK80k9ytMUv\nAbffha+h9FOlDfU5gAb/FwCCqRwRAqz9GhV5TFORxM/l+t5IC1oqK2yESvL4pR9dgq/pY0RFDOlG\nqKVgTXEdOyPAkFZHOZhPNmsaQQPAOzeeFuB2Z2pFpBwmgwg0T017CPcnkFrqU0b4d3aoE8PTa5hb\n346MCcibWLlSQ1chXl2YnXGfJbntKmehNuMZ+uCcGnN4JicejA5toGC0nUWfYmhfM05kOzC9WpAE\nooASVYcnpUBPaz2O97U65as7m+vR2VyPx8uTyrHN9TXpWRkVumMAhFhDlqHnLUVFKBgOwkH5KurL\nCQknIAfRjDEJyJN+0LFRUQybla3DMKCx6VFqyBTrE2Xi8ybko/B+649iMQvivIdPg45/pPxdiSVL\nCwWWNEIQEV4G3FEXfTdpjMuFx6ajFYc3yFqwLfJ9OUqHI/ts6q5afRM4xjLgz1ZBENIWa/0a0Qbr\nOqBV4sRFehTT5wAJkEmDc4dXTU7vbJ0zAmAi6Xs6damq7XpJGF+xuR5wQwT8FdQ36LSVccM3N/w6\nze2Jrutsd+CM9a+PIUNLKBEPHvFwtLcF3a31SlpaxiaUKPDegyVFP8iVa9gulnBtfJmRKwWfSU/M\nehhfZ2S5gKO9LQAqY/bVbVc5CwDz+HhoiIMY9SiBbhmP4MUDe0Q04uInswDUMkk9VQEAs7ktzK9v\nYXh6Dcf72oSToeeZXtAUxMYW8oJpMqmZCyOsIcvQ89ZPQOxhUAmYplgCohnRLmnSF5PWE0B2G9fO\ncja9b4duvKPd5SD15d/b+CgA1t/eS19O1Gad/pl07Tekg9PwBthAf8Zi55cAEOCp52Pb57p35doR\nEQH3IhTibOSdeJJFUj4n7dqv1dub+e84M0rsCLEC/vQKgpC2WAfLup0wl0S2nsRMmoYjA5p2hIT1\nACSsCSHAoRec49JK7WybMx7cBH1wM1WpqrPttnvkwE7JsSFg+INwnvONMaY4kJe+o0SzEl3XZYEz\n1rvxGK/f+w4mT/wa9p94AYCKHXimp9VY1AvFZOj6+fXtkFxJ++54XxvyO0Ul6g0AzXUZFHb8kIlY\n0yWqlu0qZ2F9q4iLd1k97KPlAlYLO6iryaCx1kOGEEM8itvJ/jbhKHApagDwpoH2plrncQALLc3m\ntjGbY9dVHqpDQcyHydAVZ2JhDMKnqKm17xrkxRuAIC+h1Fo7rgDTgCACgUSobD7h6OF+PyInapwn\nZdmYbmIBjuiXJ8GUqAvmJJ04Of1zNXgDXFz4Ij/NSXmGrwAPbsIfv13WvSvfpQibmyFjNQ2WaiIP\n2gVt9xiqXSY8h1hwd9hYf+p54MFNY/wZ98kZBWUmUs9evqxc7/grLDz+8APBWFpuJU6cgyXjjjB+\nG7AoyFrfBVs0ikjS35JzXMm7qreDATsDfYhTXwrHL5/nqG/IjvN+kB3IcqKSNpOdsd6tWWSf2gcS\nlFTKczpADepn5Tz8HqW/KVRMG48syC5GfQ3B0d49hrMAhJUa8jWZLpFJBlWu7SpnQVeHlHUeXjnc\nibncNgCK+fVtzOZCqVEOZBydUascfKh5Iw/MebBFGQBWh/vy4F54hJM7hXkuNrio+HcSyWl9BxAn\nqww4QrcOgBmdGGVlmLIdesEIPdraFcUNXy2ymqRm6xe579I6JNacvN6v995PXTGgXMPSJgCx7bSF\nbm1c+P7td1kba+qteiDlWpqwuYFyjwiNJ74+1B1ZWr4Mvf0A4AccADpGwUVbnKRqx3DqXv1axZol\nvP3O45USaHsJoit1hWNnWF92D4blo5a5o1qaKSHeCKzNN38IOvT5xPNcov5Iaa6xrYMKj/a24Whv\nG0Zn1jC5uqmsB3uaarBWKCkbTFaO3yZK8jmmTdaEAIAPJlbR3lhrMD2OLxUw2NkEW6JieHoNrXu6\nuqpx/7vKWXBZ0Wec369+rhsAS1XIzsLQvmZMrxasglCyHetrxdHeNvzVB5PW3BJn5FJ2UgiwEwM+\nRj+4CVCKZ1bvoPfwW0B7+vB8kpcjzvPWefnhZUKdhgQhdWXC0cCQaXOaJHtEIKHlkrikpkQ4gkVT\n7zty7qux0rXy+Vy7e/5fU+uiDHZDh5NULm+AbP7td0Hf+Vb4gZcBYHJ3lGuJw+aag1WVxdICpEx9\nDj1qJFfzWBRZXcdFWVKnTvy+CnTPSUoQ4yJkpHuQ/a5rPwhPZ0n3H1dJk2qToKAAzXRDRVGLMsec\n7bo6e6LMqihHozME6G9vwkp+TTm+RIG1TeZQyLwJAAxNiOHpnIGp8ynF/fkN+JYINwXQvq/nQKKb\ni7GfOwtQNcIBJmO9WtjB/fkN9LYxGenRmTXlYexpqsVqYUc8yAxhzI+jM2uGo1CbIXguyzAL18aX\nQhYuCvx0bAkvD+5F7+Ioeh5fYJMH8eJ3txWG57nZBr8BSnz2PEtRJF3gOX6iFKDTAzAkkCynKU8q\nAEJApERxncSSEg9hcz3xblgv19N3Z0poPdC6iKOUtfahY+JNwxvgIg/Sqy7QfRBk6KWqhGqjzBWR\nSRvFiTKSjQZSltXmy981wH0VR2DSpGuqxO3Ax0YUK6Y+7vTxzsL/NJSJDlKKLgeqonsQgGqwOdGh\nXZHGbGBNWlNXMV8GdxA4yFF2GN481a84AB/P5owKvEfLBUyuTAGg8CkEnk3WhACgbGK5ZYL0xeRK\nwZr6IOkDbFbblc6CF/ReibL/Pj/QruADplcLotZ1dbMIYAMZQgR7V8Yj+GIQhWA5IYru1nqnwthO\nieLDyTUc6moRISv+u0fLrHzz1/uPoidFCK8a4fmk544SzOFmlA0ef8VQ3QMQH0bXd/0RRCmxhDYO\nh8rWd4l3wzG7M6PvZEeCl6wCifrU1qakkSPA7ZgZVRcnzj8xAihuCqcA8UBe+93Ya5a7SCZ9lk7C\nLluKKjx74vctkugsYhfuBBhWkCaTr0sOnwZ9PBLk/O3pRyXSaC1PLYLeuZQ41RZ3D9Z7lnfKlDq1\nK9KYkt7gVtxOrAXj6lsduM7B7/ntEprqatDdWiccBlGBN51TNpZyaoLj2V46uBerhR0FAM/tUGcT\netoasF0s4f78Bnra6jG1ajoTlBrBiLJsVzoLPmUdPbaUh08hFnLZO9TpMkuUoqe1DvtaGkRuCQg9\nSA5ykU3OIMkP/42TWfx0bEnwK5R8ismaLvTpuVINCa+cO0VuOK2lDSdawXjdgyy8HUxIaGhhYdwY\neV9jUgGsKYKoWnhxHw6HqpK+i9uduc7t334X9N0/BweU6vX01baoyVmvunjSjgIAVqUggWrpu38e\nGyWqVvTMem5X1CkqRWXRNkl7ftmUdKAUGjdKiyuMQgAwI3UWRkhn+S/XndlYBcZuiWMxNw4xw8WU\n3lrTG8H8BsAQllJ+H8EDkzrypFeNcXOUgsf1Lf+9zJxY9KkA0gubZv+pCSIG+Z2SEYEO6j4UOmcA\nVvK/DCEY7GzCmEYLLWduPADH+towPzl2N7JTEtqudBYAYLNYEp2qi3Lou39us7ltLKxvCyEpAAGW\nYQ35nZKIPHDACtcz597mQEcj7kytYHg6hwxhD9yn4XekPblwClBd8E7Sc8frP0gEMHxSOfUlhZgp\nSt7XFtXg0rQ8rE4XHhu18LaFJMopiLq/JOV6UZoF+rlF7T6VHHyJBCnpddNY3ALDqy5+Fkan7gIP\nbmgfxpfeKvfgeYyKuMIwtLi82GEysB9vi5GimhsDDj4HLE8De/oSOQri/AkdHQUjZFkYvdOvl5km\nk97F4H0VlMYWRsjINktS1nj2PFvUProUHGkn55LNSI9JDhEOPhc6kkGbvS9+PRaIXXYVk6gakxyG\nBKXgUf3jWjN042vNxpZZikrB1o5jEtgRYFg3nbiPUoor9xaNSryOxlrUZQia62pEuf9WfkMVnyjT\ndq2zwBdweSGX7ZmeVvD0wgcTqwLRWqKsKsJWSknAdM1lToVnelqR3y6iqa4GDxbWlXASAaudlQcG\n8GR3VGnMGpK0gBe9Y2fsXAp8Qpofl5gU7SWa3KIWeHNCDSxiV5PGoUqr1pdqAtdVzDKZsiY9//a7\nDGzXvCcSbEqylQFDq2lGSBkASDwJlLKrHb4C+tGlSFbGVA6XzHZIQz4G3UFRxKSWJuGP3UoUEQrL\nDVmFFd10z9fKO0WJVd0yfZrMzmuiUxrLO3wnqFaZj1hJXwgkpYmBpPwedE4SbCyp/aH9HoAdiF3m\nPMmrKfxrF4KyWFpx6peDHOWIsc34WtNY64lyetm4ryFjHzip341HK0FanBM7mY7JSrBOeWQbTXXV\nXd53rbMw0NGIfS31IqfETc89dbfWiwcQGsOLTGiAEgoefVgEYGqb6ygTCqC1wWRrfJJ4BCDZpOqs\ntrCAF3HsTEj0A4B0D6oTUmMbbBOzy2wTo31CZWBQqxR3GTv1tJNPqgm8ptZJiOPa5eqmVzH4Dz+A\n91t/5F44ywSGVtuU8cw+AXntd5PjDyZGQWPKO5Xx6nlspxsVBVDYDkM9AtkJpGsLwO2L6nFaRCiq\n3Tj1JeD6BTbmr1+A39HjVh31vHDhDdQtY53QmBJeEeKXeU0kSmNbysPKaKi983T4CkszslZE9oO1\nb/SIUfNewBsPK64SkidVPE+O32bPJkagS25D1Aahr70RLw/uFRICBEBLfQb7Wuuxp7EW8+vbQieC\nz/nD02uYy22HDhIJS/QJgKc6m/DigT04ke1AZ3O9WJu8gG6ag+7V+jo2lO5Mr+Hj2Rzqm5qbUQXb\nlc7C57qbDbGO0Zk1HOxswsZWURHnuD+/YdRt8zTEQEejlXyjRJnypB6S0l8rD3Y+hVS71pSLYioR\nJBs4MGsHL5KBo0q4k5MBoaGFhfxkixDDcZkxMTiUCI17TJFnLnfyMao3YiZwox2OXa5xHb2KwQ8X\nrnJAcdVOfbiMZIMKhRTgTuX4BM9Fvd94bQjhwEWkkejUXZNhUYoIxdr8uNrG6xfcThtPPfg+K0us\nABOhL6wuSmN1hx9W9uglnCR7JKBZvijaSO+9H0bLErK5yueTI0Z4cJM5Dc+9mmpspJkndVOqlmIE\nuvRrRl0nlBDIYXRmDbmtEta38hhDSLYHsIq7E9kOFHZ8zOXCyMq+ljrM5hhGgQJ4sJjHw8U8zh/p\nwolsh1KiieB8uc0d3Jm2ky+VfIqGppZW65cpbdc5Cx6AlcKOsZCXKAxmrIynqkQSAC/sZwxx18aX\nMNDBymJs5Bsu5Ulu2bZ6fOFpU1WSW5Jda5SqovybcpDVYRhVlaWmU3dD0KEfoqn19ATmxuB98ets\nQlJSBikmW60/4iYGIeSztqAsHLh9MRGKupzJx3BMAEPRj5877S7XaJ9WxcD7MpJ1z7HAJnYaq+RQ\npEkH2Y6NLRmVx2uEUFLcOQ2is9/8wxDc19yebjHTn9fKLPy/+qbR1/61CyGehfrwr11A5vU/iDx3\nmiiYq+/jKntk8zjbJx9PnLEyIejS5qwoESMfkelJl5U7rp5k9JZLCPBNJEW4UfQpcPleyObbWOsp\n6fDjfW2YXw9LJfnxl+8toLO5XgHhN9ay+aa7tR7eTE45hq8+GY9gM79eFRrHXecs+IDw3KLswB4W\nUuIPh9e63ppYw61Ap5zXwr76uR6DfGNvU51SxtLeUCPyTQTAwc7mSDpnrvLG84PO3b+sqqiJqpSz\niHATYdQb3xcyt6WVWaGmh0wG5NnzStv0UCU9dkbawe04UwZJTclhamWIAEINC89j/ytxJyW+tMt2\njSSm53NdC1VkOdvAUdBMBoJIKHAA9IoTbK4Dn/8yMDEKZGqBzn6zDZwESwKIWaMvCSMP1ajvr4bF\nPRdjtyo5sknP6aqwKaekTnle968BK7Pshxx0KD8XLWdv/G1rexUWO9Fnjsoew3GKYKykE3YV2cgI\niAsj8TOIeFUSlUjSRk6/bMM7+jQUmrKpEgOqEBU/hkcl/uZDVSk5QwieH2jHB3xdIkBPWz1KPsXx\nvrafAxyftBVLPkZncljc2ArYsdjnMvq06FP8+P68kJPmUYb8Tgn57ZJS7fDigY6gMsJHBhT9xQUA\ne63XVmrSAVBHmZ1RBiSFA+nUXTYJcPKRoGIgKbKaTt1ljgG/3+IOcxxouBhC2glYQ5UpkdxJTe4f\ngJUhYvBUGC72S0D/M8DU3XDHllBVMa0Z+VfAWKjSLrp04bGSSxaKhlIKhl7+LsAdynNflZwjqpSB\nibGgleGmD+0nc7Z+VqkN/VoAWBoMSJzzN86VoMLGdaxebikUKD0PeOGXgVs/CkGTgTMjxsKJ86Az\nD8T5yInzzvtMnNpKaCRrr+yJYoiVjwWiidaUDY3Wp1YH5Ak4qK4xWW5UIkkb+9ob8fxAu5UfAZCx\nBQi1JWYAACAASURBVBRjS3n0tDaI7zg+4cajZTxczAvdiIGORmdZ/1aR4ivB+jMynRMb1bncws/p\nnsuxxtqMU+ZT/3xqbQtTa1uiPpYbdwD4b2dz23j7g0l85Xm2yxudWVccikNdTXhxPyth2VuYw8T7\nl9G/9gA9t2dAI/ECUlmPBVQl6rJf+OVwtx+IJNlYyiAp8CVKcegIfgIY6Fstt66EKgkBvX8dfkML\nvOdeq+rCEeYbAyuVgI1l9UclGZQaX9pVrukTHm+fgdp2TJjieylnLRQMdUVDx9/YXLfjSCImX9dE\nLf+ddPcayRHwhBwG5b7kckMgrNVPGyGKqLCJcoIMp0rWBfFLwM0fCu0HurYAfHRJccC8068bvBdJ\n+rSS1I5strHgv/+9RKDbWIdSxuNYVED1e6h2JVhq4GuScyZsoy4QSAD0tdWzdUWyhwt5PFzIC2np\no71MuPDLzzYq9M886mAv0aQi/eErn/4DoXsmhPwSgH8DIAPgzyilf6J9/zUA/xuAyeCj/4NS+mfB\nd28B+MPg8/+ZUvqduOu1NtTg/JEuI8QDQNS4RpXJHtjTiKF9zbikEW74YABJwFSufLiQx4v79wAA\no3Se+THiKJ3DsHSwIGqgqjgRGgFcUk4a5sITcQnICH6+O7r5Q6k22cyti7Amlwme+RR05lP4gDIB\nuhanpGag6z0PaN6jaFiQE+dAFx4rKPAnZa4dl8BQbG5AnjD1MjpjUdbzwXF/yzvryLI3t2R0FCFP\nHE7ExRHgX7sAFLeeCPGTWh2jfZmwYkG2qHRZ3E7S+vwejygRP679EIImqeKQyLwXMhZJcdJTpLYi\n+y4J7XYE6FY5Ps6hlPE4xI3HcfZlimhgbKl3DPA1aX8mbeNARyM8cPpEAgoYjgKgRhlkaWk9Tc0d\nB84OORLoRHjB+adXC1bQ/d97umdCSAbAvwXwjwBMALhGCPlbSumI9tO/pJT+vnbsXgD/CsDnwfr6\nRnCstr007US2A3O5LQM9WiMoOrcxMr1m8GNmCPDy4F5MrBSskYml/DZmHQNhdCaHvvbGVHgBDqyy\nYRb0BUAWoaFTd4G1Bai86kRIuabxtMmxMwp63e/oiZSG5W1HUe0Heu99VtdsC9WWsQvl/UNHrjJ5\n37FbAlFNnntV3E+UMt2TDpcbi6hsN34gFPTE/TjywUn/Bhyo96TRgajql6iUibJoSxwBhDCHEQAd\n/0g4jNWyENBowR+lqVjg54twjOJ2ktadORAjF+/elSiRKPEzUlFqS5w76XEO0K3t+EhZ7IiqE71d\n/BzlpFec8xpP1ZakGd0SKXkSHCu9G49x9vH3caX/V0CJFyzZ6lxAAKu09E/HljC0r1mQ+nmEPYsS\nZb8/d7hLKFuOzqxjeHoNozNrONrbhlMD7XiwmMdKfoelsf8B0D2fBnCfUvoAAAghfwHgdQC6s2Cz\nfwzgv1BKl4Jj/wuAXwLwH5Nc+GhvGz6eXRf1qgc7m9BUm0Fncz1OZDtwtLdVyRcBoXM/0NGIGksY\naHp1K+r1BxA/yPQFzAWsigIGqYqHYLskCYiolkvZPW09coFgV55UGtbQHjh82h6qrSDcyBcx//3v\ngT64CSF6peEo4nbD+sSQRC8g0aQs369C5AqA+vAvfxeeVNtti06k+TvqsyQTm469SCraY4zFoKSV\n3meRJdEf995PxBgZq/chf3/uq6DvfBvKwrs3C+9Lv1eWA+gaL0kcLv1Y17sioj+As+TQwCKBAAdP\n2AXLYt4fHQic9DjXIm873jv9evzCKqlT2toYJWlv3E+sQ6fNa3KKDoCNECxVf3KnJkIlFGDP+vj8\nNYzsOYW55gG4NvgHO5vwcCGv9M+j5QIeLxeUqAM3DpD8jef70dpQK9LinFuBW4YQHNzbiHxudTGy\noQnts3QW+gE8lv6eAPCy5XdfIYScBXAXwD+jlD52HNuf5KJyKIeXrnDvbXQmJ3TFe9oaFM5tXiPL\ntR1GZ9aU6ETgf2svBEUGFM/UrALoAVDeAqabawEIc/ly3Y3PJgp9p6mUmKnqiUlD1y6zaQ/QqbvR\nofYywIciihKjN2Ecp92fP3IVJCI/XBatrLbAoOcQMPlx+IOZT61ldNUwOd/N01NxE5syqQ9fiRTt\niUPJA4Df0AIqOQvk8OlE7Y7qZ71aAXpqiXiJHIXUegIJHS7bcYbDOXwl/IEDdEuyEiVxEMXTlUtt\nDowtzacDgcn5txLJsbvuudw0gU2dUnyXYqGOrayQ5zWZYXbkqkip6ikm8a7EAX5l4HkCXAyfhY8t\n3mTOQhBx62quxcIGw1QRAE21Gefx3L0gWoqcRaxZJMFFM83Bk81t7fucjUxhn6WzYHOz9Dv+fwH8\nR0rpFiHkvwfwHQCvJjyWXYSQ3wPwewBwYPAphZ2RE1xwARCZ9ersUCcyJMQgZCQZaw4k0a2vXVb9\noti/9gCnpy9FghlF41MCe6y7SEdolmjHqSVmJRg11imBbbYJ1Ko9cOyMklaRd15AtHCW7doi+hGj\nN6GbUcEwfIXVezsEa6KeTRTS2mDSkyZuAFUBcDn7RUyaRCkDjCzh5PcawZaYBCUPpBOrEhO2zI9R\n3AEduar2s1atQAAFV5OkLLfc8H0SJ1m+FycQUoAoCRABuo2L4lnHl0uzhVupFCvHrrffv38d9P/7\nP4Ghl5A5+zupHaewKsutTllWqoyXCEubGDGvCYpuqjDMirRu1/6wbfydzNTEVtEoUaFSURmfNvOO\nnYE/fAXHF28CxMOnA1/Avr0duLUcgq99APU1npGK4NbXXo8az0ONR5TNKwDkt0uCBEqPhAMyBq8q\nkIXP1FmYALBf+nsAwJT8A0qpHD75dwD+F+nYc9qxl20XoZT+KYA/BYCh4ycp98DkvJDumRUD5sZX\nDjMMA0AFQpUbJ8SQbW9THeZy28wZAcXp6Uvo3XgUCWbkVgmwR5zDeGEY2A/dg8pCzFMc9NiZoMb6\nI0BC6icpd0wz6RqlZcGOkLelnAlcmThSErrIEx7WFpggDk8X2Hj549I+LuCbHprmBD8xPACV4CnM\n6FI4QQPRZW5R92qcP4FTyx1GW+mmfK8KP4bA2khcHcKJkZUCKWhdo4GrSdw/FaDto1JVaYCQNlpj\n2ZSIofS3/L2I5Gh6C35QRspAv0G/BViOpNFNDL0EfPx37MvrF1AChMOQyqGXHFeZ4E2+j8SpMkuJ\nMO8jMnAUmS9+nTmpFoZZjFwFDRZ5HkWTF39OJOe6Fzo3pn6G6HeVZEPs2fHhKzi+eAM3es/C7zsP\neQFnG08Wl/aC8DQHLs6ubQlxQg9QwAfjSwVMr7JN66MgZeER4PmBdtTVZLBdLOGDiVU49tGp7bN0\nFq4BOEwIeQqs2uG3AfyO/ANCSB+llBcv/hqA0eDf/xnANwkhe4K/vwTgn8ddcLuo4jx4XqivvR4N\nNRmMLxVEJOHRcgFTq5t442QWgCrsATD2Ldm40uTR3jZMrBTQX1xAz+0ZyC9I3MCqhvCP7Ajw8Fpk\n6ZWCL2BIfT6xR4Wu00y6cb8tZwJP4lzF9jffactVBBYa6di0T0JlQToxGqpoOnK4caHOOEci7JeA\nlU8CxiVpr/NeU4RrjfuJSi0oOfwS0NoFcIEdKafPFoqM6jDc/CFo4NgZKQlHX1U6biLxLmUAISvp\nO9ls0TKh+vr05yPZJ62RnVIRGPtQ/eH9a8DZ3zGOd7Zfd1wJBMEb5bt7LV0WG03VSoT9katCEVP0\nEU87yCkay7OxVcRZ70NxegLL1IB0DyaTIZ8ImSr71x7A6zsHX3IWMp6k8UCZuGBrQw1ymzsYns6B\ngkUInupswlxuC+vb7B0oUZY6b22oEdwLlLKSzYGORvzNh1PwGUa2Kt7CZ+YsUEqLhJDfB1v4MwC+\nTSkdJoT8MYDrlNK/BfA/EkJ+DUARwBKArwXHLhFC/jWYwwEAf8zBjkmspS4jOpwCmFrdgkeAwb1N\n2NguCoZHTrq0sL4jyJV4SUtjradIUp87HFI3s//uhX/uq2GO9dJ32BOzUAEDwQtbReEfvhjqOw5j\ngdBRz8EEnGpyilk04n5bTlTFNvHqJD1JZb4T7Wqi0j4J0jXCASAe8OKviAlOz+Hqux3/6l8wNP3h\n0yC8oiSC3huASPege9CYhJNW47h2zHG6HMa9xy2g0GaydSmYqOf0n3qeVb2AAsRTyzQD3ImSr0/I\nL6G0N2aBjsTzlAGETNx3Wtjddl5rtMwHSN/TSrWUgWuQ03kS/geDJ8PIAgD0DqVKFSr9oaf4uHS2\nI13mPKfuCACg2vNwRUaFWFcwrggCQreAOZVHenTMj3CiePnnAQY2TQUWDfqhd2sGb+4H/utamLKe\nkZh+Mx4RKsTTqwUFiC9vZrmNzqzhlcNdCmV0Y62Hn44tiWg5McqxyrPPlGeBUvoDAD/QPvuX0r//\nORwRA0rptwF8u5zrdrfWI7+UVwAjPmWiHRkCBasgU0MXAxAkwBQlZUehs7le6EWIdMXmerC7owhJ\nlux5OzqRTHlQ6YOkfAlxCzVHPTty9tbzJlxkRRvjFhgNz5DE5InXmupIuOtPM4Hrxxl5Y8tkquye\nqQ9c/37wjTRxBucwtgABKJKOfwT69OfT0XtrfZl2Z8tNnxT1Ul1XFIIMJKjDF+qF/GKi3lfk9I0F\n7fgrTNmUs1pKuBMjX58CpBuVX08SWSm3f13mCrvHjWMjWhaRNtPTeXj2PEvpBe0vtexhEYXeIeD+\nNdBP3ksO8pUdGCnCacjYs9Yp6bI0WA3bvbrfaaqci5x/S4nmWlMnmUyQHiOAl1GrUtKARYNoYl8j\ncLCmWVTQ8Ri1R4CzQ51KuvuZnlbRDrnSgZtPWZSb4+84YN8GeKzUdhWDI8CAii8e2IPBziYrOZNP\ngeN9LVjbLFp1yRn5ElXCPnO5LVFRwaMPvRuPGVsb99RlKmDPY96/VJqmEPckkHFOGqKMS29EvdDl\n4CZ422zncyHr5bB7OeRJ1kkeCCZ1VQir2iZP0E6kNvQ4IGW55EAeV6b/Jee+aobbuW0sB+PJpPcG\nzEXdRopUjmMUidnQUiaAGdGJXECVyBbCfpFy+jZ8igwAVHbSHBh57Ewq3QFjkSBS+iZFZKVcx9Pa\n75awe6IUXZq0mQVHIcbz+9+DN/R5kLO/w0qUP3kvVapQ3AO/vg5oliMLQX+joSVZaF/6LNGmRQaX\nlkqCGlyP5iqbNvYLttGzbM7j5lajDVI0sf9Xv4GMl1EWdbaWbOPiJ7PIb5cwvlQQEe2nu5rUawct\nzAQ00Fz2+tr4kkEHXS3bVc5Cc30Gb57qN/TEMx4RQBIWBmoDAEytToVOQXCOEgXm17dFCoKpS5Kw\nosKnmHj8GN0Xw50QefY80D3IADIBiRD96JIA2gBg7IiyxTCdJUXoA+YLEfXyJeFR4NewvdRRjH62\nCSYtwtjZDmUnwCY92j0YpoGCPGm1JnIjnBu1kz12BlQgtKEgrw3637mxcGIiHoS2BQBy4hy7toPs\nxwj7VokUybn46CmTwDmRnTZ/5KqyUzXOLUe2XJgRh7Oi7KSHr4gdOB2+wiIWevVNErwBH0MHQl4D\nPZUnR1aqaVaMhSX/nsSSps1c6bxyBegi78WxyMuYhbLwSwkcND1KQ4evhNEN6VoqPTVvqJTy0qjU\nuQYIfTSM0sMP4b30ZXvUSruv3sVRvHHyS4JUyaeMeMlGCFj0Ke7OqayvHMyoRyIGOhqdpZSV2u5y\nFupqRMdOrxaUaMArh7sM5S9XaGc2t4UMITje1yIci49nc+Jc2dyYGtpDuGDbFlAAqWWcdUATJ9EB\nUHY4Hki+M3K91MrnFGzB09jnlPPE/J24HVo+UbRFpIHMvHbkeSPC61bQqDaZoqFFSUl4v/VHVkZO\nOnVXlf4FGBiK29OfN6IDLodOnvjLJUVymW1cGM/qwc2wvwmxpgfiwsqu6FhUuodkj2giZqWAo4Aq\n0Soj8iKPB32HLYWa0yyU5VaylIuxSGOuc+nP1sBKBBwsSdvhUu+0tce6sKbELyVKxxpjhEEMDa6K\niVEoka6DzzIQuCXiqkQhKAU+vQ5/7JYAJVvTccHv6chP0NPQgr7nXhOg+NzmjsEsDLhlCHgKQra+\n9kacHeoUm+CGmgw21lbmYzsxge0qZ0E2hV/Bpyjs+HjpoKoCKUcgOpvr8dOxJZGa8ClFa0Ot4VgM\ndDSid6ME/1o4CBUPVqbElQdehIyzy0u3kehAdw6A1Oj1yBx03G5P8eDBFo0T55xIbF6LLIOMkk64\ndOqumuqJmuQTLFzyefWJG0BkxEQGVbkqUGzgtLgcrG2nYkzuFhImxJAiVVKeyU15doSEjkKwMyft\n3WF6QM//S6yCiXaGMekeXcTMFtGKGw+uxTBqwS4HVGt7DlSrRNCxEtXAQMj9qLdduV9tYZM5WPSI\nig0wqfBhJMRfKZYCv6SMB4nmGYBxb8oYCZxIElSNKfOdFOkSGw+Lgy7mOjllGOiSADCrms59FfTd\nb7P3ZGkS9J1vsb3kwf8OAMPSZWZygm/BA3Csrw3drXVOHIJewj+9WsCVewvhOapDsQBgFzsLPFwj\nI0h1gKKu+PXy4F6RmuC5Im6yY4F2y04opjwvajJy5sKzJomO7i3zUj2+q42yuEUyyY7HyLNSGsmB\nQLKBzkPKCVcHvcmU1sq5bQhxS4RFnvSMnZUeXnfxMWTdFSh04bGToCgqBwtEk1VFkTDhi1+3XrNc\nYiLd5Gdn4FN+8SvsWnoJm4tV0IEBSJruUZ51FPYmWIjoxqpI08gOX9Q4tbWtkiievRKBQi61dqX6\nFOfS4UyUWwIKBOmPuYfAzEO40ohOwKSiVptcGt7FxyLuRXMw+b2HfR7QPHOWTG1jEDVnieYmjL6I\nz179Gui7fx6mCwMuC1t6FW1d0JV7px/ex/dWBsWacmqgHRMrBTTX1wi1YoBtVln0oagAHfXIwsRK\nQSF38inQ3Nbx957B8TMx2QHQ0wwyQBGAwfbI2bJ0yVCbRS0AqUJy2sKl5/SNHb7FW6ZTdw1CkiR5\nNZEiceXiHW1Om2eVz2NbaHnbnGAtH4omhO3cLoQ4YJmkzn2VTdwchf7pdUAuL83URoPctGdCNzeA\nn/wlu1YC/ICxi44olVRz7YAe7bClHsrJC8e1FbCnR3RdgLC9gZWKwWRLQTMZhVciae5cXhRFlYYu\nvCX3pQ5Wc9Aux5nRj0C6KJ4+hg+9ADz8IMTYWJwPAMpOmn1gRsvKLQE1HJgMV3JNSNDFMSgpWDWV\n81mk3G0OJh8nRhQEYJEuifJZnjPTRLF4P0bN2wJoqzkyghSL3xsAb8DkCpnsfQGlAotwF32Km49X\nGXBxfUeoFU+vFoIqPIru1nrUzBLrhhWAVXWyWrarnIXc5g7++taUAJNw7XA9JcEJmGS2x4mVgoge\nRDkJ3HguWg6nuXaGkU6EDZgjedZJvGXjpZZK9SIdD75zSZlDjArbxh5ry/3rC/nmempyIGPnyR0h\nwKikwOa6mt9kvWBgIpLev//e28r3iUWV5MnTUiqp9JcFxe9sX0qwWlJzjvHhKwwjoGsTiB9wlHpR\n4RKwLUZ6DT3gjnwZ74CcXw5bHUm7HHm/Os6BE24lHPfGWG9uD9MnnM7allMXfcLTPjCcvjiH0Pmu\naw4MefY8c8QTOMVRgMlEfaKAC8OKMNPBDCXI+fX8axdCDg5eURNQPutzZlJLVXEm3SdgT6+SbIBd\nunYB2FgCOXEe+w+ewPUPbUD6sEz/7VuTArOQmclZ8XXc+tob8eapfozOrCG/U8L4Yh5UD2eUabvK\nWSjs+II/QdYOPzvUKVISHiHIbe6gvkbNBc3mNjG9WnCmKIzcJc9XgU2WNtGRJIORZI8Ag6fCkGnA\nWkYm4sOQ4hw6GJKX6mkS1a4XPS2lLm932aFtqQ1GZCUArvF0Dp0bS8x8LqIX+s5M7ETChZZAK+0C\nYSHVhOyayqS972BAqR18l0BUCbDkRP2SMekDEM+HWEiYXG2rJh9AlBnh2NG/Y2mqxUlg8hOE02PQ\nNvnfLlxMTCQq0ulWSlIJUFMbS7vssiSOetLj0dAC+vBDKItl96BQilSiajLuArDu/OMcQmfbbZHK\niNRMXMg+VcpLLqMlRFSEKW0CYJUgH78NXopMzr/FqookMGM50bM0ETjbfcrpVblvMq//gTiuDyHe\nbXZtU9N/YA6DDFUoUWB4OoezQ13OTau8oZ1eLeBfLC1Mpbpxh+0qZ8FmHNzIlCRzGJ1Zw/B0ziir\nfbCQx6MlplY5l9sS5S4Zj+DX+0vo+X44UBjI0AS9GPm+GIEV/juM3Qo/ICQEZkWEIWWTX2q1VM+U\nqHa96PA8wVee5qUrB6Bl7ArlckAJuIa5MdYXpaLTITPaY+zMAFfUQPTZ5gYrbU1RgqnX5uPzXwbm\nx2NFlfR+wAu/DFy/EH4o8UUY9f8/A2dOvrb+XP3b7xoYCWNLM/kxUxv1PPNb4il5apKNr2NPGiUh\nWU3J0csojnIlfSBHqso619oC6Htvq7tnAJgbA3nuNTUikLUAYlOCMuXf2DYnaRxJ2zmc+J+IOU4A\ndC2y2CQbYGMsmAV+/yIVRykrbdXBjGVEz9JE4FxRsCTjgS/u06sFjC/lGckkawHy20Xj97O5Lbx9\naxJfCWgA4s69ujA7E9uIBLbrnQVCGKKUK0kGXNpMTRTqdFb0KS7fW1A9PZ9iYmYePdJAYeHDjNMT\ndnED6L8Ri7usVNc9CMw+jA1DGvcphcrUHbP7WB08hNsXWVQjId1vEoBWksnIyQL3/7P3pjF6XeeZ\n4HPuV5SKLC4iVSSLJdIixcXmIpnWlhgBLVJyq+2OMEralhM0olZ6PAjQ6KAHaGAGGLcdzKS7g8wM\nMEAD0z86iLyMZhpZrE7LkOPYI4qUOR0llETRXCVSXEosFrcS9+JW9d0zP849557lPdv9bklBSu8P\nW6zv++4999xz3vMuz/u8E1ccEFE01WMj4gHlmTltgIdrwCLXSjBTvBRbebD+ARRfi7YvcZ+/fwCc\n8Laoe/SCPcgRqjSOj58Cf+1FMS4Nl8GWrKzHX4/cBMEBAGNgT/0zx6DmO34gnu3DgyTWgzo8fYDQ\nWCfHHHH3MMCLjsKVpKzx+hp36M8997YP6Niet+/pRCqsv6X+LvhMetowcOAa81gUwMNfBesfII2f\npMhpIB2S+yw5hlNbqb31Q/Nx484URi7exMEzV8kGUoAALh4+e42MdAMw/nvB4NKhRoOxZEYZC7Nn\nFegw0bRDqq+SC+rmewfuNiokClYbDVKoetdOwbB8aLG5ISqQIVVXD1iWMOHRhvja2aat4OOnomFI\nn6gcX0L3Qxc8xI1UQLQE0QOYzEXiG9EOTdlTICJnDFR4MMEzI+chB7fRkvJQgDEdw7H7FWE4WWWj\nKffotRTPKY2rgGj81CHze2+/Krr/7XwJbgRBpHSMlMCDT7rgTYsmm7/2Xa/BoAzhTPa/4HMG5skF\nlkLhStRzR4xkJxevi8RAtCjRaicrLRnkFfEcvvaej7bEtnA52PMTsG98J2tthgxGu9STMnTlOEhc\nhh3l9JWb9pjaO3PlpgLUM+2cEYzC83Dh+m2j9UA1Gue3olSSKVwewDF/0eB9WYPxyIwyFoqC4Ym1\n9+LmZIlrt6ZwsCpBkaDGx+5fpPJHdokKAKxdPIAPLkygW0UdVt07B498RpS3cAs8x5aLdqmUOMAo\n21DQ0xMWyAiAAFEBBh1uzKsy7j9sdqYMhSkVml22vM7pH0Eh1z0GRJOwZwGzEQxbstJ5fh9im7pe\n6J65iiDH4029jlLaFm+9LBvl46dQvvmyN9XRRskkH7VK42QlQf9crXspgMvnaqZJKfcsBdY8BtY/\n4JZaUl0jib9QIE9jbC1EWpKMDrW2ZXfPSspSAFhTjGQ7ylX1vEgtI81+Ls/e06OHMi3Jtj4fJJKj\nHBtfJCEUqUD/XJPCnDfDF6QYjBQHBNm10hP9jJab6jpH+3eK6CB7GdUGakbh9QB++O5pY08smXc3\nAOCdDy8pML7IrNa4vGpkyeMIyYwyFiZud/HzDz5SpZHvnbuGqcqSk+QWev7o4Jmrxsu5fHNS6QUO\n0QXskc8sVJ/zq+PAmy9nYQjIxWinJwi6WtmWN8erosaR8h0Ade2yZOZLiGZ4nzNQ7ZBzgKlcZsD7\niVVXxO5HleWlSi/vhrqOAvPpILiyBOYPetMAxrO0cJjWkQ6TQIwNrxMe9duvApfPVTcsTarcy+eB\nvT8Dkwo5khIQKQxLAodJW9Ecc55qBkOfJ6ljWmSHUH76/aiR7OuOSI6pBUPPMU6ujou0plN6OGUa\nPND2vNVnJSeSQEUq0OkTuJw9PxHX6MxKfm/kgR5Y446hywqyayVARz9j+6eXtOvye2aj0EoeGQM2\nDM3D+qH5KtWwcdk8g+Hx5mSJA2OXDVAkA1DI6LmH+bGpzChjARC4g789eRG/tHIRvrTmXoVB2Hl0\nHEBNfrH8ntl4eMUCvHPqivptp2BG7qjLRURiaOKUk79MxRDo4jRWsdMTsY0wTfnrepNVAKJNW4N8\n/6HntA2IXsftHKQBsp7Y/Sg2ujbIi3z3JNnvQoennRbSyiRTyjObHqb2uHyHgcQE2E2X+NHdwMgB\nMWaN0S9qrNpNpoDgYdJrKFhdR59nzoGR/YrB0F7L6r3duWmA7yhDKFbZEZJWDL1hMwXJ9+8wqoqM\ntKRl8GDz0zTIt38uVEfGSCTBx4DK+gfAvvGdrPfmpceWVS9aK2r1/NLQ1TkgKo6EoGFXlZrX5dp0\nczojpVKl5wBZGdd1eER0WbZgNtYPzVfRbM5hMAQDIpJQVNURfRXHwt+evGhcZ8m8u/GlNYM4fPaq\nJ3XRXGacsQAAH166idHLp7Fy0RwjN/T6kXGlmvoKhi+tuRfDC+q+4+eu3jbAJh0mXhh/385fxmvd\nbeFjR8RmldewWqECYWXflldFiZM26QFBDgSqHXrN7fvmJuF+Xja6hEM+KlKhauuCCt/akRHAgwg/\nygAAIABJREFUTM/YKQk9XM3WPm6kAdjax0nWu9zDlAwzB8Ct1D26l8/VpaMJHVXVtXS8hpVP9/4m\n8fDVn8+eDza8TqPmrb7ooS2mon3UOHo1ZFrDwAyvAxs9LPqPaNGAzpe/6aQlVRfG/rnC4CN62vCd\nL0F20mVbn/c+l7GXFOW9G6kgf5sZQQg9O/UOgtFPrdQ8aDQBJE9EaZUO6zwitqwfmmf0GJIARUHK\nJBtOCfP5MwvFZ2sWDxjdkTcumwcAeO/cdY0eup3wwow0FgBhHJg1rULktFKVDxJsAgD8o9P43IW3\nsHRkjRPea1KSZYbImLiG9fuQwmnDq0oB70hMBh8/lVQREZPWvMHE69jfA6pafYqbn8JcZB6efOwI\nqVDNSMikCN/rZbSy54flkfgOw+Khp8Sh/MFbAhcwuMLPepe7LuU4E8Gt+j342JHsjqr6daaTDyKY\n3z5/Eg6XDXGo5RiUxkGn/dse03Ttb3Utj+FBGTgAvJVbBsizKllMvadx6O74gdC7GUyUvmcwoqAE\nvwK1/kOGnd0VFhdGAF9lFMETYdcBYeKKF7tEMQRL8KLRyhri7Dp58Qa2rh3EIysW4L1z17Fgdp+K\njOttqm/fvGGC7xrKjDUWUoSqfFg/NB9LR/4a/G+q/PCxN4Avf7Pnjewsfg8SOqTsQ58ZgCLicIsC\ngzwAu1BXuRRpo1FOLq5ADx+HuPkpBW0c8sThCZjRAJ9CdQByMs9fpRbsslDKI7GJwLD3Z+I3e38G\nfudm/XsAFNdHihjrMgPcqsboACLjHVWN+2cYN7lryXfQl/u2iwPC+DInOTZSDEo9dx2kYE4A0LVh\nMOUYHsb6pVKjnmgHVY5ppwPrcmSNnjkxvaqiPxUHBwBVJZTD7BqaI/XO9DSFSs+4qQgjEqYbMHqz\nteN7wI+9A95HU8bbDMH2wa+LHQ2fuNPFf947hifW3mv0Pbry0fmxRpNgyYwyFmyiJedz+AM2D2iV\nD92ju43P+NHdoqY8clDneLw5XkdMKOCkfcjzQ7vqem8d6KOXWOqHhfhVT/iIVtD5PVzDUEQUN391\nMHgPB+vwJJHVAS+u+Pq3BNZA5vNRK2O9nwLg4pnt5za6jU5NCmND3hegWe8SxIkq+Ro0+X6v8sR3\nxHw9/FUAzSpDemmM5B0bcdAr4iZbPJEDb/+LUPt2CiCXgafpZa6AdMPDSUFWDcJUaWIIqG1HA4Y9\n6cAGTJQqYlfNE9d/n8gDkyKkwwDU5ZeWniDTHJJQSkYoAGDqTu1oVJUwVHp3+T2zg+cSrM+6vCYZ\nlBGKf3FjYqKnSahkRhkL98yehS+uWoTZswqcv3YHh85cRR34B1Ys7MeHl26Rv106v19ZfFR+2Cc5\nSsy3gZV1K2mamx6KnkOejx2pqx0AsXll1YAO2tRzjdwMSfqePWj8ZOYd28pdSnFCowML6hDjVBwF\n7xyegIOsDiHe2fA6FF/8GkoNSGZ4bXpZqBVpsp+bAUYPERzfAzzyj8As4F0T0b0sntE+WP126/N1\nGeW7f4Xy3b/KXsdRr7ylHHa5+xUHMW9X/5B4k8pIVKRllIEYwR34Pqe4AShjyUittQDMpeaIurbT\ntjrhXVDX9YF9SYPEuEe1ZwGFwVANxVqIXDp6+dZ1fyrC83s+ethMaxmORk14Z1dQjM9djxKF99rO\nvQDcmeomNTvMlRllLMzqFHjs/kU4c+Umbk6WGJp/N8auCvAiB3BxYpL8XcGgwCZ87IhYLIn0vb2i\nmCmmuNB1yFypHfK2DnkbL4GNT4hntEGbWujMl85wxh1QWAbqPAJ0ys1dpgipCPWKlJEDQRQ8AAP1\nDoDsbBlLHfn49SlueSU2aFJybqjW4KUiuClaCF07B2QOYZClXJVk7Ieo133mWPXNPHAxGTmyS0Ot\nygan8sbiVfCVDzqGpoVdUJ/rUQqCG8CJSISiTD1E/qg5SunFkbonnbkPRCbsw99IN3giE21VMznj\nDkQ7fPcz1hUYMLwOOPuBloIxgaPyOh+sfh6Y/wDc2GItHcawdN5dOHP1NjigKvgkSP9TBscGMtkt\n8fr751RfB1vm9/fh+p2u8TcGYOvaQdUsSkc+Jy0+/QAMtML1WcBuVIBWhgr5TkQfbCVlH/JOqFEe\nPD2ANh3lTnS6tL3OUN+F1Nxlr2FtJzUQUba2wmuCXfEZE6FIkwJNMgbc/5D4/oYtFXmWbDzVjOCG\nkhwgnzFOQ7FbBEYZraHZcrokjo8dQfln/6Z+ZlYAm592DuJeKX69qSgjjx0mItKvE4ySaFEKbNji\ncgPYe5+KMn1MlVHUtX1zmCohLImKUFk5f/m7plHHnAiE7/lC95O/URHisSPCyFn9iOj9o0eutJTw\n6ksHcWr+A96xLJ13F760ZjFGL9/EmcrxlSJB+p8yODaQSzcmDVILXQoAv7J6EO98eMmokti4bB42\nDd+DM1du4tSJC7jv7iEMTXwIH1mLHQ7kO35Q56k8nUL16AGv6n9ltMLYnJ5Dm+SYr/q4A/Umcqxz\n1AeSvfj5WLNuk1LscVNGDIDkkF5S7vL0+0lNnow5I/KqdmogVdm2EfJMuo8Nmjz2DsqRfeIZZLMk\nqVAbpohsyQHyyesH+RY8FT+5Uh7aZdJG8xJ458fgnKteDUzjfvB5mBQgzzsX1H7J6DnBR916fN+B\nw4CaG4AxYNUX3HHbtN8V3fx0rMVUQyA2h8F7WLoDV8c1Q6GOsOjpBnlP73UC+zglzZPyfNE007Bd\ntsqBqduibbtu9Ggp4Y2X9+LDDc/g+AQdWRi4uw+jl2+KVgYFM6om6vYEnzI4tiqsQj+uvHeOYSws\nmXe3xr29BJ21L+DZo9/H0MQpJ0xNhwM1RaZ5eg6fusaPrlPapmzO+vAw/gp+YKfyNHmnD8Vz3xbD\niICPfLXjWfM57C8/0ucAgf4GKWRATdM8FKCTChfnAMqmI+Rp38Pw1PWeHRpGInZwNWX7DFaGaCFU\nPnrYKUXF+ZPAgiVAp1N7URnrqk6VmSVxJPhLGuVlF3z798Af3BZcI22wn2YdjkQ9vrqOfeBofWZw\n8A3g+B6UI/uEV33+ZM0BUBSK9puKhrQpvRgCqdd3yKMYM41CIsLiu05sL8TSPM73PddLuZ+Req1S\nnVw7Q0zMjEgJP7JuBT60yieljHx0AyfGb6BTpRxuTpa4M9XFhet3sHjuXfjF6avgPi81Uz41Fiop\nKzZGW25OlhpvN0O36MPp5b+MofdHYXvDdDjQ7T5J1uoT/OiAGxWgxFAw1e/FQ+ltskUqAPMHo4dr\nND8cOUTtUsZy33Zwi+XNKVt8cJsRwQh5/t5nT4wC8LEjwoiSQoTDcxVir2DNKBiU8NSNwyIRI9Fk\nrFKcA9KOHp05JlotV4eXMgJ1YhvtUAPSqyJ875lt2FIBQacAynTgJaBXhlApvIT5SHk/vjSfI0Q9\nvj7HZBpE90hlya6+v0uI/jHTeIj7JFcnpMyt44WDAUWnXkMVzXhMkvZCJM2jj7PXRmXKEDJSnRqr\nKZES1vkXTl++YYDwJT10txRVEMvvma2aSo1duYUvrbkX37o4PhadqASZscZChzGt0QYUY9ZHE7dV\n+KZPY9Gq61YLLP/cRuDYK67iCngFOoLc9shw63odPq740XN6GBhe/K0J4O1Xye9xAEVKzrEBgEfd\nw46urHkMeP+vhbdXdGhSohKCPlo3FPRmWqH0RJMogB26Xrm5ZyWbY7SksDfGDDjcuo7CYt0DEhuJ\n9QAKNa4zrAHyDr4BHHu7/rAE8OA2sPmDZmSprI5zD74meq8AEBT9c1VLa+O3AwvAAmskNh/J/AgR\n/hHDoCDq8fVnDY5RIenVp61jE1KFjx1R5F8yeunMTaCSKwoK1NMRKzcDAwu8adEmaUAFPNQpoH0G\nT0Mj27nnsMW4qrGa+tb5sgXibPJV68nzS29IJQ2IK+PnzmYPkpAZaSwwQHWfnD2rUBYZINpVl1zk\ne7605l5VemIza3Gf4iL+bpPpUMrJznvmLkypYMrdr6BuwM0qB0Yc1KmUv72E/I3vTN0B3vuv9Ydl\nSZASeQwSgjEu9uyp4sTkBhaoe6coG58nlEV0o+esiS6FqQeafHZK6cp72ePRw7y9ZjNVRI04vFSf\nBJ3YhjFg/w5wncdgKhz61e/lW6/y793zJwFZEQIIT1FruOa7bujdxda9gSERfyEjck5kKIMLIOgQ\nrH4ExWPPZEX/UiUaUbHojPmhXe4zByq5UkCByhg9vodMi4bA3SmSis1qy8gGYPU9caNL9jjOXLmp\n+hfZMveujupAufye2QYhkzzX2pAZaSxwiPTCY/cvMv7+1shFxZZVcuC81oTDZtZKUVw+CXlJhhJq\nsDCVpSytcc4BXrGHZY6xScjfTIlwmLXFMA65oEFCMMa1pgTv0jZQdail5q1DnlSy0WLnrBffDwQA\nleq5AweMo3QP7VKK3Ps8h3aBV9/tqRbf9gAtghndOIFOTFOPXkQFWni/hczvJ3iKxjOEjIkYcE19\nTpcmA57IUIMupgBEqkeXqRoF3yZ2JimSaP9G/2/HiHLnhQIz8rEjxtpRxqgnLeqAuxO9/hRsVgpu\nqokYejpBv49evuntIHn9ThfXP7qBEx/dwMZl8xR24VOehRakz2NxiTahdXri8NmrWD80z5nwXtjU\ngEQcQsOFaXggMvwL9FxGl3JgOfe3PaBHftXxcGMGiW4opCrB0Psp9203x/SFr7hpEU+lCxD2pJLF\nylmz/gERJrfr6+3QOhHm9c0br8bXhC0wV/R3LnP21HfYqKT4dT4VYNwLI408Q99Y2qoEMDxc7e8U\ncZAPs2C/H/TPRfnai1nVRqanDqg1pAGt23yvKdcqNmxBqZGHFdqBaxsCVCWXYUgefAN83+vgB3b6\nK8J8Rlh9xXTskhEFnUT51qtgy1YbOKIU3FQTyV2nsoW1bjAsnDMLl27U3EAcwIEz11CcvYavbb6v\nVUMBmGHGwsI5gsFRGgpvjVw0GnaMXr6J+xfNVtUQJRcWnT7puZa78X2NPCQ1T9tUYTrh3xzwn+3t\ne/glfIeyPu7ynqWKAyFEXqX/tpeqh1g5H7fxHBdGxH1t79BDyBTypFLF51Wo+vqDb4gxqNC+FsL1\nGCds2OKbGFwRfPcpUaLc2nMgzB8g7ikBvxYb6Nlj9cUaHHLlvu3GOovtySbGhM3SaONMUo1/G1sh\nm3wBdNpI3d/21PsHKsNMS3vo61gjOmucz49FEof95GHUXuZjRxxcjTIkJUFRRkVYLKoVfT6d9fTY\n20bfBn50dxJuKiQqRQI4AO6c97FswWwsnnuX0XL6rg4jq4FKDrxz6hKe+dRYaC46g6NEjMqSk59/\n8BG6JUfBGDqVBUflfKL5SxvlruenuxWqt8eeCqmSa736DlrqmYE0StnioaeABCPBHneTFAjgfz9k\nuBJQVN3KwwkQMvGxIxWtsiz/Mz2pnOcLlyESfQnk8/n+bvFNsK9/i/SGQ2OwrxcD9ZEGnVrrERxC\npwO27QWLewHQPcNUhVru2w7+WtXYbWS/KMDwrLkcbIfxO3tdJeBMbJHrWr1rKd0u3VfEtwfkHN+S\nlP/1nCmjUSM6K4EogNY33hDjpP1coWcGwmtKHdweQjFjjWn/TlnHXmDr8DoBmtSBuXLtSq4SuS4t\nIrBUbBPV+RVoRse9cdl8nLtW4xYG7u7Dutmz8P55t/XDpRt3lDPclswoY0EwOJ7Hheu3VM3qVMlx\n8MxVhSAtOcfGZfMxr7+PzPnU1ih3Su5IRWTkp1HjCD4m9HJOdMLHPUAd1K2GOxM2X6rh4wVOqoNM\nk0efcQ4VtmCJ8H4D1LEoCuChJw0AX5N0keFl6HwTgJnXZ0wsoYBxQr6P5esNbzhEW+1cz7MWDHR7\nt2uSiOlrXUN4G2OU0ZIK7GoQYGmhaqBujWwTlTljJRq7+QxUe55SDmmAWFcEa2NMSKpiQBhOgNNX\nhBzHhi2iffbZ45BpLLsTpEN0lmnY2GWgeg+UGJ4nKTLiATOGCMViRh4V1UmKAlfgZnOSC6thXuY1\n7eeVUnV+Ff+dX6q7afgeAMDBM1dx/vodHB+/AZ9cvjmFN09cRIcx3D1nYMD7xQyZUcaCYHB0W3uf\nv3YHBWMoOa/aUM8DAMW7kJr7cVDucmHo+elNW0U9dEv51LaEjx1xmklFwYgtIIPbJjPyjdXxXCCw\nAsY4/vzfitwrxfugKzqt1LPX8dtGCHtwG7BkZRWm7ioPPIacb9Og860FEt2uhYxDCG9jjFovEN/7\nKne/4iUqc2Tx/YDW2A2L7/c+mzNPSDukAQBWE60s1ka7GmLbC4InA6jp1a20kY11MoxVzaB1mp2F\nDJuiALdAhOQ4VQSO1Y20AhHRJA6CSHSweOgp75w2AfBmYy6KQujnJSuFcWSs8zL5oCefFzA6v/oc\nzthcbhq+Bycv3gC/ZkZIpSycMwuzZxUYuyJAr13OMTB/4b3klzNlRhkLPuEABufOwuK5/Vgy7y4c\nPnsNh89eVamIX//8sDIYau+IO6EyLzObzM12ZmX1VzDG2MB7zSFCMby+ijks5IXmpji8Y2wBi2CL\nHKudHw15LqUOXKwMiqAC1iMWPURYbCME8weDStMnTQ06bzqBWAt1+NwlPqrz5Z3ayLFxEkSInGoD\nDsTD0sZ3+weMcmHdCIzNE+Ae0tQc2U20skHO1jqRPBm62OPyNofSOCx84XWSjlqWF+7f4USa5PPw\nq+NWBI7XJFtWRNRhoY3sgxSd4Yt25QJ4qd/kYC64xPwQpGdJ6VA5N5ZRKPWSmlvOFS0/6ZhYz3bm\nyk2cCEQUPrd0Hs5dNbkYOn19s7w/yJBPjYVKzl27g/Hrd3D4rEnW1C25AXJ0ADW6lW4zs50/WREA\nVaxjFSFRrjTxXnUv0A7jktezqxAScvHBMHaiMqW8TfJ6mYcy9YyhQ9gGCtn8A8GIRUaExQE8eX5P\nzW1sTmMGHWCSNnnR3p61YPydsTrU3fH3oHDk/EmNWjdMtpXa5yJmpETnKdKIrEnqwn5XsXVif98m\nbrObQ8XActRaUEagD88jdZp6t5VU+kOPblHEYiGWTN/cpwq5lgNGngS8YvPTotookuIEYOAh2PA6\ndIbXGaRn8nsxHAcFCNc7v4r1JI3gLvi+7Ub5cmitjF6+6cUtdRhw7daUo7y6U3b+tZnMKGNh4ZxZ\n2LRsPkYuTuDa7a7zuaDONF+FDXJU3tGBHcD5EfD9O+oXvdxEuSvrV/INECVlKeIDGEbzg54wrnG9\nqUmUh3ah8+VvtlZylsNZwEcPA5ufBvb8JNh5MvtQ9hgXXs9F0QZXBw5hLJEecEaExQd4Svl9U4PR\n56mGyuy8hhHlldsHnC/qJsfjSXVR0iTCEpsH8lCPNCJzcEoAeADI6XtXvvfsVExtfAJsyUrz8LXY\nYI3fSt6PogO2aas3epkUHSsBPPAwcOJdYdRVzbhsvIihX2RTp5ZLVp3xW/vPdz8d8IqR/cCXv5nt\nWPiMLvk3wA9SjDo2No4NSNp/gCih7KsaRjEAq+6dg5X3zsH5a7dx+Ox1HDxzFQWrm0h1GMPE1Usf\npc5xSGaUsTCrU+DJzy7B6++fI7tPMgijWjI4bhiah/VD853SSSefVb3o4vFns6zfVLE3eQoVdCiM\nWyu/SrEffAM8wnKXIylRAKPdbEJONOVQNg6FUASIECocmRwdSZw3H+CpePzZ+MHfY2TFCGPL3wcM\nMK9RRXis6r9j3nMk1ZXiIXvnxmOk+CJsylC1Gl6F51Xsd37XbPXf4Fz0xNDWVq6han6/BPa9rsr3\nbG8eh3aBT00qLgKcP2mkz2wvVZfU6Fjx2DPAY8+E1z4BZm1Lf6SKfj8jJUIAXkNGZ5NUYug3XqNM\nT/UYsUyCrMozl3qfCB2A/9bIRZRcgvRFt+R5/bOw/J7Z+N0bE265RAOZUcaClPVD83H47DXVhAMQ\nxsHye/oV9zarvucQMimFT7/oVOs3R+xNTkYGCMXgC+Oy4XVgG58Al7S4CYRNvoPTrm8HEg6NsSNm\nI5yEnGhI2crvOmkHnexFjwAFQsZ6G+9UNH6qhABPWb9NwB/YykyFsRPAhU15CGIGXSjV1QtQNDQ3\nToRt+/fQPfEL4ORet+GVZ16FwS9TJ11g9BAMZX/s7bpFuCeMHCzh01NxWhdRm+WRihbaLavFGCPp\nnVQjIjT/ETAr0Hwd5fxepfU0qmdsftoBvMb5P/LA2jFDm+SXoACqHrKq0FwsG17nnEs2zTN1dvUq\nM9JYWLZgNv7x5vswevmmauc5e1Zh1Kt2CUImQF8kkwAY8MDDBi+7LT7rtxcLPBQZcGTJSmBgoTvG\nJStFFzdeRjcImZ+8dd1gaNTr22OHhulhIiknGiW/Iiz94vFnrf7xNC+Gl1vCUswlQFYl5EQgiue+\nTZK0xCQ6p7Ec8oYtAuUtwYXV88j3JcGgqWVyoXEGoze+UHwD7y50XaP8z+ro6mt45ZtXHHwDtXPA\ngfMjQtlLEiEgGEYGImRV8vvaoecl0rKihRhYYJZhsmZNpeS4KdIk8vtWypXEDMi1RjTViknK/ie5\nU7pTAuD65W8qJwa3rgcrXlKils7za7+hsAv2PrBTPezBbdLMSjIUYnNhRxwA4PX3zwH4tHSyZ5FG\ngCRnsoUBJKEFGzYR3RjZBzz2TPR+qYs/mtOUv41EBoy8HQC+6vOm0bLzpWTgpR3JcAhL5PcC9e26\nKEWj8feTOdGMw8MLFEwJjVMhY0cxC68UnIN3Oop2Odeo6SVUG4ysWM9B5ZDNcL1W8gitLE91NJwe\n4jBHiVLcAykoc2uP2Ea5wfn/8FcrTIyNUzIbXpH3sw1bAOAcbNNWsfo9h7s+Hhus6EuzsWEaUGd8\nx4oWFhu2ANVvktpjByS34iiEwTAih4mNwoyxpKQyZQ+QelQq5ciWrzcA3RSrpf08uXOm3m/CnDmp\n5CUrgZ0vJfVmSdWFsn/RmSs38Z/3nlaR88X3rfxs1oN5ZMYaCwCMdp62PLxigbcnBL86DoP0hHh5\nZGli4IUHqxeo3+qAPKpWN0BUY6RSEoCXxkLXDxP7exUbYiyEn2LJ54YGQ6HUoAfgMzJsxcwYFFFS\nd0qlfnKMGpvspk0gGPUctgL04VjkMwnqZUamhKZDDNwKkaO3JRk4a6dg+gfAvvEd03P3hH8dY6R/\nLhQpFlB77hu2oIgc7lJy1nLs0PKBPtsI82cb6J6xlnYLeI2nI9V7T0llGhGfoiNSMif3OilH28Hz\ngaibiI+8zHme4UAqOTLXqevnzJWbOHz2Ki5cv22k2BnTugj2IDPaWLDzPJ+/bz4uXL+DNYsHFFuW\nFCfnZOU5vcjzSinBRjdTHq6nesFMO8CyjOlCGqNfOuqDHOjtIEb/XNNrAIB7loJpbIihZ9GvGQ3Z\nNwgN+jYqQHsAofvoipmfOWaEr+XuS51Ll9CINQrPhp49qYb9yd+uIiRljV0YXGE+Q2b75Cbiep93\nop0YUxVsyHAKHe5UKqeOwHWAh7/qlOGleKRN1nLser1eI6V8uomhWB/icrBVihF5FMexObPBspLs\njh/fQ68Pm9WyhYhZbnWPE1XLMCB9aTb5bzuaYIyT7t6WLTPOWJANo2SK4TMLZ2PiThcbl81zDARd\n7JwTHngYmLqtDmE/8rwU6YK+u4JK2PH6uJVakO+bl4Ldb+MTBnWuk4cbXAG++lFg4iLYpm3Znr0t\nRlgVMEOhX/nnYQ/WfhY5p5m8Ab1IEL1M3McGPfKxIyhP7lWRHF59J3UuXWCsYPn0dbckr9HCfLHB\nFeDSU67WEkss32xTyPC+h2NDShJwVr4zX+OhjFSOokmuInCsf8BrzDR5N21hmFIlRqJkV3NlpQ30\n6hL9EH9Q6J6UVIwtoXflrAXJgukDHTY0hELvyAC+VtU9AEjMBwXWDqZxiMiR/G/K0BudHHQMhaXz\n7sLiuf24cPrk+0kPG5EZZSzcnOzi5b2nyb7g49fv4N6Bu70IUmOxFYVCU/PT7ztlaQbyXANAhTwn\nI+wt2R6Xa3XQuiff7Yqr+hDgVs6WVXlp534NFVSs/j30LNQY26B5tiWXFCdlbAqcSLDgJYdV9TVh\ntRcOXaOt+XIO6Uj55nQdaI5BCcTTYYGUElkNE4hSeMekr5HE/g9ekGwg7TTd6z82Rmx+WkSWItVc\nudd2oq4UoVcL6S3fYRsyEnMNoRBI002DFMDEFcF5YXUV9pKfeQzIKLaNMPSWf/ZpdBiUwdBhDF9a\nsxjLFszG7U9LJ/Pl2q0p0lAAgC7nZPWDFH2x8avjwP4d9csCaOT5gZ2iDjox/2sfwgAUQt1uPKMD\nm6LI8kO7Wlf4QQ9t7IhQjlaFg/GdHtDvMcklxdF/p7wjCvQ47GfBi4lz0OndFhOu09Z8CaXdMdZS\n7iHYRMgyWKK0N6lc7uo48ObLhlIOzU9yCd7oYZfbIIEUiro3gGDaaTrXf3yMk4oErRdmWSk10JB7\nq0tChl5ToXSQE+on1h31d1ucNJlFvuUY3ZwDx94BiOqYLFyT57teDpnqXFm2YDaeWDuIg2euYuDu\nPjyyYuGnpZPTJb7qB+M78sAYO1I1HxGMbvbBDUCVn6EogE1b03us6/cINJ7RN6FzDSsKotcgf5we\nDAL3a9vTMMbg2XAxAyeESWlj3IayGlxRdVsUCG1+ayIYvuy1WkAfQ/HctxUTYKhsq60DzWu8UcZx\npC2208hKjsvzXrJK8Ig1mxU10u5tHKDiLuZanMb1L5/JG1nTQco9MMvK+9getk/Xyb+1EiFLNAB9\nEZ8k7103Bljh1wMO6NuK1gTWppNuIL7r45CxMQs//+Ajgb+bmMQjKxZmz2lMPlFjgTH2FQD/HkAH\nwB9zzv/Q+vxfAfjvAEwBuADgv+Wcj1SfdQFIBN+HnPP/Jn4//2f3zGkyFXWYQlcq5Wsv1gjZEqpD\nYdaVLUVNNZ4JStUhjwNaFCQvR5481rEj6vCxG7yUh3aBtRQWTJUmitjBpHhq79saNxuLMcqlAAAg\nAElEQVTWEdpd4O1XwW3v0zYYW6oWYMPrHBIvcowtHWipeBE7r22vHRf3UStl33tJMXh6NYrse/Px\nU2LP6eBj5ob7e1lHocMyFlnTuTR6NVQcoKHFykl+v0cDtGlVTI6nz5bL8u474t09/FWvHjDmk6iy\nod51KDVhf5fEeyxfL5hDP3gLZz/7D/FW3wOYqsLmej+jM1duYsHg0qGsCfbIJ2YsMMY6AP4DgH8A\nYBTAW4yxH3HOD2lfexfAo5zzG4yxfw7gfwPwG9VnNznnm3Puec9s0Rvi9JWbuHTD7K1x6cYU/uIX\nY0aHSZ8YG4Sgl/W1980CFMqcrqeNqXdsFKK7U9UY87wcecp4+ZjGTQ8I1Lj0yotCEEZ5ohqGQtf+\n3as0UcT2wRiKBKV4m0miENpSeFCptVUtkCqtGUaJRoeDC7LXjvU5pZRJpR+5dxtGkR4RVFgdKasf\nBVu2OgtsGRJjz3X6FOeH+txKOegOgh7ZasNQ9wENk7/fYK5T17nPS+dXx6OsnaYxXwJ7fwa+5lG/\n/tr8NHBhxGCyda7ne0cWC6/9Xfs5+K0J8D/9XwDOcXZgBf7LlUF0ixuQNVqyn5GskJi/aPF92ZNM\nyCcZWXgcwAec8+MAwBj7EwDPAlDGAud8h/b9vwHwW73e9L1z15QFBsBg6LY7TPrEUWpXx1Hu2y6Y\nwgw0MICVwp5pE8wU9CqoA+br30L55svJOfKcXLW4nwZSK0uwh54E5g+Kfgw6tsO653SCvHIVcZuR\njmRGRxv0aHufmQbjdIe2m0rW3FYRMQDO2mmC1k+5d6vv3g5fF50gw2uje+jt1CtMEn24+B0E3/7I\ndmoy566NuU42Pq17ARqOhMXZd0PllgbNtGLyZN5mZOQzWCy85ZKV/sih3BeShbVyMt5b9Hl0WR+k\nobB03l0K2Pj6++fIUsqm8kkaC/cBOKX9exTALwW+/00AP9H+3c8YexsiRfGHnPP/ErvhnW5pGAqA\nIF/6xemrimshhlsA6kWo+g7sex1ysaDTgUHicnIvyoEF2R5frXTM5jhRwiNdUeg9AL74tSpHnlAN\nYFm9tjIy5oICzGl925Vio0rdPmaQFyVNAVCh64UaF4VAX71yG7Sd2mnTmIsZb0G66qIA1xqBpY7B\nLn/tZXypUoeva3bStte0rf/tfyv9lOEgAM3fdxPDnNpnANKM7IbrnI9q/C+ci86aAfbdKA5Gp5kW\nnyQ5YmrcBgtvVxkBIXwFA9ySY00Wz+3XnN1WuJiUfJLGAvUkpB3EGPstAI8CeEL782c452OMsQcA\nvM4Y2885P0b89ncA/A4AfGblKiOSAAgWxy+tuRc3J0uji1d08MPr6r4DOoipLIGlq4Cz1VDK0ulF\nn+LxeReqvuDt1tMSDOdp+Zy6wWyrlwd6T7BhP2Auds9P0hOWOAtUnoF9sHvbzwYoufloRd6k8Cp1\nTwlfvwUjfF2lY9Q1PQZj6JnaxID0WmGQMz5fRMwuVU0ljPq4SxOltG2wUVJs2FIBrLt1ZRQ1jgwH\nAQjk+HtYV8nYiqIQf0wEYqcYKKQBylid+ovsKd+7rLEz9g/CfTmc5125WRjEkiGWoFl33gkASGOU\nAZ+bOo332KPogoEBWDLvLnW/9UPzcPis2125qXySxsIoAJ0AYDmAMftLjLEvA/jXAJ7gnN+Wf+ec\nj1X/f5wxthPAFwA4xgLn/I8A/BEAPProo3zV4BwcH7+hPj937Q4+mvjIi1UILXZvGHnTVgFy0vJ4\nbMMW1UAoRXwLVR3kBGUvye+v5cNSPQA2vE4QjMiISbdr5NQobyCEgM7djG2JChXCrCAhUfWa4RVS\nmkF0tYF+l4MowQ/sqD9LTMcASMqthq7R63xGPatA1YL9TmONhah7KWWpSlUnSe+LnI9PMGrVNEqR\nVM4nIyVWO3XfOLKIfxKR+DnGYXCdGO+oCvcD6n3J7zTVDc4aOH/SjPomdH2l3qWTht74BFgohUCO\npxSllp0O2IPbRHqBAJ1SWCq98u6+4XV4Yuwydh4dR8mBn3/wkeILEg0Th/GvL144nT15hHySxsJb\nANYyxlYBOA3gNwH8E/0LjLEvAPiPAL7COT+v/X0hgBuc89uMsUEAvwIBfozKIysW4uRHNwy+BR9W\nIbbYQ2FkG0Ckh+RLq3GIT0mQC3XYU5+uL0QwzYLm4a6UHmFLVlZMf+Y1ADT2Bsj7tBT+tUUHgQFA\nefCNuvmT8gysg116Gp5D0iiHo6x/0hRkwLkT9WdUHw9bqR3aVadvikIpk/LQLrBDu8hyx7YPRx/v\ngO9e6u9E10oAwZp1IGIcUyVqkWf8u4rfCEWmkspGtc9TSKeo/dUzEj8n7B/4rXPoAqopF/rn9mz8\nOmsAQM18HK/c8F63oZNjRmwBFYmePxjs+cG2Pq86aOp/l3JzslTBkqmS429PXsQvrVykDIYr4+fO\nZj8kIZ+YscA5n2KM/S6An0KUTn6Xc36QMfb7AN7mnP8IwP8OYC6AP696YcgSyfUA/iNjrARQQGAW\nDpE30mTizhQ+mrjt5D98WIUUBew77PTwcrn7FeElZnirzlh0r8KzsPSNgaUPAKffEz/udoO4A/Je\nO1+Cgeimmg4p9Ex7fOttiRMqrJgK2TBRc86rHGZleFHKwKknZ6zOo9sRJmMg3PgbpaActDNQz3FZ\n/XrHD1QYkh/Y6XB3hKIATdIFIa4M+166YhcXqNaNZkiYeVZmYBDUXz3GcajkL2RotxG1ajO1E0xv\nRRoStWkMhq5lv4NejK7Yb+13JMfGlq/3GuZJz6e/M/2gHVxRARK5wlY1lcZOjlH9RLNnyjNDzcmO\nHyj9RYEnZY8jicf78NJNjF0ZU+n1vxctqjnnfwngL62//Z7231/2/O6vATyYe7+J210VrpHymYWz\nlRVmS6/eSQrRT4oSCHkCaqyaBYrF9wPv/pV+BfAY2lb/tpOTMxd10BsgiIU+CTHeHWCEHENKyqc0\na/yA/AM3KJ8Vu+etCYEX4SXALDrjwlVQlAcPSN55zSMyKk66wL7XHbrp1FrumEQ9QuteZlRLEy2K\nokB/rIp6WXTZIdHfRQ6Jk/G7HBbHhPlrZISFMAGRhkS+FEEID9AGVqiJ0WU4NgmVKPY7o4ieYik4\nck3okc/T7wNbn9d+xIWBBkSfKSc9FLqW041zaBWKrf+UjiBVAGnMX1zrsO6UkQ6WsmzBbPz654fx\ntycv4sNLNwGICMPOo+PgHFh838pWlPGMY3AsOVBUzmTBGOb3+6egV+/EUA4lRDjZpkFN2Lh8VAM1\nepoPqWhAdwo4dchFzHrQtuRzW+FBu56dOmip8PPHYTAEPUvZywFwMBWUkgqKbFUMVhkBVji8moti\nzaPAmkfNOfEg40MevDPHB9+wDDjX4yINnExvNKcOXd1DsksakRXRWMd+HocqPdND1p/RDJH7CcdS\njCYKU9EEuxI8GH3RH70U0po3/bnJMkCPIZOaPk3RazletC9donvL0TVoGObhdIEDYjT69FiRz6O7\nNcBwF3zfdqOVderz+PZwFL8DM+7Ilqxy16qu68sucNnMIJBVAWNHsHT0MB6/dz3GrnTQLbnI2Kkg\nKCvIh8uUGWcs9FWtqEcv38SFa3dw8Mw1vHfuuhfgGNoo2cqByDUnbdz+uaiXGQdG9jt104Zi40wo\ne15WYS/PAeczFiJjog7aXnKbKULNdYpSbGMMfOyICAWWXTGPD38V2PszMgxv55ND5Dcp4WD13Nte\nEACtiSuqiVnUK8yMjNmRMPbgNi8dNMUuyc+fFB5hNTYdpW+EWAPltDlSP1+YcCxmNCkiJdUuezKI\nXfFhNmIGidpXGtDZiSp4qhv0OQQqQ0lzIPRnIjEwgchZq6mWhnNjPCehN5PvBxglt+LmpdkYzKYL\nD/TOia6dDPxOXQ7c9aZBFK5Bj0DUn5KRSTm3Szt9+LVf/RZO9w3i4sRtvH++lf5RSmaUsTB7VoHP\nLJqNvaNXDLKKVDImXVK8lVQLPnqo3boO2HapfbjYG6wKa0vgpZ3vjaUMcg9aOxrBzxxD97UXlUff\na/kV6cm1DOrz3l/3/HgJducmmC8MH/H29WeKefC6twuLBjplLlPWn34tOxKGAE25/cy4dR2dL38T\n3NPczB6TLLXtRdS1InwCBqak4h5xnsUgUqrD3mzDFrcfC4XZePPl5By7DnTGhi2GF01FFUixHQjt\nmZy96OkNY5QPt9Q7hkyXGGslTjmfE/mw70f26dFTS4MrjGeO9c6J4i5C+B0LkItb16NVLGxYB7Bb\nBsOjvxqORExNCoN9eBCXb5oMxW3IjDIWbk2VRtmklFQyJil87EiycmjDu2XLNaIXgulP3id6MMiy\nwEjKoMnBrh8COLATOPY2AFGFwLa90FOKwncYxzZyW7lGigSnsEP+LXvwrrd7p37ujDUVi4x5iZAa\nRi2Sx3ZoF3jl1fVK9hTjE2DDJnWvzj2inqVvlohQMJEuAmBETmBFSRzQpdZdMlhrb61lm4PFF1UA\nrNy87kAwBpw/aRj/Ku1z5pjai/re6f78PwHv/BgG4G7KrVLJFTXXFnpfGGt3qgiQGxklr5MwDp/e\nsyOM+n93htcpozaWFkuJsnrxOyrCy41y4Nhz6QB2fmsiSCOtG41nB5bjldsr0T1xMdgHqanMKGOB\nW1q/ALBh2XysH5pnRBWkxS1JhgAYlqpTU5/Ru6GJ2MrJB1KMLUT5eShlEGOIlOJjJBREVZpF3O2K\nXGEPEYDQwRSqI+8l16hLjAQnxxMCrAPD48E73i4Afuj/Q9k/l1YaDYSKDoSew37nFKAytkap+7Zx\nQEXnP0DdS/0+FOY35PzJKupUHdqf2RT2mqnUZCQaA3gMu75ZbvRAxxgtXw/+5sv1RSo9Ve7bDrz9\nKnUXJ+oi7528tiV2amoS/NQh0SLmoaeEAbH9u7USbsEwkdLEIZO/SUmLpepVKVSENzeimvxMmtF4\net4qdMFExRQHFs6Zhbs6DJcvnB1JvnFAZpSxYMuCObNoQ0FrjMQP7FThJANAk0ivlOy9xvAP9oK0\nAEO+nD4J/gt45DbAhm//HrrnT9KkRsRBa1wbELk5mStsmKcOHQZqTKOH3X9n5hqDYdGU8GGqt0+F\nLq2UEJm7vHga/LUXlQL2SXKaglgHvueIVeS4xFQMvNNxwLG++/YqsQhKLOXj/D4Q5jfSQ52Ocd1Y\nR9cUT5h8hoBhZ3rHpQLu+VIcpW5AGINjTrvq3IoaR39URGfCWNO+OM0OFjk2j4PTJjEcG14nGHQ/\neAtY81hjwz7V8K6jYlO478YpdBgwVc3zpRuT6DCGWXf3z+nlmaTMaGPh0o1Jp9Ok2JRWmZoM9+kA\nGoP9j6YNJb0B4sXnbkgbuc22Pk8S4XgP9NDhax9SvHTK9GI5eqoKodcud9mHWGauMaa4coyBFMOP\nCmPrkRw27M9d8qO7AY8SyllLOYrSeOdERY76XD9gu1Mk4rxtBR2SHNCmIXaYvzpE+dgR8O3fg84l\n4esq6ZNGnnDAsFPesQXc86U42NrHwUf2axevgIBUKi8zCkTpDxWit1I9bb331LLYkD609XFWJEWP\nOr/1ap32eftVdAGw/oGsdU4a3gTrqRy7BM0OAfi15Ry7r89RJZRdzjEw/57FSTeOyIw2FgAX3Cg2\npdYYqejUQBUdQCM56wOodFPB3hFKBjCZ7aRnkLghSeQ2EeYXDxeulfd6yM4hZYZuowcxce0mCjJF\nvHiGyIE0XQdW6mEtx2iEu61eHzJ3aSggCGWfOx8+SX0vBkgQbuVBvSYm3XxfxvprS6QSN/ZWDLSp\nHxKax6ZHf/iZY7WhIOXkXrCEzpKp3iIlbNiDBdB4OuxqFF+Ko3joKdGvRCcr8u2TUBTSl4qU+oOX\nQKcmOtPH31oqLZXUztoX5aFdYA3Sl7oYTpvEJthr450fg4M14zmxDe8E0Cw/eRzzH3kBHdZB196H\nPcqMMhZmz+o4ta4FM8GN0jP2YRac6AHgRfwrK1vSe2reSHloF6BR+ib3AKCQ254wf9NQrwLYeAyi\n6fQMc8GVIWUWO5B8KYxepDVPTFO+nWf/lVBMR3cDs+eDH93tTUVMR4hfjiNUeeBES+yDK2McvZby\npZChhX6jFLtGcqYqiShJbPKV6i36fq+ih1UbZMAEYRZf/xb4kpVBamCbCVZKbvQpdKhSDLPU+D/O\n/Wbsi6IQ9PVUhUji9RynjSx1BHw4mZC4hncaaPbsnPvwygO/he4VhoJxPDA4ByMf3QB3rPdmMqOM\nhaKAgzT43KwrWPLan6HUrF02vM5hyfJZnxIp7d08ekMmcSWNlS9M2EQJFc7z0T/3cqCrEKcHfDUd\nnmETxsEUw8V3+DRlOAyOp0l6g/DEbFHe4GsvirGP7CcNBuXBHdgJDCzs6VmosfoqD0jMjLV2eg0X\np4oNIE3ZW84hoffnUCRnVUqCFbXhH+k06Fw/4i161ypxiAFwvGXpgFAHctO5pfa6OZ46LSU/Y8vN\ntuBtg1qVSLI0Hn4PhjF7dRzcUwGRun8pALJ1Rzg6P9Fgtg3vWBRKjvn0vFXosg44GEoOzJnVh/VD\n83Dj6pXxpBtHZEYZC2UpKiDkK+6gxOf2/ykwcQp8ZD+6l88l5ZeojcIWLCE3Q7FhS4221ZDKQB06\n8hE2UeI7HKcr9J97jZ74FHKsej2CExhjkLK34f1CQr2f2O99xp4zjqO73X9bxoIikKq84PLkXhTP\nfVs9b6+RIN/z+cCPKZ6oMf4WDhUHQFrRnFNipAa03/CJK3UUwC6BszhMyIgjFWXU0ziEkZEMHPZF\nD6E5ID2CetPnWCPEkgYM4bFPR8RLRSsqvgS29fmklBsfO2LqXisamcSNI522qTuAbNwHLgzJVV8A\nju8R85JQIWM8j6XXUkQ6CPed+AAdBnQhIuaHz14VRsO8BfcmXSgiM8pYuDnZBRjwwKI5mHNXHz77\n3l9gaOJU/YXE/BK1UbiFio6F7PnYEWDDFpXqyNm0qQupjXBuzu979QpTFEojdLYPjOlTwDZoKbMd\ns/5+Yq2Z1bMnvFMbmEZhF2oPtpKqvbjyOFuIoNhjTTmEDJR8oGwu51DxVvvYKREPx4eRGigEMyfr\nHxC/2fEDKM+wAp6m4gx8a1TxkExcARtY4HJrxIDDhB5xaMEDZYBtHtjqeYy0VLees8Tx54j9vo1o\nDedeg5Acv0W2lXtQqwierIqpWlVLEGk5sq9OD1URlxAJXo5ec+ahMpqGulN4dt6HGPvlF3Bt1gIc\nOHNNjJXhU7rnJlJyYM5dfXjys0tQ3l4DfkyjWuUA4KdIlUJulLIEHtwGlpBKcKokeuh+lnqPnAOi\nKbNbr55LUkqhCSYggGkwDpXRw+Djp0yKVoNr3sNJETIkIq2Zc8QGpkUxC4BQYudPNu7glyJJh1Cg\nFNG4VmQN6JGAENGXVPhBThHdgCm7wJ6fgH3jO9Ua03LQnINl5NiDa1Qz2ux9nwomBMyDRx/XdIJ6\nqQPVSEvZ9MoJwOecezuVZQk9TELXkSnkVIPengODu6Mshe73GHExXexL61Dr376W/tuhayPAtZN4\nd+4m7VftMDTNOGNBiFBabHAFeNGpOf+LIokCFKDzt3azIiD+cpso71AOXv696T1cIBaixpOaEwXo\n5I3rqGMKpQkmIKZAAQ0oZlG0GlzztgKPzLGT12SF9wBIff/FQ095yybV88rS1Y9OA6ffB84eqz5M\nz52GxkYeGp7omaFYiVJE3zPEvC/nPTWIVDjg0lIr8zNApzxrj3ojVpH1EppHspNiwEhqW5wxVF60\nPWb5nL2mu5z763M3Nama4qEogAe3kbo3eh2p1w7sdPuCJHj/IcZTI7qY0DeHTOuk9jnR1tvZeffj\nlTurMPWRzlTcTlXEjDMWGIAl8+4GUE28DhTd+ATY/MHkznjURrFDTbGXm0oPHLNSe6HuNe7lALFY\nkvFkXSXpXk0k1zsyPNFRuurBeEfV86IsAcbAlqz0MuzF3mOd16zD3AqYhrzmOr7nChlA/E9/H8a7\nWOq2xPVd28cP4hu3k5oIMQ42DIGT70keGFfHwceOkIZKiNCrLhMW/TeUAUT8PVV8azRl31OHvalD\ntOjM1CTZstg7f71EG40xuNwr9rzapHG9ijF3uqFYwvDoybHbJbE6NgXw9gWxr2FT/McYT8mxB957\nqNoodC19vY3NWY/uuBlJ4C0p5BlnLHAAbxz9CPcO3I0ha+L1/FVqZzy5UXLIgXIOPDJlQViptlGS\nupCd59HHWwEyOZBkPBmetFZO1it2whljoveUWq7mAOI2Pw3s+YnqI8C+/i0D2a2PIzXsK8PmXHpm\niz/TODWQovSFIWyitamWuOT1PV4cr8K2KRGrttajMX57L2ncAnz/DkX+BLgGDfX+AD+4NBV06h0r\nsUYbpwH09uhFRxhIZYUPOLATvKlX3SRaovaSf91OR5URUOMM2JKVRlO8GK7FWQu2g3doF5y+IBY7\nro/iP0UXpb53KlpNpXJCAPf7jh1BgRJdVOtF/G8reYgZZywAQJeXOLRvP4ZW3+Od+NxN7duIsZfr\nXMcH4qFasOpASo9R0shbtZgmU40nagxtKY4mBoeRkxZ/SQr/8tHD4In10clzLHsISM/s7PHqAnll\nVeq5UsKaMsUmZcnKpOt7vbiuywoo33GKF91riJzaS+XuV8DL0pgLAFmHom9cpJffAPRrp2xyrqmq\nW6pUKdv2AviJX9QkXWUX/NCupLHkRjSN38q5zyWjCxgUOdFBox36hi1G19egs0WMpXj8WeM3MXyB\nG23Nl9S1n3L2hM6OpT/+A3xu2T/EwcFHUHeT+hSz0Fw4gLPHUL77U6/XkavYQvn6bE9YP1iJ6AeI\nsLixmRPH7EtvwDrUsyxjQpn3gs/wzkvKNQxQXSWJ4d9esReyPItrrXAhr6mneBLLqoyxpoazN20F\n37e9vlciWpyKiBiK2moB7EtLxFJ0TcQJefvwAYH5aRrpyq7ECaRz5O+iIFmrPTrOnwQGFpj3SRx/\n48iG9ns27OdeUd+LrM82KprsA9875szUD6mvnKgKgG43CweWM+eOLkr8vZynz13ci/fv3YwpGY36\nFLPQVDg6vIvPXdzb+PCKXb/xLz2bwheZIK9RKRc9n0h+LzG9ISXHMo4p89jij0ZXUt+ZDqoDgPsf\nVAdz8gbmXMwp/HNujxmQnUnv1F8oIaplgApQVYoOlpmGghxHkvFW0ZI7B2nCs+vvkQrHB5WrFT1L\nqhrp4QBLKSksX3vRCWE3ytur1FG8ssVct2Y6R2GNImvb1iay3C/UBRXwz2mv0Z2Ua8TWZ+5+Djli\nsbWTayCF0sYm7bq/osd41h4jqzm/l2MfunEazx7/vzH2yy9g9qLF+L2L46eTbxiQGWUsLJwzC18c\n5Bj+m5cwdOO0t+NfE/Hl63PEZwUnRyYCm7BpeqNXIT3MzNbRqSxtzr2Xm/z+uqEQHIN6l1W/hn3b\nwQ/sDLbrJg2veiRGIx9+8A3nGrmi3qsHtCn/lkqgRIkBEtTZ+AKAsdywdAhlnzMX9vcNQ6XqIgsA\nnFWgyCZlpHqkiscPi1A6R6UpI/NXGwZTIg1RpZIklii1AivFKG9TQjqreTrENJ2mhYHVY1yw4XVg\ny1aDH3tHjCNS0aPGaK99T1WZ7WzoKdFUw0of+/Dy9biv+t6V8XNne5qUSmaUsTCrU+CxTevAF73g\nhFh7XWy95APVNXoNE/pCsg3SG4A/bJybb/SmJULdC23a3USWtpT5jG1AMuxoNXkynjFkeFkHYLn7\nFc0QSTMqqflOVZROSDNR+ZBGG2CkVijAmDcsrXmGuoFujsdF2fcqdb5Z/qGsQYK5+9SIVCWmdSri\nNXhAeT6DzsA5bHuh5gHY8YMawV8UgvIbyH7HKSkS+T1qbE2aYUnJ1XM+R8z3nE6U78//rUgbdDpg\n216I0yd7DB3b+YitHT52pOaCqKpY+IGdbnQpUBqbW9XWRuTIJzPKWACgGvKwtY+Lzd5jPl2K92DK\nPVgrzEEqJMW+furhSKU3+NgR8X1JTGS1TZb3y/FMvUQqMnc/cgDlqUN1a2bLiOFADS6KsLT52BQB\ngXhmh3aJnHvEsFNhx0O76ioQwHu4p+JKqO+mKByyVFZ/p1OTrYPcvEabnloJ5I/1fcaqpkfyHQrA\nnqUME1D2TcR4XkA8c8KB4b1W4mHhvLcAKM9I+VBGmk7+Y7Ak0sZVdrSH6IhLRaHY1ueVXpAGU04z\nLGMu9chPJLLrjbhaf0f/XHRfe9Egk8P9D9Xvvjvl7fxLGkmVLpaGfo6R43CCMCbmWgZHdOPG2Gsm\nGLuNKqK2ZEYZC5M3ruPt/Udw3/XLGBp5EXj0mWSrLTfPK3+TdbBq4dLy4Bsonvu2Y3ToFj3gB5cZ\n40pIb7iEN3U3Nd2jTrHm9QPaoPjViVSGHqgqArjbmlkDarIlK9MON9+hqs0rh0gBFM99Owlx3Ble\nh3LJymi9fSh0mfpdn9jzLVvr1qkZAODg+3egXLIy2vo3xZMF3DVTG23qSt73Ue7bDr3hFV/9qOEZ\nVk9mKsMElH0TYcMaSRXosH3WtRIdgqagPHJ/6e9Cep7KaHCNq5Q1Vkd7qvehdcT1eu5Hd9eGu/hR\nT4ZdTnQsVrWmosQWmRwmLlk31Z5Taxbm0xmAqYtTPXdj7rgNMmR+o4dgwZzOaEGOzChj4VK3D38z\n/BQ6vMSvHf0ehi6MJCnuprmxnHyTEy7V0LY+voAYKFGOnY+65ZDO/XWv0UFV1R41ZXj4QtY4+IZ5\nMWWAQJTxnT/psudJZavT4kbGTs51lRvE1XEY1L3VvKaiqVPr7VM2tA8DEBJHkVStdRVxlLp46U2T\nhMYaXNta7xIARkO0ELaAH9hh/mHiopmWAZQylGRZdpVFm8qxTWWb6hCEvPsgoZYHYCfbZctIjc+4\nSsKZyHsuvr9m9xR3D5djr30c/PT7wWZYOZKbj/cZEmx4nYgoGGXSEGnLTVvBLw3cRT4AACAASURB\nVIwIHVAUNXZEN4B9nDVSMiof1Lh8BgCxd2xjSM7NJx1JsGVGGQuAaC/bBcN7iz6PZWuXpin5jEUN\nWFGAxMiFGy7tGAuHtOgB8voGa6GWJw0CnUKgO61tMmXlU4h4ABbVsTb8okCxYQu4x2s3DJfuJPjR\n3dGqAXtzOiWL0igpCvCr4yj3bU8ORbdx2DQFnRnek9FaVy/BlD/OB9ZSkQtYfUFkw6NUwxrnR4y/\nsU3bxAFnKUMKM5RqRP1dEZ9u0FNZekoxtg68kR85T6ffFyRhX/6miHpJA4JIG6SlEyAO0KIDrNwM\nppVlkmOp3qMT4WwAEm8D5yXn1HFM5D0GV4A9923yIAZ0QiZWA1b758JoQ67pYurevtRSjgFg65jU\neZxOkKotM8xY0OS+z6F46OGkr+YsaodAJMErBsLh0vr+FW84AB8VsZtOiPPnGwAiY1A0D4CzsD3z\n4yLBAYAJWu3qGrbX7hguAZ50Z/6qzWnQdVcliwCAiSvAyb3AvtfBe8y55koT0JmeVlJzo3v3gJnD\n7qTTEpMGbRW58HUPTDasdQr11Y+KBlj7toOfOgT0zxXYFI+R2TScnYULalG5RnXDoV2CtbPCFaSs\nAyd6QfwGgGFAqEM85CmT6QSxx9nax2uGUYvGObT3e6lISDVAY+LVX54oovHfWudIvvMl0aht50ti\nDbMCeOBhFI894zXsdWAi2/iE0Um0qQHgfU4CbEqCkKfJeJiRxkKnYNiwsXeud0rsjYlb19NDzsRG\nVCFFeRDemgDe+UuR59/xA7Dnvm2GG+1cmeTP9wGddMRuCSdMnMID4JsfH7GPXhfuhMTffNlMG4hP\nkg4T/VDVGSf1SgR+fA98Odc2kN7eseWCzqznVc+09AGgOwm2aavy1nPH6zNoVeRCJ43K9PgcsOdj\nzzgYhhIgwaxNPMteALfTWWoHeN5ng2cmU38Z1/amE+Q7+uLXsqOnwWckjGBv2qWFqJ3xfDreKoUL\nwQCPWoYUBzB12/tT89lLUWLdYiWPcS9i7ZKp1xZb0dsyo4yFhXNm4YurFmH5PbOxbMHsrN+mLmon\nV2U1uNElRvNK8duXr70IboF0jN/qnAR9s4KRDePQ0Lq3Aa51qqPbi4eeIsPlIUVQAkbI1BmHDH0r\nr5YBnY74QibozafA3QhNfRi6uBARGdFBprbkeKkpBqc3QmMBrgCAXxhxDMUUUQaZ3RDn8WedyIXt\nKaUImaZ682VzDEd3A1V0oVfPshEuqIXqJ118usGHP8h9ZvUbjZ0159qhdIIBymxguMWMn+kw0EKp\nOn51HNj3OpTBe/4k+Rvv+G1cRiCq6YBEAfTaht77zAnGIZ+4YqZvRw/j7MAKLBhcOtTGGGaUsTCr\nU+Cx+xdl/aYJVacqu7Ma3OSE77whRXt89lh3vmRwEoTQ8cY9Shjd2/Sx2J5h9/I5YO/PkhWAnXPV\nQXjUIa2nP+Q4s/OhHuNFj3boRpQKieszWuXwqa5+TZRgzOD0KXvxnqxoSwPQlTPXFkCNmp8m4oRf\n1z4OPrLf+Lfvu75x5wACvePSjUU9Rz1NEjq8GxlGFjtrzrVj6YSmhhsbNsGXgNWEKRItc1KQkRx/\nSqpOkVgB4AffENgOD5+Oz5AS3R/3A7KSy5MuwsYnAEWpDtht6NuSmHGI/rkinaImiuNMZxFe+cUY\n5i8avK+NMcwoYyFXmlrFbHgd2Ohho8GNLHlL2USAXwmGqF4NIGSEkyB0D2ceju42//DBW9rYXWIl\n5/c+w8f2csWogM4s43ptWulRL1DnERCjyXqm6RifGFvHiCyEQFc+MYGyfjwK0Fv7bFvY4Iq6qVXR\n0XgXiDEm5GVDhxzgB9upg83KUbeVcvLxfLSxLqj1llrRkypNxlru217P5+hhRRjlI38zomUU6LLr\nEhPp7zyqN+0DvOzWqYWcxmKGgetPZxQbttQl4hUnTdtRBTUmvSLGWl+C7M10KE7fKtAtc1h7wjJj\njYWUiEEvB4KTjqhK3mKbSP0+5JVse4EM6efmQ1O9CdszxJrHqshCFc4f2Y9y9LA3ZE/mXIlyUHQ6\njULfbYgREdJ6NzDNGDO+3xKSO3lsz31bjG3iCjCwIIkvwFnjVorKZ+AZ635q0htdSRUD9Mi5H2ib\nkpcNAAKTjHs9Rz1F92to9IzTEG7X5eNcb6nCx45UhkJ1SOnGrGbQJBHFGQe6VuljvfOUeWBLVtbx\nQc5Fiain7bP3velsnQFqZ/sQj/Gc5ApV2WZHZwG4xkzRwfKhxXhrtB1DAZihxkLyxm7Qk4ACJZol\nb+FNpAtl6YdC+k1CiSneRPHQUwbmoHjoKfA1j6Lc+VJdpx0I2VPjKl97sfbiPVUXbUvMQGTDgogp\n1lXP90xtjCH03ZwDu8Y5CJpbfOErwJ6fJNFmm7lYLgxdD5YlRVJxPN68bGIHUG/VgJ7fdsBw8Wqh\nFJmuSJOUputtOsWpQmCyTLl00lvq+9W/g6BLgphI3SJlHixabtY/4GXP9L03tjyNrTOkj73zlqgD\n/JVtRDTXaponAdAYbaWHFICZZixM3hLhmqvj0Y1N5f9TFgEFSjSAY9Ymyt30KWG46VAkxUNPATGr\n+fxJL5hTH5dTHlk0676YIyT1tCf8nDqHhkdLhL6DIfUYsVGmp2rfS1WDAOL/3/4xlLfGS9JTMq6x\n8Ym6vXVZ9oS0NqI2ARyPbVTwq+PA+Ck5uvh9rAMI/XPJOTQqi/b8RMxH7ECIGY8fg+fv7KEWDYcm\nRiz65wJ9syoMSBWCp4CTWhRRp48PgS4BGP8t95f+9+C7sA56314l10z1uYEH0AwdYy4yjcSs6h39\n2qqyrQRVTu4884YtGL18E2V82yTLzDIWLp0F/69/rhH1IF7Glpj/N37jIWhpY3M3UUrToVjqFIIm\nZ4+j/OEfxA82wyOpeRdi98x5BuegtkLr0x1+jofUaV5/Y44SlRA5BtjHq/YvAoRFGlN9d6l15mO7\nC82587f5gwaOhzJ0Dern/TvAdY6OSOMte5+F9iMA8B/+QdQZSDUyP07P31dfLwmgUtN4qgpJ8o8Q\nGIHQvX08MuRalulGi9o95OiQBjYQHafvXfj2KlXiraeLg5iZTH2cs6+da1fpDowcgB0No555+ZWb\n6BQM3CA+aS4zy1jgHIqo54GHganbZCkfoAPe0pHToYXTlsefq5RClmxTXgETKGd8kpTjtuep8OAC\nUp4h+fsfc/jZZKG0Sp2Mpkk0QDRHCZFj2LBFHLg6zW313xQIyzSm7oAf2GEcBAAM7oqYsaEOMPug\njZTZ6SA5x6MCwM8c80avAHefeSmXE52BHCNzuqJ6wTF1p2rjqjtl9D+J7hGrHBdA3DC17p3CI6NS\nSQS1e8wJMO+X3pOCehch45ENB5hoI5FcknGTSnmMHRHRMo+jGioJ1aMvpQd/Yad7lg2vw69/fhjf\nujg+FnxBiTKzjAXG6ryatKQ9eSY27CKnVTOlQMnPdOWxqYWUdG3dqq8OctmIiOogl8I46R56xh1V\njlufG9sgyTJ4ckN9xPd1jIhNEtVLyNgH3uQHdtZfqnLtjudcdsmQIpBnFFJjYMMVI2gkrKvuZ+AU\nAJw9Dn7hQ+PQCY3HOVQP7QLmD7oHiy93bHN+aAoVm58WRGS8BI69jfLEuyi+8Z3ounG8xkO7RCQn\nofMoObepjKgN9nOO2GMXUR+3/0l8j9jkZ3FsVpPIJhteB/bkbzvU7ilOgIN3Aby8K1FMUmTsvs9j\n5bZ2eigWaURRgD24TUWAZJrabv2uGzL6vXzpESrds+yhp3Bl/NzZ6EtKkJllLCwcAvuV50jAIbmx\nbHav6sV4S340nEKqpGyYnHy7I/1zUR/oHDiwE5xzU/HJz7pp4Xm5YBWRkgwTK7KoLso3X1YUsr6W\ntslKMhNo6tv08p587IgwZpAesvXeizjUy9deNMuYVm42jAA2LECUopbbDSnq104Zm2GEWH8PhnVt\npaTjFADn0AmNxwZF8gM7gVVfcLwo3zUMY6ME2IPbgPmDKp2giMgAoOyifOtVsGWr44bU8DrRcn37\n99T6LBM7jxpzaxiZ/oMjeT/LTqidMPFXbEzK+NO4BVLKasUe0cpxiw6waauK8oXKT5s4RFRDthS6\nb+W02U20rOv7cBE5Y/d97nMa7fvz0cNePJwdIeFXzotUoRq32/o9tCYBt7zZSfds/y4IEuzGMrOM\nhVn9QcChLaTXaHutmTW8tqR4zT3l2y2UbG0gMK1zIa+jLonheTa8DgXEOcAAQBKfaMxn/NQhwiDJ\nm6MmQFNHwXg8WF4Bgbz3TVSIdvjPSRBqzXn03xRf/FodUoywfcbGCKAm7Tn4hrcENbTe6tRF+qFj\nzMHGJ2r2vLILHHtHsHBWzKBZ0RHr+9xGYRzfA358T3APqJy8dAykZHYe1Q2cEggeHKH5VWmWM8fq\nOe4SLKzEczgHmGV0ydLaVANYRp7s3yR5+xEj1suWaBuvCVEKu9oAW593yKnUYezBReSMnfyccBod\nnVJVHvnwcE40toomQnYOrkfQHPtgp3s4B3/9+5h3d99A8GKJMrOMhUpSrWPf90I869GXbKcTEjZM\nT/l2I7IAs1eE7Akg2fr08HwCVbVjyX/9W6a3zEsTwWvRK6eEag3SplSgaYgxMsU46xEjwbY+X72v\nmjjLp/BTqgRS7qmUToSnPoar8TUzSxGDoEZiMsrSYAb1SSi8Ki6uKUGwoPIGdLIgO9SORoRWSiIH\nhzeUrYehLQmhz1LXIhvOK631/SY35WeLQdIUadIW0sNeT/3AToOqXOEOAriIXiWmo43Ko7ILrH7U\niXqpvW5FExm08yRSIRUbExuu0j3bv4ua16TE/P5Z83qeBMxQYwHIC/Ha1rFDGZyYFoihcYOGy4Yt\nIh6wZCX4jh8oKzaq9KyaY2zaKpS3D1A0uCLp8BKWfBU6qyx59o3vmN4yYZCosGkC6NJOYSRXf4S8\nZ7XJAqHkHjESuHXdwQv4npcNu2yfKUrOvqdSOjqORA+DJuJqvGmCBDCsiugc2Ck4+QMNzCgJhlcV\noJsBqx8BRvYp8DG/NWFSDNtkQeoG4S6CSWOM5b19Dob+vlBF8Th3WFht6fXwbvv5AH/kwJl3D02y\ncT9ivXnxK0VR9Xqo1oKm/9RBSbS871Wi6Yt6ROLfAwvIVDQVTeRAXlo5MibFifP698Wa6czC1VuT\n1xo9uCUz1lhIkVA4DaiVGhLL7wyvS7eKPRuGAuNhycqsZ2DLzfrbaDg49fCyD9myDu3q+XNm9YHg\no1WzFyqv5yMhySRtinnPsRxkLojLa+XLdRLJzYbu512DVNheevYSR6JFcZwoUBNcjQd7IkX3KtHp\nCGKYzOiEN7yqV8889gz4qs/XB9Pbr4JrY+KjLlmQDijrRVKMe2o/O+8r0uBNXb8BoLAn8GTk+YLV\nVfa8B5yZ0Bjt/D5WPwI2sAD8/Ang7Ak5UpFq01MxBC4iV2IpFJ2nQY11ycqqyqcbZH2V11H68cBO\nYN/2RrgVfUy22PNw7b//wUTWhT0yY42FaMlOJPyX7X2OHRFKnLCKQ/e2mbv4269CdWZMCLWlRi6M\n36QoKBsLUZihXTuvCID2FvRQrT6nVntt3VCIop5jzxwLJWfOGfX9HIXv9UYDa9D3G4qBsquzZQby\nuV6PUb6XAPbE8Sq7XQFQzFWAHsPLmV8j2lCNqarCYBu2VAZyTRYkO6XmkPvYYkRnMrt9pq4pktgt\ncnjb665X2ulQ1DUatbNJmhroVpVSkAyiJ94VfBt6R9q+WeShbBgu2r9jEqpIIMdtV2ZseyHN+JNG\nx6FdBk12DLeSK6mR8xyZccaCAj15FkUM1aokE6FvWt2uVex81zk0q7z/5XPqGlmlS4HQMmVFRxXU\n1XEBXiu7jmKgIigAtL9xsIeeVGh3N0Xgel9A5aFTxCmJ3p36LAUnkrnZ9O+HFL6PDY6MLkUMUt8Y\n7bFAZ8sEAF66B31IUaq1ru5A8xYkepUh8a09+1kdwJgYBfiBnSKCYPH1NyH3MaZsmg9hdR/infuA\nmHHir2mgnY5hXlIMIs8YDX1kMYiqd2x1pLWrNpq8p9SKBCfioaX7fHwT3lJK+3vBEZrX6yVy0ovM\nLGNh8pbbDlk7zIwQboDlsRFCX1nLPB6qsjYkNj8tOj1KQ6GFXgpR6z5gYKg5ZAx44BEjB+yLoPDx\nU9CVOpasTC5t8kdaKkKazM3TJNqSIz6FDxAkRZY30msImhyLfogDQKfO58YUpbnWO8DDXxVc+1Ra\nJMGrTJGUQ1V/h/zEL4DT74kPqrJKjOyDDnANKfokjAhBsgXkRyeC94iQ9jjfT0jZtJW3l2LvHcA8\nsJPeHTFGsjxcMohaXrwyFKhDuIGxVEfO1AjjPAwRzgfn2nb34SUrNdB6AZaQXm5iCJ25chMLBpcO\nRS+eIDPLWLhzywqnMpNDXjciSgAPbnPAgE0R+jmib0gT6AdxWHb8HQNTpakHIoCN2rOfeBd47BkT\nj0BEUIRyTeziFvKw9fREUSiWQl9ttbqGh9QqN1yZIj6Fbc65VgJbFGAbn6jLTz0haMBf/540luo+\neu4+piiNFATnYP0DfvDWx0R3rN+TDa9DeXUcXBoLADBxKXyIJip6KXzsiNXLpPD2nWgqIdIe7/Mn\npmzaFhVKbxhtocZo43psAi8Awe8r/FcDY8lZG0RFgtIfVrQzOs96BLooBM9N2RXnjtbcjSzDtVNM\nmTr7zJWb+ItfjGH+osH7opOQIDPLWLirv6ab1RSnm5NlJBjQAXqxxBSENDAysQbGppC5uh4iCm14\nrSpCopcoaU2GnIhMFUGpPc98j8eXnuBXx426fv769wUJCeGtx6iIe1X2xnh9oXT9OYwIiSh1RNFx\nymJlCLpNxSznRBqjCCjKlHXSSy6/DTGorStgJR8/FTxEgbii9xnA2PiEMHZbDPcbB0GJJLxHasrG\ne88eQ9qNHQ6qjNhj+NjRTvl7eCIwTYyllLSrD8weur4dgcbQmjoC1p0CFO6GxgA55dgZUScAGL18\nE92yOjdakE/UWGCMfQXAvwfQAfDHnPM/tD6/G8D/BeARAB8B+A3O+cnqs/8JwDcBdAH8S875T5Nu\n6mHuC3lf6juGUZF2cFNI8uzDWUeC92AohIBTANzyMw+eAQ9/FXj7VXll8IkrhqLT2ff0TdXU4wmm\nJw7s1AyXruOtG8agFgrElfNkZUpbQilsf8RII8yS2AAr55+jmKkoCmn0EtiQ0JhjitSmt00F5eWI\nl69CK1Vlw+scVLzvd77resv3OnUvkxozAbJnRRaxV1PjPWIYhMoce8ZgNBiz776p+sF5Lw887JCe\npRpLqb/pKQqrReXQvWN+YWAh0DlFzp8vCpkadQKA5ffM/vvRSIox1gHwHwD8AwCjAN5ijP2Ic35I\n+9o3AVzinK9hjP0mgP8VwG8wxjYA+E0AGwEMA3iNMbaOc04wsGhy6azoZKd5vED6Qdbk4DYWTAOs\nQVthxRBwirRiAyBC1j+gMeoxsVntMj5inEb4Mjec7jl8jdpqnZFSIyYyGhgVhcBU6MjqlnK7KYeD\nkQLROC3U+HmlWOzfJSrmlEPAXguxZkC5ihQI82gEq4yIQ1ulEcZPeQl/KC80555BoKDPAN76fE0j\nXfWskOWioTnwzXEoApQSAbEjJsH3kAIybBjZCEno4LXfGWnkGO+lSoNy7u3e2ob0FIXVf7dpG/j5\nEeHcFB0Ujz0jUriUU+aLQhJRJ99cLVsw++NtJMUY+10A/w/n/FIbN9TkcQAfcM6PV/f5EwDPAtCN\nhWcB/M/Vf/8QwP/JGGPV3/+Ec34bwAnG2AfV9d4M3lF2nSSswxRrtFGIq4XIQBNLOTYOx4rVmk3F\nKKydlMKSlfLYjVq8uYeF7+/Gv7/xHb+3buU/VV+QhsZb7nOFyIzY8Dqj1JFfHRfUxESqKtnz0pXp\nVO8dLWPi5HuvjteMdhTlceCwCBqt0hCUtM0JhD/knBDrOQkoSK1rVYJbSdlVBqrJqJnmjYYiQEl9\nJoqOOlhcVk8fOZkfZOi7XyhqFZPY2otVq/lTedNHWNXUYbN/B0CUgAJi7PDrdjIKqe0xGcWKvbNl\nC2Z/rI2khiC8/j0Avgvgp5y3Eta4D8Ap7d+jAH7J9x3O+RRj7AqAe6u//431WxLEwRj7HQC/AwAP\nL18EsKInBWkoPe3foe9/HMCvnrgH7GZTi+8HAhTWvoUc6rWgxplxWOgHbmrzLsdbt/Kfskyw17RO\n9LmqDod2FIMiMzIiLoGeJUkGrVSmFge944V7emfkilwLOutnqJIoarTqc2gYrVoFA5BVmhk7oOzP\nZXlrjFlP/E5rxiSla9H4NtQ3KeFvtZYBk7EyMgZKH8TIw9oqH/VxkviMfZ/R3Gb32JRxN9kn+u/K\n3a/U2JcM3Bqg6bUDO8H3va7akDdNkTSRqLHAOf82Y+w7AJ4G8M8gvPs/A/Ai5/xYD/emUBe2EeL7\nTspvxR85/yMAfwQAj35+E2e/8lxv4fwGG6aNyEAbY/KOQydYYkyUxkU42yWYLaVznDEG/TCz6Ja9\nodHgIeIqE4qYSJ+DpsZbyCBTwM+umEOuYynqKwTniPJEmqRrKA562yjz9c5oImzYYv2UYXsQGzpy\nWBjpor67Tapfzklej9Q5CWEYfAdQCIPBhutmTJi4otre64yadofEtnEMjtJjVaVHp2Z79UX8HMcn\n5vW3dDDZ6QayLFpKxGgugVaM3qbyceBSgOpdWUROst166Jofe+kk55wzxs4COAtgCsBCAD9kjP2/\nnPP/seG9RwGs0P69HICdW5HfGWWM9QFYAOBi4m9duXOrZ+++lw0zXYQalFebnSqxKhXIkCgVHgx5\nih4F66Nb9l3L+btq3pXWYz7nM5+kG4ncVXj1naNKwogyNPTi2DDBQa+HLqfBG3G8c60M1M4nG8pe\np4jumyW8+fMnRXXD8T3CSHhwW90TpeqWygZX+AdTCbX++OhhgX0gMDk+7xoI4w/Y/EERUbPyz3oU\nq6ywMymEYuq6EcOWjx0R/1HU5Gh45B+B9Q84ET8sWUniIXSiKrbxiTDYtcX0lXoGfS2Cif0sA9fM\n5LAhU5Ga0UtVQk2n5O7RXqPMTg+KyDU/9tJJxti/BPACgHEAfwzgf+CcTzLGCgBHATQ1Ft4CsJYx\ntgrAaQjA4j+xvvOj6t5vAvg6gNcrw+VHAP4TY+z/gAA4rgWwO3rH65dQ/vAPSMbGphiE1A3TRggv\naUwZ3APq9wlKiSKzKg/tEorSQy7kfV4P3bJvHGTIFIj2mJfjSH2/QQR/St5blddZhsLQarBNW7MU\nWa8Hupozycy4f0d9aE+D0rffUVIIfeyI03gIt64D8wdrfEIpDmPcuq6BvOIh3FDqKpTrJnP5ATCg\nU2GkAUVzImKhefWta8MjZxXL656fAE/+tlXaaba1V6XHZ45pFUFV+W7fXcHIZNspVcfIvP8h0dpc\n7qGKjyXOVmk+43SBHXXJ3aO9OotOibAsS/eskU+idHIQwD/mnI/of+Scl4yxZ5reuMIg/C6An0KU\nTn6Xc36QMfb7AN7mnP8IwIsAXqoAjBchDApU3/szCDDkFIB/Ea2EkEJtdr3BTnWwhkoHm2yYXpW/\nD/FsH7IU90BKmDnkbaux6zwUVVUBl6xqNlAx8Lyhw8o3Dufvkf4Ocs5SDbQoo2VO3luFzEvRVTCB\n4dN53gQgWGwNqiiC1RRMNftqwYiy72esgUjECQZ/AQwcAklqlWHgkAe1IhOD8MarUjQdMObb33GS\nLQ8QmIyI9W6kGffmms8pO8A++dt1Skc3jqYm60gOFf2K6KYmUbmQ2PMNAGXFvumd66lJNwTvMQCn\nK5oL+PcoGdFqC+9hlQj77gd8AqWTnPPfC3x2uJebc87/EsBf+u7HOb8F4DnPb/8dgH+XfVN7AUoF\noh2sgIdKNJF8JpV0JFXscKEYoIkUVovk0C6BuNX6mfcaZrYPQrbxCXHp/TtIRRkiTQFays3bh7Om\n8NW8ZRhoSd/1cHT4nqknLyJglGYpHk8Pk1SlT4aqE2q8vYeuXSfv6S9C/TbHwHE81sX3AyP76y+s\n+2VB0ka0YrfnhnoWZ40Ta9AbESNy7D1FOBkz8TFlaVYA6TgMChcAGFgHfa+W+7YbPTbaEqqqQoqX\n0ExvLnXwDWDDliDYcTqjuYB/XbRFQ+27JwCVHgP8KbKPvXTy75XMXWgumP65ZiKoOlgBGC+2PLRL\ngEuIch67NI7fmqgpPO1a8A1bhFMTULa+PKseLlSD9oRERVlOIb7T6b2vO3m4H9pFd460D4MHt5HP\nKxVEkw2t5mjr8+DnT5IKH8gz0GLYCyOk7an4oA6ZXsQbgk4N8WvNoVAUwOanazBb4hyb7cRr7oqm\nwF5j7CUEqc7Ubecwon6b49VSaRGub/b33wSWroKqVAnNo+UgOGt8eB0wdkSg1AP4DB+wtCloWlWh\nHNhpftjpOIew6o9hVxxU9PFUKrHctx38tRfF70f2C5uoBYMhGsXzvXuruZSMktnPqAwzD/6k1TSK\nHU3z7M22Un/23MVKdD/u0sm/PzJwj7txuRZa1xvs6F6rUf4GY+E5uXxdqlpw9T3p5XgOG+8mMkob\nUZMPaeA+EyhUkCQyvYhSIBaJkM0mZh8GLEJb2yTvZ7APbthSo/DtdEfAO6eez+vJ9+AVTEcYNCVF\n4TSHqvLZPCGnS7IXdrV0ARFJcoBnnmd2IkJVBUEbVRm26AYpro6b4DleAmerYi4PbXual8iBsffr\n63YnvXPjxT40XF9seB3YoV2i14D+d6ujrfN+NMMhhKPhR3e7/w4YC6lrvfHzVtUl3lSgbazb0aWW\n+3mQY/SBtDN0UUjshmZ2eSz652ZHaVNlZhkLmtR5eABgwP0mOQ9J4iO/awOffA1GZcfFxM3h/Z5V\n2ohVXxDMZTq4z16kCeRIOQuXBDkSbGK5FnQdXuRJtfPOHAEme2REgQTHshUfNAAAIABJREFU4vnu\n3zVQa0zxmGsbECjzIjmnaygk6f0f3wNFiKRjC2xPZ/PT3siaPXa1twIsgvJ5UnK0lOikRWoubEy5\nh5jLux/t5kD6Yc38c8O2Pl8ZXuZa72V9cbv9uBb5ChEcJR3Oax8H11I3bO3jwbGkrvVYFM+XeuOj\nh8X6ujCSlMahoksfR6QhlGINRa6Son1WQzNVomulYqbDGJqRxgKVU3dY7nRPWstLOl37On1EZKEq\n79JysEa1ApFfBwJW6XKztBEDC2CD+3JAa41C/45h5Gnj2pIF7RN7jooNWwAPp0Jr92z4TDnKyQeK\n8nroAYXveO8bnxClhwk5XQCuQhpYoK1uZniu5jNOAu/82PSyiTJecm9RY5L4HK2yhw2uqBkLO31g\n214IeseK5EqX1Y8anAg+Yi5qP6qIpEztPPxVYO/PhA6w97z1/nH+pHzb4vAeP6XeY5P1JZ5NM1SG\nHkCx9Z+aqY0AwVFMioeeMjAWoRRETrTA97w+fAxgR3BZchrHSRM0iDQ0jQ4aJbpEk7ZcPcxH9Yor\n0dBMf85czptcmXHGgi+nDriNlGItY+Wil6QsbGCBIELRlJeeX8f5k4KsZ9/rKCsGLp/X5SxMDVwH\ngGT6S/UYmoQBnQhAxYFPKtnUcYw168bpK69MuV9ToyInQqF+Yx02/NYE+J/9G8fr9h3aTWixlRBg\nzNScrqOQ7PCv3lclBLQDU5gJHyOnvbfMMWmsjRKAvOoL9eHfnRK9GQCvsrXjCAAHW7YaTONEAGiA\nLbXWjC6wVctum8CMJJnq9IlxyMOdlwagOtsQHTsiIgby6Tp9kIaCvF7MuE/ZD8VDTwVTD2quciOK\n+jirf5t6SevtIvPyOstsgzROSqTBNtRzvXUvyVS3FHpfw7Tk6mHSUerhHeTKjDMWykO7tAoIkVMH\nXMXsALFCufdKkfJOn9dyVDXEFgNXJ+Ix+sB1KWBJn+SG/k2pWB4b3Ne4iuP5pDd0anJwTzcymhIj\n5N4/1+EUCCk7AEFF5nsWneSI981yGqYZh6FHudgKKWTEOs8owXNFIdJlMn3hU+7W3nKiIno/iLIL\nXDpjTrL8zKNs2YYtJptmx6X/zgHbUXOmf8fB1GjAQQBWl9SyBqF2u+CdjuNAqMe0cQeWl2njFOx5\ndCKiLe+H3OiIE0FauVl8IPWSHg0BhP40QJmarpBpoQzSMzUOav17D/wETJWBHWP1GgbBK9PAwArN\n8XRHdWeUsTBx8xbOnjiGIbkQQ5iCxBcZtE7tMOSE2YvLR5VhgKIsQIuqzJAGSAAs6QOdNRFDOSVE\nAKLj0T2fFhs6BccfseJzUwEpIpVT+dqLptedkLP25nWtNWHk+j0GiW9sqSWKIQPNOCy16AVA18yH\n9pbj/Y2fqjs7AsDlsxVjYZUGkMrcs0fZ8DoU3/iOol22jets7y6ikJ09b3X0NLqk9s2q27sDYn+/\n9aqIfPjC8/JgJzBKvYyzjZB1jhFvRxFw7G3xQdEBVj9ipom0VKMNyqyNY9HJkWVwmvjmiDzwOU/H\nYOnvRWcktdZp6B2FeH7UGLV/659Plw6dWcbCFMMrq5/Hs0e/j6GJUTP3SngLKVZaUPGpzypa4uXr\ngQsjsBm4dHEsbp1PoyhEWDXh0As1XmIbtmSx4cWeMyZJym7t494N0IbExt8kFZAqDjDJ4hTIObRJ\nkJMGBPSRHHnnhVAuvSgc+7epjJy+a7DhdSjPn6xL5jgX9M9VpQ8fPxXtDRA0dBqs6+D8EF6uUX75\n0FOGQWX3jsDxPeDH90Rr9H0YpRB/Qa/PbUsTkLT6vry/jfcqu6KUlsCikMa9bhxX/BI5Qq5/6sD3\n4GKo+SbfS6BXDam/NVyOHm2KRYSmk4RqRhkLANBlBU7PW4Wh2+cMukwjlKodWtFDdDiCftX6IGDv\nz6KALFMxWJ32qPwxsckd5WLTzALBCoKU50wJlXrHYym76Ubxpow/NRUgvxvajLGQMR7c5oDFYoe2\n4j048YvaE7VBTsslEHbSMUg+KfHtISccHAJzWmteRgd8vAUp19TH0Vbo1gY/sq3PA6ANTmOcsjRb\nlXamhaupOUyuSOjxubPBecT3DZ4IPeo2cgDc6pRKXjPTOE49SCmdLrvIsvFTIlIAGKBh+92m7GWv\nHtVBud0pgdugoh5WVDHU2rsNmXHGQqcocN+qB1BsfZIM7zTxJOVCIL1Ti5bYDks61woAxtiSlUmh\nK/TPNUu0LJpZqoIgVbGGDkgjIqIjf1WpGaBzQ8jrTTeKlxq/4xEkpAJS0NMpURQbmBQTkjcBAIrC\nuFabB18bklx3n4AbiIaLM3Adthj7N7FGnUxZ6ak1zgVJWwKITjoQBubD2icp77VJSqXpGjHvNYny\nzZeDaUSfw6A6xB7aBX7+BHD2BFLxATnGsbfyJxLdsktvjQ6irECMcj5lHI4OsX8zcaX+B8HI2kbl\nS4rMKGNh4O4Ofn3zcixbsJb8vNc8Xi/YBym6YjD6PICpEJs3dKVXefA6KsEGV5Atp5soVvn9sOKu\nkb8qBaLwDl2n8VMbIdGY2JgNp/791nUy3JiKnlb3yQgZJ49dHUKWLLk/6MF8kuIlNIquHQ9QMSVc\nrOM6RjXWU40czfAWtRx4TnTL92w52BMbCCmvUQJGg7QSUGsy5GTE5qMNIdMI3Umha0YOoDz9vjdk\nH8Op2M5WG4A/Y+zWGtOxX8GySd/eA8S1ZI+RxPlOWevFhi0mEPbkXlH9AjiRK8PZipS19yozy1i4\nqw/LFsz2ft7rZqN+38TbMzZPJOUgxZu+IGhRw78NG0lRRamsW26mQHR7eWrSCK1Nt0fsEAfpFKlT\nd8C3f1cMz0MipA65QL8L9f1pUNj13JqRBbZpW8/Xni7xpXW8a6dBdU5w3Risp/z/Z+9dg7O60nPB\nZ+1PAoQAYRAChABhA20wtvGNJCeDDW4fz+nEMx2nLzU1VY67yplU/s2fmUqmT2dqak5Oqmf+zM/M\nZMrnpNNnUrmeHp9xVyddvuDWzOluMBhzETbYIFlCEkKAhNAFSd9e82Pttfa6X/b3yT4p+a3qaqNv\n77XXXntd3svzPi9LW7XwNwhFPLOTVjnfTdCvlyBS3p+8v0+Al5O9IoonMq2S4nKuI9l6FUX3vvld\nlvo8eAFCKXP0N7pvnvorrneOuk5fl0AQ+2Xcp0stzPMhi43fx7qHdO8HDh2TCgJqZQgkz5XRR167\np6u3vKdJsqKUhZmFJYxOzTkVhiqLTbeUUpHkPknpjz5hAHhR4s57HeC/kHUt+irXI+DAxesflxYI\naxH04nug0obQDIs4FjMhKFJFFcKiX47sAcXNRwjw4JPInnnJGdLQv1mjaWqku8C+XDkJtG0A5u42\nvbBPs8U2p2zWvjoO7Fvk/X3IEAd0dc4bnfX05qCmTBfPE8/No1DvdOQyK+3M76VUhAuE9PeBFrFm\nF2OiE4dghCET0vY8GVANry352/HKlt/+I2S/9g3kPMRp6S+/NwS4dKWIe/vkeT8f8BBr1rGaMlkG\n5FQJ+ehCuotKjwUQlXT1CsxCStp6LL8Pl+zgUauh6MKuGLg5aSzXr25pj+pkQFaWsnC/jh99OIKX\nH+/2KgwAFJCjS5xWdoV4p0uiNWfLhEl5hg8HYbjsXa7fiSHQqXHgiX/ByGr4plWgv+nop2Wt+grp\nlz7xsrjpG3NBkapYRYDTqlU2SkoZ1fYzL6nPtZU5lzbLYPgitPFJ7IufB0eEHrZJPXSsStPEEJQD\nWq5rIoWpdPKaKqLHs7FlN8APNcOzAJZ257ASDYIexcNDFAR+rJfOZ1jYgL9Bz2IgAyoUVgnilbj3\nR+aI4PcUnC86S2hKLYbUELBvvbvWJP9dLbhHVNp8x7dKmYfBUJuN30fjwnDND91zZeujjgHbsKZ1\nfXTnPbKilAUAqOcUw5Nz2DYzFHU4NnOCp7afKvqkTrZefTE7OW/cMonlCnUYPA+88JrhNaAjl615\n980Q37dwLjxhFfkBUuZGWRft2yyuHFBTVT0KFhCeE40qG8ljqYNVgUoIa2NO6da+7kbVQ1gNKJPC\nGyNnIukESQKJzxQVYjks7AQ9kmSZYpWmhKFca04+YHxpe0o/9TmiZ0BZrHz9/Xzfl3TvNzgihDLA\nSbiK0EQKxqfKuNneN+/vA5Gfq61JQQ2tKP6AmI8NzjfRrwQ8i47z0iu6OpUUi+fKN5Z35xenG3qp\nQlacslDLCHYsTSB/w6GVLuMEj20/5E6scjBUPUxcOAyjzxEV6lLCKqkS+hZ6n8V4RGzGpHs/sP9X\ngY/+v/L++ZnyubrFpW3UsoKlp+YC4Tlh3Wg8gM1UBdRJmKXjX6S+VZlPpbVv+UYHjwIzUwoZT8PK\npBz/X1oExgeQvfBa2Z/hS6D8d4enSxkLXjiKFsoOpYZV2ow57gI/+sSYI1oGlMvKT9nvDI4IV2hC\nAmIqPDMOVz+QvjcYYdeL74EWCq0o2KV7Qbr32yv4JgAUQxIM0+rKmqIkIw4vE/he+rOm/9sfzDT8\nYlhhykL76hpefrwbXaf+UgIoaVZoomWQDF6MwAd4CZUS3IuuNmMPE+VALeJ0ruvQslr945bdy1Yq\n1SYp36LKZoy5u+q/bw6K5+oWl75RKx6YBBS96930dkI17X0STPW04F+qzidraEJHwCcAxnj/Xd+c\n9BwA5Sm7Ek4GgFDcQnwjxrcplEt6dwLg1WgtnqxGlHjXgRBiGDXGVj/YeZtLC8hP/AWyY7+TbPAY\nSrfrUObXSt4dn6s/ddyUcI1WvRTz98w1yd9L826RQ8cY3XiTDC/feNrejxw8ylIjNSXZZSDGzNnU\nsYyVlaUsrGrBtpkhlpbiiFMna7g2K9s3mQLtq4t6EfT9N1XFxuJe1DcS3o7dUkwPl8gHhh5LVq+r\nAV27gZ6DwNmfMldZTU2bW876DM5QitdyVl2Yzo3MU65Xt7j0jTp0CPjmhHIYFBabHpPUa9qnWEi2\nPmVHvi4AlWTfEZCIAlRVQxPWMFcgRVCMiwSmdc4nmQG1Xjfo0kOeJadFmJCp5HuHaJe1gyfAIDqS\nqaVtB3u9CKOMXUX+t3+M7Fvfq+wJsSrK+jhoPDPNcPUrz+d7n/YtXGvQ8G4l1ripygnia0dXkgEz\ntVvBrkSGppotK0pZAIo4pcwW1nvYqqULbRxIcrv6qDq5+LQ+I347eaP4gVjdi8ZGYosxNxwucbui\n85//veRGy0D2PsPutyk0FZSWVOGbuFKhU99kZWKTLAMunADN62xhOizbULle/ZtarYhEqyP6MJFq\n2lsV0ERLSGdGJPoh5HiPyqGJ1LlpI6myzCc6fAkhuvQY5cT6LW3enpNvGLUL5D5XUR552IrenTCu\n5e8dWxaaPPJcSZsNAPV6qRxWXIc2RVl5boXva5MqBljMd0vZ24F4r09qO/I8NJRx2UC0hNM+L1lx\nyoJespa0dwCA98BNQhZ7qDpDIrv96ZWTElJfLbTkLzVsHuxVSIFELL7IfdcL9hisYVoluGBaWJMB\njnz8hKIGMKvzkecMLwL6+8pCRNv2Atc/KsfLU/KYl+tNYfqTJdVrZRSM6u9zupx5+9YxCTDX6W2F\nPAehcEKjoYmQiI22bMUevhFWpARg7dwZpEuXx87XL34o1H/2l8DpH0uKCbGXINfR+QEsCuk5oHr3\nLPn5SSGEg0cLauli7Go17z35ubcV5dg1Hl7jp8L31SVmbqWGMGyeUYWgzfXNI70+QQ+nz3DQf+N1\nc+osLVVPO9e/03LJylMWxIJRizl5LWnd9S9t2oYVpz3PFefXxXBLHXtFpWiWqFQNKzYixtzIYgUh\nhsWdv/W6ZNmZVSNDaWHL4UJj31DyGtXrposehWXJ0yDrGoWyVvKYt9voocgldlOjI5fVglFAEZel\n4iByWcReXoz+PnFYutJ9Y5S6UDgh1mtUaW7KxZqymkotrvXRlX4W8sLEMjrm594G3n9TfyvTo+ZA\n5/uwKETGouQAefS4EV9PDZnKnAE+ngA5u4kOnkd98gZw9qeV5r0cLqiiZC+nRzLv71MJtgIkWFWU\na8Cu8Li+ne0Z9fEBgHuF6mU2lv6dcmDZFIYVpSws1nO8v9iJHS99D9tuWWJZrgNXdv1nmTdOmh08\nilxSRkJ1APjmpLsZXSmKNrFtOq4NKBrcOMxz36mo5sYPJ+Mgq9UMXnjXoZhiAaQK+4Y11XKSXPQq\nGQvYtz10HPTmZxCFfABwdLQNQf55hFIAefz5H6T/9pSedvNiMES6KIlsSamTXejNBu5a37GC4iVC\nJJzy9vir3s3R5YoOjV0sIRK9cMLyUGJ61BxAQLkvigJeeMcUMJtDIUr2XB48iiw0zlp2Ez76j05Q\nuNK2Y740omQvl0eSjlxmhZdkmmT+zZfc9S5ilOsQTioU/jGe0dUrGZ4SR0lEFlqzZEUpC5Nzi/jF\ntduoZTW8/PiLCjGT78Dlrv+8vw8YHwDGrsK1aIT2LsUb+d91MUCEmpsxtBH44mRiA6oIRtMXANas\nQ/2t18swjlxFUap8+EUKH3sZsyDcjRNDJRCrVgN59Lj4PUex6Y8PqBUD5++ZY7eMG5fyLUUYKDcv\n9lAi22KhCt/AwFllnim58kXIy+a5iHLJy6DIWIXUQpscvEf2DCWWJI5qW0+TzDLQuxOgI5eNAxLj\nA2ojD/86SGePGTsPAAENBZwXCfNgUcR9sViqhMNaB/RiZhLiUNXmX0zbjSjZy+WRVBVyxsyKwXPl\nnCzqXaTSbAMWAy1x3zC+q4ujxAO8Hp2aw/DkHFavbf+SwTFVaMHDwYmZdBZH14ErRHZZeYp1iIM6\nZQE53IzOd4klU6lo8XHshCiy8+4PSmsnq5UAwQjvifcZke+a4mqt2VzLct37+hLo1DhbetxSlXOd\ni0PINnYxG1eqa90JZNQBaQBjGvRU17NaOQLoV3iJHj0OUswz5fBlvTE28/zc22X6m6V+hnhnT7lo\n2/gwrgoPbXLk+7kk9TsYbfOU4YvvAeffNTOBdADlpm5kh/+59VkhIKBxcMmlxz3juFwEcjKgFy2r\ngatnRN+IZhxYQ116CLKikm3LBmqW6H3KnnkJeOYlldnVAmK0gVgVD5HFQEvBjTnTmS0cJS7g9ejU\nHH704QjqOcWWHb1N0a5WlLJACNPNahlBz0Z3QSmbKJsqKWP0gB0FHYWa1RdQCtd45OJP1cqt2AlR\nDKqQvA6QDIhGZLifEUNF22i6peHSB4TVIDgKLBXbXGOnK5WNEiS5viUpSvdyz5NMB+sSV5+VTVFr\ng2XfSNgNiUDHULRc9TMi56Ph6i8fangJbId97HyOUXBixi4/+QabO5Z1LIoCcYzT7VHkf/cnJgNn\nxIFX7gUFGLOrNzgWimfGE5pS209TsjiwUWFe1YwDPYRrC9NW8Q58HqnWOn0y6d6v1rtwAbo1EKtz\nPORwVGTIyBWycI0fB17LMjw5h3pOOUmlzg5dSVaUsrCxrRW/umcTeja2eatP2sTQQrmi4JpAPtSs\nVrnNNgGCbt+ExZ8U15QnKq8ipx+0oo47KtV40J+R9/cZ3gDrtRUxAqVWvlg0WuZ9Y2ZK8ZLoB3Jo\n7PRDiVQgSPJtLlXcrzYPmQ9MVYYpJDrrgkDHULQcIZDY+ah8Tw5QtDDo+Q77qPCc4kmKC3HY2vau\nYx4+3LYHGLsGm1cm2gOofAeVwMjZhlZZsxkMia5n+e6Vf1fqv2hjkbIPAc1Z+1FioU92ghg9HjhF\nEqtnxmRK8PGzAUV1r8eOzQdQy2qo5xSgFa06TVaUstBay/DM7k2V7k2dQDZNMD/5RpAeFYjbYJYr\njqdMVBnkRQiwdQ9I1x5W/jSywI3+XmJCi3g8ZVStjkUl+sMrPka4qo02pLFSivNkWcmcpoHlYlzY\nVqsbiGJYc/XPepg34dt62xHEOZLIGA09/TDRg+XdCC2pao0c9oDFk0QyK+gsWrSNX3Ez5wDp2gM6\nMWz95kkHnoPAyNmGI47tkpi55PRyBe4V3+7nfw+xHyaUG7e2uUz4IC4GT4znfRXPD3W/nwEwjgjR\n2hRj11qyXQuYRuvWllb81m9+F9dbOnHz+sDlxkaKyYpSFhoV5wRycA1Yr5dR0TSCj74ej8pt1jta\nD9ZaC7Jjv1NuCp74q0308AZ6DwOfvs9+9HgnfBZX6nvpfRc0sRpYLjpv2mJ1x4DSQv0LScOpsPqz\nbWBKaSPkVQVDJXlt75CSMibuMcJGJOmgEApOUeCIPP8dABXCQ46N3xo+dHzzJA+gy6L0/d1Va0N+\nBwvgN7UPoXGiw0VGl4S70LENofttivJypVrbwgoC8GtJ75RDFqz4WN1oT4xBgjfEpRiLzLNhjRjQ\nEhJk95VG61h7D66v34Md4wN45tf24/7szJe1Ib5oEQfZlZPAlt1KWWbn9RwVTXOgZqFHhUWLjUTl\nNktsB2ujFq9usaC9A2hZFbcpWSwu3maKsiJfLxafrWZ8LB7EY3Uv13dajjgu6d7PyKvOvQO+cZJH\nngMAVcGrAmS1jWXgAGLzX0qBJYRls0j3ekN0Pi9gCuW5x8qOJcVKOfB87VbhLbGRlNkYZV19CGVz\niWfIIRk5pBcxX0LzWdmLmqgk2zBoZN8RL7cG6d4vFR+DMHIAqGNgIc/y9sPhBdPHJT/1pqqkSAo9\nN1rH2nvwxr7vYInUgPsED5wcxPoHOjsbGqxCvlQWKoiNuAUFLW5oEodQ0YCkxTpQucsptkO1EeuA\nix5OIF29Xopi67380HJU0PP1zZpt4NqEI62r5bR8nO+iY0oSGEJ9ovCDZBmzUbgilWIlBcYy5tuR\nbi0ThOYlWU5kyWy3GzkhPOS5J0VZTr0WYGRBpL9PeANcXpugh0YjKYvC0PA+xHrXxBwpDt6EEHkV\nYGwjSrISCtUwaL6+uO4jPRrxWSCrTccWYM06Vu5b8oLZlNv81JulJxZge6hknPB96DrtxtJcC1Bg\nGu/MLmLjlm27kwfKIitKWZieX8Q7H4/jwLb1VoBjbJw6lbjF1nbMgrWhcpdDUlnrbPdHHQBaOEGv\nOeAS/VBOBT7RYTdq3PYtUq3BZhzWsVaTGjIwqV9T27P0hFkv595h1r1UQ8M3/2IVsmivjZwJoqwz\nCR9UEOeQfUei6jEkE01VVAYbsYBjvQFRa0730ATonZX2U7xrBsYJ0cDnWCVOZVqsZjjZMr0MvIwF\nH2WEUA+/CNwcVPhEYrLarKGPllYlRR3z9xifh65kz9xWG9u6RyEj42tt59QcfvnB9eYgGjVZUcrC\n3GKOC6N3cWlsGr99uFtRGJLi1HwRUVJspvAT5VTUij8PyzWk/ABhd3/04d1ABTqxKB3avVcSUOPy\n8z4PTwEQNz+U9Ew5ZJDnRl57JWZEAydQKA2RWVe+OaCPZarXxgClAoXFzEJ0jJTGUY9BGgPxfCmk\nwa91zfHUedCoBRzrDYhZc6TbTVIWEt8h7lLCdIxTo+Be+XkK02JF4KQRCtWKiJHu/UwROP1jMyNI\n8ubhzE+Yl0viE4nKNJGNFvYX0Q/Sc8CL7aETQ6BjV8u+HjrufE9CYOCVmyErSlngUqcUvxy4jV/p\n3SQUhkqaNGd4s3wZeUHFtO0D+SznoWUoP/ydEtz90W57YRXT5AUfZRVoYC7xfncnEEKNNzUemkrK\nFJgfBtDu2CslsM2S157i2hX9NNDeBCCZQvntU+5SQzf5qTeBmTugE0PuNrvt2BkAaoiOXaG8qzEG\nvCaGluacUiQuRlK9XsY7R3oDUsbblZbs7YfjAPR5kAAkA5/5s4KewQTgpIs8KTRmdOSyUAQAlF5I\nq/fEnz1hFcVoKcQWyuDp5C+8pijcNvIl+X1JzwEML3Yilx6xpjXD5M2xQX/H4mRFKgsA8NmdOYxM\njeDlx5mHoUqcmt6dADiaXtpMbZu7zxJebvIRnxjvLR3C0QpUsgckXe3VQwm6VWC4by+cKBd2lgG1\nmlJcS2k7cfx9ykCVbxncxGwWkT4HPZTUNoS3L0tBjqfGWooizOShe1aYG4v4Kx37NKr4jb4ZlyE6\nSbmR3lX3PlEAAtDGnswOA71IXOTh7lTuK2Aj9PeM8QbEWuS2QzOlL6kejeUwbowx9QAnQ+RJXkCo\n7l0rDJpY70nQSJBTXUGA3WrxPRpIJ7eRL+nreM0L3wWQid/vL1ro4ivKilIW2lozbF2/Gjem7wOA\nQvtcJU7NLVl94vg2d+ck1RYg//tyA+eCCyg27YtP+P4+Rotri6PLizGVzCkQSjDctzJqOIdCcVzF\npSuuDSgDVSzL0DewHUC+OWhsbpyqu9Yi4t+2ftoK2wg3rIaM1zfGEN2z4hnSlMVQ8ZsQk6NTuZFj\nweMDpVdLnkdtGyAqWCakCgrFVBrTmG8ZI7HeAN/BnMI4mNS3BpUhl4RCQdFUyXxeOzxOXmWG879w\n3hUtu8nnPYnGkEiprkYlYRnUG7k/6ut47s5NAFvL3wF0bNm6y9tIpKwoZWH9mlY8u7dTcGbrtM+x\nWrFChxqJpve1XQUxXlVcGy8A5TDg/5/EZ15soACQW4BZMRavq780EEoQIQ5ZSeB4kppKcWyATRM2\nwKBlVXEz9c4Pz3dw/cbby996vXRpF+740Dvb5ogRBtFc98FQivy7/n5S8RtdrF462bUsPUNHkOux\n4JJtsYz94vIvlOJhUeufK2famMrf5PPyDLokdGhWlWYoQ0ZfYwHSMQqULZwWsQ6FsispCi5vVxWP\nC7/PaxTIoN6KGTs927YgG2L2kbgmFngUkBWlLADA9o42vPx4N4Yn55Jon30ZAzqiP3VB6ddXsU6t\n3PEW68+2KF1gMKEQRVQfzOUNFIANmOVy59kOAf4sZaP3hBJI936QQ8fUwkuUssJL0iHgeledeMhq\nOXMr1qMMpCpYtmf4gHYy1Sv/RoaXRcbLzEypvwX6aWOIM+ajzXUfUJIMRVFClPtCEOqzF8sUStuh\nsmZdmb3hSmuT2Rbl+HNCBUs9iBYTVGs2kVZIxHg7CONCkp972xosnfhoAAAgAElEQVQfBxpThqz7\nVIM4D71vuscp2hjhylWFaqYpYewqRoHzufo97TtBhkcg4+goRVNiEStKWZhZWMLoFAs7bO9oYxvv\nx/4Dlv8tNV3StrnHLoBU69R1AOp/YwCvomCQDgaTSwVzMFiEUsH/Drm8LuAGZnGLV7YCl+yHgNLf\niKqcQjO3VJAUY6UAiRaQ//T/BCbHmEeixoiHrIBCi3vb2Y+IzdT3DF9GhKgtQog6F22APe5Slfsm\nFSjS++likzMO+i27gaF+yFabb6MTayowbjZRLEVArRwqZYEAUC1DWUHU4t2c36MKeh8oOCk4i18W\nrrrqWzc+7EujoYyUQ1OW/NzboG+9zvoxeD4KUxIjTqOEF+QKEBlFpxcneIirkCmFwmKNKIRVFDH5\nnuHB28glRWHXA21f0j1XkZn7dfzowxE8vmMDhsfvYO34x3hy7OfY9osfOQ9YcZgKF6qaMRCaVFHp\nmB6wWczEc2EelL/19zHUPBc5G0HGA1AKeut6eUhLvASu5+Q//3sVL7DtIWQBl65yAMmHXoEEzgCz\nv5EVF/P+Pqa8WLwQIlzBqY1vXy8bKMYJGzq9lrQOrqwiUda6zdXJFSFeb7381dKOHJ8vxGMxMUyJ\nHMbJBFZBKVfuOJSt7lktiyUlpCa8OYdfZCh13jdCjCwQUcBLswx9YRrAHn+29cH4nVfMJGEPr3Pd\nOPaGZgGeq3oA6JWT5r8DykLMQa5zJeT9fSXxV5aBPHpcrPFYr2gjYnidCmPEx1yp9CPLgEeeE97I\n/xTCT22tmUidbMkIfqV305d0z1VlKac4PTQFgAAbHsbg+n14+cqfYzs/YCXEvajJoFv6kRZSrHst\nFmzmEpcnQk5TpICSfoTew6VSoaB0AYx8LPdOuLmd2ArF1dmKkKIAWEISBQgPBRI4B1QFxJEuZSO7\nqnXvB3Vx9XfvL3gK3jbaKt4WmfyeWQa0rE6icI0R45vtOwIaIOCy4jJkyTK1Ha7U8uvluWHb3HX+\nif2/qtYGkUMSke5aRcFZWnDWOTHus3rzAIBR86Kjq8wCWVoEHR9wfqOQ69fnonYaDwlAXdv69O0N\nzXTLVxGy70jBXVHI0iLyt14Pkw0FvGIGVwIAKim2FEDmUAyaFZpV3lP/LoWHyKUMAPq3yYFz7zDj\nxqO8LKcHiY5cZoYggBt7juJn12vIKZAR4Nm9m5OrK/tkxSkL5ZHIYB85Mlzf8CC6exjxRWmJUWDw\nvKjJUMXFFB1O4LHWBES28hyL9URHuOepOCxuXS8306LaIr16psQLcJQuIeZh5LDSVBAV28RjDgK5\n3yJWPj6gIIExMwXZKpbd51x8m5TvECipjZfUHyQgpOKhuHrGsHwaFds3k/OoneENubZIVmMFua59\nIL4Z6dwJyCmMnTvFZiLjMazjNj6gPnB8IBmbYIieWy6tqWhFW/PmifLwsqU6dpVhWh49Hix4FbtB\nuw6o1DHQvzUAxv3hUm4qgmSbJdljX2Vz8cIJ4MY14PpHoNc/crNJRhzkioLFuRIOHmXeIS1d0Npe\nE0Kzep+sa1AByZrKgIEFCYSjff0oQeF10FotWLfD2rYEKr80uRZLnU8DIMgpMHBrFoe6N0a3F5IV\npSy0r67hyZ0dhWcBACgyAvQcOVZaDLKFDVSy9LnExLEMFG4kItv2LCVOLAMOKQWuf8QOl0ePszeU\ncvPl1E7VykfQSpMXcIqiYPRfQwKjvQOQc5JtREoVLTDSXeSyn3qTKQLFwUuOv6oqG8OXQPNcuCmx\nobOpFp48lr7UQyX7RqstQocvgV49wxrMc8W1S3m9koNHAe5F8oybAdS7PVKAShGFTbCK7rUCor6V\ny5snwiI9LBNJIWfKc5YeK89PmfkSKMNxgdoS1j7I6yCyEqe4vlvCMMlx8kePg3T1Km7v0BjHgJlT\nxfDQde4EXb0WSvaKBlqOBf0CdiuedDvSBS3jnjrvDGzSib+AUjVXXlO8wuPI5VKJEyE8CqNE+sGj\nzJjh5e19OAvPHpVrWTV5f18SgVZprAFj7Tvx0aYnlN+v3prFhZHJ6PZCsrKUhVUt+PWHtqCjrRUX\nR++ifVULntr1gHDVkB6pimBk2k2Ki0l2GQkrL9GtGyN05LIa7+fCN9OeA0aKjnJwSdaovpHJ4lvA\nMZuXizaWFF4emmWIq86ZboGR7v0g2x8qD1rL2H+eFp7zAA8w5gGqwqa6dtW4sLjf8V7ZwaPIz78D\ngaQmYOEfDVSaEputsqbEMyQPSfbYV+3YHk/9FCO+DKjepIDS4vLYpVTiNPYAPU4OWIGtrjGOBTMn\nW6g2sO3SonqhBFrWxyEG9GvFjljSBZ3Xps47GZs0dhX53/4xsm99zzpe8t+QZcCOrzADC2Dzds06\n852PvxoMR3sVTigqdHJ+o9z29XW9qJPMaOWTm02BKwBYYcoCAFwYmcQnN2fwyPYNhotGnqSxaTex\nICVy7BXFYhc8BJEHkuvwtQKBdMAhl2Kxh7R0mxVkez9dM48Zl6ixk6w/n7dFPlCwZbdTqXFJaOyT\nregGxIk7CXhPbC5uZfOFqjxwL5nzvUgG0GLuFEj/Ri3VKqh8m6fFhe1xKqx6fFkd8XilxdlmBQIv\n7TsLZklPpUNjbesgwanxhoosOcG2HIe09UFRJVb0TbsnBvRrO+yrKAYxhojhtQCEZ4T9twcQnoOF\nZTXPZtV3dnKkiDBMWemVjlyO378kD+mayTnWT0oLfYEpDXu3tEe1FSMrSlmYW6zjncsTABjdMwCr\nwhD7sZJASmIBFlJMXO/GzZ8T4kdYWmRa9JNfA87+VE0dzGrAnieA9g5l47e9p9cKKjYmwkMVnjS/\n6Bim3jZXEuRxynPGvudyvXILaPA8W2y1lujYX4wykDIfGhHnphmhTOp99CoPxd+s33/4UulVAHGC\nSkNi9QDo1NwhMq6EuLXrGxnWJVBkUtQM4FqspHibYpQbAHYWWK+1XxxgWcYwNbyoViKXgvOdNLCt\nFbBs4bRQ3j0hLJK05yZkRZSHMQ+pSp4Rm2Iug7d5erDm2Wwm4Ro/7IVxdP7dIFjS2vb2hzA/Mwo2\nBzIAFB1rWvDUro3/9DELhJBNAP4aQC+AAQDfppTe0a45DOBPAWwAUAfwrymlf1389ucAngPAwQff\noZSeDT13flG1ti+O3m1oMMvNiBqFkawLUIoxyRM3tFicLuphCWme11m1NAoozi1CkD3zUpQl57WC\nio2J5jlCXBNRB5ytbVlJKHsGeuGENc6sAiwLSYz9fV7KQFWp4t2QFVbZsg/dr3+3EH+AS7xKdORm\nr/dFT+GMPYSMzJddh0RJ6yqS8j1ilRtbe0Frf9chlqVT1NioAjD2vZMvpTSEs1qONEfRdoJnR7a8\nMXMb5NBxca1tzA3COMv7NdvTKPYxjo1yGVc+wraeA9hx7iRaaB11UNSyDC8e2NrUTAjgi/Ms/CGA\ntyml3yeE/GHx7z/QrpkF8DuU0iuEkG4Apwkh/0gp5YiN/55S+ncpD820nOiFOhUkTQpYp0LRFV2c\nC1DDLISEjlx2kpaQngOMnIdbgwVjYUnUg2oc40uMmCl74bVyAd2dKEGRWnXKVPe9TtIj2i5bKKyW\nMj1NvI8ENhKbMeeEKO/+JydVMzti24rhhYg9CJNT0mQcQWCzd4Uv9BTOaMurq1cFbm7ZHWQOjRkn\nV599ISKvy9xyAHjTd/cdYWFNcQNpDGCs9cEbBgjgrBQytWIvaZay4DPQnDJ4jn3viR8K4LArJEK6\npYwIy/s1alxYCZ0CxlVI+SLd+9H9G6/i64MDGFnfi56dPU1XFIAvTln4OoBjxX//AMAJaMoCpfSy\n9N8jhJBxAFsAVIZ3rl1VQ4aSN/vO7CJ+9OEIfmtHHVt//CfWoisAnIuduQ8LF6DlUJYnlpgkB48i\nc4QabG52GXQTTN0rQDd0fMBJSuQS1WVLQaWqZzzkobizHZusD8tgvJMELhJtF7nNpKu3PCDkdE5K\nQUc/FbE9keJ44UTxvjVvVbpmiIGw10GsFSyPFItpudqKBaVWSUmLQc67lJz85Bsqw2jK2MjZGIQA\nNwdVpdhHHx0hMRt5le+ozG0pfVdkT+hhTZoXqd9wzs1miVcZNMDV6l7SaNaG3K7xF9seWmEt2Lxa\nqSy81h57wMpe40r2IMv8P9o829G9Hzsq9y4sX5SysJVSOgoAlNJRQkiX72JCyBEAqwB8Kv35XxNC\n/kcAbwP4Q0rp/dBDW2sZvvHEDvxy4LbALNRziuGxm9iquLML97qD9hiAlWTENamcNKdy3DLEHGlJ\n3aP9faX1DQC9hwUtq4uUyDnGwmX7DmzKjzyhXd6XKGBjAkhNgNruToDyfgHAp6eRD54T7ftImHi/\nGrWWre/IEfacRTCCstn57EjK25i+psTVre9lmaOhzddGjmVVen2KpsW7Rbr3GwyjBnmUR0iPWulP\nicdHUrd7xy0QcpHXi2/duDwTevquyJ7QMxUAFq6bGLLOzSrMmT4cjxdUqlGM870EaCxrw2hf2qOc\nB3EKxiTg1bL12VdDw9p3x1zxKpV6xV0LV8no1JyodwQgufZRjCybskAIeQvANstP/zKxne0Afgjg\nVUrFyfg/ABgDUyD+DMwr8T877v89AL8HALt27cL2jjb8Su8mjExJlSe3bSmsHTW9y4tUVhZFwYjo\nmFTGJNGUEHLwqKI5Gm52l3tKf9n2jvK9K1g02cGjVrCV3CZgViDkG2CMFp8CUjO8Gh4iFNf7NpqZ\nYbQna/n1gjDISrWspT/294EAhmco1XtU1bIPSWiO+jbfUJ/0tl0ocpd3S+VqsHNuuMTq5ZDLbleo\nDSHey6PkyeBjdaUS0FpBptXeoXjQrJ4JbbzFnmQrX9X+ACNRElTfgM8adb1TjNLoWm9lf81UWacy\nmCCuMIRr74ldC16vltYufx6dnwHef5P9e/A86pM3QNa0N1WJBxDkKhmdmhOVlPlVxcjjyZ0dthYr\nybIpC5TSF1y/EUJuEEK2F16F7QDGHddtAPBjAN+jlP5Canu0+M/7hJB/C+C/8/Tjz8AUCjz99NMU\nsFeepBarGbAjlQHLh2/vMFLUXDEpQwlR2ApLyyk00UsmwjpQCxe0CUnMwlIXperGJcde8bqYUwF3\nRr/klMpYi1nbRHhGR2VXpc5IKGM3LJTNMssaBQwWvJD3KPQ+rr6mKovBOerYfAGo6XyWgyl2k3R6\nt3TvgHQgRwENJaWz/tbritKmA/mqeJhsSp4S11fvZH8vgImUFPPHBRbWPXrjAwXlN6BX7ySdO5EX\n8XkIXokiTDp4QVijvH9Ol7e2XgyejoDnTvdAiloLa9YVhEeFMnj+XeRdvWGLXAv72SQUOggqSS5l\nw9Yu/+76tz39Y1CQpirx4t08XCXDk3NYyllf5B5RAKeHprB110NfiXpQQL6oMMR/APAqgO8X//+G\nfgEhZBWAHwH4C0rp32q/cUWDAPgtABdSO8ArTwKFC2exEz1fedFw2zhzZC2bpqsWuRx/JADQ1Wsq\nGnJcNRJQQ7qL1JsmxiVDC0tZPJobF/P3FCIdmxvalUoXCwJLDq/oQLEio0OxmhJCALqVSw4dUyph\n6ocPs0ykLByNBS/V2qhsnQTEqgR45rPi+lWsZ/VgirHuFEXS4t2y9u2t16OZGPkzXEqbb556PUwe\nJc+0sF0dY+yhvsJ0ukePYxdsIGljnE78BaPCthRvivFk2Hg6XJ4xeU0BYNTjcr9rLcyjwjM4aA76\nzp8rbKXG8Ohhvy27i4MaylrSlZTUcKDP46mQxcnf3eisW+kTz6ng8bUpYPI6Wlhy1IopZNWatvi4\nnUe+KGXh+wD+hhDyGoDPAHwLAAghTwP4fUrp7wL4NoBnAWwmhHynuI+nSP5fhJAtYLv2WQC/H/PQ\nxXqOU4O3lVgOd+Es5Yz6+di+TiWd0vZxXSA+Y6Hq+IX+PrbwNPc9wBWNRfBKfz6xxYdTpQrQyMhi\n0Ny4yiKVKIutLu4AXsMlyRazvNDkjI66v+qdsz3dytWu1/vHNqFaucFppbtTrY2q1klIbPMh2svE\nldyOLmByHI2GiXwkPaWCImXAROANWF/dSpvyPpZ5arRtqecSZWGPDxRgXKm4VwQToK6ckA2dAMw9\nRld+cPOzshGjeFMFki89FBoIX4FXAy1+J+0doFlNAiz7s7XU9nNgTIatqfgV/u620IGu4Njml88w\nVO6XuTtIBmzdA/QcYBw3DSrxXvyKY4xu3luw/r3Z8oUoC5TSWwAM3xOl9H0Av1v8978D8O8c9z9f\n5bmTc4v4xbXbqGUELz/eDQD45cBt4cLJKfDu5Qlsbl/tBIbEpLjZrgnFbcmxV5hLP89BT/zQqW3H\nWj8+ZaBKHrQti0G3pKNceVnGCtTkdfa3R56LDwFUFPm7MJIWam6cESEA0ZbFe+K7PvvW95yYBX4N\nABEP5f/tA5g1c4x8KO1oL1OWAZt3AtO3jDCRdy5a5oyvDkupoIheOA9rs6+m0qbco89Th+fCxjMA\n2JVe69osKI5TUqh97nAvmNhWvMlz+APm/PIpjaHwFQFUi/3gUeZZ5cXQHFTuRvsG9gOGF1aIhzCq\n0RRl0m0yQ5K9TyM78nXQvU9bxyk2Ld9GxIX5ewwbUYSabCGbttZM+feDnWvRmhF8PN48qmdghTE4\nUsqmWz2nOP3ZHQzcnkWuzT8K4NLYXWybGbJ/+IiYsfUaBzBMaPDz96LcWFHPTwGcRYKffAAipe2A\nK4+Oflq6IetLrCBLk9zqyd6Srt7kZ9toiIUi4tpQu/d7SaIUJk7COSaqp/OlShJmQxLxXTmWxFKd\nM5ha2EgYRiohDPg9VDalzXaPmKd3J8oS2NqYKB4VmjNgq61Cp88j+cJrEV/GMtYBxdw5VpIXrApm\nyHWdzROhhJEOHmUKiuYJzQGnwm3z0IgUUoWt0lQ0goRRFee68s4OhcvlhVZDdWVavv/cKPBgUgVg\nOnieFQ2WFIYLI5OKUvCVrnb85we3AwAe2zGHS2N3MXN38mbSCzpkRSkLhFWlRkaAa7dmbXhiJrNT\nyP/RoX1GbG62a6yLStciY0BgEc8PLQhDW9dizFWfG+PKq7/1unFfM9zq0WmbHGOR50q1zdhn28YW\nsB9UsWlVdFjKsOAaLbBsnhZdGsFBkG6NgU7z0LjmYlXAq2uOhVzP/F5ZabPdw70aPIPFNiYGHmHw\nAvNaeHAvzWA1tLvD3eRErrFqtmcqxhNhWNqeCqu2cZLTow0QuhSKURU5kzDKN9eTALOR3kWlP+wv\nccqdwINp7V05CUh7iV4oam6xvIfj8m6PDX+GJsiKUhY2trXike3rcfPeAm5Ml7QMReSRrXNC8JVb\nHzoLs8Ro5jGLVN+oYg+uqOfHLAhegImX9w0cTDHPjVls2cGjyOWY7cBZ4JmXohgGfVLF0pLLHUdv\nnrZYteXZdGIItFCMbBaB0a8sU6wIHfG8nOL6ttGbp2e+uTxqVRgm5f4GrWjHuDnDDg5Qskvxzb5p\nlsfGo8eNCp3iuZEWbTqWyA2ebB4BUpqElBHfWCjsj5a9V1c6QoW69Hngm+vR4FaPsmOMhW6YEXfY\nTO6bwH/p7LT7jij/3rJuleAM4v8+NXgbba0Z5hZzwbvQDFlRygIAfHTjnsAoABCgxs3tqzE8OYcd\nSxPY+ub/A7EILVp7dGwrcYO1LQZ5MoXYEeVnhxYEB1nqqX5V3yl2sZHu/cChY07yp6qS6vmogpj2\nuTj1Z+c//3v1Xs0i0PtFnv+OwKygVr3QUVWJ2oh9h5uDaMk2FxVFuUl0wLHKbAyYUrwXL9Puet6v\nfQP5cAGczDIRDuHeJqs3z+cRTM3GsJATVWmrGRIblwcsoaS7EwyMCajsjx46ZzpiVuDkniGDV8ND\nGCbaSwhPpFyr7zmKRySAE+J4MBdmYXRqDmeGppTnnRmeUpJvWjKC1Wvbm1J6ckUpCwv1HHVJUdj1\nACNo4mDG7R1tyE/2McY0AAIU1IBr3BfHDqWTuUpc01q4smJ4QSwyN1oFbnzbe9oWrte7oLl4rVSt\nCZaRbzzljT87eNRJthJUFmSXYs5i1dyq0J9N9h0BHTxf9k+zCIwxeeyr3uI9yrs02Vq0jr3HwpPv\ns4FeddHnovCkWKjFGxHRd8thLf7uCDsY71WkWQJSOXln/5jLOz/1JvOUWUCRUcpMgvcBgXTfZsTm\nYyUlLg9InpkCh0DPv8vm28GjKtGdY+81nqdV21QO3FgjxqHApHpubX21fXNdYbYVvwsZnKeH7pgs\nHtof6jnFmrXr1jsbSZAVpSysqmWoZUQwN8qKAhcbKKiKxDLtRWuvF06IzQv1paA1Zk0PssVaA1iF\n6Pd0LFxnv7TUUVuutpJfLQHZfApY9MZfIU5fuhQXYMN6yM/OHvuqAuIKEc+4+m+8SxOtRaFEaah/\nIM7CawQY6aMWN/oYqRw1A0wpFF++1gBY0yzFdUXoKK9LFSBhxwpV8Db63tHHt9AIDoU/J3rcE+Ly\non/dGpV13cyccJHMqc/zV9uMnaMuBaYRciVv5oWmMCNRYR6dmsO1idngdbWMYH723nRUowFZUcpC\nay1TmBsBGLwLY+07Mfz8d9E9PYDu3b3VD1F9kvpyti1ixNfbH1Db9z3bkwpnxFrr8VSw3veMWbgO\nS9RFqVr+LQfOvcPYKoEkvvuyf4UUG7+rHoXeX8N9eewV0Lf/DcrMFXdho+yxrzpDD7Ei9yGXKa8b\ntBZ9fAUAghaej+o4RkLU4kofI5WjILA31pun113QuDHcVM7iSdXxJgePOlNsDQ9ewbfgO/xS5rcc\nSkgJ0fni8j6xGWakmBe+yrH6fb69K0VpsikwPuUieu9x1YKQUzATw7HDk3PeMyAD0Nu5FqBA+4YH\nNkc1GpAVpSwAEErBpbFpXBq7y8DEBW4BAE5cmUBOM7RkD+Hl9m5sq+j21d1aKWxzgCMlaeAsYqid\nQ5M0+7VvIL/+seJhCGVDRL1nYOG6+uVa0Gp+NS2tuITDUmkbUDZ+r2fHdVDN31PPBxJZJreCGOx1\nXEEBVF78KgRbuhKlHXA+Cy9EdRwjzXTLizYjcSvB+ckPvK0PAl29huVOhy9pioJUsl3ygqWMhxF2\ndI15woGsu+N1xcAIcypVXktm1uC4d9vj8jF7nJ5VQEcuC/I6evE9wQ2RovS5+hbVJwsIumrFySDY\nMoLzwiU9G9vQkhEsFfUgimxrZITgwLZ16Fq/Gu9duYU6pWjfsHFLUscdsuKUBZmxkQsnYwLK5b+U\nUwwPDaHrHbZAaZaBPP+dKHcyoE5SX852qA3Fte2hdo5FeQs5eJTlhnMq2IRiM673rIqad7Wh5PAX\noEKWosc2y6jQQfd+Vrb7wgmWl73ZXsTV2Ex9ik1LK9u0iznRiHUff1hKioKEpQlyargY4fQYrXbA\neS1wuV+RZFau/jR6+CvXa4eWC7sQ+7ysIFvS2xEuZDl75dAx5kafmYJPXN8jpBilePBsz7SSxMll\nv+UiaLLyExuii7C0rWOhZRWo45CDnnvbGg4QSlDEN+Z9oyOXgwe/MYcqgKBlLg8voVWiIsOFV5h8\ndu9mkfFwa+Y+Prk5g71b2nGoeyNODd5G3UczXkFWnLIwPDmngBy56H/JCNA9PSC5/OpBHnNdlEla\nUYME1A3GVlNBn9Tk2CtMa4XJEGfEPAWrHbWWPk15zyhxuFltbYjxK/Kr5SpvyOugE0PB5+bn3lbI\nTej1j43NJ5iClWWgEuDJC6RsUnwdsBzoQMmOKCPvHYdMiK0utJE1w7Wb+s56H6oQCNGJoZIN1QO0\nCz0P8CDW5eyVllZWPbIAIAN2UKSLoS9GwU/x4OlimyNG2e8tuwE5M6oJwOcq/TJCGoBdeUoNUSVc\nz79xKm20jI+S64/omWspCrMucoVJmYn4Z5/cQj2nGJmax+b21ejZ2IYaIU1VGFacstCzsU2AHLnr\nhoLFeGQKjCd6OtDd1ov8l5IFUTHNL3XTU5gd4Qb6iUNfdhsulZUgkWUsvx+aJi5bhQ8+CVw9DQGj\nXXLH4BuRkJs1Sob71TaLdESntTZy2WBB012rRhy4SOXLXnhN9Wycfxe5pGTYPDvNjK8D9sPLDVq1\ncGpExPDFdfBbZ8qYagDVRg6tKFd1ojtf+eZLC0mpmfLzfIcF6dwJHDomFHIXNsbpPVhSK7b60jh5\nv6ruIbY5wr65VBBtTTtIKkFZg5k5zrm7+zHgzggwecPp3UidS5Xmnm9tubw1ofojqSnJ2thyY5eC\neb8vjd3F+jWt4m/1nGJ4cg7P7N6E3z7cjdOf3cHi/fmm8D6vOGUBAB7eug4AwYFtLKNkeHIO0/NL\nuDB6V1yzqqVmtyAqxoljNz3roaoD/fr71L9TyW2oxBvL68Uhpy+A9g413caT29yIVFms+ngwMqRS\nyL4j3sVHh2VufH6TSopiq5oop/KJNkLpbMsQXwfMeZNyiPi8I/rYplpnPHThA6JVfedGxPbNq6Zm\nuuLXWLOu9CLUWLEkHzbG2p4FF+CriQFU30NciogcTsOadUmKWTMyc6yeHClzCVnNiYdJDlFVmHte\nL6LTK+IuGue8L8Hw0OtAXBq7h+f2bVay/GQipsHbc2hdveZLnoVUWaznwoWTEaZVH9i2Ac/s3oTR\nqTl8dGPaGHBb/nvMQomh+rXmt+uTCWAbkgL00/6eZcCTXwNZ06666lmLaszdZq1KFS9tMfhm5PZX\ndl3L4wECbNoBrFoNcug4S090ZFLk/X1F3Yka0/YJgK/8M5DOHvEe4l49CCV5kER82kOrK94v4jpx\nfXdaQapgW5b7xbfu72OYjSKjJPvW99hrJnBjAPrczIFzbyvu9tA8qRJWSJUSUyJleTTBI6hUWAUg\nShTXl0pP1Le+5y0Q5WyvyYqT7UDSFREx/yKK18U+o5J3webJ4ZLX2Vg2YS7FXh9D4ARoGSCECGUr\nWDQuYh90je3o1Bx+9sktZbfKKcXcYq5k+ckg/i/DEBWFk4/q/jAAACAASURBVDJRAHVKcWF0GpfG\npvHbh3dge0cbnt27WYBEZP4FfcKEFkp+7m2EqH6d6Y3aJCRdvQI1K4B+BUKd8upteQ6c/SnIN78L\nDF8CFe5FQEe5294nhRwqSINa0Y0aBuIVmRu3R5iHp3On9rtk/cnWCclKqPAnp0AO/3O7C1/HBBiL\nOHbRxV0XQxnbFCWtez9TnLhbvr7EyIMGzykkOq56BsrGKeammm6Z9/exMF4kg2eK9aor6aHx4PNM\nFB5yfs+48eX9VZRSvZ2Ed5OviSHhqiLRinlk8bqGnlG131w8XqHUEFXo+mRcg0PZ8hWNi1FaXGNr\nw9tlBJieZ+P1zO5Nym+zC0topqwoZSEjRJwbXOqUVZkETJAIAENbA8ILhV45af5bVxYcCodtEpJv\nfhfZC68h7+pV04yGL5mLnVtWkqs4lMblW0RBlLYOsvRkjrieEwPEU7ghJMYzffEZcUPukYio88Hf\n1/T0lMQ73jCEh343OK4aD0ezCJjoyGVg+CP1jzN3So8KUZH1oVz77JvfRX7ih8DYp6I5YnufBnEv\nvtS+mI1cLjzUqBIMmJ4jAIKa25fG7BNFcWgiM6fiUfJd18CBb3hJEnAvvjbJ8VdB3/o3ECqYZ81V\nEd84J8/hCGXLSo4XUFpcCoWMt8sIsHvTWgzensPF0bv46Ma0ADsOT86hrTXD4O055zOqyIpSFu7d\nXzJKUjMhCnCknlOcHrqDgVushHVLRvBbO+rYdqv8eF4wkkb1iy27zSf6FqplEgIwLVFLG8129caC\nfFgMVjpUEzJHYoB4JQ9/cchJFofh+ZHjhlmtjA9b8qb1e43+aqhxeu1DUNs3bySGauHhaMbhq7NX\n8vEgh46BTgyJvsqKghU0q4exjr1StMs4P0RmBvcAFW7ZRsR4fzm1b2kBed9fgex5PMorENV+9Pgy\namc89RsMFNiENdYo6M3ZbpGBlTfIROgSET4IVXvVANve52lVIgE0PJfkflRh+IxKP3Z45qoq/La5\nq3u/5xZzUT25nlNcGpsWoXRC4DjrqsuKUhZs4RsC4MC29bg1c1/JjrgqUWku5TmGT57A1rGfGSlU\nNiGdO0FJVrosP/gH0L1PG67UKGCajF62xCFtbaS653zis1IMPIHstqHxceKYg5Z0xzGekW4zbij6\nWiFv2ti8rn+E/G//2EiLS9145eutPBwBJS3mOeL7yHLomLMOhfE9pVx7XcmycX40EgM3xkd//31H\nQIf6S5//9Y9Ar3/EvA4W4p7k9gPKneJhojlw5icg3/6jpngGlHF38J0sR7YN0PheEeN5VLK5AC85\nnYE5oWh4LsX21baGG0k/1r9rowXTOGaBe7+f3asCG2cXlgR/kHzWUdoc4MKKUhZccmvmPn72yS2n\nJpYB2HH3arQVUoYHCvHEdZ3VIy18BIYC0UTXZUhsVoqBFzj8InDmJ2ycaq3BDZhLzEFLRy6XoE5P\nHJq3ZyvKUqV4FHM/19T0S0tKFH9G0oHV7ebhcI1JUlxVjwHXSjZGRUHgfdEP0CI90qVkGc+VPWKO\n4jgponOF1C+cUMIfAFifHMQ9XFyu4GRmP5mISVKG5ayaVPI20bYMYrYwqsaGAw18yTIAKOVnKgWt\nLAWY1H6XGUeu9ce/i0pJn+ZZq+oJ4M9X1loABOw1GkXoKq5gWmg/173fc4u58DRsWbcKHwz5CcEa\nlRWvLFAApz+bVBgdZckI8NwWim3nxhhYLsLKY5NScoUDwMX3GI9D4LBy8RHomxsQByhrhvjwFYYm\nvvfphhQYOjFUWtYTQ8z9vGU3cPanwmVfhV4YiLcmjY33+e+Avv1vS0+Rx81eRYFzHVy2jSjFfS48\nABaEfklWpRIXCXDgzBTotQ9Zau3dCeWZeX8fiO0d16yTlGSaXBxHvKMcDilSEwGw8ImuLHCJXE+6\nZZjkFuZp1JoyTIcvNUzeZh6QqochKhyoKSvLmXlipNE++CQwcFYpwATAVCYAZ0iQt0uHLzFPkkwS\nFans6N8bh19UyjvHjkkVem1dSPf+pIJptmJ6cl85ZoGfVbdn7uPTiVnUc4qhO+5aEYRoOecVZcUr\nCwAwNe9GjR7b14nN7atxxlJcypnRwF3hMhAsz42qatYYl0eTlTc3n5XcbI+Db6PSN9wqbk2T74Co\nVpyM/0ikF1beI9KDYXh/Crd9fupN4OoZhl2wuEabHaO0XpeKjbApHDpxkV4M6+J7QtGlAMN9yBv+\nxfdANVcyHbnMuAfkLcvhgQmJSyGSK3liy25gYS6c8aC15VR0IsQVvvF5HWKFdGu4HEvNFm/Ov0NZ\nacb6D6Z45wCW7qt8JP19Zd0DqTqmuNfirQKgKIkNE38tLYg0cjp4HvVrHyJ75iWnN1d+zzKE56fX\nDu21MQXTjH5r48fHZ3v3fjy+YwNOD02BAvh4vClcS9GyopUFOcHQJQO3Zos4UYZaUVxqe/Gbz8oj\n3QUQTJ78RVU164JP1GR9YJxmexxSXbapoi5MgG96aicIXCl+3rYj86aNvtiyVLY/BHr1DFwuyUZA\nibEKXuy3CKK+ZeIiqRiWFeeQ5yCPPQ9s6GRuZkudEyWmz6UiwZcR3pIsUL2Spy/jQbTFsxgIsSo6\nSX2TQkf1t14vQ4XPf6esRqoVF6uuvJvgUu87SgDjRirJKj0IpXjLmBLJE0AByeihSnVM0h1TaXZJ\nKApyqCwoisdP2+E/fR/54DknCNOg4pbez6UoOAnhIrBpPpZNKo3FxY7H8OknM9iHSdy8t6D0gbsM\nMkJAKWUFYAnB1vWrMHL3Pn9SeNwiZEUpC+vXtGDXA23Ysm4VVrXU0Naa4Wef3HKGIADgztyiQaXJ\n0yhDVp7PvawL7e+T8tfDhWLktuXUpUYOLMAT74u0Uiq54ZXYHiDAdbLC8NRvWtHn3kOxguLk9aKE\nvncimrpqP4MKj68GAd/oHcWwDJwDINzH4n0slpIRenMQfLn6qyt0AlQ7M8U8Fo4DXh8LOfWT4y3K\nH2lSNUXv+Go1APDEvyhDMFLdkiSeEl2Ji1SOlRCJ8MZVqyRrcFukhCAlrwudGAKVlf/iOyjfx7ZW\ndCUxNdOCh4lc4gpXae+J+XvB9FPb2ABQOD7E+tP6rF+js2zydi52PIYTu/4LIAeGLk/gK10qGeOT\nOzuwqqUmSAQvjU3j9sx9SVEAkMSz6pYVpSxMzy/hsztzGJmax8uPd2N7Rxs2t6/G8OQcFpbqGJ6c\nx43p+8o9U7OLyIqCHISodJsxVp5vY1dy2i++V/5Qq0VZBSIk4dGIU63wKhUMY+8PS6EkHDrGSKcK\nzIKLBTPY30TFKVT3IPS9rRtoxJimMimG+g8FY2DWINAVTczfE6A0HkLjBzUAIxbtUoBD7HWuPtvG\nh04MMdZJBVjqHxtbOEtUKkWR5hSophij7BpelHod+OSUeg2vW2JzL7vmj6yoZVlSlocIlTUIDPQW\nVEsIQbKDs7DsCRFzzBVm4PfIf4sBdSr4hN2PmXVgHnqa8YqMD1i/e1B58aSflmPD0oXp/Azo3/2J\nSlqm1QARfCGWQlk6y2b2ze+i/8pccRk78CfnlvDg5rW4M7eIB9pa0dHWirnFUjlqNmujLCtKWeCy\nJHkI+P8A4NTgbYxP31c0SQqgd1MbrhWcC+9dmcDm9tWld0FyS6bUPbfntAMAYZz7VWJ0skZcwe2p\nxvtUgFWMIuBb3D42vnLzZZYfd1mS7v0GmVXs84C0+L6+kVVlIDQs3cCYGIdbReS6ATjjGAMPXwLg\nqarIfz/5Bgu9eKiD5XdPzX5wWWdmAbDw2FjDWTRXFQRPHDxW2TW8KLUasPcZhWad7DsiXWvh07Ao\nA42EmBoFBirjF5GeHRLhvZL6Yd2rjnzdu/a8oE5NycbMHa0TGbJnXjL2G2P9OTASoewp0q0S6OHM\nT+y1aOT1x/lC5FPGEa4ba9+JCVxX/nZz+j5uFP99Z3YRV2+xFP+WjODhreuWTVEAVqiyQMA8BO98\nPA4U9SG2d7QZaFOAZUMA5aetU+Ctj2/gha9sFQpDFYtaWThaTnsKI5ztQIwNGTjbsqRwxVjpsTgK\nnY0Ph18ELC5Lfm+UJZYQBrJJo+Ebl3hR7PLhRsKhJ58YgLNHj4Ns6FRrEGipbTHKncviapbYxsfq\njn/oKbHxB9tScD+t0UA5Q1l2pH66vCj5xq0l+FLy1tj5NHJryqcrrGJ4qqTMB9K50zj06PhAsvPZ\nNVer7CeutWfdHxJCHXxMrPiuQ8dAbw6WSpwnXGU8d2kRdHwAtRdeC46HuH/kMvveXBnQFQXehxtX\nyza4MqcUr7PL8OSckoH/wNpWTM4uWq9lNNAkCodXVVaksgAAJ65MCF6F/tFpfOMJVh/i5ce7cWns\nLvrHpovfiRHyuTO7hH9/dgS/fZiFMqocNMZErFg/Xonvpg2Bsy3dlck3RWGtOg4N5+LWx0dm46sv\nATcHobssAU3JsFBXNxoGUq5L8EKkis4X4HpmI4A0oy2Zn6Nzp4iRyuGEGOWukbkZ49J3zhmOqeDF\n0wbPge55PPit9fBKdeyMP/XT5kURoYC/+xNQi7dGxKotLmjbM2zprXTYzHzAoWPq+hofAPr7WB8u\nvhdF+a6PXzoY095eTBgvNtTB55NI5bVkKuRAmebsIFATbQe+t288rF7BllZg64PAdYleffMOZEf/\nK3VOFgXkxB7rSKmU6Z1rGcETPR1OjF0tI+havwoXR1O+UJqsSGWBAorGloPVh+AhCVmjyynF2taa\nobHVaRnK8KG3UzdJb78dm28Z382d1K6hNpR+/do3kHNXppQqJ6dA+d4rFItFy2pV8XC4TlUlIzfK\nbbueV0WavVEC5qHL+QIMpLSNHTMRKOrrP+neDzJ8iX3DCBezy11c9d2jivJYDhW9HogNe9HImFn7\nEcES6hOf4SDeK7bIlRyKWVosw3Za5gOdmVK9PwBoYN14x6AJcz+l/Zi15wyz6Ur2/D0oAEdP+m7M\n93aNh8srCEChQle4TXTvj7Tn2c4MbrzK9YlkjN0Hw1PIKfN+P7t3M+YW82XzKgArVFmoFbzZ8sDO\nLtZxavA22lozTM8vISuuqWUEB7ZtwOqWDKclhqwaKctY6xZNSsGb2A3PCQRzbCoAVJRwQt+U95FT\n5XIoKVCxYmySV8+URC7tHSCdO0GK32UnjuFWbhAAGNPPZrbrREvrIRkNRKVfEws09c0nVzhBsXr5\nZlUxqyP07skeM1lpdWAvuLhIplKFV3j1up4dY0BHLjOrVzrIbLVIQkWuAJihGEIYcBUwScIGzoIc\nf7Vk2xwfYH2oF2umiesmCgBakZjMd60eZiOPHmd8K/oakOcuwGqXeLyEVb+3zSvI+8m/haGA831s\naVHBlrn25dGpOaOQITdoTw3eLpn1KTC3mKOtNRPnVkaAfVvam8rFsOKUBQJWreuBta04U5BbEAAD\nE7NKPQgCYM/mtXhq1wO4OnFPURQe7FyLp3Y+YC1jXYVSmIs3b9ex+RqbSpapKUcya1pgw1XGSTpE\nfItJ7nswHCBbtzkFrn0AUMqUhGOvlK5TyQoSlrdkicV4bv5TEGc8Xv6OF06U6GlJoQiCIiOU0dhw\ngpWIypbVUVhMtFZzunZ97548fg4l3Ipolw9PnWRKG5PYUEaswm6MdcEyiq5ep3IeOhxLgOAiUNRd\n4SEkcuwVYOsehfCNf1dROCyrAQ89BQycDdKjx0oUyHkZeF4Ay3zyhIdcrKXWdhO+t75+XIy6VoC0\nXJCuwGX5zoyx9p340YcjIgTBs/e46CEKTgPAFYVj+zqLLIkvlYXKQgFcvTWLljsET+7sEK4cww0M\n4NqtWTywtlVRFABgbWtN+XCyNLJJel2YIr5GhUJQf+t1YGaKobHzOnhuO+bvSe3IyHASTB0z3iew\nmJI8FvLYuFDCNjIkyRKrVAxKH2cfmryJCoht7OjEEATBVJaxlC4uEio6CIqMUEbVaxdBr5y0k8s4\nUPCK5c4VRkB4QXyZD80K68iHqo09EQBTZpXceuKkEhb8CLUWdyw75Hq2ACDVMSzWnLIO0wwHp3dv\naaFQjIpnSORtVP5GeR2kvQPEUvCrqsTMvWUDCqfOpw2dyBJCeIZ3rVsHANvDYCLEcPINKTPDoqzO\n34PAZYGAXjlZsmxazgy9DgQPecveBjlEwa8HSk9Dz8Y2tGQE1FpCMV1WnLLAhX8AXxlPCuDjG2bJ\n1NnFOt75+AYAggPb1hsehqqbZJyiUQCbZEsqqwGPPl/Sqfb3OfnYq4DVXO7tUDljWztOSzGQ8iW0\n8LdeNyzxlDF2cbAvhzVkTRc98UM2VlkG9B5mIRn2hkrKrBN/kKCMltcush1k8Dzy4UtmxcyINnXM\nTgzSvtlhHechrv+he79VoaSawpNaBdAHiNN/E0RNhDAlvYJlr3j3Lr4HQVomFCMN3NffZ4xL1sRv\noMynglfA8PCtWYeqbKvB50e8S1XPhpNjQoRzAnucVsperx2jeIoiqLx7puYUz0HPRqYo6N6GZ3Zv\nwujUHKbnGR9QTsvrOebhu7cnRtJG2i4rSlloa60JvEJGCG5OLwTv2bCmBfcWVBrbgYlZ8OV6aWxa\nZEVwid0krVTEBVKW7DuiWk/DcolcHosspOAmAKCCgDQ+9qYC9+QcZ5gei5i4um4puixHZbxk8qoK\ndMIuHIE1xNOAt8G2+SigKEpZkSYtg8E2TrKkKKP82vzEXwBjV8V76l6BUJt05HJxIS+7ToCuXuX3\nZntlUiQ7eBT5xffAQWVk8w7WZ/17avelmluk2w2II9371aJB9XqZd59lwOEXxVxLHSOjbfZXoKVV\n8RTp45AdPNrUbyP2J46Rev9NUBCBEQGgKMPk2CvLonR7r63o2bDeJ+8tRCL4smEbZA8hyowuRQ4e\nZZ7EsavQlQ59vdvAjacGb4tMCM4VdGvmPt69PMEUQwCPbN+gGLDbO9owNXFjLDgAEbKilIU1rRkO\nbFsPbiddHJ0Wv9k5toFff6gTt2bu4+LoXbSvasHaVTVckO6rU4pfDtzGr/RucoYmbOKycDm7Fx3q\nZ46BgpSI9BwAJQRWj1IB4lFANLnJx94Msec4txpsbE4wpqYcASgP7NCzZYUJSCKv4uIE7+nYggZj\nr67Nx4i7WoBuPpCryKJIyk4gzn+F2jRTxACAgr77A9DOnQA+v+qnLhFxahnQa8HZ2A7T5Gd5AHFK\n0SDZ20YZYQ/1ZHKERGnbkkbsGocUuuSoPoky5KIFU+kulGHrgRkhOoVzEhV6hJfM9s5OfJH4hhQ4\ndIztqZZ1CY2BV8fUKEZcrSYUKqqV9AaghBqe2b1J/F1mDwaAhaU6fnHttliVzIClSedQiqwoZeHO\n7KI46L/S1a64eXjqCc9wkDU6OWWlrTVDbWy6hAIAjEJ6chhfX3VNqUrpE6eF66se9+CTwKfvl41s\n2gHS87AA+9CJIfhcYc0QxTp21LBwFYnxkcnIQEznpqCAhAAiWbdGPz2eDZsVrf9Nf4fUaoU6xsQG\nirIpcr6sl5RNkwNTKT8cudTKsudJrJy6HV6kpAGQUN4LButnFau2GWh6HyW1CINVsPRd31CnClfC\nbAnA4tTn+sYhBLauohCLQ9VR8K5RUKsBKjx4NMlTEOMlc1YKDpBIucCSKsicMGZOwyss4Vkeeop5\nFS++B5x/V0lrHZ2aw78/O4I6pagRonitZVpnALh5b8HiHStNAa50rF7b3m5cVkFWlLIgy8fjM3hK\nKsKha2Pyv3msaCmnyAjwRE8H7i/luHnvPm4UoYylPMf1a1ex7dRfRvEcOLnIPaVus2deQj5wtrSM\nXvxv1OdoIJqqmr1PbClD+rs6tXQvmYwExHRtCvL7Eff7hTZBm4tf/5vyDo6yzHFSgI4mhsqNiI8H\nzIPK5UZVyHxCwEbhDZDDbATYrSp2LoVV8f4osXhJuDdLVlABhosY6gee/Bpw9qfWbxBKP2yGp8IX\nxgHSvSEur5jeZxkJz8NqvkyOZryT8/qAlR3z/fUxyPv7WA2G9g6mrGv4p9BBHVJ2jD4BTgbRlBRi\nLr51ZOwBsSE/jtOgLDRENI+VgXUZOAv6yHNqSe+iH3JthzqluDQ2Lc4iDljkBu6Wdavw2Z055VnM\ncw4F37BlR29TXH0rVlkAgE9uzuDFA1uDbpvhyTkRK8op8MHwFL5xeAe6Zu7jxvQEUESM1izOeDdy\nOf0MtZo1H1dUj6M5Ay5KbirdzWhYbwJE03wWQkUOHhU0twAMkJNTS1fIZHJ1I9CBmJZNAWvWMZa0\nwPspismSO43OJ/I7uMoy+0SxNur1Ekkd8KBYFS3h5iwOZQ9WQ8WTiFaN+LbtWbYqf4pkNWD7PqC+\nCHLoGJt/w1LBIC55HTj94+JP6qYcUgZ0BHqo1HIVL0RofjgplqP6bI9Dh/A4yyGhwy7m+8sKnkjL\nBJzpi66DOloJlA9ejuNxhOqqKHyx6yj0PnKbIZwG6TaxLgR2L8zswpJy7+DtGbzz8bjAIegZEMpz\npP+WsykKFuiGZUUrC1PzS/jRhyNGDqtOhtGzsU2QXQDs/9UPRQDkmG9t9x5ievqZzkUOSJSxNnpe\nfQPy5MdXdbPydm0bjE58k5JHTrrlMro508C7egXPBXEAMVOph+nIZdDRTyHH16uGY/g76FwTUQyd\n8kasuKH9HhTbBp+ffMPr5pTf3SxMVfPT/UqKnzM0xp9Nc2D0ClN6JoZYiIwrqDrXPYU1TTcEQDMz\nOC4gH75krcBY2QthyXn3tRnfZz+J1eelJMjie64+13yKmoEXcjAjcu+DXDMDCH93fq/r4PV74MJK\npbhHW0dAaezwa5IVzwicho51QVevULH52hydmsPNe2rV4+n7dVwYvasA6eWzSj6XKCBSLGUeBlB5\nYVaXFacsEABrWjLMLbFJI+ewArCmpwBA76a1uHZrFhSswlfPxjbcmrkvPlZLRrBjz4PIjj1vWvx8\nwkON/LrUPdJdEBhxxWJpwb64LAuQg9SqulldPAZWpkgHN4JLuCJkew7fWELv6KIeFi5SPUbvCVfE\niryp0vmZKKZAxTOxZh3ouz9g/SLSV3elKfpCIhLmQH537gFR8CTrNgJbH7IqCrbYcBD8aYm9y5TR\ndH6GZQDQ3FnAKeQa5+NmlFq2FF2KOYCs4glnRQFTHX1O8Ub4pBkZDLFtGCEVXVHj6X09ZqVNI6wh\n81gAoBdOMA+UZ24p90cevIBDqZRSEa3jobNrdvWmYaa8/fB7O8UcKUq/03d/ILyoo3uO4qOPb+DS\n2D1n1UgbkH57RxuO7esUdY74ucR/416Im9cHLgdfJEJWlLLQvrqGbz6xAwAUhYAP8OjUHH45UKan\n1HOKS2N38dGNe6jnFIQAXetW4ZHtGwBAYcx6dt8W7OjeB8Bt8ZCDR0vAWa1mbPqy0PkZ778Bj0WT\nuImGOBMAsM1bLhmcZZXK4fLNKZbpMhbdbCL2AWZZt1YGWtmsQvo3/8rk6/dYbkLRYndDIMmzWnRq\nmc+dbOfML55z7w5w733kA2cNbgWXoukDf7pi78r47H3ae0jFxIFJt0T1LH/TpUXkp94E2f5QGXar\nAKjzhetsbcb2OSY0IYuLHKxRzEYlMGzRD6uixufGt76HvO+vgKlx4OF/5lDspT0irytKXnAME76n\nU6l0eTs0dk3Tkyalo8eGGjVQa4xyR/v7FCzR2OpteGMIWMK05y4mn92Zw/XJERzYtk5USj7UvVEB\n33OPt+yBWLN23fpg4xGyspSFVS1iAPUcVhnEyKWWMXIRHvuhFLgxvYBbM7fw8Nb1gjErpwz/sLl9\ntbUKpYyk92IO5Il2c1DtvP5vuDdeayzS4jbnzxZV3GgOneVRxDHlGHhWA3n+O8ge+yqr8mbhhQhJ\nEHylb2Ba3QjlWtkiYa2zd+jqFbH1FHFmJChuTETzPBj3AU7LKQW0ZfBd5AAePc4288Hz5YUWl7Fr\n/G3PUZSBQOw9xt0ee42oJ3LhRKGgUeDT90E/PS28OjaLPmRR+w5/55pKDSPIsXetNDighfSkUFFl\nb4kkKW1YQ5lyTQ7ZCJkYKisqvv8m8o1bRWo3wOeU5H3gIikcIS9HCqGdolTGeCx4+XYppVwBMQPR\n1NguUKv3Hk1RAAiub3gQdW1nywjQ0cbKUet+hjqluDA6jYuj0zi+vxOHujeKM40bwBkBDmzbgK71\nq/CzT25hw6bOHd6ORcqKUha42Ap0yHSZALDrgTb8Si/Lcf3oxrSiRCzlFDfvzSMjRLiNPrszh5Ep\nhn/YFkDScze6slCzTInLkn1HQKUNn+w7Yn0X1+YeKlJit0hh4AKUg1iqriY2Zt729Y9F3n2s+zOJ\nk91SN0K0pY9372HGiX/jWhlbT9hwnYA1YZEuglNrJ7kqZSvZoSAl133QUtg4d0AuvhusLuPUjVm+\nr6prPEX4oZ8V5b0FOIz9aj2AfGmnKYe/67dY174Sey+4UWTsEQA1pFdfEpUhybFXnOj/WEmx0H0e\nJl1Bp1dOqvdeOQnIykI3A2Dn/X2Mhr5CXYrU+RXl9fEoxnp9h9j1UMV7qxLK1YBDx9Cz5yjev54p\nhzwHM/Jzitd9kM8gCuDdyxPCQFXooSlwYfQusjGOZ2gKvnHlKQs2TIIOCKllRIkNPbt3My6O3sX4\ndJnXemN6AZnW9lJOcfqzO9i6oRM7fvO72HbLj6RXJ1yuuuw0q13W4GMk5O7XtW1XFTcAykLzpd7l\n/X1AAeKJIlBxbcoyWr0exkboi54OXwK9eiZtIcshh8jNJcWSVZjvHCEIn0fKea2D74Jv2gRgQNRh\nE+z6eR38urjc7/KmbSiLLavK+LSDStgF0GxGKqYSj6+560oo/QCFcEnq5EW6p6n4Xa5GWBWzkKII\nGop24QEBYCromgGDLbuV8eHP46DtZjN76nOEG0OuEIDyfAczrr4GopXmxBCYDq7EoWOovfAaugE8\n2zaJT27OYO+Wdhzq3iju0cGM71yeUNuECmjMCBT+JJ6rswAAIABJREFUHx4i/7I2REWR0yCXNHDj\nw1vXAVq9hwsjkwJAoou+3AFWpOrqrVm0ZDW8/PiL2DYz5GR8s1qcUhGS7LGvKpp7FXEefNomQQFr\n4RVx0NkWmt42wECZjRaR0XnWt+wGAq5GRYFxcFhwiWGI87mpK8WXZeY7RwjC2LgvnADN69bDSR97\nIy2yuyiF3CTegmaJi7lU/ht2P6bkwuvlfF2Hg22uN8OtD8BaVwKwW6LGdwQMC1tkkBAivA8yRqLR\nb6TPU9ehrYR7pOwrGxlSduTrqE/eKNNiP/gH1BfmWFaTxXvZTGVU98ICKPARTHnUwcbW6/NceECb\nMb4xCpmLV4d7AEen5vCzT26hnlOMTM0LT4EuOiETl4WlOkan5nBp7K4RsmgpyAa/92VtiHSZWVjC\nwpJa56GtNTO8DTKxhUtRAMzsBllElsVuCQWr388X6qk3S2bGJjMv+mKw4tlXzwg3qJFDbgk16G0o\n2n5EOWvRrmuhaeRSZE07SGBhxqZY6ocVHAxxMRtdykEUY4nI40lHPy3nRHE4+bwpQSu3kRh4kyxE\nA2MhW9q8j0uLRXEtey488Wz0rjGJxcb4LFN97dKZKVCHEhbj3laUn/EBJYUutn8xEqMskm6tfHzd\nTYZE1rSDFqniLHzytkpD34iR4HsPA4wIlLsv48swUz1t4MW4NEvx3ICiFfJYhvYkV3VJQA2X92xs\nQwbTQD0zNIWzw1OKRwEow+hf1oaoKDP36zijlZueW8ydH8xVlTID0Lt5LUCAaxOzToVB5vLmh6h+\nIJPu/SDbHwL99DSES7nJzItOd//EEHD1tLTQF5lSI7vZA4eN3nYMg5uRNqktIhtaPbgwtX46Uyy1\n61zkKCGxpWLJ9wq6ZZSHQApdb/2t19Xnadfl5962FxwLhFRiOCL092y2G79400B6JrtG5MJH9sHm\nVo7Fxjgt02KOsj4WmUztHV4vWsi9zf8tHyawpMQ2nBkhz3ctm4T/TnoORJMhWb2hlnLZ1r44Dl4j\nvCCtG/EOa9axtVbQp4MQybMA9v9F+iQ59gpLIzYq79YRnWbpwXtVGnvHniSHvzMCTM8vYXSKZTTI\nBuyzezdbzxmOUZClRQqjj07NoaNz67boTnvkC1EWCCGbAPw1gF4AAwC+TSm9Y7muDoAHyT6jlP6X\nxd/3APgrAJsAnAHwCqU0XEIS4jgGACVtUi8HCpiFO2QZvD2HnFJkhGD3pjbcmVvEndkyY4CCpVZu\nbl+NraED13I4LqcIToLz70INZxEGwpFzjROyFhTX5/AlpoxYiksp6ZlL9jrxKS4+0mOm0bkOReN9\nHMWcguNnScVSDhrpYMwvvifCCLGbja/oUf1nfwm8/yZ71uB5UXDMdbiEwK7ed10ONz4AbHsQmYTb\ncKZnWjIEkut0uJRlz7tZN/qIYlVJYxIY20bGXnF/y1TDPJukVmMX5rnipg+RIYn51N9XYrG4WOrE\nyP0J1jzhWVgF8DM//25Z6ZH/xtOPn/wayJp2Nl+unCzTJ6X9RK+8q6dZ2uZRKI08Ze7H7EmcD+HS\n2F1cGruHi6N38dGNaTy8dZ1iwH5yc8ZplJZFEIHdm9Zi7Sp2rHOP+T/1bIg/BPA2pfT7hJA/LP79\nB5br5iilhy1//18A/G+U0r8ihPzvAF4D8KexD9+zeS22blijZEPoqZQAy4KwSQ6IQzanFFs3rMFT\nux4wUi+5l2Kb5cDVD1ndbSlPKpuVWtU96eQkIIQVqtKAgbbce5/mDUBrn8UTFXe/XNLasSD1Dd5J\nwSsVpoo5FH1hmegx1MChciqW8ruYCHa2O9t7KfLIcyYT3shlFjOW2yhQ6a7Dhf8vlttCllQgl0uM\nja6r12mJ29Izm1OnQxXfu9l+S/GiNfr8mN9dIqdloqWVZQfJBehAVatcdtPTXHg2bYBCeRzyrl7l\nOV5absfcdIYLeF94TRK9j2d+AvLtP2JtdO4s0yfl/SSHUnlXSbMUmCCWusqVeTW9UU0jT537sYp6\n6cVmygHLtruPjBDklBmwe7e0Y2RqXjlfpK+JBzevRe/mtQL/cGlsGp3rWovr/2lnQ3wdwLHiv38A\n4ATsyoIhhBAC4HkA/7V0//+ESGWhRgie2vWAcNGcGrytVJfkcmFkEiNTKvWmrMFRcLRp6Yl4eOt6\nzC4sYfD2rECiTs8vYWzjTmzTlQFH5TOr+/PdHyhWKjn+apSFaEWdKyh6MajAU7+JbO/TyAfPicVE\ntboUvM0QgZPaPjXd/VkGbNsL1BeAnoOi4FCQdEl6XzosZUwUhanIt/8I2ZGvBw/FFAvfJkmbPGBN\nXXS9l3UOSF4FOnwJOriZp9VWOXxc9Lzinm43wDVFdE8J6ep1hkN8oYQqdTpc4vNgxXi3QgptI883\n3juSvt3GtIqZO8yy5W54TgMOlOmdongdw0w5AYKyx0piZA29cyzQuuwjv7F4NvcwcE+GVGTPdSgb\nCmC3GxOU9/chA4z0Rlv9nhTh/bv+85/ieuevYsf0NWybvY6RwQGMLHYqJQVqGRHKwI3pBdQI8Mj2\nDQrg3oWhm1mo45ObMyWhIKWiyKFFVa8kX5SysJVSOgoAlNJRQkiX47o1hJD3ASwB+D6l9P8GsBnA\nJKWUm27DAKLcLO2ra4JfWwc16iWqT382adx/fH8n5hZztLVmeO8KT2OhuDVzX2h0tYzguX2dGJ++\nr7iVXn58J7Yf2e8EebncnyJtkEu97kwljEH5K4uTA5MoZQf23qdLF6OlfCoAt+ZdKBekq5dtTHoJ\n28LdL0h2OLnLzc+sC1IBl9mskp4DzgqdzbKGXRKKg9PhS+ydPMA1INbaUucHC1mtYt+AK3lFxkzo\nYLd6sGR6XilcoryPA+CaPGZyeWgPZsV1v5jjF9+DXPq7EfEpjilKZVV8QegZ/Ldo/o1hnQCMAmNX\nmYL26PNAV68SGhQK2Ll3IIK08/fcgEJ9PkaOkc+jp6Q9TwyBvv1v2XNrLcwwGh9gxsaqNpVOXFME\nfJ4p/br8rdcN6n117AgjymowGw1g4YA3Fvagvr0XtW11/Gcj/4j/d2EP6tduIyNEMDI+u3cz3r08\nIfpVp8D6NSWR4Nxi7gTb35y+b83OA4D7c7N3G34JLKOyQAh5C4ANWPEvE5rZRSkdIYQ8COAdQsh5\nALYXd6pOhJDfA/B7ALBr1y6DhIm7fbjGRlAo2lqLX+lqF4rCJzdnxPrh7I1yfGluMcf6Na3CrSTC\nETNDlkI/AffnviOgQ/3loVirWWmWU1D+hpWmkdyIRWNTRiyaN732ociooC1lTQBbmhtDXasFaXTg\nj5WUyeYS5oWptM0jFNbhz4hBwaccJDZWt6xRa8tjHVkVlcDBLvebeWD8xYFsigv/e6q1ZQ2HODAr\nYWELUC79LfdL72MMuK4Rb1OzsB3BtpcWkP/DnwJ7n2FZQjZMjkjLBEqOhzoogJp2+ImxseAvgumf\nFTwpIQ8NDyso3/HEDxmYtNYC8vx3ohVLb19k6n3+fo70RllC72z7fXhyDnVKQAlBnRBc3f8bqM+S\nApzIGBk/unEPD29drxxkGWG4Oe791gsaAsC6VTV0rV+Na7dmre9ZI8DUrfER72BEyrIpC5TSF1y/\nEUJuEEK2F16F7QDGHW2MFP9/lRByAsATAP4ewEZCSEvhXegB4BwMSumfAfgzADjw2GE6OmVW5ZKV\nAwrVC9axpgV7t7Tj7PBd1MfN+gxyPIkhWgmm5xfRtX61AZqkH2shAA3kBdgPOsqLD5EM5PirVvef\n7nr3ofwVK62/D4yRkIiUTddhZdO8SefO8sAG2CblyEQw2gbsBWls4DJbzQKPG9QV1rHl9ftQ8D4W\nQF1SD4xYayvkpq/8/J5wcSArSKtikTKh5OnerQQQmTIHc0fpb81tTo69YvVkNIp2941TqsfDm6LH\n2+YevckbwPtvglr4BfjcESyK1z4oqbIvvgfqCDVZ15cn/XM5+TtMhTac5RQaQ9szBNtkwS/B0xu5\nJ8PWvoGTkpQv15iohH8Z9vZsxojGyMjYgylailBERoAnejoUj/XLj3cbhaO+9gizxz+7M2ecZQBj\nhLw/O2MeXBXkiwpD/AcArwL4fvH/b+gXEEIeADBLKb1PCOkE8OsA/ldKKSWEvAvgm2AZEdb7bTJz\nv66UpOagxrbWzBoLaskIXjywFZfGpq3VwAgYuyMv5nFpbBqXxu7iYqEpPtS5FmN372PvlnZWM4K7\nzjloZ3xAxMpsBx0ArTwxBPhIPzCqoPyF25pz1J/4obBGY2pOCC77hHoJYpGeehOYuWOt3RADLrON\nlU1clrFs2eb9fahxZcFxfczG6DswUmo+2P4e5e2IPLCUuhsS06MLs6CzY/oUEicQVRu7mBiztU2n\noiEB4OrSfJRDeZonw4W5SbGWlbFMxBfIbfgOIaEA/MOfMkWhvNOtYOnZJwBb4w5lTHHjy+8kHcwh\nj1OzlAWlXwlz2jWG3rU3rPJLYHzASS1vw0nJ3jvbmIy178Tw5Bwe37EBN+8tKCyNcsiBKyc8HM49\n2HJRw+HJOTyzm5Ug4IyPPKT+8Nb1ACi61q9WFAzOGdQM+aKUhe8D+BtCyGsAPgPwLQAghDwN4Pcp\npb8L4ACA/4MQkoNRG3yfUtpf3P8HAP6KEPLHAD4A8Lr+AJcs5WqpTxnUyBWGmsbRfWnMHvKhKJm1\nZF4GHtr4uPBEnB6awp3ZRTy1aye6HnkO4PHBvO4nQxoOsxFy8bqnfRuXYBb0ZyP4nlGlXgIKIKWt\ndkPIsk4Rp5dETieTLC4rCFDeJOruSpOufitFg1rspZt9EmvFxYybrS1Oz+scQ11x8ShECiiuyOZQ\nFDOJEEfMH0+M2dZfq6Khpd2xjpMylGdDy2to91SvifW79Bzweq2c69NxCCn3PP0SqMK/EUF7DcLq\nEEQi+vVvKNerkSXFkxLllfMc6NHkY5YxBPyKvv4eFPDjhRw4KaOtLMPo+G28MfMZlkgGrg5cn5zD\n+PQCZheXlJADBYSR+ezezXjvyi3FQOXeaZ3xcWpuER8MTwlPw4FtG6yZfc2QL0RZoJTeAmAgRyil\n7wP43eK//yOARx33XwVgr6wUIXLRJ66ZzS3mOLavU4Ac5UE+sG0D+kenITngQaHWDwdUgg0AymS4\nemsWn92Zw2/tOYqt/X0SbsECcoxkI9TFZo0G2dsS3aeGR6PCwR5jlbgsndDmHevSJ488VxYnyu3I\namEdTwxBfM0Aw6bVI6Cg0xeSY/QpVlwVT4txKAXmmFMplcGv9Zyx+9VaSjIdiTjHICZzeCes/eXY\njs6dCrNn3t9XKuIAsLUM83GFpFQwmHLL8/VjvCZ6/yBXa7V5rbTxda1F4xAq5iNgHnR44TXmKdmy\n24pZEO3JazqlhLKiGKv1aiod4hF7UOia0JwOjaHvm+rvAYDNI1f41oGTUtrq7wO9cALXp+ZRbwfK\nE4OIIk/GOBX/X88pLo6qnuyt61fjke3rMTw5h+n5RQVrd2ZoSty7pHkfeLnqZsmKYnBc1VKSLHG3\nDgBrYSldSPG9awQ43NMhXErytXJoY2GpjtMaW+RSTnG9pRPb5YwDS1U2a8zeEafzSeyh3HC+eMRi\nVq5PtEpiLDXAbUFYvSQHj7prdujXa/TTKQybRpimCtGLYNeDgi2pJLwtySpNjT/bxtMAv3Kp14HH\nni/KZpeEOL6DWHYn48mvKZ41Oj8D+jf/yijtTLr3Mzrci++V7neprLvc5xwo+QHO/hREnlOBeakT\nctkYPJ14H5fFKh9CBWeBTXnJ+/tANnRa+Qx8vC1Ja1quyyK+YVihd/UjZg/yXZOixNrGEAh/U/09\nfGMXShcV75zn2HFvADVaxxKK+h8eycBGvZYRtK+qKb+1r6oJb0JGiAA56viEjDCDVa5nVCMEm7b1\n7PI+PFJWlLKwuiUTWz4fWB83NxeZ9rlOgQ+Gp0AprIU/5NDG6N15hauBgD2TdEikJjEFmhLBUqnt\npB72jUqsu9xlvdksNVf2h9xWCohQ6W9PdYbN8t7Skg3xShjjcOKHqsX07g+Qjw9Y3cNxbalMfSlk\nTV5XulFJEUCWlQx6jmJghidBcifjzE8EAh5r1jlLO4vUYIfHSBFP6C04L+WDLQfw6HFG/OMABlpd\n1DzkIWXouA4hKxlVEeKRCdpcvC3JoijGAA/VyJwrLnGFZYKHtStU6AAnpx7kqYpTaOyCv/cw4PC2\nmSF8/coPcH3Dg2h7/Dj651ZL3Af6TUDXulV4ZPsGbG5fjcHbs6gXxunaVS0Kf8LW9avx/7P3rkFy\nHVea2Jf3dld3V3V1N9DvwqsJAiDxkACSQ2omNCBBSqHwWHJoSGkm1o6VpYlZb6z/OmzvrHZnY8Kz\ndswv2+EfdsRuaB6rcDg8OxyNHLInZkN8gFiFhqRAUiTQDQIg0AD6Uf1+VFdVV3fVTf/Im3nzee+t\nByQ7WidCIrq7Km9m3nszT57zne8b7c8IfAIHRJ4ezeGdu6tYKkV7ToNS5AaGRhMHncIOlLNQ2o3y\nRAEFZooljOUzQtqTOxDcZD1xOb0gHAeHc8HtcDajOAtPDGfFZ+PK3Dpx2u9kO522NOVHiac37TTi\nqv6IDf/yBdmC6ejUSc323WBoPDXJkRhn9Bs2Fkd4OF1bIbcGB8s2CyJzhdL9LrUs2FMxLFa8i61M\nVssLY3kWGBhh/3VIO4uQMxASEJkRO349xGh6pNsIVJBvmhO3/Bygt18QrVG/S6ECd4XIVTKqQHGS\n2gEbWitVuGPseYz9cfYjK+eK0ZalHzYGWGNOLe+IlY9m+pqIBjrTqjEprV/U+kcKUaXFJIBC+IyM\nbFXx1x8tWMHyAWVETGvlNbx6sYDXLh0RuIO1cg1YjD67VKphrbyn4BNskexO24FyFmSjYLkjsogI\niioVzCxuVfHXH82jEXIvPHtsELV6gOliSZRW6s6FbmP5HmAxooyeGs5G1094wTt12ne9PHFSv7J1\n+mVLlcNMcXozNjhH9UdSiDMNg2JbJzVY8BcpSI4MgKtOzw2wUP1cegS/yylI6wwlhdLlzdD2bFnD\n1paUm5IX9vwoXed5jHkwaAA8tGsBJ4IQYHwK5MLLxrOf9Jkka9dxJAVGCCQcwEYdwdvfh15CrX9H\nlDnbsE4tRiKTKlV4pIdqFPCuMesAP1gYYJPmRumXRuwWBz5sZny/CCvmjmHu9KsK/m1ysA+vXSpg\npljCzUVTUhqAUvXA8XR3V8zKx3pAcf3hhpAteHd23fhMZ0ieIzuwzgI3Kv6P6TxwHMM7d1cE8RIF\nkwI9PzmgcDCcnRgwogpMW7yEyl4d5T21dEnWJO9UqqEZM3UhzDpt6+c7+LKlwlEknN6EA2MBbiW1\nFYcNESkO+ff1PQT//t/A+8p/0RlnKU0O1wFwRW8/I8ASPP+U5fBjyu6UuYjZ6FIt6AnPbJo2YjkX\npDJZHk6m26uh4JnpOAIQZZ9Yno3mlQIo3gNdfiBEtoy5pwCK90FX55pmpWzXkTc2ieJnCP7qf4h9\nv8S9s2CdjKiFJVJms0B2PrR0jPK+pVyneD9k7gJ686qSMkljSgQMAMafgHflP4/6nDaF10bEpR2T\nD5o+AV67dERxGADgpgXkCLARL5V2FeVJmx4EwEDz99YqAkf3cCMCNHKtiIhpuH078M6CbL5H0Nft\nWW8Qr2+QiZbOTuQVzXEAzjCTXjnxy0gRGC9hEtjsMbxsqXKYjrCkimavC5bEpPyic4N0nbSPnmVE\nWHya1ucR/OUfwwuFax73+F0AV7pwmyHheU6ZEAbii6v91jfnNiMk7Tyzegmp7SQrO30iyiNtEJ4u\nqhXWxIt0lcy3EDRA3/hT4TCYqZImQKYdtEgnQzpMpOiHmBObdHT439S00Au3gZtXIebKwY/SrCNC\nCjp3QeAsD3eOk1c2cL6MlYdqX0JRPZc1U3b+ONIUM8VtcdBsUPazwLFtVfHu7Hps/++tVvBgrYqz\nE3mR+gYYW+POXsP4fIMCtXqAV86MCP6FC4UhvP9g3UkP3YodKGfhULYbFybzmCnuqDWsEq/C3GbV\n6sn5hISfGVCcA7mS4vjhPqujcPxQn+B1kK2YO4a58REczfVhssNjtZmxWJIE8JIDOd9u5USaDcca\nluTh4yarCVwbZNxGhbETjFOfW+BWjmzG0ozf5lDYQ7PdJh24BOprNjLUKs11GjNKSCW+CleqLAkv\nYk1XAap0MqWgb/45K3ve3WFRmuVZZyXSL8JIQWUPlPvRzj1oxrlXAakEmLrkdASadUTadcpIwQJU\nnb4WOSyh8+jip0lbdv740hR6AoD9zPWIXJEC2RohAFc+nA70dlmdBQCo7DdwoTAkCJ+AqJSf6spz\nLdqBcha6fQ+vPDWOsxMDIlWQzfhKOmGtrCpNFgZ6cDjXoyh/8f++/2BdqXm9v2rn5x7tz4j0huxh\npinZ7JTpoXv09keLpk0wyoKcB9IvGMo1Wwh5K+0o4WOVSKfdhd7pSFx4GVR2Fjy7cmQnryn/3QBF\n8ooFDh48fkGU0CmlgHLJWDObx2PO71qrJSwloC4EvM0MpyoUScJz/zGT8aZShIGzNvKxcfbRJtkW\nm7W4d8DXogRAc++Xfo20BG6AfHqn7H2a/Qj03gfpcESWZ8nq4MWUhyeZUtrseVE7CYcFtZ/7oHfe\nc0pntxs5dd3bsxN5wfrLDpmMRVE/iMpVDculPUwvbgsuH/1wylmGXTa7WgGXMpBT4ccP96GyvdWR\nXMSBchZk4zeTAFjZqeHoUB8yXT5Ku/vK504M5wTJhW4ufQndeKml7BSkKdnslNkEjsQGxMOFLtpj\nCTnf7ubD220aGKYDp6YuAbnBpvKgzZr3+S+xTfjGW0DuMLznv9bWQtKu6I6B45AWQFfJWDO4mLT3\nttXIkkDZc9ImSkHf+gsDL6D3I5i+JqiLbdUsLtpoPPfVSKGQeMYGw3lLmgnbpxl3Wu4PMS/SfTYE\ntqavJc5xqwRuaiM0mp/6PoL3fwQy+WTqZykOEGxLmaQx+d4quBXEHxaifu6zz1hIwMzPNo8bi3Ou\nOZBRZ1Hs6/aUNs5P5pVIAHMytgEQcTjl2IXZ9UpsSiEA29MAMxWezQ+OpB5YjB1IZ0HWemCAkj1R\n/+qBpSUCGlFsukwnYeK0m37I4MRvrlxqOVMsGeWYHCvx/oN1HKmvYmItgX8gzNml3SxtGwEAVkIm\ncvM0kfYYSA92Mq6ZouzJZXzhEGHbex+wDcGiCtcpowu3GVYgBFY1c/q0lQPaBIuaFr6JSV/YohXN\nYAx0h8yWmmo3reF987sI3v4+UPyMfSB8LuKcIgIwTEJC1ZAhpNabA/ndP7Q6EnGRF/77uPLOtIBg\nnLscheLrbppwZewSDTl1CD8p13TgW5IsivRQCLIvzj3x2c9AP7uu4EpSp4O0e9Rq2kr+ro5biXOI\nxHP209cjErCQZpycfkH5XjPvh3X+HGOWcWzyAVAGuAPAcqkmFCVlfp6Z4jZmiiWslWuCjCmNrezs\nAkVqpMIJSWCESmkHylko79VDT809+QGAk4ezoiSFe3curu3JQVYH++7supC4PjHch6nDWSyXarhZ\nLInLEUTgF64qlunysVdvhKIiFH4Q4Lfv/BQTf/8Dez7u3/0rAYwKbl4VNdpxpi/ASpmZMvh42mMg\nnuDEKfhjlD2pGgHONvRNYU4VfZFz850EKRkaB3xuUjo5xkIiCxlJm1KceJDNbAtv0tiTFmtFNEgO\nHX/8JoIbb6uCPJ1Ia4xNRc4CzDdRf+4AOJk2le9pYXV5QwCQKvLi0oZwVs0ksBWivCWNkCYyb5LC\nGUDRjlFJpazkYi2ejo2xn/g88Nl1tb+WjR8wHefHXdnV7KZOCmfg/cY3GAkYd9YefAL64BPoFWC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1DOQpdnlkPK3hoN55TngGTgyOsfzTsrFva03Z2CgVm4hwmY3Ar8GxxZCwBYZA9h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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "inside = x**2 + y**2 < 1.0\n", "outside = ~inside\n", "\n", "_, ax = plt.subplots(figsize=(8,8))\n", "\n", "# we'll graph the first n co-ordinate pairs\n", "# for points inside and points outside of \n", "# x**2 + y**2 = 1.0\n", "n = 5000\n", "\n", "ax.plot(x[inside][0:n], y[inside][0:n], '.', color='#fc8d59')\n", "ax.plot(x[outside][0:n], y[outside][0:n], '.', color='#91bfdb')\n", "\n", "ax.set_xlim([-1.0, 1.0])\n", "ax.set_xlabel('x')\n", "ax.set_ylim([-1.0, 1.0])\n", "ax.set_ylabel('y')\n", "\n", "ax.set_title(r'Monte Carlo estimate of $\\pi$: {} / {} points'.format(n, nsim))\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To count the number of points _in_ the disk, we use `numpy.sum(x**2 + y**2 < 1.0)`. The array `x**2 + y**2 < 1.0` is effectively an indicator vector whose ith element is `True` (equivalent to 1) if the ith point falls _inside_ the disk, and `False` (equivalent to 0) otherwise, so the sum of the boolean elements is the number of points in the disk. To get our estimate of $\\pi$, we convert the sum into a proportion and multiply by 4. Altogether, we have" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "estimated value for pi: 3.143172\n" ] } ], "source": [ "num_points_inside = np.sum(x**2 + y**2 < 1.0)\n", "est_pi = 4.0 * num_points_inside / nsim\n", "\n", "print('estimated value for pi: {}'.format(est_pi))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How close was your estimate to the actual value of $\\pi$?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Visualizations of the central limit theorem\n", "\n", "One way to visualize the central limit theorem for a distribution of interest is to plot the distribution of $\\bar{X}_{n}$ for various values of $n$, as in Figure 10.5. To do this, we first have to generate i.i.d. $X_{1}, \\, \\ldots, \\, X_{n}$ a bunch of times from our distribution of interest. For example, suppose that our distribution of interest is $Unif(0, 1)$, and we are interested in the distribution of $\\bar{X}_{12}$, i.e., we set $n = 12$. In the following code, we create a matrix of i.i.d. standard Uniforms. The matrix has 12 columns, corresponding to $X_{1}$ through $X_{12}$. Each row of the matrix is a different realization of $X_{1}$ through $X_{12}$." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "matrix x has shape: (10000, 12)\n" ] } ], "source": [ "np.random.seed(102334155)\n", "\n", "nsim = 10**4\n", "n = 12\n", "\n", "x = uniform.rvs(size=n*nsim).reshape((nsim, n))\n", "\n", "print('matrix x has shape: {}'.format(x.shape))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, to obtain realizations of $\\bar{X}_{12}$, we simply take the average of each row of the matrix `x`; we can do this by calling the [`numpy.ndarray.mean`](https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.mean.html) method on `numpy.array` object `x`, specifying `axis=1` to take the average of each row of matrix `x`:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "xbar = x.mean(axis=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we create a histogram:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10, 4))\n", "\n", "plt.hist(xbar, bins=20)\n", "\n", "plt.title(r'Histogram of $\\bar{X}_{12}$, $X_i \\sim Unif(0,1)$')\n", "plt.xlabel(r'$\\bar{x}$')\n", "plt.ylabel(r'Frequency')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You should see a histogram that looks Normal. Because the $Unif(0, 1)$ distribution is symmetric, the CLT kicks in quickly and the Normal approximation for $\\bar{X}_{n}$ works quite well, even for $n = 12$. Changing `scipy.stats.uniform` to `scipy.stats.expon`, we see that for $X_j$ generated from the $Expo(1)$ distribution, the distribution of $\\bar{X}_{n}$ remains skewed when $n = 12$, so a larger value of $n$ is required before the Normal approximation is adequate." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "np.random.seed(165580141)\n", "\n", "from scipy.stats import expon\n", "\n", "n1, n2, n3 = 12, 32, 256\n", "\n", "x1 = expon.rvs(size=n1*nsim).reshape((nsim, n1))\n", "x2 = expon.rvs(size=n2*nsim).reshape((nsim, n2))\n", "x3 = expon.rvs(size=n3*nsim).reshape((nsim, n3))\n", "\n", "xbar1 = x1.mean(axis=1)\n", "xbar2 = x2.mean(axis=1)\n", "xbar3 = x3.mean(axis=1)\n", "\n", "_, (ax1, ax2, ax3) = plt.subplots(1, 3, sharey=True, figsize=(14, 5))\n", "\n", "ax1.hist(xbar1, bins=40, color='#1b9e77')\n", "ax1.set_ylabel('Frequency')\n", "ax1.set_title(r'Histogram of $\\bar{X}_{12}$, $X_j \\sim \\, Expo(1)$')\n", "\n", "ax2.hist(xbar2, bins=40, color='#d95f02')\n", "ax2.set_title(r'Histogram of $\\bar{X}_{32}$, $X_j \\sim \\, Expo(1)$')\n", "\n", "ax3.hist(xbar3, bins=40, color='#7570b3')\n", "ax3.set_title(r'Histogram of $\\bar{X}_{256}$, $X_j \\sim \\, Expo(1)$')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Have a look at Appendix A below for another neat visualization of the CLT." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Chi-Square and Student-$t$ distributions\n", "Although the Chi-Square is just a special case of the Gamma (refer to [`scipy.stats.gamma`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gamma.html)), it still has its own functions in [`scipy.stats.chi2`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.chi2.html): `chi2.pdf(x, n)` and `chi2.cdf(x, n)` return the values of the $\\chi^2_{n}$ PDF and CDF at `x`; and `chi2.rvs(n, size=nsim)` generates `nsim` $\\chi^2_{n}$ r.v.s.\n", "\n", "The graph below illustrates Theorem 10.4.2:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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OuWeAa4BXAx8xs/vN7Hfy9JoiIpJ/Bbk5BnwcMIIA6mkA59yAc+6LzrmPAZjZEjO7y8z2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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.stats import chi2, gamma\n", "\n", "_, (ax1, ax2) = plt.subplots(1, 2, sharey=True, figsize=(14, 6))\n", "\n", "x = np.linspace(0, 20, 1000)\n", "\n", "n_vals = [1, 2, 4, 8, 16]\n", "alphas = [1.0, .7, .5, .3, .2]\n", "\n", "# graph for Chi-Square\n", "for i,n in enumerate(n_vals):\n", " ax1.plot(x, chi2.pdf(x, n), lw=3.2, alpha=alphas[i], color='#33aaff', label='n={}'.format(n))\n", "ax1.set_title(r'$X \\sim \\chi^2_{n}$')\n", "ax1.set_xlim((0, 20.0))\n", "ax1.set_ylim((0.0, 0.5))\n", "ax1.legend()\n", "\n", "# graph for Gamma\n", "lambd = 0.5\n", "for i,n in enumerate(n_vals):\n", " ax2.plot(x, gamma.pdf(x, n/2, scale=1/lambd), \n", " lw=3.2, alpha=alphas[i], color='#ff9933', label='n={}'.format(n))\n", "ax2.set_title(r'$X \\sim Gamma(\\frac{n}{2}, \\frac{1}{2})$')\n", "ax2.set_xlim((0, 20.0))\n", "ax2.set_ylim((0.0, 0.5))\n", "ax2.legend()\n", "\n", "plt.suptitle((r'Theorem 10.4.2: $\\chi^2_{n}$ distribution is the $Gamma(\\frac{n}{2},'\n", " r' \\, \\frac{1}{2})$ distribution'))\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Student-$t$ distribution is supported in [`scipy.stats.t`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.t.html). To evaluate the PDF or CDF of the $t_n$ distribution at $x$, we use `t.pdf(x, n)` or `t.cdf(x, n)`. To generate `nsim` r.v.s from the $t_{n}$ distribution, we use `t.rvs(n, size=nsim)`. Of course, `t.pdf(x, 1)` is the same as [`scipy.stats.cauchy`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.cauchy.html)'s `cauchy.pdf(x)`." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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aJEmapG/FxPWhI+XUIUltoCMDT7GHB+CIw9okSVXSuxS6umvrgz58VJLmqjMD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\nz/Q57yeyKa0PPgx77oEn7ob922CkwQP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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.stats import t, cauchy\n", "\n", "_, (ax1, ax2) = plt.subplots(1, 2, sharey=True, figsize=(14, 6))\n", "\n", "x = np.linspace(0, 20, 1000)\n", "\n", "# graph for Student-t \n", "y1 = t.pdf(x,1)\n", "ax1.plot(x, y1, lw=3.2, alpha=0.8, color='#33aaff')\n", "ax1.set_title(r'Student-$t$: $\\tt{t.pdf(x, 1)}$')\n", "\n", "# graph for Cauchy\n", "y2 = cauchy.pdf(x)\n", "ax2.plot(x, y2, lw=3.2, alpha=0.8, color='#ff9933')\n", "ax2.set_title(r'Cauchy: $\\tt{cauchy.pdf(x)}$')\n", "\n", "plt.suptitle(r'Student-$t$ vs. Cauchy')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "----\n", "\n", "## Appendix A: Quincunx - an interactive visualization\n", "\n", "Statistician and geneticist [Francis Galton](https://en.wikipedia.org/wiki/Francis_Galton) invented the _quincunx_, or _bean machine_, to illustrate the Normal distribution. Here is an implementation built with IPython and [D3.js](https://d3js.org/) (version 5.7.0), embedded right in this notebook.\n", "\n", "In this interactive visualization of the CLR, you can:\n", "\n", "* alter the animation by controlling the time between redraws with the `delay` control (from 50 to 1000 milliseconds, changes are immediately effective without restarting the animation)\n", "* change the number of bins with the `num. bins` control (from 1 to 25, board is redrawn upon completion of change)\n", "* change the probability $p$ that the ball will go to the right (slider moves left to 0.00, right to 1.00, board is redrawn upon completion of change)\n", "* as the balls drop into the bins below, the heights of the bins will increase to form a histogram\n", "* the running percentage of balls per bin is displayed on each bin and updated in real-time (`Math.floor` is used, so some accuracy is lost)\n", "\n", "First, we import `display`, `Javascript` and `HTML` from the [`IPython.display`](https://ipython.readthedocs.io/en/stable/api/generated/IPython.display.html) module.\n", "\n", "Next we use `display` to load the D3.js file from the [Google Hosted Libraries content delivery network](https://developers.google.com/speed/libraries/#d3js). We also load the main JavaScript code in `assets/quincunx.js` and Cascading Style Sheet definitions in `assets/quincunx.html`.\n", "\n", "Lastly, we embed a small JavaScript snippet into the code cell below to provide an entry point to the `quincunx` module in `assets/quincunx.js`." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "application/javascript": [ "\n", "require.config({\n", " paths: {\n", " d3: 'https://ajax.googleapis.com/ajax/libs/d3js/5.7.0/d3.min'\n", " }\n", "});\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "require.undef('quincunx');\n", "\n", "define('quincunx', ['d3'], function (d3) {\n", " /*\n", " * Creates HTML form controls for manipulating the visualization,\n", " * sets up the initial visualization state, and then kicks off\n", " * the animation.\n", " *\n", " * This module was built with D3.js, v5.7.0.\n", " */\n", " function draw(outputarea) {\n", "\n", " var def_bins = 7,\n", " def_speed = 500,\n", " def_p = 0.50;\n", "\n", " /*\n", " * Calculate level in pyramid of triangles\n", " * for given triangle (path) element index \n", " * (zero-index)\n", " */\n", " function lvl(d) {\n", " d = d + 1;\n", " var i = 0, n = 1;\n", " while (i + n < d) {\n", " i += n;\n", " n++;\n", " }\n", " return n - 1;\n", " }\n", " \n", " /*\n", " * Calculate index for first triangle (path)\n", " * in pyramid of triangles, given the level \n", " * (zero-index)\n", " */\n", " function pos(l) {\n", " l = l + 1;\n", " var n = 0, i = 0;\n", " while (n < l) {\n", " i += n;\n", " n++;\n", " }\n", " return i;\n", " }\n", " \n", " var speed = def_speed,\n", " step,\n", " histogram_height = 100;\n", " \n", " function init(bins, p, width) {\n", " var p = p ? p : def_pp / 100.0;\n", " var margin = { left : width/10, right : width/10, top : 10 , bottom : 30 },\n", " height = 450,\n", " sx = (width - margin.left - margin.right) / bins,\n", " sy = (height - histogram_height - margin.bottom - 100 ) / bins,\n", " histogram_y = height - histogram_height - margin.bottom,\n", " values = [],\n", " ts = sy/3,\n", " bs = sy/2,\n", " dropping = true;\n", " \n", " var container = d3.select('#quincunx');\n", " container.selectAll('svg').remove();\n", " var svg = container.append('svg')\n", " .attr('viewBox', '0 0 '+width+' '+height)\n", " .attr('preserveAspectRatio', 'xMinYmin meet');\n", " var g = svg.append('g')\n", " .attr('transform', 'translate(' + (width / 2) + ',20)');\n", " \n", " var path = g.selectAll('path');\n", " path.data(d3.range(0, pos(bins + 1)))\n", " .enter()\n", " .append('g')\n", " // position the triangles\n", " .attr('transform', function(d){\n", " var x = 0;\n", " var y = 0;\n", " var l = 0;\n", " y = lvl(d);\n", " x = d - pos(y) + 1;\n", " l = (y + 2) * sx / 2;\n", " return 'translate(' + (sx * x - l) + ', ' + (sy * y ) + ')';\n", " })\n", " // draw the triangles\n", " .append('path')\n", " .attr('class', 'triangle')\n", " .attr('d', 'M -' + (ts) + ' ' + (ts) + ' L ' + (ts) + ' ' + (ts) + ' L 0 -' + (ts/2) +' Z');\n", " \n", " step = function(){\n", " // drop a ball\n", " g.append('circle')\n", " .datum({lvl: -1, pos: 0})\n", " .attr('class', 'ball')\n", " .attr('r', (bs) + 'px')\n", " .attr('cx', function(d){ return (d.pos * sx / 2) + 'px' })\n", " .attr('cy', function(d){ return (d.lvl * sy - 50) + 'px' })\n", " .style('display', 'none')\n", " .transition()\n", " .style('display','block')\n", " .on('end', animate)\n", " }\n", " \n", " function animate() {\n", " var c = d3.select(this);\n", " var d = c.datum();\n", " if (d.lvl > bins - 2) {\n", " // drop the ball into its histogram bin\n", " c.transition()\n", " .duration(speed / 2)\n", " .attr('cy', function(d){ return (d.lvl * sy + 20 + histogram_height) + 'px'})\n", " .style('opacity', '0.0')\n", " .remove(); // remove the balls once they're invisible\n", " values.push( bins / 2 + d.pos / 2);\n", " update();\n", " return;\n", " }\n", " if (d.lvl === -1) d.pos = 0; // when the ball drops into the first position\n", " else (Math.random() > p) ? d.pos-- : d.pos++;\n", " d.lvl++;\n", " c.datum(d);\n", " c.transition()\n", " .ease(d3.easeBounce)\n", " .attr('cx', function(d){ return (d.pos * sx / 2) + 'px' })\n", " .attr('cy', function(d){ return (d.lvl * sy + sy) + 'px' })\n", " .on('end', animate)\n", " .duration(speed);\n", " }\n", " \n", " var x = d3.scaleLinear()\n", " .domain([0, bins])\n", " .range([0, width - margin.left - margin.right]);\n", " var formatCount = d3.format(\",.0f\");\n", " var data = d3.histogram().domain(x.domain()).thresholds(bins)(values);\n", " var histogram = d3.select('#quincunx').select('svg')\n", " .append('g')\n", " .attr('transform','translate(' + margin.left + ',' + histogram_y + ')');\n", "\n", " var xAxis = d3.axisBottom(x).ticks(bins);\n", " \n", " var bars = histogram.selectAll('.bar')\n", " .data(data)\n", " .enter().append('g')\n", " .attr('class', 'bar');\n", " \n", " bars.append('rect')\n", " .attr('x', 1)\n", " .attr('width', x(data[0].x1-data[0].x0) - 1);\n", " \n", " bars.append('text')\n", " .attr('dy', '.5em')\n", " .attr('y', 10)\n", " .attr('x', x(data[0].x1-data[0].x0) / 2)\n", " .attr('text-anchor', 'middle');\n", " \n", " histogram.append('g')\n", " .attr('class', 'x axis')\n", " .attr('transform', 'translate(0,' + (histogram_height) + ')')\n", " .call(xAxis);\n", " \n", " function update() {\n", " data = d3.histogram().domain(x.domain()).thresholds(bins)(values);\n", " var bars = histogram.selectAll('.bar');\n", " var y = d3.scaleLinear()\n", " .domain([0, d3.max(data.map(function(d){ return d.length }))])\n", " .range([histogram_height, 0]);\n", " bars.data(data)\n", " .transition()\n", " .duration(speed)\n", " .attr('transform', function(d){ return 'translate(' + x(d.x0) + ',' + y(d.length) + ')' })\n", " .select('rect')\n", " .attr('height', function(d){ return (histogram_height - y(d.length)) });\n", " bars.select('text')\n", " .text(function(d){ return Math.floor(d.length / values.length * 100) + '%' });\n", " }\n", " update()\n", " };\n", " \n", " (function interval(){\n", " if (step) step();\n", " setTimeout(interval, speed);\n", " })();\n", " \n", " \n", " // setup event-handlers for controls\n", " document.getElementById('qxspeed').onchange = function(e){\n", " speed = e.target.value;\n", " }\n", " document.getElementById('qxbins').onchange = restart;\n", " document.getElementById('qxp').oninput = function() {\n", " var newp = (Number(document.getElementById('qxp').value) / 100.0).toFixed(2);\n", " document.getElementById('qxpval').innerHTML = newp;\n", " restart(newp);\n", " }\n", "\n", " function restart(e) {\n", " var b = def_bins;\n", " var p = def_p;\n", " var w = Number(document.getElementById('quincunx').offsetWidth);\n", " if (e) {\n", " b = Number(document.getElementById('qxbins').value);\n", " p = (Number(document.getElementById('qxp').value) / 100.0 ).toFixed(2);\n", " };\n", " init(b, p, w);\n", " }\n", " \n", " restart();\n", " }\n", " return draw;\n", "});\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\n", "\n", "
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