{ "cells": [ { "cell_type": "markdown", "id": "83dd2747", "metadata": {}, "source": [ "## Python Tutorial\n", "\n", "This tutorial is meant to show you how to work with the `symd`. This will not focus on running simulations -- see the other examples ({doc}`toc`) for that. Some of the ideas here help with re-implementing the symmetric molecular dynamics engine, but you should refer to [the paper](https://arxiv.org/abs/2204.01114) for exact details. \n", "\n", "Let's install if you have not:\n", "\n", "```shell\n", "pip install symd\n", "```" ] }, { "cell_type": "code", "execution_count": 1, "id": "cc8f42f2", "metadata": {}, "outputs": [], "source": [ "import symd" ] }, { "cell_type": "markdown", "id": "112abab6", "metadata": {}, "source": [ "### A group\n", "\n", "All 2D and 3D groups that tile periodically can be loaded with `symd` (see custom group example to make more). Let's load a 2D group using its Hall Number (1-17 in 2D)." ] }, { "cell_type": "code", "execution_count": 5, "id": "c2986890", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Square\n" ] } ], "source": [ "my_group = symd.load_group(11, dim=2)\n", "\n", "print(my_group.lattice)" ] }, { "cell_type": "code", "execution_count": 6, "id": "9bc27558", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "['x,y', '-x,-y', '-y,x', 'y,-x', '-x,y', 'x,-y', 'y,x', '-y,-x']\n" ] } ], "source": [ "print(my_group.genpos)" ] }, { "cell_type": "code", "execution_count": 7, "id": "ca9ba39f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0≤x≤1/2;0≤y≤1/2;x≤y\n" ] } ], "source": [ "print(my_group.asymm_unit)" ] }, { "cell_type": "code", "execution_count": 9, "id": "a0be17ed", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Group(lattice='Square', genpos=['x,x', 'x,-x', '-x,-x', '-x,x'], specpos=[], name='f', asymm_unit=None)\n" ] } ], "source": [ "print(my_group.specpos[0])" ] }, { "cell_type": "markdown", "id": "6da7a14a", "metadata": {}, "source": [ "You can see the group is a data structure consisting of the Bravais lattice, the general positions (group elements represented as affine matrices), special positions (itself a group), and an asymmetric unit specified as an inequality. The group in this format cannot be used for many calculations, so we'll need to convert these strings into python objects. \n", "\n", "#### Group Elements\n", "\n", "Let's get access to the group elements and apply them to some points. We'll access them using the {obj}`symd.str2mat` function. These are affine matrices, so they are shape $D+1\\times D+1$, where $D$ is the number of dimensions. Thus, we need to add work in [homogeneous coordinates](https://en.wikipedia.org/wiki/Homogeneous_coordinates), which are $(x,y,1)$ in 2D.\n", "\n", "We'll just apply the group elements to these homogeneous coordinates and plot the results. Remember we wrap the coordinates here, as done in the engine and paper." ] }, { "cell_type": "code", "execution_count": 11, "id": "0595aa5d", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "N = 8\n", "D = 2\n", "some_points = np.random.rand(N, D)\n", "homo_points = np.concatenate((some_points, np.ones((N, 1))), axis=-1)\n", "\n", "for s in my_group.genpos:\n", " g = symd.str2mat(s)\n", " xp = homo_points @ g\n", " xp = np.fmod(xp, 1.0)\n", " plt.plot(xp[:, 0], xp[:, 1], \"o\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "adbafd68", "metadata": {}, "source": [ "Now let's try applying the special positions, also known as Wyckoff sites." ] }, { "cell_type": "code", "execution_count": 12, "id": "516620bd", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for sp in my_group.specpos:\n", " for s in sp.genpos:\n", " g = symd.str2mat(s)\n", " xp = homo_points @ g\n", " xp = np.fmod(xp, 1.0)\n", " plt.plot(xp[:, 0], xp[:, 1], \"o\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "2c6817aa", "metadata": {}, "source": [ "You can see the two sub groups: points on the line and the origin." ] }, { "cell_type": "markdown", "id": "f5362784", "metadata": {}, "source": [ "#### Asymmetric unit\n", "\n", "As you add more points, you'll notice that there is overlap:" ] }, { "cell_type": "code", "execution_count": 13, "id": "511a4833", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "N = 8000\n", "D = 2\n", "some_points = np.random.rand(N, D)\n", "homo_points = np.concatenate((some_points, np.ones((N, 1))), axis=-1)\n", "\n", "for s in my_group.genpos:\n", " g = symd.str2mat(s)\n", " xp = homo_points @ g\n", " xp = np.fmod(xp, 1.0)\n", " plt.plot(xp[:, 0], xp[:, 1], \".\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "9de5a84c", "metadata": {}, "source": [ "This is because our randomly generated points do not all lie in the asymmetric unit. We can load the asymmetric unit test function and use it to filter our points" ] }, { "cell_type": "code", "execution_count": 14, "id": "0d36c030", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "False\n", "True\n" ] } ], "source": [ "in_unit = symd.asymm_constraints(my_group.asymm_unit)\n", "print(in_unit(0.2, -0.3))\n", "print(in_unit(0.2, 0.3))" ] }, { "cell_type": "code", "execution_count": 15, "id": "292259e1", "metadata": {}, "outputs": [ { "data": { "image/png": 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Mo2O/bXOFfJZcZzKRVlfn497Vc/HUIfMaUpaEKXcazzd24bljMkuGAnjtbD8euqEGwWwvesam8PRhdhyFAFUFAbQPx2zRNHMWX7h5oeSQfnOmFx+sZzCcNer84ZsXHfkkBcDNi4vRMTyJAxeHAMpyDwRAWnN/AVMaxZnuCFSFOO61rlM8vPsMdCO5+W6M52F0neKj66pEjuPDFjaQnamUTOt4wsD6rfCVNCbbeXTKVmNWe2B9FRaXBnH/4+8gpVFQSvHNl5qQ1jIkYgkBBZuUfnGoA88e6xIsILtZJ3s+8e67MCgm5k2BbBS+3IbN8EEjQKo6iKyuCSBNAQIoIR985bnv8m7Ozq44hz+6cydGnvgxACDV3o6CHZ+BHp0Q3/ve+h2L/FUVNy3owuSyGyTnbmVnWP+2mhUf56brNDOzxbKtpjuhIoDh1w6Yw2KEQCTz7L8sRSE4f6AXuk4d9QY3PbDEnHx47iHX6zi2/bxu48i4KtAoJkeT7l8COLe/ByM9k2JC03Wg9cQgTr/Z5diWR9CCDmnJhfQ0j2XMq1i3U1Q2Cek6i+qXbCjDcPcE9jzV7LxOY0xamqJpbw/O7e/FDffXIitHvkd8bDy/we2eVXMlxgVgJkzdmDbSfQPw2N5WPLC+CnXlIQkXfuiGBRJDRiFw4MXH2kfx6MtNSKR0vH1xSLwf3GHlB3wgtoerA3jkV2eQtgz4zrpSDEYTEqxi3Y2CrV7cyvIp4MD+HfeNmEGEdVOeEPV6FEcOgJs18e2WwyBg0TmHXDKdPz/gc3zOk9nsGgBN113ZVgdbhx2TIc8zZGLn2OEe6wQwr3UC42kdhAIeAuSV5ICU5ECLJhE/PwJ9LIn42AjiLaOY89kVV5O201n0lVelv2OHDiNx4QKDeBSFe04QrxdVNy9HoGGetP3vW6AzHbOFEEtkRCE5E85jP/92L4twFDbJZOV60X56SEAylAILVhdjsCMqRfdlC9m2HApyS1Jacw9ZOV7s29kijX3l7VXwBzzovzyOyyczYOEZLNMkVbYohN4LbBWh63CsKFoO97lG0BwuEslby7E1jaLxlXZ86PMrxGdSQtlIdBMQbNouw0J7nnY6ezfTdZawr14hJ+IIARauKcbhl1tFXQXnbd91TTl2n+gRQ9Uo8NieS3jj/EBGZy+uFyxizPKyBCGHFNiX1KAHAtvXVkmRL8BWDpyKqFETDkoZzuj5xi5XZ5y2Rem/Otkj3RsFwOKSIM7ZGDE6nMnhmUwhwP3rqlAezsah1mHsvWC+Xzs2zpewcjt0c8+quVLie3lFCPOLcizJX2DNvHysrsrHY3vNPIVHJbh5cTEisSSOdYxB1xn/HTDhHIBNAta8itdg2mViHMVt76vbPchE2eT/A4AEVHZjNBbRx471G/9N5OVJml5l6cxkwTtux+SBA+JvT3Ex4k1NzOvoOrupqoqSr34FgQaZAhk7fhwtv7oILV3ooF5aMWOAzR26AU9ULy9CIOTDcPeEBKtwJ9vfNm5i8wQi6eco6gF7iQrKc3DTA0vw6x+dkjB9nli1Wl9rRE72UTNJmU7p2PdMi4CQOFRhx4mPv9KBmz62GKs+UI3OsyMZ2SvcsnI9yC/NQUF5DmKRpOskEY+moCjENUEMAJNj7isCStkKKhZx//7yiSE07euWKLMcEuNOywoLAQz2ybQ6cTNdp2izXdPcJfni/neeHcXhy8P4u7Mmt/2GRUWSM3vtXL/kRGV03Gk8GchxYZ4opGD3hCdGuR1rH8XOI05uPYzztPRHXamKrtvbHLjHozggEG63Li0BNc4/Mpl5VQeYTJcPr5qLV5v6pPtDAASzveJ6OXTDo/lESkeLkXTl1tQ7jjM9MnR4rH0UR9pGpc9uWVyMz924AP/0WouAmtK6WfTE7+NoLGnkd9h4blpcjJWVYUddQH7Ahw+vmouhaAJvnO+HprNJmBjnB0wozUrZrE0RDL/WjsRtqtNpWy9M4w+Ayi+K5ypLZ0bL374dAIv0g3fcDn9tLSYPHABNJEx+IqWMzWMxXrDl85eDrPj/Ah6fk3qpMmBb1ykUlaDuujL4sjw4+Vqn5NgUlWDp9WVYsqEMFbX5OPLyZfM7wnj7HJ92UBApK2BasqEMgTznMtRu1M7+tHmWgbYodn2vUUgXVNTmS2wkbm/9ohk3fWwxtnypAY2/a3c6cctx4xNp9F6MYKBtHCtuqXQdV2QgxiAcIg8pEPQiNu5CoeSnIcDZ/b3OxLDF9jzVjMHOKOZUBjHYyaJQX5YHxMBZ3VdbxJFz4asTj0fB8pvnsufIi5ls5x8fnpL+7jkzIkkPdozEpO8pZZAFP96OjfPx5NttrowVN7jGyvIhhCA6lcLXXjwNAqCuPIQnD1zOCKXoFDjSNgp1GtYPt5VzQzjTMy5h4qAUG2oKpUiaj7OmKEcUKFk/t68IeGT/4VVz0dwXdewDgow1CwB7X+yOXNOceYJMr4n9eAD73XK4iDtyj8KYSRSMhfT5GxcAAL724mk8e7RTql/wKAQ7NtZgPJHGc8e68PThDlbQRojA/jllszZF8D0E4L8YxVDbaamAKtEaMYn4OgRdiXgUhDbXINnDaM2BVVdZOrOy/O3bheMHgKqfPInIrt0Ye/FFQNNAvF4E1q2V9uEFW6F4KxpO/yuSH/wkaj9+R0YsXtcpRnonBWxhNV2jUnWslHCljEd/7kAvqpcXuuLyXGpgyYYyd+fHnSiFM3R0+QHwgige5d9wf62QdbDa3qdbsO3Lq/Chv1iBt1+4KNg6nEFiT9hpaYqhrqjjOGWLQujjEI4tepzJ2ZcumD6hDJj3MJPVNMxxJMW3/vUq7HumRVA8AcaWmlMVFInampVz0N0yiu7mUXSek51NybyQqJcAgPL6AuDspPh7ZWUYbcOy09+8oowV0xgRY1VhDh7fe0kkYwkYlfIaS1TJrbkvirn5AbQOTEDTqdNhzsJ0AAvn5ODi4GTGbU50Oe91WqdYVBLE0lLZid+2tARNvc7kPKXApaFJeFQCTWO1Ct8yNGOOtY/iYQNOsdpaC8Rhr1nIZHwlOx00pxqUHTv8QsCgnpOdY/jB6xeQNmi/q6rCONI2ajCkTCjMvj+/L4/tbcXty0qQ1ozCK42CkXVlyubwa+3wX4yCUGcBlb8mBOJRQNO6cPJ6LP2+SCnY7Yp0+HYLNDQg0NCA0NYtiB0+gsC6tQ44J7BuLYjPB5pKIRTrRFhvQl5kIVBb40gKcnNz9lbjXG+O5QNmklDXKC6fGILqISiuDkqOCGAOLRZJYt6KQgdV86YHFiMyOMUYLrYxKSqbAax0TKLIeYO6TRVobxp2HNdae3DdhxcKBxgdibs6WKIQeHwqi541KiqUeW3BTNCQfDDgxgeYvtFMDn8mazncj/JFYQfss+m+WpNdRdnqZ6R7Er4sj8DmR3omHc4eBPBmqZi/sgiTYwlBqfUfCmPnkQ4U52Uh4Pc4uPa7TvTg8zfUsCral5rQ1BOBZjJCoSoENy0ulnBlgFVpfu1FJ0/8XRsF1tcUomN0atbwDsASo1z+4f5/O4hUWodHJSgK+pHn94jqVMtpkErreGA9w+qtk5dbQRcB8H9/cKn4m9Nb3VY/1ntqPczWleWIJTVHXUBtca6DDkoArJgbwrm+qLS9TimOtY/C6zGrhTmclMkoGFxnldSwY//1UBEryMGkMgHoLHK3QjP+6jwU7VjOJoH/BCdvtSve4XMhNe7k7Y6eW6ChwVwJPP88xp55BpEXX0TJ17+GG+cncC42Dz1dabG9P8eLeDRztAqwF23JhjLMqQzi0vEBpFO6Y5LQdYo5VUGMdE86HCSjQhKWLzC+UlSCwopcXDo+4HrC6uWFCOT5EBtPIj6ZQt+lCKjOonfAFGhbdUc12k8NSVRQQoD+tnH0tUakCNmX5f6aUN2YtFSCuk2mwBunUna3jDomMuu5QBinn4vZ1W2qYEnsA70sz2BdybxLu3R8wCGNwQYt/5lO6YIaykXs7KYqBOff7oWusUQ4l4lYXBpEc38Up7sj8KiKyMNZbbrIXNMpHn25ScKVAUaz/H1NAUANL+n3Mvz8w0ZF77NHO5E2InAYVb1uDnbHxvkAmLP+5l1ypalHIagIZ6F7LC7tRwEE/fJ7cqx9FCc7xwROzu1zN9Q4VjOawfHnCVeORvWPx3GqK+IY5+WhSTT3m+8WT27bE80Auw/1FSGc7nYeh1Lgxto5iFurYG2sK7tJbCYAH1lTiXqoaIAHZU2jGNzfY2B6BIF1pchxgWb81XnSZ4n28f+UCeCKdviSkJrPh6qfPCk5fLfJILJrN5Bmjp0mk+h79FsApSgvWIS+FV80HCSd0dkDEOJsvKJXUYkrq8WX5cHia0sRG0+i7eSQ9D3VKcJlAYz2MrhA1yhe+2kT8gqzHecjANpPDQnNnMXXllqYMk65CGL8Eq3FWJdPDKHjzDBW3FKJE691sBXJDFiwprEqYwAOKqWiMqdOKaM1XnNbJZJxdn+thU5WWuzWv1klJcl5Erf9zJCjkCyTTYwkHMnd8wd7MxY2TWdV9YVoM+6rVXbBmqDTNB2rq/NxuM190rAbHwWXWbDyzuOpWV6kYR6V4JbFxSgK+kXBkp0WuLo6H/esmisVglEAeYYQm5VN9OSBy3jy7TaBS3941VxBX0xq1OHsuXGmjKqYOQu+sjDmdwDAT99pc2j4CEhbo5gT9At1T8J3tj22sVhKwC4KAa5fWITeSFwUtnF7YH0V6stDaOqJCHqo9VCKwrD7tKaLKthbl5YIrR03UxWCJbqCBqg4Dg3X+rOw6p0B0JQO6ewahSecBX913rQOPdE+jqEnTguI570WTLPale3wLUJqNJVizt1w+NJk4PEgtG0bQlu3OA+isR9f3sgFVPt6cHmqlGEkVEPVPD9GoyqiNuVLgMkf8IpQs6KXIifkkxgqVDcqVAnbx80dhUsCiA6ZOjSRgbiEJ4tjUXMyEWJrFqaMFbKRtHZsK1gtTXH8VQtcNAsfmYilJalic0wUpQtCiI0nULOyGDUr58zYg8Bay5CV40WwIAtLNpShur4QZw/0QEvrGO7KjEsDrDCN5ynEyuFtZ+QcCHoRm27yJkAg5BOwHgER8Fh+wAfFmMG9HgULS4KzdvjcKJjMAnfU9z/+jpA3mM4IGCUxmdaxfS0rIjrYOozmvmhGTfzV1fmiNoArYnLJ4V8e7cRYLCWcOn+IybSOw5dHZkXD5NvYBd7Ed4aztU5yB1uHJQKBophiaNMxWtstSXJFIfir22rxoz2XHA4/z+9xyEdbrSjXj/7xhMS//9yNC/BW84Drc1hWFsQH8oP4s7NReACkAfS2joO6wUCEsWwmDvVibPclRrN1ceiJ1gio8bt5PwTTrHZFO3wrLk9UFameHsSOH0egoUGeDJJJBuHs3o2Sr34F8PmAVIrLM7KD6TrKRhrR7r8DOlGhUA2L/G2YbLgBB3dZlu2Elesvu74cpTUhtJ4YNL+jmemIsCWFrcblBF77aZPk6DMWahkMlMGOKBauKcbFowOSXITd+SlMXkhcaqaK2unMzlQSl0VNDv7xVzrQdzki9SDgtFHApL4Od0/IAm/GZMgZUjOtOKzGoR2mA+Qcn6uztzCLPB5FwHJ7nm6GrlPs29mCQYXim79pQtoinLa4NIgXGrskdojqAvPYjVfQAnBVtTSG5HC6J7siSGs6zvWeEUwRfsu4Jj5gRvvNfVF8Y9dpsU0yreNHey5llEAgYPCF3YnOxjhLieP3HgXGGKk0yQk2khHNr6oKY8BQ4bTnHRTLc7G+anVleVhdnY+bFxc7ruW3TX0Oto7VuLPnlh/wYXV1Pr55d70kvcDtz1aU45YxHV5EoRqjKU/bj8oGG97CGD9juy+JAdOUjlhjv8nYaR9HeiwuXhQ73v9e23vi8AkhdwL4AQAVwBOU0n/IsN09AJ4DsJZSevS9OPdMFtqyBemhIUzs24exZ59FZPduVP3kSVlVEwAoBU2loI1FUPr1r2HsuecRPyOzC7IO/wYNoWaMhhYhP3oJJbf9ORK1+fB4efTHYJLB9ij2d18wE6su5s1SkU5qDsdqd7ZEIYKx03B7tcSuKV0YQlbAKNCyYPwlNXnovRDBQFsUA21RNNxRJWAUAA7nxxus8EYmcyqD2LezxSkdkeFXY5Utdpjt4/FBmd440BbFrn9sZEJgBm7vmGzsk6HtmGULQ+i/HGFwj22cCxqKAVgqcmdIJIeKs9Bwe7VDYuP8wV6pKvfQmx3CIWk6RVNPBA+sr5J0bs70RFyVGa1GIFMyrQJm3FSF4LMb5wv5YG48yWllinBLahSf/dlRjE8loVMIGWPrY1IIwcC4OzyTyewTmNtrQcBwc640ScEqkl9o7MJThzokRkx5OBuPbK7DGSNPwFdIHoWJmVlXTA9tqkE0kUZLf1SibG5fWyXkiO3mxp4iBKgIZaEnEpfuh0aBb/6KHYOvClSFgFikjTcFslEyFsOkQkB1QCUEnj75+GrYB//iAnhLcxgF0/bbmDzaj4Chk8OhHCgEWUsLoAZnpmL/IfYHO3xCiArghwBuB9AF4Agh5FeU0rO27YIA/huAQ3/oOWdjVsgGisKgGcOpxw4f4YMyQ2RCQLxeqOEQ+r/7D6Bx9x9CKNKKUIRF9P3f/QdU/aRWFFhFR+I4u69HYL2tJ1wSq4al4u44bbgkAFBTK4fqcsl/wx1VaDnch1gkib6LEageBTfcvxjtTcOCQWJP6J57uxepqTR0naL5nT5svG+RJPPMaYlWaKWwIleaAHiDkMHOKEtgGlLBVfWF76o6t3ZdKU693inr6Eu6vu77KYbuuU7ZealRSq8qBAXlOei7xJwqISx3kk5qKJrLxt3Xyr6rXFaAy6eGpHMoCozJhv0dGYhj384WLLmORfW88G4mo5AbnpzpieC5Y12SnrzH0FSyBq6EADcsmiP+/siaSgxEExiwJispRTDbi29tqWdwjE7ZsQhhldwKU1u0s2GshVF2BoxCgEe31AOAq3IkvyarEQCf3VSDn77D6glUVcG9q+cKjJwCqC8PTdvu8fnGLrHvs0c7kdYpPApBVWGOtLrRdODGxcVYVZWP3zb14c66UtxeVyr49QqAmuJcfPp6lmC2rlwIgOrCAO6sK8U7FpkGcV0U6BqLu/YRSGkUvznTa3YyM3R+ysPZQgMnltLNRabL+6qNJRE71IepxgGENteAeBUZ8tFZBS0AAeVAo4ifHwUoRaxx4H3D8d+LCH8dgIuU0lYAIIT8EsAWAGdt230LwP8A8N/fg3POaFbIxsgYAoDEwSd+v4B7OIYfO3wko7O3G5888tYBnvYjmKhqQLOlUYjHp77rcY/2xqAocBQK6TrFnqeaoajy55qmY7Azis6mEWhpHfu7L2D5zXMlxglvDMK3581AeD/dTL1kMzUX56yjBQ3FiE+mMksTW4wQJuHA6Z7nD/Yy/R9jwp2JiUMAbPporSi0sk9CvAENV9QEIPUqAHFCZllBL6qWFuDCERkG4Lo6/MS8iQpvlqMqBOtvrsKPfz2GlEbhVQnqy0OipD7TYkfXqeCyd4+ylY5OgVfP9uOtlkFjMjC7TTX3m0qYvFvWo1vqRfesMz0RDEUTeKt5ACmduiYluVGwCUc3WDrW3qodw5MOzJ3fc2o7RjDbi0c21wnBNjul1K6FY7XV1fli32yvKuiNSY06YCOvylQ4/+WNC0imdfz0nTaMJ9ICnqFgTB0ARk7C3FdVCO6sK3Uko+0W8KmYSMiBl6IAWV5VauyyvbwA82I60j0xxN4FvZWmdOixNIp2LMdkY7+QULDCNpyPD8CEfd5HHP+9cPgVAKw13l0A1ls3IISsAlBJKf0PQkhGh08IeQjAQwBQVVWVabNZWWDdWgg+o6HcFL7nHoS2bhGJW07DBCB9LvEgMw9WrAisTKAPfPdxXGxJ4MK5KQx3TeBdAc6G6TowfwWjV1r57/biL4Aty2PjSQFVpNM6/AEP5q8scjpiAlE9zJlDvRcigmbINfw5Hm/t/MStrzUi7bv85rkOz1C7rkTkDVSVYMl1ZdLkwVcTHEY6uz9zERU3TacY7IwKLXuFMMbP0f9okxrQWNUuRbI8g/hLPJpylauQjJqTJGcP9cdTaDrRj29sWIBoruooqc9kOoUr+4MnDK3/bdVct/dWffDaefj+qy2iipdXyYrFKtyd/s026QBuX/nQUtxeVypUPXlR0uYVZVK1rUJYW0TuhI+0jUiUUkkP36gx4Mwhzsjh1+FRSEbu/TVzQ3jkrjo8b8mHJFJMTtpKfdV01oNA0p4Ho5XO5OwBoDI/4KBxLtVVrDgbwUr4oC0rwE2Li1H4chvG0zrDs9y4t5lMIQ5WDoFcQSsmg6P95nEVvG84/vuetCWEKAC+B+DBmballD4O4HEAWLNmzSzv6jRmddq6Dm95uYOHH9m9GzSZFNh+oKEBBZ/+lFDcdDVCkHPddSj6yy9g+IkfixUBTSZBn/yfSEUroFd/yISMDD5aII/1TOXwgdCWJ4A/W0UiZkYbk2MJVNcVssjVeBEUhf2QrRh3IOyTHTtlXPrqukJ0nB4W0AmHOlbdUY3zB3vFBCE1BbHh2+mUsym4dd90WsfJ1zqFd8kvC+CaW1hTF28WW91kWiUAFg2cWQRNinEP+bl1SqX8CG9Aw88ltWU0JBdmS+mUjMjy2ed7o2jZdQkqgJHTY1j58cXC4fHk4wx+xtVUlUABc2Ic0+eCWz9886LUyNzK7dcpg0QkueAM5ygO+jNquPNzcayd4+7r5hfiyQOX0TowAUoheunysVgVI60OOqlRMbnxXrjWSTGtU3x0HZPl2HmkUzhtn0rwyF11aO6LYueRTumaXjvXj4JcH4aiJlRVkpcFrzou8h4elaB1aNLh7PkkyOUh2kdiaO6PSjUCd8GLv0EW+LpcPzuBHPgQ57BLmsI3L4isxYVIdo4jfnYk0+MECBDeskBQMq20y4BF595fnSdLLQBOfef30N4Lh98NwCqoMtf4jFsQQD2Atwj70ZYC+BUh5O73M3Eb2bXbEaVbWTqAk7YZ2bUbscNHELz1VqT6+xF96WVzZ4+Hedx0GlAUBO+4HYmWFky8/rq5ja4jfvo08vMmQKo+yNJoFmWzqajcak5IJlBIzh5gycyhjhaJsrZ0Yzl8WR4meWB8HB12UkIvnxhC+6khVC8vwvjwFIa7JkEp0Nk0gnBxAGf3WaI2A8h0dIAyrPPcKHovmL12zx8w2T32ZG35orDZwctQG7XLCdsbh4/0TE+v5IyZ6uWFGfMeVqfMjbcm5NBTu9Gv+N3Y/JVFDj2jphP9UAGjYQVF04l+3HQ9o1R+eNVcEACD0cS0PG5jyNK7cMviYty0uFhAJfYGHNbuWXa7bkEhIlMpNPVEmEZghnMG/R5HY3U3rJ23XXyhsQu/2LEB6+YX4NLABIOadbNwi4I1Vf+wQSl97liX62TDe+HmB3yWXrzAUDSBmxYX4znSCZ5v/9DyMrzQyHRq7BMn28d09iphgmdzgn4zGaxTvH7OfRXFjzGRSEPTTTnlOqi4Ex7cBR9UAMRYlSuAw6kn26IINJQga3EBw9x1CiFaZHHauZsq4C3NwfibndDG4q60S87N123N5EHxRw3pHAGwiBAyH8zRfxTAA/xLSmkEQBH/mxDyFoAv/2exdITpusTSCTQ0MNqmxwNqUDDHXnyROXSPx+ifyuSUc2+6CYU7PoNESwv6vvX3gK6j79vfgSffmZQCgND4ZdRe2InmRR+FUNgiRBQf6XaBmYxDNhKUhGHTvF8uxTSUTPNyHQ4undKlyQKASE5mHA+VVUOtDj437JdqEM7uZ5OBvdE7j7rd1EGns/nXMBXS82/3Tuusi6uZJg4/B59Q9j9zAemUzvIZFmTNtWuXi4WLA6LVI+8qVreyBCdOjwGg0AAsX1nikMS9s6502uOqCnDLkhKGvRtO4rVz/aLs/0gbczJWqeR7Vs3FmQyMn70XhgTbp6486FqZCgD/tv8ynjxwWWjHczaNtdmHvUH3841djki7NJQlchCaRZAsUwMVCogJxjrRvXq2X5KQpoBDsC2TKYyli0dfbsIjm+tE20NCyIz6/H3j7J0lAJZBxQ8QgBfsl0pADL4TyQjGjr/eAX0yBd7NJ3z3AnhLcxDd04n4+RGAAhNv92DiQI8pqcuhIKNPrTXqd5xIee9VMrn9wQ6fUpomhPwlgN+B0TKfpJQ2EUIeBXCUUvqrP/Qcv4+Ftm5hDjxp4b0bnHtrAZZ4NShlzl7XgVRKsCNACNIDjPWijUVMmeVkEun+DFEcIajoewe5k71or7wNQ4X1ACVQVYJN9y/FpeMDGcv4rcYrU4e6oiiaa8ozAAAlMzt9l2HJkr3Gi8YToW7nt6tPWqmN9oIzqlN0nBlmkxo1e+5yqYbpGpTbTfUQrPpAdUb+vPUahjsnMNgexbkDPUw91G1z/hkBwsXZUk+BTGadHPnkdZMhudx0oh/LV5bgpuvnOiCX3TM4LU0HBsbjgjdOITP34ildKGOqCqAoCtIaw73tMgXWy9M0HfUVITQb0sj27TSdQrfcCp4v4M0+jrWPomdsSkBEqkKwt3nA4UC5s7dTSn0exZXzrgAi0awqRHLw7D3JrHrpZkZJhrjfbzUPiNVVXXnI0XQmE3V0xdwQVnbH4aGACiKSwQCxd3uUTB+31tJQ6DFGedbGk+byypprc1SgycVWMn3KhILeD3NrYvOujVL6a0ppLaV0AaX028Znj7g5e0rpTf9Z0X3upk3ODwkRLJ3Y4SPMyfMSVUUBVBXwetm/bMCInz6N9o9/gnH3FcVxPBIISB8FN/8ZiNeL0PhlrGj6N6w++QPUdPwatzREULepAus21wgohdv8lUWou6GcFRgR09mffrMLnWdHcfyVDnOSMJgjNz6wGPNXFs0qL0wUxpLxeBVRmEUUgrP7enD+7V5xXuv2+eUBzKkKYuN9iwCwpG5Nw5wMZ2AWHWGdk8LFAVAAZ/f1YPf3j6OvNSJw9dmMl8suR0fiTBDOZR+isLyEbvCkdW3mCVBVCSIDMzt7QD6WtZftTdfPxRe+sFpAOVz8C3D+fjPZya4I3moegNeT+SdIAaR1s+pU0yluXVoiFCGtpoDBWhTAg9fOw/KKkOttVhUIOqIC02HzVcrTho7Mqup8UDD64nR2Z12pqPC9Z9VcrJ2XLzkVhTD+Ok888+bzHpVAJWySuPuacumYmV4PQpi66Le2LofHuAgKlgh/+lAHnm/swuLSIB7dUs8mR7CcwAPrq3D7shLpuKrCcgX3bF3KVt/gvwkjEFIIfPOC8vkDLvGxSqAEPBh87CRSXRPS5+DvrbVfqEHJ5IqZdvMUB6DH0ki0u7cM/UPtiqy0FRx8F3pl7k03ieheqsT1elHy1a9AG4sgsG4tE1HbudPcMZ1G5KWXhc4OAPBmKjRmOpDgXZuRtXARoi//h/gsNH4ZofHL0P71DfR2n0Zo6xZHw/TqukLEJ1PY9FGzU5NrREyAyqX5WLe5BgBrphIuDkjRKFEMmWGLUNucqiBqVs6RFDB5zYCuUyzbyPq+jvRMouVIP6gOIV8w1NkCgsxsF7tRnUoRdDrNouPVd86TOm/FJ1NoPzPsqo554tUOnHqjU9AI6zaVS1RMfo+GuyfQfmoYdBZLnbKFIWhpPaOg23RWOHf6HqNLS4PTFli5WUqjWDE3D36PMq0kA482VVXB529cgM8bjco5TMK1cbjA2XTR8va1jFNux/C//uJpUxLYUJGcKermEAwPhu1BMSFMUpk3VucTlwoqjcMqFkcAbFxUhLqyPKnQTCWsBiCY7cXi0iA+sqZS4PZ8LHy18oWbF2JxaRDPN3aBACLHsO/CIJIGw+vRLfVM1bInhknrwPnPTaNQAnKby5w1JZh4u8cRvU81jzgSJ4E1JchZVYJEawRKwIPIy60iacuZO0U7lmP4F+ekFUO6L4bxvjYQ7/ujqXNlOvzDR1jDE7t5PCjc8RnxJ1fIjB0+AjUcQvzsOfFdaOsWjD33nNDSAYBUp9xhSC0pAVEUpHvMJXzi7DnkrFkjh4f8vy0SDvN/8iQKv7xKwpvd2ipK0syERagen4rGV9rRcWZYKDjOW1EkcG5KgYKyHAy2RcW+A+1R7P4+S77yBuHN7/RJxVcAcPhXlx1Offom4bMwyuSZOb7OGS99rRH0X87c/JxTUDkDx65+2bSv27VPrZv5slUMtkdnzB+ULQyhvzXiYOVa75+VdWTF7+3mUYDakiDO9rpPMBTAqa4I/F4FAZ+KWNI9Kc2vL53W8dieS/jcjQscbBveIWs6J80Tyvb+sc19UdbIw2K8qG0mPJxfh/Vf67jfOD+Az924QCSeeV0Bd8LWe6eArQb+6rZaHGw1J3EC1mnrp+8wMTaPqmDl3JDQiaKQVyvcuADb80by2dpXth4qw9Ct74PtApI9cm1A7MQg/LX5SFgTubod4mGDyTGYOOmxOMgYXDXv/dV5yLu1CmMvXnTe09T7w8W/Ih1+YN1aBsnYovHSh7/BdHRsKpkA0PHJBxljB8DYiy+i+t9/ioJPPYiRHz8JUAri8yHvrs0SXVMbHHQwgZKXLmFi777MXH5LtW/p5xqQF2nFUZe2ipyrzpkmRXODSMbTOLe/x8Gv1zRb4oeywqQlG8pw+OVWpu9OmcOw0iztxVfHftvm6IT1bk2SObDYYGdUUg2tqi9E++nhjJOJWAVToxTewsABWHJ2tn1qAVY5zKtxzZMA+aWmEikAjA9NuZdgUGcSGsC0/HtNB3oi8irzmrkhSZ+FR6azUdrUweCLt1oG8fRnNziYPIpCpPvJUCbTaXP4483mAdy0uFioRCoZEp2f3TgfrUOTMzKOph0zpSLqthZsra7Ox9dePC01KL9+YRH+6rZaIfJmvUeACW0l07q4VzzyH0+kpZ+APfnc3NiLzeEg6muK4a/Ow/ibnWbBk5sRgNpqXvTxJBLNtmekADlrSzHWd4lF/gTI3cgCk8HHT5nMHQ8RDcmtypne0hx3waX3KXF7ZTr8hgaUPvwN9P3doxZFMAJtLILY8eNo/+SDTBzN60X1v/+UrQhSFmpUKoXhJ36MiT17BLaf/4mPo+TLX0bycptJxeRFXTabeOMNJ9YPiLwAr/bN1FaROzd7kdPia0tdnZGqOs812BkV+YLeC6ZkMadZbrxvkaP4qqI2H54MzV64BQv8iI4mXL8nClBdX4iC8hypYIwLufHjamnqWp1buSwfRXODDiE2XQOGuyfEqoBDUg4dIktSWlUJFqwuRn9bxKHSyTZmeZBrbqnEvl+2iHqFjOJ2YDh+dCSOX++6gJOXRpAo8KJ2WVHGZCUFk/E1Tge/V8H2tVU419ckFRypqoL/+4NL8WpTH37b1IeVlWH8+nRvRtVM3qTcKoHc3Bd1NCdXCcE3767Hb870Sk1LUhqVRMYopQI24kcgYFW111SGHU1GuBUEvBiJTdPBDAyj5zkCXnTFWUhWGqfHULzkk9iZHnlypnBPCmsUGE+kHdG8dUWxQvFg07ERjGvDplol7zqVacVHCOiEy7XZ7nHO2lLkri9DengKE/u6GUNnfw9SQ1PytkZD8lTfpBBTI14FgVXFzoy1Ibz2x0rL/KM0f20tsletwtSxYwAA4vMJbF4wd5JJDD/xYxTu+AyI1ysifKgqJt56y4RzdB0jT/4EsUOHoeRZHgKlzIlrtnCWAeNOWoyqImxIOAQaGjD02OOubRWt8sBWimPMtnQkCkR1Kde9sRtvpm6P9I+/2m46YCNyzcrxoqAiB6mEJkW9Vlu4pgRjAzFXh80nq+Fum7oiwYy4uaoSLGgoxqXjA65CbCff6GQ6PgdMHR+pKE0Frrm1Ct0to8gJ+4W8QkFLjphAJZyfAhvvW4TCilwUVubOjOsTtn/T3h5QUOQCyAbw/57tx4M3z8Pj+1qnXW2U5Plxy1Kj4IbaerMaO95eV4pgthcbagqxbn4hdh7pQEleFmqKcvBv+1rNYFElkg7NR9ZU4tBlZxFQSqM40xPBX91Wi0Otw64TiICvqYzBUzAq5eLSoMSssdrqeQUStdRuC4pzkeNThWSzNUJ/fO8lQeMkYBpC1hWLPXFbHPTjFzs24IXGLvzySAesDNChaEKK5vmKgkM4t4zpIIf7JR583s2VKNqxHLHGfkwe6XMWL2SCsmyUokTHOIZ+1oT4uRE5MXt+hOFM/Lgeltwd231RfEaNyUvIKyiAWpgNb1E2i/zfB7siHX7s+HEJooGiMNljAPGzssTPxBtvwDd/HkLbtiE9xJxYemDAoZTJi6ocxitprVLK3OwOP52Wqn2tSeNwvBslS3Ror+5EzICarNWiqqo4ourcsF+qZD3/dq/QmZ9TGcSx37YJvHxBQzG6z4+JGgAhs0yYo07E0rLMs8WKq4MY7IiCUuD0m13YeN8iqVsWn3i42Fh0JC55DxGJE3as4c4JQdusqi9EIOQTNQaZCsBGe2PSJKTpFHWbTHYH319L6xjpnkR1XaGUF2G9heVjNh/uY3mO2dQFUEj788KripSC1871zwgtDU0k8MvDHVCI03mmNCp6qXLZAS533NwfxeduXCCkDwiAgWgCrxlRd1Kj+MUhd0VWClOG+OmHrsXzjV1Ce4fTLpeW5bny9hXCouzRWNJVqsBndKba0zwAg9SC6xcWYa9lJcH1cU52ncbnb6gREbpOIRQsGfWUoK6cvcM8r1BXHnJg/nxC2NM84GAPWbfdUFOIRPs4FrVOoL6GqaUONQ5KSVPAUuVqf/yZeJwUjhV9ujeGtFtwpAPeubmAhwBpipy1pYjbk7sGiSe0uQbx5hHEz41AG5iCNjCFeMuogIDeS7syHT6voOWm65jYu4+pYNqTuZQyXF5RDO0CmhGqcTXu9WwEd+L1glpzCACgKALK4TkEa9K4/7v/IHXnKm1oEKyWitp8RxQfHUngxX9sxNLrmVbN1r92TwJz+MYtcuba/Uf+43LGS0xMpSQ+enwyhW1fXs06UY0nEcjzSQ5XUQ2+OIzaNZi8/DlV7Hz2Tldc+4YnpyuX5ru2hBRGWacwf8AjGE18xZJO67h0fEBaHbHnAumHPD44ZbKgCJBfEsBofywjXEXFprw4B+j06FBSGrwep347P+Waefkm64VSVzYLhYlRW+WOuXzBt7ctB8CqYN9qHpiWLFURzkLPWFxw83nEa9W84fIJ9eUhIdKmKgQ6YPQnhtDV8SgEtyxhujhWNcyDrcNIW3R8OkYy0113nejGg9e6r4R4q0cAkmbQN++qk4rPvvbiaTx7tNOxoigyon9HQjZtdpCy9pAFgPE3O1kCtSbkiNpBIRy19Jn131mYlaYpMH6rUWDycB9cVe8MCOiqw5+FiaStBWpJDwywSSCTI+cFVVbjEXqmBKyqgqgqw/8tx82qr0fWsmUYe/ZZc1tFQenD3zCrdTUNxO9H1U+eRNHnHhLwjr07l122mFMpxbA1BjPwStDVd86ThMMEfJMhik3FNQnDlq8frqsBq6PmMgqEmJ21ZIE3IlQuz7/di7P7ehxMJACO1cy6zTVoPTE4baP4E6+xrlyqR2EibpYfZTqlSwqaSzaUwZflkfR3ateVskpa45zltWGM9cfYYYhR6WuRVuB5CX6aw740ejw6bi8P4Qc3LhBOdCiaELi3QhhT53R3RESgd9aVShWlD22qwe11pXjBkA4mnH1i+IBnj3airjyER19umraZB8Ci5btWlAsJYztzhRtfTXBlTk7vfHj3aTZR6ICmm7o4r57th9+rCCE0blbJh3ZL1G4fY994wlWRk/+ZSOnYeaRDgmZGY0l84eaFONY+mrETmEogxsTHJRKyNghH0rVJ6QIrD29ZgLFdF6UERlZtvgzTcPMYCdZMD4EASsADfdIW7GVobsRutst3nqtJ21lboKHBwbAJ33sP+i9cYBG+m9N3K1vlf1udvqrCt2gR9NFR5N21GcFbb0X/d74rwT1Zy5YhtHWLEGbj8gwAmLO39Mzl2vypnh4m85BOswRzdBxDjz0uMYlKa0K48YHFrlREznUvrQmhojYfikKYE7c6bBfLVHFKFMbdF9i2hf/vJqRGKeuNS1lwKkzXmMplsCALukZdJRf4tVlXMwDrojWdiYYkmo6hLhmD770QgaoSzFtRJMa6ZEMZQnOyBevJH/Bg432LJMllq+BaIM8nIDNOY02ndBDCnP2+7DQ8CvD5GxcIh8OjZ68hpczkDth1DkQTKA768WFDlIwzVninLK6L/1bzgOQfNN3UaJ8pwNR0ip++0yacuJtWjp3Bwh3rQz87KrBxCrMqkz/SRErHoy814ZG76sT1/mLHBvzTay3Yf2FIcPEzVYBbnb19UqAATndH2P5gExefqJ5v7Mro7L+1dbl0fYn2cSQ6x8UJiEeBEvCIiD7RGjETtTrF2O5LCG9ZgKylBUIWgXgUKEGfbRkG5KwrRWBVCaaahjB5rB/U7tSNC3E4e4BNFJmcOy/QMr5Ti7IR3FhxNWk7W4sdP46Rn/1cJFXzP/FxaGMRlHz1K5jYu08SPMteswahuzYj8tLLmDqaoQDYIoAGXUfy/HkAwMgTP4avshLhe+9Bn8XhK8FcxA4fQclXv4L42XMYe/FFTLz5JmP9WBO8igI1HDJZQ4Z2DzTNpH8qCgo+/SmUfPnLAFh/1sKKXOx7pkVKNBJAyBgA72rl6WpUB1Svhf1DIeibfa0Rd1ljyiAitwRoVo4XhDilGqzGVzN9rREcfrlVgqAUheCG+2tx9kCP4/iqqmBBQzF6L0QkhpGmU6kp/Pm3e7H1r1cBgCh6s7ZO5PCXdTXCV04AUFlXIJrM5Ps06Gd6UVeWJ+m/C3lgVcH2dZWot0XmBEwd8tEt9fj5Z9az6PXfTC66SpyO0etR8MH6MhxpG5EifAImD3Cud1w0GQeAZErHb870SqwXq0ltBQnTnQeA1iFZyK48nIXeSFz4KApWIbz98Xdw35pKEVl/sL5MsIBcYG7JiPF/M00IIATNfVEcbB3GUFSGYRcW52Ld/ALHamPs162Y2GvRbVSAnGvLMParS0LHJnz3AhnCMZw+18XJWVsCb3kuw9stlrupAuEP1WDiUK98Dn5RxPbgLKYWZyN4PaNqRvd3Q7N0fctaVoCsxQVI9kxAjyYRPz8CbXAKY7+6BG9pzlVIZzYmMXE0DSM/+amI9ENbtkjbTh0/jtBdmzF14oTzQIQAigLfokVIXrggO37Doq+8isC6dWZYQwhGfvrvgK6D+HzIuf565sxNviBbKSgKCh78JMaee14aq8N0XUws/tpao+HKWmy6r5YJkVlw4ybDQVXWFcyqWIoIXTcDjrFjq1YYiDCq51tPncf5A72uEBClwGQk4WjTyGEjXWf0v433LXJo7PPcQ3vTMNpODUn7c2fPC6+4iqiqECwx8hcAsPjaUsTGk6LlI4HsWLQ0ZROVBRazwk8c+88ryharo3RaR+Pv2tmYjE0HO1vwTDCBDqIJR8dxbiH/q7GuSPbInIJJAz+867RoPG7timX4JVb4ZCRGi4N+LC4NCpbKs0c7kTYqkHkDc/55SmN6OfsuDOHAxSEBF1kpnLwRycO7TiOtU9HW7/KgrdAoqbkGpGmN4ulDHXjuaCc+sqaSvx5ShO/m+4jxLGdTzJVK66LZumpoCFHKJr//cc8KrK7OR6J9XETuqb5JpyPWIUsPaxSTR/qQu7EcE/t7TMKFbn6vRZOIvdzqoGtSo1HK1BkXET8F8BRmgQQ8DLe3wTfawBTGXrrkGuGrQZ+owmUn4jtRTFp6375XdkU6fIcZjlRw7a34vqYxp+uC0WfV1yN+7pyI6N0seMft7D+s8A9vpxiPy/LJBo6vjUUyt1JUVTNxbLGRn/0cqe5uKan7gQ/l4PyBLrQOh6RqzLZZygCXLgixityOKAba7VEz044Z6pgQkXAmR2+1yVEnj73lSL/J2KGyWNuMCpoEuOa2SsQnU2ja182Sz0YCeNNHa0UrRkHX5FK1LjArIcBI76QjuhQQBAU6z46CKKNSPsCu1Ek1itI4QVuW+VlapxJfXadw0AetplHgR3su4ebFxQ4IxOoPeXHUs4Zz/fCquUIgTKdUqEWWh7Px6evn47F9rWLsOgV+tLcVT+xn2LnPYypjnumJCN+T1Cie3N/qcO7Tcew5tv/UoQ54VQKvR5Eap7x8qtchYFZdGEC2V3U0Hcl0fK7xz4OXFUTFf6+tQD1Uh8a8ku93HsRDoOb5YL2KVNcE0v0xhLcsgB5LM6rkry4ChjvIpHHP+9Bm1xchcWFM/lID0gMsas+9oQJT50akKB6AO4avGoJtGepenOHlH25XpMMPbd2CseefZ1i5qgoHT7xehLYaTc0tjpj4/a6JWeL3y9W61u+yspB7+23I374dQ489nhm4tJquI372nNlKMWlzjh6PmBDiFy9IevzJy5fFMahRGDa1Zw9o+a2g8/8MIGY7ReswsoIelNWEHb1cAaC/dRwDreOmE2cLGhRVBhEuDogCKKIAeUXuCpOFFTnIK8rGQPt45qIluyPpmRSU0e6W0elpkdRMzloTw5Sw3MDeX7ZIqxl7RzDpUBRO3R4DWnWlkWYwohL0ZTlVHu1ntjp7t9fj9XP92NM8kDGRmdao+IvTL58xHD9vQpJMmZEwMSS47caDx0RKF/BTU7f9PmR2L6V5fnzx1lq81TzgKMKixjhr5gRweTiGtE7x0skerK7ORyjgExOWlYopTmm5VoUwrj2XLubH5tvUQcX3aAC+s2MYPB9B1pJ8KTFrd7C+eUGEPmjoTTWPSpE1TetI9UxADWeZJ5rJLKJnar4PmktgA4A5++Ep5xcKzGSIYTlrSlhOoHFANDJnMxxb5lkbpbxXdkU6fAAmHq6qKP3614QoWqChAdjxGUzu28ciflXF1KlTLCq3Of2p48czMnRoPI7oSy9jdM0axqf3++Ueum6m6xjbuROR3buR/+cfM2mglu35hFD0uYfQGZtyrBD4NfHCsPyxFij6ndBVBYQQ5HgTmEia0U48mkb7mSFB/SPEdGgS7MM58l0TGGiLSjg51TMndwMhHz70Fyvw9gsXJQZMfmlAMF5Ugy3Dz9t7MYLeixGoHoIFq4rd75X1XovVLhWSzQohQkvoXZl983exOyHAvBVFWPWBaqxXmfOMTqXwhCHyJUHQtkNnwqwzFS1lspRGsbd5QEgYE0KE858p4KAADrUO4/uvtjhqAW5bUoz24UmkNOdENjSRwOLSIEZjSalCl1+nDuDS4KQVjcDhtlF4FODRLcvxmzO9Iqlr3e/2ZSXYawiaEUIwOCFj9XVQcVtONvZMTWGFrgrNeuiUJVj5QG0YUtayAhR9og6J9nHEGvud90VhEbtDu2Ea48lfSS7BzdKaxLX3lAZY9K9TLrgvEsO81SGnjLLVxqWZB/MH2Hsij/zHZpLssaZBG4ug6HMPmQVPDQ2o+vefYs5f/RXC99xjbsurY7npOnJvvtmUSnax6CuvChG2nGuvdZdUsBlNJATOL50vncbYM8+g41OfRuz4cVYBnJXF6J8+H0of/gbmfPGLCG/bJl7i0PhlNJz6FywlTajseBUTCZ/jBdc15jQVQrDyNotEslF6QBQmMzCnKjhthMy1Z6y2oIE5bL9NOna0L2bkwQg2ba/Fso2yBC7AonHeWMVqwQJ5eU4sY7zhfuNYxKnHPxtTpukrz3Maqoeg4Y4q0fxc9RDU3VCOD//31fjQX6xAaU0Iq6vz8YWbF+IrH1qKnZ+7Fvevr4LPo0AhDM//nFFo5DiH/e/fY93eNRYHCMH2dVV4dEs9fB6FqfHaZJMLcnyO8+27MORaNcu1aDgGbzVdh8gBWOWcPSrBirkhEZjaLa1DVPr6vYoYCwGTmfjcjQvwyOY6oeVjXRHdBS/+FQF8eJLgB8jBtnAQivVqKIuQ8+6Yh/CWBSD8nfYqCN5YKSCfyUMuVbQcS7dF3K5GAP+iMIp2LGe699M5e5XAWyarquqxtAXuBQJrS5F3xzxJCdNfnYe8myvZtpZkcqI1MyX597UrMsK3yx6r4RB6//abAMxm5fx/sePHEXnxRRNesa69KUXuDZtQuOMzGPrXH2Ly7bcdzlQpyEfHZ3YgeMftKPrLLyB27JgZ6U9nHCpSFNY+0cD9reJqgXVrRZI5tJX9Gzt8BFnLljIKpzHmUKQVoTf/F46v+IJ5DWJBbJquU7SeGEBNwxzRZBwECOT5ULuuFDUr5+Dc/l7XAi0YRwuXMI18rlHDE6lZOV7XfXRKEZ9Msa5aLiYxgQwrqgpiYizBmEIeNmFYC7Xeeur89BOTMdjC8hwMd5vMk7JFIWipzPLIXCKan4dLSVvrDtzM2g/Wmhy9va4U//RaCw5cHHINJgmAsnC2aCgCzKxPwy2t6agIZ+OB9VUi+Zsf8OFvf3UGKY3CqxLcWV+Kp2xVuJnu2lA0IYqo7HkHYlAkV1fn4+nPbsBjey6hdWgSNUU5qCnKQVPPeEbRPf4GrqgI4UjbqKBcPnjtPLzQ2IUz3RFHErcOKv4aWfDAKHLTgTlj8j0hHgXe8lzosTS8pTkIba7B1JkhZNcXzSyOpsO9WMA6aGP1QDwKvGU5GH+tHd6yDEJnYJNC3m3VmGqS8z1CSZOwMedYGpgDwMShXnPcXN/HVhH8XtqV6fBtssf93/6OqYT53HMofeRh5G/fLrYNbduGsWeeccArADCxdx/8tbXwzp3Lqmc1DSAEWUuXwjuvWuDskwcOIHjXZvgXLYKnuBi++fNYFG/PARjMH540Jh4PSr7+NcTPnmMTj5FrUMMhpulvJGmzli01r0NVkd3QwHSCLOMtHjyO0fylBvsAaLijCsl4Wkq2RgbiEi+fUiYYdvyVDoTmZOOG+2vx1i+aXe8rpXIC89QbnahZybjjl44PuD8MCiRiaSa34GLjQ3FULs1H1/lRxqL1EHScHgY1Fj8rbqmUZJH7WiNSX11XM6Jd+2TSfymzY1IUgiUbyjDcPYF9z7RA9SooKMuZtgm73ThF8LE9l9A6OIGaObmudEpuFECPxdkTAGvmFeCN8wOid+z8wgBahyZd+7tyOqW1BoDrBVFKUV8eQpaXyRkQwpzuiQya/UVBv0Ntk1ttca5EPX3T0M/h0gmZTCGsA5WVdgqwBPdje1ul+6GArRhuWlyMsnNjUKi1olkOXLxzc6Hk+SS6Jb8pybZxRme0OE+ohMkat4zKkT0/rG0WDm9dKFoWJnsmBPsncWEMuTdUQE9ojELZPCogpex6Vu8xsc/GFDLMv5BNCFZnb6WRJi6MIbxtoVQR/H7w8MlsGkf8V9iaNWvo0Uy8+HdhvX/7TbmRCcBEzO69V0T7omEKZ/HYuPLweESv29xNm+ApKkJo6xYW9R844Hre0r/7JgDIip2AuV42KGG5t9yC7BUrpC5cgXVrETt8BIP/9E/gRV9ZdXWylg+XgrBNKN1l12GgeBWW3r0aDR/bwMbQGsFvHz89rRIkABTPC+IjX1mLX/+vU7Nu+D3/miJ0nh2ZNvFKjIRVpleN0y7jkylER+KS0qaiEGz7MuPO2xu3yCdhkM/ym+eiu2UUQ51Rh3bOdNZwRxVCc7Idkx1RgBvvX+zQ4nezpw514Bu7TkvO2asS/N3d9XireWBWMsOqQlgRG5gG/E2Li5ncgK2BOQFw//oqVISzRfT9tRdPSxH9A+urxKojP+BztP6z2taV5XjpVG9GyqRCGMvnhkVzZi2XfMeyElxTGcb//J17AGG1TYtMaeRTh7oR3N0Kj0URQ7pwnjjIYIH1pSjYtkiSIQaAycZ+pLon5M5UNuP4/8ShXledev+iMOZ8ZjkS7eOsh61RjUu8CnyLwrJWPh+ypZkJH5MS8MjVvWATWclfNmS+sFkaIeQYpXSN23dXZITPLXb8OOtrazdNE41IeENz64qg79FvmU6fUpNHn06z4ildF4nXTA5f8PPdvBynXqoqJvftw8SbbwIej6SkmWhpMffVdaRHbC+SHf83rKL3bVQMH0XB2o+j4zNPIHjH7cirrUVerBuTKMJ0ZK+hzij6WiNY9YFqdDQNzwybABjrj80oPjYT64XDPrwxixVW0nWKxlfa0dk0Yur0cC43Hx5hVcALGopF43JXm2YZ7w94XFcpVAf2PN2MworcaSP9Y+2jeHj3GUckntIoRmNJFAVdaIMuZnW4r57tx94Lg0JH3pr4tGrdcLqlvUCJwIz+f/jmxWl7HZzoHJu2a5hOGcunddDpLK0AIj+Cz8Mw+uZpKJh1UNEAFVFQfL4gH5V9cYw2XsBcAMrGCiE37DjRDK9l7Fi/BJ3EGvvNJC1vPeiS7AXAKmyRgW8PMFqmVZ7BMJrWHY1QfPPykLW4QETrcuNyZ+Ij1TOBRPv4+9bPFrjSHT5P3rqZBSvn21plDPq+9feseMrjYc/FgHK45g5NpaAG81Cw4zMYefInDsxe8PMt8A0AwOsVrKFUTw/T2zGaolsnIWv3LQBSVy1h/LiEwFNczJqtGxMUr9SdPHAAIATlwXnoveavWNYyQ6aQUgjMesl1rJjJ2lZwsDNqFjZpAAhz+JmMv9OqShyTR9mikIBYPB6z8ra0JoRrbquUGD/WQixNo8gvCSCd1DAxmhCJ4exc37SaQewC4er0eb/arByva3N5qgONv2tHyfw8B57P1R1Pdo65RscKYZWtLzR2ud8j53Ck4SZSOp48cBnzi3LgNRQhASDgUxE1ioFShg78Wy2DYl9VMVv7AXJ1LeAsjLqzrlR0lHL7no/n8tCkIMdY2w7ylonRqRSaesdFk5ODrcOu11gHFT9AwGDeEJBD/RiDZeVg20nJ80GPTr9CFZamjJ0DOLtaaRQ560qhhrOgT6UcxVq+cpZ0deXbqwTe0hyzAbnFiEeRG6F4CEIfnA8AIvkqNS4HdaFy4X0RTLPaFe3wrclbUWxlcZLEoGQO/fCHoOk0iM+H/D//GGKHDiN75Ur4FyyQkqWiWMo4XsruhA3Hm1VfDwDo/+4/yM6eEIS3bRP5g9jx40xvh+v7UAqaSJjNV6w2HfRGKdLDw6z5uqY5E8aUIjR+GeV9b6OnfCPsUT5R2JvHZZJf/H8aheb8nPuDWH3nPGn7pn3dTJrARkW0mhWm4RW0l0+yWgBVJbhuG2vRZ0+K9rVGcPpN2TkyVIvRD0GdFFFdp2g5PMuuTC4DXrimWFT6BvK8iI07k6Ztp4bQdmpIEn6ztjfMtG4qC2ejuS/KJj6XKlO3+0dgVqRSMJnhiwMTTHLFcLbc2ROw6lMCCH15twNz3RsO73C5B0KAu68pRzDbK4moZYJ/hCa/wvrCPrC+SnzHRc5SGsXbF1mEvKGmEH6vInUFIwDuhBc+MGfv+g7ZJmdHG8EZbPJIH7Ro0lExa6VDjr/Z6XC6kZdb2fliaVZE1TQMbTguLn78tXZk1xdJ+YHA6hKxovCW5iDW2I9U/yRGnmuBNhIXs6O/Nt9M+lq18i1jez8StdI5rnQMn0sRT+zb59TK4TIH/B7Yq2MMjL1wx2dMRs+u3UgPDTEefzotrQCIqrL/TqfNyN5ybOL3S43SrccUhWJ8XG4yC9MVdykKwh/5CAA4evFyi+TNx/FrvghdYfwHHukTAiwzmoTvebpZgmAIAW58YDEAiHaIg51RCWdnKposnNd0xpHnUgi8kpYpagKhkgDCJQGsuqMapTUhNO3rFset21SBY79tw6HdsoSux6uIdoxuEbjdvFkqUvHZA/i8N2omk9otKsD6u2uw+s55+OGbF/GPrzQzijVjcGZk7XHix2xo9wRMI2c2TdHnFQbwj/etBABsf+wd4aQVAH/zgcVCbdLa0Ht1dT7+4dfnRHet3zb1CeVMXon71KEOVtClU3iMmcbapUshwP3rmLOnYDLLO490SGMmAL69bTkWlwbx6EtNSHdNoAEqIqD4K2TBZ9nSdcJUAW9ZLlLdE9PDOJmWSdbPVSIaiwOQm4vbV4WGjgPxKAhtrpG3Mdg2oc01SPZMgABiAhG4foZqXT4OX2UQyTa5l7NanI2Ce2rfk+j+TxbDByAgmsF//mfnl7bo2+FQKcXE669jYs8elD78DaFXz78DpaCahvC998JbXi5DNICE1Ye3bWNMG5vmPaeHApCZQlanzwu0pjNdR9aypdDGIhm3DSd70XDyn9Fbsg49ZdcBYPAOpUCwIAuDnVEH3k4pJHXOzrOj0gJBUYnQ4wecEbu1axelZiOTjtPDWHGrCd10nh1FZHAKNSvnSIqVXCuntCaEwopc9DQ3zijvUDQ3lzUsdylZVxSAgoBaWyhmoqFaGrvs+2WLmMw4/LShphAehSClsc5T37y7Hmd6ItjpIqlAYdbe8K9UhfFQNNswvR7WCvFM92lpgjBa1Epwy0M3LBDsoEe31Asn7fOarQW3P/6OaH+482gndlw/Hz/ayyJZa/Ur7xa1ujpfonty1cof7bkkCq90ypLU0z0JCuCR3Wew83PX4ta8HHwIOjzG56rh5Hkg72o64KvIRapvMrO8MD+RPZlrO2hgTYlI5FolGUKba5DqmTAxfu4DqIHLx9Io2rEc46+1I3FxTHwebx5B/PwoQClijQPIubYME/u7p00mAwA06nD2AJxSDO+TXbEO39pkJHb4iHvEzM3jQfiee6AEc6Um5cLSaYw997xTWllRhFyDiNZ37xb8//w//xgS587Dv3QJ1GAe4mfPuWreAzDllI19c2+/DbH9BwBVhTY8LK9CLEJtYnJRFLFyyFgdnEggFL+M0PhlBCc60bJoOygUqApcG6yI/ey/NcvfS68vw00PLBF/86j98MutovG628JE0ylajvRJnx1/pQM1K+dIMslcPZNLMWz6aC3eeqpZGoOo6qUMnrruwyZclJXjFbASZwGd3eeSD3ExK1WTw0lulVMUVDjme1bNxXPHuqC53X/HBxTb11WhPJyN/IAPZ3oiUhQOQLB+CICNi+SOUltXluOB9VUij7ChphA7P3etVAvw9RdPS71u0xrFrhNO6qACNgGd7BzDZ392VMg4f+HmhWKblUZ/24zX42K6zpqY3x7MgRdRqCDQwOQ6oE9HIQBAmLwABRA7ZHlX3CJ6Cviq86BF4tCTOrIWhRFvGhGO3RrZWyUZ9FhaSBiko0kQAHGDvskhFn91HvJuq8ZQ27iAcaxRPE3pzgSzxXzz8pDsjE6/vKMsufx+UjKBK9ThC5qlEUmXfPUrJrXSxbJXrmStB9etha+yEiM/+zmSl+QSZ+L3O7xWzrXXougvvyBX8BpsHy06znj4mmYyeTweBgEZXHstOi6KtvK3b5f3dZt4uFkas8PjESsCnlMoffgbMtPISgU1KJ5zm48iN9aH0XAtyhcEkRcpRIgmYPVqVijDzYgCEdlzxctELC1F7Xw7x74A8gqzHWJr3S2jWH3nPOHohTqnobQZLg44xmPF9DkibG8cw62vNSJaQboNKljgR3SYsV20NMXbL1xE36WIqa6pUaHlb1W61HSKb+w6jTXV+RLn3LFotJxOVeXWfXZbXBqUqOL7LsrMkctDk/jsz47ijfMDoNTsb2s9ptujy/I6y42Xzw3hbO+4RLl89liX1HVqQ02hax5CXCtMeIyCJWbXEA82BbJRGVAwSvrZKkclyL97IabODImoWRzA8t+5G8uRaI3AV56LKa9islsynN8aOU+dGELuDRVQsr0CFx998QLS0aTA0YVcwr+dklcQiql9b62G5Rz5ROe4TL/MAClxWWSO68dbI5kjeQ8RqwzRaP2qHv7sTAiTGZG0NhZhTtDoNAVA+hVOHT8ump1nr16Nsr//FutM9ei3GFPH64V/wQI5B6AoCN5xu3D23DilcvAHP3BG2ek0cm69FdkrViB+8YLEpEl2dkIN5iGwbi36v/PdzBdnGTcv2prYy6idY888g7HnnkPWsmUIfuiDSLW1w1NcjNwbNolkM/F6Eb73Hkzs3Qf6xhsIRVqBdqB974vor7wdqPqQmCDmXVOE9lPDM1ZRWnH6TEN2RPmEwUi9sGC+xkoDkBPD1uNk0vThpuvAS/9yAhW1+Vj1gWpXp184N0PTcgrh7Lk5xNbA+g68daALJzrH5MQiZRoy9mvPZDfWznE4e95AZSCawNnecSkotB+L9aI1x8cF1rje/gPrq1Bf7rz+DpuImUchqKsI4ZQtZ2CVKOadsTKkWM1InbKJeRllLBwfJVBeuowxnYIYKxWuTGmNmolHQc61ZYzR4mFwj4iaVSBrcQGUoA+KX3XKIGewRGsE4bsWYLKxH7Gj/VKEnbWsAMEbKxmbxz7564AWTTocrr86D/7qPAz9rEm+fyUBaMNxY0IC/EsKkHcjk42O/KYVyfZoZuxKBQJrSgEAscN9YuXxfrF1rkiHb5dWcNAt7fCO5e+po0fR/vFPoPrnP0P1//65gIUSLS3yPrrOjgUI1g3AVhec0ulmnqIiBNatZUVVFhv58ZMAYFbzzmSEILRtG/y1tWJi4tcSP33aLNLy+VC44zPO3rl2WeZ0GuGRZihz74BOVKgKk1yYLqlPAaGFw3F6N1MUICfsl5wppUD3Bdk5zqkKisjerauX3fLmZCE6HHfkHZJTGi6fHEL7mWFs+5tVwum7TSLv2ihrdZgCRVNuEvQP+AW9cb4fX3vxtGjkYW+GYjeFAItLgkJeONNVWPX2R2NOdou9gOu6BYVo6o4wnoHlSytTKJVmTVXst84e1XNG1YcoZ+HAFX8f23URcz5/jVM4zA320JhsMfEqyJ5ObM8Waad6JpzRu2HxcyMI3liZ8R7Gz424cuInDvWyYiuLpYemEL6LyS1bOfcOoTW3kxEi4Caumvl+snWuSPE0Dq3M+eIXRWIUAEtozqZBeTot8HUuuqaNRZzCaOk0+r7194gdPy4+mjZfoKoMq9+12zkGngS26/BwzN5uRu5gxvxEMonIrt3iWrSxiFOW2bDQRDsaTv4zatpexspT/4J5+VGoHgVEYSyc+dcUSfAMT2DyfrREYYyahjuqULksHw13VGH+yiLomjNyVggQi8j0x2XXM4G1xlfaZ3xEABAdigsJBjfTNdbw5Nhv2zI6+2Dh7Aqi7KYAqEy/u5/Pwjk5mBs2RfQ1nSU+P/bEQTx1qAP/9FpLRmfPWT7nZ6ElDzA/83xjlwHDyN95FEhQ0d4LQzjZFYGmA+vm5eP2ZSX42PoqfGtLPfxeJszGu275PIrkNBQCfHbjfLGdz6vg+xsX4c+ILxP3RpyYR7F5N1ci2TMxI4WJcvqrmuG4KoESNrk/0DFtL9nJRlag5TpMCod4WaJ93OiOZdtWo9BjadE3F7A1XpnONLNZedGO5Q5htffarsgIP5OJyH8mcTNVZclegzIJsLaFrslQTZOSr5JUMnfWRoer0oe/gUBDgzimqxnyx0Ku2ariaUnchrdtA8B64Wakcb7Le6Dm5SE0ypK6UFXkdhzHli9tFwnU8wd7pWg6YPy43PrR+gMeJGJp9NiLVwwLFQcc8ExkcApvPXU+YwOXQNCLWNScJCwihBnt3IFeUC4j7BLZ2yciq/kCKpIx9/uqA+j0uL9DwSwPonE5X6QSoGN0ytWhxw1N++k6Qa2ZZ2jl2D5XiFOAjdvF/iheaOxyvLKleVkozPXjdHfEEbGf7R3HdQuKRB7AytTh8NP/87vzQuBNo0xpk3P8N9QUYlHrBJw8FJupcpPuaZO3lo285bnIWQOmgmk3jcJXnov4+KhZGebSyc16Tn91HsJbFzJHbm3Y4nVG2YnWiHv+QCFIdI5j9MULAvf314Tg0JkW20NwdP8zuPdWuyIdvj1pW/UTBpdEdu1GzvXXw1NUBCWYi9Ff7gSdcNHVIAQD//g9TDU2Oh28HYxWFKGDA8iJWw4FRV95VSRmASBr2dKMY/eUl0MbHBQibURVWZKXc/yNhK8SzEX7xz8xsyongMSlS4gdPy4ooHx8k4cPI2aRhtBGR8U1cQG31L9/H+UA8kq2AMiWjhsdTmDX9xqx9a9XSf1oZ+pgpSjEFYs/8WrHtJF9bmEW5i4twIUj/eZ2hK00MuUZuBhY5hIxdgwC56LL41GQhNPhF88LYs6mMrx88CIwOOn4PsujwBGHEyIXRtnMrqdvGx5qS4I43R2RNHVUheCzG+fj5VPurKNjHWM40uacJLrG4uiJxJlujyafdyKh4ZWz/XijeQA7H7pWSDMALL/wzZeaHJNWaTSNRa0TWBzIgd46ASXgYYVJGd4B/zKGcVujWOKfRreamw6MvXSJFTB5iFHARMwCCJUwQTNWfo3w3QscPWSt5jWqanPXM+LB1JkheMtyRKLXgeHXhNwTtBpF4uwIEgAmj/TDvyTfmMAy5DuyPQjdMQ+pnglo0STT+OmbFK0O/+iTtoSQOwH8AIAK4AlK6T/Yvv9rADsApAEMAvg0pbT9vTi3m9mTtpFdu5mmDocyPMZluylZGpo5GRua27xCtoVHD8h0UACCdx8zksLaWAQT+/ZlHLvi9yPN9fkpRWjbNsEg4temhkMsT+DGOvL5kL1ihTT+qaNH0fHJB1H17z+VxqqPu8dhanExQpv/DH3f/o64Z5EXX0TxRz6Ps3QRKOGkZ1PT3s67t5s3S0X9DRVIxtNoykCLnAnGGWiLYrA9Kjl7SUPHWPITxdmj140ayiuMCdyjf7eKWwAY7pzAHDCWjJsNTjghM2pULhOwDLY9mrf3elWN4h8Kpkvz4VVz8eFVcyW5ZV2neHxfa8b+sdOtGHQKEJ3igfVVmEykseuE/EzSGhWcfG72/rt3wYu74MXS8xMYP2cpjvIQZNXmI9E2DhpzvqNq0CfgEo53T+x3NgbP3VSBiQM9MjSSZs4VKhFMGoBF3+mxuEh8ApTJDi8twMSge5I33jwi2hxyZ5tsG0doc400Pm7+6jz4qoNIZpDX5jfWTUDNanQyjbHdF9lLaVxbzIKx/VEnbQkhKoAfArgdQBeAI4SQX1FKz1o2Ow5gDaU0Rgj5CwD/PwDbnUd7b8yetAXABNC4uThK35IlSLW1Obn2M1j81CkRPdtXFqEtW8yJJx43k6uZjk8Ikq2sIMbO8eeWaGnB8JM/yUgx5Wqe9gmLT3yRXbuZDHM6nRH81vr6BKVU7J9Mgvzin1Fbdh2aF33UyGcQqB6zEAmAwPPtEf7cxfm47sML8dZT52euipzGrM7e41GwbnONKMqyQkqHX26VqnKzgz7EIqYj9gdUFJTnoqA8B3Mqg9j/zAVoRgXUTI9f0ynePtg9K4iWw81eg+XyVvMAzvZEWBMTvo3C2gh2G58RANvXVjr09QHgr26rxaHLI6IxeqaxVhUE0D5irqKWlgZx3pB4ENdBgfJwtjin9TuPSkTBFTfeACWZ1nEXvPi/kAWAgNjn9zRlPPUMOE3MImQWWF3CNrMfgwJKthdZi/PdK1c1imT3hAmhGBOHaBdImeRw4tKY+yDAEsHxsyNSNRxN6QZO76RHJtrHkeycXhLa1dw09HXjIi3XCx6AvI8wz3sR4a8DcJFS2goAhJBfAtgCQDh8Sumblu0PAvjz9+C8GY3DFlwGIT00xHDuTEJqANTcXAS2GP1u9+yZdlur0XQakV27ETt8BKmeHmllkR4akp3qTDi7BaPnHH8AGHrscQEP9RmNXITZQlcu3SxJNRjbjT3/vEPuIaMZeQeJy08pKnrfRu5kL4auuRu5N9/k0IvneH7jK+1CO0dRCVZ9oBoAELNpogSCXuQWZjlokhlqx4SF5mSh4XaTdmnn3a/bXIPu5kYB6VidPQAkYhp6L0bQf3kcS/6mTEg3FM0N4tQbndMqhSqEIFngZWtVw9zmK59HwaevmyfExAC4SgtrOoSzB9jkwJk7dtrm6up83FQ7vUSxAqBz1FqbAKyqzofPozjkGvIDPiwuDcJv6OYDQHl+Nr5w00LXcz/92Q14obELf3ZuAhhPT4+9U2SEQAAwkbNDfVLrP2EehvFrY+59FADWkHzw8VMI320yZERVLM8dzYx4OmlLvG9yWpeKoWKN/bNLxHJTGGyk5vmml1swtvVV5YKmKXLWlv5RJ20rAHRa/u4CsH6a7T8D4DfvwXlnNKmTlceD3FtvRXpgAPGmJoc3mTp6lEXFvLkIx+89HmQtXYr4mTPu4RSlpiMFmKdSVRBVZdDNLJOpkikKiv7yC8zBc9VOnw/eClmT3VNSgqL/z1+wxiipFCuqWrYUgYYGVP/8Z4js2o3EpUusN69dVI0QRgEF2HeqitxNm9iYDS2gggc/CT3KIhprFXJo/DIW35aP/O1LkMk6m0aYs1cIbvhorXDGgTyftF0smpISsdx024+wckk+upvHRMVrZCCOvU8zqizX7LHLOmQHvTP2AOBMnuZ3+qCldfReiGDT9lq0nxlmKp0wcue6WU9wzW2V8K8uxC8u9okesA9tqhFqkwQ2Lfu0jiNtI1hc4t71y25LS83trFW0XOPm9XOms/eqBDcvLkbnSExE8G6R/7NHO5G0OSsCYDSWFMJqLzR24dmjnegdm8KjLzdhcWnQ1emvrs7HRLmsF5+1rABZiwuYTMERo62gynB0SbqAY+7WCZU/awXwVgXhK8kRkXuqb9KMwA2oSHKeGmXwCIVYMWTXFyHZNp4xhzCtWVaQUInlWgBvhq5t3Lxzc5HqnTQnBZ1NSqlMsyIBvBWsmUuieURARWN9l1gTlz9GSOfdGCHkzwGsAXBjhu8fAvAQAFRVVf1B54odPmI2NAEATRONRjo++aD5naPmX5PhEEqRtWwZEhcuyHRG7pEMzN+6f+6tt8JTVMR0dX4Py73pJgCQcHqaTDrGquTnI/rKq8j9wB2I/ua3gKah79vfwcTefSLSj+zaLYrK5J0VlHz9a/DX1krS0KM7d4pJZvR//0KitfoqKx0JaDez4vg6pbh0fEDoyS/ZUObewGQ6o0BiKo0b7q+VBNR0nQqnv/+ZC9DSOlQPE1qbVhffYkThuQhWR6BpOuKTKXzoL1ZIk0jriUGRVD75WieyJmIC9ycAqgpzJKYK16DnKpGptI7ivCwAkcyDMex0dwQfe+IgHtlcJyYMXvj0yO4zwp8QAB9ZU4n68hC+seu08FVut9bu7AE2WVhhm46RGNI6FeO1Y/hWsyY6s+uLxN+J9nFMHuO6NIC3NAe568sQWFUiIuVU36Sj+QcfePbiQvhrQphs7GdCZM2jzOEqBNn1hUgPuUT8/DEbK4YpL9PImTzSN22zk+nMvzAMmtJMvF4DUtZVKAHD842iKuJVmO5Pt8v5MiG4HgXhuxaw6l3rJJamf7wYPoBuAJWWv+can0lGCLkNwNcB3EgpdeXCUUofB/A4wNQy/5BBBdatlWEcowALAGPAzMbjGFFwaOsWZC1bKmnk+xcvljtQWa8jHje1cWbICXjKy+EtL2crCkoBrxeFOz7j5Nfz8JJjHYqC5PnzcMSvySQmXn8dgCHGxvd1MW0sIom3je7cyfIDxv2x6/34a2uhjUXgr62VjmNNVAcaGkwc38BSO8+OovfCcWz5UgOGuyec738GlozVBtqiGOm+gI33LUL3+TGzQYoxoVgd9tkDPRmdffG8oAQfzVtRiCUbyliEr+lQVVmbn2sDWRlEuk4x8fYgSnIV9Hh0aJRp3vz91uWS9gzXoE+ldXg9Cm5eXIzLgxO46MLsAYBcv4rJhCaajew80iFNGKzwSU7s1peHjGrYzPduOmSFNyj52BMHRRtGxeDdb6gplLpG2R2QtzRH9JTlJvHP0xQjzzQjeMNc5K4vkznqGQY6eXIA46+0OQerU0ydyNCFzXZxXCMnfNcCqfjJtyiEVM8k6OT0cC3xKsi7rRpjL13KuE3W0gITNlIIQptrDAmFgVmvLLLqCsx7qkJUIHM46/2w98LhHwGwiBAyH8zRfxTAA9YNCCENAB4DcCelNEPz0/fBeKGUoiB30yYAjJpph1nU/HyTkmjZN6uuDuF772EJ2cNHzOYn6TTT1slgXHKh5KtfMSt7FUWGigxL9/SYzU08HhR84uOCiQOv12QWUSr0fbLXrEGqsxPpfguO6wZ6T5McJpYJEGDOXsoP2LYZ3bnTbNfo8aD65z9zTVRX/eRJlDY0YMuXGqTEqabpOH+wF+f298rsGUORMjaexOVMP2jDePR9zW2VzAGDFYR5fCoUlTFtFEIw2OHOoiAKK+4a7mwRipsdZ4ax6o5qh2AbYOjuHOx1XZEQAHVJFT0evpIBHt51Gk09EcFhd9Og55RG3sMVhIjPJhKWJDmAMz0ReBSCtFFHUFeWh0OXR5BK61AMPfrRWHJaNg63tfPy0dgxJtE/NZ3ikd1nsH1tpUgCKwCuX8jaDdZDlZQlrQnMiUO9DErR2U7hLQuZU+e9ZA2npw3HBfTDVwH2baRnPIN0Bjclzwe1wM+ibvvlKwRKwINEawS515djYn8P63d7wWWi4YQzA7YJrCkV2vY5a0sx1uVsc8jN2sxEj6Xhr87LuLJQwz5QXdb1nzo5hMS14wy24reCAOG7FvzxYviU0jQh5C8B/A5snnqSUtpECHkUwFFK6a8A/E8AuQCeJSxR2EEpvfsPPfd0JnW70nVMvPEGJg8cQM711zu21UZHZW18o19svKkJfWfPYmLvPvjmzzMdqq4jceGC63lzb71VwB32yl7/ggWYOnWKOXFXCUmNsWOMCD575UpHo3IArvUBgWuvRezgwelzBnzFYkg1825fgYYGjD33vLSpp7gYeXdtxtC//hD+pUvkrl7pNIaf+DECP/xXmQKbTGLoX3+Ior/8AkobGrBucw16Lxw36JIEsfGkRH8khPWLLazIxfmDvSAGVi6PGSJEVVUFWTleHP2PNkMZk9Ed204OQVEI5q0owlhfLKPeDtWB9qZhVNUXip69uk4lwTZuM9YTwD1ifupQB55v7BK68tYWgzxaVwhzqh+sL8OLx7twxKa/I46nA6X5Wegbm4KmUzx54LLJwSdMXA2AlHB10xZTFWBhSRBbG+aiqSeCXx7uEEG4plOc6WYTi6ZTeD2K6C07+uIF4ZStVEFWcXrRdFI6k0qIN49ACfoQ2lyD8dc7JOc2eaQPuevLxIqB68nHjvbBpdRBNgtlkZs+nszYActXGRRMm+nE1syDmf96wlnC2eauL2MyyC4JVz2WghVD06dSGPpZkym7YGtwoo0lnawlarRfPNIvX5sLlfW9svcEw6eU/hrAr22fPWL579vei/O8GxPUTGs3qVQKnqIi98pU7uh5VasF9pl4/XW2j8VJ6xFntECyslC44zPOMVjpoXwSslbhigNYzqvrmDp+nCVWeU9dbi70lVRXl7yNy4SSVV+Pkq99FQAcaqL6pAwzKPn5cptEm6UHBuRrNJz+5NtvI3bsmIj0N963CHueboau62g/NcTaHWoM3y1dyBzsdMJr/IegEIKN9y1CfDIltqW6+TvRNOb4Z0LqLp9gY1A9bEVghXCs1t0yyiApuxEGI+kAmv0abrBJFlO44992eOeD9WV49OUmxGdY/lsraK04POfJf+HmhSa2b+DvtuECFPjl4Q6RB1hVnY+j7aNc9h161wTuV3woWFqIjTfOw+rqfIbFH7WsIC2Vsazi1DZQCuEYYyqBrzIXSYvD1xMaJg71OoqLclaVYPT5FqQHptGDz/RM3T73ECTbxy3OmDrxLPsEYml4YodSgjdWIn5+xHG9di6+Qx7ZDUdzWYlQQJ6QyPsH5wBXaKUtIFMzx158UVSoZi1bitybbsLEW2/JnHguYcD/226aZkoRW7c1LLx9u4Mzbx0DwCpsrRNA/p9/zOS7c8iHM2qMceRs2gQaj0MpyIc+MgqlIB/Rl152DC/VbtSxGTi/b9Ei6OPjSPf2iuuJNzUh0dJi6unw+oC/e1Q+mKpC4RNUBgvfe490jUP/+kNMvv22mFg5VXU0UgqqZQNEha5pKCnzob9fAyjQeyGCvosRU4KZuC982Nes0XlFbT4rUnJJQs42EaxTKnR7MllWjtfxe51/TRFWfaAahw/1oNOj45/Wlbv2qiWEID8gs5FWV+eLZuQfrC/DaCyZUTdnVtcAiHOMxpLQqXulLq/upwCSaR0P7zotJX3roOL7CMCjAzg/gaLFcYy3djI6pMURBVZbpIJrQqzSNRN1VaMgAa/k8LTBKYnVw1cMSsDjcPYk4IG3IgfJSy4Ti82yVxZBn0xDyfFAn0wDXsUhXeyrzjMnAYUgd2M5Jt/plVQ6U72TyK4vclXIDG9Z6J5kNiYKqfGK5bwOU8Fe8DTbJ3djObLriljtQEpn1cFb3j84B7iCHT4AkZDkbJX00BCrHk2nWdOTe++FFptkDtTKTVcUJw9fVVH68DegjUUQv3hBcroFOz6Dki9/OeM4Irt3S9G0tcVh8NZbRTHUVGMj24HnHjwes5WigY/HDh9BdDqSOstcInn+vPM7XUffo99C6SMPy5i/i3yEnpKpksG7NiNx4SJSXV3IvuYaaGMRjO7cKa6l6C+/gNgRgxlFCJtk02l4QjVQ6r8AnQAEOvp7kwyL4cXnlFE3KaGGRAIkz202QlcEvr7k+jK5xaLNiMKUNytq85GMpzHSO4l4NIXIQEwcSxRbpXU0v9MnVg882t//zAXHBNJ+egirPlCNu+9n0hjH2kex84jZbF01WlLplApaIwAHhn+kbQSPbK4TET8hwLyiXBQEvFhYEkSe34N3WoddtW64KQRCCdPaeUsx7pfYjxB4FRj9BIhogVgHFXfCg8VQ4QXrQEV1WKAQ8YhEAxEOxygBD/y1+Uj3sAS8J5yFZMe45PQS50YyZ4uNYyoBD3OkNqOxtDve7jgI4C3Jhb8mJHINUImj0CnZPu7oPZtdVyS3OTSqbN3okDz3IDl9FYL/n+wcd8A+npIA0oMxGa6ikHIKk+/0wlOYjcCqYlBAjO39tCvS4Y/u3InoK6+KTlNqOORkzGgaa0t4+LC0r5qfD23EidmVPvIw8rdvR+z4cQz98IfmF4oCPTohqm3tFjt8RJyXJpPQxiIo+txD4nsupibBNqqK8L33AoBomSgYM3bxs+n63LqZrkMbi7DaggwsI6TT8oRBCGhsSnwWO3DA1OAhBPB6kbtpE6h1hWRcTyjSiobT/4rRvIWI+8PoKb8eAI+MCFSVYMWtlRjqisLjVQW2zo1PCBvvWyQwds6qyYSvU52zeiZFw3HATMICwGBnVDB70mldyDGrKmur6AYx6Tpw/mCvON7zjV2wbja/KBetgxOCVfPYnkt44/wANJ1CNZqw6xRIphjjhjcNt1bS8sbo00E9BKyoS6qEJYZntYnE6TpF/dwQ6ipCqC8P4eFdp7GEqvhnBIyessbEC4OiyvcVEwbgXxQ2tV5cxpWMppC1pEB2etT2r8XUwiwU3LeYQUOzfXUtgmN8Hw7BWLtYQaPIWVcKCiDGOfQAkKYSPs+rc0cy5ClczTZWPjkk2scdsE/aLY+kg/H0jd+rtarXqgCa6pt00F3fK7viHL6VbSKwZ95b1ho5GgwULTouYdRuzh4ej6AiOvj9uo6xZ55BZPduibPOTQ2HzPPqOrTouKic5SyXseefl502pUI/x9r2kO9j1bbXxiKYOnVKUDFnNOM4ajiEPovDVwoKoI+Ouk8ehGTW/6FUooKKz4x7TlQVoWgbQmOXEMmbj77SDdCNd7s8NIXau1aLSFtRCIgi95sFTDiHW2lNCBvvW+RodWg3TdMlnR8AosBKUQlL+moATB8CTaOIjSdFX11KIZ2Dt1uMBj043Dosna8g4EWXEbWrqoLXz/WbDEWrEwZw4OIQjrSNiOQut4OtwzNCPYQAj2yuE/sdbB1GWmMsG7smEAVrlNLcH8U9q+biW1uX4/yLzWBt7GXcIXtFIWsLaHXqBjbvhmML0ygSneOORCUbLKDkeKFPmM8veMNcCx1RjsYzmVqYjYJ7a0VUbtWeB5jz5xAN5/zbx6JPmWNItI8j1tjPksaWsbrh50IWWbpmU97ZX52H3I0Vs2rM4i3LkYvC+PMyaghMLSAI2ud76fSvOIcffeVV54eG8qTVvPPmAYCoJJ3WKBV89MC6tSyRai3CMqJ3znrhmH1o6xZM7JUd5cgTPxZRcXjbNia/YIOPiM/ncO7WJi78X/65Gg5N7/AJQVZ9PbKWLRN5hkBDAyaPHhXQlO420Rn7QtdNeuhMRogEXVkno9D4ZTSc/GeMhhchP9qK6jtWo/1CkYi0dUoxpyrolFkgBNGROJr2dQvYZbDThY5nM3tC1tpQXbNEim625UsNjEZ6oFfIMwDAcNckhrtakQJFLDcp/YKOd47h7+5mVMnusSk8fajD5cjMMhU38eTudBG+ToG3mgfE6iA/4INirPQUhUiTC2Amkpsbe7E5HMTKG2pADaqp9VcxdWoY4S0LGHvmWL+zGtbNofNzRDMwSygkZ281f3Ue5jy0AmMvXZqxQEobnmL0RcABu1jbD0r1AjZ54on9PfAUZpuVv/aJhkKcI9bYL2AWV1lkG1deyfZmhK+spic0+BeFM0st2PafOjN01eFPZ8E7bndllajhsMS1T54/z+SFZzIbHz3Q0ICqf/+pKVvAq3J1HZOHD2Pwhz8UzlEUPtnNiIrHnnnG0VQla/lywaThKwErBARY5J8TCSYFsXKl8xyqKs5FfD6UfO2rjtWHPjLq3M9trC7Hzr3pJmiRCBKtrdJkoeTno/i/fVFQU3tt2j+FwSTmeC8hGW3H2LOtIAUnoFzzRYZO6TqyEIeqMvhDIQRVywvRcWaYKWwaQ/F4FcyZN32ZOyHAnOqggHBKa0KiIEyIpGXYN5DnQ2lNCN0to47VhrhOsAYoPRZN/LRGMRpL4gs3L8Sx9lE8c6TT4Xyt+3ttsAxvb7iiIoRj7aPTBr6vnx/Aa+f64VFYpls3nP2OjfPx03fakErrqIOKlfDgOE3DoxBsOjaCcW0YIY+CnE0ViJ8fkROmlPHJC7YtQs6qEow81yJJC6vFASgehUXToHLl6bswqxPzV+chfNcCCYP3zc012wJy0yGSvsTrlA+2CqiNv9kJf00I4S0LZNxdpw7de8koHMnZ2NF++GpkiMc3L4jQB2vk809TW2A1e6vFmSy7vmjW287GrjiHzx3N2HPPI372LItOvV4ENl7vZLdMoxjJLau+XhRfceMR8tBjj0syDDH7RDMTts7ZPrwGQFWZjENLi5BV5slaSYL58BGzRWE67S6dACB8770CGnKTcPYvXeI6OUpmTxArCgo+9SBGf/Zz185Z+sgI+r79Hbka1+MRTKR0X59Eic0bbsG19C1c7vWip3gdOi7Hoagqlm0sx5INZTh/0NlwPJ3W0Xdp+qQepawfbe9F1rSca/ZvvG8Rzh7owdR4EtERl4JvwoTW+lojjophu9kboNgd+KqqsKsePQDUFOdi3fwC8fdM7Q3txlsKpjSGObFcN0XUaEayf08b/uxsFB4AafgwUhkEaWcSxjSlMzliHSbThAIgrGCJmzYis2e0vpiZg/QQZK8scla/Zmr6YTFvWY5wytxRWyP0RGuEOfwMRlM6Jhv7HVh7on1cKhQLba6Bf2kBEhyOmsXY3Ior7AnkrMWFrmye0OaaafX3+fEcRoDsa4owdWqYjU8FvGW5yFlbehXDn435a2sRvO02hO+9B9pYRPRxdRjXxefcd5cEaPzMGfRfuAB/ba3DaU6dOjX7QWXkG1IUfOpB6NEJjD3/vBn1G5OBXd4AMPICtmNIpiggqsrgIpvZK2MLdnwGiXPnBe0zeMftANiEyauJJW0hXUfk5f/I2CYRAJBKYfiJHzPVUYMOm3PjjYwK61L/4NvzAvxzbwMlCkBUUJ0iWMBaAZ4/0Os4PCFwFGiJvrkuTpxr9g93T0zfK9dYkvN+uEuvL8Pym+diqCuKxGQaAxYnlF6Qg55hU9dlWVkQFfkBvNDYhea+qNQoxG2lf3FgApcGJvCM0XA8E01TAVAezkJPJC75Kp4EJsYN4RW0zx7txIdXzcXSFIEHgIef3VooBFiKjSh88/KQ7IgClGLsV5eQMtg30xZEpSkSrc5+Ct6qXPir8gTNEWARPadNestyJEqkNVLXxuKYbIzDV547Y7QcO9rvYLVYk7c0rZvRugLkrC8FeRcN0Kczay5AnLt9PHNPXm4uiWcALE/SNILwlgXi3r9fjJ0rzuHbHVrJV7+C6CuvMvgDEJIJWcuWMX2cb39HcOzD99zD5JFtCUiaSEhOV5zD3gh8Gsuqr4d3XjWiL/+H7KAJgRrMY7kEjuXz9oZGxys1HBLQSGjrFlbBm8k8HuTeeCMm9uwR1xF58UXR/CSyy2Qr0VQKajAPVT9+QjrE6M6dbHWUoWpX63NpL2c1SjHx5ptiZUCTSVaoNQ2VNH/8EhRdg26wYgvpILpbnElIwGDOqiaMUVVfCFBGm8xkIz2Tcqcsm9k1dnSNStRPRZFXglODcZTrDNIhYJo0Z3vZ/qqtmQmFu9OnYMncb+w6jbuvca8L0AEMRBNYU52PYx1joJTC51Hw4LXz8MT+y9B0CgVUHF/TKZobe7HG6zH8NUUaQKgoAAy4t3NkTpIKlsvkob7MfWOtYxt3TvqptihS7VHkrCsVWLs1Sh1/s9N0ykakDkBqNh4zVDaTPROIHel3j8o1KqSLeRJXCXjYuPmKUEA57D9pwuV9Jkz2QBudZY4KrMgqu67IMdnYnb13LqOMiqIsQkSzcyXgwdSZIZGYpSmdSTL0TjLdoMaB96Xr1ZXn8K00yERCCJ5ZxcfC996D/O3bMfTY48zJGtz1VFcXgnfc7tTDp1SKqsU5rMahIXu1q/FZvKkJiQsXkHvLLZh44w2JghlYtxbDRlWrMO4sdV1SzRx78UWUfv1rmfvYUsomImvzEmOVADDnbz+3uC6jh+/Yc8/NStbZt2ABlEDAXTra5tzj5865Vw0rCuDxoGJVNbLp2+i9PIHwSDPiB3tQ+N3HBeZu7UpFKbB0YxmCBVlIxNI4+Vqn68QgjCCzsyeskUpFbT6L4DMchk8uOqWglCJvXMN98OHZYBL9Xio5eEc3KwKmiaOxCl2789cp8KuTPRlzfkmN4nDbKDwqwUfXVuHDRmMUXmxFKZtkKKVYoXiw6dgIiEZBVQW9BT6E5wRQsbgQY81jzgjUqKB1JE1dItWsZQVQgj5MnR3KnKQFu4jJQ32YPNYvcd8BmL1eeZ+CY0Y1rxW2M5qCe8JZmSEYAjnxSiAaiPAxWE2PJqEG5WI4T3E20sNxJnsgPiRQ87Omh2UoHJCSW9Tvrchlk4wlh8CbnXNLXDITwtZnQFPvT9crZeZN/s8yiQZpOHLBVzcYJ/3f/QfEjh9n21q445MHDqDvW3+PwHqnnP/Yc88jdvw4AEOJ05psNVgwUj7A40HpN/8WOdddJ85Lk0l4iooYVGI4Ot7Y3FOUITmTTsuTTyoFbSxiFk/ZjKgqg2WslbKqilRPD4vuLdIO4W3bHKuWsWeembWGv5qfj5KvfZVdzwy5EFDWrjHnuuskUbusujqhdeTb8wKq236LUKQVNJmE8txj+MCHcrD+7hrccH8tPF4FRGHsmyUbypCV48WJVzumd/aAqxInIUDDHVXYsKUGG+9bhNNvdmXO4hqTwjW3VQI5qoESECgAlnv92LFxPryWiFi1rQYIgG/eXY+/+cBifGfbcty/vsqxDaWGv5rG0hrTvQFMNo9KAJ9XwaNb6vHXdyzG/1hcAZJm0TrRKMqHkwicG8XY7kvwVeZKg/IvCmPOQysYw2QmU5jMQM6qkumdvTRgRjUceuI0Eu0M/vFX5yFnTYm5jUaZJo71VTYmIX9NyH2loQD+pQXyZGCsTjLBUGrQx9oheozjeQj880MSvOJfFMacz65Awb218sMgbHKwmnVUE4d6WRRvM5pIY/KwZTVMIXIkifZxRF5uhYMqZb3MwHsfj19xEb42FpE1cVwqSq0RrwNbT6edyVcA8dOnRV9YsZ9hxOtF+N570H/hAov8CUHBg58EACTa2szj6zqyli1FaOsWB9UytHWL3LAlkxlReaChAf7aWvR+42GhoglCENq2Dfnbt8NfWyuqiyf27WMFXB6PmR8wmqVwEyJomTAPl+reqePHkWhpQYh3CrPAOHwSjDc3Cxw/tHULO9exY6K2wFNcDPB6AKMRC89fTL79NsixY1hqJK3tbQz3PC3j8UQBSheE0HtRLuiZt6IInWdH5EItAiTjaSTjabSeGHR8pyqsAGtOZRDxyRSycrzY/8wFIMUgHA0sWj+dSuCtd9rwzbvrcaYnwuQKDMliztDRKSRJBTYBUevp4PcquGGR3MlKIUBNUY4kp3yyK4L7/+0gnv7sBof+fqJ9HIOvWfJKCiyFVJTh9CpLXBIPkwAWPHYv47FDIfCW5Tgifv8SlmDmEMy7MXtBE/Gr5jKHNx43aJ/+JXKD88CaEtYVyzDv3FyE71oAABi6MDY7KWIPEQ1V5nx2haTLb7Vk7ySiezqRtbgAWUvyhRAa8SjIWlKAiQHTqfMG6EJIzuVn4ybnzIXRpGIxwFXv5/0QUbviHL4kWKaqTu17o1cshzKI329Wrc5gNJnE8BM/ZtG4JVLmThaAgJBGfvrvrm0S42fPIX/7dgdFktM9h5/48fSceltUn+y0NBszqJh8JeItN3DhdJpdn6U5OjQN/QabJtHSguhrr2U8pW/JEtZr1z4ZcbjJkEzOXrWKaQEZVNDwvfcgfvYcAAh1zsC6tVLhmF2lM7uhAenBQaQ6OkSegedP8iKt8LQfQaBkLQ6fy5YTtwRYeVsVultGpR+OorD2iqs+UI3zB3tx/u1eJqOsEJzb3+PorKWqBEuuK5NaN/a1RnD45VYhpkYIQTSo4Nd0Ct2qDiXNHDpXmeTGBc0ogP0XhrDvwhAIWOMRj6oI/f17V8/FPavmAgDeOD8gTRQ1c3LRMRKThNOSaR0vNHbhkVXVWAQ//GDP3c4XVwuzoQ1PwaoGmbUsH77KPMEh52yZoh3LMdnYz8ZXnotIv1FVa8Q1iXMjGLowBv+isPMFUcAqbacpzppqGhIRqzVx6p2bixRPhlPAY2lwbl6ICQGlepmT5qyYaWmWYDBU0DKBcFaQuF8WoxMps88tgSTHYN928kgfvKU5iO7pnFHvx3od/L7boS27s3+/+tpeeQ7fUqyU6unB2M6d5peWXrHc4fJttei4KWQ2DZ1y4o035A8oFZGykEPm/5uFcdwcYFF+9ooVMsZvN00TDjB2+IijOfvYs8+ylYLxN0/+in8t4+ITmDTBuLCJ0n19TpVPwOx5a9QVTB07Jskvc2opPB4Qo3E68XgQ2rYNSjAXg//yL/KkqCiYOnHCPKZlcrYm46EoSNz3XQABsWvZwhBOvd4piaoRAtxwf63U93bJhjJ0t4yyQi6bHk/l0nys21wDgBVpcZNkkg145/otC/Hz356Gkmb+Zv8Fs3IWYDo3j26px2/O9OLAxSFJsUDTKbavq0RFOFuSVQCAzSvKsOuEOa43zvfj0S3LsfNIh9SPdkl/AoOPnQJXeSzasdzkghuRozY45QBt4+dGWCvCvkmpWXdoc41oAM4Fxbjmi3hf0jqUoM8pnEYBbTzp7viMyDXVNYGxrotQ82UcXZ9Mm4wcwhwpFzlztEIEWFWvsVrQY+kZaZa+StYmcfy1dodUgXC6bseg7NwEMHF0y3WnuiYw+KOTmWFAq7msXDi0NXnISYDwLwxLq6/30q44h281JZgrf6Cqjsbg1o5PwVtvFZHnyNO/dBcgc3HEnDUj5QTczBKBc1mF9o9/Qji9yIsvouTrX5t+1WFJtEr5Cm5GrsD6NwAWga9cKVMsVVXIHHNT8vPhKS6Wrl0fGzO+VKQqWk53lSSoDY0iqyInkklTWiWZlCdhcWJFnigVBTnXXovgHbcjdvgIpk6dMllRuo7Qbx6D0vAlRltWCArKctDrIrg12BlFX2sEpTUhqWUhwCiffIJQPUQ4ey7XrHoULL62VNLVycr1Irs0G009ETx47TzsOtGNvvGEqGZ9vrELLzR2SW0Jj7SNmFr4MJuUA0wWAYDoV/urk/IkpOls8njkrjrc//g7SGkU1ygqbuowI3ea0hHd0wlfJYt6rewPNxljIVhGzf0nDnRLmjJWzRduXEQtZ1UJJhv7WcJVo4BKkOqxJX0JExDTRhMSO0ZP2moX5mQja2OFM1Kfht7IVwquGDfH/A3YSp9KYfx3bQCYVEF6eArhD9UIIbjcjeXTUjUnj/YLOCiwWoaXpnP2amkAwWvLHRIQAMS5veW5DEqzwVLeshyxorjK0pnBpEjQlkjMWrpUKmqCoqD04W84+rP6a2vhLSx0tg90M48HqZ4exI4fZ46fR8hWvXtCkL16NaZOnWIRuKG7M/zEj6UIlxoJWTvkIUTOLInW2PHj7jISmYxSqCF5iehbtAiB9eskETV9ZATJSASeigrQWEyqTs6qq3NU7PJcAW/kTowJKdHSMutVDjuxFUMnIB4PSFYWa9DOISmLhSKtuHlhFyaX3eDqwI1LRtPeHpx/uxdV9YVoPzVk1LcRbP2bVdj6N6tEJS6HcI79tk1qlxiLyG9BPJrCVDQJ7UIEv8pNos9WfDUUTUhtCUdjSanrFZdDAID7H38HSY1CJcBnN9Xgif2XHcEm7zu7ujofTz90LQ62DuOWMR3kkIylCyjCkP+dtom3i6OSKm5Vguz6IiQuR1hEqxIE1tjYNtV5AupIdI5LksQk4IEa8iHd6xQQU4M+pC0tBj1F2SxSfxcCgHxy0WNpCftWC7MQvGEuvKU5Aqcff61d2pc7d2stQO4NFRbqJOCtDppVxDqV4RxrK8JpzBP0iXFI5z/UK62scq4tw1TTMDRLTcfEfjYWe53Ce2FXnsO3dGCyW/z0afQ1NZk4toFB86pQK38/9/aZe7ZwbJs78ZKvfoVF50ZC0iqFHDt8RHSqovE4Bv7xe6YcMjdFkRK5kV27ET93TnzNE5+StMJMxiUWVBXJtjbpq+T58xhtbUX2mjVy5K9pSHd3izHxe5lobnYcno+V9xzgP1uO3b8rsyhvTuzbN6MgXL4+gCV3zhN/r78uG2/v44k4c7LX0lRqn6hpFI2vtONDn1/h6HLV3zYudlUUgo4zw06GDwgUUIe0Ate48ahMQI0CiE6lRNcrbsfaR/HoS00Cl9co8KO9rRJZ4y54cRM8oDVhse/q6nws7otjsqkPqUy6NjrFxL5uhLcuzKwZM4OpRtGbdWJwKwTif4+/LjtVGksjbU84+lUgrTtUJCf2dSN3U4UJRZEM12WxyaN9LOq2Q1jDcYz96hJy1pSIqDy7vshc7VjOaV3d0ISGOZ+/RkwSAKSKXSXgMaUfFAK1wAfNrUrbYkqOx9EeEoC0kqEp3dk4Beb1z6je+XvYFefwHZ2u7GafCHRdMHZEU5BUanY6M8mkSIjao3O7nIE94pUcLAAQgtJHHpb7xFqvgRD4Fy8GMAtGDTefj/XIPXQY8XPnTDaPxWgqBf+CBYifOuXOELJi/i5Vv3w8XA4Z6bQZ8dstU+2A5R4UfOLjSJw7n1msja+gdF105OIS2O3PtACl18mrrAx2+eQQ3nrqvIjs+1oj2PW9RiHjQAhQVV+ItpNOpgU1GDp2aQWOz6+uDuNwG+so9aO9ragqzMED66sAsBaIDxvJXMelGce4C178XzCc7oUJnP31JSyom4Ponk5JdEstDUDrjzkdBgWmmkfgr8xj+uvTVZe6qFVqA1MyxKJRVykDwEh8ZmqEYrGsBSGz/Z9trBP7e5C7sRyp3kl4y3IwcaBn+klKY+Jm+dsWMTmDvV1mhGwUjsWMwqXc9WVIXB6TGTO2Q08eYROIlR9vl3qwyi/rMzRBB1huwlr1KyJ9+3Of5jLfj8Ttlefw7Z2u7IU+3AxnwJUp+X/z6Dx4x+2YtPeItSU0k62tjOpoCKyp4ZCrs58N/JJ7yy0CWnI4dOO88aYmdHzq0yj56lfcm5bbri930yaM/u9fZJ78AEBVEdq6RTSJGf/1r6FHM+iYUCrJO/OxatFxiXqauHTJyVDiFcDTRe2UYuQnP53+umzXMfLkT8yvFnzEtq3OuJqux2FwT/M7fUIZ06rZQykkSWarERC8GUhK0T37nDF4usfkop3H914SzVCsHafsVgcV10DFJuNnSUCYSs6xfgzu73U4i+kafifOjjCYZQZuf2BNCQiMZKn1cnQqwSUxo90hj/Q5Du1WcGQ1Jc+HvFurGLyRiUapUwFjJNvGkbU4P7OapGEUJpedukhSWKNjb0kuppC5Chs6m0DsYmwARCWvVerBXrHrKQ3IKxfCRM+SbeMiwheOezZy0CqRVinvpV1xDh+QO131f+e7mRt9qCpKvvoVB2PH6rD7Hv2WEGAr/frXMPT//i+k+038NGvpUgRvu81MYNoEz2Ylw6CqUi9ce/LXN38+g2MMOGhi7z6UPvwN1prQ3hPXwrMHMONKIPfGGyXZ5axlS0U/AYcRIpqsE4+H+QKjw5U1qk5clLsYqUVFmPsv/wyA9SgQtQqf/hR8lZUmtZP39H03ZulzUNZ/GL2l14ISFQwE5d6OX7/T+6XTOhpfaUfHmWHHd25JYH6YLN3FkxIW4XePyc+6fTiGjz1xEJsWzXH9rfPuU5vhgwrT7/KmhcHJWd4TO5cbELg0Z774FuQhadQpEK8iOXC70/JVB83erZqh1360H+G7F5iOdoaCu8KPLRVOq2jH8sxSyBYYA8D0QmcKoPhVjDzTnDlPYadATteSEXJyFnAXYpOS4YZx2ufg46eYIydAeOtC5K4vk3IJ/B6LV9Coh5CelwIE1pa+r52vrkiHz9UgA+vWouRrX5WYMJIEAqWCYWPdhztAXsDkmAQsDtEq02DtE9v/ne+i5GtflZUtM1jWsmXSikDCvxUFgbVrkezoEM594vXX4Zs/z/lj487PSBZP7NkzY+LUXuGbv307kp2dLHJ2aX3I76MkkWCdUCg1WT2GaUNDSLS0IH/7dtdJld/jjI1crM9MUVjR2NKlCKxfJ9U7hMYvY9XJH2A0XAtvagIXFt4LXWGtPjLCPBRoOzVz83OrKSpBXxZ1yMNnOgYF486/cX7A8V0dVPwAAXjBGDxExPVmexJpxISV7PtrQjL0oRKoeV5XTZispQWCe2+Nzq1/Ozo0USDZ6eKYNYrJI30mxJGxUA8Ib1noiJq9FbnTa99TIN6cmc8PANDhhKmsqp9gmvnW8zoYNi7XxWEXnoi2spb0WBp5t1Vj0KqZo0Jw/Oc8tEK6p/y8/HjiX76vTlmv3TZTgC53Y4VgEFnVRN9Lu+Icvl08reonTyJ8zz1MMsCipwNKBce767//dyZqBlaIZe87yyP1occeZ9G3xyP64vKErxoOSc6EV+bmf+LjM445sH6d+O/RnTuZlg03QhDaugXxs2ellUr01dfcnbm17eFMLBkDzrEb78878uMnHc5cGIeUZukpeXLcSoO1TrJFn3sIsePHWQ9fO35PKdP9b2iAf8ECqVm8r7JSWumExi8jNH6ZQVqTPWhZcA+iefOsB4M90meyBgT6dCL5huWXBlBeG8angwSvDoxhKJrAub7pdeEVwo7vhtvfCY/ZU9ayEnEFoizRIwBk1xVhfE8ntKEppIem3AXAPEQ4JasjseLVsUzVsxmgB568zPS9vdjJar7yXGQGovh5Z9pANs7OsbZgTHVNYPCxUwhvWYDc9WWzOq8+lTKTs7ZLUwIept1/9wJWWasDABGVx256/IBFFI4wCWRrZy5PSUBy+Eq217GyuMrSmcGsLB2eZAxt3SIaiUNRUPDgJ0Wib+AfvyclUGk8LiAGPmEAkKmeHHbQNPR85asI3n4bRv/3LxwOlqZSLAFpL2ZSFHgrK5FqZ+yGkZ/9HMFbbwVgVOpaYQ1NQ6KlBeF775FaEpLsbLPwyWp8QrPnHhQFSk4O9HHzBfMZXb/smLwaDrHI2e7M7c7fTaDGvh03IznuUBy1QWD5n/i4c6Ix7sPUsWOInzkjTVL527dLnbus4wuNX0btpefReM1/M2EeHu0bTpg3WrnmNtZXt/Ps9Mn60f4YRvtiSIHiUm4Svd7pJ1UFwPULi1BXlifULfmV1UPFn8EHBRy+MfJKGY6VfY2zx2lyOnkBAoTvWiAcUSZH4uq2rVK+to3S/TFkLS3IiLPz4i4r64X/t5tcgFqczYrE3sUqy2rBG+Yid30Z0sNTcuTPG54ATLrYME9xNpSQz6Fzn+qddHX2oEDk5Vakh6cw1TRsrj4MmIsrWwIyu8e/KCwpd06dGIJvXhDekhx4y3MZvdQidWFPEF9l6czCJGkFi4RCzvXXMz12Xcfo//4FSr76FYa5u8EtRqUnTaUQ2bUbqa4u98QnpUi1t5ttC12+9y9dgtiRIyYEYsAtqa4uc7tkEpFdu5kUgguGHX3lVVT9+AkkOzsx/tLLSA8OmoVR9vPaI3vuhDVNcvYAkGxrQ8cnH2Q8d76drrtPJFabRqkTHg8KHvwkkpfbED9/HulexnPnyXEe1ad6esyJOZFA79e/Ad/8+ewZuU0kvLDLeCZWWGg6RpUJ8ywyYJ6PQFc9UAHMLUqgfSALOgVOv9mFjfctQu+FiNTwhLBMrNn5yvjHreOVasAKHJpVCGs2/sH6Mjz6chOW6AoaoGIcFCEQlBIFXkoExD5DflWwQzgko43FXROW5vNgbJ1UzwTirREJouDSwv6aEHJWlUidmNQ52QhurAAAd+kCyjjwbkVD/HtR3MVvok4BD0HudU4ZaG1gGmXKGcw3LyjgGy67IJnOICjrasRTlO3A4rmGkJvMMQBGoczAduIyz9pIXHLWKRfFzWRblEFlxCxa8y8tgMdQ8rRSTd8Plg6hs1yS/2fbmjVr6FE7dXGWZoUKAKD9kw/KND9VRc6GDZh8+2135+L1iiIiCphaNNMZly6wOcLcW29lDcBnEEXLvfVWFO74jGuCt/Tvvgl/be271uDPNKZZWYaGLdlr1kANTdNDV1URvvdesaLiUgo8KhcrJY/H1PeZxoJ3bYYayGFyEbw3sTGpEb8fVT95EomWlsyJZqspCsbDCzASWghvfBwti+5jkb8x2W3YWoOK2nx0t4yassuUQlUICitzZb18ULyancIpvwYCYMXcEM71jiOtsxXDjo3zEcz2YkNNIQ62DuO3v7uI7yMAD1jtDgUBOzVxNsTIYOFtC+EtzWFRJNe54YkE3hpwNm0HbdWoPDq1Vs8Sj4LsVcVSU22rcRGzyG9aZ3dOfuri7D/IwbsZb3mY6psUbRCt39l7yHqKs+VCMzE4l0QqYM7E0z0ja0EWgam2ORMjx3pslWDOQysAwJEPeDdGCDlGKV3j9t0VF+EDkHDi3r/9puxsDQrldO39wtu2wVtezrR4nn12VhWjBZ/+FJKX2xyOMHboUGZnb6FWTrz1FtIDA8j/84+x7ldck97IEwio6l1YzrXXgmRlzVjA5GZqYSGrsrXi9IRA8fuRe8MmZ88A43tiyDKL6N2QWuAtIUVRXDoNkpVlyjW7GSHIWrgIRZ97CFnLlrKq46Ymcc9443je8zf6yqvwL10iuofZdXpyrr0W4blzkffss2ibexuohV1ECFBRm4/SmpCouKVGEpA3Vx/pnkQ6pQus/ZYpL4ZUipFsoK4ihNPdEYPNSBHM9uILNy8Up+8nbfBQ1oGKgiV8oQOBdSXQRuIuESeQs5Z1aeLdo3LXl7EGIjyqpuwY3grWDk+PpWflfIlfBZ1KS7BB3s2VZnRrfE6AjJ2nctaWsmN5VZcTIKNznMnZK3k+Z2OVaZqnAxbooyZkbmuwjGiagvjkjIirswcyOmf/0gJ4i7Knr2ewxFT+hWF4CrJkaWS78ckFMO+VUe9QsG3R+8bSueL08O1mb/Pnq6lB1U+ehBrMc9WTh6IgtHULij73EEJbt4D4fM5tbJZ7660I3norawRiM30iMyNBCYclyCV++jRGnvgxGzN3spqGyK7dTg1+AEpubmZanMeDor/8AnJv2CTvp6rwLVkib+tyDM24b7758xmEYzjGybffRv93/wGlD38D4e3bkb1mjfm9QXMV901V5QbwBtzGJzoamyGNZun21f/t77D7a+uvy4+dv307qn78BHyVlayRzQfvNKuMjfvB2zcSjwf5kYtQdA3QNRCq4dpNOVLVbVaOl0XfxNTf3/KlBqDEL+nhbwrl4hc7NuCeVXPh8yiMaUMI8gPme7O6Oh9rN1UjDSBt/LopICLt7PoiWfedAN4qxtvPrivCnM8sN5t+c8EvbtQQJnvpEhKd46be+zRGY2kznWGBDTicwD8PrCpBaHONeT7C4B7rSkOaqGaKhG1DU8I+x3UHVs5xNAbwFMla9EqOLU4ljII52dhv5bQi2RZFqmvCVab43ViqawLZdUXIWlYw47bEy2SnA6tK2L103YjVP+SsK3Xcq5mf3h9mV7zDt9MOA2vWsBUAdz7T8IgDDQ2syCmTEQKSlYXcGzah45MPSvz8WY2tuFh2SobFz5wxnTSlrEsVgNKHvyEKvQBjMnGDpIzGKgDQ/+3vCCepzpmDgk89KCtsAvCUZWiUrGmsuMyqIEpZJ7H42XMo+7tvInfTJjOBa9BcefHbnC9+0dGAPbRlC2t6ksms9yOdRt+3/h5jzzzjLEQzcgWxw0eEHPTozp3o+9tvYvLAAZbEtWjz527ahP7v/gPGnn0WFED1nWtx69pJLK8Yw4e25aPhYxvEaftaI/j/s/fn8XVUV74o/t1VR6M1WLMs+ciyBkuyLCRZso0nbDyAbYwJEJOQSXYHMnT6vs5N3+tLSKc7nTQ0zb3pF7o7TdKQ2A6EJBgM2GAMGM+WJ8mSLMuax2PN82CNp2r//ti196npHIkA79ePx8qHWDqnateuOjprr/1d3/Vd51+th6oytcScuxeKyH9BMnOOqlZtG7U4TEgfrE+PAdG6Yv307SqUtnpyC/fvSMf4g6moSw/D6F2JCFnFvuzjV7ow/HYTAjMiPPdNWavA25e70PvCdYbZa+wPAJj/QKq1W4qbskKrjyCj4JcYguDlseJ33kw87J5kkdQ169zMWx4Hv/h5GDnRao38fVxajgqE/6JQw2vEX0bI2gSQIFmcf/tiJ0LWJXjUMh0E7j5jRK5OuD0Lm0TY84Cue5ad6fnvH9GrqiPT6HuxEoEZkSB+3l2mFBkgnhuXb7a7Fhehk+cHmgYAa9LyKdpnEtLRW/gXHvBU3OqacADM+Uw1NmKitNQQUXMOPcAYLN5s3po1iP6r77FOUh8RboEkeZypCS93d3cbonKqSSJz6KL/t/sFw8c8pl7+ufPvf2KYl9LbK+QIhNkoZs5qlArqaODSLNskuWDj8EYz0GkVORyWxG/o/TsRmJaO0RMnjIVyelhGy6/MN8kvc5aPpZpZt0gpw8OexLt23Ujaj4W7rFXRdUca4J6JEkNUnHAhJS8G/e1j6LzcA55mLfV349yNW1CP+ePAxRZMzajC5y2ZIeg/0YqpLbLYnmfEhyJ5XBVsDI4X0xkV7gEvuRk32+brpYujH8tBzLfvwPi1bqtWjsnpylGBCMqOssIRMsFM123MtI9h/FoPwnemCGVHPWXTnERUJ2bQ++uKWfVuzKYMTEIZnjLAM0rPhKGpCMCehRTkh5hvM167e2iS5RH0pgL+SSEgfrIB6vK52OneCsqN/shRP+fi+yoeUwemMPRuE+ZvT8FM122MnrV2UeMsHUB7tjzxrS1cnxaUw+0z7/CD8/Ox6OABA6vDVqtGZ5OVlaxYS5K84+8aZBKcn2/pR+tISIDS18eYOYBg5hiMUu+yDwA0WUd2uk4TXih9zjKnuVrg0qUMF5/NzJRLRcHQq6/a1i0AWrTN6a0OBwIyMgy4/vwvfhHuvj5MNzfDf/FiRH7lKwjOz4c8P9xAPwUg2kHO15K/5nwA1VhOJNAUMenMoF1ECAsC3G7bqmj/gASQ3O+DSqwUSqUU7XWDQiOfQ9RxKluUj1d1Ydrtcfb3ww9/g0DI9aPoa6m0peyF70wxNNy2FD5xkwlm2scMjb+5jkzAojAEL4+zd/yaccoiAExU9cPfGQK/uBAoQ5MMY9bGFKwaXdMPHqlyXRkp2KHjoGuPMtjBpAZm21lQAAqdvfAKEMlKTicdt7m36bZRcCkGv/h5FiE1r6ZQuPtmIT44CGvMos+HEM+8fN3DTMsoev+zwmstwXTLKKZbRoXWj16z59N29sBnGNLhhVJce54rVvKGI3Ry0ruzBVhkOeNFJ0STVebOzQwbhaxfj6SDBxDz/e9j0Su/R/zf/519vsAGztFbUH6+ARbxpQQKwNCjFmC7G1/X4F2pBLQ1h7605t/p9DSUoWFEf/tbwml2/v1PmCQFF5abnmZRu763MAD/xcmYbm3F2Icfoq1oD8bLyhDB8wI6C8zOxqKDB7DgH34i7s8gP6GqGDp0iDWOcTjgn5ICR2Ki19vwT0oyiN7xXQh/vuHDTVhS/0cQlX1reZPz1PxYwzh1fuz9bdnxor9sniTjf5AgyHwfoCUUzfxqddyNgCURsDXC2Cz+yaGM+ntrzODEbpd0G3rERjyYjphv3QG/hcb+D/7JoQhZtYD1XD3fDqV/EhM3+iEFO6CMThvhBqr9p/Wh7X3hOgbeqMdU6wgCFoUh7G6n1nDEOFU6F2ljApEXmLci3iekEpQXbanONcBd3FRYuOrRj+XAL9HUA8N8LQLIYTZ5OYkg5K5EhN2bjJjH74B/3DzD24GZkWJe85bH2ffa5WYujbHR7ecLt9k4dMc/30/aPpEInxCyDcBzYOSkFymlz5jeDwDwOwAFAPoBfIlS2vJJXNvOxsvKGBVTg3Hif/SkZ/vvcIB6aSwCwAMzyLIBdtAXLREHe2ydGhXQDGvwKNQO1mADEJCAAER87atMLIxf0ySINt3YCPn+nR6tG19KoA6HpWo2OD8fi15+iRWX6WEr7VpxP3rSI6VghnrM5mMnIs8PFwuphR1jN47b7al85i9PTwsozazbH7h0KQBj0xpD7wFtHgAAt5vJUPigoqqalo+53aVIjKsqEjuLETLehekde7Dk6/cIDH+4dwI3r3ahLYiCRAbg6RVJ+MqqJGzNjhda9bJeq554NF1EBCqxln/ER4JV6Z2AQuBVAllfru8t8pSC/Zj+up6q6KYsmp8N6tcc//jVLsxbEY/g5XHem2rPBu9oCeLwnSmMM++lSjcoLxpRX86yvC6FeidO6JPOM123WectnTniguHunfBcTyIIzIjEZN2gqWsXhRTkZ4Czbpd2s2Mc7JyRUy5IwQ6o426mQqrrCEYCZY+omulzC1wyHxPX+y31DLevdrFrKJ6uY0NHGgU/P+Zbd/zXk1YghMgAfglgK4BbAK4SQo5QSm/qDvsmgEFKaRoh5MsA/hnAl6yjfTI2/OZbHihmehpDr71uqL61mJYAHDhw0PMaIYj/0ZMGPfve555jY7jdLILlTsXf33BscH4+6j/8EI3l5UjNy0Oiqc8u56WPX7lqSEQO5+WhfWICsT09iO7vhzI4KPjlvA9u3A+fYFICJuet33HoLTg/H8kvv8TgIL2QHCFCR2iq2qaz11xNkjB5s9pSxNYXFYWe2FjE9vUienDI2jrSC5TWVrTHsCD3xcSg8fZtzP/vP0BUT48Hglm5gvUemJpCX2Qku5b23Cy4v6mQTGj9yzKmHv0yzp48idSBAaRv3mwQpQu/3YZFu9IQrDmUK6++j+LL7ZCm5yNtJAzz3e2YP0YBJAnN+6nWEfSWdLMoj0DgsjfKSzGyqB/xE1Hwb1c9jllPYeQ/898N0DzzmkSLlPUa7cQhYWSDHwb7u+AkESDaeZM1A14liY2foUYR1HT32P9pWj4qhNywPsH7kY2yYi1z393ApUadHzszF4YJ0xaRgEVhloWNc6FmuscRpK8KVinUcTdiHr/DUncQkBKOG+Wl6KluRWzWIqRrDc+lYIdBtkGTRfXcB9E0dTSm0Hhpt+EeJ6sGWGctU8tIqBC/U7dqLBDzIUn9ceyTiPBXAmiglDYBACHkjwAeAKB3+A8A+In282sA/p0QQuinWPUlHE5PD5JjY0Hq6z2NzQFRWKV3vn3z56MnJoY5joEBAVVw404bhKAvPBwtycmgABa3tiJGd2z9hx/ij6dOQZEkXD11Cl+++26vOvl8zP6YGJxKWQxFkkAAhA0NQVIpUpuaMO/9D4R0sjI0jL6oSPREa/McHET83/+dpWuX2YLz8xH35A9Z7sKUYA29Z6uhJsGRkICuqSmjE3U4AEUxOteBAUFb7Q0NQc/ixQiYmsJgRASaFydDlSTIqoqHU1MR0dIqcHO93g//nAKmpjAVEIDY3l4AQE9MDAKmp1CWnw9FkiCtW4vFzS1IbmtDtJbATtr/W9w8cBCnQ0PYc6MUBaXXkNrSgr6ICLHgpG1ishWTN2/iVkcHmpOTQQBEDA2ibHTU8zkBiAbQmJwMl3MhnK5biK+rEwv48coLUEMICNqwbioP8dOLMHNiGjeiSrEsrwAAizKpSY7gRnkpgv40hFAaBkbM9Eik+SeGwj8xRPjg25e7PJW3BKDUI6OmQsF0TgCS1mYzaWK3CkIBdUZB0IlpBCMMCtyQNUCJ6vwTnw4BjEVCMsH8XalQx91oVzoR8OEYHFq1AHQybqqWo+BJRj4WtRmfz13/DPTqlfoksDfNHb1xcbLxa924faWLFaxrQ3OphokbfWKuHuk5AkophqeGEehnrF7lOQLetSsgJRz1g/UI+tMQUmkk3NeHUP+leiy7uwAjp1zsWYMtvIRq19Aqq/Vj6it1+fNQ3Z5EtKE1JGciaQuOHOaPaZvn+knaJ+HwEwG4dL/fArDK2zGUUjchZBhAFGAUqSaEfAvAtwAgKSnpz57Q2F3rcUpVoEoSJFXFoxs3Qn7oQU/EHRlpcb7tAwM4vXGDcLgF5RVYpDlEgDlM+ef/B43l5QieNw+n29uharh8y+JkxKelgiP5jeXlUDRVR1X7Pf1v/sYSgesbrjd3dEChTNaAUorhCIZblkRFImzBAvCnMZiWitMbPPO8OyEBWbM4e7t7SM3LM6iCdo6Po7HiOlJz7wCSknDq1CmokgSiqsiUHVh+13p01tfjVHs7KCGQVBUZ2utjAE4rbnbP+jwAIVABtA0MYOk//ARjd60Xz2/89m1MTkygYmrKUAAlafROVbs/CrDnSAga01INzzo4Px99J09CGR4Wz620sADuNavFuLKqIv6u9UjfvBn1H37I7osnwyn1jK99Ti2trShZwXII3fHxCLhwAVu/9CU0lpdD1bBoSim65WEkKJFwUBk91a2A5vCbL1dhPvyF42m+XIXemBGk0kjIkKFooT8v3qpJaseGXTsBaAvDlWnIlNXi1qX3IKMuDhIkbTzARTqRvmg1c06YhgztXkAgQ4YbChQNT1ChgoDAoR2jQEXrmjFEJS1A56V6gAILVqdjYR5L6pb84SpSaSQkbX58jmxMBcOLR4DFgei8VI+0FjYvBQpca8Yx3TGG1JZYSJoyUOvq27gz9y60XbiJ3vEehBUmYqHm2AcfDhRRdOIcI1juoK/LtVhUHAKizastogfL4MTNmFak1IeJOev1RpuUNtz12A7b5CgfFwB6ilvF50QpxOfaFtEjnrWs3bMbCm7dOQHl9rThPgJSwkFlXrhGoED1zHOR03aR4c8CmERw9QwcVIabKGhfPAIvWZ4/2/5LsXQopf8J4D8BJq3w545TOzEhvtSqLKO0txcNDQ1QFAUlFy9i27ZtmFiahSBFwcS5c0hOTkaXvz8UDZunFLhWsBy50dEI1sZ0uVz408WLUBQF5PZtMT4AqA4Huvz9ka79npqXh6unTkEFIKkqUvPy4HK50NLSguTkZDidHpywPzoaLUuzMD82BqSsjFV3mpKnrfM8CSTDPAGc6u5GcEkJCk2JTjvT30PJxYsoWrIETqcTLpcLr9+6BWV+OMpcLkTevg2VX0OSUA2g9sIFUEpB+XPVXq+/eBF5eXnieGGa4yaUIiwlBW+//TbKysqgKAqgb7CiTyprC4QYAmBQjC7Zq3/WLpcL/fPmASNaAxZCQAlBhaKIeSqShNqJCdS+/TY6OzsN86SEgGjj88/pnKoCY2NiAXJpnxX/TBVN1zJOCYNKFShE0b6szM6HlWFnxyrheM6HlWF91ia4rw+x9AVR8FbECaROOXE+tAwd8gjOXLwmnFNlUglyxtNxPbgOtXIL7olfg+91fQkEBG6ioC7MhciecpTIZfgg6W0sG0/DqHwb3+7+ImOcEgW/ijuEMCUElcH1oKDYPMzirw/DL6N2sAXykAx3EIuM/Sv98UTQExieHkbiwmi4rytsHKj4YP5FNAS6EK6EoGpeA7InCnCk8QgmgyaRuWgx7hhfguvBdagbbIUapBpfG2pF/s18lLvLofqpCLgRgBcSXgAAPH7jO5hWpuF/wx8vJLyAvNi8Wf92y3vKcaTxCA4PHUb6oiTcMb4EN4IbsFXeiWUowCtBRxEaT7BuNB9D0gjuHl0hnlmjsxsxQU0oiS5BYVAh8pBnGLekuwSFcYWIzVokPif953pJ96yH5TGEKyG4EdyAuqFWqFQ13Ed1UBP+T9JzyBxNxpB2bNW8BmyRd8LdI6OkuwTh/uEYjh5G+GQ4nr3xrHgWaxLWoCOpWTzDnIlCLEPBrM/mo9gn4fDbATh1vy/UXrM75hYhxAEgHCx5+/+IjY6OQlEUUEqhKAqOHTsGVYcTS5KE1atXgxCiOVxWTl9RUSGcdEtLixiDUuo5FoAsywgKCsI5bfFI37wZXwZEJB24ZAkOHjwIRVEgSRLy8/ORm5sLAOJ1QgiSYmPR2mflB2dleRJZQUFBhmtTSvHOO0za2ZfTd7lcOH78ONwavq0oClpaWuB0OlFRUcEcMQBVVdFnMwfVCzOIjyc7HOJnAGLRorKME5WVXs83myzLoJSK44ksIzkgAG0zM0zXRpaRnJwMl8uFgwcPsmuaFkgzUlhaWmp5jU2RYEVGBqTubqTm5SF982a0qCraLlwQC8gdd98NAOwzHWzB9ZPvoGVcxk21E33BixC5Kx935nm+lNGrk/Hc0CtYN5qP86FlSFi2BMvyCnADpWiouIHSgCq8OfWu5377ZVT2sbyKBAkIBqqDm8T770VcQGtAB+4YX4LK4HrU9rXgN++/jH0r9qEptB2181rgJ/nh7oJ7MdU0jD9OvIGqIKYM6SAOqFBRE9xsuG839XxO0+o0nr78NBSqQCISMpOSkT2ehuvBdYbzAuVALMVyTCmsl2tNcLNlXMNrFCjtKfVcR5lGSXeJ+FmFiillCvtv7EdOTA4K4wq9Ov7ynnJ8871vYlqdNlxHgoQv+jOYaEvSFvy046d4L4JBk++Mn8Md40tQFdyAlXF3Ye/xvcw5y/544R628BxtPIo3G96EW3WL1ye+NF9E3O4EGS9Wvohw/3A0hbajJrgZKlRIkCARCQpVQEExo86Ie3u+4nlUBtSjIsDT/zlQDsTKqRHsPb5XPHsCApnIUKkKFSpm1Bn0TvQanuEd8CAMn5R9Eg7/KoB0QshiMMf+ZQBfMR1zBEARgIsAvgjg5KeJ3+fm5opoUpZl5Ofno7u7WzhWs/NRVRXFxcUWp3Dt2jXxWkBAgMHBb9++HV1drCAkPj4e7777rrjenj17kL55M9I1yeNz584ZFpySkhKUl5cjLS1NOElKqcXZBwcHY9OmTcKRc6dtnielFMeOHUNcXJxh98Dtgw8+wAUb3aCgIFayPuZD/mEuFh8fj6KiIlRUVODatWuG50sBe1aUjSUmJmLbtm24cOECajQ1UAogKicHm3JzDTukc+fOGRcYnUmSZJyD6XlFR0ejv78flFJca2lBUVGR2OlcunSJHURYzB3XdRJwqYBzJdK/+E2kh7eh4/JxXBnxx6BjAAs1nZaOumq4qioRmxCIExGXhOPxr76KTUmbgAQZT934d0xPTcNBHMiKykJMUAxOuk6KeXEIRtLY0oQQKFSxONcZdQbD08N44Z4XRHSaF5uHnzl+hqo6jwzwXQvvwrrEdfjZpZ/BI8rMFhZV20sREOGEFKqgKrgRVcE6KWHiwIPpD2JX6i7UD9YbxvmoFu4fjvSIdPH5UFCcdJ3ESddJEBDsyd6DHxT+wHLe0cajwtnrjYLi2avPIj0iHbszWHvLX1//NbrHu8Uzy4jIwEs3XxL3OKVM4UjjEbzV8JZhTO60H8t7DMgrEIvMjDoDP8kPT6xku6Bw/3AMTw9jZGoEL918CQpVoFIVv638Lf792r9DhWp5RpuTNhvmwOeuUAUyYfkWP8kPD6Y9iNqBWnHN+1Pv/7OftTf72A5fw+T/CsB7YOmg31JKqwghPwVQQik9AuA3AF4ihDQAGABbFD41czqd2LNnj8FBxMXFoaWlBUFBQZYIX7sPyzj6YyZ1DBQeDe/cybDXt99+W7ymKAoqKioAQFw/KCjIMr7b7UZtbS18WUxMDCYmJuByueB0OsUuw85UVUVFRYXF4b/++uuotGnxSCnFu++ySLO+vt7nPHwZIQQTExNwOp1wOp3Izc1FRUWF16gaYA55+fLlCAgIEAutLMvYtm0bnE4nJiaMpfSdnZ3Izc3F+vXrxWt8sbIbOzIyEm63G0Omzlvc5s2bh/5+tsHU73TMz5dCRUvJB3CW/wtQdATovglc+AX6BuPQ2DUEYBhdjXUY6u5C2fGjUNxuUEKxMjEcDYlj6I2YNkR/PLIlINiUtAkjU1auNceek8OTEREQgYreCoOjAACZyMLJ86i4vKcc1QPVhuOGp4aFI3zq8lNQqAJ/yR9PrHwC59vP48ytM1CpdTHmDugLaV/A/an3i2vw+zAbj1R9LQbcOe9bsc92t0dBsb9qPwBYnH7fhHXHyXMk/PnmxeYhPSIdscGx6B730GLrBusM86KgaBpqsiwgBAQjUyN4sfJFFMYV4kjjEXHMtDqN8+3n8dym5wB4dhz6z2V0xrtoXWVfpe1zlomMJ1c9ieHpYfF5pkekGxbxT9o+EQyfUnoMwDHTa3+n+3kSwG7zeZ+mcQcEwBY/Nzt9PUwCMMdBCPHqYPURtTlCrq+v9+DV2th2Ntsmp62tDW1tbZBlGUVFRUhOToYsy2Jc8/llZWXIzc0V91hSUmLr7LkpioKysrI5wy12Zoaz+HOPj4/HsWPHQCmFJEmIj49HR0eHgMQAoL+/H1FRUYiOjsbatWvhdDpRUlKCVpNsRHt7Ow4cOCCgML4o8M+MEIKCggKMjY2hpqbGFpLSW1tbm4gyOUQEwPR8KWSoSIYLcE8BLeeAlvMAgLpRY6Fd/ZVi5uy157ikLQSpt+bhvVXdGI4CCuPYDs1f9hfRW7h/OH5Z9kvb+alQ0TTMYB2H5EBOVA6q+qrEYvFA2gMGR88j1hnVSDku7SnFodpD2J2xG65RFz5s+xA50TkYnh5GVFAU+ywEZ4iI65kdPce5w/3DIRMZCvV8JyICIpiz8/GnrHfObzS8IXYXdnag6gA2JW0yXPt8+3nLcTKRQUHhJ/mhMK4Q5T3lePz9xzGtGB25nrnD52K3W3BTt1hw/CV/5ETnGN4/c+sMynvKkReb53XHwc1BHIbFIMjBYFj+jDic8+SqJ4WD56ZfxD8N+y+VtP00zOVy4cCBAwa4pbCwUET8k5OTFjgnMzMTa9euBQC89tprGB4etoyrqipOnz6NjRs3IiTEWN1nPt4bfixJktcFRb8A8Sh0/fr12LZtG8rKytDR0WE5R1EUMSen04nq6mrLMWbr6OjwbLE/AsrGo/T4+HgcP35cPF8Oj+ifMXeo+jyGfgfQ19eHtLQ0n3PmUFhZWRny8/MRHx8vnLMsy8jNzcXp06fnPP/8/HyEh4cbggC+M6w4/jugvRS5uAknOgHJASSvB4KigMaTiA0YQ+ttD38ifeUalB0/CrcmlUFAIFOCrWQFtt/7HfEF1kMwJd0lhqhP75QM960qyIrMQv1gvVgsdqXusjh6b9H1ibYTACCcWdtoG9DMnJpDckChCvwkP+xbsc8QaXLTO1J/2R/fWPoN/O7m74TTH5wanPVZE8JgKpnIuNl/0+exFFQ4wJLuEnSOdcKtWqG7e5PvxeDUILYkbUFebB5erHzRsIPiY/F/+Wt8geB5EzubVqdxreeacV7UM6+bA97voSC2AN8v+D7qB+vxRsMbuNl/E7WDbCcvExnfWPoNhAWEiSDg8fcfx5QyJRYAviP7tOwz7/D1CUkOt+ij/9OnT1scXWJionj/i1/8In7zG/sq1MbGRrS2tmLbtm2GyHsuRinFwoUL4XK5LBF2ZGQksrKycPHiRQF3JCcno6SkxBaOMs+pubkZO3bsQFZWFhobPXhsUFAQli9fjrq6OvRqfHdKKWJiYtD9EZU+ly9fjp07d1ryExwesdtVcZy/s7MT7e3GvP57772HsrIyREYaJWjNeDx3/DzRHhgYKK5hvl+9LVq0CC6XS+w4ACBoshstp88BWQVwFt4LQNsZbtsKHPw3QJkCiAPY8XPAuRJwrkRHTSXKatgXnkBF4cZ1uOure5G24k5UnTmJqtMnoKoKHA4HvrL9r5EQ60m4Dze3YbKsDjdSp9AR0g+H5IBbdUMiEnJjcg1JTm4cy70/9X6xWNQP1uPpy09boB6O/yu62v4p9xT+rezfLOO6VTeyo7ORGZmJXam7DBE1hzXyYvNQ0l0iHOmMOoOwgDAc2HYAz1c8j4sdF+eE6atUxbLoZQiQAgz3mBKegqzILLzT/I54zV/yx4iW4FSpCofkgEQkCyTyXst7UKiCK51XALBdlL/sj2llGhKREBsci47b1qAIAK73Xp91zub78pf9Ee4fLhy0na1ZsAa/vufXAFikXjNQY1hYFKqgdrAW3839rlikppQpUFC4qRtPXX4K6RHpn0f4H8fMcEtraytcLlY2IFgeJjPjw2FhYRgZseKtAMPiGxoasGfPHhw6dMjrcXZ2+/Zt26g6KysLly9fhqqqkCQJ27ZtA2CFobyZqqo4duwY9u7di7Vr14qE7cTEBC5duoSFCxcajufJZzsLDQ3F2NiYYZ4OhwPx8fE4d+4cJicnDdBKUFCQYNCYo34AKC8vt10YZ2Zm0N7eblgIJEnCjh070NXVZYDI+D1evHgRe/fuFWPz5HZ1dTWCg4Nx48YNMe9bt24ZxiotKdG+1BSOxrMoGmyGc+t32ODOlQyzr/gDAArEMWkHuK7AVV8PhTJRNQqKnsZqdNRVI2GJURIge8Mmw2vvvPECqv70JggFbp+5gTOreoEo4ItLvojMyEw8c8WjRiIRCfkx+UiZn2JwxnmxeSjvKbc4e465r0tch/Pt56FoGkAExHYRARhsVNVXhfrBeuxK3cU+G1M0/8I9LyDcPxwSkcRzrOytRGFcIb6b+11c677mNao2242+GyIZzS0iIAIftHoUTiVI+GrWVw0JTrfqxtLopbjRZ+w1Id6nbjx9+Wns37Yf+1bsE4yjnnGjAqyoKVDdluh9NosLjsP/2fB/sP/GfkwqPoTXCATsU95Tjjcb3rQccrHjIq51X8O+FfvQMdZh2NkpVMGRxiOfO/yPY2a4pbe3FwcPHkReXp7XiLyrqwvnzp1DUFCQgcrozWpqahAVFYWEhASDwyeEICQkBKOj9gmdefPmYWBgQESdCxYsYDUBXV3imqqqYmJiAi0tLT4hF3MOQlVVtLS0INCkIKkoCtra2nzej97Mc09NTUVWVpZgJelNVVUcP35cPFtz1K+nts4GaenvfefOnYiPjxdQFr9Pfo/6RHVcXBy6uroMDCt+39XV1YiIiNAYItwkKABaig/DmbmcOXtu5X8AlGmg/I/AtmeA40/AOeEHmSyDW3P6ra5BtP/sR7i76HGcOvgCFLcbssOB7A2bxDAdddWoefUIJKoJFqhAXL8/+iNZD9YTbScM+LtKVVT0ViBlforlmZR0lxgwdIlIyI7KxoNpD2J4ehinXKfEe96c7zzHPEy4J0TUzpOe5mj+SOMRHG08amDxnHSdxBnXGRzYfgAv3PPCR4v0tYWBH3ut55oloVo7WGu4P0IIVsStQE1/jaBBWsalqoBb9AtBSngKgv2CsSJuBX5f/XvMqDOsathHDsEOWsuOysbJtpMGRpWdXey4iJKuEjyQ9gCbgw0URUExpUzh6ctPs12LXloDQtDiU7PPpMPXwwl6iiY3RVEsUSs3QohIZNpROL1ZcXGx5TVKKRITE9HQ0GC7aHA4hxCCHTt2IC4uznbXMTk5iczMTMiybDuO2dkDLDoeHh5GQECA7bz+XOM7Gm+Omr/OIS4+D5fLZUiKSpI0p3lMTk4KOiqn1fJ7cDgcIj/A8f3Ozk6vn1lTUxMkQiCBcrFFACpkKEimLpaYBdi/7dcA9yQ7yj0FFD8HuCeREDyBu+MacaIrDVqjQrhnZnD16GGB4btnZnDlrdexIG0JnNk5cFVVAtTjTCgoQiYdiBsKFDxws5NxUzcO1R3CG/VvICsqCw+mPYjdGbtRGFeIADkA08o0CGHJVh6pP5r56KzPEwAmlUkDfs+Tnp1jnYbXCYglCQoAChTsv7Efe5ftxZR76iNRNReHLxYJafN5FBRTboZnix0MBX5f/XsoVLF1xgQE/rI/CuMKcbLN6JCbhpsQKAfiobSHPHRJAjjgsIXDDNfVTIKE067Ts94Xn9u0Oo3X6l6Dn+RngSP198kXL4lKguXE4Tt9MdgnHe1/5pqY28EJAHDhwgVBg5RlGXl5eZhtfELIR3L6dpaZmYm0tDRUV1fD7XZbGCjcCgsLER4ejg9t+s+mpqbi61//unBq+ijXztmb78Hb+zzKNnPWP86YHIYBgEuXLgm+u8PhEJ9FS0sLhoeHDYnbkJAQBAUFidyC/loJCQninjkjR59wLSkpwdtvv+11vobxoKIANxAuTSAoeSUmmi8imbrgdAyKKB7KFGBDo+N2uW8hzvcmY1a1E0Lg8PMT0b97ZgbM80sAVUFlCRcz+xAwTdAVNYneCN9NdP7uzr/D7ozdwiF0jHXg9brXReRsF72mhKcgOSwZNQM1AtOWiYyH0h9CQkiCSB7ywiYJEjY6N2Lvsr1ecwV83I6xDq8QhwzZkywlEA7tq1lfFQlkb6avEzA8ThBR8MSP43PNi83Dtz/4Noo7ii1jZUdnG7D0lPAUNA83i/ktDl+MwrhCzPOb53Vu3pLq/D3OXuLHyETGorBFYnGzO56CQiYy1iWuQ1RQlIDWzLDaR3X6/59qYq6HDTickJycjIaGBgGdbNu2DXFxcSgvL7eNmHn0ybnhHPfljlHv7HiC9fLly16hHz384ctZJicn20YFWVlZcLlcYhxJkpCRkQEAGBoa8onB+3Lc0dHR2LVrl4FJ46tWQT+m3X3w1+zOdbvdgmnEk7ocz5dlGV/60pfgdDotRWKUUoHrE0IEI0cP41y+fNnrPWqjiJ8kqIx9Q3uAyEwgMhvAUiA+D6h+i0XzPvV+CZzBo3AQFW7q6fXr5UHBPTODusvFuLvocXQ3N6GnuRFdTUzHhigUq6rmMzEuQnEpewD1Sbe9Xvnl6pexO2O3oO6V95QziqAGw5gdkgwZX8v6mlgkHn//cQPThzuSn138maAZqlBx0nUSi8IW4Q81f4BKVVtnlxyWjJbhFtt5ypDxozt/JFg/AAzsJOsTNY7vDXKhoEibn4YQvxCU9ZZBpSrOt5/H3mV7AQAZERlWh08kxATFGF7rHe8V0TwFRdNwE26N3sIDaQ943UUEyAF4NPNRfNj2IVyjLgPNM0AOwL4V+1AzUIM3G94UO6TksGRbh8+Prx6oxlsNb+G06zT8ZX/sSt1lgdU43PZJ2WfO4ethA85uqaioMFS0dnV1YWJiQjhzfaTPq2gnJiYMDJNcrdIzKCjIUFX74IMPwul0IiIiAu+8846Fyw/AAH94g5G4E9uxY4dhHEII4uLiLPIHAOP7fxRmkNk4X11f0MTvd3Bw0LY6l+96srOzLRx/vdyD2SRJEosKv05RUZGByWOodLWxhIQEUZzFraSkxLIrAID58+ebCq+YSHk+p1pCBkoPAqCMdolXAHUGs4q7Ry9BQvJa3D2+BHX1HXBPT6O9xkfHMErRWlmOWzdvAKBQTEGBRDWROAqsvhGFqBF/NCbeto32m4ebBa8eYEncfSv24UDVAUa3NJkCBc9ceUYwP8yVuWKKNpHrgaoDXvHujIgMrEtch7O3zgouPzcCgg3ODRa2Cf+5ftBa5PdRIKHawVrDDmBancaRxiMAgD/U/MFwrIM4BNf97K2zYqdiVyQ1rU6jf6IfAXKAYM5wkyBh34p92J2xG85Qp8Df7WoW9GwqADjbflZg+TJkbHBuQFRQFNIj0jE8PSwotVx6grON+MLMx/mk7DPn8M2OBGAFSdwopSKhxyEfXh0KwBI96sflTsnOsZmrQ7lMAB/Xl0VFRRmYJuZFqKWlxcI24vpAdjYbJMONanpB5vv94IMPbHMSHD9XVRVVc2mLqLMdO3bY0jX5a+fOnUN7e7vPBayzsxMVFRXo7u7GxMSE2InY2cjwEIzVQCocUJDLVbt1iUEoPGE6B8fTV4+O9n6ccuVAUVj+xWeUDwCUQlFsOkNRCiG5q/2U0RaKtFshuLJ0yAL1UFA8dfkp1AzU4P7U+wXkok9ymm1anTbo1TyW85iFerkrdRdeq3vNkkCViGT7SBJDEvHs1WdtcXUCwhK7t87gR6t+ZOGV1wzM3nthtspd8yLEx+T5BgkS7ky4U9AfASYzMVvSNTooWiyKlb2VOOU6JXD/4elhlPeU49mrz8JN3YJRZK4KNhdO7b93P440HgEBQWZkJp69ysTSjjYexeakzeIeVagI9w/3uTB/EvaZc/iA0TmfPn3alk0CMJihoqICO3fuNDgjPgbAIsjq6mpkZWWhsLAQFy5cEOerqooLFy4gMTERQUFBhp2FPhI168uYrb+/X8gnAEYtIEII2tvbUVdXJ47n8gFmLjvgcfaSJGHJkiWora39SEnakpIS28geMC5w/Bo86ezrGpGRkYiLizMInhFCsGbNGmRmZoqcy2ymqqphIbS/rvYFogCP6jPRiER0IxntWnRvMiKx/1Sb5jj6rttsZLjGglllLfX4QyJJIEQCVRXrnAiBLDugqoqtrhCXPuY/Sypw5435AAhUieK9Vd3C6StUwat1r+Jw/WGR/OPnsbu3fg5nXGcEbLA5aTPebX4XKlQEyoECI169YDWKO42LfF5MnoVJ4y/5IyooCtPKtD1jRntWClVseeWzRfMSJGxYuAFnb50V92Z3jn5RuNF3A9X91Wz3SRnOzwuyAO/Vuubr8kidw2XFHcWGyujnK54XHHwVKg5WHYQz1IndGbtxqPYQTrSdwJakLWKR47kWDp/pi8OmlCm82/yuYQ7n288LGOyxnMd8zvfPtc+kw3e5XKioqLCwc+yMyxEAsCR7a2pqhPNrbGzEzZs30dRkxORqa2tRW1srnLwZCnI6ndi7dy+OHz9u66AB75E2wJwcFxLjtmTJEq8Rtp6yCMArs4ebnsXjcrlw9uxZr8cC1vwGj7T1MFdkZKQBZhkYGMD+/fuxZMkSA7R24cIFVFVVGeY3190JH0MvW0GpCmM7DhbVr0WpvaMHGJyz4+dAVzlQYkrYZd4HjHYB7UYue5A0Y5knpRRxi1MQuzgVt6pvYKDd0yJiflw8tn/vB+hra8EHL/6H7W6AEG1Z0aJ+cLkDFVh6OwEXIm8Zkqd2iVRzpA14EqAUFJPKpKHIaUqZwtHGozjSeASXu4x5EAKC8IBw4Vj18AXABM04zdFuLgBz+s9XPC8i7fKecvRPWEVyeTIWYIVm/Fxfi8OGhRswqUwKSqh+DgpVhKgap5uaZSfM9vCShy0QFI+0w/3D8ezVZy1QjwoVP7v0M5R2l4rnWtxRDNeoC5uSNtnWNPAFUd9vgNtJ10mccp2Cn+SHB9IeMORZPin7zDl8g2zuHIwndvnPPNlbUVFhYfGYnb1Z/oA7e/Muwel0Ij8/36vDB4CGhgaDSJq3HYHD4UBISMicnGJ9fb1Q9eRJZ/N5Fy9eRGZmJrq7u+dU2LV8+XKLJAEvZOO2ZMkSC66uqqqtWJweZ+dRf1dXl6Vi1ttCkJGRIXZY775zFIp2jAQFy3HTI49gMQkoLAJyv8K4964rQNkrjKEDAEQGotKB+g8MZ3WMh+JU92Kt8lPH0qEUXY116HO1IH3lGoPDX3H/Q0hYkiUKsU785nlrpE8BySzzDApKKO5cuQ2P5a7Fs1efNbBNuDPmx+rtbufdyInJwcjUCA5WHbR1nhQUhxsOQ1GtzlUmMivi0hQdn1j5hAGe4c6wc6wTr9a9avN8mRV3FKOkqwRPrHxCOE2zmdUon7nyzKw7Ac5qudZ9zeKIzaJqI1MjPseTIAmGDDc9NZInUs26PPxa+kUUYPmP2zO3LcnXuZie2nm08eifxdLxZZ85h+9LUdLO9MlEPSQzF8nguLg49Pb2ChGuoKAgwy5BH/GbMX49nxxgjm///v3Yu3evIfGsT95mZGQIjR9vDCO9qaqKrq4uhIeHY/v27SgrK7MsOjzSngv0I0mSbY5D/8wVRUFgYKChwld/LV9GKcWlS5eQnp5ukaqwO1eWZSG6BgBx6EfF2/8JQEUuqr1H9QCQmA/s/IXnd+dKYM/bwIXngNp3AVDg4r8bmsoDgGs8XFTa2pl7Zga1F88JeeXC+x/CHVu2i/fv2LId0UnJePeX/4KhLtP8zLdICKJ3rsbXtn4PALBvxT4h2SsTGanzUy1qkAAE1Y+zQHwVGtkVBxXEFiB1fioO1R0CBYVKVQxPG/Wh9NDH4YbDtuNwm1an8evrv/YKA30h7QtCRKxmoMbnWABLxvLod9+KfTjccBg1/TVCW16CJBKeh2oPWaiWZtrnRudGABB5DcBIjdy3Yp9IpMpERph/GPomvQv0UVD0TfTZJl/1wmq+YDjzovVJ2WfO4ftSlIyOjsadd95pKOLhyUQAhmSvNxxbb11dXZAkCQUFBYLFw5202+0WbBtCCJKSkgxFRzt27LA4YF45mpycjLy8PIyNjWFiYgJtbW2glKKurg5paWkoLCxEUVERTp8+7VU7hps+QZ2YmGh5X5IkC2TEzRxVL1iwwHKMy+WyLCLepIvnYoqioKamBrIsIzMz0ysTiRCC7du3GxYfZ1wEnNEuoE+/kzCVMnLL/waL6lvOMWE0TSsHicuZwxcNYYnhdGfwMGSiikpbu3mpqspgG0lCQLCnWxnXzHdm52DF/Q/hgxd+qT+RPW/dAhOV4MS9Kx8Wv+fF5uE39/4GRxqP4I36N4Qol94cxIGvL/26LQQxV0udn4rMyExDQrGyt1LIBnDjUfBdicaEqB21US9ZrDcZMjIjM4WDlSRJ1BR4m/uD6Q+KxeaZK89gRp1hFcfR2SiMK8TYzJhwplw8Tm8bnRtxvv28cMaLwhah6HgRVKpCIhI2LtxoiM5574GjjUdxuP6wT2evN7vk65OrnhQsH3/ZH49mPopjzccMz0cmrFvb5yydOZiepWPmkw8ODiIuLs5CB9Sfy5O3nZ0+okOdqaqK8PBwMY5eLkDP5mltbQUhBIWFhYYo2awdw3cJdtE718jhssy+xMK4s+ZzcLvdtqqfCxcutBSDxcfHo7u72xJVd3R04ODBgwbs3iw9wfXxP47TB5jjn5mZEZCUWV+fUoqJhvNA9VNA1gNM7+bAfUwKgZvkAJZ/nXHsJ/qByRGg67rn+IO7GO9ekhiOX7iHOX/Zn40j+wNpm4CaY+BePyEmALsXhcI1705M+UWg+vwZjA308ZtHyvKVaL1+TUgsOLNz0FFXrQmrfcB2gw4Hdv/4KWx9/HuoPPkB5kVEYuUDD6OvrcUA9wy0u/DqP/wQj/z9PyFhSRaun3gXDZeLEbWQGgTSAE8xVVZkFk60nfjIzl4f9b7Z8CYeSHvA8Nop1ykUdxTbdotySA74S/6CYkhBIUGyxamDHcEYd4+L39Mi0lA9UC3my7+r/Hw7y4pk0Jhes16hCir7KlE9UA0JEtyqG0caj+DRzEcN3HwHcWDvsr3Yu2wvSrpLMDI1ggNVBzyLG1VxynUKEpEgUc9Ogcsie8tXmI0zh8zJ190Zu8VuRp8bADyaSBze+pyl82eYWU+Fywdz7rmeJgjAtmvTbDZX58bnYhb7KisrQ2hoKNauXYuWlhafUI1eP8YMEwG+q4PtGoLYXctcyBUWFobR0VHDzoVfy3wdLqUwPDxs2CHwZK8kSUhPT0ddXZ3lXPPcm5qa0NraiqKiIsTHxxvqE2QCJNf8CkAn0HgSWLRWR6/kD0thzr5wj+c1HtVXvOIpslJV4J0fsMRt7leYcBqP/AGg4aTn2PEBJEydBe74Eg795++16lmIqtqVDzyMlQ88DFdVJYJCQ4WCpuL2zE1xu1F15iTComNw957HBbafsCQLN8+dNvD6+bFX3nodjSVajcJ1IDMnDNXOYe1ZyPjRqh8hPSJdRMrc6UqEOW292qRMZGxL3ob3Wt4TkeaahDWChqhQBf0T/UI0jf9vRp0Rjl6vB69QBRsWbsBp12nDrgCwRvsBcoDB4c+oM3ir4S1b5+4gDkvyVoIk4CU73Rk9HDStTCMsIAx/d+ff4XDDYcQGxYqqXG57j++1XJs/AwdxYN+KfT7F0LxZx+0O7D2+Fw+mP4isyCyDA+f//fTiTw0LM4fPqgeqP5WELfAZdPh6aQW7RB+XNOZl/uZjZ8OZFy1aBLfbbYjMuYPUF0fN1QoLCw29aGeTKdbrx5jhKzuNesA7ds7bP3Z1dfmctyRJXncueke+cOFCtLW1oaSkBLIsG2ibZiljzqTSSyVTSpGRkYGenh4hKqfvBcAL0AAgt/MPcLbrdmGtF1ii1cBJp8Cxv/GoXVa8whKzqptF/3q4hipAyQH2fv5XPMlcgC0Ap/8JaDoNUBUdo/4o/tMBuGfAWDWEICknD2t2f0U47762Fnz4219BNT9XTc6CyyhLkozsjVuE2FpHXbXpcIIbp963jLN9phA5S6JAQW1pfwQE2dHZiAmKEYJq/LX/teJ/IS82D1/O/LJBcvnsrbNQqSoStm7qZjIAkAHCIIa+iT5L8w+ZyOid6LXNFeijfd5FS4+p6yt2RXtH7Vq8elWfI3BIDgFz3J96v2Xx0Rvntu/O2G2rM28WorOcT1WcaDshInI90yclPAWFcYVoHGr0qkjK9ZC46Wmw5T3ltgudm7o/tYQt8Bl0+L6ajXPTM3P0NMHZTJZlbNmyBQBEUxWARehczZEb12uvqqoyRNbx8fG2WvEA48DbFTxxI4Rg1apVhnP0FEgeGfPmIxUVFRgbG0N9fb1ILK9atQotLS1iR8HbP/ra2QwNDYmqYfN8uOQw7zbFTVEUZGZmikj+8uXLht6xLS0tyM3NRXx8vGHxrKurM3wW+o5UTnTCGV7LIu/4rUC7WT+HAvPigNu6RZOqTOa4/A8eMTSAcSAztgN1x9lOAJT9p0xpjv/3QP7XgNxHmePf+EOg9SI6Rv1xqDUbbi1iJkSC7OeHNbtZG+fLb7yKoNBQq7PXuPjZG9nfT+XJ90BVFYqq4vqJd3Hz7IdYetdmy99hSFQMRvuMUr8AULD+Xtwblcz66EYFALFME94hOTCtsgi/ur8a1aRaOBU/yQ8PpT0kGCP6xCsvpOIJX75IUFCoUHH3wruxd9leHG08apmLW3Vb5Iv1JkkSHkp7SPDcnaFOvNHwBmKCYrAucR2KO4qFjv3Xl35dNAjJi83Dzy7+TMg9A8CSyCWGsdclrsNp12mviekDVQcAwMKNL4wrRLh/uMHhRgdGY1HYIlT2VWJGnYEKVcgZP5r5qOFYvWTFnuN7fC4c3KaUKYMyqX43oofP9JW3nzv8WcyufyzggRQAjxP5KE0/eOUsd7bp6enCwdm1CqSUIiIiAlFRUQaH39XVZUkaFxYWzkkAjFJqoFGapRwAT11Bd3e3SNjyxLI+8ieEiC5TnArqa9GzWwiSkpIQFxdnKyFNCMHo6Kg4j1NdeX0E1/qPj4+3vQ4hBCkpKdiYFQtny6tAd5QmbKZh60VHgLXfZ6wa/kWkqtHZg7CCqrFujW6pvz8KRKUxjH+sF6h/X4f/U/ZzyX7N8WsR/7Zn4Hr1NzqWjorwsACseOSbnoheuy+zs08rXIXg8AjELU5Bd3MTzAlfZWYGt4cGLQGK2dmHREZj9cNfQnRSMg797EciV3B30eOYGh3Fg8Gb8OrYewKW4LdMQJATnWMrC6CnHapURc9EjwGKoaA4c+sM9i7bi/tT77fQMH2xgAD2d7sgZIHBeVX3V6OKVqG4oxiPZj4qGoK/dPMlPLnqSQMDSO9ob/TdwN7je/H1pV/HH2r+MGuuom20DT+99FMAQHpEuqExuV47h4BgSeQSfDf3u6gfrMc/XvpHAWVx5ys+ThABK+XF5uFHq36Ef7z0j5bnYG7cQkER7h8OwNiwhQvM6W+D704+afvMOXwzrm0uROLiadzJmb9gZrokt/z8fAPv3Nz4247uaNbE4XRP/a6CJ2H1uwO98YVKfx88Grdz0Pr39RXB4eHhmJiYMOx+9AlgDg/NtX4BYIvr6dOnbc/Ri57x+7CTqdYfwzF8ziramBUL5/Ei5nwJ0SiSKvu94g9A+EJg7V9r9EkepRtmweCbuvdhYdRQFbjwCwAS4AgA7vxL4MK/wlhVq4/4XwFA4SRBkEk23JQAIBgamcLJ/b9mNQ78eVvgMYLmshJ275TaSzEQdoxdJa54hrKMlOUrEJ3EInveR9c9M4MPf/srUEoxT5aRsDIEXfPHhTOjlMIhOVDeUy6SvdPqNF6texVvNryJJ1Y+IXYGKlTc7LO28FOoIiQaMiIybBlCdsYTkRyGMTdwmVamUTtYK6pmeUMTDqPoo3tubuoWtQV6ETM/yQ8qVW0Tq4cbDiMrMsvQmLy0uxR+kh/cqltE8yVdJVgYutDgvCmoof5B77gBiJ7BZvpnfkw+ynrKDPkM/ULBG7a4qdvyp6vPVXySZt2n/7/ckpOT4XA4hIOVZdnwPhdP4w1OZFkWMsGJiYlChdJs+oXEV2GU+VrcEhISkJWVZSk+4knY0NBQ2zF4MRKHVBwOhzjP7lhJkiya8IQQJCcnIzk52VCZyq8NeNhNhYWFtvCNndXW1s5KC+XXT09P95knEF2zqIqCDDYX58QN5typwhw6IQynlxxA2cvAyaeAS88DS+5lVbGSl/hFnQGSVrFo3/om4J7QtPC9RYpaxK9MIyFoGLuTbmBRjAyAOW59A3N+L8bTVSaaxv8ebFRGEzKyoCo2iy0hkB0OJGZlg1KK6x8ex6Gf/QhBoaGQHQ5N0oFAVZhsA1UUfCfyS3go/SHEDgVgaX0IYocCsS5xnYXZAzDHZ5YdsFPeBFgl6HPXnkPDUIOX5+QxCRL8JX/sXrLbgEXbNXDZkrRFVNoCDDs/2ngUnWOdkCXZPLSYo0xkyESGv+SPLy75Ip5Y+QQk4qF16i02KNbyWtNwE2bUGcTPY7tMXvRkVri0exZmZxwWEGY5JmV+CoqyiyBBEqqa4f7heLHyRZT3lGN4etjS11g8O03j/5O2z1yEb6ZlcnyZ87kppSgtZUkWPabd2dmJjo4O65cVxkQpgD8rGu7o6PBaaTs5OYmQkBDDboP/rKoqAgMDsXfvXgObyExTnDdvHmRZxujoqKHBOef8893Jjh07BFXV4XBgcnISL730EoKDgzE+Po6srCysXr0a5eXluH3bXqo3PDwcIyMjPiEg/b1QSjE6Ouq1WpboIl6VqgivOwTn2mUMq5dkQNGid0KABblAaDxQe5wtBIrCaJOyH7BkGzAxAAy2ACOmfqYxGUDOlxgbxw5vbb/GFgyemJP82EIiMH7PnjsheASxYbFo7fXAR0LDSJZRcN8XcO3YEcHMIZIMahOpAixq3/wX30F3cxPaq41yGZGJTkQsSAQhQGPpFbGoKDMz6G5uwtK7NuP20CDbGcCzg1258h50NR7FpouRkFQCtYGiL8Z7a76WkRZDQtJbMxBuHOuPC46z9I2VIWPVglW4NXYLm5M2wxnqxPMVzyMiIAKDU4PIiMgQDVwkIhkad+vhJk75JCAIlAMtuvtcCVPPfnmx8kXRTIY7WRUqZMiICorCPL95MBsF9dr71ps5iMPijAvjCuEv+YsdBAFB01ATKvsqRTHY5qTNQjxNkiQkhSaJBYrnTgAm4qZX4Pwk7TPn8LkNDw/j9OnTIll55513imIqPTf94sWLFuxdb4mJiQY4B/AsKnMpfPI2rt6Ki4u9Yu0836BvvG6WMgBgcc68cciCBQsQFxcnXucJ3ZaWFkxOTloKzMz3ExkZiYGBAcO4CxYs8Nm7lz9v/bNtb28XOwfzs8hIikVDWycUCtZ9Sm1hrJiNP2SJ05L9EPBM+zWG4YuFABAReA3PgZgWbcnPyLop+x1wuxcY0ksKU8AvGIhfxhaHXK17VP0HABTooZ6O8VCUtHZCv0Hmzn7zX3wHd2zZjrQVd+Lqkdcx0NGO28NDmBozSvJGJjqxMGuZ6H3bUVdtYeMMtLsMEg36a3GWj4EaSwiyN24FAARc6oCkEub2VCCqaQaSUxIMHo4vy5KMtpE2EcU6iENQCb01P+FzWDBvgcVZrlqwSoiw2TUTKe4oxt7svYbELMDw9QfTHxQwFG/sAsB2Z/j1pV+3MG/M0sL7VuzD+fbzOHPrDF6rew0ykX0WdM3VeOGX3vJi8/DEyifwcvXLormKnr2jQsWx5mNiEVJVVewkCmILcF/KfWIxcEgOMcfPk7azmMvlMjBoAE/zDbPNpZtVe3s7uru7BdbNr6HX2OeWkpKC1tZWw7U/SvcoVVXR2dmJ3Nxcr8VhACz3Mm/ePNtovKOjAx0dHSgvLzc0EueLx0svveTz3gEYnD3Avuh2mjjcgoODsWnTJhQWFiIzM9OwKKqqisTERISGhnqYQxLB2lu/wlo6jRYkaoqWHUBjF9ByHki/x1MIxZk0qptBNK3eGE0UgMTkExbkepg2riuexK+dTQ0zemfOI+z4cz9n1zI5CNd4OKh5UQFAVRUTuh7AzWUlFv17bgMdtzDS2y3omAlLsvClnzyDqjMndU1SvP/dcLllqsF4VFVBJAkBwcE49LMfwT0zA0knw+Z/sx8Lwuaha/64cIbVA9Uo7S4VjoeA4KH0h/Dj1T9GeU85ksKSDPBGUmgSbo3eEs7Ijo54sfOi1zlzqx2sxa+3/lr8rm+e7pAcyInO0XZ99udLkGwhFLO0cP1gvYHBw3cmvoTZ9LUHAFMHLYwrNCiJNg012VYdP3v1WZ9Nzr1JTpf1lCE8IFwkoKfVaRyqO4S3Gt7Cb+79zefSCr7MGxfeDn5Zs2aNJcK3M30jbrsFhdvixYtx9913G7T19YqbeuMceDOdsb29HQcPHkRRURHWr18vtOL1jt/c5CUlJcVrMxI+/4qKCssCEhwc7PO+vZmvBWx8fBzHjx8HwPIe8fHxhl1De3s7JAKsXpaCwNjFSB6+CGepC4ACJ7oYXDMKiORszTsMrsm8jzFpVIUtAG6rCJfBCGHyCfqiq5ZznpyALZ6vWdnvPFW3kkO3k2DmDB6GDBUKTPgyIXBm5wCASKp6NQ37d1VVGgqveEVtV5O1UYjhUgAgSZAdDuRvux+l77wJVVXZv3a5EkrxncgvoS93HtLHY1F/tgRnx4+je74nN+Un+SEzMhM/u/gzvNnwpkVhsn2s3UAd/HNtS9IW8XN5Tzmer3he1A9Mq9Neee0O4hB8fjOkoqdbcs3/py8/bUi+ykTGk6ueFBpDvDKYm0Qk/O2qv0V6RLrQsOcsJr3DL+0pxTff+6bBGXOm02y2YeEGADBIUahQDUVr3Hhzl88d/p9hPT1GetvatWuxdetWjIyMWJyl2XjSE/AuzsZxfj30AsDSACUzMxOJiYmGAiRz1al+R2KWbOZjc62dkJCQOQm9ceVP3lu2u7vbcN8cw7e794+ipw+wBebYsWMW+WJuKqW4WFmPvYtOw5lzlyeCl2TgtplzTpmTT1zOGDm8ArbmHYtssfE0lUXzcUs9UI5eNkFysGPsZHND4z0VuQsLWdQvHoiEhLu+iEfC1+PtP75joE1yx825+ESLvO2MaMlYvkBw66irxqmDL/iM7gEgc+0GRC1MEk3SKaUApfbBi3atlSvvERLNKlWxlUTjvTs9WvvrEtd51eDRK3Pa3g9POGpQET9fJjIiAiJs9Wd4ZO8rKuaWMC8Bj+U8hhNtJ5ARkWGoJdDvELgUcUl3iQWO0sNAu1J34fmK54W8MgAQSoSkstnJ6kXPAFiEzUamRmalpwLsGadHpGN4atjQa8DbuXbVxB/HPnMOX988BDBS/fR2+fJlZGZm2jo5s6mqiu7ubgN9Ue/0zfo4viwkJMTSUnD58uWWxh7Dw8Nit6KvOAXwkeSfAWNEzhcTs2Cat+fAnfayZcu8LoyyLFvkEgwsIfBdLBWvqCBoaW2D89b/ZJTIrusMQ695xzS61lEqKMojcOa6Alz+NXybhuu3nPM4fADI+7JnRqW/0y7Bt9kqWwjS7mE6OwJG0lnGdmDnL5AAYHFNF66fMDax0HPjC3c+iJK33xBwC3fK0Cpzl6xaA1cVe6Z8sZh1Z6BZ/ZVi5N17nzhPkmQoXgoN41PSEbs4VWj1gFKG7VMguzEM/fOn0RM9AzhhUbTkbfn4YsAjcb05JAfuXXQvjjUfsxQgKVRB/6RRA/9A1QFBu7STS7az7tvdeObKM3CrbhR3FAvWC3fuerEzHp1z+AZgjlMPA+XF5uG7ud/Flc4rwpFTUNtip7zYPDy56kkD114msoFq+rubv5v1HggIqgeqPYlbXa8C/j6nlvK+uLz/wCdlnzmH73Q6sWfPHsHSmZiYwOTkJC5evGhxfKdPn7aFNey+NO+8847A8fUJYIA1EfHm7PULkCzLiI+PN0A0PAEry7Kh6Ki0tFRIGvDEM9fa/zh9bAkhCAoKmrM4HMCc/sjICOLj4zEwMICFCxdi8eLF4vny3Q+vTeD0UFVVIRGAUgVGOS0CBxQk4xbTv7n475q6pMz+4xWImmogVFO0XsGrZn2ZxKL55PUaj/53QGcFu47sD2x7BpD/6Cnk2vYME1hLXm+EfgxDOlixl2bZGzYZEq0dtTfF343idiMgeB6+/A//LHR1Th18QSwGS1atEb8TQhCbnIqcTVvhzM6B7HAwjR5fGP7MjAEO4gsTIQRElsWciCSjt7UJ3c0NuGFS4wSApN5gJPUEQ22gOEkuwxHhMLQupJSyROuyvYaGIOfbzwuBsAXzFuDd5ndtYR67JGnbaBsef/9x7Fuxb85JVAWKgZOvL4jSJ2tlIuOthrfgVt2QiASZyKIOoXOsU2DvHAL6+tKv46WbLwlNIZ9USC/Cq0caj1gWOp7vMENK/RP9YgclQRI7J0IINizcIBqyf97i8COYXvVSX9lpFueaK8MGYE6P4+DmpOmFCxcwNTVlG+WbFyA9+2bVqlUih8D17gGI6FtVVWRkZGBmZgbBwcFigfKljZOeno6JiQmLAia3NWvWYGJiwjKGmRIaFBRkiPr14zU1NWHp0qVCA8jcSpJSKhqlDNecRWk7ozVSUBSE9CF8rAHJcDG9eiIzaIWqgKJRL6H9F50G9NZD4Pkt59gEyl6Gd868ZkHhQNpWTRTNtDNRpplQWt6jbBw9g4ebDXaPJdsAAB2v/h1c4/PhXLMdy+6+R0T5+mcqSTKc2TmGxicAUHe5GEtWrcHE6Kjg71MAXY116GqsQ/SixUhfuQbN5aWYNDF79EYpRZBWu+GqqhSSzKqqIjJhIQY6bmkLBoWiqGJnoYeZCFhilIA94pg+P6xdsQMJIQnoGOsQTBneGevHq39skCXmFEQ7WmPCvAR03e4yODy9c+eyw0XZRbZsHhmyuJa3ugAVKhoGG3C16yo2J23G4NQgAuVAkaillOJu590AWJtH3hqSV+lyCMhM7zTbodpDlkpahSo42ngUJd0ltl28bo3esv3czraf9TCiJAe+mvVVvHTzJbipG2dvncW6xHXYnbH7U6FkAp9Rhw9473y1fPlyg2CX3nhVq12EL0mSqF61w6VLSkosbBg+D54s1ev8KIoi6JiAh/2iH5sQ4lUP3myJiYno6uryyaCJiYlBZmYmAGOzl23bthm0+SmliImJ8bpoAEzCobCw0CBWx02WZbH4uYLGUd5+FgoY5TJ3/Byc0L4Mi9YwbjxnzhDCHD9n4/TWaT/rYJ2WcxovfhabGAQqvXRikmSPiJrszxy+3pwrmZxCyQEYFpaaY+goO6dp6UiQ3jsN57Jc6/iEIHvjFoOj59i84najvaYKdxc9ziL5aWOir6+1GX2tzbPfHyGCERQUGsr+ZgGAUiOVUydwxyUYbp47jfbamwClmkAEhSpR9EUr+B+aEBsX9+K6PG82vCm44SXdJV4FywCGd2dGZhoWgmXRy/BQ2kN49uqzlqYgZ26dsRQ7KVBQ1lsGLnsA2CeK9d2mOCSizyOcbT8LqnrkpHmVLgABAVUPVCMhJMH2XuySvwBjCh2uPyyYPzJkQ2EbBRW7Cz5vhRr7Ha9LXIewgDCxO9BXGf+XdPiEkEgAfwKQDKAFwCOU0kHTMXkAngcQBkZofopS+qePc925mB30wSEVXnilN0mSEBbGML7w8HDcunVL7ATMkTelVMAZeuNN0fX0TXMHLDvVSW5mtc6oqChLq0DAHnJSFGXWhaG3txcHDhxAfn6+pf9uQ4OxevL27dtYu3Yturq6EB8fb2Ea8cpg/SIm9G82bvRQQOMiUJQ5iZZRPySHzsBZ0w7hRF1XgC3/4JEj7qkBbrymfyKeHzmss+0ZD0uHEI/kAiFA0p3AYLO16EpvmfcBIFquwAvOD7BFoPyPRsE1qHDdDhXNT1RVRev1MuN5mkwyp1ty00shKDMzqLtc7HG+NcaCK70FhYVjYnSEOW6tapxDfFxr/9TBF+yZOZplrF4vErwA0FlfY4CLojPTMZ4Sgu/IMYgdYkJsebF5eCDtAbxW9xq4Lg/HtwvjCg34OADROCQ6KBqZkZl4ufplwxxig2ItWvB2Ust607dvNCcveTWtWQJhRp3B4vDFggtvJ82gL8wiIAIC4glfvbM90njEthZhUfgisUi5qRubnOzzPuM6AwoGIcXPi0fPeA/TyyHsWvqxeESvL3JTqfqpiKZx+7jSCk8A+JBSmg7gQ+13s40D+AalNBvANgC/IITM/5jXndWSk5MNEgGZmZkoKipCV1eXxVkGBwdDVVUMDQ1haGgIra2tUFUVCQkJuO+++/DlL38ZISEhhnP0zb/1du3aNYHLmztgXbp0SSwidgwWjn1zWYj+futWEWCiZXxx4mbWsPdmiqKgpKQEx48fN1A0zffX19eHy5cvY+PGjdi6dSt27twp3pMkSbRa5ElsPmfh7F1XgLf/O3DgPjhr92N99wE403JYsxFuqsLEz1rOseYkla8CtkwQCgHrTPQDq76t4akqg4QytzMIpu0SMGZVlvSYxBKy9e9DOHHJwXB71xXGu3ddYa87V7KFqHCvJ5cARsmU+A7EZESScMfmbdj946dEdN9RVy1YO7Im+UEpRWtlOU7u/zW6Gup8zBeYus0YWLyClxBJQDd9bS1wVVV6NPntnhylqD5/GlPjt1F15iROHTAuDpIso2D9vXCfuImmdz7Eq//wQ3zwwi/RUcc02QPkAMhENkTkXDCMd2aSiYy/XfW3eG7Tc7g/9X48e/VZNA8bdylRQVHi3MK4Qjx79Vkcqjvkc6dguA/T844NjkV+bL7tcW0jbfCT/IT0gl62gTt5BYpYyLiGkFkkrbynHIfrDtvOJyIgwnJ/z216Dj+680fIjs7GjDqDttE2TCqTUKEibX4aksKSDOcoVMHw9DCeXPUkk6AG8wGfhmgat48L6TwAYKP280EApwH8L/0BlNI63c8dhJAeADEAhj7mtWc1vWOvr68XTspsdgwVLv7Fi67i4+M95fOSJDRtzMbFy5xOp6UxSl+fkZpGKUV8fDwCAgLQ2toqFoGCggIAsDRRj4mJQW9vr0+oZa6mry0ArOwm8zH6Cl39QqGXshCvu65o3aR00TF31jt+rpM3oKw6tuaYpTjW1mR/BuucetqzMKgzwMwEg2coA44QnWFqc8iNsuStXrMmXeOEc1YOV+LkjCDnSiA+F3jnvwNURULwKDbHN+BEV7rBBRFCsOWb3zX0r+2oq7YoWlae/ABdjXWCh683SZdsBVg17mBnOyuwohQ9LU2s4AqsyOvD3/4Km//iO1Z1Thu7euR1y2u8MlifT9DLNe/+8VO2bfoAY+cm/Xt65U1u/pK/oUm43THc7LB/wJr87RnvQfd4t21nLQoqlDA57EJAsHrBarSMtBigJv155laO+2/st9UfAoDwgHAhpSATGVmRWaL4yo7Waic2R0DEIsoLzRSq4Jkrz3xqsM7HjfDjKKWc7tEFIM7XwYSQlQD8Acw9W/pnmlngjDsvsxzvbMaLlo4fPy4csqqqFudtNpfLJc7xZV1dXQYHrqoqxsbGkJuba9ih2NLt4uORmpqKnJwccSzvBVtYWIidO3f6FEILCgoShV0AsGfPHmRmZorktl6LHmDNWVpaWiyy0k6nE+vXr/fkLjjLRUfDFIyZwj2M2mgw1Utkr7PEAuaIJ/qNjcWJxFoWyv4sEpf9Gc3TEQTrnzdl0gx6Z1L3PmuMwlk5+uQwj/rjlgJr/i9RrHVHVD+2bC0A0Z4tkSRseewvEZ2UjMtvvCqamBhgHLcb3c1N6G72/qcvmDWEwOHvj4Idu4RAGmf26D9PVavs3fwX37HNK/my+fELhAwEZwZBNwYvCsuLzcNjOY/ZOp/6wXpc7bqK+kFPkRjX5CcgcBAHdi/Zjd/c+xsAEKJh4f7hXue7NnEtDm4/iEeWPIJNzk3wl/wFm+W+xfexKlyd8zcndDmOnxWZheqBagPlsrizeFbdnFOuU3j8/cdR3lOOngnvu8Wzt84iJzpHsGyevfosa7noZSGzM/5ZmgXlOMf/07BZI3xCyAkAdl7yR/pfKKWUEOL1TgkhCwC8BKCIUvtvNyHkWwC+BTDY4uOYXTeo9vZ2jI56Zz5oc0BcXJzo6UoIQWdnp9dGKdHR0RgYGDBQKoE/r/sVt9raWqxdu1YInXG5YPOXZHx8HIWFhXj33XdFMnn79u0imdrS0oLs7GzcuHHDNl/w7ruMXcI13NPT01FfXy92MatWrRIa9gEBAQLH5+wmfacug5kLnPQdpFxXmCCZwez4bvxeKXPkyeuZYx7rBWQHi9L1vWjjlhobksctBQ4V2eD5puuobogFiUf4QVHAH7/KmpmDMi0ecA69BKz+K0Qv+jLIyeugUBnMAghJA0IIUgtWYnFeAWSHQ0T448ODXkXU9BaXki5aH3IpZM74ASCaq0iShKnx2xjp60VCxlJ01FaDUi2fYSYdmHYPQ12dOHXwBUQnJSNhSRZ2//gp0Y5RVRXbojC9Hao9JHTmizuKcb79PNYlrkP1QLXA3iUiISsyC0cajwic3KEpmto1DJGJjBC/EJR0l4gE8aHaQ3jq8lNwUzc+aP0A6xLXWRyqHlr6QtoXkBmZOavMgTfjdM/nK57HirgVhsYuBbEFogrYTd2GiuBpZRo1AzWeLm+6Rckb9VRVVfzz1X9GbFCsAcf/NJqXcyMftYrScDIhtQA2Uko7NYd+mlJq0RcmhISBwT1PU0pfM79vZ4WFhdQMaXxU47TMsbEx2x6qelu0aBFiYmLmdKzeZFkWjbb13aU4M+Kj9MbV2+bNm4W0AodLuru7Z22SwovAzAwlX71uvZmdeie31LAZfH3JuEenRm+uK8w599YxWEcvcfD29zUxNM1C4oHwRC3y1u0I9Hx8y8RkICHPKp1gnsP+HfaVtOax/uI40H0TqH4LiL+DSS77KgiSHPgg9K9w/ZLnCx8aHWtpViI7/LB8xy70tDRhyao16G5ushRq2Zns8MMjf/+0geWjt7O/34+So4e97h4NRV5gn13O5m3ov9VmSRCv+/I3sOrBR0Sj9f5bbVBmZpCzaasBnuLGjztz6wyKIxpFla6d8XaFdhLAemcoE1ng6fw1XlR1pPGIoU2g2Xk6JAeeXGlVzfy3a/82p8pXX3P3l/3xaOajqB2sFXIQfJGbi8lExtKopaLNpK/I30EcuGvhXYgKivrY/WwJIaWUUtsV4+Ni+EcAFAF4Rvv3LZuL+wN4A8Dv5ursPwnTt9Gzqyw129TUFMrLyz9SBSugbasnJrBz506cO3cOtbW1wtEnJCRYGnzMZYGVZRnDw8NwuVwGqQb+b3FxsUXUjNvY2JjXRujLly8HAENdgrcFgEcq3IzzpsgaOQ2U3GAdofa87XH6dvg9l0Ao3MMidMOEu9h/RNYiaABx2VbuvN6owhaI7pueYiwuhcAbj5/+JyN9MzIFGDBS/0AkBi913/RQQ5vOWAuuzKaqwKixcM2uDaHinkHJ22+wR1BThfxt99vKLRBJRsSCBEGnVBTWuByAJbrvqKtG6Ttv+vw7oqqK6EWL0e9q1ap8ZVtnDzBKZ0ddNV79hycNjdZ7W5tF9M9Nf1wEgHtJnEGawXBPmmM3yzFwBgulVETkXB1TfwxPoJo57nqnmROdI5qMcyvvKUfHWAcckqeAzJviJ5+nRCTLjoNTNsMCwoTQ24uVL34ktU2FKrjRdwN+kt+cjo0OisaCkAVzGvvPtY/r8J8B8Coh5JsAWgE8AgCEkEIA36GUPqa9dheAKELIHu28PZTS8o95ba9mR4c0wzuAsfx/riwXO7NrKs7F0bq7uw3z6OrqsiRj9bZo0SLcunULpaWlKC8vN9AnASZItmbNGqFpb7b6+nr4+Vn/wAghghvPF8H29nbbhTA0NBR33HEHLl26JJ4ZlzzuqjyNrJHTKIS21TXTGi34vWbv/y37NyTW/sa5oBmlvp295wQWhZ/+J4bhH39Ci8q1toZUAcPqtd1C7FJ7h1/7rqZ5rwJzjQhlB7I33ovKmwdmXcC5c3fPzAhHTYgEPapJVQURCxIx2NnOjqcUlSffZ31vKYXDzw+7f/wUAKD40Ctz2qX1tbWwXSYAVXF7pX5OjI7i6pHXDc4eYIuVsZKX5yQ8xzmohJX9SXgviuXLuO67Q3JgXeI6lPWUYXDKwNJmipxpD2FByAIRkZf3lONw/WHDnwwFxcjUiKU5Cx+DC70BHuG0cP9wg8Tww+kPY57fPNvCLoAVdz205CFkRWaJ+gAOD3FpAz20UhhX+JG1pThV1LxIOIgDIBB9bWUiix4AdvTQT8o+lsOnlPYD2GzzegmAx7SfXwbwsvmYT9PMBU4TExPYs2ePgHdCQkIQEBCAq1evYnraGp1IkgSn0zknNoz+w+eMFS6YFhcXh23btqG6uhpZWVkC89bj4Wbr7e1l7fI0KifH8PWLlCzLWL16tZCLMCtj2mne6Jug8F3D/v32X4TR0VFcvnxZQFUAY/E40Qlc/DUAnXPgyVhuHL93G2sUMD0KvP3XrNiKyPZR9GyJ20VrgakRoPuGVpulAo2ngeazxhaHYmziKeaqe886HoeMqGSfRpifBAzdgmUhiGfYtl2DcSLJCI2Kwkiv6XW+m6LUNkI0tzfUY/3KzAyqzpzEzbMfGiUXCEHW2g3odbVai7UonZW5I8kymitKLY1X2H1IFgyfJXf9DE4/rpHiFzv/AfXBPQj3D8fw9LBwvN4w9MzITIOWfV5sHvJi8gyYOAXFwaqDFljGX/LHusR1ON9+Hq/XvY63GhiowKUUuPQxd7Jnbp3xev/fyP4GflD4A/E7F2a7PXMbFNQeWpnF18tEFoqYZ2+dhZu6LZ93REAE/lv+f0P1QDX6J/oRHRQtdjl8Z/FpcfE/k5W25khbTyPkkf9sq/SWLQyz4847ICDAq5Synt4IQEBDpaWlIiJobmZfyMLCQkxNeceHzRRRfRNwboqiiC5YFRUVlu5XZlu0aJEhwcpzG21tbYbjAgMDMTk5Ka4xMTGBnbmxGmsllmnY6DHx+UnAw7+xQipFRxiGX/o7q2NvLWYOf36SqQEJWHJU5ZG5jfU3sIbkxifkIzCn2hfUg2dbTWJj2L3tnrKdS0d9PV498aJVHhkAqOr1UrLsEDr2ZrNtb8iHBHB7aNDYJhEAKEX1hTMIi46xP5EwYMVSdzI/AoHzQjDU1enV2W/55ndFYxY9rLRp77dw/k8vY2JkWMx7+roLOzZs0o5bi2NTF7xKBVNQPHWZ7Vb0Tj88wMo9Nzt7mch4YuUTGJ4eFvIJBh4/hcHpv1H/hm1ymNvYDKtxOFR7SDR7Ke5gMsiBcqCBSgowNo1dXsAhOXBXohF/L+8p97rYjEyNCCE4Hs0DwNHGo5Yq5E/aPpMO3+l0GiJr7oz1kb8v471e9VTDc+fO2Z4nSZKBuqjHz/XRN6VUCLB9EhYUFCQasc92PzExHofgTXICgGEhkgiQHDQOHNztYa+kmTZzw1p+guP2/LhV3wYGW4FlDzMVzF4TbEQVdq7kMCZmV38PCAwDGk7YNzcxO3uucmnXFFzciJYb4NcyO4B5kcBtLxRby+Ki3e54GBQvjGZKqS2eT1UV4QsSMTE6IpwlN9nhAEC8LgagFE2llxn+b75XSi27CW6pBaswb34Ern943HDO5OgIxocGbc8Ji4lFaFSMSDDrBd/uLnocpw6+YJGDuD00aKg3SHtoO+5oCkd7xG1bfF+hCp66/JSBax4dFG07H7PxHYS5QQoBgUNyIMw/TEgx+2p0ws8p7ynHU5efsiwMPIegj7IL4wotMskA+8xzYnLwWM5j4jUz1VJveiE4Hs0/lvMY9q3YhxNtJ7Alact/TWmF/6rGOfCKoqC1tVWoXAYFBc0JgzM7cYA5WDt9HT1UAngqfO12AlyALTc31yuOz1UzfSblKMWxY8fE9XzdE9e14Uns4eFhr3RRzxgq8mk1nF2DHn66exLouGY+wcNZ1x934Re6gwiL3IMjjQ6UqkDIAmBUR5tsOQc8fpLtEn67bfbkaUQyW1i8HUc02iZXwey+ae1p683Z+zBn8Kh9A5RZzK5dYWrhnVj5wMMAgKozJxlu7+VvBypFdFLynLR2iCRh5QMPM/ll09+GGeohkqTlEDow0tuDkd4etNdUGdg+ituNusvFttLNk2Oewi33zAzqDr2NXDUMy0gI3ltln9TlUg0Ac46ZkZnwl/xt8W5ufpIfwv3D8cyVZ2ydqVt1G3T3JUiQJdm2mleGjPtT78fRxqO2YxFCLFE2l0l+6tJThoIsvVQyN16P4PbGNDOdy4u2ppVpXOu+9qkVXn0mHb4Zw+fqlsePH7d1xNxhEkKQlJQk4Jw//vGPGB0dRX5+vkU3hxCCHTt2WLjoTqcTO3bswDvvvOPVCTudTqxdu9aA469duxaBgYFITk7G8ePHvTY856aqKo4dO4YdO3YgIyPDknwlhCAqKgrR0dHo7u4WC6Bectmo7iiBUJX1OYWCXHoDGPPXomcAoFZOuyR58Ht9G0IToweqwnrIGiYoAcnrjAJnHeVst+BcCdz3L8Cxv/FOzQSsSVizrfm/jLRNzs9/66+8VOLOxSQk3PUQHglfjyuXqtFYetkHXOTbEjOz8YX/+bfi94QlWYhbnIITv3nei9NX5+TseQVtwpIs9LW1WA+w2REtzFpmWZCoqkKSZSG8xvT7r1vccXtNldA14rkKQgGZEqS1h2I4ahQqVQ2Rsb/kj3D/cEPjkq9mfRVXu69iRplB/VC9YPhwTf7ooGicbz9v68DN1bYAsDR6Kfat2IejjUdxuOGwJ0EKGT+680fIi83DkcYjts9ww8INtg53d8ZunG8/b+hYxZuP//TiTwUmf3/q/dh/7378ovQXuNZzTXvsxGsTGbOm/+cY/kcwOwzfrgctt6SkJKSlpQmu+5EjRwyiZe3t7Vi7dq0hkqaUorq62tDrFmC7C86kMWP+ej38zMxMREREGBK6es79bA4f8Dh9XpiVn5+P+Ph4NDQ0oKamBn19fejr6xNUUX5OQkICEz+bGADG+xESlYDctfcANe+g5cJrSMYtlqCt7fLtzPh7XHeGa+KYI3xC7KPwEZOELFU8jB9eTFXxByaHzAukotJsnLUp4xqTCaz6rneO/mCL93syG5GsyeRwJxLWP4wFfa8yh2843ge8ZLKuhjp01FUbmDB3bNmO6KRkxolvbzNi7Kax41OXYF5EJJquXQEXV8veuFU0RgeA7mbrojg/Lh5DXR5aKVVV9DQ3QpIdhlyC7PDDpr3fwsToqEjget15ikSy5OH/gyCjPRRf/eIPEL44Cb8/8TwmmjsQtDgBKwu24ETbCeHkJpVJHLx50FO0BQkFsQVInZ8qCqm4CNlcrTCuUBRx3Z96v2iMkhmZieHpYZT3lGNX6i6hCsrnLBMZUUFRtn1r7Spgh6eG8c33vmlYiA7VHcLi8MX4WtbX8P2C7+NI4xFD/2Bu0+o0nr36LB5Me9DQgP1zDP8jmFnfBWCiZt7M5XIhJibGa/9ZgO0azNBJU1MTWltbhSSymQ66evVqoTYZGBho0cMvKioyaMrrz83JyUFjYyMkSfLawlDPo1cUBeHh4YiLixNwDzf9nLlGEAAQsGi+aOBf4VybA0zVwImruhNnYc1QhSVn9bozABCx2FPENDUCXPudNSlKVWCgxXxHHiEzngDe+X+z4i7+e/dNJsomkmcSEJ0O9NezMSUHsOvf2FvnJHe6fgAAVbpJREFUfs6qZif6Pf8O3/K9a9CbHABsfxZoeJ/RN6nK+utquxpndg5LxLpnQIiElIKVSMkvwIe//bX3JKzOaauqgqozJ0WDFO6cszdswtbHv4frJ95FR42nenZRTp5BnTNiQQJ2/Lf/YUisArB00TKbGYMHgK6mesiyjLQVd4JSYN78CMPCAbDWjd5aNnKzVBKrQGDHJIbRhpijtyCpgHrjFl7s+zk6w8eNWja6vzcVKip6K/D9gu/jaONRoU9DKBFceDMnviC2AJ23OzHhnsCahDUGzfsX7nkBf7f672zbIf7m3t/gSOMRwfnnDKCjjUcFPdLcaF0vh1zeW26BhSgomoab8NNLP0VBbAEq+yotPYK5VfZVonagViSkP43GJ9w+kw4fgKFg6dy5cz65y6qqoqSkxGf0EBoaio4OI6Shh4x4AlUPJXHaZEtLC/Lz8wV+bj4PgGEHoiiKRQ7BDqc3/x4UFOQzievn54cZoazIRGIVAC1KLJwt5+BVwcwS5eoi6msa45ZrynPHzKPrcz+3j3hlP+COR4y7gbV/zf7lCWBJBvK/xhz++r9hC8G7/xNG5oxqjPhVN3Di74H2MsbLp6puvhon35Dw89LGiI/VVa4pbH7AunNZVy6AEEiyhJT8AnQ3N30EnjYxdMziVnX6BDbt/RaDdvhz1xQ29X8H1edPY2FWNu7Ysl00P//wt7+CqqqCu2/uyiXJMrLWbbSKqWnFgvGpS7DqwUcAeJQ+hazyLMqediZp9M7X3vglJFUrdFIpFrkC0BF+2+e5KlWFLAN37GaRNHEdIqG8p1w44ePNx0FBDQ1chJa/qR0iAEOXLJWqFmhFf55CFWRFZ6Gqrwq8K5hZLlpverqpN23/aXUaw9PDhsTvp2GfWYfPzeVyYXh42NZhml+z+6LGxMRg1apViIuLQ0NDg6FXLodSgoKCcO7cOQQFBQkoyRx9l5SUQJZlS8tCTpE070DsnLuv5CwhRBRo6TX39aZ39oAnwk9GO4t843OtHHkiAff93+zn6rdYkVNXhSaPQBlNs+QAaygCatW40evqEA2SiUpjzt250rMbyHqAHX/u5zohM4Vdp/wPTAe/+i3N6c5inZUmSiX1/GuJ7jmDx6bwimrXJ7I2hpaP0GAnQ6cpRfGKvbPnqPVWNnHt7T5NRXGj8uQH1rGoNZ159ehhRCclA/Bo7ACs0MtVVYlVDz6CL/3kGVG5q4/a668UY0FaBuqvFAuGDXfu+sVDlmUIFpG4HSbXwC1ucYpHCVRnm//iOwCAoP4Z6PcVgVMychrC0BU16VWewV/2Z5Wys+zIJEgWbJwXgQHMuR5uYDLHmZGZlnaIhkSxRu3kxV08odo51imqd/0kP6yIW4Ga/hrRGnHfin2oHqhG01CToTm53viYOdE5lmMIPl1ZZHGdj6Ol82naJ6Wlw2ES7iz198tbAnL9G952sKWlBaGhoVi7dq2AalpaWkRvXH4sx8z1CdH09HSEhISI1815g8zMTCQmJgqoyY4imZmZ+ZH0fPi9bN++HRMTE2hoaPBRNEaRilZkoR4TCEIy2uGUelgUzimVF/+dOTZJ9jhuvZUc0BKqumIns0kOD0MmKIrBIjWaGJnsB+x5x6rBA9hLMxCJ/TfnalgfUbud5TwCxGayeZ5+2p6OyTXxdfLJevljALbOPjQ6Fnc+uBvdzU2oPPn+nMTTAN6K0MqmgelvGAAc/v5YetdmA/1SkmV86SfP2MI6fN7uaYaJZ67dgKiFSQgKDcXE6CiCQkMNi4ed8cSwWQ761X/4IevTq3H5o5OShaicfqdHWYEAVIniuA2TR4KEouwi3J65LSpQvWnj2MkdcG0avYYN1+jZt2IfhqeH0TnWidfqXhPjmt8P9w9H9UC1QfjtgbQHRGXulDIFiUiiFy2HYcp7yrH/xn60jLSgbbRN7AB4wZi5SIxboBz4iVTYfppaOv+lTQ+x2C1sqqoiMTERa9euNei586i7oqLCwHDRR9iqqiI8PBxdXV0GKKampgayLGPPnj3Ytm2bha1TX1+PtLQ0rxRJh8OBtWvXIiQkxKcEg9kiIyOFaqZ3o5ChYCMusaSseBDav8o048HvfZdh8xzi4Vh4VznTwql7T3P2ehkD88N1Mw15gNEylRnPhZRpBuWExLIx9AJszpUsmr/0HwyXB0zOXgIS8wFHIGt4QlW2MGU/BLSXAAPN8Ons7ZKwVYeBle+y/IAX7j0ytgOJyz1qnIBQmXRVVaKrsQ4NVy9ZThvr70V0UjKDeuycvW2SlxqOjUx0ImJBIlrKS6EobhAiITAkhHXCAsSC4/DzE/h8xur1FmfPhc96mhvFcbxByopdD+PS4T8ytU94T85yqibf0Qx1dyEgeJ5YLJbveECIxd2xZTsuv/GqbUN2pqtLIKlAdlMYTheYekWA4qWbL0GhCiRISA5PRstwi63TNzt7AoIH0x/ErtRdKO4oFvg/r8DlLQ3n+c2zjLdvxT7sztiN8p5ySyLWrbqREJKA4elhIYOsUAWnXKdQ3FGMF+55AfWD9YJL/9ym50SilyeQecEYKFvU9PTOT5Odw+0z7fB9wRsALFW4XOtdr1NjZubodeeDgoJw6tQpy7hcQz88PNzyxVEUxSCXwCEeSZKQn58v9G7MmvPz58/H0NCQ4TU939/cClEPOW3fvh1d518ChtqQi2qjszcMKHtolmWv6BQjvUXMFIjKAPrq7N+nOgdvfr/mmOc1vQAbx+l5pSaRgdV/BVz+taewK/8bDN7hMAtVgfE+YM1fM00dQ1tCw1OxT0SrKoNpWqy6LWIOHIIyGW9S3lFXjcbSK5Yon1Iqkqi25muHrbVLLNixi3HgtcIsSoDEzKVoqbgmoJjsDZsQEBwssHk9vg/AViBNb/VXioVj9jojQhCxIFHQN6mq2jZWAYBbN28gOimZNVr3cY8EBMnd8/C92O0Yj3HgpZsvQaUqJCIJGqcCBU3DTQxqobOLl/lJfqLilStuvtXwlug/q8fr9UZBUTPA6M1HGo9Y6J8qVIT7hyM9Ih3+sr9lIdl/Y7+gaxZ3FKO0uxRpEWmGJCyHk+xE3fQNUT4t+0w7fKfTifz8fEukzLtKiUbbpkbcZlyfSx3rIZvc3FxUVFT4jKi9FXrxc1RVRUFBAcLDww0LDwAL73/evHkWh+8tCpOgYseyaEzE5rNx0Qmo7wPw3fwB6fcwp/bHr5rkgX18waLTmUSCFxkCAOCNQ4w7Ad2YyjSjX7acA4ZdRpyeqmzXwWmfQVEmp6458cbTQOtFBkm1nAM6r/uWaTDMT2uQnvUA0HjS9J7MagLs4CedJSzJwpZvfhcnXtQlWgFIsgNBoaEY6esFkeRZIR0iyex+dJr6pw6+YIySKUXTtauiWxWXPSg+9IphrLrLxUJPf6Sv16uzB4AFaRkY7un2mSOS/fwQmZBoW0BmNsU9g6tHXkd86pI5UVWjr41ize6vYNO2TbhU+j5ulzWgZqAWjQvHBNyjUlUkPb0ZAcEX0r4gHGxebB7yYvOwK3UXSrpLjDAOtcJBfRN9Yhw7qx6oxu6M3Xjhnhew/8Z+0cPWT/JD74Qx6Hqn+R2QZo/UM1+AuNDbP176R8MOIzMq81ON7oHPsMPnuHt8fLxBKZMQgvvuu89QMOWLo88LrLq6ulBWVoba2loR5fuiS05NTYlI3myiSQIhiI+PF60Du7u7ReI1OTkZDofDoLzZ2dnpQ7JYvAoVBKj8E9bvDAMQoMPEZ7GQGIbP17wz+7G8acjav2b/nf4nq7Pktua/MXpmyW+9DCV5NPJlf6MWPu85y2mf536uLS66RCwAQGX3WPyvnvMS8z3SzJyhQ1VrlE8V4N19bJex8znWBtERCMRk2Ov9ezHOob965HUMdLQjMiHR3mF7M0KQsnwFmsuuQlVVNJeVYmxgwPZcVVHQ3dyErY9/T7y2ZNUaA20zNjlFYPVseO9Jf79ALTixeS960WJkrl4vErpN10p8av9wayi5jMV5BfYtGE2LQGtlOdprqnB30eMYf/kCqNuNDIQg7dY8gwQzb0CuL7RySA4Gj2gJ1ftT7wdgVNHkmHwHOkQFrB1j5sytMzhUewiZkZkG6qWYtibHcKTxCM63n2fzIRL2rdgHgFEs9aZvqPLd3O+KBQgAXKMug5LnQ2kPGSCgzwuv5mhmTrtF9dFUKFVWVuZtKKxZswZxcXGorq4WiwZn3eghGS4fzJO6doqV3Liz13ed0i9InKNvVt7kYmnem7RoES8oqpGOwkv/wZqLCAdJgMjFQGIhw60FLk5YIjU+jyVjvUX0RGZYtl8ww8uzdnmcoV10DACQWISeeR9QesDqbP1DgGndwqlMs2Nrj3mO7b7poXsmr2csINudFfU4EdXtgYX4e85VbFEwNFvh151iu4zwhSyHoBeEA+bk9DkffsWuhwXMU3zoFZ/O3tA4hVJ01FYL56i4ZyysF1/XDQoNFbsIIsmYGh83cO59Re++3u93tcL52F+Ke1qcX4jBznZELEhEZEIiSt950z7BSym6m5uw+S++Y2AwEUlC4c4HMTU+jp7mRnQ11QOUwj0zg6tHD4O6FeGMJQrE9wcakroULAn69aVfR1hAGArjCg3YuZk3r4+iJbDvLAGxtEcEmOTDP17+RziIg10HMngTFz/JD/P85mHv8b1GOIYypc3v5n4X9y2+D+80GwMmFSoudVzCte5rhqTsDwp/AGeoU8w7PSLdUiPwSTv9z6TDt5NH3rlzp+EYvbaML1imv78fv/3tb70mffWsm7kImXHjx5nzC3qOfnJyMsrLy6EoitDGDw8PN5wPMBefNF9C65CHNZOFesZPF/i6FuFm7WJ4uKoyx5n9RYZ/Zz1g7RdrnTXQV+/hvV/4BaNVFu5h51qMsGsERTGnbfdoHIFGhw/K9PD1Tcrf0SRsZX/mjJfcC9Qet08Wi2FUq65+azGL/L0taKUH2XmyP3Dndxlbiaos6axv02gyngytOn0CiuKGJEkouO8LuHbsiE8YBQBG+40wwMTosJcjjSbJ7KurFzhjt61q/yqov2IjQGdnhCBucQqqJAkK1fT6ddCTPg+hzwMMdXXg9uDArGwynkcoPXYEgx3toJSi7PhR7P7xU4hbnIKelka2YFAqKoA9PWspZgKAbV1ZuBbQhJ4IhpurVMXYzBjCAsJQP1hv0aHR8+b1pkIFVanhGmZTqYppyhYYmch4OP1hLAhZgHD/cKGqaR6zuKMYV7qu4K7EuwzvxQXHoXe8V/D6jzYeNUTwuzN2C9XQFytf/NTlFT6TDt8srcB58noWDt8B8CjdzMIBWOQzW6eskJAQ0YpweHjYZ5KYm6zpk3jT9bGTg7DTxudGoSJt6AJyMIlqxzJkua97GpRwZ8914Yv/zeMoKVikTylLWKbfwyJ9uyQrx8rNsgbVbzGHPzlifD06g7FsVA0u0bN0uEl+QOomo54OAAyZKKV8vsoU24FQyhavwEirRo9Ps+Phe7nOhecgnoEyxaCu0t+xHc7av0bHRChcVZWYGr9tiXBVRcHVo4dnh3CAuR1jsqCwcEyP30blyfdwQ6ezbzazKicALLojH203Kkz1ACqaykrZEJRyCo0wXjxlboCiKorPHYgky4hbnIIPXvglqk5/wL4X2jzdMzO48tbraL1+zbDj5cawdYBEBGH1TT9QdRz3kFghxkYIMSRfOcWRF1ndn3o//GV/W6dPQUUED9j31wUgmqcDHpkGX3LLbtUtkr7c5gfMZxW81HuTEz309GnLK3wmHb7T6cSqVatQXV2NxMREi5yBfgegqioyMjJsIZKkpCSfTVB4FymXy4UDBw6IRcPX8TxZXFFRYZtMzsjIQEhICGpqalBaWmp4j9NLzXN2QEEyXHCiE4VKJSzOWlARbZw4h3UUhWH3koPRDyNTNdhHYedHpbHo3uy0b/eyJK9ZSVPP3DH3hyUSULDHI5kwG2+ec+CJbr4qWLQ9p3yD6dr6L63k8Dwbs+ibwSg7r+ZtdFRcxCHXHXC7Fe8O2/y6TeKSSDIkidgqUPqyhCVZaLrGGEGUEEEqAGBhCZnNuTQHa3Z/Be/96l8Nydfe1iaBy5vHCA6PQF9bi+bcbT4rQhCZsFB07CKShISMLATOC8XJ/f9pv8uh1CA8R22+NwSAPDgpriZRggX9QRiMVHHXwrtsKY4UFIfqDqFvok8UQx2uP2xw1BIkPJj+IBJCEhDuH24rj8zNrbpxqO4QjjQewb4V+xAgB/hsjh7oCDRIKNcO1gp9Hn3BFY/gARhgnM1Jm1HZV4nNSZs/x/DnaiUlJUITR9/7lUMlk5OTBqql/l+9ud1ur1LH/Jzu7m50dXXZMnzMxpO0PJnscDgMyWJKKWpra23HSUpKQnt7u1i41q5di7VpEWgpO4Xk9iMeqiW14cbbOnswcbKeah2MQxmE0l7K4JDVf+WBNQZbANlhlRfoqvTSklB3jNnZZexgGjncHIHeWT6EsKRvYJiHocPpmWu/z2QPip/T8e+J6Xr6eUhW8bXQBCbRrGfPWDpyGZ2cazRYa0Zic9v6s/T9a23+LuIWpyJn01YLs0dcjztB7dz58Quw4v6HEJ2UjNbr1ww69ROjo5gav227s9ArXnJGj1kd0+Ef4PU+xgb68MELv/Ryk2xHOtzdxXafsoyM1etRe/HcrB23DPO0WyBNr8uSjDVpG/E/t30RAKM+8mg4OypbSBhQUJx0ncT59vNYl7jO4sz9ZX9kRWZheJrtgLwxcvQ7g2mFSR88mvmo15aJAFPZPHPrjEEkjUNQ5b3lBhgp3D/cAD1NKVMC/99ftR/OUKehScwnYZ9Jh19dXW34nUfdHN45edKYXAwJCbFlMLS3twsn3d1tT1mrrq5GRESE7fUkSUJkZKTgyOvVLQkhWL16tegty83bghETE4MtW7Z4CsTQCRwvgpNHz5z6KAcwamLxv+oSpF48U/dN9h5vJKJ3uLxXrdgBzHgqbste9qIrA+ZAx7qNDnPZbuDmm+wcIgFpWz3v6ZU2g6KAhg88QmU86r74756KX66gCcrmP9Hv4d8r01rErsDTI1e/8FFGI9U7/JFb2m1ozyFlI9PZ5wlmIrEFqvZdMZYzdBzykAOK29NMR5JlpCxfgYYSFrUSQpCz6V4M93ShtbLc1uHnbNqKidFRk7MHiEQYaiVJIESCqiqQHQ6suP8hTIyOoq+tBUvvYs1osjdsAgAth/CB4TqEEBTe/xDSVtxpaYYetzhFLEiyw4GCHbss0hBBoeHecwqao8/eyD5LXuWrKgpqLpzxkSCWLPdrZ/p75/9SVcXM+1WIXf1VJCzJEhTHwrhCHG08atCsAVghk5kqmROdg8K4Qjx9+WnB9+cLAgHB4vDFuDV6y6LLLxEJhXGFeL7iectcHcSBpLAkRARE4PfVv7eVbzY3SleogmeuPIMnVj4hYBxKjRLPJ9pOfO7w52JZWVlobGwUvy9btgyxsbEICgpCWVmZ5Y8xICDAaw9bHsX7upbZ1qxZI9Qxu7q6MDAwIHBKvluglOLixYuC8qmHg+warXB2kdPpZOyR0/9kKjCSgYIiD0wyKzZM4DXy5+YIhGcRUJnWTuEedg27FoZEBsIWAKOmwq7YTGDR/9bwd5U557ilxupa/nPhHs/9NZ6CwN2P/Q1737wgEIktctueYRo/nRVARxnEYqGP1jmNFABq3tY/YLYzkv01raByrd2i20g91aqPE3IfxW4Nw+cVppyyyIuhJInBUEtWrUF7TZWFqZO24k7csWU7OuqqDX1i9U1HqKoiNiUVsYtTEbc4xULvlGQZ48ODaC4rMcJCmrLmmt1fEQ5eX3XbUVeNUwdfEBH5pr3fxh1btlu0cILCwjB5e9QC8UiyjGV33yN0ea6feNdwb76b96hz4uVTVcWyzfcgLDoGnQ11aCxhVcx6fr8z29hl6nD9YUNClTvp2oFasRN4MO1BQ+KVyx5w5k9BXAG+lvU1i+b9vcn3Ii82D1uStog2iNxUqqJtpA3NtNk2EZwSnoINCzdYFoNpdRpvNLyBfSv2oWagBo1DjYZFa0vSFp/P6M+xz6TDLywsRGtrq6BG3rx5E4sWLbLVtgHgVRKZmzmRGxcXh/HxceTk5CAuLg7Hjx83HD81NYXMzExDYrigoADx8fGGKl5VVQ0N1svKysTxq1evFi0HDVRSoWNjug9KGaXQudITufu+K35H9scSifHQ2y5qzlViCVruqJ0r2blmbn17mXU8Lk1MKRuL7x7MjBe9LPLGH2rNybX7VN3WblWAZ7yuCuPOg0gs2k+/hx0XEssWqu6bbEGSHFry1wGkbwFC4tiCJnYKugVUP8+KV4CKP6BvfAlc9R1YsmqNUJcEgN0/fkpE25Un38NNDXJpKisVuvWynx8iFiTitad+jCWr1uCRv38aVWdO4rbWdrClnDlwSim6GuvQ52oBAEtPW1VRbOUcHH5+WrMSe5lklnzVqnYpxcToKAAm96x3+ByT11t86hLcvedxMWZHXTXqLhd7nLiWU/AJ58whUU0pRdziFNyxZbsFTmoouYyGq5cMej55sXnYv20/jjYeReNQI8p7y6FSFX+o+YNBdticeJWJjCdXPYmagRq82fAmXq97Hf6yv6Wf7fHm4wj2C8au1F3Ym70Xbza8icEp9nlRUAtzR29Nw024NXrLtvnJjb4bqB1gO05eGzA/YD6+kPaFTzy6Bz6jDt/lcuHGjRvid0VRhDP9KOZNkphz+ouLi3Hp0iXbcc3U0M7OTuTm5mLHjh3C6TscDsEcamlpMUT/gYGB2Lp1q3FQ1xV7pwcCOAI8sggT/RDNuTn33pvGTEwG6xxlbjodkcyOl/wYrq+vZtXEw5D7KFOy5EqYtuJmEnPG0JyrChY187nq703fF7foCMsh6OWT7RJrRGLHj3Ub7yEqneUdat/1jFfzjnG8RWuBW1cZxVP2B/KgU+pUgbEe4eARnwsc+x+AOoPrg3H4oIslMHmhE29aAmgNxzVGiuJ2o7u5Ca3XrwmGVWJmtpAkaL1ehhW7Hkb2hk1CiI0QYx7Cramcyg6HrZa98XFIyN92v6EX7e4fP2Vw+s7sHMgOh3g/KDQUl994FVPj44axDH/7msyD2dnrhdEIIZBkB5LzCtDZUGvpmztbe9H41CWCkw9CxEKUvWETY/nwYE0bg+v5RCclI2FJlihqerHyRZT1lInkqFl2OEAOwLQyDYlIeHLVk0iPSMcbDW+I6JvDOfrkqwIFr9W9xiQaVMVQkKWP6jm8Y2504k0Ln89RP8bg1CB+X/17bEra9Dktcy5mx4cPDQ2FLMs+K2r1f5CSJIn2gN6MO3OzjY2NIT4+3jBee3s7Dhw4gD179mDv3r2G5ixmaWVOywRgjHorXrFxehKQupFFxIBH6MwR4HGevjRm/OcB2/83cPafjS0MB5rZf5IMJORrkbsuOgfYfNI2s+hZHx0TiS0SADvn2u8gqJQFRexYc0FTyzmds53SICsTu8dsXOUyeb2G6+ssIMTTtFyZZnMtOWA8ZrCZJWupwq7VcsGY7NXDPjrRtct9TsMwl988hNuDg7ZsFKqq6L/VJiJqVVUN1bAAUHL0MKbGx0VfWHOjckmSkL1hE3N8Z076VN2kqoqa4nNiYVDcbriqKi1RPs8BcKhILDQ600uKLM4vFGwdng/Q7xRACOJS0tHT0mjb9jEkMhpZ6zag5OhhW6fv8PdHzqat6HO1WBYiZ3YOHvn7f0LxoVcs+RCqqmKh5fMqjCu00Bv1Fax67B+ARSSNgCArMgtNMUapYzvnbDaVqogIiDAsFhIkJq1sWigkSIyGrWnp63cen/PwP4Lpefjc0tLSsHbtWtt+sZmZmQgJCQEAxMfHo6urC9euXfPp7M2md+41NTWoq6uz/GFzltD69ettO2Rt27ZNSCsIrF4f9aZttl7YEeBx9gd2eo7d/qyneTd3qnaSxh1lDOZY9W1Ta0LtGNUNTAxqyI+GcwdFAQfu80TUkh+wnDIcfaKf6eGUHNCNoV1ToQxjL3vZI7+cfg+TdIjP03TztaYl3mQahElAwDym41/xina+bpHL/wa7L/67HXQVsRgYH/QwhHz1udWcfcd4KEbcgYa3ZianfBZYtddUQZJlQGJfcDPcwf9OeNTN6iwIVIXJDHNNee7YUpav8NlLV1TuApAkGc7sHFEcxjF/LtjX05ziEU0zOfxldzMMXdQacL4/j/aLHmd1J1p+yu2e8QrlZK3bgLLjR63OXoOA7i56XEhT8NwIp3TKDj888vdPY83ur7B8iGmXMz48KHZHfEdjdurmClYe8b9Y+aIl+lahWgqsuJyDnRSz+dzSnlI4JAceSX8E8/zmoXawFluStuCNhjcM0gsUFA+nP4ysyCycbz/voZkCn/PwP4o5nU7s2bMHJ06cEInY48ePo6ioCAsWLDA4fEII0tLSDBLIS5YssaViJiYmIiAgAE1Nnu2aXUNwALbnS5KE4eFhuFwumw5ZbkxUv4/1G7cAHK83RL02W3kieWQA3v7vHr67MsVgFE59dF1h+Ls+0RmRzCAPjoEHhnl0ZG73GYuf9M3CV32bJTX18+FNUByBDDox5xBEn1PVKGugKJ4oWvZnO43qtxh0ZIGGdMVjkBhF9NrLnp2E5Aes/h57ZqELWK6Bs384fHTtJd3Og7AdwpafsJ2J0NzxZgQAgWs8XPc7BUCQnJvvk5kCMC57yvIViFucgpP7f21IsnK1y+wNm0SU2tfWgsqTHyAkMhJD3V0GBo0kOzwBjQalMKKR1Zlmb2SJP65TrzdFVX0WTsUtTkF0UjL+9JMnjI6cUrinp7XuXtpLqrXBelhMLILD5gs2Er8+IQThcfEY6u4Sux7e3pGrj37wwi/FIqq4Z1B15iS2Pv493F30OE68+B+GZ00pxO6I72hWPfgIYocC4LpQibLAFtsK1vKecnSMdVhkinnHK73x3yXBaGOWEZGBxJBEnHGdMYyhqAr6JvpwuP4wVKriWvc1PJr5qEVrh4CIKmGJSEgOS0ZyWLJBX/+TtM+kwweA7u5utLW1id/dbjdaWlqQm5sr8HwupDYxMWHQzecCaXqnvXbtWmzduhVvv/22weF/lCYllFKUlpaivLwcRUVFup2IGzKdQXLjq0Drv3owcn23KNmfRcKGAVVPItWuUAjQNRTRoljOatFTGfWYevdN30JrNw5bm4/z63G4Z9hGTTExn+0mvFHylBlPH9zms1aJh7V/7eHi8960XHANYI5cT0Wtfx+48y+BruvsnLilHuoqt+NPaOweH/LFepP94ExJgqNPhZtKIAAy83NQf6XYp7MHGJf95tkPEbc4BbDwvtnvfW0tcN1k1bvXjr3FHGSjZSioqoI7Nm9DWHSMYAlNjd+2SBXLWqVr8aFXfBd3EWKrgT8xOurp6mVjzeWlPkXURvp6MT48JDpy6fMGK+5/yFOURSmqTn9g6aFrNp4gNs9z3vwIw9h8RyNyIrKMBSvnoWv+uAHiefz9x4XE8VxNn3glINi2eBsey3kM/1LyLzhQdUCMJUuyYRGYVqYRFhCGvdl7cbDqICgoAuQAcHE1FSpUqqJpuAltI21Yl7juc4c/V3O5XBalSkIIgoKCRPRvbnhi1r0vKChAb2+v2CFcvnwZERERhlaEHOM0/wHGxMRY9On5uIAR2ikqKkLL6ZeQ3PgqnGgHFNnDYOHNQPQNwSWHkaHTdNojC6y3+DwPvVHhRU0az3zjDz0wD28vyJUoFb0SpY0Nt3l/j6pAwwnAddX6+oI7PBALZ8bUva+LuCmDcTiUw6trqcKi98z7jGwZ1xVN+8ZcYKYZb7ICsDEzd5qYTdoCdfl5424lLAEY6YJ1h8HooQkrtmD3imS4Ss7AWbgBrj4FNRVVXh9JYEgoJsdY8tE9PY3Kkx9ANeHvqqrg6pHXBePGjPGbTZYdFufYUVdtlXhQVdu2i5LswOL8QrSUl2o8d2Lr1KfGb2Ows31O0JGtUQpF12rx7qLHUXe5WDRH6W5uMvD3iw+9IqikbGH0WEBwsCdBrDMiSQgIDjbUJSQsycLlN14VUT8AfCfyS+jLnSc0bLhujTdnz9kynInDX5MlWbRcpKAYmRpBeU85/lDzB3HM8tjlSJ2fikN1h8S5nCKaF5uHTUmbDHDTWw1vGRutUDeevvw00iPSP8fw52J6xgs3SimOHz+OuLg4Q4NzgEFAZvZMfHy8wbm73W6UlZUZxo2MjERYWJgh4s/JycGiRYvw9tu6hJ/JRFLWdQXOlnNwZiUArQPM2eujbdcVLdk6xZwWkTTndy8w2uWJmEUilVdoaswYfq4+sufOno+tTLMFI24pu65dR6g5G2UCZXavx+cBRV/xQCx8DheeMyZHxSkKRCRMVSuN07mS6dQL1tIs8gyd19mzFRW92ti9eu0TwqCusR5ApZ7K3IEmCFG15PVIcK5EwvqH2Sl11SK6JETC/PgFjM6oJTtDo6KFwweArsY6pnkvLkkgOxzoqPORP9Adm1a4Sqhx6s1VVWlllNk48bQVdxrUPD14+a8tu4CSt9+YVaph1ilrOjyc+6+43WivqUJ0UjKyN2zCzbMfQplhRUdcInn3j59iDB1d8lqfICaEIIJLOVDKdjZaXoEXopmZSCtXMnqu60IlOrIDRGLXm0wCBUVWZBaKOz1/z8tjlyM8INzAz3/p5ksYmxkz7BQqeitwX8p9FjaQWaMfYBLOdnRNlaqfJ23nalxL3szIcbvdqKiosMgj82h/x44dqK6uRlZWFrq6uiyLhsNhfFx9fX3o7zeqRHZ2diI2NtZ2XlzXPjc3F87uDz2FSLxwiPd/5QwWjuHzaJOqLCKemTAmJYlk4r8THU1ROzchn10DYJH88C1jfoBLA2c/BFQegsF5Sn4a7dL95y0GRGL3pmfk8CrZiQEv58ie3YwkaxDOAc8z4gnp+/5Fl4z2YcMutksAgLrjHnaOwUwLFlWYJhCRhGiauXaAtzm8euR1NJZeMcgVqIqCXhOuDUAwbCRZxuL8FQAgCovsnwVzfLLswIpdbKG5/Marhh60I329DIa02XHqLTg8Aq6qSvS1tRiap3Q3N7ECKnFJ8tGdvbmgihBxf9xhc5y96sxJhEXHiKi/9XoZyw1oO4Kg0FDDrrurqZ4lsyUJssNhbcSiUWD1jCRzNTLfIUhaIpx3wzpcdxgKFIPOvgQJt8aM0OW0Oo3z7cauaCpV0T/Rb9gpuCkTUdu3Yp9B+vjFyhcNOvflPeX456v/bEgOE+1//rL/50nbuZrT6URRURFOnz5tqLgFgGvXrtl2uuIKlKqqepU5jomJgcvl8tmEpK+vDz09PRaWkESA7XdmoXDrThbZ6oun3JOsyXdIHHD6GUBxs+rP1X9likolIx+ed3fq0CiTYlIK45Yb2DjljId++dcabEM8mLbk0Jgz3KET5nDjlnoYL3FL2bV6aqwLgtkkBxNfM0XGlnyC16hc08/JvI8xcMo4pdLkgIgMZGzTnMxsOCzVxOFkLT8wV9yWsudZd9xTpWtjTdeufmQHyZqcXJ2z5oyqKrjy1utCOM1ghECWHcjZvA0BwcGszy7ntOvsxqn3LWyb3T9+yhBtgxAkLMlCZ33trI1OstZtFA3Qu5ub0N/ehvaam2x8ygTSWq9fw91Fj7OIW4Nkbpx6H1zfJ33lGsO9NleUorOuxniPlIKqFHEpaXBm5+Dasbes96/h99dPvMuasGt9KgBWG8HZPaqi4MPf/gpf+skz2CDlob7pBDoixtEf4RaLjEOyusbGwUYLo8chORAdFG059nDDYUiQ4FbdKOliIml6lUyAMYfMO4zlscuxbuG6zxugfFRzOp2Ij4+3OHzu0DlLRt+AnJsdt57DPL7UMLlVVlbqjmNMDkpVTFz8DRAxxnBzQ0SqOSO9A1RVpiGz+q9Y4jH+DvYvZ7AoU+x9M81SDGmuSFW0pKbJORYUsd9LDsLjUClz1D3V7PjumyyRnLweOPO/fd/8/CQGN/U3MOe6vMhTrXru58Zdhy+ne/nXzOGHO7WF0caZUoUVVvGCLq6d43UXot0XIXP39+JUD6zUce51geEnrH/YZ2LTl/kS5hPHyLLQkpEkCU2lV+y1aCgVuYGy40c1eMa6oBqklHVR8aoHHzFUCXfUVUOSJITFxGKk1ztWX3+lGHn3sp3TqYMvWAvDtKh9YnQUdxc9zhyxoohZKTMzqLlwxnBKe7V9ToRSxirqaWn0PDdCkFqwCvPmMz2rvrYWcQ2AsXf0OxfxHBQFpw68gK6WetyhhGIZCcGt2AlMBihoShxHf6QbbaPGfNW4Mm4ZBwAyIzMRKAcaYB3OuTdz96eVaaGSOW3DvBucGvzUnD3wMR0+ISQSwJ8AJANoAfAIpXTQy7FhAG4CeJNS+lcf57pzMb1ipt70RU1BQUGG9/SFJoCHgRMVFYU777zToIrJzzf3nuVmjPxVyFCQrLZ4YBxbj2N6TVU0tUrKIvptz7B/Of3Sl7a7/aSM224+j/g8APvNB3vG1xdbCa18wpy7Wbt+Xgww3M4crwqP3APgYR3NGuFTrRDqnM055kNVIP9r7Do898GF2PTN0AGIXU1s1hyYORKQ80WtX4AGuyWvR8e513Holy9CoRLky/XYDYYXO/z8oMzMaJj1HbMmXufHL8CCtAxbVUnZ4cCmvd82aPTwvrR2zovdGotwARiSlYZDeIc2jZGmj4oBBk/xxYuqjIgYHDbf4vD1Xbr4gsF/tjVKBfxkWOAIAZlNhsHGVK47pfXZTckvEPmBGzZ1Dt6MU1IlEBAKLOoOBgAscYXiYnY/6pNu254X7h+OkekR4cyrB6qxb8U+vFz9MlpGWgAKsUNQqGJoWG5uhG7W628absI33/smfnPvb/5LRvhPAPiQUvoMIeQJ7ff/5eXYnwE4+zGvN2czK2YCrMBq7dq1AsOfmJgQWzhCCJYvXy4ail+5ckVo8fT19eHYsWOGsWRZxvLly33o8GhOEUAiurENZ+Ak3exlAZvAtOXW7R4IlzlWPYnZiX7m9OeCWQNg8gq68R2BmpImb4JCGVySD+/JWi5dwJ2pJDP+PCjD1Q3HytaCJ72EglkZc6Jfg4hMDVAAACp7b9jlqeadGrMeS7R71BeY8X/jlgrBM0yNATdeY89tTjRMyqp4V75rSDS7XnsZCpVAQaBQAlfJGaz67w9j94+fMlSgzubwh7o6RXcnQggy126AXyALQLzRE6vOnLRVm1x0Rz4A1sOWySPY70ILdz4olDP1om++ZBdyNm1Fd3ODYQEZG+gTP/PmKOxnGYqXHQvPNej/3lMLViElv8CQMOZN3GejuXLhNy4NLRY5QiDJsnD6dnIOkYlODHTcsnz3iGdw3FkViaHQGQxEKogIiEDfpOeeH0p/SAihUVC8Uf8G3iBvCPYOAcFXs74q2DgdYx14ve51qFAhQcLw9LChofn5W+cNomnT6vSnkrAFPr7DfwDARu3ngwBOw8bhE0IKAMQBOA7gk89E2JhZMRNghVP6hK25MxbH9j/44ANLT1rz1js/P19o3RQXM26wLMuIj4/XCrtY9EpAmbNHJzAvDhgf0HwwNQa3QRGsopVbxn1MRvjdfZ4oNSiKFT15g3G4Zd7HtGSK/83jxInMFovCPVpD8f3wRPGERbCWKJpYaZz5X/OcK/RxtMUnfCH7V1/wZBZI0ytjAgzm8Rbp63MFcgCQ/1XTsdqiWPo7oPyPnvoFvYU72XMTO6s5GpFYFy/TfTgLN0C+XA+FEsiEwlm4AYBHoIx3wTJo4c9ilFLUXjyHzX/xHaEfozcDp1wioIpJn7/qukeywYcS5dT4uChs8mY8Ca0vAAuJjBYRvSTLBjgle+NWMV72xi2CZqk3votwVVWK+RFCsCBtCaKTks15XizbxPIQs7GEVFX1LCSaSbIDy3fsEufaLRzTExOQJBmUqhrCqQpnz6tpCQXi+4OQc0cBijuKRTK1KLsIPyj8AVpHWgVbx02NvREoKA5UHYAz1InHch5DeU85jjYetXSy4mydjrEOg8OXIH0qCVvg4zv8OEop18LtAnPqBiOESAB+DuBrAHzqfRJCvgXgWwBr+PGxJhYXZ9HG0Ve5csvLywMAQyK3uHj2XqBjY2NwuVwIDPSU2auqigWhMroJhZtSSKDYgZOe5iRjPqQa9M4eYIqOXRWaQ9YSh8f+BhbnyBOkQhZAAhILWOWomaPOi7T0omeyP/udyypPjmi5AdUj26B3ouZzV30buPCvAFQG77z916xiN3n97A3AXVdYBG/WrfdM2vMjh5IcgQzSIpKxt61b09/R0065LAUhc9wR6S+tMB4/p7Nqi0nC+oexGzBg+IBVSOyjGk8k8kTm7h8/xR6RBuWICFaSkFq4Cs1lV0V3KTMu781uDw0KbRpvTp9TNbmzNyhVEoKC+74gcgS8QpibSPxq8hBcf0e/Y3H4+Rm0cooPvWJIDKuKgp7mRty953FMjY8bFpDIRKdRwZNSTI3fxsXXXhGvqYobAx1WlU+98R1K9KLFlupg1tycQiUUYVP+iBn0F3x9iUgYmxnDzy7+DGfbfYMVFNTApX/hnhdwtPGohfdf3lMuOmJxLR3JXCD4CdqsDp8QcgJAvM1bP9L/QimlhBC7v7a/BHCMUnprtoQnpfQ/AfwnABQWFn70b43OWlpazGMbqlwBGHRscnNzxXlzaUReU1ODhoYGbNu2zbNLkAhy659DLp1BC0lCcoQM58CNWceytc7rRhkCwBONG28MSF4DDLV5nPDkiE3rP2pUu+QFXbzoCvD8m3mf7whdH8G3nIMFWz/3c62xCGXz4fLDPHnrusJooFxTZy4mOViuIU9b8HK/wl5vOOnZmfAiND4/TjulksbOMWHM86KBlE3Ajde9LDjwwGk6qmxC8nokrP9XdNRVCwdqEBLzYkSSkVqwAt3NTZaiJRE5a4nUqjMndc5TZtg7WLS88oGHsfKBhw3aOHNpk9hcdhWNpZcFLZE3F+c6O7eHBgVriEgSIhYkmp4FRUDwPMMOQL9wmHcH5kUlYUmWoGHGJuv0/U3W1ViHV//hh9i099uGBWJh1jIGxeisp6XJkFejlKLp2hUDrOPNRnqsARiRJMRmZ6DvZi3S2+ZB6mgQVboykfFWw1uzCqhxM3PpjzQewbQyjaONRw1MnWllWuwgOC30/2+QDqXUa1ROCOkmhCyglHYSQhYAsEvnrwawnhDylwBCAPgTQsYopU/82bOeg+nhGn0lIa9yBWBoEH769Gls3LjRK4ffzhRFwcTEBIq2rUBLdSmS/QbgrHUBUOBEF4BFc5ipKWKfFwP4BTMHbv6j4hruwjlp+Hp8HpDWy3YF+d9gjlxvAaHA1G0ItcuKVxgEoi+6Mhc1Acwpc2EyPf89KIq9331Ti9Blo8PUV+MqU57F59pLwI7/Y59Mna1wCmDnqQq754Bwxlpa9W32b9Npj3O+8AvGFBJdwPzZAtfwAVBzDGKBut3HOnGt+W+M7dNfr01Bl1DmOQwhGDcDyH7o2PgrvPqrl0TAsGnvtwXt0CwrTEAQkZCI1IKVHskE3ftphauwOE9LPGoO8Fb1DbFbUAHkbLoXABMKqzpzEnGLU8SCQLTk52wQEneAqqLgxIv/AQCaVs4PLfRLqqpGnrv2OenhE66cySmZACwVsnrTF19xGIoTCUIiogy5AUVRMDE6ivxt96P+SjHSV65B2oo7jTLJhCA4LJx9z/WtQlUV8yKjER4Xh4mREZv7YDY9aS26opRiHglEP2U/U0XBHnIv+sZvYzgGeHXsvTk5ewmS4NKX95Tj2avPChaPvp8tT9ryhukU9FMTTgM+PqRzBEARgGe0f98yH0Ap/Sr/mRCyB0Dhp+3sAQ8Xv6KiAmNjY6ivrxe83OTkZIsSZmNjI1pbW1FUVIRt27ahrKzMoqoJAPGRoegeGAWFxvgJGofzeBGc7ilPohXQuiftMilQciNA0HyG0Y+0A626xO/4AEB1sgySA1iyjenoBISb9NzvBIIijZz+zuvWqHzJdo1tAo9ypL7oSi93DMLki9/dZ2o+7hELs/w71y2oOgNc/g+rEJzsp81pBrZMHEAXnWsMHr1sQs4j2qKjORD97iZzp4c/f/wJWBYVZdqT6yASkJjHdi5Tw8BYr6dxSsUrnnkr06h67zXhZLjmPac13tbpwBPCOPoDHbdsG4qAUrRUXMOKXQ8zYTBNCsHspAKCg1H6zlvCMRs6Y83WQUrj6PM2geyyFB/+9ldIWb5iVq69brICduLX9nY9rqbJFwIuDGdIrgpWnIy4lDSMDw+JuUiShObyUrTXMIom1wnK3rgVHfU1DIqhFNXnT2PFrocx0NFuqE8YG+jD2EAfstZtNDzL8PgFkGXm9sy7BYB9p3mXMl493VFcCkopgh0OEe3HDAZg2UQi5qUsxFsTpwxjRAREYOuirbg/9X4AVvllmcjCoXMZZ5nIWJe4DlFBUdiVuuu/Ji0TzNG/Sgj5JoBWAI8AACGkEMB3KKWP+Tr5/wkrLy83dJ3iWH1LS4slg68oCioqKsQ5ZktJiEZbRycAGRIotq1aBufEDY/OPAX7EiTms0ib94A19JfVGpNMDGmMEzNEY7quqnoc1hsmvZy2S7Dw6tUZVi0q+TH9muT1jNOu4b/Y9gyL6Mv/oGHhhEFAerljSxNv6K5h8y9VtOStCq8O2zwMt8QCTwWwt762XFIC1JOw1o9jYO6Yrj8zbqoBME+AeO6VKiz30Xnds3g4ApjDHzNrIxk/t/Fh5uRvnv3QwEXXR97eoEI9tdHuGKqquHrksGHuVFVFc3K9nLK+x+6yu+9B3OIUwcbpa2sxKE1SVcXYgJdKZy82J8qjxr3X6/hUnf4Ay3c8YKBT8gWh6vQHDIaRJKStuBOUAi06Z8+t5Ohh26S0q6oSX336X3D9xLuW7lidDbWGc/5/7V17dFXVmf9959wkAkIMhKcEAiERiOGVQCwMirxUUMAyYEUrPpZT7XRqWztdznRc7XRWq33Yjmumr7FVtEpbW6uCCII8hAqCCTGEAAkEAgkhvI0oEnLv2fPHfpy9zzk3uUgSJDm/tVjk3nPuOXufm3z729/3+35fQ72n/aZ2jCxLtXsEwFs+asVrTlMTHup5B8q7HEZk5U5YTiOc0ipMnZWPdY6bdD3deBrLqpbhtqzbUHS0yFesNXfYXGXQZWz/tX2vYUPNhsBuW62JizL4jLGTAHwi7YyxIgA+Y88YWwJgycXc80Kgyw87joPU1FSVsNVDPkqPXFTlxW2S8vERxGCDCaP9aeV6AEUwjYjDjUZ9GTesV/SAaxwsoEc/0WjEaziF1rzPy3W43sy+tX4Vy5YKjIbP5tRJtSCRK3Gg6J2iwEuPb0sJ4paMtw5ZICZDKwradawkrmApmUcy1OLNIci+tjp9M3MyDyGVvMAT3Lpkc3MYMZf/nzmZL0peg9XlKn/CXP8DjTZy737vam1KSci9aT527v+D8kgPlBSha2qar/AoEaaO1KwH4AtPaFfyvdNz4CBEIknImzrD0JEPolsCLpNo7bO/4c3Lk/hnj1VXxTXkUrcmXlgkHrzSDLFoVGnq6/r3W199WfH+Y4yha2oaeqT35u0gvU8gzq7iWHUV6ip3Y39Jse9Y9oSJKFm1PG4y/cq0Xvj49El17NMzZ1BXuTtQWwgAzu2rQ/cuZ9HoECwQ4DB0qT8PeNRUGmONWF61HLdl3YYkK0l5+MmWadDH9BmDoqNFiDpRn3xzW6DDVtoCftql6iIFN+RTXV2tCqiCQj1y22lbhBFnNuEgJiMG8EKq42sBeDwGidh5bqgnPeJKHFsR4Iw3USS03bNnAmDCs/WccnKf1q2KeMvCqzKB/evM88iC0p6XcecNT0Jd0IqYbRCZ8MgdPUQDkWidIUIjieTOiS9sU/7NLQyTi4ZlC3sv6glOHwDGLoIKHQUxefQuXwA3uO8+DVS+ZRrj5pB+DV9c5C4rYwK/r96YBeA7rWbhcO9eJZcJGHc3Bkyej2v31Ltqj46Dk4ebURKNB6FZL43xwu89gY0vLfF5t0GQDJNj1VUYOm48uqamGYVagL95+adnzmDa/Q+pUMuHR+t9OQfu+BAcJ2YmSxNlHxEhK38CDpQUG41h5KLi7aOr+PtCJlnlQ6Juo3HvvVP79VfeOnMcbP7LUpw5eQJeNJ49q3YSO9ev9i1sZxtOq3CXpI9ue/2VuEnww7vLQZYl/loYCEBO/5FYi71GERUDw2v7XsNtWbfh9zf9XjF0gsI1QR262god2uDrRl11kfIc9wqp6QVbRjFWwxZkFO9EXxxDNQYi84ozyDgXx9hLVKzkBl8yYqLn/GqSlsUN09bfAtGAql0rwg2+brRv/y2nIHrBGNeWubIPV3x871dixwAAxA2eNKxdemmeuLg22a5IGMB3Fb6WhTpEstWOuEVYkiEjOeyyNSIARXWUcX9Jl7STgXvfcBk8Mjmqmp5cIKUSAFKvdo29xOhFQMlLwc1kmsPe1WY/XsEQMmmINuoq/MV+cSEYa7rCI8ANdCQ5+YKGpzcz37F2FX+TMUSSk1U/27rK3Xj5P/8dsWiTUOtkwbsPxjBu1lyjQOvogf2wBYvIsix0vapnoDSyDDHZES7yNn7OfK7945GDILKM6t7cKdNVBXEsGkXZujUYPGocAOCT06d4WMWDLt2645Pkk4hKpc0dJbyrmAc73l6JSHIyblz8IMo3+FmCjuMgK388oucbkVPINX2CdhfGI3IcvUwLud1y8MwkXkRVdrwM62vWg4Eh6kTx69Jf4+HRD+PxLzwe93p6EVZbyioAHdzgA6ZR15UxvcZfCqnJcA4JT2f06NGcR196BCBCBjvCXzf6f7l8YMxkxMQ7p35HQP9WCxg+C4AnCelEeWij36iANoCMe8GA30DbSS6VEeBibf7BAFePcxcFabxVsxEva8jmXPi9bwPFS3jv2llPcc/8+TnBPXTlfVjMPRRrBJb9CzDnf8zkqDdWfyGQoRwfdEaQxWP0kunTb5RWhazBiQrNIfl5F1KREUCg7IFl28ifPQ815WWuBoxWG3Lj4gd9oZecwoktVurGheYJR8+fV8qYW175s/K24/XDlShe8RqGjb8OGbl5apGw7Ajypt6ElK5dfY1WAABEqiWiHk7qPyzHpwTqTRJ7mT1GF644Cem0/gNwZc+eaqHj141xbv2havM5NDWhcuvmQN0iIlJ9AQ7vKcfI66e1SMv25v4az34CvFuJWbmTUHBtATbXbVbe/pa6Ldh+dDuemfmMYcj1HruyAKstDb1Ehzf4ADfmpaWlSs/etm0sXrzYMPoy3i8xNM3ClInjuXGXBTxeDJ4kPPY4vyCRFBiMGOnZqkSrxT3HpC4wBb2Ie6ej7wSem+W5KOMa8JYtridvLz4sC7W8GHu3a8hrtvHdhxdkmVr8OmtH9pvV4cS4VLNMhjKHF14NnhgnQdoMju8Bnr0ZGFSY+GcCQUDeAr93r5rBNEElggeMBfqP5rmOGf/Jz2lsAPa/Y+YImMMZUnLHVPKij5Y5bpZ/gUkfPAQDsodj2PjrcP1d92HH2yvx/vK/cUkFwXQ5emC/rxhKJg2L31x2YaEU36Mgg+mSKJjjoKa8DHu2bFKLhBOL4pMPT6PhWH3gfSJJSVylcxffFci5ZOTmBVJGt73+Cub9638AgE/73hyMGW6S7+3++4bAsZ+qrcGwgkJjISAiRJJTeOhIhocES6h/znAl1ibDOJGkJL8InDaGofmFRk/h4hWvGQVzP8t+HCs3/gnvJ1XiWFqjLy4vu23JHrvfGf8dNJxvaHPvHuigBl/35AEYnjvgcvGDZRZ4u8Epp15GxqpfAmPudA02WS4X3ooAvXOAgeM9qpXEj4272/WoS15y9WfIBvLv4Ua0vpQXH1WIbTgRT6xKZkj1pmCBNBZzk4/Mw18P+sOxxfUkSpcGJHyJe+cA74+rd5OSDBkvV95ODt5pHNwsnpOlLs3HRJxeGq/imMWAQ1s9Xb0C+PlkAfn3us8QjBtkWSG8ezk33voC59txEJeMrivhjKXCrwihOkHP9N5X9SZAIC1Txsx1nKo9hBOHqrFz/Wrkz56H7W8uM2LazHFQtm41ANdYSEOZPigTHx3nz0nuErhODveIi99c1mIilYhaNPb9snJ8SVvLtnGy9pCvCnX/9m0ouPV23+7DsixkT5ioPP+DO0pQu7scvQYOQkZuHqY/8LCPPXP6iEt5luJzCVUpt3DciUXRNTUNkeRkUdPAvfGq4q2wbRujpt2smEuy8Ys7D1v1Fi5/Zx12rl9j7Eb070HG/VWNj6dgrndTE2ZSX6y57jgaejEjLl90tEjtAM7HzuNHW38EhzmGdHJbhXc6nMGvqanBkiVLlOc1duxYH8VStjvUoeL93naDYGZf2Zuf5EZm+ws8AWjZLk9eFijpHZ2qN/FK0z1vQnnBqQO5B7rpKX8jDst2mSuBSdMAaQXADeEwzzmS9qgbv5KlnmtavOF535HBoRhveKj7AKBnJtD7Gq7LE4Rew3juwYlpf6RMM/ZxCq2Yw435x8dFAtsbfiBg9i/8Hvymp8R9tMpYveGKd076daOf8qSwPO5VFQWAqNfjM0M7uiEHeJxaL3QKDIPADa94m3folbtMVLhef9d96nPpgzLxp+89FhieISIMuGYk6ipbzikENzEn1OzyV4gzxtB49iyyCq7jCeCPGtT8qorNuPfuv29Qnv+Cx3+I8XPmG8/g9JE61FXuVto+Cx7/ITb/ZamxmFw9PBd1lbvd5u1SxVb7eybL9j2DlK5dVU1E2bq3BCmBO3o90nurHdTWV182bEPmmHxVJTzjwX9WtQMyj3G24bTBNMqbehP6Dhmqisl0tVIwhghZmJcyBf8wc5FhuAv6FiBiRdDkNPEFQzRNb3Ka8NzO57CxdqOxALSm0e9wBr+0tFR9ibFYDB9//LFRcSspmnq7Q4mMjAxkTJnOG4nLdoOjF/F/utTAG99wPVAnylv0RbrwFn5er1ImPZUxcdxKVSX9qxkjJ8b7rO5b7Xr+EsNn8xBK1Xr3/P6jgO793AWFIHj0zKQ9ysWnodZjwAmY9HW+UL37dDNxdw1n6vi/g1vcBceLrj2B43LXE4Ae/YGPjviPk+U+76Cw0/BZweGahlp3h2TZ/BlvEvmEzMnxQwYK+iIqFnG99eKxXXyn40QBOxm50+aj/MCLiMV4wvb4oWrjakPzJyTW3ERAasvI8A5nr1iICaGxj04cVwYS4MnOvKkzg+WSidBr4CAc3b83fmjCOJ1EVFAaxiiu6N7dqHyFOB7EdAGA858GaMUz3tNWdrfqPXiI6gDGRB/fflk5Kpw1ccEiVfBkRyLoNXCQsWj1yczyxe3zps4EYOZPit54FafqDvsK3XRlTwA+9c4DJUXYv32bsduSCW+v1r98BqOm36IosfLaMpFvRyL44tT7MKBPfLE62Sc3xmKwyd/4vLUpmh3O4AdBCqQBQHEx5+rGYjFUl25CRvURv7RukNqjUb0aoAkU5FUqLRetVB+i3Z9+r9KlwPYXhSFmPJ5t9FoV6JXNy/9143R4OzfsdpLLeJHtEvWdhlx8ZOxfgQU3RkkILD5N8uAW93pWBMgoNCuK8xYKZpJngZFVu3IxVBRP8NeTvmHeR81NO48xzvUXxhmLlwETvx6n6lmHWCxkaEs3+CzGGVBX56u+tgv7jkRNeZkvTk6WhQlz52Po2HyjGUc8DBt/nSutIAzFjYsf5ONhvMH3jrWrsGvjWiPsI1lC0SbuKUrpZClq1nfI0DhNzE2dmeGTbsD5c+fc5CpjOOlZwCQuVLueMWYwh3RUFW9DVbFpYHUtHgBqfmCMtzmsNqu6P/nwNHoOMDV/mOP4EsUk9IP0BLk3dyDDN3F3W3HgVSAN0hPSRemKGjnvXurmzBs2DwwMe07tQdkJNzQoG5+3JjqcwR89ejS2b9+uMvIVFRWQ0sXZA9NhgcEhwLYImSU/Bpwa1yjonnCQcJi6yZ0avU8Yca/2uzJYgn/PYsIgR+DTiJf3KXqumZmRlivQwVwWiWwCou8y3vgmcKTUNYgOeOhG14QPLOBKQNumWWix8nH3iAT0LXysVsTtL/vu056Pxfjzn/yoSfGs32EKvUmohVWbg5641vv1TvoG3zWcqISbNBeSDFaE01ZHL3Irc73PoGIVMGymGsOAnBE4cagahyt2GUPKyp+gjED6oEzRReptxHR2ijAyskXg0QP73Z6vTU14f/nffOd7DZEuRpZTONHwNGUzEx/jhAjT7n8IHx6tR9Hyv4Exhr3bNnO2kWb8EhEQTBhxriX59TL2Xf4OzwXp6poq1FP2AWS9g46q4q04UNKytEfe1JtUKEciIzdP7f4ty1KdxfSmMOq8SMTIMdgRk06rQ18oJKS8tR2JYMzX7kWynYzUk4T+p67AR5FarIuZFbk2bKPxeWuhwxl8AEYbQqa2qTHsOXgENhzkUwVGZw/iQme6nszRXW71aSQlWF8d4O/d+0bzxsjb7OPNb0PF8EuXuucA3DDLZG+8LlZkIbAXqxT3kkqUEjXbOMNH98BJGLijpoEKvJfBjhD8fDBXjth7fno2cLwCPpBWYCWv6Qg+fuVbwfPxhmPk7kQKvQHuohzYEcuTxJaqnHL3Iyt9LRvImQmeTO5jFoJlTuZSzPoOREpUC7G5usrdWPvsb4xnRZalGo1Lr47TDqfjZO0hHpNmTCUAS1Ytx57NG5XBYeAa7h8GSABIQySv26V7d7UrOLynHAse/6GrOw+osJDhlTOG/SXFiJ5vdFmxwnu17YgvFwHwHUGfzKzAHrlkWRg6bgKIuMd+IX19pcyCZdlGqGjn+tW44/tPqkVTD/VIHXs1J7ED8j4r73fipX5KhVDHYYpQMPW+fwqsUvaqfKZ07daixLTeMH3I2PFGA/cr6s7hZ9mP4/2VvwOLxuBU1iC1EDiepo+ZkJ2WnfCzTBQdzuB76ZUmuMRsKjuNDCSbyVjZJEM1Fm80QzQS+g4gyBjpuwQZq9+3xjW8TpR78iVL+aIBaOGWCDD8JgAEnNireaIABl3HwzcqdCHCD9J79o6zdKk/3JKWCfQZCVS8Gef5iGt+4Wtus3OyeIhDJpn3eD8reO29srlIW/UmvqOQz5E5XLTs5ifNbllKK0e/lLj3qsdcg9wvzzXmUgmz8i2++NkRTjdVXbwCpuTE+Gfl53e/7u4AnCY39+Hl5i9eJsJtfzQZS1pvW28vWyLC9AceVnFfQx/fY4SY43BpX2kIRKw+HogIg0eNw4lD1UpWmJOfhEMTjWLb66/wvIHjqGTptPsfwprf/cq4d1XxVjEIphaSvkOGonyD35gPyBmBLt2785SQHeG7Dn0ejKH/sBwU3r5QNQ/nOj8RZI7JR/UHxYGLCAAMuGYEIknJiCSnGCEYJxZD+TvrjJ2MDJN4mTVSKVQ3+v2GZqNbWk+c++QM6ir4Arv++WeQPijTV4Tm3jOKAx8Uo19WjlIBlUZdV/mUCyuAuL0FasrLXKXTWEzpBDlwm8GUv7MOFBUFXA7Q7+QVOJ7m5giiThTLq5aHHn5L8LJvAPFLwRiY7C2LWqDyAy7VK2Pd1ZtMA2RZZugFMGPhdjIw5ktunF424BgxVxgsLaaMgC1nrBF4+/tc0lh6kQ5UjBjPCY9aorYIuOUnXEvmcLE433G7TEmPWBn+AONxqponN60kP08+byGQciV/b/hsvya+TIxaEXchkclhFuPxbjuFL2JHdwErvunOP9rIn7PeLcsXRrKA2T/n5yklz5jWE0BU3eo7jNh5fj0rSOxNgvh3yYRW0Yi5fHFWnrvGIAJgsHwmP8rnntLDzXPIHQh40k960ESEgtu+qMIGPn38AM/YVGWkwMIgCRmX1hPB3vVN54ZHm5pUc/IPj9abLCE5FiIMzhuDiQsW8fHq7BciFNx6u0EltWwbwwoKsX+7OwbLslRCOSiBKZuLN5371ODOk2Whfm+FYrwEtSIEzNh34e0LfcyavkOzkZGbZ8yvvqqS5zGmzODVz0LMbf2SZ9BnSBY++fB04CK0r2irmxDWFD8rt25WBtzbq8BLpwUCdlaMIXfKDFWUBvBdDP8OuTxDUwqXVNb720pphjBp2wz0PrUAkHV1Oqb0Pwsc34Pqg4eQiVpeTOXA1Xbf8ATnk9spplcbN14swkBS8ExvwHFgI1QfWoU4YmR6ElNeK3Oy8M49oR0nyumgR3aY1z33kbkIyTCUnmdQoWiHe7z59/DWf3o4SlIyY+fddoGTH+W3MZK+ES45fGVvPmY976BLLevQF88P/hjMBCJyF1+DuaQZZBa0ULA4TVTEAmGnuElsKcQmqbUlLwKxKMzvx5OPqdnGdzsyqe3EgFWPoe7T7lj//EuGPkzJquUYNv46DMgZ4Y/7ah6+ZduYdv9DSB+UqSp1dXqfzu32gjmOzzh6hcr4I3cZKSlduwWylCzLwsQFi5Sx8oZ/+A5E84IdB/2ycjB+znwlA139QTHK1r1lJJT1HY5uFAeOyEXZujW4smdPdE1NQ9m6t1Sz9KH5hUreWMbHg67hZdYcq65CnyFZvvnForxQTP8O6qsqOQ01aCflfT6CYbT22d8Yuv3eRvHevArAdyTT7n/I2O3oktk15WVuz13hmN2KiUi1B2JF9F28R5yZFGOxkKXTEgzBNIswpf4ZZNTxApUMaIaBbG7w1v6Av65ax5N6V/SIn7DVE7F6a8ANT7gqkQzCo/SwXobP4nHi7S9oBko73nMI18jJmMDDCAbEYiATtPr79Tv82vYyESzzDF16uWESSTX1zk/KB3uvA5gLnQMuvzD5UcHpf9EtSNINZbzFc/EynqjVGTAA99Llc1+8jIdugrp2ySSrrFpWIRstwWonA7f8ND5TSS6MsrhNb+yif0afu77wxM6jpugdH3ND/+P3hiFkoY+MEQNmIi/3hqm+XrJBDB9LVPUWr3jNbHHoQf7seUa1a5AKp36O10jZSUnIKZyI2l07ldG3bVuFMAbkjMDWV19WRjoes0U/Vnj7QqPLlu4lyy5eeihl66sv+67hhZx7UHVst6vSAvn9YEz1E7AsC9feOBNnG04bdE8ARvtIIsIgsRsCTOqlnuCVkLsdXsC1WoWspDict/r4ZHkFTpZXYKRto2ZCd9RfdbZNhNQ6nME3BNMatiCjWCRmyYJqkkEifODtDFW/A/jyq81cPA5lU6lEeouz/uBSAyc94nreMtmr0wQnPuJeT/fOrQgw7stupawu/qWHKOS94zGA+o5snn3kXcziMY70YxkTgHtXuBIMei4hXiPzjAl8wfAafF36IWMCD23tWQl3V+Tx1uUY9MWWLH/TdQnv7kwP2TQHb1JYJMkzCm6Avb3W7XClJVUlmmsYHmTMCm9faBjg9EGZBkNFNg2//q77DHEz1SpQC9WkdO1mjCN3ygwfZ18/B/BzynWWEWCyZwCXvRJk+Jo7JscURF9M5Pp2JMlYhMzq2NVCPiWixjtxwSJz4YpEMPW+rxgJ2rrK3VzdMxZVi4C3qErfDTXXylGfo+7NA1CdvKY/8LCizOrNbADgoZ534MTobm1SaUutSr9qRRQUFLCioqKLu4jXq/Py04uWcO0XiVuf9hf1XMi9vAauJYpn0RK3r2xQMVHQZ3WNG71HbEtU0s86h0SOfZb76A1XZOzfO0+9dmDs3cHJ6SDPPWh8iZ4Xb7xebX7B0mlJgz4egsIVQZ9N5DzJOCnfsIYbu4DzvIlKOxLBwu89kfB4m5tHPMPX3LGLub6cL+BfhOLds7nPtHSvi5lDc889iG3V3O9CoiCiYsZY4NagYxt84OKMboi2Q9DCFXROIotMa5/XTkjUmLTWeYkYvRCtj8+62HxWdG6DHyJEiBCdCM0Z/AS7T4cIESJEiMsdocEPESJEiE6C0OCHCBEiRCdBaPBDhAgRopMgNPghQoQI0UkQGvwQIUKE6CT43NIyieg4gIOXehyfAekATrR4VsdCOOfOgXDOlwcGM8Z6Bx343Br8yxVEVBSPA9tREc65cyCc8+WPMKQTIkSIEJ0EocEPESJEiE6C0OC3Pv7vUg/gEiCcc+dAOOfLHGEMP0SIECE6CUIPP0SIECE6CUKDHyJEiBCdBKHBv0gQUU8iWkNEe8X/ac2c24OIaonof9tzjK2NROZMRGOIaAsRlRPRDiK641KM9WJBRDcTUQUR7SOixwKOpxDRn8XxrUSUeQmG2WpIYL7fIqJd4jtdS0SDL8U4WxMtzVk7bz4RMSK6bGmaocG/eDwGYC1jLBvAWvE6Hv4LwMZ2GVXbIpE5nwVwD2MsF8DNAP6biK5qvyFePIjIBvBLALcAGAngTiIa6TntAQCnGWPDAPwCwI/bd5SthwTnWwKggDE2CsBfAfykfUfZukhwziCi7gAeAbC1fUfYuggN/sVjLoDnxc/PA5gXdBIR5QPoC2B1+wyrTdHinBljlYyxveLnOgDHAARW/32OMQHAPsbYfsbYeQB/Ap+7Dv1Z/BXANCKidhxja6LF+TLG1jPGzoqX7wEY2M5jbG0k8h0D3Fn7MYBz7Tm41kZo8C8efRljR8TP9eBG3QARWQCeAvDt9hxYG6LFOesgogkAkgFUtfXAWhlXA6jRXteK9wLPYYxFATQA6NUuo2t9JDJfHQ8AWNnM8csBLc6ZiMYByGCMrWjPgbUFIpd6AJcDiOhtAP0CDn1Xf8EYY0QUxHP9KoA3GWO1l4vz1wpzltfpD+APABYzxpzWHWWISwUiuhtAAYAbLvVY2hLCWfs5gHsv8VBaBaHBTwCMsenxjhHRUSLqzxg7IozbsYDTvgBgMhF9FcCVAJKJ6GPGWHPx/kuKVpgziKgHgBUAvssYe6+NhtqWOAwgQ3s9ULwXdE4tEUUApAI42T7Da3UkMl8Q0XTwhf8GxlhjO42trdDSnLsDuBbABuGs9QOwjIjmMMYuu6bbYUjn4rEMwGLx82IAr3tPYIzdxRgbxBjLBA/rvPB5NvYJoMU5E1EygFfB5/rXdhxba+J9ANlENETM50vgc9ehP4t/BLCOXb7VjC3Ol4jGAvgtgDmMscCF/jJDs3NmjDUwxtIZY5ni7/c98LlfdsYeCA1+a+BJADOIaC+A6eI1iKiAiH53SUfWdkhkzgsBXA/gXiL6QPwbc0lG+xkhYvJfA/AWgN0AXmaMlRPRD4hojjjt9wB6EdE+AN9C8yytzzUSnO9PwXepfxHfqXcBvKyQ4Jw7DEJphRAhQoToJAg9/BAhQoToJAgNfogQIUJ0EoQGP0SIECE6CUKDHyJEiBCdBKHBDxEiRIhOgtDghwgRIkQnQWjwQ4QIEaKT4P8Bny9Aq8dun5oAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# filter out those not in asmmetric unit\n", "some_points = some_points[[in_unit(*p) for p in some_points]]\n", "homo_points = np.concatenate((some_points, np.ones((some_points.shape[0], 1))), axis=-1)\n", "\n", "for s in my_group.genpos:\n", " g = symd.str2mat(s)\n", " xp = homo_points @ g\n", " xp = np.fmod(xp, 1.0)\n", " plt.plot(xp[:, 0], xp[:, 1], \".\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "8d54b539", "metadata": {}, "source": [ "### Fractional vs Euclidean Coordinates\n", "\n", "All the work above required the points to be between 0 and 1, which are called fractional coordinates. Namely, a value of 0.2, 0.1 means that 20\\% of lattice vector 1 and 10\\% of lattice vector 2. How can you can you work with real particles though? You can easily convert via matrix multiplication between fractional coordinates and Euclidean coordintes. In our example above, the Bravais lattice is square so let's make a square set of lattice vectors to see this:" ] }, { "cell_type": "code", "execution_count": 18, "id": "45e11369", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[11 0]\n", " [ 0 3]]\n" ] } ], "source": [ "v1 = [11, 0] # 11 wide\n", "v2 = [0, 3] # 3 tall\n", "B = np.array([v1, v2]).T\n", "print(B)" ] }, { "cell_type": "markdown", "id": "22708ba0", "metadata": {}, "source": [ "Note that we have the lattice vectors as columns. This makes converting between formats just a matrix multiplication. We can switch back and forth using the inverse of **B**" ] }, { "cell_type": "code", "execution_count": 33, "id": "4d70b71d", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Bi = np.linalg.inv(B)\n", "\n", "N = 10\n", "some_points = np.random.uniform(-10, 10, size=(N, D))\n", "homo_points = np.concatenate((some_points, np.ones((N, 1))), axis=-1)\n", "\n", "# convert to frac coords from Euclidean\n", "frac_coords = some_points @ Bi\n", "# convert back to Eculidean\n", "eucl_coords = frac_coords @ B\n", "\n", "plt.plot(some_points[:, 0], some_points[:, 1], \"o\")\n", "plt.plot(eucl_coords[:, 0], eucl_coords[:, 1], \"o\", color=None, mec='C2')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "6edd1a7d", "metadata": {}, "source": [ "You can see we are able to go to fractional coordinates and back to Euclidean with matrix multiplication. In simulation engines, we also will wrap using ``np.fmod(frac_coords, 1.0)`` on the asymetric unit" ] }, { "cell_type": "markdown", "id": "4400cdba", "metadata": {}, "source": [ "### Bravais Lattice\n", "\n", "The Bravais lattice isn't always square. To get correct lattice vectors, we can use the {obj}`symd.project_cell` function:" ] }, { "cell_type": "code", "execution_count": 34, "id": "78f4538c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "This lattice is Square\n", "[[1.31528419 0. ]\n", " [0. 1.31528419]]\n" ] } ], "source": [ "lattice_vectors = np.random.uniform(size=(2, 2))\n", "blattice_vectors = symd.project_cell(lattice_vectors, my_group.lattice)\n", "print(\"This lattice is\", my_group.lattice)\n", "print(blattice_vectors)" ] }, { "cell_type": "markdown", "id": "2b907ae6", "metadata": {}, "source": [ "There are a few other convenience functions, like counting the number of particles in a cell if you duplicate for all sites, and getting the cell volume" ] }, { "cell_type": "code", "execution_count": 35, "id": "da616840", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The volume of my cell is 1.7299725113082867\n", "If I have 8 particles in asymmetric unit, there will be 64 in the unit cell\n", "If I want to have a number density of 0.6 with 8 particles,\n", "my cell should be [5.163977476386403, 0.0, 0.0, 5.163977476386403]\n" ] } ], "source": [ "print(\"The volume of my cell is\", symd.cell_volume(blattice_vectors))\n", "print(\n", " \"If I have 8 particles in asymmetric unit, there will be\",\n", " symd.cell_nparticles(my_group, 8),\n", " \"in the unit cell\",\n", ")\n", "print(\n", " \"If I want to have a number density of 0.6 with 8 particles,\\nmy cell should be\",\n", " symd.get_cell(0.6, my_group, dim=2, n=8),\n", ")" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.13" } }, "nbformat": 4, "nbformat_minor": 5 }