{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Quasi-random samples\n", "\n", "As demonstrated in the [problem formulation](../main_usage/problem_formulation.ipynb) section, \n", "Monte Carlo integration is by nature a very slow converging method.\n", "One way to improve on converging\n", "The\n", "error in convergence is proportional to $1/\\sqrt{K}$ where $K$ is the\n", "number of samples. It is somewhat better with variance reduction\n", "techniques that often reaches errors proportional to $1/K$. For a full\n", "overview of the convergence rate of the various methods, see for example\n", "the excellent book \\\"handbook of Monte Carlo methods\\\" by Kroese, Taimre\n", "and Botev `kroese_handbook_2011`. However\n", "as the number of dimensions grows, Monte Carlo convergence rate stays\n", "the same, making it immune to the curse of dimensionality." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Low-discrepancy sequences\n", "\n", "In mathematics, a [low-discrepancy\n", "sequence](https://en.wikipedia.org/wiki/Low-discrepancy_sequence) is a\n", "sequence with the property that for all values of N, its sub-sequence $Q_1,\n", "\\dots, Q_N$ has a low discrepancy.\n", "\n", "Roughly speaking, the discrepancy of a sequence is low if the proportion\n", "of points in the sequence falling into an arbitrary set B is close to\n", "proportional to the measure of B, as would happen on average (but not\n", "for particular samples) in the case of an equi-distributed sequence.\n", "Specific definitions of discrepancy differ regarding the choice of B\n", "(hyper-spheres, hyper-cubes, etc.) and how the discrepancy for every B is\n", "computed (usually normalized) and combined (usually by taking the worst\n", "value).\n", "\n", "Low-discrepancy sequences are also called quasi-random or sub-random\n", "sequences, due to their common use as a replacement of uniformly\n", "distributed random numbers. The \\\"quasi\\\" modifier is used to denote\n", "more clearly that the values of a low-discrepancy sequence are neither\n", "random nor pseudo-random, but such sequences share some properties of\n", "random variables and in certain applications such as the quasi-Monte\n", "Carlo method their lower discrepancy is an important advantage.\n", "\n", "In `chaospy`, the following low-discrepancy schemes exists and can be evoked by passing the appropriate `rule` flag to [chaospy.Distribution.sample()](../../api/chaospy.Distribution.sample.rst) method:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:10.315249Z", "iopub.status.busy": "2021-05-18T10:56:10.314943Z", "iopub.status.idle": "2021-05-18T10:56:10.327113Z", "shell.execute_reply": "2021-05-18T10:56:10.326702Z" } }, "outputs": [], "source": [ "import chaospy\n", "\n", "uniform_cube = chaospy.J(chaospy.Uniform(0, 1), chaospy.Uniform(0, 1))\n", "count = 300\n", "\n", "random_samples = uniform_cube.sample(count, rule=\"random\", seed=1234)\n", "\n", "additive_samples = uniform_cube.sample(count, rule=\"additive_recursion\")\n", "halton_samples = uniform_cube.sample(count, rule=\"halton\")\n", "hammersley_samples = uniform_cube.sample(count, rule=\"hammersley\")\n", "korobov_samples = uniform_cube.sample(count, rule=\"korobov\")\n", "sobol_samples = uniform_cube.sample(count, rule=\"sobol\")" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:10.330216Z", "iopub.status.busy": "2021-05-18T10:56:10.329893Z", "iopub.status.idle": "2021-05-18T10:56:10.632604Z", "shell.execute_reply": "2021-05-18T10:56:10.632883Z" } }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA54AAAIUCAYAAABy0/PtAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAEAAElEQVR4nOz9eZxcV3nnj39Ord3VLbmxFgcHjO0I32/GQRYWyzhOQgxmcfz76ktwnFjBVkgG20M803b8BRSWySgJBowJA5ovi5EzEIlEJo5IohnjsBOCYzARsWU8k2sUMCaxg2QJWWpVd1VX1f39UXVbt6vvcu69z1lu1fN+vfSye6t77lme82znOcLzPDAMwzAMwzAMwzCMKkqmG8AwDMMwDMMwDMOMNmx4MgzDMAzDMAzDMEphw5NhGIZhGIZhGIZRChueDMMwDMMwDMMwjFLY8GQYhmEYhmEYhmGUwoYnwzAMwzAMwzAMoxQ2PBkjCCF+UgjxDSEE3+fDMIw0Qoh3CCH+TQixI+Ln9wghFoQQvzj4+lwhxP9O+MyPCSG2kTfWYoQQB4UQG0y3g2EYcwghbhBCPC6E+GTKv/uIEOK4EOINalrGjCpseDJG8DzvXwFcY7odDMMUC8/zbgPwNzE/vxrAvwW+fhzAz/pfCyHeIIT46tCfvRnAn5E21H5+wfO8Q6YbwTCMOTzP+ziAT2b4u98G8FDwe0IITwhxLknDmJGlYroBDMMwDKMSz/OOJ/x8TlNTrCGpTxiGYRiGGo54MpEEUjDuFkLsEkI8JIT4ByHEHiHEF4QQfyeE+KgQojL4/d8bpMD9f4Pf+Y4Q4k+GPvPtQohHhRB/A2DL0M+qQog7hBB/P/j3fiFEdfCzzwzS535XCPHXQojvCSGuFkJsE0J8WQjxiBDi+do6h2EYUgby48uDf/9LCHF24Gc/NZA3DwghPgFgcuhvrxikjn5VCPH2oZ99yffECyFeBuB3AWwa/O5/F0Jc56eaCSHOEUI8JoT4sRDiPYO/f58Q4qgQ4ncHX28bHBP4WyHEnwkhVke8jy+z3iKE2C+EODKItgbl3NeFEP9VCCECf/f/Dj7/K0KIzwohLhZC/HowHU4I8aZgunGErP6qEOIsIcR9g8/6uhBi++D3/2g4TS7wXl8btP2swLjEynWGYQrPhBDiTiHEtwdyZ0IIMR2l7w0jhLhv8L93D2TPT4o+bxnIla8LIf6HEGLV4Pf9VN0/FP3jEY8JId6t7W0Zc3iex//4X+Q/ADvQT1tbh76jYheAawM//ySA/zD09T8CqAOYAHAUwCWDn/0SgKcAnDn4+vb+FFz62/8C4IsAyoN/nwPwXwI/fxzAzsH/vxbAYQC/PPh6J4CPme4v/sf/+F+2fwD+MwAx+P83ANgT+Nk3Abxt8P8/CeAYgB2Dr9cCmAvImS0AFgH8YuDvPQDnBj77q0PP3gHgk4P/3wjgGQCTgc//xOD/LwXwNIB1g6/vAHBXzDs9DuB/DP7/FwFcCeAdAL48kHFVAH/vy1QAvw7gOwAag6/fHHjPpTYOvv6k/7PAz4Oy+nYA7wOwffDzKQBfD/z+VwG8YfD/Pz+Qp/57vRPAl4aeFSrX+R//43/F/jeQHf8K4FkD2fEIgK0AzkS8vrckQwZfL8nZwdfXAXg0IM/uAvDHQ39/LwAB4NkDuX226f7gf2r/ccSTkeEBz/OOeJ7XA3ADgOcNvFdfRV+Z2jz0+1/xPK/led4CgO8COG/w/asBfNbzvGODrz899HfbAOz2PK/reV4XwG4Avzn0O18Y/Pc76CtYXxx8fRDA+VlfkGEY4/wQwFeEEF8DcAsGckUI8TwALwHwKWDpfPjXA393JYAfeZ73wODn+wHMZ22E53kHAXwffecW0D+Lfvfg/98A4H96nndk8PWfAXh9MGIZwl8PPvernufdO/iMPxnIuUUA96CvoAF9effnnuc1B1/vAvAXKZq/JKs9z9uOvoF+hRDiQs/zTgF4VcTfbQPwvwLv9QkALxdCnBP4nSi5zjBM8fmm53k/Huh530F/ff8YyfpeHNsAfDogzz4B4DohRDnwO5/z+jyFvkPr3HyvwdgOn/FkZHgm8P+/AeBGAJs8zzs2SPU6d+j3TwT+fwFAbfD/zwbwcOBnx7Cc5wA4Evj6yOB7QU4O/tsBAM/zgl/XwDBM4Rikyf85gEs9z/uW6Fek/eTgx88e/PfpwJ8EZcezh342/PMs7EZfadoL4HIAHx18/zkA/p04XZyoAuBHANaEtMHnmaGvnwPgViGE71SbBnA88LMlGeh53jMhfx/H8O/eAeAUgE8LIToAbkPf0B3mOeg773yOBL7/xOD/o+Q6wzDFJ7i+W+ivbxl9L44wna4K4CwAT4Y8l+XKGMCGJ5OWlwB4MBC1rKb426fQj1L6rBn6+Q+Hfr4OwL+kbiHDMEXjhQBOeJ73rcHXQbny1OC/63DaCFqDfhqr//Og3AD6KWJ5+FMA7xZCXAbgsUEGBtCXUd/zPO8m/xeFEGs9z4syOsP4IYB3eZ53z+DvSwBmAj9behchxBSA53ie5wJoo5/q6jODZNZ7nvffAfx3IcTlAP6XEOLbnuf9c0ibhmUvwPKXYcaZPPoeEC5XFtF31jFjCqfaMmk5BOAiIUR9cMj8FSn+9s8B/JIQwjc4f33o558EcK0QojxQxq5FPzWDYZjR5hCAZwkhLhh8/Rr/B57n/QDAgxikowohfhLAywJ/ey+A9UKISwc//3/QjyJGcRJAY/C7+8KKZXie9yP0z2F+CsCewI8+CeBKIcSzBn/vAPif0m95+jN+PZBu9hvon/v0f/arQojG4OtbcLovvo9+tFUIIc4E8FKJZ71HCLFp8P/fRN94DUsL/iT6snltoE1f9jzviZDfZRhmPEir780BaAghrhVC/ApOyzO/GNxvoH92vxv1AcwYYPqQKf+z9x/6huHj6Bes2D343hSAvwTwf9BP2frLwc9vHfz7t8Hf/DKA30M/heyfALx88PdvB/C/0T+r+Tb0D6N/Ff30iir6BTH+fvDv/QCqg7/bjX4axkMAHADfGPztX6PvlfunwbPeZ7rf+B//43/p/wH4w4Hs+GsAdw7Wuy93fgr9c53fQD/99TOD371h8PNfQr8gxtcAvHvws4cGsuFLA1nxDfQLEz0LwLcB3A/gQ+gbtL6ce0egPb8G4B9D2nnt4LO+jP59ohdEvE9QZv164PtVAO8dfMZX0DdsG4Gf/7+Dn/0t+mc8K4PvTwK4b9D2O9E/d/o4gP+AEFk9+JsrB33yZQAHAMwOvv9HAdl85dB7fW3Qv2cNvp8o1/kf/+N/xfw3JDvehH4dD3+9vx7R+t5HQmTIe9FP2f86gJ8YfO/NAB4YfO9/AFg1+P77An9/yeDzfHn570z3C/9T98+vIMgwDMMwDMMwDMMwSuBUW4ZhGIZhGIZhGEYpbHgyDMMwDMMwDMMwSmHDk2EYhmEYhmEYhlEKG54MwzAMwzAMwzCMUtjwZBiGYRiGYRiGYZSy4v4ylRw5clK6hO4ZZ0zimWfmVTZHKdx+sxS9/UDx30G2/evWrQq7V7DQsKwrDtx+s4xT+1nWjc9Y2wi33yxFbz9AI++sjXgKUWz5zO03S9HbDxT/HYrefl0UvZ+4/Wbh9pul6O3XSdH7ittvFm6/eSjewVrDk2EYhmEYhmEYhhkN2PBkGIZhGIZhGIZhlMKGJ8MwDMMwDMMwDKMUNjwZhmEYhmEYhmEYpWitasswDGMzjuP8BIB3AbjIdd0Xh/y8BODdAE4COBfAH7uu+w2tjWQYhskJyzqGYUyQaHiOs3Cq1coQ1QqmJ6uYm1+Et9hBu9013SyGYdTxcwD+GsCmiJ//KoDVruv+ruM4ZwL4huM4P+267kgJBpZ9DDPysKyzDJa7zDggk2rrC6eoGrq+cLoNwHYAux3HKRO1zxi1WhktUcKNn/o2bv30QzjWXMSq1ZOoT0+gVkv3erVaGfWpOtasnUZ9qp767xmG0YPrun+BvhMtiisBPDD43WMAFgBcqKFp2gjKvgvecR9u/NS30RKlzHLLlPxjucsw0bCsswtquWsalr9MFIkRT9d1/8JxnF+M+ZUrAXx+8LvHHMfxhdNBkhYaQlQruPlT38a6VXXc+koH2/cdxLceP4YXn3smPnTNJtRrkPJE+cLk5k99O9PfM3Yxzh7JcX73AOuxXFk7MfjeyODLvge+dxQA8MD3juLmux/CnddeDKQcb1Pyj/q5PPeZMURK1p1xxqT03X7lcgkzM43Y32l1e2jUK2i2OqiX7SpDItP+rLS6Pdy8+8AKubtr22bMNOokz1DZ/mGOLyxiNiB/d27dhJmZfO+hs/0qKHr7AZp3oDjjKa2IUQsolZQrJXzr8WO4d/bnsX3fwdTCwG+/DmGiAtP9n5ew9lNsaCqEaRS2jUHad7et/UQcBrAq8PXqwfeWUSRZN4wv+4J86/FjmJ6sYrK60msd135T8i/Nc2X6X+e6T0ua+WOjUm/b/E9L0dsfg5Sse+aZeekPnJlp4PjxZujPlpxFdz+03Fnk9axx8sS1Py9r1k6Hyt1GvYKjT8+RPENl+4PUp+qY3fvQMvk7u7fvvGydamX+XF3tV4XO9qtylqZ5h3XrVoV+n8LwlBJOAJ2A0kF9qo4Xn3smNqzPJgz89qsWJjZMLhsJtp9qQ1MlTGXeIS9550mWd5dtf5RwsgXHcaYANFzXPQLgXgC/AGDP4NzTBIBHh/+mSLJuGF/2+WMNAC8+90zMzS+GjnVc+3UoU3mfm9T/1OueWmbLzB+blXrb5n9aKBQxW8gi66hIk2kxihkIc/OLkXI3DTb0zfRkNdJ5qUJXksWGvtGB7ZmWmVyejuNMOY6zbvDlvQAuGXxfuXDShbfYwYeu2YQfHmvixeeeuexnaYSBL0yy/n0cRTsToDvn339WqVbF3Q8+gQe+dxSdnre0oYlqOr9LnDC1GYp5UtR3T4vjOC8DcB2AZzuO807HcSYBvAHAHw5+5c8BnHQc578CuAPAtlErtuHLvkvOX4NKSeCS89fgQ9dsgrfYSf1ZKuWfrudSzn1TMltUK7j57odyy0AfPr9VfGyTdbLrzGa9J8+6oJC7tvSNKbkfhy19owNqeU+N8Dwv9hcGwmkbgNcA+CiAPwLwWwBe4LrufxxUtX0PgCaAcwDsiqpqe+TIyfiHBUhKydDhtajVyqjUq2gudjG7N52n2G+/Sk9zfaqOGwMeQgC45Pw1JBE4ai+0To97rVZGu1RaNma3X7UR7/+8i/0PPwkAqJQEHrvtilRRF5X9HQbVGFC0O8tnpIh4yuWkFggqWWeKNDLWxvS5NM+ViXhSrXsVMkRm/qxZO40L3nEfOr3T0zKLDATox3RmpoFms6U9EkGlR6SMeLKsi+gr2bWhex8OolrWUWQmxfWNrr1GldzP036T88ZHl11DKe+HoZB3MsWF/hbA3w59+8OBn/fQr2arBZ0h5Ha7i3a7i1qtjDuvvTjThGi3u6jXkPnv47A1nSEMyoIlMs+aHXrW9n0HsWNLvyDfTZdtwIb10zi10OkbqZLP9z2Sw8I0SyRomDChk/dv/e81W12ctXr5ebS080Tm3YfbwchjWwpQu90F2t3cckSl/NP1XMp1b0pmU6XxAWpkue60MNtT0cYR2XVmq95DsS5k5G7cXmFL35iS+3GE9c1Zq+solUpYs3baaBup5RGlvFeBHXHXFOg0YHzyKmFUStwwtk+uIDoEYlAghz3rp9ZN4c2vyl6hWJUwjRI6MuUqwv72o9dejHant+x7d1y9ET0PSxHftPMk6d3D2rFz66ZUhv04Q60EmzBko56pSv4lYaPxbEpm22w8t7q9pbQwQM+ebkKPYOKRXWe26j26dJy4vcKmvqGQv5TO7OG+2XLR2Xjzqx1cv/sfjDufqOWRyiAJBXaUtUvBuJw1k4HyLJZqVOf8B/P3v/ujudBnzS92lyoUZ817bw8E6dGn59A61SIxOku1KtZM17Fjy4X4pRc8e6ldrW4v8e/DcvmPNxdXfO8t9xzEra+8INc8iXv3sHbM7rXnTIHNBBVvqvN3us+yqHimTecIqda9KZndbndR93q489qL8dhtV+DOay/OnPZGLcsb9Yr2PZ31CDuRWWdRa6hcEkZlhY5zjUln94qkEyYRtqccX1jMPLbDfXPrKy/AW+7Jpw9SkVYeJe2NlPJeBYXTCiM9Ogsd1Kfq1oT1dWBjOkMUqj0wQY/Rh79yCLdftXFFZHMqRsExkaKz5L3cc2DZWVQA+OwjT6FRr2A+7npvhAus557ZCH3Pc9Y08NhtVyiZJ7ak+BSROMU7S9+ZiOZQP3NU7uEMe66vEOhuC1UEmFqWN1sd7VEamyJDTDpW6D0LHfQ8D2/cfcBo5EpHlClpn6XSCW04+hG2p/jVxLPsKcN9A8AanSWNPJLdG01lGslQuIhnlEen53ljUa1qGOoInCpUe2CCAnn/w0/i/Z93sWPLhcueZVultTDv5fZ9B3HTZRvw4nPPRLOVvGGFvVNcJWZV88S2vi0SvuIdJE/fmYjmUD+TsiqfqWqGUc8FkElm2xIBppbl9XJJe5RmlCJD40hQ74Hn4U0DA8Vk5EpHlElmn82rE9pS/VXFPhbsm6w6iwo5nEYe2V6xVobCGZ5hi3uqVrZC8DDxqDSSh4XI/oefxI79jy7dPdhud61TNqIE64b1030PlsQF72HvNNOoWqHI7dzKipwM1Iq3CScA9TMplQ5TG/UoGM9RZJXlUUqb7rQw21PRGHl0OdpqtTJa3V6swaE6EKBDh7HFsFG9j2XpS1VyOI08UjXfdTo2C2mZDYeQz1wzhR1bLsSG9dM4dHgOH/7KIXz2kacKk+bnX9viQaBRL2NuoQOvvUgitKJSJmxIpaBEJs3FttTkqPSKZqufjidD1DvVofc9w9oxWS1bd02IrVCmX5ooLED9TMpUSFNp4JTPjU1lzoCp4lNRRdRMpIXZnIrGyKMjbXpp7hpO59Whw9hybCZsT6F0ZmfpyzxHSoKOi7BnycojFfNdd5XvQhqeQWq1Mo6eamPH/keXnZPbsG6KRPCo3qBrtTK8agU/nl/EW+7JVm017rNDN/pGCc0utEwyXQpOUIhMTVTQbHcxVa9gbn4RNZx+L5uUjShlvTdwOjRkytoi5p2I3zNpLIfbMTkj+QIM6bw04WChfialIWvqPJ8u47nbkXNS+Zi6SiRKadu1bXOmzxs15ymTjSRZQTFPqM6wU7RFtQ6jyrBJ+946nNlp+zKrUU7puFDhWNZdF0J4nvTdv7lRcal65KWw123OHTWUuQQ3akGlaf+x5iLe9plHyC+2jeqbj1+3GTfsORD7PIqLhk1cHm/qwvqsxAlkXZc9yxDXrwByrQG+VD37ONugfKuap1TvliQTVLafShbFXX6eVhkzdZE65aXm1HI+z1yjuFC9yOSVdRTrPC6zi2KeUMxdG3QTmbmqYm1RfZ5pnSir7KSWudT7fpr5TSHvCnfGc5hID8REJfdiTsp1p8j3np6sRlYhzZuzHdU3UxN6ytebOCtgy/kEWYpSHCqqXyv1qlVnz0YFmfMW1OdNbCle40O1Nkyd56N8LuXZLlNXiUSd2ZIpojbMKJ+fHSeo+j5KVlDNE4rzhkXRTajlZVHeW4ascpha5lKfsdddF6LwhqfKDkuaLBQLam5+MbYKaR6i+ubUAm0VzShGobrmqCNrbET1qwcxMpuKLcgqY7Yr3yYM2ahnmnLw2Gg8m6pAHaW0yRRRG2YUik8x6vueap5QOH6KpJvIyK28uoON751EVjlsQ9X/uD1ed+HNwhueKjssabJQLChvsYOZRhV3XL0x9h2yKHFRfSN6XS2TbBSqa44i/lw6c80UWiU5YyOqXxv18shsKrYgq4zZrHybiCJxBFgOU9W9o5S2LFDK+VFSjIuG6r6nmif+3N21bXNmx88o6SZpZK2u99Ylr7PIYRtuVIjb43VnBRXe8FTZYUmThWJBtdtdiMUOnjVZxa5tL+q/w3WbV5wjzaJQRfXNfHORvM/CFr2JxWbDAreZ4Fw6dPgUbt4rZ2xE9eucpuj5OCGrjNmsfKswZJOUCtsjwCYI6zeTV4nYaDyPkkFQNGy8MgOIWTflUua5a4tuQmGcpZG1Ot7btLxO2p8oHBd5SdrjdWYFjUQuiaoqX0mVGmOrS1XlJ3y73V36zPmTK3+ep+JUu91FDcAc+hNvDjhd5ZWozyKrJHo90msiZPDHbNe2zWgMqtoWvdoh5UHy4FzasH5aqkKb//y1k1V8/LrNaNTLOLXQgbfYgdfukawB5jSyVQVtrvxKWZJftgqrtutLMq493YWgEvstg/y3oZgVQFtF2cT1Q0wf1X2fZZ7ErRvdbQm2iaIA0/GFRczufShWjsqQRtbqqLKuuyprENn9qd3uYqZRT11IjQpT1d3DGAnDUyVxG3TcgpK9CkOGPAqVjtL5cYu+dapl5H42kwucEurxC86lQ4fnEgVRnFPBf76ONTBOyCpjNivflJucrFJh892f1Os4qIg2W52liEwQamXM1DUsUVAaz7odpEwfHUZJ2nlCfWdunrYAdOtOVCuYJZIHaWUtRaAj7h5Mk3ePmjR602CTg63wqbam0RGezpOOoqNwAp+RUQf1+AXn0oe/cgi3XxV/tljm+UWpzFsU0qRC2li8BjBThdXm9EuVacDX7z4QmlZWlPTpcqWktfhUWEoeAJZhhkiSYbrPWtumz1CtO8r30p027K/b63cfCE2lNZkur3O+5FkLJo9YDMOGpyHSTKA8i1zHouAzMuqgHr/gXPrsI0/hr/7xX3DndZtXFPvw52bS820rwFI0gl5c01VYKZ9pogqrrdeXAGYKQVHLZcp3MFUIiivYFgsTZ/ds02eo1h3le+k2YpLWrcnzszqLJ+VdC1F7vG49jg3PnGQZsLQTKM8ip1wUy951egKNVRNYs3Ya5ZKw4tC8LEUylqiF2vBcesPPnguvvbgkiAAsm5tPHI2+6qdWK8OrVnCsuQjPQ/+/1YrV/WkTSV7cLJ9nal6rvMIkjVJhawTYRCEoamWM8h1MFYKyLZrFxGPCUWBLESAfqnXnLXawc2u+9wruMaJagbfY0eIclSmMk1Ve5903dc0XVWvBhHNHeJ6n7MOHOXLkpPTDZmYaOH68qbI5uVnKvR/Kma57PTQa9cj216fquDGQEw4Al5y/5vSZSE1tjFuUw/0f9jl3XL0R7/+cix+daOGj116MkhCYnrCjoE/U/MnaH9TIFAuYmWmg2Wxpbe/w3Nxy0dl462scvOWegyueX6lX8eP5xWU/u+PqjXjWZBXNkwvSa3jdulWC/EUMIyPrKOUA9byWLWZRq5XRLpVWFqwgfq7KojY69hrK8Ukzbyj7jfId1qydxgXvuA+d3ullUikJPHbbFanP5qfpDxV7b5r5M66yziftWqOcJ0ksWysLHZQFMDlUoNCEXkq57mZmGphf7GaSByZ1J1U6M9U7ycrZPPNH1VpI27cU8o4NzxzEDdhktRzZ/jQTiKqaWdrPGO7/qHfdseVCvPqDX1NmOGd9j6j5o9Poj0JW2PnvoLOSZNjcfO2ms/Gu174AjXp52fMnV03i+t3/sKIvd217EeZPzrPhmYAp5TuJNJvxKBjPuvYaqnVsUgGkegfKeZN2P6XuOzY81el1uvbrtHuybqjWXZ72m9SdVMm8PO9EoVframscafUQCnnHqbY5yJq2I5s6QRUCD6afeYsdiGplKa1gslGVSjOIetcN66el3zsPVH1hQ6pV2pQJnef9wubmj0600Ov1Vjy/US+H9mWjzqm2Mth6D2ea+WnquUmYvtctjCzrWOYezl3bNmvL2DCRPp1EmnVkU4ENJpmipzHKInMPpOniVyZ1J3/dytyDmSZ1Nus7mdhfVK0FE2ea2fDMwfCAbbnobHzx1pcBAFrdXuQklJ1AKqoIDi+WZhf45N8/nrh4oibnocNzS/+vcqKG9cXdDz6BUq2aKjffhsIBKgQ41fm+NMJtbqET3pcLdp7ttQ1bq7CmmZ+jYDzLovsMbZxyE1RE6+VS4Qwnk4WgbFDiGTl0OQpMGlU2OsnCMK07tdtd1Mul0ACK31dp+zLrO5lwVKhaCybONLPhmYPggL12U/8s3Ns+80hsiXtAfgLpKof/6p95duLiCZucd1y9ER/96iEtE3W4L7ZcdDZe+8Ln4IY96Qqz2FA4gFqAU25caYSb114M78s2VzOWIY0XNwlTRixFwYosz02CWnYaKcAwAsZzHL4B2O30rCoExdiFjkqcJo0qKqe6amzQnYB4WZxWZmZ9J1OOChVXD5mQn3zGMyf+ZC+VSqHn3fLkX1PndEflcrvvugI/9fbPLn392G1XoNvpreh/mcP3qhjui8/d8gvYsf/RyL6Jmz86z0xGPZ/yPInpsxdRfclnPOWgknWmzhDmKViR57lxpFkTMv1vYo3Jnr2RnT+mztAmkWb+m5bdYfAZTzOyjnoumzrjObzOt1x0Nt78Kgfb960s6JdnrtdqZZTrVTRy6Gym15+/10TJ4unJauq6CVneKet+oNKu0XX2f6zPeNriufU9EFHn3fJ4QMjL4UekRvrpsv7XUV6+Zd6WuQU0Ty5oS1ca7osN66cz97fpVCtqD5PpsxectmYHJq8Sse0KE5vv4ZSFOgpT9DO0Kp5pix7BpIM6G8Bk1Hx4nd902QZs33eQPNOB4uouG/b7OFkcJTNPLXRIz8/aEv0NYvqcchoKaXjamBOvIlWDWhiWBXDH1RtXLJbPfecprYuHIh2g2Yo4X2jokue0UApw02cvGBpMKcFRBWxMKBgmjec4TKwxm41nE0qOjpoHpvUIRo60c1lGtpqSeZRO9SiKZJQkESeLo2TmJ+7/PukatzG934bCmbIU0vC0cRGp8oBQCsPJegXv/5yLHVsuhPuuK7Bjy4W47ztP4bd+7nxtiyfPZh/si17U+UKDHidT2Oh9Y9JhSgmmfq5NESRK2WlijdlsPJtQcnTVPCiiMj5upJnLtjsYdDjVi2SUJBEni4f78uPXbcbdDz6BD3zxu+RrnGJ/GZVzymkppISNW0Q672Iczgv3J/z0ZBXNVgfd1qJVqYdz84v40YkWXv3Bry1975Lz1+CXN/0kjj49r6UNolrBzYHceF8Q3HntxUCKvmq3u6jXsNTfFJejZzm7YPrMA0DfF4x+qNaFyecunTH51LeXnzGpwegZQqrnmlhj7XYXGCg4efEVtuEzQHkKQQXPOKlWcqifaYMewWQjzVxWJVsp5VNwnddq5UzrNK49JtZrVpL6NUkWB/tyzdpp7PzyoWWfb8sap94vKeW7agppeJpeRJETxutX51sqbmOZ4p9lYlIrf5SbPZVSNtmoolcqY6pewXd/NIfPfecpXPOScxIFALXg8D/T7+9mq7OU9pgEpYLK6MeUEkz5XJuNWLLnplxjNjimfCiNZxNKDvUzTesRTDxxayfNXFYhW1XKpyzrNKk9RTFKZPtVVhbbvMapHSJFCkAUMtU2b9pT3vB2UVN00qZuqUhRsS0doFYro9kDbtxzAM4778OO/Y/itS98Du5+8InE8VR95ijuSh5mtDC1LmxNvzQlY4tegCeJLOlhUWeAdZ9xon4mH1GwF5m1IzuXVchW1fIp7TpNao+/diiu7lIJdb/avMZVpD/blv4bRSENzzwbEIUyUOR8+TQTU4VwtU0QiGoFN+9d/o7b9x3Etp89F9OT1diFFzcPsizeojo0mPyYWhem7v9MwpSMtdl4NnF+Nm6/NFGMhfKZNhYIYfpQrh0VstU2HVCmPe12F/VyifQOSMq/l32PNNi8xm0LwgD6nKWFMTyHJzWQrYQ/hUCzccKoQJVHxiZBEPWOqyaqiQsvch4sdDItXts2M0YfptaFrVeYcAR4Oaaip6NgPMdhw/UQzEoo144K2WqbDpi3PXnlC5V8UnU7hI1RQNuCMIC+4IfVhqc/2GeumUKrRLPpUgg0GyeMClQJV5s2+6h3PHR4LnHhRc2DskCmxatrM7NN+WP68BUmp+EI8HJMZUPoMJ7zYCoKPOwEZ2ih3guzyriosbZNB8zbnij5UqlXpdYXlXyyrV8BdU4/2f1Sp4zTFfywOofPP2S8Y8uF2LH/UZJDuBSHjYt0iDcPRTmQnoewd7z9qo14/+fdpd+JKkQQNQ8m6/VMxQx09Lepoi1FwXGcywG8DsBhAJ7rur8/9PPzALwfwLcAbALwZ67r7tfdTh+bitcAdEWuTFaRtbEAT5xC0O30Un+eLJTFOaKKaezatjlT20zIsrBn7ty6SboInE3YLOts0D2SxlpWTuiQ0XnlVph8OWt1Hc3FLmb3PpS4vqgKONmoW6usOJ+0X+qWcbqKMUkZniYEVKvbW/KgxF2om1bBoRJo41BF1EYhQM3wO55a6OAT938f+x9+cul34hZe2DzIuniH26LiSh5RreDuv38cO7ZciA3rp3Ho8BzufvAJvOFnz1V6bUcRcBynAeBjAC50XbflOM4+x3Fe4brulwK/9lYAX3dd9785jvNCAH8OwIjhqbqqsq71HvVMUzLWRuM5TqZMVtV5wHUYz416BfMn07fNxBVEYc+c3av+2iNqbJd1NugeSWMtIyd0Gg555FaYfLnl8gswO6h/AcSvr6w6T+R+Y5FubfLaJd0yTpfDJzHPJSCgfsd13R0ANjqO84qhX/MF1HsB3A7gj/I2rFGvLA32ocNzZGkXtp0xtB2b0mJVEXzHXnsR17zknFypHnnSRYJtqZdL5P09NVHBa1/4HOzY/+iyKr5TE1YnP+jiEgA/cF3X303uB3Dl0O/8CMC6wf+vA3BAU9tWoLqqso5zhCqeaVMqOZX8NJWCRrlfRqVPNlvZ3sHEmfgROodvVNbJrFHTugfFWBelYGCYfDlnTUP6/bPIJxurfoeRJe2bag/SLW902Ucysz9KQAU9Y+QCqtnqLHlQPvyVQ7j9qo3Yvu8giRVum0eFsQcKT6sN3toomq0utu87uMyDtn3fQXz8umzpbiPGegDB2MuJwfeCfADAXzqO8wEALwHwh2EfdMYZkxBCSD20XC5hZqaRurHlSilyU8oSBWt1e7h594HQVMiZRvRZtqztz/PMOI4vLGJ2KD1uZiZ7+1vdHhr1CpqtDuplfWURhp/bALBr2+YVbcnT/2nodnr9eVUto5HxcTu3blqWurdz6yZMVsuoZ2h/UEfw8Q1ZVf1h4pmKMCrr0q5RE1CMNbWMzkucrBiWL2nfP0o+RcmKLLJfl6wbJkpuTUa0JWp+p22/7Bio2KOi5D3FGMgYnkYEVKkklgb7s488hQ3rpnDndZsxPSE3qU1jaoFQ0Or2UK6UMLlqQquiRQlF/1MoWnk+Q8UcitoIpyYqmKgQP6t4a+AwgFWBr1cPvhfkkwDucl13r+M46wB813Gc813XXdapzzwzL/3QmZkGjh9vpm5sfaoemd6Uxam2Zm34kYZGvYKjT89F/l3W9ud5ZhT1qfqK9DA/PS6qT6Lav5QmN5R2pDpDJum5flqqP8OS+t+mc8C1WnmFQ67X8zLNn1qtHJoW1m0t4rjCM57Dz9y5Vf6Z69atSvwdTRiTdfODc4Np1mgW8s77vGMN0MvovPiyIq5vfPmSdX0Ny6cossj+PHtNHsLkVlQ74vagSSBV+5PGwMQelWYMouSdjOFpTEDVer3lg91exNG5BQD9SU25oVJvzqYWSB5MKVoqKGL/D6PiHXRuhLLtt0gZewDA8xzHqQ8yPC4F8BHHcc4E0HFd9wSA5wJ4avD7PwbQg6Hq4NTnMXQVFlD5TMrzONTna2T3GMrn2lZMLCzbSMYhF9V3ujNLwp45WS0Xca8xJut0nJmjmPdxYy27lm0okjSMbN+oXl8Usl+XUy1NliRlIbikMTBxzp0CGSGyJKAGX18K4F7Hcc50HGf14HtKBFRcjj9lfnhRcs1VU4TzCDad3yoiNpYrtwXXdZsA3gRgp+M47wJwcFBs43cB/Pbg134HwH9yHOftAD4K4O2u6z5tor3U5zFMzA3qZ47CPZyUzx2Fezjj+s7EOcDhZxYRk7JOx7VhVPM+bKzTrGUba4qk6RuV6yuv7LdVb6eY30E5K6oVeIud0DEo6plz4Xle4i85jvNKAL8C4AiARdd1f99xnPcBOOa67nsdx/k5ALcA+DaA8wAccF33Y8Ofc+TIyeSHDZiZaaDZbEV6M+pTddwYsPQB4JLz12RK16D8rGD7i+YFXbN2Ghe84z50eqeHqVISeOy2KzKlvVGTJiJbxP4fRtU7DHsJS14PPVEi9xqmiHjK5d8XiLSyzpa5msWDnLf91JkrabM2otpvao9J+9y4/qeU6SoyYmq1Msr1Khr1SuTYU+/PJrObWNb19TrVmVWqdBk/VZhaXwxDRTRvZqaBcqVkjZ6X9h2Da02F3k5BnJxsNOqJsiKNnDXRBxTyTsr947ruFwB8Yeh7bw38/9cBfF2qJSkISwdoNEpLSvKOLRfiw185tHT1RVi6hszENlkuOS0qUwvmWx188daX4blnNnDo8Bw+/JVDOHKypTTVLg1FTSuwjWDaSK1WRlOUcPPddqTijRu1Whmtbg9r1k5rPX9n0xUmlM8s4j2cw+9N+Vwd93DmST1uiRJu3n0gVvZQ7s+2pR6PIzpSpFUeGyhKqnAUJo5UBAnbe45m6Ddb9fa4+S1zrCCNnLUxlVsGayvHLPY8NNtdfOqNL8W9sz+PdavquPvBJ9DsYSm0vmP/o3jzqxxsuehsACsXj2woXkfqBwUqUwtqtTJOtbt422ceWbpm462vcfDRay+2ZhLbllYwCmm/RUivHlX89Xz97gNarxJRIUdsWgdU6WE6rhIJ22Mon0uZykwtf2VlD+X+zPLOHEEnW1z6IAUqjw1knY9p9AWV89TkcRvKvcdmvT3PHpRGztqYyi2DlYZn3wjqLDOC3vwqB7988XNw897li3H7voO46bINoYtHdvHacO5NRiipFEZhn/2Wew6iJIQ1k9gmQWPr+YK02GbMjxOm7uGkfG6tVsbxhcXC38MZ9UxT93AW3XiWQVb22Gw8M3KocLLFoVIh13Fnpcp5Otw3d23bjIlqGatWTyqXt5R7jw16uwrSytmse4XJwImVhqeoVpbKEQcNzJ981mToYnz+WdOhgkV28Zr2GsgKJZXCKPKzJ+zxBFMcRqdaaKPiObfJmB83TEWQqIvXDMtqHcZzms+TWfOqn2lyjzFlPCchK3tsNp4ZOUzsl6oK42SZj2nfX/U89fvm5Il5nGp3ceMePQ4Byr0nbhyKnI2mw6A2HTix0vCMmpzNVjdyMYYJlrTpTaa8BiZSjoaxaUOOiz5kVUCoF9qoeM5H1WtYBExFkGyt/ArQR2Nl1nyr29PyzCJ5pnUYz2lkj63GMyOHrftl1rWVdj6mfX9d81S3Q4B6zwsbB9NGVV6S5KxOm0MVVhqeUZNTCKRajKoXL9UEN5FyNIwtG3JSn2ZVQKgXmk2GehxJQsp0tH+cMRVBonyuKeNZBtk136hXrL6+RLcSpct49mXPrm2btckelndmsHG/1Lm2sqRP6pinuh0COvRM00YVhWEYJWd12xyqkLpOhQrZstu1WhntUgmze1eWEwaQqqqryiqwcaWM01wqnaYkssr3CX52s9VBt7WofUOmKg89XPKZury6iqsFkt7BxjbGwdepJCNznYQsacabSo7Eyeosn0dZHl52zU+umsD1uw9ofaYsMv2RRk7IjLuK60vi5qVN1wllga9TSZZ1pveiMLLM86xzNer9p2plTBLIflmG22/iOo48e49M/5u8FlC1rKMarzyfo+06Fd30B6geXW47Rel9ldcDxHkNup2e9OekKYms8n2Cnz0z08BxAxuCqhLZ1CXEdZSEz0tUWe67tm1W5rxg0tFudzHTqJNsiGnmJJUcSZTVKTFxlUi9XLLy+hLAzFUi1DJYxTUsLL+KhS+bdm3bnMvJRjn2Oq/jWCGbFzroeR7emHCVkGqor+OQGR/VV3aZvC5G9ZV/VHPW9DUsVhqePq1TLaX38eQVYnETfLIqH/oughGjC1VCQ8VCM3HnYRrChNRZq+toLnZXRqj4HrtCYdM9nACdrDZ1D6ef1mbT3Z+AmXs4R8F4TvN5bMTqIa+TjXrsdRsoQdlcn6rjTRbcSU4pb225I9ekUaXamZF1zobJOao9LwtWnvHUAUWuNGW+uqoKbEUgmBMPIfDRay8mPwNAfWaiCFXTws6V3HL5BaRVSBn9mKr8qgsTV4nYeH0JYOYqEVNnj2UwUXyKsQPqs3sm61roOmM3LNvDoJJ9qs5WBt+h1e0lrk+T57hVn2WmvMoHgDGbY2y1TYqQeJy3qNFQ2frRIcpLdte2zeRnH6iiQXk9e7q87GGev3PWNLSlFzFqoEznGZUIkk0RYMpnUkYkZL3l1Bk4lBEIyoiC6rQ4hhbqaJLJTDMd0dYw2b5z66alwl7UqIj2Zd2fssrgvPuX6mhrljlro5wb24gnlcepKJFK26IaPlFesm7Ps7ZPs3j2gv0valV88u8fx62ffgjHmov9i5unJ6TGJM04hnn+5hY61lUXZNJhovKrDKYiSBwBlsPE9SX+Z9l4D6fpyo5MOlREkyjmeRZ5Yaq66+xeNdlNtVoZpxY6cN91BT53yy9gy0VnA8g/Pjor1FLsIzqirWnnrI1ybmwjniYPIOvGltz7MHQe8KcibZvD+v/9V1+EWllgdrj6WcyYZBnHYc9frVY2eqicyQ+l7BqFCJLNEWD/M3VHgaOeaSrCQxUFNlF8irED0wVRwsgTkaNYi3GyRZdutdQHe04XSrr9qo3YsG4K17zknFzjo1M/pNpHkmSd7v3ARjk3thFPW+6tVInviVu1ehLNdhfrVtWtO9dn4/1eSaRtc5jX7s33PIxT7W4qTx6F98/k+QeGBlvv4TTlWbU1AgyM9j2cJqCUX+OgA4wSNu5deeRF3mhrkmzRpVuF9cH2fQfxm5eeJz0+UfJFp36oa//SvR/YKOfMWx6G0O391e3lCPPE3X7VRgDA/oeftCaqaKMXM4m0bY4SaM89s4EtF52Nmy7bgA3rp3Ho8BymJiqRY0Ll/UsbfeDKj3ZhqvJrEqY8q7ZGgAEzUWAV15fYlDFDeX7LZGVHJj0yY69zvzKZsZW0zsNk+86t9LpVVB9MTVRwdG4h8e/j5ItO/VDH/tXq9paMdEDPFXc23poxsoanL3ymJipotrqYmlhZqEZ2A8sryExs3GFCafu+g9ix5ULsf/hJa6KKWRaFaUMobZujBNrhEwt486scbN938PS82LoJ9YjD/yYUe9uUTqYPVeqirUasqefafJWIqWeqvodTB5FyzOspv7aN0Yfu/cpkGmPSOg+T7ZPVMo4fb5K2I28fxMmX1qnWsndotjrotha1FWOk3r8a9YqRK+4onXUUjGSqrS98Pvn3j+Nff7yAG/YcyBzWpkiV0nlA2idKKG1YP21FqD1ImpQTW0rgp2lzaKrD1k1YPVnF9n0Hl8+LmMP/JlImTMxdRi+2XiVi4rk2XyVi6pmUKWhh8vv4wqJy+a0ihTrNFQ9MPFSp3Lr3K5NpjDLrfFi2ZyFpbPL2QZJ8Cb5DvVxStp/o2L+arZXFHW294i7uGpa8jKTh6QufV//Ms1cq9ikHlEKQmTj7FCWU5ttdK85GZKWIhlCoQOv1MFkrp5oXJhR7GyuiMcsxdf7Of265Ulp6rqkq37YazyYUU5uNZ52VNoOoNJ6v332A7//MAaUzWWacKeWlyXOnOmSLzNjk7QOb6nwE9xFvsQNRrZDuq/VyacWYxV1xZ5IoXbvV7eX+bHu19Rz4wmfD+uncKUdx+ev+z7OmWqpcWFFpA91Wu5AGp08Rq+AC4akOWeaF7nsJbayIxpzGVCr0qNz/GYat93Caeqat93CmgVKO2XgvXpGh7M+kcVYhL3XvycHnqpYtsmOTpw9srPNBNU/CjhUMnyv3r7izTceKktWNegXzJ/N99khEPIc9WPODcPahw3O5PSlh3pjZl2/A0VNtaQ+dCa+3jRXgKLDJO5YXG6uNDVOENo4zpjIAbL7/03QEePi5JqLA43APZxoo5RhngdBC2Z9J41zEjKk4VMsWHXPdlK4at09QzJOoYwUAlo2Z1160UseKktXNVv52FXO1BYjyTHz02oux++8fx+1XbVxevCViQKM87mHemDdceh5u3HNA2kNnqqqUKU+cSmz0jmVFdl6YjAbZWBGNOY2pCJKt939yBFgNKu/hVFFpcxhKOcZZILRQ9mfSOBc1Y8oUOua6qXuO4+Q1xTwJ29dm94ZHi23UsaJ07Xq5hPmcn114wzNSabluM97ws+diaqKCj1+3ObSqrU/SJByeFNMTKytTJU3KUTQCTWDrIs1K0rywoaosz1174StMlmMqDdJ249mUchf2TB2VNsNQaTwX1flpkuDNAx/augk376Xpz7hxZqdBOlTPdVP6TZK8ppgnafY1G3WsKF2bgsKn2kYO7uA+xGNHT2FhbiE2FSEprD6czjBK6Z5FxFQBExOMWmoQQ4upVGjK51LKU1NpkJTPVVGBVXcl8LhnZqm0aSp9Oozh1MBd2zaPxDEWnQTnh/POv8Hd33wCd163WXmqJR8dOY3MmlKdBmtKv0mS1xTzxFY7IY0sVaVrF1571e2ZANjjyYSjIqrAqUGMj2wESVcav433f3IEeCUmosC2R4DzEoxQzMw0cJyNzlQMz48PfPG7eOB7x5bublTFqGVMZSXNmlIZjaOQdVn0riR5TTFPTB0riMMWWVr4iKcJz4TvBbpr22Y89Huvwp9e/1JMVLmU+jijKqpg2mtmU6RhnEkTQdJ9hUm307PmChOOAK/ERBTY5ggwwHLNNCYLNMXJy3GZF7ZkUuWVdVn1Lhl5nXdfDdvXZiaq5Ptzmjlry7gX3vCkUFqyKg2n2l1cv/sf+hN+D9/lNc6oWtAmU4NMpOiNK0kbh4r0S5sULFvv4TTxXJvv4TTxTGojheWaeUw7VMMYp3lhS2XmvLIu676oa5/IcqwgjKj9Ou2ctWXcC59qC+RPBcgSVh+nu7xsq7AYh99W/1J7XW1VlRKbN+Ujz9iN0xw3Ra1WxvGFRcwOFdYYTn2hnF+jXrzG5L16FM+1+R5OE8+kTp9muWYeG48rhc2Lux98Ar956XlYs3rSirN5VDLWliJLeWVdnn3RxoI+YcTt12llmS3jPhKGZxhpF2naSTguZ+9syQmXwWRbVS7orAIyb3+Myxw3iahWMCuxcVDOLxWKt+6rREbFeI6CUikyca7N1jPAAMs1G6CaH5RrdnhebLnobLz2hc/BDXsOLDuj5x9v0Am1vLPJ8Jep7O+PcbPVWdb/thhSKonbr4tan6bwqbZh6EiZsDFVRAU25ITLpgWaamutVgaEwJ9e/1J89c2/iNduOtuKanl5+2Nc5rhJZFNfKNMvqdNtWt0e2bqTld22V341lcoc9VwT54BtTZ9muWYHeecH9Zodnhc3XbYB2/cdXCZjZveaqShPLe9MHUlIy/AYX797+ZG2cahSHLdfR8myUwud0L3HlnEfScNThwGic8KbPI9lOic8zeZioq1L7dtzABe84z687TOP4B1X/jTusqDEft7+GAehbhpZJZhyw6BWvBv16HuN0yIru6nXOuWeYeqs2KgYz2FQGs4s10YDaj1veF5sWD9txXk4IL28k70qxfZr6WSuOrTBkFJJ3H4dJcs+cf/3I/cAG8Z9JA1PHQaIrglv+sC7ae9wms0lqa1UilTwc0q16or2ze59CN2eZ1z45R27cRDqpvEWO9i5VU4JptowqBXvZqujvZCMzZVfTRWCGgXjmZqwvmO5NhpQ63nD84JSruUljbwblbULyI0xxb5ok5NtmLj9enjOfvy6zbj7wSfwgS9+1+p730fS8NRlLOnwHJhOdTXtHU6zucS1lUoYD38OZbSHGoqxs8E7Nsq0213MTFS1KsHUine9XNJ+lYjNlV8pFWJTGR+jUEXZxiuIGDpU6HnBedFrL66QMTL3MKqY62nknSqd0cQa1qHL226oJ+3XwTk7NVHBzi8fWvb3tuijQewyg4mw5QAtBaYLIZi+cDnN4fG4ttan6iQFVYYPeh86PGft4XbTY8fI0zrV0lrYJE/BquFiHgCWNkZdhWRsrvxqqhAU5XNHoYoydREtm4pPUeA4zuUAXgfgMADPdd3fH/q5APCfB1+eC2DGdd3f0trIGFTreWEyZrJaxvHjzci/yTPX4+ZXGnkXt3a7nV6GnjBXuFGHLm+6yrWMXJHdr4tSbGkkDc9RUrhtmEgmy06nFTx+Wyer5WXtpVCkarUySqUSPvXGl+LQ4Tl8+CuH8OGvHMLtV23E9n0HrXRyyFSMq9Sr8CDQqJcxt9CB114s5FqhoCjKmKnrS8KUjwbMXCVia+VXSmUpjdwaBeNZBlklWJfxXEQcx2kA+BiAC13XbTmOs89xnFe4rvulwK9dC+C467q7B3+z0URbo9Ch5w3LmMmZRuzvZ53rMnOawviYrGaL4uV5rzz71PAYN1sddFu0+onJ4M4oVyuOQ8rwLIoyFqQod/QkUZSJpIq8m4sv+Jqtbi5FaklA7P6HpXG4/aqNeP/nXfzVP/4LPn7dZkxNVArl5KjVyvCqFfx4fhFvueegVk+mjRRFGbMtgrRr22bSZ5qS3SaM5ySoMj7SYsp4lkFWCdZmPBeTSwD8wHVdfwDuB3AlgKCsez2Av3EcZxbATwC4S1Vjshootul5Wec6pXMmdu1mNDyzvBfVPhUc45mZBo4T6yVZ5QSF85faKVeUoFviGc+AMvY7ruvuALDRcZxXDP2ar4ztdF33VgAfpG7ouMKFELKfMwzm7r/zrx7BHVdvzHwmLOzcxPZ9B3HrKy/ANS85B732YuHOC4lqBcebfaPT5HU5FhGljAV5PYAzHceZdRzn3QDmdDYQMHeVSJTy0ajbUbzGpgIRpgpB2XiFialCUDZfQWQB6wGcDHx9YvC9IM8DsNp13Z0APom+EUq+qGw/Y5eGrHOdcn6p0BmzvJfp+iSyZJETVHNWhVwpQrElmRlglWdsHLHNq1cUhr1JPQ94z+tegHPWNFJ7gqIExDlrGjh5Yn7Z5xTlLND0ZBVTE3yZeoA0ytgfOI5zAfpy76dd1102wGecMQkhhNRDy+USZhJSuJb9fqUUOWZZUqla3R5u3n0gNJI506gv/Z5f5XHYM9xsdVO1P80z03B8YRGzAe/6zq2bMDOT/FlR/d/q9tCoV9BsdVAv66vDN/zcBoBd2zavaEujEd9+KrqdXn9eVctLz0zLzq2bMLv3oWVjM1ktY3Kmkbr90fOws+JzkvqO4pmNWkVp/yviMIBVga9XD74X5ASAbwKA67qPOY6zGsBzATwe/KW8sk6FLFCFzFyNm+tRpJnTaRheuzLtj5J7ad+Lep8C1Mm6tHIi65wdbr+qcc9L3F5KMQYyhqcRZaxUEphcNWFk46dAtTKgmlFo//SQ4Nv/8JP47CNP4bHbrkitSMUqHo36ss/JqgCHvUOeMUhSnJutDp6eaysTfAWcQ2TK2DPPzEs/dGamEVuwYpj6VD0yNSiLs2DN2vD76hr1Co4+fTqgW6uVQ1O46mWRqv1pnilLfaqO2b0PLVMEZvf2U5aS+mS4/5dSxIbfU3GmSdJz5we78PDMipo/NjnAarXyivQvv81p53/UPOy2FiPT8KL6juKZ3XJJuv3r1q1K/iU9PADgeY7j1AdBhUsBfMRxnDMBdFzXPYF+cOF8ABjIuTKAfxv+oLyyjloWREGxHmTmatxcj/ubtHM6C3HtT5I/ad+Lep9Kaj8FcXIiOH8aEUZ10pwN22t0jHsakvbSNGMQJe9kDE/tylitVka7VFrmXdGx8VOieoGoZhTaP78Yfa4zS3EJGQGRRwEOewd/DNJsmrKKc61Wxkyjijuu3rjijGeU4EvTDtk5NIrKmEqoz33LnnGJOj+i8pmyUJ4jNFXlkPK5pqpQRkFZRdnEOaa4Z2aNApvEdd2m4zhvArDTcZwjAA66rvslx3HeB+AYgPcCuB3A+xzHeTuAnwLwG67rLlC3RUcBRZ3rIctct+FsXpL8Sfteo1SfZHj+fPHWl2Wes/Wp+rIxpqoIT4WOYksyhqd2ZUxUK5g1WN6YsYO8HkpKwSe7MWQ9hB/3nmk3TVkFtt3uogbgWZNV7Nr2osSqtrYps9TYpIzFYfIqkTDlI4vibcp4lsFUlUObjWebqigvyRvNx09G7ciL67pfAPCFoe+9NfD/zwC4UXU7+MqMPqbnF7Xcs8GYppJbw/PnA194LNRhn3Qu9PjCYmhATfd1anHocAQlGp4mlDHTd1cy5qEwcqgFn8zGkHbRypTpT7tpyq4fXyhP1vvVeE+eaMf2jenNWwe2KGNJ2HqViKln2nqViKnn2n4PpwyjYDwzyeiQP6N0ZYYqVMg96kyHtJ9B1e/D82f/w0+iJHDaYS/RxqIE1HQ4gqTKS+lWxmy4u5KJR/UmTqV06PYipl20MmX6026aMusni1AebseWi87GTZdtWKrAxoqc/dh0hYmtxrOpFDFbjWdTDiebjefgOmq2Ov3jQSz7MkMhC+J0EpM6pa71Y1OGWB6o7syl7Pew+fOjEy30ej0cfVruCGFRAmo6HEFWVuzxFjvYuZWmDDpDj47y50UtX5+2lLnMe6YtZS5THjxLqfNgO7ZcdDbe/CoHO/Y/WvgS+OMC9br1S66XKyXj15cAdl4lYuq5o3CVCOU1LJRXOwyvo+t3H2DZZ5gk2Ua5HtKiY/1QyHZbru6jWquU/U4xfyjkma4rw6j20iisNDzb7S5mJqrGFwATjo77meIWqU339YWRZtHKCKMsd/klbSBZhHKwHTddtgHb9/H9n0VCpfJd1Hs4a7UyWt3eimeq3nijsNF4pr6HUxZbjeei3E84TiSNiUmjSsf6oZqTUfJHp2ymWquUht6q1ZOYqJZx17bNmedP3oDaKN13a6Xh6WNi47cFm40rHR68KKWj5PVGZvEBcspVlk0zSYHNIpSD7Xj+WeEl8G2PSI8zNivfJjZV/5nX7z5AGgG2RWZTGbGmokW2Gs9FzcYZZWTGJOt6CK7rVreXel3rWD8q56Ru2Uy1VvP2+4r33nMAp9pdnDwxn0me5g2ojZLDy2rDc1yx3bOhw4MXpXT0BteEjMLiA+SVK+oITFah7LfDVBSEyY7NyreJTZUjwHLPNBktstF4ZtlnH6rGhCKtWsf6UTkndctmqrWat9+p3nvYceEtdjLJs1FyeLHhaSG2ezZ0ecDDlI5RWnw+OtL6hhVKALmEsskzM0w2bFa+TaxrjgDLP5MiWmQyCmzr+VmGhjRjkmZO5lnXweeIaiWzwSGDyjmpWzZTrtU8uhXFe1OeBx8lh5cdlgyzDNXVr/JWP8tb9SrP8+fbXXzx1pfhuWc2cOjwHD78lUM4crJVyMWni8gqcTnuj7Lhji4mHTZXfjVRddLW60sAM5VkVVxfYtM1EpRXOwQvfW+2Oui2wu8+ZvQgK9vSzsms61r33Fe5H6uQzUk6oIkq68NQvDelTLWl6jAFHPG0EJWeDSpPeh4PeNbnTzaqONXu4G2feQTOO+/Djv2P4q2vcfDRay8mWXy2eOepURVBN1WAhcmOjcVrADNRJI4Aq32miiiwkeJTIfsVcLoGRb1cYtlnAUHZ5i12IKqVFXMl7ZzMuq5NZK2p2o+pZbPtR8l8KN6bUqbG7blF013Z8LQQlUqY6TTePM/3SmXcvHf5377lnoMol0RuIWtKGOoQGKOYnjyu2LTB+IpOt9PLreiYOEfoP3NXjkqFPtQy20Ralc3Gsyn5bHq/ZNITN1fSzsms69rmPTft/kEtm8PW1N0PPoFSrWrFvuZD8d7UMjXMuVAUQz4IG54JmFD0VCphVAIxa78kPT/uc6cmKqF/O1XPrwSYUDB0CYxh4bflorPxxVtfBgDWCHkmGVX3cOre7KOeayKC3m53US+XOAKs4Jm23sOZBpsNCCacuLmSdk4Or+td2zZLrWsbz+PVamUcX1jMtH9QyubhNbXlorPx2hc+Bzfsoaku7kOxv+V9bx1yvIjOsbE3POMmp0lPgioljEIgTjaqaJWy9UvS/Zxx/X1qoRP6t6cW5MtjR421CQVDl8AICr/Xbjobb32Ng7d95pHCeMeYPrZXYTXxXBsjwBQy22QE2Ebj2ZQBaKMBwcQTN1ei5mS5JCJlSHBdy6ZV21iASlQrmN1r3kAZXlMq7gS3JQqY1XGRhiI6x8ba8EyanEX0JCRBcbdRLyTlVTpdNub5Sf0tet3QvxW95EWcNNYmFAxdAiMo/N712hfgLffQCnlGDzZXYTXx3FExYm2LANtoPJsyAG00IJh44ubKijl53WbUKiW8keguXx+TVxBFYYuBMrymNqynvxNc1/4ms2dkcVykoYjOsbE2PJMmpy0LlRKKu42m6uEprzL9Evf8pP6eby6iUQY+fl3/TNbHr9uMRhnodnqJiz9prE0oGDoFhi/8GvXyyM3pccHmezhNPNdmI9bUc22KAAN23sOZBhsNCCaepLkSnJPwPLxpUHWU2kChmPuU69kWA2V4TTVb4ZlsSe0yncFmS1S1iM6xsTY8kyanLQuVmrx3Gx06PJerX6KeL9Pf881FLMwt4OjTc1iYW+gXNomoOjjc7rixNqFgRAmMktc3pMuVErnyOKpzehywuQqriefaasSaeq4KRchUJdnhZ5o0ALl6t10kzck0c8Xm4AL1evYWO9i51Q4DJbimeu3F1PuaDRlsqvaMtDK3iM6xsTY8kyZnET0JqpmbX8TnvvMUbr9q4/J+2Zq/X7L0d9Tib3V7K9qdJIjyKhgUAqNRBppdKPOi8ZwuLpQbjKl5YKvxzBHglZjw6Mc9M4t8ti0CzORDdk7KzhWbHbHU67nd7mJmomqdgZJlX7Mhg03FnpFV5ua53tCEfBzrg11JF7KqvJQ3K0kX76rGW+zgmpecg7sffAI7tlyIDeuncarVQanXxfxCvnZk6e+oxd+oVzB/cnm7VV6+W6uV4VUr+HFzEVMTVRxrLmKmUUUN8RdGD1+UXJ+q4+a71V0cb+OcZuTJcrF2lMwwMQ8on0u5plVckq77uVkvu4+C8vJzQG7vonymr8Td/KlvL5sf9Vq8TGbUUKuV0er2sGbtdOZ1Tz0nVesFeaBezz6tU61cf69CB027ryX1jY79TcWeQT2/4zApH8fa8JSZnFkUPVXYsJG22100GiX85qXnYWqiglMLA6OzSaOgpe3vqMXfbC3fOFQLokq9ih/PL+Jtn3lkaWzuuHojnjVZTZ3KrGKzCWLTnGbUkigzDMwDqufaasSaei61IkQpi+LmoapnqlDiwpRuJpml8d99IJfuQr0/2uyINeUMi8MGHRSQ65ukfSavAa1iz9Ch//noNHKHGetUW6BY5zfi0gt0hcxrtTKaXeCGPQdw66cfwtFTbTQaddSnJ4ykMUWlVNTLK6e2yrH2IFZUi33LPQfhQaT6HJtTfxi7kFnzKs6hDD/XJFRr2tQ5GZvTp03cw2lz+nRUGhyTDJUcUrE/2lYEyMfGYzG23PRAcTtD3mMEeWR31HzRqf+ZPN881hHPohE1UaYmKjja6WnxQvleknWr6rj1lQ627zto1PMV5bHUTVS12Ea9vJTyK+Nhszn1h7EHWc8ztQc17Lk7t25aOoOX5fN0Hx0YfqYPR4CXQymL4uZht3P6PL7NEeCoCMGubZszfd44QSWHbNwfVUUBZdezThmqMyIXR15ZF7WW79q2OVVfZj36EjVfdM5vkxF1NjwLRHRaaXfJCwWoDZn7gufe2Z9fuvSX+plpBWnY4m80cjUhNXMLnfBFvNAXGLKbk82pP4w9yKbJ6FC+Z/facQZPRm5QG86yz9UFpfFMKYvi5uFk9XSUweb0adl6AsxKqOSQjfujypRFmXRRnamvMuOoSx7mkXVha/ms1XU0F7uY3fuQ0r6Mmy+tUy1t89ukE4fzRApEVHrB1ET2ezXT4gseFZf+AvbcjZQWL6okeLsvkNOkqPipP91Oz/r0b8YMsmky1OlatlZhlZUbYc+c3WtP5VdTVQajnkuVypxmHtqaPh2VBjdcT4BZSVY5FHW1jk3Ho7LIRKp1rjv1NWkci6K/ha3lWy6/ALN71felzNV+Oua3yWtYOOJZIKK8fTpD5r7g+eGxZuwzs3q9TB54zkOSJ9aWFBVmNJBd89QRAlursMrKDZsrv5qIAOt8btQ8VJmdQhkBjooQ1MslzBO0dZTxx3/Xts1o1CtScsiWQjZJpJWJlO+lW69I2k+Kor+FreVz1jS09KVNRaOC8tGX22tWTyrPJOCIZ8EI84boPITue0nWTdciLyPO4/Wy+ULnJOI8VUUuGsR34dmHiQhS1HN3ZrzD10QhGep1WPQIsM7nZpmHNkWAoyIEjBztdhf1ckl6/G0pZJNEWv2L8r1k5FlwLre6vdxrKG4d26q/hRXEG17L/nGpICp0NBuLRumOVNu1gplM6D730G530W53UauVQ59Zn6pn9nrZ5A2ixMaiCDIUxes8yth+D+dktYzjx5upP8tEIZmwZ2Y1nNM8VwZTV4nYeoWJKdmT9goi3fUExgWKeanjvGFaWUy53pJkqI1nQHUT2Qdeb9mdprVaWYuOZmrvjlsLuiPVbHhqRKUQNFGRMeqZeQRrUQ20JGwsiiBDUVJnRpUi3MM5OZNN8zZRSIbScE7zXBlMGbGjYDzLIrMHs8yzg7zzUqfRlUYWU64321JfbdTfZPtAp44WNV9U2QhJa0F3yrbVqbajlN5XlEPXFORJZ6M88Gzb/LGtKIIMtqbOjAvU6Wa2pU2bKCQz/My87bfxHs40MtjUc5PQdQ/n8BpgmWcHeeelram6FOstKMdFtQJvsWNF6qvJgjVRpOkDkzqaShshaS3oPgpmpeFZq5VxfGEx1QDYplANY6sQVEFewRq3+GXGOcv8YcIp8tnUUYBScVCxsdVqZbS6Pa1yV3UF1rTYWIU17RngohvPMsjuwSzz7CDvvLTVgZD3vdLIcRNzOas8VKXDF2U9q7QRktaC7nOnVhqeolpJVdY4i0Kl21C1VQhmIanvVHm90lyZoKMs9jhg40H4cYJy01QRPW2JEq7ffUCbg0eVV9gWp6UpI7boxrMMpq4gYtIhG81LwmaDI896SyPHizKXVUb7itIHKm2EpLUQJ7fDCjPlxUpNPG2+cdo8dhNFC3QdulZ9mF6271ScPzN1ZcI4U9SzqaMC5ZkZm68SMfVMPzuC6tJwXZenSz/XgjPAeT7HxFVALPPMQamb2XjekII0cnx4LjdbHXRbi9IVpfPIsjR/r3IvKcp6VmkjyKyFMLkdth53bt20VOU7K1ZGPNN6qtJ6Ckykverwuug4R2oyZdjUlQmjRtpofxHPpo4KlBEkm68SMfVMyuwIk+f4KZ9r07EV1VcB6biCiJGHUr+w8bwhBWnleHAu18slaaMzj0xJ+/eq95JgH3iLnf59lRbItyAqbYSsayFsPc7uza/vW2l4eoudyDsiw1BhqFJvvjqEoA6j0GTKsOw4p50/48Q4FbkaFaiUYOqNzYSDx2bj2ZRTrtXtGbn/U/bzbL+Hs+iGyChBrV9EyU6bnCtp0RHEyCvL0v69rr3EZv1HtXzKokeo0vetNDzb7S5mJqrSA5B2ISZNclWTU7UXVYdRaDKaKDvOYfOnUYaVXi7dG+A4FblilkO9sZk4O2Oz8WzKKdeoV6w0nk0peXHPzbIHF9lIKRo69AubjQ8ZkuQ4xXzNK8vS/r2uvUSX/pN1DGzLtFC1Hq3WNoOXu8aRNoc7Kd+5qPd46ThHavLcRNpx9udPrVZGU5Rw8916zvTKnm0wcdaYz7/G4zjO5QBeB+AwAM913d+P+L3XA/gUgFWu685pbGIusp6/i5rT9Rqwa9tmNOoVLWdnqM/r+NkRw2c8Td/DmYZmqzM293Dqfq4JGa0LG2WdDv3CtH5HcQ487h5IivmaV5ZF/f2phQ7WrJ1e8d66zmHq0H/ixqBohK3HnVvzr0crI55ZSOMpSPIYFbUCrQqvUVhFK5PpSlk8QjqjfGm8qZHtqlVRn6qjXCmRe9j5/Gs0juM0AHwMwO+4rrsDwEbHcV4R8ns/DeDfaW4eADPRl6QIUr1c0uqhpfQKp82uicNU9cR6uWTlFSam9tFRSJ9WjUlZZ6IifhCT+p3qaCvVfM0ry6L+/hP3fz/yvXVE+3ToP6MkM8LW48xENffYSPWEjZ6xvMR5/k15rvNC7TWK9Nx4PelotA3ojPKl8aZGtmuigtfv+qYSD3ucR9lURU6LuATAD1zX9SfF/QCuBPAl/xcGCttbAdwI4O06G2cq+qKikqxt84xCnpmsnugrB3mfSxlxMrWPUj53hDNEtMs62QrSqqsxm9TvVEdbqeZrXlk2/PenFjr4xP3fxwe++F0A5rIIdUTU48ag2+mRPUfXPjq8HidnGrk/M9HwDHjGLnRdt+U4zj7HcV7huu6Xhn7PWBSAmiKX4aYU2nmEpA3Kpd8GAPjirS/DB77wGPY//CQAdRtNGsEftQE+cbRJliYWlR45vKEAGNmUshSsB3Ay8PWJwfeC3AbgD1zXbTuOo61hgLkUMUrlW4XxbELWRD2TrzA5jal9dBSMZw2QybozzpiEECLxga1uD7O7D6yQX7u2bcZMg+Z+QFmG0+t3bt2EyWo5Uakul0uYyaF4lyulSFk6Wc0f9YxKu2+2OpiZacS2v9XtoVGvoNnqoF4+nQzZ7fT6bauW0cjw6t1OD1MTFez88qFl38/y3nn7HwAaOH08JPiuWd4tjLgxaNQqudvvc3xhEbND15zMzKhfRxRjIBPxtDoKoIKi3PujmqwKpy3nYobbcMfVG1ESwI9OtJQpQGkUlaj8+dvu/T/Lfi+Lkp84BkNKan2qXshzzcQcBrAq8PXqwfcAAI7jPBfAswD8WkARu9VxnM+6rvsPwQ+SVcYAeUGuWmmJIo8yM0yr28PNxMpn3g04y0ZKvelHKX0yUCgCYeRVOAE5JU9F+ymVyyQjRVX/K4ZM1j3zzLzUA9esnQ6VX416BUefzp4gl8XxVKuVV+h3x483E581M9OQ+r0o6lP1SP2AwllVq5VDnS7d1iKOt7uh7V/SFYb+hjLFmeq9k/o/zVyYH7hd5GavPHFj0C2Xcs0fn/pUfekaMABL15zcee3Fyp2eadbAunWrQr8vPM+L/UPHcbYC+DXXdV87+PqNAH7Rdd1rA7/z3wDsdF33+47jeIhItW23O14aZazbpQtL62YU2t9sd3B9QEkEgEvOX4Nd2zbHKketbi/T31HS6nq4fvc/hLThRQA8pe0YTifauXUTZiaiz48Elc6SEPgPfxLW7nR9l3YMypUSLnjHfej0TsuDSkngsduuyJweIrsGqtWynFBQzMCBdhCB7A4AHwHwjwA6ruueGPr9SFl35MjJeMEaQFaQ16fquDHgHAD6Y6p6s0lSTNJsRGvWTkfOsyzKJ0WfpFUmKceBQukbbr9NEWAZ8irzqkl6t5SK2NjKOhXyS4fRFGRmpoH5xW7mtaWjvXHzNWyu6thXqN47bq3pngtxRI1BGlkRN47U+2gaKOSdTMRTu2cMsH8zSmIU2t9tLcZ6z6JQ5dlMQ3Qbyjj69By5lytIFm+q731L8ljKknYMVHhiZddAlFdMN67rNh3HeROAnY7jHAFw0HXdLzmO8z4AxwC8FwAcx1mHfnYHALzVcZw7Xdf9V9XtM5W6SJkBQp26aOIMns2VX01km4xK+nQUptKnVWJC1lFWkPbRefxA9oxqHDKyNO/cTztfdchQHVmEuudC3BjllRlJMrXoRwBkIp5WRwFsZVTan0UImorMBJlcNREa8dPZhqxkTR0K/k25JPDGFO+vwluYwvC0IgpASV5ZFzUHbFLIfdJ6cSnnWdEjnhSe62D7TcjevM8Mi9hSzhHVa6aIEU9K0sq6PBHDYXRGfooUGYzCVMSTirj5o2su5Bkjquwmk9FdCnmXmLvnum4TgO8ZexcGnjEAvwvgt/3fcxxnneM47xx8+VbHcX5SqmWK4EufachS4trUtQJBKK8Y0I3f591OT6rPw0q0n2p38dFrL5Z+fx1l7Bk5kq4vyVJy3hZ5SD3PTMgaymdSl/c3cVUE9TMpryNQfX0Fkx5K+aXzejAda8vEVRw26Gsy+BHnqLWsay7oGKOkuVZ0fU2qp1zX/QKALwx9761DXx8B8K7BP6PYUtxmXLGlOBPVFQO2E5lict3mVO8/iillRWQU0i/jyDrP0lRpVvleNld+NZGCZXP6tKlK0AwdcfJL5/EDHWsrau5PTVSWfk4t42zR15IQ1QpmY9ayrrmgIzVZZq7J7KM2ZkgBEhHPIjJKF7iqQnUEpD0QBHPzi5ierEJUK9q9zDouJLaBuPtAx+H9Rw2bI0jAStmhAxVR4DxQPZMjwCuhjFyYiAAztMTJL52RH/+Mqsq1FTb3Z1++AUdPtZVG7YuQSWNLFFBHZJVCptqc7TGSltgIX/pMgo4IiG1RllFmbiH8uou5BbtSZRg5bI4gha3rnVs3LRmAaZH1yKqIAvvPbbY6mdtPAWWmQdEjwADfw8ksJ0l+6crU6VclrZ+e5wsdlAUwWa+TrbOwuf+GS8/DjXtWXkFlOmqvW8ejigImkbQn6YisUsjUsD3z7gefwG9eeh7WrJ40GgEdyYinzrx/m5D1PumICHPUWR9lAdxx9cZl3rE7rt4IOy4pYdJicwQpbF3P7lV//o4ycjX83Ot3H8jlCTZ1ftZ/brlSWvbcIkeA/c+iilwU5fwaE41t+lzrVAsnT8xjYbGLN+4+QBpNCpv70xMVK6P2unU8HRFnmT0pSj4BIN0H8srU4T1zy0Vn47UvfA5u2EM7Z7Mwkoan6s3GlkIdw20yocRFoeoZNva9aSbrFbz/cy52bLkQ7ruuwI4tF+L9n3MxWddj5POY0GJz+iXluk6juKg2nm0qXiOznqifa9satjWVmdGPjc4DKhkStu6G575threP7jT2druLmYmq0rUsO67DYwTAurTW4Xlz02UbsH3fQSuCQYUyPGU3R5Wbja1506aUuChUPEOm76OiAKPM3PwifnSihVd/8Gv4qbd/Fq/+4NfwoxMtLRuTreuh6NgaQTJ1/m4UjGcZZNfTKBjP1EQ9c1zO+o8qJpwHSfOXQobIrjsbDW/AXCRa5VrOOq42ZvgNz5sN68PvdjcROS+M4Zl2c1S12dg4wQBzSlwUKp6R1Pdp5khWxci2yABA29dp38/W9cAsh0oehs21nVvVXyUyCsazDLLraRSMZ0pGxXhmluOPwarVkwCAkyfmlTsPZOYShQxJE12zMWpvq0Gch6zjamMRs+F502x1rImcF8bwtEXBtXGCAeaUuChUPCOp72XnSFYlxdboHlVfR73fZKMaqYDZuh6Y/ESlgQ3PtZmJqpbzdyqN56LdwzkKxrMsMgbgKBjPzHJMjYHMXKKQIWnWnc6ovQ2ZhabIOq62pkMH502vvZj4brqcbYUxPG1RcNNOMF0DaUqJi4P6GUl9LztHsiopUX9XqlWNKyQUfR31fr1S2filzeOO7uhLmutLsmJKcRl+7q5tm60pXiO7nkbBeJZB1viw3Xhm0mNqDGTmEoXssnHvtCWzUAUye2jWcS1C9Dfp3XQ6egpjeNqySGUmWK1WRqvbw5lrptAq6RnIUfQ+DZPU97JzJKuSEvV3jXplJLzhkZdX1yuRm38RBG7RMVFIRoXSJ1NIQ5e8Cj63Xi5ZU7xGdj3ZXPnVRCEom41nJhtUY5DWaSc7l/LKLhv3zlF1uKTZQ7OMa1H077h30zn2hZlNKu/Okb1LDki+X2fpbqPdB/D+qzdisevhU298KQ4dnsOHv3JI6f1L1PdZpekXHST1vewcyXq3W9TfHTo8hx37HzV+r1Ze4t4vyPAdalFj0mjofoPRhPIOS9m716jvQqa+882UbIp8roF7OP3nTlbL+SPPlt7DKTsPqfUDvv/TPBRjkEXuxM6lKp1zWdedu0GZlXRnMbXctwXqe6DDiNsH/DHwi16a1qXD0Dn2hTE8VS3SLIIpboL5E3zdqjpqlRLefM9p4XX7VRvxgS+4hVnEOi8HliWu72XnSFYlJezvbr9qI97/eXckhHNov2zdhLu/+cSy31NxaTMTDeWGILsBUyveJoznNNSn6on7ii7j2cR6MmU8JyE7D202nplsUIxBFrmj05lKte6iZElamTWqDheTBrWK/UoFOsdeeJ5H/qFRHDlyUvphMzMNHD/eVNkcAH2F48aAYAKAS85fgzuvvTjThFyzdhoXvOM+3Dv789ix/9EVn/ue170AZzbsN1AmV03g+t0HyPpFN0nzJ2vEpFYro1SrolGvLEWx9z/8pJK+0bUGggz3S8nrodnFis1fJo1Etv3r1q0SVO23BUpZRymjfPnU6Z1uXqUk8NhtV+Do06cj20ubpcS4y4yz7HNloOyPWq2MdqmE2b3J70n9XNn+TWJmpoFms2VVdkoa4uYPZT+lRXaPSCOnWdal29NkxiDudyjlTpb26yBujYhqJZXMMrnewtoyPK6NRj1T/1Pr+Xmffevlz8dvXnoepiYq1shr2bGnkHeFiXiqgtoT4nsNou7MOWdNAydPzOdqc1bSGFuNemUkUy58ZNIiwvqp3e6iBuDoYhc79j+Kbz1+zIqzGVSE9Uu9VlaeDsREQxl9MRVBovSmUkeAZyUjIiYiz7JQe9RNpDJHPVNHOmIYnMlhnqQxSIomjWoEL0icLEkrs0yutyBR45o14Gwyg2F4DLZcdDZe+8Ln4IY9B0gjoHllts6xL0xxIVVQFyXwJ/gPjzXDP3dBzUAmHaBPW6DEpjt/dCLTT0U5SE5FkSrXjSKmCslQjrutVVjTFDCx9QqTVrdX+KtE0lRRls1M4Ts4R5+kgig2FvChJk6WRMmsUwudyLVhw34fNa6tbi/T55nU2YbH4KbLNmD7voPkhfsoZLausR97w5NaMPkTfP2qOnZuDfncNr3hJjPp0lasqpdLIy+ww0hzqbNp4cyMD1TKt6kN2NYqrGmMSVuN57jslCyYqGxJ+Uy+g3N8SHLgjIOTOE6WRMmsT9z/favXRtwNAmHIXpViQmcbHoOobMg8FbOLVo3YzlZphCq8PBzmrpYEar2elrC1TNpWljQxX2DbkGKpK/VrVKu6MeNFYkEDAymEVM+lTAnyFjvYuXXTijOeURFgyudSpX752SlU6YQmZKDNacyAfRXemT4yqbQUcsfmqqRxsmRYZp1qdfCJr38fH/jidwGoqe5KQdS4Nlsr5aPtxXtWjMECrbwGiqe3jn3EE8jvCQnzsB5f6E8iHR4WmbStLB52W6J6oR7sUgmTDfo71Wy5L5Zh8qDrHk5TUMmmdruLmYmqdESE8rlUkRjq7BQTMtDWNGaAI6g2oyOV1vT4J8ndJFkSlFlT9Qp2fvnQsr+38X7aqHGtl1eaLKqifZT7nT8G3U4PvfZipjkb156i6a1seBIQNvFn9+oLc8tMuiKfdQgVLHsfQq9UJhf+Re4nhvGxXfk2YcTGPdOEg43SsUeZTmhCBtqaxgwUL41tnNCRSmty/GXlrqwssal2R5w8jhrXMKj3Or9tqpwNWeZsUnuKprey5CTAdJhbJm3Llmplw8ikMEX171S9glOeR5oiIttPnHrF2IzWezhTYiI1Ku6ZeT7TFhlg6z2cJp5JXcHS9P4+ylCsIdVHB0yOP3XauJ8dYfp+Wpk9IGxcw+5RVVG5WEW6fpC0czapPbbq91Gw4UmA6ZLdspPOn+zeYgeiWsGq1ZNGJ6isAhrVv4cOz+H5Z03HllrPsqnlLeHOMKbRqXx3O+kqDare1FM/MwPUMsCUERv1XBPngG08AwyY399HlaLso1nHn2JNqzB6bajdQbkHqLgqxTZnk0x7ZPRWWxylnGpLQFiYe+dWvV4k2VQL0+cVgsimsHiLHXxoqELw7VdtxOe+81Ss8Ff1nkVKvbLpXB6jD+oUNJvP4Jl45ihUYR2F9OkobL0KiDlNUfbRLONPtbZUnN2jWBt51zqlPFaRbm3bmcm87bFJ7wfY8CQhbOLPTFSt8tr52CTsZYVPu91FowTced1muO+6Aju2XIi/+sd/wTUvOSdS+FPfbZel3cPoVsxsEzaMXmxVvotevAagVZxMyWSbjWdTRqxNVxCNOiYcUFmQHf/g3CnVqiRry0anB8Vap5bHWfe6KDljW7/nbU+UrK/Uq0bkrF2upQIzHOaenAlJRrcAm1II0qSwzDcXUav1cMrz8PyzpvHs1efGpgrE3W2X9z2zpN6YSCsykdLI0GFTakxc+mLYuZs4VKRG5XpmNf1mS5l+aUom23qFiakUTBuvIBplipTC7I//ZLUcOgeG5477ritI1paNZ/co1rqJPWCYpPUu2+869um88yBM1p+1uo7mYnfFVWI6Ut054jlm2JRCkNaLk8arpbJ6Wxbvk4moRlE8ysxKbIxWZ/Eq2xJBon5m0SPA1M/lCDCTFtuiSnkYnjuHDs9lWltR8tKGa+18KNa6DVkESetdpt917tN55kGYrL/l8gswu9eMvGOJOmZ4ix189NqLcby5iOee2cAPjzUx06gaEfYqvXkqq7dlabeJqEaRPMrMcqij1Saip7ZFkGyt/GrK+0/5XI4AM2mxIZpHJReH586Hv3IIt1+1Edv3HZReW6NUbEmmX01nEVCs96JklYXJ+nPWNIzJOzY8M2JTGlxa2p0e3vaZR5YLN1NtUSh8KKq3UY2zCSMwSrEseT3Up+qFnLvjAqUSbEqhGQXjOQ5bq7CaeK6tRmwRnjvOZF1DFLKAUi4Oz539Dz+JDeum8PHrNmNqoiLVxiIbMcG1PkoGdBJFcVaFyfq5hY4xecepthmwMQ1OlnFKJ8qbohI1zpONaurxN5FWFJbO0igDzS4KOXfHCco0SFNrnjL9UoXM9dPaypWStsIKUcUsTKXTUT2XMnXOVArmKKV+jjJUsoBSLobNnWtecg567UXptUUhL3UU5Upa6zr3mzzvS7HebTq6FkQmZdtrLxqTd6NnbeRA1otWFM9UGEXx0NhA1Dh//LrNuPlPD6Qaf5NRjaBHuT5Vx813F3PujhOUESRTa54ygqQieqrbK6/imbVaGa1uD2vWThuPAnMEmNEBlSyglIsUcyevvNQp0+LWuq79Ju/7xo2ZrC1gQ5GkYWT7xaS8G5mIZ15PTxovmq1FW2T6wFYPjY1EjfPURHTF3DhsKBJg69xllkMZQTK15ikjSDbfw2nqmf6edf3uA4W9wiRoOI9SBJhRB5UsoJCLwTUjqhV4i53Mc0fVlRm6s9l07TcU7xu23tPYAjYUSRomTb+YkncjYXhSpF6kGSwbjTfZPuB0InmixvnUgrqKuaqxce4y4VBtCqbWvM3GswkHjM3Gs4l7OKkNZ9nnMsWGShbklYvUayavvLTFqaxrv1H1vmnlKvUdonmxZR7EMRKGJ8UGnGawbDTeZPvARg+NDCYUiqhxFr2udeMvi41zl6FleK0AMLbmbTWeTThgbDaeTRixqiLAOo1nRj9UsiCvLkQ1f6miprY4lXXpmKreV4fhprJOjC3zII5Cn/EM5mHnzSlPk19v41mQNH1guox1WkxVSYsa5/lmF/Va2arxl4Vq7tpWYZQKx3EuB/A6AIcBeK7r/v7Qz7cD+AkATwF4EYDfc133n7Q3NILIteL10DrVMlI9kgJqmWvibA71M229wkT2DB71WTDKc8BFqcyZB5tlXZzcoZQFeXQhivlLOc9MnzcMG7OjCnVMVe+bVa6m2StV1okxPQ9kKGzEM+gx+O6Psl3WGyStF822syBF8HJkxeTZhahxtm3806Cy2u9wpK1IOI7TAPAxAL/juu4OABsdx3nF0K9NA7jVdd33AdgH4A4dbZONvticfpkXypQmE5kf1M+kjAJT7h+yEYNxiQDbiO2yLknu2LD/UsxfynlmMpvNxF6h6n2zyNW0768yqjrcL3dt24yJahmrVk9ak7khZXg6jnO54zgfcRxnh+M4/zXk59sdx/lvjuO81XGcP3cc5/+ib+pyggvWv6w3zwZsWwpq2jSfUU6hLELO+jgRtVn2SuVlgvf4wqIVQi4FlwD4geu6vpv2fgBXBn/Bdd3/4rquN/iyBGBOdaNMFT5TkQpppHhNRN/5ymu309OmvFIqzP6etWvbZquuMJFVyG1Onx6DPcdKWQcUx+inmL/U8yxKvqi+OsrUmKlwQGSxBdK+v+pAkd8vJ0/M41S7ixv30J2jpyBxVgQ8Yxe6rttyHGef4zivcF33S4Ff8z1jnuM4v4a+Z+z/VtHgYDh7x5YL8eGvHML+h58EAOzYciGef5ZcWfnIsLgFKahZ0i9sTP+lYlQu9rYlbTEvkdV+65VlqSOzewt3Tct6ACcDX58YfG8FjuPUAPwGgJvCfn7GGZMQQkg9tFwuYWamEfnzVreHm3evvL5n17bNmGksjyw3W+GXQjdbndhnhLarUopUiiarpzeupPb7HF9YxGxApu3cugkzM/ki461uD416Bc1WB/XySj+qTN/Jtl/2mbopl0vodnr9MamW0Ug3zEs0AOzatnnFu2X5vJ1bN2F270PLxnqyWsbkUD/3n/kiNOrl3M9M89wk0qyjtPPHEqyUdUC43DlrdR2lUglr1k4bXXfD7c+7ZijldRwqZG8Q2b0i93MyrLU88lpWrmbZK6lkVRxpdAdZKOSdjDsiyjO2ZHi6rvtfAr+vzDMWZpDdftVGAMD+h5/EkZMt3HntxYmGo+3nN7Lmf9tiOFNThJz1JGyfc2mM4ihHwKHDy5d9Ae+HPQxgVeDr1YPvLWOgiH0UwDtc1/3nsA965pl56YfOzDRw/Hgz8udr1k6HbmqNegVHn17e57VaOXStdFuLOJ5yntWn6pEOn+CYJrXf/6zZvQ+FOiayzI+l9TT0nsOeaZm+k2l/mmemeQcKR5Rs+2WfOz8wR+RncPgzhp2gUW2cmWksjUWeZ6Z9btLnyK6jNP2/bt2q5F/Sg5WyDlgpd7ZcdDbe/GoH1+/+B5J155Nl/UW1P+uaoZTXUVDL3qhnyOwVeUmz1qjldRxZ9koqWRVHGt1BFgp5J2N4WuMZC7Pet+87iB1bLsSRky1pj4EKL4BM+6X/VpP3KLYNlnlx03oWbWu/7JwLeudKJaHtHdJ6RIe9dR/augl3f/OJZb+jwnOrmAcAPM9xnPrA0XYpgI84jnMmgI7ruicGGSAfBvB+13UfdRznKtd196lslKnCZ5QOH1OFZCizJWwvXiOjSFM/N+qZppygVM8d5QyiAVbKOmCl3Ln1lRfgLfccJC3EossRnLQmdcwzatkbho3BAZUFfIaJev9ySWDN2tNZmEF0yEhbswVlDE9rPGNR1vvzz5rGnddeLO0xkPEC5PVGp/VCB9HlPYojT/tVMn+yPzbzCWNjW/uT5lyYd27n1k2o9cK9c5Rpu1k8osPeupLXwzUvOQcPfO/YsvbLeG5tiQK4rtt0HOdNAHY6jnMEwEHXdb/kOM77ABwD8F4AnwLwMwDOcxwHAKbQL7yhjLSbuo3KN/UGKKtM2Wo8UytFsor0KBjP1NhmPOvAVlkHrJQ7AMgNJx1Giez6UD3PdBgfNlbL12Fw+6x4/4UOep6HN+4+sGzsdbvgbXQIAHKGpzWesagFdGqhk2qCBj9ny0Vn46bLNmDD+mmcWugsHbo1mRZp62ShIo9wsT1lNYok4R+2EUadkaTugywCOmyzHL5iZrJatsr4l8F13S8A+MLQ994a+P/XqXx+1NowFX2hUopMXSViq/FsKgI8CsZzms/THQEuEqZlXRxBuRPniI8jbvx1GCU6I25x6NIn8+4V1GtRd7RveM6+KWTsd23brOTZcW2yMXMj8aSt67pNAL5n7F0YeMYA/C6A3x782qfQN0g/7DjOVwc/IyesitjtV23EJ+7/fqpKTf7n3Hr58/HmVznYsf9ROO+8DzfsOYCWKKFSrxqtqqarwq7pKpO3fvohHGsu9ss8T09IPb8oFe+GSaqANzVRwY4tF+Kf3/1L+Nwtv4AtF50dWd2Oug+oKqwNV5hj0iFTgZXiKhETmLxKhKryoa3XlwBmrjChrshp4iqgou4n44SK6y10XD+nqjJyWplu240NUVCvRZM3PUSNfaNOK1dk5oINVw8NI9ULtnjGfOv949f1z/odOjyH93/exf6Hn8QD3zsm7UnyP+c3Lz0PN+wJO3f3Im0h+rg21tCv0jQ9WcUcgBrovLCmPL2+F3DdqjpufaWD7fsOpnq+zvQJSuI8T7VaGUdPtbFj/6PLimZtWDcVuhFS98GoR9iLgu0RpLxk9YjbEgW29fwsIO/dp3yuqfRpGUxEgBk1ZFl3SeOvY89TEXHLKtN92TtZLaea1zpT36nXosloX9TYN1t088u2/T0N5mvBp6Td7mJqogLnnffh1R/82tJVKmk9Sf7nhHslysq9YUmovJC3ViujVDMT1fWFy02XbcD2fQdTP1+Hp1IVUZ4nUa3g5r3Lx2L7voN4w6XnhW6E1H1QFI/oqGNzBAkwnyFBFQXOA9UzTUWAKZ87CvdwFnk/GSfSrruk8ZdZB3nlnYqIm84IvUodNAwVa5FCXmeZB1FjT3kNkO654PdBq9vLPQcKZ3gCdBM08nMWzIXofVRNKl+YNOrhRrfqC7L9Pt+wPrzYTtLzTaZPhEGhjEdukhOVUEGpog9UCGgmHabSL2XQrYT4jILxHAWl4ZzGoCy68SyD7FqybT9haJAZ/7h1ECXv0qDCoasqfTcM3WnoNq7FrPte1NhneX7UfqVrLgz3wfW7D+Te+wt5kIEqTSLyc9qLqMPsgVxVKUB+CsqOLRcaKbPs9/kPjzUzPd+mw9JUqQ5p0zJs6gOfsL7YuXXTUmSKScZU+qUMsalrCqGUg1HrNWulQRMVWMOe62OiCivlM02kMtsoS5n85JWlUfIubXEY6uMFOgvm6E5Dt3Et5jn+Ejb2Udf/hZGkX+qaCyqKZBXS8KSaoImfo3kTD6JqUvnC5MNfOYTbr9q44oylau+S3+dT07WVd0FKPt+WMvdUCzJ0k9y6CZO1MnpT9dC5bUsf+KSpysuEQ73x6rpKpNtJ78mVRYfxnKXSoKnzNdQOHlPGcxRUci3NWrJNljL5yStLo+SdvyerXC9xskVnPQYTd0DKrMUinztNgw3nlAE1fVBIwxOg3aCCn+OHtk1vxKomlS9M/LOxO7ZciA3rp9FsddBrL2p7127Pw5lTNXz8us2Ymqgk9rVtChJAHI2plPCe170Azz2zgblWB39y//ex88uHrD4wHhyTZquLs1YvT6/lIh3psTWCFKeETFbVpavqMJ4b9QrmT6b7LFNXJVA6ePgeTsYEuuZInvEPk3ezL9+Ao6fauHnIWU69N8fJltaplraooK1FB3U6/EwY3z5J+qWuCLGKPiis4akCm6pEqZpUJa+HO6/bjKlBVeDPfecpPOsl52grJhPZxzHPt2lcglAtSFGt4D8ONprP3fIL2LH/UWN3f8kqBWFjcsfVG9HzsOTU4CId5qFSvmOVEIWGpw7jOUulQVOe8HG6h9PEM210cI4aNu7lw4TJuzdceh5uDLkFgXpvljE4dDhUKGUv1bpqdXtL504B9fqRSeNbRr+kmAtJY6OiDwpZXEgVtt3plXT4PW2RjFqtjGYXuHHPATjvvA879j+Ka156DhplfUI/Sx9TjItMf6XtU6rD8MGNJmvRJQrSHKQPG5O33HMQt77ygqW+2LnVvHe06JiqJDv8TJOVj6mK4VBWGjRVDXVc7uE08UxTBbTGiaDhYIOOFUWYvJuOuAWBem+2qdJyUPZ6ix2IaiX1XkS5rmSKYlLumSb3PR3FlmTGZrgPdm3bnLsPRtbwzDL5dFYMy0PWhRy6Se99CL2U1drykKWPZf4mrqKqTH9l6VMqoRTcaA4dnjO26aRR4qLG5Jw1jaW+mJmoWuXFLhomFGEV15fYUkmWqtIgYK4CY9hzszp4bK6ibOKZtjmeRxFT1fSTiHK2BeWdLoNwlKq7ArTrqtnqxI6Bij2Tsvp42ueqNnplxybYB/VyKX/mZa6/tpSsk88mT1McWReyDYZ1lj5O+puw8f7xwiImG/33kumvrH1KIZSCG803vvd06KZTyqggpyHN/IgbE78vmHwUPYIE2BdFyrJebYoAhz03q4PH5ns4TTzThv1x1EkyHEwgK6O8xQ52blVvEJqQLUnOwTz7AuW6qpdLsTJr1JxHqo1eUzKvsIZn3ELJOvls9DSFkXWy2GBYZ+njpL+JjOSWyqjVylL9ZVLpCG40V138XNz94BPYseVCuO+6Aju2XIi7H3xCS1Q6zfwoylopMkWPIAHFv4dTRQQ4L8PPzfM5tt7DaeKZNuyPo06S4WCCNFGfmYmqFoMwSraokH8yhneefYF6XcXJLHYepcOUzCukGyCpoEDWAgw23iM0TK1WxqmFTqaiNioOCac9NJ6lj5P+Jmq8p+oVnPI8qUPaJquXAacPia9ZO42dXz6ED3zxu0s/q5QE/tMrnq88iphmfhRhrRQdE3OS+pk67uFUWZhERfVamwrY2FpF2cQzba3iOWr4hoMN8x9IL6Nap1pGMnpUyT8ZGZdnX6BYV77MLFdKENUKvMUOjoaMgWk9rmiYknmFjHgmeajyWPGmvNgy+ILnE/d/H7dftTG115Daw501jS5LH8f9TdR4Hzo8h+nJqpRXPK3nXFXkxaTXPe38sHmtjAJFjyABtPPZRBoVtQedOvW4Viuj1e1pPz8bJf9MyASqZ5osJDJO2HZWvCiRblXyT0bG5dkX8q6rNDKTM7Hk8NfSqtWTmKiWcde2zVplnvA8T+kDghw5clL6YTMzDRw/3gz92Zq107jgHfeh0zv9cZWSwGO3XYGjT8+d9gwNWfE6N5G49melPlXHjQPP1JaLzsZNl21QdgenTPuD7fG55Pw1S/dN6aJWK6NVKi27X+v2qzbir/7xX/CGnz0XrVMtqShD6qtEFMwvG+YuFbJrYN26VUJDc7RCJetsuhcxiqT2U83nJLmflbj2U8s4ys8zJSuonzsz08D8YteaCFha0uz1LOuy6UW27Lkq9DpZKORfWPtlZVLUvqB6j0orM23KKBnG5PzxybuWKORdIVNtk8Lpo5oGGPRM7X/4Sex/+MnTgmduwWh7fHTcZTdMu91Fo1Fadj/pX/3jv+Cal5yz5OmSSSmTTTtLk36nIxWZKT5R80TXnW1BbE2/NJFGRZ2KZPM9nCaeW6uVcXxhEbN7HyJJH7RZ6WSWk2asVM71ouy5quSfrIwL2xd0HH9IKzOz7l/jIjtM7RtBCplqKxNOH8U0QNtSQmxqz3xzEaVeF81WB88/axq/+XPnkd1POpziMyV5n1feVORupzcyc5eJhzr90obrS3yoZLGJNCrq9MtRqMJKfYXJ7F6+h3PcSDtWqud6UEZlva9SNarkXx4Zp+P4gw49c5xkhw0FmAppeI7rWQzb8tdD27NVz9Ufw9RqZTS7wA17DuCCd9yHG3YfQLOL3IIjTCAdPdXG7Ms3LPu9MEFY9IqejB4oL1UflQ3UtitMqJyYo1CF1VbjedSuUhhl0o6Vrrlus/xUKf+yyjgdRkySzKTQi6hkRxF0NBsCRoU0PIHRjGgmYZvB3W530SgDd163+fTVH998gsTgS4sqpSPqqpY3XHpeovJIKZRt3hCZfFBeqj4Kzg7qK0xsUgYoZbgpR6StxrMNnnxGjrRjpWuu63JeZJVJtum9Mus3r/yNk5lUehGF7CiKjmZDAItdgQXDxJmvOHqihBv3HFh27uCB7x3Tmi8OqDtvGvm5E5XEMyGUZzJsyMtn1OBfqk4xT2y/vkTmHA31GULdV7AkkUWGR/VbvQbs2rYZjXpF27kk6itMdm7dtOKMZx4jlq9SsJ+osTq10MGatdMr5pSuc5g66lbYKJOyknQ+lOpdfZk5WS0vGweqvYJCdhRFR7PhTHNhI56MHdjiZU7yvGX1usV9bpLnkdKzZEs/M/RQXqpu8/Ulsh5h29MvdUdQkyLA9XJJewSE8gqTmYlqoSPATHqixuoT938/UjboiPbpSEMcpZTwpAwO1e9KtVdQyI4i6Wgya0nlPle8mc5kQlXFLlu8zHGetyiv29SqKiYTIgUlrxf6uTLnWIte0ZPRB9Wl6pRVWKm9/7IeYcq5Tv0O1NEK3RHgNM/VSetUK3dEyQZPPiPH8FidWujgE/d/Hx/44ncBmIsWUVexDkPXbQBha1wFcRkcqt+Vaq+gkB2jpKPF7XMUcMRzDFCZe26Ll3nY87Zr2+Ylz1uU1+3IXHtZf0w2qmismsDkqsm+l2d6AqJcxt0PPoEdWy48fY71wSfQE3JLp8gVPRl9UEaQqM4QUnv/ZT3Ctp4hBGg9+CYiwGmem+bzTJyhjSpAZdMZOCaa4FhNTVSw88uHlv3cRLRIRx0Nk1VadaP6XbPuFSpkhw06GpUsVh2p5ohnwTHlMfcx4WWWufNwZqaB44M2RCluzz2zsbSo7n7wCWz72XMxN7+It9xzcMnLs3PrJnzv6VN49Qe/tvS3lZLAf3rF87XfrcjefEYGqnPg1N5/WY8w9RnCot/DSe1Jt/kMrWwk1tRzGTXoihbJjLPqOho6oqpRa3zXts1kz5BB9btm2StUnbHNs29RyB/K94rb57qd/LdWsOFZYMIm2kevvRj1WhXTE6dTSHWlduggy+IKbmpbLjobN122ARvWT+PkwiK2XHQ29j/8JF79M8/G8eYi3vaZR5YJ69m9D+E9r3sB/uqhJ5c+z1T6hOyGyEpUsTE1fmHPpUoBBtIpIVTKH7XDxkQa8CgYzzKkke02G89MenQYY7aMM5VMitsnotZ4o17B/EmyV0lEh8M87V6hOhCTpXAcxbykfK+4fW6ymj+jhQ3PAjM80datqmOu1VkWsfvQNZsgFuiqZg6jW5hnWVz+pnb3g0/gtS98DrbvO90/t1+1EQCwYf00AIQK63PWNHDJ+WuUbYiU2LK5MtkwNX6Rz/V6mc7fxVVh1R21p4xgUCrIJiLAaZ4rgykj1lbjmcmGDtmga5x1RFWT9omoNd5s6ddbkt5Vt6PVtkAM1bykfK/YfY7A8LTyjGetVkar21N6ZsSmu92iSGrj8ES76bINeMs9B1fkZZdLQlnueVIuOHU/Zznv5J/b+M1Lz8P2fcv7Z/u+g7j1lRdgbqGDHx5rhp9HWOhYc3dqEqNUMW8cMXUPp66zi0U6gxd1DsjEPZyU/WbrGdo0sp3v/xw9KOZ4nLzTMc667nJMktdRa7xetkvlN3H3pY4ztmmgmpeU76X6rLNdsxCnJ+L1uw8om4iqJntQ6LW6vVyfJ9PG4Ym2Yf00vvX4MWy56Gx87pZfwD+/+5ewY8uFmKiW0ChDySSKWzQq+jnr4mq3u5iaqERGNP/yH/8FU7Uy7rh640qFrJ18dYotjgxWoooN5filWX82X2FiYm3pMJ51FDJR/VxTRqytxjNjjiR5N0pXpSTJ66g1bhtR/VWpV5XJfBuKAAVJOy+j9kPq91LpJLbO8NSxcFXd7RYUetfvPpDLyJJp4/BE++GxJmZfvgFvfpWDHfsfhfPO+7Bj/6M4OteGKJeVTKK4RaOin/Msrqi2PnG0iR3/83/jD+/9PxAAdm17ER677Qp8fNtmrJmuQVQrseNowmsXxdz8ImZfvmHJ8fC5W34Bsy/fwEpUQTB1D6etESQVa2t44w5Dl/FsKgJso/GcNgJso/HMmCNrFFDXVSmUyMhr03c1yhDWX2etrqO52FWmT+WRHSr6K828TLzT2YAjMwvWGZ46Fq6KZ1ArKjJtDE40912vwZrpGn7r585fkU56890PwYPI/G5xxC0aFf2cZ3H5d3IOt3XtdA2XnL8Gn33kKbz5noPo9Hp4+mQLN+w+AOedf5Mo+EyntwaFYblcwjUvPWeZ4+Gal5wjde8oYx5K5SjN+rM1gqTCABzeuI8vLCq9wkS18Zw3uyYvpoxYG41nxhxZo4BZivpEGR+6oucU8toGh3lYf91y+QWY3atWn8oiO1T1V5p5mbQfFuUoi3WGp46Fq+IZ1EaWbBvb7S68xQ6OzrVxw+4DmKyVI6qZqREmcSkdpwZFjZLeIcsz0ywuf6NAuRJ+J6e3PA25JEQqZddkeuuwMDxysoWbQ4S27L2jjFlM3cNpawSJem2Fbdyze1eu7SIZz3mza0ylMocZzkWPADPmoIoCJhFnfOiKnlPI6zC5dPeDT6BUq2qTBWH9dc6ahpXHhVQGGILz0lvsQFQrxs4p68A6bVTHwlXxDGpjNqyNO7duQrkkVgiD4II4dHguskCOKoaFOdAXzp+4//u4/aqQM5OaL9T1N4rJWhk7v3wIr/7g1/BTb/8sXv3Br2Hnlw9heqKyrP3TEWdBoxY35dinjWQMC8Pnnmmn0GbkoVKC08o5GyNI1HJVduMumvGsohCUKqgNZ/8zbThjz5hDh+7Y6vYSI05Rso96juaV18NyactFZ+O1L3wObtijrr7KMGH9NacoYJEXG4pTjcp5dOtKXfpltXdt24xG/fRdlNT3/lCX7qa+h2qpjddtxvREBU8cbeK2e/8PfnSiteJ6heCC+PBXDuH2qzYuuzLEL5Cji2B56ENHTmHHlguxYf00mq0Oeu3FyH5WUVZ7WVsGRnnSNQJprxsIG/ugk0D2HbJcpTEsDGXfkRktbLq+BKC7woRarpq4woTy+hKg+FeJUD+T+gqicbkH2XGcywG8DsBhAJ7rur8/9PMJAO8H8K8Ang/gva7rPqa9oZLokHeNerRT2l97YbLPxmvOhuXSTZdtWDqmBaiRBZFrK9BftVpZ6VUeWaGS43HyJUk26rjvVgfWGZ5AfyHONOo4+vSc0mdQ3e3mf15Q6DVbHXRb0UaW9GdWK3j9rm8um+zDwiC4IPY//CQA4D2vewHOWdMwsnEGFaP9Dz+J/Q8/iUpJ4LHbrsDRuYXQv1ElmKWM8qFFm3Zxp3ESxJFFIRsWhh/+yiHccfXGFXe5Fk0wmaKIylji2iGUc7qhViajnERRBWyKbDzLYOJOO+pnUhqyNhoIKnAcpwHgYwAudF235TjOPsdxXuG67pcCv3YLgCdc132f4zgvAPDHAH7eQHOlUS3vmq1sd6LbeFfssFzyb0UIQikLZNdWnMxvNHI3IzNUcjyuD5Jko0lnMiVShmcRlTETBIXezEwDxwkmg8wmPbwgjpxsoVEr4+SJeSMTMotipEowZzHKsyxuWSdBHFkUsrCxn65XlozgogomExRVGbNRqaGEUpkMW9uT1TKOH28StFT+mdTGc95CUDozJDgCbAWXAPiB67p+B90P4EoAQVl3JYC3A4Druo84jnOR4zirXdc9obep9lAvlzKtPRMOniSG5ZJfk0OVLEiztmx0mFLI8WCqNrCyD2Rko419k5bEM54BZex3XNfdAWCj4zivGPq1W9BXxt4D4L+hr4wxBMgemLepKl+Wsxaq8ueH2xI0yuPORWQ5P5H3HbLk74eNvVjsoDW3wIUy0hOljAW5EsADQF8ZA3CR4zir9TVxJaNScEAXYWfSdT8zdyZMYM3v2rbZikJQpp5p61VAlrMewMnA1ycG30v7O2NHFl3L1rN5QbnUay8qlQWjsLbyyvG4VG1gfK52kol4smfMILLebZu8IFk8Q6o87zpTE/K+Q9ZIhk1jX3DyKGPLZN0ZZ0xCCLkrjMrlEmZmsucQRaV/NVudXJ8rS972m6bI7e92emjUKuiWS5nT0Bo4XVOh2eqgXu77o1WmtS1/Zhf1ssj1zJ1bN2F27/L06clqGZMpxzXLWiro/DkMYFXg69WD76X9Ha2yzjTlcgmNRv/u326nh8lqGaiWpeYt1RzNQ1L/q5QFFPtU0edPs9VN7AMT8jgNFGMgY3iSKWNMeoqa053WGFJ5aFqXYZb3HVScE2ZSQaaMPfPMvPRDZ2YauVI9o4oxdFuLJOn+SeRtv2m4/X3mBzu4/MzNz/xJmvbXauUVe2SWz8yyltK0f926Vcm/pIcHADzPcZz6IKhwKYCPOI5zJoDOIGhwL/qBh78bHCt4OCyYoFPWmSZP+6nmaB5k269CFlDsU6Mwf2T7wIQ8loFC3skYnuwZy4CK9qf1sOXBRP9TenpMzR+qd6CIZJimgGuYTBnTSVGdUwxDBZVzcVzWkuu6Tcdx3gRgp+M4RwAcdF33S47jvA/AMQDvBfAhAO93HOedADYA+A/mWlx8xj0zaVzWVhJ+qvY494GM4cmesQxw+7ND4ekx3f+j8A55kW2/LVGAIitj467UMAwV47KWXNf9AoAvDH3vrYH/nwdwk+52MaPLuKytOLgPJAzPIitjDMMwaWBljGEYhmEYRg1S16mwMsYwDMMwDMMwDMNkJfE6FYZhGIZhGIZhGIbJAxueDMMwDMMwDMMwjFLY8GQYhmEYhmEYhmGUIjzPM90GhmEYhmEYhmEYZoThiCfDMAzDMAzDMAyjFDY8GYZhGIZhGIZhGKWw4ckwDMMwDMMwDMMoReoeT5U4jnM5gNcBOAzAc13394d+PgHg/QD+FcDzAbzXdd3HtDc0Aon2bwfwEwCeAvAiAL/nuu4/aW9oBEntD/ze6wF8CsAq13XnNDYxFon+FwD+8+DLcwHMuK77W1obGYNE+89Df/5/C8AmAH/muu5+3e2MwnGcnwDwLgAXua774pCflwC8G8BJ9Pv/j13X/YbWRloAyzmzsJwzC8u58YLlnVlY3pmF5V08RiOejuM0AHwMwO+4rrsDwEbHcV4x9Gu3AHjCdd33APhvAP5YayNjkGz/NIBbXdd9H4B9AO7Q28poJNsPx3F+GsC/09y8RCTbfy2A467r7nRd91YAH9Tbymgk2/9WAF93Xfe9AG4H8Ed6W5nIzwH4awAi4ue/CmC167q3AdgOYLfjOGVdjbMBlnNmYTlnFpZz4wXLO7OwvDMLy7tkTKfaXgLgB67rtgZf3w/gyqHfuRLAAwDguu4jAC5yHGe1vibGkth+13X/i+u6fungEgBrvEqQaP9gEb0VQKjHzDAy8+f1AM50HGfWcZx3o2D9D+BHANYN/n8dgAOa2iaF67p/gb7XK4rg+j0GYAHAhRqaZhMs58zCcs4sLOfGC5Z3ZmF5ZxaWdwmYNjzXY/nLnRh8L+3vmEK6bY7j1AD8BoB3amiXLDLtvw3AH7iu29bWKnlk2v889D0zOwF8EsDfWOSJlmn/BwC81HGcDwD4PQCf0NQ2Kmxev7pgOWcWlnNmYTk3XrC8MwvLO7OwvEvAtOF5GMCqwNerB99L+zumkGrbQDh9FMA7XNf9Z01tkyG2/Y7jPBfAswD8muM4vzv49q2O47xIXxNjken/EwC+CQCDMySrATxXS+uSkWn/JwHcNUgn+WUAn3Yc50w9zSPB5vWrC5ZzZmE5ZxaWc+MFyzuzsLwzC8u7BEwbng8AeJ7jOPXB15cCuNdxnDMDaRf3oh+6huM4LwDwsOu6J/Q3NZTE9g9SGu4E8AHXdQ84jnOVobaGEdt+13V/6LruG1zXfe8gFx3ov8c/mGnuCmTmz5cAnA8Ag++VAfyb9paGI9P+56JfwAAAfgygB/PrNhbHcaYcx/HTSILr90wAEwAeNdU2Q7CcMwvLObOwnBsvWN6ZheWdWVjeJSA8z0v+LYU4jvNKAL8C4AiARdd1f99xnPcBOOa67nsdx5lEv/rTUwA2AHi3ZdXPktr/GQA/A+DJwZ9MhVWJMkVS+we/sw7AjQD+cPDvTtd1/9VUm4NI9P8ZAN4H4AcAfgrAPtd1P2uuxcuRaP/PoV+I4dsAzgNwwHXdjxlr8BCO47wMwDYAr0Hf+/tHAH4LwAtc1/2PTr/62XsANAGcA2BXmupnowLLObOwnDMLy7nxguWdWVjemYXlXTzGDU+GYRiGYRiGYRhmtLE6tMswDMMwDMMwDMMUHzY8GYZhGIZhGIZhGKWw4ckwDMMwDMMwDMMohQ1PhmEYhmEYhmEYRilseDIMwzAMwzAMwzBKYcOTYRiGYRiGYRiGUQobngzDMAzDMAzDMIxS2PBkGIZhGIZhGIZhlMKGJ8MwDMMwDMMwDKMUNjwZhmEYhmEYhmEYpbDhyTAMwzAMwzAMwyiFDU+GYRiGYRiGYRhGKWx4MgzDMAzDMAzDMEphw5NhGIZhGIZhGIZRChueDMMwDMMwDMMwjFLY8GQYhmEYhmEYhmGUwoYnwzAMwzAMwzAMoxQ2PMcAIcQNQojHhRCfNN0WaoQQNSHEV4UQnhDiXNPtYRimWAghfk8I8W9CiB2Kn3OOEOIbQghP5XMYhmF0IYR4iRDiISHE4zr/likubHiOAZ7nfRzAJ023QwWe57U9z/tF0+1gGKaYeJ73BwD+RsNzngBwjernMAzD6MLzvAcB3KL7b5niwoYnwzAMwzAMwzAMoxQ2PMeLCSHEnUKIbwshPiuEmBBCTAsh9gghviCE+DshxEeFEBVgWQra/yeE+JQQ4jEhxO2D9Ii/EkJ8Twjx2sHvLqVMCCHeIoS4XwjxoBDiXCHEx4QQB4UQfxJsjBBi2yD17G+FEH8mhFg9+P5HhBDHhRB/KIT4jBDiCSHEDiHEzwohvi6E+PIgvfb/F/WigzZ8Y/BO/32QkvvLQogjQojvCyF+ZfB7fyeEeEoI8Uplvc4wTGEYyLtTAxmzSgjxxwO584AQYrvoE0zxv0kIca8Q4qQQ4hej/mboGdcLIb4ohPiOEOI3At+Pet4NQogTQoj/I4R4mRDiTCHEgYG83aS9kxiGGUmEEKWBHvh1IcTXhBB3CSGmhBBnCSH2Db73jaDcCvztOwdy8aAQ4tWB7yf+LTM+VEw3gNHKzwP4GQDPAHgYwC8D+ByAz3me9ykAEP1zoL8B4I89z/sDIcT5AP49gJ8FcAaAfwVw0vO81wohXgfgvQD+yvO8B4UQtwD4PIC/8zzvDiHEXwH4CwCvALAA4IdCiH/ved43hBCXAvgAgJ/2PO+IEOKOwddv9Dzvt4UQ/w7ASwFcAWDDoO0fBPCfPc/7phDiIgC/A+B/Db+kEOL1AH4LwGYA8wA+DeCtnue9SwhxHoDXeJ73F4Nf/yCA1Z7nfSFv5zIMU2wGBqIH4Jc9z/u8EOKPAZQ9z/s5IcQkgG8CeNLzvD0AflH0z2uu8TzvSiHEVgAn0JcpK/4GwJ7gozzPu3wgjx4VQnzT87x/ivpbz/M+LoT4vwBMe573t4O27gbwvz3Pe0h1vzAMMza8BsC5nuf9HAAIIf4SwDoAdwH4uud5O4QQawE8IoT4nud5fzf4u58E8O2BnvWzAD4nhDjX87yjAP404W+ZMYIjnuPFNz3P+7HneT0A3wFwHoAfA3jewLv1VQC/iL7BFuRvB2cpjwA4jL7RCgAHAZw/9LsnPc/7xuD/vwPgB57nPeN5XgvAY4HffwOA/zn4TAD4MwCvH4oM3Ot5XtfzPNfzvLsAHANwnRDiLM/zHgbw2xHv+QYAd3ue1/Q8zwOwF8B1g5/9KYCXCSHOHnz9KwD2RXwOwzDjxUcAfGtgdJYAvB7A/wAAz/N8J9ZvDv3NXw9+vhfAQ5J/c8/g598H8ACAX5V43u7B700Mvr4MwJdyvzHDMMxpfgzgBUKIVw5k0lYAi+gHEHzZ9DT6Tv+gXGt6nvfZwc//Hn1d8UohxE9K/C0zRrDhOV6cCPx/C0AN/ejmjQC2DIr0fBJAY+jvTgb+vxP4ugOgKvm7/te1wf8/B8DLB2kZXwXw3wH8CMCawO8/M/TZvw6gCeDbQoi/AXDB8AsGPvvXA5+9HUAPADzP+xH6ytq1A89bx/O8ExGfwzDM+PAfAPw0+pkgQN/LXwdwJPA7R9CXL0GCckrqbzzP+3Hgy6MAnp30t4PI5hMA/p9BRsg/DZyIDMMwJHie9wCAG9DXm34A4M04Lb/i5FpQpgGn5ZrM3zJjBBuezEsAPOh53rHB18OGpCp+COB/eZ73i4N/PwfgRQNvWBR1z/PeCuB5AL6GQaQh4rPvCnz2v0c/VddnN/oR0K0A7s79JgzDjAJ7AWwB8CIhxDXoK0ct9A1Cn3UA/iXmM6T+RghxZuDLtQCekvzb3eg7C6/D8tRdhmGY3AghzgDwVc/zLkc/A+43AFw++HGcbHrW0Ef5cu2HEn/LjBFseDKHAFwkhKiLflGhV2h67ifRT8N4FgAIIRwA/zPhb/5CCNHwPK8D4H4A5ZjPvtpPSRNCXAbgzsDP/wrAOehHOD6Xsf0Mw4wWzUH2w/UAdqKffeEbehicufxVAJ+I+oBBBFLmb64Z/Nw/Q//nkn/7pwBeDuAiz/MezfGuDMMwYfwy+hFPeJ73z+gbiD8C8AX0jzFBCLEGwJVYLptWCSGuHPz859A3Lu/1PO9Jib9lxgguLjQGCCF+Hf1FPyGEeBOALvoHyBcAvAP9s5gPDf77FIDXCCFuHfz5awAsCCEeBvBKAD8B4INCiF8D8CeDz/88+ncxfRDATwgh7gRw79Az1wHYBOB3hRBPeJ73ZSHEOwHcJ4RoAmjjtML1vsDvnul53gcGbflrAF8UQrTQTwfeJoSooV/QCADuFkJc5Xnenwkhng3gb4UQp9BPMb7B7w/P8xaEEPcAODUwYhmGGVMGss6Xc48BcACsQt+59RYA/7cQ4uvo75d/BsAvxBaUO2/3PO/Lg69vRV9GLvsbIcQ5OJ1hURdCfBnAWQDeNCgsFPm3fls9z3tKCPEVsMOMYRg1PADgA0KILQCm0a/lsRvAfgAfEUJ8Df0jU2/zPO/vhBAvQV/3ewLAzwshtqMf/bx6UFgIAK5N+NufEELc43ne1drekjGG6NdeYZjxQghxO4C/8DzvW6bbwjAMwzAMwzCjDqfaMmOF6N8dWgXwQjY6GYZhGIZhGEYPHPFkxgohxA8APA1gh+d5SWdKGYZhGIZhGIYhgA1PhmEYhmEYhmEYRimcasswDMMwDMMwDMMohQ1PhmEYhmEYhmEYRilar1M5cuSkdF7vGWdM4pln5lU2RyncfrNw+82Spv3r1q0SipujHZZ1xYHbb5Zxaj/LuvEZaxvh9pul6O0HaOSdtRFPIYotn7n9ZuH2m6Xo7ddJ0fuK228Wbr9Zit5+nRS9r7j9ZuH2m4fiHaw1PBmGYRiGYRiGYZjRgA1PhmEYhmEYhmEYRilseDIMwzAMwzAMwzBKYcOTYRiGYRiGYRiGUUpiVVvHcX4CwLsAXOS67otDfl4C8G4AJwGcC+CPXdf9BnE7GYZhlMPyjmGYcYBlHcMwJpCJeP4cgL8GEFXK6FcBrHZd9zYA2wHsdhynTNQ+pgDUamXUp+pYs3Ya9ak6ajUefqawsLxjRhqW18wArbKuViuj1e3xvBthWLYwMiQanq7r/gX6Hq8orgTwwOB3jwFYAHAhSesKyjgJ2FqtjJYo4cZPfRsXvOM+3Pipb6MlSiP/zixcRxOWd/bC6y4/4yiv8zKq806nrPPn3fW7D/C8G1FYtowmw/KPgsRUWwnWY7nwOjH43grOOGNS+g6YcrmEmZlG/tYZ4PjCImZ3H8C3Hj+GF597JnZu3YSZGZoB04Vs/7e6Pdy8+wAe+N5RAMAD3zuKm+9+CLu2bcZMw9w7q5w/xxcWMfupbysd36j2t7o9NOoVNFsd1Mv2HtEu8vpNQErejYusA/S1X9W6G+X+H5YXNspr2/s/ad7Z3v4cSOt2SYhqBTd/6tsr5t2d114MtLv5W8oYx/YxrtXKENUKpiermJtfhLfYQduCdtmM70y4eUj+1WrlXH1HYXgeBrAq8PXqwfdW8Mwz89IfOjPTwPHjzXwtM0B9qo7ZvQ8tW3yze/uLr3WqpfTZlAtLtv/XrJ3Gtx4/tux733r8GBr1Co4+PZfp2bLEva+q+aNrfIfbvyQA7n5oSQB86JpNqHs9K4Vnmv5ft25V8i/Zg5S8GwdZ50PZ/qg1rXLdjWL/R8mLtavqxuR1FDb0f555N+6yTsbJVq6UQufd9GQVk9XiRMRUOxmiHMtUDmeV7dcxxnnaryNgkETRnFRhjsrZvfkdlZkMT8dxpgA0XNc9AuBeAL8AYI/jOGcCmADwaOYWEWLCwzE9WY1cfCoNzzDPxIeu2YR6DUrfeW5+ES8+98yliQkALz73TMzNLyp7JmDufU2Nr+3exFGmKPKu6MStaVPrznaCxzqCe1yUvPj4dZuNyGub4Xl3miyyTsbJVp+qR8472/sxqEc2Wx10W4vkOkaUo6hRBppdkDmcVTp5dIxx1vabDAj51GpllOtVNOqVwkRc8waWohxtia4Tx3FeBuA6AM92HOedjuNMAngDgD8c/MqfAzjpOM5/BXAHgG2u6xrvTVP55r4hFkTHxi6qFdx8d39hdXrekqIhqnK+hax53N5iBx+6ZhMuOX8NKiWBS85fgw9dswneYifrq0iR932zYmp84xQgGUb1nBI1RZV3RSNsPsataVPrzmbizs1FyYtGvWxEXtsCz7vT6JR1pvSEvAzrkdfvPqBEj4yag16pTKbnqK49YvMY59Wf8lLUM86q5J/wPC/XB6ThyJGT0g/L65mpT9VxY8DjCwCXnL9GuYfDVErkmrXTuOAd96HTO93FlZLAY7ddkeiZCGvzzq2bUOvJtdlEZDnpfZPmT9Y26xrf4fbnmc8m5mTK9DO5w5AFQqesM03a9selgUat6ZMn5pXN4SL0f5i8EtVKpEwAEPkz/29tOeukq/9VzTuWdXKyLiniY+MZPF16ZJw+k1WvC6JLB1AxhhQRZ1P2gC3Pz0pe2yBK3qkNDxkkb4pM1gXUbndRrwG7tm3WGlLPk/IalpblpyHIpHG2212g3dW6gPK8b540XX9877z24kzCNeu88r2JwxuHjDeR03QZU0QZTGnTQPOuuyITJa/WxuxxJ0/MR8oLE/JaNzzv7KPd7mKmUQ81mEwdnUlCV6p1lD5zaqFDkhqvSweIky1ZdB+qeZFHf6KgqCn7YfJvslrO7Si0tyxmTvKEiPOm6bbbXdTLJRx9eg6tU61UCyRrSmSeNAfTaQhZyPO+edN02wPBmnZ888yrdruLutfDnddejMduuwJ3XnuxtLeyiOPLFJ+o+Z41DTTruisKUbI/Sl75SmmQZQZTRnlRdHjeFQ8dR2ey6Fa6Uq2j9BnR65Kkr+bRASiO6WTVfajmhWl5WOSU/WH5R4H1Ec9xihCZisSZKhAE5I8sZ3nfohYIyhqpMDm+zHhQn6qvWIdpI0ynFjpLysG4RZeyFLjxDaaoPW7UI5tRewfPu+Khek/OqlvpipRF6TPzzS7qtXLuuZlVB6CKOGbVfSjnhUl5mGce2ZiCnherI57jFiEyFYkL87bt3Ko+DYEispzlfYtaICgr1If+uVAR41OrlXF8YTF0DWeJMI1DdImqwI1vMO3atpmjmjzvCo3qPTmrbjWsR+7atjnzGkvaN6PmIMXczKoDUEUcs+o+RY4UBvHnUVpZbapIqmqsNjxNGWLjZpiEGekzE9XMm6+sYWKqMq2p6mum5hVlmsmoCkImmSiDyS9Tn9Zg4jTQ5DTQ6clqrLzKc6yjyOQx1Mdx3tmO6j05j24V1CPr5VIh982shg+VTppV97GhUi6Voz2LrDalI6vGasNz3CJEJr07VHncaQSsTYZ2HgVEdnxNClEqj/6oCkImHhUG06hHmNJENvm8ZjRh/cjzbrSIm+MUir/pyJkN+2YWw4eq37LqPpQR5yyYdhhQ6sg2ZapZrS2aOptGWckuTY686cpbFKTJ5Td59pAq3z/N+FJXSDSR+1/U6myMHFTn5sa9ImjaSrTjfl4ziqh+FDHVPsd53hWZsDnOVU31s2wPWOjgo9dejDcN9X/afsuzJoPzYmamgeMa17HpGwGodGR/Hd3994/j1T/zbGxYP41TQmCyUsJ8U3/astURz3GLEJmKxFGSxkOjMrLc6va0vG9aTybVvDLliTPtOWbUkfXc3M6t41sRlKoSLaeBposQlwW4Eu2IU6uVUapVsWa6jh1bLsQvveDZXNVUMSv2gD0H0O70cBfBOfIirknTNwJQ6ciiWsHdDz6B177wOdix/1E47+yPbbMHI5FPqyOe4xghMhGJoySNh8ZUZJmSolbIzYppzzFDQ5p7Du+89uLYe+ZmJqpjGV2irkQ7rlFNIH2EeLJeQae1OJbzbhxYmg97DizNh9uv2ggA+OwjT41VVdMoVOizcXtA2P2ro47pGwGodOTpySpe/TPPxvZ9B5eP7V4z97lbHfEEOEKUFYozBTruEy362cOiFqLKGg037Tlm8kN9XhNA4TzZaaGuRDuu64f6rtJRn3fjSth82L7vIG66bIOVkUIgfk9Vkc2mQp81HeHLC3WW3/C+d+vlz8ed123G9GRVWxYhhZybm1/EhvXT1oyt9YYnFeNWQTXvhcFRVyQkYcowMWWIFbFCrqlrbBj9cIGb/HBhJRqi+hFIjhCbrGrJ6CdqPmxYP23l+MvsqZTrXpU+W5SU4DBUGOPBfc9912twzUvPwY17Diz7/MaqCSsK9sThLXZwqhW9v+tmbAzPcYsQ5REgcVckyGBCsTJliOUdXxMGrw0V9hj1pDWYkpT8cTCY2FCnIU0/tro9jhAzy4iaD81Wx8rx172nqopM2nB9SZBhORKHqjHw971TCx3cHKIXH5lrW3+1XLvdRanXxYdi6jHoZGwMz6JGiEwYJkVMtzBpiGUdX1MGbxHHl4mGC9zQwIY6Den7scIRYmYZUfOh1160cvx176l59Nk4fTJJr9BZsDJMjhxfWIx8puoxiPr8557ZKIQDf765iHovfn/XNb529lAMWQ9U5zncbaqQS56COXkOJZs8UJ11fIfft9nqoNuS26SsLBAkQdZiCaYPzDN0cIGb9AzLGJ+0V8YEDfVxLHBDdfVOs9XhK1CYZRRtPujeU7Pos/4Rqtm9D8Xqk1F7QBZ9NE8BpDA5MhtTDEf1GER9/qHDp4su2XpFjk/c/q6zQGehIp7jFiEyFYnzFjuxVySogjKyXC+XpN+3qAWCsiITHbbpsmGmDxe4yU+cFz1LZHNco3FZr94J68d6ua+GjGtfMuEUaT7oTlHNos/mPUKVVh/Nq8+l1Y9Uj0HY599x9UZ8+CuHln4nrd5ok56lM128UBHPvJHHokWITEXi2u0uZmbqsd5G3aW8TV8RouJ94+bVZFWdAEryJpu6moaJJu11E9OTVZw8Mc+RTYkrY3wvetyVMRzZpLl6J6wfGcYG8uzxJiK0aWV4Xn0y7d/n1efS6t2qx2DF5y900PM8HDnZQqUkUl+RY5uepdPeKFTEs0gRIgpMVxiL8jaOWilvmXMNKt7X5EH+OG8yFx8yCxe4yQ9XoqWB+5EZByj2+LRzW3e0K68+mfbv8+pzYXJk59Z4/SivfEkak2WfP7cAsdjJvL/apmfptDcKZXiaMsSyGCZxh6BlsTUlchRLeZswxGQMAxPjy8WHzMEFbtJBfS/kuBrqADs8mNEizd6p2wgwca983iNUaR3lefW5MDkyM1FVJkeyjEme/dU2PUtnIKRQIYw8BYLyEpfWkPYQdJpn2pgSqSokbyrlNQmVKQi2HPYOwsWHzMEFbuShKqwU9KKPQwpyGGlTueMKVAGj34/BfajZ6qBWK4/FmisKwfl81uo6brn8ApyzpoG5hQ68kMq4uo81mThWJHOEKunv06SyUujrw3JkcqYh/bdp0T0mWfQslfqvznTxQhmeMh0zToaJqTORqgwTWw1tU4ZY3vE1UQGayQdXog1H5TnDyWoZx483Tb2aVqgq0bLDw56zWcxK/Pm8blUdt77SwfZ9B2PHSvceb6p+B9A/QpX1GWn2Gl2GDJXOr3tM0upZOuSOLl2iUKm2QHxo20T6AlDcqqgm7ghNwsazh6bOYuYZX1MVoJl8cCXalag+ZzguUFaiHZfzmmkrSTP5oDpa4s/nmy7bgO37DiaOle49nlpntKk6ahDVMoJS59etx6fVs0ZJ7hTO8Iwj78BQGmJJh6ApyLNQimiYmDK0Tb1vnvE1dRUPk49xL8zC5wxp4Kt38pPF4cFkR4URsWH9tNRY6ZYXlIauqYCLDVAaYyYCDGn2dGq5Y9JZMVKGp00RIpWHoH3yLJQiGiamDG0g3/uaiCyzclRMxtlg4sJKNHAl2vRQOTyY7KgwIn54rCk9VjrnOaWcz9NvtkZKZaHUc2zfe7Pqv2FjbNpZMVKGp00RojSYiMSZNExMGGKm0hRMRZZNX8XDZGfUFX2qSrTjHI0DTvdjuVLiir45oHZ4MNlQYUSsm67lquSqEio5n7XfTBsfYe1JqxdS6zk2771Z9N+oMa7Uq0bTdq00PGu1Mlrd3lhEiExF4kwZJqYMMVPjayqybPKOUIaJgs8Z0kDdj4DdShcFqhweu7ZtHhsjXSUqjIjmyQXUemocKrZEC7P2m01nBrPqhTbqOarmRRb9N2qMPQijGXHWGZ7+BLx+94GxiBCNU8GcWq2MUi2fp6VohrYpg9dEBCMocFvdXuHSdhha+JwhDdyP+VHp8KiXS2PRh6pRpZMkFaTMYiTYFC3M2m82HcfJqgfL6Dk6HQSq50Va/TdOtpnMiLPO8By3CNG4GCb+gmzUK0be15ShbfI8kM4IxrDAvX73gbEpcMCshM8Z0sD9mB421IuJKZ0ki5FgU7Qwa7/ZdBwnjx5s000Xtp23jRzjBbORYusMz3ExxIDxMkz8BXno8JyR9zW1qX3i/u/j9qs2WpUKogKbNmLGPHzOMD1c0Tc/bKgXGxM6SZY9y6ZoIZCt31Q54204q+mjWy+x7bxt5Bi3F43uEdZphbov8g2i6/JU4PREu3tgmAxfcKw6Ekdx4W4a/AX54a8c0v6+PjrHN3gh+6Ejp7Bjy4XYsH4azVYHvfaicoeGqfENoutCbMYcwfP4wbmWlL4YdWm2zjVqE/5+MHw5+Frux0jC5FxQ7gJYUjQ/ft3mSL2i3dZz0T1jF3n2LJN6KhV55n2UjhElx+o1xH6ubyBFybOs6NZLss6LKLl157UXAwnjEafvJY6xoT3COsNT1QS0DVOGSVbBkBd/Qe5/+EkAGCtDbP/DT2L/w0+iUhJ47LYrcHRuQdlzTY9vkTdiJh1Lc233gRVzLWo+BNMXx1HJj5JFaQ0m7kc21JnTZNnj8+xZo6KnZpn3cTpGVgNKlfNHt16SdV5kNZBl9D0bZZt1qbZ+mtCubZuNFEXRVZ1s2DB59Qe/Bued92FqomJtekkegiH/zz7yFHbsfxRH51pajE4TRQCKWqzKxFU3jP2kPTfH6YsrUVXgptvpjWw/8tU7TBImKqKqSme3pVJuHHFyX9VZzazo1kt0n7ct6hEnK1vXbncx06jj6NNzyp81bhGivKkHWaOHptKZ8qQw5MGURzTP+OZZC8Pj22x10G2pdSowekgbXZqerOLoqdZYpy+mSQO989qLOUIcQpw8ypLKbaPnn8mPqSgb9XwypYumJU7HsC3zKW6MVWXCyc6LZc9f6OCj116MNw2NvapIqWmsi3jqZtwiRHkicabuHM1D3iIAWcfXVIGPPONLWVGarxgoJlQFboDRvxcyCi5wkx6uRMtkxbYoW1aC8/2XXvBs7NhyIdZM11GqVa2KfMbpGDZmPg2PMQDUpyewavUkjjUXceunH9J+Hc6KPWLPAbQ7PdyVMtPTpsrEaZDSKB3HuRzA6wAcBuC5rvv7Qz8/D8D7AXwLwCYAf+a67n7apqpBVYQoCVMRwDyROFPRwzzk8cDl9UDm9YjWp+qp50ae8S2q94ySUZZ1SVCfmxsHuMANDWkj6idPzHNkMyejIutsi7Jlxd9/t1x0Nt78KmdFAUZbIp9xOobtcmxpj9tzui7B7VdtxPs/72rVZeN06TSZnqoy61TXRUmMeDqO0wDwMQC/47ruDgAbHcd5xdCvvRXA113XfS+A2wH8EVkLFWNLhCitt81EJM5kCXETkWVT+fO1WhnHFxYzRZbzjG9RvWdUjLqs86E+N6fzPL5NpI1sxp3XBOyKvqggat61uj2+MkYzpmUd5VlGG6NsWfD335su24Dt+w5ae24vae3ZLMfC9rjt+w7ipss2aL0Oh0qXViEHddRFkUm1vQTAD1zX9d2H9wO4cuh3fgRg3eD/1wE4QNM8eUwYJqYMMVMpr6YMkzzvW0RDW1QrmN2r36ExKht4Dgoh6/KgosBNvVyyUsmgggvc5Cdu3jXqFTbU9WNM1lErtqPihPD33w3rp626IzQMk2svj9Miao/bsH5aq5OdUpemHgsdAReZT1oP4GTg6xOD7wX5AIC/dBznAwBeAuAPwz7ojDMmIYSQali5XMLMTEPqdwHg+MIiZgOpOju3bsLMTF3qbxsAdm3bjEa9gmarg3q5b483Eh7fbHVCUzyarQ4atUqq9qeh1e3h5t0HVoTpd23bjJmG3DsnEdX/O7duwuzeh5b182S1jMnA77a6vRV9mYcs7xvW/m6nh8lqGaiWE8cWiB9fVWMLAOVKKXLjmayqPYMgsxZkxjft+rWEQsi6NAyPVdxaiprv8+0unjVZjZwXBR3rJZLaH7W3RK3TRr0cKScxWL9pZVGe9psg3bzrZpp3tmBj/0tgTNaV61Vl+gvlugojONbUeg7Q33+bbRq9I6x9BZ2rS5RKAu1SKbOuH7XH/fBYM1SXpSbY/zK6tAmS9E+KOSRjeB4GsCrw9erB94J8EsBdruvudRxnHYDvOo5zvuu6y1r/zDPz0g2bmWng+PGm1O/Wp+pLESKgL8hm9/bzpdOc85gfiGHZVtZq4Wecuq1FdMsl6fanZc3acI9Yo14hqwQc1f+1WnlF/r7/e0v580P9kdf7mOV908yfKOLG9/jgfVTkwten6pFnVnSdWwpbC2nGN03/r1u3KvmX9GC9rJMlaqzWrqpHrqWoc3PB+R42L1S0Xyd++6POa0btLVgMN5hOLXRQ662sRKuqj2zq/yzzrtvpZZp3tsCyLp2si45w0+kvqpiZaaDZbCnRc3xk9I6kv49qX6NRt0ZWZGFy1UQuXT+sb3du3YRGtYxOa5Gsb6L0wqCsiNOlTZKkf1LIOxk3zQMAnuc4ju9SuBTAvY7jnOk4zurB954L4KnB//8YQE/ys0kwlRIpk+Kh4l4mk2fx4sL6qkL0pt43aXxV5cJ7ix3s3Bqf8mrivq+i3hmVAutlXRhUlWhHJWUtC1yJNj2UFZDHdd4ZxJisK3otAdX7YF69cpT36SinhayuH9a3tV4PzZMLZPJGVi+M2yNM3ueq48hVohBxXbcJ4E0AdjqO8y4AB13X/RKA3wXw24Nf+x0A/8lxnLcD+CiAt7uu+zRZKxOw1RBTaZgkTQwTE1eVA8Dk2UMThna73cXMRFW7wZuEyeJSOiiCrBuGC9ykg+q8JhvqPO+KjElZZ0MtARXnBCn3wTx6JUX7TBo+cfipskHS6vqqZQ3FFY0m9DsfHfua8DyP7MOSOHLkpPTD0oRzZVIAVZcHDmv//GIXNwZKJgPAJeevSZ0CHEbc+1CkvGZJ36pP1Y28b9jPJ6tl5WkLa9ZO44J33IdO7/S0rpQEHrvtitwpQ3H9r7Kf40jz3JTpGHIHhAoEtayLmv9RY/Lx6zbjhj0HQsfKTyGlkoU2pXrGESUXnzVZRblSCl3L7rteg6NzbWVpdRSo7H8d864o8ycKlnXpZZ1ufSxIHv1ItV4nQ9I+HPdzGb1I1ZGp4OdnHfuZmQZ+PL9otTyO0wu7nV5i/5vS72ShkHdGU8SoMJUSmYRKz5iJSFwSKj2ZaT2AxxcWlY+vqUh73nllogI0kx0VlWhHPbqUJg201e1FrmWuRMvzjqEn71zIE5HLqx+Z3geT9v+87VOpP1Lo4rbL47x64ahnlgFyxYUKQdyl0XGXtaq8LNbUxcZxE1f2AHar28OatdOpPFKmLg8OG9+lAiCSh/GzeOBUXd6bRJ55teTNHLqsXeZyatsvhx4FogrcRMmvqLkQNJjGbayi5vjaSGMpurDSUp9F7C2jAs87pijk2cOA/PqR6X0waf+Pa59Mpd+8/RMHhS5uuzyO1QslbiWgsBtMZhTIMBIRzyTGLUKUx+PiC/Xrdx/QekdoHvKMr6k7QvOQZ17l9WZy1EIdXOAmPRQFbpqtDp/X5HnHFIS8exhFplLSHFd5RlJm/8+zBlVmco1CNC9pbPPuJXntBtNnRGUYmYhnHEWNEJmIxJmKDuchz/jmfd883res45tnXqn0ZjL5iJqLH79uc+T8Nu19N0n6yGb4NQX1cgnzsN+TnpcoecPzLj3Bvmy2OqjVymPz7qbJu4epzlTy5dLdf/84Xv0zz8aG9dM4JQQmKyXMN/Mbb6rXnsr+MZUFSEVwzzlrdR23XH4BzlnTwNxCB157cWkM8uwlece3CDr8WBieJg2xrBPQlMFr0jChNLR3bpUbX1PvmzddKOu8KrrgH2WSzs1FyS82mOQMpqg00HEgTt7wvEtHXtnN5CPvHqbScKvVyijVqjizVsavveQc3BJcO1s3oU7koFC59lT2j6njSVT4e866VXXc+koH2/cdVCID8oxvEYILhUq1zZq+kCf0bSo1wFRKpKmCOdQprzMTVal3NvW+o1IAytay60WEC9yshAvcpCdN+rGoVnjeRZD26p1RuCexCFDsYSrkgC+rbthzAP985BRuGZ4je+2ZIzLpoirkZNGPNPh7zk2XbcD2fQetlAFFuCe3MIZn3rzlohlipgxeU4YJtaEti6lzuKbGl1LwF+EsQZEY93NzbDDlh89r0pDF4VGkc2q2E6c32Gq8BGXVhvXT1s4R0/u2L1NOnpgHAKxaPblsjG12Zvt7js3ja7rqsgzmzXNJTOUtU6cGyKaTmkqJ9NMsdm3bjEa9kivNIk1Kkqn0AOq0EtvHF6BL04ldk0xqxvncXNrzmtOTVa5EO5A15UoJ9al6bCVaPq8ZDVVFX5siCkVGRm+wcX0HdZhDh+esnSM2nAGMGuNGo4RmF9amsfv2wA+PNa0d3yR5bkPF28JEPMctQmTSa9Fud1Evl3J7udNEMU2mB1B59U2OrwkvIXv+6Rn1CFPa9MWoSrRLBpOFkQ8dpI1sxqUfA6M/76KgjhAz+SlqKnNQh/nwVw7h9qs2WjlHbNi3o8bYK5XJxl6FTuTvOeuma9i51V4ZECXPTUe7fexeyQFGPkI0tNGbisRRkiaKqeLQeX2qbvw+UR3ja6rYRdyanJS4r4oZL7jATXpUF1YaJwNTVUXfZquDbmtxbPpSNUUojhJGUIf57CNPYcO6Kdx53WZMT+TLHBsmry5nQ8Q+aoynJiokY69SJ2q3u2i3u6jVyrHyNGycTGNDtBsoUMST0stoKoc8rafJRCSOkjRRTOrI8vGFRe3va2p8R6VQETM68HnN/HBhJRqo+xFYLrvr5dLY9KUOilAcJYxhHeYNP3suvPYi6V2fFLqcDft2nLynGPs8OpHsuMTJ06hxMo0N0W6gQIYnlWFiMtTMFVTjBRylITa7V//7FrUQlYlq0czowgVuaGBDPT3s8Cg+NhhGWZGVVVn1UApdzoZ9O2qMRa9LMvZZdSIq+yBqnFrdXqrPSWprWr3NFqdOYVJtAZq0KpOhZlN3GOVNXcma2mGqaIWp9zU1vnlSZ0zdJ8qMBrVaGa1uD2vWTicWZuECN9GEyZw4OTbuhZXC4AJVo0EeWWBD4RQZsuqhVGnIpud21BjPN7uoJ6SwypBVJ6KyD6IzKSqYP5niRSLIqrfZco9qoQxPCigWbtEMsXEzTEy9r6nxzSNMbMn5Z4rH0lrZfUBK0R/385pRRMkcMUg7Y0N9JWkq0bLDo3hkkQWmah1kIaseasP5TFmS9OSoMabYB7LqRFSGfdQ4NVs0Bl5Wvc0WeVeYVFsq8oaaTd0n6j87S0pkntSVIlaY8xY7mSuOUd8nmnV8W92elpRXW3L+GXuhqkQ77umLafuxLCB1zrDb6Y1VCjJX9GXCoNRVVNcByaqH2pCGLNM3pqunZtWJqFJRo8apXqYxufLobTbIO3utB0XkDTWbihCZisSZrDCXJ7I8M1Mv1PuaiiwXyYPK6Ie6Ei1HNeX7cbJeQae1aNw7bQqu6MukgWrvjlurVGTVQ01HrGT1FBsyqbLsNVSpqFHjBNCkgxddbytsxNNUQRRTESJTkThTh5EpPGZFel9bC0CZqgDN6IcLs9BA1Y9+Kqhp77QJuKIvkxaqvTu4Vn/pBc/Gji0XYs10HaUanY6XRw81OZdl9ZQiZVIF5bWoVtAog2TvihonikiwDZHvPBTS8DSZ7lrUyqVZMWWY2GqIqcLU+MZtgKbTZRh9cCVaGqj7cVxghweTF6p15K/VLRedjTe/ysGO/Y/Ceed9uGHPARxfWCTb/4ooI2X1FFuqpyYRJq+b3f5cUjEuiz0PzXYXn3rjS3Hv7M9j3ap6Jr3WhsrEeSik4Wny3KGsIVaulEgNMVML2ZRhYqMhBqgztE0K6qgNsIjne5l4qM5rLhVm8XrYtW1zITe/vKSJbMr0Y1GViDxE3bnMDg8mLVTryN+Lb7psA7bvO7hsLc/uLdb+Nyyj8iKrp6h0plHqXzp1nFqtjFPtDt72mUfgvPM+7Nj/KN78Kgdnra5n0muLLOuKs4ICmDx3GJdjr7KqmskyyFG58irz+E3msEe9r8nxNVEm3uQ6Y+ihPq8JDM5TN+o4+vSciVcyRtqrO7iib3Ql2lmuRMsQQVkRdc10vdD7X5iM2rl1E2q1cua1MqynzL58A95w6XmYnqgs/bzd7ipZo76TanbvQ2T6l04dJ0zWbd93EO953QusiwT7hMlsCgoZ8TQdxjcRITIViYtDZVTSxrOHOsd317bNxlNeTa8zJjt8XpMGruhLA1eiZXxsrxng78XNVnSWQhEIk1F5I7ZBPcV912twzUvPwY17DoTqJdRrVFQrmN1Lq3/p1HGiZN05axpWHquIktkUFNLwlAnjj5ohBkQv5FE0TGw8e6hzfOvlkvGUVz57Vkz4vCYNXOAmPWyoM1FEpVXbanz22osr1vLOrWb3vzR6rSp9xZdjpxY6uJnYEIxDxfvo1HEi9eUFO7M1omR2q9vL/dmFTLVNCuObukjYVHpo3pTXrOF01em/JlJ84zA1vnnTQfJcS8MpbXYTlb6Y5roJTl9M1493XntxpCwY56s7sqZy79y6aUX63DhfvTOqRKVV67xiIw1hMnGyWsbx482l39F5BCatXqtaX9F9FCfL+ySNj4wtQTW+/v3yK2Rd284IerTMrmD+ZL7PLmTEE4gP449bhCiPJyhPON1UUYy8nq+s0XBT45snsmyyAjSjFk5fpIMjxOmgTOWemahyZHMMKNIVGz7DazlIlr01TyZeWr02TEZRRmx1H8XxDTdZ/Ut2fHRlErbb3ULJuqjxbbbyz5/CGp5xmDJMTBlieQRA3nC6CSXLlCGWd3xNGLxcmbb4cPoiHWF92er2uBJtClRcGTPqhjpDY6jYdK902r01ryGTVq8Nk1EzE1Wy9aXbEZ/WcMur+6jSnYoi66LGt17ObzaOpOFpQ4So2+mlnlgmDJO4cLqtmDTEshrapgzeInqZmdPwOUM6ovqyUa9whDgEFVfvjKOhzvRJG7EaxrZ7pdPurXl1jyx6bVzENi+m1rSszM2r+4yC7pTHURM1vhRYbXiOU4TIlGGiMpyehInIsilhYsrg5cq0xYEr0dKQ2mCKqF45zv1I7fAARt9QZ+LJm2poW/ZO2r01r+5h4qhPko6Wdk3rjFjn1X2KrjtROGpUyWyrDc9xihCZMkxUhtPjMHX20JQwMTWvdGxWNqU/FRWuREtDJoOpNt4RYnZ4MDrJup5si0Cl3Vvz6h66I4zUEWbdEeu8uo9tVf3T6lm2OWqCmG9BBMFzN0D6CmhZK+IVtXJpVqKqelGStmKkygp3qivxAuHva2peqa5WGlVpr0Hy6eMDV6JND1Ul2vmAQjdu/Ri1ftfG7EcnT8xHytBxqEQ7PO8YPaioapqHtPKXQvfQub6odTTdOl/e/dGm/XVYTs++fAPecOl5WLN6MrJdpmwKGaw1PKPO3ajutHEzTIBwYdYgshyyKDYmDG3lhpjXUz6volC5WUVtJru2bSZ/1iiTlL4YNW/GQdEPg9JgqpdLOD4G/chX7+QnbN7t3LoJtVp5LN7fJGl1Mx3X6qWRv7rWDZWxTW24UH6e7Dvm3R9t2V+DcnrLRWfjtS98Dm7ccyB2Xpu0KZKwNtW2GXHuRkuESGE6Q1S6QWlgmIxaSmSWQhSqUZk+F/W+PVFSniZjYnyLWJzKRjh9MRwdBW7GAb56Jx1p5t3sXjvS10adtLqZjamGqtcNZTor9bEkqs+zrchUEkFZ0ur2MrUzKKdvumwDtu87mDivbUsVDmKt4Vkvl4x12igaJqYWa1bFhgKbDLHpyarSeWVqfE0Wpxol+LzmSrjATXr46p38ZJl3Rap0WWTSrN+sYxW1hvyrl2yuZUBpbFMbLlSfZ6NDIYphWXL97gOZ9LKgnrVh/bTUvLa5krjUSDmOczmA1wE4DMBzXff3h34uAPznwZfnAphxXfe38jZO9bkblfn/UcQJw6OnWtpTIlWfqYwK9wcVG1X9rzrNJgxT6Q15xzfrWohKf6qXS5jP/Vb6MSXrxjl9EaA7r6lDrthKXGphllRuW9LMVEI172xIX2OWk/VMaOhRmUYJzS5w8+749EbTUKazUu9JVJ+X5x116/xUendQzzp0eE56XtsqwxMjno7jNAB8DMDvuK67A8BGx3FeMfRr1wI47rruTtd1bwXwQYrGjVOEyPaqqiqutlE5vlGXwqv2iplKb8gzviqu8ikiJmUdMPrRuCi4om96wtK3uBJtOqjm3c6tdqSvpcVxnMsdx/mI4zg7HMf5ryE/F47jzA7+fcBxnP9B3QaVWUlZ9uKoNeSVytr1iSx9Q61fUstSis/L+o4mdH6qDImgnrVh/RQ+lOM+XBuQWTWXAPiB67q+yXw/gCsBfCnwO68H8DeO48wC+AkAd5G2UgGjXFU1jDye2jyH9E1FcvIWp8rqGTP1vnnGN+9aUFmcSjMjKetsggvc5Icr0dJANe8mq2UcP9409RqZCDjZLnRdt+U4zj7HcV7hum5Q1vlOtt2Dv9lI2QbVxX+yyIgoQ2FqQm+xy6x9Y0q/1EnWdzSh81NmSATldL1WJt/7dEaDZc54rgdwMvD1icH3gjwPwGrXdXcC+CT6ipl9CfABTEUATeVd54nEmbpjNA95ilOZumPUf3Z9qo5ypUQWWU6Czy0tMZKyzha4wE06dBRWGrU+iyKsL6nmXUGJcrIFeT2AMwcRz3cDmKNsgI6zemllRFxmgM5Mtax9I7POi37vdlZZZkLPUZUBFzevs4yv7miwzAo/DGBV4OvVg+8FOQHgmwDguu5jjuOsBvBcAI8Hf+mMMyYhhJBqWLlcwsyMurCJb5gMeyKarY7Uc48vLGJ2qKT6zEx96ecy7e92episloFqOVWEqNXtoVGvoNnqoF6Wrw/VALBr2+YVfxv27GD7y5VS5IKdrNoptEolgZ1bN2F270PLxmiyWsZkwri0uj3cvPtA6BUhM4167N/mJWlexZFmfIPkXQthqF6/ihhJWaeasPaHyaiodfXxbeERpvl2F8+arGaa03nbbwNRsiBKHjfqZSmZl3XfUYWO/g/ryyi5l3be2Tp/EkjjZPsDx3EuQN/J9tOu6y7T8LPKOgq9IqsuFEfYGpqolDLrE1mg6JuwdV4qCbRLpcw6hmmG11oaWaZCz5FhuV7WRb3cXyuqZG8WHTKNzksh72QMzwcAPM9xnPrAO3YpgI84jnMmgI7ruifQT0U7HwAGilgZwL8Nf9Azz8iXG5mZaUilr2QND9dq4UUVuq3F/p1uMdSn6pjd+9CyQZrd2w/Z+x5Q2fanYSn9YriQS0rP9fxgu4kbjWD761P1yHQB1R7frOM7M9NArbeyyIjMmKxZG141rFGv4OjTpE7fZcjMKxlkxjdInrUQRZr5v27dquRf0oPVss5Wgu2Pk1GrVk+GryuJ+Zd2Tmdtvwmi0o+jZAEWu5GFlbLKPJNQ9X/UXhElV+/atplk3hVU1pE52bLKujx6BZUuFPXZYWuoVisvGRBp1lYWHUaVzjW5aoJExzBFHlmRV8/Jm4o6f1L9XpNVh0yj81LIu0TD03XdpuM4bwKw03GcIwAOuq77Jcdx3gfgGID3ArgdwPscx3k7gJ8C8Buu6y5ItSwHps4eUl+sK8u4nUvNewYk69klU5ULTc0rmbVgogK0bmyWdTbizwk/LZwr0aaHz2vSkKWi72S9gk5rcSznHQidbFnJo1fk0YWS9rKoNdRudzHTqKdyPtt2VjNv7Ysik0fnV30emYqsOqRunVd4nqfkg8M4cuSk9MNkrOr6VB03BoQPAFxy/hrl3huZ56rwbKxZO40L3nEfOr3T3VgpCTx22xXkkbjh9icJaxWGSZ7xzesZS/Km2va+KsniXU7pFZPL0yoQ1LLONqLmxNpV9UgZdfLEvLIoRR509X9UZDNszX/8us24Yc+BSFkQ/Kxmq4Nua9EqBSgNafs/TT/eee3FAKBUrhZV1jmO80oAvwLgCIBF13V/33eyua77XsdxzgDwPgA/QN/Jts913c8Of04eWZd1H82qC+WNlKadq3n2dBU6xuSqCVy/O1qu2I6pvZJKN0vT/qyR8iztTLMuKOSdfTeupsBUhEjWG1WfqpMKDZN3iMV50lV5g2yNAKp6X1sr0pmKtDPmidr8uBJtOtJGNuPu1wSWy+OZmUbmlPiiQR0hHmdc1/0CgC8Mfe+tgf9/BsCNKtugOytJ916WR4dRkb1QL5esWgtFyaTSrYvqjpTr3psLbXiaMsRkDJPjC4vLDqLrMkxMLGRVwtxWQ1vV+9qa8mrKAcCYJUv6YhqDaRShMtTHOf3Yh6/eYXyG50LJ62VSsHXvZSZ1mCii5Ipu3SK4v5y1uo5bLr8A56xpYG6hA69tVwaH9lTUjDpmHlmnc2+mKQNmCFWlimWIK2ccLAxBWSY8qYy0iQtyAXVlqmXG10RpcJVluf151e30Qstkmxhf6kupGfsIW0dxJf3jrh0Y12s74tZnlqs7Rv26mDj46h3GJ2wuNLtAo4zUckb3XmZSR40i7Dqg+vQEVq2exLHmIm799ENadAt/f1m3qo5bX+ngbZ95pD++ew5o0WvSoHsc8+iYRZB1hY54jmOEyEQkLglV3qA8Ka8qMeXFzDu+WdeCrSnADA1c4CY9aaJxXFgpmlqtjFa3hzVrpzlCzIQSt65ap1qp5IyKvSxuX7U92r4k+/ccWOqP26/aiPd/3lWuO/p68r2zP4/t+w5afZRH9zjaGCmnpNARTyD5ItVxihDljcQFox6tbk+6n1R6g5Iiy6ovoA7DlBczz/jmWQvjfvn8KJEmshl3afo4z4m00bjpyWqszCiCh1oFfj9ev/sAR4iZSCgzjKjllsy+avO8DJP92/cdxE2XbSDL4orC15M3rA+/ykPls7OQZGtQZt7ZGCmnpNARzyRMRoiGLxvWMWnyeElMXU2Th7gNqdvpJf591vE19b55xjfvWhiHKNaoo6rAzWS1PLLzgs8Z0sARYiYr1NEfyr3MhsJ7ebL6onSoDeunlQdLfOPqh8eaucfXZJEiFcUmR32/KHzEMw6TEaKZiar2aEAeL0ne6KEJr16eyHLeaHie983qHcszvirPpTJ2ETW/0kY2x/m8JsDnDKngCDGTB5ujP6b31bx6TJQO9cNjTeV97Eef103XsHNr9vE1ldnooyrzTqec010rZaQjniYjRABSnz/wMRGJM1m5VMnZw2r8wjHlqTQVWR71MwNMH+pKtOMS6Q67+orPGaaDr95hspC0/9s8F0zvq3n1mDAdaufWTWhUy+houBu43e4uVdSVqdVSrpRQn6ov+7npqHPRq/6ruh4wjkJEPMcpQmQqEmfqXKqps4emxtdUZNlmrzGTDa5Emx//6iuuRJsP6oq+wPhGiMcJ2f1f5/m6NJjeV/PqMWE6VK3XQ/Pkgtb1lqdWi+moc9Gr/puolWK94WnKMDE1mUalYI7sZmDKECtqAaisqCiqYGqzZzh9MQtRhnrU1VdsqIdD7fDYtW3zWPYjk3//N51mabrIGoUeY7vsT5ojFH2QR58x7XwA8rXfhE5qveE5bhEiWwyTXds2ZxagaTYDU+9rytA26R2j2mBMb/bjBleizQ8b6jSo6Md6uTR2/cj0ybv/m3LUB8krC4pu9KgmaY7k7QOKLEOT+6qqc74qdVLrz3iayp+mPlcge47R5JmB4HmumZkGjmd81zQ596bel3J80+TIU98jZqKam+kzFeOEqkq0RTh7kgU+Z0gHV/RlVJN3/x/383XjsLaS5kjePqDQZ/Luq3n0OBXnfFU7L6yPeI5bhMhUJI6SNF5Mkx47qvFN43Wl9I6ZijyaPlMxinAl2vxkPWcYV1GRI5tc0ZdRR97933SaZV4oIrajvrZk5kiePjCtz+TV41Sc81WtM1gf8Ry3CJGpSBwlabyYqiLLYdXPVJHW60oVdTIVeTRdyW8U4Uq06aC8F9K/+mpUIwZxUEWIx72iL5ONvPt/Xv3QlI7kU/SILTCQIbUqpicqaLa6EPBIK+Kqjuqa1mfy6nEU7detM1gf8RzHCJGJSBwlab2YRT97WNRCRSaqRTMraXV7XIk2BdTnDAGMdMQgCupKtKMeeQG4qFoearUyWt3eir7LM2/y6oemz4gWvSLqkgzZcwC3fvohPD3XwmS9AlGrYrJBFzH050i30yOXLab1mbx6nOn2Z8H6iCfAEaKs5PWmmbhPNA95x1fJfaIKyTOvTN0nyqykUa9ErtOTJ+Y5sqn4nGGjYert9EEZIR7XyGaUzByD6ZObpb7bfYA8sphHDpqOOJrSHagQtSpu3nMA61bVcesrHWzfd/D0e2zdhHqtbL1sMK3P5LUPTLc/C9ZHPCkZtwhRXm+aiftE85BnfE1d25OHPPPKVLVoZiXNFleiDYPPGdLAFX3Tk6aSdKvbM91c6zEdWYzC15G2XHQ2PnfLL+Cf3/1L+OKtL8N8S4/hV2T5XquVMT3Rd5redNkGbN93cPn47jU/vrKYlGklr4cPxdQZkKFoMrkYs4KIcYsQ5fGmBdP/gGJULs0zvnmjpXm8rmHRCBnyzCvTnl7mNPVyaawr0UbB5wzTwRV9aUhfSbqC+ZOGGlsQbN1vvMUOPnrtxZhrdfCWew4O6XZ6onXtdhc1AHPo99McgBr0nDHNg6hW8MTRJl587pnYsH7ayvG1iWCqeVDPa3aBux98Aju2XIgN66dxqtVBqdfFfNPu8c/DWEU8ixohyhppzeNNi0v/U42JyLKpymZR0QhZss6rop8tGTWK6vWmIGq98zlDeajPawLF86KnhaqSdFNTdKzI2LrftNtdlITAW+45aCwaW9R7sacnq/jgFx/D7VdtxA+PNa0cXxl0nNv2x/j63QeWjXGlXsXNdz+ED3zxu3j1B7+Gn3r7Z3HjngPopdABi0gh386EIWabYaI65TUu/U8lplJeTW2MptK3inggfZQZdSU/irj1zoWVwhne/4B4xyj340ooDfV6uZBqlFZs3m/8dNEgOq/TsDUNOYm5+UX86EQL7/+8i2pZxF5LZSu6jP6oMfYgyOZekQqfFU5imjLEbDNMVAslP/0vSpComuRUkeW01c9MbYzRSo7a8U0y0oskxJhikObcnKhWxv6cYRhh+9/xhUU+rxlD2nmX1lBnkvH3m13bNpPuNxT7lOlorOl7JLPiy5UjJ1t42R1fxd5vPoE7rwsfX8BOnUKXfh3nzKKYe0WLmtvtUgnBVGVaU9XHTJ6NiDovpfLuK1Pvm3SmSdX9r1HnUnWkb0WdHTR9txkzeqQ9Nzc9WcXRU62xPWcIyFeind3L5zWjyDLv0laSHoeqyBS0213MNOo4+vTcsu9n3W+o9inTlWVN3yOZlVC50l7E0bmFFb9rq06hS9+MHOMFmrmXxy5SpdvGUbiIpynvUNoIERUmvXFR3nCVXiIb31elNykqGuGnb5nwEhY19YcxD9W5OX+9j0NELgyu6JueNJHNuHlX5EqjRSTrfkO1T5keb5vTkJOQlSs6dIosupIufTNyjNuLJHMvq11kKlJaOMOzKIbJ8YVFpYaJ6pTXOFQa/zYKYZVCM2rTA8wJhaKm/jBmUVHgZtShMtTH+bwmwIZ6kcm631DuUybHO4/ha2P6ahiqdYqsupIufTMu1Zxi7mW1i0wFGQpneNpoiIUN3izRHUZxQsmUYaLS+Lfx7KFqoWkishyH6TMvjP0E12Gr2yM/NzcOij6Vob5z63if1wTYUC8yWfcbG/YpKn0ky9ot0rk+1WOVVVeijHYnzYV2u4t6uaREPmc1oE0FGQpneNpoiI2bYaLaS2Qi5TUOUxtc3nll4loaZvQZXofX7z4QG13iAjdqC9zMTFRHss+GoY6oj8O8KwJZ9xvT+5Rpw49S/1Pt0Fc9Vnl0JQo5YHouZDWgTem2hTy0FVUUxVThIVOHw/MejM56qNhUsYq845v1fU0VH8gzr/Ic5h/nYiTMcmQL3Nx8Nxe4iUJ1gZvJmdGrbpNm3t157cWRsjJoqI/bvCsKWWWDaZliSt/0oSqMo6PwT9xYURS3MV2gyfRcAKLtomGW9fdCBx+99mK8aWjsVeu2hTQ8ozBliIUZJn76k0pMGSaA/CSnJM/4FtEQy2Pw5hWEJsaXsYu0BpMfXYqar+Mwp9hQz4+OSrSMXWQdI5Nja/LGAYDO2ArKpy0XnY2bLtuANdN1NFsd1EBrfA6P1ahUJjY9F2SJ6u+7tm3GZL3CVW2zkCdsnCdUHhbmTpP+ZCIlsoiVS/OML9X9oFnSMbKOb57zB1wgiJGFz83RwAVu0uHPu3KllLsCsunKpMz4YfqMKVX6qi+ftlx0Nt78Kgc79j8K55334YY9B5Smi9ZqZZT+/+2df4ylV3nfv3fuj3fvndn12ONdwK0h0I2PEsfeLeM2sogUORgLsLRqTWkyAhaU1jjE6hhclwXhoCW1wQFCwkiEHwsqWltdonRRa4m4qopQlVKKkqF4KVIO2kgBBDS72Bnvru/Mnbn3Tv+YueO7d9/zvu/5+Zz3vs9HsuSZvTNz3vec85zn92k1sTCX4OSxW/Hm215R2s7EvtaC6xRolWwdDLeDnjNTZXhSGmKTSkJRXBu8ZTBMKAxtque1zf03VT6pD0WmHHDdnD5sqNvjowNyFdYeY4dLRZ66xtSVsTXSFR686zBOnD0XJBgx2v/vfnIV4tFncPLp7+ORewSOHbmplJ2JfawFH3WjsQQkogxvtVp19AZDLNw4F6z2kCpUTpUSSZUTT5XySvW8VLn/oVNPJlMMmfjwVTfX7fUx6G1VQtHPkl95BlNV00C5XpOJAde1jGn6yMz2EMNaAwsH2kHWpwv5MdIVFuaSYDpw2v4/cfYcTh67FRcv96LVIVTleD5KI3zojtS1sCOii3iOhMP9p1crESGi8kCE9tbtpVUlLZKUVyrvJNX8hkw98XmPLeMG3TRQnU60SX1mKpV/n51oqx7Z5A7ITGh8lBeNr8ftrT66A1yz1jv790V9z+ZIV+j21KnsrlHt/8OH5qLtoJ8XgXQtm3zojtRR+hHRGZ7TekXIJCOlptsbkBi8VIZJu1WfekMMoJ9fIFzqic97bBk9XKWBVr1ujg0mfXQMdV53jAt0Umd9O4FVa/3ilc3o79nc3BxguLkVTAdWOem6vX60ez20bWISDCt0l2gEsrXQGxNC3A3gPgAXAGxLKT+i+NzbADwFYL+U8orJgKhSXkN2ERxP+XjZgQSfeOvt+Hd/di54N65QaV7jKQPnL1whC/WHel7K+XXRmlyXsnR0K0JIWeca12mgwPR3olWVdXAnWj24A3L5KLOsA/RTZ32nGapk7M03dK4yVEJesaFDEfnlSr9QlQINN+Mt2Qit5+iWSxXdD1myNZT+mGt4CiE6AD4H4FYpZU8IcVYI8Xop5dcnPvdLAH7ZdkCUOcgUhhgADLeBj913G1650PGurFAbJp/5xnn8wVtux4mz02uIUc1viPu40oilbsCW0LLOBq6bs2dvv5xeZUO9ICp5qmuoV3ndxUAsss7mfNatgfPd90AlY89feMlWj90hm2eUuNIvyuikC63n6L4jF/fch9Ifi6Ta3gngh1LK0Ur8JoB7xz+wK8TeDyDVY6YDVcpryBz8SaXm6Wd/irs/9T8AwGsalo8uWUUYTxl4+tmf4pP/TeJj991GUnsY4nmp5jemNPUQ99h6IKisM4XTQPXhek17fHVAHvSHU7vuIoZc1tmez7qps77TDNNk7Cfeejs+843ze5/RNVQo9FMVrvWLsp07FPWROu/INpU8pP5Y5DceAnB57OtLu98b53EAvy+l3BRCKH/Rdde1UavVcv9gB8Cp43egk9R3cr7rO/Zxp1NgtJqsbWxheczCX1k6ivn5xPr31uszmJ9PH/CoiHvSc9Lt9ZU/44LeYIiHTq9e4xE5dXwR852rn1k1/t5giE7SuGpeirCydBTLZ3Y8jRcv9zCb1DHoD9Fu1oFm3fnc1uszqCfNws/rEhfzm7V+lD/TmFEKnnaz2IFlOr87e3Zx72fbzTqGw20ve9YjwWUdkD/Xk3Oi2sdfOJ4eXer2+uh0kmvmyJVcNVmroUmT8wsZB/WgP7xKZo1+ZiSvAHiVXzr4ev9F192p44tKmbe+OcD17WbmuivD+smipON3JutMsY3QmESgXGQkJLNJagTqmgjVRh/D7W1cvNxDY6amHWGlymBSMQ0lNTYR9tijtLYR2ZDzW8TwvABg/9jXB3a/BwAQQtwM4HoAvzkmnB4WQvy5lPKvxn/RCy+sFx7Y/HwHz/18J0Wh+E/pkcwmWD7z3asE3/KZHcFn+6Ln5ztYW+um/lurlZ6uNehtYc3jIl64cU7hlW7svWvV+PeE4MSYi3oMW636NRtW9X5cMD/fQSdpFH7eNEyFlIv5zVo/KpLZRCl48taz7fyOWN9VZRKN8R88uD//Q2Egk3Vp70o1JzfuT2973ym47kZz5EqumqxVX6hSkNPkfFa9Zu/FXnCZZYrr96+97pIGLl9az117qnUX0/oxQWf80yjrTJ1sLhylKudQ25MjYG1j65q/lxaoGPSHaDd2HCymzj6dQEFRbJwkVAGTcWydPK4CTTpOx3EH3sxMzeu7stkPRefXhaOttr29nfmB3XSLcxirBQDwJwD+D4C+lPLSxOe3oShCv3jxcvYfGyPEYbRw4xxu+dAz6A9fGlZjpoYfPP4ma8Mkb/wUtYfJbIIHxjyMAHDnaxZSDe3J8ev8bAzMz3ewvjUwHrMLQ9t0flutOupJE52koW3wmo7Z9fxqKmPFtBbPUMq69a3BNWtFNSdfeMci3v3kaupcjQytkHIlFsMhy2BKk/PysTfiuSub1s4Wakzfv0pGmay7kaFusvZiWT+msKwz0+tcnDkh9ajQOpCtfpqGzV5z5Zy2YXz8unMfev7S3tfK0lG0hn5vU7DRO4vMrwt5l5tLJ6XsAngPgBUhxGMAzu0WoH8AwO+OPieEOCiEeHT3y/cLIf5BoZERYnN3p219gk1+u2nev02OOtV9lDbYPK9tvrvp/NrcY2tTw1LG+XUNhaxrtepY29hyXjdXlroZE1xdGTOq1zx1fJHrNS3XHVC+mq0qE4Ne56JmLuSaC31G+rhOw4ZYruIArpVfX/5ff4taq5n53KHnj+KaOZv9EHJ+cyOeLvEV8bRJifQVIfLlxQ0ViYsp4mkyv6Pxm64NH97GIlC9Z454uqWorMt67wCU/0YR2VQRMmKVJf/2H2gbRTanPeKmSj+OZd2V5f2rzhKWdeZ6XYiIpau/EUPELEvXK/L5suw1FaPxj8/FsSM34ZF7xDU3JUy+p7JHrCmyJNMIEvGMHZvIYxkjRFSROIqOXgBdZNkmGm4D1boqMr8xddibFrgTrRruRGsPd0B2A1WH9GnH93pyOW/bW32sLIXTgXT1U6qu9rq40CPG5deDdx3GibPncp87tA7rUoecNvkT14o0wLYzmmmXM6q7C6k6i4W8XHgc2/k1xfedXyqo1lXe/MbWYW9ayJrv2Lvo+US13m7MkH+qBjd772yK79dUoXu/ZtXXHaB/Ry4TLy71h53odhJ0X+jILVPdUKW3+dDnXOkR4+fm4UPpTTMnnzu0XEvTIU2vmaPSg31R+ohn1SJEVJE4INs76csjQzW/RbyNPuaXKrIMZM9vWbypZSPPiz7tESZX9Zp7BlNFI5tA+rvkek09TCLETBhMzlsf8xbrvjCtCU1b7+1O04s+50qPGNeTzl+4Uvi5Q8q1tPNofl/T6G/arOMYM9VKb3hSGWJFlBwfG5fSMMnCl2FSNUN7tK6yGp5QCBJWvPywuTnA/L5mJY0lbnDjDtW7vJLTWKmK6w5w6/Bg/GN63lLqDyp8nd8muqFqvW/P1L3oc670iHH9+/ChWXw6YAq07jjHzyNTTNdxrCm6pTc8Y40Q9QZDLxuXKhKXhy/DJNbaQ58RwM3NAZL6TFCDN48YD/BpYtqNJa7XdIOuwVSvges1J/Dh8GD8YnrexqY/+Dy/TTI+VOt9dl/6Hei2+pxLPWIkv55/7kUkQ/dnQkyRQlM7J9ZMtdLnyVHVHubRSdQb17bOKCvvn6oWz1dtomntoe/rjKlqbatW88qUH67XdEOWrFPJo3bSQL+3xfWaBes1VefYuMNj8j3mXSDP2GN63sbWu8D3+a0rG7PWuw99zpcekacT6+r/sfW0MK1PpdJT8yh9xBOgSYnMo9ujSc2x9XCMvDz1xkywO0LzMKk97A2G1n83i7J2vTX14lW9fo4phk5kk+s11ei8x95gmCmPOLLJHX1jwuQMsjlvY+pdEFutnmq914YDL/pcaLluqv/HGCk0kT+xZqpNheGZBdUCSuozJKk5toKN4moaG9SpUXqGtq4wp0rxthEkVFfTMNVAV9Hnes109N9jI9ra/1Cww6M8mJxBvtZ36N4FsdXqqdb7enfL2z4IKddN9f9p6Wlhs298phqXPtU2D9tQs02ario1xyc2Ka9UV9PYoHrebq/YxjJNp7BtzW26rmxSVaatJTdDw+TaHaF7dUdW+mIVUMkA3ffY7fUrfQWKbir3yOGhkqFVTeUOwXjvC6D4GeRrfYe+vsz0/LY5u8flTLfXR6tVv+q9qdb7NOwDU/2f6lo715jumyzd2AVTH/Esa4SIIhJXRi+P6nmTev7Sto2Gm84vVWS5jPPLxEXa2l3b2DJuzMJRTfsGNyNZN+3v0lUn2qo3qKIkq/dFHj7Wd+hMAdPz2/TsnpQz959ejaKrqQmtVh29wTBIivY0ZZCY7BvfmaKliXhWKUJEFYmj9PKYzq/qeYtQ1gZBpp7IafHiMWEo2phl+Yx5Y5Yq4LvBTRXIOhPzDHVuUBUPo94XsZxBWfpS2r519Td1157p2T0tWU57+//0qpZObKr/+8wgSWaT6M/BLN140Lfvn1KKiGfVIkRUkTgqLw9VZLmsDYJMcT2/MbUbZ9zCjVncwO9RH756Z3qh6n2RRdqeUu3bkIzvA9Rq+OzbX6v93qYly8lUJ7bR/13L2larjrWNLTzw1Hfw8J9+F893t7D/QBvJ3L7odCffunEpIp5VixBRReJce3mKRjGn5YqQos9Lta5czm9s7cYZM1zVGe41ZqlonSGgF9nk95gOX70z/cSe/dBq1THTamIhaeDksVvxmW+cx9PP/hQPfeW7OHV8MdgY0vbBF48vop00Cr+3aclystGJY5EBtWYDy099Bwf3J3j4DQInzp6LVnfK1I2b9kZyKSKeVYsQUbZAHnl5Bv2hlZdHJ4pJNb8uOxjqPC9l/YArL16M7cYZPVzVGa4scSda7uirT9rVXdyJdvqJeW2P9vG7n1yFePQZnHz6+3jkHoFjR27S6pZvi2ofDIbbWu/Nl64ROtsp1mtBdBidBQ/edRgnzp6LWnfyLVPjedIMqhYhoorEuUQniknplXPlDdN5XqrIsktivZiYScdnnWG7WcfaWpfq0YLiKkLMda/ciZbxg815mLaPT5w9h5PHbsXFy71C3fJd4Op8ndQ1ur0+Br0tKzlTRJd1rZO41okpGJ2phw/NlUJ38ilTSxHxrFqEiCoS5xKdKKaPyLJu9zNbdKO2rtYV1fxOgweyKviuM6wKLjvRVrleE+BOtIwfbM9D1T4+fGiucLd8F7g8X8flTFKfsd4zebqsD51kpBOfOr5Y2v2/vdXHytJR/Pj5rvXclr2/RikMT9dhX4pJozJMqFIidQSnD0P7/tOrlTDEbOeX4toexh86jVk4fVENN7ixhw11JjS256FqH3d7O/s4FDGfr3m6rC+dc3NzgKQ+E2T/+7ARNjcHmN/XxMG5FlaWzOeWKtjgklIYngBHiEyxrZ8MZZiU3dCmOihs5peqWzTjB64zdAN3otWHDXUmBmz1HdU+Hm7apadOkqdXxXy+5umyZe+k69tG6F7eQGuYPbdZ62Ma+muUZ6SOsO2gSnGfqA029ZNU94naYFsb4fo+Ud/PazO/VN2iGTu4ztAd42n53InWDO5Ey8SCbb+IEPu4qF6VtQ8o+jqMyNNlY+ik67rO1/UtC3lzm7U+pqG/Rmkinq6oWoTIJhJHdZ+oDTaRZar7REd/e9zDVRSb+S27Z7KKcPqiO1Rp+RwhTsdVvSancjO+cJF55HsfuyiPoUy1zNu71GnCvup8Q+lFeevDRfYkdY1o5SKeZY0QUUTiKD0rFJFlqvtE0zxcK0tH0WrVvUaWY/BMMmp8dqKtSjQO4AixC7K88HmGel4n2nazXhpPPeMfm2hVGTIPbPUqKj1lnCxdlnoObN8PtV6Utz5ssydjuIO9tBFPiqYoVJ4QqkgcVV2qi8iySfczqvlN83Atn/EfWab2TDJquM7QDRwh1ofrNRkqXETzYt+jtnoVdUSuCLZzYBOR81XnG0ovylsfttkiMdSIltLwpEp5LWvnUlPyNqCvcL2LFF+T7mdlbQBlSt5eoE7HqBLcidYeNpjsYYcHQ0kMSrEteeemrWEzDamWWdg6H2zfD/U5WmR92MjVGBwXpTQ8qWoPy9i51IasDeizzoDqeakMbco7MVV7gbqOpCq0WnWsbWxxJ1pL2GDSh6/eYWIjBqXYhiLnpu1+sdVDYz/bbfX7EHW+Pg133/I0hjvYy+NGGoOq9jAvd328NqHb6xeq0SsCZc65KpffZ50B1fNmza/PvPi0nP2VJdqU1xjqSKpArdnAMtcZFsZVveZ4J9pTxxfRSRqVepe6nWiL1mtyrSZjA3V9nS3jcujYkZvw4F2HsTCX7OiDeElXsNkvtjWUsZ/tWfr9oJ9/l6rvGtNx2fmyAwnee/cteOVCB1c2+th2dO2OT3lKdcPGOKU0PGM0xEIbJpORuNCttX0a/5Qbg8LQThOU7WYda2tdANM3v8xLmDRmqaqS76vBzXwnwXM/v0LxSN7hxkpuoLy+okrEoBTbMJJDx47chEfuEThx9pyXBi42Z0DsZ3uWft9uFu9r4uOMbLXqmGk1sZA08Mm33g6ghkf+7FmyJj0mUDd/AkpqeMYonEIbJiEicVn4NP51IsvTYohNCsr2fAcAXQeysnueywJ3ok2HO/ra49pQZ4cHXRfIqlBEKY7ZCTCSQw/edRgnzp6LMqoY+9meqd8XNDx9sCcHnlzFX/7t8/jvD/86PvjVOOcYyN4n1LK8lDWeMTZF8V2boMo5j7XxkC2x1R6WtbEURfdnpjjbW32sLFW3zjANrtfUhxsruUH3PTLuGe3Xy5fWAQD7D7T35iL2+sSRHDp8aC7aWtUYzvYsvSTWmvFJOXDzDZ1o5zj2fVJayUmR8poFlRfJNhJHcT+oDVT1CVRRdpv5tdkLMaRjVIHNzQHm55PKvmedyGaRes2qvkedes25dhOXL61zZHMC3brXWFITpxHVXMy26vid06vRRplGcqjb60cbVaTOKCuil8QogyZ1sfMXrkQ7x7HX8ZYy4plF1SJENpE4qvtBbbCNLJvOL5UXzmZ+qbo/M/pU8T3rRjar3tFXJbt6gyF3otXEVUdfxg+qudhGzVmUyVdm3ObmAMPNLfKoYhaUGWVlzSCY1MU+843z+MRbb49yjmPvDj11hqfNC3d5P+ip44tBDnIbg7eMAqCshjaFQyN24cNUA9Xa11X0q5wGmiW7OkmDDXUNXDs8GPdkzYULJ4BvA6uIYyfGuzRD6IRl1UsmdbGLl3uYSxr4/DsWnZb8uVgXMVyZksXUGZ6xRIiS+kwQw8TGc00pACgMMSpD26VDQ2d+Yxc+zPSTtfZNFP0qGEu6dYajtL5xqm6oA+zwKDPKs2vDTWaZjS5QVHfJklWx1uCF0AnLqpek6WK1rT56VzYKR47zcLUuYqjjzSJqw7MqESKqSByVAKAyxKjmlyrlNXbhw0wX3ODGHpPGSkl9ptKGehrs8Cg3yrNrc8uJbLDRBVwYBiGc4CbO/RA6YZn1kqJyQDW/vUH2PaSu1kXspRSFnkYIcTeA+wBcALAtpfzIxL+fAPByAD8DcAeAD0sp/9p0UK1WHWsbW1g+c3XjA99NUagaBEXZMMdR22rdaxGKPK9p4XlZG0CZEqrhStocl5XQsm5aMGnMUvUGN64aK7Wb9cpeGQPw1TumUMu6vOseMs8uS9lgqguM11MD5rqab51AJY87OT8XoomirV4S83U6I9TOrQbWL+v/nMm6iPkMzY14CiE6AD4H4H1SypMAbhdCvH7iY3MAHpZSfhzAWQCfsBlUrdnA8pnqRIioInG+vSIm3nufhJrfSU/jFcLmFL499aYpJTFCIevKhqv0xao3uOHGSm7gq3fMoJZ1RbKefM6FqS6gqqfW1V18RxZNI26hZLLN3MaYojyJan67vez1FUMacoja4yIa4p0AfiilHJnN3wRw7/gHpJS/J6XcHvudV2wGNa2GGJA+qZSLzadwj61LYKj5nRSMw+1tEoM3hDA2PeAiJbisKxNZTgY2mNLhOkN3uOpEW2WHxxikso66saHpGlDVU+vqLr6d4FkRtzxilsmqDt6668a3rqSa36SebXJRpyGHqj0uMluHAIwHhy/tfu8ahBAtAO8E8GDav193XRu1Wi33D6ruQOr2+pifz0sWcMOgP0S7WQeadXQM/mS9PpM61rWNLSyPpT+sLB3FfLOOlaWjV6UWrywdRbtZR9vh8/YGQ3SSnWYUeRtANX4d6o0ZpTLq+3nzxm87vyp6gyEemrhn7D1PfQdfeucdOHV88Zr3r/rbJu8/dW3NJ1bPk4d6jhtI6mH2qkOCyzrAzV7zwaS8SFvbD33luzh1/A5gkC6z1zcHuL7d1Fr7ofH5/lV70kQ2jsofJmVXrOunKEXHn/YuFzIcHkXOGBfnQEnfP6msU63/uXZzZz4CkrcGxuXgvoY73aUDKOWijq6WhlqHHpRxre7hat2E0JXS5reIrMhaF75Rn/GLmO/svB8X8q6I4XkBwP6xrw/sfu8qdoXTZwF8SEr5N2m/6IUX1gsNqtW6dnN/+reOYtDbwprDNFCfeeLz8x2srXWv+l4ym+ylEAM7k7p8Zqc+oDW8trZk8udN2cv3n8jbz/LwpY1fl2Q2UdbS+HxeYGf861uD4HUACzfOpQrGfa06nvv5lb38/rydoPv+s9aWzxx/1Rx3e32sX94o9DsOHtyf/6EwBJd1gJu95hKVvLhxf6JU8lX1muMyu+jaD42L96+qM1TtSWwNnMnG2NaPLuPjV53LKvmmqn0NccakjT8PlnU770p1blxZ34qmJi1NDq4sHUV75tr6RJt1NZKLg1YdtVYTc/sa+PkLG/jj//x/8XeXerm6mmrsafI4qddKLSva+/dZr5txWXLsyE148K7DuGE2QbfXx3Bzy7meOH7u6cgKivNSpb92kgae+/lOwoMLeVfElfItAK8SQozcAa8D8DUhxA1CiAPAXr3A5wF8Skq5KoR4S6FRKdjcHGB+XzN47aHv1MSsFGKKlFffaS1UtTSj5lQUdQBUadO26emur7cx8dJGQHBZR42L9MVur1/p9EWuM3QDd6INCqms85FS6Dp9Mk0OLp/5Loa1Gefram/tP7mKWz70DD741e/h4TcIHNyfOO1qWnayOngXZSRLjh25CY/cI3Dy6e9DPPoM3v3kapT1oiEJpb/mrmYpZVcI8R4AK0KIiwDOSSm/LoT4OIDnATwB4CkAvwLg1UIIAJjFTjG6Fb0Xe168X1RdZMvaVdU0Ohyqq+oktWYDyxbzaxMND9EVLg2btaXqgGfTRbqMUMo6CnQ70Y6U/Gu96DNYR9xd9FzhqhMtlWyMhfH32O31X3J4cCfaIFDLOtfr3+YMUxGyG33a2j9x9hxOHrsV9678hbOuprGUN9hgu99HsuTBuw7jxNlzwe0Al7jO3JzUX5d/4zDe9bpXY25fY+/fXVDb3t7O/5QjLl68XPiP+UwfWrhxDrd86Bn0hy8NpzFTww8ef9NeODmLIpOdNn6TlFcXJLMJHhgTagBw52sWMtMwR+OnGrMNNvPr4nldCAPd9W8zbpP14XL8Bw/uL1YgVCJikXVAdvpi2rx/4R2LePeTq6nrYWRojf+uTicpdfpW0feflYKcJm/kY2/Ec1c2vcvOsqXa6r7HHzz+Jly+tB7tOcSyjl7W+TjDfPxOFSqdRT72Jrz9i9929jddvn+Ka01clUX0ajNYmEsgHjW3A0xw/f59yMTRvM7ua+C5Fzfx0ETJ4/XtprW8K2U+nC024WSbNF3bdDTX6ZBFvBfU3edMsJlfF89rk+I1muN6Y0Zrjm3WFlUXacY/nL6oD3eidQNfvcOEwscZlqY3rSz5yV5S6Sw/fr4btKtpUVTnSrvTDN5ZX5eRLHHVodglOjq+L918dMa/uNHHQynXWrq4saCShielIWaquFEZvJRGiY2hvbJkNr/Uz2tTe2y6tmK4O4qxR6des9ZsKOe9ygYTG+pucP0egbiveWBoMT3DsnSMNL1pfl/Ty7pTGbkH51pRyl7VuTKcqUd/xyawM7fDzS3Sq0sm0dX/fOuqNlfy5BFv2KoAFLWHIfP+x7GtSzWtv6KqS7WtO5yfT4zml+p5Abra47y6VIqUGkYP3XrNuXZT2Yl2b34rUq85yi7IqtfkOkM1OnWv/B4ZH5j0ViiiY0zKwfErU1yeiyqdtHs5TuevSg+eTRqlqZksYgeE1H109T/fuqrq93d79oZ5aSOeVYsOUUXiikSHfVzG6yKNwGR+KS/wpZrjrIg4VQdoRo2LTrRVT1/kTrRu4PfIxICJLLPRMXyci2Va+yo9+PyFq2sjYy/ZyXrnJnNsowvr6n++dVWfNxaUNuIZa3QI2F2wgyEWbpxz5iWhisTleYV8dJMD6CLLlF4wymirKsJFtc+YdFx1oh1PX5zmyKZqr3InWn18dfTt9voY9Nzfn8dUC11ZZqNjTMO56Lx7/9JRfOXbP7rqc7r6S0zZVbpzbKsL6+p/vs8jnzcWlDbiGWN0CHhp8d1/etVphIgyEpflFfJV4ExZd+jaC1aUvDn2EVnOgxsP0cANbuzhOkN36EY2dd5jUp+pzHtk4sFGxyj7uegiY3DyXOnMAL/1T19prKPGll2lO8e2urCJjm97HuXplL7Ou9JGPGOMDgH+PGGx5aOP8BWZLBpZDv28Pj2dWXPsK7KcB+U+qypZc52n6Fe9XpPrDO1wFSGu+ntk9Al9ntvcuV32c9GFHpN2riStuvGejy2KrDvHtrpw6IwaKp0SKHHEk6r2MA+fnjCqSFwWviKTRSPLoZ/Xt6dzNMeD/vCqOaa61oYy0l4FxtPyuROtGVxn6Abu6MtQQXGe29S4x3gu6ui7vvQYmz0fWxRZd45d6MIhZSblVYmljXhS1R7mQeUJi7nm1RSKyHIeVPNr602j6ADNZLMno06vcidaC7heUx+OEDMxQXWem8rM2OTHpL67/BuH8a7XvRoLB9qpY4sxYmsyJp9Rct059qkLj+Pqman6qAAljngCNLWHeVB5wmy9RZPesqJQdcZ0/bw6d4RSzK+NN42qAzSTDXei1Sdt39rWGU5mF0w7HCHWhyJ7qkq4jnaFmK+Y1v34WfLm216Bf/aP/yEeeFLdZyTGiK3umEJEyXXmOMTZ7PKZKfuolDbimQd1hOjU8UV0kkYwT5iNBystOryydBStVr3wM4eOtLh+Xp07Qik8nTbetNhqJ5gdTOo1genvRKtCtW9ru4Y6R+Ouhjv6uoGyFqoquIzAlWm+fESvHrzrME6cPZd+3u8S437WHVOMeo3vs9nlM4eK0KZR6ohnFtQRoqQ+Y+QJo4jEpUVels+EyfU2xfXz6kTDbTydpvNr402LrXaC2YHrNdPR7ehbr6HS0bg0uKOvPrrrLubzsWy4jMCVZb58Ra8OH5ordN7HuJ91xmSq16j2eRmyGlzqcpTZU3HtRIeUMUJEFYmjzPWmqD2kel5bT6ypNy3Geg4mW0ZxVLN4R9920kC/txWV9z40yWzC9ZoWmKy7EOdjVXAZgbOZr5CddX1Fr85fuKI879vN+IwpU0xrQtP2eaczg+4AQaPkJmvNtS5HpWdEH/GsUoSIKhJHletNVXtI9bzTUndcBs9gGRjJqFPHFzmyadHRd5QKGpv3PgStVh1rG1tcr6mBy3XHuMPV2jOdr9CddX1Frw4fmsWnl+Kp3/SlL5joNap9vj1TD6qbma61GGtzTYja8KyaYUJl8KYt5pUl/4bJtBhiRaGaX5cpFbFd8lx2bNLyy4zrBjdVQGUwLZ/hBlVF4XU3/ZjOV2h9xLWeOdJ3n3/uRSRD9/vbxID0qS+YyDHVPp/d1wiqm5mutSLPXIbAQNSpttNyRUjRkDpVSmRamku7WcfaWlf7d+mkk1KlMLkurI99fgF3KRUxFvQz8cINbtygkquqq3e4QZXelTG87qYH0/kKrY9QXUVnkuJpWibkW1/QlWNZZQYhdTObtZY3t2VorBV1xLNqESJKz+pkdNgUHU8OZQqTq7Qeyvml8GxxoyKmKNzgRh/dBjeqyCY3qNKLbFZ93U0bJvMVWh+hyjwwiUCaRuhs9AUf+o1KB6sNB8a6mck4fa21sjTWims0E1QtQkQViXOJjifHZ2S52+sXvg7GBqr5pfJscaMiJg2d6BI3uEnHpMFNJ6ljZekols9Us0GVq4h6ldcds4ONPmLTJDHkHu0NhnuGCVA8AmkaoTPVF5RNgIo8ZAYqHWy9O0DSqmvvf1M9zFe0uyyN0KKOeFYxQkQRiXOJjifHZ2T5/tOrQZ6Xan6rVh/LxI3LurkqRJdcNbh5caOP+X3NSkY2XUfUq7DuGDWm+kiZ+h50ErNaRtMInet6295gmPlzQL6er9rnJvvfZ62mCWVphBa14TkNTVHK3EE1xH2iZTfEytqIiqJbNFN+0tbNuBedG9zk46PBzbQbTC4N9aquuzISOlgQ0viwwfS9dHtqmZyFqQFpKufVjqPsd1qmzsQ+HF1lCQxEbXgC5TdMythBVdWiv8jmpVIoqQwxqvm1MXipukUz5Ua1blRe9KrXzbmq12RD3a2hPu3rblooSyQxdN8Dm/eS1GeCGpCjn3VVb9vtTXdnYluy5immbrfRG56uqFqEyGZDqFr0+75P1AYqQ8x2fikM3rIUoDM0aBtMCi96laNL3FhJHzbUmXHG5/3Nt70CJ4/dioW5BDOtZlTGZ2jjw/b8DmlA6jC+/1Gr4bNvf+01sjCpZ5ssoZ0AMUYY0+YpNidOZTRNm6Yoto1cbArITYvWbYqXy1KgPI7N89q2/Dad36x1VeRvmjYqKuP8MmEwanDTUl/dUdUGN9xYSQ/TxkpVvzJmmhnN+7EjN+GRewROnD0X5RURPq9FScP2/I5xX6j2/xePL6KdNPZkYR6hmx+W5aqlRtLE31/ZxFP/+ldx/sIVfOYb50mvwStdxLNKESKqSBxl+oCryPKp44uFn5fqihDbdWXqgYwtPYShwVXd3HqFo0ucBqrP5LoDsmUh12tWk9G8P3jXYZw4ey7aDJ0iupbLNMdpPL9V+38w3NaShb4ikFnzF7vMbrXq6G4N8MGvfg/i0Wdw8unv45F7BF52ICG7Bq9UhieVIVY1w2R7q4+VpfDpAy5rD5P6TPSGGNW6yhPOMdUCMH5waTCN9lrMh68LdAx1TgNNJ23drW1ssaHOXMNo3g8fmov+7uisdeg6zTFtP3z27a8FarXSntmudCEfsjWGNFUbnSytdO7E2XN47923kDkrSmV4Vi1CRGWYbG4OMlv0+zJMYm0A5et5qdZVXgE6tZBl3BGibq4K6BrqVa/XBIob6stn2FBnrmU076adWMehdKa61msm98MXjy9isz/EA0+ulvbMdqkLuZat1D0xbHUy1Rn1yoUOWS1qqQzPqkWIqFMq0javT8OE0tCmMMQoC9NVwplayDLu4AY3+rgy1KueBsqGOuOCzc0BhptbVucktTPVh14zvh8Gw23vZ7Zvwz3GJj0jqPTSEbY6mdKO2KCrRS2VNhm6cHhEVgGxqii64+Dv5hWtmzYessG2EU8WVPMLqAvufT5v1rrqdGjmlxsPlRNucGOP6wY3MTbxcI1KRqnW3hfescjrjtGiSAOXrLPS5xleBN96je8z27a55uh3ZOkyeXM8+vl6YwbJbBJUNlDqpYD9/CrtiE26muBSRTzLFCHqDexT0GJMifTp/Ymx9tC3tyvLk08xv9RRdkYfbnCjz7gs6Q2Gxo2VqhzZdBVRX1mqzrpjzLCpoaSOWPnWW4uc2SN5NzLcdGsEbSJuRXVV1RxTR6ypo7G2OlmMpQqlMjzzXmBMhkkncRNMji0l0qdhEqOhTWWI9QZDa2Efuvsz4x9ucGPPpCy5//QqG+o5uOqAnGaoz+9rTuU7Y8KQpwu5OMNtDDffsraIw95HjWBRw91WV6Uu/6E+K13oZLGdUaUyPIH4vCIqodbt+VXUbYVBrIZJbIY2lSHWSRrG80vV/ZnxC9fN6cOGuj2+I+oMY0OeLmR7hrvQLX3K2jzZ5K1GsKDhbqurUkesAfv5i9lxQUHpDE8VsRkmSd3vq7URBmU0TKgMbarntenkR9X9mXEDN7hxAxvqbmBDnYmZPF3Idi1SR9yAfP0lSzbZ6k62hrut4eoyYk3R1Th2xwUFU2N4xmaY+MZGGJTRMKEytAG75zVdV0l9xnh+Y/AQMma47kQ7bQdWGmyou0H1HtlQZ2KmiC5ksxapz1Nb/YW6RtDWcI0hYm1DDI4LW9J6IthQ6MmFEHcDuA/ABQDbUsqPTPz7PgCfBPATAL8I4Akp5Q+sRqaJTecp265dad0LOy7a2ub8zbxObyrK2Lk0r8NvFlRd7WzXlWmXR+oubGWGWtZxJ1o9uBOtG7LeI6+76YRa1rnCRhcqAvV5aqu/2OhOI2zkou382P48dVfjMurb47joajxJbsRTCNEB8DkA75NSngRwuxDi9RMfey+AH0kpPwbgjwB8yWg0FlBGAKkw9eKVsXOpjdeNymNJFVnmBkFmxCDruMGNHi4a3Jw6vlipyGYaWe+R1930EYOsc4nPdUh9ntrqLzGkvdvOz+jnB/1h6SLWZdS3x/FhHxVJtb0TwA+llCPT/JsA7p34zL0AvgUAUsrvATgihDhgPCoDymiYUEEtSE0pm6FNta5iOGhKCrmsy1qrPK/X4sJQT+ozlX6HQPZ75HU3lZDLurJAvf5d6C82hlvZoTb8yqpvj/ChxxYxWQ8BuDz29aXd7xX5zKXxD113XRu1Wq3QwOr1GczPm+WrDvpDtJt1oFkvlPI6auQymUrR7fWNx2Az/hB0AJw6vohO0kC3199rhjR6X7GPP4/J8a8sHcXymZdSTVaWjqLdrKPt8Rlt1pWr96+7F1xR0vUThawrslap5jUNyrnO2mOdTpIr54DSrtU9XIy/qKzyse74/ZMQhawrHdsgkbuu9Jeyv3/T8VPof+MUOYdixYd9VMTwvABg/9jXB3a/p/sZvPDCeuGBzc93sLbWLfx5G1qt9JqfQW8La4aeoZDjt2F991iZnJmyjF/F5Phbrfo1NQK+n89mXU3b+8/i4MH9+R8KQxSyjmKt2kC5VovuMZWcA6q111T4OAOLUqX3z7KuOnPtEldnQlXffyxnalLvYP3yRuo5FCs2Z4NK3hUxPL8F4FVCiGQ3LeN1AP5ECHEDgL6U8hKAr2EndeMvhBC3AXh29/ulwHdxOkMPRdMQXlelIwpZV9UGNybwHnMDv8fKEYWsY4rBZ4Id/P7MmTwbur0+Br0tq7Mht8ZTStkF8B4AK0KIxwCck1J+HcAHAPzu7sc+jR0h9iiAfwvgXxmPiAhuksD4gNdVeaiKrJs2eI+5gd9jdWBZxzBMUVz3RKhtb287Glo+Fy9eLvzHqpoSEAs8flqqNP6DB/cXKxAqESzrygOPn5YqjZ9lXXXmOkZ4/LSUffyAG3lXpKstwzAMwzAMwzAMwxjDhifDMAzDMAzDMAzjFTY8GYZhGIZhGIZhGK+w4ckwDMMwDMMwDMN4JWhzIYZhGIZhGIZhGKZ6cMSTYRiGYRiGYRiG8QobngzDMAzDMAzDMIxX2PBkGIZhGIZhGIZhvNKgHoAQ4m4A9wG4AGBbSvmRiX/fB+CTAH4C4BcBPCGl/EHwgSooMP4TAF4O4GcA7gDwYSnlXwcfqIK88Y997m0AngKwX0p5JeAQMynw/msA/s3ul78AYF5K+dtBB5lBgfG/Gjvr/y8BHAXwH6WUT4cepwohxMsBPAbgiJTyn6T8+wyAjwK4jJ33/yUp5f8OOshIYFlHC8s6WljWVQeWdbSwrKOFZV02pBFPIUQHwOcAvE9KeRLA7UKI10987L0AfiSl/BiAPwLwpaCDzKDg+OcAPCyl/DiAswA+EXaUagqOH0KIXwLwy4GHl0vB8b8dwJqUckVK+TCAPw47SjUFx/9+AP9TSvkEgD8A8IdhR5nLrwH4LwBqin//lwAOSCkfB3ACwGkhRD3U4GKBZR0tLOtoYVlXHVjW0cKyjhaWdflQp9reCeCHUsre7tffBHDvxGfuBfAtAJBSfg/AESHEgXBDzCR3/FLK35NSjloHzwCIxquEAuPf3UTvB5DqMSOmyPp5G4AbhBDLQoiPomTvH8DfATi4+/8HAawGGlshpJT/CTteLxXj+/d5ABsAbg0wtNhgWUcLyzpaWNZVB5Z1tLCso4VlXQ7UhuchXP1wl3a/p/sZKgqPTQjRAvBOAI8GGFdRioz/cQC/L6XcDDaq4hQZ/6uw45lZAfBlAP81Ii90kfF/CsCvCiE+BeDDAP5DoLG5Iub9GxKWdbSwrKOFZV11YFlHC8s6WljW5UBteF4AsH/s6wO739P9DBWFxrYrnD4L4ENSyr8JNLYiZI5fCHEzgOsB/KYQ4gO7335YCHFHuCFmUuT9XwLwbQDYrSE5AODmIKPLp8j4vwzgi7vpJP8cwJ8KIW4IMzwnxLx/Q8KyjhaWdbSwrKsOLOtoYVlHC8u6HKgNz28BeJUQItn9+nUAviaEuGEs7eJr2AldQwhxG4BnpZSXwg81ldzx76Y0fB7Ap6SUq0KItxCNNY3M8UspfyylfJeU8ondXHRg5zn+ima411Bk/XwdwGsAnvcP/gAAAXxJREFUYPd7dQD/L/hI0yky/pux08AAAP4ewBD0+zYTIcSsEGKURjK+f28AsA/A96nGRgjLOlpY1tHCsq46sKyjhWUdLSzrcqhtb2/nf8ojQog3APgXAC4C2JJSfkQI8XEAz0spnxBCtLHT/elnAA4D+Ghk3c/yxv9VAL8C4Ke7PzKb1iWKirzx737mIIAHAPz73f8+L6X8CdWYxynw/q8D8HEAPwTwjwCclVL+Od2Ir6bA+H8NO40YvgPg1QBWpZSfIxvwBEKIXwdwHMAbseP9/UMAvw3gNinl74id7mcfA9AF8EoAp3S6n00TLOtoYVlHC8u66sCyjhaWdbSwrMuG3PBkGIZhGIZhGIZhppuoQ7sMwzAMwzAMwzBM+WHDk2EYhmEYhmEYhvEKG54MwzAMwzAMwzCMV9jwZBiGYRiGYRiGYbzChifDMAzDMAzDMAzjFTY8GYZhGIZhGIZhGK+w4ckwDMMwDMMwDMN4hQ1PhmEYhmEYhmEYxiv/H2v1EXKrdzu6AAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from matplotlib import pyplot\n", "\n", "pyplot.rc(\"figure\", figsize=[16, 9])\n", "\n", "pyplot.subplot(231)\n", "pyplot.scatter(*random_samples)\n", "pyplot.title(\"random\")\n", "\n", "pyplot.subplot(232)\n", "pyplot.scatter(*additive_samples)\n", "pyplot.title(\"additive recursion\")\n", "\n", "pyplot.subplot(233)\n", "pyplot.scatter(*halton_samples)\n", "pyplot.title(\"halton\")\n", "\n", "pyplot.subplot(234)\n", "pyplot.scatter(*hammersley_samples)\n", "pyplot.title(\"hammersley\")\n", "\n", "pyplot.subplot(235)\n", "pyplot.scatter(*korobov_samples)\n", "pyplot.title(\"korobov\")\n", "\n", "pyplot.subplot(236)\n", "pyplot.scatter(*sobol_samples)\n", "pyplot.title(\"sobol\")\n", "\n", "pyplot.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is easy to observe by eye that for the average distance between each sample is much smaller for the sequences than the random samples.\n", "\n", "All of these methods are deterministic, so running the same code again, and you will result in the same samples." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Antithetic variate\n", "\n", "Create [antithetic\n", "variate](https://en.wikipedia.org/wiki/Antithetic_variates) from\n", "variables on the unit hyper-cube.\n", "\n", "In statistics, the antithetic variate method is a variance reduction\n", "technique used in Monte Carlo methods. It does so by doing a type of mirroring of samples.\n", "In chaospy we can create antithetic variate by providing the `antithetic=True` flag to the [chaospy.Distribution.sample()](../../api/chaospy.Distribution.sample.rst) method:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:10.635233Z", "iopub.status.busy": "2021-05-18T10:56:10.634915Z", "iopub.status.idle": "2021-05-18T10:56:10.718497Z", "shell.execute_reply": "2021-05-18T10:56:10.718217Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "antithetic_samples = uniform_cube.sample(40, antithetic=True, seed=1234)\n", "\n", "pyplot.rc(\"figure\", figsize=[6, 4])\n", "pyplot.scatter(*antithetic_samples)\n", "pyplot.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since the uniform distribution i fully symmetrical it is possible to observe the mirroring visually.\n", "Looking at the 16 samples here, it is possible to interpret it as 10 unique samples, which are mirrored three times: along the x-axis, y-axis and the x-y-diagonal.\n", "\n", "Antithetic variate does not scale too well into higher dimensions, as the number of mirrored samples to normal samples grows exponentially.\n", "So in higher dimensional problems it is possible to limit the mirroring to include only a few dimensions of interest by passing a Boolean sequence as the `antithetic` flag:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:10.721335Z", "iopub.status.busy": "2021-05-18T10:56:10.721019Z", "iopub.status.idle": "2021-05-18T10:56:10.820606Z", "shell.execute_reply": "2021-05-18T10:56:10.820324Z" }, "scrolled": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAecAAAEECAYAAAAS3fx4AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAAijUlEQVR4nO3df5AcZ33n8fezszPjHa20w4o1vtw5FkrgCSE2ewKFqEwOE5uqEFWlEkNAF4Rxkbpz7IAXO4XxYcfYYIOxsUFKxbYClF2OzggIXIWEwJ0RF8C+JSesUwTU8ZhEJ0MSg9a71mrlXc/+6vtjeuTZ1cxO7+5M99M9n1fV1M709vR8p6ef/nY//fTzmCAIEBEREX/0JB2AiIiILKXkLCIi4hklZxEREc8oOYuIiHhGyVlERMQzSs4iIiKeUXL2kDHm940xn046jk4yxhw1xvxi0nGIdFqXlOcHjDFXJB1Hlhjd5+wfY0wO6AuC4HTSsXSKMaYcBMHJpOMQ6bQuKc/9wPNBEMwnHUtWKDmLiIh4RtXaMTDG/GdjzHFjzAFjzD5jzPeNMfuNMS8zxnzBGPOPxphrwnkvNMYcMcYcD1//tjHmh8aYbxpj7jbGfMcY8/+MMbcYY35qjPlTY8wjxhhnjHkofM8V4XzfMsZ8yRjzknB60/fUxfrGcPmTxpi3hLFPGGP+a5Pvdosx5hvh42+MMT8XTr/HGDMTfka/MeZrxph/Nsa8I/zfSWPMleG8v1S3jG/Xpov4KGXl+WpjzJQx5v8aY15njBkyxhwOP/PCBt/td40xB40xXw8/7+Jw+juMMU8bY34WLucWY8yzYVl+R7g+avGWjDGfD7/jY8aYT3Tu18iwIAj0iOEB3Ar8BBgACsDPgD8HDLANmAJ6w3kvAY7XvfdKYBr4pfD13eHfh4DvAaVwuTcDvw6cAIbCeW4GDtYt66z3NIh1K3ASeDXwq8AdK3yv9/BCDcyVwF/U/e/9wCEgB9wDXFT3v78Drgyffx54W/j8POCrSf9eeuix0iNl5Xkv8Od1r/8YeEOT77UbGAyfbwF+XPe/HcCzwPnA5cAfLlsfD4XPrwHuD5/ngENJ/15pfOjMOV7/OwiCySAIZoEfAd8LqlvwUaAfOHeF97ogCH4IEATB++qmfz0IgulwubcDVwB/EwTBWPj/B4HfMMb8/ArvWSIIgmPAB6kW/PcDH14hrp8A/9MY8y3gvVQTes3Hw7+PAKeCIDjaZBkTwFuMMVuCIPgp8OYVPk/EF6koz8DDwO8ZY84JX7+B6sFxI/8APGiMeYxq+T/fGHNuGOdoOO1h4K3AvibLmAB+3Rjz2iAIFoDXN5lPVqDkHK+puufztdfBC40oCiu8dzLi9H8HjNW9Hqub3mpZ9f4UOIfqEf/zAMaYK40xfxc+rjTGvIzqWe/7giD4D1STc6m2gLBgXk+1IH9phc+6jupO4RvhTuHXIsQnkrRUlOcgCL4L/Cvw28aYVwHfD4IgMMYM15XnT4azfxn4dhAErwuC4JJwWqlucTdTPQB/PDwQafR5B4A7gT3GmB8B71wpPmlMyTl7fgIM1b2uPf/nVS7nEuAbwB/Urk0FQfBQEASXhI+HgH9P9Yz4UPiefIPl/D7waeABY0yz7a0cHvH/AtWj8b82xmxYZbwiWdSu8vwXVM/C3xE+JwiCI3Xl+b3hGfIW4GsAxphG5fmtVM+eP2iMOa/RBxljXgx8LgiCXwvnv90Y84ZVxtv1lJyz5yHgt8ICAtWj1m8EQfDjqAsIE+M1wB8Bd1Ct5uptMOs/Ai8yxrw8fP2by5bzW8CT4bI2ANc2+cgHjTEvCY/Ev0U1yes2ApE2lOfQfuCNwIVBEPygyTzjVNuavDZ8vbw8/xxwSRAE1wKfAx5ospx3AzvD59+jWs2dW2W8kvRF7254UD17PA78FLgauIVqIfgh1UYWX6KajL5D9frMEeB54AvAb4TznQT+R90yrw+Xdxy4a9nn7Q6X9a1w2S9p9Z66914IfJ9qUj2PavV2ABwGzmsw/4fD5f0V1bPe56lek3of8AzVxijnUb0mNw18kmrjsNr330l1h/M41TP17xI2DtNDDx8faSrPy5bzdeC6FvP8DnAM+O/A7XXf421UD8aPhvP9dfi//0X1bLy2Pm6ielnqYF15/mjSv1kaH7rPWUSkCxhjHgGuD6qNLsVzqtYWEckoY8ygMWanMWYzUFBiTo9G1xFFRCQbisD9VO/DvibhWGQVVK0tIiLiGVVri4iIeEbJWURExDOxXnMeG5uKXIc+MNDH5ORMJ8PpKMWfrLTHPzS00SQdw0rGxqYC39ex7/GB/zEqvvUZGOijUOhdU1n29szZGK/3TS0p/mSlPf408H0d+x4f+B+j4luf9cTnbXIWERHpVkrOIiIinml5zdlaex7Vbtxe5Zzb3uD/PcBHqI7IsgX4jHPuO22OU0REpGtEOXN+HdV+k5tVnr8V2OScu4Pq2L8PW2vVybmIiMgatUzOzrm/ZOm4pcvtBEbDeSeodvD+yrZEJyIi0oXacSvVuSxN3qfCaWcZGOiL3Hotl+uhXC61nnEFlYVFSsVepivzFHPxXl5vR/xJUvyyVoVCDpPvpb8vz+mZOYK5eWZnF5IOS6Rt4tjG25GcTwAb615vCqedZTX3o5XLJU6enF5TQIVCjorpYeTAEQ4dn2D7lkH27BqmGCzGtpNYT/w+UPzJGhra2HomD50pe/sPLy17BZSgJRPi2sbXdDpprd1grR0KX36F6himWGsHgXOAZoN5x8Lkexk5cITRY+PMLwaMHhtn5MARTF7jfIh0ksqeZF1c23jL5GytfT3VwbT/jbX2ZmttH3Al8OFwls8DU9baDwJ3A1c45xI9RO7vy3Po+MSSaYeOT9Dfl08oIpHuoLInWRfXNt4y1Tvnvgl8c9nkP6v7/yLVVtreOD0zx/Ytg4weGz8zbfuWQU7PzCUYlUj2qexJ1sW1jWeyE5Jgbp49u4bZsXUzvT2GHVs3s2fXMMHcfNKhiWSayp5kXVzbeCYvBM3OLlAswL7d29RiVCRGKnuSdXFt45lMzhC2mptdoPJcJelQRLqKyp5kXRzbeCartUVERNJMyVlERMQzSs4iIiKeUXIWERHxjJKziIiIZ5ScRUREPKPkLCIi4hklZxEREc8oOYuIiHhGyVlERMQzme2+U0TOZq29DLgcOAEEzrnblv3/pcDHgUPAMPCIc+7Lcccp0u105izSJay1JeAB4Drn3K3ARdbaS5fNdgPwmHPuTuBjwD3xRikioOQs0k12AE8552q99T8O7Fw2z8+AofD5EPBETLGJSB1Va4vEoFDIYfK9SQ+jeC4wVff6VDit3r3Af7PW3gv8KvDhmGITkTpKziIdVijkqJgeRvYf5tDxCbZvGWTPrmGKBeJO0CeAjXWvN4XT6j0EfNo591lr7RDwI2vtVufcRP1MAwN95HI9lMuljga8Hr7HB/7HqPjWJ5dbe+W0krNIh5l8LyP7DzN6bByA0WPjjBw4wr7d2yDe5DwKXGCtLYZV2xcD91lrB4F559wp4Hzg6XD+Z4FFGlz+mpycoVwucfLkdEyhr57v8YH/MSq+9SmXS/T05Nb0Xl1zFumw/r48h44vOfHk0PEJ+vvyscbhnJsGrgb2WmtvB4465w4CNwLXhLNdB7zbWvsB4H7gA865Z2INVER05izSaadn5ti+ZfDMmTPA9i2DnJ6Ziz0W59yjwKPLpt1Q9/wx4LG442qn2vX9XG8PxQ3FpK7vSwd1w2+sM2eRDgvm5tmza5gdWzfT22PYsXUze3YNE8zNJx1a5tSu71+1/zAvv+mrXLX/MBXTQ6GwtqpF8U+3/MZKziIdNju7QDFYZN/ubTx5x5vYt3sbxWAxc0f6PjD5XkYOHGH02Djzi8GZ6/smr0rCrOiW3zhb30bEU7OzCzC7QOW5SuuZZc1Wur6vdZ8N3fIb68xZRDKjdn2/XlLX96UzuuU3VnIWkczQ9f3s65bfWNXaIpIZs7MLFAuwb/e2pHtjkw7plt9YyVlEMqV2fb8vn8vUNUh5QTf8xqrWFhER8YySs4iIiGeUnEVERDyj5CwiIuKZSA3CrLWXAZdTHV4ucM7dtuz/LwU+DhwChoFHnHNfbm+oIiIi3aHlmbO1tgQ8AFznnLsVuMhae+my2W4AHnPO3Ql8DLin3YGKiHSDQiFHcUORzS/up7ih2JE+o+P4DFmfKNXaO4CnwvFfAR4Hdi6b52fAUPh8CHiiPeGJiHSPOAZ16JaBI9IuSnI+F5iqe30qnFbvXuC11tp7gVuAB9sTnohI94hjUIduGTgi7aL8GieAjXWvN4XT6j0EfNo591lr7RDwI2vtVufckt7JBwb6MMZECiyX66FcLkWa10eKP1lpj1+6UxyDOnTLwBFpFyU5jwIXWGuLYdX2xcB91tpBYN45dwo4H3g6nP9ZYJEGZ+WTkzORAyuXS5w8OR15ft8o/mSlPf6hoY2tZ5LMqQ3qMHps/My0dg/qEMdnyPq1rNZ2zk0DVwN7rbW3A0edcweBG4FrwtmuA95trf0AcD/wAefcMx2KWWRFhUKOysKiGrtI6sQxqEO3DByRdiYIgtg+bGxsKvKHpf3MR/Eno9bYZeTAEQ4dn2D7lkH27BqmGCymqmP8oaGN0a7/JGRsbCrwfRvxPT5oHGOhkMPkezs6qEPUz/B9HaYhvnw+t6ayrE5IJFPU2EV8s9rblmZnF6g8V2H8mdNUnqt05KBytZ+hW6/ipz2WZIoau4hPztTk7D+8tCanQGpqcrLwHdJIZ86SKbXGLvXU2EWSkoWanCx8hzRScpZMUWMX8clKNTlpkYXvkEY69JFMmZ1doFiAT13xakrF3o41qBGJIgu3LWXhO6SRzpwlc2ZnFyjmejraoEYkiizU5GThO6SRzpxFRDqkVpOzb/e2jt4a1UlZ+A5ppOQsItJBs7MLEN66lFZZ+A5po2ptERERzyg5i4iIeEbV2gmIo3s+ERFJLyXnmKm3HRERaUXV2jFTbzsiItKKknPM1NuOiIi0ouQcM/X9LCIirSg5x0y97YiISCu60BmztPa2oxbmItF0Q1nphu+YNCXnBKSttx21MBeJphvKSjd8Rx+oWltaUgtzkWi6oax0w3f0gdamtLRSC/O0nP3LC6y1lwGXAyeAwDl327L/G+A94cstQNk5965Yg0ypbigr3fAdfaAzZ2lJLcyzw1pbAh4ArnPO3QpcZK29dNlsu4GTzrm9zrnrgU/GG2V6dUNZ6Ybv6AMlZ2lJLcwzZQfwlHOudorzOLBz2TxvBwattddaaz8CnI4zwDTrhrLSDd/RB6rWlpbS2sJcGjoXmKp7fSqcVu8CYJNz7kPW2pcDX7PWvsI5d+YHHxjoI5froVwudT7iNUoqvhLwqSteTanYy3RlnmKueg5UahBKWtfhar5jEvH5Ipdb+/mvkrNEkrYW5tLUCWBj3etN4bR6p4C/B3DOPWmt3QScDxyvzTA5OUO5XOLkyenORrsOScc3Ex4CzawwT9IxttIqvijfsZPSsP56enJreq+qtUW6yyhwgbW2GL6+GPiKtXYwTMIAB4GtAOG0HPDT2CMV6WJKziJdxDk3DVwN7LXW3g4cdc4dBG4Ergln+xgwbK39APAJ4J3OuecTCVikS6laW6SJrPaC5Jx7FHh02bQb6p5PAlfFHZeIvEDJWVKvURJtxzLVC5KIJEXV2pJqtSR61f7DvPymr3LV/sNUzPo3a/WClB2FQo7ihiKbX9xPcUORQmFtDXQkOd34Gyo5S6o1S6KVhcV1LVfjbmdDs4O3bti5Z0W3/oZKzhF145FbGjRLoqXi+s5w1QtSNqgGJP269TdUco6gW4/c0qBZEp2urO+6s3pBygbVgKRft/6GSs4RdOuRWxo0S6LFdfTMA2GvaMEi+3Zv48k73sS+3dsoBotqDJYyqgFJv279DSNll24fxUajsPirWdei7Vq2ekVLt9rB28iBI0ta3asGJD1W/A3z2a29bJmc60axeaVzrmKt/aK19tKw44Ka2ig2D4fvuagz4SajduQ2emz8zLRuOHJLi0ZJNO4+fsVP6hc+/Vb6DbNczqPU/XX9KDa6/iiSXrPhgdv4M6epPFdRYk6hbvwNo1Rrt2UUG6iOZGOMiRSYb6ONrHYUFt/iXy3FLyKSnCjJuS2j2EB1JJuofB1tJOooLL7GH5XiT9bQ0MbWM4lIZkWp1tYoNiIiIjFqmZw1io2IiEi8It1KpVFsRERE4qNeNCTVsjqsoyRD21N8tK5XpuQsqbXSsI7Snep3+NOVeQqFXOQdvoYJjU8713VxQzGTCV7dd0pqqVtVqbe8D/z/9PATq+oDX9tTfNqxrguFHCefn8vsmAdKzpJa3dohvjS23h2+tqf4tGNdm3wv1342uwdTSs6SWt3aIb40tt4dvran+LRjXWf9YErJWVJL3apKvfXu8LU9xacd6zrrB1MmCILYPmxsbCryh6W9hyfFH49mLT7TEn8zQ0Mbo/Vzm5CxsanAt3V8ppHRstGLVjPUZ9wtiH1bh8t1Mr71rutCIcdsTw/Xfnbtv3enlcsl8vncmspyNirnpWtpWEepWT560XRlnoXK3Kp21Nqe4rPedV09CC9mdsQxJWcRyYz6HX65XOJkRnbU0lzluUomD6Z0zVlERMQzSs4iIiKeUXIWERHxjDfXnJe33GvnsrLUSEBERLLPizPnQiFHkO9lYnqOIICJ6Tmm5xbW1A1bo2UF+d7MdOkmIiLZ58WZc28xz7Mzc/yXL33vzP1qd//eRbyoL7/qM952LktERCQJXpw5Bxje94WjS/pIfd8XjhKw+nu327ksERGRJHiRnEvFXMM+UkvF1VdFt3NZIiIiSfAiOZ9+fr5xH6nPr75P23YuS0REJAleJOdgdu6sTtD3/sdhgtnVt9putKw9u9a2LBERkSR40SBseZ+4p2fm6Mvn1tTheqNl6VYqERFJEy+SM5zdCXpfudS2ZYmIiKSJF9XaIiIi8gIlZxEREc94U60tIp1nrb0MuBw4AQTOuduazPd2YD+w0Tl3OsYQRQSdOYt0DWttCXgAuM45dytwkbX20gbzvQL45ZjDE5E6Ss6SaoVCjuKGIptf3E9xQ1F9qK9sB/CUc67WUvJxYGf9DGECvwFoeEYtIvFQcpbUKhRyVEwPV+0/zMtv+ipX7T9MxfQoQTd3LjBV9/pUOK3eHcCHnHOzsUUlImfRNWdJLZPvZWT/YUaPjQMwemyckQNH2Ld7W8KReesEsLHu9aZwGgDW2vOBFwFvs9bWJl9vrf1b59x36xc0MNBHLtdDeR23PHaa7/GB/zEqvvXJ5dZ+/qvkLKnV35dv2I96f1+ehfnFhKLy2ihwgbW2GFZtXwzcZ60dBOadcz8BrqzNbK39KHBvowZhk5MzlMulNXUUFBff4wP/Y1R861Mul+jpWVtNnqq1JbVOz8w17kd9Rl21NuKcmwauBvZaa28HjjrnDgI3AtfU5rPWDllrbw5f3mCt/bfxRyvS3UwQBLF92NjYVOQP8/2IqBXF33m1a84jB46cGbt7z65hisEipVLR+/hXMjS00esxTsfGpgLft5FyucT0dAWT7/W2K980rENf4isUcmf9lr6X83K5RD6fW1NZVrW2pNZK/aiX/L0MJTGqmB5G9h9eevBWwKsELa2dORBf9ltmuZirWltSbTbsQ338mdNUnqtop5sR7bhFrrKwyMiBI4weG2d+MTjTYNDkdU6SNibf2/C3rCysvm1JWm6/jLSVqlchEYlLs7Ok1Z7xloq9TRsMalCcdGnW+LNU7GVmqsmbGmjXthWHlmfO6lVIROLU7CxptWe805V5NRjMiGaNP6cr86taTru2rThEqdZWr0IiEpuVbpFbjWKuhz27htmxdTO9PYYdWzezZ9cwwdzqduiSvGBuvuFvWVzlfcTt2rbiEOVwYVW9CtV1XnCWgYE+jInWcM3Hm8srC4uUir1MV+ZbbhQ+xr8ail+SUjtLqnUuA2s/4y0Giw0bDEq6NGv8uVrt3LY6LUpybluvQpOTM5ED860Jf7NbdpoVdJ/iXwvFn6yhoY2tZ8qo2lnS8vK2lp3x7OwChI0GJd0a/ZarvSujndtWp7W8zzmssj4KvNI5V7HWfhG4D/g/VHsVOrVs/oAmDcLSep9zcUORq+q6iQTYsXUz+3Zva1rofYp/LRR/srr9PudG97Su9ow3DduA7zFmMb52bFuriW+t9zm3rLBXr0Lpuk7RjdJya4REp1vkpFPSsm1FaqLmnHsUeHTZtBuWvR4Dbg8fmZKm6xTdppOdE8R5hC0iUk+dkETQrKWgj9cpuk07Oyeop+EoRSRJ/t3c5aGVuomUZLWrc4LlVhyOUr+7iHSYzpwjSst1im7Trs4JllM7AxFJkpKzpFq7OidYTsNRikiSVK0tqdauzgmWS9P9kCKSPUrOknrt6Jyg0TLVzkBEkqLkLNKEepcSkaTomrOIiIhnlJxFREQ8o2ptiUS9ZYmIxEfJWVpq1kVmsYAStIhIB6haW1pq1kWmyevYTkSkE5ScpSX1liUiEi8lZ2lJvWWJiMRLyVla0qhcIiLx0kXDBKSt5bN6yxIRiZeSc8zS2vJZvWWJiMRH1doxU8tnERFpRck5Zmr5LCIirSg5x0wtn0VEpBUl55ip5bOIiLSiC50xU8tnERFpRck5AWr5LCIiK1G1toiIiGeUnEVERDyj5CwiIuIZJWcRERHPKDlL5hQKOSoLi2x+cT/FDUUKhVzSIYmIrIpaa0umnOm7/OEnUtV3eVystZcBlwMngMA5d9uy/78fOA94GngNcItz7oexByrS5XTmLJmivsubs9aWgAeA65xztwIXWWsvXTZbP3C9c+4u4IvA3fFGKSKgM2fJmJX6Ltd95ewAnnLO1VbE48BO4GBtBufcn9TN3wOcji88EalRcpZMqfVdPnps/Mw09V1+xrnAVN3rU+G0s1hrC8A7gT9q9P+BgT5yuR7K5VLbg2wX3+MD/2NUfOuTy629cjpSctZ1KkmLWt/lIweOLLnmrL7LgWr53Vj3elM4bYkwMd8P3OSc+6dGC5qcnKFcLnHy5HRHAm0H3+MD/2NUfOtTLpfo6Vlbg9SWaV3XqSRNZmcXKAaLfOqKV/PkHW9i3+5tFINFNQarGgUusNYWw9cXA1+x1g5aazfBmfK+D7jXOfeEtfbNCcUq0tWinDnrOpWkyuzsAuVSkfFntBnWc85NW2uvBvZaa8eAo865g9bau4AJ4E5gP/ArwEuttQAbqB5wi0iMoiTntl2nEpFkOeceBR5dNu2GuueXxx6UiJwlSnJu23WqgYE+jDGRAvP9Qn8rij9ZaY9fRLpblOR85jpVWLV9MXCftXYQmHfOnQqvU/0Z8HHn3A+stW92zp1VFTY5ORM5MN8v9Lei+JOV9viHhja2nklEMqtlctZ1KhERkXhFupVK16lERETio+47RUREPKPkLCIi4hklZxEREc8oOYuIiHhGyVlERMQzSs4iIiKeUXIWERHxjJKziIiIZ5ScRUREPBOphzARWZ9CIYfJ99Lfl+f0zBzB3LzGmBaRppScRTqsUMhRMT2M7D/MoeMTbN8yyJ5dwxQLKEGLSEOq1hbpMJPvZeTAEUaPjTO/GDB6bJyRA0cweR0bi0hjSs4iHdbfl+fQ8Ykl0w4dn6C/L59QRCLiOyVnkQ47PTPH9i2DS6Zt3zLI6Zm5hCISEd8pOYt0WDA3z55dw+zYupneHsOOrZvZs2uYYG4+6dBExFO66CXSYbOzCxQLsG/3NrXWFpFIlJxFYjA7uwCzC1SeqyQdioikgKq1RUREPKPkLCIi4hklZxEREc8oOYuIiHhGyVlERMQzSs4iIiKeUXIWERHxjJKziIiIZ5ScRUREPKPkLCIi4hklZxEREc8oOYuIiHhGyVlERMQzmR2VqlDIYfK9GqJPRFZF+454aD2vLJPJuVDIUTE9jOw/zKHjE2zfMsieXcMUC+jHF5GmtO+Ih9Zza5ms1jb5XkYOHGH02DjziwGjx8YZOXAEk8/ksYiItIn2HfHQem4t0pqw1l4GXA6cAALn3G3L/n8O8HHgX4CXAXc6555sc6yR9fflOXR8Ysm0Q8cn6O/La7B76WppK8tx074jHlrPrbU8c7bWloAHgOucc7cCF1lrL10223uBHzvnPgp8AvhMm+NcldMzc2zfMrhk2vYtg5yemUsoIpHkpbEsx037jnhoPbcWpVp7B/CUc652OPM4sHPZPDuBUQDn3PeAV1lrN7UtylUK5ubZs2uYHVs309tj2LF1M3t2DRPMzScVkogPUleW46Z9Rzy0nluLUq19LjBV9/pUOC3KPKfqZxoY6MMYEymwXK6HcrkUad5GSsCnrng1pWIv05V5irnqcUhp7YtclfXGnzTFn0ltK8tZNTu7QLEA+3ZvUyviDtJ6bi1Kcj4BbKx7vSmcttp5mJyciRxYuVzi5MnpyPM3MxPuZqJ/cnu0K/6kKP5kDQ1tbD3T6rWtLA8M9Hl/ALTe+BbmF+nL5yCf69hBfdbXYRTrWc9pWH9rFSU5jwIXWGuLYXXYxcB91tpBYN45dwr4CtUqs29bay8E/iGcLiL+aFtZnpyc8f4AyPf4wP8YFd/6lMslenpya3pvy7TunJsGrgb2WmtvB4465w4CNwLXhLPtoVrobwb+GPiDNUUjIh2jsiySHiYIgtg+bGxsKvKH+X5E1IriT1ba4x8a2hitcUZCxsamAt/Xse/xgf8xKr71KZdL5PO5NZXlTHZCIiIikmZKziIiIp6JtVpbREREWtOZs4iIiGeUnEVERDyj5CwiIuKZxMfnijBKzvuB84CngdcAtzjnfhh7oE20ir9uvrcD+4GNzrnTMYa4ogjr3wDvCV9uAcrOuXfFGuQKIsT/UqqjLB0ChoFHnHNfjjvONPN9JCvf9yFp2Ef4vh/wvZxba88Dbgde5Zzb3uD/PcBHqHaNuwX4jHPuOystM9Ez54ij5PQD1zvn7gK+CNwdb5TNRYwfa+0rgF+OObyWIsa/GzjpnNvrnLse+GS8UTYXMf4bgMecc3cCHwPuiTfKdPN9JCvf9yFp2Ef4vh9ISTl/HfBXQLN7mt8KbHLO3QG8H3jYWrti12FJV2u3HCXHOfcnzrlak/IewJuzTiLEH25YNwANj5YTFmWUorcDg9baa621HyFl6x/4GTAUPh8CnogptqzwfSQr3/chadhH+L4f8L6cO+f+kqUDxixXX0YmgOeBV660zKSTc5RRcgCw1haAdwI3xxBXVFHivwP4kHNuNraooosS/wVUj/j2Ag8BX2t1xBejKPHfC7zWWnsvcAvwYEyxZcV6RrKKg+/7kDTsI3zfD2ShnK+6jCSdnCONgBMWqvuBm5xz/xRTbFGsGL+19nzgRcDbrLU3hpOvt9a+Jr4QVxRl/Z8C/h4gvI64CTg/luhaixL/Q8Cnw6q43wU+Fw70ING0bSSrDvF9H5KGfYTv+4EslPNVl5Gkk/OZUXLC1xcDX7HWDtaqxcIqn33Avc65J6y1b04o1kZWjN859xPn3JXOuTvDayFQ/R7fTSbcs7Rc/8BBYCtAOC0H/DT2SBuLEv/5VBsCATwLLJL8dp8mUdZxbSQrEhiVzvd9SBr2Eb7vB1JZzq21G6y1tar2+jIyCJwD/GCl9yfeQ5i19o3AW4AxYM45d5u19i5gwjl3p7X2S8CvAP8avmVDo9ZwSWkVfzjPEHAV8OHwsc859y9JxVwvwvofAO4CngJ+Afiic+5vk4t4qQjxv45qg6XDwEuBJ5xzDyQWcApFWMd9VFvKPg38IvCRmFtre70PScM+wvf9gO/l3Fr7euAK4Dep1tDcA7wLuNA594dha+2PAtPAzwOfatVaO/HkLCIiIkupek9ERMQzSs4iIiKeUXIWERHxjJKziIiIZ5ScRUREPKPkLCIi4hklZxEREc8oOYuIiHjm/wPzq0PLxJ/75wAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pyplot.rc(\"figure\", figsize=[8, 4])\n", "\n", "pyplot.subplot(121)\n", "pyplot.scatter(*uniform_cube.sample(40, antithetic=[False, True], seed=1234))\n", "pyplot.title(\"mirror x-axis\")\n", "\n", "pyplot.subplot(122)\n", "pyplot.scatter(*uniform_cube.sample(40, antithetic=[True, False], seed=1234))\n", "pyplot.title(\"mirror y-axis\")\n", "\n", "pyplot.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here 20 samples are generated and mirror along a single axis, which is twice as many as in the first try." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Latin hyper-cube sampling\n", "\n", "[Latin hyper-cube sampling](https://en.wikipedia.org/wiki/Latin_hypercube_sampling) is a stratification scheme for forcing random samples to be placed more spread out than traditional random samples.\n", "It is similar to the low discrepancy sequences, but maintain random samples at it core.\n", "\n", "Generating latin hyper-cube samples can be done by passing the `rule=\"latin_hypercube\"` flag to [chaospy.Distribution.sample()](../../api/chaospy.Distribution.sample.rst):" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:10.822878Z", "iopub.status.busy": "2021-05-18T10:56:10.822564Z", "iopub.status.idle": "2021-05-18T10:56:10.882233Z", "shell.execute_reply": "2021-05-18T10:56:10.881869Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pyplot.rc(\"figure\", figsize=[6, 4])\n", "\n", "lhc_samples = uniform_cube.sample(count, rule=\"latin_hypercube\", seed=1234)\n", "\n", "pyplot.scatter(*lhc_samples)\n", "pyplot.show()" ] } ], "metadata": { "jupytext": { "formats": "ipynb,py:percent" }, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.5" } }, "nbformat": 4, "nbformat_minor": 4 }