{ "cells": [ { "cell_type": "markdown", "id": "2d5d625c", "metadata": {}, "source": [ "# Computing galaxy-galaxy-galaxy lensing statistics\n", "\n", "In this notebooks we compute the galaxy-galaxy-galaxy lensing (G3L) shear correlation functions on a mock catalog and transform them to the third-order aperture statistics." ] }, { "cell_type": "code", "execution_count": 1, "id": "90abdb2e", "metadata": {}, "outputs": [], "source": [ "from astropy.table import Table\n", "import numpy as np\n", "from matplotlib import pyplot as plt\n", "\n", "import orpheus" ] }, { "cell_type": "markdown", "id": "9016e231", "metadata": {}, "source": [ "## Initialize the catalog instances\n", "\n", "For this exercise we use a simplistic mock catalog built from the [Takahasi simulation suite](http://cosmo.phys.hirosaki-u.ac.jp/takahasi/allsky_raytracing) that traces two tomographic bins in a _Euclid_-like setup for the $n(z)$ and uses a linear galaxy bias. \n", "\n", "As we are dealing with two separate catalogs, we need to initialize a `ScalarTracerCatalog` instance for the lenses and a `SpinTracerCatalog` (with `spin=2`) for the sources." ] }, { "cell_type": "code", "execution_count": 2, "id": "74ff1ec5", "metadata": {}, "outputs": [], "source": [ "catname = \"data_g3l.npz\"" ] }, { "cell_type": "code", "execution_count": 3, "id": "7afc513c", "metadata": {}, "outputs": [], "source": [ "mock = np.load(catname)" ] }, { "cell_type": "code", "execution_count": 4, "id": "c1495669", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hist(mock['z_lens_true'],bins=np.linspace(0,2,81),histtype='step',lw=3,label='Lenses')\n", "plt.hist(mock['z_source_true'],bins=np.linspace(0,2,81),histtype='step',lw=3,label='Sources')\n", "plt.xlabel(r'Redshift $z$')\n", "plt.ylabel('Counts')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 5, "id": "a97bd9ce", "metadata": {}, "outputs": [], "source": [ "sources = orpheus.SpinTracerCatalog(spin=2,\n", " pos1=mock[\"x_source\"], \n", " pos2=mock[\"y_source\"],\n", " tracer_1=mock[\"gam1_source\"],\n", " tracer_2=mock[\"gam2_source\"], \n", " weight=None, zbins=None)\n", "lenses = orpheus.ScalarTracerCatalog(pos1=mock[\"x_lens\"], \n", " pos2=mock[\"y_lens\"], \n", " tracer=np.ones_like(mock[\"x_lens\"]), \n", " weight=None, zbins=None)" ] }, { "cell_type": "code", "execution_count": 6, "id": "c6af5c86", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of source galaxies:1098203 --> effective nbar: 2.848/arcmin^2 on 107.10 deg^2\n", "Number of lens galaxies:551207 --> effective nbar: 1.431/arcmin^2 on 107.02 deg^2\n" ] } ], "source": [ "print(\"Number of source galaxies:%i --> effective nbar: %.3f/arcmin^2 on %.2f deg^2\"%(\n", " sources.ngal, sources.ngal/(sources.len1*sources.len2), sources.len1*sources.len2/3600.))\n", "print(\"Number of lens galaxies:%i --> effective nbar: %.3f/arcmin^2 on %.2f deg^2\"%(\n", " lenses.ngal, lenses.ngal/(lenses.len1*lenses.len2), lenses.len1*lenses.len2/3600.))" ] }, { "cell_type": "markdown", "id": "fbffecb6", "metadata": {}, "source": [ "## Computation of the shear-lens-lens correlation function\n", "\n", "For computing the shear-lens-lens correlation function we need to invoke the `GNNCorrelation` class. In principle, it is only required to define a binning for the 3pcf (given by the range of the bins and the number of bins).\n", "\n", "**Notes**\n", "\n", "* Instead of the number of bins you can also specify the logarithmic bin-width `binsize`. However, the final value of `binsize` might differ slightly from the provided one as we fix the values for the binning range and then choose the largest possible value of `binsize` that is smaller or equal to the input value for `binsize`.\n", "\n", "* If no further parameters are passed, the default setup chooses the some accelerations of the discrete multipole estimator renders fairly accurate results for the 3pcf itself and percent-level accuracy for the third-order aperture statistics. In case you want a different setup than the default results you can change the parameters of the parent `BinnedNPCF` class." ] }, { "cell_type": "code", "execution_count": 7, "id": "301fbb64", "metadata": {}, "outputs": [], "source": [ "min_sep = 0.25\n", "max_sep = 150.\n", "binsize = 0.1\n", "nbinsphi = 256\n", "method = \"DoubleTree\"\n", "resoshift_leafs=-2\n", "nthreads = 48\n", "\n", "gnn = orpheus.GNNCorrelation(min_sep=min_sep, \n", " max_sep=max_sep, \n", " binsize=binsize,\n", " nbinsphi=nbinsphi,\n", " method=method,\n", " resoshift_leafs=resoshift_leafs,\n", " nthreads=nthreads,verbosity=2)" ] }, { "cell_type": "code", "execution_count": 8, "id": "a50abf45", "metadata": { "scrolled": true, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Done 99.95 per centCPU times: user 35min 8s, sys: 3.06 s, total: 35min 11s\n", "Wall time: 49.6 s\n" ] } ], "source": [ "%%time\n", "gnn.process(sources, lenses)" ] }, { "cell_type": "markdown", "id": "68a5a431", "metadata": {}, "source": [ "Once processed, the instance of `GNNCorrelation` contains the multipole components of the shear-lens-lens correlators $\\Upsilon^{'}_{\\tilde{\\mathcal{G}},n}$, as well as their nonrmalizations $\\mathcal{W}_n$ in their multipole basis. If required, we can use the `multiples2npcf` method to transform the to the real-space basis, in which they become the more well-known shear-lens-lens correlation function $\\tilde{G}$ introduced in [Schneider & Watts 2005](https://doi.org/10.1051/0004-6361%3A20041923). " ] }, { "cell_type": "code", "execution_count": 9, "id": "4baf8a1b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 528 ms, sys: 8 ms, total: 536 ms\n", "Wall time: 534 ms\n" ] } ], "source": [ "%%time\n", "gnn.multipoles2npcf()" ] }, { "cell_type": "markdown", "id": "93ef57d8", "metadata": {}, "source": [ "## Computation of the aperture statistics\n", "\n", "The integral transormation between the shear-lens-lens 3PCF and their third-order aperture statistics can be done by calling the `GNNNCorrelation.computeNNM` method.\n", "\n", "**Notes**\n", "\n", "* In case you are only interested in obtaining the third-order aperture statistics, you can also directly call this method right after processing the shape catalog.\n", "\n", "* One should only trust the third-order aperture statistics for radii $R\\in[\\alpha\\,\\theta_{\\rm min}, \\beta\\,\\theta_{\\rm max}]$, where $\\alpha\\approx 5$ and $\\beta \\approx 0.125$. In the plot below this range is indicated by the dashed vertical lines.\n", "\n", "* Furthermore, the binning should be sufficiently fine, i.e. the value of the `GNNCorrelation.binsize` attribute should be less than `0.1` for an accuracy of about one per cent." ] }, { "cell_type": "code", "execution_count": 10, "id": "6d666905", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 9.21 s, sys: 753 ms, total: 9.96 s\n", "Wall time: 3.95 s\n" ] } ], "source": [ "%%time\n", "radii_ap = np.geomspace(1.,30.,20)\n", "NNM = gnn.computeNNM(radii_ap)" ] }, { "cell_type": "code", "execution_count": 11, "id": "8eb15668", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1e-08, 8.290079304338584e-05)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.loglog(radii_ap, NNM[0,0].real, label=\"NapNapMap\")\n", "plt.loglog(radii_ap, np.abs(NNM[0,0].imag), label=\"|NapNapMx|\")\n", "plt.axvline(x=5*gnn.min_sep, color=\"grey\",alpha=0.5,ls=\"--\")\n", "plt.axvline(x=0.125*gnn.max_sep, color=\"grey\",alpha=0.5,ls=\"--\")\n", "plt.xlabel(\"Aperture radius [arcmin]\")\n", "plt.ylabel(\"Third-order aperture statistics\")\n", "plt.legend(loc=\"upper right\")\n", "plt.ylim(1e-8,None)" ] }, { "cell_type": "markdown", "id": "b07141ea", "metadata": {}, "source": [ "## Accounting for the angular clustering correlation function\n", "\n", "The estimator for the 3pcf described above is biased as the lenses are inherently clustered which implies that we perform the area-averaging of the source-lens-lens pairs in a non-uniform fashion (see [Simon et al. 2008](https://www.aanda.org/articles/aa/pdf/2008/09/aa8197-07.pdf) for further details). To counter this effect we need to modify the estimator and reweight the nominator by the same factor. \n", "\n", "We give the option to apply this correction within the `multipoles2npcf` method when making use of the optional `xi` parameter. The data type of `xi` is defined to be a list of two elements:\n", " * The zeroth element are the radial bin centers at which the clustering 2pcf is evaluated\n", " * The first element is the clustering 2pcf for all tomographic (lens) bin combinations\n", " \n", "This general way to pass the clustering 2pcf allows for both, a theoretical and a measurement-based model. For our example we make use of the measured clustering 2pcf from the [NN_tutorial notebook](./NN_tutorial.ipynb).\n", "\n", "\n", "_Note: Our prescription slightly differs from the original one introduced in [Simon et al. 2008](https://www.aanda.org/articles/aa/pdf/2008/09/aa8197-07.pdf) as the multiple-decomposition of the triplet counts do not contain information about the shape of each individual triangle -- only its mean shape per bin is known. Given the smooth shape of the clustering correlation function, for a sufficiently fine binning in radial and angular scales the two prescriptions should converge towards each other._\n" ] }, { "cell_type": "code", "execution_count": 13, "id": "6cffc12a", "metadata": {}, "outputs": [], "source": [ "# Load in the data that we stored in NN_tutorial.ipynb\n", "dat_nn = np.load(\"nncorr.npz\")\n", "\n", "# Define xi. \n", "# As in NN_tutorial.ipynb we computed the 2pcf for all tomographic bin combinations we need to select the \n", "# lens-lens one. This is the zeroth index. The double brackets are needed to make sure the shape matches\n", "# the orpheus convention for which xi[1].shape == (nzlens*nzlens, nbinsr)\n", "xi_corr = [dat_nn['bin_centers_mean'], dat_nn['xi'][[0]]]" ] }, { "cell_type": "markdown", "id": "e743b77c", "metadata": {}, "source": [ "We now repeat the computation of the conversion between multipole-space and real-space and the convert to the aperture statistics." ] }, { "cell_type": "code", "execution_count": 14, "id": "d4b30d07", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 6.37 s, sys: 269 ms, total: 6.64 s\n", "Wall time: 771 ms\n" ] } ], "source": [ "%%time\n", "gnn.multipoles2npcf(xi=xi_corr)\n", "NNM_wcorr = gnn.computeNNM(radii_ap)" ] }, { "cell_type": "markdown", "id": "73f461aa", "metadata": {}, "source": [ "When comparing both results we see that the clustering-induced correction boosts the E-mode aperture statistics while it does not siginficantly affect the B-Mode." ] }, { "cell_type": "code", "execution_count": 15, "id": "ac8e630f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1e-08, 0.00010657315314739559)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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gCJoiEiHhZYhRY8UnEqFSoOkWoZcRnZLBhfBEzoclEhCeQFhcWr4yNexNaepqndfPqKo19uZ5PxD3n9zHL8oPvyg/rjy+Qq2kvFlhb1news7YjjZObWjr1JamlZpioGNQilclCOWfSISElyESoeITiVApKAuJ0H/FPs3kQngiAWGJXAhP5M7jp/nKVLU1oWV1Gzp7VKJpVWt0deQkpCWw89BOIp5EcEL3BGmKfxIqI10jWlZuSVuntrR2bI2VYf6p5gVBKBqRCAkvQyRCxScSoVJQFhOh/0pMy85LjP7uZ3Qr5gn//l+1MdHnnToV6eRuh+LRLeRyGU1bNCUwLhC/KD9ORJ0gNj1WVV4uk+Nl56XqV+Ri4VLq1yQI5YFIhISXIRKh4hOJUCl4HRKh/0pJz+FCRCLHbj3m0M0YktJzAJCjpKlRLNXsTOnQrg1v1bRHT0eOJEkEJwarHqHdTrytdj4XcxfaObejnVM76tnWQ0cu5rsQhJfxOidCfn5+DBkypMBFTYUXGzJkCC4uLsycOfOFZUUiVHwlkQiJnrLlkIWxHm+7V2D+u/W48GVHNg9vQt8mzlgZ65ORo+DGoxSGb7xIo2+OMmnHVfxC4qhh4cYor1Hs8NnB4XcPM63JNJpXao6uXJeIJxGsv7GeQX8Nov2O9nx95muORR4jIzfjxcEIglAuyGQyDA0NuX//vtr2nj17MmTIkBKtKyIiAplMhr29PU+fqj/69/Lyeqnkoij8/PyQyWRYWVnlW9/s4sWLyGQykZyUYyIRKuf0dOS0qmHHvN51OTu1Pb0bOFLPwQIbE31SMnLYEfiAoesv0uibI0zYfpXjtx9jbWhPP7d+rHpnFSf7nGRR60V0qdoFM30zEjMT2Xt3L+NOjKPDjg7MvzCfe8n3XhyIIAivPZlMxvTp00utvqdPn7J48eJSq8/MzIw9e/aobVu7di3Ozs6lFoNQ+kQi9AbR1ZFTz7UyvZvX4szUDvw2ohkDm1XB1tSAJ5m57Lr8gGEbLtHom6OM3xbE0eDH6MmM6VS1EwtaL8C/jz9r31nLALcBVDKpxNPsp2y5tYWe+3oy+K/BHAg7QJYiS9uXKQhlmyRBdpp2Xq/YE2L06NH88ssv3Lhxo9AyBw8e5K233sLS0hIbGxu6devGvXv//LH0rLVn69attGjRAkNDQzw8PPD39893rjFjxrBkyRJiY2Pz7Xtm8+bNNGrUCDMzMypWrEi/fv3Uyj9r7fnjjz+oV68ehoaGNGvWrMBrGDx4MOvWrVO9z8jIYOvWrQwePFit3LBhw6hXrx5ZWXn3u+zsbOrXr8+gQYMKjfNFdHR0xDIbWiJmln6D6Ojo4OXlpXrfvJoNzavZMLN7HS5FJPLn9Wj+uhFD7NMsdl95yO4rDzE10KWjmz1d6laidU07mlRqQpNKTZjUeBLnHp1j+53t+D/wV62LtuDCAnpW78l7Nd+jinkV7V2sIJRVOekwt7J26v7iEeibFPvwli1bEhISwtSpUzlw4ECBZdLS0hg/fjz16tUjNTWV6dOn06tXL4KCgpDL//nbe9KkSSxduhR3d3eWLFmCj48P4eHh2NjYqMr07duXI0eOMHv2bH788ccC68vJyWHOnDnUqlWL2NhYxo8fz5AhQ/jzzz/Vyk2aNIlly5ZRsWJFvvjiC3x8fAgJCUFPT09VZuDAgSxatIjIyEicnZ3ZtWsXLi4uNGjQQO1cy5cvx9PTk6lTp/L999/z5ZdfkpycXGiMLyKTyTA2Ni7WscKrE4lQIf49oWJ5pyOX0dTVhqauNszwqUNgZFJeUnQ9hpgnmewNesTeoEeY6OvQwa0CXepWpG0te1o6tKSlQ0sepz1m993d7ArZxeP0x2y4uYENNzfQtFJT3q/5Pu2d2qOno/fiQARBKPPmzZtHvXr1OHXqFK1atcq3/91331V7v27dOuzs7AgODsbDw0O1ffTo0aqyP/30EwcPHmTt2rVMnjxZVUYmkzF//nx8fHz4/PPPqVatWr76hg0bpvra1dWV5cuX07hxY1JTUzE1NVXtmzFjBm+//TYAGzduxNHRkT179vDBBx+oytjb29O5c2c2bNjA9OnTWbdundr5nzE1NeWXX36hTZs2mJmZsXTpUk6cOPHaDKgR1IlEqBCjRo1i1KhRql7nbwq5XEZjF2sau1jzdVd3rkQl8ef1GP66Hs2jlEz2X33E/quPMNbXoUvdSgxp4YKHQwU+9fyUEXVHcPrhaXaE7ODUg1MERAcQEB2AjaENvWr04t0a7+Jo5qjtSxQE7dIzzmuZ0Vbdr8jd3Z1BgwYxdepUzpw5k29/aGgo06dPJyAggPj4eJRKJQCRkZFqiVDz5s1VX+vq6tKoUSNu3bqV73ze3t689dZbfP311/z666/59gcGBjJz5kyuXr1KUlKSWn3u7u4F1mdtbU2tWrUKrG/YsGGMHTuWAQMGcO7cOXbs2MGpU6fylWvevDkTJ05kzpw5TJkyhbfeeqvA75dQ9olE6A2iUCg4f/48AM2aNXvh82i5XEbDKtY0rGLNl13cuPogmT+vR/Pn9RgeJmewM/ABOwMf0NjFiqEtq/KOewXaOrWlrVNbHqU+YlfoLnaH7iY+I54119ew9vpaWji04IOaH9DasTW6cvHjJ7yBZLJXejxVFsyaNYuaNWuyd+/efPt8fHyoUqUKq1evpnLlyiiVSjw8PMjOzi52ffPnz6d58+ZMmjRJbXtaWhre3t54e3uzZcsW7OzsiIyMxNvbu9j1de7cmZEjRzJ8+HB8fHzUHtX9m1Kp5MyZM+jo6HD37t1i1fWMJEmkpeVNcGtiYiJGqJUy0Vn6DZOTk0NOTk6Rj5PLZdR3tuLLru6cntKOXZ82p7tnZXTlMi5GJPHZlsu0XniCn/zukZSWTWXTyoypP4bD7x3m+7bf07xScyQkzjw8w9gTY/He5c2KoBXEpMVo4CoFQdAkJycnRo8ezRdffKHWfSAhIYE7d+7w1Vdf0aFDB9zc3EhKSirwHM/+KAPIzc0lMDAQNze3Ass2adKE3r17M3XqVLXtt2/fJiEhgfnz59OqVStq165daMfqf9eXlJRESEhIgfXp6uoyaNAg/Pz8Cnws9syiRYu4ffs2/v7+HDx4kPXr1xda9mVIkoSY1k87RCIkFJlMltdStLxvfc5Mbc+Y9tWxMdHnUUomCw7eptm8Y0zddY3bMU/Qk+vRsUpHVr2zij96/cFQj6FYG1oTmx7LT1d/wnuXN2OOj+Hkg5MolOW/P5YglBfTpk3j0aNHHD16VLXNysoKGxsbVq1axd27dzl+/Djjx48v8HhfX1/27NnD7du3GTVqFElJSc9NPL799luOHz/OnTt3VNucnZ3R19fnhx9+ICwsjP379zNnzpwCj589ezbHjh3jxo0bDBkyBFtbW3r27Flg2Tlz5hAXF4e3t3eB+69cucL06dNZs2YNLVu2ZMmSJYwdO5awsLBC4xfKLpEICa+kgrkhE96pxZmp7Vn8vid1KpuTlatk68UoOi09Rd9V5zl0MwaFUsLZ3JnxDcdz5L0jLGy9kMYVG6OUlPhF+THq2Ci67O7CqmuriEuP0/ZlCYLwAtbW1kyZMkVtAkK5XM7WrVsJDAzEw8ODzz//nEWLFhV4/Pz585k/fz6enp6cPn2a/fv3Y2trW2h9NWvWZNiwYWr12dnZsWHDBnbs2IG7uzvz588vdN6h+fPnM3bsWBo2bEhMTAy///47+vr6BZbV19fH1ta2wEdUmZmZDBgwgCFDhuDj4wPAyJEjadeuHQMHDnwjBtiUN2KJjRd4HZfYKIxCoVB1+mvVqpVG5qyQJIlL95PYcCaCg38nQACOVkYMbu7CB42csDD+ZwRZWEoYO0N2su/uPp5kPwFAV6ZLO+d2DK0zlLp2dUs8RkEoLWKJjfwiIiKoWrUqV65cUZvOQ1P8/Pxo164dSUlJWFpaary+Z8QSG6VDLLEhlDkyWd6oM9/+DTg5uR2ftq2GpbEeD5Iy+PbPWzSbd4yv9l7nbmzetPmuFq5MbjyZY+8fY+5bc/Gy8yJXyuXI/SP0+7Mfnx39jOtx17V8VYIgCEJ5JRIhQWMcLI2Y0qk256d1YH7vutSuaEZGjoJfzkfScclJBq4N4PjtxyiVEoa6hvhU82Fzl83s6r6LHtV6oCPT4dTDU/T7sx+jjo3iRnzhs9kKgiAIQnGIR2MvUN4ejQUFBQF5CxeW9nTukiRxLiyBDWciOHLrsWq2fxcbYwY1d+H9Ro6YGf7z2CzySSSrrq3iQNgBFFLec/c2jm341OtT6tjUKdXYBaE4XudHYxEREezdu5dx48ZpO5TX0t69e7G0tKRt27YvLCtJEunp6QAYGxuLR2NFUBKPxkQi9ALlKREqS6IS09l0LoKtF6N4mpkLgIm+Du83cmJQ8yq42v0zI2zkk0h+vvYzB8IOoJTyJktr69iWT70+xd3GvcDzC0JZ8DonQoLwOhCJkAb9e4mNkJAQkQhpSFpWLnuuPGTD2QjuxqaqtrerZcfo9jVoWMVKte3+k/v8fPVn/gj/45+EyKktn3l+hptNwfOPCII2iURIEDRLJEKlQLQIlQ5Jkjh9N54NZyI4fidW9djsbfcKTPauRY0KZqqy4SnhrLq2ij/D/1QlRO2c2vGZ12fUtq6tjfAFoUAiERIEzRKJUCkoT4mQQqHg4sWLADRu3LjU+wi9rIj4NH7yu8eOwCiUEshl0LuBI5+/XRMHSyNVubCUsLyEKOxPJPJ+jDs4d+BTz0+pZV1LW+ELgopIhISXIZbYKD4xfF4osszMTLUJycoiF1sTFrxXj8Oft8a7TgWUEuwMfEC7xX58cyCYpLS8NYRcLVyZ32o+e3vupXPVzsiQcSzyGO/9/h6fn/icO4l3XlCTIAhC2SCW2NAekQgJZVZ1ezN+HtiIPZ+1oJmrNdm5StacDqf1whP8eDyU9Oy8TtauFq4sbL2QvT320tklLyE6GnmU935/j/F+4wlJCtHylQiCIAhllUiEhDKvvrMVv41oxoahjXGrZM7TrFwWHw6h9UI/Np+LIEeR10/I1dKVhW0WsqfHHjq5dEKGjCP3j/Du/ncZ7zee0KRQLV+JIAhCfmvXrqVHjx7aDkPrNmzYoDb798qVK1XLmGiSSISE14JMJqNtLXv+GPMWyz70wtnamPjULL7ed5OOS/zZF/QQ5d/LeVSzrMaiNovY3X033i55iyYeuX+E3vt7M8FvAneT7mrzUgThtTBkyBBkMhnz589X2753716N9GFp27YtMpmMrVu3qm1funQpLi4uJV6fi4tLgfUB1KlTB5lMxoYNG0q83v/KzMxk+vTpTJs2TeN1acJ/k5eSNGzYMC5fvqxaGkpTRCIkvFbkchk9vBw4Or4Ns3vUwdZUn/sJ6YzdGoTPj6fxD4lTPWevblWdxW0Ws7v7bt6p8g4Ah+8fpvf+3kzyn0TU0yhtXooglHmGhoYsWLCApKSkUqvvq6++Iicnp1Tqc3JyYv369Wrbzp8/T0xMDCYmJqUSw86dOzE3N6dZs2YaqyM7O7vA7aX1fS4ufX19+vXrx/LlyzVaj0iEhNeSvq6cQc1d8J/UjvFv18TUQJebj54weN0F+q0OICgqWVW2hlUNvmv7Hbu67+LtKm8jIXEw4iA99/Zk2eVlpOWkae9CBKEM69ixIxUrVmTevHmFlklISKBv3744ODhgbGxM3bp1+e2339TKtG3bltGjRzN69GgsLCywtbXl66+/ztc5uG/fviQnJ7N69epC67t37x49evSgQoUKmJqa0rhxY44ePapWxsXFhTlz5tC3b19MTExwcHDA19c337n69++Pv78/UVH//FG0bt06+vfvj66urlrZJUuWULduXUxMTHBycuKzzz5TLZQK/7SM7N27lxo1amBoaIi3t7fauQuydetWunXrlm/7unXrqFOnDgYGBlSqVInRo0er9kVGRtKjRw9MTU0xNzfngw8+4PHjx6r9M2fOxMvLizVr1qiNppLJZPz00090794dExMTvv32WwD27dtHgwYNMDQ0xNXVlVmzZpGbm6s6X3JyMh9//DEVKlTA0NAQDw8PDhw4gJ+fH0OHDiUlJQWZTIZMJlMtMpuVlcXEiRNxcHDAxMSEpk2b4ufnp3aNGzZswNnZGWNjY3r16kVCQkK+74OPjw/79+8nIyPjud/HVyESoTeMsbExxsbG2g6jxJgY6PK/DjU4Obkdw9+qir6OnHNhCfT0PcOnvwSqTdJY06omS9ouYafPTppWakq2Mps119fgs8eHfXf3qeYkEgRNkiSJ9Jx0rbyKOipJR0eHuXPn8sMPP/DgwYMCy2RmZtKwYUP++OMPbty4wciRIxk4cCAXLlxQK7dx40Z0dXW5cOECy5YtY8mSJaxZs0atjLm5OV9++SWzZ89WDSf/r9TUVLp06cKxY8e4cuUKnTp1wsfHh8jISLVyixYtwtPTkytXrjB16lTGjh3LkSNH1MpUqFABb29vNm7cCEB6ejrbtm1j2LBh+eqVy+UsX76cmzdvsnHjRo4fP87kyZPVyqSnp/Ptt9+yadMmzpw5Q3JyMh9++GGB1/HM6dOnadSoEXK5HLk87yP5p59+YtSoUYwcOZLr16+zf/9+qlevDoBSqaRHjx4kJibi7+/PkSNHCAsLo0+fPmrnvXv3Lrt27WL37t2qpZUgL0nq1asX169fZ9iwYZw6dYpBgwYxduxYgoOD+fnnn9mwYYMqSVIqlXTu3JkzZ87wyy+/EBwczPz589HR0aFFixYsXboUc3NzoqOjiY6OZuLEiQCMHj2ac+fOsXXrVq5du8b7779Pp06dCA3N66sZEBDA8OHDGT16NEFBQbRr145vvvkm3/enUaNG5ObmEhAQ8Nzv4yuRhOdKSUmRACklJUXboQgvISoxTRq/LUhymXpAqjLlgOQ67Q9pys6rUnRyhlo5pVIpHbt/TOq8q7PkscFD8tjgIX34+4dSUGyQliIXyqOMjAwpODhYysj45+cvLTtN9TNX2q+07LSXjn3w4MFSjx49JEmSpGbNmknDhg2TJEmS9uzZI73oo6Nr167ShAkTVO/btGkjubm5SUqlUrVtypQpkpubm1qZsWPHSpmZmVKVKlWk2bNnS5IkSd9//71UpUqV59ZXp04d6YcfflC9r1KlitSpUye1Mn369JE6d+6sVub777+X9u7dK1WrVk1SKpXSxo0bpfr160uSJEkWFhbS+vXrC61zx44dko2Njer9+vXrJUA6f/68atutW7ckQAoICCjwHElJSRIgnTx5Um175cqVpS+//LLAYw4fPizp6OhIkZGRqm03b96UAOnChQuSJEnSjBkzJD09PSk2NlbtWEAaN26c2rYOHTpIc+fOVdu2efNmqVKlSpIkSdKhQ4ckuVwu3blzp8B41q9fL1lYWKhtu3//vqSjoyM9fPgwX13Tpk2TJEmS+vbtK3Xp0kVtf58+ffKdS5IkycrKStqwYUOB9Rf0O/bMy35+ixYhoVxxtDLmuw88OTi2NR3dKqBQSmy9GEWbRSeY99ctUtLznonLZDLaO7dnb4+9fN7wc4x1jbmRcIMBfw5g2qlpPE57/IKaBOHNsWDBAjZu3MitW7fy7VMoFMyZM4e6detibW2Nqakphw4dytdC06xZM7VO1s2bNyc0NBSFQqFWzsDAgNmzZ7N48WLi4+Pz1ZeamsrEiRNxc3PD0tISU1NTbt26la++5s2b53tfUPxdu3YlNTWVkydPsm7dugJbgwCOHj1Khw4dcHBwwMzMjIEDB5KQkKBaLBVAV1eXxo0bq97Xrl0bS0vLAusFVI97/j0RYGxsLI8ePaJDhw4FHnPr1i2cnJxwcnJSbXN3d89XT5UqVbCzs8t3fKNGjdTeX716ldmzZ2Nqaqp6jRgxgujoaNLT0wkKCsLR0ZGaNWsWGE9Brl+/jkKhoGbNmmrn9ff35969e6rraNq0qdpx//0/e8bIyEjt+1zSdF9cRBBeP7UqmrFmcCMuRSSy4OBtLkYk8bN/GL8FRPJJ22oMbVEVI30d9HX0GeYxjO7VurP88nL23t3LgbADHIs8xnCP4QyuMxhDXTEjsFByjHSNCOinwWb+F9RdHK1bt8bb25tp06YxZMgQtX2LFi1i2bJlLF26VNWHZty4cYV20H0ZAwYMYPHixXzzzTf5RoxNnDiRI0eOsHjxYqpXr46RkRHvvfdesevT1dVl4MCBzJgxg4CAAPbs2ZOvTEREBN26dePTTz/l22+/xdramtOnTzN8+HCys7OL3d3AxsYGmUym1hndyKh4/0f/VVhn7/9uT01NZdasWfTu3TtfWUNDw2LFk5qaio6ODoGBgflWMDA1NS3kqMIlJiYWmNSVFJEIvUEUCgWBgYEANGzYsMwusVGSGrlYs/3j5hy/HcvCg3e48/gpCw/eYePZCL7u5k7XupWQyWTYGtkyu+Vs+tTqw/wL8wmKC+LHoB/ZHbqb8Y3G806Vd8S090KJkMlkGOu9fv305s+fj5eXF7VqqS9fc+bMGXr06MGAAQOAvD4lISEhuLu7q5X7bx+P8+fPU6NGjQLvQ3K5nHnz5tG7d28+/fTTfPUNGTKEXr16AXkfuhEREfnOcf78+Xzv3dwKXpx52LBhLF68mD59+mBlZZVvf2BgIEqlku+++07Vj2f79u35yuXm5nLp0iWaNGkCwJ07d0hOTi60Xn19fdzd3bl58yYtW7YE8hIFFxcXjh07Rrt27fId4+bmRlRUFFFRUapWoeDgYJKTk/N9z19GgwYNuHPnjqoP0n/Vq1ePBw8eEBISUmCrkL6+fr5Wvfr166NQKIiNjaVVq1YFntfNza3An4n/unfvHpmZmdSvX/9lL6nIxKOxN0x6erpGmxjLIplMRge3Cvw5thVLPvDEwdKIx0+yGP3rFQavv8j9hH86ZdaxrcOmzptY2HohFYwr8CjtERP9JzL00FBuJ97W4lUIgnbVrVuX/v375xvKXKNGDY4cOcLZs2e5desWH3/8sdoIpmciIyMZP348d+7c4bfffuOHH35g7NixhdbXtWtXmjZtys8//5yvvmcdgK9evUq/fv1QKvMPdDhz5gwLFy4kJCQEX19fduzYUWh9bm5uxMfH5xtK/0z16tXJycnhhx9+ICwsjM2bN7Ny5cp85fT09BgzZgwBAQEEBgYyZMgQmjVrpkqMCuLt7c2ZM2dQKpWq65g5cybfffcdy5cvJzQ0lMuXL/PDDz8AeSP5nv1fXL58mQsXLjBo0CDatGmT77HXy5g+fTqbNm1i1qxZ3Lx5k1u3brF161a++uorANq0aUPr1q159913OXLkCOHh4fz1118cPHgQyBuhl5qayrFjx4iPjyc9PZ2aNWvSv39/Bg0axO7duwkPD+fChQvMmzePP/74A4D//e9/HDx4kMWLFxMaGsqPP/6oOue/nTp1CldXV6pVq1bka3tZIhES3hg6chm9GzhybEIbxnWsgb6OnJMhcbz9/UmWHwslKzfvrxqZTEbnqp35vdfvfOr5KYY6hgQ+DuSD3z9g5tmZJGTkH+IpCG+C2bNn50s6vvrqKxo0aIC3tzdt27alYsWK9OzZM9+xgwYNIiMjgyZNmjBq1CjGjh3LyJEjn1vfggUL8q2NuGTJEqysrGjRogU+Pj54e3vToEGDfMdOmDCBS5cuUb9+fb755huWLFmCt7d3oXXZ2NgU+hjI09OTJUuWsGDBAjw8PNiyZUuBUwoYGxszZcoU+vXrR8uWLTE1NWXbtm3Pvcbhw4fz559/kpKSoto2ePBgli5dyooVK6hTpw7dunVTjbaSyWTs27cPKysrWrduTceOHXF1dX1hPYXx9vbmwIEDHD58mMaNG9OsWTO+//57qlSpoiqza9cuGjduTN++fXF3d2fy5MmqVqAWLVrwySef0KdPH+zs7Fi4cCEA69evZ9CgQUyYMIFatWrRs2dPLl68iLOzM5DXZ2z16tUsW7YMT09PDh8+rEq+/u23335jxIgRxbq2lyVWny+Er68vvr6+KBQKQkJCys3q889m6GzVqtUb8WjsecLiUpm+7yan7+Z1yHS1M+GbHh60qG6rVi46NZrvA7/nr4i/ADDVM+UTz0/oV7sfejp6pR638PoQq8/nadu2LV5eXixdurRU6nNxcWHcuHGMGzeuVOqDvDlxxo0bR3JycpGPff/996lTpw4TJkzA1NRUPIb/282bN2nfvj0hISFYWFgUWEasPq9Bo0aNIjg4mIsXL2o7FEFDXO1M2Ty8Ccs+9MLW1ICwuDT6rQng821BxD3NUpWrZFqJhW0WsrHTRtys3UjNSWXxpcX03t+bkw9OihWjBUF4JQsXLiy1maxfJ9HR0WzatKnQJKikiERIeKPJZHlLdhyb0IaBzaogk8GeKw/p8J0fWwLuq9YvA2hQoQFbu21ldovZ2BjaEPEkglHHRvHpsU8JSw7T4lUIgvA6c3Fx4ZNPPtF2GGVOx44dn/s4s6SIR2Mv8LJNa68D8WjsxYKikvlyz3VuPnoCQH1nS77tWRf3yur/96nZqay6vorNwZvJVeaiI9Ohb+2+fOL5CRYGmv3rRXh9iEdjwsuQJEm1XId4NFY04tGYUGSGhobihvwcXk6W7BvVkund3DE10OVKZDI+P57mmwPBpGb9s/aOqb4p4xuOZ1+PfbRzaodCUvDLrV/otqcb225vI1eZ+5xaBEEQ1D1bq0sofaJF6AXKU4uQUDQxKZnMORDMH9ejAahkYcgMnzp416mQ74Z19tFZFl5YyL2UvFlTa1rV5OtmX+Nl71XaYQtliGgREgTNEi1CgqBBFS0M8e3fgPVDG+NkbUR0Siaf/BLIRxsvEZWoPhdTi8ot2Nl9J180/QJzfXNCkkIY+NdAZp2bRUpWSiE1CIIgCNomEiFBeIF2tew5PK4No9tVR09HxrHbsbz9vT8r/O6SnfvPnCq6cl361u7LgV4H6Fm9JwA7Q3bSfW93fr/3uxhdJgiCUAaJROgN8myJjcDAwHxTogvPZ6Svw0TvWvw1thVNq1qTmaNk4cE7dF1+igvhiWplrQytmNNyDuu911PNohqJmYl8cfoLPjr8EeEp4Vq6AkEQyipJkkhLSyMtLU38waQFIhF6wzx9+pSnT59qO4zXVnV7M7aObMZ373tibaJPaGwqH/x8jkk7rpKYpr7oY6OKjdjhs4OxDcZiqGPIhZgLvLv/XX688iOZuZmF1CAIwpvo30tsCKVLJEKCUEQymYx3GzpyfEIb+jbJW/RwR+AD2n/nx/aLUWpzD+np6PFR3Y/Y02MPbzm8RY4yh5+v/Uzv/b05+/Csti5BEARB+JtIhAShmCyN9ZnXux67Pm1O7YpmJKfnMHnXNfqsOkfIY/VWN0czR1Z0WMGStkuwN7In6mkUHx/9mEn+k4hLj9PSFQhC4fz8/HBxcdF2GK+1IUOGMHPmzBeWW7t2LT169NB8QGXchg0bsLS0VL1fuXIlPj4+Gq9XJEKC8IoaVrHm9zFv8UWX2hjp6XAxIomuy0/x4/FQchX/NHXLZDLervI2+3vtZ4DbAOQyOQcjDtJ9b3d+u/0bCqXotyWUbTKZDENDQ+7fv6+2vWfPngwZMqRE64qIiEAmk2Fvb5/vcb6Xl9dLJRhF4efnh0wmw8rKKt9CrxcvXtTYPD+ZmZlMnz6dadOmlfi5S8N/k5eSNGzYMC5fvqyaCFhTRCIkCCVAT0fOyNbVODqhDR3d7MlRSCw+HELvn84S+p/WIRM9E6Y0mcLWrlvxsPEgNSeVuQFz6f9nf4ITgrV0BUJpkSQJZXq6Vl4l0RFXJpMxffr0EvhOvJynT5+yePHiUqvPzMyMPXv2qG1bu3atatX0krZz507Mzc1p1qyZRs4PkJ2dXeD2nJwcjdVZEvT19enXrx/Lly/XaD0iERKEEuRgacTqQY1Y8oEn5oa6XHuQQtflp1npfw+FUv1DyM3GjV+6/MKXTb/EVM+Umwk36ftHX+ZfmE9qdqqWrkDQNCkjgzsNGmrlJWVkvHL8o0eP5pdffuHGjRuFljl48CBvvfUWlpaW2NjY0K1bN+7du6fa/6y1Z+vWrbRo0QJDQ0M8PDzw9/fPd64xY8awZMkSYmNjC61v8+bNNGrUCDMzMypWrEi/fv3Uyj9r7fnjjz+oV68ehoaGNGvWrMBrGDx4MOvWrVO9z8jIYOvWrQwePFit3LBhw6hXrx5ZWXkLNGdnZ1O/fn0GDRpUaJwF2bp1K926dcu3fd26ddSpUwcDAwMqVarE6NGjVfsiIyPp0aMHpqammJub88EHH/D48WPV/pkzZ+Ll5cWaNWvUJhqUyWT89NNPdO/eHRMTE7799lsA9u3bR4MGDTA0NMTV1ZVZs2aRm/vP7PjJycl8/PHHVKhQQfV/deDAAfz8/Bg6dCgpKSmqFrNnLXVZWVlMnDgRBwcHTExMaNq0KX5+fmrXuGHDBpydnTE2NqZXr14kJCTk+z74+Piwf/9+MkrgZ7cwIhF6w+jp6aGnp6ftMMo1mUxG7waOHP68De1q2ZGtUDL/r9u8t/Is9+LUExwduQ4f1v6Q33v9TueqnVFKSrbc2kL3vd05FHFIDKUVypyWLVvSrVs3pk6dWmiZtLQ0xo8fz6VLlzh27BhyuZxevXrlGxU1adIkJkyYwJUrV2jevDk+Pj75Pgz79u1L9erVmT17dqH15eTkMGfOHK5evcrevXuJiIgo8FHdpEmT+O6777h48SJ2dnb4+PjkaxUZOHAgp06dIjIyEoBdu3bh4uJCgwYN1MotX76ctLQ01ffhyy+/JDk5mR9//LHQOAty+vRpGjVqpPbo7aeffmLUqFGMHDmS69evs3//fqpXrw7kjS7r0aMHiYmJ+Pv7c+TIEcLCwujTp4/aee/evcuuXbvYvXs3QUFBqu0zZ86kV69eXL9+nWHDhnHq1CkGDRrE2LFjCQ4O5ueff2bDhg2qJEmpVNK5c2fOnDnDL7/8QnBwMPPnz0dHR4cWLVqwdOlSzM3NiY6OJjo6mokTJwJ5CfO5c+fYunUr165d4/3336dTp06EhoYCEBAQwPDhwxk9ejRBQUG0a9eOb775Jt/3p1GjRuTm5hIQEFCk72uRSEUUGBgoXbt2TfV+7969Uo8ePaRp06ZJWVlZRT1dmZeSkiIBUkpKirZDEV5DSqVS2nYxUvKYflCqMuWAVPPLP6XVJ+9JuQplgeXPPDwjddnVRfLY4CF5bPCQPjnyiRT5JLKUoxZKSkZGhhQcHCxlZGSotimVSkmRlqaVl1JZ8M9dQU6cOCFVqVJFbRsg7dmzR7p586ako6MjnTx5UpIkSerRo4c0ePDgQs8VFxcnAdL169clSZKk8PBwCZDmz5+vKpOTkyM5OjpKCxYsUCtz5coV6eDBg5Kenp509+5dSZIkydPTU5oxY0ah9V28eFECpKdPn6quBZC2bt2qKpOQkCAZGRlJ27ZtUyuTlJQk9ezZU5o1a5YkSZLUrl07admyZdKePXuk/35knj17VtLT05O+/vprSVdXVzp16pTa/sGDBz83zqSkJAlQfR+fqVy5svTll18WeMzhw4clHR0dKTLyn/vCzZs3JUC6cOGCJEmSNGPGDElPT0+KjY1VOxaQxo0bp7atQ4cO0ty5c9W2bd68WapUqZIkSZJ06NAhSS6XS3fu3CkwnvXr10sWFhZq2+7fvy/p6OhIDx8+zFfXtGnTJEmSpL59+0pdunRR29+nT59855IkSbKyspI2bNhQYP0F/Y4987Kf30VuEfr4448JCQkBICwsjA8//BBjY2N27NjB5MmTSyI3E4RyQyaT8UEjJw593ppWNWzJylXyzR+36PPzOcLj0/KVb1G5Bbt77OZTz0/Rk+tx+uFpeu3rxeprq8lRlO3n+cLLkclkyI2NtfIqqc6+7u7uDBo0qNBWodDQUPr27Yurqyvm5uaq0WfPWlmead68ueprXV1dGjVqxK1bt/Kdz9vbm7feeouvv/66wPoCAwPx8fHB2dkZMzMz2rRp88L6rK2tqVWrVoH1DRs2jA0bNhAWFsa5c+fo379/gfU2b96ciRMnMmfOHCZMmMBbb71VYLnCPHvc8+81smJjY3n06BEdOnQo8Jhbt27h5OSEk5OTapu7uzuWlpZq11KlShXs7OzyHd+oUSO191evXmX27NmYmpqqXiNGjCA6Opr09HSCgoJwdHSkZs2aL31d169fR6FQULNmTbXz+vv7qx6R3rp1i6ZNm6od9+//n38zMjIiPT29wH0lociJUEhICF5eXgDs2LGD1q1b8+uvv7JhwwZ27dpV0vEJQrlQ2dKITcOaMK93XUz0dbh0P4nOy06y4Uy42rxDAAY6Bnzm9Rm7uu+iacWmZCmyWH5lOe/9/h4XYy5q6QoEQd2sWbO4fPkye/fuzbfPx8eHxMREVq9eTUBAgOqxRmGddl/G/Pnz2bZtG1euXFHbnpaWhre3N+bm5mzZsoWLFy+qOjsXt77OnTuTkZHB8OHD8fHxwcbGpsBySqWSM2fOoKOjw927d4tcj42NDTKZjKSkJNU2IyOjYsX8XyYmJi+1PTU1lVmzZhEUFKR6Xb9+ndDQUAwNDYsVT2pqKjo6OgQGBqqd99atWyxbtqzI50tMTCwwqSspRU6EJElSPec9evQoXbp0AcDJyYn4+PiSjU4oUQqFQvUDKZbYKH0ymYy+TZw59HlrWlSzITNHyczfg+m7+jyRCfn/2qlqUZXV76xmXqt5WBtaE5YSxrBDw/jy9JckZiYWUIMglB4nJydGjx7NF198oXY/SUhI4M6dO3z11Vd06NABNzc3tQ/6fzt//rzq69zcXAIDA3FzcyuwbJMmTejdu3e+Vqjbt2+TkJDA/PnzadWqFbVr1y60Y/W/60tKSiIkJKTA+nR1dRk0aBB+fn4MGzas0O/BokWLuH37Nv7+/hw8eJD169cXWrYg+vr6uLu7c/PmTdLT00lPT8fU1BQXFxeOHTtW4DFubm5ERUURFRWl2hYcHExycjLu7u5Fqh+gQYMG3Llzh+rVq+d7yeVy6tWrx4MHD1RPggq6hv9+ntSvXx+FQkFsbGy+c1asWFF1Hf/t9/Pv/59n7t27R2ZmJvXr1y/ytb2sIidCjRo14ptvvmHz5s34+/vTtWtXAMLDw6lQoUKJByiUrOTkZJKTk7UdxhvN0cqYX4Y3ZU5PD4z1dQgIT6TTspNsPn8/X+uQTCajm2s39vfczwc1P0CGjP339tN9b3f2hO4RnakFrZo2bRqPHj3i6NGjqm1WVlbY2NiwatUq7t69y/Hjxxk/fnyBx/v6+rJnzx5u377NqFGjSEpKem7i8e2333L8+HHu3Lmj2ubs7Iy+vj4//PADYWFh7N+/nzlz5hR4/OzZszl27Bg3btxgyJAh2Nra0rNnzwLLzpkzh7i4OLy9vQvcf+XKFaZPn86aNWto2bIlS5YsYezYsYSFhRUaf0G8vb05c+YMCoVClVDMnDmT7777juXLlxMaGsrly5f54YcfAOjYsSN169alf//+XL58mQsXLjBo0CDatGmT77HXy5g+fTqbNm1i1qxZ3Lx5k1u3brF161a++uorANq0aUPr1q159913OXLkCOHh4fz1118cPHgQABcXF1JTUzl27Bjx8fGkp6dTs2ZN+vfvz6BBg9i9ezfh4eFcuHCBefPm8ccffwDwv//9j4MHD7J48WJCQ0P58ccfVef8t1OnTuHq6kq1atWKfG0v7bk9iApw9epVycPDQzI3N5dmzpyp2j569Gipb9++RT1dmVeeOkvn5uZKJ06ckE6cOCHl5uZqOxxBkqT78WnSByvPSlWmHJCqTDkg9Vt9TopKTCu0fFBskNR7X29VZ+rBfw2W7iXdK8WIhaJ4XkfOsu55naX/be7cuRKg1ln6yJEjkpubm2RgYCDVq1dP8vPzUzv2WUfoX3/9VWrSpImkr68vubu7S8ePH1ed49+dpf9t5MiREqDWCfnXX3+VXFxcJAMDA6l58+bS/v371Y591hH6999/l+rUqSPp6+tLTZo0ka5evap2vfzdWbog/+4snZGRIbm7u0sjR45UK9O9e3epRYsWqvvrizpLS1JeR2cjIyMpKipKevLkiapD+8qVK6VatWpJenp6UqVKlaQxY8aojrl//77UvXt3ycTERDIzM5Pef/99KSYmRrV/xowZkqenZ766Cvr/kyRJOnjwoNSiRQvJyMhIMjc3l5o0aSKtWrVKtT8hIUEaOnSoZGNjIxkaGkoeHh7SgQMHVPs/+eQTycbGRu3/JTs7W5o+fbrk4uKiuoZevXqpDbZau3at5OjoKBkZGUk+Pj7S4sWL83WWfuedd6R58+YV+v0ric7Ssr+/Oa8sMzMTHR2dMjk028XFBXNzc+RyOVZWVpw4ceKlj33y5AkWFhakpKRgbm6uwSg1T6FQqGbobNWqFTo6OlqOSABQKiU2nYtg/sHbZOYoMdHX4atu7nzY2KnAzq05yhy2BG9hxdUVZORmoCvXZbjHcEbUG4GBjoEWrkAoTGZmJuHh4Wpzubwu/Pz8GDJkCBERESV+7oiICKpWrcqVK1dUfU41yc/Pj3bt2pGUlKSxWZALMmTIEFxcXF44C/b7779PnTp1mDBhAqamphqZwfp1dPPmTdq3b09ISAgWFhYFlnne79jLfn4X+dHYxYsXCxzPf/XqVa5evVrU05Was2fPEhQUVKQkSBBKg1wuY0jLqhwc25pGVaxIy1Ywbfd1Bq+/yKPk/JOI6cn1GOIxhL099tLasTW5yty8hVz39ebco3NauAJBEF7FwoULC+3c/CaLjo5m06ZNhSZBJaXIidCoUaPUOmk98/DhQ0aNGlUiQQnCm8jF1oRtHzfnq65uGOjKORkSh/f3J9l+KarAvkCVTSvzY/sfVQu5Rj6NZOSRkUw7NY2EjPwztAqCUDa5uLjwySefaDuMMqdjx46F9tEqSUVOhIKDg/PNsAl5vcSDg4u+TtLJkyfx8fGhcuXKyGSyAodi+vr64uLigqGhIU2bNuXChQtFqkMmk9GmTRsaN27Mli1bihyjIJQWHbmMj1q58ufYVtR3tuRpVi6Td15j2IaLPH6Sma/8s4Vc9/XcR7/a/ZAh40DYAbrv7c6ukF0oJWUBtQjCi7m4uDBu3DiNnVuSpFJ5LAbQtm1bJEkq1cdikLcYbdu2bUu1TqHoipwIGRgYqK1p8kx0dDS6urpFDiAtLQ1PT098fX0L3L9t2zbGjx/PjBkzuHz5Mp6ennh7e6sNj/Ty8sLDwyPf69GjR0DeFOaBgYHs37+fuXPncu3atSLHWV7I5XLkcrGySllXzc6UnZ+0YFrn2ujryjlxJ463l/iz+/KDAluHTPVNmdZ0Glu6bKG2dW2eZD9h5rmZDD04lHvJ9wqoQRCeT5OJ0JtCJEKvhyJ3lu7bty/R0dHs27dP9dwuOTmZnj17Ym9vz/bt24sfjEzGnj171IYzNm3alMaNG6vWb1EqlTg5OTFmzJjnrnVTmEmTJlGnTp0C16GBvIXini2iB3mdrZycnMpFZ2nh9RT6+CkTd1zl6oMUADq6VWBubw/szQrufJurzGXLrS34BvmqOlMPrTOUkfVGYqj7enXYfd0968hZpUoVjI2NtR2OIJQ76enp3L9//5U6Sxc5EXr48CGtW7cmISFBNcFRUFAQFSpU4MiRI2rTfhfVfxOh7OxsjI2N2blzp1pyNHjwYJKTk9m3b98Lz5mWloZSqcTMzIzU1FTatGnDypUrady4cYHlZ86cyaxZs/JtF4mQoE25CiU/nwxj6dEQchQSVsZ6zOtdl04elQo9Jjo1mrkBc/F74AeAo6kjXzf7mhYOLUopakGpVBIaGoqOjg52dnbo6+uLEUGCUAIkSSI7O5u4uDgUCgU1atTI97RDY4kQ5CUXW7Zs4erVqxgZGVGvXj369u37ykPn/5sIPXr0CAcHB86ePau2BsnkyZPx9/d/qdVow8LC6NWrF5A3fHzEiBGMHTu20PKiRUgoy27HPGH8tqsERz8BoHcDB2Z2r4O5YcG/e5IkcTzyOHMvzCU2Pe9xcpeqXZjUeBK2RralFvebLDs7W7VukyAIJcvY2JhKlSqhr6+fb9/LJkJF79RD3lolI0eOLM6hpc7V1bVIw/oNDAwwMCifc7EolUpu3LgBgIeHh+gr9BqqXdGcvaNasuxYCD/53WP35YcEhCWy+H1PmlfLvx6STCajQ5UONKvcjB+v/Mivt3/lz/A/OfXwFJ83/Jx3a7yLXCZ+DjRJX18fZ2dncnNzxdI2QoGetRwCBbZsCAXT0dFBV1f3lVtZXyoR2r9/P507d0ZPT4/9+/c/t2z37t1fKaB/s7W1RUdHJ1/n7MePH6vWKxFeniRJJCYmqr4WXk/6unImedemfW17Pt92lcjEdPqtOc/wllWZ6F0LQ738E2Wa6JkwpckUurl2Y9a5WdxKvMXsc7PZf3c/05tPp4ZVDS1cyZtDJpOhp6dXJiecFbRPoVCo1mMzMDAQk92WspdKhHr27ElMTAz29vaFrssCeb/sJfkXj76+Pg0bNuTYsWOqepVKJceOHWP06NElVk9BfH198fX1FX/BCWVWwyrW/DW2Fd/8cYvfLkSy5nQ4J0Pj+L6PF3UqFzwBWR3bOvza9Ve23t7KD1d+ICguiA9+/4DBdQbzsefHGOmWzMrXgiAIr4uXan9TKpXY29urvi7sVZykITU1VbUiOuQt3hoUFERkZCQA48ePZ/Xq1WzcuJFbt27x6aefkpaWxtChQ4tcV1GMGjWK4OBgLl68qNF6BOFVmBjoMq93XdYOboStqQEhj1Pp6XsG3xN3USgLbvXTlesywH0A+3ruo71Te3KlXNbeWEuvfb04/fB0KV+BIAiCdhX5QeSmTZvUOhM/k52dzaZNm4ocwKVLl6hfv75qBNr48eOpX78+06dPB6BPnz4sXryY6dOn4+XlRVBQEAcPHhQr3QvCv3Rwq8Chca3wrlOBHIXEokN36PPzOSITCu+gW9GkIsvaL2NZu2VUMK7Aw9SHfHr0Uyb5T1J1rBYEQSjvijxqTEdHh+joaFUL0TMJCQnY29uXu0dJYtFV4XUiSRK7Lj9k5v6bpGblYqyvw9fPWcD1mbScNHyDfNlyawtKSYmxrjGfen5Kf7f+6OmIfi2CoEni3qwZGlt0VZKkAm+oDx480PjCaIIgPJ9MJuO9ho4cHNeKplWtSf97AdePNl4i7mn+ltxnTPRMmNx4Mr91/Y16tvVIz03nu8DvePf3dzn76GwpXoEgCELpeunh8/Xr10cmk+UNx+3QQW05DYVCQXh4OJ06ddJIkNogOksLrzNHK2N+G9GMtafDWXToDsdux+K99CRze9Wlk0fhIy7dbdzZ3GUz++/t5/vA7wlPCefjIx/T0bkjkxpPorJp5VK8CkEQBM176Udjz2ZbnjVrFhMmTMDU1FS1T19fHxcXF959990CJzV6nZWnR2PCm+l2zBM+33aVW39PwvheQ0dm+LhjVsgkjM88yX7CT0E/8dvt31BICgx0DBhedzhD6wwVS3UIglDmaWxm6Y0bN/Lhhx+W20kH/0skQkJ5kJWrYOnRUFb630OSwMHSiO8+8KSZa/5JGP8rJCmEeQHzuPT4EgAOpg5MaTyFtk5txXIRgiCUWRpLhKKiopDJZDg6OgJw4cIFfv31V9zd3V+b2aaLQiRCQnlyMSKR8duDiErMQCaDEa1cmfBOTQx0n985U5IkDkUcYtGlRaoRZW85vMXUJlOpYl6lNEIXBEEoEo11lu7Xrx8nTpwAICYmho4dO3LhwgW+/PJLZs+eXfyIBY1TKpXcvHmTmzdvolQqtR2OoAWNXaz5a2xrPmzshCTBqpNh9PjxDMGPnjz3OJlMRqeqnfi95+8M9xiOrlyX0w9P02tfL5YGLiU9R6yjJQjFJe7N2lXkROjGjRs0adIEgO3bt1O3bl3Onj3Lli1b2LBhQ0nHpzW+vr64u7sXukr960iSJOLi4oiLixNLbLzBTA10mf9uPVYPaoStqT63Y57Sw/c0P/ndK3QSxmeM9YwZ13Ace7rvoaVDS3KUOay9sRafvT4cDD8ofq4EoRjEvVm7ipwI5eTkqPoHHT16VLW2WO3atYmOji7Z6LRIzCwtlHdvu1fg0LjWvOOeNwnjgoO3+XDVOaISX9y642Lhwk8dfmJ5u+U4mDoQmx7LpJOTGH54OKFJoaUQvSAIQskociJUp04dVq5cyalTpzhy5IhqyPyjR4+wsXlxx0tBEMoOG1MDfh7YkIXv1cPUQJeLEUl0WnqSXwMiX/iXqUwmo51zO/b22MtnXp9hoGPAxZiLvP/7+yy4sIAn2c9/3CYIglAWFDkRWrBgAT///DNt27alb9++eHp6Ankr1D97ZCYIwutDJpPxQSMn/hrbiiYu1qRlK/hiz3UGrr3Ag6QXtw4Z6hryqeen7Ou5j47OHVFICn659Qs+e3zYe3cvSkn0eRAEoewq8qgxyJtA8cmTJ1hZWam2RUREYGxsnG/pjdddeRo1JqZxF15EoZTYcDaCRYduk5mjxERfhy+6utGvifNLD5U/+/As8y7MI+JJBAD17OrxRdMvqGNTR4ORC8LrS9ybNUNjo8Ygb72xfydBAC4uLuUuCRKEN42OXMbwt6ry19jWNHaxIi1bwZd7bjBgbcBL9R0CaOHQgt3ddzO+4XiMdY25FneNvgf6MuvcLJIykzR8BYIgCEXzUi1CDRo04NixY1hZWamW2ijM5cuXSzRAbfn3EhshISGiRUh44yj/bh1a+K/WoWld8lqH5PKXax2KTY9lSeAS/gj7AwBzfXPG1B/DuzXfRU8uFnMVBBD3Zk0p0QkVZ82axaRJkzA2NmbmzJnPTYRmzJhRvIjLqPL0aEySJNUcFXK5XMwKLLyUiPg0Ju+8xoWIRABaVLNhwbv1cLI2fulzXIq5xLwL8whJCgHAxdyFsQ3G0sG5g/g5FN544t6sGRqbWfpNU54SIUEoLqVSYtO5CBYcvENGjgJjfR2mda5N/6ZVXrp1KFeZy46QHfwU9BNJWXmPyDztPBnfcDwNKjTQZPiCILyBNJYIubq6cvHixXxD5ZOTk2nQoAFhYWHFi7iMEomQIPzjfkIak3Ze40J4XutQc1cbFr5XtNah1OxU1t9cz+bgzWTkZgDQ1qkt4xqMo5plNY3ELQjCm0djiZBcLicmJiZfx+jHjx/j5OREdnZ28SIuo8pTIqRUKgkJyXs0UbNmTeTyYvWVF95wBbUOTe1cmwFFaB0CiEuPY8XVFewJ3YNCUiCXyelZvSefeX5GBZMKGrwCQShbxL1ZM0o8Edq/fz8APXv2ZOPGjVhYWKj2KRQKjh07xpEjR7hz584rhl62lKdESHTIE0rS/YS8vkMBf7cONa1qzaL3PHG2efnWIYCwlDCWBS7jeNRxAAx1DBngPoBhHsMw0zcr8bgFoawR92bNKPFE6FmGKpPJ8s04q6enh4uLC9999x3dunV7hbDLHpEICULhlEqJXwLuM+/P22TkKDDSy2sdGtisaK1DAEGxQSwJXMKV2CsAWBhYMLLuSD6s/SH6OvqaCF8QygRxb9aMEp9HSKlUolQqcXZ2JjY2VvVeqVSSlZXFnTt3ylUSVB4XXRWEkiaXyxjU3IVD41rTzNWajBwFM/bf5MPV57mfkFakc3nZe7Gx00aWtVtGVYuqpGSlsOjSIrrv7c6BsANihmpBEDRCjBp7AdEiJAgvR6mU2BJwn3l/3SY9O691aHKnWgxu7lLk1qFcZS777u5jRdAKYjNiAXCzdmNcw3G0qNxCE+ELgtaIe7NmaHT4fFpaGv7+/kRGRubrHP2///2v6NGWYSIREoSiiUpMZ/LOa5wLSwCgiYs1C9+rh4utSZHPlZGbwS/Bv7DuxjpSc1IBaF6pOeMajsPdxr1E4xYEbRH3Zs3QWCJ05coVunTpQnp6OmlpaVhbWxMfH69aZ0wMny+7xC+bUFqUSoktFyKZ9+ct0rMVGOrJmexdmyEtit46BJCUmcSqa6vYemcrucpcALpU7cKY+mNwNHMs6fAFoVSJe7NmaGytsc8//xwfHx+SkpIwMjLi/Pnz3L9/n4YNG7J48eJXCloQhPJBLpcxsFkVDo1rTYtqNmTmKJl9IJgPV50nIr5ofYcArAytmNJkCr/3/J0uVbsA8Gf4n/js9WHBhQViDTNBEIqtyC1ClpaWBAQEUKtWLSwtLTl37hxubm4EBAQwePBgbt++ralYtaI8tQhJkkROTg6QN9JPTOMulAZJkvj1QiRz/7hFWrYCA105Y9pXZ0RrVwx0i/eXb3BCMN8Hfs/56PMAmOqZMsxjGAPcB2Cka1SS4QuCxol7s2ZorEVIT09PNZTe3t6eyMhIACwsLIiKiipmuEJpkMlk6Ovro6+vL37RhFIjk8no37QKB8e15q3qtmTlKll8OITOy05x5m58sc7pbuPO6ndW8/PbP1PbujapOaksv7Kcbru7sf3OdrIV5WtiV6F8E/dm7Spyi9A777zDkCFD6NevHyNGjODatWv873//Y/PmzSQlJREQEKCpWLWiPLUICYK2SZLE/quPmHPgFvGpWQB096zMV13dsDc3LNY5lZKSP8P/5McrP/Iw9SEA9sb2DKkzhHdrvIuxXtEmeBQEoXzQWGfpS5cu8fTpU9q1a0dsbCyDBg3i7Nmz1KhRg7Vr1+Ll5fWqsZcp5SkRUiqV3L17F4Dq1auLadwFrUnJyGHJ4TtsPn8fpQRmBrpMeKcmA5u7oFOMztQA2YpsdoTsYN2NdcSm5w25tzKwYqD7QD6s/aGYpVoos8S9WTPE6vOvyNfXF19fXxQKBSEhIeUiERIjE4Sy5vqDFL7ae52rD1IAqFPZnG971cXLybLY58xWZLP/3n7WXl/Lg9QHAJjpmfFh7Q8Z6D4QK0OrkghdEEqMuDdrhsb6CLVv357k5OQCK2zfvn1RT1dmjRo1iuDgYC5evKjtUASh3KrraMHuz1ryTU8PzA11ufnoCb1WnOGLPddJSc8p1jn1dfR5r+Z7/N7rd+a+NRdXC1ee5jxl9fXVeO/yZtHFRaoWI0EQhCInQn5+fgWuMJ+ZmanKaAVBEF6WjlzGgGZVOD6xLe82cESS4NeASNp/58fOwAf51jZ8WbpyXXyq+bCnxx6+b/s9btZuZORmsCl4E512dWLOuTk8ePqghK9GEITXje7LFrx27Zrq6+DgYGJiYlTvFQoFBw8exMHBoWSjEwThjWFrasB3H3jyQSNHvtp7g9DYVCbuuMr2i1HM6elBrYrF6+Mjl8npWKUjHZw7cPrhaVZfX82V2CtsD9nOrtBddHXtyvC6w3G1cC3hKxIE4XVQpNXnnw3rK+gQIyMjfvjhB4YNG1ayEWpZeeosLZ5DC6+LHIWStafDWXY0lIwcBbpyGcPfqsr/OtTAxOCl/34r1KWYS6y6topz0ecAkCGjY5WOjKw3ktrWtV/5/IJQFOLerBkl3ln6/v37SJKEq6srFy5cwM7OTrVPX18fe3v7cvmfJxIhQdCeh8kZzP79JoduPgagsoUh033q4F2nQonMt3Ij/garrq3iRNQJ1bZWDq0YWW8kXvZer3x+QXgZ4t6sGWLUWAkRiZAgaN+xW4+Zsf8mD5IyAGhXy45Z3T1wtimZOYJCkkJYc30NhyIOoZSUADSp2IQR9UbQtGJTMcmdoFHi3qwZGkuENm7ciK2tLV27dgVg8uTJrFq1Cnd3d3777TeqVKnyapGXMeUpEZIkiaysvEnsDAwMxM1deK1kZCvwPXGXn0/eI0chYaArZ3S76oxsU/ylOv7r/pP7rLuxjv339qsWd61nW48R9UbQxrGN+J0RNELcmzVDY4lQrVq1+Omnn2jfvj3nzp2jQ4cOLF26lAMHDqCrq8vu3btfOfiypDwlQoJQHtyLS+XrvTc4ey8BAFdbE2b38OCtGrYlVkd0ajTrb65nd+hushR5H1A1rWoyou4I3q7yNjpy8Re7IJR1GkuEjI2NuX37Ns7OzkyZMoXo6Gg2bdrEzZs3adu2LXFxca8cfFkiEiFBKHueLdXxzR+3iHual6j4eFbm61dYqqMg8RnxbArexLbb20jPTQegkkkl3q/5Pr1q9MLWqOSSL0EQSpbGJlQ0NTUlISHvL7HDhw/z9ttvA2BoaEhGRkYxwxVKg1Kp5N69e9y7dw+lUqntcASh2GQyGT28HDg2oQ1DWrggl8HvVx/R/jt/1pwKIytXUSL12BrZMr7heA6/d5jPPD/DwsCC6LRoll9Zzts732byyckEPg4s9lxHggDi3qxtRW4R6t+/P7dv36Z+/fr89ttvREZGYmNjw/79+/niiy+4ceOGpmLVivLUIiQ65Anl1Y2HKXy59wZXo5IBcLI2YrJ3bbrWrYS8mGuXFSQzN5NDEYfYfmc71+L/mVutumV1+tTqQzfXbpjqm5ZYfcKbQdybNUNjLUK+vr40b96cuLg4du3ahY2NDQCBgYH07du3+BGXMb6+vri7u9O4cWNthyIIwgt4OFiw59MWzO9dFzszA6ISMxjz2xV6rjjDub/7EpUEQ11DelTvwZauW9jWbRvv1ngXQx1D7ibf5duAb+mwowPfnP+GkKSQEqtTEATNEsPnX0C0CAnC6yU9O5c1p8L52f8eadl5j8ja17Znaufa1KxQ8ivQP8l+wv67+9l2ZxsRTyJU2xvYN6BPrT50rNIRfR39Eq9XKD/EvVkzxDxCJUQkQoLweopPzWL5sVB+DYgkVykhl8H7DZ34/O2aVLQouQ7Vz0iSxIWYC2y7s43jkcdRSHlJmLWhNb1r9Oa9mu/hYCqWIRLyE/dmzRCJUAkRiZAgvN7C4lJZdOgOf93IWx/RUE/OR2+58nEbV8wM9TRS5+O0x+wO3c3OkJ3EZuStdC9DRmvH1vSp1YeWDi2Ry4rcM0Eop8S9WTNEIlRCRCIkCOVD4P0k5v15i0v3kwCwNtHnf+2r069pFfR1NZOU5Chz8I/yZ9udbZyPPq/a7mDqwAe1PqBX9V5YGVpppG7h9SHuzZohEqESIhIhQSg/JEniSPBj5h+8TVhcGgBVbIyZ7F2bLnUranRG3/CUcLbf2c6+e/t4mv0UAD25Ht4u3vSp1QdPO08xo/AbStybNUOjiVBubi5+fn7cu3ePfv36YWZmxqNHjzA3N8fUtHwNHS1PiZAkSaSn500KZ2xsLG66whsrV6Fk26Uovj8SSnxq3oSMXk6WTOtcm6auNhqtOyM3g4PhB9l6ZyvBCcGq7bWsavFBrQ/wdvHGwsBCozEIZYu4N2uGxhKh+/fv06lTJyIjI8nKyiIkJARXV1fGjh1LVlYWK1eufOXgy5LylAgJgqAuLSuX1afCWHUyjPS/R5h1dKvA1M61qG5f8iPM/utG/A223dnGX+F/qZby0JPr0dKhJV2qdqGNYxuM9UpmYVlBeNNoLBHq2bMnZmZmrF27FhsbG65evYqrqyt+fn6MGDGC0NDQVw6+LBGJkCCUf7FPM1l2NJStF6NQ/D3CrE9jZz7vWKNEl+woTEpWCnvv7mXv3b3cTb6r2m6ka0Rbx7Z0rtqZlg4txTB8QSgCjSVCNjY2nD17llq1amFmZqZKhCIiInB3d1c175UX5SkRUiqVREZGAuDs7IxcLkatCMK/3Y1NZeHB2xwOfgyAkZ4OI1pVZWSbapga6JZKDKFJofwV/hd/hf/Fg9QHqu1m+mZ0dO5Ip6qdaFKxCbry0olH0Dxxb9aMl/38LvJvklKpRKHIv47PgwcPMDPTfFOyUHySJBEREQGAk5OTdoMRhDKour0pqwY14lJEInP/vMXlyGSWH7/LrxciGduhBh82cUZPR7MfUjWsalDDqgZj6o/hRvwN/or4i0Phh4jNiGXP3T3subsHa0NrvF286Vy1M552nmIo/mtO3Ju1q8gtQn369MHCwoJVq1ZhZmbGtWvXsLOzo0ePHjg7O7N+/XpNxaoV5alFSIxMEISXJ0kSh27GsODgHcLj80aYVbU1YWyHGnStV0njCdG/KZQKLsde5q/wvzhy/wjJWcmqfZVMKtGpaic6u3SmtnVt0dH2NSTuzZqhsUdjUVFRdOrUCUmSCA0NpVGjRoSGhmJra8vJkyext7d/5eDLEpEICcKbLUehZOuFSJYeDSUhLRsAB0sjhr1VlQ8bO2FSSo/MVPEoczj/6Dx/hf/FschjpOf+0x3BxdyFzlU707lqZ6paVC3VuITiE/dmzdD48Plt27Zx9epVUlNTadCgAf3798fIyOiVgi6LRCIkCAJAalYuG86Es+FsBPGpeQmRhZEeA5o5M7iFC/Zmmu9U/V+ZuZmceniKv8L/wj/Kn2xltmqfm7WbqqWokmmlUo9NeHni3qwZGkmEcnJyqF27NgcOHMDNza1EAi3rRCIkCMK/ZeYo2H35IatPhakemenrynm3gQMftXKlmp125lJLzU7lRNQJ/gz/k3OPzqnWOgPwsvOic9XOdKzSEXvj8tVqXx6Ie7NmaKxFyMHBgaNHj4pE6DUkftkEoeQolHmzVP988h5XIpMBkMngbbcKfNymGg2raG/pjKTMJI7cP8Jf4X8R+DgQiX9u85VMKuFh60Fd27p42HrgbuOOiZ6J1mIVxL1ZUzSWCM2dO5eQkBDWrFmDrm75Hb7p6+uLr68vCoWCkJAQkQgJglAgSZK4dD+Jn/3vcfRWrGp7oypWfNymGh1q2yOXa68D8+O0xxyKOMTBiIPciL+hlhRB3mKw1SyrqSVHNaxqoCfXzIK0Qn7i3qwZGkuEevXqxbFjxzA1NaVu3bqYmKj/JbF79+7iRVxGlacWIUmSePo0b40jMzMzMbpEEErY3dinrDoZxt4rj8hWKAGoZmfCyNau9KzvgIGudj/gUrNTuZV4i+vx17kRf4Pr8deJSYvJV85Ax4Da1rVViVFd27o4mTmJe4aGiHuzZmgsERo6dOhz94vh84IgvOkeP8lk/ZkItgTc52lmLgB2ZgYMbelC/6ZVsDAqO60tcelx3Ii/wY2EG6rk6NmisP9mrm+Oh62HWsuRrZGtFiIWhJcjVp8vISIREgShuJ5m5rD1QhTrzoQTnZIJgIm+Dn2bODPsrapUtix7I20lSSLyaaRaq9HthNtqI9Ke+W9/IyczJ8z1zTHSNRKtGoLWiUSohJSnREipVPLgQd6U/Y6OjmIad0EoJdm5Sn6/+ohVJ8O48zivtUVXLqO7Z2VGtnGldsWyfW/JUeQQmhyqSoxuxN/gXvK9fP2NntGV6WJuYI65ft7LzMAMcz1ztW2FfW2iZ/LGJVHi3qwZGkuEqlat+twf0rCwsKKcrswrT4mQ6JAnCNolSRJ+IXH87H+P82GJqu1ta9kxsrUrzV1tXpskIC0njeCEYFVydDP+JrEZseQqc1/pvDoyHcz0zdSSJDN9Myz0LbA1tqWCcQXsje2xN7angnEFzPXNX5vvWWHEvVkzNLbW2Lhx49Te5+TkcOXKFQ4ePMikSZOKHKggCMKbQiaT0a6WPe1q2XM1KplVJ8P460Y0fnfi8LsTR10HC95v5Ehnj0rYmRloO9znMtEzoXHFxjSu2Fi1TZIkMnIzeJL9JO+V9aTgrwvZl6PMQSEpSM5KVltG5HkMdQyxM7ZTJUb/TpSebbM1thWj4IRCFTkRGjt2bIHbfX19uXTp0isHJAiC8CbwdLLEt38D7iekseZUONsvRXH9YQrXH6Ywc/9NWla3xcezMt51KpapztXPI5PJMNYzxljPmIomFYt0rCRJZCoy1RKkp9lPVYlSclYycRlxPE5/TGx6LLHpsaRkpZCpyCTqaRRRT6MKjwsZ1obWqsTov4mSvbE9lU0rY6xn/KrfAuE1VGJ9hMLCwvDy8uLJkyclcboyQzwaEwShNCSkZrHnykN+v/qIqw9SVNv1deS0qWWHj2dlOrrZY6xffudvK6rM3Ezi0tWTo39/HZse+9KP6+QyOQ0rNKS9U3vaObfDwdShFK4gj7g3a4bGHo0VZufOnVhbW5fU6QRBEN4oNqYGfNTKlY9auRIRn8aBa4/Yf/URIY9TORL8mCPBjzHS0+Ft9wr4eFamdU1brc9LpG2GuoY4mTvhZO5UaBmlpCQpM+m5ydLj9Mc8zX7KxZiLXIy5yIKLC6hlVYv2zu1p79yeWla1Xvt+SELhitwiVL9+fbUfCEmSiImJIS4ujhUrVjBy5MgSD1KbRIuQIAjadDvmCb9fzUuKohIzVNvNDXXp5FGR7p4ONK9mg44WZ68uDx6mPuRE5AmORx0n8HEgSkmp2lfZpLIqKapvXx9decm2yol7s2ZobNTYzJkz1RIhuVyOnZ0dbdu2pXbt2sWPuIwSiZAgCGWBJElcfZDC/qBHHLj2iNinWap9tqYGdK1bke5elanvZKXVJT3Kg6TMJE4+OMnxyOOcfXSWTEWmap+FgQVtHNvQ3rk9LSq3wEj31eeCEvdmzRDzCJWQ8pQISZJESkpe3wMLCwvR1CsIrymFUuJCeCL7rz7irxvRJKfnqPY5WBrRzbMSPvUqU6fy6z+0XNsycjM49+gcxyOP4//AX200m6GOIc0rN6e9c3vaOLbByrB4C+2Ke7NmaCwR0tHRITo6Gnt7e7XtCQkJ2Nvbo1AoihdxGVWeEiFBEMqf7FwlZ+7Gs//qIw7fjCEt+597sKudCd09K+PjWZlqdqZajLJ8yFXmciX2Cscjj3Mi6gQPUx+q9sllchrYN6C9c3vaObXD0cxRi5EKoMFESC6XExMTky8RevToEdWqVSMjI6OQI19PIhESBOF1kZmj4PjtWPYHPeL4nViyc//p51KnsjkdatvjbGOCg6URjlZGVLQwRE9HzGJcHJIkEZIUwvHI4xyPOs7txNtq+2tZ1aKdczvaO7WntnVt0cqjBSWeCC1fvhyAzz//nDlz5mBq+s9fFwqFgpMnTxIREcGVK1deMfSypTwlQkqlkujoaAAqVaokpnEXhHLsaWYOh28+5vdrjzgVGo9Cmf9WL5dBRXNDHKyMcLQyxsHS6O+vjXCwNKKypRGGeqXfX0WhlEjJyCEpPZvk9GyS0nJ4kpmDJIFMBnKZDJksb94iuSxvniC5DNU2Gf+UKawsz/YBcrkME31dalU0K3an84epD/GL8uN4ZF5na4X0T8tcJZNKdHXtykd1P8JEzyTfseLerBklnghVrVoVgPv37+Po6KjWmUtfXx8XFxdmz55N06ZNXzH0sqU8JUKiQ54gvJkS07L560Y01x+k8CApg4fJea9/txgVxs7MQC1BclR9nZc4mRgUPoJKkiTSshUkpWWTnJ5DckY2Sek5quQmKT1blfD8sz2bJ5mvtkxHcVka69Gyui1tatjRuqYdFS0Mi3We5MxkTj7M62x95uEZVWdreyN7JjeZzDtV3lFrIRL3Zs3Q2KOxdu3asWfPHiwtLV81xteCSIQEQSiPlEqJ+NQsHiRn8PDv5OhBUvq/vs4gPfvFfT4tjfVULUiSBMnpf7fkZOQlNjmK4o/HMTPUxcpYH0tjPSyM9JDLZCj//shSShKSlPevUgL+/lr61z7p730SEkolSORt++c46e9tEP80i6dZ6glYzQqmtP47KWpS1bpYrWMZuRmcfHCSZZeXqWa/blG5BV80/YIq5lUAcW/WFI1MqJiTk0NkZCTR0dFvTCIkCIJQHsnlMuzNDbE3N6SBc/7RTpIkkZyeo0qQVC1JSRmqr1MycvJaetJzuPGw8FUF9HXlWBnrqZIaSyN9rEz0sDTWx8r42b95+569tzDSK9X+S7kKJVcfJOMfEs/JkDiuPkgm5HEqIY9TWXM6HANdOU1dbWhdw5Y2Ne2obm/6Uv1+jHSN8Hbxpq1TW9ZdX8ea62s4++gsvff1Znjd4QyvOxzdkpvbWCiGIrcIOTg4cPToUdzc3DQVU5kiWoQEQRAK9jQzR5UcPUzOQCaTqSc8fyc6Rno6r11n4eT0bE7fzUuKTobEE/MkU21/JQtDVWtRy+o2WBrrv9R57z+5z9yAuZx9dBYAJzMnpjaaijIs7zGluDeXHI09Gps7dy4hISGsWbMGXd3yn8WKREgQBOHNJkkSobGpnAyJwz8kjgvhiWT9q3+VXAb1HC1pXdOONjVt8XS0RPc5rVmSJHH4/mEWXlhIbEYsMklGV7rSsnJLOnfoLO7NJURjiVCvXr04duwYpqam1K1bFxMT9R7wu3fvLl7EZZRIhARBEIR/y8xREBCeyMmQOE6FxhHyOFVtv7mhLi2r29K6Zl6LkYNlwbNPp+WksSJoBb8G/0rNpJroyfXo2K4j/ev0R0+uVxqXUq5pLBEaOnToc/evX7++KKcrFeHh4QwbNozHjx+jo6PD+fPn8yVwhRGJkCAIgvA80SkZnAqJxz80jtOh8aRk5Kjtr2ZnQtd6lfmkjSvG+vmfpATHBbNy70oepz3mluUtqltX5+tmX1Pfvn5pXUK5JJbY+Jc2bdrwzTff0KpVKxITEzE3N3/px3rlKRGSJInExEQArK2tX7tn9oIgCGWdQilx7UEyJ0PiORkax5XIJJ5N4eRkbcS8XvV4q4at2jGSJBGfEM/R+0fxDfElJTtvuY1e1XvxecPPi710x5tOo4lQbm4ufn5+3Lt3j379+mFmZsajR48wNzdXm2ixLLh58yZjx47l6NGjxTq+PCVCgiAIQulKycjhxO1YFh68zaOUvA7X7zd05MuubgV2sE7KTGLp5aXsDs3rZmJhYMG4BuPoXaM3cpmYaLEoXvbzu8jf1fv371O3bl169OjBqFGjiIuLA2DBggVMnDixyIGePHkSHx8fKleujEwmY+/evfnK+Pr64uLigqGhIU2bNuXChQsvff7Q0FBMTU3x8fGhQYMGzJ07t8gxCoIgCEJxWBjp0bO+A4fHt2FICxdkMtgR+ICOS/w5cO0R/22LsDK0YlaLWWzuvJmaVjVJyUph1rlZDPxrYL5lPISSUeREaOzYsTRq1IikpCSMjP7pAPasE3VRpaWl4enpia+vb4H7t23bxvjx45kxYwaXL1/G09MTb29vYmNjVWW8vLzw8PDI93r06BG5ubmcOnWKFStWcO7cOY4cOcKRI0eKHGd5oFQqiYmJISYmBqXyxTPKCoIgCCXD1ECXmd3rsPOT5lS3NyU+NZvRv15hxKZAHial5bs3e9l7sa3bNiY1moSxrjHX4q7R50AfFlxYQGp26gtqE4qiyI/GbGxsOHv2LLVq1cLMzIyrV6/i6upKREQE7u7upKenFz8YmYw9e/bQs2dP1bamTZvSuHFjfvzxRyDvw9zJyYkxY8YwderUF57z3LlzzJw5k0OHDgGwaNEiACZNmlRg+aysLLKyslTvnzx5gpOTU7l4NCY6SwuCIGhfVq6CFSfuscLvLjkKCTMDOSNqZFHXwYLWrVvnuzc/TnvMokuLOBSR9zlmZ2TH5MaT8XbxFn09n0Njj8aUSiUKRf5p1x88eICZmVlRT/dc2dnZBAYG0rFjR9U2uVxOx44dOXfu3Eudo3HjxsTGxpKUlIRSqeTkyZPPnQxy3rx5WFhYqF5OTk6vfB2CIAiC8IyBrg6fv12TP/7XivrOlqRl5XL8diw7Ax9wLy5/a08FkwosbrOYnzv+jLOZM3EZcUw6OYmPj3xMREpE6V9AOVPkROidd95h6dKlqvcymYzU1FRmzJhBly5dSjI24uPjUSgUVKhQQW17hQoViImJealz6OrqMnfuXFq3bk29evWoUaMG3bp1K7T8tGnTSElJUb2ioqJe6RoEQRAEoSA1K5ix85MWfN3VDT0dOQ+TM+j+w2l+PB5KjiJ/94UWDi3Y3WM3n3l9hr5cn3PR5+i9vzc/XvmRzNzMAmp4PWh78HqRE6HvvvuOM2fO4O7uTmZmJv369cPFxYWHDx+yYMECTcT4yjp37sz169e5ceMGS5YseW5ZAwMDzM3N1V6CIAiCoAk6chmDWlRlYLMquNiYkK1QsvhwCD4/nOZqVHK+8gY6Bnzq+Sl7euyhZeWW5Chz+Pnaz/T9oy/3n9wv/Qt4RUfuH2HE4RFkKbJeXFhDipwIOTo6cvXqVb744gs+//xz6tevz/z587ly5Qr29vYlGpytrS06Ojo8fvxYbfvjx4+pWLFiidYlCIIgCNpibqRHD6/KLH7fEytjPW7HPKXXijPMORBMenZuvvLO5s781PEnlrRdgq2RLXeT7/LhgQ/xi/Ir9diLI0eRw4ILCxjvN56AmAC23t6qtViKtViYrq4uAwYMKOlY8tHX16dhw4YcO3ZM1YFaqVRy7NgxRo8erdG6fX198fX1LbA/lCAIgiCUNJlMRg8vB9rUqsCcA8HsDXrE2tPhHLoZw9xedWld0y5f+bervI2XnRcT/CdwJfYKY46PYWS9kXzm+Rk68rI5ICYmLYaJ/hO5GncVgKEeQ+nv1l9r8RRrdqY7d+4wevRoOnToQIcOHRg9ejS3bxdvfoPU1FSCgoIICgoC8pbDCAoKIjIyEoDx48ezevVqNm7cyK1bt/j0009JS0t74VIfr2rUqFEEBwdz8eJFjdYjCIIgCP9mY2rA0g/rs35oYypbGPIgKYNB6y4wYftVktKy85W3M7Zj7Ttr6Ve7HwCrrq1i1PFRpGSllHboL3Tm4Rne//19rsZdxUzfjOXtljO+4Xh05dpbxL3Iw+d37drFhx9+SKNGjWjevDkA58+f5+LFi2zdupV33323SAH4+fnRrl27fNsHDx7Mhg0bAPjxxx9ZtGgRMTExeHl5sXz5cpo2bVqkeoqrPM0sLUmSagJMOzs7MexSEAShDHjevTk1K5fFh+6w8VwEkgS2pvrM8KlDt3qVCryH/37vd2afm02mIhMHUweWtltKbevapXYthVEoFfx09SdWXVuFhISbtRtL2i7BADsuhCfStV6lEq9TY0tsVKtWjf79+zN79my17TNmzOCXX37h3r17xYu4jCpPiZAgCILwegq8n8TUXdcIjc0bXt+htj3f9PKgkkX+le3vJN5h3IlxPEh9gIGOAdObT6d7te6lHbJKQkYCU05NISA6AIAPan7A5CaTSUmX6Lc6gHtxqSzt40UPL4cSrVdjiZCxsTHXrl2jevXqattDQ0Px9PR8pQkVy5J/9xEKCQkRiZAgCIKgVVm5Cn7yu4fvibyJGE0NdJnSqRb9m1ZBLldvHUrJSmHqqamcfngagA9rfcjkxpPR09Er1ZgvP77MJP9JxGbEYqRrxIzmM+jq2pXYJ5n0XX2ee3FpVDQ35LeRzahqa1KidWssEerSpQvvv/9+vj4669evZ+vWraoZnMuL8tQiJB6NCYIglD1FvTeHPH7KlF3XuBKZDECjKlYsfK8ernbqi54rJSU/Xf2JlVdXAuBl58V3bb/D3rhkR3gXRJIkNt7cyNLLS1FIClwtXFnSdgnVLKsRk5JJv9XnCYtPo7JFXhJUxaZkkyDQYCK0cuVKpk+fzgcffECzZs2AvD5CO3bsYNasWVSuXFlVtnt37TXFlZTylAiJJTYEQRDKnuLcmxVKic3nIlh46A7p2QrMDHX5eUBDWlS3zVfWP8qfaaem8TTnKTaGNnzX9jsaVmhY4tfxzJPsJ3x1+itORJ0AoKtrV6Y3m46xnjHRKRn0XXWeiIR0HCyN2DqyGU7WxpqJQ1OJkFz+cgPNZDJZuRh6LhIhQRAEQZNe5d78MDmDsb9d4dL9JPR0ZMzvXY93GzrmKxf5JJKxJ8ZyN/kuujJdJjSaQH+3/iX+ZCA4IZjxfuN5mPoQPbkeU5tM5f2a7yOTyXiYnJcERSam42hlxG8jNJcEgYbXGnuZV3lIggRBEAShLHOwNOKXj5rStV4lchQSE3ZcZdnR0HzLVjibO7OlyxY6V+1MrpTLgosLmHpqKuk5JdOvV5Iktt/ZzsA/B/Iw9SEOpg5s7rKZD2p9gEwm40FSOh+uOkdkYjrO1sZs+7i5RpOgoijWPEKCIAiCIJQNhno6/PBhfT5pUw2A74+GMGnnNbJz1dcrM9YzZkGrBUxpPAUdmQ5/hv/JgL8GEPkk8pXqT89J54vTXzDn/Byyldm0dWrLtm7bqGNTB4CoxHT6/HyeqMQMXGyM2TqyGQ6W+Ue7aUuxZjBKS0vD39+fyMhIsrPVJ3f63//+VyKBaZuYWVoQBEF4XcjlMqZ2ro2TtRHT991kZ+ADolMyWNG/IRZG/4wUk8lkDHAfQG3r2kz0n0hoUigfHviQ+a3n09qxdZHrDUsOY7zfeO6l3ENHpsPYBmMZUmeI6pHb/YQ0+q46z6OUTFxtTfh1RDMqWhiW2HWXhCL3Ebpy5QpdunQhPT2dtLQ0rK2tiY+Px9jYGHt7e8LCwjQVq1aIPkKCIAiCJpX0vfnEnVhGbblMeraCmhVMWTekMY5W+R9DPU57zHj/8VyLuwbAp56f8onnJ8hlL/ew6I+wP5h1bhYZuRnYGdmxqM0itU7YEfFp9F19nuiUTFztTNg6ohn25qWXBGmsj9Dnn3+Oj48PSUlJGBkZcf78ee7fv0/Dhg1ZvHjxKwUtCIIgCMKraVfLnu0fN6eCuQEhj1PpteIsNx7mX26jgkkFNnhvoE+tPgD8dPUnRh8b/cKlObIV2Xxz/humnppKRm4GTSs2ZbvPdrUkKCwulT6rzhGdkkl1e1O2jizdJKgoitwiZGlpSUBAALVq1cLS0pJz587h5uZGQEAAgwcPLvaaY2VVeWoRUiqVxMbGAmBvb//SIwAFQRAEzdHUvflRcgbDNlzkdsxTjPV1+KFvfTq4VSiw7L67+5hzfg5ZiiwcTR1Z2m4ptaxr5Sv34OkDJvhPIDghGBkyRtYbyaeen6ot8Ho3NpV+q88T+zSLmhVM2fJRM+zMDErkmopCYy1Cenp6qv8ke3t71eKoFhYWREVFFTPcN0/G1atEf/01yoyMUqtTLpdTsWJFKlasKJIgQRCEMkJT9+bKlkZs/6Q5rWrYkp6tYMSmS2w+f7/Asj2q92Bz5804mDrwIPUBA/4cwIGwA2pl/KL8+ODABwQnBGNpYMmKjisYXX+0WhIU+vgpH67KS4JqVzTjtxHaSYKKosjf8fr166tWZG/Tpg3Tp09ny5YtjBs3Dg8PjxIPsDySsrN5OGEiyTt2EvFhX7IjIrQdkiAIglAOmRvqsW5IYz5o5IhSgq/33mDun7dQKvM/DHKzcWNr1620rNySTEUm005NY/6F+WTmZrIkcAljjo/hafZT6tnVY4fPDt5yeEvt+DsxT+m7+jzxqVm4VTLn1xHNsDEt20kQFOPR2KVLl3j69Cnt2rUjNjaWQYMGcfbsWWrUqMG6devw9PTUVKylStNrjaWdD+DhhAkoEhKQm5hQad5czN95p8TOXxBJkkhMTATA2tpaLLEhCIJQBpTGvVmSJHxP3GXx4RAAutStyJIPvDDUy98xW6FU4Bvky+rrqwEw0zPjac5TAAa4DWB8w/H51iy7Ff2E/msCSEzLpk5lc34Z3hQrE/0Sv46i0NjM0m8ajfURSo4k5/xOHm6+TEZgIADWQ4ZgP2E8Mj3NLIonRo0JgiCUPaV5b9575SGTdl4lRyHRsIoVqwc1wrqQhOV45HG+PP0lqTmpmOiZMLvFbN5xyf8H+81HKQxYE0BSeg51HSz4ZXhTLIxLd3HXgmisj5BQAnKzYfsg9M7Poko3OdZDBgCQuGED9wcPIefxYy0HKAiCIJRHPes7sHl4U8wNdQm8n0TvFWcIj08rsGx75/Zs7baVTz0/ZXu37QUmQTceptD/7yTI09GCXz4qG0lQUYhESBt09MCrP8j1kN3ZRwXTvTh+OxW5qSkZly8T3qs3aefOaTtKQRAEoRxq5mrD7s9a4GhlRERCOr1XnOFSRGKBZauYV+Ezr89wNnfOt+/6gxT6rT5PcnoOXk6WbP6oqdrkja8LkQhpg0wGTUbA0L/A3AHiQzC7PY2q80dg4OaGIjGRyOEfEb9yJZJS+eLzCYIgCEIRVLc3Y89nLfF0tCApPYd+awI4cO3RSx8fFJVMvzXneZKZS8MqVmwe3gRzw9cvCQKRCGmXU2P4+CRUbQM5aeifnoTLkGpY9O4FSiVxS5cR9ckn5CYlaTtSQRAEoZyxMzNg68jmvO1egexcJaN/vcJK/3v5Fmz9r8uRSQxcE8DTzFwau1ixcVgTzF7TJAiKmAjl5OTQoUMHQkNDNRXPm8fEFgbugVYTAJBfWUXlapeo9PUkZAYGpJ08Rfi775Jx7ZqWAxUEQRDKGyN9HVYOaMiQFi4AzP/rNl/tvUGuouCnEYH3Exm09gJPs3JpUtWaDUObYGpQrGVLy4wiJUJ6enpce0M+kH19fXF3d6dx48aar0yuAx2mQ9+tYGABUQFYPpqLy3eT0KviTO6jaCL6DyDx119fmKkLgiAIQlHoyGXM7F6H6d3ckclgS0AkIzZdIi0rV63cxYi8JCg1K5dmrtZsGNoYk9c8CYJiDJ///PPPMTAwYP78+ZqKqUwp9SU2EsNg2yB4fB1kchTNpxL9+0OeHjkCgHm3blSaNRO5iUmRT61UKomOjgagUqVKYnZpQRCEMqAs3ZsP3Yxh7NYrZOYoqVPZnHVDGlPB3JCAsASGbrhIeraCltVtWDOoMUb6ZXsKFo3NIzRmzBg2bdpEjRo1aNiwISb/+UBesmRJ8SIuo7Sy1lhOBvwxAYK2ACDV7EJiWmtil/qCQoF+tWo4Ll+GQbVqpROPIAiC8MYIikrmo40XiU/NprKFIaPb12DOgWAychS0qmHL6kGNCpyIsazRWCLUrl27wk8mk3H8+PGinK7M09qiq5IElzfCn5NAkQ3WrqTX/oKH3/xIbmwsMmNjKs2ejUW3rqUXkyAIgvBGiExIZ8iGC4TF/TPHUOuadqwa2PC1SIJAzCxdYrS++vzDy7B9MKREgq4Rua2+4eGGM6SfOw+AVb9+2E+dglz/xVOZS5JESkoKkLdIrlhiQxAEQfvK6r05OT2bjzcHEhCeSLtadvw04PVJgqAUEqG7d+9y7949WrdujZGREZIklZn/vJKk9UQIID0Rdo+Au0cBkBoMJe6eMwk/560DY1ivHo7fL0HPweG5pxFLbAiCIJQ9ZfnenKNQciv6CXUqW6Ajf70+4zW2xEZCQgIdOnSgZs2adOnSRdXBa/jw4UyYMKH4EQuFM7aGfjug7ReADNnl9dib/I7TkjnILSzIvHaN8N7vknrypLYjFQRBEMoRPR059RwtX7skqCiKnAh9/vnn6OnpERkZibGxsWp7nz59OHjwYIkGJ/yLXA5tp0D/nWBkBY8uY3p9Iq7fj8ewbl0UKSlEjfyY2GXLkBQKbUcrCIIgCK+FIidChw8fZsGCBTg6Oqptr1GjBvfv3y+xwIRC1OiYNxt15fqQkYTe4ZFUGemFVb++ACT8tJLIjz4iNyFBy4EKgiAIQtlX5EQoLS1NrSXomcTERAwMDEokqLKgVCdULCpLZxh6EBoOASTkZxZQ0fUalb+dgczIiPRz5wnv1Zv0wEBtRyoIgiAIZVqRE6FWrVqxadMm1XuZTIZSqWThwoXPHVr/uhk1ahTBwcFcvHhR26EUTM8QfJZBjxWgawh3j2AR+S1VfWeh7+pKbmws9wcMJHr6DHITC15VWBAEQRDedEWeG3vhwoV06NCBS5cukZ2dzeTJk7l58yaJiYmcOXNGEzEKz1O/P1SqB9sGQlI4BseGU/XLb4n5PYyUvXtJ3r6dJwcPYjdmDOYfvK/taAVBEAShTClyi5CHhwchISG89dZb9OjRg7S0NHr37s2VK1eoJmY61o6KdWGkH9TsDIos5EcmUrnZE6psWINB7doonzzh8bffEvHe+1TOyMTV1bVcTnUgCILwOpLJZLi6uop7s5aICRVfoEzMI/SylEo4sxSOzwFJCfbuSN4LSL74iLjvl6L4e8Ius06dqDB5EnqVK2s3XkEQBEHQkBKdULEoK87Xq1fvpcu+Dl6rROiZMH/YOQzS4/Peu3VH0XQycZv2krR1KyiVyAwNsRnxETbDhyM3NNRuvIIgCIJQwko0EZLL5chksnyzRz879N/bFOVsDpvXMhECSEuAE99C4Pq81iEdfaRmo4g370jcijUQEIAM0HNwwH7qFMw6dhRNsoIgCFogSRJPnz4FwMzMTNyLS0iJziwdHh5OWFgY4eHh7Nq1i6pVq7JixQqCgoIICgpixYoVVKtWjV27dpXYBQivyMQGui2BT86Aa1tQZKM8s4ybR7/nsXd9Ki1aiG7FiuQ8fMjDMf8javhwsu7e1XbUgiAIbxylUsnly5e5fPkySqVS2+G8cYrcR6hJkybMnDmTLl26qG3/888/+frrrwksZ3PXvLYtQv8mSXDnLxSHvuJUkj0ArSpmIGs3k/iD10hcuw4pOxt0dLAe0B/b0aPRMTPTctCCIAhvhrK81tjrTGNrjV2/fp2qVavm2161alWCg4OLejqhNMhkULtLXutQtXagYwAx15D/1hP7Spdx/fVnTDt2AIWCxI2buNepM8m7diGJv0wEQRCEcq7IiZCbmxvz5s0jOztbtS07O5t58+bh5uZWosEJJUxXH5yaQtORUH8wyOQQvBf9Pd1x6mWP008/oF+1KoqEBKK//IqID/qQERSk7agFQRAEQWOKPKHiypUr8fHxwdHRUTVC7Nq1a8hkMn7//fcSD1DQAH0T6PAdNP0IDk6FiFNw6jtMTbdgMucrEq/lEO+7gswbN4j4sC8WPXtiP2E8unZ22o5cEARBEEpUkVuEmjRpQlhYGN988w316tWjXr16fPvtt4SFhdGkSRNNxKgVZXqtsZJS0QMG/w59toBVVUiNQXZgNDa5m6i29lssevcGIGXvXu516kzCuvV5fYkEQRAEoZwoUmfpnJwcateuzYEDB96Yx2DlorP0357bIS83CwJWgv8iyM4bxonHu2RU/JCYZWvIvH4dAP2qVanwxReYtnqrtMMXBEEol0Rnac3QSGdpPT09MjMzXzk4QTtkMhkuLi64uLjkn6dC1wBajoX/XYYGgwEZ3NiFkd9AXD6uR6XZ09GxsSE7PJyoESOI+mwU2Q8eaOU6BEEQypPn3psFjSvy8Pm5c+cSEhLCmjVr0NUtchej1055ahEqkuhrcHAa3D+d996sEooWU4n3iyFxyxbIzUVuakrlBfMx69BBu7EKgiAIwn+U6MzS/9arVy+OHTuGqakpdevWxcTERG3/7t27ixdxGfXGJkKQN//Qrd/h8FeQfD9vm0NDstz+R7TvdjKuXAHA5uOPsfvfGGSiOVcQBEEoIzSWCA0dOvS5+9evX1+U05V55SkRkiSJ9PR0AIyNjV++CTYnE86vgFPfQXZq3rnc3uXxzYokbd8DgEmL5lT+7jt0raw0ErsgCEJ5Vex7s/BcGkuE3jTlKRF65Q55Tx/D8dlwZQsggZEVKdYjiV6xEykjA91KlXBcvgyjunVLPnhBEIRySnSW1gyNzSz9TFxcHKdPn+b06dPExcUV9zTC68SsAvTwhZF+ULk+ZCRh8XABLuNao+fsTG50NPf79Sdp+3ZEfi0IgiC8DoqcCKWlpTFs2DAqVapE69atad26NZUrV2b48OGqpj2hnKvsBcMOQZOPATAMX0/V3jJMW7dEyskhZvoMor/6CqUYYSgIgiCUcUVOhMaPH4+/vz+///47ycnJJCcns2/fPvz9/ZkwYYImYhTKIl0D6LIQ3t8A+mboxJzDsdoJ7AZ3B7mclF27iejXTwyxFwRBEMq0IidCu3btYu3atXTu3Blzc3PMzc3p0qULq1evZufOnZqIUSjL6vTKe1RWwQNZRjy2WT/jPKYjOlZWZAXfIvzd90j9+9m3IAiCIJQ1RU6E0tPTqVChQr7t9vb24tHYm8q2Onx0FBoMAiRMHm+gaj8rDN1ro0xJIWrkx8StWCFWsxcEQRDUKLOzyQoLR5mVpbUYijwjYvPmzZkxYwabNm3C0NAQgIyMDGbNmkXz5s1LPEDhNaFnBN1/AOcW8Md49BJOU6VZJR67tCX5T3/il/9A5tVrVF64AB0LC21HKwiCIJQCSZLIjYsj58EDch48IDsqipyoB+Q8iCI7MoLcuESQJFw2rMSoWRutxFjkRGjZsmV4e3vj6OiIp6cnAFevXsXQ0JBDhw6VeIBCyZHJZDg5Oam+1givvnmdqbcPRh5/h0oW2zEa8gExv54j1d+f8Pfex3H5MgzfkLXqBEEQXqRU7s0apExLI/vBQ3IeRP2d7DwgJyqK7L+TH+kFrT0yXSW54ddAS4lQseYRSk9PZ8uWLdy+fRsANzc3+vfvj5GRUYkHqG3laR6hUpWVCgc+h+vbAcgwa8PDP1LJeRSNzMCAirNmYtmzp3ZjFARBEF5IUijIjYnJS3Ae/J3gRD0g++/ER5GQ+PwTyCT0jBTomSrQM81F3yTva30LPfScndBxqI6s5VhwbFiicYsJFUuISIRegSRB4Ab4awooslAYOPHw/+3dd3gU5fbA8e/uZjeddBICKfSihB5ARERQVETAjiKIXkDFi8pVfxcVsSF20UsUBRQbTaUIKKIRRCmGFor0mgghvReyZX5/TLIYagLZzGb3fJ4nTzazszNnE3hz8pbz7r6C4k07AAgcdg/hEyeiN5m0jVMIIcQ5FaxaxYln/g/lIuVQDCYbRj8LRl8rporParJjwNgkBl1YcwhpDiEtILjisV84OLAHrE4SoYEDBzJr1iwaNWp0qZdwWgkJCSQkJGC1Wtm/f79LJEKKonCqoovS09Oz7rpg07bDwpGQewRFZySr9BayliaBouDVIY4m77+PMSKibmIRQggno1nbfBGK1crh6/tSfiITnV6pSG4qe3T+kfT46zFExJ5OcIKbqQlPSHPwjwT9Jdduvix1kgj5+/uzfft2mjVrdqmXcHqu1COkaRn3snxY+hjs+R6AIo9rOb40DVthIYbgYBq/+w6+PXrUXTxCCOEknHWLjYKffuL440+gN9locWsWhobR/0h2Knt4mkNAFOidI+Z/qu7v7xpPlhbikngFwF1fwJ8zYNXz+FnW0PTWWP7eGMOpQ8dIefAhGk54kuCHHnKav4aEEMJdKYpCdsJ7AAS1Lsfw7AHwCdY4Kse4rP6qmJgYjEZjbcUiXJ1OBz0egVErISAKk/Uosd22EdD7SrDZyHj7HY6PfxxrUZHWkQohhFsrSdpE2f5j6AwKwXfc6rJJEFxmIrRr1y77kj8hqi2qG4xdCy1vQE8ZjSJXETG4BXh4UPjzzxy9405OHTigdZRCCOG2sj98H4DApiV4XP+4xtE4VrWGxnbs2FHtC8bFxV1yMMKN+ATDsAWwbhq6X18hyHstXkNb8PdvAZQfPcqRu++h8Vtv4t+vn9aRCiGEWynbu5fiP7eCTiH45m7q5GcXVq1EqGPHjuh0OhRFqTJ/48yvQZ30JUS16PXQewJExcO3D+FddJCmfXw5vqcjJbuO8Pe/xxMxeTJBd9+ldaRCCOE2sj/+EIAGUWWYbn5S42gcr1pDY0eOHOHw4cMcOXKE7777jqZNm/Lhhx+SnJzMtm3b+PDDD2nevDnfffedo+MVrij2anj4d2jaBw9DMdHt1hEY3xhsNk5Onkzm9ASk3JUQQjhe+d/HKfjpFwBCrm4EMb00jsjxqtUjFBMTY39855138sEHH3DzzTfbj8XFxREVFcWkSZMYItWCnZZOpyMyMtL+2Kn4NYT7F8Nvb6L77Q0imm7CQ9+arI2FZE2fjiUjg4jJL6BzkmWlQghRW5ypbc75dBbYFHzDy/Aa/LhDCx46ixovn9+5cydNmzY963jTpk3ZvXt3rQQlHEOv19OqVSutwzg/vQH6ToSoeHTfPkhY7D48PBpzch3kLVyIJSebxm+/jb5is18hhHAFztI2W3JyyPv2WwBCOpvgits0jqhu1HjVWNu2bZk6dSrl5eX2Y+Xl5UydOpW2spGmqA0t+sG/EiG4OUFNjtP4mhJ0Rg+Kfkkk5cGHsOblaR2hEEK4nNyvv0Ypt+AVVI7PkIfAwz22P6pxZemkpCQGDRqEoij2FWI7duxAp9OxbNky4uPjHRKoVlypsrSiKJjNZgCMRqPmXbAXVZIDC0fA0d8pyfQkdX0jbKXlmFo0J3rmTIwuuLWLEML9OEPbbCsp4WCfa7AWFtO4dyENpm0H35A6j6M2Vff3d417hOLj4zl8+DCvvvoqcXFxxMXFMWXKFA4fPuxySZCrsdlsrF+/nvXr12Oz2bQO5+J8gmH4Iug0HJ+wU8T0+RuPAC/KDx7i6LB7pdaQEMIlOEPbnPftd1gLizH6WfC/5bZ6nwTVRI3mCJnNZtq0acPy5csZM2aMo2IS4jQPE9w6HUJb4/XzC8Rec4yU9VGUnzzJ0fuGEzXjI3w6d9Y6SiGEqLcUs5ns2TMBCGlThO6qcRpHVLdq1CNkNBopKytzVCxCnJtOB73Gw91fYQz0JOaaY3hH6LEVFJAy6kEKf/lF6wiFEKLeKvjxRyzpmRg8rQT06wFhrbUOqU7VeGhs3LhxvPHGG1gsFkfEI8T5tb0FHlyJR2gjoq8+jl+UFeXUKf4e/zi5CxZqHZ0QQtQ7iqKQPfMTAIJbFaPv/ZjGEdW9Gi+f37RpE4mJiaxatYr27dvj6+tb5flFixbVWnBCnKVRBxidiH7ePTTRb+ekKZi8Q16cnDwZS2YmoeMedf5J4EII4SSK167l1IFD6D1sBPVoAs2v0zqkOlfjRCgwMJDbb7/dEbEIUT0NImHUj+gWjyVCtwwPL3+y/vJXCy9mZhLxwiQpvCiEENWQPWsWAIHNSzBc+6xbFFA8U40Toc8++8wRcQhRMyZfuPMLdL++TJjuPTy8rJzcGkjeggVYsrOk8KIQQlxE6fbtlGzaDHqF4I5GiHPPfR1rPEdI1F86nY6IiAgiIiJcY/hIr4f+L8LgDwlqbabxVTnoDEjhRSFEvaJV21zZGxQQU4qxz0Ng9K6zezuTahVU7Ny5M4mJiQQFBdGpU6cL/qC2bt1aqwFqzZUKKrq0o+tgwX2UHCsm9Y9QbOVI4UUhhDiPU4ePcHjgQFAUmt2Si+fk7eAfrnVYtaq6v7+rNTQ2ePBgPD09AWRTVeGcYnvBvxLxmXsXMaajpK4NtRdejJ41E88WLbSOUAghnEb2p7NBUfBrXIpnr6EulwTVRI232Khv9u3bx913313l63nz5lU7oXOlHiFFUexVS/V6vWsMj52pNBcWjsC8ax0pv4VQXuCBPqABUR9J4UUhhHOq67bZnJ7Bof79UcxmYvpn4vP8aoho79B7aqFWe4TOpby8nIyMjLPKgUdHR1/qJR2idevWJCcnA1BUVERsbCzXX3+9tkFpxGaz8fvvvwPQu3dvDK64sso7CIYvwrjiP8R4fMHfa0MozVYLLzZ+9x38+/XTOkIhhKiirtvm3C+/QDGb8Q49hU+3ni6ZBNVEjSdL79+/n969e+Pt7U1MTAxNmzaladOmxMbG0rRpU0fEWGu+//57+vXrd1btI+FiDEYY9D4eg14lum82fpFlauHFf48nd6EUXhRCuC9rYSG58+cDENK2CHq413Ya51LjRGjUqFHo9XqWL1/Oli1b2Lp1K1u3bmXbtm2XNFF67dq1DBo0iMjISHQ6HUuWLDnrnISEBGJjY/Hy8qJ79+4kJSXV+D4ACxcurDJMJlyYTgdXPYb+/nk06XuKwGbFYLNx8oXJZCYk4OIjwkIIcU658+djKyrGM8CMX/sm0PIGrUPSXI2HxpKTk9myZQtt2rSplQCKi4vp0KEDDz74ILfddttZzy9YsIAJEyYwY8YMunfvzrRp0xgwYAD79u2jYcOGAHTs2PGcW36sWrWKyMhIQB0rXL9+PfMrMuHzOXXqFKdOnbJ/XVBQcDlvT2it9U3oRv9EhM9deHgXqoUX/zcdS0YmEc89i85k0jpCIYSoE7ZTp8j5/AsAgtsUoevxf2oZEjdX40SoXbt2ZGVl1VoAN910EzfddNN5n3/33XcZPXo0o0aNAmDGjBmsWLGCTz/9lP/+978A9jlAF7J06VJuuOEGvC5SZG/q1Km89NJL1X8DwvlFtEc3ZjVh/sPw8NrLyS0B5C1YQNmuXUS++QaezZtrHaEQQjhc/tKlWLOy8PCxENDaEzreq3VITqFaqWBBQYH944033uCZZ55hzZo1ZGdnV3mutntPysvL2bJlC/379z8dsF5P//792bBhQ42uVd1hsYkTJ5Kfn2//SE1NrXHcwgn5R8ADKwgafD1NeudgMNko++svjgy9jZyvvpahMiGES1OsVnJmfwpAcOtidN0eUCv0i+r1CAUGBlZZzqcoCv3OWH2jKAo6nQ6r1VprwWVlZWG1WgkPr1rfIDw8nL1791b7Ovn5+SQlJfHdd99d9FxPT097zSThYkw+cMcc/MPewCvkXdI2+lF8EtJffZWiX3+h0dQ3MIY31DpKIYSodYW/JFJ+7Bh6k42gFuUQP0brkJxGtRKh1atXOzoOhwoICCA9PV3rMDSn0+kICwuzP3ZLej30nYix/R1ErZxI7g/ryNgeQPH6jRwZOICIV16jwQWGaoUQorY5um1WFMW+nUZQi2L0HQZDQONav099Va1EqE+fPrz88ss89dRT+Pj4ODomu9DQUAwGw1lJTHp6OhEREXUWh6vQ6/VcccUVWofhHEJbohv+LcHxq/Cd/19O/JhPWS4cf3ICRSu+JXzqNAz+/lpHKYRwA45um0uSNlG2cyc6g0Jwq2Lo+ajD7lUfVXu6+EsvvURRUZEjYzmLyWSiS5cuJCYm2o/ZbDYSExPp2bOnQ++dkJBAu3bt6Natm0PvIzTW6gY8n/uT2DefIKR9OegU8n9Zz5Hrr6Zk9QqtoxNCiMtW2RsU2LQEj5bx0LiLxhE5l2onQo6aTFpUVERycrJ95deRI0dITk4mJSUFgAkTJjBz5kw+//xz9uzZwyOPPEJxcbF9FZmjjBs3jt27d7Np0yaH3kc4AYMRXe9/03DOn8Q82h2jnwVzXjnHHvkPGePvwFaUq3WEQghxScr27qX4999BpxDcpkh6g86hRsvnHTF2uXnzZvr27Wv/esKECQCMHDmSOXPmcPfdd5OZmckLL7zAyZMn6dixIytXrjxrArW4OKvV6vpbbFwO31B8/v05TQcmkf7fx8jfUUj2qr8o2nIVkc8+htfNj6qFGoUQohY5sm3OnjUbgAZRpZiaNIY2t9TatV1FtTdd1ev1BAQEXDQZysnJqZXAnIUrbboqiVANKAqFc6aS9v6XWMtAp1cI6xNE8LP/QxfVVevohBC1Kf84HFsHLfqDT3Cd395RbXP538c5NGAAWK00HZCB1z0vQ0/32VLDIZuuvvTSSwQEBFx2cPVBQkICCQkJtVoOQNQjOh3+o57F+8YRpI1/kKKdqWSszqPor7uIfLAvxttfA3/plRSi3itMh9k3QMHfYPCEdoOhy0iI6VXve4BzPvsMrFZ8w8vwCveGTvdrHZJTqlGP0MmTJ+3bWrgL6RESiqKQ98VM0t9+H8VsQ2+0EdGjjICRT0CPR8FD6k4JUS+ZS2HOQJTULVgs3hhNpaefC2kJnUeo1Zd9Qx0ahiPaZktuLgf7XodSVkb0tVn4DvkX3Dj1sq9bn1T393e1J0u7bd0Z4fZ0Oh1BI8fQbNkKvNo0x2bWc+J3H46/PA3ru/GwdwVIZWoh6hdFgSWPoqRuIXVdOAcXBXF0Rx/yuQGb3heyD8DPk+CdNvDNA3B4DdhsWkddbblffY1SVoZXUDk+ERboPlbrkJyW5qvGhKgvTLGxxH67hNDHxoFeR0GKD4fnlVI87QH4YjCk79Y6RCFEda15Hf5aRNaeBhQfV3tgSncf4MT8XRxc2ZSM0tsx+8eBzQx/LVb/j/+vM/z+rjqc5sRsJSXkfvUVACFti9C1HQhBsdoG5cSqnQjZbDa3GxYT4kw6Dw/CHnuM2PnzMUVHYyk1kLImlPRF27Al9IIVT0GJay0YEMLl7PgGfnud4nQTWbvUwqnhz04k7PHxeISHY83JIXvpBg7OzuHv44MpDhiMYmoAuUcg8SV4rx0sGA4HfgGb880jzfv2O6z5+Rj9rfg3KYMe7jNB+lJUe46Qu3KlOUI2m41du3YBcOWVV6LXVzsPFudgKykh/a23yJs3HwDPADORPXLxauQH/SdDl1H1frKlEC4nNQnm3IKl2MzhX2OxFpQRcNttRL42BQDFYqEw8Vdy586l5M8/7S8zNY0l6JpWBDTYhSFz8+nrBURD5/uh03BoEHlJIdVm26yYzRwcMADLiTQiuuYRdE1rGL3aLdui6v7+lkToPP65amz//v0ukQgJxyj67TdOPPc81qws0EPD9gUEty5C13UkDHwHDEatQxRCAOQeg1n9UAozSd3cmuLDhXi2bEHswoXovb3POv3UwYPkzp1H/pIl2EpKAND5+BBwfW+CW5/CM2MFlOWrJ+v00HIAdHlAXYZvqNGi7FqT//33nHjm/zB4KbS4JQ39XbMg7k5NYtGaJEK1xJV6hITjWHJySHvhBYp+UbeD8Q0/RZPe2ehbXgN3fQHeQRpHKISbKyuATwdAxm4yjzUna0MpOm9vmn6zEM8WLS74UmtREflLl5I7dx7lhw7Zj/t07ULQ1c3wNyShO77h9Av8Iyt6ie6HwChHvaOzKIrCkcFDOLV/P2HtCwjt0QCe2OG2f4xJIlRLJBES1aUoCvmLFpM+ZQq2khL8osw06ZmJLqwF3LsQQpprHaIQ7slmhXn3wIFVFBdEkLLSA2w2Gr0+lcAhQ6p9GUVRKPkzidy5cylMTISKOnMeDRsSeMt1BMbmYzyyGEor5wnq1N6hLg9AqwEOT0iK1q4ldcxY9EZoMSgNw00vQO8JDr2nM5NEqJa4UiJktVpZt24dAL169ZI6Qg5SsnkzKQ8+hFJeTmBbiIg7gc4nCO7+CmKv1jo8IdzPyomw8UMsZm8Or47FmpNfZV7QpTCfPEnuggXkffOtOiwO4OFBg/79CLqqCd4la9Ad/f30C3wbQtxd0GEYRFxZ5Vq11TYfu38EJZs2Edy6iPB4Czz5lyaVsp1FrdcREq7BZrNhq0e1MOojn65diXz7LdDpyNsD2X+3gtJc+GIIbPtK6/CEcC+bZsPGD1FscOJAN6w5+ZhaNCfi+ecu67LGiAgaPv44LX9NJPLtt/Hu3BksFgpW/sSxF2ZzZJGB3Kgp2LqOA98wKM6ADdNhRi+YcTVs+BCKMu3Xu9y2uXT7dko2bQK9juDWRWrC5cZJUE1IIiSEAzS44QbCKxrazHVF5JX1UuuRLB0HP79QrwqzCVFvHVoNPzwNQFbZLRTvOIjO25sm06ah9/GplVvoTCYCbhlI7Nyvabp4EYF33onOy4tT+/dz8q0EDrz4MydPPUBJx9cwRw5AwQgnd8JPE+HdNjBvGOxZBjbLZcWRPWsWAAExxRh9bGrVe1Et2kxrrwdkrzFxuYLvuw9LegbZn3xC2rIUDGPvwz/na1j3PmQfgts+AZOv1mEK4Zoy98PCkaBYKfYbQNbCZAAiXnjhopOjL5VX27Y0euVlGj71H/IWLyZ33jzMx1LI/eprcitP0jXE4O+Nh2c5Hh5FeGxch95nHaVRXdGHRFFqTsezfR88QkPReVTvV/Spw0corFioEdKmCFrdCKGOeY+uSOYIXYSrzRGSvcbqlqIopE18lvwlS9B5exMzaTjef00FazlExMGw+RDQWOswhXAtJTkw8zrIPYIluBuHF57CmpVFwNChRE59rc7CUGw2itetJ3fBfMp278aSmQVm81nnWfV69rRrB0Db3bsx2GygA0NwMB7h4RjDGuLRsCEeYWHq54b/+DokmLQXXyT/2+/wa2Im6upMGPE9NOtTZ+/TWTlk93khRM3odDoavfIyluxsin//ndS3viXmnVl4/jEBTu6AWf1g2DyI7KR1qEK4Bku5WvU59whKg2hObGmENWuzOi9o0vN1GopOr8ev99X49VYXSSg2G9a8PCwZGepHZiaWjAzK0tMx5WViK8jDw9uKUgIoOqzZOVizczjFnvPfRK+373UY0iYPwq+Eptc4/s25EEmEhHAwndFIk2nvcWzkA5Tt2kXqC9OJnfENHj89Apl74dOb1GGydrdqHaoQ9ZuiwPIn4dg68GxAtvVOiv+cV+vzgi6VTq/HIzgYj+BgaNPGftxqtRJQ0Vvfstv/0O9einXjXCwHt2IpNWAuNWAxe2PxbIZFF4alyKImUllZ9vmGvo3BJ9Sszg1ywyrSl0MSITcTGBiodQhuSe/rS9THMzg67F7MKSmkPjOF6JmLMfz4bzj4Cyy8H/pNhquflEZMiEu17n1I/gp0eopbP0vm89MBx84Lqi32ttkrAF23UXh0G4VHzmHYPh+2z4O8FCBbPSeoKXQYhnLlnVhsfliTFmLa+Jy6RL/9HVq9hXpL5ghdhCvNERLaK09J4eg9w7Dm5OB71VVEJUxHt/oFSPpEPaHjfXDLNPAwaRqnEPXOnmWw4H5AwXLVixx+ZRHWzLqfF+QQNhukrIfkebB7CZQXnX4u5mooSofsA3Dts3Dt/2kWprORgoq1RBIhUdtKd+7i2MiRKCUlNLh1EJGvv45u0yxY+X+g2CCmF9z1JfiGaB2qEPXDiWT47CYwl6B0+Repi3MpXr8BU4vmNF24UPMhsVpVXgx7lsP2uXD4N6DiV7jBUy2g6BemaXjORAoqXqaEhATatWtHt27dtA5FuBjv9lfS5P1p4OFBwffLyHzvPeg+Bu79BjwbqPMbZvVTl/8KIS6sIE3dPsNcAs2vIzulGcXrNzjNvKBaZ/KFDnfDiKXw5C7o9wI0iYf+L0oSdImkR+giXKlHyGq1snHjRgB69Oghy+c1lrd4CWkTJwIQ/txzBN8/HDL2wNy71PkAngFw1+fQvK/GkQrhpMpL1J6gtGQIa0Nx3FRSxv5b3Uds6lQChw7ROsJqkbbZMaRHSJyT2WzGfI46FqLuBQ4dQtgTTwCQ/tprFKxcCQ3bwujVENUdTuXDV7fD5k+1DVQIZ2SzweKxahLkE4JlwEccf3Yy2GwEDB1ab5KgStI2a0cSISE0FDJ2DEH3DgNF4cTTz1CclAS+oWpBtLi7QbGqy4FXTlR30BZCqFa/Cnu+B4MJ5Y4vOfHadKyZWZrUCxL1myRCQmhIp9MR/txz+F9/PYrZzN/jHqNs334wesHQj6FvRYO+8UN1T6JThdoGLIQzSJ4Hv7+jPr71f2T/tMO15wUJh5JESAiN6QwGIt96E+8uXbAVFpI6ZgzmtDS1nlCfp+GOz8DDCw78BLMHQF6q1iELoZ1jG+D7f6uPe/+H4rJmZP6v/tQLEs5HEiEhnIDey4uoDxMwtWiOJT2dlNGjseblqU9eeRs88INaLC3jL3UPpRPJWoYrhDZyjsCC+8Bmhra3Ymn/MMef+k+9nRcknIMkQkI4CUNAANEzZ+IRHk75wUOkjnsMW1mZ+mSTLjD6V3UfoeIMWDrOvr+QEG6hLB/m3g0l2dCoI8rgjzjx34kyL0hcNkmE3Iy/vz/+/v5ahyHOw9ioEVEzP0Hv70/pli2cePppFGvFJOnAKBi5TB0mS98FJ7ZpG6wQdcVqgW8egKx94B8Jw+aTPecritevd5l5QdI2a0cSofNwxYKKBoOBLl260KVLF6lT4cS8WrWiScJ0dEYjhT//QvqUKdjLffkEQ9tB6uNtX2oXpBB1afNsOPQrGH3g3vkU700l84P/Aa4xL0jaZm1JInQe48aNY/fu3WzatEnrUIQb8o2PJ/Ktt0CnI3fuPLI//uT0k52Gq593fqsWlBPC1e1YqH6+bhIWUxNO/OcpmRckao0kQkI4qQY3DiD82WcByJw2jbxFi9UnYq+BwGg4VaBuNCmEK8tLheObAR1Ku6GcePoZLJmZMi9I1BoPrQMQdcdqtdp7uLp16yZdsPVA8P3DsWSkkz1zFmmTJuERFopf797QcTiseU0dHutwt9ZhuhxFUbBmZVGekkL5sRTKU45hTknBnJGBX69eBN0/AoOfr9Zhuoc936ufY64ie95Sl5oXVEnaZm1JIuRmyipXIYl6I+zJJzGnp1Pw/TL+fvwJYj6fg3fHe2HNVDj6O+QchuBmWodZ7yg2G5bMTMqPqUlO+bEUyo8dU5OflBSUknMPO5Zu3kLOl18ROnYMgffcg97Ts44jdzN/LQGgWN/VpeYFnUnaZu1IIiSEk9Pp9US++irW7ByK160jdezDxM6bi6n5dXAoEbZ9Df0maR2mU1KsViwnT/6jZ6eid+dYCuWpqSgX+uWj12Ns1AhTTDTG6GhM0THovb3ImfM55ceOkT71dbLnfE7YuEcJGDIEnYc0p7Uu/2/4OwlLmYETM3+VeUHCIeR/rhD1gM5kovH775MyYgRlu3dzcsoUoscPVxOh5LnQ91nQu3d3umK1UrByJWU7dtiTHnNqKsqFNrI0GDA2aYwpOgZTdHSVpMfYpDF6k+mslwTecQd5ixeTlfAhlrQ00p6fRPbsTwl7fDz+N9yATi9TL2vNbnVYLC+3NZasbEzNZV6QqH2SCAlRTxj8fGk05VWODL2N0s1bUFpOQ+cdBIUn1KXFLa/XOkTNFG/cSPrU1zm1b99Zz+mMRoxRUWclOqaYaIyNGqEzGmt0L53RSNBddxEweHDFir6PKT9yhONPPIlnu7Y0fPJJfK++Gp1OV1tvz33tXgKAmSZAHg1uvNFl5gUJ5yGJkBD1iGerVuh9fLCVlHDq6N94xd0Nf85QJ027YSJUfvQo6W++RdGvvwKgb9CAwKFDMDVthikmGlN0NB4REegcMPlU7+lJyKgHCLzzDnLmfE7OZ59xavceUkePwbtrFxpOmIBP5861fl+3kX8cUv8EwFzuDYAxspGWEQkXJX24QtQjOoMBr7g4AEq3J5+uKbT3ByjO0i6wOmbNzyd96uscGnSrmgQZDATddx/Nf1pJ+MSJBN1zN749e2Js3NghSdA/Gfz8CHtsHM1/+ZngUaPQmUyUbt7CsXvvI2XsWMr27HHo/V1WZWmIqB6YM3MA8IiI0DAg4aokEXIzPj4++EjXcr3m3aEDAKXbt0NEe2jUUd2EcscCbQOrA4rZTM5XX3NowI3kfP45mM349rmGZt8vJWLS83gEBWkWm0dQEOH/9wzNV/1E4F13gcFA8W9rOTL0No5P+A/lR49qFlu9VDEsprQbjOVEGgDGRpEaBuRY0jZrRxKh83DVLTbi4+OJj4+XOhX1WJVECKDz/ernrV+69EasRWvXcnjwENJffRVrXh6mFs2JmjmT6I8/xrN5c63DszNGRNDo5ZdovmI5DQYOBKDghx84NPAW0ia9gPnkSY0jrAcK0iBlIwC2qH7YKkoZGBu5Zo+QtM3akkToPGSLDeGsvDuoQ2PlBw9hLSiAK+9QN2LN3APHt2ocXe07deAAKf8aTeqYsZQfPowhKIiIyS/QbMkS/HpfrXV452WKjaXxO2/TdMli/Pr0AauVvG++4dANA0h//Q0sOTlah+i89nwPKNAkHnOxesgQGIje21vTsIRrkkRIiHrGIyQEY1QUAKU7d4J3ILS9VX3ShTZiteTkkPbSSxweMpTiP/4Ao5HgBx+k+U8rCRo2rN7U7fFq04aoj2cQM/drfLp2RSkvJ2fOHA71v57M/03HWlSkdYjOp6KIIlcMwZymDot5yERp4SCSCLkRq9VKUlISSUlJWK1WrcMRl+G8w2O7vqv3G7HaysvJ/vQzDg24kbx588Fqxf/6/jRfvozwZ57G0KCB1iFeEp/OnYn+8guiZs7Eq107bCUlZCUkcKj/9WR/NgebVBZWFZ6ElA3q43aDsVQkQsYI102EpG3WliRCbqakpISS82wdIOqPsxKhmKshMKZiI9bvNYzs0imKQsHPP3P4lkFkvPkmtsJCPNu2Jfrzz2nyv/9hionRNsDco2qimf/3JV9Cp9Ph1/tqYr/9hsbT3sPUtCnWvDwy3niDQwNuJHfhQhSbrfZiro92Vw6LdYOAJpjtE6VdNxECaZu1VD/6loUQVXh3VBOhsuTtKIqiVjPudD+sflWdNN3hHo0jrJmy3btJf/0NSpKSADCEhdLwiSfUrSu0mjyqKHByJ+xdoX6k71SPG32g73PQ/WEwXFoTqtPraXDjjfj370/+0qVkTk/AkpbGyRcmc2rvPsInPe++BRl3L1U/txsCYJ9cLjWEhKNIIiREPeTVujU6kwlrfj7mY8cwxcZCx2Gwegoc+wOyD0GI86ykOh9zRgaZ779P/qLFoCjoTCaCR40iZPRobXZ3t1ogdWNF8rMc8lJOP6fTQ0AU5B2DVc/BzoUw6AOI7HjJt9N5eBB4++00uOUWcr/8kox33iV37lw8wsMJHTvm8t9PfVOYDsfWqY/bDQbAnHYCkBpCwnEkERKiHtKZTHhdcQWl27ZRun27mggFNIEW/eDgL5D8NfR7Qeswz8tWVkbOnDlkfTLTvst7g5tvpuF/JmBs3LhugzGXqluU7F0B+36E0n+s5vLwVr+nbQZCqxvBK1CdkP7zJEjbDjOvg56PwrUTwXTpiZve05OQf/0LncmT9NdeI/O99/Bo2ND9NhetXC3WuCsEqgsC3KGGkNCWJEJC1FPeHTrYE6GAwepfz3QaXpEIzYVrn73koRtHURSFgh9+IOOdd+y/4Lw6xBH+3//i06lT3QVSkgP7f1J7fQ79CuZ/zM3wDoLWN6vJT7O+YDqjyF2XkWpStPK/8NciWP8/dTjnlvegRf/LCit4xP1YMtLJnjWbtOefxyM0BL/evS/rmvWKfVhM/fesWK2YMzIA160hJLTnXK2kEKLaKucJlSZvP32w9c3gHQyFaeov+FY3aBTduZ2c/CJ5CxcC6lBHw/9MoMHAgXWzY3teKuz7Qd264dh6UP6xOicgWk182gyE6J4XTyD9w+HOz9S5WCv+ow6hfXU7tL8TBkwFv7BLDjNswgTMGRkUfL+Mvx9/gpjP5+Ddvv0lX6/eKMo4a1jMkpUFFgsYDHiEXfr3VIgLkUTIzXh5eWkdgqgllSvHyvbtw1Zaqhab8/BUfzlv/BC2feFUiZCtpIS8xYsBCB03jpB/PeTYAnmKAhm7T8/3Sdte9fnwK6HNLWryE9EeLmVycqsBENNLnZv15wzY+Y3aI3fDFOh47yVdU6fXE/nqq1izcyhet47UsQ8TO2+u9qvmHG3P96DYILIzBKnvtXLpvEd4w3pTN+pSSdusHdf+lyWqMBgM9OjRQ+swRC3xiIjAo2FDLBkZlP31Fz5du6pPdBquJkL7flQ3YvUN1TbQCiXbtoHZjEejRoQ+Ns4xq6JsVkhNUhOfvSsg98jp53R6tbenzUC15yy4ae3c09MPbpwK7e+A7x9XV5ctfRR2zIdbpl3SpHWdyUTj998nZcQIynbvJuVfo4mdNxePUOf4WTpE5bDYFUPsh8xuUEMIpG3WmtQREqKe0ul0Z9cTAgi/Qv2r2maB7fM1iu5sJX+qS+N94+MdkwTlHoPp3eCzG2HDdDUJMnhCq5tgcAI8dQBG/QA9x9VeEvRPjbvAmNVw/cvqJOsja+Gjq+D3d8BqrvHlDH6+RH08A2OTJphTU0kd+zC24uLaj9sZFGXC0T/UxxXDYoDb1BAS2pJESIh67JzzhEDtFQJ1hZOTbMRaWSPIJz6+9i9elAFfDoGcQ+AVAHH3wF1fwjOH4d756vejLnrGDEbo9Tg8ul6daG0pg8SX4eM+8PfmGl/OIyyM6FkzMQQFUfbXX/z9+BMo5ponVU5v77KKYbFOEBRrPyw1hERdkETIjVitVrZs2cKWLVukjLuLsPcIJSej/DPhaV+5EeteOL5Fo+hOsxUXU7prFwA+3bvX7sXL8uGr2yDnsDrp+dGNcNvH0O5WddhKC8HN4P7FMPQT8AmBjL9gVn/44Rk4VVijS5liY4n6eAY6b2+K//iDtOcnVf1Zu4LKvcUqiihWcpcaQtI2a0sSITdTWFhIYWHNGmLhvLyuuAIMBiyZmVgq/npWnwg4PcSw9QttgvuHkq1bwWLBGBmJqUkt1gkyl8K8YWoFaN8wGLEEGjhJvRmdDjrcDeM2QYdhgAJJH0NCd9j7Q40u5R0XR5P3p4HBoFaifvc9h4SsieIsOPq7+vgfw2IAlrSKHiE3qCEkbbN2JBE6j4SEBNq1a0e3bt20DkWI89J7e+PVujVwxjwhULfcANi1CMq1nVtiHxarzd4gqxm+GaUuufZsAMO/c85q2r4hMHQG3L9EHfYpOA7zh8GC+9UNRqvJ75praPTKKwBkz5xJzldfOybeuranYlisUYez5m7ZJ0tLDSHhQJIInce4cePYvXs3mzZt0joUIS7ovPOEYnqpv3jLC0+vyNFI8Z+1PD/IZoOlj8H+H9UhwGHz1V+kzqx5X3hkA1z9JOgM6nLx6fGw+VP1/VRD4G1DCXvicQDSp0yhYOVPjoy4buxeon4+Y1jMVlaGNUet8i2TpYUjSSIkRD13zpVjAHr9PyZNf1XHUZ1mLSqi7K+/APDtXguJkKKoe33tmK8mFHfOgdhel3/dumDygf4vwtjf1JV9p/Jh+ZMw52bI3FetS4SMHUvQvcNAUTjx9NMUV/S21UvF2XCkYljsH8vmAftQr87HB31AQB0HJtyJJEJC1HP2wop//YVSXl71yQ73qvVzjq1TN2LVQOmWLWC1YoyKwhhZC3M9fn9brZMEMORDaH3T5V+zrkW0h3/9Aje+AUZfSNkAH/WC1VPVWkgXoNPpCH/uOfyv749iNvP3uMco27e/jgKvZXuXqxW+I+LUCeb/cLqGUIRjyi0IUUESISHqOWNMDIaAAJTycsr2ndGrENAYmvdTH2vUK1RsXzZfC/PtNs2GX19VH9/4ulpFu77SG6DHwzDuT3XvMpsZfnsd/rj4RGidwUDkW2/h3bkztsJCUseMsScO9UrlsNgZvUEgNYRE3ZFEyM0YjUaMRqPWYYhapNPp8DrfPCGAzhWTppPngtVSh5Gp7IUUL3ei9K7v1H29AK55Gno8cpmROYnAKHWO001vqV///m61JlHrvbyI+jABU4vmWNLTSRk9GmtenmNjrU0lOXD4N/XxGfODAMwnKxIhN6khJG2zdiQRciMGg4FevXrRq1cvDAaD1uGIWnTeeUKgVlb2CYGik+o+WHXIWlhI2e7dwGVOlD74CywaCyjQ9SHo+1ztBOgsdDqIHw1NuoG5GH59pVovMwQGEj1zJh7h4ZQfPETquMewlZU5ONhaYh8Wa3/O1X6VPVyuXkMIpG3WmiRCQriACyZCHia10jKolabrUMnmzWCzYYyJxnipv9BSk9Sl5jYzXHEb3PzWpW2Q6ux0OnXneoBtX5+9Sex5GBs1ImrmJ+j9/SndsoUTTz+NUh+K8tmLKA4+59PuVENIaEsSISFcgHdcHOh0mFNTsWRnn31C5eqx/SvV7SjqyOn9xS5xWCx9N3x9J5hL1LlOQz9W59a4qqhucOUdgAI/PVft7VG8WrWiScJ0dEYjhT//QvqUKc5dfbokB45UDosNPecp9snSbjI0JrQjiZAbsVqtJCcnk5ycLGXcXYzB3x9Tc3XVTen2HWefEN5O3RTUZoEdC+osrsvaXyz3KHw5FMryoEk83P2l2rvl6vpPVmsjHf0d9lW/ArVvfDyRb6m9Zblz55H98ScODPIy7ftB/bcYfiWEtjjraUVRqqwac3XSNmtLEiE3k5eXR159mlApqu2Cw2Nwuldoa91sxGrNz6dszx7gEhKhogz4Yog6r6lhO7h3AZh8az9IZxQYDT3HqY9XPQ+W8guf/w8NbhxA+LPPApA5bRp5ixY7IsLLd569xSrZ8vNRSksB95gjBNI2a0kSISFcxEUToStvBw9vyNp3STuh11TJli2gKJhiYzGGN6z+C0vz4MvbIPcIBMbA8EXgE+ywOJ3S1U+CX7i6keymmTV6afD9wwkZ/S8A0iZNomjtWkdEeOlKc+HwGvXxOZbNw+lhMUNwMHovr7qJS7gtSYSEcBHeHToCULZjx7kny3oFnP7Fs83xG7GW/PknUMP9xcpLYN49kL4TfBuqO7g3cMM5Ip7+cN3z6uPf3lDn1NRA2IQJBAweDFYrfz/+BKU7zjFcqpW9P6gT3xteAaEtz3nK6T3G3PBnL+qcJEJCuAjPFs3R+/hgKynh1MHzVJGuHB7btQhOFTk0nmJ7/aBqDotZzfDNA2qVZc8AuH+Rc26iWlc63qcuLS/LhzVTa/RSnU5Ho1dfwffqq1FKS0kd+zDlR486Js6aukARxUoyUVrUJUmEhHAROoMBr7g4AEq3J5/7pJhe6lYG5UUO3YjVmpfHqYoq1z7dqlFR2maDpePgwE/qROF7F6hJgDvTG2DAa+rjTbOrvRdZJZ3RSJP3p+F1xRVYc3NJ+ddoLFlZDgi0Bkrz4NBq9fF5ls0DWOw1hCQREo4niZAQLuSi84R0OrWnARxaU6h40yZ1flDz5niEhV34ZEWBnyaqq9n0HnDXFxDT02Gx1StNr4HWA9XCg6uer/HL9b6+RH08A2N0NOa//yb14Ue0rTG070d1WCysLYS1Pu9pZnsNIUmEhONJIuRm9Ho9er382F3VRRMhgI4VG7GmbICsgw6JoyRpE1DN/cXWvgV/zlAfD/kIWg1wSEz11g2vgN4IB1bBwcQav9wjNJTomZ+g9/GhbNcuyvbudUCQ1VSNYTFwz6ExaZu1I991N2IwGLjmmmu45pprpIy7i/LuoA6NlR88hLWg4NwnNYiEFv3Vxw7qFaqcKH3R/cWSZsLqKerjm96EuLscEk+9FtIc4seoj3967pL2izPFxODZWu2BMaek1GZ01VeWD4d+VR+fZ9l8JXeqIQTSNmtNEiEhXIhHSAjGqCgASnfuPP+JnSo2Yt0+r9Y3YrXk5nJq/37gIvODdn4LPzytPu7zX+g+tlbjcCl9ngbvIMjcc8kr/kzR0QCUH9MoEdr3I1jLIawNNGxz3tMUiwVLhlr93EO21xB1QBIhIVxMtYbHWt0IPqFQlA4Hf67V+1cOi3m2bIFHSMi5TzrwMyyu2EQ1fgxc+99ajcHleAfBtRPVx79OUXtXasgYU5EIadUjdJEiipUsmZlgtYKHBx6h5/n3I0QtkkTIjdhsNnbs2MGOHTuw2WxahyMcpFqJkIcJOlRsxLq1dofH7PWDzre/WMqfFZuoWtR9tW58wzU3Ua1tXR+E0FZQkgW/v1Pjl5uiYwAoTzlW25FdXFk+HKqY31Td+UHh4ejcZJhI2mZtSSLkRhRFIScnh5ycHOfekFFcFu+OaiJUlrz9wj/nf27EWphea/cv2XSB/cXStsPcO8FSCi2uh6EzQCaIVo/BCDe8qj7e+BHkHKnRy00VPUJmLYbG9v+kDouFtlKHxi7AHYspStusLWmBhHAxXq1bozOZsObnYz52gb/+G7aFxl3Vpdk75tfKvS3Z2Zw6oK5Es68YUxQ4tgEWDIdPrlV7B6J6qMvkDcZaua/baHkDNOurJhW/TK7RSyvnCFkyM7GVlDgiuvP757DYRXr/7DWE3CgREtpyi0Tovffe44orrqBdu3aMHz9eMm7h0nQmE15XXAFcZHgMoHPFpOltX9XKRqwlmyrmB7VujYe/L+xYqCY/n90Ie5aBYoOWA+De+WDyuez7uR2dTi2yqNOrBTGPra/2Sw0BARgCAgAoT011VIRnKyuAg7+ojy8yLAZSQ0jUPZdPhDIzM5k+fTpbtmxh586dbNmyhY0bN2odlhAOVa15QgBX3AZGH8jaD6lJl33f4sr5QY0N8H4cLBoNaclqtejOI+HRjXDfQnXyr7g04e3U7yXAyolqVe5qMsZUzBO6UE9hbdv/E1hPQUhLaNjuoqe7Yw0hoS2XT4QALBYLZWVlmM1mzGYzDRvWYCdsIeqhynlCpckXSYS8GpxexXO5NYUy9lKSuAwA3/I/oDAN/CLUzUOf/Atu/UAdjhOXr+9z4NlATTJ3LKj2yyqHx+q0ltA/iyhWY1K82b69hnvUEBLa0zwRWrt2LYMGDSIyMhKdTseSJUvOOichIYHY2Fi8vLzo3r07SUnV/8s1LCyMp556iujoaCIjI+nfvz/Nm7vxRo7CLVT2CJXt24ettPTCJ1dOmv5rcc03YlUUOPALfHkblnd6Up5RDCj4tG8JQz+BJ3bCNU+Db2jN34Q4P78w6P0f9XHiS1BeXK2X1XktoVOFaqkEuOiy+UoW+2RpqSEk6oaH1gEUFxfToUMHHnzwQW677baznl+wYAETJkxgxowZdO/enWnTpjFgwAD27dtn79np2LEjFsvZReFWrVqFt7c3y5cv5+jRo3h7e3PTTTexdu1arrnmmnPGc+rUKU6dOmX/Oj9frddRcL4qvfWI1WqluFhtMAsKCqSCqQtTfHwoCw7GkplJxsaN+HTpcv6Tg64En1jIPQJ/zoWO91z8BuUlsOs72PQp5BwAoOC4F0VWK6amTSh+YLH6139JGVBWK+9JnKHdffDHTMhKhVVvwjX/uehLysJCKbJasR44gG9dtGl/LVH/DQQ1A+8ouMg9baWl5GdnA1Dq60O5C7S71SFts2NU/t6+6LxgxYkAyuLFi6sci4+PV8aNG2f/2mq1KpGRkcrUqVOrdc2FCxcqjz76qP3rN998U3njjTfOe/7kyZMVQD7kQz7kQz7kQz5c4CM1NfWCeYLmPUIXUl5ezpYtW5g4caL9mF6vp3///mzYsKFa14iKimL9+vWUlZVhNBpZs2YNY8aMOe/5EydOZMKECfavbTYbOTk5hISEoDvP+Ha3bt3YVLFaproKCgqIiooiNTWVBg0a1Oi14tJcys+pPnDW96VVXI6+b21fv7aud7nXkXbM+Tnr//XL5aj3pSgKhYWFREZeeJjVqROhrKwsrFYr4eHhVY6Hh4ezt5o7KPfo0YObb76ZTp06odfr6devH7feeut5z/f09MTT07PKscDAwAvew2AwXHIj0KBBA2lA6sjl/JycmbO+L63icvR9a/v6tXW9y72OtGPOz1n/r18uR76vgIqSERfi1IlQbZkyZQpTpkxx2PXHjRvnsGuL2uOqPydnfV9axeXo+9b29Wvrepd7HWf9dyROc9WfkdbvS1cxN8cp6HQ6Fi9ezJAhQwB1aMzHx4dvv/3Wfgxg5MiR5OXlsXTpUm0CrQUFBQUEBASQn5/vkhm+EML1STsmXIHmy+cvxGQy0aVLFxITE+3HbDYbiYmJ9OzZU8PILp+npyeTJ08+axhOCCHqC2nHhCvQvEeoqKiIgwfVvYk6derEu+++S9++fQkODiY6OpoFCxYwcuRIPv74Y+Lj45k2bRoLFy5k7969Z80dEkIIIYSoCc0ToTVr1tC3b9+zjo8cOZI5c+YAMH36dN566y1OnjxJx44d+eCDD+jevXsdRyqEEEIIV6N5IiSEEEIIoRWnniMkhBBCCOFIkggJIYQQwm1JIiSEEEIItyWJkJNavnw5rVu3pmXLlsyaNUvrcIQQokaGDh1KUFAQd9xxh9ahCHFBMlnaCVksFtq1a8fq1asJCAigS5curF+/npCQEK1DE0KIalmzZg2FhYV8/vnnfPvtt1qHI8R5SY+QE0pKSuKKK66gcePG+Pn5cdNNN7Fq1SqtwxJCiGq79tpr8ff31zoMIS5KEiEHWLt2LYMGDSIyMhKdTseSJUvOOichIYHY2Fi8vLzo3r07SUlJ9udOnDhB48aN7V83btyY48eP10XoQghx2W2YEPWJJEIOUFxcTIcOHUhISDjn8wsWLGDChAlMnjyZrVu30qFDBwYMGEBGRkYdRyqEEGeTNky4E0mEHOCmm27i1VdfZejQoed8/t1332X06NGMGjWKdu3aMWPGDHx8fPj0008BiIyMrNIDdPz4cSIjI+skdiGEuNw2TIj6RBKhOlZeXs6WLVvo37+//Zher6d///5s2LABgPj4eHbt2sXx48cpKirixx9/ZMCAAVqFLIQQdtVpw4SoTzy0DsDdZGVlYbVaz9owNjw8nL179wLg4eHBO++8Q9++fbHZbDzzzDOyYkwI4RSq04YB9O/fn+3bt1NcXEyTJk345ptv6NmzZ12HK8RFSSLkpG699VZuvfVWrcMQQohL8ssvv2gdghDVIkNjdSw0NBSDwUB6enqV4+np6URERGgUlRBCVI+0YcLVSCJUx0wmE126dCExMdF+zGazkZiYKN3GQginJ22YcDUyNOYARUVFHDx40P71kSNHSE5OJjg4mOjoaCZMmMDIkSPp2rUr8fHxTJs2jeLiYkaNGqVh1EIIoZI2TLgT2WLDAdasWUPfvn3POj5y5EjmzJkDwPTp03nrrbc4efIkHTt25IMPPqB79+51HKkQQpxN2jDhTiQREkIIIYTbkjlCQgghhHBbkggJIYQQwm1JIiSEEEIItyWJkBBCCCHcliRCQgghhHBbkggJIYQQwm1JIiSEEEIItyWJkBBCCCHcliRCQgghhHBbkggJIdzW0aNH0el0JCcnA+rWEjqdjry8PIfeT6fT0bFjR4fc43LNmTOHwMDAGr3mgQcesL+vJUuWOCQuIRxFEiEh6qENGzZgMBgYOHBgnd73zMTB1Vx11VWkpaUREBDg0Pv88ssvVXZvdyZ33303+/fvr9Fr3n//fdLS0hwUkRCOJYmQEPXQ7Nmz+fe//83atWs5ceJEndyzvLzcKa9Xm3GZTCYiIiLQ6XS1ds1zCQkJISQk5LKuYTabaymaqry9vWnYsGGNXhMQEEBERIRD4hHC0SQREqKeKSoqYsGCBTzyyCMMHDjQvht4pcrhnRUrVhAXF4eXlxc9evRg165dVc77448/6N27N97e3kRFRTF+/HiKi4vtz8fGxvLKK68wYsQIGjRowJgxY2jatCkAnTp1QqfTce211wJw7bXX8sQTT1S5/pAhQ3jggQcueL3qxHGmF198kY4dOzJr1iyaNm2Kl5cXACtXruTqq68mMDCQkJAQbrnlFg4dOlTltUlJSXTq1AkvLy+6du3Ktm3bzvm9qxwaq7zXP02bNo3Y2Ngqr4mPj8fX15fAwEB69erFsWPHzhv/uWzatInrr7+e0NBQAgIC6NOnD1u3bq1yjk6n46OPPuLWW2/F19eXKVOmALBs2TK6deuGl5cXoaGhDB061P6a2NhYXn31VUaMGIGfnx8xMTF8//33ZGZmMnjwYPz8/IiLi2Pz5s3215w5NFb5Pfjyyy+JjY0lICCAe+65h8LCwhq9RyGclSRCQtQzCxcupE2bNrRu3Zrhw4fz6aefoijKWec9/fTTvPPOO2zatImwsDAGDRpk70U4dOgQN954I7fffjs7duxgwYIF/PHHHzz22GNVrvH222/ToUMHtm3bxqRJk0hKSgLUoZ20tDQWLVpUo9jPvF514zjTwYMH+e6771i0aJF9mK64uJgJEyawefNmEhMT0ev1DB06FJvNBqgJ5C233EK7du3YsmULL774Ik899VSN4j+TxWJhyJAh9OnThx07drBhwwbGjBlT4x6lwsJCRo4cyR9//MHGjRtp2bIlN99881nJxosvvsjQoUPZuXMnDz74ICtWrGDo0KHcfPPNbNu2jcTEROLj46u85r333qNXr15s27aNgQMHcv/99zNixAiGDx/O1q1bad68OSNGjDjnv6FKhw4dYsmSJSxfvpzly5fz22+/8frrr9foPQrhtBQhRL1y1VVXKdOmTVMURVHMZrMSGhqqrF692v786tWrFUCZP3++/Vh2drbi7e2tLFiwQFEURXnooYeUMWPGVLnu77//ruj1eqW0tFRRFEWJiYlRhgwZUuWcI0eOKICybdu2Ksf79OmjPP7441WODR48WBk5cqT963NdrzpxnGny5MmK0WhUMjIyzvl8pczMTAVQdu7cqSiKonz88cdKSEhIlet+9NFHVd5P5fcuNzfXfq8OHTpUue57772nxMTEKIqifl8BZc2aNReMpdL5vn9nslqtir+/v7Js2TL7MUB54oknqpzXs2dP5b777jvvdWJiYpThw4fbv05LS1MAZdKkSfZjGzZsUAAlLS1NURRF+eyzz5SAgAD785MnT1Z8fHyUgoIC+7Gnn35a6d69+1n3A5TFixdf8L0J4WykR0iIemTfvn0kJSUxbNgwADw8PLj77ruZPXv2Wef27NnT/jg4OJjWrVuzZ88eALZv386cOXPw8/OzfwwYMACbzcaRI0fsr+vatWutxn/m9aobx5liYmIICwurcuzAgQMMGzaMZs2a0aBBA/vwVUpKCgB79uyxDxVW+uf36FIEBwfzwAMPMGDAAAYNGnTJk4bT09MZPXo0LVu2JCAggAYNGlBUVGSPvdKZ37/k5GT69et3wWvHxcXZH4eHhwPQvn37s45lZGSc9xqxsbH4+/vbv27UqNEFzxeiPvHQOgAhRPXNnj0bi8VCZGSk/ZiiKHh6ejJ9+vRqr3YqKipi7NixjB8//qznoqOj7Y99fX2rdT29Xn/W0Mq5JvOeeb3qxnGx6wAMGjSImJgYZs6cSWRkJDabjSuvvPKyJlNX53199tlnjB8/npUrV7JgwQKef/55fv75Z3r06FHt+4wcOZLs7Gzef/99YmJi8PT0pGfPnmfFfub79vb2vui1jUaj/XHlkN25jlUOIV7sGpWvudD5QtQnkggJUU9YLBa++OIL3nnnHW644YYqzw0ZMoR58+bx8MMP249t3LjRnkzk5uayf/9+2rZtC0Dnzp3ZvXs3LVq0qFEMJpMJAKvVWuV4WFhYlZ4Qq9XKrl276Nu37wWvd6lxnCk7O5t9+/Yxc+ZMevfuDaiTsP+pbdu2fPnll5SVldl7hTZu3HjB64aFhXHy5EkURbEnDOcqHdCpUyc6derExIkT6dmzJ3Pnzq1RIrRu3To+/PBDbr75ZgBSU1PJysq66Ovi4uJITExk1KhR1b6XEKIqGRoTop5Yvnw5ubm5PPTQQ1x55ZVVPm6//fazhsdefvllEhMT2bVrFw888AChoaEMGTIEgP/7v/9j/fr1PPbYYyQnJ3PgwAGWLl160UnKDRs2xNvbm5UrV5Kenk5+fj4A1113HStWrGDFihXs3buXRx55pFpFCS81jjMFBQUREhLCJ598wsGDB/n111+ZMGFClXPuvfdedDodo0ePZvfu3fzwww+8/fbbF7zutddeS2ZmJm+++SaHDh0iISGBH3/80f78kSNHmDhxIhs2bODYsWOsWrWKAwcO2BPO6mrZsiVffvkle/bs4c8//+S+++6rVm/P5MmTmTdvHpMnT2bPnj3s3LmTN954o0b3FsLdSSIkRD0xe/Zs+vfvf87hr9tvv53NmzezY8cO+7HXX3+dxx9/nC5dunDy5EmWLVtm79GJi4vjt99+Y//+/fTu3ZtOnTrxwgsvVBlyOxcPDw8++OADPv74YyIjIxk8eDAADz74ICNHjmTEiBH06dOHZs2aXbQ36HLiOJNer2f+/Pls2bKFK6+8kieffJK33nqryjl+fn4sW7aMnTt30qlTJ5577rmLJg1t27blww8/JCEhgQ4dOpCUlFRlpZmPjw979+7l9ttvp1WrVowZM4Zx48YxduzYGsU/e/ZscnNz6dy5M/fffz/jx4+vVi2fa6+9lm+++Ybvv/+ejh07ct1119lX9gkhqkennDkALoSo19asWUPfvn3Jzc2t8VYJwrGOHj1K06ZN2bZtm9NusXE5dDodixcvtvc8ClEfSI+QEELUsauuuoqrrrpK6zBqzcMPP4yfn5/WYQhxSaRHSAgXIz1CzstisXD06FEAPD09iYqK0jagWpKRkUFBQQGgLq2v7mpDIZyBJEJCCCGEcFsyNCaEEEIItyWJkBBCCCHcliRCQgghhHBbkggJIYQQwm1JIiSEEEIItyWJkBBCCCHcliRCQgghhHBbkggJIYQQwm39PxFN4iBDbX5GAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.loglog(radii_ap, NNM[0,0].real, label=\"NapNapMap\")\n", "plt.loglog(radii_ap, np.abs(NNM[0,0].imag), label=\"|NapNapMx|\")\n", "plt.loglog(radii_ap, NNM_wcorr[0,0].real, label=\"NapNapMap (corrected)\")\n", "plt.loglog(radii_ap, np.abs(NNM_wcorr[0,0].imag), label=\"|NapNapMx| (corrected)\")\n", "plt.axvline(x=5*gnn.min_sep, color=\"grey\",alpha=0.5,ls=\"--\")\n", "plt.axvline(x=0.125*gnn.max_sep, color=\"grey\",alpha=0.5,ls=\"--\")\n", "plt.xlabel(\"Aperture radius [arcmin]\")\n", "plt.ylabel(\"Third-order aperture statistics\")\n", "plt.legend(loc=\"upper right\")\n", "plt.ylim(1e-8,None)" ] }, { "cell_type": "markdown", "id": "b6efd296", "metadata": {}, "source": [ "## Computation of the lens-shear-shear correlation function\n", "\n", "Let us now repeat the same procedure for the NGG correlation -- the stragegy is practically the same as for GNN. However, we note that due to the multipole structure of $\\tilde{G}_+$ we need to choose a fairly large value for `rmin_pixsize` as otherwise the tree-based approximations can produce an artificial $\\langle N_{ap}M_{\\times}^2 \\rangle$ mode.\n", "\n", "_We further note that the different components of the NGG correlator are ordered as $[ \\tilde{G}_-, \\tilde{G}_+ ]$ , which is different to the usual conventions, but matches `orpheus`' conventions to always start with a correlator in which not polar field is complex conjugated._" ] }, { "cell_type": "code", "execution_count": null, "id": "01997051", "metadata": {}, "outputs": [], "source": [ "min_sep = 0.25\n", "max_sep = 150.\n", "binsize = 0.1\n", "nbinsphi = 256\n", "tree_resos = [0.,1.,2.]\n", "rmin_pixsize=40\n", "method = \"DoubleTree\"\n", "nthreads = 48\n", "\n", "ngg = orpheus.NGGCorrelation(min_sep=min_sep, \n", " max_sep=max_sep, \n", " binsize=binsize,\n", " nbinsphi=nbinsphi,\n", " method=method,\n", " rmin_pixsize=rmin_pixsize,\n", " tree_resos=tree_resos,\n", " nthreads=nthreads,verbosity=2)" ] }, { "cell_type": "code", "execution_count": null, "id": "13f3ea1b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ ".........|.........|.........|.........|.........|.........|.........|.........|.........|.........|CPU times: user 1h 37min 57s, sys: 6.03 s, total: 1h 38min 3s\n", "Wall time: 2min 3s\n" ] } ], "source": [ "%%time\n", "ngg.process(sources, lenses)" ] }, { "cell_type": "code", "execution_count": null, "id": "c38ae459", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 680 ms, sys: 7 ms, total: 687 ms\n", "Wall time: 684 ms\n" ] } ], "source": [ "%%time\n", "ngg.multipoles2npcf()" ] }, { "cell_type": "code", "execution_count": null, "id": "87d45079", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 11.9 s, sys: 8.1 s, total: 20 s\n", "Wall time: 3.89 s\n" ] } ], "source": [ "%%time\n", "radii_ap = np.geomspace(1.,32.,17)\n", "NMM = ngg.computeNMM(radii_ap)" ] }, { "cell_type": "code", "execution_count": null, "id": "72f739a9", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/users/lporth/anaconda3/envs/orpheus_devel/lib/python3.12/site-packages/matplotlib/cbook.py:1709: ComplexWarning: Casting complex values to real discards the imaginary part\n", " return math.isfinite(val)\n", "/users/lporth/anaconda3/envs/orpheus_devel/lib/python3.12/site-packages/matplotlib/cbook.py:1345: ComplexWarning: Casting complex values to real discards the imaginary part\n", " return np.asarray(x, float)\n" ] }, { "data": { "text/plain": [ "(1e-09, 4.355715096918785e-06)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.loglog(radii_ap, NMM[0,0], label=\"NapMapMap\")\n", "plt.loglog(radii_ap, np.abs(NMM[1,0]), label=\"|NapMxMx|\")\n", "plt.loglog(radii_ap, np.abs(NMM[2,0]), label=\"|NapMapMx|\")\n", "plt.axvline(x=5*ngg.min_sep, color=\"grey\",alpha=0.5,ls=\"--\")\n", "plt.axvline(x=0.125*ngg.max_sep, color=\"grey\",alpha=0.5,ls=\"--\")\n", "plt.xlabel(\"Aperture radius [arcmin]\")\n", "plt.ylabel(\"Third-order aperture statistics\")\n", "plt.legend(loc=\"upper right\")\n", "plt.ylim(1e-9,None)" ] }, { "cell_type": "code", "execution_count": null, "id": "41c2fb18", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "orpheus_devel", "language": "python", "name": "orpheus_devel" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.1" } }, "nbformat": 4, "nbformat_minor": 5 }