{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# Copyright (c) 2024 Graphcore Ltd. All rights reserved.\n", "from matplotlib import pyplot as plt\n", "import numpy as np\n", "from gfloat import *\n", "from gfloat.formats import format_info_ocp_e5m2\n", "\n", "# Abbreviate RoundMode printing just for this notebook, for figure legends\n", "if \"RoundMode__str__\" not in locals():\n", " RoundMode__str__ = RoundMode.__str__\n", " RoundMode.__str__ = lambda x: RoundMode__str__(x).replace(\n", " \"RoundMode.Stochastic\", \"SR\"\n", " )\n", "\n", " assert str(RoundMode.StochasticFast) == \"SRFast\"\n", "\n", "\n", "def longstr(rnd):\n", " if rnd == RoundMode.StochasticFast:\n", " return r\"SRFast ($\\lfloor x + (SRBits + 0.5) \\times 2^{-nbits} \\rfloor$)\"\n", " elif rnd == RoundMode.StochasticFastest:\n", " return r\"SRFastest ($\\lfloor x + SRBits \\times 2^{-nbits} \\rfloor$)\"\n", " elif rnd == RoundMode.Stochastic:\n", " return r\"SR ($\\lfloor RTNE(x, nbits) + SRBits \\times 2^{-nbits} \\rfloor$)\"\n", " else:\n", " raise ValueError(f\"Unknown rounding mode {rnd}\")\n", "\n", "\n", "mode_colors = {\n", " RoundMode.TiesToEven: (\"pink\", \"red\"),\n", " RoundMode.StochasticFastest: (\"bisque\", \"orange\"),\n", " RoundMode.StochasticFast: (\"lightblue\", \"blue\"),\n", " RoundMode.Stochastic: (\"#ada\", \"green\"),\n", " RoundMode.StochasticOdd: (\"#faf\", \"purple\"),\n", "}\n", "\n", "\n", "def lollipops(ax, xs, ys, key, label):\n", " colors = mode_colors[key]\n", " ax.plot(\n", " [xs, xs],\n", " [xs, ys],\n", " label=None,\n", " color=colors[0],\n", " markeredgecolor=\"k\",\n", " markersize=2,\n", " linestyle=\"-\",\n", " )\n", " ax.plot(xs, ys, label=label, color=colors[1], marker=\".\", markersize=3, linestyle=\"\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Stochastic rounding\n", "\n", "This notebook does some simple experiments with stochastic rounding.\n", "\n", "Let's see examples of stochastic rounding and the default round-to-nearest for \n", "some input values in an 8-bit float range. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fi = format_info_ocp_e5m2 # A common P3 format\n", "\n", "vs = np.arange(2.9, 7.1, step=1 / 64)\n", "\n", "# Round to nearest\n", "rn = round_ndarray(fi, vs)\n", "\n", "# Stochastic rounding\n", "np.random.seed(1)\n", "srnumbits = 16\n", "srbits = np.random.randint(0, 2**srnumbits, len(vs))\n", "rvs = round_ndarray(\n", " fi, vs, RoundMode.Stochastic, sat=False, srbits=srbits, srnumbits=srnumbits\n", ")\n", "\n", "# Plot\n", "fig, axs = plt.subplots(1, 2, figsize=(14, 7))\n", "for ax in axs:\n", " ax.plot(vs, vs, label=\"True value\", color=\"k\")\n", "\n", " if ax == axs[0]:\n", " lollipops(ax, vs, rn, key=RoundMode.TiesToEven, label=\"Round to nearest\")\n", " else:\n", " lollipops(ax, vs, rvs, key=RoundMode.Stochastic, label=f\"SR, {srnumbits} bits\")\n", "\n", " ax.set_xlabel(\"Input float value\")\n", " ax.set_ylabel(f\"Rounded values\")\n", " ax.set_yticks(np.unique(rvs))\n", " ax.set_xlim(2.75, 7.25)\n", " ax.set_ylim(2.4, 7.6)\n", " ax.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The black $Y=X$ curve plots the input real value, the red curve shows that value \n", "rounded to the nearest representable value in the chosen float format, \n", "and the grey curve shows stochastic rounding, again to a nearest representable value,\n", "but randomly up or down depending how close the input value is to the next highest \n", "and lowest representable values.\n", "\n", "In order to get a better idea of the behaviour, we will change the plot to show the \n", "average rounded value at each input real value. At 16 bits of randomness, \n", "this almost appears too good to be true:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1, figsize=(5, 5))\n", "\n", "ax.plot(vs, vs, label=\"True value\", color=\"k\", marker=\"None\", linestyle=\"-\")\n", "\n", "# Compute mean absolute error\n", "err_rn = np.abs(rn - vs).mean()\n", "ax.plot(\n", " vs,\n", " rn,\n", " label=f\"Round to nearest, err={err_rn:.2f}\",\n", " color=\"red\",\n", " markersize=3,\n", " linestyle=\"\",\n", " marker=\".\",\n", ")\n", "\n", "# Stochastic rounding, multiple samples\n", "srnumbits = 16\n", "nsamples = 500\n", "srbits = np.random.randint(0, 2**srnumbits, (nsamples, len(vs)))\n", "\n", "rvs = round_ndarray(\n", " fi,\n", " vs[np.newaxis, :],\n", " RoundMode.Stochastic,\n", " sat=False,\n", " srbits=srbits,\n", " srnumbits=srnumbits,\n", ")\n", "\n", "rvmean = rvs.mean(axis=0)\n", "err = np.abs(rvmean - vs).mean()\n", "lollipops(\n", " ax,\n", " vs,\n", " rvmean,\n", " key=RoundMode.Stochastic,\n", " label=f\"SR, {srnumbits} bits, err={err:.2f}\",\n", ")\n", "\n", "ax.set_xlabel(\"Input float value\")\n", "ax.set_ylabel(f\"Average of rounded values, {nsamples} samples\")\n", "ax.set_yticks(np.unique(rn))\n", "ax.legend()\n", "None" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The green line is pretty much on top of the true value (some small random \n", "deviations are evident), indicating that with 500 samples, \n", "the stochastically rounded value is on average very accurate.\n", "\n", "Before we go further, let's zoom in a bit:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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Nmzdj5cqVuHbtGsaMGYN+/frh5MmTAICAgABcv34dBw8exI0bN7BixQqUKVMGADQtJEePHoVcLsdvv/329g/jf77//nucPXsW27dvx5UrV9CzZ0907NgRd+7c0RyjUqkwZ84crF27FteuXYOLiwsAYP78+fD29sbly5cREBAAAKhVqxZsbW3zfHTq1Elz3bNnz6Jdu3Y58nTo0AFnz57Nd34ASEpKgpOTU577VSoV0tPT33gMERGVDElJSZg4cSK863pr+uK7du+KGzduYPHixShTpkyJb6V5o0L64UIvCm1kPiVFCHd3IYCs/6bo96dBHx8fYWpqKmxsbIRUKhUAhImJidi5c6cQImu03NzcXGzdulVzTlpamihfvryYO3euECL/I/PW1tY5RuJ9fX1F48aNhRBCKJVKYWFhIX755RfN/mfPngkrK6s8R+azr+vt7Z1j2x9//CFMTU3FgwcPNNuuXbsmAOT4jcKrskfm165d+9o5N27cEEIIMXjwYPHNN9/kOO/UqVPCxMQkz8/+77//FgCEUqkUQvw7Mr9nzx7NMS9fvhTW1tav/RZg8ODBonfv3kIIIT755JM8R5+zs1++fDnX/Xm5f/++MDU1Ff/880+O7W3bthUTJ04UQvz724/w8PAcx1SuXFl8+umnr13z3r174s6dO3k+Hj58qDnW3d1dhISE5Dh///79AoBQqVT5eg87duwQFhYWIjIyMs9jhg0bJqpVq5bnZ8SReSKi4i81NVUsWbJElC5dWgAQFnYWwnWBq0AQhGyprESMvr9JfkfmOc98fkRGAtmjonfuZD1vpN/5Sj/88EOsWLECKSkpWLRoEczMzNC9e3cAWaPR6enpaN68ueZ4c3NzNGrUCDdu3NDqdapUqQI7OzvNc1dXV8THx2teJy0tDY0bN9bsd3JyQo0aNbR+Pzdu3ICbmxvc3Nw022rWrIlSpUrhxo0beP/99/M8t06dOjnyAUB8fDw8PDwQERGBK1eu5LjhUggBtVqNmJgYeHp64uLFiwgKCkJERASeP3+u6S9/8OABatasqTmvYcOGmq+joqKgUqnQvn37HFnS0tJQr149AMCwYcPQvXt3XLp0CR999BE+/fRTNGvWTOs/m1ddvXoVmZmZeO+993JsT01NRenSpTXPLSwscvy55PYeslWuXPmdMmnj+PHjGDRoENasWYNatWrleszs2bOxfft2nDhxApaWloWWjYiIiga1Wo2dv+3E1MCpuHX9FgDA09MTXwV+Bd+bvgD+nWKyOM8Pryss5vPDywtwd88q5N3ds57rmY2NDWSyrGmW1q9fD29vb6xbtw6DBw/O1/kmJiYQQuTYlp6e/tpx5ubmOZ5LJJJcb6Y0pFczSiQSANBkTE5OxrfffouRI0e+dl6lSpWQkpKCDh06oEOHDti6dSucnZ3x4MEDdOjQ4bUbRG1sbDRfJycnAwD279+PChUq5DhOKpUCADp16oT79+/jwIEDOHLkCNq2bYvhw4dj/vz5BX6vycnJMDU1xcWLF2Fqappjn62treZrKysrzZ9FXu8hW61atXD//v08X7Nly5Y4ePAgAKBcuXJ4/Phxjv2PHz+Gvb09rKys3pj95MmT+OSTT7Bo0SIMGDAg12Pmz5+P2bNn4+jRo7n+MEJERMXbX3/9hUlTJmHo2qHw2eCDH/v8iKn+UzFo0CCkqlOxatUqRCVElcgpJgvK4MX8P//8A39/fxw8eBAqlQoymQwbNmzIdYTRYKytgfDwrBF5L6+s54XIxMQEkyZNwtixY9GnTx9Ur14dFhYWOHPmjGbUNT09HX///bdm/ndnZ2colUqkpKRoCjxtp0msXr06zM3NERYWhkqVspZGfv78OW7fvo1WrVrleZ6FhQUyMzNzbPP09ERsbCxiY2M1o/PXr19HYmJijtFxbdWvXx/Xr1/X/ODzX1evXsWzZ88we/ZszeteuHDhrdetWbMmpFIpHjx48Mb36uzsDB8fH/j4+KBly5bw9fXF/PnzNfc3/PfP4W3q1auHzMxMxMfHo2XLllqdm5cDBw7k+oNctleL9KZNm+LAgQM59h85cgRNmzZ942ucOHECXbp0wZw5c/DNN9/keszcuXMxc+ZMHD58uGh9fxMRkd7duHEDEyZMwN69e2FhZ4G7++5CrpSj+ojq6DuwL8zMzGAGM0QMjUBkfCS8XLzYF59PBi3mnz9/jubNm+PDDz/EwYMH4ezsjDt37sDR0dGQsXJnba331po36dmzJ3x9fbF8+XKMHz8ew4YNg6+vL5ycnFCpUiXMnTsXKpVKM3LfuHFjWFtbY9KkSRg5ciTCwsLeOl/4f9na2mLw4MHw9fVF6dKl4eLigsmTJ8PE5M33TVepUgUxMTEIDw9HxYoVYWdnh3bt2qF27dro27cvFi9ejIyMDHz33Xdo1arVOxV2/v7+aNKkCb7//nsMGTIENjY2uH79Oo4cOYJly5ahUqVKsLCwwA8//IChQ4ciMjIS06dPf+t17ezsMH78eIwZMwZqtRotWrRAUlISzpw5A3t7e/j4+GDq1Klo0KABatWqhdTUVOzbtw+enp4AABcXF1hZWeHQoUOoWLEiLC0t4eDg8NbXfe+999C3b18MGDAACxYsQL169fDkyRMcO3YMderUwccff6z1n5E2bTZDhw7FsmXL4Ofnh6+++gp//vknfvnlF+zfv19zzLJly7B7924cO3YMQFZrTZcuXTBq1Ch0794dcXFxALJ+qMu+wXXOnDmYOnUqfv75Z1SpUkVzTPZNuEREVDzJ5XIEBQVh7dq1UKvVMDU1RdchXbFTuRMAEJ0YnaOdJnuKSdJCoXTw58Hf31+0aNGiwOeXpKkphRBi1qxZwtnZWSQnJ4sXL16IESNGiDJlyuQ6NaUQWTe8ymQyYWVlJbp06SJWr16d69SUr1q0aJGoXLmy5rlSqRT9+vUT1tbWomzZsmLu3LlvnJpSiKybR7t37y5KlSqlk6kpX72J9Pnz5wJAjqkaz58/L9q3by9sbW2FjY2NqFOnjpg5c6Zm/88//yyqVKkipFKpaNq0qdi7d2+O62bfAPv8+fMcr69Wq8XixYtFjRo1hLm5uXB2dhYdOnQQJ0+eFEIIMX36dOHp6SmsrKyEk5OT6Natm7h7967m/DVr1gg3NzdhYmKimZoy+7ViYmLyfN9paWli6tSpokqVKsLc3Fy4urqKzz77TFy5ckUIkfvNzUJk3QC7aNGiPK+bX8ePHxd169YVFhYWolq1aprPL1tgYGCO/0d8fHxem4oT/5mOs3LlyrkeExgYmGsGY/7+JSIiIRQKhZgUOElYVrcUMM/6O//TTz8VN2/eLJHTTBZEfm+ANWgx7+npKUaPHi169OghnJ2dRd26dcXq1avzfX5xLeap+Fq/fr2QyWQiLS3N0FGKNH7/GqGUFCHCwnKf7asg+3R9veKwr6jkKOx9RSVHYe8rKjm03JeWliZWrFghXCq4CMkICARBWI2XiiMnjuQ8LfGJCDu8XqQkPilS+fO9rxAYRTEvlUqFVCoVEydOFJcuXRKrVq0SlpaWYuPGjbke//LlS5GUlKR5xMbGspgno9KjR48cU31S7vj9a2TeNH1vQfbp+nrFYV9RycH3zfedxz61u7vYu327qFGjhgAgpBWyCvnsR1jUyeLzvguJURTz5ubmomnTpjm2jRgxQjRp0iTX4wMDA3P9VT2LeaLihd+/RiYsLOsfvOxHWNi77dP19YrDvqKSg++b7/uVfeqwcyLdSirSraRCDYj3/1eXlSlTRmweN1K4/29k3n0EREroybdfswi9tzfuKyRGUcxXqlRJDB48OMe2H3/8UZQvXz7X4zkyT1Qy8PvXyHBUkiO1fN8l8n3fjLgsfon+RfwS/Yu4biUVTpaWYvLkyVl1WUqKSPGoLsIqQKR4VC9W77uwGEUx37t379dugB09evRro/V5Yc88UfHE718jlJLCfmF97ysqOQp7X1HJUdj7ikqOXPbFx8eL77//XtjY2Ygtt7aIkLAQ8fWQ/jlWFC+O77uw5beYlwghhH7ny8nb33//jWbNmiE4OBi9evXC+fPn8fXXX2P16tXo27fvW89XKBRwcHBAUlIS7O3tc+x7+fIlYmJiULVqVa4ySWRk+P1LRFT0qFQqLF68GLNnz4ZSqYSFnQVKB5WGXCmHzEmGiKERnBteh95U577qzROG69n777+P3bt3Y9u2bfDy8sL06dOxePHifBXyRERERKRfQgikpqdi/cb1cHd3x+TJk6FUKlG/fn0s3LIQcqUcABCVEIXI+EgDpy2ZdLJoVGJiIkqVKlWgc7t06YIuXbroIgYRERER6YgQAgcPH0RCtQQ8rvkYT5VPUblyZYSEhODLL7/Ei4wXWPxgMaISouDu5A4vFy9DRy6RtC7m58yZgypVquCLL74AAPTq1Qu7du1CuXLlcODAAXh7e+s8JBERERHphxACyjQlIuMj4V3WGzYWNrh48SL8/Pxw+u/TmlaaMr5lcGn0JTjZZa3ubWNhg4ihEYiMj4SXixdbbAxE6zablStXws3NDQBw5MgRHDlyBAcPHkSnTp3g6+ur84BEREREpD/KNCU8lnug+frm8FrmhS/6fYGGDRvizz//hJmrmaaV5qn6KaIUUTnOtTa3RqMKjVjIG5DWxXxcXJymmN+3bx969eqFjz76CH5+fvj77791HpCMU1BQEOrWrfvGYwYOHIhPP/20UPIQERFR7iLjIzUF+z3lPfxy4hcAQN++ffH3vr8hc5IBAFtpiiiti3lHR0fExsYCAA4dOoR27doByPoVTWZmpm7TlVBPnjzBsGHDUKlSJUilUpQrVw4dOnTAmTNnNMdUqVIFEokEEokE1tbWqF27NtauXav1a127dg3du3fXXG/x4sW5HvfPP/+gX79+KF26NKysrFC7dm1cuHChoG8RALBkyRJs3LhR87x169YYPXr0O12zqHn58iWGDx+O0qVLw9bWFt27d8fjx4/feI4QAlOnToWrqyusrKzQrl073LlzJ8cxM2fORLNmzWBtbV3g+1WIiIhevnyJk7+ehKuda9aGBKCVZytcvHgRP/30E2q610TE0AiEDQlD+NBwjsAXQVoX859//jn69OmD9u3b49mzZ+jUqRMA4PLly5DJZDoPWBJ1794dly9fxqZNm3D79m3s3bsXrVu3xrNnz3IcN23aNMjlckRGRqJfv374+uuvcfDgQa1eS6VSoVq1apg9ezbKlSuX6zHPnz9H8+bNYW5ujoMHD+L69etYsGABHB0dC/weAcDBwaFIFqJpaWmvbcvMzIRardb6WmPGjMH//d//4ddff8XJkyfx6NEjfP755288Z+7cuVi6dClWrlyJsLAw2NjYoEOHDnj58mWOjD179sSwYcO0zkRERKRWq7F161Z4eHggeEow5naZi5BOIfitw284/sdx1K9fX3MsW2mKOG0nsE9LSxPz5s0TI0eOFJcuXdJsX7hwoVizZo22l3snxXHRqOfPnwsA4sSJE288rnLlymLRokU5tjk5OYkxY8YU+LVzu6YQQvj7+7+2uNfbBAYGCm9vb7Fy5UpRsWJFYWVlJXr27CkSExM1x/j4+Ihu3bppvsb/loHOfsTExIiEhATRp08fUaZMGWFpaSlkMplYv369VllOnTolWrRoISwtLUXFihXFiBEjRHJyco73PW3aNNG/f39hZ2cnfHx8xIYNG4SDg4P4/fffhaenpzA1NRUxMTFavW5iYqIwNzcXv/76q2bbjRs3BABx9uzZXM9Rq9WiXLlyYt68eTmuI5VKxbZt2147PjtncWOs379ERMbg6NGjol69epp/bytUqCA2bNogXqa9FGq12tDx6H/yu2iU1iPz5ubmGD9+PJYsWYJ69eppto8ZMwZDhgzRwY8XRZMqXYXz/5yHKl2l19extbWFra0t9uzZg9TU1Hydo1arsWvXLjx//hwWFhY6z7R37140bNgQPXv2hIuLC+rVq4c1a9a89byoqCj88ssv+L//+z8cOnQIly9fxnfffZfrsUuWLEHTpk3x9ddfQy6XQy6Xw83NDQEBAbh+/ToOHjyIGzduYMWKFShTpky+s0dHR6Njx47o3r07rly5gh07duD06dP4/vvvcxw3f/58eHt74/LlywgICACQ9VuLOXPmYO3atbh27RpcXFywdetWzWeU1+PUqVMAgIsXLyI9PV3TigYAHh4eqFSpEs6ePZtr3piYGMTFxeU4x8HBAY0bN87zHCIiIiCrTVORqkBobChS0lJe2xdxNQKfdPsE7dq1w+XLl2FnZ4eQkBDcvn0bAwcMhNRcColEYqD0VFAFmmd+y5YtWLVqFe7evYuzZ8+icuXKWLx4MapWrYpu3brpOqPBqdJVqLuyLu4k3IG7k7tee8bMzMywceNGfP3111i5ciXq16+PVq1a4csvv0SdOnVyHOvv748pU6YgNTUVGRkZcHJy0ssPVHfv3sWKFSswduxYTJo0CX///TdGjhwJCwsL+Pj45Hney5cvsXnzZlSoUAEA8MMPP+Djjz/GggULXmvpcXBwgIWFBaytrXPse/DgAerVq4eGDRsCyLpXQBuzZs1C3759Nb347u7uWLp0KVq1aoUVK1ZoVhdt06YNxo0bpznv1KlTSE9Px48//phjutWuXbuicePGb3zN7PcbFxcHCwuL11qJypYti7i4uFzPzd5etmzZfJ9DREQE/DsrzX9XZH348CGCpwej1bhWaDa5Gf489SeG9B+CKVOmwNnZ2dCx6R1pPTKfXdR16tQJiYmJmpteS5UqlefNk8YuMj4SdxKybkC8k3BH7yucde/eHY8ePcLevXvRsWNHnDhxAvXr189xsygA+Pr6Ijw8HH/++ScaN26MRYsW6eW+BbVajfr16yMkJAT16tXDN998o/lh400qVaqkKWwBoGnTplCr1bh161a+X3vYsGHYvn076tatCz8/P4SGhmqVPSIiAhs3bswxct6hQweo1WrExMRojsv+YeFVFhYWr/0AZWdnB5lM9saHlZWVVhmJiIh04dVZaaISonDu7jlMmjQJ7u7u2LxtM/z2+WHSwUlwnuKMWfNnsZAvJrQu5n/44QesWbMGkydPhqmpqWZ7w4YNcfXqVZ2GKyq8XLzg7uQOoPCmZbK0tET79u0REBCA0NBQDBw4EIGBgTmOKVOmDGQyGVq2bIlff/0VI0eOxPXr13WexdXVFTVr1syxzdPTEw8ePND5a/1Xp06dcP/+fYwZMwaPHj1C27ZtMX78+Hyfn5ycjG+//Rbh4eGaR0REBO7cuYPq1atrjrOxsXntXCsrq9d+3ahNm025cuWQlpaGxMTEHNd4/PhxnjcbZ2//74w3bzqHiIgIyKpXsmelcTZxRq/WvTBr1iy8fPkSXm28NIX+feV9vQ9MUuHRus0mJiYmR698NqlUipSUlFzOMH7W5tYIHxpu0BXOatasiT179uS5383NDV988QUmTpyI33//Xaev3bx589dG02/fvo3KlSu/8bwHDx7g0aNHKF++PADg3LlzMDExQY0aNXI93sLCItfpTZ2dneHj4wMfHx+0bNkSvr6+mD9/fr6y169fH9evX9fZbyy0abNp0KABzM3NcezYMXTv3h0AcOvWLTx48ABNmzbN9dyqVauiXLlyOHbsmGaefoVCgbCwMM5cQ0REb2RlZoW5XeYiNjEWQe2CkKZMQ40aNTBnzhy07dgW9VbXQ1RCFOeLL2a0LuarVq2K8PDw1wq5Q4cOwdPTU2fBiprsaZn07dmzZ+jZsye++uor1KlTB3Z2drhw4QLmzp371vsRRo0aBS8vL1y4cCHXtpHcpKWlaUbz09LS8M8//yA8PBy2traaAnjMmDFo1qwZQkJC0KtXL5w/fx6rV6/G6tWr33htS0tL+Pj4YP78+VAoFBg5ciR69eqV5whzlSpVEBYWhnv37sHW1hZOTk4ICgpCgwYNUKtWLaSmpmLfvn1a/X/m7++PJk2a4Pvvv8eQIUNgY2OD69ev48iRI1i2bFm+r5PNzs4OdnZ2+TrWwcEBgwcPxtixY+Hk5AR7e3uMGDECTZs2RZMmTTTHeXh4YNasWfjss88gkUgwevRozJgxA+7u7qhatSoCAgJQvnz5HAtsPXjwAAkJCXjw4AEyMzMRHh4OAJDJZLC1tdX6fRERkXEQQkCZpkRkfCS8y3rDxiLrN8unTp3CxCkTMWrDKMjKyFDWqSwmz5uMwYMHw8wsq9yLGBph0IFJ0hNtp8lZs2aNqFChgti+fbuwsbER27ZtEzNmzNB8XZiK49SUL1++FBMmTBD169cXDg4OwtraWtSoUUNMmTJFqFQqzXF5TSPZoUMH0alTJ81zAGLDhg15vl5MTMxrU0ICEK1atcpx3P/93/8JLy8vIZVKhYeHh1i9evUb30f21JQ//vijKF++vLC0tBQ9evQQCQkJmmNenZpSCCFu3bolmjRpIqysrDRTU06fPl14enoKKysr4eTkJLp16ybu3r2rOadVq1bCx8fnjVnOnz8v2rdvL2xtbYWNjY2oU6eOmDlzpmZ/bn+Wupry8cWLF+K7774Tjo6OwtraWnz22WdCLpfnOOa/n5FarRYBAQGibNmyQiqVirZt24pbt27lOCe3qTwBiOPHj79z5qLAWL9/iYj0LellknBd4CoQBCFbKhOXrl4S3bp10/w74FjGUQRNDxIKhcLQUekd5XdqSokQQmj7A8DWrVsRFBSE6OhoAED58uURHByMwYMHv+vPFlpRKBRwcHBAUlIS7O3tc+x7+fIlYmJiULVqVc2MJSVNTEwM3nvvPVy/fh3u7u6GjqMXlStXRnBwMAYOHGjoKKRD/P4lIspdaGwomq9vrnluss4E6lg1TE1NMWTIEAQGBsLV1dWACUlX3lTnvqpAU1P27dsXffv2hUqlQnJyMlxcXAoclPTnwIED+Oabb4ptIX/t2jU4ODhgwIABho5CRERUKKrYVIGrnWvWzawJgDpOjW7dumHWrFnFut2Z8lagYj6btbU1rK3Zc1VUDR8+3NAR9KpWrVq4cuWKoWMQERHpXUZGBtatW4eZs2Zi7h9ZN7nu9duLOUfn4IMPPjB0PDKgfBXz9erVy/eKYJcuXXqnQERERESURQiB//u//4O/vz9u3rwJAJj5+UwEBwXjzJ9nYGKi9SzjVMzkq5h/dRYNIiIiItIfIQQyRSb+/vtv+Pv6a9YvKV26NAIDA/Htt9/CwsLCwCmpqMhXMf/fxYqIiIiISD9uR9/GFZMrgDNw/sJ5WFpaYsyYMfD394eDg4Oh41ERU+DfzVy4cAFbtmzBli1bcPHiRV1m0qkCTNZDRAbG71siKgmEEFCkKhAaG4qUtBQ8ffoUo0aNQsMGDZGakYqop1H4sv+XuHPnDkJCQljIU660vgH24cOH6N27N86cOYNSpUoBABITE9GsWTNs374dFStW1HXGAjE3NwcAqFQqWFlZGTgNEWlDpVIB+Pf7mIioOFKmKeGx3ANypRylJaWRtiQNygQlLOws4LfPD3KlHDIvGZzKOhk6KhVhWhfzQ4YMQXp6Om7cuIEaNWoAyFqiftCgQRgyZAgOHTqk85AFYWpqilKlSiE+Ph5A1sw7+b2Jl4gMQwgBlUqF+Ph4lCpVCqampoaORET0TkQeK7YCwJW4K1lTTAJ4Jp4BVlmTjgyaOggjI0YCAKISohAZH1koq9CTcdJ60SgrKyuEhoaiXr16ObZfvHgRLVu21IyoFYa3TaYvhEBcXBwSExMLLRMRvbtSpUqhXLly/AGciIyeIlWhGX2XOckQMTQCVmZWOHz4MCYGTsTjLx5DrpTDXGGOFd4rMKjfILzIeIG6q+oiKiEK7k7uCB8aDmtzTgVe0uht0Sg3Nzekp6e/tj0zMxPly5fX9nJ6JZFI4OrqChcXl1wzE1HRY25uzhF5Iio2IuMjNaPvUQlR2PnXTmyetRnHjh2D1EqKtVvWIjYxFoNrDIaLQ9YinDYWNogYGoHI+Eh4uXixkKc30rqYnzdvHkaMGIHly5ejYcOGALJuhh01ahTmz5+v84C6YGpqyuKAiIiICp2Xi5dmxVa7dDv4dPIB0gELCwsMHzYcHUp3gKPMEaaSnHWKtbk1W2soX7Rus3F0dIRKpUJGRgbMzLJ+Fsj+2sbGJsexCQkJukuai/z++oGIiIjIEJ4mPMWhp4cQmxiLoHZBSFOmoU+fPpgxYwaqVq1q6HhUhOmtzWbx4sXvkouIiIio2EtNTcWyZcswb8E8/HD6B8jKyNCqWSvMmjkLDRo0MHQ8Kka0LuZ9fHz0kYOIiIjI6KnVamzfvh2TJ0/GvXv3ILWSavbt378f5qaccpd0S+tiPlt8fDzi4+OhVqtzbK9Tp847hyIiIiIyFkIIZIpM/PXXX/Ab76dZTLN8+fKYPn06urp1zbp/T8L790j3tC7mL168CB8fH9y4ceO1VRolEgkyMzN1Fo6IiIioqLt67SpuWd8CKgGR1yNhZ2eHCRMmYPTo0bC25kw0pF8m2p7w1Vdf4b333kNoaCju3r2LmJgYzePu3bv6yEhERERU5Pzzzz8YMmQImjRpotn27bffIioqCpMmTWIhT4VC65H5u3fvYteuXZDJZPrIQ0RERFSkKRQKzJ07FwsXLsSLFy8gtZIiNSMVsYmxmD57OuylnGGPCo/WI/Nt27ZFRESEPrIQERERvTMhBBSpCoTGhiIlLUVn101SJWH8ovGoVqMaZs6ciRcvXqB58+bY/8d++O3zw6SDk9BgdQOo0lU6e02it9F6ZH7t2rXw8fFBZGQkvLy8YG6e867srl276iwcERERkbaUaUp4LPeAXCmHzEmGiKER77SKqhAC23Zuw8BzA5Funw70BGRHZZgXMg/dunXD2YdnIT/27yqvkfGRXPCJCo3WxfzZs2dx5swZHDx48LV9vAGWiIiIDC0yPhJypW6K6zNnzsDX1xdnH5wFvv7fxtLApoOb0KxyMwCAd1lvyJxkiEqIgruTO7xcvHTxNojyRes2mxEjRqBfv36Qy+VQq9U5HizkiYiIyNC8XLzgaucKAJA5yfJdXL/annP52mV8/vnnaNGiBc6ePQsrpRWchBMAwN3JHXXL19WcZ2Nhg4ihEQgbEobwoeHv9FsAIm1JxH/nl3wLOzs7hIeHo3r16vrKlG/5XeaWiIiISo4MdQa2R21HbGIshnsPz/cNqYpUhaY9R5IggVghYJJpgiFDhiAoKAgOZRwQGR8JLxcvFuykd/mtc7Vus/n8889x/PjxIlHMExEREeVGaiaFrIws30V3SkoK/Bb5QZ6Z1Z4jnARafN4Cq6auQs2aNTXHsReeihqti/n33nsPEydOxOnTp1G7du3XboAdOXKkzsIRERER6VNGRgY2bNiAqVOnIiElAa5BrpAr5ahoVRGHtxzmCDwVeQWazcbW1hYnT57EyZMnc+yTSCQs5omIiKjIE0Jg37598Pf3x40bNwAAVatWRVCFIFRvUh11XeuykCejoHUxHxMTo48cRERERHonhEDY32GYMmUKjh05BgBwcnLC1KlTMXToUEilUgMnJNKO1rPZEBERERmj6Oho9BvQD7FlYvHtym9h72iPCRMmIDo6GqNGjWIhT0ZJ65F5AHj48CH27t2LBw8eIC0tLce+hQsX6iQYERERkS48e/YM06dPx48//ggTMxN8GvwpACAiPAJVKlUxaDaid6V1MX/s2DF07doV1apVw82bN+Hl5YV79+5BCIH69evrIyMRERFRDkIIKNOUiIyPhHdZb9hY2OR63MKFCxEyIwRJSUkAgI87fqzZV7FixULJSqRPWrfZTJw4EePHj8fVq1dhaWmJXbt2ITY2Fq1atULPnj31kZGIiIgoB2WaEh7LPdB8fXPUXVUXqnSVZt+ri1hOnToVSUlJ8Pb2xh9//IE9e/YYIC2R/mhdzN+4cQMDBgwAAJiZmeHFixewtbXFtGnTMGfOHJ0HJCIiIvqvyPhIyJVZc8JHJUQhMj4SAPDHH3+gRYsWmuMqVqyIzZs349KlS2jfvj0AIDUjFVFPo3L8AEBkrLRus7GxsdH0ybu6uiI6Ohq1atUCADx9+lS36YiIiIhy4eXiBVe7rDnhZU4yZMoz8dGgj3DkyBEAwPBmwzF+/HhcCb8Ca+t/p5hUpavgt88PcqUc68PWI2JoBKegJKOmdTHfpEkTnD59Gp6enujcuTPGjRuHq1ev4rfffkOTJk30kZGIiIgoB2tza8ztMhexibG4seYGmo9qDiEEzM3N8f3332Py5MkoXbr0a+flNqLPVV3JmGldzC9cuBDJyckAgODgYCQnJ2PHjh1wd3fnTDZERESkM2+6yTUpKQlSMylkZWQI3hoMIQR69+6NGTNmoFq1anle07usN2ROMkQlRMHdyR1eLl6F8VaI9EYihBCGDlFQCoUCDg4OSEpKgr29vaHjEBERkQ4pUhXwWO6haaWJGBoBU7UpfvzxR8ydPxdLTy0FAKwethqzZs5Cw4YN83VdVboKkfGR8HLxYosNFVn5rXO1vgE2NjYWDx8+1Dw/f/48Ro8ejdWrVxcsKREREVEu/tsSs/CnhfD09MTYsWMR9ygOM3vMhNVNKxw+eDjfhTyQ1aLTqEIjFvJULGhdzPfp0wfHjx8HAMTFxaFdu3Y4f/48Jk+ejGnTpuk8IBEREZVM2Te5AoBliiUCvg1ATEwMXF1dsXbtWlw4fwFdOneBiQkXtKeSS+v/+yMjI9GoUdaNIr/88gtq166N0NBQbN26FRs3btR1PiIiIirmhBBQpCoQGhuKlLQUzfb7Ufcxt8tchHQKgXqlGrZSW0yfPh137tzB4MGDYWZWoIXsiYoVrYv59PR0SKVSAMDRo0fRtWtXAICHhwfkcrlu0xEREVGx998FoKIfROPrr79G48aNNTe5fvvVt4iOjsaUKVNgY5P7aq9EJZHWxXytWrWwcuVKnDp1CkeOHEHHjh0BAI8ePcp1CigiIiKiN/lvb3ytD2th7dq1eJHyAr9O+hVeGV5YsmgJXFxcDJyUqOjRupifM2cOVq1ahdatW6N3797w9vYGAOzdu1fTfkNERESUXzUca2h645EApMamolmzZjhz5gx+2f4LPN/zhEQiMWxIoiJK62az1q1b4+nTp1AoFHB0dNRs/+abb3KssEZERET0JkII7N69GwGBAZi7K2sBqM3fbEbIjhB8+umnLOCJ8qFAd46YmprmKOQBoEqVKrrIQ0RERCVAaGgofH19ERoaCqmVVNMbfynsEqykVoaOR2Q0eBs4ERERFZrbt29j4sSJ+O233wAA1tbWGDduHNqVaQc7WzuYSkwNnJDIuLCYJyIiIr17/PgxZs6aifXr1yNFmQITExMMHjwYQUFBKF++vKHjERktrrJARERE+ZbXnPB5SUlJwYwZM1Czdk20HNkSG8I34NPPP8WVK1ewevVqFvJE74gj80RERJRv2XPCy5VyyJxkiBgaAWvz1yfAyMjIwMaNGzF16lTI5XJIraSafb/++ivMTFiCEOmCVt9JT58+xfr163H27FnExcUBAMqVK4dmzZph4MCBcHZ21ktIIiIiKhr+Oyd8ZHwkGlXImppaCIEMdQYOHz6MCX4TcO3aNQBA1apVMWvOLKRmpCI2MRaqCirYS+0N9h6IihOJEELk58C///4bHTp0gLW1Ndq1a4eyZcsCyOqBO3bsGFQqFQ4fPoyGDRvqNfCrFAoFHBwckJSUBHt7/qVARESkb4pURZ4j8+cvnMd9p/sAgP5e/WFjZYOAgAAMGzYMqUjN14g+EWXJb52b72K+SZMm8Pb2xsqVK1+b91UIgaFDh+LKlSs4e/bsuyXXAot5IiKiwpWhzsD2qO2ITYzFcO/hsJfaIyYmBpMnT8Zve37D2vC1iE2MxbPfn2GK7xSUKlUKABAaG4rm65trrhM2JEwzok9Er8tvnZvvNpuIiAhs3Lgx1wUcJBIJxowZg3r16hUsLRERERmN7DnhXypfImhiEJYtW4b09HRI7aXw2+eXNfpeToZpNtM053iX9YbMSYaohCi4O7nDy8XLgO+AqPjIdzFfrlw5nD9/Hh4eHrnuP3/+vKb1hoiIiIo/Ly8vPHn8BADQvn179JvYDz5/+QB4vZ/exsIGEUMjEBkfCS8XL7bYEOlIvov58ePH45tvvsHFixfRtm3b13rm16xZg/nz5+stKBERERmWWq3Gtm3bYNnUEkBWG4C3tzfmzp2Ljz76CClpKZgeOT3P0Xdrc2u21hDpWL575gFgx44dWLRoES5evIjMzEwAgKmpKRo0aICxY8eiV69eeguaG/bMExERFYwQAso0JSLjI+Fd1hs2FjZvPP7IkSPw8/PDjVs3sCVyCwDgRegL9O3dF6am/67aqkpXcfSdSAd0fgPsq9LT0/H06VMAQJkyZWBubl7wpO+AxTwREVHBvGlWmldFRETA398fhw8fBgDY29tjcsBkDBs2DLbWtrneS0dE7y6/dW6BVoA1NzeHk5MTnJycDFbIExERUcHlNl98NiEE7j24h8FfD0a9evVw+PBhmJubY/To0YiOjobfeD/Y2dixkCcqArQq5o8cOYLOnTvD0dER1tbWsLa2hqOjIzp37oyjR4/qKyMRERHpmJeLF1ztXAEAMieZpr89KSkJkwMm4/TL05B9LYO5rTm++OIL3LhxA4sWLUKZMmUMGZuI/iPfN8Bu2rQJQ4YMQY8ePbBo0aIcN8D+8ccf6Ny5M9atW4f+/fvrLSwRERHphrW5NeZ2mauZL95MmGHJkiWYPn06lGlKlHYqDblSDrcAN6wfvZ7970RFVL575t977z2MGjUKw4cPz3X/jz/+iEWLFuHOnTs6Dfgm7JknIiLK25tucs1QZ2D3vd0AAPVFNSZNmIS7d+8CAGStZYhqHaU5lgs8ERU+nffMP3jwAO3atctzf9u2bfHw4UPtUhIREZHeKNOU8Fjugebrm6PuqrpQpatyPc7Hxwd3795FuXLlsHr1alzYfwEyJxkAcIEnoiIu38V8rVq1sG7dujz3r1+/HjVr1tRJKCIiInp3ed3kev369RzTSdvY2mDatGmIiorC119/DQdrB0QMjUDYkDCEDw1niw1REZbvnvkFCxagS5cuOHToENq1a/faolF3797F/v379RaUiIiItJN9k2v29JOl1aXxzTffYN26dTCXmqP33N4AgKtXrqJ8ufI5zuUCT0TGId/FfOvWrREZGYkVK1bg3LlziIuLAwCUK1cOnTp1wtChQ1GlShV95SQiIiItvXqTa/KhZNTxqAOVKqvVpnPHzvBK94K7uztMJaZvuRIRFVUFWjSqqOANsERERHl7kfoC+/7ZBwDo79UfqS9S0bRpU8ybNw/Nmzc3cDoiehO9Lhr1qvT09He9BBEREemQEAJ79uxBo0b/tslUq1YNO3fuxJkzZ1jIExUj+S7mf/nlF6SlpWmeL1u2DJUrV4alpSXKlCmDadOm6SUgERER5d/Zs2fRsmVLfPbZZ4i8EonRrUbj8eHHCL8Uju7du3PVVqJiJt89871794ZcLoeLiws2bNgAX19f+Pn5oXHjxrh8+TJmzZqF8uXLY8iQIfrMS0RERK8QQiBTZCIqOgpTJk7Brl27AABWVlYYO3Ys/Pz82IpKVIzlu5h/tbV+5cqVmDZtGnx9fQEAnTt3hpOTE3788UcW80RERIUoLj4Op1NOA6bAvgP7YGJigkGDBiE4OBgVKlQwdDwi0jOteuazfzV39+5dfPTRRzn2ffTRR4iKisrtNCIiItIxlUqFmTNnonbt2pptHTp0QHh4ONauXctCnqiEyPfIPAAcOnQIDg4OsLS01Extle3ly5fswyMiItKzzMxMbNy4EVOnTsWjR48gtZJq9u3atQtmJlr9005ERk6r73gfHx/N13/++SeaNm2qeX7u3DlUr15dd8mIiIgIQFara4Y6A3/88Qf8ff1x7do1AEDlypURMjsEqRmpiE2MhaqCCvZS9scTlST5LubVavUb95ctWxazZs1650BERESU04VLF3DP8R5QA4i6GwVHR0dMmTIFw4cPRypS4bHcA3KlHOvD1iNiaASsza0NHZmICsk7zzOfrUuXLujQoYOuLkdERFTixcTEoG/fvmjZsqVm26hRoxAdHY2xY8dCKpUiMj4ScqUcABCVEIXI+EhDxSUiA9BZMU9ERES6kZCQgHHjxsHDwwM///xzjn0zZ86Eo6Oj5rl3WW/InGQAAHcnd3i5eBVqViIyLN4lQ0REVES8ePECP678EXPnzkV8XDwAoG3btpg9dzZiEJPrOTYWNogYGoHI+Eh4uXixxYaohOHIPBERkYGp1Wr89NNPqFO3Dip1q4RlZ5ahfsP6OHToEI4cOYK6deu+8Xxrc2s0qtCIhTxRCcSReSIiIgM6evQo/Pz8cPny5RzTTIaGhkJq/r/nIo+TiajEYzFPRERkAFeuXIG/vz8OHToEALC3t8ekKZM0+01NTQ0VjYiMiE7bbNq0aYPp06e/tqAUERERZXn48CH6f9Uf3p29cejYIZiZmWHkyJGIiorCuHHjDB2PiIyMTov5SpUq4dixY/Dw8NDlZYmIiIxeUlISJk2aBJmnDD/Z/gR8DdiOt8Wlq5ewZMkSODs7GzoiERkhnbbZbNy4EQCgUCh0eVkiIiKjlZaWhpUrV2LatGl49uwZUAFA6ax9ydJkvLB7YdB8RGTcdDIyn5iYmOO5vT2XkiYiopItJS0FIZtCUMOrBkaNGoVnz57Bw8MDvyz7Be5O7gA4LzwRvTuti/k5c+Zgx44dmue9evVC6dKlUaFCBUREROg0HBERkTE6cuIIykwpg8n3JuNex3twqeCCVatW4erVq+j5aU+EDw1H2JAwhA8Nz/d0kqkZqYh6GgVVOu9LI6J/aV3Mr1y5Em5ubgCAI0eO4MiRIzh48CA6deoEX19fnQckIiIyFjdu3EC3bt3wUb+P8NLmZdbG0sCO4zvwzTffwMwsq7tV23nhVekq+O3zw6SDk9BgdQMW9ESkoXXPfFxcnKaY37dvH3r16oWPPvoIVapUQePGjXUekIiIqKiLi4tDYGAg1q5dC7VaDROpCewy7JBklgR3J3c0qtLona4fGR8JuVIOAIhKiEJkfCQaVXi3axJR8aD1yLyjoyNiY2MBAIcOHUK7du0AAEIIZGZm6jYdERFRESWEQKIyEcEzgiGTybB69Wqo1Wp069YN18Kv4dHUR1q30uTFu6w3ZE4yAOyzJ6KctB6Z//zzz9GnTx+4u7vj2bNn6NSpEwDg8uXLkMlkOg9IRERU1GRkZGDdhnVwauuEmn1qIiMkA40bN8a8efPQsmVLzXG6Gj23sbBBxNAIRMZHwsvF651/OCCi4kPrYn7RokWoUqUKYmNjMXfuXNja2gIA5HI5vvvuO50HJCIiKiqEENi7dy/8/f1x78E9rA1fi9jEWKzdtBZ9e/SFRCLR22tn99kTEb1KIoQQhg5RUAqFAg4ODkhKSuJ0mEREpFfnzp2Dr68vTp8+DQAoV7kcJCMlkCvlkDnJEDE04p1HzDPUGdh9bzcA4LMqn8HMRKfLwRCREclvnVugeea3bNmCFi1aoHz58rh//z4AYPHixfj9998LlpaIiKgIEkLgVtQtfNnnSzRt2hSnT5+GpaUlJk2ahM2HNr92UyoRUWHTuphfsWIFxo4di06dOiExMVFz02upUqWwePFiXecjIiIyiCdPnmDMuDG4YnIF3Wd0h6W1JQYNGoQ7d+5g5syZaFatGW9KJSKD07qY/+GHH7BmzRpMnjwZpqammu0NGzbE1atXdRqOiIhI34QQUKQqEBobipS0FKhUKsyaNQsymQwrV67UHHfu3DmsX78eFStWBPDvTam6mrEmGxeHIiJtaN2MFxMTg3r16r22XSqVIiUlRSehiIiICosyTQmP5R6QK+Uoa1YWJqtNIH+Q1T7TqMm/N5zWqlXrtXN1fVNq9uJQcqUc68PW66QPn4iKN61H5qtWrYrw8PDXth86dAienp66yERERFRoIh//uyDT44zHkGfKUalSJfz00084depU4WbJZXEoIqI30XpkfuzYsRg+fDhevnwJIQTOnz+Pbdu2YdasWVi7dq0+MhIREenFpUuXEDg1EK5tXCFXymGaaIppo6Zh7IixsLS0RIY6o1DzZC8OFZUQxT58IsoXrYv5IUOGwMrKClOmTIFKpUKfPn1Qvnx5LFmyBF9++aU+MhIREenUvXv3MGXKFGzduhVSKynWLsyaL75PpT6oXK6ywXJxcSgi0laBJrDt27cv+vbtC5VKheTkZLi4uOg6FxERkc4IIZApMpGYmIg5s+Zg6dKlSEtLAwB0/6w7mpo3xZcNv4SpxPQtV9I/Lg5FRNp4p9UorK2tYW3NUQMiIiraUl6k4GDcQQDAD8t/QFpaGj788EPMmzcPDRo0MHA6IqKC07qYr1q16huXq7579+47BSIiItIVtVqNbdu2IWh6EEIOhAAAatasiZnTZ6Jjx45v/PeMiMgYaF3Mjx49Osfz9PR0XL58GYcOHYKvr6+uchEREWlFCAFlmhKR8ZHwLuuNsNNh8PX1xaVLlyC1kmqOO3v2LKTm0jdcKafUjFTEJsZCVUEFe2neS6oTERmC1sX8qFGjct2+fPlyXLhw4Z0DERERFcSr88XbvLRByoIUIB2ws7PDxMkTNUV5aoVUSJG/Yp7zvhNRUaf1PPN56dSpE3bt2qWryxEREb3mv6u1vurE9ROaOdpTLFNg6mqKESNGIDo6GsNHD4ffPj9MOjgJDVY3yPfqqpz3nYiKOp0V8zt37oSTk5OuLkdERPSa7NH35uubo+6qulClq6BQKDBlyhT079gfrnauAADbNFtcPnwZS5cuhbOzc4GL8ux53wFw3nciKpK0brOpV69ejhuGhBCIi4vDkydP8OOPP+o0HBER0av+W5RPXTYVm0I24enTpwAA74PemDZuGnq36Q0bCxvNeQVdjInzvhNRUScRQghtTggODs7x3MTEBM7OzmjdujU8PDx0Gu5tFAoFHBwckJSUBHt73pRERFTcKVIVmr54c6U50pemA+lAjRo1MGfOHHTt2jXPGWpU6SoW5URkNPJb52pdzBclLOaJiEqWv878hQfODxCbGIugdkFwtHZEcHAwBg8eDDOzd1o6hYioSMlvnZuvv/kUCkW+X5hFNRER6drNmzcxYcIEHPrjELZEboGsjAyT/CZh7KixsLOzM3Q8IiKDyVcxX6pUqbcurCGEgEQiQWZmpk6CERERxcXFITg4GGvWrEFmZiZMTEzw58I/MXnSZPSY3IOLPhFRiZevYv748eP6zkFERATgf9NPpiiwdMlSzJk1BykpWVNQdu3aFbNnz4anp6eBExIRFR35KuZbtWql7xxERETIyMjA+o3r4djGER69PZAxMwONGjXCvHnz8MEHHxg6HhFRkVPgu4VUKhUePHiAtLS0HNvr1KnzzqGIiKhkEUJg37598Pf3x917d7ElcgsAYPPmzejZvSfbaYiI8qB1Mf/kyRMMGjQIBw8ezHU/e+aJiCg/hBDIFJm4cOEC/H398ddffwEAXCu4IjUjFbGJsRj+yXAW8kREb6D1CrCjR49GYmIiwsLCYGVlhUOHDmHTpk1wd3fH3r179ZGRiIiKoTt372D3vd2ILROLsL/DYGlpiQkTJiDschj89vlh0sFJaLC6AVTpKkNHJSIqsrQu5v/8808sXLgQDRs2hImJCSpXrox+/fph7ty5mDVrlj4yEhFRMfL06VOMHj0aDeo30Gzr168fbt++jVmzZiH2ZWyOVV4j4yMNFZWIqMjTuphPSUmBi4sLAMDR0RFPnjwBANSuXRuXLl3SbToiIio2Xrx4gdmzZ6N69epYsmQJ0tPTNftWrlwJNzc3AIB3WW/InGQAAHcnd3i5eBkkLxGRMdC6Z75GjRq4desWqlSpAm9vb6xatQpVqlTBypUr4erqqo+MRERkpIQQSMtIw7Zt2xAwOQAPHz4EANStWxdz5s1BEpJeO8fGwgYRQyMQGR8JLxcvWJtbF3ZsIiKjoXUxP2rUKMjlWb/+DAwMRMeOHbF161ZYWFhg48aNus5HRERG7I+jf0BRXQGbFjZ48uwJKlWqhJkzZ6JPnz5QQ43d93bnep61uTUaVWhUyGmJiIyP1sV8v379NF83aNAA9+/fx82bN1GpUiWUKVNGp+GIiMg4Xb58Gf7+/vjr9F+aaSZnzpyJ4cOGw9LSEgCgVqsNGZGIqFjQumf+9OnTOZ5bW1ujfv36LOSJiAj379/HgAED0KBBAxw5cgQWFhaafaNGjdIU8tlSM1IR9TSKM9YQERWQ1sV8mzZtULVqVUyaNAnXr1/XRyYiIjIiQgg8TXiKCZMmoEaNGtiyZQuEEOjdu/cbJ0ZQpas4BSUR0TvSuph/9OgRxo0bh5MnT8LLywt169bFvHnzNDc1ERFR8SOEgCJVgdDYUKSkpWi2p6amYskPS3A88TgaDGkAmACtW7fG33//jZ9//hlVqlTJ85qR8ZGcgpKI6B1pXcyXKVMG33//Pc6cOYPo6Gj07NkTmzZtQpUqVdCmTRt9ZCQiIgNTpinhsdwDzdc3R91VdZGcmoxt27bBw8MDEyZM0By3c+dO/Pnnn2jYsOFbr8kpKImI3p3WN8C+qmrVqpgwYQK8vb0REBCAkydP6ioXEREVIf8dRX+/y/u4efQmAKBy1cqa4zp27AiJRJKva3IKSiKid6f1yHy2M2fO4LvvvoOrqyv69OkDLy8v7N+/X5fZiIioiPBy8YKr3f/WEkkAbp68CTs7O8yYMQMRVyIKfN3sKShZyBMRFYzWI/MTJ07E9u3b8ejRI7Rv3x5LlixBt27dYG3Nv4iJiIqjR48eYdqMaZg7ei5iE2Mxo+MMfPXtVwgICICLiwsy1BmGjkhEVGJpXcz/9ddf8PX1Ra9evTgdJRFRMaZQKDBv3jwsWLAAaqjRdnxbyMrIcOHcBXi+55nj2NSMVMQmxkJVQQV7qb2BEhMRlTxaF/NnzpzRRw4iIioi0tPTsXr1agQHB+PJkycAgGbNmqH84/Jo3LgxTCWmOY7PnmJSrpRjfdh6RAyNyNE2w0KfiEh/CtwzT0RExYtarcauPbtQt35dfP/993jy5Anee+89/Pbbbzh9+jSaN20OMxOz125wfdMUk5xLnohIv1jMExERQkND0bpta6jrqBH0exAqVqqIH3/8EZGRkfjss8/eOEPNm6aY5FzyRET69U5TUxIRkXG7ffs2Jk6ciN9++w1SK6lm+5WrV+Bo75iva7xpisnsQj8qIYpzyRMR6QGLeSKiEkQIgUyRifj4eMycPhOrVq1CZmYmTExMMHDQQM1xdrZ2Wl03e4rJ/+Jc8kRE+sU2GyIiIySEgCJVgdDYUKSkpeT7PEWKArvv7cYZ1Rms27AOmZmZ+OSTT3D16lUs+2GZXrJyLnkiIv3J18i8o6Njvlf0S0hIeKdARET0dso0JTyWe0CulEPmJHttBpn/ysjIwMaNGzEjZAbmHZ0HAGjQoAFCZoSgVatWWcdwvngiIqOTr2J+8eLFmq+fPXuGGTNmoEOHDmjatCkA4OzZszh8+DACAgL0EpKIiHLK7cbS3NpchBDYv38//P39cf36dUitpJqpIvf/sR+lrEoVcnIiItIliRBCaHNC9+7d8eGHH+L777/PsX3ZsmU4evQo9uzZo8t8b6RQKODg4ICkpCTY23PuYiIqORSpijxH5rP74i9evIgJfhNw4sQJAICTkxMmBk3EwvSFuZ6Xoc7A7nu7AQCfVfkMZia8rYqIyFDyW+dq3TN/+PBhdOzY8bXtHTt2xNGjR7W9HBERFYC1uTXmdpmLkE4huPjNxRwtNlExUdgetR1/ij8RejEUUqkU/v7+iI6ORrNPm3GqSCKiYkTrYZfSpUvj999/x7hx43Js//3331G6dGmdBSMiojeTmkkhKyPTFPLZbZBrNq+B/WR7yJVy2I+0x/mvzqNGtRoAAG9rThVJRFScaF3MBwcHY8iQIThx4gQaN24MAAgLC8OhQ4ewZs0anQckIqI3e/HiBX5c9iNmzZqFpKQkmFcz14y+K8wVSJImaY7lVJFERMWL1sX8wIED4enpiaVLl+K3334DAHh6euL06dOa4p6IiApPvXr1EH0nGgDg7e2N4FnBGB81Ps/R97zmhCciIuNToLubGjdujK1bt+o6CxER5dOxY8eA6llfP3z4EG5ubpgxYwb69u0LU1NTtE9vz9F3IqISoECLRkVHR2PKlCno06cP4uPjAQAHDx7EtWvXdBqOiIhyioiIQIcOHdCtWzfNtmnTpuHWrVsYMGAATE1NAXChJiKikkLrYv7kyZOoXbs2wsLCsGvXLiQnJwPI+gcmMDBQ5wGJiEqqV1d5vXX3Fnx8fFCvXj388ccfUGeocW7FObSybwXfcb6wsrIydFwiIjIArdtsJkyYgBkzZmDs2LGws7PTbG/Tpg2WLdPPUuBERCXRq6u8Sp5LILYJQABffvklZs6ciWrVqhk6IhERGZjWxfzVq1fx888/v7bdxcUFT58+1UkoIqKSLjU1FUE/BmlmpRGOAvU61MOqqavw/vvvGzgdEREVFVq32ZQqVQpyufy17ZcvX0aFChV0EoqIqKRSq9XYsWMHPD09sTxwOVztXAEA5aXlcWrXKb0X8qkZqYh6GgVVukqvr0NERLqhdTH/5Zdfwt/fH3FxcZBIJFCr1Thz5gzGjx+PAQMG6CMjEVGxJoRAhjoDx08eR5MmTfDll18iJiYGTjZOmGQ3CX/5/IXbY2/DxsJGrzlU6Sr47fPDpIOT0GB1Axb0RERGQOs2m5CQEAwfPhxubm7IzMxEzZo1kZmZiT59+mDKlCn6yEhEVKxFXo/ETaubgBtwJfIKbG1t4efnh7Fjx8LGRr8FfI4c8ZGatp6ohChExkdyPnoioiJO65F5CwsLrFmzBtHR0di3bx9++ukn3Lx5E1u2bNFMiUZERG/36NEjfP311zkW3Pv6668RFRWFgICAQi3kAcC7rDdkTjIAyHWxKSIiKnoKtGgUAFSqVAmVKlXSZRYiohJBqVRi3rx5WLBgAVQqFaRWUs2+RYsWwcykwH81vxMbCxtEDI3gYlNEREYkX/9ijB07Nt8XXLhwYYHDEBEVZ0mqJISsDcGGORvw5NETAEDTpk0xZ/4cxCHOwOmyZC82RURExiFfxfzly5dzPL906RIyMjJQo0YNAMDt27dhamqKBg0a6D4hEZGRE0Jgx287MCB0ANLt04HuQPUj1TF35lx89tlnyBSZ2H1vt6FjEhGREcpXMX/8+HHN1wsXLoSdnR02bdoER0dHAMDz588xaNAgtGzZUj8piYiM1NmzZ+Hr64sz984AX/9vY2lg86HNaFa5WdZzYbB4RERk5LS+AXbBggWYNWuWppAHAEdHR8yYMQMLFizQaTgiImN1584d9OjRA82aNcOZM2dgqbCEk3ACkHVzad3ydQ0bkIiIigWt77JSKBR48uTJa9ufPHkCpVKpk1BERMbq3j/34DvPF7tX7Ubmy0yYmJhg0KBBCA4OhqOLI28uJSIindK6mP/ss88waNAgLFiwAI0aZd0kFRYWBl9fX3z++ec6D0hEZAxUKhXmLJyD6U+mQzgJ4Gug472OmBcyD15e/07xyJtLiYhIl7Qu5leuXInx48ejT58+SE9Pz7qImRkGDx6MefPm6TwgEVFRlpmZiY0bN2Lq1Kl4JHmUoy8+2D8YXhXyN1d7akYqYhNjoaqggr3UXn+BiYioWJEIIQp061VKSgqio6MBANWrVy/0xU2ArJYfBwcHJCUlwd6e//gRUeERQuDgwYPw8/PDtWvXAACVqldC2ldpiEuPg7uTO8KHhuernUaRqoDHcg/IlXLInGSIGBrBNhwiohIuv3VugVcmsbGxQZ06dQp6OhGRURJC4MKlC5g8eTKOHD4CIGsSgICAAHz33XfINMnUui8+Mj4ScqUcABCVEIXI+Ei24xARUb5oPZtNSkoKAgIC0KxZM8hkMlSrVi3Hg4jI2AkhoEhVIDQ2FClpKZrtMTExGDBwAO453sPXP34N+1L28PX1RXR0NMaMGQOpVKpZdEmbkXXvst6QOckAZM104+WSv9YcIiIirUfmhwwZgpMnT6J///5wdXWFRCLRRy4iIoNRpilztL0c73UcC+csxPLlyyExlaDD5A6ITYxF6N+hqCWr9c6vZ2Nhg4ihEZzphoiItKZ1z3ypUqWwf/9+NG/eXF+Z8o0980SkD6GxoWi+/t+/42y32SL5VjIAoN3H7XCtzTX2txMRkV7lt87Vus3G0dERTk5O7xSOiKgoq1mmJlztXLOeJADJd5NRu3ZtHDp0CME/Br/W305ERGQoWhfz06dPx9SpU6FSqfSRh4jIoI4ePYqPPvwIc7vMRUinEFQ5XAUb12zE5cuX0aFDB3iXY387EREVHVr3zC9YsADR0dEoW7YsqlSpAnNz8xz7L126pLNwRESF5cqVK/Dz88Phw4chtZJCaiaFrIwMVy5egZ2NneY49rcTEVFRonUx/+mnn+ohBhFR4RJCIFNk4uHDhwgODMamTZsghIC5uTmGfjMUH9h9gNKlS8NUYvraudkz1hARERlagReNKgp4AywRFdSzxGf4M+FPAEB/r/5IfZGKXr16ISQkBNWrVzdwOiIiKun0dgMsEZGxyG2++LS0NCxduhS1vWojNSMVUU+j0LhFY5w7dw47duxgIU9EREZF6zYbExOTN84tn5mZ+U6BiIh05b/zxU91noqgyUG4e/cuLOws4LfPL2vfJzLUrl/b0HGJiIi0pnUxv3v37hzP09PTcfnyZWzatAnBwcE6C0ZE9K4i4yNzTCM5YM4A4B+gbNmyGDR1EGY/ma3ZFxkfyT54IiIyOloX8926dXttW48ePVCrVi3s2LEDgwcP1kkwIqJ3ZZFoAVc716yCPgGwTraGf7A/xo4dC4mFBDtX7URUQhSnmCQiIqOldTGflyZNmuCbb77R1eWIiPJFCAFlmhKR8ZHwLusNGwsbyOVyBAUFYcvWLVh9aTViE2Nxb+s9BN8MRrly5TTncopJIiIydjop5l+8eIGlS5eiQoUKurgcEVG+vdoXX71UdXzx/Assmb8EKSlZN7zuCdiDacHT4LnY87X7fTjFJBERGTuti3lHR8cc/yAKIaBUKmFtbY2ffvpJp+GIiN7m1b746MRohKwNAVKyfls4b948tGjRwsAJiYiI9EfrYn7x4sU5npuYmMDZ2RmNGzeGo6OjrnIREb2VEAIPLjzI0Rdf1aYq5v46F927d3/jzFtERETFgdbFvI+Pjz5yEBFp5dy5c/D19cXfF//G2vC1iE2MhfRvKb6f9z0sLCwMHY+IiKhQFKhnPjExEevWrcONGzcAALVq1cJXX30FBwcHnYYjIvqvO3fuYNKkSdi5cycAwNLSEre23sLoMaPh9L4TR+OJiKhE0XoF2AsXLqB69epYtGgREhISkJCQgIULF6J69eq4dOmSPjISUQknhEBcfBxGjx2NmjVrYufOnZBIJPjqq69w584dTA+ejtKlSrOQJyKiEkcihBDanNCyZUvIZDKsWbMGZmZZA/sZGRkYMmQI7t69i7/++ksvQXOjUCjg4OCApKQk2NvbF9rrElHhUalUWPLDEsh6ygAA/b36o03rNpgzZw5q1+aqrUREVDzlt87Vupi3srLC5cuX4eHhkWP79evX0bBhQ6hUqoIlLgAW80TFV2ZmJjZv3oyAgAA8TXiKLZFbAACO9xzRrk07A6cjIiLSr/zWuVq32djb2+PBgwevbY+NjYWdnZ22lyMi0hBCID0zHQcPH0S9evXw1Vdf4Z9//oFbJTfNMa1btzZcQCIioiJG62L+iy++wODBg7Fjxw7ExsYiNjYW27dvx5AhQ9C7d299ZCSiEuLi5YvYc38Pkt2TcTvqNkqVKoX58+fj8qXLSM1IRdTTKKjSC++3f0REREWd1rPZzJ8/HxKJBAMGDEBGRgYAwNzcHMOGDcPs2bN1HpCIir979+5hypQp2PnbTk07zahRo+Dv6w8nJycoUhXw2+cHuVKO9WHrETE0Atbm1gZOTUREZHhajcxnZmbi3LlzCAoKwvPnzxEeHo7w8HAkJCRg0aJFkEql+spJREZECAFFqgKhsaFISUvJ87jnz5/D19cXNWrUwNatW3PsmzlzJpycnADkXOU1KiEKkfGR+gtPRERkRLQq5k1NTfHRRx8hMTER1tbWqF27NmrXrg1ra46QEdG/lGlKeCz3QPP1zVF3Vd0crTFCCCSrkrFwcdaUtvPnz0daWhratGmDU6dO5dpO413WGzKnrNls3J3c4eXiVejviYiIqCjSumfey8sLd+/e1UcWIiom8hpJV6vV+Hn7zzgYdxBuXd2geqlC7dq1cfDgQRw9ehQ1vGrAb58fJh2chAarG2gKehsLG0QMjUDYkDCEDw1niw0REdH/aF3Mz5gxA+PHj8e+ffsgl8uhUChyPIiIvFy84GrnCgCQOcng5eKFP//8E++//z4GDx6sOW7FihW4fPkyOnbsCIlE8sZ2GmtzazSq0IiFPBER0Su0vgG2c+fOAICuXbvmWG1RCAGJRILMzEzdpSMio2Rtbo25XeYiNjEWH5p/iB7deuDgwYMAgNLOpTXH9e/fH6Ympprn2e00UQlRbKchIiLKB62L+ePHj+sjBxEVM1IzKWRlZGhTpw1epLyAmZkZvvvuO0ycPBFHE48iNjEWqgoq2Ev/XQgju50mMj4SXi5eHIUnIiJ6C61XgC1KuAIsUdGTlJSE+Qvno45PHQBAf6/+6NqlK0JCQiCTyaBIVcBjuQfkSjlkTjJOM0lERJQLva0AS0SUm7S0NPzwww+QyWSYN2+eZvvx48fxyy+/QCbLmo2G00wSERHpjtZtNkRErxJCYNeuXZg4cSKioqIAAB4eHrC4ZoHOnTvDrGrOv2bYF09ERKQ7LOaJSgAhBJRpSkTGR8K7rDdsLGx0cs1ToacwadIknPnrDACgbNmyCA4OxuDBg2FmlvtfL+yLJyIi0p18tdns3bsX6enp+s5CRHrypkWcCuLmzZvo8UUPPHZ9jFEbRsGxjCOCgoIQFRWFb7/9Ns9CPhunmSQiItKNfBXzn332GRITEwFkrQIbHx+vz0xEpGO66lOPi4vDsGHD4OXlhf379mtWaw27GIbAwEDY2trqMjYRERG9Rb6KeWdnZ5w7dw7Av/PJE5HxyG0Rp2xCCChSFQiNDUVKWkqu5ycnJyM4OBgymQwrV65EZmYmPurykWa11s6/d37n0X4iIiLSXr565ocOHYpu3bpBIpFAIpGgXLlyeR7LRaOIip5XF3Ea7j08R3tLdgtOblNFpqenY/3G9Zg5cyZi78cCABo1aoR58+bBrKoZmq9vDuDf0f5GFRoV/psjIiIqwfJVzAcFBeHLL79EVFQUunbtig0bNqBUqVJ6jkZEupS9iNN/+9Rza8F5v/z72Lt3LwICAxDwWwAWtF2AgE8CMC1wGnr27AmJRIKUtBTOSkNERGRg+Z7NxsPDAx4eHggMDETPnj1hbc0b14iKg+wWnOyR+Rf3X6BV71Y4deoUpFZSzXGXLl6CteW/3/eclYaIiMjwtJ6aMjAwEADw5MkT3Lp1CwBQo0YNODs76zYZERWKV1twLv9wGa1HtgYAWFpaYuy4sZrjLCwscj2XrTVERESGo/UKsCqVCl999RXKly+PDz74AB988AHKly+PwYMHQ6XiDXBExubZs2eaFpy9u/ZCIpFg4MCBuH37NoKDgw0dj4iIiN5A62J+zJgxOHnyJPbu3YvExEQkJibi999/x8mTJzFu3Dh9ZCQiPXjx4gVmz54NL69/e93bt2+P8PBwbNiwAW5ubgZMR0RERPmhdZvNrl27sHPnTrRu3VqzrXPnzrCyskKvXr2wYsUKXeYjIh3LzMzET5t/QkBAAB4+fAgAmN93PmbMmIG9e/Zy6lkiIiIjonUxr1KpULZs2de2u7i4sM2GyAg0b94cF/++CACoVKkSQkJC0Lt3b5iY5P6LutSMVMQmxkJVQQV7qX1hRiUiIqK30LrNpmnTpggMDMTLly812168eIHg4GA0bdpUp+GISDciIiI0X0dGRqJUqVKYN28ebt26hb59++ZZyKvSVZqFoRqsbsCFoYiIiIoYrYv5JUuW4MyZM6hYsSLatm2Ltm3bws3NDaGhoViyZIk+MhJRPuS2kuv9+/cxYMAAtGjRQnPcyJEjER0djfHjx8PS0vKN18xtDnoiIiIqOiRCCKHtSSqVClu3bsXNmzcBAJ6enujbty+srKx0HvBNFAoFHBwckJSUBHt7/vqfSjZFqkKzkmu1UtXQ9Z+uWLF0BVJTUwEA/X36Y+rUqahetXq+++JT0lJQd1VdzcJQ4UPDOZ88ERFRIchvnVugYr6oYDFP9K/Q2FA0X9/83w1rAPwDfPjhh5g3bx4aNGhQoOuq0lVcGIqIiKiQ5bfO1brNhoiKHrVajdunb8PVzjVrQwLgWdoT+/fvx7FjxwpcyAP/LgzFQp6IiKjo0Xo2GyIqWo4fPw5fX19EXo/E2vC1iE2MhcNVB3y78FuYmpoaOh4RERHpEYt5IiN17do1+Pv7Y//+/QAAOzs7PPjtAYZ/Pxz279tzvngiIqISgMU8kRERQuDho4eYMWMG1q5eC7VaDTMzMwwdOhQBAQFwcXExdEQiIiIqRAXqmU9MTMTatWsxceJEJCQkAAAuXbqEf/75R6fhiOhfCoUCgcGBOJd6Du1828Fcao4ePXrg+vXr+OGHH1jIExERlUBaj8xfuXIF7dq1g4ODA+7du4evv/4aTk5O+O233/DgwQNs3rxZHzmJih0hBJRpSkTGR8K7rDdsLGxyPS49PR2rV69GcHAwFMkKbBmwBQBw7NgxNG/aPNdziIiIqGTQemR+7NixGDhwIO7cuZNjwZnOnTvjr7/+0mk4ouJMmaaEx3IPNF/fHHVX1c2xuqoqXYWwh2H4+defUatWLXz//fd48uQJZDKZ5pjGjRsbIjYREREVIVoX83///Te+/fbb17ZXqFABcXFxOglFVBLktbqqKl2FGotqoMm6Juh7qi/u3LsDFxcXrFixAn///bchIxMREVERo3UxL5VKoVAoXtt++/ZtODs76yQUUUng5eKlmRde5iSDl4sXbt26hc4DO+Phi4dZB5UGBk8cjKioKAwdOhTm5uYGTExERERFjdbFfNeuXTFt2jSkp6cDACQSCR48eAB/f390795d5wGJjJkQAopUBUJjQ5GSlpJjn7W5NeZ2mYuQTiE49OkhjB81HrVq1cLJX08Cz7KOqWpfFUunLIWdnZ3mvNSMVEQ9jcrRlkNEREQlk0QIIbQ5ISkpCT169MCFCxegVCpRvnx5xMXFoWnTpjhw4ABsbHK/iU8f8rvMLZGhKFIV8FjuAblSDpmTDBFDIzQrqWaoM7D73m4AwNAmQ5HwJGtmqE8++QSBMwKRWToTXi5eOVZefdP1iIiIqPjIb52r9Ww2Dg4OOHLkCE6fPo0rV64gOTkZ9evXR7t27d4pMFFxlFtffKMKjZCRkYENmzag1IelAAApySl4//33MW/ePLRq1Urr6xEREVHJVOBFo1q0aIEWLVroMgtRsZPdF589kl7LuRb27dsHf39/RMdEY0tk1jSTmzZtQq8evd66aqt3WW/InGSISoiCu5M7vFy8CuNtEBERURGldTG/dOnSXLdLJBJYWlpCJpPhgw8+gKmp6TuHIzJ22X3xsYmxaKZuho8/+hgnT54EADg5OUF+QI7BgwfDuof1Wwt5ALCxsEHE0AhExke+1oJDREREJY/WxfyiRYvw5MkTqFQqODo6AgCeP38Oa2tr2NraIj4+HtWqVcPx48fh5uam88BExkZqJoWsjAwdvDog9UUqpFIpRo8ejQkTJqBUqVJaX8/a3JqtNURERASgALPZhISE4P3338edO3fw7NkzPHv2DLdv30bjxo2xZMkSPHjwAOXKlcOYMWP0kZfIaDx79gz+/v6a5xKJBD4+Prh9+zZmz55doEKeiIiI6FVaz2ZTvXp17Nq1C3Xr1s2x/fLly+jevTvu3r2L0NBQdO/eHXK5XJdZX8PZbKgoevHiBZYuXYpZs2bhZdpLTV+8TClDPe96Bk5HRERExkBvs9nI5XJkZGS8tj0jI0OzAmz58uWhVCq1vTSRUcvMzMRPP/2EKVOm4OHDrEWfvL29YR9tj7Zt28JUwvtIiIiISLe0brP58MMP8e233+Ly5cuabZcvX8awYcPQpk0bAMDVq1dRtWpV3aUkKsKEEDh85DCaNGuCgQMH4uHDh3Bzc8PmzZtx6dIldGjfAWYmZvm6wZWIiIhIG1oX8+vWrYOTkxMaNGgAqVQKqVSKhg0bwsnJCevWrQMA2NraYsGCBToPS1TUhIeH4+NPPoaiugJ+2/zgXNYZc+bMwe3bt9G/f3+YmGj9LUZERESUb1r3zGe7efMmbt++DQCoUaMGatSoodNg+cGeeSosQggo05SIjI+Ed1lvPIt7hilTpuCnn36ChaWFpi++lX0ruJRxMXBaIiIiMnZ665nP5uHhAQ8Pj4KeTmRUlGlKeCz3gFwph6NwRMr8FKSlpAEAevbsqTnOycnJUBGJiIioBCpQMf/w4UPs3bsXDx48QFpaWo59Cxcu1EkwoqLk8j+XIVdmzc70XPIcKAW0atgK8+bNQ70G9bA9ajtiE2OhqqCCvZS/JSIiIqLCoXUxf+zYMXTt2hXVqlXDzZs34eXlhXv37kEIgfr16+sjI5HBqNVq/PLLLwiYGQDXQa6QK+WwSLbAzz/+jM8/+RwSiQSKVAX89vlBrpRjfdh6RAyN4MqsREREVCi0vjtv4sSJGD9+PK5evQpLS0vs2rULsbGxaNWqVY52A6KiSAgBRaoCobGhSElLeeO+EydOoHHjxujduzdio2Mxt8tchHQKgTxIju5du2tmp4mMj9SM2kclRCEyPrLQ3xcRERGVTFqPzN+4cQPbtm3LOtnMDC9evICtrS2mTZuGbt26YdiwYToPSaQrr/a+y5xkOUbRX91nk2qDlPkpQHrW7Ez+/v74pPwnsJHZvDZfvHdZb8icZIhKiIK7kzu8XLwM8daIiIioBNK6mLexsdH0ybu6uiI6Ohq1atUCADx9+lS36Yh0LLdR9EYVGgEATl4/qdmXIk2BSTkTDP1kKAIDA+HikvcMNTYWNogYGoHI+Eh4uXixxYaIiIgKjdbFfJMmTXD69Gl4enqic+fOGDduHK5evYrffvsNTZo00UdGIp3xcvGCq52rZmTey8ULSqUSc+fOxdLVS+Hqn7XPNtUWpw6eQt1adfN1XWtza80PBURERESFRetifuHChUhOTgYABAcHIzk5GTt27IC7uztnsqEiz9rcGnO7zEVsYiy+qfkNNq7ZiKCgIDx58gQA4LXfC4HjA9GvbT/YWNgYOC0RERHRm2lVzGdmZuLhw4eoU6cOgKyWm5UrV+olGJG+SM2kkJWRoVWzVrh29RoAwN3dHbNnz8Znn32mubGViIiIqKjTajYbU1NTfPTRR3j+/Lm+8hDp1bmwc5qvo6Ki4OzsjOXLl+PatWv4/PPPWcgTERGRUdF6akovLy/cvXtXH1mI9Ob27dvo3r072rVtp9nm5++HqKgofPfddzA3NzdgOiIiIqKC0bqYnzFjBsaPH499+/ZBLpdDoVDkeBAVJfHx8Rg+fDhq1qyJ3377Demp6Tg2/xiaSJsgeGow7O25WisREREZL4kQQmhzgonJv/X/qy0JQghIJBJkZmbqLt1bKBQKODg4ICkpiUUZaQghoEhRYNkPyzA7ZLbmhu0uXbpg9uzZmqlUiYiIiIqq/Na5Ws9mc/z48XcKRqRPmZmZ2LBpAxxaO+C9L95D+vR0NGjQAPPmzcOHH35o6HhEREREOqX1yHxRwpF5yiaEwIEDB+Dv74+ou1FYG74WsYmxKH+3PPr36p/jN0pERERERV1+69wCVTinTp1Cv3790KxZM/zzzz8AgC1btuD06dMFS0v0Di5cuIC2bduiS5cuuHbtGhzKOMBvnx8mHZyEGU9m4GXmS0NHJCIiItILrYv5Xbt2oUOHDrCyssKlS5eQmpoKAEhKSkJISIjOA1LJJYSAIlWB0NhQpKSlvLYv6m4U+vv0x/vvv4/jx49DKpXCz88PWw5tgVwpBwBEJUQhMj7SEPGJiIiI9K5As9msXLkSa9asyTGdX/PmzXHp0iWdhqOSTZmmhMdyDzRf3xx1V9WFKl0FAEhISICvvy8u4zK6BnaFpbUl+vfvj1u3bmHOnDloLmsOmZMMAODu5A4vFy9Dvg0iIiIivdH6Bthbt27hgw8+eG27g4MDEhMTdZGJCAAQGR+ZY4T9YuxFnNt1DiEhIXiR+gJ1h9RFbGIsjp44iubvN9ecZ2Nhg4ihEYiMj4SXixesza0N9RaIiIiI9ErrYr5cuXKIiopClSpVcmw/ffo0qlWrpqtcRPBy8YKrnSvkSjnKmZdDn3Z98DDmIQCgXuN68NvnB7lSDpmTDBF1I3IU7dbm1mhUoZGhohMREREVCq3bbL7++muMGjUKYWFhkEgkePToEbZu3Yrx48dj2LBh+shIJZS1uTXmdpmLkE4hSJidgIcxD1GxYkVs3LgRS3csZV88ERERlXhaj8xPmDABarUabdu2hUqlwgcffACpVIrx48djxIgR+shIxZwQAso0JSLjI+Fd1jurTSYiApMDJsNnsQ9kZWSwt7LH+MnjMXLkSFhZWSElLQUyJxmiEqLYF09EREQlVoHnmU9LS0NUVBSSk5NRs2ZN2Nra6jrbW3Ge+eJBkaqAx3IPyJVyVLGvguZXmuPnTT9DCAFbe1sMGTIEkyZMgrOzc47zVOkq9sUTERFRsaS3FWB/+uknfP7557C2tkbNmjXfKSQRkPNG13uKe7h35B4ggF69eiEkJATVq1fP9Tz2xRMREVFJp3XP/JgxY+Di4oI+ffrgwIEDyMzM1EcuKmbymjM+LS0NoXtC4WrnmrUhAWgma4Zz585hx44deRbyRERERFSAkXm5XI5Dhw5h27Zt6NWrF6ytrdGzZ0/07dsXzZo100dGKgay54zPnn0m/Ntw7Nu9D5MmTcI/8n+wNnwtYhNjIYuTocfiHpBIJIaOTERERFTkaV3Mm5mZoUuXLujSpQtUKhV2796Nn3/+GR9++CEqVqyI6OhofeQkI/ffOePf//h93Dh6A0DWdKeqv1QYM2AMpOZSFvJERERE+aR1Mf8qa2trdOjQAc+fP8f9+/dx48YNXeWiYubVOeORANw4eQM2Njbw8/PD2LFjDXIDNREREZGxK1Axnz0iv3XrVhw7dgxubm7o3bs3du7cqet8VAzI5XJMmzkNc0fORWxiLKZ3mI6BQwYiMDAQZcuWNXQ8IiIiIqOldTH/5ZdfYt++fbC2tkavXr0QEBCApk2b6iMbGTmlUon58+dj/vz5yBSZaDO2DWRlZLh47iI8a3gaOh4RERGR0dO6mDc1NcUvv/yCDh06wNTUNMe+yMhIeHlx8Z6SKnvxp/BH4Qg/FI6Q4BA8fvwYANCkSROUlZdFs6bNYCoxfcuViIiIiCg/tC7mt27dmuO5UqnEtm3bsHbtWly8eJFTVZZgilQFPH/01PTFIwGQyWSYNWsWunfvzhtbiYiIiHRM63nms/3111/w8fGBq6sr5s+fjzZt2uDcuXO6zEZG5Ny5c2jzZRvNjDVwAsbNGYdr166hRw9ONUlERESkD1qNzMfFxWHjxo1Yt24dFAoFevXqhdTUVOzZs4erwZZQd+7cwaRJk7Bz505Y2FnA9YOsGWuqlaqGad9Ng4W5haEjEhERERVb+R6Z/+STT1CjRg1cuXIFixcvxqNHj/DDDz/oMxsVYU+ePMGIESNQs2ZN7Ny5ExKJBP169sOfn/2JM1+dwZVhV2Btbm3omERERETFWr5H5g8ePIiRI0di2LBhcHd312cmKsJUKhXmLpqLeZvmQXVPBWQAnTt3xuzZs1G7dm1DxyMiIiIqUfI9Mn/69GkolUo0aNAAjRs3xrJly/D06VN9ZqMiJDMzE+vXr0d1j+oIfhwMVV8VpKOk2P/Hfuzfv5+FPBEREZEB5LuYb9KkCdasWQO5XI5vv/0W27dvR/ny5aFWq3HkyBEolUqtXzwoKAgSiSTHw8PDQ+vrkP4IIXDgwAF4e3tj8ODBiFPHAaWz9qXapqJMzTKGDUhERERUgmk9m42NjQ2++uornD59GlevXsW4ceMwe/ZsuLi4oGvXrloHqFWrFuRyueZx+vRpra9BuqdKV2HT0U1o3b41Pv74Y1y7dg2Ojo6YNWYWZI4yAIC7kzu8XLiuABEREZGhFHhqSgCoUaMG5s6di4cPH2Lbtm0FuoaZmRnKlSuneZQpY0QjvSoVcP581n/1va8QX+v6nesoF1gWA88MxKmaf8Hc2hzjx49HdHQ0JoybgAifswhruh7hA0Jfv8nViN93kdpXVHIUpX1FJUdh7ysqOd62j4iIDEMYUGBgoLC2thaurq6iatWqok+fPuL+/ft5Hv/y5UuRlJSkecTGxgoAIikpqRBT/09KihDu7kIAWf9NSdHfvkJ6rWfPnomxY8cKm8qmAkHQPPac2l6s33eR21dUchSlfUUlB9937vuIiEjnkpKS8lXnGrSYP3DggPjll19ERESEOHTokGjatKmoVKmSUCgUuR4fGBgoALz2MEgxHxaW9Y9a9iMsTH/79PBa6rBzIsnOQpypZi6SzSG2jBghSpUqJQCI+uYQ7iOyCnn3ERApoSeLzfs2in1FJUdR2ldUcvB9576PiIh0ziiK+f96/vy5sLe3F2vXrs11P0fmdfdaSQly4brAVSAIospIibA0z/rBqHbt2uLw7t0i2aO6CKsAkeJRnaOSfN+G31dUcvB9576PiIh0ziiLeSGEaNiwoZgwYUK+js3vm9SblJSs0anc/lHT9b4CnKNWq0VSglycObxWJD+Pz7Hvhz0/5Gilca7rLDZs2CAyMjIK/73p+H0Xi31FJUdR2ldUchT2vqKS4237iIhIp/Jb50qEEMIQvfq5SU5ORqVKlRAUFISRI0e+9XiFQgEHBwckJSXB3t6+EBIaF0WqAh7LPSBXyiFzkiFiaASibkTB398ff575E6WDSkOulKO0pDRujrqJMg5GdPMxERERUTGW3zo33yvA6sP48ePxySefoHLlynj06BECAwNhamqK3r17GzJWsREZHwm5Ug4AiEqIQq/ve+HAmgMQQsDMzAyf//M5Ph74MT6o8QFsLGwMnJaIiIiItGXQYv7hw4fo3bs3nj17BmdnZ7Ro0QLnzp2Ds7OzIWMVG14uXnC1c4VcKYfkuQT7N+wHBNCzZ0+EhIRAJpMZOiIRERERvYMi1WajLbbZ5C0tLQ2r1qyCY3tHxCbGIqhdEBrXbYx58+ahcePGho5HRERERG+Q3zr3nRaNoqJHCIFff/0VNWvWhK+vL6RmUsjKyLDjpx04efIkC3kiIiKiYsSgbTakW6dOnYKvry/CwsIAAGXLlkXCsQT4+PhAWlUKiURi4IREREREpEss5o2cEAI3bt1AwNQA/PbrbwAAGxsb+Pr6Yty4cbC1tTVwQiIiIiLSF7bZGLG4uDgMHzkc1yyu4cvZX8La1hrffvst7ty5g8DAQBbyRERERMUcR+aNUHJyMhYsWIB58+YhQ52BZiOaITYxFidDT6Jh7YaGjkdEREREhYTFvBEQQiBTZCIjIwObNmxCYGAgHj9+DABo0roJ/Pb5Qa6UY73TekR4RMDa3NrAiYmIiIioMLCYNwIZ6gzsub8HADBqzCikvkhF9erVMXv2bJRvVB7NNzQHkLUwVGR8JBpVaGTAtERERERUWNgzX8SFhYWhQ4cOSM1IRdTTKDi6OGLp0qW4fv06evToAe9y3pA5ZS3+5O7kDi8XLwMnJiIiIqLCwkWjiqioqChMmjQJv/76KyzsLFA6qDTkSjmqlaqGq99dzdFKo0pXITI+El4uXmyxISIiIioGuGiUERJC4PGTxxgzbgxq1qyJX3/9FRKJBB0HdIRcKQcA3E28i8j4yBznWZtbo1GFRizkiYiIiEoYFvNFxIsXLzBn3hz8pfwLzYY3g4mZCTp27Ijw8HD8vPBnttIQERER0Wt4A6yBZWZmYsuWLQgICMCTZ0+w9tO1iE2Mxa97fsUnH32iOS5iaARbaYiIiIgoB/bM64EQAso0JSLjI+Fd1hs2Fja5HnP48GH4+fnh6tWrAIBqntXwYsgLyJVyyJxkiBjKaSaJiIiISiL2zBuQMk0Jj+UeaL6+OequqgtVukqzTwiBi5cvotPHndCpUydcvXoVpUqVwvz587Hu/9ZpeuOzp5kkIiIiIsoLi3k9iIyPzLUov3//PgYNHoS7DncxeNlg2DnYYdy4cYiOjsa4cePwvtv77I0nIiIionxjz7weeLl4wdXOVdMuU8G8Anx9fbF06VJITCX4eMrHAIDLly+jetXqmvNsLGzYG09ERERE+cZiXg+sza0xt8tcxCbGwiTUBLU9auP58+cAgI86fqQ5rnLlyrmeyxVciYiIiCg/2GajB2q1GlIzKWRlZAicFIjnz5/Dy8sLBw4cwL59+wwdj4iIiIiKCRbzOnb8+HG0atVK89zV1RXr1q1DeHg4OnXqBIlEgtSMVEQ9jcpxYywRERERkbbYZqMjkZGR8Pf3x4EDByC1kmq2R0REwN723+mEVOkq+O3zg1wpx/qw9Zx+koiIiIgKjMV8AQkhkCky8ejRIwQHBmPjxo1Qq9UwMzPD14O/RgubFnB2doapxDTHebnNdMMeeSIiIiIqCBbzBfRc8RzHnh0DAGzdthVqtRo9evRASEgI3N3d8zzPu6w3ZE4yRCVEcfpJIiIiInonLOYL6MSJE0j1TEVsYizeb/Y+5s2YhyZNmrz1PE4/SURERES6wmK+gNp2aAvPHz2z5pLvJkOdBnXyfS6nnyQiIiIiXeBsNgV07cm1XFd5JSIiIiIqLCzmCyi79x0Ae9+JiIiIyCDYZlNA7H0nIiIiIkNjMf8O2PtORERERIbENhsiIiIiIiPFYp6IiIiIyEixmCciIiIiMlIs5omIiIiIjBSLeSIiIiIiI8VinoiIiIjISLGYJyIiIiIyUizmiYiIiIiMFIt5IiIiIiIjxWKeiIiIiMhIsZgnIiIiIjJSLOaJiIiIiIwUi3kiIiIiIiNlZugA70IIAQBQKBQGTkJEREREpDvZ9W12vZsXoy7mlUolAMDNzc3ASYiIiIiIdE+pVMLBwSHP/RLxtnK/CFOr1Xj06BHs7OwgkUgMHadYUCgUcHNzQ2xsLOzt7Q0dh/LAz8k48HMyDvycjAM/J+PBz0o3hBBQKpUoX748TEzy7ow36pF5ExMTVKxY0dAxiiV7e3t+AxoBfk7GgZ+TceDnZBz4ORkPflbv7k0j8tl4AywRERERkZFiMU9EREREZKRYzFMOUqkUgYGBkEqlho5Cb8DPyTjwczIO/JyMAz8n48HPqnAZ9Q2wREREREQlGUfmiYiIiIiMFIt5IiIiIiIjxWKeiIiIiMhIsZgnIiIiIjJSLOZLkKCgIEgkkhwPDw+PN57z66+/wsPDA5aWlqhduzYOHDhQSGlLLm0/pzVr1qBly5ZwdHSEo6Mj2rVrh/Pnzxdi4pKpIN9P2bZv3w6JRIJPP/1UvyGpQJ9TYmIihg8fDldXV0ilUrz33nv8u68QFOSzWrx4MWrUqAErKyu4ublhzJgxePnyZSElLrn++ecf9OvXD6VLl4aVlRVq166NCxcuvPGcEydOoH79+pBKpZDJZNi4cWPhhC0BjHoFWNJerVq1cPToUc1zM7O8/xcIDQ1F7969MWvWLHTp0gU///wzPv30U1y6dAleXl6FEbfE0uZzOnHiBHr37o1mzZrB0tISc+bMwUcffYRr166hQoUKhRG3xNLmc8p27949jB8/Hi1bttRnNHqFNp9TWloa2rdvDxcXF+zcuRMVKlTA/fv3UapUqUJIStp8Vj///DMmTJiA9evXo1mzZrh9+zYGDhwIiUSChQsXFkbcEun58+do3rw5PvzwQxw8eBDOzs64c+cOHB0d8zwnJiYGH3/8MYYOHYqtW7fi2LFjGDJkCFxdXdGhQ4dCTF88sZgvYczMzFCuXLl8HbtkyRJ07NgRvr6+AIDp06fjyJEjWLZsGVauXKnPmCWeNp/T1q1bczxfu3Ytdu3ahWPHjmHAgAH6iEf/o83nBACZmZno27cvgoODcerUKSQmJuovHGlo8zmtX78eCQkJCA0Nhbm5OQCgSpUqekxHr9LmswoNDUXz5s3Rp08fAFmfU+/evREWFqbPiCXenDlz4Obmhg0bNmi2Va1a9Y3nrFy5ElWrVsWCBQsAAJ6enjh9+jQWLVrEYl4H2GZTwty5cwfly5dHtWrV0LdvXzx48CDPY8+ePYt27drl2NahQwecPXtW3zFLPG0+p/9SqVRIT0+Hk5OTHhMSoP3nNG3aNLi4uGDw4MGFlJAA7T6nvXv3omnTphg+fDjKli0LLy8vhISEIDMzsxATl1zafFbNmjXDxYsXNW2Fd+/exYEDB9C5c+fCilsi7d27Fw0bNkTPnj3h4uKCevXqYc2aNW88h/WEfrGYL0EaN26MjRs34tChQ1ixYgViYmLQsmVLKJXKXI+Pi4tD2bJlc2wrW7Ys4uLiCiNuiaXt5/Rf/v7+KF++/Gt/cZJuafs5nT59GuvWrXvrP3qkW9p+Tnfv3sXOnTuRmZmJAwcOICAgAAsWLMCMGTMKOXnJo+1n1adPH0ybNg0tWrSAubk5qlevjtatW2PSpEmFnLxkuXv3LlasWAF3d3ccPnwYw4YNw8iRI7Fp06Y8z8mrnlAoFHjx4oW+Ixd/gkqs58+fC3t7e7F27dpc95ubm4uff/45x7bly5cLFxeXwohH//O2z+lVs2bNEo6OjiIiIqIQktGr3vQ5KRQKUaVKFXHgwAHNNh8fH9GtW7dCTEhCvP37yd3dXbi5uYmMjAzNtgULFohy5coVVkT6n7d9VsePHxdly5YVa9asEVeuXBG//fabcHNzE9OmTSvkpCWLubm5aNq0aY5tI0aMEE2aNMnzHHd3dxESEpJj2/79+wUAoVKp9JKzJGHPfAlWqlQpvPfee4iKisp1f7ly5fD48eMc2x4/fqxVjzC9u7d9Ttnmz5+P2bNn4+jRo6hTp04hpaNsb/qcoqOjce/ePXzyySeabWq1GkBWj/CtW7dQvXr1Qstakr3t+8nV1RXm5uYwNTXVbPP09ERcXBzS0tJgYWFRWFFLvLd9VgEBAejfvz+GDBkCAKhduzZSUlLwzTffYPLkyTAxYfOBPri6uqJmzZo5tnl6emLXrl15npNXPWFvbw8rKyu95CxJ+H96CZacnIzo6Gi4urrmur9p06Y4duxYjm1HjhxB06ZNCyMe/c/bPicAmDt3LqZPn45Dhw6hYcOGhZiOsr3pc/Lw8MDVq1cRHh6ueXTt2hUffvghwsPD4ebmZoDEJdPbvp+aN2+OqKj/b+/+Y6Ku/ziAPz/8Mk4OSDl3CJcKnI3a3S5/rUAnWhs4prQwwS6crWa2EYhgUB47QHFisA6rsaVTdCGc2XAtNtLYbrEjZa6AWgSI1CXecrqpMYcQvL9/ND/t02UKBed9eT42/ni/7/15v1/vz/uf170/7/twUf6yBQC9vb2IjIxkIj/N7rdWt2/f9kjY734JE0JMeXwzVWJiInp6ehR1vb29WLBgwT2vYT4xxbz9aICmT35+vnA4HGJgYEA4nU7x3HPPiYiICHH16lUhhBBZWVmiqKhIbu90OkVAQICorKwU3d3dwmq1isDAQPHdd995awozwkTXaf/+/SIoKEicOnVKuN1u+e+3337z1hRmhImu01/xmM30mOg6uVwuoVarRXZ2tujp6RGff/65mDdvnti7d6+3pjBjTHStrFarUKvVor6+Xly6dEmcOXNGxMbGik2bNnlrCjNCe3u7CAgIEOXl5aKvr0/U1dUJlUolPv74Y7lNUVGRyMrKksuXLl0SKpVK7Nq1S3R3d4sPP/xQ+Pv7i+bmZm9M4f8Oj9nMIJcvX8bmzZtx/fp1aDQarFy5EufOnYNGowEAuFwuxS5HQkICTpw4AYvFgnfeeQd6vR6nT5/mO+an2ETXqaamBiMjI9i4caOiH6vVipKSkukMfUaZ6DqRd0x0nXQ6Hb744gvk5eXBaDQiKioKubm5KCws9NYUZoyJrpXFYoEkSbBYLBgcHIRGo8H69etRXl7urSnMCMuXL0djYyPefvttlJWVYdGiRbDZbDCbzXIbt9uteBPRokWL0NTUhLy8PFRXVyM6OhqHDx/mayn/I5IQfBZFREREROSLuG1EREREROSjmMwTEREREfkoJvNERERERD6KyTwRERERkY9iMk9ERERE5KOYzBMRERER+Sgm80REREREPorJPBHRDPPRRx9Bp9PBz88PNpsNJSUlMJlM3g5r0pKSkrBjxw5vh0FE5BVM5omI/kNbt27F888/P+3j1tbWIjw8/L7tbt26hezsbBQWFmJwcBDbtm2bknh8/QsCEZGvCPB2AERENH1cLhdGR0eRmpqKyMhIb4dDRET/EnfmiYimUFJSEnJycvDWW29hzpw50Gq1KCkpUbSRJAk1NTVYt24dgoODERMTg1OnTsmfOxwOSJKEGzduyHUdHR2QJAk//fQTHA4HXnnlFdy8eROSJEGSJI8xgD927w0GAwAgJiZGvv6vxsfHUVZWhujoaMyaNQsmkwnNzc2KNoWFhVi8eDFUKhViYmJQXFyM0dFReZzS0lJ0dnbK8dTW1nqMc+bMGTzyyCOKeQFAbm4u1q5dCwC4fv06Nm/ejKioKKhUKhgMBtTX19/jbv95P0+fPq2oCw8PV8Twyy+/YNOmTQgPD8ecOXOQlpb2t/eCiOhhx2SeiGiKHTt2DLNnz8b58+dx4MABlJWV4ezZs4o2xcXFSE9PR2dnJ8xmMzIzM9Hd3f1A/SckJMBmsyE0NBRutxtutxsFBQUe7TIyMvDll18CANrb2+F2u6HT6TzaVVdXo6qqCpWVlejq6kJycjI2bNiAvr4+uY1arUZtbS1++OEHVFdX49ChQ3jvvffkcfLz8/Hkk0/K8WRkZHiM8+yzzyI8PByffvqpXDc2Nga73Q6z2QwAGB4extKlS9HU1ITvv/8e27ZtQ1ZWFtrb2x/o3vyd0dFRJCcnQ61Wo7W1FU6nEyEhIUhJScHIyMik+yUi8gYm80REU8xoNMJqtUKv12PLli1YtmwZWlpaFG1efPFFvPbaa1i8eDH27NmDZcuW4f3333+g/oOCghAWFgZJkqDVaqHVahESEuLRLjg4GHPnzgUAaDQaaLVa+Pv7e7SrrKxEYWEhMjMz8fjjj6OiogImkwk2m01uY7FYkJCQgIULF2L9+vUoKCjAyZMn5XFCQkIQEBAgxxMcHOwxjr+/PzIzM3HixAm5rqWlBTdu3EB6ejoAICoqCgUFBTCZTIiJicGbb76JlJQUeazJsNvtGB8fx+HDh2EwGBAfH4+jR4/C5XLB4XBMul8iIm/gmXkioilmNBoV5cjISFy9elVR98wzz3iUOzo6pjo0D7du3cKVK1eQmJioqE9MTERnZ6dcttvtOHjwIPr7+zE0NITff/8doaGhEx7PbDbj6aefxpUrVzB//nzU1dUhNTVV/jHv2NgY9u3bh5MnT2JwcBAjIyO4c+cOVCrVpOfY2dmJixcvQq1WK+qHh4fR398/6X6JiLyByTwR0RQLDAxUlCVJwvj4+ANf7+f3x0NUIYRcd/d8ujd8/fXXMJvNKC0tRXJyMsLCwtDQ0ICqqqoJ97V8+XLExsaioaEBb7zxBhobGxVn2999911UV1fDZrPBYDBg9uzZ2LFjxz8eh5EkSXGvAOX9GhoawtKlS1FXV+dxrUajmfAciIi8ick8EdFD4Ny5c9iyZYui/NRTTwH4M8F0u9149NFHAcBj1z4oKAhjY2P/Oo7Q0FDMnz8fTqcTq1evluudTidWrFgBAGhra8OCBQuwe/du+fOff/550vGYzWbU1dUhOjoafn5+SE1NVYyblpaGl19+GcAfP87t7e3FE088cc/+NBoN3G63XO7r68Pt27fl8pIlS2C32zFv3rxJPU0gInqY8Mw8EdFD4JNPPsGRI0fQ29sLq9WK9vZ2ZGdnAwDi4uKg0+lQUlKCvr4+NDU1eeyCL1y4EENDQ2hpacG1a9cUyetE7dq1CxUVFbDb7ejp6UFRURE6OjqQm5sLANDr9XC5XGhoaEB/fz8OHjyIxsZGj3gGBgbQ0dGBa9eu4c6dO/ccz2w245tvvkF5eTk2btyIWbNmyZ/p9XqcPXsWbW1t6O7uxuuvv45ff/31H+Nfu3YtPvjgA3z77be4cOECtm/frng6YjabERERgbS0NLS2tmJgYAAOhwM5OTm4fPnyZG4ZEZHXMJknInoIlJaWoqGhAUajEcePH0d9fb28+xwYGIj6+nr8+OOPMBqNqKiowN69exXXJyQkYPv27cjIyIBGo8GBAwcmHUtOTg527tyJ/Px8GAwGNDc347PPPoNerwcAbNiwAXl5ecjOzobJZEJbWxuKi4sVfaSnpyMlJQVr1qyBRqP5x9dJxsXFYcWKFejq6pLfYnOXxWLBkiVLkJycjKSkJGi12vv+U66qqirodDqsWrUKL730EgoKChRn7FUqFb766is89thjeOGFFxAfH49XX30Vw8PD3KknIp8jib8eLCQiomklSRIaGxu98p9jiYjIt3FnnoiIiIjIRzGZJyIiIiLyUXybDRGRl/G0IxERTRZ35omIiIiIfBSTeSIiIiIiH8VknoiIiIjIRzGZJyIiIiLyUUzmiYiIiIh8FJN5IiIiIiIfxWSeiIiIiMhHMZknIiIiIvJRTOaJiIiIiHzU/wAhNJ8Uu3V0RAAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "vs = np.arange(4.9, 6.1, 1 / 77)\n", "# Round to nearest\n", "rn = round_ndarray(fi, vs)\n", "err_rn = np.abs(rn - vs).mean()\n", "\n", "fig, ax = plt.subplots(1, 1, figsize=(9, 5))\n", "\n", "ax.plot(vs, vs, label=\"True value\", color=\"k\")\n", "ax.plot(\n", " vs,\n", " rn,\n", " label=f\"Round to nearest, err={err_rn:.2f}\",\n", " color=\"red\",\n", " markersize=3,\n", " linestyle=\"\",\n", " marker=\".\",\n", ")\n", "\n", "# Stochastic rounding\n", "srnumbits = 16\n", "nsamples = 500\n", "srbits = np.random.randint(0, 2**srnumbits, (nsamples, len(vs)))\n", "\n", "rvs = round_ndarray(\n", " fi,\n", " vs[np.newaxis, :],\n", " RoundMode.Stochastic,\n", " sat=False,\n", " srbits=srbits,\n", " srnumbits=srnumbits,\n", ")\n", "rvmean = rvs.mean(axis=0)\n", "err = np.abs(rvmean - vs).mean()\n", "lollipops(\n", " ax,\n", " vs,\n", " rvmean,\n", " label=f\"SR, {srnumbits} bits, err={err:.2f}\",\n", " key=RoundMode.Stochastic,\n", ")\n", "\n", "ax.set_xlabel(\"Input float value\")\n", "ax.set_ylabel(f\"Average of rounded values, {nsamples} samples\")\n", "ax.set_yticks(np.unique(rn))\n", "ax.legend()\n", "None" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The random deviation is easier to see at this scale, but still shows good agreement between SR and infinite precision." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## With fewer bits of randomness\n", "\n", "Random bits are rarely free - generating good quality random numbers is relatively \n", "expensive, whether in hardware or software.\n", "Thus, one may have fewer random bits available in a real-world system.\n", "\n", "Let's see what happens with 2 bits of randomness:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize = (9, 5)\n", "fig, ax = plt.subplots(1, 1, figsize=figsize)\n", "\n", "ax.plot(vs, vs, label=\"True value\", color=\"k\")\n", "ax.plot(\n", " vs,\n", " rn,\n", " label=f\"Round to nearest, err={err_rn:.2f}\",\n", " color=\"r\",\n", " markersize=3,\n", " linestyle=\"\",\n", " marker=\".\",\n", ")\n", "\n", "# Stochastic rounding\n", "srnumbits = 2\n", "nsamples = 1_000\n", "srbits = np.random.randint(0, 2**srnumbits, (nsamples, len(vs)))\n", "\n", "rvs = round_ndarray(\n", " fi,\n", " vs[np.newaxis, :],\n", " RoundMode.Stochastic,\n", " sat=False,\n", " srbits=srbits,\n", " srnumbits=srnumbits,\n", ")\n", "rvmean = rvs.mean(axis=0)\n", "err = np.abs(rvmean - vs).mean()\n", "lollipops(\n", " ax,\n", " vs,\n", " rvmean,\n", " key=RoundMode.Stochastic,\n", " label=f\"SR, {srnumbits} bits, err={err:.2f}\",\n", ")\n", "\n", "ax.set_xlabel(\"Input float value\")\n", "ax.set_ylabel(f\"Average of rounded values, {nsamples} samples\")\n", "ax.set_yticks(np.unique(rn))\n", "ax.legend()\n", "None" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We still have the green line is closer to the black Y=X line than the grey line is,\n", "but now we all see the clear step effect, due to the limited number of SR bits.\n", "\n", "As a mental shorthand, we might consider that SR has given us extra precision \n", "corresponding to the number of `srbits`.\n", "Here, with `srbits = 2`, it's as if we are performing round-to-nearest in a 10-bit \n", "P5 format rather than an 8-bit P3 one. Let's just quickly simulate that.\n", "We will make a format like `format_info_ocp_e5m2`, but increase the \n", "bitwidth and precision:\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Make FormatInfo for a putative P5 format with the same exponent range as E5M2\n", "fi_p5 = FormatInfo(\n", " name=\"e5_p5\",\n", " k=10,\n", " precision=5,\n", " bias=15,\n", " has_nz=True,\n", " domain=Domain.Extended,\n", " num_high_nans=2**4 - 1,\n", " has_subnormals=True,\n", " is_signed=True,\n", " is_twos_complement=False,\n", ")\n", "\n", "# Round to nearest in P5\n", "rn_p5 = round_ndarray(fi_p5, vs)\n", "\n", "fig, ax = plt.subplots(1, 1, figsize=figsize)\n", "\n", "ax.plot(vs, vs, label=\"True value\", color=\"k\")\n", "\n", "# Stochastic rounding\n", "srnumbits = 2\n", "nsamples = 1_000\n", "srbits = np.random.randint(0, 2**srnumbits, (nsamples, len(vs)))\n", "\n", "rvs = round_ndarray(\n", " fi,\n", " vs[np.newaxis, :],\n", " RoundMode.Stochastic,\n", " sat=False,\n", " srbits=srbits,\n", " srnumbits=srnumbits,\n", ")\n", "rvmean = rvs.mean(axis=0)\n", "err = np.abs(rvmean - vs).mean()\n", "lollipops(\n", " ax,\n", " vs,\n", " rvmean,\n", " key=RoundMode.Stochastic,\n", " label=f\"SR, {srnumbits} bits, err={err:.2f}\",\n", ")\n", "\n", "ax.plot(vs, rn, label=f\"Round to nearest\", color=\"red\", linestyle=\"\", marker=\".\")\n", "ax.plot(\n", " vs,\n", " rn_p5,\n", " label=f\"Round to nearest ({fi_p5})\",\n", " color=\"pink\",\n", " linestyle=\"\",\n", " marker=\".\",\n", ")\n", "ax.set_xlabel(\"Input float value\")\n", "ax.set_ylabel(f\"Rounded values\")\n", "ax.set_yticks(np.unique(rn))\n", "ax.legend()\n", "None" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And we can observe that the \"Round to nearest (e5_p5)\" line and the \"SR\" line follow each other, up to noise.\n", "That is, with enough samples, 2 bits of stochastic rounding can be thought of as being\n", "akin to having 2 extra bits of precision." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implementation of SR\n", "\n", "The second part of this notebook goes deeper into the implementation of SR,\n", "and explores some subtleties that are not generally brought out in discussions of practical implementations. These subtleties might be summarized as\n", "\n", "> stochastic rounding of infinite-precision values with real-valued random variables is easy, \n", "> but rounding finite-precision values with limited-precision random variables can have surprising effects\n", "\n", "Note that these details are independent of the quality of the random number generator (RNG) — all of the issues discussed here happen with perfect RNGs.\n", "\n", "### Case 0: Infinite-precision inputs and real-valued random variables\n", "\n", "To begin our discussion, let's start with \"high-school\" rounding,\n", "where we implement round-to-nearest with code like\n", "```py\n", "def round(x):\n", " return floor(x + 0.5)\n", "```\n", "\n", "Then SR is easily motivated by replacing \"0.5\" with a random number between 0 and 1:\n", "```py\n", "def round_stochastic(x):\n", " return floor(x + rand())\n", "```\n", "\n", "This is a correct definition when `x` and `rand()` work in infinite precision, \n", "but needs to change subtly when they are supplied in fixed precision, as is true \n", "in a floating point system.\n", " \n", "### Case 1: Infinite-precision inputs and limited-precision random variables\n", "\n", "Let's assume that `rand()` produces only `S` bits of randomness at every call,\n", "i.e. that its implementation is something like\n", "```py\n", "def rand(S):\n", " bits = randint(2**S) # Draw a random S-bit integer (assume this is perfectly random)\n", " return bits * 2**-S # Return a float in [0, 1)\n", "```\n", "so that SR looks like:\n", "```py\n", "def round_stochastic(x):\n", " bits = randint(2**S) # Draw a random S-bit integer\n", " return floor(x + bits * 2**-S)\n", "```\n", "This is essentially gfloat's `StochasticFastest` implementation.\n", "There's a hint in the name \"Fastest\" that we may be trading speed for accuracy,\n", "so let's see how it behaves, by plotting the mean rounded value for a densely sampled set of inputs, as we did above for our default implementation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But first, let's look at the actual code to confirm that this is the implementation" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " case RoundMode.StochasticFastest:\n", " should_round_away = delta + srbits * 2.0**-srnumbits >= 1.0\n" ] } ], "source": [ "# Show the code from gfloat.round_float\n", "import inspect\n", "from more_itertools import one\n", "\n", "src = inspect.getsource(round_float).split(\"\\n\")\n", "loc = one([i for i, line in enumerate(src) if \"case RoundMode.StochasticFastest\" in line])\n", "print(*src[loc : loc + 2], sep=\"\\n\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And now test SRFastest.." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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JieLt27fizZs3wtLSUowZM0ZaV6ZMGVGrVq10tZxCpCaGlpaW4qeffhJv3ryR+0k7pr+/vxBCiOTkZGFkZCR69eqVbj/t2rXLNpnPKo40mSUBycnJwtjYWPTo0SPdNj///LPQ1tYWUVFRIiUlRZibm4tOnTplGUtacnj58mW55b/++qsAkOF/elk9x4qcn6LJvKLnkN25+fn5yS1X9DkUQvlkPrvnUdnXTmbJvKLHyeh+k44dO35Rbf7ly5dFly5dpEQOgLCxsRGHDh3KMPb//tjZ2Ynjx49n2Pbza0DaT2Zy+l5Pk9HrUJnrwJe8jzMzdOhQoaurm265IjXzI0aMEAYGBqJu3bqiRIkS4tmzZ5m2TUxMTHd+9evXF7169Uq3PCUlJdP93LhxQ/To0UOYmJhIf9/SpUun+7tt2bIlw9dCkyZNRGBgYIZtt2zZIvf/Qe3atYWBgYE4f/68XHtfX18BQPzzzz9CCCEiIyMFAPHrr7+mi3fq1KlCR0dHnDlzJsvnMiNRUVGiRo0awtraWpiamorGjRtn+OEyO3fu3BHm5uaiXr16GX7w0WRZJfNp98J8/PjxK0dFXwtr5kkhderUQYsWLdCiRQu4urriyJEjcHJywogRI7Ksj46Li8O0adNga2sLAwMDFC5cGDY2NoiMjJSrxfT29kZQUBBsbW1Rp04dTJ8+HY8ePQIAvHnzBpGRkVi3bh1sbGzkfgYOHAgA0kx5b968QVxcHBwcHNLFosjwcVnFkZ03b94gNjY2w+M4OjpKoz68efMG0dHRCpdClC5dWu5xWglEREQEAMWf4y89v/+eqzLnkJn/jo6i6HOYE9k9j1/62lH0OK9fv0ZcXBzKly+fbtuMlimjdu3aOHDgACIiInD58mVMnjwZHz58QLdu3RAcHJyu/cqVK+Hr64t9+/ahXbt2ePv2baaj83x+DUj7+Zwq3utZUeY6oKrXuapMmDABCQkJuHnzJg4fPpzhDKBpzp07l+78zp8/j927d6dbntW9FM7OztizZw/ev3+PM2fOYODAgXj69Cl69eoldw9H2ug0R44cga+vL7Zv345KlSrh2rVrsLCwkNvnjRs3oKuri969e8v9f/DHH38gISEBK1askGt/69YtAECVKlUAfCr7SSsp+Vy/fv2kYY9r1qyJBQsWIDw8PKunVWJubo6FCxfi/fv3iImJwZIlS2BkZKTQtmlevnyJ9u3bw8LCAvv27ZO7fyCvE/+WMHI0m/yLyTzliLa2Npo2bYrw8HCEhIRk2m7kyJGYPXs2evTogd9//x0nTpyAr68vChUqJDfpSo8ePfDo0SMsX74cJUqUwIIFC1CpUiX4+PhI7fr27QtfX98Mf9JusPpSWcWhLpn9p5J2gVb0OQY07/yU/Q/3c5n9x5SSkpLh8uyeR1X5WsfJir6+PmrXro05c+Zg9erVSEpKwt69e9O1S0vQu3btisOHD6Ny5cro06cPYmJilD6mKt7rWVHmOpAbr/NChQohOTlZqmlWxuzZswGkDh9obW2dZduqVaumOy9nZ2e0atUq3fJixYple2x9fX00adIEv/32G9q3b493797h3r170vqbN2+iTJkyaNeunZSc7927Fx8+fMCqVavk9nXz5k2UK1cOenp6cstLliwJY2NjPHv2LF370qVLSx8K0pL5/9bVA6k3nt6/fx9btmxB2bJl4eHhgW+++UahWu9Hjx7B1dUVFStWRJkyZdC1a1eFPwgAqfeDtG3bFpGRkTh27Fi6G4TzuoiICBgbG3/R9ZY0G2+ApRxLTk4GgCz/49+3bx/69+8vd6NXfHx8hhO1FC9eHMOGDcOwYcPw+vVr1KhRA7Nnz4afnx/MzMyQkpKS7UgSNjY2MDIyyvADxuf/gWUlszjatm0LIPMk0sbGBsbGxhke5+7du9DW1oatrS1MTU1hbm6OoKAgheLJjjLPMZD1+Snac2NjY6PSc/h8v4o8h0Bqj3dG55g2o2JOjv2lrx1FFClSBIaGhhmO0JHZqB1folatWgCQbXKjo6ODuXPnomnTplixYoXSE0Kp4r2e1XvMxsZG4etATo+RlbQbDkNDQzPsWc7MggULsGHDBqxYsQJubm6YPXs2NmzYkGl7KyurdOdnZWWF4sWLKzWSTkbSvnX5vMf95s2bqFOnjlw7R0dH1KpVC/v378eCBQvk2qaNkf65tG/U/vvh4vPRXNIeFy9eXO7G6c+ZmpqiX79+6NevH+7du4cqVarg999/z7KzJjw8HC1btoSenh58fX0RFxeHhg0bolWrVvDz88v2w1N8fDw6duyI+/fv4+TJk9INq/lJaGhoulGGKH9hzzzlSFJSEk6cOAF9ff0sLxI6OjrpeiSXL18u13uakpKSrhykSJEiKFGiBBISEqCjo4OuXbti//79GSaPb968kTte69atcfDgQbmvoO/cuYPjx49neU7ZxZEmbYSB/yYpOjo6aNWqFQ4dOiQ3xN2rV6+wc+dONGzYEObm5tDW1kbnzp3x559/4urVq+niULYHV5HnWNHzy+zc/kvV55BG0ecQAMqVK4eoqCi5ETvCw8MzHKZO0WPn9LWj7HFatGiBgwcP4sWLF9LyBw8eZNhzrOjQlGfOnMnweT969CgAxUqFmjRpgjp16mDJkiWIj4/Ptv3nVPFeT5PR61DR68CXvo8zU69ePQDI8PWemYMHD2LSpEnw8vLC8OHD8dNPP2Hr1q0IDQ1VeB/K8vf3R1xcXLrlN2/exLFjx1C9enWULVsWQGppyevXrzMsl2vdujVCQ0OlIRrT2mZ0vU8bqalr167SspSUFAQHB8sl82FhYShVqlS67f87ShKQ+q1dSkpKlr3kERERaN26NWJiYnDy5EmUKlUKDg4OOH78OJ4+fYr27dtLI/tkJCUlBT179sSFCxewd+9e6W+c3wQEBGT4IYzyD/bMk0J8fHxw9+5dAKl1qTt37kRISAgmTZokJVcZ6dChA7Zt2wYLCws4OTnhwoULOHnyJAoVKiS1+fDhA0qVKoVu3bqhatWqMDU1xcmTJ3HlyhWpl2/evHk4c+YM6tatiyFDhsDJyQnv379HQEAATp48iffv30v7mzFjBo4dO4ZGjRph2LBhSE5OxvLly1GpUqUsh2pTJA4A0sx7U6ZMQa9evaCnp4eOHTvCxMQEs2bNgq+vLxo2bIhhw4ZBV1cXa9euRUJCAry9vaV9zJkzBydOnICLiwt++uknODo6Ijw8HHv37oW/v79Ss14q8hwren5Zndt/qfIcPqfoc9irVy+4u7ujS5cuGDVqFGJjY7F69Wp88803cvMTKCOnrx1lTZ8+HSdOnECDBg0wdOhQpKSkYMWKFahcuTKuX78u11bRoSlHjhyJ2NhYdOnSBRUrVkRiYiLOnz+PPXv2wM7OTqorz46bmxu6d++OzZs343//+5/C56Sq9zqQ+etQkeuAKt7HGSlbtiwqV66MkydPphs3PiPXrl2Dq6srXF1dMWXKFADAxIkTsWbNmmx757/EpEmTcP/+fXTv3h1Vq1ZFcnIyrl+/Lv1ttm3bJrVNq5dPq2n/XKtWrTB79mwcOXIEjo6OUtvXr19j+/btAFKT8BMnTsDHxwe9evVC9+7dpe1DQkIQHx8vt297e3ucPn0a3t7eKFGiBBwdHVGzZk2MHDkSQUFB+O6772Bvb4/w8HCsW7cOpUqVwpAhQzI911WrVuHp06c4e/as3L0u1apVw19//YVWrVphy5YtGDZsWIbbjx8/HocPH0bHjh3x/v176bzSZDf0cl5w7do1vH//Hp06dVJ3KJSb1HXnLeUNGY16YWhoKKpVqyZWr14tNwRhRqPZREREiIEDB4rChQsLU1NT0bp1a3H37l1RpkwZaai1hIQE4ebmJqpWrSrMzMyEiYmJqFq1qtxwZkKkDnM2fPhwYWtrK/T09ESxYsVE8+bNxbp169LF7efnJ2rWrCn09fVF2bJlxZo1a7KdxVPROIRIHTmgZMmSQltbO905BwQEiNatWwtTU1NhbGwsmjZtmm6UByGEePLkiejXr580HGDZsmXF8OHDpRkJM5sB9r/PsyLPsTLnl9m5ZfT3ze4cMpPd7LaKPocnTpwQlStXFvr6+qJChQpi+/btmY5mk93zmEbR105mo9koepxTp06J6tWrC319fVGuXDmxYcMGMX78eGFoaCjXDgoOTenj4yN+/PFHUbFiRWFqair09fVF+fLlxciRIxWeAVaI1Jkqy5UrJ8qVKyeSk5MVngFWle91ITJ/HWZ3HVDV+zgjv/76qzA1NZUbKSWj0WyePn0qihcvLho0aCDi4+Pl1g0dOlTo6elJwxIqQpmhKQ8cOCB69+4typcvL0xMTIShoaFwdHQUbm5u4vXr13Jtvb29BQBx48aNdPtJTEwUZmZmomnTpnJtP/8xMzMTDRo0EBs3bkw3HO3vv/8uAIjbt29Ly54/fy69rwGIZcuWCSGE2Lhxo2jWrJl0HSlfvrwYNWpUunj/KykpSQQFBWW6/saNG1kOk+vi4pLpsKt5LT3KbDQbd3d3Ubp06WyHC6a8TUuIr3hXFhERZapz5864fft2ljeVk/pERUWhbNmy8Pb2xqBBgwAAgwcPxsmTJ7OcPZYot82aNQseHh5ypW4JCQmws7PDpEmTMHr0aDVGR7mNNfNERGrw37rmkJAQHD16FE2aNFFPQJQtCwsLTJw4EQsWLJAboefJkyfQ0tL64qFaiZS1ZMkSaGlpwcPDI926TZs2QU9PT6lyOcqb2DNPRKQGxYsXx4ABA1C2bFk8efIEq1evRkJCAgIDAzMc654008uXL6WbaA0MDNLNnUCUmyIiIvDq1SvpcdqoS1SwMJknIlKDgQMH4syZM3j58iUMDAxQr149zJkzBzVq1FB3aERElIcwmSciIiIiyqNYM09ERERElEcxmSciIiIiyqOYzBMRERER5VFM5omIiIiI8igm80REREREeRSTeSIiIiKiPIrJPBERERFRHsVknoiIiIgoj2IyT0RERESURzGZJyIiIiLKo5jMExERERHlUUzmiYiIiIjyKCbzRERERER5FJN5IiIiIqI8isk8EREREVEexWSeiIiIiCiPYjJPRERERJRHMZknIiIiIsqjmMwTEREREeVRTOaJiIiIiPIoJvNERERERHkUk3kiIiIiojyKyTwRERERUR7FZJ6IiIiIKI9iMk9ERERElEcxmSciIiIiyqN01R3Al5DJZHjx4gXMzMygpaWl7nCIiIiIiFRCCIEPHz6gRIkS0NbOvP89TyfzL168gK2trbrDICIiIiLKFU+fPkWpUqUyXZ+nk3kzMzMAqSdpbm6u5miIiIiIiFQjOjoatra2Ur6bmTydzKeV1pibmzOZJyIiIqJ8J7tSct4AS0RERESURzGZJyIiIiLKo5jMExERERHlUXm6Zl4RQggkJycjJSVF3aEQkQJ0dHSgq6vL4WaJiIgUkK+T+cTERISHhyM2NlbdoRCREoyNjVG8eHHo6+urOxQiIiKNlm+TeZlMhtDQUOjo6KBEiRLQ19dnTx+RhhNCIDExEW/evEFoaCgcHByynCiDiIiooMu3yXxiYiJkMhlsbW1hbGys7nCISEFGRkbQ09PDkydPkJiYCENDQ3WHREREpLHyfZcXe/WI8h6+b4mIiBTD/zGJiIiIiPIoJvNERERERHkUk3nKVVpaWjh48KC6wyAiIiLKl5jMaxgtLa0sf6ZPn67uEImIiIhIQ+Tb0WzyqvDwcOn3PXv2YNq0abh37560zNTUVPpdCIGUlBTo6vLPSERERKQyQgBChti4WBgbmwIaPLx5geqZF0Lg48ePX/1HCKFwjMWKFZN+LCwsoKWlJT2+e/cuzMzM4OPjg5o1a8LAwAD+/v4YMGAAOnfuLLefMWPGoEmTJtJjmUyGuXPnwt7eHkZGRqhatSr27duXaRy//PIL6tatm2551apVMXPmTADAlStX0LJlSxQuXBgWFhZwcXFBQEBApvs8e/YstLS0EBkZKS27fv06tLS08PjxY2mZv78/GjVqBCMjI9ja2mLUqFH4+PFj1k8cERERkYqcP38OCL8I48ibgJCpO5wsFahkPjY2Fqampl/9R9Uz0E6aNAnz5s3DnTt34OzsrNA2c+fOxdatW7FmzRrcvn0bY8eORd++feHn55dhe1dXV1y+fBkPHz6Ult2+fRs3b95Enz59AAAfPnxA//794e/vj4sXL8LBwQHt2rXDhw8fcnxuDx8+RJs2bdC1a1fcvHkTe/bsgb+/P0aMGJHjfRIRERFlRwiB06dPo2nTpmjZsqW0POTBAzVGlT3WZ+RBM2fOlHuRZSchIQFz5szByZMnUa9ePQBA2bJl4e/vj7Vr18LFxSXdNpUqVULVqlWxc+dOeHh4AAB27NiBunXronz58gCAZs2ayW2zbt06WFpaws/PDx06dMjRuc2dOxeurq4YM2YMAMDBwQHLli2Di4sLVq9ezQmEiIiISKWEEDh+/Di8vLxw/vx5AICFuZm03uHfvEdTFahk3tjYGDExMWo5rirVqlVLqfYPHjxAbGxsug8AiYmJqF69eqbbubq64rfffoOHhweEENi1axfGjRsnrX/16hWmTp2Ks2fP4vXr10hJSUFsbCzCwsKUO6HP3LhxAzdv3sSOHTukZUIIyGQyhIaGwtHRMcf7JiIiIkojZDIcPfoX5s/3xj/+5wAABgYGGDJkCNwnTgDwTL0BKqhAJfNaWlowMTFRdxhf7L/noK2tna4uPykpSfo97QPMkSNHULJkSbl2BgYGmR6nd+/ecHd3R0BAAOLi4vD06VP07NlTWt+/f3+8e/cOS5cuRZkyZWBgYIB69eohMTExw/2lzer5eayfx5kW688//4xRo0al27506dKZxkpERESkCJlMhgMHDmDRwgW4sP9XtN89H4WdO6L/gIGYMGECihcvDshSgHAm8/SV2NjYICgoSG7Z9evXoaenBwBwcnKCgYEBwsLCMiypyUypUqXg4uKCHTt2IC4uDi1btkSRIkWk9efOncOqVavQrl07AMDTp0/x9u3bLOMEUkfssbKykuL8XI0aNRAcHCyV8hARERGpQkpKCn7//XfMnj0bt2/fhrHRp9LdO3fuwKZIUTVGl3MF6gbY/KpZs2a4evUqtm7dipCQEHh6esol92ZmZpgwYQLGjh2LLVu24OHDhwgICMDy5cuxZcuWLPft6uqK3bt3Y+/evXB1dZVb5+DggG3btuHOnTu4dOkSXF1dYWRklOm+ypcvD1tbW0yfPh0hISE4cuQIFi1aJNfG3d0d58+fx4gRI3D9+nWEhITg0KFDvAGWiIiIlCcEkhLjsWPbVjg5OaFPnz64ffs2LCwsMHnyZKmZTeHCagzyyzCZzwdat24NDw8PTJw4EbVr18aHDx/Qr18/uTZeXl7w8PDA3Llz4ejoiDZt2uDIkSOwt7fPct/dunXDu3fvEBsbm274y40bNyIiIgI1atTADz/8gFGjRsn13P+Xnp4edu3ahbt378LZ2Rnz58/HrFmz5No4OzvDz88P9+/fR6NGjVC9enVMmzYNJUqUUO5JISIiogItMTERmzZthN6ba3BtVg7PnobB2toaXl5eePLkCaZOmaLuEFVCSygzCLqGiY6OhoWFBaKiomBubi63Lj4+HqGhobC3t+cIKER5DN+/RESUU/Hx8di4cSPmz5+Pd2/f4GPISQDA4t0XMPinn2Fm9u9INbIUIPxi6u/FvwW0dT7tJKt1X0lWee7nWDNPRERERHnXZ7O1rl23AQsWLEB4eDgAoKy9ndRs7NixaknKcxvLbIiIiIgoz/rwIVqarXXqlF8QHh4OW1tbrFy5ErdvB2W/gzyOyTwRERER5TmRkZHw8vKCk9OnOWjs7Oywbt06PHjwAMOGDYOhQf4v1WSZDRERERHlGe/evcOSJUuwbNkyREdHyw0xef16IPT0838C/zkm80RERESk2YTA69evsGzZMixdtlyaENPJyQme0zykZnq6euqKUG1YZkNEREREGuvFixdwd3dDkeSHmDWsPWQpyahatSr27duHW7duoUf37uoOUa2YzBMRERGRxgkLC8Pw4cNRtmxZrFixUlq+d+/vCAwMRNeuXaGtzVSWZTZEREREpH7/DjEZ+jgUc+d5Y/PmzUhKSgIANG/WRGrWrm07QEtLTUFqHn6cIaU1adIEY8aMUXcYRERElI+EhNwHwi/C3uAVdmzfhqSkJDRt2hSnT5+G7wlfdYensZjMa6ABAwZAS0sLWlpa0NPTg729PSZOnIj4+Hh1h6aQ6dOno1q1auoOQ60eP34MLS0tXL9+Xd2hKO3s2bOoUaMGDAwMUL58eWzevDnb9p06dULx4sVhYmKCatWqYceOHXJt1q9fj0aNGsHKygpWVlZo0aIFLl++nItnQUREecXt27fRp08f1KhRQ1rWokUL/PPPPzh9+jSaNm0KLfbEZ4rJvIZq06YNwsPD8ejRIyxevBhr166Fp6enusMqEIQQSE5OVncYCktJSYFMJku3PDExUel9hYaGon379mjatCmuX7+OMWPGYPDgwTh+/Him25w/fx7Ozs7Yv38/bt68iYEDB6Jfv37466+/pDZnz55F7969cebMGVy4cAG2trZo1aoVnj9/rnSMRESUxwkByFJw68Z1dO/eHVWqVMGuXbvk/i87dPAgGjZsqMYg8w4m8xrKwMAAxYoVg62tLTp37owWLVrA1/fTV0wJCQkYNWoUihQpAkNDQzRs2BBXrlyR1m/evBmWlpZy+zx48KDcJ9u0HvRt27bBzs4OFhYW6NWrFz58+CC1+fjxI/r16wdTU1MUL14cixYtyjLuzZs3Y8aMGbhx44b07UJaz25YWBg6deoEU1NTmJubo0ePHnj16lWm+0rr3T5w4ACaNm0KY2NjVK1aFRcuXJBr5+/vj0aNGsHIyAi2trYYNWoUPn78KK3ftm0batWqBTMzMxQrVgx9+vTB69evpfVnz56FlpYWfHx8ULNmTRgYGMDf3x8ymQxz586Fvb09jIyMpDvn00RERMDV1RU2NjYwMjKCg4MDNm3aBACwt7cHAFSvXh1aWlpo0qRJls/b5xISEjBhwgSULFkSJiYmqFu3Ls6ePSv3HFtaWuLw4cNwcnKCgYEBwsLCYGdnBy8vL/Tr1w/m5ub46aefFD5mmjVr1sDe3h6LFi2Co6MjRowYgW7dumHx4sWZbvPLL7/Ay8sL9evXR7ly5TB69Gi0adMGBw4ckNrs2LEDw4YNQ7Vq1VCxYkVs2LABMpkMp06dUjpGIiLK2wICrgLhF1Gl8EccPfIXhBDo2rUrLpw/r+7Q8qQClcwLIZCYmPjVf4QQXxR3UFAQzp8/D319fWnZxIkTsX//fmzZsgUBAQEoX748Wrdujffv3yu174cPH+LgwYP466+/8Ndff8HPzw/z5s2T1ru5ucHPzw+HDh3CiRMncPbsWQQEBGS6v549e2L8+PGoVKkSwsPDER4ejp49e0Imk6FTp054//49/Pz84Ovri0ePHqFnz57ZxjhlyhRMmDAB169fxzfffIPevXtLPecPHz5EmzZt0LVrV9y8eRN79uyBv78/RowYIW2flJQELy8v3LhxAwcPHsTjx48xYMCAdMeZNGkS5s2bhzt37sDZ2Rlz587F1q1bsWbNGty+fRtjx45F37594efnBwDw8PBAcHAwfHx8cOfOHaxevRqFCxcGAKmE5OTJkwgPD5dLbLMzYsQIXLhwAbt378bNmzfRvXt3tGnTBiEhIVKb2NhYzJ8/Hxs2bMDt27dRpEgRAMDChQtRtWpVBAYGwsMjddzdSpUqwdTUNNOftm3bSvu9cOECWrRoIRdP69at032Ayk5UVBSsra0zXR8bG4ukpKQs2xARUf5y/vx5tG3bFo0aNZaWde/eDbdu3cK+ffvg7OysxujyLrWPZvP8+XO4u7vDx8cHsbGxKF++PDZt2oRatWqp/FhJSUmYO3euyvebncmTJ8sl4or466+/YGpqiuTkZCQkJEBbWxsrVqwAkNpbvnr1amzevFlKxNavXw9fX19s3LgRbm5uCh9HJpNh8+bNMDMzAwD88MMPOHXqFGbPno2YmBhs3LgR27dvR/PmzQEAW7ZsQalSpTLdn5GREUxNTaGrq4tixYpJy319fXHr1i2EhobC1tYWALB161ZUqlQJV65cQe3atTPd54QJE9C+fXsAwIwZM1CpUiU8ePAAFStWxNy5c+Hq6irdkOvg4IBly5bBxcUFq1evhqGhIX788UdpX2XLlsWyZctQu3ZtxMTEwNTUVFo3c+ZMtGzZEkBq7/icOXNw8uRJ1KtXT9rW398fa9euhYuLC8LCwlC9enXptWpnZyfty8bGBgBQqFAhuechO2FhYdi0aRPCwsJQokQJ6fyPHTuGTZs2Yc6cOQBSX8urVq1C1apV5bZv1qwZxo8fL7fs6NGj0mgAGTEyMpJ+f/nyJYoWLSq3vmjRooiOjkZcXJxc28z8/vvvuHLlCtauXZtpG3d3d5QoUSLdBwciIspfhBA4e/YsvLy8cObMGQCAmamJtH7zps2Ato6aossf1JrMR0REoEGDBmjatCl8fHxgY2ODkJAQWFlZqTMsjdC0aVOsXr0aHz9+xOLFi6Grq4uuXbsCSO2NTkpKQoMGDaT2enp6qFOnDu7cuaPUcezs7KREHgCKFy8ulaA8fPgQiYmJqFu3rrTe2toaFSpUUPp87ty5A1tbWymRB1JnbbO0tMSdO3eyTOY//6RevHhxAMDr169RsWJF3LhxAzdv3pS74VIIAZlMhtDQUDg6OuLatWuYPn06bty4gYiICKkmLywsDE5OTtJ2n3+AfPDgAWJjY6XkPk1iYiKqV68OABg6dCi6du2KgIAAtGrVCp07d0b9+vWVfm4+d+vWLaSkpOCbb76RW56QkIBChQpJj/X19TPswcjoQ3CZMmW+KCZlnDlzBgMHDsT69etRqVKlDNvMmzcPu3fvxtmzZ2FoWLCm3CYiKiiETIZTJ30xb/48nDp9FkBqrtK/f3/8MtkdQOZltqQctSbz8+fPh62trVRnDHyqNc4Nenp6mDx5cq7tP6vjKsvExATly5cHAPz222+oWrUqNm7ciEGDBim0vba2drrynox6Z/8bm5aWVoY3U6rT5zGm1fynxRgTE4Off/4Zo0aNSrdd6dKl8fHjR7Ru3RqtW7fGjh07YGNjg7CwMLRu3TrdDaImJp96CtKmiT5y5AhKliwp187AwAAA0LZtWzx58gRHjx6Fr68vmjdvjuHDh2PhwoU5PteYmBjo6Ojg2rVr0NGR76n4/FsEIyOjDO/s//wc0lSqVAlPnjzJ9JiNGjWCj48PAKBYsWLp7mN49eoVzM3Ns+2V9/PzQ8eOHbF48WL069cvwzYLFy7EvHnzcPLkSX6dms9ERkYiKipK3WEQkZoJIXD+/Hns2b0Lh1aMQYsVfVC7dzgaNGmDPn36oGjRotCCDEiJBz4+wtMEK8h0Uv/v0oIMpbXSL1f3Otg4A/qfOj41jVqT+cOHD6N169bo3r07/Pz8ULJkSQwbNgxDhgzJsH1CQgISEhKkx9HR0UodT0tLS+lyF02gra2NX375BePGjUOfPn1Qrlw56Ovr49y5c1Kva1JSEq5cuSKVm9jY2ODDhw/4+PGjlOApO0xiuXLloKenh0uXLqF06dIAUr9NuX//PlxcXDLdTl9fHykpKXLLHB0d8fTpUzx9+lTqnQ8ODkZkZKRc77iyatSogeDgYOmDz3/dunUL7969w7x586TjXr16Ndv9fn5jaVbnamNjg/79+6N///5o1KgR3NzcsHDhQul19t/nITvVq1dHSkoKXr9+jUaNGim1bWaUKbOpV68ejh49Krfe19dXKjXKzNmzZ9GhQwfMnz8/0xtvvb29MXv2bBw/fjxXyuhIfSIiIrB8+fIvvj+IiPKPBt9WA64NAOKe4djYQljzxETqODLSS8ZEx81A3DMYJxXCmic/I1noZ7o8q22+xjqELADaXQd0jb/Ok6cktSbzjx49wurVqzFu3Dj88ssvuHLlCkaNGgV9fX30798/Xfu5c+dixowZaohU/bp37w43NzesXLkSEyZMwNChQ+Hm5gZra2uULl0a3t7eiI2NlXru69atC2NjY/zyyy8YNWoULl26lO144f9lamqKQYMGwc3NDYUKFUKRIkUwZcqUbKdOtrOzQ2hoKK5fv45SpUrBzMwMLVq0QJUqVeDq6oolS5YgOTkZw4YNg4uLyxcldu7u7vj2228xYsQIDB48GCYmJggODoavry9WrFiB0qVLQ19fH8uXL8f//vc/BAUFwcvLK9v9mpmZYcKECRg7dixkMhkaNmyIqKgonDt3Dubm5ujfvz+mTZuGmjVrolKlSkhISMBff/0FR0dHAECRIkVgZGSEY8eOoVSpUjA0NISFhUW2x/3mm2/g6uqKfv36YdGiRahevTrevHmDU6dOwdnZWbp3QBnKlNn873//w4oVKzBx4kT8+OOPOH36NH7//XccOXJEarNixQr88ccf0kg0Z86cQYcOHTB69Gh07doVL1++BJD6oS7tBtf58+dj2rRp2LlzJ+zs7KQ2aTfhUt72/v17CCGgo6PDMkmiAkZHWwsxMR8Q/vK11OGqra2NaqXiUxNhAIX03uGbIol4nZJ6L1hxvbAM12W2PKttvsY6xIQAkUFA4Tq58RR+OaGka9euiZs3b0qPDx48KDp16iQmT54sEhISlNqXnp6eqFevntyykSNHim+//TbD9vHx8SIqKkr6efr0qQAgoqKi0rWNi4sTwcHBIi4uTqmYNEH//v1Fp06d0i2fO3eusLGxETExMSIuLk6MHDlSFC5cWBgYGIgGDRqIy5cvy7X/448/RPny5YWRkZHo0KGDWLdunfj8T+7p6SmqVq0qt83ixYtFmTJlpMcfPnwQffv2FcbGxqJo0aLC29tbuLi4iNGjR2caf3x8vOjatauwtLQUAMSmTZuEEEI8efJEfPfdd8LExESYmZmJ7t27i5cvX2a6n9DQUAFABAYGSssiIiIEAHHmzBlp2eXLl0XLli2FqampMDExEc7OzmL27NnS+p07dwo7OzthYGAg6tWrJw4fPiy33zNnzggAIiIiQu74MplMLFmyRFSoUEHo6ekJGxsb0bp1a+Hn5yeEEMLLy0s4OjoKIyMjYW1tLTp16iQePXokbb9+/Xpha2srtLW1hYuLi9yxQkNDMz3vxMREMW3aNGFnZyf09PRE8eLFRZcuXaT33aZNm4SFhUW67cqUKSMWL16c6X4VdebMGVGtWjWhr68vypYtK/390nh6esq9Rvr37y8ApPtJO+e02DJq4+npmWEMefn9WxDdu3dPTJ8+Xaxbt07doRDRV5KUlCR2bNsqxDN/IZ75C2MjQ2Fubi6mTp0q3r59K0RijBCHHITYASEOOwiR9PHTxpmty8k26lj3lURFRWWa535OSwjlvhetXbs2Jk2ahK5du+LRo0eoVKkSunTpgitXrqB9+/ZYsmSJwvsqU6YMWrZsiQ0bNkjLVq9ejVmzZik0mUx0dDQsLCwQFRUFc3NzuXXx8fEIDQ2Fvb09b7IjjZE2Ik1wcHCO7qUoKPj+zVvu3LmD33//Hba2tnKjRxFR/pOYmIitW7di7ty5eBn+Ah9DTgIA5m45g6HDRsjPcZMcm9qjbVk5fYlKZutyso061n0FWeW5n1N6nPn79++jWrVqAIC9e/eicePG2LlzJzZv3oz9+/crta8GDRrg3r176fb/NUffIPqajh49ijlz5jCRp3wlbd4HXV21j3ZMRLkkPj4eq1atgoODA4YMGYJHjx7B5t+5VQBg8qTJ6SarhK5xamlKRolwZutyso061mkQpa+84t9h/4DUCXE6dOgAALC1tcXbt2+V2tfYsWNRv359zJkzBz169MDly5exbt06rFu3TtmwiPKEvXv3qjsEIpVLu9H7vyMwEVHeF/vxI377bSOWLFmCh49CAaSOfDZx4kT8NGQQEHVLzRGS0j3ztWrVwqxZs7Bt2zb4+flJN+SFhoamm2wmO7Vr18Yff/yBXbt2oXLlyvDy8sKSJUvg6uqqbFhERKQm7Jknyn8+fPgAb29vVHJyxIjva+LB39vwjUN5rFixAqGhoRg7dixMjNMPh0xfn9JX3rRk++DBg5gyZYo0JOC+fftyNGFOhw4dpN59IiLKe9gzT5R/REVFYfny5Vi8eDHev38PY6NP9y3dunUT+gbZzwROX5fSybyzszNu3Ur/lcqCBQt4ISciKoDSeub5fwBRHiUE3r9/h5UrV2LRr4ulCeAcHBzg6TFVaqavl/fm6ikIlC6zAVJn+tuwYQMmT56M9+/fA0idAOj169cqDY6IiDQfe+aJ8q7Xr1/Dw2MqrOPvwWNQCyQlJsDJyQk7d+7EnTt3WPqcByjdM3/z5k00b94clpaWePz4MYYMGQJra2scOHAAYWFh2Lp1a27ESUREGiotmWfNPFHeER4ejgULFmDNmjXQgoDX0HYAgO3bt6NT5y6fJoiUKTeTOX19SvfMjxs3DgMHDkRISIjc+M/t2rXD33//rdLgiIhI87HMhigPEAKQpeDZ0ycYOXIk7O3tsXjxYsTFxaFGjRpSsy6dO2c70ztpFqX/WleuXMHPP/+cbnnJkiWlKdqJiKjgYM88keZ7/PgREH4RpbSf4beNG5CQkID69evDx8cHf/v5qTs8+gJKJ/MGBgaIjo5Ot/z+/fuwsbFRSVBEuW3z5s3pJ7f4j+nTp0sTpBFR5tgzT6S5QkJCMHDgQDg7V5WWNW7cCKdOnYK/vz/atGkDLS0tNUZIX0rpZP67777DzJkzkZSUBADQ0tJCWFgY3N3d0bVrV5UHWBC9efMGQ4cORenSpWFgYIBixYqhdevWOHfunNTGzs4OWlpa0NLSgrGxMapUqYINGzbI7efs2bNSm89/pk6d+t9DKs3Ozg5Lliz54v18rkmTJhgzZozS2x04cAAtW7aEjY0NzM3NUa9ePRw/fvyL45kwYQJOnTolPR4wYAA6d+78xfvVJEIITJs2DcWLF4eRkRFatGiBkJCQLLf5+++/0bFjR5QoUQJaWlo4ePCg3PqkpCS4u7ujSpUqMDExQYkSJdCvXz+8ePEiF8+E1Ik3wBJpnuDgYLi6uqJixYrYvHmz9D4FAJ+jPmjWrBmT+HxC6WR+0aJFiImJQZEiRRAXFwcXFxeUL18eZmZmmD17dm7EWOB07doVgYGB2LJlC+7fv4/Dhw+jSZMmePfunVy7mTNnIjw8HEFBQejbty+GDBkCHx+fdPu7d+8ewsPDpZ9JkyZ9rVP5Kv7++2+0bNkSR48exbVr19C0aVN07NgRgYGBX7RfU1NTFCpUSEVRqk5iYmK6ZUIIqXdUGd7e3li2bBnWrFmDS5cuwcTEBK1bt0Z8fHym23z8+BFVq1bFypUrM1wfGxuLgIAAeHh4ICAgAAcOHMC9e/fw3XffKR0f5Q0ssyHSEELg1o3r6OvaG5UrV8bOnTshk8nQoUMHnD17Rt3RUW4ROfTPP/+IlStXivnz5wtfX9+c7uaLREVFCQAiKioq3bq4uDgRHBws4uLi1BBZzkVERAgA4uzZs1m2K1OmjFi8eLHcMmtrazF27Fjp8ZkzZwQAERERkW77y5cvixYtWohChQoJc3Nz0bhxY3Ht2jVpvUwmE56ensLW1lbo6+uL4sWLi5EjRwohhHBxcREA5H7S/PPPP6Jhw4bC0NBQlCpVSowcOVLExMRI61euXCnKly8vDAwMRJEiRUTXrl2FEEL0798/3T5DQ0MVfdrScXJyEjNmzMh0/aZNm4SFhYX4448/pHhatWolwsLCpDaenp6iatWq0u//je/MmTMiISFBDB8+XBQrVkwYGBiI0qVLizlz5igV661bt0SbNm2EiYmJKFKkiOjbt6948+aNtN7FxUUMHz5cjB49WhQqVEg0adJE+tsePXpU1KhRQ+jp6YkzZ84odVyZTCaKFSsmFixYIC2LjIwUBgYGYteuXQrtA4D4448/sm13+fJlAUA8efJEof3m1fdvQfX777+L6dOni0uXLqk7FKIC68qVK6J7t65CPPMX4pm/MDYyFN9//70ICAhIbZCSLK0TKcnyG+fGOvpiWeW5n8vx7coNGzbEsGHDMHHiRLRo0SLHHybyjORY4O3l1H9zkampKUxNTXHw4EEkJCQotI1MJsP+/fsREREBfX3FJnT48OED+vfvD39/f1y8eBEODg5o164dPnz4AADYv38/Fi9ejLVr1yIkJAQHDx5ElSpVAKSWtZQqVUr6ZiA8PBwA8PDhQ7Rp0wZdu3bFzZs3sWfPHvj7+2PEiBEAgKtXr2LUqFGYOXMm7t27h2PHjqFx48YAgKVLl6JevXoYMmSItE9bW1ulnrvPn48PHz7A2to6y3axsbGYPXs2tm7dinPnziEyMhK9evXKsO2ECRPQo0cPtGnTRoqvfv36WLZsGQ4fPozff/8d9+7dw44dO2BnZ6dwrJGRkWjWrBmqV6+Oq1ev4tixY3j16hV69Ogh127Lli3Q19fHuXPnsGbNGmn5pEmTMG/ePNy5cwfOzs74559/pNdQZj87duwAAISGhuLly5dy718LCwvUrVsXFy5cUPgcFBEVFQUtLa1s71OgvCntWyH2zBN9fefPn0fbtm1Ru3ZtHDlyRFp+6dIl7N+/H9WrV1djdPQ1KHTlXbZsmcI7HDVqVI6D0VjJsYBPNeBDCGDmALS9Duga58qhdHV1sXnzZgwZMgRr1qxBjRo14OLigl69esHZ2Vmurbu7O6ZOnYqEhAQkJyfD2toagwcPTrfPUqVKyT1+8uQJmjVrJrds3bp1sLS0hJ+fHzp06ICwsDAUK1YMLVq0gJ6eHkqXLo06deoAAKytraGjowMzMzMUK1ZM2sfcuXPh6uoq1b07ODhg2bJlcHFxwerVqxEWFgYTExN06NABZmZmKFOmjHSRsbCwgL6+PoyNjeX2mRMLFy5ETExMuoT4v5KSkrBixQrUrVsXQGrC7OjoiMuXL0vnmsbU1BRGRkZISEiQiy8sLAwODg5o2LAhtLS0UKZMGaViXbFiBapXr445c+ZIy3777TfY2tri/v37+OabbwCkPpfe3t5Sm7QPUDNnzkTLli2l5bVq1cL169ezPGbRokUBQBp9Ku3x5+tVOTJVfHw83N3d0bt3b5ibm6tsv6Q5WDNP9BUJAQgZ/vH3x/QZM3H69GkAqe+/3r17S80qV6qkrgjpK1MomV+8eLFCO9PS0sqfyXxkUGoiD6T+GxkEFK6T9TZfoGvXrmjfvj3++ecfXLx4ET4+PvD29saGDRswYMAAqZ2bmxsGDBiA8PBwuLm5YdiwYShfvny6/f3zzz8wMzOTHltZWeHVq1eYOnUqzp49i9evXyMlJQWxsbEICwsDAHTv3h1LlixB2bJl0aZNG7Rr1w4dO3bMsuftxo0buHnzptTzC6TWcstkMoSGhqJly5YoU6aMtM82bdqgS5cuMDZW3QejnTt3YsaMGTh06BCKFCmSZVtdXV3Url1belyxYkVYWlrizp076ZL5zAwYMAAtW7ZEhQoV0KZNG3To0AGtWrVSON4bN27gzJkzMDU1Tbfu4cOHUjJfs2bNDLevVauW3GMjI6MMXwPqkpSUhB49ekAIgdWrV6s7HMolTOaJvg4hBE6fOonmjsZoVE4XFy+ch66uLvr374/JkyejnL0dEH5R3WHSV6ZQMh8aGprbcWg2y8qpPfJpPfOWlXP9kIaGhmjZsiVatmwJDw8PDB48GJ6ennLJfOHChVG+fHmUL18ee/fuRZUqVVCrVi04OTnJ7cve3j5deUP//v3x7t07LF26FGXKlIGBgQHq1asn3Vxpa2uLe/fu4eTJk/D19cWwYcOwYMEC+Pn5QU9PL8OYY2Ji8PPPP2f4ga506dLQ19dHQEAAzp49ixMnTmDatGmYPn06rly5opLyi927d2Pw4MHYu3fvVyv9qlGjBkJDQ+Hj44OTJ0+iR48eaNGiBfbt26fQ9jExMejYsSPmz5+fbl3x4sWl301MTDLc/r/L//nnH7Rt2zbLY65duxaurq7SNwyvXr2SO9arV69UMiRnWiL/5MkTnD59mr3y+RjLbIhylxACR48ehZeXF27dvIGPIScBAEOGDMbYcRM+fSvM2VoLpC+68gohACD/D22ka5xaWhMZlJrI51KJTVacnJzSDQH4OVtbW/Ts2ROTJ0/GoUOHst3fuXPnsGrVKrRrlzp989OnT/H27Vu5NkZGRujYsSM6duyI4cOHo2LFirh16xZq1KgBfX19uWGugNTENjg4OMueYV1dXbRo0QItWrSAp6cnLC0tcfr0aXz//fcZ7lNRu3btwo8//ojdu3ejffv2Cm2TnJyMq1evSr3w9+7dQ2RkJBwdHTNsn1l85ubm6NmzJ3r27Ilu3bqhTZs2eP/+fbY1+0Dqc7Z//37Y2dmpJBFSpszG3t4exYoVw6lTp6TkPTo6GpcuXcLQoUO/KI60RD4kJARnzpzRyFGBSHXYM0+kYv+W0shkMhz68y/MmjULAQEBAABrK0up2ZLFSwBtvu8KuhxlDxs3bsTixYul8agdHBwwZsyYDOu18w1d41wtrUnz7t07dO/eHT/++COcnZ1hZmaGq1evwtvbG506dcpy29GjR6Ny5cq4evVquvKL/3JwcMC2bdtQq1YtREdHw83NDUZGRtL6tDFp69atC2NjY2zfvh1GRkbSp387Ozv8/fff6NWrFwwMDFC4cGG4u7vj22+/xYgRIzB48GCYmJggODgYvr6+WLFiBf766y88evQIjRs3hpWVFY4ePQqZTIYKFSpI+7x06RIeP34MU1NTWFtbKzSl9M6dO9G/f38sXboUdevWleq9jYyMYGFhkel2enp6GDlyJJYtWwZdXV2MGDEC3377baYlNnZ2djh+/Dju3buHQoUKwcLCAsuXL0fx4sVRvXp1aGtrY+/evShWrJjC3zQMHz4c69evR+/evTFx4kRYW1vjwYMH2L17NzZs2KB0cqRMmY2WlhbGjBmDWbNmwcHBAfb29vDw8ECJEiXkxtNv3rw5unTpIt3IHBMTgwcPHkjrQ0NDcf36dVhbW6N06dJISkpCt27dEBAQgL/++gspKSnS38Ta2lrhm7Qp72DPPJFqpSQnQef1FWgD6OvaB7Fx8TAxMcGwYcMwftxYIOWRukMkDaL0aDbTpk3D6NGj0bFjR+zduxd79+5Fx44dMXbsWEybNi03YixQTE1NUbduXSxevBiNGzdG5cqV4eHhgSFDhmDFihVZbuvk5IRWrVop9HfYuHEjIiIiUKNGDfzwww8YNWqUXI25paUl1q9fjwYNGsDZ2RknT57En3/+KfWwzpw5E48fP0a5cuWkmX+dnZ3h5+eH+/fvo1GjRqhevTqmTZuGEiVKSPs8cOAAmjVrBkdHR6xZswa7du1CpX9v0pkwYQJ0dHTg5OQEGxsbqX7fzs4O06dPz/Rc1q1bh+TkZAwfPhzFixeXfkaPHp3lc2BsbAx3d3f06dMHDRo0gKmpKfbs2ZNp+yFDhqBChQqoVasWbGxscO7cOZiZmcHb2xu1atVC7dq18fjxYxw9elT6EDJgwAA0adIk032WKFEC586dQ0pKClq1aoUqVapgzJgxsLS0VOiDzJeaOHEiRo4ciZ9++gm1a9dGTEwMjh07BkNDQ6nNw4cP5b61uXr1KqpXry7dvDxu3Djpbw0Az58/x+HDh/Hs2TNUq1ZN7m9y/vz5XD8n+vrYM0+kGsnJydi2bRtq1/l0P5e5uRmmTJmCx48fw9vbG0WzuR+MCh4tkVYroyAbGxssW7ZM7o5pILXMYeTIkelKNXJTdHQ0LCwsEBUVla4eNz4+HqGhobC3t5dLTChviY2NRaFCheDj45NlUqypXFxc0LRp0yw/jFB6fP/mLUuWLEFUVBQGDx6MkiVLqjscojwnMTER27Ztw9y5c/Hw4UMYGxlKdfERRhVhZf1ZqaIs5dNNrsW/lS+z0aR19MWyynM/p/R3oklJSRmWcNSsWTNHM1ASZeXMmTNo1qxZnkzko6Ki8PDhQ7lxf4nyI5bZEOVMQnw8tm7djEWLfsW9+6mly4ULF8YkdzepjRXn56BsKP09/g8//JDhEHPr1q2Dq6urSoIiStO+ffs8mwxbWFjg2bNnGQ47SZSfsMyGSDlxcXFYtmwZKleuhCHtq+Du6U2wtyuDRYsW4fHjxxg/bry6Q6Q8JMc3wJ44cQLffvstgNRZxsLCwtCvXz+MGzdOavfrr7+qJkoiItJY7JknUkxMTAzWrFmDhQsX4tWrVzA2+lRGePt2EIyM/+384RCTpASlr7xBQUGoUaMGgNQb44DUr4QKFy6MoKAgqV2+H66SiIgAsGeeKEtCICoqEmvXroH3gkV49+4dgNTBHTym/iI1MzI0ymwPRFlSOpk/c+ZMbsRBRER5kEwmk+YcYTJPJC8iIgKrVi7HlIHNMbFvY8yYMRMODg745Zdf4OrqCj0dbc7YSl8s338nquRgPUSkAfi+zTs+n0iNZTZEqd68eYPFixdjxYoVSElOwpSBzQEAv/32G7p26/7pvcJyGlIBpa+88fHxWL58Oc6cOYPXr19DJpPJrU+boUzd9PT0AKQObfj5ZEhEpPliY2MBfHofk+b6fBQz9sxTgfXvjK2vXr3CgkW/YvXq1dJ1rG7tTyMA9uzRg8M3ksopncwPGjQIJ06cQLdu3VCnTh2NrY3X0dGBpaUlXr9+DSB1giBNjZWIUgkhEBsbi9evX8PS0pLJYR7wec/815jojEgTPX/+FCW1nqIogNWrViI2Lh41a9aEh4cHOrZvB7y6rO4QKR9TOpn/66+/cPToUTRo0CA34lGpYsWKAYCU0BNR3mBpaSm9f0mzfT6SDTtMqKB5/Pgx5s2bhz27dyHi9lEAQN26deA2cRLatGmT+p5gKQ3lMqWT+ZIlS8LMzCw3YlE5LS0tFC9eHEWKFEFSUpK6wyEiBejp6bFHPg/hSDZUED148ABz5szBtm3bkJycLDfE5KmTp6Clw/tH6OtR+tW2aNEiuLu7Y82aNShTpkxuxKRyOjo6/I+GiCgXMJmnAkMI3L17Bwu8vbF56zbpnsGWLVvCc5qH1IzfUNHXpnSBY61atRAfH4+yZcvCzMwM1tbWcj9ERFRwcMIoKghu3ryJH35wRUXzCGycNQSGBvpo3749Lly4gBMnTqBB/frqDpEKMKWvvr1798bz588xZ84cFC1alJ9AiYgKMPbMU3527do1eHl54dChQzA2MsS2+cMBAOf8/VGtRk01R0eUSulk/vz587hw4QKqVq2aG/EQEVEewp55ylf+HWLy0uVLmDFzFnx8fACkls507fq91KxatWpqCpAoPaXLbCpWrIi4uLjciIWIiPIY9sxTfuLv/w8QfhF1bQX8zp6BtrY2+vbti9u3b2Prlq3qDo8oQ0on8/PmzcP48eNx9uxZvHv3DtHR0XI/RERUcDCZp7xOCIGTJ0+icePGaN26tbS8X79+uHfvHrZt2wZHR0c1RkiUNaW/F23Tpg0AoHnz5nLLhRDQ0tKSm0CEiIjyN5bZUF4lhICPjw+8vLxw8eJFAIClhbm0fvWqVZytlfIEpa++Z86cyY04iIgoD2LPPOU1spQUHDnyJ+bP98a58xcAAIaGhvjpp58w0W08gKfqDZBISUon8y4uLrkRBxER5UHsmae8IiUlBfv378eiBd64dHApOv6+ADZVv8OAgT9i/PjxqbNOy1KAcCbzlLfk+OobGxuLsLAwJCYmyi13dnb+4qCIiChvYM88abrk5GTs3r0bs2fPxt27d+Vmaw0ODoZNkaJqjI7oyymdzL958wYDBw6Uhmv6L9bMExEVHEzmSSMJgaSkBOzatQszvWbj4cOHAABLS0u4TRgnNbMpXFhdERKpjNKj2YwZMwaRkZG4dOkSjIyMcOzYMWzZsgUODg44fPhwbsRIREQaimU2pGkSEhKwYcM66L25hn4tvkH4i+coVKgQZs+ejSdPnuCXyb+oO0QilVL66nv69GkcOnQItWrVgra2NsqUKYOWLVvC3Nwcc+fORfv27XMjTiIi0kDsmSdNERcXh/Xr18Pb2xsR799hcLuTAIA5s2dj0JCfYGpqmtpQxgoCyl+UTuY/fvyIIkWKAACsrKzw5s0bfPPNN6hSpQoCAgJUHiAREWmutJ55JvP01f07W+vH2I9Ys3Y9FixYgFevXgEAypcrKzUbPXo0h5ikfE3pMpsKFSrg3r17AICqVati7dq1eP78OdasWYPixYurPEAiItJc7JkndYmOjgLCL8Ik6hameUzFq1evUKZMGaxevRpBQbfUHR7RV6N0z/zo0aMRHh4OAPD09ESbNm2wY8cO6OvrY/PmzaqOj4iINFhaMs+aefpaIiIisGzZMqxftwbPLu8DAJQta4+x4ybghx9+gJ6eHktpqEBR+urbt29f6feaNWviyZMnuHv3LkqXLo3CvCuciKhAYZkNfS1v377F4sWLsWLFCkRHR8sNMRkYGAhdPQM1RkekPl/clWJgYABtbW1eyImICiD2zFOuEgKvXr3EsmXLsHTZcnz8+BEAUKVKFXhO85Ca6erw9UcFV46Gpty4cSOA1It448aNUaNGDdja2uLs2bOqjo+IiDQYa+Yptzx//hxubuNRNOURZg/vACFLQY0aNfDHH3/g+vXr6Pr99+oOkUgjKJ3M79u3D1WrVgUA/Pnnn3j8+DHu3r2LsWPHYsqUKSoPkIiINBfLbEjVnjx5gmHDhqFs2bJYtWq1tHz//n24evUqOnfuDG1tpdMXonxL6XfD27dvUaxYMQDA0aNH0b17d3zzzTf48ccfcesW7x4nIipIWGZDKiEEHj0MwbCh/0P58uWxevVqJCYmomHDBlKTNq3bQEtLS41BEmkmpZP5okWLIjg4GCkpKTh27BhatmwJAIiNjWXPDBFRAcMyG/pSd+/exeDBg1DW8DVWTf0B+nq6aNGiBfz8/HD82HF1h0ek8ZRO5gcOHIgePXqgcuXK0NLSQosWLQAAly5dQsWKFVUeIBERaa60Mhv2zJOybt26hZ49e8LJyQm7du2Slp8+fQq+vr5o3LixGqMjyjuUvvpOnz4dlStXxtOnT9G9e3cYGKQOBaWjo4NJkyapPEAiItJc7Jknhf07Y+v169cxc9Zs/PHHH9Kqjh07Sr/XrVNXHdER5Vk56krp1q1bumX9+/f/4mCIiChv4Q2wpKgrVy6hdskUVCsKHD/mAy0tLXTv3h1TpkyBc+VKQPhFdYdIlCfxdnAiIsox3gBL2fnnn3/QqlUrNGnSVFrWq2dP3L59G3v27IGzs7MaoyPK+3j1JSKiHGOZDWVECIHTp0/Dy8sLfn5+AABzM1Np/caNGwFtvmaIVIE980RElGO8AZY+J2QynDjmg+bNmkgj0ujp6eHnn3/GzZs3st44JR6IDgaSYxU/YE62+ZLtiDQQk3kiIsox9swTkNoTf/jwYTRu3Aitqpjj9PY5sLayxMiRI/Ho0SOsWbMGZUqXyXwHybHAtQFA4E/AsZrySXZmiXdW22Qlp9vllszO72t/4OAHnDxL6a6Uly9f4tKlS3j58iUAoFixYqhbt640kRQRERUcvAG2YJPJZNi/fz9mzZqFmzdvwtjIMDUp/PgIt29cQTHb8vIb/LsONs6Avtmn5VFBQNyz1N9jQoDIIKBwnU+Jd9wzIGQB0O46oGuc9TY5PVZ222W3LiuZbZfZ+WV13l8So7JxfMm50VejcM/8x48f0bdvX5QqVQrdunXDtGnTMG3aNHTr1g2lSpXCDz/8gNhYfpojIipIeANsASQEUpISsWf3LlSpUgU9evTAzZs3YWZmhsluo6Ve72KB7eR7ebPqEbd0BkwdUn83cwAsK6f+nlHind02OT1Wdttl16Ofk28QMju/rM47pzHmJI4vOTf6ahRO5kePHo3Lly/jyJEjiI+Px6tXr/Dq1SvEx8fj6NGjuHz5MkaPHp2bsRIRkQYRQrDMpoBJSkrC9m1bofP6Cno2Ko3HoY9gYWEBT09PPH78GFNHdMo8KcwqYdQzSe0NbnUJaHv9U69wVol3Ztvk9FjZbZfTBDsnH0iyOu+cxpgbH4yy+xBAX4XCyfz+/fuxefNmtG7dWu6iraOjg1atWuG3337Dvn37ciVIIiLSPDKZTPqdPfP5W0JCAtatW4dvvvkGP//vf9JyT89pePLkCaZPnw5ra+usk8Ks1gGpSXXhOvLJdVaJd2bb5PRY2W2X0wQ7Jx9IsjrvnMaYGx+Msnue6atQ+Oork8mgr6+f6Xp9fX25CzsREeVvafXyAHvm851/Z2uNi4/Dxt82Y/78+Xj2LDWhsyttKzWb6DZRfojJtKQwMig1scsoMc9oXVbSEm9l5PRYOY0/LamNCck8Uc4slszOL7PlOY0xp3F8ybnRV6ElhBCKNHR1dcWdO3ewceNGVK9eXW5dYGAghgwZgooVK2L79u25EmhGoqOjYWFhgaioKJibm3+14xIRERAbG4sFCxYAADw8PKCtzQHS8ouPMdEwiboFADBxaIHYuHiUKFECEydOxJDBP8I48mZqw+Lfcrz4NMmx+Tepzc/npsEUzXMVvvKuWLECRYsWRc2aNVGoUCE4OjrC0dERhQoVQq1atVCkSBGsWLFCJcETEZHmS+uZ19LSYiKfT3z48AHz5s2Dk6OTtMzW1harVq3Cw4cPMXr0aBgbMZnLUGalO/lBfj63fEDhMhsrKyv4+Pjgzp07uHjxotzQlPXq1UPFihVzLUgiItI8HMkm/4iMjMSyZcuwZMkSREREpA4x+a+bN29A38BIjdERUVaUvgKn9cgTEVHBxpFs8jgh8PbtG6xcuRK/Ll6C6OhoAECFChXg6TFVaqavl/n9ckSkfkol84mJiTh48CAuXLgg1zNfv359dOrUKcsbZImIKH9JK7Nhz3ze8+rVKyxbugSzh3eA55BW8Pb2RuXKlTF16lR069YNOloAwi+qO0wiUoDCRY4PHjyAo6Mj+vfvj8DAQMhkMshkMgQGBqJfv36oVKkSHjx4kJuxEhGRBmHPfN7z/PlzjBkzBvb29liyZIm0fOfOHbhx4wZ69uzJvydRHqNwd8rQoUNRpUoVBAYGprujNjo6Gv369cPw4cNx/PhxlQdJRESaJ61nnsmfBvt3iMmnz55i7jxvbNy4EYmJiQAAl8aNpGadvusE8CZmojxJ4WT+3LlzuHz5coZD45ibm8PLywt169ZVaXBERKS5eAOs5nv06AHKGr6GrQ6wZfMmJCYmolGjRvDw8ECLZk2Bl5fUHSIRfSGFP4ZbWlri8ePHma5//PgxLC0tVRASERHlBSyz0Vz37t1Dv379UK3ap3lhmri44OzZs/j777/RsmVLaGlpqTFCIlIVhbtTBg8ejH79+sHDwwPNmzdH0aJFAaTeRHPq1CnMmjULI0eOzLVAiYhIs/AGWM0TFBSEWbNm4ffff4cQQm6IySNHjnCCJ6J8SOEr8MyZM2FiYoIFCxZg/Pjx0id6IQSKFSsGd3d3TJw4MdcCJSIizcKeeQ0hBG5cD8S8+fOwe89eafF3332HaR5TACSpLzYiynVK3e3i7u6OFy9e4MGDB/D394e/vz8ePnyIFy9eMJEnIipgeAOs+l26dAldu36PqkXisGvRaJgYG6Fbt264fv06Dh06hJo1aqo7RCLKZTn6brRs2bIoW7asqmMhIqI8hDfAqo+/vz+8vLxw4sSJf0tpJgAArly5AkenSuoNjoi+KqV65oODgzFs2DBUr14dxYsXR/HixVG9enUMGzYMwcHBuRUjERFpIJbZfEVCQKQk4+yZ02jatCkaNWqEEydOQEdHB3379pWaOVasqMYgiUgdFO5O8fHxQefOnVGjRg106tRJ7gZYX19f1KhRA4cOHULr1q1zLVgiItIcvAH26xBC4OSJ42hZ2QxNvjFA+0sXoaenh4EDB2LSpEmwL1Oas7USFWAKX4EnTZoEd3d3zJw5M9266dOnY/r06XBzc2MyT0RUQLBnPncJIfDnn3/Cy8sLwbeD8DHkJADg559/wthxE2Bra5vaUJaixiiJSN0ULrO5f/8+XF1dM13fu3dvhISEqCQoIiLSfLwBNhcIAVlyEv44sB/Vq1dHp06dcPXqVRgZGUlNfl3066dEnogKPIWTeTs7u9QxajNx5MgRlClTRiVBERGR5mPPvGqlpKRgz57d0H51GV3qFkPI/XswNTWFu7s770sjokwpNc58nz59cPbsWbRo0SLdpFHHjh3Dzp07cy1QIiLSLBzNRjWSkpKwY8cOzJkzB8+fPUXPf8tpJk2ahGHDR6BQoUKppTThD9UcKRFpIoWvwN27d0fJkiWxbNkyLFq0CC9fvgQAFCtWDPXq1cPZs2dRr169XAuUiIg0C8tsvkxiYiI2b96MefPmITQ0FABQqmRxab3H1KmcsZWIsqVUd0r9+vVRv3793IqFiIjyEPbM50x8XBy2bNmMRYsWIeRBam+7jY0NJkyYgKH/+xn4EKTmCIkoL1FqnPk0UVFRuHfvHu7du4eoqChVx0RERHkAa+aVExsbi8WLF6NSJSf83NEZ989uQVl7OyxevBiPHz/GxIkTYWZqqu4wiSiPUao7ZcOGDfj1119x7949AKnDZmlpaaFChQoYP348Bg0alCtBEhGR5mGZjWI+fPiAVatWYdGiRXjz5s2/M7amun07CIZGJmqMjojyOoWT+QULFmD69OkYNWoUWrduLXcD7IkTJzB69GhERERgwoQJuRYsERFpDpbZZEEIREZGYM2a1Viw8Fe8f/8eAFC2bFl4TP1FamZoYJjZHoiIFKLwFXjFihXYtGkTevToIbfc0dERTZo0QdWqVeHm5sZknoiogGCZTcbevXuHlSuWY9rglpjUrwm8vGbhm2++wZQpU9CnTx/oamtxxlYiUhmFa+Zfv36NKlWqZLq+SpUqePv2rUqCIiIizZdWZsOe+VSvX7+Gu7s77OzsMH/+fGn55s2bERwcjH79+vG5IiKVUziZr127NubNmyddvD+XkpKC+fPno3bt2ioNjoiINFeB75kXApClIPz5M4wdOxZ2dnbw9vZGTEwMnJ2dpWbdu3UruM8REeU6pcpsWrdujWLFiqFx48ZyNfN///039PX1ceLEiVwLlIiINEtBvwH22bMwlNJ+huIA1q1dg7i4eNSuXRseHh7o0K4t8PKSukMkogJA4Z55Z2dn3L9/H15eXjAzM8OjR4/w6NEjmJmZYdasWbh79y4qV66cm7ESEZEGKag3wD569Ag//fQTKlf+VHpar963OHbsGC5duoSOHTtCS0tLjRESUUGi1BXYzMwMQ4cOxdChQ3MrHiIiyiMKWpnN/fv3MWfOHGzfvh0pKSlyQ0z6nvCFlk7B+lBDRJohR5NGZSQpKQlhYWGq2h0REWm4AnEDrBAIvh2Egf37wdHREVu2bEFKSgpatWoFX19fqRl74olIXVSWzAcHB8Pe3l5VuyMiIg2X33vmr1+/DlfX3nCyjMKmOT/D0EAfHTt2xKVLl3D8+HHUr1dP3SESESlXZkNERJQmv94Ae+XKFXh5eeHPP/9MLaVZMBIAcOH8eThXq67m6IiI5CmczNeoUSPL9XFxcV8cDBER5R355gZYIQAhw8VLFzFj5iwcO3YMQGrpTPfu3aRmnw83SUSkKRS+AgcHB6NXr16ZltKEh4fj/v37KguMiIg0W34osxFC4J+//dC4vB6+LQ387XcWOjo66Nu3LyZPnowKDuU5WysRaTSFk/nKlSujbt26mY5kc/36daxfv15lgRERkeYSQkAmkwHImz3zQgj4+vrCy8sLAdeu4mPISQDAwIEDMW78BJQtWza1oSxFjVESEWVP4StwgwYNcO/evUzXm5mZoXHjxioJioiINNvns4HnpZ55IQSOHDkCLy8vXL58GQBgZWkhrV+xfDmgnXfOh4hI4WR+6dKlWa4vV64czpw588UBERGR5ksrsQHyRjIvS0nBn38ewvz53rhwMXVmViMjI/z888+YOGE8gCfqDZCIKIdUNjQlEREVHHmlZz4lJQW7d+/Gt3XroFPtoji/bxFsCltj4sSJePz4MRYvXozixYurO0wiohzLe4WORESkdp/f/KqJEyYlJydj586dmDNnDu7duyc3W+udO3dRqLCNGqMjIlIdJvNERKQ0jRzJRggkJsZj165dmOk1G48ePQIAWFlZYaLbeKlZIWtrdUVIRKRyLLMhIiKladqEUfHx8Vi3bi303wagf8sKeBn+AjY2Npg3bx6ePHmCSe6T1B0iEVGuYDJPRERK05QJo2JjY7F06VKUK1cOY8eOlZbPmzcPoaGhcHd3h5mZmRojJCLKXSyzISIipamtZ/7f2VpjPsZg9Zp1WLhwIV6/fg0AcChfTmo2csQIDjFJRAWCSnvmmzVrBi8vL8TGxqpyt0REpGHU1TMfFRUJhF+EaXQQpntOw+vXr2FnZ4e1a9fi1q2bXzUWIiJNoNJkvnTp0jh16hQqVqyoyt0SEZGG+do3wL5//x6enp5wdPz0/0v58uWwadMm3L9/Hz/99BMM9A2+SixERJpEpV0qmzdvBgBER0ercrdERKRhvlaZzevXr7F48WKsWLECMTExckNMBlwLgI6efq4en4hI06kkmY+MjISlpaX02NzcXBW7JSIiDZWrZTZC4GX4CyxZsgTLVqxEXFwcAKBq1arwnOYhNdOUkXSIiNRJ6TKb+fPnY8+ePdLjHj16oFChQihZsiRu3Lih0uCIiEgz5VbP/NOnTzFu3BgUE48xb3RnaEGgVq1aOHToEAIDA9Glc2eVHo+IKK9TOplfs2YNbG1tAQC+vr7w9fWFj48P2rZtCzc3N5UHSEREmkfVPfOhoaH4+eefUa5cOaxdu05afvCPP3D58mV89913GjnTLBGRuil9FX758qWUzP/111/o0aMHWrVqBTs7O9StW1flARIRkeZRyQ2wQuDBgxAsWLAAG3/bJO2zebMmUpOWLVsCTOKJiDKldM+8lZUVnj59CgA4duwYWrRoAQAQQkgXYiIiyt++tMwmODgYPw4cgPLGb7DWcwAM9PXQsmVL/P333/A56qPKUImI8jWlk/nvv/8effr0QcuWLfHu3Tu0bdsWABAYGIjy5curPEAiItI8OS2zuXHjBrp3747KlStjz++/S8vPnj2DEydOoFGjRiqNk4gov1O6zGbx4sWws7PD06dP4e3tDVNTUwBAeHg4hg0bpvIAiYhI8yjcM//vjK0BgQGYMXMWDh8+LK367ruO0u+1a9XOlTiJiPI7pZN5PT09TJgwId3ysWPHqiQgIiLSfIrWzF+8eB7flgZqFANO+p6AlpYWevTogSlTpqBKJScg/OLXCJeIKN/K0Qyw27ZtQ8OGDVGiRAk8efIEALBkyRIcOnRIpcEREZFmyq7Mxs/PD82bN0fz5i2kZb1790ZwcDB2796NKlWqfJU4iYjyO6WT+dWrV2PcuHFo27YtIiMjpQu6paUllixZour4iIhIA8mV2QgBJH6AeH0ep078icaNG6NJkyY4ffq0XLK/Yf16VKxYUV0hExHlS0on88uXL8f69esxZcoUua9Xa9WqhVu3bqk0OCIi0kyfl9mIxA/AESdonWyA0kGdcPXSP9DX18fQoUNx69bNbHYUD0QHA8mxXyFqIqL8R+lkPjQ0FNWrV0+33MDAAB8/flRJUEREpNnSkvl79+5hSM8GQNwzAIBDMYFZE3ri0aNHWLVqFUrbls48YU+OBa4NAAJ/Ao7V1NyEPqsPHHnhw0huxJgXzpuogFA6mbe3t8f169fTLT927BgcHR1VERMREWmwlJQUPHr0CACwefNmHDwbAhiVAgAkG9lj3IzfULJkydTGWSXsUUHShwDEhACRQV/xLP4jJx84vuTDiKqT4dz4wJTXP4QRFRBKJ/Pjxo3D8OHDsWfPHgghcPnyZcyePRuTJ0/GxIkTcyNGIiJSNyGQnJSAXTt3oHLlyrh4MXUUGl1dXfw8fDze1vsHaHkeuh1uAbrGn7bLKmG3dAZMHVJ/N3MALCt/Wvc1e5Nz+oEjpx9GskuGM4tT1fHnNEZN+hBGRMon84MHD8b8+fMxdepUxMbGok+fPli9ejWWLl2KXr165UaMRESkRomJidiyZRN0X19Fbxc7hD15DENDQwDA3LlzMXv2bBQuZgfY1AP0TOQ3ziph1zMB2l0HWl0C2l7/9CEgp8luVutympxmFX9W67KKJavjZRZnbsSf0xiz2ycRfVVaQgiR041jY2MRExODIkWKqDImhUVHR8PCwgJRUVEwNzdXSwxERPlVQkICfvvtN8ybNw9v37zGx5CTAIBFu87BupANwsLC0LlzZ1StWjXrHSXHpiaDlpXle+0z8+YC4Fv/0+NWl4DCdVJ///dmW8Q9S00o213/tM+s1mW1z6SPgE/11KTVzEH+g0V28We2LqtYsjpeZnHmRvw5jTG754SIVELRPDdH48ynMTY2VlsiT0REKiYEIEtBXGwMli1bhnLlymHYsGEICwtD0aJFpWbjx42HlpYWgMzHmZeja5yaeCqa9GXV85vTspecfEOgSPyZrcsqlqyOl1mcuRF/TmPM7jkhoq9K6Rlg7e3tpYt4RtJuiiIiorwlJiYaptFBMAIweZI7YuPiUapUKbi7u2PQjwOAiBtSW7lx5lUtLZHMqOc3LalN6zHOqOwlo3VZ7RP4lJyqSlaxZHW8zOLMjfhzGiMRaRSlk/kxY8bIPU5KSkJgYCCOHTsGNzc3VcVFRERfSVRUFFauXIk1q1ci7OLvAIAyZcpg9JixGDBgAAwMDABZitw22c0A+8WUTXazW5fVPnNDdrFkJbM4VR3/l8RIRBpD6avw6NGjM1y+cuVKXL169YsDIiKiryMiIgJLly7F0qVLERkZCWMjQ2ndjRvXoadvmOm2n08a9dVlldRqUm+yJsWSmbwQIxFl6Ytq5j/Xtm1b7N+/X1W7IyKi3CAE3r55Dc9pHihTpgxmzJiByMhIODo6YuPGjVIzPV29LHeTq2U2RESkMJUl8/v27YO1tbWqdkdERCr28uVL/DJ5EgonhmDGz22QkpwEZ2dn/P777wgKCkKvnj0V3leul9kQEZFClL4KV69eXe4GWCEEXr58iTdv3mDVqlUqDY6IiL7cs2fP4O3tjfXr10NbC5gz8jsAwJ49u9GufUdoa//br/OfuvissGeeiEgzKJ3Md+7cWe6xtrY2bGxs0KRJE1SsWFFVcRERUU4JAQgZnoQ9wdx53ti0aRMSExMBAE2bNJaadWjfAdDO2Re07JknItIMSl+FPT09cyMOIiJSkYcPH6Cc0WuU0QO2bd2CxMREuLi4wMPDA82auAAvL33xMdR6AywREUkUSuajo6MV3iFnYiUiUo87d+5g9uzZOHTwD3y4dwIA0KxpU7i5T0Ljxv/2yCtRSpMZIQTLbIiINIRCybylpWWWE0UBqRd3LS0tqbeGiIi+jps3b2LWrFnYt28fhBByQ0z++eefgLZqE26ZTCb9zjIbIiL1UugqfObMmdyOg4iIlCEEAgOvYd68+fh97z5pcefOnTHNYwqAhFw7dMpnvfvsmSciUi+FknkXF5fcjoOIiBR04cIFeM+fhz9WTsSexWNw5MgRtO/QEVOmTIGzs3NqKU34xVw7/uffwLJnnohIvXJ8FY6NjUVYWJg0QkIaZ2fnLw6KiIjS8/Pzg5eXF06dOvVvKc1EAMDVq1dR0dHpq8WRnJyazGtpaX0a1pKIiNRC6WT+zZs3GDhwIHx8fDJcz5p5IiIVEQJCloLTZ85gxkwv/PPPPwBSe8P79esnNatYocJXDYsj2RARaQ6lu1TGjBmDyMhIXLp0CUZGRjh27Bi2bNkCBwcHHD58ODdiJCIqcIQQOH7cB1ovL6G5ozGuXb0CfX19/O9//0NISAhWq3GSPo5kQ0SkOZTumT99+jQOHTqEWrVqQVtbG2XKlEHLli1hbm6OuXPnon379rkRJxFRgSCTyXD48GHMmjULd4Jv42PISQDAsGFDMXrMOJQqVerfhur7FpQTRhERaQ6le+Y/fvyIIkWKAACsrKzw5s0bAECVKlUQEBCg2uiIiAoCIZCSlIj9+/aiWrVq6NKlC65duwZjY2OpyQLvBZ8SeTWTscyGiEhjKJ3MV6hQAffu3QMAVK1aFWvXrsXz58+xZs0aFC9eXOUBEhHlZ8nJydi1ayd0Xl9B13ol8PBBCMzMzPDLL7/gzp076g4vQ8kpqWU27JknIlI/pa/Eo0ePRnh4OADA09MTbdq0wY4dO6Cvr4/NmzerOj4ionwpKSkJ27Ztw9y5c/Hi+TP0/recZsqUXzB02AhYWVn9O8RkiJojTY83wBIRaQ6lk/m+fftKv9esWRNPnjzB3bt3Ubp0aRQuXFilwRER5TcJCQnYtGkT5s2bhydPngAAbEuVkNb/MvkXlc/YqmppQ1MymSciUj+ly2z8/f3lHhsbG6NGjRpM5ImIshAXG4tVK1egciUnDB06FE+ePEHRokWxYMECBAcHqzs8pfAGWCIizaF0Mt+sWTPY29vjl19+yXP/ARERfW0xMTFYuHAhKjk5Yljn6gjx24ry5cpi6dKlCA0NxYQJE2BqYqruMJXCMhsiIs2hdLfKixcvsHv3buzatQvz5s2Ds7MzXF1d0bt3b40ZaYGISN2io6OxYsUK/Prrr3j37t2/M7amCgq6BQND4yy21mwpybwBlohIUyjdM1+4cGGMGDEC586dw8OHD9G9e3ds2bIFdnZ2aNasWW7ESESUNwiBiPfvMGe2F8qUKYMpU6bg3bt3KFeuHFav/jTJk4G+gRqD/HLsmSci0hxKJ/Ofs7e3x6RJkzBv3jxUqVIFfn5+qoqLiChPefv2LaZP94RV3F38MqAZEhPiUbFiRWzbtg13795Fvx/6qTtElUkbmpLJPBGR+uU4mT937hyGDRuG4sWLo0+fPqhcuTKOHDmiytiIiDTey5cv4ebmBjs7OyxYsEBavnXrVgQFBaFv3775rhyFN8ASEWkOpa/EkydPxu7du/HixQu0bNkSS5cuRadOneRmKiQiyreEAIQML8JfYL73Qqxbtw7x8fEAgPr1vpWadf3+e40fYjKnODQlEZHmUDqZ//vvv+Hm5oYePXpwOEoiKnDCwh6jtO4LlACwYX1qIv/tt9/Cw8MDbVu3Al5eUneIuY4180REmkPpZP7cuXO5EQcRkUZ78OAB5s6di317f0fUnWMAgIYNG8Bt4iQ0b94cWlpaqTO2FgBM5omINAcLHomIsnD37l3Mnj0bO3fuhEwmkxti8vix4/m2lCYrHJqSiEhzfNFoNkRE+ZIQuB10C/379YWTkxO2b98OmUyGtm3b4vTpU+qOTu1SZOyZJyLSFEzmiYg+ExAQgN69e6KSVTS2zB0KI0MDdOrUCVeuXMHRo0dRt05ddYeodsnsmSci0hi8EhMRAbh06RK8vLxw5MiR1FKaRaMBABcvXkQV56pqjk6zyGQyAOyZJyLSBEzmiahg+neIyXPnz2PGTC/4+voCALS1tdGrZ0+pWZXKldUVocbi0JRERJpDoWTeysoqdaQGBbx///6LAiIiym1CCJw9cxpNKxiigb02zvn/A11dXfzwww+YPHkyHMqVBcIvqjtMjcVJo4iINIdCV+IlS5ZIv7979w6zZs1C69atUa9ePQDAhQsXcPz4cXh4eORKkEREqiCEwLFjx+Dl5YUb1wPxMeQkAGDQoEEYN34C7OzsUhsWkCEmcyqtZp4980RE6qdQMt+/f3/p965du2LmzJkYMWKEtGzUqFFYsWIFTp48ibFjx6o+SiKinPi3lEYIgcN/HcGsWbNw9epVAIC1laXUbNnSpQVyiMmckrFnnohIYyg9ms3x48fRpk2bdMvbtGmDkydPqiQoIiJVkKUkA+EXofXyEvr07oWrV6/C2NgY48ePR/Dt2+oOL8/i0JRERJpD6WS+UKFCOHToULrlhw4dQqFChVQSFBHRl0hJScHOnTtRp24daZmpqQkmT56Mx48fY+HChShatKgaI8zbWGZDRKQ5lP6OdMaMGRg8eDDOnj2LunVTx1u+dOkSjh07hvXr16s8QCIiRSUlJWHHjh2YM2cOQkJC5GZrvXPnLqwLFVZjdPkHb4AlItIcSl+JBwwYAEdHRyxbtgwHDhwAADg6OsLf319K7omIvhohkJgYj+3bt8Nr1hw8fvwYAGBtbQ33iROkZtZWVmoKMP/h0JRERJojR90qdevWxY4dO1QdCxGRUuLj47F502/433dV8WMbJ4wc+RJFihTBhAkTMHToUJgaG3GIyVzAnnkiIs2hdM08ADx8+BBTp05Fnz598Pr1awCAj48PbvOGMiL6Cj5+/Ihff/0V9vb2GD9+vLTc29sboaGhcHNzg6mpqRojzN/Sknn2zBMRqZ/Sybyfnx+qVKmCS5cuYf/+/YiJiQEA3LhxA56enioPkIgIQgCyFERHRWLevHmws7PD+PHj8fLlS5QqVUpqNnzYMBgbG6sx0IIh5d8bYNkzT0Skfkon85MmTcKsWbPg6+sLfX19aXmzZs1w8SK/ziYi1YuMjADCL8I85ja8Zs7A27dvUbZsWaxfvx63bt1Ud3gFDoemJCLSHEon87du3UKXLl3SLS9SpAjevn2rkqCIiADg7du3mDp1KhwdK0rLvvnGAVu2bMG9e/cwePBg6OvpZ7EHyg0cmpKISHMo/R2ppaUlwsPDYW9vL7c8MDAQJUuWVFlgRFRwvXr1CosWLcKqVavw8eNHuSEmr165Ch0m8Golk8kAsMyGiEgTKN0z36tXL7i7u+Ply5fQ0tKCTCbDuXPnMGHCBPTr1y83YiSiAuL582eY6DYelZwcsWDBAnz8+BHVqlXDzp2fRs9ib7Dm4N+CiEj9lE7m58yZg4oVK8LW1hYxMTFwcnJC48aNUb9+fUydOjU3YiSifO7JkycYNmwYKleqBO8x3+PtzT/RuFFD/PnnnwgICECn7zqpO0TKAHvmiYjUT+krsb6+PtavXw8PDw8EBQUhJiYG1atXh4ODQ27ER0T52MOHDzF37lxs2bIFycnJcuU0Z8+cgZbOv5cooaYAKUvsmSciUr8cd6uULl0apUuXVmUsRFQQCIH79+/B29sbm7dslcYsb9asGTyneUjNtLS01BUhKUBbW5t/IyIiDaBQMj9u3DiFd/jrr7/mOBgiyt+CgoKwwHsetswdig0zB2HXrl1o7NISHh4eqF+/PiBL4YyteQR75YmININCyXxgYKDc44CAACQnJ6NChQoAgPv370NHRwc1a9ZUfYRElOcFBgZi1qxZOHDgAIyNDLFl7lAAwN9/+6FmrTpqjo5ygvXyRESaQaGr8ZkzZ6Tff/31V5iZmWHLli2wsrICAERERGDgwIFo1KhR7kRJRHmLEICQ4eq1q5gxcxb++usvAKmlM99//2meipo12AGQV7FnnohIMyg9ms2iRYswd+5cKZEHACsrK8yaNQuLFi1SaXBElDedP38OCL+IWiWScfrUSWhra6NPnz4ICgrCtq3b1B0eqQCTeSIizaB0Mh8dHY03b96kW/7mzRt8+PBBJUERUd4jhMDp06fRtGlTtGzZUlret29f3L17Fzt27ICTk5MaIyRVYpkNEZFmUPpq3KVLFwwcOBCLFi1CnTqpta6XLl2Cm5sbvv/+e5UHSESaTQiB48ePw8vLC+fPnwcAWJibSevXrlkDaLMXN79hzzwRkWZQOplfs2YNJkyYgD59+iApKSl1J7q6GDRoEBYsWKDyAIlIMwmZDEeP/oX5873xj/85AICBgQGGDBkC94kTADxTb4CUq9gzT0SkGZQuszE2NsaqVavw7t07BAYGIjAwEO/fv8eqVatgYmKSGzESkQaRyWTYt28f6tX7Fu2rF8Lfu+ejcCFrjBs3DqGhoVi+fDlKlSyl7jALhpR4IDoYSI796odmzzwRkWbIcdeKiYkJnJ2dVRkLEWmwlJQU/P7775g9ezZu374tN1trcHAwbIoUVWN0uSAlHvj4CLBxBvTNsm//tSXHAtcGAHHPgJAFQLvrgK7xVzs8k3kiIs2gdM/8x48fpQleypcvj7Jly8r9EFE+IgSSEuOxfesWODo6ok+fPrh9+zYsLCwwefJkqZlN4cLpt82q1zgnPco53V9OjpWWKAf+BByrqZlxRgWlJvIAEBMCRAYpHmNO/RujrlYiy2yIiDSE0lfjwYMHw8/PDz/88AOKFy/O6byJ8qnExETs2L4VA1vYo2/tRIx5HQZra2uMHTsWI0eOhIWZaeaztWbVa5yTHuWc7i+nvdcZJcqFFZjcKjfizOwbAktnwNQhNT4zB8CycvbxKSKz430W46CShXBam0MRExFpAqWTeR8fHxw5cgQNGjTIjXiISM3i4+OxceNGzJs3D3Ef3mDgJhsg7hlClhWGbscgmFn9W04jS8k88csqGc4uUc5onzndX06OBWSfKKv6vDNbl1WSr2eS+jgyKDU+ZUpsFEjY0x3vsxgL6b2Dtc4LxY9HRES5RukyGysrK1hbW+dGLESkDkIAshTEfvyAxYsXo2zZshgxYgSePXuGRlWspQTOSvctzFKefNouq1KUtGQYSJ8MZ7Uus33mdH85ORbwKVFudQloe10+Uc6N885sXXalNLrGqUl/Rol8ZmU7WcWf1fE+i/FdojU+6tqnPyYREX11WkIIocwG27dvx6FDh7BlyxYYG3+9m60yEh0dDQsLC0RFRcHc3FytsRDlVR+io2D2ITVpM3Fogdi4eNja2mLSpEn48YeeMDxT71MP9eeJ7ZsLgG/9TztqdUm+1zs5NvNe48zWZbXPnOwvp8fKSm6cd2brkj4CPtUzfv6zkvgBOOKUmpibOsj3sGcVf3bHS45F4NltOHo+DFWq1cV3332XfSxERJQjiua5SpfZLFq0CA8fPkTRokVhZ2cHPT09ufUBAQHKR0tEX11kZCSWL1+OdWtX4+mlvQAAOzs7jBk7Dv3794e+vn5qw8xKObIrRUnrNc5IZuuy2mdO9pfTY2UlN847s3U5LaXJqqQnq/izO56uMSJ1vkGyeMnRbIiINITSyXznzp1zIQwi+lrevXuHJUuWYNmyZYiOjpYbYvL69UDo6RvKb5BZAvolNduZyY19qvpYXzNGIOsPAJn5woQ9q+MlJyenNuNoNkREGkHpq7Gnp2duxEFEuUkIvH79CsuWLcPSZcsRExMDAHBycoLnNA+pmZ6uXmZ7yFhOEk117FPVx/qaMebEFybsWUlJSQHAceaJiDSF0jfAElHe8uLFC7i7u6FI8kPMGtYespRkVKtWDfv27cOtW7fQo3t3dYdIuSGrm2O/QFoyz555IiLNoHQyr62tDR0dnUx/iEgzhIWFYfjw4ShbtixWrFgpLd+793cEBASga9eu0Nbm53lSTlqZDa/3RESaQemulT/++EPucVJSEgIDA7FlyxbMmDFDZYERkZKEAIQMoY9DMWfufGzZsgVJSUkAgObNmkjN2rVtB3CyN8ohltkQEWkWpZP5Tp06pVvWrVs3VKpUCXv27MGgQYNUEhgRKSck5D4cTN7C3gDYuWM7kpKS0LRpU3h4eKBJ40bAy0vqDpHyAZbZEBFpFpV9x/7tt9/i1KlTqtodESno9u3b6NOnD2rUqCEta968Ofz9/XH69Gk0bdoUWuyJJxVhmQ0RkWZRSddKXFwcli1bhpIlS6pid0SkgOvXr2PWrFnYv38/AMgNMXn40CFAm8kWqR575omINIvSV2MrKyu5Xj4hBD58+ABjY2Ns375dpcER0X8IgWvXrmDevPnYt/+AtLhr166YNnUKgFj1xUYFAmvmiYg0i9LJ/JIlS+Qea2trw8bGBnXr1oWVlZWq4iKi/zh37hy858/DodWTsHfpOJj6+KDjd50wZcoUVK5cGZClAOEX1R0m5XMssyEi0ixKJ/P9+/fPjTiIKANCCJw9exZeXl44c+bMv6U0kwAAAQEB+KZCRfUGSAUOy2yIiDRLjq7GkZGR2LhxI+7cuQMAqFSpEn788UdYWFioNDiiAkkICFkKTp06hekzvXDu3DkAgJ6eHgYMGCA1+8bBQU0BUkHGnnkiIs2i9Gg2V69eRbly5bB48WK8f/8e79+/x6+//opy5cohICAgN2IkKjCEEPDxOQKtl5fQopIpAgOuQV9fH8OGDcODBw+wcsUKdYdIBRx75omINIvSyfzYsWPx3Xff4fHjxzhw4AAOHDiA0NBQdOjQAWPGjMmFEInyP5lMhv3796NGjRro1q27tHzEiOEIDQ3FypUrUbp0aTVGSJSKN8ASEWkWpbtWrl69ivXr18v1yujq6mLixImoVauWSoMjyteEQEpyEg788QdmzPTC7du3AQA2ha2lJvPnzecQk6RRWGZDRKRZlO6ZNzc3R1hYWLrlT58+hZmZmUqCIsrvkpOTsXPHdui8voLuDUoh9NFDmJubY+rUqbhz5666wyPKFMtsiIg0i9LJfM+ePTFo0CDs2bMHT58+xdOnT7F7924MHjwYvXv3zo0YifKNxMREbNiwARUqVMCQn36Slnt4TMWTJ0/g5eWFQtbWWeyBSL3YM09EpFmU7lpZuHAhtLS00K9fP+mirqenh6FDh2LevHkqD5AoP4iPj8dvv/2G+fPnS99slbEtJa2f5D6J5TSUJ7BnnohIsyh1NU5JScHFixcxffp0zJ07Fw8fPgQAlCtXDsbGxrkSIFFeFvvxI377bSOWLFmCh49CAQDFihXDxIkT8dOQQUDULTVHSKQ4mUwGIQQA9swTEWkKpcpsdHR00KpVK0RGRsLY2BhVqlRBlSpVmMgT/UdMTAy8vb1RyckRI76viQd/b4ND+XJYvnw5Hj16hLFjx8LE2ETdYRIpJa1XHmAyT0SkKZT+nrRy5cp49OgR7O3tcyMeojwtKioKy5cvl+ZhSJ2xNdWtWzdhYMgPvpR3pZVWAiyzISLSFErfADtr1ixMmDABf/31F8LDwxEdHS33Q1TgCIH3795iltdMlClTBh4eHnj//j0cHBywds0aqZmBvoEagyT6cp/3zGtrK/3fBxER5QKlr8bt2rXDjRs38N1336FUqVKwsrKClZUVLC0tYWVllRsxEmmsN2/eYNo0D1jH38PUH5sjKTEBTk5O2LFjB+7cuYO+ffuqO0Qilfl8JBstLS01R0NEREAOymzOnDmTG3EQ5Snh4eFYuHAh1qxZAwgZZv6vLQBg+/bt6NS5y6deS1lKFnshyls4+ysRkeZROpl3cXHJjTiINJsQgJDh2fNnmDd/ATZs2ICEhAQAQKOGDaRmXTp3Blh+QPkUh6UkItI8zDqIFPD48SMg/CJKaT/Dpt82IiEhAfXr18exY8fgd/asusMj+io4YRQRkeZhMk+Uhfv372PAgAFwdq4qLWvcuBFOnToFf39/tG7dmrXDVGCwZ56ISPPwikyUgdu3b2P27NnYs2cPZDKZ3BCTPkd9OFsrFUjsmSci0jwK9cwfPnwYSUlJuR0LkXoJgVs3rqOva29UqVIFu3btgkwmQ4cOHXD2LG/8JmLPPBGR5lEome/SpQsiIyMBpPbIvH79OjdjIvrqrl69ih49uqNK4Y/Y7j0CRoYG+P777xEQEIA///wTtWvVVneIRGrH0WyIiDSPQsm8jY0NLl68CAAQQrBGmPKN8+fPo23btqhduzaOHDkiLb906RL279+P6tWrqzE6Is3CMhsiIs2j0Hel//vf/9CpUydoaWlBS0sLxYoVy7Tt5zMEEmkcISBkKfjH3x8zZnrh9OnTAFKTk969e0vNKleqpK4IiTQWy2yIiDSPQlfk6dOno1evXnjw4AG+++47bNq0CZaWlrkcGpFqCSFw+qQvmjuZoHF5PVy8cB66urro378/Jk+ejHL2dkD4RXWHSaSx2DNPRKR5FO5eqVixIipWrAhPT090794dxsbGuRkXkcoIIXDkyBHMmjULt27ewMeQkwCAIUMGY+y4CShTpkxqQ87WSpQl9swTEWkepa/Inp6eAIA3b97g3r17AIAKFSrAxsZGtZER5dS/s7XKZDIcPPwnZs2ahcDAQACAtZWl1GzJ4iUcYpJICbwBlohI8yg9aVRsbCx+/PFHlChRAo0bN0bjxo1RokQJDBo0CLGxsbkRI5FSUpKTgPCL0H51GT/0dUVgYCBMTEzg5uaG4OBgdYdHlGexzIaISPMoncyPHTsWfn5+OHz4MCIjIxEZGYlDhw7Bz88P48ePz40YiRSSnJyMbdu2oVbtWtIyc3MzTJkyBY8fP4a3tzeKFimixgiJ8jb2zBMRaR6ly2z279+Pffv2oUmTJtKydu3awcjICD169MDq1atVGR9RthITE7Ft2zbMnTsXDx8+lJutNTj4DqysC6kxOqL8I61nnjXzRESaQ+krcmxsLIoWLZpueZEiRVhmQ1+PEEhIiMPWrVsxa/ZchIWFAQAKFy4M94kTpGZWHHWJSGXYM09EpHmULrOpV68ePD09ER8fLy2Li4vDjBkzUK9ePZUGR5SR2NhYrFy5AgbvAjGkfRW8ffMaRYsWxcKFC/H48WNMGD8h+50QkdKYzBMRaR6le+aXLl2K1q1bo1SpUqhatSoA4MaNGzA0NMTx48dVHiBRmpiYGKxevRoLFy5EzIdoDO+SOsTkwoULMWDgjzAyMkptyCEmiXIFy2yIiDSP0lfkypUrIyQkBDt27MDdu3cBAL1794arq+unZIpIFf4dYjIqOhorVq7C4sWL8e7dOwBAxQrfSM2G/u9/HGKS6CtgzzwRkebJUfeKsbExhgwZoupYiORERLyHVdxdWACYM3sWYuPiUb58efzyyy/o69obeHNN3SESFSicNIqISPMoXTNPlNvevHmDX375BY6OFaVlFStWwPbt23Hnzh0MHDgQerp6aoyQqGDiOPNERJqH3SukMV6+fImFCxdi9erViI2NlRti8vKly9DR01djdETEMhsiIs3DZJ7U7tmzp1iy+Fds2rQZ7yMiAQA1a9bEdE8PqQ2TByL1Y5kNEZHmYZkNqc3jx4/xv//9D1UqV8bCcd3w7tZfaNqkMY4ePYorV66gQ/sO6g6RiD7DMhsiIs2To+6VyMhI7Nu3Dw8fPoSbmxusra0REBCAokWLomTJkqqOkfKZBw8eYM6cOdi2bRuSk5PlymlOnTwFLZ1/X5ZCTQESUYbYM09EpHmUviLfvHkTLVq0gIWFBR4/fowhQ4bA2toaBw4cQFhYGLZu3ZobcVJeJwTu3r2DBd7e2Lx1G2QyGQCgRYsW8Jz2qZxGS0tLXRESUTbYM09EpHmULrMZN24cBgwYgJCQEBgafupRbdeuHf7++2+VBkf5w61bt9CvX19UNI/AxllDYGigj3bt2uHChQvw9fVFwwYN1B0iESmAN8ASEWkepZP5K1eu4Oeff063vGTJknj58qVKgqL84dq1a+jSpQucnZ2xf/8Babm//z84cuQIvv32WzVGR0TKYpkNEZHmUfqKbGBggOjo6HTL79+/DxsbG5UERXnUvzO2Xr5yGTNmzsLRo0cBpJbOdO36vdSserXq6oqQiL4Ay2yIiDSP0j3z3333HWbOnImkpCQAqYlaWFgY3N3d0bVrV5UHSHmHv/8/QPhF1Cklw9kzp6GtrY2+ffvi9u3b2LqF91IQ5XXsmSci0jxKJ/OLFi1CTEwMihQpgri4OLi4uKB8+fIwMzPD7NmzcyNG0mBCCJw8eRIuLi5o3bq1tLxfv364d+8etm3bBkdHRzVGSESqwp55IiLNo3T3ioWFBXx9feHv74+bN28iJiYGNWrUQIsWLXIjPtJQQggcPXoUs2bNwsWLFwEAlhbm0vrVq1YB2vwPnyg/4Q2wRESaJ8fflTZs2BANGzZUZSyUB8j+396dh9d45/8ff50sSJAFiQSpNVSb+KmliKWoEaXCdEGktFMd5aqlRlpaMkns1JKoDh2qOm0IZXRcpVoMLUJ9W7taIoSGqDJIIkgk9+8PddqI7UTOOTnyfFzXuS7nc3/u+37d55PEO598zn3y8vTll6s0deo0JW27UcSXK1dOAwcO1NtvjZT0s30DArAKwzBYZgMAJZDFP5Fnz55923aTyaRy5cqpXr16ateuHTM3D5m8vDytWLFCM96bpu+/iFfY59Pl2zhML7/yqkaOHCk/Pz8pP09Kp5gHHkY3PxtCYmYeAEoSi4v5WbNm6ddff1V2dra8vb0lSRcuXJC7u7sqVKigs2fPqk6dOtq4caMCAgLueqyYmBjFxsYWaGvQoIEOHTpkaSxYyfXr15WYmKiJEyfq0KFDBT6t9aefDqqKj68d0wGwlZvr5SVm5gGgJLH4DbCTJk1S8+bNlZycrPPnz+v8+fM6cuSIWrRoofj4eJ08eVJ+fn4aMWLEfR3v8ccfV3p6uvmxZcsWiy8CxcwwlJtzVZ/+a5EaNmyofv366dChQ/Ly8tKYMe+au1WpXNmOIQHY0s0lNhIz8wBQklhczI8dO1azZs1S3bp1zW316tXT9OnT9c4776hGjRqaNm2atm7del/Hc3FxkZ+fn/lRpUoVSyPZhWEYD+Xj6tWrWrDgn3I9s1X9mufqwq8/q3LlypowYYJSU1P1zuh3pLyrUsZPMnIvF9q/uLfZ8lwlaVtJycGDx83HzZl5k8kkJyeL/+sAAFiJyTAMw5Id3N3d9d1336lZs2YF2v/v//5PTz31lLKzs5WamqqgoCBlZWXd9VgxMTF677335OnpqXLlyqlVq1aaPHmyHnnkkdv2v3btmq5du2Z+npGRoYCAAF26dEkeHh633cdazpw5ow8//NCm57QVN9frervhIulKms7nVta8E6/rulHG5ttKSo7SfN3ArVxcXDRmzBh7xwCAh15GRoY8PT3vWedaPL3SoUMHvf7669q1a5e5bdeuXRo8eLA6duwoSdq3b59q1659z2O1aNFCixYt0tq1azV37lwdP35cbdu2VWZm5m37T548WZ6enubHvdbk4+5cXZzk6lL4S8DH9ax0JU2SVNn1vHzLnLXLtpKSozRfN3Cr+/nZDgCwHYtn5s+cOaN+/fppw4YNcnV1lXTjjVFPP/20Pv30U1WtWlUbN25Ubm6uOnfubFGYixcvqmbNmpo5c6YGDBhQaHtJmpnPz8/XlStXbHrO4pSVcUlV849Lknz+X5iyr1xVjRo1NHz4cIW/GCbPpPZyupyi/PJ1daX9NsnF/caOuZfl9m2IbbbZ8lwlaVtJyQHchru7u0wmk71jAMBD735n5i0u5m86dOiQjhw5IunGHWgaNGhQtKS3aN68uTp16qTJkyffs+/9XiR+d+HCBc2ePVvz/zlPaTuWS5KCQ/+qEX+LVL9+/cy/oOl6tnRxv+QVVLiws+W2kpKjNF83AACwOasX89aQlZWlRx55RDExMRo2bNg9+1PM379z585p1qxZmjNnjjIyMuTuVk6Xk9dLkq77NpOLa1k7JwQAAMBN91vnFulmwWlpaVq1apVOnjypnJycAttmzpx538eJjIxU9+7dVbNmTZ0+fVrR0dFydnZWeHh4UWLhVoahX86kK372bM1+f44uX74sSQoODlb036PM3VycuWc0AACAI7K4ituwYYPCwsJUp04dHTp0SEFBQUpNTZVhGGrSpIlFx0pLS1N4eLjOnz8vHx8ftWnTRtu3b5ePj4+lsXCLU6dOKW7WDL034nlNGtJd8fHxatKkiaKiohQWFiYnGVL6dnvHBAAAwAOweJnNk08+qWeeeUaxsbGqWLGi9uzZI19fX0VERKhLly4aPHiwtbIWwjKbwk6cOKEpU6Zo4cKFcnF2Mi+l+XrfJXUOfeb3N67l5/1ezPu3lJz4EBgAAICSwmq3pjx48KD69+8v6cb9hq9cuaIKFSpo3Lhxmjp1atETo2gMQ8rPU8rRZA0YMED16tXTvHnzlJOTozZtWpu7hXYO5Q4UAAAADxmLi/ny5cub18n7+/srJSXFvO3cuXPFlwz35fDhQ1L6dtV1O6vEJYvNtwndtGmTvl77tb3jAQAAwIosLuZbtmypLVu2SJK6du2qkSNHauLEiXr11VfVsmXLYg+I29u3b5969+6tpk2bmts6d+6spKQkrV+/Xk899ZQd0wEAAMAWLH4D7MyZM5WVlSVJio2NVVZWlpYuXarAwECL7mQDCxiGZORLknbu3q0JEyZq5cqVkiR3t3Lmbiv//W/WvgMAAJQiFhXzeXl5SktLU6NGjSTdWHIzb948qwTDHxj55jertm3TSdlXrspkMumFF15Q1NgxkrLsmw8AAAB2YdEyG2dnZ3Xu3FkXLlywVh7cYvPmzQoLCzM/d3JyUkREhPbv369ly5YpOCjIjukAAABgTxYvswkKCtKxY8dUu3Zta+SBJMMw9N///lfjx4/Xt99++9tSmnclSbt27VK9wPr2DQgAAIASweI3wE6YMEGRkZH68ssvlZ6eroyMjAIPFJ2Rn69v1n6lpzu2V6dOnfTtt9/K1dVVAwYMMPepV7euHRMCAACgJLG4mO/atav27NmjsLAw1ahRQ97e3vL29paXl5e8vb2tkfGhZxiG/vOf/6hdu7bqHOyh/342Sd5enhoyZIhSUlI0Oz7e3hEBAABQAlm8zGbjxo3WyFEq5efna8WKFZowYYL27t1b4M40Px04IL9q1X/rmGenhAAAACjJLC7muX/5AzIMXb+eo+XLV2jc+Ak6ePCgJKlChQoa8eZwczc/Pz97JQQAAICDsHiZjXTjDisvvfSSQkJCdOrUKUnSp59+av4wKdxebm6uPv30E7mc/UF92tXUidTj8vT01N///nedOHFC42Jj7R0RAAAADsTiYn7FihUKDQ2Vm5ubdu7cqWvXrkmSLl26pEmTJhV7wIfBtWvX9OGHH6p+/foaNGiwuT06+kYRHxsbq0qVKtkxIQAAABxRke5mM2/ePM2fP1+urq7m9tatW2vnzp3FGs7RXblyRXPmzFG9evU0aNAgpaamytfHx7z97bfelqenpx0TAgAAwJFZXMwfPnxY7dq1K9Tu6empixcvFkcmh3c5K0uz4+P0+GMNNXToUKWlpalatWqKi4vTgZ8O2DseAAAAHhIWF/N+fn46evRoofYtW7aoTp06xRLKUWVmZmrKlCl6rOGjGvZCcx3bkqAG9QP1j3/8QykpKRo+fLjc3dztHRMAAAAPCYvvZvPXv/5Vw4cP18KFC2UymXT69Glt27ZNkZGRioqKskbGEu/ixYuaPXu24uLidOHChQK3mNy7d4/KlHWzYzoAAAA8rCwu5kePHq38/Hw9/fTTys7OVrt27VS2bFlFRkZq6NCh1shYMhmGzp8/pzlz5mjmrDjzp982aNBA0VFjzd3KuJaxV0IAAAA85CxeZmMymTRmzBj973//0/79+7V9+3b9+uuvGj9+vDXylVjffL1Wla8dUfRfO+t6bo6CgoKUmJioAwcOKDw83N7xAAAAUApYPDP/2Wef6bnnnpO7u7see+wxa2RyCI2feEK6niJJWrw4Qd3DesrJ6bffjfjEVgAAANiAxTPzI0aMkK+vr/r27as1a9YoL690Fq5/vMVkj7AevxfyAAAAgI1YXIGmp6crMTFRJpNJvXr1kr+/v9544w0lJSVZIx8AAACAO7C4mHdxcdGzzz6rhIQEnT17VrNmzVJqaqo6dOigunXrWiMjAAAAgNuweM38H7m7uys0NFQXLlzQiRMndPDgweLKBQAAAOAeirTQOzs7WwkJCeratauqV6+uuLg4/fnPf9aBA3y6KQAAAGArFs/M9+nTR19++aXc3d3Vq1cvRUVFqVWrVtbIBgAAAOAuLC7mnZ2dtWzZMoWGhsrZ2bnAtv379ysoKKjYwgEAAAC4M4uL+YSEhALPMzMztWTJEi1YsEA//vhjqb1VJQAAAGBrRb45+nfffaeXX35Z/v7+mj59ujp27Kjt27cXZzYAAAAAd2HRzPyZM2e0aNEiffTRR8rIyFCvXr107do1ffHFF6X602ABAAAAe7jvmfnu3burQYMG2rt3r+Li4nT69Gm9//771swGAAAA4C7ue2b+q6++0rBhwzR48GAFBgZaMxMAAACA+3DfM/NbtmxRZmammjZtqhYtWmjOnDk6d+6cNbMBAAAAuIv7LuZbtmyp+fPnKz09Xa+//roSExNVrVo15efna926dcrMzLRmTgAAAAC3sPhuNuXLl9err76qLVu2aN++fRo5cqSmTJkiX19fhYWFWSMjAAAAgNso8q0pJalBgwaaNm2a0tLStGTJkuLKBAAAAOA+PFAxf5Ozs7N69uypVatWFcfhAAAAANyHYinmAQAAANgexTwAAADgoCjmAQAAAAdFMQ8AAAA4KIp5AAAAwEFRzAMAAAAOimIeAAAAcFAU8wAAAICDopgHAAAAHBTFPAAAAOCgKOYBAAAAB0UxDwAAADgoinkAAADAQVHMAwAAAA6KYh4AAABwUBTzAAAAgIOimAcAAAAcFMU8AAAA4KAo5kuavKtSxk/S9Wzr7vMg+wEAAKBEoJi3hzsV0dezpR9fkXYNlNY2Lbi9KPs8yH4AAAAo8SjmH8TdZraLUkRf2i9dSbvx76xk6eL+ou/zIPsBAADAIVDMF9XdCuWiFtFejaQKgTf+XTFQ8goq+j4Psh8AAAAcgou9Azis2xXKVZ6897abRXRWcuEi2rW81HX3jf5eQZKLe9H3eZD9AAAA4BBMhmEY9g5RVBkZGfL09NSlS5fk4eFh25PnXpa+euL3QvmZ3b8XxHfbJt2Yqbe0iC7KPg+yHwAAAOzmfutcivkHcbdCmSIaAAAARXS/dS7LbB6Ei/vvy2cs2QYAAAAUA94ACwAAADgoinkAAADAQVHMAwAAAA6KYh4AAABwUBTzAAAAgIOimAcAAAAcFMU8AAAA4KAo5gEAAAAHRTEPAAAAOCiKeQAAAMBBUcwDAAAADopiHgAAAHBQFPMAAACAg3Kxd4AHYRiGJCkjI8POSQAAAIDic7O+vVnv3olDF/OZmZmSpICAADsnAQAAAIpfZmamPD0977jdZNyr3C/B8vPzdfr0aVWsWFEmk8necR4KGRkZCggI0M8//ywPDw97x8EdME6OgXFyDIyTY2CcHAdjVTwMw1BmZqaqVasmJ6c7r4x36Jl5Jycn1ahRw94xHkoeHh58AzoAxskxME6OgXFyDIyT42CsHtzdZuRv4g2wAAAAgIOimAcAAAAcFMU8Cihbtqyio6NVtmxZe0fBXTBOjoFxcgyMk2NgnBwHY2VbDv0GWAAAAKA0Y2YeAAAAcFAU8wAAAICDopgHAAAAHBTFPAAAAOCgKOZLkZiYGJlMpgKPRx999K77fP7553r00UdVrlw5BQcHa82aNTZKW3pZOk7z589X27Zt5e3tLW9vb3Xq1Ek7duywYeLSqSjfTzclJibKZDKpZ8+e1g2JIo3TxYsX9cYbb8jf319ly5ZV/fr1+dlnA0UZq7i4ODVo0EBubm4KCAjQiBEjdPXqVRslLr1OnTqll156SZUrV5abm5uCg4P1ww8/3HWfTZs2qUmTJipbtqzq1aunRYsW2SZsKeDQnwALyz3++ONav369+bmLy52/BJKSkhQeHq7Jkyfr2Wef1eLFi9WzZ0/t3LlTQUFBtohbalkyTps2bVJ4eLhCQkJUrlw5TZ06VZ07d9aBAwdUvXp1W8QttSwZp5tSU1MVGRmptm3bWjMa/sCSccrJydGf/vQn+fr6avny5apevbpOnDghLy8vGySFJWO1ePFijR49WgsXLlRISIiOHDmiV155RSaTSTNnzrRF3FLpwoULat26tTp06KCvvvpKPj4+Sk5Olre39x33OX78uLp166ZBgwYpISFBGzZs0GuvvSZ/f3+FhobaMP3DiWK+lHFxcZGfn9999Y2Pj1eXLl301ltvSZLGjx+vdevWac6cOZo3b541Y5Z6loxTQkJCgecLFizQihUrtGHDBvXv398a8fAbS8ZJkvLy8hQREaHY2Fht3rxZFy9etF44mFkyTgsXLtT//vc/JSUlydXVVZJUq1YtK6bDH1kyVklJSWrdurX69u0r6cY4hYeH6/vvv7dmxFJv6tSpCggI0Mcff2xuq1279l33mTdvnmrXrq0ZM2ZIkho2bKgtW7Zo1qxZFPPFgGU2pUxycrKqVaumOnXqKCIiQidPnrxj323btqlTp04F2kJDQ7Vt2zZrxyz1LBmnW2VnZys3N1eVKlWyYkJIlo/TuHHj5OvrqwEDBtgoISTLxmnVqlVq1aqV3njjDVWtWlVBQUGaNGmS8vLybJi49LJkrEJCQvTjjz+alxUeO3ZMa9asUdeuXW0Vt1RatWqVmjVrphdffFG+vr564oknNH/+/LvuQz1hXRTzpUiLFi20aNEirV27VnPnztXx48fVtm1bZWZm3rb/mTNnVLVq1QJtVatW1ZkzZ2wRt9SydJxuNWrUKFWrVq3QD04UL0vHacuWLfroo4/u+Z8eipel43Ts2DEtX75ceXl5WrNmjaKiojRjxgxNmDDBxslLH0vHqm/fvho3bpzatGkjV1dX1a1bV+3bt9e7775r4+Sly7FjxzR37lwFBgbq66+/1uDBgzVs2DB98sknd9znTvVERkaGrly5Yu3IDz8DpdaFCxcMDw8PY8GCBbfd7urqaixevLhA2wcffGD4+vraIh5+c69x+qPJkycb3t7exp49e2yQDH90t3HKyMgwatWqZaxZs8bc9vLLLxs9evSwYUIYxr2/nwIDA42AgADj+vXr5rYZM2YYfn5+toqI39xrrDZu3GhUrVrVmD9/vrF3717j3//+txEQEGCMGzfOxklLF1dXV6NVq1YF2oYOHWq0bNnyjvsEBgYakyZNKtC2evVqQ5KRnZ1tlZylCWvmSzEvLy/Vr19fR48eve12Pz8//fLLLwXafvnlF4vWCOPB3Wucbpo+fbqmTJmi9evXq1GjRjZKh5vuNk4pKSlKTU1V9+7dzW35+fmSbqwRPnz4sOrWrWuzrKXZvb6f/P395erqKmdnZ3Nbw4YNdebMGeXk5KhMmTK2ilrq3WusoqKi1K9fP7322muSpODgYF2+fFkDBw7UmDFj5OTE4gNr8Pf312OPPVagrWHDhlqxYsUd97lTPeHh4SE3Nzer5CxN+EovxbKyspSSkiJ/f//bbm/VqpU2bNhQoG3dunVq1aqVLeLhN/caJ0maNm2axo8fr7Vr16pZs2Y2TIeb7jZOjz76qPbt26fdu3ebH2FhYerQoYN2796tgIAAOyQune71/dS6dWsdPXrU/MuWJB05ckT+/v4U8jZ2r7HKzs4uVLDf/CXMMAyr5yutWrdurcOHDxdoO3LkiGrWrHnHfagnrMzefxqA7YwcOdLYtGmTcfz4cWPr1q1Gp06djCpVqhhnz541DMMw+vXrZ4wePdrcf+vWrYaLi4sxffp04+DBg0Z0dLTh6upq7Nu3z16XUCpYOk5TpkwxypQpYyxfvtxIT083PzIzM+11CaWCpeN0K5bZ2Ial43Ty5EmjYsWKxpAhQ4zDhw8bX375peHr62tMmDDBXpdQalg6VtHR0UbFihWNJUuWGMeOHTO++eYbo27dukavXr3sdQmlwo4dOwwXFxdj4sSJRnJyspGQkGC4u7sbn332mbnP6NGjjX79+pmfHzt2zHB3dzfeeust4+DBg8YHH3xgODs7G2vXrrXHJTx0WGZTiqSlpSk8PFznz5+Xj4+P2rRpo+3bt8vHx0eSdPLkyQKzHCEhIVq8eLHGjh2rd999V4GBgfriiy+4x7yVWTpOc+fOVU5Ojl544YUCx4mOjlZMTIwto5cqlo4T7MPScQoICNDXX3+tESNGqFGjRqpevbqGDx+uUaNG2esSSg1Lx2rs2LEymUwaO3asTp06JR8fH3Xv3l0TJ0601yWUCs2bN9fKlSv1zjvvaNy4capdu7bi4uIUERFh7pOenl7gTkS1a9fW6tWrNWLECMXHx6tGjRpasGABt6UsJibD4G9RAAAAgCNi2ggAAABwUBTzAAAAgIOimAcAAAAcFMU8AAAA4KAo5gEAAAAHRTEPAAAAOCiKeQAAAMBBUcwDQCnzz3/+UwEBAXJyclJcXJxiYmLUuHFje8cqsvbt2+vNN9+0dwwAsAuKeQAoRq+88op69uxp8/MuWrRIXl5e9+yXkZGhIUOGaNSoUTp16pQGDhxolTyO/gsCADgKF3sHAADYzsmTJ5Wbm6tu3brJ39/f3nEAAA+ImXkAsKL27dtr2LBhevvtt1WpUiX5+fkpJiamQB+TyaS5c+fqmWeekZubm+rUqaPly5ebt2/atEkmk0kXL140t+3evVsmk0mpqanatGmT/vKXv+jSpUsymUwymUyFziHdmL0PDg6WJNWpU8e8/63y8/M1btw41ahRQ2XLllXjxo21du3aAn1GjRql+vXry93dXXXq1FFUVJRyc3PN54mNjdWePXvMeRYtWlToPN98843KlStX4Lokafjw4erYsaMk6fz58woPD1f16tXl7u6u4OBgLVmy5A6v9u+v5xdffFGgzcvLq0CGn3/+Wb169ZKXl5cqVaqkHj163Pa1AICSjmIeAKzsk08+Ufny5fX9999r2rRpGjdunNatW1egT1RUlJ5//nnt2bNHERER6tOnjw4ePHhfxw8JCVFcXJw8PDyUnp6u9PR0RUZGFurXu3dvrV+/XpK0Y8cOpaenKyAgoFC/+Ph4zZgxQ9OnT9fevXsVGhqqsLAwJScnm/tUrFhRixYt0k8//aT4+HjNnz9fs2bNMp9n5MiRevzxx815evfuXeg8Tz/9tLy8vLRixQpzW15enpYuXaqIiAhJ0tWrV9W0aVOtXr1a+/fv18CBA9WvXz/t2LHjvl6b28nNzVVoaKgqVqyozZs3a+vWrapQoYK6dOminJycIh8XAOyBYh4ArKxRo0aKjo5WYGCg+vfvr2bNmmnDhg0F+rz44ot67bXXVL9+fY0fP17NmjXT+++/f1/HL1OmjDw9PWUymeTn5yc/Pz9VqFChUD83NzdVrlxZkuTj4yM/Pz85OzsX6jd9+nSNGjVKffr0UYMGDTR16lQ1btxYcXFx5j5jx45VSEiIatWqpe7duysyMlLLli0zn6dChQpycXEx53Fzcyt0HmdnZ/Xp00eLFy82t23YsEEXL17U888/L0mqXr26IiMj1bhxY9WpU0dDhw5Vly5dzOcqiqVLlyo/P18LFixQcHCwGjZsqI8//lgnT57Upk2binxcALAH1swDgJU1atSowHN/f3+dPXu2QFurVq0KPd+9e7e1oxWSkZGh06dPq3Xr1gXaW7durT179pifL126VLNnz1ZKSoqysrJ0/fp1eXh4WHy+iIgItWzZUqdPn1a1atWUkJCgbt26md/Mm5eXp0mTJmnZsmU6deqUcnJydO3aNbm7uxf5Gvfs2aOjR4+qYsWKBdqvXr2qlJSUIh8XAOyBYh4ArMzV1bXAc5PJpPz8/Pve38npxh9RDcMwt91cn24P27ZtU0REhGJjYxUaGipPT08lJiZqxowZFh+refPmqlu3rhITEzV48GCtXLmywNr29957T/Hx8YqLi1NwcLDKly+vN998867LYUwmU4HXSir4emVlZalp06ZKSEgotK+Pj4/F1wAA9kQxDwAlwPbt29W/f/8Cz5944glJvxeY6enp8vb2lqRCs/ZlypRRXl7eA+fw8PBQtWrVtHXrVj311FPm9q1bt+rJJ5+UJCUlJalmzZoaM2aMefuJEyeKnCciIkIJCQmqUaOGnJyc1K1btwLn7dGjh1566SVJN96ce+TIET322GN3PJ6Pj4/S09PNz5OTk5WdnW1+3qRJEy1dulS+vr5F+msCAJQkrJkHgBLg888/18KFC3XkyBFFR0drx44dGjJkiCSpXr16CggIUExMjJKTk7V69epCs+C1atVSVlaWNmzYoHPnzhUoXi311ltvaerUqVq6dKkOHz6s0aNHa/fu3Ro+fLgkKTAwUCdPnlRiYqJSUlI0e/ZsrVy5slCe48ePa/fu3Tp37pyuXbt2x/NFRERo586dmjhxol544QWVLVvWvC0wMFDr1q1TUlKSDh48qNdff12//PLLXfN37NhRc+bM0a5du/TDDz9o0KBBBf46EhERoSpVqqhHjx7avHmzjh8/rk2bNmnYsGFKS0sryksGAHZDMQ8AJUBsbKwSExPVqFEj/etf/9KSJUvMs8+urq5asmSJDh06pEaNGmnq1KmaMGFCgf1DQkI0aNAg9e7dWz4+Ppo2bVqRswwbNkx/+9vfNHLkSAUHB2vt2rVatWqVAgMDJUlhYWEaMWKEhgwZosaNGyspKUlRUVEFjvH888+rS5cu6tChg3x8fO56O8l69erpySef1N69e813sblp7NixatKkiUJDQ9W+fXv5+fnd80O5ZsyYoYCAALVt21Z9+/ZVZGRkgTX27u7u+u677/TII4/oueeeU8OGDTVgwABdvXqVmXoADsdk3LqwEABgUyaTSStXrrTLJ8cCABwbM/MAAACAg6KYBwAAABwUd7MBADtjtSMAoKiYmQcAAAAcFMU8AAAA4KAo5gEAAAAHRTEPAAAAOCiKeQAAAMBBUcwDAAAADopiHgAAAHBQFPMAAACAg6KYBwAAABzU/wfuS8QyleisSgAAAABJRU5ErkJggg==", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fi = format_info_ocp_e5m2\n", "\n", "fig, ax = plt.subplots(1, 1, figsize=figsize)\n", "fig.suptitle(f\"Biased stochastic rounding: {longstr(RoundMode.StochasticFastest)}\")\n", "\n", "ax.plot(vs, vs, label=\"True value\", color=\"k\")\n", "ax.plot(vs, rn, label=f\"Round to nearest, err={err_rn:.2f}\", color=\"gray\")\n", "\n", "# Stochastic rounding\n", "srnumbits = 2\n", "nsamples = 10_000\n", "srbits = np.random.randint(0, 2**srnumbits, (nsamples, len(vs)))\n", "\n", "rvs = round_ndarray(\n", " fi,\n", " vs[np.newaxis, :],\n", " RoundMode.StochasticFastest,\n", " sat=False,\n", " srbits=srbits,\n", " srnumbits=srnumbits,\n", ")\n", "rvmean = rvs.mean(axis=0)\n", "err = np.abs(rvmean - vs).mean()\n", "lollipops(\n", " ax,\n", " vs,\n", " rvmean,\n", " key=RoundMode.StochasticFastest,\n", " label=f\"{RoundMode.StochasticFastest}, {srnumbits} bits, err={err:.2f}\",\n", ")\n", "\n", "ax.set_xlabel(\"Input float value\")\n", "ax.set_ylabel(f\"Average of rounded values, {nsamples} samples\")\n", "ax.set_yticks(np.unique(rn))\n", "ax.legend()\n", "None" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Yikes! The SRFastest line is not symmetric around $Y=X$ -- there is a bias towards zero.\n", "Note that it is still rounding as if to two extra bits of precision,\n", "but there is a clearly undesirable bias.\n", "\n", "Shortly, we will introduce a tool to analyse this more carefully, but for the moment, let's just try a single set of roundings, without averaging:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Stochastic rounding\n", "np.random.seed(1)\n", "srnumbits = 2\n", "srbits = np.random.randint(0, 2**srnumbits, len(vs))\n", "rvs = round_ndarray(\n", " fi, vs, RoundMode.StochasticFastest, sat=False, srbits=srbits, srnumbits=srnumbits\n", ")\n", "\n", "# Plot\n", "fig, axs = plt.subplots(1, 2, figsize=(14, 7))\n", "for ax in axs:\n", " ax.plot(vs, vs, label=\"True value\", color=\"k\")\n", "\n", " if ax == axs[0]:\n", " lollipops(ax, vs, rn, key=RoundMode.TiesToEven, label=\"Round to nearest\")\n", " else:\n", " lollipops(\n", " ax, vs, rvs, key=RoundMode.StochasticFastest, label=f\"SR, {srnumbits} bits\"\n", " )\n", "\n", " ax.set_xlabel(\"Input float value\")\n", " ax.set_ylabel(f\"Rounded values\")\n", " ax.set_yticks(np.unique(rvs))\n", " ax.set_xlim(4.9, 6.1)\n", " ax.set_ylim(4.9, 6.1)\n", " ax.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Yes, it looks as if there are more roundings-up than roundings-down, consistent with the averages we saw above." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Rounding profiles: a tool to understand the bias " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To visualize the behaviour of a conventional rounding mode, we might\n", "plot the rounding for a densely sampled set of values between two floats.\n", "\n", "In OCP E5M2 format, the values 5 and 6 are adjacent floats. Under NearestTiesToEven,\n", "all values between them below 5.5 round to 5, the other values to 6.\n", "\n", "We would express this behaviour as a \"rounding profile\" a function from the reals to \n", "the value set of the floating point format. " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 3))\n", "r = round_ndarray(fi, vs, RoundMode.TiesToEven)\n", "ax.plot(vs, vs, label=f\"input\", color=\"gray\")\n", "ax.plot(vs, r, label=f\"RTNE\", color=mode_colors[RoundMode.TiesToEven][1])\n", "ax.set_xlim(4.75, 6.25)\n", "ax.set_xticks(np.arange(5, 6.1, step=0.25))\n", "ax.set_yticks([5, 6])\n", "ax.legend()\n", "ax.set_title(f\"Rounding profile for RTNE\")\n", "None" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To consider the behaviour of stochastic rounding, think of it as selecting a random \n", "rounding profile based on the set of stochastic rounding bits. Let us plot those \n", "profiles for SRNumBits=2, so there are four profiles." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 3))\n", "ax.plot(vs, vs, label=f\"input $x$\", color=\"gray\")\n", "\n", "srnumbits = 2\n", "for srbits in range(2**srnumbits):\n", " r = round_ndarray(\n", " fi,\n", " vs,\n", " RoundMode.StochasticFastest,\n", " sat=False,\n", " srbits=np.full(vs.shape, srbits),\n", " srnumbits=srnumbits,\n", " )\n", " ax.plot(vs, r, label=f\"SRBits=0b{srbits:02b}\")\n", "ax.set_xlim(4.75, 6.25)\n", "ax.set_ylim(4.75, 6.25)\n", "ax.set_xticks(np.arange(5, 6.1, step=0.25))\n", "ax.set_yticks([5, 6])\n", "ax.legend()\n", "ax.set_title(\n", " f\"Rounding profiles of simple stochastic rounding: {longstr(RoundMode.StochasticFastest)}\",\n", " fontsize=\"small\",\n", ")\n", "None" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So, if SRBits = 0b11, then any value above 5.25 is rounded to 6, which feels sensible;\n", "and if SRBits = 0b01, then any value above 5.75 rounds to 6, again sensible.\n", "\n", "But look what happens if SRBits = 0b00. Then all values below 6.0 round to 5.0, \n", "which feels a bit wasteful. If we look at the list of step thresholds:\n", "```python\n", " [5.25, 5.50, 5.75, 6.00]\n", "```\n", "we could make them more symmetric by subtracting 1/8 from each:\n", "```python\n", " [5.125, 5.375, 5.625, 5.875]\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Put more generally, we will add an extra half bit to SRBits.\n", "\n", "From:\n", "```py\n", "def round_stochastic_fastest(x):\n", " bits = randint(2**S) # Draw a random S-bit integer\n", " return floor(x + bits * 2**-S)\n", "```\n", "\n", "To:\n", "```py\n", "def round_stochastic_fast(x):\n", " bits = randint(2**S) # Draw a random S-bit integer\n", " return floor(x + (float(bits) + 0.5) * 2**-S)\n", "```\n", "\n", "This is essentially what is done in the mode called `RoundMode.StochasticFast`.\n", "[Aside: of course you don't write the slow code, you write something like\n", "```py\n", "def round_stochastic_fast(x):\n", " bits = randint(2**S) # Draw a random S-bit integer\n", " return floor(x + bits*2**-S + 2**-(S+1))\n", "```\n", "Let's see if it works..." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axs = plt.subplots(1, 2, figsize=(16, 5))\n", "\n", "for rnd, ax in zip((RoundMode.StochasticFastest, RoundMode.StochasticFast), axs):\n", " ax.plot(vs, vs, label=\"True value\", color=\"k\")\n", " ax.plot(vs, rn, label=f\"Round to nearest, err={err_rn:.2f}\", color=\"gray\")\n", "\n", " # Stochastic rounding\n", " srnumbits = 2\n", " nsamples = 5_000\n", " srbits = np.random.randint(0, 2**srnumbits, (nsamples, len(vs)))\n", "\n", " rvs = round_ndarray(\n", " fi, vs[np.newaxis, :], rnd, sat=False, srbits=srbits, srnumbits=srnumbits\n", " )\n", " rvmean = rvs.mean(axis=0)\n", " err = np.abs(rvmean - vs).mean()\n", " bias = (rvmean - vs).mean()\n", "\n", " label = f\"{rnd}, {srnumbits} bits, err={err:.2f}, {bias=:.3f}\"\n", " lollipops(ax, vs, rvmean, key=rnd, label=label)\n", "\n", " ax.set_title(longstr(rnd))\n", " ax.set_xlabel(\"Input float value\")\n", " ax.set_ylabel(f\"Average of rounded values, {nsamples} samples\")\n", " ax.set_yticks(np.unique(rn))\n", " ax.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Good news. `SRFast` seems to have fixed things...\n", "What could be wrong? Why is that not the default?\n", "\n", "First, though, let's just squint at the rounding profiles for SRFast:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 3))\n", "ax.plot(vs, vs, label=f\"input $x$\", color=\"gray\")\n", "\n", "rnd = RoundMode.StochasticFast\n", "srnumbits = 2\n", "for srbits in range(2**srnumbits):\n", " r = round_ndarray(\n", " fi,\n", " vs,\n", " rnd,\n", " sat=False,\n", " srbits=np.full(vs.shape, srbits),\n", " srnumbits=srnumbits,\n", " )\n", " ax.plot(vs, r, label=f\"SRBits=0b{srbits:02b}\")\n", "ax.set_xlim(4.75, 6.25)\n", "ax.set_xticks(np.arange(5, 6.1, step=0.25))\n", "ax.set_yticks([5, 6])\n", "# location se\n", "ax.legend()\n", "ax.set_title(f\"Rounding profiles of simple stochastic rounding: {longstr(rnd)}\")\n", "None" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## Case 2: Finite-precision inputs and limited-precision random variables\n", "\n", "The answer is that we are still modelling the inputs `v` as being infinite precision (well, they are float64 here, but that's pretty much infinite precision).\n", "\n", "If we first assume that they are available in some finite precision, \n", "still larger than that to which we are effectively rounding, then we obtain another, relatively small, bias.\n", "\n", "To look at this experimentally, let's round from bfloat16 (precision = 8) to a P=3 format, using only 3 bits of randomness." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "nunique= 32\n", "Q,P,D,K=(8, 3, 5, 3) note P+K=6 != Q=8\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from gfloat.formats import (\n", " format_info_binary16,\n", " format_info_bfloat16,\n", " format_info_p3109,\n", " format_info_ocp_e4m3,\n", ")\n", "\n", "fi_hi = format_info_bfloat16\n", "fi = format_info_ocp_e5m2 # format_info_p3109(8, 5)\n", "\n", "vs_hi = np.unique(round_ndarray(fi_hi, vs, RoundMode.TiesToEven))\n", "print(\"nunique=\", np.sum((vs_hi >= 5) & (vs_hi < 6)))\n", "\n", "Q = fi_hi.precision\n", "P = fi.precision\n", "D = Q - P\n", "K = 3\n", "print(f\"{Q,P,D,K=} note {P+K=} != {Q=}\")\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(16, 5))\n", "fig.suptitle(\"SRFast vs SR, limited-precision inputs\")\n", "\n", "for rnd, ax in zip((RoundMode.StochasticFast, RoundMode.Stochastic), axes):\n", " ax.plot(vs_hi, vs_hi, label=f\"True value ({fi_hi}, P={fi_hi.precision})\", color=\"k\")\n", " ax.plot(\n", " vs_hi,\n", " round_ndarray(fi, vs_hi, RoundMode.TiesToEven),\n", " label=f\"Round to nearest, err={err_rn:.2f}\",\n", " color=\"red\",\n", " markersize=3,\n", " linestyle=\"\",\n", " marker=\".\",\n", " )\n", "\n", " # Stochastic rounding\n", " srnumbits = K\n", " nsamples = 10_000\n", " srbits = np.random.randint(0, 2**srnumbits, (nsamples, len(vs_hi)))\n", "\n", " rvs = round_ndarray(\n", " fi, vs_hi[np.newaxis, :], rnd, sat=False, srbits=srbits, srnumbits=srnumbits\n", " )\n", " rvmean = rvs.mean(axis=0)\n", " err = np.abs(rvmean - vs_hi).mean()\n", " bias = (rvmean - vs_hi).mean()\n", "\n", " label = f\"{rnd}, {srnumbits} bits, {err=:.2f}, {bias=:.3f}\"\n", " lollipops(ax, vs_hi, rvmean, label=label, key=rnd)\n", "\n", " ax.set_xlabel(\"Input float value\")\n", " ax.set_ylabel(f\"Average of rounded values, {nsamples} samples\")\n", " ax.set_yticks(np.unique(rn))\n", " ax.legend()\n", " ax.set_title(f\"{longstr(rnd)}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So... The `SRFast` curve now shows some bias: the dots are generally below the Y=X line.\n", "The `SR` curve is now unbiased, but shows a peculiar non-coherence in terms of the widths \n", "of the plateaus. To explain this, recall the \"rounding profiles\" above.\n", "With only two bits of randomness, we can have only four rounding profiles.\n", "Those profiles must have their steps coinciding with the steps in the \"Values with precision p=6\" \n", "curve, so in order to be symmetric, the central region must be either one or three units wide,\n", "and the adjacent steps must be three or one wide.\n", "That choice of \"three or one\" depends on whether the implementation rounds to \n", "nearest even or odd before comparing to SRbits.\n", "\n", "Let's plot all the rounding profiles together:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axs = plt.subplots(4, 1, figsize=(8, 10))\n", "fig.tight_layout(h_pad=2)\n", "h = 0.7\n", "for rnd, ax in zip(\n", " (\n", " RoundMode.Stochastic,\n", " RoundMode.StochasticOdd,\n", " RoundMode.StochasticFast,\n", " RoundMode.StochasticFastest,\n", " ),\n", " axs,\n", "):\n", " ax.plot(vs_hi, vs_hi, label=f\"Finite-precision input\", color=\"gray\")\n", "\n", " srnumbits = 2\n", " for srbits in range(2**srnumbits):\n", " r = round_ndarray(\n", " fi,\n", " vs_hi,\n", " rnd,\n", " sat=False,\n", " srbits=np.full(vs_hi.shape, srbits),\n", " srnumbits=srnumbits,\n", " )\n", " ax.plot(vs_hi, r, label=f\"SRBits = 0b{srbits:02b}\")\n", " for k in (5, 6, 7):\n", " ax.plot([k, k], [0, 10], color=\"lightgray\", linestyle=\"-\")\n", " ax.set_xlim(4.75, 6.25)\n", " ax.set_ylim(4.75, 6.25)\n", " ax.set_xticks(np.arange(5.0, 6.1, step=0.25))\n", " ax.set_yticks([5, 6])\n", " if ax == axs[0]:\n", " ax.legend(loc=\"center left\", bbox_to_anchor=(1, 0.5))\n", " ax.set_title(f\"{rnd}\")\n", "None" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conclusion\n", "\n", "Stochastic rounding provides a pretty impressive approximation of higher precision\n", "when casting high-precision values to lower precision. However, it comes at the \n", "cost that the number of random bits used per cast should match the input precision.\n", "The number of random bits can be reduced, but care must be taken to ensure that doing\n", "so does not introduce a bias. Fortunately, mitigations are available, as implemented \n", "in this library. We don't know the details of the various hardware implementations of \n", "SR, but we also know of no description of these biases in the current literature.\n", "\n", "Conversely, it might be that in some use-cases, a bias is advantageous.\n", "For example, adding gradient updates in a stochastic optimizer - it may be that it's \n", "always a good idea to make *some* change, as it can be undone in the reverse direction\n", "on the following iteration. But that is speculation - let's see how people use these\n", "ideas in practice.\n" ] } ], "metadata": { "kernelspec": { "display_name": "gfloat", "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": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 2 }