{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# PyVBMC Example 5: Prior distributions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this notebook, we discuss some considerations for using a prior distribution with PyVBMC, and demonstrate some convenient built-in priors.\n", "\n", "This notebook is Part 5 of a series of notebooks in which we present various example usages for VBMC with the PyVBMC package. The code used in this example is available as a script [here](https://github.com/acerbilab/pyvbmc/blob/main/examples/scripts/pyvbmc_example_5_full_code.py).\n", "\n", "## 0. Preliminaries\n", "\n", "In Bayesian inference – and in PyVBMC – you *need* a [prior over parameters](https://en.wikipedia.org/wiki/Prior_probability), $p(\\theta)$. The prior should be a proper probability density function (pdf), i.e. a normalized distribution. A common choice is an independent or factorized prior:\n", "\n", "$$ p(\\theta) = \\prod_{i} p_{i}(\\theta_{i}) \\iff \\log \\big( p(\\theta) \\big) = \\sum_{i} \\log \\big( p_{i}(\\theta_{i}) \\big)\\,, $$\n", "\n", "where each prior $p_{i}(\\theta_{i})$ is chosen separately for each parameter $\\theta_{i}$. Note that an independent prior does not mean that the posterior is independent!\n", "\n", "## 1. Specifying a prior with PyVBMC\n", "\n", "By default, as in the previous notebooks, PyVBMC assumes that the first argument to `VBMC` is a function which returns the log-joint (i.e., the sum of log-likelihood and log-prior). However, you may instead pass a function which returns the log-likelihood as a first argument, and supply the prior separately. Using the keyword `log_prior`, you may pass a function (of a single argument) which returns the log-density of the prior given a point:\n", "\n", "```python\n", "vbmc = VBMC(log_likelihood, x0, lb, ub, plb, pub, log_prior=log_prior_function)\n", "```\n", "\n", "Alternatively, using the keyword `prior`, you may pass one of the following:\n", "\n", "1. a PyVBMC prior imported from `pyvbmc.priors` that matches the dimension of the model,\n", "2. an appropriate continuous `scipy.stats` distribution that matches the dimension of the model, or\n", "3. a list of univariate (i.e., one-dimensional) PyVBMC priors and/or continuous `scipy.stats` distributions, which are treated as independent priors for each parameter $\\theta_{i}$. In this case the length of the list should equal the dimension of the model.\n", "\n", "```python\n", "vbmc = VBMC(log_likelihood, x0, lb, ub, plb, pub, prior=UniformBox(0, 1, D=2))\n", "vbmc = VBMC(log_likelihood, x0, lb, ub, plb, pub, prior=scipy.stats.multivariate_normal(mu, cov))\n", "vbmc = VBMC(log_likelihood, x0, lb, ub, plb, pub, prior=[UniformBox(0, 1), scipy.stats.norm()])\n", "```\n", "\n", "Below we detail the built-in PyVBMC priors (1) for various use-cases. See the [relevant documentation](https://acerbilab.github.io/pyvbmc/api/classes/priors.html) for details on other types of priors, and the examples below for some usage cases." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import scipy.stats as scs\n", "from pyvbmc import VBMC\n", "from pyvbmc.priors import UniformBox, Trapezoidal, SplineTrapezoidal, SmoothBox\n", "import matplotlib.pyplot as plt\n", "\n", "figsize = (8, 4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Bounded parameters\n", "\n", "PyVBMC implements several priors for bounded parameters. All the priors listed below apply both to the univariate and to the multivariate case, with the assumption of independent/factorized priors mentioned above.\n", "\n", "### Uniform-box prior (`UniformBox`)\n", "\n", "For bounded parameters, the first simple choice is a non-informative uniformly flat prior between the hard bounds. This is implemented by the `UniformBox` multivariate prior. Below, we plot the pdf of the prior for a one-dimensional problem (the pdf to the left and the log-pdf to the right)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lb = -3\n", "ub = 3\n", "plb = -2\n", "pub = 2\n", "x = np.linspace(lb - 1, ub + 1, 1000)\n", "\n", "prior = UniformBox(lb, ub)\n", "\n", "fig, (ax1, ax2) = plt.subplots(1, 2, sharex=True, figsize=figsize)\n", "ax1.plot(x, prior.pdf(x))\n", "ax1.set_xlim(-4, 4)\n", "ax1.set_ylim(0, 0.25)\n", "ax1.set_xlabel(\"x0\")\n", "ax1.set_ylabel(\"prior pdf\")\n", "ax2.plot(x, prior.log_pdf(x))\n", "ax2.set_ylim(-20, 0)\n", "ax2.set_xlabel(\"x0\")\n", "ax2.set_ylabel(\"prior log-pdf\")\n", "plt.suptitle(\"Uniform-box prior\")\n", "fig.tight_layout()\n", "# (Note that the log-pdf is not plotted where it takes values of -infinity.)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Trapezoidal prior (`Trapezoidal`)\n", "\n", "Alternatively, for each parameter we can define the prior to be flat within a range, where a reasonable choice is the \"plausible\" range, and then falls to zero towards the hard bounds. This is a trapezoidal or \"tent\" prior, implemented by the `Trapezoidal` prior shown below." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "prior = Trapezoidal(lb, plb, pub, ub)\n", "\n", "fig, (ax1, ax2) = plt.subplots(1, 2, sharex=True, figsize=figsize)\n", "ax1.plot(x, prior.pdf(x))\n", "ax1.set_xlim(-4, 4)\n", "ax1.set_ylim(0, 0.25)\n", "ax1.set_xlabel(\"x0\")\n", "ax1.set_ylabel(\"prior pdf\")\n", "ax2.plot(x, prior.log_pdf(x))\n", "ax2.set_ylim(-20, 0)\n", "ax2.set_xlabel(\"x0\")\n", "ax2.set_ylabel(\"prior log-pdf\")\n", "plt.suptitle(\"Trapezoidal prior\")\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Spline-smoothed trapezoidal prior (`SplineTrapezoidal`)\n", "\n", "Finally, we can use a *smoothed* trapezoidal prior with soft transitions at the edges obtained using cubic splines. This prior is better behaved numerically as it is continuous with continuous derivatives (i.e., no sharp edges), so we recommend it over the simple trapezoidal prior. The spline-smoothed trapezoidal prior is implemented by the `SplineTrapezoidal` class." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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x5coVbNq0qUKNxd/+9jfs3LkTzzzzDAYOHIgrV65g7dq1aN++fYXpcGvDzc0NvXr1wrhx45CRkYEVK1agdevWmDBhQp329/LLL2PdunUYO3Ys4uPjERgYiK+//hr/+9//sGLFCqNCcSIiSUg1HRURWY4ffvhBePHFF4Xg4GDBwcFBsLGxEVq3bi1MnjxZyMjIMGoLQJg4caLRNsP0mUuWLDHabpjWc8eOHUbbt2/fLnTu3FlQq9WCm5ub8PzzzwvXr1+vENdPP/0kPPLII4Ktra3g5OQkPPXUU8L58+crtJs/f77g5+cnKJVKo+lcK4tVEAQhICBAGDNmjNG2jIwMYeLEiYK/v79gbW0teHt7C3379hXWr19v1O7atWvCoEGDBDs7O8Hd3V14/fXXhb1799Zoutm6xCoIgrBhwwahTZs2glqtFoKDg4VNmzYJs2fPFu4/RRj28fnnn4vtO3fuXGlcNTlelE9fW9nt3n2eOHFCiI6OFhwcHAQ7OzvhscceE44cOWL0evdPN2vw8ccfC0FBQYJarRa6du0q/PLLLxWmcdXr9cL//d//CQEBAeIx7d69WxgzZowQEBBQ4T2o6XSzX375pRAbGyt4enoKtra2wsCBA4Vr164Zte3Tp4/w8MMPV7qf++M0vK/jxo0T3N3dBRsbG6Fjx47Cpk2bjNpU9XkhImpsCkGQsOqRiIjMhkKhwMSJE7Fq1SqpQzFphw8fxmOPPYYdO3YYTR1MRCR3rLEgIiIiIqJ6Y2JBRERERET1xsSCiIiIiIjqjTUWRERERERUb+yxICIiIiKiemNiQURERERE9cbEgoiIiIiI6o2JBRERERER1RsTCyIiIiIiqjcmFkREREREVG9MLIiIiIiIqN6YWBARERERUb0xsSAiIiIionpjYkFERERERPXGxIKIiIiIiOqNiQUREREREdUbEwsiIiIiIqo3JhZERERERFRvTCyIiIiIiKjemFgQEREREVG9MbEgIiIiIqJ6Y2JBRERERET1xsSCiIiIiIjqjYkFERERERHVGxMLIiIiIiKqNyYWRERERERUbyaRWKxevRqBgYHQaDQIDw/HsWPHqmz7ySefoHfv3nB1dYWrqyuioqIqtB87diwUCoXRrX///o19GEREZEJqc24BgB07diA4OBgajQYdO3bEnj17mihSIiJ5kDyx2L59O2JiYjB79mycOHECnTp1QnR0NDIzMyttf/jwYYwcORKHDh1CXFwc/P390a9fP6SkpBi169+/P9LS0sTbl19+2RSHQ0REJqC255YjR45g5MiRGD9+PE6ePInBgwdj8ODBOHv2bBNHTkRkvhSCIAhSBhAeHo5u3bph1apVAAC9Xg9/f39MnjwZM2bMeODzdTodXF1dsWrVKowePRpAWY9FTk4Odu3a1ZihExGRiartuWX48OEoKCjA7t27xW09evRAaGgo1q5d22RxExGZMyspX7y4uBjx8fGIjY0VtymVSkRFRSEuLq5G+ygsLERJSQnc3NyMth8+fBienp5wdXXF448/jvfffx/NmjWrdB9arRZarVa8r9frkZ2djWbNmkGhUNThyIiIpCcIAvLz8+Hr6wulUvIO6iZTl3NLXFwcYmJijLZFR0dXeYGK5w0ikqv6nDskTSxu3LgBnU4HLy8vo+1eXl5ISEio0T7efvtt+Pr6IioqStzWv39/DBkyBEFBQbh8+TLeeecdDBgwAHFxcVCpVBX2sXDhQsydO7d+B0NEZKKSk5PRvHlzqcNoMnU5t6Snp1faPj09vdL2PG8QkdzV5dwhaWJRX4sWLcK2bdtw+PBhaDQacfuIESPE/+/YsSNCQkLQqlUrHD58GH379q2wn9jYWKMrVbm5uWjRogWSk5Ph5OTUuAdBRNRI8vLy4O/vD0dHR6lDkR2eN4hIrupz7pA0sXB3d4dKpUJGRobR9oyMDHh7e1f73KVLl2LRokX46aefEBISUm3bli1bwt3dHYmJiZUmFmq1Gmq1usJ2JycnniCIyOxZ2tCcupxbvL29a9We5w0ikru6nDskHXRrY2ODsLAwHDhwQNym1+tx4MABREREVPm8xYsXY/78+di7dy+6du36wNe5fv06bt68CR8fnwaJm4iITFddzi0RERFG7QFg//791Z6LiIjImORDoWJiYjBmzBh07doV3bt3x4oVK1BQUIBx48YBAEaPHg0/Pz8sXLgQAPDBBx9g1qxZ2Lp1KwIDA8Xxrw4ODnBwcMDt27cxd+5cDB06FN7e3rh8+TKmT5+O1q1bIzo6WrLjJCKiplPbc8vrr7+OPn36YNmyZRg4cCC2bduG48ePY/369VIeBhGRWZE8sRg+fDiysrIwa9YspKenIzQ0FHv37hWL6JKSkowq0tesWYPi4mI8++yzRvuZPXs25syZA5VKhTNnzmDLli3IycmBr68v+vXrh/nz51fabU1ERPJT23NLz549sXXrVsycORPvvPMO2rRpg127dqFDhw5SHQIRkdmRfB0LU5SXlwdnZ2fk5uZyrCwRmS1+lzUdvtdEJBf1+T6znInNiYiIiIio0TCxICIiIiKiemNiQURERERE9cbEgoiIiIiI6o2JBRERERER1RsTCyIiIiIiqjcmFkREREREVG9MLIiIiIiIqN6YWBARERERUb0xsSAiIiIionpjYkFERERERPXGxIKIiIiIiOqNiQUREREREdUbEwsiIiIiIqo3K6kDICIiIsug0wtIyi5EWu4d3C4qxZ0SXZVtFQpF1Y9V8xrVPA2KKp5Z/XPq9lrVPbOq51X/Wg37ftTlfXrQi1X1kCn8WyoVCjR3tYWviy1Uymr/4agemFgQERFRoxAEAWdT8nAgIQO//JmF82l5KCrRSx0WWTC1lRKd/F3Qq7U7otp5ob2vk9QhyQoTCyIiImpQBdpSbP89Gdt/T8bFjHyjx9RWSjR3tYWTrTVsrVVVXmEWhNptBwABVT9Y/fNq+0DDv5ZQzZOq2V0dj6thX6vO70UDv0/VKdbpcT37DrSlehy7ko1jV7KxfP+faOfjhBHd/PH3rv6wtVHVad90FxMLIiIiahB3inXYfOQq1v9yGbcKSwCUJRKPtfVEZFsPdA9yQ0Azew5FIUno9AKu3izAb3/dxM8Xs3D4YhYupOVh9nfnsPLgJUzo3RJjegZCY80Eo66YWBAREVG9HbiQgVnfnkNKzh0AQJC7PV58JBCDQv3gbGstcXREgEqpQCsPB7TycMDz4QHIKSzGrpMp+PTXK7h+6w4W/pCAL48lYc6ghxHZ1lPqcM0SEwsiIiKqs/yiEszcdRbfnkoFAPg6azCtX1s8HeoLKxUnnyTT5WJng7GPBOH5HgH498kULPnxIq7eLMTYTb9jeFd/zB7UHnY2/KlcG3y3iIiIqE7OpuRi0tYTuHqzECqlAi/1CsKUvm1gr+bPCzIf1iol/t7VHwM6eGPFT5ew8X9XsP14Mn6/lo21o8LwkJej1CGaDV5KICIiolo7mJCBYWvjcPVmIXydNfjqHz0Q+2Q7JhVkthw11njvb+3xxUvh8HJS46+sAgz9+Aj+eylL6tDMBhMLIiIiqpVtx5Lw0pbjuFOiQ+827tjzem+EBbhJHRZRg+jZyh0/vP4ouge6IV9binGbfsc38delDsssMLEgIiKiGvvyWBJm7PwDegEYFtYcG8d2g4udjdRhETUoN3sbfPZSdwwO9UWpXsCbX59mclEDTCyIiIioRv598jre+fcfAIAJvYOw+NkQWLNAm2RKbaXCh8NDMapHCwgC8ObXp/Gf06lSh2XS+G1ARESycfXqVYwfPx5BQUGwtbVFq1atMHv2bBQXF1f7vMjISCgUCqPbK6+80kRRm4dfL93AmzvOQBCA0REBeOfJdlBUtbodkUwoFArMG9QBz4eXJRfTdpzG8avZUodlslhhRUREspGQkAC9Xo9169ahdevWOHv2LCZMmICCggIsXbq02udOmDAB8+bNE+/b2dk1drhm48qNAkzcegI6vYDBob6Y89TDTCrIYiiVCsx7ugOy8rXYdz4DE/51HN9N6gV/N35H3I+JBRERyUb//v3Rv39/8X7Lli1x8eJFrFmz5oGJhZ2dHby9vRs7RLNzp1iHl/91HLl3StC5hQsWDQ2Bkitnk4VRKRVYMSIUI9b/hjPXy6ZZ3vFKT9hYcfDPvfhuEBGRrOXm5sLN7cEzFn3xxRdwd3dHhw4dEBsbi8LCwirbarVa5OXlGd3kasGe87iUeRuejmqsGxUGjbVK6pCIJGFnY4U1o8LgbGuN09dz8cHeBKlDMjlMLIiISLYSExOxcuVK/OMf/6i23XPPPYfPP/8chw4dQmxsLD777DOMGjWqyvYLFy6Es7OzePP392/o0E3CwYQMfP5bEgBg2d87wdNJI3FERNLyc7HFsmGdAAAbfr2CXy/dkDgi06IQBEGQOghTk5eXB2dnZ+Tm5sLJyUnqcIiI6kRO32UzZszABx98UG2bCxcuIDg4WLyfkpKCPn36IDIyEp9++mmtXu/gwYPo27cvEhMT0apVqwqPa7VaaLVa8X5eXh78/f1l8V4b5BeVoO+yn5GZr8WLjwRh1lPtpQ6JyGTM+vYs/hV3DS3c7PDjG4/C1kY+PXn1OXewxoKIiEzetGnTMHbs2GrbtGzZUvz/1NRUPPbYY+jZsyfWr19f69cLDw8HgCoTC7VaDbVaXev9mpMP919CZr4Wgc3sML1/W6nDITIp0/sHY//5DCRlF2LFgT8RO6Cd1CGZBCYWRERk8jw8PODh4VGjtikpKXjssccQFhaGTZs2Qams/ajfU6dOAQB8fHxq/Vw5uJCWhy1xVwEAc5/uwLoKovs4qK0w/+kOeOlfx/Hpf69gWJg/Wns6SB2W5FhjQUREspGSkoLIyEi0aNECS5cuRVZWFtLT05Genm7UJjg4GMeOHQMAXL58GfPnz0d8fDyuXr2K7777DqNHj8ajjz6KkJAQqQ5FUvN3n4dOL2BAB2/0eahmCR2RpYlq74Wodp7Q6QUsZiE3APZYEBGRjOzfvx+JiYlITExE8+bNjR4zlBSWlJTg4sWL4qxPNjY2+Omnn7BixQoUFBTA398fQ4cOxcyZM5s8flNwJPEGjly+CWuVAu88yeEdRNWZMSAYBxMyse98Bo5dyUb3oAfPQCdnLN6uhJwKHonIcvG7rOnI5b0WBAFD1xzBiaQcjIkIwNynO0gdEpHJi935B748loSIls3w5cs9pA6n3urzfcahUERERAQA+DXxBk4k5UBjrcTEx1pLHQ6RWZj0eGtYKRWI++smTibdkjocSTGxICIiIgDAp/+9AgAY0a0F16wgqiE/F1sM7uwHAPj48GWJo5EWEwsiIiLCnxn5+PnPLCgUwIuPBEkdDpFZeaVPKygUwP7zGfgr67bU4UiGiQURERFh469lvRXR7b3RopmdxNEQmZfWng54rK0nAODLY0kSRyMdJhZEREQWrkBbiu9OpwIAXuzF3gqiuniuewsAwNfx11FUopM4GmkwsSAiIrJwe/5IQ2GxDkHu9ugW6Cp1OERmKbKtB3ycNbhVWIIfz6U/+AkyxMSCiIjIwn0dfx0A8GxYcygUComjITJPViolhnfzBwB8dTxZ4mikwcSCiIjIgiVnF+LolWwoFMAz5TPbEFHdDOlctjBn3OWbyMrXShxN02NiQUREZMF2n0kDAPRs1Qy+LrYSR0Nk3lo0s0MnfxfoBWDv2TSpw2lyTCyIiIgsmGEseP8OPhJHQiQPT4WUfZb+c5qJBREREVmI9NwinErOAQD0a+8lbTBEMvFkx7LE4vdr2cguKJY4mqZlEonF6tWrERgYCI1Gg/DwcBw7dqzKtp988gl69+4NV1dXuLq6IioqqkJ7QRAwa9Ys+Pj4wNbWFlFRUbh06VJjHwYREZFZ2X8hAwDQuYULvLjSNlGD8HWxRbC3IwQB+O+lLKnDaVKSJxbbt29HTEwMZs+ejRMnTqBTp06Ijo5GZmZmpe0PHz6MkSNH4tChQ4iLi4O/vz/69euHlJQUsc3ixYvxz3/+E2vXrsXRo0dhb2+P6OhoFBUVNdVhERERmbyfL5ada6PasbeCqCE9Fly2WN7BhMp/z8qVQhAEQcoAwsPD0a1bN6xatQoAoNfr4e/vj8mTJ2PGjBkPfL5Op4OrqytWrVqF0aNHQxAE+Pr6Ytq0aXjzzTcBALm5ufDy8sLmzZsxYsSICvvQarXQau9W7ufl5cHf3x+5ublwcnJqoCOVJ0EQsO33ZGz+31XcKmyc7r7GmvlQgcbZcePF20j7NaOpJZVKoFdrD7zzZDAcNdZSh2Py8vLy4OzszO+yJmCO73WpTo/QeftxW1uK/0zqhY7NnaUOiUg2jl3Jxt/XxcHFzhrxM5+ASmk+59r6fJ9ZNVJMNVJcXIz4+HjExsaK25RKJaKiohAXF1ejfRQWFqKkpARubm4AgCtXriA9PR1RUVFiG2dnZ4SHhyMuLq7SxGLhwoWYO3duPY/GMn322zXM+vac1GGQBfnyWBKu3LiNL17qYVZf1ESm5vT1XNzWlsLFzhrtfc0jGSIyF11auMBRY4WcwhKcTclFJ38XqUNqEpImFjdu3IBOp4OXl3EXrJeXFxISEmq0j7fffhu+vr5iIpGeni7u4/59Gh67X2xsLGJiYsT7hh4Lql5mXhH+b88FAMArfVrhbyE+jXa13kDa/rWG1VTHIqBpXqgpjict9w7e3HEGv/2Vja3HkvBCj4DGf1Eimfpf4g0AZdPMMkknalhWKiW6BbrhYEImfr+azcTCHCxatAjbtm3D4cOHodHUvehMrVZDrVY3YGSWYc3Pl1FUokeXFi54u39bsxpSQ+apk78L0nOLMOc/57H28GWM7OYPK5XkpWJEZsmQWDzS2l3iSIjkqXtQWWJx7Eo2XurdUupwmoSkZ2R3d3eoVCpkZGQYbc/IyIC3t3e1z126dCkWLVqEffv2ISQkRNxueF5d9kk1V6Atxfbfy5arn/rEQ0wqqMmM6N4CzextkJJzB3vOVt4LSUTVK9XpceZ6LgCge6CbxNEQyVO38s/W71ezIXFJc5ORNLGwsbFBWFgYDhw4IG7T6/U4cOAAIiIiqnze4sWLMX/+fOzduxddu3Y1eiwoKAje3t5G+8zLy8PRo0er3SfVzt6z6Sgs1iHI3R69eLWLmpDGWoXnw1sAAHaeuC5xNETm6WJGPu6U6OCotkIrDwepwyGSpY5+ztBYK3GrsASJmbelDqdJSD6GICYmBp988gm2bNmCCxcu4NVXX0VBQQHGjRsHABg9erRRcfcHH3yA9957Dxs3bkRgYCDS09ORnp6O27fL/sEUCgXeeOMNvP/++/juu+/wxx9/YPTo0fD19cXgwYOlOERZ+vfJsul9h3T2Y28FNbmnO/sBAH69dAO3LGzxIaKGYFgUL8TfGUrWVxA1ChsrJTr7uwIAjl+7JXE0TUPyGovhw4cjKysLs2bNQnp6OkJDQ7F3716x+DopKQlK5d38Z82aNSguLsazzz5rtJ/Zs2djzpw5AIDp06ejoKAAL7/8MnJyctCrVy/s3bu3XnUYdNdtbSmOXrkJAPhbJ1+JoyFL1MrDAe18nHAhLQ/7zqdjeLcWUodEZFZOJeUAAEItpKCUSCoh/s6I++smzqbkSh1Kk5A8sQCASZMmYdKkSZU+dvjwYaP7V69efeD+FAoF5s2bh3nz5jVAdHS/I4k3UKITENDMDkHu9lKHQxYq+mEvXEjLw89/ZjGxIKolQ4+F4WoqETWOjn5l68NYSmIh+VAoMj+H/yxbnj7yIQ+JIyFL9mj539+vl25Ap7eMojiihlCgLUViVtnwYUuZApNIKobE4kJ6Pkp0eomjaXxMLKhWBEHAzxfLEos+bZlYkHRC/JzhpLFCXlEpTl/PkTocIrPxZ0Y+BAHwcFTDw5FTrRM1phZudnDUWKG4VI8/M/KlDqfRMbGgWrl+6w5Scu7AWqVAj5bNpA6HLJiVSomIVmV/g7/9dVPiaIjMx8X0sh83bb0cJY6ESP4UCgXa+5StbJ+QxsSCyEh8+awGD/s6w87GJEp0yIIZ5gg/YSGzbVDNBAYGQqFQGN0WLVpU7XOKioowceJENGvWDA4ODhg6dGiF9ZDk4mL5VdO23kwsiJpCG6+yKZ0NQxDljIkF1crxa9kAgLAAFvyR9LqU/x3GX7tlMYsPUc3MmzcPaWlp4m3y5MnVtp86dSr+85//YMeOHfj555+RmpqKIUOGNFG0TUvssWBiQdQk2niWfdYuZcg/seAlZ6qV+Gs5AICuTCzIBHTwdYaNVdniQ1duFKAlF/qico6OjvD29q5R29zcXGzYsAFbt27F448/DgDYtGkT2rVrh99++w09evRozFCbnGGcN4dCETWN1p5l56bL7LEguiu/qAQX0/MAsMeCTIONlRKdmpfNuGEpiw9RzSxatAjNmjVD586dsWTJEpSWllbZNj4+HiUlJYiKihK3BQcHo0WLFoiLi6v0OVqtFnl5eUY3c5BXVIIbt8sWlWzlyUScqCm0Kf+sXbtZAG2pTuJoGhcTC6qxM9dzoReA5q628HTiYoNkGsICyuosTiYxsaAyU6ZMwbZt23Do0CH84x//wP/93/9h+vTpVbZPT0+HjY0NXFxcjLZ7eXkhPT290ucsXLgQzs7O4s3f378hD6HRJN0sBAC4O9jAQc1BC0RNwcNRDUeNFfQCcOVGgdThNComFlRjhsVdQsqvEBOZAsPf49kU87hiTHUzY8aMCgXZ998SEhIAADExMYiMjERISAheeeUVLFu2DCtXroRWq22weGJjY5GbmyvekpOTG2zfjenqzbIfNS3c7CSOhMhyKBQKcUFhQ3IvV7xcQTV2Pq3sh9vDvkwsyHQ87Fs2jd/F8sWHrFW8XiJH06ZNw9ixY6tt07Jly0q3h4eHo7S0FFevXkXbtm0rPO7t7Y3i4mLk5OQY9VpkZGRUWaehVquhVpvfGhDXyn/UBDazlzgSIsvi72qHM9dzkXzrjtShNComFlRj51LLEov25T/kiEyBYfGh/KJSJGbeRjsf/n3KkYeHBzw86rYo56lTp6BUKuHp6Vnp42FhYbC2tsaBAwcwdOhQAMDFixeRlJSEiIiIOsdsiq6V91gEMLEgalLNXW0BAMnZ8u6x4KU9qpE7xTr8VT6bwcP84UYm5N7FhwzD9chyxcXFYcWKFTh9+jT++usvfPHFF5g6dSpGjRoFV9eySSdSUlIQHByMY8eOAQCcnZ0xfvx4xMTE4NChQ4iPj8e4ceMQEREhuxmhrpb3WAQ041AooqbUvHz44fVb8k4s2GNBNZKQnge9ALg7qFm4TSbnYV9nHL2SjXOpeRgmdTAkKbVajW3btmHOnDnQarUICgrC1KlTERMTI7YpKSnBxYsXUVh49wT/4YcfQqlUYujQodBqtYiOjsbHH38sxSE0quvlV0v9WWNB1KT8y3ssrnMoFNHd+goOgyJT1MGv7O/yXCp7LCxdly5d8Ntvv1XbJjAwsMKCihqNBqtXr8bq1asbMzxJ6fQCMvLLCth9XXiBiKgpGZL55OxCCIIAhUIhcUSNg0OhqEYM9RUPM7EgE2Soq0hIz+cK3ERVuFmghU4vQKkAPBzMr/CcyJz5uZT1WBQU63CrsETiaBoPEwuqkfOGwm3WV5AJaulhD5VSgfyiUmTmN9yUokRykpFb9tlwd1DDirOnETUpjbUK7uUJfWqOfIdD8ZuFHkgQBCRmlhVut/V2lDgaoorUViqxGPXPjHyJoyEyTel5RQAAL9bJEUnC07EssciS8QUwJhb0QBl5WtzWlkKlVHDuczJZbTwdAAB/ZtyWOBIi08TEgkhaXk5liUVG+WdRjphY0ANdyiy7AhzQzA42VvyTIdP0kFdZb9ol9lgQVSojt+zHjLcz6yuIpODpWJbUy3nILn8l0gMZhkG19nCQOBKiqrUpTyw4FIqocoarpN7ssSCShGd5j0VmPnssyIKJiYUnEwsyXQ95lf19Xsq4zZmhiCphGArFtYiIpGH47GXksceCLBgTCzIHQe7lM0NpS8UfUER0l6Fg1FBASkRNyzDNM4u3yaJdzmJiQaZPbaVCoDgzFAu4ie53q7AYANDMnokFkRTc7G0AADnln0U5YmJB1bpVUIwbt8s+AK1YY0Emro1nWZ3F5UwmFkT3EgQBtwrKFuVytbeWOBoiy+RW/tnLLmBiQRYqsby3wtdZA3u1lcTREFUvyKNsOuSrNwskjoTItBQU61Cs0wO4e9WUiJqWq13ZZy+vqBSl5Z9HuWFiQdUS6yu8uDAemb6g8nVWrtxgYkF0r1vlV0htrJSwtVZJHA2RZXK2vdtbmHOnRMJIGg8TC6oWp5olc2LosWBiQWTMUF/hZmcDhUIhcTRElslKpRSTi1syHQ7FxIKq9Vf5UKiWHlxxm0yfYWX4lJw7KCrRSRwNkekwjOl25TAoIkkZhiLKtc6CiQVV69rNQgBlU3kSmTp3Bxs4qq0gCEBydqHU4RCZjJzC8sJtOxZuE0nJpfwzeKuQQ6HIwuj0ApJvlf04CyifxpPIlCkUCgSWJ8F/cTgUkcgwvaULEwsiSRkKuOU65SwTC6pSas4dlOgE2KiU8HG2lTocohox9K5dZWJBJLqtLQUAOKqZWBBJyaF8hk3DZ1JumFhQlQzDoPzdbKFSstiPzIOhx4IF3ER35Zf/iHHQcNpwIikZPoNMLMjiGNYCCGjG+goyHy2ZWBBVcLuoPLHgekREknI09FgUMbEgC5OUzfoKMj9BTCyIKhCHQrHHgkhSjuyxIEtlGKMeyB4LMiOGoVCZ+VoUyPSLm6i2DFdHmVgQScvQa5gv0/MTEwuqkqHGgj0WZE6cba3RrHyecPZaEJURayxYvE0kKQdN2WeQQ6HIogiCgGvZrLEg89SiPBnmWhZEZcQaC/ZYEEmKs0KRRcrM16KoRA+VUgE/F041S+bF37U8sbjFxKIhnTlzBnq9XuowqA5ua1m8TWQKxBoL9liQJTHUV/i52MLGin8mZF5auJUlFknssWhQnTt3xo0bNwAALVu2xM2bNyWOiGqKxdtEpoE9FmSRWF9B5szfrayXLTn7jsSRyIuLiwuuXLkCALh69apJ9l4cPnwYCoWi0tvvv/9e5fMiIyMrtH/llVeaMPLGxelmiUyDYThiflGJxJE0Dn7DUKUMa1hwRigyR/5urLFoDEOHDkWfPn3g4+MDhUKBrl27QqVSVdr2r7/+auLoyvTs2RNpaWlG29577z0cOHAAXbt2rfa5EyZMwLx588T7dnbyuLBSXKpHsa4sCbRnYkEkqXt7LARBgEIhrwWI+Q1DlbrGNSzIjBlqLK7fugO9XoCSK8c3iPXr12PIkCFITEzElClTMGHCBDg6OkodlhEbGxt4e3uL90tKSvDtt99i8uTJDzyB29nZGT1XLopKdeL/a6w5UIFISrY2ZRdj9AJQohNgYyWv8xMTC6rUtfIeC8NYdSJz4uOsgZVSgWKdHhn5RfBx5gQEDaV///4AgPj4eLz++usml1jc77vvvsPNmzcxbty4B7b94osv8Pnnn8Pb2xtPPfUU3nvvvSp7LbRaLbRarXg/Ly+vwWJuaNqSst4KhQKwUTGxIJKSrfXdXt47JTrZ1bEysaBKXb9VNja9BXssyAxZqZTwdbFFUnYhkm4WMrFoBJs2bZI6hBrZsGEDoqOj0bx582rbPffccwgICICvry/OnDmDt99+GxcvXsTOnTsrbb9w4ULMnTu3MUJucNryHgu1lVJ2wy6IzI21SgkrpQKlegFFJTo428prbRkmFlRBflEJcgrLioo41SyZqxZudkjKLkTyrTsIlzoYmRgyZEiN21b1g7yuZsyYgQ8++KDaNhcuXEBwcLB4//r16/jxxx/x1VdfPXD/L7/8svj/HTt2hI+PD/r27YvLly+jVatWFdrHxsYiJiZGvJ+Xlwd/f/+aHEqTKyrvsVBbVV4PQ0RNy9ZahXxtKe4U6x7c2MwwsaAKUnLKeitc7KzhqJFXJk2WwzAzFKecbTjOzs7i/wuCgH//+99wdnYWi6Lj4+ORk5NTqwSkpqZNm4axY8dW26Zly5ZG9zdt2oRmzZph0KBBtX698PCydDQxMbHSxEKtVkOtVtd6v1Iw9FiwvoLINGhsyhOLEvklFpJ/y6xevRqBgYHQaDQIDw/HsWPHqmx77tw5DB06FIGBgVAoFFixYkWFNnPmzKkwZeC9V7Dowa6XT9HZ3JW9FWS+DDNDXWdi0WA2bdok3ry8vPD3v/8dV65cwc6dO7Fz50789ddfGDFiBNzd3Rv8tT08PBAcHFztzcbGRmwvCAI2bdqE0aNHw9q69hdITp06BQDw8fFpqEOQjLaUPRZEpsSQ5DOxaGDbt29HTEwMZs+ejRMnTqBTp06Ijo5GZmZmpe0LCwvRsmVLLFq0qNqZOx5++GGkpaWJt19//bWxDkGWrpevVtzchfUVZL4MM0Oxx6JxbNy4EW+++abRdLMqlQoxMTHYuHGjhJGVOXjwIK5cuYKXXnqpwmMpKSkIDg4WL2RdvnwZ8+fPR3x8PK5evYrvvvsOo0ePxqOPPoqQkJCmDr3BFZXcrbEgIukZCriLZDgUStJvmeXLl2PChAkYN24c2rdvj7Vr18LOzq7Kk1K3bt2wZMkSjBgxotouaCsrK3h7e4u3xrh6JmeGwm32WJA5M8xolnyLiUVjKC0tRUJCQoXtCQkJJrFw3oYNG9CzZ89Ke6xLSkpw8eJFFBaW/W3Y2Njgp59+Qr9+/RAcHIxp06Zh6NCh+M9//tPUYTcKQ4+Fxpo9FkSmwJBYyLHHQrIai+LiYsTHxyM2NlbcplQqERUVhbi4uHrt+9KlS/D19YVGo0FERAQWLlyIFi1aVNnenKYNbApMLEgODEOhMvK0KCrR8UdVAxs3bhzGjx+Py5cvo3v37gCAo0ePYtGiRTWa2rWxbd26tcrHAgMDIQiCeN/f3x8///xzU4QlCa1YvM0eCyJTYJhitrhU+oswDa1GiUVeXh6cnJwa9IVv3LgBnU4HLy8vo+1eXl6VXgWrqfDwcGzevBlt27ZFWloa5s6di969e+Ps2bNVzrduTtMGNoXrOeVDoVw5FIrMl6udNRzUVritLcX1W3fQ2tNB6pBkZenSpfD29sayZcvEla59fHzw1ltvYdq0aRJHR/cSp5tl8TaRSRATC538Eosafcu4urqKdQ+PP/44cnJyGjOmehkwYACGDRuGkJAQREdHY8+ePcjJyal2usHY2Fjk5uaKt+Tk5CaM2PSIPRZu7LEg86VQKMRet2TWWTQ4pVKJ6dOnIyUlBTk5OcjJyUFKSgqmT59uVHdB0tNyulkik2JYqFJrqT0WDg4OuHnzJjw9PXH48GGUlJTU+4Xd3d2hUqmQkZFhtD0jI6PawuzacnFxwUMPPYTExMQq25jTtIGNjWtYkJz4u9khIT1fnJCAGl5mZiYuXrwIAAgODoaHh4fEEdH9ON0skWkx9FhYbGIRFRWFxx57DO3atQMAPPPMM0bT+t3r4MGDNXphGxsbhIWF4cCBAxg8eDAAQK/X48CBA5g0aVKN9lETt2/fxuXLl/HCCy802D7ljGtYkJwYkuOUnCKJI5Gf/Px8vPbaa/jyyy/FYm2VSoXhw4dj9erVRmtekLQ43SyRabEp/yxabI3F559/ji1btuDy5cv4+eef8fDDD8POrv7j72NiYjBmzBh07doV3bt3x4oVK1BQUCAW/o0ePRp+fn5YuHAhgLKC7/Pnz4v/n5KSglOnTsHBwQGtW7cGALz55pt46qmnEBAQgNTUVMyePRsqlQojR46sd7yWgGtYkJwY/o4NCTM1nJdeegknT57E999/j4iICABAXFwcXn/9dfzjH//Atm3bJI6QDDjdLJFpUVt68batrS1eeeUVAMDx48fxwQcfwMXFpd4vPnz4cGRlZWHWrFlIT09HaGgo9u7dKxZ0JyUlQam8+0WYmpqKzp07i/eXLl2KpUuXok+fPjh8+DAA4Pr16xg5ciRu3rwJDw8P9OrVC7/99hu752uIa1iQnPgaeiw4FKrB7d69Gz/++CN69eolbouOjsYnn3yC/v37SxgZ3Y/TzRKZFoufFepehw4datAAJk2aVOXQJ0OyYHD/FIGV4VWy+uFUsyQnhqFQqRwK1eCaNWtW6XAnZ2dnuLq6ShARVeXuUCj2WBCZAkPxdrHOQtexiImJqfEOly9fXudgSHpMLEhODD0WGflFKC7Vi1eJqP5mzpyJmJgYfPbZZ+KEG+np6Xjrrbfw3nvvSRwd3YtDoYhMi8UPhTp58qTR/RMnTqC0tBRt27YFAPz5559QqVQICwtr+AipSXENC5ITdwcb2FgpUVyqR0ZekbhoHtXfmjVrkJiYiBYtWogLkCYlJUGtViMrKwvr1q0T2544cUKqMAn3TDfLoVBEJsHih0LdO/xp+fLlcHR0xJYtW8Tu7lu3bmHcuHHo3bt340RJTSaFa1iQjCgUCvi52OLKjQJcv3WHiUUDMszmR6ZPXCCPPRZEJuHuUCgLTSzutWzZMuzbt89oDK2rqyvef/999OvXjyuumrHb2lLc4hoWJDOGxCKVM0M1qNmzZ0sdAtVQqb6sNtFKqZA4EiICAKvyxKJUV33dsDmq9eWLvLw8ZGVlVdielZWF/Pz8BgmKpGHoreAaFiQnvi4aAJxytjG99tpruHHjhtRhUBUMP15UKvZYEJkCQ5JvSPrlpNbfMs888wzGjRuHnTt34vr167h+/Tq++eYbjB8/HkOGDGmMGKmJGKaa9XVmbwXJh1/51MnssWg8n3/+OfLy8qQOg6rAHgsi02Klkm9iUeuhUGvXrsWbb76J5557DiUlZcNmrKysMH78eCxZsqTBA6Smk5pbNiWnL4dBkYywx6LxPWgacJKWrnxldCYWRKbB8Fk0fDblpNaJhZ2dHT7++GMsWbIEly9fBgC0atUK9vb2DR4cNS3DFV2/8h9iRHLgx9W3ycKJPRYqJhZEpkBVvvhziQxrLGqdWBjY29uLBdxMKuQhrfyHlw97LEhG7i6SdweCIECh4I+rhsb6OtMm1lgoWWNBZAoMSb5OhkOhav0tU1paivfeew/Ozs4IDAxEYGAgnJ2dMXPmTHFoFJknDoUiOfJ21kChAIpK9MguKJY6HNnIy8ur9Jafn4/iYr7PpsTw48WaQ6GITIKci7dr3WMxefJk7Ny5E4sXL0ZERAQAIC4uDnPmzMHNmzexZs2aBg+SmoZhKJSvM4dCkXyorVTwcFAjM1+LlJw7aOagljokWXBxcam296d58+YYO3YsZs+eDSWvlEuqpHwct4qJBZFJMHwWS7mOBbB161Zs27YNAwYMELeFhITA398fI0eOZGJhpnR6ARl5ZT0WHApFcuPnaluWWNy6g5DmLlKHIwubN2/Gu+++i7Fjx6J79+4AgGPHjmHLli2YOXMmsrKysHTpUqjVarzzzjsSR2vZdKyxIDIpVuUXW9hjAUCtViMwMLDC9qCgINjY2DRETCSBG7e1KNEJUCoAL0de0SV58XWxxcmkHBZwN6AtW7Zg2bJl+Pvf/y5ue+qpp9CxY0esW7cOBw4cQIsWLbBgwQImFhIz1FhYseeIyCSwxuIekyZNwvz586HVasVtWq0WCxYswKRJkxo0OGo6hmFQXk4acUVIIrlo7sKZoRrakSNH0Llz5wrbO3fujLi4OABAr169kJSU1NSh0X1KOd0skUmx4lCou06ePIkDBw6gefPm6NSpEwDg9OnTKC4uRt++fY0Wydu5c2fDRUqNKo2F2yRjvvfMDEUNw9/fHxs2bMCiRYuMtm/YsAH+/v4AgJs3b4qzB5J0DMMtWGNBZBpULN6+y8XFBUOHDjXaZjiJkPky/ODyYeE2yZAfeywa3NKlSzFs2DD88MMP6NatGwDg+PHjSEhIwNdffw0A+P333zF8+HApwyTcW2PB3mgiU2Bd/lmU41CoWicWmzZtaow4SGKpOeyxIPm622NRJHEk8jFo0CAkJCRg3bp1+PPPPwEAAwYMwK5du8Q6vFdffVXCCMngbo0FeyyITIGhx6KEQ6FIrtJyOdUsyZdh9e3sgmIUFpfCzoZffQ0hKCiowlAoMj2lnG6WyKQYknw59liwX5QA3DMUij0WJENOGis4qMuSCfZaNJycnBwsW7YML730El566SV8+OGHyM3NbdTXXLBgAXr27Ak7Ozu4uLhU2iYpKQkDBw6EnZ0dPD098dZbb6G0tLTa/WZnZ+P555+Hk5MTXFxcMH78eNy+fbsRjqDpiQvkcSgUkUkwDEuUY40Fv2UIwD2rbjszsSD5USgUYv2QoXeO6uf48eNo1aoVPvzwQ2RnZyM7OxvLly9Hq1atcOLEiUZ73eLiYgwbNqzKYVY6nQ4DBw5EcXExjhw5gi1btmDz5s2YNWtWtft9/vnnce7cOezfvx+7d+/GL7/8gpdffrkxDqHJlehYvE1kSu7OCiW/xILjAQjaUh2y8sumD/Z14VAokicfF1tcyrwtzoBG9TN16lQMGjQIn3zyCaysyk4lpaWleOmll/DGG2/gl19+aZTXnTt3LoCyBfoqs2/fPpw/fx4//fQTvLy8EBoaivnz5+Ptt9/GnDlzKl1v6cKFC9i7dy9+//13dO3aFQCwcuVKPPnkk1i6dCl8fX0b5Viaili8zcSCyCTIeVaoWvVYlJSUoG/fvrh06VJjxUMSyMgtSyrUVkq42XORQ5InQ/1QGodCNYjjx4/j7bffFpMKALCyssL06dNx/PhxyeKKi4tDx44d4eXlJW6Ljo5GXl4ezp07V+VzXFxcxKQCAKKioqBUKnH06NFKn6PVapGXl2d0M1V6oezHi1LBxILIFBg+i4Jg4YmFtbU1zpw501ixkERSDYXbLrZQ8MRDMuXNoVANysnJqdLF75KTk+Ho6ChBRGXS09ONkgoA4v309PQqn+Pp6Wm0zcrKCm5ublU+Z+HChXB2dhZvpjztuuG3C7/eiUyD4bMov7SiDjUWo0aNwoYNGxojFpII17AgS2CoH+JQqIYxfPhwjB8/Htu3b0dycjKSk5Oxbds2vPTSSxg5cmSt9jVjxgwoFIpqbwkJCY10JHUTGxuL3Nxc8ZacnCx1SFUSyn++MLEgMg2GUYly7LGodY1FaWkpNm7ciJ9++glhYWGwt7c3enz58uUNFhw1DcMPLR8WbpOM+biwx6IhLV26FAqFAqNHjxZnXLK2tsarr75a6ylop02bhrFjx1bbpmXLljXal7e3N44dO2a0LSMjQ3ysqudkZmYabSstLUV2dnaVz1Gr1VCr1TWKSWp6sceCmQWRaSj7LMqwxKL2icXZs2fRpUsXABAXRTLgl5Z5MvRY+LFwm2TMhzUWDcrGxgYfffQRFi5ciMuXLwMAWrVqBTs7u1rvy8PDAx4eHg0SV0REBBYsWIDMzExxeNP+/fvh5OSE9u3bV/mcnJwcxMfHIywsDABw8OBB6PV6hIeHN0hckjIkFtJGQUTlFOyxuOvQoUONEQdJiGtYkCUw9Mjla0uRX1QCR421xBHJg52dHTp27Nhkr5eUlITs7GwkJSVBp9Ph1KlTAIDWrVvDwcEB/fr1Q/v27fHCCy9g8eLFSE9Px8yZMzFx4kSxh+HYsWMYPXo0Dhw4AD8/P7Rr1w79+/fHhAkTsHbtWpSUlGDSpEkYMWKE2c8IBXAoFJGpMXwU5ZdW1HO62evXrwMAmjdv3iDBkDQMQ6F8mViQjNmrreCksUJeUSnSc4uYWNTBkCFDatx2586djRLDrFmzsGXLFvF+586dAZRd9IqMjIRKpcLu3bvx6quvIiIiAvb29hgzZgzmzZsnPqewsBAXL15ESUmJuO2LL77ApEmT0LdvXyiVSgwdOhT//Oc/G+UYmprhoihnhSIyDUoZV2/XOrHQ6/V4//33sWzZMnFVUkdHR0ybNg3vvvsulEquuWduUsp7LHxZvE0y5+Nsi7yifKTmFqGNl3QzF5krZ2dnqUPA5s2bq1zDwiAgIAB79uyp8vHIyMgKQxDc3NywdevWhgjR5Bimm2VaQWQaDHmFnkOhgHfffRcbNmzAokWL8MgjjwAAfv31V8yZMwdFRUVYsGBBgwdJjee2thT5RWWFlxwKRXLn46LBxYx8pOWwgLsuNm3aJHUIVAfiTxdmFkQmQVH+YZRfWlGHxGLLli349NNPMWjQIHFbSEgI/Pz88NprrzGxMDOGH1hOGis4qLkQO8mbD6ecJQskrmPBzILIJNwt3pY2jsZQ63FL2dnZCA4OrrA9ODgY2dnZDRIUNR1xGBR7K8gC+HKRPLIw9w75UjKvIDIJd0ss5JdZ1Dqx6NSpE1atWlVh+6pVq9CpU6cGCYqazt01LFhfQfJ3d/Vt9liQZbj3iiinhCcyDYbPItexALB48WIMHDgQP/30EyIiIgAAcXFxSE5OrrZYjkxTKnssyIIY/s6ZWJCluPd3C9MKItMgfhZlmFjUuseiT58++PPPP/HMM88gJycHOTk5GDJkCC5evIjevXs3RozUiFJzONUsWY67i+TdkeXCRE2lpKQEffv2xaVLl6QOhR7g3r9zdlgQmQY5D4WqU7Wur68vi7RlwjDW3JerbpMFMBRvFxTrkFdUCmdbrmVRF9bW1jhz5ozUYVANGPVYMLMgMgmGdSzkeH2rRonFmTNn0KFDByiVygeeTEJCQhokMGoa4qrbzuyxIPmztVHBxc4aOYUlSM8tYmJRD6NGjRKnHifTpWePBZHJMXwULXYdi9DQUKSnp8PT0xOhoaFQKBSVDiNQKBTQ6XQNHiQ1DkEQ7q66zcSCLISPsy1yCkuQmnsHbb25SF5dlZaWYuPGjfjpp58QFhYGe3t7o8eXL18uUWR0L6PibenCIKJ7yXfh7ZolFleuXIGHh4f4/yQP2QXF0JbqAQBezmqJoyFqGj7OGlxIy0NaDgu46+Ps2bPo0qULAODPP/80eoxDbkwT/12ITIO4QJ4MM4saJRYBAQEAygr25s6di/feew9BQUGNGhg1PkNvhbuDGmorlcTREDUNH65l0SAOHTokdQhUA/f+cOE6FkSm4d7PoiAIskr6azUrlLW1Nb755pvGioWaGNewIEvEKWcb3vXr13H9+nWpw6BKGNVYcDAUkUm4N5GQW69FraebHTx4MHbt2tUIoVBTM1yxZWJBlsTbiT0WDUGv12PevHlwdnZGQEAAAgIC4OLigvnz50Ov10sdHpUznhVKsjCI6B73fhRlllfUfrrZNm3aYN68efjf//5XacHelClTGiw4alxi4TbXsCAL4uNiWMuCPRb18e6774qzQj3yyCMAgF9//RVz5sxBUVERpyQ3EVyvhcj0KO4bCiWnqRVqnVhs2LABLi4uiI+PR3x8vNFjCoWCiYUZSSufatabPRZkQQwzoKXlFslubGtT2rJlCz799FMMGjRI3BYSEgI/Pz+89tprTCxMBHssiEzPvcMS5Zb61zqx4KxQ8pHKGguyQIZE+k6JDrl3SuBiZyNxROYpOzsbwcHBFbYHBwcjOztbgoioMsI9o9KUzCyITILinkIEua1lUesai3sJgsBuVjOWzqFQZIE01iq42ZclE6kcDlVnnTp1wqpVqypsX7VqFTp16iRBRFQZAfcWbxORKTCqsZDZz+g6JRYbNmxAhw4doNFooNFo0KFDB3z66acNHRs1Ir1eEBML9liQpTH8zafnsYC7rhYvXoyNGzeiffv2GD9+PMaPH4/27dtj8+bNWLJkidThUTmjBfLYY0FkEuT8Wax1YjFr1iy8/vrreOqpp7Bjxw7s2LEDTz31FKZOnYpZs2bVOoDVq1cjMDAQGo0G4eHhOHbsWJVtz507h6FDhyIwMBAKhQIrVqyo9z4t1c2CYhTr9FAoAC8nJhZkWXzK6yzYY1F3ffr0wZ9//olnnnkGOTk5yMnJwZAhQ3Dx4kX07t1b6vConFGNhWRRENG95NxjUesaizVr1uCTTz7ByJEjxW2DBg1CSEgIJk+ejHnz5tV4X9u3b0dMTAzWrl2L8PBwrFixAtHR0bh48SI8PT0rtC8sLETLli0xbNgwTJ06tUH2aakMvRUeDmpYq+o1Io7I7HCRvIbh6+vLIm0Td+9wZRlfJCUyK/fWOwkyK9+udWJRUlKCrl27VtgeFhaG0tLSWu1r+fLlmDBhAsaNGwcAWLt2Lb7//nts3LgRM2bMqNC+W7du6NatGwBU+nhd9gkAWq0WWq1WvJ+Xl1er4zBHqYY1LFhfQRZInHKWi+TVypkzZ9ChQwcolUqcOXOm2rYhISFNFBVVR8+hUEQm596Pol5eeUXtE4sXXngBa9aswfLly422r1+/Hs8//3yN91NcXIz4+HjExsaK25RKJaKiohAXF1fbsOq1z4ULF2Lu3Ll1ek1zZZhq1ofDoMgCiVPOcihUrYSGhiI9PR2enp4IDQ2FQqGodAIPhUIBnU4nQYR0P8PVUOYURKZJbpMg1TqxAMqKt/ft24cePXoAAI4ePYqkpCSMHj0aMTExYrv7k4973bhxAzqdDl5eXkbbvby8kJCQUJew6rzP2NhYo7jz8vLg7+9fpxjMRVpeeeG2CxMLsjzeHApVJ1euXIGHh4f4/2QGyn+zMK8gMh1GC+RJF0ajqHVicfbsWXTp0gUAcPnyZQCAu7s73N3dcfbsWbGdOXW5qtVqqNVqqcNoUoYrtYYrt0SWhIvk1U1AQACAsiGxc+fOxXvvvYegoCCJo6LqGH60cA0LItNhVGMhs8yi1onFoUOHGuSF3d3doVKpkJGRYbQ9IyMD3t7eJrNPuTJcqeWq22SJvJzLLiRoS/W4VVgirmtBNWNtbY1vvvkG7733ntSh0AMYFt9iXkFkOoxnhZJXZiHZdEA2NjYICwvDgQMHxG16vR4HDhxARESEyexTrtLExfGYWJDlUVup4O5Qllyk5nA4VF0MHjwYu3btavLXXbBgAXr27Ak7Ozu4uLhUePz06dMYOXIk/P39YWtri3bt2uGjjz564H4N05jfe1u0aFEjHEHTEsShUMwsiEyFgj0WjSMmJgZjxoxB165d0b17d6xYsQIFBQXijE6jR4+Gn58fFi5cCKCsOPv8+fPi/6ekpODUqVNwcHBA69ata7RPKlscL8NQY8GhUGShfJw1uHFbi7TcInTwc5Y6HLPTpk0bzJs3D//73/8QFhYGe3t7o8enTJnSKK9bXFyMYcOGISIiAhs2bKjweHx8PDw9PfH555/D398fR44cwcsvvwyVSoVJkyZVu+958+ZhwoQJ4n1HR8cGj7+pib9ZmFcQmQyjHgvJomgckiYWw4cPR1ZWFmbNmoX09HSEhoZi7969YvF1UlISlMq7nSqpqano3LmzeH/p0qVYunQp+vTpg8OHD9donwTcuK1FiU6AUgF4OlpWbQmRgY+zBn+k5CKdBdx1smHDBri4uCA+Ph7x8fFGjykUikZLLAwz+G3evLnSx1988UWj+y1btkRcXBx27tz5wMTC0dFRdsNmDcMslEwsiEyGUfG2zLosJE0sAGDSpElVftkbkgWDwMDAGv0DVLdPujsMytNRAysujkcWyrd8DZdUrmVRJ+Y0K1Rubi7c3Nwe2G7RokWYP38+WrRogeeeew5Tp06FlVXlp0lzWf+IQ6GITM+9Q6Esfh0LMn9p4uJ4rK8gyyVOOcsai3oTxAJh0/vxeuTIEWzfvh3ff/99te2mTJmCLl26wM3NDUeOHEFsbCzS0tKqnDbdXNY/EhML0/unIbJoCkXZ51NuK2/zcrUFSs0x1FcwsSDLZfj7Z49F3W3YsAEdOnSARqOBRqNBhw4d8Omnn9Z6PzNmzKhQOH3/rS7rG509exZPP/00Zs+ejX79+lXbNiYmBpGRkQgJCcErr7yCZcuWYeXKlUa9EveKjY1Fbm6ueEtOTq51fE1BXCBP4jiIyJj4mZRXXsEeC0uUzsJtInEoFBfJq5tZs2Zh+fLlmDx5sjjrXlxcHKZOnYqkpCTMmzevxvuaNm0axo4dW22bli1b1iq+8+fPo2/fvnj55Zcxc+bMWj0XAMLDw1FaWoqrV6+ibdu2FR43l/WPDD0WXMeCyLQoFQroBbn1VzCxsEiG6TXZY0GWzPD3n55bBL1egJLVrbWyZs0afPLJJxg5cqS4bdCgQQgJCcHkyZNrlVh4eHiIK3o3hHPnzuHxxx/HmDFjsGDBgjrt49SpU1AqlfD09GywuKSgF7j0NpEpMuT6ehZvk7kzFG+zx4IsmZeTBkoFUKITcKNAC09HJtq1UVJSgq5du1bYHhYWhtLS0kZ73aSkJGRnZyMpKQk6nQ6nTp0CALRu3RoODg44e/YsHn/8cURHRyMmJgbp6ekAAJVKJSYvx44dw+jRo3HgwAH4+fkhLi4OR48exWOPPQZHR0ex52XUqFFwdXVttGNpCoafLMwriExL2YQKguzWsWCNhQVKNyQWLN4mC2atUorJhKHuiGruhRdewJo1aypsX79+PZ5//vlGe91Zs2ahc+fOmD17Nm7fvo3OnTujc+fOOH78OADg66+/RlZWFj7//HP4+PiIt27duon7KCwsxMWLF1FSUgKgbFjTtm3b0KdPHzz88MNYsGABpk6divXr1zfacTSVu8XbTC2ITEr5R1JmeQV7LCyNTi+INRa+7LEgC+fjokF6XhHScu4g1N9F6nDMzoYNG7Bv3z706NEDAHD06FEkJSVh9OjRiImJEdtVNbNSXWzevLnKNSwAYM6cOZgzZ061+4iMjDSaurxLly747bffGihCU8N1LIhMkeEzyXUsyKxl5Wuh0wtQKRXw4OJ4ZOF8nW1xEjmcGaoOzp49iy5dugAALl++DABwd3eHu7s7zp49K7bjlXJp6dljQWSSDGvLyCyvYGJhaQwz4Hg5qqHiJSyycL4uXMuirg4dOiR1CFQDrN0mMk0KscdC2jgaGmssLIxYuO3CYVBEhgkMUjnlLMmUuI4FMwsik2L4SMptwlkmFhbGMNWsN6eaJRJ7LFi8TXLF4m0i02RYW4Y9FmTWDDNC+TKxIBJ7LLhIHsmVYY58phVEJkam61gwsbAwXMOC6C7D6tuZ+VqU6PQSR0PU8O72WEgbBxEZuzsUSl6YWFgYw1hyrrpNBDSzt4GNSglBuNubRyRHCvZZEJkUBYdCkRyks3ibSKRUKsR6ozQmFiRDhh8tnASQyLTc/UzKK7NgYmFBSnV6ZOSxxoLoXj5iYsE6C5IfscaCY6GITIrhM6mXV17BxMKSZOZroRcAK6UCzRy4OB4RAPiV996lcC0LkiGZ/WYhkg2xxkJmH1ImFhbEMNTDy0nDxfGIyvmIi+RxKBTJjyBwHQsiUyQukCez9J+JhQUxDPUwzN1PRJxyluTN8JNFycyCyKSweJvMnuGKrDenmiUSGYZCcZE8kiP2WBCZJsNHkutYkNlK4+J4RBUYhkKlsseCZEhcx0LaMIjoPuJQKHnlFUwsLEka17AgqsAwFCqnsAR3inUSR0PUsAy/WTgrFJFpkevaMkwsLEhqLodCEd3PSWMFexsVAPZakPxw5W0i06RkjwWZu7QcFm8T3U+hUMC3vM6CM0OR3IjrWEgcBxEZu7uOhbwyCyYWFkJbqkNmvhYAxB9RRFTGRyzgZo8FycvdHgumFkSmSF5pBRMLi5GRW5ZUqK2UaGZvI3E0RKbFMKEBh0KR3BjmyGdaQWRa7hZvyyu1YGJhIa7nFAIom1qTV66IjIlrWXAoFMmMAgpYKRWwUvF0T2RKrFVKWMlwsWIrqQOgpmGYo9/PlcOgiO7nyylnSaYiWjVD4v89KXUYRHSfQ29GSh1Co+AlDAuRcqu8cJszQhFV4MsaCyIionpjYmEhDD+Y2GNBVJFhbZe03CLZjXclIiJqKkwsLESKONUsEwui+xlqLAqLdci7UypxNEREROaJiYWFSOUaFkRVsrVRwa18trQUDociIiKqEyYWFkAQBPHHUnMXO4mjITJNd4dDMbEwZQsWLEDPnj1hZ2cHFxeXStsoFIoKt23btlW73+zsbDz//PNwcnKCi4sLxo8fj9u3bzfCERARyRcTCwtws6AY2lI9FArA25k9FkSVMQyHSs3llLOmrLi4GMOGDcOrr75abbtNmzYhLS1NvA0ePLja9s8//zzOnTuH/fv3Y/fu3fjll1/w8ssvN2DkRETyx+lmLYBhGJSnoxo2VswliSpjGCaYxqFQJm3u3LkAgM2bN1fbzsXFBd7e3jXa54ULF7B37178/vvv6Nq1KwBg5cqVePLJJ7F06VL4+vrWK2YiIkvBX5kWQJxqloXbRFXilLPyMnHiRLi7u6N79+7YuHFjtbN9xcXFwcXFRUwqACAqKgpKpRJHjx6t9DlarRZ5eXlGNyIiS8ceCwtgqK/wY2JBVCVDjUUqV982e/PmzcPjjz8OOzs77Nu3D6+99hpu376NKVOmVNo+PT0dnp6eRtusrKzg5uaG9PT0Sp+zcOFCsfeEiIjKsMfCAjCxIHqw5q5lExtwVqimN2PGjEoLru+9JSQk1Hh/7733Hh555BF07twZb7/9NqZPn44lS5Y0aMyxsbHIzc0Vb8nJyQ26fyIic8QeCwvAxfGIHqx5+ecjPa8IpTo9rFS87tJUpk2bhrFjx1bbpmXLlnXef3h4OObPnw+tVgu1Wl3hcW9vb2RmZhptKy0tRXZ2dpV1Gmq1utJ9ERFZMiYWFsAwtMPXmYkFUVU8HNSwUSlRrNMjLbcI/m6cmrmpeHh4wMPDo9H2f+rUKbi6ulaZCERERCAnJwfx8fEICwsDABw8eBB6vR7h4eGNFhcRkdwwsbAAXHWb6MGUSgX8XG1x5UYBrt+6w8TCRCUlJSE7OxtJSUnQ6XQ4deoUAKB169ZwcHDAf/7zH2RkZKBHjx7QaDTYv38//u///g9vvvmmuI9jx45h9OjROHDgAPz8/NCuXTv0798fEyZMwNq1a1FSUoJJkyZhxIgRnBGKiKgWmFjI3J1iHbILigFwKBTRgzQXE4tCAM2kDocqMWvWLGzZskW837lzZwDAoUOHEBkZCWtra6xevRpTp06FIAho3bo1li9fjgkTJojPKSwsxMWLF1FSUiJu++KLLzBp0iT07dsXSqUSQ4cOxT//+c+mOzAiIhlgYiFzht4KB7UVnDT85yaqjqHO4votFnCbqs2bN1e7hkX//v3Rv3//avcRGRlZYfpZNzc3bN26tSFCJCKyWKxOlLnUe2aEUigUEkdDZNoMM0MxsSAiIqo9JhYylyrWV2gkjoTI9BmmZE7JKZQ4EiIiIvPDxELmUjjVLFGNcSgUERFR3TGxkLmUW5wRiqimDEOh0nLL1rIgIiKimjOJxGL16tUIDAyERqNBeHg4jh07Vm37HTt2IDg4GBqNBh07dsSePXuMHh87dmyFVVsfVMwnV8m3yoZ0GH4wEVHVPB3VsFYpoNMLSM8rkjocIiIisyJ5YrF9+3bExMRg9uzZOHHiBDp16oTo6OgKq6AaHDlyBCNHjsT48eNx8uRJDB48GIMHD8bZs2eN2vXv3x9paWni7csvv2yKwzE5ydllPRYtOCc/0QMplQqxzoLDoYiIiGpH8sTCML/4uHHj0L59e6xduxZ2dnbYuHFjpe0/+ugj9O/fH2+99RbatWuH+fPno0uXLli1apVRO7VaDW9vb/Hm6upaZQxarRZ5eXlGNzkoKtEhI7/sqqs/ayyIasRQj5TCxIKIiKhWJE0siouLER8fj6ioKHGbUqlEVFQU4uLiKn1OXFycUXsAiI6OrtD+8OHD8PT0RNu2bfHqq6/i5s2bVcaxcOFCODs7izd/f/96HJXpSMm5A0EA7GxUcLO3kTocIrPQ3IVTzhIREdWFpInFjRs3oNPp4OXlZbTdy8sL6enplT4nPT39ge379++Pf/3rXzhw4AA++OAD/PzzzxgwYAB0Ol2l+4yNjUVubq54S05OrueRmYbk7LL6ihZudlzDgqiG7s4MxSlniYiIakOWSzGPGDFC/P+OHTsiJCQErVq1wuHDh9G3b98K7dVqNdRqdVOG2CSSy6+4snCbqOaau7HGgoiIqC4k7bFwd3eHSqVCRkaG0faMjAx4e3tX+hxvb+9atQeAli1bwt3dHYmJifUP2oxcL++x8HdjfQVRTYmrb3ORPCIiolqRNLGwsbFBWFgYDhw4IG7T6/U4cOAAIiIiKn1ORESEUXsA2L9/f5XtAeD69eu4efMmfHx8GiZwM5F0z1AoIqoZw1CotJwi6PSCxNEQERGZD8lnhYqJicEnn3yCLVu24MKFC3j11VdRUFCAcePGAQBGjx6N2NhYsf3rr7+OvXv3YtmyZUhISMCcOXNw/PhxTJo0CQBw+/ZtvPXWW/jtt99w9epVHDhwAE8//TRat26N6OhoSY5RKoY1LPw5FIqoxjwdNbBSKlCqF5DBtSyIiIhqTPIai+HDhyMrKwuzZs1Ceno6QkNDsXfvXrFAOykpCUrl3fynZ8+e2Lp1K2bOnIl33nkHbdq0wa5du9ChQwcAgEqlwpkzZ7Blyxbk5OTA19cX/fr1w/z582VZR1EdwxoW/uyxIKoxlVIBXxdbJGUXIim7kKvWExER1ZDkiQUATJo0SexxuN/hw4crbBs2bBiGDRtWaXtbW1v8+OOPDRmeWcq9U4LcOyUAWGNBVFsBzezKEoubhejRspnU4RAREZkFyYdCUeMwTDXr7mADOxuTyB+JzEZAs7JevmvZBRJHQkREZD6YWMiUYQ5+TjVLVHuBzewBAFdvcmYoIiKimmJiIVOcEYqo7gyfmyQmFkRERDXGxEKm7hZus76CqLYC3Q09FgUQBE45S0REVBNMLGSKU80S1Z2hxyK/qBQ5hSUSR0NERGQemFjIlGEIB4dCEdWexloFbycNgLJeCyIiInowJhYyVKrTizUWhiEdRFQ7LQwzQ7HOgoiIqEaYWMjQ9Vt3UKoXoLZSilddiah2AplYEBER1QoTCxm6Uj50I8jdHkqlQuJoiMxTQPmUs9c4FIqIiKhGmFjI0NUbZT+EDHPxE1Ht3V0kjz0WRERENcHEQoauGBIL1lcQ1VmAG3ssTNGCBQvQs2dP2NnZwcXFpcLjmzdvhkKhqPSWmZlZ5X4DAwMrtF+0aFEjHgkRkfxYSR0ANTxDYhHkzhmhiOrKULx943YxbmtL4aDm16UpKC4uxrBhwxAREYENGzZUeHz48OHo37+/0baxY8eiqKgInp6e1e573rx5mDBhgnjf0dGxYYImIrIQPFPKkGF6TA6FIqo7Z1truNpZ41ZhCa7dLMDDvs5Sh0QA5s6dC6CsZ6Iytra2sLW9uzBoVlYWDh48WGkScj9HR0d4e3s3SJxERJaIQ6FkRluqQ8qtslW3gzyYWBDVx90CbtZZmKt//etfsLOzw7PPPvvAtosWLUKzZs3QuXNnLFmyBKWlpVW21Wq1yMvLM7oREVk69ljITHJ2IfQCYG+jgoeDWupwiMxaS3d7nErOwV9Zt6UOhepow4YNeO6554x6MSozZcoUdOnSBW5ubjhy5AhiY2ORlpaG5cuXV9p+4cKFYu8JERGVYY+FzFy5cXdhPIWCU80S1UcrTwcAQGImE4vGNGPGjCoLrg23hISEWu83Li4OFy5cwPjx4x/YNiYmBpGRkQgJCcErr7yCZcuWYeXKldBqtZW2j42NRW5urnhLTk6udXxERHLDHguZucoZoYgaTCuP8sSCPRaNatq0aRg7dmy1bVq2bFnr/X766acIDQ1FWFhYrZ8bHh6O0tJSXL16FW3btq3wuFqthlrNXmEionsxsZAZw+J4LZlYENVb6/Iei8uZBdDrBS442Ug8PDzg4eHRoPu8ffs2vvrqKyxcuLBOzz916hSUSuUDZ5IiIqK7OBRKZgxDNoKYWBDVW0AzO1gpFbhTokNaXpHU4RCApKQknDp1CklJSdDpdDh16hROnTqF27eNe5W2b9+O0tJSjBo1qsI+jh07huDgYKSkpAAoGzK1YsUKnD59Gn/99Re++OILTJ06FaNGjYKrq2uTHBcRkRywx0JmDInFQ16cf52ovqxVSgS62yMx8zYSM2/Dz6X6AmBqfLNmzcKWLVvE+507dwYAHDp0CJGRkeL2DRs2YMiQIZUuoldYWIiLFy+ipKQEQNmwpm3btmHOnDnQarUICgrC1KlTERMT06jHQkQkN0wsZOTGbS2yC4qhUNwdG05E9dPawwGJmbdxOfM2+jzUsMN1qPY2b95c5RoW9zpy5EiVj0VGRkIQBPF+ly5d8NtvvzVEeEREFo1DoWTkUkZZb4W/qx1sbVQSR0MkD4Y6CxZwExERVY+JhYxcyswHADzkxd4KoobSyrOsXolTzhIREVWPiYWMGHosWnuyvoKoobT2KPs8XWZiQUREVC0mFjLyZwZ7LIgamqHH4mZBMW4VFEscDRERkeliYiEjhqEabdhjQdRg7GysxNmgLrHXgoiIqEpMLGTi5m0tbpbPCGUoNiWihtHOpyxZv5CWJ3EkREREpouJhUxcTC8bBsUZoYgaXnsfJwDA+VQmFkRERFVhYiET58p/8Bh+ABFRw2nvW55YsMeCiIioSkwsZMLwg+dhXyYWRA2tvY8zAOBiRj5KdHqJoyEiIjJNTCxk4lxqLgDgYT8mFkQNrbmrLRzVVigu1eOvrAKpwyEiIjJJTCxkoKhEh8vlP3YMV1aJqOEolQq0M9RZpOVKHA0REZFpYmIhAxfT86HTC2hmbwMvJ7XU4RDJklhnwQJuIiKiSjGxkIGz5cOg2vs6QaFQSBwNkTwZJkY4m8LEgoiIqDJMLGTgxLUcAECov4ukcRDJWYh/2TDDM9dzoNMLEkdDRERkephYyMDJpFsAgC4tXCWOhEi+2ng6wkFthYJinbhuDBEREd3FxMLMZRcU468bZYXbnVu4SBsMkYyplAqxV/BEeTJPREREdzGxMHOG3opWHvZwsbOROBoieetSnryfuMbEgoiI6H5MLMzcCQ6DImoyXQLKPmfx7LEgIiKqgImFmfvtr2wAQNdAJhZEja1zC1coFcC1m4VIzbkjdThEREQmhYmFGcsrKsGp5BwAwCOt3aUNhsgCONtao1N5ncUvf2ZJGwwREZGJYWJhxn67fBM6vYAgd3s0d7WTOhwii/BoGw8AwC+XmFgQERHdi4mFGfu5/IppL/ZWEDWZRx8qSyx+vXQDpTq9xNEQERGZDiYWZkqnF/DjuQwAQFR7L4mjIbIcnZo7w0ljhbyiUsRzdigiIiIREwszdfxqNm7c1sLZ1ho9WzWTOhwii2GlUuKJ9t4AgG9Pp0ocDRERkelgYmGmdsRfBwA80d4L1ir+MxI1pWc6+wEAvj+TBm2pTuJoiIiITINJ/CJdvXo1AgMDodFoEB4ejmPHjlXbfseOHQgODoZGo0HHjh2xZ88eo8cFQcCsWbPg4+MDW1tbREVF4dKlS415CE3qxm0tvjtVdqX0ufAWEkdDZHkiWjWDt5MGuXdKsPNEitThWIyrV69i/PjxCAoKgq2tLVq1aoXZs2ejuLjYqN2ZM2fQu3dvaDQa+Pv7Y/HixQ/cd1JSEgYOHAg7Ozt4enrirbfeQmlpaWMdChGRLEmeWGzfvh0xMTGYPXs2Tpw4gU6dOiE6OhqZmZmVtj9y5AhGjhyJ8ePH4+TJkxg8eDAGDx6Ms2fPim0WL16Mf/7zn1i7di2OHj0Ke3t7REdHo6ioqKkOq1GtPXwZxTo9OjV35sJ4RBJQKRV4qXcQAODjw4koKmGvRVNISEiAXq/HunXrcO7cOXz44YdYu3Yt3nnnHbFNXl4e+vXrh4CAAMTHx2PJkiWYM2cO1q9fX+V+dTodBg4ciOLiYhw5cgRbtmzB5s2bMWvWrKY4LCIi2VAIgiBIGUB4eDi6deuGVatWAQD0ej38/f0xefJkzJgxo0L74cOHo6CgALt37xa39ejRA6GhoVi7di0EQYCvry+mTZuGN998EwCQm5sLLy8vbN68GSNGjHhgTHl5eXB2dsbXRy7C1sFR3H7vOyVAqLD93jeyqrf1btuKz6/4GhX3d/3WHaw8eAl6Adg8rhsi23o+8HiIqOHdKdahz5JDyMzXol97LzzT2Q8KhdRRGSu4nY9nI9oiNzcXTk5OUofTKJYsWYI1a9bgr7/+AgCsWbMG7777LtLT02FjYwMAmDFjBnbt2oWEhIRK9/HDDz/gb3/7G1JTU+HlVTYZxtq1a/H2228jKytL3E91DOcNOb/XRGQZ6vN9ZtVIMdVIcXEx4uPjERsbK25TKpWIiopCXFxcpc+Ji4tDTEyM0bbo6Gjs2rULAHDlyhWkp6cjKipKfNzZ2Rnh4eGIi4urNLHQarXQarXi/dzcXADA65/FQak2zfUhng1rji4+GuTl5UkdCpHFmjOgJSZ9cQJ7T17B3pNXpA6nAr22EEDVFzrkIDc3F25ubuL9uLg4PProo0bJQHR0ND744APcunULrq4Ve3nj4uLQsWNHMakwPOfVV1/FuXPn0Llz5wrPqeq8we9kIjJ3hu+xupw7JE0sbty4AZ1OZ/RlDgBeXl5VXllKT0+vtH16err4uGFbVW3ut3DhQsydO7fC9pQ1Y2t0HFL4sPxGRPQgN2/ehLOzs9RhNLjExESsXLkSS5cuFbelp6cjKCjIqJ3hfJCenl5pYlHVecXwWGWqOm/4+/vX7iCIiExUXc4dkiYWpiI2NtaoFyQnJwcBAQFISkqS5cm4MeTl5cHf3x/JyckcBlBDfM9qh+9X7eXm5qJFixZGV/RN0YwZM/DBBx9U2+bChQsIDg4W76ekpKB///4YNmwYJkyY0NghVsDzRv3xM117fM9qj+9Z7dXn3CFpYuHu7g6VSoWMjAyj7RkZGfD29q70Od7e3tW2N/w3IyMDPj4+Rm1CQ0Mr3adarYZara6w3dnZmX+EteTk5MT3rJb4ntUO36/aUyoln6ejWtOmTcPYsWOrbdOyZUvx/1NTU/HYY4+hZ8+eFYqyqzpHGB6rjLe3d4XZCB/0HJ43Gg4/07XH96z2+J7VXl3OHZKebWxsbBAWFoYDBw6I2/R6PQ4cOICIiIhKnxMREWHUHgD2798vtg8KCoK3t7dRm7y8PBw9erTKfRIRkXQ8PDwQHBxc7c1QM5GSkoLIyEiEhYVh06ZNFU58ERER+OWXX1BSUiJu279/P9q2bVvpMCjDc/744w+j2Qj3798PJycntG/fvhGOmIhIniS/jBUTE4NPPvkEW7ZswYULF/Dqq6+ioKAA48aNAwCMHj3aqLj79ddfx969e7Fs2TIkJCRgzpw5OH78OCZNmgQAUCgUeOONN/D+++/ju+++wx9//IHRo0fD19cXgwcPluIQiYioARiSihYtWmDp0qXIyspCenq6UR3Ec889BxsbG4wfPx7nzp3D9u3b8dFHHxkNW/r3v/9tNKyqX79+aN++PV544QWcPn0aP/74I2bOnImJEydW2itBRESVk7zGYvjw4cjKysKsWbOQnp6O0NBQ7N27VyycS0pKMroi1bNnT2zduhUzZ87EO++8gzZt2mDXrl3o0KGD2Gb69OkoKCjAyy+/jJycHPTq1Qt79+6FRqOpUUxqtRqzZ8/mCaUW+J7VHt+z2uH7VXtye8/279+PxMREJCYmonnz5kaPGWYvcXZ2xr59+zBx4kSEhYXB3d0ds2bNwssvvyy2zc3NxcWLF8X7KpUKu3fvxquvvoqIiAjY29tjzJgxmDdvXo1jk9t73RT4ntUe37Pa43tWe/V5zyRfx4KIiIiIiMyf5EOhiIiIiIjI/DGxICIiIiKiemNiQURERERE9cbEgoiIiIiI6o2JRQ1ptVqEhoZCoVDg1KlTUodjsq5evYrx48cjKCgItra2aNWqFWbPno3i4mKpQzMpq1evRmBgIDQaDcLDwysszkV3LVy4EN26dYOjoyM8PT0xePBgoxl96MEWLVokTsVNTYvnjgfjeaNmeN6oOZ436q+u5w0mFjU0ffp0+Pr6Sh2GyUtISIBer8e6detw7tw5fPjhh1i7di3eeecdqUMzGdu3b0dMTAxmz56NEydOoFOnToiOjjZanIvu+vnnnzFx4kT89ttv2L9/P0pKStCvXz8UFBRIHZpZ+P3337Fu3TqEhIRIHYpF4rnjwXjeeDCeN2qH5436qdd5Q6AH2rNnjxAcHCycO3dOACCcPHlS6pDMyuLFi4WgoCCpwzAZ3bt3FyZOnCje1+l0gq+vr7Bw4UIJozIfmZmZAgDh559/ljoUk5efny+0adNG2L9/v9CnTx/h9ddflzoki8JzR93xvGGM54364Xmj5up73mCPxQNkZGRgwoQJ+Oyzz2BnZyd1OGYpNzcXbm5uUodhEoqLixEfH4+oqChxm1KpRFRUFOLi4iSMzHzk5uYCAP+mamDixIkYOHCg0d8bNQ2eO+qH5427eN6oP543aq6+5w3JV942ZYIgYOzYsXjllVfQtWtXXL16VeqQzE5iYiJWrlyJpUuXSh2KSbhx4wZ0Op24sryBl5cXEhISJIrKfOj1erzxxht45JFH0KFDB6nDMWnbtm3DiRMn8Pvvv0sdisXhuaN+eN4wxvNG/fC8UXMNcd6wyB6LGTNmQKFQVHtLSEjAypUrkZ+fj9jYWKlDllxN37N7paSkoH///hg2bBgmTJggUeQkJxMnTsTZs2exbds2qUMxacnJyXj99dfxxRdfQKPRSB2ObPDcUTs8b5Ap4HmjZhrqvKEQBEFowLjMQlZWFm7evFltm5YtW+Lvf/87/vOf/0ChUIjbdTodVCoVnn/+eWzZsqWxQzUZNX3PbGxsAACpqamIjIxEjx49sHnzZiiVFpnDVlBcXAw7Ozt8/fXXGDx4sLh9zJgxyMnJwbfffitdcCZu0qRJ+Pbbb/HLL78gKChI6nBM2q5du/DMM89ApVKJ23Q6HRQKBZRKJbRardFjVDM8d9QOzxsNg+eNuuN5o+Ya6rxhkYlFTSUlJSEvL0+8n5qaiujoaHz99dcIDw9H8+bNJYzOdKWkpOCxxx5DWFgYPv/8c/6AuU94eDi6d++OlStXAijrpm3RogUmTZqEGTNmSByd6REEAZMnT8a///1vHD58GG3atJE6JJOXn5+Pa9euGW0bN24cgoOD8fbbb3M4QCPjuaP2eN6oHs8btcPzRu011HmDNRbVaNGihdF9BwcHAECrVq14YqhCSkoKIiMjERAQgKVLlyIrK0t8zNvbW8LITEdMTAzGjBmDrl27onv37lixYgUKCgowbtw4qUMzSRMnTsTWrVvx7bffwtHREenp6QAAZ2dn2NraShydaXJ0dKxwErC3t0ezZs2YVDQBnjtqh+eNB+N5o3Z43qi9hjpvMLGgBrV//34kJiYiMTGxwgmUnWNlhg8fjqysLMyaNQvp6ekIDQ3F3r17KxTmUZk1a9YAACIjI422b9q0CWPHjm36gIioQfG88WA8b9QOzxvS4VAoIiIiIiKqN1ZGERERERFRvTGxICIiIiKiemNiQURERERE9cbEgoiIiIiI6o2JBRERERER1RsTCyIiIiIiqjcmFkREREREVG9MLIiIiIiIqN6YWBARERERUb0xsSCS2OHDh9GlSxeo1Wq0bt0amzdvljokIiIyYTxvkKliYkEkoStXrmDgwIF47LHHcOrUKbzxxht46aWX8OOPP0odGhERmSCeN8iUKQRBEKQOgkiusrKy0LFjR0yZMgXvvPMOAODIkSOIjIzEDz/8gH379uH777/H2bNnxeeMGDECOTk52Lt3r1RhExGRRHjeIHPGHguiRuTh4YGNGzdizpw5OH78OPLz8/HCCy9g0qRJ6Nu3L+Li4hAVFWX0nOjoaMTFxUkUMRERSYnnDTJnVlIHQCR3Tz75JCZMmIDnn38eXbt2hb29PRYuXAgASE9Ph5eXl1F7Ly8v5OXl4c6dO7C1tZUiZCIikhDPG2Su2GNB1ASWLl2K0tJS7NixA1988QXUarXUIRERkQnjeYPMERMLoiZw+fJlpKamQq/X4+rVq+J2b29vZGRkGLXNyMiAk5MTrzoREVkwnjfIHHEoFFEjKy4uxqhRozB8+HC0bdsWL730Ev744w94enoiIiICe/bsMWq/f/9+RERESBQtERFJjecNMlecFYqokb311lv4+uuvcfr0aTg4OKBPnz5wdnbG7t27ceXKFXTo0AETJ07Eiy++iIMHD2LKlCn4/vvvER0dLXXoREQkAZ43yFwxsSBqRIcPH8YTTzyBQ4cOoVevXgCAq1evolOnTli0aBFeffVVHD58GFOnTsX58+fRvHlzvPfeexg7dqy0gRMRkSR43iBzxsSCiIiIiIjqjcXbRERERERUb0wsiIiIiIio3phYEBERERFRvTGxICIiIiKiemNiQURERERE9cbEgoiIiIiI6o2JBRERERER1RsTCyIiIiIiqjcmFkREREREVG9MLIiIiIiIqN6YWBARERERUb39Pw5R8okGPaYjAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "prior = SplineTrapezoidal(lb, plb, pub, ub)\n", "\n", "fig, (ax1, ax2) = plt.subplots(1, 2, sharex=True, figsize=figsize)\n", "ax1.plot(x, prior.pdf(x))\n", "ax1.set_xlim(-4, 4)\n", "ax1.set_ylim(0, 0.25)\n", "ax1.set_xlabel(\"x0\")\n", "ax1.set_ylabel(\"prior pdf\")\n", "ax2.plot(x, prior.log_pdf(x))\n", "ax2.set_ylim(-20, 0)\n", "ax2.set_xlabel(\"x0\")\n", "ax2.set_ylabel(\"prior log-pdf\")\n", "plt.suptitle(\"Smoothed trapezoidal prior\")\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Unbounded parameters\n", "\n", "If your variables are *unbounded*, remember that PyVBMC supports `scipy.stats` univariate and multivariate distributions, so you could use standard priors such as a multivariate normal distribution or a multivariate Student's t distribution with 3-7 degrees of freedom. \n", "See for example [this page on the Stan wiki](https://github.com/stan-dev/stan/wiki/Prior-Choice-Recommendations) for a broader discussion on prior choice.\n", "\n", "### Smooth-box prior (`SmoothBox`)\n", "\n", "As an alternative to these common choices, we also provide a smooth-box distribution which is uniform within an interval (typically, the plausible range) and then falls with Gaussian tails with standard deviation(s) equal to `scale` outside the interval. The smoothbox prior is implemented by the `SmoothBox` class." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lb = -np.inf\n", "ub = np.inf\n", "plb = -2\n", "pub = 2\n", "# We recommend setting the scale as a fraction of the plausible range.\n", "# For example `scale` set to 4/10 of the plausible range assigns ~50%\n", "# (marginal) probability to the plateau of the distribution.\n", "# Also similar fractions (e.g., half of the range) would be reasonable.\n", "# Do not set `scale` too small with respect to the plausible range, as it\n", "# might cause issues.\n", "p_range = pub - plb\n", "scale = 0.4 * p_range\n", "\n", "prior = SmoothBox(plb, pub, scale)\n", "\n", "x = np.linspace(plb - 2 * p_range, pub + 2 * p_range, 1000)\n", "fig, (ax1, ax2) = plt.subplots(1, 2, sharex=True, figsize=figsize)\n", "ax1.plot(x, prior.pdf(x))\n", "ax1.set_xlim(x[0], x[-1])\n", "ax1.set_ylim(0, 0.25)\n", "ax1.set_xlabel(\"x0\")\n", "ax1.set_ylabel(\"prior pdf\")\n", "ax2.plot(x, prior.log_pdf(x))\n", "ax2.set_ylim(-20, 0)\n", "ax2.set_xlabel(\"x0\")\n", "ax2.set_ylabel(\"prior log-pdf\")\n", "plt.suptitle(\"Smooth-box prior (unbounded parameters)\")\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4. Using a prior with PyVBMC\n", "\n", "\n", "To conclude, we run inference on a couple of problems using some of the priors introduced in this notebook.\n", "\n", "### Bounded example\n", "\n", "In this example, we use the spline-smoothed trapezoidal prior (`SplineTrapezoidal`) introduced in this notebook. The code below shows several equivalent ways in which the prior can be set in PyVBMC (see the comments in the code below for details)." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Beginning variational optimization assuming EXACT observations of the log-joint.\n", " Iteration f-count Mean[ELBO] Std[ELBO] sKL-iter[q] K[q] Convergence Action\n", " 0 10 -1.41 1.15 310361.34 2 inf start warm-up\n", " 1 15 -3.31 0.26 13.00 2 inf \n", " 2 20 -3.05 0.02 0.36 2 9.32 \n", " 3 25 -3.03 0.01 0.20 2 4.89 \n", " 4 30 -3.02 0.00 0.04 2 0.947 end warm-up\n", " 5 35 -3.06 0.00 0.01 2 0.332 \n", " 6 40 -3.02 0.00 0.00 2 0.193 \n", " 7 45 -2.71 0.00 0.07 5 2.74 \n", " 8 50 -2.64 0.00 0.05 6 1.4 rotoscale, undo rotoscale\n", " 9 55 -2.59 0.01 0.01 7 0.536 \n", " 10 60 -2.55 0.00 0.00 10 0.203 \n", " 11 65 -2.51 0.00 0.00 13 0.19 \n", " 12 70 -2.44 0.00 0.01 16 0.588 \n", " 13 75 -2.44 0.00 0.00 18 0.0273 \n", " 14 80 -2.43 0.00 0.00 19 0.0392 \n", " 15 85 -2.43 0.00 0.00 20 0.024 stable\n", " inf 85 -2.42 0.00 0.00 50 0.024 finalize\n", "Inference terminated: variational solution stable for options.tol_stable_count fcn evaluations.\n", "Estimated ELBO: -2.424 +/-0.002.\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "D = 2 # Still in 2-D\n", "lb = np.zeros((1, D))\n", "ub = 10 * np.ones((1, D))\n", "plb = 0.1 * np.ones((1, D))\n", "pub = 3 * np.ones((1, D))\n", "\n", "# Define the prior and the log-likelihood\n", "prior = SplineTrapezoidal(lb, plb, pub, ub)\n", "\n", "\n", "def log_likelihood(theta):\n", " \"\"\"D-dimensional Rosenbrock's banana function.\"\"\"\n", " theta = np.atleast_2d(theta)\n", "\n", " x, y = theta[:, :-1], theta[:, 1:]\n", " return -np.sum((x**2 - y) ** 2 + (x - 1) ** 2 / 100, axis=1)\n", "\n", "\n", "x0 = np.ones((1, D))\n", "np.random.seed(42)\n", "vbmc = VBMC(log_likelihood, x0, lb, ub, plb, pub, prior=prior)\n", "# vbmc = VBMC(log_likelihood, x0, lb, ub, plb, pub, log_prior=prior.log_pdf) # equivalently\n", "# vbmc = VBMC(lambda x: log_likelihood(x) + prior.log_pdf(x), x0, lb, ub, plb, pub) # equivalently\n", "vp, results = vbmc.optimize()\n", "vp.plot();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Unbounded example\n", "\n", "We run now another example with an unbounded prior. In this case, we apply a multivariate normal prior with zero mean and diagonal covariance, with variance $\\sigma^2 = 9$ in each dimension (we chose $\\sigma$ equal to half the plausible range). \n", "Note that this is equivalent to setting a normal distribution separately for each variable. The code below shows a couple of equivalent ways in which the prior could be initialized in PyVBMC using `scipy.stats` distributions." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Beginning variational optimization assuming EXACT observations of the log-joint.\n", " Iteration f-count Mean[ELBO] Std[ELBO] sKL-iter[q] K[q] Convergence Action\n", " 0 10 -3.17 0.83 5094.29 2 inf start warm-up\n", " 1 15 -2.90 0.08 0.24 2 inf \n", " 2 20 -2.81 0.00 0.09 2 2.52 \n", " 3 25 -2.82 0.00 0.01 2 0.28 \n", " 4 30 -2.80 0.00 0.01 2 0.224 end warm-up\n", " 5 35 -2.77 0.00 0.01 2 0.211 \n", " 6 40 -2.79 0.00 0.00 2 0.161 \n", " 7 45 -2.58 0.00 0.17 5 4.77 \n", " 8 50 -2.49 0.00 0.05 6 1.42 \n", " 9 55 -2.43 0.00 0.02 7 0.778 rotoscale, undo rotoscale\n", " 10 60 -2.38 0.00 0.03 10 0.87 \n", " 11 65 -2.36 0.00 0.00 13 0.144 \n", " 12 70 -2.32 0.00 0.00 16 0.165 \n", " 13 75 -2.32 0.00 0.01 18 0.183 \n", " 14 80 -2.31 0.00 0.00 18 0.0557 stable\n", " inf 80 -2.28 0.00 0.00 50 0.0557 finalize\n", "Inference terminated: variational solution stable for options.tol_stable_count fcn evaluations.\n", "Estimated ELBO: -2.280 +/-0.001.\n" ] }, { "data": { "image/png": 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IKgBDGREREVEFYCgjommTTCYxMjKCZDJZUc9FRDQd1NN9AUQ0cyWTSRQKBSSTSRiNRgBAuVye8scrFIpJn0v+tdFoFM9LRFTpuFJGRNPGaDRCrVYfkOA09rkmBjQiokMBV8qIaNocyJWsic81dvWNiOhQwFBGRIcdblsS0aGIoYyIDgmpVAojIyMAAKfTCUmSpvmKiIgOLIYyIqooqVRqXC2Y0WiEJElIJpOIx+Pjfp8rYkR0OGEoI6KKIhfph8NhVFVVIZlMQpIkGI1GmM1m8biJpzan+tw8lUljeb1eBAKBKT3WbrfD5XId5CuimYyhbIabeJPiTYumm9FoFNuU2WwWVqtVrJ7J25Z+vx9+vx8Oh2O/nnuyFhw0c3m9XrS1tSGVSk3p8ZIkwe12M5jRQcNQNsMlk0nEYjH4/X60trbypkXTTl4V0+l0UKvVIoTFYjH09vbCbrcjlUqhWCzu1vJiX28q5DcefG0TAAQCAaRSKaxduxZtbW17fazb7caqVasQCAQYyuigYSib4YxGI/x+P3Q6nbhZ8aZFlSAcDouVMPl1WiqVMDw8jGg0Cq1Wi2w2C6fTKV6v+3pTwRVgmkxbWxuWLVs23ZdBxOaxM53RaERrayssFou4YY29yREdLPsai1RVVQXgX4X/DocDTqcTKpUKVqsVsVgMxWIRHo9HPMfEBrIcu0REhxKulM0gextf4/f70dvbi5aWFjgcDpTLZSgUCnFDlE/A7cnYcTdEE0322tvTWCSDwSDqyrLZLJLJJIrFIrLZLFpbW+F0OuHxeKBQKDA8PCxOZkqSJF6j8jamvAIsSRJfo0RU8RjKCMlkEl6vF4lEAul0erc/G3tjIzpQ5NUsAPB4PNDpdOLPPB4P+vv7YbVakcvlkE6nUV9fP+4NQjqdRmtrK1QqFYxGo3gDIb9mAUCtViOZTIpDAU6nc1q+ViKiqWAoO8yNLXzeU6gaW2eTTqcxNDSEbDaLxsZGADhgswmJxpJXtuSaxnA4DJVKJd4kDA4Owuv1Yu7cubDZbFAqR6st3G43SqUSlEolVCqVqDvzeDxiRc1ut4vXbF9fH2KxGHw+H1auXMnXMhFVLIayw9zIyAji8TjMZjOcTuekAU2SJCxfvlysKBSLRUiSBLVaDbWaLxE6+LLZLIDR12sul4NKpYIkSdDr9YjFYojFYqLGLJFIIBKJoKamBg0NDeLj4vE4YrEYZs+eLVbh4vE4MpkM8vn8uJU5tn0hokrEO+4MsqcanrF1OABEgAN231aaSn0ZEbD3VdqxtYrAaFF/KpVCKpWCQqFAdXU1GhsbkU6nUSqVMDAwgFgshnA4DACw2WwwGAzjTmhKkgSVSoVwOCxCXiqVgl6vR2Njo2i1wbYvRFSpGMoOc/JJSvnmM7F4emx/MnmEjfzYsdtBcuG1vOrW2to6XV8SHSLGhp+JoUz+M7lJLAC0tLQgmUzC5/OJ+kaDwYBIJIJ8Po/+/n6o1Wq4XC6YTCYAEG8YjEYjAoEA0uk0tFotisUiVCoVcrkcbDbbbvVkDGREVIkYyg5zY/s3yeFMHmHj8/mg1WohSRKcTqcYYTM2gOVyOTQ3N0/63GNXO3iDo4n21vNO/rNsNiuaxDocDjgcDvh8PmzduhU6nQ5OpxOZTAZ+vx/BYBBGoxHd3d2iLcbAwACy2Sz6+/uRTCZhs9mgUqnEa7lYLGJoaEgcBuC8TCKqZAxlh6mxW0eTrUpIkgStVotwOAyTyST6k02sNVOpVNDpdOJjx25tTpwGwBsdjTU2/OypHcvY14zH4wEADA0NQalUIpFIYP78+ejs7EQgEEA2m4VKpYLJZMLAwAAUCgVqa2vR1dUFv9+PUCiEJUuWYOHCheIAQV9fH4rFIkZGRiBJEmbNmnXQv24ioveLoewwNVkQA0a3e7LZLFKp1Lji6bEjbIDR8SOSJKGlpQUAxq1oyMFtsmkARPvi9/uxceNGaLVa0Xdsx44d8Pv9MBgMiEajyGQymDdvHhwOB/x+P/r7+6FUKlFdXY18Po9wOIxisYhyuQyn0wmv1wuj0YhMJgNgdBXX7/fDZrMhk8lAkiSkUimMjIxwzisRVSyGssOUfNORb15jT1+Gw2GMjIxAo9FApVKJWYJ9fX144403UCgU4HK5xNamfMOSi6rHblvK9Wi8qdFU+f1+xONx+P1+qFQqEaCGhoYQCoUQiUSg1+sBQIQxvV6PWbNmIZfLQaPRwOv1IpPJwOfz4bjjjsP8+fOxefNmtLe3o76+Hi0tLeINyLx588TA6bEF/iz4J6JKw1B2GNhbp/6x9Ho9kskkPB6PKJ4uFAro7++HVqtFMBhEoVBAoVBAZ2enKJ4+8sgjkc/nodVqkU6nIUkSisUiTCYTWlpaYDAYRA8posmMfY06HA709/dDpVKhVCqhv78fkiRBo9FAo9FAqVRCrVYjGo0ilUohk8ngiCOOADC6optOp2Gz2RCPx6FQKNDX14fW1lZotVooFArs2rULsVgMAET/s/r6emQyGfHGolwuj6t5G3t97PxPe+N2u6f0OLvdzsHltN8Yyg5DqVQKHo8H8Xgc0WgUTU1NMBqN6OvrQ2dnJ3K5HKLRqAhomUwGVqsVdXV1qK+vRyAQgE6nQywWQ6FQQCQSgdFoRDqdRiaTgcfjgcPhgMlk4g2MpmTs68ThcOD444+Hx+NBV1cXisUiAIjaxWKxiNbWVkSjUSiVShiNRsyZMwe7du1CKBRCZ2cndDodbDYbAoEAent7kUgkUFVVhWKxiIGBAWQyGSgUCthsNvT29sLhcKC5uRk2m03M0ZzYCoZtXmhv7HY7JEnCqlWrpvR4SZLgdrsZzGi/MJQd4ibrBSWPmens7BQ1YgAQj8dRLBaRTqdRKBTEyli5XEYgEEA+n8fcuXPhdDqRy+VgNBrFyoXc3X/btm1QKpXI5XIcWUP7tKdeZZIkweFwIJFIoLu7GwBEfaJGoxH1YslkEhqNBm+++Sa8Xi+8Xq84EWwymWC1WtHe3o5wOIyamhrU1dUhmUyiVCph2bJliEajUKlUyOfzGBwchE6nEycz5evbU9sOorFcLhfcbjcCgcA+H+t2u7Fq1SoEAgGGMtovDGWHuLEF/WOP+yeTSdHtXB7YLNePVVdXQ6PRIBgMwul0oqqqCp2dnUin0+KdXSqVQl1dnWg9IPeM0uv10Gg0ohkn0d7sKfSkUil4vV4MDw+jUCigr69P1JmZzWaYTCbRiywQCCCRSCCfz4+rcczlcgAApVKJTCaDoaEhEeaOPPJIHHXUUejr6xOfs7GxESaTCU6nE36/H36/Xzwfa8poKlwuF0MWHVQMZYe4sf2e5Jufw+GA0WgUpyX9fj+2bNkCAFiyZAkkSUIul0Mmk0FPTw8SiQRKpRKKxSKam5uRTqcRiUQQDofFr4eHh6HRaGAwGGA0GmEwGOD3+wGM3nhTqZT4vDzRNjONXRWTfw1MPjtVHuklByu73Y5sNovm5maUSiUAo2FL7qmXTCZhtVpRVVUFvV6PcrmMWCwmVi3k12Q8HodGo0Emk0FfXx8SiQRcLtduI5ba29uhUqkAgI2QiahiMJQd4uRtoYmNOuUGsNlsFj6fD9u3b4fRaITFYsGiRYtQVVUlVtDa29ths9lQV1cHhUKBfD4PAIhGo2hoaEBnZyeKxSKsVqtYvSiVSvB6vdDpdBgaGkJNTY0IaTzRNjNNHONVKBSgVqvhdDp3O4xiNBrFtqJcvyhJkphf2d/fD7vdjlgshlwuh1KphGAwKA6UBINBSJKEwcFBGI1GNDc3o66uDr29vQiHwwgGg/B4PLDb7VAqleK5e3t74fP5YLVakcvlxIgmGRsiE9F0Yig7TEiStFvNjtFoRCwWg9frRSwWQ7lcRldXF4aHh2E2m5FIJODz+ZBKpRCPxxEKhdDb2ytOwRmNRiQSCWSzWZRKJXFiUx5h09raCp1Oh6qqKuh0ut1Wymhmmfizn+x1IPcKA0a3E+vq6jA0NIRgMIhQKIREIoFkMomRkREEAgHo9XrU1NQgFoshFAqJPmQqlQoKhQLRaBTRaBT5fB7ZbBbRaFScprTb7YjH42JFTA50Wq1WjArb0/gnvoaJaDowlB3G5OauGo0G8+fPR7lchl6vh8fjgclkQiqVQrlcRi6XQzqdRjweh16vF+0J5BmCWq0Ww8PDcLlciEajkCQJNTU1AIDa2trdVhV4M5uZ9vU6kE8FBwIBlMtlOBwO1NXVwWw2Y9euXchms+jp6YEkSYjFYlCr1dBoNLBYLPB6vUilUigUCshms4jH42I+plqtFi00VCoVGhoaMGfOHAQCAfT19Ynh5QsXLhSBUD6kIk8RkKdZ8E0FEU0nNpc6jEmShNbWVtTX10On06GtrQ3V1dUwm81IpVLYsmULwuEwSqUSyuWy6NpvNpths9lQKpWQyWREnY7H44FWq0W5XBbNOCe2FhgZGRHbV0RjjYyMIJFIYHh4GOFwWMyrNBqNOPbYY2EymdDY2AiFQgFJkmA2m2EwGMRrs1AoIJfLIZlMijcTKpUKBoMBpVIJpVIJzc3NsFgs2L59OzZv3ox4PI5IJCI+v1z4L2/dx+NxxOPxcW0xnE4nQxkRTQuulM0QdXV1MBgMAEZXMDo6OhCNRpFOpwGM1v9oNBrYbDYsWrQI1dXV6O/vRzgcRiQSQSwWg9lsRjweh91uR6lUEh8r49YPyfY0wshgMKC+vl60Zmlvb0cgEIDdbhevK7mucWRkBOl0GoFAAMFgUAQxrVaLaDSKcrmMUqmEmpoaVFVVIZVKoaamBmq1Gv39/TCZTLBYLGhtbYXBYMDOnTsRDocRDofFNcntMfh6JaJKwFD2Ictms8hms+LXcufxgyWZTKJYLIoiaa/Xi46ODuzatUusdhmNRpRKJXF6bdOmTWhra4Pdbkcul8Pw8DAAYHh4GJlMBlVVVWhraxONZOXnkFcbrFbrQf2aqPJNFtDlLUO5xgsA3nzzTfj9fmzbtg0LFiyA1WqFXq/HyMgIdDqd6J83dis9lUpBrVaLWkiNRiPmtvb398NsNiMUCkGSJNjtduj1ejG+KRwOw2AwIBaLIZvNTlpXRkQ0XRjKpqijowMPPvggurq68IlPfAJHHXUUli9fvt/Pc8stt+D73//+Ab22ycYspdNpEZIcDgeUSqWoIdNqtaiqqoJCoYBSqYTBYIDZbIZarRYNO+VTaGq1GiqVCk6nE4VCAZIkIRwOixYZ6XQajY2NsNlsqKqqEgPL9zT6iRMADi97+jlPHGEkh365VUskEkE6nUaxWEQgEEA0GsXWrVvR0tIi5lwODAzAarWKZrByU1n5MIA8yDyfz4vt9lAohHQ6jdraWtFXL5vNQq1WiwMuDQ0NYqs+mUyKFWQZX6NENF0YyqZgx44dWLlyJU488UQkk0n88pe/hEajwfXXX4/LLrtsv57rpptuwvXXXy9+HYvF0Nzc/IGuT6FQjDvKL0kSPB4PRkZGRM2N3KHfbDbDbDaLhpvlchnBYBAajUZ0Uy+VSvD7/dBqtaJnVLlcRk1NDeLxOPL5PDweD7LZLGpqapDNZuFwOMSwc7k1hlyfw5WImUfuQwaMvg4ymYx4kxCJRPDqq69iZGREtKsARluweDweGI1G0SjWbDYjk8mIKRTygRQ50KVSKWSzWZTLZajVahSLRajVatTW1mLevHnIZrNQKpXw+/3ikIBcayn//8IQRkSVgqFsH4rFIm699Vacc845uP/++6FQKLB+/Xo8+OCD+NrXvoZcLocvfvGLU34+nU4HnU53wK9zbGd/AOjq6kIul0M4HMbChQths9lQKBRQV1eHXC6HoaEhDA8PI5VKoVQqIZfLiZNu8vaq3CtKLpbO5XJwuVxidcHhcKClpQV1dXXipOfOnTuRyWSg1+tRX1+/23gdOnyNfWPg9/uRzWbh9/vhcDhEkb986nd4eBherxeNjY1YsGABAoEAwuEwUqkUbDYbstksQqEQ4vG4CFYKhUK8aVAqldDr9dDpdNDr9bBYLCiXy0in0+LksEKhgFarhVqtRk1NDRQKhXiTwLmXRFSJGMr2oVwuo7OzE0uWLBHvqFesWAGHwwGtVoubb74ZDocD55xzzrRe59jO/vF4XBTlNzU1ob+/HzabDalUCul0GkNDQ/B6vSiXy6Lfk1qthl6vR6lUEjMyE4kEAIhTb6FQCA6HA0cddRTK5TJsNhv6+/uRyWTg8/kAQGwhVVdXw+v1ipYZbMh5+BtbR+ZwOEQgG0seau9wOFAsFuFyudDa2gq73S5qvlQqFeLxOAYGBhCPx6HVauFwOGA2m+H3+8eFLa1WC2D0dafX61EsFlEoFDA4OAitVouamhrMmTMHzc3NOOKII0QIkwMk514SUSVhKNsHtVqNj370o9iyZQsGBwdRX18PAGhpacHVV1+Nvr4+rF27Fqeddtq0/sUuv/sfe6pMXrEYGRlBb28vyuUyIpEItm3bhlwuh3w+L+p95K2gcDiMfD4Pg8GATCYDnU4nOqrHYjH4/X7Mnz8fADAwMIDe3l5YrVZYrVY0NDRAr9dj0aJFiMVisNvtu938GMoOX5P1+Bpb5J9Op9Hf3w+LxYIlS5agtrYWWq0Wer0eADBr1ixIkgSlUikK/AuFgijuz2azYhu+VCqJgeT5fB56vR5arRZarRaJRALFYlG0u7BarXC5XMhkMmLouXydfE0SUSVhn7IpOOaYY7Bz5078+c9/FqtHADB//nyce+65eOaZZ8S24XST62XkQCZJEkwmE2pra6HRaKBQKMSWoslkgkKhEO0tkskk8vk8VCoV1Go1bDYb0uk0jEaj6OofDAYRCATg9XrR2dmJUCgkboA+n09MAli8eDGsVqtYKQmHw9P8naGDTZIk0bdu4sglg8EgTktu27Zt3PBwuWYsHA6jWCyir69PvC6tViuUSiWSySQikQgKhQJqa2tx5JFHora2Vqz0yrVkZrMZVqsVWq0WKpVKbG92dHTghRdeQEdHB7q6usa17OAqGRFVCq6UTcFnP/tZvPvuu/jGN74BvV6P888/H9XV1QCAZcuWoaWlZVybi0rg9/sRiUTQ1dUFvV4vOp0rlUoxRknumC4HMfk0piRJsFqtGBwcRD6fR39/PyRJglarhcViEbU+8milmpoapNNp6PV69Pb2wmQyjSvw9/v9qKqqEs1luY15+BvbIsXv94vwk8/nEYlExJZhPp9HJpPBzp07MTQ0hEwmI94saDQaAKMtNOSVXK1Wi1AoJJrKymFM3oIvl8uioF+uRctkMggGg6JJrF6vRyAQECtmABjQiKgiMJSNIc90LJfLon5MLir+2c9+hnQ6jW984xvo6enBZz7zGcyZMwf33nuvOIVYSSRJEisC8jZOc3OzOI0JQHROLxaL4gQnAHFTC4fD4oSmXq/H3LlzYbFYRL2O0+lEPp+Hz+cbt0oRDAaxYcMGNDU1ie7ocr0btzEPb2OL/eW6MvkAisFgQHV1tegRFgqFxGlIOVgNDg7CYDAgEolAqVSK///G/j+ZTCbh8Xhgs9mQy+WgUCjENjwAMQezXC7D4/GgubkZhUIBkUhk3CEbtXr0rz+PxyN+n6GMiKYTQ9n/t2nTJnznO9/BI488Mu4vZqVSKcLa6tWr0djYiCeffBK//OUvsXDhQgwNDeHpp5+G3W6fxqvHbi0xjEYjFi5ciB07dsDr9YqtS2D0xiOvnkWjURgMBtFyQG47YLPZUCwWAfzrJufz+VAoFJDJZOB0OtHa2opIJCIK+wEgFAqJAwVWq1XcnDlXcGaYWDw/NpDLw+u1Wi38fj/cbjfC4bA4FRwMBqFSqcRrVR7pJfdCkzv6F4tFZLNZMYZJoVCIOjJ5u1NeMQuHw+jt7YVKpRKvUfkNlHxtOp1OHDDgKi4RTSeGMgCbN2/Gxz72MVx33XXjApn87lylUqFQKECtVuMb3/gGLr74YvT09EChUGDOnDlobGycxqsfNdnNEADq6+uhVCrR0dEBt9uNTCYjZmEODw8jkUiIQn6lUolCoTBu1UHeFsrlcggGgwBGVw99Ph+y2ayoUTMYDPD7/SiVSqiurkY+n8fQ0JA4cCCHMbmrOx2+wuEwHA7HuDcK8mvA5XLB6/UCALq7u2G1WmEwGJBIJEQH/nK5LFZw5QL/bDYrDqaoVCpotVoUCgWYTCYkEgmxBQ8A8+bNE6u+cn2kSqVCKpVCfX29qI/csWMHWlpaYLFYRP0Z3zQQ0XSa8aFsy5YtOP7443Httdfipz/9qfh9ecYeMBpC5K0OAHC5XHC5XB/6te7N2OAz9mZot9vhdrvFNqNSqYRSqYTZbMaWLVsAQNzo5FUHeaalSqWCSqVCOp2GQqFALpeDJEnI5XJQKpWIRCKiH5R8o7VYLDAajbDZbKIn1cSib7bHOLxVVVUB2L13HjB6CjMcDmPnzp0wm81YsGCBOMUrv6FQKpUYGBhAMplEOp0WoQqAWL2VV9AikQjUajV0Op04OKDX6+FyuZDL5WCxWGA2m1EqlURNpPzx8hsPh8PBVVwiqggzOpQNDQ3hjDPOwMqVK/Hzn/8cxWIRN9xwA3bt2oWuri58+ctfxic/+UksWLAAAHDHHXfAbDbjyiuvnN4Ln6BcLsNgMIhasUAgIG6GgUAAZrMZkUhENJBVKpXo6elBbW2t6LourwTmcjnR1kLuWyb/WblchtlsFisW8qEASZLQ3d2NeDyOpUuXim0quaVGIBAQo5z2pzcUO60feiaGG3nrcmyPvI6ODlESYDQakU6n4XA4xOD76upqmM1m8fpQKpVQqVSIRCIolUqi/ksOeCaTSbyBKpfLSKVSaGpqgsViEY1kw+EwRkZGYDKZYLfbxUEUeQzU2P9/iIimy4wOZQBw3HHHoa+vD3/729/w29/+Fvl8HkuXLkVraytWr16Nbdu24bvf/S40Gg1+//vfw2634/zzzxfvuCvBxPBiNBpFIEskEiiXy2htbUU8Hsfg4CA6OzvFaTR5jI3c5V+tViOZTMJmsyEQCCCXy4mVMbVaLVpbyKc15fqcXC6HdDqN7du3Y+nSpYjH42htbUWpVEKpVBLhTW5vwBWJw9PYbvnyr41GI3p7exGNRpFKpaBSqTA4OIiFCxeio6MDw8PDyOVyoq2K3J5FLuKXJAmFQgF+vx/FYlGsigWDQfh8PoTDYUiShFKpBIVCAYPBAK/Xizlz5kCn08FkMsHn8yGTySCfz6OhoUGs6LKjPxFVkhkdyurq6rBmzRp885vfxMUXX4yVK1fikUceEUHjoYcewjXXXIPzzjsPZ599Nu6//35YLJaKCmSTkW+ExWIR6XQadrsddrsdHR0dKJVKSKVSUKvVaGpqEtuPg4ODUKvVoiBbbiibz+cBQKyYja0xM5lMohZHPjRQU1ODYDCI+fPniwAnb2cFAgGYTCZRbzS2VQIdnuTta4PBgNraWni9XkiShCOOOAKFQgHxeBz9/f1iBddsNkOr1Yph93LbCwDQaDRQKpXQ6XTIZDJQKBTipHChUIDRaBTjmOLxODZu3AhJkjB79mxUVVWJAwPyCl0ymRQNkVtbW/k6JKJpN6NDGTBaCH/LLbegsbERp512GmpqakSB/yWXXILvfe97eOWVV3D22WfjyCOPnO7LnTJ5JUru8RQOh2G329HX14dsNjuu9stisSCRSIito3Q6LUKYRqNBLpcDADEjU16tkG9iiUQCkUhEbAU1NTUhEAigVCrBYrGgqqoKPp8PpVIJdrtdDIPmiJtD274asKZSKXg8HtFcOJPJwGw2iyCUTCbR3d0Nv98PpVIp+pMBECcxU6kUzGYzgNG5sXKRvnxKU95il3vsORwOFAoF9Pb2ioCmUqlw/PHHAxh9gzD2euXVN4/Hw2B2GPF6vQgEAvt8nNvt/hCuhmjqZnwoA4CGhgZ885vfFONe5L5H8qzHo48+epqvcP+NHbsk3xjVajXy+by4+dXX14teTnLfMXl2YDabRbFYhFarFSsTIyMjYqVQqVQil8uJk6mpVArFYlE0Am1paUEul0Mmk4FKpUKpVEK5XBatQ+Qt1mw2y9WyQ9TYQn754IYkSfD7/fD7/UilUggEAujq6kJ9fT2cTifi8TgMBoPYdpQPARQKBeh0OnECUm57kcvl0NfXJ15DOp1O9MSTxy3FYjFotVoYjUa4XC7x2tTr9eKNh8FgQH19/biTyfL0C7lPGQ+iHB68Xi/a2trECdx9kU/9ElUChrL/b+KWpEKhwOrVqxEIBMS77EORfOMZGRlBKBSC3W5HNpuFWq0WKxbRaFSMqpFnXQIQvaKy2awYr5RKpUTxtBzcHA6HaP45NDSE2tpauN1uscIBQMwoBEZXUOQQFo/HAQCtra37/FrGrszwhjm95J+FbOyqp9/vRzabxeDgoJj+kM/nkc/nYbFY0NPTAwCi5lHulZdMJmEymQBAnPiV68Dk+jL5hKXBYIDJZILFYkF/fz9SqRRqamrQ1NQk/ry1tRVOpxPZbFaM/Jps61xeuZW3NNng+NAm/z21du1atLW17fPxdru94k7T08zFUDaJhx9+GC+//DIeffRRvPjii2hpaZnuS/pA5BtPKBSCSqUSK4KdnZ2iEH/sycpisShaZ8ira/LMT3lL6sgjjxQja7RaLaqrq5HNZsXqhDw+R36MSqUSz/1+tyz3dsNkYPtwyU1X1Wr1bicuHQ4Hent7odfrUVtbi8HBQcTjcQwMDAAAYrEYQqEQCoWCmLtaLpeh1WqhVqtRKBSgUqmgVCqh1+tF7Vg+nxe1jqlUCgqFAiMjI0in02IlzWq1wmQyjWth43A4kM1mxTWOjIzA4/Egl8vh6KOPFs2Nx35tfA0d+tra2rBs2bLpvgyi/cJQNomFCxdi7dq1eO2117Bo0aLpvpwPLJVKYWRkBJlMBqlUSjTwbGlpgd/vh0qlQiKRgNfrFQXU8naQXF+XyWTE82WzWXR2doqmufI2ldwqo6OjQ9T7yKc7rVar2JIC/jUPcX9C1N56SXGF48M19mchb5WPXYFqaWlBVVUVBgYGYLfbEQwGRfjyeDwolUpipVV+XcqzUevq6kQoM5lM4tBKPB5HLpeDWq0W/fLkE51msxlz5sxBTU0NstksIpEItm/fjrq6OjQ1NYlWLclkUryxMJvN8Pv9cDgc4usau71JRPRhU073BVSio446Co8//vhhEciA0cAyPDwsti8bGhowa9Ys0fpi8eLFYkUsEAigXC7DYrGgpqYGer0exWJRbG3+/e9/h0ajQTQaFbMLg8EgwuEw4vE4/H4/Ojs70dXVhVAohP7+fmzevBnDw8Ni+1IOUMC/bu5Tqf+QJwJMdtM0Go1i1YYOPvlnMXGFaWyT4HA4jC1btsDr9UKlUqG+vh6lUmncYZpIJCJWVVOpFBKJhGgGK3f6l/8cGA1N9fX1qK2thVarFSHNbrdjwYIFaGpqgkajgdfrFQdc5JOcnZ2dYpV21qxZMJvN4wIZEdF040rZHsjNKA81Y7v5AxA3SJVKBavVCkmSxMDncrmM/v5+1NTUiNFIcv+xhoYGJBIJ9PX1icC0ePFiHH/88fjJT36CG2+8EYFAAHq9XrQbkLc8A4GAGDIttzPQarVoaWnB8PAw7HY7mpubYbVaD9gpTG5bTr+xq2dynzy5Uz8wevKxpqYGgUAAWq1WrHzJJy7lLvvyicl4PC4OnSgUCtGDTK4TAyAOoqhUKtF7b3BwEBaLBcFgEMViEaFQSPQxGxwcxOzZs9HS0rJbqCQimm4MZYeZiasVcjf+hQsXipNucgd1n8+HqqoqBINBmEwm2Gw25HI5aDQaBAIBDA8PixUxAOIU6pe//GW8/fbbeOyxx+Dz+eB0OqFUKmGxWKDVapHJZMQcTaVSiVgshmw2K07leb1ehMNhzJ07F8Do6ofVap2G7xYdSJIkIZlMYseOHRgcHERPTw/UajWUSiXq6+vR39+Pzs5OBAIBJJNJbNu2TbRNMRqNIozJhf3pdFqEL5l82jeRSKC6uhp2ux0ajQZqtVqsxsrzXJuamqBQKBAMBlFdXY1wOIyqqiokEgm0tLQwkBFRxWEoO8xMNuZG/u9MJgOtVguDwYC5c+eiWCxi27ZtyOfzUCgUWLBgAcrlMnK5HJxOp1hd6+7uBgAcccQRiEajAIAf//jH2Lx5M3bt2oXBwUHMmTNHtMtIJBJQKpWora2Fw+GA0+mE3W4X7Tny+Tz6+vpgtVpRU1PDlhgVRm6yOhXyyhYwukq7c+dOcaIyGAyiVCph3rx5sNlsCAaDIri/8MILYsaq3LOstbUVzc3NWLp0KTo6OmAymcQ4JnnUktxXT6fTwel0Qq1Wiy1Qua+eTqcTdZAOhwNWqxVVVVXihO/Y8UqT4XgvIpouDGWHgbE3kYnbePJ/j4yMiDYWLS0tSCaTqKqqEi0CcrkcbDYbVCoVQqEQdu3ahXQ6jXg8jmAwCAA45phjxMlNvV6P3//+9zjttNPEFmdDQwMcDgc0Gg2MRiOy2awIgaVSCdFoFE6nE4lEAgaDASqVareVEDq0pNNp0eIklUpBq9WKVhfJZBKZTAaBQADZbBb9/f2IRCLYvHkzhoaGIEkSLrvsMjz66KMIhULYsWMHfD4fent7AUDUM6rVami1WqhUKtH7Tu7iHwgERHsXuQ7SYrEgHA6Lgya1tbVoaGgYtzomH07hGwIiqiQMZTNEMpnE4OAgqqur0dvbi1AoBL1ej4985CMoFAqiH9ScOXPECCW1Wo1oNCpmV86bN2/cc86bNw+/+tWvcNVVVyEYDIqgZTAYxCpELBaDQqGARqMRNWtyS4NMJiNmbAIQN0j5tCiAPRb20/RLpVLwer3iVGM6nUY0GoXD4UAmk0FLSwuGhoYQDocRDoeRz+cxMjKCXbt2AQBuvfVWnHPOObjhhhvw5z//GXfffTe6u7sRi8VEg1in0ynCmUajATBaRyafzMzlcmIiQDQaRUNDA+bPny9Gimk0GrhcLtjt9nGBTG4YC3DuJRFVDp6+nCFSqRSUSiV27NiBrVu3IhqNihNvVqsVpVIJIyMjUKvV43o8yc1d5ROaE33mM5/BVVddJR4r1/MUCgWEQiG0t7fD4/Ggq6sLkUgEnZ2dKBQKSKfTiEQi6OrqwoYNGzA8PDyuo3oikUA8Hh/XoJSmh9zqYuwJ2bEjlOTVzmKxCKvVKmZYmkwmLFy4ENFoFMlkEoFAAJs3bwYAfOELX8A555wDADAYDFi1ahVeeeUV3H///Tj22GNRKBQQDofR0dEBt9uNaDQq2meUSiXMnj0bZrMZpVIJjY2NMBqNaGxshMPhQHV1NaqqqmC1WlFfXw+HwzEu2Ms91uRpEkRElYIrZTOEw+FAOByGWq0WqxZjZ1nKtTtDQ0Oorq4e1wAWAJYuXbrH5/72t7+N7du348033xRF/gqFQjx/TU0NcrkcIpEIJEkS/cyA0ZW0YrGI9vZ2MSjaaDSKzu68aU6/yU7IysEml8vB5XIhlUohGAxCqVSK7vx1dXUYGhpCuVxGLBbDK6+8glgshuXLl+Pb3/72bp9HqVTi9NNPx4knnoi+vj7ccccd+Otf/4pEIoFdu3ahWCziyCOPhNPphEajgUajgcPhQDKZxJw5c2Cz2bBixQro9XqEw2EAoz0HnU6nCPdj+5DJ/x7b3Z+IaDpxpWyGcDqdmD9/PlQqFbRaLVwulxjOrFKpUFVVBY1GA7vdDq1WC4fDIU5OAsDs2bP3+NwajQYPPPCA6Jy+c+dOuN1u5HI50cdMLvqW510mEglxctNkMsFsNmNkZES0UHA6nZg1axZD2TSTW6xMXFUyGo2wWCxwuVzi9xsaGgAA/f39yOfz2LlzJzo7OxGNRrFr1y4x8P7OO+/cZ8uZZcuW4f7778fmzZtx8sknAxgdUp7NZlEul2EymcTrqqGhAStXrsTJJ5+M2bNnQ5IkzJ49G7Nnz4bdbheh0uPxYMeOHUgmk6KL/8TTyvLWOVdoiWg6MJTNMLW1taitrYUkSZg/fz6WLVsGq9WKeDwOi8WCj33sY1i+fLmoLTMYDAAgTmDuSUNDA55++mmcf/750Gg0SCaT6OnpEYcLkskkQqEQgsEgfD4fBgYGUCwWYTQasWLFClHzk0qlxt0kDwa5czxvvPsmr4hNXEmSJGlcsEkmk4hEIhgaGoLH40E4HBYjtnK5nCjev+6660R4mwqXy4UvfelLACDGMgWDQfT29qJQKMBgMIhTxB6PB93d3ejv7x932EBuLJxKpURrFtnEpsMTQxoR0YeJ25cziNFoFEOZnU4nAIgTcnq9HuVyGSqVSrQqUKvVIpRt27Ztn8+/cOFC/P73v0d3dzdOPPFERCIRDAwMoKWlRczYTKfT6O/vh8lkEluXwOicurE3woO5QsaRTFM3scWKvJIkn7iUT+/qdDqk02mxFV4sFlFVVQW/3498Po9YLAaDwYALL7xwv69BHmxfLBbFiWD5ZKXchqOpqQnxeBylUkkU8AOjq2vyYRE59E8cqzRx2zIcDrPTPxFNC4ayGUQeTC7z+/0oFAqor69HNBrFzp07xQqSfLJNvmFt27ZNjMbZl9mzZ2PNmjW49NJL0dvbC7vdDr1eD6VSiWKxiFKphIGBAeh0OvT29opasg/L3mZo0nhj51p6PB4EAgH4/X4MDw+Pey0BgN1uR39/PywWC3K5HCwWCwqFAjo6OgAA559//vtqEiyHslKpJMKYPLRcrokMh8NwuVxiXNgRRxwBYHSKwNiJAvKbkr2pqqra72skIjoQuH05g/j9frjdbrF9I/cSq6mpQW1tLYxGI3K5HEKhEMLhMGKxGPR6PRQKBaLRKHw+35Q/17nnniu2nTweD5RKJZqamsRIpnK5jKGhIaxbtw7vvPMO3n77bXg8Hni93j1uHx2obce9zdCkySWTScTjcTEYXA7tAMTKlNyPzOFwwGAwIJvNYsuWLRgeHgYAXHHFFe/rc49dKdPr9eI1EAwGkUwmUS6X0dLSgvnz58NsNqO5uRk1NTVoa2uD2WwWh0emMhuVM1SJaDpxpWwG8Xq9iMfjSKVSsNvtMBgMSKfT8Pv94mZqsViwc+dO0ayzUCigvb0d0WgU7733Hux2+27POzw8LFpnjHXNNdfgtddeg9vtRldXFz7+8Y8jl8uJhrIqlQrlcnnc52ttbYVCoUCxWERPTw8AiBmFB2JOprzSJ9dBzZSZmfvTpX+yFVGj0Qiz2SyasQYCAWQyGQwNDYnB4MPDw4jFYujp6RFDwLdv345isYglS5bAYrFMKdgXCoVxP1+5FUuxWER1dbU44VlTU4NCoYDGxkZYrVa4XC4olUokk0n09/eLSRKyqbxmxp7OJCL6sDGUzSAGgwHxeFyEsZGREXR2dkKlUiGVSqG+vh5GoxGpVAobNmyAz+cT8wgBoKura9Ltp2g0OmkPM7VajdWrV+Mzn/kMBgYG8MQTT4jTnvX19bBarUin01AoFAgEArDZbGhpaYHBYEAoFILX64Verxf1QJPVN8m/nnjD3dufAawr218Tt76NRiPee+895PN5aDQaFItF9Pf3w+/3IxwOo7e3F7lcTvQlu/TSS2GxWKb0ufL5/LifmVz/CIy+BiVJgtlsRl1dHU488UQYjUbYbDbU1NSImje5oe3Y5+H4JCKqdNy+nEFaW1uxaNEitLa2iu0oefVDr9djYGAA3d3dGBkZEfMCzWazuJlu3bp1vz/nrFmz8IMf/AAAsHnzZjE0emhoCCMjIygUCjCZTCiVSojFYmhvb0d/fz+A0TE7ciD0eDwYGRkZF7L2dlJuX6fouE21/+S6Mo/HAwAwmUyQJAnZbBZDQ0MYHh4WdYOZTAY9PT3IZrOoq6vDKaec8r4/r7yqCowOJDeZTNDpdBgYGIDX64XNZsPixYvF60Kv1yMaje7W8JaIqNJxpWwGmXjSTA5kTqdTdGfv7u4W24dGoxEKhQLV1dXweDzvK5QBo/Vlb775Jh577DEx3kZulWCxWOB0OmEwGNDT04ORkRFIkoSlS5dCpVKJbcux26PyluPeCvb3Vcx/OG5bHogt2b2tMMo/h3Q6jVwuh3Q6LVZI5XmpkiRBp9NBo9FgYGAAAHDVVVeJEUnvh0KhgNlsFoPHAYiTnhqNBpFIRDRFLpVKUKlUqK6uRrFY/EBb3UREHzaGshlq4naUw+FAf38/jEYjgsEgqqurUS6XMTIygpqaGgBAb28vIpEIbDbbfn++7373u9i4cSO6urrQ29uLhoYGGI1G0VBWbpdRKpXg8XigUCgQDodhs9lEXZB8c43FYvD7/Whtbd3jSbrJWh0c7g7Eluy+6vay2Syi0SiCwSDC4TB0Oh1KpRI6OjpQKBQQDAZhNpuRy+XEDMsvfOELk9Yc7g+LxYJIJCLaVajValgsFlgsFmQyGbS3t8NgMMBgMIgVPIATIYjo0MLtSxIsFouYYyivUslF3HIH9k2bNr2v55YkCatXr4Zer0cikUAwGBSNYuVfF4tFJBIJhMNhhEIhRKNR8fHyXEOn04lwOIx4PC6Glu/JZDMbD2cHYkt2T88hfy/ldhF+vx+7du1CqVRCb28vSqUSEokEbDYb/H4/NmzYAGB0Nmp9ff37/6L+P3nslhwKtVotmpubccwxx0CSJHHCs66uDq2treKfmRbMiejQxpWyGWriNpV8uk6u2ZFXS+LxOAqFAsxmM4LBIO655x4x9mZ/zZ8/H7fddhv+/d//HcFgEGq1WgyVlttx6HQ6lMtllEolVFdXi1WPcDgsrlOSpCmFrQNxWvNQcqC2Le12+25F8XJn/3A4jEwmA7VajerqanGiN5fLoba2Ful0Gu+99x4CgQAA4Nprr/3AX9eOHTuwc+dOAKP1YiaTSVyv1+uFy+VCJpNBOp3mwQ2qKG63e0qPs9vtcLlcB/lq6FDAUDZDyYFFLp6Xu/2vWLEC69evRygUEjVDWq0WLS0tCAaDeOaZZzAyMjLuRNz++MIXvoCOjg7cfvvtCAQC0Ov1sFqtSCaTqKmpQTAYRLlcRjqdht1uRyaTQX19PcLhMIrFIlKplOijJp8alQPXZEFzXzfpmdYaYyL5e5ZMJlEsFkWzX7kNiUz+XsonK/v6+pDP52EymaBQKGCz2TAyMoIXX3xRbGvefffdOPbYYz/wNd58880oFAqoqqpCbW2tCOqRSAQ1NTVoaGiATqdDMBhEPB7ncHGadvLYuFWrVk3p8ZIkwe12M5gRQ9lMJd9ks9msOPUIADU1NTj22GOxfv16xGIx6HQ65PN5UfifTCbxpz/96QOtgNxyyy0YHh7GH//4R/j9fphMJmg0GuTzefj9fhEQCoUCamtr0d3djaGhIdEIVKvVIpPJIBAIYMeOHVi4cOGkfcymUlc2U1pj7KmAX/76gdGtwVKpJOq/5KA69vs4MDCAnTt3itVMo9GISCSCWCyGN954A+FwGFarFX/7298OSCDbtGkT/vGPf0CpVKK+vh5KpVIcFJG784dCIVHrKL9GiKaTy+WC2+0WK8Z743a7sWrVKgQCAYYyYiibqeQbrdFohMfjQSgUEjdnYPSGPG/ePOTzeWzcuBH5fB4OhwPJZBJ//OMfP1AoUyqVuPvuuxEIBPD8889jeHgY1dXVyOVyKJVKKBQKsFqtmDNnDpqamkRrhUAggOrqauTzedTW1or+WHKLBvnr2Z+b8kwZubSnrVyj0Shq8+RxSnL7iVgsJlbOAOC1117Dhg0bROPYmpoalMtl+P1+bNy4EcPDw1Cr1fjjH/94QAIZAPziF78AANhsNhgMBiQSCYRCIfHaOOaYY+Dz+cThk6n0sCP6MLhcLoYs2m8s9J/h5FOY1dXVMBqNyGQyCAaDiEajYpXMbrfDarWivr4eWq0WW7du3Wt7jBdffBH//u//jr6+vj0+RqvV4uGHH8bRRx+NQCCAjRs3jmuzIA8uHxwchEajgd/vRygUwvDwMAwGg+hhJm9hyqHN7/djx44douZsX7Vnh+vIpYkjqfZUwC8H2WKxiL6+PlRVVYlw1t3djVQqhXg8Dp/Ph0QigWQyOa41hdwKY3BwEADwm9/8Bh//+McPyNewbds2PPXUU1AoFKivr4dCoYBWq0WpVEIkEhGzLKurqwEA1dXVInjuq08dEVEl4koZQZIkLF++HMlkEn6/H16vV6yOWCwWeL1eUQDu8/nQ19eHhx56CD/60Y8AAIODg2J1BQBuu+02tLe3o6enB3fccYeYjZjP58c9DgB+/etf4zOf+Qz8fj88Hg9OOukksbrR0dGBSCSCE044AU6nE7lcDtFoFCaTCcViEZIkoVAowGKxIBQKARidv6jVasV8z7HtMwAcdvVjexqfNHFlzGAw7HHFyGg0ihOUg4ODUKvVSKVSohGsHMYsFguam5uRyWSQSCTEDEx5HNZVV12FFStWTFrc3NvbO+VB3wqFAqVSCbfeeiuA0fqc+vp6WCwWGAwGGI1GEcDa29uh0+nE15fNZsXUCflnLX+P2NGfiCodQ9kMsreb0tigkkqlREPXzZs3o7OzE9FoFOVyGQ0NDejr68Njjz2GX/7yl+IUnlI5uug6djuxs7MT99xzD77zne8AGB3HNPEaGhoacNddd+Giiy6Cz+fDunXrsHjxYuRyOXg8HqjVarS3t2POnDnw+/0wGo2oqamBUqlEKBRCKpVCW1sbDAaDOC1aX18Ph8MBo9EIr9eLYrEoDjRMPNxwuISzid7Ptqxer0c+n0cqlUI6nUahUBDjuGpqamCz2dDW1obOzk5EIhFkMhns2LEDhUIBZ5xxBr7yla/sMSSazWY0NjZO6ToUCgV8Ph/++te/il97vV6xZVkoFJDL5cQcV7PZDIPBAJvNNm67ktuWRHSo4fYljdvqklsfVFdXi6axzc3NqKurw9KlS9Hc3Ay1Wo3h4WH84x//2O25vF6vaJmgUCjw+OOP44knntjr5z/66KNxyy23ABhdUfF6vchms9BoNGJ8TyaTgV6vh0ajQXd3NzKZDEKhEBQKBTZv3ozu7m4MDAzAbDajqakJDocDkiShpqYGBoMBwL+28AAc9ltbkiSJxrp+vx/pdHqPj00mk2Kkltw0WK4v7O3thcfjwfPPP4+XXnoJHR0dYnt506ZNSCQSWLp0KW6++eYDuhJ1yy23oFwuj5t9WlNTg9mzZ8PhcKChoQGFQgFKpRIqlQp2u1302CMiOlRxpYz2WH/j8/mgVCqxcOFCzJ49Gxs2bMDOnTthtVoRDAaxdu1anH322eM+pqOjAwDQ1taG448/Hr/97W9xyy234IgjjkBtbe0er+H8889HR0cH7r77bnR0dMDhcKBQKECSJGQyGYyMjKCxsRF9fX1IpVIIBAJQqVSi9k0OXnKQlI2tFxu7dTkyMoJsNntYFPnvazTS2C1ceYtaXkkcGRkRbUVaW1vh8XjQ2dkJYPQ0Zjweh9frRSwWw9DQEJxOpzj1msvl0NzcjF/+8peiufB9992HJ598EkcddRQ++tGP4thjjxU1X1Pl8Xjw8MMPAwDq6+shSRIaGhrQ3NwMm80Gi8Ui+pXl83k0NDSI8U5ERIcyhjIat9Ul/1MulzEwMACVSgWj0Yj169djw4YNSKVSmDVrFoLBIJ544gmEw+FxzyU3+VywYAGuvvpqbNmyBW+88QZuvPFG3HnnnXu9jv/+7/9GZ2cnXnrpJbz++utoaWmBwWBAOp0WBf0OhwOdnZ0olUqoqqrC/PnzoVAokEgkoNPpoFQqx/VQk0+Z+v1+ETzloDZdrTAOdG+0ifVjfr8ffr9fBLRwOIyqqioRyLLZrKi5Gzv+KJlMor+/H1qtFt3d3TCbzUilUiKEyy0zNm3aJPrK3X777eLk4+OPP441a9YAGF0xfeqppwCMvhaWLl2Ks846C8uXL99neLrzzjvFz7e2tlYMOB8eHsa8efOg1+vR2NgoasuA0W3zbDZ7yAdsIprZuH1J404gyv8NjJ6QVKlUYnuzWCyiuroaCxYsgMlkQjabxZ///Odxz7Vr1y4AwLx586BUKvHjH/8YdXV18Hq9+PKXv4wHHngAiURi0utQqVS4/fbbMXfuXGQyGfT09MDv92NkZAQ+nw8+nw9DQ0PIZDLQaDSoqalBXV0djEYj/H4/+vr6RGAAxo9Zmnj68ECMJHq/DvTJwIlfixy8+vr6oNPpYLfbxc9RXlGSV8pUKpU4uSpvC+dyOahUKrEyNm/ePLS0tMBkMqG9vV0cpnjsscfQ3NwMANiwYQN++tOfAgAuvPBCXHHFFViwYAGA0dXTRx55BFdccQUuuuiivX4tg4ODopbsrLPOwsKFC1FVVYVUKoVoNIr+/n7U19ejv78fvb29og+USqXiWCUiOuQxlM1wE1snyCRJQi6XE7VGs2bNEnMFXS6XmGf497//fdzHmc1mABAtEmw2G2699VZYLBb4fD7cfPPNOO6443DzzTeju7t7t+sxm8245557YLPZRLG/3AfL7XbD4/FgaGgI4XAY6XQa69evx6uvviqamiYSCXi9XvG1jV1BkoMI8MFbYcjfN/mf/QlYBzoQyl+bHEgcDgd0Op2o/5O/Tp1OB6PRiIULF4rHOxwONDY2IhwOY/PmzeLriMViiMViSKfTOOaYY9DS0oKBgQH4fD4AwL333ovjjz8eABAMBnHTTTehWCzizDPPxDe+8Q1cd911eOihh/Dcc8/hhz/8IU455RQAo20uxvbDm2jdunWiUXGxWBRDyJVKJUwmE+bMmQONRoNgMIi+vj689dZb4uuSVwnllihERIcahrIZbk+rNnIdz+DgIIrFIhoaGrB48WIolUp4vV4Rvl5++WUUi0XxcXKPqhdffFGcxFu0aBGeeeYZfPWrX8WcOXOQSCTwwAMP4NRTT8UVV1yB9evXj/vcra2tuPvuu6HVahGPx+HxeMRqWV9fH0qlEnQ6HQYGBrBr1y60t7cjFouhvr4eqVQKAwMDk66O7enr399QNfb7NnZbdCofIzdqnWognMr1TezH5nA4sHDhQrS2torwtafvhdFoRDabxdDQEEZGRtDT04PBwUHRpT8UCuGpp57Cm2++KcLu17/+dbHiVSwW8e1vfxuBQACzZ8/Gt7/97XEF/zU1NTjrrLNw/fXXi9/bW0H+u+++CwBiVc7tdiOXy0Gj0WDZsmVwuVywWq0wm83QaDSwWCzjttAnbs8SER1KGMpmuLEnEife/OUTb/IsSvnEYzAYhF6vh1KpRDQaHdeX6vjjj4dWq0VfX5/YypQ/z3nnnYfnn38ev//973HqqadCoVDgn//8Jy699NLdgtlHPvIR3HfffQBGa6ICgQBKpRIsFos4VZhIJBCJRGAwGFBfXw+9Xo9isYgNGzbg6aefRjKZFFMI9rR6MnYG6FTDmVwTls1m4XA4przqNTYATzUMTmWrc3+3Q8eGOLlRbDQaRS6XQ1dXFzKZDEqlElpbWzE8PIyBgQG89tprSCQSOPHEE/HjH/9YPNd9992Hd955B3q9Hj/72c/EgYuJNBqN+O9cLrfHa3vnnXcAADqdDplMBgqFAgqFAi0tLeINgcfjwdy5c3HyySdjxYoV4/qfyauE8muEiOhQwlA2w42tIRt7Y0+lUkilUqipqUF1dTX0ej3sdjsMBoNoKmoymQD860YKjAa5lStXAoA4QTeWQqHACSecgHvvvRevvPIKPv7xjyOXy+HLX/4yent7xz32oosuwg9+8AMAo1tkcrsOg8EAhUIxrsFpPB5Hc3OzmArg8XiwadMmeDweeL1eDA0N4ZVXXsH27dvHhZf30yZDvg75ezfVVa+xq1UTg9SeQtpUVvvkxySTSaxfvx47duwQPz+PxyNWGscGwlgsBo/Hg1Qqhf7+fqRSKYTDYZRKJYRCISiVSgwMDCAcDuOFF15ANptFQ0MD/vCHP4jv10svvYR7770XAPCtb30Ls2fP3uM1ytMXgD2HMp/Ph/7+fvH11tTUwOFw4Mgjj8ScOXMQj8cxMjKC/v5+6PV6Uc/W398vnkNeJWQoI6JDEU9f7if5JNvhZmKz0VQqhVKpBIPBgAULFoiTe3JnfLVaDZ/Ph1gshnfeeQdXXXWVeK7LLrsML730Ep588klcffXVov5sIpfLhTVr1uCiiy7Cli1b8MUvfhF//vOfRUd2ALjpppvQ09OD+++/Hx6PByqVCoODg5AkScy+jEajUKlUiEQiWLx4MdLpNBKJBHp6etDR0QGbzYZYLAalUone3t5xMzLlf8aeiNzf79X+fI/HfowcwOQwptPpdnveqZzQHHvCNBqNIpFIiBWweDyOdDoNv98PvV6PxYsXw+l0wu/3Q6fTYceOHdiwYQN8Pp8IQ/K2s9/vh9vtRigUgk6nw5/+9CfR1mRwcBCXX345yuUyPvOZz+Css87a59ev0+nESKzJyOHearWKiRLV1dUwm83I5/OwWq2Ix+Ooq6sDMPoaLRaLbIVBRIcNhrL9sHHjRqxYsQLr16/H0UcfPd2Xc0BNvPlLkoRQKIRSqSRO4ymVSthsNjQ3N8NiscDv96O/vx+bNm3CyMiIuDnOmjULRx99NDZu3Ih77rkHX/3qVwEAPT09YhzSWNdddx2+8Y1voKurC5dddhm+/e1vi0axAPDd734Xu3btwrp16zAwMICGhgY4HA4olUqYzWZs374dKpUKVqsVvb29aG5uxrx587Bz506k02kUi0W0tLQgHo+jUCgglUqJAAT8q3+ZvLpSKpVEJ3v5eyP/Ww5AclH9njrY74lcbzW2X5pc+D4xFE3F2Mc6HA6EQiFEIhFs27YNTqcTarUa+XweSqUS5XJZfP8VCgVUKhXi8TgsFgtKpRKSySTy+TyOOOIIUUg/MDAAAPjJT34Cp9MJj8eDQqGAK6+8UvSOO/3007Fhw4a9XqdKpRI/z1AoNC54y9atWwcAmD9/Psxms7h+OURXV1ejqakJSqUS1dXVkCRJ1DayFQYRHQ4YyqZo8+bNOOmkk/C1r33tAwWybDY7bqUgFosdiMs74EwmE/R6Pd577z3RpDMQCECn06Gurg7pdBo2mw0ajQb5fB6hUAgnnHCC+PhvfvOb+PznP49nnnkG3/72t1FbWyuGi09UW1uL733ve/jGN76BrVu34t5778U111wj/lyj0eDuu+/GhRdeiO3bt+Pll1/GihUr4HA4UCwWUSgUoNVqsX79epTLZSQSCVgsFsybNw/RaBRWqxVVVVVi0kAoFEI6nYbL5drthKZsZGQEHo8HBoMBZrNZ9PmSH7O3hq0TjX3sZIX2yWQSVqtV/NlUQtlkn1/e8gsGg6Lo/8gjj0RNTQ3a29sxMjICjUaDVCqFSCQCSZLEaKJYLIZkMolSqSSmKrz00ksAgK985Sv49Kc/LT736tWr8c4778BoNOLqq6+e0sqxSqWCwWAQP4/JRi5t3rxZ/Hc0GoXFYsHcuXNhsVjgdDpRW1sLrVYrQprJZBKhDDjw/d+IiD5srCmbgm3btuG4447D1772Nfzyl78EMHrT3rp1616P90/mlltugdVqFf/IdTGVKJ1OQ6lUYmRkRGyLaTQauFwumEwmuFwusZ312muvjfvYj33sY1ixYgWy2SzuvvvufX6uWbNm4cYbb4RSqcTzzz+Pv/zlL+P+3GKxYO3atWhpaUEmk8GmTZuQyWRE2wSv14u+vj50dXVh586dcLvdGB4ehtVqRUNDgyhA93g88Pl88Pv94ga+p5otg8Eg6p8mNibdn+L6vT32/bbmGPuccuG+3EsuEAggn88DgOgJV1tbC6vVKurv5FXO4eFhmM1m1NfXQ6FQIJPJIB6P45133kE+n8dpp52Gr33ta+Lz/vOf/8Rvf/tbAMCPfvSjvU5pmEju+j9ZTVl/fz+8Xi9UKhUcDgfy+bzo1l9VVYWWlhZUV1fDZDLtMXQd6P5vREQfNoayfUgkErj22muh0+lE0fkFF1yAM888E0uWLMEnPvEJrF69esrPd9NNNyEajYp/+vr6Dtal77exxebySotGo4HT6UQ2m4XZbIbVaoXBYIAkSVAqlWLLT956kikUClx33XUAgN///veTbltO9JGPfETUpj3wwAN45plnxv25w+HAQw89BKfTiUQigTfffBPxeBzZbFbUTykUCuTzeezYsQPr16/Hu+++i40bN2LXrl3o6elBsVhELpdDJBJBMBgUBwFGRkZEJ/xAIACj0YjZs2ejubkZVVVVu62ITRbmJramGGvi5IP3Y2zhPgAxJmrsFmg2m4Xdbhfbg2OvRR5bJf9Ze3s7du7cKbafS6USJEnCs88+i0AggCOOOAK/+MUvxLD5wcFB3HDDDQCASy65ZLcRW/sih7LJasrefPNNAKN97ZqamuB0OqHT6RCNRtHY2AiTyYSamhqxdT3Z6uR0NgQmIjoQGMr2QaVS4eqrr4bdbsd5552HM888E7lcDv/zP/+D1157TZxIW7t27ZSeT6fTwWKxjPunUkxs2WCz2TBnzhxxQ1QqldBoNEin0yiVSvB6vQgGgwCArVu37hY8Pv7xj4vCe/mU3r58+tOfxqc+9SkAo7VmmzZtGvfnLS0tWLt2LSwWCyKRCN58802USiXYbDZRFF4sFqFWq5HNZqHVapHNZjEyMoJgMIh8Po+qqirYbDZRAB+NRuHz+UTfMXlWpCwcDiOZTMLj8YjWGhMbtsrfv7GnGsc6EIdDkskk4vE44vE4kskkAoEARkZGkE6nkc1mkU6nRfjN5/NIpVLYunUrgsEgMpkMLBaLOHShVqtRLBbh8/mwdetW9Pf3IxQK4c0330QoFEJNTQ3uvPNOEXDy+Ty+/vWvIxKJYOHChbjpppv2+/r1ej2AvYeyuro6sV08e/ZszJ49G42NjWKlc2+jlD5oQ2AiounGULYPBoMBF1xwAW655RZs3rwZsVgM99xzDz772c/i+OOPx+rVq6HRaHbrbH8okhuJyts/2WwWoVAIiUQCKpUKCxcuhEqlQk9PD2KxGHK5HHQ6HUwmE8rl8m7fg7GrZQ888ABKpdKUruOqq67C8uXLkclkcOmll+L1118f9+cLFy7E/fffD51OJ7r7y4XkFosFOp0OWq1W3KCDwSByuZyoQZIHnKfTaTgcDlitVlRXV4tQKTfMlU8oAqNhuq+vD9lsFu3t7ZP2PZO/f2MPEci1X+9nLqO88iaHwWQyCbPZLOqoisUi0uk0gNGt5l27dmHr1q3IZDLQ6/Xo7u5GNpsVX48c3IDRNxulUgnDw8MIh8MYGRlBR0cHhoeHodFosGbNGlH3FQ6Hcdlll2HDhg0wmUxYvXr1+zrxKG+pTtzyT6VSePHFFwGMnrwcGBhAqVRCXV0dZs+eDZVKhVAohN7eXtEaZbLVSCKiQx1D2RTo9XqcffbZuOOOO/Dd735XbNnJsyCXLl0qOs0fyuRaHfmGazQaodVqEY1Gx3Xt9/v9iMfjqK2thdlsRktLC4DRAvCJ9UKf+MQnRIG3PHppX1QqFW644QasWLEC0WgUl156Kf70pz+Ne8yxxx6LO++8E0qlEkNDQ9iwYQP6+vrQ2dkpgohWq8W2bdtEjZlSqUQmk0F7ezsGBgYwPDwMh8MBl8sFSZJQVVWFdDotVtfkxrCSJCEcDqOmpkZ8b+Su8RMbsba2tsJisYgANranGfCv9hdTaR4rr1zKYTCVSqG1tRWtra2i8N1kMsHn84k6Mb1eL+rI5O8NMNrnTafTIRKJiOeVJAmJRAImk2ncadMf/vCHWLZsGQAgk8ngK1/5ighkt99+O1wu15R+jmP5fD50dHRApVJhyZIl4/7sV7/6FYaHh2EwGGA0GsVWtFqtxsDAAIrFIjweD/r7+zEwMCCa/cp1gUREhwuGsikyGAw4/fTTcdppp4kmmPK/A4EAli5dKmpvDmVj63LkNhGNjY3Q6/Wib1lzczNcLhc+9alPYfHixViwYIHo4v/HP/5x3POpVCosWrQIACaddbknkiTh4YcfxjnnnINCoYDrr78ev/jFL8adTPzEJz6Bm2++GQDQ19cHj8eDWCyGYDAoOvt3dnbC7XYjEomgVCqJk5nyTb+jowMejwe7du0S7R/kmjmZ3EJD3rKsqakRvcA8Hg+2b98u6rwmbmvuqWHs3prHykEPGN1mbG5u3q1LvSRJcDqdSKfTyOfz2Lp1K3K5HHK5HObOnQubzYa6ujosXboUkUgE+XxerFANDQ2J75Hc+qSnpwfAaPuRz3zmMwBG33TccMMN2LhxIywWCx555BGceOKJU/4ZjvXKK68AAE477TTRrBgYfU3IBweOOuooSJIEtVoNq9U6rg+d3W4Xo7/2t9kvEdGhgi0xJlEul8fN75PJhcqydDqNH/3oR/jnP/+Jl19++cO6vINKDmNy+JFXZXp7exEKhaDX6zF79myEw2Fks1kUi0VotVrMmzcP27dvx+rVq/G5z31u3LidxYsXY/369SK4TJVer8evf/1rtLa2YvXq1fjVr36FeDyO73//++Ln84UvfAF+vx933HEHhoaGYDKZYLVakUgkYDQaoVAoUFVVJUKS1WpFqVQSW5rhcFisAlqtVtF5PpVKIRaLia/xvffeQywWQ2NjIxwOB+bOnQu1Wo1AIIBisThuOy2VSu3W40zW398vgtvYovSJIU3+3PL8ysl4PB4Eg0EMDAyIYv+6ujrE43FkMhkR3CKRCDKZDDKZDHQ6nWgjEggEMDw8jG3btqFYLOKyyy7Dd77zHXR1dQEAfvrTn+K5556DRqPBb37zG8ybN2+/fn6yQqGAf/7znwAgZmYCo/+ffec730Eul0NtbS3mz5+PXC4HvV6PhoYGmEwmNDc3w2AwiL5kTqdTtMR4Pw18iYgqGUPZ/yf3aCqXy1Mqvv/LX/6CRx99FK+88gqefvppLFiw4EO4yukhSRLsdjsSiQQCgQASiQSqq6vR1dWFlpYWBINBHHHEEfB4PBgeHsbvfvc7/Pu//7v4+MWLFwOAWI3ZH0qlEv/93/+N5uZm3HjjjbjvvvvQ0NCAr3zlK+Ixt956K3p6evDUU09hZGQEKpUKdXV1oi+ZvC3mcDhQLpfR29srth8NBgOKxSJUKhWGh4fFz14eeN7c3IxAIIBwOCz6m8mBSv7eABBbuMC/CvKBf3Wdj0QiYvuzWCxO2rl/7O/19vaiWCxix44d4vO0traKyQqSJMHn80Gr1cJsNkOpVMLn88FkMqGvr0+0tvD7/XA4HCKI+nw+WK1WEf5ef/11ZDIZnHzyybjrrrtE2P3d736HBx54AADws5/9DMccc8x+/+xkmzZtEqtdp556qvj9559/Hi+99BI0Gg0++tGPQq/Xo6amRtQD2mw28T1Tq9UinO6t7xsR0aGMoQzAjh078PWvfx1+vx/Dw8P4+c9/jksvvXTcilmpVBq3PXn00Udj+/bt+P73v/++VxAOBfINEID4+k0mE0KhEIrFIsrlMmw2G/L5PObPn4+NGzdizZo1WLVqlShIl0OZx+PZ7fs4VRdffDHi8Th+8IMfiP5Y5513HoDRLdK1a9filFNOwYYNGxCNRgH8a5UqEomgUCjg3XffhVKpRC6Xg9/vR1NTkxi/lE6nodFoMDQ0JJrjyjWCNTU1cDqdoqeXvFLj8XjEtqbf70dvby9aWlpgNBrHNTXdsmWLOHAwdmtUro2SyQcTyuUy7Ha72FY1GAxQqVQIBoNIp9Piv+XtPZvNhng8jtbWVtE2I5fLiVBms9ngcrmwefNm5PN51NTUoKenB8888wwymQwWLlyIxx57TKwE/+Mf/8Att9wCALjxxhvFadj369VXXwUAXHjhhaJ5cDabxXe+8x0AECdCDQYDli5dKlZZrVYrfD4fDAbDuDq2sauKDGVEdDiZ8aFsx44dOPHEE3H55ZdjxYoVeO+99/Bv//ZvWLRoEZYuXSoeJweJJ554AscccwxaW1tx0003ibqyw428fSnfALPZLGpqakSgCIVCCIVC4zr0L1u2DF1dXYhEIvjtb38rmo62trZCp9MhnU5j3bp1Ux4Wnclkxv160aJFOOuss/DMM8/ga1/7GkZGRrB8+XJ89KMfBQDcd999OPvss0VB+JIlS6DX66HVapFMJpHJZFAqlVBVVYXa2lrkcjkYjUYkEglxqk9eeZK3JAcHB2G329HS0oJCoSCCuryyOjw8jKqqKrGNGQgE4HA44HQ6RRuOuro65PN5sSonr7YBo+EkkUiIAeKtra0wGAxwOBzo7+9HU1MThoaGYLFYkE6nodfr4fP5xHZpXV0dtm7dilQqBafTCYVCAYPBAK1WC5fLhXg8jnw+j0wmg0KhAKVSiY6ODrz66qtIJpOoq6vDXXfdhUQigUQigfXr1+O//uu/UC6XsXLlSjQ1Ne31ZPHAwICYUzmZWCyGjRs3AgA+97nPia3ixx57DF6vFzqdDitWrBArZMlkEiqVCi0tLVCpVNBqtbuVDXDrkogOVzM6lIVCIXz961/HpZdeiv/93/8FMNoUc8OGDbjvvvuwevXqcatlTz31FK655hpcfvnl+OEPf3hYFPbvydgZjXJLB/kUYTKZhEajgdVqhclkgkKhQC6Xw7Zt29DQ0IBYLIb77rsPN9xwg7hhy3Vl6XR60hE7E3V1dU06bmjVqlUIhUJ46623cOutt+KHP/yhCGV1dXVYu3YtPv3pTyMQCOBvf/sbzjjjjHEnEkOhEC644ALkcjkolUokk0nY7XZxOlStVqO3txcqlUrMgkyn06ipqYHP5xNtJQKBAIaGhsQqj1yLJn+9IyMj8Hq9UCgUItT19vZi586dsNls8Pv9oj2FPDlA7oUmh43q6moAEEPgu7u7kUgkRJ+yUqkkWkjItXF1dXXo7OyERqNBNpuFwWCAXq9HOBxGIpFAe3s7tm3bhkKhgCVLluCee+4RhfddXV246qqrUCgUsGjRIpxzzjmijcWeWCwWLF++fI9//vDDD6NUKmHRokU4/vjjAYyuOst966qqqpBKpaBQKJBKpcRKniRJaG5uhslkEiuTE+eGEhEdbg7fVDEF+XwekUgEn/3sZwFAbFfNmjVr3OBm2ac+9Sn827/9G774xS9CqVROehjgcCMXpcvDoYHRk47BYBCzZ8/Gcccdh3nz5qGurg41NTVoamqCXq9HPB7H73//e/E8couF91NXNpZSqcR//Md/oK2tDel0Gj/+8Y/h8/nEn7e1teFPf/oTampqEIvF8MQTT4h+XZlMBrFYDG+99RaSyaTov2axWNDU1CS6xZtMJlgsFpjN5nE3/3w+j3K5jJ6eHvj9ftFAN5VKYfbs2Zg/fz4cDgdSqRQ6OzuxZcsWbNu2TaxqpdNpcQ1dXV3o6OgQNV9NTU0wGAxIp9NIJBIYGRnBwMCAmPVot9uh0WgQj8cRjUaRz+ehVqvFVq1Wq4Ver0c+n4ckSchkMujr60Nvby/C4TA0Gg02bNiATZs2oVAo4Nxzz8UjjzwiApnf78eVV16JSCSCxsZGXHrppR/4TUe5XBZTGcZ2///HP/6B9vZ2WCwWMTrpiCOOQHNzs/j+y01+HQ4HZs2axRBGRDPCjA5ltbW1WLt2rRikLW+tNDY27nZDikQiAIAf/OAHmD179od6ndNh4sggOZwBowHAYDDAbrfD6XRCr9fDZrOJodp1dXUAMK63mLwVvL8nMCej1WrxX//1X2hqakI4HMYll1wifj7AaAB85plnMGfOHGSzWWzduhUDAwNQKpUiMO3YsQP9/f3YunUrtmzZguHhYRGYFAoFYrEYSqUSSqUSQqEQdu3aJdpH5PN5dHV1IRAIQKlUYnBwEN3d3fB6vfB4POKkqrxl6PP5RO2Yw+GAXq+HxWKBSqWCyWQS3295ZSuXy4kB4eFwGD6fD1u2bBEzLeWCeL/fL9pdaLVasYJXKBSgVqvF1xMOh3Hvvfdi586dAEbrxG6//XbRYT+VSuGLX/wi+vr64HK5cOmll+62Zfh+bN++HX19fdDr9fj4xz8ufv+2224D8K83PCqVCtFoVPTIq6qqgl6vh0qlYhgjohllRocyAKJIv1Qqifqocrk8rgD7lltuwX333bffw8cPZXsa7iwXscthYseOHQiFQlCpVFiwYAGMRiPq6+uh0WiwefNmuN1uAKMHI4DRUDbZtuT+MplM+OY3v4mqqirs3LkTV155pdiiBEZPQz755JM49thjEYvFRC8xtVqNfD6PXbt2oaurCwMDA3C73aJzfiKRgNvtRrlcFitR3d3d6OvrQz6fh8ViQaFQgEajgclkQiqVglarRSAQQCAQgNfrFYcNjEYjqqurxTZkdXU1tFotGhsb0dLSgmOPPRYLFiwQTVDlxrTybEqbzQaj0SgCYzweF61IUqkU9Ho9PB4P/H6/mLwghzP51OfIyAgeffRR9PT0QJIk3HXXXbjmmmtEIMrn8/jP//xPbNmyBVVVVXjggQfEz/aDevbZZwEAJ510kghXGzZswCuvvAK1Wo3a2lrY7XYolUoRAhOJBGKxGAYGBhAIBA7IdRARHSpmfCiTKZXKcWFBXin77ne/i29961s49dRTxfbdTCA3PQUw6YpZY2OjuPEDQHNzM5YsWYKmpiYxgxIYLb4HRkcjaTQaJJNJbN269YBco91ux7e+9S2YzWa89dZbOOuss9DZ2Sn+vLq6Go888gjOPfdc5PN5vPHGG9i0aROGh4eRSqWQSCQwNDSESCSCoaEhaLVaDA8PQ6vVoqurC9lsFuFwGMFgUMz4dDqdcDqd8Hq96O7uRi6Xg9vtxpYtW7Blyxa8/fbbGBwcFPVptbW1aG5uFtuEcmiSO9dv2rQJiUQCSqUSJpMJDocD2WwWtbW1cDgcMBgMSCaTop7N6/Xi3XffxebNmxEKhVBdXS0K+QOBAHp7e0UT2d7eXmzduhWJRAINDQ147LHHcMYZZ4jvTy6Xw7XXXosXX3wROp0O9957L2bNmjXp9zocDu/Xm5JAIIAXXngBAPDJT35S/L68Smaz2eBwOMQWscFgQDabhdPpFKcv5dYhREQzxQENZW+//faBfLoPnRzK5C7qt956K37+859j/fr1u42GOdyN3a6cuGImBzZJkqBSqSBJEoaHh9HT0wOFQgGbzSb6dj3wwAOIxWLQarU45ZRTAAB//OMfD9hIqpaWFjzyyCOoq6vDzp078clPfnLcaUG9Xo8777wTN998swhC7e3t6O7uRjqdhkKhEIPJ5Vme+Xwes2fPRkNDA1wuFzQaDVKpFLZs2YJoNIpAIIBUKoVIJILBwUHE43G43W54vV4kk0lEo1HEYjH09/eL71tvby82btyIzZs3o7OzE2+99Ra2bt0qGrgaDAb4fD5s2rQJmUxGfF/l1hxqtVq048hms4jFYvB6vRgaGhKnQUdGRsScy56eHmzduhXxeBwnnngi/vKXv2DhwoXi+xKPx/HlL38Z//jHP6DVanHnnXdOWrBfLpfx3HPP4cc//jEeeeSRKf9cfv/73yOXy+HII4/EUUcdBQDwer147LHHAAANDQ3QarVQKBTi66mtrUVDQwOOOOIILFq0CLW1tdy+JKIZ5YCGsgsvvPBAPt2HTl4d02g0uOeee/CjH/0I69atE0XqM9HYMUHA+MadwGiT1Ww2KwJHKpVCXV0d6urqYDAYxhX8n3vuuZAkCV6vF6+99toBu8Zly5bhueeew0c/+lHE43FceeWVuOWWW8TJQaVSia985StYt24dLrnkEpTLZfj9fnR2dsLj8aCvrw+xWEysoIXDYWzcuBHt7e0ol8uiYWsoFEJnZye6u7vR398Pv98Po9GIQCCAdDqNoaEhFItF2O12uFwuKJVKeDwePPvss3jxxRexc+dOMcPR4/EgGo0iHA6jVCqhq6sLIyMj8Pl8SCQSSKfT6OjowM6dOxGNRsXzy01kAYgtzVwuJ1b1fD4fXnvtNdF09mtf+xqeffbZcW0rvF4vzj//fLz88svQ6XS45557RGAeq1gs4rHHHsNzzz0HANi5c+eUtp77+/tFgf/VV18ttkp/85vfoFgswmQyiaawFosF4XAY8Xgc/f39405eyn3biIhmiv0OZZ/73Ocm/efCCy8UJxYPdfIWzxtvvIEVK1ZM89VMr4mzHCfWmsnjiPL5vBjK7XA4MG/ePLFCMvZmLM9VfPTRR5HNZg/YdTqdTjz66KO46qqrAIwOuT7rrLNETRsw2jLjgQcewMsvv4yjjjoK4XAYHo9HnILM5XKiNYa8tfnWW28hl8uhXC6LQefypIBisSi2FeVmrfF4HGazGTU1NWhoaEAmk0GxWITf7xcrQ8BomK2trYXFYkEymRQnJfv7+0XI2759u9g2HRkZwdtvv43u7m7RekOpVIptv1AohN7eXvT09CAcDkOSJDz44IP4+c9/Pq6X3BtvvIFzzjkHu3btgtPpxJ/+9CecdNJJu30/s9ksfve73+Htt9+GQqEQq3Hyac+9ue+++1AsFnHssceK10AymRRtMJqammC1WjFnzhyYzWZUVVXBbrejqalJfE06nY5bl0Q04+x3kdQLL7yABx98cLdi4HK5LObbHepWrFiBeDw+o9+lj10RkyRpXGf/sQPL5aapJpMJs2bNgsViQXd3t+hftXHjRvT09ODpp58GAJx++ul47rnnEAgE8Pe//x3nnnvuAbtmjUaDH/3oR1ixYgW++c1vYuvWrfjEJz6B//qv/8K1114rGv2uXLkSb7/9Nu655x5873vfQzgcxvbt22GxWNDc3IzGxkak02kEg0GoVCr09/ejqqoKKpUKOp0OiUQC5XIZJpNJNJ1NJBIoFovYtWsXUqkU5syZA6PRCKVSiWKxiI985CPo7+/H0NAQ4vE49Hq92Abt7+9HfX09yuUyqqurMTw8jHQ6DbPZjO7ubgwNDWHbtm3IZDKoqqoSK2OZTAbpdFqs9sn1fccffzzuuOMOHHnkkeO+Pw8++CC+//3vix5ld999N2pra3f7PiYSCTz00EPw+XxQq9VYtWoVnnvuOQwMDMDn88Fms+3xZ9DZ2YmXXnoJAERABoCnn34asVgMkiThqKOOwkc/+lHRUDiVSkGtVkOn00Gj0UCv149bnSUimin2O5SdfPLJMJvNOPHEE3f7M/ld8eFgpt8Qxq6ISZIkfi3PIPT7/fD7/QBGWxo4HA7E43FRxB4IBKDX67FgwQJs3boVv/71r3HJJZdAoVDgnHPOwX333YcnnngCK1asmHTW6NDQkFgl2huz2TzpKb1vfvObeOihh7Blyxb89Kc/xR//+Ed86UtfGhcCTznlFCxfvhx33303HnroIcRiMezYsQMajQbz5s0bt6qVyWRgNpuRy+XG1dK1traKE6XxeBwqlQqlUgnxeBwKhQItLS2iYF9eVdNoNNBoNAgEAkgmk0in09i1a5eoszKbzWK1yGazIRQKiVWkmpoaWCwW0X9sw4YNCIfDAEb7611//fX4+Mc/DoVCgV27dgEYPWF5zTXX4PXXXwcALF++HBdffPGkNaAjIyP4zW9+g0QiAZ1Oh5NOOkm04QCA9evXj2so63A4xp16/b//+z8AwIknnoi6ujoRVuX2KE1NTaIe0Wg0olAooKqqCo2NjVCr1QiFQnudEEBEdDibciiTt2Uef/zxPT7m+eefPyAXRdNv7CgbhUKx26/lHlmJRAIOhwPJZBImkwm5XE4MLZebqrrdbrz22mu48cYbceSRR+K0007DO++8g23btmHLli34wQ9+sNvn37FjhwgCwGjLkv7+ftTW1o7rodXX1zfpyo1arcZll12GDRs24K9//St6e3vx3e9+F36/H1dccYU4WWqxWHDDDTfgoosuwurVq/Hss89i06ZN6OjogNPpRG1tLQwGg3h8uVwWvcEaGhrE/Mmxsxij0ag4QDA8PIzq6mpkMhlEIhFRc2cymcT30OfzQa/Xo1gsYs6cOSgUCujv74darYZSqRTjofR6PTQaDd555x1s2rRJDD2vrq7GNddcgwsuuGDcdQKjpyavv/56vPvuu1AoFDjjjDNw0kknoVAo7Haa0uv14oEHHkAymYTFYsGnPvUp8b1tbGxEd3c34vG4aNkBjLbvkLf4+/r68M477wAAfvjDH2L+/PkAgCeffFIMilcqlaI9h9wU1uFwwG63I51Ow2q1ipVD+XVIRDRTTLmm7IQTTsDQ0NDBvBaqIEajcVyh9cRfyyskOp0ONTU1OPHEE2EymWA2m1FfXw+dTifaPMg38fvvvx/AaOH9//zP/wAYPYnZ3d29z+t5/fXX8dBDD2HNmjV4/vnnp7SKplAosHz5ctxwww1oa2tDsVjE7bffjssvv3y3z9nU1ISf//zn+MMf/oClS5cinU6jt7cXGzZsQH9/P1QqFTKZDJLJJOLxOFKpFHp7e+Hz+bBt2zaEw2FRd6VUKhGJRLB161Z4vV60t7djaGgI5XIZFosFTqdTNI7VaDRQq9VIJBLw+/3YuHEjvF4v+vr64Ha7sXXrVlRVVWH27NkoFAr4y1/+gtdeew3xeBySJOHqq6/Gs88+i89//vO7tWzZtWsXLr74Yrz77rvQarW47LLLcPLJJ086iWLHjh245557kEwmYbVacf75548Lu/JJXHl1dDJr165FqVTCCSecIAJZuVzGb3/7WwDA/PnzMWvWLBHCVCqVOAwiDyM3m82w2WzIZrMMZEQ040w5lB199NE49thj0d7ePu73N23ahLPOOuuAXxhVNqfTifnz54vGqHLT2JaWFixatAiNjY0wmUwIhUJoaGgAMDo7VG7K+9GPfhSnnHIKisUifvazn+31cxWLRWzevBnAaG+tDRs24N5778XDDz+M3t5eUUu1J1arFV/4whdw8cUXw2w2Y+vWrbjwwgvxu9/9brePPeqoo/B///d/WLt2rVi16uzsxOuvv46+vj5RA5XJZJBKpRCNRjEyMiLqu0qlkjgtGY/HMTIygmQyKQZtKxQKbN++HRs2bEB3dzd27doFhUKB6upqlMtleDweEfzkoe9erxdPP/00/vKXv2BwcBBKpRJXXHEF3nvvPXzpS1+aNLy8/PLLuPTSS+Hz+dDU1IQrrrhiXEuMsd566y08+OCDyOfzWLBgAY4//nhxsENWU1Mj5lNOVoCfzWbxhz/8AQBwxRVXiN9fv349NmzYAJ1Oh6amJrS0tGDhwoVYuHAhTj75ZFRVVYmt3UAgALvdjtraWrS2tjKUEdGMM+VQdv/99+PKK6/EypUrsW7dOuzcuROf+9znsHz5clFATTOL0+lEXV0dnE4nksmkmFV4yimn4KSTTkJLSwsMBgPmzJkDq9WKfD4vbtzAaN2XSqXC888/j5dffnmPn6enp0fUtn32s5/F3LlzoVAo0Nvbi1deeQW33HILXnjhBbGdNxmFQoFjjjkGjz/+OI4//njkcjn88pe/xBVXXLHbqplCocCnPvUpvPXWW/j5z3+OmpoaJJNJbN++He+++y58Pp84VVkoFEThfaFQEPVWmUwGCoUCWq1WnDLVaDSIRCIIBoPweDzo6upCoVBAKpWC3W5HLpdDVVUVtFotmpubAYwOCX/55Zexa9cuFItFnHnmmXj99ddx++23i3FWY5XLZdxzzz247rrrkEqlcMwxx+Dhhx8WK10TH/uPf/wDf/3rX1Eul7FixQpcfvnlkzZJ1mg0qKqqAjD5atnTTz+NYDCIurq6cQ1q5VWyxsZGSJIkTodms1mYzWZYrVYUCgUMDAyIAOtwOBjIiGhG2q+WGN///vdx/fXX4/TTT8eRRx6JeDyON998E08++eTBuj6qYPKWpryqIs9uTCaTqK6uhsvlwpw5c6DVajFnzhwAwB/+8AcxHWDu3Ln4t3/7NwDA9773vT22yJAnACxatAhz5szBBRdcgC9/+cviBF8kEsHf//53/OhHP8I999yDF154Af39/ZM+V11dHe6880784Ac/gMlkwubNm3HBBRfg1ltv3a3dg0ajwZe+9CVs2LABX//612Gz2ZDL5TA4OIitW7dix44d6OjoQCwWQzqdRi6XQz6fF1uYcmd6pVKJRCKBTCaDoaEhDA8PI5/PI5fLIZlMinqyhoYGsRr16quv4oUXXkB7ezsikQgWLVqEJ598En/84x9xxBFH7PZ1lctlrFu3DldccQV+9atfoVwu46KLLsJdd901ac1dNpvFww8/LMLwaaedhgsuuGCvb7DkAvzJQtnvfvc7AMBll10mQl13d7cYtXTEEUcgk8kAGK1dGxwchM1mg8FggNVqFSuuREQz2ZRD2fDwML761a/iRz/6kRiZc+WVV+KYY445mNdHFUTuGr+n/lE2mw3pdFoUkC9ZsgR2ux3V1dXi1GAoFMIvf/lL8TFf/epXUVdXB5/PN26A+VjpdBrA+KJvq9WKk046CRdeeCEuvvhiuFwuFItFdHR04O9//ztuv/12PPvss5NubSoUCpx33nn4y1/+IoreH3jgAXzyk5/EfffdJ8LD2M/1ve99D+3t7bj//vtx2mmnQalUIplMor29XfQ627VrFwYHBxGLxcSJRLnOTJ65KXfnB0YPL8gnEAOBALZs2YL33nsPDz74IN544w2x+njrrbfilVdewcqVK3f7WgqFAp5++ml89rOfxVe+8hVs2LABer0e3/nOd/Dtb397XI8yWV9fH1avXo3NmzdDqVTiggsuwGmnnTZprdlYcpie2EB28+bNePfdd6FWq3HppZeKx9x0000ol8uw2+2w2+2YO3euOKyQTCYxMDCAjo4OdHV1IZ/Pw2QycYWMiGa0KZ++nDVrFhYsWIBHH30UZ599Nv7+97/j85//PLxeL2688caDeY1UIeS2GCMjI6JP2diDAMlkUqymGAwGbNu2DZIkIRqNolQq4fjjj8ezzz6L3/3udzj77LOxbNkyGI1GfOUrX8HNN9+Mu+66C5///OfHna4ERlfI+vr6sGHDBnzkIx8RkxeA0XYcS5cuxfLlyzE4OIiuri7s3LkTO3bswIsvvoiuri5ccsklk67E1NXV4de//jXWrVuH2267DTt37sRtt92Ghx56CN/97ndx0UUXjVs50uv1OO+883DeeedhcHAQL774Il599VWsW7cOg4ODyGaz49pDyIO2tVot9Hq9WGkzGAyidUY+nxenNMe2mli2bBkuvvhiXHjhheNOO8pSqRTWrl2L22+/HYODg+J7fuGFF+Lyyy+fdGuzVCrhn//8J5577jmUSiVYrVZcdNFFe5x3OZbf74fP54NCodhtpU5uCnvOOeeIvmePPPII/vnPf0Kv12Pp0qWora3F3LlzodFoRNsLOcArFAro9XpRe0hENFNNOZTdd999uOiii8SvzzzzTLz88sv41Kc+BY/HgzVr1hyUC6TKIQcvuX5q7LglSZJ2Kw4PhUIIBoOoqqqCyWSCXq/H3Llz0dnZiW9+85t48sknodPp8PnPfx5r1qzBwMAA/vrXv+Jzn/vcuOdZtGgR/vnPfyIWi6GjowNtbW2TXl99fT3q6+uxcuVKbN68GY8++ig8Hg9uu+02fO5zn8PSpUsn/biVK1fiuOOOw9NPP4077rgDQ0NDuOaaa7BmzRrcfPPNOP3003dbRaqvr8eqVavw+c9/HkajEZ2dnXjllVfw6quv4rXXXsPIyAhKpRIymQwymQxisZg45LAn9fX1uOSSS3Deeedh0aJFkz4mFArhnnvuwd133y0maFRXV+PSSy/FRRddNGmAA0Zb2vzpT38SA9sXL16M8847b7ef2Z5s2LABwOiW89i+cvF4HH/7298AjI5UAkZX1W+++WYAo7NJTSYTVCoVWltboVAoRGsTg8EgxnjNmjWLDWNpRhs7fWRv5DFudHiacigbG8hky5YtwxtvvIFPfvKTB/SiqDLJK2PyacJ93UBTqRSUSiVqa2thMpkQj8exfPlyeL1edHZ2Ys2aNbj++uuh0+lw9dVX4yc/+QnuvPNOnH/++eOeR61W4+ijj8brr7+Od999F0ccccQ+t9qWLFmCpqYmrF27Fn19fXjggQfQ2dmJE044ATqdbrfHq1QqnHPOOTjjjDOwdu1a3H///dixYwc+97nPYeXKlfjBD36wxxmoCoUC8+bNw7x580QwSaVSGBoawuDgIIaGhjA0NISBgQH4/f5xv59Op3HWWWfh8ssvx6mnngq1Wj3pKCOv14vf/OY3ePDBB8U2YmtrKz7/+c/jwgsvHNfTbaJXXnkF9957L9LpNDQaDc455xysWLFin99DWSQSEYchJn4P5GayH/nIR0To/da3voVoNAqz2YxZs2ZBpVKhUCggm81Cr9eLthgAxMfU1tZOehiB6HBnt9shSRJWrVo1pcdLkgS3281gdpja747+E7W2tuKNN944ENdCh4ix25Z7M2vWLFG8L9dVmc1mHHvssXjttdfw29/+Fp/85CfR1taGSy65BHfeeSd6e3vx1FNP7fZcRx99NN5++20MDg7C5/OJ04l7U1NTg2uvvRbPPvssXnnlFbz++uu45JJL8Itf/AKzZ8+e9GN0Oh0uv/xyfO1rX8P//u//4q677sK6detwyimn4JxzzsEVV1yBk046adITimNJkoTZs2eP+zyFQmHSQLg37733HtasWYMnnnhC1McdddRR+OpXv4pzzjkHHo9nj4Esk8ngf//3f/HQQw8BGF2Ju/jii+F0Oqf8+cvlMl599VWUy2W0traipqZm3Nezfv16AP9aJXv66afx9NNPiyDtcDjEFvBrr70mGvHW1tZCkiRxGIIrZDRTuVwuuN3uSSeTTOR2u7Fq1SoEAgGGssPUBw5lAMRReZqZJutdJc+DlCQJW7ZsgdPphNVqxdFHH42Wlhb4/X60t7fjv//7v/Hoo49Cq9XiyiuvxG233YY1a9Zg5cqVu7W4mD17Nnbu3Il169bh1FNPBQAxQ3Nv5IDgdruxc+dOfPazn8UZZ5yBJUuWTLpaVFVVhblz5+LUU0/FUUcdhYceeggvv/wynnjiCTzxxBOwWq1YuXIlTjjhBMydO3dKNVkApjxCaPPmzdi2bRueeuqpcX0BFy9ejHPPPReLFy+GQqHAyy+/jE2bNiGXy+32HIFAAE899ZT4i37OnDmYM2cO3G73PrdJMpmM2Brt6uoSzXOPPPJI8fvA6OnKVCqFhoYGfOITn0ChUMAtt9wCYHSbc968eaJRbrlcxpYtW2C1WrF48WLk83mxfWk0GmEwGMYdIJjqKh7R4cDlcjFkEYADFMpoZpMPAITDYVRVVYl/p1IptLe3IxqNih5c6XQamUwGH/vYxzA8PIzt27fj8ccfx4033oibbroJ9913H7q6unDeeefhYx/72LjPc/TRR+O6665DX18fli9fjoaGBnz961/f7WDAnrS1tYmC9aeeegodHR04+eSTd/v4SCSClpYWAKMnSv/jP/4DZ599Np5//nm88cYbiEajYkXIbrfj05/+NM444wzMnTt3r58/lUqhVCrt9c+feOIJ3HfffWJigUqlwnHHHYczzzxTXNPYELZp06Zxq1flchk7d+7Ee++9h2KxCL1ej4997GPw+XzjDiHsTUtLCy655BIEg0Fcc801AIArr7wSn/nMZ8Z9nuuuuw4AcO2116KhoQEvvfQSurq6YDKZUF9fD7/fLw46DA0NQaPRiDmgDocDqVQKOp1O9KAjIprpGMroA5PrzORB5XKgqK2tRXNzM5RKJRoaGpDP56FWq1EsFmE2m7FkyRK88sor+PGPf4zLL78ctbW1uOaaa/CTn/wEjz32GI477rhxKyZNTU1YsWIF1q9fjyeffBJf/vKX9+s6tVotzjnnHGzYsAFvv/02du3aheHhYZx22mli1uKetLS04KqrrsKVV16JrVu3Yt26dXj77bcRCARw//334/7778ecOXNw5pln4hOf+AQaGxunfF3Dw8N45JFH8Pjjj4vVQaPRiFNPPRWnn376pH3GJiqXyxgcHMSmTZvE97+hoQEf+9jHRMf8/SGPR0omk5g3bx4+/elPj/vzrVu3wuPxQKfT4Qtf+AIA4M477wQwOpKptbUVOp0OVVVVUCqVMJvNCAaDOPbYY9HS0iIGu7O4n4joXxjK6AMbe/LS7/fDZDIBGF3ZMhgMqKmpQV9fH9RqNQKBgNiuWrFiBbZt24ZAIIDbbrsNP/3pT3Httddi9erV8Hg8eO+998Swa9m5556L9evX4+WXX5708Mm+yPMwGxoa8NxzzyEWi+Hxxx/H3Llzcdxxx407WTgZeSv06KOPxpe+9CWsW7cObrcbr7/+Orq6urBmzRqsWbMGVqsVBoNB/KPX66FQKMRYIfmfoaEhvPDCC6JerLm5GccccwzOPPPMvRbvjzU0NIRNmzaJpq5qtRpLlixBW1vb+94GfOONN/DWW29BpVLhP//zP3drKvvEE08AAE4//XRUV1fD5/OJJtINDQ2w2WxQKpXj5qUeddRRaP1/7d13eNPl+j/wd/ZqkmZ0b2ihZUpZchQQQZEDggPxoDhR1OPGPUDFPdCvwjlHBZw4QREXqBxAQEBkyGwpYBdtaZOO7NF88vz+6O/znLYUKFBIx/26rl5AkrZP0iZ584z7Tk8HAL63jjb3E0LI/1AoI21Kq9Xi8OHDMJvN0Ol0yM7ORmJiIlauXAmJRIJgMAifzwe73Q6lUonU1FTY7Xa88847eOCBBxATE4PbbrsNc+fOxZIlSzBw4MAmwaJXr17o3r07Dh06hJ9++umUx5mQkICrr74amzZtwr59+3Dw4EEUFhaif//+RwXBY1GpVBg8eDCmT58Ol8uF1atX46effsLWrVvhcDhaPEV5LLm5uZg2bRqGDx+ODRs2tCqQHThwAL///nuTpc6ePXuid+/erQ50LQkEArw90uTJk4/aM1dRUYEtW7YAaAjJALBgwQKEw2FoNBoEAgGUlJQgNjYWVVVVyMjIQFpaGsLhMKxWK+x2+1EFaAkhhFAoI21MbEwOoEnZDIPBgOrqakgkEtTX18Pv98PlcvGZI6/Xi9deew0vv/wy7r33XsybNw8HDhzA1q1bMXjwYP71JRIJJk2ahNdffx0//vjjMetytYZarcaoUaPQt29fbNiwAWVlZdi+fTvy8vLAGOMlKlpDr9dj0qRJmDRpEhwOB6qrq+Hz+Zp8VFRUQK1W83+L/THHjh17zGbhLampqcGnn36K33//HUBDkdqsrCz06dOnTfZm/fnnn6irq0NycjKuvvrqo67/6quvwBhDbm4uUlJS4Ha7sWjRIv441NXVQa1WQyqVwmAwQC6Xw+l08lkxk8mEQCDQ5BSoeFhEp9PR/jJCSJdFoYy0KZ1OB71ez//d+FSmwWCA1Wrlp/nEmbPExES+9HfLLbcgKysL48aNw/Lly/H2228jOzu7ydccNmwYn4WRyWSnNSsENNQJmjRpEoqKirBx40bU1dVhwYIF+OGHHzBt2jQMHjz4pJYBjUZji2GxrKwMycnJpzzOUCiElStX4ptvvkEgEIBEIkFSUhIGDx7Ml4xPl9Pp5DXJ7rrrrqPaNG3fvp3PUE6ePBkA8Oyzz6KqqgpyuZwXCdZqtTAajVAoFJBKpXC5XLw8SkpKCl/GtNlsfE+iWJCYQhkhpKs6qYbkhJyIVqtFeno6f9N1Op3Iz89HVFQUJBIJEhMTYTQaeX/J2NhYWK1W6PV61NfX4+GHHwYATJkyBUlJSaitrcW7777b5HvIZDJeYNbpdB73RGNrSSQSZGRk4B//+AdGjBgBg8GA8vJyvPLKK5g9ezYOHDhw2t/jVInlJJ544gl88cUXCAQCyMrKwrPPPot+/fq1WSALh8M4dOgQAGDs2LFHdRVwu9148803AQATJkxA37598ddff+Gtt94C0FB2IyYmBrGxsYiOjkZiYiKioqL4UmUgEIBKpeKzYY2DmFjZnzb9E0K6Mgpl5JScqDk50DBrFggEEB0dDZlMhl69eiEYDMLv98Pn8yEQCEAmk8FisaBbt26Qy+X48ccf8dNPP0GlUuHee++FVCrFb7/9hg0bNjT52qNGjYLFYoEgCHA6nW12v2QyGfr164f58+fjiiuugFKpRF5eHh577DG89tpr2L59e5MelWeSx+PBypUr8cgjj+DVV19FeXk59Ho9ZsyYgSeffJKXyGgr5eXl8Pl8UKlUuOGGG466/j//+Q9qamqQlJSEG264AeFwGPPmzYMgCLBYLMjKykJCQgJMJhN69uwJs9nMlzOtVisSExObbPxvHMS0Wi1iYmJolowQ0qXR8iU5Jc2Xm1raEyS+0dpsNmRmZsLv98NgMPDm3EqlEvHx8fB4PGCMobKyEkeOHMFDDz2EZ555BpmZmbjqqqvwxRdf4N1330VOTg6vyaVQKHD55Zdj4cKFqK2thdFobNOCo1qtFtdccw0uvvhifP755/j111+xefNmbN68GTqdDkOGDMGwYcP4jGBbKikpwbJly7B582Zek0ytVmPkyJG4/PLLz8hskt/v52UzBgwY0GS5GGioxr9u3TpIpVLMnDkTarUaP/30E/Ly8hAVFYXU1FQwxsAYg8lkQnx8PMxmM/x+P4xGI++B2fjxaqlfKiGEdGUUysgpEfcBiQHheHuCTCYTr08mCAL8fj8yMjJgs9lgt9sRDoehUqmQkpICu92O/fv3Y8WKFZg0aRKuvPJKbN26FYcOHcK///1vPPnkkzx8jRkzBu+//z5CoRCcTudpbfo/FqvVirvuugsTJkzAf//7X2zatAl1dXVYs2YN1qxZw+uJjRkzBkOGDGn1wYDmfD4ffvnlFyxduhR79+7ll6ekpGD06NG83tiZwBhDYWEhwuEwDAbDUUGzurqa1yC76qqr0KNHDzgcDnz44YcAGvYKymQy+Hw+PhOmVCoRDoeh1+uRmpqKmJiYo4IeIYSQpiiUkTbRPKS1dHl9fT18Ph8yMjJQWVmJcDiM0tJSmM1myGQyBAIBpKWl4dChQ1iyZAnOPfdcGI1G3H777Xj88cexY8cOrFy5EqNGjeJfX6vVwuVyobq6GlKp9LizZQaDAbt27TrhfYmLi8PHH3981OVKpRIjRoxAdXU1ysvLUV5eDo/Hw9svqdVqdO/eHVlZWbBarXws4rik0obdAhKJhH84HA7s3r0b+/bt4xvhpVIp4uPjkZaWBpPJBJvNhuXLl7c4Vrvd3qrCsPX19cdc5nU6naitrYVEIkFsbCxCoRDf88cYwxtvvAGXy4WMjAxcdtll8Pv9WLhwIVwuF6xWKzIyMvhSZXx8PHw+Hw4ePAitVou+ffuesTBJupaSkpJW94ckpKOiUEZOSeOZMfHfLTUqbzyTBjTs2YqLi0NcXBzy8vJgtVpRU1ODuLg4XkxVqVTC6/Vi48aNeP311wE0lEx46qmnsGzZMjz66KO8yOuVV16Jzz//HH6/Hzk5OejZs+cxx7x+/fpWzdasX7/+hFX0lUol0tLSIAgCJBIJSktL4ff7sXfv3iYzXSdDp9MhMzMT5eXl0Gg0qKqqQlVV1XE/p3Gx3uPp0aMHJkyYcNTlfr8fr776KgDgwgsvxLhx4xAVFcV7i7733nvYuXMnVCoVPvnkE2RnZ2PTpk1Yu3YtgIalTolEArlcjj59+iAYDCIQCKC6uprXqtNoNAiHw0fNrB7rd4aQ5kpKSpCTkwOv19uq22u12lb1mSWkvaFQRk5J4xmw5qfomhOvLy8vh0qlQlRUFGJjY6HVamE2m9G7d2/evLx79+4AgB07dmDx4sW44YYb0L9/f9x6661YvHgxDhw4gLlz5+KZZ54B8L/q9b///ju2b9+OrKwsPiN1pkkkEkRFRaFXr14YOHAgqqqqUFpaisOHDyMYDPI9VieSmJiIrKwsxMfHQyqV4siRI2dh9A1+/vlnOBwOWCwWjBkzpsl1hw4dwuzZswEAs2fPRnZ2NoLBIB544AEADQV44+LiUFVVhbi4OKhUKr6nLC0tDT179uQh2WazISYmhocxj8fD+15SKCMnYrfb4fV6sXjxYuTk5Jzw9larlRp8kw6JQhk5Jc1nOI735ioGN61Wy9sJFRcXo6CgAHK5HD6fD0qlEjabDSqVCvHx8cjMzMTBgwfx+OOP4/vvv4dCocCcOXMwdepULFiwANdffz0PcL1798aff/4Jh8OBQ4cOISsr68w/AM2IS47x8fFNit0C4OGssLCQn5gUL5NKpae8D038OoIgIBQKIRwOIxQKgTHG+0oeT1lZGdavXw8AuPzyy5vUJAuFQrjjjjvg9XoxYsQI3mf0P//5D/Lz8yGXy5Gdnc0DVnFxMWJjY2EwGNC/f3+kp6fzgrhFRUV8pkz82gCoBAY5aTk5OcjNzY30MAg5Y6gkBjltOp2uSamDY12flpYGmUyG6upqlJWVQalU8pOMcXFxCIfDqK+vh9lsxqWXXgqtVostW7bgm2++AdCwsX/06NGor6/H008/zb++UqlEv379ADQUN21vLXzE/WRiAJPL5VAoFFAqla0OZG63G2VlZTh8+DBKSkpQVFSEwsJCuFwuVFZWorq6GrW1tXC5XHC73airqzvu4xAKhbBkyRIwxtC/f39kZ2c3uf7NN9/E1q1bodfrMX/+fEilUpSUlOCVV14B0BCE4+PjIZfLeeBWqVQ8mB2rp6VYJkX8O4UyQgj5Hwpl5KwQ65qVlZXxMg8GgwFJSUmwWCzo0aMHunfvDrVaDY/HA4PBgCFDhgAAnnjiCb6k9+yzz0Iul2PlypX47LPP+Nfv06cPlEolamtr8eeff571+3emCIKAyspKVFZWwu/3IxAIoL6+HoIgHLdobjAY5DNSzYXDYSxZsgSHDx+GRqPBxIkTm1x/8OBBvPzyywCAV155BcnJyRAEAXfffTd8Ph+MRiP69OnDi8SmpKQgISEBgwYNwjnnnMP3kgHge4DEJWsxiIlLl4QQQv6HQhk5KzweD9xuNwRBQHV1NUwmE7p164ZDhw5h/fr1qKmpQe/evWEymeB0OnHkyBEMHjyYnz689dZbUV9fj6ysLMycORMA8MADD6CiogJAQ3PwoUOHAgB+//13FBYWRuy+tgXGGNxuN0pLS+F2u0/688UZuZa+7rfffott27ZBKpXimmuuaVJKxOl04t1330UoFMKVV16JKVOmAABeeuklrF+/HjqdDn379gVjjO+bEzs1mM1m1NXVwe12o6ioiNeuE6v4A+AHF2jpkhBCjkahjJwVOp0OUVFRsFqt6NWrFywWC+RyOaqqqlBYWIi1a9fC4XAgHA5DoVCAMQabzYaRI0ciKioKmzdvxvPPPw+gIYxNnDgR9fX1WLVqFRwOB4CGJTWxNdAvv/yCbdu28T1sHYkgCDhy5AgqKyshCEKTvV6pqano3r07unXrhoyMDERFRSEmJgYWiwUmkwnR0dGIjo5uUpKjsZ9//pl3R7j66qubbJoOhUL46KOP4HQ6kZOTg//7v/+DRCLBr7/+irlz5wIAkpKSoNPpIJFIEAgE+PdXKpUoLy9HQkICHA4HbDYbL00gBjDxwAeA4y53E0JIV0WhjJw1Op0Oqamp/HSkuNesuroaDocDJSUl0Gg0SE5O5m/6jDFkZmYCAP71r3/hxx9/hFQqxbx58zBgwAAEAgGsWLGC71M677zz0K1bN4TDYfzxxx/4+uuvT1hWor0Ih8MoKChAdXU1X/YzmUxISUmBTCbjtwGa7lNTKBRQqVTQaDS8Sn5LJ1DXrVuHX375BUDDxv6BAwc2uf77779HUVERNBoNPvroI+h0OrhcLtxzzz0AGoJUQkICQqEQXC4XpFIpMjMzMWDAAN4gvq6uDmazGT6fDzabDTabjX996m9JCCHHR6GMnBWNZ0l0Oh3C4TCKi4thMpmQmZmJmpoaFBYW8n/Hx8dDoVBAo9GgX79+fAbsvvvuw5EjR6DVanlwqKurwy+//AJBECCVSnHRRRfhwgsvhFqtRnV1NZYtW4ZNmza1SePyM6Wurg6rVq3Ctm3bwBjjHQ7MZnOTwrOneh8qKirw7bffAgAuueQSnHfeeU2u37ZtG59Bu+mmm/jJ1jlz5qC0tJQfplCpVFAqlVAoFDCbzUhKSkJKSgrKy8shl8uhUqlgsVgQExPDw1njcik0Q0YIIcdGoYycFY1nScQTeCqVCmazGYmJiYiLi4NSqYRUKkVMTAxiYmJ4HSyTyYRBgwbBZDKhtrYWd911F8LhMOLj43HxxRdDLpfj8OHD+O233/gepx49euDqq69GZmYmGGPYuXMnDh48iNra2kg/FE0IgoBdu3Zh5cqVqK6uhlwuh16vR1JSEpRKJb/d6YQyn8+H/fv3AwBGjBjBC8OKysvLsXTpUgANJ1zFk6wbNmzAokWLADQcpEhJSUF6ejoSEhKQkpKC7t2782r9OTk5fIk6NjYWOTk5iIqKgs/nQ21tLQUxQghpBapTRs4KsbK7KC0tDR6PB/Hx8dBoNHA4HCgrK0M4HOZLYLm5uairq0N1dTWCwSDOP/98rFq1Cr/++ivefvtt3H777dDr9RgxYgRWr16Nffv2Qa/X8/pYUqkUw4cPR3p6OjZu3Aiv14udO3fCYrEgMTHxmOUowuFwq8Ob1WrFjh07mlwm1g4Lh8P8QxAEyGQyFBYWNrnO4/Ggvr4ewP9OKDocDtTV1TX5muLeOJfLxU+vit9LXLptSTAYhMvlAgDk5uZizJgxvIUS0HA68v333+eHKIYPH45gMAi3282XLZOTkzFw4EDez9JgMKBv376IiYmBQqGARCJBZWUlcnJyeB02kdhtgFotEULIiVEoO03izAw5scaPk7j3CWgIbCNHjsS2bdvgcrlQUlICmUyG+vp6KBQKeDwelJWVoaamBjExMSgpKcHzzz+P8ePH4+mnn4ZUKsW7776LF154AX/88Qduv/32Jv0xgYYwM2PGDGzatAnV1dWor6/HlClTcM455xw1zvnz57d6ZufPP//k+70YYzyAnQq32w232w29Xn9Uc3Wv14tQKASFQtGk4XtmZiYuueSSFr9eSUkJFi5cCAA455xz8NVXX/GxAg3h86abbkJtbS1SUlLw1Vdf8fZSr732GoqKiiCVSmE0GmGz2WA0GlFVVcWrpUdHR/N+pt26dQNjrElvQnGcMTEx9BwhhJBWoOXLk3D48GH89NNPWLJkCYqLiwE0BI2TWVIKBAJwOp1NPkjD49KnTx/0798fvXv3hlqthkKhQG1tLcLhMC+rYLFYoNfrEQwGcd1118Hn8wEAbr31VkyZMgXhcBh33303X64T6fV6XHbZZbjvvvsQGxsLp9OJhQsXYsGCBaf9MxBnxsT6YS053VAiLl+2tjDukSNH8N577yEYDCIrKwvXX399k0AGAK+//jrWrFkDtVqNBQsW8ED2xx9/YN68eQAaHjeFQsF7hooFYk0mEwoLC2Gz2aDX6+F2u+Hz+eB0OmGz2RAKhaDT6dCrV69jFpIlhBDSFIWyVtq9ezcGDRqEWbNmYerUqZg8eTJf3pFKpa0OZi+++CKMRiP/SElJOZPDbre8Xi9sNhs/ZSjWL7NarejWrRuSkpL4rJAYJkKhEGQyGdLT0yGXy5GXl4eXXnoJQEPoee655zB06FC43W7ceOONLRaRzczMxGOPPYaLL74YUqkUO3fuxFtvvdXqRseNia2SmocxmUzGK/aLH43LWpwKMdS15vfMbrdj0aJF8Pv9SE1NxXXXXXfU9//ggw/w1ltvAWioQSYu+fr9fjz44INgjEGtVsNsNiMcDsPn80EQBCQkJCAtLQ2hUAharRYmkwk5OTno0aMHEhMTEQgEEBMTQ6csCSHkFFAoawWHw4HrrrsOU6dOxS+//ILi4mJMmjQJa9aswYQJEwC0Ppg99thjcDgc/KO0tPRMD79dat7EvKKiAg6HA7t27YIgCDCbzcjIyIDVakU4HIbb7YZMJkNSUhIGDBiACy+8EADw8ccfY9WqVQAa2i29/fbb6NatGyoqKjB58mS8++67R80uKRQKTJw4EQ8//DCMRiOOHDmCBQsW8Fm31ggEAsjPz2/yMxfDmEwma9PlOnFZVPz78YiBzOVyIT4+HjfeeGOTAwMAsGTJEt5o/N5778UVV1zBr3vttddQWFgImUyGlJQUXl6jvLwcMpkMer0eJpMJZrMZcXFxyM7ORnp6OmJjYyGTyaDVaqHT6RATE9NkmZUQ0nby8vKwffv2E36UlJREeqjkJNGeslZwOBzw+XyYMmUKn+G677770LNnT8yaNQtTpkzBl19+2WJtqOZUKhVUKtVZGHX7JhYT1el00Gq1MJvNKC0thd1uR3l5OdLS0jBw4ECo1WpeOqOmpgaxsbHQaDTwer1ISUlBaWkp7r33Xnz22Wfo168fTCYTli1bhscffxw//PADXnjhBZSVleGpp546agzJycm444478MYbb+DAgQN44YUXMG3atFaNv/EsH3D6y5ONhUIhuN1u1NfX83ZJYhg7VigLh8PYsGEDfv75Z4RCIVgsFkyfPv2oYPTFF1/g4YcfBgBMnz6dd0cAgO+++w7vvvsuACAlJQUxMTHQ6XSorKyEXC5HdXU1evfuDa1WC4vFArVaDavVCgA8jDmdThQVFSE9PZ1CGSFtzGq1QqvVtvp1SqvVIi8vD6mpqWd4ZKStUChrBb1ej/r6emzcuBHDhg0D0HCqbOLEifD5fJg7dy7eeecd3HbbbREeacchvmE3738oFow9cuQIvF4vL5lx5MgRJCYmory8HHl5eXA4HHxGxmaz4cYbb8SXX36JzMxMGI1GzJ8/H7m5uXj22Wfx4Ycfora2lrdhaiw5ORl33303PvjgA9jtdsybNw/R0dFIT08/ag9WY/Hx8WCM8cK04r4yQRAgkUh4SDuVsObz+VqctVOr1TAYDEddfuTIESxduhSHDx8G0LBEe9VVV/F9YKKPP/4YTzzxBADg+uuvx+zZs/n4duzYwQNadnY2kpKSkJiYCK1Wi6ioKNTX1yMuLg4OhwMKhQJqtRoJCQlNvr5Op4PNZuN9LSmUEdK2UlNTkZeX1+RAzbHk5eVh2rRpsNvtFMo6EAplraDVajFixAisWrUKF198Mfr27QugYdZr8uTJ+Oqrr7B27VoKZSep8RIm0NCgXCaTwe/3w2QyAWgIKOI+pqqqKrjdboTDYQQCAUgkEgwdOpT3zrz++uuxdOlSJCYmQiKRYPr06bBYLHjwwQfx7bffIj8/H7fddttRM5Xp6el47LHH8M0332D9+vWoq6tDXl4e0tPTeUmH5uRyOVJSUmC32/nSdeMlxtZuyG+JRCKBSqWCQqHgH3K5/KiAxxhDUVER1q9fD0EQoFKpMH78eAwePPio265ZswZff/01AOCWW27BrFmz+G0OHz6M6dOnIxAIICkpCSNGjIDL5eKzXd27d+dFYNVqNRwOB+9zKc6UAQ3Pk/T0dP7ztNlsfCaUENI2UlNTKWR1YrSnrBVUKhUefPBB7NixA8899xwOHTrEr9NqtRg5ciQKCgpOabN4V9a4oGxaWhqMRiMyMzMxatQo9O/fn7+Z19TUQCqVwuVyQaVSIT4+Hunp6YiOjoZGo8H5558PvV6P8vJyXHfddaipqeHf47LLLsOCBQugVqtRUFCA+fPnHzU7BzT8jK+++mrceeedkMvlCAQC2L9/P6+ddixitX25XM7Dk0wm4y2QGn+0ltgj1Gg0QqvV8lpgjQWDQVRVVaGoqAiCICAnJwczZ87EkCFDjrrt2rVreSD75z//2SSQuVwu3HTTTbDb7TAajbjooosglUr5TJ3RaIRSqUROTg7OP/98ZGVlwWAwwOfztbgMr9Vq+WnLxoGbEELIiVEoa4VwOIw+ffpg+fLl+OGHH/Doo49izZo1/Pr8/HwkJycfsxgpaZn4Bi7+mZaWxmfIxBmY6OhopKWlQS6XQ6PRICcnB0OGDEF2djYsFgs0Gg2ioqIwYsQIqNVqHDp0CDfddBPcbjf/PqNGjcInn3wCjUaDwsJC/N///d9RxVlFOTk5yMjIgMViAdCwNJiXl9eqwC0GNJlMBrlcftRHW2CMoa6uDlVVVbyO29SpU3H99dcfVduMMYZVq1Zh5cqVABpaVD3yyCM8kIVCIdx1113Yv38/lEolBg8ezGcgtVot1Go1JBIJBEHg+/9MJhNkMhkMBgMCgcAxZ8GozyUhhJw8ShGNhMNhMMaOKrAplUohCAKGDh2KX3/9FbfccgsefPBBCIKA9PR0rFmzBuvWrTvqlBs5OY03/4vLf3V1dfD7/bwHZFJSEux2OxwOB29HVFdXB4lEguHDh2Pr1q3YuXMnZsyYgXfffZeHhgEDBmD69On46KOPUFFRgblz5+LWW289Zg2thIQE6HQ6lJWVwe/3Iy8vD7GxsbBYLEftNTudpcpjEav8NxYMBuF0Onn5DbVajXPOOQc9e/Y8qqo/YwyrV6/G+vXrAQB///vfcd999/GlVcYYZs+ezeuU/e1vf0N8fDyio6MRHR3Nw5g4U2Y2mwGAl/iIiopCamrqMSv1Ny4OTAghpHUolP1/+/btwwsvvIAjR44gKysLEyZMwPjx43kgk8lkEAQBAwcOxPLly7Ft2zasXr0aKSkpeOmll5CdnR3pu9DuHWvTu8fjadKwGvhfpwSlUomysjK+dysqKorPeFmtVh6QqqqqUF5eDqvVimAwiI0bN+LGG2/E8uXLERcXBwB45JFHMG3aNEydOhWFhYVYtGgRPvnkE75HUJSRkcH3ktXV1WH+/PnYsGEDqqqq4PV6MWHCBEycOBFmsxkrVqzgYz6RoqIiXg/seJxOJwYNGgSgIYjt3LkT69atw+rVqwEAFosFd955J4YOHcp/JxtjjGHOnDk8kM2ePRszZszgj4MgCLjjjjuwePFiAIDZbEZ1dTVCoRAqKiqgVCqh1WrRo0cPxMfHw+l0IhQK4fDhw9Dr9ZDJZLBarXwWjKr1E0JI26BQBmD//v3429/+hnHjxmHw4MFYsWIFtm7dilWrVuGNN96ATCZDMBiEUqkEY4xvtLz88ssjPfROoXnNMqChuKzH40FtbS1SU1PhcDj40mZsbCyGDBmC6upqaDQalJaWorq6Gi6XC1FRUTAajSgsLMTWrVtx/vnn4/vvv0fPnj0BNJR6+Oabb3Dttddiz549mDx5Mv71r39hzJgxLY4tOjoaTzzxBH799Vd89NFHKC8vx+eff46vvvoKo0ePRmxsbKtD2ck8HqtWrcLvv/+O7du3N+lVOXbsWEyfPv2Yy4LhcBizZ8/G+++/DwB4/vnnceONN/LZvGAwiBtvvBFLliyBVCpFbGwszGYzjEYj4uLi+H48h8MBACgtLYVKpUI4HIbRaERUVBQSExP5XjGxwTwhhJDT1+VDGWMMH330EcaOHYvPPvsMAPD444/jrbfewtKlS/kymLg0+e2332LYsGFt/kbclTVethR5PB6+TKfX63mPSqvVCq/Xi/r6elRWVvIDAHFxcbDb7fD7/dBoNLx8Q2FhIYYPH45ly5ahW7du/GssXboUN910EzZt2oQbbrgBkydPxlNPPcWX6RqTSCS44IILMHz4cGzatAlLly5Ffn4+36uVnZ2NESNGHNWM+2TYbDbs2bMHe/bsQWFhYZMlUYvFgqFDh2LUqFHHnWnLz8/HE088gc2bN0MikeDll1/Gtddey6/3+Xy4+uqrsWLFCigUCsTFxUGr1UKlUsFisTSZ+UpKSuJLkIWFhXz2rPHybfMgTQgh5PR0+VAmkUhQXl6OI0eO8Mv0ej3uueceqNVqfP7553jppZfw6KOP4ocffsBdd92FG264AXPmzDmpE3Xk2FqabRFrXplMJl6qQS6Xw2azoaCgAACQmJgIh8MBxhgCgQDMZjMqKioQDochk8l4fbOamhpcfPHFeOutt3gHBr1ej8WLF+OFF17Ae++9h6VLl2Lt2rV47rnn+Cb/5mQyGc4//3ycd9552Lt3L5YuXYrNmzcjPz8f+fn5SE1Nxfnnn4+cnJyjfjcYYwgGg7DZbPB4PHC73fB4PKiqqsKePXt4vTNRRkYGzj33XAwdOhSZmZnHXSL0eDx4/fXXsXDhQoRCIWg0Grz00kuYPHkyv43L5cI111yDdevWQaPRIDExEQaDARKJhJ8ctVqtyMzM5AcTVCoVBEGAwWCATqeDWq2GyWTiG/gpkBFCSNvq0qFM3LeUm5uLAwcOYP/+/XyZS6/X4+abb8b+/fvx3XffYebMmRg/fjxuvvlm3HDDDRTIzjDxRKbNZoNWq+WnFw8dOoSamhq+yV8qlcJqtcJiscBms/FSDXK5nPdvrKyshMPhwO23344XX3wR1113HYCGjfJz5szBxIkT8dBDD6GgoAC33347hgwZgpkzZ/IG3c1JJBL06dMHffr0wSeffIK8vDzs2LEDJSUl+PTTT2E2mxEbGwu/3w+fzwev1wuv13vMZuVAQ5uuzMxM9O7dG+np6cdcTm2MMYZNmzbhtttuQ0VFBQDgkksuwTPPPIPk5GR+O5vNhhtuuAE7d+7kbZJMJhMSExNRU1ODQCCAUCiE6OhoWK1WCIKAQCAAt9uN9PR09OnTB16vF1arlQcy2shPCCFtr0uHMnH24e9//zvmzJmDV155BW+++SaioqLAGIPJZMKsWbOQlpaGn3/+GRMmTMAzzzwT4VF3LSqVqkn1ar1eD0EQ0KNHD2i1Wmg0Ghw+fBgmkwnZ2dmIj49HIBCAxWJBQUEBBEGA1WpFQUEB7HY7Hn30UajValx11VX8aw4aNAgrV67EvHnzMG/ePGzZsgW333477r///ha7ADRmNptx+eWXY8yYMdi0aRN+//131NTUNKmV1phSqYROp0NUVBSioqJgMBjQo0cP5OTk8JOMTqfzhI9LZWUl3n77bWzZsgVAQ0HJZ5999qgwV1BQgOuvvx6lpaWwWCzQ6/V8351YukNcyoyLi0NaWhqqq6tRV1cHtVoNi8XSqsMJhBBCTl+XDmWi7t2748svv8S4ceOg0Wjw9NNP8zpZCoUC/fr1O+aSFjlzxCVMt9sNu93OT2eKDbD37duHgwcPwu12Q6lUIjU1FRaLBXK5HGVlZTCZTDh06BDq6urQo0cPmM1mFBQUYObMmdBqtRg/fjz/XmKB4HHjxuGWW25BSUkJnnrqKYwbNw4zZsw4ZukHkV6vx8UXX4yRI0ciLy8PwWAQGo2Gf+h0OtjtdvTr1++0HpNQKIRvvvkGn376KQKBAORyOf75z3/innvuOWqM69atw2233Qan0wmtVguj0QiNRgOJRIK6ujrU19fDaDRCLpdDr9dDqVTy/WTdu3fnJyypMj8hhJwdFMr+v1GjRmHJkiW46qqrUFFRgSlTpqBfv3746KOPUFVVhZSUlEgPsUvSarV8Y7lSqURMTEyT2mKCIEAqlfI9TuIeMwAwmUzQaDTweDxwOp0YPHgw/H4/SkpKcOedd0Kn0+GCCy5o8v169+6Nl156CV999RW+/vprrFixAn/++SceeuihVs0YqVQqfiihuWMVrG2tffv2Yf78+SguLgYA9O3bF7fffjsuu+yyo2772Wef4dFHH0UoFILBYMCIESNQVlYGmUyGUCgEnU4Hg8HAi/darVY4nU5YrVaYTCbekNxms/EN/RTKCCHkzKJQ1sill16KjRs3YubMmXjkkUd4y5wffvihyR4dcnZ4PB6oVCoeiO12Ow8kMTExsFqtKCsrg1wu58GhvLyct2ISC8y63W7ExMRAp9Nh6NChCIfDvN/jp59+etQSpVKpxK233oohQ4Zg7ty5qKiowIMPPogrr7wSY8eOPau/C06nEzt27MDmzZuxbt06AA09QqdPn47Ro0cf1QJKEAS88sormD9/PoCGx0mc6XW5XGCMob6+HiqVCr169UKPHj1gt9tx8OBBmEwmWK1W9O/fn3892tBPCCFnD4WyZnJzc/Htt9+ipqYGLpcLCQkJTZouk7NHDARiD0iv14tAIACbzcZDlsViQWVlJUKhEGQyGeLj4yGTyRAOh6FWq2E2mxEIBOB0OqHT6SAIAkaOHImff/4ZNpsN119/PRYsWIARI0Yc9f379++P//znP/jPf/6DVatWYcmSJViyZAkSExMxePBgDBkyBKFQqE3vczgcRmlpKfLz87F9+3YUFBQ0KY8xduxY3HjjjTAYDE0+r76+Hl9//TX+9a9/8d6sycnJyMrKglqthlqtRigUQjAYhNlsRkxMDNRqNfx+P0KhEEKhEBwOB4LBIILBIKKjo3mtOFq6JISQs4NCWQsMBsNRb3rk7Gt+wk9cThOXL8XQ5nQ6odFokJqaCqBhdklsE6RSqRAVFYWKigp+WtPv92PMmDH4+eefUV1djalTp2L48OF46KGHMGDAANTX1/M2R0qlEvfeey+GDBmCH3/8EXv27EF5eTmWL1+O5cuXQy6Xo3v37sjKyuLNuo9FEAQEg8GjLnc4HCgoKMD+/ftx8OBB3gxclJaWhgEDBvCG4AB4GPT5fHjvvffw9ttvo6ysDEBDE/GMjAykpqZCoVDAaDRCr9dDp9PBaDQiJiYGKpUKDocDCoUCdrsdBoMBarUaOTk5/HFvvHQJgAIaIYScYRTKSLvUUl0usXq+x+OBzWYDgCZNspOSkuBwOKDRaLB9+3Y4HA7IZDJYLBZotVrU1dWhpqYGBw8eRH19PVJSUhAOh+F2u7F+/XqsX78e48ePx8MPP4zc3Nwm3/uCCy7AY489BpfLhbVr1+Knn37Czz//jIqKCuzfvx/79+8H0LAn7aKLLkJiYiJ8Ph/8fj8CgQB8Ph+CwSD+/PNPXiojEAigoqIC+fn5Tb6X0WjE6NGjcdFFF2H06NEtLpc6nU4sWLAAb731Fn8s5HI5rFYrDAYDf4wSExOh0WhQXV0Nq9WKlJQUdO/eHYIgYNu2baiqqoJGo0FCQgIuvvhiXgC38dcUwy8ViyWEkDOLQhnpcKqqquByuVBXV8dLTGg0Gj7zU1tbi4SEBOzbt4/X20pOToZSqUQoFIJcLodEIoHZbEZCQgIOHz6M0tJSuFwu/PDDD/jhhx8wadIkPPHEE8jJyWnyvfV6PS699FJceumlYIzht99+w/r16/HLL79g69at2Lt3L/bu3XtS90eslTd69GhceOGF6N279zFP+9rtdvzrX//CO++8ww8OKBQKfl+kUikYY9BoNMjIyEB6ejpvKB4bG4v4+HhoNBr8/vvvSEhIQF1dHaxWK/r27Yvs7Owmm/vlcnmTzhUUyAgh5MyiUEY6vLq6OkRFRUGhUPCltZKSEr6pvbKyEnq9Hl6vF0ajEW63G263G1KpFBKJBAaDAcnJyXC5XLDb7fB6vVi+fDm+/fZbTJkyBY8++igyMzOP+r5iEdnBgwdj5syZqK6uxurVq7F27Vp4PB6+l0v8kEqlvCyFeJnBYMDQoUObtHdqaYmzuLgY//73v7Fo0SJ4vV4ADSc9MzMzEQwGeX9WxhjkcjkvWssYg8PhQFVVFQRBQHx8PPLy8iCVSpGYmIg+ffpArVYjISGBB66WNvdTj0tCCDnzKJSRDic2NhY6nQ7x8fGw2WxITU1FfX09EhISADQ0M4+NjUX37t1RVlYGxhg/lanVapGamopgMIjS0lIADXu9ZDIZP+lpNBqRl5cHp9OJL774AkuXLsU111yDRx555Lj9LS0WC6666qomhWkbc7lcrdqryBjDgQMHsGHDBvz222/47bff+KlTANBoNIiPj0dSUhIMBgNqamrg8/kglUp5j1aFQsGXZn0+HwRBQE1NDXbt2sU7WYwcORJarZZX8BdptVoKYIQQEgEUykiH03jWpvGsjrjvSTwtm5iYiLi4OBQUFKCurg5utxs6nQ4+nw9yuRxmsxmVlZUIBoOQSqWIjo5GKBSCXq9Ht27d4PV6eYumjz/+GIsXL8bAgQMxduxYjB07tknpiLbg9/uxbNkyvPPOO9i9e3eT66RSKa/+L5FIEAgEEAwGoVKpEA6HERcXB6VSCYvFAqlUCqfTCYVCwZdBVSoVzGYzoqKi4HA4kJiYyMOXzWaDSqWiWmSEdEJ5eXmtup3VauWHpUjkUCgjHVrzE5piCQ1xL1RtbS3C4TAOHjwIuVwOpVLJC6UKgoD6+nrI5XJoNBoYjUb4/X4olUqo1WrEx8fz4FZVVQWPx4OtW7di69ateP755xEXF4eRI0di3LhxGDly5Cmf2C0vL8f777+PDz/8ENXV1QAaTn0qFApERUVBr9dDq9UiJSUFqampKCgogEQigUwmg0QigcViQVRUFC8RolQqEQ6HoVKpIJPJYDAYYDabodVqYbFYkJmZCbfbjaKiIqSnp/N9ZISQzsNqtUKr1WLatGmtur1Wq0VeXh4FswijUEY6DTGciTNnaWlpMJlM8Pv9EAQBgiDA7/fztkMJCQnweDwIBAJQqVSIi4vjBWtlMhkYY1CpVDCZTIiOjkY4HIbX60VtbS1qa2tRWVmJL7/8El9++SXkcjnOPfdcjBkzBhdddBH/2m63Gx6PBx6PB3a7HYwxfrnb7ca+ffvw/fff82blSqUSPXr04A3YxctNJhOkUimOHDkCqVQKvV4Pq9WK6OhoVFRUQBAEfsr08OHDEAQBRqORzxqWlJQgOzsbKSkpvEVV48KzKpWK2ikR0omkpqYiLy+vSe/gY8nLy8O0adNgt9splEUYhTLSYYjhRly6bKluVuPSDQBQUVHBZ81KS0tx5MgRmEwmMMZgt9sRHR3NZ5MUCgViY2MRDAah1WohkUh4UVqxbpl4KCAcDqOurg7BYBBFRUXw+XzYsGEDNmzYgKeffvqk75vRaERcXBxiYmKQkpKCw4cPw+VyQSqVQiaT8ebhHo8Hfr8fCQkJSEtLQ319PaRSKQRBQFVVFXr16oWePXvC5/Nh8ODBiI+Px+7du5GamgqZTMYPCfTq1avJY3msJczGjzntMyOkY0lNTaWQ1cFQKCMdRvPA1VJPxuZ7zBISEhAIBKDX61FTU8NrmVVXV6OqqooXVDUYDLBYLCgqKuKnJE0mEywWC44cOQK73Q6Px8Prp0mlUsTExKBbt25IT09HZWUl7HY7HA4HnE4nr8LfOFBptVqEw2FIJBL+oVAokJycjPj4eAiCwDfhB4NBKBQKvrSakpKC+vp6+Hw+6HQ6KBQK+Hw+fpIzEAggLS0NPXr0gMFggEajQVJSEgBg+PDhKCoqgsvlQklJCbRaLdLT05s8bunp6S2WvKD6ZIQQcvZQKCMdRvNSDS0FhcZ7zMSlSfHfPXr0gM/ng81mwy+//IJgMAiNRoO+fftCq9XC4XDwul0KhQJWqxVyuRy1tbVQKBSQSCQ8VImzToFAAOFwGGazGWq1GklJSVAoFJDJZJBKpbxZus/nQ/fu3XHgwAEYjUbU1tby0hcmk4mX7GCMQSqVQq1WIxgM8mr8crmc96xUKpX8MjE0GQwG6HQ6qFQqGAwG1NfXw+12IxAI8OBWVVXVpGUT0HBStaqqCkDDqdbmS5fU+5IQQs4eCmWkw2i+hKbT6cAYO26PRpPJhNraWphMJnTv3h1msxkHDhxARUUFysvL+edoNBp+IlNc0gwGg6iqqoJcLofJZOJ7sGQyGTQaDaRSKQ+BSqUSKpUKgiBAo9HAYDCAMQalUgmfzwelUgmTyYRu3bpBIpGAMcYPFURFRfHTn+JJylAoBLVazYviiicudTodDAYDzjnnHNhsNkilUoTDYaSkpECn06Guro7vL/N6vXA6nYiOjgYAREdHQ6fTITY2lj9mHo8HLpeLP560n4wQQiKHQhnpsMRQIW7Ob96jUZzliYmJgcfjgdfrhdfrhdVqxcCBA+F0OuF2u6FUKpGWlob9+/fz5ucqlQr5+fn466+/EAgEkJSUxPdtKZVKKJVKVFVVoby8HKFQCPHx8QiFQvB6vVCr1fB6vfD7/VAoFPB6vfD5fKioqIBer0d1dTWCwSDq6+thMpmgUqn44QGj0QiXy8VPidbX18Pj8aC6uhrV1dWwWCywWq3o1q0boqOj4XQ6+alPuVzODzVER0fD7XbzE6XR0dHQ6/W8B2ZVVRXvn6nX6wE0hLLm7a1o+ZIQQs4eCmWkwxIDA3DsHo1iUAMaTjK6XC7elkmlUgEALxVhtVrh9Xr5pn/xpKPFYkFsbCwSExMRHR0NQRBQW1sLq9WKUCiEpKQkJCQkwOFwoLKyEkBDl4FwOMwr+QeDQQQCAdjtdigUCgANhwaio6OhUqlgsVh4wVcxxGVkZPDyHXa7HcnJyTAYDMjNzeXjN5lMiI2NRXR0NOrq6visnHj6Uq/XIz09nT9ezeu7GY3G44YtWr4khJCzh0IZ6bCOFSwaBzJxaU6v1yMQCKC2thZ6vZ5XwI+KikJ0dDT27t2L2tpaHpA0Gg3S0tLAGOOnMh0OB/R6PdRqNXbt2oWKigpYrVZYLBakpqbymmgOhwNutxtqtZqHLYVCAalUilAohFAoBIvFgujoaGg0GiiVSsTFxUEQBBQVFcHr9cLlcqGiooLPAvbu3RsAeB9LALyArNvtBgBkZ2cDAK/+b7Vam+wTO5W2SXTqkhBCzh4KZaTDaikwNL9MXJoT91GJG/Q1Gg0GDhwIQRCgUCgQDAb5Znm1Wg2j0YhBgwZhwIABkMlk+Ouvv1BbWwuLxQK/34+srCxIpVKYzWYoFApoNBq+HCmXyxEVFcVPXOp0OsTFxSEcDqO8vJyf9ExJScG2bdtQU1MDv9+PzMxMGI1G1NfXgzEGn88Ht9uNbt268Yr+giDwwwJiYVmZTIbExER+n5OSkhAIBOD1erFv3z6kpaUhJibm7PxQCCGEnDIKZaTT0ul0yMjI4P8WK9eLe8x8Ph/i4+MBNGzeF4uvlpWVweFwwGQyQavVwuv1QiqVIikpie/5stvtvG+k2WyGxWJBKBRCYmIiPwBQU1OD+vp6eL1ePismLpmee+65CAaDSE5OxqFDh/heMLGeGGMMoVAIaWlpEAQBycnJfGnW7/fzsYkHEMrLyxEIBBATEwO5XI5AIMCbkIv3mRBCSPtGoYx0GTExMU3CSWZmJt+LFhMTwzfAC4KAiooKVFRU8OAlnooUw1N8fDx0Oh2CwSCio6ORnJwMp9OJuro6ZGRk4G9/+xtWr16NXbt2wev18vpoWq2W950U64X5/X7U1dXB6/XCbDYjMTERgUAAUVFRUKlUGDJkCO/JKZVKATQ0JTebzXzmzOl0IhwO8/vh8XgQFRXF73fjE6rNl3qpOCwhhLQPFMpIlyQGsNraWhQXF8NkMvHrtFotDzU2mw1GoxFOpxPl5eUoLS1FdHQ0BgwYALVaDYfDAb/fD4fDwcteKJVK+P1+GAwGxMXFweFw4PDhw4iJieHLp16vF/Hx8UhOTobP54PT6YTf74ff70diYiJUKhUUCgViYmJgtVp5IVgAvENBVVUVqqur4Xa7+eyYGMhUKlWTZUubzdbiKUo6XUkIIe0HhTLSKZxoxke8vjG73c77wvl8Ph6YJBIJBg8eDL/fD7VaDaChsfnu3bshl8shlUqRnp6O1NRUHD58GEVFRQgGg1Cr1Xw/2q5du3D48GHU19cjMTERdXV1qK+vh0QigcFggN1uR319PfR6PSQSCdLT0yEIAuLi4qDRaJCVlcWXOhsfZGjc0UClUvFG5QcPHoRGo+H3rba2tsms4LFOUdLpSkKIKC8vr1W3s1qt1L7pDKFQRjqFE834iNeLhWRra2t5s29xo7zX64UgCLw5eeNQ4/F4oNFo+LIh0DCjlpWVhZqaGhQUFEClUiEmJgahUAg2mw1//fUXwuEwNBoND4sWiwU6nQ7hcBgKhQIulwuJiYmIiYlBWloa/H4/PB4PGGNISEjgYxWDWHV1NbRaLe82YLVaYbfbkZCQAEEQ+O0az/yJY23pcaFlS0KI1WqFVqvFtGnTWnV7rVaLvLw8CmZnAIUy0imcaMancSFZoGGflVarRVxcHADwGTNxr5e4hOn1enmg6dGjB4xGI4qLi3lx2UOHDqG4uJhv/NdoNOjXrx8KCwsRCoWgUChgNpuRnZ0NpVIJuVwOpVLJ94Cp1WpotVpkZGRAJpOhuroadrsdarUafr8fgUAAfr8fJSUl/ISoGL7EQJWdnY3i4uImwYtmvwghrZWamoq8vDz+Ong8eXl5mDZtGux2O4WyM4BCGekUTjTj01ILocb7rcR6ZmJYEzfGq1QqHsy0Wi0CgQDkcjmKi4tRVVUFm82G0tJSKJVKaDQauN1uFBQUQKvVolevXlAoFMjMzIROp4PZbEZ9fT38fj+6desGn88Hj8eDYDCIuro6XrMsMzMTfr8fRqMRNTU1sNvtOHz4MJKTk2EymfgGfnFmsPkBBgDULokQclJSU1MpZLUDFMpIl9G8hZBIp9M1aTXUUqcAiUTClx9dLhef5fL5fDAYDLx9UTgchs/ngyAIyMjIQFxcHFwuF3w+H1wuFywWCyQSCaxWKwAgPz8fMpmM1zoDwEOXGPYCgQDfa5aTk9MkNLbUGokQQkjHRKGMdHonOgTQvJ6Z+DliH0yv14uioiJ+29jYWFRXV/OTkdXV1byJudjKadCgQbxERjgchsvlgsFg4H01bTYbL48hdhlofKrSbrdDqVQiGAyiT58+AP43iwf8b5mVEEJI50GhjHR6J1v2oXngadyuSaxpJjYRV6vViI+PR319PeLj4yGTyXhxWqfTyUNdfHw8r7ovtmMCGoJWQkIC/35FRUUoKiqCRCKBVCpFYmIiDAYDFX8lhJAugEIZ6fSOdwigpVm0xkuD4ub5xsubQMM+NEEQoFQqodfreWgSv1dpaSk8Hg/KysrQu3dvpKSk8OtqamqgVCoRGxvLuwwUFRVBq9XyjbY6nY43SCeEENI1UCgjnd7xDgE0nkUDGpYOxb1ccXFxSE9P55X3G0tPT0dVVRUANGn67fV6kZ+fD6fTibKyMqSnp0MmkyE2NhYajQY2mw1RUVEQBIEvV9psNgQCAVRXV/Nq/+np6fygASGEkK6BQhnp8sRCq+IypdvtblKItfnMGQAenMTG4TabjXcJCIfD8Hq96N27N2QyGVJSUnjoa1ySA2hYrhRnwywWC+9fKX6f1i65UrskQgjp+CiUkS5PLLQqLlOmpaXxZUubzcZnrDweT5O9ZmJY83g8EAQBxcXFqKiogMfjgcVi4cuTQMvlK2w2GyorK+Hz+ZCeng6dTsdPfQInt5n/ePvmKLARQkjHII30AAiJJJ1Ox8teiKcwxYDUUmmMxhpfHwgEeFFXhULBG5eLYSgQCPBitI2/t0wmA9BQ/kJcxjyV4NT4fjTXfImWEEJI+0QzZaRLa2n2qHkYE0tjNCbOkgFNG4SLIUu8TSAQ4NeLJzgb708T65UJggBBEJocJGip4O3J3I/G11GFf0IIaf8olBHSjBhiWgpjInFJUy6X89ukp6fzwCXWNhOXPY/3NcRg1ng5tKXl0tO5PxTICCGk/aNQRkgzzUNMS3uyGs8+tVRRX6fT8ROU4ueJH+LtG4c/8ZBAKBTirZyoWj8hpL3Ky8tr1e2sViu1bzoJFMoIOYGWNtE3DmhiaBM1D2GNL2+spesbhzRCOruSkpJWN8Em7YPVaoVWq8W0adNadXutVou8vDwKZq1EoYyQEzjRnqyqqiq4XC4EAgEkJSWd8v6ttlxmpBOXpL0rKSlBTk5Oqwska7VavtRPIic1NRV5eXmtDtPTpk2D3W6nUNZKFMpOQn5+PlasWIF77rmnyYbukxEIBBAIBPi/nU5nWw2PnCEtzYq1FHa0Wu0xT0CejlMJWCfbWoqQs81ut8Pr9WLx4sXIyck54e1pGaz9SE1NpZ/FGUKhrJX+/PNPDBo0CC+//DIPZIyxk97z8+KLL+KZZ545E0MkZ0FLYSc2Nvao5cq2nKk6lYBFJy5JR5GTk4Pc3NxID4OQdoHqlLXCrl27cP755+P+++/HAw88wC8/lU3Yjz32GBwOB/8oLS1ty6GSM6ylemA6nY4HM1Fb1gY7Xg2y431O8zERQghp32im7AT++usvjBw5EldddRVeffVVCIKAefPmobCwEB6PB/feey/69u3b6q+nUqmon2EH1tqZr9bOVLVmRo32hRFCSNdAoewENm3aBJVKhaSkJOTn5+POO+9EKBSCTCaDz+fD0KFDsWjRIkydOvWUljNJ59TaIOXxeOB0OmGz2XgnAUIIIV0ThbITuPbaa+F0OvHuu+/igw8+QP/+/bFw4UKYzWaoVCrcdddduOuuu3DBBRcgISEh0sMlHYzYX1MsFkuhjBBCui7aU3Yc4XAYAHDHHXdgxowZ6N+/P5555hkkJCTwJcjZs2dDEASsWbMmkkMlZ4nH40FVVVWb9ZEUi8waDAYKZIQQ0sXRTNlxSKVShMNhSKVS3HHHHTj33HP50W1xqdJmsyEpKQndunWL8GjJ2XAmSk3QnjFCCCEAhbITkkqlPIANGDCAXy7uHfv000+h0WiQkZERqSGSs6Bx1f4zUYuMEEIIoVB2DOIMGdBy6Yv//ve/+O677/Dhhx9izZo1iIuLO9tDJGeROEMml8sRGxsb6eEQQkiHQX0yW49CGYDi4mKsXLkSTqcTaWlpmDJlSpMZMqBpoViHw4HNmzdj/fr1WLdu3UmVxCAdExVjJYSQk0N9Mk9elw9lu3fvxrhx45CTk4Py8nK4XC7s378fs2bNajJDJv49FArBaDTi/vvvx+233w6LxRKpoZOziPZ9EULIyaE+mSevS4eyoqIiTJo0CdOmTcMLL7yAqqoqfPzxx/j+++8xY8aMo5YkxWr+c+bMgU6ng1arjcSwCSGEkA6B+mSenC5bEkMQBHz++efIycnBE088AalUivj4eJx33nnYsWMHamtrj/qc5ORkfPDBB/B6vREYMSGEEEI6sy47UyaTyZCdnQ2dTge9Xg+gYXN/nz59YDKZWgxe999/P2666SZER0ef5dESQgghnV9XPxTQZUMZAFx44YUwGAwAGjbyS6VS6PV6KJVK+P1+frtffvkFF110EQBQICOEEELaGB0KaNClQ5kYyICGjfyCIMDtdsPj8UAub3hoZs2aheeffx6lpaVITEyk3paEEEJIG6NDAQ26dCgT6041JrZW0uv1ePnll/HGG2/gjz/+QFJSUiSGSDoAsbAsndAkhJBTR4cCunAoEwQBcrkcRUVF+PXXX3HDDTdAJpPBaDQiISEBt912G7Zs2YINGzZg4MCBkR4uacfOROslQgghXU+XPH0ZCoUgk8lQVFSEnj17YvXq1fy62tpa7N+/H5s3b8aWLVswaNCgCI6UdAQ6nY5aLxFCCDltXS6UiUuWRUVFyM3NxbRp07Bo0SIADZv9jUYjXnrpJezZswf9+vWL8GhJR6DT6RAbG0uhjBBCyGnpUsuXzQPZxIkT8c477/B9ZRKJBHK5HLfffvtRe80IIYQQQs6kLjNT1ngPmRjIFi5c2GL4okBGCCGEkLOty6QPmUyG4uJi9O7dG1dffTUWLFgAmUwW6WERQggh5BR0xkKzXSaUCYKAOXPmYOrUqXj77bcpkBFCCCEdUGcuNNtlQplMJsNrr70Go9EIqbTLrNoSQshZVVJS0uoCoIScis5caLbLhDIAMJlMkR4CIYR0WiUlJcjJyWmxd3BLtFotrFbrGR4V6Yw6a6HZLhXKCCGEnDl2ux1erxeLFy9GTk7OCW/fkfb6EHI2UCgjhBDSpnJycpCbmxvpYRDS4dDmKkIIIYSQdoBCGSGEEEJIO0DLl4QQQgjp1E7mtG8k9zpSKCOEEHJMrS1xAVCZC9L+nGxNMyCydc0olEUYYwwA4HQ6IzwSQsjpEp/H4vP6dJzsa8ORI0dw5MiR0/6+jdntdkybNg0+n6/Vn6PRaKBSqeg1jbQL0dHR2LJlC6qrq1t1+/3792PGjBn46aef0LNnzxPePj4+HvHx8Se8XWtfGySsLV49yCk7fPgwUlJSIj0MQkgbKi0tRXJy8ml9DXptIKTzOdFrA4WyCAuHwygvL4der4dEIgHQkKhTUlJQWloKg8EQ4RGeOXQ/O5+ucl+PdT8ZY3C5XEhMTDztziEtvTacaV3h50f3sXPoaPexta8NtHwZYVKp9Jip2WAwdIhfttNF97Pz6Sr3taX7aTQa2+RrH++14UzrCj8/uo+dQ0e6j615baCSGIQQQggh7QCFMkIIIYSQdoBCWTukUqnw1FNPQaVSRXooZxTdz86nq9zXzno/O+v9aozuY+fQWe8jbfQnhBBCCGkHaKaMEEIIIaQdoFBGCCGEENIOUCgjhBBCCGkHKJQRQgghhLQDFMoIIYQQQtoBCmWEEEIIIe0AhbIOKBwOR3oIpA109mo0nf3+kc6lM/6+1tbWRnoI5CRRKOsgAoEA//vpNjruCMQXyM7yQnn48GH89NNPWLJkCYqLiwEAEomkUwbsvLw85OXlnbUm2uTMys/PxxtvvAFBECI9lDbTFZ6PO3bsgNVqxY4dOyI9FHISOv+7eyewd+9eXHHFFbjgggswbNgw/PDDD7Db7ZEe1hmzZ88ePPjggwiFQp3ijX337t0YNGgQZs2ahalTp2Ly5Mm45557ADQE7M70RrBr1y707t0b33//faSHckbt378fTz75JKZOnYr3338f27Zti/SQzog///wTffr0QTgchkwmA9Dx/6PUFZ6PO3fuxMiRI3HfffdhwIABkR7OGdFZn4MUytq5Q4cO4bzzzkNycjLGjRuHjIwM3HDDDXjxxReRn58f6eG1uZ07d2LgwIEwGo2Qy+UAGt4EOuobgcPhwHXXXYepU6fil19+QXFxMSZNmoQ1a9ZgwoQJADrXG8G5556Lhx9+GA899FCkh3PG7Nu3D8OGDcOePXtgt9sxd+5c3HLLLfj4448jPbQ2tWvXLpx//vm4//778cADD/DLO/J/lLrC83HPnj0YNmwY7rvvPsydOxcAUFVVhd27dyMUCkV4dG2jUz8HGWnX5syZwy666KIml82bN4/16dOH3X777ezgwYMRGlnb27lzJ9PpdOzBBx+M9FDaTHFxMevRowfbuHEjv8zlcrEvv/yS9ezZk1111VURHF3bKSgoYBKJhM2ZM4cxxlgoFGJLlixhc+bMYV9++SXbsWNHZAfYRkKhELvpppvYDTfcwMLhMGOMsT/++IPdc889zGw2s4ULF0Z4hG3j0KFDLDo6mt14442MsYb7/cYbb7B77rmHTZ8+ne3atSvCIzw1nf356HK52MiRI1l0dDS/7IorrmADBgxgEomEjRo1ir355psRHOHp6+zPQXmkQyE5PkEQ4HK54Pf7oVAoIJPJcNddd0GpVOLVV19Ft27d8NBDDyEcDnfovWYlJSW48MILMWHCBLz66qsQBAHPP/88Dh48CJvNhrvvvhvDhg2DyWSK9FBPil6vR319PTZu3Ihhw4YBAKKiojBx4kT4fD7MnTsX77zzDm677bYIj/TUMcawYcMGAEBWVhYAYMyYMairq4Pb7QZjDCaTCU8++SQmTZoUyaGeNsYYDh48iP79+/MZo0GDBiEmJgZKpRJPP/00YmJiMHHixAiP9PRs2rQJKpUKSUlJyM/Px5133olQKASZTAafz4ehQ4di0aJFmDp1KhhjHWb2rLM/H2UyGW699VY8/fTTuPzyy+Hz+aBQKPD4448jISEB//nPf/DJJ5/AbDZj2rRpkR7uKensz8GO+y7eRSQkJCA/Px+VlZWQyWR8w/+MGTNw3XXX4bnnnkNZWVmHDmRAw+bwlJQUSKVSbNmyBZdccgnWrFmDYDAIuVyOqVOn4p133oHX6430UE+KVqvFiBEjsGrVKuzevZtfrlKpMHnyZKSnp2Pt2rWRG2AbkEgkuOqqq/Dqq6/immuuQXJyMiwWC7744gscOHAAn376KbKysvDmm2+isrIy0sM9LXK5HOeeey4OHDiAiooKfnlaWhpuvfVWnHfeeVi8eHGH+z1t7tprr8VTTz2FH374AWPGjIFarcbnn3+OFStWYNOmTbj55ptx1113oaKiosMEMqDzPx81Gg2uvPJKvPjii9i5cyecTicWLFiAyZMn47zzzsNbb70FhUKBlStXRnqop6zTPwcjOk9HWmX48OGsT58+LBAIMMYY8/l8jDHGgsEgS05OZu+9914kh9dmli1bxsaMGcNMJhMbO3Ysq6qqYqFQiDHG2LPPPsu0Wi3bu3dvhEd58nbv3s3i4uLYlClTjlpunjt3LsvNzWUejydCo2s7Pp+PzZ07lw0fPpxt3bq1yXXLli1jarWa7dy5M0KjaztLlixhGRkZbN68eczlcjW57tNPP2U6nY4VFhZGZnBtQBAE/vd///vf7O9//zv7448/mtymsrKSGY1G9sknn5zt4Z22rvB89Hq97Pvvv2crVqzgr6Hin3feeScbMWJEk59zR9OZn4O0fNmOsf+/LDB37lzcfPPNGDZsGNatWwedTgcAcLvdiI6O7nBLes2JS6+XXXYZwuEwvv32W8yYMQMxMTF8g/+TTz6JN998E7/88gt69eoV4RG3XjgcRp8+fbB8+XKMHj0a4XAY//znPzFq1CgADeUGkpOT+aGGjkytVuOWW27B6NGjkZOTA+B/P9u4uDh069YNBoMhwqM8fZMnT8Yff/yBRx55BGq1GldccQXMZjMAIDc3F2lpaU1K2HQ04kZ3qVSKO+64A+eeey7/eYqvSTabDUlJSejWrVuER3tyusrzUaPR4KKLLoJUKuWnZsU/7XY7zjnnnA69utKZn4Md+zevE2KN9meIfw4cOBDz58/Hfffdh169euG1116DTqfDxo0bUVVVhXPOOSeCIz59UqmU3+8rrrgCvXr1QkZGBoD/PQZFRUVISkpqt4EsHA6DMcZf+MTLpFIpBEHA0KFD8euvv+KWW27Bgw8+CEEQkJ6ejjVr1mDdunVQKpURHH3bMRgM6N+/P/+3+MK/bNkyGI1GREdHR2hkbUP8mb788svw+Xx45JFHUFhYiMsuuwzdu3fHwoULEQgEYLFYIj3U09L4Odm4pIL4fPz000+h0Wj487S96UrPR3aMPX3N74PP58Nzzz2HdevWYc2aNWdreKdFEATIZLIm97GzPwcljHXQWgOdWEub9hljqKiowKOPPoqNGzcCaHgDXLRoUaepQ3OsFxcAmDVrFr755husXLkSSUlJZ3lkx7dv3z688MILOHLkCLKysjBhwgSMHz8ewP9eVMQ/S0pKsG3bNqxevRopKSmYOHEisrOzI3wPWk+8H621f/9+vPPOO/jggw+wdu1a9OvX7wyOru3U1NSgqqoKMpkMaWlpTd7gGj8GL7/8Mr777jts3boVvXr1wpEjR/DDDz902OfkiQ4M/fe//8V3332HDz/8EGvWrGmX/yHsCs9Hj8fDg2drZp+XLVuGJUuWYO3atR3m9/PPP//ErFmz8MUXX0Cr1Ta5rjM/BymURdjBgwfxzjvvwG63Iy0tDU8//fRRt2n+QvnXX39Bq9VCqVTyKduO5GTe2JctW4bVq1fj448/xtq1a9vdm8D+/fsxdOhQjBs3Dunp6VixYgUUCgXOP/98vPHGGwCAYDAIpVLZoU6ptaSgoADfffcdrrnmGiQkJLR4m8b3cc+ePZg/fz62bNmC999/v8kMWnu2Z88eXH/99QiFQigoKMCTTz6Jxx57rMnvbCgU4ktcJSUlKCwshEQiQffu3dvdfxqOpbi4GCtXroTT6URaWhqmTJkCoOnPsPHfHQ4H5s+fj6+//hoffPAB+vbtG7GxH0tXeD7u27cP999/P2w2GyorK/HKK6/g2muvbXE2SVRUVITFixfj6quv5iek27OdO3di2LBhuOeee/DSSy/xyxvfx87wHGzR2du+RprbuXMni42NZZdffjn7xz/+wXQ6HZs9eza/PhwO8zosjDVs3uzIjhw5wv8ubjptrvH9ZYyx119/nQ0bNqxd1kUKh8Ps8ccfZ1OmTOGXOZ1O9txzz7FzzjmH3XrrrU1u/80337DKysqzPcw2ceDAAWY2m5lEImGPPfYYs9lsR92m+c+OMca2bdvGKioqzsYQ28TevXuZxWJhDz74INu7dy977bXXmEQiYSUlJfw2HXmDtGjXrl0sKSmJjRkzhvXq1YulpKTwGnMtqa+vZ4wx5vF4mN1uP1vDPCld4fko/n7ef//97JNPPmEzZ85kCoXimHUAly9fzp9/x3rNbW/EepUPPfRQk8vFg26MdY7n4LFQKIuQgoIClpGRwR599FHGWMMv3N13390klDU2c+ZM9sADDzC32302h9lm8vLymEKhYJdeeim/7HgvEtXV1fzvtbW1Z3Jop+XGG29kI0aMaHKZ0+lkr732Ghs0aBB78cUXGWOMff/99yw5OZk98cQTHe4Fxe12s5tvvpndeOON7F//+heTSCTsoYceajGYMcbYK6+8wp5++umzPMrTZ7PZ2IgRI9i9997LLwuHw+ySSy5hGzduZDt27GClpaX8ujfffJO9//77Z3+gp6mwsJBlZGSwRx55hAmCwCoqKtgrr7zCRowY0eQ/TqKZM2eymTNndojXns78fKyurmYXX3wxu+eee5pcfsEFF7C7776bMdb0P0bfffcdS05OZo8//jgTBKHF/zS1NxUVFSw+Pp6NHTuWMdbwHnHfffex8ePHs+zsbPbGG2+w/Px8fvu33nqrQz4Hj6fjHr/owBhjWLhwIQYPHoynnnoKQMOmTLfbzdt93HLLLTh48CD/nOTkZLz//vsdsvZKRUUFpk+fjoEDB2Lv3r248sorAYDv7WjugQcewIwZM1BYWAgA7XJzOPv/q/65ubkQBAH79+/n1+n1etx8880YMGAAvvvuOwSDQYwfPx4333wzbr755g536kkqlWLgwIG45JJL8M9//hOff/45XnvtNbzyyitH9WCtqanBtm3bsGLFClRXV0doxKdGIpHgkksuwZ133skve+655/DTTz/hn//8Jy699FLccsst2LBhA2pqarB48WJ88cUXcDqdERz1yREEAZ9//jlycnLwxBNPQCqVIj4+Hueddx527NiB2traoz4nOTkZH3zwQbt+7ekKz8f6+nrU1dVh8uTJAMBbQWVkZKCmpgZA0xZYEyZMwE033YTp06dDKpV2mKXaYcOGobq6GsuXL8eECROwe/duZGdnY/To0Xjrrbfw6quvoqSkBBUVFfjoo4863HPwhCIcCrssl8vFfv31V/7vl156iUkkEjZz5kz2+uuvs/T0dDZ8+PAmn9OeZ4yO59NPP2VXXHEFW7t2LVu6dClLT09nV1xxBb9eXBoRLV26lJnNZlZWVna2h3rSDh48yKxWK7v55pt5vRzxf6QlJSVMIpGw7777LpJDbBPNZ0k+//xzJpFI2IMPPsiXs0KhEKutrWXV1dWsvLw8EsM8bU6nk//9s88+YxKJhH3xxResurqa/frrr2zw4MHsqaeeYow1LAEWFxdHaKSnbtmyZeytt97i/xYEgTkcDpaamsq2bdvW4ud0lNeezv58LCgo4H8PBoOMMcaefPJJdt111zW5XUf5ebWkvLycXX/99Uyj0bCLLrqoyXL5J598wqKjo9n333/PGGuoOdcRn4PHQ6EsAppPlxcVFbFrrrmG/fTTT/yyAwcOMIlE0uSyjsrj8bDly5czxhoC2JdffnlUMAuFQiwcDvPHpnlBwPZs9erVTKVSsTvvvLPJkl5FRQXr379/kz57HZ34c2Lsf6HloYceYmVlZey+++5jl112GfP7/REeZdsoKio6KqSMHz+ejR8/vkMsBR2Lw+HgfxfvRzgcZpmZmey3337j1/38889nfWxtoSs8Hxu/hzzxxBN8uY8xxl544QU2d+7co/6z25GUlZWxxx57jP33v/9ljDVdls3MzOxU/ZGbozplEdB8ujwtLQ3z589vUgS2srISffr0abd1gForHA5Dq9XyPmRyuRyXXnopJBIJHnroIVx55ZX46quvIJPJsGDBAowYMQI9e/bkBXI7glGjRmHJkiW46qqrUFFRgSlTpqBfv3746KOPUFVVhZSUlEgPsc2INYPC4TD+8Y9/QCKR4LrrrsO3336LQ4cOYcuWLVCpVJEeZptIS0tDWloagIbf42AwiKioKPTr16/DLAW1pHEJBYlEAkEQ4Ha74fF4+Gm2WbNm4fnnn0dpaSkSExM71P3tCs/HxnXkxH8DwOzZs/Hcc89hx44dHboAbmJiIh599FGo1WoADb+njDHU1NQgJiamw5a7aJUIh8IuS/xfTOP/qTb2+OOPs+HDh7fbk06ny+v18qXMK6+8kt17771MIpGwv/76K9JDO2Xbtm1jI0eOZGlpaax79+6sR48ebPv27ZEe1hnR+GTwhRdeyMxmc7s8IduWZs2axVJTU5ssIXVEzWdQQqEQq6mpYQkJCWzfvn3spZdeYjqd7qhWWR1NZ38+irNlTz31FJsxYwZ79dVXmUqlOuYSdGcwe/ZslpWVxYqKiiI9lDOGQlkEiKcOCwsL2QcffNDkuoKCAvbYY48xo9HYKfoEMnb0m4D4Zu7z+fjeJLPZ3CleTBwOByssLGS7du065unEziIUCrH777+fSSSSTvO72pIvv/yS3XnnncxisXT4N/VjvfYIgsByc3PZ8OHDmUqlOqrXZUfVFZ6Pzz33HJNIJMxoNHaan1tzn332GZsxYwYzmUwd/jl4Ih3j2EknEgqFIJPJUFRUhJ49e2L16tX85NDevXsxd+5cfP311/j11187TPXz4xEEAXK5HEVFRfjwww8B/O+EkFqtxqpVq6DVarF+/Xrk5uZGcqhtwmAwID09HX379oXVao30cM643r17Y/v27Z3id/VYevXqBZvNhvXr13foZZOWXntEtbW12L9/PzZv3owtW7Zg0KBBERxp2+kKz8exY8cCADZu3Nhpfm7N9erVC2VlZR3+OdgaVNH/LBIrEBcVFSE3NxeXX3453nnnHb7273K5sH//fsTHxyM5OTnCoz19je9vz5498Y9//IMHMwD48ccfcd999+Gzzz7DwIEDIzhScqpYB62KfrLq6+uhUCgiPYxTdrzXHsYYBEHA22+/jYsvvhg9evSI9HDJSfJ4PB1qH+6pEDsxdHYUys6S5i+KEydOxMKFCzv0ZszjOVEABRoa5DocDsTHx0dwpIR0bq197WnctoYQEhkUys4CsddjVw1kLd3fEzU+JoScvq722kNIR0fvimeBTCZDcXExevfujcsuuwyLFi3qtC+KjfeQHe9NgAIZIWdeV3rtIaQzoJmys0AQBMyYMQMSiQRvv/12p39RLC4uRq9evXD11VdjwYIFkMlkkR4SIV1SV3vtIaSjo1B2ltTW1sJoNHb6GSJ6EyCkfekqrz2EdAYUykibozcBQggh5ORRKCOEEEIIaQdoKoMQQgghpB2gUEYIIYQQ0g5QKCOEEEIIaQcolBFCCCGEtAMUygghhBBC2gEKZYQQQggh7QCFMkIIIYSQdoBCGSGEEEJIO0ChjBBCCCGkHaBQRgghhBDSDlAoI4QQQghpByiUEUIIIYS0AxTKCCGEEELaAQplhBBCCCHtAIUyQgghhJB2gEIZIYQQQkg7QKGMEEIIIaQdoFBGCCGEENIOUCgjhBBCCGkHKJQRQgghhLQDFMoIIYQQQtoBCmWEEEIIIe0AhTJCCCGEkHaAQhkhhBBCSDtAoYwQQgghpB2gUEYIIYQQ0g5QKCOEEEIIaQcolBFCCCGEtAMUygghhBBC2gEKZYQQQggh7QCFMkIIIYSQdoBCGSGEEEJIO0ChjBBCCCGkHaBQRgghhBDSDlAoI4QQQghpByiUEdLGPvvsM2g0GlRUVPDLbrrpJvTr1w8OhyOCIyOERBK9NpATkTDGWKQHQUhnwhjDOeecgxEjRmDevHl46qmn8N5772Hz5s1ISkqK9PAIIRFCrw3kRGimjJA2JpFI8Pzzz2PBggV4/vnnMW/ePKxcuZK/6H7//ffo2bMnsrKysHDhwgiPlhBytpzoteHyyy+HyWTC5MmTIzxSEik0U0bIGZKbm4u9e/fi559/xsiRIwEAoVAIvXr1wpo1a2A0GjFw4EBs3LgRFoslwqMlhJwtLb02AMDatWvhcrnw4YcfYunSpREcIYkUmikj5AxYuXIl8vPzIQgC4uLi+OVbtmxB7969kZSUhKioKIwbNw4///xzBEdKCDmbjvXaAAAXXHAB9Hp9hEZG2gMKZYS0se3bt2PKlClYtGgRRo8ejVmzZvHrysvLm+wdSUpKQllZWSSGSQg5y4732kAIAMgjPQBCOpOioiKMHz8ejz/+OKZOnYpu3bph2LBh2L59O3JzcyM9PEJIhNBrA2kNmikjpI3U1NTgkksuwaRJk/Doo48CAIYOHYpx48bh8ccfBwAkJiY2mRkrKytDYmJiRMZLCDk7WvPaQAhAG/0JOatCoRBycnKwdu1a2uhPCDnK2rVrMX/+fNro30XR8iUhZ5FcLsfcuXMxatQohMNhPPzwwxTICCEAgDFjxmDnzp3weDxITk7GkiVLMGzYsEgPi5xFNFNGCCGEENIO0J4yQgghhJB2gEIZIYQQQkg7QKGMEEIIIaQdoFBGCCGEENIOUCgjhBBCCGkHKJQRQgghhLQDFMoIIYQQQtoBCmWEEEIIIe0AhTJCCCGEkHaAQhkhhBBCSDtAoYwQQgghpB34f6tdo7OGS0eZAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "D = 2 # Still in 2-D\n", "lb = np.full((1, D), -np.inf)\n", "ub = np.full((1, D), np.inf)\n", "plb = -3 * np.ones((1, D))\n", "pub = 3 * np.ones((1, D))\n", "\n", "# Define the prior as a multivariate normal (scipy.stats distribution)\n", "scale = 0.5 * (pub - plb).flatten()\n", "prior = scs.multivariate_normal(mean=np.zeros(D), cov=scale**2)\n", "# prior = [scs.norm(scale=scale[0]),scs.norm(scale=scale[1])] # equivalently\n", "\n", "x0 = np.zeros((1, D))\n", "np.random.seed(42)\n", "vbmc = VBMC(log_likelihood, x0, lb, ub, plb, pub, prior=prior)\n", "vp, results = vbmc.optimize()\n", "vp.plot();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Acknowledgments\n", "\n", "Work on the PyVBMC package was funded by the [Finnish Center for Artificial Intelligence FCAI](https://fcai.fi/)." ] } ], "metadata": { "interpreter": { "hash": "cf2c3e35bb9d622e963fe7adafe5d3d77a0ee2382f730f35475e9a620896d84b" }, "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.13" } }, "nbformat": 4, "nbformat_minor": 2 }