{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Gradient Descent Optimizations\n", "\n", "Mini-batch and stochastic gradient descent is widely used in deep learning, where the large number of parameters and limited memory make the use of more sophisticated optimization methods impractical. Many methods have been proposed to accelerate gradient descent in this context, and here we sketch the ideas behind some of the most popular algorithms." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Smoothing with exponentially weighted averages" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "n = 50\n", "x = np.arange(n) * np.pi\n", "y = np.cos(x) * np.exp(x/100) - 10*np.exp(-0.01*x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exponentially weighted average\n", "\n", "The exponentially weighted average adds a fraction $\\beta$ of the current value to a leaky running sum of past values. Effectively, the contribution from the $t-n$th value is scaled by\n", "\n", "$$\n", "\\beta^n(1 - \\beta)\n", "$$\n", "\n", "For example, here are the contributions to the current value after 5 iterations (iteration 5 is the current iteration)\n", "\n", "| iteration | contribution |\n", "| --- | --- |\n", "| 1 | $\\beta^4(1 - \\beta)$ |\n", "| 2 | $\\beta^3(1 - \\beta)$ |\n", "| 3 | $\\beta^2(1 - \\beta)$ |\n", "| 4 | $\\beta^1(1 - \\beta)$ |\n", "| 5 | $(1 - \\beta)$ |\n", "\n", "Since $\\beta \\lt 1$, the contribution decreases exponentially with the passage of time. Effectively, this acts as a smoother for a function." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def ewa(y, beta):\n", " \"\"\"Exponentially weighted average.\"\"\"\n", " \n", " zs = np.zeros(len(y))\n", " z = 0\n", " for i in range(n):\n", " z = beta*z + (1 - beta)*y[i]\n", " zs[i] = z\n", " return zs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exponentially weighted average with bias correction\n", "\n", "Since the EWA starts from 0, there is an initial bias. This can be corrected by scaling with \n", "\n", "$$\n", "\\frac{1}{1 - \\beta^t}\n", "$$\n", "\n", "where $t$ is the iteration number." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def ewabc(y, beta):\n", " \"\"\"Exponentially weighted average with hias correction.\"\"\"\n", " \n", " zs = np.zeros(len(y))\n", " z = 0\n", " for i in range(n):\n", " z = beta*z + (1 - beta)*y[i]\n", " zc = z/(1 - beta**(i+1))\n", " zs[i] = zc\n", " return zs" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAD8CAYAAACfF6SlAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niimIMv4KhUIxBVHGX6FQKKYg/w+fK83aExSN4QAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "beta = 0.9\n", "\n", "plt.plot(x, y, 'o-')\n", "plt.plot(x, ewa(y, beta), c='red', label='EWA')\n", "plt.plot(x, ewabc(y, beta), c='orange', label='EWA with bias correction')\n", "plt.legend()\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Momentum in 1D\n", "\n", "Momentum comes from physics, where the contribution of the gradient is to the velocity, not the position. Hence we create an accessory variable $v$ and increment it with the gradient. The position is then updated with the velocity in place of the gradient. The analogy is that we can think of the parameter $x$ as a particle in an energy well with potential energy $U = mgh$ where $h$ is given by our objective function $f$. The force generated is a function of the rat of change of potential energy $F \\propto \\nabla U \\propto \\nabla f$, and we use $F = ma$ to get that the acceleration $a \\propto \\nabla f$. Finally, we integrate $a$ over time to get the velocity $v$ and integrate $v$ to get the displacement $x$. Note that we need to damp the velocity otherwise the particle would just oscillate forever.\n", "\n", "We use a version of the update that simply treats the velocity as an exponentially weighted average popularized by Andrew Ng in his Coursera course. This is the same as the momentum scheme motivated by physics with some rescaling of constants." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def f(x):\n", " return x**2" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def grad(x):\n", " return 2*x" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def gd(x, grad, alpha, max_iter=10):\n", " xs = np.zeros(1 + max_iter)\n", " xs[0] = x\n", " for i in range(max_iter):\n", " x = x - alpha * grad(x)\n", " xs[i+1] = x\n", " return xs" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def gd_momentum(x, grad, alpha, beta=0.9, max_iter=10):\n", " xs = np.zeros(1 + max_iter)\n", " xs[0] = x\n", " v = 0\n", " for i in range(max_iter):\n", " v = beta*v + (1-beta)*grad(x)\n", " vc = v/(1+beta**(i+1))\n", " x = x - alpha * vc\n", " xs[i+1] = x\n", " return xs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Gradient descent with moderate step size" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ncldKKR/0/9N5W3MoaLYUAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "alpha = 0.1\n", "x0 = 1\n", "xs = gd(x0, grad, alpha)\n", "xp = np.linspace(-1.2, 1.2, 100)\n", "plt.plot(xp, f(xp))\n", "plt.plot(xs, f(xs), 'o-', c='red')\n", "for i, (x, y) in enumerate(zip(xs, f(xs)), 1):\n", " plt.text(x, y+0.2, i, \n", " bbox=dict(facecolor='yellow', alpha=0.5), fontsize=14)\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Gradient descent with large step size\n", "\n", "When the step size is too large, gradient descent can oscillate and even diverge." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJztnXd4HNX1v9+76r1YvVnuvQjL2MZgXCgGQu+YlgCGAElI\nfiSQEEAhcSAk4WuSAMGAsektNINDCzbGvXewLdvqkmVZlqze9v7+GC1q2ySttNLqvM8zz065M3NW\n5TN3zj33HKW1RhAEQfAsTO42QBAEQXA9Iu6CIAgeiIi7IAiCByLiLgiC4IGIuAuCIHggIu6CIAge\niIi7IAiCByLiLgiC4IGIuAuCIHgg3u66cVRUlE5NTXXX7QVBEPol27ZtK9FaRztq5zZxT01NZevW\nre66vSAIQr9EKZXtTDtxywiCIHggIu6CIAgeiIi7IAiCByLiLgiC4IGIuAuCIHggIu6CIAgeiIi7\nIAiCB9LvxD2zuJLHVuynvtHsblMEQRA6zdNfHWLTkRM9fp9+J+65pdUsXXeUr78/5m5TBEEQOkXO\niWr+76uDbDpa2uP36nfiPmtkNHGh/ry1JdfdpgiCIHSKd7bmYlJw1ZSkHr+XQ3FXSi1VShUrpfY6\naDdVKdWolLrKdeZ1xMukuDo9iTUHj1NQVtOTtxIEQXAZjU1m3tuWx6yR0SSEB/T4/ZzpuS8D5ttr\noJTyAv4CfOECmxxy9ZRkzBre25bXG7cTBEHoNmsOHafoVC3XTU3ulfs5FHet9RrAkYPoZ8B/gGJX\nGOWIlEGBzBw+iHe25mI26964pSAIQrd4e0sug4J8mTs6tlfu122fu1IqEbgceK775jjPNenJ5J2s\nYf3hnh91FgRB6A7FFbX877tirpyShK937wx1uuIui4EHtNYOYxOVUguVUluVUluPHz/erZuePy6O\nsAAf3tqS063rCIIg9DTvb8+n0ay5Jr13XDLgGnFPB95SSmUBVwHPKqUus9ZQa71Ea52utU6PjnaY\na94u/j5eXJ6WyBf7jnGyqr5b1xIEQegptNa8syWX9MERDI8J7rX7dlvctdZDtNapWutU4D3gbq31\nh922zAmunZpMfZOZ93fk98btBEEQOs3mo6UcKaniml4aSLXgTCjkm8AGYJRSKk8pdZtS6i6l1F09\nb559xsSHMjk5nDc356C1DKwKgtD3eHNzDiH+3lw8MaFX7+uwzJ7W+npnL6a1vrVb1nSB609P5oH/\n7GFb9knSUyN7+/aCIAg2KauuZ+XeIq5NTybA16tX793vZqi250cTEwj28+aNzTKwKghC3+L97fnU\nN5q5/vSUXr93vxf3ID9vLp2cwKe7CymvbnC3OYIgCIAxkPrWlhwmJYczNiG01+/f78Ud4PrTU6hr\nNPPhThlYFQShb7A95yQHj1VyfS8PpFrwCHEfnxjGhMQwGVgVBKHP8ObmXIJ8vbh4Uu8OpFrwCHEH\no/f+fVEFO3LL3G2KIAgDnPKaBj7ZXcClaYkE+TmMW+kRPEbcL5mcQJCvF29ukoFVQRDcy4c78qlt\nMHP91N4fSLXgMeIe7OfNpWmJrNhdIAOrgiC4Da01r2/KZlJSGBOSwtxmh8eIO8ANp6dQ22Dm/R2S\nClgQBPewNdsYSL1hmvt67eBh4j4+MYzJyeG8vkkGVgVBcA+vb8wmxM/bbQOpFjxK3AFumJZCZnEl\nm3uhRqEgCEJrSqvqWbmniCtOSyTQ1z0DqRY8TtwvnphAiL83r8vAqiAIvcx723KpbzJzw7TB7jbF\n88Q9wNeLK09L4rO9RZyorHO3OYIgDBDMZs2bm43UvqPiQtxtjueJO8CCaSnUN5l5Z6sMrAqC0Dus\nP3yCoyVVbh9IteCR4j4iNoRpQyJ5Y3M2TVJjVRCEXuDVjVlEBPpw4YR4d5sCeKi4A9w0YzC5pTWs\nOdi9cn6CIAiOKCyv4cv9x7hmajL+Pr2b2tcWHivu542NIzrEj1c3ZrvbFEEQPJw3N+WggRv7wECq\nBY8Vd19vE9dPTWbVgWJyS6vdbY4gCB5KfaOZN7fkMmdUDMmRge425wc8VtwBrp+WgkkpCYsUBKHH\n+GJ/Eccr6rhpet/ptYOHi3t8WADnjInhna251DY0udscQRA8kFc3ZJMcGcCskdHuNqUNzhTIXqqU\nKlZK7bVxfIFSardSao9Sar1SapLrzew6N01PpbSqnv/uLXS3KYIgeBgHj1Ww6WgpC6YNxsuk3G1O\nG5zpuS8D5ts5fhQ4W2s9AfgjsMQFdrmMM4YNYmh0EMvXy8CqIAiu5ZUNWfh6m7gm3T3VluzhUNy1\n1msAm4latNbrtdYnmzc3Akkuss0lmEyKm6cPZmduGbukkIcgCC7iVG0D72/P55JJCUQG+brbnA64\n2ud+G/BfWweVUguVUluVUluPH++9+PMrpyQR5OvF8g1ZvXZPQRA8m/e25lFd38StZ6S62xSruEzc\nlVJzMMT9AVtttNZLtNbpWuv06OjeG3wI8ffhyilJfLKrUPLNCILQbcxmzasbszktJZzxie4ryGEP\nl4i7Umoi8CJwqdb6hCuu6WpunjGY+iYzb23JdbcpgiD0c9YcOs7Rkipu6aO9dnCBuCulUoD3gZu0\n1ge7b1LPMDwmhDOHR/Haxmwam8zuNkcQhH7MKxuyiQr244LxfSOPjDWcCYV8E9gAjFJK5SmlblNK\n3aWUuqu5ySPAIOBZpdROpdTWHrS3W9w8YzCF5bV8uf+Yu00RBKGfkn2iilUHirlhWgq+3n13qpDD\nUiFa6+sdHL8duN1lFvUg88bEkhQRwMvrs7igj2RuEwShf7F8fTZeSrGgj6T2tUXffez0AF4mxc0z\nBrP5aCn7CsrdbY4gCP2MyrpG3t2ay4UT4okN9Xe3OXYZUOIOcG16CgE+Xixbl+VuUwRB6Gf8Z1se\nFXWN/HhmqrtNcciAE/ewQB+unJLIR7sKJCxSEASnMZs1y9ZnMTk5nLSUCHeb45ABJ+4At56RSn2j\nmTckW6QgCE7yzUEj/LE/9NphgIr78JgQzhoRxasbs6lvlLBIQRAcs3TdUWJC+nb4Y2sGpLgD/GTm\nEIor6iRbpCAIDsksruDbQyXcNH1wnw5/bE3/sLIHOHtkNEOjgli69ihaSxFtQRBs8/I6I/vj9X08\n/LE1DuPcPRWTSfHjmak8/NE+tmWfJD010t0mCYLQBzlZVc9/tudx+eREooL9unSNxYsfoayse2N8\n4eEp3HffY063H7DiDka2yL99cZAXvz0q4i4IglXe2JxDbYOZ284a0uVrlJXlkJGR2i07MjKyOtV+\nwLplAAJ9vblhWgpf7C8i54QU0RYEoS31jWaWr8/irBFRjIwNcbc5nWJAizvALTNSMSnFy+uPutsU\nQRD6GJ/sLqC4oo7bzxrqblM6zYAX97gwf340MZ53tuRyqrbB3eYIgtBH0Frz0tqjjIgJZtaIKHeb\n02kGvLgD3HbmUKrqm3h7s+R6FwTBYOORUvYVnOInZw5BKdcXv16zJptLLnmTxMSnUOoPLFu206XX\nF3EHJiSFcfqQSJatz6JBcr0LggC8+O0RIoN8uTwtsUeuX1lZz/jxMTz99HwCAlwf2yLi3szCs4aS\nX1bDyj0yqUkQBjqZxRX87/tibp4xGH8frx65x4UXjuDPf57HVVeNxWRy/ZuBiHszc0fHMCw6iCVr\njsikJkEY4Lz47VH8vE3cNH2wu03pMiLuzZhMijvOGsq+glNsONwny8AKgtALFFfU8v72fK5OT2JQ\nFyct9QVE3FtxWVoiUcG+LPn2iLtNEQTBTbyyPpsGs5nbzux/4Y+tcaaG6lKlVLFSaq+N40op9Q+l\nVKZSardS6jTXm9k7+Pt4ccuMVFYfOM6Bogp3myMIQi9TXd/IqxuzOW9sLEOigtxtTrdwpue+DJhv\n5/gFwIjmZSHwXPfNch83Th+Mv4+JF6T3LggDh9dfh9RUAvx9+fSpG3mgdLu7Leo2DsVda70GKLXT\n5FLgFW2wEQhXSvWPhMdWiAjy5dr0ZD7amU9heY27zREEoad5/XVYuBCys1Fak3TqOEN/90tjfw9S\nWVnPzp1F7NxZhNmsyckpZ+fOInJyXFPf2RU+90Sg9eyfvOZ9/ZbbzxqKWcPStZKSQBA8gpoayMyE\n1avhtdfgL3+Bn/0MLr8cfvITqG6XW6q6Gh56qEdN2rq1gLS050lLe56amkYefXQ1aWnP88gjq1xy\n/V7NCqmUWojhuiElpe/mRU6ODORHE+N5Y1MO984ZQVigj7tNEgTBGlrDqVOQlwf5+canZWm9XWrF\n+RAWBklJUF9v/do5PVuGc/bsVLR+tMeu7wpxzweSW20nNe/rgNZ6CbAEID09vU8Hk985axgf7Szg\ntU3Z3DNnuLvNEYSBh9kMJSVtRdqagFdWdjw3JgYSE2HwYJg50xDxxETj07IeHGy0TU2F7OyO1+jD\nHVBncIW4fwzcq5R6C5gGlGut+/00z7EJoZw9MpqX1x3ltjOH9NgsNUEYkDQ2QlGRfdHOz+/Yq/by\ngvh4Q6AnTID581sE2yLaCQng14n49EWLqPvJbfjV17XsCwyERYtc813dhENxV0q9CcwGopRSecCj\ngA+A1vrfwErgQiATqAZ+3FPG9jZ3nT2M61/YyHvb8rixH89UE4Repba2Raxt9bqLioyeeWv8/FpE\nesaMjqKdlASxsYbAu5Cdsy5i6Xn3smjLm4QUFxo99kWLYMECl96nt3Eo7lrr6x0c18A9LrOoDzF9\naCSTksNZsuYI101NxttL5nwJA5xTp+z7tvPzDVdKe0JDW0R63LiObpKkJIiMhB7IvuiIf68+zLop\n56LeewL8PKc4ned8kx5AKcXds4dx56vb+HRPIZdO7tdBQIJgG63hxAn7bpK8PKiwMrkvKsoQ5+Rk\no8fd3redmGiIex8ks7iCz/YV8bO5wwn2IGEHEXeHnDsmlhExwTy3+jCXTErokbzOgtCjNDW1+Ldt\nuUny86Guru15JlOLf3vMGDj33I5ukoQE8Pd3z/dyAc+tPkKAjxc/ntn1+qh9FRF3B5hMirvnDOOX\nb+/i6++LmTcm1t0mCUILdXVQUGDfTVJYaAh8a3x9W0R62rSOom3xb3t7rkTkllbz4c58bpmRSmSQ\nb4/eKzw8pdMFrq1dozN47m/OhVw8MYG/f3GQf63KZO7oGOm9C71DZaVjN8nx4x3PCw5uEehzzuno\n205MNFwpA/zv+IVvj2BScMesnu+133ffYz1+j/aIuDuBt5eJO88exsMf7mXjkVJmDBvkbpOE/ozW\nxqQae26SvDxj8LI9gwa1CPTUqdZ73H3Uv92XKK6o5a0tuVyRlkR8WIC7zekRRNyd5OopSTz91SGe\nWZUp4i7YpqkJjh1zPPGmtrbteUoZ/u3ERBg1CubN6yjaCQkQ4JlC1NssXZtFY5OZu2YPc7cpPcaA\nEPfFix+hrKx7U4nDw1NYOOsW/rzye3bknCQtJcJF1gn9hvr6tv5tawJeUNDRv+3j0yLSU6fCZZd1\ndJPExRnthB7nZFU9r27I4sIJ8f0+ra89BoS4l5XlkJGR2q1rZGRkcce0wTy3+jD//DqTpbdOdY1x\nQt+gqspxfpLi4o7nBQW1iPScOdbdJFFRRuSJ0Cd4ed1RquqbuHeuZ6cVGRDi7iqC/Ly57cwh/O2L\ng+zNL2d8Ypi7TRIcoTWcPOnYTVJW1vHcyMgWkZ4yxXp+krCwAT8w2Z84VdvAy+uzmD8ujtFxnj02\nIeLeSW4+I5Ula47wz68P8fxN6e42Z2BjNhu9aXtukrw8I91ra5QywvySkmDECJg9u6ObJDHRyC8i\neBTL12VRUdvo8b12EHHvNKH+Ptw6cwj/+N8hvis8xZh4z376u42GBsN/bc9NUlBgJKBqjbd3S+86\nLQ0uvrijqyQ+XvzbA5DKukZeWneUeaNjBsRb94AV98cf/5b33/+eAwdK8PPzZvr0JB5/fB7jx8c4\nPPcnM1N56dsj/GtVJs/c0G9LxrqP6mrHbpJjxwyXSmsCAowp7omJcPbZ1vOTREeLf1uwymsbsymr\nbuBn80a425ReYcCK++rV2dx9dzpTpyaiteaRR1ZzzjmvsH//PURG2g83Cw/05eYzUvn3N4c5dKyC\nEbEhvWR1H0drKC937CY5ebLjueHhLQKdltbRt52UZLQR/7bQBarrG3lhzRHOGhHF5ORwd5vTKwxY\ncf/88xvbbL/66uWEhT3BunU5XHzxKIfn33HWUJavz+Lp/x3iXwOh9242G7MhHU28aV+uDFr820OG\nwFlndRTtxEQj6kQQeohXN2Rzoqqe+84ZGL12GMDi3p6KijrMZk1EhHOTRCKDfLmluff+82MVjOzP\nvfeGhraFE6wJeH6+0a413t7GxJrERJg0CS66qKOrJD7eyGMiCG6iur6R55t77VMGR7rbnF5DxL2Z\nX/ziMyZPjmPGjCSnz7njrKG8sj6Lf/Tl3ntNjfXCCa23i4o6+rf9/VsE+swzrecniYlxeeEEQXA1\nr2zIprSqnvvOGeluU3oVEXfgV7/6nLVrc1i79id4daIgh6X3/pw7eu+2CgO3F3B7hYETE41SZdYm\n3kREiH9b6PdU1TWyZM0RZo2MZsrggTWrfMCL+y9/+RlvvbWPVatuYejQzv/yW/veXRY5o7VRzcae\nmyQvz7nCwNZ63JbCwILg4bT02geOr92CU+KulJoPPA14AS9qrZ9odzwFWA6EN7d5UGu90sW2upxf\n/OK/vP22IeyjR0d16RoRQb48UbeHtJ/+FX1jCcpR/cXWhYFtuUkcFQYePx7OP7/7hYEFwYOprGtk\nyZrDzBoZzWkDMBeUQ3FXSnkBzwDnAnnAFqXUx1rr/a2a/R54R2v9nFJqLEbR7NQesNdl3HPPp7z6\n6m4+/PA6IiICKCoyesHBwb4EB3diAPD11/nRPzNQNc1RItnZcNttsH690XtuL+CdKQzcvnCC+LcF\nwWleXnuUk9UN/L9zB5av3YIzPffTgUyt9REApdRbwKVAa3HXgGWqZhhQ4Eoje4Jnn90KwLx5r7TZ\n/+ijZ5ORMdv5Cz30UIuwW6irg2ef7dh2+HC49lpITzfSuloEfNAg8W8Lggspr25gybdHOGdMLJMG\nSFx7e5wR90Qgt9V2HjCtXZsM4Aul1M+AIOAcl1jXg2j9qGsulGMnlXBKilHizBJCmJlpLG++afi9\n4+MdLzKwKQid5oVvj1BR28ivBmivHVw3oHo9sExr/Xel1AzgVaXUeK11G/+DUmohsBAgJaVz9QD7\nLCkphiumPYMHQ1ZWS9WdwkLby7ZtxmdVVcfr+PkZub6tCX/r/RKWKAgAnKisY+m6o1w0MZ6xCQM3\n95Mz4p4PJLfaTmre15rbgPkAWusNSil/IApokwBba70EWAKQnp7eLrC6n7JoESxc2GZmZp2vP36L\nFhkbShlul0GDjIFQe1RU2H4AFBXBwYPwzTfWwxtNJkPgHb0JxMXJoKvg0Ty/5gi1DU38cgBGyLTG\nGXHfAoxQSg3BEPXrgBvatckB5gHLlFJjAH/ASuVeD8QSFfPQQ5CTQ2VMPL+bej3XTjufmZ29VkiI\nsYx08CpZV2eIvb23ge3bjXS47QdvwchTbusNoPUS0o9n3QoDkqLyWpavz+KyyYkMjxnYf78OxV1r\n3aiUuhf4HCPMcanWep9S6jFgq9b6Y+D/AS8opX6JMbh6q9btpzx6MAsW/CDy3g1NbP3barI/+54P\n75mJ6gl/uZ+f4fYZPNh+u6YmQ+Bb9/7bPwTWrDE+24degpHvxZlxgchIGRcQ+gT/+PoQZq355QD2\ntVtwyufeHLO+st2+R1qt74fOd1Q9EX8fL+47dyS/eW83n+8rYv74ePcZY4mNj3dgg6Vakb03gR07\nYOVK6xOnfHxs9/5bLzExRj4aQegBjpZU8faWXG6clkJypBRakf+0HuCKtESe/+Ywf/viIOeMicW7\nEykN3IJSRu87MhLGjbPftrLSvkvo8GFYuxZOnLB+H0fjApaHhL9/z3xXwWN56suD+HqZuHeufV/7\n4sWPUFZmJ8rNCcLDU7jvvse6dY2eZkCIe3h4ChkZWd2+hrN4e5m4/7xR/PT17by/I59r0pMdn9Rf\nCA424vWHOyhTVl/veFxg1y6jKEdTU8fzw8OdcwmFhIhLSGBvfjkrdhVwz5xhRIfYDxgoK8shIyO1\nW/frrp70BgNC3N3xhJ0/Po6JSWEs/vIgl0xKwN9ngIUp+voaYaKOQl6bmow8OvYeAuvWGZ91dR3P\nDwx0HCYaH29EK0mFJo/lb18cICzAh4WzhrnblD7DgBB3d6CU4oH5o1nw4iZe25jN7WcNdbdJfRMv\nLyO1QmwsTJ5su53WUFZmPUTUsr57N3z+uZEtsz0+PsY9HL0JxMbKuEA/Y8PhE6w+cJwHLxhNWIDU\nxrUgf8U9yMzhUZw1Iop/fp3J1VOSCQuUP7wuo5QxWzciAsaOtd+2qsq+S+joUSP3T0mJ9ftER9sP\nEbUsAc4VdhF6DrNZ8/h/vyM+zJ9bz0h1tzl9ChH3HubBC0bzo3+u5dlvMvntBWPcbc7AICgIhg0z\nFnvU1xs+f1thooWFsHevcczauEBYmHPjAqGhMi7QQ3y6p5DdeeX87epJ3XJ9PvPMZp5/fhtZWWUA\njBsXw+9/fxYXXdR/QypF3HuYcQlhXD45kZfXZXHLjFQSwqW312fw9YXkZGOxh9nseFxgwwbjs7a2\n4/kBAc6FikZFybhAJ6hvNPPXzw8wOi6Ey9MSu3WtpKRQ/vKXcxgxYhBms2b58p1cdtnbbNu2kIkT\nY11kce8i4t4L/Oq8kXyyp5CnvjzI366e5G5zhM5iSe0QE2PUirWFpTqWvYfAvn3w1VdQXt7xfG9v\n2+MCrR8OcXHGGMIA541N2eSUVvPyj6fiZerem9Gll45us71o0Tyee24rGzbkirgLtkmKCOTWM1J5\n4dsj3HbmEMbED9xkRh6NUoarJiwMRo+237amxn4eoZwc2LQJjh/vWN8WjF6+My6hQM+czHOqtoF/\nfJ3JjKGDmD0y2qXXbmoy8+67+6msrOeMM/pvGLOIey9xz+zhvLM1l0Wffsert53eM2kJhP5DQAAM\nHWos9mhoaJtCwtqyf7/xQGhs7Hh+aKhzeYTCw/vVuMCzqw5TWlXP7y4c47L/pT17jjFjxkvU1jYS\nHOzLBx9cy4QJ/bPXDiLuvUZYoA8/nzuCxz7Zz+oDx5kzOsbdJgn9AR8fo6BLogOfstlszAq2FSZa\nWAibNxuf1dUdz/f3d25cIDra7eMCuaXVLF13lCvSEpmQFOay644aFcXOnXdRXl7Le+/t55ZbPmT1\n6lsZP75//q+KuPciN04fzKsbs1m08jvOGhHV99MSCP0Hk8kQ3uhomDjRdjut7aeWLiyE776Dr782\n5hW0xzIvwdGDIC7OGLDuAZ78/AAmBfefP8ql1/X19WL48EgApkxJYMuWAv7v/zbw0kuXuvQ+vYWI\ney/i623iwQtGc+er23hzSy43TXeQ1VEQXI1ShqsmNNQo9WiPmhqj928rTDQ/H7ZuNdxG1sYFBg1y\nLo9QcLBju19/HR56CJ2TwwMhUcz/6W9ICL+gaz8DJzGbNXV1VkJg+wki7r3MeWNjOX1IJIu/PMil\nkxMI9ZeoB6GPEhAAQ4YYiz0aGx2PCxw4YHxaSk62xlHJyW3b4A9/gJoaFJB06jiJ/3wUJsS31FPo\nJg8++BUXXTSC5OQwKirqeOONPaxencWnn7YvXdF/EHHvZZRSPHzRWC7+11qe+TqT314oE5uEfo63\nNyQkGIs97JWcPHrUSCS3Zo1Tt1TV1UaBHBeJe1FRJTfe+AFFRZWEhfkxcWIs//3vAs4/30GCvD6M\niLsbmJAUxtVTkli67ijXnZ7CkKggd5skCK7FkguouNiYBezos6LC+nWCg63XEAD7xek7ybJll7ns\nWn0FEXc38ev5o1i5p5BFn37Hi7eku9scQXBMQ4MRd28RZXuCXVxs3QWjlBGjHxtrTApLT29Zb/8Z\nE2PE6aemWi9C7yjj6ABHxN2FdLYIwITiU2zcUc5Pd0UTG2oUp+gPRQAED0Fro1dsS5zb77NWmB2M\nso+WzJ4JCZCW1iLO7QU7KsqIuOkEJx96FP97fkpAQ6uUz4GBRnF6wSYi7i6ks0UAGs1mXt2QjZdJ\nceO0wZhMql8UARD6ME1NRry7s4JdU2P9OhERLaI8frz1XrVlvYcLpjwaPBmfC3/OX7a9hXd+ntFj\nX7TIZf52T8UpcVdKzQeexiiQ/aLW+gkrba4BMjAKZO/SWvffYeZewttkYtaIaFbsLmBXXhlpKRHu\nNknoi9TUOOcGOXbMSHBmNne8hrd3W1EeNcq2YEdH91iMemfZklXKx7sK+Pk9t+N97pPuNqdf4VDc\nlVJewDPAuUAesEUp9XFzUWxLmxHAb4GZWuuTSqn+OaXLDQyNDiIlMpANR04wKi7E3eYIvYFlsNGZ\ngcbiYtuDjSEhLaI8bBjMmGHbfx0e7vaZpZ2lscnMwx/uJSHMn7vOlmI3ncWZnvvpQKbW+giAUuot\n4FJgf6s2dwDPaK1PAmiti11tqKeilGL2qBhe25jN2kNWikcI/QNLDhhHPexjx4xBSVuDjdHRLYJ9\n+unWhdrSu/bQpGAWXt+Uw/dFFTy34DQCfcWD3Fmc+YklArmttvOAae3ajARQSq3DcN1kaK0/c4mF\nHsTjj3/L7373NffcM5V//evCH/ZHBvmSlhLOtuyTnKi0MtNP6H0sg43O+K2PHYOTJ61fx9+/RZQT\nE1sGG60J9qBBnR5s9FRKKuv4+xcHOHN4FPPHx7n02uHhKd0e2woP7/uROq56HHoDI4DZQBKwRik1\nQWvdJjmFUmohsBAgZYCFMW3cmMeSJdtt5oaeNmQQ3xdVsCP3OE1m3e381IIVLIONjvzWlk9rhTfA\nGGy0iPKECTBvnvWBxthYI067H2Vb7Cv89bMDVNc3kXHJWJdnUB0o0WjOiHs+0DqpcVLzvtbkAZu0\n1g3AUaXUQQyx39K6kdZ6CbAEID09fcB0UcvLa1mw4H2WLr2EP/zhG6ttfL2NwdWnq/N5c3MON0re\nGeewDDboSUQlAAAgAElEQVQ6I9iOBhstojxmjO3IkD402Oip7Mg5ydtbc7lz1lCGx8g4VFdxRty3\nACOUUkMwRP06oH0kzIfA9cDLSqkoDDfNEVca2p9ZuPATrrpqDHPmDLEp7gAjY4OJDvHnyc++Z/74\nOKKC/XrRyj6C1oaLw5mBRmcGG2NjYfhwmDnT9kSZiAjpXfcRGpvMPPTBXuJC/fnZvBHuNqdf41Dc\ntdaNSql7gc8x/OlLtdb7lFKPAVu11h83HztPKbUfaAJ+rbU+0ZOG9xdeeGEbmZmlvPba5Q7bKqVI\nSw5nRUMTf/70O566dnIvWNgL1Ncbg4jOCra1ohMmkzEBxiLMp59uf2ZjgNSq7Y8s35DN/sJTPLfg\nNIL9ZBC1Ozj109NarwRWttv3SKt1DfyqeRGaOXCghN/97mvWrv0xPk5WZg8N8OHOGcP416pMrkpP\n4oxhUT1sZRew5AR3ZqCxuNi5wcakJDjtNNuCLYONHk9ReS1PfXGA2aOiXT6IOhCRR2MPsmFDHiUl\n1Ywb9+wP+5qaNGvWZPPvf2+lqup3+Fnpndw7dzgf7yrg4Q/38t9fzMLXuxfik5uaDJ+0szMbbQ02\nRka2iPLEibYjQ2JiZLBRaMMfP9lPo1nz2CXjpQylCxBx70Euu2w06elt06D++McfMWJEJL/73Vn4\n+lrvifr7ePGHS8fxwf1PUvvkAnyPF3ZtynVNjfORISUl1gsu+Pi0HVQcM8Z2ZEhUlAw2Cl1i9YFi\nPt1TyP3njSRlkGfH7/cWIu49SHi4P+Hh/m32BQX5EBkZ4LAu45ytX3LGF8/gV9/cQ87OhoULoaoK\nzjrLuQgRW6lSQ0JaRHnECGOw0ZZg97PCyUL/o7q+kd9/uJfhMcHcMUtmoroKEfe+ykMPtQi7hepq\nuPNO6+1DQozUqDExMG2a7YFGGWwU+hhPfXGQvJM1vHvXDPy8vTqdXdUakl1VxL3XWb36VucadrYQ\nQUUFZGYaOUtKS1v851FRLUt0dNvtQYMMt4sguIk9eeUsXXeUG6alMDXVKE7d2eyq1pDsqiLufZeU\nFNsFCnbsMMTbshw/3nbbsu/wYWO9vNz2fcLD2wq+tYdA631hYf0uAZXQN2lsMvPg+7uJCvbjgfmj\n3W2OxyHi3ldZtMjwsVdX/7Crztcfvz//2YhIiYyEkSOdu1Z9vdGbb/8QaL+dnw87dxr76+qsX8vL\ny+jxO3oItF6CpIyg0JEX1x5lX4ER0x4WIG+QrkbEva9iiYp56CHIyeFUdDy/P/16Lpw0j/mdvZav\nL8TFGYszaG08VBy9GZSUwHffteyzNrUfDB9/Z94OxF3k8Rw+XslTXx7kvLGxEtPeQ4i492UWLPhB\n5AOazGT+ax0Pf7SX6UMjCQ/swZBDpYzedlAQDHYyx43ZbPj7bT0EWi9Hjjh2F4WFde7toB/mKx+o\nNJk1v3lvNwE+XvzpMudj2jMyVndI3xEbG0RR0f09YWa/R8S9n+DjZeKvV0/k0n+t47FP9vPUNX0s\nNYHJ5Dp3UfuHQn4+7Npl7LM1eaq1u8iZt4OoKCMfuoR59jqvbMhiW/ZJ/n71JGJC/R22b82oUYPa\nBCV4ecnvzxYi7v2IcQlh/HT2MP75dSYXT0xgzuh+XvCqu+4iey6j77+HtWvtu4v8/Tv3dhAVJe6i\nbpJzoponPzNSDFxxWmKnz/f2NhEXF9wDlnkeIu4upDeKANw7dzif7S3it+/v4fP7ZhEWOIDEpi+5\ni5x9OxB30Q+YzZpfv7cLL5Piz5dP6FKKgSNHTpKQ8Hf8/LyZNi2RP/95HkOHSu1ha4i4u5DemDTh\n5+3F36+ZxOXPridjxT7+z1MyR/YU3XEXORpMLiiA3bvtu4tMJsNd5OzbgaV8nge6i15en8Wmo6U8\nedVEEsI7P5Fu2rREli27jNGjoyguruJPf1rDGWe8xL59dzNIUhZ0QMS9HzIxKZx75gznH/87xPnj\nYpk/Pt7dJnkWnXUXgZEWwtHbgcVdVFJiVIRqarJ+LYu7yNm3g0GD+nxOn8ziSp787HvmjY7h6ilJ\nXbrGBRe0ze8+fXoSQ4c+zfLlu/jVr2a4wkyPQsS9j2NrKnaTWZN0pJiHHm5i9dhY/O2kFJap2L1A\nV9xF5eWOB5NLSiAry9hnz10UGtrxIWDvodCL7qLGJjP/791dBPh68fgVXXPHWCM42Jdx42I4dEhK\nR1hDxL2PY28qdkllAm9uyiE1KoAfTYy3+U8jU7H7ICaTUQEqIsJ5d1FDg9Hjt/dm0Fl3kb3B4/b7\ng4I65y56/XV46CG8cnJ4JiSK4gcfISb0POfPd0BtbSPff1/CnDmpLrumJyHi3o+JCvZjxrBBrM0s\nYX/BKcYlhrnbJKEn8fHpGXdRSUnX3EX23hC+/RZ+8xuorkYBSaeOk/SnByAlonNpq1tx//1fcPHF\nI0lJCaO4uIo//nENVVX13HLLpC5dz9MRce/nnDY4gqwTVaw+eJzEiICendwk9D+66i6y9WaQkwMH\nD8L69W1SYzhFdbUx47qL4p6Xd4rrr/8PJSXVREcHMX16Ehs33s7gweFdup6n45S4K6XmA09j1FB9\nUWv9hI12VwLvAVO11ltdZqVgE5NSnD8ujtc2ZvPZviKumZKMyeR5kRaCC9Ha6NGXlrZdTpxwvM9W\nziEAPz/D1RMZCXv3Wm/T2WynrXjrrau6fO5AxKG4K6W8gGeAc4E8YItS6mOt9f527UKAXwCbesJQ\noS2FhRU8+OD/WLnyEBUVdSSlhDH/zjQGRwYxY9ggd5sn9AZaGwVZbAmzvf319bavGxDQItKRkTBq\nlPHZel/rxbK/VZ2AmoRkAgrzOl47xf48DsF1ONNzPx3I1FofAVBKvQVcCuxv1+6PwF+AX7vUQqED\nZWW1zJy5lDPPTOHTT28gOjqQI0dOcqSqjs1HT5ASGUhihBTk6DdoDadOOS/Mrfc3Ntq+blBQWxEe\nO9a2MFuWiIhuF3MpKq/l6RkLeHTFYvwbWvX0AwONbKdCr+CMuCcCua2284BprRsopU4DkrXWnyql\nRNx7mCefXEd8fAivvHL5D/uGDIngrEYzb2zK5r97C7lx+mC74ZFCD2A2txVpZ9wclsXWICYYhcRb\nC/GECbbFufXi59d7372ZJrPmF2/tYM+42dx37kj8n3jMcMV0pQaw0C26PaCqlDIBTwG3OtF2IbAQ\nIEVez7rMhx9+z/z5w7n22vdYteooCQkh3H77adxzz1QumBDP21ty+WL/MS62Ex4p2MGSssBZN4dl\n38mTtvPYgBGL3lp8k5Oti3PrfRERfX6CUmv+9XUmm46W8rerJxE7ZT7c9RN3mzRgcUbc84HkVttJ\nzfsshADjgdXNQhIHfKyUuqT9oKrWegmwBCA9PV13w+4BzZEjJ3n22S388pfTefDBG9m5s4if/ey/\nANx77+mcOTyKNYeOszuvnEnJAziSoKmprUg765c+edJwldgiLKytCKem2nd1WETag5OOLV78CIdy\nD/HNwWLGRgax5+MI9q7ofMfCUW4lwXmcEfctwAil1BAMUb8OuMFyUGtdDkRZtpVSq4H7JVqm5zCb\nNenpCTz++DkApKXFc+hQKc88s4V77z2dtJRwck9Ws+bgceLCOpdStU/S2GiIdGfcHCdOGOfYQilj\nlmZrAR42zPGgYXg4eEsEcXuKjh8l7TIfppqSuGHaYHy9uzb7VSbcuQ6Hf6Va60al1L3A5xihkEu1\n1vuUUo8BW7XWH/e0kUJb4uNDGDs2us2+MWOiePppY3q6Uorzxsbx+qZsPt1TSH1jH3lJamgwesWd\nDb+zN+1eKaNXbBHhqChjxqejgcPwcCMHvNBtmsyazUdLSWwI59qpyV0Wdgu9kV11IOBUF0RrvRJY\n2W7fIzbazu6+WYI9Zs5M5sCBtvk0Dh48weDBLTNUA3y9uHBCPO9tyyNry3704MGo3FzXDGzV1xsi\n3ZnwuxMnoKLC9jVbZ2+MjITYWBgzxnEInhTsdjv//PoQxRW1zB4VQ0xI998UJQ+Sa5D3y37IL385\nnTPOWMqiRWu49trx7NhRyD/+sZk//3lum3YJ4QFcbDpB8cHdqJzmgb7sbKPwNsBVV3Ut/K6y0rZx\nXl5tBTg+HsaPd9yTDg0Vke6HrD1UwtP/O8SYyCDGJ4S62xyhFSLu/ZCpUxP58MNr+d3vvuaPf1xD\nSkoYf/zjHO6+e2qHtqk7N+Ct20VwVFfDTTfBjTfavom3d1sRTk6GSZPsDxoOGgQhIR6Zi1zoSH5Z\nDT9/awfDo4M5zTtcIrP6GCLu/ZSLLhrJRRc5ziaoTp2yfsBeNAgYE2ACA41kUb6+hth7eRnCrbUR\nidLQYLhoamuNB4afn9EuIEAE3sOpbWjirle30dBo5t83TeHVZ1622i41dTHZ2R3HTC68cASffnqD\nlTMEVyHi7umEhbHLVE5G+7xRQYFwwQWGONfVGZ/tl7o6qC+GyjzC8zX3VfkZvnZHCaN8fY0By/Bw\nY7DT2fWICMOH7sEhg56A1prff7iXPfnlvHBzOsOibdc03bLlDpqaWjoShYUVTJmyhGuuGdsbpg5o\nRNw9nblz0S99QMaVLbuavLwwXXo+auJ4py+TkZEFGcuMjfp6I4Ll5Ekj3LCsrGXd1r4jR1rW7U2Z\nB+OtwZkHgbXjISHiu+9hXtuYzXvb8vj5vBGcOzbWbtvo6KA22y+9tJ3QUD+uuWZcT5ooIOLu+Uyc\nCNFrIdwQ5NrAYFYlTiA+PJkuV1/19TVyeEdHO27bHq2Nnr+tB4G19dxco/hEWZn9sEgwhD0szLkH\ngbX1buZV8XQ2HD7BH1bsZ+7oGO6bN8LxCa3QWvPSSzu48caJBATI21lPI+I+EAgNhfuMwVM/rWnY\nXcg3B48TEeTL4EFBDk52MUq15BhPTOz8+U1NRv4WZ94YLOvffdeyXlNj//p+fl17Y7C4lDx4glPO\niWp++vo2UqOCWHzd5E6nlv7yyyMcPVrGHXec1kMWCq3x3L9EwSpKKeaPi+Odrbl8uqeQ66amEBnU\nf3KX4OXVUp6uK9TVtQi/PTeSZV9JCWRmtuy3l+ALjCRfXXljiIgwzu2jA9EVtQ3ctnwLAC/enE6o\nf+d73i+8sJ2pUxOYNKkTlaSELiPiPgDx9TZx8aQE3tqcw4pdBVw7NXngZJD08zMmSMXa9xVbxVLk\nwtk3hrIyY17Bzp3Guq3IJQsmk/MPAmvH/V2caqK5BqrOyaEuMpbxM2/k6qceIDWq8297xcVVfPTR\n9zzzzIWutVGwiYh7H8cVU7F9fTv+Mwb7evHdJ4d59bXd3FFaS2JCCAsWTCAjYzbe3Zw+7rEoZfSu\ng4MhKanz5zc2triUHD0ULJ8FBS3rtopdW/D379obQ3g4hIWx+J9/oKysuVLS4cOwYQPQBCkARYTs\nfYovMjbyxbBhHW69c+daMjJ2Eh4exn33zelwfNmynfj5eXP99RM6/3MTuoSIex/HFVOxMzJu7bDv\nL39Zxysv7WDR4vMoNGlMJ+t5+pFv8PPz4uGHz+72PQUrWCaGRUZ27fzaWucGoC3rxcVGvVPLPnvp\niIGy4d5k3N08t8H7BAxr74IyQ/geuG9eh3NXr97J7NnhZGR0TNamtebFF7dz3XXjCA7uRy7Afo6I\n+wBl/fpcLr54FD+9OY3NR0+w/vAJZswZzKZN+Y5PFtyDvz/ExRlRSqdOGZFDlk/L0nq79brlLSA3\n15h8Zo2GRig/ZSy2cBStZIXVq7M4dKiU1167otPnCl1HxH2AcuaZKTz77Ba+/76EqaMGsXtPMRvW\n5nLPfdMcnyx0ndpa+yLsjGDby+1jwcfHiN4JDTU+w8KMCk4zZ7Zstz++4p9wdyr4+dH04kt4WUv0\nFhbWcZ8D5swZgtaPdvo8oXuIuA9QHnhgJhUVdYwd+wxeXiYaG81cddtkok+P43BxJcNibM86HJCY\nzYaodkeUy8vtF6a2EBjYUYCTkqwLsq1tf//OR95sehtiYjhRWceOpInMPrgR79bRQT7eMHeu7fOF\nPoWI+wDl7bf38coru3njjSsZNy6anTuL+MUvPiMiLgiTSXFFWhLvLt9IWZnxGr5zZ6VV3313CQ9P\n6fkUrw0N3RflU6cc5+MxmVqE1vIZHw+jRzsnyJZPN8bKn6pt4IMd+ej4oZwxfBDe335jfP+wMEPY\nJ050m21C5xBxH6D8+tdfcv/9M7juOiMFwYQJsWRnl/PyyzuZeeFwPtqVT9HxUp5YNAiA1ath9uxU\nl9thNxJIa2PSUWdE2Nq2o4lLYIRIthfc4cOdE2TLEhTUZ+PUnaG2oYkPtudT32jm6vRkAkOGwpQ0\nKirqePjhVXxw8dcUF68gLS2Op5+ez9SpXZiEJvQaIu4DlOrqBry82oY8enkptNZcnpbIO1tzKc07\nhnnDQUx19bDfByKHOt9zM5tbMkbW1RmLtfWNx430w7YE21EeGjBCE1sLbmQkDBnivAsjLMwQ9wFM\neU0Daw+VkFgbyeVpiUSHtPw8br99Bbt3H2P58stISgrltdd2c845r7J//90kJkoO976KiPsA5eKL\nR/LEE2sZMiScceNi2LGjkKee2sjNN08kNMCH6wLKyTl1HFNd8wn1DfDRR0b8c2SkfcGuq4M6J3zL\nJgVHfeBAXYvYJifDuHHO95hDQqRcXjepqmvkJ8u2UF7bwI8mJpAUEfjDsZqaBv7zn/385z/X/PDm\nlpExmxUrDvLcc1v505/EB99XEXEfoPzznxfw8MOruPvulRQXVxEfH8wdd5zGI48YMe7Ba7/B1N7F\n3GSGXbudv0lQoCHEtpbgYGgqgD8sd90XE35g8eJHWiYl2aDJbGZd5gmOV9QR15jJ8n+VtDne0NBE\nUpLmk082s2PH9z/s9/Iq56uvthMVpbjvvjn4+4exenVZ89hMVpdtltqnrsMpcVdKzQeexiiQ/aLW\n+ol2x38F3A40AseBn2its11sq+BCQkL8WLx4PosXz7fewF4886yzWnLAW3rq1tarqo2lsMj2tZYD\nf/+PIfYhIS1LV7clF/wPlJXlkJGRavN4Y5OZj3cVMKg0jPPHxXHsQAmzZ4d3aDd0aAhKneCqq2IJ\nDvZl795ilKomMjKAEyeMv5Pp041ZqatXZ5FhSQ0tuBWH4q6U8gKeAc4F8oAtSqmPtdb7WzXbAaRr\nrauVUj8FngSu7QmDhV4iLAzoKPCrSwJ5avExtm0rpKCggpdfvpRbb21JHqy15g9/+IYlS7Zx8mQt\n09LjeOYvsxg3NKSj+NfXw85jMGyeUTy7osLws1dUQE5O221HU+8t+PlZF/+uPDA8uKKURdhzSqs5\nd2wsY+JDOXbAetvLLx/DRx8d4KmnNmIyQXx8MBMmxFBQYKfgueB2nOm5nw5kaq2PACil3gIuBX4Q\nd631qlbtNwJ2inMK/YK5c+GbD9rsavDyYlNoKiNHh3PzzZO4+eYPOpz25JPr+PvfN7Bs2aWMGhXF\nY499w7lXfcyBA/cSEmdl0HJyFmT83bE9DQ0tD4D2DwJH28ePG8VCLNvOTAICw5fvireJkBDDBeXO\nIiK7d8PXX0N5OTo0lO3D0sgJTOC8sXGMdVDYOjIygB//eDL19U3U1TUSEuLHu+/uJyIigJISu6cK\nbsQZcU8Ecltt5wH2pjHeBvzX2gGl1EJgIUBKivjW+jQTJ0LyVvAvhto68PWh8rzzCakOI9rHi3NO\nS+yQz1trzeLFm3jwwZlceaVRRm358suIifkbb7yxhzvvTO+6PT4+3cvL0hqz2cju6OzDof12QUHb\nY47SAFsIDnbdw6Iz7qfdu2HFCiO9AKDKT5G2cy0Js88lKcFxHV4Lvr5e+Pp6UVPTwOHDpZx77lAO\nHXLeDKF3cemAqlLqRiAdsJp5Smu9BFgCkJ6e7mBGiOB2IiNh+tDmjTIipk3hylO1fLAjn3e35nVo\nfvRoGUVFlZx3XkvWwIAAH2bNGsz69XndE3dXYjK1iGR30dpwGXX1QZGd3Xa7rs7xPaElLt+e6+nw\nDlhfAN9++4OwW/AxN5G0fQPMcpxuIjOzFK01UVGBlJbW8OWXR4iKCmTy5DhWrHCQxlhwG86Iez6Q\n3Go7qXlfG5RS5wAPAWdrrZ38CxX6G7Gh/lw9JYn3t+fT2KQpr2lJQlVUZLg7YmPbpi6IjQ0iP99D\n/bNKGb75gICu5YgHI5a/qspwF508CYWFxttBYWHLUlAARUXGenW18RA4ftxYbDEY+KLtrjXZ8Lf1\nsK0QCirKeTl8Z5sxk/ffP87zzxeyfXslJSUNrFo1iejoRr766iinTtUREODN2LHRzJ07pMM8CaFv\n4Yy4bwFGKKWGYIj6dcANrRsopdKA54H5Wutil1sp9CkGBftxdXoSP1OwNauUrJKqLhVw6HdYeumV\nlS1i3JWl/bnODhaDkZrAUrXJsgQFtd22LPtXwoWxmFetwlRj3KOyHsbHwM2T4OYPO16+qsrMGWeE\ncuONsdx8sxH6OG5cDOPGxbjiJyj0Ig7FXWvdqJS6F/gcIxRyqdZ6n1LqMWCr1vpj4K9AMPCuMqIL\ncrTWl/Sg3UIn6GrBj507K1m92lj392+bDTA80BdvkyLQ14uPdxVwhU8pcV+sA+DY4hdIufW8H2az\nHjtWRVxcLycia2pyLMBdEWgHOdHbEBjYUXDDwozasc6Is7XFtxP50DNyKRgZy/6jpzj74EZ8mpq4\ncARcOALw8ebWTzp6Rm+6yXj7KCmxkRZY6Dc45XPXWq8EVrbb90ir9XNcbJfgQrqamCsj41aH+WTS\nUyOZVJVP7M61eHs1ERcMX+6qYuqKFQDUjhzLt99m89e/nmv9AlobLgZX9YItizP5ZCxYomLai2x8\nvPOi2/7cwEC3z5zNO1nNf7bnEZI8nIZhg/BZ2y4J2OOfuNU+oWeRGapCp6isrCczsxQAs1lTmF9B\n+ndbKWxqIiUM7psGf14Lo6MaGVm8gj9tX0Wwt5kbvL+HZXuN2PbWyyt18NgrzhsQEGBdXOPiOtcD\nbt8b9qB4dq01z6zKZOORE5wbMphLJiUS4JsK6WntWoq4ezIi7kKn2Lq1gDlzWtIFPProah4FbpkE\nyy6D38yEmka4ZyWcrGlkWlIZX1wHIbmHrV/QWsyUyWRUG4qJaSlmHRtr7AsNNUQ8KMjoHVtbDwrq\nWj5zD6C2oYnfvr+HD3bkMzYykCtPS8JbBj4HJCLuQqeYPTu1Y1WdxYuhOe+7UpAx21iaggLxuvpq\nYwJSfb3x2Xq9vh42lsLs6YZ7parKiASxrJeXG9EhVVWdc7NYDLEl/u0fBPa2bR3z8+sbD4/XX4eH\nHoKcHBoTk3hm7q18ED+N+88byfFvIkXYBzAi7kL3mTu3zSQZMGazfp00mQSfCCak2inNtj4LnMlF\nYjYbwt9a/Ns/DJzdtjwwWh93Nr7cgsnU9QeDM219fBw/PF5/HRYuNL4D4J2Xy91vPsk5f3yKSXMv\nImNNH3j4CG5DxF3oPpYc783T2wkLQ589myodxf++O0ZhWQ1zRsfg051epMnU4iPvCRobO//wsHWs\ntLTjcVtFqW3h5eX4QbBixQ/CbiGgoY5Jzz0JD9xt9bLtx0xycsrZubOIyMgA/P3D+PjjEoqLG6is\nNGbdfvrpCTIza4iM9CYysuOs2PZZICWrY99BxF1wDRMntink4QtcpjUbD59gc1YpRadquXBCPFHB\nfbQohrd3SyrinqChwTVvHVVVUFwMVVXoykqs9s1zbKf5tTpm8uhqbrllEsuWXcayZTu5446Pfjj+\nt7/lNbc7m4yM2R2uJ1kg+y4i7kKPYVKKM4ZHkRQRyGf7inhzcw6zRkYzMTEM1Rf81b2Jj09LgREX\nsObgcUacPp74citzBu3kbbI6ZtKKW2+d3GbGqtB/kdEWocdJGRTIgmkpJEUEsur7Yj7cWUBlrRPl\n84QOVNc38vsP93Dz0s28fNEdmAMC2jYIDIRFi9xjnNCnkJ67YJOuzmy1hdaaI8freTnvOI+Zspic\nHM7EoaNddn1PZ0tWKfe/u4uc0mpuP3MIvzp/PqYLx/wQLUNKiiHsCxa421ShDyDiLtikqzNbHXG0\npIr7393FquyTNIVFk3OimpRBgY5PHKCUVzfwxGff8+bmHJIiAnjzjulMHzrIOLhggYi5YBVxywi9\nzpCoIN65cwYZF49lW1Yp5y3+hudWH6a+sRN5WwYAWms+3lXAvKe+4e0tOdxx1hC++OWsFmEXBDtI\nz11wC14mxa0zh3DeuDge/Xgff/nse97ZmstDF45h3piYgTfg2o49eeU89sk+tmSdZEJiGMt+PJXx\nia4ZjBUGBiLugltJCA/ghZvTWXWgmD9+sp/bX9nKWSOieGD+6AEpZvllNSz+8iDvbc8jMtCXx6+Y\nwDXpyXiZOv+wc/WYia17CH0TpbV7CiKlp6frrVu3uuXeQt+kocnMKxuy+cf/DlFe08BFE+L51Xkj\nGRbdy+mC3UBJZR3PrjrMaxuzAbh5xmB+fs4IQv07UU5PGBAopbZprR2WNRNxF/ocp2obeHHNEV5c\ne5TahiYumpjAXWcPZVyC5/XkC8pqeOHbI7y1OZe6xiaumpLEL84ZSWJ4gOOThQGJiLvQ7ymprOOF\nb4/w+sYcKusamT0qmp/MHMKZw6M6FOfub+zNL2fZ+iw+2pmPWcOlkxO4e/Zwhsd4/luK0D1E3AWP\noby6gVc3ZrFsfRYllfUMiQrixumDuSItkYigTlQmcjM19U18vq+IVzZksT2njAAfL65JT+KOWUNJ\nipBQUME5RNwFj6OusYn/7ili+YYsduSU4eOlmDMqhitOS2T2qBj8fdxb+cgaTWbN5qOlfLAjj5V7\niqisayR1UCA3zUjlqilJhAWIT13oHM6Ku1PRMkqp+cDTGDVUX9RaP9HuuB/wCjAFOAFcq7XO6qzR\ngmAPP28vLktL5LK0RPYXnOL97Xl8uLOAL/YfI9DXi9mjojlvbByzRkYT6cYefXV9IxuPnODzvcf4\n6vO6yUYAAAYfSURBVLtjnKiqJ8jXiwsmxHNFWiLThw7q924loe/jsOeulPICDgLnAnnAFuB6rfX+\nVm3uBiZqre9SSl0HXK61vtbedaXnLriCxiYz6w+f4PN9RXyx/xjHK4y87GPjQzlzRBTpgyOYlBxO\nbKh/j9lQXt3A7vwytmeXse5wCTtyTtLQpAn282bO6BjOGxvLvDExBPpK5LHQfVzmllFKzQAytNbn\nN2//FkBr/XirNp83t9mglPIGioBobefiIu6CqzGbNbvyyliXWcK6zBNsyz5JfZMx6zUu1J/R8SEM\njw5mWEwwyRGBxIX5ERvqT4gT4Ya1DU0cO1VLUXkt+WU1HD5eyeHiKg4cq+BoSRVg1NYYnxDGGcMH\nMXNYFNOGRuLn3fdcRUL/xpVumUQgt9V2HjDNVhutdaNSqhwYBJQ4Z64gdB+TSZGWEkFaSgT3zh1B\nbUMT+wtPsTOnjF15ZRw8VsmGwyeoa5fmwNfLRLC/N0F+Xvh5e/2QI72hyUxlXROVdQ3UNrQ9x9uk\nGDwokJGxwVw1JYnJyeFMSAqTuHShz9Cr74lKqYXAQoAUOzmnBcEV+Pt4cVpKBKelRPywz2zW5JfV\nkF9W80NP/GR1A5V1DVTVNVHX2PRDW2+TiSA/b0L8vQn19yY21J+4MH/iwwIYPCiwe5WlBKGHcUbc\n84HkVttJzfustclrdsuEYQystkFrvQRYAoZbpisGC0J3MJkUyZGBJEdK6KHg2TjT9dgCjFBKDVFK\n+QLXAR+3a/MxcEvz+lXA1/b87YIgCELP4rDn3uxDvxf4HCMUcqnWep9S6jFgq9b6Y+Al4FWlVCZQ\nivEAEARBENyEUz53rfVKYGW7fY+0Wq8FrnataYIgCEJXkREhQRAED0TEXRAEwQMRcRcEQfBARNwF\nQRA8EBF3QRAED8RtKX+VUseBbLfc3HmiGLgpFAbyd4eB/f3lu/dtBmutox01cpu49weUUludSdDj\niQzk7w4D+/vLd/eM7y5uGUEQBA9ExF0QBMEDEXG3zxJ3G+BGBvJ3h4H9/eW7ewDicxcEQfBApOcu\nCILggYi4t0IpdbVSap9SyqyUsjlirpSar5Q6oJTKVEo92Js29hRKqUil1JdKqUPNnxE22jUppXY2\nL+1TP/crHP0elVJ+Sqm3m49vUkql9r6VPYcT3/9WpdTxVr/v291hZ0+glFqqlCpWSu21cVwppf7R\n/LPZrZQ6rbdt7C4i7m3ZC1wBrLHVoLlg+DPABcBY4Hql1NjeMa9HeRD4n9Z6BPC/5m1r1GitJzcv\nl/Seea7Fyd/jbcBJrfVw4P+Av/SulT1HJ/6O3271+36xV43sWZYB8+0cvwAY0bwsBJ7rBZtcioh7\nK7TW32mtDzhodjqQqbU+orWuB94CLu1563qcS4HlzevLgcvcaEtv4MzvsfXP5D1gnlJK4Rl46t+x\nU2it12DUnrDFpcAr2mAjEK6Uiu8d61yDiHvnsVYwPNFNtriSWK11YfN6ERBro52/UmqrUmqjUqo/\nPwCc+T22KfwOWAq/ewLO/h1f2eyWeE8plWzluKfS7//Pe7VAdl9AKfUVEGfl0ENa6496257exN53\nb72htdZKKVthVIO11vlKqaHA10qpPVrrw662VegTrADe1FrXKaXuxHiLmetmmwQnGXDirrU+p5uX\ncKZgeJ/E3ndXSh1TSsVrrQubXz+LbVwjv/nziFJqNZAG9Edxd1nh936Kw++vtW79XV8EnuwFu/oK\n/fb/3IK4ZTqPMwXD+yOti5zfAnR4i1FKRSil/JrXo4CZwP5es9C1DPTC7w6/fzsf8yXAd71on7v5\nGLi5OWpmOlDeym3ZP9Bay9K8AJdj+NbqgGPA5837E4CVrdpdCBzE6LE+5G67XfTdB2FEyRwCvgIi\nm/enAy82r58B7AF2NX/e5m67u/mdO/wegceAS5rX/YF3gUxgMzDU3Tb38vd/HNjX/PteBYx2t80u\n/O5vAoVAQ/P//G3AXcBdzccVRjTR4ea/9XR329zZRWaoCoIgeCDilhEEQfBARNwFQRA8EBF3QRAE\nD0TEXRAEwQMRcRcEQfBARNwFQRA8EBF3QRAED0TEXRAEwQP5/7BjpZmPKc/ZAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "alpha = 0.95\n", "xs = gd(1, grad, alpha)\n", "xp = np.linspace(-1.2, 1.2, 100)\n", "plt.plot(xp, f(xp))\n", "plt.plot(xs, f(xs), 'o-', c='red')\n", "for i, (x, y) in enumerate(zip(xs, f(xs)), 1):\n", " plt.text(x*1.2, y, i,\n", " bbox=dict(facecolor='yellow', alpha=0.5), fontsize=14)\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Gradient descent with momentum\n", "\n", "Momentum results in cancellation of gradient changes in opposite directions, and hence damps out oscillations while amplifying consistent changes in the same direction. This is perhaps clearer in the 2D example below." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n7kII4YKkuAshhAv6f3MS+I+bWdT4AAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "alpha = 0.95\n", "xs = gd_momentum(1, grad, alpha, beta=0.9)\n", "xp = np.linspace(-1.2, 1.2, 100)\n", "plt.plot(xp, f(xp))\n", "plt.plot(xs, f(xs), 'o-', c='red')\n", "for i, (x, y) in enumerate(zip(xs, f(xs)), 1):\n", " plt.text(x, y+0.2, i, \n", " bbox=dict(facecolor='yellow', alpha=0.5), fontsize=14)\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Momentum and RMSprop in 2D" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def f2(x):\n", " return x[0]**2 + 100*x[1]**2" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def grad2(x):\n", " return np.array([2*x[0], 200*x[1]])" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAD8CAYAAACfF6SlAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nDEKUv0AgEMwg/n9MwCO8MPvyrwAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-1.2, 1.2, 100)\n", "y = np.linspace(-1.2, 1.2, 100)\n", "X, Y = np.meshgrid(x, y)\n", "levels = [0.1,1,2,4,9, 16, 25, 36, 49, 64, 81, 100]\n", "Z = x**2 + 100*Y**2\n", "c = plt.contour(X, Y, Z, levels)\n", "pass" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def gd2(x, grad, alpha, max_iter=10):\n", " xs = np.zeros((1 + max_iter, x.shape[0]))\n", " xs[0,:] = x\n", " for i in range(max_iter):\n", " x = x - alpha * grad(x)\n", " xs[i+1,:] = x\n", " return xs" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def gd2_momentum(x, grad, alpha, beta=0.9, max_iter=10):\n", " xs = np.zeros((1 + max_iter, x.shape[0]))\n", " xs[0, :] = x\n", " v = 0\n", " for i in range(max_iter):\n", " v = beta*v + (1-beta)*grad(x)\n", " vc = v/(1+beta**(i+1))\n", " x = x - alpha * vc\n", " xs[i+1, :] = x\n", " return xs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Gradient descent with large step size\n", "\n", "We get severe oscillations." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true }, "outputs": [], "source": [ "alpha = 0.01\n", "x0 = np.array([-1,-1])\n", "xs = gd2(x0, grad2, alpha, max_iter=75)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAEICAYAAAC3Y/QeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-1.2, 1.2, 100)\n", "y = np.linspace(-1.2, 1.2, 100)\n", "X, Y = np.meshgrid(x, y)\n", "levels = [0.1,1,2,4,9, 16, 25, 36, 49, 64, 81, 100]\n", "Z = x**2 + 100*Y**2\n", "c = plt.contour(X, Y, Z, levels)\n", "plt.plot(xs[:, 0], xs[:, 1], 'o-', c='red')\n", "plt.title('Vanilla gradient descent')\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Gradient descent with momentum\n", "\n", "The damping effect is clear." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": true }, "outputs": [], "source": [ "alpha = 0.01\n", "x0 = np.array([-1,-1])\n", "xs = gd2_momentum(x0, grad2, alpha, beta=0.9, max_iter=75)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAEICAYAAAC3Y/QeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nOihuAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-1.2, 1.2, 100)\n", "y = np.linspace(-1.2, 1.2, 100)\n", "X, Y = np.meshgrid(x, y)\n", "levels = [0.1,1,2,4,9, 16, 25, 36, 49, 64, 81, 100]\n", "Z = x**2 + 100*Y**2\n", "c = plt.contour(X, Y, Z, levels)\n", "plt.plot(xs[:, 0], xs[:, 1], 'o-', c='red')\n", "plt.title('Gradieent descent with momentum')\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Gradient descent with RMSprop\n", "\n", "RMSprop scales the learning rate in each direction by the square root of the exponentially weighted sum of squared gradients. Near a saddle or any plateau, there are directions where the gradient is very small - RMSporp encourages larger steps in those directions, allowing faster escape." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def gd2_rmsprop(x, grad, alpha, beta=0.9, eps=1e-8, max_iter=10):\n", " xs = np.zeros((1 + max_iter, x.shape[0]))\n", " xs[0, :] = x\n", " v = 0\n", " for i in range(max_iter):\n", " v = beta*v + (1-beta)*grad(x)**2\n", " x = x - alpha * grad(x) / (eps + np.sqrt(v))\n", " xs[i+1, :] = x\n", " return xs" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": true }, "outputs": [], "source": [ "alpha = 0.1\n", "x0 = np.array([-1,-1])\n", "xs = gd2_rmsprop(x0, grad2, alpha, beta=0.9, max_iter=10)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAEICAYAAAC3Y/QeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-1.2, 1.2, 100)\n", "y = np.linspace(-1.2, 1.2, 100)\n", "X, Y = np.meshgrid(x, y)\n", "levels = [0.1,1,2,4,9, 16, 25, 36, 49, 64, 81, 100]\n", "Z = x**2 + 100*Y**2\n", "c = plt.contour(X, Y, Z, levels)\n", "plt.plot(xs[:, 0], xs[:, 1], 'o-', c='red')\n", "plt.title('Gradient descent with RMSprop')\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### ADAM\n", "\n", "ADAM (Adaptive Moment Estimation) combines the ideas of momentum, RMSprop and bias correction. It is probably the most popular gradient descent method in current deep learning practice." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def gd2_adam(x, grad, alpha, beta1=0.9, beta2=0.999, eps=1e-8, max_iter=10):\n", " xs = np.zeros((1 + max_iter, x.shape[0]))\n", " xs[0, :] = x\n", " m = 0\n", " v = 0\n", " for i in range(max_iter):\n", " m = beta1*m + (1-beta1)*grad(x)\n", " v = beta2*v + (1-beta2)*grad(x)**2\n", " mc = m/(1+beta1**(i+1))\n", " vc = v/(1+beta2**(i+1))\n", " x = x - alpha * m / (eps + np.sqrt(vc))\n", " xs[i+1, :] = x\n", " return xs" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": true }, "outputs": [], "source": [ "alpha = 0.1\n", "x0 = np.array([-1,-1])\n", "xs = gd2_adam(x0, grad2, alpha, beta1=0.9, beta2=0.9, max_iter=10)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAEICAYAAAC3Y/QeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nv5lZhdz8zcwq9CcxsgHWtrWEuAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-1.2, 1.2, 100)\n", "y = np.linspace(-1.2, 1.2, 100)\n", "X, Y = np.meshgrid(x, y)\n", "levels = [0.1,1,2,4,9, 16, 25, 36, 49, 64, 81, 100]\n", "Z = x**2 + 100*Y**2\n", "c = plt.contour(X, Y, Z, levels)\n", "plt.plot(xs[:, 0], xs[:, 1], 'o-', c='red')\n", "plt.title('Gradient descent with RMSprop')\n", "pass" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Implementing a custom optimization routine for `scipy.optimize`\n", "\n", "Gradient descent is not one of the methods available in `scipy.optimize`. However we can implement our own version by following the API of the `minimize` function." ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import scipy.optimize as opt\n", "import scipy.linalg as la" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def custmin(fun, x0, args=(), maxfev=None, alpha=0.0002,\n", " maxiter=100000, tol=1e-10, callback=None, **options):\n", " \"\"\"Implements simple gradient descent for the Rosen function.\"\"\"\n", " bestx = x0\n", " bestf = fun(x0)\n", " funcalls = 1\n", " niter = 0\n", " improved = True\n", " stop = False\n", "\n", " while improved and not stop and niter < maxiter:\n", " niter += 1\n", " # the next 2 lines are gradient descent\n", " step = alpha * rosen_der(bestx)\n", " bestx = bestx - step\n", "\n", " bestf = fun(bestx)\n", " funcalls += 1\n", " \n", " if la.norm(step) < tol:\n", " improved = False\n", " if callback is not None:\n", " callback(bestx)\n", " if maxfev is not None and funcalls >= maxfev:\n", " stop = True\n", " break\n", "\n", " return opt.OptimizeResult(fun=bestf, x=bestx, nit=niter,\n", " nfev=funcalls, success=(niter > 1))" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def reporter(p):\n", " \"\"\"Reporter function to capture intermediate states of optimization.\"\"\"\n", " global ps\n", " ps.append(p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Test on Rosenbrock banana function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will use the [Rosenbrock \"banana\" function](http://en.wikipedia.org/wiki/Rosenbrock_function) to illustrate unconstrained multivariate optimization. In 2D, this is\n", "$$\n", "f(x, y) = b(y - x^2)^2 + (a - x)^2\n", "$$\n", "\n", "The function has a global minimum at (1,1) and the standard expression takes $a = 1$ and $b = 100$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Conditioning of optimization problem\n", "\n", "With these values for $a$ and $b$, the problem is ill-conditioned. As we shall see, one of the factors affecting the ease of optimization is the condition number of the curvature (Hessian). When the condition number is high, the gradient may not point in the direction of the minimum, and simple gradient descent methods may be inefficient since they may be forced to take many sharp turns." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the 2D version, we have\n", "\n", "$$\n", "f(x) = 100(y - x^2)^2 + (1 - x)^2\n", "$$\n", "\n", "and can calculate the Hessian to be \n", "\n", "$$\n", "\\begin{bmatrix}\n", "802 & -400 \\\\\n", "-400 & 200\n", "\\end{bmatrix}\n", "$$" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": true }, "outputs": [], "source": [ "H = np.array([\n", " [802, -400],\n", " [-400, 200]\n", "])" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2508.009601277298" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.linalg.cond(H)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2508.0096012772983" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "U, s, Vt = np.linalg.svd(H)\n", "s[0]/s[1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Function to minimize" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def rosen(x):\n", " \"\"\"Generalized n-dimensional version of the Rosenbrock function\"\"\"\n", " return sum(100*(x[1:]-x[:-1]**2.0)**2.0 +(1-x[:-1])**2.0)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def rosen_der(x):\n", " \"\"\"Derivative of generalized Rosen function.\"\"\"\n", " xm = x[1:-1]\n", " xm_m1 = x[:-2]\n", " xm_p1 = x[2:]\n", " der = np.zeros_like(x)\n", " der[1:-1] = 200*(xm-xm_m1**2) - 400*(xm_p1 - xm**2)*xm - 2*(1-xm)\n", " der[0] = -400*x[0]*(x[1]-x[0]**2) - 2*(1-x[0])\n", " der[-1] = 200*(x[-1]-x[-2]**2)\n", " return der" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Why is the condition number so large?" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": true }, "outputs": [], "source": [ "x = np.linspace(-5, 5, 100)\n", "y = np.linspace(-5, 5, 100)\n", "X, Y = np.meshgrid(x, y)\n", "Z = rosen(np.vstack([X.ravel(), Y.ravel()])).reshape((100,100))" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAD8CAYAAABjAo9vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Note: the global minimum is at (1,1) in a tiny contour island\n", "plt.contour(X, Y, Z, np.arange(10)**5, cmap='jet')\n", "plt.text(1, 1, 'x', va='center', ha='center', color='red', fontsize=20)\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Zooming in to the global minimum at (1,1)" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": true }, "outputs": [], "source": [ "x = np.linspace(0, 2, 100)\n", "y = np.linspace(0, 2, 100)\n", "X, Y = np.meshgrid(x, y)\n", "Z = rosen(np.vstack([X.ravel(), Y.ravel()])).reshape((100,100))" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAD8CAYAAACYebj1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.contour(X, Y, Z, [rosen(np.array([k, k])) for k in np.linspace(1, 1.5, 10)], cmap='jet')\n", "plt.text(1, 1, 'x', va='center', ha='center', color='red', fontsize=20)\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### We will use our custom gradient descent to minimize the banana function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Helpful Hint \n", "\n", "One of the most common causes of failure of optimization is because the gradient or Hessian function is specified incorrectly. You can check for this using `check_grad` which compares the analytical gradient with one calculated using finite differences." ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1.52226677 0.65004796] 1.489680875137234e-05\n", "[ 0.52565945 -0.97450204] 5.561538106652017e-06\n", "[-1.90395551 -1.40865775] 4.959629801043568e-06\n", "[1.56241883 0.02916979] 1.1141498255202488e-05\n", "[1.41686433 0.97694193] 1.2788749325180071e-05\n", "[ 1.67198246 -1.43445961] 4.925842873021741e-05\n", "[1.50075383 1.26752343] 1.646225036670931e-05\n", "[ 0.12793507 -0.8359048 ] 3.0161708019548927e-06\n", "[0.35530784 0.59406072] 1.7619515805981918e-06\n", "[-0.01477088 -1.9624893 ] 6.263297131400611e-06\n" ] } ], "source": [ "from scipy.optimize import check_grad\n", "\n", "for x in np.random.uniform(-2,2,(10,2)):\n", " print(x, check_grad(rosen, rosen_der, x))" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/plain": [ " fun: 1.060466347344834e-08\n", " nfev: 100001\n", " nit: 100000\n", " success: True\n", " x: array([0.9998971 , 0.99979381])" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Initial starting position\n", "x0 = np.array([4,-4.1])\n", "ps = [x0]\n", "opt.minimize(rosen, x0, method=custmin, callback=reporter)" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": true }, "outputs": [], "source": [ "x = np.linspace(-5, 5, 100)\n", "y = np.linspace(-5, 5, 100)\n", "X, Y = np.meshgrid(x, y)\n", "Z = rosen(np.vstack([X.ravel(), Y.ravel()])).reshape((100,100))" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAsYAAAD8CAYAAAB0FmJXAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nnWB1YCTNnwcAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ps = np.array(ps)\n", "plt.figure(figsize=(12,4))\n", "plt.subplot(121)\n", "plt.contour(X, Y, Z, np.arange(10)**5, cmap='jet')\n", "plt.plot(ps[:, 0], ps[:, 1], '-ro')\n", "plt.subplot(122)\n", "plt.semilogy(range(len(ps)), rosen(ps.T))\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Comparison with standard algorithms\n", "\n", "Note that all these methods take far fewer function iterations and function evaluations to find the minimum compared with vanilla gradient descent.\n", "\n", "Many of these are based on estimating the Newton direction. Recall Newton's method for finding roots of a univariate function\n", "\n", "$$\n", "x_{K+1} = x_k - \\frac{f(x_k)}{f'(x_k)}\n", "$$\n", "\n", "When we are looking for a minimum, we are looking for the roots of the *derivative* $f'(x)$, so\n", "\n", "$$\n", "x_{K+1} = x_k - \\frac{f'(x_k}{f''(x_k)}\n", "$$\n", "\n", "Newton's method can also be seen as a Taylor series approximation\n", "\n", "$$\n", "f(x+h) = f(x) + h f'(x) + \\frac{h^2}{2}f''(x)\n", "$$\n", "\n", "At the function minimum, the derivative is 0, so\n", "\\begin{align}\n", "\\frac{f(x+h) - f(x)}{h} &= f'(x) + \\frac{h}{2}f''(x) \\\\\n", "0 &= f'(x) + \\frac{h}{2}f''(x) \n", "\\end{align}\n", "\n", "and letting $\\Delta x = \\frac{h}{2}$, we get that the Newton step is\n", "\n", "$$\n", "\\Delta x = - \\frac{f'(x)}{f''(x)}\n", "$$\n", "\n", "The multivariate analog replaces $f'$ with the Jacobian and $f''$ with the Hessian, so the Newton step is\n", "\n", "$$\n", "\\Delta x = -H^{-1}(x) \\nabla f(x)\n", "$$\n", "\n", "Slightly more rigorously, we can optimize the quadratic multivariate Taylor expansion \n", "\n", "$$\n", "f(x + p) = f(x) + p^T\\nabla f(x) + \\frac{1}{2}p^TH(x)p\n", "$$\n", "\n", "Differentiating with respect to the direction vector $p$ and setting to zero, we get\n", "\n", "$$\n", "H(x)p = -\\nabla f(x)\n", "$$\n", "\n", "giving\n", "\n", "$$\n", "p = -H(x)^{-1}\\nabla f(x)\n", "$$" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from scipy.optimize import rosen, rosen_der, rosen_hess" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Nelder-Mead\n", "\n", "There are some optimization algorithms not based on the Newton method, but on other heuristic search strategies that do not require any derivatives, only function evaluations. One well-known example is the Nelder-Mead simplex algorithm." ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/plain": [ " final_simplex: (array([[0.99998846, 0.99997494],\n", " [0.99994401, 0.99989075],\n", " [1.0000023 , 1.0000149 ]]), array([5.26275688e-10, 3.87529507e-09, 1.06085894e-08]))\n", " fun: 5.262756878429089e-10\n", " message: 'Optimization terminated successfully.'\n", " nfev: 162\n", " nit: 85\n", " status: 0\n", " success: True\n", " x: array([0.99998846, 0.99997494])" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ps = [x0]\n", "opt.minimize(rosen, x0, method='nelder-mead', callback=reporter)" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAsUAAAD8CAYAAACfIdlUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ps = np.array(ps)\n", "plt.figure(figsize=(12,4))\n", "plt.subplot(121)\n", "plt.contour(X, Y, Z, np.arange(10)**5, cmap='jet')\n", "plt.plot(ps[:, 0], ps[:, 1], '-ro')\n", "plt.subplot(122)\n", "plt.semilogy(range(len(ps)), rosen(ps.T));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### BFGS\n", "\n", "As calculating the Hessian is computationally expensive, sometimes first order methods that only use the first derivatives are preferred. Quasi-Newton methods use functions of the first derivatives to approximate the inverse Hessian. A well know example of the Quasi-Newoton class of algorithjms is BFGS, named after the initials of the creators. As usual, the first derivatives can either be provided via the `jac=` argument or approximated by finite difference methods." ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/plain": [ " fun: 1.3642782750354208e-13\n", " jac: array([ 1.21204353e-04, -6.08502470e-05])\n", " message: 'Optimization terminated successfully.'\n", " nfev: 38\n", " nhev: 26\n", " nit: 26\n", " njev: 63\n", " status: 0\n", " success: True\n", " x: array([0.99999963, 0.99999926])" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ps = [x0]\n", "opt.minimize(rosen, x0, method='Newton-CG', jac=rosen_der, hess=rosen_hess, callback=reporter)" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAsUAAAD8CAYAAACfIdlUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nDAaD4aLn/wFDgK7TUY6ycwAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ps = np.array(ps)\n", "plt.figure(figsize=(12,4))\n", "plt.subplot(121)\n", "plt.contour(X, Y, Z, np.arange(10)**5, cmap='jet')\n", "plt.plot(ps[:, 0], ps[:, 1], '-ro')\n", "plt.subplot(122)\n", "plt.semilogy(range(len(ps)), rosen(ps.T))\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Newton-CG\n", "\n", "Second order methods solve for $H^{-1}$ and so require calculation of the Hessian (either provided or approximated using finite differences). For efficiency reasons, the Hessian is not directly inverted, but solved for using a variety of methods such as conjugate gradient. An example of a second order method in the `optimize` package is `Newton-GC`." ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "text/plain": [ " fun: 1.3642782750354208e-13\n", " jac: array([ 1.21204353e-04, -6.08502470e-05])\n", " message: 'Optimization terminated successfully.'\n", " nfev: 38\n", " nhev: 26\n", " nit: 26\n", " njev: 63\n", " status: 0\n", " success: True\n", " x: array([0.99999963, 0.99999926])" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ps = [x0]\n", "opt.minimize(rosen, x0, method='Newton-CG', jac=rosen_der, hess=rosen_hess, callback=reporter)" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAsUAAAD8CAYAAACfIdlUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzsnXlYVeXah+/Fhs08CM6AKM4DKE6gghMqDjmVaWZlmdlk\n4ynznOaT1ddgp9HKIc0sTStzzFlQUUFUBHFABVERRZR5hr2+P5ZbxT3vTYn63tfV5TnrHda7da+9\nnvWs3/t7JFmWEQgEAoFAIBAI7mbsbvUCBAKBQCAQCASCW40IigUCgUAgEAgEdz0iKBYIBAKBQCAQ\n3PWIoFggEAgEAoFAcNcjgmKBQCAQCAQCwV2PCIoFAoFAIBAIBHc9IigWCAQCgUAgENz1iKBYIBAI\nBAKBQHDXI4JigUAgEAgEAsFdj/2tOGn9+vXl5s2b1zhWyhUkJJyoZ/W8+ZWQUwaB7iBZMf7KFSgo\ngJuWZpLCwiouXqygZUsXJDNOXFBQQXZ2KS1behrsX10tc+ZMPvXqOeHl5VSjrbJSw9mz+TRo4Iq7\nu/ra8dzcMi5fLqFVK2+9cyrjCqhf3xkPD0ezP5+W0tIqMjIKadHCA0dHlcXjBaDRyKSm5tG0qSse\nHmrTA26iuLiSrKwi/P31/xsUFpaTnV1Cs2aeODjUfOYtKCgnJ6cEf3/dtlOncvH2dqZevZrftRvJ\nyipGowFfX1ez1pqZWY5KJdG4sWWfMzsbKirAz8+iYdfPWwIqCRo7WzceoJISKijEhQZIN+UO9u/f\nnyPLcgPrZ7/90PebLRAIBLcLZv9uy7L8j//XrVs3+WZi5LfkzfJLOsctYeEJWeZHWU7Nt278rA9k\nGXtZzrdw/MqVF2XYLO/enWtW/+XLU2X4Ut6zJ8tgn+pqjdyw4f/kBx9cqdNWVFQuOzj8V37llY01\njv/wwwEZ3pH37z+vd87y8irZ23u23jnNISurSHZxmSNPnLjBqvECWX7vvXiT//bGmD59g+zk9H9y\nXl6p3vYHHvhNrlfv/+TS0kqdtkcf/VP28PhQLiur2ZaUdFGGWfK8eQeMnrtlyx/lUaPWmLVOjUYj\nN2wYI0+efNis/jfSd4As9wq3eNg1An+X5Qkx1o+XZVlOkhfLK+QxcrVcpdMGJMi34HfzVv6n7zdb\nIBAIbhfM/d2uM/IJd5pSSCYystVzdPBS/kzJs25852Dlz+Rky8aFhXkCsGdPvln9+/dXUmDbtp01\n2MfOTmLo0EA2bEijulpTo83VVU2vXv5s3366xvGRI9uiUkksXar/A6jVKsaPb8/KlccpKCg3a603\n0rixKy++2IWlS1M5ePCSxePvdnJySvnkkwOMHt2CsLDGFo8vL69i6dIURo1qjaenbkb3woUiVq48\nyqRJQTg51XwJVFWlYdWqY4we3RZHx5pt69adBGD48FYGz33mTCGnTuUzcKB56dvTp8vIzq4gNNTT\nrP5aZBmSkq9fi5ZSUgXpRdDestPqUEQmrjTEDvFGRCAQCO4W6kxQ7IYvVZRSjpURLdDOQ/nzqHmx\nqQ7aG3GShUFx48aONGvmRFxcgVn9GzRwplMnH2JizhvtN2RIIFeulHLw4AWdtoiIZiQmXqC4uOLa\nsfr1XRgzph0//JBIaWml3jkffTSY0tIqli8/YtZab2bGjK74+DgxY0YsysOXwFxmzdpHUVElH37Y\n26rxq1ef4PLlUh57rLPe9jlz9lFRUc3zz4fqtCUknCc3t4wRI1rrtG3cmEbnzg1p2tTd4LljYjIB\nGDDAvKB4717lIgwL8zCrv5azZyEvz/qg+Hg+yEAHG4PiQs7jjq9tkwgEAoHgtqLOBMXaG1AhmVbP\n4aEGPxc4YmVQ7OcHXl5wKMnysaGhHsTFmX/ifv2aEhubRWVltcE+gwY1B2DTpnSdtt69/amultm3\nr2Zg/dxzPblypZTFiw/pnbNnz6Z06FCf+fMTzV7rjXh6OvLmmz3YsuUsGzeesWqOu5GTJ/OYMyeZ\nqVM70L69fs23KebPT8Tf34PBg1vobV+zJpW+fQNo3dpHp23z5lNIEgwaFFjjeFFRBbGxZxkyJFBn\nzI1ER2fi7e1Ep066c+sjPj4fZ2c7OnVyM6u/Fu0DaVAni4ZdQ/tAbEumWEZDkQiKBQKB4K7jjgqK\nQbkZWpspliQlQ5WoP540SmioJxkZyitjc+jb15fi4kqjMoRGjdwICmrI9u0ZOm09eyp/X/HxNf++\n+vYNIDTUl9mz9+idU5IknngihLi48yQm6magzeHpp4MIDPTglVd2UVWlMT1AwGuv7UatVvHOO7pZ\nXHM4efIKmzalMXVqF1Qq3cs2K6uQxMQLDB2qXwIRE5NBcHAjfHxcahzfufMMlZUag4G2lh07MomI\naIKdnXlbWOPjC+ja1V1nQ58pDiYq12GwlZniI/nKJrs2liWoa1DKZaqpEEGxQCAQ3GXUmaDYhfrY\n4WBzUNzBC47lg8bKN/vduymZ4kr96gOD9Oyp3IXj482LyCMimgKwY4dxCcWAAQHExp6loqJmRrl+\nfReaN/di166a2VpJkpg0KYgTJ66Qnp6rd87JkxXN6Zw5+81a682o1So++aQPKSlXmDcvxao57iZi\nYjL5449TzJzZjSZNzHNuuJlvvz2Avb0dTzzRRW/7pk2nAPQGxZWV1ezZc46IiGY6bdu2ZaBWq+jT\nx9/guc+fL+LkyXz69jUvSKys1HDgQKHFemKA/QegTRtwN6zkMMrRfGjlDmobpMCFnAMUSZdAIBAI\n7h7qTFAsYYcbTSnEeJBoivaeUFwF54qtG9+tK5SVwdGjlo3r2tUDOzvYt888XXGTJq60auXJrl3G\nP2///s0oLa0iISFLp23ChI6sW3eCtLSawe/gwS2B64HSzdSr58yDD3bk559TyM8vM2u9NzN2bEv6\n9fPlzTf3kptr3Rx3A9XVGl54YQfNmrnz8sv6A1pTlJdXsWhREmPHtqVJE/3R4p9/HsfX153g4EY6\nbUlJFykpqaR3b93ANzo6g7AwX1xcHAyef9cu5bsXHt7ErPUePlxEWZmGHj0sT9fuPwBdQywedo2j\n+bZvstP+BrnT1LaJBAKBQHBbUWeCYlBuQkW1EBSD9bpi7Q15/wHLxrm6qujY0Y34ePOCYoDwcEVX\nbGzDWni4EshER+tKKJ57ricqlcTnn++tcbxtWx+aNfNkwwb9QTHAk0+GUFJSya+/WrfhTpIkvvgi\ngtzcct5+O86qOe4G5s8/wqFDOXz6aR+jgacx1qw5wZUrpTz+uP4NdsXFFWzYcJKxY9vplTdoXUp6\n9aoZFBcUlHPgwAX69dPNIN/Irl3ncXGxJyTEPGte7TWgfXtiLtnZcO6c8mBqDZUaOFlYG84T57HH\nGSes034LBAKB4PakDgbFF9BgePOZKTpevSEettLEonVrcHODAwctH9ujhwcJCQVmuzL06dOEnJwy\nUlMNL7ZBA1dCQhqxZs0JnTZfXw/GjevAzz8n19D2SpLEiBGt2bTpFCUl+nUgPXo0pWPHBixYYIWA\n+iqdOzfgySc7MWdOMsnJOVbPc6dy5UoZr7++h379fBk3zrDdmSkWLEjE19edQYP0635XrDhCWVkV\n48d31GnTaGTmzt1PWJgfzZt71WjbseMMGo1sRlCcRVhYYxwczNMk7NtXgLe3Ay1aWFY9Q3vNWZsp\nTi1QAuMOXqb7GqOQ87jRBMmqEkACLasSM1lz6LxwqREIBLcNdSoodsMXmSpKuGj1HD5O0MTZ+qDY\nzg66dLYuKO7Z04OcnErS0krN6q99Ha21uzLEuHHt2bs3k3PndLPQ99/fgStXSomJOX3TmA6UlFSy\nYcNJvXNKksTUqV2Ijz9PUpL1f9+zZoXh5eXIM89Eo7FWyH2HMnPmbvLyyvnqq75I5pQ61MPp03ls\n3JjG44931rvBDmDevAO0betDeLhucLtlSxonTlxh+vQeOm2//34MT0/Ha28j9FFYWMGhQzn07m2e\ndAIgLi6fHj08LP7M2msuxDqVCYevqoiCbA6KM8UmOxuRZZnf9p/juaUHeWLxfi5YKdMSCASCf5I6\nFRRrNXy26oqDvCBZ/x4zs+gaojhQVFuYsA4PV+7GO3eaF5G3bVsPPz83Nm0ybm12333tAFi1KlWn\nLSqqFU5O9qxZU7Otb98AGjVyZeFCw9ZrDz/cCUdHFd9/b8UTwFW8vZ345JM+7NqVxQ8/WCfFuBPZ\ntes88+al8OKLXQgKqm/1PPPmHUSSJKZM0R8pJiScZ/fus0yb1k1vELpoUSI+Ps6MG9ehxvGqKg2r\nV59g5MjWOsU8biQ6OhONRja7aEdubiUpKcX06WO5huHAQQgMVGwRreFwnuI80c4G+UQ1lRSTjRvm\nPwQIdJEkiUWP9eSNEe3ZdfISgz+L4Ze4M+LBWSAQ1GnqWFCsZGds1RV39FI23FRb6RYW0gVKSuCE\nrmLBKO3bu+LlZU9srHlBsSRJDB7sz7Zt53Sq1t1I27Y+tGnjrVdC4eLiQHh4M7Ztq+llbG9vx1NP\ndWfdulROnLisd14fHxcmTOjA4sXJVlW40/Loo+3p27cpr74ay8WLJVbPc6dQUVHNk09up1kzd959\n1zoLNoCysirmzk1k5MjWBAToj/T+97+9eHk5MXWqrhC3vLyKdetOMGZMO53Ad9eus1y5UsqYMW2N\nrmHTpjO4uNibnSnesycfWb7+gGgJBxNt22R3OE+xYnO0wXmimAuARmSKawGVncTUiEA2vtiXTr6e\n/GdlMg/O38vpHCt3QQsEAsHfTJ0KitV44ICrzZniTl5QWg1pRdaN176+tVRCYWcn0aePF7t2ma/d\nGDy4Gbm55ezfn22038iRrdm+PYOiIl0f5IEDm5OcnM2lSzVvNk8/3R0HBxUffxxrcN5nn+1GUVEF\nixZZUbHkKpIk8f33AygpqeTFF3dYPc+dwscfH+DIkSvMmdMPV1frNtcBLFuWQk5OCdOnd9fbXllZ\nzfr1Jxg7th0eHo467TExGRQUlDN2bDudtjVrTqBWq4iKMl60Y9OmM/Tr54ujmZFmbGwe9vYSPXta\nlq7Nz4e0NOulE6AExR1tlE5oH8jd7nDnCUmSXCVJSpAk6Z6/+1wBPq788kQoH90XRMr5AqI+38H3\nMaeosjZrIRAIBH8TdSoolpBwqwUHik71lD9TrNQVd+gAarWSubKU3r09OXashCtXzDM6joxUXktv\n3XrOaL9hw1pSUVGt14UiIiIAgN27z9Y43qiRG48/HsLixUl6g2lQioD06uXLF1/EG81Wm6JdO29e\nf70Hy5adYM0a3Qp8dwtHj17hvffimTChNSNGGC+IYQxZlvn883g6dWpAZGRzvX1iY8+Sl1fGyJFt\n9LZv2nQKtVrFgAG661i//iT9+wfg5qY2uIYzZwpJTc1j8GDDmuOb2b07n5AQd1xdLUvXagvmWBsU\nl1TBqcLa0BNr7dhur0yxJEk/SJKULUnS4ZuOD5Uk6bgkSSclSZp5Q9NrwPJ/cH1M6NGMLS/3o2+b\nBnz41zHGztnNkfPmu/UIBALB302dCopB0RXbminuYKMDhYMDdOpofVAMymtkc2jY0IWgIB+2bj1r\ntF94uD+urg56bda6d2+KWq0iNlZ3jvvua09FRTXbtxsOVF96KZS0tDz++suwhZs5zJzZjaAgH6ZN\n28bly+ZtNryTqKys5pFHNuPuruaLL/raNNfevZkcOpTN9OndDW5YW736OGq1Sqd0s5YtW9IID2+m\nYwWXnp7HsWOXGTaspdE1bNumPKhFRpoXFFdWaoiPz6dXL8tFvQdt3GR3NB9kaidTrMYdNZaVp64D\nLAKG3nhAkiQV8A0wDOgATJQkqYMkSYOBI4Dx11N/A408nJj7cDe+ebArWfmljPp6F7M3Hae8ynrH\nIYFAIKgt6lxQ7EZTSrhENeaVS9Y7hwM0d7M+UwzKzflQEljqJtSjhycqlcSePeaffOBAP2Jjsygv\nN3xjcHS0p1+/ZmzZclqnzcnJnm7dmrBx4ykd+6OIiADc3dWsXau7SU/LmDFtaNzYle++s9Cc+SbU\nahWLFw/m8uUynn46+q6zYvrggwQSErL57rsBNGrkYnqAEebM2Y+7u5pJkzrpbddoZJYvT2Ho0Fa4\nu+tKJ3JzS0lKusiAAc112jZtSgNg6FDj0olt287SoIEzQUE+Zq05KamIkhLNtQdDS0g8BI0bK/9Z\ng/YBuFMtZIpvtywxgCzLO4ArNx3uCZyUZTlNluUKYBkwGugPhAEPAk9IkvSP3gckSWJEcBM2v9SP\n0V18+WrbSYZ/sZNdJ4Sto0AguLXUuaBYcaCQKeKCTfN08rI+UwyKLVtODmRaWHXa1VVF585u7N5t\nfvWQ/v19KSurJi7O+GeOjGzB8eOXOXtW95XjlCkhJCVd1Klip1arGDq0FWvWpBrc+e3goGLq1C6s\nX3+S9HQb/tKALl0a8O67oaxYcZJffjEciN9pJCRc5L339vHQQ21t8iQGuHSpmOXLjzJ5crBBecOO\nHRlkZhbywAO63sSgSCtkGb2lnTdvTsfPz522bQ0Hu7IsEx2dSf/+vmZbq2nfjvTqZXlkmnhIueas\nJSUP1HbQ0sry0FqKrnoU3yH4Aje+PjoH+Mqy/Losyy8CvwDzZFnWq5uSJGnaVd1xwqVLl2p9cfVc\n1cwe35kfp/SkvErDQwvieHhBnJBUCASCW0atBcWSJKkkSTooSdJaW+bRbnCx2YHCE45fNfO3Bu0N\n+pAV+8969fJk374CqqvNy5T27euLJJn2K9ZqS7UVym7kkUc607ChK99/v1+n7d5725OVVaTjZXwj\nTz7ZFTs7iW++STBrzcZ49dWu9O7dhGeeiSYj486/wRUXVzJp0iaaNnXlyy9tk00AfP/9QSoqqnnm\nmW4G+3z7bQKeno6MGqXfPWLNmuM4Oqro2bNm1lOjkdm+PYNBg1oYDXbT0ws4e7aI/v3Nz5ru2ZNP\n06aO+PvrZq6NUVEBR45C52CLhtXgcJ5ixWZvwy9aFeWUcvmO32SnRZblRbIsG/y9lmV5rizL3WVZ\n7t6ggXnVDK2hX5sGbP1XP94Y0Z6kc/mM+GonLy9PJDPv7pNgCQSCW0ttZopfAI7aOok2S1MbtmyV\nGjhpZUwWfPUGbY2uOCzMk6KialJSzLO/8PZ2IijIh+ho40FxUFBDfHyc2bxZVx+sVqt45JFg1qxJ\nJTu7pgvF6NFtcXdXs3ix4Qjfz8+DcePaM39+IoWF1tuzgWIH99NPg5FlmQcf3ERl5Z2tF3zuuRhO\nnMjjxx8HU6+ek01zlZdX8c03CQwdGkj79vr9jc+dK+D3348wdWpXXF11M8mXLhWzeHESDz8cjLNz\nTT1xUtJFrlwpZeDA5kbXof0u9u9vnj8xwN69ip7Y0qIdR45AZaVtzhNH8myXThTdppvsjJAJ3CgI\n97t6rM7haK9iakQgO14dwLS+gaxNymLAp9F8uP4o+QaqcgoEAkFtUytBsSRJfsAIYL6tc6lxQ42H\nzZvttBtuUsxXMdTAw0MpJGBNpjgsTNFUxsWZH5H36+fLnj0XqKgwHEDa2UmMGtWa1atPUF5epdP+\nyCOdqarS8Oefx2ocd3Z2YOLETixdmkxWVqHB+V96qSf5+eXMn2/Fk8BNBAZ6MnfuQHbvzmLmzN02\nz1dXWbAghYULj/LGGz0YMMD8ANIQP/98mAsXinnpJcP+xp99tgeAZ5/VrVIH8NNPSZSVVfHSS710\n2tavV+Q1AwcGGF1HTEwm9es70b59PbPWnZ1dQVpa6bXvviVonSeszRQXVUJG8fUNttZy3Y7tjpFP\n7ANaS5LUQpIkNfAAsPoWr8koni4O/HtYe7a/0p+RwU2ZuzONvp9sZ/7ONLEZTyAQ/O3UVqb4c2AG\nUCvGk+40pYgsm+Zo5wkStm226xpiXbnnli2d8fFxIC7O/Ii8b19fSkurOHjQuHbv/vvbU1BQrjdb\n3KlTQ5o399K7qW7GjD5UVWn49FPDAWpoqC/9+jVj9uw4o8G5uTzwQBumTw/ms88S+f13/eWmb2cS\nEy/x7LMxDBrkz9tv97R5Po1G5uOP9xIS0ojBg/XbuVVXa1iyJIl7721Pixb6A9affkqiZ09fOnTQ\nfeX9669H6N3bD19fD6Nr2bnz/FVZj3lZX+13PTTU+Lz6OHAQXF2hdWuLhwJw5OplZqvzROFtHBRL\nkrQU2AO0lSTpnCRJj8uyXAVMBzaivMVbLstyyq1cp7n4ejkze3xn1j0XQWd/L2atO8rAT2P482Cm\nqIonEAj+NmwOiq+av2fLsqwrZq3Zz+xNG240sVk+4WIPLWx0oOjRXSkocFl/QTiDSJJEz54eFgXF\nERGKjlFrg2WIyMgWeHk58fvvx3TaJElixIjWbN2arhPUtmzpzYMPBvHttwkGPYsBZs7sTWZmIb/+\nWjslmz/9NJyePRvx2GNbOH7chtrbdYzc3DLuvXc99es78csvUahUtj9fbthwiuPHL/PKK2EGg9HY\n2LNculTCffe119t+/HgOiYkXmDQpSKctNfUySUnZjB+vf6yWs2cLSU8vuPadNIe4uHxUKomuXS0P\nihP2K9IJlZWV6I5cvcY72CyfyMIRLxywzTnkViDL8kRZlpvIsuwgy7KfLMsLrh5fL8tyG1mWW8qy\n/P6tXqeldGjqweIpPVnyeCheLg68+Gsiw7/cyU97M8gvFbIKgUBQu9RGprgPMEqSpNMolj8DJUla\ncnMnSzZtuONLKZepwraNFh29rmeRrKH71X1O1mSLQ0M9SUkpprBQV+agj0aNXOjSpT4bNugW57gR\ntVrFiBGtWLv2pN5iG4MGBVJSUkl8vK508LHHulBaWsXmzYb9iKOiFC3r55/H14qlmqOjihUrhuHo\nqGL06LXk5pbZPOetprKymgkTNnDuXBErVgyjQQPnWpn388/jadrUjfvvNxy0/vbbEZyc7Bk+XEmr\nZmcXk5Fx/clvzRrlLcHo0bob8FauPA7AvffqVri7kY0bzwAwaJD5RTvi4wsICnK1uGhHVZWi2++h\nv2ifWaTkgaMdBNpoLVxI5lX3G0FdI7x1fdZMD+fzCYrw/M0/D9Pj/S08v/QgO09cEtljgUBQK9gc\nFMuy/O+rmYnmKJq1bbIsP2TLnO4o2szaKOKRaoMDRdcQ5c99Vhgy9OrliSxjkTXbsGEBxMZmkZ9v\nfKPb6NFtyMkpYc8e3cC3X78AJAm9xTrCw5vh5eXEn38eNzi3JEk8/3x3Dhy4wM6dxguKmEuzZu78\n/vtw0tIKGDt2vVE/5rqOLMs880w0mzefZe7cgfTqVTuv2pOTs9m8OZ1nn1VKc+ujqkrDihVHangT\nz5mzj7feir7WZ926EwQFNSQgQDdtumpVKt26Ncbf33g296+/MvDzc6NjR2+z1l5dLRMXl2+VnvjI\nESgru/4Aag1H8qGtjc4ToA2KbdeFC/4e7OwkxoT48tcLEax9LpwHevgTk3qJhxfEE/Hxdj7bdJwz\nl0tu9TIFAsFtTJ3zKYbru78LMS4lMEWHqw4UpwzvLTOKlxe0agX7rahp0auXUsRj507zJQNRUQFU\nV8ts3278cw8Z0gKVSmL9el2dbr16zgQFNWLHjjM6bQ4OKsaMaceqVcf0btTT8sgjwdSv78Inn+wx\ne+2m6NvXl4ULBxETk8njj2+9bQt7fPBBAvPnH+H117vz6KPGZQiW8NFHe3B1deCpp7oa7PPXXye4\ncKGIyZOvG/q+805/fvxxDAAlJZXs3n2WqCjdSnWXLhWzd28mo0bpLwmtpapKw9atZ4mKama2nvjQ\noUIKCqrp29e8TXk3knBVdGVrUNzRxk125RRQQcGd5DxxxyJJEp18Pfnv6E7E/SeSryaG0LKhG19t\nP0nfT7bzwNw9/L7/HCUV5r2lEwgEAi21GhTLshwty/I9ts6jbHSxo9BG9yDtbnRbdMXdul6/cVuC\nu7s9ISHu7Nxp/sl79WqMm5vDtdfXhvD0dCI83J916/RvXhs+vBXbtqVz8uTNBa5gwoSO5OeXs27d\nCYPzu7g48Nxz3Vm79iTJybVXCXbSpLbMmhXGzz8f59//vv0cKRYvPsobb+xl0qS2vPdeWK3Nm56e\nx7JlKTz5ZFe8vQ1LMb77bj+NGrkyYoT+HWm7dp2hoqKayEjdSnV//XUKWYYRI4wXFomPv0h+fgVR\nUbpFPwyxY4fyHY+IsFzUu/8AuLsrD5/WUFwJp4ugvc2b7JTfGpEpvr1wclAxsnNTFk/pSexrA3ll\nSBuy8sv414pD9Hx/KysSaudtl0AguDuok5liFWpcaWBzUNz+qgOFLZXtunWFM2eU6naWEhHhRVxc\nAeXl5uk31GoV/fr5snWr6Qz50KEtSUrK5sIFXS/k558PRaWS+OqrOJ22QYMC8fPz4NtvjWtCpk/v\njru7mvfe22XW2s3lP//pzpNPduKjjw7w7ru666urLFuWymOPbSUy0o8FCyIt9uI1xocfxqJS2fHy\ny4YdLA4ezGL9+hM8+2wPg/KKzZtPYW9vR3i4bkC7YUMaDRu6EhJivI7y5s1nkCSIjDRfT7xzZy7N\nmzvh52e5R/P+A4pMyc7KXyKt5aLt5Z21QbHIFN+uNPVyZvrA1kS/0p9fp4XhV8+Zb6MN758QCASC\nm6mTQTEoNydb5ROuDtDKHZJtMD3Qvta1RkIREeFFebmGhATz/YoHD/bnxIk8k5XghgxRLLv0WbM1\naeLOAw904ocfEikoqKlPtre34+mnu7NlSxpHjhh2AfH2dua557rz229HSUmpvRKvkiQxZ05/Jk9u\nxzvvxDNr1r5am/vvYsWKEzz00CYiIpqyatU9ODpaaZOgh7NnC1i0KImpU7sYtUl7//2deHo68vzz\n+v2Li4srWLDgICNGtNYpDa3RyGzenE5UVCB2dsaD+S1bztK9e0O8vc0LcGVZZteufKuyxFVVig94\nN8OKEZMkXb22gy1XbtSgkEwk7HGlkW0TCW45kiQRGujDvV19ScspJrvg9t/cKxAI/hnqeFB8HtlG\n6+OgepBsQ6ZYW2XLGgeKPn2UQCE21vwFaHf8m7Jm69KlMfXru7BpU5re9ief7EZRUQVr1uhuqps2\nrRtubmrYXvTOAAAgAElEQVTefjva6DlefjkUZ2cHPv649rTFoGyYWbAgkocfbsubb+7lv/+tHaeL\nv4Nly1KZOHEjvXo1Zu3ae3B1dTA9yAJmz96LLMOMGbqFNrTk5ZWxevVxpk7tiqen/mB16dLD5OaW\n8corvXXaEhMvkJNTcu1ByhBFRRXs3XvRoizxyZOlZGdXEB5ueVCs3WSn3dBqDcm51+0XbaGQTNxo\njB2198AjuLWEBfoAsDddV0YmEAgE+qjTQXE15ZRioUnwTQR5wYkCKLFyz4WXF7RsaV2muGFDNa1b\nu1gUFHfo4E3Dhs4mJRR2dhL33NOK1atPUFam++F69fLH19edFSt0/Ybr13fhpZfC+O23I5w6ZfiG\n4ePjwrRpIfzySwoZGTZ42+lBpbJj4cJBPPJIO95+O46nn46mqqpWar/UCrIs88knB5g4cSO9ezdh\n/fpROhlYW8nJKWHevEQefLAjAQGGd4qtWnWMykoN48d3NNjn++/307FjA/r00Q1otVXsIiObG13P\njh3nqarSEBlpvq5W+93WPgBagvZB05ZMcXKeco2bSICbRHGeENKJO4kOTTxwc7Rnb5pt9xCBQHD3\nUKeDYrDdli2oHshcN/i3hq4hipeqNfTp48nu3flmZ0IlSaJ/f1+io8+ZHDNxYkcKCsrZsEFXN2dn\nJzFmTDs2b07T6zTx+ONKek5f0HwjL78ciiTBRx/V/sY4bWA8c2Y3vv/+MPfcs4aCAsOFRf4pqqo0\nPP10NDNmxHL//a3YtGk07u61GxADzJ4dR2lpJa+9ZjhLDLBkSTLNm3vRo4d+D93jx3NISDjP1Kld\n9Wqdly07Qni4P02auBs9z/bt51Cr7ejTx3yv3tjYPLy87Gnf3tXsMVpsrWQny0qmOMhGPbFMNUVk\niaD4DsNeZUeP5vWIE0GxQCAwkzocFGu9im3bbBd0VWtoq4QiLQ3yrJijd28vcnIqOXnS/EIkAwb4\nkZlZzKlTxrOzAwYE4OPjzPLlR/W2Dx3aipKSSnbt0nWzCAjwIizMj+XLjVd99ff34PHHuzB/fiJn\nz5qvjTYXOzuJDz/szfz5A9m69Ry9eq0gJeXW3cSysoqJilrF998f5rXXurJs2VCcnOxr/Tw5OSV8\n9dU+JkzooLccs5YzZ/LZujWNyZM7Xwt4e/deQGjo/Gt9fv9d+fcfN66Dzvjk5GxSUi4xcaJu281s\n355JWFhjnJ3N/7y7d+fTu7enSa2yPg4chC6dra9kd7EMcsqvX+PWUkw2MlUiKL4DCQv04dSlYrIL\nha5YIBCYps4GxU54o8LJ5qC4pRs4q2zbbKfVPFqTLe7dW3ktbomEon9/5eZsyq/YwUHFvfe2Zc0a\n/RKK/v2b4+Bgx6ZN+ndgP/BARw4evEBy8kWj5/n3vxWd6qxZtetEcSOPP96RDRtGkZNTSvfuvzJn\nTtI/rjNeuzad4OBf2LPnAj/8EMn//V8fq4I9c/jooz2UlFTy5pvhRvt9953iEnKjN/GePedqVCz8\n889jhIb64uenu1FvxYqj2NlJjBtn3FM5P7+cgwcvXfvumUNubiVHjhTTq5flJsEajbLJTqvZtwbt\nNW2784TyNkoExXceoVd1xXFpQlcsEAhMU2eDYgkJd5pSZGNQrLJTinjYYsumvXEftGKzXfv2rnh6\n2rNnj/ma3LZt6+Hn58aGDcb9ikEp2VtUVMHWrbouFG5uanr29GXbttN6xz70UDBqtYq5c40bMTdr\n5slTT3VlwYJEUlP/vixuZKQ/SUkP0r+/L88+G8OoUWs5fbr2s9M3c/lyKU89tZ2RI9fi5+fGgQMT\neOwx05lVazl/vpCvv07g4YeDjGaJi4oq+PbbBMaObU+LFtfTobL8NrL8NqAU5UhIOH+t7PPN/P77\nMfr2bUbDhsblDdu3n0OjkRkwwHw98d69yne6d2/Lo9ITJ6CoyMZNdlevaVszxVqXGxEU33l0auqB\nq1oldMUCgcAs6mxQDFoHCtuCYlAySbbIJxo2hKZNrcsU29lJhIV5WhQUS5LEiBHN2bRJKcZgjAED\nAnB3V7NqVare9pEj25CQcJ6DB7N02nx8XLj//g78+OMhLpsoj/r6631wdLTnnXd2mv05rKFRIxfW\nrRvF559HsG3bOdq1W8Lrr++hqKj2tcZVVRq+/voQrVv/xLx5Kbz8chf27h1Pu3bmlTe2lg8+iKWq\nSsPbb0cY7fftt/vIyyvj1Vd1HSW0bNmShiwrUpmbSU29zJEjOYwd29bkmtatO42Hh5o+fcwvW71n\nTz52dtCzp/Gy0frQXku2ZIoP50JDJ2hguT1yDYo4jwOuqLH8cwjqNvYqO3q08CZOOFAIBAIzqNNB\nsRtNKeYS1VTaNE+QF1wohcs2yMq6hsABKzfbhYV5cPhwEYWF5ltgDB8eQFFRJbt2Gd9o6Ohoz5Ah\ngaxff0qv3ODJJ5UiHB9/rH+j3MyZ4RQVVfDxx7FGz9OokRvPPdedZctSOHy49qrc6cPOTuKFF7pw\n/PjDjBvXig8+SKB165+YNWsf2dnGg3dzKCqqYM6cJDp2/JnnnttBSEgDEhMfYPbsiFr1INZHRkY+\nc+ceZMqUzgQGGk5xVlZW88knu4mKaklYmOHs7dq1J6hXz4lu3XSD2TVrlKqFo0cbL+0syzLr12cQ\nFdXMYGEQfezdm09wsBtubpZrrg8cBAcH6GBDQv5wnu2b7ECRT7jji8TfI5UR3FrCAn04mV3EpcJy\n050FAsFdTZ0OipXXmRqK0c1yWoJWc2iLhKJ7Nzh6FAoLLR/bu7cXsoxF2eKBA/1Qq+1Yt+60yb73\n3NOKzMxCDh3S1QZ7eTnx1FPdWb48hbNndc/fqVNDHnoomC+/jOfiRd3qeDfy6qthuLmpeeutHWZ/\nDlvw83NjyZIh7N49juDg+rz55l78/RcyefJmVq1Ksyh7XFFRzZYtZ3j++Rj8/Bby7LMxeHio+eOP\n4WzZMoagoPp/4ye5zrvv7kCSJN54w7iWeOPGU1y6VMIzz/Qw2Ofs2XyWL0/h4YeDUal0L+W1a08S\nFNTQqN0bwKFDOZw/X8zw4c3N+gygZNnj4vIJC7NcTwywLwE6B4PaSlMPjaxUs+tYK0FxJm6Y77gh\nuL0IbaG8+YlLFxIKgUBgnNsgKLbdlq3T1YRcig1Bcc8eigWUNX7FvXt7olJJxMSYv9vPzU1NRERT\nNm40rSseOrQloJTy1ceTT3ZDo5FZuvSw3vaZM8MpK6vi11+NO1H4+Ljw6qthrFx5nN27bas2aAm9\nejVh48bRHD06iSee6MjKlacYM2Yd3t7zGDDgD55/PoavvjrEunXpbNlyhs2bz7BhQwbff3+YV17Z\nxYgRq/HxmcfgwauYOzeFoUMD2L17HPHx4xk7tmWtlmw2RlLSRRYtSmL69O74+xt/Vf/DDwdp2NCV\nYcN0ZRFavv02AY1G5uWXdS3dCgrK2bXrLCNGGB6vZcOGDACionTLQxsiMbGIgoJq+vWzXNBbXa1c\nRz0Nx/smOV2keI/bqieuooxScoSe+A6mk68nrmqV2GwnEAhMUvteU7WIG8orYVt1xU2dwUttm664\nR3flz/h90L+fZWPd3Ozp0cOD6GjLLDCiogKYMSOWc+eK8PMzXLKrcWM3QkIasXbtCWbO1NWftmzp\nTViYH7/8ksyMGX102jt0aECXLo1ZsiTJYBlhLS+/HMq33x7glVe2EBs7+R8LKAHatfPm66/789ln\nEcTGZrF+/Wm2bTvHwoVHKSrSL7FxclLRqpUXkya1ZcSI5gwc6FfrVenMZcaMbXh5OfHGG7r/Bjdy\n4UIRa9ak8uKLodfkDNOmraFRI1fee28gAOXlVcybd4BRo9oSEKCbLt2yJZ2qKg3DhrU0ua4NG87Q\npUt9mjQx32tY+122Jig+flx542JLUKx962Or80TR1bdQIii+c3FQ2dG9ubfYbCcQCExSp4NiNW44\n4nntxmUtkgQdPW3LFNevDy1aKK99raFfPy8+++wMJSXVuLiYp9scMsSfGTNg8+YzJt0Q7ruvHW+8\nEcPp03k0b64bKdx/fwf+9a9NZGTk6Q2iJk/uzEsvbeTQoQt07tzY4HlcXdW8914/pk5dx4oVRxk/\n/u9zaTCEWq1iwAC/a04JsiyTnV1KenrBtap4dnYSfn5u+Pm5/W22apawceMpNm5MY/bsQdSr52y0\n7zffxFNdrWHatG7Xjs2bp7yi0AbFGzeeIienhCee0F8O7o8/juPl5USvXsaDvaKiCnbvzuKllyzb\n8RYTk0vr1i40aeJo0Ti4fg1pHzStQRsUd7BOvXEN7QO39gFccGcSFujDRxuOkVNUTn03y7+zAoHg\n7qBOyydA2WxXGw4UHa/astlifduju/VBcd++9aislC3SFQcF1adRIxc2bz5rsu+kSZ0AWLJEv0Ti\nnnuUzVZr1+p3qXjkkc44Odlf88U1xqOPBhMc3JCZM7fr9Uf+p5EkiUaNXAgLa0x4eFPCw5vSu3cT\nmjVzrxMBcXW1hldf3UZgoBfTpxuPBJVNgAmMGdOO1q19DPZbtuwwPj7ODB4cqNNWWFjOypXHmTCh\nvcmNczExmVRWahgyxHzphEYjs2tXHv36WZem3ZcAbm7Q1rQphkFS8qCZK3jYWGiw6JpHsdAU38mE\nBiq64njhQiEQCIxQ54NixavYtkwxKEFxboXiQmEtPbpDRgZcumT52D59vLCzg507zZdQ2NlJREb6\nsXXrWZOFLJo39yIiwp9ly/SXbW7TxoeWLevpLQkN4O3tzKRJQSxcmEhmpnFvYJXKjtmzB5GenscX\nX8Sb92HuYhYsSCQ5OZsPPxyAWm08SP38871cuVKqI3OZMqULn38eBSibBtetO8HYse30Br2rVqVS\nUlLJQw8FmVzbli3ncHJSWWTFlpxcRF5eFX37Wifo3ZeguLlYW8kOlAfc2tlkdx4nvLHHePZecHsT\n5OuJi/ArFggEJrgNgmI/yrhCJcU2zaPVHtoioeh+9W22NZvtPD3tCQ52Y+dOyxYwaJA/2dmlHD5s\n+sd8woQOpKRcIiVFf9QeFdWSbdvSyc3V/2Tw+usRVFfLvP++aS/iQYNaMHJka2bNiuXCBeOuFXcz\neXllvP56DBER/tx/v/GqckVFFXzyyW7GjGmnY8O2YMFoXnghDICdOzMoKChn5Ej9qdZly47QrJkH\nvXubLsSxZctZwsObWlTKWvsd7tvX8qi0okKpZGeLdKJKA8fybdcTgyKfEHriOx+hKxYIBOZwGwTF\nyg2rANvcDjrWgi2btvqWtRKKiIh67NmTT2WlxuwxkZH+AGzdavrz33dfOyQJfvvtqN72adO6UVJS\nyTff7NPb3qJFPZ54oivz5h3g1CnTrxlnzx5EeXkVr722zWTfu5W3397B5cslfPHFEJObEpctO0xB\nQTmvvKLrJnEj69adwNFRRWRkC522vLwyNm1KY/z4DialIxcuFHP48GUiI82vYgdKUOzv70hAgOXZ\n1ZQUKC+//oBpDacKoUJju55YRqaQcyIovksIbeFN6sUiLhcJv2KBQKCfOh8Ue6DcsG3VFTdyVqpf\nJVlmAFFzLR6KDtKaTDFARIQXpaUaDh403+y4WTN32rTxYv360yb7Nm7sRp8+/qxceVxve+fOjRk+\nvDVffhlHaal+t4Y33uiLLMvXNnYZo3Vrb2bM6MXixcnExGSY7H+3kZh4ga+/TuDpp7sREmJ486KW\n77/fT8eODejd299gn+LiCn76KYkhQ1ri6qorqF279gSVlRrGjWtn8nxarfqgQYbPdzOyLLNzZy4R\nEdZJJxKuVhS3JVOsvYaDbbRjKyePSorxwPzPL7h9CQtUNPpCVywQCAxR54NiVxojoaIQ05vNTNG5\nHhyyISgG6BZy/cZuKeHhSrp61y7L0tWjRrUgOjqTggLTxSrGjm3LoUPZpKfrP8drr/Xh0qUSg57F\nTZu6M3x4axYuTKS83PQmuv/8pw/Nm3vyzDMbTJakvpvQaGSefnoDPj7OzJpl2sNvz56zJCSc56mn\nul/LKJ8/X0jhTVW45s8/QE5OCTNn6i/+sXLlcXx93enRw/TGsdWr02nc2IWuXRua8YkU0tNLycqq\noE8f69K0CfvBywsCdfcHms2hXFBJ0MFG+YT2QVtkiu8Ogv08cXYQumKBQGCYOh8U22GPG01qxYEi\nuJ6iKa4yX72gQ/dukJkJF3WLx5mkSRNHWrRwJjbWsqB45MgWVFZq2LjRdDZ25MjWgPKKXR8REc1o\n3dqbn35KMjjHs8/2IDu7mBUr9G/auxEXFwe+/HIIR47k8L//xZnsf7cwb95B9u7NNMuCDeDDD3fh\n7e3Mo49et0bz9f2MiIiF1/6/RiPz9df7CAvz05tNLiurYuPGNEaNam1SOlFeXs3GjRmMHNnCIoeO\n2FjFPUX7gGcp+w9At66KTaK1JOVCWw9wsrEit1aSdTdmiiVJCpQkaYEkSb/d6rX8Uyi64nrsFUU8\nBAKBAep8UAzKZjtbNcWgZIrLNZBq3FzBKN1s2GwH0KePJ7Gx+SbdJG6kd+8meHs7sXbtaZN9W7f2\npk0bb9asOam3XZIkHnoomOjo05w7p/8vYvDglrRt68Ps2XvQaEyvc+TINowZ04Z3391JWpqNqfg7\ngKysQmbO3E7//gE89FAnk/0PHMhizZpUXnghFDc3RRKhzdLfWLp769Y0Tp68wnPP9dQ7z/btpyku\nrmTUqDYmz7ljRyaFhZWMHKmrSzZGbGweHh4qOnY0XEzGEBUVkHxYCYptISnXdukEQCHnUOGIM4at\n724nJEn6QZKkbEmSDt90fKgkScclSTopSdJMAFmW02RZfvzWrPTWERbow/GLhVwpNr9EvEAguHu4\nLYJiD3wp4gIabHs9r72RJtsQt4V0UbJc1gfFXly8WEFamvnecPb2dgwd2oy//sowK0gdO7YtW7em\nG3SFGDdOKbixerV+7bGdncTrr0eQmHiBX3/VL7O4ma++isLBQcXUqessCvjvNGRZ5plnNlBaWsl3\n3w0zublOlmX+9a9N1K/vwgsvXK8mqM+6bcmSZDw9HbnvPv0uFitXHsfV1YH+/QNMrnPdutM4Oaks\n3mQXG5tHr15eqFSWp3oPH1YCY1uC4vwKyChWHnBtRbvJTro9fgbNYREw9MYDkiSpgG+AYUAHYKIk\nSf98xZ06Qtg1v2IhoRAIBLrcFncDd/yQqaKYCzbN084T7CXbdMXu7tCmjfVBsfa1c0yMZYsYPrw5\nly6Vsn9/tsm+jz4aTHW1zE8/Jettb9++Pq1aebNqlf6gGGDSpGA6d27E669vM6tAh5+fB59+Gsn2\n7RnMnXvQZP87leXLj/Lnn6n897/9aNvWdAZy9+6zREef5q23+uLp6XTtuCRJyPLbyPLbAJSWVvLH\nH0cZN64Djo669mklJZX8+utR7ruvnVn2auvXZzBggB8uLuaXvL5ypZKUlGKr9cTaa8aWoDi5ljbZ\nwZ1nxybL8g7gZm1AT+Dk1cxwBbAMGP2PL66OEOTrdVVXLCQUAoFAl9skKFZuXLbqih1VSmCcbIMt\nGyib7awNijt2dKVhQzXbt1sWFEdFNUOS4K+/TOuK27WrT1iYLz/9pD/LK0kSo0e3JTr6NJcvl+jt\nY2cn8ckng0lPz2PhQvOC3KlTuxAZ2ZxXXtnK6dM2/iXfhly4UMQzz2ygZ8+mvPxyqOkBwOefx+Hl\n5cSUKSFG+23dmk5RUQXjx3fU275qVSoFBeVMnhxs8pwnT+Zx4kQew4aZzijfSHR0LrIMAwZ4WzRO\ny4GDioNLC8sUGzXQOk8E2RgUV1NOMdm4Y1mm/DbEF2rsUj4H+EqS5CNJ0ndAiCRJ/9Y3UJKkaZIk\nJUiSlHDJmopFdRC1vR3dAuqJzXYCgUAvt0lQrLVls11XHORlmy0bQM8ecO4cnD9v+VhJkhgwoB7b\ntuVaJDOoX9+Z7t0bmhUUAzz0UCeSk7NJStK/I3DKlBAqK6v5v//bZXCOQYMC6dq1Cd98s8+stUqS\nxIIF9yBJ8Nhja82SetwpyLLMU0/9RXFxBYsWjcTe3vSllZGRxx9/HGXatK567dVuZNWqY7i7q+nf\nv7ne9sWLk/D39zBLOrFhg/IdsjQo3r79Cq6uKnr29LBonJa4eOXasbPhVycpD+qpwc/F+jlAqWQH\n8jXLx7sNWZYvy7L8lCzLLWVZ/tBAn7myLHeXZbl7gwYN/ukl/m2EBXpz7EIhuUJXLBAIbuK2CIrV\nuOGIZ605UJwpVrSJ1hJ6dZ9TnJUVjgcMqMf58+WcPGlZzemoqADi4y+Sl2fafH78+PaoVBK//qrf\nQaJDhwY8+GAQ3323n/z8Mr19JEnihRdCSUm5xF9/6d+4dzMBAZ58/vlgoqMz+PTTvWaNuROYPz+R\nVatSef/9/rRvX9+sMbNm7cDe3o7nnrueVd679xw5OTWz91eulLJ8+RFGjWqrV2t86VIxmzenM2lS\nJ7OcJDZuPEPLlp60amWZg8T27bmEh3uhVlv+s1FSAknJ168da0nKVbLEtrhXwF1lx5YJNew1/K4e\nu2vR+hXHCb9igUBwE7dFUAzKzas2guKgWths16ULODhYHxT3768sYvt2y36Uo6KaodHIbNtm2rO5\nQQNXBg5szvLlRw1meV9+uRdFRRXMn29YCzJxYieaNfPkgw92mp3Zfuyxztx3Xztefz2a/fuzzBpz\nO3PsWA4vvriZQYNa8NJL5skmUlMvs3BhIk891Q0/PyXzWlZWRa9eCxg0aHGNvp9+upvCwnKD3sS/\n/36M6mqZBx4wvX+qoqKa7dsziYpqZtY6tWRnV5CSUsyAAdbpFg4cgOpq24JiWVYqUgbXSnln5a2T\n250fFO8DWkuS1EKSJDXwALD6Fq/plhLs54WTgx1xYrOdQCC4idsoKK4dW7ZrDhQ2SF6dnKBzsPVB\ncZs2LjRpoiY62rLIPDS0Ee7uDmzceMas/vff356TJ3Nr2HrdSNeuTQgPb8a8eQcMBrwODipmzuxD\nbOxZoxvzbkSSJObOHU7jxq488MBKg5noO4GSkkrGj1+Ji4sDP/440mzP31df3YyTkz3/+U/EtWNZ\nWUqlwxv/vYqLK5gzZx/jxnWgUyf9RTZWrDhG27Y+BAebLsKxZ88FiosrGTzYMm9e7cZQ7QOdpcRd\nrSzes4dVwwHFdaKw0nY9MSiZYhcaYI+j7ZPVESRJWgrsAdpKknROkqTHZVmuAqYDG4GjwHJZllNu\n5TpvNdd1xSJTLBAIanIbBcW+VFBABeaXSNaHnwt4OtiWKQYl45WwX8l+WYokSfTrV4+YmDyLdMUO\nDiqiogJYtSqd6mrTFUhGjWqNJMGff6Ya7DN5cmeOH79MQoJhgfQTT3QjKKghL7ywgWIzdXje3s4s\nXTqW9PS8O9qm7YUXNpGcnM2SJaNo2tTdrDGxsWdYvfo4b7zRl0aNrvv9urvrBmhLlx4mP7+8hl3b\njeTklBATk8G4ce1M2r8BrFmTjlptx8CBlgXF0dG5uLmp6NrVvM94M3Hx0Lw5NGpk1XDg+jVbW0Hx\nnSadkGV5oizLTWRZdpBl2U+W5QVXj6+XZbnNVf3w+7d6nXWBsBY+HLtQQF6J0BULBILr3FZBMdju\nQCFJ0MnLdgeK0J5QVARHTBd900u/foqu+NQpy3TFY8cGcvFiCXv3mrana9TIjT59/PnjD8MZ3nHj\nOqBWqwyWfQbFJ/mbb4Zz5kw+X39tfno8PNyfDz4YwG+/HeN//7MyrV6HWbToEPPnJ/Kf//QmKqql\n2ePef38nPj7OOkU4PD2VoPjDDyOvHZs37wBBQQ31VrADWL06lepqmXvvbWvyvLIss3LlKSIj/fHw\nML6x72ZiYnLp08cLBwfrfjLi90GP7lYNvYb2mu1onSPcNWRkCjl/xwXFAvMJa+mDLEO80BULBIIb\nuOuCYlAyTYfzFI2itWhfA+9LsG58v35KumvnTsui8xEjmuPgYMeqVelm9Z8woT3JydkcOKBf2+vl\n5cTgwYGsXHnMaDY3IiKAwYMD+eKLuGvV1szh1VfDuPfetsyYsZVt206bPa6uk5Bwnqee+ovIyOa8\n+24/s8ft25fJX3+d5F//6qXjOOHgoEKW376mHT558grx8Zk88khng1ngX389SkCAJyEhjU2e+/Dh\ny6SlFTB2bKDZ6wXIyVH0xP36WSfmzc6GjAzbN9kl50JzN7AwntehjFyqKBFB8V1MsJ8nTg52QkIh\nEAhqcNsExa40QkJVK7ZsnbwgrwIy9Vv0mkXr1uDpqWTArKFdOxfq13ewuIiHp6cj/fv7smpVmln9\nH3ooCGdne+bNSzTY595723P6dB7bt582OteMGX3Iyipi4ULDc92MJEksWjSSNm18uP/+P0hNvf03\nt5w7V8Do0Sto1MiVpUvHmGW/Bkqm9o03tuPt7cz06aYjxGXLlOz9hAn6vYlPn85j8+Y0Jk8OMks6\n8eefaUgSFpd23rVLeXCLiLBOt6B9cLQ1U3w4T7l2bUX7YH0XbLITGMDRXkXXZsKvWCAQ1OS2CYrt\nsMeNxlf9RW1Dq0k8bIOEws4OunezPlMsSRIREV4WZ4oBRo1qQWpqHqmppgNqLy8n7ruvHUuXplBa\nWqm3z8SJnfD1deeNN7YZzRZHRrYgPLwZ77wTTWGhaVs4Le7ujqxdOx6VSmLEiF91LMduJwoKyhkx\n4lcKCytYu3YCDRq4mj32zz+PsWnTKd56q+81/XBlZTWRkYvZsKGm5Z1GI/PLL8mEhzfD31+/XmDR\noiQApkzpYtb5V69OJzS0MY0bm79mUN5mODra0aOHdf7E8fuU68WWSnYV1XAsX/EZt5W7yI5NYISw\nQB+OXiggv0T/76JAILj7uG2CYqg9WzZttsnWzXY9uiveq2VWmitERHiRllZKZqZlE2gzfWvWmCeh\neOyxzuTnlxvccOfs7MBbb/Vjz55zRv2IJUmpcnfxYjEffRRr0ZoDA+uxatX9nD2rZFkNBeh1mcrK\narOBtCgAACAASURBVCZM+IOUlEv89tt9BAWZdnvQUlJSyYsvbiQoqCHPPns9S3zo0EW2bUtn5Mil\nNfovX57C0aM5PPVUN73zaTQyixYlMWhQCwICTItss7KKSUjIZuTI5mavWcuOHXmEhnrg6Gjdz8W+\nBOjQHlwti8VrkFoAVTJ0rIWguIhM7FDjgnl+0oI7k7DAq7ri00JCIRAIFGwOiiVJ8pckabskSUck\nSUqRJOmF2liYPtzxpYgsZKywfLgBb0fwdVGqY9lCj+5QVQVJSdaN176OtjRbHBDgQadOPqxfb151\nu/79A/Dzc+eXXwxvpnvssS40berOV18Z3xAXFubHQw8F8/HHsRw+nG3Runv18mPJktHs2XOOiRP/\npLLStn/Hf5Lqag1Tpqxlw4Y0vv12GEOGWKbL/frr+KsbFYfXkFsUFCgZdy8vp2vHNBqZ99/fSYcO\nDZg4MUjvfDt3niEjI59HHzVd1hlg/frTANxzj2XSiaKiKg4eLCQ83LpoVJaVoNhW6YS2CmVwrTlP\nNEW6vXICglqms78njvZ2QkIhEAiuURt3hSrgX7IsdwDCgGclSTJdRcAK3PFFQyXFWBaM6aNLPUi0\nMUHQ/WoSz1oJRUiIO15e9mzZYvlCRowIYMeO8xQUmLYUsrOTmDixIxs2pBmULjg4qJg2rSsbNpzk\n1Cnj6/nf/6Jwc1Pz2mtbLF73uHHt+fLLIaxalcqDD94egbFGIzNt2nqWLDnMrFn9eOKJEIvGFxSU\n8/HHsQwd2oq+fWuWVta6OTRufN2abd26VA4fzubf/w436Hu8ZMlh3NzUjBlj2nVCmfM0fn5uBAX5\nWLT2mJg8qqtlq4t2ZGRATo7tQXFiLqjtoJ2NzhNwPSgW3N0IXbFAILgZm4NiWZazZFk+cPV/F6IY\nxP8tYj13/ABqZbNdF29Fo1hmQ0zm7w8NGyp+xdagUkkMGFCPLVuuWOzjO2xYc6qqNGzdarq6HcDE\niR2pqtKwcqVhe7bHH++KJMGSJcZT3/Xru/Daa31Yv/4EMTGnLVk2ANOn92D27EH89tuxOp8x1mhk\nnnhiHT/8cIi33grn9df1V5UzxqxZO7h8uZT33hug09a+fQMefbQLixePuXbsm2/24efnwQMPdNI7\nX0VFNb/9dowxY9rg4uJg8vwVFdVs3nyW4cMDzNqQdyNbtlzGycnO6kyx9trorl8FYjaJVxTphJWO\ncNeopoIiLuKOZT7NgjuTsEAfjmQVkH8byrkEAkHtU6vvDyVJag6EAHG1Oa8Wj6s3stqobNe5nqJR\nPGKDhEKSlJu9tUExwKBB3mRklJGWZplfce/ejfHwUF97LW6KLl0a0bJlPVasOGqwj5+fB/37N+fn\nn5NNBunPPx+Kn58HM2ZsQaOx3Nvu5ZdD+eyzQfz++zHuv/+POqkxrqioZvLk1fzwwyHefDOcd97p\na/EcqamX+fzzvUyZ0oXu3XWzk/Xru7Bw4WhCQpoAkJGRx6ZNp5gypYtBV4stW9LJyytjwgTzXsjE\nxmZRVFTJsGEBpjvrnOsK4eFeODmpLB4LyrXh4ADB5qk89CLLSqa4Sy1JJ0CDx9UHbMHdTVigtyLx\nEX7FAoGAWgyKJUlyA34HXpRluUBP+zRJkhIkSUq4dOmSVedQ444jnhRgXnbUGF28lT9tlVD06A5H\njkKhlYX2IiOVhWzdatlCHBxUDB3ajNWrzatuJ0kSEya0Z9u202Rm6vzzXOPBB4M4ceIKO3caLyXt\n7OzA++8PJD4+k+++s04/8tJLoXz11RBWr05lwIAlXLxYZNU8fwe5uaVERS1lyZLDvPdeP959t6/F\nWVYly7wGFxcHPvjgekGO4uIKBg1azP79uk4qP/2UhCzDlCmGJRq//noET09Hs3XNq1crVewiIy3L\njl68WM7hw8XXvqPWEL8PgoPA0YZqyhdK4VIZdLZ+GdfQvmXyEJliAdDZ3wu10BULBIKr1EpQLEmS\nA0pA/LMsy3/o6yPL8lxZlrvLsty9QYMGVp/LA/9akU+0dAdXezhkowNFWChoNNbritu0caFpU0e2\nbbN8IePGtSI7u5SdO82zqXv88S5oNDJz5x402GfixE40aeLGjBmbTWaLH344mKiolrz66maTOmRD\nTJ/egz/+GEdSUjZhYYs4csS6B6baJC0tl969fyQ29iw//TSKN94ItzggBli0KJEdOzL47LOoGuWc\nt28/zdat6TzzzPoa/TUamSVLkujbN4CAAP1yhStXSlmx4ijjx7dHrTadvdVoZH777SRRUQG4u1tW\n9SI6WvlORkZal6KtqlKC4l5hVg2/hvYarY1MsfKWSRJ2bAIAnBxUdG3mRZzIFAsEAmrHfUICFgBH\nZVn+zPYlGccdPwo4i4wN5egAO0nxPLU1KNZW6dqz17rxkiQxcGA9tm2zXFc8fHhznJ3tWbHCsI3a\njQQG1mPYsJbMm5dIVZX+7LKrq5r33x9IXFwmq1cb1h9r1z5//ijs7e147rm/LFr7jYwZ05YdOx6m\nrKyKsLBFLFmSbPVctvLbb0fp1u0HLl4sZvPmB3noIf3uD6bIyyvj3//eSq9efjz2WE0fYe0DxM1x\n9i+/JHP8+GWDNmwAP/6YRGlpFc8+a97Otfj4i5w7V8T997ey7AMA27bl4ulpT0jI/7N33vE13f8f\nf557s/eSGAkZVoSYIcSoTW21VWm1WlpVLVo6KeX37dAqnUbVqNLatbcQmyAxEjESQqYksnPv+f1x\ncq2S3HvPaSN6no9HHleu83nfT5I7Xud93u/X29HktQBnz0J2tnxRbLiao4zzRAL2eKJFRupa5aki\n1N+dqBsZal2xioqKIpniMGAY0E4QhFPFX88qEPeROOFDIdnkI9NPDelybGS6vHHPrq4QGAiHZFRR\nt2vnRnJyIVFR2Sats7e3pGvXaqxdG2d0Xe+oUQ1JTLzDpk2PF9LDhtWnWjVnPv/8YKnxvL2d+Oij\n1mzeHPu3ARSm0KRJZY4ceYkGDbwYNmw9Q4euJSPDTANoM8jOLmDUqL/o3381NWu6cfToS7RpY3oN\nroGPPtpNSkoOc+c++7csc5Uq0hAMS8t7md6CAh0ff7yHBg0qMnDgoxvsRFHK8oeGVqF+fS+j9rF6\n9SUsLTUmT7ED2LUrjTZtXIye2PcwhteEEpniqvbgqoCOzSRebbJTeYBQf3f0IvScG87ry08wd1cM\nO8/d4sbtXJMTFSoqKuUbJdwnwkVRFERRDBZFsUHx16bSV5qHoUFGibri4OJxz/GmadG/EdpUEgDm\nvn8a7K527zb9El6fPv7cuJHNkSO3jDr+2WerU7GiPQsWPH5Us4WFhrffbs6BA/EcOVL6sJSxY5tR\nvbob48ZtIUfGdCgfHyd2736eTz9tw++/RxMc/DOrVp37Rz+YRFFkw4aL1K8/n/nzT/Heey0ID3+B\ngADz05KHDiUwb95RRo9uQqNGlf72/4bYffvWvnvfkiWRxMWlM2NGu8fasB04kMD586m88opxE+xE\nUWT16ku0a+eNi4tpijIhIY/Y2FzatjW/kPfQYcmdxdfX7BCA5FFcX4EssYiOLG7gpJZOqNxHiK8b\n73apTS0vR84kZPDFtouMXHyMFrN20WDadgb+GMEn66P4/eg1TifcJiO3kLxCHYU6vSqaVVSeMizK\negOmcr8tmycyWtq517hz+jZUdSj52JIIbQaLFkNcHAQEmL7e19eWatVs2Lv3NmPHVjVpbbduvmi1\nAuvWxREaWrHU4y0ttQwbVo/Zs4+QnJz92DHFI0Y0YPLkncyff4KmTUsWEVZWWn78sTvt2//Ku+9u\n59tvzb9QoNVq+OCDlnTo4Merr25iwIDVtGrlw+zZHWnc+O8CUw7R0cm8/fYOtm6NIzDQg507h9K2\nra+smHfuFPD886vx8XFixox2D/xfbGwafn4uNGxYiZSUibi72wGSeJ09+xD163vRtevjyxx++SUS\ne3tLBgwwznUiKiqNS5cymDTJ9PnKhnriZ56RcXJwRHptmFGOfZc8HVzIhL6mvSweSTbJ6ClQM8Uq\nD6DVCIx+5t4bd1ZeIRdvZRGdmMW5xEzOJ2ay8lg8OQWPto7UagS0GgFLw61Wc/fWy8ma2pWcCKzk\nRGBFR2pVdMTRpnQbRRUVlbKh3IliWzywwFYRW7Z6xb1MkWnQXYZDU2gz6TbikHmiGCTxsXFjCnq9\n+NhM4aNwdbXhmWeqsG5dHDNntjBqzQsv1OPzzw+xYkU0Y8eGPPIYJydrBgwI4rffzjJ7dmfs7Utu\n0mrXzo9x45rxzTeH6d69Jp07m17Dej+hoVU4cWIkCxdG8v77e2jSZCHt2vkyblwI3bpVR6s17yKH\nKIrs2HGZ2bOPsHnzJZydrfn6646MGdP4gXIGc5k8eQdxcens3TsCZ+d7U+oiIuJp0WIh48Y14+uv\nu9wVxAB79lwhKiqZhQt7PrahLyenkJUrz9G/fyAODsY1zK1dG4cgQM+eppdO7NmTjqurBcHB5p0t\npqXBhQswfJhZy+8SfRt0onL1xIBqx6ZSIo42ljSu5kbjaveukuj1IvHpOZxLzCQhPZdCnYhOry++\nFSnU69HpRIr0IkV6PUU6kQKdnoT0XDZG3mD54XtuPt6utndFcu1KTtSu6Eg1d3u0Jrzvq6io/DOU\nO1EsFHeOS36j8nCyAj8HOCOzPDkoCBwc4PAReH6oeTHatHFl8eJEoqOzqVvXNCHSs6c/48btIzb2\nNtWrlz5koW5dT+rX92T58qjHimKAkSMb8ssvp/jhh2O8807pgnvmzPZs3x7Hyy9vIDp6DI6O8opA\ntVoNr7zSkAEDAvnuu+N8991xevVaha+vM7161aRLlwDatKmKrW3JmZeCAh3h4fFs2hTLhg0xXLyY\nhpeXPVOntmb06EaPzZabSnj4NebOPcrYsU1p1erBeuS9e6WR3I8ajT1//klcXGweO6wDYMOGGLKy\nChg2zPjGv/Xr42ja1IuKFU3/+fbsSadVKxeTTtDu58hR6dZwwmguhvHOStqxOaqiWMVENBqBau72\nVHM3/bUkiiKJGXmcv5nJucQszt+UMtA7z93C0ApipdVgbSllmC00AhpButVqBbSCcDcbrdVocLSx\nwN/DHv8K9vh7OOBfwR4fNzsszUwUqKio3KPciWKQxj0nE6VIrGBX+Q4UWq00xOPwEfNjtGkjidk9\ne9JNFsXdu/sybtw+Nm68wltvGVdvOnRoXSZN2kV0dDJ16jzaIi8szIeuXaszdepenn8++AFbsUdh\na2vJggU9adFiAe++u4Pvvutm0s/xOJydbZg8OYwJE0JZu/YiCxac4ocfTvDNN0exstLi7++Cv78L\nAQGuWFlpEUUoLNRx9WoGFy+mERd3m4ICHVZWWtq0qcqUKWEMGlQHa2vlnv7Z2QWMHLkeX1+XBzyJ\nDRw/nghA5coPOjkkJGTy55/RvPxyoxLF/bJlZ6lc2YE2bYyrI0hMzObo0SSmTze9y+369TwuXcpl\nzBjzxePhI/eG28jhdDrYaiFARnmTgUwSsMIJa5zkB1NRMRJBEKjsYktlF1va1b7XIJtXqCM26Q7n\nEjOJTb5DQZEenV68+1WkF9EX3+pE8W4mOiO3gO3Rt0jNLrgby0IjUNXNThLKFRyKRbMDjjYWCIKU\nTJJuDeVM938vYGWhoZKTjdknwSoqTwvlVBR7c429FJGHBTalLyiBYFfYkCDVLpo5tAuQrNm++hry\n8sDGjC35+9vh72/Ltm2pvPGGaTWP/v7OBAW5sW5dnNGi+MUX6/Phh3v59ttjfP9910ceIwgCs2d3\npk6d7/jii4N8/nmnUuOGhnrz1luhzJ59iI4d/enTJ9Ckn6UkLC219O8fSP/+geTmFrJv3zV2775K\nbGw6sbFphIcnUFSkR6MR0GgEfHycCAz0oGfPmoSFedOuna/RpQemIIoiY8ZsIiYmlR07XnjkY1gW\nzyd++P+mTNkJwIQJj8/EX758m7/+imXSpOZGl4389dcVALNcJ7Ztkxo+5QztOHwEguqAo3lubnc5\nnS6Nd1YiCZZFgupPrPLEYGOppW4VZ+pWcTZrfUZOIXEpd4hLzr53m5zNvpgUCh5juVkS9lZaAis5\nUaeyE3WKb2t6OWKjQFmZikp5oVyKYqe7zXbXccXMIt5igl1BXzzuuZG7+XGaNYXCQoiMhGZmXjLu\n3NmdJUsSKSjQY2Vlmgp47rkAPv30KImJ2VSqVPolPg8PO4YOrcuvv57hs8+ewdXV9pHH1arlwZAh\n9fjuu2NMmhRmVKnBrFkdCA+/xosvrqN+/Yr4+ytQEPoQtraWdO4cQOfO8v7+SvDLL6f49ddIPvmk\nDe3aPVqEfvppW1q08KF795p37zt+/AZLlpzmvffC8PV9fNnL3LnH0GgEXn/d+LTrqlWx+Pk5Ua+e\n6U/qbdtSqVjRyux6YlGUyid69zRr+QOcuS2v3v9+MkmgCjL94VRUnhCc7SxpWNWVhlUffH/V6UVu\n3M4lLiWbnPwiRKTXpIhYfMtd1wzD/TkFOi7ezCI6MZM/jyfwa3FToVYjUL2CwwNCuYqLLRpByjRr\nNAICoBEENAIgSP8Witc621qaNfhIRaWsKJei+H4HCrmi2NBsdzpdnihuWlyae/iI+aK4Uyc3vv8+\ngYiIDNq0MU1IDhpUk2nTjvLHH7GMHVvfqDVvvhnCwoWRLF58hrfeavrY46ZMacnSpaf58cfjfPBB\n61LjWllp+f33fjRq9BMDBqzi4MGRRk1fK4+cO5fMG29spm1b37/9bi5eTKV//1WsWTOQgAA33njj\nwd/xtGn7cHOz5b33Wj42fnZ2AQsWnKJfv9p4ext32T85OZedO+OZNKmRWaOpt29P49ln3c3+MLt8\nGVJT770mzOVWLiTl3XuNyiGfTArIVDPFKk89Wo2Aj5sdPm52pR/8CAxNhVE3Mom+kUl0YiYRl1JZ\nc9L0Pp5Kzja0quFBqxoVCKvugVspDdsqKmVNuRTFDlQCNIo021V3lMomTsusK65SBSpXvtdgZA5t\n27qh1Qps355qsigODHSjXj13fv89xmhRXL++F6GhVfjxxxOMGxfyWBEUGFiBjh39+fHH47z3Xkuj\nhjn4+bmyaFEv+vT5nSlTdvLFF6WXXpQ3cnMLGTToT+zsLFm6tO/fShu+/PIgp0/f4uuvDzFnzoMl\nKufOJbN+/QU+/rjNAy4VD7NiRTQZGfmMGWN8lvjPP2PR6UQGDqxh2g8EnDyZRWpqIZ06mX+GaKit\nlyuKDa9JZZwnpPcKJ9WOTUWlRO5vKny23j0bzNQ7+UQnZpKUmY8I6IvTznpRvPu9vjgtrRehoEjP\nyfh0tpy9ycpjCQgC1K3sfFckN67mipWZg4FUVP4pyqUo1mKFPZ6KDPDQaqRM1CmZohgkEXDkmPnr\nnZ0taNrUie3b05g+3fT1AwfW4IMPDpGQcAdvb+MufY8a1ZCXXtrIgQMJtGz5eMHw+ush9O79O6tW\nRTF4sHEOCL1712b06CZ8+WUEISGVHzuprTwiiiKjRm3k9OlbbNo05G8NdABnzkhOE1FRyX/7v6+/\nPoSNjQWvv16ycvzxxxMEBVUo8W/zMCtXxlKrlgvBwR5GrzGwfbtUT9yhg/n1xEeOSnX1QUFmhwCU\nH+8MqJliFRUzcXewplWNRzdll4ROL3I64Tb7Y1LYH5PMj/vi+G7PJeystIT6u9Oqhgchvm44WFtg\naaHBUitgqdE88G+1AVDl36JcimKQSiiUyBQDNHSDVVel+io55U9NQ2DtOsmj1c1MTdGxoxvTp1/m\n9u1CXFxMM3nv1686H3xwiDVrLhmdLe7fP5A339zGokWRJQqv7t1r0rBhRSZM2E737jWNtlubPbsz\nZ84kMXz4WqpVcyE09Omww/r884MsXXqaTz9tS9euj87IpqXlAlC37oMfJElJ2SxdeoahQ+uVWKN9\n5kwSR48mMnt2R6NLGZKScti79zrvv9/ErPKHHTvSqFfPgYoVzbfTO3IUGjUES5kzCk6mgY8deMjr\npQUkUazBAns85QdTUVExGq1GuFv7/Gb7GmTlFRJxKfWuSN51/u82lY+KYRDIlV1sCfV3o3mAO838\n3HFVSzJUFKTcimInqpDEaUT0CDKnVTd0g59i4Go2+MqwfmrRXLo9GAHdzXQj69DBjWnTLrNnTzq9\ne5v2AV6rlit167qzapXxdcUODlYMGBDI779H8803nR7rzqDVavjhh+6Ehs5nxoz9zJrVwaj41tYW\nrFkzkGbN5tO79wqOHHmFqlXN67Z+Uli79jzvvbeDAQOCeP/9Vo89Ljk5B+BvJwKTJm2nsFDHxIkl\nez8vWhSJpaWG5583PsO+Zk0cer1Iv36mD0/JzdURHn5blhVbXh4cOw5vvmF2iLucTJdem0qQxXUc\nqIzA01nbbiqCIPQGugFOwAJRFLeV8ZZU/iM42ljSKaginYKkCazxaTmcTsigQKejsEgaelKouzcA\npfC+7/OL9FxKvsPKYwksjpC832tXdKR5gDvN/d1p5u+Ocym+9SoqJVFuRbEj3ugpIIdk7PEqfUEJ\nGD54T6XJE8UhTcDCQp4obtbMGTs7DTt3ppksigH69vXn00+PkpSUg6encY0Wr7zSkIULI1mw4BTj\nxj2+4a5p0yoMGVKPb789wvjxoaX6Fhvw8LBj48bBNG++gB49fiM8/EXZgz3KisOHExg8+E+aNq3C\nokW9/paN3bv3CiNHruePPwawadMQ7OwsCQq693c8duwGixdHMmlSC2rVenx5Q3Z2Ab/+eoaePWvi\n4WF8w8zq1ZeoXt3ZLNeJgwczyM/XyyqdOHECCgogzLjhio8luxAuZMDAaqUfawyZXMcZBWZFPwEI\ngrAQ6A4kiaJY9777uwDfAFpgviiKsx4XQxTFtcBaQRBcgS8AVRSrlAnmNAUWFOk5nXCbiEupRMSl\nsvzwNRYduIIgQFBlJ0kgF2eRNYLBHaPYm/m+7zWCZD3qZGuBp6MCl6RUyj3lVhQbGmYyiZctiuu5\ngkaQLtf2lvG5aWcHDRvAgYPmx7Cy0tCqlSs7d5pX5Ny3bwDTph1l/frLvPyycUWdoaFVaNnSh6++\nOszrrzcpsZHu44/bsGLFWf73vwN8+WVno/cVGFiBlSv78+yzyxgw4A/WrRtU7hwpYmJS6dHjNypX\ndmT9+sHY2f09I/HRR3u4dCmdV17ZwNGjrzzwf6Io8s472/D0tOf990t28Vi0KJLU1FzGj3/8ScrD\npKfnsWtXAu+808Cs0omdO9OwsBBo1cp8u4cDEdJtc5nOZ2duS9ZRDRTIFOsoJJtEfAiTH+zJ4Bdg\nLvCr4Q5BELTAPKAjkAAcFQRhPZJAnvnQ+pdEUTRcs/6geJ2KSrnBykJDE183mvi6MbZ9DfKLdJy8\ndptDcalEXEpl8cGr/Lz/skkxQ3xd6dPQm271KuH8iPd2lf8G5VYUG2zZMomnEk1kxbKzgFpO9xp7\n5BDWAn78WfIsNremsn17VyZNiiUxMZ9KlUzLqAYHe+Dn58SaNZeMFsUAEyeG0qvXKtasuUD//o8f\nuFGjhjuDBtXl559P8NFHJTsnPEynTgH88EN3XnllA88/v5rly58zysniSeDatQw6dFiCKMLmzUPx\n9HyoFjgoCDE6mj3F38acqQQ8KIr37bvKvn1X+fbbrjg5Pf7vqtPpmT37CKGhVQgLM77BbtOmqxQV\n6end2zybwl270ggJccLR0fy3hYMRUL06eMk7T+Vk8WtRifKJO9xARP/UOE+IorhPEATfh+5uCsSK\nohgHIAjCCqCXKIozkbLKDyBIZ02zgM2iKJ74Z3esovLPYm0hNe2F+rvzVgdpWuCZ6xnkFOgkdwxR\nRK+/55AhPuSYcS01mzUnrzNlzRk+WR9F+0BP+jSswjO1PFWHjP8Y5VYUW+OENS5kck2ReA3dYP8t\n+XFaNIev58CpUxBipiVV27aSEti9O50hQyqatFYQBPr2DWDOnEhSUnLx8Hj0UI6H6datOgEBrsye\nfbhEUQzwzjvNWbbsDF99FcHUqW1N2t/LLzciIyOPCRO2Y2mpZfHi3k+8ML5xI4sOHX4lIyOP3buH\nU7PmQ6UJdnaQm8v9udka+YmS/ULUvXHkn30WjpeXPSNHNizx8davv0hc3G3+7//ambTPVatiqFzZ\nnqZNTVekmZlFHDuWxeTJviavNSCKkijuooD73qk0cLWCqqXPiikVg0uN01NSPvEYqsADdjwJQEmO\n6WOBDoCzIAjVRVH84eEDBEEYBYwCqFr1qf7dqTxl2FhqCfE17Yz69bbVOXM9g9UnrrMh8gabz97E\n1c6S7sGV6duoCg18XNRBJP8Bnmw1UgpO+JBZbLUklwauEJ8Dafny4hguG0ccMj9Gw4aOuLpasH17\nqlnrn3++FoWFelatijV6jVarYezYJkREXOfkyZul7K8SgwfXZdasA5w/n2Ly/t55pwWffdaO5cvP\nMHDgHxQUT096EklIyOSZZ34hMfEOmzYNpWHDSg8e0KEDYm7u39YJANHRd7/ft+8q27ZdYvz4UGxL\naQT59ttjVK3qRO/etYzeZ2pqLps2XWXQoBpm2Rft2ZOOTifSrp35/mdxcZCUJL90AiSLxPqu8txg\nDEgnzhocqSw/2FOCKIpzRFFsLIria48SxMXH/CSKYhNRFJtUqGC6FZeKSnlCEASCvV34pGcQh6a0\nZ+GIJoRV92DlsXj6fHeQdl/uZc7OGPZdTObgpRSOXknjxLV0ziRkcC4xk9ikLC6nZBOflsPNjDzS\nswvuTg5UKT+U20wxSKL4KnsQERGQ9+lpqF2MTIe2piVnH8DbW/qKOAxvjjUvhlYr0LmzO5s3p6LX\niyaLnPr1PQgKcmPp0guMHm2cpzDA8OHBTJ68m++/P85PP5XcKTh7dmc2b47ltdc2snv3cJPPoCdP\nboWtrSXjx2+lZ8/fWLWq/xPXfHf2bBLPPruMjIx8tm8f9mg7uZ07S33m5eYWMnLkevz8XP42YOnw\nCgAAIABJREFU1e5hoqOT2b37KjNntjUpg75yZSyFhXqGDatt9Jr72bQpBQcHLWFh5tcTG04EDS4s\n5lKklwZ3jK5Z+rHGIPUdeKLlyXp+Kcx1eKA+xLv4PhUVFROx1GpoV9uLdrW9yMwrZMuZm6w+mcBX\n2y+aFMfDwZoGPi408HGmgY8r9bydVXeMJ5xyL4qLyCGPNGyRMaMZKSsFUi2jHFEMUqbsYIS8GF27\nurNixS1OnsyicWPjxvsaEASBoUNrMWVKBFeuZOLra9x6FxcbBg8OYvnyKL74okOJda9eXg7MmtWe\n1177iw0bLtKzp/FZTQNvvRWKo6MVr766kbCwhWzYMJhq1RSY6asA27Zdon//VdjZWbJnz/C/Z4hB\nyhJDqaL4yy8jiI1NY+fOF7AvxVPzhx9OYGWlZeRI4yz1DCxbdoGgIDfq1zd9YIcoimzenEr79m5Y\nWZl/8SjiEDg4yB/aEZMJeTqor5AdWybxT009cQkcBWoIguCHJIYHAUPKdksqKuUfJxtLBoT4MCDE\nh8SMXK6n51KkFynSiRTqJas4nV5PoU6kqPj7Ir1Idn4R0YmZRMbfZse5e7WZARXsaeDjelco16ro\nqNYtP0GUc1F8r9lOrij2tIVKthCpQLNd82aw6g9ITIRKj9BSxtC5s/TzbN2aarIoBhg0qAZTpkSw\nYsVF3nvP+EbEMWMas3BhJN9/f5x33y3ZV2vkyEZ88UUEH364m+7da5p12X7kyEZUrepM//6raNp0\nPmvXDqR587ITMKIoMm/eUd56awt16lRg48Yhj/ZVDgqC6OiSBXGdOty4kcXMmeE891wg7dr5lfjY\nGRl5/PrrGZ57rnaJQz0e5tq1LA4cSGT69FCzat7Oncvm2rU8pkzxNXnt/Rw6DM2aglamqUhksfFK\nAwUm2enRkcUN2c24TxKCIPwGPAN4CIKQAHwsiuICQRDeALYiOU4sFEUxqoQwKioqJlLJ2ZZKzsb1\n6dxPRm4hpxNuExl/m1Pxt9l7MYk/T0iln1YWGpr7uzOtVxDV3BVoolCRRbk+PTE0zigx7hmkbLES\n455Di9tbDh02P4aXlzWNGjmyebN5dcV+fs6EhlZkxYoYk9Y1blyJzp39+fLLw+TkFJZ4rIWFhqlT\nn+H06VusXGn+52/HjgEcOvQyjo5WtGnzC7NmhaPT6c2OZy5pabk899xKxo7dTJcu1QkPf+nRgrhD\nB8T76oUfia0tREUxdeoeCgt1/O9/HUt9/HnzjpORkc+ECSX1R/2dlSulv/GgQebVG2zZIj3HunQx\n/8QyJwciT9977svhVBpYaiBQgRkv2dxEpOipyhSLojhYFMVKoihaiqLoLYriguL7N4miWFMUxQBR\nFGeU9T5VVFQknG0taVWjAm+0q8H84SEcfb8D4e+2Zd6QRrwQWo2T19Lp+s1+fjtyTa1DLmPKtSi2\nxgVL7BUVxecyQG7fV6NGYGUFh4/Ii9O5szuHDmWQmVlk1voBA6oTGZnCxYumKf0pU8JITs5h4cJT\npR47cGAQDRpUZNy4LSQlZZu1T4DatT04cuQVevWqzeTJO2nbdjFXrtw2O56p7N59mfr1f2Djxot8\n+WUn1q8f/OjykWXLEEurI7aygpwcYmJSWbjwFKNGNcbfv+S0Z3Z2AbNnH+HZZwNo1Mi0ywsrV8bQ\npIknAQHmqcht29KoXduOatVMz4AYOH4CdDplmuwi06GOMyhhY33PeeLpEcUqKirlG0EQ8Ha1o1tw\nJT7oXoet41vTsKoLk1ef4eXFx0jKyivrLf5nKdeiWEDACR+ylHKgcINCPZzPlBfH2loa4iHHgQIk\nUVxUJLJrl3k1HYZRv6a4UAC0auVDixbefPHFYYqKSs7YarUalizpQ0ZGHm+8scmsfRpwc7Nl5cp+\nLF7cm1OnblKv3vd89tl+cnNLzljL4fr1TIYM+ZN27X7FxsaCiIiRvP1288eWgojjxpXe0rlwITqd\nnhEj1uHgYMWUKY8fBW1gwYJIUlJymDLFtAETly9ncPRoEgMG1DBpnYHcXB1796bfLdcxF8NVkaZm\n2hDeT2T6vRp/uRhEscHXXEVFReVJo5KzLUteasbHPeoQHptCl6/3szWqZBcolX+GMhHF+VlZisWS\nbNmUyRQHF38QK1FX3KwpHDsOReYleQFo3twZe3st27aZtyEfH0eaN6/IH3+YJooFQWDixFCuXs1g\n7doLpR5ft64n77/filWrotmxI86svd7/2C+8UJ/Tp0fTvr0f77+/i9q157Fs2elSBboppKTkMH36\nPmrVmsvq1ef46KPWREa+RuPGj7ftKhr1GqSWUs7Svj0MHcqcOYc5eDCeOXO6ULmyY4lLior0fP31\nEcLCvE0a1gH3Tnj6969u0joD4eG3ycvTKyKKAwJArnNXch4k5irXZJdFArZ4YIlpY2QfR3qcvOe3\nioqKyqPQaAReDPNj49iWVHax4dUlx5m4KpKsvH8uKaTyd8pEFGdeU2bgBkgZoHwyyEdmeheo6QTW\nmnuNPnJoHlpcZxlpfgwrKw1t27qa7VcMUp3pqVMpnDljmp9wjx418Pd3YfZs42pAJk4MIyDAlTfe\n2ERhoXzfYV9fF9auHcSuXS/g5mbL88+voVq1r5kxYx/JyeaXaURHJ/Pqqxvw8ZnNhx/upn17f6Kj\nX2fq1LaPHNtsQAwKQvvzj6U21rFjB1eu3Ob993fRvXtNnn8+uNQ9rV17gcuXb/POO6YX5C5ffpGQ\nEE+jHUYeZtu2NKysBFq3Nj81axja0UyJLHHx+V+wQiYkkvOEclniI/PUicgqKir/HDW8HFk9Oow3\n2lbnzxMJdP1mP4fjzNcAKqZRJqK4KD8fUa9M1s9QK6hECYWFBuq5KjPuuWXxVfDwA/LidOzoRmxs\nLleu/H1AhDEMGVITS0sNv/xyzqR1Wq2GN98M4eDBBA4fLt3u1MbGgq+/7sKFC6l8991Rs/b6KNq2\n9ePYsVdYu3YgQUEV+OCD3VSp8hVt2y5mxox9RETEk5aW+8jmBL1e5OrV22zZEss772ylZs1vCQr6\njsWLIxk2LJizZ0ezbt2gUut9GTOmdKcJK6u70+vee28HAN9996xRbhDffHMUf38XevY0rVHu5Mlk\nIiNTGD685AmEJbF9eyotWrhgb29+AW9cHNy8Ca1amh3iLoZGVyUyxSIiWVzHUcF64rQY0xpXVVRU\nVEzFykLDhM61WPVaC7QagUE/H2Lm5nPkFz25g66eFsrEkk0URTKvX8fZR/6H1T1btgQ8qCM7XiM3\nWHlVyn7Jmabl7Q2+vrD/AIx70/w4HTpI6mD79jReeaWKyes9PGzp0cOPJUsuMGtWCywtjRc/L71U\nn08/Deejj/axdevgUo/v1q0GXbpU5913d9C2rR/BwaaPG34UWq2GXr1q06tXbaKjk1m8+BTbt8fx\nwQe7gd0AODhY4ePjhFarQafTU1ioJz4+g/x86U3EykpL27a+vPlmM/r3r4OXl4NxDz5mDOL335cs\niC0tYeFCAPbuvcLvv0fx0Uet8fEpvfFt796rhIfH8/XXHdFqTTtHXbQoGisrDYMHm+c6kZRUQGTk\nHWbMCDBrvYH94dKtEqL4RCr42EEFG/mxckmhiFxFM8VpsaaVIqmoqKiYS+Nqrmx6sxXT/zrHj3vj\n2HshmVGt/aniYktlF1sqOttgaeLnhkrJlJlPcVpsrCKi2A5PNFiRpVBdcSN3+CkGrtwBv5JLQUul\nZQvYvlOewA4MtKdKFWu2bEkxSxQDDB9em9WrL7F16zW6dy/ZK/d+HB2teffd5kyatIsDB+JLrXcV\nBIHFi3sTHPw9w4at4ciRl7G2VvYpVqdOBf7v/zryf/8HycnZHDgQz+XL6Vy5cpuEhCxEUUSr1WBh\noaF371rUrOlOjRruNGlSGQeHkgdn/A1jBDHAokUwdCjJydkMHbqa6tXdmDix9IY5URT54IO9VKrk\nwKhRDU3aWkGBjt9+u0ivXv64uZmnILdtky7JdewoLy0bfgBcXSHQ/IT1XU6kSa9BJTCMgFeqyU6v\n05F+6ZIisVRUVFSMwd7agpl969Eh0JN3/zzD2yvv1WQKAng6WlO5WCRXdra5+29vV1tqV3RCa8b8\ngP8yZSqK/dq2lR1HQIMjVchUaKJpo2J9cCJNAVEcBkuXS5eXA8xMxgmCQLduHixffpP8fD3W1qaf\nFXbpUg0PDxuWLDlvkigGaZjHF18c5uOP97Fjx9BSj/f0tOfnn3vQs+cKpk7dy2eftTd5v8ZSoYI9\nvXubN9a4NMQxY8AYQTx6NAwdiiiKvPDCWlJScoiIGGmUAN++/TLh4fHMm9cZWxNHf27ZcpWUlDxe\neMH8n3/jxhS8vKzMGg5zP+EHIawFaGQmLLIK4WImDPWXF+duvGJRrFSmODM+Hl1BgSKxVFRUVEyh\nfaAXB97zICE9lxu3DV950m1GLuduZLIj+hb59zWkezhY0SHQi85BFWke4I6NCVeK/6uUiSgWBEHR\n2jwnvEnDtJnkj6OeK1gIkih+rpq8WGHFA+H2h5svigF69PDgp5+us29fOh07mp5Gs7LSMmhQTebP\njyIzswAnJ+Mzpvb2VkyaFMqECTs5dOg6oaGlZ6t79KjFiBEN+N//DjB4cF3q1VOmjOLfoujV0Wh/\n+qF0QVynDnz3HQALF55ky5ZY5s7t+uiR0A8hiiJTp+7Hx8eJkSMbmLzHJUsuUKGCLZ07VzV5LUBh\noZ4tW1Lp27eCWZMIDSQnw4ULMOIFs0PcJTINRO6dmMolk3gssccaZbr2UtV6YhUVlTLE2kJLQAUH\nAio8uvxPFEXSsgtIzMgjJimLneeS2Hg6kRVH47G30vJMLU86BXnxTC1PnE1MxPxXKJNiFK21taK1\neY54k00SOvJlx7LRQh0XOKlAs12dOuDiAgcOyovTrp0b1tYa/vrLNAeJ+xkypCZ5eTrWrjX98u+r\nrzbCzc2WmTON7xr84ouOuLpKrhHZ2eUku7ZsGYVVfIwTxKNH322sS0rKZuLE7bRqVZXRo42zYNi7\n9xoHDyYwaVKoySUmmZkFbNhwmYEDa5hUI34/Bw9mkJFRRPfu8jzUDkZIty1LnghuFCeKX3NKieIs\nruOED0Lpf02jUOuJVVRUnmQEQcDdwZq6VZzp09CbuUMacfzDDvzyYgg9G1Th8OU0xq04ReNPtzNs\nwWGWHLrKzQx1UMj9lIkotrC2VjhT7APFneZK0MgNjqdKtcBy0Ggka7YDEfLi2NlpadvWVZYoDg2t\niJ+fE8uWmZ5Rd3CwYuzYJqxfH0NUVLJRa9zd7Vi6tA9nzybx2mt/PfmjK5cto2jky1jeSDBOEBdn\niAsLdQwa9AfZ2YX8+GN3o7OuM2cexMvL3qws8Zo1l8jP1zFkiHkNdgB//ZWCpaUgu574wEHJeKNJ\nE1lhAEkUe9lAJWUshckkHkfMq8N/FGmxsVjYmj/1T0VFReXfxtpCyhDP7FuPI1Pa8+foFoxs5UdC\nei4frj1L6MydjF56HL3+Cf+M/pcoG1FsY0PapUuK27IpNcSjoRskFQ8RkEtYCzh3DtJkZp67dfMg\nNjaXmJgcs9YLgsCQITXZsSOe69fvmLx+7NgmODpaMWXKbqPXdO5cnU8+acPSpadZsOCkyY/5b5GW\nlkvqa+OxyDfijPk+QQwwfvxWdu++ws8/9yAw0Lisa0REAtu2xTFuXIjJtcQAS5dewM/PidDQiiav\nNbBpUwqtW7vi6CivgurAQWjcCGwUcIs4qWCTXQFZ5HMbJ8wrL3kUaTExuMmpg1JRUVEpQzQagcbV\nXJncNZBd77Rhx9utebmlH5vP3mTFUWX0U3mnzMoninJzybpxQ5F4jlRGQEsGygwFMVy+VaKEwlBX\nLHfkc9euklrYtMn8bPGLL9ZBrxdZuDDa5LXu7nZMntyC9etj2LfP+N/zlCmt6NjRn7FjNxMVlWTy\n4/7TbNoUQ2DgPFzvGJEBf0gQL1kSybx5R5kwoTkvvFDfqMcTRZF33tlBpUoOjB1r+rSLuLgMduyI\nZ/jw2kZ5ID+K+Pg8oqKy7z6nzCU/X5raGKZA6USeDqJvSyekSmB4L1BUFMfG4lbdvMmBKioqKk8S\ngiBQ3dOR97sFEurvxv9tOU/KHfklqOWdMiufAOVq9DRY4kBlMhUSxfUVFMVNQ0CrlS+KAwLsqFHD\njq1bzZ9sExDgTPv23ixceM6sSyVvvdWUKlUceffdXUaXQ2i1GpYs6YOjoxX9+q0iLU2B9LtMRFHk\n6NHrjBixlm7dluPlZU9RpRIcCrTavwniS5fSGDNmE61aVWXWrA5GP/aaNReIiLjOtGmtTbeIAxYs\niEajERg5MsjktQY2b5ZOrOSK4hMnoKBAGVF8Nh2KROVEcSZXAXBWSBQb7NjcatRQJJ6KiorKk4Ag\nCEzvXY+cgiI+22TakK+nEUVEsSAIXQRBuCAIQqwgCO+VdrxF8bVWJbu5nfFRTBQ7WkJ1R2VEsZ0d\nNKgvv9kOJBGze3c6ubnmT7V5+eUgrlzJZOdO0y+V2Npa8sknrTh06Drr1xtfm+zl5cCqVf2Ji0un\nV68VFBSU3VSepKRsOnZcQtOm81m5MoqJE1tw6NDL7Ok0imweKmWws4OlS6Go6AFBnJqaQ7duy7Gw\nkAS/sUM3ior0TJmyh8BAD0aMMC6z/PD6RYvO8eyz1fD2NnL4yCPYvDmVqlVtCAy0NzsGwMHiE73m\nobLCAPdea0pmii2wxRYPReJlXb+OrqAAV7V8QkVF5SmjuqcDo1r7s/rEdQ79x0dKyxbFgiBogXlA\nV6AOMFgQhBJHy2mtrNBYWipqhO9EVe5wSxEHCpA+nJUY9wzQojkcOSppKzl06eJOXp6e/ftvmx2j\nT58A3NxszCqhABgxoj7Vq7vyySf7TWqea9PGl8WLexMefo033tj0rzbeZWXl8+ef0QwbtoZateZy\n4EA8s2d3JjHxHXr3rk3LlgvpvFjPN0Ej0TsUm1NXqwY//QRDH/Rmzs0tpGfPFVy5cpsNGwZTrZrx\ndl/Llp3lwoVUpk9vg4WF6S+9LVuukpiYzciR5k9uLCzUs3NnGl26uJtdfmHgYAT4+4OXAo57p9LB\nyRL8zNf6D5BJ/D/iPOGuZopVVFSeQt5oWwNvV1s+WHuWgiJl+r3KI0pkipsCsaIoxomiWACsAHqV\ntsjV319hB4qqgF4xB4qGbhB3B24r4CbWojnk5EBkZOnHlkSbNq5YW2vYssX8Mzlray1DhtRkzZo4\n0tNNt2KxsNDw4YctOXXqFqtXXzBp7aBBdZkypSU//3yCuXOPmPzYpvLRR7sRhKk4Oc2iX79VbNoU\nQ6dOAXz1VSd0Oj1Dh64mLGwhyck5rFjxHJPPfIfmjdclO4UrV/4miPV6aUBHREQ8S5f2pWVL4y/N\nFxbqmDZtPw0betGnTy2zfp6FC6Px9LSlWzdfs9YDRERkkJWlo3NneaUToiiJ4ubNZIW5y8k0aOAG\nSg1fyuSa4vXEgFpTrKKi8lRia6VlWq8gYpPuMD88rqy3U2YoIYqrwAO2DwnF95WIW/XqpCmaKVbe\ngQLgdLr8WC2LJ/7u2y8vjsGabf36ZFmZ1hdfDCQ/X8fvv5t3UjJkSF2Cgirwzjs7yMkpNGntp5+2\no2fPWowbt4WFC/9ZRwqd7sGz3dzcQlaujGLMmE1MmLCdc+dSeP/9Vpw//zoDB9YtMXMqiiITJ27j\njz+i+fzzjvTrZ1q2du7cY8TF3WbatDZmZWiTk3PZsOEKw4bVNtubGKQpdpaWAu3by6tTiI2Fmzeh\nVUtZYQDQ6aXXWQNX+bEA8skkn4y77wlKkBYbi9baGscqylm8qaioqDxJtKvtRecgL+bsjCE+zTyn\nq/LOv9ZoJwjCKEEQjgmCcCw5OVkSxbGxil1GNzhQKCWKGyjYbOftLV1m3itTFAP07l2BS5dyiYrK\nNjtGw4YVqFvXncWLz5u13sJCw7x5nbl6NYNZs0wrltZoBFaseI5OnQJ4+eX1LFr0zwnjGTPaExU1\nhv/9rwNDh9bj1Vcb8+mnbVm9egCJie9w6dKbTJ/eDnv7khveRFFk/PitfPXVIV5/PYS3325u0j5u\n3Mji44/30bVrAN26mZdp/O23ixQV6Rk+3PyxzqIosnZtMu3aueHsLM+KzXCC16a1rDAAxGZBdpGS\nTXZSb4FSTXYgiWJXf380WnVMqoqKytPLxz2C0AgCn6yPevLnC/wDKCGKr8MDKRnv4vseQBTFn0RR\nbCKKYpMKFSrgGhBAYXY22bduKbCFew4UStmyVbSVBgkoIYoB2rSSxj3LtWbu2VPywl2/3rghGo9C\nEASGD6/NoUM3iYoyrxSjTZtqDB4cxOefH+LatQyT1traWrJ27SA6dgxg5Mj1rFwZZdYejKFOnQpM\nnBjG0qV9mT27Cx980Jo+fQKpWNG44lVRFHnvvR18881h3nqrGd9+29XkTO+UKXvIz9cxZ04ns7LE\noiiyaFE0DRp4UK+e+Y1j58/nEBOTQ8+e8pvP9u6DChWglnmVIA9gqN2vr1Cm2HBirLgdm9pkp6Ki\n8pRT2cWW8R1qsvN8EtuildFn5QklRPFRoIYgCH6CIFgBg4D1pS0y1OYpXUKhVKYYpGyxUqK4dStp\ngMc5mY4nlSpZExLiJEsUA4wYEYi1tZZ5886YHWPWrLaAJPpMxcbGgjVrBhIWVpUhQ/7kxx+Pmb2P\nfwq9XmTKlJ38738HGTOmCV991dlkUXvs2A0WLz7N+PFNqV7dvFRoRMRNTp1K4dVX65q13oDhOWM4\nsZLDvnApSyyzVw+QXmOWGmm8uhJkEq+o84QoipIoVpvsVFRU/gOMCPOldkVHpq6PIjtfpkNAOUO2\nKBZFsQh4A9gKnANWiqJYaurvrihWyKsYJFF8h0R0mFbn+jiauEPUbchV4DnRupV0u3ef/Fg9e3pw\n+HAmN2+a77Th4WHLoEE1+PXX82RmmtdNWLWqM2+/3ZRly85y9Kjpg1js7CzZvHkonTtX57XX/uLj\nj3c/MZdr8vOLGDZsDbNmHWDUqEZ8++2zJgtiaVDHTjw97ZkyJczsvcybdxonJyuef15eWnb9+mQa\nNnTE21ve+Llr1+DqVWhl/o/0AMdSoZ4LWCtUmSCNd/ZWzHniTmIiRbm5qh2biorKfwJLrYbpvety\nIyOPOTuVM0QoDyhSUyyK4iZRFGuKohggiuIMY9a4VKuGoNUqbMvmA+i5o5ADRRN30IkQqUCznZ8f\nVK4M+w/Ij9Wjh5TpkzPdDmDMmHpkZxeydKl5tcUA777bAk9Pe0aP3kyRGTYuDg5WrFs3iJdeasC0\nafsYNWoD+WV8ZioCnTsvZfnyM3z2WTt++KE7GjNsEVauPMe+fdeYOrUVTk7WZu0lKSmHVatiGTEi\n0KxhHwaSkwuIiMhQpHTCUE9sONGTgyhKojhEmaQuIIliReuJi9+jVOcJFRWV/wpNfN0Y2MSHBeGX\nOX8zs6y3869RJhPtQPIqdq5aVfFMMaBYXXGTYteqYwp4WQuC1Km/P1wSAnIIDnbAx8eaDRvkieKQ\nEC8aNarA99+fNTtD6+Rkzdy5nTl+/CbffGOezZqFhYb583vy/vutmD//JGFhC7l0SaG6FRO5cSOL\nggIdBw/Gs2xZXyZPbmVWHXBqag5jx26lSZNKvPxyQ7P3s2jROQoL9bz2mrzSic2bUxDFeydUctgf\nDk5OUK+e7FBcyoKMQmisUJNdAXfIIw1HSphQaCJ37djUTLGKisp/iPe61sbRxoIP1pw1awpueaTM\nRDEU27Ip6FXsSGVAQxYJisSrYgeeNnBcoQEvrcLg+nXJAlcOgiDQrZsH27enkZ9vfueeIAi8+mpd\nzp5N5fBh8wvq+/WrTY8eNfjoo31cvWpa0939e5k+vR1r1w4kLi6dhg1/5Pffz5q9J1PR6fRMn76P\nJUskM+k9e0YwZIj5qm/ChJ2kp+exYEE3swZ1gFTT/NNPZ3nmmSoEBspTjRs3plCpkhWNGjnKigPS\n1Y6wFtL0a7kYXluN5dkm38XQU6C084Sg1eJcrZpiMcsaQRCeEQRhvyAIPwiC8ExZ70dFReXJw9Xe\nisldAzl2NZ0/jiujq550ylYU16hBakyMYnWkWqxxwEuxcc+CIH1YK5EphnuervvD5cfq1s2D7Gwd\ne/fKq+0YPLgm9vaW/Pij+QJUEATmzu2MIMAbb2yRtZ9evWpz8uSr1K3ryaBBf9K9+3JiYv7ZsZOH\nDiUQFraQDz/cTe3aFbCy0tKihfket7t3X+GXX04zcWIowcHmj3vbtSueuLhMRo2SlyUuLNSzdWsq\nzz7rIXuKXWqq1CzaUqF64uNpYKWBugo22QE4KulRHBODq58fWkvL0g/+FxAEYaEgCEmCIJx96P4u\ngiBcEAQhVhCE90oJIwJ3ABtQKIugoqLy1NGvsTchvq7M3HyO9GwFppk94ZSpKHavWZP8jAxyUuSV\nAdyP5ECh3Ht8YzeIzoAcBcpcg4LA2RkOmGbt+0jatXPDxkbDX3/J+905OloxeHANVq6MISPD/Ma9\nqlWdmTq1NRs3xrJ+/UVZe6pWzYW9e0fw5Zed2LfvKkFB3zFp0naSk833Zn4Uly+nM3jwnzRvvoCr\nVzNYurQPPXvWlNWeVVCgY8yYLfj5ufDhh/ImW/z8cxRubjb06eMvK86BA7fJzNTRrZv8wl3Dc1eJ\noR0gZYqDXcFKoSa7LOLRYoU98stEDKTFxOBes6Zi8RTgF6DL/XcIgqAF5gFdgTrAYEEQ6giCUE8Q\nhI0PfXkC+0VR7Aq8C0z9l/evoqJSTtBoBKb3rkdWXhGzNpvff1ReKFtRXGxxlHpRnoi6H0d8yOIG\nepRp1mrsDnqFmu20WmnksxLNdnZ2Wtq3d5M93Q7gtdfqkZNTxIIF0bLivPlmCPXqeTJq1CbZAtbS\nUsvbbzfn4sWxDB0azOefH6Rata8ZM+Yvzp83/0RAFEV2777MgAGrqFHjW9atO8+HH7acwaUiAAAg\nAElEQVQmJkZ6HLl+BZ9+up/z51P59ttO2Nqan1m8fv0Oq1fHMXx4bWxs5A3aWL8+BSsrgQ4d5Bfu\nhh+QpmCHNJEdClGEE2nQSKF6YjA4T1RBQBmVLYoiqTExuD1BolgUxX3Aw0X3TYFYURTjRFEsAFYA\nvURRPCOKYveHvpJEUTTUXaUD5nWBqqio/CeoVdGRkS39+P1YPMeulE2/z79FmWeKAUXrip3wRqSI\nbG4qEs9Q63hCoSv4LcOky89pCjyv+vatwJUreZw8mSUrTuPGnrRqVZk5cyLNcpAwYGmpZenSnqSn\n5/Hqq5sVKYupWNGBRYt6ER09hkGD6rJgwUkCA+cRHPw9H3ywi8OHE8jLK/kEKCenkE2bYnjzzc1U\nr/4t7dr9yo4dcYwfH8rFi2OZNq2tLGcHA+Hh8Xz22UGGDw+mWzd5nrbffhuJXi8ydmywrDiiKPLn\nn0l06uSOo6M8cQ2SKG7SGGzkuboBcPkO3C5Qrp4YDKJYudKJrBs3KMzOvnsC/wRTBR4waU8ovu+R\nCILQVxCEH4ElwNzHHPPAFFIVFZX/LuM61KCKiy1T1pyhQIZOeNKR/ykpAxdfXzQWFopmig1TrDK4\npkgHurcdVLCRMlpKENZCut0fDr16yovVq1cFRo06z59/JtGokZOsWG+/3YA+fTaxdm0c/fqZbz0V\nHOzFjBnPMHHiThYvPs2IEfVl7ctAYGAFFi7sxaxZHVi69DTr119g5sxwZszYj0YjUKOGG4GBFXBw\nsMLCQoMgQHx8JjExqVy7loEogq2tBW3b+vHxx23o37/O4zO5ZtTdZmbmM2zYOqpVc2bOnE6yftbs\n7EJ++imKPn388fNzlhXr+PEsrl3LY+pUeSUYALm5cPwEjBsrOxSgfJNdEbnkkIwf8n7/92M4YX/a\nBneIorgaWF3KMT8BPwE0adLkv9F6rqKi8kjsrCyY1iuIkYuP8dO+S7zR7ul6TzRQpqJYY2GBq7+/\nwqJYyhJJzXYtZMcTBOnyrlIOFM2aSlm2PXvli2J3dyvatHFh9eokZsyQ56Hao4cf/v5OfPPNKVmi\nGGD8+KZs2BDDW29tp0MHP7y95Qn2+/H0tOftt5vz9tvNSU3NYefOy5w5c4uoqGQuXEglN7eQoiI9\ner1IlSpOhIVVZfhwV8LCqtK6dTXZpQiPY8KEHVy7lsn+/S+Y7UlsYMmS86Sn5zN+fAPZ+1q9Ogmt\nVqBHD/n1xAcjoKAAnmkjOxQgnWhaCMo32SnpPGF4byoHmeLr8ECK3Lv4PhUVFRVFaB/oRbd6lZiz\nK5Zn61XCv4JDWW9JccpUFEOxLZuCXsUW2GBPRcW8ikESxZ9HQb5O/tQtGxtoHiqJYiXo08eTsWMv\ncP58NrVr25sdR6vV8PrrwbzzTjinTiXToIH5jUparYaFC7sTHPwzw4dvYOvWwWbbkpWEu7sdAwYE\nMWBAkOKxTWHTplh+/vkUkyY1p0ULeVcnRFFkzpxIGjWqQIsWlWTvbc2aJNq0ccHdXX55yJ69Ul28\nUk12J1IlQazUJLsMrgLgjHLWaakxMWitrXGuqpzQ/oc4CtQQBMEPSQwPAoaU7ZZUVFSeNj7uUYd9\nMcm8v+Ysy19pJtvR6EmjTGuKQbosmaagLRtImSLDB6QSNHKHIhHOKNBsB9D2GYg8rUxdce/eknhd\nsyZJdqyXXqqDnZ0Fc+eelh0rIMCVefM6s2vXFT76SKEzgCeQy5dv8/zz6wgO9mTq1Nay4+3alcC5\nc+mMHVtf9pvNhQvZnD+fQ58+nrL3BbB7DzRuBI7yrY7vNdkpWE+cwbVi5wnzbfAeJi0mBreAAARN\nmb9V3kUQhN+ACKCWIAgJgiCMFEWxCHgD2AqcA1aKohhVlvtUUVF5+vB0suG9rrWJiEt9Kr2Ly/yd\n3r1mTQpzcsi6cUOxmE5U4w430FGoSDxDd/xJheqKn2kjiQLDuFw5eHvb0KSJE+vWyW+EcXGxZujQ\nWixffpG0tDzZ8UaMqM8rrzRg5syDbNigXInMk0JubiHPPfcHogirV/dTpDTju+/O4O5uw6BB8i/X\nr10rPSd69ZJvT5adDUeOSid0SpCQAyn5SjtPXMWJqoo5T0CxKH7CSidEURwsimIlURQtRVH0FkVx\nQfH9m0RRrCmKYoAoijPKep8qKipPJ4NDqtKkmiszNp0j9Y75Vq5PImUuig0fOEo6UDhTFREddxQq\nqfNzAGdLadCAEjQNuVdXrAS9enlw+HAmiYnyn5xjxwaTm1vEvHnys8UAc+Z0plGjirzwwgazp909\nqbz55jZOnrzF0qU9CQhwlR3v0qUM1q6N4+WX6ygisNeuTaZxY0d8fORbRUQcgsJC5eqJDSeYDRUU\nxRlcu9tToASiXk/apUtPnChWUVFRKUs0GoGZfeuRnV/E9L/OlfV2FKXMRfFdr2JFbdnuOVAogSBI\nH95KZYqtrSW/4r37lInXq5d0eXzjRvlDUOrV86BbN1/mzIkkJ0d+pt3GxoJVq/qi14s899wfZD8l\nE3F++SWS+fNPMXlyC9n2awb+97/jWFpqGDdOfoPdzZv5HD6coUiWGKTnqlZ7zz1FLidSQQDqyz+X\nAKCALPJIU7SeOCM+Hl1+fnloslNRUVH5V6nh5cjoNgGsOXmd/TFPj2VjmYtiJx8ftFZWimaKHfFG\nQKPYuGeAJu4QmQYFOmXitWkt1RWnK1CnXLeuPb6+NoqUUABMntyYlJQ85s+XN8zDgL+/K8uW9eLk\nyVsMHrwWna58exzu3HmZV17ZRLt2vkybpkzqNDExm19+OceLLwZSqZL5DZMGNm5MQRShZ0/lRLFS\n9cQAR1Mh0BnsFZqcbDgBdlLQeeJptWNTUVFRUYIxbavj72HP+2vOkquUOCpjylwUa7RaXAMCFHWg\n0GKJA5UVdaAI8YB8PZy5rUy8Nq2luuJwBabbCYJA376ebNuWyu3b8rO7YWGVCQurxOzZp2QN87if\n7t1rMGdOJzZsiGHixJ2KxCwLoqKS6dv3T2rXdmf16ucUc9X45ptTFBWJTJjQSJF4f/yRhJ+fLcHB\n8i1zcnPh8BHpOasEoiiJ4qbyXeLukvkPOU9AubBjU1FRUfnXsbHUMqNPPa6l5fDNTuUSm2VJmYti\nKLZlUzBTDFLGKFNBB4qQ4i75o/IrFACprtjKSrkSioEDvSgsFO82V8ll4sRGXLmSyR9/KHey8vrr\nTXjzzRBmzz7C998fVyzuv8WtW3fo1u137Ows+OuvgTg7KzDWDcjMLOCHH87Sr18AAQHyhnUApKQU\nsGNHGgMGeCpil3P4iORP3LqV7FAAXMuG5Lx7ryklyOAaFthii3JKOy02FgtbWxwrV1YspoqKisrT\nRPMAdwY08ebn/XFE38gs6+3I5skQxTVqkHbpEqJeucvqzlTlDjfRoUxnpK8DuFvDMYWGeNjaSoM8\n9ocrEy8kxAlfXxtWrbqlSLwePfyoWdOFL788qahd3ldfdaBbt+q8/voWFi9Wppnv3yA5OZuOHX8j\nKSmbjRsHUrWqfPFqYOHCaDIyChTLEq9Zk4xOJzJwoDLWZPv2S3X1LcMUCcfR4tdQiKKZ4nic8EFA\nOc/MJ9GOTUVFReVJY8qzgbjYWjJ5zRl0+vI9/PKJeLd3r1GDotxchW3ZqgIimSjjoycIUl3xUYVE\nMUiZt+Mn4M4d+bEEQaBfPy+2b08jPV1+CYVGIzB+fAOOHUti717lBmNptRpWrepL+/Z+vPjiBpYs\nOaNY7H+KlJQc2rdfTkxMGuvXD6BxY/lDNQwUFur45ptIWrWqTEiIMiJ21apbBATY0qCBMgXA+/ZD\n/WBwUWjy3NEUsNRAsEJNdiBNsFSydAKkTLFaT6yioqJSMi52VnzUow6R8bdZEnGlrLcjiydCFLtV\nl8YKK+lAYRj1qmSzXYg7RN2GnCJl4rVuBTqdZHelBP37e1JYKLJ+vTIlFMOHB1Kxoh1Tpx5RJJ4B\nW1tL1q3rT7t2vowYsYEVK57cGQNpabl06LCMmJg0Nm4cQIcOforGX7LkAleuZDJpkjJZ4pSUAnbt\nSqd/fy9FSicKC6Xnp1JT7EC62lLfVblJdvlkkE+Gok12ep2O9EuX7r43qaioqKg8np71K9O6ZgU+\n33qBG7dzy3o7ZvNkiGKDV7GCzXYOVEbAgkziFYsZ4gE6EU4pZM3WojlYWMCu3crECwlxwsfHmj/+\nkD/dDsDW1oL33mvMnj3X2b1b2ck1dnaSMG7Z0ochQ9YyZ85RReMrwdWrGbRuvYTz51NZt64/7dsr\nK4gLCnR8+ulRQkI86dbNV5GY69ZJpRP9+yszxe7wYcjJUa7JTi9KoljpemJQ1nkiMyEBXUGBmilW\nUVFRMQJBEJjRuy46UeSjdVGKll3+mzwRotjJ21txWzYNFjhSWXFbNlCuhMLBAUKbwQ6FzBgEQeC5\n5yQXisxMZdLZr75al8qV7RXPFgPY21uxefMgevWqybhx23j77e3oy7oeqfiFfOz/2zvv8Cir7I9/\nbia9VxIghCRAAqxU6aCCIIJSRERhsaAuKmvd1RVZV3821rYKuqKra8GCHRWlSAcFpElvgVATSgqp\nJCFt7u+PdwaQTRDIvZkZuJ/nyZNkHM+9L5N55/ue93vOWXuIrl0/IDOziNmzR9K/f7LypT76aAf7\n9hXx9NPq5sdPn55NYqI/HTqosU4sWmJZh1RNsksvhqJKuFShKC46IYrVDe5wXqCbTLHBYDCcHU0i\nA/lLvxQWbM9i7tYjrt7OeeEWotjLZiMiOVlpphisD0mVbdkaBULDAPhVoa+475Wwbj0UKGr1Nnx4\nLBUVktmz1bTJ8Pf35tFHO7J06UF++kmdt9hJYKAPX389nPvv78SkSasZMWI6RUWuHRtZLeGKKz7B\n39+bFStu48orE5WvUVlZzT//uZbOnRswYIAaL2xhYRULFuQxfLiarhMACxdBxw4QqWjy3FrHn6Xq\nIjtvAglAndLOM+3YDAaD4Zy5s1cSrRuG8uSMrZSUK/Ka1iNuIYpBX1u2ErKoUtSBAqxssaoOFABX\n9gG7Xd3I5+7dw4iN9WX6dDUWCoCxY/9AgwYBPPecHouDzebFa6/155VX+vHddzvp0OFd1qxRV3R5\ntpSVVTJ//h4qKqpp3TqalSvH0Lq1muEXpzNt2k727i3iiSe6KBOwM2fmUFkpuf56NdaJkhLLT9z3\nSiXhAGtUur8NWqtr3qGn80R6Ot7+/qYdm8FgMJwD3jYvHh2QSnZxOWv2KfKa1iPuI4pTUpS3ZbNu\np0qKFXWgAOu2745COFb3Bg+AZZ8ICFDnK7bZrEEes2blUlys5iotMNCHhx/uwPz5GaxereeWiBCC\nv/61Kz/9dAtVVXZ69PiQF19coWx4yO+xeXM2Xbp8wLr1WXjbvFi27Fbi4uo++KImqqvtvPDCWtq1\ni2bQoERlcb/8MotGjfzo1k2N4ly+wiq0UymK1x6F9hGgaOYJ4Ow8oc5PDHA0LY3IFi1MOzaDwWA4\nRy5tGoEQsDGj0NVbOWfc5owfnZpKVVkZhRnqCuNCNXSg6BQFElin6ALI19eq7F+0RE08gD/+MY6y\nMruyQR4A48a1ITranwkTftFqoO/ZswkbNvyJoUNTeOyxxbRv/y4LF+7Vtt7Ro6U88MBcOnR4l+zs\nUkbc0AofHy/8/Ly1rfnRRztISyvgH//orCxLnJdXyZw5Rxk5MhYvL3XWCR8f6NlDSTjsEtYdVesn\nLqdIeecJgKM7dxrrhMFgMJwHIf4+NIsJZlOmIl9oPeI2ojgqJQVAqYUixNGBQqWv2PmBrtJX3Kc3\nbN0KWWrmbtCjRxhNm/rz2WfqsrohIb488UQXFi3KZN48df+eNREREcBXX13PN98Mp7S0kn79PuW6\n675SaqkoKirnlVdW0qLFW0yZ8itjx3Zg69a7SE5W1Iy3FsrKqnjyyVV06RLL8OHNlMWdPj2bykrJ\n6NFxymIuXmINmAkKUhNvZxEcqzpZsKqCQvYBKM0UV1dWkr9nD1GpqcpiGgwGw8VE2/gwNmYWelwX\nCvcRxY4PoNy0NGUxvfAmlPgTH5wqiAuARoqL7fpcYX1X5Sv28hKMGhXHvHl5ZGdXqAmK1YkiKSmU\n8eNXaO8SIYRg2LCWbNt2NxMn9mbx4v106fIBvXp9yBdfbKOk5NyPS0rJ1q05PPDAXOLjX+eRRxbS\nqVNDNm78E2+9NZDo6EANR/Jb/v3vjWRmHuOll3oqyxIDfPrpEVJTA5V1nSgstAbLqOo6ASffMyoz\nxYWOUe5hJCqLWbBvH/aqKiOKDQaD4Txp3ySc3GPlHCo87uqtnBNuI4qD4+LwDQ7m6M6dSuOG0fTE\nB6cqLo2yCoaUxbsUQkKszJwqRo2KpbpaKi248/Oz8eyz3di4MZevvlJbFFkb/v7e/P3vPcnMvJ9J\nk67i8OFjjBz5LVFRrzJgwGe8/voali7dz5Ejx/7nirS0tJItW7L5+uvtjBs3h+TkKVxyyTu8/fZ6\nhg5NYc2a25k3749ccomawrTfo6CgnBde+JWBA5tyxRWNlcU9ePA4S5fmM3KkmoEdYI0ft9vVi2J/\nG7RSWGRXyD58CcUPdRl+5znI2CcMBoPh/Ggbb52TN2V4loVCn3HyHBFCEJWSQp5yUZzIAZZSwTF8\nUVM41TkaZmZCYQWE+dY9nre35SterChTDNCmTTCtWgXx2WdHGDcuXlnckSNb8MILv/LEE6sYPrw5\n3iorps5ASIgfDz3Uhfvv78SSJfuZOTOdWbPSefDBeSeeExzsS0CAN0IIpJTk5JSe+G9BQT707ZvI\n+PHdGTYsldhYPUV0Z+KVV9aTn1/OxIndlcb98ssspIRRo9RZJ5YsBT8/6N5NWUhW50KHSLVFdoXs\nJ4ymSjtPnBDFJlNsMBgM50WrhiH42AQbMwsZ2Kahq7dz1riNKAbLV5y5apXSmGFYPWCLOEA0rZXE\n7BptFdutPQp9Fb3WfXrD7Dlw+DA0VBBTCMHIkbE89dQeDh48TuPG/nUPitU+7bnnunHddbP44INt\njB17iZK457J+375J9O2bxKRJV3HgQCHbt+eSlpbH7t35VFRUn8gYN24cQosWkTRvHkGbNg20Fs/9\nHllZpUyatIERI5rToYPaNm+ff55F+/bBpKYqMv9iieJuXcFfzZ8NlXbr7so9KWriAUjsFHKAJK5S\nFxRLFPtHRBAYpdDnYTAYDBcRft42WjUMZaPJFJ8/kSkpbP3yS6rKy/H281MS0ymKC9mnTBQ7R9Su\nylUnins7xuguWQqjRqqJedNNsfzf/+3h66+zefBBdYVIQ4Yk0atXQx5/fCU33NCciAhFyuk8SEgI\nIyEhjKuvVle0poMJE1ZQUVHNc88pTL0Ce/eWsXp1ES+8oG7yWkEBrN8AT/5DWUg258PxauuCUhUl\nZFPN8RPvcVXk7dxJtMkSGwwGQ51oGx/GjPWHsNulsq5IunEbTzFYmWJpt5O/Z4+ymAFE40OQUl9x\nhB+khMIqdR3P6NABwsNh/gJ1MVNTg2jXLpgvvlDU1sKBEILXX7+C3NwynnlGz0CPC4k1a7L44IPt\nPPRQe1JSIpTG/uor67W98cZYZTEXL1HvJ17tmGTXRaEo1tF5AqxMcaTxExsMBkOdaBcfTnF5FXty\nS1y9lbPGvUSx44NIZVs2gSCUBOXFdl2jrUyxqm4jNps1JGH+QnUxAUaOjOOXXwrZvbv09598DnTo\nEMPYsX/gjTc2sWOH502tqS+klDzwwE/Exgbyj390Vh5/2rQjdOkSSlJSgLKY8+ZDcLB6P3G0HyQp\ntHI7+4+r7FFcUVJCUWam8RMbDAZDHWnXxCq28yQLhXuJYkevYpVt2eBkBwqJOrXZJRqyjkOGwgug\nq/pCZiaoPPybb45DCPjoo8Pqgjp47rnuBAV58/DDy5THvlD47LOdrFx5hOef705oqIKqzFPYsKGY\nTZuOceutaosY5i+0ssQ+Pupirj5qvWcUdqGjkP0E0gAf1LXSy0tPB0znCYPBYKgrzWKCCfS1edQQ\nD7cSxf7h4QRGRyvNFIMliisp4TjqMprO28BrFPYrvqqf9V2lhSI+3p9+/SL56KPDynsLx8QE8Pjj\nnZk9ez/z5+sd6OGJlJVV8dhjK+jYMYbbbmulPP6HHx7Cx0co7TqxZw/s3m1doKmiuBK2Faj1E4Oz\n80Si0pgnOk+kKKwINBgMhosQm5egTWNriIenUCdRLIR4WQixQwixSQjxrRCizs1Co1JStPQqBpQO\n8WgXAT5eJ72SKkhOtr7mL1QXE+C22xqyb99xli1Tf7X2wAPtaNYsjD//eQllZVXK43syzz67moyM\nY0yadJnyIoPKSjvTph1h8OBoIiPVpXQXOP72nBdoKvj1qNWtpbNCUWynkmIOKvcTOy/II5urK1x0\nN4QQCUKI74QQ7wshHnP1fgwGw4VLuybhbDtUREWV3dVbOSvqmimeD1wipWwL7AQm1HVDUSkpyjPF\nTs+hynHPfjZLGKvMFIOVoVuyFKoU6svrrmtAUJCNjz9Wb6Hw87Px9tt9SE8v5LnnLoCiO0WG7o0b\nc3j55fWMGdOKyy9XN6jDybx5eeTkVCq3TixYBPHxoNJS67xw7Kyww1kxh5BUq+88sWsXIY0a4Rtc\n/32szwaHkM0WQmw57fEBQog0IUT6WQjdNsDXUso7gA7aNmswGC562saHUVFtJ+1Isau3clbUSRRL\nKedJKZ3ybSVQ5ykRkS1aUHzoEBXHjtU11An8CMWfCOXFdp2jrF7FKl0J/fpCcTGsXq0uZlCQjeHD\nG/DVV9kcP16tLrCDvn2bcNttLXnppXVs3qwwde4q6mh8ra62M3bsIiIj/XjllV6KNvVbPvnkMFFR\nPgwcqC79arfDwkXQ70q13t81R60Cu2iFnfuc72WVRXZg2Sfc3DoxFRhw6gNCCBswBRgItAZGCSFa\nCyHaCCFmnvbVAOtcfacQYhHwYz3v32AwXES0c0y22+ghvmKVnuI7gDl1DeJsheQseFFFKAknqtVV\n0Tna8kvuLFIX88o+liBZuFhdTLAK7goLq5g1S49ofeWVXoSF+TJu3BLl3mVP4623NrNmTTaTJ19O\nZKT6Hs7FxVXMmJHDjTfG4uur7i28YQPk5VkXZipZk6s2SwxW5wmBFyF1vw7/De7ejk1K+RP8T3FE\nFyBdSrlHSlkBfA4MlVJullIOOu0rG7gd+D8p5ZXAtfV7BAaD4WIiPiKAyCBfj+lA8bufqEKIBUKI\nLTV8DT3lOY8DVcC0M8S5SwixVgixNien9ga/zqpv9b5iSxRL1PlanMV2Kn3FkZHQof1Jb6cqrrwy\nkrg4Xz755IjawA6iogL41796sXz5Yd57b6uWNTyBQ4eO8fjjK7nqqiaMHKlHXH37bTZlZXZuvlld\ngR1Y1gmwLsxUkXMc9peo9RODlSkOphE21PmpjxcUUJqb69aiuBYaAxmn/J7peKw2fgQeEEL8B2ov\ntDjbc7bBYDDUhhCCtvFhbPKQYrvfFcVSyn5Syktq+JoBIIQYAwwCRktZuyFTSvmOlLKTlLJTTEzt\nY26dH0hHlfuKm1JNBSVkK4vZMhSCvC0LhUr69YVfVkKJwnZvNpvVpWD27FxycyvUBT6F225rSZ8+\n8fz1r8vYs8cz3gAqkVJyxx0LqaioZsqU3giVHoRT+OijIyQlBdC9e5jSuAsXQevWasaMO1mjwU8M\nVqZYuXXCcc650NuxSSm3SClvkFLeI6V85AzPO6tztsFgMJyJdvHh7MoupqTc/Yvx69p9YgDwKDBE\nSqlkOoRvUBAhjRppaMtmfYAWKfQV27ygY+TJD35VXNkHKith+Qq1cW+/vREVFVJLwR1YV4RTp/bD\nZhPccst8qjyk2lQVU6ZsYu7cA7zySi9atKhzI5Ya2bOnlIUL8xgzpqFS0V1RAT8vg74Ks8RgXTAK\noKNCUVxFOcc4oqXIDvDETPFBoMkpv8c7HjMYDAaX065JGHYJWw66f7KsrobEN4AQYL4QYoPjdlyd\niWzRQmMHCsXFdtGwPg8qFNav9eoJvr5q+xUDtGkTTNeuobz77iHOkNSvEwkJIUyZ0psVKw7zyivr\ntazhjqSl5fO3vy1n4MCmjBvXRts6779/CC8v6wJHJb+shLIytdYJsIrsWoVBiMJBIMVkAlL9eOdd\nu0AIIps1Uxq3HlgDtBBCJAkhfIGRwPcu3pPBYDAA0NZRbOcJFoq6dp9oLqVsIqVs7/i6R8WmIlu0\nUO4p9iGQQBooF8XdoqHcDhvz1cUMCoLLesGPc9XFdHLnnY3Ztq2EVasUVgeexh//mMINNzTnySdX\nXhjdKH6Hqio7t946n8BAH957r68220RVlZ2pUw8zYEAUTZqoLeD7cS54e6sVxVLCyhzopvjOewF7\nAZQP7sjbuZOwhAS8/dUXR6pCCPEZ8AuQKoTIFELc6egAdB8wF9gOfCmlvHiN/QaDwa2IDvajcXiA\nR3SgcKuJdk6iU1Mpzc2lLE/dBDqAcBJPfKCqwvmB/4viOpQBV8OWrZCR8fvPPRdGjowlKMjGe+/p\nu7sqhODNN3sTHu7HqFFzKSmp1LaWO/D006tZvTqLN9+8goYNg7StM29eHgcPlnPnner7Hv84F3r2\ngNBQdTHTiyG33LpwVEkh+7DhRzBqCw1z09LcvR0bUspRUsqGUkofKWW8lPI9x+OzpZQpUspmUsqJ\nrt6nwWAwnEq7JmFGFJ8vUY7JAblpaUrjhpFEMYeoRl2hWZMgaBwIqxQnRAf0t77Pm682bkiINyNG\nNOCLL7IoKVHfs9hJTEwA06b1Z9u2PO66a5E2u4armTlzL889t4bbb2/FTTfpFVTvv3+ImBgfBg1S\nqzIPH4YNG60LMZWsdFwodlecKS5kH2E0RWBTFlNKydG0NKJbtlQW02AwGAwWbePDycgrI69ET6G/\nKtxSFEc7RPFRxaI4nETArrxfcbdo9ZniP/wBGjeGORosFLff3oji4mqmT89SHwKp788AACAASURB\nVPwU+vVL4Nlnu/Hppzt5883NWtdyBXv3FnLLLfPp0CGGKVN6a10rN7eC77/P4eabGyrtTQwnL7yu\nvkppWFbmQrC35SlWhURSwF7lRXbHDh+m4tixExfkBoPBYFBHuxO+YvfOFrulKA5PSsLL21tDpjgR\nUF9s1y0G9h6D7DJ1MYWwRMrCRWpHPgNcdlk4yckBfPihni4UpzJhQieuvTaRv/71Z9au1SvC65Pj\nx6sYMcIaBjZ9+kACAry1rvfpp0eorJSMGaN2rDPA3PkQGwvt2qmNuzIHukZbXVpUcZx8KigmjCR1\nQTl5VyraiGKDwWBQTpv4MISAjRnuXWznlqLY5uNDRLNmyjPFwcRhw1e9r9hxN1u1heLq/lBQAGvW\nqI0rhGDMmIYsWpTP7t1KOunVipeX4MMP+xEXF8SwYbM5dEjd+G5XIaVk3Lgl/PprNh9+2I+kJLX9\ngmta7/33D9GhQwht24YojW23W11O+vcDL4Vng9Iqq/hUdZFdoWPWhOpMsfNcYzLFBoPBoJ5gP2+a\nxQSbTPH5Ep2aqlwUC2yEkqA8U9wxCmxCvSju19fKGM9T3JoNrC4UNpvg7bf1tzONigpgxoxrKSgo\n59prf6C42L09Rb/HM8+sZurU7Tz1VBeGDEnWvt7KlYVs3HiMu+9WX2C3bh3k5kJ/xdaJdUehWlqZ\nYpXoEsW5aWn4BAYS2lj9v7HBYDAYLAvFxsxCt64xcltRHJWaSl56OvZqtcVgYSSe+GBVRaA3tI04\nWVikishI6NwJ5s5TGxegUSM/hg2L4b33DlFWpq/gzkn79jF8+eUANm8+ysiRP3rsYI8PP9zOU0+t\nZsyYVjz5ZJd6WXPKlExCQ22MHq222wKcvOC6qp/auM4LRNWiuIB9BBCFHwrbZGC1Y4tKSUGoTJcb\nDAaD4QTtmoSRe6ycQ4XHXb2VWnHbT4Co1FSqKyoo3K82qxtGU8op5DgKGwtjffivOQp2xRdAV/WD\n1WugUIMN589/jicvr5Kvv1Y3+vpMDByYyJQpvZk9ez/337/Ura8Wa2LRogzGjl3ElVfG8/bbfbT1\nIz6VnJwKvvoqi1tvbUhwsHrf8rz50L6d5SlWyapcSAyGBgFq4xayX3mWGBzt2Ix1wmAwGLRxYohH\nhvtaKNxWFEdrassWrqnYrms0FFXCDsXitf9VUF0Ni5eojQvQu3cEKSmB/Oc/meqD18Ldd1/Co492\n5D//2cJf/7rM/YRxLftZuvQggwfPJCUlnOnTr8HXV107sDMxdeohKiok99wTrzz2sWOw4hf11gmw\nRLHqLLGdKorIUD60o6q8nIK9e40oNhgMBo20ahiCj02w0Y0n27mtKHY20VftKz7ZgWKf0rhdNRXb\ndesKwcF6ptsJIbjnnsasWFHI5s31VwD3wgs9ePDBdkyevIFHH13ufsL4tAzwzz8f5Nprf6Bp0xAW\nLhxGeLhfvWzDbpe8/fZBLrssnD/8IVh5/CVLobJSvXXiSBkcKFEvios5hKRKeaY4f/dupN3u9oM7\nDAaDwZPx87bRqmEoG02m+NwJjInBPzxc+bhnP8LwI1x5pjg1DMJ8YLViUezraxXczf6x1iRmnbj1\n1ob4+Xnx9tv1ly0WQjBp0mXce28b/vWv9UyYsML9hLGD5csPcc01PxAfH8SiRcOIjQ2st7UXLcpj\n9+4yLQV2ALNmnxwprpJVDm+9viK7RKVxnecY047NYDAY9NI2PowtBwuxq/aaKsJtRbEQgigNHSjA\n8hWrFsVeAjpHq88UAwy6xhr3vFnD/IuoKF9uuKEBH398WOuEu9MRQvD661dwzz2X8OKL6xgzZgEV\nFfW3/tnw9dfp9Ov3HQ0bWoI4Lk7fCOeaeOedg0RG+jB8eAPlsaWEWXOsLLGf4sT36qNWN5YOkWrj\nFrIfgRchqLWSOC1akS1aKI1rMBgMht/SLj6c4vIq9uSWuHorNeK2ohgsC4XqTDE4O1AcQKJWhHWJ\nhs35UKZ42MbAAdb3WXPUxnVyzz3xFBVV8/HH+od5nIqXl+DNN3vzzDNd+eijHQwc+D0FBeX1uoea\nkMDLL69jxIg5dOzYgOXLb6BRI/X2hTORmXmcb7/NYcyYhvj7q/cvb9liXWgNukZ5aFblWN1YVM8z\nKWQ/ITTGho/SuEd37iQoNhb/ML39pg0Gg+Fip10Tq9jOXS0Ubi+KizIzqShRe0URRlPsVHCMI0rj\ndouGKml1oVBJo0bQob11u1sHPXuGcemlIUyefKDeb2kIIXjiiS589NFV/PzzIbp3/4otWxT/A54D\nFZV2KirsPProcm68sTkLF15HTIziFgpnwZQpmdjtkvvua6Il/mxrGN+JCy5VVNutTHF3xUM7wLJP\nqLZOwMl2bAaDwWDQS7OYYAJ9bW47xMO9RbHD45eXnq40rrNQR7WFwikEVmjocHbtNfDLSshX20kO\nsITpQw8lkJZWyrx5rhGkt9zSknnzhpKfX07nzl/w5pub6t1nvGFDDh9/vIOqKjuPP96Jzz4bgL+/\n3vHNNVFaWs3bb2cybFgDkpL0CPLZc6wLrUaN1MbdUgDFldBDsSiupJRSsrW0Yzu6c6fpPGEwGAz1\ngM1L0KZxmNt2oHBvUaypA0UoCYBQ3oEi2h9SQ2G54iEeANcMsEbyzpuvPjbAjTfGEhfny+TJGXoW\nOAt6945n48ZR9O7dmHvvXcp1183iwIFi7etWVFTz0ku/0rXrl1SUV+Pvb+O557rj5aW/D3FNfPLJ\nYfLzq3jwQT1Z4oICWL4CrhmoPvYKx9++alFcxAHA+d5Vx/GCAkqys4kyfmKDwWCoF9o1CWfboSIq\n3HCIl1uL4sjmzQE4umuX0rje+BFMQ+WiGCwx8EuO+k4RXbpYE+7m/Kg2rhNfXy/GjYtn7tyjpKW5\nzgAfGxvIrFlDePXVXsybd4CWLT/h6adXUVpaqXwtKSUzZ+6lTZtPGT9+BQMHNuW2Ma2wuUgMO/f0\n+usZdOgQQq9e4VrWmL/A6n098Gr1sVfkQFyANbhDJQWO92q4ps4TJlNsMBgM9UO7+HAqqu2kHdGf\n9DpX3FoU+wYFERofr6UDRThJFLBXedweDeBoOexS/FrbbNaQhR/nWRljHdx9d2N8fARvvOG6bDFY\nBXh/+UsH0tJuYfDgRJ56ajWpqZ/wyivryM+v+3hIu10ya9Ze+vX7jsGDZyIEzJo1mO++G0Sg6uqw\nc2Tx4ny2bi3hwQebaJuYN+dHCA+Hrl3Vx16RbV0Yqt56IXvxIYhA1I7eOyGKjafYYDAY6oW28VZR\n80Y39BW7tSgG68MqT3GmGCxRXEIWlZQqjev0Ff+iwUIx8GrIyoKNG9XHBoiN9eOmm2KZOvUwRUWK\nW2icBwkJIXzxxUCWLr2e5ORQHnlkOfHxH3DPPYtZsODAObVwk1KyY0ceL7+8jpSUjxk0aCY7duTz\n6qu92LTpj1xzTaK+AzkH/v3vDKKjfbjpJsVzlx1IaV1YXdUPvBXr/6wy2HNMT5FdAXsJIxGBWrV9\ndOdOhJcXEcnJSuMaDAaDoWbiIwKIDPJ1yw4Urk2LnQWRKSls/eIL5XHDSAKsivZoWiuL28oxxOOX\nHLitmbKwwMlxvHPmQocOamM7eeCBJnzyyRH++9+DPPyw+qKm8+HyyxuzdOlw1q/P4fXXNzJ16nbe\nfnsLwcE+9OvXhHbtomnRIpxmzcJOtC+TEjIyiklPL2THjnwWLMhg794iALp3j2PixG5cf30zfHzq\nZ1zz2bBrVynff5/D+PGJWtqwAWzaBIcP67FO/KLJTyyxU8A+klA8eg9LFIcnJuKtulmzwWAwGGpE\nCEG7+DA2uWGxnduL4qiUFI7n51OSk0NQjLpP23CHKC5gr1JR7CWsSV46OlDExcGlHWHmLPj7Y+rj\nA3TuHEafPhG8+uoB7ruvCX5+7nMzoUOHGD74oB9vvHEFCxdmMGvWPhYuzGTGjD1n9HBHRPjRq1cj\nHn20IwMHNqVp09D62/Q58PLL+/Hx8eKBB/QU2MHJXtcDNPmJfbygY5TauCUcoZrjyv3EYBXxGuuE\nwWAw1C9t48NZunMXJeVVBPm5jxR1n53UQnTLlgDk7tihVBQHEIUvIVp8xd1j4JlNVmuqELVzBhgy\nGJ56xrJRxOq5w8748YkMGLCeadMOc8cdekYM14WgIB+GDElmyBDrlvfx41Xs3VvEnj2FVFbaTwjk\n+PhgmjULIzLS34W7PTsOHy7nww8PcccdjYiL05e1/P4H6NwJGjZUH3tlDnSMBNVJ7oIT452TlMaV\ndju5aWkk9umjNK7BYDAYzky7JmHYJWw5WEjXZMWZlDrgPmnAWjhVFKtEIByT7fYpjQuWKJbAag0j\nn4cOtqwBM2epj+2kf/9I2rcP5uWX97vtfPJT8ff3plWrSK69NonrrmvGsGHWV+fOsecmiKdNg3fe\ngdJSSEy0fq8nXn89g6oqySOP6LOsHDkCq1ZbF1aqqbTDWk1DO6wLVy/CFLdjK8zIoKqszHSeMBgM\nhnqmbbzVXcndLBRuL4rDEhLw9vfX1IHCEsWqxz13dQiDlRqK7dq2hYQE+EGjKBZC8Le/JbJjRymz\nZmlQ9u7ItGlw111QZPmO2b/f+r0ehHFRURVvvZXJ8OENaNYsUNs6zgupoRpE8aZ8KKvWNclur2O8\ns9oMuvNCO6ZVK6VxDQaDwXBmooP9aBwe4HYdKNxeFHvZbESlpJC7fbvy2GEkUU0FxzisNG64r1Vw\np6MDhRAw+FpriEdZmfr4TkaMaEBCgj8vvaR26p/b8vjjVob4VEpL4cEH4cABrUu/++5BCgur+Nvf\n9BY2fj/TSoBfcon62M6/9W7R6mMXsE+Ln9gpik2m2GAwGOqfdk3CjCg+H6JbtiRXU69iOOlZVEn3\nGFiZq36IB8DgQZYgXrRYfWwnPj5e/OUvCSxbVsDKle51e0MLtQnfo0ehaVNISYFx42D6dMjLU7Zs\nZaWdyZMPcMUV4XTuHKYs7umUlcGChdYFlY72xytzoGEANAlSG7eSEsd450S1gbFEsX94OEENGiiP\n7U4IIZKFEO8JIb4+02MGg8FQn7SLDycjr4y8kgpXb+UEHiGKo1q2pGDvXqqO131ww6mE0gSBlxZf\ncbdoPUM8AHpfAcHB8MNM9bFP5c47GxEV5cMzz+zRu5A7kFCLX7VhQ5g0yRLFn3wCN9wA0dFw6aUw\nfjzMm/e/GeZzYOrUw2RklDN+fOJ5xzgbFi6yhPHgQXrir8yFblqGdlh3KrR1nkhN1TYkRQVCiPeF\nENlCiC2nPT5ACJEmhEgXQpyxF42Uco+U8s7fe8xgMBjqk5O+YvfJFnuEKI5OTUXa7eSlpyuNa8OX\nEBprEcU9Hcmn5Rpas/n5WT2LZ87Wk4l2EhLizSOPNGXOnKOsXn2BZ4snToTA0/y8gYHw8svw0EMw\nc6aVIV6+HJ56yroqmTQJrr4aIiKgTx947jlYuRKqzm7wSUWFnYkT99KlSygDBuitvp05y9ry5Zep\nj324FHYXQ09tRXbqO0+AlSl2FvK6MVOBAac+IISwAVOAgUBrYJQQorUQoo0QYuZpXxd2GtxgMHgs\nbeLDEAI2ZriPvvAMUaypAwVAGIla7BMtwyDSF37OUh4agEHXwMGDsGGDnvhO7r03nqgoH55++gLP\nFo8ebXWeaNrUSnc2bWr9Pnr0yef4+ECPHvDkk7B0KeTnw5w58MADUFAATzwB3btDVBQMGQKvvw5b\nt/72ymXaNMvY6+VFecMEeuyfxVNPJWvNVkppXUD1v8q6oFLNMseF32UaWgQWsg9fQghA7UVDeVER\nxw4fdntRLKX8CTjdr9MFSHdkeyuAz4GhUsrNUspBp31puCw3GAyGuhPs503zmGC38hV7hCh2NtfX\n4SsOI5FSsqmkRGlcLwG9GsByDcV2AAMduSPnMAZdhIR48/DDCcyefZS1a4v0LuZqRo+GffvAbre+\nnyqIayIoCAYMsLLJ69dDTg58+SWMHAnbtllFepdcAo0awc03w913w9ixVmcLKQnJO8h7XpMZkDdX\n62Ft2GBdQF07UE/8ZdkQYIMOkepjF7CPMJoqH+/sPJd4aJFdYyDjlN8zHY/ViBAiSgjxH6CDEGJC\nbY/V8P/dJYRYK4RYm5Oj6URmMBguano2j2bZrlwOFmjsHHAOeIQo9g0OJjQ+XltbNjjpXVRJrwaw\nswiyNbzWcXHQpbM1jEE3997bhIgIb5599gLPFteV6GgYMQLefhvS02HvXnj3XctaMX++lXk+rWVI\ngP044tFHobJS27ZmzraS39doEsXLcyw/sY/is4nETiH7tVgnnOcSd88Uq0BKeVRKeY+UspmU8vna\nHqvh/3tHStlJStkpRuHgJIPBYHBy1+XWEK43Fu1y8U4sPEIUg/XhpUMUO6vadVgoTviKNSVZrhsK\na9ZCRsbvP7cuhIZ689BDCXz/fS4bNmioHLxQSUyEO++ETz+1JmfUZpE4dMjyL7doAddcY2WYp0yx\nivj27oXquvXR/uZb6N7NupBSzbFK2JCnx09cQhbVHCcM9a3qctPSEDYbkc2aKY9dDxwETp0FHu94\nzGAwGDyKRuEBjOrShK/WZnLg6PkXravCY0RxVGoquWlpSMWVZQFE40MQhRrGPV8aBX5eeortAK6/\nzvr+3Qw98U/l/vubEB7uzT/+sVv/YhciQtTe4SIqCv72N2jf3hLI774L991nFfElJ1uCuVUry6f8\n8MPwn//AokXW1ZDdfsZl9+yBDRth+DANxwSsyoVqefICUCXOAlgtnSd27CAiORmbr6/y2PXAGqCF\nECJJCOELjAS+d/GeDAaD4by4t09zbF6C1xa6PlvsUaK4vLCQkiy1lWsCQTjJJ6rcVeJng05R+kRx\naiq0bg3ffKcn/qlERPjw2GOJzJqVy9Kl+foXvBCZOBEZUEOHi9deg3/+E776yjIAHztmmYCXLIH/\n/tfqftGqlaVw33zT6pfct68lsoOCoE0buP56q0Xcu+9aRYCHDoGUfOu4YLpu6Gl7OaXgry4jrZdn\ng8CyT6jGOd45VFOmONoD/MRCiM+AX4BUIUSmEOJOKWUVcB8wF9gOfCml3OrKfRoMBsP50iDUn1u7\nN+Xb9ZmkZx9z6V68VQQRQjwM/AuIkVJqmQvs/ADLTUsjWPF94HCS2cMcJNUIbEpj92wAk7ZDWRUE\nKPnX/i3DhsLzL0JurmVp1cn99zfh9dczmDAhneXLO7l1f1e3ZPRoZv6QQ5svnqepyEEkJFit4E4v\n6BPCKs5r1AiuuOK3/81uh8xM2LXrt1/bt1tt4071JgcFMZgWtAluQfJ7LSx7RosWsGkTPPLIyf7K\nzpHWjj2eC8uz4ZJwa4qjavLZQyiN8VY83lna7eTt2kWz/v2VxtWBlHJULY/PBmbX83YMBoNBC/dc\n0Yxpqw7w2sJd/HtUB5fto84yTQjRBOgPaJ2F6+xAcTQtjcTThUIdCXeMey7mIKHUcov7POnZAF7a\nCmuP6mlZNWwoTHzeGuRx+xj18U8lMNDGU08lc9dd2/nhh1yGDDHFN+dCQUElt81rT7eBPzJ79nm+\n6b28rAxxQoKVLT6VqiprMp9DKJdu3EX6e7voGrEeXvzmzN7k0lKrtVxQEMTGnvwKqn1EXbUdfsmF\n0err4AAoYA8x/EF53MIDB6g6ftxTO08YDAbDBUdUsB9jeiTy1tLd3NenOalxIS7Zh4rc5STgUUCr\nszUsIQFvf38tbdkisKofC9irXBT3cOjGX3L0iOKOHaFJE5jxg35RDHD77Q15+eX9PP54OtdeG43N\nZrLFZ8vLL+8nP7+K559vrmcBb2/Lg5ycDFdfzafvwdipsHExRLWqtNrM7dwJg2oZa5eXB8NOMx+f\nKpIbNPiNYM4MiqXdrlgGNIiFggYQFqZspF05RZSRS7jjvakS5znEE+wTBoPBcLFw1+XJfPzLfibN\n38l/brnUJXuokygWQgwFDkopN+q+lS68vIhs0UJLB4oQ4vHCh3z2kIDaLHS0P6SE6vMVCwHXDYF3\n37eSfacPZVONt7cXzz6bzMiRW5g27TC33tpI74IXCEeOlDN58gFGjoylXbv6uQL+7ntISrIsxwif\nk/aJpk0ty8TpNG4MM2ZAVtbJr+zskz/v3g0rVlheHSlpCvwM8E/H/+/n9z/CuTZBTWSklfWuhQKs\n9n/hNbVjmzYNHn/cyorXZkE5A85ziPPuk8FgMBhcT3igL3delsTkBbvYcrCQSxqH1fseflcUCyEW\nADWZeB8H/o5lnfhdhBB3AXcBJNRWhf87RKemckTDCDcvvAmjqZYOFGBli2dmWpPFdFw7DB0C/54C\n8xdYP+tmxIhY/vWvA0yYsJvrr29AcLAGs/QFxoQJ6VRWSp59tn5agB07BgsWwri7a/ibmzjR8hCX\nntL+JjAQXnwRLj2Lq/OqKsjN5fEfs9mVnsUXqVmI7KzfiulDh6yBJtnZNY+99vaGmJhaRXNFbDph\nsYWExwZBdJX1fLAE8al7Pw8/dG5aGn6hoQTFarh1YzAYDIbz5o5eSXywfB+vzt/J+2M61/v6v6tm\npJT9anpcCNEGSAKcWeJ4YJ0QoouU8kgNcd4B3gHo1KnTefVVi0pNZfu331JdUaG8lVI4SRxkFRKp\nfHpWjxiYuht2FVtZY9Vcfpl153rG9/Ujir28BK+/nkKPHmuZOHGfPjvABcKqVYVMnXqY8eOb0ry5\n5lS+g7nzoLy8lr8Hp3g832yrtzfExfFFWBzt+oHofYbn2u3WOOyaMs+nfm3fbn0vLwesJrxWI94U\nS9VHRVmCOT39xHNOUFpqHctZ7v9oWhpRqammUNRgMBjcjFB/H+66PJmX56ax7kA+HRMi6nX9807x\nSSk3Aye6kwoh9gGddHWfAGuAh6yuJi89nZjWrZXGDieJvcznOHkEEKU0di/Hv9LPWXpEsY8PDLrG\n8hVXVlq/66Z793BuvjmOV1/dz9ixjUhOrh+x52nY7ZIHH0wjLs6Xxx/XVJFWA9O/tXRkr561PGH0\n6HPuNHEqB0thdzH8+fdsuV5e1kaioqz+gWdCSiguhqwsVmWNJzTLl1ZZl/9WTG+tpfPYgbOv883d\nsYOkK6886+cbDAaDof4Y0yOR95ft5dV5O/nkT13rdW2P6VMMJ0ey5mzfrjx2+CnFdqppGQYx/vCT\n2hbLv+HGEVad1MJF+tY4nRdeaI63t+Bvf3N9w2135dNPj7BqVRHPP9+ckJD6sZmUlVndSK6/7qTr\nQDU/O/6Wr1DpQBACQkOpbpFARi871cMHwZ//DE8/DW+9Bd98Y/mha+IsLVnlRUUUHzxIdKtWCjdu\nMBgMBlUE+XkzrnczlqXnsmrP0XpdW5kollIm6swSw0lRnKtBFJ8c97xHeWwh4PIGsFSjKO5/FYSE\nwFdf61vjdBo39uexxxL55pscM9CjBkpKqhk/Pp1OnUK59daG9bbuj3MtT/GIG/St8VMWhPhAOw13\ntgo5gMRec5HdxIn/W00aGGg9fhbk7tgBQIwRxQaDweC23NytKQ1C/Hhl3k7lk4zPhEdlin2Dgwlt\n0uTEB5tKfAgkiDgtmWKAy2NhfwlklGgJj78/DBlkdRw4dX6Dbh55pClNm/ozbtwOysvPPHL4YuOp\np/Zw6FA5kyen4OVVf/7Vr6Zbg1z69Na3xk/Z0DMGvDWcQZzvwRrbsY0eDe+8Y2WMhbC+v/PO2RfZ\nOc4dJlNsMBgM7ou/j417+zRn9b48lqVrzbf+Bo8SxWBleHRkigHCSdQmii9z+Ip1WihG3GBZKBYt\n1rfG6QQE2HjrrZZs317Ciy/uq7+F3Zz164uYNOkAf/pTI3r2DK+3dZ3WiWFD9Vknco/D1gI9fbcB\nCtmLNwEEUcsCo0dbPZftduv7OXijc7Zvx8vbm4hk9f2PDQaDwaCOkV2a0CjMv16zxR4niqNbtSJ3\nxw6kXX1WMpxkjnGYKsqUx24bAaE+8LOmfsUAV/eH4GCY/o2+NWpi4MBobroplokT95KWpikV7kFU\nV0vGjt1OdLQPL73Uol7Xnjdfv3VimeNv+LIGZ37e+VLAXsJIRGg4PeVu305kixbY6qMa1WAwGAzn\njZ+3jfv7tmBDRgGL0zSKp1PwSFFcWVpKUWam8tiWr1hSSA2DDeqIzcsa+fyzxkyxvz8MHgTfzqi5\nNaxOJk9OITDQxj337KhX/4878sYbGfz6azGvvZZCRET9iq+vp0NEBPRWO4PmN/ycDX5e0DlafWyJ\npIB9NfuJFZC7ffuJ2gSDwWAwuDc3XBpPQmRgvWWLPU8UO4vtNPiKnR/EBexTHhuszNq2Qjh6XEt4\nAIYPswaO/bxM3xo1ERfnxwsvNGfJknw+/PBw/S7uRmRkHOcf/9jNwIFR3Hhj/Q6HKC+HH2ZZEw51\nJkKXZUOXaPC3qY9dShZVlBLuKHxVSXVFBXm7dxs/scFgMHgIPjYvHujbgq2Hipi79X9GYCjH40Sx\ns2pcR1u2QBrgQ5CWDhRwsl/xMo13AQZcDQEBVsawvhk7tjE9e4bx0EM7OXBAo/J3U+x2yR13bMNu\nl0yZ0rLeh0MsXASFhTD8en1rlFTCuqP6/MTOC9IwDZnivN27kdXVJlNsMBgMHsR17RuRHBPEpPm7\nsNv1Zos9ThQHxsTgHxGhJVMsEISTpE0Ud44GXy+9ojgoCK4ZCN98B9XV+tapCS8vwUcf/YHqasmY\nMVu1//G6G2+8kcGCBXlMmpRCUlJAva//9XQIDYV+ffWtsSoXqqROP/EewOtEi0SVmHZsBoPB4Hl4\n27x4qF8KaVnFzNys9060x4liIQTRLVtq7EDRjAL2YUe9ovS3QecovcV2ACNvhCNHYPESvevURHJy\nIJMnp7B4cT6vvXb2U8Y8nW3bjjF+fDqDBkUzdmzjel//+HFrit2woeDnp2+dn7NBAN1j9MTPZzeh\nNMYb9QfhPGeYTLHBYDB4FoPaNKR/61iCfDX49k7B40QxWB9qOjLFABEkUqEBkwAACWlJREFUY6eC\nYtQX8oFloViXB6UaC+EGXWsN8vjsc31rnIk77mjEkCHRTJiwm23bjrlmE/VIZaWdW2/dSnCwjXff\nbVXvtgmAOT9CURH8cZTedZZlQ5sICPPVEz+f3TX3J1ZA7o4dhDRujG9wsJb4BoPBYNCDl5fgnVs7\n0beV3lodjxXFJVlZlOWrn6IWQTPA+nDWQa9YqLRbt6F14e9vjfid/q2VQaxvhBC8804rQkJsjBq1\nhdLSevZx1DNPPLGbX38t5u23WxEbqzFNewY+/RwaNIAr++hbo8oOv+Tos04cJ5/j5BFBcy3xc3fs\nMNYJg8FgMNSKx4pi0NOBIoTG2PClQJcobgBeApZoLqIcNdIquvpxrt51aiM21o+PP/4Dmzcf4957\nL9w2bTNmZPPii/u5++7GXH+9JrX4OxQVwcxZcOMN+gZ2APx6FEqqrOmMOnB6+XVkiqWU5O7YQVRq\nqvLYBoPBYLgw8GhRfDQtTXlsgY0wksjXVGwX7gsdImGpxn7FYGUMo6Ph8y/1rnMmBgyI5oknkpg6\n9TDvvnvIdRvRRHp6Kbfdto1OnUJ57TXXia0Z31t3BEbdpHedxY4Lud6aRLHz7kyEBlF87PBhKoqL\nTTs2g8FgMNSKR4riiORkvHx8tLRlA8tCUcAeJOqn5oElKn7JgTKNvmIfHxgxHL7/AUpcOGTuySeT\nueqqSO6/P43164tctxHFlJVVc8MNm/Dygq++aoOfn+veSp9/CQkJ0L273nWWZEHrMGigqbFGAXsI\nIg4fgpTHdt5VMkV2BoPBYKgNjxTFXt7eRLVooSVTDNbt2yrKKEGPx6F3HFRo9hUDjLwJysqsW+uu\nwmYTTJt2CdHRPgwbtokjR8pdtxlFSCn505+2s3HjMT755BISE+u//ZqTvDxrtPNNI0BnfV+l3Sqy\n6x2nb4189mjJEoMRxQaDwWD4fTxSFIP+DhSANgvFZQ5f8WLNvuJePaFRI9daKABiYnyZMaMdOTkV\nDB68kZISzy68e+KJ3Xz66RH++c9mXHONhlnH58A331ojvW8aoXcdp5/4Ck3WiQqOUcIRfZ0n0tLw\nDQ4mpFEjLfENBoPB4Pl4rCiOSk0lf/duqisrlccOpSkCm7YhHmG+0D5Cv6/Yy8uyUMyeAxoadZwT\nl14ayueft2HduiJGj95CdbVnFt69//5BJk7cx9ixjXnssURXb4dPP4fmzaFjR73rOP9WdYniQsck\nO2f3F9UcdRTZuaJdnsFgMBg8A48VxXHt2xPXoQNleXnKY9vwoQFt8UJfKf+AxtYwD91NGW69GeLi\nID1d7zpnw+DBMUyenMJPP+Wze3epq7dzztjtkqlTD9O/fyRTprheYFVUQGWl9Rrr3kqV3eqcEqvJ\nKVLFcUJorC1THBAVRZMePbTENhgMBsOFgXBFqywhRA6wv94XhmhAs5PX7TDHfHFgjrn+aCql1DTT\nzz2pwzn7Qvy7NMfkOVyIx2WO6fw4q/O2S0SxqxBCrJVSdnL1PuoTc8wXB+aYDe7IhfgamWPyHC7E\n4zLHpBePtU8YDAaDwWAwGAyqMKLYYDAYDAaDwXDRc7GJ4ndcvQEXYI754sAcs8EduRBfI3NMnsOF\neFzmmDRyUXmKDQaDwWAwGAyGmrjYMsUGg8FgMBgMBsP/cNGKYiHEw0IIKYRw7UiyekAI8bIQYocQ\nYpMQ4lshRLir96QLIcQAIUSaECJdCPGYq/ejGyFEEyHEYiHENiHEViHEg67eU30ghLAJIdYLIWa6\nei+GmrkQ34tCiH1CiM1CiA1CiLWu3s/5IIR4XwiRLYTYcspjkUKI+UKIXY7vEa7c47lSyzE9JYQ4\n6HitNgghrnHlHs+V2s7tnvxaneGY3Oa1uihFsRCiCdAfOODqvdQT84FLpJRtgZ3ABBfvRwtCCBsw\nBRgItAZGCSFau3ZX2qkCHpZStga6AfdeBMcM8CCw3dWbMNTMBf5e7COlbO8uLaTOg6nAgNMeewxY\nKKVsASx0/O5JTOV/jwlgkuO1ai+lnF3Pe6ortZ3bPfm1OtPnlVu8VhelKAYmAY8CF4WhWko5T0pZ\n5fh1JRDvyv1opAuQLqXcI6WsAD4Hhrp4T1qRUh6WUq5z/FyMJRQbu3ZXehFCxAPXAu+6ei+GWrno\n3ouegpTyJ+D0UbBDgQ8dP38IXFevm6ojtRyTR3OGc7vHvlae8Hl10YliIcRQ4KCUcqOr9+Ii7gDm\nuHoTmmgMZJzyeyZu9obTiRAiEegArHLtTrQzGeui1u7qjRhq5UJ9L0pgnhDiVyHEXa7ejEJipZSH\nHT8fAWJduRmF3OewDb7vSTaD0znt3H5BvFY1fF65xWt1QYpiIcQCIcSWGr6GAn8HnnT1HlXzO8fs\nfM7jWLcvprlupwYdCCGCgenAQ1LKIlfvRxdCiEFAtpTyV1fvxXBR0ktK2RHLFnKvEOJyV29INdJq\nSXUh3EV9C2gGtAcOA6+4djvnx5nO7Z76WtVwTG7zWnm7amGdSCn71fS4EKINkARsFEKAZSNYJ4To\nIqU8Uo9bVE5tx+xECDEGGAT0lRduH76DQJNTfo93PHZBI4TwwTrBTJNSfuPq/WimJzDEUYjhD4QK\nIT6RUt7s4n0ZfssF+V6UUh50fM8WQnyLZRP5ybW7UkKWEKKhlPKwEKIhkO3qDdUVKWWW82chxH8B\njyvKreXc7tGvVU3H5E6v1QWZKa4NKeVmKWUDKWWilDIR65ZeR08XxL+HEGIA1u3mIVLKUlfvRyNr\ngBZCiCQhhC8wEvjexXvSirCu7t4DtkspX3X1fnQjpZwgpYx3vH9HAouMIHZLLrj3ohAiSAgR4vwZ\nq1h7y5n/L4/he+A2x8+3ATNcuBclOASjk2F42Gt1hnO7x75WtR2TO71WF2Sm2PA/vAH4AfMdGfKV\nUsp7XLsl9Ugpq4QQ9wFzARvwvpRyq4u3pZuewC3AZiHEBsdjf/fASmvDBcQF+l6MBb51nEO9gU+l\nlD+6dkvnjhDiM6A3EC2EyAT+D3gB+FIIcSewH7jRdTs8d2o5pt5CiPZY9oJ9wN0u2+D5UeO5Hc9+\nrWo7plHu8lqZiXYGg8FgMBgMhouei8o+YTAYDAaDwWAw1IQRxQaDwWAwGAyGix4jig0Gg8FgMBgM\nFz1GFBsMBoPBYDAYLnqMKDYYDAaDwWAwXPQYUWwwGAwGg8FguOgxothgMBgMBoPBcNFjRLHBYDAY\nDAaD4aLn/wFDgK7TUY6ycwAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ps = np.array(ps)\n", "plt.figure(figsize=(12,4))\n", "plt.subplot(121)\n", "plt.contour(X, Y, Z, np.arange(10)**5, cmap='jet')\n", "plt.plot(ps[:, 0], ps[:, 1], '-ro')\n", "plt.subplot(122)\n", "plt.semilogy(range(len(ps)), rosen(ps.T))\n", "pass" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 2 }