{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Solve Cournot oligopoly model via collocation\n", "\n", "**Randall Romero Aguilar, PhD**\n", "\n", "This demo is based on the original Matlab demo accompanying the Computational Economics and Finance 2001 textbook by Mario Miranda and Paul Fackler.\n", "\n", "Original (Matlab) CompEcon file: **demapp07.m**\n", "\n", "Running this file requires the Python version of CompEcon. This can be installed with pip by running\n", "\n", " !pip install compecon --upgrade\n", "\n", "Last updated: 2022-Oct-22\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## About\n", "\n", "To illustrate implementation of the collocation method for implicit function problems, consider the example of Cournot oligopoly. In the standard microeconomic model of the firm, the firm maximizes profit by equating marginal revenue to marginal cost (MC). An oligopolistic firm, recognizing that its actions affect price, takes the marginal revenue to be $p + q\\frac{dp}{dq}$, where $p$ is price, $q$ is quantity produced, and $\\frac{dp}{dq}$ is the marginal impact of output on market price. The Cournot assumption is that the firm acts as if any change in its output will be unmatched by its competitors. This implies that\n", "\n", "\\begin{equation*}\n", " \\frac{dp}{dq} = \\frac{1}{D'(p)}\n", "\\end{equation*}\n", "\n", "where $D(p)$ is the market demand curve.\n", "\n", "Suppose we wish to derive the effective supply function for the firm, which specifies\n", "the quantity $q = S(p)$ it will supply at any price. The firm's effective supply function is\n", "characterized by the functional equation\n", "\n", "\\begin{equation*}\n", " p + \\frac{S(p)}{D'(p)} - MC(S(p)) = 0\n", "\\end{equation*}\n", "\n", "for all positive prices $p$. In simple cases, this function can be found explicitly. However,\n", "in more complicated cases, no explicit solution exists." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Initial tasks" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from compecon import BasisChebyshev, NLP" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The model\n", "### Parameters\n", "\n", "Here, the demand elasticity and the marginal cost function parameter are" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "alpha, eta = 1.0, 3.5" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "D = lambda p: p**(-eta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Approximation structure\n", "\n", "A degree-25 Chebychev basis on the interval [0.5, 3.0] is selected; also, the associated collocation nodes `p` are computed." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "n, a, b = 25, 0.5, 2.0\n", "S = BasisChebyshev(n, a, b, labels=['price'], y=np.ones(n))\n", "p = S.nodes" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "S2 = BasisChebyshev(n, a, b, labels=['price'], l=['supply'])\n", "S2.y = np.ones_like(p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Residual function\n", "\n", "Suppose, for example, that\n", "\n", "\\begin{equation}\n", " D(p) = p^{-\\eta} \\quad\\text{and}\\quad MC(q) = \\alpha\\sqrt{q} + q^2\n", "\\end{equation}\n", "\n", "Then the functional equation to be solved for S(p),\n", "\n", "\\begin{equation}\n", " \\left[p - \\frac{S(p)p^{\\eta+1}}{\\eta}\\right] -\\left[\\alpha\\sqrt{S(p)} + S(p)^2\\right] = 0\n", "\\end{equation}\n", "\n", "has no known closed-form solution." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "def resid(c):\n", " S.c = c # update interpolation coefficients\n", " q = S(p) # compute quantity supplied at price nodes\n", " marginal_income = p - q * (p ** (eta+1) / eta)\n", " marginal_cost = alpha * np.sqrt(q) + q ** 2\n", " return marginal_income - marginal_cost " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that `resid` only takes one argument. The other parameters (`Q`, `p`, `eta`, `alpha`) should be declared as such in the main script, were Python's scoping rules will find them." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solve for effective supply function\n", "\n", "Class `NLP` defines nonlinear problems. It can be used to solve `resid` by Broyden's method." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "cournot = NLP(resid)\n", "S.c = cournot.broyden(S.c, tol=1e-12)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot demand and effective supply for m=5 firms" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "prices = np.linspace(a, b, 501)\n", "\n", "fig1, ax = plt.subplots()\n", "ax.plot(5 * S(prices), prices, label='Supply')\n", "ax.plot(D(prices), prices, label='Demand')\n", "\n", "ax.set(title='Cournot Effective Firm Supply Function', \n", " xlabel='Quantity',\n", " ylabel='Price',\n", " xlim=[0, 4],\n", " ylim=[0.5, 2])\n", "\n", "ax.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot residual\n", "\n", "Notice that `resid` does not take explicit parameters, so to evaluate it when prices are `prices` we need to assign `p = prices`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to assess the quality of the approximation, one plots the residual function over the approximation domain. Here, the residual function is plotted by computing the residual at a refined grid of 501 equally spaced points." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "p = prices\n", "fig2, ax = plt.subplots()\n", "\n", "ax.hlines(0, a, b, 'k', '--', lw=2)\n", "ax.plot(prices, resid(S.c))\n", "ax.set(title='Residual Function for Cournot Problem',\n", " xlabel='Quantity',\n", " ylabel='Residual');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot demand and effective supply for m=1, 3, 5, 10, 15, 20 firms" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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Gm5sb//33X6WPrdfrOXbsGLa2tvTp06fUek9PT7p27cru3buJioqy+L1U5J4LpntiTEwMU6dO5e6776Zfv3506NABX19fq5QcaYgIhUhgQckb8PUoFArgWvppamoqAN7e3mXO4e/vX2U55syZw1NPPcXp06eZN28e8+bNw8vLi0GDBjF16lRatmxZ4blKHig3Mm7cOD777DPWrFnDo48+SkxMDKdOnaJv377mh0RF8ff358EHH+TBBx/EYDAQFRXF6tWrWbJkCadPn2bu3LnMnTu3UnPeSNOmTcscLwnYLvm/3O72N1Id5+fUqVMsWrSIU6dOcenSJfMNvkShkMpIaS7rN1hiASqJ0yp5W77Zb7Am0ruNRiO5ubkAZuU2OTkZMFm1bsWN8R1lKccl5+TGOkc3S/EvKipi2bJlbN26ldjYWFJSUjAajbcsCVDWcW+8vuHW59fFxcXCClNRajrt/mYvHEql0kKZLPlu1yc6VJXs7Gx0Oh1+fn7m3+qNlNwX09PTLcYrcs8FePnll7l06RL79u3jm2++4ZtvvsHV1ZX+/ftzzz330LFjx2r6No0XoRAJLKiO+iolF3NFKSuw1s/Pj+XLl7N//342bdrEzp07uXjxIosWLeKvv/7if//7n9mVVx43+05jx47l888/Z+3atTz66KPmYOESc/Wt0Gq1nDt3DoPBUOoNT6FQ0LFjR3NQ5WOPPca6det4//33yz2/t6qpdLMbbck+N66v7PY3UpXzA6Zg888++wyZTEbr1q0ZNmwYrVq1IiIigpUrV7J48eIy97PGb7AixMXFodPpsLW1NSubJb/dIUOGYGNjc9N9b3z4lnfuyyMlJYUpU6aQkJCAq6sr4eHhDB8+nHbt2tGqVaubBv9WV/2kqspfFcq6X0DFv1vJ/tVZS6pEcbnVnCXX3Y1W24rK4eTkxMKFCzlx4gQbN25k586dnD17lhUrVrBixQpef/31chVzwa0RCpGg0pS8NZako95IyRvY9ZRc9GU98MvKwinZp3v37nTv3h0wpdd+9913LFmypFIK0c3w8fGhR48e7N69m/j4eDZt2oSTk1OFXAJZWVlMmDABDw8Pdu3addObWr9+/XBzcyMrKwuNRoOtra05jqmsG3uJBaIsbpZFUhKHc6O7oLLb30hVzk98fDyff/45TZo04aeffjJn5JXw+++/lzvHrSj5Dd6sNUpZv8GqUpLK3rVrV7PC5eXlxcWLF3n00Udp3759tR/zZsybN4+EhASmTJnCzJkzLRSUEndkVfD29ubChQskJSWVshIVFxeTm5tbY0UJb3V9aLVai8yr26HEHVVi3buRNWvWYGNjQ79+/VCpVBWa09XVFZVKRXJyMnq9vkyFsaTadVULtIaHhxMeHs5LL71EWloaixYtYsGCBcybN48pU6ZUWGZBaURQtaDSeHt706JFCy5evEhMTEyp9WXVgSm5eWZkZJRad+zYMYvPiYmJjBkzplSNj4CAAGbNmoVcLre4mVXlTa8k4PeXX37hwoUL3Hnnnbd80y/B29sbPz8/0tPTWb9+/U23y8zMJC8vj6ZNm5pjN0piXspKfT9+/PhN59q1a1epsezsbA4fPoybmxvt2rWr0vZlcbvnJyoqCqPRSN++fUspQ1qt1hyjcrtVxsPCwnB0dOTQoUNlBsDu2LHjtua9Gfn5+WYlbtKkSebxTp063fJ406ZNY/LkyZw7d65a5Sn5nTzyyCOlHr4lMURVqeBe8hKyadOmUut27dpVo9Xhr78+bnSp3nivuB1KEjLKuj4KCwt5/fXXmT17dqWsYCqVig4dOlBcXFzmbyE9PZ3Dhw9jb29foevuRoqKirjrrrsYPXq0xbinpyfPPvssPj4+FBYW3vKFSlA+QiES3BYlhQNfffVViwyalStXsnnz5lLblwRCL1261CLAcfny5aUCsP38/MjOzmbHjh2l6oesW7cOo9Fo8TZe8oC+maXpVgwePBhHR0cWLVoEVNwdBPDEE08AMHPmTFauXFnqIZGcnMyzzz6LXq/noYceMo+XnIudO3cSFxdnHj916pQ5U6UsTp8+zXfffWf+rNFomDlzJsXFxUydOrWUm6iy25fF7Z6fEutTSYB5CQUFBcyYMcOs0N7u275arebuu++muLiYV1991aK+y4IFCzhz5sxtzVsWycnJTJ8+naSkJHr06GHO+gKTcmRjY8N3331n8SCUJImvvvqK3bt3k5KSUi1Bw9dTcn63bt1qMb5nzx5zk+OqWFLGjh2Lo6Mjv/76K3v37jWPJyUlVTkWrjxcXV3x9vYmOzvbIssxMzOTDz74oMrz9+zZk8DAQPbu3WtRZNNgMDB37lw0Gg0jRowwv2iV3F/KK0hZck+cM2eOhZUuPz+fl156CZ1Ox/jx40sFtVcEOzs7lEolZ8+e5Y8//rBYd/DgQVJTU/H396dJkyaVnltwDeEyE9wWkydPZs+ePWzatIkhQ4YQGRlJamoqx44do0OHDqUsHcOHD2f+/PmcPXvWXLX40qVLREdHM2rUKIsbX0mG0uOPP84TTzxBeHg4vr6+XLlyhRMnTmBnZ2dRpK958+YArF+/nvz8fAYMGMBdd91Voe9ha2vLnXfeydKlS2nWrBmdO3eu8DmYNGmS2Y03Y8YMPvzwQ9q1a4ejoyPJyclERUWh1+uZPHmyRRZIYGAg/fv3Z+vWrYwfP57u3btTUFDAwYMHGTFiRKlU9xJ8fHz49NNPWbt2Lc2bN+f48eMkJycTGRnJo48+WuXtq/P8dOjQgY4dO3Ls2DEGDx5Mp06d0Gq1HD58mIKCAoKDg4mJiSkVYFoZnn76aY4cOcLWrVsZMmQIHTt25OLFi5w9e7bM32B5bNy40SK1XaPRcOXKFaKjo9HpdHTs2JF58+ZZ7OPv78+7777Lq6++yiOPPELbtm0JCAjg3LlzXLx4EXt7e+bNm1ftMU33338/u3fvZvbs2axevdrsujt79iyenp7IZDJyc3PRarWlYlYqgpeXF3PmzOHll19m2rRpdO3aFQcHB/bt20dAQECpzL7q5qGHHuKDDz7glVdeYdmyZdjb23PgwAF8fX1p27Ytp0+fvu255XI5n3zyCdOmTePNN99k8eLFNG3alNOnTxMfH09oaCjPPfecefvmzZsTGxvLY489RqtWrW6qlA0bNox7772X33//nVGjRhEZGYmdnR0HDx4kOzubLl268NJLL9223G+88QZTpkxh9uzZLF68mBYtWpCZmcnhw4fN6wVVQ1iIBLeFXC7niy++4LXXXsPDw4Pt27eTkZHBa6+9xiOPPFJqe0dHR/78809Gjx6NVqtl+/bt2NjYsGDBgjKVl759+/Ljjz9yxx13cPnyZTZv3kxycjKjR49m+fLlFhaidu3a8dxzz+Hi4sKuXbvMN4iKUuL2KK/yclm88MILLF26lHvuuQc3NzeOHz/Opk2buHLlCoMGDeLnn3/m7bffLrXfZ599xuOPP46bmxs7d+4kJSWFF1988ZbtMAYOHMgnn3yCwWBg27Zt2NnZ8eKLL/Ljjz+W6caq7PY343bOj0Kh4JtvvmHq1KnY29uzY8cOYmJiiIiIYMGCBeb2KjdaOCqDvb09P//8M0899RQ2NjbmauEfffQRw4cPr/R8586dY/Xq1ea/rVu3kpycTLdu3Xjvvff4448/yux0P3r0aBYvXsyQIUNITk42yzF+/HhWrlxJeHj4bX/Hm9GvXz+++eYbIiIiiImJMVfmfvDBB/nnn3/o1asXer2+Sq7D4cOHs3DhQnr27Mnp06c5dOgQAwYM4Oeff66RoPXreeihh3j33XcJDQ3l6NGjnDx5ktGjR7No0aLbynC7kfbt27N8+XLGjRtHWloamzdvRq/X88ADD/DHH39YWHFeffVVOnXqRGJiIvv3779lm4xZs2bx2WefER4eztGjR9m9ezf+/v688cYbLFy48KZlBypCu3bt+P333xk8eDAZGRls3ryZmJgYBg4cyJIlSxgwYMBtzy0wIZPKynsVCBoRjz/+ONu3b+e///6rk924ly9fzmuvvcbUqVN58803q3378qjr50cgEAiqA+EyEzRKiouLUalU/Pvvv2zfvp3evXuLh/11iPMjEAgaG0IhEjRKXn75ZbZu3YpOp0OpVPLss89aW6Q6hTg/AoGgsSFiiASNkvDwcNRqNc2aNeOzzz67rVTYhow4PwKBoLEhYogEAoFAIBA0ehqly8xoNGIwCD1QIBAIBIKGgEpV9czHRqkQGQwS2dmF5W8oEAgEAoGgzuPpWbpJbmURMUQCgUAgEAgaPUIhEggEAoFA0OixukK0c+dOpkyZQocOHYiIiODBBx+sUAO/+Ph4nn76aSIjI4mMjOSVV14ps1mmQCAQCAQCQXlYNcvswIED3H///bRq1YoJEyag1+tZtGgRqampLFq06KYl77OyspgwYQJarZb7778fg8HAjz/+iL+/P0uXLi23d49OZxAxRAKBQCAQNBCqI4bIqgrR2LFjycnJYd26deYeL+np6QwfPpx27drx888/l7nfZ599xvfff8/q1avNXaT37NnDQw89xJw5c5g0adItjysUIoFAIBAIGg71Oqg6JyeH6Ohohg0bZtHwzsPDg65du3L06NGb7rt27VoiIyPNyhBAz549adGiBWvXrq1RuQUCgUAgEDQ8rJZ27+joyIYNG8rs/puVlXXTbso5OTnEx8czdOjQUuvatWvHtm3bKixDTk4Whw7tR61W06VLjyp1IhZUDEmSkMlk1hZDIBAIBAILrGYhUigUBAYG4u3tbTEeHR3NkSNHiIiIKHO/lJQUgFL7AXh6epKfn09eXl65x5ckidWrl3P27Gmioo6xa9cW87ozKXmM/G4/n22LqcxXKhNFxlncf+2B45YXqzxXYkEC9267i7ePzMQoGas8X21TtHwpmWOHU7RimbVFqTRGg8SWH86w4cuTJF/IsbY4lSYlJpqlM59k0/y5pF+q+u9aIBAIGhpWzzK7noKCAmbMmAHAo48+etNtgDKtOTY2NgAUFpYfH6TRFJObe+3BlpBw2by8Jy6TlDwNi48kojdWLcRKlXIYRV48dmeWIM+Oq9JcMXkXSCpMZEfyVnan7KzSXNZAd3A/UmYGBf/7iOI1q6wtTqXQFunJiC8gN7WIHQvPcWz9ZQz6+qOUpl+8QFFOFklnTrDu4zfY/uM8clKSrC2WQCAQ1BnqjEJUVFTEE088QXR0NI8++iiRkZFlbmc0lv8QksvL/1oKhaW3UKvVmpddbFWmY0mQWaClKui8r1m61Je3VWmuLh5dcVSaAscWx/5OfWtDZ//IE8gcTfLnfzwXzbYt5exRd7B1VBE5LhCl2vTbOrcnhU3fnCYnpcjKklWM1n2G0rrfMORXXdGXju7nn/deZs+i7yjIyrCydAKBQGB96oRClJuby7Rp09i/fz8TJkzg+eefv+m2Dg4OAGg0mlLrSsZKtrkVSqXSIpbFYDBgMBgA8HC4lrafXkWFyODeGoODyb1XVYXIXunAmObjATiTfYrjmTcPPK+LKIOCcf74M7C1BaORvHfeQLt3t7XFqjDNO3ow+Ml2uPubfl85KUVs+uYU5/en1HnlVKFSETnxAcbM+h9Bkb1BJkMyGrmwZysr3nmeQyv+oDi/fFezQCAQNFSsrhBlZGRw//33c+TIEe6++27ee++9Wwbd+vn5AZCWllZqXWpqKs7Oztjb25d7XJlMVqpekU5nUn48HKtPIUImQ9usHwDqxD2gL67SdOMD78JGbnIN/n7hl6rJZgVUYeE4v/8xqFSg15P7xgy0hw5YW6wK49TElgGPtKZNX1+QgUEvcXTNZXb9fp6ivCr+VmoBJw8v7rj/SUa9+gEB7TsDYNTrOL15DSvefpYTG5aj01TtNyoQCAT1EasqRPn5+Tz88MOcOXOGBx98kNmzZ5ebgeTs7ExAQACnTp0qte706dOEhYVV+PhqtY3F5xK3WXVaiAC0zfoDINMXoUraX6W53GzcGdFsDABHMg5xKiuqyvLVNuqu3XCa8wEoFKDVkvvqi+iO1x9rl1whp/2gAPpPa429i+m3cuVcDv9+eZL4qPpRLd3NvxkDHnuJYS+8g1dwawB0xUUcW7OUFW8/y5mt6zHo6r6CJxAIBNWFVRWi2bNnc+bMGe6//35ee+21Cu83ZMgQ9u7dS0zMtWyZPXv2EBcXx/Dhwys8j0plaSEqUYiaXK8Q5Zd2zVUWXdPeSDJT7Ib64qYqz3d30FRUclOcU320EgHY9OqN01tzQC4HjYbcl59Hd+qktcWqFJ6BTgx5qh3Nwt0B0BYZ2PtXDHuXxKAp1FtZuorhFRTC0OfeZOATM3Dzbw5AcV4uB//+leVvP0f09o0YdDorSykQCAQ1j9UqVcfExDB8+HCcnJx4/fXXy6w7NGbMGOLj4zly5AidOnWiadOmAGRmZjJy5EgUCgXTpk1Do9Hwww8/0KxZMxYvXlzh1h3Lly8mOflaps3YsZPw8wsAYPCCvWQX6RgX7sPrg0Oq/H1dVt6FOnEvBudmZN67G6pYi+ezkx+z+vIKAL7p9RMhLq2rLKM1KP53PfnvvQ2ShMzRCZfPF6AMCbW2WJUm/mQmh1dfQntVEbJ1VNFlbCB+oa7WFawSSEYjcYf3cnzdMvLSks3j9m5NCB86luDu/VAorVa6TCAQCG5KvW7d8eeff/L222/fcpuzZ8+yfPlyXnvtNebOncv48ePN62JjY5k7dy6HDh3C1taWvn378sorr+Du7l7usUsUojVrlnP58kXz+PDhYwkMDAJg8sLDXEgvoHeQO/8bV3E33M2wO/YdjrtnA5B5z2YMTar20E8uusJ92yZhkAz08u7DnM4fVFlGa1G8eiX5H70PgMzFBZcvvkEZFFzOXnWP4nwdh1ZdJCk62zzWopMHHe9shsq27EKjdRGjwUDcwV0c37Cc/PRU87hjE0/aDxtHcGRv5AqhGAkEgrpDvVaIrEmJQrRx41ouXDhrHh88eDitWpksLdOXRbHvUhZtvB359d5OVT6mIjsW9z/6AJDf4zWKOj1V5Tk/PvE+6xPWAPDDHb8R5Fz/lIgSiv7+i4J5nwAgc3PHZd78eqkUSZLEpWMZHF17GZ3GlLVo76Km6/gWeAc5W1m6ymE06InZv4MT61dQkJVuHnfy8Cb8zvG06NLLnMYvEAgE1qRe9zKrC9zoWru+FlGTq5lm1RFUDWBwDULvarI+2VzcXC1zTgm+H/nVf+EfMb9Uy5zWwm7CJOyfmA6AlJVJzjNPoL9w3spSVR6ZTEZghAdDp7fDO9ikABXmaNn+81mOrLlkVpLqA3KFklY9BzD2rc/odvc07F1N1te89BR2//Y1/7z3MrEHd1eoNphAIBDUdRq1QlQ6qPpaALXn1cDqzAIthipWqzbP33wQAMrkQ8iKs6o8n79DAAP8THNuu7KFi3lVq4Rtbeyn3If9408DIOVkk/Pck+jPn7OyVLeHvYsNfe4PodPI5ihUpsvswv5U/v2q/rX+UCiVhPYezLi3PqPrxAewc3YFIDf1CrsWfsU/775EzL7tGA31I5BcIBAIyqJRK0S3shCVpN4bJMguqp4sG20Lk/Iik4yoL1VPleapLR9EhgwJiV/O/1Atc1oT+6n34/DUswBIOTnkPPsk+rPRVpbq9pDJZbTs5sWQp9rh0dwRgMJsLTsWnuPAiji0RfVLgVCo1LTpN4xxb39Ol/H3YetksoDlpl5h9+/fsHL2i5zbtVlkpQkEgnpJo1aISnqflaC5riBdtRZnvIrOpytGtekhUh3p9wDNHQMZ6DcEgB3JWzmfc7acPeo+dvdMxeFZUzNcKS+XnOeeQnfmtJWlun2cmtjSf1prIkY2M7f+uHgknQ1fnCTxdNUthbWNUq2m7YDhZsWoxGKUn5HKvsU/sOKd5zizbQN6rahjJBAI6g+NXCGytfhcXHydQmRRi6iabuwKFdrmpiKN6svbwFA9b9IPtHoYxdU6Rz+f+75a5rQ2dhPvxuH5lwGQ8vPIff4pdKfqXxHKEmRyGa26eTN0ehg+LU1KcXG+jt1/XmDP4gsU59c/q4rKxpa2A4Yz/p3PiZz0EPZuTQAozM7k4LKFLH/rGU5tWiMqXwsEgnqBUIiu4+YWoqoXZyxB23wgAHJtXpWrVpfg7xDAnQEjAdiXtqdeVq8uC7vxd+Hw0qsASAUF5L7wDLoTx60sVdVwcLWh9/0hRI5vgdrOpMQmnMpiwxdRXDyWXud7opWFQqWmdZ8hjHtrHj2mPIqjhxcAxXk5HF75B8vfnE7UvyvRFhVaWVKBQCC4OUIhuo7rG8Z6OFxzp1WXywxA23wAktxUw8Umbn21zXtvywfN1at/Ovddtc1rbezGjMdxxkxTM9LCAnJenI72YPUoktbiWiZaewLaugGmKtcH/o5j52/nKciqPgW8NlEolbTq2Z+xs/7HHfc/iYu3qe+gpiCfo6uXsPzNZzi2dqloIisQCOokjVwhunkMkY1SjpONSXFJqy6XGSDZuqLz7wmAOnYDSNWTsuxl582oZuMAOJpxmCPph6pl3rqA7cgxOL42y9Tmo7iY3BkvoNmx1dpiVRk7JxU9J7ek5z3B2DqafmvJ53PY8OVJonddwWion+nscoWCoMjejJr5MX2mPYubfzMAtEUFnFi/nOVvTufgsoXkZ6aXM5NAIBDUHo1aIbK1vbmFCMDzqtssNa9639g1QXcCoChIQZlSfU1NpwTfj63C9J1+OvdtvXS/3AzbO0fi9PZ7oFSCTkferNcoXr/G2mJVCwHt3Bk6vT2BER4AGHRGTvybwH9fnyb9cr6Vpbt95HI5gZ26M3LGXPo/+iJNmpnqcOm1Gs5s28CKt59j929fk30lwcqSCgQCQSNXiMqyEF2vRHg7mdanVLdC1GIoEqZeZjYx66ptXncbd8YHTgLgdPYp9qXuqba56wI2/Qfi/MGnYGMDRiP578+maNkSa4tVLdjYK4kc34J+00Jx8jAptTkpRWz54QyHV1+sdyn61yOTy2ka3oXhL7/LoKdfxyfU1ApHMhqI2b+Df957mS3ffkJabP2sOSUQCBoGjVohUiiUKK9rVilJEjrdNfdYTSlEkoMXet+uANjErodqtORMajEFB6Wp5s33ZxdgkOpPZeSKoO7WA5f/fYnMwQGAgs8/pXDhjw3GGubVwpkhT7Wj3QA/5EoZSBBzII0NX5zkclRGvf6eMpkMv9btGTJ9JsNffpfmEd3MTY4Tog6z/n9vseGzd0g4dbRef0+BQFA/adQKEdw6sLpEIcop1lOsq17Fwuw2y72MIr36auw4q52ZHHwvABfz49iYUH2B23UFVXhHXL74BpmLKwCFP3xL4YIvGsxDVKGU066/P0OfCsMryNSfpzhfx76/Ytn56znyM+t/GrtH82D6PvwcY9/4lFY9ByC/+mKSGhPNlq8/YvXcGcQe3IXR0LAUeoFAUHcRCtEtAqtLFCKoAbfZVYUIwCa2+txmABMC78bT1pT6/NO57yg21P8H6I0oQ0Jxmf8dci/T9yxa/Af5H72P1IAeoE4etvR9MJRuE1pgY3816PpCLv9+eZIzO+pv0PX1OHv70mPKI4x/5wvaDRqFytYOgOykeHYtnM/K2c8Tvf1f9Nr6mXknEAjqD0IhukVxxusVotT86r0hG50D0HmGm2SIqV4rjo3ChmkhjwKQoUnn77iGEWdzI8rmgbjM/x55QFMANGtWkffma0iahvPwlMlkNO/owbBn29Oi89Wga71E1H8JbJx/itTYXCtLWD3Yu7jReewUJsz+kojR92Dr5AJAfkYaB5b+wt+znubYmqUU5WZbV1CBQNBgafQKUelMs9qxEAFogocDoMw6hyLrQrXOPch/KEFOLQH4M/Y3sjX1r0VERVD4+OL61bcogk3fVbtjGzkvTseY1zAUhRJs7JV0HduC/g+3xtnT9JvNTStm289n2ftXDIW5DaNNhtregfZDxjBh9hd0v+dhc5FHTUE+JzYs5+83n2HPou/ITk60sqQCgaCh0egVoopaiGpCIdJe5zZTx26o1rkVMgWPtX4SgEJ9Ib9e+Lla569LyJt44PLltyg7dgJAf/wYOU8/hiE1xcqSVT+egU4MfrId7QcHoFCZLt/4qEw2fB5Vr2sX3YhCpSbkjkGMffMz+kx7hibNgwEw6nVc2LOVf959ic1ff8iVsycbTOyYQCCwLo1eIbKzs7P4XFRUZF62VSlwsTXFbtSEQmRwC0bvFgKATczaap+/i0c3OjcxZbOtvryChIL4aj9GXUHu5ITLJ5+j7jcAAENsDDlP/B/6uFgrS1b9KJRy2vTx5c5nwwhoZ6p0rdeaahc1JDcalNQy6sHwl+Yw9Lm3aBrexZyZlnjqGP99+R5rPnyN2AM7MRrqb2kCgUBgfRq9QmRra2/xubjYst9STaXel1DiNlOlRSHPjqvWuWUyGY9etRIZJAM/nP2mWueva8hsbHB6+z1sx98FgDE1hZynHkUXdcLKktUM9i429LynJX0eCDHXLmqIbjQw/Za9W7am/6MvMvaNTwnpPQiFylQ4NSvhErt+XcDyt57l5KbVaAsLrCytQCCojzR6hcjOzlIhKiqqZYWo1Wjzsu2F1dU+fyuXUAb5DQVgR/JWTmedrPZj1CVkCgUOz72E/SNPACDl5ZLz3FNodu2wsmQ1h09LF4Y8ZXKjKdWl3WgGfcNwo5Xg7O1L97sfZsKcL+k44i5snZwBKMzO5MjKRSyb9TQH//6V/Iw0K0sqEAjqE41eIbK3v7nLDGpeITK4h6Bv0gYAm/OrauQY00IfRSU3vU0vONNw6vXcDJlMhv39D+H46ixQKECrIW/mKxSvXmlt0WqMEjfasGfa0zSstBstJabhuNFKsHV0JvzO8UyY/SU9pjyKi48/AHpNMWe2rmfF28+y/afPSb9YvQkLAoGgYdLoFaIbXWY3sxDlawwUaGsmRkHT0mQlUmaeRZFxttrn97HzZUKgyY10OvskW678V+3HqIvYjhiF8/sfX2v18dH7FP78Q4NWCO1d1PS4uyV9H7zmRstLL2b7L2fZu+QChTkNpyRBCQqVmlY9+zP69Y8Y+MSMa61BJIlLR/ax7pNZrP/f21w8sk8UehQIBDel0StEpV1mN1iInGs20wyguNUo87LNhX9q5BhTgx/ETe0OwHfRCyjSF5WzR8NA3fMOXD5fgMzFVNem8KfvyP/wXSR9ww7A9Q42udHCh1znRjuZxfrPT3JqSyJ6bcNTDGRyOf7tOjJk+kxGvjqXoMjeyOQKANJiz7Ljp89Z/tYzRG1cRXF+npWlFQgEdQ2hEN2QZVZcXFRmg1eoOYXI6BKIzqsDADbn/6nW3mYlOKgceDj0MQDSilNZEvtHtR+jrqJq1x6XBT8g9/UFQLN2NbkvP4cxv/52kq8ICqWc1r0t3WgGnZFTW5NMvdFO1O/eaLfCPSCQO+5/kvHvfE67waNR25v6+xVmZ3L0n8X8Pesp9iz6jqzEy1aWVCAQ1BUavUKkVCpRXc1WATAajTcvzphbc+4GTasxJnly4lCm10zg89CA4bR0NqX5L4n9g9Sihlen52YomzXH9esfUbY2xWvpDh0g56lHMKQkW1mymqfEjdb/4da4+posooU5WvYtjWXLD9FkJjbcrCwHtyZ0HjOZie9+RffJ/4err6mquUFnqme0eu4MNn4xh8snDmE0Nqzgc4FAUDkavUIEt65F5OVog+zqck1ZiAA0LUeal2squFohU/B02+dMxzNq+C56QY0cp64ib+KByxffoL6jD3C1VtFj09CfjbayZLWDZ6ATgx5vS5cxgdg4mOprZVzOZ9M3pzmwPI6ivIaTpn8jSrUNIb0GMur1Dxk8faZFPaPkc6fZ9t2nrHzneU5vXivS9gWCRopQiLh16r1KIcfdwWRBqkmFyOjoh9a3GwA251eDVDNvq+HuHennOxCALVf+42Rmw6zRczNkdnY4vfshtnfdA4AxI53s6Y+h3bPLypLVDnK5jKAuntz5XHtCe/kgV5iUgotH01k/L4ozO65g0DVcS4lMJsM3NIz+j77IuLc+o+2A4aiuXv/5GakcWvE7y954iv1LfiJHtAcRCBoVQiHC+rWIStBcDa5W5CeiTD5SY8d5tPWTqK+m4X91eh7GGlK+6ioyhQLHZ17A4ZkXTFaCoiJyX3uJohXLrC1araG2VdJhWFOGTg/Dr7UrYErTj/ovgQ1fniThdFaDjS8qwcnDmy7j72Piu/OJnPQQzt5+AOi1Gs7u/I9V777EpvlzSTh1FEm40wSCBo9QiAB7e0uFqKDA0mReawpR8AgkmelfUlPZZmBKw58UNAWAc7nRbExcX2PHqsvY3XUPTu99ZE7LL/jfRxTM/6JRPfycmthyx9RW9HkgBGcvk+u4IEvDnj8vsP3ns2QnF5YzQ/1HZWNL6z5DGDPzYwY++Sr+bTua1yWdOcGWrz9i5ZwXObNtA7rixpGdKRA0RoRCBDg4OFp8LiiwzD66XiGqybdmyd4TnX8vAGwurAFjzaVGTw66lyY2HgD8cPYbCvWNM27CpndfXL78FpmbqSRB0eLfyXvzdaTrAusbAz4tXRjyZDsiRjZDbWdKVU+Ny+O/Bac49M9Figt0Vpaw5pHJ5fi37cDAJ2cwdtb/CO0zBOXV5s95ackcXLaQZW88xcFlC8lLazwJCQJBY0EoRFRcISrWG8ktrtn6NSWtPBSFqaiS9tXYceyU9jzS2tTeIlOTwaKY32rsWHUdVZu2uH7zI4rmLQDQbt9CzrNPYszKtLJktYtcIaNVN2/ufC6cVt29kMlNFSBiD6axfl4UZ/ckN7g2IDfD2duXbpMeYuK78+ky4T4cPbwA0BUXcWbbBlbMfp4t33xMUnRUg3ctCgSNBaEQUXGFCGrBbRY0DEmuAq7WJKpBBvkNpY1rOwCWxi0mqbDxBpEq/Pxx+fp7VBGdAdCfOkn24w+jv3zJypLVPjb2SiJGNGfIU2H4tDT1CdMVGzi+Pp6NX53iyrls6wpYi6jt7Gnbfzhj3/yM/o+9ZK6CjSSRcPIIm756n3/ee5lzuzaha2RWRYGgoSEUIuqWQiTZuqFt1hcAm5i1YKg5V4VcJjen4euMWr49M7/GjlUfkDs54/zJ59gMuRMAY1IiOY8/jO5YzQW412VcvOzofX8Id9zbCqcmV11HGcXs/O08O349R25q44mnkcvlNG3fmSHTZzJ65ke06jUQxdX6ZTnJiexb/CN/z3qawyv/ID9TNJUVCOojQiECHB1vrRB5OV4r3FjTChGApqUp20yuyUadsLNGj9XGtR2D/IYCsDNlG0czDtfo8eo6MrUaxzfexu7B/wNAyssl54XpFP+3wcqSWQeZTIZfqCtDnm5Hh2FNUdma4ouSz+fw7/xTHF13GW1Rw26DciOuvk3pMfn/mPjufDqNmYyDmykWT1tYwKlNa1jx1rNs+/4zUi6cEe40gaAeIRQiwMbGFoVCYf6s0+nQaq8pPh6ONsivVmesDYVI22IoksJklapptxnAI62fxFZhsgDMP/05BmPjesDdiEwmw+HhR3F8/U1QKECnI3/2mxT+8mOjfcAplHJCe/lw53PtCerqiUwGklHi/N4U1s2L4sL+VIyGxnVubBwcCRs8mnFvz6Pvw8/h3bI1YGoqe/n4Af6dN5s1H77Ghb3bMOgabtFLgaChIBQirj4Ab3Cb5V/X50opl+FRC8UZS5DUjmgDBwGgjl0PNdyI1dPWk8nB9wEQm3eBNfE1r4TVB2zvHInzp18gu2pBLPzxW/LffwdJ1/Azrm6GrYOKLqMDGfxEOzxbOAGgLdRzZM0l/ltwipSYXCtLWPvIFQqaR3Rj6HNvMWLG+wR374tcaYoDzEq4xJ4/vmXZrKc5unoJhdmNK1BfIKhPCIXoKuXHEZksKLWhEAEUX+1tJtcVoL64ucaPN6nFFHzsTM1Pfz73PbnaxvdgKwt1566WjWE3rCP3xWcw5uZYWTLr4uprT7+HQul5TzAObiZrZk5qEdt/OcuuP86Tl9E4A4ybNG1Br3sfZ+Kcr+g4chJ2Lqamupr8PKL+Xcnfbz7Djp+/IC3ufKO1NgoEdRWhEF2looHVqfm1oxBpmw/AqDa9gdvWUG+z67FR2PB466cByNXlsPD8DzV+zPqCskUQrt/8hLKtKcNId/QwOU/8H4bEBCtLZl1kMhkB7dwZNj2M9oP8UapNt5Ok6Gz+/fIkx/+NR1dcc7W06jK2Ts6EDxvHhNlf0PvB6XgEtgJAMhq4eHgv6z99k3WfzCL24C4M+sbtohYI6gpCIbpKaZdZnsVns0JUw8UZzSht0QYNA0B9aQsyTc1bbHr79KNjk04ArLq8gri8mBo/Zn1B7t4Ely8WoO5v6gNnuHyJ7MemoYtqXL3gykKhktOmrx93PteewAhTgLHRIHF2VzLrPz9B7OE0JGPjtIbIFUpadOnJ8JdmM/ylObTo2gv51XjFjEsx7Fo4n+VvTuf4+r8pys22rrACQSNHKERXcXZ2tvice4NLxNvZpBBpDRJZRbUTQ1LiNpMZNKjj/q3x48lkMp5u8zxy5BglA/NPfy7M+tchs7HF6e33sJv6AABSTjY5zz2JZvN/VpasbmDnpCZyfAsGPdaGJk0dACjO13No5UU2fXuatEt55czQsPEIbEnvB55m/OwvCb9zPLZOpntOUW42x9cu4+83p7Pr1wVkXI61sqQCQeNEKERXcXJysfhcSiGqxVpEJegC7sBo1wQA2/Mra+WYQc7BjGo+DoAjGYfYnbKjVo5bX5DJ5Tg8/hSOr7xuykDTasl7eyaFv/0ilMeruAc4MuCRNnSbGISd89Xg4qRCtv4Qzd4lMRRk1871U1exd3Gj44i7mDD7K3rd9wTuTU0V0o16PbEHdrL2o5ms/9/bXDyyD6OhcbocBQJrIBSiqzg7WypEeXmWLioLhSi3lm7ociWa4JEAqOJ3ISvKqJXDPtjq/3BSmeKXvj7zJVpD436AlYXtqLE4fzwPmYPJElL43QLyP3wXScSDACZrY/MOTbjz2fa07e+HQmW61cSfzGTDFyc5uSURvbZxP+wVKhXB3fow4pX3GPb82zTv1B2Z3HSe0mLPsuOnz1n+9rOc/O8fNDfENAoEgupHKERXcXKydJnl5+dhvK7ruTUsRHCd20wymBq+1gIuahceavUoAFeKklgat7hWjlvfUHfthsvXPyD3uZqBtnY1uS89izGvcbuGrkepVhA2wJ9hz4TRtL2pga5BZ+T01iQ2fHGSyycyGr1lTSaT4RUcSt9pzzL+nS8IGzwatf3VUg9ZGRxZ9SfL3niKvX/+QPaVeCtLKxA0XIRCdBWVSoWdnb35syRJFoHV7vYqlFerM9amQqT37YLB0Q+onWyzEkY1G0OQUzAAf8T8SlqxaEdQFsoWwbh+8yPKNm0B0B0+aMpAS2q8feHKwsHVhh6Tgun/cGtcfU3XWWGOln1LY9n6QzSZiQVWlrBu4ODWhE5jJjPx3a/oPvn/cPUNAMCg03J+92b+ee8V/vvyPRKijiAZG0ejXYGgthAK0XXcKrBaLpPhVcup9wDI5GhajQZAdeUA8rzaedAq5EqebPMsAMWGIr6PXlArx62PyJt44PLFN6j79APAcCmO7McfRnfqpHUFq4N4Bjox6PG2dBkbiI2DEoD0y/ls+vY0B1fEUZTXeIteXo9SbUNIr4GMev0jBk+fSUBYJ5CZXsiunD3Jlm8/ZuWcFzmzbQPaokIrSysQNAyEQnQdNwZWl4ojcqy9atXXo2k11rxcG608Sujk0YXe3v0A2JT0L6eyomrt2PUNma0tTnM+wO6eewGQsjLJeeYJNNu3WlmyuodcLiOosyd3Ptee0F4+yBUykCDuSDrrPz9B9K4rGPTC+gEmd5pvaBgDHn+ZsW/+jzb9hqGytQMgLy2Zg8sW8vespzm4bCF5aSlWllYgqN8Iheg6bgysvjHTrMRCVNsKkd6jHXpXk/vKphbdZgCPt3kaldykCH51+jOMknhQ3QyZXI7DU8/g8OKMqxloGvJmvUrRsiXWFq1OorZV0mFYU4ZOD8Mv1BUAvcbIiX8T+PfLkyRFZzf6+KLrcfb0oevEB5gw5yu6TnwAJ08fAHTFRZzZtoEVs59nyzcfc+XsSXHeBILbQChE13GjQpSTk23xuaR9R2q+FkNtFpqTydBcDa5WpZ9EkVV7BRN97f24O2gKAGdzovk3YV2tHbu+Yjd2As4f/g/s7ECSKPj8UwrmfyFiPm6CUxNb7ri3FX3uD8HZ03SN5Wdq2PXHeXb8eo6c1Jrt5VffUNvZ06bfMMbO+pQBj72Mb6ipgjqSRMLJI/z35Xusfn8G53ZvRq8VGaICQUURCtF1uLq6WXzOvqERY0mmmcEokVVYu92rNSFjzcs2tVSTqITJQffhYesJwE/nvqOohpvNNgTU3Xrg+uW3yNxNmVVFi38nb/abSFrR9fxm+LRyYchT7eg4vBkqW1M155QLuWycf5Kj6y6jLRYlDa5HJpcT0L4Tg6fPZPTMj2jVayAKlcmam30lnn1//sDfs57m6Jq/RBVsgaACCIXoOlxd3S0+Z2dnWZievZ3U5uXadpsZXIPQebYHrsYR1aJJ3E5px8MhjwGQoUlnadyftXbs+owytDWuX/+IollzALSbN5Lz4jMiLf8WyBVyQnp4M/y59gRHeiKTgWSE83tT2PB5FBePpQt3UBm4+jalx+T/Y+K78+k0ZjL2bqaCrpqCfKI2rODvN6ez+/dvyEoSafsCwc0QCtF12NnZYWNzrd6QXq+3SL23Vi2iEjQtRwGgzI5BkXm2Vo892H8YLZ1DAFgc+wcZxem1evz6isLPH5cF36MMCwdAf+wIOU89giFFBMDeChsHFZ1HBTL4yXZ4NDfV5CnO13Pg7zi2/hhN9hWRWVUWNg6OhA0ezfi3P6fPtGfwCGwJmKpgx+zbzur3X2HT/LkknTkhFEuB4AaEQnQdMpmsDLdZlnn5eoUo2RoKUfAI87JNzNpaPbZcJufx1k8DpjT8n899X6vHr8/IXVxxmffVtbT8uFhynngY/YXz1hWsHuDqY0//h1vTbWIQto6mNiDpl/L57+tTHFl7CW2RcKOVhVyhILBTD4a/NIdhL7xDsw6R5rT9pDMn2DR/LqvnzuDCvu0YdKLUgUAAdUwheuONN7jvvvsqtO3EiRMJDQ0t9ffMM89USYbSbrNrcUSudirUCtNNJTWv9mNBjC7Nr7nNLtSuQgSmNPzuXr0AWJ+whpjcC7UuQ31FZmOL0+y52E6YBIAxLZWcpx9Fe+SQlSWr+1zfBiSkpzcyucljfGFfKus/jyLuSDpSbSY51DO8gkLo98jzjHvzM1r3HYpSbXqxy06KZ8/v37D8rWc4sWEFxfnClSto3CitLUAJS5cuZenSpURGRpa7rSRJxMTEMGjQIIYMGWKxzt/fv0py3KgQZWVdU4hkV4szJmQXW8VlBiYrkSotCmXWORSZ5zC4h9Tq8R9v/RQH0vZhlAx8E/0lH3Wdh+zqm6fg1sgUChyefRG5tw+FC75AKigg96VncXr7PWyuWo8EN0dlq6Djnc1o0cmDI2suk3YxD02BnoMr4og9lEqnkc1x83Owtph1FidPbyLvepAOIyZybtdmorf/S1FOFkW52Rxb8xdR/66kZfe+tOl/J85evtYWVyCodayuEBkMBr7++mu++uqrCu+TkJBAYWEhAwcOZMyYMdUqz61cZmBym1lTIdIGD4d9HwBgE7OOwlpWiJo5BjKq6RhWXV7O4fSDHEjbRzevHrUqQ31GJpNhP/le5B4e5L/3Duh05M16FemVmdiOGGVt8eoFLt729JsWSnxUJsc2xFOcpyMjvoBN35ymZXdvwgb6o7JRWFvMOouNvSPth4yh7YARXDyyl9Ob15KVeAmDTsvZnf9xdtcmmnXoStjg0Xg0D7a2uAJBrWFVl5lGo2HcuHF8+eWXjBkzBm9v7wrtd+GCyVUTHFz9F6ubm6WFKDPTssO8t7k4Y3G1H7siGFyD0Dcx9c2yiamdZq838kCrh3FQmt7Ev43+CoPUuLuW3w62g4eZahXZ2IDRSP4Hcyha/Ie1xao3yGQymoWb3GihvXyQyWVI0tVstC+iSDydVf4kjRyFUklwZG9GvjqXwdNn4t+uo2mFJHH52AHWffwGG798j6ToKBGALWgUWF0hys/P57PPPuPDDz9EqayYwer8eVMwaolCVFhYfRknrq5uKBTX3i4LCwss5vdyNClEGQVa9FaKW9C0NAVXKzOia7VIYwmuNm5MDjbFel3Mj2NL0n+1LkNDQN2tBy7/+wqZoxMABfM/p+C7BeLhUwlUNgo6DGvKkOuy0Ypydez+8wK7/jhPYY4oTFgeJe1BBj4xg9EzPya4e19kctM9MPnsSTZ99T7rPprJpaP7MYriooIGjFUVIkdHRzZu3Mjw4cMrtd/58+dxcHBg7ty5REREEBERwaBBg1i7tuqBxnK5HHf3JhZjGRnXOr2bizNKJqXIGmiCR5qXbWKsUzl6fOAk3G1M5+mXcz+gM4pMldtBFd4Bly+/QXb1N1f02y8UfPoBkkFY3SqDi7cd/ae1psuYQHNRx6TobDZ8cZJze5MxiqDrCuHqG0Cvex9n/Duf06b/cHMAdkZ8HNt/nMeqOS9ybvdmkZkmaJBYVSGSy+UVtgpdz4ULFygoKCAvL4+PPvqI999/HwcHB1544QVWrlxZZbmaNPG0+FyWQgTWqUUEYHALRu8eCoC6ltPvS7BV2HJfywcBuFKUxLr41VaRoyGgbNkK1wXfI/czJQQUr1pB/rtvIelFSnllkMllBHXx5M5n29Ms3OT61muNHFsXz+ZvT5OZWGBlCesPDm5N6DrhPsbP/pIOIyZi42CyvuWlJbPvzx9Y/tYznNy0Gl2xqFovaDjUqbT7ijJp0iTefPNNvvjiCwYPHsyECRNYsmQJTZs25eOPP8ZQxbfr0grRtSKEno7XqlWnW8lCBKAJGgaYepvJ85OsIsPwpqPxtfMD4PcLv1BssE5cVUNA4R+A6/zvUQSZCulpNm0kb/YsoRTdBraOKrrfFUyfB0JwdDe9wGQlFbL529Mc23AZvU64fSqKraMTHe6cwPjZX9J14gM4uHkAUJSbzZGVi/j7TVPKvrZIFMoU1H/qpUI0efJkpk6dajFma2vLmDFjSE9PNwdd3y4eHh4Wn9PTr1mIPByuU4jyracQaQMHm5fVFzdbRQaVXMUDIQ8DppYeKy8us4ocDQW5hwcuX36NIqQ1ANqtm8l78zUk4Z64LXxaujDk6TDa9PVFrjAFXZ/bncLG+SdJuyRq7lQGlY0tbfoNY9zbn9Hr/idx9Q0AQFuYz7E1f7H8zWc4vm4ZmsJ8K0sqENw+9VIhuhnuVxtpVjXI2t3d0kKUlZVhtjq52auRXy27k1FgvYBNvVc4BntTVp46bqPV5BjoN4RAxxYA/Bn7G/k6cUOsCnJnF1zmzUfZph0A2p3byZ35CpJGBAffDkqVnPaDAhj8RDvcA0yZkfkZGrb+GM3RdZfRa0WsVmWQK0yZaaNe+5B+j7yAW8DVPn1FBRxf9zfL33yGo2v+EkUeBfWSeqcQpaSkMGLEiDLrFsXFxQEQEBBQpWPY2dnhcNVnDmA0GsnMNLnNFHIZbvYmK5E1XWbI5GgDBwKgTtgNWuvERyhkCqaFPApAni6PlZeElaiqyJ2ccP7fl+b+Z7q9u8l9/WUkjXBJ3i4u3nYMeKQN4UMDUChlcDVF/9+vTpEal2tt8eodMrmcZh26MnLGXPo/+iJNmppeinTFRURtWMHyt57hyKo/Kc4T51ZQf6h3CpG3tzd5eXksXbqU/Pxr1ogrV66wfPlyunXrhqen5y1mqBheXpY1kVJSks3LJW4zqypEgLaFqUq3zKhFnbDDanL08u5DsFMrAJbFLaFIL+IJqorc0RHnTz9H2SECAN2BfeTOnIGkte5vrj4jl8tofYcvQ54Kw6OZ6YWnIEvDtp/Ocnj1JWEtug1kMhlNw7sw/JX3GPDEK+ZCjnpNMSf/+4flbz3D0X+WoC0UAe2Cuk+dV4ji4+NZtWoV8fHx5rE333yT5ORk7rnnHhYuXMiCBQuYOHEiSqWSt956q1qO6+1tWbo+JeWKedmsENVADJEkSby9PprfDsaXu602oBeS0hYAmzjr1QKSyWTc2/IBAHJ1OfxzeaXVZGlIyO0dcPl4HqpOnQHQ7d9L3jtviEDrKuLkYUu/h1vTcXhTFCrTLTDmQCr/LRCZaLeLTCYjoF0Ed740h4FPvopnC9MLkl6rIWrjSpa/9SxRG1ehE1ZOQR2mzitEBw8e5JVXXuHgwYPmsUGDBjF//nzs7Oz45JNP+Pnnn+nYsSN//vlntVWv9vLysficmlrzFqK4jEKeXHqCzefSy98YQGmHNqAPAOpLm8FovTfc3j79aO4YCMBfsYvQGETMS3Ugs7PDee6nZveZdsc28t9/R9QpqiJyuYyQHj4MffpaQce8jGI2f3eG09uSRN2i20Qmk+HftgPDXniHQU+/brYYaYsKOPrPYla8/RzR2/8VdYwEdRKZ1AjL4up0BrKzb+3W0Wo1/PDDfIuxhx9+ChsbG77efZGf9l1GBux5vjdKuYzD8dnM3xmHt5Mtl7IKsVMpeCCyKUuOJHIpq4gBrTzoFeTO59tjSx1rep8W9Ah056PNFwj3c2bfpSyCm9hzX9em5X4X21N/4LRtBgBZd61F79Wh4ieimtmU+C/vH38HgKfbPs/4wLusJktDw5ifT+5zT6I/Gw2AzcgxOL7yumisWw0YjRJndyVzaksiRoPpdujRzJHIiUE4utmUs7fgVkiSRHzUYY6t/ovsK9es3g7uHnQYPpGgrncgV4i+c4Kq4+npVOU5hEJ0CxYvXmjRy2zUqAk0bdqcpceS+GizKbV/3WPd8HS04XB8Nk8tPcHCqZ0I9Xbkmb+jyNcY+PbucAo0Bu78dh//PBKJp2P5N9i3N5ytsEIkz02gyW/dASjoNoPCLtPL3aemMBj1PLBjMkmFiXjZevN7v6Uo5VbvH9xgMOZkk/PMExhiTe1abO+eguPTz1lXqAZEVlIB+5bGkpducuso1XI6jWpOYEePcvYUlIfRaOTi4T0cW7uU/PRU87iLjz9dxt+Lf9uO1hNO0CCoDoWozrvMrMmNbrOSOCKLWkTXuc38XGwJ9TaZ3wNc7ejSzAWVQo6rvQoHtYKt59OZ8uvhUn97L2betoxG5wD0LqYMD5UVA6sBFHIl9wTdC0BqcQo7k7dZVZ6GhtzFFZf/fYmiaTMAipcsomjJIitL1XBw83Ng8BNtadnNCzBVuT7wdxwHV8aJYo5VRC6XE9T1DsbO+pTu9zyMnYsbADnJiWxe8CH/fTWXrMTLVpZS0NgRr++3wMfHl+joU+bPSUmJQBnFGa8mpKkUlvqlUm7pzujU1JVJEf7VLqeuWR+UUXGorhwCXSGo7Kv9GBVlsP8wfjz3LTnabJbGLaaf70Dh1qlG5E08cP7fl+Q8/jDGjHQKvpqH3NMTmwGDy99ZUC5KtYJOI5vjG+LCgeVxaAr0xB1OJzOhgB53B+PsaWdtEes1coWSkDsGERTZh+jtG4j6dyW64iKuRJ9gzQdRtOw5gI4jJmLn7GptUQWNEGEhugV+fpYuq+TkRAwGAx7Xte+wVoPX6ykJrJYZdaiT9llVFhuFDaOajQUgOuc0p7JPWlWehojCxxfnj+chszcVGsx79210R49YWaqGhW+IK0OebIdnoMkMn5NSxKZvTnP5REY5ewoqglKtJmzwaMa+9RkhvQchk8mQJInzuzez4p3nifp3pQi8FtQ6QiG6BS4urthffegA6PV60tJScLNTmceyi6x/0er8eyDJTIGJqvidVpYGxjQbj1JmMj4ui1tsZWkaJspWITi9+wEoFKDTkfv6S+gvX7K2WA0KO2c1fR8MpXUfUwkOvdbIvqWxHFl7CaNBuNCqAzsnF7rf/TCjXv/QHEek1xRzdPUS/nn/FRJPH7eugIJGhQiqLoeNG9dy4cJZ8+fu3e+gU6dI7vh8Fxq9kamdA3iuX1BNiVphXP8eiyr5EPombci6x3o1iUr44PgcNiauR46cRf3/xsvOu/ydBJWmeMM68t97GwBFs+a4fPszckfHW+8kqDRXzmWz/+84tIWmGlBeQU70uLslNvYi6qA6STpzgkPLf7fISGvWMZKuE+7Hwa2JFSUT1HVEUHUt4Odn2QYkMdF0obpetRJlF1vfQgSg8zNlmikyopFprF8uf3zgJACMGFmfsMbK0jRcbIcNx+7+hwAwXL5E3juzRI2iGsA3xJXBT7TF1dcUn5cam8emb06TnSyqslcnfm3CGfnqXLqMvw+VrSle6/KxA6ya8yIn//sHo0EUJRXUHEIhKgd/f8s4oitXkjAYDGaFKKcOuMwAdL5dAZAhoUw+bGVpIMQllFbOoQCsj1+DQRIP6ZrC/uHHUPfqDYBu324Kv//ayhI1TBxcbRjwf61pGmZqIl2QpWHL92dIOpttXcEaGHKFgrYDhjPmjU8I7NwTMFW8PrLqT9Z+/AaZCRetK6CgwXLbCpFer+fo0aOsW7eO9PR08vPzycnJqU7Z6gSurm43xBHpuHIlEVc7k6m8LsQQAeh8OiNhyuZSXTlYztaVx/bEz7gtGoDbnwNxXjsNWWH51bRHNB0NmFLwD6dXv0wCEzK5HMdZ76AINJVfKPrjVzS7rR9L1hBRqhV0nxRE+8EBIDPFFe3+4zwxh9KsLVqDw97VnT4PTWfw9Jm4ePsBkJVwibUfvcHRNX+JoGtBtXNbCtH69evp168fU6ZM4cUXX+T8+fMcPnyYvn378sMPP1S3jFZFJpPRrFmgxdjly3HXXGZ1RCGSbF0xNDFZZFRXDlTr3MrUE9gf+5bsCSvJmrwZg2sLHPZ/XO5+A/wGY6sw9Vpbe/mfapVJYIncwRHnuZ8gczAp7/nvv4MhJcXKUjVMZDIZbfr40mtySxQqOZIEh1dd5OTmRBphSGaN4xsaxshXP6D9sHHI5HIko4GoDStY+9HrpF+8YG3xBA2ISitEu3bt4sUXXyQwMJAZM2aYbwABAQGEhITw6aefsmrVqmoX1Jo0a9bC4vOlSxevc5nVHZ+2zjcSAFXKUTBcKwegStyD67LROP37BG6Lh+D691jUcf/hsmoy7gsjcdj1Nqr4nbgtHlLqT3V5G3qvcDKn7kSycQZ9MfKCZCRbt3LlcVQ50tdnAAB7UneSo214FsS6hCKgKY6vvA6AlJtL3mzRCLYm8W/jRr+HQlFfDaw+vS2JQ6suij5oNYBCpSJi5CSGv/wubgHNAci+ksD6T9/k+LplGEXcnKAaqLRCNH/+fMLCwvj1118ZM2aMeTw4OJhFixYRERHBwoULq1VIa9O0aTOL4oJZWRk4K0wKR55Gj76OpODqfLoAIDNoUKaftlinTD1OUaenyLpnI5LaEfsjX5EzciFZkzZgF7UQg3srsu7ZWOpP16yfaQKFCnXsBpos7IoqaR/FbSZVSKahAcMBMEgGUbm6FrAZMBjb0eMA0J84TuHCn6wsUcOmSVNHBj7SBoerPc/iDqdz4O9Yc080QfXSpGkLRrz8Lh1H3oVcoUCSJI6v+5uNX8whP7OCTbEFgptQaYXozJkzjBgxArm89K5KpZKRI0cSFxdXLcLVFWxsbPHx8bMYsy26dvHlFNeNt3C9d0fzsjLdsiCiwbkpes8w07JLc7T+PUGhRrJzR1I7oo5Zf1MLUQnaoGFkPBxFYdcXcFl9L0jlK4Lt3TvgbmNKl912ZXPVv6SgXByeeR5FkKnLeNFvP6M/d7acPQRVwcnDloGPtsHF+2pW1IlM9i2NEbWKagi5Qkn4sPEMf/k9XHxMlf9TY86yZu6rXDq638rSCeozlVaIVCoV+luY4bOzs1GpVDddX1+50W1mzE40L+fUkdR7g0sgRpUphkSZdkOFaMUNTWVvaLqq8+9xUwuRPDsOZdK1uKTiNvcgz0tApinfBaaQKejr0x+AYxlHyNTcft82QcWQ2dji9MY7pqKNBgN5c2cL11kNY+uoot+01ua0/IRTWez7S1iKahL3gOaMeOU9WvUaCIC2qIDtP87j8Mo/hAtNcFtUWiGKjIxk2bJlaDSaUutSU1NZtGgRnTt3rhbh6hItWgRbfC7MSkaN6SFToKkjF59Mjt7DZAVSpkVV27SKwlScNz6JrMikzNicW4HBPbRCcUQA/f1MfbaMGNmZvLXa5BLcHGWrEOzufRAAw4XzFP3RsNzYdREbeyX9HgrFPcD0UpJwOovDqy+KQOsaRKm2ocfk/6Pv/z2P2s503k9tWsPmrz9EU5BvZekE9Y1KK0QvvPACaWlpjB49mgULFiCTydi8eTNz585l5MiR5Ofn88wzz9SErFbF3b0Jbm7u1wYkiWaKbAAKtHXn7bvELabMiAZD9ViudH7dKOzyDK4r78Jt8RBszq8iZ/iPFd6/rWs7mth4ALA3dU+1yCQoH/sHppldZ4W//oIh+YqVJWr4qO2U9HkgBFcfk6Uo7nA6Uf8lWFmqhk/zjpEMf+VdXH1NdeOuREex9qOZZCXFl7OnQHCN22rdcfbsWd59910OHrSsLRMWFsYbb7xBx44dq0u+GqEyrTuu58CB3Rw6dM1HHW9wYZO2FR+MasPAEM/qFPG2sYlehvPm5wDIvOc/DE3aWFegq3wSNZd18atRy9WsGvwvNje68AQ1gu7EcXKeegQAdf+BOM+ea2WJGgfF+Tq2fH+G/EyTJb3TyOa07OZlZakaPjpNMXt+/8YcS6Sys6f/oy/i06qtlSUT1DRWa90RGhrKb7/9xr59+/jrr79YvHgxO3fuZNmyZXVeGaoKQUEhFp/95Lmo0ZOvqUMWousUIGXmeStKYkmkZw8AtEYtxzJEZ/baQhXeAZtBQwDQbt2M9qj1q5g3BmwdVfR5MBRbR1M85dF1l0mNs35LnYaOysaWPtOeJWLU3QDoigrZNP8DEWwtqBC3pRCdPHmS559/HoPBQHh4OB07duSnn37imWeeISYmprplrDM0aeKBi4ur+bNCJtFckUWBto7EEAEG12vB34qsulO0rHOTrihkCgAOpO21sjSNC/vHp4ONySJX+O18EdNSSzi62dBrSkvkChmSUWLP4hjys0rHXgqqF5lMRvuhY+l1/5PI5AqMeh3bf/qcmAOiervg1lRaITp06BBTpkxh9+7dZGVlmcc9PT05fPgwEydOJDo6ulqFrCvIZDJatgy1GGulyKg7QdUAKnsMjqYSAYrsuqOcOqgcCHMLB+BIRvVaKb4+8wX3bBnHIzsf4JGdDzD76Kxqnb++o/D2xu6uyQDoT51Ed6h6K5kLbk6Tpo50GRMIgLZQz76/RDp+bREc2ZuBT7yCUm0DksSe374m9uBua4slqMNUWiH6/PPPadGiBRs3bqRly5bm8WnTprFu3TqaNm3Kp59+Wq1C1iVat7b0RXsr8snPz7aOMDfB4GoKpFVkx1pZEkvC3TsCcCk/jlxt9bkPTmVF8UbEbL7vvZDvey/kzYg51TZ3Q8Hu7ilgZ6qTU/jzD8JKVIsERnjQsrspfigzoYBTW5OsLFHjwa9NOAOffBWl2gZJktj963zhPhPcFGX5m1hy5swZXnjhBVxdXUutc3FxYdKkSXz55ZfVIVudxMXFDV9ff65cuVaHyJhxGehgPaFuwOAWBAk7UWbFgCTBdVW2rUmYW3vz8unsKLp79eJYxhF+OPs1XnY+xOdfxlZpy+Sg+1hxcSnxBZfp7dOP7l49+ebMV6Xme7T1E3Rw78T53PMsif2dzwoSCXBoxpNtn8Hbzqc2v1qdR+7qit34uyj641f0UcfRR51AFV53frMNnQ5DmpIWl0dOShHRO67gF+pKk6aO1harUeDdsjUDnniFLV9/hF6rYdev87F3a4JnYMvydxY0KiptIVIqlRaushvJz8/HaGzYJuHQUEsrkSo3vk59Z4OLKY5Ipi9EVlx3CiG2cQ1Dhkk5O5l1rU5SdE40k4Pu5fveC3FQOrAo5lfe7/oJ397xM6su/U1zx0Cz9ef6v66e3cnQpBPRpDPTQh7lh96/0catHbMOzxAWkDKwmzQZlKZ3oOKVy6wsTeNCoZLT/a4g5EqZqRns6kui51kt4tOqLX3/73lkcjkGnY6t335MfkaatcUS1DEqrRB169aN33//nfj40vUdUlJS+P3334mMjKwW4eoqLVuGoFReM64pDcVculR33FMGR1/zsiK/7tSecVQ50sIpCICz2WfM4752vrRyMcVm+dr7E9GkEyq5Che1K/ZKB3YmbzfHB13/dzBtH772fnzQ9VNaOAUjk8m4u8UUkgoTSS6qO9+7riB3b4K6r6nZrmbbFoy3eLERVD8u3va07m26NrOvFBJzINXKEjUu/Nt2oNukhwAozstl+4/zMIgK7oLrqLTL7Nlnn+Wuu+5i9OjR9OnTh8DAQGQyGZcvX2b79u3IZDJeeOGFmpC1zqBW29CyZSjR0afMY1FRx2jRom6YYI0O1xQief4VuFqssS4Q5BRMbF4MF/Ov9btTyS1bvShklj/Ljk0iGBc4scz5YnIvEJN3niH+d5rHJAmUskr/tBsFdmPHo928EXQ6NJs3YjfxbmuL1Kho3duXS8cyKMjScHprEoERHqhsFNYWq9EQcscgspMTid62gYzLsRxdvYQu46ZaWyxBHaHSFqKgoCCWL19O37592blzJ99++y3ffPMNW7ZsoXv37ixZsoTg4ODyJ6rntG/f0eJzQsJlMjMzrCPMDRivsxDJC+qWpSTwqoUoQ5NOjrb8XmjlIZfJ+OrUPK4UmgJV/7m8nCDnYDztRBG8slB2iEDuY/p9aLZtsbI0jQ+lSk74kAAANIV6LuwXVqLapvOYKbg3NYUVnN6ylrS4ulOvTWBdbus1unnz5sybNw9JksjKysJoNOLm5oZC0XjedDw9vSlUuWCvu/ZQP3nyGH36DLSiVCaM9l5IMgUyyWCyENUhgpyuKcsX86ruZmzhFMz0ds8z89DLGCUjnrZevNHxnSrP21CRyWTY9BtA0eI/0J84hjEjHXkTD2uL1agIaOuGi5cdOalFnN2dTEgPbxSq2yoJJ7gNFCoVvR98mtVzZ2DU69m35EdGvPwe8kb0/BKUTZWuQplMhru7Ox4eHo1KGSohz6G5xefo6FMUFVW+JUi1I1dgtDM95OSFdesNtJljoHk5vuAyHZt04qc+f5jHnm33Ig+G/J/588rB62nhdGuL42D/YfzU5w9+6fsnH3f7XGSYlYO6T3/TgiShPShqEtU2MrmMNn1NVjptoZ7EMyKWq7Zx8fYjbPBoALISLhF7cJeVJRLUBcq1EA0cOJDXX3+dgQMHmj+Xh0wmY9OmTVWXro6jdfSlIOsMDjJTE1W9Xs+JE0fp1q2XlSUDycYFClOQa+pWuwBPWy9kyJCQSCuuW8paY0HZpq2pJlFREbrjR7EdNtzaIjU6/Nu6obZXoi3UE3s4jWbhTawtUqOj/ZAxnN+zlaKcLKL+XUlQZG/kcmGpa8yU+9/38/PD3t7e4nN5f76+vreYseGgVik4qfO2GIuKOoZGY/3y/JKtCwAyTdXjdKoTlVyFu43p5p9alGJlaRonMqUSVZiparjumOgrZw0USjnNO5iug7S4PDSFItuptlGo1IQNGgVAXloyCSfFtdDYKddC9Ntvv1l8/uKLL3Bzc6sxgeoTaoWccwZPIkhGjemGptVqOHXqOJ06Wbf0gFHtDICsjlmIwGQlytCkCwuRFVG2a4/u4H6MCfFIxcXIbG2rZV5Jksh//x0UQS2xn3yvacxgoGD+5+j270UyGLC7Zyp2YydUy/HqM36tXTm/NwVJgpQLOcJKZAVa9uzP0TV/odcUE3tgJ83Cu1hbJIEVqbR9cNy4cSxYsKAmZKl3KOUy9Ci4IFnGrBw7dsjqViLJxqQQyeuYhQigia3pxp+lqTtFIxsbyuaB5mXD5UvVMqf+Yhy5zz1ZKnut+J8VGOIv47rwT1y//4XipYvRnT51k1kaDx7NHFGqTbfglNi69+LSGFDZ2NK8o+nlNeHkUfRarZUlEliTSmeZZWZm4uEhslLAFCsFEIMPHVSp6HSmi6m4uJhjxw5ZNZZIUprcnDJ9kdVkuBkOSlPLgkJDHQhAb6QoAgPNy4bLlzAW5FP47Xzk3j4YLl9CZmuH3b0PULxsCYbLl1D37Y+65x0UzP+81FwOjz+NulsPilcsw2bkGOReli8I2h3bsB09FplSiczJGfXAwWg2rkfVtl1Nf806jUIpx83PgbSLppYeAusQENaJmP07MOp1ZFyOwbtlG2uLJLASlVaIRo0axZIlS+jZsycBAQE1IVO9oaRDmBYlHTt25uDBveZ1x48fJiysAw4OVupXpLj6rzXWvdgEe6UDAIX6AitL0niRe1yr02TMzkLRpAn66DO4vjADZUgoOS89S9Hvv+DyxTdIBQVkjhuO3ZT7cPv5j5vO6fj8ywDoDlg2zzSmpiD3uhZrp/D0QhtzoZq/Uf3ExduOtIt55KYKhchaeAWHmpfTLl4QClEjptIKkVwuJzY2lqFDh9KsWTOaNGlSKjJfJpOxcOHCahOyrnJ9z9SOHTtz8uRxc9q9Xq/n4MF99Os3yCqySSXVn+ukQmSyXhXohYXIWsgcrynqxtwcFIDc1w9liOnhoPAPQObggEylQubqiszBAe32rRSvWVVqrhIL0c2QjEauvT4AEiCyeQCwc1YDoNca0WsNKNWNr3yJtbFzdkVla4euuIiCzHRriyOwIpVWiHbv3m0OqtZoNCQlJVW7UPUNSQKVSk2XLt3ZufNa/MSZM1GEhXXAw8Oz9oWSm/61MqOu9o9dDnKZ6WEoSXWnIW5jQ6ZUIrOzRyoqRMrPN42pLFuooLS8PagiOmM3YVKlj6Xw9sF4XSNNY0Yack9RSRzAxv7aOdYU6oVCZCXsXd3JSU6kKCfb2qIIrEiFFSKdTseFCxf4/PPPadmyJXZ2djUpV71CwtS1um3b9hw/fpjcXFMgsyRJ7NixmXHj7jbHG9WaTHXYQlTSiV5G7Z4TgSUlCqmshouqqu/oQ/Ha1ah79kYqKkKz+T8cX3y1Ro9ZbxCXQN1C/D8aNRVSiH755Rfmz59P/tU3SbVazZQpU3jxxRctur43Nm5UchQKBb169WP9+mtuheTkJM6ePU3r1rUbQCorUYTkdfH/Y1KIqGUlUXADJZ2+lapbb1dFbMdOwJCUSPZDU5H0emxHj0MV0alGj1lfMOol87JcIa4Ha2G4mhAjV9TF+6Wgtij3v79y5Uo++OAD/P39GTNmDHK5nP379/PLL79gMBh4/fXXa0POOo107Z5GixbBNG8exKVL1/p07d27g8DAYGyrqdZLhTCY0v4lhU3tHbOC6CUDAAqZcA9YC0mrNStEMhsb1BGdUf+62Ly+JEC6hCZr/qvw3E4z37L4LFMqcXzmhSpI23ApyjM9iGUyS/eZoPYw6PXm2CHHJlYIbxDUGcq9AhctWkTHjh1ZuHAhNjamh6skSTz//PMsWbKEl156CbVaXeOC1id69+5PQsIlDAbTg7+oqIjdu7cxcOCwWpNBZrhaT0NR9/43+bo8AByVVsrAE2BMu1YUU+4pHgLWIj/T9OJi66RCrhCB5tYg+0q82Y3v7NU4uiwIyqbcKzAmJoZRo0aZlSEwuYoefPBBtFotsbFV71heX9EbTDEYqhtuZM7OLnTu3M1i7OzZ08TG1l6qcYlCVBctRPk6k+vVUSUUImthSL3WNuX6lHhB7ZKVaCo94epjX86Wgpoi6cwJ87J3y9ZWlERgbcq1EBUVFeHk5FRqPCAgAEmSyM1tvBVWdUbTW4WqDN9/REQXLlw4R+Z1aZzbt2/C19e/dgLSrxZklJR1USG6aiFSlf5dCWoHQ9y1FxmFf+OuJ2YtCnO1ZguRe4BDtc0rSRIHlsfh4m1H6zuuWTxWzj2KvfO1eLHQO3zN/dQaK5IkcfGIqX6ck6cPTh7i5aAxU65CZDQay8yQUlzNTClxCzVGdCUWInlZ50fJoEHDWLZsEUajabuiokK2bdvIsGGjazzrTF6cDYBk41qjx7kd0jWmFGx3G3crS9J40Z85DYDM2Rm5r5+VpWmcJEVnm5d9WrlUy5y5qUUcWXOJjIQCXLyvvXjlphWhtlMw5KmwajlOQyH94gWyEkyta4Ije1tZGoG1EVF8VUBnMFmIlDfx/Xt4eNG5czeLCtZxcTGcOHGUDh1qNstGVpwFgNG2bjXilSSJlKJkALzthL/eWujPmHqJKUPb1HpJCIGJS8czAFP8kLufA6lxuUT9l4C9i5q89GIUagVtevtyfl8KeenF+Ld1wy/UheMb4kvNFT6kKT6tXLhwIJUWnT2xd7WMHcyIz0cmk7HlhzPoig0EtHOjTV8/5GW8zDUmTmxYDoBMrqBlz/5WlkZgbSqkEGVnZ5cqwJiTY6q1k5mZWWZxRj+/hv/WabYQ3SJdtlOnSC5diiX1upiNvXt34O3tg49PzZ0jebGpcapUxxSiHG02xYZiALztfMrZWlATGJISMVy6CIAqvKNVZWmsZCUVkHHZFEsXGOGB7KpikplYQKeRzXHzc2DHr+c4syOJftNao9cYWP3xcVrf4XNLK0+nkc0BSImxbOpsNIJ3sDPhQwIwGiR2/n4elY2CkJ6N9xq8cvYkiaeOAdCye1/sXerWvVJQ+1RIIXr//fd5//33y1z30ksvlRqTyWScPn26apLVA/RXY4jUt8gOUSgUDBkykr/++h2t1hQvYDQa2bhxLZMm3Yutbc3EE8nNFqK65ZZKKkw0L/sIC5FV0O7ZZV5W9xJuAmtwdrfJSiqTQXDXa1l+Dq42uPmZ4okc3W1Q2dijUMpRKOUobRQknM4i7nBaqflKLEQ3I7iLZSZhaE9vzu9LbbQKkU5TzL7FPwKgVNvQYcREK0skqAuUqxCNGzeuNuSol2j1JguRspy+TM7OLgwYMJQNG/4xj+Xn57Fhw2pGjZpgjseqLmTaPHOXe6Nd3VKIYvKuZdoFOQVbUZLGi2bbZsCUXaZo2crK0jQ+sq8UcjnKZMH1b+uGg+u1xAe58oa+kDdYn71aONGqe+UDfy8eS8fVx96czSZJmK1SjZEjKxeRl2ZSSjuMmCisQwKgAgrR3Llza0OOesmtssxuJCioJR06dOb48cPmsaSkBHbs2Ey/foOrNY5DnpdgXjY6N622eauDmNzzANgp7PG1b/hu1bqG/vIl9MePAWAzoHp/d4LykSSJ4xvjQQKZHNoPqp0Mv5yUIhJOZdFzckuMBokL+1Np1kgzzGL27+DsTlOhUa/gUNr0H25liQR1BVEJrAoUaU0Zdnaqill4une/Az8/f4uxM2dOcuzY4ZvscXsocq8pRAanupVSfeGqQtTCKcjc5FVQe2hWX2srYzNqjBUlaZxcOpZBygVTqZKgzp44edRO9fp2/f1Q2yvZ+NVJNn51kibNHAnq7FErx65LpMWeY++fPwBg4+DIHfc/hbwcC7+g8SCyzKpAoc6kEDlUsEO1QqFg6NDR/P33InMDWDAFWdvb2xMa2rZa5JLnXctCMdYhhUhr0HA+9ywAIS6iAFptY8zPp3jNSgCUHTqibNbcugI1MorytBxddxkAW0cVYTdYh7xaODNs+rWA6ZIA6RLGvhZR4WNFjg+y+KxUK4gc16KyIjcoMhMusvnrjzDqdcjkcvo+/Lxo1SGwQKjGVSBfY+oFZV9BhQjAzs6OESPGoVZbFkzcsuVf4uJiqkWuEguRpLDBaF93LvgzOafRGXUAhLt3tK4wjZDi5UuRrjZotrvnXitL07gwGiT2/RWLrtj0EtV5VHPRu6wWyUqKZ9NXc9EWmSqD95j8CD4h1fMCKmg41CmF6I033uC+++6r0Lbx8fE8/fTTREZGEhkZySuvvEJmZmYNS2hJobbEQlS5G5ubmztDh460MNVKksTGjWtITLxcZbkU2abAZYNzM1OgQh3hROYx87JQiGoXY0E+RX8tAkAR3FJkl9UyUf8lkHbRVKE9MMID/7YiiLe2SI05y7+fvUNxvslV2XXC/bTs0c+6QgnqJHXmFWXp0qUsXbqUyMjIcrfNysrigQceQKvV8n//938YDAZ+/PFHzp49y9KlS2ul2azeKFF8Ncusoi6z62natDmDBg1n48Y15jGDwcDatSsZPnwsAQHNbls2ZYbJLaVvUrfcUkfTTbFSTR2aiSrVtUzRwp+QrtYOs3/gYRFMXYtcPJpuTrN39bGj08jbv7YFlSMh6gjbf5qHQWeyTHceN5U2/e+s0WPGHtjJqc1rABlKtZquEx/Ao3kwRqORw8t/I/HMCSSDgbYDRxDae3CNyiKoHFZXiAwGA19//TVfffVVhff55ZdfSE5OZvXq1QQHm1K3O3TowEMPPcTKlSuZNGlSTYlrpiSgGsDB5vbS5lu2DEGrHcS2bZvMY3q9nrVrV3DnnaNp1qzyPn+ZNg9FvqnWj8E99LbkqglytbmcyDoOQFfP7laWpnFhuHyJoqWLAVCGhaPuN8DKEjUerpzL5uDKOADUdgp6Tm6J8jZeoASVQ5IkTm5cxdE1f4EkIZPL6THlUVp271ujx81JSeLwykWMmPE+9i5uJJw6yrYfPmPinK84t2sTuanJjH79I3SaItZ/+hZNmrbAI7BljcokqDhWVYg0Gg133XUXZ8+eZezYsezdu7f8nYC1a9cSGRlpVoYAevbsSYsWLVi7dm2tKEQFWr152b6CWWZl0bZtOBqNhr17d5rHDAYD69atYujQkbRoUbmLRZF5zrysb1J3FKL9aXswSiYlspe3cNfUFpIkkT/vE9DrQSbD8bkXhXWolki/lMeexTFIRlAoZdwxtRWO7rWTVdaY0WmK2fP7N1w6uh8wFV7s/dB0mrbvXO6+yedOc+SfxTi4NyE35QpKGxvCBo8metsGclKv0LxjJP7tIji84o9S+3YaMxkXbz96THnEXNeoSbMginOzMej1xB8/SKteA5ErFNjYOxLYqQexB3cJhagOYXWFKD8/n88++4zhw4czYED5b645OTnEx8czdOjQUuvatWvHtm3bakDS0hRYWIiqdhojIroik8nYs2eHecxoNLJhw2r69h1E27btKzyXMv2MebkuWYh2p5gUPkelE+3dOlhZmsaDZvUqdAdNDwab4aNQhraxskSNg7SLeez87RwGnRGZDLrfFYxHcydri9XgyYiPY9cvX5GTYmon5ejhRf9HXsDNv+IZlRmXY+h290M0adqCTQs+4OTGVQx59k10xYUsm/kk7QaOZNRrH9x0/5LMNUmSOLT8NwLad0ahVFKQnYmD27XaTw5u7mQnVT1mVFB9WFUhcnR0ZOPGjSiVFRcjJcXUE8zbu3S1Vk9PT/Lz88nLy8PJqWZvPnnF1yxEjrfpMruejh27oFAo2blzi3lMkiS2bfuPvLxcIiN7VujNXpl6FACj2gmDS2CV5aoOivSFHEjbB0A3rx4o5Vb31DYKDMlXKJj/OQByTy8cnnrWyhI1DlJic9n1+3kMOiPIoOu4FiKIuoaRjEZObVnLsdVLMBpML6u+rcPp89B0bBwcKzWXYxMvmjQ1hSs4eXijtrVHoVSicHRGZWvH5eMHOb9na6n9Oo2ZjH9b08teiZWqICuDQU++apaR6+7h0lVXnqDuYNUnk1wur3RRrIICU9qknV3pHmA2NqZU9sLCwhpXiLKLdOZlNztVtczZvn1HFAoF27b9ZzF++PB+8vJy6ddvcLnKoyr5CAB674g6k2G2I3kbxQZTK5H+voOsLE3jQNLryXtnFlKh6XpxfOV15DV8TQhMHewProjDaJCQySByQhDNG2lF6NoiLz2FvYu+I/mcqX+mTC6nw/AJhA0Ze1tFFxU33GNlN7RW8m7VltZ9S3soSsjPTGfrtx/j4u3PkGdmobya5OPg7kFRTpZ5u6KcLOxdRXJJXaLevaobjcZyt6mNyqNZ1ylErtWkEAG0bdseW1tb/vtvHQbDNbfcuXNnyM7OYtiwUTg6lv1gk2lyUGaZKkHrvDtVm0xV5d/EdQC4ql2JFAHVtULht/PRnzwBgO3ocai797SyRA0bSZKI3plM1H+mGmByhYzICS1o1l4oQzWF0WDgzLb1HFuzFINOC5gsOnc8+DSeVorL0RUXsfHzOQR3602H4ZYNY5u278yFvdsICOuEXlPMxcN76XbPw1aRU1A29U4hcnAwdYLWaDSl1pWMlWxTk2TXkEIEEBTUijFj7mLdulUUFxeZx1NTk1m69A+GDh2Jn1/pCtTKlGPmZb1P3VCIkouucCzDZLUa6DdUuMtqAc32rRQtNgV9KlqF4PDMC1aWqGFj0Bs5uvYysYdMXehVtqZsMu8gZytL1nDJiI9j36LvyYiPM4+16jmALhPuQ2VjvcD16O3/UpCZxuXjh7h8/JB5fPD0mYT2Hkx+egqr587AaDAQ0msgPq1Ecci6RL17Ovn5mRqCpqWllVqXmpqKs7Mz9vb2NS5HiUJkp5JjW4Uss5vh4+PHhAn3sGbNCnJyss3jRUWFrFq1lB49etOhQ2eLuCLVlQPmZZ13xcv81yRrL/9jXh4aULP1PwSgP3uGvHffAkDm6IjznA+Q2diUs5fgdinM0bJn8QUyE0yuSXsXNb3va4WLd83fgxojxXm5HF3zF+f3bAHJ1FzbydOn2ipP+4S0ZfTMj82fu016yGL93R9+f8v92w8dS/uhY2+6vuvEB6okn6BmqXcKkbOzMwEBAZw6darUutOnTxMWFlbGXtVPiUJU3dah63FxcWPixCn89996Ll++9iYkSRJ79uwgPv4SAwcOw97eZBFTJ+wCQN+kLZKt9YM4NQYNqy+vBKCtaztaOodYV6AGjiElmZxXXoDiYpDLcXrjHRT+daeXXUMjNTaXvX/FoCkwJVi4BzjQa3JL7JxrvjBsY8Og13N2x0aOr/8bXVEhADK5grBBo2g/bJw5TkcgqAr1TiECGDJkCL/++isxMTHmWkR79uwhLi6Ohx+uHZ9sVmHNK0QANja2jBgxloMH93Lo0D6LdfHxl1iy5Ff69x9KC18Ps8tM27Ru1PnZnLSRXJ2pOvKEwLutLE3DxliQT+4rLyBlZgDgMP150Z6jhjAaJM7suMLprYklRgqCunoSMbwZCmXdSGRoKEiSRMLJIxxeuYjcq6n0AH5tO9B1/H24+PhbUTpBQ6POK0Tx8fEcOXKETp060bRpUwAeeeQRVq1axYMPPsi0adPQaDT88MMPtGvXjjFjxtSKXLVhISpBJpMRGdkTT09vtmzZYBE/VVRUxLp1KwkLcGOEpMAWA9qAO2pcpvKQJInlF/8CwMPWk94+/awrUANGKioi95XnMcSaetjZTrwbu4lCAa0JCrI07F8WS/plU5NcuVJG51HNadGp7jRRbigknzvN0dWLSYs7bx5z8vSh64T78G8XIQqMCqqdOq8QHTx4kNdee425c+eaFSJ3d3d+//135s6dyxdffIGtrS2DBg3ilVdeqZU+ZgCZVy1EbvY1rxCV0KJFMJMm3c/mzetISkq0WHcyIYtLPMAI2Tbc/brVmkw3Y1/qHmLzYgAY22yCCKauISSNhtzXX0Z/wtQWRd27Lw5PP2ddoRogkiRx+UQmR1ZfQqcxZX86edjS/a4g3PxqPomjMZF+KYajq5dwJTrKPKaysyd86Dha9xtWKi1eIKguZJJUYvRtPOh0BrKzC297f6Mk0XPeLgxGiQcim/J078r3HKsKRqORI0cOcPDgXsr697Vq1Zo77uiHnZ11AjslSeLJPQ9zNicaB6Ujf/b/G0eVqIFT3Ug6HXmzXkW721QFXBXZHee5nyAT8RTVSlGuliNrLpF4Jts8FhzpRYehAaIvWTWScTmWExtWEH/iWnaWUm1D637DaDdoJDb2lSuwKGhceHpW/RkjVO3bILNQh8FoUkS8HGv/4SOXy+nSpTsBAc3YsuVfsrOzLNafPx/N5ctxREb2pF27DrVSl+l69qft4WxONAATAicJZagGkDTF5M56Dd3e3QAoO0Tg/N5HQhmqRiRJIu5wOsf/jUdXbLIK2Tgo6TquBX6hrtYVrgGREhNN1IYVJJ05YR6TKxS06jWQ8GHjsHN2tZ5wgkaFUIhug7T8azE8no7WS2n28fFj0qT7OLb6Sw4mGZCuq0yt0WjYuXMrp06doHfv/vj7N6sVmSRJYuH5nwBwUDowoUXNN9ptbBgLC8h77SV0Rw4DoGwXhvNH/0NmKxqHVhf5mcUcWnWR1Ng881jT9u5EDG+GrWPtuckbKpIkcSU6iqh/V5ByIdo8LpMrCIq8g/Bh43Hy8LKihILGiFCIboPUvGsKkZeTdWu8KJVKBun+oyPJrFSMItXgYrE+MzODVauWERwcQvfud+Di4lqj8mxP3srZHFOD2fGBk3BSieJ01YkxL5fcl55Df/okAKqIzjh98AlyexHHUh3odUbO7rpC9M5kUy8ywM5ZRefRgcIqVA0Y9HouHdnL6S3ryEy4aB6XK1W06tmfdoNG4uguAtQF1kEoRLdBar7WvGwNl9n1yPMSUaWdwBeY2sGRfTa9OXRoHzqdzmK7mJhzxMVdoG3b9nTu3A2HSjY8rAhag5bvoxcA4KJ25a4Wk6v9GI0ZQ/IVcl9+DsNFU00qVfdeOL87F5kVK/M2FCRJIik6m2Pr4ynIuvbCExzpSfjgpqhsRaxQVdAU5HNu1yaid2y06OelVNsQ0nswbQcMx97F+rXTBI0boRDdBiUuM4UM3O2tqxDZxK43LxuChxHh2Z6QkDbs27eLs2dPW2xrNBo5efI40dGnCA/vREREF2yq8WG64tIyrhSZaoU82OphHFUiCLK60EWfJnfGC0iZmQCo+w/EadZsZCrhvqkqeenFHF13meTzOeYxVx87IkY2x7O5iH+rCrkpVzizbT0x+3eg115TNG2dnAntM4TQ3kOwvUlvRoGgthEK0W1QYiFq4qBGIbduLQybs8sBMDg3R+9hqtLt4ODIwIHDaNcunJ07t5KWlmKxj16v58iRA5w6dZwOHToTFtYR2yrGn+Ros/n9wi8ANHcMZGTT2qkH1RjQ7NpB3jtvmCpQA7aTJuPw5DOlunALKoemUM+ZHUlc2JeK0WBKklDZKmg/KICgLp7IFaLOze1gNBpJOnWMs7v+I/H0cXOLDQBXv6a0HTCCFp17ohDKvKCOIRSi26Akhsja8UOKzPOo0kyZGcWh4+GGQmWmfmiTOX8+moMH95Kbm2OxXqPRcODAHo4ePURYWAc6dOhkbgNSWX44+w0FelOxusdaP4VC1B2qMpIkUbx0MQVfzTM9VORyHJ55AbsJIlC9Khh0Rs7vT+HM9ivm7DFkENTZk7BB/tg6iAf17VCUm82Fvds4t3szBZnpFuv823WkTf/h+IaGiYKKgjqLeGrdBilXFSJvKytENudWmJc1IePK3EYulxMa2paWLUM5fTqKQ4f2UVRkWYNJp9Ny9OhBTpw4Qtu27QkP71Sp4OuozOOsjTc1ce3q0Y1unj0r/2UEFkjFxeR/PBfNxqsuUVtbnN5+DxvRjuO2kYwSl09kELUpkcKca3GAnoFOdBjWFHd/EZheWSRJIuXCGc7t3MTl4wcwGgzmdUobW4Ii76B132G4ihYbgnqAUIgqicEokZRjcl34u1gxmFUyYnvO5C7TeUdgcA265eYKhYL27TvSunU7Tpw4yrFjBy1agAAYDAaioo4RFXWMFi2CCQ/vhJ9fwC3f6HRGHZ+d/AgAtVzNM+1eFG+AVcRwJYncmTMwnD8LgNzLC+f3P0YZ2sbKktVPJEniyrkcTm5OJPvKtZcBZ09bwoc0xTfURfxmK0lxXi6xB3dxfs8WcpItq+a7+Tcj5I5BBHW9A5WtnZUkFAgqj1CIKklavgb91aKM1lSIVEn7UeQlAFAcMr7i+6lUdO4cSVhYB06dOs7x44cpKioqtV1cXAxxcTE0aeJJeHgErVq1RllGyfylsX9yMd+U9XRfy4fwdxDd1auC9tAB8t6eiZRjcm8qO3bCefb7yN3crSxZ/cNkvcjl5JZEMhMKzOO2jiraDfCjRScRJ1QZjAYDiaePEbNvO/FRR5CM16xBcqWSwIjuhPQejGeLVkLBFNRLhEJUSRKvWocA/KyoENme+gMASa5C02p0pfe3sbGhU6dI2reP4MyZkxw7doj8/LxS22VkpLF160b27t1BaGhb2rRpj7t7EwASCuL59YKpCGNzxxZMCppShW/UuJEMBop++4XCn78Ho6n+je1d95iCp0XvpkohSRKpsXmc3JJIxtUmrAAqGwUhvbwJ6emDykYEpFeU7OREYvZtI/bALopysy3WOXn60KrXAFp274uto6g5JqjfiDttJUnMvqYQ+btYxxwsK8rAJmYdAJrg4Uh2TW57LpVKRXh4BO3ahXP+fDQnThwhPT2t1HbFxcUcP36E48eP4OPjR+s27fg640u0RlMsxvNhL6OSi2DU28GQnkb+7DfRHTVVnkZtg+Mrr2M79E7rClYPSbuYx8nNiaRdvKbcK9VyWvUwKUI29uKWVxG0RYVcPLKXC3u3k37xvMU6pdqGwM49CO7eF6+gUGENEjQYxN2hkiTmmhQiuQx8nK0TVG175i9kVxWR4rD7qmVOhUJB69btCA1ty5UriZw4cYS4uJgym8cmJyeRnJxEsCwItaOKFi1b0t6tQ7XI0djQ7t1N3nvvIOVkA6BoHojT2++hbNnKuoLVIyRJIvl8Dmd2XCH90jWLkEIlp1V3L0J7+WAjMsfKxaDTkXj6GHGHdhMfdQSj3rK4q1dwa1r26EfziG6oRDFQQQNEKESVJDHbFG/j7WSDSlG7TVMBUzD1aZO7TO/WCp1vt2qdXiaT4ecXgJ9fALm5OURFHSM6+mSpAGwAtaQmOC8Yjkr8EfMTrVq1JiSkDW4i3qVcJJ2Owu8WULT4D/OYzfBROD73EjI7EYhaEYxGiYRTmUTvSCY7+VqwtEIpI7ibF63v8BV9x8pBMhpJiYkm7uBuLh3dj7aowGK9vas7wZF9CO7eB2cvXytJKRDUDkIhqiTWzjBTJexGmXMRgOJ2U0vVHqpOnJ1d6NWrL9269SI29jynT0eRlJRQ5ra5uTkcPryfw4f34+npTUhIG4KDW+EoqtCWQh8bQ967b2E4fw4AmZ09Di+9iu2QYVaWrH5g0Bu5dCyD6F1XyM+4pqgr1XKCI70I6emDnZNQhG5FVuIlYg/uJu7wHgqzMizWKdU2NOsYSYsuvfBt3R653AovfgKBFRAKUSVJNCtE1nmLtzthCmKWFDYUh06slWMqlUpCQtoQEtKGBYc/5+yZ0zTPb46tsWylMC0thbS0FHbv3oa3ty9BQa0IDm6Fs7NLmds3FiSDgaLFf1D447dwtdecIqQ1zm+/i6JpMytLV/fRFuuJO5zOud3JFOVdc+fY2Ctp1cOblt28UNuJW9rNyE29wqWj+4k7tIfsK/EW62RyBf5tO9CiSy+ahndGqbZujTWBwBqIu0clyNfoySw03Yj9XWvfQqTIisHm4n8AFIdORLJ1rdXj70nZxbKUJeAO2mZ6Xgx4hZjz57l4MQbDdQXZricl5QopKVfYu3cHHh5eBAW1JCiolTlTrbFgSEwg77130EcdNw3I5dhNuR/7h/4Pmdq6/fDqOvlZGs7vTSHucBp6rdE8buesIvQOX4I6e6BUi6yxsihRgi4e3UdWwqVS6z2DQgnq2ovmEd1Elpig0SMUokpwKfNanEJzd/taP77d8e/Ny0UdH6nVY6cUJfPhiTkAOCgdeKPzO/g7BNAyKBSNRkNs7HnOnTtDYmL8TedIT08lPT2VAwf24OrqRvPmLWjePAhfX38UDbQvlyRJFK9aTsGCL+BqvSd5QFOc3ngbVbv2Vpau7iJJEhnx+ZzbnULimazr22Hh5GFL694+NAtvgkIp3Dk3Up4S5OLjT1DXOwjs3BMnDy8rSCgQ1E2EQlQJLmZeK2AY6F67LjNZUSa20UsB0DQfiMGtZa0dW2/U8+6xt8jTmVKZX2z/mkUBRhsbG9q0CaNNmzDy8/M4f/4ssbHnSElJvumc2dlZZGdncfz4EVQqFQEBza8qSC1wcHCs8e9UGxgS4sn/+H10Rw6bx2wnTMLh8aeRVbGZbkPFaJBIOJ3JuT0pFsUUAbyCnAnt5Y1PSxdkVm6qXNcoTwly9Q2geUQ3mkd0x9VXFE8VCMpCKESV4OJVC5FCBgG1HENkd/JXZAZTAGlRx0dr9dg/nfuOU1lRAIxuNo5+vgNuuq2joxMREV2IiOhCXl4ecXHniY09T1JS4k330el0xMVdIC7uAgCenl40bRpI06bN8Pb2K7NCdl1G0uspWrKIwp++B63pfyb38sbxtVmou0RaWbq6iaZAR9yRdC7sT7XoMyZXyGgW3oSQHt64+ta+VbauIkkS2VcSiD9xkEvHDgglSCCoBurXk8bKlChE/q52qGvTVK8vxi7qFwB0HmHo/GuveeqOK1tZHPs7AC2dW/Fkm2cqvK+TkxPh4Z0ID+9EYWEBcXExxMScJykpHqPReNP90tJSSUtL5ciRAygUCnx9/QkIaEZAQDM8PLzqdNaL/mw0eR++Z+5DBmA7biL2jz2JvIFYvqqTjIR8Yg6kcjkqE6P+ml9Mba+kZaQXwZFeImPsKkajkbS4c8QfP0T8iUPkpaeU2kYoQQLB7SMUokpw6arLrLlb7VqHbM8sQV6UDly1DtVSZdi4vBg+OPEuAA5KR96MeBe14vayT+ztHWjXLpx27cLRajXEx1/i0qU4Ll2Ko6io8Kb7GQwGEhIuk5BwGTC55/z9mxIQ0Aw/v6a4ubnXiUq5UnExhT9+R9Ffi8ytNxTNA3F85XVU4R2tK1wdQ68zEh+VyYUDKWQlWv7vnT1tadXDm+YdPVCq6q7iW1sYdFqunD3J5ROHSIg6THFebqltXH2b0jwiUihBAkEVEQpRBdEbjMRfLcoYWJsB1QYt9kfmmxadm6NpOapWDpuny2XW4VcpNhQhQ8bMjm8T4NC0WuZWq20IDg4hODgESZJIS0vl0qVYLl2KIzX15nFHwNUA7gvExprca7a2dvj6+uHr64+vrz8eHl61HqCt3bOL/M8/xVjiFlQqsbv3Qezve1BkkF1HfpaGmAOpxB1OQ1t0LStRJgf/Nm607OaFZ6BTnVBwrYmmMJ/EU8eIP3GIxFPH0GtvKIoqk+EVFEqz8C40De+Ck6e3dQQVCBoYQiGqIIk5xeYu981rMaDaNnopivwkAAo7PwWKmncfGCQD7x59i6RC0wN+WsijdPeqGTedTCbDy8sbLy9vunbtQWFhIfHxF0lMjCc+/hIFBfm33L+4uIi4uBji4mIAU80kb29fs4Lk4+OLSlUzSonhShIFX/wP7a4d5jFl2zAcZ8xEGRRcI8esbxiNEikXcriwP5Ur53PgumwxW0cVQV08Cerqib1z41Yc8zPTSTh5hPjjB0k+f8aikzyAXKnCr3V7moZ3IaB9J+ycGndNL4GgJhAKUQWxzDCrJQuRQYf94a9Mi47+tVaI8cez33IwfT8AfXz6MSX4/lo5LoC9vT2hoW0JDW2LJEnk5GRfdZldIjExvswWItej1+tJTIw3p//LZDKaNPHE29sHLy8fvL19cHV1r1IckqTRULT4dwp//cUcNC1zcMD+/x7HdtxEZA20hEBlKMjWEHcknYtH0i2CpAE8A51oGemFf1tX5NZof1MHMBqNpF+8QMLJIyScPEJ2UulyFWo7BwLCImga3gW/th1E/zCBoIYRClEFsUYNIptzK1DkmW6UJutQzb9F/5uwzhxE3cIxiBnhb1jNhSGTyXB1dcPV1Y2wsA6mh0h6mlk5Sk6+gk6nveUckiSZ6x+dOnUCAJVKfdUqdU1JcnBwrND31O7fS/68TzAmXHuA2QwbjsMT05E3smKTN2I0GEk6m0PsoTSSL1hag5RqOc07NOH/27vzuKrqxP/jr3sv93I3dhBFcFdUcM3lm01Zmtovtyy1SdO0sbFlpsVG07aZrzVjNt+yKWemMXXMb9too9mMbVO26zdKzRRBQVwAkR0ud+Gu5/fH4V5AQEAuXK58no8Hj3v5nMM5H1E4bz9r/3HdiOzeNWeLOawW8jN+Iv/YIfKP/4i9kdZPfWQ0ScPH0GvEWOIHDEapEr+iBaGjiJ+2FsoplddEidKpidR1wKwXjwv9wZcBcBu6Uz3k9na/5eHSg7xw9DkAwtXhrL3qOXQhnefhpVQqfd1ro0ePw+PxUFpaQkFBvu/DarU0ex2n01GvFQnkQd/x8d2Ji+tOXFwcsbHd0OsNvpDkvlCA5ZUNOL76wvc1qn4DMK5YiXrEKL//WYOJuayanB+KOXO4lGpz/R3SoxL09L0qjt7DY1Bru1bLmSRJmArPk3fsMHnHDlGUcwKpkdmVMb37k5g6isSUUUQn9e3yY6gEIVBEIGqhrGL5QTsgztAh9ws9scu3iat19P1wmbO7Wuqc+Qy/Pfg4LsmFWqlm7VXP1Vt8sTNSKpXExXUjLq4bw4ePkh9Apsp6AamiorxF1/IuC+AdiwSg0+mJjYom4kIhxgPfEllcjFGhQKXTo1+2XO4eC7I1kvzF7fKQf7ycnIPFFOVU1TsWEqqk9/AY+o2JIyqhY35eOgu300lhdgb56YfJO3a40anxIaFaEgYPJzF1FD1TRqILj+z4igqC0EDX/G3eSi6PxOmaLrMBsR3wC95VjSHtBQDchniqh97RrrersJez5vvfYHbJD7ZVw55gePTIdr1ne1AoFERERBIREcngwSkA2Gw2ioouUFR0gcLCAoqKLlBdXd2i69lsVnJtVnIBxssLKqokidjYOGK7xRJ74jixsXFER8e028DtzkReDNDK6cMlnPupDIfVVe94TJKBfmPiSEqN7lJ7i1WVFHE+4wj5x49w4WQ6LnvDf19hsfFyAEodTXz/wajUYm0lQehsRCBqgXPlVpxueUBER7QQ6dLfQGWWZ3hZx66AkPab1WZ323ny4GMU2OSZbEsGLmNyz6ntdr+OptPpfFuCAL5WpNqQdIHi4sImN6e9mFuhoLC0hMLSknrlYWHhREfHEB0dQ1RUbM1rNOor4MFXbXZy9kgpZw6XUFloq3dMo1PRe2Qs/a6KIyK+Y9fnChSXw05hVgb5GUc4f/wIpqKCBucolCq69U+Wu8JSRxPerYfoChOETk4EohbILq4dlzKwnQORwlGF/gd57JArsl+7jh1yS26eO/IMxyuOATCl500sGrC03e7XGdRtRRo4cDAgL/5YVlbKhZMZXNj/DaU2C5WRkbhb0R1WVWWiqsrE2bOn65WHh0fUhKOYmsAUS1RUFCEhnTsouV0eCk5UcOZwKQVZFUh1h74oIL5fOH1GxZI4NArVFb6AoiRJVBae5/xxuRWoMDsDj8vZ4DxdeCQJQ0aQMHQEPYcMR6PvWt2FghDsRCBqgewSORApFdC3nWeY6X7chLK6DADL+FWgbJ+/IkmS2Ji+gS8v7ANgRPQoHk1d3SX/F6uotqH/5w567HibHk75QefRhOL8+QIsV0+gtKqS4uJiSkqKqK62NXO1+kymSkymSs6cyam9n0JBeHgEUVHRREREERUVRWRkNJGRUeh0+oD9HTTXJWaMCaXPqFj6jIxBH9G+Y9oCzWGzcuFkOvnH5VYgS3lJg3O8rUA9h44gYcgIonr26pI/P4JwpRCBqAW8A6qTInVo1e03NkJhLUH34yYAnHHDcfS/ud3u9b/Zf2fPuV2APL1+7VXr0HTAtP7ORHI6qf7Xe1i3bUEqL/OVh06Zhn75A6jiu9c/X5KwWi0UFxdRUlJMaan8ajJVIknSxZdv+r416ytVVlY0OKbRaIiIkJcaqBuYIiKi2q377VJdYupQFUnDoukzKoaYpJYtTRCMJI+HsvyznD9+hPMZRyjKyWqwOCKAITqWnkNHkjB0BN0HDkWj6zyzMAVBaBsRiFrgVEnHzDDTH3wFpVO+l+Xq1fKeBu1gz9ldbMvaDEC8rjvPjdtAmDq8Xe7VGUkeD47PP8Py2l/x5Of5ykOGpmJ48BHUKcMa/TqFQoHBYMRgMNKnTz9fucvlpKKinLKy0pqPEsrKSjGZKltdN4fDQXFxIcXFDWcnGQxGIiOjCA+PICIikvDwCMLDI4mIiCC0lYv2Oe1uzmeUc/ZIKYU5pia7xHoOibxiB0iby4opyDxKQeYxCk4ew26uanCOSq0mfuBQetZ0hYmxQIJw5RKBqBlmu4sCk7wacXvOMFNWnkV37H8BcPS8Bmfite1yny8K9vFyujyDLUITyfNjXyJOG9cu9+qMHAe/x/rqRlyZGb4yZY8EDL+8D83kqZf1sAsJURMb243Y2G71yp1OJ+XlZZSVlVJeXuILTFWNbNDZEhaLGYvFXG/9JK/QUC0REd6A5A1LcnDyLjrpcUsUnqrk7JFS8jMqcDvrr4lzpXeJOawWLmQdpyDzKOczj1JV3Pi+eeHxCfQcMpyEoSOIHzCUELEfnSB0CSIQNcPbOgTtO6DaeOD3KDzyqsuWq9e0y472h0p+YN2R/0ZCQqfS89yYF0gy9vL7fTojV/ZJLK/+Ged3B3xliohI9Et+gXb2rSjaoTtKrVb7FpKsy+l0UF5eRkVFeYMPVyODdVvCbq+mqKiaoqKGLUsqpQqNSo/Hqkbh0KB0a1GpQlGiRasx0Htod/qMvPK6xNwuFyVnsijIPMb5zKOUns1utGtTozfSIzmFHsnD6DF4GGEXBVtBELoGEYiakVVnhln/dmohUucfIPTUBwBUD7oVV/xIv9/jZGUmTx1cjdPjJEQRwtqr1pEcOcTv9+ls3AXnsW7+G/b/fATeh6FWi+72hejuWIjSYOzwOslbh8jbhtQlSRIWi/mikCQHp6oqU6vGKdXl9rixeapAjfxRRyVQUqDiRFUYYWERhIXVfQ0nLCwCg8HQpr3fOookSVReyON8TTdYYdbxhjvFA8qQELr1S6bH4GH0SE4lOqlvUPz5BEFoXyIQNcM7w0yvVpEQ0Q6bK3rcGL75bwCkEK08dsjPTledYlXaw9jcVhQoeHzkb7kqdqzf79OZeMrLsb6xjerd70LNzDFUKrQzb0G/5BcoY2IDW8FGKBQKjMYwjMYwEhPrt9y53S4qK+UZa5WVFZhMFTWfV2AymfA0MgC4pdxud5ODvEFeEdxgMPrqZjQaMRjkV29ZoGbHWSvLKThxTB4LdOIYtsrGVyaP6tnbF4DiBwwmRHPldQkKwe/UqZMcPfojt9wyP9BVAWDv3t307z/It9DtlU4EomZkFMobMA7qZkDZDr/wQ0+8i7pEXgfIOuo+PMYEv17/nPksv/nuIUxOedzKgymPcn2PyX69R2fiqarC9o83qd7xDpKtdkNezfWTMNxzH6pevQNYu8unUoX4Fn6sy1ntJi+jlFNHCijMK8KtrMYdUo1bZcOjqsajqcaDq4mrtozH4/Gts9SUuqFJfvWGptrgpNPp29wS47BZKczO4MLJdAoyj1FR0HA8FcibpMoBaBg9klPE9hiCIDRLBKJLcLk9ZBfLgWhwfJj/b+CwYPi/9YC8RYd11H1+vXyB9Ty/SXuQcoc8pfy+wb9mdu9b/XqPzkKyWrG9+w9sb7+BVGe2UMjI0Rju/RXqlNQA1s6/XA43BScrOXe0jIKTFXhccleamkjUgD5SQ+/hMfQaEUNENx3V1TZMJpMv1Fz84WikW6m1Whqa9HoDBoMBvd6AXm/0vZdn78nv67Y2Oe3VFOecpOBkOhdOplN2LqfRrkO1Vkf8wKH0SE4lYfAwwuMTrqjxUMKVKy3tW06ezESr1RIREQXIrbYHDnzN+fN5SJKH2NhuXHvtDWg0ofzv/25m4MDB5Oefw263M3LkGC5cOE9xcSFKpYqbb56NwWDkzJkcDh78Do/Hg81mJTl5KOPHX0N+fi7fffct4eERlJWV4PF4mDjxRnr06InFYuazzz7CYrEQFhaGzda6ddeCnQhEl5BTasVRs2XH4G7+H2uiP/wXVNYiACz/tQbU/lvTpNhWxKPf/ZqS6mIAlg66h3n92ndPtECQ7NVU7/4n1jdeR6rT5RMyJAX9PfeiHjPuingwul0eCrNNnDtayvnMClyO+jPENPoQElOi6D0ihtgkIwpl7Z9Zq9Wh1eoaDO72stvtTYalqipTqxejbIrH48FsrsLcyPT2uhQKBWqlEoXTgdtSBU4HSpcThcuBwhCOwuVE6XYTl9SHhJoAFNunP0qV+HUmBJfTp7M5dSqb+fMXERISwocf7gHg0KE0lEoF8+YtRKFQ8H//9w0HDnzDxIly677b7eK22xaQlXWCTz/9gHnz7iQ2No4PP9xDZmY6o0eP48cff2Dy5JuIjIzCYjGzfftrDB8+GoDCwgKuu24SsbHd+PHHH/juu2+45Zbb+eqrz4iP78H48ddQWVnOP/7xRsC+N4EgfoNcQmaR2fd+cLx/A5GyKh/94VcBcHYbgT3Zfy03ZfZSHk17kAs2eY+lBf0Xc2f/JX67fmcgOZ1U/3sPtu1/x1NS7CtX9R+Aftm9aK65NuiDkMctUXTaRO7RMvKOl+Osrj9OSB2qoufQSJKGxRDfLwyl6vK6o0JDQwkNjSM2tvHlF5xOB1VVVVgsZszm2lf5w4zFUoXd3vZWJi9JknC43aBUQVhkk+dZFQqKiks5YU5Df/wYOp0enU6PXl/31YBOp0On06NSXZnrKQnBKy/vHP36DUBTs7TD4MGpHD16mLNnc7Db7eTmngPA43Gjq7MIaL9+AwGIiIhAr9f7fnbDwyOprq5GoVAwffotnDmTQ1ZWJuU1C896Z7GGhYX7lgmJi+tGZma6rz4TJkysuXYUiYlJ7f0t6FREILqEzJrxQ6EhSnr7ecsOw4E/oHDLDxHzNb/12yKMlY4KVn73EHkW+Qfp1j7z+cWg5UEfDrwklwv7Jx9h3fYanoLaTTVVvXqjv/uXaG6YjCKIZwxJHomSc2bOHS0jL70Mu6X++B+VWklCciS9hkXTfWBEh+wjplZrGh2/VJfT6bwoLHnDU21oqq5uuAt8W3hXDrdaLZSWNn9+aKi2kcBU+1obqAxXxKa8QvDxjrGTJImf/ewG36bUTqcDl6v2P0R1w71S2TDoO51Odux4g759B5CQ0JPBg1M5fbp22YmQevs0Ki56X9slrWinxYE7KxGILiGzUG7aHxRnJETpv0ChzvsWbZbcNFrdfwauhHF+ua7ZWcWqtEc4bZb3zZqRNJsHhjx0RYQhyePBse9TrFs34a75XxOAskcP9EvvIXTKTShasRlrZyJJEuX5Fs4dLSP3WBk2U/21iJQqBd0HRtBrWDQ9kiNRh3a+lg61Wk1UVDRRUdH1yiVJoqroAgUnj3H+xDEKzmRjdzjwhKiRQjRIIWrfh0KrR1KrcV/e6gLNstursdurqagoa/bckBA1Op3c1eh9beq9TqcjNFQrpu4LrdarVx++/fZLRo68Co0mlJMnjwOQlNSHo0d/JDGxF0qlks8//w9qtZobbpjaoutWVpbjcDgYP/4aVCoVJ04cx+12N7t0R69efUhPP8qECddRVWXi/Plc+vbt3+Y/Z7AIzidIB3B5JE7WrEHk1+4ytxPjV08CIIXosFzztF8uW+U0sSrtYbJMJwB55/qHU1cGfRiSPB4cX3+J9e+v4T6V7StXxsahu+tutNNntcuiiu1NXjPHRu6xMs4dLcNSXr/LSaGUt89IGhZDzyGRaHTB8aMqSRLm0mIKs45zIes4F06mY70ogKhqPvSR0XTvM4geg1KIH5SCMVpeCsHlcmK1WrFYzFitFiwWi++9/Ln83t8tTnW5XE6qqpytWlVcboFqeYhSqzVB//MptE3v3v0oLS1h5843CQ3VEhsbh81mY8yY8ezf/xU7drzhG1R9zTUTW3zdmJg4evfuy9tvb0OpVBETE0tUVAyVlRWX7Dq+7rpJ7Nv3MW+9tQ2j0UhMTNfZxQBAIV3uam9BzOl0U1FhveQ52SUW7nj9IABPTRvErNTulzy/pXSHX8W4/1kAzP+1GttVv2rzNaucJlZ+9zAnTZkATOw+iSdH/g6VMjgeoo2RPB4cX36OddsW3Dm1QUgRGYX+zrvQ3nIrilbu3xVo3t3k89LLyU0vw1x60bgbBcT1CaPXsGh6Do1Ca+j8QU8OQEVcyDpOYVYGhVkZje4MD6A1htN9UIr8kZxCWGx8mwKB2+3CarVis1l9r7XvLdhsNqxWS01555sto1Qq0Wrl1iWtVlvvtbEy76tGI4KUIFwsLq7tM8GD94nZzk4U1hlQ7acZZkpzAfrvNwDgiuyPbeQv23zNxsLQE0EchuQgtK8mCJ3ylSvCw+XVpefejkIfPDuMe0NQ7rEy8tLLMZc1HHwck2QgaVg0SSnR6MI7975ZkiRRVVJIYU0AupB1vEELkJdap6f7wKG+EBTZI9GvD3KVKqRmNe3mNyb2eDxUV9uaDU7e4x6Pp9lrtpXH4/G1erWGQqFoNjyFhobWKdP5ykS3niA0LTifmh0go2b8kEaloF+Mfx7Ahv3P+nazN1/3DKja9vAzOUysTHvI1012fY/JPDHit0EZhiSPB8cXn8lB6HSOr1wRHo7u53eivW0eSn377SXnT5IkUX7eSl56GbnHyht0hwFEJxpISo0mcWgUhqjOu2qydwzQheyaFqDsjEsGoPj+g4kfOITuA4cSldin0zyAvWsg6Vvwb0iSJOx2O3a7DZvNRnV1w9eL3/tzll1L6ue9b2tpNBo0mtCamYWhaDRyi1Pdz+XXuufUvnaWv09BaA/B9+TsICdqptwPiDMScpnTmeu6eCC1M+m6Nl3P5DDxm7QHyTadBOCGHpN5PAjDkOR24/j8M6yvb8F95rSvXBERIQehW+cGRRDyDozOTS8nL73xEBSTZCAxJZrElCgMkZ0zBEmShKmooGYMUAaFWcexmSoaPVejM9BtwGC6DxxK/MAhRPXsfUU8MBUKBVqttt5Cec1xu93Y7dUtCk/e9y5X21YQvxwOhwOHw9HsWlBNUas1dQKUtsngVP+4xhe8xNIHQmcWXE/PDuL2SL5ANMQfA6r9PJC6YRi6kcdHPB1UYUgOQp9i3bYV99m6QSgS3R0L0c2Z1+m7xiRJoizPQm663B1mrXA0OCeml5GklCgSU6LQR3S+ECRJEpWF531dYIXZGU0HIL2B+AFDfAEoMqHXFRGA/EGlUrW4BcrL6XT6Zr5VVzf+2liZ0+ls/uLtxOl04HQ6sFjMzZ/ciJCQENRqOVB5w5W31Uqj0dQpC23iWKgIVkK7CZ4naAc6V27D5pTHEPhj/JDupy2ElGcBYBn7MJ6wy9+vrNJRycq0B8k2ydeb1GMKa0Y8FTRhSHK7sX/2H2zbt+I+e8ZXroiMQnfHnehuua1TByFfCKoZE2StbBiCYnsZSUyNInFoNPqIzjUmSJ7dll8zCPo4hdkZVDcxkyrUYCR+wNCaLrAhRPZICuo1njobtVqNWq3GaGzdYNDa1qiLQ5Pczdd0uOq4br2muFwuXC4XNtulJ7U0R6VSNQhJTYWnuh9qdf0ylSpEDFAXfAL+FM3NzWX9+vWkpaUBcP3117N69Wqio6Mv+XVz587l6NGjDcqnTZvGyy+/3KY6ZRbVNie3dcq90nweQ9qLQM1A6hH3XPa1Lg5DkxOmsnr4k0ERhiSXqzYInTvrK1dERdcGIZ0ugDVsmuSRKM0zk3usnPzjjYQghRyCklLl2WH6TjQwWvJ4qLiQ7ws/hVkZVJubCEDGsNoWoAFD5EHQIgB1OpfTGgXyIG6n04HdbsfhsNcEqLrvq33vGzvujz3v/MXtdmOz2do8e1ChUKBWa2rCqfwqByd1nbKmjmsanKPRaESraRAL6JO0vLycu+66C4fDwbJly3C73WzZsoUTJ06wc+dO33LmF5MkiVOnTnHjjTcydWr9hap69uzZ5np5V6gOUSroH9u28SuGb59F4ZL/N2S+7tnLHkhd6ajgN989xKmq4ApDksuF/dNPsL6+BU9e7c7kiqho9AsWob3lNhTazjd9XvJIlOSayUsvJy+94WKJKCCudxiJKVEkDo3qNLPDJI+HioK82mnwpzKwNzFeRGsMJ37gEOIHDKX7oCFExPcUAegKplQqfbPSLkdzgar+a3WjxzobSZJwOPwb9lQq1SUDU8Nj6poWrcbLQ0JCRMjqIAF9mm7bto0LFy7wr3/9i/795dUwR4wYwdKlS3nvvfeYP39+o1+Xl5eH1Wpl8uTJzJ492+/18gaiAbEG1G0YUK3O+xZt9vuAdyD1tZd1nUpHBY9+9yA5VfJ6PDcmTOWxEU+hUnTefnTJ5cL+n4+wbv97/SAUHY1+wWK0s2/tdEHIu21GbnoZ+enl2KrqhyCFAmL7hJGUIrcE6cICv06Q5PFQfj7X1wJ0ISsDh7Xx8R3asHDiBw71tQBFdO8puguEFmtroJIkCafTWRNA5LFI8iBvu2+wt1xW+3lTxzrz8nlutxu32+3XhUO9ISskRP6Qw1KI733ta0id4+oWHVepVOL3QI2ABqK9e/cybtw4XxgCmDBhAn379mXv3r1NBqLsbDkY1P06f/FItQOq29Rd5nbUGUitx/KzyxtI3TAMTeOxEU922jDk22ts+1Y8+Xm+ckV0DPqFi9HOmtOpgpDHI1F6ziyPCTpeTnUjISiuTxiJNVPktcbAhiCPx0N5/llf91dhdgaOJtax0YVH1rQAyd1g4fEJ4hefEDAKhcI3dqctJEnC5XI1EqjqBikHTuelP3c47B2y3pQ/eEMW+H91doVC0Uygqh+8Lh3I5HK1OhR9Jx4L2pSABaLKykpyc3OZNm1ag2MpKSl88cUXTX5tVpbcbeQNRFar1W/f/LyKaiwOeRO9tgQi3ZGLBlIbWz+Q+uIwNKXnTawa/kSnDEOSJGH/aC/W1+sHIWVMLLo770I7c3anWlm6/LyFnIMl5B8vp9rcSAjqG05SahQ9hwQ+BNmqKjmd9g0XsjMoys7EYbtUABrqmwUW3q2HCEDCFUce9yM/gFs7jupibre7Zuac0/cqhydng/JLH/e+d3bq1qvGyC138p/Bn2JjuzFjxpw2/x11pIAFosLCQgDi4+MbHIuLi8NsNlNVVUVYWMMZGFlZWRgMBtatW8cHH3yA1WolKSmJRx55hOnTp7epXtkltQ+bwfGXuRS4JKE/tBEAV9QAbCOWXdZlXs3Y6AtDU3v+P1YOf7xThiEA+38+xvyHtb7PlbFx6BYuRjvzFhShnWu6uaXczmebMvDU2UVUoYRufcNJTInqdNtmfPzSWkyF5xuU6yOj67UAhcV1FwFIEFpBpVKhUsn7y/lDbetV44GpNkxdHKSaDluBWK/KH0pKijh8+IdW7cEWaAELRBaLHDx0jcwsCq15gFqt1kYDUXZ2NhaLhaqqKp5//nlMJhPbt29nxYoVOJ1ObrnllsuuV+8oHXq1ioQILclxl5lsJQ8eYw/wuDBfv/6yB1LHauWN9W5Omskjqas6bRgCUEZEgEqFMjpGbhGaPqvTBSEvZYiCkFAVzmoX3fqFy2OChkQS2olCUF2hBvlnQB8ZXdP6I7cCGWO7iQAkCJ1I3dYr8E+vhTdkuVxykKr/6vK9b6q89njDMqfT2a7dhuog23g7YJu7Hjx4kAULFvDss88yb968esc2bNjAq6++yjfffENcXMPddt9++208Hg8LFy70lVVXVzNjxgxsNhtfffXVJRfuam5zV7PdhU6tQqVsw8PG40LhsiFp2rbhnMlhIlzT/F5NnYHHbEah1aII6dwz3wBcTg+SR0Id2nlDppfH48FhMRNqDBMBSBAEv3K73Y0GpvrhydVkecNA5sLtdpOQkMj110/psFAU1Ju7Ggxy60tjUzG9Zd5zLnbHHXc0KNNqtcyePZuNGzeSnZ1NcnLyZdfNGOqHb4sypM1hCAiaMASgNPpnE9yOEKIOnmmsSqUSbQs2MBUEQWgtudtQRSdt0O9QAXsqJCTIg4yLi4sbHCsqKiI8PLzVA6W9izlarW1bBVUQBEEQhK4lYIEoPDycxMRE0tPTGxw7fvw4qampjX5dYWEh06dPZ+PGjQ2OnT4t74mVmJjo38oKgiAIgnBFC2i/wdSpUzlw4ACnTp3yle3fv5/Tp09z8803N/o18fHxVFVVsXPnTszm2gXoCgoK2LVrF+PHj2903JEgCIIgCEJTAjaoGqCsrIwZM2agUqm4++67sdvtbN68mV69evHOO++g0WjIzc3l0KFDjB49mqSkJAA+/fRTHnjgAQYOHMi8efOwWCy8+eabOJ1O3n777WYXbGxuULUgCIIgCMHDH4OqAxqIAHJycli3bh0//PADWq2WiRMnsmrVKt94oF27drFmzRrWrVvHrbfe6vu6Tz/9lL/97W9kZmai1WoZN24cK1asaNHq1SIQCYIgCMKV44oIRIEgApEgCIIgXDn8EYiCZ+6xIAiCIAhCO+mSLUSCIAiCIAh1iRYiQRAEQRC6PBGIBEEQBEHo8kQgEgRBEAShyxOBSBAEQRCELk8EIkEQBEEQujwRiARBEARB6PJEIBIEQRAEocvrUoEoNzeXX/3qV4wbN45x48axatUqysrKAl2toPT111+zYMECRowYwahRo1iyZAk//vhjoKt1RcjMzCQ1NZVXXnkl0FUJWmVlZTz55JNMmDCB0aNHs2jRIvHvsw2OHTvG0qVLGTlyJKNHj+bee+8lJycn0NUKOk8++SSLFi1qUC6eTa3X1PeyLc+mLhOIysvLueuuu/jxxx9ZtmwZS5cuZd++fSxduhSHwxHo6gWVtLQ07rnnHqqqqnjkkUd44IEHOHfuHHfeeSc//fRToKsX1FwuF2vWrMHpdAa6KkHLbDazcOFCPvzwQ+644w4eeughCgsLueuuuzh58mSgqxd0cnJyWLRoESdOnOD+++/n3nvv5ciRIyxYsIDCwsJAVy9o7Ny5k507dzYoF8+m1mvqe9nmZ5PURbz44ovSkCFDpOzsbF/Zt99+Kw0aNEj6xz/+EcCaBZ/Zs2dL119/vWS1Wn1lxcXF0tixY6UlS5YEsGbBb+PGjVJKSoo0aNAg6eWXXw50dYLSiy++KCUnJ0tpaWm+sqKiImn48OHSypUrA1iz4PT0009LgwYNktLT031lR44ckQYNGiQ999xzAaxZcHC5XNIrr7wiJScnS4MGDZLuvPPOesfFs6nlmvtetvXZ1GVaiPbu3cu4cePo37+/r2zChAn07duXvXv3BrBmwaWyspLMzExuuukmdDqdrzw2NpaxY8dy+PDhANYuuJ04cYK//vWv3H///YGuStCSJIndu3dz/fXXM3bsWF95XFwcq1atYsyYMQGsXXDKy8sjKiqKoUOH+sqGDx9OZGSkaHFrht1uZ86cObzyyivMnj2b+Pj4BueIZ1PLNPe99MezqUsEosrKSnJzc0lJSWlwLCUlhWPHjgWgVsHJaDTy0UcfsWTJkgbHysvLUalUHV+pK4C3q2zChAnMmjUr0NUJWnl5eRQWFjJhwgRADkgWiwWAhQsXMn/+/EBWLyj17t2bysrKemNaKioqqKqqolu3bgGsWednt9sxm81s2LCB9evXExISUu+4eDa1XHPfS388m7pEIPL2czeWzuPi4jCbzVRVVXV0tYKSSqWiT58+Db6XmZmZHDp0iFGjRgWoZsHttdde4+zZs6xduzbQVQlqZ8+eBSAmJob169czZswYRo8ezZQpU9i3b1+Aaxecli1bRvfu3VmxYgWZmZmcOHGCRx99FLVa3eigVqGW0Wjkk08+4eabb270uHg2tVxz30t/PJu6RCDy/g+xbjOaV2hoKABWq7VD63QlsVgsPPbYYwD88pe/DHBtgk9WVhZ//vOfeeyxx+jevXugqxPUTCYTAH/605/48ssveeKJJ1i/fj1arZYHHniA/fv3B7iGwSchIYHly5fz/fffM3v2bGbNmsWBAwd44YUX6nWjCQ0plcoGLRl1iWdTyzX3vWxMa59Nrbt6kPJ4PM2eo1R2iWzodzabjfvuu4/MzEyWL1/OuHHjAl2loOJ2u1mzZg1XXXWV6M7xA++sHJPJxMcff0xERAQAkyZNYsqUKbzwwgu+7jShZV566SX++te/Mm7cOObPn4/b7eadd97h4Ycf5uWXX2bSpEmBrmLQEs+m9nM5z6YuEYgMBgMg90FezFvmPUdoOZPJxPLlyzl06BC33XYbjzzySKCrFHS2bNlCZmYmb731lm+MhreVw2azUVZWRmRkpPil2EJ6vR6AqVOn+sIQQHh4OJMmTWL37t1YLBbx895CJpOJLVu2kJqayrZt23zjMKZPn87cuXN56qmn+NnPfoZGowlwTYOTeDa1j8t9NnWJ37IJCQkAFBcXNzhWVFREeHi47xep0DKlpaUsXryYQ4cOcfvtt/P73/8ehUIR6GoFna+//hqn08m8efO4+uqrufrqq5kzZw4gh6Wrr76a8+fPB7iWwcM7fiA6OrrBsejoaCRJEl0QrXDmzBkcDgczZsyoNyhVrVYzc+ZMSkpKxAKNbSCeTf7XlmdTl2ghCg8PJzExkfT09AbHjh8/TmpqagBqFbzMZjO/+MUvyMjIYMmSJaxZsybQVQpajz32mK9FyKukpISVK1cye/ZsbrnlFuLi4gJUu+AzcOBANBoN2dnZDY7l5eURGhraaFgSGudt+XG73Q2Oebt7WtLtIzROPJv8q63Ppi7RQgRyE/qBAwc4deqUr2z//v2cPn26yVHrQuPWrl1LRkYGixcvFmGojVJTU5kwYUK9j9GjRwOQlJTEhAkTfIMrhebp9XomTZrEF198QVZWlq88NzeXffv2MXnyZLE0RCsMHDiQbt26sXv37nrdOna7nffee4+oqCgGDhwYwBoGP/Fs8p+2Ppu6RAsRwD333MOePXtYsmQJd999N3a7nc2bN5OSksLs2bMDXb2gcerUKfbs2UNYWBhDhgxhz549Dc4R308hkFauXElaWhqLFy9m8eLFqNVqtm/fjlarZcWKFYGuXlBRqVQ8/fTTPPjgg8ydO5e5c+fi8Xj45z//SU5ODs8//zxqtTrQ1Qxq4tnkH/54NnWZQBQdHc0bb7zBunXrePnll9Fqtdx4442sWrVKDAhshbS0NACqqqqaTODih1gIpMTERHbs2MEf//hHtmzZgiRJjBkzhlWrVpGUlBTo6gWdKVOmsHXrVv7yl7+wYcMGAIYOHcqmTZu47rrrAly74CeeTf7hj2eTQpIkye81EwRBEARBCCJdZgyRIAiCIAhCU0QgEgRBEAShyxOBSBAEQRCELk8EIkEQBEEQujwRiARBEARB6PJEIBIEQRAEocsTgUgQBEEQhC5PBCJBENqdyWTitddeY86cOVx11VWMHz+en//85+zcuROHwxHo6vmUlpbW2/x19erVJCcn1zvH4XBQWFjY0VUTBKGdiUAkCEK7ysrKYs6cOfzpT39i8ODBrFy5kvvuu4/IyEieeuop7rzzzkZ3++5oX375JTfddBNlZWW+sttvv53nn3/e93l+fj4zZ87k22+/DUQVBUFoR11m6w5BEDqexWJh+fLl2O123n33XQYPHuw7tmTJEj7//HMefvhhfv3rX/PWW2+hVAbu/2g//fQTJpOpXtmoUaMYNWqU7/O8vDzOnDnTwTUTBKEjiBYiQRDazebNm8nPz+cPf/hDvTDkdcMNN/DAAw9w+PBhdu/eHYAaCoIgyEQgEgSh3fz73/+mT58+TJw4sclzFi5ciFqt5l//+hcAkyZNYtGiRQ3Ou7hckiTefvtt5s6dy6hRoxg2bBg33XQTmzZtou4WjZMmTeLpp59mz549TJ8+nWHDhjF16lTefPNN3zmrV69m48aNAEyePNl3n7pjiHbt2sXixYsBWLNmDcnJyeTk5JCcnFyvW83rj3/8I6mpqVRWVrb4+yUIQuCIQCQIQrsoKiri3LlzjB49+pLnGQwGhg0bxsGDB1t1/Zdeeonf/e53DBgwgDVr1rBixQpCQ0N54YUXeO+99+qd+/XXX/P73/+eadOmsWbNGnQ6HWvXruXLL78E5LFCU6ZMAeSwc++99za439ixY33l3rFF/fr1IyUlhY8++qjB+R9++CHXXnstERERrfpzCYIQGCIQCYLQLoqKigCIjY1t9ty4uDgcDgcVFRUturbT6eSNN95g+vTpPPfcc8yfP5+lS5fy5ptvotFo+Pjjj+udX1BQwPbt23nwwQdZsGABmzdvRqFQ8P777wPyWCFvS9CNN97INddc0+CeSUlJTJgwAYCRI0cye/ZsAGbOnEl+fj4//fST79zDhw/7BmALghAcRCASBKFd1O22ao53MLXb7W7R+Wq1mv3797N27dp65eXl5RiNxnpT5wH69u1bbwxTXFwcsbGxlJSUtLiOTbn55ptRKpV8+OGHvrK9e/ei1+u54YYb2nx9QRA6hphlJghCu4iPjwdo0ZT64uJiQkJCiIyMbPH11Wo1X3zxBZ999hmnT5/m7NmzvvE6F4ex6OjoBl+v0WjweDwtvl9T4uPjGTt2LB9//DGPPfYYHo+Hjz76iMmTJ6PT6dp8fUEQOoZoIRIEoV1069aNXr16NTs2yGazcezYMYYNG4ZKpWryvLqtR5IksXLlSh588EHy8vIYNWoUq1at4pNPPqFHjx4Nvra9p/N7u82OHDnC999/T3FxMTNmzGjXewqC4F8iEAmC0G5mzpzJuXPn2LdvX73y9evXs2PHDtxuN++88w7V1dXMmjULkMPLxatXu1wuysvLfZ//8MMP/Pvf/+b+++/nrbfe4vHHH2fu3Ln07NmzxeOQ/GnatGloNBr27dvHZ599RmRkZKPjkARB6LxEl5kgCO1m2bJlvP/++zz55JNs3brVN46nrKyM119/nXfeeYesrCwGDRrE3LlzAXkQdk5ODtXV1Wi1WgD27duH3W73XdcbegYMGFDvfjt27MBms+FyuVpdV28r0qXGPnlbsC7uagsPD2fixIl8+eWX2Gw2pk2bhlqtbnUdBEEIHBGIBEFoN3q9nk2bNrF8+XLmzp3LzJkzGTFiBMOHDycrK4v09HQArr32WkJC5F9HM2bM4JlnnmHZsmXMmjWLs2fPsmPHDnr27Om77qhRozAajaxbt47z588THh7Od999xwcffEBoaCgWi6XVdfWOM9q8eTPXXXcdkydPbnBOVFQUAO+//z6SJDFnzpx69X7ooYcAePbZZ1t9f0EQAksEIkEQ2lW/fv3YtWsXb7/9Nh9++CEff/wxKpWKpKQkVqxYgdlsZsuWLRw4cIANGzawYMECKioqePfdd3nmmWcYPHgwGzduZOvWrb7ZY7GxsWzatIn/+Z//4S9/+QsajYa+ffvy4osv8tNPP7F9+3ZKSkpaNOXfa/r06XzyySfs2rWLtLS0RgNR//79WbRoEbt27eLo0aOMHz+eXr16AfKq20ajEaPRyJgxY/zzzRMEocMopNbMjRUEQWgHJ06cYNu2bTzxxBMYjcZAV+eyOBwOJkyYwO23387KlSsDXR1BEFpJBCJBEAQ/2L17N6tXr+aDDz6gf//+ga6OIAitJLrMBEEQ2mDr1q0cOnSIr776ihtuuEGEIUEIUmLavSAIQhu43W6++eYbRowYIQZTC0IQE11mgiAIgiB0eaKFSBAEQRCELk8EIkEQBEEQujwRiARBEARB6PJEIBIEQRAEocsTgUgQBEEQhC7v/wMb91IcGFJOqQAAAABJRU5ErkJggg==", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig3, ax = plt.subplots(figsize=[9,4])\n", "\n", "ax.set(title='Industry Supply and Demand Functions', \n", " xlabel='Quantity',\n", " ylabel='Price',\n", " xlim=[0, 12])\n", "\n", "lcolor = [z['color'] for z in plt.rcParams['axes.prop_cycle']]\n", "\n", "for i, m in enumerate([1, 3, 5, 10, 15, 20]):\n", " ax.plot(m*S(prices), prices) # supply\n", " ax.annotate(f'm={m:d}', [m*S(1.2)+.025, 1.4-i/12], color=lcolor[i], fontsize=12)\n", " \n", "ax.plot(D(prices), prices, linewidth=4, color='grey') # demand\n", "ax.annotate('demand', [10, 0.6], color='grey', fontsize=12);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot equilibrium price as a function of number of firms m" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m = np.arange(1,26)\n", "x0 = np.full_like(m, 0.7, dtype=float) #initial guess\n", "eqprices = NLP(lambda p: m*S(p) - D(p)).broyden(x0)\n", "\n", "fig4, ax = plt.subplots()\n", "ax.set(title='Cournot Equilibrium Price as Function of Industry Size', \n", " xlabel='Number of Firms',\n", " ylabel='Price')\n", "ax.plot(m, eqprices);" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.7" }, "vscode": { "interpreter": { "hash": "ad2bdc8ecc057115af97d19610ffacc2b4e99fae6737bb82f5d7fb13d2f2c186" } } }, "nbformat": 4, "nbformat_minor": 4 }