{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Qualitative analysis and Bifurcation diagram Tutorial\n", "\n", "*This tutorial assumes you have read the [tutorial on numerical integration](http://nbviewer.ipython.org/github/diogro/ode_examples/blob/master/Numerical%20Integration%20Tutorial.ipynb?create=1).*\n", "\n", "## Exploring the parameter space: bifurcation diagrams\n", "\n", "Bifurcation diagrams represent the (long-term) solutions of a model as a function of some key variable. The idea is that, as this parameter changes, the solutions change in a \"well-behaved\" way, and that helps us understand better the general behavior of the model.\n", "\n", "In this tutorial, we are going to study a simple predator-prey model (the Rosenzweig-MacArthur), and see how the amount of resources for prey ($K$) changes the dynamics.\n", "\n", "### The Rosenzweig-MacArthur consumer-resource model\n", "\n", "This model is expressed as:\n", "\n", "$$ \\begin{aligned}\n", "\\frac{dR}{dt} &= rR \\left( 1 - \\frac{R}{K} \\right) - \\frac{a R C}{1+ahR} \\\\\n", "\\frac{dC}{dt} &= \\frac{e a R C}{1+ahR} - d C\n", "\\end{aligned} $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Rosenzweig–MacArthur model solutions\n", "\n", "We use the same method as before to integrate this model numerically:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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oVeEA/aO70tPt3yYiIiLvwhDnYXIwc2U41VElztUQl5FhffviRe12RERE5B0Y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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "from numpy import *\n", "from scipy.integrate import odeint\n", "from matplotlib.pyplot import *\n", "ion()\n", "\n", "def RM(y, t, r, K, a, h, e, d):\n", " return array([ y[0] * ( r*(1-y[0]/K) - a*y[1]/(1+a*h*y[0]) ),\n", " y[1] * (e*a*y[0]/(1+a*h*y[0]) - d) ])\n", "\n", "t = arange(0, 1000, .1)\n", "y0 = [1, 1.]\n", "pars = (1., 10., 1., 0.1, 0.1, 0.1)\n", "\n", "y = odeint(RM, y0, t, pars)\n", "plot(t, y)\n", "xlabel('time')\n", "ylabel('population')\n", "legend(['resource', 'consumer'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the parameters chosen above, the long-term (asymptotic) solution is a fixed point. Let's see this in the phase space, that is, the space of Predators ($P$) vs. Prey ($V$). We note that the arrows are \"circulating\", but always point inwards, and so the trajectory moves toward the middle, to the fixed point." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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58vb2xpEjR5CZmYm8vDxJJ9gv9PT08Pfff2tEfy95viSiX4+IzU9OTg5Wr16N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rVr5s9LS6PcIZ7stG/PKkMN4do1eUUrT3xGj6bkf2Pk7/FjClmuXk26bqNGkfRH585UlTlwIP1t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\nI0bY1KlTbdy4cbZ///5W/cb7Wrf3uIOw1mbXP+7ffvvNPv30U0tLS7NQK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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot the solution in the phase space\n", "plot(y[:,0], y[:,1])\n", "# defines a grid of points\n", "R, C = meshgrid(arange(0.95, 1.25, .05), arange(0.95, 1.04, 0.01))\n", "# calculates the value of the derivative at the point in the grid\n", "dy = RM(array([R, C]), 0, *pars)\n", "# plots arrows on the points of the grid, with the difection \n", "# and length determined by the derivative dy\n", "# This is a picture of the flow of the solution in the phase space\n", "quiver(R, C, dy[0,:], dy[1,:], scale_units='xy', angles='xy')\n", "xlabel('Resource')\n", "ylabel('Consumer')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Messing a little with the parameters...\n", "\n", "Increasing the carrying capacity $K$ from $10$ to $15$, we now see oscillations..." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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++eW6rzVr1gyHDh2K1+WEoZotgiCkQyu2WO576JSzlSqiJNliURqRSCZk/nFA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\nvXr1qqYSXP5069YNw4YN8/y1b98eAFCvXj2kpaVRW1Qjqampn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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# now K = 15\n", "t = arange(0, 1000, .1)\n", "pars = (1., 15., 1., 0.1, 0.1, 0.1)\n", "y_osc = odeint(RM, y0, t, pars)\n", "plot(t, y_osc)\n", "xlabel('time')\n", "ylabel('population')\n", "legend(['resource', 'consumer'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And, looking again at the phase space plot, we now see that the flux (the arrows) inside circles outwards, towards a limit cycle, and the arrows outside points inwards. The limit cycle corresponds to the periodic solution we just saw." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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IELRs2dJsnoXMzEzMnj0bq1atAsAX0s6dO2PPnj3Iy8vTWtfV1RWDBw/G8OHDMXToUNSp\nU6fK/e/btw/Tpk1Dnz598Ntvv4GIcObMGURERCAiIgLHjx/X+Uz79u1LhVdVRE9GRgYSEhLQo0cP\nnWX379/H9u3bER4ejp07d+rsi7p162LEiBEIDQ3FwIEDLSKG8/LyEB0djbCwMKM5VqGhoRg6dCjc\nLDBEXLIhPDwcERERNWJDTSHEVi3jURJb778PfPmlZbZtYwO0asVhPpmMRUdODucDKZWV366VFQsa\nJydujo7qRzs7Xi55xKRHuZyFjkKh24qLgYIC9pLl5qpbVWw0hEzGgqxhQxackrCUQqDW1sDDhzy3\nY26u+fuvKWJjuUxIRcjOzsann36KJUuWQGnkYPTq1Qt79+41Oqy+MuTk5ODjjz/G0qVLdTwaEi1b\ntkRwcDCCg4MRFBRk1gTiu3fv4vXXX9caPdayZUtcuXJFZ92AgAAMHToUQ4cORf/+/eHk5FTl/vfs\n2YPp06dDoVAgKSkJRUVFOHDgACIjIxEZGYmbN29qrS+TydC9e3cMHz4cI0aMQKdOnSotAHNzc7Fh\nwwZMmzZNZ1lKSgoiIyMRERGBPXv2oKCgQGt5nTp1MGLECISEhCA4ONgs+6IshYWFiImJQVhYGMLD\nw5GcnKy13MHBAcHBwQgNDcWIESNQt25ds9ugVCpx5MiR0nBjTeRYSTZI4carV6/qtUHyvPn7+5vd\nhupEiK1axqMitsztzbKyYnFlb8/iobAQuHzZdE9V3bosQvz81I/16wPe3oCXl7q5ulreE0fEIiw3\nl8OCDx8CGRn6W3o6kJam9sxVNaTp6Qk0aQK4uOh6yAoLOXfKSC5zrSE3l0VyeVy4cAEzZ85ETEyM\n3uXe3t4ICgpCUFAQ+vXrh9atW5s1f+TkyZN45ZVXcKKcCTWtra3Ro0cPDBo0CMHBwejWrVuVK4ET\nEbZs2YKZM2ciNTUVly5dgoODA3bu3IkdO3Zg7969yC2jym1tbdGnT59Sr1dV9kdubi4++OADfPLJ\nJ/DQmK1dyumJiopCVFQUDh06pCOI69evj+HDh2P48OEYOHCgRURPfn4+9u3bh4iICERGRuqIHjs7\nO/Tv37/U62WO/LqyEBFOnjyJ8PBwhIeH4/Tp01rLZTIZevToUSp6zH1+Skh5XuHh4Thy5EiN5Fhp\n5nkZskEKN1ZFjNcUQmzVMmpabL3+OvDf/5pnW+7uLIoAFicJCcYLa1pbA+3aAW3bcjhRas2a6V54\nFQoWFWlp3O7d44mks7O1W04Oh+SKi3WbZtK8TKZ+LpezKHRwUD9qNldXLh6qr3l4sOjTNzCKiIWZ\nJLxSU4Hbt4uQkFCIrCw33LnDIcTU1Mrtbzs7QoMG+XByykFRUSEKC4v+14qRn++KkpLGAGpnvsSz\nzwIbN+pfRkT4+++/8c477xgN7QGcSyWJr6CgILNc3JRKJVasWIH33nsPOTk5+PTTT9G9e3dER0cj\nOjoa586d0/mMm5sb+vXrh+DgYAwaNAhNmzattB2ZmZmYM2cOBgwYgLEaMdri4mIcPnwYO3bswI4d\nO3D+/HmdzzZq1AhDhgzB0KFDMWDAAL15QVUlMzMTu3fvRmRkJHbs2KETWrKzs0NQUFCp+GrSpInZ\nbVCpVDh16lRpeOvUqVM663Tq1AkhISEIDQ1Fly5dzFpAVCIxMbE0vykmJgaKMndfTZs2LfX0PPXU\nU1UW5PpIS0tDZGQkwsPDsXv3bqM5Vn369DFraQtNG6KiohAWFobo6GgdD6Rkg5RrZgkbzI0QW7WM\nmhRb5riRcHbmUBjAwsLY1Fvt2nH4qGtXoHNnfm1nx8sUCg6XJSSwt+bWLXW7c8f4dmsamYwFl4+P\nunl6KgDcR3HxbeTkXMG9e6eQmBiHO3fisW3bZowcObL080VFwN27/D3v3AESE3kfXL8O3LjB71X8\nV5cC4DoABZydndCxYzs4Ozvg/n0ZLl7kUGltIykJaNBA/To3Nxfz58/Hd999B4VCgXr16uGtt95C\nTEwMDh06pJNHA3BYSVN8tWrVqtKiJzk5GW+//TZkMpnWyL2UlBTs2bOnVHyl6lHTAQEBpSHHAQMG\nVKqEQH5+vtFcoDt37mDXrl3YsWMHoqOjdXK+bGxs0Lt371KvV9u2bc3uXVAqlTh+/DgiIyMRFRWl\n4+kBuKSDFG7s1auXRRKqk5KSSsONe/fu1Rno4OvrWxpuHDBggEVyrLKysrBr1y6EhYVh+/btyMzM\n1Fru4eGB4cOHIzQ0FIMHD7ZIHav8/HytHKv09HSt5W5ubhg6dGhpPS93d/dqt8HV1VUrz8sSNpgD\nIbZqGTUhtsxRzqFuXfbmlJSwl0kfHToAwcFAnz7AU09xSAxgz9SxY8DJk0B8fAGOHMlCZmYdlJSY\n/85SJmNBZ2MDyGSE4mLl/2oUqUAkg7W1LZRKebVNbSOTKVG/vhwNGsjQoAGLh4AA7ebpqS2Ei4pY\ngEni6/p1bgkJLFArEqq0tn4IH5/78PCwh4uLC5ydnSGXWyMpqer5c9XNxx8Dn37KNYpmzZqF6Oho\nZGZmwtXVFQqFAvHx8YiJiUFMTAxiY2PLFV/9+vWrVHL52bNnDc4nR0S4cOECoqOjsXv3bhw4cEDn\nrl4mk6Fr166l4qtXr15mv7NXKBSIi4vDjh07sHPnTpw5c0ZnnYYNG2p5vSxxsU9KSsL27dsRFRWF\nPXv2ID8/X2u5m5sbhgwZUppk7+3tbXYb8vLysGfPHoSHhyMqKkqnrpaDgwMGDBiAkJAQjBgxAvXr\n1ze7DQqFArGxsaVhtrI5b1ItLcnbY6kcq3/++ac03Fg2/8/a2lorz8sSOVaSDdJ+MGSD5Hl7lPK8\nhNiqZVS32EpIAFq0qNxnZTIOFdrbc+ir7JlgawsMGgSMGAEMG8a5VioVcOYMsH8/cOQIiywj5XN0\nsLLi0GS9eizw6tYF6tThR09PzmVydVU3Fxe2z9YWkMkUOH78n1Ivw7Fjx7RySfr374/Vq1fD3t4e\nVlb2AOyhUtmhsJA9P4WFXEoiK0t/y8zkPK1794C0NBVSU5VQKKp+V+7sTAgIkJWKryZNOLTavDk/\n17wOl5SwF+zKFSA6+jY2bz6Pu3edAbQEYHoirr19Bnx9s+Hp6Qh3dxc4OdkjN1eGM2ceba9iWc6f\nv4i2bdvovK9QKHDixAkt8VX2Qg/wKDJNz5c5R/YBQFFREeLi4kq9XvHx8Tq5LI6OjggKCioVX23a\ntDG7xyk5Obk01ys6OhpZWVlay62trfHUU0+Viq/27dub3QYpsTwqKgqRkZG4deuW1nKZTIYnnnii\n1OvVoUMHs9ugUqlw/Pjx0tGNZ8+e1Vmna9eupXlelsgtIiJcvHixVHAcPXpUZx0pvyk0NBSdO3e2\nSH7TlStXSoVXXFycznnZqVOnUuFlSRuk/VBTNpiKEFu1jOoUW0uXAm++WfHPyeWcu6RUsgDRxMoK\nGDAAGD8eGDWK85ju3AEiIoA9e4ADB1iQGKcYLi7JGDYsAK1asaCQhEb9+pzbVRF27tyJZcuW4cCB\nAzoJw8bw8PBARvnGGiU7uwS//74DK1ZsxoULaQB8ATTQaPX/91gHlZnXXS7neQ2bN9duLVoAjRvz\n8YiNjcVHH32EmJhTAFrhrbd+RmqqN86cUSIx0Rn5+aa55R0dgfbteVCCREkJD3RITKyw6TVCdjYL\n8LKYKr7S09Mt4l2RePDgAfbu3VsqvhL17Ni0tDSzlFEwRElJCf7555/SXC99+U3Jycnw9fW1mA1E\nhEuXLpWGGw8fPqyTZH/37l2LeJk0SUxMLA037t+/X6eobFJSEhpoxrItgFRLy1Adq+qw4d69e1p5\nXmW9sXfu3LHIAIOyNkh5XjVlgzGE2KplSAdszpw5WLhwocX6mTIF+O03823P3x+YPh2YOhXw9QXO\nnwc2bwbCwzk8aJhcACcAHANwHMA5ANfg4GCL3NxcsySpEhHOnTuHjRs34u+//9YZgmwIX19fnRFM\nVeHIkSP47rvvsGXLltJyAUuWLIGbmxuuXUvEpUuZuH69GElJcjx44AKiRnBwaA0/v95ITKx41Xo7\nOx5g0KYN0Lo1oFSeQ3j4QgQHB+Drr+eXrvfgAXDunAoHDjzAkSM5uHRJjpQULygU5Vfhlsu5jyZN\nWARbW7MIv3CBvaaPOrdvs8e1LMXFxVri6/Dhw2jatKleT4elICJcu3YNu3fvRnR0NPbv34/GjRvr\nzXOyJCkpKaW5Xrt370ZAQIBeAWZJHj58iF27diEqKgo7duxAo0aNEB8fX6025OTkYPfu3YiIiEBU\nVBT8/f2r3QbNkGdERAT8/f3LHQlrbvLz87Vs8PPzq/b9kJ+fj7179yIsLKzGbCiLEFu1DOmAffDB\nB5g/f375H6gEEyYAf/5pnm317g3Mng0MH87hs/XrgbVrOVSoD3d3FdzdT+HWrV8BHABwEYBu/Ydv\nv/0Wb731lt75zlQqLqmQmsqP9++rHx880K6HJbXCQvbClJQQ8vNLkJ9fhIICxf9KTygBKGFvbwM3\nN2fIZCrI5SrY2ang4+MMBwf26jg6skfPyYnDp+7uPPpQei699vHh54Y82rdu3cIPP/yAX375BS+/\n/DK++eYbnXWk+kWZmZno3LkzVCr+vlKifEKCdjNQ31IvVlaEZs1kaNOGByV06MCtaVP1KEoiTkCP\njc3FkSMFuHvXB6dPc45YecjlPKK0WTP1PigqAs6eZS/no8ylS1yipCzFxcVITk5GQA3OSVRSUoLk\n5OQazVMpKSlBampqjXoQlEolUlNTLe7NqQ02pKWlWdy7J2wwDSG2ahnSAdu5cycGDx5s9u1/+y3w\nn/9UfTvDhwPvvQf06gXs2wcsW8ZeLH11swIDgZEj+TOdOvHFODs7Gzdv3sT169dL240bN3D9+nUk\nJiaiRYtOWL06Frdu2ePKFRYZt29zS0p69CusW1uz6KpTR7vVq8dJ8H5+gKtrDi5e3I2JE5+pUl9E\nLHSl0ZsJCRzau3SJn5eUmLYdBwdt8dWhA4cNvbzU62RlsWg6fVrdzp0rPynfxoa35e+vLiybnQ2c\nOPFo1wU7f56Fo0AgEBhDiK1ahiUP2JkzLHaqwpNPAl9/zeUa1qwBFi/mi3pZevQAJk7kvC1jN8GS\nB+XkSXU7e5Zw+7b5Eh3t7DhJ3saGRZD0KM1pqFQCSiWhsFABlUoOmcwaJSWcFK8nbcfseHryPmrQ\ngMVIQADnW0mPPj6VL8tRXMwi7NIl4OJF9eOVK7r5doZo0IBLc3Tpom5+ftpeq3PnWDhJ7fz58kcy\nursD3bvz95OmZrpyhcXcozoK8u5dzhsUCAQCTYTYqmVY6oBVtbxDo0bA998DgwcDq1YBCxeySNKk\nfn3gpZeAyZMNj3BUKvnCfOgQcPAgP5YZaW0UV1cWJP7+3J+PDydsS49SFXnNSaOrUqZHqswuCa/8\nfA7ZSaMPyzapanx6Onub7t2retV4R0dojUSUEuCbN+fjUpm6h0olewvPnWNxI7Xr102r4eXjoy2+\nunRhYSgJsIIC9nppCrBLl8rfdsuW7AGTwpm5uTxitUzpnUeGoiLt0aACgeDfiaXFlvnL2wosQmWF\nlpUV8M47wEcfAWFhnM9StlRD797AzJnsxdInbO7dA3btAnbs4MfyBvi5uXFCd8uW3J9URd7fn5dV\nJzKZunJ8JepMgoiFGZeD4Imm797llpSkfkxONpwAn5/P3qiLF3WX2djoCrBWrTgp3phHzMqK92mz\nZnzcJHJzObldU4CdOcPfQZP0dD6Wu3ap33N355Bx9+7s2ezeHejZU708JweIjwf++UfdygrtK1e4\nSbi4AE88wcLayopFYnw8e84eBaQivBIqVfVN3C4QCP49CLFVC6jsn3/LlsAff7Bnpl8/9k5oMmIE\n8OGHfGEtS3IysGkT8NdfXE/LkEfD1ZUvpl27qj0kAQGPzwVLqkXm7m68nplKxblLUrX4W7d0H/Xl\nqSkUugJFwsuLRVfbtvwotXr1DO9fZ2c+nprHlIht0Az1xsfr5lplZgJ793KT8PPTFl+BgUBQkHq7\niYna4uvkSW1PYE4OEB2tfm1tzefIlCn8HVQqLr56/HjVPYjmQPOm5sUXgV9/rTFTBALBY4QII5oZ\nc7siAwNyrQBhAAAgAElEQVTLK72gnxkzgHnzgPnzea5EzaM8dCiwYAHn8WiSn88Ca/VqDhHqOzPc\n3LgOV9++7BHr0EH/PIICbaTRiDdusLiQEuGvXuWcrIpMt+Purk6E79iRH9u1Y6FlKvpy7eLj2XNn\nDJmMBV/37jy4olcv9sRJIqWwkMOP//wDxMUBsbHlb7N5cz7P7e1ZjCUl8Wezs03/PtXBmTO8rwUC\nweOHyNmqZZjzgKlUFRcyDg7AypUctnnhBe28rPbtgUWLeModTS5f5tGI69bphpsAvriGhnIV+See\nqFoOVUUgYgGYl6eefFqhUD+qVNqTUEuPNjZ84dacjJqn96keuyuKSsXhSEl8SUnwFy+yh9EUZDIu\n/SCNQuzYkVtFvYxJSZxjJbXjxzk0aQwPDw43SuKrWze18CNir15srLrpC6dq0rAhC3lPTz6et2+z\n+K9ifVqzI0KOAsHjgxBbtQxzHrCK/pHXrw9s3creqW+/VXumHB2Bzz8HZs1SJ2MT8YXvm2+4OnxZ\nWrQAxo7lZq6h8yoV5z5JJSCSk/m1lIyens4X1JwcddNXiqIyyGS8H9zcOPTp5qb93MuLE/Q1k/Wl\n566uNXdRzczUFl8XL3JOlqn1rjw8OGwXGMitSxcWZaZ+H6WSQ5yS+Dp6lPPAjJWjsLJioSeJryef\n5Hw9iQcPODQtia/jx40XfG3QgOfj9PJSe+QOHuSJ0h8V3n+fvcUCgaB2IsRWLcNcB6xDBx5pZipt\n23L47+23OQQj0b8/jz7UrOUYGwt88AFfsDRxcACeew54+WX2VFRWYDx4wILg8mVuV66wx+bOnUe/\nvpY+7O1ZyGo2X19+9PPjEYV+ftXn8QNYhGkmwJ89y+eLKeFINzd1fl1gIHuiKiLACgo47BgXx+3w\n4fJHG/r7s2CSWosW6v4KC1lwHTwIxMTw9ox9j/r1eRve3izsbt3iaaQyM02zvzrIzeWRtAKBoHYg\nxFYtw1wHrCJCp2tXvqueMkUddrKxAb74Avi//1Pn05w/D8yZw6MKNfHzA956i6fqcTdtmr1SMjPZ\nS3H8OF+AT52q2MTUZXFyUk9ALTVnZx41ZmvL30t6lMvV9Z2kR5WKQ4yFhdCagLqggMOR2dncKlKx\n3RTkcvbANGqkbgEBLGKaNeN9bIaZi4yiVHLphzNnuJ06xXlYppTm8PRUJ8L36MECzNQpBIk4F00S\nX3FxLPyM/bPUqaMtvtq1U4fMi4t5MEdMjFp8GauX1rgxDwCpU4f7PHuWxVd11FgzhWnTgJ9/rmkr\nBAKBMYTYqmWY44BVRGj16AG88QbPayh5A/z8gC1b+IIJsCCaNw9Yvly72GTLljwacexY070yWVk8\nWm3/fq6xdfasaXWdnJ35oijV2PL3Zzvr1FFXavf21h2KbymUSvY+ZGVxe/BAe9og6Xl6Oid4JydX\nLWxlZ8clHqRyDVJr1YpzlCwZpkxOZtElJcHHx5uWC9a0qbYA69zZ9OOTlcUhx7g4Pk+OHDHurXJz\nA556ioVX//7clyS+FAoWXwcOsPiKjWXhbIgOHTjny8WFhds//7Atj0qh1YIC9pYKBIJHByG2ahlV\nPWAKhelFFtu35yKks2erLyS9ewMbNwJ16/LrrVuBV1/V9m74+wOffMLFS00pqHnpErBtG3vE4uKM\nX7RcXPhC2bGjdq0tX9/an0xcUMAjCpOTud29y168xER1q8zUNU5OvI9at1Y/tm7NYsdSBTdTU1l8\nnTihzsUqz3Y7O/aiPvmkOh/Lx8e0/oqLWeRJxXBjY/UPxpBwc+MRr/36sfhq107tGZTEl1SmIi7O\ncM6XtbW6bIWdHXs0Dxx4dOp8LV7MXmWBQFCzCLFVy6jqATNVkAQEcNhw3jz1e+PGAb/9xheVjAwu\nVKo5YbWDAyfyzp5d/p311avAhg3A339z/pU+5HIWVU89xRfewEAWCJYOlz3K5OWpBZg06fS1a9yu\nXzd9ih2AhYJUkV2zNWpkfuEqjRo8epTbsWMsxsqzt0ULdRJ82TIQxpBmIjh4UN2M5X15e3N9L0l8\ntWyp3gf5+Rxq3LsX2LOH7TZWF27AAD5vra15BOiuXSw+HwXEv7FAUDMIsVXLqMoBy8zk0WPl4ezM\nSezffad+7803+bVcziGbceO0c6dCQri8g+aosLLk5bG4WrWKL176aNECGDKEp/158snqrwhfm1Gp\n2CMmiS+pzMOlSyzMTB156erKnp727Vk0dO7MoTNHR/Paq1BwmPjoUXXdrOvXjX/Gw0MdDuzbl20z\nxXtKxAMpYmJ4YvT9+4172nx9WXgNHMilTDTn78zI4O1Ini99BWMlWrTgzzdowMJSGiFpbHRkdSHm\ncRQIqg8htmoZVTlgpnorpk7lytbSxXn2bJ5cGgCWLuXX0tB8d3d+b9Ikw9tPTAR++IGTePUVkuzZ\nExgzBhg5kvOOBOansJC9LJcu8QhOzYmnTamsLpezV6lLFxY4UqvogIfySE1lMX/4MIuvEyeM2+fs\nzKJcEl9du5qW96VSsUdVEl4xMcbDjq1bs2gKDmYPmGaB16Qk9njt2sXV7B880L8NGxsWik8+yTam\npgK7d/NxqWnmz+cRxAKBwDIIsVXLqOwBMzVXKyiIvQxSeOfNNznvQ6EAXn8d+OUX9bpPPsmhQM27\nfk0uXuT6Wxs36uZhtWnD+WDPPccJ3IKaQaFgD5hU2kFqiYmmfb5xYxY43btz69KlYpXmy6OwkAWX\nVALi8GHDYgbg8HXPnmrx1bOnacniSiVXpt+3j9uhQ4aT5K2tOaQpia+uXdXJ9kolhxl37WIhZSwH\nsV49LuTbujWLv7g47tvcI1krg/jXFlSE7OxsnD59Gq6urlrNVszCXooQW7WMyh4wU7xa/v6cnyKF\nVyZOBH7/nS86o0Zpz2n37rt8N6wvhHP1Kud6/fWX9p+2nR1vc/p0TiqujoR2aU7BBw+4ZWTwY2Ym\nfy/NVljIHjulUv2oVLJXx9qaL6hSs7PjHDVHR27Sc6mIqbu7+lFqpoS7HhWys1l0nT6tLrlx/nz5\nXjC5nIV0t24svrp143Ckuf5zVSr2zB04wHlYBw4Yn67H3p5vCvr359a1q2nHQaHg8GZ0NLejRw2H\nYd3dOU9r0CCeqkrz5iE7mwWUNCn3zZv6t2FtzYNPgoN5e9evA1FR/F1rGoWidp27/2aSk5Nx5swZ\nuLm5wc3NDa6urnBzc4OzszPkFkx2JSKsWbMGr7/+OvI1aqLY29vrCDBXV1e89957eOKJJyxmz6OI\nEFu1DEuJLbmcR/pJoZS+ffnOPDub776PH+f37ey4uOmECbrbePgQ+Owzzt3SrADu48PJ9DNmcAkG\nc1JSwl4YKVH8+nVOxJZG86WkGK9GXl3IZFxrysdHXYrCx4dHddavzzk9DRrwc2/vR3MQQHExh95O\nnVILsNOny683ZWfHgxukKXd69uScKHNAxMdcEl4HD/LxN4SLC3u9Bgxg8dW+vWn7OjOTw43R0fy7\nMJZb1rYti66hQzlsKAlNIj5Hd+0Cdu5kEWaoXEXjxmqvV36+OtxZ00V779wx7MkWqDl9+jTS09O1\nBI+bmxscHBwgs+BdJhHh+++/x7vvvguFxp2RTCaDi4tLqS2urq7w8vLC0qVL0bhxY7P1f+nSJTz3\n3HM4b2Q47oIFC/D++++brc/aghBbtYzKHLCK/rYDAlhcyWScJCxVmvfw4Lvtnj211ydiD9g772iH\neHx8uMjpq6+ap9p1ZibbdeoU23T+POcc1fQFyNzY2LDo8vdXFy/VbA0bWq5kQ0UpKeFjIM1zeOwY\nH5vyBG5AgFp49erFCfjm8p5Icx3u38/eWGMhUS8vPseDg9kzpTkTgjFu3lR7vfbsMVxd3tmZhZ0k\nvjQHkBQUsECMiuJmyOtlb6/2zDk5scCNitKel7Qm2L6dv9OjSklJCeLi4uDk5FTqUXFxcbG44AGA\nnJwczJgxA+vXr9d638rKSkuAubq6onXr1li6dCnszFgE8NixYxg7dixuGbjzsLW1xYYNGzBq1Ciz\n9SlRUFCAt956CytXrtTb70svvYTJkyejZ8+eFj8OjxJCbNUyLC22bGw4QblpU/5zP3WK3/f15Tv6\ndu201795k0cu7tmjfs/BgUXW7NmVz9+RqoZLxU2PHjU+6ksfPj5qb1GdOuxZkpqHB9vm6MgXMCcn\nttvaWh0ytLZmr4dKpR1aLClhL09BAXsdpMe8PM63ycxkD2FmprppFjEtb+Ll8pDJ+KLdrBnQvDk3\n6XmTJtVXuNUQBQUsCCQBdvQoe3SM4ejIk5D36cPhtCeeMM/oRyI+R/ftY+G1bx/Pk2mI5s1ZdA0a\nxPmLrq7l96FUcl7Zjh3cjh83nPPUpo1aePXure31unqVRdT27SwWDYVsAwN59G/jxuy9jYzk32xN\n/tN+8AGnFegjPT0d+fn5cHFxgbOzc7Xm8Rw6dAjjx4/H3bt3S9+zsrLSG9qaOHEiJk6caLa+iQir\nV6/GG2+8gQIDLsxGjRph7969aNq0qdn6lcjMzMTUqVOxZcsWnWVubm548cUXMXnyZHTp0sUiomfD\nhg14+eWXkWMgCbFJkyaYNGkSJk2ahObNm5u9/0cNS4stkMCsxMfHEwCKj483af3oaCL+GzatLVxI\nVFBA1KeP+j1fX6KrV3W3vXYtkYuL9ufHjiW6fbty3y0nh2jzZqIpU4j8/cu3VS4natWKaPRoojlz\niFauJNq7l+jmTaKiosrZUB3k5xMlJhIdP04UGUn0009EH39MNG0a0dChRB06EHl6Vuy4ae6Tpk2J\nRowg+s9/iFavJvrnH6KsrJr9zmlpRGFhRO++y+eWvb3x72FjQ9SzJx/XyEiihw/NY4dKRXT+PNGS\nJUQjRxK5uRm2wdqaqHdvos8/Jzp6lKikxLQ+7t0j+uMPokmTiHx8DG/f1ZVozBiiNWuI0tO1t5Gd\nTbRlC58T9esb3kbDhkSvv86/xRUriJ5+msjRsXLnjrnaoEHa3+Xhw4c0ZswYAkAAyMbGhjw8PMjf\n35/atGlD3bt3pwEDBtDIkSPpxRdfpNTUVPMc7P+Rnp5Ow4cPL+1fXxs/fjwVFxebtV+Jc+fOUevW\nrfX226xZM/rqq6/ozp07FulbpVLRsmXLyNbW1uB3b926NX3xxReUmJho9v4TEhIoMDCwtK///Oc/\nFBAQoGNDjx496IcffqB79+6Z3YZHhYpeuyuKEFtmpqIHrCJ/kv368QXluefU7/n4EF26pL3NvDyi\nyZN1//Sjoir+fTIyiH75hWjwYCJbW+MX327diGbO5IvTqVMsCh9ncnJYGERFES1fzuJpzBiirl2J\n3N0rfhGsX58oOJjonXeIfvuN6OTJmtuHxcUsNpcsIRo3jsjPz7jtMhlRx45Eb7xBtHUrnzfmoKSE\nxejnn7OwsrY2bIOHB+//X38lSkkxbftKJdGxY0SffsriUS43/P169SL68kuic+dYFEqoVETx8USf\nfELUpYth+1xc2L6ff+bfyLRpRHXr1qzw8veXvoOKVq5cSQ4ODgYv+ra2trRt2zbzHNgyqFQqWrRo\nEdnY2Ojte9SoUbRt2zYqstBdWm5uLk2ZMsXgd5fJZNS/f39avXo1ZVngzujkyZPUrFkzAkBeXl40\nZ84cql+/vo4NQUFBtGrVKrPaUFhYSG+++SYBoGvXrpFSqaRDhw7RK6+8Qu7u7lo2WFtb04gRI+iv\nv/6i/Px8s9nwKCDEVi3DUmLL3Z09UgsXqt9zdOQLhSY3bhB16qT92eefr5jnRKEg2raNPQuGBJa9\nPdGAAUTz5xPFxj7+wqqiqFTsDTlyhOj334k++oho/HiiwEAiJyfTj7uVFVGbNuyRXLCAaPt2IjM7\nFkzm1i3+LtOnE7VsWb746tKFhWNkpPk8d1lZ7IF7/XWi5s2N29ClC9GHHxLFxZnu9Tp69Br17Pk9\nNWiwn2xscoz8HjPoiSeO0YYNGVRYqL2N27eJ/vtfoiFDDP9+rKyIgoKIvv+eaONGovfeI2rbtmaF\nl7U10YULF6hdu3Z6BYevry999dVXFvGwqPf/UWrcuLFB0ePp6UkzZsyg2NhYUmkqXjPx+++/k5OT\nEwGg3r170+TJk0tfS83BwYHGjRtHUVFRpFAozNZ3VlYWjRs3jmxtbUmpVFJJSQlFR0fTCy+8QM7O\nzlo22Nvb09ixYykyMtJsHr+tW7fSyZMntd4rLCykLVu20OjRo3W8b66urvTSSy/Rvn37SKlUmsWG\nmsTSYkvkbJmZisR9R4/muQtNYeVKrnbdvz/nKMlkQHg4MGKEep2jR/m1VBrCyYkLlY4fb1ofKSnA\njz9yBXl9ExU3bMi5KCEhnC8jJtOtHCoVJ09L1eOl4qUXL3LpC1OoX59rZkktMJDz36oznzUtjaut\nHzzIeXunT/NlWx9WVlzWQZpu56mnOAdPHyqVCps2bcKDBw9Kc1U0HzWfp6c7Izm5LVJS2mPvXsOJ\n8J6ePOvBsGH8aGxOx8TERLz44ouIiTkEoCeAEQBCALTRu76zM8+q8PTTwPDh2oVkc3I4lzI8nHO3\nDB3f7t25fEvHjsDp00VYsiQRaWnNANTksFfDJ1Pv3r0xYcIEjBkzBl5eXmbtNSsrC9OnT8fGjRsB\nANOmTcOZM2dwXBpy/T8aN26MiRMnYtKkSWjZsqXZ+r98+TKee+45+Pv7IzIyEnl5edi6dSvWrVuH\n6OhoqDRqjNSpUwfjx483W24VEeGXX37BM888A09Pz9L38/LyEBYWhrVr12L37t1aNvj4+JTaEBgY\naLGk9oyMDGzatAlr165FbGys1jI/P7/SY9GubOJwLUHkbNUyKqKOTb3jDAwkSkrSDjl89JH2tsLD\niRwc1MubNye6cME0m8+dI3rxRQ4Flu27Xj2iN9/knBgL3EgKNFCpiJKTiXbtIvrmGw4Fd+xoPHyr\n2Xx8iIYP55DYjh1E9+9X1R4VFRYWUlZWFt27d4/u3LlDCQkJdP78eYqPj6e4uDjav38/7dixg7Zt\n20bnzydReDjR22/relfLNjs79owuXMjh0rI3xikpKfT0008b9HBIzcvLi86fP09E7JGNjSV6/32i\nzp2Ne926dyf67DMOd+s7r5VKJS1atKjM3XwTAmYREE1AsUHvUHAwh5WTkrS3qVAQHTxINHs2UbNm\nhu1r25Y9cu+/f5AcHN4iYIfB/qqr+fr60uTJk3U8LFJYaf369ZSbm1u1E67MubdixQqys7OjP//8\nk4iILl++TB999JFez1fXrl1pyZIlZssny8/Pp6VLl+q8n5ycTIsWLaJOnTrp2NC6dWtasGCBRT1/\nRPzb+O6776hz5846NrRq1YoWLFhAt27dsqgNN27coM8//5xatGihY0OnTp3o22+/peTkZIvaYG5E\nGLGWYQmxdfgwUd++6tcDB2qHRTZs4LCEtLxfP9MSli9e1M7/kpqVFSfybt9uevhFYDmKizk3bN06\nDsv162c8cVyzNW1KNGECh6vi4kgn5GWM27dvmyR4ANDgwYN1whn37/OAipkzORRqzE4fH84NW72a\nSMpFVqlU9Oeff5KXl5fBfl999VW6e/euXvvv3iVatYro2Wc52d1Q3w0bEr32GgvUsvvn3Llz1LFj\nRz19uxLwLFlZrSVb2yyD2+7eneiLL3TzKlUqvsn57DPjwrRhQwX5+W0gYDgBz5O390GSyfJrTHQF\nBChpw4YNFBISQtbW1lr7xMnJiSZOnEhRUVFmC22dOXOGtm7dWmbfqejw4cP06quvkqenp5YNVlZW\nNHToUPrjjz/MKv70ce7cOZozZw41aNBA5/zo27cv/fLLL5SZmWlRG86fP0/vvvsu+fn51YgNKpWK\njh8/TrNmzSIfHx+t/uVyOQUHB9OaNWsoJyfHYjaYCyG2ahmmHrBXXzXtz+2FF4iWLVO/btCAR1NJ\nbNigndQ7fnz5I/1SUoheekk3GdjdnXNHyt6R11ZUKpVF8joM9ZWSkkKHDh2iX3/91ayJxLt27aIZ\nM2bQmDFjqH///tSpUyfy82tIDg5tCXiGgAUE7CQgvdzzyc6O6MknOZl/61YehVgeYWFh5O/vb1Dw\nODg40L59+6ikHGWemsrn67RpRI0aGbezVSuiWbNYAN28mUrPPPOMwf4BUGBgIH366ad08uRJvce8\nuJgoJoZHW7Zvb7hfZ2eiZ57hAQrS76ywsJDmzp1LMpmMAJCdnR316NFDo38rAvqQXL6EHBxSDW67\nZUvu/8gRXU/e9etE337Lx0YmM2RfMj3xxAmKilLRggUJ1KpVPMlkhoWepduIEYX0008/UZ8+fXSO\nh7e3N7322msWy62SKCoqorCwMHr22WfJzs5OR/xNnjyZdu3aVe65WRVKSkpoz549BnOrnnvuOYqI\niLDYaErJhr1799KLL75o0Ibw8HCL2lBcXExRUVE0fvx4nYEWjo6ONGHCBNqxY4dZ89zMicjZqmWY\nGvc1JaxuY8MT8A4erK79tH8/50sBXJdo6FB1vZ9p04CffjJccVuh4HkUP/9cu5ZUnTo8vc/LL5tv\n3jwiMil3ID+fc39SU7llZHDezcOH/JiTw3WhpCZN2aNSqetrEXHNLRsboKSkEDk5D5GVlQ4bm2L0\n7h0IR0dZaa0uNzeu4aU5TY+XF+fwODsbPy5EhNTUVCQkJODatWu4du2a1vPc/+1UZ2dnnD592my1\neYgIYWFh+M9//oNrRgpiderUGYsXhyE52Q/Hj8tw7BhXkpfm0TREs2ZcuLRXL66j1aqV7n7Iy8vD\np59+iu+++w5KA5MJenp6on///ggODkZwcLDRytdEXNtLqvi+f7/+SdABzg3s1w+oV+8Utm17BQ8f\ncu6Or68vHjx4gOLiYq31GzZsiBEjRiA0NBT9+vXTW4zy9m3OoYqI4NpeZTYBgH9HPXtyjuLTTwPp\n6bF4/vnncevWLeTn5yM9PR1btmzBpk2bcPjwYaj/SjtCJhsNZ+eJyMnRfw74+QHPPMMTvPfsqf2b\nTUkBwsKALVt4v+grQFuvHvDss0BIiAqnTl3CmjVZuHy5FYg8dVeuBubMyYSX10qsX78eZ86c0VoW\nEBCA8ePHY+LEiWjbtq3FbMjMzMTmzZuxbt06xMTEaC2rV68eJkyYgEmTJqFTp04Wy2vKz8/Htm3b\nDOZWjRs3DpMnT0bXrl0taoNmfpfm79Xb27vUhm7dulnMhuzs7NI8t71790JTZtStWxfjx4/HpEmT\nLFZDrDKInK1ahqnq2JQ7x1de4XpM0uvp09WfP3VKu4bWtGm6d8uaHD3K9aE0t+/mRvTVV0Tm9Lan\npaXR22+/TTt27CAitikxkWjnTg5lzZpFFBrKthgL7dREs7fnofCBgVxPa+pUrq/1009E4eFKmjdv\nGzVooJurUbYNGTKEdu7cSTdv3jTrKJ2ioiL6/vvvycPDw2j/devWpaeffpoWLlxI+/Ydori4Avrx\nR/aSljeCD+CQ3jPPcNmHU6e0Q8lnzpyhnj176ngQ9NnRtGlTmjFjBm3evJkelhPXVig4XD5vHpdY\n0AyLl23OzskELKFBgxZTWlo2bdq0iV544QXy9vbWscHJyYlGjx5Nv/76q8EaQdnZHO584QUib2/D\n/bZpQzR7diGNHPkZnTt3XmsbycnJtHz5curfvz/J5XINGxqTTPY2ubmdJplMqXe7vr4cao2J0Q3b\nZ2TwCNCRI9kraejzb7xBtHt3CX3xxSlq0eIQyWQZNfY7WrHiFr3//vt66zV16NDB4iMaiYgSExPp\nq6++orZt2+rY0KZNG/riiy8snteUkpJCixcvpi5duujY0LJlS5o/fz7dvHnTojakpqYateHzzz+3\nuA1JSUn0zTff6A3HS3lulj4WpiDCiLUMUw5YUVH5f1g2NkSLFqlf16unzsO6eZNfS8tCQ/liRUT0\n888/a8XHi4s52VYzZCiXE82YoR2OrCoZGRk0d+5HZG/fi4Bp9NRT56h794qVOahI4wtXMQGFBBQQ\noKi2i4mtbTHZ2iYQEEnAMgJmE4fz2hNgT2Uv9uauDfTgwQN6++23dWoSWVlZ6fyZAZzErCl20tK4\ntMecORy2MnQRl5q7O4v+r7/m2lvFxUr66aefSmvwhIeHU3x8PH311Vc0YMAAnXAOwPkbFUlezswk\n2rSJBa+xoqH29kTDhhH9+CPRrVslFBsbS++++y61adNGxwaZTFZuccqSEk6yf/dd43lm/v4qevNN\n/QLp3r179PPPP9PgwYPL5DV5E/AS9euXp3cwCsCDYF59lYv/lo22ZGVxMVZjJVnq1+cbml27imne\nvGPUtOkBAh5W22+jbNu69Ti9/vrreoVwQkKCyedDZVGpVHT69GmaPXu2Tt0qAHRVXzVoC3DhwgWa\nO3cuNWzY8F9tw9mzZw3muVXH+WAMIbZqGdIBW758ucF1TPmTeuEFoiZN1K83beLP5udre6h69uQi\npkQ8QsTR0ZHq1q1LGRkZdPMmUY8e2tvt1InoxAnzfNfCQqKoqHwKCjpI1tYxBOSa/CdsY8Pfr08f\nTtKfNYvrSP30E9FffxHt3s01xC5fZs/YvXtcRFShIEpLu0crVqygoKCg0jwadbMiwI4AV/Lx6UDX\nrhGdPct5MtHRvB9/+YXzYz78kOs1jR1L1L8/Ubt2RHXqGC5saVpTklyeSJxDtYQ8PT+i6GiuvWTu\n1JWEhAQaPXp06Xc/f/48xcTE0JdffkkjR46kOnXqEMBVsMs7jnFxLKZGjCg/+d7dnQdQzJ+fRSNG\nvEvz5n2itb38/HzatWsXzZ49u3TUVosWLSr9PVUqojNn2Avbt6/xwqadO7M38vhxoqtXr9HixYup\nX79+ZGVlRa1bt65w3wkJfNNjLJfKx4dFYWSkboJ9RkYGrVmzhkJCQsjOzo7atGlDRHzj9PvvfKNk\nSDh5e7M3Ozpav/Bat8745xs04AEV+/cX0vvvx1GjRjFUk8IrMnI7TZo0iZycnKhdu3aVPBsqT9m6\nVX9Cwf4AACAASURBVO3atau2nE4JpVJJ+/btoylTppCLi8u/1gbNHDMXFxdq3759tfavDyG2ahnS\nAfv1118NrmPKH9Prr6ufDxig/uzLL6vfb9FCPbxfpVLRwIEDSfJkvP32Dq0pZaytuQp3VfMj79zh\nhP1hw4js7UvK/R5NmxKFhKinpjl4kLdhrnzV5ORkWrp0KT355JNaosvFxUVnFJOpKJXs/Tl1Snu6\nnqlTeaqTli3L9wbpa46OLHbHjuXt/f03T7NU1UjjwYMHqWvXrjrnnEqlouvXr9Phw4crtL2SEv7u\nS5ZwONHYlDYsNkpo3DiejunGDd3tpaWl0QlzKXxir9fmzeVPlePry2IlPJzo7t2HdPr06Sr1m5LC\nU+4MHmxY8Lm4EE2cyJ7DsoV+s7Ky6OzZszrblTxWo0YZniapTh3+Tzh0SPd8yczk6YBCQgwLrxYt\nuML90aN5tHx5Ik2axIMBakp4XSo7PLOaycvLEzYIG7QQYquWIR2wY2VLu2tQ3h9Rjx7aF7jjx/lz\n69er33Nw4HIAEqtXryZXV1f6v//7P/r003Stu/CmTTlnq7IkJXHdp27djNvt61tEQUHJNG7cEZo6\n9Te6efNB5TutBLdv36ZFixZR9+7dCQCFhYVZrC+lki++R47wcfn8c6IhQ9LJ3f0q2dkVVOjC4+TE\neUqvvcaC5dgx9mBWzB4l3dCndMyASsVlQv77Xy6j4OVl/Ps0a8bfJSzM8nM+ak6VExho2CYHBw6/\n/fZb1euPEbFnat06FqOG5jo0JrwMkZPDnt0xYwxvt2FDrtV14oSutzQzkz1mI0YYFoSBgeytS0hg\nwT9qlOm13Mzdxo6t+rEQCMyBEFu1jPIOWG5u+X9AmgUZpT+jq1e170RXr1Zvs7i4mNauXUtZWdn0\n0Ufa2woJqdwkwUVFPEx/4EDD4ZN69XgqoLVrOdT3KHH9+nXavXt3jfSdlnaPUlKIDhxg8fTOO3zx\na97ceOK3ZpPLOWdowgQO7+3ebVqZhupAqSQ6fZov2MOHG/eQSJNFz5/PItLSddvu3mVP5IgRhr1E\nVlZcq2zp0spPyq5JXh4LquefNxyCrYzwystjMfTMM4Y9qc2acTj8/Hndz9+/z/siKEj/b1gm42U/\n/cSlJ1atYi+64dITlm1HjlT9WAgElUWIrVpGeQesvD8cT0/1KD1ra777VKm0i5pOnqx7R6tQcMhE\nc1vvvlvxEFVyMlfgrlNHv30dO7IXwVDlbYFxioq4wOXWrbwfn36aKCDA9AuSnx97lxYt4tF7j8Kc\nlMXFnPP1+eecg2csp8rLiwXkunU8d6QlycvjEOL06doDSsq2rl05X/Dixar3WVTEE5O/8IJx4TVh\nAnv+TB07kZXFNzXDhhnev+3asajVN7gsKYnPGUPePxsbvjHbuJFDwYsXl+/JtmQTxZQF1Y0QW7WM\nqootDw9tUUXEd5zSe40bc6hBE4WCL8Ca2/n++4rZnZDAOTD6wglNmnCOUTUNWPlX8vAhe8KWLCGa\nMoW9m4ZGrJW9SHbvzgMM/vyTL7Q1LYKzs1nklDdZtExG9MQTXEU9Pr7quWvGUCpZnM6ezWF1Qza1\nasWeojNnqr4fTRFe7u78u9u713SBcf8+e0z79zfsherdmz1WGRm6n79yhYW+ocnE3d05NzQ2ln/z\nn31W/sTjlmwCQXUgxFYto6piS7OdOcOhI00BtnOn9vZUKk7c1rz4/m8qMZO4dYs/Xza8ZW3NeSP7\n9tX8xfvfSlERnwNr1vB8g0FBpiU116vHHrOFC1nASaNVa4obN/jCP3q08dpq9eqx0Ny0SfeGwpyo\nVDxC9bPPjM+h2KIF0QcfcMjUXMLrxRdZzOjrz9eX6K23KjYPaXIyC/SePfVv09aW9/uWLbojJaV8\nt9mzeeSivs83bcq1z65d4xyxN98sf8CEpVrZ/z6BwJwIsVXLMJfYGjyY1588Wf3e+PG625s7V1to\nbd9ump0FBTxhcdm8FldXDj8amG5OUMOUlLAAW7GCL9ymeBysrNj7NWcOT39Tk9OUSdPmzJnDEy4b\nstnWlgvL/vij5aePunmTw2a9exv2FDVvzuF1c4TPi4p4lOvEiYbr0DVtyh42UyeTl77HggXsndO3\nTcljdfCgrhexpIRozx7OOzNk05NPsmi+d48oIoJvxmoqsV6EGQXmRoitWoaxA7Zxo+l/JtHRRCdP\nav9Rlq0JqVn0VCbjhHZT2L5dN5Ti5sY5N5YePVYZSkpYHGZncwglJYUTm69f5/ynCxc4DHrnDl8I\nsrL4Lv7f4pF78ICP6ccfEwUHl1+Z38qKw3fvvceJ9xaer9cot26xoAoJMTz6DuC8qs8+M4+XyRjJ\nyVzapG9fw8KrWTP2eOlLSq8oeXn8uzVWqLRjRx4NbOoNkOSxeustLpKqb5sBAfwd9KUG5OZyflhw\nsP59YGvLaQuRkZx399NPLMRqQnQFBlb9GAgERGJuRLNy4cIFLFu2DKmpqdi6davRdX/44Qe8+eab\nWu/5+Pjg7t27sLa2Nvg5Y/MrmToFVPPmwJUrwLBhwM6d/N7ixcBbb6nXiY7mOROlo/ff/wKvvmp8\nu2lpvI7mV7eyAt58E/jwQ54zsLrIywNu3gRu3ODH9HTgwQN1y8hQP8/Pr3w/traAnR3Pi+jlBXh6\ncpOeaz56eQH16/O8dY6O5vuu1Y1KBVy6BPzzD7fDh/m1IWxsgO7def7BoCCeI9HBodrMLaWwkOcC\nDQ/ndveu/vUaNQJGjQJGj2ZbrawsY09qKs9PuHEjcPAg79eytG8PjB8PjBsHGJkK0iQePuT+/vyT\n50Qs259cDgQHA88/z3M1mnKOlpTwHKrr1vG29f2WnnwSmDIFeO45wMVFe9ndu8D69cCaNcCFC7qf\n9fUFXniBPy+Xcz+//86/6eomKQlo0KD6+xU8Hoi5Ec3A/v37aeLEiSSTyUgmk1FwcHC5n+nYsSPJ\n5XKtNnfu3HI/Z0wdm3q3tnAh0f796teNGmnnWyQmatc6+uij8vfB7t26d7l9+xKdO1f+ZyuLSsXe\nprAwzvsYP549KoZGOj5KzdOTPQrDh/PURgsWcO7Uvn3sRatqcdjqJjWV6zfNmFF+6NHWlkcVfvwx\nh5xq4rtK3pl584znVdWty3OI7t5tWTtTU7nOWL9+hmcY6NmTy0lUYFYigyQn8yCX7t319+XszGHk\nfftMH1iQk8OjQAcP1v8dHB05bUHfNlUq9rS//bbh3+9TT3FJmuxsLr46dWrNFU4VCCqK8GyZAaVS\nCSsrK7Rv3x4XLlzAwIEDsXv3boPrx8fHY8WKFZg7d27pezKZDPXq1YNjObeTVfVsWVsDd+7wXfuR\nI/zemjV8NwsARUVAnz7AsWP8evhw9gLI5fq3p1AAH38MLFyo9oLVrQssWgRMmGC6t80UHj4EDhwA\nTpwATp4E4uOBe/cqty0bG7W3ydWVPVQ2NupHzSaXA8XFvG8KC/mxbMvJYfuq4iXTxMoKaNIEaNFC\n3Vq25Mf69c27Xy1BSgp7kfbv58eEBMPrurkBAwcCQ4cCQ4bUjPfg9m0gIgIIC2ObS0p01/HwAEJC\ngGeeAQYNAuztLWNLaip7u/78U/0b1UQuB/r359/XM8/w+VsVrl5lj9HatcCtW7rLGzYEJk0CJk8G\nWrc2bZupqcAffwC//qrfYxUQwB6rF17Q9diVlLDHffVqPiZlj4WTEzB2LDB1KtChA7BpE7BqFRAb\na5pt5uT4caBr1+rvV1D7EJ4tM9K3b1+TPFuvvfYaWVtbk5eXF/Xt25e+//57yjexpHdVPVtPP83e\nBOl127bayaDvvKNeFhCgf2i3xL17XJlcc/tDh5qvOGZREY92+/BDvgM3dU7BBg04Gfn553kI+po1\n7JmIj+ccnuxsy+Xl5Odz7su5c5yovWULz5W4cCFPKTR+PNsWEGBa6QV9zcmJp+V57jn2Dm3axKO5\nLFnaoKrcucNej6lTtefk1Nc6dOBBFDExNeP1ysjgKulPP224cKlURDQ8XHcUnjm5eZPoyy+J2rfX\nb4e9PdG4cTwSsez8hhVFqeTf27RphvPyunfnwROZmaZtU6XiYrOvvWZ4lGRQEP9G9Y1qTUvj3FFD\nk3a3bMm/reRkLjkxdy6PuhTeLsGjhkiQNyOmiK2CggLy8PAoDTlKrXnz5nRTX7XAMhg6YFlZpv0h\nbNzIycLS67Vr1duIi1MnrNrZsTgxxNWr2knw1tY8+XJVL/h5eRyOGjXK8KglqXl6cpLt3LlcCfvi\nxUejCKepSFPyHDvGc/EtWcLD5MeMYTFlLKFbX3N2ZvH76qucVPzPPzVflsEQiYk8tc24caQ1x6Y+\nUTNqFNd9unOn+u3MzWUxO34826LPRjc3rnUVFWV6EdHKcP48J50bEqt163LS+smTVb+ZyM/nxPph\nw/TPSuDgwCHB/ftN76uggLc5ZIj+Gyc3N66dpm+KSZWKz+eXX9Z/HKys+DzZuZOPQUQEi2VjBXAt\n1Q4erNq+FzyeCLFlRkwRW+np6fTrr7/SF198QS+88AK5urqWCq4+ffqU24ehA2bKn4CjI9eykV43\nbKj2HBQUaA/pXrjQsA1xcdo5XQ0aVG1uRIWC/ySff954Dka7dpzTsXkze6ge99GAKhWXJdi3j0fU\nvf0253g1a2b6tDwyGd/9P/cc0RdfcHHL7Oya/mbalJTwOfXRR1xV3Nh0Lu3asYdw377q93oVFrKg\nmjLFsJfGw4PopZeIdu2quqfJECoV/97eeIPI21u/HW3b8m/YHGUtUlO5dEXHjvr7atqUK8tXRAwn\nJfH52KKF/m1268YCW9+5mpfHnsegIP2fDQjgHMiUFLb922+JWreuftGFf9XVT1AeQmyZEVPDiJrk\n5ubS+++/TzKZjORyOWWW45+XDti6desoPj6+tAGGWnLpD3/sWL4zlF4vWqTe7nvvaf/RGbpQ7Nyp\nHVpp377yHof0dC4HYWiqkzp1iCZN4hCDqMuljTQtz+bNLFJCQ3mgg6kCrH17nmZm1SoubfEohSDT\n0tjjOmGC8Ump3d05lPf339UvIKVaVs8/bzjkVrcuV96vSBHRytgRFsalEvSVdpDJiAYNYo+SOby+\nJ08SzZypXQhZanI5e602bjQ9tKpSceX9KVP0e3Kdnfk8PXZM/z68do3rk+n7D7G25nkfd+9WV/h/\n/nnDoWFLNhOCFoJaSnJysta12FBbt26dEFvmojJiS2L8+PEkl8vLzd2SxJbpbV7pD/6339ShOWdn\ndc2rq1fV+UM2NoZHEO7fr/1HNWCA6bkbmly8yKJP35+emxvn9VRkehGBGs1peV56iesEGZpkWLO5\nunJI9qOP2Htz/35NfxOmpITDR/PmEfXoYdjrJRUpXbGC83eqk4ICngB6wgTDntlmzfg7XLliOTsy\nMozXpPLwYKF06lTV+yoo4JkkDNXK8vZmD2RFpuDKzOQRmYZGh3bsSLR8uf7/nOJivvEYPFi/PU2a\ncO5bairXjfv+e8PFWS3ZvLyqvu8Fjxbz5s2r0DVZiC0zoE9s3b9/n8aPH0+vvPIKFf0voePGjRs6\nomr58uU0aNCgcvuorGfLxoZDAdKP/uWX1dscOVL9/ocf6u83Lk47h2r06Irnp1y+zJ8r+wckl3N+\nxZYttSvnqragUHC+z5o1nM/VubNpYchWrXj9v/4yT7kBc5CeTvTHH5zrZay4as+eHD6qbo9Cfj7n\neI0ebbiIaNeu/Fs010ASfVy7xoNDGjfWb0PnzkQ//MDCo6rcusWzRRia8Lx/fz6HKvJ/ceIE/0fp\nE6+OjuztMiQab9xgT72+gqs2NpwTGRPDnrIDB1gk10Slekvm9wmqD+HZqgF69OhBMpmMevfuXfre\nokWLSnOytm7dShcvXiSZTEaenp60YsWK/2fvusOjqLr33fSENCDUFDooPRQBRZogTaUpReFDEREU\nURAQwYKIfugnggj6CdKkN0VARLpSRHoNRUrohCQkIQkpuzvn98fLZO6dmd1sm8X8vrzPM08mO7tz\n787O3Pvec95zDlksFsrOzqbevXvThQsXCm3DVc1W+/ZiTp0DB/C57duV1ypU0C+1cuKEWOi2a1fn\nBoqbN5F/ST3Bh4VB0HvxouPnKoZnkJWFieazzyAsdiSCq3ZtRJWtXGksUXAUeXnQRr32mu3ae4zB\nuvfvf3u/0HlaGiJR27bVt7b4+SFYZc0a4yZeqxUW6f799S3JAQGQF8iuNnfb2rYNwQR65KVsWUSZ\nOjDMFSAzE9ewWTP93/bRRxHlque2zM+HS7NDB/3P1q0LS2hmJkj8F1/Y1pCZTI5ZiF3ZvvrKvete\njKKBYs2WB3Dw4EH68ssvKTAwkHx8fCg4OJhmzpxJFy5coJMnT1JsbCzVrl2bkpKSyGw205tvvknR\n0dEUGBhIjRs3pgkTJlCSg7OXq2Rr8GBlv0EDrOokiahRI+X1efO07aWkiKvj9u0dtz7l50Ooqo4q\nLF8eerF/Yume/1VIEkoUrVxJNGoUksMWFslVpw6ix1atQhqQB93/gwfhBrVXE7FePegEvU28rl5F\nSZyGDfX7Vbo0XHwHDxqn70pPB7lo2lS/D9WqEU2Z4hkiffs2vm+NGvptdegAC6AzQQ7HjuF+04tG\nLFMG1qzERP3Pnj8PoqeXMDUiAou+c+dw7bdvR0CJ3v0fEoL3G0W8/peQkpJCf/75J6V6wrxaBFCc\n1LSIQS8x2pQpjL37rv3P9e7N2MqV2J8+HSV0NmxAkkbGGGvYEElC+eSlZjNK9uzYgf8bNUJZkRIl\nCu/nkSOMDRrE2NGjymuhoYyNHcvYqFGOncMI5OUh+WhGBmPp6djk/awsJFC0WlHKxGpVNiIksQwK\nQqmZ4GBlPygIiSVLl2YsKgrJL+1UXCoyyMpCKR45OenBg7gWthAfj8SknTsz1rz5g70GZ88ytmYN\ntsOH9d/TqBHK4PTujRI93kJCAhKI/vADYzduaI/XqcPYiy8iiWi5csb04cQJJBxdtIixlBTxmL8/\nkh6/+irKK7mTQFeScP/8978o46VOUFqhAmNDhzI2ZAhj5cs7ds7MTCRMnTWLsZMnxWM+Pow99RRj\nr72G0kPqZMz5+bgnZs5kbO9e7bk7dWJs+HD8TUpibPZsxr77DklaeQQE4LmXJDwnnkZ2tndKepnN\nZrZy5UpWrlw5VqtWLRYTE8NMXsqYTERs8uTJ7IMPPmClSpViNWrU0N0iIiK80h+jUZzUtIhBjx0X\ntlqqWFExj5tMiOyTJNGtuHattq0RI5Tj5crB8lEYcnORC4h3Gfr6YtXuDddTXh7cnitWEH3+OcLj\nu3eHK6lMGWNWo3pbZCRE0c2aIVfRSy9BIP3993DZnD79YAs0u4K7d4l+/ZVo7FjcO/Z0X5GR0MbM\nm+d9wboaFy7AytK8ue3+Pvoo3Dk3b3qvXxYL3KD9+um7+Pz84OL95RfjgkXy8mCZbN9e/7rUrAn3\nWnKy+23dugV3rp6OzN8f2qm9ex237EkSclr17atvhapeHUJ4Wxb0Q4cQRKJ37atWxfdOTcU1WrbM\nduBBRAQ2R9OxOLN99537170wHDt2jCpUqECMMQoJCaGGDRtSnz596IMPPqAlS5bQwYMH6a6B4b7f\nf/89+fr6EmP6gvKyZcvSE088QZcvXzasD95AsRuxiMEVssVH3bRujc9s3qy8Vr++Vq+xYYM4EO7e\nXXjfrlzR1lqrXx+uESOQloaJ6JNPMODWret6VvYHtck1Ep9+Gu67776DePfmzX9+HrGMDKKNGxF1\nZq++IGNwn737LiZHo/JPOYLLl0G8GjfW76ePDyLaFi/2LhlOT0deKVsTekwMqgXYcpN5An//DSKt\ntygJCECajT//dP++tFpBMrt3109u2rgx0fz5zgXL3LwJ93BMjPZ8sjbUllYsJYVoyhQrlSqVrvls\ncDCCROQo0sOHES2tR9DCw6F9tJWDzd3t3LlzZDbo4bl06RLVrFnTJuFhjFFsbCzt2LHDkPZ/+eUX\nCgkJ0W03JiaG/nInkeM/BMVuxCIGPVNkYVbf0qUZS03F/jffMDZsGEzsW7fitRUr4EqRcfs2Y/Xq\nKXUHZ82CWd4etm2DS0Z2Sfj7M/bee4yNGweTuydw6xbcmH/8wdiuXXCFOHp3+fig5l5sLFx9kZGo\nycf/DQ2F68vXV7uZTHBB5uRgy81V9nNy4IpMTcWWkqLsp6W5/n3Dw1EPUa6J+PDDjDVowFi1arZr\nVT5I3LqFmna//srY5s1wzeohIgL3X7ducPlERnq3nzLOn8e9v3y51h3FGFzdPXuiLuATT+A+8Ab+\n/hsuvgULUGOSh8mEa/fKK4w984znni0eeXmMrV0L95ksIeDRpAlcbX36uF8f8vJluBjnzFHGKBmR\nkRY2eDBjw4f7OezmtVhQT3HWLIxJPEwmXLO33mKsdWvtuJmSksZatZrCTp9uxxjrqDl3w4bX2Cuv\nZLEXXqjIrNZwNm8e2lHXkwwLU9y/58871m9nsHbtOtat2zMeP29KSgrr2rUr2y8XxuUQFhbGVq9e\nzZ588kmPtyvjwIEDrGvXriw5OVl4PTw8nA0dOpS99dZbrEKFCoa1bzSK3YhFDK5Ytngx540byHMl\n/1+tmuiikCQkyJSPd+1a+Er2yy/FFWrlyvZL/TgKSSI6fhwr1iZNCv+efn6wbvXrB2vXsmVIZHjl\nyoOzppjNEAsfPYoSIrNmobzQCy8oNRKdLSlSogRSG8hlef76659XlsdshjV0wgTbViT5N+vYEcJt\nb7rw1DhxAskxbSWGrVABdUNPnvRen8xmJCx9+ml9C1DZsri+nvSuXLx4kUaPHk0zZ86kTZs20dat\nV2jkSKtuSaWoKFgrHZEXFIacHFiz6tbN07n+Fipffhf16TOd/vvf/9KOHTvoxo0bJBUyMJ08ifQR\nwcHavjdooG89u3fvHj399NPEWE1i7CtiLFPzWR+fYzRmzEnKzcXYuW4d0luo3+fvj4CM+vWNsbgb\n4VXLysqizp0761qY2rdvT9u2bSv0uruD8+fPU/Xq1XXbDwgIoMGDB9NZI5PVGYhiN2IRgytkS97i\n4/H+4cOV1778Ujz/8uXKsTJl7OdXkiS4kPg2OnVyP3fP6dM4r72CxT4++D4jRhAtXYrJsqjmrbFY\nMGFt3QoyNmIECEjlyvZL16ivx0MPwZ06bRoSgRpZINlZ3LqFPF/2aiGaTHCjffGFc+kBPAmrFa7O\nIUNsu4MeeQTlk9LSjOnDxo0baerUqbRmzRo6dOgQ3blzh65elWjyZH29k48PFki//uqZSgC//fYb\nhYaGFkxy/v7+VL16PapX70sqU+aKbvs9eyKKz915WJKINm1Kp6ioTcSYHvHaS4w9S5UrV6eTDjLf\nlBRoxfTSg5QpA/csP86ZzWZ66aWX7n//CGLsbWLssuaz5ctjISjr2Y4cQYZ6PWJVqxYInl7mfXe3\nmTPdu+Zq5Ofn08CBA3UJD2OMmjVrRmvXriWrQWUnkpKSqGnTpsQYo0GDBtHIkSOpRIkSBe2bTCbq\n1asX7d+/35D2jUIx2SpicIdsjR8PkbMcOh0SIk4Yd+9CTC+/f80a2/0wmyEu5c8/YYLrQt6sLKw0\nbWlWGFN0P7/+6lrm+qKIe/dg3Vu9Gkkqe/SwnahSvQUGwgI2ahRSOjyIQs56sFiQ4+utt4ji4mz3\nv0EDJMs8fty7+rW8vDxaunQprV27iaZOvUSdO+eSv7+k6V9QEKyoW7Z4ttyR2Wym1157TZjgwsPD\nqX79+vTMM92pR49Z1KDBWfL1tWr6VK0aNGnuVgA4cuQIlS9f3saE24IYW0Imk1nTfr16eI7dJfrZ\n2dnUvn1/Yux94kuOyVtsrIW+/NK59DH5+bB26wVKBAYSvfqqkhJEkiQaN24c9539iLE+xNhfuvfB\nkCFI2kwE78GECfqLipgY3NeOltZyZqtQwb1rzkOSJHrnnXdItmgtWrSI6tSpI9wHderUoUWLFhmi\nI8vKyqIuXbrQmDFjiIgoNTWVJk2aRFFRUUIf2rVrR7/99puh1jZPoZhsFTG4Q7Z270Z0mPw/n0We\nCJOyfOypp2xPcBYL8tDI7zWZUGbDFdy8CVGuXjZwX1+Y57/6ylhhcFGEXJZnxgyQ3kaNHMuCHROD\nOnrTp4PEPOiaiJIEl/OECUiaaqvfNWogh5Y8oRmNgwcPUkxMTMGg7utbjiIi3qeQkDO6/atUCcWY\nPVXDU5IkmjZtGplMJhuEh1FAQCXq2fOIrsUmMJDoxRfdK82TmJhIDz30kG7bHTp0oCtXzDRxon5d\nwvLlcT3cIX1ms5kGDRpEjAUQY/8ixo5q2gkLk2jUKOfHhz//hJVVHUFoMsFKt28f3jdt2rSC7xwY\nGHh//1FibBUxZtF8tlcv1HEkgmv/229h1VL3OyqKqGVLx+QRrmyewvTp0wsqolitVlq7di01a9ZM\nuBcqV65Ms2bNKrTUnLMwm820a9cu4bXs7GyaOXMmVa5cWehDfHw8LVu2zLAAAk+gmGwVMah/sDNn\nHHv4IiNhjWrTRnmND/A4fVoZeIKCbGd1lySUypDP4e+PNAvO4tIlZP7WSw5Ypw7cmw86UWZRQ34+\noqW++YZowADbCSXVg/6zz+Izp08/+AjIM2fg8mnc2GKzzyEhCVSz5rfUtesrNHjwYBo9ejRdN6BS\n+a1bt6hly5Y6ZKMBMTadGEvR9M3XF1F2Gzd6Jl3D2rVrbUZpffTRRyRJEpnNKHVlK1N6q1Y47kp/\nUlNTbVwDRjVq1KDvvvuOMjJyaPlyfYtRcDCqR7gqs5EkicaPH1/QZkjI08TYBp3rLlHfvs6Ty6tX\nIVnQS5TaqhV0lj/8sJj8/PyoQ4cOdPDgQerVq9d9ElyZGPuSGLur+Wy7doj4liQsaDZs0Nd1hYVB\nMtCpkzElgzzxPB8/flzzm2zfvp06dOgg3A/lypWjKVOmUIYXslWbzWZaunQpNWjQQOhD1apVoTKs\nawAAIABJREFUDSF+nkAx2SpiUP9gjj50vXtj9Sf/X6uW+CA+95xy7KOPbLf/zjvK+/z8MIg4g9RU\nojff1IrCAwJgodm378FP+P90WK1WSklJoYSEBNqxYwddu3bN5nuTkzFhTJiAwd5WoWR5q1AB+Y7m\nzCGaP/93ql27NkVHR1N0dDTFxMRQbGwsxcXFUVxcHFWqVIkqV65MlStXpq+//trj3/PKFaL+/f8i\nH5+dxJjWZQbLwhYaMGCbYW7lvLw8GjJkiC7Z8PMrQaNH76OOHSVdbV2lStD0uJtn7ODBgwV5kNRb\n7dq1afbs2QWTy7lzRCNH6uvNKleGHs5ZrVlOTg716tVLmFTVk+ynn35KaWlptHcvyLueoP/pp1E6\nyJXne8aMGWQymWjo0KF08OBB6tBhBDH2HTF2T9NO586w+jrTTno6Slfpla2qXZto1Kjj1KVL94L3\nnzp1igYMGHA/P1Q4MTaGTKabms/Gx2MxKhPdw4dhUVNfn4AABCN1765P/NzdjNKzHjhwgHr27ClY\nYCMiImj8+PEOV0VxB5Ik0aZNm6ht27bCPVmmTBmaPHky3blzx/A+OIpislXE4CrZ+vZbROjJ/3/y\nCX9O5fVy5WznF/rmG+V9JhP0D47CbIaQU61jCA3FytLZCelBmYslSaJz587RnDlzaNKkSYZqBaxW\nK82ZM4cGDBhAHTt2pIYNG1KFChXIz8+vYFB55JFHKNcJgYzFgtX/tGmY/Pial3pblSr5VLnyT8RY\nB2IskPQm/FdeecXQ65CQkEA1a7Yhxt4ixg7o9jMwUKJevWDBMSIw4NtvvxWuO79Vq1aN3n33O3r7\n7WzdydrPD/UHd+1yfSFx5coVql+/fkGbVapUEfoQFRVF7733Ht28H9KZlYXnlc+xJ28lSqDszfnz\njrdvsVhoxIgRxBij2bNn0549e6hbt25CH0JDQ+ntt9+mq1ev0sWL0OTpkftmzYh++sl5F/aKFSvo\ntddeK/j/9OnT1LfvG+Tj8wExlqRpp0ULRAo6005uLtHcufrXrUIFC02fLkb+XrhwgYYOHUoBAQH3\nn49XyGT6W/PZatUQcStHP54/D4uf2rJvMiHB7LPP6hfSdnfzRHJaPSQkJNDAgQOFZyQ4OJjeeOMN\nryUj/euvvzTELzQ0lEaNGkVX/wGC1WKyVcTgKtk6cULUB1y6pJyzc2fldVsGij/+EK1R337reJ+P\nHEH4M9+fkBBocJyNXMzKyqJ3332X5syZ49wH70OSsIo9dw6T348/Ei1ahBQK06ZBZzJ+PPRrb79N\nNHq0RIMHp1DHjoepdu2fKDR0GjH2DjH2OrVtu4BWr0aCxj17kFIjJcWzOqj8/Hz67rvvbIqVn3ji\nCafIlhoWC4qSf/45XBnqOpbilkWM/UyMDSHGYoWJ3gg3Ho/s7Gx6+eWX77dZixj7iBjTTmqMgUAO\nGQLtjCc54O+//14g0PX39xfIj6zpOXLkBK1di6oBetauBg1gNXQlVcfdu3cLwvKPHj1KO3bsoGee\neUaYXAICAugI50uzWhFQ0qmTti8+PpjUHc0XKUkSffHFFzSTC39LSEigQYMGkb+/f0Ef/P396eD9\nTMbp6RDsx8Zq23/4YaIFC5yrj6hnqbh8+TINGzaK/P3fJMYuatqpU4fohx+ca8dqBVFr2VLb77Jl\nYQXjk6pfv36dRo0add/l60OMPUuMHdR8tnx5XA95QXvzJlLB6GlWW7ZEAIa9qGxXt4QEx6+FM0hM\nTKQ33niDgoKCCu4HPz8/r0YOnjlzhgYPHnyfAGvvyQeFYrJVxCD/YD/99BMROfZgRUYiJ4v8v5wC\ngghmbfn1SpX0rQJXrogFXCtUWESZmZmF9jU/n2jSJK3LsH9/5yPjJEmiVatWUWwsJvmyZcvatKbc\nvQsCsWwZ3DgDByLKMTbWuAKy/ObnB3dEw4ZETz4J/dS774LQ/fYbiJ6z/CgrK4smT55MYWFhwgQf\nExPj3IkKQX4+SqZ88gmqDdgvQXKcGJtC5co9S2azd3y/CxcuLNAwlS9fgR555A1ibAb5+ibr9rFB\nA1hUPZWmITExkRo2bEg+Pj5ktVppz5491L9/fwoICKDq1asL4fCJiSDuehnZIyNB6PlFjyMwm830\n+uuv0549ewpeO3fuHL3++usUEhJCNWrUsBmSf/o0dJIhIdr+tG4NSYAjCwW9Z//atWs0ZswYCgsL\no5o1a5JFJRDLz0eKFvWiizE8l1995X6uuKSkJBo37j0KDh5MAQFnNe1UqoTUKs4+e3v2EHXrpu13\nqVIY3/h7Kzk5md577z2KiIigmjVr0aZNFnriCe1no6JQ9Fu+lLIbUy/YoGVLREraKmLuzrZ1q3vX\n3BaSkpJo/PjxFBERQbVq1dLcD97A9evXaezYsTbvSW+jmGwVMcg/mFw2wZEHqksXDDLy/7wmq18/\n5XW9iEKLRUzHEBT0B5UqVZY2FCLWSkwkatpU7Ef9+ogCchZWq5W++eYb6tChA7Vo0YLq169PHTp0\noLt371JmJvL7/Oc/+C41azqem+pBbxUroibfwIEYaNetg3vB3piQnJxMb731Fvn7+1N4eDidOHHC\n+QvqBNLSUDvvxRftuzXKlYNbZMsW5ywIriAhIYHq1KlDcXFxRER09epV2rFjF23aBGKrZ50LCsKx\nP/5w39qVlZVFvXv3Fqwst2/ftrl6z82F9bRZM22/ZOvS3r2Oty9JEuXo1LJJTU11aCC/c4fo00/1\nf886dZC6wVWNT3p6Oh09etRO31FiS89iFBWlJS+u9+EYrV+P50vdTnQ0CLgz5YCIiI4dgztYPb6E\nh0MTybvoMjIy6NixYwX/HziA31n92dKl8VvImvKcHCzKqlXTJ11jxohBTp7aVq1y75rbQnp6unAd\nHgQKuye9hWKyVcTgihvx00/FSCX5vrt0SbFcREUhp5MavM4rKiqTnn/+DUouxPG/ZQsGEflzvr4Y\njDwh0szLg/j1ww8x+DiTfb1MGeQBat8eIvCRI3FtZs5ESozly0F4tm5FmozduzE579wJYe+2bbBM\n/fQT0axZGTRy5Fn6/HO4Q996CwkNO3WC5TA62vWs0YGBIKZ9+8KtuXGjNrnsxYsXqX///l4dRKxW\n1LmcNImoceM80hetY8X/0kuYVI1KrJqdnU1DhgzRXa1mZqLgtx65YQzBIf/5j3vRrpIkubRS3r8f\n5FrPwtq8OcTU3pIj5uTApamXmiAmBpICI4O6du2CKFzddkQEnm9PWSN37cKCU2+xM2OG86Tr9Gk8\n62qrb4kSRKNHE9nThZ86hUWhmnSVLAkrvBzoYTbD9Vmzprbfjz6KMcdW8XB3Nmd0uMVwDsVkq4jB\nFbL1888KKalcWVnZjx6tvGfiRG1bBw8qn/PxIVq71j7JkiREO/GRNtWqOa4JsYXsbGirnn++8Eid\nwEBY1AYPhg5pzRqsSB3wenockgQrQkIC0aZNEMiOGwcS1ayZ8wLY6GiI2idOBCm8fp0My+LsCG7f\nlmjs2BPUvbt+YV7GsOp/4QX8fs5Oao6gMGH+8ePIyK+XudvfH1G4mzd7P9/Y7dsgrXr3QFwcUp94\n6561WjFG6CUULlcOxNTIvhw7hmdbHaEXEYHs7p4KKDt4UCxFxpOur75ynlieP49xRr2oCgmBbMCe\nHvX0acgp1N85MhLPt0w0LRaiJUv0BfvNm4N0dezoedJ1X6VSDA+imGwVMbhCtubPV/bffBPnyc2F\nNYsxhB2rV/lmM6xA8ufGj7ffL6sV1h2+3S5dXB8orVZYmPr00deYyFuNGhBDz50Li53RLixPIysL\nurklS2D969kTA6ujFru4OKyUZ87E939QsoTMTGSp793btsg+IgKT0++/e5/c3LtHtHgxtEl6fatZ\nE1YOL6QIEpCbi+eTf9bkrWRJkA2jIsj0sGcPCL26L6VKwfJiVIkiIpRoevll7b0fHu5Z0nX4MFIs\nqL9j+fIIknF2UXD5MqI71dbK8HBINuzdU2fP6lvJIiLgVZBJrsUCq5Ne4t9HHsF79ax37m7bt7t+\nnYshophsFTE4S7Zq1IAoVv5/40acZ+lS5bV+/bTtfPmlcrxhQ/suwPx8rNL4dt97z7UJ9fZt6Jeq\nV9f/PpGRaGvBAs8UwP2nIi8PhXSXLEFUZJs2+hFL6i08HCvdSZPg+nwQ9RHv3SNauxYaKVupJSpV\nAoE/fdr7/Tt7FlUL+KAPeQsLQ+1Qb2WqlyFJWFzoTZjBwbDOeSmCnogQQfzcc/r6pPfeM5Z0XbwI\nUq5Hut5/33Oluo4cQfkr9fWOjYUb2ll37vXruHfUlq5SpTCm2UqpQ0T0999wvatJV9myWATIz7HV\nCldznTrafrdrh0WXHll2dzOIH/xPoZhsFTE4S7Z690aINWN4kOVw5bZtlffc19oX4No1JT+OyWTf\nDWg2o0SFfC4fH1iZnMXVq7C6BQdrv0Pp0hh8N20qusWmPQGrFYPy8uUgC23a6F8v9UTdsSPcu0eP\net+ilJeH1AMDB9pOqNqkCdw4XsiBqOnbqlW2BcedOkF/6O0kuydPwtqhJht+fnjd1WzsriAhAaRZ\nz/Ly8cdi+gNPwxbpKlUKEgFP6cmOHoVFWf3716oFa62zz0xiIvqtvmblyuE+t2c5u3ABpEvtXqxU\nCRZQmQBaraiXWreutt/dukHvpecydXf7/7zANRrFZKuIgf/B0tIKfzjefFPZb94c57h2TVmx1qih\nnUwGDFA+M3So7b5YrZhE5fcGBECb4wyuX0dYs16piieewGD3v0ywCkN+PkTX06aB9OqFjvNbmTLQ\njM2di/vAm8jKgqWuUyf9DOO+vliVb9jgfXfo8eNwR+u5rBs0IFq40Pv34eXLeH7VffLxgQ7Om1bB\n8+dRpktttSldGsTH3bQN9nDpEtpWk67oaKLZsz0XUHD0qL5gv3FjBMY4S7r//htWeLV1MCYGxMne\nPX76tFjVQ94eeggkS+6L1Qr3uDoXl8mEtpctI93UE+5uRugv/7+jmGwVMfA/mJ7OQ729+KKy/+67\nOMe0acprH34onv/YMWVwKFXKtshTkuDakM/j7w/Lk6O4dw8rY/VEIrtMzp1z6fL8z0OSsDpesABE\nuGJF+/dH48YQ5B4+7F0Lzs2bcFXHx+v3Ky4O94fBuVI1uHMHVsDKlbV9qlABdRuNKg1kC8nJeE7V\n1RdMJkgAjEpQqYdLl1BWS89qM326sZPwxYtYCKrJS40acK15ymq7axfR449rf/82bVxLXXPqFNI+\nqM9Xv37hY+ahQ/oJaRs3RmCHjPx8JJpWVzDw94eMZPFiaLs8TbqK4TiKyVYRA/+DOfIw8KbkLVtw\nDr5grHqg5ld2U6fa7sfXXyvv8/FB1J+jWLdOm1E6LAyReka7knJy4IbZtQsRN3PmILng2LFEb7yB\nFfSAAVhVPvMMhLS9esEd268fjg0divd//DEmmHnzoFH6809MCEau8p2FJOE3njED38deNGdMDL7b\nxo3eXbmePInfPjpa2ydfX+hqfvvNuy5QsxlWVb30EeHhWLh42+159y5SlfBpVWTS1bevd92L587B\nuqYmPnFxyClm5G91/Li+iyw+3nNJOiUJz4FeItHnnsOCxlkcOaJvOevQQUnHYwu//64fLdqpE54f\nGdnZsDSqiXlwMPRuixfr672KSZfxKCZbRQzOkK3ISMWn7+sLN86lS+LKisfevcqx2FjbE+7WreLK\ndv58x/qemiq6KOV+DR+OMjeegiThe/78M/JUPf88ctPo1a0zagsNhcj/iScQYTV5Mlxoe/YgZ9aD\nKradn48+fPCBbasSY4go7NsXhNRbxMtsxm9mq9RN1aqwLHmT5EgS8q316KHtU1AQCLo3hetEiFCb\nMkWJJuafpcGDvaurOXlS32oTH68s7ozC3r360aVPPeU5F6vVCo1kjRpiGwEBSDDqipVz+3ZYptSE\n+V//sv/byQlhGzQQP+vjAykGn4svPR3kSh0ZXKECFpgLFhBVqVJMuryJYrJVxOAM2apbV9HGNGyI\nz3/2mXKcL0ZNJK4WbZUeTEwUcxa9845j/d62Tasn6tABJnZ3kZEBy8cHHyAip7BcXP+ErWRJrFQH\nD4Y7bdMmaKi8TcKuXoX7oXNn26WMwsNBkjds8J5u6dIlpMLQ06AFBoLAeuLecQbnzunnVfLzg0XU\n2dI77iIzE1YMdTmgwEAk7HUnaauzOHxY39315JOFW23cgSTh2VEvHPz8QIQ9tYjLz0eePHUEa1QU\nKm84qxuzWhERrnZXBwXBymsvXYTVioVbXJz42bAwWD75wIGkJMgy1Hq3Bg0QuDJrlucLXr/1lmvX\n+P87islWEYMzZItfuQwZgs/zZTL+/ls578mTyuvR0fqTqtksmrK7di1cyGy1YgDgBdEREbCGuUos\nJAkD+CefwGKlJ7bW28qXhwu1b19MRp98gtIYa9YgInP/frgozp3DCvPWLaIbN0BIEhPhOjh7FjqK\nnTvhDl2yBGRl8mQM7r17E7VqhUgmV0hfuXIgPu+9B6vSlSveI2CZmWjzpZe0bgieJA4aBOumN9x6\n+fkQBPMVEPitSxcQeW+S1KtXMaGo9Yb+/njOEhO91xci/G4ff6xNDRIaCj2evZQDnsaWLVriI1tt\njNTfWa2IwFO7oiMjsZjx1CIhIwMuZPXCpHZtkBdnkZsLjWBkpHYcWLDA/jN27x7GVvU4ExeHcYn/\n7Nmz+rnFnnoK496ECbYTE7u6eTt9yj8dxWSriMEZssVPmN9/j9w4svuvVi3xvC+9pLz3yy/12/7o\nI+U9lSoVnmsnK0tbwPXJJ12Pgjt+HFop9YpOvUVHYxAZPx7ROCdPGlt2xBbkDPKHDoEwfPEFkh8+\n+ST0Uc4QsF69ENhw4IB3yrnk50OzMnCg7fxelSrBmnjxovH9IUJE3Ntv6/enYUNohbyZ1DY5Ga4a\ndX/8/eHW8Xa0Z0oKng/1pFmxInSF3orwlCPkKlXSkr8pU4zN/ZaVhXFKTYSrVydav95z7SQmYtGm\nvg87dXItuCc1Ffe2Oiq7eXM88/Zw6xbuN/Wis2lTon37xPfu3EnUqJH4Pl9fjEuHD2vzJXpie1CS\niX8aislWEYMzZIs3HZ84gZxC8v9yJnkikCY5X1NEhH5pjsOHFaLm4wPdjz0kJYmFqE0mDILOWkPu\n3oUYv35929/z4YcRcbN0qff1M+4gIwM5zObPR+mk9u31y8qotxIloAX76CPoVowmX7m50FI9/7zt\nXFlt2sCy4I3ggIwMBG/oke7oaLjKvRkxmJoKS6TawhAUBPLjqcznjuL6daJhw/RdR54SkDuCnBx9\nq0316rAKGzkJX7+OSGy1zu7ppz27ONi7Vww4YgyE6f33XVvgXbyozfllMsF9XZhb+ORJWMXVz8TL\nL4uftVqRykTPCvjNNxiTWrXyPOn6X0cx2SpicDYakTGs8iwWPHTya3zI8YwZyutvvKFt02wWBZ3q\ndBFqXLwoVq2PiHAuLQQRXHZvvqnvivP1hXXo66+9Z1XxFiQJ32nVKrgrOnQoPHN8RARcBLNmYVVt\n5CR27x7C7Dt31nffhoVBv3TkiHF9kGE2w3LZpIm2H3JhX2+W30lNhTtGTUgjIyHs93aU6pkz+lF7\nTz3l3dQqycmIclXfL506GZ8r7NAhrYg+KAj3hqcsbJIEEb06wrpyZZBKV7B5s5KMmn/Ov/qq8MXV\nb79pk52WLAm5A2/dzM5GpQm1FbBxY1jEfvrJdiUPV7f33nPtevx/QDHZKmJwhWw1a4YBQV7JBAUp\nqy5JEkOB+TBiGXzpnrp17esfEhNF90F0NNx/juLSJf3sy/L3mDnTu8LffwIsFmjUZs6E60IvRQK/\nVakCorptm7FutWvXoBlRR2rJW8uWIGZGu/YkCaHxzzyjtWSULAk9nZGZztVITiYaNUqr66lYsXAd\njhHYsUOrowoIgJvdm3quI0e0FhN/fxBUI938kgRSro5Grl7d+UWgPWRlIWBIbVF01ZqWn4+xV73Y\nqlsXFjV7MJuRlkb92SZNtBVBbtzQRombTFg03bgB+YIjpcKc2bxdg/SfgGKyVcTgCtkaPBgCSfn/\njh2V8+3erbz+2GPa9pKSFOuSyWT/Ib9yRRTlP/SQ42Hod+4gakYd6RUUhIfeGcLmDvLzMTEnJUEI\nff06EnAmJUETk5Pz4DUIcmqL779HoW513iV+i4yE+2/FCuMGODk9wssv67sZK1bECvrmTWPa53H2\nLNxHarJeqhSIoTdJ1+XL+qVXGjcm+uMP7/WDyLbrKC4OASLeuqdtWYGqVTM+VURGBgJj1PfGs8+C\nVHgKCQmIilaPYx9/7JpQ/+ZNMTm1PBa/9lrh7vKbN20TKXWB899/11rESpVCENGNGwhy8CThYv9j\n7KCYbBUxuEK2vvoKE7P8/6efKucbPFh5feFCbXtDhyrHX3nFdr/S00ULWa1ajk2uVivSTKhzBoWH\nw13pqdDtjAyYxpctg0h32DBYQh59lKhmTRAWPWua3ubrC5N+dDQGp3btYHF64w1YUX74AQNXYqJ3\nxOxWK9wlU6agL+qVtbwFBMDduGKFcS6tzEzoPmrX1rbv749EmEamApDx998Q96uJTunSuE56ukSj\ncOqUvjuvVy/vu8EzM5FaQL2oefJJMTrZaGRnw6Kl7kf//sbnUTt2TIzKlhcl7kRIq2HLmla/PtHB\ng66dc98+bX6uihXh7isMtojUDz+I3zk/H5YstXyjaVMI9f/4gxyqXOLMxs9H/59RTLaKGFwhW9u2\niSujXbtwrvx8xSoSEqKdgE+fVghIaKiYNI9HXp5Yf6t6dcfCvC9d0hYBDgmBX98dUXFyMiKPJkxA\naoDCoheN3Hx9kYyzSxe4lmbPxvUvLJLTHaSnY6Dv1w+kUK9fJUrg+Lp1xkSHSRLuux499LVdXboo\n96GROHcOK3t1H8qVQ94kb5BhGdu2aQM9goJg9TMyQk8PZ86AYKn7MmWKd6/JqVNa4lOyJKInjbS2\nSRJcuuocZR07ejbIJiMDzz2/kPP1hbvRFdep2QwypE5W2qNH4dGvtohUp07a73zjBizi/Pt8fJDI\n9e5duCg9nc/wQXsMjEYx2SpicIVs3b6tCB0DApSM4L/9prynd29tW3wY8OTJtvv02mvK+6KiHFsh\nz5+vfVh793Yt+3VmJsjV8OGwqDn7kIeHgxA1aoSBv317iIh79sQg1q0bdBedO0Ns27gx2qlY0b3c\nNFWrwoXxySfI0WNE1FpeHiLQhg+3XaS6dGlovIxy1SYmwpqi5+58/HGkmDB6oD1zBvezmnQ99BAi\nLb010FsssOSqE0l6Wj/kCCQJLkS1Sy8+HpZSb0G2bqujFrt0Mb42ZnIyrK18u6GhCDbxpLbu0CFt\n5veaNV1fcCQmaiMPw8Ic6/eNG5AfqL/zzJnaz+7YobVSV68OS9mNG8akivj/imKyVcTgLNkqVQru\nPPl/XpfFuxBXrxbbuXBBWY2VLm3b7bJkiXKOwMDCU0Lcu4ekmHwf4+Kc12tkZCCXz9NPa3PT6JGp\nRx+FG/Szz6AZ+fNPDOTuJjuUJKz0LlzAOX/8EavHt94CUYuPd24FWLs2+jl/PvJKeZIEWCywrrzy\niu0UE02bwuJjROqE7GxEkOpZGhs2RC1Co8Xjp0/rl5dp2xbpUbwFPYsHY+ibN7RtPDIzcb/ywQW+\nvkhb4c38dLduaa0pJUviOTeaDG/YoNWztWrlWTdvfj50W/x4ZTJhIeSKW1t2Vaqz2rdt65h17uef\ntYXqW7bUJiPNz8eCUD3ODhuG+3jnThBHTxIuWyT7xo0blJqa6vzF+gegmGwVMThLtpo1Q5Fk+f+x\nY3Ees9m+C/HVV5XPTJqk35czZ0Rz9vff2+/79etazcGgQY4LtyUJK8H+/W1blPz8kPdm5EhM3omJ\nD948LUkw8W/dCrIxbBj6KOc2s7dVqoRrtHSpZ7UseXmYYPr10y/TExyMdo8d81ybMvLz4cJRh7Yz\nBnK6aZPxv9mePUQtWoht+/pCd+fNvFjHj+u70TypH3IU+/ZpdT0PP+y6xshVrF+vtcL26GG8lis9\nHRUA+HbDwpAs15O/xalT2gLn1asjk7srSE0V0/rIC8wFCwrvt953DgxEqhK1O/n0aSxa+ffGxiqF\n68eNc1z36uimRm5uLjVv3pyeffZZWr9+PZm96fN2E8Vkq4jBWbL1wgvI8i3/v2oVzvPHH8przz0n\ntnH9urKKCQvTn3zMZnHAePFF+w92QoJo0QgOxorVEeTnQ7yvngjkrWJFCPl/+qlohRRbLBh4Fy9G\nJGaTJoUPVg0b4vc8cMBzVqA7d+BCsFWYuk0bXFtPZyC3WmEJ5JPf8m3++adn21NDkmDRVRfkLV3a\nu2RHknB/q/VDHTp4v95iXh4kA7wVw88Pr3lzXktJwUKAvx5RUSjEbDS2bdPWLOzbV9FZWiwWsrj5\nMFgsSMzLL7jk61zYqW/cuEHjxo2jv1V6ja1btS7h7t0dI6nbt4u5ERnDgvD8eW2/P/oojRjLEt47\nYIBSLaNhQ88SLnUfzp49SyVKlCDGGJUrV45GjRpFx70Vru4GislWEYP8gy1b5hjZmjgR+iP5/wsX\ncJ4JE5TXFiwQ2+DJma1C01OmKO+pUcN+dNv+/aLbqnJlxywm+flIxKfndipZElqxP/7wft4iI5GV\nBZ3E5MnQjtkqDi2TzCFDoL3z1ER4+DBKd+jl1alcGROEpyP5bBUTlicLvdxvnkRODq63Orlj69bG\nJ93kkZys1cCUKAE9k7etXKdOacu6NG/u3YhFIpBhdaTyqFESXb1qrJkrI0Ob6iAuDlolSZJo2LBh\nNGPGDMp082E4d47okUfEdh5/vPD6mlOmTCGTyURdu3alTZs2kfX+IJieru132bJwGRaG7GxUsuB1\njaGh+guPGTPWE2ObhXYqVMinnTttux3d3XgsWLCAGGPCFh8fT1999RXd/ocmYiwmW0Xl4h52AAAg\nAElEQVQM8g/Wtq1jZGvxYkWLEBGhPDR81m0+x4zZrLzf11c/wuXiRYUE+PjYz7114IAYERcfX7gm\nRZJg8dDTAbRoAbO+O1qStDS4TFatgkXn/fdBWrp3R4RW69aYWOLjkc6ifn0MiK1bI1qpWzdMiqNG\ngXTOmweX3IEDMOl7EvfuYcU6bpx28uO3qChY93bu9IwFSi6TpPcblCoF17KnIyqtVqSlUGet9vEB\nATTavXf1qlY4HBCAskjerLm4YYO2dma3bt5P5puXh0WZevJdskSiM16sMpyUBG0mfz2io69R9+6j\n6JgRfm4Oy5eLwn2TCdfk778vUkhICEVERNDYsWPp6tWrLreRn48IbP46R0RAOmALZrOZmjZtWkA0\natWqRV9//TXdvZ9Ibs0aLUl9+WXHUr7s26e1cj37rHZs69u3HzH2IjGWxr3XSt27n6KsrDxKSNC6\n6v38HJNP2Nrk+UiSJHrhhRc0hIsxRn5+ftS9e3fauXOni7+IMSgmW0UM8g/GmGNk6+eflf22bXGO\n5GRFDFu/vnj+devEAV4PfO2uUaNs9/XECXGgat268KSSFy/q1/fq2tX5yB1Jgq5s7lwQkTZtbEfk\neXIrWRKusX79QOQWL4Yb1RMk6Pp1JBns2tW2bq1iRZAzT5RksVqhyejYUdtOeDiykHuaBOTnQ6Sv\nzlFUpgyIrdGWzF9/1boW4+ON0a/ZQkaGGMDCGCwUv/yCidaoAVsPe/fquZiOUqtWT9Ivv/xCkhfM\nbpKEfIG8tcTH5y4x1ps6duxIW7ZsMawfV65oS/488QTRxImzhAn++eefp4NuCNx27dIW737pJdsL\ny5MnT1JAQIBANMLCwmjEiBF07tw5unVLS1Lr1tUK4PVw9642kCk6Gi5WGXfu3KHo6GhiLIYY26Ei\nVYdp8ODPKC3tLk2dqnVLV6hgOx+gIxv6eJeqVaumIVtRUVH0+eefu2119DSKyVYRg7Nka9kyZX/k\nSJyDf23MGPH8vMtRTx+xbZtyvFw52xqpa9fE1XmrVvZLg0gSrEzqVU+rVtrK9faQmIhB+emn7WdW\nd2Tz84NryZ30DvwWEoKV3uuvgwAmJLjnHsrKgpvluedsrxYffxxuYk+UZTl1CtoMta4sJAR1HD0d\nwZidjYSHavdeixZwdxqJ7Gy40Pnv6u+PaLKkpFQ67SX/4tq1WgvF2LFE7777ATVv3pyWL1/uFZFw\nZqbWPRUcfJoYq0a1a9emefPmUa4XkoUdOqRXr+8/xJgvxcfH05IlSyjfADOkxQLROH8/xMRI9NBD\n/9JM9q1bt6aff/65wLXnDNLTtako4uNtR0VOnjxZ0768derUiQ4dOkxz54rPUIkSiCJ3BKtXayOX\nx4xRLL2bN2++354PMTaWGMsveF9QkIW+/x5j3NGj2hQSsbGFlx6zt0kS0YEDB8jf31/43iVLlqT1\n69c7fe2NRjHZKmJwhmyVKAHiIf8vRwvyebH43D63bimm7NhYrSXGYhFF6vPm6ffx3j1Rf9OkiX2d\nT3KySPIYw0PoaBmRM2egM1PnsdHbypXDKvXVV+ECnD8flpuDB+FGSktD/9XjpCQh8WR6OtygZ85A\nL7Z6NTKmT5wIV+QTT2B1qq7RZ2srWxZkaeZMaJNcJV+ZmXA7PPOM/ooxMhJ6DE8Iri9cwHdVZ/8u\nXRrJDj095165gmvEt+XjI7kcMu8MDhwQKyMwRtSypUSdOr1KrVq1oiVLllCOnLjOINy6BUsm34dH\nH7VStWqtiDFGsbGx9NlnnxkeEi9JWCSIi490YqwzMcaoQoUK9O9//5vuGOzvvXtXS0gY+40YK0mM\nMYqLi6Np06YVuNQ8id9/F63jfn5WMple1yU7NWrUoB9//NGldhYtEglSyZIYp9TIz8+n+Ph4TduN\nGzemn3/+uUDIf+qUluy8+qqSc9Eerl0Tk1YzhkWwLAcZPnw413YjYuyM8N5evbAov3cPaS74YyVL\nwrvi6Hip3iZMIJo6dWpB+4GBgQX777zzzj8qWrGYbBUxOEO2HnpIJFa7d+McMinx8REtU998o7x3\n/Hht28uXK8ebNrXtznnlFeV9VarYzjxPBFejOvLntdcKjyrMyYF7Tl3Ylt9KlQKJ+/e/MUh6M6Q/\nNxfi6nXrYJ159lkkMS3sNytTBmVm1qxxnUjcukX0n//g91ef38cHYfQ7d7pO7P7++2/Kz8+nq1eR\nKkEthK1SBcTP016dLVu0SWvLlMmgjRuNDUHNzcXzwGtqwsOtFBExmBhjVLp0aRo1apShOiZJApHl\niXRkZD4x1rZgcgkJCaFhw4YZbnU7flz9O1iJsbcL+lGiRAl688036ZKBoZSShPHKz0/i+nGeGKtb\n0I/IyEiaM2eOx9u+cUObroOxBcSY4tKrVq0arVy50i0r2/HjohXPZIJ+UD3uHj16lPz8/ASyVa5c\nOdqncglkZWFs4fvdsKFjQQ9WK4Jj+AVWhQpwfWZnZ1OtWrWIMUYRERHEWAgx9l+hnZo1QfiI4DFR\n5wZr1kwbjevM1rlzZwoODqaEhASqV69ewXV4/PHH6VphqfW9hGKyVcTgDNlq314siJqSAhIjTxoN\nGojnbttWee+RI+Ixq1W0am3dqt+/RYuU94SE2I8k27BBLFxctqz+6o1HRgYix2y5CJs2xfHjx/+Z\nUYppaYg2/PxzEEFb5XQYQxBCly7QL8lBDBaLhTIzMx3Sp0gS0icMHKgfGfTooxj4nCVF+/fvp/Ll\ny1P79u1p0qRJtGzZPurTx6w5f8uWnk8UmpcHi2RwsFWY7KtWXU3z5y8zVD+0Z49WU8PYDGJMcWN0\n6dKFUjxV0FMHf/4phvf7+FiIsVeFiTYuLo7+NDhvxt27sFiI12J+AeHo0KEDrVu3ztA+EGERFRZ2\nj+tDJjH2NMXFxdGvv/7qkivPEeTnQ5Yhfv+dJFvX/Pz8aO7cuW63k56uravZtatW+zpx4kSSXWhB\nQUEkW3mW6PgL580TrZMlS4paLHv480/R9efnh0XAX3/tJ19fX5o3bx599tln5OPjQ4x1I8buFLy3\nRAnkPiRC0IPaWtuwoX4aGEe3p59GDqPs7Gx6+eWXC56HMmXK0ObNm935GTyCYrJVxOAM2XrxRSVD\ncFQUPs+X6HntNeW8vAuxenXtBMwnRm3RQn+CPndONH2rU0rwmDtXNB03bmy/tldmJiLg9DKfP/QQ\nVl3OLGDy8mB5Wr8e7tVPP0XJmhdeQABA164gq61awYTepQtef/55oldesdKQIbdo8OBjtHw5yFNi\nomsCeIsFOpSpU6Ez48knv/n4oIbZkiUSffHFNxQeHk5xcXHUvn17Sk5OLrSdpCSQUHXGaMbg8nXU\nZStjx44dBSb70NBQ2r17Nx06hGvGn9vPDxoPT2jGeJw/T1Sr1m2hrapVsw3XcqWlIeeSeA33EGMV\nKSAgwCvC9ZQU3AtiH74mxvzI399fY9EwClarmCYG227y8YnyCtGScfmyRKGhZ7k+WIixwfR9YVmW\nPYAVK0S9pMl0lmJiWhdM9PNsaS2cgNWK8Ym3rDZsKGZZz8vLo/r169OLL75I+/fvpwoVKhT0YeHC\nhZpzHjsmRhr7+SHwxhEkJYkLc8bwTLz77ieUkJBARES//fYblSxZkhirQowdEd779tuIepckWOD5\n7xUXh8AiV8XzvEdmwYIFFBwcTIwxMplMtFJmeg8IxWSriMEZsjVihLLfsiU+/9FHymv8oue775TX\n331X2y6fC+aZZ/6rMc1KklhUetAg299BTbSee852SLIkYTWkFVJa6PnnJdq1q3CScPcuVm6ffIJV\nYvXqns90zBisR7VqgZi9/TbcnKdOOUfCcnOhoxs2zLZ4NCyMqGvXW1SqVHeqXbuOU6v3/Hz0S61D\nYgyryu3bHe/runXryNfXlxo1akT3uJCpX3/ViphjY+FS9SQsFqLHHltLjOUKk8bUqcYXMZ49W112\n5RZVqdKX0oysMM7BYsE9xl/jwMAdVKNGvOGaKTVWriTy9c3lnoOzdOKEd/tw9OhZ8vFZLlyPceOy\nvZKfbP9+0S1WurSVatd+mWrVquVRHd3mzWJ0d0yMWM/00KFDBcTq2rVr1LhxY6pZs6bN+yEjQ2td\nevNNx8YrsxkBJPxn69aVKDFRGYsuXLhA9erVo2rV6lGfPnnCe1u3VuQl27eLLsTAQIx/jsgubG0y\nTpw4QQ899BBVr16d0o2oQeYEislWEYMzZIsv4TB4MD7fvbvyGp8aoEcP5XV12YiDB5VjtWvnUURE\nJB09elR4z7x5ynsqV7ZtyZg3TyRaI0fadvclJmpTDvj6StS06UmaNes3m9FPViuEzRMngkC4Kr70\n1BYcjLxdo0fDkubofCxJsHpNmKDnvsJWtWo2ffut85YjOXu7unwSY0i94Wiag0WLFtEtHVFeTg6u\nvzop66BBhaf/cAZ5eXn07LMTqUEDSWinZ09j6jvy2L9fdOkFBUnk7cXzvHmijqZxYws5YOj0ODZu\nTCKT6VZBP+LiiM6e9W4fPvhgIsXELBPug1df9XzlAz1cukRUs6aFIwwSff+95xOjJSSIGtfwcLGu\nLL/wys7OpsuFFEm0WLTu0M6dHa/E8eOPYu3XihVFCUpWVhZdvHiRJAlFsvl7lSeLV69qSxj16aMV\n5rtCuDIzMzXZ9h8EislWEYMzZIvPRv3ZZ/i8PGmHhiokx2xWMoaXLq0dnHjB++jRZzV6kNu3Rffe\nr7/q9/2330SL0siRti0Qq1eLqzjGYDGylzvq9GnklyosnLhECbjO+vZFHqzvvkM5mt27MUFcvYrv\nlJEB0pCZCdfNtWtwXx06hO/4ww9EX3yBXGPdu0PT5kjCPpMJ7Y8dizYdmQysVuhTBg3SL2wdEYHz\nOVvEWJKg26pfXzyfjw/E7+4SlnPnkChWJIiFFyx3BmazmfLytCvtmjWNn/CTk7VBGvKz5i3s2kUU\nEaFo2GrVcqwQsacxffp6qlpVIb1RUVrtp5HIzc2lFStW0BdfiL9H377eKTWUlkbUrp3y/f38yBDy\nfeuWmJTaz8++ZMMRzJ4tuu7q1rVdDFqNM2dES3ZoqO05YO9eUcoQHq7oxXJzYdHif7t27ZAj0VXC\n5c1C6oWhmGwVMThDtvhw+eXLkQFY/v+xx5Rz7tkjDkw8MjKUYtNhYUR372rZEe+u7NdPv9+nT4ti\n8BEj9IlWXp72gYuNxQpK7/0WC/RG6gKp/FavHvRpP/yAyd9oF9O1axD6f/IJohDVCSHVW1QUROw/\n/uhY2oTsbLgCH3tMey7ZBO9sIJjFguujLo1Uvrz7kYWSBAsMr0fz8UHWbE9bHdavF0l6ZKS48jcC\nubnaKK933vFuiZ0TJ8RJrFKlwku+GIEbN0TiXrq054MkHMGSJaIV5fnnvWPhyssT01L4+DheA9YZ\nZGUh6TR/zzmqubKF7dvFRXPVqrbze6lx+zas9/JnfX1RZkoPN2+KQnh/f4w9MhYsEC3i9etD2+Vq\nvsMVK9y7Lp5CMdkqYnCGbPH++L178TDJ/7/+unLODz9UXlfrOefMUY4NHartT2Kiol0JDhZL/8jI\nyBBXPt266bsOMzK0Aus+ffStKxYLcmTplZPx88N3/+475GiyhcxMmLF//hn5yCZMACnr1w9i9S5d\n4Mbs0AH/9+0Ld+zbb+PhX7wYq7KLFwsfyG/fBikcMQJRoLZcmyVL4jrv3evYZH3oELJMq6MN/f1h\nmXKkCC2PnBykylAnEu3Y0fGVri1cuKAliJ06eT4lx8WLYuSsnx8KPRsJSULCU/67DR3q3YjYS5dQ\np5SfLN2oIuMy0tLExU/Zst6tMSljwwaRcA0Y4B3CZbGI2ddNJts5Cd1tR523atYs98557pxYPSE6\n2vHf7t49bYTq+PH641hWlja7/eTJynt37ULqHvlYTAxImLqMlaNbtWruXRdPoJhsFTE4Q7b4iJHr\n11HrTm8VxKeHUJOTDh2UY2otFxEiHuXj48bp95lf9devr58/Sr0iDgy0XYB3+3b9yvJ16xJNm6ZP\nMMxmhC1PmQKLnzYLtXtbYCDaf/ZZRA5t2WKfRCQngwD06qVYDtVb9eoQezviyrt+HZowdTRjiRLQ\nTjlrTk9MFPV9MhF0d5VoscDix7uTa9SAFsWTuHtXO5j/5z+ebUMP33wjEulhw7xr4bp5U8yBVb26\n/gLIaKSni9aLihVBtr2NdetEwvXSS975PaxWrYV+/nzPtyNJkA/w7Xz1lXvnvHZNzNFXpozjFRus\nVsgq+P7Y8mJYLNprNHiw4vI9c0YkfuHhsLLb82IUtj1IFJOtIgZHyVZQENxnjMHqYbXC0iEf//13\nnM9sVib72FixreRkZVKsUkX7wCQmKmG7kZH65GL1aqXNsDD9Aff2baKHH1beV6qUkoCVx507epmj\nEQX566/a/qWnwzzdrZu+zskb28MPw4r444+2yVdODtyO/ftrLUqMgUCNGOFY8sHUVFjo1OepUgUu\nNmexbp22RmH//u6nctixQyxDExYGS4QnYbGISX0ZQ/oQo7FkiePaRCNw/bq4mIiPNz7Tvh7u3BEX\nRbVqeTexsIyffhL1SB984J12JYnorbeUdn199UugeaKd8ePF+/zLL9075+3b4m8XEYHFqqOYMUNc\ndAwfrv8MSBI0jnzf+/VTCJdan+bvDwuXeiFVFAhXMdkqYnCUbMXGKhop2YTKR/bJQurDh5XX+vQR\n25o9Wzn2zjvavowerRyfOFF7PDVVnFD1VnZpaeJDXamSfqHUzZu1wvf4eEzaPCQJCVd79tRP5MmT\n0UcegdXtww/xAG/ejCjG8+dhHUtJQf/S0/HQX7gAt+POnagv+eWXuAbdu4NUqcvXqDcfH4ipv/rK\ntnvz7l30RZ3HhjEMXi+84BjpunkTREOdr6Z7d+dF9KmpRL17i+epV899S8WlS2KJJT8/aAs9CUkC\nwXoQhIufbD791Pg2eVy5Ikawdu3qHZG4GsnJ4kKqXTulrp43sWqV+HsY7VaWIUmipjUkhOivv4xp\n5/33xfvcXdG82h0cGSmmmigMCxaI1/y112wvOpYtE8dPnnBlZYnl3Hx9YeHivSpFgXAVk60iBkfJ\nFr+ybdMGn5VNsuHhyk0/c6byPrX5mdd8qYvZZ2YqZC4wUN91x+sJevTQPmhms6jRio7WTuCSBNcf\n/9BGRCARKa+/kAXe/MDOb2XLQnM1ezay2ssPstUKS8CePZggv/gC5OvttxE2/sorsEyNHAnC+dln\nGKg3b4bwl88PZjYjr9bChbAiPvKI/XxeLVrAVWorFcKpU+iDOsLR1xe1CR3R45w6pSVupUtj8nEG\nkoTrw1sIS5YUa2u6gqwsuF55QmqEu0UdoeautsURzJ0rtunttBAJCWKwwIgR3m1fxoUL4qLrlVe8\na+mTMW2a0gd/f+1CzShYreJiJSrKuCjZiRPFxYu7idOzssT0CxUqOC6aJ8JYqHar29Ixrl+vDWqQ\nx2mzWdTB+fpC0jBmTNEhXMVkq4jBUbLFJ4Tr1w8RU/JN36SJcr6XXlLexyeezs1VXFEVKmgHx2+/\nVT6nl8D0+HHFxRgSok8MeMtYVJRWiKmO7GEMGjL+XJIEN4G6Zh5jKDo9YgTElvIDnpSEVdTIkUj0\nque2c2YzmXCtn3oKmrW1a2ERk5GRAffYyJH6Yn7G4MYdNMh2aaPUVFhG1CWKgoMhZi/MUiBJ+M7q\nemSDBjmv5Tp9WrzWvr5iJJErsFig1eD79s037p1TDzzhMpng4jYan36qtBkUpF20GI3t28UJ7EEl\n0d6zR4wwM0IwXhgkCQsnfrHgrYjN3Fwx6XPVqo7n23MGkiQucsPCiFQpEZ1GZqaY1Lp6decCbxYt\nErPEv/GGbbKt1tjxUaRWq5g70tcX9/PnnxcNwlVMtooYHCVbvAvhzTdh4eBvYBmyP9xkEq00O3Yo\n7//Xv7T94M3LeuJJ3uz7ySfa4z/9pBz381M0ZDJyc7V++UmTxFXRpUvaDMiMgUStWKGQkIsX0Yfm\nzb2X4LR2baziNm0CaSTCAHPqFKLW+Gg5fuvaleiPP/R/+4wMVABQ68/q1NHXuKlx+7Y2WqhRI+fT\nRGRkaOu1zZjh3DnUULtbTCbo3DyNd99V2ggJcX8iKgySJLo7qlY1PtmqGrwcICzMMTe0EVi8WFxg\neDvpKREsJF26KP147DHvuVfT0xUdLWNw6Rth4bNYxLQQ0dHuR6UmJ4ui+fh4xxOfEuG35wnXtGm2\n36smXAMGKNfJatVauFatEqPm/6mEq5hsFTE4Srb4nDuffgrrivy/LBC1WBQXVfXqYjv8pKTOE3Ph\ngnKsbl3tgMHrwGJjIQDnkZwsWllmzhSP5+eLA2JQkHbiXbZMScQqb48/rrgGLBZYLtQJNdVbpUpo\n6/XXYfn4/ntY7WbNQr/kv19/jQjOOXPgbh0/HiS0aVPb0YTyFhEBC926dcrALknQhw0dqv0ejCGL\nsy19REoKiAk/eDEG61lhebokCaZ93jUZFeW8jsRq1YrPv/jCuXPo9Y2PrAoO1o+AdbeNAQOUNipX\nNl60nZcnZsd+7jnvutEkCQssuf2mTb2TAkEPvAUzPt6xvHKeRlqauBj1lmCeCJY0PpeVu0J2W8jO\nFu+5xo2VRZ+ruHJFTL3QubNzqU34KiMmExbctvDzzyLh+vBD5Zge4dq8GePyP5lwFZOtIgZHyRaf\no2TuXKL//lf5X042d+6c8lqPHmI7fD4ktaCaFxxPmaLtI6/BURMpIrg15ePPPCNOPJIkZqwPCRHr\n9ZnN2km+YkWYkyUJD+LKleIqjN/q1IH26qefQOC+/BL9adRIvGb2tsBABB107QpX6Pz5EOX/+CPC\nnps2ta3VqlgRyTz5cPzMTKLp07UJRU0mmM1tlVc7eFBbbqdRI8c0FceOibq+EiWc11/pRUG5m8BR\nksTKB+XLez4bek6OmJagTx/jyc+lS6J+ytuJFu/eFd3Y06d7t30ZWVnis8lPot7E3r3KM+rjo7Ws\nG4n165Xv7+eHvhiB27dFOcmoUe6fMyFBHCedDTZ57z3HF1Nr1oieCH5ssVpFCUxEBPo2efI/l3AV\nk60iBkfJFm+52LBBvMnlUgpr1iivvf++0kZenpKtt2pVbR/4CV49EV6+rDwg5cppNUG7dimfLVlS\nmwOIF7EGBCDyT0ZmpmjxYgwWI9mcfeyYOInKW5UqsO4dOQKi+cwz7mu19LayZUE0Fy7ECnb1avSP\nz5zPf7dXXxWJUX4+InjUpKtcOdsuNYsFubj4yMuoKNuuSB5paSgIK3/O3992mQ174Iub+/u7n7E9\nNxdWSvmcLVp43tVz5YpIfpYu9ez59bBypfibejsNwu7dIrl+ECV9iPAcylGygYEPJv8WEaQF8vWo\nVct9y48z4EtLVa4sSjg8iUOHxLHBE+lVtm5VrOomE8qwOQq1lbVcOfu6OV5nGRCA+UOGxSLKGapU\nAcFUl+36pxCuYrJVxOBMUlN5279f1I3I5TN4CxUvnD1wQHmd13cRwcolH2vYUNs/Phv9Rx+JxyRJ\nFFrOni0eP3hQNB3zE+C9e2JUnb8/XH6ShIl44kRtmoPHHoO15uBBuPwcqVuods3pbX5+had58PVF\npOXy5SCJ69dDR6G2eAUEwDrGi2VzciD6VLsXX3zRtqD9yBHRcuHv75jmKScHaTLkzwUHO6b/Uv+u\nr76qnKNUKSRGdAcpKeKqXH0veQIrVoiDvhGCZR6SJGpp3njD2Pb0wNeZs1Vayxt4+22lH08//WD6\nYLGAyMv9+Pxz77VtNkNbKrdtKyG0J8C716Ki3H82iUSiWrq0/UodaqgXU82b2w7ykSREXvP9P39e\nOZ6ZKaYOevRRjGl8IIQzW5ky7l0XeygmW0UMrpCt8+fFTPDyipo3w/JCYT4dhFr4PH++cmz8ePGY\nxQKNlkxa1KLMn39WPlu3rqgbyckRo9zGjhXPywvhIyIU12JamlaXVbs2koSeOKGtHyZvJUsiyjIy\nEqTGXk4uW6QsKAgDTcWKsEbpaa/kB/i99+AOvH4d300tci9TRhsdd/26NkigcWPbFgn1tZDDowuD\n2SwSrlKlnLd6WCxiUETbtu7rgvbtU8hpQIB+/jV3wX/vkSM9f341rl1TrKr+/s4HJ7iL9HQlDYPJ\n9GDqFhLBrckny9269cH04/BhxRIfGuoZIuIozpxRxh0/P9vRyO5CkkQLUOfO7rvNrVbxeW/Rwrnn\nXb2Ysqeby88XUwQ1aCBq/a5eFTXKcgRj586uES5nLHXOoJhsFTG4Qrb4DO0hIcqDxluK+FU9v5LY\ns0dsn9fT8CZdIriu5GNdu2r7zq9m1q0Tj/G+9iZNRJM+n0slLExJUXH1qjYNwYQJmFDGj9dauiIj\nYVmrU0db1sYTW5UqGHS6dBEHEnkLD4cFLisLhHf8eDEcXh4o+GzfkoTQad7tWaGCbeJhNovlkfz8\nUL+xMOTmigPaI484L15OTRUTz3pC/DtunHK+Tp3cP58aly8rFs/AQPfrPzoCXuf28svGt6fGf/6j\ntN+rl/fbl7FokdKP9u0fXD94a99LL3m37Q8+UNpu2dK4WpopKeKz6Uo1CTXu3IELVD6nsxHJ/GLK\nx0c7n/BISxO1fmPGiMcPHRLHyLlz0b9q1Vwby43QcBaTrSIGV8hWXp4iauQ1WDIhiIgQ2+DF8eow\ndfkzQUFajQNfE2vRIvEY75p8+GFxULl2TZnwfH3FKLx160TiIFu0bt0S3WZRURC5Xrgg1lhkDKue\n3r21YnIjt8cew/Xo00frcqxaVSFAiYla61v9+lqLx/HjIoErX952gVirVYz6iohwLNz/zh2xFtmE\nCYV/Ro3t2xVLQWSkbXG/o8jOFjVsjmjRnAVP5r1h3UpLU3R8QUFiXjZvIDsb9488yTnjAvIkLBZx\nMvR2DjIZKSmKfs/f37vWrZwc8RrYi9BzF7zbvFo1bZS4K+B1gGFhzl87vnh7pVGGW/cAACAASURB\nVEr2XflHjyqWQJNJ1PMSiaXhQkMxF5w4UXi0uK3N0ygmW0UMzpKtoCBMvvIE2LQpzmOxKJafBg2U\n80uSMvDExIht83qtli3FY5KkkAFfX634l48gVGu1+PphfJbrO3eUSYExpF8ggm6J99NXqwah+e7d\nYqSMvz/aVeeE8ubWtCnSVAwerNVrjRoFS5QkIdKGd0NWrKglSCkp4veOi7OdXNBsFs38zZo5Vibl\n0CGFHAYEuJYLiXdPv/22859Xg3ddG6HvSUpSAkJKlnQ+0asrGDlS+U7e1ArJ4PWa3ihfZAt8lLRa\nH+pN8KlueAmDN8AvKB95xLjIWEkSE6t6qoQUv7B77jnnPmuxiNq1wiy9fALTuDitMYBPevrYYzj/\nqlXiuKv2JniLcBWTrSIGZ8lW2bKwLsj/y66YK1eU1555Rjk/T6iefFJse+1a5ZjajHvxonKsbVvx\nWF6ekv08OFgsT5OcrFi1goPh8pTBk7CuXZVBiHdzxsXBFbR3r+garFUL+bLKlHlwREveTCaQyKNH\nRVeqfI3lSKSEBDEdQ0yM1uqQmor8RPJ72rWz7XrIzBTPN3Wq7fuKBz/xqFOCOIKrVxXyEhjovvA8\nP1/J72MyGZP1+1//Ur6zNyITz55V2mvc2Pj21LhyRQkGqVz5wZTPIYJ1RR4bQkKMi8orDDduKFaT\n8HDbJbSMgCSJ1nhH3P6ugq/sUaKEZ6yqqaniOLtxo3OfT0xUFpomk/1EwxaLGEE9cKB4/O5d0Tov\nE0p+Lilf3nFrlye1hMVkq4jBWbJVowYsJPL/8urxr7+U1157TTk///rQoWLbvK5KXTB44ULlmHql\n/NtvyrG+fcVjX36pHHvzTeX1S5cUC0twsCK255OzBgdDVJqYKFq02rdHiofCIgaN3tTldZo3x6A+\nY4aoJ2vbVtFHJSeLWaZbtNBapK5fF8XF335r+37Zt895t15WlnJ+k0mM/nEUfMkQtSXTFfDuhs8+\nc/98avAVE9T3qFHgSbM3XVcy+KCZhATvty+Dz6vnbM1OT4JPlLlkiXfbXrpUHL+MxLBhSlt6eRJd\nwQ8/KOds0sR58s7rCNu3t/95npwxBokKj927FULp54d7OztblGHw9R4L2zyFYrJVxOAs2WrSBBOu\n/L8cbv7LL8prfGJB3u+tNjPz+VHU2c15U7K6wCsf5q2OjuNXdLwGiXezyNqh/HxRp/X993CX8ekk\n2rVD/jCezDhKukqUwIM+fDjyu8ydC/fewoUghWPHwjXHZ1G2t0VGoiQHn3KiVi2sJv/4QxwwhgxR\nvntSkpjhWi/twZYtyvGoKFFUrwaf9sNRosLX9Bs92rHP8Dh0SPm82uXsCvgEvHJhdU8iP1/RUZUs\n6R1LDy+OXrjQ+PbU4HMYuVtuyR3w93KfPg+uHzt3Kv1w1h3mLsxmkQy4W17HHs6fVxZgMTGOyQsK\ngyQhobLcf2etczk5otj+l1/sv59PZ9GunfZ55QNrZOs8f5+Fhyul6rxFuIrJVhGDs2SrTRuYdeX/\n5RBbfiXCD7S8pUktcpf1Qr6+2kg1WzUWiaAJk4/xZuvz55W2mjVTXr93TxQQJyfjdb7+1eOP4wHj\n01RUrQoTNJ+sslo1+2QrLAyWvd27nRt0zp2DW65OHfvXPyAAiVp5gibXY/vzT8Xdxphoft+/XyGM\nJUogIECNvn2Vz371le2+8te5enXHiERysrI6fPhhx6+LDElSIkV9fT0jxpUHY73gDE+ATy/iSBZ+\nd8FbfN96y/j21Dh2TGn/2We9374Ms1mRAMTGPth+yNbo0FDP3LPOgE8ObO959gT4lDKeqmawfLly\nTrUExdnP165tPzIzL08kp+p0Dbx1njGMtUTiwrNZM3H8tbc5UwfSForJVhGDs2SrUycxc7Vcv44n\nVbxGhbcoqaM9ZBKjzipvtSpht+oai9nZyqStToI6a5bSFm9F47VhchFsSRLdLvv24dy8q27vXjHD\n/KOPKjmF1JuPDwTq7moWJAmJU9URkPwWGYkUGrzYXy7EOneu8lqdOiIR4oMKPv5Y2/bJk8rxwnQ/\nvDDWUbcgn/DRlZU2P7B5osZh797K+YzIucVXWVCnJjECt28r7bVrZ3x7apjNykKkfn3vt8+jVSvl\nWvC6TW+Dv2fdrYTgLPjnuXVrY9vaulVpy1OWYrV1zllOIUmQWsifL6x82LJlynsbNtSSMz74olUr\nnJ/Xl5lMqPDhyDzKPMBkjCZbPqwYDxSBgYzdu6f8HxKCvykpymulSyv7N28q+zExyn5WFmPp6drX\nGWPs8mWljTp1xGMnTjAmSdhv3Fg8tmuXsv/kk8r++vXKfp8++HvyJGNHjmC/SRPGmjVjbMUKxlJT\n8VrfvoxZrYxt3Kj0sXRp8XvKKFWKsZ07GZs6VfzursBkYqxjR8YOHGDszTfF1+PisJ+eztg33zC2\nZg1eZ4yxKVMYy8tj7KWX8F0YY+zUKcb+/FM5x9ixyv7Kldq269RhrH597B8+rPw+eujQQdnfs8ex\n7/boo8r+uXOOfYZHw4bK/okTzn9ejerVlf3ERPfPp4b8ezHG2K1bnj+/GmXKMBYUhP2kJOPbU8PP\nj7EqVbB//jymlAcFfmw4fPjB9aN1a2X/+HHvtl27NmM1a2J/1y79scsVmM1mzWvt2jFWrRr2d+9m\n7O5d99vx82Ns9Gjl/7lz5fPvdujzJpM45s2ZY//9vXsr983Ro4z9+qt4fNAg5Xr+8QeOlyql9JEI\ncxM/rtjD6dOOve9BoZhsPWAEBOiTrbQ05bVSpZT9jAxlPzJS2b9+XdlXk62rV5V9+QGWcfKksi8T\nAxkyeQoMFI/t3Yu/fn6MtW2L/W3blOP9++PvsmXKa2+9xdjs2cr/Awcy9ssvTIPgYMa2bGHs8ce1\nx9xBQABj06YxNmIE/idi7OGHFTK3ciVjtWox1rMn/k9KwoBqMjH26qvKebZsUfYrVWIsPh77J08y\nlpurbfexx5T2EhJs948nwVeuOPadKlVS9vnf2FHwRJa/B12FrfvUUyhZUtm3R1w9CfkayYsGb0N+\nlu/dYyw7+8H0gTHGatRQ9vkFn7fBPyf2nidHcdWJB8dkYqxrV+xLkmdI571799hsfmDk2urcGfsW\nC2Pbt7vfFmMYmwMCsL9+PcalESNGsFy9wUsHTz3FWPny2P/5Z/uLHh8fxt5/X/l/wQLxuL8/Y598\novw/fTr+Dh2qzG2rVjH28ssOdY3Vru3Y+x4UPEq2hg4dynr27Fmw9ejRg73xxht2P7Nt2za2du1a\nT3bDJk6dOsWGDRvGevToUeh7t23bxtq2bcuGDx/OOnXqxI7IzMPDCAxkLCdH+V8mW/y9L7/GmLjC\nCQtT9pOTlX35YZBx44ayX7GieIwfa6pWVfYtFsb+/hv7tWvjwWAMfZVXEA0agBwxJlrB2rVjzGxW\nLDTR0Yw98ohCriIicD7ZosZjwgTGGjXSvu4JmEywWMmkYN8+xl54AftmM2P79zPWrZvy/qNH8bdF\nC+W1s2fFc9aqhb9E+oSHv972VsI8kXCUqAQGKvtWq2Of4eHnp+xbLM5/Xg3+9/T1df98avDf0Yjz\n60G2dMp/vQ3+N3LlN7YHqxMn5Bd2niK62dnZbN++fU595uGHlf1Tp9zvw4cffsgynFgZ1Kvn2fY3\nbNjA1vOuAg4dOyr7mza53xZjmDPatcP+1auMbd6cxI4cOcI2bNjg0Of9/WHtZwxjhppAqdGlC2Nl\ny2J/3TrtoqVnT2Im0yXGGGNbtxK7do2x8HBlUWyxMHbpknbesgV+Lv2nwaNka9y4cWzt2rVs7dq1\nLCsri40ZM4Z9/fXXdj/ToEEDNnHiRPar2sboQezcuZP179+f1atXj3333Xcsu5Al4v79+1mXLl1Y\nkyZN2MyZM1mZMmVYmzZt2MWLFz3eN7UbUSYvPNmSXRmMKWQrKEhZofCvMwYyw4NffaiJ2LVryj5v\nEUtKUiZP3n3DEwrZBMwYHgjGMAnWri26Llu0wOfu3MH/jz0muq3KlFH2X3mFGYrgYGXAzMhgrFw5\n5VhKimidycrCX3ukhv+f/z1k2Pod1cjMVPZDQ22/jwf/m5co4dhnePADH0/oXYX8+zKGAdPT4Cd5\nR6+Ru5CHCk+3l8n/4HbAkzxPkq179+6xefPmOfx+I8jW9OnT2bFjx5z6TGiosjBx19p48+ZNtnjx\nYnZWvYKyA96y5gmytXTpUrZ7925dV2KbNsqYsnOn+23JePppZX/OHEwOS5Yscfjzgwcr+2vW2H+v\nvz9jAwZgPz9f9HYwxlha2h1GtIAxxhiRiS1ejNdHjFDGtOXLGRsyxLG+eWIcMwoeJVvyDfPhhx+y\nzZs3s0d5UYkNREVFsZ9++omNHDmS5efne7I7BXj88cfZ4sWLWR21YMkGPv74Y2Y2m1nlypUZY4xV\nrVqVZWZmss8//9zjfQsI0J+QCyNb6smMn3jVx3huae9zvHWFt5TJKxP16zxxk10L5cuDcN2+rRyL\njhYHxrg48bj8gISFiW0ZgdxcZZAMC4MWhu8nP4DKqyn+NbWLVnZl+PgwFhWlbY/XEcTG2u4X7xLh\nya098C5g3qXoKPi+8RYDV8HrxmStkSfBr3XuP5ou4Trvc7eDzEzFnc8vCNzFtWvX2HTZZ1IIZK2Y\nn592EeUOPvroI3bmzBmH389bDOwtGhxFcnIy++yzz1gyP6A4CNnKrsNPnMLXX3/NzGYzO+2E2Id3\nVbmik+SRlpbGNm7cyLKzs9mhQ4c0x0NDFfdtYqLnNHs82dqzB6v7jRs3sjReu2IHVasq1+HIkcLd\n2y++qOzLZErGhQsXGGOLCv5fuJAYEdz3sgPq7l0s7GVDRFGFR8nW5s2bWa9evdiHH37o1OeqVKnC\n/vWvf7GFCxd6sjsF8L3vcyjtgNo6Ly+PbbsvQAq6P6qY7i8vjbC+BQSI7hef+7+ILbIlv64e8PR0\nXzLsDZR8O/zNzA9kvGWHf5235Mj9llfivJtHkkR3SE6OaImRP5uZabw25v33FXdezZrKSis0FO7L\nb79V3ivr0fgBQtZgMYbBViZiTZporUu5uYxt3Yr9iAjREqgGrwVr2rTw70GkuG79/UWxu6OQtXeM\nuU+2iJTzhYXpk6G8vLz7g6tr2L9f2XdVn7Fhwwa2Ui+aQQc8F/GUHkSSJPbiiy+yew6K5GRLcnS0\n51ynx44dY1OnTtW1ptgC7wLXW1Q4i48//phlZmay2/yqy0HIY4k7ZCsrK4t9e/9hd4Zs8c+4u7aB\n1atXF/wGO22YruSFV16euNB1B7GxyuIhJQUMPj8/n61evdrhc8jjoNUqPpd6qFtXGV8OHRLnHHiL\nLjHG/mCMMXbmjKlgEclLOnbvVvS0heGHHxx7n7fhUbK1Y8cONnHiRJc+O2DAAJu+a2/i4sWLBWJB\nP54hMKxIHRUSOgqTSVyxyGSFf5B5UuOKdoQflORVoQzeNeFj427gySBP1vQIXkYGK1iZyLh2TbS8\nHD8uah9kdx1jiog+O9szETgyzGbGxoxh7IsvlNf4B3/oUMY++kiJouvYEavKvXsRVckYJhlZIMsY\nY5MnK/u9emnbXLhQ+Q7dutmeLC9fVgIMqlTRRozqYe9exdLz+OOFWxtOnDjB8vLyCv4/d06MHnV3\nAj10SHFXt2wpkmvGGCMiNnjwYJbiYghXdjY0dozhXlJbGB3BhQsX2IABAxxadDGGCCkZ6uARVzFt\n2jS2bdu2goWcPVy5oiw+1IEtrsJqtbIhQ4Ywq9XqFNniRfHu3ivnz58vIDquWLbkcUfPbe8o5s2b\nx9Lv+0OdIVsmkzJOuuvWXbp0acH+77//rvse3hruaOCMI5DvJ4ulHGMM96IzrkR+0ckv2mxBjui2\nWBQtLGOMW3ytK3jtr78w4XTsqPzG69aJEdv2MHCgY+/zNjxKti5duuSwq06N2NhYQzRRzuIOJzwx\n6TCbdA+HQclZQpQ28ZcnPnrH1SZlvqsnTpwQzNK8ZYqbbxlj4kqNNwfzLkVei8O7U/gBWA7PzcxE\nZGRCwi+sRAmorvfuheVIjtw7ckS0FPDj7aRJeP+kSYw99BCIjqvm819++YXt33+AbdoEaxFPtHjU\nqIHrLXt2/P0hpL9+HeHLMt57T7mWv/zC2KL71u+ICJA1HsnJjH3wgfL/8OG2+zlpkkJoBw78P/au\nOzyqavvuSe+9EJJgQk2jBwhNlN5EQFERELADKooKoviwgO0pImDFhoWHomDhAYpioRMIRDqEXpJQ\nElJJMpl7fn8sD/fcO3dm7kxmBvN+Wd93vun3nrnlnHX2XntvfYR63jz5uWim18LBgwdp4sSJ5Ctc\nCB9+KH9+xx2292cL4mpSK/5kzpw59MUXX1x1zduLH3+UibEoHNaLyspKuuWWW+jy5csUpZMt8DQl\nRMrUJ44iNzeXZs2aRURE/jp8IuL826NH3fdPRPTOO+9c1UnZQ7ays+XnDg7xV/Hss8+S99+rPnst\nW8XFsmZMDOixB7W1tbRw4cKr58AedyqRvGjSCvDRizNnztDmzZvJ29ubPDw8LOq2RKmGA0ZAi1CS\n96YUHBxMW7dupVM6GZ2oENITlZmZKT/fsUN+fuzYMfLw8CAieb5aseIkEcFC3qcP3jtzhiguTlfX\n/rHwsv0V/SisYzIavaJRVyJYDPHTQKhu4YS+1VJZWRz5+spXEZ9oLUWK8c/VN7pIzhYtepe++WYl\n5f/NhsRxXW2YE/+uGJQjaqfEaMYmTbDaqKlRaobatZMjZr7/vpgeeWQYeXmtIaL+VFgIN9kdd8jW\nlLVrIZwX81bx/omrpjvuIFqwADmyhgzRJwRnjCg7+xINHfo7eXpOtLoCDQyE+FeU4y1YAHLYs6ec\nUqN7d6IpU/A8N5fozjvl77/6qlILJ0kQdPLB0df3v5SZOZiIzFnU778TcZ1yaKgchWMNmzYRrViB\n540aaVvVRJw+fZr6CcvC/HyiRYvw3MeHaPRo2/u0hkuX5P8QEGDeH8YYtW7dmgYPHkwxDoryRPeu\nI/01GAw0d+5cWrJkCUXrEGCdPEn02294npxs3QWsFy1atKDly5fTjz/+SBFiJIYFiGRPzC9VF0yc\nOJGio6Np+/btFKRT9c+YbFWMjNSf90h7W4zefvtt6t27Nx0/ftxuT4HohXaUbF25coU2btxIn3/+\nOV25coWMRiPV1taaeTK0UFoqewocCUrhqKqqoqNHj9Lbb79N4eHhlJqaSgUFBZSoEnZaikqvK0RP\nw4AB91D//kSjR4+2GTzGER8vP9cj9RKlESJxDwsLo23bttHs2W9evd4vXpRFq927y/m5ysuxSLc3\n5Ud+fv7VudAa7LFwOgRnZkgNCAhgpx0sGlVaWsp8fX2d2R0z9OrVixkMBtavXz+L36msrGReXl7M\nYDCwTz75hDHG2OzZs5nBYGBJSUk29yFnkNfXOnWazaZPN88KL5ZrEDM287IycXHK/a5YIWY3Xs0W\nLlx49TMxE/zHHyt/J9Z/+/FH5Wc8o3pkpDJzeseOcobfwkK8J9Ytu+kmxp566il2331rrr7XvTtj\nly8rC1JPm8aYr6/+DME+Psg0PGUKMux/8glKSCxZwtjChYw9+SRqHYplIOxtb7zB2MqVyn4mJ8vl\neLZulTMcEzE2bJjy2EgSY488In/u71/OXn5ZddD/xrlzyjJBPGu9NZSVoXg5/83779v+jRoTJ8q/\nd0YZGrGqwaRJlr8nOVjQcONGefspKdbLhOiBSccGnn7aenWAuqK2ttbq50VF8r0RGema8kd6jgNj\njG3bJh+LoUOd2wd7r4l335X78tprzu2LHmzfLu//3ntdv78HH3Q847s1zJghb1ddK1cPJAllvohs\nV8dgDGM/3584/Yrnv1kzfO7nxxi/PcQC4P/+t7LGr7UmlrKbPXu2XXOyqzLIO9WylZCQQPPnz6fX\nLflrrOA///mPbvO+M3Hp0iV6+OGHKSQkhBYsWED+/v7Uu3dvWrduHZWLYiIiGjhwoB1b/oKIbKuO\n09LiFDoqbsUS9T2iZYYvRlVdU1hWunYdpHBbiTlK1IFYYtSYGJlHBJ1KQQEsFydOyN/t1w8aHcbg\n3rnnHrg5GjeGFWzVKqJXXnmZWrSA7uXQIVhj/vMforfekkOBFyxAZMx33+lzFdbUYHuilsZZCA2F\nZmvnTqLHH5ffT08n+uknWPo+/ZRo0iR5tZmVRbR0qWxtNJmgC1uwAK89PIiWLw+kIUMmmu2vtBQ6\nLp56o1cv21YtxuCu5PnPMjORhdkefPst0Sef4HlQENHTT9v3ezV275b/r7+/9e1pueVtQZKU5+PJ\nJy1rC/XCw8YGLlwg4hlrvLzsP8Z64GlD7b5kiezyHzeubvokS7B1HDhsuYjrAnuvCTERMncxuRNi\nloiUFNfvT3T22HC62AUxaMqRKD+DAf25fFmftlaUKIpSFvH8JyXBcllVhRYYqJyfjh3T70ocN05O\nrv3AAw/QsGHDbP7mwIEDNJb/yBVwJnObOHEi8/b2Zj+qTSQ2cODAARYXF8cGDBjgzO6YoUuXLsxg\nMLCePXtefe+NN95gBoOBGQwGt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LwckYpa7rmuXaFH4jXLi4uR42riRFirXJ1NPiwM7rsn\nnoCV6cQJeXK5eBGuzGnT4Erlg5+6eXqC6H3+ueWJsqoKE8Xw4dou0bQ0/F5vdNXZszg3ardlUBCE\n3dz8bi+qqpDSQtQOEYEQOTOpZmUlJnLx2vfxgeXRlZO7yQQrqUjAQ0MtJ591FaqqzAvpjhp17VyH\nJpN5AMtTT11boiUuBomuTcBCWRks5bwPWVm4dl2JM2eUKWVmzXLetisrUeGBb/vttx3bzr//rVwg\n2MLFi7IHw8NDezG6bJlyPOTXnkjSJk9WVlSx1RxFA9mqZ9BLtkTz9N69ylqIXK8j1oHipW8Yw+DM\nf9+kifngKJpftSogieG0HTuaa7OMRsZuvFH+TrNm5ukNqqrgrhL/U1KSuWXlzBkQFy1dExEGtUcf\nhb6Ju6lKSpA07733QIhGjADxSU6WNQeWGo8+zMiA5euuu+BS/OADWNwKC3G8JAkuwh9/RI6lW2+F\n1czWORsyBJYJSytDoxF9f/BB86SnRCCSw4ZBjK93Utu9G/9DTdh8fJCiQk9dRS3U1OBaaNLEnIwu\nXOjcKLSfflKuiolwvF0dXXbqlNL1TYRryR5NnDOQl2ee7mTatGuTxoAxTMDimEMEsfO1IlqSpMzd\nRASXmrtRWQntnDimuTr6sLpaudju29d514UkIT0N33a7do5tOydHHn8MBmTTtwVR0qJVXqmyUjn2\nrF6N9y9dkomnwcDY2rX2VRpxFA1kq55BL9kSycfvvyv1Kzz3yW+/ye/9XRP7KsQJRK1n2L9f/qxl\nS3MXkNGojPKZO9f8f5w/rxRCtmypTGjKGG7kxYvNrVd9+piX07h0Ce4BcYWl1eLjMdg8/DBcPD/+\nCFH2qVNy7T2jEVa0khJs9/x5rEb5/zSZsKo6cADRjitXgjw89hisTG3amFtxLLWMDKysfvjBsqam\nrAyu1HHjtAkWESyETzxhfgwt4coVRIyKIeBqksUtg/bCaIT2Qk1+DAZowOqi91LjwAFzrYW3NwIT\nHLXE6UFtLaxZ6vP8yCPutSRJElz9YqStnx8iYK8VDh9WRtx6eLjfnSqithb3u3iennjC/cSvrEwZ\naBIa6noNodGo1OA2aeLc+0+MuA0MtF0eTAsVFcoyVk8+afs3v/6qrDGqlfZGrETBA8MYU2rLbr1V\nmXvPVqvLNdNAtuoZ9JIt0UKzfLnypvjwQ2xLjFLs3l25H3EVqEWWRMuUVkTLtm3yzeDtbZ7qgTFM\n5mJy0ehopTuT4+BB82g4IvThm2+UFhJJgqXm+eexytJ7E/Hm7w9CExcHS1eLFuhjXBwytQcHW8+n\nZa35+cF1Nm0aXIlioW8RNTUgky+8AHcqzyytbgEBsP6tXavPSiRJIJZTp2qTtvBwWB8cLY5cWgrC\nq5UwdvBgrF6dhTNn4DJTu2F79nR9vb/sbPNcZwkJ7ilkLSI/HwkpxX40b+7c42wvvv5aSUADAxn7\n73+vXX/KypR5vYiQrNndRKu4WGldCgpyPOGnXhiNyohLX1990X168dtvyvvvq6/s34YkKV3fHTrY\nLjh/7pzSJfrSS+bf2bJFtpR5esqk9r//VZJdMRpUT6sLGshWPYNesiWWUZk/H7mW+Gux1hQX9Pr6\nKlfkYiFQrarrYi2x9HRt0/FTT8nfadxYO3nmiRPKCEYvL+go1NYySYK4XG0t4dueNg3JW9WD6MWL\nsBpNn45IPkuWIWc2Ly8c1wED4GJcuhQEwBIhKi6GG+z557ECs5YPLDiYsdtvxzb1ip7374elR6xh\nKLbUVGjcHC3fcuYM/qdWxvy+fbUJtKO4cAH7Et3k/Hr/6CPnCu3VOHvWXOBPhOCGuhbetgeShAWT\n+njffbfrUwdYQkkJjoPYn5SUa1tc+q+/lFGvXl7IFedunDihtPSFhWGsciXUZal8fLAocxY2bFCO\nU45mvRetT/7+tqNCjUalNX7AAPN7vrBQGXzALWXFxcoAotmzLVf50Gp1JegNZKueQS/ZEifWxx+H\nFYm/HjxY3p44eahdc2IiSPVNIEnKlZrWIFZdrczzlJmJ0Hg1ioqUljIiWHS0TOw1NZhULemfEhIg\nhF+6VFtrJEm4GX//HWLZ555DGogRIxCd2aYNtp2YCEtbWBhWUQkJIFCpqfgfAwdiMHvsMVj+PvoI\nK70TJyxrFiQJffrpJ4hBx43TTlSqbk2bQqO1dq0+F5UkYaKZO9dyAlVfX/R/wwbHBpHaWhDum2/W\nFvkPHOjckjAnT8JFp46QDAmBJs6Vdf4uXYLwXq0LTE+3nlDWFdi929z1GxVlXj7LnVi3zlyXN2bM\ntSN+jCFzvyg/CA52f8ACY9BXRkXJ/YiOxjl0JcrLla51b2/GVq1y3vY3bFDeC4MGOaa/FPMuEtlO\nZixJqIDCvx8fb+4SVeuBr78ec0Z1tfL93r21JRSWWuvW9v8/NRrIVj2DXrKVni4/HzUKFypfiSQn\ny9sT67ap3YXz5smfiSV9OMTK7JGR2lqAwkJlzqiuXbUtMjU1mNDUObQef1zb3WYywVpnKRKPt8RE\nDDxz50Ikv3evazU1tbWwgGzfjkiYOXNAaLt3Vw661lpsLGOjR8N6cfy4vv1euQLyM3my+cTHm8GA\nAeeDDxwvr3PyJGMvvqhMjMibjw+IrjOtGXv3QmOhFrD6+MCa6Uz9iRrFxRBRq3VZYWFInlhT47p9\nq3HxIhYFahf2uHGuPQbWcOmSMqKZCJPw4sXXTgh/8aK5BqddO/cXupYkXCPiQqR5c9fn8zpzRrlI\n9vJybi1ONdEaMMAxbeSyZcqx3lYJKUlSZqf38jI3DkgStKb8O3FxWNyqRfxRUQhE0ku0yEkspoFs\n1TPoJVtt2sgXM88Qz3UmBoNMeMSyPT16KPd16ZIczh4erh2efPvt8u/vuku7z3v2gIzx73XubDnC\nbf168xxaQUHQElmK0CsqgmVp4EBz95JW8/CA6zEzE5F7998PM/icORC6f/wxVllffolB4euvkULh\nww/hbnv9dbjlHnoIK/jBg6HFatzYfj2Xlxf68dBD2N/Ro/omKqMR2qHXXsP+1RYfsXXuDG2Co1qs\noiIQNEsrwcaNcTzsqbFoDbW1jH3/vTJqizd/f4idteqfOQslJSCUaheDtzfOkyWtnStQUYHkueq+\nNGt27TKwm0wgVOI9TQRrgd7FgSuwYoVSPkGEgAxXBkpo4eJF80jMgQNdn+dt505lrr7gYOdeI0uX\nKsdXR4nW4sVKEirWKtSCJCmzxBOZe1IkSRklL+ZwFBO5+vlp63+tNWctHBrIVj2DXrIVHy/nu2rU\nCL8VV6FitmKua9AqwSP6/RctMu/PuXNKMb46qzzHrl1KvVSTJigDo4XKSrj31MSJu742brR8A1y5\nArfGjBlwRbq7HqK1FheHdBGPP45ovV279A9WV65A5/H661iVWUtR4eODTPYLFjiegqC4GOdy+HBt\ngb7BAPfBd985L4VDfj5Ijlb2/IgIDJqutOKcO4f8Q2J5Hz5w33+/awmeGjU1SE2iLhweGAhN47XK\nnbVtm3mdzcBA5FZypV7OGs6fVwrBiUBOly51f1/WrDE/ZzNmuDYFhyRBEiG6TZOSYBV2Bkwmc7Lj\nCNGSJNxf4nbuvdc6mZEkaKvE37z/vvl3xGhTgwHjK2PKQC+DQSl90dPU1rO6oIFs1TPoJVuensqS\nLZcvw2LDX4vJ/KZNs0yWcnLkzxIStAf5zz6TvxMQYPkmz81VChT9/EDgLN1sJ0/CdaI12bdogRXR\njh3Wb9baWvTnP/8BgRs9GpakuDjHowq1msEAUtuhAzIZP/AAjvE330CjYY9+xWSCu2HJEpjFMzNt\n13Fs1AgC6RUrHM8WXliIVefAgZb316oVCJE6Ea2jMBoRITRqlHaum6QkWOVcqf/JyYGbQf2fPT1x\nTN2ZM6uqCpOJOqLTwwMuWketk3XF4cPm1hoikBytsHt3oKYGrjp1aa6bbnL/cSovhwtfvUBwZu1B\nLVy8aB5t2a2b83J3lZaal5+6+277yX51tdKVRwRpijWCXlVlHpCiXvCbTEodl8GAVCiSBGG8+Fux\nuoOeNnq03YfLKhrIVj2DPeV6br5Zfr51KwTn/PWIEfI2xRI8gwaZ71O82RYs0O7X3XfL32nSxPIA\nfO6cedj8oEHW3Q+nT4MQqi0OIgm86y7cZCdP6jf7Go0YlHNy5MLRX3wBi8Lbb+O/zpuH1dHChXCl\nLVkC1+KaNTimhw5hZe2IdYcL5n/+GfuZOBHuSGsuQd5iYhi77TaITA8ccMzUbTRCg/HMM0g+a2lf\nsbFIIGiL2Nrzv3fuRAoKMYRbHDCHDgUJc5VFoLYW+dG0XKNeXriejhxxzb61UFGBa0yr3NKIEa7P\nx2QJ+fkgEWoinJoKl/+1wq+/KnWpnNx88YV79WKShAWO2ho7YIDrCd8vv5iX+Jo0yXlu0+3blbkQ\nPTwQ2W7v8T19WnmfGQy2a2MWFprXd1Un0C4pAbEWt7tkCca1CRPsI1ZazdloIFv1DPaQLTF526ef\nYhXA3U9xcfJNYzLJompPT/NV0Y4d8nYs1b2qqFCWoMjIsCzCrqw0TzLo5wfdj7WositXYHm74Qbr\nVqnYWOiYZs3CyjI399oV4a2sRHbv336D5uupp2Ah6NDBdrZ69eQ2fjxI4L59jk8op0+jH7fearlY\nNxEmj6lTkQvIWYTn8GHkxFFPkiKBfPpp51nNtHDyJFJsaOUCi4iANtDRZK6OoKAA171a/0QEC6Oe\nTNquwNmzOP9qV35MDK5BdwYHiNi719ySQ4SFijMLmetBXh4WimI//P1xfFxJ+IqKEJ0sCswjI6Fz\ndAaMRtwjoq4qLMyxaM4fflBe235+CFSyht27TYoAHH9/82jbw4eVkdweHvCwlJRgoVZXonXRBcLM\nBrJVz2AP2XrwQfn5jBn4/YAB8nti8kcxJ9brr5vvVyRu99yj3bf8fGUerNatra/u1qyB+0vsc6NG\nSItgyxVWWAh3y8CB2vURtVrjxggCGDUKZG/OHLjNli9HXzZsgMvv0CEMpEePwuJ28iQIwMGD0Flt\n2QLy9N//YiW9YAEGp0cfBSHq3x+EwpGcXgYDopZGjIAw+tdftdNl6IEkYVD66COs9GyZ0du1w3Ww\nfbvzJot9+5BLp00b7X36+ID4ff+97WSGjqKqCgkX+/fXrouZkgJrpjsJeXY2rMFaBc1vusm5ySft\nwalTcF2r+xUYCDf8tUrncOwY3FDq89e5s3bCZFeirAw6IvUx6t+/blGPko2bTpIQRKO2BvftW3cr\nWmFhIVu7di17771fzTR5mZn2/6+qKqVgnQgLOK3FQ1FREVu1ahV76qmZrFWreczXt1YxZmdnK7+/\nZo0yYCQ8HN6BXbtsl0TT02Y5s3CkgAayVc9gD9kSL3buHhQFg6Ip9+BB+f2kJHNrRkGB0hJjKcol\nL08ZEZSUhG1bQkkJQnrVepnwcLi39OhlqqrgCn3uOZTyseRu/Cc1Dw9EXfbrB+3Cxx9jgq1Lvqjq\nalghFywAoVQTWXWLiIDm5tNPnRtJuHkzzp21HGI9eoAsuypCS5LgHn7kEe3rwcMD98SaNe4TdpeV\nwRUthubz5uUFMuHqHEyWkJODyFq1u9DfHwEd7rYacXDypx4f4uJwzzh67iRJYhcuXGDbtm1jy5Yt\nY8d0DDQ1NbBaqclOfDwsL3oXKFeuXGG5ubnsq6++Ys899xy74447WKdOndj3VkxTR45grBD3GxgI\n15o9x0CSJHbs2DH27bffslmzZrEhQ4awxo0bMyJv1qjRmywgQLq6fU9PBKXYa8Xctcu8esfw4fB0\nSJLE8vLy2JIlS9h9993H0tLS/p7PYhnRKsVvMjOVcpSqKiwGRa9GWhqOzXvvaS9c7Gv/ZXfeeadN\n0usoGshWPYM9ZGvyZNmEGxWFwWDPHvlzsV4UY8pQ+xUrzPf99tvy5zExlgfgI0eU6RuCg2E9soZD\nh1B6RMvy0LcvIotKSvQdI0mCJerbbyHmHj8eolEtfZCrmq8vrHw9ekBb9dhj0OSsXo1VYl2tODU1\nGNQWL4YFMzPTclkfsU89e2JVvnWr89yDRUUIQBg71nousS5dkKrClYLzvXvhlrO0wk1OxjXhTldh\nbi60NFr1MkNCIOR1R38kSWKlpaXs+PHjbMeOHay0tJytXm1eSJtP5NOn111oXV1dzU6ePMm2bNnC\nvv32W7Zw4UI2c+ZMdtddd7G+ffuyd999V3NyO3wYFnStRdhrr+mzQpaXl7M9e/awH374gc2fP59N\nnTqVDRs2jLVu3ZoFBQX9PY4Se+WVV6xOsJIEy6i6AoOnJ4ioJSu8JEls69at7KOPPmJPPPEEGzJk\nCGvWrBnz8PC4um8iYoGBgewnCz66CxfgzlUfh+HDQUT1YN26dWzatGnsxhtvZGFhYYp9o/Vhvr7H\nFdtv3tx+F3ZZGY6H6H709YWofdmyr9jIkSNZbGysxv5vZkTnFft/8EHlOc7JMa97O3w4LHqjRztj\nzO7LevXqxapcGObbQLbqGewhWwMGKDUFx45h4OClDHx8lC6qtWvl72Zmmq/UJEmZDO7GGy2ThnPn\nzF1HDz1k23Kzfz9cllpZyX18QAjfe0//QKNGZSVcg1u2IG3B++/DbTl7NgaK++8HaRgzBjfx7beD\nLN12G0jbAw9g8JsxA5a0t96CVmDVKoQJ79/PV3CO9U8NScJEvHYtEv/dfTdcJ3pWccHBuAbmzoXl\nz1nC2ZoapN94/nmQSa1zRQTi3LMnLKiOni89OHwYBEosfi42Pz+cz/XrXWfFMplM7PDhw2zXrl1s\nw4YN7JtvfmZTpmSz5s0LNfuUmQntnDMz35eXl7N58+axmTNnsvvvv5+NHDmS9erVi2VkZLC4uDjm\n4+PDiIj5+MSy227bqlm+KTISZLUuKTYWLVrE2rVrx2JiYjQmVjRvb2+2ePFis9/u3o17Tq3JDAyE\nBlOvS/3SpUusW7duFvdPRMzX15d9bSX1vskEzaeoReVt1CgsEG3h559/ZpGRkRb7EBkZybZp+EEr\nKqBvVOs6ExPt12adP3+eDRkyRGP/8YxomWL7Hh4Yp+11F//4o3ky5bQ02VJbXFzMJk6cqNp/I0b0\nueI3sbHKbPdGI2QIosXV2xsSi1WrtJMr29/8WUpKCitycSK0BrJVz2AP2WrWTJmjhBcKFd2LYokE\nSVKWd9EKWz5/XumeGj/eMrEoKzNfdSQl6Uu0d/YsBhtrOqOkJBCzDz+ERcNZ+Z6uBUpKYKn65hus\n3O+9FzlhrInY1cQmJQWkYv58RPs563iYTLDOzJsHsm0td5mfn5H16FHAnnrqMPv557/YwYMHmcnJ\nDIe7CJ97TnsiRDMxf/+tLCrqGZaY2JpNnTqVlbuypg9jbM6cfzOiYYzoK0ZUadYnD49KdvvtJWzH\nDtf1YenSpczLy8vC5N6RBQUtY76+JrO+NW+OyFZn6NaMRiN74IEHLBKMmJgYtlGoc1Rbi4WPumQX\nEa7/Z56xnNDYGqqqqljPnj01+xAVFcU2WyjaaTRCi5mWZt6fG26wTyNmMpnYggULNPuQmJjIDqhS\nyvNyZGJtPyK4c59+2jHNXE1NDXv//feZr6/v3/sOYUQvMKIyxT66drW/iPnRo8rSQERYCM6Zo1yI\nl5eXs9mzZzNvb29G5MWIHmVEJYrfDR+uPM/bt5tHrrdtC32WOq+a4w3Xox43cl3RQLbqGewhWwYD\ntAT89aOPYhsbNsjvDRmi3P6qVfJnKSna/volSw4rBuynn7ZMuCRJ259+yy36SleYTEjL8NBD2mHx\n6pu8QwdEJr3xBgbw3FzH807ZQk1NDXv33XdZbm6uVUJRXQ235ubNIFMLFkB7MHo0XGt6y/iIrUUL\n/P5f/7rMmjQZx1q37s5uuukmNmnSJPbSSy+xXbt2Ofy/qqvR11dfRWSPLaF/8+a1LDT0Q0bUmxF5\nX51MUlNT2Xon5QeoqoJ1b/JkW9fBRkb0EMOqmVhYWBj74osvXKbDMJkQLHHffYyFhtZa6FMu69dv\nJbtwwfUhfLm5uSw9PV2Y1CMY0cOMaLdm3/r0gWTAmSk2tm7dapHktG/fnp38Ozvs5csg8FrF5aOj\nYb1wNDhk06ZNLDMzU7MPrVq1Ynl5eWa/qayEpVurPx07YpFoz2X0xx9/sIyMDM0+pKamstOC77iq\nCuOkVn61e+91PJfZL7/8wpo3b/73fv0Z0ZOM6JJiH1FR9uvfLlzAol3t3uzTxzxlyurVq1l8fPzf\nfejFiPYofhMeLrGPP5aPbUEBxnD1cXj6acbefdexwCPz9g0jIubv769pWXQFGshWPYM9ZIsIAwTX\nQfFimiaTvHLy9FRGskiSMr/Jyy8r93/+/Hnm5eXFoqIeYAaDLKZ8/HHrA9HBg1gVqm+gceP05zOS\nJAjAZ89mrGdPIzMYrui+uaKiINrs1w+106ZOhXvtnXcgEP/6axA7+KwNAAAgAElEQVTN9euhZ9q+\n3bxt2wbit2YNJqj33y9jAQEPM6IpzN9/LuvceQMbM6aG3XQTjmFqqmNESmxNmsAV/MQTKFGxfbty\ndXv69Omr7iEiYmlpaWz58uW6rUmShGjLb76Rs+7bKnkUG4tj+PHH+O3BgwcVE0lAQAB79dVXWXUd\nhWmnTmGVf8st1q1pmZmMPf54PiNKVPRj8ODB7KwLkh1JEiKknnzSGvE7z4gWsoiIweynn352eh8s\nYdeuXYzIkxENZHARVZn1LSQEE6Wr6vTJY5Sy3X777ay8vIJlZ4Ocqgt7EyGv06JFdbewZWdnX92v\nbNEh1qtXL3ZJlZPmzBlM5FrpN7p3t59kcWzbtu3qfrOysq5qtbKysq6mFqiogCVanS+LCFGpdc2v\ntnnzZgZL0gPM11dJsry9Jfbww/YFqVRUYNxUuzejo5GWR+s4bdiwgRG1YLD4ir8zsXvvla66rKur\nEcCl3nZqKuQaPXo4g2QxNmfOK6x3797MYDCw75xZONIGGshWPQM/Yd7e+sjW4sXQ+PDXPOrs2Wfl\n9154QbmP7GxZM+HnpyRDNTU1bPTo0eyZZ55hixYp93X//dYjVyQJSefUQnWDAQPL2rX6V1fFxcXs\nwQenstGjF7H77jvKbrsN2c21BPb/5GYwYMLu1QuruTlzEAywbZs+i5zJZGJ33HEHa9myJVu6dCmr\ntWGiOH8eKSueew5WTT1BA1FRSJA7fz4CLMy1fBKbPn06IyI2cuTIq5YLe1Fejr5NnWo9ktHHBwT0\n3XdlYbkkSezVV19lRMRCQkLYxx9/7FRrVnU13BeTJ5u7eHgLDJRYRsYuFhp6ByPyYoMGDWKFzkrl\nbQOSBCL+yCOM+fuXaPavSxdEQ7ojfcOUKVPYG2+8wYiIGQwG9q9/vc7eeUey6Pbt3x/BI870OE+b\nNo39+OOPbO7cuYyI2Lhx4xQC6G3bsGjQqlzQty8WVnW9hGbMmMF+/fVXJkkS8/T0ZIMGDWLl5eXs\n/Hnc61r338CBcl2/uqCiAlb00NBi1T5MbMyYWrsCVa5cwf2mJoX+/tDSWQpeOnkSgQ4eHkrXdWTk\nUbZ1K062JCHBMC8bx1toKCJRtfKqOdqO/D2ZTZw4kb311lt1PcR2oYFs1TPwE7ZwoT6y9fDDynpU\nvGbUyZMyoUpIMCdJjz0m/6ZbN8skavFiJcG5/nrLRaY5ystRykbLHNy8OcTO1tJFWENFBQbRzz4D\noRg/Hn1KTNQeVF3ZgoJgmcrKgnXm4YdhKVyyBNmfDxxwjmg9OzubGVUCLaMRx3D5clgCR47ULyZN\nTobF8YMP9Gen/+6779jq1avt6jd3V770EvQ61koSRUXhXH77rWWykJuby/r16+cw2VOjtBQWzzvv\ntKyd8/KCq3XpUlzXkiSxiIgI9uabbzpdq6aFfftwfsVM38pJrZZNm+a8Onn2YNu2Hczffyjr3fuU\nZlWE4GBEaYr5/lyBWbNmseeee45JksTKyjBmdeqkfS7vvNM1Oc4kSWJjx45lO3fWsHvu0Q5wuflm\n5+z70iUsoLWs6h07nmQ5OfotzmVlkGSo6z16eMA6aclwnJ+P8U4dIR0VxdiMGXmsutrIJAnCenUq\nFIMBBOv22503ZqvHsH3XoCSDq8mWgTHGqAFOQ05ODnXs2JF27NhJmZkdbH4/K4votdeIrr8er0eP\nJlq6FM+HDSP68Uc8/+QTogkT5N9VVBBlZBCdOIHX06YRvfGG9j7+8x+i8eOJjEa8btwY7/F9WkJJ\nCdGiRUTvvUd05oz5523aEI0aRTRoEFG7dkSenjb/rlUwhn1euCC3khKiykr838pKuVm6av38iPz9\niQIC8MhbWBhReDhRRARaeDiRj0/d+qsHkkR09izR3r1oe/bgcf9+oupq278PDyfq1EnZGjd2TV+r\nqoi2bSP680+iP/4g2rIFx1oLnp5EXboQ9e9P1K8fnts6/+Xl5RQYGEgGg8HhPh47RvTTT0SrVhH9\n8gtRTY35d3x8iPr2JRo+nGjECKKoKPE/VtH+/fupQwfb96ajOHCA6OuviZYvJ9q3z/xzX1+ilJQj\n9MwzSXTzzd5uuQ7V/fvsM6JPPzVSQYG32eedOxPdfz/R7bcTBQW5vj8FBQV07lwj+uADoi+/JCov\nV34eGUn04INEkyYRxcc7f/+SRLRqFaO33iJav155bRoMGOOeeQbjXV1w6hTR/PlEH3yA8UzEoEFE\ns2fjPtKD4mKMzW+9RXTpkvKzYcOIXn6ZKC3N/HdnzuA377yjvLdDQ4mefJJo6lSiwEDcY//6F1F2\ntvL3KSlEzZphjCgr09dXa/jiC6IxY+q+HWeAz907d+50zfjgEgr3/xgiO9bD6L29YeLlK/PgYNma\nsnGj0qKkjl7bulVpbeDRjFrYskW7Tpee3FhGIzRQWvl+eAsPh3Xm7bcheq/PkYf2wmSCruS332Bt\nevJJrPwyMmzrq8QWGIhUDNOmIS9WXp5ry4pcvAi34KxZsC7aSlfRrBmumRUrGCsudl2/RJSVoaTI\nlCnmeZTEFhoKq8fXX7su4MISamuRVmTGDO0IOd5uuAGRue46diJOnYLeRh09Jh6/yZMRcesuXLiA\n3HZaSWSJENm2eDGE8a7A6dOwMGlZlENC4D04erRu+5Akxtatw3igTpfh6Yno5Nxc/ds7fhz6UK2c\ncCNHmmdz59izB5ZntXU6IAAlsIqKMI6tWoWoR/W2GzWCG1FPXVi97Z+GBjdiPYO9ZIsI9e3Ewpxi\nwtLeveX3P/7YfH8LF8qf+/jA/WUJBQXQHon7TkhA4Wa9HpWTJ2G2zsqy/p/8/KBBmTwZIupNm6BH\ncmcRWmfhyhXo4tavh4vxxRehfxs0CIRKbzki3jw8MHDdeityYX37LXJRuaqoM2Mgv7t3Q9dx112W\n3VpiS0xETrPFi0H83AFJwoT/yiu2XZeNG+P6+vln15USsoSyMpy3CROsB1l06wYtnTuTtHKcOwfh\ncrdu2n3z9ISL9euvnZfjzRauXIHrfNgwbRdUYCDcX9nZrhkrjEbkwRo6VLt+a/Pm0FHVlbBfvoxj\nr9Y58bHxoYdAnPRAkjCu33yzNmEbO1ZbqC9JWAAOHmzeB19faC8LCkBmP/gA0e3q7wUHg2jZSshc\nn0kWRwPZqmdwhGzNnYuIGv561Ch5e3/8Ib8fG2seai1JSqIWFGQ9z0xtLQZ/9QqlfXsI4O0Z4E6e\nhCVr5Ej94b6hoVhdjx6NDNhvvgkrzu+/Iwnh5cuuLc9iMsGad/o0BqiNG3nkIgSxjzyCvvXpg6Sv\ndclq7+2NwXboUKxGlyxBnhxXT2wmE7RcX3yB1XmvXtqRZeqWnIxr6ZNP5AS7roYk4Ty8/Taue2vH\n28sLlr85czAZu6uMD8fp04iOHTjQ8uRjMCBC7loRrBMnsO9evSwHo7Rvj++4KTaA1dZiHLv/fmXN\nPLF17Ih70FVWyf37YcFRa5v4ORs4EPqkulxTkoSx94EHtO+3xo2xuNJ73MvLsTjSKgzv44PjqWV5\nq6zEPaxlxeRl1goK0I/ZsxGpqHVOfH21Camj7Z++0G7QbNUziH7fjh31+X379iVavRpanIsXiby9\n4VuPicHnt9xCtGIFnj/2GNG8ecrfG41Et95K9MMPeB0cTLRyJVGfPpb3efw40QMPEK1bp3y/a1f4\n7UeORD/0wmQi2r2b6LffiHbsINq5kygvT//v1QgORgsJkZ97exN5eaF5esrPDQYcg5oaPIrPa2qg\nLSgtRVPrQeoKHx+ipCSiFi3QmjeXnzdpUncdmy3U1BAdOoRjv3Mn2u7dtv+njw9Rhw7QDHbtipaY\n6Nq+EmHY3b+f6Pff0f74A9o8S0hKIho4kGjAAKLevXE9uAvV1USbN0MbtmYN0a5d2t8LDET/hg0j\nGjyYKDrafX1kDLqwlSvRLPUxPR0arNtvJ2rZ0vX9kiSiTZugXfv2W6L8fPPvNG4Mvc64cUStWzu/\nD/n5RMuWQReUk2P+eWIi0d13ozVp4vh+Cgqwj08+wbWtxg03EE2ZQnTzzbbHVMbQ148/hn6tpET5\neXw8tGv33SfPDxyHDkFf++mnRJcvKz9r0gS63nvuITp8mOjdd4k+/1yfbrSuqKmxby65VmjQbNUz\nOGLZ4rqt6dPl9156Sd7miROy9sfDAy45Na5cUebJ8vaGZcMaJAnWLK1w7/h4WBDqsjovLobrbd48\naH369UNSwPqS/sHXF660rl0RefPEE3ANrFgBy0pBgfusK5IEXdjq1UhmOmYM8rJZc7OJLTERlqN5\n86Dfc2GJMQWqqrC/efMQ8WlpFc1bSAhSXixYAEunO1fDkgT9zOuvo4ySNfdwQgJcmGvWuM8Fx1Fd\nDR3Q1KnWKzi0bIkUMu6KdKytRULmRx7RzktFBIvPuHFw/brCbV5aikjn/v21rTKenoyNGAGtYl32\nX10NN/LQodrlsAIDMebt2aNvexcvYmxRl1DjrUcPaHLVUec1NXDLinITsbVrx9iXX0KT9cEHsCC6\na/x0t+W5rmiwbNUz2GPZCg9HVAkRIpc6dIBlhDGsuo4elVcEL72EiBgiouRkWC/Uq/zKSkQzcgsX\nEdH06URz5lhfWUgS9v/ii9rRUz17Et1xB6xn6tWUI6iuhmXt3DmsPgsK8JifT3T+vNISVVaG5uhV\najAorWS88dehofhPMTGwSIjPg4Pxe3eipgbn/dAhtIMH5Ud+rdhCkyZEHTvKrUMH55w3PcjPRxTj\n5s143LnT+uo5JARRsTfcQNSrF6Javbzc01ciWJDXrYP16pdfcP1ZQseOsF4NG0bUtq17r42CAljX\nVq0i+vlny5bLjh3lKMy0NNf38coVol9/JfruO0ROax0/Hx9E240aBeuOsyMcS0pwXJYvJ1q7Vvt6\n69QJVrQ77iCKjXVsPyYTovCWLSP65huioiLz7/TogajxUaNsW2Fra3HsPvqI6PvvzSNrAwJgiXz4\nYaL27ZWf5eYiovTLL4kKC5Wf+frid5Mm4di//z4i3J1t1beE+sooGixb9Qz2WLZEQeJdd+H3YiHp\nDz+Ut2s0KjPH33679qrfaIQvX9xP9+76ssBLEmO//gohppb1ycMDYtt//QsrWGsJUp0JkwmC5OJi\nRDAVFMDKc/IkNAtHjuD5uXP4/PJl6BaMxn+mToBHL27YgHP8xBNIGtuiheWi0VrNywsC/TvvRH6w\nn36qW4Fie1FeDs3bW29B56YnT1hoKP7rG2+gPqQrgwK0cPo0cm5NmqQtCBZb48aI4Pr8c9u56ZyN\nigpYzR5/3LK1g1tqbrgB58BJ6cts4uJF6A9HjLAcnebjg/P8+eeOl/SxhqIiVJYYOtSyfi45GZY9\nR3MCMobxY8sWWOvEmrNii49HhvvDh/Vtb9MmCOQt6ROzsmCFUkeK5+fjvhHr44qteXNYZffvx/Xg\nTivW/wKTaBDI1zPYS7Z4mZPwcLhcNm9WDhYioTl+XFkq4dlntfsgSRCei9E+/v5w5ehNyXDsGMSc\n1iak4GCQwxdegHvLkWK0/4uQJIhPt26F+P/ll0GA+/cHoXIksicxEa6t6dMxgeXmujcCr6IC1+bC\nhSAgGRn6xLPNm2Mh8e67iIZ0J7mSJEy0ixejD8nJ1vsaFITJ+623INp3J1GvrYW4eu5ckCdr10hk\nJFxxy5a5J42EyQRi/OKLcKlbOu/+/khxsGSJawjWqVMIpBgwwLL7vFEjuHc3bXL8/JlMOBfTp1te\nQAQEoNjy2rW2r2lJwrU/Y4bl7UVHg1irXb7l5RhDBg3SPu7e3nDPf/cdxoVBg+xbsNW1ff+9Y8f4\nn4gGN2I9g70C+T59YEomgpB05EgkiuTC9UWLIK7k+P57uAj4WfvoIwg8tbB1K9Gdd8Jlx5GeTvTm\nm0hEqQeMIRHnsmUQ6R86ZP37110HV0ZqKoS4vEVE6NvfPx2VlbLL89w52RXKn587h+SFlpKBWkNA\nAI5VSgpRq1byY8uWEGG7C8XFRH/9BVcFF97v2wc3ijUEBMBd07UrUbduEN+7UyxuMqHPGzbIzZpb\n0NMTCTz79ZMTs7pLyMsY3MW//IJ7ff16c1Ezh8EAV/CAAURDh6LPrg68uHwZfVu9Gu7LggLt70VF\nwa16880I9AkIcF4fGINY/Icf0Hbv1v5e48aQONx6K647R46N0YhgjZUrMcaePWv+He4OHT0a58Ha\nPcnHzZUrESSgJZz39SUaMoRo7Fg88uS2FRU47suXE/33v9pjSVYW3KLR0fjOihXmiVJdCUlyv8TC\n1XC1G7GBbDkZ9pKt8eOJlizB85tuwqCydSsmLCJkPj90SKm5eestokcfxXMPD6IPPySaOFF7++Xl\nRDNngrSJuPFGouefhx7LHpw+LU8Qv/xiPZJMRGQkUdOmiKaJi8MAyVujRvifoaHQSblas8MYdB3l\n5RigSkqQhbmoCI+WnufnW54Q9SIwEJq7pCQ8tmghk6qEBJxPd6G2lujIERArTq7++gvn2Ba8vBBB\n1rEjUWYmSFbr1u6NOjp3jmj7dmS937YN2a6t6VJ8fUGoevZE69rVfdGNjGHRw0ngr7/K1R+0kJwM\nAti3L6IwIyNd27+aGhzDdevQtm/HhKqFtDREXd58M46hM4lfaSmI59q10GFpkR4iaFo5wcrKcuy+\nqahApvSVK7EvrXvb0xPn4I47oIULC7O8PUnC2M0jQ48etby90aOxvdBQuS+2CFaTJuhHYiKI3Hff\nWV9MOBsvvYS55H8VDWSrnkE8YY0adbBZXmLsWITAnzmDG/HoUViHJkyQSdj48QjnFfHooyBdHAsX\nEj30kOX9bNtG9MgjGERFdO+ObQ0fbj/JkST0d8cOTHQ7dmAlWtcVVmAgBiEuZPfxwSTOm/iaCBaN\n2lrzx9paTCIVFTKx4o+WJpK6IiAAg6FIqMTnkZHuXxHW1qLMzf79KNWyf7/cqqps/97TE6WhOLHK\nzASx8vNzfd85KipgYePEats27RJSIkJCcH1zctWpEwiXO2AyYULcsIFo40Y8aqU/4AgPh5WbE6ym\nTV3bP8Zw/vnC6Y8/LBPVgAD0bdAgtKQk5/YjNxfkau1apIuordX+bmamHKDQpo1j91FeHkjN6tUY\nd7XE9D4+OA/Dh4NQWrPO1tRgOytWwCJmyQLYowcIlhhkVFQEq+H331smWFFRsHpFRWFh++OP+gNl\nnIX/LwyhgWzVM6hPmK0BITISUSNz5uA1z6NVWAhrB8+zsmIF3IccjOG7IuF64gnUxLJEmiQJNRGf\ne848B1ZCAkjd+PGwtjgKkwkE7MgR5HPh7dAhWCLq69UWFAQLHLfKidY58fm1iGDkKC/HcT9yREmq\nDh/WriGohdBQTGRt2+KRN39/1/ZdRFUV6kfm5MgEa+9e227MhARYOXr2RIRj69aud7eJfd6+XSZX\nmzfDSmMJvr6YgPv2RWvf3rV9ZQwRrTy/2e+/W7eKpKWBcAwejGPpTGKdnw/r1c8/o1kiKH5+IHnD\nhsFt50hN0OpqEElOsI4c0f5eSAhIzYgRyOsWHGx5m+fOydtbt06bpHp6Irp2xAiQtoQEvJ+XB8L0\nww+4VrSu6chIHPuwMBCrNWusX0uuwMWLrrem/tPQQLbqGewlW0RIiHfvvRiwg4Kg+QkPh3vwvvvw\nnfBwaBbE5HuMoVgoJ2pEGLg//xzEwBJqaxEy/O9/a6d66NwZiVRHjkQqCmfBaASJVOucCgtBKktK\nMKjw5yUlzglX9vGBtSwoCI/i86AgDKyRkWgREfJz/joiwn0WEVuoqlKSWfHRmuVEDQ8PnNu2bZXE\nqkkT95LF0lJc17t2oeXkgCDaIlZBQbB0dOkiN1cV6NbCmTOyC3PjRlh1rRHa4GDoiXr0ABns3Nm1\nBFaScBw3bpTJlTpFgIjYWNmq1revcws+X76M/f/6K9qBA5a/27w5yM7AgUgHYq9WUW2x++03y/rJ\nxEQQrOHDIauwVBDcZMJ5Xr0aFihL2jE/P+htR4yAJCQyUv4t151Z+u+RkUh74u+PMW/TJoyX7sTy\n5bC8/X9FA9mqZ3CEbE2ciMn8vffweuZM+McZQ76U5cvxfufOGDzUItR33kHWd25+j4oiWrwYg4g1\nMIbBb8ECDCRaE1xqqiwg7tXL+orPFWAM/VJnhueNSJlRXv0ouhvrA6qrQbZPnNBu587Ztz1vbwjs\n09LQUlPx2LKlewkkY+j7nj0yucrJ0VdlwMMDbkyRWKWmus9qVVICMrV9u9xsnYfYWNl92aMHiKwr\ntYjl5ejXpk1yjjN19nERPL/ZjTfi3s7IcB7JLivD/n/7DePLzp2W3fYBAdCk8SoBjizu8vPlPGm/\n/GL53Hh64lwMHgySZS0P2alTMmH7+WftnFpEGGsHDsRYO2AAFgFnz0IL9tNP+L0lt19SEn7v4YHv\nWLK6uRJz5xI9/bT79/tPRAPZqmdwhGwFBWGAzMwEmfDzw42XkIBVYbt2RCdP4rs33QSXonrg/vNP\nEDPRJD9iBNyMesqwFBTA2vXZZxBJa8HTE1aQbt3QeBJWd0169R2SBN0Ft+ydPVt3MsUREyOXCWrR\nAmQkNZWoWTP3k83Ll+H227NH+ahHa+LpiUmwQwe41tq3x3NnJ8K0hOpqXP8isTp40PbvWrSQiVXP\nnjjurrQQnjqFMYOTq9xc69bA4GA5eewNNzjXbVlcDAvan3/CZZeTY7kvHh7QzvXpg9a9u/2kv6gI\n++LWsr17LX83NhY6s8GDZdecFkpKsD0eIHD4sOVtduwoE7bMTCxyN26UdWeW+mMwwPrq748x/syZ\nugfcOIK33oJ+twFKNJCtegZHyBYRalUdOSLXPRwzBu5FIgz+PXpgxUgEl+P775tH4Fy4ALfj99/L\n7wUEQAA/fboc+WILeXmIpvnuO0TXWBOT+/lhcmzdWm7NmoHgWTLL/6/BaES0IidSllpBgWXxrx40\naoTgCV5/sWVLmVzpPbfORFkZtHgHDiiJlS3hOoefHyw+nFC1b+9e4X1VldLSxutK2tK3hYSAMHTp\nAmtzly7W3fZ1hdGIMWDTJplc2TrGsbEgMt26gWS1b+88y9qZM+gDJ1h//WVdi5mRIZOr66+3/1q9\ndEkmcr//bn1/AQHYB7fGW7LYXbmCsY0TrO3bLRPEkBC4BwcPBnGLiQG5Xb8eZO+PPyy7Kj09lVZ2\na9ZGV2LNGljgGmAZDWSrnsFRspWejpu2eXN5tbNqFVZPRLipBw2SXWcTJkDTpV6dMobSDNOmKQWw\nERFwNU6ZYp/w8fJluAPWrYOgc98+fSJ3gwG6j+uug7k8KQmWuuhomM6jovA8IsK95VksgTEMmLw8\nEC8ZVFQEseilS3jkTXztrAE0NlY+Vjx6kT9v0sS9InUO7v47cAAWHrFZCsvXQnw8Jj5OyDt0QMoL\nd537oiKZVPHHgwdta8O8vWFZ7txZbi1bui5FhyTBqrJjh9x27bKet81gwLHl5Kp7d1w7zrCs1dbK\nRG/zZrRTp6z/Jj0dhIe7Ke0tj3PuHPbH9WaWLO1EOA+ZmdCZ9euHVBRalrLKSrg2OWHbts0yqfby\nQqAF32anTlgIr1+P9vvv+q20tq4vV6K01P2yj/qMBrJVz6A+YTk5MDvrwYoVuInvuQev4+JAbsLD\n8XrZMqSK4Dfw0KEgVlo3VHExog7ffVcptAwIgEbsgQcw6dmLy5cxUG3dikFwzx5YwupyFYWHgwBy\n8XpAAJr43N8fg5eHByYRrUciDKDqVl2tfK0mVby5Kh2EwQBiKeYW442T0SZNnJsQ0l4UFeE88nbk\niEyq7AlSCAuTSRV/TE93X1JbxuByz81VEitbBIGjZUvZWtW5M9zmrtK28cSmIrHKyZEt2JYQGAgy\nwIlVly7W8z/Zg8JCObXG1q14tJbKxWAAGb3+emg6e/SwL5GtJGGM41a7jRut5x8zGGCl69UL7tCe\nPeXxUURZGfr/xx9o27ZZF5yL2tTrr8dCYsMGEKv1660HF/yT0DCbO44GslXPoHXC9K4w27WDK2Po\nUJh9iWDZ+v572YL17bfI18IHjowMFEVt1Up7m8ePE82eDT2Wmkx06QIL2S231C3Td2UlIoD27MHj\niROY8E6c0J/0tD4iPFy20kVGWiZUsbHXXqTPGM6FSKjEZm/unshITFA8IWtGBlp8vHuiGRmDW3bv\nXkzWe/ei7d9vm6wQwXqRno57rn17PLZt6zzSotXfU6eUxGrHDn2anaQkOSt/9+4gsM6wCFZWgtyJ\nuctskdKAAJDQ7t3Rp+7d7TtmJSXIybd1q2wps2YZ9vDA+eGFynv21N7f6dMyYdu0CWTb2uKpWTNZ\nv9ajB+4NnnB240ZYrOsDsrNh2WtA3dFAtuoZ6kK2iKDT6tULAz+PgHn6aUSNcKxfD4LEB+qAACQ1\nnTjR8r6OH0eZng8/hF5BhKcnIoJGjoSr8rrr9PfXFioqMIAfP47J8eJFDGzcBcefFxVh8NdKMugK\nGAxy2gfeeBJVsUVEyGRKfAwP/2e4PzkYg2tTFNsfP658bW8JIQ8PuKNSUsxbVJSz/4FlXLwoEyqR\nWOkliMHBIFO8tW8PnaGrLFbV1XC7ipn5d+/WN4EnJsqJYzMzYRV3Rr6jykr0IydHbnv26MtdJron\n27TRv3AwmXC+uJVs61YcF2szjp8fyFyPHvJ+1eSqthZ9F8mVraoHLVrIhK1jR7gqebLZLVvcW+qm\nLkhL007X04C6o4Fs1TM4QrZ8fGT9QKNGEB1nZyOUmA+Gn3wCKxTH4cMINxbztvTvD7ehtezTly/D\nyrV4MQZfLaSkQEx5/fX2uwXqitpakMHKSgyAlZVyYwyrVUmSn4uPjGEC9fFRNvV7fn5wxbizNE5d\nwBhW/2fPQpysfuRWREcmDIMBLszmzbWbu8TqJhP+x6FDaAcPyuJ7e1w4ycmy+5JHMyYnu+Zcc+ua\nWOooNxd91xMI0agR9EAisbJX36SFkhKQO5FYHTxo200eEA2JIWMAACAASURBVKDMXda5s75IZiJs\n+9gxORFtdrbt8klEEJt3747WowfOlxhYwxiIlGh927nTfMEowmDA+efbbNwY19aWLSB8e/a4TjLg\nChiN/6yF3f8qGshWPYMjZMtggFmb5xx6+GHkvlLXQPzyS9TG4qioQBb5xYvl9/z88JunnrIe9cMY\nBuSvvkKhVLFYtRopKdCIdOiA1q6dewsj/y/DaJSjGC2RqbNn67by9vWVhfZqMpWc7N58WyUlMqES\nSdWRI/ZZNbngPiMD7sCMDLg1XZUiglurRFL111/63eTR0UqLVWamc5KwXrqkJFX25C5LS1PmLktL\n0zepcxE/J1Y5OdDF2QoU8fKCxT4rC/vLysI1KI6PJSVK1+bWrZYzzHMEBGBboot13z7Zmnbpku3/\n9E9CcbHr3NkNsIwGslXPoHXCTp2y7Zrr0EFZq271aliXHn0UxIsIg9I77xA9+KDyt6tWoeSPGA4e\nGYnyPZMm2Q61ZgyD5erV0IrZSvdgMMB6lpIi63ZatsRk3rjx/++8W4zBenj+vL5mKVmiPfD1xfUl\nRi+KLSbGvVa8y5ch/M7LUz4ePmx74lQjOtqcVKWnu24yqqwEAVTXkTx6VF9kmZcX7gmelZ8/1jU1\nBC+DxdNrcJcgz79nDd7ecgQob61b6wvIqK3F8eBEjqfH0BM0kZgIEsTJVYcOyoja0lI55caOHXi0\nlt+KIzkZ22vbFuS6pgbbyc4Gca9vsKc0DmOMDNeqHpiA/fv3k4+PD0VHR1NISMg16dP27dtp3759\nFBERQZGRkVcfw8PDyceBvEMNZKuewdIJ03Mtjh0r59aKjsagFhcHcvXBB/L3nnwSGebFVWhZGdHz\nz0O7JYY0h4Tg9w88oL+4bXGxLBbdsAGDoN78UF5ecEtddx36HhuLyZ4/8udRURh4/wHjhgKSJLsx\nS0tBHIqL8cib+Fr9/NIl55bZCAqCbiY+XvsxIUHOQu0uMAaiqCZU/Lm9lgRvb1g4WrWSBff8USvS\nzBkoLTUvyn3gANyxekfE6GhluaO2bdHvulgKGUPCW3VC2P37rbvOOPz8YHkWiVV6ur6cd0Yj9rNz\nJ9H27bW0e7cH/fWXh679JiRgXx07yvsVLXfFxbAE7tolBwccPmz7WIeEMLruukJKS6umuLhACg8P\npTNnvCk7G8elLnnrrhWqqx3PQVhcXEx9+/alyspKiouLo0aNGlGjRo2uPhcfIyIiXEaCfvrpJxo0\naBAxxsjHx4diYmIoOjpa8cifx8fHU9++fcnTyavwkpISysrKooMaWYeDg4MpIiLiKgHr1KkTPfPM\nMxRoxSXTQLbqGepCtjp0ABHhkYgdOiD0OCgIbsHXXpO/26cPaiDGxSm3cfw40axZKDgtnlmDAZqu\nu+9GtKM9aQauXMGgz1e3PEdRXesWenriv4lCdf48KAgTh5eXsvyOuvFcNrW1aPy5+rG2Vk77IDa1\nLkzPxOIMBAXJ5DMmBpaPxERzMhUS4p7+iOCRi5ZKBp08ab/YngjkhJOo5s1NlJ7uSa1awVLhCk2K\nJEHvw2tHcg3Y/v325Qjz85PLHInkqq7WqpISWey/Zw/ajh1VVFmpTygXFCQnhOVNT+4ynh5D3O+e\nPTg+ehYKsbFXqF07ibp186POnT2pfXtZayZJIN3c1cqbntQbvr44tqmpss6yooLo118v0qlTIURU\n/7Iku0LQvmvXLuratStV2/C733jjjfTee+9Ry5YtndsBIqqtraVJkybRhx9+aPV7t956K7300kvU\nokULp+6fMUbHjh2jzz77jF544QWL3wsNDaVnn32WHnroIfK1sQpqIFv1DHUhW0Soi/jll/Lg1L8/\nqsT7+BAtWgSNFl/NRURAED9qlPn2jxwBOVuyxHwADQwkuvlmRDT26+dY4jvG4LY8eBATmBj5dvz4\ntcuUfK0QHAx3bVSUkkQFBVWQJBVQx45NKD7em2JiQDquRU6tFStW0JYtWyg9vQM1atSRfHyaUn6+\nF50+LYvsOZlylHQmJMBK1ayZ+aNIHLOzs2nEiBHUqlUrSktLo7S0NEpPT6e0tDSKsiPUkVvZxKLc\n/HlenuyW14cyMhgOUljYOUpMLKWUFKLOnYOoa9fGlJraksIdNLMVFSmTwe7bB3JjK4JOhok8PY9T\naOgZSkgoppQUI3Xq5Ec9e8ZR586ZVq0Xly4prWT8uZ70GEAeEe0kohyhwfdtMIRQTEwfSkgYQikp\nt1FeXjDt2aOPiPv4gLAmJoJYeXlhMcRJX30SsItIS7uH5s+/g/r27es0q1JlZSXt3r2bdu7cSTt3\n7qScnBzat28fSRYOUuvWrenll1+mwYMHO6UPjDE6ceIEbd++/WrLycmhSisnumfPnvTaa69RVlZW\nnfdPhGOwY8cO2rJlC23evJm2bt1K58Ws3Sp4eXnRpEmT6F//+pfu8aSBbNUzWDtheq57Pz+ijz9G\npnce2j58OBKa+vrCrXfbbUrty8CBENNrLWAKCxHJ+P772skCvb0RdThwIEKj27VzjpWhpASTYGGh\n+WNhISaB8nIM+uKjO69Gb285aapWItXgYLixwsLkJr7mz0NDLR8zSZIoKyuL/vrrL+rYsSNlZWVR\n165dqWvXrhQfH+/0/1RRIdddPH0ahJg/njplor/+KiZJcjxvg58fdGC8bJBIqJKT7YtefOaZZ+il\nl14yez8mJkZBwFJT06hp0y6Un+9PR4/KpIo/lpba9x/Cw8XC3BLFxFykzZs/pnfemWn1d9HR0TRp\n0iSaOXMm+an+KI+mVGfZP3jQvlxzwcGlRLSXyso2E9EeItpLRPuJSGaNXl5eNHbsWHrqqaeo1d8J\n9q5ckXPdieQqP1/ffr28GCUmVlBExDny8dlDFRUb6PTpH6i4mEfOJBFR279bm78f9VWNDg7G9eHt\nDXe3jw/u80OHlFUu6h92E1F7IiJq06YNvfjii3TTTTfVieCUl5dfJVY5OTm0c+dOOnDggEViJSI5\nOZlefPFFGj16NHnUQVdw4cIFys7Opu3bt199vKgz8Vhqaiq9+uqrNHToUIePAyd3W7Zsudpyc3Op\nVsNn7OXlRYGBgVQirO6HDRtGr7322tV7Qy8ayFY9Q13JFhG0VW+9BYsVX5n36YPkpWFhEFROmoTX\nHN7eRPffj5xcWlFOkoT8XF99hcSolnIUBQXJCQt5OLqj7pJXX32VunTpQr169dJ146lL5hiNsgvQ\nUjOZZBej6GrkzxcsmEeff/4JRUdH0PXXd6V+/brRgAE9KT4+3C2JRisrK+nNN9+kWbNmmX2WkJBw\nlXh17dqV2rdvr2nq5qkf8vOtt3Pn7LFYWOwx+fico5YtfalHjwRKTjYoSi7FxDimsysqKqLvvvuO\njh8/TsePH6cTJ07Q0aNHqeDqqsGPMKE3JaLkvx+bUnBwWzIaE6mqyr4VANeB8RqSLVsSxcSUUF7e\nj1RQ8Bfl5R2hvLw8ysvLoyob5i8PDw+65ZZbaPr06ZSamnk1ilJshw/bF03p43OFAgKOUW3tbiov\n58RqH3GrkRZ8fX1p7NhHaPDgx+jy5TjF/o8e1W8NSkw0UWjoafLxOURXrmyngoJfqLh4CxEZiSiR\niFKJKO3vlkpErYlIX0HD667DGCJWdigrQ1qI+j7TNG2aQc2aNaZ169Zdfa9Vq1b0/PPP06hRoxwi\nOAUFBbRs2bKrVquDBw+SpSk5LCyMOnbsSB07dqTCwkJasmQJERHFxsbSs88+S/fdd59DwvCCggJa\nunTpVavVcQuh6R4eHpSRkUGdO3emzp07U6dOnah///504cIFiouLoxdeeIEmTJhAXg6s1vPz8+mL\nL764Sq4KLETSxMbGKsbMzMxMGjFiBP3000/Uvn17euONN+jGG2+0e/9EDWSr3sEZZIsI7sNHHoEV\ni1trW7ZENvmUFAxc336LGoiiO8LPj2jCBBOVlLxA8+dPoZiYGLNt19Sg1uJ//4tmrTwGEchb27bc\nEoDHlBTr4uWysjLq0KED5eXlUUpKCj344IM0fvx4CnNjTHN+fj4lJCSYrQo9PDyoS5cudOedd9KD\nDz7o0OCgFydPnqSkpCTVuwYiCiOiaCKKptDQ5tS581BKT+9FjEXThQtY8V+4ICd9tVUcWR9qiegc\nEZ0hotN/P/J2koKCLtHdd99EU6ZMdrrO48CBPEpL60dETYjoOhIJFZr9Vj4PD0zunEyJxKpJE/Oo\n2CNHjuj8X4FE1Iy8vFKpY8fb6brretP586GUl6e/yDZHXJwyGWxQ0Bm6555uhOOvhKenJzVv3pya\nNEmmdesOElEKEaWQl1dratToBqqquo4uXtQvMo6IUBaI51Gdp08fpIyMoWROqlKJSJ+mICAAOi1O\nqDjPOH3afbpHV6Jt2xsoM7M5tWvXjtq3b09t2rSh4OBgWrZsGY0ePZqSkpLoueeeozFjxtRp/Ni/\nfz+lp6ebvR8eHn6VWPGWnJx8ddE6YcIEWrlyJc2YMYOmTp1qVfhtC/v27aOMjAyz95OTk68Sq86d\nO1P79u0V+9m/fz9lZWXRjBkz6NFHH61TH/bs2UNt2rRRvOfp6Ult27albt26XSVXSUlJioW70Wik\n1q1b08yZM2ncuHF1sug1kK16BlsnzB7CNWIEUj+MHClHeAUGEs2fj/qJBgPcRq+8guzwylxMEgUG\n/kH//ncLuvfeBItWHG7O/+03oj//RB0xva6HsDC5YHJyMia4uDi0oKAyuuWWbnT8+F7y8vKi9PR0\n6tGjB82aNYsa1VVZrBMlJSXUr18/ys7OvvpeXFwcjRgxgkaOHEnXX389eTto3mIMK/aSEmWkothK\nSoguXDDSV1+tperqQOLkiiiKiJxL8AID5WMfFydHKiYmEkVHV9PAgekUH+9F4eHBtGPHDsVvW7du\nTVOmTKExY8ZQkIOJqsrK4EY7dQqP4vNTp4jOnWMkSfabxLy9cW01bYqWnCyTqqZN7Yv8MxqNFBsb\nS8nJyXTddW0oPDyT/PzSqbY2mYqKImnFilySpKZEFGdzWyK8vGBFE1Oh8EAAddoVo9FI8fHx1LRp\nU2revA1FRGSRt3drqqpKpvPnw+nwYU86eNBENTX6SZW/P/arJlZRUdCtiVGXKCjOqLravnPh6SmR\nn5+BfH0N5OsL8l/f8ldZwvXXD6XMzFZXiVWrVq0sjgtPP/00NWnShO6++26HrEhqmEwmatq0KbVq\n1UpBrNSkQo358+fTuHHjKNIJ5QVMJhO1aNGCUlNTFVYrW1qnI0eOUFhYGEU7Ieu1yWSilJSU/2vv\nzsOiuPL1gb8N3ezIvogLKqBB4wKCIIg7iEoUcUlcJhr3qImZSWbizHWiMUYzydy5icbExBvMohmd\neE3ib5IYvcbgTDbngo5xSdCoAZRNQAHZeqnfH5VquqHZuyga38/znKerm4b6Ut1Qb586dQqDBw82\n67VqKcBVV1fDYDB0KOhJGLZsjDXDFiD2bD37rHj7/ff1j0+bJk7zIE3nUFwsDoh/7bXGA1T9/IAF\nC8TDkrGxzc+DJQhil7807410cdz2Dnh3cdHD19cOPj4q+PiIn7a9vcWdkOkYqYa3UlOrxU/N0kWo\nm7pVqcTDiqaHHrVa4Mknn8aZM99jwoQkjBs3CQMHDoHBYIe6uvozERveWnrs7l2xSeHqzh35B/Gq\n1eJrJw26Nw1TDVtLJzlI8/O89dZbWL58OdRqNdLS0rB27VokJCQ0+4+9srLxJKums9fn5LT92orm\nv2cJgoP1iIryQViYvTFYDRjQ/nnbdDqxRunEjWvXxHblioArV1Ttumanr299qDJtAwY0fQmbigrz\nqTHEJtbQljMigca9ZFKgc3Cov3i4NJbt0iXx1hanRpBLYKB4qL0jY8YNBkOHek+o62LYsjEtvWDf\nfy+ehdMW48eL0zw895z5fFtOTuKcW089VX+mV2mpeP3DnTstH/Lw9xfPRExOBiZMaN08RoIg/pOS\nPiFfuiT+U79+XdzR8h966zg6GuDvr4Kfnwp+fmixeXhYfx6yBx98EOHh4Vi5ciX8/YNQXFw/3qth\nkJJu2zoAvSF///q516Tb4GDg8uWjCA93wvTprRvTZ8pgEOs2DVOmt7m57XtfBgZavmxRSEjTE6mW\nlVkKVGJry6WGAKmXTMB996nMQpW/f+OzLi9fFlvHx+l1P3//OzB9utJVkC1h2LIxrXnB2rMD7ddP\nvKzOzZvAmjXircTHB/jd78TJS6XQpdMBn38uTv3w8ceWx/yoVOLcPBMnigPiY2Mbz9vVEtMehLw8\n88Ha+fnizqasTAyBth7KNJr6MxE9PMzPUjRtDb/m5qaDr68arq7yT+IqHd4sKBBbfr75cn6+AYWF\ndsjPF3tDO/rXr1aLhypNg5Tpbd++5rOGt1ZdXf2ZlDk5ME5PIYWpn39u/zg2aXqKhm3AAMs9hHq9\nWIs0NcbVq+aBqj1XAfDzEwOcaaDq1Utc1/Xrjc+4tMaVBrqjESPEef+IOophy8a05gXLyhLP8msr\njQb44x/FaSGef168jI9pgHF3B1asANatE8e2SMrKxLm6PvoIOHq0+QGsffqIF8cdPlwc+zFsmHUu\n5CuFgNJScaxHRUXTh+tMbw0GcQfU0q0giNtHrW58a+kxBwfzQ5aWDmM2PKTZGWcvNmQwiNvs1i3z\nAfOmtw0fs9YAZWfnxrPWN1wODGz7YT6DQQx/pkGq4XJbL+tjytOz/tJF0nhCaXnAgMbhT+ols9RD\ndu1a+3vJevZsfB1KFxfxb6mkRPzZV6/Wt478zveCjsy8TtQShi0b09oXrCM9HMOGiYcJg4KAzZuB\n999v3EMxYQLwyCPiIHvTMc9VVeJg+BMnxHbuXMvrc3ERByVLO42wMHGnJc143p6ei3uNTtf0YHrp\nkj+WQlRpqfXHhmk0Ykjq2VO8lZalQfVSoPL0bPv7tLpa7NWU2o0b9ctST9WNGx27pJGra32IMg1S\n0vQUDQ/3SeEuJ8d84l3ptr29ZCqV+DdgOteYdOkkOzuxV9c0UHWkN+5eMXkyYDKzAlGnYdiyMa19\nwQSh471FqaniOC57e/FsxHffbTzXj6MjMGWKeEbj9OnizsBUURHwzTfixae//Va8mKv5WY0t8/Gp\n30lLM6RLzd+/fkC81Fxcut41ES2RBtGbtsrKxo/dvSv21DW8hqJp6+iljVpiby++ttI2bxikTJe9\nvNq+/evqxPAgHSJuGKSk5Y4MlAfEunr2FENM377irely//7i+02qXxDEQGqpd0y6f+NG+w9he3iY\nBzofH/Hv1tFRvL150zxQ3b7dsd//XrFjB/DYY0pXQVSPYcvGtOUFs1bgmDkTePpp8dP1W2+JM8Zf\nvmx5fRER4qfHyZPFMVoNx6jo9eI4lO+/F3u9vv9evLzItWvWG3Nlby/uxNzdxUH+ps3R0fJj0qEq\naZupVObLDR/TasVWVyc2abm5x6qrzQOUkmPMXF3rw5N0RmLDZdPHPDzaHt61WrH3rKBADFLN3XY0\nREm8vRsHKNPloKD6Q0XSZK7SoH1LYSo3t33XaZRIvWTSrPhOTvU9U/b24vpzcuqbtbbDveLHHy1f\n2YKoq2HYsjFtfcHaE7g0GnFH1DAMDB8OrFolTvNw/rx4jcWPPmp63iw7O3E+nthYsY0YIc7XY+mS\nKzqduLORTjG/fl08LGR6aMjWB8Bbm7Nz04PoLTVf3/rWnmsn1tWJhyAtjeVqeL+wUFy2FkdHsWcz\nKEhsTS1L0+GYHm6UesUs9ZR1dPyZFO769hUDqUZTP12InZ0YqqUglZfXscOb96q//hV46CGlqyDq\nGIYtKzl48CB2796N8PBw5OXl4eWXX8YAaZIqC3bu3In169ebPebn54cbN240O2Nwe16w9gQulUrs\nATAYGu8gHB2BqVOBBx8U5+O6cEEMXcePt3zmjr29OHfPsGHiGVJhYfWtucnfDQbznbrUiorE3oA7\nd+pbebl4W1EhHvasqWnbpU6szd5e3JZOTmIYaGtzcxOb6XUTPTzaNuGmqdpa8dBYWVl9a+p+SUl9\niJLj4t8uLvWHIAMCxFtLQUqaQqS8vL43zLRnzNqHGwFx20vjBk17pExnNS8rq5/CQu5Dud0ZAxV1\nd3KHLfmuU9KFfPjhh1iwYAF27NhhnMRx7NixuHDhAjwaTvH8i7feeqvR3D9Lly6V5dIuOl3bL/4s\nCOJOWboGoJ1d/eDb2loxXH30kRgiEhLE8PXee+Ihpy++EGeL/+Yb8VCh6QBsvb5+tumGfHzMD/1I\nLTBQHCfk7y/2jFm48kOLDAaxfil8SQFMWjYY6k8CEATzZUuPaTTi7+7g0PyydHFca5Bek4oKcQcv\nXeNRutC21MrLGwco02W5L3fi7CwGJyk8NXfr5ib2/jQ8rHj9OvDdd41DVQuXGWw1Dw8xxPXoYX5Y\nzzRI3b0rbueMDPaqWsORI8ADDyhdBVH3dE+ErWeeeQaCIBivUTdgwAB89dVXeP3117Fhw4ZGz8/M\nzER0dDT+53/+x/iYSqWS7TIz9vbiTrilWcAt0evrlx0cxMCiUtUHD+k6iCdOiJOf+vgAY8aIAWzR\nInGc18WL4nQU//63GL4uXrR8OKWkRGzN9Y6pVPVjiUznnDK9dXcXd/im0ypIzcGh/kLSjo5i70VT\nF5m2txd/z9ZMDSHdVlWJPUBSiGtrkwbJm4Yn01ClxE7fy8t8/FZTY7ykZZ3Oci/kTz+JJ0k0fNya\n4c/RUQxyDg71oalhb5RKJQbSn3/u2HgsMhcWJg4v4PQJRJ2v24et3NxcXLhwASqVCk6/DEaSeqw+\n/fRTi2ErPT0db7/9Nj788EPcf//9mDVrFlauXAlnGec4cHMTdzDSpKTtIfVsSWc6WpoyoKREnOT0\n44/F+3Z24mHDyEhxzNe8eeIp7HV14tlVppMrXr0qHgIyDXgNCUL9Tppaz9lZDE3e3uKt1EzvN/ya\nq6u4vcvLxde1tLR+HrPSUuCHH4Cvv66/L43XkmNckqenGICl0NQwPEn3a2vFQ3rNvYeo/W7dEj9Q\nEVHX0u3D1vnz543LDQ8BZmdnN3p+TU0N/vrXv0Kv16O0tBSnTp3CqVOnsGvXLhw7dszYOyYHd3dx\n52mNsxRbOzeTwSBefufSJXFAvcTBQTyLKDRUPEsrNVU8Y6t3b3GnWlVVP0C+qMi8SWGrrVNI2CJX\nV/F1c3MTby21hl/r0UMMS6a9OzU15tddNG3Z2eb3pbFacm9f6bCd9H601BMl9aLeudPx2eipZdeu\niX+HRGRbun3YKv3lOhfShXhN3bYwKU5lZSX+8pe/ID8/Hz/++CM+/PBDVFRU4MqVK1i8eDEyMjJk\nr9lagasj6urEQw4mWdWMRlM/tkdqQ4fW98B4e4vBQjrUp9OJvRnSoTjpgs/V1fXLVVXmF5KWml7f\n9GOm43mkW0sXqzZdVqvFnqSGU0w01dRq88ORpoHDdLoI0wtWS+3mzfoLWDc8SaCr9+509fq6m82b\ngU2blK6CiOTQ7cOW+y8DoSxd6NbS4HhfX18sWbLEeH/Xrl3Ytm0btm/fjn/+85+4c+dOk4PqTV26\ndKlV9fXs2RM9LVyQUBDEQ32pqa36MZ1Oq63v2WoLe/v6s/fc3MQwIw1YtzSI3c3N/PGmBsQ3t6zX\n18+tJQ28l+631GpqOOs3dVzfvuJhXV5tgahz5efnI7+p+Y9MtHaf3V7dPmwNHjzYuGxocGzN9GtN\ncXV1xfPPP49r167h4MGDcGjl6NJFixa16nmbNm3C5s2bLX5t5syu0ctlTXp9fe8OUXfw8MNAenrb\nrxFJRPJ744038OyzzypdRvcPW6GhoRg4cCCys7NR2WCineTkZJSUlOCxxx5Djx49sGPHDjg4OODa\ntWsIDAw0GxA/ZswYlJSUtHqQ/L59+xAeHt7i8yz1ajUk9dR0p9BFZAuuXxfHLBKRbVq1ahVmzJjR\n4vMuXbrU6k6S9uj2YQsAXnjhBaSlpRkHxOfl5SEoKAgrV67E3r17ceDAAQBi+Bo0aBCGDBkCLy8v\nbNu2DcuXL0dtbS0yMjLw+uuvt3qd4eHhVp8YjaGLqOM8PcXLUPXurXQlRCS3pobqdDYrTefYtaWm\npuK9997D3/72NyxatAguLi44ffo0vLy8MGXKFPTu3Rvh4eGIi4tDWFgYHn/8cTg7O2P9+vWIiYnB\ntm3bsHPnzmZnnO9M0likP/9Z6UqIuo6PP67/22iulZUxaBFR57pnLtfTWeSe8r8poaHipJRE3UVw\nMPDPfzIYEZH85N533xM9W/eCK1fqP7mfPq10NUSN9ekjfiBoTe+TIIjjpRi0iKg7YNjqhqKjzXda\nP/6odEXU3UyYIE5c29rgJAhATg7QRY7EExF1Koate8DAgY13fG2dH4u6n169xMv5SBf5bkv74gvx\nOotERNQyhq17VK9eTe9I/9//U7o6ao3p04HMzPaFJSlwjx7Ns1uJiOTGsEWNpKS0bmf94YdKV2pb\nxo8Xt1lVVfvCUcP297+LFxBnWCIi6truiXm2SB6pqfJcfFgQgIIC8bqM//oX8O23wIUL4kWupXlp\nHR3F5uAgXvJHWnZwMP+ap6c4yPq++4D77wcGDxav38iAQtS9VFZWwtXV1eKl2Trb6dOn0bt3bwQF\nBSlax9WrV3H06FFER0dj2LBhcHR0VKSOkpIS/O53v8PQoUMRFRWFESNGwM3NrdPryMzMxNq1axER\nEYHIyEiMHDkSQ4YM6ZTtwrBFXY5KBfTsKbbERKWroc5WW1sLBweHLrHTBIArV67AYDAgLCysS9S0\nZ88eeHp6YvTo0eit8OmaR48eRXp6OmJjYxEbG4vIyEg4OTkpUsvFixfxwAMPICoqCjExMYiJiUF0\ndDS8vb07vZbc3FzExMSgV69eGDVqFKKjozFq1ChERUW16tq61tK/f38cPHgQa9euhUajwbBhwxAd\nHW1s4eHhUKvljwE+Pj7o2bMnfv3rXwMQr1UcHh6OId+qQQAAIABJREFUkSNHIioqyhjAXFxcZK1j\n5MiRGD58OHbv3m18TKPRYOjQoejbt6+s6+Y8W1am1DxbZFl2djbKy8sRGRkJO7uucdT83XffRZ8+\nfTB69GjFdkymTp06hffffx/jxo3DuHHjFP80npOTg4kTJ2LkyJEYM2YMEhISMHToUNgrdPHB/Px8\nDBo0CE5OToiLi0N8fDzi4uIwcuRIRV6/Y8eOYcqUKQBgfB9JLSIiotXXb7UGg8GAuLg4fPfddwDE\nHdeIESOM4Ss2Nhb9+/fvtJC6atUqvPnmm2aPhYWFGcNXTEwMhg8fLus20mq1KC4uxowZM5CZmdno\n64MGDcKoUaOMIWz48OFWfR/pdDoUFxejsLAQhYWFyMjIwPbt2y0+18XFBREREYiOjkZUVBRmzpzZ\n4R4nvV6P4uJiFBQUoLCwEAUFBSgoKMD169fNQk5DdnZ2GDx4MCZMmIA//vGP8PPza9f6DQYDiouL\njRegNm0FBQW4cuUK/v3vfzf5/XLtuxm2rIxhq97nn3+OMWPGwNXVVbEabt++jf79+8PR0RFTp07F\ntGnTkJSU1KmfLhs6fPgwZs+eDScnJyQkJGDSpEmYPHkyRowYoUigMBgMiI6ORlZWFgBx5zRu3DiM\nHz8e48aNU6T35JlnnsFzzz1nvN+jRw/ExcUhISEBCQkJiI6O7pSgo9PpcPv2bWzduhWvvPKK2dcc\nHBwQFRVlDF9xcXHw9/e3+vrLyspQUlKC0tJSlJaWoqSkBBs3bkSehVOKHR0dERUVZQxfcXFxCAwM\nbPf6DQYD7ty5g1u3bqGkpAS3bt0yWy4pKUFWVpbFUCHx8/NDbGwsZs6ciSVLlrT5PV5VVYVbt26h\nuLgYxcXFxmVLjxUUFOBOC1e579GjB5577jmsWbOmVb06BoMBpaWlKCoqQlFREYqLi43Llu6XlZW1\n6vfSaDSYOXMm1q5di/Hjxzf73JqaGmN4KioqMi5bul9SUtKq9Ut69OiBRYsWYcWKFRgxYoTF5wiC\ngLKyMmNwahikTO8XFxfDYDC0qQZA7HVatWoV5s+fbzHw1dXVoaCgoFF4ahioCgsLodfr27x+CcOW\njegqYau0tFSR7nNTGzZswM6dOzFz5kzMnz8fU6ZM6dRP3VqtFpcuXcLLL7+MvXv3Gh9Xq9WIj4/H\n9OnTMX36dISHh8v2ybuurg7nz59HdXU1qqurUVNTg6qqKqxbtw7FxcVmz/Xy8sLEiRMxefJkTJo0\nCaGhoVapq7a2FufOnUNlZSUqKipQWVlptlxRUYHTp0/jH//4h8XvDwkJMQtf7elur62txdmzZ3Hn\nzp1WtVu3biEnJ6fJn+fg4IDo6GjMmDEDjz/+eKuCV01NDc6ePYuysrIm2+3bt83uV1RUtPp39PHx\nwaZNm/Doo482uROvqanBmTNnjKHJNEBZeqy8vLzV6zcVEhKCJUuW4OGHH270elVXV+PMmTONQpOl\nQFVSUtKuHafE3t4e06ZNw7JlyzBt2jRoNBpjDVlZWU2GJtPlqqqqdq/f1NChQ7F8+XIsXLgQPj4+\nZjU0F55u3brVoW3QUFhYGFasWIHFixfD3d0dmZmZLQaotrwPG3JxcUF1dTUa7upjYmKwcuVKzJgx\nAz/88EOLQUqr1bZr/W5ubggMDERAQADOnTtn9ru4uLhgwYIFWLx4MQRBsNgbJbW2hkjT9UvXR+zZ\nsyd8fX2xa9cus+ckJSUhKSkJTz31FMOWregKYauurg5jx45FVFQU/vjHPyIgIKDTaygrK8OIESPM\ndpheXl6YPXs25s+fj3Hjxsnei5Ofn9+qQ2LBwcGYPn06HnjgAUyZMsWqwSsvLw99+vRp1/dOmDAB\nr776KgYPHtyhGnJzczs8HsHNzQ1paWlYsGABEhMT23xI9ueff0a/fv06VINErVZj6tSpePjhh5GS\nktLqHq5r165Z/fqmUphYsmQJpk+f3uJA2+vXr6N///4dWqc0CLxSOlvkFy4uLpg3bx4eeeQRJCQk\nNPk+vnr1KkJCQtq9fjc3N/j6+sLX1xc+Pj4QBAHHjh0ze87AgQOxdOlSPPzwwxYvAtyRGpycnODn\n52dsvr6+xuWKigq88MILZrUuWLAAy5cvR1RUlNk2aW8N9vb28PPzg7+/v/FWaqb39+/fb9ypOzo6\nYs6cOVixYgXGjh1rrOOnn35CaGhom2vw9PREQEAA/P39ERAQYGym96XlW7duYcCAARAEwdiLtXLl\nSgwfPrzdNTg4OCAwMNDYAgICLN4PCAgw9lIVFxejV69e0Gq1GDp0KFavXo2FCxfCw8MDV65cQVhY\nWJtq8PX1RWBgoFmQatgCAwMb9ZJ9+OGHSEtLg4+PD5YuXYpVq1YhJCRE9n03B8h3QxUVFfj+++/x\n3Xff4b333sMLL7yAVatWdeqYpbq6ukZduWVlZdi7dy/OnTuHhQsXtrobv71a8/s6OzubjVmwdg+X\ns7Nzo8fUajUMBoPFT8vBwcGYN28e5s2bh5EjR1qlnob/bJycnODu7g43Nze4ubnB3d0dtbW1jQ4F\naTQaTJ06FQsXLkRKSkqHBq+aHra1s7ODh4dHk83T0xNarRYvvvii2c+Ijo7Gr371Kzz00EPtGs/h\n5eVlXHZwcICXl1eLzdPTE15eXrhw4QLWrl1r/P5hw4ZhyZIlWLBgQZs+zJj2Nru4uMDHxwfe3t7w\n9vY2Llt6TFr28vKCo6MjkpKScPz4cQDAmDFj8Mgjj2Du3Llwd3dvsQZfk9lo3d3dzYJTw+WGj/n4\n+DQKlFu3bsWxY8eMYW/ZsmWIj49v9r1r+vp5eXmZBaaWlpsblrBhwwYAQFxcHJYvX465c+c2OQZJ\nOuSrUqng4+NjFpSaWvb394enp2eL/1sMBgMWLVqE+++/HytWrMCiRYssHmmQ3jsqlQp+fn5NBibT\n+/7+/m06e+6ll14y9mLNmzev0faTarCzs4O/v79ZaGoqSHl6erb5f9OhQ4cwf/58rF69GrGxsWbf\nLwVye3t7swDVVJgKCAho91GSS5cu4b333sOcOXM6d8ylQFaVmZkpABAyMzMVq+H27dvCv//9b6Gg\noEDQ6XSK1TFv3jzBzs5OiIqKEn77298Kn3zyiXDnzp1OW79OpxN++uknYe3atQIAY/P39xeWLVsm\nHDlyRKiqqpK1Br1eL/z8889CUVGRUF5eLmi1WkGn0wkhISHGenr37i385je/Eb799lvBYDDIUkNu\nbq5QVlYmaLVai8/57W9/a6xn3LhxwhtvvCGUlJRYtYa8vDyhoqKiVb/j9u3bBQBC3759hT/84Q/C\npUuXOlyDwWAQbty40a7XfM6cOYKvr6+wfv164cyZMx2q4ebNm0J1dXW7f8aPP/4o9O7dW/j9738v\n/Pjjj+2uoba2tt01SHQ6nTBv3jxhz549Qnl5eZtqyM/PF+rq6jpcg+nP/NOf/iRcuHCh1c8vKCho\n8m+iI4qLi4Vvvvmmxfe6VIOc/6dv3LjR4nMKCwtl31e09PMLCwsFvV4vaw3NkXvfzcOIVtYVDiN2\nBTU1Nfjf//1fjBkzBp6enorVUVFRgeDgYPj5+WHmzJlITU1FTEyMYme2AeInvPXr12Pu3LmYN28e\nYmNjFT1TsrKyEg888ACmTZuGhx56qN2HPa1FEARs2bIF48aNw9ixYxU/i1Sv1+Po0aNITEzs1DGH\nTSktLYWHh4ei72GJIAhdYjoMoo6Se9/NsGVlDFtdS05ODqqqqnDfffcpXYpRXl4egoKCFA8REoPB\n0GVqISJSAsdsEXWA3BPVtYfSE1E2xKBFRCQv/pclIiIikhHDFhEREZGMGLaIiIiIZMSwRURERCQj\nhi0iIiIiGTFsEREREcmIYYuIiIhIRgxbRERERDJi2CIiIiKSEcMWERERkYwYtoiIiIhkxLBFRERE\nJCOGLSIiIiIZMWwRERERyYhhi4iIiEhGDFtEREREMmLYIiIiIpIRwxYRERGRjBi2iIiIiGTEsEVE\nREQkI4YtIiIiIhkxbBERERHJiGGLiKgbEQQBgiAoXYaZ8vJypUsw0mq1yM7O7jLb6MyZM/j555+V\nLgMAkJWVhePHj6OqqkrpUnDw4EEcPnwYZWVlSpdiFQxbJAtBELrUP1jJ5cuXu+Qf7xdffIGCggKl\nyzDzww8/YP/+/SguLla6FKOCggI8/fTTOHHiBGpra5UuBwBw6tQpLFmyBO+//z6KioqULgcAMHv2\nbCxevBj79+9HYWGh0uVg48aNGDlyJDZs2IATJ06gpqZGsVo0Gg1+/etfo1+/fli2bBkOHDig6Osm\nCAL69euHsLAwPProozh06BBKSkoUqSU4OBhz586Fl5cXJk6ciOeffx7fffcddDpdp9cSGhqK2bNn\nw8fHB1FRUdiwYQOOHz+O6urqTq/FGlRCV4n33URWVhZGjhyJzMxMREZGKl2OotLS0lBTU4O0tDTM\nmDED/v7+SpeEc+fOYeTIkYiLi0NKSgpSUlJw3333QaVSKVrX3r17sXTpUkRERGDq1KmYOnUqYmNj\noVarFatJq9Vi8ODB+OmnnxAZGYnk5GQkJycrXtfs2bNx+PBhuLi4YPz48UhKSsKUKVMwaNAgRV5H\ng8GAUaNGITMzEwAwYsQIJCUlISkpCfHx8XBycur0mk6ePImJEyca7w8bNgxJSUlITExEQkICnJ2d\nO7WewsJChISE4O7duwAAJycnJCQkIDExEYmJiRg2bBjs7Drns78gCMjMzER0dLTZ48OHD0diYiIm\nT56MhIQEuLi4yLJ+g8GAmpoas7ZixQp88cUXxueoVCpERkZi8uTJmDx5MuLj4632mun1elRXV6Om\npsbi7auvvopDhw6ZfY+HhwfGjx+PyZMnY9KkSR36n6nT6VBdXW3WpHU3bFu3bkV2drbZ9zs4OCA+\nPh6TJk3CpEmTEBUV1ab/R1qt1vjzq6qqjMtnz57F8uXLZdt3M2xZWVcJW4cPH8bEiRPh6empWA1f\nf/014uPjAQB2dnYYM2YMZs2ahVmzZiE4OFj29RsMBlRUVJgdVhEEAYsWLcJnn31mfF7//v2NwWvc\nuHFwdHS0ag137tyBXq+HXq+HTqczLpver62tRXJyslkvkqenJ5KSkjB16lQkJycjMDCw3TXcvn0b\nOp0OWq3W2EzvN/W1jz/+GHv37jX7eT169MDkyZORnJyMKVOmoG/fvq2uoa6uDnV1ddBqte1evnjx\nItLT0xuto2/fvsbgNWnSJHh5eTWqoayszPhzamtrLd6257GzZ8/i9OnTjWpydnbGuHHjjOHrvvvu\nw+3bt1FbWyt7+/rrr6HX6xvV5ODggNjYWIwZMwaxsbHo378/tFotamtrUVNTY/G2tY8197XCwkJo\ntVqL7w8vLy9ER0cjMjISERERcHNzaxRIpJ/Vmsdbem5Luz21Wo3w8HAMGTIEY8aMgUajafSzpJDQ\n1sfq6uqaXXdT9YSEhCAhIQH9+vVrMig1vLX0mDV6qTw8PJCQkID+/ftbXKelZs31m/Lz88OoUaPg\n6uraaJ2mYUq6b+lvwpRs+26BrCozM1MAIGRmZipWQ3V1tRATEyM4OTkJCxYsEE6cOCHo9fpOraGo\nqEiws7MTAFhskZGRwtatW4WLFy/KVkN+fn6T62+qubq6CrNmzRLeeustIT8/v8M13Lhxo801NLfN\n/uM//kP44Ycf2lRDXl6e1Wqw1MLDw4Xdu3cLOp1OsRoaNmdnZ+H5558XampqjDXk5uZ2ag0NW1RU\nlPDKK68oWgMbG1vzTa59t3LHAkg2d+/eRW5uLmpqavD+++/j8OHDePDBB/GnP/0JAQEBnVKDVquF\nwWBo8utZWVm4cuUKsrKysH79eowdO7ZT6mrJ3bt3kZOTg7y8PBQWFra7N0lircNtAwcORGJiIlJS\nUhAWFtam79VoNFapoaGIiAikpaUhLS0N4eHhzR5WcHBwaPPPd3BwgEajgYODg9kyAFy9erXR852d\nnTF16lTMnj0bKSkp6NGjR7trUKlUcHR0hIODQ5O3pstFRUXIyspq9HNGjx6NOXPmIC0tDf369UNx\ncTHWr1/fqhocHR2NTVpXW9qePXsaDXQePXo0kpOTsWnTphbXr1ar4eTkBEdHxyZvm/taw+f8+c9/\nRk5OTutegF84OTmZNelndeRxR0dHGAwGLFiwoMVeFnt7ezg7Ozf6GdZ6rKamBsnJyc3W4ODgYPwe\nS7fNfa0131NdXd3i/1+NRgM3Nze4uLgYv7/hz2mpNfe86upqjBw5stkaVCoVnJ2d4eHhAQ8PDzg7\nOzeqpyP3L1++jMmTJzdbQ0cwbHVDLi4uSE1NxeDBgxEbG4thw4bJtsNtiq+vL9LT07F06VKzxyMi\nIoxjf0aPHi1rXd7e3sZxECqVyhgGtm3bhmPHjhmf5+joiEmTJmHGjBlISUlBr169rFaDl5cXTp48\nCXt7e6jVatjb2xub6X0AmDhxIm7cuGH83ujoaMyaNQupqakIDw/vUA1ffvklNBoN1Go1NBpNo+Wm\nvvbSSy9hw4YNAMRtGBcXh7S0NMyaNQv9+/dvdQ2enp7IyMgwC08Nw5TpfbVa3WR4e+ONN7B69WoA\ngLu7O1JSUjB79mwkJyfD1dW12e2QkZHRbICSbu3t7ds0JuWhhx5CVlYWVCoVxowZYwxYvXv3trgd\nWgpKGo2mQ+PPTp06hVdeeQUAEB8fj7lz5yItLQ19+vSBVqvF+PHjmw1J0jawlvPnz+Pxxx+Hs7Mz\npk2bhrS0NPj4+MDb27vJoNTRbdCcXbt2QafTISwsDImJiZg2bRoGDRrUqAa5xybqdDp88sknmDNn\nDgIDA5GSkoLU1FSMGDHCWIPcY9l0Oh1OnToFZ2dnqFQqTJkyxTg4fe7cuQgODpZ9LKRpDVIA+v77\n77Fq1SrMmTMH8+fPR2xsrKzb4tatW7L9bIBjtqyuq4zZ6grS0tKQkZGBKVOmIDk5GUlJSR3uKeqo\nmzdvYsCAAejRowdSUlIwY8YMJCYmNruT7gwHDx7EokWLMH78eKSmpmLmzJmNdtSdrbq6GmFhYRg8\neDDS0tIwc+ZM9OzZU9GadDodRo8ejSFDhmD27NlITExUZAC6qevXr2PlypXG8YhKv8cBYPv27XBz\nc0NaWppVPzy01wcffABBEDB9+nTF/9YA4MCBA4iKikJoaKjSpeDKlSuora3FkCFDlC4FxcXF0Gq1\nCAoKUroUFBUVwdfXt9NOnJB7382wZWUMWyKtVousrCxERUVZ9RNyR2VmZqKurg6jRo3qUnWdPn0a\nYWFhjQZ1K6msrAyCIMDb21vpUozq6uqgUqk6vae2OYIgKH42KxF1jNz7bh5GJFloNBrExMQoXUYj\nLY0LUMqoUaOULqGRrhT8JO0Z+yU3Bi0iagknNSUiIiKSEcMWERERkYwYtoiIiIhkxLBFREREJCOG\nLSIiIiIZMWwRERERyYhhi4iIiEhGDFtEREREMmLYIiIiIpIRwxYRERGRjBi2iIiIiGTEsEVEREQk\nI4YtIiIiIhkxbBERERHJiGGLiIiISEYMW0REREQyYtiysuLiYrNbap/8/Hxs3rwZ+fn5Spdi87gt\nrYPb0Xq4La2D29F65N53M2xZ2a1bt8xuqX3y8/Px7LPP8p+IFXBbWge3o/VwW1oHt6P1yL3vZtgi\nIiIikhHDFhEREZGM7pmwdfDgQUyYMAFr1qzBjBkzcPXq1Waff+LECUyYMAHr1q1DcnIyzpw500mV\nEhERUXdyT4StDz/8EAsWLMCcOXPw2muvoaysDGPHjsWdO3csPv/06dOYNm0aoqKi8Oqrr8LPzw/j\nx49vMaARERERNXRPhK1nnnkGgiCgX79+AIABAwbg5s2beP311y0+/7nnnoNWqzV7fkVFBV588cVO\nqpiIiIi6i24ftnJzc3HhwgWoVCo4OTkBAFQqFQDg008/bfT82tpanDhxAgAaPf+zzz7rjJK7ncLC\nQqVLaFJRUREEQVC6DIu66na7c+cOampqlC6jkcrKSlRWVipdRiO3bt2CXq9XugwzVVVVKC8vV7oM\nM5WVlbh7967SZZjpav8futp7qSttn676f0nS7cPW+fPnjctqtdrsa9nZ2Y2ef/XqVeML1vD5eXl5\nXfrF7Kr+8Ic/IDIyEps2bcL//d//wWAwKF2S0eeff45+/fph3bp1+Pzzz1FbW6t0SUa7d+9GeHg4\nfve73+Ef//gHdDqd0iUBAPR6PQYMGIBZs2YhPT0dBQUFSpcEANBoNIiIiMDUqVPx2muvIScnR+mS\nAADXr19Hz549sXjxYhw6dKhLhBwHBwfExcUhKSkJO3fuxPXr15UuCWq1GsOGDcO0adPw+uuvIzc3\nV+mSutz/h5ycHON76YMPPlD8w8VHH32EkJAQPP744zh+/Djq6uoUq0UQBISEhCA1NRX//d//3WX+\nLxkJ3dy+ffsElUolqFQqISMjQxAEQVi8eLGgUqkER0fHRs//5z//aXz+O++8IwiCIGzatElQqVSC\nnZ2dkJ+f3+L6AAj79u2z/i/TSnq9Xli9erWwa9cuIScnR7E6JFeuXBHs7e0FAAIAoWfPnsKKFSuE\nI0eOCHfv3rX4PZmZmQIAITMzU9batFqtEBYWZqzN1dVVmDVrlpCeni4UFhbKuu6WlJWVCR4eHsba\nvL29hYULFwoHDhwQbt++3eqfI8e23Lhxo7EuAMKoUaOE5557Tjh79qxgMBistp622rVrl1ldw4cP\nFzZu3Ch8++23gl6v79DP7sh2TElJMdak0WiExMRE4ZVXXhGuXr3aoZo64p133jHbVkOGDBE2bNgg\nfPXVV4JOp5N13U1tyx07dpjVNGLECGHjxo3Cd9991+HXrz264v+HGTNmGOtRq9UCAOGpp55S5L1U\nW1sr9O3b11iPu7u7MGfOHOGdd94RiouLO72ezZs3m71/oqOjhS1btghnzpxp8f+S3PtulSB0kT5A\nmRw5cgSpqalQqVQ4efIkxo4diyVLluDdd9+Fn59fo0M1586dw4gRIwAAb7/9Nh5++GFs3rwZW7Zs\ngUqlQmVlJZydnZtcX3p6OpYtW4ZHH30U8fHxLdbn6+sLPz+/jv2SDVRVVWH9+vXIysoCAISFhWHs\n2LEYO3YsBg8eDDs7+Ts0S0tLMWvWLOP9pj6BOTg4YNSoURg7diwSEhLg7+8PALh06RIWLVqEffv2\nITw83Co1NKWmpqbJXqOhQ4ciISEBY8eORWhoqPGQsrVraEpVVZXFnkB7e3tERkYaa+vTp0+TP+O7\n777DmjVr4OzsDHt7+3bXYkqn0zXZyxsQEGCsKyoqCo6Ojh3eDq1lMBhQVVVl8Wuenp6orKyEWq1u\n1GvdGnq9HtXV1e3ajnV1dU1+6lepVFCr1dBoNJ3ytykIQqsO10nbqT3bqiXNvX86q6bWbofm2NnZ\nGetpz2tnjRpMSe8ltVrd6veotWswJW0fjUbT7P9OOWswZW9vb2wN6XQ6aLVavPXWW1i6dKn1Vy5L\nhOtCLl++bOyVOnnypCAI9T1b48ePb/T8qqoqQa1WCyqVSti7d68gCPU9W/369WtxfTt37jRL1mxs\nbGxsbGy20Xbu3GnNCGJk/Y8sXUxoaCgGDhyI7OzsRr0rycnJKCkpwWOPPYYePXpgx44dcHZ2xsSJ\nE3H8+HGLz2/JQw89BABwcXGBo6Nji8+Xo2eLiIiIxGsdtuYSPLW1taiqqjLuw62t24ctAHjhhReQ\nlpZmHBCfl5eHoKAgrFy5Env37sWBAwcAiGEqNTUVW7duRUZGhtnz3dzc8NRTT7W4Ll9fX6xbt06+\nX4aIiIhsSrcfsyXZv38/du7cidDQUJSXl2P37t0ICgrChQsXMHXqVLi7u+PkyZPGMUPHjx/HM888\ng9DQUBQUFGDHjh3tHjtERERE9657JmwRERERKaHbz7NFREREpCSGLSIiIiIZMWwRERERyYhhi4iI\niEhGDFtEREREMmLYIiIiIpIRwxYRERGRjBi2iIiIiGTEsEVEREQkI4YtIiIiIhkxbFnRwYMHMWHC\nBKxZswYzZszA1atXlS7JZl24cAGPPvooZs2apXQpNkun02Hz5s0IDg6Gq6srEhMTcfHiRaXLsll7\n9uzB4MGD4eLigpEjR+LkyZNKl2TznnjiCfTv31/pMmzWk08+CTs7O7MWERGhdFk26+zZs3jiiSew\nbt06/O1vf0NNTY31frhAVnH48GHBzs5OePXVVwVBEIQxY8YIvXr1Em7fvq1wZbbl5MmTwsKFCwWV\nSiWoVCohMTFR6ZJs1qOPPirY29sL9vb2xu0ZGBgolJeXK12azdmyZYuQkJAgJCYmGrenm5ubUFJS\nonRpNuvAgQOCSqUS+vfvr3QpNqmurk7w9/cX7OzszNru3buVLs3m3L17V1i1apXg6ekpHDlyRJZ1\nsGfLSp555hkIgoB+/foBAAYMGICbN2/i9ddfV7YwG5OQkIB9+/ZhyJAhSpdi065duwYvLy9UVlai\nuLgYycnJAIDCwkJ88cUXCldnW27fvo3hw4fj1KlTOHbsGN58800AQFVVFXJzcxWuzjZdvHgR69at\nU7oMm3bkyBGsWbMG2dnZxnb58mUsXbpU6dJsil6vx8yZM/Hmm2/i4MGDeOCBB2RZD8OWFeTm5uLC\nhQtQqVRwcnICAKhUKgDAp59+qmRpNsfe3h4A4OPjo3Alti0oKAjPP/88nJyc4OXlheeffx6A+L4M\nCgpSuDrb4unpiRkzZhjvjxgxAgAwbtw4DB8+XKmybFZFRQU2btyIJUuWKF2KTUtPT8e2bdsQHx+P\ntWvX4tSpUwgODoZGo1G6NJuybds2nDhxAhMnTkRSUpJs62HYsoLz588bl9VqtdnXsrOzO7scIjg6\nOprdr62tBQCEh4cjOjpaiZK6hbKyMjz55JNwdnbG1q1blS7HJj3++OPYvn07XF1dlS7FZt24cQPH\njh2DVqtFUVERjh07hmXLliE+Ph5lZWVKl2dpxCCkAAAHLUlEQVQzampqsGPHDgBiD/awYcMQEhKC\nJ554AlVVVVZdF8OWFZSWlgIABEEw9mhJbt++rURJRGaOHj0KR0dHvPXWW0qXYrMuX76MadOmISMj\nA9XV1Zg0aRK+/vprpcuyKS+99BKmTZuGQYMGKV2KTdPpdHjjjTewZcsWzJ071/jh6vTp03jiiScU\nrs52nDlzBiUlJQCA5557DidOnIBer8eOHTuwZs0aq66LYcsK3N3dAaBR0AIADw+Pzi6HyExxcTF2\n796Nt99+GzExMUqXY7PCwsLwzTff4ODBg3B2dkZtba3xUzG17Msvv0RBQQHmzp2rdCk2Lzg4GEuX\nLsXGjRtx8OBB3Lhxw3hY9siRI8oWZ0NycnIAiPtuV1dX+Pn54aGHHgIAHDhwAHq93mrrYtiygsGD\nBxuXDQZDk18j6mwGgwGPPPII/vznP+PBBx8EII6ZofabO3cuNm3aBACorq5WuBrb8fbbb+O//uu/\njFMUbNmyBQBw/fp1Tv/QQd7e3khPT0dcXBwcHByULsdmeHp6AhCPSt26dQuAeHIbAGi1WqsekmXY\nsoLQ0FAMHDgQgiCgsrLS7GvSWWBESnj66acRExODiIgInD9/HqdOncLTTz+tdFk2xWAwGA81SKS/\nazkH1HY3ERERSElJMbawsDAAgLOzMyZPnqxwdbbn8uXL0Gq1Zo/FxcUhNTVVoYpsT3x8PJydnQHA\neGaxFFYDAwPh6+trtXUxbFnJCy+8AKB+QHxeXh6CgoKwcuVKJcuyWdJkcladVO4e8+abb+I///M/\nsWnTJgwdOhTDhg3D+PHjOTC5jZ544gn4+/vj97//vfH9+PXXX2PSpElYvXq1wtXZjvXr1+PIkSPG\nNn/+fABAQEAA9uzZo3B1tuXo0aMYNGgQQkJC8MEHHwAQxw7/+OOP2L59u8LV2Q43Nzds3rwZAHDi\nxAkA4r4bADZu3GjVddlvltZEHXLfffchNDQUe/fuxZdffgmDwYCPP/4Y/v7+SpdmUzIzM3Hw4EHs\n378fBoMBRUVF8PT0hK+vL7y8vJQuz2YcPXoUixYtAiCORzBtjz32GO6//36FK7Qdzs7OOHfuHD75\n5BPs3bsXP/zwA7y8vLBjxw7jVCXUdhkZGcjIyICnpyfWr1+vdDk2xd/fHzdu3EB2djYOHDiA48eP\no6ysDC+++CLHCbdRfHw8evXqhc8++wxnzpzBv/71Lzz77LNYvny5VdejEgRBsOpPJCIiIiIjHkYk\nIiIikhHDFhEREZGMGLaIiIiIZMSwRURERCQjhi0iIiIiGTFsEREREcmIYYuIiIhIRgxbRERERDJi\n2CIiIiKSEcMWERERkYwYtoiIiIhkxLBFREREJCOGLSIiIiIZMWwRERERyYhhi4iIiEhGDFtERERE\nMmLYIiL6xRdffIHf/OY38PPzg52dnbG5uLigZ8+e8PLyMi7HxMTgySefxNWrV5Uum4i6OJUgCILS\nRRARdSVvv/02li5dary/ZMkSpKenAwB+/vlnbNq0Ce+++y4AwNHREe+//z5mzZqlSK1E1PWxZ4uI\nqIHevXs3+bXg4GCkp6djyJAhAIDa2lr86le/Qn5+fmeVR0Q2hmGLiKgBtVrd7Nft7Owwc+ZM4/2q\nqirs27dP7rKIyEYxbBERtUPD3q/r168rUwgRdXkMW0RE7VBSUmJ2PygoSKFKiKirY9giImojvV6P\nDz74wHjfyckJCxcuVLAiIurKGLaIiFognbRtMBhw4cIFzJ8/H+fOnQMAeHh44MCBA+jXr5+CFRJR\nV9b8KFAiIsKhQ4fw+eefo7CwEKaz5WzevBmrVq1CQECAgtURUVfHni0iohbMnTsX2dnZ6NOnj9nj\nd+7cYdAiohYxbBERtYKbmxv27Nlj9tjLL7+ML7/8UpmCiMhmMGwREbVSYmKi2czygiBg8eLFKC8v\nV7AqIurqGLaIiNrgL3/5i9k0D7m5uVi7dq2CFRFRV8ewRUTUBj169MDu3bvNHtu/fz8OHTqkUEVE\n1NUxbBERNVBdXW12v6amxux+SkoKFixYYPbY6tWrkZeXJ3ttRGR7GLaIiEwYDAZ88sknZo999dVX\njS40vWPHDvj7+xvvl5aWYs6cOY1mliciYtgiIvrF1q1b4enpiddeew0qlcrY8vLy0LdvX0RGRhqf\n6+3tjV27dgGA8XmnT59G7969cf78eaV+BSLqglSC6Qx9RERERGRV7NkiIiIikhHDFhEREZGMGLaI\niIiIZMSwRURERCQjhi0iIiIiGTFsEREREcmIYYuIiIhIRgxbRERERDJi2CIiIiKSEcMWERERkYwY\ntoiIiIhkxLBFREREJCOGLSIiIiIZMWwRERERyYhhi4iIiEhGDFtEREREMmLYIiIiIpIRwxYRERGR\njBi2iIiIiGTEsEVEREQkI4YtIiIiIhkxbBERERHJiGGLiIiISEYMW0REREQy+v/GOP7zPiGHtQAA\nAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(y_osc[:,0], y_osc[:,1])\n", "R, C = meshgrid(arange(0, 6., .4), arange(0, 2.1, 0.2))\n", "dy = RM(array([R, C]), 0, *pars)\n", "quiver(R, C, dy[0,:], dy[1,:], scale_units='xy', angles='xy')\n", "xlabel('R')\n", "ylabel('C')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The bifurcation diagram\n", "\n", "We have seen the solutions for two values of $K$, $10$ and $15$, so we want to plot those as a function of $K$. In the second case, there are oscilations, so instead of taking all of the solution, we just pick the minimum and maximum of the solution (after a long time). When the solution is a fixed point, the minimum and maximum should coincide." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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eBi1cmKz58+erW7dbNGNGgqKjo72aGdVnlXXQTF9mQ5I2bNigESNGKCcnp8Lz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\nAMAXVDRxoFZOErCK1NRUbd6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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(10., y[-500:,0].min(), 'og')\n", "plot(10., y[-500:,0].max(), 'og')\n", "plot(10., y[-500:,1].min(), 'ob')\n", "plot(10., y[-500:,1].max(), 'ob')\n", "plot(15., y_osc[-500:,0].min(), 'og')\n", "plot(15., y_osc[-500:,0].max(), 'og')\n", "plot(15., y_osc[-500:,1].min(), 'ob')\n", "plot(15., y_osc[-500:,1].max(), 'ob')\n", "xlim((0, 20))\n", "yscale('log')\n", "xlabel('K')\n", "ylabel('min / max population')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is a very poor bifurcation diagram: it has only two points in $K$! Let's try with many values of $K$.\n", "\n", "What happens when we change the carrying capacity $K$ from very small values up to very large values? For very small values, the resource is not going to sustain the consumer population, but for larger values ok $K$, both species should be benefited... right?" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "## this block calculates solutions for many K's, it should take some time\n", "# empty lists to append the values later\n", "ymin = []\n", "ymax = []\n", "KK = arange(.5, 25, .5)\n", "t = arange(0, 6000, 1.)\n", "# loop over the values of K (KK)\n", "for K in KK:\n", " # redefine the parameters using the new K\n", " pars = (1., K, 1., 0.1, 0.1, 0.1)\n", " # integrate again the equation, with new parameters\n", " y = odeint(RM, y0, t, pars)\n", " # calculate the minimum and maximum of the populations, but\n", " # only for the last 1000 steps (the long-term solution),\n", " # appending the result to the list\n", " # question: is 1000 enough? When it wouldn't be?\n", " ymin.append(y[-1000:,:].min(axis=0))\n", " ymax.append(y[-1000:,:].max(axis=0))\n", "# convert the lists into arrays\n", "ymin = array(ymin)\n", "ymax = array(ymax)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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1IKenp2ZhCFEjebh4sP7R9Qz4fAA/nf2JjPwM+nzWh2VDlvFI+0eq9Z6entC5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OAAAI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\nBSPNJwAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# and now, we plot the bifurcation diagram\n", "plot(KK, ymin[:,0], 'g', label='resource')\n", "plot(KK, ymax[:,0], 'g')\n", "plot(KK, ymin[:,1], 'b', label='consumer')\n", "plot(KK, ymax[:,1], 'b')\n", "xlabel('$K$')\n", "ylabel('min/max populations')\n", "legend(loc='best')\n", "# use a log scale in the y-axis\n", "yscale('log')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Well, the first prediction was OK (notice that the plot above uses a log scale), but for high $K$, the minima of the oscillation go to very low values, so that the populations have a high risk of extinction. This phenomenon is the so-called **paradox of enrichment**.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Consumer-resource dynamics in a seasonal environment\n", "\n", "A special type of bifurcation diagram can be used when we have parameters that oscilate with time, and we want to see how this interacts with the system. Let's consider the Rosenzweig-MacArthur equations again, but now we make $r$, the growth rate of the prey, oscilate sinusoidally in time:\n", "\n", "$$ \\begin{aligned}\n", "\\frac{dR}{dt} &= r(t) R \\left( 1 - \\frac{R}{K} \\right) - \\frac{a R C}{1+ahR} \\\\\n", "\\frac{dC}{dt} &= \\frac{e a R C}{1+ahR} - d C \\\\\n", "r(t) &= r_0 (1+\\alpha \\sin(2\\pi t/T))\n", "\\end{aligned} $$\n", "\n", "We integrate this in the usual manner:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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S14cOAZ9+yr9++231JxejAwXU+q0FmrVpaPCduuPAAfP2/vUv8fULL/iWZI3A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7TxvMz2BcyPnSpeqb/tc3rsAOV70JPsMdXC6blhpYUUz03b/N5Xsx82z/FIC9LCAeNBCzf9+0hB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\nTze+5TNob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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def RM_season(y, t, r, alpha, T, K, a, h, e, d):\n", " # in this function, `t` appears explicitly\n", " return array([ y[0] * ( r * (1+alpha*sin(2*pi*t/T)) *\n", " (1-y[0]/K) - a*y[1]/(1+a*h*y[0]) ),\n", " y[1] * (e*a*y[0]/(1+a*h*y[0]) - d) ])\n", "\n", "t = arange(0, 2000, 1.)\n", "y0 = [1., 1.]\n", "pars = (1., 0.1, 80., 10., 1., 0.1, 0.1, 0.1)\n", "y = odeint(RM_season, y0, t, pars)\n", "plot(t, y)\n", "xlabel('time')\n", "ylabel('population')\n", "legend(['resource', 'consumer'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that, even with small $K$, the solutions oscilate due to the oscilation of $r(t)$.\n", "\n", "Now we use a tool that is an all-time favorite of physicists: the resonance diagram. It works exactly as a bifurcation diagram, but the parameter that is changed is the period (or frequency) of the external oscilation." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "ymin = []\n", "ymax = []\n", "t = arange(0, 6000, 1.) # times\n", "TT = arange(1, 80, 2) # periods\n", "for T in TT:\n", " pars = (1., 0.1, T, 10., 1., 0.1, 0.1, 0.1)\n", " y = odeint(RM_season, y0, t, pars)\n", " ymin.append(y[-1000:,:].min(axis=0))\n", " ymax.append(y[-1000:,:].max(axis=0))\n", "ymin = array(ymin)\n", "ymax = array(ymax)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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vazHBGQDMfXgu5vedDwBQMRUmfz8ZF+9fNHOpCCGkdTF6gLZ48WJ8//33+Oef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\nI9JstedzUijq3ioUQEmpCpkFhcgsKEJ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8ELfybhn9+dbWwIIFwPXrwJw5ldNv3LkjLBs1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(TT, ymin[:,0], 'g', label='resource')\n", "plot(TT, ymax[:,0], 'g')\n", "plot(TT, ymin[:,1], 'b', label='consumer')\n", "plot(TT, ymax[:,1], 'b')\n", "xlabel('$T$')\n", "ylabel('min/max populations')\n", "legend(loc='best')\n", "yscale('log')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see a strong peak! (remember that this is a log scale). The frequency at which this peak occurs is the **resonant frequency** of the system, and is related to the natural frequency of the system (that exists even when it goes to a fixed point with constant parameters!). The external oscilation excites the natural frequency and drives large amplitude cycles, just like when we push a seesaw (ou gangorra, o balancín)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What if I really want to explore a 10-dimensional parameter space?\n", "\n", "First: good luck. Second, you will probably have to sample the space, rather than go through the whole thing. The recommended method to do it is using so-called [Latin Hypercube samples](http://en.wikipedia.org/wiki/Latin_hypercube_sampling), that uses a random sampling while ensuring a roughly regularly-spaced distribution. Notice, though, that this method is a way to sample the parameter space and do useful statistics with it, so the result will only make sense if you know how to properly interpret the outcomes. That said, there are implementations for both R and python:\n", "\n", "* [R-Cran pse: Parameter space exploration](http://cran.r-project.org/web/packages/pse/)\n", "* [PyDOE: design of experiments for Python](http://pythonhosted.org/pyDOE/randomized.html)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.5" } }, "nbformat": 4, "nbformat_minor": 1 }