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@ravy101
Created March 19, 2019 09:28
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Created on Cognitive Class Labs
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{
"cells": [
{
"cell_type": "code",
"execution_count": 60,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import matplotlib.patches as mpatches\n",
"import math"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# The Question\n",
"\n",
"**Consider an equilateral triangle inscribed in a circle. Suppose a chord of the circle is chosen at random. What is the probability that the chord is longer than a side of the triangle?**\n",
"\n",
"Lets start by creating a plot of the problem that we can re-use.\n"
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7f711c7580b8>"
]
},
"execution_count": 61,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"\n",
"def draw_question(cent, rad, poly_sides = 1):\n",
" fig=plt.figure()\n",
" ax=fig.add_subplot(1,1,1)\n",
" ax.set_aspect('equal')\n",
" top_point = (cent[0], cent[1] + rad)\n",
" plt.plot([0,2.4*rad],[2.4*rad,2.4*rad], color=\"white\", alpha=0)\n",
" plt.plot([2.4*rad,0],[0,0], color=\"white\", alpha=0)\n",
" centreCircle = mpatches.Circle(cent,rad,color=\"red\",fill=False)\n",
"\n",
" centreSpot = mpatches.Circle(top_point,0.8,color=\"blue\")\n",
" poly = mpatches.RegularPolygon(cent, poly_sides, radius=rad, fill=False)\n",
"#Draw the circles to our plot\n",
" ax.add_patch(centreCircle)\n",
" ax.add_patch(centreSpot)\n",
" ax.add_patch(poly)\n",
" return ax\n",
"radius = 40\n",
"centre = (1.2*radius,1.2*radius)\n",
"n = 3\n",
"draw_question(centre, radius, n)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Interpretation\n",
"\n",
"We will consider for the sake of this experiment that the randomly selected chord is line connecting 2 randomly selected points lying on the circumference of the circle, point 1 and point 2 are independent, and all points on the circle are equally likely."
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.patches.Circle at 0x7f711797c7f0>"
]
},
"execution_count": 62,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ax = draw_question(centre, radius)\n",
"plt.plot([centre[0]+radius, centre[1]], [centre[0], centre[1] + radius], color=\"blue\")\n",
"ax.add_patch(mpatches.Circle((centre[0]+radius, centre[1]),0.8,color=\"blue\"))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## By Intuition\n",
"We can see that our triangle divides the circumference of the circle into 3 even arcs. If for the sake of visualization we assume that our first point lies at one of the vertex of the triangle, we can see that if the second point lands in either of the 2 adjacent arcs, a line connecting the points will be shorter than the nearby triangle side. If the point lands in the arc opposite our first point, the line will be longer than the sides of the triangle. Meaning that a line connecting the first point to the second will be longer than the sides of the triangle if the second point lies in 1 out of 3 equal arcs. If all points are equally likely, then the probability of this is 1/3.\n",
"\n",
"Since we are working with a circle, the selection of the first point is arbitrary and the probability of the distance between point one and point two is 1/3 regardless of the selection of point 1.\n",
"\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f711cc9d160>]"
]
},
"execution_count": 63,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ax = draw_question(centre, radius, n)\n",
"plt.plot([centre[0], centre[1] + radius], [centre[0] + radius, centre[1]], color=\"red\")\n",
"plt.plot([centre[0], centre[1] - radius], [centre[0] + radius, centre[1]], color=\"red\")\n",
"plt.plot([centre[0], centre[1]], [centre[0] - radius, centre[1]+radius], color=\"green\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Visualizing\n",
"\n",
"We have our circle and triangle, we know that the circumradius of the triangle is equal to the radius of the circle, we will call this r.\n",
"\n",
"We can calculate the length of a side of a regular polygon by 2r * sin(pi/n) where n is the number of sides of the polygon.\n"
]
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {},
"outputs": [],
"source": [
"#with a triangle we have 3 sides\n",
"n = 3\n",
"def calc_crit_len(rad, poly_sides):\n",
" return 2* rad * math.sin(math.pi/poly_sides)\n",
"critical_length = calc_crit_len(radius, n)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So we have the length of our triangle sides, that is our critical distance. Lets visualise our circle as before, and overlay a circle with radius equal to the length of the triangle sides indicating every point that is closer to point 1 than our critical distance."
]
},
{
"cell_type": "code",
"execution_count": 65,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.patches.Circle at 0x7f7117a17e10>"
]
},
"execution_count": 65,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ax = draw_question(centre, radius, n)\n",
"critical_circle = mpatches.Circle((centre[0], centre[1] + radius),critical_length,color=\"yellow\",fill=True, alpha=.5)\n",
"ax.add_patch(critical_circle)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here we can see that 2/3 of the circumference is within the critical distance to the first point (the area covered by the yellow circle) and 1/3 of the circumference is outside of the critical distance (not covered by the yellow circle). This confirms our intuition."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Experiment\n",
"Now we will randomly generate pairs of point and compare the chord they form to our calculated critical length. To do this we will randomly generate pairs continuous variable between 0 and 2 * pi, then map these to points on our circle's circumference.\n"
]
},
{
"cell_type": "code",
"execution_count": 66,
"metadata": {},
"outputs": [],
"source": [
"import random\n",
"def RandPoints(r,n=100):\n",
" points = [(random.uniform(0, 2*math.pi), random.uniform(0, 2*math.pi)) for x in range(0,n)] \n",
" return [[(math.cos(p[0])*r,math.sin(p[0])*r),(math.cos(p[1])*r,math.sin(p[1])*r)] for p in points]\n",
"\n",
"#generate pairs of points\n",
"sample_size = 200\n",
"points = RandPoints(radius,sample_size)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lets sanity check our data by plotting the points to make sure they are on a circle."
]
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig=plt.figure()\n",
"ax=fig.add_subplot(1,1,1)\n",
"ax.set_aspect('equal')\n",
"for p in points:\n",
" plt.scatter(p[0][0], p[0][1])\n",
" plt.scatter(p[1][0], p[1][1])\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Our points look good, lets create a function to calculate the straight line distance between 2 points, ie the length of the chord."
]
},
{
"cell_type": "code",
"execution_count": 68,
"metadata": {},
"outputs": [],
"source": [
"def chord_len(p1, p2):\n",
" return math.sqrt((p1[0] - p2[0])**2 + (p1[1] - p2[1])**2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lets now use our points and our distance function to see how many of our pairs of points form a chord longer than the critical value for this triangle. We will save this function to re-use later."
]
},
{
"cell_type": "code",
"execution_count": 69,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Radius: 40, Sides of polygon: 3, Critical Length: 69.28203230275508\n",
"Total chords: 200, Number of Chords Longer than critical length: 74\n",
"Experimental probability estimate: 0.37\n",
"Expected probability: 0.3333333333333333\n"
]
},
{
"data": {
"image/png": 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vtGMH/PSTURB6Gle+Nz+4Rq3TcOrGKfaczlW+/nThJ6aUHUBNr2KcSDpDh/tOkGY3QUNXvLJwZuTVV2CzQWKiUfo5nbBundnPQVqa0XGsX290DFWrwnPPwZw58M03RqmYkmIcnC5dIuHyKV6qBwcjLHN9jqejZcEnnxDV+3kATu3bbHQXS5bAlCmweDHUqUPKrev4lC5nnKZiY02bwOgcFi0yvgjXr0NkJDtSjoPgesp1VndfTbVC1QDYe2kvB68cpHO1x0kaORSWL2fh+I4E5Y9i3IyfqHs8i587NPyHbtHro2FkQ7Of4QHdA9cSPvV/LEfD3VCNP2r7b+AQFu1e5Ppy3/MUeroFSvA1X565VYz/wL5wdMsTte6KNk7JK7PO2zFPONCP537MPZmaauT6Fi10JhD5jTScRk49K6r6SaDvolDYUFSjN5rySFFteOR+zavy6zqLPF/7KlWkZ54xnEHdutK1a3f3wJmZ2v/y88Jhnu9S3KtScrK0bp00apRUrZpOB5p2xlXH+D+MGmXEk5UrpeBgVR5g10Ov15befde0Z/bsvHWkpkotW+qCv/HLsMah72sUMGVkY8y6MbKNt2nejnkqOCVcOwugm+H5lJ5wOW9Z/fr9aj8Ue8aUXfsJ9EgHIz5kgU4E3fme/tOAW2T4g5HtVxA9OHuijkOlnja/gS+gkY3QoRAjy2ZYaF5l1OshtGP+ZGnPHunqVcnp1OWky7KPt2vkmpF5y8/IkL7/XnrmGb3RxCgSm3ZDr9ZC3xRDzsBAOW9zCMrZUuy/MPhLlZJ27TJy+tatUufORnSwLOOItHbt3T3zvn3SffdpY5R55pBh6P2d799xWebVBHk47BrRNSJvO4KCpObNVXaQhx7uhDRlilFYBgVJ587lKeNSwimVH+ovayyq1Qsj8nh5SbNmyZmVpZJvlFTkK5HCgarOrqrDqz4wz9S//y+3vXjxPG3ZHWHeVcmBaGckqvgU+lvh3P+TPK3/aIcmN0H4A7FxSj+lZisJCz+LbGORzwgU9ALyGGPO4TBedFPuR+f8fuVL7esrlSihfSUCtbG0r5z16xutfViYGdzZ12VaqHoflP95dM7fOOUcDDVf+hU1AtXuYfRxeTSr6m1Ewc8vb12xsdKtW7kPMWOGOe/paQhDu3bS5s2//MAZGdLkyWZChoVpxZwhLoVnn8/6/OItMTNi1G1ZN+nIEaObsCxTV2CgogejHu2y21W4sCFKbdq47r2SdEWV4irJe6K3fMbYNLgF5v7775dAX3WsLBzINt6mSRsmKT0z3dw4eLC57vvv72xQ//7mv/BwOUFvVzPvqMHj5v0xDo1umPf9nAhCFQZ5/Uc6NLkJwh+EA10a51FWnQlAH99jJulFf1S3pxlowcPRvX3NfsykCD31Ym090QYtqB+k1aXsulUqxnju3Tbxf3XLl087ahYR41DYSA/Zx5gBvLAi+rGAqWNbwWyvR29U6Sl0sXCw9PXX0ltv5SoIQ0OlFSsMdxIZKVWvbr7MY8aYtoARHz77TMrKMg+8Z4+5DszEvnDBJeY8sOABlX2r7C/2U/359VXv3Xq5J/bskdq3l0D5h1rqO7CYsWjc/pxFi+rqM31U9eXi8p7orfjd8cas2ClaAmVEF9WHXcprRCMziX/4en7eShMTpagoQ1TT0vL+98EHpo6AAB0p4q+J9Yy4gAOVHoC8RxuxLqctOd6kjEP2Majfyv8sEeJuCYJbqfjvoH9/yixZiwUsqATpFhS+BVXOQrnLZiQ9cBw2zYOSV2FXQbj/tMWKNy4TN/pvvPs59Nhwg/tPZnHsxgmuplwDpxOnrw/fF4X1j9WDTZtg1y4TeDRvnnEMatyYqgnelEmABK9MxnwHWPBYB9gUBa9+ZSIgAarGGkXmF8Uyub5tY64Dzj33GAVgu3bG8SghwSgNCxY04c2nTsHrr8Pp0/DQQ1C+PLRvD1WqmEzMS5bA0qWQPz8JKcbTsWF0Qw5eOcjlpMt3dFVUUBSnbtwWXFWhggla2rqVVG87PoePw7VrMHCgUTxaFjeuX6B56jz23DrGJwvTKTRsIgCl2z5JYtH8eJw8TfLh/cxvGEijs17c17Y/vPdebh0BASYX4/79MHVq3gbVrWt+b91i1H1JjGls8jku+wiOh0KvH8E/w1yyqgREDIW4arg8mpLnxv13hlffDdX4o7b/OA7BbleOqSrTylXe/ZJ5K83D0tyqRoywjUOPPJFP3dobJWDRwShyhIfyOby0bfV8KTNTDeY3ULmZ5Uw96enSmjXG2adwYeUoAgf3LiocyO6wqfCkMHmP99RzTXC16Zyf+eqNbISSPP4J1wFSzZpG4Td7tlH4/fST4RgmT86NJ/D1NRzE9euubhj29TB5T/TWppObhAMtP7D8jq4auWak7OPtysjKuOM/r4leeuHdR10igKKidLNwuGr3Qh5jLX368YvSmDGa3bm4cBjWPdlufDlyOKLZa14y+geQevUyis0cPPywEW8OHnSdSs9M14wmxpw7rAmaWgd9tHisuj1XTB5j0LGg3H4JeMFwBk89iKr2Mvu3PNHAFvzH6BVwcwi/D+L3xBMzIwbbeBvO7JBcG2DPtmcJuOUJqTk9m22C8wqNoNePcHwG9N8Ki4sm8mV5T/KlQUCxMlzyziTF5qTB9gFsv/ATXYs/RKkN+7n+cDvInx+aNIF334UaNcxX8NIlivceCkAWTtI9baQpg4BsF+BhTWDhsCaEWX5cC/JifwQUHwSNH4fToXYTz/Doo66vMQBbtxq35759oXVrww0UKgQjRxpTZJEixjQ4caJpU5s2sGwZVy4eI8w3lOqFquNt92bjyY139FtUUBRZyuJ84vk8551ykp6Vjk+x0rBxI3zxBUkRQbRqdoWtheGjj8VDs9ai55/n83blABjUxs7eDvdjL16CpeVMboj2XScYt+nmzY1rda1a8PPPppIZM0w4drZJ8/tT31N1TlUG103kQDj0OBPO0M1Q+YoHn4RcoHvBZhQjiMu+5nYvJ7Q9COmesOVdeO1Lwz0M+RtkPt6dTS/993AK7nwI/wL6f9Gft7e/jbKt2Rf98+b/s2EyEOfLgARf8E4BS9mU4soVrMhIfCZP4OKthTivf09gSCFOeJwkf/p1pjaZyjs75nLo2mFqza3By+s8WL4RUvN9De07G9a+eXMzsLNRJNCkUi6arygXrp+m5VF4tQ7UOwnT7odgn+0UDIjmUsdSVK9Ymc/ef5UmnZKpFgvffHyQez/I9mXo1MnEDMybZ4iD02mCmI4dgzNnTNxB+fLG7+DsWbh508RBrFwJK1eS0BXCQsA7siD7/exc/GgeLL5m4hmyt2hPw3+fun6CokFFXc+QlmkSafl4+IBlkdy0IW0uh/P9CYsPNkbS8cBFdGA9l4vnZ31sKr7+vkyevp1yEeWQxJLx4TQ6dpWIa2mGoF24YAreu9eIJX36wIgR8MorJDzTh+HTGvBO8iYi/SNd7/C+41dJ9rJYcOpTUn1TeaHzG5xrlsKrA6oyfbWIuQabixrfEZtg0DZTRdQN886rjI1jE1D3hf/8VPFuDuEuseml/ny2Ls5FDDwzzWD6e0cXr2yfmtAU2BMJ49vkY2NOCvQePfDt1ZeFA9bS4Z4OnLxxkjJWJEnXLzFszTDqrD/Ci2vAEjzfOJPwMV5UGp8fLVhg5He/vOmIiwQWwZ4Fs74w6yPc8oJUO3w8rhPtyrbjeup1ztw8w/nUKzB+PBV2nGaj11P4pDtp2OkWW4oAkZFGlp87FypWhODslEMbNpjJP2iQmVxLlhgHpkOHTDKV69dh9Wpo25YEf8skRgkKwgoJw+PqTZxfrYLJk026toceIurxgQCcatvQZE6uXRs6dSJ16GAAfHftI3Xtatq924xvT3zLe+3fp8uq0xzu0hgLiExIJeomNHcWp1yE4RR2XtjJEesqXVKKG+Y+KQmWL4fZs6FlS3Nu1ixUtCgLlo6mzCAbC25tYlCpx/Dz9KO4fxHuvQC+aU6OFQ9lpudOOpfvTLhfOM1Wd+dCkJkeMTfgljfEfW7ed04A2tpikORpuIWYqXN+g1H258NNEO4G8fFUHfs25/IBgpKXISADWj4G+/9uKYmcwWLFxZG5cwfLHoxmaHPA6SSpilmnxvvoCT4+Wo2j8REcHHeJc6+IQXsDWHivxSstAhhW7wUCvQK5Zs/gyM0TVJ1dlTXH1iDlJT9FfCL5YBm0Xnea5zbDhhhoWrAO804u59naz2JhkZieyI7zO7iUdAlCQyk1KY6N/bYSlm6nyWPwnd8lwyEMHWom+e0Zkry8jGKxYUOjmHM9pAVBQdCsGaxYwZVKJQkvVg4SEym29zQZdtgz9injzXjmDGzZQtFZxtvvVOv6JkrS3x/27SNlsTlvX7CQDvNb8M2F73lnhXi0/gBOFw/j+La1XAr2JNNucTQESm/YZ/JBrl7Nkr0fYbfstB/3ofHmzMoyYeX33WfyQCYmsv+J1jTsCU/UvkiZK+KntyH1w4WcvHaCBQn12FrCG4APKttI9MhiUNUBtPygJYevHuaGhxEJTwXB9K+g8iWzhB1mGLCgcm76t0LXsv6/o+uvhbtRNPxR219VqZhY0ET8xbY2Ci1hzIoFnkNhw9DoVr5GkZWjnHvzTde9qekpWlnSnH+nrr8SS0TlmrKqV9eXT9RT2QGo6PSi2nVhl5q+39SYvt4o7YpkDJgcYGzk8xto48mNpuDkZDnL3SOBTgQaBVvUuEBFvhKpgEkBavdROzV+r7H8J/kLByr5Rkkdu3rM3BsXp3MBqNyEAvIZZ9fqMh7GJm9ZxuehefO8SUk8PIw5dMQIKSnpjv6JmBqhvp/3lZKSlDzjVR0Nyb6vdGlp7lwpJUWSFPJSiPqvzOsodPTqUeFAlWfcIxzo7Td76qdBD2tOHW+tKGfTuXJF5SxQQMeCjfJwXpVcxW3xZ1DzJ72MMjTHZOnnJ+XLp+TZM/XC4j7ymOCh0IkBmlfHV1khwdreqopwoOe7hkkeHhrQEm0phEKHo5aPokYvlZN9vF1Rr0Xpob5BEqhhD7ThtWdd5tocpXFO1iphEtT8lYFbqfjvI35PPOFTwwmMTaDos1DyCqRkfxFKJsCG+ZBmhxk1RdaH2f7unTrB00+b5CLr1+P93DBaHTF/Pb45ia1Zp/gotg63Du/H2raNB9/dQGiVOpy+eZpnVz/Lsi7L+KTLJ6RlpXEz/SYWFinpKYxrMI5DCYeoN78e7ec24WaZGKz9B1h6j1kHYXGzwgQXiOFK8hXKR5ZnxcEV1ChUg6QMo+S4knSF+9+9nz171sDw4RSs2Yjvhuzm4eTiRCdkmmFtWXDjhsmXuGsXvPkmhIWZZ3E6TfxBTIxJxJoNp5xcTblKmG8Y+PnhO+g5Hn6xMhP7lzcKyz59zD1TplDeoxAnb+Rdqi8xzeRg33n9AJMaTWJV+DWqhCxm/pNVKfvdfgruO4V1/jw/DzdrBZfqHAvdu/NjQTgWCl1+SjdcSFqaidFITiY1OZFbzw7gk41z6b4jk4Nvil4XC0FGJtW++Imdb1tMXp0Js2dzLtKPeVXhqq8Rudal7qftIYtTN05x3ZkMQGC6jWoDXoS0NI60rkMmhkMIzA4RSfKEE8Nif+vh9+fgbqjGH7X9lTiEfiv7yXJYrngBHOjR9uZrkJjtsPJOZfT4x920qnKABMr09JCWLJF69szNI5DzpY2MVMqFMxr29TDZxtsU/Vq01hxdI0n62+m/uTzt7pt7n64kXVFSepLGrR8n+3i7K+/B7gu79caXDm0tbCnDQu9XNOHSO0oH6tmVA+U3yU8Dvxwoy2EpfGq4asypIZvDhEmvO7ZOhacVVvBoT20s6SXt3i09+6yclqXzoV5q/rhNC9fNkJ56ynwJvbykgQOls2dNWrUcD8YcrqFECWnVKl1NvmryE2ye7uq7Z758Rn6T/JSekWbcoJs3l0DJPnYtaBwunTolScrIynBxRA3mN1DISyHyedFH0zZPU2ZWZp738ebmGcKBzhePlK5f1/B3HpHHGJQQ6Gna5ump04+2VocuJs3c5QCbUoMDpGHDTIxGx446XDJMN2/7qguU4oEKPme4PRxoVAtPeY1BdXpZerOGuSbJyzI3PQbPAAAgAElEQVRp5d56S/GfT1bVWJRkz825sOvJVqaRixaZnI1/wdyNuD0V//9YtHvRHcSg+ECU6GHs+U4Mm/nZxMfyJB2Jq4ZWlMH44nfrJi1dKh0/bv6vVctV/uZTm1X6zdKuXAY3U2+q1BulVGFWBXlP9NY9b92j0zdOS5K+Pf6tqw3eDg99Xs5DTtCK8h46EWTyCsaM9NeUjVOEA205s0WFpxVWkelFhAOVeqOUcKDtZ7fr5OI5KvM0atzTrsTogqZd/fop8co5NXqvkSyHpdnbZ5s29+5t/Cx8fKRnn5W2bDFeiyAFBrqe+XBZEz/w3sa3XM/38b6PhQP9cPqH3E7duVNbG5Y2eSA8PJT5eHd1e6dVnj6u804dHbpy6BffycAvBypgop+cNkvOfk+p2IxiajG3gVStmjJsaHrnIgoYgXxHoSl1UfqMaYYoR0VJJ05o8d7FwoEmfjdRWrhQstuVbEctHs2t39HUS/V62xU0wtL+sLyE4/Yt3W7JWaBAbn5IkLp3l7y99UkZVGJgdt7GwWhR13K/wwj91+EmCP8Gol+LzjNQbdmRhWUHGBk20QPlfw4dLhHiGhBOUNPBYbI7bIr/8b3cwlauNNe0bJmnjuT0ZA35aogsh6ViM4rpiRVPCAdavHex8k3Op6jXolyTo9rsaqo9IlLRg0w7Wj7prWPByGmz6cmR5V3cBQ706vev6pP9nwgHinwlUmEvh5msx2vGSwULKjnCtPloCFo1Z1ie9rSKb5X3a3/kiOF2bDbjkPTcc9LYsYZ7CA2VihbVD4VNm1aWtZk8B198oQvXzggHeuX7V/I889RNUxU1GCUP6KueHQ3n0+wxQ3ifXjngDq7gdjRf2FxVZ1eVBg3StkK4kqT87ci3uneEyZTUcmCYjj1suBHZbFKfPlJwsDJiolVhRLBqzq2Z6xi1ZYsOhxqXchxoUGu74poGu9557Gex2rR5sQQ61r21FB+vTZ3u0/polBYZ5nJK+6VtdhWU7wVTjt/Iv0ZehbslCG4dwt8jPp5T13PlXEtmsZOFy8wiKL3bQulBUO8UhJ+9Ztx+ASsmhmUvHadudD26f9aTuTvmmgK2bDG/gYF5qvH19GVa82lseGIDNsvG/J3zAThw5QDf9vyWlIwU6r5blx/P/8io08XZ8NIl9s2EUgkWawqlUW4AjJ/cjDItHwegX/V+AAz9Zihf/PwFTYo34UbqDZdb8bl334Dz5/G9fI30Af0YPLURD56byivfv+JqzycPf0Lncp0Z8vUQJn43ERUvDvPnw4ED0KEDTJ9utscfN45Jp09z5f7KAIQnOo1fQqtW5C9fk7c3hXB0y6o8zxwVFMWpYOhc5wwLKmZR7wQ8sdsMwR6vr8e+fIVr/YW/x+GrhykVWgomTmRJrQA8nbDp6HrqLHqAK+F+LAvoxcq46xTbecI4TjmdMHcuknCePc0nc26wqNYreNiMEii1aiXKP21x3RcaH4Xnv8tieLXreGVCpYCSzGgxg/VJewEoUPJezrSuT9PKu5k9rSteF68YC8r338Po0XlWuvo5FCY3gEbHjWk62QtGaa1xLPtPwN1QjT9q+zM5hNszHOUEC+V8kT8ul8sFLC2D6vfzNSz8aDTkqWI6HYiRVSUlpSfpwUUPCgeatnmayTjk7W3cZ38Ft9Ju6ZkvnzGZeiZ4auOJjTp05ZCip0dpSkNPOTGu0Z8/Xkt7apr66vbxEA4UMTVCONDO8ztV5e0qKjytsLwmeslzgqc8JngoaHKgAkagm14oKyhI2rBBkpSWmaaHP37YaNxXPy9ndjqzjKwM9VjeQzjQsK+Huc5LMuHODz+cKzbUqaP37jV9dLjbg0Z2DgqSqlRRps3oG5z332/WYbh5U5tObHJ9gT3Ge+i1za9p8Y6FwoH2VMteJ6JkSSkuLo/rcVpmmmzjbRqzboyysrKUf0KgWj6KRja2NOSrIbqZetNc+N13JkgrXz6pcWPJbteFCsVd704FCxqdiKTnV5scDn5j7Er3sNTuYeQzCjXogX5+fawkqcn7TZRut6QRI/T48sflPdFbx68dv/MFbt0qYfQ5Mc8Yy9PqYsgag2xjblsbovGfxyngFhnuHot2L5LfeC/hMERgei2THCPTQvcMMIumXPZB1/J56q3q5uUu6VVbgcNNohKPMejxWU21+8JuSWYAd1zc0cilzX3kDAk24cT/BENWD3FNmGGfD9LNxvVcA61DbLA6P21yLN4sml/B47xV4vUSipkRY3IAvF1VXZd2VeCUQJ24dkKxn8WqzMBcPUjT7ujTTe/mqS/LmaWnv3haOFCP5T1cYcNZzixXnsb+K/sry5mVt6G7d5t1GkDTG5h+u+qLMb1mR0Kev7ekXq6DUkuZCZnp56MWffyEAwVNCdLPV36WJC3cZQjC4UsHjc6lRg0zLCMiTH7HhAQduHxAONBLm15StdnVTP+09TO5HA8fztu206ddZWT4++nHQjYNGXqvnDlmSS8vLZ/xlKtf5q15Rcuq+AgHmlzXmJNVrZrS01PlN8lPSf7euvikIZzDVg81EZTHjhmdysqV0vz50ssv61DFQhJmPY29ESaWxAlaXvrv1qv4k+AmCP8CbtcZDG+E0iyz8o8TFF/BnF9SDmV17CiBljeL0tkbZ7SoIjoSZmlQS5v8JpnB/uCiB7Xu2DqlZ6arx4J2woGe6xQoZ8sH/2k7riZflddELzWaXFZ7IswAyrChLsOKy28k2pkfZXl7SceOafWR1fKa6KUKM01GZt8XfV0WiV0/b5R691aGDZUfYMnK1oGUfKOkriZfzVOn0+nUhG8nCAdq/UFrJaUnuc4P/Xqoi1j8UlCSfvxRo/qWkn1sdrtAqlRJGjtWmYH5lGpH23o9qC/mDleLx2wufcywTkHSiy9Kp05p7o65woHO3DiT0yDp22+NzgUkf399MqSlCeIab5f3RG/Zx9uVcHSv4VIaN3Yla3UhJUVZT/TUmIamD6+OHGKumThRa4qbfIm+o1DoGC9dOXdUIeMMQfg53HLpBlKiCuujcijTy1PX/T10Otgm5+2+GbdtG6NMEpxFFXN9FNKy82Nc8zI6pxwu5cx9f46S0U0Q/gXkWBTChpqJ06t1bvRiDpdQfoiPsiy0rW0NMQ6d3LpGmRa6HOwl1amjhOQEvfjdi66sPdVmV9OHM/vpqZamzL59C9/5pf0FjJzQUAm+ZvBc9EPFBllyvN9Lq0paygI5htZ0XfvFz1/IY7wRHQasHKC2H7YVDlRgqKX4SpacfXprS7SHGJerIA2aEqQJ307QjdQbeeqN2xYny2Hp/nfudxGN24lF5yWdlZb5dzkFJPX9vK8iJofkTmDLTCrnqFH6uLKXnKB+2X3Q7aOHFTMxXI/2y++69o3HywoHunL1zJ2dsXu3zrRvrJfrmPu/aFRERV6KVKv4bDPfzJmmnPezszRlZUkJCdKBA/poZn+172IS1wqktm31wxNN5T/a5hIF361sUqUxDpV52mSyul1JnG4ZU/LZALS/dS1p6FBp6lTDFaxcKW3Zoq83vSe/F/1U+s3SOn1o+y+mf8+w0LkAs58F2n5P8N0NzN8QboLwLyCHQxjeGA1pio4FG1+DFx4wL/HDqmYNhMUDG+ns9dOyj7dra/OKSvOyK92G0oY97yorJSNFs7fPdpn7ig221HSg0V53W9btl7+0OZg9W1k2m7JAt3xsurnuKz31SS8dDTbtmNDI4w7ZfsWBFca8OD5cKd266ofC6N4BhlOoNzhIu0oEKOqVwi6CcM9bxiMw9OVQvbzpZd1Ky82a9PG+jw3XMauCzt486zo/bfM04UCt4lspJSMlT5M7LemUmxRl82apQQPXRDgUmpsUpncblPVwFzWYXVt1361r2O6xYzW1pembWxHBJrx7+3bJ6dTZm2fVeXEn4UAFx/orZLSHfihmxJP3mkZKbdsaq0ZgoPmqR0T8Q83/nkgU8oKlYsO8VPkZL0UNRqsrGF2Q12h0pHR4nuvf6l1Jp0M9lAU6VNBLGTlZmG7DigMr5DXRSxVnVdSFxAuSpKxCxpyb7eqlTFCCt0mfl2blEoUlTQv9q8P038LdEgS3lQGY1HgSfnjS8yezuk+hRGjUA5odM/93/imDculBjC9zgQKBhegd2oTK3+whoUFNPJ3wU+l8rrJ8PHyIrRbLgQEH+GRrcfLb8vFN2HX8Mm3E74nnoQ8fckX4uZCeblZF7tsXy+lkfyQMntaUfA80J+7jZIpfhz2FPRlX18Q2T908lT6f9yHTmUnbsm2JPVuQb1+5gseHH7G7QiSFqjRgbmhP9nvdoMpjSXh5+WKzzKu+knSFrb23UrNwTYavGU6JN0rwxpY3SM1MpVO5TqzqtooT109Q5506/JxgwoeH1B7C7Naz+fLwl7T6oBW30m+5mp6QnEC4X7g5qF2b058u5LlRNTgYBkvLm6Qw3a5HMbvyaGzLVxC1ZhsnT+6Gw4fhnntIrV/H9FtwGMTFkVWjOm/U86TslMJ8tmcpE9dB6ZNJlD2fyZJS6XhlwkMbLxlvyc8/h9BQY5kICYEXXiBr+jRG9YqhU+9AEr5fA2fOcGziEJo9Bj4ZYrLng+wMTadwpi8DG6ZQIBEW+D1KiWsWt+P8+cM8OfZervlC6fPpeDzSzUR5ZuPDPR/ScUlHyoaX5emaTzN542Rqzb2PpCvnORdgYh6ueUGap4l3KXkNdhQy99qA+7ac+2smWLkbqvFHbX8kh9BvZT+XzG0fb9eQ4ZVdX4dZ1dCjne252YoffVQf7fpAONBHez7SqUdbK9WO9nVtogwben5p3zsrSE6WPDzkfGG4Nnato4f6Brm+0kWnF9Wei3vMdefP5yYGASkgQM+9/5h8XvTRjXfjlKPRv37uuEskyDcpn3Cgx+a2VOYjZoWl/QU9VL2vpYKvFlSpMcFyhoYqoUFNDVjZ/w4nq08PfCpJ2nRykxouaCgcZp2Dt7e9rbTMNG0/u10RUyMUPjVc285ucz3Swl0LZR9vV+15tXUt5ZqUmqqKr5dV27cbyvnVV1o3sZeGt/LW1Aaeeq6P4boe6WDErpznG5Wd7ixnoZoRjZHnGKSICG2tE62qA72Nf0J3dDjMku69V4XHBuixmU1U9OUCajO/mXTzpomRyFnRKWfhmC++0Lj144QDLdu/TJJ09uZZFZtRTKEjPbS3kIeaPGa0/lGvGsetVSWQWrQwokZQkKudJwNRlWf99EOlUDmLFJHsdmWWLK6Nn76lNh+0MZaSCR6uPvWb5Kc2r9eSQKea3qccsePR9mYFris+xqktvnwul1D0OdvvPs5zgFtk+HX0W9kvzwQJGYZu5OTPa9dOunlTWaHGgWdFeQ/tOrNDmVmZKjeznMrNKK0Mb0/F1wnUztKBOlg8SKXfLH1nJZs2mfKWLze5B8uX1/5L+1Xv3XquetvOqq+t94bn5lEMC5MuXtQPp3+QfQw6F5idCXnLFklGps8xK3boaum8P8qwW1r5SHWFTgjQ+zvfl+WwVLEfSvbxcC16MmjVoDzPGzk1Mo85ce2xtao9r7YRcV4tqgXLx2n/srcV82K4AhzeWjPiYemJJ6TWrbXsoVLyHIOq9LPpsh8qNAQ9+VBe9vy12kaB2KVXkNaUsOlS/tyl6OfUMRP+ZJSZfM8+V175JgVowBcDZDkMQVu8d7Gcu3dLQ4boVkGzOE1sF8PeL1z1cm4fZ2WZ/q1Z00xAm00T61vqt6CzJJOctfzM8gqYHKAt3y/R1hjP3H4Yh8ImByt9ztumbW3aGJNqtuIwR3+UkD9I5wsE6JFnCutsAC59RsCkAPVY3kNzts/RzvM7jSi4ZYsEulmrqmbWNeXkrM496gFT5tfFTJ7L40HZ5sg/CG6C8A9w+zJo1lizrPqScuin/MiZmSnVM+a+lDo1FT21kAq+WlAnruW6v35U0dK8+OeVakffdq4pHNxpn542zXTvuXPGvblUKddfcVuNAi9nbYUGPdHKWmHKum7WQnCmpmpe9Wx5+NVX8xQ7adlgfVTB2Ph3FDAyev5X8gsHupF6QxPfMiay+iMKKPXqZenoUc1fOlo40OhprV3P3Xh4AV1q08iYCaOj5fTz1ZclUdXY7ESjTxsTWvl+RsZeUjdUqlxZatpUq3o3lM84u+5xhMtznE33PGNX41gfxX88Tm+tnyocqMPiDkrPTFeLRS1UfmZ56ccfpehofVUie7WpmgXkbNrE9cW2OSw98+XAO5SdO09vM16IgyPlNdpMJtWubTiEG9nXOp1Ke+VlF9Fx+voq8elY1XzrXnlP9NbaYyatfNvx9yhkuOFQrHFoezEfackSObOVkwllo/MQtnmVjULQCfq8RTG1nWGIZscuKLVH97xZqyXpo4+0ugSKetYQnM/rmLTzmRaq0xMdCTZlrStqPBgZh6Kft2vRrN8/YevdEoT/SR2CU9lZTJwgG8yvAl26QJV+EObwpWXURka3C+Sr2UNZ0Dme5Ixkmi9qTiO/CpS7YjG+TSDtQ2rjnQXbSpo8W6uPrM5byZYtJhFIwYImr0Batt4gI4On3tvLZ/Fi5AaYthqORNhp3SKBSvF1WbBzARkd2tJrexZv1YCTvTqZ+yRYsIBhvebTYb840qImVmwsHY570+z7iwD83L4Bo4YsZ9ZK2OB9gYf7R5BRqgSRI14EoPX0lTTJjrxc63OB0hW/463ySWTWr4v1VD8e7P0S22vOY3nxkXjFFKd/a3DeU4bi+cvSpclV4ubEwtdf02LuehZ0iucQV8mwnCQVK8y8lw+QVKwwT383jDal2/Bhxw/xtHtSL6oe+y7vI6FMFBw8SFT7HgBs9bpMswJrWFMCPJ2wdbZ4fcYhAk9fytONh2+eAGB7YWhRojlBL75iIjL79DF926MHfPcdwyucY2ElcHrYSWvZjHaJc9lxaReLT9Sg0bVg9lzcw6c6gE8mOG3QsUAjIv3CoUsXXv/4OZ5tBqEHjYdqjq9k46RI0rp2Am9vNjhP8On1v/F4Znk+inke7/fjTd6FgwcBuJ56nd4/v0rzx8z9RbwjeLjhZdJtxtu1+nk4H2DyZdQ5CzmZVk4GZBF79i+UsPVuqMYftf0hHMKiRWKcWSNhdmUUNBw91BV9HYPq90A926Jy/cljqvOeaNjctj19NLKRObe7f0dlWajomHwqMr2I2n/UPm890dFmARTJ+NQXKCBdvGhWPAaXvLqgsqVSkwvqtbd7quKLxhpQeAh6qb5dK0qhCyUKGO+72yMN/25bU8JwPB9UMMcbygWo1xMmhqHT1Or622JjJfhsw1wdPr3L9Vw5lpCKsyrquxPf5Wl+ljNLH+750BWEFTTF6EDGrhuruK1xCpgc4OqXkJdCNGXjFFkOSw8uelCpGamucjac2GD0FgeN3uJy0mWjtxljbPfV+nuo9NMYL0IfHxMnMX68Wa1J0qQNk1ztXbQrO3rQ6TSrWfftKwUGan1Mtg/J0CrKCAlSu/6hxhoxoqWc2YFYD/XJJ89xlssDdVY15D3G0uJ6oRLodK1yuvBsrARKvi0hrbNRI6V7mP7tN7iUWU07KEjq0cOIeP7+2jHteRWaVki2caho9hoc5d4qp/XfLlCOLiET9HHZ3HJnVkNV+uSOseghv68+ATeH8AuIj4fYWIpehzXvQa+d0G8bfF4GTgbDt+/Bu5/C4kZxxLWK45EKj1Auohyedk9sTvg0JpXJ9U1RLXyW8VB3O6ftiSBYc+grrh0/aNKNLVtmUpVnZpq06T/8YPIRRkWZ1GQ5eQeA0pfFpZvnmX5oAcumneWrhVDmCrzQKIvuneGFey9zJuu6ifVv1QoWLOCdyZ2p+ZSd6z/vhpQUSm435pBbXjCnKvTpV5gvy3sxvdl0liZvZ3LWtwBc8rcoWaQSFSMqAnD6xmkWtV/EjbQbNFjQgG6fdOPszbMA2CwbXSt0ZV//fSxou4AQ3xAAJmyYQL8v+1GzUE2WdlkKQEpGCiPWjqBWkVp88vAneHt4u7q8RuEaeNm92HRqE2uOraHOO8aqUCy0GAcvdaZoQiY+Ni/w9TV5Gn19Ydw4k85t7VoOXz2Mv6c/3nZv2pRpYwq1LPN1fvttbp44RM/e4ZRM8WXUjJ/o3eAGKyKvMvhYAeYUuUjE08n0bgMrCyYyeLPJmPT+lkL02wFXG3xJlw0JMHcuRX48QuSKbzgT4oFvpvmAZ0aGs+zit3hmOhlecwgzpx/Ctmu3ySD13ns4nU4u+UMBx6uUPHQFYfJlzEqoxa5+uyjy3U8ArClurA6NThlLxpbCMLAVFL0JOTn4TuVzQv+/AJdwN1Tjj9p+dw4hO0dBDsUWaEYN48PuUowNH26uTUszfu87d0rffKPMdm111QcNao7q9/VU24dRgedzKbw1znAWPdqht2qgHwqbWHuBsnIWRvH0NNmHwGjIZ8yQPvhAPy2PU8SkYH1e2jJOLR9+qO27vlLrfsGyjUWeYy31XNDOrJ4sadtZI1fP/2m+aWpqkqxxaExLXxUe7edq04YTG/Typpddxy9+96IkaebWma5zvT/traT0JI1dN1beE73lP8lfL296OY8TUpYzS29ueVNeE7zyKCZzyrYclrwmeinkpZA8Vokc1JhTwxV1WfKNkir5ekm1jDfRny1eraKaT3mYeI/HHstdhTp7xeo6w8PlNcFT7T660/X7ctJlNX2/qSyHpZpzaip8lGlfzopLib52bW5TRc1fqybLgbp0RPsjsjktDw/ju3Dliinshx+UFBni8hUQaGUZmwY1z+YUEhLy1L32w8laVdZD4xsYfYDXaDSsmWV0HJ9+qoOXD2p9SQ8djfTUlUolXWUm20zUbOEh6IY36pvttOVyb/6dcijwRykVgaLAeuAAsA8YlH0+FPgGOJz9G/LPyvpdCcKiRXew2pmYNFj9WhrT15kIH5P44zbz099vWTZLl7O9355u66WNzcvpqVYmzVa5oX7KNzavJjtH9Agajt6tYindhjZ1rKmvDn+lk9dPurT9F2tXkkCjm3vqyIxxUnCwnD4+im1r070zK8r3RV+Xc9D6Y+sVNT0q12Nv2jQVeA71ntFIZ2+cdXlL2sfbNW3zNI3/drxwoPIzyyvLmaVLty7J5rDJPt4u23ibTl83uReOXj2qhz58yCgV3yytrw5/pWNXj6nRe42EAzV9v6kOXj7oMn/e7uy05+IexcyIUb7J+Vxp3jKzMjVz60yXaDFyzUilZKSo7YdtVWFWBUlSg/kN1GB2balVK9PHjRpJ06ebperJDU9+/9XHtfnEJs342ww9svQRFX+9eJ425ChWm7zXRAc2rJDT01OKitKpCG9X+LrNYenR99ublagqVDD1Za8zkXr2lGpMKKqd+Y15cGk2e3+8RHaim7dMvocLiRdccSqeE8y77vxUWG7aONC1+XGqNCVa6TZ0bWAf6YEHzH+WpUn1sk2/Zcy1GRZq+JhxexaYdH2/A/5IglAQqJq9nw/4GSgHTAVeyD7/AvDyPyvrdyUI0dG/OsmPBZsgpeceLyB17WoyBU2YYKLuli41OgCQ1q6VMzNTS7tVkzCuzvN2zJPfJD9FvhKpmnNryul06tSD92tp8yj171NIVfoi39G5fgAet63anGO/7tu7gLJA+0oE6Zuy5st4rVoF6dAhdVrSSRFTI3T+5nlN+HaCwqcaM1yBVwrIPt6uq/t/lPz8VH1okFosbCFJOnX9VJ467n/nfgVOMfkZ+37eV06nUw8uelAhU0wegTrz6uTpqi9//tKlX7CPt8t/kr/m7pibx1SZE/yUs7X7qJ2+PvK1yrxZRn6T/DRr6yzVmFNDONC9cfcKh8naJJlkJ4FTAiVJ9829T80XNjd6gdmzJX9/OYODdXbWy1o19lGXvuGmF9oXhu6NNT4TreNbK2BygEq8XsKlZ+i5omeue/iECRKow+R7c4mzAy2sbDNLyH32mfE/yM4lme7loVnVUYW+qP4Txvq0NyJ3jDhDQ7Ro89vKNzmfy6+j+pzq2nRyk2n7vHl5xtT2QtmcyKZNLmJ36NHm8h6NOnfODX4SaFTD3IQqCyvyu6wdebcE4d/WIUg6L+nH7P3EbE6hMNAWyFlX6z2g3b9b1/8X8XviiWl/khIDIdHTLKRyO4pdh4ft9zK77C2uvjsT3ngDxowx3oMtWpjU3i1bQqNGWHY77S+FcqJIPhL8Ydy34+havivXUq6x7ew2riZdoejGXXT8/ioz30/gx3zPkzRJ/PwGfEBHBtZ5lvsK32fWIQCSM5L5IOIC9Z6E2aVucN4znZ5tIbTVXqK/bMq5xHNcTr7M9B+m81CZh/j56Z+JaxWH3WYnS1lUWVCLuCqZFCxTnTOJZwAoGlSUUqGlyO+fH4Ad53eQmJZIqE8os3fM5plVz/BIhUe4lnaN/P752XxmM+uPr3f1R9nwshTKV8h1nOnM5OzNs6RmpgLw5eEvmfvjXEJ9QwEI9Qll7bG1NFvUjJKhJfGyedH/y/4cvnqY+A7xrO+xHguLjafMAi5RQVHcTLvJjdQbpGamYlkWKw9/wdhSZ3hifBW2BSZSqP9wtq37AIAiGd7YvX0olwA/zYFTm+/DBw/SMtPoWbkno9aNon3Z9sxtM9flkcnw4ZyuGM3K5F0A1IuuB0Czpn1h82azPN2PP4KvL5nFY/iwokWvnRa7ZsPAH2DVMm/KXwbsJs/yZ+HX6P71UySmJ5LfPz+L2i9iS+8t3B91v9FppKWRBUxvm59r3v/H3luGV3Vt7d+/tT3uihMkAQJBAsG9uFNcihQoFGtpoVDaUqClQAWXFpfibkWDQ4IHCZIQIe62s7P1/TCTHVJoT885fZ7/9Zzzjl69SLLWmmsumWMNucc9oGFicXAgJgaMRswSjKv2BBujxPKTpXTnFsAMWCQRxxrXE6aenPqvvur/tvytQUVJkioD9YGbgJfFYkkCoTQAzz84ZpwkSbckSbqVlvZmT8B/V7wsPxQAACAASURBVHasmci4PcPJ1MDhXWCQw/ROYHodqdq4MTPHbCRfn8/q8N8121i3TgQEP/9c/G4wILt2jXLdB1PdtToJeQnIJBkGswELFsKWTof8fEEL/sUX8P33SBaongmDP97MD51+4MbYG+R/lk/E0CtsOqZg+H0xr7WNJUb0gy31AZkg+ryfLF7oJdeWELQuCLfFbiy9tpR6XvWonK9AptMzsaOeM8lXeZH5ggytIERp6NsQjULDsLrD0Bl1aBQaMnWZlHcsz8rwldxMuImNwoaWFcRCGXpgKGaLmVVhqwhcE8jd5Lv80uMXXk59SZ+APnx18Stqra7FV6Ff0WdXH+p41qGvf1/sVfaYMWOrtKVDlQ6ceH6C7KJsNAoNObocZJIMFxsXAr0CuRJ3hUJDIYWGQgAG7R/E47THnHpxih6/9mDh5YXctctj07JR3JrUF71KPKQPawzHNjULFi1CsrXl16f72ff8EAMtYj7tq7RnZ7+dVvITgELJROfu2ejlUMFkj8lioqFPQzwXrxb9Kg8fhmbNQKdDEfWSgEQDIRPVLGoBPaMVdHok0sSRLiIJ2esZzLoM8yq9R9TUKIbWHVqqfADLsaNM7wIf10/h19+WilQzwLBhcPEiG5qouCiLY6nrQLyLkd9GCbbVhcWtBJkKQKESK6nN/wuRhDXxNwwkSfbARWChxWI5IElStsVicX5te5bFYnH5szEaNWpkuXXr1t8yHwB27KDy7eHEOVho+goGPIS73rDqBKTaC8sAuVxkBvz96bazG2EJYcROi8VWaSui3lWqiK5FZ8+KMcPCRIR7925Su7Whwo8VMJqN1HSpwbOMp6w/bGH0PWD6dPjxR/H1GDoUtm8XisXNTYxjsYg8ekqKUB4//YT+/dFEpD0iPDGca/HX2P9kP1qD1no5zhpnvOy8UMqV5BXmkJgVj0FR9pJlkow6HnXwtvfmdPRpHn7wkHW31rEifAVKmRK1XI3OpMNoNuLv5k96YTpBXkGcfXmWyk6VicmJoXO1zqzvvr5Mh6XQmFBGHx7Ny+yX2KvsOTP8DMtvLicsIYzlnZfTd09fikxFVHWpKrINTw5QZCzCgoUBtQbwOO0xj9MfIyFhsohF5m7jjtaopZZHLX545wca+DTATmVnPWfjn+oQnv2I9MXgNnoSLF5MQn4idVbVwTe9iBeuUD9dwdkOW7HvN7jMfRhxYATbIrYBcGGLxCfvSHQa8BkL2i0os9+Lx1eJ6d6Cid0hwQH27JPo5tWC9PDLuOpKv5gJ9qKRL+7uQqFoNKWDWCz82MGej1pp+ajxVL7X9IJ27UQLucWLScxLpNYkaJAE5waeQOralXNV4JN34K4P+KfB5xdhfA8oKE7QbO+7naGBQ//yq/6PRJKk2xaLpdE/2u9vsRAkSVIC+4EdFovlQPGfUyRJ8ine7gOk/tHx/2MyZw5xjhYGPoRke5jWFbY0gGpT4cOusKsOpH09E/z9AZjVfBbp2nQ23t0ojt+wQbQGK7EOAC5eFP+2aoWnnSc/dfoJs8VMbOozTJIFuUyORa0WykAuh0OHoHlzcYy+mLf75UvR4iwlRTQ8efoUJk5EpdTQ0LchExpNYGufraTMSKF1pdbWU9d0qwnAw9SHxOYJZaA0ib/X9RJUbg4qBx6kPuB09GkA6qypw46HO3BUO2IwG/C296a2e20AIjMiSdemWxd+TE4Mq7qs4sSQE2WUAQhFk5yfjJedFxISrTa14lr8NQqNhfTb2w+lXImbjRvxOfGYzWaCfYOtX+w9j/fwKO0RZouZ4XWHs7GnuL/z2s7DXmVPI59GtKzUsowyMJlNRBREYau0xW3CdFi1Ckv9IEbvHUahEmJ8bahhcODEFiP2/YeIbtbFdHXbH2y3KoO+ft0JyXVizREznSt3eOMVGX/rC7oMl0ixhx9PgVvNICa63cDzU9GZqaS/Y7mSeq70dNFS7zXZf3oZH7fU0u+5kiWdf4AjR0CthjFjICKCyV0EXf/ao/B4ZFe6DYEOI0W7v6374cFqGPoQvgwtHXPUgZHsiNjxxnz/p+XfVgiSJEnABuCJxWL54bVNR4CRxT+PBA7//tj/cYmNpWIO7K8Fw+7DvdXwxQXxcK5VgMH9wdPwDQ3WNWDW2VkUGYsIKR/C0mtLMRQWwHfficXcunRRcvEi1KwJ3t4AjFc1pUaOAp1MoB+DY01YiorEV//MGeGrqovVvk4Hq1aJlzcpSeTck5OFFfIWsVfZc2rYKXrUEPn31IJUIj+MJLv5Uc5tgUX6VshUauJz43mQ8gCA3KJcqrtWx8/FzzqOWq7GViHawL3IesH91PtlzrPp3iZcNMJ42/dkH0azscz2a/HX6LqjKxWdKnJvwj2eT35Om8ptiM2JJTEvEVulLU5qJzIKMzCYDex6tIvYnFhG1x/NN22/wdfe19oCLzYnlm41uqGUKYnLiUNn1GGjtHnj2q/EXUFn1FHNrZrgcTx3jrWV0jmdfhO50Yy3vQ+n5zzF9c4TYcFFRkJICJGdGjLu0FjrdW/ov40to+rTKAmaHr5d9rrvbuL8y/Oo1Db8rH6Xpq9gSMBj1gQZsDFJOJsUeBQW71yhgrDoQGBJGjSA5GSuxV9j6I0ZBCfAkoTaPE9/hu7AHtKb1uNA/Gk+/G0aB2pBvSIX+g2EwIlwxg+axsGjleCuBaNcuA6fdgJfAU/BgIkPdw1/63vxPyl/h4XQHBgOtJMk6V7x/12BRUBHSZKeAx2Lf//fk2JSy4XnIOQVfHQDbIywviFc2ALpi+GGx2zmt52Pg9qB769/T8ftHbmdeJvYnFhGrmjHfX08ltdJNE0m0aG4REHs2YOsWXO+vemAWQZVMiEgA0wKCa5cES3LoNSfHDRINHHR68WYN2+WNT3fIhqFhv0D9lPHsw4vs18y5ehEHCdOpx1VmDnnJGPqiwYmF0cKy6W3f2/83f2tDVoAkvKTSC4QTVDre9dHQsJJ5YREaSAlS5cFwIWYC9gssKH26tr039Of0YdH035rexzUDoyuP5pZZ2dRa3UtzkSfsR6bWZhJkamIj0I+4rdhv9GmchvicuKo4VaDz1p9Ruz0WHrW6Gkd32+5H3YqO15kvqDQUGgNsL4uux/uBiCkXAgAL4Iq8lGrQlRmGU75Bs4esMcnMVdYdw8fwu7daN2deNfvDiaD8P+/9J+Ak9qJBT7PuBPkhXzulxAXB0B4QjjvH30fmSRjc8/NTLG9SL0PIE1eRFuvEFZr2xDvXDqfPR6pDA9JYmZHiUwNWO7exVDOh0e9m1MpzURYeaja5h59vwpAE5fIHPsw+u3px6pnwlK5aZ/FQ0+wMUDlLAGfPhQAXaJED9AhEdDpuVAOgYninNlKC5ED37Rq/iflb4sh/B3yt8UQJk6ENWusv+plkOQALUbDiPuw8Dyiq1BWFiiEWZtXlMfF2IucfnGa9XfWU2QSL5WnnScdqnbgnarv0CXXC8/WXWDrVtHrcNEiaNYM8/Zt1F9Tj0JdPo9XwYxuSpYe0gqT2WwWpuPmzeKccrlAKa5cCZMm/eVLisqMotqKagBMvQE/TjuF1KkTF15eoN3Wduzsu5MhB4Ywv+18Pm/1ORaLha47u3I/+T4j6o1g96PdxGTHlBlTQqJ5heZcib8CgAwZZsw4qBwIcA8gMiOS3KLc308FAF8HX1ILUularSvtqrRj/qX5ZOmymBQ8iTkt5/DhyQ/Z93gfM5vP5Nv232K2mAlYFcDzzOdUc63Gi8wX1vPNbjGbhe0XWsc2mU14f+9NujadZZ2XMSl4EiEbQrideBsnjRNXyn1BranzKTQUkrPgc3IH9yNHn8vcs7M5/fIcAHZ6mHEdXgZVZqtzDN2Utdk37wnhAY4MG+lAXG78P7znchNkLgJHA3zd2ZbNbZxwytHh/iqLZSfAPwOMMlCY4bkbPOrdjKp25QlavocrV3cxMnw20dkCRVrR1oddjwJoevIhltRUIt0FQvZogJznTiailsPJavBbNWgZAyP7ARYwzgP537BG/2oM4T9TIUjSP94+ZYoI+rxFtq2ZwIjUdUxz706qjyNno8+SWpDK1Ovw02/w5dByNA5LoHX70dgvXAKdOnEw/xZ9B8G2AyKL0aP5KDb4z0QaM0bQdQM0biyCkj16CD/zn5QRXzfA+fpdVoTAmPpjWNd9HRYs+H7vS/uq7TkXLbpKr+2+FoCFlxby+YXPyZmVw8uslwStC0KOHDNmqwn/j0QpUxJSLoRnmc9IKUjBw9YDFxsXYrJi0Jv11v287LxQyBQk5iVip7JjfIPxpGnT2PpgK6ODRrOuxzo23d3EuGOi5Vk5h3KkFaShN+vRyDUMDhxMiwot0Jl03Eu+x893BI1928pteZX7iueZz5GQ8LH3QWfSkavLxWgxvnXOr4vaKBqyVtM7MPmxPVMOJfHuQBn7AszWfeSSSOH2qN6DKVFuOK7bjNPchTjNmIOHwhFZdi7S7NmwUCitwvQkun5ehQUnimgaX9bMtjjYk+FqS8X38yg0FqJAxrJjZt4/nc7ljV9y9MwqjtaEKJGxJShNQbfHRibcgnKiqx1P3aDRONAYIW0JSP+/Qvg35c8UgiSJCP/t28IP/L2YzRjq1KJaj2gq1mzC5dGXMVvMRKREYNurH3ZPovGbYkGnFIvlw9sKFh0txODhSvMRBvIMBcQ4mpl+Hb69qEBp5yAshKVLxfi+vsJslcvfPPefidlMSv3qyJ5HM3vjEH55upOBtQeyrc82PjzxITsf7sTPxY/yjuU5NuQYACefn6Trzq7s6LODZWHLCEsIo5prNT5o9AFX465yJvoMefo86ylKvtivi0quQm/SY6uwZWyDsUwKnoSdyo5nGc9ot7Ud3at3x0njxMvsl7zKfUVibuJbF6pCpkAlU6E1at/Y9mfiaecpOlcDTcs3xc/VDye1E45qR5zUjjiFPSD3yD7mtjTgqXbllSmTCo4VuDfuLk57j9Dl8jgSNEYerVdwpJqJCtkWvAogYBLkaqB1pdZMbTKVvnv6cmTQEXpU6QSNGgnrEcS7kpAgymF378ZkNjFg3wAOPjnIwX0Kej0qBsEDd7ygQQrMbQtb60FAroq+TiGcS77Gqbq25BblojaKng09nkL3VzZU0Hhhjo1FZilV0RLQZQgMixCuxP+mQlD8ox3+48TTU6T+6td/+/b9+1E+ecqMKe8xJX4zV+Ku0KJiC+pdeQ5hUWBjQ1an41xRJvHqk/EMuZbPEw94Z3gmBUqooIWrGyAkAQ7VNJK/7DOGxTqJseVyuH79n1cGAOvW4fUgmjF9Fdg5ufFdh++YeXYmWoOW8Q3Hs/7OelRyFa9yX1kP8bEXQbDhh4ZT8ra9yHzBx6c/xlZpS3XX6tgp7QhPDMdgNmDGjFqutrpLAHqTHhkytEYty8OWszxseZlpHXt+7I2p2ipskclkaA1azBYzckmO0WwsE6yUkKxWSki5EIK8g7gSf4WHqQ+RSTI8bT3JKMygQC9iIVt6b2FEvRFvnCu/cT6NpTAc02LJLMwEFaxo9S2udm4UDBnAxfgJfJhTh+UNHjKtCzRIhJu/wJIz4Pz9Kga0nsiCSyIV2bxicxHv+eUXCAmBatWgBBvzUDRt+eTMJxx4coAf3vmBXuZsePg1sR4q5rTQozHCL0ch3hH274ZGSXoSHC6R3FDCo3tPOtTtRcfggdjpzMJVdbYT4KgRw+HYcWtERy+JIPjQRwKwxI4dInX9vyD/cRbCjogdzNk4jLG3YdYV2B8AAx//bqdFi2DmzDcPtlggKAiKitDeC6fSiqqElGvC0Sf1YUFx/vrHHwV6sUULyMiAgADSfjvIueenkX84hR7PRNXh5K5wKEiNVFjEi7VKvDMNyF4zO/+qWCwWCmKfk9O8IbkN6vBhfxtuJ91hTbc1HHt+jJ0RO6nsVJmk/CTkkpwiUxFutm5kFWZhMBv+tZv4O1HJVbSs2BJfB19ydDmkFKQIENRrAJryjuVp6NOQkPIhNCnXhAY+DZAkia8vfs2ym8tQy9UUGgvRyDWoFWraVm7LgcgDb5zrdUVRIoNqD2JDrw0CG/K7ezPy0Ei2P9hO64qtCI27SM10eHLQF2nzFk5U0tNtZzeCfYIJTwqnhIPg8A7o8RwkhQLGj2dw9Qc8VGUR8UFE6eDTp5d1KZ2cWP7b10w9NZUpjafwU+efyF2/nBnHp7GxAWCBYzshIA2qTAMXNPx4QU3vmzk4FSGyTn37CkCUTieCyRoNlsxMJhwdT7cZP9PzeenpLlaEkX0hzgkq5sBCqT1Dfzj7Lz/D/0qXYUfEDsYdHYfWoGXDIfDKh0H94cVy8NJSWmIbFwfly785wJEj0KuXCBoOH87803P44vo3PFgNgVVDRBnzwYMCfVZQIFyO0FBR6ty7N0RFkdC0Dg2aPyTVHio7VuLrzbEMfQDdh0BM3QoEVm1KNddqeNp5UmAoIEeXI2C8RaX//v5vVkKXvyglpr9ckmOnskMhUzCtyTRWh6+mvGN5ZrecLUxuTYnp7cRnZz9j0/1N1uMtxf9JSFRwqkBcThz9AvqxptsaPOw82Pd4H+/ufZdfevxCZmEmt5JuEZ4Qzsvsl9Z51HSrSXC5YMo7lOfsy7PcSrxlXfDb+2xn2MFhgFACQd5BfNDoA9bcWsP95PvW878ulZwqUcujFgHuAdTyqMWLrBcsurKIwXUG8+vDXwHY1eAbBn66FdPTSDp+Vo4LqgTr8a5qF9rczWLnITlqvQlsbLDo9RRJJq51rUu7db9Z08kUFIj0ckICSBIWCeRfQC//XqzsspJPz3zK7oidVsSrfZHIXO0MFICjp+EhuO08KFr92dpCYiIYfqeg5XJWXlzC5LMfceV+I5ofviOC0IBODkubwsLWoFOCyggbfT9g6Ae/Q9L+RfmvVAjui93JKMxAKmZCel3UJgkHnQUHixL7qv44qB2wV9njoHIQPyvtcPj1APa5OuxnfoEqIwvt+tXMDkonSFOJ7Rfc8Lr7jNvOWtpEm3kWVJENc7rQ5EAYPfbcI18t8V0zMwd6VCM6+yUmi4nxYbD2BHzZBr5u8/Y5yyU5jmpHXDQuONs4Wxeok8YJR5UjTrHJOO7YR0GLxtwP8iE6K5qI1NIvmaPKkUpOlXiU/qiM4uhVsxdruq1h7a21LLi8gNxZuXT/tTsms4lLoy6VmcPuh7sZdnAYRrMRW4UtWqOWKY2nsCJshXVR2qvsKTQU4qxxZl33daRr05lwfAIJHyWUqXtI16ZzO/E24YnhhCeGcyvxFol5Io8mQ4YkCaSiTJJZ5/tps0/54cYP1POqR0x2DM5qZ6Kyo1DJVMxrO4/V4auJz43HWeOMs9qZpPykMm5NSfrUUe3I122/RleYx6bzS4mUZ1v3GVVvFLE5sdxJvsPLPhdxHjEObt7E4OLEKfccukXLkKnUIkM1cyZ4eMCpU9ClC2aZRKHMQvAX3lhcnInMiLSOW85kx7yLEkOu5WNjhA7DYcwjJYMfyQSqMSkJZs+GOXNEIPvnn8vc+9XBEDqpG7tXpSJpNHD5MnkqOF4D9gXAb1Uhvxim4VYI6Yv+tfX6XxdD2BGxw2rCVsmCqTdhV22olwIRXuDUoAl5d26QZ2OmwKAlszATnVFHkakIg8kABgOmKmaMcuDMdDFo8e27aYgl63EseUpoEw0H/OGb4DjWT15Hg2TYEyhjZgcLeTZyNMZCPOw8SM5PpnEiXKkkca9vM2ySr6JQ2zCx6RSKTEVEZUVxP+U+cTlxZOmysFXaUterLq0qtsLVxpVnGc+IeHGVObOOkaqBhu3C4LmCel71CPQMJDI9kqujr9LQtyEWi4WxR8ey+d5mAKtJK0kSDXwaYLaYeZDyAE87TyuACcTinXh8Insf70WGjPIO5fGy9yLQK5DlYcsJ9g0mPDEcEC5BZHokWbos+u/tb0VNutm4lXkO7rbudKrWiU7VStF8iXmJhCcI5XD91XXOvTxXRnkdjDzIO37vcOr5KcyYrc9xYvBEZrWYxSfNPmH3o918FfoVzzOfU9+7Pol5iRQZi6juVt06R51Rx9RTxYVBJWEaC3SMBg/tfbao7/BZ6zk4Vq8jrL1mzVBcv06PLND26oKtxl64hGvXYpg8kauDmrO/vy3vhmlRm+CJORkyBJ7DU+7Izg25tN98HFb2IU8lJ0duwq5pKwZdiQNVhsCtmM2iwEmjET/LZFYrAGBiOHww5iRZSjO7htZjUx0FEW5GihTgVAjtX8LhWmLfjD+HrPwt8h9jIVT+qTKxObH/eEdAjQJHW5dSk1nlyMpFEXilF/LVB/4ow+6g9vBG1X8g+TZyll3/kQ/CLKw4CRFtAsis4E6LnVcpcNSwZXwIl+q7kH/8EHkVPMkr74EqLQtdUjx5ashWQ86bQLy/JK46Cb90C1K1anhVDKCyc2VcNC5k6bJYEbaCMfXHUN+7PqvCV/Ek/QmOKkdy9bm4aly5MfYG1d2qE58TT8WfKrKyy0oi0yPZ+XAnaZ+ksenuJmacmUG2Lhu1XM3pYae5lXSLj09/TOSkSH658wtLry9FI9egM4kqx2WdlxGeGM7OiJ3WBf3DOz8wven0f+q6Om7tyLOMZ8TlCpCQQqZAKVNSaCwss1+/gH70C+hHcLlg/Fz8MFlMbL2/lSknp1BgKKCqS1Wis6LxtPOk0FBIgb4AlVyFyWKyxk8aeQQRnxRJikJnHVej0FDTrSbN5JX5bspRXjmCWbLgrnTi3Ph3OJp1g1PKOLJtQG6Gg7+KupdmY0Fvq2Z+2/lMW3Ub5Zlz8PQpFjc3sm1lnKtkpvHA6VQcOUWA17KzS3s5jBsn3E2tFrPZjKywkCRb2NjKnlCPfEIrC1CSUyHUToVF56B8DpglqDkZTHIolwvfvfev1Tj817kM0rzSVOOwe9A8Dry1sLgZdBvyJQPH/IBj63dwyi1CfTYUXrwQLc1BwJHbtBG0XRERot352rVCqy9cyOhbc/m1DsTebolnQrbYZ9gwWLZMNAp58ADq1ROxh8GDwd+fg4oo+hbX29zrdRK31l04NPddpmkP4GrjioetB1FZUVbTVy1X42XnhUapQW/Uk1OQQbYhD4skTGKlXNRs6016/qqo5Woc1Y5kFGbgpHbCXmVPfG48rhpXMnWZyCU5MknGmPpjqO1ZG6PJyPTT0xkWOIyJwRPZ82gPP90sDazJJTnHhxynlkct2mxpQ3SWAN1423uzsstK+gb0RfpHGBBg/sX5fBn6JfW86nEv5d4f7qeSqaxYB2eNM418G6GQFJyKOkW7yu24FHupTIozwD2AJ+lPAPC190WtUBM1JYqf7/zMicXjmX7fhhfOJh73bcmTciqepD+hy+kYVp+A4X1ge11AApVZoqrGF0NaMjEOJjYdEmlCnUrCnPAKX7W7cCn694fJk/mtf306RcGp9pXpfDkR7t8XQcTGjSEzk4Ju72B3XNSWxDrDlrqiic1Dz+IsggX80+GzyzD8AeSqQWMAdbEh0X0wXKgC64/CzbpuLN+e/pffgRL5r3IZdkTsKBOd/vac6L60rR48q+nGtexAiM2DIe9D5cpQp47g7VsrADzMni1SgY8eicjylCki4zBtGixfzifusDkIVhiuMD/DR3QM6t69dALFRTU0aSJYgKOiaNuwNoJACoafncSDXHh8YS+mxpCmTcNgNjC6/mialm9Kk/JNqOZarbScVq+Hhg0pyM/k0uHlnE68wpnoMzxKE+O5aFwoNBaiM+po4N2Aua3nopQpydRlMuLgCFxtXCkyFmG2mGlduTVX465SoC+wpvCydFlWMI7FYmHt7bVl7uf2iO1sj9j+xn02WUx03tEZTztPtAYtNgobbBQ2JOcn039vfxxUDrSq1Ipg32CcNE44qIrjNGqHMj/X9qyNBVEIBlDTtSZPM59az+Pn4kdUVhQuGhdWdV9l5Zq4FHvJ6r+fjzn/xvxKlMHsFrP56cZPvBf0Hvn6fOZemEuNzi1o9f2vNB87mqurzyB1qsyTGibWNhKL8KfTMjJaNSRfm0VkzgsipQQozhbnqsBeD85FFlZM64SmaQsCnHMJ6NEey/P7PHEXpn3HFccxN29O1vD+rPyuHzVauDD4SCaP7pxm3mBR2ZjkWDpfmQXqZCrpZKhIyydaml+9jym4BfaRz5BjTYrwyyE4V01gEnpEZsCbj+Zvk/8IC2HKMHc+OpbBc1dw0EFIkjDVq0yDlUO3M3TuXoEQjIsT+d/Jk2H1avFlP3UKZswQkeBjx0T9gcEgFvavInKNTEbfd81cqKEi7sMXOHiWrQQ0jxmD+cA+rk7uTev5W8lXy6g43UKWRtxbGRKF8y1c/7A36hkzuRx3mU/PfMrERhNZ2XXlm1/VhQtFheWRIwLVWCxxOXHMOD2D/U/2C4abYgXo7+5Px6od6Vi1I8MPDkdr0HJvwj06b+9Mnj6PIK8gQmNDreNUdalKUl4SJ4aeoHWl1hSZisgryiNfn8+W+1uYd3EeKzqvwNvBm3x9PjsjdlprF5QyJWaL4D9QyVXUdK9JSn4KMdkx1rLmf0cUkgKjxSisIpkSSZIYWW8kFZwqsPzmcgoNhTioHEgqSHorkApEXCOjMIP5beaTXZTN99e/Z37b+TxJf8LJ5yfJ0mWhNEHreDnpahPrev1Co57j+XV8M2ZXiyUup9iVMcKQGDvGhZlp/KIQpRkeuUOdSVACGlBZ5NxZbSLHUUW3sbY0fpjNzKvwSUdIc5KTrTCRV+z7OxTBp1fBWQuBaRBcrwu2R08RV8mFg92rEq/Rs3TpA75uBV9cEmQ+DgahGFJtRabMwr8GVPrvcRl27KBo5DAUZvCbKnD+02/Ahnowtg9YJqWJKrWpU0vRgunpAnTi5QXPngnr4MEDqFULtFro108oCrAiG29O7UeIy36WdlzKoDqDuJlwk5uvbhKWGMbKmZfIUJlp9kpo/Y/mNsapbWeejahBdwAAIABJREFUpj9l92NRpLNjHwwZVop/+PTMpyy5toQFbRcwp9Wc0ut59kykqnr0gL17rX9+lPqIUYdHEZ4YTv9a/VnZZSXddnYjLieOBj4NuBR7qYwPPrLeSJqVb8a036ZZ/z618VSWhS1DKVNyfMhxOvp1fON2ZhVm4bXUi8mNJ/N9p+8Bke9vsL4B95KFee9j70NyfjLtqrTj7AiRGy8yFvH1xa9ZdGURCrkCvUmPk9qJgbUH0qtmL9QKNXl6oXTyivJYdHURqQWp6Iw6bJW2aA1aa+ahJGvwV+HVr8vbcAwlopAUlHMsR5B3EA2UFTFv3EjVhAJetgxkn0M8D9XZOOpl5KrMVHGuwtkaC6n68Xx48qTMOEn24mv/a224XgFerICpnWF5yJvnVJmguakca9Ym4FkALkVgUimR6w2EV1YRHKMn+H245QtXNkHFbPCfBFnfwcpgmBwGCgs89BBKxAJcfa89LTb9c5iE/x6F4O4uAEJAgaK0onFuOzC7uZJq9yXyyVPh3j3h54NgNGra1Io+46uvhAuRnS2o0q5ftw5vbNEcxZWr/LJ1OrOTt5NRmGENqCllSpo5B3J+yh3MGhUKnR7L/PlIxfwJV+Ku0HKTYCSqmQaRXl8LajZEs5gSUM2GnhsYXX+0cFPatYO7d8VL6OOD0WxkydUlfHXxKxzVjqzuupp3a78LwC93fuH9o+9zc+xN6nrV5Vr8Naafms6D1NJMApT64s5qZ7KLsvmk6ScsfmfxH97S3rt6E54YTty0OKtZfyvxFsE/ByMhIUkSFosFhUzBpVGXCClfuhLCE8J57/B7PE57TGXnysRmx6KSqxhRbwQfN/2Ymu4iOzHq0Cg2398MYCVmWdZpGQWGAmafn01lp8p8EPwB8y/NL9NctrFvY8ISw6y/O6gcKDAUMLD2QDQKDREpEdxJvlMmiyFDBhJ/juewwJLT0P0pBH0gmrSC4IGYecnMN+fgTBWomypgxUmuClLURlFodhqqToGXxfUJGklF+XQ9ChMkO8Dwe/DFRbA1ivdTJ4M9dUSsYHK4yFpFNPXjy01RHJ3cibhhPRja6kMRPzKD8+/CRmk2cPrmPxdc/F8lSPl/KhmlaDk7o7igxgkQkA6Zukwefj+LPP8qpcogKkoog0ePROBHJhMuRFISlmbNsFy/jgXIc1Tz/pQq7My7SpotvB/1IwqZArPFzKA6g7gx5gZ5n+URWnsJMkCh00PbtkhzSr/2Tco1wUHlgK3SlqceEKEvrbCTSTI29NzAO37vMO7oOI49OyYqIkNDBQ+Djw8PUx/SdENTZp+fTW//3jye+NiqDADerfUuarmabfe3oVFoaFelHY3LN7Zub+DdgIG1B1q7M2cXibz85bjL7H20V0B93yJDAoeQmJfIpdhSvEIj30YMqjMIpVy4DBYsaBQaOm/vzK3EUiUeXC6Y2+NuM7P5TOJy4vC296Zj1Y5svb+VgFUB9Nndh72P9nLkaWlxV0xODGq5mnGNxlmvLyYnhrW31qKUlSXALFEGAW4ByCQZBfoCWlZsyW9Rv7Hp3ibup9zHbDHTqmIr67yVciUyScawusPY2HMj05pMs8K6X5dT1cA/U5jrJSKX5BTaivL1KxXBQyvYtpI1Riwy6PlMlC+XKAMAnUXPCzeI9IRsG1jRFDxmQfuRAsUa6wJftYEpXaHhOJjZEb6qGIXjbIkpVZ6w9f5Whg1W81Vr2FFXVOvmKSG9OFvlXggXF45/67P7d+X/voXwB1FtM3Du+Ao6dpvMjI7wcEQn1ir7UHnCLKEEvvtOtAMDToxuSeN9N3DLNSAhylAnjHChVtUm7Jxxg6K6tVAePIKrjSsN1zekwFDA44mPxdezQwc4d05kG16+BEfHMvPou7svF2MvklmYSUdjJU7PjymzPa8oj7Zb2vI47THndygIcauH8cI5Fl9fyryL83BSO7G622r61+r/1uscuG8g51+eJ2JCBHMvzOWXu79Yt4WODKWhb0O6bO/Clfgr1kDi6356I99GIv7g15Gm5ZuiVqjRGrR4LfVicJ3BrO+x3jpedFY0/iv98XHwIS4nDjly3OzcMJgMnBtxjvo+ZetDbry6wXuH3uNpxlNG1huJl50X626vI6coxzqHEhkaOJTtfbdbW877OviSmJeIhISzxhk/Vz+r4rFX2pNvKLUa3Gzc6FajGz1q9CA1P5VJJyfR0KchsTmxvJj8gnx9Pt9c/ob1t9dbEZBvWAsWUca89SD0ewxBE+BJMQvo0Puw/SC0GQHP3SHRUewfkCnj4Qozr2pX4OWM0VRZvxcePyalvDP723qz2i4SGyMsPQPHm3ngY+dF7fMPGXEfUj1s+DykkCRHiRyVhRhnyLeTo5PzRizmgzBYfQJ21oEhxUZtjBNUzv7ra/e/w2XYsUOk//5IPv8cyzff8MvBubxa8x1f/KYjupwN33zUmB7bwuj4qJA4R2FNlKiVu1MH4vjFAvxc/JDi46FSJZFenDIFgD2P9jBw30D2vbuPfolO0LHYD797V9RB/E7W3VrHhOMTcCwSX4esWTk4asoqjZT8FJp/W40sYz7b265kbtwmbifdZmDtgazosgIPO48/vMSjT4/Sc1dPHNWOFOgL6OPfh31P9qGSqxhVbxRPM59yKfYSXap14UzUGSRJoshUxLQm03DWOHM6+jQ3X93EZDFhq7SldaXWdKzakfMx57kSe4XkGcllOjFNOzWNZTeXASKtqTfpcbFxQULiwsgLBHoFlplfoaGQz89/zo83fqSCYwUkSSI5PxkXjYuVtAVg37v7qOddj767+xKRGoGvvS+OakdrVuFtsQE/Fz9WdllJR7+O6E16kvKTeP/I+9xMuEmBoYDWlVojl+REZ0W/gW58m8glOS75JiJXwiMP6DdCRb5aRqeHOg7thqDx8MgT5BYJhdnCyW3QMh4yurXl4LzBHIo8BKfPMPecgSYJIhCol0H5fCA6GpYsEdyaeXmiiMpgEG6iTCas1aIiGDMGw7IfefbbTu59OYEH3vDcBaaECbbw7sW9Oc2A7J9Yu/8dCqFyZVFH8BaJ9bHBFVviPVTEKrV0uZ3D7towupeoO3+yEuIbVqPS7RdIFsRDOX5cFC6VyLZtApPwWvzBZDZRc2VNXOX23Pz0GZK2UJTLhoe/dR4x2TFUWVaFbtFKjlc1MCpoFBt7bSy708mTRA3tSvCHSrLkBtxs3FjXfR39avX708t/kvaECccmcCnuEm42bpwfeR6lTEmt1bVo4NOAh6kPMZgMbOuzDUmSGHpgKDXdapKjyyG5IJmF7RYyu+VscnQ5hMaEcib6DGeiz/As45n1HG0rt2V0/dF0qNoBb3tBWlLpp0pW8ld/N38iMyJxUjuhkqsIfS+UWh613pjr6ajT9Py1J0WmInr79yakXAizzs2ybrdR2FBkKkKGDLlMTpdqXTj09FCZMZQyJVjAYCmtCZBLclRy1RugprfJ65YRlA1aett5075qe5w1zqTevsSZggiybcDeKGNWYUPmfB/OgZqwuAXcrAByZOzYa6Z1DPh+LKDyTkoH2lRtx6h67+H4yzba/vBa8da8eeI9unZNcGnu3i0YtErW34IFQiHMny/wCwMGwIwZ1tTj7yXeWUaFrL+e1fmvUAgWmQQWKFCKDsKRruJrLwMKVOBUBPHOEuVyLJx/vwPGGR/hauuGdlA/ml99hdIikGCSTC4q36KjBV9BiYwdCwcOiKyErDTcsv7mKsaf+pBzW0Rt++sWxNuk5sqaVL0bQ2h5ExalgrzP8qxAIwoK0PvXIMGQQY33i0CloKZbTa6OvoqTxumt42kNWhZeWsiSa0uwV9kT5B3E1birpHySImojFjniY+9DUn4Sc1rMYUH7BUSmRxKwKoA6nnWwUdhQ070m2x9sZ1bzWXzT/psyqc+4nDhOPT/F5FOTgVIwVKBnIB2rduReyj3OvzxPDbcapBak0rxCc44/P46d0g4HtQOhI0OtwUMQkOLuO7sTGhNK52qdOf78OBIStkrbMlRv/4yUBEpL3KDfS6BnIAX6AqKzo7FV2qI36a3l1yXWhpPaiZwiQWJYkuLUm/S4aFzoGaOm39VMOr5So9HqoaiIBHvwmwbdn4l37dbPEOUC495zIdWQQ7STGXPxa6IxQJcX0CgBgpPEvy6SjSiwMxgEa1ZgoIhlgUAx9u5dWjynFQo3y8cFVXoWdq/VRRUo4e7XH9Bi1l8vdPqvCCq+cpJhlmBOe1CbwFMr0kAGGTgWiRRNeYsjshMn6bDuDJ2rd6Hx+ae0ufIKhUU05kyzgY8mVsVsNpVlVwaBYGzZsowyABix9gbeebCobTGuK+Qt+abXpJNfJy76GhiSV5kiU5G1/t5gMnB99DuoXiUyva8te4Yc4PiQ4zzNeErv3b0pMr5p4p54foI6q+vwzZVvGBI4hKcfPuW7Dt+hN+vZ+2gvaoUahUxhLYcuWXAl3AdGk5E0bRpbem9hfMPxLLq6iMknJ5fxqSs6VWRco3GMrT8WGTIuvneRb9t/i4edByvDV3L+pQAFvcp9RV5RHkazkbH1x1JgKCBbl02rTa3Ydn8b2x9sZ9HlRdRZXYdzL89RzbUakenCBbBg+YfKoKJjRXrXFP19ZL97VUsQjCaLCW97b+xV9tZtarmaiNQIK32Z1qBFKVMypM4QTg49yZpugl4vpyjHygxdogwc1Y7Maj6LtR/+RvdnEnkNA1naTRDQrmwsWIxWnIBtac3RmKB2Olw95sXzj16S83IglzbCnEsS9TNVRHjCnA7wznBwnQXVxxYyuG0mP9TTcnn7QvItrz3fTz8VSqBt2zJxMRe1E3fnTSDeWYYZETuY3teO2G7N//Te/avyf1Yh7IjYwcx2ZnQK6FlcfOZTACHxcMdHmFkSIH3/vXADcnJEEHGEINmQZDI0XuW49ut37K2s5cdGRsybNxF/qZjwIzFRwJtbtSp74o0b0WzezvQwGWcqGrldUVGawfgD6eTXiUKFhW45nkhI/HjjR24l3GLEF3VovPca5zv4sWHpc/oE9OEdv3fY1GsToTGhDD843LpQX+W+ov+e/nTb2Q21Qs2FkRfY3HszHnYeNPJthL+7P1vub2HQvkEYzUaCvIPoWr0r+57sEyQlMjlB3kHk6fNILUhFJslY020NHzf9mFXhqxh9ePQbbMtDAoegM+mIzY5lXMNxLO+8nP0D9lsj+FqDFpPFxG9Rv7Hh7gYkJHRGHanaVEYcGsHwg8P57PxnRGVF4W7rjquN6x8qgUY+jVDLSmMV1VyqEZ8bb3UbzJhRyVTW7aOCRnFiyAmalGtCcn4yJlOplVBkKsJGYYMMGWq5mgVtFxA1JYr2VduzImwFHxz/AABbpS3jG47nwsgLaGdruTHmBsG+wcw8NxO3Q01Z0NKCx9lrPDMLkpQER5Ga9CmUU/9essCvODkJxueNGylau4p1PXx4L0LGtTV6nq+AzG3lODPsNN8k1aZuClytJPFxBxOtoufi1P8FdSbCe30kVjk/J2xYW4rq1xWl12PGCDbumBh8bjzk63YyljeG1qPgF/8Cxu8axsTjf3+36P+zLkNJMVP7KKEQJocLBXDPC4JSXtvR01OgEqdNE7XtJddbtarIDlSujNagZdVvCxg94Fvu+kicWj2deSm1sBs5VsQGGhVbWvfuQXAwGI3k/rySijFTeSfdiT1r/7zTToG+ANcFDkzJ8ONuk0qce3kOuVni9gY5NYsc0DyPBmfnMscsvbaUT858wqTgSfi5+PFF6BcYzUbmtprLjGYzUMlVZfaff3E+X4R+AQgeAieNE5OCJzHy0EhujLlBk/JNmHJyCmtvrcVgNpD/WT62SlvStel8FfoVq2+tppFPI3rW7ElqQSpJ+Ukk5iUSlhCGxWJ5KyJQQkImyZBJgj/h9xRpCpkCo9lIhyod0Jv0XI67bPXbG3g34F7KvTKIy9fFTmmHWqEmszDTauLLkOHj4IPepCdNW9rlq4TmDYR1AEIpOKocGVh7INHZ0YTGhGKymPCy8yKlIAUHlQPpn6ajkqvI0eVw8sVJDkYe5MTzE+Tr80Wdh8HEg/VylDZ2+MXm8mNzGdOumkt9eldXqFED/Pyw7NnD6K+C2Gm+z8VBpwnpN0WA3ZRKKPko1agBMhkpHwznliKV8PsnCfeF8HKQVtySQmmCQK0DwW2G0OiFluBF26idBllqaDYGXriX3iO1ETYM+Gt4hP/4GIJsnqzMi3RvDVTPECZddkUPXA0KYXolFnNaOzsL4BEIlOLFi2XjBUDOd/NxmvUF3YZA/2g1Qx+AlJmFUm0DmZmC/z85WRQwbdnC7B62LAox8nTyM6q7Vf/T+baf7Ei8vQmLjy8vsl7gqpeT9J0J1a974N1339jfYrEwZP8Qdj3aBUCXal1Y2XUlVV2qvrGvyWyi355+HH56mM5+nfFx8OHki5Ps6b+Hdlvb0aFKB1pUbMH5l+etNQC+Dr6ka9PfWizlqHLE19EXXwdfkvOTeZL2hHlt5lHdrTq+Dr6sCFvB1birbOi5ga47uzK58WRWhK1gdovZDKw9kI/PfMzZ6Lcj6WTICCkfQkRqRBk+x9fTkAvaLkBn1LHg8gJsFDYEeARwN+mu9XkrZUpcNC6kalNxUDmQp89DKVNaKxzdbNywVdoSX8ys7KBy4L1679GkQhPGHRmH1qhlUvAk6nrV5WDkQc5Fn8NgNuBl50Wvmr3o7d+btpXbCrzG+qlonz9h+0EIbVmRllfikFvJDyVo2xbLrl3kV6vIIwcdL45sZliDkQJtGhEhPiDh4aJ+pgQIN2CA+PnxYwgKwnLvHvFOAq0Y7gvhQR7cctdb4xs2BghMgaBkwSa9rxZWivhKJntivi69j38k//EKodMEey67F1CohNYv4fQ2EVgc1ge2HILQICeaRhuwzRFfrDJa/elTgXD8vej1ULs2OslMSn4yj+y0TJ9agyXtv6PHxGVIoaHg5yc0/9OnpLRsQKVPlYyo/16ZfP0bw5r0dJ3uyTm3HNxt3PEukHgoS2N9TF3e33jvDSxFVmEWs8/NZt3tdWgUGgqNhWzquYnh9YaTpk0jKU98vZPyk3iV+4pfH/7Ks4xnqOQqzBYzJrPprV/dksUDQsEEegbi6+CLj4MPvg6+XIy5yNwLc2lVqRVHBx/FQe1AREoEddfWZXXX1XwQLEzt3rt6E50Vzf0J92m/tT0PUh7g7+7P9VfXcVQ7kq3LfuPcr0sJ2rGkJkJr0KKRC8B/Sal1iciR06hcI+6n3CfQM5ApTaaw5OqSMmhMF7ULWUVZZY6r41mHnjV6klGYweZ7m62xAovFgtaotVodVV2q0se/D338+xBSPsSKzCyRg08O0m9XX8xfw/oG8FNzGXt2mamd9lqqenBblmkvsPkwolHw5MnCldDphPm/f78gXsksBoKp1SKjoNEIOv6xY9+4R+Z2bYna+D1hPRqwIxBCi3v5FCrhg5uwpknxvbSA+at/vIb/s6sdd+wg0qaAQgU46URl4y8NoEU8NE2SobCY6XA3hwhPcHaACnlWjlGMJ46hfJsyAJEbXrwYTd++VAIKPx6JTLrJ7Yl96BkK8e5KKhw/Lgqhbt7EqwBGV3+XDfe38FWbr8owB5XI3aS7vHf4PR64CW3/Zesv6PnRWvrVTuOrgGRGmg3IJBmpBakk5Caw6+Eufr7zM/n6fGp71sbX3pfrr64z6sgoxhwZ81bTHQQ7sbutO4/THhNSPoQbr26wuttq4nPi+fbKt1wdfZVg32DsvrHDYDYwMXgi3Wt0LzNGi4otqOJShREHR9BhWwdODj1JoFcgtT1qs/PhTqtCyCjMwE5lx8qwleTp88gozOBqvKCaz9Hl/OFja12xNR52Hux/st8aGylJX/5eEYDo/Xh48GGux1/nZsJNZjafyd7He3mQ+gBHtSNySU6WLsuqDOyV9rSu3Jrjz49TwbECc1rO4WnGU0wWExvvbCxz7+a0nMOA2gOo41nnD0u2c3Q5fHjyQwIL7bGQz/AYJ1a0N6JTFHDfC+KcoZlzIPV/vcC8cvZYmtdF+uwz0eotN1fUxigUMHCgcFUHF9fDFxUHE5s1EynIElm5UnwcPvsM2fkLlGvYhjZ6AXe+XgFG34ZRD+CuR6lCqPjHt/tfkv+TCiH/k6nEj4Nx4ZBpJ1pj/VoXej+BtcfMGGVwdXBz9MmJVL8oOP4k4IUzBId2pVtCN3r796aTXycc1A5lB+/dW7Rae/IE/87DiCjsizy0F7trw+D+BkZGLmKBzwLK3bwJ7u7M6PQ161bu4qcbP7G4Y2l9gN6kZ17oPBZdWYSLjQufxVdmlXccsesWU/HaK8pXlLhVmIrHEg/y9flvxdmn5Kcgk2Q0Kd+EO0l3yCvK46MmH9G0QlN87H1YHb6a7RHbmdNyDvPbzie3KBfv772tUOV6XvUYUGsAi68u5tizYzSr0IwA9wAepD6wUpv/XoYEDsFOaceAfQNou6Utp4edZkjgEOacn8Peh3s5GXWSG69uYDQbufHqRpljXydTcdG4ML/tfAI9A2m9RXS6uhJ/BZPFVCZV+EcVi152XuiNelpubImN0obyjuUZtH+QdeySTlMlcQqAfIO4j0PrDGXHwx24Lna1gpEkJLpV68bZl2cpMhXxOP0xjmrHP+Vv+OzcZyTnJ3NojwxJpcImM4f7t9siS7rAkmbw6TvgXPSI5s29OPwrSDfDREZqkJgnjUth5OTnv3mCO3fg/Gtl3Hl5MGsW0b3bkNqlFSEPMrAFer9QYLvHiH8GVM4VDWSwgK0BRtz5w+n/S/J/0mUwSxLTOotuzi1eweFqUC1bpIDiHOGDATacLFfIx9cE3Xaon5xjVU00ToD9vWtwzO4VWoMWuSSnhlsN6nrVpbZHbZw0TlgsFlrP20zt0/fYPi6EwVvvkIueTWMbcqqBA5djLyOTZDxboyC3nAffz27D+ZfnScpPItAzEK1RS6Y2k4zCjDfMdo1eVGLm2MrY3ESF1qRDKVPiY+/Dq7xXyCU5jcs1ppFvIxzVjlZ+BIvFQr4+n433NqI36RlZd6QgNU0Mp2n5prSp1EYUHGHhUOQhorKi0Jv09KzZkwD3AHY/3E12UTbvN3ifUy9OEZEaQYuKLQgpF2KdY8l7UPL7y+yXHIk8gkKuQCVXlSkwArHAvO28KedYDo1CY+3+BAIs1KJiC3KLcolMjywDGpKQBD+jsdDKkvS6//9XKx0lJALcA4jNicVkNr3VwgDhcpgw0aRcEyo4VWD/4/242biRpcvCggV/d39qutUsvdfF500rSONy3GX8lF4EPkhhzTkNShM45BahMlnYWA+Q/X/kvXdcVOe2x/3dM0PvIE2qgljA3gUVK6KJvWuMPXZjS2KMJdEYuzEaWzRq7F1jr6ACYkVERCwoVaR3BpiZ/f7xwCgn5Zzz3nvfzz33Xf4hZc/MZpe1n7XWr8CUXsIIxtbIGp9cBaOv5fDZAyhTwOClDanwcEVGZujpV3x69AVlCuj9iQK0OiGOAsiGBuw/rOFxQwemDLPkVe4rJCQ2hlsx+XIOJ+vCT60FrubUYbhbUwDs5odBxzfgWvDfVzL8RyaETFMJGzV8GwhLQwTxw0gLt12FUpLLHJhyHxbfgKMN4OeWEOkmThzwXnniL+LRFkEksSsFj3xBQPmQvGKphtwVsLgTLOv41+/z/0VUCZd++KSremIqJSUqhQqtrEWj02CkNEIn66jQVaCUlHpIclU9rZN1aLQaIZzyFzekidKEUq2QUzcxEOjCDy3r/ypUClW13saH/g//CC4yVZmilbV/CTWuEqZVa9R/SDZVStEKSaF/TwkJT2tPtDotSQVJuFq4YqQyIqM4Q9+QdDJ3wsLQQp9YX+W8Qifr8CkxQVlUzNETBmRZqWj9rIhyJfQZDJcPwLJ+dmxvb0p6UToVugosMebcDjWt0qDX5/bk1/MEYM6hJPqHviPNAoaMMUMqFONXSSmSw5pLYF0u4TtFxtbEFm8bbwyVBkz+LY7hN3I47As7m8Dl/ULro8UE0Khg2TUY+fj/5wkhx0yJbYmOcgUY6kCLsNa2VYNGAo25MeYFako+GYbW0wOLpSuIOruT9C2reJYdz7lW1tx2LNdfyFWgFx06bEqEnHZcDbHiyDOEoDn2VHi44mTuhJO5EwHxasZ+eZAxk2uy2zGN+jXqI8syL3JeoJW1jGw0klVdV2FjIgAtEhL06IEUGsqqtpD7zWySC5I5+vQoEhL2pva8+fwNhkpD/Y1d9aT88EaXZZkxp8ewJ3oPNUxr8HL6yz+gGSu0FdRcW5NcdS4zWs9gXdA6MoozcF7rzIL2C+hdtzctf2mJr70v/ev3527qXSJTIvUd7aqwNramjUsb2ri24ac7P1Ghq6CwvJCwMWEE7Aqgg3sHHmc8/kMDsYZpDYG0rOwpqBQqjg06Rp96fcgpzaHRlkakFqbqkYbuVu56QZKqc1FVQhirjFFr1HrKc9V48UNeQ9XX7d3bc3roadKL0gnaF0RmcSZqrVrfSFUpVPi7+XMj8QZZ87KwMxXisCGvQ5h2YRpPM5/Sw7sHG3psYN/jfSy9uZSLg88Q1Hq46AHExgofhZs3kSoxDzpJQtGzJ5w9S2lFKVvvb+WHkO/IrMij13P4LgSaNf9IGL/MmAHHjomSQpaFAKudHXJODhEDWuF/TKhuJQa3xX3ncaQqp+nnz4UcPOI6VwIlKnCfBdlmYgLxy5B/Pnr8P41UtCl5X3OWK0CtgieOQkjCWAfmBWpOdHOlfaP7lK1bybk60Oz+OPo1jmdsFFz5KY+mr9U4mztT26Y27tbuWBuLOU77JHFQNrSBz3vAFW8wKi6jqVNTJrWYxM89f2ZshS8Av37/hN/6/kZaYRrPsp+hlbUM8xvG3n57cbZwxlhljLHKGKMKHUb3HqJUKPm1twsb7mzg9/jfGVB/ADIyGSXDcNJzAAAgAElEQVQZ7H28F6VCqZ/r/+NTH2BJ6BL2RO8h2DuY3NJcBhwZ8IexoYHSgOENh6OTdSTkJpCnzuPxu8d4WnnyY+SP9D0kkH+xmbEsvbmUawnXyC/LRyEpaObcjBVdVxA/LZ7cL3O5MPICX7f/mk09N+lLisDdgQDcTLpJvjofA4UBloaWnBpyiu87f09WSRavc997M5wbfo4+9foAYGtiS4B7ABKSHmmYlJ9UDVOhQ4etiS0/Bf+EuaE5EhIP3z7E1dL1T0ekdWzFuPdW0i0c1zgy+dxk2ri2Qa1VIyGxs/dO1nRbgyzL3Ei8gYTED2E/6B2uOtXqxKPPHrE+aD0RyRH4bvbl+5vfM9R3KEFvlKKu79dPGPWmpSFptcL9GVAYGgpreI0GEwMTZrWdRULuKJZfl4hwg+afwQDzczzpUA/u3xdqy5IkkoGREQ8P/Ui2uQLjsDtoKk+1x9X7SPXrC7NirbZa01EJhLtC+7EiGYCYOiy49oHAzn8x/iNXCBqlRKEhRDtCujkMfAoH/WDoEzCQ4VoDExbOaszEm8WM3hvDns2foWvTmpoWNfF6nILXgPFgY4OUmVnNVi23NJfcYf1wO3ODXsMhrLaSUsX7ZaeMjIHCgN3XLQl+o+L+1b3MujSL2MxYmjs1J+pdFDpZx9SWU1kSuETf3OObb7i/63sm9VHywFGLhMSDzx5Qv0Z9aq6tiSSJuvrF9Bd/ABxVxbKby1gYspAxTcawo/cO9j3ex6enPmWY3zD29d+n1waISo/ixNMTrL+zvlrDrSrsTe31oB4rIyuC6wTzsc/H9PDuga2JLYVlhUSmRBKWFMatpFtEpkT+KXGop3dP4rLiyC/L5+bom3hYe/DFlS/Ycn9Ltc9d2GEh33X6DhC28c5rnf9wY9cwrUFWiRAO/cr/KxzMHFgUuqha36K5c3MxHqzfj5ySHDrs7oCMjIOpA0XlRRwdfJTQN6H8Hv878dlCn7GqFPmk0Sf0qduHgUcHopTE+ZYkieENhzO37Vw9QzO1IJUm25qQVZKFs7kz65LqM2TXXaTMLBg6lIrrVymsKOJk/waM2//0vaT6nTuigSjLUKcOlJeTX1HI+gAV63yyKTKQGRYjSlifSgzbxSEt6Fn/AZ+9tmPLniyh6vX2LaxbJ6T8rl8XGIaMDLRJiZxqqGJdCw0R7kKKrfA9qBMJ0C3+Jz2X/8slg04SC2qNAtLN3o8VJUA2NBSOy2vXCjSiry9c/QeQzMiRgjo9cGA1mTIyMsDFBTQaaNaM8rAbPPplKeEHV3FzcCtulL/Qd7dNyqHUUFx0Pbx7sKLLCh6kP2D0qdFISFgaWbKww0JGGbTgu2878XMLGccSiYnBC/nu5necHHKSvvX6MvfyXNZHrkcn69jaayuftfij8MWq8FV8efVLRjYaye4+u1EqlJRry5lzaQ6b7m3C194XhaQgNrO6WYuEREePjiTlJ+lx/XYmduhkHXnqPNQL1OSqc/U3f1hSGI/SH+mNVJo4NaGNSxsKygr4/fnvFJYV6pfqzubOFJQVcG3UNYrKixh/ZjyJeYkEuAeIZpyNF61cWnHs6TGWd1lOZEokZ56f+aeq0R+iDg2Vhqzquor+9fvjZvVex7L3wd6EvgllddfVTLkwBWRY1W0VAxsMxP9Xf7Q6LV93+Jq7KXc5+vRotV6EgcIAY5UxQV5BnH95npKKEoK9g5nXbh4xGTHMvDiTxR0Wc+b5GR6mP6RjsT0b51zDferXmJ84y4WW1gQevoN5rffkLb014JMngrDUsKFIFps3k93Nn9Wjfdho/ZwyFYyKFupJQSMhqOd0vu+0DItBI4Rkn0YDX30Fy5fDgQMUTf+MX32K+bENvLaBmgUw/Q5MuycMZX9sKz7eo0DBm7V/z3z8v5sQ9u+n8NORWPzJ319oKGHRrqMAg3z6KUybBiEhQmL9w9DphJ5iVhZcuCBgpRqN0NKPiBB4hPh4Qa/WaATqTKNBjonhbPiv5M6ewkp/SKgpatyqMFYagyTm4b72vtx4cwM7NeSYwNQSP5btSMAkMxe7VXaMbDiSLR9t4UX2C3w2+eBmKS74lzNeVlslrL+9ntmXZxPsHczA+gN5mP6Qe2n3iE6Prnah17WrS996ffX8/+Nxx6moxDgEuAfwsc/HHIw5SFF5EQZKA2IzY/XSZSDq9TaubQhwC6C9R3tau7TmasJVvrj6BQm5CfSs05PFHRfjv9Nfjyj8yv8rckpz2P5wOz52Puz4eAcrwlZw/uV5bI1taerclGuvrwFijFhQVqBfbVTJuf3j2FFCoq1rWyJSIvi196+MaTqm2qkLeR1C598680OXH+hbry/1f65PY8fGRL+LxtTAFAmJiHERNHJsBAitxwFHBnDuxTlA0Kyr9qFejXo4mTkR/S6aXHUuCklBI4dG3J1wF0VEBDtmBfJ1H3Py5VL2npQY8khD9q6fsW8VKB40IKDJgYFw+bKgLi9eLH7n7i7o9FOmwJYtvDODFQGwpaVg2A5Te7P8i0u41KgtxH/r1hVApoAAUs4dZOPN1WwL/4l8Y9EonxMBtXKg0BAaZMGZujCmH5iWC3n2Ef+ksfh/NyEYGSGXl/9hSCAD4d9PIiDXXNCRnZzESbl1689Vle7dE7LppqZiqbZ0qRCwAPH1h8zHc+fgo4/4fUoXDmVc58AxmdsnN9K27zRySnM4GXeSQ08OcS/t3h+ac7Yl4FwIBvaObNmTSZs3Wvoc6kPMuxhezXiFJEl029uN6PRoMksy2dxzM0HeQdxLvcf2B9u5/uZ6tS68uaE5zZ2b07JmS1q6tMTZ3JnPL37Ow/SH+vGdlZEV7lbuxGTEMLj+YNq5t+NW0i0uv7pcDS7czLkZQ32H0t6jPc2cm+kT0f20+8y+NJtbSbfwtfdlXdA6unt1R61R63ETTqZOpJekIyExt91cprSYwsKQheyL2acvr2yMbWju3Jyrr6/SrVY3rry+8qen9MMmYWOHxpgZmZFSkMLL6S/f08QRmogttrcguzSb+GnxbL2/lVmXZhE/NZ4BRwfwJOMJhgpDVnVbxfTW0/WjRJ2sw2ejD69yXzHMbxi96vRi2oVpFJQV6H//YWJytXTly3d1GLsxjIIXsTQ/FMjsY2lMug9HbvzMp9luKD7u/f4PMDAQD6E2bQQK8eVL0XfYvBm5WzekkBD9pjG1LdjcUscOn2KUSEz2Gc5XfdfiuGEHD3/+hnXtVRz2A51Ww8BYmG3amdZHIkSyAEqVAp2YYQadR8O3oTAihvccnb+I/7sJ4S+AJHp56iNHRFcYxDIsKOhPtwf02Rtf3/e8dIVCNJJM3zsN30mORNetCz5JJcQE1qdjyGukggJxIXwQZZoy5l+dz/o76wHweycYcrkfODc5mTnh6+DLtdfXiP4sGnszezbc2cDK8JWYGZhRqimttuy3NrZmqO9Q2ri2oaVLS+rY1iEqPYqzz89y5vkZvRKyscqYMk0Z45uNp6Z5TU7Hn65mguJh5UFz5+aceHZCf3NObTmVTT036bdJKUjh62tfs/fxXhzMHFjaaSljm47V9wQGHR0kVIEqo2oK4GPrw8vcl+hkHSYqE6a1mkbImxBe577mxugbdNjVgRz1e/1GG2MbAj0DOfnsJABuFm4kF77XmwTYFLyJqa2mVvvZnkd7GH16NPv772d4w+H02NeDxPxE2rq2ZdejXazrvo5rr69x7sU5Onh0YFefXdS2qY0syzisdsDVypVH6Y8I9g5mQ48N9D7Umze5bwj2DuZk/EnsjO3IVr8nqhnpFNS09eB13mtebzXBM70UxSJoZejJps1vaJEGWFiI62XTJrEiXb5c+Hx8+y3Fb15gtmufUDfig2n399/zur4TS49MY7dPKQYKJU6WNUkqSMaiDMbX/IgZC8/iqbCF4cMFOa/S/q3qvQ76waJOsCQURjyRqtnD/Vn8/y4hAKIr+/KlWH55eAiNw7/bXqMRzZysLLGdmZmo/yIiACHssShkEWtvr6VrgT0X12UgOTkJWmp4eLW3upZwjSnnp/A8+zlNnZoSlR5F2F5D1Fs2si3vKheenqaIv6+fq5B+rVxacTf1Lj28e3BqyCk0Og1XE65y5vkZzr04R3pROgpJQSuXVgJUg4LH7x7zIP2BOERIeNl48TJX6G2dHnKa3vXEE63dznZkFmfyMvcl7VzbET4unKLyIlaHr2Z1xGp0so5ZbWYxv/18LI2E1JtO1jH29Fj2RO/Rr1aqOAhVYW1sTbmmnNgpsZRqStl0dxOb71cX8JCQuDzyMg/ePuCb69+gkTW0cW3Diq4rCNwdWK0Z+WTyE3wdfPWvLakowWejDzUtahI5PpIyTRm2q2xp4tSEyJRIFnVYxLedvkWWZfZE72HmxZlodVpWdVtFoGcgvpt9+eVjYbT62dnPaOXSit19djPw6ECeZDwRWg1Tn5GYn8jl0F85dPp7wjwltJKMTxbEV+bNb37/nB33t5MhlTD+ISwPN6ZGjhrs7ITg77Vr0KULiQF+eIQJMpNWIaHUfXCfXb9OSUBrfgvfzMori3ljKAwXjHQSn0fIzL9rgFVhhfAF+fRTQdk/d47Eore4FImkkmoGTaYIbM1/Z8nwHzl2/MtISHjvouTj8/fJAKC0VCQBEEuu0lJ9vyEyJZKm25qyOmI145uO5+j3z5E++USUF/Xq6d8ivSidESdG0HVvV7Q6LZdGXuJWjXnYlsCS4TV5bF6MSqHCEYs/2QHRlKzqfKu1apSSkrupd/G28aapU1P6He5HjdU16Hu4L0dij+Bu5U4nj0542XgRmRLJnug97H+yH2MDY6a1nIa9qT22JrbsH7AfEDiAS68u6T9vYIOB+kQRlxXHrqhd+Gz04bub39G7bm/ipsbxQ9cf9MlAlmWGHRvGnug9wHsBULVGzeKOi4meFE0jh0bkqfNwsXQhaF8QDTY3+EMyqLKYH/v7WL669pX+fea2nUtinpDB+3Ai0vKXlsS8e+9yvTZiLamFqawLWodCUnAj8QZqjZrIlEhGNR7FksAlgJgejG4ymieTnxDgHsDU81MZcFhI0bV3b8/4ZuM5NugYUW+j6H+kP7VtaiMhkZCTwOHYw9S2qc2kaBUhv0nUKJFp4dyCyWku+v345eaP5FCCW4mKnU3Ba6KaTV0s0ORmg4sLKaViTOgR9oRiY3FelSM/oXLnSDeHhWUXcF/vzuQb86jh2YCDDlOI2mtKrxewsj3UmlLBD8PdKbp0RlzDixeDnx92agjxFLZznnMg1xRKDGFBUHVC1n8l/uNWCLIk/aF/oI9du4SackqKYCU++mvfQGRZ0FCPH69Wf5WdPsE3xhGsi1yHq6UrO3vvpGvtruKX589Dr17Qti3asFtsf7Cd+dfmU6opZVTjUfjZ+/E84R6LphxmSYCGrS3Fy1wtXWlZakvLC49pufE4zet2YujxoVx5deVfguiaGJiAjF5rwNLIEn83f9q7tyfAPYCWLi0xVgm2YHxWPP6/+mNlZEVaURqe1p5C32DOWwyVhiTmJeK5wbPaZ7RyacX6oPW0c2tXeWhkYjJiOPb0GBvubNDX2m6WbhgoDFAqlLzIecE37b/hRc4LDsce1r+XjbENGp2GwvJCvfGKu6W73tjVQGFAvRr1SMhNoLiimLPDzhKZEsnysOWilpcUuFq66vEJIaNCqGVTizob6xDkHcTxwccBGHB4ACeenaCjR0cuf3L5T8e1siyzM2onU85NQaPTsKXXFiY2n4gkSYS+CaXXgV6UVJQwtslYEvISuPHmBts/3s7IUWt4WPySyV/6Ej42HPMuwWgSX6NKTsVvjgmxFqWYahWUKN8v0xunw+qrCp7WkJkZKZPvYo9VaqboU/XrR8y6r1jfwYD99SqoUEn0qdeHOW3n4O/mL/AmSUnQqxcPs5+wqJOwg7cvhvmqQPrM28mR2UHstHjJSzuBlC0yRC/X9t85dvyPWyFUadN3+eT9z857wXlvSP9qulCv6dpVjIBK/0Z4c+1agRyTZTEyMhcSXHt/HMea22uY2GwiTyY/eZ8MQJQgQNTr2zRY6c6U81OER4Ess+PhDj6/9DnNNh3DvkCDd4/hGCmNGNRgEMmzkjlhN4X5YdDVsS02JjZMaTFFYNz9hlaT//rHkJEp15brk4FKITQX69Woh4+dD3Xs6uiTAUDdGnU5O/wsb4veIssydiZ25JTmcOHFBQC9o1JVfOn/JbfH3aata1vupd7jq6tf4bPJh8ZbG7P0piBMmRmYcXnkZeKmxqGRNZRUCPrwslvLOBJ7BAOFAROaTcDKyErYpCkN9DBpOxM7fTIY4TeCCl0FMRkx+vGqscqY5znP9bbyXjZe5Kvzmdl6JuXacjru7siYU2Mo15azsutKAJ5kPOFU/CnMDc05PfT0X2I3JElifLPxeibopHOT6LG/B8n5ybRyaYWNsQ1KScmpZ6f4NvBbenj3YMKZCWy1iOeinwm/D/0d8/xSiIhA1UYky8ghV1gbaoQtosdUswDavlWRYwLdR+o47CtTZzosapTJmXoSJzdMJqhwM42mwGGfCiY8N+f5DhNOtt0gQFpVq1hXVygpodlbOHsAbu4UzejZRqF4/eTFfM+XOBVB/1h4uxZsP7i03VV2f3n9/LvxP54QJEnqIUlSvCRJLyVJ+uqfv+LvY2awcL7RKeC1Nbw1g56vBPnjHUU8swP7xpdoMU7L+P1D2Pd4H2kFaVRbCYWEiCSgUEDHjpQs/po0e2NkYGxILvfqr2fLR1swNzQnITeBw08OM/fyXE4eXsJnH0GLiZCZn4ax0ohmzs34vM3nHBl4hLQ2xxgbWY5ixkzmTNvP5BaTOfnspFgSG4qLNjUnkW33t/HT3Z8AOPTkECXl1bkAVeYkVf8rUNDdqzvTWk1jcovJGKuM2XJ/CwOPDsR5rTPeP3nz6alP2f5gO7EZsbRyacWRQUco05YRmxmLvak9O6N2MvvSbHw3+1YDGuWU5jDn0hw8N3jSakcr1kSswUhppP/sejXqsa77Ojbe3UiN1TVIyk8isyST+vb19UpJdezq8MvDXwSs2y2AnNIcyrRlqCQV2aWiSedi4cLaoLVCzLSSmARgYmDCi+wX+v1p69qW/LJ8xjYdy6w2s9DIGi4lXKJrra5423qTVphG973d0ck65rSd85dCtFWRlJ9EamEqXwd8zeaemwlPCsdvix8DDg8gtTCV3/r9hrWJNT339+Sz5p/RpMCMWT0ge8jHeFh7iFWhTqeX0jPPKWJ2aBmvrBays+m32JXCbWcNGglGPYIHzsLheVML6D1Upv/F0YQqk+n6Ck4egg1tvsU7B5g8ufpkYNkySEjgpYOKr7vCkMHw2AlsNAa4lgkUUrIVmGqFqpJnpfyDJEPPO7kCV/PfEP+jJYMkSUrgOdANSAHuAcNkWX76Z9v/KyWD5QIFHz2T2XFaHBwZoUJrqBW8hjlBEptbyKirDwBQKVTYm9rTDnd2LX2MVFFBmZ0Vr47vZNzNOdz/8hXpbja4v8mlyMaUMT+0ITQ/Wn9BqxQq7Ao0ZJhBX+qxc+UzrHYfRDGkkupaXg7NmgkefGwsWFiQnJ9M7Z9qM7D+QJxT8jj55iJvbP7kOCHhaO7I4g6LmXtlLsUVxSgkBeaG5uztu5frb65z6tkpEvMTxZzerS296vTCy8aLlIIUwpPDCUsK0yMQbYxtaOvWlph3MSQXJGNvYk9maSYSEmOajKGpU1O9ojIIAFB3r+4EegRy/uV5vYiqpaElheUCjORm6Ubfun3Z+mArM1rPwMnciXlX5gEC/bgkcAmOZo4MPzGcCm2F3tlpWstprLktPDU7eXYiLCkMY5UxntaexGTEcH/Cfdrvao9ao0ZGZnbb2ay7vY5NwZuY0nIKnj966lcY67qv47fHvxGXGUeZtoxnU59VU3f+s9j/eD8jT47kwcQHNHNuRkJuAoOODOJh+kPcLN24Pe42CklB8P5gYjJiWHBdxzNPU47WKhGK1FueI925Ixp8HTropwlx276nv3oPUbOeE1Ib1rSDcDcYFgMHGkG5SiT0pk5NKX/6mEfWYmxobWhJZ50n3U49ptv0H/EaNZPS2GhOjGjKjqYyoZ6g0EHPRAPGP4SesRWodHB5Ri8Wlp7jngt4Z8PXt+B4fThXtxKLEGHHiJC/ton/XzFlkCSpLbBEluWgyu/nA8iy/MOfbf+vJIRfm0lMD4a0teJAGMjwzgQcSitHOrduwejRFCa/4tZHDbk2sRv30u7xIucFefkZXN+lwy8DWk2AZ5X+J4GvIWSPAC5uvAhORXC1iSWHlwzE06YWF19eJDw5nCZvYavrJFrP3yRu/sJC4cFoZCQy/MKF8PvvFAd1Zk/0Hg49OUREckQ1Jp+hwoDmNVvQw6sHESkRXHp1iUYOjbgx5gbWxtYsv7WcBdcX0My5GQ/fPsTG2IZNPTcxxHcITzKecDr+NKfjT/PwrSDC16tRjz51+9Dbpzd2pnbcTrlNeFI44cnhenv0qrA3tadMW6bvCUhI1DCtQfy0eNZHrmdV+CrKteXVXKUH1h9I33p9aebcjOKKYix+sCDALYDw5HBkZNwt3YmZEsPpZ6cZfXq0XiOxsUNjojOicTRzRCfr0Mk6skuz+bbjtziaOzLp3CRAuEsF7hETBisjK/rV78fFlxfxd/NndJPRBO8PJsA9gLCkMP0+t3Ftw9uityTMSPhbPQOASWcncSDmALlf5qJUKKnQVtBqRysSchMo15RjbGDMTz1+IrUglUVX5qNRwAapB7HNPdgduY38tQYYjh6H9Nln0LQpZbNmYLT+J5p8Bvn1PYn7voA3cg4/+ivZ3VBLmQp6PhfK35ENBLFqwGsTFlwq5bmHGZfnD+ZKwtX38m4G5pSpiylXynjqLJlQUIdPdz7AJfBj4TM6ebIQWdFokO1s2VQrhx0txOrBtAxKKiHMHnnwZv1f38v/W3oILsCHA+aUyp/9v46xUbD9d8g3ggt1BPXZvioZgDBXiYjAwsSKnidiWJtUjwsjhL7g7dg2tE0RyzqjDyD+HRLFfPeqF4zuK96rc3QBr64eZUnoEu6n3WeWUz9Cd0HrtgMF/2HNGtFT2LiR8qcxnDmwhAGzXHCKn4D5D+ZMPT+VW0m39OCYTmYNub8NioPDiBgXgb+7P6FvQgGY3HKynlxVNffv6N6Rhg4NKSovYsSJEbT7tR1F5UUs6riIBxMfkPh5IhuDN+Jq6cra22vx3+VPx90diUgWKD170/duT1Vt2MySTH0yMJAMkJHJLMnEaa0TS28upUxbhiQJnYO74+8SNzWOpZ2X0rxmcyp0FawKFwIwYclhyMj0q9ePlMIUvrj8BaNOjdJ7Pg5uMJhHkx+xuedm3hW/q0ZF9rbzZkLzCXjbeAMQmSxEVoK9g6ltU5uk/CQC3AO4mXiTuZfn4mXjxZWRV2hQQ5i/yMjcT7tPkFfQP00GIEhP/u7+emm0dbfX8Sj9Ebv77CZmSgy+9r6MOjWK+dfn831qPfo8gxlcxMHMgY1GfTFSV7De4RVaE9GnuRgiRpc9uk7i5+aLGdQtl/rTYHcjHaOi4elmiUPHJc4fUlA7XSBJT3qU0nY8xDdy4fsuy/kq4CsaWHgBUFxehK4yAScqCjmtjWVLS7ihTKY8/KaYMhgYwPDhSNk5TL0PUdvgm1CqeTUk/X3l9C/H//QKYRAQJMvy+MrvPwFaybI8/YNtJgITAdzd3Zsn/oUTkz5UKoE3+IuQlUrizu2m9PA+mu26hITQTXhlDb+dEvTo67Vg+Hhr5nf8hnHNxmER3Bd1Vjpbto0nLCmMEWsu0zeqVOgg2EDRB0QSa0NL3K09cTJ3Qv3wLi+V+bw1l/ViFyqFijq2dejp3ZMxTcfQwL4B/Y/058aLqyQtLcI8NIIbzuUE7w/Gy9aLt4VvCa4TzN5+e/WfMfjoYK69vsa+fvvoeaAnnzT6hOuvr5NamMrABgNZ0WUFXrZe+u3z1Hmcf3GefY/3cfnV5T8Yl3Sv3Z1nWc9IKkiiT90+pBelcy/1XjXIcJXmoKWhJb/0/oVg72BMDEyQZZmjT48y/9p8EnIT9NtPaTGFQQ0G0em3ToDAUKgUKmrZ1OLO+DuYGJhwNPYog48N1r/G09oThaQgbmocy24sY+mtpTiYOZBRnEHYmDDWR64nNjOW6a2mM/W8ACUdH3ycZ1nPWHB9gR7fAdDRoyNXPrlSDcn4j5FVkoX9anuWd17O/PbzeZnzkoZbGhLsHcyJIcJVKTYjlhbbW1CmLePyASXNS22Yu/Fjfn30K6GR9Wlz4xWWc8pppHLh3pJU7nib8MxOZsMndYjKisG+GKbehcn3waFKYb5lS0hIoMLHix+W9mD95e/IM62+b40cGjEh3owR225jXg53f/uBK9l3ufz4JHddQKsQgqod8aTbrVS6OfnT4M4rpKT3z9eBg+B4JVTDPQ8S/wNWCCmA2wffuwJpH24gy/J2WZZbyLLcwt7+rz0Mq+JZu7r6QZ0WSK+cOpSoBBW6VKFFNfwTlheJZHCvUQ0Wh8Lu3yVKVfDODEKXjePNnGTmtJuDtcIUZeQdzLr0YFTjUVgZWzGpSyn5pgpu/qYg5VRtZjT+jFEvzGmUDnnlBTzOeMzlhMvctM4jzUIssE10KnztfZnaYiqLOy5mTNMx+Nj5IEkSX/p/Sa62iF+aQXjmA3od6IWHtQdXP7lKkHcQl19droZOnNxiMjmlOWQWZ9LevT3XXl/j8eTHfBf4HedfnKf+z/WZe3kueeo88tR5HH96nGU3l3Hh5QW0shYjpRF17erqsQSXEy7rmYOn408T9Taqml9jJ89Oes+DHHUOA44MwGqFFb4/++KyzoUhx4ZgpDRiUQch817ToiYuFi4E7RcoUGOVMY2dGoMERwcdFWNS4MjTI9iaCGUZpaTUU7K33t+q1yPIKM7QlwFV2ghNHIVHpo+dD03BZFMAACAASURBVCUVJSy4voDhDYdzb8I9GjoIZuKNxBv0P9Kf0oq/niRVlRntPdojyzITz0zEUGmoR2dml2TT51AfLI0tud73JB1fadnpmkmuOpeZLafjHR5HeH0zlMYmxKtTAbjkXs7oYDXq1y/45ZySpPWCxehQpnovpT9oEKxZQ3bMXYzu3KNG5S5+uJ7RaivoGJaMjRoMDI3x7zGBJT8+IuJhU7L3OHLyEHyaZMMLRxWzulTg5xuK68BkRveF/Q3FdWxWhXOToWf8Xx6Gfyv+pxPCPaCOJEm1JEkyBIYCv/+T1/xtmMU8I9wFUi2Enn2so2gs6iShulxmbUGdXIk92o8BaNRvMiVmRih0MkYayPp5NcuH7Xg/6rt3D9RqrriWU29TPQ7GHGRw+0k8nD8G6xIdJckJpO3fxm91injsKF5ioDDAx9aHwBot2XwWFt4AZYWG2MxYNtzdwNDjQ/Hb4ofx98a4rnNlUcgiPIydWBIIQdHzqGlRk+ujruNo7kiQVxAZxRlEp0fr/8ZAz0B87HzY9nAbSwKXkFaYxoGYAyzsuJAX018wsMFA1t5ei8NqB+xW2TH+zHjisuKobVObff328Xrma+a2m0sL5/cPhA85FuW68mqswzupdzBSGRH1WRRZ87LY0nMLtaxr8TTrKW+L3gICxLQ6QnA9isuLWRCygHJtOX4Ofqg1au6k3mH7R9v1Tb6i8iLOPT+HLIuG5Omhp8kqzsJEZcK3N76tJqxShVB0t3KnpKKEI0+PAGBvYs/Y02MJ9Azk196/6vUiHM3EiTj7/CxB+4L+UuX5VuItjJRGtKzZkl2PdhHyJoTV3VZT06ImFdoKBh4dKMxghpwi8GkJBloZ508mc+7FOWIu7sGlEDZ656KVtZQbixWUYbmOE+ctefJjOeNtu2JcBQbQaiEvD40Czthl0df4FK5zJL6quEDNQthzEvJnvuPggIO4WboRmx1Ho49SaD8GEg3VIom8fg0//ICVbETfZ/Bzx1U8n/GCWw5f88vv0CYFzvjAyAHgNA/2VvkDSXD+73ur/3L8jyYEWZY1wDTgEhAHHJFlOfa/8p6J5jqavoPl/tAmFbq8EWWAWYXIwDbZxUjz5mF+4gzl1hbkrV+OYUml0KYk0XjLcQFVrozUswcBGJaxBaVCibmhOVsfbCWofCc+MyRqzoVjfmLePNm0A5dGXqJwfiHx0+MJCfdm8mNDvrtrSvaTnoR8GsKabmvoW7cvta1ro0BBamEqVxKukKhOp8AYinVqEnITCNgVQP/D/YnPEqn90JND+lWCJElMaj6JiOQI7Ezs6ODRgWU3l7EhcgMjT4zUA4E0Og06WYeBwoDZrWczpcUUtj3Yhut6VyacmcCr3FcoJAUjGo7g/oT7uFiI9o2EVK2sKKko4dvAb7E1tmVJ6BKmX5xOWlEaSzstJXteNhFjIxjcYLB+XFmVXIyURvoeSRXbsirOPT9HqaaUXHUum3ttppdPL659eg2lQklOaY6eE2GiMqFCV8HqiNW4W7kDsOX+FuxN7bmdehtvW29ODD6BkcqIt4VviX4XzYzWMxjmJxSMw5PDCdwdSHrReyfpqriZdJPWrq3JVecy5/IcOnh0YHyz8ciyzPQL0wl9E8qOj3fQ1q0tnDoFjo4Mm/gTX7T9glqJBfQfDKcaCOyGmYklFYYqlFqZtX4FFO74WYij6HTQogWvrGUWdJVwnwW9k1cRmRLJnAbjeLZFxY3dMCrZFgtrB4b6DSWx0S6OHwLXAgjzAM9Z0KNmCAkBvsL7MUlMVX5/cZZR3zWlyczltE2ROHoEMlbDne3Q/aUwmK2K5P+EHsK/G//KlCHFUsKlUJhsWpQJP8eLtSE4oRLFKMuU3LjKu89G4B7/DqUMOoUCRY8eMHYsxaOHc6epA1dn9uZA8jm2bUqkZiE0miJ8C7SyVg+8aW3flI9PxvLxMx1+KRVI165B585iRy5cEF3gJUtEX+ObbyA0VFCoK0Or0/Iq9xWn40+z6No3lGnLhR/BX6ATjZRGeNl40cy5GXVr1OXb0G9p7NSYMk0ZTzIFLt7LxgtDpSFxWXHYmdjhbetN1NsovQJRHds6DG84nL71+tLYsTG1N9TG0tiSuMw4rIytyFfnM6DeAM68OPOntmoSEl1rd2Vzr81423pToa1gRdgKFocuroaqDPYKxtLYkqNPj+oTmYHCgOY1m+Pv5s/VhKtEv4tmsO9gDg98j2R8lP6INjva6KnbKoUKLxsv3uS94eCAg/Q/0h+VpMLU0JSCsgLuTbhHi5pipVNFbor6LAo/Bz+GHR/GsafHMFAY4G7lzpVPrlDLRhgYFJYVYrPShq8CvuJFzgtOPztN9KRo6taoy8Y7G5lxcQZf+n/Jiq4rBJPQ3p6s/sG0bxmjt6C3KpcoNJQwMzSjTFvG2+XlpJpDsykSjbX2nPwpg5uDWrLTNZMQ6Y0YF76Acc496bXqlOhv9OwprhUfH0Gpz8sTdPrMTLC0ZN/pZcy8OIMcSQ0ydE815utbEh3jSxneH1aGqrBRmKK5dhXrgC5QWIgG2NYSpvV6f94cMSd98V8btvxv6SH8t0fNQrESSKlkETafKFSTZKC00lJn8cYBfFf3HQpZTA/OtLJkzkQPWueuwmquhi5dUvghZjOpOYn4J0NYrfc02R7ePfi196+kz03n9pQHfD14Iw1TKkT9t3q1AJMUFYlxUL16QtBi1iyBNJszpxrrTKlQUqYpY2XYSuyNbfnxAuiQ2ddvH+Fjw9nSawtjm4zVKytVyYPvi9nHwpCFaGQND94+IDYzVkCGJSWvc1/zPPs5loaWZJdmczf1Li1dWtKvXj9sjG14mfOSxPxE7E3tiUqPIrMkk8fvHjOwwUCeTnnKgAYDuJRwCU9rT0A4JlWFm6UbVsZWXEm4gu9mX1r90gqPHz1YFLoIGRknMycAlnZayqmhp0jKT8LMwIyv/AXebHjD4SglJRsiNxD9TpRAd1PvMub0GHY83EFcZhyNHRtzdNB7URqNTsO4puMwUhmx9OZSQICVqkqaD/UWL766iJO5E40dG6NSqDjQ/wB96vahQlfB26K3+P/qr+c/3E65jVbWolKoOBJ7hIUdFlK3Rl0uv7rM55c+p0/dPizvshyAnAsnWe9XhLvbUZ5lP8PJyI6fz0Gq9TKiJkXhbePFxPByigwgzh7mKNsTpcjA83MY6XaPxIpMll2DpH01OHNIom949vtmZxVr9u1bQZGeMUNYCqrVsHIlI7378W69isWxDhhr4LKLmsBhpXQYDYOfgkuxAvNzV7Dee0QkAwMlSsD6g9aJESrW9t/6b91HfxX/cQkhrZIjFJAEtXMFuWNsf9hY6cwbWwMUufmsuyS2VQDRhnlseryT4vJirEwqGz8SNH0L5uVg2KkrF0dcJPuLbI4PPs6YpmNwMHMQ240fLyiuCoWgU//0kyCbJCbC9u0Cg2BqKmivDx7AgQP6fX2a+ZQuv3XBSGXE9W77mXIfaqvs+enuT7R1bcukFpPY0XsHK7qsANAv6UGwB80NRJ9DRqZCV4FW1qJDh1bWUlBegInKhJY1W9LEqQndvbqzr/8+pracyv7H+/Hc4EmL7S307sgHBhzA3syeEX4jyFXnEpspKrcqsZNAj0CSZiWRNS+LE4NPUNumNvfS7ul7CEZKI9KL07E2tmZB+wV8ff1rbqfcZmfvncxtNxcDhQEOZg6EjQ1jZKORAHTy6ERjx8acfX6WCWcm0GBzA2qsrsGXV7+sdk4NlYYs77xcP0EoLC/kwIADGKuMuZV4CxCrrcuvLlcbNxooDTg88DC96ghOQqmmlA67OxCRHMGtxFtISPzy8BcaOjRknv88nmU9Y/BRYc6yr/8+UgpS+OTkJ7g9GMHsHmBuaceuPrtINVvElHtg1mcgjRwbcS97AMtCBCrQQAcrdTdRyGI1VdPYgWubi1lwW4VLcj5YWgr9xMLKp3V8ZbevsFAYtezdK8qCVq3IH9yHqOmDkAqLiCGDpHUwRhwCwt2h31Bo/LUte99doWLDOujUCZVGeEsGJIv98ciDnQ4T/iV/x38l/uNKhjA3iabpYFaJI3jkAMs6CLPMG3vgs15QoYR54bDSH8ZFQbsU+GicCRddRVp1t3JnnNcgJkzfjXNituCbT5785x9YViYSgiwL+7esLNFAmjABtm17v51OJ3T1MjIgPp744iQC9wQKcc/RN6irNgM3N7b+OILJefvZ+tFWkvKSOB53XK8B6GzuzBf+X9C1dldi3sWw+d5mvd+BhISh0hCNToOJyoSiivd6gx8KjEB1WXNDpSFanZaseVlYGlvS91Bfzjw/o9+2kUMjHmc8xkRlQt6Xefx872cWhy6mXFvO5BaT2fFgBxVyRTV1JiczJ9KL0+lXrx9HBx1FqVDy8cGPeZT+iIixEdTeUBuFQkHJ1yUoFUpkWeZ59nPCk8O58eYG+2P2/2E02rpma+6kCaZqI8dGRE+KJnB3IMUVxdybcI87KXdos7MNBwccZKjf0GqvVWvU9DnUhyuvruBo7ki+Oh8vWy/eFb0jqySLyPGReNt603pHawrKCvjlo1/YF7OPY0+PIcsy/eNgjNyYj45UkuG6d4fkZOSnT7m1aR47r6/laCMlITu1lCthwBAoMISFFj1ZXXwFqyIN18K98L77Urg1PX0qRHV69hTWgbm5QqPj8GHxfU4OP6zpy+53F3m8Ts3l1jXwzzbFJrcUqaychz4WTG2UQqQbmEgGlMoVuBYqmBVlhGdKKf2fi5Wv/ziYchc+SbOr1hf7s/g/WzJ45kOUkyAzAQwdBMf9INYBki1g4kPY3RT8psK+JhA8UvQbth8pxUNrwdZeW3kz8w2LPl6Dc93mIltPmSLITn8Wjx5BRYXI7unp4sZXKGDRourbKRTiPZKTebnuGzr/1hmtTsv1T69Tt0ZddAYqbrvCM3UKCknBpLOTWBm+EldLVzb33EyAWwAanYZLry7RdGtThp8YTlhymN7z8ManN7g48iJaWcuyzstIm53GxREXWdV1FcMbDhcjzsrB1od+BOXacrSyFptVNhguNeTM8zNIlf/sTOxo4twEG2MbSjWl1FxXk9mXZxPgHkDM5Bii30VToi1Bo9NwoP8BGjo0xMfWh6zSLCQkTj47idNaJ8acHoOPrQ8pBSkMPjoYjaxhmN8wPRhIkiTq1qjL2KZjaePaBq2spZ1bOz0pyUhhpE8GILABY06PwdzQnIdpwrHq4suLSEh0q93tD6fIWGXMqSGn6FSrExnFGTiaOfIk4wmZJZnMaD2Dpk5NGXB4AG/y3uBk7kSfw304HnccGZmvDDtx/Ah8NKhSuTg/Hzk0lMhmjtRb4ULHnLWc8lPxafOx1C8wJCAJDsY1oFEGLCw9z+e3KiixMKZ9jzRi7REkOUNDwZcBAWWXJHQ52WIalpPDrsbwnfoiOx+4YaAy5OP247CNT0Laug0mTaLZvRTCT9ux56RgNkoyaK0tmdOhlIHDYH4XYRMQ6Qbj+sBul793H/934j8uIXzRDZ7bwclKSYJ2lSWmTQlcqy0ccu1KwEQLOoVEsRGM7gdOxRIbT6iZdHYSjbc2Zue97ciRkUKRZtAgmDsXZs/+o/JMlb7Cd9+JPoFOJ1YI3333x53r2JHXg7rSOWc9ZRVqLo+8TEZxBtPPT8d9X3PajYfN6jC8bUU229VnF0FeQeyL2UdYsuAi3Eq8hVbWYm5ozqquq0ielYy5oTm/Rv9KoGcggZ6BrAxfibWxNUHeQczzn8fE5hOroQS3f7SdL9p9QXev7lgYvtdhqEoUcuW/7NJsfov+TS+rll2aTSePTqzosoIjsUcIeROCQlJwYsgJhjUcRkFZgfB1NDAjalIUhwceprtXd07GnWRd5DoAIlMF8nBgg4F/ODwV2gpWhq+kjWsb7Ezs9CQqMyMz/TZWRlZoZS0nnp7g3Itz6NDhsk5I17tauhKXFVdNx7IqTAwEOzHAPYDE/PfgNgdTBzrt6URoYiganUYPrnK3cufqJ1f5IbMxGBmh6d6Vs8/PsmZRV6SKCuYY38DxZTq7Y+uQNieNLTEeWBaWIxka0uWdGb9H1aNRtopvAxEkKCNjOo6Bh4p3QkotJET0DbRatAoJxZWrpFaWsD4tg0jvcY2A0FcoRoyEH38UuPnGjUUZamaGoqiYUdEQ/6OGWaluZOiEkrAsiZVvt08rj6kK5vyNKNi/G/9xCeFgI5jeCx5XlvhV1twv7eFqbfH9rpNgpDIWAqMKT57bwvzOMh/HVrAvqwMSEj/v+AypoICD9u9I3LpSNHvWr4cRI96bcYJICDVripKhSlnJz0+cuBMnqu1bUn4SnVvFkWss0zHXiu77utNpTyd2RO2gpXNzfjsBVwzG0dunNwpJwahTo/ji6hcUlxfj7+YPQKmmlKktp/J65mvm+c+jhlkNRjQcwaEnh8gtzWVJxyW8LXrL9gfbKSwrZNr5aXTc3RGdrOP6qOscHnSYCc0n8H2X7+lfv381JJ+TmVO1JmJVfChMEpIYQuNtjfkmRGhKtnVtS9TbKI49PUZqYSrZpdns6rNL+Eb6DmZ///1kzsvkxOATeqEXEMrI7Xe1Z03EGl7mCEGWAzEHSMxPZEH7Bag1asq15dSyrkVOaQ4mShM6eXbSjzRdLF24PfY2EhIeVh7kqnNJLkim/a72WK2wot3Odsy7PI9Tz06RWSxIXWaGZpwbfk4PyLI2tmZByALCk8OxMbbB1tiW4vJiZreZzZPJT+hSqzOvrh5hwaeueOz04+ODH1PrVgxFFkb8esmImw8a8en2u5iF3RE8FaVSwIjv3cMp8CPubNPRJdeGBwXPKKsoxawcOnVKIqmZF3JUFBuWCSyMpNXx2t0C10KQ69fH/2AYVvOXiNVEbKzoQf3wA/TuTblCJuHAz2iqNDTVMvm1XaoZCbvlw7D3sBVy/gEF+V+J/7geQo1VNcRTqgyKfoD1bWBRIITuhgaZQuE41gGW9jRjy8JI/J5mUdqtE3u2T8F31S6avyyl71wX2hp68cUPN2kwXUGKFfSt24dVUfZ4rdwOnTrByZPC0tvbW4yJSkqEbNqYMbBxoxgjZWZCdDRqZ3sOxRxixsUZ+qeteRn08g6mb6tRWBlZcfHFBU5d2UiSNSgkBS4WLqQUpLCo4yJ+i/6N13mvMVGZ0M6tHVdHVZeNj06Ppsm2JvwY9CMz28yk857ORKdHY2YoxEhntp7Jss7LMDM0Q5Zlzr84zxdXv+Bp5lNqWdfidd5rGjs25v7E++SU5jDxzEROx58GxL4M8R3CwScH/3CslZISA6VBtSeyhKR3hPZz8NP/vyJ8BTsf7kRGpqNHRzp6dOR0/Gn9tKF+jfq8K36HnYkdcVPjCNwdSFhymN57saZ5TeKmxdFxV0e9FuTyzss5FncMtUbN08ynnB9+nnJtOeHJgrx1P+2+fhrhY+eDv5u/nhr+Z+Fr78uvfX6lkWMjTsSdYOfNH7medQ8FEsF1ejLe71P6BIxDKisTAr1hYaL+b91aSPo/evTeyr1/fzh3Dt2rlwyJmMWxp8cYGAuPnMClUFyP5+spCX6mBYUCydVVqHOdPo3cqBGSWs3bwBY4h97nt5mB7FU+4aU2iyQbIfa67TSMewSh7jBpkjNWtjV5kPag0mtAfzJEyCD/E0v4/xVsx383/pWEsD9mP+OOjGTNRZhaualWEtjvgDEw/AnMrDQlVkRECAFVa2v49lu048aiadiAZBMNfqNLMNMpGNF+Kshw4MkBskuzmf/alWX73kKD+igOHBQai0OHwqFDQs154kRo2pTikjwu2OVyvI0lZ1xL9DP9Hl49GOM1kB69ZvC6ti1dBpeSXZqNkdKIbnFl9Kvdi4+/2sX9tPv0OtALGRk/Bz/Wdl/L8afHOfjkINlfZP8Bo992Z1vy1HncHnubkSdGcu7lORxMHTg59KRe6ejh24fMvTyXkDch1LGtQ//6/VkdvhodOr70/5LP23zOvCvz2Pd4n55DAFDLuhbpRemUakr1nosqSUW/ev1ILUol6m1UNQ0FUwPTagpOVWFpaElBeQF1bOqwIXgDvg6+aHVafo//nV8e/qKfbDibO1NaUUpemUAYBrgFEJYcxoYeG6hnV08PiVYpVAz3G87+mP1YGlmSOS9T35cA0Ux8kPaAW0m3OBl3kofpD/WrnT9zle7u1R0vGy+x2lLnUku2ZlxIPp/ujsK11v/D3luHR3ltff+fmYm7u0ASQrBAEtw9aIFS3KXQ4tqiJcXdnQIBQnGnuHuRAEFDCEQgkBAnPrJ/f+xkIKftc/qc0+d5fz3vu65rrsxM7nvPvm3tJd/1XVUlp0Dv3mBrKzsz29pKZZCeLsl0GjWSsaKyZWWW6dtvYeVKot5HMWndl5xUxtIiFm66Q8piSHQwxP+9mmwHK6xSs5k4oSp7XNO4OPsNvhmSQfmsL/TubohzhhoLJw8MnFwoVOeT9yqaeHMNmj/Jjib+b27UctNdQe0kqSBzDMFCDf07yM9LT4NtyYLm5SW1et26sqPO0aN6QNE7O0OGDXbliFkiRiojelXpha+dL3uf7MXp+kMO7gVhZoplZr60FPz9ybp4iuOxJzlwbSOnkq6Qbwh2uaAzNyFfJWv5X6S94NTLU3x7KZdFZ2HuD03x7/YtrfxaYWHtSOKofkypnUtEVAQmBibSrx31Ck9rTw4+O0jnvZ250v8KDbwblDrmElCOg5kD6fnpsrWZpohXo1/xIe8DUy9MJSIqAgczB2Y0moG/vT/td7Wnmks13ma/xc3Sjei0aAo0BUysO5EpDaYQuC6Q2IxYKjhUKFUqXd+zPq8zX6MTOi71u0TPgz15nvqcXHUuXSt2RYeOqOQoXqS9KDVHA4WBPo1ZIpZGllR0rEhMegxKhZIB1QYQlRxViuexrV9b4rLieJfzjnN9zhG8MVifdXAwdSA1P5XmZZtztm9pGvd8dT4RUREsu7WMZ6nP9L0eAD192+9JXc+6jKs9jk7dZqC0s4fLl2XAOCAAsrKkm1i9OnToIFPN585JvouWLeUAgYGI6Gj2HJnDwrid3H9/n1pJSiq+1xEeJFGtOw7Jv/7p8MYC9gQbsKFzGcqmaXB5FMdLOwWvbAXJ/0CWZW1sjW+BGb5P3+Fr5Izvs2R8sMX3/H2CV1Qknd821rU3tSf1u78my/C3VAglvIofDcFSDfsqgEuuxCYoFArp62k0EkHYvr001c6fh6Tiuqo+fSAiAkaPJnratyy7tYzwB+H6FuotfFqQcPEQ06efp8AAjgTA1r5VuJMTTZG2CFcLV7784ECzI4+Y1NaIRJMi/DKUPHLS4WrhSofyHejs05ZmbUegsLKGyEhytPks7ODA4lpadAYqxtUZR5dKXai+sToT605kfvP5ZBVkYb/Qnkn1JzG76Wz98ablpTHy5Eh2Pd6FtbE1Z/ucJV+TT6PwRjQt05TriddRKBSMqTWGSfUnEZ0WTdNtTSljU4YFzRfQdV9X8jR5hPqGsqr1KsrZy36Ig44MYsuDLcxsPJOZl2fqH+Yv/L9gZK2RdNnXBQRkFmYyq/Espl+azoW+F2hSVlY45qnzGP7LcMIfhtPWry0nXp7AQGmgb+0OsmkNCn7TTr5E7EztUGvVelerhH9xXO1xRL6L5FL8JQC+qvAV+7pKQFNKbgpr76xl7Z21fMj7QJBLEP2r9WfK+SmYG5nrLZ8KDhV4nfla7/JYGVvpy78B/FOhnmtN6jfqQ72JK/G/9RJFnTrSNZw+HWbPJm/pQp50bczL/RsInL2ZSqmgAdbXhJFtSh+LXyo0joctQdJ9VQCvbCH3M4Y3hQCPHCW+qTp8MsE3Q4Gvoz8+i7fg6xyAXcIH6aJ26SLZw0uyWRMnsvPCcga0VqP+LAxkiIqtX277y5q9/q0VQq4BmGmKG29SzHsfHAyxsVLTt2gBZ89C586STPXtWxkgXLZMZhRsbSX3opsbKbkprL69mjV31pCen05Zm7JYxL3lqVURWqXssmtmZU/HgI54Wnty7uFh0qMfEGsHW48qCU22JPbCfkIqNNXj+9mzB22P7mxb3p+p6lO8z3lP9wI/5n1/Vo8U7L6/OydfniRhTALWJtbU31KfQm0hd76+A8CBpwcYdmIY6fnphLiGcC/pHq9Gv+LQ80NMODMBtU5Nzyo9md9sPp7WnjxOeUyj8EZYGllS3a06B54dwMzQDFsTWxLHJpbiECgpT1YpVKWwDSVEqjVca3A18SquFq4sbLGQPof6SJbl4q5IUclRhGwMoVeVXjQr24y+h/tybcA1uuzrgqeVJ19W+JKHyQ85En3kD1vGl/R2+D1xt3AnJS8FtU6No5kjZ/ucZfXt1eyI2kGhtpD2/u0ZV2ccDb0a0mxHMy7HXS6Fx7A0sqRnlZ50CujEmFNjSMxOZGLdicy+Oht7nQmBsTlEVrAhrSiTiinwZC380M2J+z5mTIqII9rNiEGtivS++rlwWTuztBbMb2WKgaUNGp2GtPy0UtaIkUYCmJq+BqccOO4Pzr6B7DDsjv+3UzAxsZDWyLNnEr14/Lgk7xUCmjWD+/clN+jNm7LhC8hFTqvliL/Mpq2uBV5ZMOfBf82UVCL/sTiEz8VcI69VqYNo2FCeZIDERHmijxYXWN6RDxk3b8rOToWFkvNep6NQU4i9qT0BDgEoUPA68zWPbIqwKoSxz21JXgjdrmex+f5mwi6FcSvrMS+clBzZBd1D+mGXmkONWZtRflbkerGGI9XHmjEoIxxvSw9uHHFgV0pDvTIASXKaXZitD4SF+oZyL+keTz88pcu+Lny17ys8rDy4+/VdwjuEoxEagjYEMfrUaP2DWd21Op7WnrzKeEXLHS31N+mxF8eY2mAqA4MG/m5FYAn9uU7o9DEQa2Nrmvs0p6VvS64mXkWlUPEu5x0LrkuC0xIyVK1Oy+Cjg7E1sWVJyyXsfSop5fVXXgAAIABJREFU4ut61qV3YG8i30cyOHgwQ0KGkKfOY3nocsbXGQ+Aj40PIAOUnysDM0Mz/fcKFLzNeau3Nj7kfaDahmpsebCF2h612ffVPnZ13kUt91o0Dm/MpbhLemVgamBKeIdw3o1/x/p262np25JdnXdhZ2rH/OvzaVq2KWm6HC6XUVCQLy2GL4oBheEuKRw3jqP+IBjUuqhUzCKiuLpwZW0Q5uZ4WXvRwrcFU+pPYWtMJa7cCODNbjfy58DlE87s2g913oCNlSNRKVHs3jsNA3NLed8VFckUtouLhL+r1dJqvXhR9op0dpbZrBIp5gDp8AJWngLdjxC3HHpd/tQA56+Qv6VCSDKDf7RrRPELBwfpLoC0FMLDoYRn4fp1qYUvX4bmzfkwdxqcP8+aLmXwWu7FmNNjyC7MZmqDqZx63YA9e8FarWRZQAYe48EpS8OW2EBsjK3R6DRoERi7eSJ2bEd8840MPG7fzou0F3TY3YGmO5qR7mTJrv1wM6kNdTIt5Y3wmQS5BhHqG8ryW8vJV+fT0rclAkGtn2pxNPooc5vO5dfBv0q68KMDAcguzOZ4j+Pc+foOzco2Y8H1BcRmxNJgawNSclPILsymrmddHn37iNlNZ1PWpiy56txSSmHXo116CLFAYG9mj4WhBV7WXlx4fYG4zDisjK0Idg0GJNMxoOc3WHV7FXeS7rCi1QpUShWnX56mS8Uu+q7KGp2G/U/3M+fqHJzNnXEwd2DpzaV0DOioD/wFOASQPCGZc33OsbTlUrpV6oaTuZMeJ/F7ohM6Lsdfpsv+LljMs8BsrhlXE6+W2qZD+Q48/fCUvof7UnV9VSznWRK0MYjE7EQKNAWciT2DaRFolIJ8hQ47hTkdXii47QaJxZyXJWr9c0RlbnGct7tzcxY0X8C2jtuI6BTBrKaz6P8AGhj64v4mG6WAkGipaBrEw1vDfGrizrx6OmYGf+SNlw1ERUkY88aN0kqdOVPWwtSpI1GwIIOXxsalOpT/Ruzs/vh//4L8Nin9NxB3R2/Sk+KxVX+6cIriF2Fh8gsTE1lAUlQkH9SGDSEigmedG3IgIIUDFS7zICOCvRVh6OFEjJoPpjC4Knfe3eHCsZXM2J6NgYBrfRtiEVKHyHf3CDM5g1IXBQUwu/GP5Gjy+Vq3gev3tHw4tgVq+rBp/2DWxIOJoQlzm85lTO0xmN7rB4sWyy5R/6AQACbVn0STbU1YcWsF1xNlRyhTA1NuD76NocpQX9XnYuHCkJAhbLy3EZVShUKhYEajGTQMb0iVtVXI1+TjZObEunbr6BTQSe8eeFh5ALJVm62pLZvubWLo8aHU86ynh0YH2AegVCpJy0ujUFtIVHIUx3scp025Nhx6foieB3pSqC2k8rrKrG2zlmkXptGmXBu6V+7OjqgdqHVqulTsAkBV56pUcKjA+nvrefD+AcNqDGPQkUHU9qhNddfq+tJnRzNHnMydaObTjGY+zQB4mf6SgNUBpR5ED0sP3nx886fvj91PdgMStm2sMsZIZYRSoSSnKEevaD6agIkatIZKTHMKqPlGcK2SJcd//sjUxvDMw4iegT0ZVn0YVZyrcLe8JUkmUpFFvr3NgqMyNexg5kBdz7rUd46lXnYuIfk5GAPk52OuUOCfLgjBnZvaaJokKJjVSJBz8wNly9tTq7YnNd1rSpd23jy5WJV0Kj90SFoKhYUys/G/JH/LGII+PfR7olDIE2tmBnl5iLFjePhdPw6Ma80Bu/c8KzYW6jgE0bpyJ2zzoWufeXzUFVBtqMDI0ppftxpSNj4LpaERiqwsUKnILcqlcXhj7iXdRaWTac4vy3dkZJ0xqHdF0HzKT0xoAcvqQLdXpoybdZ7qZYr7db96BRUqyOBmo0byYn8mOp0Ov1V+xGfGY6QyorxDed59fEe3yt1Yf3c9RiojJtadyPi64zFSGeG5zJPaHrU50PUAy28uZ+I5yX7cpWIXtnbYirmReanxbyTeoN6WepzoeYLnqc/13aSH1RhG+13tcTRzJLMgk0FBg9h8fzNqnZry9uV5PuK5fozeB3uz7+k+fd7fQGnArUG3CHELod3P7XiU8oi40XF6JTT7ymymX5yOpZElhkpD7MzsONb9GLU216KKUxWuJ16na8Wu7OkiS6Nj0mJYfms5Wx9s1ac4Pa08effxHbU8aukV5b8jSoUSVwtXvF9+4JF1EcLYkB9bzidhyQ8sPyhdpu+7O+Aw4jsGBg3UszqRmSnjTSXX69xZogPd9XiI6/FXicmIBcBYqKieqKVeAtR7o6BugsC0bUdaWRzmuhc0ioNLZcHcwIw8TT6T609mRmY1jL7qCp6eckFbuFAWRfn4SJciKkpW2P6eKP55X0e52X9yDKHXp4hqofKT+yCQ3XqEnS23bfP4vjmUYxVBG4KYWz4Z5xxYeVJBzCZTTC1s+PHyj4z89QeGdDenbCa8eNacFIuZ+MWkonJzR1GzJqhU5Kvz+WL3F0S+j2Rn559JcJrH5Gtw/skxGm9rzBe6CKY2hZmXFMx8V56fI/K50LsuX+75Uvq2ZcvCyJES5PLhQ6lDic+Mp9XOVjLNh46ZTWZSzq4cKXkprLmzhgHVBhAzMoYZjWdgYWSBkcqIQUGDOBZ9jCprq+iVAUBtj9q/UQbwyUJYf3c9486Mo3OFzoR3DOfbX76VVOGuQah1apJzklHr1DiYOpCYlVgqEJhZkEklx0p6CjOtTkvjbY354cIPnIk9Q9eKXUsFLINdpKuh0WlQKpWc7HWS1XdWk1uUS2u/1oDEEYw6MQqfFT74r/Zn7d21pWIKidmJaITmTykDb2tvVArVp4DuZ2KsMsbPzo9A50DscjS8NiviownkKNSMPzueZo9zSbKAmoPhVafGVHCsQHZh9qdA4SZJrIqfhJwrc/Oo4FiBwcGD2dphKy9q7OD9Ijh4zp4RPt3RKuTC0KG7wPE7CHE+jG86BCZLZVDfrQ65mjx8bH1YeHkuCSP6oDUxljGvQYNkfc3u3VIpdO78x8oAZGr9L5S/pctQIjurwF1XWHYG7rrI9lYHK8LhChkkWoOBFpq+1tKvwRgskzMYE7YNHYKPxvmkp7/lu3rf0SmgEyFuISgdZuEaFganrkkSlCtXoHt3CjQFdNzTkYuvLxLeMZweVXpAFehiZ8S1c+O54g1qrYa5DeFAZQXjU+HDgG58t3UPX1Y4R5Pnh6jiVIXxbQfSd4UBimfPQAh0CNbfXc/3575HCMGKViuYf20+Uy9M1QfSxtQaw5LQ0kVXKbkpxKTFIBB6SHB4h3AiHkWw4PoChoYM/Y1ScDF3QYGCoy+O0rdqXzZ/sZlBRwfx7uM7KjhWQAhBBYcKnIyV3Z26VOrCurvrOP3yNJ0qyCh3al4q1sbWPE55jIWRBYWaQqq5VGPWVclhYGVspW/FBrD5/mZAQrEHBQ1i2oVp7HmyB0sjSz0s+uiLT2x6JgYmstmtpoACbemsg5HSCLVO9npQKpQEOATgZOakT0kuabGErpW74rnMk6Utl9KlUhf2PdnH7se7ufvuLoXaQuIz4zHUCPKUGj5vs2leBM1fwf4qKh56qbjzbD/7n+2X/zM0p5JTJSo9eELlOlCjbRMaTHuJyMn5FDoWAr77Dudc6NRvPp22RMBlyDeAu25wvayK625ajgZ86gJ+Lekmtia2xGbE8v1DMzw/5KHSQoGZMcYGxijOnPkU96pS5Y8fADMzmDPnj///L8jfVyEolUxtpiPeRvZXiHSFFAupBEJj4fur0OMx2BVA0c/LmdsA1ArZx8GqEO4/aQBj534ab+pUCUlOS4OOHeHCBQprBPPV3q84E3uGzV9spm/Vvrz7+I5pF6axNWYrtr5WrDqrZtBLS46sH8uih+sYYhfNdOU7Rn7pyKZzCr7aPIuFL7bS/8pYnjdRMu9sOrd2LmSS5iSX4y/TwqcFA6oNYPHNxXrugXnN5hERFUFUSpR+ehqdhvV31zPtwjRyi3KxMLIgpyiHpS2X0q9aP/zs/Ki/tT7r765nfN3x+v10QsfoU6MRCAIcAtjaYStHnh9h+8PtTG84nYfJD4nPjMfCyIICTQGGSkMMVYbYm9qz/9l+vUJIy09Do9WQWZjJhb4X+PrY1zxKfoSfnR9xmXH8cOkHVt2WtPBJH5NIzk3Wz2H1ndUoi43Rz7kcP5cShGSBtgAjlZF+u5KO2P52/rxIf0HPyj2JeBTBMySQysTAhCW3luhX84beDfGw8mBsnbGMrTOWrIIsNkZuJCZ8KWt+es9jR3jsDJP7uuJp6kLg6YeYanRsq6ylSKfVl5K7W7rjY+tDbk46J9xy2eoP7mmbeAOM3j+YyIK1ErYdn0elt9eobA5OeXkyYA2YaqBBAjRIkLEQnVLB81+2cc0xn1XXlvA4U4K6FgTnsawqOBvYYPU+k/sbCkkb1heXfVI5l/ApxNrCRyPo2APmnIdeSfYSOdvrr+FBKJG/p8sAMHSonov+nI+M5i49Ca+Xwx03GNEOntpLZmZDHYRdlsoAQBEaCps3lyIz4ehRqQxMTWHxYtRK6Ja9mV9ifmF92/V0r9yd2VdmU25VOXZE7WBs7bG8HBfHiLV3MVUa073nXO7W2MSF+4EEx+YxLfADXj1TuHVgBQe7HOBK/yu8KmfPlKbQ5PkkbiReZ0C1ARiqDOl5sCepeals7bAVNws3Tr08RahvKFfjr5KnzuNG4g1qbKrByJMjqe5WnV6BvfRAn5IUZj2verTwacHCGwvJLZL+sEanof/h/qy/tx5XC1e8rLxIzUtl6PGhBLsGM63hNJzMnIjPiudOkkzJOps78+D9AzoGdORY9DGSc5KJfBfJm+w3xGXFUdGxIlMuTCE9P52swixepr/UZw0+5H3g/vv7pZRBiejQoUBBobZQ3yauU/lOtPBpgYHSgKzCLELcQtjaYSupE1L1pdwF2gLalmvLw28eYmVshbGBMcYqYwSC5mWbc2vQLbQ6LdMvTcfUwFSyPyMrK/c+2UuH3R04tuk7Vmx9T6KPHZWyDfH2qIiBULBg4X3WHNeRa6zktq8xNiY2DKg2AA9LD95+fMvVhKtM2PCE94vhu6vg7x0EQAUTD/I1+ex7vIdRaRE06wfOE8ExaSxNvjFlRBvYIomj9e6scsBAKnoGM2TldR5NeMWiswq2H4CfD0jcQqahlucuKhbVBZf9p+g01JqBRwYy5NokfnWDTGOokgLpJjCkvbSO/2plAH9nhbB2LR7FRMKbjsDGYzDyNnh8hP4PYMd1Z6q/BxWgUCo/mWAAp0/LqrX+/WXvvqwsGDFClp9u2YLmTQI9uxlwJP40K1utxMLIgvKryzP94nRC/UJ5OvwpS0KXYGtqKwkxbtwAb28U7drRpGE/Tuwx4NHzpnS1qMl6+9eUW12OuVfn8tSigHkNoX48+KYKtj7YyqmXp/gy4Esih0TSv1p/JtSdwOX4y3hae1KoLaTj7o7U21KP1LxU9nXZRwOvBmx7uI2RNUfiYelRqpAnrHEYKbkprLu7jkJNId32d2NH1A5mNZlFHY86vPn4hiHHhpBdmM32jtv10ffMgkyCnIOo6FCRD3kfuJl4k2sJ1/hY9BGXJS6EbAzR+/YvUl/w8P3DUoi/EnEwdcDKyEr/uZZ7rVKNZbtX7s7R7kf1PSAORR/iwfsHjKk1hmfDn3F1wFUal2lMp72dEAiMlcbU8ajDrTe3KNAWUM+zHoeeH9KTtZS1LUtVl6pcHXAVrU6LWqfmRMwJwi6F4b3cm277u2H+5AVn9xlj6OePz48rMSpQ03DMMl6/7kDDBNCYGnOlsiUfKSSzIJMdUTvoFNCJAdUG4JoNXZ7KhzrH0Yqc4hXl7fsY7r+NZN+mLF6uVPBlmjPtYpSEvNGRbW/O9qpwuJgFuUApXdnkwzuhcmXUe3fzrl9nhndfSp9HcNdNgZOLD7lFuQS5BuG7ZCsJjkYs2J/Nnrvb2FQhl9pDoGVf+KorVE4pbgFf7a/jQPhc/p5ZhmKJCFQwtD0MvgcrTktrQChAowSTFbIHn16WLZOcB1qtzFCkpkqcOkhl8eEDnD2LtmkTevc0YXcFDRMdO3LJ8C13ku4Q7BrM0pZLaVSm0e/OhcxM6WpcvizBUL/8Anv3khixjpWFl1haS6BTgkOBihxDHRoETb0b87bwA08+PMHWxJavg7+mX9V+1N9aH3dLdx5/eIxSoWRi3YlMaziNLfe3MPrUaPpV7ceWDluYc2UOP1z6gZiRMXqOhdCIUCLfRVLNpRrnXp1jWegyRtcazZDjQ9jxUCL8mpdtjqO5I9Gp0US+j/zdw/k9BKECBWVsyuBr54uvrS8X4y7yIVd2gwpxC2Fc7XF0PyDZjOxM7Egv+ASaaeXXCrVWzfnX5/XfTWkwhRmNZuhZndbcWcOU81PQCi0FmgL87f3Z3Xk3wRuDmVRvEtlF2ay9s1ZfexL+IJybg27ia+uL42LHUq5Ga7/WfOfQkUZ9pqEwNZUYlB9+kCXr8+fLwqSePaWVuHMnr1rXZvWvq1l5e6U+5bn2jBHf3CjiqZMCzzqhWB0+iTA2Jm1oHxLM1AQv2M7KwVVY7PCCRJNPJfO2hQrezxcYCfhgBo55sgBvfmMDltbQUKSC56sh08qQgVOrEJkaJV3AwhwCHAO44jkD2/ZdWNLUlAkN8un+GJQC9lbiU7HTn6hwLHXt/pOhyyXyxs6AOHMtwe8lhLmUlFzsEmnUSO/fATJmUL68RCoWi9bYkAFDnNlh/4bJN1SMuKGl5URnvuuwkN6BvX83gl1KCgrkePv2gZMTap2GbiNdWLXoKZvrGrOolpYclZyobxpMtWpLjxn7uZN0h5W3V3Lo2SF0QoeRyohCbSHWxtbYmdrxavQrtj/cTr/D/egY0JF9XfZhoDQg6WMSXsu8GFdnHAuaL+B9znt2PdrF+LMyhhDiGoJWp+Vl+stSlGsgffMiXdEfFgDVcKtBnjqPmPQYffPW7R2306dqH0DWV7gscWF8nfFUd6su6x4+Ex9bH+p61GXno5363L+TuRMdy3dkY+RGAM73PU/Tsk15+uEpg44O4tabW7T2a427lTtb7m/BwcyB5AnJ9DnUh/1P96NUKMlT5zG53mQmN5hMwBqJKlUqlCRmJ2JuaI6pgSnZRdkcaLqBdj1mQH6+LGMuSeEFB0t27MaN5fslSyTtXXFa8dabW7TY0QJLpSm35n3AKwvGhMLhigqCa3Vk15AzKFq3wejIMWjeXLqatrZkaD7y6OIeHn0/gIBUaPZInu/35nDDE758Do3CymDmF8CoXa8IPfGCiT/W55xjNk8/PC3FSWGoNOTEaQca3XpPtSGC+omw4TiUGQ3xxdlPyyIF2XP+ebqxRP6z047FEvfdEOq9+R1lALJbr4vLp89Xrsi/hoYSEjpnjnQXim8E3exZDBrjyw77N8y6AGOvaXHJU/Dggj99A/v8c2UAEgy1ezdFo4azzisFkZ5OuVsxNJjkyIy6hVRJN+DyL05EdIrAwsKWgYa/4LPMm+uJ15nXdB6dK3ZGIPSrXJG2iNeZr1l7ey0DjwykaZmmLGy+kKvxV9l0bxMrbq3A2cKZJTeWYDrHFLelbnplAPAo5RGPPzz+jTJwtXDF09oTndAR6CThz2vbrCV5QjJdK8rWaw29GzK76WyKtEX6pjbOFs76MQ4/P4xGp5Et1WJLVyF2rdgVOxM7Ih5FIBBYG1ujRClbthV3UwKJZZh5eSZBG4KISYsholMEv/T8hRuJNyhrU5aU3BQKNAXMbDyTQk0heeo8lAolSTlJTDo3ifT8dN5+fEtGQQYqhYrEsYk8H/GcQPuKdDo9gD1OKdIK9PeXSiEtTcLXPT1lWu/4cQlY+wxjUNujNid7nSQ7P5PWvSDFHNq9kIS9R6OPkkwu2Uf3kWWgZeuwunw4/DNkZWEbEETDU88YfjFHrwwAChvUxWqezBR1TrbD6MFjWp54wbrqsFR3jdcZr6nhVoNQ31DMDM0wVBqiEzr61v9AlpFgw3F4XOztfn8NekTJJsczz/3PLOR/awsBPhU6/a44O38iRQUJAw0KklDQtm1hyhQA1L5laNo0kWvuWpQ6WHYavrZphumZCzKt5O0NkydLosySdl1/IHeT7jLwyEAepTwi8L3s0utr5ML8rBp0XnAMhbU1ZGYi4uM516ocC7+w55yZbDKiQKHH/w85NkTPQgzo2Yg+R/ApUKBSqkqtLvCp9Le8fXma+zQn6WMSh55LMNTR7kcpa1uWmptqUsezDotbLCZ4YzD7u+ync8XOnHp5itY7WxPoHEjXil2ZdnEaVZyq6Fu3h7iFAJKf4XHKYwo0BWh0Gn2rNn3naPsAWVvh25L+1frz1b6vGFFjBJvvb9YDj7ytvYnPiqdH5R6saLUCR3NHErIS8F7uTY9KPdj1ZBcxI2PY83iPPlVpbmBOriYXY5UxXSt1JS4zjuuJ1wl2DZYFYR8/kh3amHYV7nPNCza138Sg4EEwfDisWydTdbduyeCxn5+kLxs9uvRFTE7mckMvWncpwi/XiAsbi3i6aS7tE+bzatZH7PMEIwa5ssHtHU9Wg38GFJkYYlSg5jdiYyPvQWdnec89fYruTSL3zkdwP/8VUclR+tfn3bUUKOgfKdhyFA6Wl63bOj0HqyKIdJHEwcr/xrP7f4WFAPyxMgBITi7dGLaoSLoJ9+/LWneVCq0SBlVN4Jq7Fs98I369H8KowmqYnjony6UrVJCddL75RlocPXrIoOQ/NJwt0BQw6dwkam6qycv0l7I4x82CFSfh6Y+pfNVnHgpHR8jORp0QR6ylmqwWDUnPlMrAUCm7MW+K3ESNTTVKKQOQiuBzZVBSZ9ApoBNWxlYYKA0wVhkT0SmComlFhPqGkpafxsBqAzn18hSNvGXsIzE7kS77umBlbMXOL3fiaukKoC8Zbu7THFMDU56mPGX21dl4WnnqeQhtTW05Fn2M+lvqc+vNLQo1hZgamOrnJxB4W3sDsuZBIFjeajltyrXBytiKXHUuoX6heuVWogw2td+Eo7lcBk+/lDwJLfwkmWr4/XC9MgAo1BWiVCiJHhHN9k7b2dBuAzqhIyM/A1FQAJ06YXX7Iafa76GFbwsGHxvMipvLYds2qdy3b5cWYknBW/v2v71vFi2iUYyaYz9DjJWWFn2gcvkG3Km6Brs8QZKVksHDNpN5sRb+GXKXaEs1McVrhVYl70oBMrYUHy9dlGPH4O5dlMuWU6Nic4aEDGF1m9VcGXCFjO8ziB8TT0SnCNwt3aWLFgiXveGLFzLD4JInreH6byDP1f53bvh/X/72CgH7TyemQCXNq7w/QlcIIW+MvDyedGlEq14C79GwI1DHqLsGxC0oovrpR5IlB6QCuHQJnJykD9q/P5w5A61aSathyhR48YIbiTeosrYKC64v0K/O4+qM48TA84S0GYRhoYaLnYIY0BGiHAVLe5TFf0U5utif54kjOOfwG1ryz0WFivF1xtOhfAd91N7b2puhIUOZ3nA6KoW0Eja130SvwF6olCrCGoeRmpdKxz0dMTEwYWuHrQBsuLeBF2kv+Lnzz7hYuOibxJQoBAOlAXXc66ARGgwUBoQ1DtNXQoZGhPLF7i/0tGhqneQxKGdXDnNDc1r7tSZmZAwNvBpw480NWvvJDtemhqZ8WeFL9jzZw4mYE/pjbenTkl2Pd+G/2p/wB+HohI5TsafwtPLEWCmb0c65JoE3vra+DKg2QN++LrYYKvz2o2zCGpsRy8FvG0veiy1bMOvYhaPdj8rS5zNjmROci2jfTlKfgVQIlSvL6/q5pKRIWv6aNWn2Gg7ltuOpI4T+OhLniWEIQ0MMBFSo2Qaza7/q7z/vgWMpV1w7tl4aUWiKn667e5dTFFhZIlXr15eW5j+IQqHAy9qLXpV78Mx/BUHvFWgNYFxLOc4j5+JUI1LRWCxa8Yf3y78jf19gUomsWAG9e7OzimzptvA87K5Y3NoNCQhR6UqbVhoF3DRKJdYK3lpD/zhbJt1Tk2KZC6IIzAWU9Ao0A35aLi0DVT68iIQzZ1Ds2YtYPR/N6nlsawiJQYCBXEWFECy5uYQlN6Xv6DMS1Co1idYfCB/2aR5KlLgb2eIXn0YZr+Z4V21EGdsyqLVqhp8Yrn8QtWjR6XSsabMGrU7LoeeH2BS5iSHHhwAS1KNSqLgcd5lWfq1QKBT42fnhY+PDq8xXrGq1CktjS8wNzYlKjuK7ut8R6BxIap6so7c1sSUhK4G0PJnKcrWSVkM5+3KlmtB+LPyIjYlNqarJ4dWH42ThxIxLMxhTW1aLIuSxnY49zcmYk5S3L098ZrweCl3JsZJsjNt6BXGZcUy7MI0BRwaw6NoiYjJiMDM0o9ehTzl2TytPbgy6gU7oOB17mqSPSZx+eZpg12B9/KJykQ0j7X+lxpIfsOr6BYoCaX5vsuuH0aNDTGsGqYGuzMjPRJGZCbevwJgxUPCZma5QwOI5IArARAEVfKibbc2O65b0Cn1I8zqCK9FgnwtP3AxxS1VzbXRrms2OQLF6FR+NAAsLuvSdwccHE8myMsIyu4gbB1fx5iM0M4J71WzxzozTW0R6ycyUNTobN6J49YodVtClK0S6Q5Vv4aU9mBV7JN0fg+p/AIMA/wExBACGDaOM8TrirfknPsT/k/8n/57s3gdV30OFkf9nft8zE84kNSNgz7l/vvFn8mdjCH9/CwFg7VoSfpQAHYsCmHFZdtZxzZH6oVAF8TayH2SjeDgQABd9oZ6xHz3jrFA8jEKh0aA1MkBRpEGJ5Gp8bSM7QsXZwDsL6BsFtvmyU1SW6aefNzM0w93ADucsDY4JqThkanAwsMShSi10IcEcSr1GZuQNht+BJIvieZmbg6mJDFa+jIV168jt/AXLDO6QlpfGqFqjKGNThtcZr1lyawkWhha4WbnxIu2FPhJtYWTBmNpjMFAacCz6GLeTbgNgdv9HAAAgAElEQVTgYuFCvjofndDhaunKm+w3mBmakZmfib2ZPdMaTit1+lbcWoEOnewRERWhpzMrkZJOUP2r9edl2kuuJV7D19aX4TWHczPxJvue7mNEjRH42Pmw4NoCtELLiBoj2P14N8/TnqNUKBkSPIQbb24QlRxFsEswke8j6RPYh5tvbvIy/SUqhUqmGXOTSxGkWhtbE9Y4TD8XIQTTL04nV53LnCZzuLRlOm2idVCvHgcqKrieeJ3RtUbjZeYCK1dB6gcoLEJ07Mgx50wuxV9idLQtXqlqFGE/ympBJCcEvxyHCxc/4UicnWUcCsDcnIcDWpNrtB+bQph3ywIxZgypK+fhkqH9VH4/80c4egzu3ZUB7MjiWJCDA8LNDU1cLBd71KYgKpIK0Rn4ZUiX4J2fCwYNGuFSPgSFQsHEs5+K1j6XRGsIWPbfUwb/HfnPUAiAV3HEOscEfvWQUICTvtBauposqw1N4lU8cdRy0Re6PIZozzdM8jZEZaOhyxMYfkdD1eRiKjbgjiu07gX5Jkr80uGJg46IQ1A9Cdr0UTDBrj2T283D1K+C/saioACOHkVs2YKYcwal7hy1vSDpq1A6FSVhePGRJMG4dBMUeWD/ALZvJ2fXU5rH/UKam4oTvU7o+QEA9j3bR0JWApf7X+bg04OMOjUKrdCSq87lVcYrJtSdwNQGU6myrgo5RTnkqfPIKszCwtCCGq41eJH2gnx1Ph3Kd+By/GVG1PwE2CrQFLDtwTaiUqJKoR5LMP29qvQiNj2W20m3yS3K5cabGxirjHkw9AHGBsasuLWCOh51WNl6JRvvbSQ5N5nh1Yez/FdJ+DKq5ii2PtjKtcRrhPqGEpUcpXc5dkTtwNvam3nN5jEoaBCtdrbCwsiC2IxYPTAquzAbrU7LiJojMDaQcYXUvFTmXpvL+3OHOLNNR2LrenguvMKAoo9UXFuRS/GXuHO5PAYHk6BfP0mSs2cFYz09mXs+jJFzZ3K7fhka1hqh7x5Faiosmw5VasGCK/AR8DGHV8hre+cyhIQQvbEyxponnG/izdEjyZie+BT7Wd3MiuHNpqP48SzcANp0hlsPZOxq9hiZlt4wgUkPn8D7DDQe7vz6RTBLKmZyNO0G2sQ9uGRcpoJDhT+8z/Ul2f9D8p/hMiDp2Xsf/MSRUDcebrvDg/VQKRVW1IQN1eGZEzSIg6tlSu9vZ2xLxZgMapr60eGjO7X2XMe4UINQKHjXrQ1dAx5zXcTT7yGEH4ZCcxOMc4uRfB4eMp/dsCE0asRtiyyGnxxB0vO7/JDoQ//7AuOXryUGQq2W6a66dWXEGyjcuom2eT9xMflXDhR+Qcf5R0rNbcmNJUw4O4HWfq05//o8AQ4B/NT+J3Y+2slPkT/J6L1vKOXsyrH6zmoUKGjn3w5jA2MOPJUty1QKFb0De7Pt4TZyJkulse7uOpbfWk5GQYb+t4yURsxtPpciTRFTLkzBy9oLc0Nz0vPTSclNQSAYU3sMy0KX6Zmgj/U4RkPvhvis8EErtGQWZNLQuyGb2m/C396f86/O02pnKwyVhvqUo1Kh5HC3w7Qp1waVUkVyTjIuS2RVpr+9P9Fp0TQr24yLcRfRCR0+tj4saL6AzhU68y7nHUEz3dEoYf0xaHgtAWc7TwD2P91Pl31dWHoKxrafI4OHGo1swAqSY7NlS9r1AG3bVhzoegCzQp1EmZ4vRlEqlbI3R4cOsoHPF1/AkSMS4u7mhi4/D4MZCkJjBIf2gLEGolwVVBsqGFhtID8NP43i7VuJdZla3CKuUiV48UJe//LlJVqyXTtJBAxk5GdwIuYER6KPyJ6Tf8AYFfFlxL/U2PXPugySP+D/J6+QkBDx7whhfHrNkH+tJiFSzBAjWsnPtYeoRJ6RQqyqgTjSqaJ45ITIPXZQiCtXhAAhjh6Vg2VliXwnO7GwLsLme4TyB0SfroYifvIwIdq1E0KlEmLHDiHWrBGiWzchXFzEBzPE1+0RihkI16km4udFfYUuMlIItVqImzeFaNBA/gYIYWsrRL16Qq1EdOquEIQhwkfUF8LISIjY2FLHVaQpEoowuU2NjTVEWl6a/n/peeli7pW5wmWxi/7YTWaZiLTcNBGZFCmMZxkLtyVupc5N1XVVhcFMA/3nz9/fTLgphBDiavxV/XfW86yF2Rwz/eeo91FCo9WI8qvKi6rrqgq1Ri2ab2suCEOYzTYT6+6sE1qdVnws/CjW3l4rKq+trN9X+aNSP+bnMv/afEEYwmuZlzCcaSh67O8hVt5aKQhD7Hm8Rz9Gvc31xK8HV4lb7vI8O821LTWO7uRJ0bYnwny6SsQ/uyXP9ezZnzYYMUIIU1Ox5foaoQhTiEYzvEW2k43cztFRiLAw+X7nTiGsrOT7kyflvuPG6a/flmB5Pdr1QBSqEDoQM5a0F8ofEGpl8TV2dxdCoZDvFQohvvlGCCcneb/82fv4H17/qgB3xZ94Bv/+acc/EgVUeweHd0N4VVhdGzo+hyuPQjAtEox4as4XNrWo7BKIWf+vJbYAoFYtdELHxpjduAzP57uWUOsNRG41ZntcEF4L1kuEm4GBjFK3bYv2551sODaD8tNs2BKiZFxWRZ7vdaLHxO2SBdrRUa4WJcjJSpUgKwvdjet83R4OBQiWn1XRr/t8Oe7kyaUOJfxBuH7FGFt7rJ7XEGRWY3KDycSNjqOxd2NAVggGrg+kZURL7EzteDD0AdVdq+srCB8mP0Sj0+Bo5sjC5gsZVl2mPgYFDaK2Z21A0qApUKBCRVZhFgWaAhQosDWxpbJTZQ4+O0h0WjS9A3tTY1MNzr0+h7ulO9Ejo2nk3YjRJ0fjtsSNYSeGYag05Kf2P+Fq4aqHSn++AqbnpzP7iqSddzRzxNLYkuWtluNlLck/fGx9eDD0ARvbbeRl8jNqRY1kflNDDHSQps4mMStRDvTyJYoePVgdWx5hbMzIQzILo2cuFkJaDA0aMGDvC3YeM+SaiKd51wLSTZEEpwkJsqX79u3S/QNp0T17BitXyrgAMOC9K+uOw/Hy0L2PCRolhIXOY1fZCRiUIIrfvpUsWSDdjiVLJBP4pUtyLn8gJViOP/v9Xyn/UQqhBGJbIvHWso78u1Bo+0JGiA0fPpbchubmsonL3r2St279eihThku5T/Ff5c/Q40PJEvnMyq3FqZ1QtcBKbr9qlaS4cnODtDSET1kuVnfg2NJvqeZYhQffPmTxsidYvYiXgJQdOyTHfkyMDGwAxMYiFDC+syXhQTDjljGjr2tljtrbW87pumQJWnZzGUOOD6GSQyUA5l+fj/idm+li3EUuxV+idxXpNmUVZJGal0pafhplV5Tl7ru7+ocw2CWYlr4tSc9P5/tz3+trCwZUHaAfz9LYknJ25fQdpL7w/wKB0OMAZl+Zjb2pPZPPTeZZ6jMMlYZMbTiVfof7UXFtRTZGbqRDQAduDLzBvSH3GBA0gKzCLKq7Squ1pERbrVXz1d6vyCnKoaJDRe69u8ey0GU4mTvpFUJCVgIqpYqvTeoSs0IwNcqG43461CrJ9zD5/GT4+FGa/UolZX4+QVjjMI4WRXG4qZsEl4GkrktIkLyFa9bQo3IPDgbN54FNAY1HW5PsYSsVhr+/XCCaNpUPsqenVP7m5rKBK4BOxzfPLVh5Ag6VKaBXVxWamWF0HbxMfw5fOxuTfvKgfntu35auSHKyVDB/IHOazdEzUJeImaEZc5r9tWQovyt/xoz433r9uy5DRFREKfO32hBpVob2RuQZ8Mlc79pVCAMDafbn5wvx88/imQOi7WBz/b5llpcRD949EEKnk9srlUJUqyb3nzdPpH5MERfaVBQCxEcjOa7OyUmIMWOEiIyU+/2jbNok9+/RQ/zYzlIQhhjVCqEzMhTC0vLT/EDojI3FxQFNhPdoROc9nUVMWox+bpdeXyo1bFpemnBb4iYqrakk8tX5wn2JeynzvORlO89WEIb44cIPQgghEjITRP0t9Usd88a7G0VuUa4QQoiKqyvq/9doayP9+5EnRurfNwlvIghDWMy10Jv8c6/MFck5yaXmmJiVKAhDrL69WtjMtxGEIeZemSuGHhv6ydWZbSJabG8hdMXnLjU3VRCGWHZzmRCvXwvh5iaEq6sQsbFi1IlRpY7tRNvyQqdUCnH2rBBCiKIPySLwW4T7DAuRffWcEB06fDq/gwcLER8vJzZtmjjrgzCbZSLKLfAQ8dZIt61FCyF69RLCy0uIw4flfpUrf3IBStwAEEvqyfPcs5uh0LQK1f+/+nAjUWGZn9AaG8vvZs2S7iAIsWrVP72XvZd5C0WYQngv8xYRURH/3cehlPB/o8vQq0ovwjuG61kpoh1ls4zJlyWDjX5dVatloEmrJfn2Bb5VnaLyMDjrkosKJbObzCZmZIwk21AoJFV2mTKQmoro3BkmT+ZYM0/aBD/jZaAH5obmsHYtigYNJMotOFhyKyxe/GlFAYl4BFZ+6c6M6h/p99aRZVfNUAwYKFvNFYsAXpoX0nDrReJWwN7VKfj9cpOqFn4YKY2Yf31+qeMecWIEKbkpfB3yNVXXVdWj9wwUBvSu0pvL/S8zosYIfS/Glb+u5FLcJbILs/n1za+08m0FSLLXIceH4LHUg9AdoTxNfar/jfvv7lPOTs5x1e1VKBVK6nnU42LcRQBqutfkSPcjvBr1iskNJuNk7lRqjiVt3wLsAwhykWb3lAtT2HBvA/U96wMys7G+3Xo9N6OdqR3mhuYkvHsuTe28PLly+/jwLucdSoWSZmWbYaZRssommoWdHDldRkb9DU+eZsMxSCKH6XOay+I2V1eoUUNyJHp5SeTgypU0D/6KM33PkZybQoMB8NLFCLZuhbg4ud3YsdLte/z4E9TZ3Fxv9o+7rmPemwB+rqBmoWtxWsvEhBXfX+RdYSr3XXToTE1lgVXZsnLMixdL37w7d8p7TKmEMmXoFQVxY+LQzdARNybuXwok/kvyZ7TG/9br37UQSsR7jFw1tlVBZBohPMYiXlt9ZiEYGIhcVwcxqyHCPMxIKGcgRrRG9O5mJJ752QiRkPDbQW/fFlpDA3Ep0FrMaiDHyW5aT4jnz4WwsxMiJESIwkIh0tKEWLtWiFq15G8plUK0aiXEzz8Lcfiw2B4o59Zxd0ehfvZECBMTITp1kr9x9arQqpTi2/ZyxZnWBKH9zGpQGyjFwC/k/veTIoUQQmyN3KpfXUtWS9WPKmE8y1j02N+j1CGk5qYKo1lG+u3M55gLi7kW4knyE0EYYumNpeJK3BVRb3O93w1oWc61LPW5JNAYdinsn16T9XfWC8IQ8Znxovn25sJ0tqm0YsKUwmuplyAMsfj64t/sV2FlefHlEGshTE2FuH5dCCGETqcTLotdhOdSTzF4sJNYVFfOx3WRq1BNR8wdFijybCyEAPFtV3OhDFOIuzf26607vfzwg/wuKkoInU7c87cU9t8hXGbZiEfJj6RFEhT06b5p2VLOo+Szi8un92fOiNlnpounDjKIrS3vL4QQIup9lPipvpkoUiI05qZCaDRC9Osn7xmtVs4jIkIIM7NSFqIwM5Pf/0XCn7QQ/o8rgc9ff5VCiAhUCLMpMjNQ5RuE9feIEaHFD5UCsaUawm2SoSAMYTxdIb5rqRIalVJo7kcKYWEhRN26QhQV6cdLzU0VQ48NFWOKx7jzXR+h27hRuhxVqwqxebM8lRMmlJ7I8+dCTJkihKenECCKTI3FT0GI0SP9RX5RntxmwQK57/79Qq1Viz6zQwRhiO86WggdCFGnjhA//ihEcLDQqpQiwwRhORnRpB+i0QhzoZjxKXrvuNBRKMOU4mbiTTHqxChhNMtIpOSklJpSycMeuDawlKug/FEpxp8eL+4l3RPmc8xF5TWVxbBfhv1htHvC6QnCd4WvqLimolBr1f/0mow7NU6YzDYRWp1WhGwI0bszzoucBWEIx4WOvx0nN1eEjrQV1YcoPkX6hdC7T6OXthRZRoiskMrCa4mHCJrlKdLc7IQA8cweEd7aTUQnPRIui11E8GxPGf1/8kQOkpEhhLW1EF9+KT/v2iUEiCeNKwnXxa7Cbr6duOOGvMYKRWlFADIDMW6cVPggRFaWdAlAhPZCfPu1m971SV67SL/fjSNrhNi2TX5+8ED+trd36bFLXt7e//S8/ln5swrhP8plKJFe9b5h4zGJKnT7CK9XSCLW074Q/A0M7AgeqWquboHJvxoSllcdVbUgVNWCpDl54wZMm4ZO6Pgp8ifKry7PT5E/oRgzBnXb1lRfthtFUJBEs716BTNmQNeu0kUoyVaAzDfPmQNxcdzfuYTd5dX0eATLV73ApHwlycHfoQMEByOGD2dQeCd2aO4xO8GP+afUKOztZdu5d+/gzh3ik54RMgSKVAouloXLDrlYFsKEa7D/iDE5mR9YZPMVtQsdGRoyhCJtEeEPwkudm8pOlTFQGBCVEkVj78Yc6noId0t3dELHqturaLi1ITYmNhzveVxfyfiPokDBjTc3iM2IZVGLRXpKtP9KYtIlq1NmQSaPUx6jUqgwUBroW6VpdVp9gRUg3bquXfGKyyDB00oWlBXL1firWOfDrBWPKDCAN1XLMvtwNve1iZyuYcvHiaPYUB0G104mJLwOjb0bE6lJZE1r+08BxhUrJK7ghx9kNmHUKAAqrj/A1QFXsdQZ0LQfXHMvttG8vGTZfPXiVH7nzrIQyshIFkmlpMDs2QhLC6qmG7LOPYkxp8YghMCpcVv93PdsGMkxt2K+hBK3IT7+909aQsI/Pa9/ufwZrfFHL2AR8ByIAg4BNp/9bzLwEogGQv/MeH+VhVCsEoX3GITjBMSRcogmfeXK5jkW8W0baYprlAq5CltYCDF8+Kd9v/lG3HVF1FzkLwhDNNjSQES9j5L/S00VwsNDCF9fuSo8eCDzzRYWUqM7OwuRXDqg9uubX4XFXAtRabGPSDNBiLFjhWjeXB+U0lStKrQKxPYqxQG09+9lvrpcOaFRIE74IVqPd9FjEfRBuCmIyI51RIGtzJfnGMp8uAAhXF3FuVqOYnoXB6F9FKUPcs68NFO//9hTY/Vz9FnhI1Q/qvQuR8n7kleDLQ1+g1lwWOAgzsee16+E/5WUX1VedNzdUTTd1lQowhSicXhjUXNTTUEYwvBHQ2Ex10JUWVtFZORnSFO6Vy8hQMxa1F4QhsgrsaiEEAMO9BWXfA2ETqEQOYbyeLUtW4iqi3xFmeVlREG/3kLY2Ijod49Fh10dhNlkRMveCLMfVCI+M16IzEwhbGyE6NhRDjh+vDxnlSoJceyYEKGhItEKUX4EwnQq4sy6CULUqCGEvb0Q5crJbTdsEKJxY2lBfP21dCesrIQwMRE6I0MxdlI1QRhi/OnxQqdWC2FhIXTm5v8fe1cdHtXRvd+7Gg9xSCCKhwQLTrEAxQrF3Vq8QIDilgQvXqBI8RJoKbSFQvGiLV5cihQSCB4kxGX3/f1xVhJIC99X/36c55lnd+/eOzN37p0zZ468h99XcKcSpfBZQQ+yaVNy1SqrlPE/ICHsBlCKZCiAqyYmAEVRSgJoByAYQAMACxVF+Y0EdX8C+fnhljPwyAHo0kIw8t//CfhxGfDQZNFRGymW+eRkS8jzk7Qn6NvAgAq9gLiH17Cmxlwc6HYAIV6m2FM3N0Fjio0FevWS1N1Hj0oYbXy8oPJ062bJpnPx4UU0XNsQnvae2FVtMVzTIebF3buBuDikT4xE/MOrUBHofB4YNHITcOoUYhdNRaTPNXiPUKNRJ2C7w32ARHEXUexpFA0ydSroP12G4mPzod0HXtC0aSf4gaZ7eutCEiZsSIAqJFQUmi1a4P5hkWCCXIKw6swqPM94jozsDDxKeQQDBYY8J/aCWUpoVaIVAKBaoWp4y/ctAOL2HL4mHKGLQ7H0p6W/muE525iNG09vIPZpLPbe3AsPew/kt8+P2GexAIDKhSrj6zZf4+eEn/HuF+8ifVB/UbJNmgS/egLNFv88Xir75Rd8OPAL1PwlGwqAk+W80HZkYah27sKM5osQ+ywWC29/DTRpgqL5g7Gp3SYc843G4q1AOgwos7gM4iYMlejC8eMFVm+WKffFvXuiNDx/HgXTtDi4Eihq44MmD+ZgU9IJiXi9dk3OTU8Hbt4UXAy1WsLiR44E0tOhZGZhloMAwsw6MgtjDowHy5eDYmOD2vEaNC7SCNvyPYLhu61At274xU31csj+n5Bz4XXodzEEkrtImuF6jgIoaPreDMAXJDNI3oRIChV/T1v/MU2eDN/noq1OtAXStIBrGlAoSXDtX7xxY8UKWH5qOYrOL4qlZ1cgong3XFlhj05j1kPJfgGjrXp1Sc65fj2wbJm4Lh86JBh72dnA9u3Axx/j5tObqB9TH3q1Hrs774Z3PnGvNed3fOJujxpe21C4TyZ2r46EIZ8zMn48CEPjRtg34X2sCQUe2hhgmwUMvuGJ2PlqfL5BNNsqlQoE8e4X7+JOyj18OGoL9DGfi417xQqgbFnoUtJhUIC4Qk5AyZJ4evEkPk8U/4YPN8TjafpTDBtXGe8MdEdyugQ0EURFn4o42uMoImtGWlyNx+0bB5WiwrXH13D41mEoUNCvQj+saLoCakVtsU4M3z3cMtHNFPcsDlnGLJx5cAYjqo2ARqXBpUeXLFsEtaJGvaB6WPXuKhyIO4DO9xfBMDgCGD3a6otwai/Qvj1YpAiC72TisZ8n8PPPODS9PzbY/IKnaU9RL6ge6ucLw6SwVDxrWt/SfqmjN+CvuKBVyZZ4mv4UP+xahhNhBRB//5q4D5spKEieacWKQFYWPNNU2Nd8E8reNaJVWwVrL6+3Jk5JSrJakL76SrYStWtbqlLy58e8hvPQu3xvTP1hKqKrZgGJiVDu3cemn8ui5RUV1AYjZlRXUKRvNno0BWKdASOA5AJuYtn6k0Kcf4v+SB3CewBM2SXgA+B2jv/iTcf+OurYEZOL9LHYGrPVkvYNAAJfyIxOAFUPdkWPLT1QwqMETvU+hTntVsL5k2Wyhzf7o+ekkSPFFDZwIHD+vHi3bdkiqbgAcOhQDJxSHWlZadjVeRcCXQJlvwkAGRl4kPwAtVbVwtkHZzH77TnY5pkIz6GE3SjCdaSC95oDRhUwZwdwfyYwe81D+PYfg70q2W+WdiqGEK8QXHtyDRNrT0QFnwpSt6Mj0L27rHzXr2NfhyrA8+fAwYMYHvIAz22ESd73c0ftm8AG1WVsWJGM/scl+emJe01xJGgqKrmGome5npbbfZ4pqc3uJt+FoiioXLAyNl3ZhG5luuF079M42O0gwgPDMfvIbATNC0KL9S2w7+Y+kLQkX61WqBqmhE9BSmYKzj88jwre0udzD88hy5CFDvsfY9ZOYGMwMKhuNkjC92eZdHEj+gBbtoBqFY57Azf3fg0ULYrqvtVB0JLu7aObQXhqC0xzOCMdNxiArVuhNG6MmFafI5geGFUPyHx4DwUbtQWTk2F0cRFnpOMSLYpNm+RZBQbCZeAI7P7KAW+p/NG5+iN8OqSmSASPHwtj12jk+5IlIiGaycsLiqJgYeOF6F6mO6L1R7CotCws6omToA0SSe+BLdHsijCCgMGAOgooNdzhb2EGwGswBEVR9iiKciGP0izHOWMAZANYaz6UR1V5+moqitJLUZSTiqKcfPRC3sPfSx37LrRGhxHYHSRfzQlbkrXWzpY6+DM+e/czHOx2EKFeAjyKtm0FrnvGDHFXzkkqlXghOjvLeSkpEry0dCmejhqMh7ZGzFp5FzvrrkIpz1JyjYkh3E67j2orquHK4ysIdAnEwB0DMe/YPCQzHUY1UPwR8WXpSbg+6h4G1R0Lp0xTiO6ECSh+Pxt9Tyq4GX8eFx9c+O0BCApC4PwYBEQAI6fVw7KQTPQ9ITef/OgOyma64aktUPV9ILGAC9K1QImV30JVJxxwdsZXvWVrYJOtQK2oMLjyYABANrNx7sE5XH18FYduHYKiKHjL7y1saL0BNyNuYkS1ETgYdxB1PquDYguKIXp/NABg9burYaQRSZlJsNXawlZjC19nXzxJe4I9y8cAAwdiiGczDK0wCLfWfIK7of7wadIeCoFbTd4CXF3x3NkG7Tvbooy/bPEq+VSCVqXFobhDAIkyX/2ITk8LYu5Pn4hL85EjMmFr1oQ2eiI+XfEIt52BjeVsAABLygF49hTHagQh6/JFoLOgSiMgQKIT9+6F4/hJ2LYkBQ0fu6J33AJk2GitYdHZ2ZK3s1w52UaayeRzolJUWNpwEb64VBLdz0iKNxQvDiXuFgigz0lgUwlBZW5vStR1K/FvUCaa6XUUDb9VAHQFcASAXY5jowCMyvF7J4Aqr6rrD1UqmijmXAztJtvxprNVWWMEuKws6D/QqoQz5HMWZdOLlJYmHoqurlbvtpy0Z48oB7t3J0kmZSSx0tJKrNdNJXU7O5M3bpAkjQ8ecH1J8X3IGTikjlZTiVLYYn0L/nh5l5gpS5Yk09OljU8/JQEeLwDecRJF5FM9uCYUrB0dyPwz8zMtKy3P+7+fdJ9BHwdZ2is6OT/tI7Xs0EG8595pBzqPUXP+ou5EFHgz7iy5dSs5bBirD3Skepx4e/ZrBF70s+fsamrW7WnDestqWpSMfbb04dWEq7naTc1M5byj83L5PQzdOZSj9owiosCm65pSN1HHwdsH02WiAzu1VMgaNcilS2ksUYIE+Es+8PCozvSeUYDd+xQgdTq2Hx7Eup/VzdVWlWVVWGVZFfL4cRJg7LKZ1E/Us9umbqKcVKlIrdby/HtHhVE9HjxVqxhvTRtNAqzWHbztoqERoLFbN3luOp0oDk3mxIwfDrD1l60Z7wj+VNlPnq+9Pfn8uXSkf3/xKwHI2Fg5duYMWa4cCfBoQYVeH4Kzq+TwdgR4Mr983nSWcfKb4/da7/Z/Qvgr/BAgCsNLADxeOB4M4CwAPYAASFS5+lX1/WVddG8AACAASURBVBkMgRSmYHbwea4Dj/jIwPdv+IJWt0+fvCu4dk1ci6tUyeWfYKGxY0mA6Z+tYPjqcKqiVfz60tcWTfkzd0fO/CKCgXP8rRr66e4W56CB2wby+uPr1vq++076Exkpv41GXqxRgpkqcHdpRw4bWoafhYLpGvD7AKlvSXRTce+lOO78EPcD229sT+0EraXNdhvbcf/N/ZZj5Yc6cf/Q1kQU2LG5nHMsohV54gTjn4mrsRKlUIkCh9QD9/uBmVq1Zbx2Btuydk899dFaKlEKm3/RnIdvHSYpEZp1VtehbqKOJRaUoMs0F6qirK7U5ujIPZvnsGczFe3HKEzx85a6Q0OZFfMZ66+sQ3W0msXHuTC8C5i8ZAGVKIUT9k/INfzDdw2ndoKWqaOGitb/7l0OndOQSiSYroYc691bLAsNG/JJi4b0HAZW+LgUsxs1pDEggA+qlaHBxGjbzqhMswMbjx8X60GzZiTJbEM273k78SfTJDYOGmTtyDvviJUJkMVlzBipw8tL/EzqhfPdTjL2Cyq8bFUwQJy9fq+bcl70VzGE6xBdwRlTWZzjvzEAfoGYHRu+Tn1/FkMgaXH+uGcPdnkXvOiew0SXsxw8mPf169czT+cjkszKYlaN6mzeQUx1q06vYrYhmzsubeGVQGc+1YMFB4EOYxSqxsuE8Jnlw49++IhPUp/k3V7HjrKqnT/PE3dO0G2kio9cbPjYBnQYJTEDdedXpDE0hBV6gkEDwWwFvFOuCMd3LkjHkaDTVCe239ie6mg1bSfZ0neOr2VCaiZoGJ8YT5Jstq4pHSeI5+CWYFlJ575rDac2SxhF5hVhZvJzNuvnxjVtijOuYjEmacH79uJV6TJKJnzVqYXZYr6YKVefWc2AuQFsv7E9q6+onotBeQwD0/Qa7g0Qc+oXrYqT27ZZTKTP05+z3BQ/qseBhcY5cMuVLUQUuO/mvlxDZT5+uKK3PGcPDz6xASv0Mq3EM2eS06bJdxPzXje1IxEFzq+iFi9T0/P/fnQHjm8kXoM/1gzk8/69RcK4cMHSnjE4mNkKuKUI2GtDF2YbsuWP0FAyIEC8DE1SDrt0Ee9Vkhw9mqlqsFk7uf9lZXO/e7dd1H8KMyD/IobwR5c/lSHExFi3B3kxAnPR6ci33xZpYdo08WA7fJi8c4fs21fOMWMmmMhgNLDbWllpx7f14vhdo1lodiHxCBzhzNF1FboPk5cgpA8YE9WSGdkZv93fR49Id3caKoQxeF5x+szy4ZF105mtgPsCFI7eHEF1tJrPnj/iZz0rEVHg1LcUXnGV+8jSa5nZtjX7RxShy2QnS/CRyzQXaido6T7d3dLUqbunLJN0+Q/zySVLWDXCkW6mPg9q78rmbcBBm/uRJIfuHErNBA3P3T9HzThw+eLe5IwZTG7WkPNq2tI/Qq4rPEjFBf0qUBWlsNnScCIKnHZIcA/at9UwTS193V1EzXzRti9tBXj8OO+76Og8Rhjte5veE0kgh08CjUYm7trCL0uanquiyEq9axf392tMAjy0e7n4ENSoIZJezZo0Zmez/oxQOo4C7zhCRP/y5ckHD2g04SC820HFNA14qkEZJmckW9t0c6MR4EfV5T47fNWBmdmZIkk4O8s7UqiQMLecFBpKAkzWgA06ip9DminoLlmLP9RV+UV6wxDyoDR7m19nBDmLl5foDPJiFjqdiIFt2pDR0TSuXMkBnzYnosDAKV5UImXPXW15NdZZVceyIr7THtxdrYAwpYoVxaf9VbRuHQlw0Nvglxe+pM8sH86vKy/cxfplheEsCiUiQfdhYNneYEKdyjTu3Uv26cNUB7nfeEdwSZ18LNlPXJw7f92ZSpSSiym9s04cgMbvHc9bz26ZHIbECWm5aSV77qgnBwzgld1fEJHggmMLWHV5VZZeVNpSz84r21i6L9izXyGGDXexMBrtWLBiXw1vBEsk5qdlwcteap5fNpWtv2xtcbpqtLYR997YS+Pdu+Lw5efHcVs/JKJA3QQdwz4Nk4ZSUkS3Yppkz2wVflkClngHkjRUq8oLPlqWi/ahQYHEJTg6WrZW19+pRpsxYKuuJrfkw4dlRTc5Cj1v3YyZGhULDQK9Z3lz5emVNGz6xvo+eHhwysEpRBQ4bkTFXE5hFr2CmcyLCcBr+cDzHqITMkB0BwM6uv3X7/Xr0BuGkBflkBJ+tSiKTPgzZ8ikJBEVv/tOApaGDycbN7Yoqc57glXes3rzFRwEdm6tYc2u8lsfqWLJDxS2jfBhWuMGcp3ZK615c3mpf4P23djLb4uC6XoNu856i/qJen5/ZSefu0qcQ+AA0UFMPDCRsw7PIqLAnUGgsVIlLt45hbqxYMs24KUqRZilFvH5lLeKhz5sTfdh4M2nNy1tmaWEKsuqcPbh2bm8FNWRCocMDub28vlIUyjvzz42nN3Wl4u2RhNR4NWEq7z86DKdpzozdFEon6c/p9Fo5MT9Ey316MeAHVrI97UhYLaTg+zNZ83izm/nWHQq2rHgT0F2zNJrmXr8MDf/vNlSh/cUNyZ+2F/0AYAwhKVLObCzBx3GqqzxEA8fkioVz/YQRre2fgE5f8UK+f/6dVJROLmOMOytvetIvARAhoWJ56lKRQ4ezB/ifmClpZVoNxq866pllp1pYSlfnnz6lBeaVSEB3nYEDW5uZMuWuR9kaqrluWcrEk8z6a0cQWKj8adtFcz0hiH8Grm5/TZDAGTvHhYm0Gcv0PP051y6pDcr9bA+UN8pnhwyox5DIz0lYGeYwnG1RV+RZ/0ODtaVZMoU2YKcPZvLypGYnki/OX6sHu3PNDsddwWCFZaEUTtByzK9RP9xMb+agTN9aTQamZ6VTu9Z3qz+UTGmaxVW7w6qo1TccW0Ho/dH02Mo+Fn38jxZQPqQqQIT6lUnN260WDPsJttRO0HLcovLUR2ttuAhtNvQjqP2jKJmgoZpD++SCxfybkkJ2DJo1PymGLh2QmsWnxNEzxmejH0aK3qAHTv4Xi/RRbzfUsfuY0OoMelQvIepeazPO2ThwiTkfooNVLHmYBc+CA4gAbZvIVucrl91IaLA1q1AzTgwvAuY3ral6HuMRjI+nutKSb0n75yUAVy1Svo3cCDL9Ab9B4Hp7zaR81NSLO1mhAazZH8V/Wb4MDmwIFm8uGwZnZ1Fmnj0iKQoai91a0ICPOchY5hcraJERKpUPNewHO1GgYl2anGd/vZbWUCqVMll4SBE0VnpfZEk/QaBMbX+XOmAfMMQfp1iYl7NEMxlxgyS8jL8eOtHvrfpPdpPFhAV73ES+ltkircFz7DUwlJccWoFP9kWTSUSrPOBA5MunpEXd80a0UsAEjlXoEDebTo7k6VL81RFX86rBK7pUoZLysl/Q5voOfC7Abz86LLFghFdA/z50c80GA1sub6lRC8OFuXex3UduWqTrOBdv+nKbEM2A+YGsO34YH5UFUz1MK2yLi5k377sMDTQgkWJKDBgbgARBV58cJEbLm4gosATd06QJO88v8PgDxQealuFj5zkhX9gD955r7VEcJYpw+c60H6MQnWUwowHd8l69fhVidw4jjVW1uCWw6toWLeW0UMrUImULQ4BZut1vJPfgdfyyTXRNcCPhlSyWEwMRlP48IIFvO0k58w9MleOtWghk9XdnbuDRWE6e1e0MIR27WjZAgI8NLUvEQUOqwfZcvj7y/8Tclgzzpwh1Wpmvd+dTwq4WJ5XfIAbn361juzShRtKyLFF5cFHdqaFpUoVYQy/Fq8A/Km6AzO9YQi/RTn2c+aSalJw5dxSPLQHZy3oyBILSljE2fc3v89hu4ZRiVKoMk2e+p++xZ3Xd9JoNFrE7YYzyzJFCwmcyUlmpdOnnwrwqpubKKOio8np08kPPmBs9RCe9QSf6fN4eWxsZBWrV48ZOg0NAPd2qMYPRpdhgcGgJlpN7QQtK80L5c6K7rKizilr0ReYlXqIAmcemEbu2EG2b2+xn5/zBO1HgcGzrL4LWYYs/vLkFzFvnlxiuZV6n9Wj/1x/Vl1ckc3agPeL+lj7qddzQIQEh4UsLEW2bk0CnDm3jUVXMefIHIvlo8SCEpy8phcRBc5q6ysYEqaV1QCxrPRvAP5YEGzZTZjxB9/0lMCq8HCyeHH6z/Vny/UtxXfE3l7C2E39qT+rDF2mufDJ5HG0SGkODmTRouS+fezRVLZGZ+6ckslrZydbRlKCrSpXFhDWxYstdf5U2J76MQLCe6KA9d35oImKJaf78+7S2WL1UBTpT17MIDz8L3nl3zCEV1FMjMUUeaggmGV6QNkAtxcGW7UGteNMSM1DnLl042huv7qdVZdVtdjnO69+l+cD7MlKlWhMT7dEErZcb7Ii9OsnQ7x1q7XdgAAB1rC1JS9dEkitYsVo1Ol4fNbQXFBlnjM86TFay593fyHozmq1iLotW5Lly9No3nrkKKPD5dofahfmmnIaflJZzRS9SnAZrl/nwyfx1ERrqJ2gZcT2CGu/EhO5sn91Dnpbrt8TAO4PVLNPa5kYRqORzlOd2XtLb8sla86uodNIcHjdHNujsmXJ99/nkfBiVCJB+9Fg106myfDRR2z5hUgxe2/sJSn+CmvPrWWZebI90Y4DvYeAT5y0ouA7fpyZjx/RcbTCqoOd+SA0iBkqMMKEoj2uiT2NikK2bMk+q1rRc4YnjWY/DvP4dO/O0/dOU4lSOLweBB7NPGabN5PFi/NxkYL0+MidlaYVFgVkq1Zyk5mZ5IgRcq4Zhdlc8uXjhY712HBSCX5ZErzloiEBnl0UTftoPT2HgT6Dc2wNQhWrpKBWy8L0F9EbhvC6pCi87Wh9yOlq8IAvOLOKiH5nPcB1YXqW72UVpT2me/DiAxPQxoYNNAIcNiqMiAK7fNPFqthKSxMAFTc38vZtOVa8uMC4u7uTpUvzQUIcZ28dyyNBoqwbU19DdZSKXb/pKrbqn5ZZ+2q2pW/cyNP3TrPc4rIcUwvMUMC0sDK8MGEAR9cW0Jd3Oqp411klkyXnS6woTHC15Q+FwANVC5IjR5KLFpHbtnHUYlm9HcZrObYWeMvDhAVoZ0d27swPh5VmpcUmLf+9e7zas6VFijlSwpEffFiCNBqZkZ3B4E+C6T3Ng4gCJ5sQpujlxQFtBHXp9L3TUk9CAjlpEo06LfcEgMUixMRoN8mWEdsjePPpTR69fVSsOB8HkiSNyck8vXYWqwx2IqLEY9N8f+c9wPRihUUxDAjzTUwkz59nl9Ya6scpjOtt2jI0aCDOQwC5cyfXnF5NRIELwyASTZ06Vs9DczGHPwPkSZO+IiODiSWDeDW/jNec9gGMrqOmbqxINgPfFoWq3ei/Rl+QF71hCK9Lfn4Wv4Q5lcAvS4AJNlbxL0sBj/qAS6ro2LI1GNIbvNO1hWipKT4IfUdIzoB+Cxpa97VmunJFxMW33hIlZWgojc2a8tIKQdGZV0X2+28vq8WTtYqRAPfXL0bNOLDz151zYw1kZdFQpgwTXe3pNlJFrxlenLSkE4fWEzu2/0Q3FplXhG4fuRFR4PZr2wXW7dIlsmZNedyVK/Neywb83h+MddNYJw7Atq2E4c2pJCJw1f527NHVVURvE8TXfXvQUKY0DVotDQr4dYiWNfo7WKSjW89uWb5/PLkpEQV+OaAOuXkzU5s04Gch0sblioEihpsBSAFy+HDeeRJHRFlzR6ij1Sy9qDQRBbp9lHsypWels8YQV2rGgRUG2HJkOLg98AWHMx8f0be4uzPO34X6iXp2baURMX7zZrn/GjXInj1pLOjD8C6Sy+Oug4mZmBWC7u7CyAMDrXV7eLyMpJSjnPES56vAgaDnhya35EH4k1/ovOkNQ3hdiomxSAjZCvjERsRRrw/Bup3B1aHycqTl1DEoCqkozK5Xl/0XNCaiwOEdvWjM52yxceeiNWtIgJmjRnBpC3+WHSYr28Iq8rLFrVvE+MR4ukxx5vKGgtN3sKQ9kxPu5armYOxBNhvuyywFPBhehI9THzMpI4m6cWD3ZvLCNZlSiqooFVXRqlwAKDQYyIED5R7ataXzVGdqJ2jFH+L2bWYfOkBdlJqaceDC8uDREBcG9wMbdX5ZGWaecM/1Cu+XK8bxNcFtk7qxYg8wesMA6ibq2PajClwfLH06c+cnkuTyo4v5Vjc5FmuOLTFLMB06WKw6dVbXYZF5RXjr2S2LE5RZOvvm8jdWJpmSwmfOepYe7Ur7SXacsbIne71jlYieujkwo0hgLoXesPoKlUiZrHlN4quuoH6sMMecUhU9PETf4Ogo4j4gUsTQoVZsxlKlSIAdermzVB/B8rQbjVyKWiXyDUP4ZzMEkocalGSyyWMsVSN72A4twGMFwDsOwuHzfwj+0qyGBLrUqEFjjpU1wdWGxmbNRLwsXVpW5Rx0NeEqj9YPpkEB63QBSw2z56ITi5iU+IgsXZpGDw+2n1+LtpNsWXlpZfZ9V0ejWi1BVfHxTExPZL+tgm/oP9efN3q3lbZNkOPl5gUTkWDPpgpPe4ErDi9kp6870X6yfa4sTzQaLRiObw90JaLAY/HHSJILji+wvLQ1V9bk2ftnxfFpRqCIzgANeh33+oFbyjnygqdYAXJOJgPAWl1AlxEiSUx6W7T7ycMHkS1aMNFBx4Vh0sb9mdHknDlyrXkVdnMj27Thxqi2YtGYPojGsWM5p4aOdfs6WPpXarANV4a7McNBVue7DiZ0rGEQRKo8JnqmRk2jSsUnNtK/tzuZ/lOrZdU3g6kWK8YJtcRJaluwXiwOaabAscxMkQjM8Qo/CaPj5cu0bEHs7KhECaZnTl8Oc/Gb9GbL8I9nCCR5qFs4Y53lpb6aD+zQXLYHpfqKYuyIj2llXLmSKZkpbLyqPiv0AA9UL/jyC+jkREOnTjw98QN2n16NiASdxqp528eJGXoNjRUrWBu+dImZei13BoKNPmtAREksBHfsIB0cmJrfnXWHelGJUjho+yBxoU1NldUqIICZiU8tZs8b5lV30CCeu3+OiMJLgUAkyc8+45wq8tK3X9OcRqORBWYWsLy0C47OJzdvpmY8qBsLPinoRk6ezOyERxbPy9VnVguDOXqUx+sH84lpIj6ylX089Xp2aaenz5DcYzOrirTxzFZ5edxylGPe4IYSMuZPbMDt5USqGt69IENGyHfv4Rp+VFPDZx9F8+fFk+k20YEXPcAMFZhYPIBPnIRhzasobY5vKAxkZn3RY+yuH0R26iSQeDnaTteAxYfo6R8Bpny3yTpuJ0/SopcArHEvO3bIb5O+4baLmu1bgOrxuZmBZvyf74D0a/SGIfwXFDM4/CXOrh4vGnejSVTOUIE1ZgZTiVKsCr9Ll0TzD1gkh0Qb6wuf5OLA1ObvkKNGifjp6GiB4L72+Bo/aCYv7rB6YPdNEkb9MPkhR85qyNuOYJKNipfWfpy7swcOkACnjrRCpi+uqKbRhPDMbdvYZF0Tun3kltsP30TffSEehK7DwS8/H0dEgboxUs/Cus5MV1vHYNyg0mSrVoyrWJzHvMFf3NUiQuusEkK8A9iyNbjPz7qlqPK+oENTr+f54q6s1wns104mc7qtVsbCwSF38hNTyVLJMYNK4SU38Ga35mzUAfxqfTSNiYnc8fNW1u0uWwnHSB2HdPfhriC5dnoVcGsFF6k3NJSpl88z5sB8PrOTrcNlD9B3MFhqbjHR+eQ0Q2s0pK0t9/vJvY9soBW8xEmTyIgIOcfsJWmOVTDrZ3KUZK04Vlm2ClEK+27966wKL9IbhvBfUszg8Fx7PtvRgrN/09nqq1C7C/j5jK6Wa4xGI4/cPsIxMxpyR2HTiwzwaqdGzFowX1Yh80Q1lxIlaJgxne+PDWW+Cfb8tpSOmSow9fBBrj23lu7T3amdoOWsLwfTEBoiL+ry5bn6erVfO+rHgq4jJO6g3UjxvqO7O+ngwB+GtyOiwHkDKgqgaK1asg3x9+fZIrJKri8JljVZUKaYgnWiakrAD6LAsn0UOo1SGFfChz8WAvcVt+WXoWoaevcWC8XUqTQuXMgSg3XUjwVPm/fmnp50G6liryYgFYXXywewSwuFw7ZGUIkEjQqs0OqZmaJ72b9fPAyjo3mjeW0e9QGTbNV5u5ub9AJP9QJCO6Q+uKyM/BfWA6zTVWFGiaJW78+IiFwWl5rd5P4+7OghzN7GhvzmG6nX3590dmb3j6pSE6niuWpFXm4fIMeNkyxQvyLl3HZR/2GZl34vvWEIv4P85vjlkhKG1JMHPLYWeCMfmGRC+s1q1IAxu2ez7GIJNHKc4sj+3/XnrSUzrYonf3/B4c/OFtCMsLCXXFmT9Qr3B6iYZatnor2Wg+qB81oV4sOInuLL0Lq1THLzZPfxodHBnhV7iEb8UCFZjdyHQWzoOequ3kNN36FqZpYOEUvHO++QnTvz8cCeRBTYvINVYXeusBPdou3Zb20Hnru8X5yXfpxJRIH6iXqGLAzhohOLxErw6LJsGfbu5YYOgjA8rRp4Oqwgw7sqvPzgklz/7Uhy/HjecRNpYmgDFW3HQJCKDYZffQapGSl0mGRHu2gdO0f4ke7ubNpWFJ45GQILFszT6SdJC94sYEtjgwYSiKYo4kegKGT16ry3eR1D+qvpN0gYfYehAVy3ebK1jsWLmZCSQPfp7qyyrAoNjx6KVGT2Ynydoih/3Uv7CnpdhvA/mZfh99KLyTavm5ItT9wPFEgCHLKAu/aAYfsONGoyBN22xuNr7yG4X2I55j+tjELZtpKnAQDu3we6dhWotbp1gStXAIMBGWrgjj0wtC6wMpQIvWeEJi0DTilZmLMbGLDxNjzmLROYtpMnJS9AgQJAQoKkCetdBscLAsUTtah+GxhhqIQEe+D0dIE5Q8uWAICRRbrhloMBX6weJunMvv0WmDIFLmp72GYBP3lmQ20ECicApW4kw1PthIfaTDy2IQAgyDUIDjoHZBoysab5GlQrVA32GcDzj6cDISF42qgOBhQ4g9IPFCyqACwa3wjfBxCrzq4GABQpWgWPhvdHoQ8y8dmw+khXjLDJhuS/CAgAxo4Frl4V7MNTpyRfQqtWsPUNRN3zqUhlJsqfewRUq4aEYH9s7FgamDpVIOwAGY/ixS3PKtPNBXsCgOXlgNPOaTh/bg8yNn0lU/T5c/n84Qfkb9YBs3cScfmA2fUdUP1KGh5OFuzMR975EPtuLbjZuWFmvZk4En8Ey86tAh49sqZyex3y9f2P3rt/BL0O1/iryj9FQiBNyTaHqsXLLAJcFSLbgN/EUnixmKUEV1erg4tOx0xbPdv1yMfNRWVlLjfMiQ07gCM/LMOU8JpyXkCA9XqNRlLDDR1Kdu5MAtznD7qOVHg8/jjZoQONWi1L9gMnH5gkkoDJbm7UalhqVhCDPwmm4dJFgXrTakm1moXG2Fmkg6DZ/mSjRqzZDawR6csNF74kosCKSytazH5jN/ajIWIgn5o1+aGh7NHegerx4E/fLWP9NfXpN8ePRecXZfAnwRZJYu25tWI1KGrPHt1c6T0jv2wNKlSw6g9y+vr7+5OdOnHIdEFV+tgUn9BuYzsGfRxEHj0q50VFibnyhXG/0a+DxZfBfH/FBmu5sjSY4mh6DmFhpL8/3+4EuoxULEpRc8lWwIdutnwSVoq1hnsx31gt7zlA0rC9rnTwF8QovC7hjYTw+6hjSEfEllmN7Ggg9mOg63nggT2QrHvFhaGhwOrVwJMnArwaFiY5Gs6dA1atAnQ6aNMy0OLHZ+jcWo3Q+0DtnzPQZthKTJlxCnY79gDVqgkw6OnTwI4dwPDhAuA6bx6wZg2MAGrEAncW2qLC5hPAmDFQnJzw+XY77L6+E5g9W1bOoCAonl4YueUZLj66iO+aBwNffAH06QNcv44UJxtLt28n30XCumXw9PDHo4RbSPh0LgDg+O3j2O46EK0f58fHPy3Es+Wf4FioKwaMLoN9/sCyYskY4t0S5Rq9jy6hXRCXGIeKPhVx6dElqBQVAl0CsePyFrinq1HunoJ0TzfYPHoK9OwJnDgh08fLSyQoQIBoy5cH2rRBYoA3FCj4wYSo7Ovki9vPb8P4zdeCdtyvH3D9uuQwyEEBC9fhhxVA5CVPdLpiA+9EIP/TLHRvDhQYkIkRqzrhzuIZwK1b+MirE57ZANMWtLVc/2TuVBzoWA3f+xlx9tEFRG98jFRkYcjbkGf7OtSnz9+GnPy76HW4xl9V/kkSgpkutwm3SAWZKikpqteQFFQqgdHq3l32uGFhZEYGjw5owT6NwAo9xa31hJ9WLBPHj1sbjY2VIKjKlXNhOBpTUjhsdEWOrQ1eDXDO3Z634BHGhCpMunZJVk6tlixZklkqCf+tElmQRlNWKbNZElECjWbWF/Tb2pdukbacbIrXjy8o7Zwv4UYlChyzOYJ9vu1Fp7FqFh4ABk72tKSPT85Ipv1ke777+bvi4j3RkYY+vek5TGHHFtLPlm0VlhxqKxGAW7aQT0wQckaj2PUjImSvDjDBQc0Vbzmycj8dn6clcsEx8ZW4Fxooma8mTJB7N8cYeHgIoO1HH/FGfpEEjKbV3ghw61v52XZ9a6qiVdSOV9i1lYbnLx9gl686iUuzl02ubEmpmalccWoFwxaEsm9DGY8thWGp91exNezt//T38j8lvFEq/nH0bS1vAb+AgGAcKvgbL4O7+0tKQ4sY6urCxRVU9DNBjE0fUd0a/WhvT544YW3UjOE4erTlUPR+CWV2n+4uwVNnz1rda8PCaNBYAVAtfTCF4C4wOQQdjBXbedN1TS0MYeaPM1lteTUWmVeEkeslFLh/A/G/MDo4SGRmRgbbbGhDhykOnN2/vOXaPb/skcl88SK5ZAm7DAmk0yjxX3AfBv5USLYbazqXJvfvZ+PPGrDcknK/PeCZmXyyfjU3lAAzNSZrQpAPLw7rzgJDwGM+kIAjjSZ3dmYz+AnJuR93YPYL4x/nrPDuoJ68se4TDmgIeVFCWQAAG/tJREFU2kWJT0XN6ABqx4FdujiKExYpGBFbt5LdutGYLx/TNGCR/qB/hDivZajETyImJI+F4B+0VTDTG4bwB9PlNuHMUr1iZTCXGjXIXr1o0R+UK8dsvc5yXYYKvOyuiJ6gXTs533xtt25WCO/33pO96N69/Pz855ZJaEY2Jil5ICtUIFUqZjdubJVcHBxy+QkYtFp+XRz8pGNRxh7aagF7RRR4Iu4o98+O4Pf+sHgSVu2tZaEoZ4k1KFqUvHGDF+6fpxIJNmsr59SeGCSIRzlAZ3aXyydOOFEqBg2ERdJ4kHSfJBm+OpzVlld75Xh/adJhHD+3g6Nbu/JSYbH9ZyumyEovL2GG5nvU6SRc2WgkV6ygQSPmyix7O9LRkY/dbLmvmI3VCqPV8vGCGZy0YQC9hprGIhKc2jWIWZ07Whm1nZ1F/7OhuJzXr6HEJujHmGITckoG/0BmQL5hCH8u5eFI81IhyQMHmF1UbNgj64DaMZJ0dGVp0OCWB2ZjzlWmSRPBSyhalOn5Peg5UqIAP/jug9x9MachNwUJpdiYpITly8UG7+oqEXpNmzIxB75Cgi24tYSag+uDF4pJX27lU7Fle2mn4qcVWXZxWfLQIQFQcXUlw8LYuhWEmUQK1iMLF5Zt0fLl5NWrzM7OsqR4n14VrPyBnuUWlbV0t+ryqgxf/WoMgAHbBtBush0zszM5as8oqqPVjD26ixPfyuH0ZVZE2tuTjRqJL0OO0OYznuLYRHt7sls3Xnp4iT3bSpCWwcNkxlWrmaZV+HEbPwuT9Bui4tyBFZk0dCA/L6PmXj+p77ajPL9aXXPHJhiAvzSU+b+h12UIb5SK/w29wpxEAEZFwZdD3kbRdo8wOhxYUwZQK8CRQkD124Dqxk1J/bVkCRAeDtjmSL1uNEqmqCpVYLh1C9r7j7DqKwMKad0wLWyknPPgATB6tPRl3DjJN9m8OezSDXhkCxgGDwLS0iRh6LVrQPfuMCxZjJJ9gW7NpB9FHxgwexcQfOUJaGODG146FHloQNVbQNqDeLjHPwGGDJG06U+eACdPwj9VA6MKcFLZ4nLrWlL3ihXAe+8BRYpArdaggVc1AIB7GnDMIxMNijS03Fp6djpsNFZl5q/RwbiDqFywMrRqLTqEdICBBmx9dgzTqwPjaxIIDrYk1EVKCrB/v6Rj+/FHMc96eaH0Q+BweU/5v3lzlHArhtkXCyLOGRjX1BHZpYIBgwE2WcTAL+MwfbdU51goCINcj6OQeh7OuhlQ/DGQogVK9QN2FQb2B1j7WSgRODy1L7Bw4Svv6d9AbxjCf0OTJ7+k2c5J2Sopn4Skwy7hGc6+XRp3nRSka4AVm4HCTyAp4nx8JIP0nj1iI//2W8DeHtDrLXWp0tNx1wFoeA3YOfsxHLwKAfnyAd7eYo8vW1YSze7ZA3z9NR5NHgO3NECVlAT06CGlRAlg2DC4KLbQKSqsLgN8UxwoOhDwHgJsH9ESB8u5wfVpOqZ+D/y4AjgWfRdzlsQJ46lSBQBw08cen5TJhrc6H1KQiZOPz4uYmZMMBlTYdhYAsLpRQRBEdd/qlr/Ts9Nhq7XFb9Gz9Gc49+AcavjWAACU8iyFUp6l8PmxZfBNBOK89MDFi3Jyo0bymZoKZGXJ5717QHo6EjwccJ2PQTs7uYfBg+Fw4SoKpmoweflNqC5eBN3cJJfj4MHofxzwfwpof76GH5cC4TeAjSUB/0HAlyWBVG3uftpmAl3dwlF95P8GMwAA5aUH+jdSWFgYT548+Xd34/Vo7VpZFU2ZnM30fQAwrRqw/FsgfzJw3AeY+hagIlDOszSiT9gDhw/LybVqCWNQqWS1IyVx7OTJyK5YAZttYhF09RGCHgOOWS+0r9FIXkEAUBRhLr6+oK8vdl7cjHoX0qAmZMLcvw+cOoUkHTCphiQWtc8GPI22iNekIfAp8IsrUDNejQQnLVRp6Qh8pqB4qi3yPZEU7wSQkE+HG/aZ8H8KrA0FMtXAB2F94ahzsG54DhzAoQcnccob0Kl0yDJkol5AOEq4FwdIxJxdgwL2+RHuX/tXN1zxz25j743vUT+wLvLbewEkLj68gHP3z8ErGTCogHo3FWGc6ekyBuXKScLdgwct9VCRr9CooTKYxtc0VmkpibB5moTYQFf4FwqBEh8P/PILznkB+mzA9xlga5Cqx9cCBh8FthYBurSUwfBLUWNyYC907PvvYAaKovxEMuyV571hCL+T6tYFvv/eksn2tjNwzBtofflv7dWfQuZ7VEzfCQAqFVQajWRENhqBjAyk6hRkqwCjaVJq1Fo46h0BRUFC+lPoNDo42TjL5HyxqFR4mvEMzzKew8/FHypFBSgKspIScTM7AXoDkKEGij7J0TF3d9km3LkjWxsA0GjA7Gxr1mHFxB38/ETCOnsWSW4OOGuXjIJwhPuDZNhn0nJ+lgJomDtrMQGoogA/jRtixyT8OYP8J9HrMoS/XZGYs/xrlIp5kN9Q9UsJZYeGC9x2za4SDUhIbkmalVA2NuKNqFKJReHkSRovXuSkBe34syu4JgQsPAD8urw9OWQIuWABLZYLszItJ65iSAhZqRKvFLTjwvJgktran6d60Hsw2L4lOPQ9X9qPAj+sCwZGgK5Rtnz+7CGZkcHMtBRqxonicF4NG7JwYT64eYGuH7myyrIqzE56Tu7Zw/jKwdwTYM08RECUrfnzc1hXH747QyDl/Ob4UT9Rz+fpkrjEZZoL+3/X/zfHsuryqqy8rLL1wL17pIMDq74nwDWIApNt1dYoxUOHJA9mTjnD25ssX55ZABf1Ki9KV7MyWK8n9Xoaq1RhukaOmX0VnmvBI96S8+KSe27ZJUsB7aJ1f3ug0n9DeGNl+GspZmFfdmtmSslleoHmVBYE4/UlwVin3NBslgkEWBxxGBDAbT1r87wHeNsJdBwF1uuhp9GUG4CkMAZA/BNCQqzXu1ihwQkBCjnrq7dEWUbXlIl01hMs1Q90GyZowa1bgf7D9eIG/N135MOHdJsipsO59Z3I2Fh2+KoDtRO0vPDAmt+QRiOdovS0GQM+LVtCnINsbGh0dLT04Zd84LryenZrBm7ZNpc0Gmk7yZbDdg371XFMzUyldoLWeo7RKBYXSIJUs3b/8sfjBIzGzFRzjue0aRJMVrQoz4V6cV5tU/BTzZq5IdtMjHtjcdB9KLg+WNKs7QgQ0/CL562q+O9kBuQbhvC3UMzCvhzQSOFNZ2uKrlatJD7/V30Xcpgwzcwk1lXFJhNK0DZax19cYM1KbTRKJilfX3mxPT1z16XRkLVrk2PHcms1Dz50FuekJJ3gHjRtBz6xU1E9Diw9XpLK1OymUDc2d5RkhZ4y6Sb1LMZtGwW2PXJf5Ev3a07/NqKu6T62bWNswi8s0xuc0sqL20Js+Mg2x6Ty9ua6UuC3EQ3lPvKIdtx3c594BF7ZIgfmz7dc/8BJbTEN7g4yjZuTk5gcTSZEtm4t/giLFpEAU1ytDIru7jJGwcESup1j7J7rwHfagRlqeW7zw0QiMMJkVvyL4NL/LHrDEP5GijkXkyvLcc6tRF7FzCyOeYMf1gNjTFmIZjRxtUoBFStaobtyFjs7gSufMsWK/BMezuWLehGR4OMje9mji8ClHfGRa74rDH5TBAyLLEDnKBtxHBr4vmQb8vKyYAUc9AV9B4ElPgDTg4tJO/PnS3BRWpolB4XdaPBhPh3p68vd+5YRUaB2gpYDtg2gw2R7Nh4TwAFNtcxo09KShIWAODS9+y45e7a4LWdnc8L+CVSiFMmKvXr1Sz4f5jR5O1qXk2ObNgljtLUVaeGFTEkZBbxoAPj9DFMYuV4vyEcvgKOmq2HB1jRA/Cz+CTgGfxS9YQh/M8WcixH048j/LELyvpOaXsMUlusFZr0gttLOzvqy55VdKC1NcApNW5BvioFzlr5PRIEVhjiSisJRjfSWlW93oAkQpYZgINLXl9RqWX9u+VwISj9EvS9ie06GpNXyuW9+jq8pzjkj5jUlPTz4SU1rBOWu67vY9ZuutJssxz478xkRCS7fMIZcuVIcmnKiGDs68lioG1fVcZNVPOe9q1SkqytX1hfJ5lg1f5nURYvmPq9sWYmTKFpUEK71esaUVnGKCQo+VQNma9W/+QzinP4+uPQ/i94whH8KxcT8pmfjY70gMLVpJchM7zcV2DZzDsZfLZ6eAjGuUpHff5+7zaQkGiZO4DMbxbLv3rZtHn8qIbqBSc1EKWl0dmLoaFf6DM6xZ9brObyDTDrfCNBnlo+1XqORvHVL8kF27swstcJnegGktR8NPnS14aDGatqMATu3UjH98gXuub7bAh5jDnpaeHxh7v7evk3On09D1apMV+dxrxoNWbIkCTCjXjiv5Xvhf0URSeq+uEfz1i05HhBAI8CI+rnBV434daZgAHjI/58Zj/B76A1D+CdRHqnjzCWiAWgzBlxaFvykvEzeMr3AkeGi8bZMCPM1Li55pwWztZVJ07WrZHnavZvtI0sx3wiwcg+FBo2anVoIBHns2AHizqxWc305PREF9moMYS6+voxobkvdWJk4P7uBj3t1Friz1FS5n7t3RYvv788is/zZcWZVqqIUDh9Rno36OjO0T47J5+rKfUX1nFfPiU266YgocMUpUxBSXJxsF3KkXCPAdKcc9/didiqVivHOJstA4SBr2rWbNwXtOg+8grwktAQ7xZJrIlf5B8cj/B56wxD+aRQTk2fm6XS1pJFHlGQ29o+wKhePmvb87NmTXLfOCrLSqhUZH0/u22dNXJqTaZjKyjJS78aaHox117DEB+KHT0WxhA5n2dtKGPNwGxpNCrygaDeqx4HbPnib2wsrzNSZVlMbGwEc9feX72fOsM2GNvSf68+OX3Wk3WQ7FppdiMp4cF1T01agbFneCfRglgq87C79+byCbW6rSMGCpI0Ns9Uqbi0MGnW6l+7Fsk3y9rYoQC2KWr3+5QxLLxQjwFsOLzAJczo/RZHP/0FGYKbXZQhvXJf/KurYUUBLSCAmBsmuDjACuOcAxJuwQfTZwMfb5TNdDdxxNF27bBng7y+AIq6uwMaNAqJCAp9/DkyYIF6L06cD8+cD4eGIKaPCoAaA93PAOT4B512ycdkDaH0Jct348YCiQJOShr4ngRt26fj+xHr8/HZ53DA+hkENGAcOwMqpreE3zhEZWzYJqMmxY0BsrHgItmiBEetuIfhYLCJK9UBaVhrin8eDKiBsybdA587A6dNwLFgYn4UAt0z3aZOUJq7aZoqPB9LToTYY0fg6oLzg/Wmh2Fjg4UM8tAdO5Qc2FYPVY9PssZgHEcADO6BQsvXYXRe1PJPYWHGoio39dwKa/MH0hiH8HdSxIxweJ+HzhX1Rq6facjhFD7RpDSwpDyTYAWXvm/4ggapVgZAQwR5UFCAuDqhTR4KiMjIkuGnCBKBBAzzcvA49W+mQaAM8d9SiXmdiWTlAZQRaPHQDChe21gug1UXBipyGHxB3/Sfos4Dyd4ByHYZg9tep6LL/GU7+tEXaSUwE6tUD2rUDdDqU2XICWz8HworXwZb1ahDEtD1A4UJlBA8SgOPBI3jvLOCYIc3aZEPuw0yKAur1yMrpFqgogqRkpmHDhKFevoz8ycDqMkCXd4E+9bOxx9dg8aLMixQA+VOtv40AYof3+g8e2P8jeh0x4q8q/9Nbht+gmHMxtIvW5UJ6thudA3xDpRKwjlmzLFmU8iwqFenkxP0Ni9N9GJg/2pH+A0FNpMKiswNZe3JRsdnndM5Rqdi2FZh/iLR73Bv8oZAoOuOdXo39YNRo+FQHpjrZ8ptSAobyY6Ec57i6kgULilUjQNrY62/6LzCQ/OorMiuLV07uYqbK5A+xcKFAnAcEvNSeWR8wo4o1HdwdB3DiW7Bk33rV1uFym3+3T8F/Q3ijQ/h3Ucy5GPqNtLGmDs+JxJMz1j4PPYS5mPNPbi4iE29Vafl91lN+LwrL+7oP65lMjJFgcD+xOFx0l0nG5s15uGMNTqoOPvR0INu2FT1CyZIv2fLnVJZ2fvKStG+5JqJOxy2F5f/9AQq5dKlYLUgyM5NJ7s40Arw/02RGNRqtCVHymNQEuN9PoN8r9JB6BzR4BUNwc/uf1hP8Fr0uQ3izZfiHUMeQjoidmgbjw76Ina9Gx/OQgKG+L8TaP378q3XYGEQcnlYD8EkEiiYIXPz8irJdaHw775DtendtkKkF1AQueQA1ugPeSUD/4wC++w4lTsRhUk1g/KzGorOYMUNg3k24EEYAibYqXPZUIV8aUPYBoGTk1gMomZnINIUP6zIJ4+LFwKxZEpDUvDkcEhKxp6gGnlPnWoKc8OxZnv01KECx/sDU6kC8E3DFXY4vqJTHyeHhVpaQkPBGT/AKesMQ/mm0cKEoyUj5fE3gjVhn4AcfYFYVAT8Z9YMoJ7cVBdaFAmoj4Pw0FT+7AttGtAK2bwfmzAEKFECiSiZv91NyzbFCQMu2QLoGQGYm8l2NwzdfAHWnrofR3Q0oXRqYNEmwEjQaqADoM4047Q3kgx7jZzZGvkg9Eo7tA9q2lcmt1+OJhwMAwDUdUP30k+gFChYEvvsO2QrgmJwN5fGTX79JE2kIxHwNfPGVKGGfm/BWfJNUEs2oKPIZEyM4EW/otUnzR1SiKMpQADMAeJBMUBRFAfAxgEYAUgF0I3nqj2jr/z25ueUpJQQOAjQGwQrIlwa8d1qUd0YFSDVBxz+2k9U85duN+O7USXzvkYT4qo9xyF+AQZpcFRCQdaWFwXRoCez9TK5t8Iu5pafyQYqC0cYGN33s0ad6Ik55GhH6xIjOG3/ElI4ZmDquNmbtMl2WkYGsVNEqVuwJDP0RGHfIVBVkkle++/rDUMF0bqzJcqHNBiYX7g3E/jvwCf6p9LslBEVRCgGoB+BWjsMNARQxlV4AFv3edt6QiT7+WLYSL1ChRCBLAxhVwDNbYEJNyTi1MVi2CwCwKwgo+USwGhrvjsXsdY/hkgE8tAc2fikMpNVlAAQ8U4BO515uPlEHCxYCSSAtDQFxidi0XpjPO+ez4Bf7DJ3OAYsqAJuKAF+UBIaHA18ESx0DjgI145ALX+GhHZD2H76NKVpgdDjglgqs9O77rwEr+SfTHyEhzAEwHMDmHMeaAfjMpMw4qihKPkVRCpC89we09/+bzHvgiAiLpJCezwGFklJwK5/V+DatOjCvErDkW2BHDPBVCeDHQsA1VyBNC2gNMqGWhQEDDwO6bJmkqVqg3QVga1Gg3i/AbUfghDfwzlVAS8A2OzdoyD4/IN4RWBsCUAGKPQb0BmDyHsA5HbAxAu9eAtpdku3MwQBBH/rFFchUAXoj8FgHfNAQ+OLr/2AcVCrY9+iNdf8jWIb/FPpdDEFRlKYA7pA8K7sEC/kAuJ3jd7zp2BuG8EdQx465lGM2APqeX4szW3qDKSlI0wK+icDk74GOF2TirywDfB6ad3WT9wEf1gcWfwck2gDuqUCyHggYBNz4GGhxRc4jAK0ReGIjegAAqBovDMDeAOwsJgwBAAomA/N2yHcjBGPSKxmocRPw+VCuqRAP7IkB3DKBDV+94p51OgFzfaMU/FPplQxBUZQ9APLn8dcYAKMB1M/rsjyO5ek7oihKL8i2Ar7/xuSY/xDqGNIRHUNMk2XtWiAiAnz8GLedgBF1czMDhbKamynBTpiBAiCsp6zsvk+AW66A3yAg6Kk4SW3YAJzykv2+mSEcLggc8Aee2AJNrgCRNYHH9kCSDngrFjjkCzyzA+445+5vhha47m79naoBNNlAhg5wyHzhBQoPf6Mc/IvolQyBZN28jiuKEgIgAIBZOigI4JSiKBUhEkGhHKcXBJCnyojkpwA+BQRT8T/p/Bv6FTJJEAqAQmvXovGC3jjsm4JbzqKJb+RTG6vTjyA1S9z3RocDS7cA9lmAGsDFnOxfBfziZrI4ACj3IHdT3ZsDcfle7oJC4KLJ0bDKLWEYaTnyYtplAmP3ifQQ7wRcdQG+re6GSiM+tjK2N/SX0x8GsqooSiyAMJOVoTGA/hArQyUA80hWfFUd/0qQ1X8prT2/FmO+H4NbibfgqrLH0J3J6HcC+LYY0Kup6BksRGDcPmDCwTzqCQF6vWO1ZAACT17/OnDGW+IXfBOBLqeAz8rJ70KJQIOrwNIKQMFkFaYG9X6jEPyT6S9HXX6BISgAFgBoADE7dif5ypn+hiH8A2jtWvxfe3cTGkcZx3H8+2v6cpEStSqioj2ImKhQERF6CXqw2iJehHoQwYKVVqigYNqAJwtqDxbRKvGNCoVYFVGqoqF4TUWpL8T6EqoWRKyCoggqKX8Pz7PTNdlk02bXZwd/Hwg7Mzs7+0uG/e+zO5P5b3lzM6OX/cGJJdCnJdx9zWb2vAV/jj7NivwvCEEa1gt4cY14aCj4fmU6oemmZQM8e+UOGBmBY8fSCUw7d/rzf0G+DLuZVRZaEHymoplVXBDMrOKCYGYVFwQzq7ggmFnFBcHMKi4IZlZxQTCzSk+dmCTpJ+C7U3jIKuDnLsX5Lzh/Wf+n/BdHxDntVuqpgnCqJH24kLOvepXzl+X8s/kjg5lVXBDMrFL3gjBaOsAiOX9Zzj9Drb9DMLPOqvsIwcw6qNYFQdIDkkLSqjwvSU9ImpL0qaSrS2ecSdIuSV/kfK9L6m+6b3vO/qWkG0vmnI+kdTnjlKTh0nnakXSRpPclHZE0KWlbXn6WpHFJX+fbM0tnnY+kPkmHJR3I86slHcr5X5a0vN022qltQahxP4hx4IqIuAr4CtgOIGkA2AgMkq40tUfS7AYMheVMT5H+1gPA7Tl7L5sG7o+Iy4HrgK058zBwMCIuBQ7m+V62DTjSNP8o8HjO/wuwabFPUNuCwMl+EM1fglT9ICJiAuiXdH6RdHOIiPciYjrPTpAuQAsp+1hE/BUR3wBTQNvrUBZwLTAVEUcj4m9gjJS9Z0XED43OYRHxO+lFdQEp99682l7g1jIJ25N0IbAeeC7PC7geeDWv0pH8tSwIzf0gZtw1Vz+IXnUX8E6erkv2uuRsSdIlwBrgEHBeo3lQvj23XLK2dpPeAHMfLs4Gfm16c+nIfuhIb8du6HY/iG6aL3tEvJHXGSENZfc1HtZi/V48BFSXnLNIOgN4DbgvIn6b0VyoZ0naAByPiI8kDTUWt1h10fuhZwtCt/tBdNNc2Rsk3QlsAG6Ik8d9eyL7AtQl579IWkYqBvsiotE07sdGi8H80fJ4uYTzWgvcIulmUqOulaQRQ7+kpXmU0Jn9EBG1/gG+BVbl6fWkIbhIXx59UDpfi7zrgM9JnbKblw8CnwArSAXvKNBXOm+L/EtzttXA8px5sHSuNpkFvATsnrF8FzCcp4eBx0pnXcDvMgQcyNOvABvz9DPAlsVuv2dHCKfpbVJzmClyP4iycVp6kvSiH88jnImIuCciJiXtJxWLaWBrRJwomLOliJiWdC/wLqnR0wsRMVk4VjtrgTuAzyR9nJftAB4B9kvaRDpadVuhfKfrQWBM0sPAYeD5xW7QZyqaWaWWRxnMrDtcEMys4oJgZhUXBDOruCCYWcUFwcwqLghmVnFBMLPKP/rGbcQxwIU/AAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"def chord_experiment(rad, n, ex_points):\n",
" crit = calc_crit_len(rad, n)\n",
" green_count = 0\n",
" red_count = 0\n",
" fig=plt.figure()\n",
" ax=fig.add_subplot(1,1,1)\n",
" ax.set_aspect('equal')\n",
" for p in ex_points:\n",
" chord = chord_len(p[0], p[1])\n",
" if chord > crit:\n",
" col = \"green\"\n",
" green_count += 1\n",
" else:\n",
" col = \"red\"\n",
" red_count += 1\n",
" \n",
" plt.scatter(p[0][0], p[0][1], color = col)\n",
" plt.scatter(p[1][0], p[1][1], color = col)\n",
" plt.plot([p[0][0], p[1][0]], [p[0][1],p[1][1]], color = col)\n",
"\n",
" print(\"Radius: {}, Sides of polygon: {}, Critical Length: {}\".format(rad, n, crit))\n",
" print(\"Total chords: {}, Number of Chords Longer than critical length: {}\".format(len(points), green_count))\n",
" print(\"Experimental probability estimate: {}\".format(green_count/len(points)))\n",
" print(\"Expected probability: {}\".format((n-2)/n))\n",
"\n",
"chord_experiment(radius, n, points)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Summing Up\n",
"\n",
"Now we can run our experiment and find that the frequency of having a chord longer than our triangle side. We find that it is close to our predicted value of 1/3."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Generalizing Our Solution\n",
"\n",
"We can also extend this principal to other regular polygons. If a polygon divides a circle into n even arcs, the probability that a random chord is longer than the length of the side of the polygon will be the number of arcs, minus the 2 adjacent arcs divided by the total number of arcs.\n",
"\n",
"P(Chord>Side) = (n-2)/n\n",
"\n",
"Lets try a pentagon. If our reasoning is correct, the probability should be 3/5."
]
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.patches.Circle at 0x7f7115e3f8d0>"
]
},
"execution_count": 70,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"new_n = 5\n",
"crit = calc_crit_len(radius, new_n)\n",
"ax = draw_question(centre, radius, new_n)\n",
"crit_circle = mpatches.Circle((centre[0], centre[1] + radius), crit, color=\"yellow\",fill=True, alpha=.5)\n",
"ax.add_patch(crit_circle)"
]
},
{
"cell_type": "code",
"execution_count": 71,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Radius: 40, Sides of polygon: 5, Critical Length: 47.022820183397855\n",
"Total chords: 200, Number of Chords Longer than critical length: 107\n",
"Experimental probability estimate: 0.535\n",
"Expected probability: 0.6\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"sample_size = 200\n",
"points = RandPoints(radius,sample_size)\n",
"chord_experiment(radius, new_n, points)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Our experimental probability appears close to our prediction! \n",
"\n",
"Our generalized solution appears to be plausible!"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
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