{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Statistics " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Considering the amount of data produced nowadays in many fields, the computer manipulation of this information is not only important but also has become a very active field of study. Despite of the fact of increasing computational facilities, the effort necessary to make statistical analysis has become more complicated, at least in the computational aspect. This is why \n", "becomes fundamental to some aspects, leastwise in a raw way. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- - -\n", "- [Data Adjust](#Data Adjust) \n", " - [Linear least square](## Linear least squares)\n", " - [Example 1](# Example 1)\n", " - [Non-linear least square](##Non-linear least square)\n", "- [Random Numbers](#Random Numbers ) \n", " - [Example 2](#Example 2)\n", "- - -" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "import numpy as np\n", "%pylab inline\n", "import matplotlib.pyplot as plt\n", "from matplotlib import animation\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#Data Adjust" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Given a data set, the first approach to find a function that passes through the points would be using a\n", "interpolation polynomial. But we should take special attention to the way data set is gathered, i.e., usually\n", "is a sample obtained experimentally or in a way that has associated an intrinsic error. \n", "Then, forcing that the approximate function passes through all the points would actually incur in incrementing the error. This is why it is necessary to build a different procedure to build the function that fits the data.\n", "\n", "The fitting functions, though, are build using a lagrange polynomial and the order of this polynomial constitutes\n", "the approximation that is going to be used. But the fitting function is not going to take the exact value in\n", "the known points, they are going to desagree in certain tolerance value. \n", "\n", "\n", "This type of procedure is also used to approximate functions to a simper type of function. Although the procedure\n", "is very similar is not going to be include because of the lack of use of it that commonly has. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Linear least squares" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Approximating a data set to a linear langrange polynomial would be \n", "\n", "$$\n", "y_i= f(x_i) = a_1x_i + a_0\n", "$$\n", "\n", "\n", "the problem is that the values $y_i$ are not precise, then it is proposed to find the best approximating\n", "\n", "line despite of the fact it does not coincide with the data at any point. The best linear approximation in \n", "\n", "the absolute sense requieres that the values of $a_0$ and $a_1$ would be found to minimize \n", "\n", "$$\n", "E(a_0,a_1) = \\sum_{i=1}^{N}| y_i - (a_1x_i + a_0)|\n", "$$\n", "\n", "\n", "To minimize the function of 2 variables it is necessary to set its partial derivatives to zero and simultaneously \n", "\n", "solve to the resulting equations. But the best procedure for determining best linear approximations is to minimize \n", "\n", "the sum of the square of the diffences between the y values on the approximating line and the given y values.\n", "\n", "This is, minimize the next expression with respect to $a_0$ and $a_1$\n", "\n", "$$\n", "E = E(a_0,a_1) = \\sum_{i=1}^{m}[y_i - (a_1 x_i + a_0)]^2 \n", "$$\n", "\n", "\n", "i.e., a minimun to occur. Then, it is needed to take the partial derivatives with respect to $a_0$ and $a_1$ and\n", "\n", "equating them to zero.\n", "\n", "\n", "$$\n", "\\frac{\\partial E}{\\partial a_0} = 0 \\hspace{1cm} \n", "\\frac{\\partial E}{\\partial a_1} = 0 \n", "$$\n", "\n", "Afterwards, \n", "\n", "$$\n", "0= 2\\sum_{i=1}^{m}(y_i -a_1x_i-a_0)(-1) \\hspace{1.5cm} \n", "0 = 2\\sum_{i=1}^{m}(y_i -a_1x_i-a_0)(-x_i) \\\\\n", "a_0 m + a_1\\sum_{i=1}^{m}x_i = \\sum_{i=1}^{m} y_i \\hspace{1.5cm} a_0\\sum_{i=1}^{m}x_i + a_1\\sum_{i=1}^{m}x_i^2 = \\sum_{i=1}^{m} x_iy_i \n", "$$\n", "\n", "where the coefficients $a_0$ and $a_1$ can be easily obtained\n", "\n", "$$\n", "a_0 = \\frac{\\sum_{i=1}^{m} x_i^2\\sum_{i=1}^{m}y_i - \\sum_{i=1}^{m} x_iy_i \\sum_{i=1}^{m} x_i }\n", "{m\\sum_{i=1}^{m} x_i^2 - \\left(\\sum_{i=1}^{m} x_i\\right)^2} \\hspace{1.5cm}\n", "a_1 = \\frac{m\\sum_{i=1}^{m} x_iy_i^2 - \\sum_{i=1}^{m} x_i \\sum_{i=1}^{m} y_i }\n", "{m\\sum_{i=1}^{m} x_i^2 - \\left(\\sum_{i=1}^{m} x_i\\right)^2} \n", "$$\n", "\n", "Now, using the error definition one can find the error associated to the approximation made,\n", "\n", "since the coefficients $a_0$ and $a_1$ are already known. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A body is moving under the influence of an external force, the variation of the position measured for different \n", "times are compiled in table 1 \n", "\n", "| t(s) | x(m) | v(m/s) \n", "| :------: |:-------------: | :-------:|\n", "|0| 2.76 | 33.10\n", "| 1.11| 29.66 | 21.33\n", "| 2.22|46.83 | 16.57\n", "|3.33 | 44.08 |-5.04\n", "| 4.44| 37.26| -11.74\n", "| 5.55| 12.03| -27.32| \n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Finding adjusting parameters \n", "def Linear_least_square( x,y ):\n", " \n", " #Finding coefficients \n", " length = len(x)\n", " square_x = np.sum([x[i]**2 for i in xrange(length)])\n", " sum_xy = np.sum([x[i]*y[i] for i in xrange(length)])\n", " sum_x = np.sum(x)\n", " sum_y = np.sum(y)\n", " a0 = ( square_x*sum_y - sum_xy*sum_x ) / ( length*square_x - sum_x**2 )\n", " a1 = ( length*sum_xy - sum_x*sum_y ) / ( length*square_x - sum_x**2 )\n", " \n", " #Returning a_0 and a_1 coefficients\n", " return np.array([a0,a1])\n", "\n", "#Line function adjusting the data set\n", "def Line(a0,a1,x):\n", " return a0+a1*x\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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wYLi4uMDW1hbDhg0r9fGBgYEYN24c3nnnHTg6OiIsLAzZ2dm4c+cO7t27hzZt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\nAMTzXWkU9zHAwMBAzJ8/H23aPPr4Snx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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#========================================================\n", "# Adjusting to a first order polynomy the data set v \n", "#========================================================\n", "#Setting figure\n", "plt.figure( figsize = (8,5) )\n", "\n", "#Time\n", "t = np.array([ 0., 1.11, 2.22, 3.33, 4.44, 5.55])\n", "\n", "#Velocities measured for every time t[i]\n", "v = np.array([33.10, 21.33, 16.57, -5.04, -11.74, -27.32])\n", "\n", "#Making data adjust\n", "a0, a1 = Linear_least_square( t,v )\n", "\n", "#Finding error associated to linear approximation\n", "E = np.sum([ ( v[i] - Line(a0,a1,t[i]) )**2 for i in xrange(len(t))])\n", "\n", "#Plotting solution\n", "plt.plot( t, Line(a0,a1,t), \".-\", lw = 3.,color = \"green\",label=\"Lineal adjust\" )\n", "plt.plot( t, v, \".\",color = \"blue\", label = \"Data set\" )\n", "for i in xrange(len(t)):\n", " plt.plot(np.array([t[i],t[i]]), np.array([v[i],Line(a0,a1,t[i])]),\"c-\")\n", " \n", "#Format of figure\n", "plt.xlabel( \"$t(s)$\", fontsize = 18 )\n", "plt.ylabel( \"$v(m/s)$\", fontsize = 18 )\n", "plt.xlim( (t[0], t[-1]) )\n", "plt.ylim( (v[-1], v[0]) )\n", "plt.title(\"Linear data adjust with error %f\"%E)\n", "plt.legend()\n", "plt.grid(1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## **Activity** " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " \n", "Using the next data set of a spring mass system, find the lineal adjust. \n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##Non-linear least square" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In general, it can be used any polynomial order to adjust a data set, since it is satisfied that $n **Activity** " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " \n", "Adjust the position column data in the table 1 to a second order polynomial. What is the acceleration suffered\n", "by the body?\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## **Activity** \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " \n", "The air drag for a sphere that is moving at high speeds can be expresed in the following form \n", "$$\n", "f_{drag} = -\\frac{1}{2} C \\rho A v^2\n", "$$\n", "\n", "where C is the drag coefficient(0.5 for a sphere), $\\rho$ is the air density (1.29kg/$m^3$) \n", "and A is the cross-sectional area. \n", "Generate points that have a bias of the value obtanied with\n", "$f_{drag}$ using np.random.random. \n", "\n", "\n", "Afterwards, use a second order polynomial to fit the data \n", "generated and find the error associated to the approximation. \n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Random Numbers " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In nature it is not uncommon finding phenomena that are random intrinsic, this is why it becomes a necessity to produce random numbers in order to model such events. But, let us think about the operations that a computer can do, they are done following certain stablished rules, how then can be generated random numbers? \n", "\n", "This is achieved until certain point, it is only possible produce pseudo numbers, i.e, numbers obtained following some basic rules. At sequence of numbers apparently random but that are going to repeat after some period. \n", "\n", "Now, the most basic way to understand the generation of a pseudo-random number consists in following the next recurrence rule that produces integer random numbers\n", "\n", "$$\n", "r_{i+1} = (ar_i+b)\\%N \n", "$$\n", "\n", "$r_i$ is the seed, $a$ and $b$ and $N$ are coefficients chose. Notice that $\\%$ represents the module, then the numbers obtained are going to be smaller than N. \n", "\n", "Now, consider the case when $ a= 3 $, $b = 2$ and $N = 5$ and the initial seed $r_0 = 3$. The new seed is the number obtained\n", "in the last step. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Random numbers produced using a = 4, b = 1 and N = 9\n", "\n", "[ 8. 6. 7. 2. 0. 1. 5. 3. 4. 8. 6. 7. 2. 0. 1.]\n" ] } ], "source": [ "# Randon number function \n", "def random_number(seed):\n", " return (a*seed + b)%N\n", "\n", "#Constant values \n", "a = 4\n", "b = 1\n", "N = 9\n", "#Amount of random numbers \n", "N_iter = 15\n", "rnumber = np.zeros(N_iter+1)\n", "#Initial seed\n", "rnumber[0] = 49\n", "\n", "for i in xrange(N_iter): \n", " rnumber[i+1] = random_number( rnumber[i])\n", "\n", "print \"Random numbers produced using a = %d, b = %d and N = %d\\n\" % ( a,b,N ) \n", "print rnumber[1:] " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that after N random numbers produced the apparently random sequence starts repeating again, i.e., N is the period of the sequence. Then, it is necessary to take N as big as possible but without incuring in an overflow. What happens when the initial seed is changed? \n", "\n", "\n", "\n", "To generate random numbers can be used numpy library, specifically the set functions random. There is also another library\n", "used random, but it contains few functions comparing with numpy. \n", "To generate a random number between 0 and 1 initiallizing the seed with the actual time.\n", "\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.6935313352397631" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.random.seed()\n", "np.random.random()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To generate a number between and a number A" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "43.75232924187592" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = 100. \n", "A*np.random.random()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To generate a random number between a range -B to B " ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "-12.581424504749194" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "B = 15\n", "B - 2*B*np.random.random()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#Example 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "###Random walk\n", "\n", "Start at the origin and take a 2D random walk. It is chosen values for $\\Delta x'$ and $\\Delta y'$ in the range [-1,1].\n", "They are normalized so each step is of unit length. " ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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D2ZlO77xToetQoNHwTUoKuRoNI2vWxKYELXZQRATnioq4olZjZ2ZGJTOzMgtLkw3YDz+A\nUond1avY3rpFg1atAO5pJ6OwkP9eu8Yfmzbx5+3b5Pv5mazPs7hJE8/miqGihLQwdwsEFYCJmVuW\n4ZtvoFUrPOLjCfvkE8N9Q0aPJrOgAGbNItPFhQ4fffRENKrH6aw1ZPRo1DVrYrl5MwV+fgYLghwV\nxcXvvycnO5s6lpb81awZ9W1sDJ8bExbGkCVLGNu/f7kEdElzSVerKSwoYMPChYY+Srrv+s2bJKel\nUTRhAnz/PSiVSFlZ3LCxof3IkfddE/13J339tfYhm5tLlosLWU5OXAsLu+dcXSPL5Go0tHBwoMar\nrxIzYgT5vr7/mKMOwZNBaNICQQVwj5k7Nhb27aORuTnVatUy3Jd26RKn/P0p0mleUH6N6mEEbkmm\n2ofV5Ir3f/3yZZJ8fdGY6/b8hw9Dbi52ajV1atfGSalEKmF8evPz0oULyyWkS5qLtG8fDQ8dolqN\nGoa2pdRUVC1b3jNntx07OD12LKhU2jcDAkyut4iLo6hYykdZllGkprLHx8fkuyM2Vvt9+/ubHGvI\naMOAq1lYUMPSkhoWFhzasYOPzpzROtk9o1o0iGdzRSE0aYHgGaK4t6+1QoHnrVucee01Eo1MnNYq\nFR4xMfzdsuVDa1QP4x1dkc5a9/Qvy0hz5sDYsTB6NNStC0CWszMncnJAljFLTWXEyJEm7UiSVG4B\nXdpc2LuXxHHjSNS1ZRMfz4rg4Hvua3LiBI1ff52z8fFo/P2R5sxB9vc3WZP3BwxgUAnruyIkhMvL\nlnHa6Ltj504YNw7LuDi+6tOH8PtkqfJ99VWWDR1KrI+P0KIFZUYU2BAIKoigzp1xOnQIZBnvxEQO\n79qF98mT2oc5GN6fNHAgyvh4gIeK2Q0PDaXpiRMm7TY9eZKwrl1L/Yx+E2F98CAA1o8QK3xP/0A1\njQblwYPg56f9GzkSBg3S/jVujLu5eYnjM+5/8KhRBI0YQfuRIw1/QSNGMLiYx7h+Lja6uVjGx+Np\nPA/deoSHhjImLAzLhATt+yoVqkaNkFq0wDcxEQBPScIqIUFr+p4+naMpKbz1zTfkrV9/z/qGd+1K\n21dfRdq/X/t+XBzk5QHQLDn5vutvPG77JUseOU5b8O9BCGmBoIKYc/kyn73xhuEhbGZmxgevvWYi\nkAM6deJEkyY01QnvBwnXktA/7Msr6PP8/HDWbSKqHDqk1SAfkladOqHQ9a9UqRg0aBA+J0/Cm29i\n/r//mQg4aedOPvvggzLFT8fXqcOuHj0Mf/G1a9OtU6d77jXeKNQ4epTm4eGY68ZjZbQezTp2pIpu\nzqhUvBQczNEvv+RsdjbMmkWWgwOKbdvg1i3o2JHcTz4hY9w4NK++Crqc0MrYWMaGh7P2+nVCunSh\nXkKCtr34eJT16mG9eHGZhW54aCi9qlYt93cu+PcizqQFggqgwwcfcAtwNDcnbuNGLBo1QgPkFxWh\nAPJdXLA6fpzt27cT6OjI2qgohqxaRWT//g91Lvl9SgpfTphA0qBBBKxcyYH7eEfnFRUx48IF2jk6\nkrl/v6FfixYtiM/MZEKdOlgqyrZfP5yZyfzLl/k7J4f8r7/m8IABeK9YweHISNZFRzNk1SrebtSI\nBUolmsBA2LsX/vc/HKpXRwKsbt/m5RYtSjw7Lyl87X6e3/rQLy8zM1IdHcm6dIlCV1csU1Nxq1mT\nHhMm4GFtzeU9e/hi/Xq+6duXAj8//tqyhej0dBNzNnv3YvvXX2RPmqTtW6OBKVNg+nSq//ADP339\nNSdychhesya/RkXx5g8/oGndmoDERJrY2bGsHGb7Zz30SDybKwZxJi0QPCWKO07lyzKnb94kPT1d\n6zVcowZ5kmTikMS+fQzz9CTQ0RHQalSbtmx5KI3qz1u3MFMomNGrFwO/+46XwsJKfeifyc3ly0uX\n+Lh2bWpZWSEb9StJEk1tbRl9+jSja9XC3dq61Pkmq9WkFBSgkCTyNRqqK5Vcv34duyVL+FTnnR29\nYwc2GRmobt5ESkiAVq3gyBGYO5cMSYK4OHLPnClRM9ZTu00bjhw8SJ6vL5bx8ffVUMNDQ2m7dCn7\nW7XShjZ9/z0A+ba2ZGRn89/PP+fOpUso09OprNHw4/btSDt2kF9UhHz8OBidVZtt3Up2164oYmPR\ntGwJ8fFgb4/iyy8xUyjoMno0rRwcWCvLuJuZUTsvjxsJCYwbMMCwlmXlWRbQgmcPoUkLBOWkJO9i\ns1mzUBYWkqf35L5yBdzcQK2Gt9+m6owZXN22DYWRxvowGlVSdjar09KY5u6OLMsMHTGCah99xGxP\nz3vu3XD9Oseys/mkdm2U9+m3QKPhs4sX2T1nDoXm5ibXNLLMtfPnOde2LWoj87hSpWJVo0Zs2bLF\n4Pxlsi4673batNFuVmQZFi8mwN6eA8uX3zNvWZaZev48XZ2cGBkRQWz//tRdvpw6dnbISqXJ/bGb\nN1NUowY21tYUaTRk3bkD//mPqbe2LryKjAztufGNG+DkpDW/29tTo6iIFIUC2coK82bNGFWrFrPf\nfJOmgwZxYtAgWLwYMjO1n3VzAwsLkCSkzEwa2diQYW2N1fHjnNq37x8ndP8Nz+apU6dy5swZVq5c\nyfnz5/Hw8KCwsNDk/89HRWjSAsFToiTv4moKBWnBwdCy5d0bY2LAzAybhAS+GT36ngdAeR/uN9Vq\nvrlyhS90AlmSJJYtXMj0CxfILirCVpe8Q60Tuk1tbflU52l9v34tFAqm1K3L2DZt+ColxUQYm8fF\n8Vm7dnz2+efcOn7cMF+ra9dYfOkSHkYC1GRdAgLgjz+goEDbkEqFwsmJ0a+8UqqA7lalCv4ODob4\n6Xn9+7Pvzh0WX7mijb/WYXb2LEWBgdzRh0LFxWnPj1u2vOut3ayZ9premhEXB0VF0KoVMnAZtJsI\npZLmSUnMHjuWIaNHc6egAOk//4GiIurXqEFyaipcvw7BwRAQgAycBCxVKla9+uo9c/mnFVH5p/Kw\nG6sDBw4wefJkDh48iJmZGe3bt2fhwoW4uLhU8AjvIoS0QFBOiheWsIiPZ+TQoazftIm4Fi0Mgsx2\n82ayp0yh6apVhD9iuE2BRsOUc+f4j4cH5kbCfsjo0RzNz+dnWaa6Ukm+RsPFvDxaWlvz6cKF5epj\nTu/eLAsIIN1IGFtfu8baixeRLSygYUOtCRvIBOKLhX3p16VPfDxqf3+sQkNRbtxIZuvWEBeH1c2b\nDJoxg7e++QYbhYKGnp7IwPncXLwtLZm2aBFgehQQBmweNIhEoyQgPlWqcHLLFrL1oVB+figmTEDT\nsiWeksSVgwfJ8feHOXNAH17l56c9YzYKn6qjUnHT0pKPBwxAkiRCO3bkp6QkZN2GIBmwiI1Fffo0\nskp1ty1Z5sXERMLHjLlnDf9pRVT+qTyspeD27du89957hISEYGZmxocffsjgwYPZtGlTBY/wLkJI\nCwQPgbHW2DwxkXFjxuBpbU0/lYr8gAAUBw5g3aQJ0vfflzujFphqZDJwLi8PF6WSjywsTDSy0I4d\n+UUnFJJ079nEx9OnDEKhJK3Pxs2N9JQUmDQJ0ArjhLg4/i84mHe/+OKuYJRlnA4douWHH5q0pZZl\nFMePw8GDFKSmosjMhAULICODnJdf1nZSVERmq1Zc0/VpFR9PVmwsQSNG3M2zLUm0HzkSD3NzxvTo\nwXs6wW+TkMDHvXox9vPPObd/P7RuDTExOAJ3vvqKGjY2VD5xApWPD5ULC8nXbaQUMTFoGjbU/jcw\nEKVKhf+rr3J6926ONGrEsXPnUL7wApoffwSjDUHz5GROHzvGzSpVQN/f/v1k3rnDkNGj79GO/8kl\nLCvCSvCobURGRrJhwwZ+//13QFtso3nz5vzyyy8A1KpVi+joaLy9vRk5ciQbNmzgzp07eHl5sWDB\nAtq0afPAPtatW8eYMWOIjo6mcePGJte6dOli8nrYsGG0b9/+gW0+CkJICwQPgV5rNE5raXhA+/vj\n//ffvDdzJoNHjuTsCy+U++FUkkZ2Mz6ej4sJ30cRCqVpfZY//0y+LN/VXJOS6DN2LPsSEvhWJ6iU\nKhVNO3Qg5OhRqltY0LFlS365dEnbVq1asGkTmuBgclq2hOHDtVq4v7/WwjBtmlbY6/JfK69d45qz\nM0kpKch2dtpz/HfewSY+ng8bNWK3lxcv/vYb8X5+ND15EuehQwkYOJBzv/4KgYFw+DC3Zs3CbPp0\nPIcMIb2wkJPffcf3I0ca1sYzIYEr5ua4xcfzd6tW+CQl8cvYsTBo0F0HQI2GXZ07s/fgQXKNSm/u\nrl2bhebm2kxquv6SmjdHOnz4nlSikiQR1LlzhdauflaoCCvBo7bRvn17Runi5q9cuYJareaALlTu\n7NmzZGdn4+3tDUBAQABTp06lUqVKLFiwgF69enHhwgUsdAVgiiPLMpGRkcyaNYvt27fjcZ/ENHp2\n797NCy+8UKaxPywiTlogeEiKx7wWT1YxyM0N9Zo1bLx1i7VubsSVIQZYlmVuq9U0CAqi9pEjD0xY\nUjyxR3mEQklJUSofOkSzdu20WqNRez+lpeHYvz9Vtm83CO6NQ4awsWlThtWowX/r1CHnwAFtW/7+\n4OSE1ZYtWkE/YID2bFiSsExIwD8gQBvj3awZNGxI5vjxJL71FvLw4VC/PqSnQ2QkZtu28fHGjcR8\n9RV2WVnYL1lCly5diM3M5KfBg3HJzdU6eOnM0FXd3Pg4PJx1gwfzRrVqhmQm9kuWMGvoUN6oXp3/\nDBlikkxEkiRDEpWQiAiSVCrM//gDZBmbTZsIDg5G/eabOO3YoTWZf/MN+PsjHznCyWHDTL5HWZb5\n4tIlmnXooE2WIss4HjpE2osvotZoHuWn9kzwMEl0KroNd3d37O3tOXToELt37yYkJAQ3NzeSk5PZ\ntWsX7dq1M9zbt29fKleujEKhYNSoUeTn55OcnFxq219++SXz5s1j165dZRLQR48eZcaMGcydO7dM\nY39YhCYtEDwkJaW1LB5aZa5QsLt5c/6oVYtXwsNNwn6KoqMZlZzMjN9+41WjIhyO5ubUsLSkb7du\nfKYz15rFxJBx5w4dPvrIcJ9eg1s+f75BYyyPabX42bpSl+xjaq9eBHTrxvXAQCzXrGFks2ZU/eMP\nHM3NqeboyO2vvsJaqcRMocDd2hp3a2vCqlZlZf/+DFKp0AQEYNWyJS+npxOVkIA6IEB7PhwQgPPh\nw7SdPp2/P/2UlKFDUU6dito4zea2bdClCxw5Qmb16mTm5XFe51FtfuMG0du2oXr9dQC+GjOGN+fO\nRfb3xzohga/79qW+rS2A4XvRfx/hXbsSrvtONhcLfbtHu4uLg0WLeKNtW8afO8c0Dw86jBrFwKQk\nckHrDFcslWiXjz5izJkz9K5WDT8HB5Q6K8vC/v1p4OjIuLNn6eToyLpZs55bx7KSfi+127Zl2vnz\n5Wqndps2HDQ6viivpSEoKIidO3dy+vRpgoKCcHR0ZNeuXcTExBAUFGS4b968eSxfvpwrV64gSRIZ\nGRncuHGj1Hbnz5/P5MmTcStDCdPTp0/TtWtXFi5cSOvWrcs89odBCGmB4BEo/nApLR91V2dn+rdr\nx/8dOKB1vtq/n3wrKy7duoWdjQ27FiwwPKyn6R7Wcq9eROlyPXvEx3M+MNAkD7jeTFjc9D5k9OhS\nBQFgck0GzJKTIT4eH2trPh85knU3btCyTx+iv/kG97ZtSapRgytGebrNpk1jWAlOU9YtW1J59Wpu\n+vvzYmIia5cuJfCtt4j19aWeJHFtyRK+6t+fcE9PvHv3Zsj33/POSy/xrX4jolJRSanklrGTlpFH\ntVKlYrzRGWGvbt2Yv349cYB3sc2Jfn4lfR8lbaxMjgz8/HD66SeKZs3iM3d3HJVKeoaGMn/9emLf\nfx/Pr7/mQsuWFAKoVPTo2pVxZ88yqU4dXC0tDW0ax6N/Wa8eW27dIq1xY+Lu3CHvOXUsM14rn6Qk\n1owdW25Tvly3rjZpje74orzn9UFBQfz++++cP3+eiRMn4ujoyKpVqzhw4ADDhw8HYM+ePcydO5cd\nO3bQpEkTAJycnO7rMLZ161ZCQkJwcXEhLCys1PsuXLhA586d+fTTT+nbt2+5xv4wCCEtEFQwpT20\nlk2bxq//mgxkAAAgAElEQVQdOmjPY6OiwMUF2d6ekwB37iBlZGBmbm7Sjl74zhgyhLnr1pFQSqlD\nY6Egy3Kp534lXbOMjcXqzz8ZGxFBdUtLghwdOdmuHR1iY+kyciRfTJhAjl6AAb7u7oYsacZn7Sdy\ncjCTZRSzZmGjMzPqx//ZBx+YWBj0450zaRJ733qLWB8fnA8fZtK77zLqm29QFxXBoUMmGqtPYiJh\nRpsDSZIYGx7+wHKXJW2kir/uGhJy9xz54EH8hw1jnpeXIaxN/130XrgQCzMzrHfsIPPECbhyhfFu\nbtT84guO+/mZbowkycS5LMTJiY6DB9Ng0CDOPaeOZSX5YjzpNoKCgoiIiMDV1RU3Nzfs7Ozo168f\nGo2G5s2bA5CZmYm5uTnOzs4UFBQwe/ZsMjIy7ttukyZN2Lx5MyEhISiVSrp3737PPSkpKXTs2JEP\nP/yQd955p1zjfliEkBYInhAKhYJ3O3bki0WL4IUXtNWijExl8r59OLm58XZyMqdzc7lWUEBOlSoo\nJYkfa9WiWuvWWCQkUODnd4+Z0FhjfJAz2fvTp5Nz9KjhmsW1a9hYWPDbtm2cadoUK4WCBfXqYfb9\n90iSRN3evRmgc6ayTkhgXM+ehn5LcgQy37ePD3RxygZzc2go4aGhJY7XEBfdty/769fnzYYN2X7i\nBFf8/JD270du3bpUs+ijZG4D6DFiBKq8PBzMzbE+e5bM48dRp6ZSrXFjPhw79h6rg21mJqfMzLSZ\n5XRYqlRcTkzksouL1rHMKJHKkawszhVzLhvTowcjnzHHspIcG0vjUdf8Udvw8vLC3t6etm3bAuDg\n4ICnpyfVqlUzjL9Lly506dKF+vXrY2trS0REBLVr1za0ofdHMH4N4O3tTVRUFKGhoaxYsYKQkBCT\nvpcuXcq5c+eYOnUqU6dONXz2QRuAR0FkHBMIngD6h6Asy8Rs2kThkiUwfrz2rFYnLM0mT6ZG48ZY\nKhS4m5mxZN48allZoeDu/y/63Nb3y2kN2qxoA5KTyfX1RRkXR69q1RgdHk5zOzvGTJ/OFxYWhphn\n0NZjdjxwAK+6dbFWKEyEyuBRo1h38iSZ1aujTE3Fu359bBUKw3n4g/JtPyizmnFd6SsFBYw7fRqL\n+HjW/vEHrmo1fw8fft/5Pkzmtiv5+SxOSeHa3r2svn79HsvCf194oVSLhKEetW6+tZctI6RzZ374\n+WcYN67UOtU/NmqEb8eOfHnpEgdmzyauDN/jk8IkW1yHDg98NldE/vFnPYf5oyIyjgkEzzjG2sn1\nW7dIzMnRhhjVrQvffYfCxQWNPnXm3r0U2dtzsaAAKSODmubm1C2WS7s8ZsIuXbrg8NNP5OrODhdH\nRLAtPZ3116/zVbt2KKdMMXHYkvfuJX3cOOKku/WY9eekoR07strFBQICUAMJgGLfPtIOHqTpsGGk\nXL+uza4WGIhZTMw9muGDHsTGWnUNS0sa2NpyyMeH1+Pj6RISwtBymrOLr70eWZappVDQJCICgI9r\n18a+f3+O68799WvRLDmZsHHjAEq0SIx+/30G6c7RbRISmPHGG2z8808s8vIoWLQI7O3hzBkTU73N\nL78wJyCAy7/9hqe1NVlqteFY4FkQVOGhofxn3ToO+/iU6f6KGPOzMO/nASGkBYLHREmmYGJjoXFj\nUKmobmdH5l9/kaVLkMG4cSBJyHv3crWEGFwom5lQlmWmX7jAzNdfZ5ROwDkqlfSsVo2rBQVEeXvz\nY9u2rNbFPNskJFAVuHC3ARqfOEF3nTAzjv/WCx3N3r0kd+iArM/L/c030KoVHvHxhBl5qpeV4vnC\n33ZzI2X8eHq6ud3jjV0WSlp7C5UKZ2dnBrq44KZz8AIYExZGv4QE8v38UKpUNOvYkaScHBra2Jhc\nk/bv58z164yLikJz/jwcPYp09SrbU1J4IziYjTVrmqYhNXISLLC0JM7NDQIDuaLr1/hY4GmRWVjI\n2uvXScrJwa9DB04dPEjOUx2RoDiPVUjXrVsXBwcHzMzMUCqVxMXFPc7uBIJnipLOhtm5E8aNwxxo\nU60aRRoN6+fPh/bt795z5AiJw4aRKEn3eP6W5j1uzLLUVLpXqUKbV18lZvt2g4D7v9RU3Cwt6VKl\nCsEzZrDtpZe4Hhio1Q4/+IDen31GkasrZGZy7Px5HLp1A7QPCWsHB1i0CKyssPbx4cdhwxj9889c\nNEq7qViwgFnvvPPIGlIR0LVKFdq+9x4LFQquHzlCZd1YZMBakmjg4WFiji9Ja7Y5cOCuw5ss0/DE\nCdZGRpZ4rj1v/XpifX3xSUpi/PDh7MvI4Ke0NDSNGlH955+56OuL04ED3G7blhtGZuz8AwcoqF6d\no40b47x6NSnGaUgnTNCmId20iQx3d9i8WSu0dePxPXOGcKOz7Yrkfslzls2fz87bt9mWno6NQkF4\n1aoMdnVF9vDg2NChxD6WEQkelscqpCVJYufOnTg5OT3ObgSCZxK9ebq/rvSiUqVCnZcHQPWjR2k4\nYwYAcWvWcFmt1n5o7957YnCLe/7eTwjGZWSQq9HQVlcS01ChKi2N5dOnIymVLNR9Pv/mTfjyS5Ju\n3eLrbdtQFhZSlJkJFy6Qry/M4eBAPpAty9pKUi1b4n3ypCEXuV7LtFYoaCVJhljk8mI4s5ckLuXl\nscfKiptpaST7+aHRj0UnHDOAzGLm+OJas1V8PL4WFtwxisf9tFevEteu+DFCXWtrk6MGr169+OC7\n7+gYFsaeP//kqtH347h+PVdatiT18GEq5eWRMnMm1Kyprb5VuTLMmgXVqsHVq9Cggfa1mxtSVhaZ\nNja4du9Orixjffs2DXXhdRURN13SmljHx1PD2ZkJZ8/SoXJlZri7Y1bsWGJMWBi9IiMful9BxfPY\nzd3COUzwb8ZYm26SmIjf4MGs0cULd6lTh0WXL/PG4sX8PGYMKa1bY/7XX0gvv4ya8mUPA22VrNVp\naYYqWaB98G66eZPrajUjQkNNH9xubvDHH9yZMYPdkgQ9esCePZCaqs1fbZykITYWl/PnyUpIYKyu\nIIWxBuqdmMif69eXaawlaXnXb94kOS3N4DV9HrBWqfCMieHvDz+Eb7812bw0OHEC7/ff51hWFrXa\ntqXOr7+SaKQ11zpyhOhlywh5770yxePe7xhh4CuvsGfbNpYOGsS6qlUNyTxQqbjVrBmxtWuTf/Ag\n2NnBpUvarGnGa7dvH2zYAK6u2o1O587IAQHa0DuAmBgyzMy4ptuEVETcdElWHJcjR1i8bBmVS0mL\nqf+c4NnisXp3e3h4UKlSJczMzHj33Xd5++2373YsvLsF/wK82rQhxcqKXMBclrG2siLvzh0cCwsZ\nsGoVjWxtOZOby+mdO1n/+++sfustbdKMB3j+Fhd0MnA6NxerEyeo6etreP92YSGZhYW0s7W91xNb\no8Fm2jRy9PWS4W4d7JQUqFoV3n1XW4N5zhzWDBvGZqP60aD1Ch6yahWR/fuX+QFv8CROSNCGKkna\nOs2W6enaety6GtxW336rTfqhn7+u1KRSpWKIqyutX3oJa4UCazMzVNu28fnly+T5+ho8qcNDQ8s1\nvvt5G+uvFfewX7loET5DhpClF4b+/trz+Q8+uHt88ckn0K2b1kEwNlYbIz99uuG6YsIENP/5DygU\nJXrHPyzGHtvGa2JMSRumXQsXimdzBVBR3t2PVUinpqbi6urK9evX6dy5M4sWLTLEtgkhLfg3MHra\ntHvCnYiJoW5qKn0++ohOlSsT5OiIAhg6YgTLFi5kXXT0AwWLSciMDqv4eIbl5PCtre09YUMLvLx4\nsUMHfo2KYqG+PnNcHPz9t/YmLy+TkCFiYuDUKcjPh9xcSE/HvWFDallagpE51jh8qqxCxSDoGjQw\nZBUz6dfMDCXwmacnET16aLOW9euH7fTpZE+ZUqIQKy087WHG9yCMBX/U9u3EpaVxMicHbt6EqVNN\nQ7D27tV6emdlaQU3wLRp0LmzVtuOi4PTp8HdHVq1QrFvHw0PHaJqjRqGeT2s6bssIXsl/Y7KEoIl\neDDPRQiWq6srAFWrVqVHjx7ExcUZhDRgCAYHbXWTx13ySyB40sydPJklHTualHi03LyZ49u2YatU\nmty7rFi+6ft5NJdkznzx5EnmLF1qyOClf7/yoUMU9e7NdbWavt2789eIEST4+lLr6FHWL17Mq++/\nz5WoKBNzMtHRSGZm2jrSQUHQpg3ngHMA+/ZxIT6eoJEjkdBm1qrfti1uPj4lOioVFzCSJNG+c2cS\nLl2isFidZtstW8j+9FN8Vq1ilC7l5JiwMG0K0Y4d+b6UcKzSwtPK4mhXFoqXDrXJzGTYrFnkWVuT\nUakSODhob1y0CCwttUVC/P21lbMyMqBTJ63wDgiATp0wj46mMDBQ+95772EzfTo5LVsi793LSZ2X\nPzya6Vu/Jn2//ZaxAweWuAYlOjcKKpSdO3eyc+fOh/78Y9Okc3JyKCoqwt7enuzsbIKDg5kyZQrB\nwcHajoUmLfiXYKJNx8QwRq1m7qef3vczZUn0YKwFWapU/LdxY4OJ935mTr0muLx/f95ds4ZbaWmQ\nlga9emnHqIvCsJRl2LoVy/x8MmbMuPsQnzPHEC4G2oxbQ7Oz+T97+3s0+OJ95xUV8dnFizS1tWXe\n+PFabbqwUBsKFh/P+zk5fH/ypIkVQa8N//DVV7w9cmSpQvdxaM0lrbUei59+QqpXj3xjS8C+fVoT\n/h9/gLMzBARg/dtv5L3yCnJ8PHzwAV6LFtHd25svjh6Fli1RShIdr1/nr/Pnsb19m/RPPik1MUx5\nkWUZnyFDOLh8+X0T3xj/XnLGjv3HP5unTp3KmTNnWLlyJefPn8fDw4PCwkIUioorDFlRmvRjK1V5\n7do12rZtS7NmzWjRogXdunUzCGiB4N/E3MmTsd2yBWQZ802bmD1x4gM/U9b0jPqyfzWPHuVY48YM\niIhg0datmP35p6Hc48ItWxisq8EryzLu7dpRz9qa+IYNadmuHXTooDW36ko0olKBnx/NkpPp06gR\nk0aOxDw+HtAWuahqXHZRlnE+fJgDoaGYqVT3LUF4MjubMWfOMNTVFR97e6oEBqJQqagbH2+4f86k\nSYbyn/oSkh0++ojTCgUdIyI4LWnzYZe2Zo9DQBdfa/38mqnVNEtKMnmPrVu1Jm4vL62gLShg0Hvv\nEZCcbAhTq9+1K59OmEDVs2fBz4/Khw4xYfx4+lWvzpLhw7FISADK7zioX6/2I0ea/Mnm5vdtw3hu\nrkeOPNI6PS887G/k5MmT+Pn54eTkhKOjI61bt2bv3r0VPDpTHpu5293dncOHDz+u5gWC5waFQsG7\nHTrwxYIFvBEUxOLUVEbUrPnI7RqbeD/v3x9/V1fea9JEW2VJV8UnE4iPj+cVd3dmnj9PtkZDczs7\ndv/wA3bm5qyyteXcxx+TOGwYrF6tNde2bAkqFZ1DQlAGBGCrVOK7aROxfn74JCURNnQokxISUPv5\nYa5S0a97dwY0bsy2119nlC7WWh9i1OGjj5BlmaKCAvI0Gi6lpLBUowFJ0qY7zcjgVlYW5l99xdi3\n30ahUBgEbUlhRA8y/z6uLFaSJGGdmaldHwcHpMxMsmxsOJuSAjNnwuTJWgvEzZug0Wgd8T74AMtP\nPyXH358xYWEMXrmSAEliWf/+TDx/nkmTJzPp++8JDA5m+507jJw1ixqWljj//DNXfH3LXXijtPUK\nrVLlgXMbExZG79GjSa9X76HX6HniYS0FNWrU4Ndff6WuLizw66+/pmfPnly9erUCR2eKyN0tEDwB\nNBoNDQMCSIqL4/+uXaOulRUdK1d+5HaLm3iLNBrqDRzI+SFDDCZT16VLmTd/Pt2dnbE3N92XTz9/\nngbHjtE/ORm1jw+89x589x2Vf/iB9Hfe4bWqVfmufn32bN1qcJYK69rV4JDU/McfeWfmTC7m57N5\n9mxO/P03BVevgovLXfO4Wo2ljQ3WV6+S0acPmpYt7w4gNhZp/Xoc7Ox48YUXkIzm5WFuTuLt23e9\n0ZcswT49neYNGtxz35OoxTxh9Wo+O3vWJLxKeeAA6t9+08Y/f/qp1ov7r7+01ol9+1C6uLD61VcJ\n69rVYLJXKBSoNRr83n2XxL/+wszLC3OFguwLF5CrVkUBaNRqGru741y5cpnnZ+woxpgxWnN7Xt5d\n73hAungRTzc3/i6m/cmyTKfwcA60bk3umDElPpvHDx6M5dmz9/gd5Ht4MLuMsdWP2kZkZCQbNmzg\n999/B7TFNpo3b84vv/wCQK1atYiOjsbb25uRI0eyYcMG7ty5g5eXFwsWLKBNmzbA/c3d69atY8yY\nMURHR9PYqDRqcQoLC1myZAlLly7l0KFD91x/LhzHBAKBFoVCQVJcHAqFgsEuLni/8w62lpZY6Uoh\nwsMJnOImXjOFgrlvvGGoWmWTkMCiPn0Id3Ex+ZzeEep8fj4uFhaQnAzHjmGjVFL43Xe8ExZGe29v\nXh4+nDhbW6zNzLDJzGTh1q0s3LIF68xM7JcsYWL//oTrPJEbdevG0MTEu0LBODNXTAwvZ2SQeuoU\nsS1a3BXgKhUeTk6kvvQSu400QLNZs7hRrZr2vogIqF4d1GoyZZndd+4YhL+Nj88TqcWcr9Gwu0ED\nPH/9lTOBgXfLZ546xTl7e9IWLwZzc62jWG6u1uxdWIhlQQELt2whavt2lht9T0qFgsmvvsqbkoS6\nXj3tWul8ATS6dTtJ+RzHDBpxfDyFPj7g4WEaVbBvH3JUFHnOzveknJUkiW1r12o96Utpv31oKNLA\ngYTk3E0cutnGBmnEiDKv46O20b59e0bpjm6uXLmCWq3mwIEDAJw9e5bs7Gy8vb0BCAgIYOrUqVSq\nVIkFCxbQq1cvLly4gEUpceKyLBMZGcmsWbPYvn07Hh4epY7D0dGR7Oxs3Nzc2LFjR5nG/rAIIS0Q\nPCH0TimSJPHJK68wMCmJQn9/w/WH9eQtNc2lj0+JJtPBo0YRe/68NptXYCAX9Rf27MHb2Rmv/Hw+\ne+MNJElibo8ejD13ziBwr+nGGZCaik1GBgu3bmXR1q2A1lpQ6eRJbkyceE/yEWnjRg42aYLm2jWk\n2FhknUld4eTEi127oty1iyQjD2MHWSaxcWPkwECD8DIJ1dK997hqMQ8eNYpNsbHk6TK35ckyyDL5\nKSnahC/t2sG+fcQePQrZ2VrvbqVSG18eHKyNiQaygN179hC7aRN/vfceSkki7eJFCgGr27exsrcn\n+9w5OHECCgq0MeIPyDh3P8JDQ6m+ejUpQ4YgTZyoXWf9hmj3bpg1i8uSxGXu/b0pFApG9OhB31I0\n2pDwcEbNm0dwbKzWqx/Y0rQpX+iOVsrCo7bh7u6Ovb09hw4dIjk5mZCQEI4cOUJycjL79++nXbt2\nhnv79u1r+PeoUaOYOXMmycnJNG3atMS2v/zySyIjI9m1axdubm73Hcft27fJyclh2rRp9OrVi4SE\nhMd21CKEtEDwFOjdrRtz16/nsJ/fQz+QS+NB1bJCO3ZkTVISmthYk1zStlu2sG/3boxr7Y7u2ZOf\nhgzhkJHgcDh4kNDXXyfu4kUT7dcmPp53nZ35Mj5eK2j0BSZUKuTXXiNVknilVSvO7N7N4RYtIC4O\nP3t7Vg8cyMdWViTpQpQs4+NZPGIEn0ZGcrpVK21bixebhoipVFgHBDy2WsyhHTvyU3Y2BZ6eJpsD\nae9e5E2boG1bOHIE5s7VOtrpEq0Yio20bn13rDt2UNC1Kxd0ghuAmBhyzMzutq2LDzc/dQqFSkVB\nQABWD1FrOquoiA6dO/PbDz9Qq3ZtTuq/gwMHtOflekr4vd1Uq9lbv36pbUuSRMiYMWzVacJblEq6\n1K6NNG1amccnASG1a7P14EFC1Gq22NjQRRdqV1aCgoLYuXMnp0+fJigoCEdHR3bt2kVMTAxBQUGG\n++bNm8fy5cu5cuUK+prPN27cKLXd+fPnM3ny5AcKaD02NjbMnj2bxYsXc+zYMYMGX9E8Nu9ugUBQ\nOpIkMTE8HKXOa7q8nrwPIjw01OAlXdI175MntUUgdIk3FPv383/jx6NQKEzGIEkSE8LDsTl40DDO\nr/r0wS4wUJs5y8iz2WzTJtZcuoTVH39o296wwcRbvOnJk/w6eDATe/bEevFirG7fZlzPnliYmeHY\nqhW+iYkgy3geP05SkyZc0VWQQpK05R91Zk3F/v3g7493YmK5q2OVZ/2aFRRoNXajOTY4dQqznBz4\n8su7mwY/P/jf/7T36V/v36/9TFwczhYWOMbGmnqB69dI//q338DPD4vTp2mu8xh3PXKE5CZNyDf2\npn8Al/Pz6RAcjKuFBSfffRfbzZvv9ldYiLXR92j8ezuXm8vU8+eZbZRStiRCwsPZ3LSpVgP28SF4\nzRptApdy/IWsWcNmHx+DFh1cDk0ctEL6r7/+Ys+ePbRv394gtHft2mUQ0nv27GHu3Ln8+uuv3L59\nm/T0dCpVqnTfs+CtW7cyc+ZM1q9fX+axFBUVodFosLGxKdccyoPQpAWCp0T74GBcf/6Zi2XILV1e\n7heOpNe0ByQlkRsbC/7+eCYklFqRqbj5vNfo0UiSxLF27fjGSFvODAkhE3C3tib1u+8wz8wka+FC\naNUKm4MHmdCzpyFZyyezZpHp6MjCrVuZu3kzJ06fpigjA774Aiwt2TB/PjmZmShOnkQTGKjN2vX3\n39CyJRabNqGuUoWxFVBx637VosaGh9Nn40bUOg1fGRuLT8eOZNvZcWn//rtCNyYGi5wcCnSlPykq\ngj//hMBA2LGDqnZ2IMuk66+rVNCwoVZ71r/29oavv6Zn27ak1amD7XffMXfAAJpXr87YM2cYUL06\nfvqEKfdh0KhRxOXlQWIidvPnk5+fr91QZGRgVaMGtmvWkOvjg80vv7CwZUsWbd1KZlERaWo17paW\njDS/v0jQa9OjhgwptwZcUW0EBQURERGBq6srbm5u2NnZ0a9fPzQaDc2bNwcgMzMTc3NznJ2dKSgo\nYPbs2WRkZNy33SZNmrB582ZCQkJQKpV07979nnu2bduGs7MzTZs2JTs7m0mTJtGgQQPqPUaveCGk\nBYKnhCozk3deeYXPSzFLPyoPio2dt349sWUoMVma+XzRlCms0GdTU6ng/ffxW7mS2GXLeHvkSL77\n73+xb9SI/OHDabpqlWETIkkSsyZMYFBysom5nP37YcsWTk6dCpKEUqWidm4uZxYu1HpNA3zzDUWN\nGxOUllYhWvT9wrwCO3XC7McfUcfFgb8/1Y8do89bb/FV797UfuklcvUZxFasQKpVC7Zt06ZSvXgR\nZXY26gULIDOTxPHjtQ3PmaMV3CoVVv7+yL/9Rr5R1rGqo0cTuXYtMhAUE8PRRo0IVirJ+PZb+uTk\noAZqWVqi4F4nw8GjRrE/J4dTFy9qTfFNmpAFd3OJL1hA3v792G3ZgtlXX2FlY8NeFxftBkhH6v79\n3NDFaN+PkPBwtmzaVG4NuKLa8PLywt7e3pC90sHBAU9PT6pVq2b4bXbp0oUuXbpQv359bG1tiYiI\noHbt2oY2jI909K8BvL29iYqKIjQ0lBUrVhASEmLS9+3btxk+fDiXL1/Gzs6O9u3bGzzNHxciBEsg\neEr858IFRtWowYcREY8tCcf9WBsVpY3dzc9n24YN9+2/tGxeo6dN44sjR6BlS2wUCkOGMX3GtF82\nbuSt//73njzkJuFCurNby6lTyf/0UzAz0+YHX76cjp98QmSPHhR9+632vsWL8be358CyZRWSHaqk\ncbgtXcqg6dOxMTfnt+hojq1bh1S5MisHDyY8NJTBo0bx55kzpFy5og01u3IFwsJMK1/t3w/LlkGt\nWjBlirbtAwe077dpQ+MTJ7BxciL+wgXD2q1o2JCe+rrZskzvjz5iX24uZGaSUlCAbG9v4tWuX+vb\najX9V6xgy+3bqH19tUL5/fe1znv6fOFA5S++4E6bNmji402v6+bttWgRlwMDyS1DxrGyZMQry9o/\n6d/8k+S5KLBx346FkBb8CzE2r57Ly8PdygqNRoOnUvlEYn2NMU63WRaBV9JDVaPR4OLjw/UvvqDF\nqlUlFr4wFu7G879++TJJvr5ojh/XCjqFQvtnbg6FhZjfvEk9X1/efOklpp89iyYwEGVcHIvq1+fd\n116rsHVYGxVFv6Qk8v38MI+L4203N95/7TW2pafTw9mZ6WPHsicuDtcWLVAoFHfH3arVXYH4+ecw\nfvxdZ7GJEyErC7N69SgCsLLCunlzHNet40atWkSEhTGjVy8cPD3JDwrCPi3NEP+t15JL0vL1Xu1m\nkZHYurtTJEmoNRrMJYmc3FxtnvA33rh7v1HlsCY2NhzbuZOi99/XrnNsrCElK3FxWEsSlQ4d4urq\n1eLZXAEIIS0QPIeUlAO6tDKCT4KK0GZ+3biRoSVoy8X7GDxqFHFpaSTm5t7VClNStDe1b28IWwK0\nwigpicYZGTjXqMH+7dspdHXFWqGgoZcXDmZmFZbIpHi1qNVff01MZiZ9ExOZVKcOClkmMyaGJVev\nar83vQe3kZbK9Onw8st3K1/t2wf6OO9Dh6BqVaS8PHxffJFL58/TwNMTD3NzKjs48KVSaaKF638P\nhqQxubkmpUQle3scsrK4o9HApEl3xxATg1lMDEUREUhz5iCPHYv08cfIc+ZgO3MmtlZW3MzLo8jB\nAaytkRo3xnLzZvJmzMD3xx/xHz+es7t3s/Wdd8SzuQIQQlogeIxURHalkijJvFpR9YOfFmUtbFFi\nWcSYGPjjD+pVrcppS0vTutagrW2tVmNuY0Ohu3uJwqwiNjdro6Lo/emn1G/cmKpVqnBdrcZCocBB\noaCumRkR06cT9sEHnNNncouNRVFUpD3T3bMHdu7UaqVTp2qLj7z66t1NR1zc3RCtYmPv8fLLuLz0\nEtcnTzb8HmouXcrgGTNQSBIn//qLdQcOoNEnPNFhHheHtGYN6nnz7obQTZtG47p1UQ0cSL25c7nm\n4E9CjkEAACAASURBVEALCwu2ZWVpU73qP68vAqJSoaxcGfNbtwym/KOZmbzo4CCezRWAENICwWNk\n89q1JWdG+vFHQsLDH6ntB1Wpeh4pi0Ze0gaFOXNoAPQYMIA527ejqV+/xKQlAYmJnLtwwUSYPWhz\ncz/P7eLatz4tZmzr1qVaOdZGRdEnKQm1nx/WKhU1Y2L4e/hwXGbP5qqrq1bw3b6tddZSqe6e92o0\nMGECfPZZiWP/NSqKQUa/h+UNG/KG7my6oKiI2v36cU2thmHDDJ/3X7mShq6urLSzM6mu1sLHR1vh\nrF8/Nm3ZwvcLFlDd15ebX3yhNXHLstY0b2cHAQEEJCbSxM7OUCYVxLO5ohBCWiCoIErSmjUaDScS\nE1l744YhM1JPZ2eaNGpkcn77MNq1sbByXbqUSytX8taYMWUWKM8zJtp0bCweO3eyZe1abhQWEvTW\nWxTIsokw4ptvsA4IYGXjxmhk2USYPWhzU96jBY1Go02LWYqV445aTZNBg0h56y1arFzJ6LAwhuoE\n4vvz53PDyUn7uWHDtJsLoxKc72Rn862tLfl+fveMwfj3UGvZMi6sXIkkSRRqNHx89izuR48ydvFi\nCoODKWzRAkVcHBpgZq9eTH79deQ5c1BMnEhrPz9OnT3LrZwcnPLzaeDnhwSk3bzJqbQ0iiZMwDI2\nFvWZM2jS0w3rGta16z2ezuLZ/OiI3N0CQQXRPjSU/775Jh5FRYbCDbclCUWNGmxUKHhFo2GLUolf\nixb47NhBSG6u4bObbWz4r5kZU4KCymwa14c0fTRkCME2Ngxp1QrbnBzMcnIosrcn0dWV6x9/fN80\noeXREp8kDxqXccy1Ijqaz8eNo56tLSdv3ODtV1/l26VL0ejiiaX9+5H9/bH99VcW6tJbmiUnw9Gj\nFKSm8r/Ll+8rpI37KktWN4VCwZiwMProKnwVT/ix/OpVJvbsycdLlmCj0fD11q3YZGay6M8/qVqz\nJjcvXUI2N9eGj2k0FEZFIQcGolm9mvjAQCx27ybf1xezTZv46sIForZvN+TN1oe4hYSGcjgrC287\nOyacO8c7bm7U9/Rk1caNJB06xJ2AABqc+H/2zjs6qnJ7/58zmZkkk04SWgIEQgs1SAoQQMBrQhMp\nFix0UIGrICiigDQRFKWIqKCAChaagrQQEAVSmBQ6KRBIAoT03jOZOb8/3kwJ5V6v5bvu9TfPWqww\nZ05955yz3733s599hVOff86jFy/i7uVF/kcfYRg5ktMW4eycyEhy8vLghRfQxMfT+sQJUmWZrsnJ\nZNfWcnv6dLrt2MHo1177n02z/P8Cq5G24v97hI0Zw7bWremdmspg40JZZl9mJl+oVDxWW8vRhx7i\nw1WrmDtqFKGpqWbd4caNeXbAABTvvfcfNQ2I27uXTiUljLx5kxEWilJ7FQrGjx79bw3K72nj+Edg\naXyTr1+nSpaREPrTHQMC/iUj2SY6mryEBAbMmgVAmU6H4t13aVxaStAjj/DezZvMv3GDD/v3Z1Rk\nJKd+/pm8Pn1oFhvLHZWKoWFh7HF1bbBPhVZLkYcHBllG8S+MzMDQUBLi46kLDPxNqm5jhg3Db88e\nLt7VKrJKrydPp2PFyJHEnzjB4LAw4dWPHk1O/bbKqCh8oqJIlWVUERHYyDK69etxdnQkslkzUY71\nySeUhYWRoFAwq/63mjRnDtd1OhyuXyclLo7hp08jAYF2drisXk2nuDj0L77I0sxMFm3axPJx42ik\nUjHQ1ZUlu3bh1qEDhpdfFichy6LJx8MPm8LbXRMTmTt9OlM2beKRkSNxsbFh5ebNf0ltvhV/PqxG\n2or/7yFJEhPffZfvn36asHrjIwMnZZlesswrSiXDX38dRZcuhK1cadYuVigYPGIEoUFBzHF3J7Sy\n0my8PT1Zo1aLxgk+PuDgYDrepDlzuJKTw/zSUn4xGHgMTNutadSIyn79TAZl8ty5D/RMOxQVce43\neol/FA8qByoBcs6fR6qu5kJZGXuTk6ksKgKL8+LHH0keOZIkC9KXIiqK4KZNOVhYSEZ1Nbd69cLb\nzo5XP/2UgU8+SeT69WhsbHAuLyc6L4+6yMgG++yRksKKGTMIfPFFHO3s7hkfZ1mmfMoUvLt1o0dE\nBHG/UdVNkiQWPvEEz3/6KfayzIBZs5AkiTu1tbgqlURJEm1UKp4YNowP7/LSfZKTGfbcc2z67DMG\nBgcT3qgR+rg4cps1g6NHRb10vUSqzYoVHMjM5ODPP5sZ7506kV1aKohdzZuTo1bz0+OPo1YoUEsS\nG4qLefKhhxg9dCj78vMZ6eGBs1rNy8uWsd5SvSwwULTLnDfPdB+NHjqU8IgIVEFBvO7jQ+qpUw8U\ng3Fzc7Ma7z8Bbn9CK1qwGmkrrABg8BNP8KWvL0frvelwIAwI79EDm5oakzKSsYvPCa2W2zY2tD12\njG+2bKHAYOAn4HHggEJBbFER4ydOxLdJE9HTV69HBmrc3Hi9Uyc2ajRs8vJi9s2bRNQf60cgrUMH\nwNzdSZble4yjbVwc5Q4O2EsS9hYtKf+qZhNw/9AxsbEi/yrLyHV1lBiNcGysubnGmTPoe/RAiowU\naluffy4IVhkZ/OLgwM8//ECdwcCxsjKuRUYiSRIzJ0wgcs0aUt9+GySJUkD97bcotFoMvXqZrrW7\nkxODBw1iVX0NtQlRUdhFRdHjs8/4+tNP2fsvmo3cD08MG8bKvXuZPGoUL127dt9ohTFEPeHsWSp7\n9sQuIYF/jhrFo6Gh3IyMZNmCBdx6+WUuTp8O8fFC0jQmRpDJoqMp0+uJy88HWSYlNxfZKMm6ebPQ\nKR88mLp6Nng1UB0Twws6He8vWkRxXR0L0tJ4rkkTvs7OZou3N847d1Jar16mDgykpSSRCricO0fj\nKVNMMrGL0tJQKhTolUrTBMQI4+SvsLCwwXj8lJ/PlfJy9i9bZipT+1+uRvhfg9VIW2EFZm/6s3pv\nOgIIVasZMmsWocnJSAYD2NgIEQ57e2okiaY6HWlJSUiAO/AJMAL43GBAV1pKHSAXFpry3EWShOzo\nyFdqNTf1egoGDaJmxw5O1tURCnzbujVDpk3jq7lzKevUiYGzZyODKQ+LTgfTpqE7dAh9587YKBQ4\nJCZS9YCWlH/2+FgaJRutFrlRIwz1L2p1VBS1xj7LAQHCa+zVSzR2WLIE51WrqEpIoNbfH/R6DJMm\nYVJSjomhOiLC1OO4tY0NPX18iDV+L8v463RkXrpEZnBwg2t95+mn+eLxx8m16ObF+fPIAwcyt1Mn\nk1b4kaNHf7OMqCRJfLZuHbdqaui6b98Dc9qmiUt8PIaCAn7w8+PHkyeR1WpmLliAa0UFqoQEdIGB\ncOIE3LolJirnz8PixSRKElJUFKrUVPRG7kJuLowaJcbNos2ktH8/33fpwqe9e1Pt6oqNJPG+QoHO\nYMCleXPKamqQ1q1DDgmhR3KyKbz90bhxXKqs5Hp1NYPc3PC2tQVg+COP/Nt0iSzLfJyZibtKxZs+\nPrT7Dyc7Vvw5sLK7rbCiHrIsM3bQIBqdPMnjssxRYI27O1JNDfObNsXW1RVJoyEjL48RSUmMstg2\nHDgH5AIeQE9gGzAJzHlu4IhGg+Lrr8lSKpmcnEzQV1+xOCmJfZLEqF27CBszBt+hQ8n6xz+ovrue\n2MbG/DkoCE18PNMrK9mcmPhAIZE/E3eLfsiyTOz48XT56isCBg7km9xcYZBiYuDGDcjPB09PbNq2\nZYyHB8eOHaNo2rR7ypF4+21YuhQUChPz+XplJQvT09EFBpqWfZ+Tw9GIiHuudeeBA4y9eNGknAUQ\nnJzcwNv7T0VbZFnmrbQ0eiYmmoyZfXw82+9ihu85eJBxa9eiCw1FHxxsWm4fH09rOzuIiyNx4kTa\nrl5Nhrc3uuxsUT8dFGQWRVEqRX14WRlUVop/Go1ghy9cCDExDExMROvvT6VeLw5gWaYWFUXHs2fJ\nSkqirF07OiiVBLVsiU1dnal2PaKwkMnJyZzw96e9RoPBYKD75MlcnjDhvkz2WoOBxenpDHd3J8TF\nxTQmv6Ue3op/DSu72worfickSaJVy5accnCgtLwc99atWarXI9vZcTs1lXEqFWE6HTIwGRiJOZcc\nDqwB5gBngDfrl+9EhLKN6611cqL62DFCXn8dj++/59JTT7F3+XIuODuTdPIkq06fxrtdOzIPHmyQ\ng1WHh1O7eLF4qdeHmDtfucL7W7ZQNGvWX9ay8e7xsWy0IcsykzdtYsm4cYweOpSkKVPQBgTgcPQo\nFYsWoXjhBQybN+O1bRtvfvopTzZuzKTNm9E1bkyNZZ9jvR6+/lq0u8zJYdH16zjo9TxUV4e2Ppc8\n4tVXuXzzJs7nzjF66NAGRLb06mpsLl9GXx/uvV+f6f/UqEiShFqSeGzIELrWh/ndzp2j6dSpDdYb\nM2wYh8PDuZKSQmxQkOn3qj5wANsuXagxGFCsXElufj6G4mIR6q+tFRtHRUFREYSGis+WhjcmBnbv\nFprmhw5x7ORJQqZNQ/v880Jz26K3thQZSfK8ecLof/op6UFBLK8vrbLkNNRUVtJblnFQKHCRZfo8\n8ggp8fFiImSRLinQ6ViclsacFi1oY2/fYEysBvr/HlZP2gorLBC+Zw/y+PEMqS+zmg9USBI59S9X\n4ysrFZiHyEEfBDYCQUABkAG0BlyBkwiDPRj4QaFgXEAAnr6+NHV352p6OsoLFwjIyaGNszNXnJ2R\nnZyQgSSlkrwxY6B3b+zj45lRWcknFy+i9/CgduxYVHFxONjYMGboUAKdnBjh4UEzW9vfVJr1R8q3\nLL0poIFntefgQSbv2MELnTqxOTGRh1u14uf0dL4eP55T7duzzMeHuXPmMG7JEv4xahR6Ly+4fRs8\nPKDeW0OWUdy5w67Zs0WTiXoVMEc3N4rr6ii5eJEqV1ek2lpK68cLWRYKZfb20LfvPV7078GkOXM4\nV12NQZLQl5aSnJNDx8aNyU1NpUmPHrir1dQYDJTq9ZTrdEjZ2WT172+KJKgyMtCNHWvan/rbbzHI\nMnVxceDmBi1bws2bYGcn5EMTEmDDBvOkbMkSatu2hbw85gYEUFBcTGxuLolVVcLT7tsXQkKwiY6m\ndWQkqS4uwhuXZZMOOLKMlJVFXK9eDQl/UVG0SUjA4OFB6fXrFC5caPKir1ZVsTEzk+WtW+Pyb9pW\nWvH7YPWkrbDiD8BIDBus1SIBDwM6WWaE0ftBeM0A3yNy0McBBdCbu0LbwC+IXHUYcNpgoGN+Po41\nNUhAN1nGJj+fNjodjvn5/JKfD8AeW1smzJ+PJjycyl69aFyfw3TZv5/ywkJqZRm78HD8OnXi+1df\n5dvCQlb16IFelqnOyqKgV68GRCpjrtFonPOLikiqrLynq9JvKd+625uy/L8x9/v+woUUzZrF5ytX\n0jg4mJWHD2N39Chdqqvxtbdn7IQJ6PPyxLEHD27YPUqrpU1eniky0G/rVrQ9eggjYyRV9enTcJuo\nKOjUCaetW5Ht7Xl9/Pg/7O0NGzSIXXflbG/ExRHcrBknPT0beL2KqCja5OcjHz4MAQG4HTtGu1at\niJVlk9F1upZMjb6GcldX4TlbSISi1cL58yiiozGEhKBJSGBMv37sSE7GMTkZp3Xr6Hb5MruuXQNL\n7fA+fdAcOYKqZUsoLBSTFGdnypo04VReHrY9ejC4e3fcf/mFSkvC3/nz3Hj5ZXj3XbydnCheuZKy\nJk3w/+c/KdbpGODggMvatX9o/Kz482D1pK2w4i5YSoIesbdnl7c3W69dM4Ws5wAfAs+0aoXbrVuM\nNBjY2rQpupwcfrAo4RoN6FxcuKVSEVBZyYERI/j6+++pUSh43KI2+gdAgzDwMtDbz4+LkyYxo6rK\nlG8ePXQoy3buZNmJExiKikS4MygIxYoVGJRKaNJE7EyWBZNYp4POnYVXlpWFd+vWqLKySO/fn5qA\nAPPFPiCH+3thzP1atqp8PjlZeJhGnD4Nx45BSQm4ugq9awuZUMdHHiF2+nT8HBzMKmBVVVBTI7Yv\nKxOa3iBCx8XF2A8axFcdOxIeEfGnhGTvJ2HaYds2Ij//nOHTpzeUNjXmlYuKQK1Gk5ODj7c3ST17\nIl++jFRdTXODnszKfHBoLM7f0xNefFFsv2gRap0OW0dHyhYuRLVsGR06dOCmVkthfDy5dXWsv32b\nPUuWcL2uTnjMOTmgVuNVU8MdBwdkOzt44QVx8vW/qfeFC6R+/TUHjhwxk8SiokQDkMaNUaakoB8x\nAvmuCd3fQab2vxlWWVArrPiDkGWZOb17s0arZU5wMKFz56KYOJGwykoOAipAZ2OD8oUX2HL6NM2v\nX2fI4sVs++EHJiUkMFiv56CtLW/rdKz4/nt+3biR44WFlHbvjpubG5oNG+iP8L5l4LJCQVODAScg\nSKlk3MKFdM3IIPqLL5g2a5bJ6MiyTK/Jk4ktKxO5TbUaVUoKuscea+hZnj4N6ekwbpxpkSY+nqU+\nPmzct4/0KVPuK7v5V7yYZVkmePJk4saPNx/zvfdM4Vri4sSKQUEQE0OjX36h48qVRJeVofr8czq6\nuFCelUWaqyv4+d2r652UBB07EpySQsyWLcBvyz//lpD/3RrrQVothmbNyM/MFK0qjc016hnTyLIo\ntzJ2x3r/fdHdy9gO0oiYGDGRGj8eW62Wmk8/RT19OrWSZK5zPnYMj0aN6Ny0qWmzjLw80q9fhzFj\nxDrGTlzR0eJ+sCSjde+Od3w8iiZNyDt/nipJEmS9t94CZ2exw4ICYfBXrPjbNHv5X4A13G2FFX8Q\nkiQR9tprzJk8mcGvv07o6NHM+fBDQrVatjg4sLeigjkBAazduJFQWWbutGmE/fOfhN6+zdyaGsIu\nXOC4vz/9/PwY/MQTVNjbk71iBf9s3Jj2K1fiu3s3r2dnYzKJBoPJm/7W1xdFYiKvjx+PQqFo4BVK\nksTrY8YwPjmZKoMB9Hp0EyeaQp/GF60yPJw6o0Gs/1t36BCftG+Pobwc3nkHvL1F72FJQvnzz3x0\n65ZJpvLPHst5Y8YwLiGB6oAAEdIdOFB0jQoJEcZm40YIDERx+DCb3niDMQ89RIFOx8OXL3OpshKe\nfFKsExvbgDBFbCxOubnIlZUPDHE/yBhLWVnE35WrvbsEybI2XHPkCDlNm5KcmYns6CjEQlJSxDmN\nGweXLkF2tvCoV60SO8jPh9OnsSsuptri9+HQIVDqRZQjIgJnPz+qf/mF2saNxf6KilCWl5M/cCAn\n7/Jy2xYVkWoch/rJgOrEz+geGSRWiowU3504we033hDH9PWF5GRxn4waJYx5bCxcu0aTK1coqy+r\n+6tr7a34fbAaaSusuA/Cxozh6JEjhI4e3cBoV7dowcyUFGrKylg6cCAATrW1vBkQAN26UVxby0xJ\norqkhBY3brBkwACq27RBGRBAwEMPIe3ezbgXXmDdO+9wymDArv545yUJjSxTnptLo+hoPmralA0R\nEQ28O4Ms4zdgAE137iStrk70Yk5OhvJy4U2FhMDp09QplZCVZV4WGUlt69akPfOMMBLLlolQeL1X\nWgbE/8mSopbGMSk1leqiIujZE3nfPiGPKcsi9Nq3r8gzb9iAu0bD/uPH2RARgSRJeAAOKSlUXLki\nQuM6nfmazpyB7Gy+eOMNjkZEPJDd/iD51K9CQ/+trrclm33Cww/zqYMD8l0ELPXFi9R++y20aydC\n9xYEOPR6KCujun17FGdiMPTuA5Gn4XYGNG4Ka9ZQ1qoVZePHm/epVkObNkLI5JNPRO66/vyq9uzm\ntqyDMnvTOEjRUbStLSE5Yidy7xA4vhPcWkB+hnmfAQGwd68Y98BAsxBNaSkdmjWj5soVtP8HtfZW\n/D5YjbQVVtwHkiSx5osvTF6F0Wi/HBbGtmefZVdiokmkJFypRNqyBVmjoXrvHk7KMhuTk5GSk/nR\nRsFKKY9OXYKQnnsOduzgww4d8HJxoV9REcEIUhn14a895eVMmD2bm/37A0JdrLmnJ4vS0pAAP42G\n10aNYu7GjVSHhgojZ0Ek4sABFK6uGCZPhn37xLILF8SJGj3rsDDYskVIltYbAJucHD66efNP86bv\nMY6xsbBhA3KPHvDss8Lj27sXQkKwvXYN15oabHv0YEdyMlL//g3ypMTEiEnFwYMil92nDxw6hEdt\nLbF+fnw4ePADvb8HNdkYOns227Kzsav38FVxcXQeMIA8nY7GarVpkoEkoSkrI66gAJvoaBHONuaS\nDxxg+7JlTHjtNaplWRhpI0pLxSTq449RvPUqNilnMfTqjeL4MQyTp0K//iI6UFraIOJBURG2hw9T\n07u3ueVlvecrjx5Dta4afvoWon4S43D0e5a+9jZvrVtO6kerwScVrqfh69iGrHoPWRkfz4COHTne\nvr04TmysYJjfucPL9fryVpGS/15Yc9JWWPEbYbxfX+3Vi7WxsWYiWWAga7RaACZ07MCXV6+Z8s29\nveDiP+zZPmY7B3+J4kZdHZq9e3EtLiarshJ/YC3mOup+jRoRtXu3qTmCZvlyenTpgtJClKONUolU\nW0vErVtkzp4tXrxarfBMPT1pdOsWhfPnC4/Zw8Ocq6zPjdrHxeH+3XfcfvLJBixjRVQUHc+dw9PL\n6w931LqHeGUwwMsvm8uMVq2iG3DR1lZMNOrD2PZxcShPnqRs7tyGYideXiKcXFkJzZrBhQv0HT6c\nzHPnyHZyQqFQmMYIROOPIcHBbFuzhhW7drEkI0M02YiP56N27Ujw82NBy5b4DxtG/sKFOL3zDn5+\nfuTX1VFrMOCck0N6//4N5Vi1Wupu3ED/zDOg1eJ2/DgFERHMXbqUtUqluA4jTp+G48dBqURqpUN2\n1EG6O5RmQXYFGIVPysrENTo7I2VmopRlAv39ifbwEIpjq1bB/PliEjZ9Osp3llDX9zRk2ELpINoW\n3+bqiQsEjgglISUZ/BpBtQI/Dz/Ss7KpWrSIoO3bif78c1wGDaJiyRIxOcjOxtfJiWuHDwNYRUr+\nD2HNSVthxV8E4wts8Ouvm5tsaDQMfuMN03fPvLOC/c+MZZTewH4F+DtAh9u+jB4+GlmyZUJKCrzw\nAt+uWIEa+BI4DAwDDtna0nfqVOLOnqX27FmoqqLSzo6o0noBTVnGJiuLKzk5lDVrhmxsxtC3rwgF\nJyXRzNERLwcHij7+GLlRI8jLEx5zaakgK/XpgyEujtDt2/l2xgyqLaQnDefPk1jfy/mPdNQyeqFl\nJSVIMTHCK46OFk1GFArQarEtKMC/b18SDx+mztVVCHc0akRVbS12CgXSxx+L3O+dOzTv3p07V64g\nPfqo2NecOfDww0RlZeHl6Um1QiHKyXQ6wXCOjaXq+nV69O3La6mpxP3yC/ZpaZRdvgw5Obx99Sqt\njx9noUrF+P79WbNhA2VhYUKMBBEOn/Xoo6zbt69B6ZL68I+oZJlyeSzs24eiRQsGzp6NQZZFW82Q\nEPPEIjoahgxB8d3XKPUl1DrUwZ1UePJlSLsFbdrcU4blm5dHvzZt+GL1apoN/we5vXpBUTZ89JFY\nNzqSnj42nM1QoWtdg82+KN5d+gWfxX9Gh/6tSAjuC30fBiAJUH77LfYbNzJv0iRsbGx4cdAg1qxb\nB6WlSNXVrJo//76ldFb8d8HqSVthxX8IWZaZ4+XFmqws5gQHsyYmpoH85ISOHfjq6jV6e0HiIDuO\ne75AEErkRx6h9+7dQlbzn/8kOimJOfX7XAu8GhxMUa9e/HjpEmWhofeygrVaXH/+GbuqKrIHDxbh\nTiPD9/33wdMTxwsXqPHwQOfs3DA/evs2cx5+mM8TE1n21FPsjIjg7MWL1A4bJo6xfLnwdlUqaNYM\np5wcerRv/7u8aRMr+qGHzOf33nsir/zuu/D++3wzYwZqSeLZK1fQBQebyoYasLe1Wmx27eKx3r05\nFhVFVVUVhuBg4X2CYCnX13nTvbswkPVENPu0NLwCAmhmZ8fFxERKHB3F+vWGXBEVRf/z5/l5506a\nPvQQeWvWmKIXRobz3kOHeC7xCrVBwRBzEpJXiuMWDQKPpmCRS5a2f4Xc2ldMmKKiBIHswAHoeB2b\n6jz055zAtyWUOkKLNmLC1Lq1yEEDpKfTqWVLPNzcqCm+Rnl+FVeqFaAxQH4VdOiI7e1bjO3WneTb\nMWg7a/E/70//F/vzXLfnuJp/lbcWfcOtV+eZJgpBX39NZ0dHttQbYIPBgKu/P2Xt2uGhUnHxyy9p\nZmeHFf+3sJZgWWFFPf6Istb9MH/SJGxv3EAqKiKjqAj7rCyq2renSXAwq+obJMiyzLTlzyIt28m3\no2VannHjydZdUQAUFXE1JQWdwUCiWs2Kqioel2WWA5mArlMn7BUKEvPzuWJrC3V1+Lm7i/OXZbh1\nC7/mzSls2pRdSiW88YbIWcbGinIaW1sYOFAY27vFMjZuRNG2LQa9HoWNDbIsIysUcP06bNsmQuN3\niWw8qGb2341rg1C38fzS0lA5O4vStawsZu/fz/gmTXj0xRfJmTZN7GTOHOjWzeyNpqejAjQlJZQ8\n+aQoK7vbAzUa959/FmHhuDgUqalMb96cbU5O9yhtGWuEiYvD3tsbpUpFWUUFNGoETk7YZGWxc9Ys\nxgwb1vA6PlwAATEgg/23Hrh07U72ywtMXb0cs7MpNzLnFy0CWzUUZ8K8sbSPTaMoNYO8PmEQXJ9r\n/+YbMQm7q6xMFRvDfA/o2rgrT184jxxiDqGrz8TQJ/YUOWUZJJckQx2EdAlBISkoKCtg8eRVPHvx\nInV9+qCMjeXDtm15edSoBr/TzO3b+fLAATaPH09shw5Mb96cjhZtVK3462ENd1thRT0exOz9T8O4\nRuNcmZ9PZVISjWSZFsAJYEF6OorlywGo1dey8MRCpk99jeWnclBkx9GkdxtCDsYTVllp2t9zwKC6\nOvYgmnIkIx5E78RE3gP2KBRMCAyEtm15Zdcuxuh0pm1/KCtjq48PTcrKyDHW1B46JJjEQ4YICWWb\nOgAAIABJREFUJu9bbzXooMSJE9CiBYZHH4XevTHJqMTECJWqOXNEz+vDhwVbvH67yjNneMPDgzHD\nhjUwzHmFhUKxzNHR5JlajuvkuXMpLS4WIeB6MhtKJbr6iYeiWTO2vvIKH7i64h8SQo6Rsd20KXTs\n2MAI62JiKLGxEcb+pZeE8InltcXFCRUuY0ogNhaX9HR230qnuqS0YV/r/ftFjXFwMHTuTBXc47nb\nJyayPjycDRERAJSVlKBYtw5DXgloWmCbmMvW1RtQKh15LiGB2rw8GDCA8kmTxIThk0+E4dWegake\nSBo/rj42UBx//usQVM/WHjsW5s4VUQGLsjLNoYMs/TUSgC47d3CpjzmE3iThFB4BjkQmX0NOlaEl\nRMZdBo9WqJUOTN2wGmqAlBRck5Ko3r2brdnZTG7a1GSo/QcN4rGYGJ4dNoynZZkl6ekMbtSIvpak\nNyv+q2A10lb8bfEgZu/dZSYmD/kuz7CmTRtWbdvGgGHDTApkRoQjZEAjunVjzejRlFSXsPDEQub2\nmYuPqw8/RBxn2j+nETo9lF1XlxF6PtFEDrupVDKuru4eCVEj2Wxt8+ZUjhwJQUGsPnCA0Tqdadv3\nNRq0VVVIKpVgO587J5S4amrEy/7MGejatQEruGl1NbdOnsS2b18MlgZu/354/HGIiBDG/W6pzatX\nsasX6rjfhAet9r7jOmzQIHYmJyOfOSNC8goFjB5tIkvVAoUxMcxu1YoWfftyc+ZMCvv0EZ2f7mrR\nyOHDgjSm1wvCU12duQwrOlpcc2wslJdjs3YtyooKinr0QNWunZiMGMfhzBnR19v42aI+23SsAz/h\noiwnqllTDH1CjDcCNkuX4lhWRfnZrkh5RXz6SwwAtikp1Mqy+B369DGfS2KiCK2fUBJguwHt95H8\nWlzMoG49zH22ExLEmF+9ClGR0LcfREXiZOfAwNmzSb6WTPmdDGHse/VGER2Jsugm2sgynKudKexT\nKG4YnyroOJra3v0xCddGRTHR15d5rVoRVVLC3OvXyf74YzINBu7odHiqVKINan30I/7VV3n7rbfQ\nK5V/WtTJij8PViNtxd8WkiQxY+RIEuLjBbP3AWIN9zXCGg3S8OGwdSthaWnMcXMjtLLSZCyPAqH2\n9gx+/XXulN3h3dPvsmzgMtw17iaj7w38OPgQN0vy+AnRjONHhQK1iwsfFxQ06I61GegKfClJBDVp\ngv7oUbTBwaS5uHCotJThwF6Viktz50L//sggPOHwcOFFGgyCCVxaKuqOU1NFCPjmTXTdutH84YdR\nlpdTa9l9qqwMdu2CDh2EwbYU3Dh/HgYPpjwujsVpacidOuH23XcNNaB//RXmzWswrpPmzOG6Tocy\nMVGEzzdsEDXbx44J41W/rSIjg29raxkaH8/ySZOYuW6dMLzXrjUwwk3s7ckpLhYG3M5OqGMtXizO\n9dgxU3MOhWMm/SUffPz8qLKx4fuICHGsigphPPfvF0b65k0R8u7XT5QhabXQq5cQWblzk8yujeDY\nIUi5Km6E2lp6tm5N34dDWKO2ozqkH6fq7xFbrRbbiAh0ubkYjOfs7y/6RtvbwbVcLnl50nT4EFRe\nLWljqOLGDz+ISYgxMjBzGhzbCSF94cJFbs9/k9uShLRiBXKzpnD0ACQlY7h5jTS1mgGansx86Tme\n++E5alNqIbQGft0FvfqZxtbz55957/hxAEJcXOis0TC+a1e0RUXUBASQWn/+xujHmBYtyAgJ4ZOs\nLGotJGP/CHnQij8P1py0FX9b3K6u5t2MDLSrVnF2/Hi6ffUV57dtu8dIW8qAmsqqvL1Zs349Uo8e\n4OND+N69JkO+X6HA1mDgaHAwU/Z/wdbzW1kxaAX2KtEj6/mBA3E7eRJ3WeYGwhCXA20R3bNaqdVE\n6HS8J8sMQ3jlEmAAlru4MGT4cKb8+CPu1dW85OxMTnExhxAMcJW9PSgUpKnVZDs7k6fRwMcfi/pd\nvf7++dqgIJEDbd0ajhwR+ee330YaPBg5JkbkpVu2FIbQxcUcOr5yhfYBAdi6ulJcV0dVcTGFRUUY\nPDyguhplURF1LVs2IJl16dOHN9PS0MmyORx99aoI795V+6xOT+fbESMYPXQog0aNIjokhNqePUWu\n/f33zaQzSRKe/a+/Cs3unBxBcMvMFNdcVUFg10ac2X2GDv37kynLVA0dau4vHRcHjo4iDF1VJdTC\nFi+mw9atuKhUxI4bh9OiBYKs139Aw/FLSsKvtBQPLy9iEuKpe6ehhGYnjQYXd3fWnTljLpWaMUOI\nlqTfgHETzftbvgxqq8FWYya9Fd+C8nRo2guqqkXUAFDfukWtwSB4BoWFok68pBj7snI8KivRP9yJ\nO1520KQbXNSCpjX07iuEWvz8eOIuHoHBYKD9hAlcnzz5vhKgsizTeeJEkiZOtEqE/sWw5qStsAI4\nX1bG9pwc1rRty8ExY5i8aRO+YWGcLS+np5NTg3UlSSJs2jQiEhIIq6sTZVXr1iGNHm0WtQBklYpQ\n4ANbNe2rq9HaZPPjC8MZ0GIA9mHmvrvPzZiB7tQpRlg8iM8BNwAvQFdbi5ebG1uKijiFCP9+iGh1\n6Vpdzcnz57kjyzjb2OBYXEwWoqnHLCCsqopw4ExVFau7dxddpBQKETqdP79hqDg21tR7WnXtGrqr\nV4XXvHYt1NZi8913GDw9MWg0wrO0rPONiYHqaq4aSV0gDOUPP4jj9etHXX14vAw4FRWFS7NmNA4J\nofuhQ8SPGyf6Hs+YAa+8IjxZC/UsEhJQFxby0dGjbIiIQO/tjXN4OPkBAUJBbc0acU7G9X/4Abp3\ng45+YJRC/fBD4RXvWoNDXQtyKnLw6upOaotgkQawDEGnpcG4cUhvv408fDiqjeux9c3mcmQWrEjH\n4KCE4xFwPU1ca20t6HTYlpWS+o9HSQoMFFKq9eFymzPRDO7XnsUT30CWZda3a4e8YoUwvl9+CWnX\nxX42bTKLn1QWw4iR0Lu/+d6LPIV89V2cos5T/chQdG3bQlCQOXQdEwM2NqbceVVMDFWHDuHwUBDq\nS3E0O/k1GZ2icDgcREWvELomJjLmPqphCoWCVU8/zYQHSIBKksSyJ59k/NmzVFklQv+rYDXSVvzt\nEF5QQEJ5Oat9fVFIkqmF4ucTJrD85k2qDQZCjOVJADU1hCUkMMffn9D4eI527cqa0aOBhrlYjbs7\nU99/n7OPD+NC3F7KHs1Ak6HhsbDHGhx/8BNPMNnXl8csOmfVAeMQrS0BKCpiL/AdMA34wdaWTGdn\nFhUU8PiVK6Z9HbG1ZbONDXJlJaH1+woHYlxccFQqqdTrxYpaLQ/5+nIlIUF0uYqMFF5xvcKUbuhQ\n0YyiVSs4ehR8fKjr1El4l+fOidCxZZ3vvn0iTL1tm3nZnTvQpYswYKdPNwiPN9Zq8VuzhrcXLCAv\nN1cYl8BAEe52chLer7Gm+8wZcHGhPCiIU0bi1unT8PMxWPOhyF2npZlU2DhzBkXuHQxpBigta6Bb\nzf594N0Yl0AXdl3ZxY5VG+n4+PNUDBlizj936yY80ugoVLoqak+cQJ+exrXy1ugNwMMDqOhnNpzE\nxkJyEty5g6aLL0U7tsPly+K79HQIDES//yeWlRTyztY9KAwKFE090Ts6ipD8pEli3ZgYcR2AFBWJ\nJv8WFb9+3yA07ZtwluwCFVvWrOWDfYeJvVuf/MABwRgH0+cnX3oJjVsKRfkGBj8/iylrLvLCI6Fs\ntlANexADX3PmDJUPkAC15HB0vHLFKhH6XwKrkbbib4VtWVkYgAWtWpmWWfZArly6lC+SkthlY4Ob\nSgWyjJyWRk1wMGFvvGFqqmHZI9n44qrs35/dWi2VGTfArzOcV2BT4cxHx05y8Jcotq1ZY3o5VrVt\ny/5r1xgJ7Ae6INjgj2HOQ38BpCkUPGowMESh4NGSEjYrFIwwGEzrRPj7M23OHGrHjkWSZcIBV0ni\nqpcXn8+axcQPPqCid29UR45g6+eH+sgRahISRCjY2PmookI0WUhIEHnoGTNEmPj8eXPTCkdHs1GL\njgZ3d9FOsX37hoSyyEhBlMrLMxvdqCgaqVTsWr0aKS+PmgEDxH6nT4evvhINKGRZCJZcuSK2ra0R\nJLDERPHdqVPCc75wQYR9W7YUpLGgIPhxL4HrV5O59VNu52ZBTDT0CYHTp6CkGBq14ZcYHb/GRPA2\nEVTcvCmu79w5cW0//QSdOmF3NgHDuPEQHIxBlkVnKK1WpAD69msYgbiTDGU3KPI8hcLRE4ORdW5k\ncHfqiCxJ6MdNRG8cm7s7YiUkiL+yDMd2MWXsRDbknEfWRkOvEGxjtaycOo0jh9x5YsQTSDb2PLt2\nrZhUBQejSUigsqBApDLqyW9NgLceH8S+lFJWbxTGO/xoOO+/vZSiWbNMGuYPqmyY7uHRwJhbwqhV\nPmnTJtqEhVm96P8SWHPSVvwtYJBlVt28ib+jI0Pd3R+4nmWvaNMyOzukHTtEt6upUxtodsuyzLJd\nu1hx86boiRx5WoQyLXKNiqjTdIzcT0F+BaWO7lS5eoKzM31+/JHIsjIesbWlpVpFXVk5LoAnkAdk\nOzriVF5OBjAfoeG9RKEgQJYZLsuCvPb114SOHs2rvXuzVqvlVeB648Z4PPEEWz/+mNeWLWPN2bO8\n1rMnLh07svj4cQzXrt1T80xMDKpvvkFnrF0uLxc11amp0LatuWXkzJlChlOjEVrUN26I/LDRgH3y\niQitJycLg/vee6IsyscHqbwcP3t7bicnU/rkk8K4BASIvz170nj/fopsbdE9+ui9rRu3bxdhbKMX\nCSKPnpuLbWIMr216ia2ZTmTt+hUKMmDFBnjrZWjfs0GzEEBMDFJSBHM9MtKkyNY//zapeWXcmTrV\nfD0bN6LOz6V26HAIChLh5/BwKDkLo2tAgsBLgSQWaKhYvFjsf+NGyL4NSgW0aieW1dbC7esQNkIc\nzximTrkC+Xl4K6oZ+d5n7Fo0ltziapi/EY933sGvUyckhQIJqJVlLiQno9HryV+4kFZbtuDh7k5C\nQoIQm1mwgF1vvkmJVw6DWg+ijVsb0z1q2cPbuOzuftjB27ff0/70bsiyTPvgYPT+/jS2tcVOoTAt\ntzK9/xz814iZhIeHM3v2bPR6PVOnTuWNN95oeGCrkbbid+B+YTy9LHNJq8U3IAAnpTk4dL8Xy/1I\nYmFNmlDz1FMN7snWSiUj33yTUyUlDHBxYfFrr3J+4hS8P99MdlEBdfPeNL38pKWvIA+4DGm20PEt\nU85R8+uvPLN8ORXe3owHtt68yfOSxOMW9/0+RMjbB7AFkm1t0et07DEYeNLJCd/Ro3nvyy8J37OH\nQ+PHkyvLTNq+nbD6fKHBYKBjUBDJsbFIkkTQ5MnE17egpF7iE1mGBQtgxAjxOT5ehKB9fODiRXEi\ngYHmjloODtCpE+zZIwygb72SlpGIFhsrGMyFhaLcq1cvs5GMihJ128OGCU/dGGo+cIBFM2ey78gR\nEq9eRf/uuxbn9jo0LYUqX5g3D6ZNM3fKkmUkhQIZGcWtW/SePI7ka0kUnE0EBxWS0gG5oFDki8UP\nLJjuhQXQ3EuE6D/4AOmt+TgpdKibNqYAB2RnZ0GQq6oEXR1tmzUjdfJknBa9SVnGRWhXBQ+DIkVB\nh/wOSDUuJIYON5d+KZXma46NheQrcPEgKNvCylXw5psiCnErFXJymPnBOjYMGc5TK5/i4N6fkVoP\nZEa37nzq4HCPt9srN5fI9HT89Xpsmzfn9P794O+PIj2dvgMGUJx7gQvfn/y3z8rOAwcYl5KCLiCg\ngTCNpTG/H3YfOMDEq1fvOS/j9vd7BpOvJUPeTTp2btLgWWvjLCYSN0rvLXFs49yGbRu2/dvr+Lvh\nv8JI6/V6OnTowPHjx/Hy8iIwMJDvvvsOPws6v9VIW/F7YJKctHiBKGNjmVRRwTfOzg98sVjC0pve\nr1Yz4emnKZk82fS9FBOFW+YNWmh0uOTepKSqmKLsKoqa9WDbuHFEx8WwRm2H5+koOqekYFNVQZ2L\nMDhyfjVJQX3Qv/QSEw8f5tw33zB/xQoefeUV+jZpQqPiYn6yqHserlQypa4ODSJvPRyRcz4KuCkU\nHBo8GDtfX1rb2OBaUgLA2rsYtwaDAUW9x7Pn4MEG/abp3RuiorDdv5+aVasEmWv6dGG0vbyEVGdx\nMTRpgrKggDovL6TMTORWrVDm5lKnUoka7MWLzV709XpSVEaGyLl+9plJUpMFC4RnnpUlmNgZGcKj\nvHOHro/3wiU7nbRrt8gcPgl6izaanDoABjVU1IkJQlGRqKu+K8ze6Ngxuvj7c6sgn7TUVGjaTHj8\n/v5iHUtv+tRJ+GKLyKlHR6KK/pBXgmfxiaMzVQGB5vWioujv4cHLXl5M3rGDaR3bsm7PSgyOBhgs\nfgj7DvZ8NeorZq7/lLxFi5AWvIX8zgrzNW/ciKq0EF3hJXB/SEwSnJwEiaykGJtLCfTp0xqFQsGN\nwhvUXq8FpQZHjTu5Lu6UNWnSQGXNvbYWVV0dbi1akBIQIKRQX3lF5Pejo1H+tAuHRo2QZZnGZZVc\ni4675zk5U1LCmzdukLV2LSmTJv1HTO37eeEBX3+NdssWFArFfZ9BW+0Z5JOrqA0uMS3TpGv4evTX\nQip33wQqW1Xe892Yx8bc9xwmvTzpb2vY/yvY3bGxsbRt2xYfHx8Axo4dy/79+xsYaSus+D24n0CJ\nf1ISn23ZwsWpU/+tcAmItpNzPviAUK2WX1xdaVlTwyXZol3g8R8p7JdAoQS0BvUNNTvm7CD8+ClG\nDx3KqCFD2P6PQVT0H8Arx48zqq4OssW+f1BA+O1buB88yJeNG1Pbpw829fm/hRs3cnbsWA4gCGRH\ngRCDgeU2Njym13NFkoiTZc4ALsA1wP72bRTJyWg0GmwDAli1des9L1qjgW4wPs8/j8PSpVT06oXn\nzz/z8cKFjD97lprAQPj4YzQGA5VGtbLHHoPdu6nz8oLaWmS1Gi5cQHZ3F2FchUKwraurRZ5YpRIH\nq6kRHalWrhTG+Z13xBiWlZlKiWjVSnjdTVzJ/nQvbpJEW6Dt5ffBzg65upokIK9HJxg+TNQLG8Pq\nlnXb+/ZRNGoUp+7Oj6vV9xcmuXhJeLIKBRzaiW2dzPaIzdTUNYaeAeb1jh1FGzaA0qsncUiOI059\nB42dhvLKcvED+YLzbWe6h3Sn0/ZGnF6/HgwG5A0bBDGvuBiSk2nUypGcNr2gey8xudi8uT4SAC6+\nHYnMLUC2NUB5GTQBSdUclX1zyhU25nPR6SA0lAKVCgIDyQak998XEy1j97ALF6h7bz0ln38OlRU4\n27syYNYsQBgxb4UClxkzuFBeznedOhH71FP/cRtKY27ayARXx8fTacAAlt+8KeRk71Mz759yFVnT\ngVg51kS66FreldHDBQHzg+0foJW19/3ufhj26LD7GvZXQl/5Tdfwd8JfYqQzMzNp0aKF6bO3tzfa\n+lZ+VljxR3D3C0QVF0fr/v1ZmpFBi759ORsfjy4wEHV8PFMff9z0Yro7RFfZqBEvqlQUd+/ODxUV\n9IqOpiAkBE1CAs0NtSbBB899EHzblsvpH+MNLB04EFmWGahScTgpiR99fRmZkmIWJZEUqHNySdu7\nl+CSEjR2dnzu48P8ujqau7mRqVCQZzDwGMJjvu7pyRPPPkuXtWtZVj+7Dgf0wDCDwRSOPqLRoFiy\n5N++aI3jM3HTJnoFBxO7aROfzJ3LmKFDWTNlCtrnn8d++3Y+XraMmdevU+XpKQzvc8+ZQ+FLlkBc\nHPq6OmEoZVksk2WR67Yo1VKdOYNu505zmFlTXwNsRFmZIIh5+VDh7dtQ5rS0lD0qFROefhomT643\nzPUM8+JiWL9etKY0GMDREflYhGCdd+okJg/XU8HJWeTGy8tFtyhjnXdZGeRmwLrV0OEG5W1qKKcc\nIkvgTBT07gtRp6H0JjURBzjv6Q7tWpJdWoTk3g5upwHF2KR40Kj9QEJfm4e+uhJDabUIZxt/h6go\nyE6mxOsqA3KdSIuLI6NPnwbefaFxLGJOmpp0SO1Hc9tCl9uYSrDZswd9x44mQp1UWChq2fv0EcQ0\n40Ske3fQ6bjdty+363dhGxfHNZWKsQoFv/j7o1YoaFFf2WAklP1WWE6GeyQl8eVrrzW497o+88w9\n5VyyfqgQWWldiyZDw+vjzQTM6U9P5+yBs+ja6O757r7Hf2wMq75cRULLhN9s2P+u+EuMtJUVaMVf\nCcsXyEPJyeysZ2PLPj4iTBcQQOfERCrGjuWtGzdoolYT1K8fu27cMIfoZJnU/Hw2v/IKvoGBfDZg\nABN79KBLYiJzZy/iuR+eQ9dGR52LmheTahl+6pTp+OEaDb2/+grHkyfJ8WnK/tRrjNQb2KuAcy7w\nSX4eY4zRrMpKwoFvAOeqKlyBYkQ5lg1Q27gxb37wAWO++ooRhYVIQCgwBBiKmQm+1cYGv/Xr+eXg\nQVMzj381PkeOHqXRtGm0+ugjxgwdap7cbNrEi2++ycSRI9k0ZQramTPxXb2a69u3Cza3ra0ggxkM\nwtgZa5vfflsY0vDwBqVausOHUVdVUbtmjajZDg+/l8h1+hTY2lEZEMDqI0cYXX+dMvCBWk2lUUAj\nIMDMGG/VSuTM+95ryACRPy8rB7WtMMhNm5p+V0pKUPn64lyaRMGFkzChBk66glMrqAAiDkPyNbiZ\nDoUVMGoyWJRgyadPI+35HlndCn11DUmdOps9/I0bzecgy3BoPzTzxr7PTN59Yhy3IyN52qhZvmpV\nQ+8+OhIeH4EqLQvvhATSLHS5iYtD1bMnYX5+HLTQLzfIMtL77yP37o3m+EEqw+pTN7oqmp2OJsvi\nt1AnJLDxo48Y1bix6RQtKxv+Exjvlwd54ZbPoNu5c4yeO5dHxj+C4qICfEAXr2N17Wo+2vMRkl4i\neEIwvoW+JLdOpmt5Vw4cPSC+uyuc3dKhJUOmD+FC9gWqfaqxzbClxqfmNxn2vyv+EiPt5eXFrVu3\nTJ9v3bqFt5HYYYElS5aY/j9gwAAGDBjwV5yOFX8zPOgFYrl8wbhxjKmP5mTV1LAvMBDXPXvMITqg\nXefOjBk2DEmSsF2wgLWzZuG5ahUjHhvF7I2zudP6Du08/DnuLzHMgmh2tGlT1hQVEdapE+dqKnjH\n7iSPV0CkAaZ1MfBdHIyuooGE6DOADiENasSPgF3XrigWLuSFUaOI+PZbwqqqOACkN2rE4cJChtVv\nP7WsjO3R0bgVFLDE4jmx1Bi3HJ8vPvqI73Jz8VuxwjQ+wwYPxmf3bj4YO9Y8Vps3s2rmTP757rvk\nhIU1ZIRv3242mgkJwou+ds28LDoajVJJpZ+fYFNXVQlDfeJEQ+N05DA0bgKJiVxp3JiDxcU8ZjAI\nmdNevcS+g4JEDv34cTEJKCoSy0MaGjKmTxceNwg2+P06fl27Rg+djv4TnuGjzz5CTlOha1EF7UdD\niEU99KmTkK+FQ983LMGKikJe97H583urzB5+YKBZtjQuDjp1AekWOoPMkOeewcWrBYrUFPRXr0JF\nuYgGaDQoOnfGpqgM3VEd5FbT+qm+3K6P+iiiozEEBmKXkMC8Tz/lyODB6I2iNIAyNwfdurV4u3iS\nfuoUtb374XD0COvnLWRivTdLXBxjhgxh8H0qG36vYRvzL7xwSZKwK87CZt0aJBeJDm9Nouj2Jarr\nquEQ6Px1aNtq4Rr45/lzZscZCisKUexTUOZdRlx6HCm3U9CPMhWwobqholmLZnT27ExA8wDslfaE\nfxKOVtb+T3vRv/76K7/++uvv3v4vIY7V1dXRoUMHfv75Z5o3b05QUJCVOGbFnwpZlpn6yiv3eAkP\nWg7w3YEDjE9OFjred5HKZFlmztSpqKOjkV0cuJ1/h5y8HDq26IiiqpritDS2yzLh9vZIH35I2GOP\ngVKJrFTSe2gQnS+kcaEPhCpg/U349gY8boCDgAowqFR86ezM9wUFJuP9rKsr3964geTm1oB1PtrT\nk6c3b+arMWM4bDAwB6FI9kzbtky6c4fBFuVjPyqVrAoNJaO4GNzc6OjrC0ByfDxVrq7oDQYC2rcH\n4GZ1NYbLl2nVs6d4/oCU1FQ6+PoiZ2ZyOjNT5JeNrPVFi3Dz9qbwxReFBzljhvh78+a9sp1nzgiR\nlKZNhZf7xBPCkEVGCqPu5gYvvECfHTtw3rGDwzU19HZwQLtvn1DlmjFDKKbJNdCkhSC0ZWQIprdl\nSZNOJ+qaR4ww56ItWeyrVqGoqWHX66/Ttqc3s2fPpqquCm1nLQ4ngqhYtsq87uKZMCipISs/OgqX\nX36l5K23zOstmgMjxkJQsPl65s0Tx751BciB7iHQtp9Yv76RCGDOm8fF1cuFRqL4fCN2jcuowRf9\n6vXYLZhHrUdTXHya0KF1W8rPnOOyv7+5LluWsTlyhOZOThTY2FBZVoq3kxNtWvkQeeEChmbNcMzN\npW3HjlxLSEDn5oadJNGlbVtU9e/ZNkolkWdOk+ukued5eRD5zPj9g4z87v27eWbxVPQjS6H1JMg6\nhHQhD/mCDE+JdZz3O6O0U1LcphhDe1P/NWyu2uB53ZPswdmm2Wzw5WBidsdQoavgjWNvsG7wOvYf\n2s/kDyez7bVtDySZ/a/hv4LdDXDkyBFTCdaUKVN48803Gx7YaqSt+IN40AvkQctXZWSwc8kSzo8f\nf1+2qyzLHN2yBcNLLzJUb36hHFGr+bJlS75PTWVOcDBrYmIabLd7/25efO0Zip7T8+hJyI4E3zro\nBlwCnIAqSeJm48a8kZ/PKL2eHwFtS3fKOrcg0dMZA1B+PIWgnHyq27enpacncTExtNTpKAeeV6ng\n8cc5GhPDmsxMk6Hv7eeHduNG1N99h9S2LTWWZUEREYLAZTzX0lK8DQayKivRv/WWIDepVEjl5XS0\ntyfl9GkML70kjENMDN4HdpAna6ixdxKGpmlT0eO5qgqdp6fwfJs0EYbpzBlo3VqEnsMgpUV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yug5BYEBsAP38HDUfU1zdOxUH0DKdMZueg2yDKtvb3JP3aMqr59bdfX4dgx9IsXw5vzhOM9ehhP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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Initial positions\n", "x0 = 0.\n", "y0 = 0.\n", "pos = [x0,y0]\n", "#Number of random steps\n", "N_steps = 1000\n", "#Number of random walks\n", "N_walks = 3\n", "\n", "\n", "def Random_walk( pos, N ):\n", " \n", " #Initializing the seed\n", " np.random.seed()\n", " \n", " x = np.zeros( N ) \n", " y = np.zeros( N ) \n", "\n", " #Initial conditions\n", " x[0] = pos[0]\n", " y[0] = pos[1]\n", " \n", " #Generating random positions\n", " for i in xrange(1,N_steps):\n", " x[i] = ( np.random.random( ) - 0.5 )*2 + x[i-1]\n", " y[i] = ( np.random.random( ) - 0.5 )*2 + y[i-1]\n", " \n", " return x, y\n", " \n", "\n", "colors = ('b', 'g', 'c', 'r', 'm', 'y', 'k')\n", "axisNum = 0\n", "plt.figure( figsize = (8,6) )\n", "\n", "#Plotting random walks\n", "for j,c in zip( range(N_walks),colors):\n", " \n", " axisNum += 1\n", " x,y= Random_walk( pos, N_steps ) \n", " color = colors[axisNum % len(colors)] \n", " plt.plot(x,y,\"v-\", color = color, lw= 0.5, label = \"walk %d\"%(j+1))\n", " \n", "\n", "plt.title(\"Random walks\")\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## **Activity** " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " \n", "Radioactive decay: Spontaneous decay is a natural process in which a particle, with no external stimulation, decays into other\n", "particles. Then, the total amount of particles in a sample decreases with time, so will the number of decays. \n", "The probability decay is constant per particle and is given by \n", "\n", "$$\n", "P = -\\lambda \n", "$$\n", "\n", "Determin when radioactive decay looks like exponential decay and when it looks stochastic depending on the initial number of particles $N(t)$ .For this, suposse that the decay rate is 0.3$\\times 10^6 s^{-1}$ . Make a logarithmic plot to show the results. \n", "" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }