{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "

\"Zeros\" in a Forced Response

\n", "

MCHE 485: Mechanical Vibrations

\n", "

Dr. Joshua Vaughan
\n", "joshua.vaughan@louisiana.edu
\n", "http://www.ucs.louisiana.edu/~jev9637/

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "\t\"A
\n", " Figure 1: A Four-Mass-Spring System with Excitation Force on the First Mass\n", "

\n", "\n", "This notebook demonstrates the eigenvalue/eigenvector problem using a four-mass-spring-damper system shown in Figure 1. We'll just look at one example set of parameters. The same techniques apply for other parameters and for larger matrices. \n", "\n", "The equations of motion for the system are:\n", "\n", "$ \\quad m_1 \\ddot{x}_1 + (k_1+k_2)x_1 - k_2 x_2 = f $\n", "\n", "$ \\quad m_2 \\ddot{x}_2 -k_2 x_1 + (k_2 + k_3)x_2 - k_3 x_3 = 0 $\n", "\n", "$ \\quad m_3 \\ddot{x}_3 -k_3 x_2 + (k_3 + k_4)x_3 - k_4 x_4 = 0 $\n", "\n", "$ \\quad m_4 \\ddot{x}_4 -k_4 x_3 + (k_4 + k_5)x_4 = 0 $\n", "\n", "We could also write these equations in matrix form:\n", "\n", "$ \\quad \\begin{bmatrix} m_1 & 0 & 0 & 0\\\\ \n", " 0 & m_2 & 0 & 0\\\\ \n", " 0 & 0 & m_3 & 0\\\\ \n", " 0 & 0 & 0 & m_4\\\\ \\end{bmatrix}\\begin{bmatrix}\\ddot{x}_1 \\\\ \\ddot{x}_2\n", " \\\\ \\ddot{x}_3\\\\ \\ddot{x}_4\\end{bmatrix} + \n", "% \n", " \\begin{bmatrix} k_1 + k_2 & -k_2 & 0 & 0 \\\\ \n", " -k_2 & k_2 + k_3 & -k_3 & 0 \\\\\n", " 0 & -k_3 & k_3 + k_4 & -k_4 \\\\\n", " 0 & 0 & -k_4 & k_4+k_5\\end{bmatrix}\\begin{bmatrix}x_1 \\\\ x_2\\\\ x_3\\\\ x_4\\end{bmatrix} = \\begin{bmatrix}f \\\\ 0 \\\\ 0 \\\\ 0 \\end{bmatrix}$\n", "\n", "Define\n", "\n", "$ \\quad M = \\begin{bmatrix} m_1 & 0 & 0 & 0\\\\ \n", " 0 & m_2 & 0 & 0\\\\ \n", " 0 & 0 & m_3 & 0\\\\ \n", " 0 & 0 & 0 & m_4\\\\ \\end{bmatrix} $\n", "\n", "and \n", "\n", "$ \\quad K = \\begin{bmatrix} k_1 + k_2 & -k_2 & 0 & 0 \\\\ \n", " -k_2 & k_2 + k_3 & -k_3 & 0 \\\\\n", " 0 & -k_3 & k_3 + k_4 & -k_4 \\\\\n", " 0 & 0 & -k_4 & k_4+k_5\\end{bmatrix} $\n", "\n", "Using $M$ and $K$, we want to solve:\n", "\n", "$ \\quad \\left[K - \\omega^2 M\\right]\\bar{X} = 0 $ \n", "\n", "for $\\bar{X}$. This is an eigenvalue problem.\n", "\n", "For information on how to obtain these equations, you can see the lectures at the [class website](http://www.ucs.louisiana.edu/~jev9637/MCHE485.html).\n", "\n", "We'll use the [Scipy version of the linear algebra module](http://docs.scipy.org/doc/scipy-0.13.0/reference/generated/scipy.linalg.eigh.html). It allows us to solve the \"general\" eignevalue problem." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# We want our plots to be displayed inline, not in a separate window\n", "%matplotlib inline \n", "\n", "# Import the plotting functions \n", "# Note: Using the 'from module import *' notation is usually a bad idea. \n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Let's also improve the printing of NumPy arrays.\n", "np.set_printoptions(precision=3, suppress=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To see how to solve this eigenvalue problem, we will use some example parameters, set up below. All the spring constants are equal and the masses are equal." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Define the matrices\n", "m1 = 1.0\n", "m2 = 1.0\n", "m3 = 1.0\n", "m4 = 1.0\n", "\n", "k1 = 4.0 \n", "k2 = 4.0\n", "k3 = 4.0\n", "k4 = 4.0\n", "k5 = 4.0\n", "\n", "M = np.array([[m1, 0, 0, 0],\n", " [0, m2, 0, 0],\n", " [0, 0, m3, 0],\n", " [0, 0, 0, m4]])\n", "\n", "K = np.array([[k1 + k2, -k2, 0, 0],\n", " [-k2, k2 + k3, -k3, 0],\n", " [0, -k3, k3 + k4, -k4],\n", " [0, 0, -k4, k4+k5]])" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# We'll use the scipy version of the linear algebra\n", "from scipy import linalg\n", "\n", "eigenvals, eigenvects = linalg.eigh(K,M)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "The linalg.eigh function returns two arrays, one of the eigenvalues and one of the eigenvectors. The eigenvalues are the square of the two natural frequencies. The eigenvectors are returned in normalized form, with each ''row'' of the array representing an eigenvector.\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "The resulting eigenalues are 1.53, 5.53, 10.47, and 14.47.\n", "\n", "\n", "So the natrual frequencies are 1.24rad/s, 2.35rad/s, 3.24rad/s, and 3.80rad/s.\n", "\n", "\n" ] } ], "source": [ "print('\\n')\n", "print('The resulting eigenalues are {:.2f}, {:.2f}, {:.2f}, and {:.2f}.'.format(eigenvals[0], eigenvals[1], eigenvals[2], eigenvals[3]))\n", "print('\\n')\n", "print('So the natrual frequencies are {:.2f}rad/s, {:.2f}rad/s, {:.2f}rad/s, and {:.2f}rad/s.'.format(np.sqrt(eigenvals[0]), np.sqrt(eigenvals[1]), np.sqrt(eigenvals[2]), np.sqrt(eigenvals[3])))\n", "print('\\n')" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "The first eigenvector is [-0.372 -0.602 -0.602 -0.372].\n", "\n", "\n", "The second eigenvector is [ 0.602 0.372 -0.372 -0.602].\n", "\n", "\n", "The third eigenvector is [ 0.602 -0.372 -0.372 0.602].\n", "\n", "\n", "The fourth eigenvector is [-0.372 0.602 -0.602 0.372].\n", "\n", "\n" ] } ], "source": [ "print('\\n')\n", "print('The first eigenvector is ' + str(eigenvects[:,0]) + '.')\n", "print('\\n')\n", "print('The second eigenvector is ' + str(eigenvects[:,1]) + '.')\n", "print('\\n')\n", "print('The third eigenvector is ' + str(eigenvects[:,2]) + '.')\n", "print('\\n')\n", "print('The fourth eigenvector is ' + str(eigenvects[:,3]) + '.')\n", "print('\\n')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Responses\n", "Now, let's look at the response and see how it reflects the four modes of the system." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Define the equations of motion\n", "\n", "# Define the system as a series of 1st order ODEs (beginnings of state-space form)\n", "def eq_of_motion(w, t, p):\n", " \"\"\"\n", " Defines the differential equations for the coupled spring-mass system.\n", "\n", " Arguments:\n", " w : vector of the state variables:\n", " w = [x1, x1_dot, x2, x2_dot, x3, x3_dot, x4, x4_dot]\n", " t : time\n", " p : vector of the parameters:\n", " p = [m1, m2, m3, m4, k1, k2, k3, k4, k5]\n", " \"\"\"\n", " x1, x1_dot, x2, x2_dot, x3, x3_dot, x4, x4_dot = w\n", " m1, m2, m3, m4, k1, k2, k3, k4, k5 = p\n", "\n", " # Create sysODE = (x', x_dot'): - Here, we're assuming f(t) = 0\n", " sysODE = [x1_dot,\n", " (-(k1+k2)*x1 + k2*x2) / m1,\n", " x2_dot,\n", " (k2*x1 - (k2+k3)*x2 + k3*x3) / m2,\n", " x3_dot,\n", " (k3*x2 - (k3+k4)*x3 + k4*x4) / m3,\n", " x4_dot,\n", " (k4*x3 - (k4+k5)*x4) / m4]\n", " return sysODE" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Import the ODE solver\n", "from scipy.integrate import odeint \n", "\n", "# Set up simulation parameters \n", "\n", "# ODE solver parameters\n", "abserr = 1.0e-9\n", "relerr = 1.0e-9\n", "max_step = 0.01\n", "stoptime = 10.0\n", "numpoints = 10001\n", "\n", "# Create the time samples for the output of the ODE solver\n", "t = np.linspace(0.0,stoptime,numpoints)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example Free Vibration\n", "Let's start by looking at some free vibration. For this set of parameters. In the code below, we choose initial conditions:\n", "\n", "$ \\quad x_1(0) = x_2(0) = x_0$\n", "\n", "$ \\quad x_3(0) = x_4(0) = 0$\n", "\n", "and \n", "\n", "$ \\quad \\dot{x}_1(0) = \\dot{x}_2(0) = \\dot{x}_3(0) = \\dot{x}_4(0) = 0$" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Initial conditions\n", "x1_init = 0.5 # initial x1 position\n", "x1_dot_init = 0.0 # initial x1 velocity\n", "x2_init = 0.5 # initial x2 position\n", "x2_dot_init = 0.0 # initial x2 velocity\n", "x3_init = 0.0\n", "x3_dot_init = 0.0\n", "x4_init = 0.0\n", "x4_dot_init = 0.0\n", "\n", "# Pack the parameters and initial conditions into arrays \n", "p = [m1, m2, m3, m4, k1, k2, k3, k4, k5]\n", "x0 = [x1_init, x1_dot_init, x2_init, x2_dot_init, x3_init, x3_dot_init, x4_init, x4_dot_init]\n", "\n", "# Call the ODE solver.\n", "resp = odeint(eq_of_motion, x0, t, args=(p,), atol=abserr, rtol=relerr, hmax=max_step)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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Xvme1/N/8znVV7Pzje5IQHeaTY1a8/Aq1y1xzicU9/FCT20SFB3PTmf0AmP3V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\nu3cVcknOHXUH8W3v2Xx1+8xiGXz2CKsTQs02VTHrzZwq0MR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BVm/if9vPsuLABT5aeYyh\nn21h0tw9bDyaiqWU7ZvwuqG0GBpb5k1sSMwwfhrwM60iXacG4+zYv5SlY+fJNJRyiYEtqmLV6Ugf\nf79NwqJ6dcIXLUDuoTInFw6lcmZnMqve+Jv8Soq/ST2ejiSTuP3ZLgRVcT6Rw5791T260/3kLp5M\nj0OSYG8JMXo3C0KIf7cox4/z2HXdNff7P/Iwqm63Yc3MJPPJqQjLtWXg0g02By1C3gydAZ7+3z42\nHUulSmwENdtVK5ofPcUXfx0nU2ukVa0QhrapXuIx1qwsW51gqxX/xx4t9/ZkId5y33U6m1KSpJPA\nCCHEQUmSRmCrQSmEEPKrjlkD/CaEmOPS3lYy7s6m1Ol0+HrgSb48pD84Af2atQRNfx3/hx8q9rnR\nbOX+73ZSPdSP98a0LDXg0tsQQnDh0CWCavmjSjrNlYGDkHx9idq1A3m48ysMlYn5wgWu9BuANTOT\ngOeeJf2eCew7ncG+sxnsOpmGrqAeZ4MqAUzt34hWtR0PCnY3zo792RtP8v2mU/RuGs2bgxqQ8cAE\nDFu3IouOJmLJb24p5lwaJp2J5dPWkXYqg6Z3NKTLI+08du1CzAYz+lxDuePY7NnffOEiqe07IPn7\nI23bTUiwBrUdNf8bGf3WbaSPvQt5lSpE7dqBpLCni+463Dn3W1JTudynH9b0dAKemELgC/+WY7YK\nK7tTdtEktBmz/z7Pb7vPIZdJLH+6O2EBFctGdZZ1h1N4dfEhVAoZP03uTM0SxrIQgoyJk9GvXImy\nVUsili1FUlYsgcgD9133ZFNiC9L/W5KkmcDsgvc+BJAkqZckSXHYVsviytH2fxqVyrOD3xn8htsK\nKlwtAHs1cplErs7ElsTLzN9yypNdqxCSJFG9RRU0gRpyPvkMAM0D93ulI5arM7HiwAWy80sWQFRU\nq0bIjC9sBcU/+ZQqifGM7FCT98a0ZMWzPXh6QCMiA9WcSMll8rw4PvjzCDqjucS2PI0zY99iFaw4\ncAGAwY1CSL/rHpsjFhFB+MIFHnXEAJS+Sga+1ovYAQ2od5t7aheWhUKlqFBCgT37K6pVRVG/PiIv\nj9CTR24YR8xisrB9Vhxndzu+rar96X8A+N1zt8ccMXDv3C+PiiLk669AJiP3yxno1qwp+kwmyehU\ntTOB6gCeHtCIJ/s1pGdsFIG+npWquZCRz3t/HgHgyf6NSnTEwJZYoV+5EkmjIfSrGRV2xMB77rtO\nO2MFxbXHYPP21mOr9fiSJEm3A4uxZVtmA95fVdTLOHToUGV3oVTUvW9HCgjAdOgwppMni30ul0m8\nNrwZkgTfbzpFfFJmJfSy/Bxd9BuGDRuQ/PzwnzypsrtTjITkLO6duYO3f09g0e5zpR6n7tmTgCdt\nS/iZj0/BkpICgEalYHTHWiya0pWHe9ZDKZdYtvc847/dyeHDKWz+ehd5aVpPfZ1iODP2d51MIzVb\nT9VAH2o+8wjGuDjkVaoQvvg3lDGejXEpxDdYzW2T2hPdONIj18s4l8WlxCsua68s+6u6dwPwajX+\nTckbeeCvcexLte1e5GfoSFh5nI1f7MCQZ1/BHcCSkYF+7VqQydCMHePu7l6Du+d+9W1di4LcM594\nCtPJ4g/MkiRxV+favD2qBUpFxeLVnEEIwauLD5FvsNAzNophbUvenjTE7SX79ekABH/wnsseurzl\nvlsuiwsh1gshJgkhRgshZhe8t0EIEXrVyzMBGzcR3lIjqyQktRrfOwYCoFtaciB/u7phjOtaB6uA\nVxcfJD3XOwIjHSGs4DtpHnygWE23ykQIwS87zjJx7h5Ss/XEVgtiSCmxFIUEPD0VVdeuWNPSyJj8\nGML4741I7SNnQo8Y5j7SkbqR/pxLz+fXz7aTuPYk5+NT3P11SsWZsb9oly2+r8/+v7AcOYK8Th3C\nf19aaY5YaVhMlnLJTJTF6e1JLJm6ipWvrXdZ+2XZX92jOwCGzVtccj13YLQYSden82Hc+5zPTSYg\nyp9qzaMxak0c/etEmefrli4DkwlVjx7Iq7gmS9hRPDH3+0+aiPqOOxB5eWQ89HAxqSKL2cqBxQlc\nLihE7ilydCaOp+QQHazmpcFNSqy1a0lNJWPiRJtu4IQJRUllrsBb7rsucX8lSartinb+64R5KOC4\nvBRtVS5ZirCWfBN4uGcMLWoGcyXHwIsL4zGaXX8zcjWGvftIO3iejc2eJbfHyLJP8BAms5W3f0/g\nyzXHsVgFd3WqxXcPticysOQMo0IkuZyQr2cgi47CGBdH1svTiiVW1I8OZO4jHekTG0V0ps1pFlXd\nW9XAHo6O/TOX89h9Kh0fs5GeO/9AGRtLxLIlKKrbd1A9jRCCpc+sZsGkP0g77Uj1OMdIOXKZdR9u\nxWq2XlNbtaKUZX9Vx46gVmE6fBhLmmdv1o7Sp1Zfula7DZ1Zxwdx72Ew62k/riVKtQK50r6dhBBo\nF9hqrGrGjPZEd8nVmbicowc8M/dLkkTIpx+jqF8f8z//kPnYFIT53zCF4+tPsueneA5VUDDXWYL8\nfPj50c78NKlzidujwmAgY+JkrKmX8enYgaBXp7n0+t5y3y33X3JhfNh1yvt7JElyncv6H6Ow1pW3\n4tOpI/Jq1bCcP49xx84Sj1HIZbw7piVRQWoOJ2fx0cqjbs+w1Jl1GMz6cp+f++mn5Kkj0KrCOLLR\nuSK67iJXZ2Lqz/tYGX8RtVLOe2Na8mT/Rg5vH8jDwwmb+z2oVeT/uoC8WbOLHaNWynltSBNUChn5\nYb5UrV0+TSNX4OjY/2XBJgB6/LOD8A6tCV+8yGuzXv3D/ci9rOX35//i4uFLZZ/gAOoAH8LrhtBp\nQhs6jG/lkjahbPtLvr6oOnQAwLCl7AoNlYEkSUxp9STV/KuTlJPEt4e+JbJ+OA8sGEPzIbF2zzUl\nJGA+dgxZSAjqPr3tHusK9EYLE2bvYuxX2zCYLB6b+2X+/oR+PwcpOBj9+vVkv/Z6URZ8YdWCsnQG\n3UHtCH8CSnLErFYypz6NMS4OWXQ0od/OdEmc2NV4y323XM5YQfD+OqANttixwldbYLGXl0PyWjQV\n0ErxBJJMhl/BU6N2wYJSjwvzV/HB2FaolDL+3H+BX3acdVufhBA8un4iz255BrPV+WB0Q1wchs1b\niDAVFIA9kILFZCnjLPeSlmtg4tw97D2dQai/DzMfaEfP2Cin2/Fp0YKQz2xJCTlvvY1uXXE5PaVa\nybg5w3j8myEE+ZVco05r0vJr4i+k69wnaVDW2BcWC+ff/4Q1qbaV1pH1NIT99COyoCC39akiSJJE\n35e607hfDBazFW26ayQvQmoGM+KzO2g+uHGJ2znlxZG5R9XdtlVpL24sT29iWVwyGXmVE6Lgq/Dl\nhXYv4SNXseHcOjYkrXPITvkLF9nOHz4MyQMB3T9sPc259HyqBvvio5B5dO5X1qtL2Nw54OOD9ocf\nyftuFsIqMOYZCa0VTN0uJQvqVgY5772P7o/lSP7+hP/4g1sevLzlvlue2pQPAxOBJdhU9ttgC9pv\nU/DzUmCSJEkTXNjP/wTesndtD7+CGn+6VauxZpWuztyoaiCvDG0KwIy1J1gVf8Et/ZEkCV+FL0k5\nZ9ly3vng4tyPbbpikQ+MJbZ/fSLqhSJVoizH5Rw9k+ft4fTlPGpHaJjzUEcaVyu/w+E3+E4Cnn0G\nhCDzsccxJhwpdoxvkBqluvTMsZ+P/cSviT/zd/KGcvejLOyNfUtaGul338v2ldsxKlS0Uetp9u40\nj2a7lQe5Uk63RzsyYeFY6ve4Vq/JarFisbOFr8vSE7/0CCteW+/SQP3ScGTu+TdubHOpYQp/H0nl\ngxVHeeT73VzMrBzNtdpBtZnY3JaEMydhNlZhP1RC6PVFgtaaMe4P3E9K0/LTdlvdxecGxSJJksfn\nflWHDoR8/u+Dmn75H4z5ZjBD3u9X5tZ3dr6RHSeuYHZDPOTV5H0/l7xvZoJCQeisb1E2sb+6WV68\n5b5bXgX+iQXB+0uEEAeEEGcK/l0ihBgFTCp43cIJvKVGlj0UNWqg6toVDAby/1hu99g+Taswtb+t\nVtw7fxxh2/HSBWMrwoj6tjivxScWlTnxXo1h1y4M27YhBQaSPXAAt03u4NBk5C4uZel4dN4ektPz\naRAdwHcPtqdqSMX1bwKeehLfoUMQWi3p99yL+fQZh8/NN+Wz4ZxtRa1tlPv0s0ob+4Y9e7jcrz+G\nbdtoqUtlVE0FL03s49JVIXejUF3rNJp0Jn56YAk/3LOIVW/8zYVD125h5qTm8evE39n9wwEuHLxE\nxhn3ZyY7MvcoGjRAFh2NNS0NUylCmT1io2hUNZDzGTomfr+bM5crp55t75p9GB97P4Pq3olMsv09\nZ6fkcvD3o5iN165869auQ2Rlo2za1G03/EKEEHy08ihmi+DO1tVoUVDuyJNz/z+Z/zB2xSh2tdIQ\n+Iot/irzyamIzevw8St7C/Cb9f/w9M/7eWjObvadcV085NXkzf+B7NdeByD4w/dRF6zKugNvue+W\n567TujCDsjQKVO5dJ8/9H0GrrTxpAWfwG2vbqsxfuLDMY8d0qsX42+pgsQqmLTpI4sVsl/ene42e\nRPpGcj7vPDsvOl6zMqdgVcz/4YfQVnL9wvQ8A4/Oj+N8ho5GVQOZMb5tqduGziIVlAxRdbsNa1oa\naWPvwnLRljlZVjyf1qTFaDHSOrINdYLcp8Z9/dgXZjM5n31O2sjRWC+l4tO+HTErlvDMhNupHmq/\nkLm3I1PICKkRhElvJnn/RY6uvjbTT6lSEFwjiFrtqtH/lR407l/f7X1yZO6RJOnf1bFStioDfZV8\nPb4drWqFcCXXwKR5ezh6wfV/82UhSRIjGozinsb/1pZMWJHIrnn7Obj02tXhwnnMzwOB++sSLrH3\ndAaBvkoe6/1vPVxPzv1rzq4m35xPmu4KAZMnETD1KbBYyHh8Crq/yq4/PKxtdaKD1CRezOGx+XFM\nnreHNYculqhZaLUKzl7Jc2oVTfvT/8ie9goAQW+/5fbVSm+575ZHgX8v8I4QotRChZIkDQdeFkK0\nrWD/vAp3K/DfKAidjpTWbRE5OUSuW4sytrH944Xgo5XHWBqXzCtDmzKoVTWX92nVmZV8e/Ab6gbV\n47MeX5S5cmLYsZO0UaORgoKI3rUDWWCgy/vkDGsPp/Da4kPEVgvii/valBjMWlGsWi1pY+/GtH8/\nipgY4jo/jzbHzOivBtm1V6o2lSBVEGqF/SxOV2E6eYrMp57CdCAeAP/Jkwh84XmXB+5WNnlpWtLP\nZBJZPxzfYM/YtqLkL/+TzMmP4tOpExGLF5V6nN5kYdqig2w/cQU/Hzkf3d2aNnUqVzLmYkIqf05b\nh4/Gh3vmDMPHT2mrLtChIyiVRO/bizzUfUkseXoTY2ZsIz3PyMuDmzC4DIkad2ARFu7/axzZhiy+\n7Pk11dTVuXw8Dc2K+Wi//hoUCkI++Ri/kSPstqM1mFm4M4lfdp4lT29zwuQyiZioAKKD1SjlMjK1\nRo6n5JCnN/NIzxge7GFfekYIQd5XX5Pz/gcABL0xHf+HbopoJ7cp8M/CFqT/riRJLSVJCgSQJCmw\n4Of3sJVIKj3C+xYlkp5+Y9R8k3x98Rs6BACtA6tjkiTx/KBYVjzbwy2OGNi2JULVoZzOPsX+y/vs\nHiuEIOeTTwDbqpgsMPAa22en5JLr4e2Vno2j+OK+Nnxzfzu3OGIAMo2G8B/no2jciKzz2Vw4mk5+\nhhbKeB6L0kS53RFLT09HWCzkzZ3HlX79MR2IR161KuELFxD0yrSbzhED8A/XUKtdda9wxByde9S3\ndQWZDOPevVjtrCiolXI+GNuSvs2qkG+0MPV/+9jqpjAFR6naNIoabapiNpgxam3ae7rFi0EIfPv2\ndasjBvDd3ydJzzPSrEZwsXnQU3P/8YzjZBuyiPaLplZgLTbP2MmKV9eTN3A8/o8/BmYzmU8+Re43\nM+2ummtUCh7sUY9lT3Xj2Tsa07R6EEIIjqfksPnYZdYnXGLfmQzy9GaqhfjSugxHXFgsZE97xeaI\nSRJBb73pMUfMW+67TkfACiFmSZLUB1tZpBeA65+qJWC9EOJjl/TwP0RycrLXaJ6Uhd/YMWh//And\nkqUETXsZyafsLbVwN9Y685H7MLrBGL49NLPMrD/j9h0Yd+1GCg4q+oO/2vbLnl2NXCnj7tnDkHuo\n9ItSIaNDjPtLMMlCQghftJDT974JQFTaYcyn2qCsX/pWmMlsZcGuJDrVDycmyj1aZCkbN2KZNx9T\n/EEAfEeOJPjN6V6bLXmz4ejcIwsJQdmyJab9+zFs34Fv3z6lHquQy5g+vBkBagVL4pJ5cUE8rw9v\nRt9mnhVUvZq+L3QrquEphEC7yLa6Vxh64S4SL+awZI+t7uPzg2KRXZck5Km5f3eKTZKoQ5VOZCRl\ncWprEnKlbdtc89KLyCMjyX59OjnvvIv51CmC334LyU7dxgBfJSPb12Rk+5rkG8ycuJRLhtaAyWwl\n0FdJvcgAIoPsP2xY0tPJfPRxDNu2gY8PoV9+ge+dg1z6ve3hLffd8irwFwbp53CttEU2tuD+vi7r\n4X+I5s2bV3YXHEbZvDmKxo2xZmaiW112nIEnGFh3EDN7z6J3rdJvEEIIcj62rYoFTJyILMDmXFxt\ne02YH/mZei4cTnVvhysJeWgodd99mjDSqHNmDVcGD0X/98ZSjz+eksPX604wae4e/rmU49K+WHNy\nyHptOiFTn8EUf9CmJTRnFqFffHbLEfMgzsw9/8aNbSrzWJlM4tk7GjP+trpYrILpSw6x5tDF8naz\nwlxdw9O4ezeWs0nIoqNRdevmtmtarIIPVxzFKmBUh5rUjy7+QOOJuV8Iwc4CZ6xjlY6kJNjmt8b9\nG6AJs8Vh+k94kJBvvrbpEy5YyJXBQzGfcSzhx0+loGWtEHrFRtOveVU61Y8o0xEz7NrF5b62BB1Z\nWBjhv/7sUUcMvOe+67AzVrANWRRYI4SYJYQIAUKwyVqEFJRBshvcf4vSMRhunPJBkiShufduALQ/\n/ljJvfmXav7VirKnSsKwdatNQDAkBM2DD/z7/lW2r9PZprNz+bj7JQUqi6iWNRn+6yNE9myDyMkh\nffz95H79TYmSBY2rBdGjcSR5ejNP/rSP5PSKB7wKg4G8Od+T2rkr2u+/B0Dz8ENEbd6I74ABFW7/\nFs7hzNxTpDe22TEpGUmSmNy7Pg/3rIdVwBtLD7P2cOWV3iokf9FvAPiNHIHkxgSe5fvOc/RCNhEB\nKh7uGVPiMZ6Y+7MMmVzSphDoE0ijsMY07BPD7c90oeN14sF+g+8k8s8/kdeujenoUS737kvud7MQ\nFtfpL1rz8sh6eRppI0ZhvXQJn3btiFyz2lbpwcN4y323TGdMkqSZBSr7mUBmgdJ+kairECK7QNbC\n8ykzNxlHS0kX91b8RoxA0mgw7tqNyUtUjO0hhCjSFfOfNBGZv3/RZ1fbvsWQxrS7pwWN+pQ8cd4s\nyPz8CP1upk2HzGol5933SBs9BvN1qd5ymcSbI1vQtm4oGXlGnvhxX1EZF2cRJhP5vy0mtUcvsl+f\njjUzE58O7Un75GOCp79+ze/kFp7DmbnHp2ULpKAgLGeTMJ896/B5E3rE8FCPfx2yTG3Zxbtdzdns\nszz59+PsSdrKxfUHyNRUx2+0+7YozRYrMzfYsmWfGtAIjarkyCBPzP2BPkGMajCaKa2eRC7JUaoU\nxHSrU2IohjK2MZGrV+I7bChCryfnzbe4MnAQ+r83VqiiijAayZs/n9Su3dD+8CMoFARMfYrw3xZ6\nvB5oId5y37WbTSlJUhw2iYrrswEEcEoI0aD4WTcv7s6m1Ol0+NrZn/dGsl56Ge2PP6EZdx/B771b\n4fYytUb8VQqHy/44g/7vjaTfNw5ZaChRu3Ygu0p5+Ua0vSvRr99A5rPPYb1yBcnPj4DHH8P/kYev\niRfJN5iZ8uNejpzPpk6Ehm8fbO+w/IZVqyV/wULyvpuF5YJNAFhRvz6BL7+Euk9v9Hr9f9r+lY2z\n4z/9kUnoV64k6J238b9/vFPXWrQricSLObw8pAkKD2v67Uvdyxs7XydAqOk9uzdmhR9jZo8gMMo9\nDwEGk4WJc/dQN8KfV4c1LTVr2ZvnH/36DWS99DKWi7btZWWrVviPH4fvoDvsxpNdjSU1lfwFC9H+\n9D8sKSlF7YR8+EGZ2fjuxgO2dyibslRnrEBp/7uCH9cDpwv+Xxfojc0h+0AI8XLF+nnj4G5nzGq1\nIpNVjuBoeTEdP87lXr2RNBqi98UVxWCVhys5ekZ8sZUwfxWvDG1CmzquC6oUQnDljkGYDh4i8NVX\nCJg08ZrP3W377HwjMklyW6akowghOLsrmejYSHyvi+ewpKeTOu0lllv30yo+m1rWEDQPTUBz911F\n0h/Z+UYmz4vj9OU8YqsFMWN821Kf9oUQGPftJ3/hQnR/LEcUZN8pYmLwf3QyfiOGF6noX23/fIOZ\n9/88SrMaQYzqUMtdprjFVTg7/rW//ErWc8+j7tuHsHlz3dgz1yKEYNq2l0hIP8yd/2uB1RRL/R51\n6DW1S6X2y5Nzf16aFnWgGoWP41uzVp0O7Q8/kPfVN1gzbSLEkkaDqnMnVJ07o2jYAHm16sg0fgir\nwJqZiSUpCVNCAvqtW4tkaqDgIez551AP6O8V4s0esH2FnbG12GLB2gohzlz3WTCwAagthKj8NAQP\n4W5nLD4+npYtW7qtfXdxZeQojDt3EfT2W/g/cH+529GbLDw6L65IJHJgi6o81qcBYS7IwtStWUPG\ngw8hi4wkasc2ZNc9CbnT9rtPpvHSwngig9QseLyrW67hKKe2JbH+o6007lefbo92KPb5gsRf+SXx\nf3RPsDJ2ZgIAkp8f6tt7oR7QH5+27cjwD2Hi3DhSsnS0rRPKJ/e0RqWUI4TAkpyMMf4ghm3b0G/Y\ngPXSv0kQPu3a4T/pEdR9+yJdN/ldbf83lx1mVfxFOtUP57N727jRGrcoxNnxb75wkdT2HZA0Gqok\nHHIom9pbOHdqP9/++iQ9N1k5F/I4gVUDGPWFZ4PGr8dTc//FhFRWvraeRn3rc9uk9k6fb9Vq0f2x\nHO3PPxdlPjuESoW6Zw8048eh6tq12N9/ZeIB2zvkjNmTtmgLPHS9IwYghMgqWDmLK2fnblEC3lIj\ny1n8x48nY+cutD/8iOb+8eV+2lEr5cya0J4ft55h3pZTrDp4kU2JqUzoXo/RHWqVe+tSWK3kfFSQ\nQfn4Y8UcMSjZ9ulnMzn0+zHaj2uJppyq738dushbyxKwWAVtXbjSV15Ob08CIKRG8UzFfFM+y0/9\nDkDvh98ltH0aebPnYNyxA92fK9D9uQIAWWgo0+vG8mLT0ew9A8++OI/nDi1GkXwOkZt7TZuy6Gj8\nhg3Fb+wYlDGlx+AV2n9V/AVWxV9EpZTxRN+GLvnOtygbZ+ceRbWqKBo0wHziBMa9+1B17uSmnrme\nkBXbeGzmWXwH30n71wYhV1a+Y+CJuV9YBTvn7sNqEQRElK84tkyjQXP3XWjutlXx0G/ZjPHAQcwn\n/8FyKRWhy7cdFxKCvGpVlLGx+LRpjaprV2R+3lk5w1vuu/acsWBgf2kfCiH2SzYChRCuzXf/j+IN\nWiflQd2/H7KoSMz//INhy5YK1RFTyGU82KMefZtX4fO/Etl2/Aoz1p5g2d7zPNIrht5Nootp9Njj\n95PL2JjwOw+lnCSiShU099xd4nEl2T5pz3lObDyNOlBFpwedW6ERQvDz9rN8tc4WvHu5b4U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PnnAch8+hksF1Nc0q75/HkypjwBQOBzz6JqV756cpIk8VSHqUxu8Rh3N7rH7rHhdWyCkae3e14/\nzVliBzSg5fAm1GhVteg9SZKQSd73Z3+zjv0bBVfZ33fwnQBFQfOVhVWnI3/Z7wBo7nJ8i9IeAcCY\noxk8kKonNsLfJW0W4ir7bz6/EStWagfVdUl7/wW8Ze7xvln5P0xiYmJld8Ft+D80AdVtt2H9f3t3\nHh1Vle8L/LsrMxVCBuYhQqBbQJAhiPME4SnOusC+rddGbyt0t/Z99u0WLtqO/a4K7VN7cABXt9rO\ngnoHX4tNnBW1maMdgkAEIgqETEClUhlqvz/qVChCVchJ6tRvV873sxYLkqo6tflyOPXL3vvsXVOD\nmvkLoHt4O3GwoQE1198AXV+PjJkzkX3LzT063rat2zB71EU4Mb/zrTFOmD4cqekpaNjTrfWQE2r0\nmSfg1HlT4EmCPR9787mfDOKVf9allwAAmv62GsE4LgBrl//1N6APHkTalClIGz8uLsc8qagABUP6\nIvDtIZT+Nr53I3cn//pvGrD9o53tXwd1EO9XvQcAOHf4ufFqWq9nyrXH/Ku0i3i9XukmOEalpCDv\n8T8iZdgwtGzciLpf3QYd7N68K93UhJof34TWLRVIHTMG+b97BKqHi/Z1NfvMvhm4fMkFmH3XjB69\nHx2tN5/7ySBe+acWFiK9uBi6sRFNf30rLse0S2uNw08/DQCh5XXixJPiwYV3no+sfpnY88U+tAQ6\nXzjaDrv5H6isxRsLV+Gdhz7GoX2HAQBfHPgC+xr3oX/WAEwccHLc2tbbmXLtYTFmEFPGrp2Skp+P\n/D89BdWnD/yvv4H6xXfYLsiCPh9q5t2A5k8/hWfQQBS88Bw8ecfuNWeXnez7F+X3ivXGTNLbz33T\nxTP/PleHthzyvdz5/EunNH/2GVq3VMAzYACyLrk4Lsf89vAebK7ehH5D+mLuHy/BnEcuQloP1xaL\nZCf/5sYWvHlXKZp9LSg6oxDZA0PFROmu0N6gJYUlSFFmL/JsElOuPSzGDGLKHllOSp84EQXPPB2a\n0P/886j72c1d3s+u9ZtvcGDu1Qh8/DE8Awag/wvPI3V49zbm7agr2Vc3VqM1GL+fhp3y3ZZ9eO/F\nT9Daan5bw9xw7pssnvlnXXYpVGYmmtesQevu3XE7blcdfvpZ1PTJwx1X/hq/f7cSB/0tx3/RcTy2\n6Y+485M7sLl6E7JyMpE7vF8cWnqEnfw9qR7kDO6LE0tGY8a/nQmlFBpbGvHpt2sAADMK47sdVW9n\nyrWHxZhBfD7f8Z/UC2SceQYKnv4zVHY2/P/zJvZfcimaN26M+XwdDML36grsv2A2WjaXIWX4cAx4\n/TWkjYvPXBDg+Nn/48CX+PHfrsfP370Z6/c5tz9pTwVaA3jjwbfw1StfY9X6t6Wb02VuOfdNFc/8\nPTk5yLzoIgBo36A7UVr3fIumVavg69MXW7UXL326C3N+9yGeKN2G/Q3dX25j8sApAIBnomwi3ljv\nR/nb2xDwdX/nATv5p6an4KqHZuO8n5/evs1ZoC0ApRROH3IGBnsHH+cIFMmUaw83CrfB6Y3C3aal\nogI1P74JbTt3AgAyS0qQddWVSJ88CSo7G8F9+xFYswa+l15Ca8VWAEDGjBnI+92jSMnv+dCkHbVN\ntbjj48XYc/gbAMBDZz2M7Y/tQf/R+Zj+z5MT2pZYaptq8fDrj2DEKyeiyevHlU/8LxT2s7epMlE8\nBD7+BAd+8E9IGTYMgz5b0+M5nV3V8OASHP7DH5F12aU4cNeDeHRVBTbsrGt/fNzQHEw6IQ+FBV5k\npnnQGGhDVa0PG3fWoaBvBh66ZmrUtcMCrU342Ts/QUOgAS9e/ArSU47sW7vu5TKsf6kMucNycMHt\n58a916wl0Irmw83wFnS+bM+h5kPITMlEWopZy9ZQ1zYKZzFmg9PFWE1NjTG32SZK0O/HoYcfweE/\n/xloin2HpWfwIPS7/XZkXXmFIxf2rmTfEmzBXyvfxJbaLbhx7AK8cf0qaA1c+6cr4c23v75ZPG3Y\ntx6/3/go0rb2wbR3z8boq0agZF7y3FHlxnPfJPHOXweD2HfGWWirqkLBi88j81znz8Xg4cPYO/00\n6IYG9P/PN5BxyjRorVFWVY9XP9uFj7dWI9Aae45qYUEfvPLzs2LuTFHbVIvGFh+G9z16jpGvphF/\nvfdd1O6qR15hP1z9h0tttz1W/rvWfYMPH/scTQcDuOapK8SvM71RAq49XSrG4jcDkXqsqqrKdR9I\nnqws9LvjdmT/ZAEaV6xA4L0P0FpZiWCjD568fKRPnoTMWSXImj0bKj39+Afspq5kn+ZJw+VjrsTl\nuBIAUDhtOHZ+XoWv1+zGhEs6XxLDKVprPPXFMrxZGVrX6aQpQ3HBReegsCg+c+kSxY3nvkninb/y\neOD94T/h4NLfwvf0MwkpxnzPvwDd0ID06acg45RpoXYohUmFeZhUmIem5jZs2FmLbXsP4Zu6RrS0\nBpGRloIhuVmYMLwfTi7M63SLsPzMfORn5h/zfW9BH1yx5AKsfXFzt4ulaPnvXrcHq37zPgBgyISB\nyOxrxrY9vY0p1x72jNngdM9YMBhs37qGEqs72e/bWo3SpR/h7J+eisJpw9q/3xJsweqdbyM/swAT\n+k9AdnrfeDe33f7G/bjxbzcg1ZOKa8ddhyvGXJmUd1Lx3JflRP5tNTXYe8qpQHMzBn38IVJHjozr\n8SPpQAB7zzgTwb37UPDsM8gsmenYe9nhq21E3e4GDB4/EKnpsf9fRsu/dlc9Pnryc4w6bQQmXDI2\nKdYLTEYJuPZwmDLenC7G/H4/srKyHDs+xRbP7Nfu/Tt+81loH04FhaJ+RZjQfyJG547B9/NOxNDs\nocc5gj1l1ZtRkNUfw7KHHf/JhuK5L8up/Otu/QUaV6yE96YbkXvP3XE/fpjv5ZdR/8vbkDr2RAws\nXd1pD1civX3/+9j5+TdITU/B6HNG4txbTjuqbbW76rH9w53Yv70aBSPzcdr1U41pu1sk4NrTpX9Q\nltoGKS8vl26Ca8Uz+8kDpuBH4+fhpIIJSFEp2NGwA/+14z/x8PqH8NPS+diwb32nr28NtmJz9WZ8\nUPU+3q96D23Btk6ff/KASRiWPQxtLZ0/z2Q892U5lb/XWnS18eVXEHTorjXd0oJDf3gMAND35puN\nKmYmXDIW/Ufno7W5DV9/uhttLUfPWSv97UfYuPJL7Nm0D5VrEr8MCJlz7WHPmA3sGeu9nMo+0NqE\n8tot2FpbgcqGHagP1OGWyf8bhTmFMV/zytaX8cKW59q/vvv0e1E8aFqn71Oxejs+eOwzXHzPTAyf\nPCRu7U8UnvuynMy/+oqr0Lx2LXLu/DX6/mRB3I/ve+FF1C9chJRRozDo/XehUs2bCt1Y54dSClm5\nR28uvnvDt9hbvh85w7MxsngE54UJMKVnzLyz1sUyMvgfUUpPstdaY/e6PRj4vf7HXGwzUjMxZeAU\nTLHWKeqKaYOmYUf9dqSoFIzoW4iTCiZ0/v5BjY2v/QPQQDCYnD9c8dyX5WT+fX9+C2p+NA+Hn1wG\n77wfwRPHDz7d1ISDDz8CAMi57VdGFmIA0Ccv+t+5cOpQFE4danvektYab+38Kwb1GXTcH9Soc6Zc\nezhMaZCysjLpJrhWT7Lf/1UNVv2f9/HOwx/HpS2jc8fg9lN/jUXTF+OacdciMzWz0+fX7q7Hwe8O\nwVvQB8MnJeeCjzz3ZTmZf8aM85E26WQEq6vR+PwLcT324Wf/guDevUgbP759k/JEevDv9+OBz/8D\nbbpnUwTs5r+peiOe3Pw4niv/S4/el8y59rAYM4gpe2S5UU+yzx2eg9SMFOzZvBd13zTEsVVd03dg\nNk6cORrn/OzUpL3jiue+LCfzV0qh7623AgAOPf4Ego2NcTlu24EDOPTo7wAAOYsWJmxh2Ui7Du7E\np9+twaqve7Yput38X/tqJQDgrGFn9eh9yZxrT3JeuXspE9Y6caueZJ/hTcf3zy8CAFRvq4lXk7os\nvU8azvvX049aXiPZ8NyX5XT+mbNKkHbyRAT378fhJ56MyzEP3v8A9MGDyDj/PGTMnBGXY9p13fh5\nAIDny/+Cuqa64zw7Nrv5H2o+iPzMAsweFZ+N0N3MlGsPizGDVFRUSDfBtXqa/Wk3FGPmr87C6LNH\nxqdBLsNzX5bT+Sul0O/eewAAhx5/HK179vToeIG169D4yqtAejpy77tP7A7K04ecgakDi+Fr9eFP\nXz7V7ePYzf+Bs5fisZlPwJvm7fZ7Uogp1x4WYwbxevkfS0pPs0/LTMWYs0ciJZX/pbqD576sROSf\nMX06si6/DGgKoOGuu4/ZcLurgo2NqLv1FwCA7AXzkVo0Kp7NtEUphQWTfoqMlAx8+M0HWPPtJ906\njt38+6T1YSEWJ6Zce/jJYRBTxq7dKBmz37f1AN57dA38DU3STemxZMy/N0lU/jl33AGVnY2mVW/D\nv/K1bh3j4H2/QdvOnUgdNxY5v7g1zi20b4h3COadFFpP7YlNjyHQav//I89/OaZkz2LMIFVVVdJN\ncK14Zq+17vZP/Xbe48PHPsNX71XiwI5aR98rEXjuy0pU/qnDhqLffaHdKervvAutX39t6/W+V1fA\n99zzQHo68n//eyhDliW4aNTFmD54OlqCLQgEm22/nue/HFOyZzFmEJ9DK1TT8cUr+9bmNrx44xt4\n+z/ed7Qg++7LfajdVY8+eZkYOnGQY++TKDz3ZSUy/z5Xz0Xm7AuhDx1CzfX/gmBD1+5ADnz6KeoX\n/TsAIPe+e5E2fpyTzbTFozy4/dQ78dzsF5GTnmP79Tz/5ZiSPYsxg4wdO1a6Ca4Vr+yVR6El0Ipd\na/dgb3l1XI7Z2XsV/3ASUtKSb2Pwjnjuy0pk/kop5D36CFLHjUXr9u04cO11CNZ1fidi4JM1qLlu\nHtDcDO/18+C97p8T1Nqu8ygP0lLSuvVanv9yTMmexZhBamoSvywChcQr+5RUD06afSIAYOs7O+Jy\nzGiGThyMG1f+EOMv+J5j75FIPPdlJTp/T3Y2Cp59BinDh6Nl40ZUX3YFmjdvPuZ5uqUFh554Egeu\nuRba70efq+e2D3P2Jp3lX9dUi8aW+KzNRscy5dpj5t4RPaSUmgMgH0AxgGUAiqyvZ2mt50q2rTNV\nVVXGrHniNvHMftKV4+BvaMKo05ydGJqsC7xGw3NflkT+qcOGYcAbr+PAddehtWIrqi++FJkXXoDM\nGTPgyclBy7ZtaFz5Gtp27gQAZP/0J8i5fbHI4q5Oi5X/9vptWPzRIozOHYMHz14q0LLez5RrT6/b\nKFwpVQKgUmtdqZSaCuAdADMB1ANYD2CU1rq+O8d2eqNwu/uTUfwwe1nMX5Zk/trvx8Glv8XhZ54F\nmo+d/J4yciRy770HmSUzBVqXGNHy39+4H7d98G+oC9Th0qLLcdPJ84Va17sl4Nx370bhWutK64/T\nANRqrTdYX+eFn2MVbbkRr1mZuBZGFwgEnN49nmJIhuzbWoP44r+3YOiEQRj4/f7SzYmrZMi/N5PM\nX2Vlod/ddyF7/k3wv/n/0FxWBu3zIWXYMGSeey4yzj0HKq17c7FMoLXGzoNfY6h3KDJi7DPbMf/q\nxv24e82vUReow8T+J+P6CTckqrmuY8q1x9hiTCk1H0BXhxTnhnu7tNalEd8vBhCryFoQHrJUSq1Q\nSpV2t8csXsrLy1FcXCzZBNdyMnutdVxWCP/iv7fg82c3oujMQsxaeE4cWmYOnvuyTMg/ZcgQZN90\no2gbnLC9fht++cEvMLDPIPxq2kKMzT92wnhk/tvqvsIDf78fB/zVGJUzCoun34E0T/IWo6Yz4dwH\nDC7GtNbLASzv4WFKACzo+E2rVyxycaa1AK6Ow/v1yPjx4yXf3tWcyr7h24N4/ZdvYeJlYzHth5O6\nfZzGej/Wv1QGABg7a0y8mmcMnvuymL9zhvcdgTG5Y7C9fjtu/2gRHi9ZhsHewUc9J5z/7oO7sejD\n29CqWzE2fyzuOu0eZKdnSzTbNUw593vtJA2lVC5CE/fXRXyvxPpjEUJzyMLqAS40yRQAABC3SURB\nVIyOcZz5Sql1Sql13333XfsCcVVVVe17WtXU1GDTpk0IBoPw+/1Yv349/H4/gsEgNm3a1H63RkVF\nRaevT0tL69Hre/r+bn59RUWFI++/paICLU2t2PDql/j8rbXdbn9roA1BrTHizCEYMWWocfmZmj9f\nz/ylX9/Y0Igl5zyE8/LPxwnekeiTmhUz/2BLELkpebj4hEvwm9Pvx/byHeLt7+2v9/l8jr5/V/Wq\nCfxWsbVCa52nlFoIYLHWOs96bA6AUq11vfUYtNZLrcfmAyjWWh/TixbJ6Qn8mzZtwuTJkx07PsXm\nZPaf/2UjNr32D5wwfTguvOO8bh+nraUNnlSP2KbITuK5L4v5y2L+chKQvSsn8NcCeDVceAEIF16V\nCN1hGe4Ni9YTJjpfDDBnjyw3cjL7addMQkZ2OgaPG9Cj4/SGxV1j4bkvi/nLYv5yTMm+V/WMdZXV\ngzY33BMWLtiOd0el0z1jRJGaDgagUhQyvOnSTSEiou7pUs9Yr50z1hnrjsv8iG+NRqgnTVR4DJoS\nL9HZt7UGO927snLNbrxw0xv4r39/O4GtksNzXxbzl8X85ZiSfW8bprTjAWs4sx7AaullLQDA6/VK\nN8G1Epm91hqv3vI/0G1BTL9uMorOPOGo1fS/er8S7z2yBgAw7OTBsQ7Tq/Dcl8X8ZTF/OaZk79pi\nzFoIdsNxn5hApoxdu1FCs9dA9gAvvi3bi3f+7yeo3dWA6dcdmUDqSfEgKzcTk686CRMvM2MTW6fx\n3JfF/GUxfzmmZO/KYUpThW+bpcRLZPbKo3DxPTNw9s9OxbBJg9F/TP5Rj485eyR+9OwcnHz5uF55\n52Q0PPdlMX9ZzF+OKdm7tmfMRD6fT7oJrpXo7D0pHoy/4HsYf8H3Evq+puK5L4v5y2L+ckzJ3pV3\nU3YX76YkIiIiG3g3ZbIJr/RLicfsZTF/WcxfFvOXY0r2LMYMYsrYtRsxe1nMXxbzl8X85ZiSPYcp\nbXB6mDIYDMLjYX0sgdnLYv6ymL8s5i8nAdlzmDLZBAIB6Sa4FrOXxfxlMX9ZzF+OKdmzGDNIeXm5\ndBNci9nLYv6ymL8s5i/HlOw5TGmD08OUfr8fWVlZjh2fYmP2spi/LOYvi/nLSUD2HKZMNhkZGdJN\ncC1mL4v5y2L+spi/HFOyZzFmkLKyMukmuBazl8X8ZTF/WcxfjinZsxgziCl7ZLkRs5fF/GUxf1nM\nX44p2XPOmA1cgZ+IiIhs4JyxZFNRUSHdBNdi9rKYvyzmL4v5yzElexZjBvF6vdJNcC1mL4v5y2L+\nspi/HFOy5zClDRymJCIiIhs4TJlsTNkjy42YvSzmL4v5y2L+ckzJnsWYQXw+n3QTXIvZy2L+spi/\nLOYvx5TsOUxpA4cpiYiIyAYOUyabmpoa6Sa4FrOXxfxlMX9ZzF+OKdmzGDOIKWPXbsTsZTF/Wcxf\nFvOXY0r2HKa0welhymAwCI+H9bEEZi+L+cti/rKYv5wEZM9hymQTCASkm+BazF4W85fF/GUxfzmm\nZM9izCDl5eXSTXAtZi+L+cti/rKYvxxTsucwpQ1OD1P6/X5kZWU5dnyKjdnLYv6ymL8s5i8nAdlz\nmDLZZGRkSDfBtZi9LOYvi/nLYv5yTMmexZhBysrKpJvgWsxeFvOXxfxlMX85pmTPYswgI0aMkG6C\nazF7WcxfFvOXxfzlmJI954zZwBX4iYiIyAbOGUs2FRUV0k1wLWYvi/nLYv6ymL8cU7JnMWYQr9cr\n3QTXYvaymL8s5i+L+csxJXsOU9rAYUoiIiKygcOUycaUPbLciNnLYv6ymL8s5i/HlOxZjBnE5/NJ\nN8G1mL0s5i+L+cti/nJMyZ7DlDZwmJKIiIhs4DBlsqmpqZFugmsxe1nMXxbzl8X85ZiSPYsxg5gy\ndu1GzF4W85fF/GUxfzmmZM9hShucHqYMBoPweFgfS2D2spi/LOYvi/nLSUD2HKZMNoFAQLoJrsXs\nZTF/WcxfFvOXY0r2LMYMUl5eLt0E12L2spi/LOYvi/nLMSV7DlPa4PQwpd/vR1ZWlmPHp9iYvSzm\nL4v5y2L+chKQPYcpk01GRoZ0E1yL2cti/rKYvyzmL8eU7FmMGaSsrEy6Ca7F7GUxf1nMXxbzl2NK\n9izGDDJixAjpJrgWs5fF/GUxf1nMX44p2XPOmA1cgZ+IiIhs4JyxZFNRUSHdBNdi9rKYvyzmL4v5\nyzElexZjBvF6vdJNcC1mL4v5y2L+spi/HFOy5zClDRymJCIiIhs4TJlsTNkjy42YvSzmL4v5y2L+\nckzJnsWYQXw+n3QTXIvZy2L+spi/LOYvx5TsOUxpA4cpiYiIyAYOUyabmpoa6Sa4FrOXxfxlMX9Z\nzF+OKdmzGDOIKWPXbsTsZTF/WcxfFvOXY0r2HKa0welhymAwCI+H9bEEZi+L+cti/rKYv5wEZM9h\nymQTCASkm+BazF4W85fF/GUxfzmmZM9izCDl5eXSTXAtZi+L+cti/rKYvxxTsucwpQ1OD1P6/X5k\nZWU5dnyKjdnLYv6ymL8s5i8nAdlzmDLZZGRkSDfBtZi9LOYvi/nLYv5yTMmexZhBysrKpJvgWsxe\nFvOXxfxlMX85pmTPYswgI0aMkG6CazF7WcxfFvOXxfzlmJI954zZwBX4iYiIyAbOGUs2FRUV0k1w\nLWYvi/nLYv6ymL8cU7JnMWYQr9cr3QTXYvaymL8s5i+L+csxJXsOU9rAYUoiIiKygcOUycaUPbLc\niNnLYv6ymL8s5i/HlOzZM2aDUqoawC4H36I/gAMOHp9iY/aymL8s5i+L+ctxOvsDWusLj/ckFmMG\nUUqt01pPk26HGzF7WcxfFvOXxfzlmJI9hymJiIiIBLEYIyIiIhLEYswsy6Ub4GLMXhbzl8X8ZTF/\nOUZkzzljRERERILYM0ZEREQkiMUYERERkaBU6QYQoJSaD6DW+rJIa71Usj1uYmUPAMXW74u01vVS\n7XEzpdQKrfVc6Xa4jVJqIYB6WNcgrfVK2Ra5Q8S1JxdAAYAHeO1xjlJqKoDF0a4xJnwGsxgTFv4P\nGb4AKqWmKqWWaa0XyLas91NKzddaL4/8GsB6AKPlWuVO1oVyjnQ73EYptQKhH0Aqra+1UiqPRYGz\nrAJ4eWTO1r8FfxiJM+va8gPry6IojxvxGcxhSnkLIgsCrfUGACWC7XEFpVRux+9Z/w75Sinmn3j5\n0g1wG+tDaG24ELOMZiGWEKdEybky2nWJekZrvUFrvQjAKzGeYsRnMIsxQdZ/vKlRHqpnQeC4IgDL\nolz8KhHlpydyjlJqjta6VLodLrQEwFFDkh0KM3JOkdVjEymXhXBimfQZzGJMVhFCczU6qkX0E4Ti\nxPrppzjKxa8IoYKMEsD6QNog3Q63sT6Ecq0/z1FKlSilFrJnJmFuArDeGq6E9cG/TLZJrmTMZzCL\nMVn5ODJpMFI9QhM6yUFWQdZOKTUHQCV7aRKqiL0xIsIfQrla65XWOb8cwDuyzXIH69ozGsBipVRd\nxPcosYz5DGYxRoT2noLFAGZKt8UtrOFJ3rknIx+hnrH2QjjcS8wpEs5TShUhdMPKKISK4NURd1eS\nC7EYkxdt4nIugJpEN8TllgCYyzkbiWF9GLFHTE4lcKQAi8ApEomxSGu9VGtdb00uLwawhIWwCCM+\ng7m0hax1sOZtdJAPz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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Set the plot size - 3x2 aspect ratio is best\n", "fig = plt.figure(figsize=(6,4))\n", "ax = plt.gca()\n", "plt.subplots_adjust(bottom=0.17,left=0.17,top=0.96,right=0.96)\n", "\n", "# Change the axis units to serif\n", "plt.setp(ax.get_ymajorticklabels(),family='serif',fontsize=18)\n", "plt.setp(ax.get_xmajorticklabels(),family='serif',fontsize=18)\n", "\n", "ax.spines['right'].set_color('none')\n", "ax.spines['top'].set_color('none')\n", "\n", "ax.xaxis.set_ticks_position('bottom')\n", "ax.yaxis.set_ticks_position('left')\n", "\n", "# Turn on the plot grid and set appropriate linestyle and color\n", "ax.grid(True,linestyle=':',color='0.75')\n", "ax.set_axisbelow(True)\n", "\n", "# Define the X and Y axis labels\n", "plt.xlabel('Time (s)',family='serif',fontsize=22,weight='bold',labelpad=5)\n", "plt.ylabel('Position (m)',family='serif',fontsize=22,weight='bold',labelpad=10)\n", "\n", "plt.plot(t,resp[:,0],linewidth=2,label=r'$x_1$')\n", "plt.plot(t,resp[:,2],linewidth=2,linestyle=\"--\",label=r'$x_2$')\n", "plt.plot(t,resp[:,4],linewidth=2,linestyle=\"-.\",label=r'$x_3$')\n", "plt.plot(t,resp[:,6],linewidth=2,linestyle=\":\",label=r'$x_4$')\n", "\n", "# uncomment below and set limits if needed\n", "# plt.xlim(0,5)\n", "plt.ylim(-1,1.35)\n", "plt.yticks([-0.5,0,0.5,1.0],['$-x_0$','$0$','$x_0$','$2x_0$'])\n", "\n", "# Create the legend, then fix the fontsize\n", "leg = plt.legend(loc='upper right', ncol = 2, fancybox=True)\n", "ltext = leg.get_texts()\n", "plt.setp(ltext,family='serif',fontsize=18)\n", "\n", "# Adjust the page layout filling the page using the new tight_layout command\n", "plt.tight_layout(pad=0.5)\n", "\n", "# save the figure as a high-res pdf in the current folder\n", "# It's saved at the original 6x4 size\n", "# plt.savefig('FreeVibration_mode_1.pdf')\n", "\n", "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Frequency Response – Force on $m_1$\n", "Now, let's look at the frequency response of this system. It will tell us how many frequencies there can be zero amplitude response for each mass." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true }, "outputs": [], "source": [ "F1 = 1.0\n", "F2 = 0.0\n", "F3 = 0.0\n", "F4 = 0.0\n", "\n", "F = [F1, F2, F3, F4]\n", "\n", "w = np.linspace(0,6,1800)\n", "X = np.zeros((len(w),4))\n", "\n", "# This is (K-w^2 M)^-1 * F\n", "for ii, freq in enumerate(w):\n", " X[ii,:] = np.dot(linalg.inv(K - freq**2 * M), F)\n", "\n", "# Let's mask the discontinuity, so it isn't plotted\n", "pos = np.where(np.abs(X[:,0]) >= 15)\n", "X[pos,:] = np.nan\n", "w[pos] = np.nan" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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ltTlCMHp7wRMJsPJyMBmtpc6ERfcJmWq+RBWtk3qoojlPp5FZuxZgDKE5+8g2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\ntwdGT4/5dU+P+f3OTvC+vjF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LP+Ocf9f6+iEAP7N+tBDAIuujBgN3F8+2N0b7AcbY+wDm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\nhIwQQgghhBBChPj/OkMFTfnD5nAAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Set the plot size - 3x2 aspect ratio is best\n", "fig = plt.figure(figsize=(12,8))\n", "\n", "plt.subplots_adjust(bottom=0.17,left=0.17,top=0.96,right=0.96)\n", "\n", "# Change the axis units to CMU Serif\n", "plt.setp(ax.get_ymajorticklabels(),family='serif',fontsize=18)\n", "plt.setp(ax.get_xmajorticklabels(),family='serif',fontsize=18)\n", "\n", "\n", "plt.subplot(2,2,1)\n", "plt.plot(w,X[:,0],linewidth=2,label=r'$\\bar{x}_1$')\n", "# Define the X and Y axis labels\n", "plt.xlabel('Frequency (rad/s)',family='serif',fontsize=22,weight='bold',labelpad=5)\n", "plt.ylabel(r'$\\bar{x}_1$',family='serif',fontsize=22,weight='bold',labelpad=10)\n", "plt.ylim(-4,4)\n", "ax = plt.gca()\n", "ax.spines['right'].set_color('none')\n", "ax.spines['top'].set_color('none')\n", "ax.xaxis.set_ticks_position('bottom')\n", "ax.yaxis.set_ticks_position('left')\n", "\n", "\n", "\n", "plt.subplot(2,2,2)\n", "plt.plot(w,X[:,1],linewidth=2,linestyle=\"-\",label=r'$\\bar{x}_2$')\n", "# Define the X and Y axis labels\n", "plt.xlabel('Frequency (rad/s)',family='serif',fontsize=22,weight='bold',labelpad=5)\n", "plt.ylabel(r'$\\bar{x}_2$',family='serif',fontsize=22,weight='bold',labelpad=10)\n", "plt.ylim(-4,4)\n", "ax = plt.gca()\n", "ax.spines['right'].set_color('none')\n", "ax.spines['top'].set_color('none')\n", "ax.xaxis.set_ticks_position('bottom')\n", "ax.yaxis.set_ticks_position('left')\n", "\n", "plt.subplot(2,2,3)\n", "plt.plot(w,X[:,2],linewidth=2,linestyle=\"-\",label=r'$\\bar{x}_3$')\n", "# Define the X and Y axis labels\n", "plt.xlabel('Frequency (rad/s)',family='serif',fontsize=22,weight='bold',labelpad=5)\n", "plt.ylabel(r'$\\bar{x}_3$',family='serif',fontsize=22,weight='bold',labelpad=10)\n", "plt.ylim(-4,4)\n", "ax = plt.gca()\n", "ax.spines['right'].set_color('none')\n", "ax.spines['top'].set_color('none')\n", "ax.xaxis.set_ticks_position('bottom')\n", "ax.yaxis.set_ticks_position('left')\n", "\n", "plt.subplot(2,2,4)\n", "plt.plot(w,X[:,3],linewidth=2,linestyle=\"-\",label=r'$\\bar{x}_4$')\n", "# Define the X and Y axis labels\n", "plt.xlabel('Frequency (rad/s)',family='serif',fontsize=22,weight='bold',labelpad=5)\n", "plt.ylabel(r'$\\bar{x}_4$',family='serif',fontsize=22,weight='bold',labelpad=10)\n", "plt.ylim(-4,4)\n", "ax = plt.gca()\n", "ax.spines['right'].set_color('none')\n", "ax.spines['top'].set_color('none')\n", "ax.xaxis.set_ticks_position('bottom')\n", "ax.yaxis.set_ticks_position('left')\n", "\n", "# # Create the legend, then fix the fontsize\n", "# leg = plt.legend(loc='upper right', fancybox=True)\n", "# ltext = leg.get_texts()\n", "# plt.setp(ltext,family='serif',fontsize=16)\n", "\n", "# Adjust the page layout filling the page using the new tight_layout command\n", "plt.tight_layout(pad=0.5, w_pad=3.0, h_pad=2.0)\n", "\n", "\n", "# save the figure as a high-res pdf in the current folder\n", "# plt.savefig('Spring_Pendulum_Example_Amp.pdf')\n", "\n", "# fig.set_size_inches(9,6) # Resize the figure for better display in the notebook" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Frequency Response – Force on $m_2$\n", "All we need to change to examine the case in Figure 2, which has the force input on the second mass, is the $F$ matrix we defined above. Then, a replot of the frequency repsonses will show at what (and how many) frequencies each mass has a zero amplitude response.\n", "\n", "

\n", "\t\"A
\n", " Figure 2: A Four-Mass-Spring System with Excitation Force on the Second Mass\n", "

" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true }, "outputs": [], "source": [ "F1 = 0.0\n", "F2 = 1.0\n", "F3 = 0.0\n", "F4 = 0.0\n", "\n", "F = [F1, F2, F3, F4]\n", "\n", "w = np.linspace(0,6,1200)\n", "X = np.zeros((len(w),4))\n", "\n", "# This is (K-w^2 M)^-1 * F\n", "for ii, freq in enumerate(w):\n", " X[ii,:] = np.dot(linalg.inv(K - freq**2 * M), F)\n", "\n", "# Let's mask the discontinuity, so it isn't plotted\n", "pos = np.where(np.abs(X[:,0]) >= 15)\n", "X[pos,:] = np.nan\n", "w[pos] = np.nan" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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0UwD8o0fnfa3uvuQVVOlkAjIb6RtmtpLOJBYuRHZ24p88Gb/GTxQL1Sh7hswt\nGTIY7HgoFZ8j8zVmArL2DQdkbvYlN2F08h46ay6lpOvi30IqRdUJJxDcRs/xLcNRjEZWZzpDVkiT\nCqdRXa4IkGrLZMhG558h09mXvIQqnUxAZiNTNW0FPxJi/30RgPA++2g5myRLoRrlyhLclCFzqNOi\nr7ERGKy9Hwo3+5KbMDp5D501jz74ILFnn0XU1FD3fz922pySUYxGxTSpcBqrV31AZkXaAPA35R+Q\n6exLXkKVTiYgs5FI5kO7Gxn4738BqNh3H4ctKY5CNbLWrQNw1fDQbEBmbeQsVynwNaQDstRGAjI3\n+5KbMDp5D101T61bR+dFvwCg/pe/cNW9/PMUo1GuZFHHM2R9mZJFRTPIAKxP0wFZIRkyXX3Ja6jS\nyQRkNuLWeuBUewfxufPA7ye8155Om1MUhWqUygRkPhdt4iM5y1WSdXMlixsOyNzqS27D6OQ9dNRc\nJhK0f/8sZGcn4X33oeqE4502qaQUdYYsV7KoYUCWy5BVKVnP6upC9vcjKisLGkStoy95EXOGTENm\nzJjhtAklYeCxxyCZJLz3l7U86Ls+hWqUWpvJkI01AVmx+LMlixtZ162+5DaMTt5DR827fn0x8dff\nwDdmDA1XXal12f1IKEYjqz2dDfBrOLQ4d9Zb0eeU1IqVAPgnTSro35SOvuRFVOlkAjIbiSluH66K\n/oceAqDq61932JLiKVSjXCelsWPtNMdRsjPVsi39la2bKe2wMkHuULjVl9yG0cl76KZ59zXX0nfb\n7RAM0njzTfjHjXPapJJTjEbWuvRe5xuTf9dAp7GKaEFfCMkV6cxJoY3OdPMlr6JKJxOQ2cjixYud\nNsF2ksuXE3/9DQiHqTj4q06bUzSFaCSldGXJot+pDNn48QAkV63a4M+40ZfciNHJe+ikec8Nf6bn\n8ivA56Ph2qsJ7zrTaZOUUIxGqSLauDtNrvlWpgqj5OtlMmSBTSYWdL1OvuRlVOmkZnKeR5g2bZrT\nJthO7+1/AympOvIIfJmBvjpTiEbWunUQi+FraMBXpaY2XQWOlSxOTG9eqY0EZG70JTdidPIeOmgu\nUym6fn0xfbf+FYBRV1xO1ZFHOmyVOgrVSKZS6SyTEMqyTHaSPZesqtwymTlb5C9wcLAOvmRQp5MJ\nyGwkHA47bYKtWN3d9P/jXgCqT/+2w9bYQyEaJT/J3HQnq5nWrgrHArJx40AIrHXrkMkkIvDF25Db\nfMmtGJ0CFiTiAAAgAElEQVS8R7lrnvr0UzrO/RGxF/4LoRANV15B1dFHOW2WUgrVyGprA8vC19SE\nCAZttqr0WG2ZjoeKArLUihVA4SWL5e5LhjSqdDIlizayYMECp02wld4bb0L29BDaYw9C06c7bY4t\nFKJRKlMnHpg02W5zHMXXnN60sm17VSGCwfT5BMsitWbNkD/jNl9yK0Yn71HOmkefepp1BxxE7IX/\nIkaNovnuOz0XjEHhGqXWrgX0Lc23IukMWXZvKzWpjz8BIDCpsICsnH3JMIgqnUxAZiOTCkxblyOp\ndevovfkWAOouON9ha+yjEI2SmZuuv8CbbrninzAB2HjpYKkITJkCQHLp0iG/7yZfcjNGJ+9Rjpon\nP/6YyKmn0X7at7Ha2gjtuSdjn3mK8B57OG2aIxSqUSpTDRLQtBoke9bb31z6828ymSTx4YcABLba\nqqD3KEdfMnwRVTqZgMxGmjRsE7shun59MTIapeKgAwnP3MVpc2yjEI2S2ZvuFlvYbY6jZLuNpdau\nRaZSStcObr01AMn3Pxjy+27yJTdjdPIe5aR5csUKOi/4KWv3+woDTz+DqKmh/pe/oPkfd+eaB3mR\nQjVKfpJ5+DhZv2oQmUzmHi76J04o+XrJjz6CeBz/pEkFD6IuJ18ybBhVOpmAzEZaWlqcNsEWok8+\nSfTBhxCVldT/8hdOm2MrhWiUaFkCDAYRbkGEw/hGj4ZUaqMt6EtBYJttAEi8//6Q33eLL7kdo5P3\ncFpzKSWxt96iffa5rN1rb/ruuBMSCSqPOYaxL75AzZlnIPx+R210mkI1ylaDBDbd1E5zlJBaswZS\nKXzjxiIUnPlJvJf+HQcze1khOO1LhpGhSifT1MNGqqurnTahaJKffELHj/8PgLqfXpArLXML+Wok\nk8lcWV1g68LKEsoZ/4TxWJ9+SnLVKvwT1D1RDmZKPJJLhg7I3OBLXsDo5D2c0jyxdBkDTzxB/333\nk/wgk1n3+ag8+mhqZ/8wd08xFK5RctkyAAIaZshSmY6HgU3UlJclMx/SA1MLD8jM/VMPVOlkAjIb\n0b0e2OrqIvLt05GdnYT335/q00512iTbyVej5PLl6bKEiRNd0fb/8/gnTCDxzoJMqYe60tTANuls\nY2LJEmQq9YUn2rr7klcwOnkPVZpb0Sjxt94i9sqrDDzzDMlMpQKkm05UfWMW1SedqGXwUGoK0UhK\nSSIzbym47bZ2m1Rykh9/DKjrhhyfPx+gqIZn5v6pB6p0MgGZjbS2tmrrYFZPD20nnUzyvRYCW2xB\n45+uQ/jcV9Gar0aJd98FBkvs3IZTjT38o0fjnzSJVGsrifdaCE3f7jPf19mXvITRyXuUQnNpWSSX\nfUTi3UUkFi4iPm8e8XlvQyKR+xlRV0fFAQdQ+bVDqfjKV7Rsy66KQjRKrVqN7OxMz9scP65ElpWO\nXAmhgqMFMpUiPnceAKEiho2b+6ceqNLJBGQ20tfX57QJBZFatZrIad8msWgR/smTabrnbnx1dU6b\nVRLy1Sg+Zy4AoV12LoU5jhPI3GSSHy1XvnZot92ItrYSf+ONLwRkuvqS1zA6eY9CNZepFFZbG6lV\nq0guX07yo+UkP/oo/d/7HyA//75CEJyxPeE99iC8z96E99wTEQrZ8DdwP4VolH34GNxuO4QQdptU\ncrIZ1MDUqSVfK/FeC7K3F//kybnmWIVg7p96oEonE5DZyFQFNwK7ib38Cu2zZ2OtXYd/yqY033M3\nAQUdipwiX43ib80BILzrrqUwx3Gymb/kkiXD/KT9hPfYjej99xN79VVqPjd4XEdf8iJGJ++QikRI\nLl3KZokkAy++CIkkMpmAZAoZjyF7+7B6epA9PVg9PVg9vVjtEay160itW4cViYBlbfD9/ePHE9x+\nOsHttyc4fTrhL+2Kb9QohX9D91CIXyYWLgQgOE2/ckUp5WBAqcD++KuvAhAq8nOBuX/qgSqdTEBm\nI5FIRJs2plZPD92XX0nfrbcCENpjdxpvvhl/Y4PDlpWWfDSyenvTNfV+P8GddiyxZc4Q3DZ9o0ks\nWYKUUumT0fDe+wAQe+G/WP39+Kqqct/TyZe8jNHJO8RefJGOH86mb4cdqH7nnYLew9fUhH/sWPxT\nphDYfDMCm00hMGUKgS23xN/cbK/BHqYQv4xlg4wv6ffwMbl0KVZHB76xY3Jl+KVk4JlnAaj4yn5F\nvY+5f+qBKp1MQGYjra2tZe9cMh6n/95/0n3FlVhtbeD3U/ujc6k9+4eIgPv/OeSjUezFlyCVIjRz\n5meCBTfha27G19iI1d5OatUqAhMnKls7MHECwZ13JjFvHgPPPEvVEYfnvqeDLxmMTl7C1zya0MyZ\nrJx1DI11dRAMpJvxBIOIYBBRU4Ovtnbwz9pafA2j8I8Zg3/MWHyjm825L0Xk65dWf3/6TJTPp+Uw\n7fhrrwMQ3vVLJX+oaHV1EXvjDfD7qdhvv6Ley9w/9UCVTu7/BK6QGTNmOG3CBrE6Oui79156b7kV\na80aIJ1ur7/4V4TK2G67yUejgWeeAaDiwANKZY7jCCEIbLMN8ddeI/HuYqUBGUDVkUfQNW8e/Xff\n85mArJx9yTCI0ck7VOz9ZSr2/jJNloXv5JOdNsewEfL1y9jLr0AiQXDHHbQsE40+9TQA4X32Lv1a\njzwKySThvfYq+ndl7p96oEon97XRc5BYLOa0CZ9BDgwQfeopImd8l9U7z6T7N7/DWrOGwNRtaPjz\nDTQ/8C9PBWMwco1kLMZA5iZfccD+pTTJcUI77wRAfM4c5WtXzToWUVVF7KWXiC96N/d6ufmSYWiM\nTt7DaF7+5KtR9OGHAaj86ldLYU5JsXp7ib38MghBxUEHlny9vn/cC0DVN2YV/V7Gl/RAlU4mILOR\nxZkZHk4hpSTx4Yf0/f0OIqeexurpM2g/7XQGHn8cEgnC++xN099uZ8wzT1N1xOFadlIqlpFqNPDU\n01gdHQS23da1Le+zhHffHYBYpuxDJb76eqpOOhGA7ot/g5QScN6XDCPD6OQ9jOblTz4aWT09DDzx\nJACVXz+yVCaVjOiDD0E8TuhLu+IfPbqkayUWv0fi7bcRNTVUHHZo0e9nfEkPVOlkShZtZNq0acrW\nkpZFasUKEkveJ/Huu8TnziM+bx6ys/MzPxfcbjsqjzyCqqOOwj9hvDL7ypWRatR3zz0AVJ94gusD\n19CuM8HnI7FgAVZfHz5FU+mz1J0zm/777if2yitEH3iQqqOPUupLhsIxOnkPo3n5k49G/ff8AxmN\nEtpjd+2GbEvLove22wCoVlBG2/OnPwHpyg5fZWXR72d8SQ9U6WQCMhsJh8O2vp8VjZJauZLUihWk\nVqwkuWIFqZUrSX74IckPPkRGo1+4xjd2DKGZu1LxP/tRsd+++MebIGx9RqJRfNG7xP77IlSEqTrq\n6wqschZfbS2hnXYiPncuseeep/Lwr6ldv6GB+p9dSOdPzqPz/AsITtuWsILhnobisfueZyh/jObl\nz0g1sqJRem++BYCaM88opUklIfrIIyRbluAbN5bKrx1W0rUSH3xA9OFHIBik5vvft+U9jS/pgSqd\nTEBmA3JgAKunhwXLlrH9JptAMolMpsBKpb9OpSAWx+rrQ0b7kX39yL4+rP5+ZH8/srubVKQdq6Md\nKxLBirRjtbcj+/s3uq5v7BiCW29DYJutCe28E6FddsE/caLrMzrFsGDBAnbcceMt7HuuugqA6m9+\nE1+Du8cAZKk49BDic+cSffxx5QEZQNUJx6czZA8+RNtxJ7D6z9ez8557KrfDkB8j8SeDuzCalz8j\n1aj3xptIrV5NcPp0Kg7Qq3mV1dFB18W/AaDu//6vpEPDpZR0XngRSEn18cfZNqvV+JIeqNKpJAGZ\nEKJOStldivcuR6L/+Q8dP5xN9Q47sLbA+SxDEgzinzAe/8RNCGwyEf8mm+DfZCKBzTYjuNVWngkW\n7GTSpEkb/f7ACy8w8ORTiIoKas+y5ymYDlQedijdv/ktA089Taq9Q/k8OiEEDVdcjhVpJ/bSS9Rc\ndTXRri4qDzlEqR2G/BjOn3RGCLEj8F2gEXhTSnnlet/bCTgA6JBS/sUhEx3BzZq7hZFolHjvPXr+\nmC7Bq//1LxE+fVoKSMui4/9+grVmLaGZM21psLExov/6N/FXX8XX0EDteefZ9r7Gl/RAlU6lypCd\nCVxRovcuO0RlJb6mJmrXrEZMmAB+P/j96blefh/CH4BQEF91DaK6ClFVhaiuRlRV4auqSs9raWzA\n19iEv6kp/XVTE6KmxmS7bGZjsySsri46L7gQgNof/wj/mDGqzHKcwKRJhPfbl9gL/6X/nnuo/cFZ\nym0QlZU03nYrHbPPgcf/Q/trr1Nx6KHU//xn2p1t8ApunaEjhNgfuA94JvPSz4QQ3wN2llL2SCnf\nFumb81uApwIyt2ruJobTyOrqov37P4BYjKoTjs81dtIBaVl0/fwXDDzxJKK2lobrrknPwysRyY8+\novNnFwFQd9GFtj6sNL6kB6p0EtmuZiP6YSG+M8If/a6UUrtx7zNnzpRzimj93dLSwtSpU220yGA3\nG9JIWla6I+UzzxCcPp3Rjz7suSGmA889T+Sb38I3bhzjXn4RYcOh5UKQUvLuww/T+L8/SZ+T9Pup\nPPIIqk8+idCuu2r1JNft2HDPK8snTkKIe4EzpZRd6712APAT0vvbciFEPekMmVb/IM0+5342ppGM\nRmk7+ZvEX3+DwNZbM/qxR/BVVSm2sDCsaJTOn5xH9IEHIRik+c47CH95r9Kt19ND29HHkli8mIrD\nDqPxpj/b+pDc+JIeqNrn8s2QNQDHAcuG+bnN83xfV1CtuDudIX+G0khKmX7i9swziFH1NN58o+eC\nMYDwfvsS2HZbku+9R+8tf6F29tmO2CGEoH7nnRnz3xfovuxyog88QPTf6f/8EydSccjBVOyzD6Hd\nd1PeEdLwWVx8z5uzfjAGIKV8BnhGCHGjEOISoAMY+RNNl+BizV3DhjSyOjqInPpt4nPm4Bs3lqY7\n/65NMBZfuJCOs88h+cEHiOpqGm+5qaTBmIzFaD/9DBKLF+PfbDMarrjM9ool40t6oEqnvDJkAEKI\nn0gpLy/2Z0qNEOJMoD3zv5tLKS8b7ppinxwa9EMmk3Rd9HP67rgTQiGa/nY7Ffvs7bRZjjHw0stE\njj8BUVXF6Cf+Q3AL55+tJFesoO/vdxB94EFSq1YNfiMQILjdNILTtye0/XSC06bh32wz5effDEVR\nrhmy3B421JloIcRPSD+Y/KeUsnT1UsNg9jnDSIkvXEj7984itXw5/gkTaLr7ToJbbeW0WcOS+vRT\nui+/gv677wEpCWy5JY03XE9wu9K1IpexGO1n/YCBJ57EN2YMox96wJTNG4phRPtcIQHZ/lLKZ4f5\nmZ2klG/n9cY2ktmkkFLenPn/nUmXmXx3Y9cVu1G1traaQ5plzvoapdra6Dh7NrEXX4JQiMabb6Ly\nQL06TZWC9h/8kOiDDxHcfntGP/QAwoHWvEP5krQs4m+9ReyF/zLw0ssk3nkHLOsL14r6egJTNiUw\nZQr+CRPwjxmDb+yY9J9jxuIfOyZ9htOczywaG+55ZSlCphzxUmApcAmwi5Ry/ud+5ljSAZkjJYtm\nnzNsiPU1kokEvTffQvflV0AiQXDaNJr+fnvZj8RJtrbSe9PN6TlpAwMQCFB96inUXXC+LTPANoTV\n10f76WcQe+klRF0dzff9k9D07UqylvElPVC1z+Xd1GO4YCzzM44FYxm+K6XcJfs/Usp5mfr/ktLX\n11fqJQxFktUo+tjjdF7wU6z2dnzNzTTe+hfCM3cZ5mpvMOoPvyc+dx6JhQvpOPdHNPzpjyU9ND0U\nQ/mS8PkI77Yb4d12o+7887B6ekgsWkRi4SLii94l2dJCcvlyZFcXiXcWkHhnwYYXCAbx1dXhq69H\n1NfjG1WPrz79n6itTTfqqco04KmqQlRVpv+szDTiqapEVFRAOIwIBtMtl0MhzwV5br3nZcoVv5cJ\nzJ75fDCW+Zn7hRBbqLcuh9nnDEOS1Sj22mt0XngRyfffB6D61FOo//lF6XtXGSKTSQaee57+e+9l\n4OlnIJUCoOKgA6n72YUEt9yypOtbHR20fetUEvPm4Rs9mua77ixpJs74kh6o0mlEGTIhxBQp5fLS\nm1M8QohRpA9ai8+9Phc4P3MOYEhMKYf7Sbz3Hl2/+z2x518AILzXXoy6+irb5oq4hfiiRbQdMwvZ\n20vVSScy6g+/Vx6UFYKUEqutjeTy5SQ/Wo61Zg2pdetIrfsUa906UuvWYq37dMih6raQCc7SAVoQ\nEUoHbITTr4lgKP0zmQ6s+AOIgD/9p98HgcB6r/nTv/NA4DNfi0wX18FOrn7w+dLNTnw+EAJ8AsR6\nr/l86Wd0n3lNpP9EfPE1sf712dfSr6//mqiqIrT99sX8xsoqgtVlrzP7nGFjxBe9S8+VVzLw1NMA\n+KdMYdTvfkPFfvs5a9gGSCxdRv+999J/3/1Y69alX/T7qTzySGrP+h7BbbctuQ3JlSuJnPRNkh98\ngH+TTWi+524Cm29W8nUNnqDwDJkQ4mgp5b8zX98InCGE+O7681Yyc1jkUE8OHWZzoHOI19uBnRls\nY2w7kUjEtDEtU+Lz3qb3r3+lbflyqt+ej6itpe7886g+5Vuma98QhKZPp+m2v9J28jfpv+turI5O\nGv94rbInq4X6khAC/+jR+EePJrzrhhu9ylgMq6sr/V9nFzL7dVcXsrc3M7Q9mh7knh3g3h/NvN6X\n/l5sABmLQyKBjKf/JJFAJhJIjzz5HDjkYLb4yy1Om1EwGu91Zp8zfIHEkiV0X3EVkZUrqX7nHURF\nBTU/OIvas75fdlkxq7ub6KOP0X/ffcTffCv3emDzzak64Xiqjjka/9ixSmxJvPcebSd/E2vNWgJT\nt6H5jjvwTyh9SafxJT1QpdOGPomu/0lmKfA94DOlipmyxC2EEP9XItsKpZHBQ87r0wl84TcqhDhT\nCDFHCDFn8uTJtLa2Auma0ZaWFiAtxvz587Esi2g0yty5c4lGo1iWxfz584lEIgAsWbKkqOtbWlrM\n9XZev3gx/f9+gKVnz+bt11+j/+FHiHz9SFbecD11zz1D1Snf4p0FC8rXfoev/6ixgeY776Bvjz34\ncKcdWPeN4+ld/rGS9T/44IOS/v0HLAvR3My7fX30br4ZFQfszyfbTaPjwAOonX023SedyJoTj6fh\n8suQF/+a1nNm03jPXdT+8x+suOxS6p97hrFz3mLdXXcQfu0VJi5fRs+zT5N6+UXGtywm+ezTdD/6\nMGNffZnAE4+z9p//oOmRh6j5132suutOqu++k4Y7/s6aO/6G77ZbabzpRjpvu5WBm29i1NVXMfDn\n6+m46Ubqf/db5BWXsfqWm6j52YWEf/FzVt58I6ELzqNq9tmsvuFPpC44n+ozvkPk8svo++UvqD71\nFPp+cRGRS/5A1UknkTxnNquuvZqK476B/5RvseKP1+H75smEj/o6q666ksQZZ1Bx2GG0/fqX9Pzo\nXCoOOpCec2bT9oufE/7K/xD/5kmsuuxSgvvsAwcfzIqrroCDDiSw+26s/MasovQvA3Td68w+Z67P\nXZ/4cCnLL/4N8559luiTTxI5+ihW/vl66l58gZpzz+GdlpaysF+mUrz7wgssueZaVu+0Mx899xyt\nM2YgqqpInv1D1t5zF80vPEfgtFOZv2KFkt/f4pde4tOjj6Vn7DhWXvoHmu6/j3jDKFfsc+Z6e65/\n7733lOxzQ5YsCiEukVJekPl6ox0TMzX2s9Z/ougkmRr6m6SUW3zu9fuAZVLK8zd0bbGlHJZl4TPZ\nFsdJrV1L35130XfHnViffgqAGFVP9YknUvmtbxIyh2jzIvHee0S+dSqpVavwNTXReMP1JW03DMaX\ndMEGnRwtWdR1rzP7nAHSQ4u7r76W6AMPpBscBYNUn3Qi1T/8AcEyatqRikToz+zJqdWrc6+H9tiD\nqlnHUnnYofhqapTbFZ87j7YTTkT29VFx6KFKq0DA+NJQSMtCxmIwMICMxZBf+DP9NbFY+v+zFSrJ\nJDIRh3jic68lIB5Pv5ZIQiLzdTyR+TqZqWyJp19b/31SSUgk8W2+OWMfeqCYv1ZRTT3Wj9LuF0L8\nGXhKSvkFi6SUXWV4kL1xiNdGAZFSLhqLxah0aJiuYbAsMfroY+nyMSCw7VRqvv1tKo/6Or7KSqKl\nOjvkYoLbbsvoJ/9Dxw9+SOzFl2g74UTqzj+PmrO+X7JyT+NLeuACnXTe68w+51GSH39Mz7XX0X//\nv9KNLwIBqk44gdpzziYwcSLRaJRymKSZWLqM3j/+kf6HHoZ4HAD/lE2pOvZYqo49hoCDD0cT7y6m\n7eRvIvv6qDz6KBquuVr5OWmdfUnG45ky/25kbw+yrx+rry9d0t/Xj+zry5T4p7+WfX1Yff2D3+/v\nHzLgyv47KSeSm6k5SziSLoujgAOB7wohJOna9KeBeUD2MdsugONPDTPMIW3z52kkbXPJWLx4Mbvs\nYjr1qUTG40QfeZTe224j8XbmiIfPR8Whh1Dz7dMI7b77ZzrfGY0Kw9/YSNOdd9Bz5VX0XHsd3X+4\nhMTCRTRccxWiBBuK0UkPXKaTTnud2ec8SGrtWrqvvIr+e/8JyST4/VQdfxy158z+zJwspzVKrlxJ\nzxVXpgNGywIhqDjgAKpPP43w3ns73o021d5B5PTvILu7qTjsMBquvsqRplVO6wTpRliyq4tUWwQr\n0obVFiH16adYkQhWRwdWV3f6bHV3+k+ruwvZ2ZXOUpWKijAiXIHI/hkOIyoyf4bDkP26ItM0KxhC\nhIKZr9N/imAw3fk4GEw3w8p+HQoiApmfCwXTjbZCmUZbn3+fQAACAeYvW4aKRwcjCch+CszKfL0r\ncABwIenNIPt0cdYQ1zmClLJTCLFMCDFKSrn+oedRG+s8ZQfTppWuParhs1gdHfTdeRe9t92GtTbd\nlUmMGpUu1/jWNwlsssmQ1xmNCkf4/dSd9xOCO+5Ix9mziT76KMmVK2j66634x4yxdS2jkx64TCdt\n9jqzz3kLGY3Sc9PN9F5/A7K/H3w+qmYdmw7Ehnh675RGMpmk99a/0nP5FelOtn4/VSedSO1Z3ycw\nZYojNn0eKSWdP/4xqdZWgjvuQON116Q/eDtAqXWSUmJFIqRWrCC1chWplStJrlxJalX669TadViR\nSK6iKC8CAXx1demxMbU16dmeVdX4qqu++HV1NaKqEl9V5uvqKkRlenRMLtDK/Ek47HjA/nmmVVcr\nWWdD/wrX/208vd5csbeB7BDKzYFjgc2zXarKiEtJb67nQ25gZkk3KYCwAwN0vUZq9Wp6/nQ9/f+4\nN/eEJrDN1tScfjqVRx817MBIo1HxVB50IIGHHiByymkk3p7Pp0cdzeh/3Y9/3Djb1jA66YELdNJ5\nrzP7nAeIPvU0XRf9nNTKlQBUHPxV6n76U4JbbngEnhMapdato/37ZxF//Q0AKg47jPoLLyibQCxL\n9JFHGXj6GURdHY033+Ro90m7dJJSklqxgsSiRSQ/+JDE0mUkly4luXQpsrt72OtFTQ2+5mb8zc34\nmpvwNY/G39yEr6FhcFZnfXpup6+uHlFfl57LWWaBU6lQ5U8bCsjeWu/rocoikFIuAy4DEEL8QUr5\nU5ttKxgp5c2ZrlIHkLZ/cynld0u97oIFC9hxxx1LvYwnSUUi9P7penr//ncYiAEQ/p/9qDnzjLxK\nIIxG9hCcOpXRjz1C5ORvkVi4kLbjTqD53/fjt6k1rNFJD1ygk7Z7ndnn3E0qEqHrF78k+uBDAASn\nTaP+V78kvNeew16rWqNESwttJ56EtXYdvjFjGHXZpVQeWPIZ5XkjYzG6L/4NAPU/u5DAxImO2lOo\nTlZfH/E33yT2+hskFi4ksWAhVkfHkD8r6uoITJ6Mf8J4/BMnpv+bMCH93/hx+JuaSnLswE2o8qch\nAzIp5b/W+/pyIcQlwD8+P4dFCFEHzKTEh4gLQUp5s+o1J5nufbYjUyn67riD7ksvzz3pqTjsMOp+\ndE5BwyKNRvbhb26m6e67aJs1i2TLEjrO+iFNd99pSy2+0UkPdNdJ973O7HPuZODFl+g4ezZWWxui\nsjI9M/Pbp4343qpSo8R779E26zisjg5Cu32Jxhv/bHsJu1303/8vUqtXE5i6DVUnnuC0OXnplHj/\nfaKPPU7svy8Sf/vt9BnC9fA1NhKcsT3BrbcmsOWWBLbYnMAWW+BrbvZMJqtUqPKnERXOSikvEEIc\nI4RolFI+t963jgNuyvznecyAP3tJvP8+Hef+iMQ7CwAI77cvdRecT2j77Qt+T6ORvfgbG2i+607W\nffUQYi+/TM+111H34x8V/b5GJz1wm05mrxset2leTshUip5rr6PnqqtBSkJ77EHDlZcT2HTTvN5H\nlUaptjYip5yG1dFBeP/9abr5xrIbQJ1FSknPDX8GoHb22SXrEJwPw+mUamuj/+576H/gQZLvvz/4\nDZ+P4E47Et5zT0I77Uhwxgz8EyaYwKtEqPKnEZ9kXP9J4nqv3SKEWMZgBypP09LSwtSpU502Q3uk\nlPTfey9dP/s5cmAA//jx1P/m11QcfHDRNxyjkf34x42j4U9/JHL8CfRc90cqjzhio+cbRoLRSQ/c\nqJPZ6zaOGzUvB+TAAO1nz2bg8f+AENT++EfUnntOQRUHKjSSUtLxw9mkVq4kuNNOZR2MAcTnzCG1\nfDm+cWOp/NrXnDYH2LBOiQ+X0nPtdUQfeSTXcEOMqqfyq1+l4qsHEd5jD3x1darN9Syq7nlFt5aR\nUj5rhyFuoFpRJxY3I1Mpun52EX133AlA5bHHMup3v7FtaKTRqDRU7P1lqk44nv57/kHXry+m+Y6/\nFfV+Ric98JJOZq9L4yXNVWF1dhL59unE33gz3Wzixhuo2Hffgt9PhUb9//wnsZdewtfYSNOtt5R1\nMAl/2ooAACAASURBVAYQ/Xd6tGDVUUc50uJ+KD6vUyoSofuSS9NjDVKp9Aifgw6k+uSTCe/9ZUQo\n5JCl3kbVPU9IKYf/KY8wc+ZMOWeO5x+AOoYcGKD9rB8w8ORTEA4z6pI/UP2NsugybRgBqUiEtbvv\niezvZ/QTjxdVWmrwDKbGRjFmnysvrJ4e2o4/gcT8d/CNG0fznX8v6Hy0SqxolLW774nV1kbDdddS\ndczRTps0LGt235NUayujH3uEUBk2pYk++hidF/4s3Ybe76fq+OOpPfsHjg7PNtjGiPY554toXURr\na6vTJmiLTCRo//5ZDDz5FGJUPc3/uLskwVg5aySlJLV6NfF5bzPwzLP0P/AA/Q89nD7I+/rrJD/5\nBFnIvBBF+JuaqD75JAB6by5udm4562QYxOjkPYzm9mFFo0ROPY3E/HfwT57M6IcftCUYK7VG/Xfd\njdXWRnDHHag8+qiSrmUHyY8/JtXaihhVT7CMHhS2tramq4J+fTHt3/0eViRCeK+9GPP8czRcdokJ\nxsoEVfc8Z6bhuZS+vj6nTdASKSWd553PwFNPI0bVM/r++0r2hLCcNJJSkli4kIHnnif28isk3luM\n7Oza+EXhMKEZMwjt9iUqDz+c4HbTyuogb/Wpp9B78y0MPP441u9/i6+2tqD3KSedDBvG6OQ9jOb2\nkB5Q/L/EX38D37ixNN97j21t2EupkUyl6L0p3dyz9pzZZbX/bIjYK68CEN5zr7IpVwTo6+mh/Xtn\nMfD44xAIUP/LX1B96ill0XDEMIiqe54JyGzEHHQujP477qT/n/chKitp/ntpyzXKQSOrv5/+e/5B\n39/vIPnhh5/5nhhVT2DTTfE1NaWDGctCJpNY6z4ltWpVOoP21lvE33qL3j9dT3DaNGrPPYeKQw4u\ni5t4YNNNCe32JeJvvEn0P08UnOUsB50Mw2N08h5Gc3vo/fONRB9+BFFdTfNddxKYPNm29y6lRrFX\nXiW1ahX+TSdTcUD5zRobini2U/OuMx22ZBBpWYz5841EH38cUV9P019uIbznHk6bZRgCVfc8E5DZ\nSCQSMS2B8yS+aBGdv/wVAKMuv5TQLjuXdD0nNZJS0n/f/XRfcgnW2nUA+MaMoeLAA6n4n30J7bgj\nvnHjNvrE0eroSJc0Pvss0UceJbF4Me1nfpfQ7rvRcNWVebdHLgWVhx9O/I03iT3/fMEBmfElPTA6\neQ+jefHE571N9x8uAaDhumsI2vyBr5Qa9f/r3wBUHXtsWTwEHAnJlhYAAmV0Nq/3zzfStnQZNdXV\nNN91B6GddnLaJMMGUHXP08ObNMHU1ueHTCbp/N+fQDxO1cknU3VU6WvRndLI6uig/Ttn0PmjH2Ot\nXUdwxvY03nwT4958nYbLLqHykEPwjx8/bPmHr6GBiv2/wqjf/45xc96k/ve/wzd6NPHX32DdIYcR\ne/NNRX+jDZPtDjbw4kvIVKqg9zC+pAdGJ+9hNC8OGY3Sce6PwLKoOfMMKg8+2PY1SqWRtCxizz8P\nQOXh5dE6fjiklCQyAVlw2/LI7sbemkP3pZfR8bVDabj+TyYYK3NU3fNMQGYjM2bMcNoErei77XYS\nixbhnziR+l/+XMmaTmiUWrWaT486hoEnnkTU1tJwzdWMfuxRKg87FBEMFvy+Ihym5pRvMea5Z6k4\n8ABkVxdtJ5zoeFDm32wK/smTkZ2dJN59t6D3ML6kB0Yn72E0L47uq64muXQpga23pu7880qyRqk0\nSixejBWJ4J8wgcCWW5ZkDbtJrViB7O3FN3o0/uZmp81JP4i+4AJIpdi6vYPKA/Uo+/Qyqu55JiCz\nkVgs5rQJ2mB1d9N99TUA1P/2YnxVVUrWVa1Rqr2DT2d9g+QHHxCYug1jnn6Sqln2lnr4GxtovPUv\nVB1/HAzEaD/9DJIrV9r2/vkihCA0M12rn8jU7ueL8SU9MDp5D6N54SSXL6f3L7cC0HDVFSWb3VUq\njWIvvgRAeN99tGjmAZB8/wMAgltv7bAlafruvJNkyxL8kycT/sFZTptjGAGq7nkmILORxYsXO22C\nNvTe+ldkVxehPXan8qCDlK2rUiOZSNB+5ndJLV9OcPp0Rt9/X8na2Aq/n1GXXkJ4v32x2tvpvOCn\nODljMLT9dADiCxcWdL3xJT0wOnkPo3nhdP3uD+kS/VnHlrRMrVQaxee/A0Bo111L8v6lIJV5OOnf\n1L6mKYUi43F6/3QDAPUX/Yz3li1z2CLDSFB1zzMBmY1MmzbNaRO0wOrpofeW9Jyquh//WOnaKjXq\nvfEm4q+9hm/sGJpu/yu+hoaSricCARquvgpRX0/suecZePw/JV1vYwRnpGe9JBYUFpAZX9IDo5P3\nMJoXRvzttxl4/HFEZWXJShWzlEqjxKL0/Tw0o3xmeQ1HtlrEP2GCw5ZA/wMPklq9msDWW1NxyMHG\nlzRBlU4mILORcDjstAla0P/vB9LZsV13Vd7mVZVGyY8+ypVkNlxzDf7x45Ws6x8zhrrzfgJA91VX\nIS1LybqfJzh9OghBoqWloGHWxpf0wOjkPYzmhdFzfTozUn3aqSXfD0qhkdXZSerjT6AiTGCrrWx/\n/1KRWrUKAL9NM96Kof+uuwGo+d6ZCJ/P+JImqNLJBGQ2smBBYedlvISUkv477wKg+tRvKV9flUbd\nV18LsRiVxxxDxT57K1kzS/UJx+MfP55kyxJiL76odO0svpqa9IeORCJXMpIPxpf0wOjkPYzm+ZP4\n8EMGnngSwmFqvnN6ydcrhUaJd9NlW8FtpyEC+kxMyu4/dg3dLpTkxx8TnzsXUVVF5eGHA8aXdEGV\nTiYgs5FJJTof5CYSCxeSWLwYX2MjlYcconx9FRolli4j+sADEAhQ95P/Lfl6n0eEw1SdfBIA/ff+\nU/n6WfxTpgDpbGG+GF/SA6OT9zCa50/fX28DKak69lj8Y8eWfL1SaJS9jwe30qO7YpbUuk8B8I0Z\n7agd/Q88CEDFwV/NNTEzvqQHqnQyAZmNmGGZwxN99DEAKo88AuFAul6FRv133QWWRdWxx5Ssicdw\nVM2aBUIQfeJJrL4+R2wIbDYFgOTyj/O+1viSHhidvIfRPD9kNJr7MF5z2ilK1iyFRsnMLCb/ZOeb\nY+SD1dEOgM/hf7cDTz0FQOURR+ReM76kB6p0MgGZjbRkhg8ahkZKSfSxxwGoPPRQR2wotUYykaD/\nX/8GoDqTpXKCwMQJBHfaCeJxYq+84owNm24KpEs18sX4kh4YnbyH0Tw/ov95AtndTXDHHQhuu62S\nNUuhUeqTTwAce8hYCDKZRHZ1gxD46usdsyPV3pFucBUKEf7yXrnXjS/pgSqdTEBmI9XV1U6bUNYk\n32shtXw5vqYmQrt9yREbSq3RwPMvYLW1Edh6a4I77ljStYaj4iv/k7bp2ecdWd8/bhwA1tq1eV9r\nfEkPjE7ew2ieH/3/uBeA6uOOU7ZmKTQazJDpE5BZXV0gJaK+HuH3O2ZH7OWXQUrCu+6Kr7Iy97rx\nJT1QpZMJyGzE1ANvnIFMg4mK/b/i2M2x1BoNPP00AFVfP9LxwZkV++0L4FiGLBuQpQoIyIwv6YHR\nyXsYzUdOqr2d2GuvQSBA5ZFHDH+BTZRCo9Qn6YBMpwyZ1dEBgL+x0VE74m+9BUB4rz0/87rxJT0w\nZ8g0pDXzBMkwNLFXXgUg/OUvO2ZDKTWSUjLw3HMAhPffv2TrjJTgdttBKETqo4/STwoV48scXi8k\nIDO+pAdGJ+9hNB85A888C5ZFeM89lJbM2a2R1d+PFYlAOJy7r+uA1Z45P1biGaDDkR2oHdzps1Uz\nxpf0QJVOJiCzkT6HmifogEwkiL/xBoDy2WPrU0qNkkuWYK1Zi2/sGILbOT/wUYRC6aAMiL+jvr2u\nf1x647bWrEVKmde1xpf0wOjkPYzmI2fgyScBqPjqV5Wua7dG1pr0QzX/2LEInz4fG8shIJOJBInF\n7wIQmjHjM98zvqQHqnTSx7M0YOrUqU6bULYkFixE9vUR2HxzZUOSh6KUGsXnzgMgvPvujpcrZgnt\nuAMAiXfeUb62r6YGUVWFHBhA9vTkda3xJT0wOnkPo/nIkNEosf+my/QrDzpI6dp2a5SKtAHOdyrM\nF9nTC4Coq3PMhsSS92Eghn/KFHyjRn3me8aX9ECVTiYgs5FIJOK0CWVL/O23ARxr5pGllBrF56UD\nstDOO5dsjXwJbj8dgIRD3Zx8mdp9q7Mzr+uML+mB0cl7GM1HRuytt5DRKMHtt8c/Qe1DSLs1sjLv\n52/WKyCz+vsBEJm5X06QfP99gFy1yvoYX9IDVTqZgMxGTD3whokvXARAcPvtHbWjlBrF52WCzjIK\nyAKbbwFAcukyR9bPPhHMNyAzvqQHRifvYTQfGbFXXwO+2MhBBbafIYuUxyyvfJHRdEDmq6oc5idL\nR3LpUgCCW2z+he8ZX9IDc4ZMQ2Z8rj7YMEhi0UIAQg4HZKXSSEajJD/4AAKBsjg/liWwRSYgW7Ys\n73NcdlBoQGZ8SQ+MTt7DaD4y4q+9DkB4D/Vnpu3WyGrTtGSxrwwyZMvSD0MDm38xIDO+pAeqdDIB\nmY3EYjGnTShL0sHKh+D3E9zW2ZrpUmmUWLoMpCQwZQoiHC7JGoXgb2zA19CA7OvDWrdO+foi01nM\n6syvy6PxJT0wOnkPo/nwWP39xOfPB5/PkTJ9uzVK6Zohy5YsOjjvK1udkn04uj7Gl/RAlU4mILOR\nxYsXO21CWZJoaYFUisBWWyIqnSsdgNJplPzwAwACW21ZkvcvBv+kTQBIrVylfO1shkzmmSEzvqQH\nRifvYTQfnsTb8yGZJDh9O3y1tcrXt1sjqyMdkDk9zytfcgGZQyWLUsrBDNlmU77wfeNLeqBKJxOQ\n2ci0aeVTqlZOJBa/B0Bwu+kOW1I6jZIfpuvEA1uWYUCW6WqZWuVAQNZQWMmi8SU9MDp5D6P58MQX\npMeMhHbayZH17dYo2yVX1NbY+r6lxuqPAiAqnSlZtNrakNEoYtSoIVvvG1/SA1U6mYDMRsJlVKpW\nTuQOtZZB9qhUGiU/+BCAYDkGZBMmAA4FZLmSxfwCMuNLemB08h5G8+HJjhkJ7uDMGSG7NbJ603OY\nfDXqs33FIPszdjt0hiy1NjO/bQOjfowv6YEqnUxAZiMLFqgfvqsDgyn7zRy2pHQaJZcvByAwRCcl\np8kGZEknArLM/Bcrzzlkxpf0wOjkPYzmw5PLkDnUtMFujWRvZp6XZhkyp8+QpVavAcA/buyQ3ze+\npAeqdDIBmY1MmjTJaRPKkuRHy4GhuwypplQapVavBsA/cWJJ3r8Y/OPHAWCtWaN87Wx3q+zGOFKM\nL+mB0cl7GM03jtXRQerjTxAVFQS22soRG+zWKPtATWiXIXP2DJmVzZCNHTogM76kB6p0MgGZjTRp\n1oFIBTKZJPnxxwD4N5viqC1QGo3kwEB6cGYggK+52fb3L5ZsZyyrvUP52qKyAsg/IDO+pAdGJ+9h\nNN848UXvAhCYNg0RCDhig90aZTNkPt0yZA63vU8NE5AZX9IDVTqZgMxGWlpanDah7EitWAGJBP7x\n4/E53GERSqPR+jdd4Ss/l/JlOmOl2tuVr53LkEUH8rrO+JIeGJ28h9F84yQ/SHfcdXLEi90aWb3Z\nph56Zcis/jIJyMaNG/L7xpf0QJVO5ffpUWOqHZx1Ua6kVqwEwD+5PFLzpdAoV664gYO7TuNvzGbI\nIsrXLrRk0fiSHhidvIfRfOPkAjIHGzzZqZFMJGAgBj4foqLCtvdVQjwO4Nhs0OwZMt8GzpAZX9ID\nVTqZgMxGTD3wF8k2ksg2lnCaUmg0GJAN/RTMaXKt59s7kFIqXTvbbtgyZ8hcidHJexjNN06iDEag\n2KnRYEOPWoQQtr2vCmQyAeBY6ag5Q+YOzBkyDWltbXXahLIjVWYBWSk0ynVSKtMMmaisTGeqEonc\nPJn/Z+/Mw+Qqq/z/fWvpvZNOdxIW0ywJSIjQIQnoqLgSQBRxC4srzPw0wWXcRkFEx1FHMQjIIDIE\nYWYEcSGgMwMiEhYZFUSyESA0hCzQnYQsne6kl+rqqrrv74+7VHV3VXdV9Xvf5b7n8zz1JKmuW/d0\nfXPuqXPPec8ri1jQslhZQka+ZAakk32Q5hOTfcndAiWhcJsXkRo5/vqxJrPWjwEARtyEDMmkktPn\netyulFJry8mXzECWTpSQCWRwcFC1CdqR2+VVj47UI1kJQ6Pcq35bgp4VMqBgsEeP3LbF/FCPVEXH\nkS+ZAelkH6R5aZyDB+Hs3QtWX6904q5Ijbj3XqrWYU0Fns0CAJiihIx7+28W2xQaIF8yBVk6UUIm\nkPnz1S3i1ZWgnU+TClkYGvlJTlzDCYs+wQbNkitk+aEelSVk5EtmQDrZB2lemswWrzo2b57SAU8i\nNeLpNACYt34MADLqKmQ8lQIfHgZqasBKDDQjXzIDWTpRQiaQHsnVBxPI7darZTEMjZxed5x8qbtg\nOsCa3EWpvH9A7nkLhnpUsn6NfMkMSCf7IM1Lk9u+HQCQmHusUjtEasQVD8aYCkGFTMEaMufgQQBA\nrKWl5No78iUzkKUTJWQCoX7g8eRbFvVIyMLQKJ+QtQh/b1HEvA09nUHJCVky6d6dzOWCiVflQL5k\nBqSTfZDmpcl2dwMA4oqHNYjUiA97FTLDEjLOOeAlZCoqZI7frthS+nsB+ZIZ0BoyA+no6FBtglbw\ndBr84EF3w2RNqkdhaORvuOzv96UjQYVsQH7Put+uUcnoe/IlMyCd7IM0L01up7fNi8L1Y4BgjbyW\nRdTWiHtPGfjJWDyuZDpkPiGbXvI15EtmIEsnSsgEkvYvXAQAwOlxNyKOtbVqMy43DI2MaFlsdCdk\nyV5DBgCswU3InAoGe5AvmQHpZB+keWn8hCwxZ45SO0RqFKwhM61CFlTHFI28L6NCRr5kBrJ0imxC\nxhhbzBhbLfOcmzdvlnk67cl5GxHrVDkSrRFPp90pVIkEWHOz0PcWSazZTci4gqlOQSAfKf+iRr5k\nBqSTWijO6UWu26+QqW3RF6kRHzEzIQs2hU6ombAYJGTTS1fIyJfMQJZOam4dhAhjbDGAC71/zpV5\n7gULFsg8nfYE0wdb2xRbkke0RoV3wXSpAhaDeXvIyN6HDABYjRvIeQVryMiXzIB0UgPFOf3gnCO7\ny0vIFFfIRGpkeoVM2ch7b3nARDdqyZfMQJZOkUvIOOfrAaz3AtZSmeeuNeyCFTaFLYu6IFojx5ta\nqHN1DMhv6umoqJDVuGsPKknIyJfMgHRSA8U5/XD27weG02At05VvoixSI1OHeqgceQ+Ut38b+ZIZ\nyNIpsi2L5cIYW84YW8sYW3vUUUcF01S6urrQ2dkJwB15uXHjRjiOg1QqhXXr1iGVSsFxHGzcuDEY\nifnXv/51Ssd3dnZG6vhtcfe/18BrX6uN/Rs2bBB6/mde3Y3BhQsRa2rS7vMvPP6Fo9rB43EM53LS\nz99/wgnovvIK5IbTZR//t7/9TavPj44vfvzjjz8+peMJOVCcC//4/du3o/vKKxBvP0q5/SLjXC6d\nRveVV+DQEUdo/fmPPX7D9u0YmT0bqK1Vcv7n5811z9/URHHO8OOlxTnOeSQfABYDWFfJMUuWLOFT\nYf/+/VM6Pmoc/MFK3n3kHH7wuh+pNiVAtEbDf/oz7z5yDt/7ofOFvq9oBv/nf3n3kXP4/k8ul37u\nvR/8EO8+cg4f/svjZR9DvmQGAnRSHitMflCc04eh/73XvcZe8veqTRGq0aF/u4F3HzmH933/KmHv\nKYPMtm28+8g5fPcb36Tk/L1fv5J3HzmH99/2HyVfQ75kBrLinPUVMpG0temzVkoHcn7LokZDPURr\n5O/rFfPGyutKrNEbe58qf/S8KPIti+UP9SBfMgPSyT5I8+Lk9uwBAMS9SpJKRGpk6sbQ+U2hFbcs\nNpZuWSRfMgNZOlFCJhC/dEm4ON6UxbhGFx3RGgULdxWvGZgMP5jydPnruISRrHwNGfmSGZBO9kGa\nFye3bx8AIDZrlmJLxGpk6lAPZBSPvfcSslhj6e8G5EtmIEsnbYd6MMaWAzi/zJefzznvC9Oecmhs\n1LtKIht/yqJOFTLRGvn7eqlexD0p/qaeCvY9YcG5y0/IyJfMgHSaGhTnooPjJWTx2bMVWyJWI1MT\nMp51h3roXCEjXzIDWTppm5Bxzm8BcItqOyqhvb1dtQlaESQrE+zDIRvRGgUXXc0TsnyFTEFC5rcs\n+lOvyoB8yQxIp6lBcS465PbtBwDEZs1UbIlYjUydsshHFE9Z9LtnJvgyT75kBrJ0opZFgfiTVwgX\nHoyE1ydZEa0RH/B+R0rISp+7ijVk5EtmQDrZB2lenKBCpkHLolCN/Ou2YQkZ/AqZqpbFoclbFsmX\nzECWTlFOyKT3yQ0q2ONJZ5wBt0LGmvTZo0u0Rs6AP9SDErKS+Hco/Z7+MiBfMgPSSTkU5zRBpzVk\nIjUytmXRjzfKWhbdAVoTtSySL5mBLJ20bVmsFsbYXAAr4G6WuZgxtgruWODQ20Lmz58f9imMgXMe\nVMhiGlXIRGuUr5Dp3QseJGQVVKmEnTvhXmb8qVflQL5kBqSTGijO6QV3nGDNdHym+pZFkRoFUxZr\n1CQ2VaO4QlbOxtDkS2YgS6fIJWSc820ALldx7p6eHhpj6sFTKSCXA6urA1PUw10M0Rrx4WEAAKuv\nF/aeoVBbByC/HkAqXkKGChIy8iUzIJ3UQHFOL5y+g0AmAzZtGlhdnWpzxGqUzbl/Kqo0VYvyCplf\nWZzg/wP5khnI0inKLYvSoX7gPNwb6MGa9WlXBEJYQ+YnZBoE4YlgKqcsVlEhI18yA9LJPkjz8Tg9\n7kAPHapjgFiNeM7bzyseF/aeUvD3IVNVISuj1ZN8yQxoDZmBdHR0qDZBG4IJi5olZKI1ChIyzfvr\nC9eQcc7lntyvkFaQkJEvmQHpZB+k+Xic3l4A+mzxIlSjnF8hMysh86f6qhh7z3M5wJ8q7A21Kgb5\nkhnI0okSMoGkVQxM0JR8hUyf9WOAeI3KaUvQAZZIAPE44DgVJUZCzu3dWa2kQka+ZAakk32Q5uNx\n+tzt4WItLYotcRGpEfdaFlnMrIQsSIgUVMj8dXeoqwVjrOTryJfMQJZOlJAJZPPmzapN0AbHH+ih\n0YRFQLxGplTIAIWTFoMpi+XvQ0a+ZAakk32Q5uNxet2EjGmSkAnVyDG0QhYM9VCwhixoV5z4Ri35\nkhnI0okSMoEsWLBAtQnaEEwfnKZXQiZaI1PWkAGFkxZH5J7Xr5D5rS9lQL5kBqSTfZDm48lXyKYr\ntsRFqEb+UA/T1pDlHPdPBXaXu1UA+ZIZyNKJEjKB1BpQJZGF038IgH77c4nWyJSWRQD5jT1lT1qs\nokJGvmQGpJN9kObj4Zq1LIrUyL+RZlzLon8DUIHdwfeCCdaPAeRLpiBLJ0rIBLJp0ybVJmiDvweZ\nblMWRWuUb1nUPyFjdX7L4rDc8wZTFsuvkJEvmQHpZB+k+Xh0W0MmVKOcPz7erISMO26FjMXlf80t\nt0JGvmQGsnSihEwg7e3tqk3QBl2nLIrWyE/IYECFjNUoWkMW7ENWfoWMfMkMSCf7IM3H4xw8CECf\nlkWhGils/ZsS/jThmL4JGfmSGcjSiRIygdAGf3mCKYuatSwK12jYb1nUv/VA1VCPavYhI18yA9LJ\nPkjz8ehWIROpkbH7kAUtiwoSMn9ZwCQJGfmSGcjSiRIygXR2dqo2QRv40BAAgDU2KrZkNCI14pyb\nNdTD62eXPdQjXyErPyEjXzID0sk+SPPx6JaQCdXI1AqZ17IIpuBrrhdjJ7tRS75kBrJ0ooRMII2a\nJR8qcVJ6JipCNfITm5oaMAV34SrG348lI3kfMr9CVsF5yZfMgHSyD9J8PLolZCI1Cjob4vL385oK\nateQlbcdDvmSGcjSyYBvkeZA/cAF+JWj+nrFhoxGpEYm7UEGACzhTjvkFazlEoK/GDxXfkJGvmQG\npJN9kObjcfrcNWRsuh4JmVCNvH3IVCQ2U4LWkBGCoDVkBtLV1aXaBG1wUikA+iVkIjUyqV0RgLIK\nWTB22G99KQPyJTMgneyDNB8N5xz8kLfNiyb7bgrVyJ+OmzCrQqZ0DVmZY+/Jl8xAlk6UkAlkcHBQ\ntQnawL2ELKZZQiZSo3LvgukC81pOeAWVKjHn9TaGdsofe0++ZAakk32Q5qPhQ0MA52B1dUF7tmqE\nxjlT9yHz15ApHeox8c1a8iUzkKUTJWQCmT9/vmoTtIFrWiETqZFpCZmyCpnf6pIrPyEjXzID0sk+\nSPPR8AFvz02NJgoL1ci/bpu6D5mK9d1lfjcgXzIDWTpRQiaQnp4e1SZoAx/2EjLN2vmEauQnNkk9\n7opORn78vOQ1ZP50Lqf8lkXyJTMgneyDNB+NM+DePWdN+gxoEKqRn5CZNmVR5Royf8pi7cQti+RL\nZiBLJ0rIBEL9wHl0rZAJXUPmJTb+sAztSXp2yq6QeWOHOa0hixykk32Q5qPhg26FLNaoT4VMaJwL\nWhYN+7qocg1ZxvtukJz4uwH5khnQGjID6ejoUG2CNuQTMr0qZEI1ogpZeecNKmTltyySL5kB6WQf\npPlouIYVMqEa5Qwd6qFwDVmw5+YkCRn5khnI0okSMoGkvb5hAuApPcfei9TIuApZsEFz+YmREII1\nZOVXyMiXzIB0sg/SfDSOt+CfaVQhE6qRoS2LKteQ+Xu3sUk+M/IlM5ClEyVkAtm8ebNqE7SBa7oP\nmVCN/AqZIXcOla0h86Zz8QqGepAvmQHpZB+k+WiClkWNKmQiNQpaFg1LyFSuISu3qki+ZAaydKKE\nTCALFixQbYIW8GwWGBlxL4ST7MMhG5EaBRUyQ1oWVa0hq6ZlkXzJDEgn+yDNR5NvWdSnQiZUI0Mr\nZFqsIZvkMyNfMgNZOlFCJpBaU8afh0zhhsmMMcXWjEaoRsGGmWa0LOYrZKrG3pffski+ZAak0LGo\newAAIABJREFUk32Q5qNx/LH3jfpUyERpxDk3NyHz15DFFVbIJllDRr5kBrJ0ooRMIJs2bVJtghYE\nAz00G3kPiNXI3AqZ/i2L5EtmQDrZB2k+Gu6tIYtpVCETplHBYAzdbq5Ohr+GzJ/yK/Xc/k3PSZJY\n8iUzkKUTJWQCaW9vV22CFuT34NDv7o9QjfzWv7gZCZnfPlFJYiTyvJW0LJIvmQHpZB+k+WjyG0Pr\nUyETplHWrHXSo3DcNWRKxvX76+4m+dzIl8xAlk6UkAmkra1NtQl6kHYTMkyyKaIKRGpkXIXMT4wk\nJ2SIeXdWK9gYmnzJDEgn+yDNR+NPWdRpHzJRGqmcVDhlHHVryIIulEkqZORLZiBLJwO9TF86OztV\nm6AFfMQdEcpq9KuQidSIB1MWzVhD5gcH+WvI/ESw/ISMfMkMSCf7IM1Ho2OFTJhGZbbeaYnCNWTB\nZMpJ1pCRL5mBLJ0oIRNIo0aLelUStCxqNmEREKyRv9eIIRWyfOtg+YmRkPP6a8gqaFkkXzID0sk+\nSPPROAP67UMmTCNTN4UG8nFOwRqyfKvnxIks+ZIZyNKJEjKBUD+wC/dbFjVMyIRqlDWzQia9ZbGK\nKYvkS2ZAOtkHaT6a/D5k+iRkojQKKj0Gtiyq3Rja37uN1pBFAVpDZiBdXV2qTdCDoEKmX6IiUiNu\nWIXM76WXPdSjmkSQfMkMSCf7IM1HE0wVrtdnqrAwjaJQIVPRbumtL5+sQka+ZAaydKKETCCD3uJe\n2+EZfVsWRWrkb/5oSrBS1bJYzdh78iUzIJ3sgzQfTeG+m7ogTCN/r00Ve3lNlWBkv/xx/UGFbJLu\nGfIlM5Clk4Fepi/z589XbYIW5NeQ6TfUQ6hGQYVMv0pgURS1LDI/mFeQCJIvmQHpZB+k+Wh0TMhE\naeSv+52s9U5LVK4hy5W3hox8yQxk6UQJmUB6enpUm6AHGq8hE6kRL3O0rTb4vfQGtCySL5kB6WQf\npPloeNqbKqxRQiZMI4OnLPKc+jVkk+1RSr5kBrJ0ooRMINQP7JLfGFq/hEyoRoZVyIKNoaW3LFZe\nISNfMgPSyT5I89HoWCETpZGf1JiYkIGrX0PGaA1ZJKA1ZAbS0dGh2gQt0HnsvUiN/AoZM2QNmbKW\nRX+YSAVj78mXzIB0sg/SfDR+QgaNEjJhGnmtd8zEhEzhGrJg7d0ka8jIl8xAlk6UkAkk7bUu2I7f\nwoGkfgmZUI38xMaQCll+/LyqlsXyK2TkS2ZAOtkHaZ6Hcw4Mey2LtfqsmRamUTBl0eCEjCkY6uEn\nspN8buRLZiBLJ0rIBLJ582bVJuiBxi2LIjUyrULmL8yWPva+ipZF8iUzIJ3sgzQvwK+O1dZqtVeX\nKI3y+5AZmJBx/y8qK2QTfzcgXzIDWTrpcwWJAAsWLFBtghYEiYqGLYtCNfIXPFOFbGL8LyqcT/y6\nAsiXzIB0sg/SPI+O68cAgRr5scLAlkXuxxsVFTJ/DdkkQz3Il8xAlk6UkAmkVqOWBZXovIZMpEY8\n47clmFEh8/cDq6R1UATMC4icl39e8iUzIJ3sgzTPk0/I9PpMhGkUDPUw8Kuil5AxBQlZUCFLTvzd\ngHzJDGTpZKCX6cumTZtUm6AFwRoyDRMyoRp5d8Emu+jqQn7KouQKmR8QnfIrZORLZkA62QdpnkfH\nkfeAOI2CibwmtixCYYUsGIYy8XcD8iUzkKUTJWQCaW9vV22CHgRryPS7+yNSo6BCZsqmmQa1LJIv\nmQHpZB+keZ6gQlarV0ImTCOvq0FJlWmqKGxZzK8hmziRJV8yA1k6UUImkLa2NtUmaIHOLYtCNcr5\na8hMScjUtCzmK2Tln5d8yQxIJ/sgzfPo2rIoTCM/qdFoYEnZqFxD5q2jn2xjaPIlM5Clk4FeNjmM\nseXeY5X3aJFx3s7OThmn0Z4gIdNw2IVIjfJryPT7PYvhT8qS3rJYRYWMfMkMSCd1UJxTj65DPYRp\nFIyOF/N2UgkSMgXn9qdTTnKzlnzJDGTpZMit/fJhjC3nnN9S+G8A6wDMC/vcjY2NYZ/CDLyEDBqO\nvReqkV8hM2WPFlUti1VUyMiXzIB0UgPFOT3QNSETphFVyKrDn8A8SYWMfMkMZOlkoJeVptgdQi9o\ntTLGloZ9fuoHdgn2LtGwciRUI9MWPCtqWQymLILWkEUN0kk+FOf0QdeETJhGjsKkZqqobFkMvgPR\nGrIoQGvIqmMugGKtG9u8n4VKV1dX2Kcwg6y+lSORGnHDgpX6jaHLT8jIl8yAdFICxTlN0HXKojCN\ngjZzM2JcUVRWyCbZEod8yQxk6cR4Bes6TIAxtphzvn7Mc70AzuecP1Tk9csBLPf+eQKAF6Zw+pkA\n9k/heCJ8SCMzIJ3MYKo67eecv0uUMbZAcY6YBNLIDEgnM5AS5yKXkI2FMbYMwBWc8yUSzrWWc35q\n2Ochqoc0MgPSyQxIJz2gOEcUQhqZAelkBrJ0ilrL4ii8lo4rAJyh2haCIAiCEA3FOYIgCPPRdsqi\n12JxfpkvP59z3lfk+ZUT/IwgCIIglEFxjiAIggA0Tsi8qVG3TPrCEjDGLgOwknO+TZxVk1K1vYQ0\nSCMzIJ3MgHSaAhTniJAgjcyAdDIDKTpFcg2Zd9fxocIgxRhbWmyxM0EQBEGYBsU5giCI6KBthaxa\nvH1Y1vpByuuvp0WTBEEQRCSgOEcQBBEtIlUhY4zNBbC1xI9nUI89QRAEYTIU5wiCIKJHpBIyVXit\nIwe8f87lnF+t0h5iPJ5GAOCPhb6cvrjoDWNsNee83IEHhGS89Ut98K59nPO71VpEhAnFOf2hOGce\nFOf0Rmaci1zLomz8C6AvEmNsMWNsFed8hVrLCB/G2HJv8XzwbwDrAMxTZxUxEYyxxQCWqbaDKA5j\nbDXcL3t+yxxnjFF1JqJQnNMfinPmQXFOb2THuUjvQyaJFYUXQc75egBLFdpDFOCtrRiFp1ertw6D\n0JNW1QYQxfG+6D01ZrLfPErGIg3FOY2hOGcsFOc0RUWco4RsCngXwcVFftRHF0FtmAtgVZGAtc37\nGaEZjLFlNClOa1YCGNW2IXnsOiERinNGQHHOMCjOaY/0OEcJ2dSYC7e3dCwHUDyAEZLx7uQuKXJX\nYy7cYEVohNfCsV61HURxvC98Ld7flzHGljLGLit2h56IDBTnNIfinFlQnNMbVXGO1pBNjVbkFzkX\n0gegTbItRAm8YBXAGFsGYBvdndKSuTQcQmv8L+ctBeuJ1gJ4GPlBAkS0oDhnABTnjILinN4oiXNU\nISOswrvDcQWAM1TbQozGa+GgIKU3rXDvHAZ33f278tS+RhB6QHFOXyjOGYGSOEcJ2dQptiizBUCP\nbEOIslgJ4HwaQKAX3t5K1FqjP9uAfHAqgNrXog3FObOgOKchFOeMQUmco5bFqbEWXp/pGFpB/cHa\n4e0nsZIGEGjJUgAtY+8++XuAFE54I9TBOd/GGCv1Y/ryF00ozhkExTmtoThnAKriHG0MPUUYY1sx\nZjEtY2wr55z2/tAIb4TpQ4VBijG2lPrr9YUxxjnnJa+KhBoYY+vg3n0v9KWt3nP0BT2CUJwzA4pz\n5kFxTk9UxDlqWZw6K+H2agMIpufQxU8jvLtRaws29xt3h4ogiLK53HsACK552ygZizQU5zSH4hxB\nCEV6nKMKmQC8u1Lb4LZ1zOWcX63YJMLD69neWuLHoe24TlSP9yViBYBlcPcBWUV3ePXCm+Dm72/U\nxjm/fKLXE+ZDcU5fKM6ZB8U5/ZEd5yghIwiCIAiCIAiCUAS1LBIEQRAEQRAEQSiCEjKCIAiCIAiC\nIAhFUEJGEARBEARBEAShCErICIIgCIIgCIIgFEEJGUEQBEEQBEEQhCIoISMIgiAIgiAIglAEJWRE\nqDDGljHGeIWP1artJiaGMbacMdai4Ly9Y/6vLJvk9Vu9/ZPKff/Lpm4lQRA2QXEumlCcI2RCCRkR\nKpzzuwHMAHBmwdMPAZjnPT8PwBIAhZuMSr8AEuXjfZE4U9Fmo8fC/T8z6bkZY4vhbup4VwXv3+cF\nN/o/SBBEWVCcix4U5wjZJFQbQEQf74L2EGPMf2oN53yb93f/grOeMbYGwBrZ9hHlwxhbBWAu53yJ\nivN7/5f6GGNrASyd5OUXAniokoDKOb+FMbYEwDq4AZEgCGJSKM5FB4pzhAqoQkZoA+f8IQDrAbSq\ntoUYj9c2sRzA5aptKZPlAKppC7ocwFwvKBMEQQiD4pzeUJwjVEEJGaEbvwa1cujKTwGs975QaI3X\nxtGCyto4AAR3J68GsNx7H4IgCJFQnNMXinOEEighI5TCGGthjPGCpx4C3TnUDu+uYQtcfUyg4jaO\nMfgtRSsE2UMQhKVQnDMDinOESighI1Qzqj+ac74ewFWMsZVjpwx5QW21txh13dgFqd5EpDXe69dN\nNEmIMXaZ9xruHbOs4PmV3t/H2rC04PhRE7NKnGNCe7yfF77PcsbYYu+YXu/3XDnB77C84HcY9Vrv\ncyp8715/ClORn5U8RwH+BfupMTZUpJP3s5Xez3y71k00RapAq17vs5lbhr3LAYxqxfBs88+71Xvf\n1SV+/7UF70MQBDEVKM5RnKM4R0wM55we9JDyAMC9x2Xev5cC6HX/G457bQvcyUG93jHL4N7NaSl4\nbnnB61cVPue9Nwewush7r/Zf672fb8dlY95jrA1Lx9jnn6OY/WXZ473/Vu9na7xzrfJs8c+7qsj7\nr/E/yzG2rCp4zfKCz7xlzPHL/M+1Qu3mVquT99xW7zHXe24x3IXFo/QsotU6771Xeu/rf2bj7Pfe\nk495ztd4ccHn7n+GK0v8zr79i1X7Dj3oQQ8zHqA4R3GO4hw9qngoN4Ae9jwKLnbjHhMc419M1hRc\n8PyL1FLv3/5Fd82YY1cWCTD+a1eNee2yAnuWjvnZumLPF/5OJd5rUnvG/I5jbV1c4v39ALS64LnL\nSrzW/6yWj3n+MgDrytStpcC+lhKvqUSndWOO9YPs2M/Lf35rEdt9e4oFqlUY/4Vg1VjNC2wsFahK\nBkN60IMe9Cj2oDhHcY7iHD2qeVDLIqGCq+GOWj0fZeyz4bGUc36L9/clAJbw/KJbvxQ/dlrQmjE/\nL/z7qKlE3N1HRhSV2FPIQwW/E7jb1tIHAGPaF4q9vz9eeezv4b927MSoFQCuKmHHWIK1DnzyXvWJ\ndNpW4pgD3p9jWzR8m0d9jpzzqzExF8BdNF9IK4ALirSMXA6gp8T7+L9rOa0jBEEQhVCcKw7FudFQ\nnCMA0D5khBp6uLs/yzbGWCvGX9CLUXgB74M7NtjHv5CMvRD6Pd2Ly3it/5yIi1Il9ow9/1gOeMe1\nAG5vesH7BK/3Ai0bd7Q7fWkV3PG2iznn65m3kaTg4OxTUifv3DP8YOcF38VwFyYD4xe5n+r9Wexz\n6UORKWXe+oeWIr/bGrh3Llczd5+gh7zn7g7pcyAIwm4ozhWH4txoKM4RAGioB6Gecse1ri/25Jg7\nav7CX38B8uqC17WMee0BhEAl9hQ5fF0Zpwjen+c3HS2JFxT8C/EV3p8rANxS/IiiBJ9VCbsLKapT\nIYyxVYyxXriB4kyUvqPon6vY3cpSx5yP8XdP4d3NLLzjuBTuXdWt/iLwCc4/6edMEAQxARTnCl5f\nxikozrlQnLMISsgIpfD8XhiTUarcXhhwZnDOWYlH35jXFhs5XNEY4hIX7UrsqYbguDKnMAH5lo1l\nns0VbSTp2eqfd7LPqJRO/p4pvXBbLc7gnM/jnK/A+LYLn4k+o1IBc9zUKe/cSznnl3POGdzgeHXB\n+5e6c+3/rhSoCIKoGopzFUNxzoXinEVQQkYoh3M+tu+7GEUvFmMu+KcWe413gRz72sVjXlPYIlEu\n485XiT3VMOZu4dKxP/dGBI/6Pbweff+4hwH08co3vfTH405m+0QXdT84fsqzyadU8PPfq1hAHvec\n18aBEr/b6sKfe0FrBrz+/bFBv/D/wxhbCYIgKobiXPlQnAugOGcRlJARUcC/8zgu4HkXp9VFXjt2\nI8SJ9uEodcEM3mNMcKjEnmoo+v7ee68scVfSX/S8GJW1cfj4d9dOq+JYH//zG2uf/3uM/aLg3/Ec\npdWYBcuFQW6yFpVii8wfAoq2xfhfMqr5rAiCIERDcQ4U50BxLrpUO56RHvQo9wH3AlU4bne191zR\n0bJjjvVH8V5W5uvWwA06fu90sCdHwWu3FtixFO542a0osg+L9/pgLC3cC/1ieONlC36n5YW/T5X2\njBtLW2DTsoLnWgqO2erZ77930dG1GD3Sd+5En+UEn3EvxozmrUQn5EcGb/U+j+XecYXjkFdi9L47\nawqe9/8fFe7Pstr/3ItpV+RzXIPRe7SsQ/Exwf7o5qo+K3rQgx52PSjOUZzzXkNxjh5VPZQbQI9o\nP8YEqGKPohcCjN7s0X+UvBB7x1xWcMHs9S5ipd5/VUFwWoPRG1cW24dlacF7r0N+089RNlZiT4nP\nptcLKpcV+dnYfUr838G/+E+4j4j3+jUTvaZMLQv3kClbJ+/3Wu393P/clxe8d6/3eS0bc9zKMVot\nxujgxgFcAqB3Att7veP84Oh/ZsW+HPhBfVwAowc96EGPsQ+KcxTnCl5LcY4eVT2YJwxBWA9jbCvc\ngHUmr7z3XHsYY6sB/JpPYfwtY2wV3EA1T5xlemHD70gQhJ1QnCvrPSIfA2z4HU2D1pARREQpXMDr\nLbBeOpUgBQDcnRb1kBf0Ioc3Gngp3M0+CYIgCI2hOFc5FOf0hBIygoggXiDZWrAw+Kcosvi6Grxg\ntaaMvVqMhLtjiqsd10wQBEFIgOJc9VCc0w9qWSQID28TxxYAK7i7waKxFLSlXA33d2rlnJ+v1iqC\nIAhCJRTnCEJPqEJGWA9jbBVjjCM/jnaVd6E3mRVwx+4ug7sfCwUpgiAIS6E4RxB6QxUygiAIgiAI\ngiAIRVCFjCAIgiAIgiAIQhGUkBEEQRAEQRAEQSiCEjKCIAiCIAiCIAhFUEJGEARBEARBEAShCErI\nCIIgCIIgCIIgFEEJGUEQBEEQBEEQhCIoISMIgiAIgiAIglAEJWQEQRAEQRAEQRCKoISMIAiCIAiC\nIAhCEZSQEQRBEARBEARBKIISMoIgCIIgCIIgCEVQQkYQBEEQBEEQBKEISsgIgiAIgiAIgiAUQQkZ\nQRAEQRAEQRCEIighIwiCIAiCIAiCUAQlZARBEARBEARBEIqghIwgCIIgCIIgCEIRlJARBEEQBEEQ\nBEEoghIygiAIgiAIgiAIRVBCRhAEQRAEQRAEoQhKyAiCIAiCIAiCIBSRUG1AWDDGlnt/XeL9eTnn\nvE+VPQRBEAQhEopzBEEQ0SCSCRljbDnn/JbCfwNYB2CeOqsIgiAIQgwU5wiCIKJD5FoWGWMtY5/z\nglYrY2ypApMIgiAIQhgU5wiCIKJF5BIyAHMBrCoSsLZ5PyMIgiAIk6E4RxAEESEil5BxztcDWFKk\nj34u3GA1CsbYcsbYWsbY2gsvvJB3dXVxALyrq4t3dnZyALynp4dv3LiRO47DU6kUX7duHU+lUtxx\nHL5x40be09PDAfAnn3xySsd3dnYadfyuxafyJ2+6ie/butUY+5977jkh5+976GHefdQx/Klf/NIo\n/bre/0H+xG238UPPP6/k/NsXLeFP3HYbHxocnPD4devWafn50fGjj3/88cendHw513RiPBTn5B6/\n7sEH+YvvPpcf+McvGGG/qDiXSqX4nvecy5+86Sa+Z+1ao/R76tFH+fZFS/jeiy+Rcv793d38yZtu\n4jsXnFT28RTnzDheVpxjnEc/JjLGlgG4gnO+ZKLXnXrqqXzt2rVVnyeVSqG+vr7q401j1wkngg8M\n4Ijnn0Ns2jTV5pSFKI2GH34EPZ+4GLXveDtm/vwOAZbJYc9b3obstm2Y/dijSB53nPTz72w/GnAc\nHPnKDrB4vOTrbPMlUxGgExNli+1QnAuPwV/8En1fvQwNF16AGdddq9qcSRGp0d73nIvMxqcx677/\nRc2iRULeUwbDjz6Kno99ArVveytm/uLO0M/nHDyI3QtOAps2DUc+/1xZx9joSyYiK85FrkI2Fq+l\n4woAZ4R9rtra2rBPoRV8eBgAwAz6vYVpFPP8y7AbGvkbMIq+B8e8S47jTPgy23zJVEgnPaA4Fy58\nZAQAwGpqFFtSHkI1Yv4126xYB/+GX27iWCMMP6ax8mOrjb5kIrJ0inxCBmAlgPNljALetGlT2KfQ\nBp7JANmse9EzJEgBAjXyL7qTJBba4SVkLKbI9cv83GzyJZMhnbSB4lyYeAkZasz4Ai1SIz9WcMNi\nHYu5CRnP5aScL3+vs/yEzEpfMhBZOkU6IWOMXQZgJed8XE99GLS3t8s4jRbwoSEAAGtoAKvgAqQa\nYRr5CY1hNw3B/bt4is4fLy+42+RLJkM6qYfiXPgEFbJaM24+CtUoiHVmJWR+rIEjJyHzP59Kvg/Z\n6EsmIkunyCZk3p4sdxcGqbDHAbe1tYX59lqRT8jM6n8Wp5GpFTLvT0VJNIt7Wx9msxO+ziZfMhnS\nSS0U5+RgWsuiUI1ihsa6hBdrZLUs+iWyCmKrjb5kIrJ0imRC5gWktX6QYoy1yNibpbOzM+xTaIMz\nlAIAsPoGxZZUhjCNvIuucUNxfHtVtSwmykvIbPIlkyGd1EFxTh48nQZgTkImVCOv9c+0NWT5lsWJ\nY40w/IR1gmFVY7HRl0xElk4JKWeRCGNsLoA13t/H/nhGmOdubGwM8+21gqfcClmswayETJRGwRos\n0xKyKhYei4QlEuCYvK/fJl8yGdJJDRTnJBOsITMjIROpEStzEJN2+C2LktaQBeeJlR9brfQlA5Gl\nU+QSMu9uoZJvmzb1Awcti4aNbBWmkf8lyLS++iraKoSS8O4eTlIhs8mXTIZ0UgPFObnwTAaAORWy\nMNaQmTbUQ/aURf/z8Stz5WCjL5kIrSEzkK6uLtUmSKNwqIdJCNPI0LH3qhMyfw0ZnyQhs8mXTIZ0\nsg8bNTdtDZlQjYI1ZJIqTYIIWhZl2e1XyCpoWbTRl0xElk6UkAlkcHBQtQnS4P4aMsOGegjTKBjf\nblZC5q95Y0yR6yfLW0Nmky+ZDOlkHzZqztNmtSwK1Shm6D5kCcn7kAUJWfmx1UZfMhFZOlFCJpD5\n8+erNkEaPOUnZGZVyIRpZOoaMsVj7/MVsonvWtrkSyZDOtmHlZqPeEM9DBl7L1QjZuoasvLa40XB\n/cSvgpZFK33JQGTpRAmZQHp6elSbIA1TWxbFaeRNWTQtSCkee58fRTxxkLTJl0yGdLIPGzUPWhaT\nZiRkIjViZe4dqRvSWxa987AKWhZt9CUTkaUTJWQCsakf2DF0qIcwjZjha8hUjb33ghXP0BqyKEA6\n2YeNmnPDpiyKXUMmeYNlUQRTFvVtWbTRl0yE1pAZSEdHh2oTpOFXyEwbey9KI/+uoXFBSvXY+2R5\nFTKbfMlkSCf7sFLzEW/KoiEti0I1ivvrfg2LdcGURTl2V9OyaKUvGYgsnSghE0ja2zzSBvjAAACA\nNTcrtqQyhGkkeaSuMFSPvS8zuNvkSyZDOtmHjZrzEbM2hhapEUtI3mBZEH7roLSWRW99diUtizb6\nkonI0okSMoFs3rxZtQnScPrdhCzW1KTYksoQpVEwnELWppOiUNyyyBL+5zZxcLfJl0yGdLIPGzXP\nj72vVWxJeQjVKJF0/5ykzVw7gqEe+m4MbaMvmYgsnSghE8iCBQtUmyAN3n8IAMCmmVUhE6ZR0J9u\nVkLGg42sFW8MPUlwt8mXTIZ0sg8bNTdt7L1Ijfw2c57NCHtPKUhuWQy6ZSqokNnoSyYiSydKyARS\nW2vG3TMROAN+hcyshEyYRsG0QLMSMijuWGTe3dbJKmQ2+ZLJkE72YaXmQYUsqdiQ8hCqkaEVMhaT\nOx3Sb41kFawhs9KXDESWTpSQCWTTpk2qTZAGP9QPwLwKmSiNgpG6hvXVK19DliivjcQmXzIZ0sk+\nbNScZ7yhHoZUyERqlK+QGRbrpFfIKp+yaKMvmYgsnSghE0h7e7tqE6ThDLgJmWkVMmEaJQwf6qFq\nDVm8vOBuky+ZDOlkHzZqnh/qYUZFQ6hGfjdIxrCWRdldLFW0LNroSyYiSydKyATS1tam2gRpmFoh\nE6aR7LtvolA89j5fIZs4IbPJl0yGdLIPGzXnw96UNUPG3ovUKBjEZFiFLGhZlDb2vvKWRRt9yURk\n6UQJmUA6OztVmyCN/Boys6YsitIoGKlLLYsVEawhmyS42+RLJkM62YeNmvPhFACAGbLvplCNTK2Q\nyb5p6lTesmijL5mILJ0oIRNIY2OjahOkwB0HvN+rkBm2D5kwjUzfh0xRy2K+1XPihMwWXzId0sk+\nbNOcOw7gVciYIUMYRGrEkuXdRNMOA6Ys2uZLpiJLJ0rIBGJLPzAfHAQ4B2toqGgTRB0QplGZa6F0\nIxh7r3hjaD7JxC5bfMl0SCf7sE1z7m0Ky+rqgjY43QllDZlhsa5QKxmTFoNzVNCyaJsvmQqtITOQ\nrq4u1SZIgXubQpu2fgwQpxHz2xIkjdQVht+xqOj0LFHeXUtbfMl0SCf7sE1znvLaFevrFVtSPiI1\nMrZCBsgd7BGMvS8/utrmS6YiSydKyAQyODio2gQpON6m0KZNWAQEamToXUP1LYvenjaTfG62+JLp\nkE72YZvmJiZkQjXyh3qYtoYMyLcPyojTVbQs2uZLpiJLJ0rIBDJ//nzVJkjB8Stkhq0fA8RplN90\nkqYsVoJfIZtsGIotvmQ6pJN92Ka5iQmZSI38CplxNx8heXNovwpXQcuibb5kKrJ0ooRMID09PapN\nkAL3K2TNZk1YBARqFC9vg2PtCPrcVVXI/IldEwd3W3zJdEgn+7BNcxMTMqEa+ROFJ7lma4nEwR7+\nzVlWwZRF23zJVGTpRAmZQGzpB3b6+gAAsZYWxZZUjjCNZG86KQDOeT4hUzSMpdztAmzZS/dQAAAg\nAElEQVTxJdMhnezDNs1NTMjCWEOGrMEtizLidBUti7b5kqnQGjID6ejoUG2CFJwDvQCAWGurYksq\nR5RGwQQnzuW0Q4igoF2RqZqyGAT3iQOkLb5kOqSTfdimeZCQ1dUptqR8hGqUKG8yro7IbFkMhp74\n66TLwDZfMhVZOlFCJpC0Nx436jgHDgAwMyETqpFpVTLfToVbFQQVsknWI9jiS6ZDOtmHbZrnK2Tm\nJGQiNWJJf4CVgRUymcO3vHMEk4TLwDZfMhVZOlFCJpDNmzerNkEKTq+5FTKhGsmc4CQCDRKycgOk\nLb5kOqSTfdimOR8eBmBWy6JIjVjCH3tvyI3HQvz1XDkJFTJ/CmUFFTLbfMlUZOlECZlAFixYoNoE\nKQQVshnmrSETqVFQ7TGkZdG3U+nmpmVWyGzxJdMhnezDNs15yryETKhGBlfIWMyP0TLWkHlDPfzP\nqwxs8yVTkaUTJWQCqa2tVW2CFExeQyZUI6qQVUywQHySNk9bfMl0SCf7sE1zE9eQiY1z5q4hkxmj\ngwpZBfHVNl8yFVk6UUImkE2bNqk2QQo5g9eQCdUomBhoRoVM9YTFwnNPtsmoLb5kOqSTfdimOR/w\n9t1sMmebF5EambyGzL8BKGVTa38NWbL8lkXbfMlUZOlECZlA2tvbVZsghWAN2QzzEjKRGvktizBk\nc2iueFNoAGD+naZJAqQtvmQ6pJN92Ka5MzgIAIg1Niq2pHyExjl/DZmJFbLaGgAAT4+Efy6/ClfB\nDU/bfMlUZOlECZlA2traVJsQOpzzgqEeMxRbUzlCNUqY2bLIVLYs1vgBcuKpRTb4UhQgnezDNs15\nfz8AgDU3K7akfIRqlJQ4qVAwfrzBSPgJGa+iQmabL5mKLJ0oIRNIZ2enahNChw8NAek0WF0dYgYt\ncvYRqVGwYNiUlkUd1pB5FbLJEjIbfCkKkE72YZvmzoBbIWMGVciExrlgyqKBLYt+vBmRMLY82Ies\n/KEetvmSqcjSiRIygTQadMGuFmf/fgBAzNA7O0I1CvYhM+POYZA4KpyyGATI4YkDpA2+FAVIJ/uw\nTXM+4FbIYs3mrCETqpFfITOwZZHV+AmZxApZBQmZbb5kKrJ0ooRMIDb0A+f27AEAxA47TLEl1SFU\no2CPEzPWkPlr3VS2LKLMCpkNvhQFSCf7sE1zHlTIzEnIxK6V9qYsGlghQ428NWT5fcjKT8hs8yVT\noTVkBtLV1aXahNDJveomZPHDzUzIRGoUBCpTEjIdWhbrvKEekyRkNvhSFCCd7MM2zR2/QmbQlEWh\nGplcIauVt4YsWKNdQUJmmy+ZiiydKCETyKA3jSnKOHv3AgDihlbIhGrkJzaGJGRatSxO0tNvgy9F\nAdLJPmzTPKiQGdSyKFKj/DVbQlIjmGCIlIw1ZFVUyGzzJVORpRMlZAKZP3++ahNCx29ZjM+erdiS\n6hCqUbDppBkJmQ4ti+UO9bDBl6IA6WQftmnuDLr7kMUMalkUqZG/ITYfHhb2nrLIJ2R6Tlm0zZdM\nRZZOlJAJpKenR7UJoZPb41bITF1DJlIjP7HhhuxDFmwMrUOFbJKEzAZfigKkk33Ypjnv9zeGNmcA\ng9A4Z3BChhq/RV5CQjZSeYXMNl8yFVk6UUImEBv6gZ09tIYswLh9yLyELK7Q7WvKm7Jogy9FAdLJ\nPmzSnGcy4IODQCwGZukasnJvoumIv4ZMSrul9/n4CWw52ORLJkNryAyko6NDtQmhk/PXkBnasihU\nI8P2IfMref7+aSood6iHDb4UBUgn+7BJc+fQIQAAmzYNTGFnQaUI1ai2FmAMGBkxZ4CVR9CyKCGZ\n5Gm3ghjEuDKwyZdMRpZO5lxhDCBt4B2kSuCcI7dzJwAgfsQRiq2pDpEaMb9CZsg+ZFpMWSzzbmvU\nfSkqkE72YZPmTm8fACDW0qLYksoQGucYM3awh9Q1ZH6FrLb8hMwmXzIZWTpRQiaQzZs3qzYhVJze\nXvDBQbBp04wLUD5CNQqmLJpRIdOhZbHchCzqvhQVSCf7sElzfvAgACA2w6x4J1wjr+rDU4atI5Na\nIas8IbPJl0xGlk6UkAlkwYIFqk0IlZzXR5uYM0exJdUjUiPT9iEL7FTZslhmQhZ1X4oKpJN92KS5\n0+dVyKZPV2xJZYjWKFgXZdhgjyA5klohK38NmU2+ZDKydIpsQsYYW8wYWy3znLUV3BkxkdwrbkIW\nbzc3IROqkV9pMqVlUYOx90gm3fUI2eyEiWzUfSkqkE5qoTgXLkFCZlhHiGiNgkmLaTMTMl1bFm3y\nJZORpVPkEjIvQK0EcCGAuTLPvWnTJpmnk062uxsAEG9vV2xJ9QjVyKuQUcti+ZS7HiHqvhQVSCc1\nUJyTg6kJmWiNgmu2aRUymWvI/MnBFXx5t8mXTEaWTuVvmGAInPP1ANYzxhYDWCrz3O0GJyrlkHvl\nFQBAwuDfU6RGzEtsuCEVMp5190lhifI3rgyFulq39WV4GKivL/qSqPtSVCCd1EBxTg6mtiyK1ihf\nITNsCEWwhkzm2PvyEzKbfMlkZOkUuQqZStra2lSbECrZl18GAMSPMvciIlSjpHuxh78hpO5kvMQx\nqfY+jB/cnaFUyddE3ZeiAulkHzZp7uzbBwCIzZql2JLKEK2RqZtD+/uQYUTPoR42+ZLJyNKJEjKB\ndHZ2qjYhVLJbXgIAJI87XrEl1SNSI6mbTgogXyFTm5DFGhoBAHxosORrou5LUYF0sg+bNM95CVnc\nsIRMtEbGtix6HRg8Vfrmnyh4FRtD2+RLJiNLJ+sTMsbYcsbYWsbY2qOOOirYkburqysQoaenBxs3\nboTjOEilUli3bh1SqRQcx8HGjRvR09MDABgcHJzS8Z2dndoev2HdOmT37MHIa16Dpw/0GGe/f3xN\nTY2w8/O6OnRfeQV6wc34/UcyGJk9Gy+de65S/bZ/+lKMzJ6N3MBAyeMzmYx+nx8dP+74vr6+KR1P\nyIHiXHXHD49kwONxPD+t2Sj7RcY5x3Gw/bzzMLhwIXg6bcTv7x+frm8Aj8exdenS0M8/cMJr0X3l\nFeDJZNnHU5wz43hZcY5xzst+sUl4vfU/5ZwvKfeYU089la9duzZEq8xlZONG7HvPe5GYfwIOe/gh\n1eZoQd/Xr8Tgz27H9O99F02XXKLanEkZ+u1v0fu5z6P+vPei9d9vUmbHvmUXYOSJJzDz179C7elv\nVmYHoQVMtQEmQ3EuXF5945uRe+UVHPan/0Ni7rGqzVHGgUs/jdS992HGTTei4X3vU21O2Yxs2IB9\n556H5MIOzL7/d6Gdh+dy2HXUMQBjOLLrZTBGlzViFGX9h7C+QiYSP2uOIlFoVwTEapRv4zBjoTP3\n15ApHuoRa3RbFp0JWhaj7EtRgnSyD1s055zn15DNNqtlUbRGMlv/RMK8WMMHh0I9j79sgdXWVpSM\n2eJLpiNLJ0rIBDI4WPoLpulkXnITssTxxym2ZGoI1chfvGvK5Kmsm5CxGrUJGWvyguRAaS2i7EtR\ngnSyD1s054OD4KkUWF1d8MXeFERrxJqaAEx8zdYR1uja7QwMhHsif21dBRMWAXt8yXRk6UQJmUDm\nz5+v2oTQyG7ZAsD8hEykRkGFzJCEjGe8aZCKK2T5u5alL3JR9qUoQTrZhy2a56tjs41rQROtkX/N\nDj2xEUyssQEAwIdCrpBVMWERsMeXTEeWTlFOyFpln9Bf9BdFMs88CwBInniiYkumhkiNjNubxa+Q\nKR57H7QsDpYO7lH2pShBOimH4lxI+BMWYzNnKrakckRrFGtuBgBwwxKy4ObfwADCnJfgT59kNZUl\nZLb4kunI0ilyCRljbC5jbCWAlQAWM8ZWMcaWyzh3VPuBc/v2IbdrF1hjIxLz5qk2Z0oIXUMWbDpp\nRkKWr5Ap3oesjL7+qPpS1CCd1EBxLnxyu18FAMQPm63YksoRvoasILExCZZMuksLHCffVhgC3NtT\nk3kVuXKxxZdMR5ZOar+ZhQDnfBuAy1Wcu6OjQ8VpQyfz9CYAQPLkk8DiccXWTA2RGgUti4bsQ5av\nkOmyhqx0cI+qL0UN0kkNFOfCJ9fdDQBItLcrtqRyRGvkV8hMa1kEgFhDA5x0Gs7QEOLecBLROP2H\n3HM1NVd0nC2+ZDqydIpchUwlaUMqJZUysslNyGoWLlRsydQRqZF5Uxb12hjamWANWVR9KWqQTvZh\ni+Y576543MCETLRG5dxE05X8QJLwbOf97nuz5qaKjrPFl0xHlk6UkAlk8+bNqk0IhZGNTwMAkgvN\nv5sjVCNDpyxCdYVs+jQAAD90qORroupLUYN0sg9bNM96FbL4nNcotqRyRGsUC6YVmjcV0G8jDHNC\npDPQDyBfSSwXW3zJdGTpRAmZQBYsWKDaBOHwXA4j3iaiNYsXK7Zm6ojUiNX5UxbD600XSbBXirf2\nTRWxlhYAgNN3sORrouhLUYR0sg9bNM91eS2Lc8yrkInWyK/8mFghi01zbwA6h0rHm6mSr5BVlpDZ\n4kumI0snSsgEUlvhyFMTyDz3HPjBg4i3txvZSz8WkRoZN/a+ytG8osknZH0lXxNFX4oipJN92KA5\n5zxYQ2ZihUy0RtL28wqB2IwZAADnQG9o5/A/l1hTZS2LNvhSFJClEyVkAtnkrbWKEunHHwcA1L75\nTYotEYNIjYybspj2KmS6JGS9pQNkFH0pipBO9mGD5s6+feDDw2At04MKi0mI1ijmV8j6+4W+rwxi\nre7OEBPFm6nit99XWiGzwZeigCydKCETSHsEKkhjSf/FS8jeFI2ETKRGrNawfcj81kpdErIJKmRR\n9KUoQjrZhw2aZ7e8BABIzjtOsSXVIVqjwmt2mPt5hUFQIQsxIQsqZBUmZDb4UhSQpRMlZAJpa2tT\nbYJQnFQKI48/ASA6FTKRGhnbslinNiFj06YB8bi7Wae/N9oYouZLUYV0sg8bNM9seREAkDjezIRM\ntEasttbdiyybNa5KJiMh8z+TSqcs2uBLUUCWTpSQCaSzs1O1CUJJP/YY+PAwkotOQfzww1WbIwSh\nGtV5FbKh0hsc60SQkCke6sEYQ2z6dACAc7D4Quuo+VJUIZ3swwbN/QpZ4vjjFVtSHWFolF+LdUD4\ne4eJlArZoer2IbPBl6KALJ0oIRNIo7ebfVQYfuAPAID6s89WbIk4RGoU9NUbMgo4mLLotVqqJAiS\nPT1Ffx41X4oqpJN92KB55sUtAIDka1+r2JLqCEOjWGv4iU0YxGZ47ZZhDvXocZPU2MzKKik2+FIU\nkKUTJWQCiVI/MB8eRmrNGgBA3dlnKbZGHELXkHn94qZMnvI3sFY91AMAYocdBgDI7dlT9OdR8qUo\nQzrZR9Q155wj690RT7zWzApZGBrlK02l1/7qSHzWbABAbt/e0M6R278fABBrm1nRcVH3pahAa8gM\npKurS7UJwkg9uAa87yCSr3udsXcJiyFSI1ZXB8TjQDptxDoyPqzHUA8AiB/uJWS7Xy368yj5UpQh\nnewj6prndu6Ec+AAYjNmIP4a80beA+FoZGzLorfcolSsEYHf6RGfVVlCFnVfigqydKKETCCDg2a0\nrpXD0F13AQAaLrpQsSViEakRYyxYxOsYoD1PuWvdYg0Nii1BsCbRKVEhi5IvRRnSyT6irnnmaXfE\ndXJhBxhjiq2pjjA0inmDDXIl2sx1JT57FhCLuVsZlBgiNRX48LA71COZdAdWVUDUfSkqyNKJEjKB\nzJ8/X7UJQsju3IX0Hx8DampQ//73qzZHKKI1ijW7F2ATJk/xoRQAgDXUK7Ykn5DlXi1+1zIqvhR1\nSCf7iLrmI08/DQCoWbhQsSXVE4ZGwU20EtdsXWHJJGKzZgKcI7dXfNuin6DG2toqTuCj7ktRQZZO\nlJAJpMewO0elGLz1VoBz1J/zLsS9hbxRQbRGrMmrkPXrv47MnwbJdKiQ+WvISgT3qPhS1CGd7CPq\nmo+sXQsASJ5yimJLqicMjeJH+K1/u4W/d9gENwB3ibfd2bfPPcfMytoVgej7UlSQpRMlZAKJQj+w\n09uLwZ/fCQBo+vSliq0Rj2iN8pMWTaiQ6ZOQBX39JVoWo+BLNkA62UeUNXeGhjCyfgMQi6H2Da9X\nbU7VhKFR/IgjAIS7FissEkcfDQDI7dgh/L1z3TsBAPE5la83jLIvRQlaQ2YgHR0dqk2YMgO33gY+\nNITat70VNSefrNoc4YjWiHn7juheIeOOA57yWhbrdWhZnLhCFgVfsgHSyT6irPnIk08CmQySHScH\neyWaSBga5RMy8ypkiePcDb4zL70k/L2z3e6X9ficORUfG2VfihKydKKETCBpAybtTURu924M3LwK\nAND8hc8rtiYcRGsUVMg0X0PGh4cBzsHq6sDicdXmuC2LiQScPXvheIliIab7ki2QTvYRZc3Tf/4L\nAKD29NMVWzI1wtAoXrBVCc/lhL9/mCSOmwcAyG7dKvy9c13d7jmqGI0eZV+KErJ0ooRMIJs3b1Zt\nwpQ4eNVK8OFh1L37HNS+4Q2qzQkF0RrFWrxNJ/v03puF9x0EALDplU2BCguWTLptJJwjt237uJ+b\n7ku2QDrZR5Q1H374EQDmJ2RhaMTq6txJi9ksHG/fLVNIzPMSspfEJ2TZV/wKWeUti1H2pSghSydK\nyASyYMEC1SZUzfCjjyJ1zz1ATQ2mX/l11eaEhmiNYt5CXt0DlHPQTRj9BFIHEvPmAgAyRe5amuxL\nNkE62UdUNc+88AKyW7aAtbSg9u/MviEZlkZB2+LOXaG8f1gk5rqxJrtjh/DR99ktW9xzeG2RlRBV\nX4oasnSihEwgtRpsuFsNTm8v+r56OQBg2lf+CYljjlFrUIiI1ijYm2W/3tOSnINuhUyndRHBXcsi\nCZmpvmQbpJN9RFXz1L33AQDq330OWDKp2JqpEZZGiWOPARBO61+YxBoaED/2WCCTQeb554W9rzMw\ngFxXF1BTU9X3pqj6UtSQpRMlZALZtGmTahMqhudyOPC5f0Ru924kFy1C04rlqk0KFdEaxb2EzDmg\neULmtVRqlZBN0Ndvoi/ZCOlkH1HUnDsOhn7zGwBA/bnvUWzN1AlLo8TxxwMIZzhG2NSeugQAMPLU\nWmHvmX3hRQDuzUWWSFR8fBR9KYrI0okSMoG0V7GoUzWHvn8V0n98DLHWVrSu+veqLiomIVqj2Ewv\nITOkQsam69OymDz+tQBQ9I6lib5kI6STfURR8/RjjyH38iuIz5lj/PoxIDyNgptoBiZkNaeeCiC/\nz5wIRjZudN/7pNdVdXwUfSmKyNKJEjKBtHnVElPov+HH7lTFeBytN/87Eq+pfFGqaYjWyF9DlvM2\nh9QVp0+/lsXkghOBRALZF16EMzB62wDTfMlWSCf7iKLmA//5MwBA48c/psUU2qkSlkbJ49wKWXaL\ngQnZ608DAKQff0LYlEg/ufOTvUqJoi9FEVk6UUImkM7OTtUmlAXnHIeu+xEOrbwaYAwzbrgetW9+\nk2qzpCBao/js2QAAZ88ecM6FvrdIuL+GrEWfhIzV17tJGefIbHpm1M9M8SXbIZ3sI2qaj2zahPTD\nD4PV1aHhwxepNkcIYWmUmHsswJg7HGN4OJRzhEXi+OMRb2+Hs3+/u/n3FOG5XLBNgp/sVUrUfCmq\nyNKJEjKBNDY2qjZhUng6jb6vXob+a68DYjG0XHM1Gt7/ftVmSUO0RrFp08CmTwdPpeAcOCD0vUXi\n9PYC0GvKIgDUnHIKAGBk/fpRz5vgSwTpZCNR0/zQD68BADRecnGwJth0wtKI1dcjccJrgVwOI88+\nF8o5woIxhrqzzwIADN9//5Tfb2T9BjgHDiB+1FHB2rpKiZovRRVZOlFCJhDd+4EzW7dh33nvx9Av\nfwVWV4fWW29B40XRuCNYLmFo5Ld65rq7hb+3KHKvvgogv7mnLgRtJN6dRh/dfYlwIZ3sI0qapx54\nAOlHHgVrakLTpy9VbY4wwtSoZtEiAEBmzE00E2g47zwAwNDqu6dc4Rt+4AEAQN2ZZ4IxVtV7RMmX\nogytITOQrq4u1SYUhWcy6L95Ffa96xxknn0W8aOOwsx7VqP+7LNVmyadMDSKt88BAOS6DEjIvH1k\ndKH2rW8FGEP6ySfhDA0Fz+vqS8RoSCf7iIrmTn8/Dn7jnwEA0y6/DHFvPXAUCFOjmsWLAQAjG6be\n9ieb5OJFSJ58MpzeXgzdfU/V78OHhzH067sAAPXnvbfq94mKL0UdWTpRQiaQwcFB1SaMgnOO4Ycf\nwd6z3oVD3/1X8KEh1L//fZj9h98HrWK2EYZGce/uSXbHDuHvLYrcbi8hO/xwxZaMJt7WhuTCDmBk\nBOk//Sl4XjdfIopDOtlHFDTnnKP3y19xt3tZ2IHGiz+h2iShhKlRjTc+Pv3EX8EdJ7TzhAFjDE2f\nXgEAOHTtdeOGSZXL0Oq74fT2InnSSahZsrhqe6LgSzYgSydKyAQyf/581SYAcBebpn7/e+x793vQ\n84mLkX3xRcSPOQZtd9yO1p/ciNi0aapNVEYYGiW99xS54aRI+MgInP37gVgMsdmzVJszjvpzzgEA\nDN39m+A5XXyJmBjSyT6ioPnAj2/E8P33gzU3o/XGGyMxWbGQMDVKHH884kccAWffPmSeM2sdGQDU\nn3cekosWwdm7F4e+9/2Kj3f6+nDommsBAE2f/UzV7YpANHzJBmTpRAmZQHp61O5Fle3uxqFrrsWe\nN7wRBz65HJlNzyA2axamffNKHPbwGtS98x1K7dOBMDRKnqh3QpbbtQvgHLHZs7XcZ67hQx8EYjEM\nP/QQcgfc4SOqfYkoD9LJPkzXfPD2O/IThn90rTs5MGKEqRFjDLXvfCcAYPjhR0I7T1gwxtBy1feA\nmhoM3n4HBn9+Z9nH8lwOvf/0FTj796PmtNNQ/95zp2SL6b5kC7J0ooRMILL7gTnnyLy0Ff03/gR7\nz30v9rzhjej/0fXI7d6N+DFHY/p3v4PDn/gLmi+9FKyuTqptuhKGRokTTnBHAb+0FTydFv7+UyW7\ndRsAIHnccYotKU78iCNQ+5bTgZERDP361wCot94USCf7MFVzzjn6b/wJ+q74OgCg5arvB9X5qBG2\nRvVnnQkASP32v7Xe7qUUNSefjJbvfgcA0Hf513Do+n+bdG8ynkqh94tfwvADfwBrbsaM66+bUnUM\nMNeXbEOWTvrdLjeYjo6OUN+fOw6y27Zj5G9/Q/qJv2LkiSeQ2707+Dmrq0Pd2Weh8SMfQc2b3ggW\no3x7LGFoFKuvR+LYY5Hdtg2ZF15ATcj/Dyols2ULACBx3DzFlpSm6ZOfRPqx/8PAzavQeMnFofsS\nIQbSyT5M1Nzp70ff17+B1G9+AzCG6d/+FzR+/GOqzQqNsDWqfdtbEZs5E9mXXkJmw0bULF4U6vnC\noPFjH4UzOIhD3/ku+n94DYYf+AOaP/sZ1C49A7H6+uB1TiqF4QcfRP911yP70ktgDQ1ou/2/kDjm\nmCnbYKIv2YgsnSghE0g6nUZ9gSNXC3cc5Ha/itzLLyO7fTsyzz2HzHObkdm8GbxgEh0AxGbMQO07\n34n6c85G7dvfPupCQoxHlEZjqVmyGNlt25B+4q/aJWTZICHTs0IGALXveDuSpyxEZuPTGFh1C5Ir\nloeiEyGWsPyJ0BfTNB/+vz+h7/KvIffKK2B1dZhxw7+h/j3vVm1WqIStEUsm0fChD2Jg1S0YvPNO\nIxMyAGhesRzJ+Seg98v/hMwzz+DApZ8GamuRmDsXsZbp4If6kdn6EjDsdr4k5s7FjH//CWpOOknI\n+U3zJVuRpRMlZALZvHkzlixZUvRnPJsF7++HMzAA3j8Ap/8QnH37kdu3D87evcj5j65uZF95BSjR\n+hY/4ggkFy1C7ZveiNq/ewMSJ5xAlbAKmEijqVB7+ukYWn030n/+M5pXLBf+/lNhZONGAEDy5JMV\nW1Iaxhimf/3r2H/Bhei/4cfYfdppOPXNb1JtFjEJYfkToS+maJ554QUc+sFKDD+4BoB7/Ztx4w3a\ntm6LRIZGDR/9KAZ+eiuG7vkNmr/8pWA/TtOoe9vbcNif/4ShX/0aQ3ffjczGp5Edsx48ecpCNFxw\nARovuhCstlbYuU3xJduRpRMzsf83LE499VS+du3aio8bfvRRHPrB1Ug3N6Fm337wbAbIZMFzWffP\nwcGKNyGMzZyJxDHHIH700UieOB/J170OyZNeh3hra8X2EXlSqVQodzpyr76KV5ecBtbQgCM2bQTT\n5K6X09+P3Se+DkgkcGTnZu3XEvZ+6csYums1nL97A17zs/9CrKlJtUnEBAjwp6ktwiAqpto45xPW\nNVQE3HGQ/svjGLjlp0g/4g6cYI2NaP78P6Jp+afAamoUWygHWRod+Nw/IvXb/0bDhy/CjGt+GPr5\nZOAcPIjs9u3gQymw+jokjj0WsZaWUM6lsy8ReWTFOaqQCcA51I/Ms8+CxePIlloYGouBNTcj1tQE\n1tyEWFMzYjPbEJ81C7HDDnP/nDUT8dfMQeKYo+mLaEjUCry7VUj88MORXNiBzNObkHpwDRred14o\n56mU9J/+DHCOmo4O7ZMxAJj+nW9jZMNGZJ5aiwMrLkXbbbcaYbethOVPhL7opjl3HGSeew6p+36H\n1G//G7mdOwG4a6obLroQzV/4POKzZyu2Ui6yNGr+4heRuvc+DP3yV2i48ALUnnaalPOGSWz6dGn7\ntOrmS0RxZOlECZkA6t76Fsz6/e/wbH8/Tp41CyyRBJIJsHjC/bOxEay+fsoTeYips2nTJpwS0sW2\nYdkyHHx6E4buukubhCz1hwcBAHXeVCzdiTU3o+0/bsO6hx7CnG9/B/s/fjFaV92MeOsM1aYRRQjT\nnwg9Ua055xy5HTswsm490n/+M4b/+BicffuCn8fnzEHDRRei8eJPWNtRIkuj5HHz0PyZT6P/hh+j\n94tfwuzf3RdaNSmKqPYlojxk6VRVQsYYOwXAqQCe4pw/XfDcSgCtAG7mnN8mzMCrhowAACAASURB\nVErNic2YgZoZM3B0Tw+SbW2qzSEmoL29PbT3rn//+3Doe99H+o+PYeTZ51Bz0utCO1c58FQKww+5\n6yfqzj5LqS2VkJh7LI55w+vhzJqFkccfx76z34UZ/3Y9at/0RtWmEWMI0590hTH2Fc75Nf6fqu2R\njUzNnVQK2ZdeQvbFLci8+CIyz3cis349nN7eUa+LH3EEas84Aw0feB9qXv9669dVy9So+Qufx/Aj\njyLz7LM48NnPoe2//hMsmZR2fpOx8fppIrJ0qngNGWPsQwBWA+gD0ALgZgBfA7DeewDAYgA/4Jzf\nKs7U8Jlqbz1B9H3rXzB4622ofctb0PbLO5VWRQfv/AX6LrscyYUdmPW7+4yr0GZ37sSBSz+DzHr3\nslJ/3nsx7atfjeRGrhaj3X9KxthX4d5YLMViuLFuGef8eDlWiUOHOMcdB/zgQeQO9MLp7YXTsx+5\nXbuR27kTuV27kNu5y/1z926gyHeU2MyZqFmyGDWvPw11b3+7O9zKsOtblMh2d2Pfu94Np7cXdee8\nC603/cSa9XoEUQahrSFbyjkPbj95weunAJZwzg8WPH8zAKMSsqnS2dmJ+fPnqzaDmICwNWr+x89h\n6O57kP7TnzD0y1+h8SMfDu1cE8FTKfT/+EYA7h5fpn1Z8XWadc9q9P/kJvTfeCNS/3svUvfeh7qz\nzkTjxz+G2tNPpzuxionoNe9uAKsAbAWwrcjPGQDremizr7yC9BN/xfbmJhzbc8DdSNd7+H/n2Sx4\nKuU+hoYKHik4Q0Pghw65CVhfH+A4k580mUTi2GOROP54JF97PBLHH4+axYsQnzPHuGuaTGT7ZWLO\nHLTdeQf2X/QRDP/+Aey/8CK03rIK8VmzpNlgIhG9fkYOWTpVk5CtL/wH5/yHjLGvFiZjHuuqN8tM\nGhsbVZtATELYGsVnzkTLd76N3s9/AX1XfgOJo45C7elvDvWcxTj4g5XIdXUhceKJqD/vvdLPP1V8\nnVhNDaZ96YtouOB89F/3Iwz95rcY/sODGP7Dg4i1tqLuXWej9vTTUXv6mxGndmHpRPGaxznfDuAs\nxtgZAFo45/cU/pwxFsQ9NRaqYWT9evR9+Z+Ac96Fvt8/MOX3Y9OmITajBbHWVsRmtCJ+5JFIvOZI\nxI88EnH/zyOPpJsuVaDCL2sWLsTMu36Fnkv+HiN/ewp7zzwbLd/718jv+TYVonj9jCKydKqmZfGr\nXjD6IOf8N95z08cmZP7rBNpaEYyx5QAOeP+cyzm/erJjdGjlIKJB3z9/C4O3/QdQW4sZ1/4QDR/4\ngLRzD9x6Gw5+61+ARAKzfnMPapYslnbusMnt24fBO3+B1H//T7DhtU/iuOOQPPkkJE86CTUnnYTE\n8cchNns23UnXG+3F8dr0eUG802btmMw4N7J+AwZ+djtYIg7E42DxOJBIuBOEE4ngOVZfD9bQ4P3p\n/70BrKEBseYmNwFraaFEK6Lk9u7Fgc98FiNP/BUAUPvOd2La5ZcpX1NNEAopK85Vk5BNB3AFgE/B\nbVPcMeZnvXCHe9zFOd9Q0ZsLwgtS4Jzf4v17MYAVnPMVEx031YSsq6uLFmlqjiyNeC6Hg9/4JgZv\nvwMAUPfud2Pa1y5Hct7c0M7p9Pfj0PevCs7ZcvVKNH70I6GdL0wm04lzjuzznRh+5BGk//wXpJ/6\nGzA8fjN11tCA+NFHI3HsMUi0tyM2ezbih81GfPZhiB02G/HZs8GamylpqxIB/mTEB+/FtgsAPAW3\nbV95QkZxjiiFao2442Dwjp/j0PevAh8YAODGwKbln0LNqUvoeuuhWieiPGTFuYpbFr1K2Ne8x7if\nMcbOBLDNa/tQxQrOebCtNud8PWNsadgnHRwcDPsUxBSRpRGLxzH9+99D8sQTcfC7/4rh++/H8O9/\nj7qlZ6D+A+9H3Tvegdi0aULOld2xA0N334PB//qZO32spgYtV30PjRddJOT9VTCZTowxJBeciOSC\nE9H8uc+Cp9PIdHYi88yzyDz7LEae24zc9u1wenuRff55ZJ9/vvSb1dQgNn168GDTpyPW4v172jT3\nDn9Dg3u337/TP7YC0NAAVlPj3vWvrbVmypst1zwv7v2UMXYsAJWxrRCKc0RRVGvEYjE0XfwJ1L/n\n3ei/8ScYvP0ONwbefz+SJ5+Mxr+/GPXnnYeY5Zsiq9aJKA9p3xvLrZAxxo4prIbpCmOsBUAv55yN\neX4dgMs55w+VOpZaFokwyO7cif5/uwFDd60GMhn3yVgMyRNPRHLRIiSPm4fE3LmIH344YjNmIDaj\nBWxMoOLpNJz+fjh9fci90oXsjh3IPP88Rp78G7Jbtwavq3n9aWj5139F8nULZP6K2uL09SH78svI\n7tiBXFc3cnv3wtmzF7l9e5HbsxfO3r3gQ0PiT5xIeMlZDViyxp04lkyCef9GTY3396T72lgcSMSB\neAIsHvNaweJee1jhc157WCLhJn1jWsaCVrJYDIgxgMXc1wUPBoAVPMfcP/3XMTb+ueC9xr4fA2to\nQE1Hx1Q+KW1ulZsS4wCKc4RZ5HbvxsB//QxDd/4i2LKATZuGhg9+AI0f+QjFKyLqTK1lccwasZvh\ntiiuKBxlzxhbBLe3fuPU7RWD17bxMOd8xpjn1wBYM1GP/VQDVU9PD9posIDWqNQot3cvUvfeh9S9\n92FkwwYgmy39Yv9Lbzzujn0eGSn5UtbQgLpzzkHjBeej5s1vikQ7iEydeCoF5+DB/KPvoDsN7uBB\nOIcOFZ8Wl8r/mw8NuVPlRkbAMxkgPb51MqoMn/MuzLv1p1N5C2X/WU2NcQDFOWJidNWIDw9j6H/+\nF4M/vzPYzgQAkosWofFjH3GrZg0NCi2USxg68WwWfGAAzuAgeH8/+OAQeDoNPpJ2/0yPACMj3nPu\nn0inwTMZ8Gw2Pzk1mwOcHJDNgjuO+2fOAXLZ0T8vmLIKh7vfVzh3j0H+3+4DgOOA+//2f+447s8K\nXuu+xskfx8e8d+HxcP/q/lmQ0wQ/4yV/ls+Bih3n/pF6+1sx90c/moosZcW5ifpqTiv4+1YAlwJ4\nuPAF3hqxeYyxr1RsXni0Ir/IuZA+AOP+5zPGljPG1jLG1h511FHo6uoC4PaMdnZ2AnCdZuPGjXAc\nB6lUCuvWrUMqlYLjONi4cSN6enoAAC+88MKUju/s7KTjQz5+x44dys7PZs5E/CMfxivfvBItG9ej\n9a5f49WfrkLuy19C7Vvegr1f+TL6LlgGJJPoPfss7LnkYiCdxuCJJ6L7G18HmzULucWL0H3dtYh/\n6pNo+udvYs+vfoGaP/8fWm+4HttntqG7u1vrz7/c47ds2SLt/AeGhhA//HBs5Rx7jzgC9WediZ43\nvB7db34Tpn3pi8heugI7zl+G6ddeg/rrr8PLX/w8mu64HTPvuxe7r78Oyd//Dkc88zQO/c9v4Tz2\nKI7sfgW5v/wJ/X/4PQ5/ZhNq/u+P2HvPasx87I9ofuB+7P7VL9D0m3vQetevsefOOxC7/Wdo/c/b\n0Pez/0T6tlsx4yc/xvAtq9B76y1o+eHVwPU/wqu33oLm73wbtd/9Dnbeegtq//mbaPzqV7D75pvg\nfPMbaPrcZ3Hg2h9i8NvfQuM//D0G//mb6Fl5FRo//jFkv/gF7LrhetR9+CLEL7kY3T++AbGPfxy1\nH/ogdv3oWmRWfAr1556L/d/+F/R/+YuoO/ss9H/x89j/rW+i9p3vxMjHP4ZdP1yJ5NveBpxzDrqv\nuwY4+ywk3vh32HnB+VP6/BVjaowDKM7R8RMcrzLOTXQ8q6tD18IOpG+6EbPXPIjBb30Tez5zKTIb\nNmDn7T/HU3fcgQNXfB2Hnn5aS/tFH19unNuwfj32PPMMhh9+BM/eey+23H4Hei+/Ap3XXIuNP74R\nr57+Vmz58Efw5M03Y+fc4/DyO87AUw88gO4PfxR7P/BBbNy4Aa9cfQ0O/MMn0bluHbY98AD6Lrsc\nO/7yF2zZvRuHrv4hXn3kUXROa0b/qltw4Lf/jeePbkfv7+7HwC9+iRePORr7Ol9A6u67saOtDbsy\nGQzffz92M4aXjz4a6UcexYG+g9j61tMx/MQT6N+yBS+dczYGtm5D+qm12Lb0DPSmRzDy1FPoWnQK\n9h42G5kNG7D38MPRfeqpyGx6Bn2xGLa/770Y6ezE4P792PbhCzF0oBeZl7Zix/kfwsGGBmRfegk7\n3/F27J9/AnI7dmD/iSdi15lnIvfyKzg0YwZe/vhHkd21C6l0Gts/9f+QGhlBdvduvHzJJ3Bo5kzk\ndu3Crnefg/0LO5DbvRv7T1mI3ee+B86rr6L/sMPxyv/7B+T27ccwB3Z89jMYBpDr6UH3WWdJiXMT\nVch+wDn/mvf3CScmeguez9dhI2ivh34V53zemOdXw13bdnmpY6d659BxHMQsWTtiKiZoxDn37jY5\n+b16amsjUfkql//f3rnHyVGVef93+jI9t0zmkgRymUQShRAkaBI+AqKs6yDeRUxAd8V1FzfZXXXX\n1TUR9X1f1F0xqCsqXgK6u+5FdMMKiuuFRFEU5JKEJMKQAEkkkwAhmckkk8lMX8/7R9Xp7unpnunu\nqq5zTvfv+/nUJ0l3ddXT9ctTTz91nvMcG3Qivuikc4TMyhgHMM6RqbFJo8zYGMbu/jFO/9d3kcj7\nfxm9YDna/vRP0fK2tyLU3q7RwtpRTCc5Po74w48g+eijSPz+90g+9jjShw4VXSC9KKEQRHs7Qu3t\nEO3tEG2tEM3NzhznpiaIWHOuZL6pCSIWc/7d1JQrfY+E3TL6EiXx4RBEuGDfsFvVI/LK4oUqdYdb\nDp97H0I4v2lUmbyYuAkRmvjZ7L6hgs+776PIn8Vem/A7Srgvifx/Tto/IwSic+aUd/2L47mpR776\ndwghvgHgHinlnZN2dJp5VGhfTeku8longMFanjQej6OlwSepmo4NGgkhnBthA2ODTsR6nWyOcQDj\nHCmBTRqFWlrQdvUatF29Bsm9ezH6X7fj9B13ILlrN4Z37cbJGz+HjvUfReuf/omTDNQRSic5Noax\nn/4Mp++8C4kHHoAcH5+4YziM8IL5iCxchPDChQifMQehnh6EZ89GaFYPQj2zEOqY4XQMbm5uqIe3\nQZAYG0MQi3SU+6uvE8DlANYJISSArQC2wFkkWj3SWAnAhKeH2+DYW0g3Cha19pv+/n6sXLly+h2J\nNqiRHVAnO6gjnWyKcQDjHJkCWzWKnnMOOj99A2ZevwFjP/kpTv3bd5DcsQPD138co9/7HrpvuQWR\nxWfpNtM3+n//e7zk/gdw6rZvQZ7ILeUbPe88NF10EZqWn4/o8vMROessrtunkaD8qdyE7HoAa9y/\nXwigD8DH4QQE9ZRxTZHPBY6UclgIsV8I0SmlHM57q3OqzlN+sGwZOwWZDjWyA+pkB3WkkzUxDmCc\nI1Nju0aipQWt77gKLVe9HeM/+SlOfOrTSO7ajReueD26bvkKWq64QreJnhn/xS8x63Ofw0i/syRL\n9GUXoO2aa9D8+isQ9lYeR3wmKH+aKiHLH/PckrfI86MA1EKUiwGsBrBYdasyhI1wAuwGINuRqqZB\nCgBisVitT0E8Qo3sgDrZgeU62RzjAMY5UoJ60UgIgZY3vRGxS1+J4Y9dj7Ef3Y2h961F1z9/Ea1r\nVus2ryqklDj19W/g5GdvRDgcRvTlL8fMT1yP2MUX6zaNlCAof5pq1ucjeX8vVhoBKeV+KeVNUsq/\nEkLc6K9p1SOlvBXAPiFEnxBiNYA+KeW6Wp939+7dtT4F8Qg1sgPqZAeW62RtjAMY50hp6k2j0MyZ\n6Pr61zDj7z8EZDI4/pF/wPh99+k2qypGbv4yTn72RkAIPP/1WzD7h3cyGTOcoPyp5AiZlPJ/8v7+\neSHE5wB8r3A9FiFEB4BVqPFE4kpxg1Wg9Pb2Bn1KUiHUyA6okx3YrJPtMQ5gnCPFqUeNhBDo+IeP\nQCYSOPW1r2No3V9jztYtiMyfp9u0shn7yU8x8oUvAqEQum75CpovvrjuGpXUI0H5U9l9Ud32wEuE\nEH9c8NY1cMoklkz+VGNh4kKMZCLUyA6okx3Uk06MceVRT5rXK/WsUcfHNqC5rw/y5EkMb9iQt7Cv\n2WSOH8fwx64HAHR88hNofdvb6lqneiIonSpaqEJK+T9Syl8WvHYbnO5UH/PTMBtRC8QRc6FGdkCd\n7KDedGKMm55607weqWeNRCiEzps+BzFzJuL3/grxe3+l26SyOPmFLyIzOIimiy9C+9q/BFDfOtUT\nQenky8qBUspfSClPTL9nfdPW1qbbBDIN1MgOqJMdNIpOjHE5GkVzm6l3jcJnnIEZH/wAAODkP3/J\n+FGy9AsvYPT27wEAOv/xM9l1wupdp3ohKJ3sWMrdEuqxbrveoEZ2QJ3sgDo1HtRcHzKdRvroUaQG\nBpDafwCp/QeQPnYMMpmcsF8jaNT2Z+9BqKcHyUcfReKhh3SbMyWj//VdIB5H8xWvQ3Tp0uzrjaBT\nPRCUTuWuQ0bKYGBggA5mEFJKZI4cQfrIEWSGhpA5cQLPxWKYl0oj1NWF0Ny5iPQugGhq0m2qkWSG\nh5F87HGkBwchwmGEexcgeu65gVwv+pIdUKfGg5rXHiklUk8/jcSDDyHZ34/kE3uQeuYZZI4dAzKZ\nop8J9fQg8uIliJ59NgYvezVedOGFCM+aFbDlwRFqbUXrn7wLp756C05//78Ru+gi3SYVRUqJsTvv\nAgC0vefaCe/Rl+wgKJ2YkPnI6OiobhMamszx44g/+CDiD/wOyV27kXzqKciTJyfsc+J916H5W9/O\nvRCLoemC5Wh+7WvRetVVCM+bG7DV5pHYuRMnv/BFxH/1a6CgFES0taG577Vov+46NK1cUTMb6Et2\nQJ0aD2peG6SUSGzfgbE77sDYlq3IPP980f1C3d0Qra1AJAxICXlyBJkTJ5AZHERicBCJhx7GiVgM\nz79vLZouuQRt77wGLW95c10+eGy7+mqc+uotGPvx/6Lzxs9CNDfrNmkSycf7kdq3D6GeHsQuvXTC\ne/QlOwhKJ2F67W2QrFq1Sm7btk23GaQC0kPHMf7jH+P0j+5G4sEHJycQnZ2IzJ+PUE83QjNnAnDK\nPjJDQ0gffhbpgYHczqEQWq+5Gh3rP4rwnDlBfg0jkFLi1C1fw8mNNznXsakJTeefj/DcuZDJBFL7\n9iP19NPZ/VvefiVmfvpTCHd3a7SaWI6YfhfiJ4xzZiFTKYz96G6M3HILUnufzL4e6ulB7FWXIrp8\nOaLnnovoi1+M0OxZENHo5GNkMkg/9zxSTz+F5GOPI37//Yg/9BAwHgcAhBcuRMeGj6LlbW/Lzl+q\nF164/Aok+/vR893/RPNll+k2ZxIj3/wmTn7mn9D6rnei6wuf120O0UNZTscRMh8ZHBxkG9OASO7Z\ng1Pf/hec/sEPskEHTU1oWrkCsYsvRtOFFyK69ByEZs+eEIAKNUoPHUfioQdx+s4fYvxnP8Pp27+H\n8Z/fg66vfRXNr3510F9LK6e+eouTjAmB9r/+K7T/zd8g3N01YZ/UoUMY/ff/wKlvfxtjd96FxPYd\n6PnOvyJ69tm+2kJfsgPq1HhQc/8Yv+83OPGJTyK1fz8AIDR7Nlqvejta3n4louedBxEqb5q/CIUQ\nmT8Pkfnz0HzZZUi88xrMjUYx9sMf4dRt30Jq3z4cf/8HnZGkm26adF+3mdgfvwbJ/n6M//JeIxOy\n+P2/AwDELrlk0nv0JTsISic29fCRgfzRFlITUgcPYuj9H8ALr70cp797OzAeR+yPLkPXzV/C3F2P\nYvYdm9HxkQ+j+dWvQnjOnElPAws1Cnd3oeUNb0DPrd/EnHt/idirXoXM0BAG3/NejN1zT5BfTSvx\nRx7ByZs+DwiBrq/dgpmf/ETRoB1ZsAAzP349zrj3l4hesBzpgwdxbPXVSO0/4Ks99CU7oE6NBzX3\nTub0aRz/+w9j8F1/gtT+/Qi/aBE6v/h5nPnwg5j5f/8Pms4/v+xkrBgDAwMIdXSg7dp3Y84vt6Lz\npo0Q7e0Y/+nPcOzKtyNVRxo2/5GThMXvv1+zJZORqRQSDz8MAEXnuNGX7CAonViymIfXUo5MJoOQ\nh5soKY1MpXDqa1/HyZu/DCQSQCyGtndeg7brrkN0yeKyjzOdRjKTwYlPfRqj3/o2REsLZv/kx76P\n/piGzGRw9C1vRXLnLrR/4P2YeX15yy1lxsYwdN37EP/1fQifdRbm3PMzhFpbfbGJvmQHPuhUX/VT\nFsA4p5fUM89g8Lr3IfXEHqA5ho4PfQjt69b6OsermEapQ4cw+N6/QOqJJxCePx+z7/4hwmec4ds5\ndZEZG8Nz55wLSIm5e5/wLQb5QfLpp/HCZa9BeP58nPnwg5Pepy/ZQVBxjv8TfCQej+s2oS5JHTiA\no2+70hnBSSTQ8o534Izf/Bqdn/2nipIxYHqNRCiEmTf8P7Rc9XbIsTEM/c0HIFMpL+YbT/y39yO5\ncxdCZ8zBjL/727I/F2ppQfdttyJy7lKkDxzAiU99xj+b6EtWQJ0aD2pePcl9+3H0qncg9cQeRBYv\nxpyf/gQzPvgB3xtuFNMosmABZv/gDkRf/nKkDx/G4J//BWQi4et5dRBqaUH0nHOATAbJxx7Tbc4E\n1JzAyDnnFH2fvmQHQenEhMxH+vv7dZtQd4zf9xu88Oa3ILlzF8Lz56Pn9u+i+ys3IzJ/flXHK0cj\nIQQ6N34O4d5epJ54AqfdBR3rldO33w4AaLv22oqfLoba2tD91a8ATU04/Z//iYRPAZG+ZAfUqfGg\n5tWROnQIx9asQeb5I2i66BU1rb4opVGoowM93/lXhBcsQHLXbox86eaanD9ooi+7AACQ3LlLsyUT\nSe7dCwCILi2ekNGX7CAonZiQ+ciyZct0m1BXnL7rLgy++1rI4RNovrwPc7beg+ZXv8rTMcvVKNTa\nio6PXw8AGPnGNyDTaU/nNRU5Noaxn98DCIHWq6+u6hjRc89F+3v/DABw8sbP+WIXfckOqFPjQc0r\nJzM6iqE/vw6ZIy+g6eKL0PMf/47QjBk1O99UGoV7etD1lZsBITDyta8juW9/zewIiqblywEAicfN\nSnCSe9yErMQIGX3JDoLSiQmZj8RiMd0m1A2n77wTxz/4d0A6jfa//it0/8u3Eero8HzcSjRqedMb\nEV60EOlnDmL8F7/wfG4TiT+yDYjHET3vPETmz6v6OO0f/ABEezviv/o1kv1PeLaLvmQH1KnxoOaV\nc+KGTyHZ34/wWWeh51u31Xye03QaxV7xCrS+651AOu101rWcyIuXAEC2W6UppJ56CgAQOaf4SCh9\nyQ6C0okJmY/s3r1btwl1Qfy39+P4hz4MZDKY8ZEPY+YnP+Gp41Q+lWgkwmG0XXstAGDshz/y5fym\noTpTxS59pafjhLu70bpmNQDg1Hf+3bNd9CU7oE6NBzWvjPFf/crpCNzUhJ5v34ZQZ2fNz1mORh0f\n/nugOYbx//1fJN3EwVYiS1RCtg+mNKqTUmbXOY0sWlR0H/qSHQSlExMyH+nt7dVtgvWkDhzA4Lp1\nQCqF9nVrnaDhI5Vq1PLGNwAAxrf+ArIOJ+AmHnJb8r7SW0IGAG3XvhsAMHb33Z4ni9OX7IA6NR7U\nvHxkIoHhj38CANDxDx8pWbrmN+VoFJ47F63vcB6ijf7bd2ptUk0JzZ4NMWMG5PAJZI4f120OAEAO\nD0OOjUG0t5es7qEv2UFQOjEh8xEu8OcNmUxi6P0fcOaMve5ydHzi476fo1KNIosWIbpsGeSpU4i7\nyUu9IKVE8gmnvDC6/HzPx4uecw4i55wNeeIE4g884OlY9CU7oE6NBzUvn9Hv3o70MwcReclL0L5u\nbWDnLVcjNff39J13Wd1xUQiBiPujOX3okGZrHFKHnwUAhKeYCkBfsoOgdGJC5iN79uzRbYLVjHzl\nq0ju2o3w/Pno+vLNEOGw7+eoRqOmSy4GACS2b/fbHK2kDx2CPHUKoVmzEJ41y5djtrzxjQCA8Z/9\n3NNx6Et2QJ0aD2peHpmxMYzc/GUAQMf6j0JEIoGdu1yNosvOReTcpc5DtN/8tsZW1ZbQ3LkAgPSz\nz2q2xCH97GEAQHiKjtD0JTsISicmZD7S1tam2wRrSe7di5EvfwUA0HXzl3xp4FGMajSKrVoFAEh4\nWEzVRNQaKX6W0TS/5jUAgPgDv/N0HPqSHVCnxoOal8fYXT9E5uhRRM8/H81veH2g565Eo5Y3vxkA\nMPaTn9TKnECIzFMJ2XOaLXHIPH8EABA+88yS+9CX7CAonZiQ+QjrgatDSokTN3wKSKfRdu27EXNH\npGpBNRo1rVwJAEhs3wGZyfhtkjZSh5wJx+EXFZ9wXA3R5edDtLYitW8f0i+8UPVx6Et2QJ0aD2o+\nPVJKjP7rvwEA2v/yfRBCBHr+SjRq7usDAMR/81tjGmJUQ3ieUxpozAjZ4CAAINTdXXIf+pIdcA6Z\nhQy4HXVIZcTv/RXi9/0GoqMDM9Z/tKbnqkaj8Ly5CM2eDTkygvThwzWwSg/pQ853iSxY4NsxRTSK\nplVOAht/8KGqj0NfsgPq1HhQ8+lJ7tyJ5OOPI9TTg5Y3vynw81eiUXTZuRCdnUgfPoz0M8/U0Kra\nElYli88ZMkLmNhcJTzH/iL5kB0HpxITMR0ZHR3WbYB1Symyd/Yy//SDCUzxN8oNqNYq85CUAgNRT\nT/tpjlbSA87k57CPCRmQG1FMPvZY1cegL9kBdWo8qPn0jP3obgBAy5VXQmhYa6oSjUQohNgllwDw\nXmquk9AsJ/HJDA1ptsRB2THVCBl9yQ6C0okJmY8sXbpUtwnWkXjoISS2b4fo7ETbe66t+fmq1Sj6\nkhcDgPXrteSTOqwSstKTjqsh6q5qn+zvr/oY9CU7oE6NBzWfGpnJYOzuHwMAWt76Fi02VKqRqmpI\n7LJ3XSyV+GQG7UnI6Et2EJROTMh8ZNCtGSblM/L1bwIA2v/izxEKYOJkKeHwzwAAIABJREFUtRqp\nhSfTBw74aY5WMsecaxGeM8fX40aXnQvAW0JGX7ID6tR4UPOpST66E+nnnkN43jw0rXi5Fhsq1ajp\npS8FACQfr76qQTehHsNGyNzEMNRTOiGjL9lBUDoxIfMR1gNXRvrZ5xC/914gGkWbux5KralWIzWK\nlDKkg5MflPMErxrCCxdCtLUhc+SF7MTmSqEv2QF1ajyo+dSM33cfAKD58j6IkJ6fWJVqFD3PrWp4\n4gnIVKoWJtUcFcfSQ0NGNCcpJ77Sl+yAc8gsZPny5bpNsIrTd9wBZDJoft3rppz46ifVaqTWElFr\ni9iOHB+HHB0FolGIGTN8PbYIhRA5+2wAQOrJJ6s6Bn3JDqhT40HNpyb+W2c9r9irLtVmQ6UahTo7\nEe7tBcbjSD1t5zzpUGsrRHMzEI9Dnj6t2xxkTp4EgCmX8KEv2UFQOjEh85F4PK7bBGuQUmL0+/8N\nAGh75zWBnbdajcLz3ITsUH0kZJkhpwNUqLurJi2ZI2e9CACQqrJrF33JDqhT40HNS5M5fRqJ7TuA\nUAixi2u3fMt0VKNR9iHavv1+mxMY2XlkmssWpZTOA08AYoqpGPQlOwhKJyZkPtLvYc5Mo5HctQvp\nP/wBoTPPQOyyVwd23mo1CnV1QrS0QI6MZJ982Uy6RuWKisgiZ22z1B+qS8joS3ZAnRoPal6axCOP\nAMkkoue/FKHOTm12VKNRxF2PMnXwoN/mBIa65pnhYa12yLExQEqI5maISKTkfvQlOwhKJyZkPrLM\n7S5HpmfsZz8HALS8/vUQ4XBg561WIyEEQrNnA8g1w7CZbH17V20SsvDChQBQ9bo29CU7oE6NBzUv\nTeLRnQCApgsv1GpHNRpFXvQiANU/RDMBMaMdACBPndJqhzq/aG+fcj/6kh0EpRMTMh+JaVhvxFbG\nf34PAKD5iisCPa8XjVS3pLQhXZy8oBatDHV11eT4kUVOQpaqssSTvmQH1KnxoOalUWsvNmmeG1SN\nRqqqwebFoUWbkwBlTuld3ytXrtg65X70JTsISicmZD6ye7e9a3gESeoPf0DqySchOjoQu/iiQM/t\nRSM1mpQZsn+ETE16DrXXZqmB8JlnAgAyR45U9Xn6kh1Qp8aDmpcmufv3AIDo8vO12lGNRmFVZm5x\nQqbimTw1otWOjJuQhdqmHiGjL9lBUDoxIfOR3t5e3SZYQfz+BwAAsUsvhYhGAz23F43CPWZMGPYD\nlZCJ1qmf4FWLWtssfeQIZCZT8efpS3ZAnRoPal6c9NAQ0ocPQ7S2IrJ4sVZbqtEo0rsAEALpw4et\nbX2vOgZL3SNk2ZLFqR940pfsICidmJD5SE9ArdttJ37//QCA2CsvCfzcXjTKLjw5WAcJWRkdoLwg\nWlogOjuBVAqZKtYioy/ZAXVqPKh5cZK/d0fHzjsv0HnRxahGIxGLITRrFpBOI3P0aA2sqj0hN55l\ndM8hG3UfeE4zh4y+ZAdB6cSEzEf27Nmj2wTjkVIi/sDvAACxS18Z+Pm9aGRKS10/yKgRspaWmp0j\nPNcpW0xXUbZIX7ID6tR4UPPiJPfsBQBEl52r2ZLqNcpWNrzwgp/mBEZuhExvQqYSwlDr1A886Ut2\nEJROTMh8pK1Gow31ROrpp5E5ehShOXMQWbIk8PN70aieErLsHLIa/p9VwT1zpPLgTl+yA+rUeFDz\n4qj1uyIvfrFmS6rXKHSGKjW3NCFTI2QjukfI3AqUaUoW6Ut2EJROTMh8hPXA05PY8SgAoGnVqpos\nSDwdXjTK3uw116f7Qa3nkAF5Cazb0bES6Et2QJ0aD2penNR+NyFbfJZmS6rXKPcQrbpmTLoJuSWC\nctSQhGyaH/L0JTvgHDILGRgY0G2C8SR37QIANL3sAi3n96JR9mZ/ug4SsjLb8nrBy4gifckOqFPj\nQc2LkzqgEjK9DT2A6jWyvmTRjdHaR8jicQDOvLypoC/ZQVA6MSHzkdFR+3+o15qE2z606QI9CZkX\njUS2pa79OsvTYwBqPELmrnFWzQgZfckOqFPjQc0nkzl1CpnnjwCxGMLz5+s2p2qNQrNnAwAyx475\naU5gqBJ8OXZaqx0ykQAAiKamKfejL9lBUDoxIfORpUuX6jbBaGQigeTj/QCA6Pkv1WKDF43UmiIZ\nzeUQfpBdJ2WaScdeUAlZeqjyhIy+ZAfUqfGg5pNJ/cFZuyuycKH2DotA9RqFujoBAJnhYT/NCQ41\nIhVPaDUjO0I2TUJGX7KDoHRiQuYjg1W0924kknv3AokEIosXIzRzphYbvGhUVyNkY2bPIaMv2QF1\najyo+WTSzx4GAIR7F2i2xKFajUKddidkotlJyFRCpA13hAyxqRMy+pIdBKUTEzIfYT3w1CSfcFqH\nRs9bps0GLxqpCbq6W+r6QXadlFrOIVMli5xDVrdQp8aDmk8m/eyzAIDw3HmaLXGoViPrEzJ3REp3\nQiaTSQCAaOIcsnqAc8gsZPny5bpNMJrU008DACJnn63NBi8aZRedrIO6bzk+DgAQzc01O4eX8hf6\nkh1Qp8aDmk8m/exzAIDwvLmaLXGoVqPsQ7ThE36aExiqiYb2hKzMOWT0JTsISicmZD4S1z1Mbjip\np54CoHedFk8aNTcD4TCQSGRvuLYik27AiE4dMLyQa0FceQJLX7ID6tR4UPPJZEfI5pkxQlatRtkR\nsirKzE0gl5CNa7VDqjls0yRk9CU7CEqnuk3IhBArhBCbgzxnf39/kKezjuSTTkIWfYm+hMyLRkKI\nXFtd2+eRJVPOn9FIzU4hZswAAMiRkYo/S1+yA+qkF8Y5M1AJWcSQhKxajURHByAE5MhItuzOJkTM\nqfjQPUKGhGp7P3VCRl+yg6B0qt2vMU0IIVYAuMb9Z6ALgixbpm9ulOnI8XGkDx4EQiGt67R41SjU\n1ob0iRPOwpPdXT5ZFTwy5SRkIlK7W4CXEk/6kh1QJz0wzplFrmTRjISsWo1EKAQxcybk8DAyJ08i\n3NPjs2U1RjX1GDekZHGaChT6kh0EpVPdjZBJKXdIKTcA+H7Q545NswhgI5M6cADIZBBetGjaxRJr\niVeN1JwrNQfLWtTTz2i0dueIxZzjJxIVP7GkL9kBddID45w5SCmRfv55AEB47pmarXHwopGXUnPd\nZH9baJ5SUO4cMvqSHQSlU90lZJUihFgrhNgmhNi2cOHCbDeVgYEB7NnjdAUcHBzEzp07kclkMDY2\nhu3bt2NsbAyZTAY7d+7MtsR88MEHPX1+z549dfv53YefhQyHkXn5y7Ta/+ijj3r6fOLMOTj46Rsw\ndtqu61/4+XhXF2Q4jF1PPlmz8+/duxeirQ2jF1yAnbt3V/T5hx9+2Ojrx887n3/ggQc8fZ4EA+Nc\n7T6/97HHgGQSoxe9Arv27jXCfi9xDh0zkJgzBzsPHrTi+ud/fteTT0KGw4jP7NB6/eOxZhz89A0Y\nj0YZ5+rg80HFOSGlLHtnm3BLOm6TUq4s9zOrVq2S27Ztq/qcg4OD6LFtiD8gRr7xTZz8x39C23XX\nofPTN2izw6tGL7zxTUju2o3Zd/8ITSte7qNlwSGlxLMLFgIA5h38Q00XMn3+okuQHhjAGQ/8FpFF\ni8r+HH3JDnzQSfhlSyPCOKef1P4DOPKqVyO8aCHOfOB+3eYA8KbR0bdeicT27Zh11w8Qu/BCny2r\nPYd7FwGZDOY9c6CmJflTcfTKq5B45BHM+sEdiL3iFSX3oy/ZQVBxruFHyPyEjlWa9KFDAIDIgvla\n7fCqkVpXRCYs7o6UTjt/hkI1TcYA5JqgjFS2dht9yQ6oU+NBzSeSdp+ch7rNuS5eNFJrU9pYsgiY\n0fpe/T6YrmSRvmQHQenEhMxH1NAlmUz60GEAQHjBAq12eNUou/CkzW3vg5g/5pKdj3Cqsk6L9CU7\noE6NBzWfSGbISchMaoDhRSORvWfbmZDBiIRMzSGbeu4RfckOgtLJ2C6LQoi1ANaUufsaKaX2peXb\n3K5yZDKpw84IWVjzCJlnjdw2ttl1RiwkiA6LCjGjuuBOX7ID6uQNxjn7yRxzR8h6ujVbksOLRl66\n45qAaI5BAoDOTovq98E0be/pS3YQlE7GJmRSylsB3Krbjkro7e3VbYKxmDJC5lWjbAmCxSNkMoA1\nyBSh1uqCO33JDqiTNxjn7CejShYNGiHzopFwf3xaX7KocVpBuV0W6Ut2EJROLFn0EdV5hUwkc+IE\n5MgIREsLQl161+7yqlGuZNHiOWRJN1hEal+ymC0fqXCZAPqSHVCnxoOaTyQ7h8ygETIvGuVKFiub\n92sKJiwOXW5CRl+yg6B0queELPC746ilT5RqTf7omBB6m6p51Sj39M3iETJVshjAHLJq122jL9kB\nddIO45xmMkNDAMxq6uFFI+tLFo2YQ+aee5o5ZPQlOwhKJ2NLFqtFCLEYwDoAfQBWCCE2AdjulobU\nlKVLl9b6FFZiyvwxwAeN1A3W4jlkQTb1UAkZKgyO9CU7oE56YJwzB1WyaFJTDy8aWV+yqKpYNCZk\n6veBmGYOGX3JDoLSqe4SMinlfgAbdJyba0oUJ/3scwCA8Lx5mi3xrpG6wdbFCFkQTT1aqhshoy/Z\nAXXSA+OcOWSGnT4rusvx8/Gike1t77Nzo9VcaQ2UG2PpS3YQlE71XLIYOKwHLk7m6FEAQHjOHM2W\n+DmHzN6ELDdCFkBCxjlkdQ11ajyo+USku8ai6Jih2ZIcnuaQWV6WL8JOXFNJkRbUWp/TrPNJX7ID\nziGzkOXLl+s2wUjSbkIWmjVLsyXeNTKiHMIjuad3Ac4hq/B60ZfsgDo1HtR8IpkRZ41FteaiCXjR\nyISmGJ5QDxo1JWRSSiCTcf4xTUJGX7KDoHRiQuYjcVtvYDXGpBEyzxrVQdt7JNwRsiZzm3rQl+yA\nOjUe1Hwi0k3IREeHZktyeNHIhKYYXlAPGmUqqccAlYwJMW0TM/qSHQSlExMyH+nv79dtgpGkjx4D\nAIRmz9ZsiXeNbC/nAHKBKtARsgoTMvqSHVCnxoOa55DJpHNvC4UgWlp0m5PFi0a5MnNLkwXdc8hU\nQhaa/uc1fckOgtKJCZmPLFu2TLcJRpIdIZutv2TRq0b1MYfMDVRBNPWocg4ZfckOqFPjQc1zZNT8\nsRkztC/pko8njWKqk7CdCZlqpKFthKzM+WMAfckWgtKJCZmPxGJTrznRiEgpkT7mziEzYITMq0a5\nOWT2JmTZEbIgmnpUOYeMvmQH1KnxoOY55Cl3/tgMcxp6AN40Es12lyxmHzSm0lpOL90RMlHGCBl9\nyQ6C0okJmY/s3r1btwnGIUdGgPE4RGtrdsFJnXjWSK0rkrA0WAGQ2REyc0sW6Ut2QJ0aD2qeI9th\ncYY5DT0AbxrZP4fMnhEy+pIdBKUTEzIf6e3t1W2CceTmj+kvVwS8a1QXJYtBjpBVWbJIX7ID6tR4\nUPMcmZGTAMwbIfOike0JGaLug0Zdc8gqSMjoS3YQlE5MyHyEC/xNJjM0BAAI9ZiRkHnVSETdhCyp\n6embD8iESsiaan+y7AhZZcGdvmQH1KnxoOY5snPI2s1KyLxolEvIKnuIZgq6R8hkBU096Et2EJRO\nTMh8ZM+ePbpNMI7M8DAAINTZqdkSB88aRdynXmk99em+oNZnCXIOWYUjZPQlO6BOjQc1z5GbQ2ZW\nyaInjZo4QuaJCuaQ0ZfsICidmJD5SJsBc6RMQxqWkHnWKKyevtmbkOXa3pubkNGX7IA6NR7UPEfm\npLsG2Qxz1iADvGmkmnrA0rb3wi0VlGnzSxbpS3YQlE5MyHyE9cCTyY6QdZmRkHmeQ5YdIdN0s/cD\nlUwGkZCpUbhUZdeLvmQH1KnxoOY55CmnZNG0ETJPc8jy5klLKf0yKTh0j5Cl3ZLF8PQ/r+lLdsA5\nZBYyMDCg2wTjyJw4AQAIzZyp2RIHzxqF9bbU9YVsjfv0T/A843ZyrHTOHX3JDqhT40HNc2RGzGx7\n70UjEYk4D+symYofpJlAbg6ZHttlxvltIMqIr/QlOwhKJyZkPjI6OqrbBOMwbQ6ZV42yN3uLR8hk\nWgWM2i9kWu0IGX3JDqhT40HNc0j3WgjDSs88xzmbOy2GNc/zrqBkkb5kB0HpxITMR5YuXarbBOMw\nLSHzrJEqWbR5hEyVoZQRMDyjRsgq7HhFX7ID6tR4UPMccmwMACBaWzVbMhGvGlmdkKlmGtoSsvJL\nFulLdhCUTkzIfGRwcFC3CcZhWkLmVSMR1lsO4QsVtOX1SnaErMJ6fvqSHVCnxoOa58gmZC3Nmi2Z\niOc4l10/0r6ELNvUQ8W5gMmeV0wfX+lLdhCUTkzIfIT1wJMxLSHzrFE9NPVQTw7LCBheqbaen75k\nB9Sp8aDmOXIJWYtmSybiWaOYu0aljSNkkerK5H1DzSErowKFvmQHnENmIcuXL9dtgnFkjjsJmTAk\nIfOsUR009cgtXFn7OWS5jleVlSzSl+yAOjUe1DyHqQmZV42ylSA2Pnh0Kz+k9jlk0/+8pi/ZQVA6\nMSHzkbiNT5NqjGlt771qpNreWxmoFO4csnKe4HlGnSOTqaiEhL5kB9Sp8aDmOeSYs76iaQmZZ42q\nbMZkAiIv5uhApsvvYkxfsoOgdGJC5iP9/f26TTAKKSXkyZMAzGkL7FmjiP0jZIHOIROiqlEy+pId\nUKfGg5rnyI6QNZs1h8yrRlbPldbdZbGCkkX6kh0EpRMTMh9ZtmyZbhOMQo6NOT/+m2MQ6ke5Zrxq\nlJ0wbPMImQpUASRkQHXzyOhLdkCdGg9qnsPUkkXPGmW7CVsY57R3WSy/ZJG+ZAdB6cSEzEdibmci\n4iBPnQIAhNraNVuSw7NGdTBCpkoHRUAJWTUjZPQlO6BOjQc1z2FqQuZVI5FdrsS+OKe7yyIy7rIy\nZcRX+pIdBKUTEzIf2b17t24TjEKechfNbDdn0UyvGlldyqGQ5QcMP6hmhIy+ZAfUqfGg5jlMTcg8\na5QdIausGZMRaC5ZlKpksYw5ZPQlOwhKJyZkPtLb26vbBKPIjJo3QuZZo4jm+nQ/CHAOGYDcBPEK\nRsjoS3ZAnRoPap5DjpvZ1MOzRtkHjxbGubA9JYv0JTsISicmZD7S09Oj2wSjUCWLJo2QedZI9xon\nfhD4HDJV/lL+NaMv2QF1ajyouYOU0timHl41EuohmoVzpdXIVLbbYdCo85bR1IO+ZAdB6cSEzEf2\n7Nmj2wSjyGRLFs0ZIfOqkdC9xokPBD+HTI2QlR/c6Ut2QJ0aD2ru4o6OoTkW3L20TDxrpEbIKrhn\nG0O2ikWP7eq3QTkli/QlOwhKJ7PuIpbT1mbOSJAJyGzJojnXxbNGKvDqmjDsB4HPIVMjZOWXLNKX\n7IA6NR7U3CGj1iAzbHQM8K6R0JzUeEIlQrpGyDLllyzSl+wgKJ2YkPkI64EnIg0cIfNeW6930Ulf\nCLhkMfvEsoKnrfQlO6BOjQc1d1HzxwzslOd9rrTqjGtfQpbrsqhrHbLyH3jSl+yAc8gsZGBgQLcJ\nRpFRc8gMegrkWaN6GCELuKlHNSNk9CU7oE6NBzV3kMkEAEA0mZeQedVIjZBZud6m5qYe2ekMZZQs\n0pfsICidmJD5yOjoqG4TjEKePg0ACBk0QuZVIyEEAI1rnPiA1NRlsZL5CPQlO6BOjQc1d5AJlZA1\nabZkMp41snm9zbAZJYuijJJF+pIdBKUTEzIfWbp0qW4TjCLXZdGchMyzRvVQsuiWVAQ1EV2NkFWy\npg19yQ6oU+NBzR1k3EnIYGBC5lWj3NqR9q1Dlu2yqKtksYIui/QlOwhKJyZkPjI4OKjbBKNQXRZN\naurhWaO6KFkMeg5Z5U9b6Ut2QJ0aD2ruokbIYuYlZJ41snqEzJB1yMooWaQv2UFQOjEh8xHWA09E\ndVk0aYTMzzlkUnUrtA2VTJZRUuEHak0bziGrP6hT40HNHWQiDsDMkkXPc8hUYwwb19vUXLIoKyhZ\npC/ZAeeQWcjy5ct1m2AUuS6L5oyQedVICAG488hge0Imghohc5t6VDCHjL5kB9Sp8aDmDtk5ZFHz\nEjLPGkVVmbl9CZlQa6jpGiGrYI42fckOgtKJCZmPxONx3SYYRSa7Dpk5I2S+aGR52aIMeg6ZWhi6\nghEy+pIdUKfGg5q7JNz7mYEli541snqETJUsarK9gjlk9CU7CEonJmQ+0t/fr9sEo1BdFkVri2ZL\ncviiUUhzjbpXAp9DVvkIGX3JDqhT40HNHUzusuhVI9XUw8oYp+KapgKWStre05fsICidmJD5yLJl\ny3SbYBTSfaogmps1W5LDF43Cdo+Q6ZpDVkn5C33JDqhT40HNHUyeQ+ZZI9VlMWlfl8XslAJd8dk9\nbzlzyOhLdhCUTkzIfCQWM2+BSJ3I8XEAZiVkfmgk3LlX1jf1CHwOWfnBnb5kB9Sp8aDmDrm29+Zd\nD68aWT1Cpjs+q2tWRskifckOgtKJCZmP7N69W7cJRmFiQuaLRpaXLEq3xj24dchU16vyrxd9yQ6o\nU+NBzV0MbnvvWSOVTFg4hywb16SmLosVlCzSl+wgKJ2YkPlIb2+vbhOMQiVkiJmTkPmike2LQ8vy\nu0D5QrjyhIy+ZAfUqfGg5g5qxF+ojoQG4VUj9Z2sbOoR0lyyKNUDTzHtrvQlOwhKJyZkPtLT06Pb\nBKPIjpC1mJOQ+aKR7hu+V4KeQ+YmfpW0IaYv2QF1ajyouYPJc8g8axSxd4QsN4dMV8li+V0W6Ut2\nEJROdZmQCSHWutsmd+sM4rx79uwJ4jRWIKUExt2AZVCdtB8aZeeQ2Z6Qiemf4PlCFSOK9CU7oE76\nYJzTTHYOmXkJmVeNtK/l5YVsyaLmOWRllCzSl+wgKJ0igZwlQIQQa6WUt+b/G8B2AEtqfe62NnMW\nQNZOtlwxFthcpXLwRSPrSxbVXwJOyCoI7vQlO6BOemCc00+27b1BDxwVnjVSnXGt7LKotwuydJeV\nKafLIn3JDoLSyZxfyj5Q7AmhG7S6hRB9tT4/64FzmNjQA/BJI9sXhlZPDoMaIauiZJG+ZAfUKXgY\n58zA5HXIPM8hs3iELFsir6mpRyUli/QlO+AcsupYDKBY6cZ+972aMjAwUOtTWENuDTKznh76opGa\nQ5a2MyFTiIASMlHFiCJ9yQ6okxYY5wzA5ITMs0YRi0fIdM/xzpSfkNGX7CAonYS1aymVQAixQkq5\no+C14wDWSCm3Ftl/LYC17j/PAbDXw+lnATjm4fOk9lAjO6BOduBVp2NSytf7ZUyjwDhHpoEa2QF1\nsoNA4lzdJWSFCCFWA7heSrkygHNtk1KuqvV5SPVQIzugTnZAncyAcY7kQ43sgDrZQVA61VvJ4gTc\nko7rAbxWty2EEEKI3zDOEUKI/RjbZdEtsVhT5u5rpJTDRV7fOMV7hBBCiDYY5wghhAAGJ2Ru16hb\np92xBEKI9QA2Sin3+2fVtFRtLwkMamQH1MkOqJMHGOdIjaBGdkCd7CAQnepyDpn71HFrfpASQvQV\nm+xMCCGE2AbjHCGE1A/GjpBVi7sOyzYVpNz6ek6aJIQQUhcwzhFCSH1RVyNkQojFAPaVeLuLNfaE\nEEJshnGOEELqj7pKyHThlo4Muf9cLKW8Sac9ZDKuRgCg2kJv4A8XsxFCbJZSltvwgASMO39pGO69\nT0p5h16LSC1hnDMfxjn7YJwzmyDjXN2VLAaNugEqkYQQK4QQm6SU6/RaRhRCiLXu5PnsvwFsB7BE\nn1VkKoQQKwCs1m0HKY4QYjOcH3uqZE4KITg6U6cwzpkP45x9MM6ZTdBxrq7XIQuIdfk3QSnlDgB9\nGu0hebhzKybg6tXtzsMgZtKt2wBSHPeH3iMFnf2WMBmraxjnDIZxzloY5wxFR5xjQuYB9ya4oshb\nw7wJGsNiAJuKBKz97nvEMIQQq9kpzmg2AphQthFw23USIIxzVsA4ZxmMc8YTeJxjQuaNxXBqSwsZ\nQvEARgLGfZK7sshTjcVwghUxCLeEY4duO0hx3B98ne7fVwsh+oQQ64s9oSd1A+Oc4TDO2QXjnNno\ninOcQ+aNbuQmOeczDKAnYFtICdxglUUIsRrAfj6dMpLFbA5hNOrHeWfefKJtAH6BXCMBUl8wzlkA\n45xVMM6ZjZY4xxEy0lC4TziuB/Ba3baQibglHAxSZtMN58lh9qm7eirP8jVCzIBxzlwY56xAS5xj\nQuadYpMyOwEMBm0IKYuNANawAYFZuGsrsbTGfPYDueCUB8vX6hvGObtgnDMQxjlr0BLnWLLojW1w\n60wL6Abrg43DXU9iIxsQGEkfgM7Cp09qDZD8Dm9EH1LK/UKIUm/zx199wjhnEYxzRsM4ZwG64hwX\nhvaIEGIfCibTCiH2SSm59odBuC1Mt+YHKSFEH+vrzUUIIaWUJe+KRA9CiO1wnr7n+9I+9zX+QK9D\nGOfsgHHOPhjnzERHnGPJonc2wqnVBpDtnsObn0G4T6O25S3uN+kJFSGkbDa4G4DsPW8/k7G6hnHO\ncBjnCPGVwOMcR8h8wH0qtR9OWcdiKeVNmk0iLm7N9r4Sb9dsxXVSPe6PiHUAVsNZB2QTn/CahdvB\nTa1v1COl3DDV/sR+GOfMhXHOPhjnzCfoOMeEjBBCCCGEEEI0wZJFQgghhBBCCNEEEzJCCCGEEEII\n0QQTMkIIIYQQQgjRBBMyQgghhBBCCNEEEzJCCCGEEEII0QQTMkIIIYQQQgjRBBMyUlOEEKuFELLC\nbbNuu8nUCCHWCiE6NZz3eMH/ldXT7L/PXT+p3OOv924lIaSRYJyrTxjnSJAwISM1RUp5B4AuAJfn\nvbwVwBL39SUAVgLIX2Q08BsgKR/3h8TlmhYbPQvO/5lpzy2EWAFnUcf/ruD4w25w4/9BQkhZMM7V\nH4xzJGgiug0g9Y97Q9sqhFAvbZFS7nf/rm44O4QQWwBsCdo+Uj5CiE0AFkspV+o4v/t/aVgIsQ1A\n3zS7XwNgayUBVUp5qxBiJYDtcAIiIYRMC+Nc/cA4R3TAETJiDFLxc+BIAAAII0lEQVTKrQB2AOjW\nbQuZjFs2sRbABt22lMlaANWUBW0AsNgNyoQQ4huMc2bDOEd0wYSMmMb3wVIOU7kNwA73B4XRuGUc\nnaisjANA9unkTQDWuschhBA/YZwzF8Y5ogUmZEQrQohOIYTMe2kr+OTQONynhp1w9LGBiss4ClAl\nRet8socQ0qAwztkB4xzRCRMyopsJ9dFSyh0AbhRCbCzsMuQGtc3uZNTthRNS3Y5IW9z9t0/VSUgI\nsd7dR7qfWZ33+kb374U29OV9fkLHrBLnmNIe9/3846wVQqxwP3Pc/Z4bp/gOa/O+w4R93euUf+zj\nqgtTkfdKniMPdcN+pMCGinRy39vovqfs2j5VF6k8rY6712ZxGfauBTChFMO1TZ13n3vczSW+/7a8\n4xBCiBcY5xjnGOfI1EgpuXELZAMg3W29++8+AMed/4aT9u2E0znouPuZ1XCe5nTmvbY2b/9N+a+5\nx5YANhc59ma1r3s8Zcf6gmMU2tBXYJ86RzH7y7LHPf4+970t7rk2ubao824qcvwt6loW2LIpb5+1\nede8s+Dzq9V1rVC7xdXq5L62z90Wu6+tgDOxeIKeRbTa7h57o3tcdc0m2e8eUxa8pjRekXfd1TXc\nWOI7K/tX6PYdbty42bGBcY5xjnGOWxWbdgO4Nc6Wd7ObtE3xGXUz2ZJ3w1M3qT733+qmu6XgsxuL\nBBi176aCfVfn2dNX8N72Yq/nf6cSx5rWnoLvWGjrihLHVwFoc95r60vsq67V2oLX1wPYXqZunXn2\ndZbYpxKdthd8VgXZwuulXt9XxHZlT7FAtQmTfxBsKtQ8z8ZSgapkMOTGjRu3YhvjHOMc4xy3ajaW\nLBId3ASn1eoalLHOhkuflPJW9+8rAayUuUm3aii+sFvQloL38/8+oSuRdNaR8YtK7Mlna953gnTK\nWoYBoKB8odjxVXvlwu+h9i3sGLUOwI0l7CgkO9dBTl+rPpVO+0t8Zsj9s7BEQ9k84TpKKW/C1FwN\nZ9J8Pt0Ari5SMrIBwGCJ46jvWk7pCCGE5MM4VxzGuYkwzhEAXIeM6GFQOuuz7BdCdGPyDb0Y+Tfw\nYThtgxXqRlJ4I1Q13SvK2Fe95sdNqRJ7Cs9fyJD7uU7AqU3PO052fzfQikmfdrovbYLT3naFlHKH\ncBeS9Dk4K0rq5J67SwU7N/iugDMxGZg8yX2V+2ex6zKMIl3K3PkPnUW+2xY4Ty43C2edoK3ua3fU\n6DoQQhobxrniMM5NhHGOAGBTD6Kfctu17ij2YsETNTXxV01A3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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Set the plot size - 3x2 aspect ratio is best\n", "fig = plt.figure(figsize=(12,8))\n", "\n", "plt.subplots_adjust(bottom=0.17,left=0.17,top=0.96,right=0.96)\n", "\n", "# Change the axis units to CMU Serif\n", "plt.setp(ax.get_ymajorticklabels(),family='serif',fontsize=18)\n", "plt.setp(ax.get_xmajorticklabels(),family='serif',fontsize=18)\n", "\n", "\n", "plt.subplot(2,2,1)\n", "plt.plot(w,X[:,0],linewidth=2,label=r'$\\bar{x}_1$')\n", "# Define the X and Y axis labels\n", "plt.xlabel('Frequency (rad/s)',family='serif',fontsize=22,weight='bold',labelpad=5)\n", "plt.ylabel(r'$\\bar{x}_1$',family='serif',fontsize=22,weight='bold',labelpad=10)\n", "plt.ylim(-2,2)\n", "ax = plt.gca()\n", "ax.spines['right'].set_color('none')\n", "ax.spines['top'].set_color('none')\n", "ax.xaxis.set_ticks_position('bottom')\n", "ax.yaxis.set_ticks_position('left')\n", "\n", "\n", "plt.subplot(2,2,2)\n", "plt.plot(w,X[:,1],linewidth=2,linestyle=\"-\",label=r'$\\bar{x}_2$')\n", "# Define the X and Y axis labels\n", "plt.xlabel('Frequency (rad/s)',family='serif',fontsize=22,weight='bold',labelpad=5)\n", "plt.ylabel(r'$\\bar{x}_2$',family='serif',fontsize=22,weight='bold',labelpad=10)\n", "plt.ylim(-2,2)\n", "ax = plt.gca()\n", "ax.spines['right'].set_color('none')\n", "ax.spines['top'].set_color('none')\n", "ax.xaxis.set_ticks_position('bottom')\n", "ax.yaxis.set_ticks_position('left')\n", "\n", "plt.subplot(2,2,3)\n", "plt.plot(w,X[:,2],linewidth=2,linestyle=\"-\",label=r'$\\bar{x}_3$')\n", "# Define the X and Y axis labels\n", "plt.xlabel('Frequency (rad/s)',family='serif',fontsize=22,weight='bold',labelpad=5)\n", "plt.ylabel(r'$\\bar{x}_3$',family='serif',fontsize=22,weight='bold',labelpad=10)\n", "plt.ylim(-2,2)\n", "ax = plt.gca()\n", "ax.spines['right'].set_color('none')\n", "ax.spines['top'].set_color('none')\n", "ax.xaxis.set_ticks_position('bottom')\n", "ax.yaxis.set_ticks_position('left')\n", "\n", "plt.subplot(2,2,4)\n", "plt.plot(w,X[:,3],linewidth=2,linestyle=\"-\",label=r'$\\bar{x}_4$')\n", "# Define the X and Y axis labels\n", "plt.xlabel('Frequency (rad/s)',family='serif',fontsize=22,weight='bold',labelpad=5)\n", "plt.ylabel(r'$\\bar{x}_4$',family='serif',fontsize=22,weight='bold',labelpad=10)\n", "plt.ylim(-2,2)\n", "ax = plt.gca()\n", "ax.spines['right'].set_color('none')\n", "ax.spines['top'].set_color('none')\n", "ax.xaxis.set_ticks_position('bottom')\n", "ax.yaxis.set_ticks_position('left')\n", "\n", "# # Create the legend, then fix the fontsize\n", "# leg = plt.legend(loc='upper right', fancybox=True)\n", "# ltext = leg.get_texts()\n", "# plt.setp(ltext,family='serif',fontsize=16)\n", "\n", "# Adjust the page layout filling the page using the new tight_layout command\n", "plt.tight_layout(pad=0.5, w_pad=3.0, h_pad=2.0)\n", "\n", "\n", "# save the figure as a high-res pdf in the current folder\n", "# plt.savefig('Spring_Pendulum_Example_Amp.pdf')\n", "\n", "# fig.set_size_inches(9,6) # Resize the figure for better display in the notebook" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Licenses\n", "Code is licensed under a 3-clause BSD style license. See the licenses/LICENSE.md file.\n", "\n", "Other content is provided under a [Creative Commons Attribution-NonCommercial 4.0 International License](http://creativecommons.org/licenses/by-nc/4.0/), CC-BY-NC 4.0.\n", "\n" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# This cell will just improve the styling of the notebook\n", "# You can ignore it, if you are okay with the default sytling\n", "from IPython.core.display import HTML\n", "import urllib.request\n", "response = urllib.request.urlopen(\"https://cl.ly/1B1y452Z1d35\")\n", "HTML(response.read().decode(\"utf-8\"))" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.2" } }, "nbformat": 4, "nbformat_minor": 1 }