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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Computational Mechanics Boundary Values - Project 05\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this final project, we will consider all six strings of a guitar and the deflection of the neck of the guitar. Here are the inputs for each of the strings, all L=0.64 m:\n",
"\n",
"|string|density (g/m)|tension (kg)|\n",
"|---|---|---|\n",
"|E|0.401|7.28|\n",
"|B|0.708|7.22|\n",
"|G|1.140|7.32|\n",
"|D|2.333|8.41|\n",
"|A|4.466|9.03|\n",
"|E|6.790|7.71|"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1. The neck of the guitar can be considered a cantilever beam with an applied moment, shown above. At the tip we have a moment equal to the sum of the (tensions in the strings) $\\times$ (bridge height). Here we will consider it as $h=4~mm$. \n",
"\n",
"a. Use a finite difference approximation to determine the deflection of the guitar's bridge if the Young's modulus is E=10 GPa and it is a rectangular cross-section $2\\times4~cm^2$ and $I=\\frac{4\\cdot2^3}{12}~cm^4.$\n",
"\n",
"b. Demonstrate that your finite difference solution has converged. _e.g. decrease the step size $h$ and show the solution converges to a final value._"
]
},
{
"cell_type": "code",
"execution_count": 74,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"plt.rcParams.update({'font.size': 22})\n",
"plt.rcParams['lines.linewidth'] = 3\n",
"from scipy import linalg\n",
"from IPython.display import Audio"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__A:__"
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"w 0 = 0.004 mm\n",
"w 1 = 0.016 mm\n",
"w 2 = 0.0361 mm\n",
"w 3 = 0.0641 mm\n",
"w 4 = 0.1002 mm\n",
"w 5 = 0.1443 mm\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 720x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"\n",
"L=0.64 #m\n",
"h=0.004 #m\n",
"\n",
"#Young's Modulus\n",
"E=10e9 #GPa\n",
"\n",
"#Rectangular cross-section\n",
"I=(.04)*(.02)**3/12 #cm**4\n",
"\n",
"str_den = 1e-3*np.array([.401,.708,1.140,2.333,4.466,6.790])\n",
"str_ten = np.array([7.28,7.22,7.32,8.41,9.03,7.71])\n",
"M = np.sum(str_ten)*h\n",
"N=6\n",
"dx = L/N\n",
"\n",
"a=[7,-4,1,0,0,0]\n",
"b=[-4,6,-4,1,0,0]\n",
"c=[1,-4,6,-4,1,0]\n",
"d=[0,1,-4,6,-4,1]\n",
"e=[0,0,1,-4,5,-2]\n",
"f=[0,0,0,1,-2,1]\n",
"A=np.array([a,b,c,d,e,f])\n",
"b = np.array([0,0,0,0,-M*dx**2/E/I,M*dx**2/E/I])\n",
"w=np.linalg.solve(A,b)\n",
"for i, x in enumerate(w):\n",
" print('w',i,'=',round(x*1000,4),'mm')\n",
"x = np.arange(0,L,dx)\n",
"plt.figure(figsize=(10,10))\n",
"plt.plot(x, w*1000,'o-')\n",
"plt.title('Deflection of Guitars Bridge')\n",
"plt.xlabel('Distance along beam (m)')\n",
"plt.ylabel('Deflection (mm)');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__B:__"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1080x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#6 nodes\n",
"N = 6\n",
"dx = L/N\n",
"A = np.diag(np.ones(N)*6)\\\n",
"+np.diag(np.ones(N-1)*-4,-1)\\\n",
"+np.diag(np.ones(N-1)*-4,1)\\\n",
"+np.diag(np.ones(N-2),-2)\\\n",
"+np.diag(np.ones(N-2),2)\n",
"A[0,0] = 7\n",
"A[N-2,N-2] = 5\n",
"A[N-2,N-1] = -2\n",
"A[N-1,N-3] = 2\n",
"A[N-1,N-2] = -4\n",
"A[N-1,N-1] = 2\n",
"b=np.zeros(N)\n",
"b[N-2] = -M*dx**2/(E*I)\n",
"b[N-1] = 2*M*dx**2/(E*I)\n",
"w_6 = np.linalg.solve(A,b)\n",
"num_6 = np.arange(0,L+dx/2,dx)\n",
"\n",
"#30 nodes\n",
"N = 30\n",
"dx = L/N\n",
"A = np.diag(np.ones(N)*6)\\\n",
"+np.diag(np.ones(N-1)*-4,-1)\\\n",
"+np.diag(np.ones(N-1)*-4,1)\\\n",
"+np.diag(np.ones(N-2),-2)\\\n",
"+np.diag(np.ones(N-2),2)\n",
"A[0,0] = 7\n",
"A[N-2,N-2] = 5\n",
"A[N-2,N-1] = -2\n",
"A[N-1,N-3] = 2\n",
"A[N-1,N-2] = -4\n",
"A[N-1,N-1] = 2\n",
"b=np.zeros(N)\n",
"b[N-2] = -M*dx**2/(E*I)\n",
"b[N-1] = 2*M*dx**2/(E*I)\n",
"w_30 = np.linalg.solve(A,b)\n",
"num_30 = np.arange(0,L+dx/2,dx)\n",
"\n",
"#45 nodes\n",
"N = 45\n",
"dx = L/N\n",
"A = np.diag(np.ones(N)*6)\\\n",
"+np.diag(np.ones(N-1)*-4,-1)\\\n",
"+np.diag(np.ones(N-1)*-4,1)\\\n",
"+np.diag(np.ones(N-2),-2)\\\n",
"+np.diag(np.ones(N-2),2)\n",
"A[0,0] = 7\n",
"A[N-2,N-2] = 5\n",
"A[N-2,N-1] = -2\n",
"A[N-1,N-3] = 2\n",
"A[N-1,N-2] = -4\n",
"A[N-1,N-1] = 2\n",
"b=np.zeros(N)\n",
"b[N-2] = -M*dx**2/(E*I)\n",
"b[N-1] = 2*M*dx**2/(E*I)\n",
"w_45 = np.linalg.solve(A,b)\n",
"num_45 = np.arange(0,L+dx/2,dx)\n",
"\n",
"#60 nodes\n",
"N = 60\n",
"dx = L/N\n",
"A = np.diag(np.ones(N)*6)\\\n",
"+np.diag(np.ones(N-1)*-4,-1)\\\n",
"+np.diag(np.ones(N-1)*-4,1)\\\n",
"+np.diag(np.ones(N-2),-2)\\\n",
"+np.diag(np.ones(N-2),2)\n",
"A[0,0] = 7\n",
"A[N-2,N-2] = 5\n",
"A[N-2,N-1] = -2\n",
"A[N-1,N-3] = 2\n",
"A[N-1,N-2] = -4\n",
"A[N-1,N-1] = 2\n",
"b=np.zeros(N)\n",
"b[N-2] = -M*dx**2/(E*I)\n",
"b[N-1] = 2*M*dx**2/(E*I)\n",
"w_60 = np.linalg.solve(A,b)\n",
"num_60 = np.arange(0,L+dx/2,dx)\n",
"\n",
"x = np.linspace(0,L)\n",
"w_an = M/(2*E*I)*x**2\n",
"\n",
"plt.figure(figsize=(15,10))\n",
"plt.plot(num_6[1:],w_6*1000,'o',label='6 Nodes')\n",
"plt.plot(num_30[1:],w_30*1000,'o',label='30 Nodes')\n",
"plt.plot(num_45[1:],w_45*1000,'o',label='45 Nodes')\n",
"plt.plot(num_60[1:],w_60*1000,'o',label='60 Nodes')\n",
"plt.plot(x,w_an*1000,color='b',label='Analytical Solution')\n",
"\n",
"plt.title('Deflection vs Distance')\n",
"plt.xlabel('Distance along guitar (m)')\n",
"plt.ylabel('Deflection (mm)')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"2. Here we will record the first three frequencies of the 6-string guitar. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"a. Consider the G-string on the guitar, L=0.64 m, $\\mu=1.14~g/m,$ and T=71.81 N [1]. \n",
"\n",
"__Guitar string equation:__ $\\mu\\frac{\\partial^2 y}{\\partial t^2}=T\\frac{\\partial ^2 y}{\\partial x^2}$\n",
"\n",
"a. Calculate the first, second, and third natural frequencies using 6, 30, 45, and 60 nodes. Plot the mode shapes and determine the number of nodes needed to converge for the first three modes. "
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {},
"outputs": [],
"source": [
"L = 0.64 #m\n",
"mu = 1.14e-3 #g/m\n",
"T = 71.81 #N"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [],
"source": [
"#6 Nodes\n",
"N6=6\n",
"dx6=L/(N6+1)\n",
"k6 = T/dx6**2/mu\n",
"A6 = k6*(np.diag(np.ones(N6)*2)\\\n",
" -np.diag(np.ones(N6-1),-1)\\\n",
" -np.diag(np.ones(N6-1),1))\n",
"e6,v6=np.linalg.eig(A6)\n",
"isort = np.argsort(e6.real)\n",
"e6=e6[isort]\n",
"v6=v6[:,isort]\n",
"\n",
"\n",
"#30 Nodes\n",
"N30=30 \n",
"dx30=L/(N30+1)\n",
"k30 = T/dx30**2/mu\n",
"A30 = k30*(np.diag(np.ones(N30)*2)\\\n",
" -np.diag(np.ones(N30-1),-1)\\\n",
" -np.diag(np.ones(N30-1),1))\n",
"e30,v30=np.linalg.eig(A30)\n",
"isort = np.argsort(e30.real)\n",
"e30=e30[isort]\n",
"v30=v30[:,isort]\n",
"\n",
"#45 Nodes\n",
"N45=45 \n",
"dx45=L/(N45+1)\n",
"k45 = T/dx45**2/mu\n",
"A45 = k45*(np.diag(np.ones(N45)*2)\\\n",
" -np.diag(np.ones(N45-1),-1)\\\n",
" -np.diag(np.ones(N45-1),1))\n",
"e45,v45=np.linalg.eig(A45)\n",
"isort = np.argsort(e45.real)\n",
"e45=e45[isort]\n",
"v45=v45[:,isort]\n",
"\n",
"#60 Nodes\n",
"N60=60 \n",
"dx60=L/(N60+1)\n",
"k60 = T/dx60**2/mu\n",
"A60 = k60*(np.diag(np.ones(N60)*2)\\\n",
" -np.diag(np.ones(N60-1),-1)\\\n",
" -np.diag(np.ones(N60-1),1))\n",
"e60,v60=np.linalg.eig(A60)\n",
"isort = np.argsort(e60.real)\n",
"e60=e60[isort]\n",
"v60=v60[:,isort]\n",
"\n",
"#Natural frequencies\n",
"f6 = e6.real**0.5/2/np.pi\n",
"f30 = e30.real**0.5/2/np.pi\n",
"f45 = e45.real**0.5/2/np.pi\n",
"f60 = e60.real**0.5/2/np.pi"
]
},
{
"cell_type": "code",
"execution_count": 87,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"First three natural frequencies of 6-element string (Hz)\n",
" 1st natural frequency: 194.4\n",
" 2nd natural frequency: 379.1\n",
" 3rd natural frequency: 544.8\n",
"First three natural frequencies of 30-element string (Hz)\n",
" 1st natural frequency: 196.0\n",
" 2nd natural frequency: 391.5\n",
" 3rd natural frequency: 586.0\n",
"First three natural frequencies of 45-element string (Hz)\n",
" 1st natural frequency: 196.0\n",
" 2nd natural frequency: 391.9\n",
" 3rd natural frequency: 587.2\n",
"First three natural frequencies of 60-element string (Hz)\n",
" 1st natural frequency: 196.1\n",
" 2nd natural frequency: 392.0\n",
" 3rd natural frequency: 587.7\n"
]
}
],
"source": [
"print('First three natural frequencies of {}-element string (Hz)'.format(N6))\n",
"print(' 1st natural frequency: {0:.1f}'.format(f6[0]))\n",
"print(' 2nd natural frequency: {0:.1f}'.format(f6[1]))\n",
"print(' 3rd natural frequency: {0:.1f}'.format(f6[2]))\n",
"print('First three natural frequencies of {}-element string (Hz)'.format(N30))\n",
"print(' 1st natural frequency: {0:.1f}'.format(f30[0]))\n",
"print(' 2nd natural frequency: {0:.1f}'.format(f30[1]))\n",
"print(' 3rd natural frequency: {0:.1f}'.format(f30[2]))\n",
"print('First three natural frequencies of {}-element string (Hz)'.format(N45))\n",
"print(' 1st natural frequency: {0:.1f}'.format(f45[0]))\n",
"print(' 2nd natural frequency: {0:.1f}'.format(f45[1]))\n",
"print(' 3rd natural frequency: {0:.1f}'.format(f45[2]))\n",
"print('First three natural frequencies of {}-element string (Hz)'.format(N60))\n",
"print(' 1st natural frequency: {0:.1f}'.format(f60[0]))\n",
"print(' 2nd natural frequency: {0:.1f}'.format(f60[1]))\n",
"print(' 3rd natural frequency: {0:.1f}'.format(f60[2]))"
]
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {},
"outputs": [
{
"data": {
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Ed9+RFG1ULquPTs1WUW6RCsYVdElYpeWlevV/fqELXtjV4qhc706YKEW53tZLmvMT6YVtFU5B6lHSnLe7JC4AvZMxZp21dqrbcQC9TbcOF2yMmS/pYknPWGtvarZ6vpzJFe8yxqy21n4Y3iZd0gPhOncy6zswcEWSiob5Q47eqdQxTr8Oybkla0SU/h2Nb6FKLSxskiCc1Q1xFowrUMHtBdLtLdfxZGY6t3E183nKF+8nsCVBVRsPKvTwxC/mS+nCIYcBAOjN2n0rlzEm1xjzRuQhp7VDkn7RrLyxTEnHh5dNhFtZfiNndve3jDE+Y8zTkjZLmijpWUn3dfwtAegPovXJ8JcNUWBLgjJCTsfzJ6YdfguV8Xqb3ELVW6TPma1DsU2HJY7cVpYRqlNgS4L8a1MVOuCJ2l8GAID+riN9TFIkndboEZlfZHyz8naz1v5I0mWS1su5Lex8SR9KukbSJdba6MPlAOj3ovXJsCGp6q0UFe3eI299vV6bFKOHLjTakeKMPV6bnqbM2+b1ylaG1MJC7Z79Le1MNaqXtCNFeuhCo3UTjIp27wnPp9L0kty4vwwAAP3dEfcx6U3oYwL0D6XlpVq0fpEqqyv15PxamWiVjDThqhiVhnZp0bChqowxykjK7NI+I92p8XvMiHWSrIId2/Tuk9FHELOSvnVTrDKSMvrMewTQOvqYANF1ax8TAGiv0vJSlawuUbDOaSXZ2WL/kSxpznIVSOqLP9ELxhVETS48L+dF7YOyM0WysvJX+1WyuqRhHwAA9DduDRcMAE0sWr+oISmR+lb/ka7Q2tDGDc/rglq0flFPhwYAQI8gMQHgmsYzod/yy606a9MX3coa9x9pmD+kl/Yf6QqphYXKvG1ew3wpkT4or01qOqniMWu2H/Hs8QAA9Gb0MQHgisioW407uAc9h/8Yz0zK1AvfeMGNEF2VvzRf/mp/k7KzNtXph89LcbVfXLeN19uvEzagP6KPCRAdLSYAes7GJc4kiSVpqvrvnx426pY3JF268osf3d4Yr4pyi3o6yl6hKLdI3pimt3ZdtqppUiKFR+669Trnc21h1ngAAPoCOr8D6Bkbl0i+a6XaGklSaL+Vooy7NXyvZGQG/ChUkffdMIJXUoaG7d0atW7oQIwU2Op8vpKUM6unwgQAoMuQmADoGcvnNSQlkuRJrHMmE2wmNitLG7+7vCcj67Waj+C1+YHoI3d5EsN9c2prnM+ZxAQA0AdxKxeAblVaXqr8pfnKGSLlj8pSaVKiJCk9Z59MTH2Tuv151K2uEG3kLhNTr/ScfZKk0qRE5Q+uU85jOcpfmq/S8lI3wgQA4IjQYgKg2zSZm8QY+WM9Khk+VJJUMOaAJKnq7SEKVRt5MjOVPmc2nbhbEflsqhYsVKiiQp7EkNJz9il1TI1KkxJVMnyogoMGScx7AgDogxiVC0C3CPh8evv2m5QWqNPnKc58HJHRtjJrQ3phW4UUmyAVLubWoyPRrM9O/qgs+WM9OmtTnS5daTVsr/R5ivR8/lDNv/01l4MF0BijcgHRcSsXgC4XGQp4aKBOg+TM4H71c7ZhnpJKT4yUehRJSWfkzHI+v9SjJBlVemJ01qY6Xf2c1Yi9avjcZz27i7lOAAB9AokJgC5XtWBhq0MBZyRnSXPeJinprJxZzudYskcZyVm6dKWVN9S0ijfkfB8AAPR2JCYAulzI749aPmzvwJ6bpDsV5RZp+N7o61r6PgAA6E1ITAB0OU9mZtTyPakxKjmzhM7Y3aBgXIFC6WlR17X0fQAA0JuQmADoclGHtfV6dcIt80lKutHoG26O+rkzBDMAoC9guGAAXa7JsLZ+P0MB9xA+dwBAX8ZwwQAAAD2I4YKB6LiVC0CHBXw+bZ6ep3cnTNTm6XkMR9vH8P0BAHojbuUC0CErH5mnIQufVFyt09oaqqiQf26xJHHLUB8QmWMmMpxzqKJCW26+Ubur3tS07xe7HB0AYCCjxQRAu5WWlyrm4S+SkggbDDJXRh8RbY6ZuFqrmIefVGl5qUtRAQBAYgKgvTYu0aKVN2poIHq/NObK6Bta+p6GBqwWrbxR2rikhyMCAMBBYgKgbRuXSL5rVTlI+jwlehXmyugbWvqePk+RKgdJ8l1LcgIAcAWJCYC2LZ8n1dYoI1SnJ6YZBZv1TjsUa5gro49InzNbh2JNk7KgR3pimlFGqE6qrXG+bwAAehiJCYC2BbZJkop279G6CUYPXWi0I0Wql7Qz1Wj37G/R8b2PSC0s1O7Z39LOVKN6STtSpIcuNFo3waho9x6nUvj7BgCgJzEqF4C2pY6SAltVUH1AkrTouDRdMzFGGfVS0bS7mM29j5n2/WKVnjNFt628UZWDpIxQnUp27m74fpU6yt0AAQADEokJgLblFTt9D2prVFB9wPkBG5sgFS6WSEr6pIJxBSrYX93wvTaITXC+bwAAehi3cgE4zGET8H0STkJSj5JknGXhYilnltuhojNyZrX4vTIJIwCgpxlrow/92ZdMnTrVlpWVuR0G0C80n4BPkozXq8zb5tGPZIDgGAC6lzFmnbV2qttxAL0NLSYAmog2AR8TKA4sHAMAADeQmABooqUJ+JhAceDgGAAAuIHEBEATLU3AxwSKAwfHAADADSQmAFRaXqr8pfnKeSxH/3NmUPXxsU3WG6+XCRQHkPQ5s2W83iZl9fGx+p8zg8p5LEf5S/NVWl7qUnQAgP6K4YKBAa60vFQlq0sUrHP6FPxt/F5VXxCjH6xOU+yOgDyZmUqfM5tOzwNI5LuuWrBQIb9ftSNS9bsza/TS+L2SJH+1XyWrSySJOWwAAF2GUbmAAS5/ab781Yf3HchMytQL33jBhYjQ23CMAF2LUbmA6LiVCxjgKqsrO1SOgYdjBADQE0hMgAEuIymjQ+UYeDhGAAA9gcQEGOCKcovkjWna0dkb41VRbpFLEaG34RgBAPQEEhNggAn4fNo8PU/vTpiozdPz9OVN9So5s0SZSZkyMspMylTJmSV0akaDgnEFhx0jdx8s1HE/+HXDcRTw+dwOEwDQx9H5HRhAAj6f/HOLm8zqbbxeZd42j1G30G4cR0Dn0PkdiI4WE2AAqVqwsMmPSUmywaCqFix0KSL0RRxHAIDuQGICDCAh/+FDvrZWDkTDcQQA6A4kJsBAsHGJtOAEeRJqo672ZGb2cEDoy1o6XjwJtdKCE5zjDQCADiIxAfq7jUsk37VSYKvSc/bJxNQ3WW28XqXPme1ScOiL0ufMlvE2HaXLxNQrPWefFNjqHG8kJwCADiIxAfq75fOk2hpJUuqYGmWeEpAnMSRJ8mRl0WEZHZZaWKjM2+bJk5UlSfIkhpR5SkCpY5zjTLU1znEHAEAHeNwOAEA3C2xr8jR1TE34B6SRSt51Jyb0eamFhU5CW5ImKcrojs2OOwAA2kKLCdDfpY7qWDnQERxfAIAuQmIC9EOl5aXKX5qvnMdylD8yTaUpaU0rxCZIecXuBIf+Ja/YOZ4aKU1JU/7INOf4W5qv0vJSl4IDAPQl3MoF9DOl5aUqWV2iYJ0zz4S/NqCS4cOk+MEq2LHN+Z/svGIpZ5bLkaJfiBxHy+dJgW0qHTFKJYPjFKwNSJL81X6VrC6R5MwgDwBAS5j5Hehn8pfmy199+HwSmUmZeuEbL7gQEQYSjj+gbcz8DkRHiwnQzxyzZrtuWVmvYXulz1OkJ6YZvTYpRpXVlW6HhgGg8XF21qY6XbrSho/FrQrE+xgBDgDQIhIToB8J+Hz6z+et4sLzKI7YK139nJVUp/JT6YyM7peRlCF/tV9nbarT1c9ZeZ2RqTVir+Sf6/RrIjkBAERD53egH6lasFBxtU1vz/SGpMtWSUW5RS5FhYGkKLdI3hivLl35RVISYYNBVS1Y6E5gAIBejxYToB8J+Q+/t1+Shu21+godj9EDIh3ch9/+k6jrWzpGAQCgxQToRzyZmVHLYzOzejgSDGQF4woUmxX9mGvpGAUAgMQE6EfS58yW8XqblBmvV+lzZrsUEQYqjkUAQEdxKxfQj0Q6FVctWKiQ3y9PZqbS58ymszF6HMciAKCjmMcEAACgBzGPCRAdt3IBAAAAcB2JCQAAAADXkZgAAAAAcB2JCQAAAADXkZgAAAAAcB2JCdCHBHw+bZ6ep3cnTNTm6XkK+HxuhwQcMY5nAEBjzGMC9BEBn0/+ucWywaAkKVRRIf/cYklibgj0ORzPAIDmaDEB+ohP7v5Fw4+4CBsMqmrBQpciAo5c1YKFUY/nT+7+hUsRAQDcRmIC9AGl5aXyVO2Jui7k9/dwNEDntXTceqr2qLS8tIejAQD0BiQmQG+3cYkWrbxRO1Oir/ZkZvZsPEAXaOm43ZkiLVp5o7RxSQ9HBABwG4kJ0JttXCL5rlXlIOmJaUbBZr3Cgh4pfc5sd2IDOiF9zuyox/MT04wqB0nyXUtyAgADDIkJ0JstnyfV1igjVKfXJsXooQuNdqRI9ZJ2pEhLZgylozD6pNTCQi2ZMbTJ8fzQhUavTYpRRqhOqq1xjn8AwIDBqFxAbxbYJkkq2r1HJcOH6rVJMXptkrPKG+NVyZk3uxgc0Dlf/t7Nuv5LJQrWfdEJ3ltfr6Ld4f5U4eMfADAwkJgAvVnqKCmwVQXVByRJi4akqdITo4x6qegrJSoYV+BygMCRixy/i1beqMpBUkaoTkW79zQc70od5WJ0AICeRmIC9GZ5xc699rU1Kqg+4Pxgi02QChdLJCXoBwrGFahgf3XDcd4gNsE5/gEAAwZ9TIDeLGeWk4SkHiXJOMvCxU450F9wnAMAJBlrrdsxdNrUqVNtWVmZ22EAAAC0yRizzlo71e04gN6GFhMAAAAAriMxAQAAAOA6EhMAAAAAriMxAXqJgM+nzdPz9O6Eido8PU8Bn8/tkADXcV4AwMDBcMFALxDw+eSfWywbdCaaC1VUyD/XGSqVmd0xUHFeAMDAQosJ0AtULVjY8OMrwgaDqlqw0KWIAPdxXgDAwEJiAvQCIb+/Q+XAQMB5AQADC4kJ0At4MjM7VA4MBJwXADCwkJgAvUD6nNkyXm+TMuP1Kn3ObJciAtzHeQEAAwuJCeCi0vJS5S/N11d2/VyPXZSo2vQ0yRh5srKUeds8OvhiQEstLFTmbfPkycpqOC8qf3yxvnnwXuU8lqP8pfkqLS91O0wAQBcx1lq3Y+i0qVOn2rKyMrfDADqktLxUJatLFKz7onOvN8arkjNLVDCuwMXIgN6Jcwb9hTFmnbV2qttxAL0NLSaASxatX9TkB5YkBeuCWrR+kUsRAb0b5wwA9G8kJoBLKqsrO1QODHScMwDQv3U4MTHGXGqMecUYEzDG7DfGlBlj/ssYcyT7GmWMudcY874xpsYYEzTGbDbGPGiMGdfR/QF9SUZSRofKgYGOcwYA+rcOJRPGmPsl/UnSVEmvSPqHpOMk3SdpqTEmpgP7OlnSW5KukZQoaZmkv0tKkHS1pA3GmDM7Eh/QlxTlFskb03TEIW+MV0W5RS5FBPRunDMA0L952lvRGHOJpB9JqpT0VWvt5nD5SEkvSbpYTpLR3pt975eUJum3kv7LWlsb3l+spAclfU/SbyRNbm+MQF8S6ay7aP0iVVZXKiMpQ0W5RXTiBVrAOQMA/Vu7R+UyxpRJmiLpu9baPzRbd7aklXKSlmxrbX0b+/JKqgk/zbTWVjZbnyVpe/hpkrX2QGv7Y1QuAADQVzAqFxBdu1pMjDGj5CQlhyT9pfl6a+0qY8x2SdmSTpe0uo1d1kkKhV/fRFkfyZaq9UUCA/QZz765XXcve18Ve2qUlZagG84/XjNOznY7LGDA4BwEgL6nvbdynRxebrLWtpQorJWTmJysNhITa22tMWa5pPMl/bcxpvmtXLeHqz5i+8NEKxhQnn1zu256+i3V1NZJkrbvqdFNT7+lwa8u19HPPKaQ3y9PZqbS58xmAkWgCwR8PlUtWNhwbn168Xd1U1X6YeegJJITAOjF2tv5fWx4+UkrdT5tVrctP5K0WdJ/SCo3xjxjjHlG0seSviWnr8pP2rkvoNe4e9n7DT+IIk4rX6NhD96jUEWFZK1CFRXyzy1WwOdzKUqgfwj4fPLPLW5ybg178B6dVr6mSb2a2jrdvex9l4pOqe0AACAASURBVKIEALRHexOT5PCyupU6+8PLwe3ZobW2XNKZkp6XNErSjPAjW9I7kl6OtKIAfUnFnsMbFa9453nF1zU9nG0wqKoFC3sqLKBfqlqwUDbYdNLF+LpaXfHO84fVjXZuAgB6j/YmJpF+IF12W1V4KOC3JR0r6euShksaISc5GSLpKWNMcSvbXxWeQ6Vsx44dXRUW0GlZaQmHlY2o2RO1bsjv7+5wgH6tpXMo2jkX7dwEAPQe7U1M9oWXya3Uiazb10odSZIxJk3Ss3JaV75mrf0/a+3n1tqd1tq/SvqanE7vc40x46Ptw1r7sLV2qrV26ogRI9r5NoDud8P5xysh1pnS598GvapX465VXGIoal1PZmZPhgb0Oy2dQzGJVv826NWG5wmxMbrh/ON7KiwAwBFob2KyJbwc3Uqdo5rVbU2BnNaRN8K3dDVhrf1Q0j/ldM6f1s4YgV5hxsnZmj/zRF2RvEZ3xv5OowbtVHrOPpmYpqNoG69X6XNmuxQl0D+kz5kt42066aKJqVdmzh7dFfeIvj7oVWWnJWj+zBPp+A4AvVx7R+V6M7ycZIxJaGFkrlOa1W3N0eFloJU6kXb4oe3YH9CrzDg5WzNWPiUFDkmSUsc4p0zVxsEKHfDIk5XFqFxAF4icQ1X//VOF9lt5EuuUnrOv4ZxbNMInzZnvZogAgHZqV2Jird1qjFkvKVfSNyVFm2BxlJwJFl9vxy4rwsspxpjY5p3cw0MGTwk//bg9MQK9TmBbk6epY2rCP5aMVPKuOzEB/VBqYaFS131HUbtBNjsPAQC9V3tv5ZKkyH853WWMOTZSaIxJl/RA+OmdjWd9N8bMN8a8Z4xp/t9Vz0s6IKflZIExJr7RNvGSFsu5NWy3pGUdiBHoPVJHdawcwJHjfAOAPq/diYm1dqmk30jKkPSWMcZnjHlazlwkE+V0Zr+v2WaZko4PLxvvq0rOPCZ1kv5Lzjwm/2eM8clpIflPSQclfc9a29rtXkDvlVcsxTYbBSg2wSkH0LU43wCgz+tIi4mstT+SdJmk9ZLOljNz+4eSrpF0ibW2rpXNm+/rMUmnSvqjpEOS8iWdJ2c0rkck5Vprn+1IfECvkjNLKlwspR4lyTjLwsVOOYCuxfkGAH2esbbLpiZxzdSpU21ZWZnbYQAAALTJGLPOWjvV7TiA3qZDLSYAAAAA0B1ITIAuVFpeqvyl+cp5LEf5S/NVWl7qdkjAgMX5CAB9S3vnMQHQhtLyUpWsLlGwLihJ8lf7VbK6RJJUMK7AxciAgYfzEQD6HlpMgC6yaP2ihh9BEcG6oBatX+RSRMDAxfkIAH0PiQnQRSqrKztUDqD7cD4CQN/DrVxAFwj4fPrNA/VKC9Tp8xTpiWlGr02KkSRlJGW4HB0w8GQkZchf7ZcknbWpTpeutBq2V9qTGqPAUJ9SCwtdjhAA0BwtJkAnBXw++ecWa2igToMkjdgrXf2c1Vmb6uSN8aoot8jtEIEBpyi3SN4Yr87aVKern7Masdf5B29ooE7+ucUK+HxuhwgAaIZ5TIBO2jw9T6GKisPKd6XGaM+f76KjLeCS0vJSpX37Rg0NHD73rycrS+NXLHchKoB5TICW0GICdFLI749aPnRvPUkJ4KKCcQUaurc+6rqWzlsAgHtITIBO8mRmdqgcQM/h/ASAvoPEBOik9DmzZbzeJmXG61X6nNkuRQQggvMTAPoORuUCOikyuk/VgoUK+f3yZGYqfc5sRv0BegHOTwDoO+j8DgAA0IPo/A5Ex61cAAAAAFxHYgIAAADAdSQmAAAAAFxHYgIAAADAdSQmAAAAAFxHYgIAAADAdSQmAAAAAFxHYgIAAADAdSQmAAAAAFxHYgK0Q8Dn0+bpeXp3wkRtnp6ngM/ndkgAuhDnOAC4z+N2AEBvF/D55J9bLBsMSpJCFRXyzy2WJKUWFroZGoAuwDkOAL0DLSZAGz65+xcNP1gibDCoqgULXYoIQFeqWrAw6jn+yd2/cCkiABiYSEyAVpSWl8pTtSfqupDf38PRAOgOLZ3Lnqo9Ki0v7eFoAGDgIjEBWrFo/SLtTIm+zpOZ2bPBAOgWLZ3LO1OcawAAoGeQmAAt2bhElfsr9MQ0o2Cz3lhBj5Q+Z7Y7cQHoUulzZkc9x5+YZlRZTcsoAPQUEhMgmo1LJN+1ygjV6bVJMXroQqMdKVK9pB0p0pIZQ+kUC/QTqYWFWjJjaJNz/KELjV6bFKOMUJ1zPQAAdDtG5QKiWT5Pqq1R0W6jkuFD9dqkGL02yVnljfGq5Myb3Y0PQJf68vdu1vXH3qigMQ1l3vp6Fe3a7VwPcma5GB0ADAy0mADRBLZJkgqqD6hk5y5l1oZkrFVmbUglZ5aoYFyBywEC6EoF4wpUsqPZub5zlwqqDzRcDwAA3YsWEyCa1FFSYKskJzkpqD4QLj9KIikB+qUCz1AVbNt6+IrUUT0fDAAMQLSYANHkFUuxCU3LYhOccgD9E+c9ALiKxASIJmeWVLjYaSGRcZaFi7nPHOjPOO8BwFXGWut2DJ02depUW1ZW5nYYAAAAbTLGrLPWTnU7DqC3ocUEAAAAgOtITAAAAAC4jsQEAAAAgOtITAAAAAC4jsQEAAAAgOtITAAAAAC4jsQEA17A59Pm6Xl6d8JEbZ6ep4DP53ZIAHoZrhMA0P08bgcAuCng88k/t1g2GJQkhSoq5J/rzPKcWljoZmgAegmuEwDQM2gxwYBWtWBhw4+NCBsMqmrBQpciAtDbcJ0AgJ5BYoIBLeT3d6gcwMDDdQIAegaJCQY0T2Zmh8oBDDxcJwCgZ5CYYEBLnzNbxuttUma8XqXPme1SRAB6G64TANAz6PyOAS3ScbVqwUKF/H55MjOVPmc2HVoBNOA6AQA9w1hr3Y6h06ZOnWrLysrcDgMAAKBNxph11tqpbscB9DbcyoUBp7S8VPlL85XzWI7yl+artLzU7ZAA9DFcRwCg63ErFwaU0vJSlawuUbDOGfrTX+1XyeoSSVLBuAIXIwPQV3AdAYDuQYsJBpRF6xc1/JiICNYFtWj9IpciAtDXcB0BgO5BYoIBpbK6skPlANAc1xEA6B4kJhhQMpIyOlQOAM1xHQGA7kFiggGlKLdI3pim8xF4Y7wqyi1yKSIAfQ3XEQDoHnR+x4AS6Zi6aP0iVVZXKiMpQ0W5RXRYBdBuXEcAoHswjwkAAEAPYh4TIDpu5QIAAADgOhITAAAAAK4jMQEAAADgOhITAAAAAK4jMUG/FvD5tHl6nt6dMFGbp+cp4PO5HRKAforrDQB0DsMFo98K+Hzyzy2WDQYlSaGKCvnnFkuSUgsL3QwNQD/D9QYAOo8WE/RbVQsWNvxIiLDBoKoWLHQpIgD9FdcbAOg8EhP0WyG/v0PlAHCkuN4AQOeRmKB/2rhEnqTok4d6MjN7OBgA/V1L1xVPkpU2LunhaACgbyIxQf+zcYnku1bpJ+yWialvssp4vUqfM9ulwAD0V+lzZst4vU3KTEy90k/YLfmuJTkBgHYgMUH/s3yeVFuj1DE1yjwlIE9iSJKVJ1nKvG0eHVEBdLnUwkJl3jZPnmRJsvIkhpR5SkCpY2qk2hrnugQAaBWjcqH/CWxr+DN1jJOgOIxEUgKgm6QWFip13XckRbmNtNF1CQAQHYkJ+p/UUVJga/RyAOhOXH/QDdatWxcn6duxsbEXSsqx1ia4HRPQEcaY3fX19c/X1dU9PGXKlC0t1SMxQf+TV+zc011b80VZbIJTDgDdiesPuti6deuGeDyeR1NSUk4cOnTooaSkpAMxMTHVxhi3QwPaxVqrQ4cOxe7Zs+dbn3322dfWrVs3s6XkhD4m6H9yZkmFi6XUoyQZZ1m42CkHgO7E9QddbNCgQf8+dOjQE8eMGbMrNTV1v8fjqScpQV9ijFF8fHztyJEjd40cOTItJibmqpbq0mKC/ilnFj8EALiD6w+6UExMzOXDhw/fTzKC/iAtLW3fZ599doGkm6Otp8UEAACgl7LWDvd6vYfcjgPoCnFxcbXW2iEtrScxAQAA6L0MrSXoL9o6lklMAAAAALiOxAT9Qml5qfKX5ivnsRzlL81XaXmp2yEBgCSuTwDQXiQm6PNKy0tVsrpE/mq/rKz81X6VrC7hH38AruP6BPSc/fv3m1tuuWXkCSecMGHw4MEnJSQknJydnX3iBRdcMO6FF15Icju+I3XddddlGWOmXHfddVlux9LdSEzQ5y1av0jBumCTsmBdUIvWL3IpIgBwcH0CesZ7770XN2nSpEl33HHHKL/fH3fqqafuO+eccwJDhw4Nvfjii2kvvvhiitsxom0MF4w+r7K6skPlANBTuD4B3W/v3r2D8vPzj9u6dWt8UVGR/6677vLHx8fbyPrKysqYqqoqfvP2AbSYoM/LSMroUDkA9BSuT0D3u+mmmzK3bt0af/HFF3++cOHCisZJiSRlZGTU5eTkHHQrPrQfiQn6tIDPp3sW79P/zg/p/vtDOmtTnSTJG+NVUW6Ry9EBGOiKcovkjfE2PD9rU50eeKBOC+du1ebpeQr4fC5GB/R9wWDQPPHEE8Ml6ZZbbumypkhjzBRjzBRJ+u1vfzvkpJNO+lJiYuLJSUlJJ59xxhnHLVu2LLmlbT/44IO4yy+//OhRo0adGBcXl5uSknLSaaeddtyDDz44tKVtDh48aIqLi0cec8wxk+Lj43OHDx8+ecaMGWM/+OCDuLZiXbFiRdJFF100buTIkTmxsbG5Q4YMmTx9+vRjW4pxw4YN8TNnzhyTlZV1YmxsbG5SUtLJ2dnZJ5533nnHPProo2nt+Xy6C81a6LMCPp/8c4sVG3Tu3x6xV7r6OashcSn68vduVsG4ApcjBDDQRa5Di9Yv0jFrtus/n5fiap3/zA1VVMg/t1iSlFpY6FqMQF/26quvJu7Zs8eTkZFxKDc3N/iPf/wj6a9//Wvarl27PCNHjqwtKCgInHvuudVHuv/Zs2dn3XvvvZm5ubn7zznnnMC7776b8MYbbwwuLCw87rnnnnu/+b5XrFiRNGPGjPH79u2Lyc7OPpSfn79n165dMWvXrh28Zs2awcuWLUt56qmntgwa9EXbQF1dnS644IJjXnrppdT4+Hh7+umn701OTq5fvXr14NNOO23COeecE2gpvltvvXXkbbfdNkqSJk6ceCA3N3e/3++PW7VqVeqqVatSf/nLX35y/fXX74zUX7NmTcL06dO/VF1dPWjs2LHB6dOnB4wxtrKyMu7VV19NCQaDg6644oo9R/p5dRaJCfqsqgULZYNNO5V6Q9L3Vns1/naSEgC9Q8G4AhWMK9DmB/IUqq1oss4Gg6pasJDEBL3K4298MnTx8s3ZO/YdjBsxOP7QtXnjt19++uhdbscVzb/+9a8ESRozZszBSy65ZMzTTz89rPH6hQsXZp5//vm7ly5d+nFycrKNvpeWPfroo+krV6589ytf+coByUkiLr/88tFPPvnk8OLi4qxzzz13c6TugQMHzGWXXTZu3759Md/73veqHnrooa0ej/NTe+3atd6vfe1rxz/77LPDfvWrX+2/4YYbGpKFO++8M/2ll15KTU9Pr12+fPn7J5xwwsHI/mbOnDn2mWeeGaYoli5dmjJv3rxRI0aMqH3yySc/mj59ekOS9MILLyRdcskl43/2s58dfd555+2L3Mp29913j6yurh70s5/9bPv8+fObtDAFAoFBa9euTejoZ9SVuJULfVbI7+9QOQC4iWsW+oLH3/hk6G1/e2d01b6DcVZS1b6Dcbf97Z3Rj7/xSYu3Iblp165dHklau3Zt8jPPPDPsqquu+uztt99+e8eOHf96/PHHP0xPT69dtmzZkCuvvHL0kez/pz/96fZIUiJJMTExuueee7ZL0rp16wYfPHiwYSrz3//+90MqKyvjsrKyDj3wwAPbIkmJJJ1yyinBn/70pxWSdN999zXpZPbggw+mS9LPf/7z7ZGkRJISExPtI4888qnX662PFtu8efOywvvb0jgpkaT8/PzqOXPm+EOhkLn33ntHRMp37NjhkaTCwsLDWmFSU1PrO9O61BVITNBneTIzO1QOAG7imoW+YPHyzdkHQ/VNfh8eDNUPWrx8c7ZbMbWmvt75zV5XV2dmzZq186GHHto2adKkg8OHD6+77LLLAn/5y18+NMbo6aefHvbOO++02V+juUsuueSwH/DZ2dmhlJSUukOHDpnPPvssJlL+8ssvD5akmTNn7mreAV+SfvzjH+80xujTTz+N//jjj2Ml6aOPPordtm1b/KBBg3TVVVcd1iqVnZ0dOuuss/Y2L/f7/Z633347KTk5uW7mzJmHrZekvLy8fZJUVlbW0NdkypQp1ZL0wx/+cPQzzzyTUlNTY6Jt6xYSE/RZ6XNmy3i9TcqM16v0ObNdiggAWsY1C33Bjn0Ho/54b6ncbYMHD25oTbj66qt3NF//1a9+9cDEiRMP1NfX64UXXhjc0f0fe+yxh6KVJycn10lSTU1Nw29pv98fJ0ljx46NOgJYYmKiHTFiRK0kbdmyJTa8jJOkESNG1Hq93qi3mh199NGHxfDBBx/EWWu1f//+mNjY2CmRzvqNH9OmTZsgfdGqJEklJSWfnXHGGfs2btyYNHPmzPFpaWknT548+Us//OEPs9esWePqbVzSEfQxMcZcKumHknIkxUh6T9LvJf3GWhu1qamN/SVI+rGkb0oaLylO0meSyiQttNa+1tF9YmCI3JNdtWChQn6/PJmZSp8zm3u1AfRKXLPQF4wYHH+oKkoSMmJwfNQf6G5rnAQcf/zxUWM8+uijD27atCmxsrIytqP7j4mJabtSmLVOXmFMy40QkTqdFQqFjOQkSPn5+a12Vh82bFgo8vfgwYPrV69e/cGKFSuSSktLU954443kf/3rX8kbN25MevDBBzOuv/76invuuce1+0s7lJgYY+6X9CNJQUnLJdVKypN0n6Q8Y8w3rbV1HdjfWEkvSDpWUpWkVZIOShoj6euSNkgiMUGLUgsL+UcdQJ/BNQu93bV547ff9rd3Rje+nSveM6j+2rzx292MqyVnnHFGQ/+Pzz77zJOVlRVqXifSYpCcnNzh/0DviKysrEOSVF5eHh9t/YEDB8zOnTtjJWnMmDG1kjR69OhDkrRjx47YYDBoorWafPrpp4cliuPGjTskSR6Pxz711FNbOhrr9OnTqyP9UoLBoHn44YeHXnfddaN//etfZ33nO9/ZNXnyZFfmfWn3rVzGmEvkJCWVknKstRdZay+W08rxrqSLJV3Tgf0lSfqHnKTkNkmjrLVft9bOstaeKilT0pJ2vxMAAAB0yuWnj94196KJn6QPjj9kJKUPjj8096KJn/TWUbnGjh1bm5OTUy1Jf//73w+7VWvHjh0xmzZtSpSk0047rVs7dn/1q1/dJ0nPPPPM0Nra2sPW33///cOstTr66KMPjh07tlaSjj322Nrs7OxD9fX1+t3vfnfYAAMVFRWe1157LaV5+dixY2vHjx9fs2fPHs/f/va3Dt+i1pjX67XXXnvt55MnT6621mrdunWJndlfZ3Skj8lN4eWN1tqGodGstZ/JubVLkn5mjGnvPm+RdIykP1hri621Tb5Ba+3n1toPOhAfAAAAOuny00fvWvPzc9/6+M6CdWt+fu5bvTUpibjxxhv9knTPPfdkrV69uqGfxIEDB8yVV145ev/+/TGTJk06kJeX162JyZVXXrk7IyPj0Pbt2+OuueaaUXV1X9xEtG7dOu9dd92VLUnXXHNNk2F6r7rqqs8k6Y477shq3EG/pqbG/OAHPzg6GAxG/W1dXFxcIUnf//73xz799NOHJS/BYND86U9/Sn3xxReTImV33nnniA0bNhzWovPOO+/EffjhhwlSy31kekK7buUyxoySNEXSIUl/ab7eWrvKGLNdUrak0yWtbmN/cZL+I/z0zo4EDAAAAERceumlgVWrVn328MMPj5w2bdqEnJyc6iFDhoQ2bNiQtGPHjtj09PTaP//5z+WNJzXsDomJifbxxx8vv/jii8c//PDDI59//vm0yZMnV+/evduzZs2awbW1tWbGjBmfN57wUJJuvvnmquXLl6e8/PLLqbm5uSecfvrpe5OSkurXrl2bfOjQoUEXX3zx59HmMrn88sv3fPjhh9tuv/32UZdccsn40aNHHxw3blwwLi6uvqKiIu7jjz/27t+/P+auu+76NDIM8KOPPjripptuOnrUqFEHjzvuuJqkpKT6HTt2xK5bty65trbWXHTRRbvOOeecA81fq6e09xs6ObzcZK2taaHO2mZ1WzNF0jBJW6217xpjzjTG/MIY85Ax5r+NMWe0My4AAAAMcA899NC2xx577KPc3Nz9H3zwQcKqVatSExIS6n/wgx989uabb75z4okn9kgrQF5eXnVZWdk7l1566Y66ujqzbNmyIRs2bEiaPHly9QMPPPBx81nfJcnj8eiFF1746Oabb96elZV1cPXq1Smvv/764NNOO23fG2+88c6YMWNaHHigpKTks1deeeWdWbNm7ayvr9fq1atTXnnlldS9e/d6Tj311H2/+tWvPvnud7/b0OJ16623bv/2t7+9Izk5uX79+vXJf//734ds2bIl/pRTTtn3yCOPlD/77LMfd+PH0ybTntEBjDHXSlok6dlwv5JodRZJulbSr6y1P2ljf1dJekjSCklbJX03SrWnJH2nlUSowdSpU21ZWVlb1QAAAFxnjFlnrZ3anrobNmzYMnny5J1t1wT6hg0bNgyfPHnymGjr2ttiEpmYpbV78/aHl+3pgBPp3PNVSf8u6R45neCHyBmNa7ukSyTd3874AAAAAPRh7U1MIgMyd83gy1+8rkfSI9baG6y1H1lr91hr/0/SjPBrfdcYMy5qQMZcZYwpM8aU7dhx2Hw6AAAAAPqQ9iYm+8LL5FbqRNbta6VO8/1J0m+br7TWlklaJye+adF2YK192Fo71Vo7dcSIEe14SQAAAAC9VXsTky3h5ehW6hzVrG579idJLXWyiZRntGN/AAAAAPqw9iYmb4aXk4wxCS3UOaVZ3dasb/T3YcOfhQ0PL/e3sB4AAABAP9GuxMRau1VOMhEn6ZvN1xtjzpY0Ss6s8K+3Y3/bJf0z/DQvyv6GSMoNP2W4LQAAAKCf68hMM/PDy7uMMcdGCo0x6ZIeCD+901pb32jdfGPMe8aY+TrcHeFlsTHmpEbbeCX9RlKqnH4mbSY6AAAAAPq2ds38LknW2qXGmN9I+qGkt4wxL0qqldPikSLpWUn3NdssU9Lx4WXz/fmMMfdI+omkfxpj/inpc0mnSsqSM2Twt217JloBAAAA0Kd1pMVE1tofSbpMzm1dZ0s6X9KHkq6RdIm1tq6D+7tB0kxJr0k6UdKFkg5I+rWkk621mzuyPwAAAAB9U7tbTCKstU9IeqKdda+QdEUbdZ6R9ExH40D/F/D5VLVgoUJ+vzyZmUqfM1uphYVuhwUA3YbrHoCBrEMtJkBPCfh82nbLzxWqqJCsVaiiQttu+bkCPp/boQFAtwj4fPLPLW5y3dty841a+cg8t0MDgB5BYoJe6ZO7f6FBB2ublA06WKtP7v6FSxEBQPeqWrBQNhhsUhZXaxXz8JMqLS91KSoA6DkkJuiVPFV7OlQOAH1dyO+PWj40YLVo/aIejgYAeh6JCXqfjUu0MyX6qpbKAaCv82QeNoClJOnzFKmyOnrSAgD9CYkJepeNSyTftXr+y1Kw2dAMQY/0fP5Qd+ICgG6WPme2DsWaJmVBj/TENKOMUJ1zfQSAfozEBL3L8nlSbY2+nLlHv/+atCNFqpez/P1F8fry9252O0IA6BaphYXaPftb2tnouvfQhUbrJhgV7drtXB8BHOaOO+5Iv/DCC8eNGzduUlpa2kkejyd3yJAhk88888zjHnjggaH19fWtbv/ggw8OnTJlyvGDBw8+KTEx8eQTTjhhwvz580fU1XVoFoxe57rrrssyxky57rrrstyOpb06PFww0K0C2yRJBdUHpJHS7VelqdITo4xQnYqm36GCcQUuBwgA3Wfa94tVuutB3TYkteHaV7Jzt3NNVI3b4QG90uLFizN27drlGT9+fE1ubu7+xMTE+m3btsW98cYbg19//fXBTz/99JBly5Z9FBMTc9i23/nOd45+/PHHR8THx9szzjhjr8fjsa+//nrKzTfffPRLL72U8txzz33k8fBzuafwSaN3SR0lBbZKcpIT5x9jSalHSSQlAAaAAs9QFWzbeviK1FE9HwzQB/zhD38oP+OMMw6kpKQ0aRopKyvzfu1rXzt++fLlaffdd9+woqKizxuvf/TRR9Mef/zxEcOHD69dsWLF+yeeeOJBSdq6datn2rRpx//jH/9Imz9/fvrcuXOrevL9DGTcyoXeJa9Yik1oWhab4JQDwEDAdRDokPPPP39/86REkqZOnRq88sorqyTpxRdfPGz4nHvuuSdTkm699dbtkaREko466qjQ4sWLP5Gc1pi+fktXX0Jigt4lZ5ZUuNhpIZFxloWLnXIAGAi4DgJdxuPxWEnyer22cflHH30Uu2nTpsTY2Fh7xRVX7Gq+XUFBwf709PTanTt3xq5YsSKpva9njJlijJkiSb/97W+HnHTSSV9KTEw8OSkp6eQzzjjjuGXLliW3tO0HH3wQd/nllx89atSoE+Pi4nJTUlJOOu2004578MEHWxz55+DBg6a4uHjkMcccMyk+Pj53+PDhk2fMmDH2gw8+iGsr1hUrViRddNFF40aOHJkTGxubO2TIkMnTp08/tqUYN2zYED9z5swxWVlZJ8bGxuYmJSWdnJ2dfeJ55513zKOPPprWns+nLdzKhd4nZxb/AAMY2LgOwk1rHxmqVXdla39VnJLTD+nsG7frlO8f9uO9t3vvvffiHnvssRGSVFhY2GQitH/+85+JknTsscfWJCcn22jb5+TkVL/44otpZWVlieedd151j8LelgAAIABJREFUR1579uzZWffee29mbm7u/nPOOSfw7rvvJrzxxhuDCwsLj3vuuefeP/fcc5vsb8WKFUkzZswYv2/fvpjs7OxD+fn5e3bt2hWzdu3awWvWrBm8bNmylKeeemrLoEFftCnU1dXpggsuOOall15KjY+Pt6effvre5OTk+tWrVw8+7bTTJpxzzjmBluK79dZbR952222jJGnixIkHcnNz9/v9/rhVq1alrlq1KvWXv/zlJ9dff/3OSP01a9YkTJ8+/UvV1dWDxo4dG5w+fXrAGGMrKyvjXn311ZRgMDjoiiuu6PRkcyQmAAAAcKx9ZKiW3TRa/5+9O4+vqrr3//9e5GQgIwIJGZAkCA4oREMQh2o1wagX830w9NLWYi3VcsVSA1hxKjHFAVAQUItI9Yr3B1VbFO4vTUUqOFADX0hQUFGZBZITEqZAhpNxf/9IThpCAgmcZCfh9Xw8zuOYvffZfPY27HXerL3Wriqv/QZcfMhHHz4eLUkdPZwsXLiw12effRZUWVlpnE6nzxdffBFgWZb57W9/m//LX/7ylC/Ne/bs8ZWkqKioiub217dv3wpJ2rt3r29ra1m6dGnYJ5988u1NN91UKtWGiPHjx0e/8847vdPS0iJHjBix071taWmp+cUvftH/5MmTXr/+9a8LXnvttQPuAfebN2/2u+OOOy5btWpVr3nz5hU/8sgj9WFh9uzZYR9//HFIWFhY5dq1a7+/6qqryt37GzNmTOzKlSt7NVXbihUrgmfOnNk3NDS08p133tmdmJhYH5LWrFkTMHbs2IGPPfZYv9tuu+3kkCFDyiXphRde6FNSUtLtsccey501a1Z+w/0VFRV127x5c/fGf8654FYuAAAA1Pp0TlR9KHGrKu+mT+dE2VRRi2VlZQW+//77vTIyMnpmZ2cHStIjjzyS+/zzz+c13ra4uLibJPn7+zc7l3BgYGBN3banT+d1FtOnT891hxJJ8vLy0ty5c3MlKScnJ6i8vLz+oUVvvvnmRfn5+T6RkZEVixYtOthwFrBhw4a5pk+fnidJr7zySnjDP2Px4sVhkvTkk0/mukNJ3TFZb7zxxn4/P78mj23mzJmRdfvb1zCUSFJycnLJ1KlTnVVVVebll18OdS8vLCx0SFJKSsppvTAhISE1jXuAzhXBBAAAALWKC5oem9Dc8g7k3Xff/cGyrJyTJ09uyc7O/ua+++4rmDdvXmR8fPwV+/bt8264rWXV3r1ljGlyX+dr7Nixp32Bj4qKqgoODq6uqKgwhw4dqg87n332WZAkjRkz5qivr+9pt5X97ne/O2yM0f79+3337t3rLdWOkTl48KBvt27dNHHixNN6sqKioqpuvPHGE42XO51Ox9dffx0QGBhYPWbMmNPWS1JSUtJJSXKHO0kaOnRoiSRNmjQpeuXKlcFlZWVtcuIIJgAAAKgVGNb0rU3NLe+AAgMDraFDh7pee+21g0888UTu999/333ixIn9Gm4TFBRUI0klJSXNfhd296oEBga2elquAQMGNHm+3PsqKyur/3OdTqePJMXGxpY39Rl/f38rNDS0UpLcAWvfvn0+khQaGlrZeGC/W79+/U6rYceOHT6WZam4uNjL29t7qHuwfsPXLbfccoUkHT16tL7rJj09/dD1119/ctu2bQFjxowZ2KNHj2vi4uIunzRpUtSmTZs8chuXxBgTAAAAuP340dxTxphIksO3Rj9+NNfGqs7Zgw8+eHjmzJl9161bF1JeXm7cPRLuEJCbm9tsT5B7XUxMTJOB4Uyaephjc1rSe+Pe5nxVVVUZqTYgJScnn3Gweq9evarc/x0UFFSTlZW1Y926dQGZmZnBGzduDPzyyy8Dt23bFrB48eLwhx9+OG/u3LnO862PYAIAAIBa7gHuXWBWLknq3bt3tZeXl1VdXW0KCgq8Lr744ipJGj58eKkk7dq1q3txcbFpamaubdu2BUhSQkJCaeN1nhQZGVkh/XtAfmOlpaXm8OHD3pIUExNTKUnR0dEVklRYWOjtcrlMU70m+/fvPy109e/fv0KqnUb5vffe29faWhMTE0vc41JcLpdZsmRJz2nTpkW/+OKLkffcc8/RuLi4Voe4hriVCwAAAP827L6j+v2Or5R+PEe/3/FVZw0lkvTBBx8EVVdXm6CgoOqIiIj6HoABAwZUDho0qLSystIsXbr0tOeEZGZmBh46dMi7d+/elUlJSR4Z2N2cm2+++aQkrVy5smdlZeVp6//0pz/1sixL/fr1K4+Nja101x8VFVVRU1Oj119//bT68/LyHJ9//vlpD5WMjY2tHDhwYNnx48cdf//734POp24/Pz/roYceOhIXF1diWZZycnL8z2d/EsEEAAAAndTq1asDX3311Z5NDcZes2ZNwKRJk6Il6Wc/+9nhhrNdSdLvf//7fEn64x//GPX111/X91bk5uY6UlNToyXpoYceym/NbVnnYsKECcfCw8MrcnNzfSZPnty34ZPmc3Jy/ObMqZ0RbfLkyadM0ztx4sRDkvTss89Gbt++vb53pKyszNx///39XC5Xk9/z09LS8iTpvvvui33//fdPCy8ul8ssX7485KOPPqp/sOTs2bNDt27delqPzvbt23127drVXWp+jExrcCsXAAAAOqUdO3b4pqamxjz66KP9rrzyytLQ0NDK4uJir/379/vu3r3bT5JuueWWohdffPG0MTITJkw4tnbt2sLly5eHJiQkXHnDDTeccDgc1oYNG4KKi4u9RowYcfzxxx8vaOtj8Pf3t5YtW7Zn9OjRA5csWdLngw8+6BEXF1dy7Ngxx6ZNm4IqKyvNqFGjjjR84KEkPfHEEwVr164N/uyzz0Li4+Ovuu66604EBATUbN68ObCioqLb6NGjjzT1LJPx48cf37Vr18Fnnnmm79ixYwdGR0eX9+/f3+Xj41OTl5fns3fvXr/i4mKvOXPm7HdPA7x06dLQxx9/vF/fvn3LL7300rKAgICawsJC75ycnMDKykpz1113Hb311lvP+5Y3ekwAAADQKSUnJ59MTU11XnHFFaV79+71W7NmzUWff/55cFlZWbfbb7/92P/8z//s/vjjj3c193T3ZcuW7X/11Vf3Dho0qHTTpk1B69evD+7Xr1/5c889t3/16tW7G/eytJWkpKSS7Ozs7XfffXdhdXW1+fDDDy/aunVrQFxcXMmiRYv2Nn7quyQ5HA6tWbNm9xNPPJEbGRlZnpWVFbxhw4ag4cOHn9y4ceP2mJiYZmdSS09PP7R+/frt48aNO1xTU6OsrKzg9evXh5w4ccJx7bXXnpw3b94P9957b/0tfE899VTuz3/+88LAwMCaLVu2BK5evfqiffv2+Q4bNuzkG2+8sWfVqlV7PXEejKdG+dspISHBys7OtrsMtFJRRoYK5i9QldMpR0SEwqZOUUhKit1lAUCHxrWz8zPG5FiWldCSbbdu3bovLi7u8Nm3BDqHrVu39o6Li4tpah23csEWRRkZcs5Ik+VySZKq8vLknJEmSTSwANAMrp0AujJu5YItCuYvqG9Y3SyXSwXzF9hUEQB0fFw7AXRlBBPYosrZ9DN4mlsOAODaCaBrI5jAFo6IiFYtBwBw7QTQtRFMYIuwqVNk/PxOWWb8/BQ2dYpNFQFAx8e1E0BXxuB32MI9SJOZZQCg5bh2AujKCCawTUhKCo0pALQS104AXRW3cgEAAACwHcEE7SZzT6aSVyRryFtDlLwiWZl7Mu0uCQA6Na6rALoSbuVCu8jck6n0rHS5qmvn33eWOJWelS5JGtl/pI2VAUDnxHUVQFdDjwnaxcItC+sbTzdXtUsLtyy0qSIA6Ny4rgLoaggmaBf5JfmtWg4AODOuqwC6GoIJ2kV4QHirlgMAzozrKoCuhmCCdpEanyo/r1MfCubn5afU+FSbKgKAzo3rKtC8yZMnRxljhhpjhqalpfVpapuxY8fGuLdp6hUbG3tle9ftSdOmTYs0xgydNm1apN21tBSD39Eu3AMxF25ZqPySfIUHhCs1PpUBmgBwjriuAk379NNP/RcvXhxujJFlWWfdPj4+vjgmJqa88fLw8PDKNikQzSKYoN2M7D+SBhMAPIjrKnCqsrIyc99998X27NmzMi4uruSjjz7qcbbP3HvvvYcfeuihI+1RH86MW7kAAADQJUybNi1y9+7dfgsWLPghODi42u560DoEEwAAAHR669atC/jzn/8cnpKScvTuu+8usqMG9/gUSfrzn/980dVXX325v7//NQEBAddcf/31l3744YeBzX12x44dPuPHj+/Xt2/fwT4+PvHBwcFXDx8+/NLFixf3bO4z5eXlJi0trc8ll1xypa+vb3zv3r3jRo0aFbtjxw6fs9W6bt26gLvuuqt/nz59hnh7e8dfdNFFcYmJiQOaq3Hr1q2+Y8aMiYmMjBzs7e0dHxAQcE1UVNTg22677ZKlS5eetWeqJbiVCwAAAJ1aaWmpue+++2KCg4OrXnvttQOt+ewnn3wStG3btu4lJSVeYWFhlTfffHPxqFGjTnh5eZ1zPVOmTIl8+eWXI+Lj44tvvfXWom+//bb7xo0bg1JSUi79xz/+8f2IESNKGm6/bt26gFGjRg08efKkV1RUVEVycvLxo0ePem3evDlo06ZNQR9++GHwe++9t69bt3/3KVRXV+vOO++85OOPPw7x9fW1rrvuuhOBgYE1WVlZQcOHD7/i1ltvbTacPfXUU32efvrpvpI0aNCg0vj4+GKn0+nz6aefhnz66achzz///A8PP/zwYff2mzZt6p6YmHh5SUlJt9jYWFdiYmKRMcbKz8/3+de//hXscrm6/epXvzp+ziesDsEEAAAA9d79/t2ei7cujjpSdsSnV/deFQ/EPZD708t+etTuus4kNTU1at++fX5LlizZExERUdWaz65cubJXw59feuklXXLJJa6//OUve6699tqyc6ln6dKlYZ988sm3N910U6lUGyLGjx8f/c477/ROS0uLHDFixE73tqWlpeYXv/hF/5MnT3r9+te/LnjttdcOOBy1X9E3b97sd8cdd1y2atWqXvPmzSt+5JFH6sPC7Nmzwz7++OOQsLCwyrVr135/1VVXlbv3N2bMmNjGx+W2YsWK4JkzZ/YNDQ2tfOedd3YnJibWh6Q1a9YEjB07duBjjz3W77bbbjs5ZMiQckl64YUX+pSUlHR77LHHcmfNmnXKw5KKioq6bd68ufu5nKfGuJULAAAAkmpDyfObn48+XHbYx5Klw2WHfZ7f/Hz0u9+/2+ztRHb75z//GfDf//3ffUaMGHH8N7/5zbGWfi4uLq70mWeeOZCdnf1NUVHRF/v27dv29ttv77rsssvKdu/e7XfnnXdeunfvXu9zqWn69Om57lAiSV5eXpo7d26uJOXk5ASVl5cb97o333zzovz8fJ/IyMiKRYsWHXSHEkkaNmyYa/r06XmS9Morr5zykKLFixeHSdKTTz6Z6w4lkuTv72+98cYb+/38/Gqaqm3mzJmRdfvb1zCUSFJycnLJ1KlTnVVVVebll18OdS8vLCx0SFJKSsppvTAhISE1jXuAzhXBBAAAAJKkxVsXR1VUV5zy/bCiuqLb4q2Lo+yq6UyKi4vNb37zm9iAgIDq119/fX9rPpuWllbw5JNPFgwdOtQVHBxcEx0dXfmzn/2s6Msvv/w2Li6u5OjRo46nnnoq4lzqGjt27Glf4KOioqqCg4OrKyoqzKFDh+rvE/vss8+CJGnMmDFHfX19T5vf+He/+91hY4z279/v6w5Ku3fv9j548KBvt27dNHHixNN6s6KioqpuvPHGE42XO51Ox9dffx0QGBhYPWbMmNPWS1JSUtJJScrOzq4fazJ06NASSZo0aVL0ypUrg8vKykxTnz1fBBO0iaKMDO1MTNK3VwzSzsQkFWVk2F0SAFwQuP7ifBwpO9LkoOnmltstNTW17w8//OD79NNPH4iOjvbIc0f8/PysRx55xClJ69atCzmXfQwYMKCiqeWBgYHVklRWVlb/HdzpdPpIUmxs7GnPUpFqe0BCQ0MrJWnfvn3ede8+khQaGlrp5+fX5MNa+vXrd1oNO3bs8LEsS8XFxV7e3t5NPljylltuuUKSjh49Wt91k56efuj6668/uW3btoAxY8YM7NGjxzVxcXGXT5o0KWrTpk0euY1LYowJ2kBRRoacM9JkuVySpKq8PDlnpEmSQlJS7CwNALo0rr84X72696o4XHb4tBDSq3uvJr9o22316tU9unXrpuXLl/devnx574br9uzZ4ydJb775Zujq1at7xMbGut59990fWrLfwYMHuySpoKDgnG7las3AefdDII1pvhOiJQ+KbImqqioj1Qak5OTkMw5W79WrV/1YnaCgoJqsrKwd69atC8jMzAzeuHFj4Jdffhm4bdu2gMWLF4c//PDDeXPnznWeb30EE3hcwfwF9Y2im+VyqWD+AhpGAGhDXH9xvh6IeyD3+c3PRze8ncvHy6fmgbgHcu2s60xqamq0efPmZqfhPXjwoO/Bgwd9T5w40eK0UFBQ4JAkf3//JsdpeFJkZGSFJO3Zs8e3qfWlpaXm8OHD3pIUExNTKUnR0dEVklRYWOjtcrlMU70m+/fvPy1g9u/fv0KSHA6H9d577+1rba2JiYkl7nEpLpfLLFmypOe0adOiX3zxxch77rnnaFxcXJO9Pi3FrVzwuCpn04G5ueUAAM/g+ovz9dPLfnp0+rDpP/Tu3rvCyKh3994V04dN/6GjzsqVm5v7lWVZOU29xowZc0SSZsyYcdCyrJzvvvtue0v3+/bbb/eUpMGDB3tkUPeZ3HzzzSclaeXKlT0rK0+/G+1Pf/pTL8uy1K9fv/LY2NhKSRowYEBlVFRURU1NjV5//fXTJibIy8tzfP7558GNl8fGxlYOHDiw7Pjx446///3vQedTt5+fn/XQQw8diYuLK7EsSzk5Of7nsz+JYII24Oh12t+D2uUR5zR+DADQQs1dZx0BlrTtr+1cDTqrn17206Mfj/v4q233bsv5eNzHX3XUUHI+srKyur/99tshVVWnzixcWVmp9PT0PkuXLg2TpClTphxq61omTJhwLDw8vCI3N9dn8uTJfaur//3A+pycHL85c+ZESdLkyZNPmaZ34sSJhyTp2Wefjdy+fXt970hZWZm5//77+7lcria/56elpeVJ0n333Rf7/vvvn/alzeVymeXLl4d89NFHAe5ls2fPDt26detpPTrbt2/32bVrV3ep+TEyrcGtXPCsbX9V2GW5ch7zl1X9778PxsdbYVOn2FgYAHR9YVOnnDLGRJKMV43CriqSMh6qXTBknE3VAR3H7t27fX/5y19eMmnSpOqYmBhXRERERXFxsdf333/fvbCw0Ltbt2568sknD44dO7bJmas8yd/f31q2bNme0aNHD1yyZEmfDz74oEdcXFzJsWPHHJs2bQqqrKw0o0aNOtLwgYeS9MQTTxSsXbs2+LPPPguJj4+/6rrrrjsREBBQs3nz5sCKiopuo0ePPtLUs0zGjx9/fNeuXQefeeaZvmPHjh0YHR1d3r9/f5ePj09NXl6ez969e/2Ki4u95syZs989DfDSpUtDH3/88X59+/Ytv/TSS8sCAgJqCgsLvXNycgIrKyvNXXfddfTWW28tbfxntRY9JvCstTMVcvEJRQwrksO/SpIlh3+VIn5Uxf3NANDGQlJSFPH0TDkCpfrr77AihcSUSZVl0tqZdpcIdAjDhg0rnTBhQkFsbKwrLy/PZ926dT02b94c1L1795qf/OQnRz755JNvn3nmmTbvLXFLSkoqyc7O3n733XcXVldXmw8//PCirVu3BsTFxZUsWrRob+OnvkuSw+HQmjVrdj/xxBO5kZGR5VlZWcEbNmwIGj58+MmNGzduj4mJaXbCgvT09EPr16/fPm7cuMM1NTXKysoKXr9+fciJEycc11577cl58+b9cO+999b3lD311FO5P//5zwsDAwNrtmzZErh69eqL9u3b5zts2LCTb7zxxp5Vq1bt9cR5MJ4a5W+nhIQEKzs72+4yIEnpPSQ19TtlpPQzTv4AAPAUrsUdmjEmx7KshJZsu3Xr1n1xcXGHz74l0Dls3bq1d1xcXExT6+gxgWeF9G3dcgCA53EtBtAJEUzgWUlpknej5+x4d69dDgBoH1yLAXRCBBN41pBxUspLUsjFkkzte8pLDLYEgPbEtRhAJ8SsXPC8IeNo/ADAblyLAXQy9JgAAAAAsB3BBAAAAIDtCCYAAAAAbEcwAQAAAGA7ggkAAAAA2xFMcF4y92QqeUWyhrw1RMkrkpW5J9PukgAAzeCaDaAjY7pgnLPMPZlKz0qXq9olSXKWOJWelS5JGtl/pI2VAQAa45oNoKOjxwTnbOGWhfUNnJur2qWFWxbaVBEAoDlcswF0dAQTnLP8kvxWLQcA2IdrNoCOjmCCcxYeEN6q5QAA+3DNBtDREUxwzlLjU+Xn5XfKMj8vP6XGp9pUEQCgOVyzAXR0BBOcs5H9Ryr9hnRFBETIyCgiIELpN6QziBIAOiCu2ejqiouLzR/+8Ic+V1111RVBQUFXd+/e/ZqoqKjBd955Z/81a9YENPe5xYsX9xw6dOhlQUFBV/v7+19z1VVXXTFr1qzQ6urq9izf46ZNmxZpjBk6bdq0SLtraSlm5UKrFWVkqGD+AlU5nbo0IkJ/mzpFIT9JsbssAMBZjOw/UiP7j2xwHX9EOyNeVNjUKQpJ4TqOzuu7777zuf322y/dv3+/b8+ePauuvfbak76+vtaBAwd8P/roox6DBw8uS05OLmn8uXvuuaffsmXLQn19fa3rr7/+hMPhsDZs2BD8xBNP9Pv444+D//GPf+x2OPi63F4402ixVV/k6rNF/5/uyfqL/KorJUlVeXlyzkiTJBo1AOgEijIy5JyRJstVO0NXVV6e9j72pBa+84V2DP6RHrn9Mo26JsrmKoGWO3HiRLfk5ORLDxw44JuamuqcM2eO09fX13Kvz8/P9yooKDjtO+/SpUt7LFu2LLR3796V69at+37w4MHlknTgwAHHLbfcctk///nPHrNmzQqbMWNGQXsez4WMW7nQIqu+yNXj73+l/5P9v/WhxM1yuVQwf4FNlQEAWqNg/oL6UOLmW12pe7d/oNzjZXr8/a+06otcm6oDWu/xxx+POHDggO/o0aOPLFiwIK9hKJGk8PDw6iFDhpQ3/tzcuXMjJOmpp57KdYcSSbr44ourXnrppR8k6aWXXgrv7Ld0dSYEE7TICx9+r7LKaoWWHW9yfZXT2c4VAQDORXPXa/f1vayyWi98+H17lgScM5fLZf7yl7/0lqQ//OEPLZ77evfu3d7ffPONv7e3t/WrX/3qaOP1I0eOLA4LC6s8fPiw97p165odn9KYMWaoMWaoJP35z3++6Oqrr77c39//moCAgGuuv/76Sz/88MPA5j67Y8cOn/Hjx/fr27fvYB8fn/jg4OCrhw8ffunixYt7NveZ8vJyk5aW1ueSSy650tfXN753795xo0aNit2xY4fP2Wpdt25dwF133dW/T58+Q7y9veMvuuiiuMTExAHN1bh161bfMWPGxERGRg729vaODwgIuCYqKmrwbbfddsnSpUt7tOT8nA3BBC2Sd7xMklTYvenfO0dERHuWAwA4R81drxte393XfFyYjr79Ts+dN908+NsrBg3dedPNg4++/U6zX4zt9q9//cv/+PHjjvDw8Ir4+HjXP//5z4DJkydH3X333dFTp06N/Oijj5oMFf/3//5ff0kaMGBAWWBgoNXUNkOGDCmRpOzsbP/W1jVlypTIBx54oL+3t7d16623FvXp06di48aNQSkpKZc2VdO6desCEhISBi1fvjxUkpKTk49fddVVJVu2bAmcNGlS7OjRo2NqampO+Ux1dbXuvPPOS55++um+ubm5vtddd92J4cOHn8zKygoaPnz4Ffv27Ws2nDz11FN9RowYcfk//vGPi0JDQytHjBhxPDo6uvzTTz8N+Y//+I/L5s2b17vh9ps2bep+4403Dlq5cmUvPz+/msTExKKbbrqpKDQ0tPJf//pX8BtvvBHa2nPUFMaYoEUie3RX7vEyLR10p1K/XHHK7VzGz09hU6fYWB0AoKXCpk45ZYyJJLm8vLV00J31P0f26G5HaegAjr79Ts+C2bOjrfLybpJUVVjoUzB7drQk9fz5z07rWbDbl19+2V2SYmJiyseOHRvz/vvv92q4fsGCBRG33377sRUrVuxtGED27NnjK0lRUVEVze27b9++FZK0d+9e39bWtXTp0rBPPvnk25tuuqlUqg0R48ePj37nnXd6p6WlRY4YMWKne9vS0lLzi1/8ov/Jkye9fv3rXxe89tprB9wD7jdv3ux3xx13XLZq1ape8+bNK37kkUcOuz83e/bssI8//jgkLCyscu3atd9fddVV5e79jRkzJnblypW91IQVK1YEz5w5s29oaGjlO++8szsxMbF+UoA1a9YEjB07duBjjz3W77bbbjvpvgXuhRde6FNSUtLtsccey501a9YpPVNFRUXdNm/e7JGLBj0maJFHbr9M3b299MnFQ7Xw6p/oUPceqpFU2TtMEU/PZOA7AHQSISkpinh6phyRkbKMUYH/RVp49U/0ycVDJUndvb30yO2X2Vwl7HJk0aIodyhxs8rLux1ZtKhDzohw9OhRhyRt3rw5cOXKlb0mTpx46Ouvv/66sLDwy2XLlu0KCwur/PDDDy+aMGFCdMPPFRcXd5Mkf3//mqb2K0mBgYE1ddt6tbau6dOn57pDiSR5eXlp7ty5uZKUk5MTVF5ebtzr3nzzzYvy8/N9IiMjKxYtWnSw4Sxgw4YNc02fPj1Pkl555ZVTnoa6ePHiMEl68sknc92hpO6YrDfeeGO/n59fk8c2c+bMyLr97WsYSiQpOTm5ZOrUqc6qqirz8ssv1/eCFBaKWtBGAAAgAElEQVQWOiQpJSWlqPH+QkJCakaMGHHajGfngmCCFhl1TZRmjRmsqB7d9enFQ/XkT5/Vzrc/0pB/fUooAYBOJiQlRQPXrdWgb7fr2Bt/087BP5KRFNWju2aNGcysXBewqsOHm7z9p7nldnPf3lRdXW3GjRt3+LXXXjt45ZVXlvfu3bv6F7/4RdHf/va3XcYYvf/++722b99efwyWVdt5YoxpesfnaezYsad9gY+KiqoKDg6urqioMIcOHaoPO5999lmQJI0ZM+Zo44H7kvS73/3usDFG+/fv9927d6+3VDtG5uDBg77dunXTxIkTT+vJioqKqrrxxhtPNF7udDodX3/9dUBgYGD1mDFjTlsvSUlJSSclKTs7u36sydChQ0skadKkSdErV64MLisra5MTx61caLFR10TRWAFAF8O1HQ05eveuqCosPC2EOHr3bvaWJzsFBQXV9wr813/9V2Hj9TfffHPpoEGDSr/55hv/NWvWBA0aNOhIw8+VlJQ0+4/07l6VwMDAVk/LNWDAgCbPV2BgYPWJEye8ysrK6v9cp9PpI0mxsbGnzRwm1faAhIaGVhYUFHjv27fPOzY2ttI9fiQ0NLTSz8+vyTEy/fr1O62GHTt2+FiWpeLiYi9vb++hZzoGd2+UJKWnpx/asGFD0IYNG4LGjBkz0MfHx7r88stLb7jhhpMTJkw4eu2113pkYBrBBAAAAJKkXg8+mNtwjIkkGV/fml4PPtgh55Bu+GX+sssuazIM9OvXr/ybb77xz8/P9278udzc3GZ7gtzrYmJimgwMZ+Ll1fK7v1rSe+Pe5nxVVVUZqTYgJScnNz3Vap1evXpVuf87KCioJisra8e6desCMjMzgzdu3Bj45ZdfBm7bti1g8eLF4Q8//HDe3Llzz3uKVoIJAAAAJP17gPuRRYuiqg4f9nH07l3R68EHczviwHdJuv766+vHcRw6dMgRGRlZ1Xgb97/8u8eMSNLw4cNLJWnXrl3di4uLTVMzc23bti1AkhISEkobr/OkyMjICunfA/IbKy0tNYcPH/aWpJiYmEpJio6OrpCkwsJCb5fLZZrqNdm/f/9poat///4VkuRwOKz33ntvX2trTUxMLHGPS3G5XGbJkiU9p02bFv3iiy9G3nPPPUfj4uJaHeIaYowJAAAA6vX8+c+ODlz/2VdXfLs9Z+D6z77qqKFEkmJjYyvd0/quXr06qPH6wsJCr2+++cZfkoYPH14/QHvAgAGVgwYNKq2srDRLly49bTrkzMzMwEOHDnn37t27MikpySMDu5tz8803n5SklStX9qysrDxt/Z/+9KdelmWpX79+5bGxsZXu+qOioipqamr0+uuvn1Z/Xl6e4/PPPw9uvDw2NrZy4MCBZcePH3f8/e9/P+18tYafn5/10EMPHYmLiyuxLEs5OTmtnla5MYIJAAAAOq1HH33UKUlz586NzMrKqp+2trS01EyYMCG6uLjY68orryxtHDB+//vf50vSH//4x6ivv/66vrciNzfXkZqaGi1JDz30UH5rbss6FxMmTDgWHh5ekZub6zN58uS+DZ80n5OT4zdnzpwoSZo8efIp0/ROnDjxkCQ9++yzkQ0H9peVlZn777+/n8vlavJ7flpaWp4k3XfffbHvv//+aeHF5XKZ5cuXhzR83srs2bNDt27delqPzvbt23127drVXWp+jExrGE/ds2anhIQEKzs72+4yAAAAzsoYk2NZVkJLtt26deu+uLi4w2ff8sL2X//1X32XLFnSx9vb2xoyZEjJRRddVLV169aAwsJC77CwsMqPPvro+8GDB5/2xXn8+PH9li9fHurr62vdcMMNJxwOh7Vhw4ag4uJirxEjRhz/4IMPdjecvvds3E99tywrp6n1UVFRg/Py8ny+++67rxqOiVm7dm3A6NGjB548edLr4osvLo+Liys5duyYY9OmTUGVlZVm1KhRR95777193br9O2tUVVUpKSlpwGeffRbi6+trXXfddScCAgJqNm/eHFhRUdEtMTHx+MqVK3tNnTrV+eKLL+Y1rCM9Pb3PM88807e6ulrR0dHl/fv3d/n4+NTk5eX57N2716+4uNhrzpw5+6dPn14oSZdffvmg77//vnvfvn3LL7300rKAgICawsJC75ycnMDKykpz1113Hc3IyNjbknO0devW3nFxcTFNraPHBAAAAJ3aa6+9dvCtt97aHR8fX7xjx47un376aUj37t1r7r///kNffPHF9qZCiSQtW7Zs/6uvvrp30KBBpZs2bQpav359cL9+/cqfe+65/atXr25VKDkfSUlJJdnZ2dvvvvvuwurqavPhhx9etHXr1oC4uLiSRYsW7W0cSiTJ4XBozZo1u5944oncyMjI8qysrOANGzYEDR8+/OTGjRu3x8TENDuTWnp6+qH169dvHzdu3OGamhplZWUFr1+/PuTEiROOa6+99uS8efN+uPfee+tv4Xvqqadyf/7znxcGBgbWbNmyJXD16tUX7du3z3fYsGEn33jjjT2rVq1qUSg5G3pMAAAA2hE9JriQ0WMCAAAAoEMjmAAAAACwHcEEAAAAgO0IJgAAAABs1+pgYoy52xiz3hhTZIwpNsZkG2N+a4w575BjjHnOGGPVvX5/vvsDAAAA0Dm0KkwYY/4kabmkBEnrJf1T0qWSXpG0whhzzk+gMcYMkzRdUuefJgwAAABAq7Q4mBhjxkp6UFK+pCGWZd1lWdZoSQMlfStptKTJ51KEMcZX0lJJhyT977nsAwAAAEDn1Zoek8fr3h+1LGune6FlWYckTar78bFzvKVrpqRBkh6QVHQOnwcAAOiKrK7wzDlAks72u9yiEGGM6StpqKQKSX9r4g/5VFKupHBJ17WmQGPMcEkPS/qLZVkZrfks2kZRRoZ2Jibp2ysGaWdikooy+N8CABca2oKOwRhz2OVy+dhdB+AJFRUV3saYY82tb2nvxjV1799YllXWzDabG217VsYYP0lvSToqKbWln0Pb+eSNmdr3xKOqysuTLEtVeXlyzkijQQKAC0hRRoYO/uHJU9qCg394krbABtXV1csKCwuD6DVBV3D8+PGgmpqaD5pb39JgElv3/sMZttnfaNuWeFbSZZJ+Z1nW4VZ8Dm0gc0+mvJa8I5/KUy9+lsulgvkLbKoKANDefnjhOXUrrzxlWbfySv3wwnM2VXThqqmpeevYsWPb9u3b17OoqCiwqqrKi5CCzsSyLJWXl3sfOnSo56FDh45XV1cvaW5bRwv3GVj3XnKGbYrr3oNaskNjzA2SpkhaZVnWuy2sA21o4ZaFml/U9MWuyuls52oAAHZxFBxv1XK0naFDhx7Pycn5z6NHj/7s5MmT/6HaCYj87a4LaA1jzLGampp3qqurlwwdOnRfc9u1NJiYunePRHRjTHdJb0o6odqZvs5lHxMlTZSkfv36eaKsC15+iVNHgqXQE6evc0REtH9BAABbHG6mLTgcLGnbX6Uh49q9pgvZ0KFDKyT9T90L6LJaeivXybr3wDNs41538gzbuD2n2uefTLMs65z+Kd6yrCWWZSVYlpUQGhp6LrtAI+HVlv5yi5GrUVytcEhhU6fYUxQAoN19kNzztLbA5ZA++JGktTNtqQlA19fSYLKv7j36DNtc3GjbMxktqUbSvcaYTxq+JN1Rt82kumWvt7BGnKfUI0eVc4XRa/9hVBhc+z/ocLB07MZShaSk2F0eAKCd/OjXT+jNO1TfFhQGS2/eIf0o4rhUdNDu8gB0US29leuLuvcrjTHdm5mZa1ijbc+mm6Qfn2F9/7pXjxbuD+dppKOndPiIFl7aQ5MHeSm8qlqpx45rpKOX3aUBANrRyP4jpdhH9czl1cp3NGgPSkqlkIvPvgMAOAct6jGxLOuApC2SfCT9Z+P1xpgfS+qr2qfCb2jB/mIsyzJNvVQ7fbAkPVK37OqWHgzOU1KaRlZYWnMwT9v2HdCag3kaWWFJSWl2VwYAaGcjb0rTmkPH/t0elJRK3t1pEwC0mdY8pX1W3fscY8wA90JjTJikRXU/zrYsq6bBulnGmO+MMbOEjm/IOCnlpbp/DTO17ykvMcgRAC5EtAkA2llLb+WSZVkrjDGvSpok6StjzEeSKiUlSQqWtErSK40+FqHa55QwpVNnMWQcjQ4AoBZtAoB21OJgIkmWZT1ojPmXpN+qdnyIl6TvJP23pFcb9pYAAAAAQEuZrvD00ISEBCs7O9vuMgAAAM7KGJNjWVaC3XUAHU1rxpgAAAAAQJsgmAAAAACwHcEEAAAAgO0IJgAAAABsRzABAAAAYDuCCQAAAADbEUwAAAAA2I5gAgAAAMB2BBMAAAAAtiOYAAAAALAdwQQAAACA7QgmAAAAAGxHMLnAFGVkaGdikr69YpB2JiapKCPD7pIAAJ0Q7QkAT3PYXQDaT1FGhpwz0mS5XJKkqrw8OWekSZJCUlLsLA0A0InQngBoC/SYXEAK5i+ob0TcLJdLBfMX2FQRAKAzoj0B0BYIJheQKqezVcsBAGgK7QmAtkAwuYA4IiJatRwAgKbQngBoCwSTC0jY1Ckyfn6nLDN+fgqbOsWmigAAnRHtCYC2wOD3C4h7QGLB/AWqcjrliIhQ2NQpDFQEALQK7QmAtmAsy7K7hvOWkJBgZWdn210GAADAWRljcizLSrC7DqCj4VYuAAAAALYjmFwAMvdkKnlFsoa8NUTJK5KVuSfT7pIAAF0I7QwAT2CMSReXuSdT6VnpclXXzjfvLHEqPStdkjSy/0gbKwMAdAW0MwA8hR6TLm7hloX1jYWbq9qlhVsW2lQRAKAroZ0B4CkEky4uvyS/VcsBAGgN2hkAnkIw6eLCA8JbtRwAgNagnQHgKQSTLi41PlV+Xqc+BMvPy0+p8ak2VQQA6EpoZwB4CoPfuzj3wMOFWxYqvyRf4QHhSo1PZUAiAMAjaGcAeAoPWAQAAGhHPGARaBq3cgEAAACwHcEEAAAAgO0IJgAAAABsRzABAAAAYDuCCQAAAADbEUwAAAAA2I5gAgAAAMB2BBMAAAAAtiOYdDFFGRnamZikb68YpJ2JSSrKyLC7JADABYo2CUBrOOwuAJ5TlJEh54w0WS6XJKkqL0/OGWmSpJCUFDtLAwBcYGiTALQWPSZdSMH8BfUNgJvlcqlg/gKbKgIAXKhokwC0FsGkC6ly5jWz3NnOlQAALnTNtT3NtVUAQDDpKrb9VQ7/6iZXOSIi2rkYAMCFrrm2x+FfLW37aztXA6AzIJh0FWtnKmzwCRmvmlMWG4cUNnWKTUUBAC5UYVOnyDQayWq8ahQ2+IS0dqY9RQHo0AgmXUXRQYXElCliWJEc/lWSLDn8qxSRcIxBhgCAdheSkqKIhGOntknDihQSUyYVHbS7PAAdELNydRUhfaWiAwqJKau96Ncvv9i+mgAAF7SQuN4KiTnQxIq+7V8MgA6PHpOuIilN8u5+6jLv7rXLAQCwA20TgFYgmHQVQ8ZJKS/V9ZCY2veUl2qXAwBgB9omAK1gLMuyu4bzlpCQYGVnZ9tdBgAAwFkZY3Isy0qwuw6go6HHBAAAAIDtCCYAAAAAbEcwAQAAAGA7ggkAAAAA2xFMAAAAANiOYAIAAADAdgQTAAAAALYjmHRSmXsylbwiWUPeGqLkFcnK3JNpd0kAALQIbRiApjjsLgCtl7knU+lZ6XJVuyRJzhKn0rPSJUkj+4+0sTIAAM6MNgxAc+gx6YQWbllYf0F3c1W7tHDLQpsqAgCgZWjDADSHYNIJ5Zfkt2o5AAAdBW0YgOYQTDqh8IDwVi0HAKCjoA0D0ByCSSeUGp8qPy+/U5b5efkpNT7VpooAAGgZ2jAAzWHweyfkHhy4cMtC5ZfkKzwgXKnxqQwaBAB0eLRhAJpjLMuyu4bzlpCQYGVnZ9tdBgAAwFkZY3Isy0qwuw6go+FWrk6kKCNDOxOT9O0Vg7QzMUlFGRl2lwQAwDmjXQPQELdydRJFGRlyzkiT5aqdYrEqL0/OGWmSpJCUFDtLAwCg1WjXADRGj0knUTB/Qf3F281yuVQwf4FNFQEAcO5o1wA0RjDpJKqczlYtBwCgI6NdA9AYwaSTcEREtGo5AAAdGe0agMYIJp1E2NQpMn6nzvtu/PwUNnWKTRUBAHDuaNcANMbg907CPRCwYP4CVTmdckREKGzqFAYIAgA6Jdo1AI3xHBMAAIB2xHNMgKZxKxcAAAAA2xFMAAAAANiOYAIAAADAdgQTAAAAALYjmAAAAACwHcEEAAAAgO0IJgAAAABsRzABAAAAYDuCCQAAAADbEUwAAAAA2I5gAgAAAMB2BBMAAAAAtiOYAAAAALAdwQQAAACA7QgmAAAAAGxHMAEAAABgu1YHE2PM3caY9caYImNMsTEm2xjzW2NMi/dljPE2xiQZY+YZYzYaY5zGmApjTK4xZoUx5pbW1gUAAACg83K0ZmNjzJ8kPSjJJWmtpEpJSZJekZRkjPlPy7KqW7CrH0v6Z91/50vKkVQiaZCksZLGGmOetiwrrTX1AQAAAOicWtPLMVa1oSRf0hDLsu6yLGu0pIGSvpU0WtLkFu6uRtJ7km62LCuibl8/tSxrsKSfSaqWNMMYc2srjqVTK8rI0M7EJH17xSDtTExSUUaG3SUBAGA72kfgwtGaW7ker3t/1LKsne6FlmUdkjSp7sfHWnJLl2VZ6yzL+ollWeubWPeupKV1P45vRX2dVlFGhg7+4UlV5eVJlqWqvDwd/MOTXHwBABc02kfgwtKiYGKM6StpqKQKSX9rvN6yrE8l5UoKl3SdB+r6ou69rwf21eH98MJz6lZeecqybuWV+uGF52yqCAAA+zXbPs5Kt6cgAG2qpT0m19S9f2NZVlkz22xutO35GFj37vTAvjo8R8HxVi0HAOBC0Gz7eLRU2vbXdq4GQFtraTCJrXv/4Qzb7G+07TkxxoRL+lXdj++dz746i8PBrVsOAMCF4Izt49qZ7VoLgLbX0mASWPdecoZtiuveg861GGOMQ9IySSGS1lqWdUHcRPrBjyRXo/nRXI7a5QAAXKg+SO7ZfPtYdNCWmgC0nZYGE1P3brVVIXUWq3b64QM6y8B3Y8zEumeoZBcWFrZxWW3rR5d46c07pMLg2unKCoOlN++oXQ4AwIXqR79+Qm/eaU5vHyOOSyEXxDBU4ILS0ueYnKx7DzzDNu51J8+wTbOMMQsl3afa6YiTLMvKP9P2lmUtkbREkhISEto6MLWpkTelSeWP6JmJ/sp3eCm8qlqpJ0o18qYX7C4NAADbjOw/Uhq5Uc9c/p7yvbrVto/HjmtkhSXdzqPOgK6mpcFkX9179Bm2ubjRti1mjJkn6SFJhaoNJTvP8pGuZcg4jZQ0cu3M2q7pkL7SiBekIePsrgwAAFuNvOVpjew5uHZMSZGzto28PY02EuiCjGWdvbPBGHOxage3V0jq0dTMXMaYA6qd3vdHlmV93uICjHle0iOSjqg2lGxt6WfdEhISrOzs7NZ+DAAAoN0ZY3Isy0qwuw6go2nRGBPLsg5I2iLJR9J/Nl5vjPmxakNJvqQNLf3DjTGzVRtKjkm67VxCCQAAAIDOrzVPfp9V9z7HGDPAvdAYEyZpUd2Psy3LqmmwbpYx5jtjzCw1Yox5WtKjko6rNpR80XgbAAAAABeGlo4xkWVZK4wxr0qaJOkrY8xHkipVO4tWsKRVkl5p9LEISZfVvdczxvwfSX+o+3GXpN8ZY9SE7yzLmt3SGgEAAAB0Ti0OJpJkWdaDxph/SfqtpB9L8pL0naT/lvRqw96Ss+jZ4L8T6l5N+VQSwQQAAADo4lo0+L2jY/A7AADoLBj8DjStNWNMAAAAAKBNEEwAAAAA2I5gAgAAAMB2BBMAAAAAtiOYAAAAALAdwQQAAACA7QgmAAAAAGxHMAEAAABgO4IJAAAAANsRTAAAAADYjmACAAAAwHYEEwAAAAC2I5i0k6KMDO1MTNK3VwzSzsQkFWVk2F0SAABdAm0s0DU47C7gQlCUkSHnjDRZLpckqSovT84ZaZKkkJQUO0sDAKBTo40Fug56TNpBwfwF9RdMN8vlUsH8BTZVBABA10AbC3QdBJN2UOV0tmo5AABoGdpYoOsgmLQDR0REq5YDAICWoY0Fug6CSTsImzpFxs/vlGXGz09hU6fYVBEAAF0DbSzQdTD4vR24B98VzF+gKqdTjogIhU2dwqA8AADOE20s0HUYy7LsruG8JSQkWNnZ2XaXAQAAcFbGmBzLshLsrgPoaLiVCwAAAIDtCCZtKHNPppJXJGvIW0OUvCJZmXsy7S4JAIAujbYX6LwYY9JGMvdkKj0rXa7q2rnVnSVOpWelS5JG9h9pY2UAAHRNtL1A50aPSRtZuGVh/YXRzVXt0sItC22qCACAro22F+jcCCZtJL8kv1XLAQDA+aHtBTo3gkkbCQ8Ib9VyAABwfmh7gc6NYNJGUuNT5ed16gOf/Lz8lBqfalNFAAB0bbS9QOfG4Pc24h5kt3DLQuWX5Cs8IFyp8akMvgMAoI3Q9gKdGw9YBAAAaEc8YBFoGrdyAQAAALAdwQQAAACA7QgmAAAAAGxHMAEAAABgO4IJAAAAANsRTAAAAADYjmACAAAAwHYEEwAAAAC2I5gAAAAAsB3BxAOKMjK0MzFJ314xSDsTk1SUkWF3SQAAoA7tNNA5OOwuoLMrysiQ88knZVVUSpKq8vLkfPJJSVJISoqdpQEAcMErysiQc0aaLJdLUl07/fh0af9Ghfz2WZurA9AQPSbnqWDOs/WhxM2qqFTBHC52AADYrWD+gvpQ4mZVSQX//Tdp219tqgpAUwgm56nqcFGrlgMAgPZT5XQ2vbykm7R2ZjtXA+BMCCbnyeFf1arlAACg/TgiIppe7l8tFR1s52oAnAnB5DyFXect41VzyjLjVaOw67xtqggAALiFTZ0i02hErfGqUdiQk1JIX3uKAtAkgsl5CnkgXRHXldb1kFhy+Fcp4rpShTyQbndpAABc8EJSUhQxaYwcAdWqb6eHFSlkoKSkNLvLA9AAs3KdryHjFJIqhaydWdslHNJXSnpWGjLO7soAAICkkN8+q5Cb4mrHlBTl17XVabTVQAdjLMuyu4bzlpCQYGVnZ9tdBgAAwFkZY3Isy0qwuw6go+FWLgAAAAC2I5gAAAAAsB3BBAAAAIDtCCYAAAAAbEcwAQAAAGA7ggkAAAAA2xFMAAAAANiOYAIAAADAdgQTAAAAALYjmLRC5p5MJa9I1pC3hih5RbIy92TaXRIAADhHtOtAx+Kwu4DOInNPptKz0uWqdkmSnCVOpWelS5JG9h9pY2UAAKC1aNeBjocekxZauGVh/cXLzVXt0sItC22qCAAAnCvadaDjIZi0UH5JfquWAwCAjot2Heh4CCYtFB4Q3qrlAACg46JdBzoegkkLpcanys/L75Rlfl5+So1PtakiAABwrmjXgY6Hwe8t5B4It3DLQuWX5Cs8IFyp8akMkAMAoBOiXQc6HmNZlt01nLeEhAQrOzvb7jIAAADOyhiTY1lWgt11AB0Nt3IBAAAAsB3BpAWKMjK0MzFJ314xSDsTk1SUkWF3SQAAwINo6wH7McbkLIoyMuSckSbLVTvXeVVenpwz0iRJISkpdpYGAAA8gLYe6BjoMTmLgvkL6i9UbpbLpYL5C2yqCAAAeBJtPdAxEEzOosrpbNVyAADQudDWAx0DweQsHBERrVoOAAA6F9p6oGMgmJxF2NQpMn6nPoDJ+PkpbOoUmyoCAACeRFsPdAwMfj8L96C3gvkLVOV0yhERobCpUxgMBwBAF0FbD3QMPGARAACgHfGARaBp3MoFAAAAwHYEEwAAAAC2I5gAAAAAsB3BBAAAAIDtCCYAAAAAbEcwAQAAAGA7ggkAAAAA2xFMAAAAANiOYAIAAADAdgQTAAAAALYjmAAAAACwHcEEAAAAgO0IJgAAAABsRzABAAAAYDuCCQAAAADbEUwAAAAA2I5gAgAAAMB2BBMAAAAAtiOYAAAAALAdwQQAAACA7YxlWXbXcN6MMYWSfjjP3fSWdNgD5VzoOI+ewXn0DM6jZ3AePYPz6Bld4TxGW5YVancRQEfTJYKJJxhjsi3LSrC7js6O8+gZnEfP4Dx6BufRMziPnsF5BLoubuUCAAAAYDuCCQAAAADbEUz+bYndBXQRnEfP4Dx6BufRMziPnsF59AzOI9BFMcYEAAAAgO3oMQEAAABguy4ZTIwxdxtj1htjiowxxcaYbGPMb40x53S8nt5fZ+Gp4zbGXGaMSTXGLDPGfGeMqTHGWMaYn7RV7R2JJ86jMcbbGJNkjJlnjNlojHEaYyqMMbnGmBXGmFva8BA6BA/+Pv7OGPNXY8y3xpgjxphKY0yhMeYjY8x4Y4xpq2PoCNryemaMea7u77ZljPm9J+rtqDz4+7i0wTlr6vVdWx1DR9AG7XV3Y8x0Y8xmY8xxY0ypMWavMeZvxpgbPV0/AM/qcrdyGWP+JOlBSS5JayVVSkqSFCRppaT/tCyr2q79dRaePG5jzAJJqU2s+k/LslZ4puKOyVPn0RgzQtI/637Ml5QjqUTSIElX1S1/2rKsNI8eQAfh4d/Hg5LCJH0tKVe15zFa0nBJRtL/ShpjWVaNhw/Ddm15PTPGDJO0QbX/4GUkPWJZ1lxP1N3RePj3camkeyV9LmlXE5s4Lct63ANldzht0F7HSlojaYCkAkkbJZVLipF0taSZlmU948FDAOBplmV1mZeksZIsSU5JAxss7yNpe926VLv211lebXAe75f0vKRxki6R9EndPn5i97F2lvMoKVHSCkk3NbHup5Kq6vZ3q93H3ZHPY93nfiQpoInlV6o29FmSJth93B39PDbat6+kb1Qb9FbW7ev3dh9zZziPkpbWfeZXdh9bJz+PAaoNdpakmZK8G63vJelSu4+bFy9eZ37ZXoBHD0bKrrso/bKJdT9ucBHsZsf+OgY6qggAAAcTSURBVMurrY/7Agom7fb7I+n1uv29Yfdxd/LzOKNuf3+x+7g703mUNKfu8ykNvmh31WDi6XbmQg0mnj6Ps+o+85bdx8aLF69zf3WZMRLGmL6ShkqqkPS3xusty/pUtf+aFy7puvbeX2dxoR63p9lwHr+oe+/rgX11GDacx6q6d5cH9tVhtOV5NMYMl/SwasNcxvlX23FxffSMNmivfST9pu7H2Z6rFEB76zLBRNI1de/fWJZV1sw2mxtt25776ywu1OP2tPY+jwPr3p0e2FdH0m7nse7+9AfqfuxqX7Db5DwaY/wkvSXpqJoeR9bVtOXv463GmBeNMUuMMU8bY27vwhOsePo8DlXtrVoHLMv61hhzQ91EDK8ZY/5ojLn+fAsG0D4cdhfgQbF17z+cYZv9jbZtz/11FhfqcXtau51HY0y4pF/V/fje+eyrA2qz82iMmaDaW0a8VdvTdINq/7FmlmVZK1tZZ0fXVufxWUmXSfqZZVmHz6WwTqYt/17/soll240xP7Ms66tW7quj8/R5HFz3vrPBZAINpRlj3pN0zxmCEIAOoCsFk8C695IzbFNc9x5kw/46iwv1uD2tXc6jMcYhaZmkEElru+CtNG15Hm/UqV9gqlQ7xuTFVu6nM/D4eTTG3CBpiqRVlmW9ex61dSZt8fv4pWpn2Vur2i/qwZLiVRv64iR9ZIyJtywrt/XldliePo89695vluQlaa6kxZKO1C1bpNrB9ick/bq1xQJoP12pm9j97AFPzX/s6f11FhfqcXtae53HxaqdXvOApPFt/GfZoc3Oo2VZ91uWZST5q3ZGrgWS0iVtNMZEevrPs5lHz6MxprukN1X7Re9BT+yzk/D476NlWQssy3rZsqztlmWVWJbltCwrU9K1qp3uNkxSV5su2NPn0f1dxqHaCUAesSxrt2VZxy3L+v8ljar7s+41/6+9ewmRo4jjOP79JfGJBjUiRpGE+DgYxEV8gBIVQkBEBQ8K4tFTDPGwZMlFvASTKD4IRPagMRePggHxIHgwIMqiCQRBggoOaGBF0EAEQTH/HKoGh8nssLtWTz/m94Ghdnpq/9P9p2Z6qrurWtpS6D3NrAJd6picy+VVY+r0Xzs3pk5V8dpiWre7tMrzKOkQ8AJpitvtEbG4mjgNV3keI+Kv/KNwjvQD8G7g8GpiNVjpPO4H7gBmI6Jr45rGmdj3Y0T8TZppCuDx/xOrgaraXwO8O/xiRHxDOiu1Bnh0GfHMrCZd6pj0crlpTJ1bhupOMl5b9HI5bdtdWi+XleRR0pvAS8BvpE7JDyuN0RK9XE6qPR7N5ZOSLikQryl6uSyVx6eB86Qj0J8PPoDHcp2dedl7q1jfpurlclLtsX/X95sLxGqSXi5L768BflqiTn/5jcuIZ2Y16dIYk/50qVslXbHEALf7hupOMl5bTOt2l1ZZHiW9DsySrp/eERHfrX41G2/S7fEsaazJOtJ1678WiNkEVeRxDWnygKVsyY9rlhmvDSbdHjfk8s+xtdqndB5PDvy9gXTAZtj1uexaLs06pTNnTCLiZ9KX06XAM8OvS3qENPPOIvDVpOO1xbRud2lV5VHSQWAO+IPUKTlVZIUbqob2+DCpU3IW6MwsUxV8P26OCI16kKYPBpjLy2bKbUm9amiPz+by67G1WqaC9ngGWMhPt4+Idy1pQgFIN3Y0s4bqTMck61+P+5qk2/oLJd1AmpUD4GBEnB947YCk05IOcLEVx+uI0nmcVkXzKGkfsJf0o3lHREzLGatieZS0TdLzki4bfhNJDwFH8tMjEfFv0a2onz/XZZRsjzOSnpC0dmj5OkmzpMs1Ad4uvhX1K90eX83lK5JmBv7ncmCeNHPhCXxAzazRunQpFxHxoaR5YCfwraTPgH9IR1DWA8e4eFDrRtI8/BsLxWu90nmUdA//7WgA7szlfkl7Bt63U3dKLplHSU8BL+enPwK7JTHC6Yjo1J2PC7fHW0njSA5LOkk6Int1Xt5vl5+Qpg3ulNKf62lVOI+bgY+A3yV9D/xCao93ATeRxvHsjYhPq9ma+lSwv/5Y0hvAHmBB0gLpctf7Sbk8AzwXEZ5x0qzBOtUxAYiIFyV9AewiXf+8ljSA8H1gfqVnN0rHa4vC270eeGDE8ttHLOuUgnm8buDve/NjlONApzomUDSPx4F9wDbSrFIPkqYuXSTdnPKDiDhWePUbY1q/z0ormMdTwCHSj+dNpLucB6mDchR4JyJOFF79xqhgfz0n6UtgNymXV5Ju1PgW6ezLqLEnZtYg8sEDMzMzMzOrW9fGmJiZmZmZWQu5Y2JmZmZmZrVzx8TMzMzMzGrnjomZmZmZmdXOHRMzMzMzM6udOyZmZmZmZlY7d0zMzMzMzKx27piYmZmZmVnt3DExMzMzM7PauWNiZmZmZma1uwB6KRcqlFRffgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 720x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(10,10))\n",
"\n",
"x6 = np.linspace(0,L,N6+2) \n",
"plt.plot(x6[1:-1],-1*v6[:,0]/np.max(-v6[:,0]),'o',label = '6 nodes') \n",
"x30 = np.linspace(0,L,N30+2) \n",
"plt.plot(x30[1:-1],-1*v30[:,0]/np.max(-v30[:,0]),'o', label = '30 nodes') \n",
"x45 = np.linspace(0,L,N45+2) \n",
"plt.plot(x45[1:-1],-1*v45[:,0]/-np.max(v45[:,0]),'o', label = '45 nodes') \n",
"x60 = np.linspace(0,L,N60+2) \n",
"plt.plot(x60[1:-1],-1*v60[:,0]/np.max(-v60[:,0]),'o', label = '60 nodes') \n",
"plt.title('First Mode')\n",
"\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left');"
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(10,10))\n",
"\n",
"plt.plot(x6[1:-1],-v6[:,1]/np.max(-v6[:,1]),'o',label = '6 nodes') \n",
"plt.plot(x30[1:-1],v30[:,1]/np.max(-v30[:,1]),'o', label = '30 nodes') \n",
"plt.plot(x45[1:-1],v45[:,1]/-np.max(v45[:,1]),'o', label = '45 nodes') \n",
"plt.plot(x60[1:-1],v60[:,1]/np.max(-v60[:,1]),'o', label = '60 nodes') \n",
"\n",
"plt.title('Second Mode')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left');"
]
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(10,10))\n",
"\n",
"plt.plot(x6[1:-1],v6[:,2]/np.max(v6[:,2]),'o',label = '6 nodes') \n",
"plt.plot(x30[1:-1],v30[:,2]/np.max(v30[:,2]),'o', label = '30 nodes') \n",
"plt.plot(x45[1:-1],v45[:,2]/-np.max(v45[:,2]),'o', label = '45 nodes') \n",
"plt.plot(x60[1:-1],v60[:,2]/np.max(v60[:,2]),'o', label = '60 nodes') \n",
"\n",
"plt.title('Third Mode')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"b. Use the number of nodes necessary for convergence to calculate the first 3 modes of vibration for the other 5 strings on the guitar. Display the first three natural frequencies for all six strings. "
]
},
{
"cell_type": "code",
"execution_count": 85,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"First three natural frequencies of 60-element high e string (Hz)\n",
" 1st natural frequency = 195.5\n",
" 2nd natural frequency = 390.9\n",
" 3nd natural frequency = 586.0\n",
"First three natural frequencies of 60-element high b string (Hz)\n",
" 1st natural frequency = 247.1\n",
" 2nd natural frequency = 494.0\n",
" 3nd natural frequency = 740.6\n",
"First three natural frequencies of 60-element high g string (Hz)\n",
" 1st natural frequency = 196.1\n",
" 2nd natural frequency = 392.0\n",
" 3nd natural frequency = 587.6\n",
"First three natural frequencies of 60-element high d string (Hz)\n",
" 1st natural frequency = 146.9\n",
" 2nd natural frequency = 293.7\n",
" 3nd natural frequency = 440.3\n",
"First three natural frequencies of 60-element high a string (Hz)\n",
" 1st natural frequency = 110.0\n",
" 2nd natural frequency = 220.0\n",
" 3nd natural frequency = 329.8\n",
"First three natural frequencies of 60-element high E string (Hz)\n",
" 1st natural frequency = 82.4\n",
" 2nd natural frequency = 164.8\n",
" 3nd natural frequency = 247.1\n"
]
}
],
"source": [
"\n",
"#Using 60 Nodes\n",
"\n",
"N = 60\n",
"dx = L/(N+1)\n",
"g = 9.81 #m/s**2\n",
"\n",
"#Density\n",
"mu_g = 1.14e-3 #g/m\n",
"mu_e = 0.401e-3\n",
"mu_b = 0.708e-3\n",
"mu_d = 2.333e-3\n",
"mu_a = 4.466e-3\n",
"mu_E = 6.790e-3\n",
"\n",
"#Tension\n",
"T_g = 7.32*g\n",
"T_e = 7.28*g\n",
"T_b = 7.22*g\n",
"T_d = 8.41*g\n",
"T_a = 9.03*g\n",
"T_E = 7.71*g\n",
"\n",
"k_e = T_e/dx**2/mu\n",
"k_b = T_b/dx**2/mu_b\n",
"k_g = T_g/dx**2/mu_g\n",
"k_d = T_d/dx**2/mu_d\n",
"k_a = T_a/dx**2/mu_a\n",
"k_E = T_E/dx**2/mu_E\n",
"\n",
"A_e = k_e*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"A_b = k_b*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"A_g = k_g*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"A_d = k_d*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"A_a = k_a*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"A_E = k_E*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"\n",
"e_e,v_e=linalg.eig(A_e)\n",
"isort_e = np.argsort(e_e.real)\n",
"e_e=e_e.real[isort_e]\n",
"v_e=v_e.real[:,isort_e]\n",
"e_b,v_b=linalg.eig(A_b)\n",
"isort_b = np.argsort(e_b.real)\n",
"e_b=e_b.real[isort_b]\n",
"v_b=v_b.real[:,isort_b]\n",
"e_g,v_g=linalg.eig(A_g)\n",
"isort_g = np.argsort(e_g.real)\n",
"e_g=e_g.real[isort_g]\n",
"v_g=v_g.real[:,isort_g]\n",
"e_d,v_d=linalg.eig(A_d)\n",
"isort_d = np.argsort(e_d.real)\n",
"e_d=e_d.real[isort_d]\n",
"v_d=v_d.real[:,isort_d]\n",
"e_a,v_a=linalg.eig(A_a)\n",
"isort_a = np.argsort(e_a.real)\n",
"e_a=e_a.real[isort_a]\n",
"v_a=v_a.real[:,isort_a]\n",
"e_E,v_E=linalg.eig(A_E)\n",
"isort_E = np.argsort(e_E.real)\n",
"e_E=e_E.real[isort_E]\n",
"v_E=v_E.real[:,isort_E]\n",
"\n",
"\n",
"#Natural frequencies\n",
"f_e = e_e.real**0.5/2/np.pi\n",
"f_b = e_b.real**0.5/2/np.pi\n",
"f_g = e_g.real**0.5/2/np.pi\n",
"f_d = e_d.real**0.5/2/np.pi\n",
"f_a = e_a.real**0.5/2/np.pi\n",
"f_E = e_E.real**0.5/2/np.pi\n",
"\n",
"\n",
"print('First three natural frequencies of {}-element high e string (Hz)'.format(N))\n",
"print(' 1st natural frequency = {:.1f}'.format(f_e[0]))\n",
"print(' 2nd natural frequency = {:.1f}'.format(f_e[1]))\n",
"print(' 3nd natural frequency = {:.1f}'.format(f_e[2]))\n",
"print('First three natural frequencies of {}-element high b string (Hz)'.format(N))\n",
"print(' 1st natural frequency = {:.1f}'.format(f_b[0]))\n",
"print(' 2nd natural frequency = {:.1f}'.format(f_b[1]))\n",
"print(' 3nd natural frequency = {:.1f}'.format(f_b[2]))\n",
"print('First three natural frequencies of {}-element high g string (Hz)'.format(N))\n",
"print(' 1st natural frequency = {:.1f}'.format(f_g[0]))\n",
"print(' 2nd natural frequency = {:.1f}'.format(f_g[1]))\n",
"print(' 3nd natural frequency = {:.1f}'.format(f_g[2]))\n",
"print('First three natural frequencies of {}-element high d string (Hz)'.format(N))\n",
"print(' 1st natural frequency = {:.1f}'.format(f_d[0]))\n",
"print(' 2nd natural frequency = {:.1f}'.format(f_d[1]))\n",
"print(' 3nd natural frequency = {:.1f}'.format(f_d[2]))\n",
"print('First three natural frequencies of {}-element high a string (Hz)'.format(N))\n",
"print(' 1st natural frequency = {:.1f}'.format(f_a[0]))\n",
"print(' 2nd natural frequency = {:.1f}'.format(f_a[1]))\n",
"print(' 3nd natural frequency = {:.1f}'.format(f_a[2]))\n",
"print('First three natural frequencies of {}-element high E string (Hz)'.format(N))\n",
"print(' 1st natural frequency = {:.1f}'.format(f_E[0]))\n",
"print(' 2nd natural frequency = {:.1f}'.format(f_E[1]))\n",
"print(' 3nd natural frequency = {:.1f}'.format(f_E[2]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"c. Create an audio signal that has the 18 frequencies (6 strings $\\times$ 3 modes) in an array and display it using the `from IPython.display import Audio` library. \n",
"\n",
"_Hint: you don't need to solve the differential equations here. You can use the calculated frequencies to add sine-waves together:_ $\\sin(f_12\\pi t)+\\sin(f_22\\pi t)+...$"
]
},
{
"cell_type": "code",
"execution_count": 86,
"metadata": {},
"outputs": [
{
"data": {
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\" type=\"audio/wav\" />\n",
" Your browser does not support the audio element.\n",
" </audio>\n",
" "
],
"text/plain": [
"<IPython.lib.display.Audio object>"
]
},
"execution_count": 86,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"freq = np.array([f_e[0], f_e[1], f_e[2], f_b[0], f_b[1], f_b[2], f_g[0],\n",
" f_g[1], f_g[2], f_d[0], f_d[1], f_d[2], f_a[0], f_a[1],\n",
" f_a[2], f_E[0], f_E[1], f_E[2]])\n",
"N = 10000\n",
"dt = 3/N\n",
"t = np.linspace(0,3,N)\n",
"samplerate = int(1/dt) \n",
"waves = np.sin(2*np.pi*freq[0]*t)\n",
"for i in range(1,18):\n",
" waves += np.sin(2*np.pi*freq[i]*t)\n",
" \n",
"Audio(data = waves,rate = samplerate)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"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": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 4
}