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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy import linalg\n",
"from IPython.display import Audio"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Computational Mechanics Boundary Values - Project 05\n",
"\n",
"![6-string guitar diagram](../images/guitar.png)"
]
},
{
"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": 2,
"metadata": {},
"outputs": [],
"source": [
"#part a)\n",
"\n",
"h= 0.004 #inital conditions\n",
"L= 0.64\n",
"A= 2*4*(1/100)**2\n",
"I= 4*2**3/12*(1/100)**4\n",
"E= 10*(10**9)\n",
"g = 9.81\n",
"\n",
"c = 10**-3 #conversion from m to mm\n",
"\n",
"d_e = c * 0.401 #density of each string\n",
"d_b = c * 0.708\n",
"d_g = c * 1.14\n",
"d_d = c * 2.333\n",
"d_a = c * 4.466\n",
"d_E = c * 6.79\n",
"\n",
"T_e = g * 7.28 #tension in strings\n",
"T_b = g * 7.22\n",
"T_g = g * 7.32\n",
"T_d = g * 8.41\n",
"T_a = g * 9.03\n",
"T_E = g * 7.71\n",
"\n",
"M = (T_e + T_b + T_g + T_d + T_a + T_E) * h\n",
"\n",
"x = np.linspace(0, L, 1000) #analytical colution x\n",
"y = M*x**2/(2*E*I) #analytical colution y"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def guitair_deflection(N): #create a function inputting N to make finding numerical solution to parts a and b easier\n",
"\n",
" dx = L/N\n",
"\n",
" A = np.diag(np.ones(N)*6) + np.diag(np.ones(N-1)*-4, -1) + np.diag(np.ones(N-1)*-4, 1)\\\n",
" + np.diag(np.ones(N-2), -2) + np.diag(np.ones(N-2), 2)\n",
"\n",
" A[0, 0] += 1\n",
" A[N-2, N-1] += 2\n",
" A[N-1, N-2] += 2\n",
" A[N-2, N-2] -= 1\n",
" A[N-1, N-1] -= 5\n",
"\n",
" b=np.zeros(N)\n",
" b[N-2] += -M*dx**2/E/I\n",
" b[N-1] += M*dx**2/E/I\n",
"\n",
" w = np.linalg.solve(A, b)\n",
" num = np.linspace(0, L, N+1)\n",
"\n",
" print('The deflection of the guitars bridge is',w[-1]*1000,'mm')\n",
" \n",
" plt.figure(figsize=(8, 4))\n",
"\n",
" plt.plot(x, y, '-', label='Analytical Data');\n",
" plt.plot(num, np.block([0,w]), 'o',label='Numerical Data');\n",
"\n",
" plt.title('Guitar Bridge Deflection');\n",
" plt.xlabel('String Position (mm)');\n",
" plt.ylabel('String Deflection (mm)');\n",
" plt.legend(loc='best');"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The deflection of the guitars bridge is 1.4155029504000065 mm\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 576x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"guitair_deflection(6)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The deflection of the guitars bridge is 1.4155029504414147 mm\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"guitair_deflection(50) #prove convergence by increasing N. Data converges as it still matches with analytical trend."
]
},
{
"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": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"First 3 natural frequencies for 6 nodes = 402.47700552834937 784.7721334018921 1127.7155095836151 Hz\n",
"First 3 natural frequencies for 30 nodes = 458.0496190688014 914.9234313348556 1369.4486482745983 Hz\n",
"First 3 natural frequencies for 45 nodes = 463.1365985017925 925.7332004468656 1387.2504388904606 Hz\n",
"First 3 natural frequencies for 60 nodes = 465.7064394892608 931.1040853515676 1395.8843487101847 Hz\n"
]
}
],
"source": [
"mu = 1.14*(18**-3) #new initial conditions, L is same as question 1\n",
"T = 71.81\n",
"\n",
"nodes = np.array([6, 30, 45, 60]) #define the node counts we want to know about\n",
"\n",
"for i in range(0, len(nodes)): #create a same length loop to find natural frequencies for all four nodes\n",
" \n",
" N = nodes[i]\n",
" dx = L/(N)\n",
" \n",
" k = T/dx**2/mu\n",
" \n",
" A = k*(np.diag(np.ones(N)*2) - np.diag(np.ones(N-1), -1) - np.diag(np.ones(N-1), 1))\n",
" \n",
" e, v = linalg.eig(A)\n",
" isort = np.argsort(e.real)\n",
" e = e.real[isort]\n",
" v = v.real[:, isort]\n",
" \n",
" print('First 3 natural frequencies for {} nodes ='.format(N), e[0]**0.5/2/np.pi, e[1]**0.5/2/np.pi, e[2]**0.5/2/np.pi, 'Hz')\n",
"\n",
" modes_y = np.pad(v, ((1,1), (0,0)))\n",
" \n",
" x = np.linspace(0, N, N+2)\n",
" \n",
" if i == 0:\n",
" modes_y_6 = modes_y #use logic to assign each freqeuncies to the print command\n",
" x_6 = x\n",
" \n",
" elif i == 1:\n",
" modes_y_30 = modes_y\n",
" x_30= x\n",
" \n",
" elif i == 2:\n",
" modes_y_45 = modes_y\n",
" x_45= x\n",
" \n",
" elif i == 3:\n",
" modes_y_60 = modes_y\n",
" x_60= x"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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KVr8Lm76BgP4QNBEcHG1zbk3LZ/bu3Uv9+nfo0KqZKrvfjYhsU0rdft8hukavmSElGWLWGDX3/Ssh5SoUqwCNBhiFe/UW5tSmRaDjv8GlOPz+Edy4Ck/8CE5FbJ9F0zQtl+iCXrON1Otw6DeIWgD7V8CNy1C0LPj3MZrla7TKH7VnEWj7FhRxh9XvGIV9cAQ4u5mdTNM07b7ogl7LO6k3jFvgohfCvmVwPdG4rc23l1Fz92wNjvn0T7DlSKNX/s8vw/Te0HcmuJYwO5Wmado9y6efsprdSkuBI38YhfvepcbodK4lof7jRuHu1cbo/GYPmgwxavYLh8NPPWDAfChaxuxUmqZp90QX9NqDS0uFo5FGs/zenyHpPBQpDvW6Gc3yXo/a73Vuv95Gb/w5g2FqNxi4CIpXNDuVpmma1XRBr92f9DQ4utFSc18CV88Ztd+6XYyae612xj3qBUHdLtB/DszsB+GdYdBiKFXd7FSapmlW0TcKa9ZLTzcK9+Vj4PP6MK077JxpzAjXJwLGxMCTU4yafEEp5DN4tYVBi+BaAoR1gfgYsxNpWoE3fvx4fHx88Pf3JyAggD///NPmGTJPopN1uYgQGhp6c9nff/+NiPDpp59affzY2Fh8fX1zJeud6Bq9lrP0dDix1WiW37MILp8CJ1eo3dFolq/d0WjaLgyqNYfBS40pbsM7G834lfL2P6imFVabNm1i6dKlbN++HRcXF+Lj47lx44bZsW7h5+fH7NmzCQkJAWDWrFk0bNjQ5FS30zV67XZKQdw2WPUOfOkHoR1ga5gxMt2ToTDmkHHLmU+vwlPIZ6jsD8NWgmMRmNoV4vTATJqWF06dOkW5cuVwcXEBoFy5clSpUgUwZqxr06YNTZo0oVOnTpw6dQqAmJgY2rdvT8OGDWncuDGHDh1CKcWYMWPw9fW9WTCDUSNv27YtvXv3pl69evTv3//muPYrV66kXr16BAYG3py4JjvVq1cnOTmZM2fOoJRi5cqVdOnS5eb6HTt28PDDD+Pv70+vXr1uDpO7bds2GjZsSIsWLZg0adLN7dPS0hgzZgzNmjXD39+fH374IVfeS12j1wxKwakdxjX36IVw8Rg4OIN3e2g31rhOrW8vM5Srbcxp/1MP49F3FtR8xOxUmpZ3VrwFp3fn7jEr+UGXj++4umPHjowbN446derQvn17goODadOmDSkpKYwaNYrFixdTvnx5Zs+ezTvvvENYWBj9+/fnrbfeolevXiQnJ5Oens6CBQvYsWMHO3fuJD4+nmbNmtG6dWvAaGqPjo6mSpUqtGrVig0bNtC0aVOeffZZfvvtN7y9vQkODs7xZfTu3Zu5c+fSqFEjGjdufPOLCcCgQYOYOHEibdq0YezYsXzwwQd8+eWXDB069ObyMWPG3Nw+NDSUkiVLsmXLFq5fv06rVq3o2LEjNWvWfKC3Whf0GqQkGQXW8T/BwcnoJd/2bajbFdxKmZ0ufypdw6jZ/9QTZvSGPj9BnU5mpwIgJT2FoSuHciTxiNlR8pyDOPBqk1fpVbuX2VG0XObu7s62bdtYv349a9euJTg4mI8//pimTZsSFRVFhw4dAKMWXLlyZS5fvsyJEyfo1cv4W3B1NfoJRUZG0rdvXxwdHalYsSJt2rRhy5YtlChRgubNm+Ph4QFAQEAAsbGxuLu7U7NmzZtT3A4YMODmXPPZ6dOnD8HBwezbt4++ffuyceNGABITE7l48SJt2rQBYPDgwTz11FO3LR84cCArVqwAYPXq1ezatYt58+bdPMbBgwftu6AXkc7AV4AjMEUple3XOxFpBmwGgpVS82wYsXBY+bZRyHf+GPyD9b3i1ipeCYYsg+lPwKx+xnC5vk+YnYqVR1ay89xOutbsSimXgv1FbfOpzXyz4xu6e3XH2V7GZ7BHOdS885KjoyNt27albdu2+Pn5MW3aNJo0aYKPjw+bNm26ZdtLly5le4yc5nPJXPt2dHQkNTUVyH762TupVKkSzs7OrFmzhq+++upmQX8nSqk7Hl8pxcSJE+nUKXcrDaYV9CLiCEwCOgBxwBYRWaKU2pPNdhOAVbZPWQjsWQzbwqHlaHj4ebPT2J9iZWHwz/C/YJgfYgyZ23igaXHSVTqhu0PxLuXNR498hIMU7G44kScief6X51l6eKmu1Rcw+/fvx8HB4WbNeseOHdSoUYO6dety7tw5Nm3aRIsWLUhJSeHAgQP4+Pjg4eHBokWL6NmzJ9evXyctLY3WrVvzww8/MHjwYM6fP8+6dev45JNP2LdvX7bnrVevHkeOHOHQoUPUqlWLmTNn3jXruHHjOHv2LI6O/wzjXbJkSUqXLs369et55JFHiIiIoE2bNpQqVYqSJUsSGRlJYGDgzaluATp16sR3333HY489hrOzMwcOHKBq1aoUK/ZgfaHMrNE3B2KUUocBRGQW0APYk2W7UcB8oJlt4xUCF4/BklFQpTE89i+z09gv1xLGqHmzB8CSkXDjimlfmv44/geHEg8VikIeoFWVVtQrU4+wqDCCagXhmB/mS9ByxZUrVxg1ahQXL17EyckJb29vJk+eTJEiRZg3bx6jR48mMTGR1NRUXn75ZXx8fIiIiGD48OGMHTsWZ2dn5s6dS69evdi0aRMNGzZERPjvf/9LpUqV7ljQu7q6MnnyZLp160a5cuUIDAwkKioqx6wtW7bMdvm0adMYMWIE165dw8vLi/DwcADCw8MZNmwYRYsWvaX2/swzzxAbG0vjxo1RSlG+fHkWLVp0n+/gP0ybplZEegOdlVLPWJ4PBB5SSo3MtE1V4H/AY0AosPROTfci8hzwHED16tWbHD16NI9fgZ1LS4HwrnBuHwxfB2Ue7BqQhjFxz/xnjAGEHn0XWr9uTJJjI0opBqwYQEJSAkt7LcXJoXB0wVl5ZCVj1o3hi7Zf0L5Ge7PjFBh6mtr8616nqTXzK392n4BZv3V8CbyplEq728GUUpOVUk2VUk3Lly+fKwELtN8/gri/oPsXupDPLU4u0DscGvaFtf+GNf8y7mawka1ntrLr3C6G+AwpNIU8QIcaHahWvBpTdk/J8XqsphVWZhb0cUC1TM89gJNZtmkKzBKRWKA38K2I9LRNvALs8B+w/nNj/ne/3manKVgcnaDHt9DsWdg4EZa+Ygw6ZAOhUaGUcS1DT+/C9V/E0cGRob5DiU6I5s/Tth85TdPyOzML+i1AbRGpKSJFgKeBJZk3UErVVEp5KqU8gXnAC0qpB79gUZhdjYcFzxn3gnf5r9lpCiYHB+j6CQS+YnR0XDjcuFSSh/Ym7GXDiQ0MqD8AV6cCNvywFYJqBVHOrRxTdk8xO4qm5TumFfRKqVRgJEZv+r3AHKVUtIiMEJERZuUq0NLTYeEISLoAvcMK36h2tiQC7d83BhvaPceY/S71ep6dLiwqjGLOxQiul/PgHgWVi6MLgxoM4s9TfxIVn3PHKU0rbEztlquUWq6UqqOUqqWUGm9Z9r1S6vtsth2i76F/QJu/hZg10Gm8MSqVlvceeQ26fgr7lxm34N24muunOHbpGKuPrqZP3T6UKFJ4Ry98qs5TFC9SnNDdoXffWNMKkYJ//41mOPk3/PI+1OsOzZ4xO03h0vxZ6PkdHPnDmBAn6WKuHj48OhwncWJgffPu388P3Iu483Tdp/n12K8cTjxsdhxNyzd0QV8YXL8M84aBewUImmjTW740i4B+8NRUOLEdpj1u9JXIBeeunWNxzGJ6ePegfFF9t0n/+v0p4liEqVFTzY6iPaCEhAQCAgIICAigUqVKVK1alYCAAEqVKkWDBg2y3Wfs2LH88ssvdz32naaGjY2NRUT417/+GVckPj4eZ2dnRo4cedv2OXF3d7+n7fOSLugLOqVg6atwIdaYK14Pb2ueBpYJcOIPQHgXuJT1JpN7F7EngjSVxlCfobkQ0P6VdStLL+9e/Hz4Z05fPW12HO0BlC1blh07drBjxw5GjBjBK6+8cvO5g0P2Rde4ceNo3/72sRTS0u56h/ZNXl5eLF269ObzuXPn4uPjc+8vIB/RBX1Bt3Om0RmszVtQI/vRmzQbqt0eBiyAS6cgrDOcv/+JZxKvJzJ7/2w61ehEtRLV7r5DITHEdwhKKX7a85PZUbQ8kpaWxrPPPouPjw8dO3YkKSkJgCFDhtycEMbT05Nx48YRGBjI3Llz7zg1bFZubm7Ur1+frVuNKahnz55Nnz59bq4/evQo7dq1w9/fn3bt2nHs2DEAjhw5QosWLWjWrNktLQIAn3zyyc2pZ997771cfS+sUXhG1SiM4mNg2etQI9AYpU3LHzxbweAlxmQ44V1g4CKoUO+eDzN7/2yupV5jmN+wPAhpv6q6V6VLzS7MOzCP5/yeo5RrwZ7YxxYm/DWBfeezHzL2ftUrU483m795X/sePHiQmTNn8uOPP9KnTx/mz5/PgAEDbtvO1dWVyMhIAPz9/bOdGjY7Tz/9NLNmzaJSpUo4OjpSpUoVTp40WuBGjhzJoEGDGDx4MGFhYYwePZpFixbx0ksv8fzzzzNo0KBbvkisXr2agwcP8tdff6GUIigoiHXr1t2cKtcWdI2+oEq9DvOGglMReGIy6DHA85eqjWHIclDpMLUrnNxxT7snpSYxY+8MAqsGUq/MvX9JKOiG+Q4jKTWJmfvuPiGJZn9q1qxJQEAAAE2aNCE2Njbb7TLmks9uaticdO7cmTVr1jBz5szb5qPftGkT/fr1u3mcjC8SGzZsoG/fvrcdf/Xq1axevfrmfPX79u3j4MGD9/iKH4yu0RdUa96D07uMa8Ilq5qdRstOxQYwdIUxp/20x6H/XKj+sFW7LopZxPnk84T4huRxSPtUu3Rt2nq0Zca+GQz2GUxR56JmR7Jr91vzzitZp5fNaLrPKmPWt5ymhs1OkSJFaNKkCZ999hnR0dH8/PPPd9w283GzO4dSirfffpvhw4dbff7cpmv0BdH+FfDnd/DQCKjbxew0Wk7K1oJhK4w7IiJ6waHf7rpLSnoKU6OmElA+gCYVm9ggpH0K8Qsh8Xoi8w/ONzuKZrLMU8MCt0wNeyevvfYaEyZMoGzZsrcsb9myJbNmzbp5nMDAQABatWp1y/IMnTp1IiwsjCtXrgBw4sQJzp49++Av6h7ogr6guXQSFr1gDIjTYZzZaTRrlPQwavZlahmD6uxdmuPmK4+s5OTVk4T4hdxTLaWwCahgfBGaFj2NlDwegljL/8LDw3nxxRdp0aIFbm5ud93ex8eHwYMH37b866+/Jjw8HH9/fyIiIvjqq68A+Oqrr5g0aRLNmjUjMTHx5vYdO3akX79+tGjRAj8/P3r37s3ly5dz74VZwbRpavNS06ZNVUaPyUIlPQ2mBRmD4wz/wxjPXrMfSRdgxlPGvfY9v4OGtw9nm67SeXLJkwDMD5pfKOacfxDr49bzwq8vMK7lOHrV7mV2HLuip6nNv+xpmlott63/DI5GQrdPdSFvj9xKGz3wPVsZE+FsuX0o13Vx64i5GMMw32G6kLdCYNVA6pauS1hUGOnKNrMIalp+oz8pCoqjG4055v36GPOha/bJxR36zYU6nWDZq7Dhq5urlFJM2T2FKsWq0LlmZxND2g8RIcQvhNhLsfx27O79HzStINIFfUFw7TzMfxZK1YDun+shbu2dsysETwefJ2DNWPjt36AU285sY+e5nQzxHYKzg7PZKe1GhxodqFa8GqG7QymIlyrzkn6/8p/7+Z3o2+vsnVKwZBRcOQMhq8GluNmJtNzg6GwMWeziDus+getXCHVKpIxrGXp69zQ7nV1xcnBiiM8QPtz8IX+d/ouHKj9kdiS74OrqSkJCAmXLltWdPvMJpRQJCQm4urre0366oLd3W6bAvqXQcbwxCItWcDg4wuNfQ5Hi7Ns+mciqlRkdMBI3p7v3GNZu1cO7B9/t/I4pu6fogt5KHh4exMXFce7cObOjaJm4urri4eFxT/vogt6enY6CVe+Adwd4+AWz02h5QQQ6jSfs8i6KXTlC8L514GMZ8VCzmoujCwMbDOSLbV8QHR+NTzn7nqTEFpydnalZs6bZMbRcoK/R26sbV40hbt1KGbdi3WE2J83+Hbt8nFVJx+lTNoASe5fC7P6Qkv1IYNqd9anTh25/9Q4AACAASURBVOLOxQmNuv1uBk0ryHTpYK9WvAnxB41x7N31POQF2dToqTiKIwPbfwndv4SDa4z77a/bdtANe+dexJ2n6z3NL0d/4Uji/c8aqGn2Rhf09ihqPvwdAY+8Cl5tzU6j5aFz186xKGYRPbx7UL5oeWg61Oikd3Qj/NTDuONCs1r/+v0p4liE8Khws6Noms3ogt7enD8CP78MHs2h7dtmp9HyWMTeCNJUGkN9hv6z0K+3cfvd6SiY2h0unzEvoJ0p61aWXt69+Pnwz5y+etrsOJpmE7qgtydpKTA/BBCjVueo76UuyC7duMSc/XPoWKMj1UtUv3Vlva7Qfw5cOGLMaX/xuDkh7dAQ3yEopYjYE2F2FE2zCV3Q25PfPoQT2yDoayhdw+w0Wh6bvW82V1OuEuJ3h6lovdoaQ+ZejYewzpBwyJbx7FZV96p0qdmFuQfmcjH5otlxNC3P6YLeXsT8agyH2mQo+OgBUwq65NRkpu+dTquqrahXpt6dN6z+EAxZCqnJRmF/Jtp2Ie3YUN+hJKUmMXP/TLOjaFqe0wW9Pbh8xpjkpHx96PyR2Wk0G1gYs5DzyecJ8b1DbT6zyv7GNLcOThDeFeK25X1AO1endB3aeLThf3v/x7WUa2bH0bQ8pQv6/C493Sjkr1+Gp8LBWY+KVtClpKcwNWoqDcs3pGnFbGedvF35OjBshTGuwk9BEBuZtyELgGf8nuHi9YssOLjA7Cialqd0QZ/fbfwaDq81avIV9NzQhcGq2FWcvHqSEN+QextjvLQnDF0JJT1g+pNw+I88y1gQBFQIoHGFxkzbM42UtBSz42hantEFfX4Wt9XogNegh3FtXivw0lU6obtD8S7lTZtqbe79ACUqw5DlRqG/cDgk6c5mOXnG7xlOXz3NsiPLzI6iaXlGF/T5VXIizBsGxasYE5vo2aMKhfVx64m5GMMw32E4yH3+9yxWFnp9D1fOwup3cjdgARNYNZA6pesQFhVGuko3O46m5Ym7fpKISAUR6SUiL4rIMBFpLnK/n0CaVZQyBsVJjIPeocZ1V63AU0oxZfcUqhSrQueanR/sYFUaQavR8Pd0iPkldwIWQCJCiG8IRxKPsPbYWrPjaFqeuGOBLSKPisgqYBnQBagMNADeBXaLyAciUuJBTi4inUVkv4jEiMhb2azvLyK7LI+NItLwQc5nN/6OgOgF8Oj/QbXmZqfRbGT72e3sOLeDwT6DcXbIhcGQ2rwF5erCkpcg+dKDH6+A6ujZEQ93D0KjQlFKmR1H03JdTjXzrsCzSqlmSqnnlFLvKqVeV0oFAQ2Bv4EO93tiEXEEJmF8iWgA9BWRBlk2OwK0UUr5Ax8Ck+/3fHbj3H5Y/gbUbAOBr5idRrOhKbunUMa1DL1q98qdAzq7Qo9JcOkE/PJe7hyzAHJycGKo71B2x+/mr9N/mR1H03LdHQt6pdQYpdSxO6xLVUotUkrNf4BzNwdilFKHlVI3gFlAjyzn2aiUumB5uhnweIDz5X8pScZ1+SLFjFnpHBzNTqTZyP7z+4k8EUn/+v1xc8rFWyirNYMWL8LWMN0LPwc9vHtQ1rUsobv1FLZawWPNNfpSIjJaRD4Xka8zHrlw7qpA5gG64yzL7iQEWJFDzudEZKuIbD137lwuxDPB6nfhTJTRkap4JbPTaDYUGhVKUaeiBNcNzv2DP/oOlPGCJaPgxtXcP34B4OLowsAGA9l0ahPRCXp0Qa1gsaZT3XLAE9gNbMv0eFDZdSPP9gKZiDyKUdC/eaeDKaUmK6WaKqWali9vh/Oz7/0ZtkyBFiOh9n1fEdHs0PFLx1kVu4rgusGUdCmZ+ycoUtRowr94DH4dl/vHLyCC6wZT3Lm4rtVrBY6TFdu4KqVezYNzxwHVMj33AE5m3UhE/IEpQBelVEIe5DDfxeOweCRUDoB2+lpqYTM1eiqO4siABgPy7iQ1WkLz5+DPH6BBT6jRIu/OZafci7gTXC+Y0N2hxCbG4lnS0+xImpYrrKnRR4jIsyJSWUTKZDxy4dxbgNoiUlNEigBPA0sybyAi1YEFwECl1IFcOGf+k5YKC56F9FToHQZORcxOpNlQfFI8i2IWEVQriApFK+TtydqNhVLVYfGLcEOP756d/vX7U8SxCOHR4WZH0bRcY01BfwP4BNjEP832Wx/0xEqpVGAksArYC8xRSkWLyAgRGWHZbCxQFvhWRHaIyAOfN9/5YwIc2wTdv4CytcxOo9lYxJ4IUlUqw3yH5f3JXNwhaCKcPwS//yfvz2eHyrmVo6d3T5YcWsKZq2fMjqNpucKagv5VwFsp5amUqml5eOXGyZVSy5VSdZRStZRS4y3LvldKfW/5+RmlVGmlVIDlYeUMH3biyHpY9wk07Af+fcxOo9nYpRuXmL1/Nh1qdKB6ieq2OalXG2M45U2TjCGWtdsM8RmCUoqf9vxkdhRNyxXWFPTRgG7ny21XE4wm+7K1oOsnZqfRTDBn/xyuply1bira3NRhnDG08qIXICXZtue2Ax7FPehcszNzD8wl8Xqi2XE07YFZU9CnATtE5Idcvr2u8FIKFr8A1xKM6/Iu7mYn0mwsOTWZiD0RtKrSivplbTwroWsJCPoK4vfDuv/a9tx2YpjvMJJSk5i5b6bZUTTtgVlT0C8CxgMbyd3b6wqvP7+HAyuhw4dQuXCM6qvdalHMIs4nnyfEz8a1+Qze7SFgAER+CSf/NidDPlandB3aeLRhxt4ZXEvRDZqafbtrQa+UmpbdwxbhCqRTO2HNWKjTBR4abnYazQSp6alMjZ6Kf3l/mlY0sdtJp39DsfKw6EVIvWFejnwqxC+Ei9cvsjBmodlRNO2B5DSpzc8i8riI3Da7hoh4icg4EbFBV+EC5PoVmDsUipY1BjDRU88WSitjV3LiyglCfEMQM/8G3ErD41/C2WiI/Ny8HPlUowqNaFyhMVOjp5KSlmJ2HE27bznV6J8FHgH2icgWEVkuIr+JyBHgB2CbUirMJikLiuVj4MIReHKKMWe4VugopQjdHUqtkrVoW62t2XGgbhfw62Pc/XE6yuw0+U6IXwinr55m+ZHlZkfRtPuW06Q2p5VSbyilagFPYcwe9yrgo5TqoJRabKuQBcLO2bDzf9B6DHgGmp1GM8n6E+uJuRjDML9hOIg1XWRsoMsEo3a/+AXQNddbPFL1EeqUrkNYVBjpKt3sOJp2X6z6pFFKxSqlNimldiildM+Ue5VwCJa9CtVbQus3zE6jmWjK7ilULlaZLjW7mB3lH0XLQLfPjP4jG74yO02+IiKE+IZwOPEwa4+vNTuOpt2XfFKlKMBSbxhTzzo4wZM/gqM10wtoBdH2M9v5++zfDPYZjLPDbV1fzNWghzEG/h8T4Ow+s9PkKx09O+Lh7kHo7lCUynbeLU3L13RBn9d+/QBO7TA635X0MDuNZqIpu6dQ2qU0T9R+wuwo2ev6KRRxN8bCT08zO02+4eTgxFDfoeyO382W01vMjqNp98ya+ehfsmaZlo0Dq2HTN9DsWajf3ew0mon2n9/P+hPr6V+/P25ObmbHyZ57eWOUxhNbjSFytZt6ePegrGtZQqP0FLaa/bGmRj84m2VDcjlHwXPpFCwaARV9oeO/zU6jmSw0KpSiTkV5ut7TZkfJme+TULcbrB0P8TFmp8k3XBxdGNBgABtPbiQ6IdrsOJp2T3K6j76viPwM1BSRJZkea4GCOS98bklPg4XPQUqSMcSts6vZiTQTHb98nFWxq+hTtw8lXUqaHSdnItD9c3BygSUjIV33NM8QXDcYd2d3wnbru4o1+5JTz7CNwCmgHPBZpuWXgV15GcruRX4BR9ZB0DdQvq7ZaTSTTYuehqM4MrDBQLOjWKd4Jej8MSx6Hv6aDA+PuPs+hUDxIsUJrhtMWFQYRy8dpUaJGmZH0jSr5HQf/VGl1O9KqRZKqT8yPbZb5pLXsnPsT1j7H6MJtNEAs9NoJotPimfhwYUE1QqiQtEKZsexXsO+4N3B6Ex6/ojZafKNAQ0G4OzgTHhUuNlRNM1q1nTGe0JEDopIoohcEpHLInLJFuHsTtIFmB9i9K7v/oUe4lZj+p7ppKpUhvoONTvKvRGBx78ybgtdMko34VuUcytHr9q9WHxoMWeunjE7jqZZxZrOeP8FgpRSJZVSJZRSxZVSJfI6mN1RCpaMhsunoHc4uObza7Fanrt84zKz98+mQ40O9tnMW7Kq0ZE0dj1s0zXYDEN8hqCUImJPhNlRNM0q1hT0Z5RSe/M8ib3bFg57l0C7seDRxOw0Wj4we/9srqRcYZivHc/91HgQeLU1Zly8eNzsNPmCR3EPOnl2Yu6BuSReTzQ7jqbdlTUF/VYRmW3phf9ExiPPk9mTM3tg5dtQqx20GGV2Gi0fSE5NJmJPBC2rtKRB2QZmx7l/IvD410aL1c+jjX81hvkO41rqNWbum2l2FE27K2sK+hLANaAj8LjloUd/yXDjGswbCi4loNf34KAHG9Rgccxizief5xm/Z8yO8uBK14AOH8Ch3+Dv6WanyRfqlqlLa4/WzNg7g2spevoPLX+7a6mklBqazcOO2yJz2aq34dw+o5B3t6Ne1VqeSU1PJTw6HP9y/jSt2NTsOLmjaQjUCIRV78Clk2anyRdCfEO4eP0iC2MWmh1F03JkTa/7OiLyq4hEWZ77i8i7eR/NDkQvhG1TodXL4N3O7DRaPrEqdhUnrpwgxC8EKSh3Xjg4QNDXkHYDlr6im/CBxhUb07hCY6ZFTyMlXU/vq+Vf1rQz/wi8DaQAKKV2Afl8HE8buHAUlrwEVZvCY/p7j2ZQShEaFYpXSS/aVmtrdpzcVbaW0dn0wErYNcfsNPlCiF8Ip66eYsWRFWZH0bQ7sqagL6qU+ivLssI9YE5ainG/PAp6h4JjPptyVDPN+hPrOXjhIMN8h+EgBbC/xkPDwaM5rHgDLuv7yB+p+gi1S9cmdHco6UqPNaDlT9Z8EsWLSC1AAYhIb4yhcQuvtf+BuC3w+JdQ2tPsNFo+Ero7lErFKtHVq6vZUfKGg6Mx5XJKEix7tdA34YsIIb4hHE48zO/Hfzc7jqZly5qC/kXgB6CeiJwAXgaez9NU+dmhtcZY9o0HGcPcaprF9jPb2X52O0N8huDsUIBbecrXgUf/D/YtNfqpFHKdPDtR1b0qobtDUYX8i4+WP1nT6/6wUqo9UB6op5QKVErF5nmy/OjKOVg4HMrVgc4TzE6j5TOhUaGUdinNE7ULwTATLUZClcaw/HW4Gm92GlM5OTgx1Gcou+J3sfXMVrPjaNptrOl1X0pERgMfAuNF5GsR+Trvo+Uz6enG/PJJF+GpcChS1OxEWj6y//x+1sWto1/9frg5uZkdJ+85OhlN+MmXjOv1hVwP7x6UcS1D6O5Qs6No2m2sabpfDngCu4FtmR6Fy+ZJEPMLdBoPFX3MTqPlM2FRYRR1Kkrfen3NjmI7FRtAmzchaj7sXWp2GlO5OrkysMFANpzcwJ6EPWbH0bRbWFPQuyqlXlVKhSulpmU8cuPkItJZRPaLSIyIvJXNerG0IMSIyC4RaZwb571nJ7bBLx9Ave7QrACMdKblquOXj7MydiVP1XmKki6FbDKjwJehkp9xb/2182anMVVw3WDcnd0JiwozO4qm3cKagj5CRJ4VkcoiUibj8aAnFhFHYBLQBWgA9BWRrIOCdwFqWx7PAd896HnvWfIlmDcM3CtC0EQ99ax2m2nR03AQBwY2GGh2FNtzdIYe30LSeWO+h0KseJHi9KnbhzVH13D00lGz42jaTdYU9DeAT4BN/NNsnxs9TpoDMZbOfjeAWUCPLNv0AH5Shs1AKRGpnAvntkpyShKvTOvG/JR41JM/QtEH/n6jFTDxSfEsPLiQHrV6ULFYRbPjmKOyPwS+CrtmwYFVZqcx1cAGA3ESJ8Kj9LS+WvbOnD/PoB+aMu+3L2x2Trnb7SAicgh4SCmVq11rLffjd1ZKPWN5PtBynpGZtlkKfKyUirQ8/xV4Uyl12xcNEXkOo9YPoOeJ1TRN0wqTbUqpbCfXcLJi52iM2etyW3Zt4Fm/dVizjbFQqcnAZICmTZuqrVtz5zaX6LPR9F3Rl+vnW1CDfnzbvwneFdxz5diafbt84zId53WkZZWWfNb2M7PjmO/ENpjSHgL6Q49vzE5jmuOXj9N9YXcGNRjEa01fMzuOlg8opZiy/gjrfwknxnMB9ZzLETrg91ydCyOnY1nTdJ8G7BCRHzJurcul2+vigGqZnnsAWafFsmabPOVTwYc+dfvgWmYz564fJeibSBbvOGHLCFo+NWf/HK6kXCHEL8TsKPlD1SbQcjT8HWFMaVtIVStejU6enZizfw6J1xPNjqOZLPFaCs9FbOPH5RvxqDCHJAcH3u3yg00nvLKmoF8EjAc2kru3120BaotITREpgjFRzpIs2ywBBll63z8MJCqlbD787siAkbgXccfXby0NqhTnpVk7eGfhbpJT0mwdRcsnklOTidgTQcsqLWlQNmsf0kKs7dvGgFJLRsP1y2anMU2IbwjXUq8xa98ss6NoJtoVd5FuE9fzx77T/NfjR5a6O9PfKwivcvVsmsOakfGmAXOAzbl5e51SKhUYCawC9gJzlFLRIjJCREZYNlsOHAZiMGbRe+FBz3s/SrmWYlSjUeyI38ozna4yvI0XM/48xpPfbeRowlUzImkmW3JoCQnJCYT46tr8LZxdjYF0EuNgzXtmpzFN3TJ1eaTqI8zYO4Ok1CSz42g2ppTip02x9P5uE+npit8e2s4U51OUcXZnxMO2vzvFmpHxHgd2ACstzwNEJGvN+74opZYrpeoopWoppcZbln2vlPre8rNSSr1oWe+XXSc8W+ldpzd1Stfh822f8nIHT6YMakrchSS6T4xkZdRps2JpJkhNTyUsKgy/cn40q9TM7Dj5T7Xm8PALsDUUjqw3O41pQvxCuHD9AgsOLjA7imZDV66nMmrm34xdHE0r77KsfNKFvw/+wE5XF15u/hbuRWzfx8uapvv3MW6FuwiglNoB1MzDTPmSk4MTbzd/m1NXTxEeFU77BhVZOioQr3LFGDF9Gx8u3cONVD1NZWGwOnY1J66cIMQvxKbX2ezKY+9CGS9YMhJuFM5WryYVm9CoQiOmRU8jJT3F7DiaDew9dYmgiZEs332KNzrXJbRPbRyWjeDzsmXwL9OAIO8gU3JZU9CnKqWy9igplFM0Na3UlC6eXQiLCuPElRNUK1OUOSNaMKSlJ6GRRwievIkTF3UzXUGmlCI0KhSvkl48Wu1Rs+PkX0WKQtA3cCEWfv3Q7DSmCfEN4dTVU6w8stLsKFoem7P1OD0nbeDK9VT+9+zDvNCmFg5LRzHZ8SrxDvB2i3/hINYUubnPmrNGiUg/wFFEaovIRIyOeYXSq01fxUEc+GyrcTuVi5Mj7wf5MKlfYw6euUK3r9ezdv9Zk1NqeWX9ifUcuHCAYb7DTPtPazc8W0GzZ+HP7+HYZrPTmKK1R2u8S3kTujuUdKVb/AqipBtpvD53J2/M20VTz9IsG/0ID3uVha1hHIlZQUTJEvTy7oVvOV/TMlrzSTUK8AGuA/8DEjHmpC+UKhWrxDN+z7Dm6Bo2n/rnw6ubf2WWjGxFpRKuDA3fwier9pGapv9jFzShu0OpVKwSXWt2NTuKfWj/PpSqBotfhJTC19olIoT4hXAo8RB/HP/D7DhaLos5e4WekzYwf3sco9vV5qdhD1G+uAuc2YNa9X9M8PDG1bkooxuPNjWnNb3uryml3lFKNbM83lVKJdsiXH412GcwVd2rMuGvCbdce/Mq786iF1vxdLNqTFp7iP5T/uTspUL9VhUof5/9m+1ntzPEZwjOjs5mx7EPLu7GHBEJMbD2P2anMUVnz85Uda/KlKgp3G0kUs1+LN5xgqBvIjl35TrThjbn1Q51cHQQuHEN5g1lXfFSbOAazzd8nnJu5UzNak2v+zUiUirT89IiUqgHtHZxdOGNZm8QczGGOfvn3LLO1dmRj5/057OnGrIrLpGuX0ey8VCujh6smSR0dyilXErRy7uX2VHsi1dbaDwYNn0DcabdOGMaJwcnhvgMYde5XWw9U/hef0GTnJLGu4t289KsHTSoXILlox+hdZ3y/2yw8i2ux+9nQqUqeJX0om9986eutqbpvpxS6mLGE6XUBaBC3kWyD49We5RWVVox6e9JJCQl3Lb+ySYeLB7ZipJuTgyY8icTfz1Ierr+Nm+vDlw4wB9xf9Cvfj+KOhc1O4796fghFK9sNOGnXjc7jc319O5JGdcyhO4ONTuK9gCOJVyj9/cbmb75GMNbezHzuYepVNL1nw2iF8L2aUT4d+Z4cjxvNn8TZwfzW/+sKejTRaR6xhMRqUEh7XWfmYjwRvM3SEpNYuLfE7Pdpk7F4iwZGcjjDavw2ZoDDJm6hYQrhe9DriAIiwrDzcmNfvX6mR3FPrmWhMe/gnP74I//mp3G5lydXBnYYCAbTm5gb8Jes+No92Fl1Gm6TVzPsYRr/DioKW93rY+zY6Yi9MJRWPISpz0aM/nqIdpVb0fLKi3NC5yJNQX9O0CkiESISASwDijcE09beJX0on/9/iw4uIDo+Ohstynm4sSXwQH8p5cfmw8n0O3rSLYdPW/jpNqDiLscx8ojK3mqzlOUdClpdhz7VbsDNOwHkV/AyR1mp7G5PnX7UMy5GGFRYWZH0e5BSlo6/166hxHTt1GzXDGWjX6EDg2yTEmdlgLzQwDFF54+pKl0Xm/6uil5s2NNZ7yVQGNgNsZQuE2UUoX6Gn1mIxqOoIxrGT7666M73j4jIvR7qDoLnm+Ji7MDwT9s5sd1h3XHHDsxNXoqIsKgBoPMjmL/Ov8HipW3NOHfMDuNTZUoUoLgusGsPrqaY5eOmR1Hs8LJi0kE/7CJKZFHGNLSk7kjWlCtTDaX7taOh7gtbH/0NZaf+IOhvkPxKO5h+8B3YO2NwGnAWYxb6xqISOu8i2Rf3Iu483KTl9l5bifLDi/LcVvfqiX5eVQg7etXZPzyvTwXsY3Ea3rErPwsPimeRTGLCKoVRMViFe++g5Yzt9LQ/Qs4E2XU7AuZAfUH4CROhEeHmx1Fu4u1+8/S7ev1HDhzhW/6NeL9IB9cnBxv3/DQWoj8krRGg/jo3AYqFauU72a0tKbX/TMYzfWrgA8s/76ft7HsS1CtIPzK+fH5ts+5mpLzcJ8lXJ35bkBjxnZvwNp9Z+n+zXp2xV3McR/NPDP2zuBG2g2G+AwxO0rBUa8r+D0F6z6BM9lf8iqoyhctTw/vHiyOWczZa3pgrfwoNS2dT1ftZ2j4FiqWcGXJyFZ096+S/cZXzsHC4VC+LvO9H2Lf+X281vQ13JzcbBv6Lqyp0b8ENAOOKqUeBRoB5/I0lZ1xEAfebv428Unx/LDrh7tuLyIMC6zJnBEtSEtT9P5uExGbYnVTfj5z+cZlZu2bRfsa7alZstBN75C3Ok8At1Kw6AVISzU7jU0N9RlKmkpj+p7pZkfRsjh7KZkBoX/yzdoYgptWY9GLrfAqf4dJaNLTYdEISE4kMehrvt79Pc0qNaNTjU62DW0Fawr65IwBckTERSm1D6ibt7Hsj195P3p59yJiTwRHEo9YtU/j6sZwia28y/KvxdGMnrWDK9cL14defjb3wFyupFzJd81wBUKxstD1Uzi1AzZ+bXYam6pWohqdanRi9v7ZJF7POo2IZpaNh+Lp+nUkO45f5NOnGjKhtz+uztk01WfY9A3E/AKd/sM3J37h8o3LvNX8rXw50ZU1BX2cZcCcRcAaEVkMnMzbWPZpdOPRuDq6MmHLBKtr56WLFSF0cDPe6FyXZbtOEjQxkn2nL+VxUu1urqddJ2JPBC0qt8CnrI/ZcQomn57QoAf8/hGc2292GpsK8QvhWuo1Zu+fbXaUQi89XfHNbwcZMOVPSro5sfjFQHo3uUtHuhPb4NcPoH4Q+2sFMufAHILrBlOndB3bhL5H1vS676WUuqiUeh/4FxAK9MzrYPaonFs5nm/4PBtObGBd3Dqr93NwEF5o683/nn2YK9dT6fHNBuZsPZ6HSbW7WRyzmPikeF2bz2tdP4Ui7kYv/PQ0s9PYTN0ydQmsGsiMvTNISi18cwDkF+ev3mDI1C18uvoAjzeswpKRgdStVDznnZIvwbxhULwy6vGv+PivjylRpAQvBrxom9D34Y4FvYiUyfoAdgORwB0uWmh96/fFq6QXE7ZM4Ebavd0+9LBXWZaNfoQmNUrzxrxdvD53J0k3Cs+HX36Rmp5KeFQ4fuX8aF6pudlxCjb3CtDlvxC3BTZ/Z3Yam3rG7xnOJ59n4cGFZkcplLYdPU+3r9ez+VAC43v58mVwAMVcnHLeSSlY+gpcPA5PTmHV2b/YemYroxqNytdjbORUo98GbLX8m/WhB2y+A2cHZ95s/ibHLx/npz0/3fP+5Yu7EBHyEKPb1Wb+9jh6TtpAzNkreZBUu5M1R9cQdyWOEN+QfHm9rcDx6w11u8JvH0LCIbPT2EzjCo0JKB/AtOhpt0yOpeUtpRQ/rjtM8A+bcXZ0YMELLen/UA3r/q/vmAFR8+DRt7lW2Z9Pt3xK/TL1ebL2k3kf/AHcsaBXStVUSnlZ/s368LJlSHvTskpLHqv2GJN3TebM1TP3vL+jg/BqhzpMG9qcc1eu0+ObSJbs1N0ibEEpRejuUGqWrMmj1R81O07hIALdPgcnF1g80ujNXAhkTGF78upJVh5ZaXacQiExKYXnIrYxfvle2tWvwNLRgfhWtbImfu4ALB8Dno9A4KuERoVy5toZ3n7obRwdcui0lw9YNWCOiDwhIp+LyGcioq/PW2FMszGkpafx+bbP7/sYreuUZ9noQOpXLsHomX/z7qLdJKfopvy8FHkikv0X9jPMdxgOYu14UtoDK1EZOn0ExzbClilmp7GZ1h6t8S7lTVhU2B1H1tRyx+64QRApLgAAIABJREFURLpPXM/afWf5V/cGfD+gCSVcrZxwJiXZuC7v7AZP/MjxqyeZGjWVbl7daFShUd4GzwXWDJjzLTAC4/p8FDBCRCbldTB751Hcg6G+Q1l+ZDnbz2y/7+NULunGzOceZnhrL6ZvPkbv7zdyLOFaLibVMguNCqVi0Yp0q9nN7CiFT0A/8O4Av7wPF2LNTmMTDuLAMN9hxFyMuacOvJr1lFJEbIrlye82kpammDOiBSGBNe/tstyasXBmN/T8DkpU5tMtn+Lo4MgrjV/Js9y5yZoqSxugk1IqXCkVDnQF2uZpqgIixC+ESsUq8dFfH5H2AD2KnR0deLtrfX4c1JRjCdfoNnE9q6JP52JSDeD/27vvsKiu7eHj301vgg0RFXsXsbfYewFssaRo7BpjbDGxxFyTX+J7bTEaS2xENMYUTWKD2HtJ7Api7wUQEJQmdfb7x2ASr0hAZjjDsD/PMw/tzNnLQWads88+a52LOMfph6cZXGsw1pbat5YscIQA34UgLGDrWP3CpwKga4WulHYqjV+wnyqaZWDxyWmM++kc/9kSwmuV9Yud65ctkrOdXA6EEyug6XtQtTPHHhxj3719jPQamW/KYmcn0V8Byv7jaw8gyDjhmBd7K3smNZzE5ejL/Hrt11zvr2NNNwLHtaRCcUdGrTvNzICLpKar6T5D+Tb4WwrbFqZ3ld5ah1JwuZTR966/dQhOF4x68FYWVgyqNYjzkec5/fC01uGYjcvhsXRffITAoFA+6lyN1YMaUcTRJmc7efJAf+unex3o8BmpulRmn5yNRyGPfNXkKjuJvhhwSQhxQAhxALgIuAohtgohtho1OjPQuVxnGro1ZPHZxQapguVR1IGN7zZjULNy+B25Rf8VfxD6WN2Hm1vXYq5x4P4B3qrxFg7WmXSnUvJOg8FQoTXsmqG/jakA6FW5F0XtiuJ3oeCsTzCmjafu0XPpUeKS0/hhRFPGtK2MhUUO76DRpcNvI/QtaPv4g5UtP1z6gVtPbjGl0RRsLHN40KCh7CT6GUBX4NOMRzfgC2B+xkPJghCCqY2nEpsSy9JzhlnaYGtlyf/18GTxm/W4Eh6H96LDHLiiGmTkxuoLq7G3sufNam9qHYoiBHRfBFIH28YXiCl8Oys7BtQYwNEHR7kcfVnrcPKtpynpfLTxPB/9EkT9skX4fVxLmlYs9mo7OzQP7hwF7/lQrBJRT6NYdn4ZLUu3pLVHa8MGbmTZSfSngMNSyoNAGOACHJNSHsz4nvIvqhWtRr+q/fj5ys9ciTZcqU/fOqXYNrYFbs52DPY/yZc7r5CmpvJz7H7cfbbf2k6fqn0obFdY63AUgCLlocNncGOv/t7lAqB/9f44WjvybfC3WoeSL92IjKfn0qP8cuY+49pVZt2wJrgWsn21nd0+AgfngNcbUOcNAL4+8zXJ6clMbjTZgFHnjewk+kOAnRCiNLAXGAKsMWZQ5uj9eu/jbOPM7BOzDbrgpqKrE5vHNKd/Qw+W7L/OgG+PExGXZLD9FwRrQ9YihMhX19wKhEbDoVxz2PExxIZpHY3ROds4069aP3bd2cXd2Ltah5OvbDuv7xMSGZ/MmiGN+aBTNSxzOlX/TGI0/DoCilQA7y8BCI4MZvP1zQysOZDyLuUNF3geyU6iF1LKRKA3sFhK2QtQXT5yyMXWhbH1xnLq4Sl23tlp0H3bWVsyp48XX/atw7l7j+n29RGO3Ygy6Bjm6tHTR2y6vgnfir6UdCypdTjKP1lYQPfFkJ6iLztaAKbwB9YYiJWwYk3IGq1DyReS09L5z+YLjP3xLDXcnQkc14LWVV1ffYdS6hffJURCn9VgWwid1DHrxCyK2xdnlNcowwWfh7KV6IUQzYC3gcCM75l2GSAT9XqV16letDrzT80nMdXw98L3aVCGLWNa4GJvxQC/4yzZdw2dzvzfHHNj/aX1pKSnMMRziNahKJkpVgnafQJXt0PwRq2jMTpXB1d6VO7B5uubiUyM1Dock3b3USJ9lv3Buj/vMLJVRX4c2RR3F/vc7fTEKrjyO3T8HErVBWDrja0ERwXzQYMPcLR2NEDkeS87iX4CMA3YJKUMEUJUBPbnZtCMJjm7hRDXMj6+cGOjEMJDCLFfCHFJCBEihBifmzFNgaWFJdMaTyM8IZzVF1YbZYxqJQux9f0W+HiV4stdVxmy5iTRCTlrrlNQxKfE89Pln+hQrgMVXCpoHY7yMk1HQ5nGsH0yxJv/otMhtYaQLtNZd2md1qGYrF0h4XgvPsydRwmsHNiAj7vVwNoyl5Usw4Jg13So0ln/fw6IS4ljwekF1HGtg3fF/FtEKzttag9KKbtLKedkfH1TSjkul+NOBfZKKaugv+4/NZNt0oBJUsoaQFNgjBCiZi7H1Vx9t/p0q9AN/wv+3I+7b5QxHG2t+PqNuvy/Xp78ceMR3osOc/pOtFHGys82XN1AXGocwzxVK1qTZmEJPZZCSiIETtI6GqPzcPagc7nObLiygdiUWK3DMSmp6TpmBlxk5LrTVCjuSOC4lnSqZYBLbikJ+hK3DsWg5zf6Oz+A5eeXE5MUw7Qm0/J1Seys2tQuzPi47dk98/985HLcHsDajM/Xkkl/eyllmJTyTMbnccAloHQuxzUJHzT4AEsLS+adnGe0MYQQvN2kHL+99xrWlhb0X/EnfodvqspbGZLTk1l3cR1N3ZtSq7hacmLyXKtC22lwaSuEmH9b16G1h5KQmsDPl3/WOhSTEfr4Kf1X/IHfkVu806wcG99thkdRA9W8+H0yPLoOvVeCY3EAbj6+yQ+XfqB3ld7UKpa/3yOyOkR5Nm/0JX/fM//PR264SSnDQJ/QgRJZbSyEKA/UA45nsc1IIcQpIcSpyEjTvrbl5ujGSK+R7Lu3j2MPjhl1LM/SLmwb24L2NUowM/ASo9ad5slT1RJz642tRD2NYlhtdTafbzQbC6XqQeCHkGDei02rF61O89LN+f7S9ySlqbtoDlyJwHvRYa6Ex7H4zXp83sMTWysDLRUL2gjnvodWH0KFVoC+Pv6ck3Owt7JnXP3cTmBrL6s2taczPh5EXw3v4rN757Nz/7wQYo8Q4kImjx45CVAI4QT8CkyQUr50HktKuVJK2VBK2dDVNRerLvPIOzXfwaOQB7NPzjZ6L2oXe2uWD2jAf3xqsu9yBD6LDxN8P/dV+vKrNF0a/hf88SzmSZOSTbQOR8kuSyvo8Q0kPYHtU7SOxuiGew4nOimaTdfNfwbjZdJ1kvm7rjBkzUncnO3YNrYFvnVKGW6A6Jv6Ozo8mkLrv68g77+3n2OhxxhTbwxF7YoabjyNZDV1L4QQnwkhooDLwFUhRKQQYkZ2diyl7CCl9MzksQV4KIRwzxjHHch0hY0Qwhp9kl8vpfwtp/84U2ZjacOURlO49eQWP1760ejjCSEY1qICP49qRlq65PVlx1j3550COZW/584e7sXdY1jtYTnrYKVoz60mtJ4MF37RNxsxYw3cGlDHtQ5rLqwx+smAKYqIS2KA33EW77tO3wZl2PRecyq6OhlugLQU/XV5Cwt43U9/IIn+st7ck3OpXLgy/ar1M9x4Gspq6n4C0BxoJKUsJqUsAjQBmgshctubbyswKOPzQcCW/91A6N+BvwUuSSlfvam7CWtVphUtSrdg2fllRD3Nm6nIBuWKEDiuJa9VLsZ/Nl9g/E/niE9Oy5OxTYGUEr9gP8o7l6dd2XZah6O8ihYTwa22/kws0XwXmQohGF57OKEJoey4tUPrcPKUfhHxEc7ei2FeHy/m9qmDvY2B7+re9zmEntUv9Czs8de311xYw4P4B0xtPBVrC/PoYplVon8HeFNKeevZN6SUN4EBGT/LjdlARyHENaBjxtcIIUoJIX7P2KY5MBBoJ4Q4l/HolstxTYoQgsmNJpOUnsSiM4vybNyijjasHtSIjzpXIyAolO5LjnA5vGCs7j0aepQrMVcY6jk0X6+iLdAsraHnUkh8BDunax2NUbUq04rKhSuz+sJqdNL8y1vrdJKl+6/ztt+fFLKzYsuYFvRt6PHvT8ypa3vg2GJoOAxq+P717fCEcPyC/ehYriNN3M3nsl5W73TWUsoXTjOllJFArg5zpJSPpJTtpZRVMj5GZ3w/VErZLePzI1JKIaX0klLWzXj8nvWe858KLhUYWGMgm65vIjgyOM/GtbAQjGlbmfXDmxKXlEbPpUf57o/bpJtxgZ3U9FSWn1+Om4MbPhV9tA5HyQ33Ovoz+/M/wMUXJgTNhoWwYKjnUK4/vs7O24atqGlq7sckMnjNSebtvIK3Vym2vt+CaiULGX6guHDYNApK1ILO/++5H80/NR+J5MOGHxp+XA1lleizqrKiKrAY0EivkRS3L86sE7Py/Ki9WaViBI5rQaPyRZmxJYRe3xzl/L3HeRpDXkhKS2Lc/nGcjzzPuPrjsLY0jym5Aq3VR1C6gf46qxnfctelQhdqFK3B9CPT2Xtnr9bhGFxKmo5vDlynw1cHOXkrmi96erLojbo42VoZfjCdTp/kUxL0JW6t/66kdzL8JDtu72CY5zBKORlwwZ8JyCrR1xFCxGbyiANq51WABYGTjRMfNPiA4Khgtt7IbYmCnCtRyI7vhjZm0Zv1CHuSRM9vjvLJ5mCeJJrHAqCE1ARG7xnN0QdHmdFsBt0rddc6JMUQrGxh4CYo00if7M+YZyU5awtrVnVaRY1iNZh0cBLbbmzTOiSDOXY9iq5fH2Lujiu0rurKnkmtGdi0nPEWyR5dCDcPQNc5UKL6X99O06Ux+8RsSjmWMsty2FndXmcppXTO5FFISqlOhwzMu6I3dVzrsPD0QuJS4vJ8fCEE3euUYu+k1gx+rTw/HL9Lu/kH+PX0/Xy9Mv9J8hNG7BrB2YizzG45m75V+2odkmJIdi4w4Deo2Aa2vg9/Ltc6IqNwsXVhVcdVNHRryMdHPs73hXQiYpMY/9NZ3vI7Tmq6xH9wI1YMbEjpwrmsVZ+Veydh30yo1QvqP7/M7Jerv3A15iofNvoQOys748WgEbUayURYCAumNZ5GdFI0K86v0CwOZztrPvWtxbaxLShbzIFJG8/Tf8WfXAnP+4OP3Ip6GsXgHYO5En2FBW0W0K2iWa3lVJ6xcYA3f9IvqtoxBQ7NM8tOdw7WDiztsJTWZVoz8/hMo/XLMKa0dB3+R2/Rfv5BtgeHM659FXZNbEXb6lnWTMu9p4/h16HgUhp8v/6rxC1ATFIMi88upknJJnQo28G4cWhEJXoTUqt4LXpX6c36S+u5+eSmtrGUcuHXd19jzuu1uRoRR7dFh/nv75dIyCe34oXFhzF4x2AexD9gaYeltC3bVuuQFGOysoU+a8DrDf1Z255PzTLZ21rasqDtArqW78qC0wtYdGZRvplxO3M3hu5LjvJ/2y5St2xhdk5sxQcdq2JnbeRmqFLCtvHw5AG8vlo/C/QPS84uISE1gamNp5ptXQ0jrHZQcmNsvbHsur2LOSfmsLzDck3/41lYCPo3KkvHmiWZu+MyKw/dZOu5UD71rUkXz5Im+0dx+8ltRuweQUJKAis7rqRuibpah6TkBUsr6LkMbJ3g6NeQHAfd5usLopgRawtrZrWchYO1A6uCV5GYlsjkRpNN9nbRmIQU5u68zI8n7lHS2Y5v3q5P17x8/zizFi5uhg6fgUej53506dElNl7dyNs13qZykcp5E48GVKI3McXsi/Fe3feYc3IO++/tN4miLkUdbZj9uhd9G3rwyeYLjF5/hlZVXfm8ey3KFzet/sxXoq8wavcoJJLVXVZTvWj1f3+SYj4sLKDbl2BbCI4s0K+u7vHNX1XPzIWlhSWfNvsUB2sH1l1cR0JqAp81+wxLCyOfHeeATifZePoes7dfJjYpjREtKzC+Q1XjrKZ/mYjLsH0qVGwLrz3f6VxKyewTsylsW5jRdUfnXUwaMM1DwAKuf/X+VC5cmbkn55Kcnqx1OH9pUK4I295vzqe+NTlzJ4ZOCw+xYPdVklLTtQ4NgKDIIIbuHIqlhSX+XfxVki+ohNCfvbWfAUE/w8ZBkGY6f0eGIoTgo4YfMbrOaDZf38zkQ5NJTTeNO2UuhsbSZ/kxpvwaTOUSTgSOa8F075p5m+RTn8IvQ/QzPL1WvDCzs/3Wds5EnGF8/fE42zjnXVwaUIneBFlbWDOl8RQexD9gbcjaf39CHrKytGBI8wrsm9SaLrVK8vXea3RacIj9VzJtV5BnToafZMSuETjbOPNd1++o6FJR03gUE9ByEnSdB5cD4If++rN7MyOE4L267/Fhww/ZdWcX4/aP07TbXVxSKv+3LQSfxYe58yiRL/vWYcOoZlQvqUEi3fkxRFyEXsuhkNtzP0pMTWT+6fnULFaTnpVf6JJudlSiN1FN3ZvSsVxH/IL9CE8I1zqcF5RwtmPRm/X4YXgTrCwFQ/xP8u6604Q+fprnsRy6f4jRe0bj7ujO2q5rKe1UOs9jUExUk5H6qftbB2Fdb33nOzM0qNYgZjSbwdEHRxm9ZzTxKfF5Or6Ukq3nQ2k//yBrjt3mrSZl2TepDX0alNFmLc/FLXBqNbw2Diq/uJJ+VfAqIhIjmNZ4mkld7jAWlehN2KSGk9BJHV+dMt2ePq9VLs6O8a34qHM1DlyNoMNXB1lx8Aap6XlT4W/n7Z2M3zeeSoUr4d/FnxIORr5NR8l/6r0NffzhwWlY62u2vez7Vu3L7JazORtxlhG7RvAkOW8Oam5ExjPg2+OM+/Esbs52bH6vOTN71sbFQaNyK4/vwtaxUKo+tPvPCz++G3uXtSFr6V6pe4FZqKsSvQkr7VSaoZ5D2X57O6fCT2kdzkvZWFkwpm1ldk9szWuVijNr+2W6fX2YP28+Muq4m65tYvKhyXi5euHXyY8idkWMOp6Sj9XqCW/+CJFXwL8bxIZpHZFRdKvYjQVtFnA15iqDdww2alfMpynpzNt5mS4LDxF0/wlf9KjF5jHNqeNR2Ghj/qv0NPh1uL7UbZ/VYGXzwibzTs7D2sKaCfUnaBCgNlSiN3FDPIfg7ujOrBOzSNOZ9j3sHkUd8BvUEL93GvI0NZ03Vv7JBz+fIzLO8Auhvr/4PTOOzaCpe1OWd1xOIRsjNL9QzEuVjjDgV4gNBf8uEHNb64iMom3ZtiztsJQH8Q8YtH0QofGhBh9jz8WHdPjqIEv338C3Tin2TWrDwGblsbTQ+JbbA7Pg3nHwXQhFK7zw48P3D3Pg/gHerfMurg6uGgSoDZXoTZy9lT0fNvyQqzFX+eXqL1qHky0darqxe2Jr3m9bmW1BobSbf8BgnfGklKw4v4I5J+fQoWwHFrdbjL2VEctmKualfAsYtEV/rX51F/0Zvhlq6t6UlR1XEpMUw6Adg7j95LZB9nsvOpHha08x/LtTONhY8tPIpnzVry6uhWwNsv9cuXkQDs+HegOgdp8Xfpyansrck3Mp71yeATUGaBCgdlSizwc6lutIk5JNWHx2MY+T8kdnOXsbSz7sXI0dE1pRp0xhZmwJoefSo5zLRWc8KSULTi9gybkl+Fb0ZV7redhYvjg1pyhZKt0ABv8OunTw7wph57WOyCjqlqjL6i6rSUlPYdCOQVyJfvWDmuS0dJbuv07HBQc5diOKj7tV5/fxLWlasZgBI86FhCj4bSQUrwJd52a6yfeXvud27G0mN5pc4LpXqkSfDwghmNJ4CgmpCSw5t0TrcHKkkqsT64Y1ZvGb9XgYm0Svb44yfVMwjxNz1ulYJ3XM/HMm/iH+9K/Wn5ktZmJlYV5FUJQ85FYThu4AawdY4wt3/9Q6IqOoXrQ6/l38sbKwYsjOIQRFBuV4H0evR9H168PM23mFttVKsOeD1oxsVQlrSxNJH1LC5tHwNEZ/Xd7mxSJekYmRLD+/nNZlWtOyTEsNgtSWifymlH9TpUgV3qj+BhuvbuRy9GWtw8kRIQS+GZ3xhrxWgZ9O3qPd/INsPHUPXTam89N0aUw/Mp0NVzcw1HMo05tMN9lyn0o+UqySPtk7ucK6XnBjv9YRGUVFl4p81/U7XGxcGLFrBCfDT2breQ9jkxj741ne9jtOuk7iP6QRywY0oJQxO8y9ij+/gWu7oNNMKJl5B/WFZxaSqktlcqPJeRycaVDvlvnI6DqjcbFxYdbxWfmmkcU/FbKzZoZvTba934IKxR356Jcg+q/8g8vhsS99Tkp6CpMOTCLgZgDj649nYoOJJltjX8mHXMrAkO1QtCL80A8uB2odkVGUdirN2q5rcXd0Z/Se0Ry6f+il26al61h9RN9hbmdIOBM6VGHnhFa0rWaCt66GnoXdn0I1b2g8ItNNzkWcY+uNrQyqNYiyzmXzOEDToBJ9PuJi68K4+uM4E3GG7be2ax3OK6tZypmNo5ox93UvrkfE473oCDMDLhL/P53xElMTeX/v++y7t4+pjacyvPZwjSJWzJpTCRi0DUp6wc8DIWij1hEZRQmHEvh38adS4UqM3zeeHbd3vLDN6Tsx+C45yucBF2lQrgi7JrRiQoc86DD3KpLj4Jeh+t9fjyXPtZ59Rid1zDoxixL2JRhRO/MDgYJAJfp8plflXtQoWoP5p+eTmJqodTivzMJC0K+RB/smtaFfQw/8jtyi/fwDBAaFIaUkNiWWd/e8y/Hw43zR/AvervG21iEr5syhKLyzGcq9Br+NgFP+WkdkFEXsiuDXyQ8vVy+mHJrCpmubAIhOSGHKL0G8vuwYjxNTWD6gPmuGNDK5plXPCfxQf4vk6376318mNl/fzMVHF/mg4Qc4WDvkbXwmROTHKeB/07BhQ3nqlOkWmMmtcxHnGLh9ICNqj2Bc/XFah2MQZ+7G8J/NFwgJjaVZFVsSiy7jbvxN5rScQ6fynbQOTykoUp/ChkFwbSd0/AKam8ff1/96mvaUCfsncCz0GB3dRrLvRDXik9IY1qIC49pXwTEvm8+8inM/wuZ3oc00aDM1001iU2Lx3eRLOedyrO2y1uwv+QkhTkspG2b2M3VGnw/VLVEX34q+rAlZw73Ye1qHYxD1yxZhy5jmTOrqxgXdLG48vklbl8m0Kt1e69CUgsTaHt5YD7V6w+7/wL7/p1/VbWbsrewZXWMmjml12f1wJUVLHSJgbAumdath+kk+6joEToJyzaHVRy/dbNm5ZcQkxTCt8TSzT/L/RiX6fGpCgwlYW1gz91Tm94zmR+GJoQRGfYKDQwINbCfz2zFnOi44yP7L2nbGUwoYS2v9dHC9gXBorr4Lmhkl+9ikVD7bGkLvpSdIDXubOoXbE2m9hd8f+Jn+It+0ZH3rWSsb6L0KXtKQ5nrMdX68/CN9qvahRrEaeRyk6THxQzflZUo4lGBUnVEsOL2AIw+O0KJ0C61DypWbj28yYtcIktKT+LazH57FPTnWJIr/bL7AkDUn6VTTjU+716K0qd3ao5gnC0vovhhsC+lv30qOA9+vX5pY8oNnHeZmBl4iKj6ZAU3K8WGnahSy78R/j/8X/xB/ElITmN7UhG9f3fMZhAfBGz+CS+ZdKqWUzD45G0drR8bWG5u38ZkoE/1tKtkxoMYAyjmXY86JOaSmp2odziu7+Ogig3cMJl2m49/FH8/ingC8Vqk428e3YkqX6hy+FkWH+QdZduAGKWl50xlPKeCEgM7/hdZT4Ow6fbOUtJwVejIV1yPieGvVccb/dA53Fzu2jGnOFz09cXGwxkJYML3JdIZ6DmXD1Q18fORj0+yrcWWH/qCr8Sio3u2lm+29u5fjYcd5v977qtFVBrUYL587dP8QY/aOYVKDSQz2HKx1ODl2NuIs7+15j0I2hVjVaRXlnMtlut39mEQ+33aRXRcfUrmEE1/08KRZJRMpv6mYv6OL9Nfsq3SGfmv11/Lzgacp6Szed41Vh29ib23J5C7VebNx2Zc2n/EL9uPrM1/TzqOdaZWYjg2FZc3BuTQM3wPWdplulpSWRI/NPXC0cWSDz4YCVT1TLcYzY63KtKJVmVYsO7+MyMRIrcPJkWOhxxi1exTF7IuxtsvalyZ5gDJFHFj5TkNWD25Iclo6b676kwk/nSUiLikPI1YKrObjwGeBvgLb+r76qXwTtzujw9w3B27QvU5p9n3YhgFNy2XZYW547eFMbTyVfff28f7e903jFl5dur6OfVoy9PV/aZIH8L/gT2hCKNMaTytQSf7fqERvBqY0mkKqLpWFZxZqHUq27burfyMpU6gMa7qswd3JPVvPa1dd3xlvXLvK/B4cTvsvD7L2mGE64ylKlhoOhd4r4c4x+K4nJEZrHVGm7kUnMmzNSUZ8dwonWys2jGrG/H51KO6UvQ5zb9d4my+af8Hx8OO8u+ddYlNeXrkyTxz+Cm4fhm7z9E1rXiI0PpRvL3xL5/KdaVSyUR4GaPpUojcDZZ3L8k7Nd9h6YyvnI02/E1fAzQA+OPABNYrWwL+zP8Xti+fo+XbWlnzQqRo7J7aibtnCfLo1hO5LjnD2boyRIlaUDF79oP86/YKwtb4Qbzp3hCSnpbNk3zU6fHWQP24+Ynq3GgSMa0HjCpkXk8lKz8o9mddqHsFRwQzfOZzoJI0Oau78AQf+C7X7Qt23stz0y1NfIhBMajApj4LLPzRJ9EKIokKI3UKIaxkfX7piQghhKYQ4K4QIyMsY85uRXiMpYV+CWcdnoZOmu1htw5UNfHz4Yxq4NWBlp5W42Lq88r4qFHfku6GNWfpWfaLik+m97BjTfst5ZzxFyZHq3vDWBoi+qW9z+1j7WhZHrkXRdeFhvtx1lfY1SrB3UmtGtKqYqw5zncp3YlHbRdx8cpMhO4bwMOGhASPOhsRo/QLIwuXA+6tMS9w+czzsOLvv7GZ47eHZnh0sSLQ6o58K7JVSVgH2Znz9MuOBS3kSVT7mYO3AxIYTCXkUwpbrW7QOJ1P+F/z54s8vaFmmJUvbL8XROvflNYUQeHu5s3dSG4Y1r8CGU/rOeBuy2RlPUV5fZcn+AAAVRElEQVRJpbYwcDPER+qT/aMbmoTxMDaJ9384w4Bvj6OTkrVDG/PN2w1wdzHMYsGWZVqyrMMyHiY+ZNCOQdyLy6ODGilh61iIf6hvPWvn/NJN03RpzD4xm9JOpfPlguS8oFWi7wGszfh8LdAzs42EEGUAb8Avj+LK17wreFPXtS4LzyzU/rraP0gpWXJ2CV+d/orO5TuzsM1C7KxevqDmVTjZWvGJT00Cx7WgYnFHJv8SRN8Vf3ApzHReB8XMlG0Cg7dBaqI+2T+8mGdDp6Xr8Dt8k/bzD7Lr4kMmdqjKjgmtaF3V1eBjNSrZCL9OfsSlxDF4+2BuPr5p8DFecOpbuBwAHT6F0vWz3PTnKz9z/fF1Pmr0EbaW2VuHUNBolejdpJRhABkfX9b/cCEwGfjXuWghxEghxCkhxKnIyPy1+txQhBBMazKNmKQYlp1bpnU4gD7Jzz05lxVBK+hVuRdzWs7B2tLaaONVL+nMhlHNmNfHi1tRCfgsPsIXAReJS8q/dQYUE+ZeR9/mVljAmm7w4LTRhzx1OxqfxUeYGXiJhuWLsHtiK8Z3qGLUDnOexT3x7+JPukxn8I7BXHxkxIOa8Auw42Oo3AGajsly0+ikaJaeW0oz92a082hnvJjyOaMleiHEHiHEhUwePbL5fB8gQkqZrb8cKeVKKWVDKWVDV1fDH9XmFzWL1aRP1T78ePlHbjzWZjrxmXRdOp/98RnfX/qeATUG8Nlrn2GZB5XFLCwEfRt6sG9Sa/o38mD10Vt0+OogAUGhpl/iU8l/XKvB0B1g6wxru8PtI0YZJjohhcm/nKfP8j+IfZrK8gEN8B/ciHLF8qbDXNUiVVnbdS12VnYM2zmMsxFnDT9ISoK+9ax9Yei5HCyyTlGLziziaepTpjaeWuDr2WdFk4I5QogrQBspZZgQwh04IKWs9j/bzAIGAmmAHeAM/CalHPBv+y9IBXMyE5MUg/cmb2oWq8mqjqs0+QNITU9l2pFp7Ly9k1FeoxhTd4xmf4jn7j3mk83BXHgQS4vKxZnYsSr1yxZWbwyKYcWG6m+7e3wH+n8PVToaZLdPnqay5dwDvtp9lfikNIa3rMi49pVxsNHmPvGw+DBG7B5BRGIEC9su5LVSrxlmx09jYPsUCNoAAzfp10FkIeRRCG8GvMmAmgOY3GiyYWLIx7IqmKNVop8HPJJSzhZCTAWKSilf+psSQrQBPpRS+mRn/wU90QP8cOkHZp2YxcI2C2lfLm87wCWlJTHp4CQO3T/EBw0+YIjnkDwdPzPpOsn643eYt/MKcUlplC5sT7faJfHxKoVXGReV9BXDSIiCdb0g4pK+MU6tTJcf/au4pFR2X3xIYFAYh65FkpouaVKhKDN7elLFrZCBg865qKdRjNo9iltPbvFl6y9pV/YVp82TnsDlQAjZBDf2gy5V35Gu3SdZPk1KycDtA7kXd4+AXgEUstH+NdGaKSb6YsAGoCxwF+grpYwWQpQC/KSU3f5n+zaoRJ8jabo0+m7ry9O0p2zusdngi99eJiE1gbH7xnIq/BSfNP2EftX65cm42ZXZG6hHUXu8a5fCx8udWqWcVdJXcifpCazvB/dPQPclUO/tbD0tPjmNvZceEhAUxsGrkaSk6SjlYoe3lzveXqWoY2IHpE+Sn/DenvcIeRTCzBYz8amYrbdnSIqFqzvgwm9wYy+kp4BLWf1BUa1eUKpelrfSAWy7sY2Pj3zM5699Tq8qvQzwr8n/TC7RG5tK9Honwk4wbNcw3qv7HqPrjDb6eE+SnzB6z2guPrqYsz98jTxJTGXXxXACgsI4ej2KNJ2kfDEH/Rtr7VLUcC9kUm+sSj6SkgA/vQ0390PXedBkZKabJaakse9yBIFBYey7HEFymg43Z1u61XbHx6sU9TwKY5FFyVqtJaQmMG7fOE6Gn8z6wD45Xp/cQzbBtd2QnqyvW1+rl/5RusG/Jvd/jum7yRc3BzfWe6833U57eUwl+gJs0oFJHLx/kK09t1LKqZTRxjHYVJ5GYhJS2BkSTmBwGMduPCJdJ6no6ohPbXd86pSiqglMlyr5TFqyfmHZ5QBoPwNa6iu2JaWmc+BKBNuCwth3KYKnqem4FrKlm2dJfOqUokHZIiad3P/XSy/VpSTqewOE/AZXd0HaUyjkDjUzztzLNPrXxXaZ+er0V/hf8Gd9t/V4uXoZ+F+Tf6lEX4CFxYfRfXN3WpVpxfw28402hlEW52jkUXwyO0LCCQwK48+bj9BJqFLCCR+vUnh7uVO5hJPWISr5RXoabHkPgn7mVrURLJBvsfdyBAkp6RRztKFr7ZJ41y5F4wpFs2w2Y+qeW3xbqi1jYmIR13bqaww4loCaPcCzN3g0faXk/sztJ7fptbUX3hW8mdlipgH/BflfVoletfcxc+5O7gyrPYyl55ZyIuwEjd0bG3T/d2LvMGLXCOJS4ljRcQX1StQz6P61UMzJlreblOPtJuWIiEti54VwtgWFsXDvVRbsuUr1koXwybhuWqF43tzapOQ/KWk6Dl97xO8p79JYRtP/yiqacxenOtPxrlOaJhWKYpWLErUmIy0Z6+t7mRMZg2NCEitC95OQkMpkr/4Iz95QrjkY6LbauSfnYmtpy4QGEwyyv4JCndEXAElpSfTc0hN7K3s2+m40WPvGqzFXGblrJDqpY3nH5dQsVtMg+zVVD2OT2B4cRkBQGKfu6Bvo1CrljLeXOz61S1G2mIPGESpaS03XcfR6FAFBYewKCSc2KQ0Xe2s61yzBWN33eFxaBV5vQI+lYJmPz7PSUvTrD0I26VfNJ8eCfRFkdV/mOsD3oQfoXaU3M5rOMFjtjEP3DzFm7xg+bPghg2oNMsg+zYmaulfYe2cvEw5MYFrjabxVI+suUNkRHBnMu3vexc7SjlWdVlGxcEUDRJl/hD15SmBQGIHBYZy9+xgArzIu+Hi50622O2WKqKRfUKSl6/jj5iMCg8LYERLO48RUCtlZ0almSXy83GleuTg2Vhb6+u2Hv4R9M6GGL7z+LVjlo5Kt6alw6yBc2ASXt+nvLrBzgeq+4NkLKrQGS2uklHxz/huWn19O5/KdmdViVq6rYaakp9BrSy8sLSz51fdXo1bXzK9UoleQUjJy90hCHoUQ0CuAonY5b135zMnwk7y/932K2BXBr5MfZQqVMWCk+c/9mER+Dw4jMCiM8/efAFDXo/BfSb9UYcM0GFFMR7pOcvzmIwKCw9hxIZzohBScbK3oWNMN79rutKxaHFurl5zJ/rkcdkyBSu31hXVsTPigMD1N3ws+ZBNc2gZPo/UVAKt76xfUVWwLVjaZPnXNhTXMPz1fvz6o9fxc3eL7bfC3LDyzkBUdVvBa6fy9BshYVKJXALjx+Aavb32dXlV68WmzT19pH4fvH2bigYmUdirNyo4rcXN0M3CU+dvdR4kEBocREBRKSKi+oU7DckXwzkj6bs55U89AMbx0neTk7WgCg8LYfiGMqPgUHGwsaV/DDR8vd1pXdc1+vfkz62DbOPBoAm/9rD8zNhW6dLhzVJ/cL26FxCiwcYJq3fTJvXL7bM9EbLiygZl/zqRRyUYsarfolTpWPkx4iO9mX5q6N2VRu0U5fn5BoRK98pc5J+aw/tJ6fvL5KcfX1Hfe3snUw1OpUrgKyzsuz9WsQEFwKyqBwKBQAoLCuBwehxDQqHxRfL3c6eLpjmuhfDRtW0DpdJIzd2MICArj9+AwIuKSsbO2oH11fXJvU60E9javeA36wm/w2whw84QBv4FjMcMGnxM6Hdz7Ux/TxS2QEAHWDlC1i361fOUOYP1qM1OBNwOZfmQ6tYrV4psO3+Bim7ODmqmHp7L79m4299yMRyGPV4qhIFCJXvlLXEocPpt8KFuoLN91/S7bBWE2X9/Mp8c+pY5rHZa2X6pKTubQ9Yh4AoP0Z/rXIuKxENCkQjF86rjTpVZJijmppG8qpJScvfeYwIzkHvYkCVsrC9pWK4G3lzvta5QwXJ35q7tgw0AoUl7f397Z3TD7zQ6dDu6f1N/nfnELxIWBlT1U7aQ/c6/S2WCXFfbd3ceHBz+kgksFVnRcQXH74tl63tmIs7yz/R1G1B7BuPrjDBKLuVKJXnnOpmubmHFsBrNazspW9br1l9Yz+8Rsmrk3Y2HbhThYm/A1xXzg6sM4AjKS/s3IBCwtBK9VKoZ3bXc61ypJEcfMr3kqxiOlJPjBEwKC9GstHjx+io2lBa2rueLj5U77Gm442Rpplfytw/DjG+BYHN7ZCkXKGWcc0C8IfHBaPy0fshli74Olrb4BT61e+jN4W+PUifgj9A/G7x9PCYcSrOq4CnenrA9q0nXpvBn4JtFJ0WztuVW97/wLleiV5+ikjrcC3yIiMYJtvba99LqZlBK/YD8WnV1EO492zGs9DxtLlYQMRUrJ5fA4AjKm9+88SsTKQtC8cnF8vNzpVLMkLg5qdbGxSCkJCY0lMGMh5d3oRKwtBS2r6JN7h5puONvl0et//xR8/7p+uvydLeBa1XD7lhLCzumn5UM2w5O7YGmjXwzo2Vuf3O2cDTdeFs5FnOO9Pe/hZOPEqk6rKOf88oOajVc38vkfnzOv1Ty6VOiSJ/HlZyrRKy84H3meAb8PYKjnUCY2mPjCz6WULDyzkNUXVuNd0Zsvmn+BtYVKOsbyLOkEBIURGBzKveinWFsKWlVxxdvLnY413SiUV0nHjD07uHp2a+StqIS/Dq68vdzprOXBVfgFfec7qdO3aXXPRXlXKSE8OOPMfRPE3AILK6jUDmr1hmpd9T3fNXDp0SVG7R6FhbBgZaeVVC3y4kHNk+Qn+GzyoVLhSvh39lc9J7JBJXolU9OPTOf3W7+zucfm546sdVLHf4//l5+v/Ey/qv2Y3nS6ahyRh6SUBN1/8teZ5oPHT7GxsqB11TyYRjZT1x7GsS0ojMCgUG6Y8uWSqOvwXQ9IjoMBv4BHDipZSgkRF/9O7o+ug7CEim300/LVvcHBNBbQ3nx8kxG7RpCsS2Z5h+V4Fvd87ufP3n82+GygWtFqGkWZv6hEr2QqMjES382+NHBrwNL2SwF9e9sZR2ew7eY2htQawsQGE9XRtIaeLQwLOK9fGBYe+/fCMJ867rSrbsCFYWbmRuTfCyCvPsxHCyAf34PvukPcQ3jzB32izkrE5b+Te9QVEBZQvqV+Wr66r7ar+bNwP+4+w3cNJyYphiXtl9CoZCNAX3Gz77a+9K3al0+aZt2XXvmbSvTKSz0rarG0/VKaujdl8qHJ7L27l7H1xjKi9giV5E2ITic5fTfmr2nnyLhk7K0taVejBD613WlbvUT27+M2U7ejEjLqGIRxKSz2uVsaO3uWpEShfFLHIO6hfhr/0XXot1Y/1f5PUdf1q+VDNunP4hFQvoX+zL1Gd3By1STsnHqY8JCRu0fyIP4BC9osoEXpFgzbNYyrMVcJ6BlAYTttLi/kRyrRKy+Vmp5K76290UkdZQqV4VjoMaY0msKAmgO0Dk3JwsuKt3TIKN7SKifFW/K5e9GJf61tuPDAjIoUJUbD+j4Qeg56r4TS9fWJ/cImeBgMCCjbTJ/ca/aAQvmzeFVMUgyjdo/i2uNr9Kzck1+u/sJ/mv7n5b3tlUypRK9k6ciDI4zeMxoLYcFnzT6jV5VeWoek5EBauo4Tt6JfKMfq7pJPE1wOpKbruP0oEYB6ZQvjXdvMyg4nx8EPb8CdI39/z6PJ38nduZR2sRlQXEocY/aO4WzEWaoVqcbPPj8brBlOQaESvfKv1lxYQwWXCrT2aK11KEouPGuwsuNCODGJKVqHY3QCgVcZF7y9zLiRUOpTfSOcQu765F7YPKvDJaYmsiJoBd4VvTNdia9kTSV6RVEURTFjWSV6dc+UoiiKopgxlegVRVEUxYypRK8oiqIoZkwlekVRFEUxYyrRK4qiKIoZU4leURRFUcyYSvSKoiiKYsZUolcURVEUM2aWBXOEEJHAHQPusjgQZcD95Xfq9fibei2ep16Pv6nX4nnq9XieoV+PclLKTLsZmWWiNzQhxKmXVRwqiNTr8Tf1WjxPvR5/U6/F89Tr8by8fD3U1L2iKIqimDGV6BVFURTFjKlEnz0rtQ7AxKjX42/qtXieej3+pl6L56nX43l59nqoa/SKoiiKYsbUGb2iKIqimDGV6BVFURTFjKlEnwUhRBchxBUhxHUhxFSt49GSEGK1ECJCCHFB61hMgRDCQwixXwhxSQgRIoQYr3VMWhFC2AkhTgghzme8Fv+ndUymQAhhKYQ4K4QI0DoWrQkhbgshgoUQ54QQp7SOR0tCiMJCiF+EEJcz3j+aGX1MdY0+c0IIS+Aq0BG4D5wE3pRSXtQ0MI0IIVoB8cB3UkpPrePRmhDCHXCXUp4RQhQCTgM9C+L/DyGEAByllPFCCGvgCDBeSvmnxqFpSgjxAdAQcJZS+mgdj5aEELeBhlLKAl8wRwixFjgspfQTQtgADlLKx8YcU53Rv1xj4LqU8qaUMgX4CeihcUyakVIeAqK1jsNUSCnDpJRnMj6PAy4BpbWNShtSLz7jS+uMR4E+gxBClAG8AT+tY1FMhxDCGWgFfAsgpUwxdpIHleizUhq494+v71NA38iVrAkhygP1gOPaRqKdjGnqc0AEsFtKWWBfiwwLgcmATutATIQEdgkhTgshRmodjIYqApGAf8ZlHT8hhKOxB1WJ/uVEJt8r0GcpyouEEE7Ar8AEKWWs1vFoRUqZLqWsC5QBGgshCuzlHSGEDxAhpTytdSwmpLmUsj7QFRiTcSmwILIC6gPLpJT1gATA6Ou/VKJ/ufuAxz++LgOEahSLYoIyrkf/CqyXUv6mdTymIGMa8gDQReNQtNQc6J5xXfonoJ0Q4nttQ9KWlDI042MEsAn9pdGC6D5w/x8zXr+gT/xGpRL9y50EqgghKmQsmHgD2KpxTIqJyFiA9i1wSUr5ldbxaEkI4SqEKJzxuT3QAbisbVTakVJOk1KWkVKWR/++sU9KOUDjsDQjhHDMWLBKxjR1J6BA3r0jpQwH7gkhqmV8qz1g9AW8VsYeIL+SUqYJId4HdgKWwGopZYjGYWlGCPEj0AYoLoS4D3wqpfxW26g01RwYCARnXJsG+FhK+buGMWnFHVibcaeKBbBBSlngbylT/uIGbNIfG2MF/CCl3KFtSJoaC6zPOIG8CQwx9oDq9jpFURRFMWNq6l5RFEVRzJhK9IqiKIpixlSiVxRFURQzphK9oiiKopgxlegVRVEUxYypRK8oiqIoZkwlekVRFEUxY/8feDBPXuyBq0gAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 576x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(8,4))\n",
"\n",
"plt.plot(x_6, modes_y_6[:,0], label = 'First Mode')\n",
"plt.plot(x_6, -modes_y_6[:,1], label = 'Second Mode')\n",
"plt.plot(x_6, -modes_y_6[:,2], label = 'Third Mode')\n",
"\n",
"plt.title('6 Nodes: First Three Mode Shapes')\n",
"plt.ylabel('Displacement (m)')\n",
"plt.axhline(linewidth=1, color='k')\n",
"plt.legend(loc=1);"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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xfLDjA34/9TuTWk6ibLGyuXIOu3R2L2ycCMd/h+K+0GMqBA4wClUzObmCUwXG9y8PiVeM5/oJVwAFTsWgmLfRkt/EbnjFiv3beHDQoEE0bdqUNWvW0KlTJ/73v/9RtWpVq47TvXt3XnvtNTZt2kRMTMzN5Rmr5NOl/z5k9XuhlGL48OF8+OGHd/ul5Bl9Ga1pGgCxCbGM+WMMb255k2olqrGk2xL61eqXJ32pyxQrwzftv+HdZu8SGh1K7xW9WRWxKss/qgXaxaPw43CY3s5oFNfpA3hxDzwwxPxCPiMRox1AqapG6/zi5UGlwuWTEHscUpPMTgjA8ePHqVq1KqNHj6Z79+7s378fDw8Prl69muO+I0eOZNy4cbe08gdo06YN8+bNA4z2Ad7e3hQvXvyW5T///DOXLl0C4OGHH2bJkiVcuHABMJ7xnzyZ7Qyy+UIX9Jqm8fup3+m1ohebTm/ilYavMOuRWVQqXilPzyki9KvVj6XdllK9ZHXeCnmLVze9SmxCbJ6e1ybEnYGVo2FqUzi6Adq+Di/tg+bPG3fRtszRCdzLgE9to/Yh8RpcCDda9Zt8obZo0SICAgIICgoiPDycYcOG4eXlRcuWLQkICGDs2LHZ7uvr68tLL7102/IJEyawe/duAgMDeeONN5g9ezZgPLvfvHkzDRo0YP369VSqZPy++Pv78/7779OxY0cCAwPp0KED586dy5sv2EpSEK+gGzVqpHbv3m12DE2zedeSrvHJrk9YdmwZtUrW4oPWH1CzZM18z5Galsrsg7P5eu/XeDh7MKH5BB6s9GC+58hzN2Ih5D+wczqkpULjJ4zW8+4+Zie7zaFDh6hTp07OG6YkwKVTkHwdXDyhREWbaqVfEGX1vRGRPUqp2/sdop/Ra1qhtT96P2P/GMv5G+d5qt5TPFf/OZxM+gPt6ODIyICRtKrQire2vMXo30fTs3pPxjUbZ1qmXJWWBtu/gs2fG8+6A/vDg29CySpmJ7t/RVzBuwZcjzZa6V84ZHTrM/nZvfYvXdBrWiH0z/V/ePG3F3Er4sacznOo71Pf7EgA1CxZkwVdF/DNvm/4/u/vcXdy5/Umr5sd6/4kxMFPT8ORX6BGJ2g/3njOXZCIgHtpcCluPLe/fBISLoOnvru3Bbqg17RCJjktmbGbxxKfEs/MTjOpWsK6Vsn5xcnRidENRnMj5QZzD80lqHQQnap0MjvWvbl4FBYOMhqsdfkMGj9ZsO9ynVyNboHXLsDVc5AUbhT2bnc3wJKWu3RjPE0rZKb8NYW9F/YyscVEmyvkMxrTcAyB3oGM3zaeyLhIs+PcvSPr4fuHjC5pw1ZAk6cKdiGfTgQ8yoBPLeNu/tIJiI00RvrTTKELek0rRH49+SuzwmYxoNYAOvt1NjvOHTk5OvFZ289wcnDi1T9eJT4l3uxI1lEKtnwB8/tBycrw9Cao0srsVPnPyc24u/coZ1TjRx+C+DizUxVKuqDXtELi9JXTvLP1HQK8AhjbOPtuRraknHs5Pmz9IccuHWPyn5PNjpOzpOuwZKQxul1Abxi5HkrkbTdFmyYO4FEWfGoao+ldOg6XTlom49Hyiy7oNa0QSEhJ4NU/XsVBHPis3Wd2NV1sqwqteDrwaVZErGDZ0dvHOrcZl07CD50gbBm0nwiP/WBMLKMZE/H41DT638fHGm0W0lJz3G3y5MnUrVuXwMBAgoKC2LFjRz6EvdWmTZt49NFHs1wuIvzwww83l+3duxcR4bPPPrP6+JGRkQQEBORK1uzoxniaVgh8tPMjwmPDmfrwVCq4298UnM/Vf47Q6FAm75hMHa861C5V2+xItzqxBX4cZhRegxdDjQ5mJ7I94mCMqOfoYszEFxMBXlWznShn+/btrF69mr/++gsXFxcuXrxIUpJtjMCXrl69eixatIgnnngCgIULF1K/vm30YMlI39FrWgG3MmIlS48u5al6T9HGt43Zce6Jo4MjH7f+GE9nT17d9CpXk3Ie0jRfKAU7voM5PaCYDzz1my7kc1LMyxg/IPkGXDwGqclZbnbu3Dm8vb1xcXEBwNvbm/LlywPGjHVt27alYcOGdOrU6ebIc8eOHaN9+/bUr1+fBg0aEBERgVKKsWPHEhAQcLNgBuOOvF27dvTp04fatWszePDgm0Mw//LLL9SuXZtWrVrdnLgmK5UqVSIhIYF//vkHpRS//PILnTv/2/YlNDSUZs2aERgYSK9evW4Ok7tnzx7q169P8+bNmTp16s3tU1NTGTt2LI0bNyYwMJDvvvvuHj/kW5l6Ry8ijwBfAo7A/5RSH2VaPxhI70R7DXhOKbUvf1Nqmv06cukI721/j8ZlGzMqaJTZce6Ll5sXn7b9lJHrRjJu6zi+aPdFnozDb7XkBFgzBkLnQs3O0Hs6uBY3L09e+vkNOP937h7TpxY0GG50QfSqDkVufZzUsWNHJk2aRM2aNWnfvj39+/enbdu2JCcn8+KLL7JixQp8fHxYtGgRb7/9NjNmzGDw4MG88cYb9OrVi4SEBNLS0vjpp58IDQ1l3759XLx4kcaNG9OmjXHBu3fvXsLCwihfvjwtW7Zk69atNGrUiKeeeorffvuN6tWr079//zt+GX369GHx4sU88MADNGjQ4OaFCcCwYcP46quvaNu2LePGjWPixIn897//5fHHH7+5POOwvD/88AOenp7s2rWLxMREWrZsSceOHfHz87uvj9q0O3oRcQSmAp0Bf2CgiPhn2uwE0FYpFQi8B0zP35SaZr+uJ19nzKYxuDu780mbTyiSi3OJm6VBmQa80vAVNp7aSPDBYPOCXDkHs7oahXyb/4MB8wtuIZ9XHJ3BqxqkpcDFI8aFUwbu7u7s2bOH6dOn4+PjQ//+/Zk1axaHDx/mwIEDdOjQgaCgIN5//32ioqK4evUqZ86coVevXgC4urpStGhRQkJCGDhwII6OjpQpU4a2bduya9cuAJo0aYKvry8ODg4EBQURGRlJeHg4fn5+1KhRAxFhyJAhd/wy+vXrx+LFi1mwYAEDBw68uTwuLo7Lly/Ttm1bAIYPH87mzZtvWz506NCb+6xfv545c+YQFBRE06ZNiYmJ4ejRo/f9UZv5m98EOKaUOg4gIguBHsDB9A2UUtsybP8n4JuvCTXNTimlGL9tPKevnuZ/Hf+Ht5u32ZFyzTD/Yfz1z1/8Z89/CPQJJKh0UP4GiIkwCvmEK9BvDvj3yN/zm6HzRzlvc6+8qkNsBMQchVLVbmnA6OjoSLt27WjXrh316tVj9uzZNGzYkLp167J9+/ZbDnPlypUsD3+n+Vwy3n07OjqSkmL09b+bmqKyZcvi5OTEhg0b+PLLL9m2bdsdt1dKZXt8pRRfffUVnTrl7gBRZj6jrwCczvA+yrIsO08AP2e3UkSeFpHdIrI7Ojo6lyJqmn1aEL6AdZHrGN1gNI3KZjnPhd0SEd5r9R7l3Msx5o8x+Tvb3eXTMLu7MS3rE+sLRyGf15yLglcNQCDmmDEbHnD48OFb7mZDQ0OpXLkytWrVIjo6+mZBn5ycTFhYGMWLF8fX15fly5cDkJiYyI0bN2jTpg2LFi0iNTWV6OhoNm/eTJMmTbKNU7t2bU6cOEFERAQACxYsyPFLmDRpEh9//DGOjo43l3l6elKyZEm2bNkCQHBwMG3btqVEiRJ4enoSEhICcHOqW4BOnTrxzTffkJxstFs4cuQI169fz/H8OTGzoM/qkibLSy8ReRCjoM920Gul1HSlVCOlVCMfH9ubCUrT8sv+6P18uvtT2vm2Y0TdEWbHyRPFnYvzRbsvuJxwmTc2v0GqFV217tvVf2BOd0i8CkOXQdm87RJVqKQPnetQxKgxSbjCtWvXGD58OP7+/gQGBnLw4EEmTJiAs7MzS5Ys4fXXX6d+/foEBQXdvIsODg5mypQpBAYG0qJFC86fP0+vXr0IDAykfv36PPTQQ3zyySeULVs22yiurq5Mnz6drl270qpVKypXrpxj/BYtWtCzZ8/bls+ePZuxY8cSGBhIaGgo48aNA2DmzJk8//zzNG/eHDc3t5vbP/nkk/j7+9OgQQMCAgJ45plnbtYy3A/TpqkVkebABKVUJ8v7NwGUUh9m2i4QWAZ0VkodsebYepparbC6nHCZvqv74iiOLHp0EZ4unmZHylNLjyxlwvYJPFf/ubxtbHgj1qiuv3TSKOQrNc27c9kIq6epzU2pyUZBn5JgjCroVjJ/z28n7naaWjPv6HcBNUTET0ScgQHAyowbiEgl4CdgqLWFvKYVVmkqjTdD3iQmPobP231e4At5gN41etO9Wne+3fct287c+dnoPUu4AnN7GwXQwPmFopA3jaMTeFc3Bti5FAnXY8xOVCCYVtArpVKAF4B1wCHgR6VUmIg8KyLPWjYbB3gB00QkVET0bbqmZeN/f/+PkDMhvNHkDep6FbBpULMhIrzT7B2ql6zO61te5/z187l7gqQbML+/0bWs32yo2i53j6/dzqGI0RrfxcMYWOfaBbMT2T1TB8xRSq1VStVUSlVTSk22LPtWKfWt5f9PKqVKKqWCLK+C1apI03LJjnM7mBo6la5Vu9K3Zl+z4+QrtyJufN72c5JSk3jtj9dIzmYAlruWkgiLhsCp7dDrO6hl25MAFSgOjlCqKriWgCtnjO6MJj1mLgj0yHiaZueSUpMYv208lYtXZlyzceYOImMSP08/JraYyL7ofSwIz7mVdI5SU4zJaSJ+he5ToF6f+z+mdnfEwRhBr2gpuHYeruveVPdKF/SaZucWhC/gzLUzvNnkTYo6Fd5JVB7xe4QW5Vvw3f7viEu8j+lQ09JgxfMQvhoe+QgaDMu9kNrdEQHPSuDqadzZx182O5Fd0gW9ptmxuMQ4vtv/HS0rtKR5+eZmxzHdqw2NcfC/3//9vR1AKVg7BvYvhAffgWbP5W5A7e6JQInKRgO9yyeNqYC1u6ILek2zY9P3T+d68nVebfiq2VFsQq1SteherTvzw+cTdTXq7nZWCjaMg90zoOVL0Oa1vAmpWSUmJoagoCCCgoIoW74CFYIeIqhDf0r4lMPfP+tuf+PGjWPjxo05Hju7qWEjIyMREd59992byy5evIiTkxMvvPDCXeV3d3e/q+3zki7oNc1Onb56mvnh8+lZvSc1S9Y0O47NeOGBF3AUR6b8NeXudtz8GWybAo2fNOaTL4RtHWyJl5cXoaGhhIaG8uyzz/LKK68QuncvoRsW4ZCWYoyRn8mkSZNo3779bctTU60fUKlq1aqsXr365vvFixdTt65992LRBb2m2akpf03BycGJ54OeNzuKTSlbrCxD/Yfyc+TPHLh4wLqdtk+D39+H+gOh86e6kLdVTm7gWZHU1FSeGj6YunXr0rFjR+Lj4wEYMWIES5YsAaBKlSpMmjSJVq1asXjx4mynhs3Mzc2NOnXqkD7o2qJFi+jXr9/N9SdPnuThhx8mMDCQhx9+mFOnTgFw4sQJmjdvTuPGjW+pEQD49NNPb049O378+Fz9SKxh/9NZaVohtD96P79E/sIzgc9Qumhps+PYnCfqPcHSo0v5bPdnzOw08849Ef6aA+vehDrdofvX4KDvfzL7eOfHhMeG5+oxa5eqzetNsh3VPHsu7hw9cYoFUz/g+68+pd/Tr7F06dIsZ5lzdXW9OaZ8YGBgllPDZmXAgAEsXLiQsmXL4ujoSPny5Tl79iwAL7zwAsOGDWP48OHMmDGD0aNHs3z5cl566SWee+45hg0bdsuFxPr16zl69Cg7d+5EKUX37t3ZvHnzzaly84P+idY0O6OU4vPdn+Pl6sXjAY+bHccmFXMqxqj6o9jzzx5+P/179hse3QArR0P19vDYD+Co733sgZ+fH0HN2sCNGBoG1CQyMjLL7dLnkr/T1LBZeeSRR9iwYQMLFiy4bT767du3M2jQoJvHSb+Q2Lp1681pajNPPbt+/fqb89WHh4fnytSzd0P/VGuanfnt9G/8deEv3m32LsWcipkdx2b1rtmbeeHz+M+e/9DatzVODk63bhATAUufgDIB0C8YijibE9QO3NOddx5ycXEBj3KQkoRjynXisxkkqVgx4/fjTlPDZsXZ2ZmGDRvy+eefExYWxqpVq7LdNuNxszqHUoo333yTZ0fMM4sAACAASURBVJ55xurz5zZ9R69pdiQ5LZn/7PkPVT2r0rtGb7Pj2DQnBydeafAKkVciWXpk6a0rE68Zo96JAwyYe8sc6JqdEIESlcDRGRLibk5vm5U7TQ2bnTFjxvDxxx/j5eV1y/IWLVqwcOHCm8dp1aoVAC1btrxlebpOnToxY8YMrl0z8p05c4YLF/J3WF9d0GuaHVlyZAknr5zk1YavUsRBV8jlpF3FdjQs05Bv9n3DtSRLQaCUMSBOdDj0mWGMvqbZJwcHcPMCcYRLJ+AO0xVnNzVsdurWrcvw4cNvWz5lyhRmzpxJYGAgwcHBfPnllwB8+eWXTJ06lcaNGxMX9++ATR07dmTQoEE0b96cevXq0adPH65evXoPX+y9M22a2rykp6nVCqKrSVfp+lNXqpeszg8dfyiUQ93eiwMXDzBwzUCeqvcUoxuMhpD/wsbx0GGS0V9ey5Ip09Teq5QEiD5iTIjjXbPAt7Wwp2lqNU27CzMOzOBS4iXGNBqjC/m7EOAdQGe/zsw5OIfzYUvh14lQtxe0GG12NC23FHE1JsFJTTLu7FWa2Ylsii7oNc0OnL9+nuCDwXSt2rXQTEGbm15q8BJpKpWvN78FPnWgx1TdV76gcXE3ntknXYPLp/Rsdxnogl7T7MBXe79CKcXoB/Rd6L2o4FySwYkOrHRz4nDn98BZ91awht092i1aymiNH38Jrp43O02euJfviS7oNc3GhceGsypiFYP9B1PevbzZceyPUrBqNE+ePY6HUzE+P7rI7ER2wdXVlZiYGPsr7N3LgJtlatsCNtudUoqYmBhcXV3var+C3WJB0+ycUorPdn+Gp4snT9Z70uw49unPafD3Yjwfepdnvcvwya5P2HpmKy0rtDQ7mU3z9fUlKiqK6Gg7nAdeKbgWB6d2gUdZo5FeAeHq6oqvr+9d7VNwvnpNK4BCzoSw49wOXm/8OsWdi5sdx/4c/wPWvwt1ukHrMQxIS2H+ofl8tvszmpVrhqODo9kJbZaTkxN+fn5mx7h3l4rCt23AqxqMXFeoB0TSVfeaZqNS01L5Ys8XVPSoSP9a/XPeQbvV5VOw5HHwqg49vwERnBydeLnhyxy7fIyVESvNTqjlpZJVoMfXcPYvoztlIaYLek2zUSsiVnDs8jFebvAyTo5OOe+g/Ss53hj5LjUZBswHF4+bqzpW7kigTyBf7/2aG8k3TAyp5Tn/7tDkGePxTfgas9OYRhf0mmaDbiTf4Ou9X1Pfpz4dKncwO459UQpWvwLn9kHv78G7+i2rRYTXGr3GhfgLzDk4x6SQWr7p+B6UC4Llz8Glk2anMYUu6DXNBs0+OJvo+Ghea/SaHhznbu2cDvsWQLu3oNYjWW7yQOkHaF+pPTMOzOBi/MV8DqjlqyIu0HemcQG4ZCSkJJmdKN/pgl7TbMzF+IvMPDCTDpU7EFQ6yOw49iUyBH55E2p1gTZ3nnP85YYvk5yazLTQafkUTjNNqarQ/Ss4s9sYGbGQ0QW9ptmYaaHTSE5N5uUGL5sdxb5cOQuLRxh/1Ht9a0x4cgeVi1emX61+/HT0J45fPp4/GTXz1O0JjZ+C7V/D4Z/NTpOvdEGvaTbk/PXzLDu2jMdqPkal4pXMjmM/0tJg2bOQdB0GzANXT6t2e6b+Mzg7OvPDgR/yOKBmEzq+D2UDjZ+Vy6fNTpNvdEGvaTZk7sG5KKV4POBxs6PYlz+nwok/4JGPwKeW1buVci3FYzUeY+3xtZy7di4PA2o2wckV+s4yprNdMtLolVEI6IJe02xEXGIci48splOVTlRwr2B2HPtxbj9snAi1H4UGw+5692H+xj66BX4h4VUNun8JUTvh10lmp8kXuqDXNBux6PAibqTcYGTASLOj2I+kG7D0CSjmbTS2uoceCuXcy9HZrzNLjy7lckLBGhtdy0bAY9BoJGybAkfWmZ0mz+mCXtNsQEJKAvMOzaNVhVbUKmV91XOht/4duHjEGPmuaKl7PszjAY8TnxLPgsMLcjGcZtM6fQhl6sGyZyAuyuw0eUoX9JpmA1YcW0FsQqy+m78bh3+G3T9A8xeg2oP3dagaJWvQ1rctCw4tID4lPpcCajbNyRX6zTae0xfw5/U5FvQiUlpEeonI8yIyUkSaiEiuXCCIyCMiclhEjonIG1msry0i20UkUURey41zapqtSUlLYVbYLAK9A2lUppHZcezD1X9gxfNQth48PC5XDjkyYCSXEi+x7OiyXDmeZge8qkG3L+H0DvjtfbPT5JlsC2wReVBE1gFrgM5AOcAfeAf4W0Qmisg9T6clIo7AVMux/YGBIuKfabNYYDTw2b2eR9Ns3YaTG4i6FsXIgJF6FDxrpKUZw5kmXYfHfjBGPssFDco0IMgniNlhs0lOK7h3d1om9fpAwxGw9b9wdIPZafLEne7MuwBPKaUaK6WeVkq9o5R6TSnVHagP7AXuZxDuJsAxpdRxpVQSsBDokXEDpdQFpdQuQP/WaQWSUooZB2ZQpXgVHqx0f9XPhcbO6RDxK3SafFdd6awxMmAkZ6+fZV1kwW+gpWXwyEdQJgB+etoYeKmAybagV0qNVUqdymZdilJquVJq6X2cuwKQccSCKMuyeyIiT4vIbhHZHR0dfR+xNC3/bD+7nfDYcEYGjMQhd56IFWz/hMGGcVDzEWj0RK4fvm3FtlTzrMbMAzNRSuX68TUb5eRm9K9PjoeVLxrj4hcg1jyjLyEio0XkCxGZkv7KhXNnVUd5z5+uUmq6UqqRUqqRj4/PfcTStPwz48AMSruVpmvVrmZHsX3J8bD0SWPUu+5f31NXupw4iAOPBzzOkUtHCDkTkuvH12yYdw1jprtjG2HPTLPT5CprbiHWAlWAv4E9GV73KwqomOG9L1Dw6kw0LRsHLh5gx/kdDPUfirOjs9lxbN/GCXDhoNGVzj3vLua7+HWhTNEyzDgwI8/OodmoRk9A1Xaw7h2ILTjzH1hT0LsqpV5VSs1USs1Of+XCuXcBNUTET0ScgQHAylw4rqbZhRkHZuDh5EGfmn3MjmL7jm6AHd9C0+egRvs8PZWToxPD/Iex+5/d7Ivel6fn0myMgwP0mAoORWDZc8ZQuQWANQV9sIg8JSLlRKRU+ut+T6yUSgFeANYBh4AflVJhIvKsiDwLICJlRSQKeBV4R0Si7qelv6bZisi4SDae3MiA2gNwd3Y3O45tuxYNy0dBaX9oPyFfTtmnZh+KOxdnxt/6rr7Q8fSFLp/A6T+Nme4KgCJWbJMEfAq8zb/P0BVQ9X5PrpRai/FoIOOybzP8/zxGlb6mFSizwmbh5ODEoDqDzI5i25SClS9AQhwMW24McpIPijoVZWDtgUzfP53jccep6nnff+40exLYHw6tMvrWV+8AZTL3/LYv1tzRvwpUV0pVUUr5WV76p17T7lH0jWhWRqykZ/WeeLt5mx3Htu3+AY78Ah0mQZm6+XrqQXUG4eLowqwDs/L1vJoNEDEG0nH1hGVPQ0qS2YnuizUFfRhwI6+DaFphEXwomFSVyoi6I8yOYtuiD8O6t6F6e2j6TL6fvpRrKXpW78mq46s4f/18vp9fM1kxb6OwP/83bP7E7DT3xZqCPhUIFZHvcrl7naYVOleTrrL48GI6VO5AxeIVc96hsEpJhCVPgHMx6DEtT7rSWWN43eEopZh7cK4p59dMVrsr1B8EWz6HqN1mp7ln1hT0y4HJwDZyt3udphU6Px7+kWvJ1/TkNTnZ9CH887fRAtqjjGkxfD186VSlE4uPLCYuMc60HJqJOn8EHuWNWe6S7LNyO8eCPmOXulzuXqdphUpiaiJzD82lebnm+HvZd+OePHVmD2z9Eh4YArU6m52GkQEjuZFygx8P/2h2FM0Mrp7QcxrEHINfJ5qd5p7caVKbVSLSTUScslhXVUQmiYi+LdE0K62KWMXF+IuMrKd/bbKVnGB0pfMoB50+MDsNALVK1aJlhZbMPTSXhJQEs+NoZqjaFpo8Y4zlcHyT2Wnu2p3u6J8CWgPhIrJLRNaKyG8icgL4DtijlNKdTDXNCqlpqcw8MBN/L3+alm1qdhzb9cdHEB0O3acYd1I24omAJ4hNiGXFsRVmR9HM0n4CeFWH5c8b3T3tyJ0mtTmvlPo/pVQ1oC/wHkZXu7pKqQ5KKf0Tr2lW+vXUr5y6eoonAp7QU9FmJyq9yn6o0dLehjQq04hA70Bmhc0iJS3F7DiaGZyLQq/v4OpZ+OVNs9PcFaumy1JKRSqltiulQpVS9tkaQdNMkj4VbeXilXm40sNmx7FNyQnGHPMe5YzpZ22MiDAyYCRR16LYeHKj2XE0s/g2gtZjIHQehK8xO43V9LyYmpbHdp7fSVhMGMPrDsfRwdHsOLZp04dw8bDNVdln9GClB6lSvAozDszQU9gWZm3+D8oGwsrRxvDMdkAX9JqWx374+we8XL3oXq272VFsU9Qe2DbFJqvsM0qfwvZQ7CG2n91udhzNLEWcjSr8xCuw+mW7mLvemvnoX7JmmaZptzsYc5Dt57YzxH8ILo4uZsexPTZeZZ/Zo1UfpbRbaT2FbWFXxh8eegfCV8P+RWanyZE1d/TDs1g2IpdzaFqBNPPATNyd3Olfq7/ZUWyTHVTZZ+Ts6MxQ/6HsOL+DAxcPmB1HM1PzF6BSc1j7fxAXZXaaO7pTP/qBIrIK8BORlRlevwMx+RdR0+zT2WtnWX9yPX1r9sXD2cPsOLYnardRZd9gmE1X2WfWp2Yf3J3cmXNwjtlRNDM5OBoD6aQlwyrbrsK/0zS124BzgDfweYblV4H9eRlK0wqCheELEYSBtQeaHcX23KyyLw8dbb/KPiN3Z3d61+jN/EPzOd/wPGWLlTU7kmaWUlXh4fHwy+uwbyEE2ebv+p360Z9USm1SSjVXSv2R4fWXUkp3JNW0O7iRfIMlR5fQvnJ7yrmXMzuO7dn0IVw8YqmyL252mrs2sPZA0khj0WHbfz6r5bEmT0PFZkZhf9U2Zzm0pjFebxE5KiJxInJFRK6KyJX8CKdp9mplxEquJl1lSJ0hZkexPbdU2dvnuAK+Hr48VPEhFh9ZTHxKvNlxNDM5OBiTL6UkwupXbbIK35rGeJ8A3ZVSnkqp4kopD6WU/V2Ca1o+SVNpzDs0j3re9ajvU9/sOLbFjqvsMxviP4S4xDhWH19tdhTNbN7V4cG34PAaCPvJ7DS3saag/0cpdSjPk2haARFyJoTIK5EMqTNED3eb2aYP7LrKPqMGpRtQp1Qd5h6cqwfQ0YxW+BUawtqxcP2i2WluYU1Bv1tEFlla4fdOf+V5Mk2zU3MPzqW0W2k6VOlgdhTbcnoXbPsKGgy32yr7jESEof5DOR53XA+goxmt8HtMhYQrRmFvQ6wp6IsDN4COQDfL69G8DKVp9urYpWNsP7edgXUG4uRw2wzPhVdyAqwYBcUrQMf3zU6TazpV6YS3mzfBh4LNjqLZgtJ1oO3rRvX9oVVmp7npTt3rAFBKPZ4fQTStIJh7aC4uji70qdHH7Ci2Jb3Kfugyu6+yz8jZ0Zn+tfozNXQqx+OOU9WzqtmRNLO1ehkOrYA1Y6BySyhayuxEVrW6rykiv4rIAcv7QBF5J++jaZp9uZRwidXHV9OtWjdKuJYwO47tiNptVNk3HAHVHjI7Ta7rW7Mvzg7OzD803+womi1wdIIe0+BGDKx7y+w0gHVV998DbwLJAEqp/cCAvAylafZoyZElJKYm6i51GaUkwvJRRiv7Du+ZnSZPeLl50bVqV1ZGrCQuMc7sOJotKBcIrV6BfQvgyHqz01hV0BdVSu3MtEwPmKNpGSSnJrMwfCEtyregWolqZsexHZs/Ncay7/Zlgaqyz2xwncHEp8Sz9OhSs6NotqLNWPCpbcxwl2DuBaA1Bf1FEakGKAAR6YMxNK6maRbrT67nQvwFfTef0bn9sOULqD8IatjPWPb3olapWjQt25T5h+aTnJZsdhzNFhRxMarwr56DDeNMjWJNQf888B1QW0TOAC8Dz+VpKk2zI0opgg8GU6V4FVpWaGl2HNuQmgwrnodi3nYx/WxuGOI/hH9u/MOvp341O4pmK3wbGv3r98yC45tMi5FjQa+UOq6Uag/4ALWVUq2UUpF5nkzT7MS+6H2ExYQxpM4QHMSaa+dCYNsUOL8fun5uE62O80Mb3zZU9KjI3INzzY6i2ZIH34JS1WDli5B4zZQI1rS6LyEio4H3gMkiMkVEpuR9NE2zD8EHg/Fw9qBbtW5mR7EN0Ydh00fg3xPqFJ7PxEEcGFxnMPui97E/Wk/wqVk4uRkD6Vw+Db9OMiWCNbcfa4EqwN/AngwvTSv0zl47y8ZTG+lTsw9FnYqaHcd8aamw4gVwdocun5qdJt/1rN4Tdyd35h7Sd/VaBpWbG7Pc7fwOTm7L99NbU9C7KqVeVUrNVErNTn/lxslF5BEROSwix0TkjSzWi6UG4ZiI7BeRBrlxXk3LLTfnnK9lm/NQ57sd30HUTuj8MbiXNjtNvivmVIzeNXqzIXID56/b5pSlmknaj4cSlY0L4aQb+Xpqawr6YBF5SkTKiUip9Nf9nlhEHIGpQGfAHxgoIv6ZNusM1LC8nga+ud/zalpu0XPOZxJ7An57D2p0gnp9zU5jGj1XvZYl52LGZE6xEcZIkfnImoI+CfgU2M6/1fa7c+HcTYBjlsZ+ScBCoEembXoAc5ThT6CEiOTbX9SkhKu8+P1DfLpQdzLQbrcqYpWecz6dUkZjI4ci8Oh/oBDP2pc+V/2SI0v0XPXaraq243q9oYyKWMiC37/Ot9NKTtMrikgE0FQplavz7ln64z+ilHrS8n6o5TwvZNhmNfCRUirE8v5X4HWl1G0XGiLyNMZdP0DD3MyqaZqmaTZuj1KqUVYrcpzUBgjDmL0ut2V1yZ/5qsOabYyFSk0HpgM0atRI7d6dG5UO8PPfc/i/vz5l5Dl31rl8xDdDG+HnXSxXjq3Zry1RWxj16yg+bv0xXap2MTuOueLOwNSmUOEBGLayUN/Np1NK0X91f5JSk1jWYxmiP5NCTSnFzK2RfLD2EO5+3+JVPJH1fdfi6OCYa+e408+YNVX3qUCoiHyX3rUul7rXRQEVM7z3Bc7ewzZ5qkPdQZQv4k5oyYs8cGUj3b4K4ee/9cCAhd3cQ3rOecCosl/9MqhU6DZFF/IWIsIQ/yFExEWw/Zyeq74wu5qQzPPz/2LS6oM0rnWNVOcTPF5vaK4W8jmxpqBfDkwGtpG73et2ATVExE9EnDEmylmZaZuVwDBL6/tmQJxSKl9L2SIORRhU/2n+cnVlcLF5NPRO5rl5f/He6oMkp6blZxTNRhy7dIxtZ7cxoPYAPef8/h/h6Hp4eByU8jM7jU15pMojeLl66QF0CrHw81fo/vVW1oX9w5uda+NbZRfuTu70qtErX3NYMzLebOBH4M/c7F6nlEoBXgDWAYeAH5VSYSLyrIg8a9lsLXAcOIYxi96o+z3vvehdsw9FHV2ZW9SBmaV/ZESLKvwQcoIB0//kXJxubFPYzAufZ8w5X7OQzzl/7QL88jr4NjH6CGu3cHZ0pn/t/mw5s4UTcSfMjqPlsyV7oug5dSvXE1NY8FQzejQqxoaTG+hdozfFnPL38a81I+N1A0KBXyzvg0Qk8533PVFKrVVK1VRKVVNKTbYs+1Yp9a3l/0op9bxlfb2sGuHlBw9nD3rX7MO6YkWJPrKaCdWOMnVQA8LPXaHrlBA2H4k2I5ZmgssJl1kVsYpHqz5KSdeSZscx19qxRn/gHlMhH6sh7Um/mv1wcnBi3qF5ZkfR8klCciqvL9nPa4v30aBSSdaMbk0Tv1LMD5+PQjG4zuB8z2RN1f0EjK5wlwGUUqFAoaujG1RnEKnAwvLVYO1rdK3uwsoXW+Hj7sLwmTv578YjpKbduQeDZv+WHNVzzgNwcCUcXA7tXgefmmansVl6rvrCJfLidXpN28ai3ad58aHqBD/RFB8PF2PMjSNLaF+pPeXdy+d7LmsK+hSlVOaf0EJXolX0qMhDlR5isVsR4hMuwy9vUM3HneXPt6TXAxX478ajjJi5k5hriWZH1fJIcloyCw4toHm55lQvWd3sOOa5EQtrxkDZQGgx2uw0Nm9InSHEp8Tz09GfzI6i5aFfDpyn21chnIuLZ+aIxozpWAtHB6Nx6oqIFVxNuspQ/6GmZLOmoD8gIoMARxGpISJfYTTMK3SG+g8lLvkaq+p3h/2L4PAvuDk78nnf+nzUux47TsTy6Fch7Dl5yeyoWh7YELnBmHPev5Dfza97G+JjjSp7x0LeGNEKtUrVoknZJswPn09KWorZcbRclpyaxuQ1B3l27h6qlnZn9YuteLD2v8M/p6k05h2aR6B3IEGlg0zJaE1B/yJQF0gE5gNxGHPSFzoNSjfA38uf4NQLpJX2N7oVxV9GRBjQpBI/PdcCJ0cH+n+3nR9CTpDTYESa/VBKMffQXKoUr0KrCq3MjmOeoxth33xo9QqUCzQ7jd0YUmcI56+fZ+OpjWZH0XLR+bgEBk7/k++3nGB488r8+EwzfEveOrnV5qjNnLxy0rS7ebCu1f0NpdTbSqnGltc7SqmE/Ahna0SEof5DibxykpCWzxitjte/c3N9QAVPVr3Yiodql+a91cYVXlx8somJtdyy98Je/r74N4PrDC68c84nxMGq0eBTG9qMNTuNXWnj24ZKHpUIDgvWNwAFxOYj0XSZsoVD564wZeADTOwRgEuR2xulBh8MpmyxsrSv3N6ElAZrWt1vEJESGd6XFJF1eRvLdnWq3InSRUsz558QaDka9gZDxG8313u6OfHd0Ia807UOvx66QLevQjhwRjfCsXezw2ZTwqUEPapnno6hEFn3Flw9Dz2nQREXs9PYFUcHR4b6D2X/xf2ERoeaHUe7D6lpii/WH2b4zJ2U9jAaZXevn3UDu/DYcHae38mg2oMo4mDNQLR5w5pbE2+l1OX0N0qpS0Dhm3/SwsnRiYG1B7Lj3A4OBz4G3jVh5UuQePXmNiLCk62rsuiZ5iSnptF72jbm/nlSX8nbqZNXTvL76d/pV6sfbkXczI5jjqMbYO9caPkSVNBTSdyLHtV74OniyawDs8yOot2jC1cTGPK/HUz57Rh9G/qybFRLqvm4Z7t98MFg3Iq48VjNx/Ix5e2sKejTRKRS+hsRqUwhbHWfUd+afXEr4sbcoz8aDZLiTsPGCbdt17Cy0YeyRXUv3ll+gNELQ7mWqBvj2Jvgg8EUcSjCwNqFdM75+MuwcjT41IF2b5idxm65FXGjf63+/H76d05eOWl2HO0ubYu4SJcvQ9h7+hKf9gnkkz71cXPOfvyI6BvRrD2xlp7Ve1LcuXg+Jr2dNQX920CIiASLSDCwGXgzb2PZNk8XT7pX686a42u46F0Vmo2CXf+DyJDbti1VzJkZwxsztlMt1uw/S/evQgg/f8WE1Nq9uJRwieXHltOtWje83bzNjmOOdW/DtX90lX0uGFh7IEUcihB8MNjsKJqV0tIUX/92lCH/24GnWxFWPN+Kvo0q5rjfwsMLSU1LtYkxN6xpjPcL0ABYhDEUbkOlVKF9Rp9ucJ3BJKcl8+PhH+Ghd6CkH6x4wRgpLBMHB+H5B6sz/6lmXEtMocfXW/lx92kTUmt3a9HhRSSmJjLMf5jZUcxxZD2EzoVWL0OFBmansXvebt50q9aNFcdWcClBd8O1dTHXEhkxaxefrT9Ct/rlWflCK2qV9chxv4SUBBYfXky7iu2oVLxSjtvnNWubD6cCFzC61vmLSJu8i2Qf/Dz9aOPbxigIHB2h+1dw6QT8PjnbfZpV9WLN6NY0qlKS/1uynzE/7uNGkq7Kt1WJqYksCF9A6wqtqVaimtlx8l/8ZUsr+zrQ9nWz0xQYw/yHkZCawKLDi8yOot3B7shYuk4J4c/jMXzQqx7/7R9EMRfrGtStPr6aS4mXTO1Sl5E1re6fxKiuXwdMtPw7IW9j2Yeh/kOJTYhl7fG14NcaGj0B26fC6V3Z7uPj4cKckU156eEa/LTXmPTg2IWr2W6vmWd1xGpiE2IZUXeE2VHMse5towuprrLPVdVKVKN1hdYsCF9AYqoeSdPWKKWYvjmC/tP/xMXJgZ+ea8GgppXuON975v3nHpxLnVJ1aFSmUR6ntY41d/QvAY2Bk0qpB4EHAD2LC9C0bFNqlqxJ8CFL39gOE8HTF1aMguTshxpwdBBe6VCTOSObEHMtie5fb2VF6Jl8TK7lJE2lMfvgbOqUqkPjso3NjpP/dJV9nhpedzixCbGsjlhtdhQtg8s3knhqzm4+WBtOR/8yrHqxFQEVPO/qGNvObiMiLoKh/kOtvjjIa9YU9AnpA+SIiItSKhyolbex7EP6ADpHLx3lz3N/gosHdPsSLh6BPz7Kcf/WNXxY+1JrAsp78tLCUN786W8SklPzIbmWk5AzIZyIO8HwusNt5pc136RX2Zf211X2eaRJ2SbUKVWHOQfnkKbSzI6jAXtPXaLrlBD+OBLNhG7+TBvcgOKudz/Ec/DBYHzcfHikyiN5kPLeWFPQR1kGzFkObBCRFcDZvI1lP7r4dcHL1evfVrTVH4YHhsLWL+H0zhz3L1PclflPNeW5dtVYsPOUrsq3EbPCZlGmaBk6VulodpT8t+4to8q+x1RdZZ9HRIRhdYdxPO44IWdu762j5Z+0NKOqvu+32wFY/GwLRrT0u6cL/GOXjrH17FYG1B6Akw3NA2FNq/teSqnLSqkJwLvAD0DPvA5mL5wdnelfuz9bzmzh+OXjxsJOH0BxX1j2LCRdz/EYRRwdeP2R2sx6vDHRVxPp9tVWluyJyuPkWnbCYsLYdX4XQ/2H4uRgO7+s+eLIOgidp6vs80GnKp0oU7QMs8JmmR2l0Iq9nsQTs3fxwdpw2tcpw9rRrQmqWCLnHbMx99BcXBxd6Fuzby6mvH/ZFvQiUirzC/gbCAGyHwqoEOpXsx/ONgNDAwAAIABJREFUDs7MPTTXWOBa3GjAFBsBG8ZbfZx2tUqz9qXW1K/oyWuL9/HqolCu6wF28t3ssNkUcypG7xq9zY6Sv+IvwaqXdJV9PnFycGJInSHsOr+LsJgws+MUOjuOx9Dlyy1sPRbDpB51+WZIAzyL3vuFfWxCLKsiVtGtWjdKupbMxaT370539HuA3ZZ/M7925300++Hl5sWj1R5lVcQqLidYRgv2aw3Nnodd30PE71Yfq0xxV+Y92YxX2tdkeegZun0dwsGzeoCd/HLu2jnWR66nT40+eDjn3F+2QPnlLd3KPp89VvMxijkVY3bYbLOjFBqpaYqvfj3KwO//xM3ZkZ9GtWBY8yr33Rbnx8M/kpSWxNA6ttGlLqNsC3qllJ9Sqqrl38yvqvkZ0h4MqTOEhNQEFh9Z/O/Ch98F71qw4nmjgZOVHB2El9rXYN6TzbiWkELPaVv1WPn5JL1WZnCdwSYnyWdH1v07/Wz5/2/vvsOiOtYHjn8HpIMUBUUERbGjYtfYW2LvLYnRaGKJGjUx8UZvfvem3HSTGJPYe0+MiS1Ro8bexYpgQ1BQaYL0srDz+2Mx0cSCsstZlvk8D8/CsnvOy3kO+56ZM/NOA62jKTFcbF3oX60/v0f+zq20W1qHY/HiUrMYtvgoX+64RK/6FZ5qVP2D5OTlsPbCWlr6tKSKm/mlxwIVzBFC9BNCfCWE+FIIoe7PP0A192q08G7Bmgtr0OXlL01r4wB95xpW/Nr65F2hLaqW4bdJrWlRxVArf8LqU6RkqWVvTSU1J5X1l9fzXOXn8Hb21jqcopOZZKhl71Ub2k7VOpoS526J1D9v/Skmsf9yPN2+2U/wtSQ+H1CPrwcH4VzAAjiPszViK7ezbjOslnlW0CxIwZzZwFgM9+dDgLFCiO9NHVhx9FLtl4jPjGdb5La/nvRpaFi7++xaCNv8xNss62zHkpeb8E7Xmmw7H0P3Wfs5E1Xw3gGl4NZfWk+6Lp3hdYZrHUrR2jYN0uNVl71GvJ29ebbys6y/vJ7UHDXjxthy8/R8sf0CwxYfw8PJlk0TWjGosa/Rps1KKVkRuoIAtwBaVGhhlG0aW0Fa9G2B56SUS6SUS4BuQDuTRlVMtfRpSRXXKqwIXXF/N3ubt8A7CDZPhrQnrzVkZSUY27YqP45pgV4PA+YeYuH+q6or34h0eh0rw1bStHxTapeprXU4RefiVjizRnXZa2x4neGk69JZf2m91qFYlJt3Mhky/wjf7w5ncGNfNo5vRfVyxh17czzmOBeTLppVgZy/K0iivwjcW5XfFzhrmnCKNythxdDaQwlLDCM4NvivX1jbQN95hjXrN0+Cp0zQhmVvW9G+hhf/+zWMV5edICk9x0jRl2zbI7cTmxFbslrzmUmGi0/VZa+5OmXq0KR8E1aGrUSnV7fnjGFnaCzdZu0n7FYK3wwJ4tP+9R65rOzTWhG6Ag97D7pX6W70bRtLQRJ9GSBMCLFHCLEHCAU8hRCbhBCbTBpdMdSzSk/c7Nz+OYrWqyZ0/A9c/NXQgnpKbo62zHupEe/1rM3+ywl0/WY/h8ITChl1ySalZNn5ZVRxrUIrn1Zah1N0fpuquuzNyMt1XiY2I5btkSV+cdBCydLl8d6m87y6/AQ+bg5smdia3kE+JtlXRHIEe6P3MqjGIOyszfd/qCAjEf5j8igsiH0pe16o9QKzT8/mYuJFanjcUy24+Ti4+JthYF7l1uD2+DWNH0QIwcst/Wlc2YOJa07x4sKjvNa2Km90ro6NdUEXJFTuOhZzjAuJF3ivxXtYiRJy/M6ug3M/QrtpqsveTLTyaYW/qz/Lzy+nu393s+0GNmeXYlOZuOYUF2JSGdGyMu90rYldKeO34u9aeG4hdtZ2DKkxxGT7MIaCfKqdAPZLKfcCtwBX4JCUcm/+c8rfvFDzBZxsnFhwbsH9v7CyMrSepN6w8I2+cDWuA31c2fx6KwY18mX2nnAGzD1MZMLjK/Ep91t6fike9h70qNpD61CKRtI1+PVN8G0Grd/SOholn5WwYnjt4YQlhnEs5vHls5W/SClZceQaPb89QEJaNktGNOG/PeuYNMlHpUbx69VfGVhjIGUcyphsP8ZQkES/D7AXQvgAu4ARwFJTBlXcudq58kLNF/g98ve/yuLe5V7ZUCI3Yp+hmE4hOdmV4rMB9Zj9YkMi4tPoPms/64Oj1UC9ArqSdIUDNw7wfM3nzbrrzWjycuHn0YZxIv3mg7VxphcpxtGjag887D1UAZ0nkJiew6jlwfzfhhCaVynD1kltaF/Dy+T7XXRuEdbCulgsY12QRC+klBlAP+BbKWVfoI5pwyr+htYein0p+3+26gEaDoNqz8GO/0DCZaPsr1tdb7ZNbkMdH1emrDvDpLWn1Zz7Algeuhx7a3sG1xisdShF48DXEHUEun9puOhUzIqdtR3P13ye/Tf2E34nXOtwzN6Bywl0mbmPfZfi+U+P2ix5uQmeLqa/YL+VdouN4RvpW60vXo6mv6gorAIleiFEC+BF4Nf850zXH2IhPOw9GFR9EL9F/EZUStT9vxQCes0yFNT5ZYyhlWUEFdwcWDOqOW89W51fz92i68z9BF9LNMq2LVFCZgJbrm6hd0Bvs6tNbRLRJ2DPJxA4AOoN0joa5SEG1xiMvbU9y0OXax2K2crJ1fPJb2EMXXSU0g42bBjfkpGt/LGyKppxDUvOLwEJrwS+UiT7K6yCJPrJwDTgFynleSFEFaDgxdtLsOF1hlNKlGJhyMJ//tKlPHT/Cm4EG1pZRmJtJZjQoRrrxrbA2kowcO5hZu68RG6eWvP671aHrSZXn8tLtc2vNrXRZafC+lehdAVDa14N9DJb7vbu9A7ozebwzSRkqhk1f3c1Po3+cw4xb99VXmzmx+YJrahdoXSR7T8+I571l9bTK6BXsamgWZBlavdKKXtJKT/L//mqlHJiYXaavxreDiHE5fzHBzanhBCLhRBxQoiQwuxPK56OnvSv3p9NVzY9uI51YD9D62rvp3DrjFH33dDPMOe+T5APM3deZsj8I0QnZRh1H8VZhi6DHy/9SHvf9lQqXUnrcExv6ztw55rhvrzD0y/DqRSNl2q/RK4+lzUXnn4qrqWRUvLj8Si6zzpAVFIG815qxEd965pkbvyjLDu/jDyZx6uBrxbpfgvjUcvUzsx/3Hx3zvy9X4Xc7zvALillNQwD/N55yOuWAl0KuS9NjQwcCQIWhSx68Au6fQGOZQ1r1+uyjLpvF3sbvhocxMzBQVyISaXrN/vZdOamUfdRXG0M30hydjIvB76sdSimd/4XOL0SWr0JlZ7ROhqlACqVrkR73/b8cPEHMnTqAj05Q8f41SeZuv4sDfzc2DapDc/VKV/kcSRmJfLjpR/p5t8N39JPNz1aC49q0a/If5wBfPmAr8LoDdwdVroMeOBCOVLKfUCxvslc3qk8vav25pfLvxCXEffPFzh6QO/vIC4Udv/PJDH0aeDD1kmtCfByZuKaU0z58UyJHqiXp89jRegK6pWtR5BnkNbhmFZytKEao08jaPew62nFHA2vM5zk7GQ2hm/UOhRNHQ6/Tddv9vH7+Vimda3JyleaUd7VXpNYVoauJCs3i1frFZ/WPDx6mdrg/Me9GKrhhd6dO2+E+fPlpJS38rd/Cyj0sEUhxGghxAkhxIn4+CevJ29Kr9R9hTyZx9LzSx/8gmqdofFIOPQtXN5pkhh8PRxZN6YFEzsE8MupaLrOLLkV9X6L+I2o1ChGBI6w7KIk+jxDT1FeLvRbYCjFrBQbDbwaUN+zPovOLSI7L1vrcIpcli6PD7eE8vyCI9jZGNaNH9O2apENuPu75OxkVl9YzbOVn6WKq/ktRfsoj+q6F0KI94QQCcAF4JIQIl4IUaBKeUKInUKIkAd89TZW8PeSUs6XUjaWUjb29PQ0xS6emq+LL92rdGfdxXUkZj2kg+K5j6FcIPwyGlJM071eytqKN5+twU+vPYNtKSteWHCUD7eEkqXLM8n+zJFOr2P26dnU8qhFB78OWodjWoe+hcj90O1zKFNV62iUJySEYEKDCcRmxPLTpZ+0DqdInYtOpse3B1h0IILhLSrx68RW1Kuo7diS1RdWk65LZ1TdUZrG8TQe1XU/GWgJNJFSlpFSugPNgJZCiDcet2EpZScpZeADvjYCsUIIb4D8xwf0aVuWV+u+SnZeNsvPP2TKjI0DDFxquE//0ytGm3L3IHcH6g1rUYlFByLo8e0BzkaXjKVvN17ZSHRaNBMaTLDscrc3T8EfH0Lt3hD0otbRKE+pWflmNCnfhAVnF5CZm6l1OCany9Pzzc7L9J19kLSsXFa80pT3ewfiaKttYae0nDRWhq6kvW/7+8uaFxOP+qQbBjwvpYy4+4SU8iowNP93hbEJuLtM2HDA4m9C+bv681zl51hzYQ3J2ckPflHZatBzJlw/BHs+Nmk8jral+KB3IMtHNiUtK5e+sw8xc+cldBY8DS8nL4d5Z+dRr2w9Wvu01joc08lJN0ylc/KCHjPVVLpiTAjBhKAJ3M66zdoLa7UOx6SuxKUxYM4hvt55iZ71K7B9chtaVzOP3tkfLv5ASk4KY+qN0TqUp/KoRG8jpfzHTVwpZTxQ2Jt9nwKdhRCXgc75PyOEqCCE+O3ui4QQa4DDQA0hRLQQonhUJ3iIUfVGkZGbwaqwVQ9/Ub1Bhsp5+7+CK6a5X3+vNtU92T65DT3reTNz52UGzDnElbg0k+9XCz9d+omY9BgmNJhg2ffmt0+H2+HQb55hsKdSrDUs15CWFVqyOGQx6TrLW8tCr5csORhB91n7uZ6YwewXG/L14CBcHc1jTEmGLoPloctp6dOSOmWLZ1HYRyX6Ry10XqhF0KWUt6WUHaWU1fIfE/Ofvyml7HbP656XUnpLKW2klBWllA+Zo1Y8VHevTgffDqwMW0laziOSaZfPwKsW/DwGUh4w/97IXB1tmDmkAd+/0JDriRl0n7WfJQcj0Ostp15+Zm4mC84toHG5xjT3bq51OKYTtgWCl0LLieDfRutoFCOZ0GACd7LvsDJ0pdahGNWNO5kMXXSU9zeH0iqgLNvfaEO3uuZVhGb95fUkZiUW29Y8PDrR1xdCpDzgKxWoW1QBWprR9UeTmpPK2ouP6Iazdcy/X59h6II14f36e3Wv5832yW1oGVCW9zeHMnTRUW7csYz7gj9c+IGEzATLbs2n3IJNr4N3fWj/rtbRKEYUWDaQ9r7tWXZ+2cNv/RUjUkrWB0fT5et9nIm6w2f967JweGO8XLSZNvcw2XnZLAlZQtPyTWngVXyXc37U9DprKWXpB3y5SCnNo0+lGKpTpg6tfVqz/PzyRxfC8KxhKJF77QDs/azI4vMqbc+i4Y35tF9dzkTdocvX+4r9anjpunQWhSzimQrP0KhcI63DMQ29Hja8BrpM6LcQStlqHZFiZOODxpOqSy32K9vdTstm7Mpgpqw7Qy3v0myd1IbBTfzM8gL8l8u/EJ8ZX6xb81CwWveKkY2uN5qk7CTWXVr36BcGPQ9BQ2HfFxBedMsLCCEY0tSPrZPaUMu7NFPWnWHMimDiUo1bua+orApbxZ3sO0wImqB1KKZz5Hu4uhu6fAKe1bWORjGBGh41eK7yc6wKW/XwabpmbltIDM/N3MfuC/FM71aTNaOb41fGUeuwHkiXp2NxyGKCPINoUr6J1uEUikr0GgjyCqKZdzOWnl9KVu5jkme3L8CzJvw8ClJjiibAfH5lHFkzujnTutZkz6V4On+1j5+KWes+OTuZpSFLaefbjrqeFnrHKfIA7Pgv1OwBjV7WOhrFhMbVH0dWXhZLQpZoHcoTiUvNYtyqYMauDKZcaXs2v96K0W2qYq1R8ZuC2Hx1M7fSbzGm/hiz7G14EirRa2RMvTEkZCbwy5VfHv3Cu/fr706Z0hdtcRtrK8GYtlXZOqk11cs589a6MwxfcrzYLJCzPHQ5qbpUy23NJ0fDj8PBowr0maOm0lm4Km5V6O7fnTUX1hCfYV4VQB/k7r34zl/tY2dYHG8/V4MN41tSo7yL1qE9Uq4+l4XnFlKnTB1aVmipdTiFphK9RhqXa0xDr4YsDlmMLu8xdee9ahqWFo3cD3s/L5oA/6aqpzM/jG7BB73rEByZyLNf72PZoUizHpmflJXEytCVPFvp2WJZ5OKxdFnww0uQmw1DVoN90S3VqWjntfqvkavPZcG5BVqH8kg37mTy8pLjTFl3hgAvZ36b2Jrx7QOwsTb/tLM1YitRqVGMrje62LfmQSV6zQghGF1vNDHpMWwKL8BigEEvQP0XDAPzru4xeXwPYmUlGNaiMtvfaEPjyh78d9N5Bs07THi8ec67XxKyhKy8LMYHjdc6FOOTEn6dAjdPQt+56r58CeJb2pc+AX346dJPD17+WmN6vWT54Uie/WovxyMTeb9XHdaNaUGAl7PWoRWIXupZcG4B1dyr0c63ndbhGIVK9Bp6psIzBJYJZOG5heTqCzCFrvsMKFsd1o+C1FjTB/gQFd0dWTaiCTMG1udyXBpdv9nP97uvmFVVvfiMeNZcWEN3/+5UcSteC1AUyIlFhqVn20yFWj20jkYpYndHgc87O0/jSO4XHp/G4PmH+c/G8zSs5M72yW0Y/kxlzRaieRo7ru0gIjmC0fVGW0yZbMv4K4opIQRj6o8hOi2arRFbH/8GWyfD/frsVPi56O/X30sIwYBGFdnxZhs61fLii+0X6fP9QUJumMcc34XnFqLT6xhbf6zWoRjftcOw9V9Q7VloN03raBQNeDt7M6D6ADZc2cD1lOtah0Nunp7Ze67Q9Zv9XIpNY8bA+iwf2RRfD/McUf8wUkrmn52Pv6s/nf06ax2O0ahEr7G2FdtSw70G88/OJ68gibtcbcNI/Ih9sG+G6QN8DC8Xe2a/2Ii5QxsSm5JN7+8P8vm2C5quiHcr7RbrLq2jT0Af/Er7aRaHSaTchB+HgZufYelZK/UvXFKNqjuKUlalmHtmrqZxnL+ZTJ/ZB/l820U61PBix5ttGNCoYrG8t70nag+Xki4xqu4orK2stQ7HaNSnhMbu3quPTIlkx/UdBXtTg6FQbwjs/dSQ8M1Al0Bvdr3Zln4NfJi9J5xus/ZzIlKbub53uzOLe5GLf8jNNiT5nHTD4DsHbZftVLTl6ejJ8zWfZ8vVLVy9c7XI95+ly+OL7Rfo9d1BYpKzmfNiQ+a+1MjsqtsV1N3WfEXninT176p1OEalEr0Z6FSpE1VcqzD79Gx0+seMwAfDFKruX0KZAPhpJCRdM32QBeDqaMMX+V122To9A+Ye5p31Z0lKL9TSCE8kKiWKjVc2MqD6ALydzatmdqFtnQrRx6HvHMNaCEqJNyJwBA6lHJh9ZnaR7nffpfj8sTnh9AnyYeebbehqZjXqn9TuqN2E3A7h1bqvUspK22VxjU0lejNgJayY0ngKEckRrAp9xMp297JzhsGrIC8HVg+CTPNZT75NdU9+f6MNo1r7sy44mvZf7mHtsetFMhVv7tm5WFtZM6ruKJPvq0idWGJYrKbVm4Y15hUF8LD34MVaL7I9cjsXEy+afH+3kjMZtyqYYYuPAbB8ZFO+HFQfN8fiXXI5MzeTz459RoBbAL0CemkdjtGpRG8m2lRsQzvfdsw+M5uY9AJWwPOsDoNXGpYk/XEYPG4+fhFysivFv7vX5reJranu5cI7P5+j/9xDJh2sd/XOVbZc3cKQGkPwdDSPdayNIuoY/PY2VO0IHdRiNcr9htcZjouNC9+d/s5k+9Dl6Zm3N5yOX+5lV1gcUzpXZ9vk1rSpbhn/ZwvPLeRm+k3+3ezf2FhZ3lIuKtGbkX81+Rd6qWfGiScYZOffBnrNgoi9sGWyYX61GalR3oUfxjTnq0H1iUrMoNd3B/jvxhCSM41/UTL7zGzsrO0YWXek0betmdQYQ1EcVx/ovxAsaICQYhyudq4MrzOcPVF7OBd/zujbP3L1Nt2+2c8nWy/wTNUy7HyzLa93rIZdKcs4F6+lXGNJyBJ6VOlB4/KNtQ7HJFSiNyMVXSryat1X2R65ncM3Dxf8jUEvGOZTn1oJ+780XYBPSQhBv4YV2TWlHS81r8SKI9fo+OUeo66KdzHxItsjtzO01lA87D2Msk3N5eYYyttmpxhu0zhayN+lGN3Q2kNxs3Pj+9PfG22bcalZTF57iiHzj5Cpy2PhsMYsHN6k2E2ZexQpJZ8c/QQ7azumNJ6idTgmoxK9mRkROAJfF18+Pvrx40vj3qv9dKg7EP74EM79ZLoAC8HVwYb3eweyaUIrKro7MmXdGQbPO8LFmNRCb/v709/jYuPC8DrDjRCpmdg+HaKOQO/voHyg1tEoZszJxomRgSM5ePMgwbHBhdpWbp6eJQcj6DhjL7+di+H1DgHseKMtnWqXM1K05mPX9V0cvHmQ8UHjKetQVutwTEYlejNjZ23H9GbTiUyJZFnoE6w7LQT0/h78noEN4+D6EdMFWUiBPq78/NozfNqvLpfiUuk2az8f/RpKWnYBqgM+QEhCCLujdjOszjBc7VyNHK1GTq2E4wvgmdchsL/W0SjFwJCaQyhjX4ZvT3371D1lwdeS6PXdQd7fHEqQnxvbJrdmyrM1cLC1jG76e2XoMvjs+GdUd6/OkJpDtA7HpFSiN0OtfFrR0a8j88/Of7Ja1qXsYMgqcK0Ia543DNIzU1ZWhjXvd09px6DGFVmwP4KOX+5hy9mbT/wh9d2p73Czc2NoraEmiraI3QiGLW+Cf1vo+J7W0SjFhEMpB0bVG0VwbDBHbj3ZhX5ieg7/+uks/eccIjE9h9kvNmT5yKZU8Swe9emfxoJzC4hJj+Hfzf5tcdPp/k4lejM1tclUpJR8ceKLJ3ujowe8uM7w/aqBkKFN0ZqCcney5ZN+9fhl3DOUdbZjwupTDJp3mNNRBZsuuC96HwdvHmRE4AicbS3gQ+l2uOEizbkcDFgC1pb9AaQY18DqAynvVJ4ZJ2YU6NZfli6PeXvDafvFbtafjGZMmyrsmtKWbnW9i2Vlu4KKSI5g6fml9Krai4blGmodjsmpRG+mKjhXYHS90ey4toODNw4+2ZvLVIXn1xjWKl/7oqGimplr4OfOpgmt+LhvXSIS0unz/UFeX3OKqMSHr3ufnJ3M+4feJ8AtwDJa88nRsLw36HMNF2tOZbSOSClmbK1tmdZ0GpeSLjH/3PyHvk6vl2w8fYOOX+7lk60XaFLZg62TWjOtWy2c7Cz74lJKycdHP8bB2oE3Gr2hdThFQiV6Mza8znAql67MJ8c+ISfvCavL+TWHPrPh+iHYON7spt09iLWV4IVmfux5uz0TOwSwIzSGjl/u5ePfwkjO+Gfr5PPjn3M76zb/a/U/bK2Ld8EO0uIMST4rGYb+DF41tY5IKaY6+HWgR5UeLDy7kNDbof/4/dGrt+k7+yCT1p7G1cGGVa82Y/HLTahWzkWDaIve79d+58itI7ze8HWLHoB3L5Xozdjdq/NrKddYen7pk2+g7gDo8H9wbh3s/tjo8ZmKs10p3ny2Bnveak/voAos2H+VtjN2s/hABDm5hqVw90TtYVP4Jl6p+wp1ytTROOJCykiE5X0MC9a8+BNUCNI6IqWYe6fpO7jZu/HuwXf/7MK/Gp/G6OUnGDz/CLEp2Xw5sD5bXm9Fy4CSkezAMADv8+OfU8ujFoOqD9I6nCIjjDWP2Zw0btxYnjhxQuswjObNPW+yP3o/G/pswMfZ58neLCVsmmAYxd17NjR40TRBmtD5m8l8/FsYB6/cpnIZRyZ2rsC3l8biYe/B2u5rsbEuxpWsslMNLfmYc/DCj1C1vdYRKRZiT9QeXv/jdV6q+QrpMZ1YdfQ6dqWsGNc+gJEt/S1yJP3jfHXiK5acX8KKrisI8rKsC2ohRLCU8oEVf1SLvhiY2mQqQgg+P/b5k79ZCOgx0zCCe/NEuLrX+AGaWJ0Krqx8pRlLRjTBxtqK6fs+IiEjkaFVpxbvJJ+TAauHwM3TMHCZSvKKUTUv35oaTu1ZEbaE1acPMaSpL3vebs/49gElMsmH3wlnRegK+gb0tbgk/zgq0RcD5Z3KM7b+WP6I+oN90U+xLK21DQxabljt7oeXIN70i18YmxCC9jW8mNpPh43rKaxTOvPGigQmrD75yAF7Zis3x7A+wbWD0G8+1OymdUSKhdDrJRtOGQbanTjZBhtRmmqBW/hPzxp4uthpHZ4m7g7Ac7RxZHKjyVqHU+RUoi8mXqr1Ev6u/nxy9BOy855iFL2Dm6FruJQdrBwAiRHGD9LE7mTd4aOj/6OmR012v/ohEztWY2dYLB2/3Mt/NoZwKzlT6xALJi8X1r8CV3ZAz5mGsRSKUkhSSnaExtLzuwNM/uE0bo42rB7Zjm86fkxUWgRzzszROkTNbI3YyrGYY0xqOMlySmQ/AZXoiwkbaxumN5tOdFo0i0MWP91G3CsZpm3lpMLiLhD7zxG55uzjYx+TnJPM/1r+D3dHB97sXJ09b7WnfyMfVh+9TtvP9/B/G0K4eceME75ebxgzEbYJnvsYGr2sdURKMSel5PfzMfT49gCjlp8gLTuXrwbVZ/OEVjwTUJbWFVvTN6Avi0MWm2TRG3OXlpPGjBMzqF2mNv2rlcwqkyrRFyPNvZvTpXIXFp1bRFRq1NNtpEIQjNhq+H5pN4guXF3sorLj2g62RmxlTL0x1PCo8efz5V3t+aRfPXa/1Y7+jSqy5th12n1hpglfStj6NpxZA+2mQ4vxWkekFGNSSrbnJ/jRK4JJz85lxsD67HqzLf0aVsTK6q+CN283eRtPB0/+ffDfT9cjWIzNOTOHhMwE3m32LtYldPVHNeq+mIlNj6XXhl40Kd+E7zoWYv3pxAhY0QfSEwzFdfzbGC9II0vMSqTvxr6UcyzHqu6rHrledHRSBrP3hLPuRBQCwaAmFRnXLoAKbg5FGPEDSAn7/lVQAAAXe0lEQVQ734ODMw316zt/aBgoqShPSErJ76GxfLPzMqG3UqhcxpHXO1Sjd1AFSlk/vO128MZBxu4cy4jAEbzZ6M0ijFg7l5MuM3DzQPoE9OG9Z97TOhyTMrtR90IIDyHEDiHE5fxH9we8xlcIsVsIESaEOC+EmKRFrOamnFM5xgWNY2/0XvZE7Xn6DXn4w4ht4OpruGd/4TejxWhsHx/9mJScFD5q9dEjkzxARXdHPu5bl91vtWNA44r8cDyKtl/s5t0N57Rt4e+fYUjyjUeqJK88Fb1esi0khm6zDjBmRTCZujy+GlSfnW+2pX+jio9M8gAtfVrSv1p/lp1fxpn4M0UUtXaklHx09COcbZ2Z3LDkDcC7lyYteiHE50CilPJTIcQ7gLuU8l9/e4034C2lPCmEcAGCgT5SysfeWLbkFj2ATq9j4KaBZOVlsaH3BuxL2T/9xjISYdUAwxSvPnOg/mDjBWoE2yK38fbet5nYYCKj6o164vffuJPJ7N1X+PGE4VbHoMa+jGsfgE9RtvCPzIFt70C9wdBnLlipO2ZKwen1+S34XZcJu5WCf1knXu8QQK/6j27BP0haThr9NvXDztqOdT3XFe6zw8xtDt/M9APT+W+L/zKguuUPeH1Ui16rRH8RaCelvJWf0PdIKWs85j0bge+klDset31LT/QAx2OOM3L7SMbUG8OEBhMKt7HsVMNCKpH7odsMaPrkCdUUbmfepu/GvlRwrsDKbisLtcLUjTuZzNlzhR+OGxL+wMa+jG1TFb8yjsYK98GClxnqF9TsYZgrrxapUQooN0/P76GxfPvHFcJupVClrBOvdwygZ70nT/D3OnzzMKN3jGZ47eG81eQtI0ZsPlJyUuj1S68/PzushOVfXJtjor8jpXS75+ckKeU/uu/v+X1lYB8QKKVMechrRgOjAfz8/Bpdu3bNqDGbo2n7p/FbxG/MbDeT9n6FLLaiy4KfRsDF3wxlc1tP0bR7WUrJlL1T2BO1h3U911HVrapRtnvzTiZz9oTzw/EodHo9nWqVY2RLf5pX8TDual36PPjjQzjwNVTtaBgHUapkzmFWnkxypo4fj0ex9FAkN+5kUqWsExM7VqNn/QpYWxnnHP3w8Iesu7SOZV2X0cCrgVG2aS50eTrG7xrPsZhjrOq2ijpli3mJ7ALSJNELIXYC5R/wq38Dywqa6IUQzsBe4CMp5c8F2XdJaNGDoW7zq7+/yqWkSyx4dkHh/2HzdLBhHJz7EZ6ZCJ0/0CzZb43YytR9U5nccDKv1H3F6NuPS8lixZFrrDp6ncT0HGp5l2Zky8r0rF8Be5tCjszNvAPrXzXMk2/0MnT9AkoV80V3FJOLSEhn6cEI1gVHk5GTRzN/D0a28qdTrXJGS/B3pevS6b+pP6WsSrGu5zocSmk8WNVI9FLP9APT+fXqr3zwzAf0rdZX65CKjDm26AvUdS+EsAG2ANullF8VdPslJdEDJGUlMWzrMBKzElnedXnhW756PWydCscXQMPh0ONrKOIpKQmZCfTZ2IdKLpVY1nVZobrsHydLl8fG0zdYfCCSi7GplHW25cVmlXixuR9eLk9x/zL+Iqx9AZIioevn0MT4FymK5ZBScij8NosPRPDHxThsrKzoWb8CI1pWJtDH1aT7PnbrGK/8/gpDaw3lX03/9fg3FAMzjs9gWegyJjWcxKt1X9U6nCJljon+C+D2PYPxPKSUU//2GgEswzBo74mGTJakRA8QnRrNS1tfwlpYs7LbSso7Pagj5QlICX/8zzBSvE4/6DuvyFqkUkom7Z7EwRsHWddrHVVcqxTZfu9+4O66EIet9VN84F7cCutHgY29oeRwpWdMG7RSbP39ArOMky1DmxfiAvMpfXz0Y9ZeWMuSLktoVK5Rke3XFJadX8aMEzN4vubzTGs6zbi34ooBc0z0ZYAfAT/gOjBQSpkohKgALJRSdhNCtAL2A+cAff5bp0spHzsPrKQleoALiRd4edvLeDt5s7TLUlztjNAaOPgN7PgPBHQ2JC5bEw9cA7Zc3cK0/dOY0mgKLwe+bPL9PcjV+DSWHYq8rwt1REt/Otd+SBeqlIaLoj8+Au96MGQ1uFYs+sAVsxebksXKe24Z1Szvwiut/I1zy+gpZOgy6L+pP0IIfur5E442pv8fN4W7nxudK3XmizZflMjCOGaX6E2tJCZ6MHTFjd05lrpl6zKv8zzjTJ0JXgqbJ4NvMxiwGFyfcJncJxCVEsWQX4fg7+rPsi7LNP9n/fugKF8PB55v6kffBj54u+bf08xOg43jIHQj1B0EvWaBjWXc71SMI08vORSewLoT0WwNuUWuXppuEOhTOBFzghHbR9CvWj/ea/Ge5vE8qUM3DjF+13galGvAnE5zsLMumYNeVaIvQbZFbmPq3qm0923PV+2+Mk6yDPkZNo4HKxvo+inUf97og/RCb4fy2s7X0Es9K7quoLJrZaNuvzBy8/TsCI1lycFIjkUmIgS0CijLSzWg05nJWCVcMAxcbDFBFcJR/hQen8b64Gh+OXWDW8lZuNiXon/DioxoWZlKZZy0Du8+s07OYsG5BfSq2ov3nnnvsYWpzMX52+cZuW0kFV0qsrTLUlxsXbQOSTMq0Zcwq8JW8emxTxlYfSD/1/z/jHOFnngVNoyH64egelfDqmsuhRwLkO/wzcNM3j0ZVztX5nWeh7+rv1G2awqRCen8fDKayONbeT/nC6yQ/Fj5feq17UdTf+1bZ4q2kjN0bDp7k/XB0ZyOuoOVgDbVPenfsCKda5fTpHu+IKSUzD87n+9Of0crn1Z82fZLs+/Gj0qJYujWodhb27Oi2wq8HL20DklTKtGXQDODZ7IoZBHjgsbxWv3XjLNRvR6OzoVd70Mpe0NxnboDCtWK3RqxlekHpuPv6s/cTnPN/59VSjgyB/n7u2SWrso3nu+x4pI1GTl5+Hk40q+hD/0bVsTXw7w/JBXjyc3Ts+9yPOuDb7AjNJacPD01yrnQv5EPfYJ88CpdfKrPrb+0ng+OfECdMnX4vuP3uNs/tLyJphIyExi2dRipOaks77rcrBsHRUUl+hJISsm7B99lU/gm45eATLhsmG8ffQxq9YTuX4Oz5xNvZmXoSj47/hmNyjViVodZlLYtbbwYTUGXBVvegDOrDZXu+s4FOxfSs3PZFhLD+pPRHL56Gymhqb8HAxpWpFs9b5ztVDU8SxR2K4X1wdFsOH2ThLRsPJxs6VW/AgMaVaROhdLFtndn9/XdvL3vbbydvJnbeS4+zqYbl/M00nXpjNg2gojkCBY+t5D6nvW1DsksqERfQun0Oib+MZFDNw/xdbuv6eDXwXgb1+fB4e8MI83tnKH7V1CnT4HeKqXkm5PfsChkEZ38OvFpm0/NfwBN5AHYNg1izkK7adBm6gNr1t+4k8kvJ6NZf/IGEQnp2NtY0bFmOTrW8qJ9DS/cnVThnOJKSknIjRR2hsXye2gsYbdSsLEWtK/hxYBGFWlXwwvbUpZRavVU3Ckm7JqAnbUdczrNuW9paC3dW/VuVodZtKlovqtuFjWV6EuwDF0Gr2x/hct3Lhunet7fxV2ADa/BzZOGOffdvwRHj4e+XKfX8d6h99gUvolB1Qcxvdl0zUfXP9KtM7DrA7iyE1wqQPcZULP7Y98mpeTk9Tv8fDKa30NjiU/NxkpA40oedKzlRcda5ajq6VRsW30lRZYuj0PhCewMi+OPsDhiUrIQAhr6udOznje9gnzwsNCLtytJVxi7cyzpunRmdZhFk/JNNI2nJFe9KwiV6Eu4xKxEhm0dRlJWEsu6LCPAPcC4O8jLNSzBuudTcHA3DNR7QDLM0GXw1t632H9jP+OCxjG23ljzTXS3w2H3RxCyHuzdDLX/m456qqlzer3k3I1kdoXFsiMsjrBbhuUaKpdxpFOtcnSsVY4mld0LtVCJYjxxqVnsvhDHzrA4DlxOIFOXh5OtNW2qe9KxVjna1/CkjLOZ90AZSUx6DGN2jCE6NZpP23xK50qdNYvlbtW7p13J0tKpRK8Yv3reg8SEwIaxEHMO6g0xTMVzMAzmScpKYsKuCYTcDuHd5u8ysPpA4+/fGFJuwb7P4eRysLaF5uPgmdfBwe3x7y2gG3cy+SM/6R8Jv01Onp7S9qVoX9PQ0m9b3RNXh+IxvckSSCm5EJPKrrBYdobFcTrqDgAVXO3pVNtwIda8igd2pcy458mEkrOTmbBrAmfiz/DvZv9mcM2iX8q6pFe9KwiV6BXgr+p57nbujAsaRxf/LsafL5ung30zDJXiHDyg8QhuVu/EmGMfcjPtJp+3/ZyOfh2Nu09jyEwyVAI8Mhf0Omg0Atq8DS7lTLrbtOxcDlyOZ0doHLsvxpGYnkMpK0GQrxuNKrvTyM+dRpXcS0wLsijk6SWXYlM5cS2J4MhEjkcmceNOJgD1K7r+2ctSy9tFJZR8mbmZTN07lT3RexhTbwzjg8YXybG5kXaDZeeXsebCmhJd9a4gVKJX/nQy9iQfHP6A8ORwyjuVZ1jtYfSv1t/4c2ZvnoZdH3Dp+n5eK1+WzFK2fFvtJRo1GW9eleNyMuDYPMNyslkpUHcgtJ8GHkVTY/9eeXrJ6agkdobFceTqbUJuJKPLM/x/VinrRKNKhqTfuLI7VT2dVRIqoLTsXE5fv0PwtSROXEvk9PU7pGbnAuDpYkfjSu60re5Jh5pexWoqXFHL1efy4ZEP+fnyz/Sv1p93m79rsgWnLiReYEnIErZHbkcIQe+qvZnWbJr5D9rVkEr0yn30Us+BGwdYHLKY4NhgStuWZnCNwbxQ6wXKOpQ12n5OxJxg4q4JOEjJ3MQMqiVeBztXw9z7BkOhQgPtKsnl6eDUCtjzGaTFQLXnoOP/Qfm62sTzAFm6PM7dSOZEZBLB1xIJvpZEUoYOADdHGxr5udOwkjuNK7lT39fNbIuxFLUbdzI5EZnIyWtJnLiWRNitFPTScKrVKOfy58VSIz8PfD0c1AXTE5BS8t3p75h/dj7tfNvxRZsvjFNqO3/bR2OOsvjcYg7fOoyTjRMDqw/kxVovmuZWo4VRiV55qDPxZ1gaspRd13dhY2VD74DeDK8znEqlKz3xtnR5OsISwzgVd4rTcafZF70PHxcf5nWah7djObh2EE6tNNSFz82EcoGGhF93EDiVMcFfdw8p4fYVuH4Eoo7A1b2QHAW+zaHTf4vFSnNSSq4mpBMcmfRn6zQ8Ph0AG2tBNS8Xqno5U6Ws05+PVTydcLS1vHn8UkpiU7IJj0/janwa4fHphMencTk2jZiULAAcba1p4OdmuP1R2YMGfm6UtldjH4xhzYU1fHL0E/xK+9GyQksaeDUgyCvoqRJyrj6Xndd2sjhkMWGJYZR1KMvQWkMZWGOg+dfWMCMq0SuPFZkcybLQZWy6sgmdXkenSp0YUWcEdT0f3sJNyUnhTNwZTsWd4lTcKUISQsjKM3zIVnSuSDPvZkxuOBk3+78NZMtKNoxmP7USbgQbaujX7AYNXoKqHcAY9+Bysw23D6KOwPWjhseM24bfOXgYFulpNByqdynW9emT0nM4ef2vlmt4fBrRSZnc+29dwdX+nsTvTFVPZ6p4OuHtam/2rdksXR5X49O5mpBGeJzh8Wp8Olfj00jPyfvzdU621vl/mxNBvm40ruxBzfIuaiaDCe2+vptVF1ZxNv4smbmGMQ4VnCoQ5BVEA68GNPBqQIBbwEPvqWfmZrLhygaWnV/GjbQbVC5dmRGBI+hRpQe21pY5ZdGUVKJXCiwhM4HVYatZe3EtqTmpNC7XmBGBI2jt05obaTf+TOqn4k4RficcicRaWFPLo9Z9/+CejgWslBcbCqdXwZk1hkTs5Anu/uBYJv/L/Z7v878cPPIf3f66KMhIhKij+S32o3DjJORlG37nURX8mhuSu18LKFutWCf3x8nS5RF5O52r8emEx6VxNSE9v+WbTlr+vWkwtHgrujvg4WSLh5Mt7o75X062eDjZ4O741/MeTrY42loX+sIgN09PcqaOpIwcEtN1JKbn5H+fQ1J6DkkZuj9/jk/N5mby/RctPm4OVPF0omp+UjdctDhTrrSd2V+0WKpcfS4Xky5yKvbUn715cZlxADjbOFPfsz5BXkE09GpIYNlAsvOyWXthLasvrOZO9h3qe9ZnZOBI2vm2w0qoC7OnpRK98sTSdemsv7Se5aHLic2IxbGUIxm5GcBf/7x3k3pg2cDCD+bLzYFL2+DCFkiLNSTujETISIDcrIe8SRim79k6GbrhwdA74F3fkNjvJndnM6+fX0SklMSlGrq7w/NbxTeSMrmToSMx426izUH/kI8E21JWuDva4GJvw5OmVF2enqQMHSlZOh72keNgY224sMi/yCjjZIt/Wec/E7t/WSccbNU4BHMnpfyzUXA67jQn407e1yiwFtbk6HNo59uOkYEjjV/Eq4RSiV55ajq9jm0R2wiODaamR83HdseZRE6GobV/9ysz6f6fs1LAs4ahte7T0LxG9Rczer0kJetuS1tHUnrOnxcBdx/v7RUoKGsrw0XCn70ETrZ4OP6V1N0dbVUSt2D33ubLyM1gUPVBVHEr+pktlkwlekVRFEWxYI9K9OqGiKIoiqJYMJXoFUVRFMWCqUSvKIqiKBZMJXpFURRFsWAq0SuKoiiKBVOJXlEURVEsmEr0iqIoimLBVKJXFEVRFAtmkQVzhBDxwDUjbrIskGDE7RV36nj8RR2L+6nj8Rd1LO6njsf9jH08KkkpH7jIiEUmemMTQpx4WMWhkkgdj7+oY3E/dTz+oo7F/dTxuF9RHg/Vda8oiqIoFkwlekVRFEWxYCrRF8x8rQMwM+p4/EUdi/up4/EXdSzup47H/YrseKh79IqiKIpiwVSLXlEURVEsmEr0iqIoimLBVKJ/BCFEFyHERSHEFSHEO1rHozUhRKQQ4pwQ4rQQ4oTW8RQ1IcRiIUScECLknuc8hBA7hBCX8x/dtYyxKD3keLwnhLiRf46cFkJ00zLGoiKE8BVC7BZChAkhzgshJuU/X+LOj0cci5J6btgLIY4JIc7kH4/3858vsnND3aN/CCGENXAJ6AxEA8eB56WUoZoGpiEhRCTQWEpZIoteCCHaAGnAcillYP5znwOJUspP8y8G3aWU/9IyzqLykOPxHpAmpZyhZWxFTQjhDXhLKU8KIVyAYKAP8DIl7Px4xLEYRMk8NwTgJKVME0LYAAeASUA/iujcUC36h2sKXJFSXpVS5gBrgd4ax6RoSEq5D0j829O9gWX53y/D8IFWIjzkeJRIUspbUsqT+d+nAmGADyXw/HjEsSiRpEFa/o82+V+SIjw3VKJ/OB8g6p6foynBJ2s+CfwuhAgWQozWOhgzUU5KeQsMH3CAl8bxmIMJQoiz+V37Ft9V/XdCiMpAA+AoJfz8+NuxgBJ6bgghrIUQp4E4YIeUskjPDZXoH0484LmSfp+jpZSyIdAVGJ/fdaso95oDVAWCgFvAl9qGU7SEEM7AemCylDJF63i09IBjUWLPDSllnpQyCKgINBVCBBbl/lWif7howPeenysCNzWKxSxIKW/mP8YBv2C4vVHSxebfk7x7bzJO43g0JaWMzf9Q0wMLKEHnSP791/XAKinlz/lPl8jz40HHoiSfG3dJKe8Ae4AuFOG5oRL9wx0Hqgkh/IUQtsAQYJPGMWlGCOGUP7AGIYQT8CwQ8uh3lQibgOH53w8HNmoYi+bufnDl60sJOUfyB1wtAsKklF/d86sSd3487FiU4HPDUwjhlv+9A9AJuEARnhtq1P0j5E//mAlYA4ullB9pHJJmhBBVMLTiAUoBq0va8RBCrAHaYVheMhb4L7AB+BHwA64DA6WUJWKA2kOORzsMXbMSiATG3L0PacmEEK2A/cA5QJ//9HQM96ZL1PnxiGPxPCXz3KiHYbCdNYbG9Y9Syg+EEGUoonNDJXpFURRFsWCq615RFEVRLJhK9IqiKIpiwVSiVxRFURQLphK9oiiKolgwlegVRVEUxYKpRK8oiqIoFkwlekVRFEWxYP8P0jF4R4PomB8AAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 576x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(8,4))\n",
"\n",
"plt.plot(x_30, modes_y_30[:,0], label = 'First Mode')\n",
"plt.plot(x_30, -modes_y_30[:,1], label = 'Second Mode')\n",
"plt.plot(x_30, -modes_y_30[:,2], label = 'Third Mode')\n",
"\n",
"plt.title('30 Nodes: First Three Mode Shapes')\n",
"plt.ylabel('Displacement (m)')\n",
"plt.axhline(linewidth=1, color='k')\n",
"plt.legend(loc=1);"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(8,4))\n",
"\n",
"plt.plot(x_45, -modes_y_45[:,0], label = 'First Mode')\n",
"plt.plot(x_45, modes_y_45[:,1], label = 'Second Mode')\n",
"plt.plot(x_45, modes_y_45[:,2], label = 'Third Mode')\n",
"\n",
"plt.title('45 Nodes: First Three Mode Shapes')\n",
"plt.ylabel('Displacement (m)')\n",
"plt.axhline(linewidth=1, color='k')\n",
"plt.legend(loc=1);"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(8,4))\n",
"\n",
"plt.plot(x_60, modes_y_60[:,0], label = 'First Mode')\n",
"plt.plot(x_60, -modes_y_60[:,1], label = 'Second Mode')\n",
"plt.plot(x_60, -modes_y_60[:,2], label = 'Third Mode')\n",
"\n",
"plt.title('60 Nodes: First Three Mode Shapes')\n",
"plt.ylabel('Displacement (m)')\n",
"plt.axhline(linewidth=1, color='k')\n",
"plt.legend(loc=1);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### The number of nodes required for convergence is at least 30, as below that number (for the 6 node chart) the frequencies and graph are widely different from the ones with higher node numbers."
]
},
{
"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": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"First 3 natural frequencies for e string are: 456.7938585088082 912.4151337342006 1365.6942523972568 Hz\n",
"First 3 natural frequencies for b string are: 454.9075716133499 908.6474020147027 1360.0547475670016 Hz\n",
"First 3 natural frequencies for g string are: 458.0470676085916 914.9183349639862 1369.4410200753891 Hz\n",
"First 3 natural frequencies for d string are: 490.9672964382031 980.6742868679936 1467.863900468321 Hz\n",
"First 3 natural frequencies for a string are: 508.7429943110854 1016.1800526522501 1521.0085913724106 Hz\n",
"First 3 natural frequencies for E string are: 470.0908041390909 938.9748919260811 1405.4486446323556 Hz\n"
]
}
],
"source": [
"N = 30\n",
"dx = L/N\n",
"\n",
"d_all = np.array([d_e, d_b, d_g, d_d, d_a, d_E])\n",
"T_all = np.array([T_e, T_b, T_g, T_d, T_a, T_E]) #create arrays with other strings' data\n",
"\n",
"frequencies = np.zeros(3*len(T_all))\n",
"\n",
"for i in range(0, len(T_all)): #similar solving method to 2.a\n",
" \n",
" d = d_all[i]\n",
" T = T_all[i]\n",
" k = T/dx**2/mu\n",
" \n",
" A = k*(np.diag(np.ones(N)*2) -np.diag(np.ones(N-1), -1) - np.diag(np.ones(N-1), 1))\n",
" \n",
" e, v = linalg.eig(A)\n",
" isort = np.argsort(e.real)\n",
" e = e.real[isort]\n",
" v = v.real[:, isort]\n",
" \n",
" labels = np.array(['e', 'b', 'g', 'd', 'a', 'E']) #define some labels let use only one print command\n",
" \n",
" print('First 3 natural frequencies for {} string are:'.format(labels[i]), e[0]**0.5/2/np.pi, e[1]**0.5/2/np.pi, e[2]**0.5/2/np.pi, 'Hz')\n",
" \n",
" if i == 0:\n",
" frequencies[0] = e[0]**0.5/2/np.pi #use logic statements to assign each freqeuncies to the print command\n",
" frequencies[1] = e[1]**0.5/2/np.pi\n",
" frequencies[2] = e[2]**0.5/2/np.pi\n",
" elif i == 1:\n",
" frequencies[3] = e[0]**0.5/2/np.pi\n",
" frequencies[4] = e[1]**0.5/2/np.pi\n",
" frequencies[5] = e[2]**0.5/2/np.pi\n",
" elif i == 2:\n",
" frequencies[6] = e[0]**0.5/2/np.pi\n",
" frequencies[7] = e[1]**0.5/2/np.pi\n",
" frequencies[8] = e[2]**0.5/2/np.pi\n",
" elif i == 3:\n",
" frequencies[9] = e[0]**0.5/2/np.pi\n",
" frequencies[10] = e[1]**0.5/2/np.pi\n",
" frequencies[11] = e[2]**0.5/2/np.pi\n",
" elif i == 4:\n",
" frequencies[12] = e[0]**0.5/2/np.pi\n",
" frequencies[13] = e[1]**0.5/2/np.pi\n",
" frequencies[14] = e[2]**0.5/2/np.pi\n",
" elif i == 5:\n",
" frequencies[15] = e[0]**0.5/2/np.pi\n",
" frequencies[16] = e[1]**0.5/2/np.pi\n",
" frequencies[17] = e[2]**0.5/2/np.pi"
]
},
{
"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": 23,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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0W9amjDdWpfL33Izc9X9NOxmucv8Yh/xN1ySyr46aaakVA3upOr3I52+6GrnLzgZgFR3nrhuH/L856xRRItK491iRfLse8+MPYfp1L4uQrlzhO6qctc7KRNLSbBjYS/kVy37lHEAi2V+6Orvbmda+9bOPE01Dw6myiF3nzmZ7ikSldzNtzv4c+SYq8Wq98ny0jjsn8Pq6eGFRd9D8Ldcif/O1MaSsXO7vlyB31YUV1uLvsBoM7KG1X4R0/pzigJsAXfE1eLIXRH8czI/eR+66cTAn/q/mbamayN34d5jvvxtByvzlX3uR/fGrkL/+SpgvPJl2MqKzbElJBsRf7m8XIXfd5VXvTufOhn71ZXVvrrJEQs08NJ+zn9VnCWvaGNir1dqK3LWXIXf9lYnuNveXPzmeJX9S68oVMGd9mvh+k6KLF1oPXPrFqmpbu4bi5ab7ACatrdDPPkb+3lujTmYZ8/H7kRt/hZWeKgd8MT/7GK0XnGrfPCaJN6ptYv5J69LFMN96tXihx/miZh65m66Gzpvdtsz89KOidXLXjUPub8kNNaKrVyH35z8gd/4fy1/L5VzeEdF+Xbo7m2+9BnPym7HtsxYM7CHpEuvCn3/o7hQTYf+fj+9E9pK79Czk/3mV62u6cgX0m9WR7EcXzodZcUawClfBaorTly31fMl8/SXkLj6jrLVy/vq/InfeKeH3FQNz2iTkrjwf5kcVGgy6vfelp4FcK7SJb9yqF8/Nh86fE8mNlM6ZFajbZu6ma5B/6J6KvXpazx0L843/QT/9CLl/jGtbnr/p6vZ9FurHa/zNm35ViiWH3fzfc8ULHJcA88WnakqHr5Xl31H+obuRv++O+PZZAwb2sFbZObbl7cVPurzKoqgmk7v0LOSu+Us027rmL8jff2ck2wrDfOlpAO592wvd6koDu1sRuPnuZJgTHnLdR+7um2BOm1RrUl3pF59Z/8/9IpbtU7Ry117WVtICoKr7B503B7nxV8B8JkBbgcJNRJCb3kLplYeyIFutMNdPv3SvKi9Ni0r+xadj23YcUh15riG53Z2mkHOuW1GN++0zNnfr1ZfA2HgzYO3gs/rpqpWQLl3dX3Qd0rS4NEDnzwUq5Ihar7scxtAtYU6dBMz3HuJSp09BfvoUGMOGV0o2dQQ1/mYKddyh2liY8Y59H5uSwG5ODX+DrKtXAfkcZI1u7duZ8hbyzz6O7K9OhUh5flcnvwkcdrS17luvwnzz1bJ16glz7A1Oc62h32O+9SpMO2cXN21tReulZ0XbsGvhfJivvQAstCb+06UeXWYcF4HcJWd6Fk+r22Abjm6PumAuctf+Bfr5JwCA/M3XurczmPsFzGce8w3qUdAli5Cf8GDFiUl0+bK6y7m7t8+It2JZ1ax9QKkUmwHovNnI3Xurd1F7mCon+ziYLz5ddP6Yb77q2n4kEWG+fkcadfkymK+/VPEtunwZ1NFQL/e3i5D7y9lF6+QfuAtYsgjIV77hyT90T+KNpsNiYG9w5pOPFD1XM4/8049CV3n3/8w/dA/yNyQz+IX5yvPAyhXFxY1Rbft1a6hH7wFoii94+nnwumPntUa/XFa+5SqG/tTW8DdhbnL33GId13lz/de78vxwLZ4T6OKnc62GWDpvDlovPgO6fBmqjZrmzBnIP/NY5fWefgy5C0+LrP1H3DRfHMBzd90InTYJWOQ+gmKhVb+zrr5Sd01dsgg65e225/mH70H+kf9Um+Tiba/42qqjr6KdRyXmGy+372dhhRElbbnLzysO5PU870dEGNhL1ekANU7m80+0PdblxY29dOokmC89DfPJh5NOlrtGraaI+DzQhfOQu/DUAA0CAwg6tn21xa1x/ga+sXJcuesuB1avgr4/vepN5W8bH6jBlDnZPuYx1sF60S+XhbuhEJe6a7tNhy71aL1ulyTha0c3twDBS1eXpKu0+5nj5kBnf47Wv15QcZuFdQEgf+t1RS3qwzLfmYj8oyFuNtT0zdD4vzfAKiG65+lXy1PtfsrA3oDMl59tf1JSfGZOeQsAHP08Y0pD0Pmja8wFpjZBS8TBzfzQmqjGfH9adBtVE2pXR5RxFCnmX3o6tsZ6YbXdcMY8v3n0qjuPc1ec5zngS96R+yziFUAqFZXHeEOWf35C2w1GGLWM4ZC//87K07E6PrP5xsvIXXJm0YA7Ucr95WxowOlhc9dcWlRKqUsXR1ZiFwQDexSc9bEJN0opK46q9o41pPzNyYwVbb5WuQ7N873/e67q9+oC/zGqS4tLK6bliQesBx6Dh2g+h9yDdxf1sNBlS6wizdIhPu0Yk3/lOeSuvqS4Hv0buw7VnrkOsCYvCtSX3g626lHkW63U6m6j9E31dfRu9bGaz8F89L8eb/DYUMXAHTyw6/TJPjtyEab4OuwNxsqVyD9+f/h+6F67Cdh9UF1b/fsfk/yzlat+ABRNCa2qyP31AuTvvSXYeyPAwB4hXTAXuT+fAnP6FOiCuci/+kLobeRuugatV5wX/A0BA0zu3lvQeu7Y0OmpWa31trXcqIS4GJWOnuXaoC4KHjd++t406NuvIf/YfY40WIOBlA0oUnjdbjOQcwRt881Xqk6aLrYaIbbdhEQkd9VFxftxnhPS9o+v/ItPw5z6dsX12vbxzer2my/7ZsmvGsT8oLxKwHmTZb7wlDVOQ1TtEKrs1la2zFky96X3GAyuys7Fkp4gjiqEsmL7wKxt5u65Ba3XuneFzT98D8zXXoT58jOhtqwfhx/T3nkOqHPMCrtk0HztJZhT3vK8ydAZ4UrcWq/4c/t7ExiBsoCBPUKFGd/MGVORG39l6Atk/qmHrYDi0lir5rRNe8f6P+SFSVevsnKSFXJdlSZzqFXQ0dR0vn+DMi/5O/9V1fsCcfZcqJSbCZLZKVxwC0WjNeSwddVKtJ47Fq2XnRNZ4zldtgT6zWqY096xAqZP3WT+qUcQJMqZzzyK/H9us7Y/Z1bFm9TcRacjf/v44nTNmOqdjjtuKLu5y09o//3qkoXIXXpWWSmQrlpZVSmd+vZKaT8ezhsOt/YEtcyypqXVMyU30Vp0I1Rjldq77wAVfpvmc09Avw4+HG7YoYDNWZ9WHBvD/N9zyP/3dqt3SxTC3mxFhIE9Cm0Xa8fJH6Abmi6cX1RHWlR3HlSIHwIQ/q7RfOV56NuvwaxQ+lCp6LpqIjDfnWyNpvbhexVX9y9GVqs18NzyBj069wvXxi6aa0X+tvFly0N10XE2Qio0dAqlZGc1zNOt36xG/qlH2nIkbbmekOeRn9yV5yN37WXI33sL8nfc4JaK9ocrVyD/eLgb4KDDeOrHH4ZrTJXLwfzs4/auoIvbb1YLN67O34+uXmV1o/QYiMiPcwS3Mo7D4378HKvWMEpgaRdA37rpCjd9rf+4DK3njrV7OTiUnLo69wv/Lroroq0fLyp1mD658hvsm9DSRsm++6jDCaMY2EtF8SUFbPCVu/oS5K6+pPb9OVXKEVa4gLeeOxb5CQ+2L7CPhznxf67dvgryd/6zbJmqWt2yfJjvTYU5c4b3CqptuZv87ddX1W/fKXfVhchdN678BdN075LnebGLp6FSpQt1pb7rlZgvPg3z5WfaiuyL5rt23oAE/B3kJzzoPl9CmJuPkpbT+s3qCkHGf3M5R/sP841wk/nkb/y7e1fQwj4dX3vu4jOsfUwLXkUQTO3XoNy4c+K72XZjVxPoJzORv8dZl1z8O8ldd3mFbnUhP3ul653jRt9vONoyoaaLrZTm5AM/A3sk7DPE/v6c/UOdzJkzkH9+AlqvPN8/mAHQ+XOsgRAiaD1cOgSq53r2j9M1GH+1HLkwdf8A9KP3i7q76coVMEvqrvP/vtE9R2wzX3iyqBhePXJrreeOdc2J10KXLELu8nCfufqd2d+z8+ap7dg5Lgxm9ReJ/AtPAoW6w1yrVYfssbnClMC6ZJHvYEbmK8+HHqxD3/MuEgfsYVYvPctvC/7bD9pjI5TkLs6mXW3mJnffHcj997ZA28lXuKku+0hR9fN3Vtu5BM8gpQyBqzdcbgCLGsX53aBG/JXqqpVo/fvFPoNCJdeVmoG9VDVdRgK+JX/beJjPPQEsW2LXLbYrrcPOXXsZzLdeRe68U2rKpeq8OcgV5UC8E1voKge0F01rLaOolTRey982HvmbrvFtUe46RrujLtD0abxSqSuZ+dwTvq+Xre8XgBbMtdPjH6SCypdUw2g+h/yD91hPamiR7WQ++zjUnszCfOoR5C4/t7gEx3kRtItpc1dd6DmYUVlr/YDyd9/sv4LPjaiqCS05Hn6tqXWRR3dAt3VL6oDdboh11SorDTX8LrRSvatPqZpOftMz41C27tuvVVqj+KlfdyyX3hxx9AAqlArWUsedv+MGq9fBpNerjt06c0aILsPWNVU/mQksWoB86XUmhaJ6jhWflpK7upzHjGmARw7aS+HGZMXXVheqf1xW8S2t546FbD4c0rN3e3oCjlim+ZznyG+lMx+156jdT3TzvSnI//smZH/5e+8d+tx4mc8GmAQjIoVcR/6uG6PZYOn54JyW0nnBrfWmv6Q6pWhmsRAXIFWzqH+2qon8/XfB2G6XGhPoz3zm8bKAZU56HZkRO7unM8SAQGVdmdy6Tc2bDXPCQ5BBG7Uv8+jC6DVrWe6K8z3TEFmjrSDCxBu3xrMBArv52ovI7LJH4N3kH7wbxslnwfygthbk5vNPwnzxKcjGQ6reRv7+u2pKQ0H7jVhyAZ6BvV741YeF6DPdVoT6wXTXKQXNWZ8Ur29fzHXqJMguuwfeT1vSbr2urVtW2zbnz/UYdclRhztvDrBOv+K02bnxQu8CN2G7m9TCfMs/x2N+/EEs+82H7PYTRun3okVdyEqG4PWp2jBLZ7tasQI6+U3kXbqNRaltFLmihRHlHANW5ZhT3kZmvYEV1/OuovArHk4wdxfznAYA3Gdu8+uvXvj8VfZuaduMXVLjPdw0Ks/6HKJ7pe92Yhowxw8DeyRcWsXbWs8di+yvT4estbbnu/0apQGAfu4zX7Hf+9zq6hw3ELn77oAxZFjb82pa5ZcGdQDIefRXLVyA9bNPkL/lWmDd/u7bTGBM70CNwxb6Nz7K3/KPSNJS2t6irMogyqo5v1bizouwiH+1R0kL49xl9ljccV/E3Mbt/3QmdOBgSP8B8e3Xeb58vRz5/94e7u2rV0E6d4k4USmr9rz0a/MT0YiE+m6AFvCrVlmllQMH17QvsUsRtfA7LsmIRT0uRBCsY49A/uF7fPvVVpphq1KjNP0owpyhc5S8yW/WNMpY1XeihT7vHsMzmo/fX2WKQvAaijVhumyJb+PBonXzudCtvKumCvO55Ko22nbrMhpYpeFw9d3JgScZ0rmzoaYJc9o74YZdrnAjmLvhr0UD6OSffrTogp67+IxIG3eqmql3s9K3X49+o18tL7tpjIva3Wer64LarnXcucjd+g+YE63fpnpUzSSpbnPsIvIJgOUA8gByqjoi3RR5q9w3vI4nlvnKpagsIP+Wy97yXoE70eF40+97qvk81G10vJKiSv3S+o7yN11TU7/lMEpv+DSfh2Qy7Qsi7oFQkPvbRWXLAg2HG4DOmWV1dezSFVi1EsbI0ZFsFwD0i8+Q/89tMDbfGgBgvvR02Tq568Yhe8q5kewvd94psbdniErYDEA1c6yn6qsvywY3Slu959h3V9Xh9RzUAxEEnjwgaZHMNhaWx9zY6miVH7v04zpy5/8h2Ip2C/ykgjpQXmqiVbaAryuFG0e7OqJsMJUkRDhlqOk1iUy1ophExqUUwW145vwL3rPy6bve3f2iVDpAT4Rbjmm7wdVtjr0ReY4vvGQx8v++KdnEBFUnoyapat2kJVENMkd4GtMZ6zerQ4/qFqp42mfd1nHnhNpv4F2GGvgkon3OmwNdtQLGBhvHvi/XBrsuvXrMoJOpxMhrTIyaxVSaFUY9B3YFMEFEFMB1qlpUESkiYwCMAYBBgwalkLxynidKCq0iPZVeoGO7a6139XET4TWlZykzoVyMpxRuuvIP3BWsEZTTgtpaU7epsp40//pLFcYHT/44Frq8Gme7jLjoFNPMkOrR7Y/iU8+BfRdVnS0i6wB4UkTeU9W2AcvtQD8eALKkliYAACAASURBVEaMGBHZr6WmfInXxS+F3A75Kx3kpN4VD9PZMYQO6kC4uBnDOWA6ZucjSkvd1rGr6mz7//kA7gOwfbopqsyz1WsdBXatk9bgpXLn+QxKE4NYWvRSQ9H3poRYOaK8Q8STnFSSylTNlDrfwC4iO4nI1SIyWUQWiMhnIvKoiJwoIj3jSpSIrCki3QuPAewNIJqxO+Pk0X3GfH5Cwgnx4TaaVgfkNcc5ucs/fK81Hn9MxbXRiamoe5X/tMVB5f8d0UiFRD48A7uIPAbgZwCeALAvgP4AhgI4E0AXAA+IyMExpWtdAC+JyDsAXgfwiKom36mWiCz2oCK5gG0Cmo7PnPKNwm0eBmpOfnXsx6hq6WgRXwF4y/4bJyJ94kiUqn4EYKs4tl1x32nslKhRzP2CxbsNKn9vsFnhqPF55thdgnpV6xARUfo0oRHdKH1VNZ4TkWBjYBIRJUQLQxUTdXDVdne7LtJUEBHVyJwxDdKpU9rJIPKkSxdDevWuvGKNqgrsqhrTkD11oCOOfkbUBNKYRYsoFLd57WNQMbCLyLNwaVOmqnvEkqK0hZj7nIiIqN4EybE7Rw7pAuC7AELMd0hERERJqRjYXYrdXxaR8lH9mwaL4omIKHq6ckUik3gHKYp31vQbALYF0C+2FBERETWjKicXCitIUfybsLKxAqsI/mMAP40zUURERFSdIEXxGyaRECIiIqpdtQPUsCieiIioDlU7bes/I00FERERRaKqwK6qB0SdECIiIqpd4JHnRGQdWP3YAQCq+lksKSIiIqKqVcyxi8jBIvIBrNbwzwP4BMBjMaeLiIiIqhCkKP7PAHYE8L7dQn40gJdjTRURERFVJUhgb1XVRQAMETFU9VkAw2NOV3o48BwREcVBkhh3Llgd+1IR6QbgBQC3i8h8cKx4IiKiuhQkx34IgBUATgbwOICZAA6KM1FERERUHc8cu4iIWr62F5kAbnZbJ84EEhERUXB+OfZnReRXIjLIuVBEOonIHiJyM4Bj400eERERheFXx74vgOMB3CkiGwJYCqArrJuBCQCuUNVJ8ScxYcm0bSAiIoqFZ2BX1VUArgFwjYi0AOgDYKWqLk0qcURERM2jflrFQ1VbAcyJOS31gS0GiIiogVU7CQwRERGFkkzOsW4Du4jsKyIzRORDETk17fQQERE1groM7CKSAXA1gP0ADAVwlIgMTWbvLIsnIqI4pFzHLiLL4R7lBICqao/YUgVsD+BDVf3ITstdsAbKeTfGfRIRETU8v1bx3ZNMSIn1AXzueD4LwA7OFURkDIAxADBoUFFX+5pIS6fItkVERJS0wEXxIrKOiAwq/MWZKLiXVxSVHqjqeFUdoaoj+vbtG92eu8VZEEFERBSvep2PfRaAgY7nAwDMjnmfNtaxExFRDBIaAK1e52N/A8CmIrKhiHQCcCSAB2PeJxERUcOry/nYVTUH4CQATwCYDuBuVZ0W5z6JiIiaQd3Ox66qjwJ4NO79uOw48V0SERFFJeh87CvB+diJiIiql1C+sWKO3TEfO1AyHzsRERHVlyCt4g8XkQ9EZJmIfCkiy0XkyyQSR0RE1DQSahUfpI79UgAHqer0uBNTF7r3TDsFRETUjBIqig9Sxz6vwwR1AGLU5fD5RETU8JKJ7EFy7BNF5N8A7gewurBQVf8bW6qIiIiaTsqTwDj0ALACwN6OZQqAgZ2IiKjOBGkV/5MkEkJERNTc6qQoXkSuclm8DMBEVX0g+iQRERFRtYK0FOsCawjZD+y/LQH0BvBTEbkyxrQRERFRSEHq2DcBsIc9fjtE5FoAEwDsBWBKjGkjIiKikILk2NcHsKbj+ZoA1lPVPByt5ImIiCh9QQeomSQiz8Fqq78bgAtFZE0AT8WYNiIiouaR0CRjQVrF/1NEHgWwPazAfrqqzrZfPiXOxBEREVE4nkXxIrKZ/f82APoD+BzAZwD62cuIiIgoKEl/gJrfARgDYJzLawpgj1hSRERE1IzSLopX1TH2/7snkhIiIiKqmV9R/HYi0s/x/Mci8oCIXCUivZNJHhEREYXh193tOgDfAICI7AbgYgC3wBp1bnz8SSMiImoe0mfdRPbjV8eeUdXF9uMfABivqv8B8B8RmRR/0oiIiJpIz16J7MYvx54RkULgHw3gGcdrQfq/EwWX4SlFRE2uDlrF3wngeRFZCGAlgBcBQEQ2gVUcTxSdhE54IqLUJNQq3jPHrqoXABgL4CYAI1XbUmQA+FX8SSMnY9Q+aSchXkaQ0Y07uL79Kq9DRKHIwMFpJyFyvldTVX1VVe9T1a8dy95X1bfiTxo5Zb6zd9pJiBdz7JVlMmmnoGnJ1jtU/94mDAwdShNee5hNSgvrlIsYI3ZKOwl1RwZsUPw8y3MmLsbADSqv5EE2GhJhSohqV3eBXUTOEZEvRGSS/bd/2mmi+Bnb7Jh2EuqerLte2kloXrXk2tZYs/I6lKwQN8HGzqPiS0dK6i6w265Q1eH236NpJyYOmQO+m/g+pZ6Dp2HA2HVPAIBs0SBTESRY591y9jhgzW6J7Y+CS7O0Sb41LLV9J8HYfd/q3ijBQlv2t2fC+Nbm1e2jjtVrYG9+ffpWXqfnWkVPM98/rqZdGhtsVNP7Y2e3z5Q+66SckBJrre26WNbpGI3Z5NtbFi/okUxf3EYhRnptH7JHHg+0dPJ8PXPY0d6vHX9SHElyJYOCX3uyvz+3/X3r9I8jOe3bL7nGVr2d4dtFsp2o1GtgP0lEJovIv0TE9ciLyBgRmSgiExcsWJB0+lz5/YjKVw5QVNSp5AfbpUugTWdPGNv+ZM3u7Y9FkDn6Z4G2kTgRSL/1rYcx/5jDyh7907STEIvMD38ebL2Djih+fsgP4khOypqvARUA36Cf7GcO1s0re9alkChKpoJUrXRdo/b92LKHHNl+be0/wHvF0mt6TFIJ7CLylIhMdfk7BMC1ADYGMBzAHLjPLgdVHa+qI1R1RN++AXK/CZCNgzeikSAnXkkXMBm8SbCNd+1q/d+jJ1p+f45zpzA2/Xb75kfvX+GHnyxj2FbInvgHGJulVzSWOeqnMLbbpWiZ5zCQCfVJjYuxyWaVV+rVG1JyAZT1B8WUonj5p7vxvstC40rZfLj3Ot8aBmP7kcgcepTLiwkG9u49Aq1WVvpRTRK79wSyLZ4vGyN2BhAyIxZAkBsSSajRdCqBXVX3VNXNXf4eUNV5qppXVRPA9QC2TyONsSv5UYnrXV7JOjX+EGXQhkXPMyNHA2v3qWmbVXFrBGZ/trYg2qVrgglyaGlBZv/DPV8uKpZu8MAeRHbMyWXLpHMXGLvvl0JqaiNbbuu63AjSlXTt+sg8OGV+YhWlS2fv34oYBjL7HQZ0s0vuOnVufzHB89fYdGhi+2r53Z+QGe3T5nqt3mg5e1xRJicK9XQ1qLuieBFxlsMeBmBqWmkJw9jxO3AG4uyvTgu3AbegLeFzR8aOu5Uty/7xfGRPvxjiUjea2WWPUNuvmqOeWrq6XIhKW7EGuYnpFf0kg1KhHULmiB87nikyRx4faQ7W2H5kqPUzPziuuv3se2ig9Upz6/XM2OsgZM+4ONybevREZtQ+qJQ1rLt2H7CCNgAYo4KPceFsFyIJtuaXzbeGsUs1M4CXfC+9g2VEZP2BPi9GHPbsKsS2zZfubph3iUpc6i6wA7hURKaIyGQAuwMozzLUIWOLrYueS6UTMNDdsiBz3P8he8p5gdOR2eeQ8q106QppcS+aMjbf2iqSj1n2hN85ElR+EZU1iouxZLMtKm7T+HbldcKq1BCqqNREAeNbw5D92W+iS4BLztAv2AeunindZo0tuY06aywEWEWhkm1B9sQ/Rt5a3CuwG3tYv50w1XBl2y4pSQv9/s5dXG/oK0oysGcyyOx5YM3bMXYaVfs2Ij53M3v4l14ZW42IdH9B1F1gV9VjVHULVd1SVQ9W1Tlpp6kgc9z/lS2T/gOQ/e2ZkPV87hBLGPu7dHVzvXAoJNsS/s66W3egV2/fImVf60bfeE06Oxv+Vc6NZ3bYNfI0RK5z58rrBGBss6N7Y8pCdUT3npHspyB7+kXudX0+9ZKlpEe0afKTOeLYUOtLn3Xc20U4bsqy/3eKte2g3anWcK8/lbWsUqPM949D9qRTQ6UztE7e55ux14HInvgH7/cWSsScVVwBMheZg78fNHXlu/ztmch87xhkf3lK1duACFB0rgUt8Pa+xkReClVoC+V1PFMY2a7uAntdKSkeNjbYuHydNdZo7zIR8PuTfuV1zO71PS4b7Na9fFnpuzJZtPzmjBD9M4v3kwlZHAwgXGv7IDcqcfwWXI57UNJ/QFujm/aFtScyc+ARyBx0BIyty5uSGNvsgMyBR8DY6TvW7tbzaW0bgng0mEwjZxGEMXRL7xdD3YQ6vq9M1qpnHW4dd9mwcsmHXy8C6dQZ4ixtcbQjkQolS0F7gYhPo1IxMr5zfcugjWDsdSAyB34v0L4KjBqG2kWPnjCGDa+5W2jGOU9GtRXZSbbZqYMhahnY/VQ4iYwDvovM4T9se15anOxFgp5kLidIy9hzgr03BGPr9qKplrPHVTUKnAS44WhfOfTmI2GsV31deHbMyeWDCkXQ+MjYtuRYO79zERjb7gixx4ivdiANZz2883ytRlVFvlEqCV7G0K2Cv9fnvKvUn1m696ipuN2P4VJ95pqG9QZaAxVVQUSQ2Xn34i5edRCAAunUXtpnDAvxfTtV+KxS2kPEI1cvPg3uCqU3ZdfPFBrZMrD7cvlCCnfXRgaZETuX1w0P28pz5DTZ9NvI/PgXkL7ed9ZF64dKa3CyyWYwdtur/fmaIYJyFPvvGqRqwf/TZ0/+U01pMCrUi0WtYmPKiH/8ztkAjc22QObYXyL769Nh1DiqX9kF0H2tmvZRtCWXkowatuZ4GC6NsvnWlVcqUvJ92vszdii/MYptDgCfHDwAQBVGWlVe1VYvBS1GX7tP2RgefrIBx3TwG39E1uhmZYxKb9ZTwMAeUmY3e9jTzdwb52S/92NkC7miklbbsslmMDbcNPjOAl18wl9Esz/8efC6xaBcApOx/UgY2+yIzLG/LF6+5wGQjb9V0+5qruN1tIytuvFSiKlm3RpTureWLW6cV63SnI0xeBOIxwh6QIh6bGc9tVfd6VrR9VYobbQmEbX/8DsWruuLIJIblkqbKCmWLxoGOuTNnwQZ3TLWcSx8PmyVNzNBu/xKtgXZX46tvKIHI8yNXB12e2VgDy34jzv7899AHK3liwY+iaoYLKJGTFJN/Wql4stBG1n1x3bLbWPfQ2Hsvi+kU2dk9jygmmRWnRY/mR+NCfcG+6Ygs0fI3gQl33n2e8e0v2TXI1cz7G9Z3T8A9O5r5dgCXriNoVsWX6B693EvdnSsk8iQuiXXTKO0LrzOrqnZX53m3oguYDpLu2kZm5TfAGe+92P3AWfKtxZsp17vrmI6WmPk6MDrZsecbI2T4HcNC3qd7LoGsqdfhOwfz3e+uf3RRnaGKsDUx9k/nh+4O2i9YmD34/djDPBDlTW6IVMYyKNX75KuUt4bMEbZuekAY3JH1To5c/APkD09eB9gY/QBlet8S36TmR12RcauApCSvp+1MlwGH8n+zqe43k6bsfMoSEsn6wbEZZYn165mhYuDs1V8t8ojaxl7HeT92kZD0HL2uKqCZWmPDGP0/hDDQMuJf0DL6RcF3o46zsmWX52GbF0MP1z8O3EdZCbgWO2GzwhtUZHefYob0ZWmYZsdgc5dgueUXS4TxrCtIm/oaGzr0v2xUlG+C2cDP9/ctSqk/wCPgbnCyRxzArK/GAtp6VTcfsnRxTezi33DEWCgIenStW2MgPIXa0lpchjYw0rgizV22R2yxdbI7Fu5UU3muz9yrbcLSwzDs6+795ucj6W8y1+CuSlj1N5lLfOle8/i1rDZlvagXLiw2v8b2+yIjE/gdeUIhLV0Cwoj890f+b5ujN7fHiwpPWWD/NTQG6FiA9ZNN/MdUtUpcKNVwLVrWVGgqngjJ+5P1+6LllMvqKqEydgmbAt1l4PnNThLT59MhMvNZrASg/gZ+xwCY6MhroNvifM7tH/3xd1uq9EYkZ2BvWoho1aIehjJZpE9/EeeLXWdRWTSq3egG4B4lBQt//y3qe1fjIxrl8Hs785G9v9OgbHrnjD22BfZ355pPd92Jxi77wuj4sh7biMCuiwLW1cZphdBCJmRo6tvjOWTwypUIwUZUyFz4PcCB9vKSn83haKWjNUff72B7WN013zRdqgwWUelEQqd3Fvuh7/rFZ9+7IG34XXz7nYPYHevzB7/q+IXjIzn+evVlbJ8xaJcgfdqFW6AMkF7afRZx+ruF2ZMhIhmfksDA7sPGTS4fGGhiCZow6mgdUQhAn/mkCMDrxsVZyv6Ns6PVocNSADrQiZ9+yGzx36Qzl0g3XpA+vazRsLaba/KpRQx3KDLkKHI/p/PYCKF9foHqK6osUV15qifts0GWMiRGi7tH4x9DrZ6dAQoOpVMFrJ2REOwlp5Wha5/I/doCyLGHvshc/D3i0abK1TNVF9XWtvvVhx1uaEaYkWq0mfwGlDFQPb//tBWPF+Wy11jTe+eNJWqBu3XM3s5RqFzuUZm//QXZH91WmTtOArd/STgZDRAeYNXGTgYmZHtGYG2eSOC3lBGcGMWFAO7j8yRx5ctkyFDYey4GzL7VTmqW1zWWhsy2GUAnVrZ9WxGSQtuWX8gpG+lH10NwT5Q24F0bibaAl/IoGrYgSez+76BRr8Sl7HwS3OKkm2pqSGmMWRo+YBJLhcqyWTD9ehwvjfC+dvFMNBy9riiXh2SbYGx9Q5FReWyTj9rvRDduYpa+Vc6pJVetwNI5iCvKhqvDUR4Jxl2U3ZVhQwcDOm7rnsduWEg+8uxkH7ruXd9rHQu2jdjzmuH9C7voSBieA/Lnda4/V26ttfRd+qMzGFHWVWhARoZZn7487bRDpPAwO7Deada6JsuRgaZfQ4JP2dwpRxtmKJct4Frfn06sseWD3lbM4/fqbHhpq59jLOnX4zsb86AbL2D70hZFXfbpat3X9eAE0FEwW1c6cz2I62GbgEbbRVI7z7W+2poOCiOY1KYYU22iChHGFOpS211/hH3799jf+/ql76OgBHVbu2qC3EbtdKDM2BWnHOihHFAuJHlivZrVxn4tRfJnnJe29gdMmBw+wuF3Gjgc8jRPmVvuyox4Ax6hRkHjf0OC7ivKtnXvrbrWEmOW1o6BS6NMTbZrGK1QpQY2AMq62YTlNcdrH1jYGyzI4x9DoF8K8S0hiH74FYj85MTkR1zcvsoSi5FWEV39Pbr0tIC6dUb2YO/X/Pcw9VM8lLtyFye3KaYdSFdIqzfDUjsQBTZHM92sWfYPt4A/FumG/XT4Ciz6+hIuloaO34HyGQhAUsxMkcdj+wvfu/d2trBOViK2/DTvunaytlrIMBxL/xu1+yGzH6HIfOz3/i26vdUS/fdQnWYRwlYaZWUtHSySmOCDn1da9fiLjWOLZ9CNWUys743MBm+HXTSG9XfwRdaY5YERunRyxqNrNda4XN+CQwFaQyyinwz/QcEaqAiNUxU4jm3d5XbzJ58FrBqZdXpqUbU3fcC7jXSrRnbj4QM2ABGNdPQ+p6T1aezMFSxbLktsGRR1duJmrH+IBhnXuL9+vYjkZ8xDTLAOpbSqXMskyvVyhixM2SNNa0RM8WIdApif45zoncfGKP2LbkpcaxZQwld9rQLq36vfGtz6EcfQHr3sS//9dmOyA0De0U1DvLQrQcyhx3tOs50LSdsU/HIxRg7fwfm04+ULW/vtuT+3UiPXoHGAPC1dl9g0QJYP+Zg54Cxx34wn3mstv2mSESqv7B37wEsXdy+rSoG2imV+cFxEHushOxhR9e8vcoCjmoWYNREY6MhMHxKjzKj90f+3zd6DpFqjD4AMnCDQOnxTMNOFapA1GqzEGa4XK8ug8aofWA+8UBVI9mJCDLfcWmcG4FaehIY2+0CY6sR0A+mR5iiZDCwJ8Bt8BQKwKvPbQLzSGePOxE6ZxbEKw0ugk4CFJ36yUFkDjoC+Vuva3tubLgp8jVu09gsfFVM3LK/Pj3QYESVtA2N69Gi2tn6uup9RDD4S1CZHXcL3vWsQYgI0LlL8a/MrjZw6znilPnxL5C/5R/WkwTnvS9gYK/A2GJr5Ce9Xv144hRAuACVxCQL0q2770xO7jw+R0x91p2MnUbVnMOrSksnKziF6UPefwAwZ5b7a737AIsXRpO2Wnhk3qtqf+DGvjkompI0YlFOLpP9zRmRbauuVZgQS4xMoHY8zhtbY0Dyv0sG9goqFalFqkdPGNu4DO1IbYyRo+syJwcUD8mKnmsBy5ZYj2ObC7o9+mT2DjlqXkSyp54PQKBegRoom7gle+RPkLviz+7r9lsfGnFgzxx/EnTOFxXXKx7yOdIklO+rpSX6hp6hExFiVZeul1Xtss860EULioZ7rRfZUy/wH5+kfgrIKmJgryMtIaYizf7ylEATGkQp87PfIH/DX2PYcvArjDNIyOCNgVeeQ+aYE2JIUxUcP3xjy21hvvhUemlJSKHhp981r7Re1rdfewztQo2BGwIDG6TEreaGsSF+S7VWHbWEDx+Zw46Gzvo00a5fQXkNNyubbQEZvj0yCU/1XAsG9gaVyMxaJYz1B9Vcb+ok394COn1K9ekZMhTyx/PDjQEeq/bwZgzfrkME9jY1BCTZaFPoRx8UnkWTnlo5kpE94XfppQPWJCf6ycxU0+DG2H5XmE8+XLY8+7s/eeZ8pXOXqqZsNvb/btkUvkmRbBbZQ36Qyr6rxcBONcmOPafqMbplrT41l27VT1BH8ZSmSfR4SKFRThyyx/wCrefac2fXSZ93Y8gwmG++AiCtroyOtGw0BNiovFeN+8rJHT+vOvxaur56yWznMjUxeeIANVQT6dY9/KxwBYWqBI+LURL99ZPgPayox/pH/RSGz1zv2ZPPgrH3wVXN3R63oC2x26YmLpWxWx3v7vF6QoxC96uwI0ymLLLBiqih8Syg1Bgj9wBav4GxXcARpOqdxwhTRsgeFcaQocAQ75EIpUcvZCr1Ua4DmYO/D126xP1Fr5xlYRjPBHoS+ArRzbHhdOoMmFFWqlG9YWCn1Einzsjsk9aUswlJcEaneuC8tTG2Djt/uMeGOhDpu27N2zD2PRTI5Txfz/7hvEiPr7FDc/VfbwYM7ERRKcmxZ35wHCTgWPONLnSliWdgqZPql65W243EWkKLAKpt897XotKMdlEW16feZY9cMbATRcwYYTX0qdf+9nXBpf2EFA3kkW6WXTLZdIJWndzXUGNLpSJJRI4QkWkiYorIiJLXThORD0VkhojENywTUdQKOfaO2ICpMJd3wIlOjB2K21VkTzoVmR+NiaAfd6Pr6J+/echWI1xnxUxCWlegqQAOB3Cdc6GIDAVwJIBhANYD8JSIDFFVtvSg+lcI7B3w2iy9+yDzk5Mg6wVrFS+dOlvD0bZ+Yz23pwqVXr2tvHqFoT2J6l320KPS23caO1XV6YBrd6ZDANylqqsBfCwiHwLYHsAryaaQqBqF4uMOGNkRvvV/9uSzgNbW4m3ssjtk3f5VjNNPRAX11qdjfQCfO57PspeVEZExIjJRRCYuWLAgkcRROoqmn/ToUlYX7OFVkx7qt1FJ1zUgPYoHMxHDsEYUTKlI3tjrQBi7xTOFKFFSYsuxi8hTANzGPT1DVR/wepvLMtcruaqOBzAeAEaMGFHHV3uqRaEBk/nK8ymnpDJjxE7AsiUwdtsz7aRQlTI77552EohqFltgV9Vqrm6zAAx0PB8AYHY0KSKKl2Rbmr9fPhHVvXorin8QwJEi0llENgSwKYDXU04TERFRw0iru9thIjILwE4AHhGRJwBAVacBuBvAuwAeB3AiW8RTkQ7fHYqakbHLHtYDnt4UgbRaxd8H4D6P1y4AcEGyKSIiSk9m9P7IjPae+IcojA44kgbVInvCWOjsz9JLQD23iiciqgMM7BSK9FsP0q9jjH9OEVqnHzB/btqpIOoQ6q3xHJEr2Xx42kmgGrC3AFFyGNiJKH5ZFg4SJYWBnYiIqIkwsBNRAtiPiygpDOzUEGRde8qAnmulmxCqDuM6UWJY8UUNwdhlFGSjTWGsN7DyykREHRgDOzUEEQPCoN7AmGUnSgqL4omIiJoIAzsREVETYWAnovhx8h6ixDCwExERNRE2nnMhG38LssHGaSeDiIgoNAZ2F9kfjUk7CUTNhUXxRIlhUTwREVETYWAnIiJqIgzsRERETYSBnYiIqIkwsBNRYqT/gLSTQNT0GNiJKH5sFU+UGAZ2IoqdFAJ7lj1sieLGXxkRxa/f+jC+szeMbXZIOyVETY+BnYhiJyLIjNon7WQQdQgsiiciImoiqQR2ETlCRKaJiCkiIxzLB4vIShGZZP/9I430ERERNaq0iuKnAjgcwHUur81U1eEJp4eIiKgppBLYVXU64GgpS0RERJGoxzr2DUXkbRF5XkR29VpJRMaIyEQRmbhgwYIk00dERFS3Ysuxi8hTAPq5vHSGqj7g8bY5AAap6iIR2RbA/SIyTFW/LF1RVccDGA8AI0aM0KjSTURE1MhiC+yqumcV71kNYLX9+E0RmQlgCICJESePiIioKdVVUbyI9BWRjP14IwCbAvgo3VQRERE1DlFNvhRbRA4D8DcAfQEsBTBJVfcRke8COA9ADkAewNmq+lCA7S0A8GnEyewDYGHE22xUPBbFeDyK8Xi047EoxuPRLo5jsYGq9i1dmEpgbwQiMlFVR1Res/nxWBTj8SjG49GOx6IYj0e7JI9FXRXFExERUW0Y2ImIiJoIA7u38WknoI7wWBTj8SjG49GOx6IYj0e7xI4F69iJiIiaCHPsRERETYSBnYiIqIkwsJcQkX1FZIaIfCgip6adnqSIyCciMsWeLneivay3iDwpCUu9HQAABeZJREFUIh/Y/6/lWP80+xjNEJF90kt57UTkXyIyX0SmOpaF/uwisq19DD8UkaukQWc58jge54jIF44plfd3vNa0x0NEBorIsyIy3Z5q+jf28g55fvgcjw53fohIFxF5XUTesY/Fufby9M8NVeWf/QcgA2AmgI0AdALwDoChaacroc/+CYA+JcsuBXCq/fhUAJfYj4fax6YzgA3tY5ZJ+zPU8Nl3A7ANgKm1fHYArwPYCYAAeAzAfml/tgiPxzkAfu+yblMfDwD9AWxjP+4O4H37M3fI88PneHS488NOdzf7cQuA1wDsWA/nBnPsxbYH8KGqfqSq3wC4C8AhKacpTYcAuNl+fDOAQx3L71LV1ar6MYAPYR27hqSqLwBYXLI41GcXkf4AeqjqK2r9Um9xvKeheBwPL019PFR1jqq+ZT9eDmA6gPXRQc8Pn+PhpWmPh1q+sp+22H+KOjg3GNiLrQ/gc8fzWfA/aZuJApggIm+KyBh72bqqOgewftAA1rGXd4TjFPazr28/Ll3eTE4Skcl2UX2heLHDHA8RGQxga1g5sw5/fpQcD6ADnh8ikhGRSQDmA3hSVevi3GBgL+ZWr9FR+gPuoqrbANgPwIkispvPuh35OHl99mY/JtcC2BjAcFjTK4+zl3eI4yEi3QD8B8Bv1WUaaeeqLss6wvHokOeHquZVdTiAAbBy35v7rJ7YsWBgLzYLwEDH8wEAZqeUlkSp6mz7//kA7oNVtD7PLiaC/f98e/WOcJzCfvZZ9uPS5U1BVefZFzETwPVor3pp+uMhIi2wgtjtqvpfe3GHPT/cjkdHPj8AQFWXAngOwL6og3ODgb3YGwA2FZENRaQTgCMBPJhymmInImuKSPfCYwB7A5gK67Mfa692LIAH7McPAjhSRDqLyIawptd9PdlUxy7UZ7eL3JaLyI52i9YfO97T8AoXKtthsM4PoMmPh532fwKYrqqXO17qkOeH1/HoiOeHWNOM97IfdwWwJ4D3UA/nRtotC+vtD8D+sFp6zgRwRtrpSegzbwSrteY7AKYVPjeAtQE8DeAD+//ejvecYR+jGWiw1qwun/9OWMWHrbDunn9azWcHMALWBW0mgL/DHtmx0f48jsetAKYAmGxfoPp3hOMBYCSsYtHJACbZf/t31PPD53h0uPMDwJYA3rY/81QAf7KXp35ucEhZIiKiJsKieCIioibCwE5ERNREGNiJiIiaCAM7ERFRE2FgJyIiaiLZtBNARPEQkUK3GwDoByAPYIH9fIWq7hzDPrcGcKKq/qzG7ZwE4GtVvTGalBF1HOzuRtQBiMg5AL5S1cti3s89AM5X1Xdq3M4aAF5W1a2jSRlRx8GieKIOSES+sv8fJSLPi8jdIvK+iFwsIj+055meIiIb2+v1FZH/iMgb9t8uLtvsDmDLQlAXa47um0Vkgoh8IiKHi8il9nYft4cmhb3Pd+0JRC4DAFVdAeATEWnYWQOJ0sLATkRbAfgNgC0AHANgiKpuD+AGAL+y1/krgCtUdTsA37VfK1UYPctpYwAHwJqy8jYAz6rqFgBWAjhARHrDGoJ0mKpuCeB8x3snAti19o9H1LGwjp2I3lB7mkkRmQlggr18CoDd7cd7AhhqDWUNAOghIt3VmpO7oD/a6/ALHlPVVhGZAiAD4HHHtgcDeBjAKgA3iMgj9vOC+QA2q/GzEXU4DOxEtNrx2HQ8N9F+jTAA7KSqK322sxJAF7dtq6opIq3a3qjHBJBV1Zxd3D4a1qRLJwHYw16ni71NIgqBRfFEFMQEWEEXACAiw13WmQ5gkzAbtef17qmqjwL4Laz5vAuGoLxon4gqYGAnoiB+DWCE3cDtXQC/KF1BVd8D0LMwBXBA3QE8LCKTATwP4GTHa7sAeKqGNBN1SOzuRkSREZGTASxXVbfGdWG2szWA36nqMdGkjKjjYI6diKJ0LYrr7KvVB8BZEWyHqMNhjp2IiKiJMMdORETURBjYiYiImggDOxERURNhYCciImoiDOxERERN5P8BedrBTXLHplYAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 576x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"N = 100000\n",
"dt = 3/N\n",
"t = np.linspace(0,3,N) #redefine required terms\n",
"sample = int(1/dt) #define sample time period, assuring it's an integer for funtions below\n",
"\n",
"signal = np.array([frequencies[0], frequencies[1], frequencies[2], frequencies[3], frequencies[4], frequencies[5],\n",
" frequencies[6], frequencies[7], frequencies[8], frequencies[9], frequencies[10], frequencies[11],\n",
" frequencies[12], frequencies[13], frequencies[14], frequencies[15], frequencies[16], frequencies[17]])\n",
"\n",
"#define signal using all the natural frequencies calculated above\n",
"\n",
"out_file = np.sin(2*np.pi*signal[0]*t)\n",
"\n",
"for i in range(1, len(signal)):\n",
" out_file += np.sin(2*np.pi*signal[i]*t)\n",
"\n",
"Audio(data = out_file,rate = sample) #use IPython.display function\n",
"\n",
"plt.figure(figsize=(8,4))\n",
"\n",
"plt.plot(np.linspace(0,len(out_file), len(out_file))*dt*1000, out_file, color='salmon') #plot using my favourite python colour!\n",
"\n",
"plt.title('Audio Signal from 18 Frequencies')\n",
"plt.xlabel('Time (ms)')\n",
"plt.ylabel('Signal (a.u.)');"
]
}
],
"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
}