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{
"cells": [
{
"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": 186,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"g=9.81\n",
"\n",
"dE=0.401e-3\n",
"tE=7.28*g\n",
"dB=0.708e-3\n",
"tB=7.22*g\n",
"dG=1.140e-3\n",
"tG=7.32*g\n",
"dD=2.333e-3\n",
"tD=8.41*g\n",
"dA=4.466e-3\n",
"tA=9.03*g\n",
"dE2=6.790e-3\n",
"tE2=7.71*g\n",
"\n",
"h=.004 #m\n",
"E=10e9\n",
"I=(.04*.02**3)/12\n",
"L=.64 #m"
]
},
{
"cell_type": "code",
"execution_count": 187,
"metadata": {},
"outputs": [],
"source": [
"M=(tE+tB+tG+tD+tA+tE2)*h\n",
"x = np.linspace(0,L,100)\n",
"w = (M*L**2/(2*E*I))*(x/L)**2"
]
},
{
"cell_type": "code",
"execution_count": 188,
"metadata": {},
"outputs": [],
"source": [
"N=9\n",
"hp=L/(N+1)\n",
"\n",
"xnum = np.arange(0,L+hp/2,hp)\n",
"\n",
"A=np.diag(np.ones(N)*6)\\\n",
"+np.diag(np.ones(N-1)*-4,-1)\\\n",
"+np.diag(np.ones(N-1)*-4,1)\\\n",
"+np.diag(np.ones(N-2),-2)\\\n",
"+np.diag(np.ones(N-2),2)\n",
"A[0,0] += 1\n",
"A[-2,-1] = -2\n",
"A[-1,-2] = -4\n",
"A[-1,-3] = 2\n",
"A[-2,-2] -= 1\n",
"A[-1,-1] = 2\n",
"b=-np.zeros(N)\n",
"b[N-2]=-hp**2*M/(E*I)\n",
"b[N-1]=2*hp**2*M/(E*I)\n",
"w1 = np.linalg.solve(A,b)"
]
},
{
"cell_type": "code",
"execution_count": 189,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The finite difference solution converges to 1.1465573898240995 mm\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"plt.plot(x,w,label='Analytical Sol')\n",
"plt.plot(xnum[:-1],np.block([0,w1]),'*',label='Numerical Sol')\n",
"plt.ylabel('Delfection [m]')\n",
"plt.xlabel('Length of Beam [m]')\n",
"plt.title('Deflection along Beam (10 steps)')\n",
"plt.legend()\n",
"print('The finite difference solution converges to',w1[-1]*1000,'mm')"
]
},
{
"cell_type": "code",
"execution_count": 190,
"metadata": {},
"outputs": [],
"source": [
"N2=1000\n",
"hp2=L/(N2+1)\n",
"\n",
"xnum2 = np.arange(0,L+hp2/2,hp2)\n",
"\n",
"A=np.diag(np.ones(N2)*6)\\\n",
"+np.diag(np.ones(N2-1)*-4,-1)\\\n",
"+np.diag(np.ones(N2-1)*-4,1)\\\n",
"+np.diag(np.ones(N2-2),-2)\\\n",
"+np.diag(np.ones(N2-2),2)\n",
"A[0,0] += 1\n",
"A[-2,-1] = -2\n",
"A[-1,-2] = -4\n",
"A[-1,-3] = 2\n",
"A[-2,-2] -= 1\n",
"A[-1,-1] = 2\n",
"b=-np.zeros(N2)\n",
"b[N2-2]=-hp2**2*M/(E*I)\n",
"b[N2-1]=2*hp2**2*M/(E*I)\n",
"w2 = np.linalg.solve(A,b)"
]
},
{
"cell_type": "code",
"execution_count": 191,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The finite difference solution converges to 1.4126762098710648 mm\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(x,w,label='Analytical Sol')\n",
"plt.plot(xnum2[:-1],np.block([0,w2]),'*',label='Numerical Sol')\n",
"plt.ylabel('Delfection [m]')\n",
"plt.xlabel('Length of Beam [m]')\n",
"plt.title('Deflection along Beam (1000 steps)')\n",
"plt.legend()\n",
"print('The finite difference solution converges to',w2[-1]*1000,'mm')"
]
},
{
"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. \n",
"\n",
"__A: 45 nodes needed to converge.__"
]
},
{
"cell_type": "code",
"execution_count": 216,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"First, Second, and Third Natural frequencies of 6-element string (Hz)\n",
"[194.43708661 379.1242858 544.80061022]\n",
"First, Second, and Third Natural frequencies of 30-element string (Hz)\n",
"[195.99464595 391.48617646 585.97276757]\n",
"First, Second, and Third Natural frequencies of 45-element string (Hz)\n",
"[196.04043699 391.85229959 587.20727994]\n",
"First, Second, and Third Natural frequencies of 60-element string (Hz)\n",
"[196.05687232 391.9837462 587.65070938]\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from scipy import linalg\n",
"\n",
"L=.64\n",
"mu=1.14e-3\n",
"T=71.81\n",
"\n",
"\n",
"N1=6\n",
"dx1=L/(N1+1)\n",
"N2=30\n",
"dx2=L/(N2+1)\n",
"N3=45\n",
"dx3=L/(N3+1)\n",
"N4=60\n",
"dx4=L/(N4+1)\n",
"\n",
"k1 = T/dx1**2/mu\n",
"k2 = T/dx2**2/mu\n",
"k3 = T/dx3**2/mu\n",
"k4 = T/dx4**2/mu\n",
"\n",
"A1 = k1*(np.diag(np.ones(N1)*2)\\\n",
" -np.diag(np.ones(N1-1),-1)\\\n",
" -np.diag(np.ones(N1-1),1))\n",
"A2 = k2*(np.diag(np.ones(N2)*2)\\\n",
" -np.diag(np.ones(N2-1),-1)\\\n",
" -np.diag(np.ones(N2-1),1))\n",
"A3 = k3*(np.diag(np.ones(N3)*2)\\\n",
" -np.diag(np.ones(N3-1),-1)\\\n",
" -np.diag(np.ones(N3-1),1))\n",
"A4 = k4*(np.diag(np.ones(N4)*2)\\\n",
" -np.diag(np.ones(N4-1),-1)\\\n",
" -np.diag(np.ones(N4-1),1))\n",
"\n",
"e1,v1=linalg.eig(A1)\n",
"isort1 = np.argsort(e1.real)\n",
"e1=e1.real[isort1]\n",
"v1=v1.real[:,isort1]\n",
"\n",
"e2,v2=linalg.eig(A2)\n",
"isort2 = np.argsort(e2.real)\n",
"e2=e2.real[isort2]\n",
"v2=v2.real[:,isort2]\n",
"\n",
"e3,v3=linalg.eig(A3)\n",
"isort3 = np.argsort(e3.real)\n",
"e3=e3.real[isort3]\n",
"v3=v3.real[:,isort3]\n",
"\n",
"e4,v4=linalg.eig(A4)\n",
"isort4 = np.argsort(e4.real)\n",
"e4=e4.real[isort4]\n",
"v4=v4.real[:,isort4]\n",
"\n",
"x1=np.linspace(0,L,N1+2)\n",
"plt.plot(x1[1:-1],-v1[:,0]/np.max(-v1[:,0]),'--',label='6 nodes')\n",
"x2=np.linspace(0,L,N2+2)\n",
"plt.plot(x2[1:-1],-v2[:,0]/np.max(-v2[:,0]),'*',label='30 nodes')\n",
"x3=np.linspace(0,L,N3+2)\n",
"plt.plot(x3[1:-1],v3[:,0]/np.max(v3[:,0]),'ro',label='45 nodes')\n",
"x4=np.linspace(0,L,N4+2)\n",
"plt.plot(x4[1:-1],-v4[:,0]/np.max(-v4[:,0]),'s',label='60 nodes')\n",
"plt.legend()\n",
"plt.title('1st mode')\n",
"\n",
"print('First, Second, and Third Natural frequencies of {}-element string (Hz)'.format(N1))\n",
"print(e1.real[:3]**0.5/2/np.pi)\n",
"print('First, Second, and Third Natural frequencies of {}-element string (Hz)'.format(N2))\n",
"print(e2.real[:3]**0.5/2/np.pi)\n",
"print('First, Second, and Third Natural frequencies of {}-element string (Hz)'.format(N3))\n",
"print(e3.real[:3]**0.5/2/np.pi)\n",
"print('First, Second, and Third Natural frequencies of {}-element string (Hz)'.format(N4))\n",
"print(e4.real[:3]**0.5/2/np.pi)\n",
"\n",
"eG=e3"
]
},
{
"cell_type": "code",
"execution_count": 193,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, '2nd mode')"
]
},
"execution_count": 193,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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ee+5h69atdOzYMaj7NQmiR+cWTz9wxZijFmsljP79o12DmJGcLYIuvSGtC9QdgtR053taV+jSKyQv361bNwoLC3nppZcYOXIkvXr1oqqqiuzsbKqqqujZs6fP67zTU7dr1w6Px9Pm9NTgpKh+6qmnOOGEE446PmzYMMaPH88LL7zA2WefzUMPPdS4v4FJHs1mCP3fAL9lj+vQnawuaX7Px7X586Gtaa0TVAKG+QAd2AVjZsK1/3S+7w+uD3T37t2Nu4F9+eWX/POf/2To0KEAXHjhhSxevBiAxYsXM2XKlIBfd+jQoVRUVLB582YAHnnkESZOnMjQoUP56KOP+PDDDwF47LHHGq85++yzuf/++xuDyDvvvAM4u6gNGjSIm266iQsvvJC1a9cGdc8mPrXU7bFu5nrW3f4Ff9h6HcWj/85rl78awZpFmKWYaBSqHcrOARbg7DL2kKoWNzl/K9DwU08FhgFZqvqZiFQA+4A6wOMrM15YTPOaGXD+r4J+uaqqKqZPn05dXR319fVceumljdM5586dy6WXXsrDDz9M//79eeKJJwJ+3fT0dBYtWsQll1yCx+Nh7NixzJ49m7S0NEpKSjjvvPPo0aMHEyZMaOyKuv3227n55pvJz89HVcnNzeX555+nrKyMRx99lPbt29O7d2/uuOOOoO/bJJZDT88h7aL7+Fq0K2IiKug01CLSDvgvMAlnM/pVwOWq+p6f8hcAt6jqGe7zCqBAVT8N9D0tDXX42M8x8bWUkO3XW3rTdUYZ4wa2sPgqgfhbSJeo+YfCmYZ6HLBZVbe4b/Q4MAXwGQiAy4HH/JwzxoRLABvN/7/jb+epPl0jWKno8vVh3xAcmgbMTDpRPn1lhGoWWaEYI+gLbPd6Xukea0ZEMoBzgKe8DivwdxF5S0Rm+XsTEZklIqtFZPXu3btDUG1jkkhpqbNYauvWFov98aoCOqUl5xySBv7GUKo5kLCLzUIRCHxNXfHX33QB8LqqfuZ17FRVPQmYDNwgIqf5ulBVS1S1QFULsrLif06zMRE1b56Thx/I3FPrs0jX9sfTr3uGz3PGdcNV0a5BWIQi9FcC/bye5wA7/JSdRpNuIVXd4X7fJSLP4HQ1rQhBvYxJeo194E12GMvcU0v5nE2oCHc+s5av9uzMlafkRq2ecWNv/G3tG4hQBIJVwGARGQh8jPNh/82mhUTkOGAicIXXsU5Aiqrucx9/HfhZCOpkjKGFbo7j2gMg/fvz0ykBbEFpHAm6CC3oQKCqHhG5EfgbzvTRhaq6QURmu+cfdIteDPxdVb33vusFPOMujEoF/qKqLwVbJ2NM62rap/H5D24nO9oViSfz50e7BmERkgVlqrpMVYeo6ldUdb577EGvIICq/klVpzW5bouqnuh+jWi4Np7V1dUxevToo1JC33nnnfTt25dRo0YxatQoli1bFvL3tTTUpq2KL/4uHa66ovWCScZfcrpMOiXsIrTknR7QMJVu2zanuTd/fkh+yQsWLGDYsGHs3bv3qOO33HIL3//+94N+fWNC5bL75pLZOUHTRwTB3/qBwrJCn2swEmHNQXKmmPCeShfCPOSVlZW88MILXHvttW2+1tJQm5Db90mLp4dlJ896gVDwO96SAJlKkzMQeE2la3TwYKt52Vtz8803c++995KS0vzH+tvf/pb8/HyuvvpqvzuUvfPOO9x333289957bNmyhddff52amhpmzJhBWVkZ69atw+Px8MADD1BTU8N1113Hc889x7/+9S8++eTIf/qGNNSrVq3ilVde4dZbb+XAgQONaajXrFnD6tWrycnJCep+TYx79V4y/aQaj+UdxkzkJWcg2LatbccD8Pzzz9OzZ0/GjBnT7Nz111/Phx9+yJo1a8jOzuZ73/uez9ewNNQmJC7pCt1S4IJfU/7djaxbupl1H21j3fadvH3Fu7x75dq478owoZWcYwT9+/teYRnE1LDXX3+dpUuXsmzZMmpqati7dy9XXHEFjz76KL16HUlvfd111/kd1LU01CYYjWsGzh8AXv/EMvfUUvJGFzLve4rMdsn5t1/YlZbG9UBycv6rmD8fMpqsoMzICGpq2N13301lZSUVFRU8/vjjnHHGGTz66KOAk5m0wTPPPMPIkYHP27Y01CZQLa0Z6Pvie3zZoUeEa5REguxWjrbkDARFRVBSAgMGgIjzvaQkbBH9Bz/4AXl5eeTn5/PKK6/w61//OuBrvdNQ5+XlkZKSwuzZs0lPT29MQz1hwgQGDDiyucjtt99ObW0t+fn5jBw5kttvvx2AsrIyRo4cyahRo9i4cSNXXZWYy+VNcxl7DpJzvKWPCIbfaaV7aoPqVo4FQaehjgZLQx0+9nOMXy2ll173k31QURG5yiSq3Fzf3coDBsTFzzecaaiNMbEuQVfERtz8+c5Uc3fWYeGCExrTdeAViONtbUFydg0Zk2zieCAzpjTpVm4MAk3E29oCCwTGJAi/fdi2ZiC0ioqcbqD6+mjXJGSsa8iYBPHSN5Zz2R/eYPOu/Tz3nQkMyuoc7SqZOGGBwJg45G+v3fqOnblv2rMWBEybWNeQMXHIXx90Sup+Jg3v5fOcMf5YIAihL774ojFp3LBhw3jjjTcA+Oyzz5g0aRKDBw9m0qRJfnMNBcPSUBsTeS2uLcjNjZs9jpOya8hfszrYKV9z5szhnHPO4cknn+Tw4cMcdKeYFRcXc+aZZzJ37lyKi4spLi7mnnvuOeb3MUkuTj5cksFRnxcNWY29E1rOmuV8j/FZWyFpEYjIOSKySUQ2i8hcH+cLRWSPiKxxv+4I9NpwCEc62b1797JixQquueYaADp06EC3bt0AWLJkCdOnTwecpHHPPvtss+stDbUJWJynM0hYblbjwgUnkPenkc7X7weR5ykmb3EehWWF0a6hX0EHAhFpB/wOmAwMBy4XkeE+iv5LVUe5Xz9r47Uxb8uWLWRlZTFz5kxGjx7Ntddey4EDzq6cO3fuJDvb2RAwOzubXbt2+XwNS0NtAhLn6QwSlvt7ice1BaFoEYwDNrvbTh4GHgemRODamOLxeHj77be5/vrreeedd+jUqRPFxcVteg1LQ20C0qOz0wftg60ZiKI43tg+FGMEfYHtXs8rgfE+yp0iIu8CO4Dvq+qGNlyLiMwCZgH0j8EfeE5ODjk5OYwf71R/6tSpjYGgV69eVFVVkZ2dTVVVFT179vT5GpaG2rTo5z3Bcwj+p5by728C71iQkeGseL0stvuiE1pD+ok4FIoWga9Po6afXm8DA1T1ROB+oKGTPJBrnYOqJapaoKoFWVlZx1zZcOnduzf9+vVj06ZNgNOvP3y408t14YUXsnjxYgAWL17MlCmBN3osDbVpNGctNUO/wZcjO8MF6ehxKc7/oH45Yc2eawLUkH4iDoWiRVAJ9PN6noPzV38jVd3r9XiZiPxeRHoEcm04ZKZn+p01FIz777+foqIiDh8+zKBBg1i0aBEAc+fO5dJLL+Xhhx+mf//+PPHEEwG/pncaao/Hw9ixY5k9ezZpaWmNaah79OjBhAkTWL9+PeCkob755pvJz89HVcnNzeX555+nrKyMRx99lPbt29O7d2/uuOOOVt7dxIJms9wG9YZBkHleHeU9z4HzfxW9ypmjFRXB4rZ1CceCoNNQi0gq8F/gTOBjYBXwTbfrp6FMb2CnqqqIjAOeBAYA7Vq71hdLQx0+9nOMPS2ml07Lh2k2nTSWhGt6eiiELQ21qnpE5Ebgbzgf7AtVdYOIzHbPPwhMBa4XEQ/wJTBNnQjk89pg62RM0rAgEHOi/WF/LEKyoExVlwHLmhx70Ovxb4HfBnqtMcaYyEmolcWq6ncmjWldPO5WZ0w8iOXuIkigXEPp6elUV1fbh9kxUlWqq6tJT0+PdlVMg9JSDvXt13o5E/PCkc0glBKmRZCTk0NlZSW7d++OdlXiVnp6uq02jhVu3pq0gwfJ3NPJ52pVWzxmQiVhAkH79u0ZOHBgtKthTGi4eWsAyudsOnI8TjZJN/ElYbqGjEkk6i+fkOUZMmGQMC0CY+LdUQOKi0Y0Hs/cU3ukVRCD6VVM/LMWgTExwu+AYsP4QEaGk8/GxJ1MOrXpeKRZi8CYeDBggBMELJ9QXCqfvtKZADBvntO9179/TP0+LRAYEw9sgDj+FRXFzAd/U9Y1ZIwxSc5aBMYYEwWxtNrYWgTGxIju+N7i0BaOJaZYWm1sLQJjos3deezVpsdT0+DHvve3NiaUrEVgTDSVlkJJGvrTvdTftx/WHYbUjpB3CcxZF+3amWgpjWx6cWsRGBMtbj4hDh5EANlTjz5XgyAwqit06RXtGppoadj7OEKzjEISCETkHGABzuYyD6lqcZPzRcBt7tP9wPWq+q57rgLYB9QBHl+75xiTaArLCqn2VMPvBx11PHNPLeU/3wGX7IxSzUxMOHjQWXMQL4FARNoBvwMm4exBvEpElqrqe17FPgImqurnIjIZKAHGe50/XVU/DbYuxsSLFlcRf7rfdh5LAn73Tt9T6zyIYF6pULQIxgGbVXULgIg8DkwBGgOBqv7bq/xKnE3qjTG+WD6hpNA4RTQ3F7ZubV4ggv8OQjFY3BfY7vW80j3mzzXAi17PFfi7iLwlIrP8XSQis0RktYistj0HTEKzfELJZf58J4+UtwjnlQpFIPC1N6TPbcJE5HScQHCb1+FTVfUkYDJwg4ic5utaVS1R1QJVLcjKygq2zsbErhhNQ2DCpKgISkqcfFIizveSkoj+OwhF11Al4L2fXg6wo2khEckHHgImq2pjx5iq7nC/7xKRZ3C6mlaEoF7GGBMf3DxEjauNPcWw+Micm3CvNg5Fi2AVMFhEBopIB2AasNS7gIj0B54GrlTV/3od7yQiXRoeA18H1oegTsbEtI4p3Xwet1XEyS1aq42DbhGoqkdEbgT+hjN9dKGqbhCR2e75B4E7gEzg9yICR6aJ9gKecY+lAn9R1ZeCrZMxsWxfTS2HP7qdgn7dWDRzXLSrY+LFz3uGbaV5SNYRqOoyYFmTYw96Pb4WuNbHdVuAE0NRB2Pixb8++JQ9X9Zyy6Qh0a6KiSdhXGluK4uNibBz87JZcevp9Oue0XphYxqEcaW5BQJjwiyW0g0b44slnTMmzGIp3bCJbf4mC4R7EoG1CIwxJkb4bCGWlsJt8+DylLDtdWyBwJhwinA6YZNgvDLUAk4qijBkJrWuIWPCad68aNfAxLN5844EgQYNmUlDyFoExoTTtm3AiGjXwsQrNwNp4YITnMy03hbnhWzCgbUIjAmnHp2PpBVuwlYRm1a5GUibBQFXqCYcWIvAmHBw9yHmf2op//4m8I4FGRlOUrHLLLmcacX8+UfGBMLIWgTGhMOctTDyEg7nd4EL0tHjUpw8vf1yIp5Z0sSxhsykYWaBwJhw6NKbfXQktf4wtfmdkVu6wtJbYNt2CwKmbSLw78W6howJoWariAc5GdozpQPl+20fYhObrEVgTAj5XUWsh20fYnPMwr3i2FoExhgT48Kdk8paBMYYk+QsEBhjTJILSSAQkXNEZJOIbBaRuT7Oi4j8xj2/VkROCvRaY+JCaSnk5ka7FsYck6ADgYi0A34HTAaGA5eLyPAmxSYDg92vWcADbbjWmNjWkBhs61ZbRWziUigGi8cBm91tJxGRx4EpwHteZaYAf1ZVBVaKSDcRyQZyA7jWmNjmlRisfM6mI8cHDICKiujUyZg2CEXXUF9gu9fzSvdYIGUCuRYAEZklIqtFZPXu3buDrrQxIeMmBgv4uDExJhSBQHwc0wDLBHKtc1C1RFULVLUgKyurjVU0JozcxGABHzcmxoSia6gS6Of1PAfYEWCZDgFca0xMalxF/NMuwMjG45l7ain/4XYnYZgxcSAULYJVwGARGSgiHYBpwNImZZYCV7mzh04G9qhqVYDXGhOT/K4iPq69JZYzcSXoFoGqekTkRuBvQDtgoapuEJHZ7vkHgWXAucBm4CAws6Vrg62TMVFnQcDEkZCkmFDVZTgf9t7HHvR6rMANgV5rjDEmcmxlsTHGJLmkSDrXLDWwK1T7fZoktO+TaNfAmJBJihaB30G9EO33aZKPvnoPmZ46n+dsFbGJN0nRIjAmZNy9iAUo9z6ems8bJSAAABSMSURBVAY/3hWdOhkTpKRoERgTMu5exKR2dJ6ndoS8S2DOuujWy5ggWCAotV2jTBssXY5ndhl6+070vv3wzl5I6wpdekW7ZsYcM+samjXL+W7zvk0Ljppw8MvcxuOZezyUv7QSzo9OvYwJhaRoEfjd73NPrZM1ct68CNfIxBv/q4hT4XnLimLiW1K0CBqniKakgPrIaWdZIk0w7N+PiXNJ0SJoZFkiTTjYvx8T55IrEMyfDxkZRx/LyLAskSY49u/HxLmk6Bpq1DAgPG8ehd9Nd7JEAniKYXExYKuNzTGwiQYmziVXiwCc/7QVFUeCQBO22tg0dchTRweO83nOVhGbRJBcLQJjjkHZqu1Uv/9DHrlmHP8z2HbHM4kn+VoExrRBTW0dv315M+NyuzPhqz2iXR1jwsICgTEteHTlVnbtO8R3vz4EEV9bbBsT/4LqGhKR7kAZkAtUAJeq6udNyvQD/gz0BuqBElVd4J67E7gO2O0W/5G7UY0xUeErZXmXYTB3VSblg8qjUyljwizYFsFcYLmqDgaWu8+b8gDfU9VhwMnADSIy3Ov8r1V1lPsVsSDgd7WxDf4lNUtZbpJRsIPFU4BC9/FinMy8t3kXcDepr3If7xOR94G+wHtBvndQfE4RLS2F2+bB5SnOIqH5821qoDEm4QXbIujlftA3fOD3bKmwiOQCo4H/eB2+UUTWishCETm+hWtnichqEVm9e/duf8WOXWmpk4Bu61YnDcXWrc5zy05qjElwrQYCEfmniKz38TWlLW8kIp2Bp4CbVXWve/gB4CvAKJxWwy/9Xa+qJapaoKoFWVlhmMI3b56TgM6bJaQzxiSBVruGVPUsf+dEZKeIZKtqlYhkAz63aBKR9jhBoFRVn/Z67Z1eZf4IPN+WyofUtm0ULjjB50KzzLJCW21sjElYwXYNLQWmu4+nA0uaFhBnzt3DwPuq+qsm57K9nl4MrA+yPseuf39bbWzI3OtnH+J99RGuiTGRE+xgcTHwVxG5BtgGXAIgIn2Ah1T1XOBU4EpgnYisca9rmCZ6r4iMAhRn+um3gqzPsZs/38k5ZJKTuxdx+brD8FwN1Hqdy8iAkpKoVc2YcAsqEKhqNXCmj+M7gHPdx68BPlfiqOqVwbx/SBUVNSaeM0lozlr424/xtHvO+U+x/DDsrYecHLi72GaPmYRmuYaMAejSG9K6kFp/GEZ3hfzDMGYmnP+r1q81Js5ZIDBJy9cqYnJzyOxwHOVdxsH+nb4vNCbBWCDwkpme6XNg2FYbJya/q4gP77GWgEkqFgi82BRRY0wysuyjxhiT5CwQBGrfJ7BoMuyzfmNjTGKxrqEANA4qpgBPH1lobfsbxzHLIWVMI2sRtObnPS01caJxEwxm7qn1edomB5hkYy2C1sxZC09PinYtTCi5CQbL52w6+viAAVBREZUqGRNN1iJoTZfe0a6BCbVt29p23JgEZy0CkxSOWjy2aETj8cw9tUdaBv37R6FmxkSftQhMUvA7ztOQcTYjw0k8aEwSskAQANvfOMENGOBkF7XEciZJWddQAGyKaIKzAWKT5KxFYIwxSS6oFoGIdAfKgFycjWUuVdXPfZSrAPYBdYBHVQvacn0s8pm5EltkZoyJP8G2COYCy1V1MLDcfe7P6ao6qiEIHMP1McUWmcWJn/eEO48j0+NnC0ob5zEm6DGCKUCh+3gxUA7cFsHrjWmR58Y1vFnybV7c9jod5TCkdoRh58PX50OXXtGunjExIdgWQS9VrQJwv/f0U06Bv4vIWyIy6xiuR0RmichqEVm9e/fuIKttkkJpKfuHFHDKbUtIX1ANGxTqDkFaVwsCxnhptUUgIv8EfC2vndeG9zlVVXeISE/gHyKyUVVXtOF6VLUEKAEoKCjQtlwbcaWlNhUxio4av/m/TMDp/snc46F8W67tPGZME60GAlU9y985EdkpItmqWiUi2cAuP6+xw/2+S0SeAcYBK4CAro878+ZZIIgi/4vHUuHJ9+H/VUS2QsbEuGC7hpYC093H04ElTQuISCcR6dLwGPg6sD7Q62OV30Vme2otZ00ss9+NMc0EO1hcDPxVRK4BtgGXAIhIH+AhVT0X6AU8IyIN7/cXVX2ppevjQfll5ZCbC1u3Nj85YECkq2NcXx72PTuokeUTMqaZoAKBqlYDZ/o4vgM41328BTixLdfHjfnzYdYsOHgQgMIFJxzJXbM4r7GYrS2IDFXlB0+tbbmQ5RMyphlbWRyMoiInR82AASByJAg0YWsLIuOBVz/kuXd3tFzIxm6MacYCQbCKipxcNT/rEe2aJLV9NbUser2CC0/sY0kCjWkjSzoXKraTWVR1SW/PkhtOpXunDqS3L492dYyJKxYIQsV2MouKiY8X8tkhy/lkTDCsa8jELU9dvc8gADYuY0xbWCAIoRbXFuTmOiuOTcj8/IX3o10FYxKCdQ2F0FFdEaWlR00tBZznYDNXQuDxN7fx2R8XwdRo18SY+GeBIFzmzYODB49eWwDgKYbFxdaHHYTPDhzmZ8+/x4p/l/LKVJutZUywrGsoXNxUBra2IPS6d+rAI9eMI/NzSx5nTChYIAgXS2UQcgcPe3hlo5OXcMwjQ5Gu7viLD7ZmwJjAWddQuDSknzAhoarc+sRaXlxfxcvfKyR3zlrYPY3y778K3rGgY0f44x/hMhuHMSZQFgjCpWFA2FMc3XokiN++vJnymhvoNHQ/F7zgHjwJ+ONIMvd6KL9pI2R1gV8/YIPxxrSRdQ2Fk30ghcRL6z/hl//4Lymp+32er+6aCs/dAr+5wH7mxhwDaxGEWWZ6ps+BYevDDsyuvTV8969rOLFfN7a0VPD8X0WqSsYkHAsEYeZ3imhpKfTvB9sroV8O3F1sf8360LNrOos6fEDBPf/HqLuOi3Z1jElIFgiioHDxyVRzAO7qBnRzDnqKyVx8P+XTV0a1brGitq6erdUH+Oo/ljL+7rnuwjwLBMaEQ1BjBCLSXUT+ISIfuN+P91HmBBFZ4/W1V0Ruds/dKSIfe507N5j6xItqDrTpeDL66XMbuOD+1/HM/eHRq7ONMSEX7GDxXGC5qg4GlrvPj6Kqm1R1lKqOAsYAB4FnvIr8uuG8qi4Lsj4mATy6ciuPrtzGVV8bQOrHlY3Hbc2AMeERbNfQFKDQfbwYKAdua6H8mcCHqupjo19jYOWWau5cuoHjh/6Cv+zay18WjTjqfOaeWsrnbHJ2hauoiE4ljUkwwbYIeqlqFYD7vWcr5acBjzU5dqOIrBWRhb66lhqIyCwRWS0iq3fv3h1crU1MqtrzJd8ufZv+mRl4ZK/PMtXHtYeMDNt72JgQajUQiMg/RWS9j68pbXkjEekAXAg84XX4AeArwCigCvilv+tVtURVC1S1ICsrqy1vbeJEj85pXFKQw0NXFbRcsKTEZlgZE0Ktdg2p6ln+zonIThHJVtUqEckGdrXwUpOBt1W1MVOY92MR+SPwfGDVjm/+1hYA5C3Oa1Y20bOU1tcre2tq6ZbRgR9OHtb6BRYEjAmpYMcIlgLTgWL3+5IWyl5Ok26hhiDiPr0YWB9kfeKCrw/2pgGgQTJkKb1v+Qc89VYlS248lR739QPPIRhoSfuMiZRgxwiKgUki8gEwyX2OiPQRkcYZQCKS4Z5/usn194rIOhFZC5wO3BJkfRJTAu9s9sLaKn6z/AO+veM/ZI4YAnd8Cr+ri3a1jEkqQbUIVLUaZyZQ0+M7gHO9nh8Ems3xU9Urg3n/pJGgO5tt2LGH21Z9gy7D9lMMFI/pCjizhKRe0RRpdo1NFTUm9GxlcTw4eNDZ8SyBAsGn+w8x689vIdm+E8lpirDux9XwwDTYvxOmJW6ryJhos0AQL7Zu5eBnH5PRvW+0axISqSnC0N5deLOlQh9/YsnkjIkACwQxwt9MIqlX8v400nny3DlHlY/H2USqSl290i2jAw/PGEve4hYK2y5vxkSE7UcQI8ovK2fd9HWsS53Lum9vYd2M9aybsd5nPzk4s4n+8OqH7DnoO+1CrHpk5VYu/+NK9tYEUG9bNGZMRFiLINY0jAPMmwfbtrVY9O4XN9IuRbj2fwZFoGLBO/Uvp7G39nPoCKeWBXBBAo2JGBPLrEUQi4qKnDw69fUtFvvvo9fzzQ9fA+CJ1duZvvBNXv3vblQ1ApVsm63VB5wgECCbHWRM5FiLII51+Hg7HW64Htq3Q084jfeq9jJ94Zt8JasTM08dyDdO6ktGh+j/ivcf8nDdn1dDd/9l1k1fF7kKGWOOEv1PCXPMGgeRPcWwoZjMr2byoyGPsvC1Cn787HpeWFvFY7NOjm4lger9h/DUx14rxRjjsEAQ41rKS9RUdU01F4/O4aJRfXlr6+fU1jkfvnu+rOUnS9ZzxckDGDPgeER8D0CHy4DMTiz/8lLy6RXR9zXGBMYCQYw7aopobi5s3XqkJeCHiFCQe6QfZmPVXl7euItn1+wgP+c4Zp6ay3l5feiQGr4hosKywqMDWD8LAsbEKgsE8WT+/CPpJvzwl7105Y/O5Om3P2bR6x9xS9m73L1sI/+4ZSLHZbQPfT1LS6n2BJ4sL5NOoa+DMSZgFgjiScN0Sk9xwJc0/FWe0SGVK04ewDfH9edfmz/lzY+qG4NA6X+2MqpfN0b0CcHm8KWl6HWz4AH/U1rX/bgaPq6CzAy4z/YWMCbaLBDEm6IiWBx4IGgqJUWYOCSLiUOczX0OHPJQ/OJG9tV4OHlQd2aeOpCzhvWinZ+FbL406wZqIQgAsH3HsVTdGBMmFgjiUFsGkKHlzW46paXy2g/OoGz1Nhb/eyvfeuQt+nXvyC8vGcW4gS3M9/SSDHsmGJPILBDEobZsbONL0w/u4zLaM+u0r3D1qQP5x3s7WfTvCvoe3xGATZ/so0NqCgN7OP34zf76N8bEPQsEScpfK2FyXjaT87Ibjxe/+D7l/93NGSf05OoJA4MOArZi2JjYE1QgEJFLgDuBYcA4VV3tp9w5wAKgHfCQqjbsZNYdKANygQrgUlUNPA+BadTW7qKmqmuqmwUHUdAU6DwU3gTefL3tr7vuJ/uc2U42IGxMzAq2RbAe+AbwB38FRKQd8DucrSorgVUislRV3wPmAstVtVhE5rrPbwuyTkkp2O4iXzQU684qKkLwIsaYcApqRZGqvq+qm1opNg7YrKpbVPUw8DgwxT03BWjISL8YuCiY+pjYYt1AxsSHSIwR9AW2ez2vBMa7j3upahWAqlaJSE9/LyIis4BZAP1tw5KABNtd1FbrUudaF5AxcajVQCAi/wR6+zg1T1WXBPAevjoY2pyBTFVLgBKAgoICy2AWgMbuotLSxv0N8haNCMt7ZdLJgoAxcarVQKCqZwX5HpVAP6/nOUDDiqKdIpLttgaygV1Bvpfxpaio8UM6M0TTPy1ttDGJIxJdQ6uAwSIyEPgYmAZ80z23FJgOFLvfA2lhmCA0G1QuLaXw819Q3aX5cJHgu+lmff/GJBYJZjcrEbkYuB/IAr4A1qjq2SLSB2ea6LluuXOB+3Cmjy5U1fnu8Uzgr0B/YBtwiap+1tr7FhQU6OrVPmeqGmOM8UNE3lLVgmbHY3Fbw9ZYIDDGmLbzFwhsz2JjjElyFgiMMSbJWSAwxpgkZ4HAGGOSXFwOFovIbmBrAEV7AJ+GuTrhZvcQOxLhPuweYkO07mGAqmY1PRiXgSBQIrLa1wh5PLF7iB2JcB92D7Eh1u7BuoaMMSbJWSAwxpgkl+iBoCTaFQgBu4fYkQj3YfcQG2LqHhJ6jMAYY0zrEr1FYIwxphUWCIwxJsklRCAQkXNEZJOIbHb3Pm56XkTkN+75tSJyUjTq2ZIA7mGoiLwhIodE5PvRqGNrAriHIvfnv1ZE/i0iJ0ajni0J4B6muPVfIyKrRWRCNOrZktbuwavcWBGpE5GpkaxfIAL4PRSKyB7397BGRO6IRj1bE8jvwr2XNSKyQURejXQdAVDVuP7CSW39ITAI6AC8CwxvUuZc4EWcFPsnA/+Jdr2P4R56AmOB+cD3o13nY7yHrwHHu48nx+nvoTNHxtbygY3Rrndb78Gr3MvAMmBqtOt9DL+HQuD5aNc1BPfRDXgP6O8+7xmNuiZCi2AcsFlVt6jqYeBxYEqTMlOAP6tjJdDN3REtVrR6D6q6S1VXAbXRqGAAArmHf6vq5+7TlTi71cWSQO5hv7r/Y4FOHMO2q2EWyP8HgO8ATxGbuwIGeg+xLpD7+CbwtKpuA+f/eYTrCCRG11BfYLvX80r3WFvLRFOs1y8Qbb2Ha3BaabEkoHsQkYtFZCPwAnB1hOoWqFbvQUT6AhcDD0awXm0R6L+lU0TkXRF5UUTCsxl3cAK5jyHA8SJSLiJvichVEaudl0hsVRlu4uNY07/SAikTTbFev0AEfA8icjpOIIi1/vWA7kFVnwGeEZHTgLuAYPf1DqVA7uE+4DZVrRPxVTzqArmHt3Hy5ux3d0B8Fhgc9pq1TSD3kQqMAc4EOgJviMhKVf1vuCvXtBLxrhLo5/U8B9hxDGWiKdbrF4iA7kFE8oGHgMmqWh2hugWqTb8HVV0hIl8RkR6qGitJ0AK5hwLgcTcI9ADOFRGPqj4bmSq2qtV7UNW9Xo+XicjvY+z3AIF/Nn2qqgeAAyKyAjgRiGggiPqASggGZFKBLcBAjgzIjGhS5jyOHix+M9r1bus9eJW9k9gcLA7k99Af2Ax8Ldr1DeIevsqRweKTgI8bnsfCV1v+Lbnl/0TsDRYH8nvo7fV7GIez53nM/B7acB/DgOVu2QxgPTAy0nWN+xaBqnpE5Ebgbzij9AtVdYOIzHbPP4gzM+JcnA+hg8DMaNXXl0DuQUR6A6uBrkC9iNyMMwNhr98XjqAAfw93AJnA792/Rj0aQxkYA7yH/wWuEpFa4EvgMnX/R8eCAO8hpgV4D1OB60XEg/N7mBZLvwcI7D5U9X0ReQlYC9QDD6nq+kjX1VJMGGNMkkuEWUPGGGOCYIHAGGOSnAUCY4xJchYIjDEmyVkgMMaYJGeBwBhjkpwFAmOMSXL/H2Q9uGGSPxy2AAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(x1[1:-1],v1[:,1]/np.max(-v1[:,1]),'--',label='6 nodes')\n",
"plt.plot(x2[1:-1],-v2[:,1]/np.max(-v2[:,1]),'*',label='30 nodes')\n",
"plt.plot(x3[1:-1],v3[:,1]/np.max(v3[:,1]),'ro',label='45 nodes')\n",
"plt.plot(x4[1:-1],-v4[:,1]/np.max(-v4[:,1]),'s',label='60 nodes')\n",
"plt.legend()\n",
"plt.title('2nd mode')\n"
]
},
{
"cell_type": "code",
"execution_count": 194,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, '3rd mode')"
]
},
"execution_count": 194,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(x1[1:-1],-v1[:,2]/np.max(-v1[:,2]),'--',label='6 nodes')\n",
"plt.plot(x2[1:-1],-v2[:,2]/np.max(-v2[:,2]),'*',label='30 nodes')\n",
"plt.plot(x3[1:-1],v3[:,2]/np.max(v3[:,2]),'ro',label='45 nodes')\n",
"plt.plot(x4[1:-1],-v4[:,2]/np.max(-v4[:,2]),'s',label='60 nodes')\n",
"plt.legend()\n",
"plt.title('3rd mode')"
]
},
{
"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": 220,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of E string (Hz)\n",
"[329.63523775]\n",
"[658.88613556]\n",
"[987.36880161]\n"
]
}
],
"source": [
"\n",
"N3=45\n",
"dx3=L/(N3+1)\n",
"\n",
"k3 = tE/dx3**2/dE\n",
"\n",
"A3 = k3*(np.diag(np.ones(N3)*2)\\\n",
" -np.diag(np.ones(N3-1),-1)\\\n",
" -np.diag(np.ones(N3-1),1))\n",
"\n",
"e3,v3=linalg.eig(A3)\n",
"isort3 = np.argsort(e3.real)\n",
"e3=e3.real[isort3]\n",
"v3=v3.real[:,isort3]\n",
"\n",
"print('Natural frequencies of E string (Hz)'.format(N3))\n",
"print(e3.real[0:1]**0.5/2/np.pi)\n",
"print(e3.real[1:2]**0.5/2/np.pi)\n",
"print(e3.real[2:3]**0.5/2/np.pi)\n",
"eE=e3"
]
},
{
"cell_type": "code",
"execution_count": 209,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of B string (Hz)\n",
"[247.05411832]\n",
"[493.82018258]\n",
"[740.01047461]\n"
]
}
],
"source": [
"k3 = tB/dx3**2/dB\n",
"\n",
"A3 = k3*(np.diag(np.ones(N3)*2)\\\n",
" -np.diag(np.ones(N3-1),-1)\\\n",
" -np.diag(np.ones(N3-1),1))\n",
"\n",
"e3,v3=linalg.eig(A3)\n",
"isort3 = np.argsort(e3.real)\n",
"e3=e3.real[isort3]\n",
"v3=v3.real[:,isort3]\n",
"\n",
"print('Natural frequencies of B string (Hz)'.format(N3))\n",
"print(e3.real[0:1]**0.5/2/np.pi)\n",
"print(e3.real[1:2]**0.5/2/np.pi)\n",
"print(e3.real[2:3]**0.5/2/np.pi)\n",
"eB=e3"
]
},
{
"cell_type": "code",
"execution_count": 210,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of D string (Hz)\n",
"[146.88611909]\n",
"[293.60097554]\n",
"[439.97350639]\n"
]
}
],
"source": [
"k3 = tD/dx3**2/dD\n",
"\n",
"A3 = k3*(np.diag(np.ones(N3)*2)\\\n",
" -np.diag(np.ones(N3-1),-1)\\\n",
" -np.diag(np.ones(N3-1),1))\n",
"\n",
"e3,v3=linalg.eig(A3)\n",
"isort3 = np.argsort(e3.real)\n",
"e3=e3.real[isort3]\n",
"v3=v3.real[:,isort3]\n",
"\n",
"print('Natural frequencies of D string (Hz)'.format(N3))\n",
"print(e3.real[0:1]**0.5/2/np.pi)\n",
"print(e3.real[1:2]**0.5/2/np.pi)\n",
"print(e3.real[2:3]**0.5/2/np.pi)\n",
"eD=e3"
]
},
{
"cell_type": "code",
"execution_count": 211,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of A string (Hz)\n",
"[110.00809489]\n",
"[219.88792527]\n",
"[329.51137616]\n"
]
}
],
"source": [
"k3 = tA/dx3**2/dA\n",
"\n",
"A3 = k3*(np.diag(np.ones(N3)*2)\\\n",
" -np.diag(np.ones(N3-1),-1)\\\n",
" -np.diag(np.ones(N3-1),1))\n",
"\n",
"e3,v3=linalg.eig(A3)\n",
"isort3 = np.argsort(e3.real)\n",
"e3=e3.real[isort3]\n",
"v3=v3.real[:,isort3]\n",
"\n",
"print('Natural frequencies of A string (Hz)'.format(N3))\n",
"print(e3.real[0:1]**0.5/2/np.pi)\n",
"print(e3.real[1:2]**0.5/2/np.pi)\n",
"print(e3.real[2:3]**0.5/2/np.pi)\n",
"eA=e3"
]
},
{
"cell_type": "code",
"execution_count": 212,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of E2 string (Hz)\n",
"[82.43894585]\n",
"[164.78177157]\n",
"[246.93246912]\n"
]
}
],
"source": [
"k3 = tE2/dx3**2/dE2\n",
"\n",
"A3 = k3*(np.diag(np.ones(N3)*2)\\\n",
" -np.diag(np.ones(N3-1),-1)\\\n",
" -np.diag(np.ones(N3-1),1))\n",
"\n",
"e3,v3=linalg.eig(A3)\n",
"isort3 = np.argsort(e3.real)\n",
"e3=e3.real[isort3]\n",
"v3=v3.real[:,isort3]\n",
"\n",
"print('Natural frequencies of E2 string (Hz)'.format(N3))\n",
"print(e3.real[0:1]**0.5/2/np.pi)\n",
"print(e3.real[1:2]**0.5/2/np.pi)\n",
"print(e3.real[2:3]**0.5/2/np.pi)\n",
"eE2=e3"
]
},
{
"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": 217,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
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G6EeTCE3IxskxCMTIgYfthpaFT0PvQhCAjb8+fbe8iDw4O4h78jwnfNW95T79/8ZBKcHVgr5C3gM2gs9CtgH8QTWAdn+QvxO+iT51/hf+Z36X/xh/loA/QEGAzsDdgKqAN79M/rd9SHxTuy156DjU+D83bfcitxi3RnffOFI5DvnEuqT7JHu8e+o8L3wRvBn70buD+3l6+PqFup96QXpj+jy5//miuVs45Dg89yo2N3T1s7uyY7FJ8IrwADA+8FTxiHNVda74fnulf36DIcckSt3OaVFo08ZV9db010sXSVaHVWHTuVGuD56NpcuZCcdIeEbtxeLFDoSkhBcD2EOcQ1mDCgLrQn5BxwGLARDAngA3/5//VX8U/tg+lv5IPiK9nz05vHF7irrNucf4ynfotva2CHXudbT14na1t6b5JvrffPV+ygE/AvXEk4YDhziHbUdlhu4F2kSFAwvBTr+rvf78XntaOrn6PPobeoc7bDwzvQZ+Tf92QDIA+EFGgeDB0MHkQaxBegEeQSdBHwFKweoCdwMnRC0FN8Y2xxpIFQjeCXBJjMn4ib0JZwkEyOUIVIgdh8aH0Mf5B/fIAQiGyPlIykksiNcIhcg5BzdGC8UGA/hCdYEQgBo/Hb5iPej9rH2iffq+Ir6F/w//b39Wv33+435M/YY8oHtxuhH5GPgdd3E24PbyNyM36fj2ujN7hn1UvsLAecFlgnlC7sMHQwtCicHWAMa/8j6vfZD85bw1+4Q7jTuHO+V8FryKPS79dr2W/cl9zf2o/SN8ijwre1a62Xp/Oc95zLnz+f46H3qI+yn7cXuQO/m7pftR+v859Xj/9612TzU1s7CyTXFU8EtvsO7ArrJuO63Q7ecttu17bTWs6+yp7EBsRCxLLKytPS4NL+bxzTS59547Yr9oQ4tIIwxG0I+UWpeL2k+cW92w3hgeJF1vHBcavZiEFsoU6pL6kQjP3A60zYzNGUyLzFRMI4vqy59LeUr1SlPJ2EkJCG0HTAasRZJEwAQ0QyxCYgGPgO5/+X7tvcy82zuiem/5FDgiNy12R/YBNiP2dPcxeFA6P7vofi3AcQKRBO7Gr4g+CQzJ10nhyXnIdMctxYTEGwJQgMM/iT6zvcn9y/4wPqa/mMDtwgmDkYTuRcyG3wdex4wHrMcMRrlFhMT/g7lCvoGYAMnAFH9yPpz+Cz2zfM18U3uC+t356rjz98a3M7YK9Zw1NHTc9Rm1qPZC95q43np5O9R9mX8zwFNBq0J2QvPDKYMigu1CWoH7wSDAlkAl/5J/Wj82vtz+/n6LvrX+L/2xfPZ7wbrceVX3wnZ6NJczczIlcUCxEfEesaPyl3QnNfv3+XoCfLj+ggDIQrrD0MUJBenGPwYahhGF+gVpRTGE4UTAxRLFU4X5xnfHPQf3yJaJSknHyghKCsnSyWlImof1hsoGJoUYRGgDmwMwwqVCb8IEQhXB1oG6gThAioAwfy1+Cj0Te9f6p/lTeGf3b7awtiq12TXyNec2J7ZhtoQ2wPbNtqX2C7WHNObz/fLjsjCxfHDccODxE3H2csO0rXZeuLw65/1B/+tByUPGBVNGa0bQhw6G+AYlhXNEf8NnwoVCLUGugZBCEYLrQ88FagbmiK1KZ4wBDelPFFB6URlR8tIMUm0SHVHlEUrQ01AAz1MOSA1cjA3K2YlAB8SGLkQIgmIATb6ePOj7QPp2+VX5JDkgOYE6tzur/QQ+4MBjge4DJkQ3xJZE/gRzw4WCiUEa/1n9pzvjemq5E7htd/43w/iy+Xg6uvwefcQ/jYEhAmgDUsQZRHnEOgOmAs1Bw0CcPyo9vnwm+ux5k/iet4n20TYu9V302nRjs/wzabM0sujy0rM+s3d0BTVqtqa4cLp7fLN/AYHLxHcGqQjKSsfMVQ1rTcwOPs2RzReMJYrSibTIHwbhBYQEjMO5woSCIsFHwOcANL9nPro9rvyLe5u6cHkduDj3F7aNNme2cLbqN845T/sbvRf/Z4GtA8pGJIfmiUEKrEspS3+LPkq5ickJBUgGxyJGKIVkRNnEhwSjhKKE84UEBYKF3oXLRcFFvQTBRFUDRAJbwSv/wv7tfbX8ofvzOyY6tLoUefo5WjkqeKL4P3dAtus1x/Uj9A4zVjKLMjmxqvGisd8yWXMEtBB1KPY5dy54NnjFOZQ54zn5OaO5dnjH+LH4DXgxOC94k/mjOti8qL6+gMFDkgYQSJxK2MztzknPo1A5kBOPwI8VDeqMXArEiXzHmYZphTWEPwNCAzSCiEKtglLCaEIhAfOBWwDXgC5/Jz4N/S872HrVee947LgP95h3AbbFtpy2fzYnNhC2OzXqNeQ183Xj9gM2nfc+N+s5JnqrfG++YcCsQvPFHAdHiVuKwQwnzIcM30x5i2hKBYiwho1EwEMsQXDAJn9c/xw/YQAhAUcDOUTXxwJJV0t5DQ5OxBAO0OoRGZEmUJ8P1Y7dDYjMagrOSYAIRQcfBc0EyoPTQuHB8wDFgBw/Oz4rPXa8qbwQe/V7oHvVPFK9Ef4Hf2GAjIIwQ3WEhUXMBrrGyQc0hoJGPcT4g4hCRUDIP2d99zyFe9q7OLqaOrQ6trrPO2k7sXvXfA78EPvcu3f6rbnNOSk4FTdjtqS2I7Xmdew2Ljaf9284B/kTuf26czrm+xF7MbqOOjQ5NvgttzH2HbVI9Me0qDSxtST2OndkOQ67In0GP1+BWANbBRlGiQfmyLTJOQl+SVEJfkjSCJZIEYeGxzVGWMXqRSHEd0NjgmKBNH+bfiC8UDq5uK72wnVF88gylHGw8N1wlDCKsPDxNDGA8kPy7HMuc0Nzq7NusxmywLK6siFyDfJXMs9zwfVydxu5sHxaf70C+AZnSebNFhAYEpdUhlYf1ufXKZb4FiqVGxPlEmHQ549Hzg6MwQvfiuSKBsm6yPQIZ0fLB1mGkIXyhMVEEkMkgghBSECuv8B/gH9svz9/L39w/7a/80AcwGoAVoBiQBJ/7n9DPx5+jz5ifiM+GD5Cvt2/XsA3QNKB2kK3QxSDn4OMQ1UCvIFNgBt+frxWuoT46/cr9eB1HnTytR+2H3ehuY38Bb7lgYnEjYdQSfbL682jDtfPjc/Oz6sO9g3FzO+LR0odyL/HNcXDxOnDpQKxgYpA67/SvwB+eH1AvOG8JXuVe3q7G7t6e5W8Zf0ffjI/CYBRQXJCGILywzTDGALdggzBNL+oPj88VDrBOV53//a0NcN1rfVs9bP2MDbMN/D4h3m8ej/6iLsTuyQ6xDqCejF5ZfjzuGx4HngR+El4wPmuekK7qvySPeR+zn/BwLWA5gEWwREA5ABiv+F/dj70Pqu+pz7rv3YAPoE2AkiD4AUkhn7HWwhoyN5JN0j2CGMHi4aBBVbD4EJwANW/nD5K/WQ8ZTuIewU6kXoj+bQ5PPi8ODP3qfcmtrS2H7XydbW1rrXeNn/2ynfvuJ35gXqF+1h76XwuvCP7zPt0Omu5S3hvdzZ2PrVkNT31G/XGNzt4sLrTPYeArgOjRsLKKgz6z12RgVNe1HaU0VU+1JRUKdMYkjiQ3w/dDv3Nxs13zIuMeMv0S7ELY4sBysVKa0m1COcICcdnRknFvASGRC2DdALXQpICWsImweoBmQFqgNhAYT+GvtF9zXzKe9o6zzo6eWm5Jnk0uVC6MbrHPDy9Ob5jv6EAm4FAwcUB5EFiQIu/sf4uvJ27HHmHuHf3ALaudgT2f7aRd6b4pjnyey28e31Cvm/+tr6S/kd9n/xt+sg5SDeIteO0L/KAMaIwnTAzr+KwIvCq8W7yZDOAdTu2UTg9+YI7n31X/22BYIOuRdAIfAqjzTVPXFGDk5WVP5YyVuQXEZb+VfXUiZMQ0SaO6My0SmSIUIaJBRhDwIM8gkDCe4IXwn8CWkKWgqRCegHVQXpAc79RPmc9CvwS+xJ6WXnx+Z+537pouyr8E31Lfrz/kgD5waZCUEL3At9C1EKlAiLBoEEvAJ3AdsA/QDYAVIDPAVVB1YJ8ArdC+EL0AqWCDcF0ACT+8P1se+z6R3kOd9D22PYqtYU1obW0tfB2RHcgd7Y4OTihOSq5VbmmeaS5mTmNeYp5lfmy+Z/517oQen16UDq5+m26IPmO+Pg3pLZi9MgzbvG1MDru3y49baxt+u6usAQybbTUeBn7mj9sgyoG6spNTbVQD1JQk/fUjJUdVP9UC5NcEguQ8Y9hTinM04vhitGKHQl7CKCIA8ebxuIGFEVzBEKDigKSQaTAiv/K/yl+Z33B/bL9MTzx/Kk8TLwTu7m6/folOXj4R7ei9p71z7VIdRh1CvWj9mE3uLkaOy79HP9GwZDDoEVfRv3H9EiCSTBIzciwh/MHMMZFhcqFU0UtRR6Fo8ZzB3pIosoRS6oM0Y4wTvMPTY+6zz0OXk1ty8AKbEhKxrHEtcLmgU7AM77U/i29dXzhvKb8ejwSvCo7/ruQ+6W7Qvtxuzl7IXtuO6B8NXylvWX+J/7bf68AFAC9AKGAvgAVv7A+nH2t/Hp7GjokeS14Rfg3d8W4a/je+cz7Hrx6PYS/I4ABwQ2BvUGNwYUBLwAfvy198ryKe406kDnieUz5UTmqOgt7JLwhfWu+rr/XQRdCJML8w2DD2IQwBDWEOIQIBHAEeYSnxTkFpcZiBx4Hx8iMSRrJZIlfSQbInIenhnTE1QNcwaD/9f4tvJa7enocuXt4j7hNuCc3zDfs97v3bjc99ql2M/VldIlz7PLecitxXrD/cFDwUPB48H6wlHErcXWxprH2MeBx5/GVcXdw4PCpMGhwdjCn8U0yr3QPdmW44XvqfyCCoIYDiaPMnY9S0a1THxQkVELUCZMPUbDPj42NS0uJKMb+RN/DWYIxQSYAsQBIQJ4A5EFNAgyC2MOrhEEFWMYzRtIH9wihyZDKvstkTHbNKk3xDn6Ohs7BzqtNxI0US+cKTYjdxy9FWoP2wleBTACcwArAD8BegOOBhkKsQ3pEF0TuRTBFFgTgRBgDDYHYAFL+231OvAf7HPpceg56cXr7+9z9fT7AwMtCvwQBRfwG3offyH2IfIgnx48GxIXchKoDfgImQStAEb9Yvru98713/P78QTw5O2T6xfph+YG5MHh6t+03kjext484Kfi7eXi6Uvu3/JT91n7rv4bAYAC0AIWAnYAKP5t+5T46/W28y7ydfGX8YTyFPQI9g/40fny+h37D/qZ96rzTe6u5xfg6NeUz5bHaMB7ui62xbNosx21zLg+viTFIM3K1bnej+f577v3sf7OBBwKuw7UEpsWQxr4Hdsh+yVUKtAuRjN/Nz47QT5MQC5Bx0AJPwA8zDegMsEsfCYkIAYaZRR1D1ULDQiRBb0DXwI5AQcAjP6O/Ob5gPZa8ovtO+ik4gfdq9fT0rjOhMtPyRzI18dbyHTJ6Mp5zO/NHs/uz1rQd9Bw0IPQ/dAz0nrUHthW3Ubk8ew5998CiQ/BHP4psjZNQk1MQ1TdWe5cal1uWzlXKFGtSUlBgTjVL7QnfCBuGrAVShIrECkPDA+TD3cQdxFaEvYSLRPzEkoSPhHiD0wOkAy8CtYI1wayBFAClv9n/Kz4WfRu7/zpKOQo3kTYztIezo3KaMjux0fJf8yD0R/YA+DH6O7x8vpPA4kKOBAPFOEVpxWAE6sPhgqGBC3+/Pdy8vrt5epp6ZjpYeuW7u7yC/iF/fEC7gcnDFsPZRE3EuERhhBeDqsLtQi/BQYDugD4/sr9K/0G/Tn9n/0R/m3+nv6Y/mD+DP68/Zz92/2n/icAeAKjBaAJUA6BE/IYVR5XI6cn+yocLeMtRS1PKygoCyRHHzMaKBV8EHYMSgkVB9kFfQXSBZMGcwccCD8IlwfzBToDcP+x+jf1UO9c6cDj4N4W26rYzdeP2OXapN6G4zLpPe869b/6bP/1AikF7wVNBWMDaQCo/HH4GvTz70DsNenw5nzlzuTI5ELlC+bz5s7ne+jp6BbpE+kA6QnpYOk56sLrHu5f8YP1dPoEAPYF/AvAEe0WMhtJHgMgRCALH24cmxjUE2UOoQjbAlz9XfgG9Gnwgu0562Xp1udU5q3ku+Jn4K/dptp712vUxtHlzx/Pxc8X0j7WR9we5I7tRPjSA7oPchttJiswPThPPipCv0MfQ3xAJzyDNgQwHSk/IswbExZIEYYNzQoCCfoHeQc8BwIHjgayBU0EUQLD/7T8R/mj9fTxY+4T6xzoi+Ve44rh+d+V3kPd8duV2jPZ3te51vPVxtVx1jLYPdu437PlJu3r9b7/QQoFFYYfPimnMUs4yjzjPnc+kDtfNjwvmSYEHRYTagmVABj5V/OY7/rtdu7k8Pr0WfqPACsHuQ3VEyoZfh2wILkiqiOnI+IilSH5H0QenxwnG+cZ3Rj5FyEXOBYhFcQTFBIQEMYNUwvgCJwGvQR1A+0CQgN9BJUGagnGDGUQ9RMgF5IZ/RooG+0ZQBcxE+sNrwfUALv5yPJa7MjmUeIe3z3dntwb3XTeX+CF4pXkReZZ57DnPecS5ljkT+JF4JDeht123ZveHeEG5UPqp/Dq97H/kwcnDwQWzxtBIC4jgyRLJK0i5h9DHBwYyROdD98LwAheBr8E0wN2A3UDlwOfA1YDjgIrASH/dfxB+az15vEl7pvqc+fM5LLiIOH/3yffZN553SvcRNqa1xPUrM95yqLEZ74SuPyxe6zip3ekbqLiodaiM6XJqFitkrIiuLm9D8Pxxz/M888i0/fVsdid2w3fTuOj6D7vM/d8APcKYRZgIocuXjpsRT9PdlfHXQViJmQ/ZIRiQ1/eWsNVX1AeS1lGV0JGPzg9JTzsO1o8Lj0gPuo+TT8WPyY+bDztOb42AjPiLowqLSbpIdkdChp7FiAT4g+kDEsJvwXyAeT9o/lP9RbxM+3m6XPnFOb55T/n6+nl7f3y6PhF/6QFkguZEFEUZhagFugUTBH/C1MFu/239dbtp+at4FXc8tmw2Zjbi99F5WXscvTm/DcF4QxvE4MY2RtQHeIcpxrTFqgReAuXBFn9B/bi7hnozuES3OzWXtJizvbKHsjkxVzEo8PdwzLFxse6yyHR/tc+4LnpMPRP/68K4hVyIO4p8jErOGA8dz5zPnY8wDinM44t4iYPIHQZYhMSDqAJEAZJAx4BUf+Y/az7TflK9oTy+e286P7iA90e163RDc2TyYXHE8dRyDjLo89U1fnbMOOU6sHxXfgi/t0CeQb6CH0KMgtaC0ALKwtfCxEMYg1eD/oRFxV/GPQbLh/lIdkj1yS8JH4jIyHLHaQZ6hTgD8kK4gVdAVz97PkL96P0kPKm8LTujewK6hbnquPV37fbg9d209fP6szwyhjKgso0zBzPD9PM1wHdUOJc58rrT++y8djywfKJ8Wvvt+zO6RrnA+Xp4xnkxuUH6dPtAfRN+1sDxAsVFOQbzSKFKNUsqC8DMQox9y8aLskrYSk4J5cltSSwJI8lQCebKWgsYi9AMr40nTawN9k3DzddNd0yty8bLD0oTCRvIMMcVRkiFhwTJxAlDfIJcQaNAkH+lfmk9Jrvseor5k7iWt+I3fzcyN3i3yTjU+cb7Bnx4vUL+jT9Df9i/xz+RvsQ98bx0Ouq5djf3Nov1zPVMNVJ13vbnuFo6W7yNPwuBs8PkRgAIL8ljylSKwor2Cj3JLYfbxmCEkwLIQRI/fb2UPFo7ETo3uQr4h7grd7U3ZfdAt4o3yDhAOTZ57XsjvJL+cMAuAjcENEYMyCdJq8rGi+gMCEwmy0qKQojkhsuE1cKjgFL+fvx9et255nkW+Oa4xnlhOd+6qXtnPAS88v0pvWa9bz0OPNM8Ubvd+0s7KjrHeyl7ULw2/NB+DL9XgJzBx8MGhAsEzQVKhYbFjAVohO4EcAPBg7ODE0MpQzfDe0PqhLhFUoZmxyGH8chJiN8I7oi5iAcHokaaRb/EY0NUgmABTgCiv9w/dP7jPpq+Tj4wfbZ9GHyTO+g63fn/OJq3gLaCtbA0lnQ+c6szmvPE9Fw0zvWJ9ng2xvemN8s4MXfbt5M3KDZwNYP1PnR5NAt0RnT1dZq3MLjo+y29ooBoQxxF3YhNipMMW82czlPOho5CTZlMYor3CS+HYsWkQ8KCRwD1v0z+R/1evEg7u7qxueX5F3hJN4G2yvYwdX60wbTDdMo1GLWsdn83RXjxOjH7tr0vPo3ACUFbwkVDSkQzhI2FZkXLxoqHa8gzySIKbwuOTS1Odo+SkOmRplI3khLR9JDhz6fN3AvaSYJHd0Tbws8BLL+HPuo+Vv6F/2XAX0HUg6SFbccPyO7KNIsRy/8L/UuUSxIKCUjPx3tFogQWAqcBH//Fvto9230EPI48Mnure3S7DTs1+vH6xrs5+xE7kLw5vIo9u75Df5LAmMGBwrnDLsORQ9dDvELCwjUAo38jvVF7ibnqOA52zfX6NRy1NzVCNm53ZjjN+od8c/31/3RAnEGhggBCfEHgwX9Abj9E/lw9Cvwj+zS6RPoWOeN54voGur76+zts+8g8RXyiPKF8irypvEy8QzxcPGP8o70fPdS+/L/KQW0CkMQgRUaGsUdRyB6IVAh0R8eHWsZ+xQXEAsLHAaEAW396vn69ov0dvKK8JLuVeyk6V3mbuLa3bfYL9N8zeDHo8IKvk66nbcMtp+1PrbBt+65gLwvv7jB4sOHxZrGJMdMx0/Hf8c6yOPJ2sxu0d3XROCk6tb2lAR6EwojtTLmQQ1QpFw9Z4ZvTXWHeEh5xHdMdD5vB2kTYshaf1N+TPZFAUCjOtA1bDFXLWwpiyWfIZ0dhRlpFWIRkg0fCiwH0wQkAyECugHPATMCrQIBA/ICSQLeAJv+fPuX9xbzN+5G6Zbke+BC3SrbW9rn2sHcw9+t4yzo3uxf8U31VPg2+s36E/oi+DP1l/Gz7fnp2+bC5Afk6uSM5+vr4/Ez+XkBRgobE3wb8SIUKZktTzAkMScwhC18KWUknR6GGHsSzAy4B2wD/f9w/bf7uPpV+mr62PqH+2n8ev3B/kwAMAKABEkHkApNDmgSuRYHGw8fhSIcJYsmlyYWJfQhOx0OF60PbQe6/gH2uu1R5iPgdttz2CLXa9cW2dHbN9/Y4kPmDOnd6nPrruqJ6CPluOCa2y7W4dAfzErIs8WTxAjFEseVylvPHNWF2zvi6OhA7wj1FfpV/soBiQS1BnkIAgp7CwINqg50EFASHRSuFc0WQxfcFnIV6hJDD44K9AS1/hz4hPFK68jlS+EU3kfc9dsS3Xjf7uIr59vrqfBG9W356/yj/4wBtAI7A00DHwPoAtcCEgOuA6wE+gV2B+wIIgrbCtwK+wkbCDsFcQHu/Pj37vI57kXqfudA5tPmYOny7XH0ofwnBpIQXRv+JesvqDjNPw5FQEhbSXZIykWnQW08iDZiMF0qziTzH/Ub4hiyFkoVgBQhFPUTyxN4E98S8RGtECAPXw2HC7YJBQiEBjkFHQQbAxIC2wBJ/zL9c/r59r/y1+1n6Kri7NyF19HSLM/mzDvMUs0z0MjU29oa4hzqavKF+vABPwgWDTcQhREFEeAOWQvPBrABcvyD90vzGvAm7oftM+4D8Ljy+/Vt+an8VP8cAcgBNwFk/2T8aPi185zueOmj5G3gG93e2tLZ/tlU27fd/ODy5GbpK+4b8x34JP0uAkUHegzeEX8XZB2II9UpKTBONgU8BUEERblH6UhpSCNGHkJ7PHQ1XC2aJJwb1xK2CpcDxf1o+ZH2LfUK9eD1Uvf3+Gj6Rfs8+xf6u/ct9JPvLepU5HLe99hQ1ODQ+M7MznbQ79MS2Z7fQOeW7zb4vADNCB4QeBa8G+Mf+yIgJX8mRielJ8MnvSegJ2wnDidpJlclryNLIQ8e6xngFAYPhQiZAYv6q/NN7b7nP+P+3xPefN0f3sffLeL85NbnYepK7EvtNu3064rpEubA4dbcoddz0pbNSsnBxRXDTMFWwBHAT8DXwHXB+ME+wjbC6MFvwf7A18BKwarCSMVlyTLPw9YR4PHqGvcoBKER/B6sKyo3/EDASDRONFHEUQpQSkziRkRA5zhGMc8p5CLOHL4XyxPzEB0PIA7IDdwNJw56DrAOtQ6CDh0OmA0KDY4MOQwcDDsMjwwDDXkNxw3EDUQNJgxSCsQHigTHALL8kPi19HjxLe8g7ojuh/Ae9DX5kP/bBqwOiRbzHXEklCkHLZIuHi66K5cnCCJ3G2IUTQ25BhoB0Pwc+iH53fku/NL/cASjCfkOBBRiGMEb6B21HiQeSBxNGWoV5RABDAIHIQKI/VD5hPUf8g7vOeyD6dTmGeRM4XTepdsD2bnW+dT109rTydTW1v/ZL9474+ro8O799L766P85BIgHvQnbCgALYAo/CfAHyAYZBikGKgc2CUoMRxDzFPsZAB+VI1Qn2yngKi4qsSd3I6wdmxaqDksG/P019mjv8ekT5vLjkuPb5JbneOsl8D71Yfo5/34DAAeiCWILTwyMDEcMswsEC2UK9AnDCdAJCApNCnQKTQqrCWYIYgaTAwEAxvsK9wfy/uw06OjjUeCU3cPb2Nq52jTbCdzp3ITdjt3D3PLaAdjw09fO7Mh2ws+7WbV1r4CqxqZ/pMujr6QUp8+qoK89tVe7o8Hgx93NgNPF2L3dkOJx557sVPLK+CcAgAjOEe8bpyaiMXo8vEb0T7NXm11jYeFiC2L4XuNZIFMcS1JCRDluMEIoHyFKG+0WFBSxEp0SoBN0FdEXbhoOHX0flyFJI5EkeCUQJnAmrSbYJvomDicFJ8YmLiYXJVwj3yCOHWQZcRTbDtYIqgKr/Cz3hfL+7tPsJez67DvvsvIR9/H73wBmBREJfAtZDHkLzghyBJ/+sPca8GLoFuG82s/VstKp0dfSNdac28LiQ+up9HT+IghAEWUZQyCmJXMpryt0LO4rWCrxJ/gkqCEtHqkaLhfEE2MQAA2NCf8FTwKF/rD67vZo807w1O0r7H3r5+tz7RbwsfMN+OD80gGGBpoKtQ2PD/APvQ74C74HRwLk+/D00u3x5qngR9v+1unTBNIw0TfRzdGe0lLTltMp09rRmM9rzHnIBMRhv/W6K7dotAizU7N0tXy5Wb/exsLPptkg5MHuHPnQApALJBNvGW0eMCLiJLcm6ye+KGUpDSrTKsEr0izvLfguwy8pMAIwNS+1LYUruyh7JfghbR4WGy0Y4hVUFJETjxMvFD8VexaVFzwYJRgLF8EULRFPDEQGQ/+V95Tvpucu4IfZANTQzxbN1Mvzy0PNgs9g0ozVt9ie2w7e7t874Q3ikOID47Dj4+Tk5uzpJO6Z8z766QFXCjETEByHJCosmzKKN8Q6MDzUO9M5azbtMbosNSfAIbEcTBjAFCESaxCBDzUPSQ93D3wPGQ8dDmcM6gmtBsoCav6/+QL1afAo7GPoM+Wj4qvgO9823n3d8dx63Arco9tT2zvbiNtv3Cze9eD35E/qAvH9+A8C8As7FnsgLirRMuo5DT/qQVBCNECzOw41qSwFI7IYSw5nBJH7O/S67j/r1ull6q/sXvAE9S36Yf8vBDkINgv2DGcNkQyVCqYHBQT5/8f7r/fm85PwzO2a6/fp1+gl6NDnyucL6JfoeunM6qjsLu978qX2svuaAUIIeg/9FnYehyXJK90waTQoNu01qDNpL10p0yEuGeQPdQZe/RP19+1U6FTkAuJJ4fbhv+NK5jXpIey17q/w4PE28rvxkvD27i7tjetk6vvpjOo57Azv9PLG9z/9DAPSCDMO1RJvFskYxRleGasX1xQjEdwMUwjaA7v/Lvxc+Vn3I/al9b31PPbx9qz3Rfig+LD4evgS+Jj3OPcg93z3b/gP+mH8Vf/GAn8GOQqlDXEQTxL/Ek8SKBCLDJUHfAGL+h3zl+td5M3dM9jI063Q485UztDOFtDX0cPTjNXx1sPX7Ndw12zWFtW205/SLNKu0m7UoNdc3KHiTeok89H87wYPEcAamCNAK3IxBzbyOEM6JTrXOKY25jPrMP4tXCstKYMnWiaaJRgloST6I+siRSHlHrobxhchE/ANagjOAlz9Uvjk8zrwau1461Xq4+n46Wbq++qM6/rrMuw07BDs6evq60rsPu327pbxMPW++SP/JwWAC88RqhenHGAgfyLHIhchch3+FwMR6wgzAGv3Ju/z51Diot4t3RHeROGY5rvtQfam/18J4xKuG1EjdSngLXgwQTFaMPotZiruJeUglhtHFiwRbgwjCFgECwE4/tX73flQ+DT3mPaV9kT3xPgt+5D+8AJCCGQOIhU0HEEj6CnCL2s0jDffODc4hzXgMHMqkCKfGRgQfwZV/Q/1Ee6k6PLkA+O+4ujjMuY36Yzsxu+E8nj0afU/9f3zxPHN7mTr4Oed5O7hHOBb38ffYeES5Krn6Ot+8Bv1cPk3/TsAXAKQA+IDcgNvAhQBnf9D/jf9m/x//N38nf2V/pD/TgCTACYA2f6P/ED5+fTb7xvq9+O53anXCtIVze/Iq8VIw67BtsArwNK/cb/TvtS9X7x2ujC4u7VVs0qx6q+Er1ywp7KCtvC72cIJyzbUA94H6NvxGvtvA5sKexAFFU8Yixr/GwMd8x0rH/4gqyNbJxgs0jFbOG4/skbFTUJUyVkKXshg4WFPYSZflVvhVltRXktDRVo/6DkaNQ0xwi0pKx4pcSftJVwkjiJgIL0doxoeF08TXw9/C+MHuAQlAj4AC/98/nP+xf45/5P/m/8e//j9GPx/+Uj2nfK77urqdeem5Lri3uEr4p7jGuZs6UrtXPFE9aT4KvuV/L38mfs9+d71zfFt7TLpk+UA493hc+Ls5FLpiO9O90QA9QnYE2IdByZLLckyNTZnN1c2HTPyLSInDx8gFsIMWAM/+r3xDOpS46LdA9lx1eLSTNGk0OfQFtI51FvXhtvD4BLnZu6k9p3/EQmvEhcc3yScLOkyajfbORA6/DezM2stdyVEHE8SHgg6/hv1Ku2z5uPhxN493RfdAN6U32bhC+Mi5FrkgeN94VfeN9pc1R/Q4soOxgbCIb+kvbq9c7/DwoXHf81n1OzbuuOH6xHzKvq1AK0GGgwVEcEVQxrAHlEjBijbLL4xijYMOwg/PkJvRGVF+UQYQ8I/Ejs2NXIuFCd1H+0XzBBXCr4EHAB0/LH5qvcl9uL0mvMP8gzwbu0m6j3m0eET3UXYrdOXz0TM68muyJnIoMmey1nOiNHX1PPXjtpq3FzdVN1f3KXaZtj41b/TINJ/0TPSfNSB2EneuuWc7pv4UANFDgEZDiMFLJQzgTmyPSdAAEFxQME+QjxIOSI2FjNWMAMuKSzAKrAp1SgFKBQn3iVHJEIi1B8QHRYaExc5FLkRvw9sDtMN8g22DvwPjhEvE54UmRXqFWgV/xOvEZAO0AqtBnICcv74+kv4nvYP9qP2QPi3+sD9AQEbBKwGXAjiCA8IzgUuAlr9mPdK8d/qzeSI33Xb59gT2BDZz9sj4L/lPewr8w36aQDVBfgJkAx+Db8MbwrBBgECiPyx9trwVuts5lDiIt/v3LDbUtu4277cRN4r4F/i1OSJ54Tq0e1+8Zb1G/oF/z0Enwn1Dv4TcBgAHGYeZR/SHpkcwxhzE+0MiwXA/Qb24u7P6D7kheHf4GDi+uV664ryvPqMA3EM4hRhHIUiAietKXwqiykSJ2Ij4B72GREVkhDKDPMJLQh+B9MHAgnRCv4MRQ9lESkTbBQZFTIVxxT3E+0S0xHXEBsQtQ+vD/0PhxAjEaERyhFoEU4QWw6CC8YHRAMr/rf4NfP07UHpY+WM4t7gYeAC4Zji4uST51DqwOyQ7njvRu/h7Ujrlef84sDdNdiw0ofNBMlixcbCPcG/wCvBT8Lvw8nFn8c9yYHKW8vXyxXMTczGzNLNxM/q0oLXtt2T5Qfv4vnTBXISRR/DK2Y3rUEpSoVQhlQWVj9VKlIdTXNGkj7oNeAs2SMkG/8SjwvnBAj/4PlW9U7xrO1d6lfnmuQ44krg895Y3p3e4d8z4pXl9+k07xj1X/u8AeAHfg1UEi8W8RiWGjAb6Br8GbYYaRdjFu0VPhZ1F5oZlhw7IEIkUCgFLPsu2DBPMS4wXC3mKPQi0RvdE40LXwPO+0z1OPDY7FHrpuu67VDxEfaY+3MBMwdwDNMQHRQoFuoWdRbyFJ4Svw+kDJYJ1wabBAQDIwLyAWACTAOOBP4FdAfTCAYKBwvbC5MMSQ0ZDh4PbBAPEgEULxZzGJoaaByYHeodIR0TG6cX3hLSDLoF4/2v9Yvt7OVA3+jZMdZK1EHUA9ZZ2e/dWeMa6a7ul/Nj97n5Wvou+T32tfHi6ynlAN7l1lLQt8pwxr7DyMKTwwjG9skazyHVtNt/4jXpme9+9cr6dv+MAyAHTwo0DegPexLxFEAXUhkEGy0cohw4HNAaVxjMFEMQ4wrnBJr+T/he8hrtzuiw5eHjaeMz5BHmv+jn6yrvJvKD9PL1PfZF9QjzoO8/6y/mxeBf21jWBNKlzmnMZcuVy93MDs/q0S7Vltjm2/HeneHn4+Tlu+en6e7r2e6r8p732P1kBTQOHBjVIv4tKTncQ55N/1WfXDdhnmPKY9Jh611kWJxRAkoCQgc6azJ3K10lNyAFHLMYHBYQFFkSxRAmD1sNUgsGCYQG4QM7Abb+bvx7+uv4vfff9jX2lfXO9K/zC/K/77bs9OiO5LLfo9qz1T/RqM1Iy27KU8sVzrXSEtnv4PDpp/OX/UAHKhDoFygesiJ0JXsm9SUvJIghbh5SG58YrxbJFRMWmRdDGt4dISKvJiMrGC8zMiY0uzTVM3QxsC26KNQiThx8Fa4OMAg7Avz8iPjm9Ary3u9D7hjtPuyd6ynr4erQ6gnrqevM7I3u//Am9Pj3VvwRAeoFkwq3DgISJhTiFAoUjBFwDdwHEQFo+UfxHulg4XPardRM0HDNGswpzGLNcc/00YDUrtYj2JjY4tf11eTS5s5IynLF1MDlvBa6xrhCube7NMClxtrOhdhI47PuVPq8BYgQZhoWI3MqbDAHNVg4gTqpO/c7jzuKOvc42zYvNOcw8Sw/KMsilhy0FUcOhAaw/hf3EPDy6Qvlm+HR38HfYuGQ5Azpge6F9Kn6egCPBY0JLwxNDdwM8Aq6B38Dmv5p+U30n++o657om+ah5ZrlWual5zfpy+ok7BHtde1H7Znsketp6mbp1ej/6CfqfOwX8Pr0CPsKArcJrxGMGeYgWyeZLGMwmDIzM04yGjDjLAEp1yTFICUdQRpOGGgXkxe6GLIaPx0dIAIjqSXWJ1wpHioTKkMpyCfDJV4jxCAaHnsb9hiOFjUU0hFED2cMFwk7BcUAufss9krwUOqK5Erf6Nqx1+rVvtVC12naC9/f5IXrh/Jm+aH/vgRYCB8K6AmpB38Dqv2G9onuOOYa3rHWcNCyy7TIksdEyKXKcM5N09nYp95V5Ifp+e168fXzbPX59cn1E/UX9BLzPfLE8cXxT/Je8+X0yfbs+C/7d/2z/9wB+QMcBmQI8wrwDXsRrhWVGicgSibOLHQz6jnaP+dEvkgWS7xLlEqiRwJD8jzFNeItuCW7HVYW5A+qCs8GXgQ9AzoDBwRIBZYGjQfSBxwHPQUlAuH9nvil8lPsEuZR4Hvb7Nfr1aPVI9da2hjfFuX761/z2/oJApMIMg63EgoWKRgpGS4ZZxgKF0gVTxM/ES4PHg0KC90IfgbSA8AAOv08+dH0FfAy61/m2uHh3bDad9hU11PXZdhl2hbdKOA/4/nl9eff6HXoi+YV4ybe79e+0PbICsFzuaiyFq0Tqd+mmaZFqMar5bBXt8S+z8Ydz17XVd/Y5tbtVPRt+kgAHAYbDHQSSxmwIJ0o9jCHOQlCJUp+UbdXelyCX51guF/aXChY4FFYSvNBHzlFMMgn/R8iGV0Tug4tC5UIwQZzBW0EdANUAusAJv8F/Zj6Avht9QjzA/GG767uie4S7zfw0/G587L1ifcO+Rz6nvqR+gf6Jfkg+Db3rfbF9rf3qvmu/LkAqgVACykR/hZTHLkgziM/JdYkfSI+HksY9hCsCPP/V/dp77DooeOT4L3fMeHa5H/qyfFH+nsD3wzzFT8eYyUVKycviDFAMm8xRy8ELOYnLSMRHsIYYRMEDrYIegNP/jL5JfQ173TqA+YL4r3eTNzt2szaB9yt3rbiBehj7ob1Ef2fBMULHRJOFxAbOB21HZgcDRpcFuERBA0zCNUDQwDD/Xr8dPya/br/hgKiBacILAvUDFENbgwWClAGRAE3+4D0iu3D5pfgZ9uA1xfVRdQE1TPXmdrr3tLj9Oj87aDypvbq+V/8Cf4F/3r/mf+W/6D/3/9sAFEBhwL2A3sF6wYXCNQI/wiACFIHgAUkA2oAh/2y+iX4Efaa9NDzsvMk9Pv09fXH9iD3s/Y59X/yae736EXijdog0mbJ08DeuPuxjqznqDunn6cIqkquIrQzuxjDZMuw06Hb8eJw6QvvyPPF9zX7Vf5qAbcEcgjCDLgRURdtHdwjWyqbMEw2IDvXPkBBQ0LeQSxAXD2yOX41GDHULAEp2yWOIyoirSH6IeIiKiSOJckmnSfaJ10nGyYaJHchXB4BG6EXeRS+EZkPIA5bDTwNow1nDlAPKRC8EOIQfRCFDwYOHAz4CdUH9AWWBPQDOQR7BbcH0AqTDrMS1RaUGosdXR+9H3geeRvMFqAQQwkeAa/4ffAP6eXiad7q25fbeN1w4T/nh+7T9p//YwifENwXvR38IXMkGiUGJGIhbh11GMcStAyCBm4ApvpG9WDw+esP6JvkluEB397cPdsw2tPZQ9qa2+3dROGZ5c/qufAS94b9sgMuCZENehCaEbkQvA2pCKgBBPki733koNkaz3LFI72NtvSxeK8Vr6aw6LN+uP69+MP/ybXPztQa2YTcFd/z4FnikOPr5L3mTOnR7HDxL/f+/bIFDA67FmcftSdRL/M1ZzuNP1xC4UM+RKNDSUJsQEc+BzzRObY3uTXMM9Qxry83LUgqySasIvIdsBgKEzQNbQf3ARX9//jh9dTz2/Lf8rTzGvXC9lT4evni+U35jPeP9F7wH+sS5Yne5deP0ejLSsf6wyTC2sEOw5fFM8mQzU/SEteA207fSuJX5HjlyuWC5evkWeQn5KrkLebk6O7sT/Lr+JEA+AjJEaIaJCP1KssxcTfGO8Q+fEASQbtAtD88Po081zo7Occ3djYzNdgzODIfMF4tzilXJfMfsBmyEi4LagO2+2L0v+0R6I3jVeBz3trdaN7r3yPiy+Sh52jq8ewg7+3wYvKe88z0IfbS9w/6/vyuAB8FMgq1D10V0hqyH5gjKSYaJzcmaSO7HlcYixC8B2X+C/U17GHk/d1a2arW/dU+1zXajt7i47jpmO8M9bD5M/1g/x0Adf+F/Yf6xfaT8knuOOqq5tnj7uH/4BDhGuIG5LrmGuoM7nzyXfer/GcCmghJD3YWHB4pJnsu3jYQP71Gi00ZUwpXC1nbWFJWZlEtSuJA3DWRKYscXg+kAuz2tOxg5DLeR9qV2O3YAdtn3qXiPOeu643vffJC9Lv06/Px8Qrvguu15//juuAx3pvcGdy03Fre5eAd5L/nhusu733yR/V09/748Pln+o36kfqg+uf6hfuL/Pr9wf/BAc4DtgVDB0QIkwgZCNAGxwQgAhD/0/uz+PX12fOU8kby9/Kb9Av3DPpS/YgAWANuBYgGcgYWBXcCtP4D+rL0Hu+o6bHkkOCK3c3bbNtd3H3ejeFB5UHpMu3A8KfztvXW9gv3dPZK9dXza/Jn8R3x1fHD8wL3kftRAQ4Idw8vF9Ee9iVBLGIxIDVbNww4RjczNQ0yGy6oKfwkViDnG84XGRTCELMNzArnB94EjgHl/dj5dPXU8CTsmed04/PfUd26207bFdwC3vHgquTm6FTtoPF89aT45/oo/GT8s/tA+kz4IfYQ9GjybPFO8S3yCvTR9lH6Sv5rAmAG1gmCDDEOwg40DqIMQgpkB2YEtAG5/9X+WP95AVMF3ArqETIaUiPRLC826D6ERphM1VAGUxhTFlEpTZRHq0DOOGAwwSdHHzoXzw8pCVkDYP41+sb2APTU8TXwIO+b7rHucu/x8DvzVfY6+tL+9gNuCfAOKBS7GE4ckR4/HyseRBuVFksQsAgnACn3NO7O5XLeidhj1C7S99Gh0/HWidv44LzmUew38QP1XvcT+BD3ZfRF8ADr+uSo3oDY9NJpzi7Leclkye3K9s1M0q3Xzd1e5BXrtfEK+PX9ZANVCNMM7BC0FDgYgBuJHkEhiyNAJS8mJyb3JHoilx5JGaASwwrwAXb4se4I5eDbldN3zL/GjcLov7e+zL7iv6fBxMPhxbLH/MiYyXzJtchrx9vFUMQew5jCCMOoxJ3H8cuU0VvYA+A56KHw2fiJAGYHOA3jEWMV0hdfGVAa9RqjG6wcVR7RIDwklijFLZQzujngP6hFskqsTlBRcFL3UetPbky2Rw1CyTtBNcwutig7I4MeohqYF1AVqRN3Eo0RvRDmD/AO0g2WDFELJgo9CcMI3QioCTILdw1gEMATWxfoGhgemiAmIoMiiiEwH4AbpBbbEHkK3QNt/Yr3ifKt7iDs8eoP61Hsc+4h8f/zrPbT+Cz6hvrL+QT4U/X28T7uieo456nkK+P34i3kz+a/6sPvivWw+8cBYgcaDJkPnxEHEssQAA7XCZUElP4t+MLxqusz5pfh/N112wLaktkG2jzbDt1Z3wLi+OQ06Lnrke/K83H4jv0eAxMJTQ+bFb4bbCFUJiQqkSxfLWQskyn6JMMeOhe+DsYF0fxd9OTszeZn4t7fPt9r4CvjIeff6+bwtPXP+c38YP5V/qD8WPm19Azvyehk4ljcHNcX05rQ2s/v0NHTXtha3nnlYu279S7+bAY4DmUV1xuDIW0moiozLjMxrjOpNSA3Azg4OKI3HjaNM9sv/Cr5JO0dBxaKDccEG/zl84PsSOZy4Szegtxj3KPd+N8H42bmpelY7CHutO7f7ZHr1efW4tjcNNZRz5nIcMIwvR+5abYhtT+1orYVuVe8IMArxDrII8zLzzHTatae2Qbd4uB25QDrsPGg+dUCOA2WGKQkATFAPe9InVPjXG5kA2qDbetuVm74axpoEWM6Xe9WglA3SkBEuT6rOQo1vzCnLJwoeiQmIJEbuxazEZcMkwfYAp3+DvtW+Iz2t/XL9aT2EfjP+Zj7IP0i/mf+yP02/Lr5dfah8obueerT5ufj/OFG4d/hxOPV5tbqde9O9Pb4//wHAMEB8wGHAIT9Efl28w7tSuad33zZUNRv0BTOXc1KzrzQedQx2YreIOSV6Zbu4fJJ9rn4Ofrh+uL6dfrc+Vj5Iflm+UT6xfvi/YIAggO0BucJ7gykD+4RwhMjFSIW3BZ1FxQY2RjgGTUb1BypHo4gUCKyI3EkUiQeI7MgAh0YGBoSSgv+A6D8n/Vv73nqGOeK5fDlSehu7Bny5vhaAPEHIA9nFVYalx31Hl4e5hvCF0YS3Av7BCL+xfdN8g/uQev+6ULq7evH7oby2PZn++D//AOGB1oKZQyqDTgOLQ6qDdEMwwuVClQJAAiQBvAECwPIABX+6fpH90XzBu/A6rLmJuNm4LjeVt5m3/fh/uVR663xtfj6/wEHUA1xEv8VrRdMF84UShD2CSgCTfnd71rmQN3/1PTNXshjxAjCOcHHwXPD9cUAyU7Mps/f0uXVu9h12zneNuGh5Knodu0d85/55ADACPAQHxnuIPon5C1bMiA1CzYSNUgy2S0LKDghwRkQEoYKfQM7/fD3tvOQ8GruIO2C7Fvsd+yp7NDs3OzL7K3sn+zH7FLtaO4s8LTyBvYU+sD+2AMgCVIOJxNcF70aIx2AHt4eXB4xHaQbBxqxGPEXDBgyGXob3R47I1Mo0i1RM2M4mTyTP/5ApUBxPm06xTTELcwlVR3bFNsMxgX8/8D7OPlp+Dj5bvu+/sYCJAdyC1QPfhK5FOcVABYXFVAT3RD7DeUK1gf8BHgCXQCt/lr9Tvxr+5H6o/mO+Ej31/VN9MrydfF+8A/wT/BZ8Tfz3vUv+fn89ADUBD4I3wpnDJsMUguBCDcEpP4N+M/wVukQ4m3bzdV70arObs23zVrPDtJ31SrZu9zB3+fh6uKp4h/hbN7N2pjWONIhzsfKmMjvxw7JGswZ0e/XY+Am6tL0/P8yCw0WLiBIKSYxpje+PHRA3kIbRE9EnEMeQuo/Cj2AOUU1TjCRKgkkuRyxFBAMCAPX+cfwK+hZ4KDZQ9R00E3Oy83RziTRc9RY2GTcJOAp4xjlqOWw5CjiJ97m2LrSDsxYxRS/t7mmtTOzj7LOs+a2qrvZwRvJDtFQ2YPhVumN8AL3qvyPAdIFoQk2DckQjxSwGEIdSSKzJ1ctADNqOE49ZUF0RE1G10YRRhBEA0EoPc84TjT4Lx0s+ii9JnolLSW6JfEmkyhUKukrCi15LQotoytCKfkl7CFPHV0YVhN0DugJ1QVNAlD/yvya+pj4lPZh9N3x8u6c6+znB+Qn4JLcltmE16XWN9de2SjdheJF6R7xsPmGAicLGRPsGUMf3CKVJG0khyIkH6EabRX+D84KSgbOApwA2f+FAIcCpQWRCegNRhJDFoMZuhuzHFAckBqJF2cTZg7NCOcC+/xI9wHySe006cfl+uK+4ADfrt273CLc69sn3PHcad6z4O3jLuiA7dfzFPsCA1gLuxPCGwAjCymDLRswnjD3LjArdiURHmcV7AsgAoT4jO+d5wHh5ttW2D3WadWR1VvWZ9dU2NHYndiS16TV6NKNz93LMcjsxHLCH8E/wQXDjMbOy6jS3NoW5PPtCPjoATILkhPFGqMgFyUnKOophSonKgQpSyclJbIiBCAiHQcaqhb7Eu4OfgqwBZUATvsK9gPxe+y46PnldeRR5JzlTOg+7DHx0/a8/HwCpAfIC48Otg8ZD7IMoAgiA5L8X/UF7gXn1+Dk23/Y3dYR1w7Zqdyb4YvnEe7H9Ev7SAGABswKHw6HECcSNBPwE50UexXAFo8Y+Rr5HXMhPCUYKccsBDCUMkY0/TSsNGEzOjFrLjMr1yedJMUhgR/wHR8dAx17HVUeUx8tIJ8gZyBWH0odOhoyFlYR2gsCBhoAcPpI9dzwV+3M6jnpheiH6AfpxOl+6vrqCeuO6oDp6efr5bfjiOGi30Peo93m3R/fReE45MDnj+tK75LyCPVY9kL2ofRu8cLs1+YG4L7YfdHIyiHF/MC4vpS+sMAHxW/LotM73cbnxfK5/SoIsxEEGuYgQCYRKnIsji2dLd8skivxKSsoYyauJBQjkyEhILEeNx2vGxsaihgVF90VDBXMFEMVkhbHGOIbzB9YJEYpQi7uMuU2xTk3O/U61DjENNkuRSdaHoAUNAr7/1X2vO2U5ifhm9332x3czd2x4FzkWug37Irv+vFK81rzKPLT75XsvOil5LHgP92i2hrZ0NjT2Rfcd9+745voye328tn3N/zm/84C7gRWBiUHhgenB7cH3Qc2CNAIqQmwCsoLzQyQDekNsw3XDE0LHQlfBj4D7/+r/LD5Nfdl9Vf0EfSA9Hf1u/b99+X4HPlS+EP2xPLG7VbnpN/81sXNdsSTu5+zFK1aqMCldKWCp9KrLLI8upjDys1Z2NHiz+wB9jH+RAU8CzIQURTVF/saAh4cIW8kDSjxKwQwHDT/N287KD7vP5RA9z8OPuU6nDZoMYgrSSX2HtcYJxMTDrUJEQYXA6kAmv61/Mf6o/gn9kTz++9l7KzoDOXJ4S7fgt0F3ePdNuD+4yTpdu+v9nr+dwZKDpgVFxyNIdol9SjvKuwrJCzWK0crtSpUKkUqlio8Kxcs8yyPLaAt3ywLK/UngyO4HbQWsw4LBij9gfSR7M7loeBZ3SjcIN0t4Brlkesn8137rQOXC6ISaBidHBMfuR+cHuMbyhebEqsMTAbM/275aPPf7evok+TX4LDdFdv/2G/XbNYH1lfWedeK2aTc1+An5oXsz/PM+zAEoQy3FAkcLiLKJpcpZionKe8l8SB/GggTCAsIA5D7GPUJ8K3sL+uS67btW/Ej9p37TAG3BmoLAw8+EfIRGBHKDkALyAbBAZP8ovdN897vi+1x7JLs2O0V8A/zgfYi+rH98gC9A/kFnQeyCFEJmAmrCa0JugnhCScKgArSCvgKxwoQCqgIbwZQA0r/bfrg9NjunOh44rrcrdeN04TQqM7zzUbOas8Y0fjSr9Tl1UzWqtXc093Qx8zNxz/Cfrz1thWyRK7dqyCrM6wcr8Kz7blOwYPJIdK82vHibOry8GH2tPoD/nwAZQINBMcF4welCj4OzBJRGLce0iVkLSM1vzzpQ15K5k9eVLVX8lktW41bQ1uFWoVZblhcV19WcFV8VGBT71H4T0tNwklDRcY/WjkhMlIqMyIYGlcSQwspBUEAsfyC+qj5+/k++yX9WP+AAU0DegTVBEYEzQKEAJv9Ufrx9svzJ/FD70ruTu5K7x/xl/Ns9kv53/vY/fP+Af/r/bf7hviU9DDwu+uZ5y7k0OHF4DfhM+Op5mjrJvGD9xL+YgQHCqAO4BGWE6sTJxItD/oK3AUsAEv6kvRS787qNuel5CPjpeIV41LkNuaf6G3rie7n8YL1XvmD/fcBwAbWCykRlBbmG94gLSV/KHwq1SpHKaQl2h/0FyAOrgIK9rjoTNtjzpXCbLhbsLeqradGp2Cptq3js227ysNxzN3UnNxW49Ho8+zG72/xMfJe8lHyaPL48kj0ifbT+Sb+ZwNpCesPpRZLHZMjQCkgLhQyDzUVNzg4ljhQOIs3YzbwNDozQDH1Lj8sBCkkJYcgHhvoFPcNbQaF/oP2vO6M50rhSdzL2PvW7daU2MjbRuCz5aTrpvFG9x380v8mAvsCTgI7AP/86PhW9LDvXOu05wDlb+MX4+7j0uWI6MfrOe+M8nL1rPcT+Zb5QPk0+Kz29PRf80Ly7PGf8ob0t/cq/L0BOghUD7EW9B3AJMQqvC96M+Y1ADfdNqU1izPKMJ0tOyrOJnEjMSAIHeUZqxY1E2QPGQtFBuYAD/vi9JXubOiy4rjdyNkg1/DVTtY52JPbJ+Cr5cPrDfIl+K/9XgL6BWUInQm5CeoIdQepBdsDXAJyAU8BDwK1AyYGMwmWDP8PFxOLFREXdReZFnkUMBHwDAUIyAKd/eX4+/Qn8pvwb/Cd8QL0YPdo+7z/+AO/B7sKrAxnDd0MGQtBCJAEUgDa+373j/NU8ADutex/7FbtIO+28er0ivhm/FgARQQbCNcLgQ8nE9sWrhqnHsYi+SYgKwsvfTItNdM2JzfsNfUyMC6iJ3If4RVNCysA/fRI6pPgUtjl0Y3NZ8tsy23NGtEI1rbbm+Eu5/Dree988c7xavBt7Rfpw+Pf3ePXStKFzfXJ5ceDx+LI9sua0JbWot1s5aXtAfY//isGpQ2VFPcaziAiJv0qZy9gM942zTkQPIQ9Aj5lPY47bDj9M1QulycDIOUXlw98B/b/Xfn88wrwn+247DXt1u5I8SP0+vZf+ev6TftJ+sX3xPNr7v3n1OBa2QTSQ8t9xQnBI77ovFy9YL/AwjDHWczi0XPXv9yO4bzlPeke7IDul/Cf8tb0d/ew+qD+TAOoCI0OwBT3GuEgKCZ+KqAtXi+eL2EuvivkJxQjnh3TFwkSiAyQB0sD0/8n/Tr77PkW+Yn4Gvil9xP3W/aG9az09POO86vzfPQo9sn4YvzjACQG6gvlEbsXDh2CIcUkmibYJnYlhiI5HtYYvRJWDBAGVACB+9r3kfW19Dn19fap+QP9qAA/BHQHAwq+C5IMhAy2C2AKyAhCByEGsQUwBsgHhwpiDjITtxifHokkEirYLocy2jSmNdg0eTKtLqwpvyM6HXAWtg9QCXgDVP70+Vn2c/Mm8VDvz+2D7FbrQOpF6XTo6ufL5zzoYOlR6x3uvfEc9gz7UACgBaYKDw+MEtwU0hVYFXcTURAmDEgHHgIT/ZH4+vSa8qfxM/Iy9Hb3sft9AGcF8gmjDQ4Q3hDZD+kMHQimAdr5IfH85/HeiNY6z2/JdsV8w5DDosWEyfDOkdUH3fDk7+yz9Pj7jAJPCDINMBFPFJsWHBjcGNsYEhh0FvATcRDkC0EGiP/J9yjv2uUq3G7SCslmwOa45bKsrmysN6wBrp6xxbYSvRLERssx0l7Ybt0Z4TjjxuPg4sXgy91e2vHW+9Po0RHRutEG1PzXg91m5FvsCfUR/hMHvQ/LFwwfaSXkKpIvmjMwN4s64D1dQR5FL0mFTQFSdFafWjxeBWG4YiJjH2KlX79bkFZRUExJ00E/OuUyDiz2JcQghhw5GcEW8xSaE3oSXBENEGoOYQzyCS8HOwRGAYf+Mvx5+n/5WfkF+m37Zf2y/woCIASmBVcG/QV7BMkB/f1E+eTzNO6U6GnjD9/U2/DZgdmH2uLcWeCb5Ebp8O0y8q31Ffg4+f34bvex9AXxv+xC6PTjOOBk3bvbZdty3NTeYeLc5vjrXfG19rD7CwCYAzwG9wfbCBAJyQhFCMAHdAePBzAIZAknC2MN9A+tEl0V0xfnGX0bhRwDHQcdshwtHKUbRxs3G44bVRx+HeseaSC5IZEipCKsIW4fwhuZFv8PHwg8/7H17Otj4ozZ09GVyxPHccSww7DEMsfcykPP8NNu2FHcQt8A4W7hjeCA3ojb/9dN1OPQMc6ZzGzM4s0T0fzVd9xK5CDtm/ZSAOMJ7xIqG1YiTigALW0wpjLJM/gzVzMIMiQwvi3bKn4noSM9H04a1xTmDpcIEwKU+131u+/96m3nSeW+5ODlqOjx7Hjy3viv/2kGhgyCEecUWBaVFYMSLQ3DBZ38KvLz5ovbiNB2xs+99LYmsoSvC6+asPOzx7i8vnPFlczW0/7a5+GD6Nju/vQX+0sBwAeVDtwVkx2nJfEtOTY7PqtFPEyoUbRVOlgmWX5YXlb4Uo9ObUnlQ0Q+zTi2MyEvGiuZJ4IkqyHfHukblRi7FEEQIgttBUb/4viF8nrsD+eJ4iLfAd043L/ced4x4aPkgOh37Drwh/Mt9hL4M/ml+ZL5NfnU+Lf4IvlK+lT8Sv8bA6AHlAyiEWcWexp8HRQfAh8hHWoZ+RMIDewEFPz18g/q2+HE2iDVK9EAz53O4c+S0mLW9try3/nkvOn87Y/xYPRx9tb3s/g2+Y757Plz+j/7XPzE/WX/IQHVAlkEiAVIBogGSgaeBaMEhwN/AsQBjAEDAkYDYAVFCNML0w/+E/4XfBskHqof2R+QHs0bqxdhEkAMqwUV/+z4nfOG7+vs9Oup7PHukvI694L89wEpB60LKQ9bESISeRF8D2cMiwhKBA4AQfxB+Vv3xfaZ99X5WP3qAUEHBg3cEmgYWx10IYQkdCY/J/YmtiWqIwAh5R2CGvcWWBOuD/YLJQgsBP7/j/vg9vvx+uwF6FHjGt+h2yXZ3Nfq12PZPNxU4GzlLOsr8fD2Afzo/zoCqgIEATn9Xfes74LmV9y30TfHab3YtPatG6l9piymFqgFrKqxobh5wMHIDdEB2VPg0+Zs7B7xAvVB+Az7mP0XALICggWRCNQLMw+HEqIVURhoGsAbRRzwG88aBhnEFkcU1hG1DyMOUw1nDWoOUxABE0EW0hloHbggeSNxJXcmeSZ5JZMj+iDtHbgaqRcMFR8TERL6EdkSmRQKF+8Z/BzlH10iJCQKJfYk5SPuIT4fEhy2GHkVphJ+EDEP1w5uD9sQ6xJXFckX5hlWG80bEBv9GJAV4BAlC64E3f0e9+PwlOuN5xDlRuQ35c3n0uv68OP2Iv1KA/QIxg17EeMT7BScFA8TdRANDRoJ4gSiAJL81fiF9anyP/A57oPsDevJ6bDoyecm5+LmJecX6OTpreyM8IX1iftzAgUK7RHGGSQhliewLBQwfDG7MMgtuCjEIUMZpA9lBQ37G/EI6DTg5Nk+1UXS3NDL0MHRYdNJ1RvXhdhL2UrZfNj41u7UptJ30LzO0s0Jzp/PvtJx16ndOuXh7Uj3DQHMCiAUshw5JH8qZi/kMgQ13jWYNVs0VDKmL28swSijJBEg/xpgFSYPSQjMAML4SvCV5+Tegta/zuzHU8Ivvqi7zLqQu8q9OsGHxUrKFc980xvXo9nh2r3aQ9mf1h7TIc8fy5PH98S5wy/EmMYMy4LRz9mn46XuU/owBr8RjRw2JnMuFTUOOms9VD8DQMA/2D6VPTk8+jr3OUE50jiYOHA4NTi+N+k2njXRM4Yx0y7aK8go0CUlI/MgXR9zHjUejB5RH0kgMSG9IaYhqiCZHlQb2BY5EaUKXwO9+xz04Oxl5vrg3dwx2gHZOdmw2iXdSuDL41HnkepM7VvvrfBJ8U3x7vBp8AfwDPC18DHymfTs9xT83wAMBksLQhCdFBAYXxpnGx8bmhkHF60T5g8VDKAI5gU5BNID0AQ2B+UKpA8jFf4ayyAeJpMq1i2pL+Uvgy6VK0Qn0CGGG7gUug3aBlkAa/ot9bLw+Ozz6ZDnt+VU5FbjueKB4r3ig+Pv5B7nJuoT7uLyffi4/lQF/wtXEvQXaxxZH2wgaB8vHMMWSw8OBnP79e8i5IvYv808xGq8krbZskKxqLHKs0q3vLurwKPFP8opzirRJNMb1C/UmNOh0qDR79Df0LfRqNPO1inbo+AN5yvusfVR/cAEuwsNEpIXOhwGIAkjYiU2J68o8SkZKzksVC1gLkYv5S8bMMEvuS7wLGAqFycyI+IeYhr6FfARiw4BDHwKDAqoCi8MZQ76EI0TuRUYF08XFBY5E60OggjpADT4y+4s5dnbVtMbzIrG7MJowQLCncT6yMTOj9Xr3GTkkusb8r/3WPza/1cC+QP4BJwFKwbrBhYI1Qk8DEwP7xL/FkUbhx+EIwYn3CnmKxUtbS0CLfYrdCqsKM0m/SRWI+YhpiCCH1ce+BwyG9cYvhXNEfwMWwcNAVD6bvPC7K3mjuG73Xjb8to83Ebf5+PX6bnwIfia/68G+gwiEucVJhjXGBEYAhbrEhwP5gqaBnwCv/6C+8v4jfam9OTyD/Hu7k7sCukR5WngMduf1f7PqMr/xWXCMcCtvwrBW8SXyZPQC9mh4uTsX/eXAR4LlBOuGj4gLySKJnEnGifKJcwjbCHxHpUcghrSGIwXqhYXFrgVcBUjFb8UORSXE+cSRRLSEbQRDxL8EooUtxZsGX8ctR/DIlYlGSe8J/0mrSS5ICwbLxQLDCID7fns8KbomeEy3MXYhNd+2Jnbm+Al58Hu6fYQ/6wGRA10EvQVoRd5F5sVRhLODZgIDwOd/Z74YvQg8fXu6u3r7dXudfCQ8u30U/eX+Zn7Sf2l/rn/mABfASYCAwMBBCAFVAaBB4EIJglACZ4IHQeiBCgBvPx/96fxeutK5W3fNNrp1cPS5NBR0PXQotIP1ePXvdo33fPeo98S3yXd4tlv1RHQJcobxGu+jrn0tfmz4LPMtb65mb8dx/PPs9nr4ynuA/ggAUAJORABFqQaSR4oIYIjnCW3JwkqtizQL1IzJDcZO/s+iUKDRa9H3UjwSNpHpUVqQlY+nTl9NDEv7yniJCggzBvIFwgUbhDSDA4JAAWTAMD7kfYo8bjrhebd4RTeettU2tnaJN034fbmKO549n3/wQjJER0aTyEJJw0rPi2bLUcseimIJcwgrBuHFrIRbw3qCTYHSgUJBEEDtQIlAlABAwAb/ob7TviS9IbwbeyW6FHl6OKZ4Y7h2uJ15Tvp8u1K8+b4Yv5cA38Hgwo4DIgMegsuCdwFzgFa/dn4ovQD8Tnubuy46xXsdO2x76DyD/bP+bb9owGHBVkJIw30EOMUBRlrHRwiDyctLEkxKjaHOhA+cUBgQZ5A/z1zOQcz5ypeIdEWuQubAAH2bOxO5P/duNmO13HXLNlq3L/greWw6knvCPOR9aj2MvY29Nzwa+w+58HhZNyT167TA9HGzxHQ4NEX1YPZ4t7m5D/roPHE93f9jgL1BqQKng3uD6YR1RKDE7UTYxN8EuoQkQ5TCxsH2wGW+1/0XezP4wLbVNIryu7C/rytuDm2xbVUt8i65b9TxqPNWtX23Pvj/Omj7rXxGvPc8ibxQu6O6nfmb+Ll3jjctNqK2svbbd5I4h3nm+xr8jP4ov10An4GqQn7C48Nlw5TDwsQChGSEtgU/xcUHA0hyCYRLaUzODp/QDBGD0vvTrdRYVP8U6ZTilLcUM5OjkxASvpHwkWNQ0JBuz7OO084GDQOLygpbSL+GgwT3QrDAhf7L/Rc7t/p4+Z55ZflFue46SjtBfHo9Gz4O/sN/bn9Lf15+8f4W/WN8bvtS+qZ5/PlkOWQ5vLom+xW8db2wvy5Al8IXg10EXMUSBb7FqkWhxXXE+IR8w9LDh4NjQyhDE8Ncg7XDzsRVhLiEqISZxEWD6sLOgfxAQ383PWy7+fpyeSb4I/dvtst28rbb93m3/LiT+bA6Q7tD/Cq8tj0oPYX+Fr5i/rH+yf9tP5nACwC2gM7BRAGFAYJBbkCAf/R+TrzZeua4jfZr8+Axim+JbfcsZ6unq3ormey4bf8vkjHQ9Bn2TPiMuoH8XX2XPrD/M/9xP38/N371vpN+qD6Ffzc/gQDhgg6D+UWOh/gJ38wvzhTQP9GlUz6UCZUH1b1Vr9WlVWQU75QK03VSLlDzD0EN1sv0iZ6HXIT6wgp/n7zSent387XSNGizBLKrcloyxfPb9QH22Li9Okw8Yz3kfzg/zsBiADV/U75R/Mq7HTkqdxK1cvOj8nZxdLDf8PIxHzHUsv3zxHVTNpe3w3kN+jM69nuePHV8yX2nvhv+7/+ogIcBxsMeREAF3IchiH6JZEpGyx7LaottizAKvsnqCQMIWwdCBoSF60U6BK+ERkR0xC9EKIQUxCmD4EO2gy+CksIsAUrAwEBef/Q/jf/zACYA4QHYwzvEdEXox39InsnwyqTLMAsPSseKJEj4B1oF5AQxQlsA939V/kE9u/zBfMa8+3zLPWB9pf3IPjj97z2n/Se8eDto+k05engFN0D2vTXD9dn1/PYlNsV3zHjm+cC7B3wrfOF9ov4vvkx+gv6gPnM+C/44/cY+O/4dvqn/Gv/mAL/BWUJkgxUD4UREBPxEzcUAhSBE+wSehJkEtMS4xOeFfYXyBreHfIguCPgJSEnPScNJoIjpR+fGq8UKQ5wB+sAAPsH9kXy5u/27mHv9/Bq81r2V/nz+8L9a/6s/V/7gvc28rnrZ+Sw3BLVCs4SyJPD3sArwI/BAsVcyl7Rs9n84tLs1PalAPwJnRJeGikh9SbHK6ovrTLcNEA22jajNo41ijOFMHAsRycRIeUZ6xFgCY0AzPd57/TnleGj3FPZvtfe143Zidx14N7kSOkz7SrwxPG38dbvG+yl5rjfttccz3XGUr5At7uxKa7PrNCtK7G7tj6+VseW0Yvcv+fI8k39BwfLD4MXMB7nI8ko/CypMPIz7TalORQ8JD62P6BAt0DSP9E9ozpINtIwaypKI7kbCBSNDJYFbP9C+jv2YvOq8fLwBvGn8ZDyffMy9IL0UfSa827y7/BT79ntwuxP7LXsFu6C8O/zO/gs/XUCwAeuDOYQFxQGFo4WpRVgE/EPngvEBsgBEv0D+e31DfSH81/0ffaw+bD9JAKxBvsKsA6PEXATQhQRFAQTVRFQD0cNjwt1CjUK+wrWDL4PkhMZGA0dGyLsJjEroi4NMVAyYjJSMUAvXSzmKBslOiF4Hf4Z5hY1FOQR2g/1DQ4MAQqsB/wE7AGJ/u/6TPfa89fwg+4W7bzsju2Q76nyrfZW+04ANgWrCU4NzQ/sEIkQnA4/C6UGGwEB+7v0tO5N6dbkiOF/37veHd9q4FTie+R/5gDorOhF6Knm0ePZ3/baedXEz0PKZMWOwRi/Q74xv+vBWcZHzGzTa9vg42TslvQi/MICSgidDLYPohF6EmISfhH1D+UNZwuHCEoFrwGv/UL5afQq75rp2uMd3qDYrNOQz5nMDMsgy/fMltDp1brct+R37Xv2PP8yB+AN2BLLFYkWCxVvEfoLEgU4/fn07uyo5arfYdsX2ffYAtsa3/3kU+yx9KL9tAZ/D6kX8R4rJUkqUS5gMaAzRDV/NoI3cThkOWM6ZTtTPA89cT1VPZk8Jzv4OBQ2lDKiLnEqPiZGIsMe4hvCGW4Y3hfxF3cYLxnRGRIarBlnGBsWuRJKDvII6gKB/BD29++U6jrmKeOK4W3hw+Jl5RHpd+058vr2Yvsk/wkC8wPeBN0EHgTdAmMB///2/oX+1f74/+YBfwSMB8IKzQ1UEAMSlRLWEa0PHAxFB2ABwPrF89rsaebT4Gzcb9n+1x7Yudmg3I/gOOVC6lvvNPSR+Ef8QP98ARADHgTTBGEF+QXDBtsHUAkcCy0NYQ+MEX8TCxUJFloW9BXcFCgTARGaDi4M+wk3CA4HmgbgBs8HOwnoCogMxA1DDrINzwtqCHID8/wX9Sbsg+Ki2ADPHcZtvla4IrT8sfCx5rOmt+G8MsMsyl7RYdjf3pjkZelA7TvwhPJa9Aj23vcn+iL9+wDJBYgLGhJMGdggaiiqL0E24TtMQFRD5UT9RLJDKEGUPS85NDTaLk4ptSMiHp0YJBOsDSUIgwLB/OD28PAS63DlQeDD2zXYz9W+1B/V89Ym2oPewON46TjvhfTi+N77Gv1U/Gv5Y/Rn7cfk9dp40OrF57sIs9SruKYCpNqjQKYSqwqyyLraxMPPCds55vLw6frsA+cL3BLiGCIeziIZJzUrSC9rM6c38zs6QFhEJEhzSxxOAlARUUZRr1BlT5JNZUsPSb9Gm0S8QilB2D+qPnI9+Dv7OT03hTOsLpsoVCH2GLUP4QXc+w7y6+jd4ETaaNV60orRiNJG1XzZyt7F5PvqAPFy9gP7gP7MAO0B/AErAbz/8/0Z/G36IflR+AX4K/ig+C75k/mL+dX4Pfed9OrwMOyW5lngzNlO00XNEsgPxILBmcBnwePD5MctzWrTO9o84QvoUu7L80X4qvv5/Un/xv+l/yf/if4F/sv9+f2g/r3/PwENAwMF/gbdCIkK+QsxDUQOVQ+PECISQBQSF7UaMx+AJHsq6DB5N9E9iEM2SHtLCE2jTC9KskVRP1E3FC4NJL8ZrQ9UBiH+ZvdY8g3vdu1k7ZDunPAh87L17/eC+S/61Plr+A327PJM74Lr6OfS5I7iVuFO4YPi6ORZ6J3sbvGB9of7OABcBMQHWgoYDAkNSQ37DEgMWgtSCkgJRwhNB0sGJQW7A+oBlP+h/An51PQb8Azr4OXf4FLchdi31RzUz9PU1BPXWtpe3sHiHOcB6wzu5O9J8BjvTuwM6JPiQdyL1fHO+cggxNXAa78XwOrC0MeRztjWN+Ax6kL07f2+BloOfRQCGeEbMR0fHewb5RlaF5gU5BFzD2gN1gu8CgsKrAl+CWQJRAkOCbsIVgjxB6sHqAcOCP4IjwrMDK8PHxPwFukawx40IvAktSZPJ6AmnyRiIRYdABh7EusMugdNA/7/D/6q/dv+jQGPBZQKOxAUFq8bnyCHJB0nNSi+J8glfiIjHg4ZnBMuDhwJsQQkAZP+BP1j/Ir8Qv1N/mj/WQD0ABsBxgAEAPn+1f3Z/En8aPxr/Xz/qgLxBjAMLBKYGBgfRiW+KiIvIzKKMzYzJTFvLUUo7SG9GhETRQuvA5z8QPbD8DTskujK5cHjU+Je4cXgdeBm4J3gK+Es4sDjBuYY6QXty/FT93L95QNcCnUQyRXxGY8cWB0YHLkYSBPyCwYD7/gq7kLjxtg6zxLHqsA9vOO5kLkXuy2+c8J7x9PMENLV1tza990Z4E/hxOG14XLhTuGe4azis+TY5yrsnPEL+ED/9gbfDqoWDR7GJKUqiC9hMzQ2EDgQOVM5+jgdONA2FjXrMj4w9CzvKBIkRR58F7sPFwe9/enz6uke4OTWnc6gxzTCib6zvKq8Rr5EwUrF78nAzlDTOdcr2u/bbNyt29vZPNcv1CDRgc7BzEDMSc0K0JPUz9qK4nTrKfU2/yEJexLdGvchlCeaKw0uDS/RLqEtzSupKYMnnSUoJEIj8iIvI9wj0yTlJeMmpCcIKPsneSeMJkol0yNLItQgjh+LHtIdVx0CHascIRwtG5sZOxfvE6kPcwpvBNj9+/Y58PvprOSw4Fre6N163xDjh+ie7/f3HQGSCtATWRy8I6EpzC0gMKMweS/hLC4pwCT6Hzwb1hYHE/cPtA00DFgL7gq8CoUKDgorCbsHtwUoAy4A+vzJ+d72fPTe8i7yh/Lq80H2YPkF/eEAoATrB3MK9wtKDFgLJQnQBY0BpPxm9ynyQ+3+6JXlLuPc4ZnhS+LI49vlSOjW6lLtlO+F8RzzZPR09Wz2c/eu+Dj6Jfx0/hIB2wOXBgMJ0wq7C3ULywmaBtwBqPsv9MPrzOLD2SnRf8k5w7q+SLwIvPu9/MHGx/XOEteZ3wPo0u+Z9gX84P8WArUC6AH4/zr9FPrr9iD0BPLV8Lvww/Hk8/324PpR/xAE4giPDe4R4RVcGWEc+x5AIUcjJyXuJqMoPyqwK9YsjC2lLfgsXyvBKBglbiDjGqwUEA5iB/0APPtu9tbyoPDd737wWfIn9Yr4FPxS/88BKAMJAz0BsP1u+KnxtOn54PfXM88yx27ATLsXuPm2+7cEu9u/M8aqzdjVVN7A5szuPfby/OICGwi+DPwQChUfGWkdDCIaJ5EsWzJSOD8+4kP7SEhNlFC0UpFTJlODUcZOHUu8RttBrzxmNx4y6yzNJ7cikB04GI0ScQzQBab+//YB7+Lm7d541+LQiMvAx8/F4sUKyDbMNtK62VbijOvS9Jz9ZQW7C0YQyhIxE4YR+Q3UCHcCVPvc83/soeWQ34PaldbJ0wfSJtHt0CHRhdHn0SLSI9Lu0ZbRQ9Eq0YTRjNJ41G7Xg9u54PnmFu7R9d394wWQDZQUrhqtH3kjEiaPJxwo9SdiJ60mHibxJVMmXicTKWMrJi4oMSs07jYyOcQ6fztROzo6UTi8Na8yZS8YLAApRyYFJEAi6yDhH/Ae2h1bHDMaKxcfE/8N1QfGABP5DvEc6anhItvo1UvSgNCf0JzSTNZi23jhGOi/7u30K/oY/mkA+gDF/+T8l/gy8yDt0+bB4FTb6tbJ0x3S99FM0/nVx9ly3q7jMOmy7vnz2Pgy/fgAKgTRBvwIuAoUDBUNtg3sDZ8NtAwMC4sIGwW0AF/7NfVp7j3nBuAj2fjS6c1LymXIY8hSyiDOmtNv2jLiaOqJ8hL6hgCBBbgIAwpeCeoG6gLA/d/3x/H76/XmHOO/4A7gGeHO4/3nX+2Z80j6CAF+B1wNaRKCFqAZzxszHfkdXB6THtIeQh/8HwghWyLZI1klqyaaJ/cnmidpJlwkeyHjHb8ZRBWyEEMMMgiqBMoBnP8Z/iX9mvxE/Ov7XPto+vP48vZt9IbxcO5v69Lo6+YF5mPmMuiF61XwfPa5/bAF9w0XFpkdDiQWKW4s6y2JLWErrifEIgod8xb0EHcL2wZjAzoBawDmAH0C7wTsBx0LLA7OEMQS5xMlFIQTHhIgEMENQAvYCLwGEgXvA1MDKwNWA6MD2QPCAykD5wHo/yX9s/m59W/xHu0R6Zjl+uJx4SfhLOJ85Pnnc+ym8Ub3BP2TArMHLgzoD9QS/hSDFo8XVBgJGd4Z+RpsHDseTyCAIpUkRiZJJ1QnJiaQI3of5hnwEtQK4wGC+CDvL+Yd3kbX8tFMzmDMGsxJzaDPw9JI1sjZ4dxC37TgGeF04ObeqtwR2nzXUNXx07fT5tSs1xfcGuKM6SnynfuCBXUPDRnuIckpZDCVNUo5gTtJPLk78TkQNzIzby7VKG0iOBs2E2kK1wCT9rvrfeAb1eXJOb97tRKtXqazoU2fT5+7oW6mJ62DtQS/HMkz07PcEuXa67XwcfME9InyQ++U6vXk794N2dTTus8azTTMI83kz1HULNoh4dHo2vDg+JAArwcTDqwTfhikHEQgjyO2JugpSS3uMNw0CTlYPaFBtEVeSXJMxk5EUOBQo1CnTxNOGkzySdJH6kVeREJDlkJHQi9CG0LLQf1AdD/6PGs5uDTrLiUonyCnGJYQ0AiyAZX7u/ZS827xAvHm8dnzhfaH+Xn8+P6wAGAB5AAy/1/8nPgz9H7v3+q75mvjOeFY4ODgyuL05SLqA+879Gj5K/4xAjsFHwfLB0oHvQVaA2MAJf3m+en2ZPR68jnxm/CH8NPwTfG/8fPxvfH/8Kzvy+1z69DoF+aH417h1d8a30rfb+B+4lTlweiE7Ffw7/MN93r5EfvE+5z7tPpA+Xz3sfUn9CDzz/JV87/0/fbp+Uv91QA2BBgHLgk3CgkKkQjZBQgCXv0t+NXyvO1F6cflg+Ok4jXjJeVG6FHs7vC69VH6V/5/AZMDeQQyBN4CuAAP/kD7rfi49rf16/WB94f68v6YBDsLihInGrIhzSgnL3s0mThoO+I8Ez0XPBQ6NjenM40vBSsiJu4gZxuJFUkPogiWATD6ivLN6jPjANyC1QnQ4ctKyXLIcck+zLXQktZ13enkaOxp82T54/2DAAYBUv9w+5b1Hu6B5UzcHNOMyi/Dhr3yubW46rmFvVfDE8tT1KHegul+9Cn/KAk3Eioa7yCJJg8roi5tMZkzSzWeNqE3VDivOJw4ATjDNss0CzKDLj8qXyUQIIwaFxXzD2ULogfWBBUDYQKjArEDTgUzBxIJoQqdC9ULKguYCTUHKwS+AD39Afpg96r1HvXj9Qf4dvsEAGgFRQswEbkWdBsCHxghhyE8IEUdzRgZE4IMbgVF/mn3MfHd65nncuRc4jbhx+DO4AThIuHx4EbgDN9H3RDbl9ga1uTTQdJ50cvRY9NW1qPaLuDI5izuDPYQ/uIFOA3SE4EZLx7ZIY8kcya0J4IoESmMKRMqtyp2K0Es9ixtLXQt3iyBK0IpFyYJIjkd2RctEoUMNweVAun+avw5+177xPw9/38CMgbxCVMN9g+FEcIRiRDTDbcJaQQ2/nj3lvD16fLj2t7j2ijYqdZI1s/W+ddx2ePa/tt/3DrcF9sd2W7WQ9Poz7nMFcpYyNPHxMhTy4rPWtWX3AHlQ+4A+NUBZgtfFH0ckCN9KT0u3DF1NCk2IjeEN2039TYjNvU0XzNKMaAuSys6J2oi5RzJFkAQhwnlAqj8GveC8hbv9+wv7KnsN+6P8FPzFfZi+M358fmD+FP1VfCi6XjhNdhUzmTE/bq1shWskqeCpRSmU6khrzy3QcG2zBPZy+VW8jf+CQl/EmgasSBfJY4oayorKwgrOSrtKEYnXCU3I9UgLR4zG9oXHRT+D44L6QY2Aqj9d/nZ9QTzIPFH8H/wuPHQ8472q/nW/Lv/CgKAA+wDNQNcAYH+2vq49nnyiO5O6yrpbehO6ejrNfAQ9jX9SQXgDYUWwh4uJm4sQTGFNDI2YjZGNSYzVzAzLRIqPyf2JFwjfCJKIqQiVSMeJLok6SR0JDQjGSEnHnsaRRbFEUcNGAmBBcECBAFiANsAVQKiBIEHqArDDYQQpBLrEzgUexO/ESIP1QsTCCEEQQCv/Jn5IPdQ9SL0f/NC8z7zQfMf87Xy7PHB8EHvj+3Z61vqVOn/6JLpMOvn7a/xYvbG+4cBRQeVDA8RUBQJFgIWIRRrEAgLPQRq/P3zdOtK4/DbyNUb0RPOvMwCzbPOidEs1TzZXN034YrkJuf36ALqY+pN6gDqwenY6YLq8etA7nbxgPU2+l//sATbCZAOhxKBFVQX6xdFF3UVohL/DsgKOwaQAfn8mfiE9MHwRu0A6tfmruNw4A/djNn11WvSHc9FzCPK+Mj/yGXKQ82a0U7XKt7d5QHuIvbE/W0Esgk8Dc8OUQ7OC3gHogG8+knz2ev85DnfAdus2G/YWdpV3i3kjOsH9Cf9cQZyD8MXEx8qJe8pYS2bL8wwMjERMbAwTTAeMEUw2DDXMTUz2DSfNmY4DDp1O5A8Wj3YPRw+Pz5cPo0+5T5sPxxA3UCIQehBvEG/QK0+SjtqNvUv7id2HskTPwhI/F7wCuXN2iDSZsvnxsnEDsWSxxLMLNJo2UPhN+nF8H/3Df0zAdkDAgXPBHgDRwGP/qH7yfhF9j/0y/Ln8XzxYPFh8Ubx2fDu72fuOOxt6SXmkeLz3pXbw9jC1s/VEdad12zaY95P4+vo6O7x9LT66f9VBNYHXQryC7YM1wyTDCwM5Qv4C5EMzQ2yDzQSMRV8GNobDR/aIQ4khCUqJv8lGCWaI7chqR+qHe8boRrWGZAZuRkmGpcawRpPGvAYWBZQErcMhwXe/PPyHujN3H/Rt8b7vL+0aK47ql6o1ah+qxuwU7a6vdvFQc5+1jfeJuUg6xXwEvQ597754fvm/QkAgQJyBesI6AxPEfYVpBoaHxgjYybLKDAqhCrNKSEopyWRIhUfahvBFz4U+hD7DToLnggHBk4DSwDe/O/4efSI7zvqxeRk32XaE9a50pXQ08+H0KzSHtah2uDfdeXw6uPv5fOi9t33efd79QvycO0N6Fvi2twN2G3UYdI00hHUANjl3YLlgO5v+NYCOg0mFzMgESiKLoQzBDclORk6ITqDOYg4cTd0NrY1SzUzNWE1uTUXNlY2UjbuNRk1zTMUMgEwsi1JK+koriasJOsiYCH0H34ezRyoGtcXJhRwD6IJwgLv+mDyZ+lo4NXXJtDMyS7FnMJJwkfEgsjDzrHW19+v6aXzJ/2sBcMMDxJbFZAWvRUTE9wOeAlSA9n8cvZ58DXr1OZs4/zga9+U3kbeTd563qjevt633p7ejN6p3iTfLeDv4YzkEuiA7L3xnffh/ToEVwrgD4gUCxg8GgMbYRp0GG0VkxE6DbsIcASqAKr9nfuc+qj6rPt//e3/uQKoBYIIGwtaDTUPthD2ER8TXhTkFd0XaBqUHVohoCUwKscuEDOuNkg5izoyOhM4HTRhLgwnah7dFNkK2wBe99Lulefs4fzdy9s72xTcBN6q4J7jd+bZ6HnqJuvJ6mrpKudG5Avh0N3x2sTYk9eU1+nYmNuR367ktupm8XL4kf+ABgkNAxNVGPgc8iBRJC0nmimrK2kt0i7YL18wQjBWL24tYioUJncgkRl9EXAIs/6e9JjqDOFg2PDQBcvPxl7Ep8N7xJXGlckRzZfQutMb1nHXjddg1v/TnNCEzBvIz8MTwFG95bsRvPy9q8EDx8nNqtVA3hnnwu/S9+3+zARGCU0M7Q1MDqUNQQxtCnkIqwY9BVgEEQRrBFcFuQZrCEYKIwzjDXEPxRDmEeYS4BP3FEoW+RcVGqYcoB/qIlkmtynDLD8v7TCeMTAxmy/tLE4p/yRTIKwbchcKFM4RBRHaEVoUcBjlHWMkfSuzMn05Vz/IQ21GAEdfRYhBozv1M+Aq2yBkFv8LIwI7+ZfxbevX5tPjQ+L44bTiMOQq5mTorurn7ADv+vDm8tv0+fZb+Rj8Ov+6AoQGcgpNDtURxhTcFtsXlRfwFecSkQ4aCcUC6Pvf9A3uz+d64k3ec9v92eLZANsj3QfgX+Pe5j/qR+3Q78TxJ/MO9J/0C/WJ9Uz2gPdA+Zf7eP7BAT4Fqwi6CxsOhg+9D5oODgwlCAoDA/1m9p/vHulS45/eVtuu2cLZiNva3nXj/egJ7yj17fr0/+4DqAYJCBYI8wbcBCECHv8w/LH58Pcn93r39PiH+w7/UAMKCPEMuhEgFuwZ8hwcH2IgzCBuIGQfzB3BG1gZnhaQEyQQRQzYB8EC5/w69rnueOaa3VvUCMv+waK5XLKNrIioi6a3pg+pc62isz671MPgzNjVOd6N5Xbrs+8n8try9/HK77XsL+m05b3it+D638PgMOM/583snfNd+64DLgx6FD4cNiM1KScuDTIANSk3vzj5OQ87MjyCPRI/4UDdQuREykZcSGdJvkk+SdJHeEU8Qj0+pjmqNH8vWiplJcEgfhyaGAQVmxE3DqkKxAZmAnr9+vf88arrROUb347Z/9TO0U7QvtBC09/XeN7N5n7wFvsIBsYQvhpuI2UqVC8KMnwyxTAgLeQnfSFjGg4T8AtsBc7/Rfvn9671evQZ9Ez0z/Re9cL1zvVr9ZL0UfPI8SDwi+487V7sFexz7HrtG+808ZrzFvZx+Hf6/Pvl/Cj9zvz2+8/6lfmL+Pf3F/gc+Sf7P/5WAkQHywydEl4Ysh08IrAl0Cd2KJcnQCWcIeUcaRd9EXQLnwU8AHr7bPcT9FbxCu/37NzqfOie5R3i5d362HvTnM2mx+/B1ry0uNu1i7TqtAO3wrr3v1XGfM3/1GzcVONY6SzunvGd8zT0jfPt8anvJe3G6u7o7+cK6GjpFuwH8Bf1D/umAZEIgQ8tFloc2SGOJnAqhC3cL5QxyTKZMxg0VDRONPszRjMTMkQwuy1kKjgmPiGSG2IV8A6LCIkCRv0T+Tf25PQw9RT3avrp/jEEzAk4D/ATdBdXGUcZEherEi4M2wMW+lzvPuRT2TLPY8ZXv2W6v7d0t3C5gL1Ww5TKztKc25rkce3f9bf94ARaCzMRhBZvGxQgjyTwKDotYzFRNd844TsoPoU/1j8BPwA93Tm2NbYwGisiJRQfMRmuE7QOWAqdBnEDsQAv/rP7Bvn59WfyQe6I6Vvk69592WfUA9CszLXKXcrPyxTPGtSs2nfiE+sD9MT80gS6CxYRoRQxFsYVfROWD2sKagQJ/r/3+fEX7V/p+ub35Ubmv+cm6jHtkfD68yn36vkd/LT9uf5G/4T/pf/b/1QAOgGhApEE/wbOCdcM5Q/DEjwVJxdjGOUYsRjiF6EWJRWuE30SzhHQEaMSUhTQFvoZmh1nIRElRSi0KhssSiwqK7soGCV4ICAbaBWsD0cKiwW4Afn+XP3Y/Ef9bf7//6YBDgPlA+oD8QLlAM/9zvkc9QPw2ur45bLhTt4C3Ofa/9ow3EneA+EO5BLnu+nB6+3sIu1a7K7qTuiC5Z7iAOAF3gPdPt3k3gnipuaY7KPzd/u4AwQM+RM9G4ghnyZiKsIsxy2ILSks1Sm4JvoivB4VGhAVrw/sCbwDGP359WfueOZR3ijWQ87zxpLAeLv2t0+2rrYluaW9/8Pky+rUkN5J6IXxufltAEIF+wd+CNwGSgMj/tf38PD86YvjHN4b2tfXfdcW2YjcmuH45z/v//bM/j4GAA3QEoQXDBttHcQeOh8CH1IeXx1SHEobWRqCGbwY9RcVFwcWthQbEzcRHA/nDMEK3ghyB7AGwwbJB84JyQyaEA0V3hm6HkgjMicoKuwrVixWK/wocCX1IOMbnRaKERANhAkqBykGjAY9CAkLow6sErgWXBozHeceOx8PHmEbThcSEv8LeAXn/rb4RfPk7snrEOq36aPqnuxg75Ty5fX9+Jb7dv19/p7+5v1z/HT6JPjA9YHzmPEq8Env9u4g76fvY/Ak8bzxBPLi8UrxQ/Dm7l3t3uuo6vrpEOoa6zbtcPC79PX55v9FBsIMBxPDGK8dlyFbJPclfSYaJgslmyMcItsgHyAZIOcgiiLrJNUnAisXLrUwejIQMy4ypy9mK3clAx5MFa8LkgFn95fth+SH3NDVgNCbzAjKmsgUyC/IocgryZbJwsmhyUDJvshOyC/IqMj6yWHMB9AC1U3bzOJJ63j0+/1tB2cQhBhtH90kpSiuKvkqnynLJrMimB27F1YRngq6A8T8xvXD7rTnkeBS2frRlMo6wxa8YbVer1iqmqZrpAKkhaX/qF6ucrXuvWvHbNFu2+XkUe1D9GP5fvyE/Y781/nB9cXwb+tR5vzh8d6b3UTeFuET5hnt5PUWAD8L4xaGIrQtCTg2QQZJXk89VLdX9FkjW35bOFuBWn5ZRljjVlRVjFN6UQxPNEzqSDJFHUHHPFc4/TPqL04sUSkNJ4wlxSSYJNIkMiVqJSclGyQAIqQe6xnUE38MJQQc+8vxqOgt4M/Y8tLnzt7M6cz0zsrSG9h83nXliOw78yL55f1HAS4DmwOvAqYAzv2A+hn38PNQ8XDvce5Y7hXvgfBl8n/0jPZN+Iz5J/oM+kL54/cZ9h/0NPKZ8IjvMe+x7xLxR/Mz9qP5W/0XAZQElAfmCWoLEgznCwILjwnDB9oFDQSRAokBDAEaAaABeAJuA0YEvwSdBLAD2AEM/1b73fbd8aHsg+fd4gjfT9zq2vjafdxe32XjQuiX7fjy+/c7/GX/OgGcAYgAGf6H+h/2QfFT7LnnzuPc4BbflN5T3zThA+R750zrJe+68s31M/jX+bz6/PrF+lX68vni+Wj6uPv1/SsBUQVGCtUPuRWmG0shXyaiKuMtBzAJMfYw8S8qLtorPymRJgEksSGzHwkeoxxiGx8arxjoFqYU1RFvDoAKKQaaAQ79xvgH9QvyAfAB7w3vDvDQ8Qz0ZvZ4+Nv5Lfod+XP2EvID7HDkqNsV0jrIqL7ztaquSakzpqulzaeMrLmzAL3yxwvUweCH7dr5RwV3DygYOR+lJH8o7SokLGEs4SvbKn0p6yc2JmkkgCJyIDMeuxsFGRcWBBPmD+QMKwrqB04GfAWMBYUGWwjuCgkOaRHAFLsXCRpmG50bkBo/GMUUWRBNCwUG8QCG/DD5TPcg99P4afzCAZsIlBAzGfAhPCqPMXA3eztsPSE9mzr+NYovmyeaHvcUJAuFAXL4KfDT6IDiK9272AzV9NFHz+XMtMqsyNbGSsUsxKzD+8NHxbbHYctM0GfWjN2C5f7tq/Yv/zAHYg6EFGkZ/hxEH1YgYyClH2Ee3hxbGw4aHBmVGHcYqRgFGVkZbRkMGQcYPxapE00QSgzTBy4Dqf6V+kH37/TQ8/vzbvUJ+JL7uP8aBE8I7QuUDvIP0Q8XDsgKCQYcAFr5KvIA60nkbN692XfWudSF1MHVOdin27bfD+Rh6GHs3O+u8tH0UfZT9wn4sfiL+dT6vvxp/+QCJwcVDH0RIhe7HP4hpiZ5KkstAi+cLycvxy2pKwUpEyYKIxUgUR3KGnsYUBYkFMsRFg/ZC/AHRgPb/b73GPEi6iXjc9xd1jDRLc1+yjjJUsmoyvzM+89F03HWG9no2pTb89r52LvVb9FnzAzH1sFBvcW5y7emt4q5iL2Rw3DL0tRO32rqpfV/AIoKYxPGGoggniQYJx8o7ifOJgwl8iLFILoe+RyWG5Ya7hmLGVMZKxn9GLgYVxjfF2EX8xayFrkWHhfvFysZwRqRHGoeDSA1IZwh/iAmH/EbVBdgEUQKSgLY+WLxaulz4vjcYtkA2AHZbdwn4urpU/Ph/QMJIxSsHhUo7y/mNck5jTtHOy85kzXVMF8rmyXrH58a9hUTEgQPvQwiCwgKPAmMCMsH1wacBRkEWgJ8AKf+Bf3C+wT75vp0+6X8Y/6CAM4CBgXnBjUIughUCPMGngR1Aav9hPlT9W3xKO7M65XqqOoQ7MHulfJR96n8SQLeBxYNrhF1FU8YORpFG5kbaRvyGnIaHhoiGpMadButHBEeYB9OIIcguR+cHfsZtxTQDWMFrPsB8czlitq3z9DFQ71otn6xoq7Tre6utrHYtfK6m8BwxhTMQdHC1X3Zcty03m7g0+Ed44fkQ+Zz6CzrbO4f8h72N/os/r4BtATfBhoIWAicB/4FpQPFAJv9Y/pV95/0YPKn8G3vn+4Y7qztKu1k7DbrielZ57jky+HL3v3bstk62N/X3thc22jf8uTM66zzM/zuBGYNIhW0G8EgCiRvJfIkuCIGHzoaxhQlD88JNwW6AZ3/Bf/4/1sC+wWKCqsP+xQZGq0ecSI1JeImfCceJ/glSyRcInYg2h7AHVAdnB2kHlcgkCIkJd0niCr2LAAvjTCRMQ8yFDK3MRIxPjBPL04uOC37K3gqhCjtJX8iCh5qGIwRcwk7AB32auuJ4PTVK8yxw/u8brhTttG257lwvx7HhNAZ20bmavHq+zkF5AyXEiAWdhezFhYU9g+9CuEE2v4R+ebzoO9t7GLqeOmW6Y/qLew57nvwyPL+9Az38vi7+n78W/5uANMCmwXKCFUMHxD+E70XHhvlHdgfySCcIEgf2hx3GVkVyRAcDKsHywPGANb+Gv6b/kcA8QJZBioKDA6gEZIUmhaFFzkXsxUME3QPKgt8BrcBKP0N+ZP11PLO8GrvfO7H7QPt6es36rfnSOTh35Xaj9QVzn7HL8GOuwC327Nhsrqy8LTvuIW+Z8U2zYnV9N0O5oDtBPRt+az9ywDuAk4EMAXhBawG1geUCQcMPA8pE68Xnxy9IccmfSujLwszlTU1N+030jcEN6o17TP1Md8vvS2RK04p2SYNJLwguhzgFxESRAuCA+76vvFA6NDe1NWyzczGdMHnvUW8kLyrvlfCPsf1zAbT+dhc3tHiDebq513ogOeN5dbiwd/B3EXat9hu2KnZidwQ4R/nfO7W9sr/7AjXESgajiHQJ8ksczDbMiY0iDQ+NIczoTK8MfwwdTAoMAgw+i/ZL38vxy6TLdErfCmhJlojzR8pHKEYZRWeEmkQ0g7TDVQNLw0vDRkNsgzDCyUKwAeVBLwAZfzV92Hza+9T7HLqE+po64TuWvO5+VEBswldErwaQCJcKJgsli4cLhMrjyXJHRoU+gjy/JDwZeT22LTO98X6vtm5krYLtRK1arbLuPK7nb+Zw8DH+ss/0JPUANmV3V/iZeej7Ajyd/fF/L8BLwbcCZUMNQ6mDugNEwxSCecFIgJe/vb6RfiW9iT2Evdl+Qr90gF3B6YN/RMcGqwfYCQCKHcquyvnKysryikSKFUm4CT3I8gjayTfJQgotCqcLW8w1TJ8NBs1fjSFMiwvjSrWJE8eSxcoEEEJ6gJm/eH4cvUS86Lx7fCw8JzwY/C872/uVexj6aXlQuF43JbX9NLwzuHLFMrAyQbL7c1i0jfYLN/v5ijveveS/yIH8g3ZE8EYpxyXH6ch9SKcI7UjTiNtIgkhDR9dHNgYXhTUDi0IbACp9xHu6OOG2U/PsMUXvem1erAHrbGrdKwvr56zYrkHwAzH78001HDZUd2m31/gkd9x3VPan9bL0lDPocweyxXLs8wH0ADVcNsO44LraPRa/fkF9Q0PFR4bFCD2I+Am/Ch9KpgrgSxiLVYubC+iMOQxGTMaNMI07zSFNHczxjGDL80s0inFJt8jVCFRH/QdTB1QHecd5R4QICQh3SH7IUohqR8NHYMZNRViEFsLfwYyAtL+sfwK/AH9l/+rAwEJOw/oFYkcmiKeJygr4yyYLDcq0CWZH+kXKg/bBYD8mPOX693ksN823HjaYNrC21re2uHt5UPqk+6i8kj2bfkQ/Dv+BQCNAfICTgSzBSkHpwgcCmoLawz6DPQMPAzGCpQIuwVlAsv+L/vh9y31WvOh8ivzBPUh+Fz8cwEUB9wMYRI7Fw0bih2AHtcdlhviF/sSNQ3zBp0Amfo+9dPwhu1r63bqhOpb67DsMu6O73nwufAn8LXubux46QnmbOLv3uPbkNkz2PDX19jb2tvdnOHX5TnqcO4v8jb1WfeC+Lf4E/jK9h/1YPPe8ebwuPCD8V/zTPYx+t3+DQRzCbkOixOeF7QaohxTHcgcFhtjGOQU0BBkDNUHTgPt/sH6yvb88kDve+uW533jKd+k2gnWgtFNzbHJ/MZ5xW3FC8dwyp3Pdda63hPoDvIm/M8FgQ66FREbOh4LH4EdwhkXFOoMvQQi/K3z7Otf5W3gXd1W3FvdTODv5PHq8/GP+V4BCQlDENYWoByWIb8lMikOLHkukzB5Mjs03TVUN4w4ZDm4OWQ5SDhRNnYzwC9KKzwmzyBBG9QVyBBSDJsIuAWpA1oCpAFQAR0ByAARAMX+v/z1+XX2ZvII7q7pu+WS4pjgIeBw4ank0+nR8GP5LAO4DYIY/SKfLO00gTsSQHlCskLcQDc9GTjtMSIrKyRuHUIX5BF7DRAKkQfZBbIE2wMRAxgCvADd/mr8aPnv9SfyQu536v7mCOS54SjgW99H39Lf1eAl4pTj+eQ05jHn8Od+6Pnoiulk6rrrue2H8Db0xfga/gQEQQp5EEoWTxsoH4IhHSLUIKIdnhgAEhsKVgEp+Anvbua/3k7YUtPkz//Nfc0izp/Pl9Gu043V7NaW12/XdtbF1InSBdCFzVfLx8kTyWjJ3cpzzQ/RhtWa2gTgeeW06nvvpPMb9+H5D/zS/WX/CgELA6UFDglnDbwSARkRILEnli9qN9I+dEUFS0VPDFJIU/9STVFgTnVKzEWrQFA77DWlMI4rqibtIT4dfxiQE1gOxQjWAp38OPba78TpPOSK3/Hbp9nN2G3Zctuv3tnij+dg7NTwdfTX9qP3n/ax8+Xubeie4OfX0s7vxdS9DbcRsj6v0a7gsF21F7y/xOzOKNr15drxZ/09CBUSwBonIksoPy0kMSQ0aDYYOFI5LTqvOtY6lzrfOZw4wTZENCsxhi12KSUlySCdHN0YvRVmE/IRZRGuEaUSEBSkFQ0X9RcMGBAX0xQ/EVwMUQZf/973OvDk6E/i5tz92NLWgdYH2Drb1d935azr9/Hb9+f8uQAOA8ADyAJFAHH8nPcr8onsIedU4nPet9tA2hTaHdsw3RLgfuMs59fqRu5R8d7z6vWC98X42Pnp+iT8rf2f/wQC1wQDCGILxQ75EcgUBBeLGEgZPBl6GCUXdBWlE/wRvBAdEEoQWRFMEwoWaBkmHfYghySFJ6opviqdKkEpvCY9IwofeRrrFcMRXA4FDPEKPAvgDLkPhxPyF48c7CCZJC0nUyjPJ4ElaiGqG3wUMwwvA9z5n/DY59jf19j40kbOssofyF3GOcV+xP/Dm8M/w+zCtcK9wjHDScQ3xirJQ82S0g7ZmuAA6ffxJ/ssBKYMNRSHGl0fjyIOJOQjNSI1HyobYBYkEb0LaAZRAZP8Nfgt9GfwxOwi6WXleeFY3Q3ZttSA0KjMdMkrxxLGYMY7yLDLsdAV15be1+Zr79n3qf9sBsULcQ9KEU8RoQ+CDFIIgQOS/gD6R/bM89vyo/Mt9mL6CADOBkoOCRaTHXgkVyriLuYxSzMWM2UxaS5lKqElaiAHG7UVpRD4C8EHBQS9AOD9X/sw+U73vvWP9NfztfNI9LD1B/hY+6D/yASmCvsQdxe9HWojHCh7Kz4tNi1PK5cnOyKIG+QTxwu3Azf8wfW/8HztJezE7DnvSPOT+Kf+BgUvC6gQBhX6F1AZ9xj/FpUTAg+hCdgDDf6g+OPzFPBZ7cDrO+ur697sme6e8LPyp/RV9q33rfhl+fT5f/oy+zX8qP2g/yACHwV+CBEMow/4EtUVBxhnGd0ZaBkbGBsWohPzEFgOGgx7Cq0J0AntCvQMvQ8PE54WGBopHYcf8iBBIWMgYB5eG5UXUxPtDsAKHwdSBIoC4gFUAr8D6AV8CBkLWA3RDigPFQ5oCw8HGgG1+Snx1ecm3pHUhstqw5K8ObeBs26x7LDQsd2z0LZfuki+UsJTxjXK882b0UjVINlJ3enhG+ft7FvzTfqXAQAJPRABF/oc4CF2JZMnIignJ8AkHCF/HDcXlhHuC4UGkwE//Zf5lvYj9BXyPPBh7lPs6OkI563j5N/R26jXqtMg0FDNe8vRynDLW8170J/UgNnE3gjk5ej+7ALwu/EL8vfwpO5W62rnT+OC33vcrtp52iHczN9+5RXtU/bbAD4MARimI7UuxTiCQbNIOk4UUlhUM1XgVKJTvlF0T/pMd0oFSKxFaEMqQds+Zzy4OcQ2ijMTMHYs0ihMJQ0iOB/qHDEbDBpnGR4Z+xi+GB8Y2RatFGwR/AxfB7AALPkm8QrpU+GA2g/VbtH3z+TQStQX2hHi3Ov69tcC0w5MGqgkYC0INFg4LDqGOYw2hjHRKt0iHhoKEQkIdv+T94vwdepN5QPhdt2C2gPY2tXy00PS0tCyz/7O2M5hz7bQ69IE1vbZo97c42Tp9O4/9Pz46/zW/58BPQK9AUQACv5U+3L4svVe87Hx1fDb8L7xYPOO9QX4ePqa/CH+0/6H/i390PqU97Tzf+9Q64Pnc+Rs4qjhROJG5JHn8esZ8ar2QPxxAeQFSQlsCzIMoAvVCQ4HmAPS/xz81fhQ9s70d/Ra9Wv3hPpp/tICbgfqC/wPZhMAFrQXhBiIGOoX3xalFXkUkRMYEygTxxPqFHIWMhj1GYIboRwlHe4c7hsqGrsXzBSSEUwOPAuaCJgGUgXVBBMF7AUsB5EI0QmhCrsK6AkDCP0E4QDV+w/22++O6YHjCN5o2dbVbNMt0vzRqNLq02zV19bS1xXYaNet1eTSLM+9yu3FIMHFvE+5Jbeftvu3XLvCwAzI/NA321Tm2vFT/UoIYRJIG8si0yhjLZQwlzKoMws0BDTQM6IzmzPOMzs00zR9NRg2gjaeNlQ2mTVvNOYyFzEnLzoteSsBKucoMSjUJ7InoCdmJ8QmeiVQIxogwBtBFrkPXgiAAIX43vAC6mfkc+B33qTeCuGS5f3r6vPb/D0GcQ/aF+QeDyT6JmsnSSWqIMQZ8xCoBmf7ue8n5C3ZM8+Lxmu/7bkUtsqz6rJGs6m05LbMuUK9McGRxWXKs8+F1ePbzeI26gjyG/o6AigKoBFbGBgeoiLSJZon/yciJzkljSJ2H1EcehlGF/kVwRWzFsUY1hupH/AjTyhmLNovWjKqM6YzQzKUL8crGyfkIXgcMRdeEj4O+gqgCCcHaAYqBiIG/AVkBREExQFb/sb5GPR77TXmnN4U1wTQzcnHxDPBOr/svjvA/cL3xtnLT9EB157c5OGh5rvqLu4K8XLzl/Wv9/L5kfyv/18DogdlDIARvRbdG5sgtSTyJyYqOSskK/cp1CftJHwhwB31GVEW9xL+D2UNGwv+CN0GhAS7AVX+Lfo29XbvC+ks4iLbR9T8zaHIj8QOwlDBacJQxdrJwM+m1hvep+XU7DTzb/hD/I7+Tv+i/sP8A/rD9mvzYPD87YfsMOwK7Q7vFfLm9TP6qP7rAq8GrQm3C7IMnwyUC74JWQeqBPwBlP+t/XL8APxb/Hf9Nf9pAeQDbgbYCPkKtgwBDt0OWw+UD6wPxA/9D2wQHBEFEhITHRT1FGIVKRUYFAUS3Q6hCm0Fev8U+aDykexd53njTOEn4T7jouc/7tn2EgFxDGUYUSSZL6s5CEJOSD9Mwk3oTOJJBUW7PoA31C80KA8hwRqMFZgR7Q58DR8Nng25Di0QuhEpE1IUGhV1FWgVABVRFHETdhJqEVIQJg/SDToMPQq6B5AErAAI/K/2v/Bt6v/jyt0q2H7TH9BazmPOWtA71OjZIOGL6bvyNfx4BQoOfxV9G8ofRyL4IvwhkR8FHLUXABNADsQJxgVnArP/lf3o+3P68vgh9730kvF/7XvolOL029jUkc18xva/Wrr1tQOzpbHmsbGz3LYmu0LA2sWWyynRUtbm2szeBuKp5N/m3Oje6h/t1u8p8y735/s+AQ0HGg0iE9kY+R0/InsliidgKAgonCZLJE8h5B1KGrcWVRM/EH0NBAu7CHoGEgRVARr+QvrD9aXwCOsi5Trfp9nE1O7Qds6ezY7OU9Ha1e/bQeNq6+/zUvwQBLoK7g9pEwgVyhTREl8PzgqOBRMA1vpC9rHyafCQ7y/wMvJt9Z75d/6kA9UIwg0xEv8VGxmKG2Ud0R7/Hx8hYiLsI9UlJCjRKr8txzC3M1c2dDjfOXc6Kzr5OPU2QDQIMYQt7Cl1JkkjhSA0Hk0ctxpHGckXAxa+E8oQCA1tCAUD9vx99u3vpekN5Izffdwn27rbQt6r4r3oH/Bd+PAASgnYEBcXlRsAHigeAxyuF2kRlgmqACz3pe2Z5H/cttWE0BDNY8toy/XMzM+j0y/YJd1E4lfnOuzW8Cb1L/n9/J8AJQSVB+8KJg4jEccT6hVmFxUY2xeqFoQUfhHDDY0JJwXjABn9F/oj+HH3Gvge+l39nwGSBtML8xCCFRcZWRsHHPsaMxjKE/0NIgek//b3j/De6UHkAeBH3SDcedwj3tjgQeQB6LvrGu/a8cvz1/QA9WD0JvON8dnvTu4o7ZbsteyM7Q7vGvF98/v1VPhK+qj7S/wf/Cz7i/lu9xT1yPLa8JXvOu/77/LxIfV0+bz+uAQZC4cRqxcyHdkhbSXQJ/so/CjzJw0mgSOHIFEdCBrHFpgTdRBHDewJPQYPAkD9t/dt8XLq6uIO2yvTm8u/xPm+oLr6tzi3ariFu1vApMb8zfDVBt7C5bXsg/Lq9sj5HvsP+9r53Pd+9TbzdPGh8BLxAfOM9rH7TAIjCuMSKhyQJbAuKze0PhNFI0raTUJQd1GiUfFQlk+8TYdLC0lTRllDD0BfPC84azMELvgnVCE1GskSSQv7Ayb9Eff58Q/ubusd6grqDevp7FLv9fF89Jr2Dvit+GL4N/dL9djyKfCW7XnrJerh6d3qLe3I8IL1FPscASgHugxXEY0U/BVjFZ8StA3JBin+N/Rw6V3eiNN2yZvAVLnjs2qw7a5Tr2yx8rSauQ+/BcU2y2rRe9dU3e3iT+iI7avyy/f0/CYCXQeBDHYRFBY0GqwdXSAxIiQjQyOsIpEhMyDZHtEdYx3NHTsfxCFkJfopTy8SNeI6VkACRYJIhUrQSkRJ5EXVQFg6yjKZKj4iMxroErwM9Ae4BA8D3QLsA+sFeQgqC5cNXQ8tEM8PJA4qC/sGxQHO+1/1y+5g6GLiAt1i2I7UftEZzzzNustqyibJ1cduxvjEj8NdwpnBgsFWwk/EmMdMzG3S6NmM4hbsL/ZwAHQK0hMtHDcjuiiVLMYuXy+LLoUskSn5JQAi5B3SGeUVJhKODgULageYA23/zfqq9QrwBurH443doNdR0vDNxsoLyeLIU8pJzZDR3dbK3OfiuejM7bbxI/Td9Mzz/vCj7ArnnODV2TjTR814yC7FssMsxKPG/soF0WvYzeDF6eny2Ps9BNsLhhItGNIciiB3I8QlmickKX4qvCvlLPEtzS5gL40vOS9PLsYsoir4J+okqSFtHnMb9xgqFzMWIxb4FpkY1hpuHRMgcSIzJBElzyRMI38ggByAF80RyAvfBYcALfwu+db3T/ik+rr+VwQkC7ASfRoIItEoai56MsQ0LTW9M5wwDSxpJhkghxkcEzMNFQjyA+IA4P7Q/YT9vv07/rn++v7P/hr+zvzx+pz48vUh81jwxu2P683pjOjJ53DnZueG56jnq+dx5+3mIOYb5f/j/eJN4ivi0OJr5Bvn7erS76L1H/z0Ar0JEBCAFasZQBwHHeQb3xgfFOwNpgbE/sL2H+9T6MLitd5Z3Lnbvdwv38HiEee160HwVPSc9935+vrt+s/50Pcz9UXyWe++7Lbqd+ke6bbpMety7UnwgfPg9jD6R/0FAF4CVgQBBoEHAAmrCq0MJA8jEqoVoxnmHTYiSibSKXos9S0ELnksPylcJO8dMRZvDQgEYfrd8N3nst+X2LTSFc6yymzIFMdzxk7Gb8aqxuLGDcc1x3LH78feyHXK48xP0M3UWtrb4Bzo0e+d9xT/yAVRC1MPiBHHEQYQYwwYB4IAF/lY8dLpD+OJ3afZs9fX1xjaWt5i5NzrY/SH/dcG7g9xGBkguiY8LKEw/DNxNi04XTkwOsk6QTukO/A7GDwHPKI7zzp6OZk3LTVIMgYvkisgKOckGyLrH3UeyR3hHaEe2R9IIaEikCPHI/8iAyG4HRwZThOJDCMFhv0r9ozvIOpN5mTkkuTk5kDravEC+ZEBjgpoE5MbjSLuJ2gr0CweLGwp8yQGHwcYYxCECM4AlPkU83btyOgE5Q/iw9/v3Wbc/NqT2RnYi9b41HvTONJb0Q3RctGj0qvUg9cV2zrfv+No6PfsNfHw9Af4avod/Dn95P1W/sr+f/+rAHoCBgVPCEEMrxBWFeYZBB5UIYAjQiRrI+UguxwVFzcQfwhcAEb4sfAM6rDk3eC13jjeRN+b4eXkueim7DzwF/Pj9Gf1hvRB8rnuJ+ra5Czff9ky1JnP98t8yT/IQchuyaHLqc5Q0mLWsNoZ34fj9udy7BHx8vU4+/8AYAdiDvwVEB5wJtku/zaKPiVFgEpXTnpQ0VBdTzpMnUfOQSY7AjTCLLwlOh9uGXgUWhACDUkK9wfOBY4D/ADu/UX6/vUq8fDriuY94VbcIdjg1MbS8NFi0gfUsdYa2vDd1+Fx5WvoguqI623rPeoi6GDlUOJa3+ncZdsp23rcg99O5MfqufLT+7AF3Q/jGUwjsSu8MjA47DvrPUA+GT2wOk43PTPGLikqmSU5ISAdUBnDFWsSNQ8QDPAI0wXDAtT/I/3V+hP5Avi/91r40vkU/Pb+PAKbBbsIRAveDD8NLwyQCWEFw//y+EjxNek44dTZiNPBztjLBstezM/PI9UB3PbjfuwL9RL9EwSnCYENdg+AD7wNZQrRBWcAmfrX9IrvC+ue527ljOTy5ILmEulq7FDwjfTw+FT9oQHQBeQJ6Q3wEQwWShqvHjMjwic4LGcwFjQLNww56Tl+Obk3oTRSMP8q7SR0HvIXxhFLDMwHgQSKAukBiAI0BKYGigmCDDQPTxGTEtYSCRI7EJMNUQrEBkYDMQDX/Xj8QPw9/WD/egJHBmkKdA76EY4U0hV8FV4TaA+rCVcCtvkp8BzmBNxP0mTJlcEeuyO2r7KzsBCwlrAQska0B7cpupK9NsEZxUvJ5M0A07rYJd9H5hbud/Y8/yQI5xAxGa8gFCcdLJwveTG1MWswyy0bKq4l3iACHGwXXBP+D2gNlwtuCr8JTQnQCAYIrgaaBK4B5v1V+Sf0nu4J6b7jFN9Z283YmtfN11zZHdzT3ynkw+g+7T/xd/Ss9rv3ofd19mv0yfHo7ibs4Olq6Abo3ugA62Du0/IY+Nv9uwNXCVIOWRIxFbQW1xaqFVQTEhAvDPwHywPr/5n8BPpJ+HD3b/cs+IP5S/tb/Y7/yAH8AyYGUQiRCv4Msw/HEkcWMhp5HvgifSfIK48vhjJjNOs08jNmMVAt2SdGIfQZVhLsCjgEtf7M+s747Pgx+4D/lgURDXAVIh6NJhouQDSOOLA6eDrfNwEzICyXI9oZZQ+6BFP6mvDm53bgb9rb1a7SytAF0C7QFNGL0nDUrNYz2QXcKN+p4pTm7uq37+H0UPre/1QFegoRD9wSqBVRF8QXBRcvFXQSGA9vC9YHqAQ8AtcAqwDOAT0E0gdSDGkRsxbHGz0gtSPjJZYmtSVLI34fjxrUFLEOjgjPAsz9xPnj9jP1pPQJ9SH2mPcV+T76xPpl+vr4c/bf8mTuQunJ41PePdne1IHRW8+Nzh3P9tDx09DXS9wX4ejleuqZ7iLyBPVF9/n4QvpM+0L8Tf2N/hMA4AHkA/4F/weyCdsKRgvFCjoJmwb0AmX+I/lz86XtDuj94rnedttV2VzYedh/2TLbQt1d3y/hbOLb4lXi0OBZ3hrbU9dU03jPGsyRySLIAMhDyebLys+21FzaYuBq5hbsGPEz9UL4Pfo5+2P7A/ts+v75FfoI+xr9ewA/BV4LsxIBG/kjPC1qNiQ/Fkf8TahTBVgUW+5cvl27XSFdMFwcWxFaKFlqWM1XN1eBVn5V/lPUUeBODEtVRslAiDq9M6EsbyVhHqsXdBHSC8oGTwJC/nj6vfbg8rPuFur55GffgNl806nNZ8gbxC/B/7/awPLDWcn+0Kna/OV88pP/nAzvGOkj9SyeM403ljizNgoy5yqzIe4WKAvz/tvyXefi3LrTFswOxp/BtL4lvcO8Xb3CvsvAWcNYxsDJkM3K0XPWjNsO4efm+ewd8x35wf7LAwUIPQtSDTYO7w2cDHEKtQe8BOMBiP/6/YH9Sf5jAMgDTAitDY4ThhkkH/cjnSfDKTMq1ii3Jf4g8xr2E3MM3wSv/UX39vH67W3rSupy6qrrpu0P8IjyvvRn9lH3XPeH9uf0pvID8ETts+qX6CznnOb95k7oeepV7ajwMPSp99P6eP1z/7EANwEcAYYAr//Q/ir+9P1d/oH/aAEIBEIH5gq1Dm4SzhWWGJkatxvmGzEbthmnFz8VwBJqEHYOEA1QDDcMsgyXDawOqQ9CEC8QMA8VDcgJSgW5/0n5SvIX6xjktN1I2CPUe9Fu0PbQ8tIl1j3a1d6F4+XnmOtV7uvvRvBu74zt3eq153Dkb+EN35ndTN1H3pLgGOSu6BXuAPQc+hgArgWiCs8OJRKnFG8WpheAGDYZ/xkJG3YcVx6rIF4jTSZGKRUsfy5RMGQxnDHxMG4vMC1gKjcn7iPBIOEddBuQGTYYVBfFFlUWyhXkFGkTKxEODgsKNgW9/+D5+PNm7pLp2+WW4wDjOuRE5/rrGfI++e8ApAjQD+oVexojHaMd4BvmF+gRNwpDAY73ou0J5ETbwtPXzb3JjcdBx7vIxMsX0GXVXtu24Srohe6h9GX6yP/GBGUJrA2bETAVYRgYGzwdqx5FH+weiR0XG54XOhMeDo4I3QJr/Zr4yfRM8mPxN/LQ9Bn53P7CBWQNRRXgHLUjTilKLWMvdi+CLakpLSRrHdEV2A33BZz+I/jN8sLuB+yG6g/qW+ob6/brm+zE7Dzs5uq+6NflXuKP3rHaE9f/07XRZtAx0B7RH9MV1s/ZFd6p4lDn2+sm8B30wvcl+2f+sgE3BSYJow3JEp4YFh8MJkstiTRyO69B50bNSiJNvk2PTJ9JEEUYPwI4HzDIJ1Af/RYKD5oHvABr+oz0++6K6QrkVN5L2OfRNMtUxH69/bYlsVGs2agHpxWnIqkwrSCztrqWw1LNa9dd4abq1fKK+YT+nwHfAmICZwBD/Vn5FvXi8BztEur65/Hm+Ob7583pNuz07sTxa/S39on41Pmf+gP7Jvs6+3L7APwO/bj+CAH7A3YHUgtcD1oTERdOGuYcvx7RHygg4h8rHzseTh2fHGEctxy2HVofjSEkJOImgym+K0wt9S2OLQcsainYJY8h4RwtGN0TUxDsDewMgQ23D3sTlhi1HmwlQCyuMjc4aDzmPnA/6z1bOus05C2oJaocaBNcCvgBnfqP9Prv7uxb6xrr8OuV7brvE/JZ9FX23PfY+EP5J/mY+LP3lfZZ9Rb01vKa8VrwBe+E7cLrrek953bkbeFH3jjbhNh11ljVdtUN10naOt/Z5fvtXPeaAT8MxxaoIF8pdTCMNWM43TgDNwIzKS3jJasdChWEDJQEov3698jzGfHW783vtfAy8uXzbvV49r32EPZd9KnxEe7H6QrlIeBW2+rWEtP1z6XNIsxayy7LdcsEzLLMXs3yzWzO185Oz/vPDtG80jbVo9gc3aPiKemF8Hj4tADfCJcQfxdCHZwhXyR2Jeck0yJyHw4b/RWXEDQLHwaSAbX9k/oo+FX28PTB85HyKfFg7x3tW+or57TjL+Dk3CLaNthl1+fX2dlC3QviAejW7iz2lv2iBOYKAxCzE8gVNRYQFY0S+Q65Cj8G/wFq/uD7rvoH+//8igCFBbALuRJGGvkhdiluMKU27js2QHpDy0VGRxJIVkg1SMtHKEdORjJFvEPOQUQ//TvgN90y+SxGJuseIRctD10HAQBm+cvzYe9B7GzqzOkx6lnr9Oys7i3wK/Ft8c/wR+/o7ODpcubz4sLfPt2+24jbytyV39njZ+ny7xX3Xf5JBWMLOxB2E9cUQBS3EWUNjweYAPH4FfF+6Z/i2dx12KDVbtTU1K7Wydnf3afi2ucz7X7ylPdc/NEA+QTmCKwMYhAYFNcXnRtYH+8iPCYTKUgrsiwzLbgsQyvlKMUlGSIjHi8ahhZsExgRrA80D58PxRBkEicUrRWSFnUWAxUAEkwN5gby/rL1ievw4G7Wj8zZw8S8rrfXtFu0MLYmuvC/JcdKz9zXW+BO6FHvGfV2+VX8wf3d/d38Bvuf+O/1NfOi8FrubOzb6pzpmei65+jmE+Y05VLkg+Pp4rHiD+M35FfmlOkA7pzzTfrmASIKrRIkGyEjQyoxMKQ0bTd3OMs3izXzMVEtACheIsYciRflEgEP7wukCQII2AbpBfMEuAMDArH/r/wH+dX0TfCw60vnbeNf4FzekN0K3sPfluJI5orqAe9L8w339vnI+2H8uPvn+SH3svP772TsWulA52vmGedt6Wrt9vLY+cIBVQolE8kb2iMCK/4woTXXOKM6HjtwOs44cDaMM1Uw7ixwKeUlSyKVHrEajBYWEkgNKQjNAlj9+vfw8nvu3epR6AXnFueJ6ErrL+/080P5vP74A5UIPAyqDrUPUQ+RDaQK1gaFAh3+Cfqx9m70fvMF9AP2WfnI/fUCdAjNDYYSMBZtGPcYpxd5FIkPEQlnAfL4I/Bt5z3f79fM0QPNq8m/xyTHrccjyUfL3c2u0JPTb9Y52fTbsN6I4Zjk/OfI6wfwtfTD+Q//bwSyCaIODBPHFrgZ0xshHb4d2B2sHX0dkh0sHoEfsyHPJMUobi2KMsM3uDwDQT1EEUY4RotE/kCqO8Y0qCy8I30abBEGCbsB4/u491T1rvSa9c736fp7/gsCKgVuB4cIPAh0BjQDn/7u+HHyg+uC5MzdsNdx0j7OMMtLyYPIvsjXyajLC87k0B3Ur9ec2/HfwuQk6ijw1/Yt/hUGaA7rFlQfSidvLmQ00zhxOws8hzroNlAx/ClEIZEXWQ0SAzH5GPAW6GPhFtwt2InV9tMv0+nS1tKx0kLSZ9ES0E7OOcwFyvDHPMYoxevEqsV1x0TK981X0hnX6ttt4EzkPOcE6YXpuui+5sXjHeAn3E3Y+dST0nDR0NHZ05LX49yd43TrD/QL/QMGnA6GFoUddCNFKAMsyy7MMDwyVTNNNFI1gjbwN5g5ajtKPRE/lUCxQUNCOkKOQUtAiz50PDU6ATgHNm80UjO5MpYyyDIdM1EzGjMqMjswFC2PKKMiYhsAE8kJJgCS9ovtl+Uu37PacdiO2Avbw99r5pnuzvd2AQAL2xOJG6Eh2yURKD0ofyYPIz8ebRgBElwL1wS+/kT5hvSO8FDtseqL6LXmBeVb46Lh0N/u3Q3cT9rY2M/XWteS14fYOdqX3ILfzeJC5qfpx+x074vx//LT8yD0FPTo8+HzRvRc9Vj3YfqG/rkD1QmaELIXuB5AJd8qNi/2Mesy/zE9L9AqBCU4Ht8Wcw9sCDUCJ/1++Vf3rvZg9yv5uvul/oAB5QN5BfMFJQX/Ao7/+Pp/9XXvNukg447dzNgV1Y/SStE90U7SUtQW12LaAN7C4YTlMunD7DzwrfMo98P6jf6KArYG+gouDx0TiRYrGb0aARvGGe0WcRJnDP8EhPxU897pmOD312nQRsrTxTTDccJxw//Fz8mEzrnTCdkY3pniWOY36TbrbOwH7UXtbO3E7Y7u/e8w8jD17Pg//ewBrQYwCygPTBJmFFMVDBWjE0MRLg64Cj4HIAS2AUsAFAAwAaADSAf1C18RLhcFHYYiXidIKxMuqi8LMFAvpi1JK34oiyW0Ii8gJR6uHMsbbxt7G8gbKRxwHHccIhxjGz4axBgVF1oVwxN8EqwRbRHIEbUSFhS7FWUXzhirGbYZthiGFhYTdw7SCHACrvv69Mzum+nV5dLjzuPn5RLqIPC/934A1wk2EwQcsiPFKdotsS8tL1osZSeaIGAYLA98Bc37jfId6sjiwNwb2NrU6tIo0mjSe9M01W/XDtoA3UHg0eO35/7rqfC39Rn7tQBkBvELHhGpFVEZ2hsXHescUBtYGC0UEA9UCVYDfP0k+KPzPfAc7k/txu1W77rxmvSU90H6QvxG/RH9hfui+IT0ae+i6ZTjqt1P2OTTttD7zsrOGtDD0oPWANvV35Xk2OhE7JHuke8z74Xtr+rx5p7iFN6w2c/VvtK60OrPX9AT0uzUwthi3ZfiLej37dXzs/mO/20FYguHEfIXtx7eJWMtMTUfPfdEdExKUylZx13lYFNi+2HcXxJc0lZlUCRJcUGwOTsyYStYJUAgGxzQGC4W8BPEEVYPUQxxCIQDcf069gDu/eSE2/jRxMhSwAW5L7MJr7OsL6xhrRawBLTUuCu+sMMUyRnOltJ81tLZtdxV3+vht+Ty587ravDS9fr7vgLoCS0RPBi+Hl8k2ij4K5otui1qLNYpOybmISwdYhjVE8cPaAzVCRMIFAe5BtYGOgexBw4ILQj7B3MHogajBZ0EvAMtAxkDnAPDBIkG1Ah3CzkO0RD3EmQU2hQxFFISRg8tC0cG5QBv+1D29/HK7hztJu0B76Ly3fdi/sUFiA0eFfobmSGKJXknMSekJOsfQBn+EJcHjv1o86jpx+An2RXTvc4zzG7LT8ylzjLStNbr25rhkeeo7cfz3Pnf/80FogtWEdoWFhzmICIllygTK2csaywHKzQoASSYHjcYMRHsCdYCYPzy9ujyifD/71LxbPQV+fj+rAW5DKET7RkyHx0jdiUmJjkl1yJHH+IaEBY5EcEM/AgoBmkExQMiBE8FAwfoCJ8KzwsnDGcLagkhBp0BB/yb9anujOec4C/ajtTuz3TMKcoEyejIrMkby//MKM9q0azT39UG2DPagtwV3xHileW06Xfu0vOo+cr/+AXtC1sR+BWCGccbqhwlHEsaSBddE9kOFwpyBT4Bw/0x+6T5Gvl5+Yz6Dfyp/Qf/1f/K/7L+cfwH+ZL0R+926X3jwN2m2IvUudFk0KPQb9Kl1QbaQN/y5LjqMPAE9fL4zfuE/SH+yP2y/CP7bfnc97n2O/aK9rb3tvlv/LP/RgPoBlgKXQ3KD4URhxLfEq4SIxJ7EfQQyhAxEU0SMRTaFjEaCR4pIksmJyp2Lf0vjTEMMnYx2S9aLS0qkCbEIgofmRuYGB8WLhS1EpARjxB5DxUOMwyuCXQGigIO/jT5R/Se75zrn+j+5v/mzOhy7Nvx0Pj2AN0J/BLEG6IjESqdLvEw2TBILlgpRSJuGUkPWwQy+VPuPeRW2/DTPM5RyirIqsejyNrKDs4C0nvWS9tP4HPlqur071P1y/pdAAMGrAs+EZQWhRvfH3QjGya4Jz4osScuJuQjFiEWHjwb4hhdF/IWzxcJGpYdTCLiJ/YtFTS+OXA+s0EiQ3BCdT8qOrAySilcHmAS3wVp+YTtquI+2YbRpcufx1bFlMQMxWXGQshMyjTMws3QzlDPTs/mzkbOo802zTPNw80Cz/jQmtPP1mraN9784YLlmOgZ6/HsH+6x7srulu5K7h3uQu7g7hHw2/Ew9PD26fnb/IP/mQHjAi4DXgJrAGj9ffnp9PrvB+ts5nvifd+k3Qvds92A30HireVx6TPtm/Be80D1IPb09dL05/J38NbtYut26WXoc+jL6X/sgvCr9bn7VQIgCbQPrxW9Gp4eLCFbIj0i/yDjHjscYxm1FocUHhOsEkoT+xSpFygbPh+oIx4oXywzMHAz/zXcNxU5xzkZOjk6UDqDOus6jztoPFk9OD7OPt4+Kz58PKg5lDU8MLQpJiLQGQIREwhg/z/3/e/U6ejkR+Hk3pzdO92B3Sje7t6Z3wDgD+DJ30jfvN5m3o/ehN+M4d3knOnO71z3EACXCYQTWh2QJqMuFTWAOZg7NDtNOAYzoCt/IhkY9gygAZ72aOxi49Xb7dW50S3PJM5ozrbPydFd1DTXH9r83LbfSeK45BHnYem16xPuefDc8iP1Mffh+A/6m/pu+n350veH9cvy3e8K7aTqAelt6CjpWesO7zn0qvoUAhMKLxLmGbYgJSbPKWgrxyroJ+4iHxzgE64KEwGi9+HuS+dA4QHdr9pD2prbb95p4iHnK+wf8aD1ZPk5/Aj+0P6p/r/9SvyI+rf4Dve79dv0efSU9Bv18vX49g/4HPkM+t36l/tV/Dv9d/43AKwC+wU7CnAPjBVlHL4jSiusMoA5ZD8ARAhHS0itRzNF+0A/O0w0gCw+JOgb2BNXDJcFtf+v+m/2yPKC71nsDelk5TThadwD1x/R7sq3xM6+jblMtVmy8bA4sTiz27bwuyvCLsmP0N3XsN6r5IbpE+1B7x7w0e+d7tHsyurl6Hjny+YV53To7ept7szy1PdB/c4COQhLDdkRzBUfGeAbKx4qIAoi+SMfJpgocSumLiEyuzVDOX48MT8lQS9CMkImQRc/KDyNOIk0ZjBwLO0oGSYZJP4iwSJBI0ckiyW7JoAniyeWJnEkBCFTHH8Www9uCOEAg/m48tvsM+jy5CfjyOKn44Dl+eep6ijtDe8E8MnvN+5H6xHnzOHH22XVEc86yUfEkcBavsu98b65wfzFecvi0eLYH+BJ5xruW/Tp+bL+tgIFBrUI4wqsDCkOaA9vEDkRtxHVEXoRkRAKD+MMKAr1BnkD8/+s/PT5Hvhz9y34dPpT/rcDcgo2EpwaLCNjK8AyxzgRPVI/Xz8xPeg4xjIuK5gijRmYED4I9AAW++D2bfSz84b0nvae+Rf9mgC9AyAGegebB20G+QNfANf7pPYV8XvrH+ZB4RHdr9kp133VndRx1ODU0dUx1/bYIdu+3eLgqOQt6Yfux/Tr++MDiQygFdse2ic1MIA3VD1VQTxD3UInQCs7HDRFKw4h6xVbCtz+3/PJ6eLgXNlG05jOLsvRyD/HMcZixZvEs8OYwk/B8L+qvre9Wr3VvWO/L8JOxsDLZdII2lri/OqH84/7rwKUCPwMxA/kEHIQoA66CxkIIQQ4ALz8+vks+HX33PdO+aX7pf4JAosF4gjUCzEO3w/WECQR5BBCEG8Png79DbEN0A1hDlgPmhAAElkTdBQiFT0VsBR1E5wRRw+oDAIKmge5BZ8EfwR6BZkHywrmDqwTyhjmHaAiniaWKU4rqiupKmcoHiUdIcUcgBi0FMER8g96D28QxRJQFssa1h8FJeQpBC4AMYoybDKRMAMt6SeHITQaVxJYCp8CiPta9UnwcOzQ6VPo0OcS6Nzo8OkZ6ynsA+2c7fbtJO5E7nnu5+6w7+nwnvLL9Fz3Mvoi/fz/jQKuBDsGIwdmBxcHWwZmBXYEzgOvA08E1AVNCLIL3w+WFIMZQx5oIoclOicyJzYlMCEqG1MT/gmW/570pOk43+HVE84nyFXEsMIkw3zFYslszh7U+dmE31LkC+hz6mvr8eog6SnmUOLj3TTZkdQ+0HHMUcnzxlvFgcRTxLzEpcUAx8LI7cqOzbnQidQZ2YLe1OQR7Cv0AP1XBuoPYRlZIm8qQzGBNuo5Vju9OjM47TM6Ln8nLiDDGLERYwsvBlEC5v/q/j7/pQDSAmcFAwhJCuoLpwxdDAMLqQh5Ba8BmP2A+bf1f/IN8H7u2O0M7vHuUPDl8WrzmvQ+9S/1WvTH8pfw/+1I68bo0+bC5d/lYedo6vnu/vRF/IcEag2LFoQf8yeEL/I1EjvNPiZBNUIhQh9BaD8zPbM6DDhWNZcyyC/ULJ0pBCbqITsd7hcJEqcL9AQr/pL3d/Em7OPn5ORN4yjjZeTc5k7qZ+7M8hz3+foW/jYAOgEbAfX/+f11+8X4TvZ19JTz8vO/9Qr5w/22A5kKAhJ9GY0guCaQK74uAzBBL34s3iehISIayREICU4ABPh+8AHqt+Sy4O7dU9y62/PbzdwY3q/fduFf42vlpece6u/sK/Dh8xb4wPzDAfsGLwwiEZAVOBngG1wdkh1/HDYa4Ra+EhgORQmaBGUA6vxT+rf4Dfg4+Pz4EPoc+8X7tfuk+l74zPT17wDqM+Pq25jUuM3GxzPDXsCMv+HAXcTayRTRptkY4+bsifZ//1gHvA1uElEVZxbRFcgTlxCVDB4IigMl/y770fcq9T/zC/J78Xfx5vGx8srzKvXX9tz4T/tF/tEBAwbcCk4QOhZwHKwioSj1LVEyXzXYNok2VTRAMGgqCyOCGjgRpwdN/qH1D+7r52/jtOCx30DgG+Lq5Ebow+v67pLxRPPl82bz1vFb7zbss+gp5ezhSt9/3bPc+NxE3njgYeO95kXqse3C8EbzIfVK9tH22vab9lf2Vvbc9if4Y/qo/fUBNgc5Db0TcRoAIREnVSyNMIkzNjWUNb805TJFMCgt2imgJrojVSGKH2EezB2tHdkdGx5CHh0eiR1xHNAatBg9FpYT9BCODpcMNwuJCpIKQAtwDOYNXQ+DEAcRnxAPDzAM9QdvAs37WPRx7IfkEd2G1k7Rvc0NzFbMjM6A0uPXTd5B5TzsuvJC+G/89v6t/4r+pfs3947xDOsd5CzdoNbP0P7LWsj4xdfE48T5xevHi8qrzSbR39TJ2OLcM+HN5cPqKvAN9m/8RAN0CtcRNxlYIPkm2izFMZM1LTiUOeE5Qjn5N1U2rjRcM68y5zIsNI82ATpWPkhDekiCTe9RVFVPV5RX8lVYUtdMn0UAPV8zLynrHgcV7QvvA0b9B/gs9I7x7u/37kzuiu1X7GfqhOeR447emNjj0bnKdMNyvBK2qLB7rL+pkaj3qOGqLq6usiq4Z74uxVHMqdMd25/iLOrE8W75KAHuCK8QTRiZH1omSiweMYw0TjYtNgc0zy+ZKZMhCRhhDRMCo/aV62zhl9hw0TPM+ci7x0/Ibcq3zcLRHNZY2hTeBeH64t/ju+O24gvhB9//3EnbMtr42cXaqNyX33LjAej97BfyAfdw+yj/AALnA+EECAWMBKgDogK/AT8BVAEhArID/gXoCEEMzQ9KE3UWFhn9Gg8cRhyxG3UaxxjpFiMVvRP3EgIT/RPwFc8YcxynICQlninHLVcxFDTUNYE2HjbANI8ywi+VLEUpDCYVI3sgRx5uHNEaRBmQF3wV0xJtDzELHwZQAPf5XfPf7Ojm5eE+3lDcXtyQ3uviUOl88Q77hwVcEPYawSQ1LeEzcTixOpU6MjjBM5QtEiawHeMUHAy/Ax78b/XX71/r/OeT5f/jE+Ol4pHiuuIR45LjQuQv5WrmBOgJ6nvsT+9u8rP17/jq+2n+NgAlARUB/P/j/e36U/dh83Dv4OsQ6Vfn+eYj6OXqMO/U9If74gJ0Cr8RSRijHXMhdyOTI8ghPx47GRsTTwxPBZH+gPh086rvQ+0+7H7syO3P7zjypPS49iX4rvgw+KH2EfSo8KHsR+jp49bfVtyj2eXXL9eA18XY2tqR3bXgFOSA59fqA+7+8Mzzg/Y6+RD8IP96AikGIwpPDoQSixYiGgQd7R6jH/oe3BxMGWYUYQ6JB0AA7/gD8uPr6eZZ41vh+OAZ4ork++cJ7EfwQ/SW9+X58PqQ+sL4oPVh8Vbs4eZs4WLcJdgF1T3T6tIQ1JPWQdrW3v/jZum57rHzFfjD+7D+5ACAAq8DpwSjBdcGbwiGCiYNRhDJE4IXOhuzHrAh/iNzJfsllCVQJFoi6R9DHbAaehjiFhgWOxZVF1YZGRxnH/siiSbEKWksPy4jLwQv7S37K2ApXSY5IzwgqB2xG3oaEBpoGmIbzRxoHu4fGSGsIXghYyBqHqMbPhh8FK0QKA1ECkwIeQftB60JngyGEBEV1RlaHiQivCS5JcwkwSGIHDUVAAw+AWP17uhq3GDQUcWqu8Gz0a30qSyoXahZquKtr7J5uPq+9MU0zZXU/NtZ46HqzPHR+KH/JQY+DMIRgRZFGtwcFh7SHf8boRjTE8gNzAY+/4j3HvBv6eLjy99m3c3c/d3O4PvkJOrW75f16vpe/5MCSQRaBMYCsP9Z+x32a/C66oDlKuEQ3nHcbtwF3hfhaOWl6mzwVvb8+wIBIQUlCPYJlAoZCrUIpQYwBJ4BM/8n/aP7wPqE+uX6y/sW/aH+SADyAY0DEwWOBhUIyQnOC04OaBE1FbwZ9B69JOQqJjEyN688RUGhRINGuUYvRetBDj3TNoovkydTHzAXhA+aCKQCu/3Y+d32kPSp8tLwt+4I7IXoBOR33u7XlNCxyKLA0rizsbOrMqeBpNCjN6WrqAOu/LQ8vVzG8s+T2eHikOto80r6LwApBVkJ7wwfEB4TGRYwGXYc6B90I/gmSCowLX4vBTGkMUwx/i/QLeoqhifkI0sgAB0+GjMY+RaSFu4W4xc4Gaga5huoHKwcwRvHGbgWpxK9DTcIYwKV/CP3WfJ67rHrE+qe6TPqouup7fzvTvJX9Nz1tfbS9jr2DPV+89TxXfBo7zzvEvAM8jX1dvmg/mcEbApDEHoVoxlfHGMdghyuGfwUoQ7vBlH+P/U67L/jQNwc1pvR584MzvzOj9GJ1aHaiODu5ovtIvSE+pAAOgZ8C14Q6xQuGTEd9CBuJI4nNypILJ8tGS6fLSUsrylVJkUivx0SGZgUsRC3DfkLswsIDfsPbxQnGskg4ifwLmg1xDqLPltA8D8pPQ44yzCwJywdwRH8BW/6m+/15dXddNfo0iXQAM80z2rQQNJT1EjW0de02NDYHNim1pDUDNJWz6vMRcpUyPzGUMZTxvrGK8jIya3Lus3Vz+/RCNQr1nHY/dr13YThyeXd6sfwevfW/qMGnQ5uFrkdIiRUKQktES9TL9ctwCpNJtIgtBpjFEsO0AhHBOsA3f4c/o7+/P8aApAEAQcRCXIK6ApPCqAI8AVsAln+CPrU9RTyGO8d7Unsqewt7qrw4PN79yD7cv4ZAc4CXAOoArEAkv19+bj0lO9r6pPlWeH73afbcNpW2kbbGd2f36Li7eVS6azs6O8B8wL2BPkn/JP/aQPHB7sMQxJKGKYeHCVkKywxHzbwOVs8MD1ZPNU5xTVfMPIp2iKBG04Uow3RBxcDnP9l/WP8bfxI/an+RQDSARED1gMIBKgDzwKrAXsAiv8g/4X/8ACHA1MHQgwmErcYlx9bJpAsyDGeNcQ3BThKNp8yLC06JiYeXhVXDIQDUfsT9A/ua+k05l/kyOM75HjlPOdI6WLrYe0o763w9fET8yL0QfWN9h/4BPo+/L/+bgEoBMIGEAnqCjIM2AzaDEwMVAsmCgMJMQj1B4oIHArCDHcQGhVuGh0gvCXUKuguhDFDMtUwDy3nJnseEBQNCPb6YO3s3znT2MdGvuG25bFkr02vbLFuteq6asF2yJjPa9ab3O7hQeaO6ePrYu037pjut+7D7t7uIe+V7zTw8fC38W7yAPNg84nzg/Ni80jzW/PJ8730W/a7+OX7zP9MBDIJMg73EiMXWRpFHKIcQhsSGB4Tkgy0BOb7l/JD6WbgctjI0bHMWcnKx/HHnMmCzEjQi9Tr2A3dqeCN46Pl7eaJ56vnlueX5/nnA+nq6tDtwPGp9mL8rAI8CboPzhUoG4QfsyKgJEwl1iRwI18h9h6IHGga3hgfGFAYexmTG3ke+iHZJdEpoi0SMfIzJzamN3g4tjiFOBE4iTcWN9g24TYwN7M3Rzi8ONc4XTgTN8s0ZjHaLDUnnCBNGZYR1AloArP7CPav8dLuhe287VDvAPJ59Vv5Qv3PALADpwWOBlsGIAUKA1gAXf1r+tj37fXj9Nr02PXI93f6oP3pAPYDZQbeBxsI6wY5BA0Aj/r686bs9ORN3RjWsc9jymXG08OvwuTCRcSaxp3JB82X0BPUUNc22rvc6t7Y4KTic+Rn5pvoIev97SPxevTe9yL7Gf6WAHkCqwMrBAgEZgN6AoUB0gCrAFIB/QLNBckJ3A7WFG0bQCLiKN8uxTMxN9M4ezgWNroxnCsTJJEbmBKzCWoBOvqG9Jjwlu6A7jPwbPPK9938JwIuB38LuQ6TEOAQkg+4DHoIGAPh/Cn2SO+P6EfiptzV1+3T99Dwzs/Nh80MzljPaNFF1PzXndw74uTonfBc+QcDcQ1XGGIjLC5DODJBiUjhTelQa1FPT6FKkUNtOqEvrSMeF4QKZv4682LpHeGN2rHVaNJ40JTPYc+Gz63PkM8Az+LNOswjys7HfsV/wx3CnsE8whvESMe4y0TRs9e53gDmMe338w76P/9sA5AGvQgaCt8KTwuzC00MWA39DlQRXRQDGB4cdiDLJNcoWywgLwAx5zHWMeIwNS8ELY8qFijXJQQkwSIeIhYikyJrI2okUiXoJfYlUiXjI6chrh4gGzUXMhNgDwkMbAm6Bw4Hage3CMQKSw30D2ESMRQOFa4U4xKWD9EKvQSf/dD1u+3S5YTeN9g808rP/M3OzRvPptEc1RzZQd0q4YLkCOeT6BTpmOhG51nlHOPg4Pbeqd0z3b3dWd8D4p7l/uno7hv0VPlV/uwC9gZgCiwNaA8zEbISDxRwFfYWsxirGtMcER88ISUjmSRpJWwliyTAIhgguBzVGLcUrBAHDRUKGAg9B5sHLAnOC0UPPBNRFxgbJx4bIKggmR/YHHIYlRKNC78DpPu483nsV+av4cDeqd1m3s/gnuRz6d3uZPSP+e/9KwEAA0oDAgJA/zP7JPZo8FvqWuS63sTZrtWg0qrQz88C0C3RNdMA1nXZg90h4k3nC+1h81X65AEGCqASiBuDJEYteTW6PKZC4UYaSRRJrkbmQds6zjEdJ0MbyQ5FAkr2Xuv44W/a+tSs0XHQFNFD05bWmtrW3tziSebV6E/qp+ro6Tvo2uUQ4y7ggt1R29LZJNlT2VHa+9sf3n/g2eLw5I7mjefc53/njOYw5aPjKOIC4XDgpuDG4eDj7ObM6lHvOvRA+Rj+ewIyBhAJAQsDDC8MrQu2CowJdAivB3EH4wcWCQgLoQ23EBQUdhecGkodTx+NIPggnCCaHyYegBzzGscZQBmSGd4aLh1zIIUkJikILtQyMDfLOl49uz7MPpc9Pzv/Nyo0HjA+LOwoeyYrJSIlZibgKFYseTDiNCA5vTxMP2tA0j9TPeA4ijKCKhAhkhZvCxUA7vRV6pjg7td60EfKTMVzwZi+l7xJu5G6WLqYulO7mLyAviPBncQAyVTOkNSd21Djbeur87v7SQMHCrIPGBQbF7gYBRktGHIWIhSUERwPBw2RC+EKAwvpC2oNRQ8pEboSnRN8ExQSOA/YCgIF6f3W9TDtbOQI3H7UPs6jye3GOsaGx6vKYs9M1fnb7uKx6dXv+fTZ+Er7QvzP+x36a/cG9EHwb+zc6MflXeO64efg3eCH4cjigeSR5t/oWuv87cnwzPMY97/60f5VA0cIkw0TE5IYzh16IkYm4ygOKpQpWSdeI78duBafDuAF+Pxm9KvsOuZu4YneqN3G3rnhNebU6xvyiPiX/s0Dxwc5CvgK+glYB0oDIP46+ATy6etN5oHhxN082/PZ3dnY2rXcON8o4kzleeiR64juY/E49Cj3XPr//TYCHgfCDB0TFBp5IRApjzCmNwc+aUOUR19KukuuS1dK6kepROFA4jz2OFw1RTLKL+4tniy0K/kqLSoOKV0n6SSPIUUdFBggEp4L1QQV/rD38/Eh7Wjp4eaN5VPlBOZh5x3p6ep67JHtAe6z7avsB+v76NDm2uRx4+rii+OJ5fro2+0F9Dj7FgMyCxITOho1IJ8kLSexJx0mhiIdHTMWKw5zBYH8xfOj62/kZt6t2VHWSdR707/T5tTC1ifZ8tsN32riCub06TXu2fLq92X9PgNaCY0PoRVSG1kgbyRUJ9Uo0yhGJz8k6x+MGnoUGw7aBx4CR/2e+VT3f/YT9+f4tPsg/8ICLQb4CMYKUwtyChsIYQR6/7T5cPMd7Srn/uHx3UTbGdp12jzcNt8U43fn9esp8LTzSva099f3tPZm9CDxJ+3N6GjkSuC93PzZMNht17TX9NgO29vdMOHi5M7o2+z58Cb1afnR/W0CUAeADP0RtBeHHUIjqShyLU8x9jMkNaY0XzJOLo4oViH7GOUPjgZ4/R719e1b6JPkweLj4tXkU+j97GPyCPhx/SwC2wU7CCQJlAimBpYDtf9j+wv3E/Pa76nttewV7cfuq/GO9Sn6LP9EBCUJjA1HETYUURagFz8YUxgKGJEXEherFmwWVxZeFmMWQhbOFd8UUBMKEQUOTwoJBmQBp/wc+Bn07PDc7h7u0u7+8I30UPkB/0cFvwsEErIXcxwHIEAiESOCIrcg6h1gGmgWURJgDs8KxAdMBWID6QGzAIv/MP5q/An67/YT84LuZOn244beb9kP1b3Rx89iz63QpdMq2P3dx+Qc7ITzhvqvAJ0FBAm0Cp8K1giJBQIBoPvM9fPvf+rK5R/isN+W3tLeTuDi4ljmder+7rvzf/gq/asB/gUrCj8OThJpFpoa4h40I3onjCs8L1YypjT9NTk2SDUtMwMw+ytcJ30iwB2JGTcWHBRyE1sU1xbFGuQf2CUtLGIy8zdgPDk/J0DzPoc78zVrLkEl4hrID3YEbPka79/l/t2c173STM8WzdfLQcsCy8zKX8qNyT3IbsY2xL/BQ78CvUG7P7oyuj+7eb3gwF7F0MoE0cPX0t775RDt7/OF+soAyAaNDC0SvhdPHeQidCjmLRAzuTefO3c++j/lPwY+PzqMNAct5CN0GSEOYgK69qfroeEL2TLSP806ygzJeckvy8bNztDT02/WSdgj2d3YdtcN1dvRM85zygLHQsSKwh7CK8O+xczJK8+c1c3cY+QB7E7z//nb/7oEkghpC1sNkQ4/D5oP1A8YEIIQIRHyEecS4xPEFGkVsBWGFeEUyRNaErwQKA/eDSINNA1JDoYQ+hOdGEweyyTKK+kywDnmP/tErkjFSh9LukmyRkBCrzxfNrUvFynjImcd3BhgFfoSlBEFERMRexH3EUkSPhK1EaQQFg8tDRwLIgmFB4YGYAY6ByUJGAzxD3AUQxkFHkkipSWzJyMouiZbIwwe7xZIDnIE2/n87k/kR9pL0anJmcM3v4O8Zruzuy+9mr+uwi3G48mnzWLRCNWd2C3cyd+A41/naeuW78/z9ffb+1L/JgItBEUFWgVvBJwCEAAM/eL58PaW9C7zBPNR9DL3pvuJAZsIfhDAGOIgXyi7LokzdzZPNwI2pDJvLbkm9R6iFkYOZQZy/8n5rfU983byOPNC9UL41vuV/xsDEAYuCEEJNAkFCMwFswLw/sD6YPYK8urtIerA5svjN+Hy3uTc9toX2T3XbdW10zTSD9F10JTQl9Gd07jW59oQ4AjmjOxM8+n5BABBBVAJ8Qv/DHEMWwruBnICSP3V94fyxO3l6S3nweWr5dTmCOn861LvpPKN9bD3wviT+A33PfRL8HzrLebG4LbbZ9c51HfSUdLc0w/Xw9u84ajoLPDp94X/sgYzDeASpxeMG6ceHiEhI+IkjyZPKDwqXSysLhQxcTOaNWM3ozg6ORU5MjiiNoU0CjJuL+4sySo1KVsoTygSKYsqjizYLhwxBTM9NHk0fTMhMVotOijtIbka+xIaC4UDqPze9nPym+9p7tPutPDL88X3RPzmAE4FKwlADGcOkw/RD0MPHQ6fDAoLmwmHCOwH1wc8CPgI1AmLCs8KUgrNCAkG5AFW/HL1au2J5C3bx9HJyKbAx7mDtBexqK88sL2y+rayvJHDP8tk06zb0+Oh6/Pytvnn/44FvgqKDwEULRgOHJcfsCI2JQEn5yfAJ3Am6iMxIF8bpBVDD5AI6AGu+z726fHs7mvtbO3U7m3x5PTR+MD8OQDMAhgE0wPUART+sPjo8RvqwOFa2XLRi8oYxXTB2r9kwAfDlcfEzTDVZ93y5VruNfYs/fsCgAetCo8MSg0ODRkMqQr8CEcHsgVaBEwDigIOAsoBsQG6AeEBLQKvAoQDzQSzBlwJ5gxmEeAWQx1mJA4s5zOTO6VCsUhQTSlQ+VCXT/1LQ0akPnY1JiszIB4VaAqCAM33h/DV6rnmFeSw4jziXuK34uviruLG4Rbgmd1o2rbWyNLzzpDL9Mhsxy/HX8gCywLPMtRM2vvg5Oep7vL0d/oD/3UCywQSBnEGHAZRBVIEWwOgAkYCYwL3AvMDOwWlBgYIMwkHCmoKUgrFCd0IvwebBqoFIAUtBfMFgwfYCdgMVRAMFLEX7BpsHeUeGx/pHUYbQhcLEuoLOgVl/tf3/fE07cjp6uet5wjp0evH75b03fk4/0gEvghcDP0OlxA7ERERVhBQD0sOkA1bDdkNHw8oEdgT/RZRGoUdQyA8Iioj2yIyIS8e6hmUFHUO4gc3AdP6CvUi8FDssOlD6PfnougL6vDrDO4d8O7xVfM99KP0mPQ99LzzR/MR80XzBvRk9WP38fnw/DIAhwO5BpcJ+gvLDQQPtA/7DwoQHRB0EE4R4RJRFa0Y6hziIVMn5yw0MsY2LDr6O9k7ijnwNBIuGyVcGkQOWAEu9F7ne9sH0WzI8sG/vdK7CLwcvrHBW8akyxjRTdbs2rTefeE74/vj3uMY4+Thg+Aw3yLegN1k3dvd4N5p4GHiseRF5w/qCO0z8J/zX/eN+0AAjwWBCxMSKxmgIDMolC9mNkQ8ykCeQ3NEFUNvP4o5kzHYJ8Qc2BCkBL34r+374wfcHNZe0szQQNF30xHXntun4LblYOpO7kDxFPPG823zN/Jl8EHuGOww6sPo9+fg53booekx6+3sle7o763wufDz71ru/+sL6bflSuIQ31XcXNpd2XzZytpC3cfgMeVF6sbvdPUV+3oAhgUpCmcOVBIRFsYZnR28IT0mLiuHMC028TuVQcxGREusTr1QP1EOUCJNj0iGQlA7SjPfKoEinRqUE7YNNwkwBpoEUgQdBaoGnwieCk8MZw2vDQkNdAsICfYFgQL8/rj7CPkv92H2uPYz+Lf6Ev76ARsGFgqSDTwQ0xEsEjUR9w6TC0IHSwIC/br3xPJj7svqHOhe5obldOX95evmCOgg6Qvqr+oD6w7r6+rC6sLqH+sL7K/tJfB485z3dPzQAXQHGA12EkgXVxt6Hp0gwiECIokhkyBkH0Mecx0oHYQdkh5DIG8i1yQpJwkpFyr7KWooMCU2IIMZQhG+B139l/Ly5/fdJtXtzaDIdMV5xJzFpMg+zfzSZNn03zDmqesF8AHze/Rr9OnyIfBU7M7n4OLZ3QDZkNS00IfNFctdyVbI78cYyMbI8smcy87NmNAN1D7YOt0C443pvPBi+DkA8wcvD4gVmxoMHpIf+h4xHEMXYRDbByD+s/Mn6RLfBNZ+zubIg8V3xL3FK8l2zjjV+dw45XftQvU6/BcCtAYHCigMRA2hDY4NXw1lDeMNDQ8AEcETQBdWG84fayTpKA0tozCHM6U1ADerN8k3iTceN7s2jTa1NkM3Njh5Oec6TjxyPRc+Aj4GPQI77DfNM8YuCCnWIn4cTRaREIoLaAdGBCkC/wCdAMwARQG/AfQBqAGwAPX+efxW+b318fFB7gLrgugJ58jm3OdD6uPthPLZ94T9HQM/CIoMsA94EccRnxAeDn4KDwYtATz8mved84fwhO6i7dbt+O7N8AfzUvVY98v4bPkP+aL3K/XL8bbtMemM5BngJ9z32LzWk9WF1YTWb9gX20TeuuFB5ano0Ouk7iTxXvNw9X/3svky/Bv/fgJfBqsKPg/lE2AYaBy4HxIiQyMtI8khKR93G/MW7xHIDNwHhwMWAMP9rfzY/Cr+cABfA50Gxgl4DFsOKA+xDuUM0QmfBZgAFft89TrwtutG6C3mkeV45sjoS+yu8I71e/oE/78CUwV9BhQGEASEAKL7r/UG7wnoHOGg2urUPdDMzLLK+cmayn/Mi8+c05HYT96/5NLrgPPF+5wEAQ7iFyYioywfN1BB3kpmU4Ra1F/9Yrhj2WFRXTJWskwqQQ006SVVF/EIVPsE72/k49uI1WDRRs/1zgrQFNKX1BnXLNl32rra19nP18HU6NCWzCjI/8N6wOu9kLyTvAG+0MDexPfJ2M861tbca+PG6cLvTfVl+hn/gAO9B+8LMRCVFCIZzB15IgInNCvXLrMxmDNhNPgzYTKxLxYs0CcuI4geNhqMFs8TMhLREaoSpBSMFxsb/R7UIkkmCSnWKoQrAitbKbEmPCNEHxsbExd3E4QQYw4lDcEMFw3wDQYPChCrEKEQsQ+1DaEKggaBAeD77/UO8J3q+eVu4jfgc98k4DDiYOVn6eftefK49kT60Pwi/h3+vvwd+m728/EA7evnC+Or3gvbVNid1ubVH9Yj18nY3to13aTfDuJl5Knm6Og868ftrPAM9P/3jvyzAVYHSg1UEy4Zix4gI6cm7CjNKUIpWydDJD4gnxvHFhwS/Q28CpoIuwcnCMkJbAzID34TKBdgGsYcDR7+HYAcmBltFT4QYwpEBE3+6Phz9Drxbu8g70bwtvIr9lD6v/4TA+oG7wniC5kMBww6ClcHmgNO/8H6RvYp8qru9eso6krpUOkg6pfrie3M7zrytPQo94/57ftQ/sYAZwM9Bk4JkgzyD0cTWxbtGLQaahvLGqUY2BRdD0sI1/9S9iTsy+HO17PO+sYOwUG9wbuavK+/vcRiyyHTb9u543LrGPJH97T6O/zZ+7D5AvYn8YnrmuXI33ja/tWY0mfQdc+yz/rQG9PY1fbYO9x635Lic+Ue6KLqF+2e71byXvXI+Jr8ywBGBeQJdQ7EEpsWyRkpHKYdPh4GHiQd0htWGv4YGRjtF7MYkRqRHachqCZTLFUyTDjRPYJCB0YdSJhIa0emRHVAHjv8NHIu6ifHIV8c9RezFKcSxRHqEdwSVRQLFrMXDBnnGScaxxnZGIMX/RWGFGMT0hIFExsUGxb0GHkcZiBjJAwo+yrKLCItvyt4KD8jKRxmE0IJH/5r8pvmJNtv0NbGnL7vt+Kycq+KrQOtsa1jr+qxIrXuuEC9FcJ0x2vNCdRa22LjGOxi9Rf/+gjFEiMcviRALF0y3DaWOYE6qzlCN4oz2y6aKTEkBh9zGr0WERR+EvIRQBIjEz8UMxWYFRIVUxMoEHcLSgXL/Tz1/ut/4jXZl9AOyfPChL7iuw+767s/vrrBAMasyl3PutN913Pag9yu3Qrewd0L3SbcU9vN2sLaUtuL3G3e4uDM4wPnXeqw7dzwy/Nz9tn4Efs2/Wr/zwGGBKMHLAsXD0YTjBerG1sfUiJHJPwkRCQJIk8eORkCEwEMoART/ZH2zfBo7K3px+jC6YLszfBJ9oX8AQM8CbgOBxPTFeQWJxaqE58PVAovBKT9K/c68Tfsd+gx5oTlbObQ6HrsJ/GI9kr8IALHBwkNwxHkFWoZZBzpHhMh/iLAJGUm7CdKKWcqIytYK+IqoimDJ4EkqCAZHAgXtxF1DJUHaQM7AET+pP1m/ncAqQO0Bz0M2xAhFaYYDBsLHHYbOxltFTkQ6QncAoD7Q/SS7c3nP+Mb4HbeSd5y37vh2+SC6F/sKPCi86X2HvkS+5r84f0f/44AZwLaBAUI8guSEMIVRBvNIAMmiioJLjQwzzC6L+0sgSinIqob5xPIC7kDIfxa9a3vTOtP6LTmYeYp59HoFOuv7WPw+/JQ9U337vg8+kv7Ofwh/R/+Qv+NAPkBbAPABMQFRgYQBvgE3wK6/5L7ivbb8NTq0uQ633Ta3tbH1GXU0tUI2d/dD+Q36+HyivqxAd0Howy3D+gQKxCXDWUJ6QOO/cf2DfDS6XfkRuBv3QHc8dsV3S7f7+EC5RHoz+r/7HXuIO8C7zXu5exL66fpOeg8597mQOdy6G/qJ+158D70S/h3/KAArwSaCGMMGRDUE7IX0RtJICYlZyr4L7E1WDujQD9F1EgLS5xLTUr+Rq9BeTqaMWgnUhzWEHgFvPoV8ebocuLg3TDbQtrX2pjcHN/z4bDk8eZo6OHoR+ij5h3k9+CG3SraR9c51U7UwNSu1hna597j5MTrMvPL+i4CBQkED/QTsxc1GoUbvxsNG6AZqxdhFekSYBDZDVcL1AhDBpMDtwCq/Wv6D/e385Hw2e3T68Pq6up97KHvYvSy+mYCOwvRFLceciiAMWg5vj8vRINGo0adRJ1A8Dr3Mycs9iPcG0AUew3IB0gD/v/P/Yr87/uw+3/7Fvs5+sH4nvbW84Xw3OwX6XvlS+LD3xDeTN163YjeSuCH4vTkROcr6WXqvuoY6m3o0OVu4ojebtp61gjTa9DrzrvO98+i0qXW09vt4aboru+09nH9qwM7CQ0OHxKDFVoYyxoDHSwfZSHGI1Im/yizK0cujjBWMnMzwTMvM7oxdy+SLEUp3CWqIgQgNx6BHQse5B/8IiMnDyxeMZo2SDvuPhpBcEGxP747nDV4LZ0jdRh+DEQAU/Qs6UTf9NZ30ObLOclJyNfIjcoPzfnP8NKm1d7XcdlP2n/aG9pM2UPYN9dY1tDVvNUs1iDXithS2lvcg96u4MXiveSY5mToO+pB7JvubvHZ9O34q/39Ar0IrA59FNUZUx6aIVYjRSM+ITUdQBeTD4EGd/zw8XPnh92l1DXNhMe+w+3B98Gkw6HGicrszl3Tddfi2mjd695q3wPf7t123PPawNk12ZvZKtsA3iDidefO7en0dfwbBIQLYxJ3GJMdnyGaJJYmtScpKCYo4ieMJ0wnOSdbJ6wnGCiDKMooyyhrKJgnTyadJJ4ifCBtHqsccRvwGk8boBzgHvMhpCWtKbQtVjExNOg1LTbJNKMxvyxEJncetxV6DEADi/rV8ors/edi5c3kL+ZZ6QHuyPNC+gABmgexDfwSSheEGqsc2B02HvodXx2cHN4bRBvbGpoaZhoVGnEZPhhCFk0TPQ8ECqsDVPw39J/r5uJv2pnSwMsuxhzCqL/Zvpq/wMEQxT7J/c3+0v7Xxdwu4Sflsujj69zuxfHL9Bf4xvvp/30EcgmiDtoT3BhoHT8hLiQOJs0mbiYOJdsiFyARHRkagBeJFWgUORT7FJUW0hhmG/UdGyB0IachaiCRHQsZ6BJdC7kCaPnj767mS94v17zRN87FzGXN9s821MfZO+AW59/tIfR4+Zf9SAB1AR8BYv9r/Hf4zPOu7mDpGuQH30ja79UD0oXOccvGyIXGucR1w9TC+8ISxELGrcltzorU+duX5CruY/jeAiwN1RZmH3QmqSvGLq8vZy4WKwMmkh86GH8Q5gjqAfn7YvdY9OvyCfN/9P72JvqK/b0AXAMTBaUF9AQAA+b/3fsz90Tyce0Z6Y/lFOPV4ePhN+Ox5RzpOe288V322vr6/pgCogUYCAwKoAv9DFMOzQ+QEbUTRBY2GXQc2B8yI04m+ygLK2As6iyrLLgrOipjKHMmqCRAI2oiSiLqIkEkLiZ5KNwqBS2dLlYv6i4qLf8pbyWeH80YVRGgCSMCVfui9Wfx5+5H7o3vmvIz9wD9lwOFClMRkhfjHP4gtSP3JNAkZSPxILsdERo+FoYSHA8hDKEJkAfSBTsElgKtAE3+Tvua9y3zGO6C6KPiwNwl1x7S8s3ZyvnIZcgWye7Kvc1D0TXVSNk03bvgsOP45ZDniOgB6S3pRemB6RnqNevw7FDvSfK39Wn5IP2VAIcDuAX6BjIHXAaLBOcBrv4p+6r3gfT38UXwje/b7x3xKvO/9Yz4M/tZ/an+3v7J/Vn7nfe/8grt4Oaw4PTaI9am0tXQ6tAB0xPX9txj5PnsRvbP/xgJsRE7GWsfFSQmJ6kowyiqJ6UlACMIIAMdLhq2F7kVQxRWE+YS4xI6E9oTuRTVFTIX4BjxGnodjSA0JGwoIi0xMmA3YzzgQHREukZTR+xFSEJIPOwzWSnYHNAOyP9U8BfhsdK4xau67rG+qzKoO6egqA2sEbEtt969pcQPy8LQftUi2arbMt3p3RTe/N3w3TbeBt+G4MbiwOVa6WftrfHw9fH5ef1dAIYC7AOcBLIEWgTHAzIDzALDAjQDLgSsBZwH2gk5DIcOkhAxEkMTuxOcE/0SBRLsEO8PUA9NDxcQ0BGCFCEYhhx1IZ8mpyssMNEzQTY9N542VzR+MEMr8STpHZcWag/NCB4Dp/6R++75r/mm+pH8Gf/fAYQErgYWCIgI6wdCBqsDWgCY/LX4B/Xf8YHvHu7Q7ZnuYfD48h72hvng/N3/NwK8A0sE2QNyAjkAYP0h+sD2fvOS8CjuWuwv65zqhurD6iXrfOub62Lrv+q06VXoyeZF5QvkYeOJ477kK+fm6u/vLPZt/WsF1A1LFnIe8yWFLPIxHTYBObQ6YDtBO506vDnjOEk4FDhROPY44TnXOo87tjv3OgI5mjWUMOMplyHgFwkNdgGc9fbp/94p1dLMP8aWwdy+9b2pvqfAjcPwxmfKkM0b0M3Rh9JC0hXRKs+/zB7KlMdsxejDPcONw+jETcepytzOwtMw2f/eDuVE65Lx9vdz/g8F1wvPEvEZLSFjKGIv6TWsO1ZAkUMNRYdE0kHaPKw1dyyLIVUVXAg6+4ru6uLn2PnQdcuNyEnIhsr9zkXV3dwz5bPtzvUG/fMCUAf3CeYKOgotCA0FNgEI/d/4CvXK8UjvmO227Izs9uzG7cru1u/E8H3x9/E58lfycfKt8jLzJPSd9az3TPpt/ekAlAQ1CJELcA6jEAoSlxJPElARyA/3DSUMnwquCZAJcgpoDG8PahMgGEUdfyJrJ6Yr2C66MBox5i8mLQQpwiO3HUsX6RD7CtwF2AEg/8b9wv3t/gsBzQPaBtgJcQxiDngPnA/QDjAN7QpLCJgFJAM5ARcA6v/BAJwCWgXHCJ8MjhBAFGMXshn2GhAb+Bm/F4sUlhAnDIgHBgPm/lz7kPiU9mb18fQS9Z71ZPY09+n3afio+K34kPh2+I74CfkZ+ub7if4KAloGVQvBEFQWtRuLIHskOCeGKD0oVCbcIgUeFBhkEVkKXgPW/Bb3Y/Lj7qXsluuM60XscO227r7vO/Dw77fuhOxp6ZHlPOG93HDYsdTS0RjQsc+t0APTi9YD2xbgX+V36vfuhvLb9Mj1N/Uy89vvbes15ovgytpM1V/QRMwnySTHPsZsxpPHkslDzIHPLtMz14XbI+AU5WTqIPBS9vz8DwRyC/gSYhpmIa8n4yyvMMoy+zImMUkthScYIGEX1g38A2P6l/EZ6lTkluAI363fZOLk5snsmPPH+s0BKQhrDT0RbBPkE7gSGBBUDM4H8gI0/vv5pPZ29KDzM/Qp9mL5q/3DAmUISA4rFNcZIx/1I0MoDSxfL0ky2TQbNxE5tDrvO6Y8szztOys6TDc7M/QtiCcdIPAXUQ+dBj7+mvYU8ALroecW5mfme+gc7PrwsPbR/OkCjwhjDSARmBO+FKMUcxNxEfIOUgztCRYIDwcEBwcICwrsDG0QQBQOGH4bPB4EIKUgBSAnHiUbMheSEpENgwi1A2n/z/sC+QT3wPUM9a30XfTU887yEPF07ubqbeYn4UbbD9XTzufIn8NEvxC8LLqmuXm6irysv6bDOcgjzS3SKNf024Pg2OQE6SXtXfHR9Z361P95BX0LvhEFGA8ekCM4KLsr2S1lLkktiypNJswgXhpqE2IMtwXY/x77z/cS9vH1VfcH+rr9DQKXBu0Kqw6AETIToBPKEswQ2Q08CkwGYwLZ/vn7+/kA+RD5Fvrl+z7+0wBQA2IFwwY3B50G6QQpAoX+M/p/9bjwM+w66BHl5+LZ4e/hHuNI5ULo2+ve7xr0Zvik/MQAwgSoCIQMbBBxFJ8Y+BxsId0lGyrnLfowBDO5M9YyKDCTKxYlzxz7EvIHJ/wa8FTkYdm8z8/H6MEwvq68Qr2pv4LDWsitzfjSwdee20Heet8936Hd2to81yrTE89qy5fI9MbExjDIRcvzzxHWYt2a5Wfudvd4AC4JZBH5GNwfCyaPK3ow3zTNOFI8bD8VQjpEv0WIRnVGbEVgQ09ATDx6NxIyXSytJl8hzBxFGQwXTRYYF14Z8hyMIckmNixWMa41yzhNOu05iDcYM78svSRuG0MRuAZN/HfynekS4gjcl9e41EjTDtPE0xrVwtZ32AHaO9sY3Jzc5NwZ3W3dFt5F3yDhvOMa5yXrtO+J9Fn50v2fAXcEGwZgBjQFoALG/t75N/Qp7hboW+JN3TLZPdaI1BfU2NSl1kvZkdw74BLk6+eo6z7vsfIU9ob5L/00AbgF0AqFEMkWfh1wJF8r/TH5NwQ92EBDQyVEekNZQfM9kTmKNEUvJSqLJcUhDh+EHSgd2x1jH3AhniOGJb4m6ibAJQ8jxB7uGLoRcQlxACv3Du6O5Qze29cy0yrQwc7ZzjnQmtKm1QbZadyF3ybiKeSD5T3mcuZP5gTmx+XI5TDmFueG6Hbq0Oxw7yjyyPQk9xT5gPpc+6/7j/sf+476DvrP+fz5svr8+9L9GAChAi0FdQcuCRAK4Ql4CMQFzwHC/N32ePD+6eHjkt562u7XK9dL2Efb9N8J5hzttfRN/F0DawkMDvEQ6xHxEBkOnQnSAyL9/vXf7jXoYOKr3UfaSdir103Y/dl43HffsuLo5ePof+uo7VvvpfCg8WryKPP38/H0I/aP9yr53/qS/CT+d/9zAA8BTwFFARYB9wAlAeQBdwMYBvQJIA+cFUcd5iUlL5k4yUE2SmRR41ZbWoxbXlraVi9Rr0nHQPs22CzvIsQZzxFpC88GGwRHAywEigYNClYOBRO9FzEcIyBtI/4l2icZKdwpTiqXKtsqLiuZKxAsdiygLFYsWyt0KWwmHiJ2HHoVRg0PBCD60u+L5bLbqtLLyljEf79VvNO63Lo9vLS++cG/xcPJyc2o0UnVptjN29re8eE75dzo8eyI8Z/2HvzcAaQHLg0yEmYWixluG/IbExvkGJUVaBGyDNMHKgMT/9f7rvmx+OH4HPoo/LL+WQG2A2IFAQZLBRQDTP8D+mvz0+ud4z3bKtPZy7LFCMEVvvO8nr31v7zDpMhRzmLUetpH4IXlCeq87Z3wv/JI9GT1SPYk9yL4Yvn0+tv8CP9jAc4DJAZDCBIKgQuODEgNyQ05DsYOoA/1EOgSixXfGM8cLiG8JSgqFy4pMQUzXDP3MbYuminBImoa8BDDBmH8SvL86OXgW9qZ1bfSrNFN0lHUXdcE29necOJu5Y/nqeiv6Lbn7uWd4xzhzN4M3TPcidw93mXh++Xc68/yifqwAukK2RIvGqkgGCZjKoMtiC+MMLcwMzAsL8YtHyxGKkAoCSaSI8ogoR0NGgwWrBEJDU8IuAOK/wz8h/k7+Fn4/vks/coBogdmDq0VBB3uI/IpoS6iMbcywjHKLvspoCMgHPYTqAu8A7H87fbC8mDw1O8M8dPz3PfI/CsCnQe3DCYRqhQcF20YqRjxF3UWcBQgEr4Pdw1uC7EJOwj5BskFfwTwAu8AXv4p+0/34/IM7gDpBORh32PbTthX1qXVRNYp2DPbKt/D46voiu0J8uD11fjC+pv7bPtV+ov4T/bo85zxqe9B7oHtde0R7jbvuPBe8u3zLvX09SD2qfWb9BjzVvGZ7y3uYe177bTuL/H39Pf5AADLBvYNFRWzG2IhuyVvKEopNihAJZYggRplE7QL5QNv/Lz1IfDc6wzpsuev58/oxuo+7dvvSPI49HD1zPU/9dLzpPHo7tfrtOjA5TLjOuH333bfuN+t4DviROSp5k3pHuwR7yvye/UY+SD9sQHmBswMYxOXGj4iGirYMRg5cT95RMtHFkkdSMJEBz8VNzUtziFiFYAIwvu37+fkv9uQ1IbPrMzky/PMg88s033XB9xl4EPkZ+ex6SHrz+vt67zriOue60bsue0c8H/z2PcF/dAC9QgkDwwVYRriHl0ityTnJfolECVVIwAhSx5qG44Y2RVeEyURJA9KDXwLoAmeB2cF+QJfALf9Kfvr+Dn3UfZp9qz3Mfr6/esC1AhmD0EW9xwQIxsosSt9LUkt/SqlJnAgrxjLD0IGnvxj8xLrFOS53jLbi9mw2Wvbbd5W4rjmKOtA76zyLfWd9vL2PPaj9F7ysO/i7Dbq5ecb5u7kY+Rt5OzkuOWh5nvnHuht6F3o9edK54bm2+WF5cHlw+a36LjrzO/j9Nf6bwFmCGoPKhZYHLQhDiZMKW4riCzILGosuCv+KoUqjipHK8osFy8YMqA1bzk7PbBAgkNrRTZGxEUNRCNBLz1tOCYzqy1IKEMj0h4VGxIYuRXfE0cSpxCtDgoMeQjHA9r9s/Zw7k7lotvU0VfIo78luD+yOq5CrGOsia5+sva3ir7NxUnNjtQ62/3gnuX/6B3rDOz36xTrpOnp5yHmgeQw40fi0OHF4Rriu+KR44zkoOXL5hnon+l7687tvfBm9Nr4H/4iBMEKvxHPGJIfoiWYKhIuvi9hL90sNCiMIS4Zfg/7BDP6tu8U5szdRdfI0nnQVdA10tDVw9qW4Mvm4uxq8gD3YPph/Pz8R/x2+s73pPRU8TXuleux6bPoq+iU6VTrwe2m8Mnz8vbw+Z/86v7NAFYCnQPGBPoFYAcZCTwL0Q3QECIUoBcaG1oeKSFWI70kSCX1JNcjEiLcH3YdKBs3GeEXVBerF+cY9BqhHasgvyODJpoosimIKfQn5SRvIMMaLhQWDfEFPf90+Qb1TPKG8dHyJvZc+yoCLwr0EvobwiTXLNMzazltPcQ/ekCwP5w9gDqmNlUyyi04Kb0kZiAuHP4XuBM0D0wK4QTg/kP4GPF/6anh1dlH0kjLHMX8vxO8d7kpuBa4Fbnxumi9OMAfw+jFasiSymLM8M1kz/fQ6dJ61ebYXd354r/pmvFc+r0DaA33FgEgIigAL1Y09TfMOec5bTidNccxRy15KLcjSh9pGzQYsBXME18SMBH9D4EOgAzICTwG2AGw/PD23vDM6hrlKOBN3NTZ8di82S/cJ+Bj5YrrM/Ls+ED/wgQbCQEMTA3sDPEKhAfhAln9P/ft8LTq3eSf3yHbedeq1KvSadHO0MLQNNEZ0nDTQtWf15/aV97a4jDoVe4w9Zf8SgT7C0kT0RkqH/Yi5iTCJHEi+B2CF1sP6wW2+0nxPOce3nDWmtDlzHLLPswez8TTx9mr4Orn/u5u9dL64P5rAWoC8wE4AIX9NPql9jvzTfAi7vHs0+zP7dTvvfJc9nn62/5QA68H3AvJD3gT9RZYGrkdNSHeJL4o1CwNMUs1YTkcPUVAp0IURG5EqEPJQfA+TzsqN9IynS7fKuQn5iUKJVslxyYhKSMsdS+yMnM1VTcEOEI37DT9MJMr5iRMHSkV8QwWBQT+FPiK84zwIO8u74DwyfKs9cL4qPsA/oL/+P9L/3v9pvoA98zyWe766fnlmOIE4Fjeld2o3WzerN8q4afi6ePB5A3lv+Tc43zixeDo3hvdlNuB2gbaM9oL23ncXd6F4Lriw+Rr5ofn/OfD5+vml+X8417iCOFG4F7giOHo44vnYexD8u74DwBFByoOWxSAGVUdrh96IMkfwh2nGs0WkRJTDm8KMQfRBGwDCAONA8sEgQZhCBoKXAvmC4kLLQrTB5cErABa/PP30PNG8J7tEuzB67Ts1e748dj1JPqA/pECBgaZCBsKdQqpCdQHKAXqAWr++vrs94j1BPSG8x30w/Vf+Mr70P85BNAIZA3NEfIVxhlKHYggkSN3JkYpBSyrLiAxQDPSNJg1STWgM10wUCteJIob8hDXBJn3sOmq2yHOsMHptk6uQqgGpbOkOaddrMSz8LxSx0/STN275yHxHvl1/wkE5QYuCCQIHAdxBYIDpQElADj/+/55/6MAXAJ2BL4G/ggHC7EM4w2RDsEOgg7yDTANXQyXC/MKegooCu0JrAlCCYgIWAeXBTMDLgCc/KX4hPSE8PnsOeqY6FzouOnG7IHxyPda/9oH2hDaGVki2invL0A0lTbUNgs1ZTEwLM0lsR5VFy4QpgkTBLL/n/za+kj6tfrb+2n9D/9/AH0B3wGOAZAA//4H/eb63fgx9x/21PVv9vb3Wfpy/QkB2gSaCPsLug6dEIARUhEZEPANAwuQB9cDHgCj/Jv5KPdg9UD0uPOl897zM/R49Ib0RvSw89Dyw/G38Ojvlu8D8Gnx8/O798D86QIECsYR0Rm/ISEpkC+xND04CDoDOj044zQ9MKUqfyQ2HioYshINDmAKtgf8BQcFlARXBPsDLwOsAT3/xPs9977xeeux5Lnd69ah0CzLzMatw+LBZcEUwrzDF8bZyLDLVc6J0CLSDNNJ0/PSN9JS0YrQJ9Bs0JLRwtMQ13vb7+BD50LurPU//bwE7QuoEtMYZR5jI+An9yvGL2kz8zZrOsc970C3Q+ZFO0dxR0ZGhUMKP8o41TBYJ58cDREbBU75K+405NnbcNUx0S7PVc9s0RzV8dlm3/HkCuo17hHxVfLg8bDv6+vT5sPgKtp80y7NqsdJw07A4b4Nv8TA48MyyHDNVtOf2QvgaeaS7HDy+Pct/RYCwQY1C3gPhBNNF7gapx3zH3UhDSKjISwgsR1QGjsWtxEZDcAIDQVdAv8AMAEQA6MGywtMEs4Z4SEJKsQxlTgMPtFBq0OBQ19BdD0OOJUxfipJI3EcZRZ/Ef8NBwyXC5EMvw7SEXMVQxnpHBYgjSInJNMkmiSXI/Uh6R+sHXMbaRmpFz4WIRU2FFUTShLeEN0OGQx0COMDcv48+Hjxaepf46/crNaf0cTNQsspynTKBMypzifSNtaP2vLeKOML54jqn+1j8PfyhPU7+Ej7zv7fAn8Hlwz8EXAXqBxMIQYlhCeDKNcnbCVLIZ4bqRTJDGwEDPwf9BTtS+cJ43jgn99o4J7i9OUN6oLu7PLv9jz6nfz0/UH+mv0w/EH6F/j99Tn0AvN+8r7yufNP9U/3d/l8+xT9+f31/eH8rfph9x3zEu6E6L7iEd3I1ybTW8+KzL3K7ckBytHKLszmzc3PvNGc02PVGNfR2LDa3dyA37/is+Zm68/w0PY2/b0DFQrkD9MUkxjlGp8btRo1GE8UTA+LCXwDl/1O+Aj0G/G+7wvw9/FY9eX5Pv/xBIkKkg+nE3YWzBeVF90V1BLCDgoKGQVjAFn8Wfm196H3M/lo/BwBGQcSDrAVmB1yJe4syTPUOe4+CkMnRlJInkkeSuZJAkl3R0FFWEKrPis6yzSILmonix8UF0UOagXf/AP1Ou7g6D/ljuPn40XmgupV8Fz3Hf8PB6gOYBW/GmUeEiCrHzgd6RgNEw4MawSn/ET1uu5s6aDlf+MP4zXku+ZT6qHuQ/PW9wX8h/8pAtQDgwRJBEkDtQHB/6D9f/uA+bT3G/al9DbzqPHP74Ttp+ok5/viPt4R2a7TWc5jyRzF08HJvzC/I8CmwqPG7stG0lzZ2+Bt6MLvmPbA/B0CrwaGCsYNoBBMEwIW8hg/HPofHySWKC4tqjHANSI5hjutPGg8ozpgN78y+ixhJlQfOxh9EXwLhQbQAnoAf/++//kA4gIWBS8HyAiLCTEJjgeUBFIA8/q69P7tIeeH4I7aiNWy0TLPEc5Czp7P7NHl1D7Yrtvy3tjhPuQZ5m7nWegC6ZnpVOpj6/DsFO/a8Tv1HPlX/bcBBwYPCp0NjBDHEkkUIhVvFV0VIhX0FAYVgBV7FvsX8BkzHIkeqyBHIgsjrCLtIKkd0hh7EtMKJQLW+FfvJea63YbW5dAYzUPLYstVzdfQj9UN29zgheae683v0/KP9AD1Q/SQ8jfwk+0G6+/ooudh51TojOr+7Yby7Pfo/SkEYAo/EIYVBBqdHUUgBSL0IjUj8SJQInkhiSCRH5celx2CHEQbyBn7F9UVWBOXELIN2QpICEIGCQXbBOkFUAgVDCIRQhclHmMlgSz9MlI4BjywPQQ92TktNCQsCyJPFnoJJ/z47oziddctzg/HUsIIwCDAY8KDxhzMwdIB2nPhuuiO7731K/vV/8UDGAfvCW4Msw7TENYStRRcFqsXeBiaGOgXQxaZE+gPRQvUBdH/gPkx8znt5Od44yngFN5C3aPdD99O4RnkJuco6tzsD++g8IXxyvGV8RrxnfBn8MDw6PEO9E/3rPsOAUgHFg4lFRkclyJJKOssSjBQMv4ycDLaMIEutivLKA4mwiMUIhsh1CAhIc4hkyIeIxkjMiIlIMQc9hfEEVEK3wHE+GjvPua13TnWIdCwywzJPcgwybXLhs9O1LDZUN/Y5P7pju5l8nr11feP+dD6w/uU/Gz9Zv6U//UAfAIOBIgFwgaWB+QHmAetBi8FOwP9AK7+ifzO+rb5avkF+oj73/3aADoEqgfOCkUNuA7aDngNeArfBdL/lPiB8Ajopd/S1wHRlcvUx+jF2MWJx8DKKM9Y1NzZQd8Z5Aro0epI7GXsQesM6Q/mn+Ib397bO9lz17LWDteC2PPaMd4A4h3mQ+oy7rnxtPQS99X4EPrk+nz7Bfyu/Jz97P6rANoCawVCCD0LOA4REaoT9RXxF64ZSxv1HOMeTyFyJHcofi2NM5Q6Z0K+Sj5TeFv1Yjxp3m17cNJwvW4+an1jxFqAUDRFdDnaLfoiWxloEW4LlgfiBS8GOwioCwUQ2RSrGQsemiEPJD0lESWSI90gIh2aGIMTGA6NCAgDo/1l+EzzSO5G6S7k8N6D2evTOs6TyCXDKr7iuY22Y7SRszS0ULbVuZu+YsTeyrTRhtj73sPkoulv7R/wv/F08nryHPKt8YDx4PEK8yb1QfhR/DABogZaDAISPhe9GzYfdyFmIgMiaCDIHWcamBawEgMP2AtlCckHCgcUB7oHvgjUCaoK8wpqCt4INAZrAp/9A/jh8ZPreeX0313b+tf81XzVcta92CPcVeD55K7pF+7h8cn0o/Zb9/b2jvVV84bwZ+0/6k/nz+Tm4q3hKOFO4QniOeO95HTmRugk6gvsCO4y8Kryk/UT+UT9NwLpB0QOGhUmHBIjeyn1LhgzhDXsNRw0ATCqKUkhMxfaC8X/iPO65+zcm9MuzOrG7sM3w53E28eRzFPSr9gz337lQetF8HD0xfde+mz8Lv7q/+UBXgSCB2wLIRCOFY0b4yFNKH8uMTQfORQ96z+UQRBCdUHlP449ozpVN9EzNzCcLAcpcCXGIe8dzhlNFVoQ8gojBQz/2/jR8jftW+iL5AjiB+Gj4d/joeex7MDyaPk2ALUGcAwCERwUihU7FUATzA8xC9gFOgDV+iT2kvJ38ArwYvFz9A756P6dBbwMzBNYGvkfWCQ7J4MoLyhXJi8j+h4FGqMUIQ/FCcMEQABO/Oz4DPaV82nxa++D7aLrxen551Tm+eQQ5MLjM+R/5bLnxuqi7hnz7PfP/G8BegWhCKUKWQurCqEIXwUhATj8A/fp8VHtlOn/5sPl9+WV53fqYO7+8vP32vxSAQoFvwdKCZ0JxQjrBkwEMwHz/d36O/hH9iT14PRt9af2Vvg0+vX7Tv38/cz9oPxz+lr3f/Ml75nqNOZL4i7fHN093KXcR94B4Zjkv+ge7VnxHPUa+Bv6//q8+mX5Ifcu9NXwZ+026oznpuWy5Mnk7+UW6CHr5+468+r3z/zGAb8GsAuhEKEVxxoqIN0l6CtFMt04hD/7RfNLElH2VERXqlfmVdVRb0vQQjY4ASyrHsMQ4wKp9aPpUd8V1zDRu82pzMXNvtAn1YLaTOAH5j/rmO/Q8sT0bvXp9GXzKPGB7sPrPOkv58/lOeV05XbmHuhD6rHsNO+d8cTzkPX59gT4xPha+er5m/qQ++T8o/7MAE4DCQbSCHULvw1+D40Q0xBMEAcPKQ3nCoUIUAaUBJgDlQOwBPUGVQqiDpoT4RgQHrcibSbRKJopmSi/JSEh8xqKE1ELxgJr+sDyOOwx5+vjh+ID4znl6ei37TvzBPmi/rED4gf4CtUMdQ3tDGoLKAltBoADpQAV/vX7XvpS+cP4lPie+LT4rfhn+Mn3y/Zz9drzIvJ78BbvJO7R7Tnua+9k8Qz0PPe9+lL+uAG0BBMHswiHCZcJBgkKCOkG9wWIBe8FcAc8CmoO9hO6GnYizypXM5c7EkNWSf5NvVBkUeNPTUzRRrw/azdKLsgkTBsyEsIJLQKK+9T19PDA7AXpiuUd4pTe19rh1sLSns6ryinHX8SRwvvBx8INxcnI3s0Y1CrbuOJe6rPxVvjz/UoCNAWkBqcGYwUTAwEAf/zc+Gb1W/Lp7yvuJ+3R7Aztsu2W7ozvb/Ak8Z3x3PHx8frxG/J88kLzivRi9sn4p/vT/g8CFAWQBzAJqwnECFcGWQLe/Bj2V+4F5pvdndWPzujIDcVHw73DbsY3y87Rzdm34gDsGfV9/bIEXgpBDkAQXxDIDr0LmAfAAqL9o/gi9Grwse0V7J3rO+zQ7TDwK/OR9jX69f26AXwFOwkCDeAQ5xQkGZodQyIMJ9IraDCZNCg43TqGPP48MzwnOvQ2zDL1LcIolCPJHr4avRf9FZwVmRbUGBEc/R8yJEEovCs9LnAvHS8nLZYpkCRdHlwX/g+9CBICa/wg+HL1gfRM9bL3c/s6AKAFOAuVEFQVJBnLGygdNB0CHLsZlxbXEr4OjAp0Bp0CGv/r+wH5P/Z/85fwYe3A6aHlA+H526LWMdHhy/HGo8Ixv8e8grtsu3q8jb54wQHF6MjvzODQkdTr1+zap91C4PTi/uWk6SjuvfOG+osCvgvvFdYgECwuN7VBKUsaUyZZCF2YXs1dxlq8VQhPE0dUPkQ1VSzsI1YcxhVTEPkLmQgBBvADHwJLADj+uPuz+Cb1IvHM7FnoBeQP4LHcGNpk2JzXtNeL2OvZkdsz3YTeQd8w3y7eKtwv2V/V8dAtzGjH+MIxv128tLpaul67tL09wcjFFcvh0OfW6Nyz4iToKe3B8fz18/nH/ZcBgwWZCdsNOhKTFrMaWR4/IRkjpyOyIhog2RsGFtUOlga0/aj09usg5KLd4Ngm1p3VS9cP26Xgruex7yn4jQBdCCgPlBRoGIoaBRsAGsIXoRQFEVQN9Ak6B2sFsgQjBbcGUwnIDNoQSRXTGT4eWCL+JRwprSu2LUgvdjBUMfIxVzKBMmQy6DHwMFovBy3fKdUl7yBDG/4UYg6/B3MB4vts92f0GPOr8y32ivqLAN0HERCjGAchrygZL9YzkDYXN141fjG1K10k6hvcErcJ+wAX+WPyHO1e6SfnWOa35vzn0unj6+Ptju+28EPxMvGW8JXvYO4v7Trss+u+627sx+227xjyvPRq9+X59ftr/SX+FP47/bH7nfkx96j0PfIo8JLumO1D7YrtTu5k75XwovFS8nDy2PF38FLug+s56LbkSeFE3vnbr9qd2uDbft5g4lLnCe0p80v5A//vA7sHKQoXC4IKgwhVBUcBvPwd+NbzR/DC7YHsn+wd7tzwpPQq+RL+/gKTB38Lgg50EEUR/hDBD8ENQQuICN0FgQOjAWUA0//g/3IAXgFwAm8DKARvBCkETQPkAQ8A/f3s+yD64fhu+Pr4qfqH/YgBjQZgDLkSSRm7H74lDStuL74y7zQGNh82YjUDNDYyLzAYLgssESogKBom1CMXIacdSxnWEysNRAU1/CzydOdt3IjRQccQvme2pbAPrcir1KwOsDS15Lunw/nLVNQ33DTj8eg37evvF/Hj8JDvdu326nToUOba5FHk2uSC5jvp4ew/8RP2FvsAAJUEoAj/C54OfBCnETQSRBL3EWkRsxDgD/QO5g2nDCELQAnzBjMEBgGE/dX5NPbo8kTwn+5J7orvlPKC91D+2AbVEOIbgiclMzU+G0hQUF9W9VniWh5ZzFQzTrtF5ztIMXQm/RtjEhIKVQNW/hv7jvl4+ZD6ffzi/mQBtQOVBdgGagdLB40GUQXBAwgCTwC3/lD9IPwa+yf6Ifnh9zz2D/RA8cTtpOn75PTfzdrM1T3Ras2VyvLIosivyQ3MmM8Z1EvZ4N6K5P/pA+9s8yT3Lvqk/LD+jAB9AsUEoAc6C60P+xQLG6ohkChlL8Q1STuXP11CZEOPQuA/dzuRNYUuuyaiHq0WQw+8CFoDQf92/Ob6X/qc+kz7Fvyk/K389/tg+t33f/Rt8ODrIed84j3eqNrw1znWjNXf1RHX8dhE28bdN+Be4hDkNOXC5crlbOXX5EPk6+MH5MbkR+aZ6LXrge/S8234E/1/AXUFwghDC+kMug3RDVsNkQy1CwgLxAoYCx0M2Q04EA8TIBYeGbIbiB1SHtId3xtsGIgTYA05BnD+bPab7mnnMuFC3MfY09ZY1inXAdmG21PeAOEt44jk1eT34+vh0N7g2mvW09GBzd3JSMcRxm7GfshBzJ3RXtg+4OjoA/I0+ykEngxdFEMbQCFTJokq+C24MOEyhzSyNWQ2kzYuNiE1VTO5MEUtACkAJG8ehxiSEuYM3AfLAwMBwf8mAD8C8wUNCzkRCxgGH6UlZCvML3kyKDO1MSYupyiIITYZOBAfB4H+6PbP8JPsc+qI6sPs9vDS9vH93QUeDjsWyB1rJOAp/y21MAkyFTL/MPYuLCzMKPwk0yBgHKUXmRIzDWQHJAF3+mjzFOyo5F/df9ZT0CrLSsfwxEXEW8UtyJvMa9JQ2e7g4Oi/8Cz42P6GBBUJewzJDioQ2RAdEUIRkRFFEooTdBX+FwobZB7EIdkkSifIKAwp5Cc3JQkheBvCFDYNOAUz/Y/1sO7n6G7kZOHL34bfYuAV4kfknubA6F/qPus560HqZejJ5aXiPt/g29XYX9av1ObTDNQS1dTWH9mv2z/eieBO4l/jnuME45zhiN/53CzaYdfb1NHSctHY0A3RB9Kq08/VRNjU2lLdld+F4RzjZeR/5Zjm6Oes6R/sc+/M8zb5qP/8BvgOSheQH2InVy4ONDg4nDohO8s5wDZBMqosZybtH7EZHRSLDzsMTwrJCZAKagwMDxkSMRX3FxcaUhuCG5oaqxjfFXUSvg4PC78HHgVrA9ACYQMXBdIHXgt2D8sTDRjuGysfkCH8ImQj0CJXISAfWhw3GeYVjhJNDzEMPwltBqkD3QD1/d76lfci9JvwKe0C6mXnmeXg5Hflh+co61Xw6var/joHKhD5GCEhHSh5LdMw6TGdMPksLSePH5IWwwy4Ag75VfAN6ZnjPeAU3xXgE+PB57vtjPS6+8wCWQkGD5ET0ha7GFYZwhgtF8oU1BF9DvEKUQeuAw4Abfy8+O708/DG7Gfo6ONm3wnbB9eZ0/rQYM/3ztfPCdJ61QXaa99g5YfrgvH29o/7Df9HATEC2AFoACX+YfuC+Or1+vMD80Hz1vTG9/j7NQExB40N4hPJGeMe4SKLJcUmjSb+JEsiux6gGlAWHBJKDg8LiAi6BpEF5QR8BBMEYgMoAi8AVf2M+eD0d++N6W3jct3311TT1s+4zR/NFc6J0FPUN9no3hLlX+uA8TL3RPyZACoEBAdGCRoLsQw/Du8P4hErFMoWrxm4HLkfeyLJJHAmRyc1JzMmTiSmIW0e3ho9F84TyxBiDq0MsAtWC3ILxAv9C8cLygq6CFkFgwAw+nbyjOnG347VYMu+wSi5ErLcrMmp/Kh0qhCujLOMuqLCVssy1MXcs+S166HxZvYS+sn8wf48AIMB1gJuBHUG/ggKDIYPShMmF98aOh4DIQ4jQCSSJA0kzSL9INQeixxdGnwYEhc2FvEVORb3FgQYNhlfGlYb/Bs/HB4cqhsFG1wa6BniGYAa7Bs/HnohiCU1KjgvMjS2OFE8lT4dP5w94jngM64riCHPFQAJrftx7u3htNZGzQfGOMHxvie/p8EfxiXMPtPq2qriDeqz8Fb2yPr5/fD/ygC0AOb/lP72/Db7dvnG9yz2nvQN82Pxi+947SLrj+jT5Q/jbOAf3lrcT9sm2/rb0t2i4Enkk+g97ffxcvZd+nj9kf+NAG8AVP9y/Rf7pPiA9hX1xfTf9Zz4Fv1FAwULDxQBHmkoyTKjPIFF/EzHUrJWq1i/WBlX+1O0T6BKGUVvP+g5szToL4wriSe+I/kfBhy0F9oSXQ04B3kARvnU8WnqVePp3G7XJNM30LzOr87xz0/SgdUx2Qbdp+DE4xzmhOfp507nz+Wc4/PgGt5Y2/LYHtcD1rbVONZ311HZmtsf3q7gHuNO5S7nv+gS6kfriuwL7vnvffKy9Z/5N/5TA7oIHg4jE2cXjBo6HDAcQxppFrcQZAnEAEb3ae2147La2tKWzDLI2cWSxULHrcp9z0fVmNv84QXoV+2v8eL05PbE96r31PaJ9Rj0zPLn8Z7xEPJH8zr1zvfV+h7+cQGaBG8H0AmwCw8NAA6iDhsPlw9BEDoRmhJqFKEWKRncG4ke/SAEI3MkKCUXJUQkyyLaIK8elhzeGtMZtxm6GvccayD6JGgqZDCKNms8lkGhRTNIC0kGSCVFh0BxOkEzaCtnI74b5xRIDy8LyggmCCwJows4D4MTERhqHB4gziItJAskVSITH2salBTYDYkG+/5690nwnumZ407evNnZ1ZLSzs95zYPL5cmlyNHHg8fax/jI+sr4zfrR99bW3GjjbOqV8Yz49v5/BOAI4wtqDXQNGwyWCTUGVgJm/s769fcu9rj1sfYb+dX8ngEhB/IMnRKsF7MbWh5gH6AeGhzqF00SlQsmBG781vTC7YbnXuJt3rzbO9rE2SDaD9tP3KPd2d7N33Hgx+Dl4O/gE+GD4Wzi9OMw5iXpwezf8Ej1tPnY/WIBCwSVBdYFvQROAq3+D/rA9BzvgulR5OLffdxX2o7ZJtoN3B3fIOPW5/zsVPKn9838rgFFBpkKvw7WEvwWTBvXH54kkimNLlkzrjc5O6U9nT7bPSg7ajakL/kmrhwmEdoEVfgq7OfgEdcWz0XJzsW5xOrFJMkLzjHUG9tN4lLpxu9Z9dv5Nf1w/64AJgEcAd0AsQDaAIwB5gLzBKoH7gqSDmESIRaYGZcc+B6mIJ0h5SGXIdUgxB+KHkcdEhz0GukZ3xi2F0kWbRT9EdkO8wpMBvwAMfsq9TrvvekT5Znhn99h3wLhhuTS6anwtviJAakKkxPKG94idyhZLGousi5dLbIqEyfuIrke4xrQF88VEBWmFYUXgBpSHqIiCycmK5Iu+zAjMuIxLjAWLcAoZiNSHc8WLBCtCY0D9P33+Jn0zvB87YHquecB5ULia9983IPZmdbj04nRtc+LziXOjs7Bz6TRDtTI1o/ZH9w13pnfI+C+33LeXdy32c3W+tOi0SfQ488d0QXUq9j/3s/my++K+ZADWQ1iFjEeYCSkKNIq4yryKDglDCDUGQUTEAxjBVr/O/o09lfzm/Hf8PTwm/GU8qHzjPQx9Xv1avUO9Yn0BvS088PzWfSR9XP39vn+/FoA0QMfB/0JLQx5Db0N7QwSC0wI0wTuAPL8NPkJ9r3zifKR8uLzbvYQ+pD+pgMDCVUOUhO8F2UbNB4lIEohwiG8IWoh/yCkIHkgiSDOICwhdiF0IeIgfh8MHWAZYBQNDoMG/P3I9E/rBeJl2eTR68vOx8LF3cUPyCfM1NGs2DPg4+c778T1Gfvy/iUBqwGcACz+qPps9t3xX+1P6fnlmONN4iPiEeP35Kzn/Oqy7pzyk/Z5+j7+3wFmBeIIaQwNENwT2Bf6GysgRSQbKHcrIC7iL5MwGTBrLporyyc7IzgeGxlFFBIQ0wzIChgKygrIDN4PuRPyFxUcpx8zIlMjtyIvIK4bSRU8DeEDrfki783kNdvW0hXMOsduxLbD9sT1x2PM39EA2GHeo+R56qjvDvSi92z6ifwh/mP/ewCSAcYCIwSpBUcH4AhNCmUL/gv3CzwLxAmdB+MEwwF2/jz7VvgD9nb00vMn9HH1mfdz+sj9VwHgBCcI+wo+DeYOARCyEC8RvhGrEkIUxxZtGlIfdSW6LOQ0nD10Ru9OiVbCXChhXGMfY1RgAltUU5hJNT6nMXYkJxc8CiT+M/Oo6Z/hG9sD1inSUs88zaXLU8oayd3HlMZGxQzECsNpwlLC6cJExGzGVsnmzO/QNtV52XHd3+CN41XlJeYC5gflYuNU4SffKd2k29ra/Nok3FbegOF35f3py+6Q8/33zfvJ/s0AzAHSAf4Ah/+q/a/73vl1+KT3ifcr+Hr5UPt2/an/ngETA8kDlgNkAjcAL/2C+Xz1efHZ7fzqOenS6PPpp+zc8GD25fwGBFMLUhKPGKEdNiEXIywjfCExHo8Z7xO6DV8HSgHb+2H3FvQY8m3xAfKs8zj2Y/nr/I4AGARfB0cKxAzZDpMQBxJKE28UhRWNFoEXSxjRGO0YexhaF3IVuBI1DwULWgZ4AbX8a/j99MXyEfIZ8/r1sfoYAe0IzBE8G7Mkoy2DNdk7QUB6QmZCDUCgO3A16y2SJfEckxT2DIgGmQFb/tv8Bv2t/oYBNgVbCZENfBHOFE4X1xheGe0YnReYFQwTLBAiDRIKEAclBEsBcf56+0r4xvTZ8HrsrueN4jvd7dfj0mDOqMr4x3/GW8aVxx3Kz81w0rnXV9324kfoB+0G8Sr0c/b69+34jvkp+g77ifza/isCkQYCDFgSUhmZIMQnZi4QNGA4BDvGO5A6aTd8MhEshyROHN0TrAslBKP9YviJ9BvyAfEI8erxVvPy9Gv2dvfb93P3MfYd9FPxAO5a6pzm/uKw39Pce9qo2EvXRtZy1aXUtNN/0vDQA8/FzFnK7sfExR/ERsN6w+/Ex8cOzLbRmth94A/p9fHO+jkD4QqCEeoWAxvNHWIf8x+8HwMfDx4gHWkcChwOHGcc8xx8HcIdfR1nHEYa7xZPEmsMaAWC/Qv1aewJ5Fzcx9Wi0CzNicu8y6vNHtHF1UDbJ+ES56Dsg/GE9YX4h/qk+w/8Dfzu+wj8p/wR/nIA6ANxCPYNRRQfGzQiMinEL6E1izpXPuxASEJ6QqBB5D91PYE6NDeuMwYwRyxuKHMkSCDeGywXMhL/DLAHdQKN/UD53vW58xrzOvQ+9y788QJRC/UUaR8iKoo0Bj4FRgRMnU+OULlOL0omQ/o5KC9AI94WoQoc/830GOxA5WTgf91u3O7crd5I4V7kkOeL6hDt8u4d8JDwXvCl74/uQ+3p65/qdely6I7ntubP5brkXeOf4Xjf6dwG2u/W1dPw0H7OuczYywDMRc2pzxLTUtcp3EbhUub06tvuxPGA8/vzPfNo8brug+sk6ALlgOL24KfgwOFO5EDoae2A8yv6AgGcB5QNlBJeFssY1RmSGTUYBRZcE5kQGw44DDMLOwthDJ4OzBGyFQIaaB6KIhYmxShkKtUqFio5KGcl2iHWHaIZhRW6EW0OugupCS0IKwd6BusFTQV2BEUDqQGj/0L9q/oP+Kb1rPNY8trxUPLE8yv2Zvk//XABrAWfCfoMeA/nECgRNxAqDisLewdoA0f/aPsX+I317/NI84fzhvQG9rv3Tflo+r36EPo4+Cj17/C6683lf9802VXTRc5ZytTH28Z7x5/JGc2h0eHWd9wD4ivno+s4783xYfMN9AL0gfPY8lXyRfLo8mv05vZa+q7+tgM1CeEOaxSJGfkdhSENJIMl7iVoJRkkMyLuH30dEBvJGL0W8xRiE/gRmBAmD4UNpAt8CRcHjQQLAsn/Bv4H/Q39TP7mAOkEQwrGECgYBiDqJ1IvuTWlOqs9fD7pPOo4nzJPKmMgYBXdCXz+1vN86ubibN1C2nfZ8Npz3qXjGOpR8dL4IADUBpYMJhFhFDsWvhYJFkYUphFcDpUKeAYhAqP9AvlB9F3vU+oo5effqNqP1czQm8w6ye3G78VzxpnIbszl0dnYDOEr6tTzmv0QB9MPiRfzHegiYCZwKEcpLSl4KIknvCZpJtAmHihhKootajG8NSQ6PD6YQdVDnESuQ+ZAPjzQNdUtnSSJGgkQigV1+yTy2unF4vbcY9ju1GPShtAVz9LNh8wPy1fJYsdGxSrDQcHHv/a+BL8WwEXCkcXnyR7P/NQ7243hpOc67RXyDfYN+Rr7SvzH/Mn8jfxT/FX8wPyy/Tb/QQG5A3EGMwnCC+cNcA87EDoQcw8BDhUM8AncBygGHQX4BOYF+QcpC1MPOBSFGdUevCPPJ6wqBCyfK2MpVyWhH4MYWRCOB5T+3PXN7b3m6eBy3FvZjtfY1vfWndd32DnZo9mG2czYdNeZ1WnTIdELz3HNmcy9zAfOitBB1BLZzN4w5fHrwPJR+V//tQQyCcYMdQ9XEZISVBPOEzEUpBRBFRUWHBdEGGwZbhofG1ob/xoAGl0YKxaRE8cQEw6+CxQKVwm5CVoLPg5NElUXBx0FI+AoJi5rMlA1jTb5NYwzYS+5KfIihBv2E9UMqQbtAQP/K/6E/wUDgwisDxcYRCGtKsgzFTwnQ6ZIVkwZTu1N6Us8SCFD3Dy0NewtvyVdHekUegweBN37u/O+6/TjcdxS1cDO68gHxEjA3r3tvIq9tr9bw0zIRc7w1OrbyeIk6Z3u5vLJ9S33Gfex9TfzBfCE7CXpWOaC5PLj3+Rf52frzPBD92v+0gUCDYUT8hj0HFEf7R/NHhMc/RfdEhEN/QYAAXD7jfaC8mTvLe3B6/XqkOpX6g/qiemi6ErnheVp4x3h1N7H3C/bPdoZ2tXadNzh3vPhcuUa6aDsvO8u8sLzWvTt84nyUfB/7VXqIucy5M3hLeB738rfF+FK4zfmpelV7QPxdPR49/D50Psj/QX+pf49/wgARgEmA8wFQwmCDWQSrBcOHSsioiYUKissqCxhK1AoiSNFHdcVqQ00Bfn8cvUP7yvqBee95VLmouhx7GnxKfdH/VwDDgkRDjISVBV1F6wYIBkIGaAYJRjNF8AXGBjYGPQZTRu3HP8d7h5THwYf7h0EHFMZ+xUqEhkOCwpBBvUCWQCN/p39hP0p/mT/AgHMAooEDgYzB+kHMQghCOAHpQerBzQIeAmjC88O/RITGN0dDSRCKg0w/TSiOJs6oDqCODc02C2iJfMbQhEYBgb7mfBT56Dfz9kN1mPUs9TE1j7auN7A4+Doru3O8fn0A/fb94r3L/b98zDxDe7T6r3n+eSm4tLgf9+g3h7e4t3Q3dbd5t0C3jPej94z30Hg2uEX5ArntOoD79Xz9fgf/gMDUwe/CgMN7g1lDWwLIgjEA6r+Pvn882Dv4uvr6c3pueu/78j1mP3UBgURpBsfJucvezhsP2lEQkfpR3JGEkMUPtc3vzA1KZghORpTEw0NdgeIAiz+OvqM9vXyVu+V663np+Od37jbKtgq1e3SotFq0VPSWNRf1zvbrt9t5Cvpm+158Y/0vPb090T4zvfH9nT1HvQQ84/y0PL28w/2EPnX/C0BzwVxCsMOfBJgFUUXFRjUF5kWkhT3EQ4PGQxYCfwGJAXcAxUDrQJuAhUCWAHx/579MvqX9dLvBOlr4V/ZS9GmyerCir3quVi4Arn3uyHBScgc0S/bCeYq8RX8WgadD5oXKB47I+MmRimbKiMrIyvcKoQqQyovKkwqjCrVKgIr6ippKl4puCdxJZgiSB+rG/UXXxQeEWMOUgz9CmYKeQoSC/4LAQ3cDVEOLw5SDawLRAk3BrgCDP9++2H4Afaf9Gj0c/W49xP7R//7A80ITQ0OEawT1xRYFBkSJA6nCO8BYfp28q3qiON73efYEdYh1RrW3Ngt3bXiDenF72v2l/zwATUGPQn5CnUL0wpGCQ4HbQSlAe/+d/xa+qX4Vfdb9p71AvVq9MHz+vIV8h/xMfBt7/vuBe+w7xbxRfM49tj5+/1nAtgGAgubDmERIRO+EzMTlhEZDwcMvQikBSoDtAGdASUDcAaACzMSQxpOI9csVTY2P+5GAk0MUcdSEVLtToRJHUIcOfYuKiQ0GYwOlgSg+93zZ+096EnkYuFU3+rd7tw13J7bF9ug2kPaFdo02rvawdtV3XffFuIS5T3oWesm7l/wxvEq8mrxe+9q7F3okeNV3gbZB9S4z3HMeMr+yRrLyM3m0T7Xhd1m5IXri/Iq+SX/VASmCB8M2g4AEcQSXRT8FcsX3hk7HM4ebiHjI+UlJSdYJzsmmiNZH3gZExJiCbz/hPUx6z7hHtg70OfJWsWswtXBrcLxxEnIT8yY0L7UaNhO20PdN94y3ljd5Nse2lfY4dYG1gTWBtcg2VHchOCQ5T7rUvGM97P9lQMRCRIOlxKoFl4a1B0pIXgk1CdDK70uKzJoNUU4kDoSPKA8GTxsOqM32zNKLzsqCyUeINsboxjJFocW/RcrG+8fByYYLbA0Ujx7Q7RJkU7DURZTelICUOJLaUb9Pw85FDJ6K58lyyArHcsamRloGfQZ5xrjG40cjhyiG5kZWhbnEVkM3wW4/iv3g+8H6PXgfdq+1MXPjssKyBzFp8KLwK++A72Euzy6Qrm1uL24gbklu8O9ZsEHxozLyNF62FffC+ZB7K3xDvY6+R77wftJ+/H5Dvj99SX06fKg8ovz0/WA+Xv+iARVC3YScRnHHwEltCiOKlwqDyi5I5Ad7BU5DfUDpfrI8dXpLOMW3rvaJtlH2fHa5t3a4XzmfOuR8IP1Jfpf/igChgWICEELxg0kEGISdxRRFs8XyBgPGXUY0RYJFA4Q6gq9BLv9LPZs7tzm5N/m2TfVGNK00BfRMtPX1sLbm+H853/uv/Rl+iz/5gKBBQQHjAdLB4EGcQVhBIgDFAMaA50DhgStBdgGxQcvCNgHjAYtBLMAMfzS9t3wqeqZ5Bbfhdo914DVeNUw15Xadd+E5WXsrPPr+rkBvAetDGAQwxLjE+YTCROXEeQPRQ4GDWYMkAycDYcPORKIFTwZFR3SIDUkDSc2KZwqPisrK34qXCnuJ1omvyQyI7shUyDmHlMddxsqGUsWwhKIDqgJRASS/tr4cvO57g3rxOgj6FnpeOxv8Q74AgDkCDESXxvgIzEr4DCVNB02ZjWIMr0tXyfgH8MXjw/GB9wAMfsD93T0hfMY9PT1y/hE/AAAowPhBnoJQgslDCYMVwvdCeMHmAUpA7oAZ/42/Cj6Kfgh9u/zcfGM7i3rT+f74k3eb9ma1AvQBMzFyIHGXcVtxazGAck/zCfQcNTO2PXcpuCy4wDmjud16OfoJumF6Vzq/+u37rryJvj3/goHHxDZGcQjXi0iNpE9OUPDRvVHuEYaQ009ozWGLHEi6BdtDXYDafqO8hfsE+d64ynh6d9735jf/N9u4MLg3OC04FTg0d9N3/De3t443xLgdOFV45/lL+jX6mftse+N8eDyn/PU85rzHfOa8lXylPKZ85r1vvgR/YkCAgk9EOcXoB//JpwtGDMlN405MzocOWY2TTIgLT8nDiHxGkIVRhAxDBgJ+Qa2BR8F8gTnBLcEIATzAhEBdv4y+3H3cPN479nr4ujZ5vDlRube56PqYe7S8p33Yvy8AFIE1wYVCO4HYwaPA6r//frh9bnw4euy53HkUOJq4b7hN+Oo5djog+xj8Df0x/fp+ob9mP8oAVECMwP2A70EqAXKBigIuwlpCxENhQ6ZDyAQ+w8TD2oNEAsuCP4EyAHe/pH8Lfvx+gb8ef46Ah0H1Az9EiAZwB5eI4cm2icVJxgk6B6xF8YOlgSr+Zvu/+Nt2mjSWMyIyB3HGMhYy5rQhNet36Lo8PEu+wAEIQxfE58Z2h4cI3gmDin7KlgsOC2jLZgtCi3nKxsqkCc7JBkgNhuvFa4PcQk9A2D9JvjY87Lw3O5s7lvvjPHL9M/4RP3PARcGzgm0DKIOig94D5UOHw1lC74JhAgHCIgIMAoMDQwR/hWYG3ghLidFLEkw1jKdM2oyKy/wKekiZhrMEJIGNvwu8uroxuAD2sfUG9Hrzg3OQs5Cz8DQctIa1IfVmtZL16HXtNen16PX0tdX2EvZutqe3OTea+EG5Ibmueh26p7rI+wI7GXrYeo06R/oZudL5wXou+mA7E/wCvV6+lcASgb2C/wQCBXYFz0ZJRmbF8UU4hBHDFQHbQL1/T76iff/9av1fPZG+Mb6qf2TACsDHAUjBhQG3ASCAiv/D/t89sbxR+1T6TDmEeQR4zPjX+Ro5g7pBewB77bx5PNe9Qv26vUT9bPzB/JZ8PXuJe4n7invRPF39Kz4tP1NAy0JAA9yFDoZGx3tH5ohJSKlIUIgMB6tG/QYPha5E4QRrw85DhUNKAxVC3wKgglYCP4GgwUKBMMC7wHQAa0CxARDCEYNyxO2G8okrS7wOBBDgky+VENbqF+hYQNhy10eWEhQskbfO2Qw2CTNGcYPLQdMAE77NPjg9hb3gPi8+l39+v8zArkDUgTdA04CtP8s/OL3C/Pe7Y7oROMi3jvZmNQ30BLMH8hWxLnAT70uuna3VLX5s52zc7Sntla6i787xkDOX9dF4Y/r0fWY/3kIGhAxFpAaKh0SHngdqhsIGQEWCBOKEOQOXQ4hDzsRkxT3GBgekyP+KOkt8DG/NBY21zX+M6kwDix9JlIg8Rm8EwsOJAk4BVsCiwCp/4P/1/9ZAMAAxgAyAN3+svy0+fn1qfH47B7oWOPZ3szaS9dh1AjSKdCjzk7N/8uSyurI/MbLxG3CCsDXvRS8BLvnuvK7Tb4Iwh3HbM2+1MfcLOWK7X/1rvzMAqMHFgsjDecNkw1xDNMKEgmGB3cGHQaXBuoH/wmlDJYPfRIAFcYWfxfvFvIUgBGvDLEG0/9z+P7w4umK41LehNpO2MXX4dh922PfSeTg6dTv3PW4+zwBUQbzCjIPMBMXFxYbXB8LJDkp7C4RNYQ7DUJnSEROU1NJV+dZ/lp2Wk5YnVSQT2dJbkL5Oloz3Cu+JC8eShgWE4kOigr2BqcDegBW/Sn69vbR893wTe5Z7D7rNetr7Pju4vIP+Ez+SwWpDPETphpOIHgkxyb6JvIktSBvGnASJgkW/9L07+r74XTau9QT0ZrPSdD00lPXAt2R44fqbPHW92n94gEYBfoGkAf2BlgF6wLq/4n89/hZ9cjxUO706q/neORI4R7eANv+1zXVzNLv0NHPn8+D0JfS49Ve2uPfOuYW7Rv05PoJAS0G/glCDNkMxQsmCT4FaAAU+7v13vDx7FzqaelG6v3sdPFu95H+bgaIDl8WeB1oI90noCqbK9kqhCjcJDkg+hqCFS8QTwshB8kDVgG//+X+nf6x/un+Ev8C/57+3f3F/G/7Avqq+Jv3AfcC97b3JflB++z9+AArBEQHAAojDH8N9A13DRQM6wkwByEECQEx/tv7P/qC+bL5yPql/BT/0wGXBBIH/QgdCksKdwmpBwUFwgEs/pf6WvfJ9Cnzq/Jo81z1ZfhH/LEARAWWCUEN6Q9EESERbA8vDJMH3AFi+4r0wO1q5+XheN1U2o3YHNjg2KPaHN3+3/jiwOUb6N7p9epi6zzrq+rl6SXppuid6DHpeep57CDvTfLM9WX52Pzq/2gCLgQrBWAF5QThA40CKQH4/zf/HP/N/1kBvwPlBqEKtg7jEuEWcRpaHXkfvSArId0gAyDZHqUdrRwxHGQcYx03H8sh9CRuKOUr+y5PMYgyXTKcMC8tISifIfQZhxHQCFMAlvgR8i/tO+pk6bDqBu4m87T5PwFICUoRxxhMH3wkFCjtKf0pVCgbJYsg6Rp9FJANYQYo/wz4KvGR6kjkUt6u2GDTcs73yQvG0sJ5wC2/G79lwCXDX8cEze/T5NuT5JztmPYb/8EGNg05EqUVcxe+F70WwxQ2EogPLQ2QCw4L5ws9DhESPRd7HWkkjytnMm04Ij0ZQANBqz8FPCY2RS64JOoZUw5xAsD2quuM4arYLtEoy5PGVcNHwT3AB8B7wHnB7sLRxCnHBcp5zZ3RgdYu3J3iuuld8U75RwH8CBkQUBZcGwcfMCHRIfog1R6iG7EXWxP+DvEKfgffBDYDigLMAtIDZAU5BwcJhQpyC6AL9QpvCSQHPgT8AKb9ifru9xP2JPU19UL2Kvi0+pT9bgDkApUELwVxBDUCcP42+brySetE4xnbOtMXzA7GbMFlvg29XL0uv0jCXcYVyxjQENW52dzdWuEq5FvmDehv6bbqHOzT7QPwxfIg9gb6Wv7uAo4H/QsEEHMTJhYMGCYZiRlcGdAYIxiSF1gXoxeUGDgahRxhH50i+yU4KQ8sQC6ZL/svWi/GLWIraygqJfIhGR/uHLIbkBubHMoe9yHjJTkqmC6XMtI18jeyOOo3jjW1MZQseybOH/4YgRLFDCoI+QRdA2QD+ATnB+ILiRBuFSIaOx5dIUAjtyOsIikgTRxOF3AR/gpFBI79E/cE8X/rk+Y+4nLeHdso2H/VE9Ph0PDOUc0fzH3LjMtrzDDO5dCB1OnY791T48ro/u2b8lP25vgo+gj6lPj09XHyau5O6pnmxOM94mDibuSE6JruhPbv/2oKcRVvIMsq9jNzO91A8kOTRMhCvD65OCAxZCj+HmQVAQwxAzj7PvRW7nrpkOVx4u/f2N0D3EvanNjv1kjVutNd0k7Rp9B70NPQqNHn0m3UCtaJ17DYSNkn2S/YVtap00zQecx8yK7Eb8Ecvwq+fL6ewIPEHcpD0bLZD+Pz7PD2lwCJCXMRHBhjHUch3yNXJfAl8SWmJVQlMyVoJQMm/CY0KHspkSoyKxorDirkJ4ck/h9oGgEUGw0WBmD/Y/mF9BvxYu99727xGvVH+qQA0QdfD+EW8B00JGkpYy0PMHYxtDH5MH8vhi1KK/8ozibNJAIjYCHNHyYeQRz2GSYXuxOwDxIL/wWlAED7EPZZ8VntQeo16EPnY+d56FXquuxh7wLyXPQ29mz37/fJ9xf3EPb39Br0xvNF9M71h/h4/I8BnAdUDlcVNBx5IrEneSuBLZQtniuwJ/khyhqJErAJvwAz+Hzw+unx5IbhwN+I36ng3uLP5STpg+yf7zryK/Rf9dv1t/Ue9UH0W/Oh8kHyX/IL80j0BfYj+Hz63/wg/xMBnAKnAzMESwQMBJkDHgPFArYCCwPSAwYFjwZICPgJYwtEDGEMhQuQCXoGUgJH/Zv3rPHl67nmmeLt3wbfHuBI43boc+/q92MBVwswFVUeNyZbLGIwDjJIMSAuyiiaIf0YcQ96BZr7RfLe6a/i6Nyd2MbVR9Tz05LU6tXC1+rZPdyj3hThkeMm5uPo1+sM74byOvYS+ur9lAHeBJIHfQl4CmsKTwk2B0YEuwDk/Bj5tfUX85DxX/Gr8n/1yfla/+UFDQ1kFHcb1SEcJ/sqOi3CLZgs3inQJb8gBhsFFRcPiwmdBHIAFf15+nv45vZ79frzJPLJ78vsIOnZ5BzgKNtH1tHRHM56yy7KZso3zJzPcdR72mnh3Ohu8Lj3Yf4cBLUIDwwrDh8PGw9fDjMN5Au8CvcJwwk5Cl8LIw1iD+8RkBQLFy0ZyRrEGxEctxvOGnoZ6hdPFtoUsxP0EqkSyhI+E9wTcBTAFJIUshP9EWAP3wuYB74Cm/2E+Nrz/u9G7fvrTOxN7vHxC/dS/WMEzAsOE60ZOR9UI7olRyb8JPkhgB3qF6URJwvjBEf/q/pQ91r1zvSU9Xn3Nfpx/dEA/QOkBoMIcQlWCTUIIwZIA9n/DPwd+D30lvBC7U3qs+dl5UrjRuE83xfdzNpe2N7VbdM40XbPYM4vzhPPL9GQ1DPZ+t6y5Rjt2PSZ/AIEwwqbEFwV9BhsG+ccoB3mHREefx6EH2khXyR6KLAt1jOjOrRBlUjGTspTLVeQWLBXaVTBTt5GDT22MVglfxi8C5f/ifT16iTjPN1H2TDXytbT1wDa/9x/4Dvk9+eH687uwPFc9Kf2rPh1+gT8V/1e/gL/I/+d/kn9CPvE93TzJe715xvh4Nmc0rPLisWFwPm8KrtAu0e9LcG+xq7NmNUK3ozmpu7w9RP80gAPBMoFIQZNBZkDXwH8/sX8B/v5+bn5TPqb+3j9o//NAacD4gQ7BYIEnwKS/3P7dfbe8ADrMuXM3xnbVtes1CjTwtJb077UrNbc2Arb99xz3mPfwN+d3yDfgt4J3v/dr95Z4C/jTue97GjzJvu2A88MFxY4H98nwy+uNn08IkGlRB9HtUiZSflJBUrhSaRJVUnuSFZIbUcLRglERUGqPTI57TMBLqknMSHzGk8VoxBDDXILWQsFDWEQOBU3G/Mh7iikL5A1OTo8PVE+Uj0+Ojg1gy6BJqQdbhReC+wCf/tl9c7wzO1R7DTsNO3+7jrxjvOl9Tz3Hvgv+Gf30vWO88Twpu1j6ijnGORK4cXehtx92pLYq9au1IvSO9DDzTvLx8iZxuvE+cP+wyrFn8dqy4TQytYE3ublFu4w9tL9oARSCrAOohEqE2kTmhIMESAPOQ25C/YKMAuPDBsPuxI6F0ccfSFqJpwqqC0yL/cu0yzEKOgigBvmEokJ5v929rPtA+a43wfbCdi41vTWhdgi23reOuIS5r7pCu3S7wjyq/PL9H/15/Ud9jn2S/ZU9k32I/a59fL0sPPb8WfvV+y/6MbkpOCf3AbZKtZa1NjT0tRi14TbF+Hf54fvpvfJ/3kHRA7KE74X8BlTGvgYERbsEesMfQcWAiL9/vj19TX0zfOw9LX2m/kU/cUAWAR+B/cJlwtLDBwMJwufCcUH4AU6BBQDnwL8AjYEPQbwCBkMeA/CErIVBxiRGTEa3hmmGKwWJhRVEYAO7wvhCYUI+wdJCGIJIgtRDawP6xHEE/QUSBWeFOoSNhCkDGcIvwP3/lb6IvaU8tPv9O357M7sUO1S7qDvCPFd8oPzavQa9ar1RfYi93/4nPqt/dwBPQfKDWAVwB2UJm8v2DdRP2JFoEm5S3lL0EjUQ7887jPaKQ4fIRSnCSsAIvjm8bLtmuuR62nt2vCG9QP75ADBBj4MDhH7FOUXvxmSGnQahBnkF7cVGBMbEMgMHQkRBZUAmvsS9vzvX+lU4gHbnNNnzK7FvL/buku3OLW9tNu1d7hhvFHB78bZzK7SEdi23GTgAOOI5Bzl8uRa5LHjW+O44x7lzuft64Dxbvh6AE4JfBKHG/AjOyv8MN80rDZONtAzYC9KKe4hvRkrEawIpgBu+UDzQO536tTnNeZn5TDlVeWg5eblDOYH5t3louV55Yjl+OXt5oToyuq+7U/xXfW8+Tn+nAK1BlsKcg3wD9wRUhN8FI8VxhZeGIoabh0dIZMlryo9MPI1cTtWQDtEw0agR5pGl0OdPtM3fS/7Jb8bSBETB5j9PvVR7gPpZOVk49TibOPV5KvmiugZ6grrKOtY6pjoAebE4h/fYNvS17/UZNLt0G/Q7NBO0mzUEdf+2fPct98a4v7jWOUw5qPm2+YR537nXujj6TDsV+9T8wz4U/3pAocI2w2bEoEWWRkDG3UbvxoFGX8WdRM2EBANSwolCMYGRQaeBrwHdgmUC9sNDBDvEVkTMRRxFCgUdxORErMRGhEEEaEREBNaFW4YIhwzIEwkCSgEK9csLi3FK3goQiNCHLgTBAqe/w314Oqk4dnZ5tMX0JXOZs9o0l7X692j5Qrup/YF/7wGfQ0KE0UXJBq1GxYcdBv/GeoXYBWIEnsPSQz4CIUF7QEr/kD6NfYg8iHuZeoj55Xk+OKB4lzjo+VY6Wnup/TO+4MDYQv4EtoZox8DJL4mvCcAJ7IkFiGLHH8XbBLJDQMKcwdWBsoGygguDLAQ8BV8G9sglSU+KX0rFizoKvcnZSNwHWwWvg7QBgv/yvdc8fbrtueg5KHik+FB4W3h2+FR4qTisuJv4tzhC+EX4CXfWN7T3azd792Y3pTfw+D54QTjsePU40nj/+H130DdC9qQ1hfT8s9yzd/Ld8thzK3OUtIq1/jcauMj6r7w3PYn/FsAUQP5BGEFtgQ5Az8BKP9R/RP8uPtw/FH+UwFTBQ8KMA9UFBAZ/hzEHxsh1iDmHlsbYxZDEFYJAgK0+s/zr+2b6MPkQeIS4R7hO+Iz5Mfmu+nZ7Pfv/PLc9Z/4W/su/joBpgSLCPgM7RFVFwsd1yJzKJQt6TEpNRc3hjdiNq4ziC8mKtEj5By9Fb8OQgiSAuj9ZPoO+Nf2nPYo9z74n/kR+2L8dP07/r/+Hf+B/yQAQgEVA80FiQlRDhYUrBrQISspVTDiNmU8fkDeQlNDxkFFPv04OTJgKuYhSRkGEZAJRANn/hz7afky+T36OvzI/n4B+APVBcoGngY0BYkCsv7a+T70JO7Y56HhwNtq1sTR5M3QyoPI78YDxq3F4MWZxtvHtslBzJfP19MZ2W3f1OY974H4ZQKaDL8WaiAuKaAwZDYyOt87XTvDOEk0SC4wJ4Uf0hegEG4KogWGAkMB2gEnBOIHqwwIEnkXehyTIF0jjCTyI4UhWR2kF7EQ3giVAD34NvDS6FLi2tx82C/V2NJP0WHQ28+Nz0/PBs+ozjjOxM1nzUHNcc0QzjDP1dDz0m/VItjY2ljdbd/i4JPhauFo4KPeRtyR2dLWXdSM0q/RCdLI0wTXtdu64dXotPD1+C8B+Qj1D9MVXRp4HSYfhR/MHkYdSxs0GVcX/RVcFY4VlRZVGJsaHx2LH4YhuSLYIqwhFx8XG8cVXg8sCJEA+fjP8XvrVOad4n/gCOAr4cLjk+dV7LjxbPcp/bEC2weMDL4QfBTfFwYbEx4nIVYkrCcgK5wu+jEINYs3STkJOp858Tf2NL0wbStCJYkemhfSEIwKGQW4AJX9v/st+777Of1Z/8sBPwRqBg4I/ggoCY4ITgeXBakDywFIAGL/Sv8hAPEBpQQTCPkLBhDcEyEXfRmsGnwa2hjPFYMROgxNBiYAN/rt9KzwxO1t7L7ssO4c8r/2PvwwAigItw16Eh0WZRgwGXcYTRbZElQOAwkuAxr9BPcd8YjrVuaL4R/dAdke1WTRxs1EyubGwsP5wLW+Ir1qvLO8FL6VwCnEr8jxzajTgtkn3z/kfOik65DtOe6x7S7s/OmB5yzld+PS4qPjNea26jDxhfl0A5wOfBqDJhkypTyeRZBMJVEtU5xSjk9ASg5DaDrOMMAmvBwwE3kK2gKA/Hr3xfNJ8ePvae+u74zw4/Gf87T1I/jy+ir+0gHuBXcKVg9sFIYZaR7RIngmGSl6KnAq5CjXJWQhvRssFQwOwQa2/0n51POX77vsS+s361HsU+7n8K3zRPZS+I35v/nR+MP2tvPh75HrHufm4kHffNzP2lzaJtsW3frfiuNx51Hrze6U8WTzEvSN8+LxNu/H6+Pn4uMf4O7cl9pP2TDZP9pl3HffNeNW547rkO8c8wD2H/hx+QL68vly+bv4CfiX95T3JPhX+S37kf1gAGwDfwZlCe4L9w1sD04QrxCzEI8QfhDCEJcRLxOvFSIZgB2nIl8oXS5KNMk5gD4eQmREK0VkRCBCiD7eOXY0sC7sKIYjyx71GiQYWhaAFWUVxBVJFp4WbRZuFWwTShAGDL0GpQAL+kzzzez15h7ilN6L3BrcPN3O35HjNehY7ZPyg/fN+yf/XQFVAg8CnwAz/gP7U/dq84rv6uu16AXm4uNG4h3hTOC03zjfw95I3svdW90V3SDdqN3c3uPg2ePM57fsfvLz+NP/0AaUDckTHxlWHUIg0yEUIi0hYR8GHYQaRxi2Fi0W8hYuGeccAyJBKEIvkTajPe1D40gKTABNgEtrR8tAzjfFLCAgYhIbBN71M+iU22jQ9cZpv9O5KLZItAG0GbVUt3S6Rb6dwlzHbMzC0VbXJN0i40Ppb++E9Vb7rwBYBRMJrQv5DN0MVAttCFUETP+o+c3zKu4s6TjlouKp4W3i8OQR6ZPuHfVE/JADigrAENIVdRl8G9sbpBoFGEcUwQ/VCuMFRQFD/Q/6wvdZ9rr1s/UD9mH2gvYl9hP1LfNq8Nvsp+gN5Fnf4Nr31u7TBtJq0TLSV9S81y3cZeES5+Hsf/Kl9x38wv+HAncErQVVBqYG2gYpB8AHvwg2CiAMZQ7fEFkTnBVsF5YY9RhwGAUXyBTdEXwO6ApqB0kExQEQAEz/f/+cAIEC+QTAB48KHA0nD4IQDhHJEMcPNg5YDH0K/QgwCGQI1wmtDPIQjxZTHe4k/SwQNa08ZEPNSJZMi06UTr1MLUkrRBI+SzdCMGMpCyOEHQAZmBVHE+4RXBFQEX4RnhFuEbYQUw81DWQK9wYaAwP/6voJ95TzsvB47u3sA+yf65frvOvb68jrXuuF6jjpgud95VTjN+Fd3/ndNt0x3fXdeN+f4TjkBOe+6Rvs1+287qTuhO1r64LoDeVj4evdD9s32b/Y7Nnn3LjhROhM8HH5OwMjDZYWCR/7JQEr0y1GLlksLygOIlYafBEBCGn+KvWy7FTlSt+x2ovXwNUk1X3VidYF2LTZY9vq3DTeN9/334Hg5uA44Ybh1uEl4mjiiOJq4u7h+OB031jdqtqG1xrUpdB4ze3KY8k0ybDKEs580/HaVORl78f7AgmOFtojUzBzO8dE90vOUDpTTFM7UVZNBEi5Qek6BTRtLW8nOyLoHXAatxeKFa4T4RHmD4gNpQotBysDu/4O+mP1A/E37ULqWuii5yro5um37GbwsPRF+dX9EwK+BaYIrgrRCx8MvQvcCrsJlwiuBy8HPgfpBysJ6Qr6DCQPKRHHEsUT9RM6E4sR9g6eC7cHhgNV/277F/iK9ezzUPOx8/P06fZW+fX7g/6+AHgCkQMABNMDMQNRAnwB/QAjATECWwS8B1UMCxKjGMofGSccLls0YznSPFo+zD0bO1s2wy+mJ3AemhSlCgsBP/ia8GDqteWg4g7h0OCn4UbjXeWh587psesn7STuq+7Q7rTue+5N7kruiu4X7+3v+vAd8i/zAfRq9EP0dPP08czvGO0E6szms+MA4ffe0d223bre2uD74+znauwj8cT1+Pl4/QoAkQEEAnoBIgBE/jT8VfoE+Zj4WPlv++v+uwOuCXQQphfNHmslBSssL4kx4DEXMDgscSYQH3sWLg2qA3T6AfK76vHk1uB/3uPd4d5B4bzkBOnJ7cHyrfdb/KgAhQTtB+QKeQ23D6wRWhO9FMgVYxZxFtAVYRQMEsUOjQp8Bbv/hfkp8//sZee34kbfU90J3XTeg+EE5qrrEfLC+EH/DwW/CfIMZw7+DbkLvgdSAtn7wvSN7bXmr+Da237Yw9ay1jTYFdsK37rjw+jF7Wvybfad+eL7PP3D/aL9Ef1O/Jj7Jfsg+6T7tfxK/kIAdgKzBMQGeQiuCU0KUArHCdYIrAeJBq4FXQXOBS4HlAkCDWERhBYsHAgiwicCLXQx1jTzNrI3DzchNRQyJS6dKcgk8R9ZGzEXlxOUEBwOEgxHCocImwZRBIMBH/4j+qf11/D060vnL+Pz3+HdMd0H3mjgPuRV6V7v9/Wv/A8DqAgXDQ0QWRHpEMwONAtsBtcA5voN9b7vXOs26IDmUeag50jqDO6b8pj3pfxlAYsF1wgfC08MagyFC8UJWgd2BEoBBP7C+pr3lPSr8dTu/esW6RLm8eK934/ckdn61gjVAtQq1L3V5tjA3UnkaOzm9XQAsgstF28iBC2CNpQ+/ESbSXJMoU1iTQZM7Ul6Rw1F+0KBQcZAzkCEQbJCDEQ3RcxFZ0WvQ1xAQDtNNJMrRiG1FUYJcvy275Djcti+zrrGlMBavP25Vrkouim8Cb91wiTG18lezZvQgdMQ1lPYXtpD3BXe3N+Z4UHjv+T15cHmAeeX5nHliuPw4MPdN9qO1hvTMtApzk7N3M39z7zTCNmz33Hn4e+S+AgBzAhxD5sUDBihGV8ZahcEFIwPcQopBS0A6Puz+Mv2UvZF94T50PzUAC4FdQlADTQQBxKIEqIRWQ/PCzkH3wES/CT2ZPAU62jmgOJp3x3dhtuF2vTZr9mW2ZfZqtnb2UDaANtG3EPeJOEN5RLqN/Bm93f/KAgsESUasSJwKgwxPzbcOcs7FTzbOlc41jS0ME4sAighJOwgjx4eHZUc2By6HQEfbiDEIc4iZCNzI/wiFiLqILAfpx4SHiweIR8MIe4jsSchLPYw0zVTOgs+mUCoQfhAaT75OcYzESw0I6AZ0Q9JBoP96fXS73fr8eg66Crpg+vu7grzcPe++5r/vgL3BCkGTgZ1Bb0DUQFh/hv7qfcr9LfwUu356aDmNOOh39vb3Neq01zPFcsHx23DicCZvte9br53wPPDysjLzq7VGN2h5N3rZPLc9/z7mP6j/y//b/2w+lb30/Ob8CDuwezJ7GTunvFc9mj8aQP4CpoS1BkxIEol0CiSKn0qoCgoJVwglRo4FK0NVweJAYj8fPh49XfzXvIC8i7yp/I286vz4vPJ81vzpvLC8dLw++9i7yXvV+/+7xHxdvIM9KT1EPcj+Lb4svgP+Nf2K/U580Dxhu9T7uvtg+4/8CvzNvc4/OsB9wf1DXYTDRhZGwsd8Rz2GigXuBH0CkMDH/sI837r9OTL30fcjdqg2mLclt/o4/ToTu6M8074Rvw9/xYB1AGOAXUAy/7Y/On6Rfkn+Lv3F/g9+Rv7kP1qAHgDgwZbCdsL7A2GD7QQjREyEs4SiROFFN0VmReyGQ4cgR7RILwi/SNSJIQjbiECHkkZaROgDEIFtP1h9rnvIOrv5WbjrOLK46rmHevc8JD32f5VBq0NlRTUGkkg7CTKKAIswi49MaYzKDbhONk7BD9BQllFBkj4SdxKZkpYSIhE5z6FN48uUCQsGZsNHQI191zt++Rl3szZQte51gDY0NrI3n7jhOhu7d3xhPUs+Lb5Hfpv+c/3avV18iTvqOso6Lzkc+FN3j/bOdgq1QHSts5Oy9nHdMRNwZi+kLxyu3C7tLxVv1LDlcjvzhnWvN125d7sk/M++Z39iAD4AQMC4ADh/mv88fnq98X24/aK+OL77gCQB4UPbRjPISYr5zOQO6xB30XsR7ZHRkXFQHg6vTIAKrEgQhcZDokF1f0k94jx/uxx6b7mwORN40LiheEI4crg1OA74Rfig+OV5Vjoz+vp74n0gfmY/osDGQgCDBIPIhEhEhMSFhFYDx0NtApuCJ0GiAVjBU4GSwhFCwcPShOyF9wbYh/nIR4j0SLmIGMdbRhGEkkL4AN//Jb1jO+26k7nb+UW5R/mS+hG66vuEfIT9Vj3mfip+Hj3EfWd8VntlOip4/Lexdpr1xrV89MB1DnVedeW2ljeheLm5kzrl++08573YPsP/8cCpgbDCi4P5xPfGPYd+yKxJ9MrFi86MQMyTDEELzMr/CWbH2IYshD1CJgB/vp79U7xnO5r7aftH++M8Zv07fcn+/b9FwBfAboBLgHd//j9xfuP+aP3RPap9fP1LPdD+RP8Xv/bAjoGKQlfC6MM0gziC+YJCAeMA8b/E/zV+GT2DfUG9Wr2OflU/YICdgjODiYVFRs9IFAkEidkKD4otCbwIy4gthvVFtYR/QyCCIwEMQF3/lL8rvpy+YL4xvcw97r2b/Zi9rL2hfcA+UT7a/55AmgHFQ1LE8EZICAFJg4r3i4mMa0xVjAjLTgo2CFhGkgSDgo4AkT7n/Wc8XLvL++/8OfzUfiJ/RADYAj4DGQQShJsEq4QFw3RByABYvkC8XHoIOBz2L7RP8wZyFrF9cPLw7DEbcbKyJPLms680eXUC9gu21fej+Hf5EnoyOtJ767yzfV1+HH6jfub+376Jvie9AXwleqd5Hzendhw013Pw8zpy/vMCdD/1Krbu+PM7Gj2EQBTCb8RABnWHiUj7CVKJ3gnwCZ6JQEkpyKzIVYhpyGjIikkBCbpJ4UpfiqCKkspqCaCItwc2BWxDbkEUfvg8dPoiuBY2X3TH89MzPnKB8tDzHPOV9Gv1EbY8duW3yrjr+Y16tXtqPHF9Tv6Df8uBIIJ3A4EFLcYsRyyH4Mh/yEVIc0eSBvAFoIR7AtkBlEBEf3y+S/45/cd+bX7fP8mBF0Jvw7vE5kYeRxiH0QhJiIsIo4hlSCRH9Qepx5EH84gUSO9Jugqki9oNA85Kz1kQHFCIENVQhJAczytNwky3SuGJV0fsBm9FKwQiw1PC9QJ4wg3CIMHfAbeBHQCHP/K+ov1he/t6AriKtua1KbOisl2xYPCuMAHwFLAbsErw1TFvsdCysrMTc/T0XHURddz2h3eYeJP5+jsGfO8+ZcAZgfUDY0TQhiuG6AdAB7THDoadhbeEeAM8QeKAxwABv6M/dX+4QGNBpMMjRP+GlwiGSmtLqIymjRZNMYx7ywEJlYdThNmCCL9//F25+rdqtXqzsPJNcYqxHzD98NmxZLHScplzcfQXtQg2A3cJeBm5MzoSO3C8RX2FPqK/T8A/wGbAvQB/f++/Fr4CfMc7fHm9eCW2z3XRdT10nbT1NX32anflOZN7lr2O/5yBZQLRxBOE48UEBT5EY4OKwo5BSUAXfs79wr0+vEe8W7xx/Lt9Jn3evo//aH/ZwFuAqgCIgL/AHX/xv08/CH7tfot+6j8Mf+5AiAHMAyoET8XrBytIQsmoSlbLDwuVi/PL9MvlS9ILxYvHC9rL/4vwjCSMT8ylDJaMmMxiy/BLAopfiRMH7YZCxSgDs0J3gUTA5UBdQGnAgMFSwgrDEQQLxSMFwUaWBtcGwQaYReeEwEP3gmUBIb/Cvtr9930fPND8xj0w/X993D6w/yj/sb/+f8e/zT9Ufqn9nvyIO7t6TrmUuNx4b3gQ+H24q7lMuk27WjxcvUI+ef73/3W/sf+xP3x+4D5q/av88PwFu7H6+XpbOhJ51rmd+Vx5B/jX+Ee31fcG9mM1d3RTc4hy6DICMeNxlDHXMmlzAfRTdYv3F7iiuhm7rbzUPgf/C3/mAGaA30FkwcyCqoNOxIOGC4fiCflMPI6PkVJT4VYZ2BtZilqS2ujaStlAV5qVMxIpTuFLQIfsBAWA6v2x+us4nnbM9bH0gzRy9DI0cPTgdbP2YTdg+G35RXqk+4r89D3cfzxAC8F/QgnDHkOwg/XD54ODAwvCCwDP/239vjvbemE46XeK9tb2VvZNNvL3ufjLuox8XT4c/+vBboKOQ7zD88P1g04CkAFUv/g+GXyVuwd5w3jYOAw33vfHuHh43XnhOuy76zzKPfx+ej7A/1U/fv8K/wg+xT6QPnS+Of4i/m3+lD8Lv4eAOoBXANIBI0EHAT5Aj0BEv+r/Ev6M/ii9sr10PXE9qH4Tfua/ksCGwbDCfwMjw9SETESMBJnEQUQSA54DOAKxwlpCe4JaQvWDRUR8RQiGVUdMiFlJKQmuieIJwwmXSOvH0sbiRbLEXEN0gk1B8oFpAW6BuUI5wtqDxATcxY1GQEbmxvcGrwYUBXHEGcLhwWH/8b5nfRV8CXtKetk6sPqGOwp7rDwY/P99UH4BPor+7H7ovse+0/6ZvmV+An45vc++BX5Xfr3+7j9bf/gAOIBSAL8AfQAQf8A/WX6r/cl9Q3zqvEu8b3xYfMO9p751/1uAg8HYgsVD+MRmxMjFH8TzhFFDzMM8QjeBVcDrAEbAcUBrwO+BrgKSg8LFIoYUBzwHg0gYx/MHEUY7REGCusAEPfy7BTj9dkD0pfL8cYzxF/DXcT9xvzKCtDU1QncX+KZ6IfuC/QU+Z39qgFFBXYIQAuiDZEP+hDFEdUREBFiD74MLAnBBKn/I/p+9BfvU+qV5jjkhuOy5NHn2OyY88P77QSUDikYGSHXKOgu6TKaNN0zvTBrKzkkkxv5EfEHAv6k9D/sHeVs3zjbcNjo1l7WhdYK153X+tfs11XXLdaE1HrSQtAYzjjM3co3ymfKfct0zTnQpNOH16rb2d/j46XnB+sH7q/wHPN29ez3rfrj/a0BHQYtC8UQtxbFHKIi/CeBLOQv6zFsMloxwC7GKq0lxx95GSgTPQ0SCPMDFAGR/2j/fgCmAp0FGgnRDHwQ4xPfFmAZbBsgHaweTSBEItMkMiiGLOAxNThgPx9HHE/vViVeTGT6aNZrn2wva4RnumEOWtVQeUZtOykwHSWtGicRwQiWAaj73PYK8/rvbO0j6+jokeYC5DThMN4M2+3X/dRn0k/Q0s7+zc/NM84JzyLQSdFJ0u/SFdOj0pPR9c/szazLd8mVx1LG7sWfxobIrssI0GvVmNs/4gTpie9y9XP6U/7xAEwCfQK3AUcAif7e/Kj7Qfvs+9X9DAF/Bf4KPBHYF2IeZiRzKSktOS91L8otSiojJaEeIxcVD+kGDf/f963xrez56JDmWuUo5b7l1uYp6HXpguoo60/r8OoT6tDoROeR5djjM+K04GHfNt4h3Q3c39p/2drX69W401zRAs/kzEjLfsrSyovM4s/41NbbZORs7pv5gAWdEWIdQyi4MU05qz6aQQhCDEDgO+E1hy5aJugdvRVYDiAIYANDAND+7P5gAN4CCgaBCeAM0w8UEnQT3RNSE+wR1g9JDYIKwQc9BSEDiwGFAAsACQBfAOsAhgEQAnECoAKgAoYCcgKNAgcDDQTFBUsIpwvND50U4BlPH5UkVyk8LfEvNjHdMNUuKisFJqYfZxitEOYIfgHZ+kX1/PAe7qvsiuyJ7WPvyvFp9PL2IfnG+sX7G/zc+zL7VPqD+QP5EPnZ+Xn79/08AR4FWgmfDZER1RQWFxEYlRePFQgSKA0xB30AdfmH8iTsseaC4tTfx95e33/h9uR76bfuTfTg+R7/vgORB3cKaAxwDagNOA1LDAwLoQklCKcGKgWhA/cBEADR/R/76vcy9Abwhuvl5mTiT97z2p7Yk9cC2Anaqd3H4i3pjvCI+KwAigi2D88VjBq9HVIfWR8BHo8bXRjTFFYRSA76C6QKZQo7CwgNkA+AEnkVExjqGaQa/xnNFwQUtA4QCGIACvhz7w7nR99/2APTCc+szOzLsczMzgHSCdac2nXfWOQX6ZPtvfGU9ST5ffyz/9YC8wUHCQUM1w5WEVoTtRQ7FcsUTxPEEDoN2AjXA4P+Mfk89P3vwuzI6jTqD+tH7anw7PSw+Yv+CgPHBmYJoApPCmwIEgV/AA37J/VL7/fpo+W24n7hK+LI5D/pVe+19vL+kQcWEAUY9B6LJI4o3Sp1K3IqAShnJO0f5RqaFU8QOgt+BjICWv7t+t73GfWO8jPwBO4O7GbqLOmG6J/om+ma66ruzPLn99D9RQT4CogRlBe7HKUgDCPDI7ci8x+hGwcWfw91CFsBo/qx9N3vYexf6tfpsOqz7JnvC/Ou9iz6OP2a/y0B6gHfATEBGgDd/r/9B/3t/Jn9Hf9yAXwECAjRC4gP3BJ/FTMXyBcqF14VgxLQDpMKJAblATL+Xvur+UP5Nfp0/Nf/HQT1CAEO3RIsF50a8Bz5HacdARwjGT0VjRBUC9gFVgAF+wf2dPFU7aDpSOY341fgmt352nvYNdZM1O/SV9K+0l3UYdfn2/jhgelX8jX8vgaIERoc/SXALgE2eDv4PnZACkDpPWg67DXqMNgrJCcvIz8gfh71HY0eDiAqIn4koCYmKKwo5SeYJawhJRwnFfEM2ANB+pPwOueU3vHWjdCJy+/Hs8W0xMLEpsUlxwnJI8tSzYPPsNHh0ybWldhF20beoeFT5UfpYO1w8UP1ofhU+y39C/7f/bD8nPrT95v0RfEr7qTr/+l76UDqXOy97zf0gfk9//8EVgrVDhoS2hPkEykSug7MCa0DxfyH9W3u7edv4kHemduL2gnb59zd35DjlueG6/numfEk83DzdPI/8P7s8Ohl5LTfN9s/1xDU3tHI0NnQCNI81FDXG9tw3yfkIelK7pnzE/nB/rUEAQuxEckYPiD2J8UvbzeuPi9FoEq0TidRy1GJUGhNikgwQrY6ijIqKhcizhq+FD8QkA3MDO8N0xA0Fbca8iBzJ80tmzOMOGY8Cj90QLxADECfPro8oDqNOLA2JTX0Mw0zSzJ9MWIwui5GLNUoRCSKHrMX6A9mB4D+k/UB7S3lbd4G2STV29Ii0tXSttR518TaOt6C4U3kX+aQ59HnKue35aXjL+GT3g3c09kO2NfWNNYa1nHWE9fV14zYEtlL2SrZstj51yPXYNbo1fTVttZY2O/aft7w4hrovO2I8yX5PP55ApkFbwfoBw4HCwUkArr+NvsS+MH1rvQr9XT3nfubAT0JLxICHDYmOzCGOZJB70dGTGBOK060SylH1UAVOVEw+SZzHR0UQwscA8n7VfW67+Lqrub+4rLfsNzq2V3XENUX04rRhdAi0HLQfNE505TVZdh725jefeHr46vlluaX5q3l8uOV4dneD9yS2bzX4NY/1wbZRtzy4N7mxO1F9fL8VwQAC4UQkxTwFoIXUhaKE3MPbArlBFb/M/rl9cHyAPG+8PfxiPQy+KP8fAFcBuMKvw6xEZMTWRQRFOESAhG9Dl0MMAp6CHAHNwfeB2AJogt8DrwRJxWGGKkbZx6pIGYioyNyJPAkOiVwJakl8yVMJqUm3ibLJjYm5ySoIk0fuhroFOgN5gUp/Qr0+Opp4tXardRS0AzOBs5K0L3UJNso41jsOPZCAPwJ8RLFGjchIyaGKXYrJizaK98qiCkhKOYmBiaWJZYl7CVwJuomGifEJq8ltSPAINEcARh+EogMbQZ/ABP7bvbM8lHwCu/q7s7ve/Go8wP2N/j4+QL7JvtM+nD4qfUh8hLuwul45XnhAt4/20rZKdjQ1x/Y69gA2inbNdz+3Gzded0x3bHcJNy/27nbRtyR3bffvuKZ5iTrKPBb9Wz6B//bAqYFOQd/B3wGVQRHAar94PlY9n7ztPFH8WzyNfWT+VX/KAakDUoVlhwCIxcocSvJLPcr+SjxIx8d4BSkC+gBK/jh7nfmQd992U/VwdLF0TzS+NPG1m/av96M47ToIO7C85T5k/+7BQcMZhK/GOsevCT2KVwusDG6M040UDO+MKssRyfYILwZXRIxC6sENv8q+8f4MPhm+Ub8jgDjBdQL5BGXF3UcHCBAIrQibSGDHioasxR/DvoHkgGp+5H2hfKk7/HtT+2L7V3uce9x8Arx8/D77wTuC+sn54biad0d2PXSQ85QylfHf8XbxGjFEMetyQzN99A21ZjZ+N084lvmW+pL7kfyavbQ+o3/pgQYCscPihUnG1wg3yRpKLkqnyv+KtEoLyVJIGca5hMtDasGyADi+0D4EvZp9Tn2Vvh6+03/aANkB+AKhg0YD3IPkA6KDJUJ+wUZAlL+B/uS+Dv3MveN+EX7OP8pBM8J0A/QFXobgSCsJNgn+ikcK2Ar9SoWKgIp8ScUJ4omYiaVJggnjyf0J/cnXCfsJX4j+x9hG8UVVA9JCPIAofmp8lns8eai4oXfnt3Z3BDdDd6T317hM+Pf5D3mPufj50Hof+jN6GHpcOom7KPu8vEK9s36BABuBboKkg+nE7MWghj4GBQY8xXKEucOqQp3BrkCzv8D/oz9gf7XAGUE4wjwDRoT5xfhG5wevx8PH28c5heeEd8JCQGR9/LtqOQo3NbU/s7SymrIvseyyBTLos4V0yTYiN0G423omu138vj2Gvvb/joCNgXAB8YJKwvMC4QLLQqqB+YD4f6r+G7xa+n44H/YdNBQyYnDh7+fvQe+18D+xUrNZdbb4CTsrPfbAiUNDhY1HVoiYiVXJmYl2SIRH34akhW6EFUMrgjzBTcEbgN2AxQEAgXxBZcGsAYJBoYEHwLm/v/6ovYS8prtf+kB5lPjlOHS4AThEuLU4xrmruhf6wHud/Cx8q/0gvZI+CT6QvzI/tUBewW8CYYOtBMQGVcePyN7J8cq6iy9LTItVitNKFckxB/2GlEWOBIFD/0MTQwHDR8PahKkFncbfiBUJZQp7CwaL/svhS/MLQIrbSdiI0EfZRsjGL0VXxQaFOMUlBbxGKkbZh7LIIMiSCPlIj8hVB48GiYVVA8UCbcCj/zh9uXxvu186hjoduZt5cnkU+TW4yXjJOLE4AzfE90A2wfZX9dB1t3VWNbG1yXaYd1P4bblUerU7vbydvYh+dn6lftk+2z66Pgd91z18vMn8zTzPvRV9mv5X/34AfAG9gu4EOwUVBjHGjMcohw0HCIbtBk9GA8XdxayFukXJhpZHVIhxyVWKpIuBjI/NNo0hzMUMG8qqSL3GKsNMgEK9Ljmw9mpzdbCnrk8ssqsSqmip6OnEKmkqxevJrOXtzu89MCsxVzKAs+k00LY3dxp4dXlA+rQ7RDxmfNC9e31ivUb9LfxjO7b6vjmQuMe4O/dCt2z3RXgO+QP6lnxwfnYAhwMARX/HJcjYSgTK4YruinVJSEgCRkLEbQIlAAz+QXzae6d677qxeuN7tbyTPiP/jkF7wtbEj4YaR3IIVklLihoKi8sqy0EL1cwtDEeM4c01zXpNpQ3sjcfN8M1ljOeMPUsxChCJK0fRxtOF/UTYxGnD78OkA7tDpcPRxCvEIkQlQ+qDbEKsAbEASX8H/YN8FDqSuVS4a7ejt0D3gTgaePv50Ht+/Kz+Af+mwIvBpQIvAmzCaMIygZ4BAICw/8H/g79A/31/dr/jALTBWQJ6QwMEH4S/hNeFIkTgxFtDnsK9QUuAYD8Ovip9APybfDx74Lw//E09N72ufl+/PD+2wAiArQCmALiAbcAQf+t/Sb8zvq5+en4U/jY9033f/Y59UfzgvDQ7C/oseKB3N/VHs+byLvC371duni4Xrgfuq+95cJ9ySTRddkK4oHqg/LL+SwAmAUXCssN6BCyE3EWahnXHOAglSXsKsEw1TbUPF5CDEd5Sk5MRUw0ShBG7T8BOJ0uKiQiGQMOSwNw+dHwuOlU5Lbg0t6H3pzfzeHO5FToGezj74jz6fb7+b78PP+DAaMDpwWUB2IJAgtYDEQNnw1HDR4MFgosB3UDGP9P+mX1tPCW7GbpdecA5y3oBOtu7zH1+PtTA8UKxRHNF2UcKR/RHz0ecBqUFPgMBwRF+kDwh+ai3QjWFNAAzOTJtslKy1jOg9Jk14/cnuE35hXqCe387vLvA/BW7yHunewB64DpP+hY59PmrebY5j3nxudb6O/ofOkL6rLqkevS7KXuNvGs9CH5nf4UBWUMVhSZHNUkoyyeM2g5rz04QORAsD+6PD04jDIQLDslgx5XGBcTDQ9nDDULaQvYDEIPUhKvFf4Y6xszHqkfNiDhH8ceGh0bGxQZTRcIFncVuBXQFqsYHRvlHbUgNCMMJewlliXeI7QgIRxNFnMP5Qf//yH4q/Dv6THknt9L3DPaPdk52e/ZG9t83Nbd+t7H3zDgPOAA4KDfSd8p32vfMeCS4Y/jHeYb6V3sq+/I8nz1k/fr+HP5Lfk2+Lv2/fRI8+vxNvFs8b/yS/UR+fn9ywM+CvUQiReQHawiiSbvKL0p8yivJiwjuh67GZcUuA96CykI+gUCBTwFhAaeCDkL+g2DEHwSmBOiE3sSIhCxDFwIaQMx/g75W/Rq8HztvOs96/rr1O2Y8AP0yveg+zv/WwLTBIMGYQdzB9EGmgX3Aw8CBQD3/fD79Pn69+z1sPMp8T7u4OoK58ziRd6p2TnVRNEbzhDMa8tizBTPhdOX2RDhl+m78v370QSyDCYTxRdHGocahBhnFHgOIAfe/jr2w+395VnfMdq91hTVKNXO1r7Zm93+4X/muepY7hvx2vKG8y3z7/EC8KbtIeu36KbmHuVD5CTkwuQS5vvnYuoo7TTwc/Pc9nP6Q/5hAuYG6wuAEa0XaR6bJRMtkjTGO1NC10f1S1ZOu074TAJJ70L1OmsxwSZ6GyYQVQWR+03z6eyi6JPmtebe6MnsGvJp+En/TwYiDXkTIRkCHh8ijiV5KBMrki0pMAAzLTayOX09ZUEvRZVISksBTXdNeEzmSbtFDEAHOfIwIyj8HuIVNQ1KBWL+p/gs9Ojwu+5z7c/sh+xT7PPrM+vx6R/owuX14t7fr9yh2efWrtQW0zDS+dFd0jnTX9Sb1bjWiNfq18zXMdcx1vTUttO80k/St9Iu1OHW5Noz4KzmFe4e9mT+fAb7DXwUqxlNHUAfhR84HpYb8ReuEzcP+gpVB5cE9wKLAk0DGAWsB7QKzg2UEKQSqBNgE6QRag7DCdwD/Px19ajt9OWz3jTYr9JLzhbLBcn+x9XHVshKyX3Kw8v9zBvOHM8R0BHRPdK606bVGdgd26/evOIf56nrI/BU9AT4B/s//aH+OP8k/5n+2/05/QP9hv0C/6QBgAWQCqwQlRfzHlwmXi2GM204uzs2PcE8YTpBNqowACq8Il8bbBRaDo8JVQbWBBgFAAdTCrkOyRMQGRoeeCLQJdonayh2JwYlQyFnHLsWjxAzCvEDCf6n+Ovz5O+Q7OPpyect5v3kKuSw45bj6uPE5D7mcuh161Hv//Nq+Wf/uQUTDB0SeRfLG8AeFiCkH1sdTxmwE84MEQX1/Pr0pu1y58bi7t8X30nga+M/6G/ujfUh/a4Ewgv2Ef4WpxrdHKodMh2wG24ZvxbyE1IRFw9oDVcM3gvkC0AMvQwmDUYN8wwTDJwKnQg1BpYDAAG5/gX9I/xF/Ij98/9zA98H+AxrEt4X8xxPIaQksyZXJ4EmOySmIPgbcxZhEA4KvQOq/fv3x/IV7tXp8OVD4qje/tou1y7TBM/Lyq3G5cK1v2S9N7xmvBq+Y8E6xnzM7NM13PPkuO0V9qL9BgQECXYMVw7ADukNIAzHCUQH/wRXA5YC7gJ1BCEHyAooD+gToxjuHGMgqyKDI8AiWCBfHAMXjxBcCdIBWfpW8x/t/Ocb5Jbha+CH4MPh7uPR5jTq5u2/8aT1hvli/UEBMAU9CXMN1BFYFucaWx+DIyIn9ynAK0QsWCvgKN0kZB+nGO8QmQgNALz3EfBt6R/kXOA63rHdm9604KXjCOdy6nvtzO8g8U7xTPAx7i/rlufD4yLgHd0W21zaKduW3Z3hF+fA7T31Iv36BFIMwhLxF58bqR0HHtAcNBp0FuMR2AyqB6gCFv4i+u32gvTe8vDxnPHF8U/yJPM19H/1CPfh+B771f0XAfAEXglLDpUTBRlXHjwjXydtKh8sOiycKj8nOyLFGzEU5wtiAyf7tvOF7fnoWubM5VTn0Or873n20/2IBRgNCBTuGXoeeCHTIpgi7yAaHmoaOxbnEcENEAoCB7MEJQNCAucB3gHuAeABgAGqAEv/Yf0A+0z4efXA8l/wjO507Tbt2e1R737xK/QW9/b5f/xr/oL/m/+m/qj8v/ke9gnyzu2/6S3mXeOD4cHgIeGX4gDlK+jZ68fvtfNq97z6kv3o/84BZwPjBHoGZAjWCvgN4BGPFu0bzyHxJwUuszOgOHw8BT8PQIc/ej0QOo41SzCxKiwlKCADHAYZYhcmF0EYghqbHSshviTgJx8qFit4KhIo0SPBHQ8WAA3yAk34fu3x4gfZENBHyNDBt7zzuGm287RjtIm0OrVWtsS3erl5u8m9esCcwzrHWcvvz+bUG9pc32zkDOn67P3v6PGg8iLygvDu7avqEOeB42bgI94O3WzdY9/94iLomO4J9gv+IAbLDY4U/Bm+HZofeB9lHY4ZPxTaDdIGoP+4+ILyUe1f6cfmhuV/5XnmLOhG6nTsZ+7g77LwyfAn8OfuN+1V64jpGOhJ51PnX+iB6rrt9fEO99L8BQNuCdIPABbUGzghIyacKrEueTIINnM5wTzwP+5CmUXERzVJsEn5SN1GNUPzPR833y51JTwbpBAuBl78t/Ov7Kfn4+SD5Ibmwerq8Jj4TgGECqwTRRzaIxQqti6lMeoypzIbMZcucysLKLIkriExH1QdGhxuGygbEhvvGoEakxn5F5wVdxKbDikKVgVdAID7/PYJ883vYO3E6+fqpurP6ijrdOt66w7rDupw6D3mkeOc4Jvd0tqI2PzWYdbZ1m/YF9ut3vjisOeB7BfxHvVT+ID6iftq+zX6GfhR9Sry8+7964vp0+f45gPn5+eB6Zzr+O1P8F/y7/Pa9Az1jfR88w/ykPBR76vu8u5r8ErzpPdz/Y4Eswx/FYEeNycgL8I1sTqcPU0+sjzbOPoyWytkIocYPg79AzP6OPFS6a3iXN1c2ZXW4dQS1PbTYdQp1TTWcdfb2HXaTNxr3t3gpeO95hLqhO3m8AX0pvaT+Jr5lvl2+D/2DfMW76TqFubS4UXe1NvZ2pbbMN6u4vLovfCx+VkDMA2rFkMffyb8K3cv0DAKME8t5igzI6kcxRUAD8oIgANk/5r8Kfv5+tv7if20/wYCMATuBQoHZQf3Bs4FDAThAYj/Pf05+675vfh4+N/44Pla+yP9DP/lAIYC0AOyBCoFSAUoBfAEywTmBGYFZQbvB/wJcwwpD+IRXRRUFoQXthfGFqQUXREVDQ8IngIp/R345/Pq8Hnvy+/78QD2sfvFAtwKgBMzHHYk1CvsMXM2QjlNOq45mjdeNFgw8CuMJ4cjLyC5HT8cwRslHDwdxB5zIPwhGSOOIy8j6CG3H7Ac+BjAFEEQtQtOBzYDhv9F/Gr52/Zx9P7xUu8/7KTobeSa3zzaetSLzrPIO8NvvpG62bdqtlG2grfcuSa9F8FexaTJmM320IzTPtUJ1gXWYNVb1ETTbtIo0rrSWNQf1xXbJeAg5sTswPO8+l8BXQd1DH0QZBM0FQ4WKRbMFUUV5BTwFKAVFRdaGVoc6h/FI5Yn/iqdLRovKy+fLV4qciUBH1MXww7CBcr8VPTU7KzmKuKA38Xe8N/g4l7nIO3U8yT7vwJbCrwRtBgkH/okMCrILsMyJDbmOP06VDzPPEo8nzqtN1gzlC1mJusdUxTrCRL/NfTO6VfgQ9j10bnNvcsJzITO8NLt2AXgredW73H2fvwSAeUDzgTKA/sApvwp9/bwh+pX5NTeXNoz13zVPtVi1rTY7Nu237fjmOcL69Ptye/b8BHxhPBh797tN+yn6mPpkehL6JvoeunU6ozsf+6M8JXyiPRe9h342vm1+9X9ZACKA2MHAQxhEWoX8h22JGgrrDEjN3M7TT51P8g+PzzzNxoyBSsXI8QagRLCCusDTf4Z+mj3L/ZG9mv3S/mF+7f9hf+kAN4AGABU/rD7Zfi/9Bvx1u1N69DpnOnU6oHtjvHO9vr8uwO1CoUR0RdNHb8hBCUSJ/MnyifGJiElGSPnIL0evRz5GnMZGxjVFnoV4hPnEWgPVgyuCIIE9f83+4f2KvJi7m3re+mo6P3oaurJ7N/vY/MC92f6Rv1c/3sAkACg/8f9PftN+E31mfKK8G7vfu/f8Jjzk/ej/H4C0Qg5D1YVzRpTH7IizCSfJUUl6yPVIU0fpRwlGg0YhxanFWcVpxU0FsUWCRetFmEV5RIND8UJFgMp+zvypujP3ifVHMwWxGy9X7gVtZqz3LOzteG4Gr0LwmDHzMwP0vXWX9s+35PibeXh5wjq+uvI7XnvCvFs8obzO/Rp9PXzyvLk8E7uKOul5wzksuDy3SrcstvR3LrfgOQa61rz8vx4B2wSPx1eJzwwXjdhPAU/LT/nPGc4AjIsKmohSxheDyYHEQBz+nz2PvSo84v0n/aM+fL8bwCsA14GTghdCYIJyghTB0kF3gJHALT9Sfsi+Uv3wvV79GHzW/JS8TPw9+6g7ULs+erw6VXpW+ku6vLruu6J8kj3zfzVAhQJKg+4FGIZ1hzWHj4fBx5IGzgXKBKADLQGPwGV/B75Kvfw9oX42vvCAPMGDg6iFT0dbiTUKiAwHjS2Nu435zfXNgY1xDJgMCMuRizvKiwq9CknKpIq9SoMK5IqSikHJ7EjRh/aGZoTxQyoBZb+4ffX8bbsrejS5SfkmOP+4yXl0ObD6MPqouw/7orvhfBC8eDxhPJZ84T0IfY++Nb61P0MAUcEPwepCTwLuAvsCr0IKgVLAFj6mvN07FHlod7R2D/UNdHjz1rQjNJN1ljbVOHb54Tu6/S6+q7/mwN2BkoIOQl8CVYJEQnyCDQJAAppC2oN4w+iEl8VyBeIGU4a1hntF3wUhA8jCZQBJvk38DHnf96E1pXP8snHxSDD9cEkwnrDtsWUyM7LJc9q0njVQdjD2g7dPN9s4cHjVuY+6X7sDfDU8673a/vY/sEB/QNqBfsFtAWwBB4DPQFa/8L9xvyo/J39vv8LA2gHmgxNEhkYih0sIo4lUScxJwYlziCuGuwS8Ak5AFr25ext5HLdX9h91fLUwNbD2rXgOOjb8CP6kwO6DDQVshwAIwIotCspLoQv9C+rL9suri1JLL8qHCleJ34lbyMlIZkezRvLGK0VlRKvDy4NQgsZCtUJhwouDLIO5RGFFT4ZshyBH08hyyG7IP0dkRmVE0cMAgQ5+2vyHOrQ4vfc7tjz1iLXc9m73a/j7Or98mb7qwNfCyQSuBfyG8seVCC4IDUgEx+cHRccvRq4GRsZ5Bj8GDsZbBlSGbMYXRcpFQQS8g0ICXUDdf1Q91TxzesB5yPjVuCm3gfeWt5s3/zgxuKB5O7l2uYg57PmmOXn48nhct8c3f3aR9kc2JHXpNdC2EbZfdqv257cFt3r3AbcZNoa2FbVWdJ1zwbNa8v7yv/Lrc4d00rZE+E26lr0Ff/vCXUUNx7VJgkupjOgNwg6CjvqOvo5lTgSN8E14TSYNPc08jVjNxM5ujoKPLY8eTwdO4E4nzSHL2UpdyIOG4ITKwxgBWb/c/qk9gP0fvLw8Sby4PLb89f0nPUA9uv1VfVK9OTySfGj7x3u3+wF7Jvrn+v+65jsPu2/7ejtjO2I7M7qYeha5ejhS97R2s/XmNV11KLUQtZb2dndiOMZ6inxRPjz/sEESQk5DF4NpQweCvwFkgBK+pzzCe0O5xriht6O3FDcxN3C4AflOOrq7671GPvG/2kDzgXYBokG/ARjAgH/IPsS9yTzm++s7IDqLOm26BjpQuod7JPukfEM9f34af1ZAt4HBA7UFE0cYSTwLMY1nT4fR+lOkFWuWuJd3l5tXXdZCFNOSpw/YjMpJosYJwua/mzzFerp4hnertuN23bdD+Hn5YTravEn91b8rQD+AzYGXwedByQHOAYfBR0EawMwA4MDYgS4BV0HHgm/CgMMtQysDM8LGAqYB3ME2wAR/Vb57/UX8/zwuO9U78Hv3PB28k/0Jfa699P4SPkB+fv3SvYU9JHxBO+y7OHqzOmf6XTqTewX76fyxfYq+4z/oAMpB/UJ6Av+DEcN7QwoDD0LeQohCnQKngu0DbIQexTXGHkdCCIiJmYpfysoLDYrmShjJMEe/Rd2EJkI2ACj+VnzSu6q6o/o8ees6IHqIe0w8E7zJPZl+Nj5Xfrq+ZL4e/bf8wHxKe6d65rpTOjN5yPoPun96jLto+8X8lT0L/aF90b4dfgj+HL3jPag9d30avRj9NP0tfX09mf43Pkb++v7Fvx4+/r5nfd49Lnwo+yH6L/kpeGN37zeYN+L4TTlL+o38O/26f2uBMoK0w9yE2oVnhUVFPMQfQwRBxwBFPtr9YnwwuxR6k/puelr6yfumPFf9RT5VvzQ/j4AdwBr/yP9xfmK9bvwquur5griDd7m2rfYj9ds1zvY4dk73CXff+Ix5irqZu7o8rr36fx+AoII7A6oFZIcdCMJKgIwCjXNOP06XzvOOT82yjCmKSkhxxcIDoAEx/tr9OzurOvs6sjsMvHz97EA+Qo/Fu4hci1BOOVBA0pdUNtUgVdzWO1XOlavU6BQWk0bShFHUkThQa4/lz11Oxs5XzYfM0kv2SrdJXQgyhoWFZAPcQroBRcCDv/J/DH7HfpU+ZT4mfcj9vrz+PAL7Tbol+Jd3MvVLc/YyBvDPb51uua3m7aHtoW3X7nQu42+SsHGw8vFOscJyEbIFsixx1zHYscOyKHJTMwr0EHVdduW4lzqcfJ0+gICxAhvDs0SxRVYF6QX4BZZFWQTYRGmD4IOLQ7HDlUQvhLOFT0ZsRzHHx4iXSM+I44hOB5FGdgSMAugAon5UfBg5xLft9eI0avMLckGxxzGScZdxyrJgstBzlDRotQ62CHcauAp5W/qRPCk9nz9pgTvCxUTyRm9H6MkNyhGKrMqeSmxJo8iXR16F1ERUgvlBWgBJP5E/Nf7zPzz/gMCoQViCd0Mrw+DER4SYBFKD/oLrQe3An79a/jp81rwCe4r7dXt/++B8xr4c/0oA9AICA50Es4V5henGBcYUhaNEwkQEQzyB/QDUwBA/dT6HPkR+KH3rvcW+Lj4evlH+hr79/vu/Bf+j/9xAdcDygZJCkEOjBLzFjMb/h4FIv0jqCTZI30hnB1eGAYS8wqUA2n87vWd8ODsA+s364bt1vHm91f/rwdmEOoYsCA5Jx8sFy/8L8wupyvOJpkgdBnQESAKzAIu/If2APKp7n3sXesg65LrfOyv7QDvVfCh8eXyMvSd9UX3Rfmx+5b+7QGkBZYJjg1NEY8UDheMGNYYzhdpFbYR2gwSB6sA//lp80Tt3+d44zjgLd5L3W/dX97W34PhFuNK5OTkweTT4yji5t9H3ZXaIthC1kLVXtXB1nrZf92r4sToeu929lr9zgOJCVEOBRKgFDMW7BYHF9AWlhajFjoXhxiiGocdFyEaJUMpOS2ZMAYzKjTDM6cxyC01KBshxBiJD9YFGvzC8jLqveKf3P3X5NRH0wXT7tPJ1VrYZtu73jLiseUs6aPsHvCq81P3IfsS/xUDEQfZCjoO9RDMEoQT7RLnEGkNgwhgAkb7jvOn6wbkJt1111bTEdHO0JjSUda+24XiNupR8lb6xwE4CFMN4RDLEhsT/hG6D6oMNQnEBb0CcgAj//T+7v/5AesEfwhmDEgQ0hO4FsAYxRm2GZ8YnRbkE7EQSQ3xCegGXwR5AkcBxwDmAIQBegKaA7oEuQV8BvkGNQc+BzEHLgdZB9AHqQjsCZALeQ18D14R2RKkE3oTIBJsD0sLxQUC/0H34e5P5grekdZd0NjLVskKyQPLLc9O1Q3d9+WH7zL5bgLACsIRKRfNGqcc0hyGGxUZ3RVHErYOhQv9CFEHmQbUBugHqQnbCzsOhBB6EukTshTDFCAU3hIeEQsP0wyhCpsI2AZkBTkERgNrAoMBZwDz/gz9pfrD9370AfGG7VTqu+cF5nrlT+an6Ivs5vGM+DIAfwgFEVQZ/CCZJ9gsgDB0MrYyZTG8LgkrqSb/IWodPhm+FRQTUxFyEFAQuRBsESESkhKDEscRRRD9DQULiQfIAwgAmfzB+b73u/bM9uv3+Pm6/OP/FgP0BRwIOAkECVQHGARe/075LPJP6hzi/NlY0orL4MWNwa++Sb1FvXy+tsCzwy/H7cq3zmTS3tUa2R/c/t7N4afkoOfG6hzulPEV9Xj4jvsj/gQACAEQAREAGf5I+9j3FvRf8Bbtn+pV6YDpUuve7hX0xfqdAjILAxSDHCckairdLikxHTGrLuspHCOZGtgQXQaz+1zx0Ody34nYPNOWz4LN1sxSza7OntDa0iXVUddF2fvaf9zu3W3fKuFP4wLmW+lm7R3yafcn/SUDMAkQD5UUlhn4HbEhxyRPJ2spRCsGLdku3TAjM6o1YDgdO6w9yz8xQZlBxECFPsQ6hTXoLiknoR67FfMMxwS1/Sf4d/Te8nTzLvba+icBrgjwEGkZlSH7KDcv/zMoN6k4lzgmN540WTG0LQwqsyboI9chkCAKICYgsSBqIQoiTCLxIckgtR6pG7AX5hJ4DZsHigGB+6/1PfBC68fmxOIj38fbi9hN1fHRZs6sys/G8sJBv/m7WLmftwa3uLfMuUO9A8LZx33OkNWt3GbjV+kj7ojxWPOK8y/yfO+961TnseJI3oja0ddx1pjWW9iv223gVuYY7Vj0ufvkAo8JhA+jFOQYVhwdH2ghcSNwJZYnCSrZLAMwbDPlNi46+jz5Pt4/Zj9gPbI5XTR/LVAlHhxLEkQId/5O9STtRebg4A7dyNrz2VvavtvT3Uvg4OJT5XfnLulu6jvrqevT69nr2evq6xjsZOy+7AvtJu3m7B7srOp36HbluOFe3aLYz9M/z1PLbsjnxgjHAMnizKDSC9rV4pLsxfbkAGcKzBKkGZsegCFFIgEh8R1uGeoT5A3eB1YCu/1h+oP4PPiD+TT8DgDBBO4JMg8zFJ4YNhzRHlwg2yBmICMfRB39GoEY/hWTE1cRUA96DcgLJgqACMcG8gQFAxEBNP+W/Wj84Psv/H/97P99AyYIwQ0TFMsaiiHqJ4It8zHvNDw2vzV7M5UvTioCJCAdIBZ8D6YJ+wTDASQAJgCrAXoEQAiVDAwRNRWqGBgbRBwRHH4aqxfSEz8PTgpgBdAA8/wD+in4dPfX9yz5PfvC/W4A9gIUBZAGQwcdByAGYgQIAkT/SfxL+Xf28PPH8f7vh+5H7Rjs0epH6Vjn7eT+4Zbe0drd1vPSV89NzBTK4cjVyP7JUsytz9bTgdhY3f7hHeZn6aLrruyG7ELrF+lR5lHjf+BG3gvdIN3C3hDiCueQ7WP1LP6DB/YQEBpoIqApdS+7M2Y2gjc3N781YDNnMB0twymKJo4j2SBgHgQcmhnyFtkTIxC0C38GjgAD+hPzBuwz5fjer9ms1TTTddKF017W39rP4ODnuO/29zYAIwhwD+MVWBvBHyEjkCUuJyIolSioKHMoAyhUJ1cm7iT5IlMg2xx9GDITBg0bBqn++PZi70foCeID3YDZtte915HZCt3l4cHnLO6o9LX63P+2A/kFeQYsBS8Cv/01+ALyouuU5VDgPtys2crYqtk53EbghuWc6x3ynPi0/gkEVwhvCzwNvw0UDWUL6gjgBYYCFf+6+5j4xfVH8xzxO++W7SPs3erF6enoYehO6NboIupW7I7v1vMn+WX/XAbGDUQVcRzcIhooySubLVwt9ip3JhEgFhjzDi4FVfv38Z/pw+K/3c/aCtpj26vekuO06aDw3ff6/pIFWQsYELkTQRbPF5gY3xjvGBEZhRl9GhYcWB4zIYMkEyijK+wurzGwM8U01TTdM+4xLC/KKwMoGSRJIMccuxk7F0oV2RPKEvIRIBEiEMoO9wyWCqYHOQRyAIX8qvgi9Sny8e+f7kHu0O4u8CnyevTT9t/4S/rS+kH6evh/9Wvxd+zz5kDhzNsE103T/tBV0HPRW9Tt2O/eCebV7eH1u/34BD8LTBD3EzMWEhe9FnIVexMoEcYOlwzPCooJ0AiRCKoI5QgHCdAIBQh0BgAEnQBY/FL3wfHq6xrmouDO29zX/NRI08PSWNPh1CTX39nK3KPfLuI/5L7lpeYC5/jmtuZy5mbmyObE53Tp5OsI78Py5/Y6+3z/bQPUBocJawt8DMsMgAzSCwULYwoxCq4KBAxKDnoRcxX6Gb0eWCNhJ2sqFCwMLB0qLyZPIKoYkA9rBbz6CvDh5cPcINVMz37LyskeykzMBtDs1JLah+Be5rvrUfDs83P25PdW+O/35fZz9dXzQfLj8NvvOu8D7y/vru9r8FTxWfJ086r0Cfap96n5LfxT/zMD2wdHDVwT7xm+IHgnwC00M3Y3MTomOy46Qzd9MhsseSQNHGETCAuVA5D9Z/ly9+H3u/ri/xEH4w/aGWYk9i75OPBBc0k0TwdT4FTVVBFT2U96S0lGl0CrOrs07y5XKfEjrx50GSEUlQ65CH4C6fsK9QXuDede4Dna39SI0GPNissFy8XLps1z0OvTwtev22rfu+J65Y/n/ejW6ULqceqd6gDrzOsl7SDvuvHd9F34+/tv/2kCoATPBcgFcATJAe/9G/mc89TtL+gb4wDfNNz42nHbpN124a/m/uwB9Ev7bAIBCbIOPxODFncYLBnPGKAX6hX/EywSsxDED3wP3A/QEC0StxMoFTUWmBYVFoAUxBHiDfMIJQO5/Pj1M++36Mvipd1p2SfW2NNl0qTRY9Fq0YXRhtFO0c7QB9AQzw3OLM2kzKrMbc0Pz6HRINV02XHe2ONg6bnulvOx99P62/zA/ZL9efy0+o/4Y/aG9Enz7vKg83P1Xvg7/MwAwQW8ClsPQhMhFsAX/hfbFnUUCRHqDIEIPASOAN/9hPy7/KX+QAJsB+oNYRVqHZAlYi10NGs6Aj8OQoBDZEPeQSU/fzs3N5ky6i1lKTUldiEzHmkbDBkGF0MVsBNBEvMQyw/aDjgO/g1HDiYPpBC5Ek4VNxg3GwEePiCTIashOSAFHfQXBBFbCD7+D/NM54bbVtBUxgq+77dZtHmzWbXZubHAesmx08TeGuog9VH/PgiZDzMV/xgQG5Yb1hojGdYWRRS7EXUPmw1BDGQL8grKCsMKsApqCtMJ2Ah2B7oFvAOiAZb/wf1J/Er70/rf+lr7Hvz6/LH9Bf67/aD8k/qF93/zoO4e6UDjW93K1+XS/s5TzBDLRMvnzNTP0NOP2Ljd8uLn51Ds9+/A8qb0wvVD9mr2hPbk9tj3ovlw/FkAWQVPCwISIRlNICInOy0+MuM19zdnODs3mDS8MPkrrCY4IfkbQhdSE08QRg4sDdsMGw2oDTYOfQ48DkINcwvHCFEFNAGr/Pb3XvMs753r4+gd51bmguaD5y3pReuQ7dHv1fFz85X0NvVj9Tn14fSK9Gb0nvRU9Zj2aPiu+kL97P9oAnIExgUpBnMFkAOGAHb8mPc68r3sh+f/4oLfYN3N3OHdmODK5DXqfvA59/X9PQStCe8NyBAZEuURSxCGDecJywWUAaL9RPq79y32o/UO9kP3Avn++uL8W/4e//L+sf1Q+9z3fPNs7vjodeM73p3Z5dVK0/LR7dE4077VWtng3R/j6OgR73n1C/y6AogJdxCOF9AeOSa5LTM1eDxJQ11JYU7+UeVT0lOTURNNWkaRPQUzHydjGmYNxwAh9QXr7OIy3Q3aitmP29ff/uWH7eT1f/7IBkMOhRRDGVUcth1/HegbPxneFSYScw4YC1cIWQY2BegEWwVmBtcHeQkXC4MMmw1MDpEOdQ4NDnYN0Aw4DMQLgAtoC2wLbAs/C7QKmAm/BwUFVwG4/Dz3EfF66sfjWN2L177SQM9QzRLNjs6w0UXWAdyH4mrpPvCY9h38hQCmA24F7AVJBcYDswFs/0n9nPuo+pr6hfth/Q8AWAP1BpYK6g2mEI8SexNaEzUSLxB/DW0KSwdsBB4CogAiALQAUwLeBB4IzQuUDxsTDRYfGBsZ3RheF68U+RB4DHgHTAJH/bT40vTO8b/vqO527gXvJfCe8TjzwPQP9gn3p/fu9/X33PfN9+73ZPhH+aH6avyH/ssA/QLYBBUGbwauBasDVgC6+/n1VO8f6MLgqtlG0/zNIsr1x5PH+sgKzIHQBdYr3HzihejX7RvyDvWO9pb2RfXR8onvzusC6IrkveHi3ybfnd8+4ejjYOdf65PvqfNU91T6fvy6/Qr+hP1U/LH63vge97H1zPSV9CH1cfZ1+BD7F/5aAawE4gfdCooN5A/3EdoTrRWUF7QZKBwCH0Mi2iWlKXIt/zAHNEI2bzdcN+s1FjP4LsMpyCNvHSwXfxHiDMQJgQhUCVgMgRGbGFAhLCujNR5AAkq/UtZZ416kYf1h9V+3W5BV4E0ZRbM7IjLPKBIgKhhBEWMLiAaUAl//tvxp+kr4OPYc9Ozxru9z7VHrY+nC54Hmp+Uu5QXlCeUR5erkYeRH43fh3N5x20vXkdJ+zWDIi8NZvx68JLqfuay6Tr1owcLGDc3l097aieF952Ts+u8c8sPyCvIp8HDtQeoJ5zTkJ+I14ZnhduPL5oDrXvEb+F//ywYEDrcUohqZH4UjaCZbKIYpHSpZKm4qiSrHKjErvStKLKgslizPKw0qEieuIsYcVxV5DGACV/e86/rfhNTIySzABLiOsfCsNKpMqRSqVKzMrza0TLnUvpvEgcpz0G7Wetyo4gnprO+Y9sj9JAWKDMMTjhqiILUlgynSK34seSvOKKgkSx8RGWUSvAuLBUAANvyv+dD4nfn5+6f/UASLCeQO5xMnGEsbEx1cHSQciRnGFS8RJgwWB2oCgP6k+wz60vny+k39rADHBEkJ2g0nEuYV3xjvGgkcNByOGz8afBh8FnUUkRLyEKgPsw4GDoUNDg17DKkLegreCNQGaAS5AfD+P/zd+f33y/Zl9tT2EPj5+Vz89v54AZED8wRbBZgEkwJS//T6uPX07xDqgOS33yHcGNre2ZTbOt+p5J3rs/Ny/FYF2g2AFdoblCB7I30kqiM1IWwdsBhxEyEOKwnuBLMBq//r/m3/EgGqA/UGqwqFDkISqxWZGPYauxzxHaseAh8TH/UeuR5jHu8dSB1UHO8a9RhEFsQSag49CVYD5Pwk9mXv+ug9433eAdv32HjYf9np23rf2+Om6GjtsPEV9T336ff39mb0V/AK69rkNN6R12rRMcxGyPHFXcWWxofJAM6401baeuHA6NHvYfY4/DcBWAWnCEYLYg0wD+MQpxKbFM0WORnFG0geiyBQIlgjaiNaIg8ghhzSFyISuAvlBAv+hve18ensYelG56bmdeeQ6bzssvAg9bP5Hv4cAn4FJggICi8LtgvBC34LGQu5CnkKaQqECrkK5grgCncKfgnMB0kF8AHQ/Q/56/O07sbphOVO4nngSODk4Vfli+pH8TX55gHaCokTbBsIIvcm7ynIKn4pMSYiIa0aQRNZC28D9/tS9czvlOu76Dnn6OaR5+zoruqM7EPun+9+8NHwn/D/7xbvE+4o7YHsRuyQ7Gntze6o8NnyOfWd99r50ftq/Z/+dv8GAHUA7gChAboCXgSkBo4JDA34EBUVGhmyHIQfPCGVIVogdR3pGN4Slwt0A+v6fPKt6v7j3t6k24jan9vY3gHkxeq78mX7QATRDKMUWxu1II8k5ibTJ4wnVyaJJHkidyDLHqcdKR1THRUeRh+vIA4iICOlI2UjOyITIO0c3BgGFJsO1gjzAiv9q/eY8gfu/elz5lbjjeD83Y3bMdnn1rvUy9JC0VbQQ9BG0ZbTW9er3ILjwusz9YD/Pgr4FCwfXCgUMPU1ujk/O4Q6rTf/MtwsuiUeHooWfQ9jCZAEOwF5/z//ZACmArIFKQmsDOIPghJVFDwVMxVJFKMSdhD9DXQLEQkAB1sFKgRhA+ECfwIGAj0B8f/2/TL7n/dJ81Tu+Oh44yXeTtk/1TjSZ9Dmz7TQt9LB1ZDZ1d064mzmH+oX7SnvQ/Bn8K/vRu5m7EzqOehm5v/kIeTW4xPkvOSn5aLmd+f05/PnW+cq5nDkVuIT4PDdO9xC203bkdww3zDjeOjT7vL1bv3SBKYLcxHPFWcYBBmTFyEU4g4nCF0AAvia76vnsOAO2xLX6tSi1CjWTNnI3UXjZunK7xz2E/x1ASUGFQpODecPBRLSE3kVHhfdGMca2xwQH1EhfyN8JSondShQKb4p0CmkKWUpQylxKR0qaytxLS0wjDNgN2k7Uz/BQlRFrkaCRpREyEAdO7Yz1yrgIEoWnAtiASb4X/By6qLmD+Wz5WXo2+yv8mj5hwCNBwUOjhPeF8waTBxxHGcbbxnXFvETDhFzDlQM0Qr0CbEJ6AlpCv0KaAtyC+4KvAnOBygF4QEf/hH67vXs8T3uBetd6EzmxuS04/DiTeKf4bvggd/g3dbbdtnj1lDU+dEg0ATP2s7Kz+XRJdVs2YDeGOTW6VrvQPQu+N76Hvzd+yj6Lfc386ru+emh5Rzi2t81323gn+PI6MDvQPjlAT4MzRYTIZwqAzP7OVA/7ULYRC9FJET2Qek+QDs1N/YyoC4+KsslMyFYHBsXWhEACwEEZ/xI9NLrQePg2v7S7cv4xVzBRL7GvN28bL4/wRHFjslezinToteI27HeB+GM4lnjl+N+40zjPuOL41rkxeXO52TqYu2V8L7znvb2+JX6Wfs0+zD6cfgt9qvzQPFC7wHuxO277v/wjvRI+fL+OwXDCyAS6hfCHF0ghiIoI0siGSDVHNoYkhRrENIMJgqxCKQIEAroDAAREBa+G6AhSydWLGIwKDNyNCo0UDL+LmUqxCRhHokXhBCSCeYCp/zp9rnxFe346FrlNOKJ32Ddzdvt2uPa1tvr3T/h4+XY6wfzQ/tGBLkNMBc3IFgoIi8yND83Gzi8Njsz1i3pJu0eaxb0DRcGVv8c+rf2UvXx9XP4lvz6AS4ItQ4RFc4aix/9IvokdCV9JEIiBR8WG84WgBJ7DvsKKQgZBsoEJAQCBDQEhQTCBL8EXgSOA08CsQDT/tj87Po4+d338/aA9n320PZQ98v3CfjR9/H2Q/Wy8j/v/eoW5sfgWdsc1mLRdM2NytXIWsgUyd3Ke82h0PjTJ9fX2cHbtNyV3GrbVdmS1nXTYtDFzQfMiMuSzFnP7tND2iniU+te9dX/OwoZFP8ckSSMKsouRDEPMlwxbC+QLB8payW/IVUeVRvSGMsWLhXZE6YSahEAEE0ORAzpCVEHogQNAsz/Gf4s/TH9Q/5sAJ8DuQeDDLgRBxcdHKogaSQmJ8EoMSmGKOYmhiSrIZ0eoxv9GNgWUhVvFB4UORSIFMgUsRT/E3cS7w9TDKcHCgKx++P09u1I5zLhBNz710HV4NPK09PUudYq2cjbM94V4CXhMuEk4AHe7dol1/vS0M4Lyw3ILcavxbzGYMmKzQvTnNng4HHo5u/a9vT87QGcBesH4gihCFsHUQXOAhwAgv05+275Pfiw98L3YPhy+dj6ePw7/hMA/wEHBD0GuAiUC+cOvxIfF/UbISFsJo8rNzAHNKQ2ujcEN1Y0ny/yKIMgqRbXC5oAjfVL627ifdvl1vDUwdVR2W7fwefV8Rz9+wjaFCMgVioLM/o5/T4NQkZD2kIRQT0+sjrANq4ysS7sKmwnMSQoITYeOxsXGLMUAREADb4IVgTx/7r74feV9PfxIfAY79LuMu8L8CjxSfIx86nzhPOp8hLxz+4F7O3ozeXy4qrgPd/i3rzf2OEl5XjpkO4V9Kf54P5dA80G8AigCdYIqwZVAyT/d/q99WTx0+1i61Dqwuq87CTwxPRM+l8AlgaMDOIRTRaWGaEbbBwSHMEauRhFFrETQxE4D7gN1wyUDNUMcQ0uDs0OCw+vDogNeAt1CIkE1f+G+tr0FO946UTkqd/J27TYZNbF1LDT9tJl0srR/dDjz3HOs8zEytXIIsfvxYHFGsbqxxLLnM911XTcV+TK7Gv11P2iBX4MIhJgFiUZfBqIGocZxReaFWATaBH3DzsPTA8lEKYRmhO3Fa0XJBnNGWYZwhfMFI4QLQvmBA/+CPc78A/q3uTz4H7eld0x3i3gTuNF57jrR/Ca9GL4Y/t4/ZL+v/4d/uL8S/uf+SH4DfeU9tT22veg+RD8Bv9UAs8FSAmZDKoPbBLhFBYXJBknGz4dgB/8IbMklSd+Kj0tkS8yMdYxOjEmL3krKiZQHyAX7g0pBFX6//C66A7ict1D27jb4d6l5MLs0fZLApgOExsWJwkyZzvKQu1HsEoaS1JJm0VSQNw5pTIWK4sjURygFZoPTQq0BbwBTP5D+4n4B/ay843xoe8E7tHsI+wT7LPsBu4C8I7ygPWi+LX7df6gAAACbALNASMAif0r+k32QfJg7gXrgegX5/TmKuiw6lzu7/IQ+Fv9YgK+BhIKFAyVDIQL8AgGBRAAa/qD9Mbun+lr5XLi4eDI4BjipuQv6F/s2vBB9T35h/zp/kgApAARALz+3fy7+pr4vPZV9Yf0YvTd9Nz1Mfeg+Oj5xfr/+mb64Phm9gjz6u5E6lnldODi2+XXt9SA0lDRJtHs0XfTldUI2JXaBt0w3/ngWeJa4xnkwuSH5Z/mPuiL6p/tgPEa9kf7yQBXBpsLPhDuE2gWexcSFzMVAxLADcEIbQM1/of5yvVT82DyD/Ng9TX5Uf5gBAMLzRFWGEEePyMcJ74pJityK9UqlCn9J2AmBSUpJPQjdySrJW8nkSnNK9ctYC8jMOMvei7WK/4nECNCHdYWHhBsCRADU/1r+H70nvHI7+bu0+5j72Lwo/H68kr0hPWl9rj31fgY+qD7hf3Z/5wCwgUnCZoM2A+YEooUZBXoFOoSVg83CrUDF/zA8yXrzuJB2wTVh9AmzhvOetAx1QfcoeSF7in59wNdDtEX3x8xJpEq7ixaLQYsQClnJeUgJxyQF3YTHBCsDTUMsgsFDAMNdA4dEMYRPBNYFAEVLBXZFBMU7RJ6EcsP6Q3WC4kJ6wbhA0YA+fvY9tDw2ekC4m3ZVNAFx969SbW0rYqnKKPZoMygEaOWpyquebYZwI7KUtXf377phfLp+bz/8wOlBgUIXwgRCIAHEQccB+oHqglyDDgQ2RQaGq4fQCV4KgMvnzIZNVk2XjY+NSUzUDADLYcpHiYAI1YgMx6WHGwbjBrHGeIYpxfjFXITQhBUDMAHsAJh/Rn4JvPS7mHrBunk5wPoWOm+6wDv2PL69hf75/4tAsAEhgZ8B7UHUgeCBnoFbwSOA/kCwQLjAkcDxQMkBCUEhAMFAnf/u/vN9sDwxekl4j/afdJSyy7FdcB1vWW8Wr1IwALFPMuU0pXaw+Kl6svx2feM/MD/bgGvAbYAyv4//G/5svZT9I3yh/FO8dnxCfOt9I32afgG+jP7zPvD+xv77vlm+Lv2LvUC9HPztPPp9CH3WPp3/lMDuAhnDiAUpxnKHmUjZCfHKpot+i8MMvcz4TXmNxU6bDzWPitBNEOsREpFyETmQnc/YzqxM4ErFSLGFwcNVgI6+DDvrecM4ozeSN003iHhvuWe60PyI/m2/38FFgosDZYOSA5cDAYJlwRy///5qvTV79Pr4egi56LmUucN6Z7rx+5F8tb1Qvld/Ar/OQHuAjMEHgXGBUIGowbxBioHPwcZB5oGoAULBMYBxf4N+7b27fHy7BHoo+MC4ITddNwJ3WDfeOMx6Uvwa/geAeQJORKaGZQfyyMBJh0mJyRQIOcaVxQcDbwFvP6V+KzzTfCj7rvuf/C98y34d/06AxoJwA7kE1QY8hu2Hq8g+CG5Ih4jUCNxI5YjwyPsI/UjtSP6Io4hQB/pG3EX0hEeC30DK/t28rbpSuGN2dLSW81VydXG1cU6xs/HU8p5zfLQc9S815za99zH3hjgCOHE4X3iZ+Ou5HTmyOim6/fujfIw9pj5f/yd/rr/rP9i/uX7Vfjv8wPv8ekf5fPgyN3n24LbrNxa32Hje+hL7mX0Wvq7/yQETAf+CCYJ0AclBWoB+Pwy+ITzUe/y66rppuj16I7qS+328Ef17vmd/gsD/QZJCtYMow6/D0oQbBBVEDAQJhBQELwQZxFAEigT+BOFFKcUOxQsE3YRJA9XDD0JEwYcA58A2/4D/jr+i//sATsFPgmsDTASchYhGvUcux5bH9ceUB0AGzoYXxXbEhURbhAvEYkTjhcrHS4kQywANec9ckYfTnVUElmtWx9cZFqaVvxQ4EmvQdg4zi/6JrUeRRfWEHoLKwfQAzsBOf+O/Qb8cfqu+Kn2YfTh8T7vmOwP6sPnyuUz5P7iHuJ44ezgUOB730veptyD2ufX7tTD0aLO0cucyUrIGcg5yb/Lp8/R1ADb3eH/6PHvOPZh+wr/5QDHAKn+o/r29APuQeY73oLWos8aylLGlMQJxbLHb8z/0gnbH+TL7Zb3EAHdCbARVhi3Hc4hriR3JlInayfqJvAljyTPIqggBx7TGvAWQxK+DFsGK/9N9/bubuYG3hzWDM8tycvEHcJDwUPCCMVhyQnPqtXm3FrkquuH8rX4DP59AhMG6QgsCxQN2Q6yEMoSOxUOGDQbjh7pIQclpieCKWQqISqkKPAlIyJvHR8YixISDRUI6QPXAA3/n/6C/44BhQQNCMILOQ8OEuUTeRShE04RlA2kCMcCXvzR9Y3v+ulz5TvifeBI4I7hJuTR50DsHfEQ9sf6/v6AAjMFCwcVCG4IPQi0BwMHVgbPBYQFewWtBQUGZgatBrgGawa1BZMEEgNMAXD/r/1G/HH7Yfs//B3+9wC2BCQJ+w3iEnYXVRshHo0fYh+GHf4Z8hSnDn4H7f9z+JTxyet85/zkeeQA5nnpq+5B9c/83QTwDJMUYBsGIVElLCifKc0p8ChVJ00lLCM8Ibwf1B6YHgMf+x9VIdYiQCRRJdAljyVvJGQicx+0G0sXaBI9DfoHygLO/Rf5qfR68Hfsgeh75Eng2Nsg1yzSFs0LyEXDCb+hu1W5Yrj0uCS77b4wxLDKFtL72ebhXenr7yj1xviR+nv6mPgg9Wrw6Ooa5YnfuNoe1x3V99TO1p7aQ+B3597vCfmAAtALjRRbHPgiOCgOLIUuuy/jLzcv9S1XLJAqwigEJ1kltyMKIjYgHB6lG8EYbBWyEbENlAmQBeMBzP6D/Db7Afvs++j9ywBcBEwIQQzeD8gSsBRXFZYUYBLFDu8JHgSl/eD2MfDx6XDk6d+C3EXaJ9kD2aXZy9oz3Jrdyd6a3/vf8N+U3xTfrd6l3kDfvuBP4w7n/usI8vb4fgBDCNsP1xbOHGghXiSHJdgkZSJiHh4Z+hJkDM4Fpf9G+vv19vJJ8evwu/F98+r1sfh++wj+DgBoAf4BzgHuAIT/v/3c+xL6mPiW9yr3Xvct+IT5RPtF/V7/aQFLA/EEVwaJB6AIvgkMC7MM1g6LEdoUtBj2HGchuSWWKZssay6uLiItnCkQJJMcYBPPCFj9hPHp5SHbutExyubEGMLewSnExMhYz3bXnOBC6uLzA/0/BUwM+xE9Fh8ZyBpvG1gbyxoLGlEZyBiGGI8Y1Rg4GZEZsRlsGZoYIxf6FCYSvg7oCtcGwgLm/nX7nPh59hr1evSD9BT1/vUS9yD4/viT+dP5xfmC+Tf5Gfln+WH6Pvwp/zkDbgisDrsVTx0DJWosETOJOHA8fT6BPm88XTiGMkAr/CI6GoIRVwkxAnH8WfgM9on1rfY3+c38AwFqBZAJEQ2ZD+sQ6BCKD+UMJgmIBFP/z/lC9Ofu7ulw5XrhBN772kHYttU807vQJc59y9PIRsYBxDXCF8HWwJnBdsNzxnzKbc8K1QvbGuHg5gnsTfB08131A/Z49enzmvHc7grsgOmS54Xmiea15wPqVe108RX24vqC/50D7AY1CVoKVAo4CTMHhQR9AW/+q/t6+RL4lfcJ+F75avvw/aIAMwNSBbkGMwejBgMFagIL/yj7Gfc88/Hvju1a7IbsKe498Z71EftEAdoHbQ6aFAkabx6ZIW4j7CMpI1Mhox5hG9IXPBTZENcNUwtZCeUH5wZDBt4FmgVgBSYF6wS8BLME8wSlBfAG9gjNC3kP7BMBGX4eFSRrKR4uzDEdNMk0oDORMK0rJSVOHZUUfQuWAnD6kfNs7lvrk+ok7PTvx/U+/d8FJA98GF4hSinZL8A01TcMOXs4VDbcMmkuVSn4I6Melhn/FPkQiQ2kCjEIDwYYBCsCLwAU/tb7gPkp9+/09fJb8T/wr++x7zXwH/FB8mPzRvSr9Ff0GvPZ8IvtPukb5F3eUthT0r3M6McixKbBlsD5wLvCq8WDyerNf9Lh1rbat92z35bgaeBX36PdqNvP2YXYNdg62dvbQ+B65mru1/dsAr0NThmeJDAvlDhsQHZGjEqlTNZMTEtGSBBE+D5NOVIzPy04J1IhkRvpFUcQkgq1BJ/+S/jC8RzrgeQk3j/YEdPSzrbL3clYySDKG8wXz9XSB9dc24PfN+M+5nbo0ulg6kLqsOnw6E3oFeiM6ObpQ+yp7wT0JfnI/pQEKwoqDzUT/xVRFw0XNhXqEWMN8gf4AeH7Evbs8L/swukU6Lbnj+hv6hLtK/Bq84L2NPlS+8X8jv3F/ZT9Of32/BH9yf1Q/8MBLQV5CX8O/xOpGSQfEiQdKPkqcSxjLMoqvCdmIwwe/ReVES4LHQWs/xH7cffd9E/zs/Lp8snzKfXk9t34A/tR/dD/kQKwBUYJaw0rEocXbB20IyUqdTBNNk87ID9rQfBBg0AYPcQ3vTBYKAUfSRWzC9QCMvs/9VPxoe838Pvyrffq/TgFDQ3YFAwcKiLMJqcpkyqMKasmKSJXHJIVPw7EBn3/s/ih8mntG+mv5Q/jHOGv36He0t0q3Z3cJ9zU27Xb3ttn3F7dyt6n4ODiU+XQ5yDqBOw/7Z7t9+w261vogeTX36XaQ9US0HnL18d/xa3EhsUOyCrMotEj2Effneax7RX0bPlx/f3/BQGlABX/pPy3+bv2H/RI8onxH/Io9KP3c/xbAg0JKRBLFw4eGSQlKQItli/mMAwxNzCnLqIscCpRKHwmFiUuJMMjwCMAJFYkjSR1JOUjvyL3IJIephtZGNwUZxExDm4LRAnJBwQH5AZHB/wHxwhlCZcJJQnnB8YFxAL5/pH6zvX98HLsgOhv5Xnjv+JM4wvl0OdW60TvOvPS9q/5gfsO/Df7+fhx9djwfeu/5QjgvtpA1t3SydAh0OHQ7NIK1vHZSt674u7ml+p+7YLvm/Da8GXwdu9R7kDtiexp7ArthO7Z8PHzofeu+9T/xgNBBwkK8gvlDOEM/AtiCk0IBAbRA/4BxwBeAOAAUwKqBMAHZQtYD1gTIRd7GjUdMx9qIOAgrCDyH90emB1MHBYbBhoaGT0YTBcVFl4U7BGLDhMKcASo/dv1Ru1E5ELbwdJGy1XFZcHXv+/AysRfy33Uzd/T7AD7sAk9GAcmfTIlPalF00uUTwBRTFDETcdJvkQQPx85PzOuLZkoFCQhILIcrBnvFloU0BE+D5sM6gk6B6EEOgIiAHP+OP15/Cr8NPxy/Lb8zfyB/Kj7HvrT98v0IfEE7bfojuTj4BLebtw+3LDd1uCl5e7rZ/Op+zsEmwxCFLQahx9sIjMj0SFiHiIZaxKwCnACL/pr8pHr/OXl4Wvfit4g3/bgvuMi58vqZO6p8WT0d/bZ95f4zviq+Fz4F/gE+EX46vjx+Ub7xvxA/n//RwBmALb/Gf6L+xv47fM07zLqM+WA4GHcDtmz1mXVI9XZ1V7XfNn224zeAeEn497kG+bo5mPnvOcv6ADpb+q37ALwZPTa+UYAdAcVD80WMx7iJHYqoS4mMegx5TA+Li0qBSUsHw0ZFxOsDR8JrAVxA3ACiwKOAy8FFgfnCEsK9QqqCkkJyAY6A8j+r/k79L3uhune5P/gDt4b3B/b/9qO25Lczd0C3/3fleC14FrgmN+T3n/dl9wc3EncUN1U32XifOaB60TxivcM/oAEoQoxEAQV/RgWHFse7R/3ILEhTyIHI/4jTSX6JvUoGis2LQovUzDPMEYwki6jK4MnWSJmHAIWmA+aCX4ErgCE/j/+/v+8A1UJexDJGL8h0yp4Myc7aUHiRVRIpkjgRi5D2D08N8gv8CcjIMcYLRKTDBoIzgSfAmwBBwE4AcQBdwIkA6gD8QP3A74DUgPEAiMCeQHJAAwAL/8V/pn8lPrh92D0/++96qzk9t3Z1qTPtsh0wkS9grl6t2C3SrkuveHCFcpj0k/bUuTh7Hv0sPor/7cBRQLsAOT9hvlB9JXuBOkM5B3gjd2X3FXdwN+y4+joD+/F9aX8TANnCbIOABM5Fl4YgxnKGWIZehhAF9sVZBTnEl8RvA/hDa4LAQm9BdABN/3/90nySexA5njgQtvq1rXT1dFs0X/S/dS92H7d7+K46Hru3/Oa+HL8RP8EAcEBngHRAJv/QP4C/Rr8r/vW+4v8tP0k/50A2wGUAogCgQFj/yP82Pey8vvsD+db4U3cUtjI1fvUGdY02Tne+eQn7WH2MgAnCsoTsRyIJBIrLDDSMxk2LTdMN702yDWwNK4z6TJzMkoyWjJ9MoIyNDJdMdIvdC01KhsmQCHSGwsWMBCLCl8F6ABW/b/6K/mM+L74kvnO+jT8iP2Z/kT/dv8x/4n+pP2y/Oz7ivu8+6j8Xv7bAAYErQeNC1UPrhJBFcEW8havFfASyQ5sCSgDYfyE9QjvX+nu5AHizOBf4avjfueL7G7ytPjm/pIEVAneDPsOlw+9DpcMZgmABUUBGf1Y+VP2RfRU84rz2vQd9x36lf07AcgE+AeWCnoMkQ3VDVINHwxZCiEIlQXNAtn/u/xu+eL1BPLA7Qbp0OMj3hrY39Guy9XFq8CNvNe52LjQuea8IsJryYrSJN3F6Ob09QBfDJsWMh/MJTAqTSw7LDQqlCbRIW8c9xbvEc0N7gqUCdwJwwslD8ATPhk6H0klBSsRMCQ0CjekOPE4/zfzNfoySS8VK4wm0iEBHSIYMhMlDuoIawOa/W737/Ax6lvjodxD1orQwcssyAXGdcWPxkzJi80U05bZs+AE6B/vovU5+6T/vAJ3BOUEMASUAl4A4f1r+0b5qPe29nn25vbZ9xz5bPqC+xr8+fv1+vr4D/ZR8vjtTumt5HHg99yP2njZ2dm72w3fnuMl6UbvmfW1+zIBvAUPCQMLjAu7Cr4I1wVbAqX+Efv195j1LPTN8330Kfao+MH7Mv+4AhUGFAmPC3MNvw6HD+kPExA1EH4QFhEbEpkTjRXfF2oa/RxfH1YhriI+I+wisyGgH9gcjRkBFnoSQA+RDKEKjQlcCf0JRgv6DMsOYhBqEZMRnhBiDtQKAgYeAHH5W/JN673kH9/X2jrYfNez2NLbrOD05kbuL/Yz/tkFtwxyEs0WpBn3GuAalBlaF4gUdhF7DuEL4QmgCCsIewhxCeIKlgxTDt8PChGyEcIROBEjEJ4O0AzkCgUJWQf7BfwEWgQGBOcD1gOsA0ADcQIoAWH/Jv2W+t/3P/X68lfxlfDp8HLyN/Ul+Qv+nAN4CS0PQxRBGL0aYBvyGVsWqxAYCfz/z/Uf64jgqNYTzkvHt8KbwBPBFsR2yePQ9Nku5BDvGPrNBMoOvRdvH8ElrSo+LpMw0DEeMqQxgTDKLosswiloJm8iyR1tGFsSoAtWBKz82PQj7dnlSd++2XXVntJP0YfRLNML1tvZRt7s4mznbeuk7tvw9vH18fHwHe/C7DLqx+fW5azkgORz5Y3nt+rC7mvzXfg7/aoBWAUACHYJpAmUCGYGUwOl/677xfc79FHxOO8H7rvtOu5S78HwOfJr8wz04fO+8pPwZ+1e6bHksN+02h3WSNKFzxTOHs6xz8DSI9ee3OPimulp8Pz2Cf1XAsMGPwrTDJgOtw9hEMoQIhGSETQSExMtFGwVtBbeF8QYQRk8GakYjRcAFioURBKPEFEPzQ4+D80QjxN/F4AcWSK9KE8vpzVfOxhAgUNmRapFVESJQY09uziCM1YurinzJX4jiiI0I3glLCkMLrgzwTmsPwJFVklMTKNNNU38ShBHoUH2OmQzRyv2IsQa8BKqCwwFG//I+fb0f/A47PvnpuMl33LamNWw0N3LTccww7K/+LwauyO6CLqyuvi7qL2Jv2TBB8NKxBrFdMVpxR/FzMSxxBHFMMZFyHfL2M9e1ePbKePZ6o3y1vlCAG4FBAnJCqUKoAjmBMf/rPkU84zsn+bQ4ZHeNt303dfgy+WV7Nz0Mf4UCAMSfhsSJGErJTE0NYM3HzgsN980dzE4LWIoLyPNHVsY7BKIDSsI0QJx/Qr4ofJI7R3oR+P53mrb0dhg1z3Xf9gl2xzfNOQq6qnwT/ez/XEDLgigC5cN/Q3aDFUKsAZAAmv9mfgy9JLwAe6v7K7s9e1a8KDzdvd++1z/uAJKBd8GWwe/BiYFwwLd/8L8yflC93H1i/Sp9M/15fe++hn+qwElBTkIpgo5DNgMgQxJC1wJ+QZsBAICCwDK/nH+HP/SAIAD+gYCC0wPhhNcF4UaxBzxHfkd4xzLGuIXZxSiEN4MXwlfBgoEeQKvAZ8BKgInA2UEtgXtBuwHnwgHCTAJNwlECYMJHwo+C/UMTA8xEoEV/xhhHE0fZSFRIsEheR9aG2MVsw2NBFT6gO+e5ELa/tBXyb3DgcDRv7bBEMadzPzUt95K6Sz03P7nCPERuBkXIAYlmSj5Kl0sBy03LSotDi0DLRYtQi1yLYUtUS2sLG0rdym6JjMj8R4TGsUUOQ+mCUEEN/+m+qL2KvMt8IztHuuy6BvmL+PU3/7bttcb01/OxcmaxTLC3L/fvm2/osF+xePKlNE/2Xfhyem78dn4vv4dA8gFsAbqBawDSwAv/M/3pvMq8MDtt+w/7WfvHvMw+FD+HAUnDP4SNxl0Hmsi7iTpJWUlgSN2IIccAhg0E2YO1AmtBQwC/v56/HL6zPhs9zf2HPUQ9BjzQfKn8WrxrvGW8jr0qfbh+cn9OQL2BrULIBDiE6cWJxgwGKQWhBPtDhkJXAIe+9Dz6ezb5gbiuN4h3VLdOd+n4lPn3uzc8uH4hP5pA08HCQqLC+ILOAvNCewH6QUXBL4CFgJBAksDJAWnB5sKuw27EFETOxVHFlYWYhV5E8IQdA3RCSUGtQLC/3v9/PtM+1r7AfwJ/TD+Lv+8/53/o/61/M75BfaD8YjsXedW4sXd9tkl13/VGtX11fnX/drJ3h7juude7NjwA/XK+Cv8NP/+Aa4EagdSCn8N+hC6FKIYhBwfICkjUiVMJtclwSP1H3gachMnC/sBaPj07i/mpN7P2BbVvtPo1JDYht595gTwmPqmBaAQ+Bo1JPgr/DEfNmE43jjLN3E1JTI9Lg0q3CXkIUweJxt2GC0WNBRtErwQCA9CDWcLfgmdB+AFawRhA+ICAgPMAzYFKgd/Cf0LZw53EO8RlRJDEuQQeg4hCwsHfwLS/V/5gvWO8sbwVfBM8ZrzFvd2+10AYQUQCvsNwhAaEtMR3w9QDFsHUgGe+rPzDu0m52TiGt993aTdgd/q4pbnKe0681v5If8uBDsIEgudDN0M6wv1CTcH8gNpANz8efll9rHzX/Fi76Dt/OtV6o7ol+Zn5Afij98h3ezaI9n315bXH9ij2R/ce9+L4xPoy+xi8Yz1APmH+//8Wv2o/BH70/g+9qvzd/H473bvI/AX8kr1mfnB/mkEKAqMDyIUgxdaGWwZnBfxE44OuAfN/zj3cO7r5RXeS9fS0dLNW8teyrbKLMx+zmPRmdTj1xnbIN7z4KHjReYJ6Rnsoe/E85f4IP5OBP0K9xH1GKkfwSXxKvUunTHQMooy4zALLkMq3CUwIZYcYRjUFCISZhClD84PuhA3EgoU9BW9FzYZQRrRGusapxosGqgZTxlSGdYZ9RqzHAIfuyGqJIgnCSreK8AseCziKvUnxCOCHngYCBKjC74FzAA0/UX7NPsT/c8ANQbuDIkUhhxZJHgrZTG3NR04bDiWNrQy+yy8JVodQhTmCq8B+vgR8SjqXuS53y3cn9nr1+fWbNZX1o/WCNe717DY8NmJ24Td5d+l4q/l4ugP7P7ub/Ek8+TzgfPg8fzu6erT5QHgzNmd0+TNDcl9xYXDXcMexcDIG87l1L3cMeXD7fr1Y/2hA3MItgtqDbENygwOC+cIxgYZBUIEkgQ9BlgJ2Q2YE1AaqCE5KZgwXDcoPbFBwkRBRixGmESwQao9xjhDM10tRSceIfwa4hTKDp8ITAK6+9f0ne0T5lDeetbHznTHxcD/uly2DbMwsc2w1bEktIK3pbs8wPTEfMmTzQbRvNOy1f/W0ddl2AfZA9ql2yneuuFp5izs3vI++vQBnQnLEBQXFhyFHy0h+iD5HlUbWhZpEPMJcgNc/Rz4C/Rq8Vrw3/Dh8iv2ePpy/78EDAoJD3wTPBc2Gm0c+B37HqUfJiCrIFghQiJuI88kRyaqJ8YoYilMKVoocSaJI7EfDBvRFUkQxAqZBRoBj/0t+xj6WPrc+3/+AwIgBoIK1w7REjAWxhh6GkkbRxuXGmwZABiLFkEVRxS0E4gTsBMFFFEUVhTRE4QSQBDlDG0I7AKU/Kr1j+6u53nhYNzH2PvWMNd32cHd2ONp6wj0Nf1nBhgPzBYaHbQhayQyJR4kYiFHHS0YeBKQDNYGnAEi/Y357/ZC9Wz0RfSc9Dv18/WY9g33QPcu9+H2aPbd9VX15PSW9Gv0VvRA9Ab0f/OA8uLwiO5j63bn3OLE3XHYONN5zpfK8MfXxojHJsqyzg3V9NwG5szvvPlEA9kL+hJBGGMbPBzPGkUX6xEsC4cDifu886Xst+ZI4pTfst6a3yfiGeYf697w+/Ye/f0CYQgmDT0RqxSGF+4ZChz/He4f7SEDJCsmTyhOKgEsOy3ULaktpyzHKhkouiTaILUcjRimFD8Riw6rDK8LjAskDEUNqw4MEBoRixEjEbcPNQ2jCSIF6v9F+oz0He9Q6nfmzeN24nvix+Mr5l7pBu3C8Cv05/an+DX5ePhx9kTzK+946ozlzeCf3FrZRdeL1j7XUdma3NngvOXk6vHvifRe+DX76/x2/eb8XvsX+VH2VfNn8MPtmOsD6g3prejL6EDp4emA6vfqJ+sD643q2ekN6Vvo/ucw6CvpGusc7jjyX/dr/SEENwtUEhwZNR9TJDUotCrBK2cryCkeJ7Ajzx/NG/YXiRSxEYUPAw4WDZIMPwzgCzcLDgo/CLkFgwK+/qH6evam8obvfe3h7Pbt5/DB9W38tQRIDrcYhiMvLi04BkFUSMtNPVGdUv9RlU+nS5FGtkB5OjY0Pi7KKP4j6B+AHKkZOhcCFc4ScRDEDbIKMAdHAw3/n/ol9sfxqe3n6ZLmreMu4f7e/twH2/jYsdYg1ELRKM70ytvHIsUXwwvCSsIUxJbH4szr04XcY+Yd8TT8GQc8ERIaHCH4JWQoRSioJcIg7BmgEWwI6P6u9U7tReb04JrdUtwV3bjf9uN06cvvj/ZY/coDnAmXDpwSnxWpF9IYOhkDGVEYPhfcFTMUPRLuDzMN9gknBr0BvPw090rxMeso5Xrfddpk1ovTHNI20t/TBdd52/jgLOey7SX0I/pW/3sDZwYMCHUIyQdGBjkE+gHf/zb+P/0k/ff9q/8aAgoFKwgmC6ANRA/PDxAP8wx+CdYEO//++IPyMexv5pfh8N2s293aettf3U/g+uMH6Bns2e/98k31qfYI9332LPVP8yfx/O4R7aLr2OrO6ofr8+zz7lbx5/Nt9rX4lvr2+8v8Iv0W/dT8kPyG/O/8/P3P/3kC+QU3CgUPKBRbGVMexyJ6Jjwp9CqeK04rMCp/KIUmkiTyIukhqSFQIuMjSiZYKcgsRzB7Mwo2ojcCOAE3kTTAMLsrxyU9H4UYCBItDEwHqQNuAacAQAEMA8EFCAl+DL4PbRI9FPgUghTbEh0QfwxHCMoDZP9p+yb42PWl9Jr0rPW795P68P2LARsFXAgXCyMNag7oDqcOww1dDJsKogiRBnsEaQJVAC7+1/sz+SH2iPJZ7pXpT+Su3uvYUNMwzuTJwcYQxQrFzMZYypDPNtbx3VDm0+719jb+HwRYCKIK5QosCasFtgC/+kj04O0S6F7jMODW3nvfJeK25vDsd/Tb/KEFTQ5nFocdWCOhJz8qLCt4KkYoyCQ1IMcatRQtDlMHQgAL+bXxSOrI4kLbyNN4zHzFCb9eub60bLGlr5mvabEbtZ66xMFIysrT3d0I6M/xwPpzAp0ICw2pD4YQzQ/GDcwKRgeeAzkAb/2A+5b6u/rf+9j9ZwBBAxMGjghtCn4LpgvjCk8JGgeLBPUBs/8Z/nb9Bf7q/y4DwQd1DQUUHxtiIm4p6S+DNQM6RT0/P/4/pz9uPpU8YDoQON418zNlMjgxWTCmL+8u/C2ULIUqqCfkIzgfshl5E8IM0AXs/l74afJC7Q/p4OWw42bi2eHS4RPiYeKF4lfiwOG84F7fyt043OfaG9oU2gnbHd1g4MbkKepL8Nr2dP2xAy0JjA2FEOgRpBHHD38MFQjqAm79FvhV85LvHe0v7N/sJu/e8sX3hP24A/kJ4w8eFWUZixx9HkMf/B7cHSQcHBoLGDAWvRTQE3UToRM4FAsV5hWMFscWZRZEFVMTkhAUDf4IfwTQ/yn7wPbD8k/vc+wu6mzoDefq5dbkp+M+4obgfN4y3MvZe9eB1SbUr9Na1FXWutmH3p/kxuuo89z76QNWC6oRexZ5GW4aTBkmFjgR3QqLA877NfRS7afnouOT4afh5eMw6Efuz/VV/l4HahABGbkgPSdQLNIvvTEhMiQx+C7ZKwIoqyMDHzAaShVdEG8LfgaIAY38k/er8vDtieml5XniOuAb30PfyOCu4+LnN+1r8yj6BgGdB34NSBKmFWAXVxeNFSUSYA2XBzcBufqR9C7v7uoV6MjmDufL6Mbrre8e9K748vyHACADhASXBFgD5gB1/Ur5u/Qc8MDr7efX5JviQeG34NrgdOFJ4hnjq+PP42jjbeLq4ADf49zU2hvZ/tfA15LYl9rX3Ubiv+cL7uH08/vsAoAJbQ+BFJ8YwRv1HV0fKyCXIN8gOiHXIdUiQCQQJi0oayqULGwuuS9GMO0vmS5LLBkpLSXEICYcnxd6E/oPUA2ZC9gK+grPCxcNgQ61D14QLRDoDmwMsQjOA/n9gffK8EfqbeSu32vc8Npt2+7dX+KL6B7wsPjHAeYKlBNiG/YhDieHKlgslSxqKxQp3CUNIu8dwRm0FecRZg4tCyoIQQVTAkH/8/tc+H30aPA87CXoWeQO4Xrey9wh3IrcAd5t4KPjZ+d164PvS/OR9ib58frt+y782/st+2j60/m1+Ub6r/sA/jEBHwWMCSkOlBJpFkUZ0RrKGgoZiRVkENkJRQIe+ujxMuqF413eH9sT2lzb+N7A5GzslfXD/3AKFhU3H2EoOzCENhk78D0ZP7o+BD0zOoM2LTJhLUMo7SJpHbsX3xHOC4UFCf9j+K3xCuup5L7egdko1d/Rxs/pzkLPstAF0/TVK9lN3ADf7+DX4Ynh898h3TvZiNRizzfKesWdwQW/Br7WvozBHcZazPfTjtyl5b3uV/f+/lEFCwoEDTMOsQ2yC4MIfQQCAHP7Jfdf81XwH+7C7CrsNOyw7GjtKO7F7h7vJ+/i7mbu2O1q7VDtwu3t7vPw5vO/92f8rgFWBxUNmRKSF7kb1h7DIHMh8SBhH/ocAxrNFq0T8RDbDp4NVg0JDqUPBxL4FDoYixusHmohniM2JTQmrSbIJrYmsibyJqkn+CjxKo0trzAkNKc35DqGPTY/qj+qPhc87jdMMm0rpyNkGx0TUQt2BPf+Jfs2+T35K/vP/tgD4QlzEBEXQh2YIrgmYSlxKt8pwidKJLUfUxp0FGcOcQjKApj96/jE9Bbxxe2y6rvnxeS+4Z3ea9s92DTVd9Iz0JDOsc2rzYPOLdCJ0mjVjNiy25Le6+CI4kXjE+P84STgwt0i25rYhtY91QnVI9ao2Jnc2eEt6ELvsfYI/tMEqQovDyESXRPgEsgQVA3cCM0Dnf7B+ab1qfIL8fDwXPIy9Tb5F/5wA9gI4Q0qEmIVSxfGF8sWbxTcEFAMFAd0Ab/7NvYR8Xrshug+5ZniieD13sjd7txe3BbcIdyT3IrdJt+H4cbk8egG7vHzifqRAb0ItQ8ZFowbuh9fIk8jeiLuH9gbgRZLEKgJEwMF/er3H/Tk8VvxgfIy9S35Ff58A+4I9Q0mEiwVyhbiFnUVpxK1DvQJxQSS/8D6qvaZ877xL/Hq8dLztPZS+mH+lgKvBnIKtQ1hEHMS9xMIFcgVYBbxFpkXZRhUGVcaShsCHEgc4xueGlAY3hRCEI4K6QOU/N/0Ke3X5Uzf4tnj1YLT2tLn043Wltq4353l6etA8lL43f2yAroG8wlwDFMOyg8GETgShBMBFbUWjxhvGiEcZh39HaMdIxxXGTEVvQ8lCa8Buvm38SHqeeM23r/aY9lR2pfdG+Ok6tbzQP5fCaoUmh+1KZQy6zmKP2JDf0UJRjpFW0O4QJ49UToEN9wz6zAuLpQrASlRJmAjDiBDHPUXKRPvDWgIugIT/Z/3hPLg7cDpI+b34hvgYd2W2oTX/tPgzxnLq8W0v2W5BrPxrIenLqNEoBmf55/KosCnpK4ytwfBrcug1ljhVOsj9Gr77wCbBHsGuwaoBaMDHgGN/l789Pqa+oD7t/0yAcgFNwsqEUUXKR19IvgmYyqdLJ8teS1OLFAqvifWJNYh8B5MHAAaExh7FiMV7BO2EmAR0g/+DeQLkgklB8IEmgLbALP/Q/+g/8wAtQI2BRYIDQvPDQoQdBHQEfUQ0g5xC/oGrAHf+/b1XvCD68PnauWr5JnlJegf7DvxFPcz/R0DWgh8DCoPKhBgD9MMqggsA7X8svWW7tPnzuHc3DnZA9dB1trWothb27veeOJJ5vHpQ+0h8ILybfT69Uj3fPi6+R37t/yL/osAnwKbBFEGjAcbCNgHqQaIBIQBwv16+ff0jfCW7GnpUueN5j7ncekT7fvx5Pd7/l0FKAx9EgkYihzXH+EhsiJrIkMheh9bHSwbLBmLF2YWwhWQFa4V6BUBFroV2RQwE6MQLg3lCPYDpf5I+T707e+y7N3qpuot7G/vS/SA+rMBdglNEbsYSB+NJDkoFyoUKjsotyTNH9YZNRNVDJsFYf/u+Xj1GvLb763ucu7/7ifwvPGU85H1oPe7+ef7M/6wAHQDiwb9CcENxBHfFeMZlB2zIP4iQCRNJA0jgSDAHP0XfhKfDMUGWAG+/Ev5Q/fJ9uX3fPpT/hEDTgiODVUSLRavGI4ZnBjPFT8RKgvqA/H7vvPW67jk1d6F2gTYbNe22L3bPeDe5Tvs6vKE+av/EwWFCeIMHQ9CEGsQvg9kDooMUwraBzAFVgJG/+37NvgO9GXvNOqG5HHeHtjD0aPLCMY6wX69DrsRupe6mrz6v4LE58nSz+fVytsp4cLlaekM7LTtg+6z7o7uZu6R7lvvAfGq82T3G/ygAa0H4w3WExcZOx3lH84gzB/XHAYYlBHZCUIBTPh370PnH+Bq2mTWMtTa00TVPtiG3Mnhs+fw7Tf0TPoFAE4FIAqHDpoSdhY2GvIduCGJJVcpBi1tMFwzoDUHN2o3rTbJNMkxzy0RKdQjaR4oGWMUZhBpDZML7gptC+gMIg/NEZEUFRcFGRwaJxoNGc8WiBNtD8QK4QUeAdL8R/m49kj1A/XZ9aP3JfoW/SYACQN4BUAHQAhyCOgHzAZbBeEDrgISAlECoQMcBsQJfg4UFDgaiSCgJg8sczB4M900gTRdMoouPynHIoAb0hMlDNwESv6u+DP06fDH7rHteO3k7bfute+p8Gzx4/EF8tbxaPHU8DjwsO9R7yjvM+9j75zvue+O7+7usu296wPpjeV34fXcT9ja0/bPBM1dy0rL/8yS0PvVDN175d/uvfiIArcLxBM9GsgeLyFfIW0fkxsrFqsPlgh3Adj6LvXf8DDuRe0i7qjwm/So+W//hQWFCw8R1RWdGUEctR3+HTQdfBsBGe4VaxKXDocKRgbUASj9Nvjy8lXtYucp4cbaZ9RGzqTIzMMFwI69mrxIvZ+/j8PqyGzPvdZ43jLmgO0E9HL5k/1OAKwBzgHwAGX/if3A+2b6zvky+rb7Xf4PApcGqgvrEPYVaRrpHTAgDiFxIGQeEhu+FsERfwxhB80CG/+N/FD7cfvk/H//AgMhB4ELyg+oE9UWHhlkGqIa5RlPGBAWYBN5EJEN1AphCEgGiAQRA8gBjQA8/7X95PvC+Vf3v/Qj8rzvzO2U7FbsRe2F7yXzGvhA/lgFFA0RFeYcKyR9KosvGTMHNU81DDRwMcMtXimeJOEfeRupF54UaxIJEVoQKRAzEDEQ2Q/rDjgNpgo0B/kCKv4J+e7zNe8761PowOau5izoL+uO7wX1PvvUAWAIfA7NEwwYCBusHP0cGhw3GpgXiRRYEUsOnQt3CeoH9QaABmEGYgZGBtEFzAQLA3QAAP25+L/zPu5u6I3i1dx9167Sg84GyzHI78UhxKHCSsH7v6G+Nr3Hu3O6abnnuDG5jbo5vWjBNMegzo3Xw+Hn7Ir4JwQ1DycZfCHHJ7krJy0MLIwo9CKwG0cTUgpvATn5OvLk7IzpY+hz6aTsvPFp+EMA3gjIEZYa7iKGKioxvjY4O6Q+F0GxQpND3EOkQ/pC40FcQFg+yDufONI0YTBYK9El9R/4GRsUnw7JCdQF7gIzAagAOAG3AuEEXwfQCcwL8wzsDHYLagi+A4r9AvZ57VjkFNsn0gnKIMPAvR+6U7hSuPG567zmwHrFPsrLzsvS/NU12GvZrtko2RnYzdaY1cvUrdR01ULXHdr13aDi4+dz7QDzOvja/KQAdQM6BfsF0wXwBIwD6QFJAOb+7/2E/bL9c/6w/0IB/QKwBCoGSAfuBxYIygclB1MGigUFBQAFrQUzB6MJ/AwkEeoVDBs5IBolVSmcLK4uYS+hLnosEimlJIYfExquFLcPggtOCEMGbgW+BQkHDwl9C/sNMBDLEY4STRL7EKMObQuaB3oDav/H++n4GveP9mP3lvkK/YkByAZvDBsScBcXHMwfYCK9I+Yj9SIbIZYerhurGM4VUBNUEe0PFw+7DrIOyA7FDnAOmQ0ZDN4J5wZEAxz/n/oK9pvxke0f6m3nkOWK5EzktOSU5bbm5Ofs6KXp+unm6Xjp1Ogu6MPn2eev6H3qae2B8bv27vzXAx4LVhIMGcgeICO4JVEmzCQuIaEbcxQODPcCvPnx8CLpyuJK3uLbrduh3ZDhLOcM7rr1tP17BZ0MtRJ2F68aSBxDHLcazhe+E8EOEwnpAnP81PUn733o5OFk2wrV5c4PyavD5b7yug64dLZbtu+3Tbt+wG7H8s/E2Yfkyu8R+9wFsQ8jGNoemyNLJvQmvyX1IvgeORoxFVgQFgzECJsGtwUTBooH2wmyDKsPYBJuFIIVXBXbE/UQwwx4B1wByfog9MLtCeg+45jfMt0Q3B7cMt0T33/hMeTq5nXpret87eXu9+/S8KLxk/LT84X1wfeN+t79lQGGBXQJHw1FEKgSGhR8FMMT/BFKD+QLDggXBFEACf1++t/4SPi7+CP6Vvwa/ykCOwUMCGAKDgwCDT4N3gwPDBILMQq3Ce4JDQs+DY4Q8hRAGjgghSbDLIkycDceO0s9yj2NPKI5OjWdLywpUyKDGykVpw9HCz4IoQZpBnIHgwlQDIQPyRLNFU4YGRoUGzwbohptGdAXCBZQFOES5xF+Ea4RbBKbEw4VjBbaF7sY/Bh1GBAXyxS1EfENsAkqBZ8ASPxW+O70IfLu70Lu9uza67PqSulp5+rktuHO3UfZTNQezwjKX8V3wZu+Cb3lvDy+/sD8xPDJfs8/1cbarN+W40HmhOdZ59nlPuPe3yPcg9h51XjT4NL70/PW0Nt24qjqDfQz/p4IzBI/HIckRys8MEEzTTRwM9YwuCxfJxchLBrkEnkLGgTr/AD2Zu8m6UTjyd3D2EfUdNBuzWHLesrgyrTMBtDX1A/bf+Lg6tnz/vzcBf0N9BRhGv0dnh86H+sc7xieE2sN1QZkAJv66vWv8ijxcfGB8yz3KfwUAn0I6Q7lFAca/B2LIJshMSFuH5Ec5hjKFJkQrQxRCb8GGgVvBLEEwQVvB4EJuwvkDcsPTRFaEvASIBMHE8wSmRKWEuQSlhOvFCIWzxeIGRMbMRylHDYcvBofGF8Ukg/mCZwDB/2A9mLwBeuz5qHj8OGk4afiz+TZ53nrWu8p8572ffmi+/38mf2W/Sf9ivwE/Nj7QPxl/Vr/HAKOBX4JpA2vEUUVEhjNGT8aSxnuFkUTiQ4MCTEDaf0j+Mnzt/Av71nvO/G+9Kv5sv9vBnoNYBS5GisgbiRVJ8wo2CiXJzcl9iEVHtUZcBUVEeEM4ggWBWwBy/0R+iD24fFH7VLoFeOy3VrYR9O8zvnKN8ikxlzGZsexyRnNZNFK1nzbpuB95b/pQO3n77XxxfJD83DzlfMA9Pb0s/Zd+QH9kwHqBsUMzRKgGNYdCiLnJComryVvI4cfNBrNE8IMkAW5/rb49vPP8HnvDPB88p32KPy8Au4JShFeGMceMSRfKDArmyyvLJErdCmUJi8jgR+7GwQYchQPEdgNvwqyB50EcwEr/sf6WPf488vw/e246ybqZOmC6X/qROyn7mnxQPTV9tH45PnI+VD4ZfUR8Xvr6uS93WfWaM8+yWPEPMEUwBjBTsSVyanQJ9mT4mHsAfbn/pUGqgzcEAoTMRN0ERIOYwnLA7r9mvfM8aLsV+gR5dvirOFo4enhAeOB5EHmJOgZ6hzsO+6K8CfzMvbF+fb9yQI3CCQOZBS8GuogoyahK6MveTIHNEQ0QzMsMT8uxyocJ5cjiyA8Ht4cihw/HeQeQyEVJAYnuSnXKxAtJS3vK2AphSWEIJoaEhRDDYEGHQBa+mX1V/Eu7tLrGOrF6JfnS+am5H3iuN9Y3HjYTNQa0DzMEcn5xknGSMcjyunOjdXg3ZXnSfKH/dEIqxOgHUsmYC2uMiA2wTezNy82fDPsL80raycDI8UezRonF88TshC5DcgKyAeqBGgBD/6y+nn3j/Qo8nPwnO/A7+7wH/M39gj6UP7CAgsH2ArfDeMPvhBhENkOTQz8CDUFVgG+/cb6vPjX9zX41/mg/FUApQQwCYoNSREPFI8VlRUMFP8QnAwqBwkBq/qB9AHvkeqD5w3mSuYw6JrrRfDb9fX7KQIPCEsNjxGnFHQW8hY1FmEUrBFQDosKlQafAsv+K/vF95L0gPF67mnrPOjr5Hnh9t2C2kXXb9Q10sXQSNDY0HrSItWs2ODcd+Eb5nXqMO4A8azyFfM08iPwFe1b6VTlcOEe3sfbx9pe26/dvOFj52DuUfbB/isHCg/dFTYbvx5CIKwfDh2cGKYSlgvfAwD8bfST7cjnS+NA4K/ehd6c37zhpuQU6Mnrju8486/25fnd/KL/RALYBGoH/wmTDBIPXxFQE7YUXxUfFdMTZhHaDUUJ1QPQ/Yv3a/HZ6z/n++Nb4pPivuTW6LTuGfar/v8HpREoGx8kLywUM6Y42Dy3P2pBK0I+Qu5BfkEsQR9BbEETQvlC9EPKRDpFAEXkQ7dBYz7oOV80+y0FJ9Yf0BhXEskMcwiLBTEEYQT/BdAIgwy4EAMV/RhEHIkekB86H4IdgBpiFmkR5AsmBn8AOPuH9pLyau8K7VrrNepr6cnoHuhA5xTmi+So4n3gKN7P25zZt9dB1kvV3NTk1EfV2dVj1qnWc9aQ1d7TT9HszdnJUMWhwCm8ULh9tQ20TLRvtou6lMBbyJTR19uo5oHx2vs2BSsNZxO6FxYakRphGdcWWxNcD04LnQejBKUCzQEnAqADDgYxCbkMUxCrE3cWfBiRGaYZvxj1FnMUbhEhDskKmAe6BEoCVADW/r397/xN/Lj7FftU+nD5cvh095f2Cvb79Zj2Bfhb+p39ugGOBt0LWhGqFnAbTh/zIR0jpCJ8ILYchBcwER0KuwKA+930Nu/d6gboxOYK56voXOu+7mPy2vW2+Jv6Q/uF+lb40fQr8Lfq2uQF36rZNtUF0l3Qa9A90sPV1dow4YbofPC3+N8ArAjgD1MW7BumIIokqCcXKu8rQi0YLnEuQy54LfcrpClkJigi6xy8Fr4PJQg8AFv45PA+6srk3+C/3pTeaeAq5KTpiPBu+OEAZAl7EbYYuB47IxsmUCfzJjYlYyLQHtsa3hYrE/8PhQ3MC80KaQpwCqcKzAqkCv0Jswi7BiAEAwGc/S/6DveJ9O7yfPJd86X1Svko/gAEgwpNEfgXHR5fI3EnHypNK/sqRClaJoMiDx5SGZ0UNxBWDB4JmgbDBHsDmALlASgBLgDK/tr8Uvo195fznO9x60nnV+PH37rcQdpe2ADXB9ZI1ZHUrtN00sLQiM7Ny63IWcUXwjm/Gr0SvHG8d75JwvDHVs9D2GDiPu1e+DUDPA34Ff8cCCLpJJ8lTCQ0IbkcUheBEcwLrwaVAtX/oP4N/xEBhAQjCZwOjhSZGmIgmCX8KWUtvi8FMUsxrjBTL2It/ypHKE4lHCKsHvMa3RZZElUNzAfAAUn7h/Sw7QLnyOBL29XWpNPk0a/RBdPM1dHZyt5f5Cvqyu/d9BP5MfwX/sH+SP7i/Nv6jfha9qX0wfPz82L1HPgL/PsAoQaYDHAStxf+G+keLiClH0QdIhl5E5kM6wTk/Pj0me0r5/3hQ94V3G/bNNwv3hzhseSe6J3sb/Dn8+r2bvl5+yH9gv68/+4AMQKRAxAFnwYlCH8JhQoOC/gKKQqaCFMGcAMfAKD8Ovk99vTzo/J+8qDzDvax+VT+qwNcCfkOFxRLGD0bpRxbHFMapBaBETwLNwTl/Lr1JO+F6SrlROLo4AvhiOIk5ZHoe+yL8HT09ffk+iv9zf7k/5sALgHbAd8CcgS5BsgJmw0XEgwXNxxLIfQl4SnMLH8u2S7TLYArCyi2I9AetBm9FEEQhgzECRoIjwcUCIIJpQs7DgIRthMfFhEYdBk/Gn4aTRrRGTgZsBhgGGYY0RicGbQa8xspHRsekB5SHjUdIRsPGBMUVA8QCpEEMP9B+hb28fIC8Vvw8/Ch8iT1Ifgt+9f9sf9VAHj/4/yH+HXy5eou4sDYIc/exYS9lbZ8sY2u9a3Cr9qzBLrrwSTLOtWw3xHq8vP5/OQEiQvQELwUWxfLGC4ZpxhYF1oVvxKPD88LeweTAhr9Gfem8ObpCuNS3AjWfND+y9bIQ8dtx2fJJs2E0kLZBeFk6erxH/qRAeIHxwwSELURwxFtEP4N1gpdBwAEIAET/xL+PP6Q/+4BHQXKCJIMERDgEqkUKBUxFLoR1g20CJ8C9vsf9YjumOin4/vfvt0D3b/dzd/24vXmeus48Ob0Sfk2/ZMAWwOaBWcH5gg7CokL7Qx3DisQ+xHQE4YV8RbnF0AY3he1FsUUKBIFD5kLKQgEBXUCwwAkALsAkwKcBasJfw7DExUZER5UIosldCfoJ98mbiTHIDYcGhfdEewMrAh0BYMD/wLuAzgGqgn5DcoSvBdtHIUguyPfJdomriZ7JXQj3iAGHjwbyRjpFsYVcxXsFRUXvxisGpQcMh5BH44f8x5iHeEajReVEzUPsQpNBkkC2P4Y/Bf6zPga+NH3tPeB9/b21fXw8ynxee3u6Kvj5d3h1+jRR8xExxfD6r/Svc+8y7yhvSC/DsEzw1/FbMdFyevKccz+zcbPBtL91ObY7d0r5KHrM/Sp/bMH6xHaGwcl+CxCM5A3qDlzOQA3gDJILMYkfxz+E9MLgAR2/gf6avev9sX3efqA/nYD8QiADrgTPRjDGxYeHB/PHkIdmRoAF64S1w2tCFcD9P2W+EfzCe7Y6LTjoN6k2dfUWNBTzPvIh8YvxSTFicZyydrNpdOb2m7iuuoN8/D66wGTB48LoQ2rDbIL4Ad+AvT7u/Rb7V3mP+Bx20XY8NaB1+bZ6t0943vpNPD09lD97QKGB/AKIA0mDisObQ05DOEKswn2CN4IiwkJC0gNKBB0E+4WUxpiHeMfqyGiIsEiFiK/IOoeyRyTGnwYrBZCFUkUvxOOE5cTrxOqE14TqBJ1Eb8PmA0hC4wIGgYRBLcCTQIFA/0EPQiwDCgSXxj9HpklySskMU41/jcDOUs44zX1McMspyYEIEQZyhLsDOwH8wMOAS3/JP62/ZT9a/3o/MT7yPnW9ujyF+6T6KTiodzq1t7R180dy+PJRcpAzLnPe9RA2rXggOdK7sf0tvrt/1ME6Qe+CvIMrg4fEG0RuhIaFI8VDBdxGJMZPRo2GkgZSRcbFLUPIwqKAyT8OPQf7DTk1NxQ1uvQ1swmytvI3Mj8yfzLls6E0YDUVtfd2QXc0t1c387gXeJF5MHmAOol7jnzMPnj/xEHaA6GFQAcciF9JdwnYCj6Jr8j5R6/GL0RXQomA6H8RPd384XxlfGt87H3Y/1oBFgMuxQZHf4kCCzmMWM2YDnZOuM6oTlGNws0KjDYK0MniyLHHQAZORRvD5sKvgXaAAL8S/fa8t3uhesE6YjnM+cX6DLqa+2Q8Vr2bftjAM8ERQhnCucKlAldBlIBp/qv8tnpp+Cl12DPV8j6wpe/Xb5Wv2PCRcedzfnU1tyy5BDshfK893/7t/1t/sj9Bfx2+XP2V/N38Bnuceyf66nrhOwQ7iHwhPIG9Xj3tPmk+0H9kP6o/6YAsAHnAmsETwaXCDoLGw4PEeETUxYoGCYZIhkAGLoVYBIZDiQJzANr/lv59PSD8UHvUO657mjwL/PN9u36Nv9JA9YGlwleCxUMxAuLCqUIWwYGBP0BlAARAKYAawJcBVkJKg5/E/0YQh7vIrEmRimFKmEq6ShKJsUisB5nGk0WuhL7D0YOug1bDhQQtRL/FaQZUR23II8joyXNJv8mQya0JHwi0x/zHBQaZhcNFRwTkhFhEGcPeg5qDQcMKAqwB5AE0ACK/Ob3IvOB7krqxOYo5KHiR+IW4/bktucT67zuW/KY9Sj4zflf+s/5KviU9Urylu7O6knnV+Q74iDhHeEq4ibk2Ob06SXtEfBj8tbzOPRy84rxo+796u3m2OIp30rcm9pl2tzbEN/2413q/fFz+kwDEgxMFIwbeCHLJVooGSkWKHgldyFbHHIWChBqCdICcvxs9tXwtusP597iH9/T2wTZw9Yr1V/UhtTI1UjYHdxR4djnke9C+JwBPgu5FJgdaSXDK1Mw3TJGM5Ux9C2tKCQi0xo9E+ULRwXJ/7f7O/le+AD55Pqt/esAJgThBqsIIwkECCkFjgBS+rDyAeqv4C7X8s1sxfq96Ldps5Wwba/br7axyrTeuLi9JMP1yA7PXNXX24HiXul18Mb3Sv/tBo4OABYIHWUj0igPLeUvKzHOMNMuWiubJuUgmxopFAAOjAgsBCsBu//u/7gB8wRcCZwOUBQUGoQfTSQvKAErtyxeLSAtNyzrKowpZSi5J7cneigDKjks7i7eMbo0LjfnOKA5JDlWNzQ02C92Klgk2R1bF0QR7gunB6QEAgPEAs0D7AXYCD4MxQ8VE98V5hf/GBcZMRhmFuAT1hCCDSEK5gb6A3MBW/+i/TH83/qA+ef36fVr81zwwOys6EjkyN9s23fXKdS30UrQ9M+x0GjS59Ts1yjbSN744PLi/uP84+PiyeDc3WHardYe0xbQ7M3ozD7NBM800qvWKdxc4uHoUe9G9Wj6cf41AaUC0QLkASQA6P2Q+4D5FPiZ90b4Nvpo/b0B/gbbDPkS8hhlHvciYSZsKP8oFyjKJUUiwR2EGNgSAQ09B7sBnfzx97nz6O9r7CrpDuYH4w7gKd1r2vDX4dVp1LPT49MU1U7Xhtqc3lvjfOit7ZLy0vYb+i383fwe/AH6t/aM8uXtN+kA5brh1d+r33bhU+U06+nyH/xjBjURAhw7Jlkv6zaYPCtAkkHeQEM+EDqpNH8uBSiqIc0bvhayEsUP+g0+DW4NVw7CD3gRSBMKFaIWAxgrGSIa+Bq+G4EcSR0THtAeZR+sH3gfmR7hHCsaXhZ3EYcLtQRD/X/1zu2X5kbgO9vI1ynWeta62MbcXeIj6abwbPj1/8gGfwzIEG0TWxScE1oR2A1rCXMEVP9n+vr1SfJz74PtZ+z76wzsXOys7Mbsfuy9637q1ujv5gTlXeNI4hHi+OIw5dTo4+1E9ML7EATSDJ8VCx6xJTYsVDHdNLw29zauNRQzay/+KhkmAiH2GyAXmhJsDo4K6gZgA9L/Hvww+P/zku//6m/mFeIv3vzat9iU17TXJdne277fj+QH6tHvkfXu+pf/SwPjBU4HmAfmBnUFkwOXAdv/sP5Z/gP/wQCJAzQHfwsUEI4UhRiTG2AdqB1EHCoZdBRXDiYHSv8192HvQeg74p7dodpb2cbZwNsM31/jYei27QjzDfiK/FkAagO/BW4HmQhoCQgKoQpPCyUMJg1GDmsPdBA4EY8RVRFzEN0OmgzACXgG9QJ1/zT8bvlU9wf2lvX39Q33pfh9+kj8uP2A/mL+Nf3l+nv3HvMP7qToRuNj3mjauNeh1ljX79lW3lnkpOvJ80f8lAQoDIUSQhcTGs0aaxkKFuwQagr1Agn7IvO46zLl4t8C3K7Z6NiY2ZPboN594ujmo+t58EH14vlO/oMCiQZpCisO1RFhFcIY3huSHrMgFiKQIv8hTyB8HZgZzRRWD4QJtgNQ/rX5QvZC9OnzTvVp+A/9+ALGCQIRLhjIHlokfSjkKmEr5ymOJoohLxviExQMOgTD/Av2XfDo68Ho4OYj5lnmQOc=\" type=\"audio/wav\" />\n",
" Your browser does not support the audio element.\n",
" </audio>\n",
" "
],
"text/plain": [
"<IPython.lib.display.Audio object>"
]
},
"execution_count": 217,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import Audio\n",
"r=20000\n",
"t=np.arange(0,3,1/r)\n",
"\n",
"out_E=np.sin(t*eE[0]**0.5)+np.sin(t*eE[1]**0.5)+np.sin(t*eE[2]**0.5)\n",
"out_B=np.sin(t*eB[0]**0.5)+np.sin(t*eB[1]**0.5)+np.sin(t*eB[2]**0.5)\n",
"out_G=np.sin(t*eG[0]**0.5)+np.sin(t*eG[1]**0.5)+np.sin(t*eG[2]**0.5)\n",
"out_D=np.sin(t*eD[0]**0.5)+np.sin(t*eD[1]**0.5)+np.sin(t*eD[2]**0.5)\n",
"out_A=np.sin(t*eA[0]**0.5)+np.sin(t*eA[1]**0.5)+np.sin(t*eA[2]**0.5)\n",
"out_E2=np.sin(t*eE2[0]**0.5)+np.sin(t*eE2[1]**0.5)+np.sin(t*eE2[2]**0.5)\n",
"\n",
"data=100*(out_E + out_B + out_G + out_D + out_A + out_E2)\n",
"Audio(data=data,rate=r)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
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