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@Wesitos
Last active August 29, 2015 14:10
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{
"metadata": {
"name": "",
"signature": "sha256:5ea41d7698d73c14b35671298c66dff0eb85e306d37c14f8c4ecad8c2e748be6"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"import numpy as np\n",
"from numpy.polynomial.hermite import Hermite\n",
"from scipy.constants import hbar, pi"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 38
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Soluciones del oscilador armonico cuantico\n",
"========\n",
"Ecuacion de Schrodinger para el oscilador:\n",
"$$ - \\frac{\\hbar^2}{2m} \\frac{d^2 \\psi}{d x^2} + \\frac{1}{2} m\\omega^2x^2\\psi = E\\psi $$\n",
"Resolviendolo, las soluciones ortonormalizadas son:\n",
"$$ \\psi_n(x) = \\left(\\frac{m\\omega}{\\pi \\hbar}\\right)^{1/4} \\frac{1}{\\sqrt{2^n n!}} \\boldsymbol{H}_n(\\xi)e^{-\\xi^2/2} $$\n",
"\n",
"Donde $\\left(\\xi = \\sqrt \\frac{m\\omega}{\\hbar}x \\right)$ y la energia de cada estado es $\\left( E_n = \\left[ n + \\frac{1}{2}\\right]\\hbar\\omega \\right)$\n",
"\n",
"La probabilidad de encontrar a la particula en cierta posicion es igual al cuadrado del modulo de su funcion de onda asociada\n",
"$$ \\rho_{cuantico}(x) = \\left|\\psi_n(x)\\right|^2 $$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def sol_oscilador_cuantico(n, m, w):\n",
" def psi(x):\n",
" xi = np.sqrt(m*w/hbar)*x\n",
" coef = np.power((m*w)/(pi*hbar), 0.25)/np.math.sqrt(2**n*np.math.factorial(n))\n",
" return coef*Hermite.basis(n)(xi)*np.exp(-xi**2/2)\n",
" return psi"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 39
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"[psi_0, psi_1, psi_2, psi_10] = [sol_oscilador_cuantico(n, 1.3e-17, 1.3e-17) for n in [0,1,2,10]]"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 87
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"x = np.linspace(-8,8,400)\n",
"f,axarr = plt.subplots(4, sharex=True)\n",
"f.set_size_inches(16,8)\n",
"axarr[0].plot(x,psi_0(x)**2)\n",
"axarr[0].set_title(\"Densidad de probabilidad para el oscilador cuantico para n= 0,1,2,10\")\n",
"axarr[1].plot(x,psi_1(x)**2)\n",
"axarr[2].plot(x,psi_2(x)**2)\n",
"axarr[3].plot(x,psi_10(x)**2);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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P+BAYzZKDH60FPAMcCrxSy35MTCVJeS1cCL/6Fay7Ltxwg3NolprbboPLL4eX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Ljn7Jy7++Wee8+5v6fvb8MGteL2tLFj9d1asEAt2LW1ehwxomdfd8AAtX5VVem1GhtVKF60qGdf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\n",
"text": [
"<matplotlib.figure.Figure at 0x7fd5bea27e90>"
]
}
],
"prompt_number": 90
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\u00bfC\u00f3mo es la probabilidad de encontrar una part\u00edcula para el caso cl\u00e1sico?\n",
"============\n",
"Clasicamente, la probabilidad de encontrar una particula en cierta region es proporcional al tiempo que pasa la particula en esa region.\n",
"$$ \\rho(X) \\propto dt = \\frac{dx}{dx/dt} = \\frac{dx}{v(x)} $$\n",
"Y como en un periodo la particula pasa por cada posicion 2 veces, la densidad de probabilidad estaria dada por:\n",
"$$ \\rho(x) = \\frac{2}{\\tau v(x)} $$\n",
"Donde $\\tau$ es el periodo del movimiento. Expresando la velocidad en terminos de la energia $ \\left( T(x) = \\frac{1}{2}mv^2(x) \\right)$ y $\\left(T(x) = E-V(x) \\right)$\n",
"$$ \\rho(x) = \\frac{2}{\\tau} \\sqrt{\\frac{m}{2T(x)}} = \\frac{1}{\\tau} \\sqrt{\\frac{2m}{E-V(x)}} $$\n",
"Para el oscilador armonico se sabe que:\n",
"$$\n",
"\\begin{cases}\n",
"V(x) = \\frac{1}{2}m w^2 x^2 \\\\\n",
"\\tau = \\frac{2\\pi}{\\omega} \\\\\n",
"\\end{cases} $$\n",
"Y haciendo $ \\left( E_n = \\left[ n + \\frac{1}{2}\\right]\\hbar\\omega \\right) $ para hacer la comparacion con el caso cuantico llegamos a:\n",
"$$ \\rho_{clasico}(x) = \\frac{1}{\\pi} \\sqrt{ \\frac{m\\omega}{(2n+1)\\hbar-m\\omega x^2 }} $$\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def dens_clas_armonico(n, m, w):\n",
" def rho(x):\n",
" coef = 1/pi\n",
" return coef*np.sqrt(m*w/( (2*n+1)*hbar - m*w*x**2))\n",
" return rho"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 42
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"[clas_0, clas_1, clas_2, clas_10] = [dens_clas_armonico(n, 1.3E-17, 1.3E-17) for n in [0,1,2,10] ]\n",
"x = np.linspace(-8,8,400)\n",
"f,axarr = plt.subplots(4)\n",
"f.set_size_inches(16,8)\n",
"axarr[0].plot(x,psi_0(x), x,clas_0(x))\n",
"axarr[0].set_title(\"Comparacion entre densidad de probabilidad cuantica y clasica para n=0,1,2,10\")\n",
"axarr[1].plot(x,psi_1(x)**2, x,clas_1(x))\n",
"axarr[2].plot(x,psi_2(x)**2, x,clas_2(x))\n",
"axarr[3].plot(x,psi_10(x)**2, x,clas_10(x));"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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T7+bzyz5n8k+TOXLckTw751n2FO/xOvxatWHXBu76+C4Oe+wwmqU3Y+H1Czml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iv5Zf/SS0NtHdC/Pzt4o0cDRUV8/0ydyo5BsJwfb8TH84v3K6/U3V+PP86OcXM0aNxw\nA784TpgAzJnDz8DkyZw2I9hMmsSNPnffzdfgsss4/UObNsGtd/hwfraHDwcqKlh1dskSftaDidHI\nztf8+cAVV/B9NmYMO6AxMcGtG+BGs/37Wb01NZXtSUvjFErNSffufJ3vuYd/aysq+Hxs3Rr8a6+G\nOXO40WziRE7HlJ/P98b27fw/IJxLdDSnurrllrptlZWch/bYsbqG3EOH2GEtKwPKy+umigp+BqKj\nuZHCYuHJvey5zWjkZ8f9O91w2ds2rft/Kfz0k/qc0EJ40tQtfQ94DOiEmvXRYAfUMxvYJgB/AeAW\n7t8GYBKA/Q0+KwuAtM8JgiAIgiAIgiCcnxwF8CtfBZrqAT0JwDMgLRXcw+mrTErNtob4NEQQBEEQ\nBEEQBEH4ZWMGe7FdAESgaRGia9C4CJEgCIIgCIIgCIIg+GQIgJ/AIbRTa7al1UxultTs/x5AkEer\nCIIgCIIgCIIgCIIgCIIgCIIgCIIgtBCuBvA1gAMAvgFwVWjNETTyFDgFz38BzAmxLYJ/PAtAAdAC\nNB0FlcwDP3ffA/gXgPjQmiOoZDCAwwCOAJgcYlsEbaQC2AEgE/x/NzG05gh+YAK/a24KtSGCZhIA\nrAP/7/0AHt4nhAdTwb+bhwD8A0CLSQK4E8BtNctDwD/wQnhwM4CtACw16+1DaIvgH6kAtgDIhjig\n4cQgAO5MdH+pmYSWjQk8LKUL+DfTm36C0HLpCOCymuVY8DAkuX7hxR8BfABgY6gNETTzDoBxNctm\nSKNruNAFwDHUOZ2rAYxtrHBzp9c9hbobKQHe1XKFlsljAF4B4KhZPxNCWwT/+Cs4RZIQXmwF91oD\nwF6w0rjQsrka7IDmgH8zVwG4K5QGCZooADcaAIAV3BOTHDpzBI2kgAUy/4am0w0KLYt4ADcAWF6z\n7gRQGjpzBA2Ugf/vosENB9Hw4ec1twM6BcACAMfBYWVTfRcXWhAXArgRrHK8E8CVIbVG0Mpd4BRK\nB0NtiBAQ41CnOi60XDoByPNYP1GzTQg/ugC4HNz4I4QHGQCeR13DnRA+dAV3cKwAsB/AMrAjI7R8\nzqLOx8sHUAJgW2OFm8oD6g9bweErDZkGHkcxEcB6AL8Ft3AMCoINgn/4unZmALDSPoEAAAHxSURB\nVIngWPyrAKwB0K35TBNU4Ov6TQXwG49t0ircsmjs2r2AujFM0wDYweMqhJYNhdoAQRdiwWPR/gDu\nCRVaPsMAFILHfw4IrSmCH5jB2TSeBGvFLAR3Xk0PpVGCKroDeBrcaFcKYC2A34FD4UNOmceyAdKt\nHk78G8BNHutZANqGyBZBG5cCOA0e+5kNDpHIAZAUQpsEbTwE4EsAkSG2Q1DHNeDx1m6mQoSIwg0L\ngP+AX6iE8OHP4OiDbPCwrwoA74bUIkELHcHXzk1/AJtDZIugjfvBYe9uHgTwWohsOYf9qHNiBoJb\nN4TwIA3An2qWLwJ3sQvhiYgQhReDwapy7UJtiKAaM4Cj4JbgCIgIUbhhADstGaE2RAiImyAquOHI\nZ+D3TACYAcm6EC70AauGR4F/Q98B8ERILfLgSvA4iu8A7AaPqxDCAwuA98DSyt9CQlvCmWMQBzSc\nOAIgFxxSdgDA66E1R1DJELB6ahZE7yDc6A8eP/gd6p67wSG1SPCHmyAquOFIH3AHlaQeCz8moS4N\nyzuoy5whCIIgCIIgCIIgCIIgCIIgCIIgCIIgCIIgCIIgCIIgCIIgCIIgCIIgCIIgCIIgCIIgCIIg\nCIIgCIIgCIIgCIIgCIIgCIIgCIIgCIIgCIIgCIIgCIIgCIIf/D9gTBw+ormz6AAAAABJRU5ErkJg\ngg==\n",
"text": [
"<matplotlib.figure.Figure at 0x7fd5ba786810>"
]
}
],
"prompt_number": 92
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"x = np.linspace(-15,15,1000)\n",
"clas_100 = dens_clas_armonico(100, 1.3E-17, 1.3E-17)\n",
"psi_100 = sol_oscilador_cuantico(100,1.3E-17, 1.3E-17)\n",
"plt.plot(x,psi_100(x)**2, x,clas_100(x))\n",
"plt.title(\"Comparacion entre densidad de probabilidad cuantica y clasica para n=100\")\n",
"plt.gcf().set_size_inches(16,6)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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62DPtFtffP8j+QwIwZhQAAABx6e3v1biyccO9GhgmhbrpAjnKSsropgsAAIBY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\nuyA72eQpU3IbGL291piZO9f/Wq2t1ijyvndDgwV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Wr71dfTa/r8+4IorHISutamqs+4oq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\nDQ0NDQ0NDQ0NDQ0NDQ0NDQ2NTPD/AUbMIDyzL46bAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x7fd5baa552d0>"
]
}
],
"prompt_number": 99
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A medida que vamos aumentando el valor de n, la densidad de probabilidad quantica va tomando la forma de la densidad de probabilidad clasica. Es decir:\n",
"$$ \\rho_{clasico}(x) = \\lim_{n \\rightarrow \\infty} \\rho_{cuantico}(x) $$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Momentum y velocidad\n",
"=====\n",
"Expresando las soluciones del oscilador armonico cuantico en el espacio de momento:\n",
"$$\n",
"\\begin{split} \n",
"\\phi_n(p) &= \\frac{1}{\\sqrt{2\\pi\\hbar}} \\int_{-\\infty}^{+\\infty}dx \\psi_n(x) e^{-ipx/\\hbar} \\\\\n",
"&= \\frac{1}{\\sqrt{2\\pi\\hbar}} \\left(\\frac{m\\omega}{\\pi \\hbar}\\right)^{1/4}\\frac{1}{\\sqrt{2^n n!}} \\int_{-\\infty}^{+\\infty} dx \\boldsymbol{H}_n\\left(\\sqrt \\frac{m\\omega}{\\hbar}x\\right)e^{- \\left(m\\omega x^2 + 2px \\right) / 2\\hbar} \\\\\n",
"\\phi_n(p)&= \\frac{(-i)^n}{\\sqrt{2^n n! \\sqrt{m \\omega \\hbar \\pi}}} \\boldsymbol{H}_n \\left( \\frac{p}{\\sqrt{m \\omega \\hbar}} \\right) e^{\\left( -p^2/2m \\omega \\hbar \\right)}\n",
"\\end{split}\n",
"$$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def sol_oscilador_cuantico_momentum(n, m, w):\n",
" def phi(p):\n",
" xi = p/np.sqrt(m*w*hbar)\n",
" coef = complex(0,-1)**n/np.sqrt( 2**n*np.math.factorial(n)*np.sqrt(m*w*hbar*pi))\n",
" return coef*Hermite.basis(n)(xi)*np.exp(-xi**2/2)\n",
" return phi"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 45
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"phi_0, phi_1, phi_10 = [sol_oscilador_cuantico_momentum(n,1.3E-17,1.3E-17) for n in [0,1,10] ]"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 120
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"x = np.linspace(-1.0E-33,1.0E-33,200)\n",
"f,axarr = plt.subplots(3, sharex=True)\n",
"f.set_size_inches(16,8)\n",
"axarr[0].plot(x,np.abs(phi_0(x))**2)\n",
"axarr[0].set_title(\"Solucion para el oscilador armonico cuantico en el espacio de momentos n=0,1\")\n",
"axarr[1].plot(x, np.abs(phi_1(x))**2)\n",
"axarr[2].plot(x, np.abs(phi_10(x))**2);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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CCvAAcHI0PQj4nPoJqSRJeXXnnTBggAlpQwccEJo0v/xy88tKkhSHbJLSXYET\ngT2BadHjAGBY9ACYAMwFZgMjgbNzHqkkSU0YORKGDWt+uUrTvj388Idh+0iSVIxaXLXaBjbflSTl\nxauvwv77wzvvQIeWjJZQId57D7beOmyf1VePOxpJUrnKZ/NdSZKK2siRoTbQhDSzHj1g8GAYMybu\nSCRJWpE1pZKkkvbVV2GAo+nTw19l9sgjcOmlMHVq3JFIksqVNaWSpIo0dizsuqsJaXP23RcWLgyj\nE0uSVExMSiVJJau2Fq69Fs52eL1mtWsHZ50VtpckScXE3jeSpJL1zDOwZAnst1/ckZSGH/4QeveG\nBQugW7e4o5EkKbCmVJJUsq6+Gn7841ALqOattRYcdRRcf33ckUiSVCebTqijgIOAj4CtM8xPAPcT\n7lMKcDdwRYblHOhIkpQz774L227rbU5aKnX7nLffho4d445GklRO8jnQ0Whg/2aWmQj0jx6ZElJJ\nknJqxAg46SQT0pbaemvYdFO4++64I5EkKcgmKZ0EfNbMMoW8tYwkqcItXQo33gjnnht3JKXpvPNC\n02dJkopBLnrh1AK7ANOBCUC/HKxTkqRG3X47DBgAffvGHUlpOvhgeP99bw8jSSoOuRh99yWgJ7AE\nOAC4D9g004LV1dXfTScSCRKJRA6KlyRVkpoauPJKb23SFh06wPnnw5//DHfcEXc0kqRSlUwmSSaT\nbV5Pts1uewHjyTzQUUNvATsACxu87kBHkqQ2u/9++M1vQi1flZ1HWu3LL2HjjWHyZOjTJ+5oJEnl\nIJ8DHTWnW1rBA6PphgmpJEltVlsLf/wj/PznJqRttdpqcOaZodZZkqQ4ZfOTPgYYDKwDLAAuB1KD\nyI8EzgHOApYTmvBeADyfYT3WlEqS2mTSJDj9dHjjDWjfPu5oSt9HH8Hmm8PMmbDeenFHI0kqda2t\nKS3kdWaTUklSm3z/+2GQnmHD4o6kfJxzDqy5Jvzud3FHIkkqdSalkqSyNmMGDBkCb70FnTrFHU35\nmDsXBg4Mf9dYI+5oJEmlLM4+pZIk5d1vfxtGjDUhza1NNoH99oO//z3uSCRJlcqaUklS0ZsxA/bZ\nB2bPDgP0KLfefBN23x1mzQpNeSVJag1rSiVJZevyy+GnPzUhzZfNNoMDDoDhw+OORJJUiawplSQV\ntWnT4KCDQi3pqqvGHU35mj0bBg0KtaVdu8YdjSSpFOWzpnQU4VYwrzaxzNXALGA60L+lQUiS1JjL\nL4eLLzbDn5IvAAAgAElEQVQhzbc+feDQQ+Gqq+KORJJUabLJYncHvgRuBbbOMP9A4Nzo707A34BB\nGZazplSS1CIvvABHHBFq7xzgKP/eeQe23z7cB3bddeOORpJUavJZUzoJ+KyJ+UOBW6LpKUAXoFtL\nA5EkKV1tbehH+stfmpAWykYbwfHHw69/HXckkqRKkouBjnoA76Y9nw9skIP1SpIq2D33wOefw+mn\nxx1JZamuhnHjYObMuCORJFWKXI2+27CK1na6kqRWW7Ys1JIOHw7t28cdTWVZe2249FK44IJQWy1J\nUr51yME63gN6pj3fIHptBdXV1d9NJxIJEolEDoqXJJWb4cNh221hzz3jjqQynX02jBgBDz8MBx4Y\ndzSSpGKVTCZJJpNtXk+2nVB7AeNpfqCjQcBwHOhIktRKH34IW20Fzz8fRoRVPB56CC68EF59FTp2\njDsaSVIpaO1AR9m8YQwwGFiHcGuYy4HUz9PI6O+1wP7AV8BpwEsZ1mNSKklq1gknQI8e8Kc/xR1J\nZautDbWkiQT8/OdxRyNJKgX5TEpzxaRUktSkhx6C886DV16Bzp3jjkZvvQUDBsBzz8Gmm8YdjSSp\n2JmUSpJK2qJFodnuzTfDXnvFHY1S/va3MBLy009Du1wNjyhJKkv5vE+pJEl5d/HFsN9+JqTF5txz\n4euv4frr445EklSurCmVJMXu3/+G44+HGTOgS5e4o1FDr70W+pZOnQobbhh3NJKkYmVNqSSpJH36\nKZx4IowcaUJarLbcEi66KFw4+OabuKORJJUba0olSbGpqYGhQ2GLLeDPf447GjWlpgYOOgi22w5+\n//u4o5EkFSMHOpIklZyrroK77grNd70XZvH7+GPo3x9uuin0/5UkKV2+m+/uD7wBzAIy3a0sAXwB\nTIsel7U0EElSZZk8OdyLdMwYE9JSse668K9/wamnwvz5cUcjSSoX2SSl7YFrCYlpP+A4YIsMy00E\n+kePK3IVoCSp/MyZA4cfDqNGQa9ecUejlhg8GC64IDTlXbQo7mgkSeUgm6R0IDAbeBv4BhgLHJJh\nuUI2BZYklahPP4UDD4Rf/jIkNio9F10Eu+wCRx3lwEeSpLbLJintAbyb9nx+9Fq6WmAXYDowgVCj\nKklSPcuWwaGHwiGHwFlnxR2NWquqCq65Bjp0CP9Hh4yQJLVFhyyWyean5iWgJ7AEOAC4D9i04ULV\n1dXfTScSCRKJRDYxSpLKwLJlcOSRsP768Ic/xB2N2qpDBxg3Lty/9KKL4MorQ7IqSaocyWSSZDLZ\n5vVk8/MxCKgm9CkFuASoAf7YxHveAnYAFqa95ui7klShliwJNaRdu8JttzmwUTlZuBD23x8GDAi1\np+28A7okVax8jr77ItAX6AWsBBwDPNBgmW5phQ+MphciSap4ixfDAQfAeuuFkVtNSMvLWmvB44/D\nyy/Dj34E334bd0SSpFKTTVK6HDgXeBSYCYwDXgeGRQ+AI4FXgZeB4cCxOY9UklRy5s6FXXeFLbaA\nm28OTT5VftZcEx59FN55Bw4+GD7/PO6IJEmlpJC9P2y+K0kV5Ikn4IQT4LLL4Nxz7W9YCb75Bi68\nEB55BO6/P1yMkCRVjnw235UkKWvffAO/+Q2ceCKMHQs//rEJaaXo2BGuvhouuQT22ANuvdWReSVJ\nzbOmVJKUM9Onw2mnQbducP310LNn3BEpLtOmhX2hR4+wL/RoeDM5SVLZsaZUkhSbTz8NtwUZMgTO\nOw8mTDAhrXT9+8MLL8DAgWH6qqvCbYEkSWrIpFSS1GpffRXuObrZZvDll6Gm9NRTba6rYKWV4PLL\nIZmESZNg003DgFfLl8cdmSSpmJiUSpJa7K23Qs3oRhvBSy/Bc8/BdddB9+5xR6Zi1K8f3HcfjBkT\nktJNNgkXMz75JO7IJEnFIJukdH/gDWAW8PNGlrk6mj8d6J+b0CRJxeTTT+HGG0MT3QEDQm3of/4D\nd9wRasCk5uy6a6g1vf9++O9/oW9fOOoouPNOWLIk7ugkSXFpLiltD1xLSEz7AccBDQd4PxDoA/QF\nzgBG5DhGKaNkMhl3CCoz7lP1ff01TJ4MV1wBiUSo3Xr0URg2DObNgz//GTbeOO4oi5f7U+P694dR\no2DOHNh/f7jhBlh/ffj+9+Gvf4VXXoGamrijLD7uU8o19ykVi+aS0oHAbOBt4BtgLHBIg2WGArdE\n01OALkC33IUoZeYXqXKtUvepmhp4/3146ikYMQLOPjsMTtOlC5x5Jnz2Gfz852GZO++EI4+EVVeN\nO+riV6n7U0ustRb84Afw2GMhQT3lFHjjDTj88LD/JRLhvqejRsGzz4bmvpU8kL/7lHLNfUrFokMz\n83sA76Y9nw/slMUyGwAL2hydJKlZNTWhVjP9sXQpLFoEixeHv6nHwoUhufzgg/A3Nd2lC2y+eXj0\n6wfHHw/bbQerrRb3p1OlWHvt0JT3qKPC808/Df2Vp06FiRNh5Eh4882wf3fvHmpWU4/u3aFrV1h9\ndVhjjbrH6qtDp05hwKXUo2NHaOeIGpJUVJpLSrO9HtlwnMUKvo6pQrjgArj99tAvqaHmrqLnc77r\nLu11f/FFqJHJx7pz9V6oS0L/97/w99tvYeWV6594d+pU/+Q8dYLetWvo/5lI1J3Yr7cerLJK02VK\nhbb22qH/8pAh9V9fvDhcSGl4YWXWrPoXYFIXZFLHSfqjQ4e6YyaVpLZrF/pJpx7pz1syL58+/DAM\nGFWsHHW79LaBg9OpWDR36AwCqgl9SgEuAWqAP6Ytcx2QJDTthTAo0mBWrCmdDfRufaiSJEmSpCI2\nhzDeUE51iFbcC1gJeJnMAx1NiKYHAc/nOghJkiRJUuU6AHiTUNN5SfTasOiRcm00fzqwfUGjkyRJ\nkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJ\nkiRJkiRJkiRJkiRJkiRJktpiFLAAeDWLZc8EXgGmAZOBbaPXNwKmRq+/Bpyf+zAlSZIkSeVod6A/\n2SWlq6dNHww8EU13jB4AnYG3gQ1yFJ8kSZIkqcDaFbCsScBnDV7rDTwMvAj8G9gsen1x2jKrAZ9E\n099ED4BVoukl+QhWkiRJklR+elG/pvRJoE80vVP0POVsYDbwAbBx2usbEJr2LomWkSRJkiQpK72o\nS0pXIySW09Ier2V4z3HA0xle7w78l7qkVpIkSZKkJvWiLildA3g/i/e0A75oZN5NwJFtD0uSJEmS\nFIds+pR2AqYALwMzgd9nWCZBSBxTNZ6XZbHeRcBb1CWVVcA20XR67edBhOa6AD0IfUkBugK7ps2T\nJEmSJJWpVaO/HYDngd0azE8ADzSzjjGEmtGvgXeB0wg1pw8TEt7XqEtmhwMzCAnuY9QlqfsA06Pl\npwEnt+KzSJIkSZJK1KrAf4B+DV5PAOMLHo0kSZIkqaRle0uYdoTayQWEQYdmNphfC+xCqMWcwIpJ\nqyRJkiRJK6hq4fJrAo8CFwPJtNdXB74ljKZ7APA3YNP0N/bu3bt2zpw5rQ5UkiRJklTU5tCKu6O0\nNCkF+AWwFLiyiWXeAnYAFqa9VltbW9uK4qTMqqurqa6ujjsMlRH3KeWS+5NyzX1KueY+pVyrqqqC\nVuSY2TTfXQfoEk2vAgwhDDKUrlta4QOj6YVIkiRJktSEDlks0x24hZDAtgP+CTwJDIvmjyTc1uUs\nYDmhCe+xOY9UkiRJklR2sklKXwW2z/D6yLTpv0cPqWASiUTcIajMuE8pl9yflGvuU8o19ykVi9b0\nKW0t+5RKkiRJUpnKZ59SSZIkSZLywqRUkiRJkhQbk1JJkiRJUmxMSiVJkiRJsTEplSRJkiTFxqRU\nkiRJkhQbk1JJkiRJUmxMSiVJkiRJsekQdwCSJLXEwoVw2WUwezYkErDnnjBgAHTwF61ZS5fCM8/A\n00/Ds8/CPvvAz34GK68cd2SSpErWXE1pJ2AK8DIwE/h9I8tdDcwCpgP9cxadJEmRmhoYPRr69YN2\n7eCcc+CTT+BHP4KDDoJvvok7wuL26aew3XZQXQ3t24dkdOpU2HprePzxuKOTJFWyqiyWWRVYQqhV\nfQa4KPqbciBwbvR3J+BvwKAM66mtra1tU7CSpMr14x/Dc8/B9dfDDjvUvb58ORxyCPTsCSNGQFU2\nv2wV5uuvYcgQGDgQ/vzn+vPGj4dzz4VLL4UzzognPklSeagKP8It/iXOpk/pkujvSkB7YGGD+UOB\nW6LpKUAXoFtLA5EkqTH33w8PPghPPlk/IYXQbHfs2JCw/uUv8cRXzGprQ7K51lrwhz+sOP/gg+HR\nR0NS+tprhY9PkqRsktJ2hOa7C4CnCc140/UA3k17Ph/YICfRSZIq3vz5Iam6/Xbo0iXzMquvHpLW\nv/wFHnqosPEVuyuvhBkz4LbbQrPdTDbfHP74RzjuOFi2rLDxSZKUzbAQNcB2wJrAo0ACSDZYpmEV\nbcZ2utXV1d9NJxIJEolEVkFKkirTt9/CSSfBeefBzjs3veyGG8JNN8EFF8ABB4R+p5Vu4cJQOzp1\nKnTu3PSyp50Wakx/+lO45prCxCdJKm3JZJJkMtnm9bS0ve8vgKXAlWmvXUdIUsdGz98ABhNqVtPZ\np1SS1CJ/+xvce29otttYLV+62trQb/KSS+Dww/MfX7H71a9g3ryQrGfj88+hf/+w/F575Tc2SVL5\nyVef0nUIfUQBVgGGANMaLPMAcHI0PQj4nBUTUkmSWmTJklDLd/XV2SWkEAY5uvRS+N3vQoJayRYv\nhmuvhYsvzv49XbrAb38Lv/yl20+SVDjNJaXdgacIfUqnAOOBJ4Fh0QNgAjAXmA2MBM7OS6SSpIpy\nww2hye4227TsfUOHhn6Rjz2Wn7hKxciRsPfe0Ldvy953zDHw8ceQg9ZYkiRlpZAD59t8V5KUlWXL\noHfvMHhR/1bc/fpf/wq3jpk4MfexlYJly2CTTeCRR1qe1APceiuMGmViKklqmXzeEkaSpIK68UbY\nccfWJaQQavvmz4dnnml+2XI0enS4dU5rElKA448P269Sk3pJUmFZUypJKir/+x/06RMGONpxx9av\n55prYMqUcCuUSrPNNqEvblsGuR89OtQ4P/FEzsKSJJU5a0olSWXh1ltDUtWWhBTg6KPDPUuXLs1N\nXKXi9dfDrWD22KNt6znxRJg7F55/PjdxSZLUGJNSSVJRGTECzj+/7evp1g223x4efrjt6yol48bB\nUUe1/T6tHTvC2WfDddflJi5JkhpjUipJKhpTp8Jnn8E+++RmfUcfDXfckZt1lYLa2vB5jz46N+s7\n5RS4775w/1JJkvLFpFSSVDRuuAF++MO21/KlHHFEGIH2q69ys75iN2NG+KyDBuVmfeuuC/vtB7ff\nnpv1SZKUiUmpJKkofPllqOU77bTcrXOddWCnnULf0kowblyoJa3K4TCGP/pRuL2OYxVKkvLFpFSS\nVBTGjYPdd4f118/teo85Jqy73NXWhs95zDG5Xe9ee8GiRfDii7ldryRJKSalkqSicMMNcMYZuV/v\nYYeF25osXpz7dReTadOgpibcnzSX2rULtaU33JDb9UqSlJJNUtoTeBp4DZgBnJdhmQTwBTAtelyW\no/gkSRXglVfgvfdg//1zv+6uXWG33eCBB3K/7mKSGuAol013U049Fe68s/wTe0lSPLJJSr8B/g/Y\nEhgEnANskWG5iUD/6HFFrgKUJJW/m28OiU/79vlZ/2GHlX+/0gcfDJ8zH7p3D/c9vfvu/KxfklTZ\nsklKPwRejqa/BF4HMvX4ycO1WUlSufv229AX8vjj81fGkCGhCW9NTf7KiNN778EHH+S+6W6644+H\nMWPyt35JUuVqaZ/SXoSa0CkNXq8FdgGmAxOAfm2OTJJUESZNCrce2SJTG5wc2Wij0Ix3+vT8lRGn\nJ54IAxLlq6YZ4OCDYcoU+Oij/JUhSapMHVqw7GrAXcD5hBrTdC8R+p4uAQ4A7gM2bbiC6urq76YT\niQSJRKJFwUqSys+YMXDccfkvZ9994fHHoX///JdVaI8/Hj5fPq26Khx0UOhbes45+S1LklQakskk\nyWSyzevJtsltR+BB4GFgeBbLvwXsACxMe6221pucSZLSfP11uAXM1KmhNjOfHngArr461CqWk5qa\n0OdzyhTo1Su/ZT34IPzhD/DMM/ktR5JUmqrCaHst7taZTfPdKuAmYCaNJ6Td0gofGE0vbGRZSZKA\nUMO32Wb5T0gBEomQuC1dmv+yCunVV2GNNfKfkEKojX3jDZg3L/9lSZIqRzZJ6a7AicCe1N3y5QBg\nWPQAOBJ4lTAg0nDg2JxHKkkqO4Vqugshcdtuu9CHtZwUouluykorweGHw9ixhSlPklQZCjlirs13\nJUnfWbIkNN19803o1q0wZf7617BoEVx5ZWHKK4R994Wzz4ZDDy1MeU8/DRdcANOmFaY8SVLpyGfz\nXUmScu6hh2DgwMIlpFA32FG5WLYMJk+GPfcsXJl77AELFoRmvJIk5YJJqSQpFnfdBUcdVdgyd9wx\n9If88MPClpsvzzwD22wDa65ZuDLbt4cjjwz/P0mScsGkVJJUcMuWwaOPwiGHFLbcDh1CrWK5jMD7\n2GMwZEjhyz3iCLj77sKXK0kqTyalkqSCe/zxMOjQ975X+LL33htycEu1opBMwl57Fb7c3XaD99+H\nOXMKX7YkqfyYlEqSCu7uu8MornHYbbfyuM/mV1/Ba6+FfrmF1r49HHaYtaWSpNwwKZUkFdQ338D4\n8SGpicNWW4U+pR9/HE/5uTJlSqht7tQpnvJtwitJyhWTUklSQU2cCH36QM+e8ZTfvj3svDM8+2w8\n5efKM8+EWt+4JBIwe3YYOEqSpLYwKZUkFdQ998TXdDdl991h0qR4Y2irSZPC54hLx44wdGj4f0qS\n1BYmpZKkgqmpgXvvjT8pLfV+pcuXh+a7u+wSbxxHHmkTXklS25mUSpIKZvJkWHdd6Ns33jgGDIAZ\nM8JgQaVo+nTYcENYa61449hnn7AdP/gg3jgkSaUtm6S0J/A08BowAzivkeWuBmYB04H+OYlOklRW\niqHpLsAqq8C228ILL8QdSevE3Z80ZeWV4cADQ+23JEmtlU1S+g3wf8CWwCDgHGCLBsscCPQB+gJn\nACNyGKMkqQzU1hZPUgohqSvVfqWTJhVHUgqOwitJartsktIPgZej6S+B14H1GywzFLglmp4CdAG6\n5SJASVJ5mDYNOnSArbeOO5Jg991Ls19pbW2IO85BjtLtvz+8+CJ88knckUiSSlVL+5T2IjTNndLg\n9R7Au2nP5wMbtD4sSVK5SdWSVlXFHUmwyy7w/PNh0KBSMmdOGPl2ww3jjiRYdVXYd1+4//64I5Ek\nlaoOLVh2NeAu4HxCjWlDDU8zahsuUF1d/d10IpEgkUi0oHhJUim75x4YPTruKOqsvXa4V+orr8D2\n28cdTfZS/UmLJbmH0IT3llvgBz+IOxJJUiElk0mSyWSb15PtT1pH4EHgYWB4hvnXAUlgbPT8DWAw\nsCBtmdra2hXyVElSBXj9dRgyBObNg3ZFNO77sGHQrx+cf37ckWTvhz+E7baDc8+NO5I6ixdDjx7h\n/9ulS9zRSJLiUhWumLb4smk2pwZVwE3ATDInpAAPACdH04OAz6mfkEqSKliq6W4xJaRQ14S3lEye\nHP/9SRtafXXYc08YPz7uSCRJpSib04NdgROBPYFp0eMAYFj0AJgAzAVmAyOBs3MeqSSpZBXTqLvp\nBg0qraR00SJ4553iGSwq3RFHwF13xR2FJKkUFbJHis13JakCvf02DBgAH3wQRt8tJjU1sM46MHMm\nrLde3NE078knobq6OG9l89lnsNFG8N57oeZUklR58tl8V5KkVrvnHjjkkOJLSCE0J95pJ5jScEz5\nIvX88yHeYtS1K+y6K0yYEHckkqRSY1IqScqre+4JTTuLVSk14Z0ypXiTUgj/57vvjjsKSVKpMSmV\nJOXNBx/Aa6/BXnvFHUnjdtqpNJLS2triT0oPOQQefRSWLIk7EklSKTEplSTlzf33w4EHwsorxx1J\n4wYOhBdfhOXL446kaW+/De3bh3urFqt114UddgiJqSRJ2TIplSTlzd13F3fTXYC11gr32Hzttbgj\naVqqlrSqkEMUtsKRR9qEV5LUMialkqS8WLgQXngB9tsv7kiaVwr9Sou96W7KYYfBQw/B//4XdySS\npFJhUipJyovx42HvvaFz57gjaV6pJKWDBsUdRfO6d4ctt4Qnnog7EklSqTAplSTlxT33wOGHxx1F\ndoo9Kf36a5g+HXbcMe5IsuMovJKklihkz5Ta2traAhYnSYrL4sWhn+a8edClS9zRNG/58nCfzXnz\nwt9i85//wA9+AK+8Enck2Zk3D7bfPoy+3LFj3NFIkgqlKgx80OIc05pSSVLOTZgAu+xSGgkpQIcO\nYdTYF16IO5LMSqU/acqGG8Imm0AyGXckkqRSkE1SOgpYALzayPwE8AUwLXpclpPIJEkl68474eij\n446iZYq5Ce/zz5dGf9J0NuGVJGUrm6R0NLB/M8tMBPpHjyvaGpQkqXR9+SU8/jgcemjckbRMMSel\npVZTCiEpve8++PbbuCORJBW7bJLSScBnzSxT5HdNkyQVyvjxsOuu4f6fpWSnnULyV1MTdyT1ffop\nLFgAW2wRdyQt06cPrLcePPts3JFIkopdLvqU1gK7ANOBCUC/HKxTklSi7rgDjjkm7iharnt3WGMN\nmDUr7kjqe+EFGDAA2rePO5KWO+IIuOuuuKOQJBW7DjlYx0tAT2AJcABwH7BppgWrq6u/m04kEiQS\niRwUL0kqFosWwVNPwejRcUfSOqkmvJttFnckdZ5/vvSa7qYccQTsuy8MHw7tHFpRkspOMpkkmYNR\n7bJtdtsLGA9sncWybwE7AAsbvO4tYSSpzN12G4wbF5rwlqLhw+HNN2HEiLgjqbP//nDWWXDIIXFH\n0jr9+sGoUaU3UJMkqeXivCVMt7SCB0bTDRNSSVIFGDeuNJvuphTbYEc1NaH5bqnWlIJNeCVJzcsm\nix0DDAbWIdwa5nIgdSvskcA5wFnAckIT3guATD/p1pRKUhn7/PNwf8r580PfzFL0v/+FAZo++gg6\nd447mlBru99+8PbbcUfSei+/DIcdBnPnQpXDIkpSWWttTWk2fUqPa2b+36OHJKmC3Xcf7LVX6Sak\nACuvDFtvDVOnwh57xB1Nad4KpqFttw2DNE2dCjvuGHc0kqRi5LADkqSc+Oc/4YQT4o6i7YqpCW85\nJKVVVXD88aG/sSRJmZiUSpLabP58mDYNDj447kjartiS0nIYIOikk2DMGFi+PO5IJEnFyKRUktRm\n//pXGNCmU6e4I2m7QYNg8mSIexiEpUth5kzo3z/eOHKhb1/YeGN4/PG4I5EkFSOTUklSm9TWhqa7\nJ50UdyS5sdFG4TO9+268cbz0UridyiqrxBtHrpx0UthPJElqyKRUktQmL78MX34Ju+0WdyS5UVVV\nHE14y6Xpbsoxx8CECbB4cdyRSJKKjUmpJKlN/vlPOPFEaFdGvyjFkJQ+/3zpD3KUbp11YPBguPvu\nuCORJBWbMjqFkCQV2vLlYQCbcmm6m1IMSenkybDzzvHGkGs24ZUkZWJSKklqtSeegJ49YbPN4o4k\nt3bcEaZPh//9L57y330Xli2D3r3jKT9fvv/90Nw77v66kqTiYlIqSWq1G26A00+PO4rcW2016NMn\nJKZxmDwZdtkl9G8tJ506wbHHwqhRcUciSSomJqWSpFb54AN46ik4/vi4I8mPOJvwlmPT3ZQzzoAb\nb/SepZKkOtkkpaOABcCrTSxzNTALmA6UwR3VJEnNGT0ajjwS1lgj7kjyw6Q0P7bdFnr0gEceiTsS\nSVKxyCYpHQ3s38T8A4E+QF/gDGBEDuKSJBWxmprQdHfYsLgjyZ+4ktJly+DVV2HAgMKXXShnnAEj\nR8YdhSSpWGSTlE4CPmti/lDglmh6CtAF6NbGuCRJRezxx2GttcKAQOVqs81g4UJYsKCw5U6dClts\nAauuWthyC+mYY+C55xzwSJIU5KJPaQ8g/WdlPrBBDtYrSSpSI0eG2q5y1q5duE/olCmFLTc1yFE5\n69wZjjsObrop7kgkScWgQ47W03B8wNpMC1VXV383nUgkSCQSOSpeklQoH3wATz8Nt9zS/LKlLtWE\nd+jQwpX53HNw1FGFKy8uZ5wBBx4Il10GHXJ1NiJJKqhkMkkymWzzerIdbL4XMB7YOsO864AkMDZ6\n/gYwmDA4Urra2tqMuaokqYRUV8OHH8J118UdSf49/DD8+c9hlOFCqK2F9dcPtaW9ehWmzDjtsgtc\neCEccUTckUiScqEq3MusxTc0y0Xz3QeAk6PpQcDnrJiQSpLKwNKlMGIE/OQncUdSGAMHwn/+A99+\nW5jy3nkn3Jt0o40KU17cLrgArroq7igkSXHLJikdAzwHbEboO3o6MCx6AEwA5gKzgZHA2bkPU5JU\nDG69NfSz3HzzuCMpjLXXDjWXr71WmPKeey7cCqaqxdeYS9Nhh4Va9+eeizsSSVKcsunFcVwWy5zb\n1kAkScWtpibUat14Y9yRFNagQaE57Tbb5L+scr4/aSbt24fa0iuvhHvuiTsaSVJcctF8V5JUAcaP\nhy5dYPfd446ksHbfHf7978KUNXEi7LFHYcoqFqedBpMmwaxZcUciSYqLSakkKStXXgkXXVQ5TUtT\nEglIJsMgRPn0ySehT+n22+e3nGLTuTMMGwbDh8cdiSQpLialkqRmPf88zJ8Phx8edySF17t3SMRn\nz85vORMnwq67VubtUc49F26/HT7+OO5IJElxMCmVJDXr8svhZz+rzISpqgr23DPcmzWfkslQTiVa\nbz049lj405/ijkSSFAeTUklSkyZODP39fvCDuCOJT6oJbz4lk6GcSnXZZTBqFLz/ftyRSJIKrZA9\ng35DP2EAACAASURBVGpr890hR5KUU7W1YaCfM86Ak09ufvlyNWdO2A7vvZefPrUffwx9+4Z+pZVY\nG51y0UWwZAn84x9xRyJJao2q8CPZ4l9Ka0olSY165BFYuBBOOCHuSOK1ySYhWczXCLETJ8Juu1V2\nQgpw8cUwbhzMnRt3JJKkQjIplSRlVFsbmlT+5jfhfpKVrKoqNK3NV7/SSm+6m7LOOmHQo1/9Ku5I\nJEmFZFIqScrojjvC30occTeTfPYrffppk9KUCy6Ahx+GV16JOxJJUqFkm5TuD7wBzAJ+nmF+AvgC\nmBY9LstFcJKkeCxaBBdeCFdfXXn3JW3Mnnvm536lH30U+qr275/b9ZaqNdeEX/8azj4bamrijkaS\nVAjZJKXtgWsJiWk/4DhgiwzLTeT/t3fncVJU5/7HPzPAsCuiEUXQQfZ9EQFBYTSiuBs0GvNLjHGN\nJl5vND+9JvGKN/qLiYkmrjG54L7FuCskgjoqKCqyDSD7IgiCAiKbLEP//ni6Ms3Q013ddaqru+f7\nfr36RU93dZ0zMzVFPXWe8xzoH3/c6qqDIiKSezffDCefbOtmiikvh7IyWLDA7X4rK62IUn1PkU50\n+eWwaxc8/HDUPRERkVzwE5QOAhYDy4FdwNPAWUm20710EZEiMHMmPPkk/O53Ufckv3jzSt980+1+\nlbq7r9JS+Mtf4MYbYf36qHsjIiJh8xOUHgasTPh6Vfy1RDFgKDALGI+NqIqISIHZsweuvBJuu82K\nzsjeTj0VXn3V3f5iMdvfqae622ex6N8fvvc9q8grIiLFzU/xeT+zZ6YD7YFtwCnAi0CX2huNGTPm\n388rKiqo0K1hEZG8cu+9NiJ48cVR9yQ/nXIKXHYZbN4MLVsG39/06dC0KXTrFnxfxeg3v4EePWx0\n+oQTou6NiIjUVllZSaWDKoB+Um6HAGOwOaUANwJ7gFSJXcuAo4ANCa/FYq6rQ4iIiDMzZsBJJ8H7\n70OnTlH3Jn+dfLIFpueeG3xf//3fsH073HFH8H0Vq4kT4aKL7Pg8+OCoeyMiIqmUWHXEjKd1+knf\nnQZ0BsqBMuB84OVa27RJaHxQ/PkGRESkIGzeDOefD3/+swLSdM46C156yc2+XnrJ9id1GzkSLrzQ\nAlNV4xURKU5+o9hTgD9hlXjHAr8Froi/9yDwU+BKYDeWwnstMLXWPjRSKiKSp370I6v+Om5c1D3J\nf6tWQd++8Pnn0KhR9vtZvhwGDYI1a1R5N51du2D4cBudvu66qHsjIiJ1yXakNJcVcxWUiojkoQcf\nhLvugo8/hubNo+5NYRg40FJujz8++33cfbdVOtaNAH+8IP7ZZ2HEiKh7IyIiyYSZvisiIkXqlVdg\nzBj7VwGpfy5SeJW6m5nycnjqKfjud2HOnKh7IyIiLmmkVESknpo6Fc4805YkGTQo6t4UltmzLaBc\nutSqFWdq40YLstasgWbNnHevqD31FNxwA0yZAu3bR90bERFJpJFSERHxbe5cOPtseOQRBaTZ6N3b\n/q2qyu7z48dDRYUC0mxccAFccw2MGgVffBF1b0RExAUFpSIi9cyUKbbm41132bqbkrmSEhg92kbt\nsvH00/Z5yc5111nRo2HDYNmyqHsjIiJBKX1XRKQeeflluPRSeOwxW29TsrdokQVFy5dnNuLpfW7F\nCmjaNLTu1Qv33w+33QavvQb9+kXdGxERUfquiIjUac8eqxZ7xRV2Aa+ANLjOnWHwYHjiicw+d889\ncNllCkhduOoqW1v3pJOsKq+IiBQmjZSKiBS5zz6zdUh37IDHH4cjjoi6R8XjjTdsfmNVlb+CR199\nBUceadsfdlj4/asvPvoIvv99OO44W2qnRYuoeyQiUj9ppFRERPZSXW1rYB51lK3r+NZbCkhdO+EE\nC0bfeMPf9uPG2TxeBaRuHX00zJhhz/v3h3/+M9r+iIhIZjRSKiJShCZNgl/8wkaM/vQnGDgw6h4V\nr7Fj4YUXbGmdVHbvhk6d4O9/V8XjML3yih375eXwhz/UVEoWEZHwaaRURKSe27XLAp5jj4Wf/ARu\nugnefVcBadi+/3348ENYsCD1di+/DG3bKiAN2xlnwJw5cPrpcOKJtp7sG2+A7ouLiOQvP0HpKGA+\nsAi4oY5t7o6/Pwvo76ZrIqlVVlZG3QUpMoV4TMViFhDdcAN06GDVSK+9FubPh3PO8TfPUYJp2tR+\n5pdeavN2PYnH09q1ts2vfpX7/tVHjRrB1VfD0qVw2mk277dXL6vUO39+1L3LXiGeoyS/6ZiSfJEu\nKG0A3IsFpj2AC4DutbY5FegEdAYuBx5w3EeRpHQiFdcK4ZiKxWxdxkcftSDoiCPgwgvtInzCBKis\ntPUvGzaMuqf1y/XXw8EHw+WX14zIecfT9u1w9tlw0UUWIEnuNG9uv5OqKnjgAfj8c/j2t6FnTwtU\n//EPu2FQKArhHCWFRceU5It0ly2DgMXA8vjXTwNnAZ8kbHMm8Ej8+QdAK6ANUECneRGR/FFdbRfP\nq1bZY+VKG/GpqoLZs6GszKqMDh9uo2/du2tENGqlpXajYMQIuP12uPFGez0Wg4svtvmNN98caRfr\ntZIS+3sZPtyWkPnoI7uB8/DDdnOneXPo08dGU8vLoX17aNfOHgcdZL9fEREJT7qg9DBgZcLXq4DB\nPrZph4JSCdHs2TZa9OabdW+Tbv6Qn/lFxbhNPvXF1Tau2pk3D557Lvh+9uyx+Z07d9rDe5747zff\nwNdf7/tYv95Gbg48sOaiuF07u1A+4wwr2tKmjYLQfNS8uc0bHTIE3n7bbiRMmmQFjt56S7+zfFFa\nauvLDh5sae+xGKxYYf+vzJljjwkTam4Kbd5sc4EPOAD222/fR1lZzaNRo73/9Z6XlLh5pPt/TyRT\nGzdG3QMRk+6/yHOw1N3L4l//AAtKr07Y5hXgdmBK/OtJwPXA9Fr7Wgx0DNJZERERERERyVtLsKmd\nGUk3UvoZ0D7h6/bYSGiqbdrFX6st486JiIiIiIhI/dYQi3bLgTJgJskLHY2PPx8CTM1V50RERERE\nRKT4nQIswNJv46UbuCL+8Nwbf38WMCCnvRMRERERERERERERERERERERERERERERERERERERERER\nERERERERERERERERERERERERERERERERERERERERERERERERERERERERERERERERERERERERERER\nEREREZGiMA5YC1T52PYnwGxgBvA+0Df++hHAx/HX5wLXuO+miIiIiIiIFKPjgP74C0pbJjw/A5gU\nf94o/gBoDiwH2jnqn4iIiIiIiORYaQ7behfYWOu1jsAEYBrwDtA1/vrmhG1aAF/Gn++KPwCaxp9v\nC6OzIiIiIiIiUnzK2Xuk9A2gU/z54PjXnquAxcAaoEPC6+2w1N5t8W1EREREREREfCmnJihtgQWW\nMxIec5N85gLgrSSvHwospCaoFREREREREUmpnJqgdD9gtY/PlAKb6nhvLHBu8G6JiIiIiIhIFPzM\nKW2PjVTOBeYA/5FkmwoscPRGPH/tY79fA8uoCSpLgD7x54mjn6dh6boAh2FzSQEOAIYlvCciIiIi\nIiJF6BCgX/x5C2AB0L3WNhXAy2n28xQ2MroTWAn8GBs5nQDMxIJeL5j9ExYAzwBepyZIPRGYFd9+\nBnBh5t+OiIiIiIiIFLIXgW/Xeq0CeCX3XREREREREZH6pBxYgY2YJhoBrMdGMccDPXLbLRERERER\nESl2LbD1RM9O8l5LoFn8+SlYVVwRERERERGRlEp8btcIeBWb//knH9svA44CNngvdOzYMbZkyZKM\nOygiIiIiIiIFYQlZLNnpJygtAR7B0nN/Xsc2bYB1QAwYBPwdS/VNFIvFYpn2T6ROY8aMYcyYMVF3\nQ4qIjilxSceTuKZjSlzTMSWulZSUgP+Bz39r6GObYcAPsKVXZsRf+yVwePz5g9iyLlcCu4FtwPcy\n7YiIiIiIiIjUP36C0smkX8/0vvhDRERERERExLd0waZI3qqoqIi6C1JkdEyJSzqexDUdU+KajinJ\nFxnn+wagOaUiIiIiIiJFKts5pRopFRERERERkcgoKBUREREREZHIKCgVERERERGRyCgoFRERERER\nkcgoKBUREREREZHIKCgVERERERGRyCgoFRERERERkcgoKBUREREREZHIKCgVERERERGRyCgoFRER\nERERkcgoKBUREREREZHIKCgVERERERGRyCgoFRERERERkcgoKBUREREREZHIKCgVkaIxdy4MHw6P\nPgq7d0fdGxGRaG3dCn/4A5x4Inz5ZdS9ERGpm4JSESkK69fDmWdCRQWMHQvdu8Ozz0bdKxGR3IvF\n4M47oWNH+OAD6NABzjsPdu2KumciIsmV+NimPfAocDAQA/4K3J1ku7uBU4BtwEXAjFrvx2KxWNYd\nFRGpy+7dMGoU9O8Pd9xhr1VWwujRUFUFhx0WafdERHJq0iS46ip47jno3Ruqq+GMMyxIveeeqHsn\nIsWspKQE/MWYe/EzUroL+DnQExgC/BToXmubU4FOQGfgcuCBTDsiIpKt666DRo3g9ttrXquogAsu\ngL/9LbJuiYhE4v774dprLSAFaNAAnnwSJk6E//3faPsmIpJMxlEs8CJwD/BGwmt/Ad4Cnol/PR8Y\nAaxN2EYjpSLi3IwZlrZbVQWtWu393pw5cPLJsHy5Ba0iIsVu1Sro0wdWrICWLfd+b8ECGDzY3tt/\n/2j6JyLFLcyR0kTlQH/gg1qvHwasTPh6FdAu086IiGRq7Fi47LJ9A1KAXr2gUyd4+eXc90tEJAp/\n+xt8//v7BqQAXbta0aOnn859v0REUmmYwbYtgH8A1wBbkrxfOyLeZ1h0zJgx/35eUVFBRUVFBs2L\niOxt+3a7uJo+ve5trrrKUtnOOSd3/RIRicKuXRaUTpxY9zaXXAI33wxXXJG7folI8aqsrKSysjLw\nfvwOrTYCXgUmAH9K8v5fgErAu/em9F0RCd2TT8Ijj8C//lX3Njt3whFHwJtvWkVeEZFi9eyzcN99\nVuitLtXVdk6cMKFmzqmIiCthpu+WAGOBeSQPSAFeBi6MPx8CfMXeAamIiHNjx9pd/1TKymybv/wl\nN30SEYnK/fdbdkgqDRrARRfBuHE56ZKIiC9+othjgXeA2dSk5P4SODz+/MH4v/cCo4CtwI+B2gl1\nGikVEWeWLYNBg6yoR+PGqbddvhwGDoR166BUqzOLSBFatQr69YPVq+1mXCpLlsCQIf7OnyIimch2\npNTPnNLJ+BtR/VmmjYuIZOuhh6yYh58LqvJyqzQ5fz706BF610REcm7yZDjuuPQBKdh6pb16wSuv\nwLnnht83EZF0NGYgIgWnuhoefhguvtj/Z4YNs4s2EZFiNHmynef8uuQSmwIhIpIPFJSKSMH56CPY\nbz/o29f/Z449FqZMCa9PIiJRmjLFznN+jR5tgeymTeH1SUTELwWlIlJwJkyAU0/N7DPHHquRUhEp\nTps2waJFMGCA/880a2Yjq5MmhdcvERG/FJSKSMH55z9h1KjMPtOtG2zcCGvWhNMnEZGoTJ0KRx3l\nbz5polNOsfOpiEjUFJSKSEH54gsrWJRJmhpY1d1hw5TCKyLFJ9PUXc+oUZZ5osURRCRqCkpFpKBM\nnAgVFZmPCIBSeEWkOE2enF1Q2qWLnUvnznXfJxGRTCgoFZGCMmGCpZxlQyOlIlJsdu2y4m/HHJP5\nZ0tKakZLRUSipKBURArGnj3wr3/BySdn9/mBA2HePNiyxW2/RESiMnMmdOgArVpl93nNKxWRfKCg\nVEQKxowZ0Lq1XYBlo0kT6N8fPvjAbb9ERKKSbequ5/jj4cMPdbNORKKloFRECkaQ1F2PUnhFpJhM\nmWLntWy1aAGDB8Obb7rrk4hIphSUikjByGYpmNpU7EhEikUsFnykFOy8qhReEYlSSQ7bisVUc1xE\nsrRpE7RrB+vWQdOm2e9n3TqrOLlxoxX5EBEpVCtXwtFH2/rLQc5nc+fCGWfA0qXu+iYi9VOJnYwy\nPiNppFRECsLkyTBoULCAFODgg6FxY1i92k2/RESiMmcO9O4d/AZbjx6wdSt8+qmbfomIZEpBqYgU\nhHfegeHD3eyrVy+7mBMRKWRz5tj5LKiSEju/vv128H2JiGRDQamIFIS334YRI9zsS0GpiBQDV0Ep\n2PlVQamIREVBqYjkvS1boKrKKkS6oKBURIqB66D0nXfc7EtEJFMKSkUk773/vq0vGnQ+qUdBqYgU\nuupq+OQTmw/qQs+esH69FU0SEck1P0HpOGAtUFXH+xXAJmBG/PFrJz0TEYl75x13qbtgF1/z5sGe\nPe72KSKSS0uXQps20LKlm/2VlsJxxymFV0Si4ScofQhItzLg20D/+OPWoJ0SEUnkssgRwH77wUEH\nwbJl7vYpIpJLLlN3PZpXKiJR8ROUvgtsTLONVvsTkVB88w18/DEMHep2v0rhFZFCpqBURIqJizml\nMWAoMAsYDzia3SAiAh9+aHOmXKWoeRSUikghCyMo7dvX5pSuW+d2vyIi6TR0sI/pQHtgG3AK8CLQ\nJdmGY8aM+ffziooKKioqHDQvIsXMdequp1cvGD/e/X5FRHJhzhz45S/d7rNBAxg2zM67557rdt8i\nUpwqKyuprKwMvB+/abflwCtAbx/bLgOOAjbUej0Wi8X890xEBBg5Eq6+Gs480+1+Z8yACy+0pWZE\nRArJjh3QqhVs3AhNmrjd9x13wKefwj33uN2viNQPJSUlkMXUThfpu20SGh4Uf147IBURydiuXTB1\nqlWEdK1bN1i8GHbudL9vEZEwLVwI5eXuA1LQeqUiEg0/6btPASOAg4CVwM1Ao/h7DwLnAlcCu7EU\n3u+576aI1EfTp8ORR8IBB7jfd9OmcPjhsGiRLREjIlIowphP6hkwAJYvhw0boHXrcNoQEanNT1B6\nQZr374s/REScevvtcOaTerxiRwpKRaSQhBmUNmwIQ4bAu+/CWWeF04aISG0u0ndFRELxzjuWShYW\nVeAVkUIUZlAKWhpGRHJPQamI5KXqapg8OZz5pJ58CUr37Im6ByLiVz78vSooFZFio6BURPLS7Nlw\nyCHQpk14bfTsGX1Q+vzzdnG5ZUu0/RCR9JYuhfbtoz1vbN0Kq1dDx47htXH00VZMadOm8NoQEUmk\noFRE8lLYqbsAnTrBypXRVeD95hu47jpb2uEXv4imDyLiT3W1LSNVXg7XXgtRrXK3aJEFpA1drDRf\nh7IyGDTIslVERHJBQamI5KWwixyBXXi1b2+jH1G46y7o3x8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PJwVo2dLWcF2xInhf5s7N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"text": [
"<matplotlib.figure.Figure at 0x7fd5ba91e190>"
]
}
],
"prompt_number": 121
}
],
"metadata": {}
}
]
}
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