{ "metadata": { "name": "", "signature": "sha256:8c8ab14e1aa7498b6a4c4a592eb9c7f600010b5ffa93376676a9020bc2e7dccb" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "La radiaci\u00f3n del cuerpo negro y el fondo c\u00f3smico de microondas (CMB) en Python: parte II" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Autor: [Eduardo Mart\u00edn Calleja](http://balbuceosastropy.blogspot.com.es/)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "En este post, continuaci\u00f3n del [anterior](http://balbuceosastropy.blogspot.com.es/2013/09/la-radiacion-del-cuerpo-negro-y-el.html) examinaremos con ayuda de c\u00f3digo escrito en Python la representaci\u00f3n gr\u00e1fica del espectro de radiaci\u00f3n t\u00e9rmica de un cuerpo negro a la temperatura de 2.725K. A continuaci\u00f3n incluiremos en este gr\u00e1fico los resultados de las mediciones del espectro de la radiaci\u00f3n del fondo c\u00f3smico de microondas (CMB) por el dispositivo FIRAS del sat\u00e9lite Cosmic Background Explorer [COBE](http://lambda.gsfc.nasa.gov/product/cobe/), para comprobar la exquisita precisi\u00f3n del ajuste de los datos reales al espectro de un cuerpo negro a la temperatura indicada.\n", "\n", "En particular tratar\u00e9 de aclarar al m\u00e1ximo mediante ejemplos un aspecto que personalmente me ha resultado algo complejo. Se trata de los diferentes sistemas de unidades en los que se puede presentar el gr\u00e1fico del espectro de la radiaci\u00f3n t\u00e9rmica del CMB" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Importaciones y referencias" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "\n", "from __future__ import division\n", "\n", "import quantities as pq\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "\n", "# Generar un cuadro con versiones de las librer\u00edas utilizadas en este notebook\n", "#https://github.com/jrjohansson/version_information\n", "%load_ext version_information\n", "%version_information numpy, matplotlib, quantities, pandas" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
SoftwareVersion
Python2.7.9 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)]
IPython2.3.1
OSLinux 3.13.0 44 generic x86_64 with debian jessie sid
numpy1.9.1
matplotlib1.4.2
quantities0.10.1
pandas0.15.2
Sat Jan 24 00:01:48 2015 CET
" ], "json": [ "{\"Software versions\": [{\"version\": \"2.7.9 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)]\", \"module\": \"Python\"}, {\"version\": \"2.3.1\", \"module\": \"IPython\"}, {\"version\": \"Linux 3.13.0 44 generic x86_64 with debian jessie sid\", \"module\": \"OS\"}, {\"version\": \"1.9.1\", \"module\": \"numpy\"}, {\"version\": \"1.4.2\", \"module\": \"matplotlib\"}, {\"version\": \"0.10.1\", \"module\": \"quantities\"}, {\"version\": \"0.15.2\", \"module\": \"pandas\"}]}" ], "latex": [ "\\begin{tabular}{|l|l|}\\hline\n", "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n", "Python & 2.7.9 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)] \\\\ \\hline\n", "IPython & 2.3.1 \\\\ \\hline\n", "OS & Linux 3.13.0 44 generic x86\\_64 with debian jessie sid \\\\ \\hline\n", "numpy & 1.9.1 \\\\ \\hline\n", "matplotlib & 1.4.2 \\\\ \\hline\n", "quantities & 0.10.1 \\\\ \\hline\n", "pandas & 0.15.2 \\\\ \\hline\n", "\\hline \\multicolumn{2}{|l|}{Sat Jan 24 00:01:48 2015 CET} \\\\ \\hline\n", "\\end{tabular}\n" ], "metadata": {}, "output_type": "pyout", "prompt_number": 1, "text": [ "Software versions\n", "Python 2.7.9 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)]\n", "IPython 2.3.1\n", "OS Linux 3.13.0 44 generic x86_64 with debian jessie sid\n", "numpy 1.9.1\n", "matplotlib 1.4.2\n", "quantities 0.10.1\n", "pandas 0.15.2\n", "Sat Jan 24 00:01:48 2015 CET" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "En esta entrada vamos a utilizar la funci\u00f3n que definimos en el anterior post para calcular la radiancia espectral seg\u00fan la f\u00f3rmula de Plank" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def B(wl,T):\n", " '''wl es un array de longitudes de onda con unidades de longitud\n", " T es una temperatura expresada en Kelvin\n", " el resultado es un array de r.e. con unidades W/(m**2 * nm * sr)\n", " '''\n", " I = 2 * pq.constants.h * (pq.c)**2 / wl**5 * \\\n", " 1 / (np.exp((pq.constants.h*pq.c \\\n", " / (wl*pq.constants.k*T)).simplified)-1)\n", " return I.rescale(pq.watt/(pq.m**2 * pq.nm *pq.sr))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Radiaci\u00f3n del cuerpo negro para T = 2.725K" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Caso 1. Unidades: $\\lambda$ en mm y B en $W m^{-2} mm^{-1} sr^{-1}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ya se ha avanzado que el fondo c\u00f3smico de micrrondas constituye un ejemplo perfecto de radiaci\u00f3n de cuerpo negro correspondiente a una temperatura de 2.725K. Vamos a representar gr\u00e1ficamente la curva de la radiancia espectral correspondiente a esta temperatura para hacernos cargo de las magnitudes. En primer lugar, y para hacernos idea del rango de magnitudes en que nos movemos, calculemos la longitud de onda en la que alcanza su m\u00e1ximo, para lo que utilizaremos la ley de Wien:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "TCMB = 2.725 *pq.K\n", "lmax = pq.constants.b / TCMB\n", "print lmax.simplified" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0.0010634012844 m\n" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Es decir, los fotones del CMB poseeran una longitud de onda de aproximadamente un mil\u00edmetro. Con esta informaci\u00f3n podemos asignar un rango de valores a las longitudes de onda para el c\u00e1lculo de la curva de la radiancia espectral, y ajustar las unidades de B:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "wl = np.arange(0.1,10,0.1) * pq.mm\n", "I = B(wl,TCMB).rescale(pq.watt/(pq.m**2 * pq.mm * pq.sr))\n", "\n", "fig, ax = plt.subplots(figsize=(10, 8))\n", "ax.plot(wl, I*1e7)\n", "ax.set_title('Espectro del cuerpo negro para T = 2.725 K \\\n", "\\n (Longitudes de onda en mm)')\n", "ax.title.set_fontsize(20)\n", "ax.set_xlabel('Longitud de onda en mm')\n", "ax.xaxis.label.set_fontsize(15)\n", "ax.set_ylabel('Radiancia espectral ($10^{-7} W m^{-2} mm^{-1} sr^{-1}$)')\n", "ax.yaxis.label.set_fontsize(15)\n", "ax.grid()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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sCvykWhySVq3Yf78GTabUO1RPb+EppM+0E8oTvSWtQxoerYzzWeCPwKRs7qt+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\nGaGYfObMit5WSmTWLNhxR3jrLejePe5oRESkmlRsEXN3f83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"text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Caso 2. Unidades: $\\nu$ en GHz y B en $W m^{-2} GHz^{-1} sr^{-1}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A menudo nos encontraremos con gr\u00e1ficos en que B viene expresado en funci\u00f3n de la frecuencia $\\nu$ medida en $Hz$ en lugar de obtenerla en funci\u00f3n de la longitud de onda $\\lambda$ como hemos estado haciendo hasta ahora. La f\u00f3rmula de Plank se escribe en este caso:\n", "\n", "$$B_\\nu(T) = \\frac{2 h \\nu^3}{c^2} \\frac{1}{e^{\\frac{h \\nu}{k_B T}}-1}$$\n", "\n", "Donde $\\nu$ es la frecuencia de la radiaci\u00f3n, medida en $Hz$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Escribamos la funci\u00f3n para calcular B de acuerdo con la f\u00f3rmula anterior:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def B_f(wf,T):\n", " '''wf es un array de frecuencias con unidades en GHz\n", " T es una temperatura expresada en Kelvin\n", " el resultado es un array de radiancias espectrales\n", " con unidades W/(m**2 x GHz x sr)\n", " '''\n", " wf = wf.rescale(pq.hertz)\n", " I = 2 * pq.constants.h * wf**3 / pq.c**2 * 1 \\\n", " / (np.exp((pq.constants.h*wf \\\n", " / (pq.constants.k*T)).simplified)-1)\n", " return I.rescale(pq.watt/(pq.m**2 * pq.gigahertz *pq.sr))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hagamos una prueba de la funci\u00f3n:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "B_f(10**13*pq.hertz, 7000*pq.K)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 6, "text": [ "array(0.20777704540401157) * W/(m**2*sr*GHz)" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Y construyamos la gr\u00e1fica:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "wf = np.arange(0.1,1000,1)* pq.gigahertz\n", "I = B_f(wf,TCMB)\n", "\n", "fig, ax = plt.subplots(figsize=(10, 8))\n", "ax.plot(wf, I*10**9) # Escalamos las unidades\n", "ax.set_title('Espectro del cuerpo negro para T = 2.725K \\\n", " \\n (Frecuencias en GHz)')\n", "ax.title.set_fontsize(20)\n", "ax.set_xlabel('Frecuencia ($GHz)$')\n", "ax.xaxis.label.set_fontsize(15)\n", "ax.set_ylabel('Radiancia espectral $(10^{-9} W m^{-2} GHz^{-1} sr^{-1})$')\n", "ax.yaxis.label.set_fontsize(15)\n", "ax.grid()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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qp2w7L5KuZ3wi8M86p8WpFtO82bLOJlseC5TPhbc1KdFs+EkdZs1OEc15ElF2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"text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Caso 3. Unidades: $\\nu$ en $cm^{-1}$ y B en $W / (m^{2} cm^{-1} sr)$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "El hecho es que la unidad preferida de frecuencias cuando se trata de representar los valores de las frecuencias del CMB es el \"n\u00famero de onda k\", que expresa el n\u00famero de longitudes de onda en una unidad de distancia. Se expresa normalmente en unidades de \"ciclos / cm\", o bien $cm^{-1}$ al ser el n\u00famero de ciclos una magnitud sin dimensi\u00f3n. Veremos a continuaci\u00f3n como se pueden hacer las conversiones de GHz a ciclos / cm" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Conversi\u00f3n de 160 GHz en cm**(-1)\n", "\n", "frec = 160 * pq.gigahertz\n", "wl = pq.c / frec\n", "print 'longitud de onda en cm = ', wl.rescale(pq.cm)\n", "k = 1/( wl.rescale(pq.cm))\n", "print u'n\u00famero de onda en ciclos por cm = ', k" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "longitud de onda en cm = 0.18737028625 cm\n", "n\u00famero de onda en ciclos por cm = 5.33702552317 1/cm\n" ] } ], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "# La conversi\u00f3n se puede hacer de forma m\u00e1s abreviada\n", "# simplemente dividiendo por la velocidad de la luz:\n", "fec_en_wave_number = (frec/pq.c).rescale(1/pq.cm)\n", "print fec_en_wave_number" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "5.33702552317 1/cm\n" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Como curiosidad, la unidad de frecuencia 1/cm es denominada, en el sistema cgs de unidades, un \"kayser\"." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "La ley de Plank se escribe de forma diferente de la anterior cuando la frecuencia se introduce en ciclos por unidad de longitud ($k$). Su forma en este caso es la siguiente:\n", "\n", "$$B_k(T) = 2 h c^2 k^3 \\frac{1}{e^{\\frac{h c k}{k_B T}}-1}$$\n", "\n", "Aviso: no se debe confundir la unidad n\u00famero de onda (ciclos por unidad de longitud) con la unidad de n\u00famero de onda angular, que se suele representar tambi\u00e9n con el s\u00edmbolo $k$ pero cuyo valor es $2 \\pi$ veces la unidad anterior.\n", "\n", "Definiremos a continuaci\u00f3n una funci\u00f3n para calcular la radiancia espectral seg\u00fan la f\u00f3rmula anterior." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def B_k(wk,T):\n", " '''wk es un array de frecuencias con unidades en cm^-1\n", " T es una temperatura expresada en Kelvin\n", " el resultado es un array de radiancias espectrales\n", " con unidades W/(m**2 x cm**(-1) x sr)\n", " '''\n", " wk = wk.rescale(1/pq.m)\n", " I = 2 * pq.constants.h * pq.c**2 * wk**3 * 1 \\\n", " / (np.exp((pq.constants.h*pq.c*wk \\\n", " / (pq.constants.k*T)).simplified)-1)\n", " return I.rescale(pq.watt/(pq.m**2 * pq.cm**(-1)*pq.sr))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Una primera comprobaci\u00f3n:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "f = 5.35 * pq.cm**(-1)\n", "B_k(f, TCMB)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 11, "text": [ "array(1.1502029877502701e-07) * cm*W/(m**2*sr)" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Y a continuaci\u00f3n obtendremos el correspondiente gr\u00e1fico en las nuevas unidades" ] }, { "cell_type": "code", "collapsed": false, "input": [ "wk = np.arange(0.1,20,0.1) / pq.cm\n", "I = B_k(wk,TCMB)\n", "I = I*10**7 # Expresamos las unidades en m\u00faltiplos de 10^(-7)\n", "\n", "fig, ax = plt.subplots(figsize=(10, 8))\n", "ax.plot(wk, I)\n", "ax.set_title('Espectro del cuerpo negro para T = 2.725K \\\n", " \\n (Frecuencias en $cm^{-1}$)')\n", "ax.title.set_fontsize(20)\n", "ax.set_xlabel('Frecuencia (ciclos / cm )')\n", "ax.xaxis.label.set_fontsize(15)\n", "ax.set_ylabel('Radiancia espectral $(10^{-7}W m^{-2} (cm^{-1})^{-1}sr^{-1})$')\n", "ax.yaxis.label.set_fontsize(15)\n", "ax.grid()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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VFykmVeREREREKpRy5ERERETKgHLkRERERGpIi6QDECkXo0ePplevXr8/njcP\nJk2CDz+EqVPhyy/BLNxat4ZVVoHVVoM114SFF04sbElAelkRaYjKixSTKnIiKX74AUaMgMceg9Gj\nYdlloWtXWHllWG65sE1dHcyYAS+9BO+/Hyp5G20EW24Ju+8OHTsm+QpERKSWKEdOBHj7bRg2DO68\nE7bYAnbZJdz/6U+NP/e770Kl74kn4H//gz//GQ48EHbdFVrop5KIiOSokBw5VeSkpk2fDqedBg88\nAAMGhArY8ssXvr9ffoH774crrghdsaeeCnvuqQqdiIg0ToMdRHJUVweXXAJrrRXy3d59F3r2HN2k\nShzAIovAHnvA2LFw9dVw3XWwzjowalQ8cUt50Lxgkg+VFykmtRNIzfnsM+jfH37+OeS5rbZa/Mcw\nC12zvXuHFrp994XNN4cLLwx5dyIiInFQ16rUlKefhr33Dt2oJ59cui7PH3+EwYPh9tvhhhtg221L\nc1wREakcypFLo4qcpLruupCzdtdd0LNnMjGMGQP//GcYTHHuuaErVkREBJQjJ5KRO5x0Epx/fshd\ny1aJK0Uey+abw8SJ8Mknodt1+vSiH1KKQDlPkg+VFykmVeSkqrnDUUfByJHwwgvQpUvSEcHSS8M9\n98A228AGG8CrryYdkYiIVCp1rUrVcodjj4Vnn4WnngqjU8vNvffCIYfA8OGw/fZJRyMiIklS16pI\nin/9K0zU++ST5VmJg5Ar98gjcNBBcMstSUcjIiKVRhU5qUrXXBNau556Ctq0ye05SeWx9OgR5pn7\n97/h4osTCUHypJwnyYfKixST5pGTqvPUU3D66fDcc7DMMklHk5s11gjx9ukD8+bBccclHZGIiFQC\n5chJVXn7bejVKwwm2GyzpKPJ32efhfiPOAKOPjrpaEREpJQKyZFTi5xUjR9+CDln559fmZU4gBVX\nDN2svXpB8+YwcGDSEYmISDlTjpxUBXc49FDYZJNw+a1ClEsey0orhelSLrggXAlCyk+5lBWpDCov\nUkxqkZOqcMMN8Prr8PLLSUcSj44d4bHHwvVa27aFvn2TjkhERMqRcuSk4k2aFK6SMHZsGDRQTcaN\ng512ClOU9OiRdDQiIlJMmkdOas6cObDvvnD22dVXiYPQVXzDDbDzzuGyXiIiIqlUkZOKdv75oevx\nwAObvq9yzWPZYYdwhYq//jUM6JDklWtZkfKk8iLFpIqcVKxJk+CSS+C668DyaoiuPEcfDRtuCHvu\nGeaZExG9N9LNAAAgAElEQVQRAeXISYWaOzdUbA49NJ7WuEowZ04Y9NCjB5x7btLRiIhI3JQjJzXj\niitgqaXggAOSjqR0WraEu+6CESPChMciIiKqyEnFmT4dzjwzVObi7FKthDyWtm1DJe7QQ8NVLCQZ\nlVBWpHyovEgxqSInFeeEE2D//WH11ZOOJBnrrw//+U8Yyfr990lHIyIiSVKOnFSUsWNh771h8mRY\nfPGko0nWIYfArFlwxx3VP9hDRKQWKEdOqtq8eTBgAFx4oSpxEEbsTp4M116bdCQiIpIUVeSkYtx8\ncxjgsNtuxdl/peWxtGoVBj/8+9/h8mRSOpVWViRZKi9STKrISUWYPRtOOy3khqkb8Q9du4aWud13\nD+dIRERqi3LkpCKccw68+ircfXfSkZSnf/wDWreGyy9POhIRESlUITlyqshJ2ZsxI4xQff556NIl\n6WjK03ffwTrrhKtc9O2bdDQiIlIIDXaQqnT22aHrsNiVuErOY2ndGm68MUyQ/M03SUdT/Sq5rEjp\nqbxIMakiJ2Vt+nS46SY49dSkIyl/ffqEgSCHHQZqiBYRqQ3qWpWydtRR0KwZXHRR0pFUhp9/DhMG\nn3JKmG9PREQqh3Lk0qgiV9mmT4du3cKlqJZbLuloKseECdCvXxgcstJKSUcjIiK5Uo6cVJXzzoP+\n/UtXiauWPJb11oNBg8K5q6tLOprqVC1lRUpD5UWKSRU5KUvTp8Ott4brqkr+TjwxdLNqOhIRkeqm\nrlUpS8cdB3PnhslupTDvvgubbBK6WDt2TDoaERFpjHLk0qgiV5m++w5WXRUmTlSOV1OddVaYf+/h\nh3VFDBGRcqccOakKV18N221X+kpcNeaxHH88fPIJjBiRdCTVpRrLihSPyosUU4ukAxBJ9euvMGwY\nPPFE0pFUh4UWguuvh512gq23hmWWSToiERGJU2xdq2bWCWgHGPANMM3df45l54XHpK7VCnPDDeF6\nqo89lnQk1eWoo0KX9U03JR2JiIhkU9IcOTNrBuwG/APoBHwFzAR+A9oAS0d/Pwlc7u7fFXSgJlBF\nrrLU1cGaa8JVV0Hv3klHU11+/DHMyXf99bDVVklHIyIimZQsR87M1gP+B7QGDnb3td29j7vv5u57\nu/u27r4h0Bd4CRhmZscUciypHY88AosvDr16JXP8as5jWXzxkHt46KEwe3bS0VS+ai4rEj+VFymm\nvCtyZrYZ0Af4m7tf4+7Ts23r7j+7+1Puvg/wkpkNLjxUqXbDhoUuQI2uLI5ttoENN4TTT086EhER\niUveXatmtpS7zyroYE14boHHU9dqhZg8OXSnfvwxLLxw0tFUr6+/hrXWgiefhHXXTToaERFJVZKu\n1aZUxEpZiZPKcvnlcPDBqsQVW7t2MHQoDBgA+o0jIlL5NI+cJG7WLLjjjpC/laRayWM58MBw+a7b\nbks6kspVK2VF4qHyIsWkipwk7sYboW9fWH75pCOpDc2bw5VXhuuxzlIbuYhIRWvyPHJm1s3d34op\nnlgpR6781dVB165w882w8cZJR1NbDjoIFltM17MVESkXRZtHzsw6ZFsFHOnux+Vz0FJRRa78PfVU\nuIzUa69ptGqpzZgR5u17+mlYZ52koxERkWIOdjgQGAncnHa7CdgjnwPmwsyGm9mXZvZmA9sMM7P3\nzex1M/tz3DFIaVx7LRxySHlU4motj6VtWxgyBI44QgMf8lVrZUWaRuVFiimnipy7nwYMc/fe6Tfg\nvCLEdSPQL9tKM9sWWM3dOwMHA1cVIQYpsi+/DC1ye+2VdCS16+CDwwTBt9+edCQiIlKInHPkzGwx\nd/8pw/KW7j4n9sDCtVsfcve1M6y7Ghjl7ndGj98BNnf3L9O2U9dqGTvvPHjvvXB9VUnOCy/ArruG\nufyWWirpaEREaldR55FLr8SZWftoeeyVuBysAHya8vgzYMUE4pAC1dWF634efHDSkchGG4WrPgwZ\nknQkIiKSr6ZMPxJ7blye0musanqrIKNHQ6tW0KNH0pH8oZbzWM4+G265JbSQSuNquaxI/lRepJha\nJB1AgT4HVkp5vGK0bAH9+/enU6dOALRu3Zru3bvTK7oqe/2bS49L//jaa6F379GMGVMe8QBMnDgx\n0eMn+bh9e9hll9Hstx+MG5d8PHqsx3qsx7XwuP7vqVOnUqiC55Ezs0HufmnBR258/53IniO3LTDA\n3bc1sw2BS9x9wwzbKUeuDM2cCSuvDFOnQps2SUcj9X75JUxHct110KdP0tGIiNSeQnLkyrJFzszu\nADYH2prZp8DpQEsAd7/G3R81s23N7APgJ2C/5KKVfI0YEXKyVIkrL4ssAuefD8ccAxMmhCtAiIhI\neWuWdACZuPue7r68uy/k7iu5+/CoAndNyjYD3H01d1/X3SckGa/k5+abYd99k45iQalN3bVq113D\nyNXhw5OOpLyprEg+VF6kmJpSkVOfpeRt8mT49FPYaqukI5FMzODii+G00+D775OORkREGtOUHLmF\n3f3XmOOJlXLkys9JJ4WpR84/P+lIpCH77Qft28O55yYdiYhI7SjatVZzOPCuwAbAUHf/sck7jIkq\ncuVl3jzo2BGeeAK6dUs6GmnItGnh+qvjx4eBKSIiUnxFnRC4EesTKnKdY9qfVKFnnoE//al8K3HK\nY/nD8svDUUfBiScmHUl5UlmRfKi8SDHFVZH7FOjl7q/FtD+pQuU6yEEyO/ZYeOklGDcu6UhERCSb\nuLpWuwBDgOuAF9z95ybvNAbqWi0fP/0EK6wA778P7dolHY3k6tZb4aqrQmXO8mrsFxGRfCXZtToY\n+A64AJhpZi+Y2blmtmlM+5cK9+CDsPHGqsRVmr33htmz4f77k45EREQyiasiNwm4xt3XA5YDzoz2\nfXRM+5cKd8cdsNdeSUfRMOWxLKhZMzjvvDDaeM6cpKMpHyorkg+VFymmWCpy7n42sKSZ/d3dZ7n7\nI+5+grvvGsf+pbJ98w2MGQM77ph0JFKIrbeGDh3g+uuTjkRERNLFlSO3KNDB3d9pekjxUY5cebj2\n2jBi9c47k45ECjVhAmy3Hbz3HiyxRNLRiIhUpyRz5E4C7jOzFcxsiJm9aWbnmZmu1ij897/l360q\nDVtvPejTBy68MOlIREQkVVwVuS/dfQ1gReDfwMHAjdHfUsM++wzefBP69Us6ksYpj6VhZ54Jl10G\nX3yRdCTJU1mRfKi8SDHFVZFrb2bNgJ2ASe7+QtTN+m1M+5cKddddsPPOsPDCSUciTdWpE/TvD0OG\nJB2JiIjUiytHrhtwLdANOMTd7zSzNYCN3f2GJh+g8LiUI5ewDTeEoUNDwrxUvm++gdVXh+eeg65d\nk45GRKS6JHat1QyBLA18BfzH3U+O/QC5x6GKXII++STkVk2fDi1bJh2NxOX88+HFF+Hee5OORESk\nuiQ52GE+7j4T6AIMLcb+pTLcfXeYcqRSKnHKY8nNkUfCyy/D+PFJR5IclRXJh8qLFFNRKnIA7j6l\nXC7VJcm4+27Ybbeko5C4tWoFp54Kp5ySdCQiIlKUrtVyoa7V5Hz6KXTvHkY4VkqLnORuzhxYYw24\n7jro3TvpaEREqkPJu1ajQQ4iC7jnnsrqVpX8tGwZRq+ecgrot5KISHIarciZWYcst47AfiWIUSrQ\n//5Xed2qymPJzx57wA8/wMMPJx1J6amsSD5UXqSYWuSwzYHAXsCnGdZ1Bo6LNSKpeJ9/Du+8E64E\nINWreXM466zQKrfddtCsaBm3IiKSTU45cmY20N2HZVh+pLtfVpTIYqAcuWRcfnkY0XjzzUlHIsXm\nDhttBIMGwZ57Jh2NiEhlK9o8cma2mLv/lGF5S3efk88BS0kVuWRsuSUMGAA77ZR0JFIKI0fCIYfA\n228rJ1JEpCmKNtghUyUuWl62lThJxsyZoTWuEq/koDyWwmyxBXTsCDfdlHQkpaOyIvlQeZFiKiir\nxczaxx2IVIdHHglf7IsumnQkUkpnnRUuxfbLL0lHIiJSWwqaR87MBrn7pUWIJ1bqWi29XXYJ047s\nu2/SkUip7bwz9OwJRx+ddCQiIpWpZNdaVUVOMpk9G/70J5gyBZZZJulopNQmTQojlT/4AJZYIulo\nREQqT9lca1Vq01NPwfrrV24lTnksTbPWWiE38uKLk46k+FRWJB8qL1JMqshJbO67L3SvSe0aPBiG\nDYNvvkk6EhGR2qCuVYnF3Lmw3HIwYQJ06JB0NJKkww4LXavnn590JCIilaWUXauqHcl8nn8eVlpJ\nlTiBU0+FG26AadOSjkREpPoVWpG7JtYopOI9/DBsv33SUTSN8ljisfzysN9+cO65SUdSPCorkg+V\nFymmgipy7v5r+jIz62RmfzGzHma2qpm1anp4UikeeqjyK3ISnxNOgNtvh88+SzoSEZHqVlCOHICZ\nNQN2A/4BdAK+AmYCvwFtgKWjv58ELnf372KIN98YlSNXAh98AJttBp9/rgunyx9OOgm+/x6uvDLp\nSEREKkMp55FbDziFUEl70N2nZ9muFbAp8E9gortflPfBmkAVudK45JIwh9j11ycdiZSTGTOga9cw\nAKZjx6SjEREpfyUZ7GBmmwF9gL+5+zXZKnEA7v6zuz/l7vsAL5nZ4HyPJ+WvWrpVlccSr7ZtwwjW\ns85KOpL4qaxIPlRepJgK6Qh7w93/k29Tl7uPA2pgqtDaMmsWjB8PW26ZdCRSjo45Bu69N1ztQ0RE\n4ldwjlwlUNdq8d15J9x8Mzz6aNKRSLkaPBg++QSGD086EhGR8lZI12qLYgUjtaEaph2R4jrqKOjc\nGd5/P9yLiEh8NMZQCjZvHjz+OGy3XdKRxEN5LMXRujUMGgRDhyYdSXxUViQfKi9STE2uyJlZtzgC\nkcozYQIsu6yu5iCNGzgQnngCJk9OOhIRkeqSU46cmWX7qjbgSHc/LtaoYqIcueI64wz49lu4qKST\nykilOvdceP11uOOOpCMRESlPRZtHzsyGAnsBn2ZY3dndV8znoKWiilxxbbopnHYabL110pFIJfjx\nR1h1VXjmGVhrraSjEREpP0WbR87dTwOGuXvv9BtwXiHBSmX79lt44w3o2TPpSOKjPJbiWnxxOP54\nGDIk6UiaTmVF8qHyIsWUT47cDVmWXx1HIFJZnnkmtMgtskjSkUglOfxweO650MUqIiJN15RrrbZ3\n9y9jjidW6lotngMPhLXXDqMRRfJxySUwZgzcd1/SkYiIlJeSXKIrxR5NeK5UMPcwArFfv6QjkUp0\nyCHw8svw6qtJRyIiUvk0j5zk7e23oUUL6NIl6UjipTyW0mjVCk46qbJz5VRWJB8qL1JMqshJ3h5/\nPLTGWV6NvyJ/OOig0CI3YULSkYiIVLam5MgNcvdLY44nVsqRK46ttoIjjoCddko6Eqlkw4aFQTMP\nPJB0JCIi5aHUOXJSg376CV58EbbYIulIpNIddBCMHw+vvZZ0JCIilaspFTk1ddWgMWNg/fVhySWT\njiR+ymMprVat4MQTKzNXTmVF8qHyIsXUlIrcNbFFIRWjPj9OJA4HHxxGsE6cmHQkIiKVqeAcuUqg\nHLn4dekCd94Jf/5z0pFItbjkEhg7Fu69N+lIRESSVTY5cma2sZkdaWatirF/ScaUKfD997DuuklH\nItXkkEPghRd0tQcRkULEUpEzs/XM7DIzG2pmvYAXgOHAgDj2L+XhiSegb19oVqVDZJTHkoxWrcI1\nWIcOTTqS3KmsSD5UXqSY4vpKPhZ4C2gBXAh8CVwFrBfT/qUMKD9OiuXQQ+H55+GNN5KORESkssSS\nI2dmh7r71SmPuwDbAM+6e2JTfipHLj6//Qbt2sGHH0LbtklHI9XowgtDF+vddycdiYhIMpLMkasz\ns3b1D9z9PXe/NMlKnMTr+eeha1dV4qR4Dj0UnnsO3nwz6UhERCpHXBW5McAjZna4ma0R0z6ljDz1\nFGy9ddJRFJfyWJK12GJw3HGVkSunsiL5UHmRYoqrInc2oTLXG3jKzL42s3vNrH9M+5eEjRwJffok\nHYVUu8MOg2efhUmTko5ERKQyxJUjd4i7X5PyeDWgJ9DF3U9q8gEKj0s5cjH4/ntYYQX4+mtYZJGk\no5Fq95//wCuvhPkKRURqSSE5ci1iOnYrM1vE3X8BcPcPgA9i2rckbOxY6NFDlTgpjcMPh1VWgbfe\ngm7dko5GRKS8xdW1Ogp4zMx6m1nLmPYpZeKZZ2qjW1V5LOVhscXg2GPhjDOSjiQ7lRXJh8qLFFNc\nFbnTgI+By4FZZjbKzAab2V9i2r8kaORI2GKLpKOQWnL44TBqFLz9dtKRiIiUt7hy5E4BbnP3j6Np\nSHoCmwOruPtfC9xnP+ASoDlwvbufl7a+LXAbsByhi/gCd78pbRvlyDXR119D584wYwa0iKsjXiQH\n554bLtt1xx1JRyIiUhqF5MjFVZFbHtgC+MDdX4yWbeTuLxS4v+bAu8CWwOfAeGBPd5+css1gYGF3\nPzmq1L0LtHf3uSnbqCLXRHfdBbfeCg89lHQkUmt++AFWXRXGjIE1NKmRiNSAJCcEHgBcDSyUsqyD\nma1f4P56ECqFU919DjAC2DFtm+nAktHfSwLfpFbiJB611K2qPJbyssQScPTR5Zkrp7Ii+VB5kWKK\nqyL3GbCcu4+tX+DudwKbFbi/FYBP0/a/Qto21wHdzGwa8DowqMBjSQNqZaCDlKcBA+Dpp+Gdd5KO\nRESkPMVVkesMZGoN+7nA/eXSH/ovYKK7Lw90B64wsyUKPJ5k8Mkn8N13sNZaSUdSGr169Uo6BEmz\nxBJw1FHl1yqnsiL5UHmRYoorfX0EMM7MzgQejrpDAToWuL/PgZVSHq9EaJVLtTFwFoC7f2hmHwFd\ngVdSN+rfvz+dOnUCoHXr1nTv3v33N1V9c7ceZ3585ZWjWWstaNasPOLR49p8PGBAL1ZdFW65ZTQd\nOiQfjx7rsR7rcVyP6/+eOnUqhYplsAOAmW0ODAf+BLwPLAIMdve8x5yZWQvC4IU+wDTgZRYc7HAR\nMMvdh5hZe+BVYB13n5myjQY7NME++8Amm8AhhyQdSWmMHj369zeZlJezzgrdq7femnQkgcqK5EPl\nRXKV5JUdcPcxZtYZ2ISQz/aqu79f4L7mmtkA4AnC9CM3uPtkMzskWn8N4fquN5rZ64Qu4hNSK3HS\nNO5hoMNppyUdiQgceWQYwfree9ClS9LRiIiUj9ha5MqRWuQK9+67sNVW8PHHYHn9NhApjjPPDBW5\nW25JOhIRkeIoyfQjZra1mfUo4HlLm9kJ+T5PklE/7YgqcVIujjwSHnssVOZERCTIuyLn7k8Cq5jZ\nRWa2emPbm9liZjaIMMr0kgJilASMHFl7046kJp9K+VlqKRg4MOTLJU1lRfKh8iLFVFCOnLuPMLNR\nwElmti4whTDAYRZhGpI2wLKEaUF+BC5090vjCVmKra4uXOfyElW7pcwMHAirrQYffBDuRURqXZNz\n5MzMgHWBbkA7YGFgBvAx8Ly7z25qkE2ITTlyBZg4EfbYQ5OwSnkaMgQ++ghuuinpSERE4pXIqNWo\npjQxukkVeOaZ2rksl1SeQYNCa9yHH4aRrCIitSzvHDmpfrV0fdVUymOpDK1bh0t3JZkrp7Ii+VB5\nkWJSRU7mM3cuPPccaO5KKWdHHQUPPhha5UREapnmkZP5jB8PBxwAb7yRdCQiDRs8OFwPePjwpCMR\nEYlH0eaRi6YQudTMHjSzQdEltDCzXcxsSCHBSnkaOxZ69kw6CpHGqVVORCT3rtUrgPeAa4C2wN1m\ntqS73wscXqzgpPTGjKndipzyWCpLkrlyKiuSD5UXKaZcR60+7+7XRn8/YmbLAf82s3OLFJckoK4u\n5Mdde23j24qUg6OO0ghWEaltOeXImdkBwOvAP4DT3P37qHt1f8Jkv0sUN8zCKEcuP2+8AbvtFq6z\nKlIplCsnItWiaPPIufsNZtYTeI1wpQbcfS5wrZl9knekUpaUHyeVqL5VTld7EJFalPP0I+4+1t1v\ndvc6ADNrHy1/vFjBSWnVcn4cKI+lUrVuDUceWdpcOZUVyYfKixRTU+aR2yO2KCRx7mqRk8o1aBA8\n9FBolRMRqSUFzyNnZoPc/dKY44mVcuRy9+670LcvTJ2adCQihRkyJJTfG29MOhIRkcIkcq1VqQ5q\njZNKV38NVuXKiUgt0SW6BFB+HCiPpdLV58qdeWbxj6WyIvlQeZFiUkVOcFdFTqrDoEHw8MPKlROR\n2tGUHLmB7j4s5nhipRy53EydChttBNOmgeXVMy9SfoYOhSlT4Kabko5ERCQ/pc6Ru6YJz5UyUp8f\np0qcVIOBA6FzZ+XKiUhtKLhr1d1/zbbOzDY2syPNrFWh+5fSUbdqoDyW6lCKXDmVFcmHyosUUyw5\ncma2npldZmZDzawX8AIwHBgQx/6luDRiVarNwIHwyCPKlROR6ldwjtx8OzG7HXgW6AD0BVYCHgda\nuvueTT5A4XEpR64R06bB2mvD119DMw19kSoydCh8+CHcfHPSkYiI5CbJeeSedfero7//ZWZdgG0I\nlTspY88+C5ttpkqcVJ/6eeXefz/kzImIVKO4vr7rzKxd/QN3f8/dL3X3CTHtX4pE3ap/UB5LdVlq\nqdDFWoxcOZUVyYfKixRTXBW5McAjZna4ma0R0z6lBDTQQarZwIHw6KOhVU5EpBrFlSN3DzAF6ARs\nBCxM6FZ90N1vavIBCo9LOXINmDEDVl0VvvkGWuhibVKlzjgjDHpQrpyIlLskc+SedPff55Uzs9WA\nnsDqMe1fiuC552DjjVWJk+o2cGDIlXvvPejSJeloRETiFVfXaiszW6T+gbt/4O7D3f2kmPYvRTB2\nbBjoIIHyWKpTMXLlVFYkHyovUkxxVeRGAY+ZWW8zaxnTPqXIxo2DTTdNOgqR4hs4EB57LLTKiYhU\nkzhz5H4A/gKsDLxENADC3cc3+QCFx6UcuSxmz4Z27UKeXCtdf0NqwJlnhorcLbckHYmISGaF5MgV\n1CJnZjukLZoAnO7u3YCOwOXA0sDphexfiu/ll8NEwKrESa048ki1yolI9Sm0a/VMM1so5fE5QHcz\n28Ddv3b3e9x9oLv/NYYYpQjGjYNNNkk6ivKiPJbqttRSYZLgOHLlVFYkHyovUkyFVuTaAqeY2RYA\n7l7n7g+4+0vxhSbFpIqc1KL6XLl33006EhGReBSUI2dm/3D328xsfWAL4FF3fyv26JpIOXKZ1dXB\nMsvAO+9A+/ZJRyNSWmefDZMmwX//m3QkIiLzKyRHLq7BDv2ANYE73H16k3cYE1XkMps0CXbaKUyS\nKlJrfvwxTIT9zDOw1lpJRyMi8odSDnZol/rY3R8HLgX6mNkRZrZYIfuV0lC3ambKY6kNiy8Oxx8P\ngwcXvg+VFcmHyosUU6E5cmdlWLYo8BzwJnCLmR1qZnHNUycxUkVOat3hh8Pzz8PEiUlHIiLSNIXm\nyP0AvAEsQ5hmpDULXu7rF2CUu2/X1CALpa7VzFZdFR58ELp1SzoSkeQMGwZPPx3eCyIi5aBkOXJm\nNhkYAWwGTAaeAr6NbjOBb93957x3HDNV5Bb0xRew5pphIuBmai+VGvbLL9C5M9xzD/TokXQ0IiIl\nzJEDznH3Ie6+JeEKDhsBn7j7JHefVg6VOMls3DjYaCNV4jJRHkttWWQROOUUOO20/J+rsiL5UHmR\nYiro69zdb0n5+25gKLC3mZ1pZq3jCk7ip/w4kT/sv3+YU27cuKQjEREpTKFdqwe5+3UZlncE/g28\nA1zm7r81PcTCqWt1QRtsAOefD5tvnnQkIuVh+HC47TYYOTLpSESk1pUyR+5T4NZsq4HeQHvgZHcf\nkfcBYqKK3Pxmz4Z27eDrr2HRRZOORqQ8zJ0La6wB114LvXsnHY2I1LJS5sitAJwEHAnsDWwLbAh0\nIYxkHQNcAyxS4P6lCMaPDxOgqhKXmfJYalOLFnD66XDqqZDr7z6VFcmHyosUU/qUIbm6H9jd3efE\nGYwUl/LjRDLbc89w6a4nn4S+fZOORkQkd4V2rbZ39y+LEE+s1LU6v+22C8ndu+6adCQi5eeuu+CC\nC+Cll8Dy6tgQEYlHybpWK6ESJ/Orqwsz2atFTiSzv/0Nfv0VHn446UhERHKn2cRqxNtvwzLLwHLL\nJR1J+VIeS21r1gyGDg3zytXVNbytyorkQ+VFiinnipyZKUW+gik/TqRxO+wQBj/ce2/SkYiI5Cbn\nHDkzew/Y392fK25I8VGO3B/22Qc23RQOPjjpSETK2+OPwzHHwJtvQvPmSUcjIrWk2DlySwDTzOwg\nM+uaX2iSNLXIieSmb19o2zZMEiwiUu5yqsiZ2WLA4u4+BbgB2MDMRprZJ2b2bFEjlCb74guYOTNM\neirZKY9FIIxYPfvsMLfcr79m3kZlRfKh8iLFlGuL3GnAQma2mLvXufst7r4F0BXYsXjhSRxeeAE2\n3DAkc4tI4zbdFLp1g+sWuBChiEh5ySlHzsyWAToA7dz9yaJHFRPlyAUnngiLLRZG44lIbiZOhG22\ngQ8+CO8fEZFiK1qOnLt/4+6vpVbizKx9vgFKMl54ATbaKOkoRCpL9+6w+eYwbFjSkYiIZNeUzrY9\nYotCimbOHJgwAXr0SDqS8qc8Fkk3dChcdBF8++38y1VWJB8qL1JMypqqcm+8AZ06wVJLJR2JSOXp\n0gV22gn+85+kIxERyayga60CmNkgd7805nhipRw5uPxyeP11JW2LFOrTT0M361tv6cooIlJcJbvW\nqlQO5ceJNM1KK8G++8JZZyUdiYjIglSRq3IvvhimHpHGKY9Fsjn5ZPjvf+Gjj8JjlRXJh8qLFFNT\nKnK13WdZAb76KkwEvPrqSUciUtnatYMBA2DIkKQjERGZX1Ny5BZ29yzznpeHWs+Re+ABuOqqcO1I\nEWma77+Hzp1h1ChYc82koxGRalTSHLlyr8TJH1d0EJGmW3JJOP54OPXUpCMREflDwRU5M1vLzM42\ns2hewG4AACAASURBVOfM7EMz+9rMPjWzcWZ2sZl1izNQyd+LL2qgQz6UxyKNOeIIeOkluPrq0UmH\nIhVEny1STAVV5MxsD+BeYDHgfuAC4CTgfOAhYEngcTP7e6GBmVk/M3vHzN43sxOzbNPLzF4zs0lm\nNrrQY1WjuXPh1Vdhgw2SjkSkerRqFVrkNJ2PiJSLgnLkzOwy4Ch3n9fANosAl7j7oQXsvznwLrAl\n8DkwHtjT3SenbNMaGAf0dffPzKytu89I20/N5shNmAD//GeY+0pE4jNnTsiRu+oq2HLLpKMRkWpS\nyhy59xuqxAG4+y/AewXuvwfwgbtPdfc5wAhgx7Rt9gLucffPouPNQH6naUdEiqNlSzj7bDjhBKir\nSzoaEal1hVbkuprZIDPrZGYL1BzNbAUzGwCsV+D+VwA+TXn8WbQsVWdgaTMbZWavmNk/CzxWVdJE\nwPlTHovkqm3b0bRsCSNGJB2JVAJ9tkgxFVqROwHoArwFzDOzn83s2+j2G/A28BdgYIH7z6U/tCWh\norgt0Bc41cw6F3i8qqOKnEjxmMH558O//w2/avy+iCSoRSFPcvefgCPM7HigK9AeWBr4AZgOvB51\niRbqc2CllMcrEVrlUn0KzHD3n4GfzWwssC7wfupG/fv3p1OnTgC0bt2a7t2706tXL+CPX0nV9rhb\nt17MmAFffjmar79OPp5KeVy/rFzi0ePyfdyrVy9Gjx5N+/Zw9dW9GDSovOLT4/J6XF9eyiUePS6f\nx/V/T506lUIVPCFwTjs3W8XdpxTwvBaEwQ59gGnAyyw42GF14HJCa9zCwEvA7u7+dso2NTnY4aGH\n4LLL4Mknk45EpLpNmgR9+sB778FSSyUdjYhUupJOCJyjYwt5krvPBQYATxC6ae9098lmdoiZHRJt\n8w7wOPAGoRJ3XWolrpapW7Uwqb+QRBpSX1bWWgu23TZ0s4pko88WKaaCulajgQWN1RgN2KqQ/QO4\n+2PAY2nLrkl7fAFhDjtJ8eKLYQZ6ESm+oUOhe3c4/HBYIX1IlohIkRU6j9xgwvQfnze0GdDD3Rct\nLLSmq8Wu1blzYeml4eOPoU2bpKMRqQ0nnggzZ2qiYBFpmkK6VgutyLUEznH34xrZ7hZ33yfvA8Sk\nFityEyfCnnvC5MmNbysi8fj2W+jaFcaMgTXWSDoaEalUJcuRi0akTsph00cL2b8UTvlxhVMei+Qq\nvay0aRNa5U4+OZl4pLzps0WKqeDBDu5+Uw7baLrMEtMVHUSSccQR8NprMG5c0pGISC0p6vQjSavF\nrtWuXeF//4N11kk6EpHac8stcPXVoTK34DVvREQaVpKuVTPb2sx6FPC8pc3shHyfJ7n79luYNg26\ndUs6EpHatPfe8NNPcP/9SUciIrUi74qcuz8JrGJmF0WT8jbIzBYzs0HAv4BLCohRcjR+PKy/PjRv\nnnQklUl5LJKrbGWleXM477yQKzd3bmljkvKlzxYppkIv0TXCzEYBJ5nZusAUwqWxZgFzgTbAskB3\n4EfgQne/NJ6QJZuXXoINNkg6CpHa1rdvmE/u+uvh0EOTjkZEql2Tc+TMzAjXOO0GtCNcLmsG8DHw\nvLvPbmqQTYitpnLk/vpX2G8/2HXXpCMRqW0TJ0K/fvDuu7p0l4jkrmTzyFWKWqrIucOyy4ZRcyuu\nmHQ0InLAAdCuHZx7btKRiEilKMdrrUqJfPQRLLSQKnFNoTwWyVUuZeWMM0L36kcfFT8eKW/6bJFi\nUkWuSig/TqS8LL88DBoEJ52UdCQiUs3UtVoljj6a/2/vvsOkKrL/j7+PoAhiQF1WlBUUMaAiGFBU\nFDOKEXP4KkZcsz8xrXmNKKsuiLvrmteEGVQUFAVEiYsIZhEwAAYUBCMC5/dH3VmGdkJ33+6+HT6v\n5+lnpvvevvfMWDZnqk5Vsc46YXV5ESkOP/0U1nYcOBB23DHpaESk2GlotYKpR06k+DRpAjfcEP7Q\nWro06WhEpBwpkSsDixbB22/DttsmHUlpUx2LpCuTtnLssSGJGzgwf/FIcdNni+STErkyMGUKbLgh\nNG2adCQikmqFFeDWW0Ot3M8/Jx2NiJSbjGvkzGwC4EBdY7hVx93dM97OK1cqpUZuwICw7Mjddycd\niYjU5rDDYOut4S9/SToSESlW2dTIZbOzw7sZnFv+WVQRGDcOunRJOgoRqUufPqGO9aSTwsQkEZFc\n0KzVMrDJJvDEE9C+fdKRlLYRI0bQtWvXpMOQEpBtW+ndGxYsgLvuyn1MUrz02SLp0qzVCjRvHsye\nDZtvnnQkIlKfyy+HQYNCXauISC7kYq/Vo4BTgbZA4+jl6jVyzWPdIF5sZd8jN2xYWN5Ak6JESsMd\nd4RkbtgwsIz+7haRclfwHjkzOwZ4AJgGtAQGAc8DDYAFwIA415f6af04kdLSqxd88QUMGZJ0JCJS\nDuIOrV4IXAucGT2/091PBFoDc4EfY15f6jFuHHRKbF5wedFaT5KuOG1lxRWhb1/4f/8vrAEp5U+f\nLZJPcRO5tsBoYEn0WA3A3RcCNwFnxby+1MFdPXIipah7d9hoI/j735OORERKXawaOTObDZzi7kPM\n7FOgj7vfGR3rATzo7oktU1vuNXLTp4dlR2bNSjoSEcnURx+F/VenToUWLZKORkSKQRKzVicCVYte\nDAKuNLPTzKwn0BcYG/P6Ugf1xomUro03hlNOCTs+iIhkK24idyMwM/r+KmAccCdwL/AN0Cvm9aUO\n48crkcsl1bFIunLVVi67DIYPhzffzMnlpEjps0XyKetEzsxWJMxOfR3A3ee5+0FAU6CZu2/v7p/k\nJkypiXrkRErbqquGHR/OOQeWLEk6GhEpRVnXyJlZA+BnoJu7v5rTqHKknGvkFi2CZs3gq6+gaWJV\niCISl3uodT3hBDj11KSjEZEkFbRGzt2XAB8D2jUwAVOmwIYbKokTKXVm0L8/XHFF2KlFRCQTcWvk\nLgOuMjPt8llgGlbNPdWxSLpy3VY6doSDD4arrsrpZaVI6LNF8qlhzPdfBqwJTDazL4Cvoterb9Gl\n5WrzYNy4MBwjIuXhuuugXbswvLrllklHIyKlIu46cvfXc4pHOz0kopxr5DbdFB5/HNqrL1SkbAwY\nAE8+Ca++qn1YRSpRNjVysRK5Yleuidy8edCqVfjaoEHS0YhIrixeDNtsA5dfDocfnnQ0IlJoBV8Q\n2MyuNLN1aznWwsyujHN9qdmECbD11krick11LJKufLWVhg2hXz/o3Rt++ikvt5AE6LNF8inuZIer\ngZa1HFsvOi45pokOIuVr113D1l033ZR0JCJSCuLWyC0FdnD38TUcOwi4193XihFfLOU6tLr//nDi\niXDooUlHIiL58MUX0KFD+KOtTZukoxGRQilIjZyZnQD0jJ7uCkwCFqSc1hjYEhjm7j0yukEOlWMi\n5w7Nm8Nbb0HL2vpCRaTk3XwzvPYaDBmiiQ8ilaJQNXI/A99GD4Dvge9SHjOAPoDWKc+xGTNgpZWU\nxOWD6lgkXYVoK+efD599Bk8/nfdbSZ7ps0XyKeN15Nz9ceBx+N/yI3919+k5jktqMX686uNEKsGK\nK8I//gHHHgt77x32ZRURSRW3Rq4DsK67D6nhWHfgc3efEiO+WMpxaPX882GddeDii5OOREQKoWdP\nWHtt6Ns36UhEJN8KvvwIcBtQW//QdtFxySHNWBWpLDffDA8+GPZXFhFJFTeR6wi8WcuxMcDWMa8v\n1SxaBG+/Ddtum3Qk5Ul1LJKuQraV5s3hr3+FP/8Zli4t2G0lh/TZIvkUN5FrADSp5VgTYKWY15dq\npkyBDTeEpk2TjkRECunUU8OuD/ffn3QkIlJs4tbIvQb86u7dajj2ItDE3XeNEV8s5VYjN2BAWHbk\n7ruTjkRECm3SJNh3X3jvPVgrsdU5RSSfkqiRuwrYw8zGm9mZZtbDzM4ys/HA7sAVMa8v1ag+TqRy\nbb01HHmkJjqJyPJiJXLuPgrYC1gC9AOeBG4HfgP2jI5LjmjpkfxSHYukK6m2ct11MHQojByZyO0l\nS/pskXzKeB25VO4+AuhsZqsAzYB57v5j3OvK8ubNg9mzYfPNk45ERJKy2mrQvz/06gWTJ8PKKycd\nkYgkLVaNXLErpxq5YcPghhtAf9iJSI8esOWWcM01SUciIrmURI1c1Y03N7PjzewvZtYieq2tma2W\ni+uL6uNEZJn+/eHOO+H995OORESSFiuRM7OmZvYEMBX4N3At0CI6fD1wZbzwpMq4cdCpU9JRlDfV\nsUi6km4r660HV18Np52mteVKQdLtRcpb3B65W4HOwB7AqkD17sAhwL4xry+Au3rkRGR5p58e1pbT\nckQilS3uOnJzgfPc/SEzawgsArZ190lmtjsw2N0TW762XGrkpk+HLl1g1qykIxGRYjJ1Kuy+e1gs\nvEWL+s8XkeKWRI1cY2BuLcdWJSxLIjFp2RERqcmWW4bh1XPPTToSEUlK3ERuInBCLccOpfZ9WCUD\nGlYtDNWxSLqKqa1cfnnY8WXw4KQjkdoUU3uR8hM3kbsc6GFmw4FTotf2M7OHgCMIOz9ITErkRKQ2\njRuHOrkzzoD585OORkQKLfY6cma2E3ATsAPQAHBgLHCRu78RO8J4sZV8jdyiRdCsGXz5Jay6atLR\niEixOvNM+OUXuOeepCMRkWxlUyOXswWBzawxYWeH+e7+U04uGlM5JHITJ8KJJ4aiZhGR2ixcGGrm\n7roL9t476WhEJBuJLAhsZo3M7DSgP2EtuX5mdpqZrRT32qJh1UJSHYukqxjbyqqrhiTutNNCUifF\noxjbi5SPuAsCbwZ8DAwAtgCWAlsCdwCfmFm72BFWOCVyIpKuvfcOy5FcemnSkYhIocRdR+51YHVg\nf3f/rNrr6wPPA9+7e5fYUWYfX8kPrW6yCTzxBLRvn3QkIlIK5s0LQ6yPPAK77JJ0NCKSiYLXyJnZ\nz8Ax7v5MDccOAR5195WzvkFMpZ7IzZsH668fZqI1aJB0NCJSKgYPhgsugLffhiZNko5GRNKVRI3c\np0BtidrK0XHJ0oQJsM02SuIKRXUskq5ibysHHgjbbQdXXJF0JALF316ktMVN5C4BrjOzHaq/aGad\ngeuAi2Nev6KpPk5EstWvHzz6KLyR6CJQIpJvcYdWJwCtgLWBr4BvgObRYy7L98i5u3fKPtSs4ivp\nodX994eTToIePZKORERK0bPPQu/eMHkyNE1s12sRSVcSNXL3ExYATuem7u4nZnDtbsDthEWG73b3\nPrWctx0wBjjC3Z9OOVayiZw7NG8ett5p2TLpaESkVJ1wQkjiBgxIOhIRqU+iCwLnkpk1AD4E9gRm\nAROAo939/RrOexn4CbjP3Z9KOV6yidz06dClC8yalXQklWPEiBF07do16TCkBJRSW5k/P8x6v+ce\n2GuvpKOpTKXUXiRZiSwIXEsga8S8RCdgmrvPdPffgMeAg2o472zgScKQbllRfZyI5MIaa4S9WE8+\nGb7/PuloRCTX4i4IfIaZXVTteQczmwV8Z2aTzCzbQcH1gM+rPf8ieq36vdcjJHf/iF4qza63WiiR\nKzz9xSzpKrW2svfe0L07nHde0pFUplJrL1Ja4vbInQVU3wymH2Eo9Njo2jXWtaUhnaTsduCSaOzU\nSK9Or2QokRORXLrlFhg1KqwxJyLlo2HM968PfABgZs2BnYA93f01M/uVsHVXNmYBf6r2/E+EXrnq\ntgEeMzMIs2b3NbPf3H25j6mePXvSunVrANZYYw06dOjwv7+Oqtb2KbbnO+7YlSlT4OefRzBiRPLx\nVMrz22+/vSTah54n/7zq+2KJJ53nEyeO4Jxz4PTTu7LjjvDOO8UVXzk/L8X2oueFeV71/cyZM8lW\n3Fmr3wLHuvtLZnYEcC+wursvMbPdgCHu3jiL6zYkTHbYA5gNjKeGyQ7Vzr8PeK5cZq1OnBiWHZky\nJelIKsuIESP+9z+ZSF1Kua1ccAHMnAlPPglWVuMYxauU24sUVhKTHSYAZ5rZ5sA5wEvuviQ6tgEh\nCcuYuy8mDNsOBd4DBrr7+2bWy8x6xYy56GlYNRn6oJV0lXJbuf56+PhjuO++pCOpHKXcXqT4xe2R\n2xx4DmhNmJywt7t/GB0bBnzp7sfnIM5s4yvJHrnjjw+bXZ9yStKRiEg5eucd2G03GDMGNtoo6WhE\npErBe+Tc/V1335Cwk0PrqiQu0hu4IM71K9W4cdCpoHtgCCxfsyBSl1JvK1tsAZdfDscdB7/9lnQ0\n5a/U24sUt7hDq1WaA8eZ2V/MrEX02s/Arzm6fsWYNw9mz4bNN086EhEpZ2efDauvDtddl3QkIhJH\n3KHVpsB9wKHAb4RZsNu5+yQzexz4zN175yTS7OIruaHVoUPhxhtBf8CJSL7NmQMdO8LTT8OOOyYd\njYgkMdnhVqAzYXbpqiy/ltsQYN+Y1684muggIoXSogX8859hiHXBgqSjEZFsxE3kehAW5X0NWJpy\n7DOgVczrVxwlcslRHYukq5zaysEHwx57hKFWyY9yai9SfOImco2BubUcWxVYUssxqYG7EjkRKbzb\nboOxY+Hhh5OOREQyFbdGbiQw292PjhbxXQRsG9XIPQj8wd0TG14ttRq56dPDsiNfpO5hISKSZ5Mn\nw157wZtvQtu2SUcjUpmSqJG7HOhhZsOBqlXP9jOzh4AjgKtiXr+iqDdORJLSoQNcdRUcdRT8qvUG\nREpG3HXkXgd2B1YC+kcvX0PY1WEPdx8fL7zKokQuWapjkXSVa1s580xYf324+OKkIykv5dpepDjE\nXkfO3d9w9y7A6oTN7Vdz953c/Y3Y0VUYLQQsIkkyg3vugWeegcGDk45GRNIRq0au2JVSjdyiRdCs\nGXz1FTRtmnQ0IlLJ3ngDevSA//4XWrZMOhqRypFEjZzkyNtvQ5s2SuJEJHk77QTnngvHHAOLFycd\njYjURYlckVB9XPJUxyLpqoS2cskl0KgRXHNN0pGUvkpoL5IcJXJFQomciBSTFVaAhx6C++6DF19M\nOhoRqY1q5IrExhvDU0/BllsmHYmIyDKvvw6HHQbjx0Mr7dUjklfZ1MgpkSsC330HrVvDvHnQoEHS\n0YiILK9vX3j88ZDUNWqUdDQi5SuRyQ5mdpSZDTezz8zsm+jxddXXuNevBBMmwDbbKIlLmupYJF2V\n1lYuuADWWy98lcxVWnuRwoqVyJnZMcADwDSgJTAIeB5oACwABsQNsBKoPk5EiplZqJV76SV45JGk\noxGR6uLutfoW8BRwE8vvs7oq8ArwhLv3zUmk2cVXEkOr3bvDySeHdZtERIpV1X6sI0dCu3ZJRyNS\nfpIYWm0LjAaWRI/VANx9ISG5Oyvm9cueu3rkRKQ0dOgAffqEyQ8LFyYdjYhA/ERuAdAk6vaaDVT/\nG82AtWNev+xNnw4rrxzqTyRZqmORdFVyWznppLBgcM+e4Q9RqV8ltxfJv7iJ3ESgffT9IOBKMzvN\nzHoCfYGxMa9f9saOhR12SDoKEZH03XEHzJ4NN9yQdCQiErdGrjPQyt0fM7NmwP1Ad0KCOAE4xt0/\nyUWgWcZX9DVyZ50FG2yg2WAiUlpmz4bttoO77gp1viISX1GsI2dmKwON3P37nF44u1iKPpHbZhvo\n3x923DHpSEREMvPmm3DwwTB6dFjUXETiSWQduVTu/ksxJHGl4Kef4IMPYOutk45EQHUskj61lWDH\nHeHaa0Myt2BB0tEUL7UXyaeGmb7BzCYAJ7j7e9H3TpjYUBN3905xAixnEyfCFluEyQ4iIqWoVy+Y\nNAlOOCFsM7iCdvAWKaiMh1bN7H7gr+4+Pfq+Lu7uJ2YZW2zFPrTapw/MmQO33550JCIi2fv1V9ht\nN+jWDa68MuloREpXNkOrGffIuXvPmr6XzI0ZA0cfnXQUIiLxNGoUeuO23x422wwOPzzpiEQqR9wt\nujqY2X61HOtuZu1rOiZh/aUxY6Bz56QjkSqqY5F0qa38XosWMGgQnHFGKBuRZdReJJ/iVjPcBtS2\nCtp20XGpwYwZ0LAh/OlPSUciIpIbHTuG5UgOPhhmzUo6GpHKEHcdufnAEe4+rIZj+wCPuXuzGPHF\nUsw1co88Ak8/DU8+mXQkIiK5ddNN8MQTMGoUrLJK0tGIlI4klh9pANT2v2kTYKWY1y9bY8ZoRwcR\nKU8XXxxm5B9/PCxdmnQ0IuUtF1t09arl2GnRcamB6uOKj+pYJF1qK3UzC0OsX32lWayg9iL5lfGs\n1RRXAcPNbDzwADAHWBc4HtgK2Cvm9cvSTz/B+++HXR1ERMpRo0bwzDNhJmvbtmGdORHJvdhbdJlZ\nV+BGoBNhYeClwDjgEnd/PW6AcRRrjdyoUXDhhTBuXNKRiIjk1/vvQ9eu8PDDsOeeSUcjUtwKso5c\nKncfAXQ2s1WAZsA8d/8x7nXL2dixGlYVkcqw2WZh4sNhh8Err0B7LUolklM520zF3X909y+UxNVP\n9XHFSXUski61lczssgv06wfdu8MXXyQdTeGpvUg+xe6RAzCzjYGWwO92DXX3Ibm4R7moWghY23KJ\nSCU56ij4/HPYd18YPRpWXz3piETKQ9x15NoBA4HNaznF3b1B1jeIqRhr5GbMgJ12CotlWkaj4CIi\npc0dzj4bPvgAhgyBlbRAlchyklhH7l+EteIOATYFNkx5tIl5/bJTNayqJE5EKo0Z/P3vYZHgk0/W\nGnMiuRA3kesI9Hb3Qe7+kbvPTH3kIMayovq44qU6FkmX2kr2GjSARx+F6dPD7P0iGzTJC7UXyae4\nidx0aqiLk9ppxqqIVLomTeC552DYMOjTJ+loREpb3Bq5vYCbgcPc/ZOcRZUjxVYj9/PPsPbaMHcu\nNG6cdDQiIsmaPRt23hkuvRROPTXpaESSl8Q6cjcQdnL4wMxmAPMJiwJ71Vd37xTzHmVj4kTYfHMl\ncSIiAOuuC0OHwq67wpprwqGHJh2RSOmJO7T6LjAEeBh4E3gveq3q67sxr19WVB9X3FTHIulSW8md\ntm3hhRfgz3+G4cOTjiY/1F4kn2L1yLl7zxzFURHGjIEjj0w6ChGR4tKx47LdH4YMge22SzoikdIR\ne6/VYlZMNXLusM46MH48tGqVdDQiIsXnuedCrdzQobDVVklHI1J4Sawjh5kdZWbDzewzM/smenxd\n9TXu9cvFtGnQqJGSOBGR2hxwAPTvD926wXvvJR2NSGmIlciZ2THAA8A0whZdg4DngQbAAmBA3ADL\nxejRYXaWFC/VsUi61Fby5/DD4ZZbYO+94eOPk44mN9ReJJ/izlq9ELgWuAk4FbjT3SeZ2arAK8CP\nMa9fNpTIiYik57jj4JdfYM89YeRIaN066YhEilfcdeR+APYHRgKLgL3cfUR07BDgNndvHT/MrOMr\nmhq5TTYJxbzt2ycdiYhIabjjDrjttpDMtWyZdDQi+ZdEjdwCoEmULc0G2lWPB1g75vXLwtdfh8cW\nWyQdiYhI6TjrLDj9dNhjj7B4sIj8XtxEbiJQ1cc0CLjSzE4zs55AX2BszOuXhTfegB13hBViTy2R\nfFIdi6RLbaVwLrwQTjwRunaFL75IOprsqL1IPsWtkbsRqJqHeVX0/Z2EBHEC0Cvm9cuC6uNERLJ3\nySXQoEFI5l59FdZfP+mIRIpHzteRM7OVgUbu/n1OL5xdLEVRI7f99tC3L3TpknQkIiKl67bbwvIk\nr76qCRBSnrKpkdOCwHn244/wxz/C3Lmw8sqJhiIiUvL69YNbbw3J3IYbJh2NSG4VZLKDmU0ws3bV\nvh8ffa3pMT7T65eb8ePDCuVK4oqf6lgkXWoryTnnnFA3t9tuYaH1UqD2IvmUTY3cu8Av1b6vS/l2\n96VJ9XEiIrl15pmw4oqhZu6ll7QigFQ2Da3m2T77hCn0BxyQaBgiImXnkUfg/PPDHq2dOiUdjUh8\nqpFLkXQit3gxrLUWTJ8evoqISG499xycdBI8/ngYbhUpZYWqkdslk0em1y8nU6eG1ciVxJUG1bFI\nutRWiscBB4Rdc444AgYPTjqamqm9SD5lUyM3IoNzHWiQxT3KgurjRETyr2tXGDIkJHULFoS9WkUq\nRcZDq2ZWvay0BXAv8CLwDPA10BzoAewDnOzuL+cm1MwlPbR6xBHhg+X//i+xEEREKsa770K3bnDB\nBXDeeUlHI5K5gtfImdlgYKq7X1bDseuBrdx9/6xvEFOSiZw7rLde2J5rgw0SCUFEpOJ8+mlI5rp3\nh5tv1taIUloKUiOXYndqH2odCVRs6emMGWCm1cdLiepYJF1qK8WrVavwB/TYsXDssfDrr0lHpPYi\n+RU3kZsHHFzLsYOB72Jev2SNHh225LKM8moREYlrzTXh5Zdh0SLYd1/4PvENI0XyJ+7Q6hnAHYQa\nuUEsq5E7GOgGnO3uA7K8djfgdsJkibvdvU/K8WOBiwADFgJ/dvcpKeckNrR62mnQvn1YQ05ERApv\nyRI491wYNQpefDGUu4gUs0TWkTOzg4DLgI6EpGsJ8BZwg7s/m+U1GwAfAnsCs4AJwNHu/n61czoD\n77n791HSd7W775ByncQSuXbtwmKVHTokcnsRESHUK998MwwYEJYn0WeyFLMkauRw90Hu3gloDKwL\nNHb3TtkmcZFOwDR3n+nuvwGPAQel3HeMu1d1mI8DWsa4X07NnQuzZsGWWyYdiWRCdSySLrWV0mEG\nF18Mf/sb7LVXMmvNqb1IPmWzjlyN3H0x8GWOLrce8Hm1518A29dx/snAkBzdO7Y334TOnaFBxa6g\nJyJSXA4/PEyEOOQQ+OijsESJapilHMRO5MzsKOBUoC2hVw7CQsAGuLs3z+KyaY+HmtluwEnATjUd\n79mzJ62jqaNrrLEGHTp0oGvXrsCyv5Jy/XzkyK506ZK/6+t5fp5XvVYs8eh58T7v2rVrUcWj5+k/\nHzOmKwceCK+9NoLzzoO99sr//dVe9Ly251Xfz5w5k2zFnexwDHAfcD8hmbuXUCd3IDAfeNDd2Iof\nfgAAGPBJREFUr8niujsQat66Rc8vBZbWMOGhPfA00M3dp9VwnURq5LbZBvr1g51qTC1FRCRJP/wA\nxxwDCxfCk09qG0UpHknUyF0IXAucGT2/091PBFoDc4Efs7zuRKCtmbU2s5WAI4HlKhvMbH1CEndc\nTUlcUubPD932222XdCSSqep/IYnURW2ltDVtCs88A9tuC506wZQp9b8nDrUXyae4iVxbYDRhpuoS\nYDUAd18I3ARktfhGVG93FjAUeA8Y6O7vm1kvM+sVnXYl0Az4h5m9ZWbjY/0kOTJ6NOywA6y0UtKR\niIhIbRo0gFtugWuvhT32gIEDk45IJDtxh1ZnA6e4+xAz+xTo4+53Rsd6EIZWm+Ym1KziK/jQau/e\n0KwZXPa7TctERKQYTZ4cJkEcfjjceKMmqklykhhanQi0j74fBFxpZqeZWU+gLzA25vVLzogRsOuu\nSUchIiLp6tABJkyASZPCThDfVeyeRFKK4iZyNwIzo++vIqzndidh0sM3QK+a31ae5s+HDz9UfVyp\nUh2LpEttpfysvTa89BJstVWonfvvf3N3bbUXyadYiVy0KO9j0ffz3P0goCnQzN23d/dPchFkqRg9\nGrbfHho1SjoSERHJVMOGoW7u5ptDz9ydd4adIUSKWewtumq9sNnOwKXu3j0vN0gvhoLWyPXuDWus\nAZdfXrBbiohIHnz8caiZ23RT+Pe/YdVVk45IKkHBauTMbBUzO8zMepvZyWb2h2rH9jCzUcAoYKNs\nrl+qRoyAamvLiohIiWrbFsaMgdVXD0Ot+V6iRCRbGSdyZrYx8D7wOHAz8G/gYzPrbGb3AC8TlgU5\nFtgsh7EWte+/V31cqVMdi6RLbaUyNG4M//oXXHFFWKLkrruyG2pVe5F8yqZHrg/wM9AZWIWQrE0A\nXgQOA4539y3d/VF3X5qzSIvcqFGqjxMRKUfHHRc+4++8Ew49FL79NumIRJbJuEYuWjvufHcfWO21\nNsDHQC93/3duQ8xeIWvkzj0X1lkHLr20ILcTEZEC+/XX8Bn/xBPw4IOw225JRyTlplA1cusAM1Je\n+zT6OjmL65WF4cNhzz2TjkJERPKlUSO49Va4+2449tiQ1C1alHRUUuniriNXparba0mOrldSvvwS\nZs+GrbdOOhKJQ3Uski61lcq2zz5hN4ipU2GnneCDD+o+X+1F8inbRG6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"text": [ "" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Caso 4. Unidades: $\\nu$ en $cm^{-1}$ y B en $MJy / sr$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pues bien, Existe a\u00fan otra unidad de medida de frecuencia, el Jansky, que es en la que est\u00e1n codificados los datos que podemos descargar del COBE, y que est\u00e1 definido como:\n", "$$ 1 Jy = 10^{-26} \\frac{W}{m^2 Hz} $$\n", "\n", "Un m\u00faltiplo suyo ser\u00e1 el Megajansky = 10**6 janskys\n", "\n", "Su uso est\u00e1 especialmente extendido en radioastronom\u00eda. Para poder trabajar con facilidad en Python con estas unidades definiremos dichas unidades mediante el paquete *quantities*" ] }, { "cell_type": "code", "collapsed": false, "input": [ "Jy = pq.UnitQuantity('jansky', 1e-26*pq.watt/(pq.m**2*pq.hertz), symbol = 'Jy')\n", "MJy = pq.UnitQuantity('megajansky', 10**6 * Jy, symbol = 'MJy')" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Veamos un ejemplo de conversi\u00f3n de una radianza espectral a estas unidades:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "I = 3.34 * 10**(-18) * pq.W * pq.m**(-2) * pq.hertz**(-1) * pq.sr**(-1)\n", "I.rescale(MJy)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 14, "text": [ "array(333.99999999999994) * MJy" ] } ], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vamos a formar ahora el gr\u00e1fico poniendo en abcisas frecuencias en ciclos/cm, y en ordenadas el flujo radiante en $MJy*sr^{-1}$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "wf = np.arange(0.1,1000,1)* pq.gigahertz\n", "I = B_f(wf,TCMB)\n", "I = I.rescale(MJy*pq.sr**(-1)) # convertimos a MJy * sr**(-1)\n", "\n", "wk = (wf/pq.c).rescale(1/pq.cm) # convertimos frecuencias a 1/cm\n", "fig, ax = plt.subplots(figsize=(10, 8))\n", "ax.plot(wk, I)\n", "ax.set_title('Espectro del cuerpo negro para T = 2.725K \\\n", " \\n radiancia espectral en MJy / sr')\n", "ax.title.set_fontsize(20)\n", "ax.set_xlabel('Frecuencia (ciclos/cm)')\n", "ax.xaxis.label.set_fontsize(15)\n", "ax.set_ylabel('Radiancia espectral ($MJy \\, sr^{-1}$)')\n", "ax.yaxis.label.set_fontsize(15)\n", "ax.grid()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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66goMzbNpS+6CrNelNasmcGL8WeyVF14kfKBvGs9MbE/m7NOyeqgIeZ+d24iL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\nCrk2TJ8Oyy0HXbpkHYlIPpxwAnToEG6AEBGR6lKPXBtGjoTzz4fRoys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"text": [ "" ] } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Espectro del CMB seg\u00fan datos del COBE" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Una vez explorados los distintos tipos de unidades en que puede presentarse el gr\u00e1fico del espectro de radiaci\u00f3n del fondo c\u00f3smico de microondas, utilizaremos el \u00faltimo formato, ya que es precisamente en estas unidades en que se pueden obtener los datos del sat\u00e9lite COBE.\n", "\n", "Solo nos resta descargar los datos del espectro del CMB obtenidos con el instrumento FIRAS del COBE, los cuales est\u00e1n disponibles p\u00fablicamente en [FIRAS CMB Monopole Spectrum](http://lambda.gsfc.nasa.gov/product/cobe/firas_monopole_get.cfm). Para leer el fichero y poderlo manipular con facilidad, vamos a utilizar la librer\u00eda Pandas de Python (a la cual dedicaremos un post en este blog m\u00e1s adelante)\n", "\n", "El primer paso va a ser descargar el fichero que se encuentra en la direcci\u00f3n indicada. Se trata del fichero \"firas_monopole_spec_v1.txt\" en el que, abriendolo con un editor de texto, se observa que las columnas est\u00e1n delimitadas por espacios, y en el cual las 18 primeras filas son comentarios y deben saltarse, si bien debemos leerlas ya que en ellas vienen descritas las unidades utilizadas y el significado de cada columna de datos.\n", "\n", "Una vez descargado el fichero en alg\u00fan subdirectorio de nuestro disco, creamos ahora un dataframe de Pandas con las 5 columnas de datos. El separador utilizado es una expresi\u00f3n regular que significa utilizar como separador entre columnas cualquier n\u00famero de espacios" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#En este caso he descargado el fichero en el directorio ../datos\n", "df = pd.read_table('../datos/firas_monopole_spec_v1.txt', \n", " skiprows=18, sep='\\s+', header=None, \n", " names =['freq', 'I', 'residual', 'uncert', 'poles'])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Mostraremos unas cuantas l\u00edneas de la tabla obtenida:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "df[0:10]" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
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freqIresidualuncertpoles
0 2.27 200.723 5 14 4
1 2.72 249.508 9 19 3
2 3.18 293.024 15 25 -1
3 3.63 327.770 4 23 -1
4 4.08 354.081 19 22 3
5 4.54 372.079-30 21 6
6 4.99 381.493-30 18 8
7 5.45 383.478-10 18 8
8 5.90 378.901 32 16 10
9 6.35 368.833 4 14 10
\n", "
" ], "metadata": {}, "output_type": "pyout", "prompt_number": 17, "text": [ " freq I residual uncert poles\n", "0 2.27 200.723 5 14 4\n", "1 2.72 249.508 9 19 3\n", "2 3.18 293.024 15 25 -1\n", "3 3.63 327.770 4 23 -1\n", "4 4.08 354.081 19 22 3\n", "5 4.54 372.079 -30 21 6\n", "6 4.99 381.493 -30 18 8\n", "7 5.45 383.478 -10 18 8\n", "8 5.90 378.901 32 16 10\n", "9 6.35 368.833 4 14 10" ] } ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finalmente vamos a utilizar las dos primeras columnas del dataframe para superponer estos puntos del espectro del CMB medidos por la misi\u00f3n COBE a la anterior curva del espectro de un cuerpo negro a la temperatura de 2.725K. En el gr\u00e1fico resultante se podr\u00e1 apreciar que los datos del espectro del CMB se ajustan perfectamente al espectro teorico, pudiendose concluir que la radiaci\u00f3n del fondo de microondas c\u00f3smico sigue un patron perfecto de cuerpo negro." ] }, { "cell_type": "code", "collapsed": false, "input": [ "wf = np.arange(0.1,1000,1)* pq.gigahertz\n", "I = B_f(wf,TCMB)\n", "I = I.rescale(MJy*pq.sr**(-1)) # convertimos a MJy * sr**(-1)\n", "\n", "wk = (wf/pq.c).rescale(1/pq.cm) # convertimos frecuencias a 1/cm\n", "\n", "fig, ax = plt.subplots(figsize=(10, 8))\n", "ax.plot(wk, I)\n", "ax.set_title(u'Espectro del cuerpo negro para T = 2.725K \\\n", "\\n con datos del espectro del CMB del sat\u00e9lite COBE')\n", "ax.title.set_fontsize(20)\n", "ax.set_xlabel('Frecuencia (ciclos/cm)')\n", "ax.xaxis.label.set_fontsize(15)\n", "ax.set_ylabel('Radiancia espectral ($MJy \\, sr^{-1}$)')\n", "ax.yaxis.label.set_fontsize(15)\n", "ax.set_xlim(0,25)\n", "ax.set_ylim(0,400)\n", "\n", "ax.scatter(df['freq'], df['I'],c='red', s= 50)\n", "ax.grid()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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8FudIHpRsbUL+/8Q5q78uIhNwb9uzVHVxwLExNiubqi4UkcXAniKytar+iBsm\nBOfrMzQgn3399wG43sj9cb0Ur6nq1zWcP13mBGyrzzUTlJcSrPNZuJv8Buqop1BQ1TkiMh/oKyI3\n4oZZBWe8psL56ic7iCvo7jgXiaG44esuqlpVSx5F/vsV9U/UBGbgDOZ40m176VKGc0O4xg/hvoRz\nEZmnqtWJiUXkINxQdDFuCLRFQpJ0fJJjZXushjSK63nMNLFzt01Sr7GZpaG33RRYpKobwuv4e3pn\n3JDyRBHpr6pB7XycqvZtLCEzjRlyjUtb//1FCmljDtVfJdkf2942YF/QdOn1/jsSsC/ZuZck2R/4\nQBaR23Bvll/iboJf4IY6wfn37JHCuRNlSFb+mAwbyq+qt4nIdzgfwStxPikqIjOAP6nq3BTPmU65\nt/Pfh7N5uIcNouF8++pCzPDegY0TAZKdw/1QfVpEfgUMwPVcXgIgInOBQRrsu1JTmffA1c2PbCxv\n4GSTOFli5U2nzadDkC7qc80ky2uzelHV9b6dxZO2nurAVzjDeLN4WHXgfpxT+om4a/NNVX0r3Uy8\nEfYZMFxcjK/f4PwKb6rl0Ppca6m2vbRQ1RV+UsENuOHdE/yu70RkNHCjulmh+HTTcC9xU3FuAz/i\nDPwiXC9W8zROHytbX7yPdBLSnoiSxrmP858gUq3X2DWWbhuN6TuVZ8Tu/jsojMgmqOoKYIaInIkb\nbblZRB5R1TVpypfVmCHXuMQMrFQaeSwO0M5J9u+SkC6TxPLcKcn+zWQSkR1xxtN84MjEN3JxU9Lr\nIkNa5VfVR4BHxM0sPBLXM9UXmCwi+6tq4gM46JwplzvumFGqOrCGvOtKLP8KVU15Vp6qTsS9gbbE\n9QT/CjfR4QURKVLV9xIO2Ql3o0tkZ9xNPCZH7PtkVX0hBVFibX7XGlOlT5BBlMlrJj6vTXpnRWQL\n3HDXZwHp09JTmswESoFjgIfqmdcjwM24SRztcL1p9WUOzpBL9kITT32utVTbXtqo6hf4MCwiciBw\nNHAZzjgvYKORfh2uB65EVcvj8xCRQThDLh1iZftUVafXTfo6Ezv3lap6Vz3zmol7MTiGml9ogo47\nHzcpobY4hLGJC7NSzVxVPxaRZbiXuI44V58mg4UfaVxm++8TJMnYSxwV/rs0yf7ShHQZw7/FfATs\nJsFR4EsCtu2FG56ZEmDE7eb3JxKbvbdZL6GX4WMvQ1DYiBrLr6rLVfUlVb0Y5x+yLW6WY1LqWO7X\n8T44NeU2bDdcAAAgAElEQVRdV1R1JfAu8DMRqXVYPOD41ao6XVUH4BzTC3G9MImUJG7wdbA7brji\nR7851oZTLe97uAfFoSKSyrBQ0jaRApm8Zubi2nPi8B644dlN7p311VOKjMX5b54hIjUOc0ktoU5U\ndTluUsauOP+2mob0UiVW7lSeKzEdHCUiQelLAral2/bqhaou8IZNrJcq3jjbB1iaaMR5gtoMuLad\nrF3HylZT/L76UNN1lcl6/Q8uflxXETmmpoQJbfQ/uJe+I0Tk2CSH4EOhHI6bTPKfVIXyL1+xsDhN\nLkalGXKNiLpYS6/ifHT+nLhfRLbz4S9Q1VnA+7gb3RkJ6c7EPUze14B4OxliLK593BxvdPrwKVcG\npI/1WnSLvzH7WD/3E3wDiYUp2DOJDA/hLrq/J+S5PS4ciBLXMyEiyR7gsbf+VUn2x5NWub3/3aNA\nFxG5LuihJCJ7i4sBVldG4QywhyQghpmIbCMiRXH/i0UkqL5jvRxB/kt/kE3XbCwA/o6r/7Fx6Z7F\nGdiXiUiQQYiIdPU9gXjforuBlsCYRANDRAq9PmPU1iaSkuFrZpz//ku8YSYiLYARSY5JS0/poqqf\n4nrOCoEXReSwoHReL5NSyPI6XFiKE1LwaasRX0exhd3Lakvve75exr3gXZ6Q1ykEGxVptb10EZED\nRSSohzB23cTfPxYC24nIwQl5XAgcn+QUS4EdfRtKZCzOkOkvIr0CZCsUkd/VVoYaSHpdeZeTmcDp\nInJB4n5//oNFZIegfQl5rWTjfXKCiATWhYh0xb0Ex45bgXMFARey6ciAY47EzZBW4I9pttnLcSOQ\nS4F30jguJ7Ch1cbnt7gb3d/8w2YG7mG5L+7Nbz82Dtn0wd3sJoiLTP2+338qzh+jdwPKOdKf5wyg\nQkSm4Lqlz8JNIjg5PrGqLvETDM4F5onIyzg/mONwN8B5bDoxAeB/ON+pc0VkHa7cCoxX1c+AW3G9\nR6cAb4nIS0ArL8P2uBm4r8bl97SIrABew4VCEFwvXBfcBJAa4xrVpdyey3H6Gwb8TkRm4Xx/2uEc\nhLv4elmUwvk3Q1XH+of2pcDHIjIZF35jW9zM0m44g/ZSf8gdQDsvx6c4J/vDcD1Si4DHA07zCk5v\nE3Bt6wTgEFy93RIny3oROR03YedFEXkVeAun491xb8sdcA+/mH/kDbjYa72AD0TkRdySUrvj2sdA\n3LqS4PyOqoER/iG5zJ/3xhSrKyPXjKq+KiJ34vy93hGRJ3G9YafgHgZfkfBmXwc9pY2qjvC9C0OA\nN3z9x2Zr74QzgPbBhbGoLa/PvXzpclpcj3UE5yrSC1fOObhYjqlwGa436Hb/wH8bJ/upuDhqmxg0\ndWx76XA87qXxVTaG+9gNp/Mo7sUmxu24a+QVEXkC17a64GZO/wcX4yyR//o0k0RkJm7y1zxVfUFV\nv/cvG08Dz4rz652Dux/ugxvibYEbEq8L/8VdZ/eLyFO462+ZqsZWV/g17tp7UNwyWXNwhuVuuPvA\nQTgXjVonjqnqv7wxfZcv6zycnpfh/PG6+jy/TThurLiYnLcAM0WkDNdzq7j7VwlOD1dp8KoOANvI\nphM2tsZNdij2x16qwXEciyR4oocXTYNWg8gewp42m48f3A3vJpwhsxrXFV2Bm2LeMiFtR9xD7kvc\nA/kL/3+z0BK4m3uUgKn2JJmWXoucW+EMm8VezgXAH3E3y6Ap7i1xoQs+9Ok/Be705Z0ORAPO0QV3\nk/nBy76J/DiH4UE437tVuGG6cuCcgLwuwQXU/BjX67QU95AbCLRuqHL7Y5rhHkyzfFnW4Iyml3Fv\nqNvGpS0hjfAjccf1xD3gluAeAl/ijNZhxIVowRmd/8LFQFvh6+xt3762S8hznJelPS5swnu+zJ/j\nepi2TCLLDrieqfm+rlfgjKYncA+FSEL6iK+f133alT79GGCvhLS/YWPsqur4doPruYiSJB5WutdM\nCnV+mdf/Gt8e7sQ9HBaSPJRESnryaVMOP5Jw3P44g32+1+9Pvpwv4nrGEuP1bQg/kkLew30dJ4Yf\nGcvGkAzxIRp+8OUbQFwMtxTPtTcu0O4y3yZm4V7e+gTJkG7bo4Z7YpI6HYkzgr/xOv/E5/uLJHqe\njTPivsf1gh6VTHbcS+ho3LW1zqdJvIfu6dvYB7jrcLlvfw/jfAMT9bHJtUAN93ncPSzWloPC52yJ\nu9e+6et0Fe5e+jzOb7BVmrrdDfecm+v1u9ZfE1Nx98Rk95b9fD39z+u3yv++m4BQVAnlTmybP+Ge\nQ48ChwUc1yfJcZuEIEn3+mzsj/jCZA1+SOhNXNiJXiKyLS7a/J64B+PZqvqDTzsI58gexTlqTglH\nasPITcQtldYbaK+uF9QwDMPIIbLRR+4PuLeGmIV5DfCyqnbEWfLXwIYZRefglh3qAYxO4jRrGIZh\nGIbRJMkqw8fPbjwJeICN/icn47qV8d+n+t+n4NYcXKeqi3CzDY9oPGkNwzAMwzDCJasMOdxiwn9i\n06jpO6lqLGjkEjbOQGzHxtUK8L8zHavKMJo6Sv2C1BqGYRghkjWzVsVFov9GVStFpCQojaqqiNT0\n0NlsXy3pDcNwfCq1hjY0DMMwGgNVTfmGnDWGHC4K/8kichJumvXWIvIIsEREdlbVr8UFFP3Gp/+C\njUt1gJshE7gMULZN6DBSY+jQoQwdOjRsMYw6YvrLbUx/uYvpLrdJ96U6a4ZWVfVaVd1dVTvgYm5N\nU9XfAc/hpgjjv5/xv5/DxR8r9MFa9yV4IW0jR1m0aFHYIhj1wPSX25j+chfTXX6RTT1yicS60W4C\nnvARsxcBZ4NbPsUHYlyAWxD+UrWuN8MwDMMw8oisiyOXaUTE7LscpaysjJKSkrDFMOqI6S+3Mf3l\nLqa73EZE0vKRM0POMAzDMAwjS0jXkMsaHznDSKSsrCxsEYx6YPrLbUx/uYvpLr8wQ84wDMMwDCNH\nsaFVwzAMwzCMLMGGVg3DMAzDMPIEM+SMrMX8PHIb019uY/rLXUx3+YUZcoZhGIZhGDmK+cgZhmEY\nhmFkCeYjZxiGYRiGkSeYIWdkLan4eUSjUaLRaMMLY6SN+enkNqa/3MV0l1+YIWfkJBUVFfQqLaVF\nYSEtCgvpVVpKZWVl2GIZhmEYRqNiPnJGVhLrZYtEIpvtq6io4ITiYoZXVdHbbxsPDG7dmsnl5XTu\n3LnxBDUMwzCMDGI+ckZOk0pP25ABAxheVUV/oJX/9AeGV1UxdODAEKQ2DMMwjHCwHjkja0jsaSsH\nFuF62v755GwWLz6YWbOqGTt2Nh3ZDqWAtvzAPnzEYcylG1M4Uhbw07q1gT15RuNSVlZGSUlJ2GIY\ndcT0l7uY7nIb65EzcpbEnrYWQEdK2anqCXr9ak/++1/o0gUici2PcRrP04s7uJIeTOJj9uYsnieq\nbzJ6tFBVtXn+NjHCMAzDaGpYj5yRFUSjUVoUFrK8uppWwCd0oD9jWEgHBvA3Lpcn+Gndj0QiEXqV\nltKzrIz+CXmMRnjk0D/Sbu+RvPYaXH899O0L8+dXMGTAACaVlwPQo7iYYaNGUVRU1OjlNAzDMIya\nsB45I6dRYAyXcARzOJ4pLOBAejMOkTUb0gwbNYrBrVszBljlP2OAIa1bMXrsb3nySXj2WZgwAQ45\nZBXHHHUJPcvKWF5dzfLqanqWlXF8t25UVFSEU0jDMAzDyBBmyBlZQSQS4fijjuZYxnIfFzOTbnRh\nJM1Yz3jgxO7dN/i9FRUVMbm8nImlpbQpKKBNQQETS0uZMnPmhl62Ll1g6lRoVj2a9asn8hNX0hKb\nGNGYWCyr3Mb0l7uY7vKLLcIWwDAAfvgBvl39FG9FZnBLtBt7sopPcT1tg1u3ZsrIkZuk79y5M89N\nm1ZjmJLq6ijvffRn5jGa3/IklRQxhv604Cd6A1fMmEE0GrWJEYZhGEbOYj1yRuisXAknnghdumzF\nK7PbMbX057QpKKBXQE9bIpFIpFZDrAMLeYWjqKI1RzON79mmIYphJGCz5nIb01/uYrrLL2yygxEq\na9ZAz56w115w330g3r2zpp62dIifGFGN8Cf+zn85lt9wPK+UHsRz06bVswSGYRiGkTlssoORM6jC\nb38LO+wAY8ZsNOLAGXAzZ86s9zniJ0asQRnGQHbnaa6VmVx+zT/qnb+RHPPTyW1Mf7mL6S6/MEPO\naFTiY7mNGAFffAEPPwwN5aaWODGibUEBBaXlXNx/SwYOPJhlyxrmvIZhGIbRGNjQqtEoVFRsGsut\n80EDWfj1cObNK6Rdu8aRIX64VhUGDIDXX4cpU6B168aRwTAMwzBqwoZWjawjtvRWLJbbe9U78978\nq1m7oidff914sdziJ0aIwK23wj77uOHd6upGE8MwDMMwMoYZckaDE7/0Vkvgch5kAKO5ac1/a4zl\n1tB+HgUFboLF0qUwePDG7baUV2YwP53cxvSXu5ju8gsz5IwGJRqNMqm8nN7+/71cwlK241r+Rm/g\nJR/LLSyaN4cnn4THHoMbb1xIr9JSWhQW0qKwkF6lpVRWVoYmm2EYhmHUhvnIGQ1K/Bqq37AnXXiT\nmXTjAP7HKqBNQQFr1q4NPSjvE08s4NxzduQ6unMNCwAYjwtGPLm8nM6dO4cqn2EYhpEfmI+ckVVE\nIhF6FBczHvgD/+CP3MYB/A9gs6W3wuSRey7jdwzkSZ5AaWVLeRmGYRg5gfXIGQ1OZWUlJV3/SvOf\nRvA+P6M5azf0dtW0akNZWVmjRCiP7zW8lLEAjOMCgKzqNcw1Gkt/RsNg+stdTHe5jfXIGVnH/vsX\nsdX2j7LXIfezY8H6wEXus4W7uYw5HME4+oQtimEYhmHUivXIGQ3OiBHwxhvw1FOZW3or08Qv5TWf\nn3E003iDw5nEp0wsLbWlvAzDMIxGId0eOTPkjAZl6VLYbz949VXo2DFsaZJTWVnJ8d26Mbyqit7A\nSP6Pf3ICS1udwsuvlGddz6FhGIbRNLGhVSOrGDECzjyzbkZcY8ZCSlzK6wYZxbdb78SFly8wI66O\nWCyr3Mb0l7uY7vKLLcIWwGi6fPYZjB0L77wTtiSp0blzZ56bNm3D8O/HH0c48ki48MLs7k00DMMw\n8hcbWjUajH79YMcd4W9/C1uSunPHHfCf/0BZmVsJwjAMwzAaEvORS8AMuXD47DPo1Ak+/BC22y5s\naepONApdu0L//tC3b9jSGIZhGE0d85EzsoJbbnE9cvUx4rLBzyMSceuxDhoE334btjS5RTboz6g7\npr/cxXSXX5ghZ2Scr7+Gf/0Lrr46bEkyQ6dO8Nvfgi3wYBiGYWQbNrRqZJw//Ql++sn5lzUVVq6E\nAw+EcePg6KPDlsYwDMNoqpiPXAJmyDUuP/4I7dvDvHmwxx5hS5NZnn4arrsO3noLtrD53oZhGEYD\nYD5yRqg89BAcf3xmjLhs8/M49VTYeWcYMyZsSXKDbNOfkR6mv9zFdJdfmCFnZIRoNMratVHuuAOu\nuipsaRoGEbj9dhg2DL7/3pU5FnPOMAzDMMLADDmjXlRUVNCrtJQWhYW0bHEWy75bQPPmlRnJu6Sk\nJCP5ZJKDD4bu3b/lsEOeokVhIS0KC+lVWkplZWbK3JTIRv0ZqWP6y11Md/mFGXJGnamoqOCE4mJ6\nlpWxvLqaX+qVnLHiBo7v1o2KioqwxWsQKioqmDaxC9990Y3XqvdjeXU1PcvKmnSZDcMwjOzFDDmj\nzgwZMIDhVVX0Bz7hID5mX+7hKYZXVTE0A7E6stHPY8iAAfx11WcM56/8hVG0BPpDxsrclMhG/Rmp\nY/rLXUx3+YUZckadiEajTCovp7f/fy+X0I8HaMZ6egMvzZjR5PzH4st8GXeziPZMogdAky2zYRiG\nkd1kTfgREWkBzACaA4XAs6o6SESGAv2AWFz9a1X1JX/MIKAvEAWuVNUpAfla+JEGIBqN0qKwkOXV\n1UBLdudzKiliDz5nFdCmoIA1a9cSiUTCFjVjxJe5FfA0pzKUoVRSxBq0SZbZMAzDaFxyNvyIqq4B\nSlW1E3AIUCoiRwEKjFLVIv+JGXEHAucABwI9gNEikjXlaepEIhF6FBczHniCs+nKbPbgcwDGAyd2\n797kDJr4MgOcyjO0ZDWPcV6TLbNhGIaR3WSV4aOqq/zPQiACLPP/gyzTU4DHVHWdqi4CPgKOaHAh\njQ0MGzWKwa1bM4xL6MN9rALGAINbt+aGkSPrnX82+nnEyjwGWA0M5Rr+wHCua9U2I2VuSmSj/ozU\nMf3lLqa7/CKrDDkRKRCRecASYLqqvut3XSEib4nIgyLS1m9rByyOO3wxsGsjipv3FBUVcdeDc/iq\n+d6cJ5NoU1DAxNJSpsycSVFRUdjiNQhFRUVMLi9nYmkpbQoK6FUwk4Jtv+XCy99usmU2DMMwspes\n8ZGLR0TaAJOBa4AFbPSPGw7soqoXisidwGuq+qg/5gFgoqo+lZCX9unTh/bt2wPQtm1bOnXqtCHO\nTuzNxf7X7f8555TRrBk8/HA3AGbOnJlV8jXk/2g0SllZGZ98EuH660v48EN4883skc/+23/7b//t\nf/b/j/1etGgRAA8//HDTWGtVRAYDq1X11rht7YHnVfVgEbkGQFVv8vsmAUNU9fWEfGyyQwOxfr1b\nimvaNNh//7ClCZfzzoMDD4TBg8OWxDAMw8hlcnayg4hsHxs2FZGWwHFApYjsHJfsNGC+//0ccK6I\nFIpIB2BfYE5jypzvTJ0Ku+3WcEZc/NtKtjN8uFu+a+nSsCXJHnJJf8bmmP5yF9NdfpE1hhywCzDN\n+8i9jut5mwrcIiJvi8hbQHfgjwCqugB4Ajf0+hJwqXW9NS6PPAK/+13YUmQH++wDp58Ot90WtiSG\nYRhGPpG1Q6uZwoZWG4YVK2D33eHDD2GHHcKWJjtYuBC6dIEPPoDttgtbGsMwDCMXydmhVSO3eOop\nKC42Iy6eDh2sV84wDMNoXMyQM+pEYwyr5qKfx7XXwj33mK8c5Kb+jI2Y/nIX011+YYackTaLF0Nl\nJfTqFbYk2Yf1yhmGYRiNifnIGWlz223wzjvw4INhS5KdLFoEhx1mvnKGYRhG+piPnNHg/PvfcNZZ\nYUuRvbRvD2ecAaNGhS2JYRiG0dQxQ85Ii88/h/ffh6OPbvhz5bKfx6BBMGYMLF8etiThkcv6M0x/\nuYzpLr8wQ85Ii6eegpNPhsLCsCXJbjp0gJNOgtGjIRqNEo1GwxbJMAzDaIKYj5yRFkcd5WZmnnRS\n2JJkP//+9wJ+95udWb9+d0TW0KO4mGGjRlFUVBS2aIZhGEaWYj5yRoPxxRewYAEce2zYkmQ/FRUV\nXHrBEey3biZ/1/NZXl1Nz7Iyju/WjYqKirDFMwzDMJoIZsgZKfPUUy7kSGMNq+ayn8eQAQMYXlXF\nvYzgH/yJZmxBf2B4VRVDBw4MW7xGIZf1Z5j+chnTXX5hhpyRMjZbNTWi0SiTysvpDfyC1+nAQh7n\nXAB6Ay/NmGE+c4ZhGEZGMB85IyW++goOPBC+/hqaNw9bmuwmGo3SorCQ5dXVtAKmcBx/5DbmczBr\nUNoUFLBm7VoikUjYohqGYRhZhvnIGQ3C88/DiSeaEZcKkUiEHsXFjPf/j+NlWrCG5+nFeODE7t3N\niDMMwzAyghlyRko895wLO9KY5LKfx7BRoxjcujVjgNXA1YzgKq7lulatuWHkyLDFaxRyWX+G6S+X\nMd3lF2bIGbWyahWUl0OPHmFLkjsUFRUxubyciaWltCkooI88y7ct2zHi9koLP2IYhmFkDPORM2ok\nGo3y/PNwxx0Rpk0LW5rcJDax4YEHIrzwghumNgzDMIwgzEfOyAgVFRX0Ki2lRWEhp582jiWf3UVl\nZWXYYuUkkUiESCRC794wZ45b4swwDMMwMoEZcsZmVFRUcEJxMT3LylhWrezISZz78W2NHsy2qfl5\ntGwJ/fvDbbeFLUnj0NT0l2+Y/nIX011+YYacsRmxYLb9gQV0YVuWMZhP8iqYbUNx6aUwYQJ8+23Y\nkhiGYRhNAfORMzYhMQbadQxnPVtwE4NYBRYDLQP06wd77AHXXx+2JIZhGEa2YT5yRkZ5nl70wrzz\nM8nVV8Po0bBmTdiSGIZhGLmOGXLGJsQHs/2M3fmSdvyC1wAaPZhtU/XzOPBA6NwZHn00bEkalqaq\nv3zB9Je7mO7yCzPkjM2IBbMdxIkcw2R+opoxwODW+RPMtqEZMABGjQIb9TcMwzDqg/nIGYFUVFTQ\n84Qqvll6PwXyKCd2784NI0daMNsMoQpFRXDTTRZo2TAMw9hIuj5yZsgZgaxbBzvsAO+9F2XHHbHJ\nDQ3AI4/A+PHw8sthS2IYhmFkCzbZwcgIr70Ge+8Nu+wSCc2Ia+p+HuecAwsWwFtvhS1Jw9DU9dfU\nMf3lLqa7/MIMOSOQyZPhhBPClqJpU1gIl18Od9wRtiSGYRhGrmJDq0YgXbrAyJHQvXvYkjRtvvsO\n9t0XPvwQtt8+bGkMwzCMsLGhVaPefPstfPQRdO0atiRNn+23h9NOgwcecMGYo9Fo2CIZhmEYOYQZ\ncsZmvPwylJS4ob8wyRc/j2OPfY8bhi6hebOWtCgspFdpKZWVlWGLVW/yRX9NFdNf7mK6yy/MkDM2\nY9IkC4nRWFRUVPCHiw9n158+YLz2Ynl1NT3Lyji+WzcqKirCFs8wDMPIcsxHztiE6mpo1w5mz4YO\nHcKWpunTq7SUnmVlbMeZ3MXlzKAEgDHAxNJSnps2LVT5DMMwjMbF4sglYIZcerz1Fpx1FnzwQdiS\nNH2i0SgtCgtZXl1NM7ZgLz7hBX7FobzNKqBNQQFr1q61GH6GYRh5hE12MOrF1Klw7LFhS+HIJz+P\nZqynP2O4kyvCFiVj5JP+miKmv9zFdJdfmCFnbMK0aXD00WFLkR9EIhF6FBcz3v+/mPt4kjNYyraM\nB07s3t164wzDMIwasaFVYwPr1rlwGB9/bDHNGovKykqO79aN4VVV9AYuZixVvMcrre9mysyZtrat\nYRhGnmFDq0adefNN2GsvM+Iak6KiIiaXlzOxtJQ2BQU8LnczqfnVTJxuRpxhGIZRO2bIGRvItmHV\nfPHz6Ny5M89Nm8aatWv5ad1rdD5sJz7/PPeNuHzRX1PF9Je7mO7yCzPkjA1kmyGXb0QiESKRCFde\naeuvGoZhGKlhPnIGAKtXw447whdfwNZbhy1NfrNuHbRvDy+9BIccErY0hmEYRmNiPnJGnZg9Gw4+\n2Iy4bKBZM+jfH0aPDlsSwzAMI9sxQ84AsnNYNZ/9PPr1gwkT4Mcfw5ak7uSz/poCpr/cxXSXX5gh\nZwDZacjlM7vs4gIzP/JI2JIYhmEY2Yz5yBmsWOHWV/3mG2jZMmxpjBjTp8MVV8D8+SApe0sYhmEY\nuYz5yBlpM2sWHHaYGXHZRkkJRKMwc2bYkhiGYRjZihlyBuXl0L172FJsTr77eYjA738P99wTtiR1\nI9/1l+uY/nIX011+YYacQXk5FBeHLYURRO/eMGkSLFkStiSGYRhGNpI1PnIi0gKYATQHCoFnVXWQ\niGwLTAD2BBYBZ6vqD/6YQUBfIApcqapTAvI1H7kaWL0adtjBGQqtW4ctjRFEv35u6bRrrw1bEsMw\nDKOhyVkfOVVdA5SqaifgEKBURI4CrgFeVtWOwFT/HxE5EDgHOBDoAYwWkawpT67w+usufpwZcdnL\npZfCvfc6fznDMAzDiCerDB9VXeV/FgIRYBlwMvCw3/4wcKr/fQrwmKquU9VFwEfAEY0nbdMgm4dV\nzc/D0bkz7LwzTJwYtiTpYfrLbUx/uYvpLr/IKkNORApEZB6wBJiuqu8CO6lqzENoCbCT/90OWBx3\n+GJg10YTtomQzYacsZFLL7WVHgzDMIzN2aIuB4nIFkAXoAjY0W/+BqgE3lTV9XXJV1WrgU4i0gaY\nLCKlCftVRGpyeAvcd/7559O+fXsA2rZtS6dOnSgpKQE2vrnk4/+1a2HWrDKuugogfHkS/5eUlGSV\nPGH+P/vsEgYOhEcfLWPXXcOXx/TX9P+b/uy//W+c/7HfixYtoi6kNdlBRA4ArgDOA9oA64DvAQG2\nAZoBPwL/Au5U1ffqJJU712BgNdAPKFHVr0VkF1xP3f4icg2Aqt7k008Chqjq6wn52GSHJLz2mgtv\nUVkZtiRGKgwcCAUFcMstYUtiGIZhNBQNNtlBRMYCc4HdgauAA4AWqrqLqu4MtPDbrgL2AOaKyENp\n5L+9iLT1v1sCx+F6+J4D+vhkfYBn/O/ngHNFpFBEOgD7AnNSPZ+R/cOq8W8rBlxyCYwbB1VVUaI5\nMPPB9JfbmP5yF9NdfpGyIQesAPZV1V6q+rCqvh/f1aWO91V1nKr+CmdYpbPk9y7ANO8j9zrwvKpO\nBW4CjhORD4Cj/X9UdQHwBLAAeAm41LreUicajTJjhma1IWdsyooVFej6N9h6q760KCykV2kpldad\nahiGkddkTRy5hsKGVjeloqKCIQMG8NKMV4jqNxx3ZF9uvut6ioqKwhbNqIGKigpOKC7mjKpjmcf/\nMY1fMh4Y3Lo1k8vL6dy5c9giGoZhGBkgZ+PIGQ1PzBjoWVbGK3ogHVnC6a8+w/HdulFRURG2eEYN\nDBkwgOFVVdzFC3zB7nzIIfQHhldVMXTgwLDFMwzDMELCDLk8ImYM9AcqOZKjmJXVxoD5eTii0SiT\nysvpDWxBlAt5kPu4GIDewEszZmSlz5zpL7cx/eUuprv8wgy5PCHeGAB4lSM5kleB7DYGjM25kAd5\njPOoolXYohiGYRghUy8fORE5yAftzVrMR84RjUZpUVjI8upqWgF78xEv8CsO4H+sAtoUFLBm7Voi\nkUjYohoB9CotpWdZGf1j/3mO03iatYxlYmkpz02bFqp8hmEYRmbIuI+ciOyR5LMncEG9pDUajUgk\nQo/iYsYDX7MTy9iG/XgfgPHAid27mxGXxQwbNYrBrVszBlgFnM+9DOcSBrduzQ0jR4YtnmEYhhES\nqZoeJz8AACAASURBVAyt9gOm4dY5jf+MA85tMMmMjBMzBobSlcN5jTUoYyBrjQHz89hIUVERk8vL\nmVhaSpuCAs6RKXzdvAN3PvBm1s44Nv3lNqa/3MV0l1/UukSXql4vIt+p6h2J+0TkioYRy2gIYsbA\n2ad+yMLFs2kjBZzYvTtTRo7MWmPA2Ejnzp15btq0Db6MN94Yobx8R8611ynDMIy8JSUfORFprapV\nAdubqeq6BpEsQ5iP3OYcdRQMGRLl6KOx4dQcZvFiOOQQ+Owz2HLLsKUxDMMwMkGDxJFLNOJEZCe/\nPauNOGNzfvoJ5s2Drl0jZsTlOLvt5ozyCRPClsQwDMMIi7qGH7HBnBylshI6dsyNHhzz86idSy6B\ne+8NW4pgTH+5jekvdzHd5RcWRy7PePVVOPLIsKUwMkWPHvD1185ANwzDMPKPOsWRE5E/qOo/GkCe\njGM+cpty5plw2mnwm9+ELYmRKYYNg6++gnvuCVsSwzAMo77YWqtGUlRh1izrkWtqXHih85NbuTJs\nSQzDMIzGxgy5POLTT913+/ahipEy5ueRGrvuCt26weOPhy3Jppj+chvTX+5iussv6mrI2VhlDhLz\nj5OUO2yNXCGbJz0YhmEYDUddfeSaq+pPDSBPxjEfuY1ccYXrjRswIGxJjEwTjcJee8HTT0PnzmFL\nYxiGYdSVRvGRixlxInKGiNwiIjkQzMJ49VXo2jVsKYyGIBKBfv3gvvvClsQwDMNoTOrrI3cY8HNg\n3wzIYjQgq1fD//6XW7015ueRHrFJDytWhC2Jw/SX25j+chfTXX5RX0Puc6BEVS2KVZZTWQkHHggt\nWoQtidFQtGsHJSXZN+nBMAzDaDjq5CO34WCRjsANwP3AbFVdnSnBMoX5yDluuw0++gjuvjtsSYyG\n5KWXYPBgePPNsCUxDMMw6kJjx5EbCvwA3Ap8LyKzReQmETmqnvkaGWbOHDjiiLClMBqa44+H776D\nuXPDlsQwDMNoDOpryL0D3KuqnYGdgRt9nn+sr2BGZslFQ878PNInmyY9mP5yG9Nf7mK6yy/qZcip\n6t+ArUXkbFVdrqovqur/qeoZGZLPyADffec+++0XtiRGY9C3LzzxBPzwQ5RoNBq2OIZhGEYDUi9D\nTkRaAd+o6hMZksdoAN54Aw4/HApybB2PkpKSsEXISb7+uoIWW5Sz3baX0aKwkF6lpVRWNv58JNNf\nbmP6y11Md/lFfR/t1wBPi8iuInKDiMwXkZtFJJIJ4YzMkIvDqkbdqKio4ITiYs787m8cohexvLqa\nnmVlHN+tGxUVFWGLZxiGYWSY+hpyS1T1AGA34DrgYmCs/21kCblqyJmfR/oMGTCA4VVV/IMpLGM7\n3qMz/YHhVVUMHTiwUWUx/eU2pr/cxXSXX9TXkNtJRAqAU4F3VHW2qv4PWFZ/0YxMoAqvv56bhpyR\nHtFolEnl5fQGClAu4n7u42IAegMvzZhhPnOGYRhNjPrGkTsIuA84CLhEVSeIyAHAkar6YIZkrBf5\nHkfuk0+guBgWLw5bEqOhiUajtCgsZHl1Na2AL9mFg3iXz9iDCCtpU1DAmrVriUTM88EwDCNbadQ4\ncqr6rqr+UlXbeiNuW2A+sE998jUyR64OqxrpE4lE6FFczHj/vx1fUcp0HuM8xgMndu9uRpxhGEYT\nI6PzGFX1e6AjMCyT+Rp1Z84c+PnPw5aibpifR/oMGzWKwa1bMwZYBfTmPv7KxQxu3ZobRo5sVFlM\nf7mN6S93Md3lFxkPSKGqn2TjUl35ivXI5RdFRUVMLi9nYmkpbQoKOFOm8m2L3bj93jcpKioKWzzD\nMAwjw9TLRy4XyGcfuXXrYJtt4MsvYeutw5bGaGxiExtGjIiweDGMGROyQIZhGEatNPZaq0YW8+67\nsOeeZsTlK5FIhEgksmGlhxUrwpbIMAzDyDRmyDVhcj3siPl5ZIZ27aB7d3j88cY9r+kvtzH95S6m\nu/yivkt0nSoi+2dKGCOzvPFGbhtyRua4+GK4776wpTAMwzAyTX3jyN0PnIwzCF8BZvrvuaqaFZFH\n89lHrqgI7r3XjDkDolHYay94+mno3DlsaQzDMIxkpOsjl5HJDiLSEfil/xwHbAc8BQxS1S/qfYL6\nyZaXhtyaNbDttvD999CiRdjSGNnAjTdikx4MwzCynFAmO6jqB6o6VlX74VZ5GIPrmXteRPbKxDmM\n9Jg/Hzp2zG0jzvw8MssFF8CECbByZeOcz/SX25j+chfTXX5RXx+5/iLytIj0EZFWAKq6EvhQVe8D\njgH6ZUBOI03mzoXDDgtbCiOb2HXXcCY9GIZhGA1HfX3kbsctyXUGblh1DrAcqFLVPn7d1WJVvTcT\nwtZRxrwcWr3oIucjd+mlYUtiZBMTJ8LQoS5QtGEYhpF9NPbQ6nu43reTgA7A7cBDwCUisg3wNnBw\nPc9h1IG5c82p3dicE06AJUugsjJsSQzDMIxMkJYhJyL/z96dx0dVXn8c/zwZiEBU0GIVcQEVURQk\nUVGqCYkggoj7VrSISxW3qgX9aSuLoBZtobi17gvuW6uIgAthCKAgOlE2ERfQgoKgCBrEwOT8/piJ\nxkAgM5mZO3fm+3695pW5dyZ3TnscPXnueZ6nsOZxdKQt7Jw70sy+NbNXzWyimW0wszVE+uWuTWC8\nUg8//QSLFsEhh3gdScOozyPxAgG46KLULEWi/Pmb8udfyl12iXVEbohzrmnNE2Y208xmbenN0UkQ\n2nc1xebPh/32g6ZNt/1eyT4XXJDaSQ8iIpI8MfXIOeeqgI3Ae0BZ9DHTzNYmJ7yGy8Yeufvvh7ff\nhkce8ToSSVcnnQQnnggXXuh1JCIiUlOye+T+A/QAXgXygWeAb5xz5c65O5xzJznnGsV4TUkwzViV\nbbnkkshi0SIi4m+xFnIfmtl0M7vFzI4DdgK6Ak8AbYBHgHeiEx3EI5lSyKnPI3mOOw5WrEjupAfl\nz9+UP/9S7rJLTIWcmQ2pdRw2szlmNtrMTgJaAeOAUQmMUWLw449hFi403090kOSqnvTwwANeRyIi\nIg2RkJ0dqpnZT2Y2Fvg81t91zu3pnJvqnFvgnJvvnPtT9Pxw59yy6O3bcudc7xq/c4Nz7mPn3CLn\nXM8E/k/xnVAoRN+SEnbIO4Iff1zAWX1KKPf5GhPFxcVeh5DRLrggsjhwRUVyrq/8+Zvy51/KXXZJ\naCHnnLvfOXc8kQkRsdoIXGNmBwFHApdHFxQ2YIyZ5Ucfk6Kf1QE4C+gA9AL+5ZxL6P8evwiFQhxX\nVESfYJA7LJ9+vEefYJCehYWEQiGvw5M0tcceUFgITz1VRTgc9jocERGJQ6zryPXbxlv2IrIo8MpY\nAzGzFWb2fvT5D0QWG25d/dFb+JWTgKfNbKOZLQU+AbrE+rmZYNigQYysqGAgMJ8CjuA9BgIjKyoY\nPniw1+HFTX0eyRUKhfhqyQ1cfPEcmuTm0rcksaO4yp+/KX/+pdxll1hHsPps7UUz62Vm+5vZuAbE\nhHOuDZFZsdXr013pnPvAOfeQc65F9NzuwLIav7aMXwq/rBEOh5lcVkb/6PF7HMqhvAdAf2DStGka\nbZHNVI/iDph3O3vQirKqjhrFFRHxoViXCvm9cy4fmAHMBGaY2ae13+Sc293MvownIOfc9sALwFVm\n9oNz7t/AiOjLI4HRQF2rX21xwbgBAwbQpk0bAFq0aEHnzp1/7iGo/svFz8dV0XXyNtKIuXzDumgh\nB1BlRjAYpHv37mkTb32Pi4uL0yqeTDoefdNNjKyo4ACgBzfyBH/kHq5gcUUFV1x4IW9FR+aUv+w9\nVv50rOPUHFc/X7p0KfGIdUHgq4HOwI/AUUS24FpFpLCrfpQDY83sypiDca4xMAGYFJ00Ufv1NsAr\nZtbROXc9gJmNir42GRhmZrNr/U7GLwjct6SEPsEgR3II/XiKhRwEwL3AxJISxpeWehugpJVwOEyT\n3FzWVlXRDFhGazoxl/+xJ471NM/JYUNlJYFAwOtQRUSyTlIXBI4WV8OAOcCpwG+IjI4tjh6XAWuB\n82K5LoBzzgEPAQtrFnHOuVY13nYKMC/6fDxwtnMu1znXFmgHvBPr52aCEWPGMCQvj9EcyiG8x3oi\nRdyQvDxuGj3a6/DiVvOvFUmePVjO0czgWc5K6HWVP39T/vxLucsuMRVyAGb2uZk9DOwG9AWCZvYX\nMysCWgDHEinsYnUUcC5QUmupkducc3Odcx8A3YBronEsBJ4DFgKTgMsyfuitDvn5+bxWVsb03U/k\nOReieU4OE0tKeH36dPLz870OT9JMIBCgV1ER42qcu5j7uZ+LGQf07tZNo3EiIj4R063VzX45sh3X\nKUCFmU2scf6fZnZNAuJrsGy4tVrtiCPgttvCFBai/xDLVpWXl9OzsJCRFRX0B8LksDdLsSZnUPrW\nv/UHgIiIR2K9tdqgQq7Gh+4KHA/MMbP5Lo2qpzQKJak2bYLmzSPbLu2wg9fRiB+EQiGGDx7MpGnT\nANhnr4c45PA+PPfcLh5HJiKSvZLaI1cXM1tJZGuuDs65kcCOibiu1N+iRbDnnplVxKnPI7kKCgoY\nX1rKhspKNlRW8mbZAN58c5eE7fSg/Pmb8udfyl12iWn5Eefc7sC+QFugTa2frYks3Ptl9PjcBMYp\n2/D++9C5s9dRiB9V34bfc0846ih47jk4/3yPgxIRkXqJdfmRSmAFsLTG4/Maz78ws3i250qabLm1\nOngwtGwJ11/vdSTiZxMmwC23wNtvex2JiEh2Svat1U+AR4BSYDLwkJk9ZGZTzOzT6iLOOffbGK8r\nDaQROUmEXr1g2TKYO9frSEREpD5iLeSeN7NhZjacyJptxc65odHHZc65Q6Ib19+V8EilTmaZWcip\nzyP1GjWCCy+E++9v+LWUP39T/vxLucsuMfXImdmwGs8/ITJCB4BzbmegK3AWkcWBJUWWL4/8B3i3\n3byORDLBhRdG/ii4/XZo1szraEREZGsSsvzIZhd17jkzOzPhF45DNvTITZgAd98Nkyd7HYlkir59\n4bTTYMAAryMREckuniw/sgUjk3Rd2YJMvK0q3rr4YrjvPq+jEBGRbUlKIWdm87b9LkmUTC3k1Ofh\nnd694X//a9ikB+XP35Q//1Lusku9Cznn3DnRje3r+/6Ac05ryaVAphZy4p3qSQ8PPOB1JCIisjX1\n7pFzzs0FmgKPEpm9uriO9x0EnA70B34ws0MSE2p8Mr1Hbt062H13WLsWtL2qJNIXX0B+fmRkTpMe\nRERSI5k9cp2J9L6dDixyzq12zk13zr3snBvvnHvLObcGmAf0BYZFf0eSaO5cOPhgFXGSeHvtBV27\nRnZ6EBGR9FTvQs7MqsxsnJnlA/nALcBnQGMiy5h8BAwHOpnZYWb2REYPhaWJTL6tqj4P7118cfxr\nyil//qb8+Zdyl11iWkeumpl9AHyQ4FgkDu+/D4cd5nUUkqmOPx4uuwzmzYOOHb2ORkREakvKOnLp\nJNN75A49FO65B4480utIJFMNGwZr1sCdd3odiYhI5ou1R06FnI9t3AjNm8OqVZCX53U0kqk06UFE\nJHXSZUFgSYFFiyIN6ZlaxKnPIz3stVdkxPf55yEcDhMOh+v1e8qfvyl//qXcZRcVcj6WyRMdJL10\n7/4p1/xpPk1yc2mSm0vfkhLKy8u9DktEJOvp1qqPDRoEu+wC11/vdSSSyUKhED0LS6haP5+JnEAn\n5jIOGJKXx2tlZRQUFHgdoohIxtCt1SyiETlJhWGDBnHz+nVcw/08yqU0AwYCIysqGD54sNfhiYhk\ntVh2dpgDGLC1KrH6dTOzLg0Pr+EydUTODFq2hAULYLfdvI4mOYLBIMXFxV6HkdXC4TBNcnNZW1XF\nWnajAwtZShuas471QPOcHDZUVhLYworUyp+/KX/+pdz5W6wjcrGsI7cghvdmXuWUZpYtg8aNM7eI\nk/TTihX05HUe5w9cwT1ehyMiIqhHzrdeeSWyftzkyV5HIpmub0kJfYJBBgJBunE59zCfg7kPmFhS\nwvjSUq9DFBHJGMkckZM08v77cMghXkch2WDEmDH0LCyEigr+wDSqcAyiiMfz3uP10aO9Dk9EJKvF\nPdnBOXe2c26Kc+4L59yq6OPr6p+JDFI2N3du5k900FpI6SE/P5/XysqYWFJCi5wcFrt/8+xvh/P6\n9Onk5+fX+XvKn78pf/6l3GWXuAo551w/4DHgE2AP4GVgAhAA1oEaaJJt7lztfSmpU1BQwPjSUjZU\nVrJq9VjWV5aw2251F3EiIpIacfXIOefKgReBUUAlcJiZhZxzOwBvAs+b2T8SGmmcMrFHbv16+M1v\nYN26yIQHkVS75BLYc0+48UavIxERySypWkeuHTADCEcfOwKY2fdEirsr4ryu1MPChdC+vYo48c6l\nl8J998GmTV5HIiKS3eIt5NYBzaJDXV8CHWq85oCWDQ1M6jZ3LnTq5HUUyac+j/TVuXNkD9YJE+p+\nj/Lnb8qffyl32SXeQu5doLqUeBkY6py72Dk3APgHMCsBsUkdsqWQk/R26aXw7397HYWISHaLt0eu\nK7C3mT3jnNsJeBToQ6QwnAP0M7NPExlovDKxR+6YY+D//g+OO87rSCSbbdgQGZWbORPatfM6GhGR\nzBBrj1zMhZxzrjFwBLDEzJbXON8E2M7M1sZ0wSTLtELODHbZBebNg1atvI5Gst3118PGjaDl5ERE\nEiMVkx2qgFKgfc2TZrYh3Yq4TLRiBTiXHVtzqc8j/V1yCYwbBz/+uPlryp+/KX/+pdxll5gLOTML\nAx8DWVBKpJ/q/jhX71pdJHnatoUuXeDZZ72OREQkO8XbI3cycBtwhpnNTXhUCZRpt1b//nf48kv4\n5z+9jkQk4tVX4aab4J13vI5ERMT/UrWO3F+BnYH3o1t0zYk+3qn+Ged1ZRu0o4Okm1694Ouv4d13\nvY5ERCT7xFvILQBeBcYR6ZdbEH0srPFckiCblh5Rn4c/BAIwcODmS5Eof/6m/PmXcpddGsXzS2Y2\nIMFxSD1s3AiLF0OHDtt+r0gqXXgh7L9/5Nb/zjt7HY2ISPaIt0duKPCgmX25hddaAX80sxEJiK/B\nMqlHbv58OP10WLTI60hENte/f+S2/7XXeh2JiIh/papHbjiwRx2vtY6+LgmWTbdVxX+uvBLuuQfC\nYa8jERHJHvEWclvTGliThOtmvWyb6KA+D385/PDIItWvvALhcJgpU6Z4HZI0gL5//qXcZZd698g5\n584DBtQ49S/n3Lpab2sKdAReb3hoUtu8eXDxxV5HIVK3E05YwkXnr2HtusOpMuP4bt0YMWYM+fn5\nXocmIpKR6t0j55w7EzgzengqMJXNR94qgQ+Bf5nZN4kKsiEyqUduzz2hrCyyCKtIugmFQvQs7M7G\n9QuZQg86sJBxwJC8PF4rK6OgoMDrEEVE0l7S91qNfsijwAgz+yzmX06xTCnkvv0W2rSB776DnGTc\nEBdpoL4lJfQJBlnBMFawG/dyKQD3AhNLShhfWuptgCIiPpCqyQ5jgQPqCKCPc04t+QkUDod5//0w\nHTtmVxGnPg//CIfDTC4roz9wCffxLGfxCnkA9AcmTZtGWLMgfEXfP/9S7rJLvGXBP4Ej6njt8Ojr\nMXHO7emcm+qcW+Ccm++c+1P0/M7OuTecc4udc68751rU+J0bnHMfO+cWOed6xvW/JI2FQiH6lpTQ\nJDeXY3tcw7Il4ykvL/c6LJGtasUKjmcik+jtdSgiIhkv3kIuH3irjtfeBuJphtkIXGNmBwFHApc7\n5w4ErgfeMLP9gSnRY5xzHYCzgA5ALyKTLzJmvCoUCnFcURF9gkHWVlVxnh3M776aTM/CQkKhkNfh\npURxcbHXIUg9BQIBehUVMS56fCV3MZnbCJPDOKB3t24EAgEvQ5QY6fvnX8pddom38AkAzep4rRmQ\nG+sFzWyFmb0fff4DkUkTrYETgceib3sMODn6/CTgaTPbaGZLgU+ALrF+broaNmgQIysqGEjk/9CF\ndOJy5jKyooLhgwd7HZ7IZkaMGcOQvDzuBToym51ZzZUcz5C8PG4aPdrr8EREMlK8hdy7wCV1vHZx\n9PW4OefaEBn1mw3samYroy+tBHaNPt8dWFbj15YRKfx8r2a/EUAVjvkcTEfmZVW/kfo8/CU/P5/X\nysqYWFJCi5wcQgzh+Z2G8fr06Vp+xIf0/fMv5S67xLXXKjAMmOKce4fIKNlXRAqr/sAhwLHxBuSc\n2x54EbjKzL537peJG2ZmzrmtTUH1//TULfiMfWjJapqzjvVeByOyFQUFBYwvLSUcDvPGG0EGDDiM\nJk28jkpEJHPFVciZWZlz7ljgb8CdgAOqiIyg9TCz6fFc1znXmEgR97iZvRQ9vdI5t5uZrYju4/p1\n9PxyYM8av75H9NxmBgwYQJs2bQBo0aIFnTt3/rmHoPovl3Q77lVUxLhgkAOAMlrRkXkA3Agc3qnT\nz/1G6RJvMo6Li4vTKh4dx3bcq1d3jj02yA03wEsveR+PjvX907GO0/G4+vnSpUuJR1zryP3qAs7l\nATsBa8ysogHXcURG974xs2tqnL89eu4259z1QAszuz462eEpIn1xrYE3gf1qLxrn13XkysvL6VlY\nyMiKCpYxlEpy2YcbGZKXp1tV4hvLl0e2lVuyBJo39zoaEZH0l6p15H5mZhVmtqwhRVzUUcC5QIlz\nrjz66AWMAo51zi0GjokeY2YLgeeAhcAk4DJfVmx1qNlvdCuHMNotYGJJSVYVcTX/WhH/CQaDtG4N\nPXvCI494HY3ESt8//1Lusku8PXIAOOcOAg4lclvzETP7yjnXDlhpZrX3Yd0qM5tB3YVljzp+51bg\n1lg+x0+q+43atzdeeOEkOnbU8g3iP1deCQMGwJ/+lF0LWouIpEK8W3RtDzwCnEZk/bdGwOFmFnLO\nPQd8YWZpsUaGX2+tVvvxR9h5Z1i3Dho39joakdiZwWGHwYgR0KeP19GIiKS3VN1aHQN0BboDOxCZ\n7FBtImhJ90RZtAjatVMRJ/7lXGQ07o47vI5ERCTzxFvInQpcb2ZTicxWrekLYO8GRSU/mz8fDj7Y\n6yi8oT4Pf6uZv7PPjvyzPG+ed/FIbPT98y/lLrvEW8g1BVbX8doOQOavVpsi2VzISebYbju47DIY\nO9brSEREMku8PXLTgC/N7PfOuUZAJXBYtEduHLCLmaXF7VW/98j16QMXXwwnneR1JCINs3p1pE1g\n0SLYdddtv19EJBulqkfuRuBU59wU4KLoueOdc08AZxLZ+UESQCNykilatoQzz4R//9vrSEREMkdc\nhVx054ZjgFzgrujpm4C2QHczeycx4WW3desioxht23odiTfU5+FvW8rf1VdHCrkNG1Ifj8RG3z//\nUu6yS9yrOpnZTDMrBHYkso7cDmZ2lJnNTFh0WW7BAujQQWtvSeY48EA49FB48kmvIxERyQxxb9Hl\nnNsOOI/IFlmtgK+Ad4BHzawyYRE2kJ975B54AN56S6viS2Z54w245prIDFZX7y4QEZHskJIeOefc\ngcDHwD3AwUSWIOkI3A18Gt0HVRpI/XGSiXr0iBRwb74J4XCYcFiT3EVE4hXvTbv7ge+Afc3sSDPr\na2ZHAPsBa4D7EhVgNsv2Qk59Hv5WV/6cg1NP/Zxzzp5Nk9xcmuTm0rekhPLy8tQGKFul759/KXfZ\nJd5C7jBgmJl9UfNk9HgYcHhDA5NIj1w2F3KSmUKhEPf8o4Cfvt2bWVXtWVtVRZ9gkJ6FhYRCIa/D\nExHxlXjXkVsE3GRmT2/htd8Dw82sfQLiazC/9sitWgX77w/ffqs+IsksfUtK6BMMspKhLKc193MJ\nAPcCE0tKGF9a6m2AIiIeirVHLt5C7mRgNHCOmc2qcb4r8AQwyMxeivnCSeDXQi4YhCFDYPp0ryMR\nSZxwOEyT3FzWVlXxA7vQno/4mHa05BvWA81zcthQWUkgEPA6VBERT6RqQeC/EtmK6y3n3FfOubnO\nuRXAzOj5vzrn5kQfWlMuDtneHwfq8/C7beXvt6ziNF7kXgamJiCJib5//qXcZZdGcf7eAmA+UJ+K\n0X/DYWlAhZxkokAgQK+iIsYFgwwErmYsx/IG1/J3xlFJ727dNBonIhKDuNeR8wu/3lo9+mi4+WYo\nLvY6EpHEKi8vp2dhISMrKugPnMhkducZJuU9z+vTp5Ofn+91iCIinklJj9xWPryFmX2XsAsmgB8L\nOTPYaSf4+GPYZRevoxFJvFAoxPDBg5k0bRpVdgzNmj5AsGwNhx6qIk5EsluqFgS+zDl3XY3jzs65\n5cC3zrmQc26PeK4rEcuXQ5MmKuLU5+FvW8tfQUEB40tL2VBZyU+Vk9n/gDZ8+aWKuHSi759/KXfZ\nJd7JDlcA39c4vhNYDpwTveZtDYwrq6k/TrJFIBCgUaMA110Ht9/udTQiIv4T7/IjPwB9zWyqc+63\nRPZZ7RE9PhW4x8xaJTjWuPjx1uo//gHLlsHYsV5HIpIamzZF1k188kno2tXraEREvJOq5Ud+AraL\nPi8GfgTKosdrgBZxXlfQiJxkn0aNYNAg+PvfvY5ERMRf4i3k5gCXO+cOAv4ETDaz6p2v2wJfJiK4\nbKVCLkJ9Hv4Wa/7OPx9mzICPPkpOPBIbff/8S7nLLvEWcoOAg4B5wJ5EFgiudjaRhYElDlVVsGgR\ndOjgdSQiqdWsGVx+OYwe7XUkIiL+0aDlR5xzLYFvajahOec6AV+Z2aoExNdgfuuR+/RT6N4dli71\nOhKR1Fu9OtIrt3Ah7Lab19GIiKReqnrkqv0WONc59xfnXPXkhh+J9NBJHHRbVbJZy5Zwzjlw551e\nRyIi4g/xriO3vXPueSLbdD0IjASqC7lbgKGJCS/7qJD7hfo8/C3e/P35z3D//fD999t+rySPvn/+\npdxll3hH5MYAXYHuwA78es/ViUDvBsaVtebPh4MO8joKEe+0bQs9esCDD3odiYhI+ot3HbnVpTRq\nyQAAIABJREFUwNVm9oRzrhFQCRxmZiHn3DHAeDPbPsGxxsVvPXIdO8K4caDtJiWbvfcenHIKfPIJ\n5OZ6HY2ISOqkqkeuKbC6jtd2AMJ1vCZbUVkZ+Q/XAQd4HYmItw49FNq3jywQLCIidYu3kHsXOK+O\n104D3orzulnt449hr72gaVOvI0kP6vPwt4bm769/hVGjIKw/Cz2h759/KXfZJd5C7kbgVOfcFOCi\n6LnjnXNPAGcCwxIRXLbRRAeRX3TrBr/5Dbz4IoTDYcKq6ERENhP3OnLOuaOAUcCRQAAwYBZwnZml\nzYLAfuqRGzIEcnLgppu8jkQkPdxxxycM/StUrG+Pc9CrqIgRY8aQryZSEclQKVtHzsxmmlkh0JzI\n7g47mtlR6VTE+Y1G5ER+EQqFGPmXzuxY8QPPWS/WVlXRJxikZ2EhoVDI6/BERNJCQxcExszWm9ly\nM6tIREDZbMECFXI1qc/D3xqav2GDBnHz+gpGcyv/4K80BQYCIysqGD54cCJClK3Q98+/lLvs0uBC\nThLjxx9h2TLYbz+vIxHxXjgcZnJZGf2B03iRb/gNQYoB6A9MmjZNPXMiIjRwr1U/8EuPXCgE558P\nH3zgdSQi3guHwzTJzWVtVRXNgEcYwJOcw5scy3qgeU4OGyorCQQCXocqIpJQqd5rVRJE/XEivwgE\nAvQqKmJc9PhcnuBj2jGbLowDenfrpiJORAQVcmlDhdzm1Ofhbw3N34gxYxiSl8e9wEY2cTW3czF/\nYUheHjeNHp2QGKVu+v75l3KXXVTIpQntsSrya/n5+bxWVsbEkhKa5+RwrXuUj3KP5p6H52j5ERGR\nqIasI3c28EegHZEtuyCylpwDzMx+m5AIG8gvPXJ77QXBIOyzj9eRiKSf6okNo0cHKC+Hp5/2OCAR\nkSRJSY+cc64f8BjwCbAH8DIwgcjCwOuAe+K5brZauxa+/RbatPE6EpH0FAgECAQCDBwIb74Jixd7\nHZGISHqI99bqtcBI4PLo8b/M7HygDbAa0JpyMViwADp0iOzqIL9Qn4e/JSN/O+4IV10FN9+c8EtL\nLfr++Zdyl13iLR3aATOAcPSxI4CZfU9k264rEhJdltBEB5H6u/JKmDQJPvrI60hERLwXbyG3DmgW\nbT77EuhQ4zUHtGxoYNlEhdyWFRcXex2CNECy8te8uUblUkHfP/9S7rJLozh/712gEzCRSH/cUOfc\nJqASGArMSkx42WH+fDjhBK+jEPGPK6+M7ILy0UfQvr3X0YiIeCfeEbm/AUujz4cBs4F/AQ8Dq4BL\nGhxZFtEeq1umPg9/S2b+NCqXfPr++Zdyl13iKuTM7G0zeyb6fI2ZnQRsD+xkZkeY2afxXNc597Bz\nbqVzbl6Nc8Odc8ucc+XRR+8ar93gnPvYObfIOdczns/02tdfw8aN0KqV15GI+Muf/gSTJ6tXTkSy\nW1rtteqcKwR+AMaZWcfouWHA92Y2ptZ7OwBPAYcDrYE3gf3NrKrW+9J6HbmpU2HYMCgr8zoSEf+5\n5Rb48EN44gmvIxERSYxY15Grd4+cc24OcJ6ZLYw+r178d0vMzLrU99o1fmm6c67Nlj5+C+dOAp42\ns43AUufcJ0AXfNafp4kOIvG78krYd19YtAgOOMDraEREUi+WW6sLgA01ni+M/qzrkUhXOuc+cM49\n5JxrET23O7CsxnuWERmZ8xVtzVU39Xn4Wyryt+OOcPXV6pVLBn3//Eu5yy71HpEzswFbep4C/wZG\nRJ+PBEYDF9bx3i3eQx0wYABtotsmtGjRgs6dO/88Pbv6H3ivjmfODHLggQDpEY+Odey3486d4Y47\nilm0CJYvnwJA9+7d0yY+Hes41cfV0iUeHW/9uPr50qVLiUdcPXLOuc7A7mY2cQuv9QH+Z2Zz4woo\ncmv1leoeubpec85dD2Bmo6KvTQaGmdnsWr+Ttj1yZtCiBXz6KbTUynsicbviiuW89PxCVq7uBUCv\noiJGjBlDfn6+x5GJiMQmJXutAv8EjqzjtcOjryeEc67mfM5TgOoZreOBs51zuc65tkR2m3gnUZ+b\nCsuWQbNmKuJEGiIUCvH0I4ex9utDeLvqANZWVdEnGKRnYSGhUMjr8EREkireQi6fyBZdW/I2UBDP\nRZ1zTwNvAe2dc/9zzl0A3Oacm+uc+wDoBlwDYGYLgeeI9OpNAi5L26G3Omiiw9bVvk0g/pKq/A0b\nNIhb1q9gKH/nb4ygGTAQGFlRwfDBg1MSQybS98+/lLvsEu/ODgEgr47XmgG58VzUzH6/hdMPb+X9\ntwK3xvNZ6UCFnEjDhMNhJpeV8SzguJuxXM0cDuNw3qU/cOW0aYTDYQKBgNehiogkRbw9clOBn8ys\n1xZem0RkH9ZuCYivwdK5R+6886CoCC6sa+qGiGxVOBymSW4ua6uqaAbcyyX8h1N5neNYDzTPyWFD\nZaUKORHxjVT1yA0Dujvn3nHOXe6cO9U5d4Vz7h3gGGBInNfNKhqRE2mYQCBAr6IixkWPL+QhPmMf\nplLMOKB3t24q4kQko8VVyJlZGXAsEAbuBF4AxgIbgR7R12UrwuHIIqYdOngdSfpSn4e/pSp/I8aM\nYUheHvcCG9nEXxjGhdzKjc3yuGn06JTEkIn0/fMv5S67xDsih5kFzawrsCOwF9DczI4ys+kJiy6D\nLVkCu+wCO+zgdSQi/pafn89rZWVMLCmheU4OF7vnWJ23Kzfe8oGWHxGRjJdWe60mQ7r2yL30Ejz0\nELzyiteRiGSOcDgMwKuvBrjxRnj/fciJ+89VEZHUS1WPXPWH7e+cO8Y5d3ztR0Oumw3UHyeSeIFA\ngEAgQN++kTUan3nG64hERJIrrkLOOdfBOTcPWAS8CUyo9dA40zaokNs29Xn4m5f5cw5uvRWGDoWN\nGz0Lw9f0/fMv5S67xDsidx+RteJOAQ4A9qn12Dch0WUwFXIiyXXMMdC2LTxc50qUIiL+F+86cj8A\nvzeztB95S8ceucpKaN4c1qyBJk28jkYkc73zDpx6KixeHLnVKiKS7lLVI/cZoBIkTosXQ5s2KuJE\nkq1LF+jaFcaO9ToSEZHkiLeQGwT8xTmnW6hx0G3V+lGfh7+lS/5uvRXGjIGvv/Y6En9Jl/xJ7JS7\n7BJvIXcrsDuwyDm3OLrDw5yaPxMYY8ZRISeSOu3aQb9+MGKE15GIiCRevD1yjwIG1HUP18zs/AbE\nlTDp2CN38slw7rlw+uleRyKSHVavhgMOgLfegv339zoaEZG6xdojpwWBPbDffjBhQuQ/LCKSGqNG\nwZw58OKLXkciIlK3lC4ILLGrqIDlyyPFnGyd+jz8Ld3yd9VVkUJu5szIDhDVu0DIlqVb/qT+lLvs\nEnch55w72zk3xTn3hXNuVfTxdfXPRAaZST78ENq3h0aNvI5EJLs0bQoXXriUvsfPZ7vGuTTJzaVv\nSQnl5eVehyYiErd4d3boBzwGfALsAbxMZEeHALAOuCdRAWYaTXSov+LiYq9DkAZIt/yFQiHuur0T\nees28ZidwtqqKvoEg/QsLCQUCnkdXtpJt/xJ/Sl32SXeEblrgZHA5dHjf0UnN7QBVgMVDQ8tM6mQ\nE/HGsEGDuHn99zzMtQxjFI1ozEBgZEUFwwcP9jo8EZG4xFvItQNmAOHoY0cAM/seGAVckZDoMpAK\nufpTn4e/pVP+wuEwk8vK6A8cy5u042Puif4d2h+YNG2aeuZqSaf8SWyUu+wSbyG3DmgWnQ76JdCh\nxmsOaNnQwDKVCjkR741mELfyF1bpX1Ui4nPxriM3HnjLzEY55+4EzgSGApXRn5+ZWY+ERhqndFp+\nZM0a2GsvWLsWcjRfWCSl+paU0CcYZGD0+CrG8hPb0ZlLmVhSwvjSUk/jExGBFK0j55zrCuxtZs84\n53YCHgX6EBnhmwP0M7NPY75wEqRTITdjBgweDLNmeR2JSPYpLy+nZ2EhIysq6A98y04cyCIaNe1L\n6cx7yc/P9zpEEZHUrCNnZm+b2TPR52vM7CRge2AnMzsiXYq4dKPbqrFRn4e/pVv+8vPzea2sjIkl\nJTTPyaFtzlra7v8U+x30Jp07q4irLd3yJ/Wn3GWXhK1mZmYbgA2Jul4mUiEn4q2CggLGl5b+PLHB\nLEB+Pvz3v3DqqR4HJyISh3rfWnXOzQHOM7OF0efb2mu1S4JibJB0urVaXAw33gg90qJ7UEQApkyB\nP/4RFi6EJk28jkZEsl2st1ZjGZFbwC8jbgu28d70qJzSiJlG5ETSUffu0KkTjB0L11/vdTQiIrGJ\na7KDn6TLiNyKFZEibtUqcPWus7NbMBjUCuU+5qf8ffIJHHkkzJsHrVp5HU168FP+5NeUO39LyWQH\niV31aJyKOJH0s99+cNFFcN11XkciIhKbWHrkimK5sJmVxRVRgqXLiNzYsZG/+u++2+tIRGRLfvgB\nOnSAxx+Hbt28jkZEslUye+SCMbzXgEAM78948+fDYYd5HYWI1GX77eGf/4TLL4fycmjc2OuIRES2\nLZZbq51qPI4DlgMPElkI+PDoz4eAZUCvxIbpf5roEDutheRvfszfqadC69Zw551eR+I9P+ZPIpS7\n7FLvETkzm1/93Dl3KzDOzP5a622TnHO3AFcBbyQmRP+rqoIFC+Cgg7yORES2xrlI+0PXrnD22bDb\nbpH15gIB3WAQkfQU7xZdPwCnmNlmxZpzrifwXzPLS0B8DZYOPXJLl8LRR8OyZZ6GISL1dNFFXzFx\n/CJWfRNZ9LFXUREjxozRNl4iknSpmrW6Bji5jtdOBr6N87oZSbdVRfwjFArx0tOdqFzVhv9WlbC2\nqoo+wSA9CwsJhUJehyci8ivxFnJ/Ay51zr3qnLvYOXdy9OdEYCAwKnEh+p8Kufioz8Pf/Jq/YYMG\ncfP61TzCnxjM3QTIZSAwsqKC4YMHex1eyvg1f6LcZZu4Cjkz+xdwCrALcA/wn+jPlsCpZnZPwiLM\nACrkRPwhHA4zuayM/kBfJtCOjxnNIAD6A5OmTft5n1YRkXTQ4J0dnHONiBRwq81sU0KiSqB06JHr\n3BkefFDLj4iku3A4TJPcXNZWVdEMWMreHMa7zOJIdudTmufksKGyUpMfRCRpUr6zg5ltMrMV6VjE\npYNNm+Cjj+DAA72ORES2JRAI0KuoiHHR4zZ8zl+4lUu4j8eA3t26qYgTkbQSdyHnnDvbOTfFOfeF\nc25V9PF19c9EBulnn3wSWZcqLy3m8PqL+jz8za/5GzFmDEPy8rgXWA9cxJ18QnOuy72Ym0aP9jq8\nlPFr/kS5yzZxFXLOuX7AY8AnwB7Ay8AEIrs5rCPSLyeoP07Eb/Lz83mtrIyJJSU0z8nhNzlGm8Pu\nJ3f7u2ndWsuPiEh6iXcduXLgRSKzUyuBw8ws5JzbAXgTeN7M/pHQSOPkdY/c8OGR26s33+xZCCIS\np+qJDYFAgGuvheXL4amnPA5KRDJaqnrk2gEzgHD0sSOAmX1PpLi7Is7rZhyNyIn4VyAQ+Lkn7qab\nYNYsmDTJ46BERGqIt5BbBzSLDnV9CXSo8ZojMotViBRy2porPurz8LdMy1+zZnDvvXDppfDDD15H\nk3yZlr9sotxll3gLuXeBTtHnLwNDowsCDwD+AcxKQGy+9+OP8Pnn0L6915GISCL07AmFhTB0qNeR\niIhExNsj1xXY28yecc7tBDwK9CFSGM4B+pnZp4kMNF5e9si99x5ccAF88IEnHy8iSbB6NXTsCC++\nCL/7ndfRiEimibVHrlE8H2JmbwNvR5+vAU5yzjUBtjOztfFcMxPNnRv5F76IZI6WLeGuu+D88+H9\n96FpU68jEpFs1uAFgauZ2QYzW+ucO9o592qirutnc+dCp07bfp9smfo8/C2T83f66ZCfDzfe6HUk\nyZPJ+ct0yl12iamQc87lOedOd84Nds5d6JzbpcZr3Z1zZUAZsF88wTjnHnbOrXTOzatxbmfn3BvO\nucXOudedcy1qvHaDc+5j59wi51zPeD4zmebNUyEnkqnuvjuyFMnMmZHjcDisfVhFJOXq3SPnnNuf\nyBpxe9Q4vQ7oDVwEnA8sAG4FnjWzqpiDca4Q+AEYZ2Ydo+duJ7KP6+3Ouf8DdjKz651zHYCngMOB\n1tHY9q/9uV71yJnBb38b6Y/bffeUf7yIpMB//wtXXbWBg9uczBsz3wCgV1ERI8aMIT9fiweLSOyS\nuY7cbcCPQFcgDziQyMSGScDpQH8z62hmT8dTxAGY2XRgTa3TJxLZRYLoz5Ojz08CnjazjWa2lMgu\nE13i+dxkWLkSqqqgVSuvIxGRZNl77xBffzmen6Yfx9qqKtZWVdEnGKRnYSGhUMjr8EQkC8RSyB0B\nDDWz2Wb2o5l9BAwkshjwYDN7IikRwq5mtjL6fCWwa/T57sCyGu9bRmRkLi1U31Z19a6ppTb1efhb\nNuRv2KBB3By+lA85i/c4mmZE/qU4sqKC4YMHex1eg2RD/jKVcpddYpm1uhuwpNa5z6M/309MOFtn\nZuac29p90i2+NmDAANq0aQNAixYt6Ny5M8XFxcAv/8An+nju3GI6dUre9XWsYx17exwOh5k4bRqX\nY/ybSzmfR7iLjjRlA/2BK6dNY8qUKQQCgbSIV8fZc1wtXeLR8daPq58vXbqUeMTSI1cFHGlm79Q4\nFwA2Et1rNa4INv+cNsArNXrkFgHFZrbCOdcKmGpmBzjnrgcws1HR900GhpnZ7FrX86RH7rzzoKgI\nLrww5R8tIikQDodpkpvL2qoqmgEDeIRcKrmfS1gPNM/JYUNl5c9bfImI1Eey91p9zTm3qvoBrIie\nn1LzvHPu6xivuzXjgfOiz88DXqpx/mznXK5zri2R/V/f2cLve0JryIlktkAgQK+iIsZFj+/kT7xJ\nD17iJMYBvbt1UxEnIkkXy4jc8Biua2Z2U8zBOPc00I3IXq0rgaFEtgB7DtgLWAqcaWbfRd//F+AC\nYBNwlZm9toVrpnxEbtMm2HFHWLUK8vJS+tEZJRgM/jwELf6TDfkrLy+nZ2EhIysq6A+8ze84lRdp\n1PQo3pz5gq9nrmZD/jKVcudvSdvZwcyGxxVRDMzs93W81KOO999KZLmTtLJ4Meyxh4o4kUyXn5/P\na2VlDB88mCunTQNm0XbP19mldTmdO+/odXgikgXi2mvVT7wYkXvmGXj++chejCKSHaoXA66qCnD0\n0XDuuXDllR4HJSK+k5K9VmXrtDWXSPap7ocLBODJJ6FrVzjmGDjoII8DE5GMFutkB6kHbc2VGLWn\n0ou/ZHP+9tsPRo2Cfv3gp5+8jiY+2Zw/v1PusosKuSTQiJyIXHBBpKC77jqvIxGRTKYeuQT77rvI\nRId16yBHZbJIVluzBgoKYMwYOOUUr6MRET9I9jpysg3z5sHBB6uIExHYaSd49lm45BJYEt0XJxwO\n/zwxQkSkoVRuJJj64xJHfR7+pvxFdOkCN9wAfftW0KfbsTTJzaVJbi59S0ooLy/3Orw6KX/+pdxl\nFxVyCab+OBGpragoxMeLpvJTWW/WVlWxtqqKPsEgPQsLCYUSsruhiGQp9cgl2O9+B3/7G3TrlrKP\nFJE017ekhOLgB9xFiDu4ipMYD8C9wMSSEsaXlnoboIikjVh75FTIJVBVFbRoAUuXws47p+QjRSTN\nhcNhmuTmsraqig84kpN4mTkczt58wXqgeU4OGyortS+riACa7OCpzz+H5s1VxCWK+jz8TfnbXFdm\n8X/cxum8wAa28zqcrVL+/Eu5yy4q5BJo7lzo2NHrKEQknQQCAXoVFTEuevxnxtCWJVzOPTwG9O7W\nTaNxIhI33VpNoJtuiqzifuutKfk4EfGJ8vJyehYWMrKigv7AD+TRmVl8n3sfZbMuID8/3+sQRSRN\n6Naqh95/Hzp39joKEUk3+fn5vFZWxsSSEprn5NA650cOOOI2GueN4aefVMSJSPxUyCXQ+++D/rBO\nHPV5+Jvy92sFBQWMLy1lQ2UlGyorKZ31OI891pgzzoCVK72ObnPKn38pd9lFhVyCrFkDq1fDvvt6\nHYmIpLNAIPBzT1zfvpE9Wc88EzZu9DgwEfEl9cglSDAIf/0rzJyZ9I8SkQxSVRUp6PbbD+64w+to\nRMRr6pHziPrjRCQeOTnw5JPw2mtw//2/nNeerCJSHyrkEkSFXOKpz8PflL/6a9ECJkyAoUPh3nsX\n07ekxPM9WZU//1LusosKuQTRRAcRaYj99oMRIxZz2aUtOCy4XHuyiki9qEcuAX76CXbaCb75Bpo2\nTepHiUgG61tSQvPgvrzDdczmCHbiO0B7sopkE+21WksqCrnycvjDH2D+/KR+jIhksJp7st7IaD7g\nECbTi8Zs0p6sIllEkx08oP645FCfh78pf/H7O9fShA1cwd149ae28udfyl12USGXAOqPE5GGqrkn\na4Aqnub3zOJIbuP/GIf2ZBWRLdOt1QTo1i0y26x796R+jIhkuNp7sn5FK7rwFpW5t1A26zLtySqS\nBXRrNcXM4IMP4JBDvI5ERPyu9p6sB+SspFOX4eRu/y9WrVIRJyKbUyHXQEuWwA47QMuWXkeSedTn\n4W/KX3xq78k6dfajvPxyY845B1K5Aony51/KXXZRIddAmuggIslQc0/Wo4+Ge++NbOW1ZInHgYlI\nWlGPXAMNHRr5OWJE0j5CRASAu++Gu+6CGTNgl10i56q38dJECJHMoB65FNOInIikyhVXwBlnQM+e\nMG3aB2mxlZeIeEuFXAOpkEse9Xn4m/KXHCNHwgEHfE2PY36ke3BO0rbyUv78S7nLLirkGmD1ali7\nFtq08ToSEckWzsH3X53N4VULmcBL5LAdzYCBwMiKCoYPHux1iCKSQuqRa4DXXoNRo2Dq1KRcXkRk\nM9VbeX1bBRfyNJXk8jxnaCsvkQyhHrkUeu89OOwwr6MQkWwUoIonOJeNNGYAj1JFvf+9LyIZRIVc\nA7z7Lhx6qNdRZC71efib8pccNbfyymUjL3A6X7I7F/Egj5KTsK28lD//Uu6yiwq5BtCInIh4YcSY\nMQzJy+NewNjAc5zATNry50aPMfT20V6HJyIppB65OK1aBe3awZo1keZjEZFUCoVCDB88mEnTpgFw\n7NHHsWr9sxx44A488gioRU7En2LtkVMhF6fJk+H226G0NOGXFhGpt5oLAq9fH9n9oVUreOwxFXMi\nfqTJDimi26rJpz4Pf1P+UqPmVl7NmsErr8DKldC/P2za9Mv7wuHwz0VffSh//qXcZRcVcnF67z1N\ndBCR9NOsGYwfH2n/6NcPZs8u1w4QIhlMt1bjtNdekduq++2X8EuLiDTYhg3Qu/d3zJw+h7+HT+aP\nrAdgHDAkL4/XysooKCjwNkgR2YxurabAqlXw/few775eRyIismVNmkCzqtM4NLyc53idn2ihHSBE\nMpAKuTi89x4UFGi2arKpz8PflD9vhcNhXp8R5A0u4HDmUEyQFewKQH9g0rRpW+2ZU/78S7nLLirk\n4vDuu5roICL+kIPxT67hNF6kkOksZW+vQxKRBFKPXBxOOQV+/3s488yEXlZEJKH6lpTQJxhkYPT4\nLq7gNv6P8+jLvJKdGK/1k0TSjnrkUkBbc4mIH9TcAWI9cCF3czxX8zfeoOepD3gdnogkgAq5GK1Y\nARUVsM8+XkeS+dTn4W/Kn/fy8/N5rayMiSUlNM/JoXlODitKvuXhR77lllv25YGt1HLKn38pd9ml\nkdcB1JdzbimwDggDG82si3NuZ+BZYG9gKXCmmX2XzDhmz4YjjtBEBxHxh4KCAsaXlv5qBwiAo46C\n44+HpUvh5pt/+XdaLIsGi4j3/DQiZ0CxmeWbWZfoueuBN8xsf2BK9Dipqgs5Sb7i4mKvQ5AGUP7S\nS80dICCyV/Rbb8HUqXDOOfD2279eOHj0TTdp4WCf0ncvu/ipkAOoPQ52IvBY9PljwMnJDmDWLDjy\nyGR/iohI8u2yC0yZAt9++y1FR4c5KriYtVVVrK2qok8wSM/CQkKhkNdhishW+KmQM+BN59y7zrk/\nRs/tamYro89XQnSRpCQJhyMTHbp02fZ7peHU5+Fvyp8/NG0KjTacRp+qF7mb2cyjC82AA9DCwX6l\n71528U2PHHCUmX3lnNsFeMM5t6jmi2ZmzrktrjMyYMAA2rRpA0CLFi3o3Lnzz0PP1f/A1+f4ww+h\nefMgc+fW7/061rGOdZzux+FwmNeml7GWIGMJchzXcwcvsTfjaAO8Gn1PIBBIi3h1vO3jaukSj463\nflz9fOnSpcTDl+vIOeeGAT8AfwSKzWyFc64VMNXMDqj13oStI/fgg1BWBuPGJeRyIiKeC4fDNMnN\nZW1VFc2AhRzISbxMX15hONfxmxxjQ2Xlr/rrRCR5MnIdOedcM+fcDtHneUBPYB4wHjgv+rbzgJeS\nGYcmOohIpgkEAvQqKqL679MOfMhsjmABB3EYUyg58hQVcSJpzBeFHJHet+nOufeB2cAEM3sdGAUc\n65xbDBwTPU4aTXRIrdq3CcRflD//qL1wcBPWcCC9Wd54BuWLn2bqVK8jlFjou5ddfFHImdkSM+sc\nfRxsZn+Lnv/WzHqY2f5m1jOZa8h9/z0sWQKdOiXrE0REvLGlhYPf6XwIM2Yfz1NPNaZfP7jlFqiq\n+uV3wuGw1pwTSQO+7JGLRaJ65KZOhSFDYMaMBAQlIpKmai8cDLBsGZx1FjRvDoMGfcDYm69mclkZ\nAL2KihgxZgz5+fmexCuSaTKyRy4dzJql/jgRyXy1Fw4G2GMPCAahZcuV9Dy2JfsEA1pvTiRNqJCr\nJ010SD31efib8udvtfPXuDGs+d/ZXG7n8wKPMYzbCZDLQLTeXLrRdy+7qJCrBzNNdBCR7BYOh5lc\nVsYo3uADDmEx+9OVt1lEe/oDk6ZNU8+ciAfUI1cPn30GhYWRPhFX77vWIiKZo/Z6cwbcz8XcyM3c\nyFAGuQf4aeNPWqpEpIHUI5cEM2ZECjkVcSKSrWqvN+eAS7if6RQylgHs1Pwdvvhi8yLc5ux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