{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# QuTiP example: Homodyned Jaynes-Cummings emission" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "K.A. Fischer, Stanford University\n", "\n", "This Jupyter notebook demonstrates how to simulate quantum statistics of homodyned emission from a detuned Jaynes-Cummings system. The\n", "purpose is to understand how well the first polariton of a dissipative Jaynes-Cummings system can act as an ideal two-level system. This notebook closely follows an example from my simulation paper, An architecture for self-homodyned nonclassical light, Phys. Rev. Applied 7, 044002 (2017).\n", "\n", "For more information about QuTiP see the project web page: http://qutip.org/ " ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline\n", "%config InlineBackend.figure_format = 'retina'" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from qutip import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction for the two-level system\n", "\n", "The quantum two-level system (TLS) is the simplest possible model for quantum light-matter interaction. In the version we simulate here, the system is driven by a continuous-mode coherent state, whose dipolar interaction with the system is represented by the following Hamiltonain\n", "\n", "$$H_\\mathrm{TLS} =\\hbar \\omega_0 \\sigma^\\dagger \\sigma + \\frac{\\hbar\\Omega_\\mathrm{TLS}(t)}{2}\\left( \\sigma\\textrm{e}^{-i\\omega_dt} + \\sigma^\\dagger \\textrm{e}^{i\\omega_dt}\\right),$$\n", "\n", "where $\\omega_0$ is the system's transition frequency, $\\sigma$ is the system's atomic lowering operator, $\\omega_d$ is the coherent state's center frequency, and $\\Omega_\\mathrm{TLS}(t)$ is the coherent state's driving strength.\n", "\n", "The time-dependence can be removed to simplify the simulation by a rotating frame transformation, and is particularly simple when the driving field is resonant with the transition frequency ($\\omega_d=\\omega_0$). Then,\n", "\n", "$$\\tilde{H}_\\mathrm{TLS} =\\frac{\\hbar\\Omega(t)}{2}\\left( \\sigma+ \\sigma^\\dagger \\right).$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Setup the two-level system properties" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# define system operators\n", "gamma = 1 # decay rate\n", "sm_TLS = destroy(2) # dipole operator\n", "c_op_TLS = [np.sqrt(gamma)*sm_TLS] # represents spontaneous emission\n", "\n", "# choose range of driving strengths to simulate\n", "Om_list_TLS = gamma*np.logspace(-2, 1, 300)\n", "\n", "# calculate steady-state density matricies for the driving strengths\n", "rho_ss_TLS = []\n", "for Om in Om_list_TLS:\n", " H_TLS = Om * (sm_TLS + sm_TLS.dag())\n", " rho_ss_TLS.append(steadystate(H_TLS, c_op_TLS))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The emission can be decomposed into a so-called coherent and incoherent portion. The coherent portion is simply due to the classical mean of the dipole moment, i.e.\n", "\n", "$$I_\\mathrm{c}=\\lim_{t\\rightarrow\\infty}\\Gamma\\langle\\sigma^\\dagger(t)\\rangle\\langle\\sigma(t)\\rangle,$$\n", "\n", "while the incoherent portion is due to the standard deviation of the dipole moment (which represents its quantum fluctuations), i.e.\n", "\n", "$$I_\\mathrm{inc}=\\lim_{t\\rightarrow\\infty}\\Gamma\\langle\\sigma^\\dagger(t)\\sigma(t)\\rangle-I_\\mathrm{c}.$$\n", "\n", "Together, these emissions conspire in a way to result in zero second-order coherence for the two-level system, i.e. $g^{(2)}(0)=0$.\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# decompose the emitted light into the coherent and incoherent \n", "# portions\n", "I_c_TLS = expect(sm_TLS.dag(), rho_ss_TLS)*expect(sm_TLS, rho_ss_TLS)\n", "I_inc_TLS = expect(sm_TLS.dag()*sm_TLS, rho_ss_TLS) - I_c_TLS" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualize the incoherent and coherent emissions" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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TJKlgfPwx9OiRrLz0xhtwxBFZRySpmEOYJElS7hk2LEkeBg82eZC0DSsQKbEC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\nsBnvbcS8a66xrOuMM6yvzKxvRS7p7osv7AbC66/b81q14Jx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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 275, "width": 392 } }, "output_type": "display_data" } ], "source": [ "plt.semilogx(Om_list_TLS, abs(I_c_TLS), \n", " label='TLS $I_\\mathrm{c}$')\n", "plt.semilogx(Om_list_TLS, abs(I_inc_TLS), \n", " 'r', label='TLS $I_\\mathrm{inc}$')\n", "plt.xlabel('Driving strength [$\\Gamma$]')\n", "plt.ylabel('Normalized flux [$\\Gamma$]')\n", "plt.legend(loc=2);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction for the Jaynes-Cummings system\n", "\n", "The quantum Jaynes-Cummings (JC) system represents one of the most fundamental models for quantum light-matter interaction, which models the interaction between a quantum two-level system (e.g. an atomic transition) and a single photonic mode. Here, the strong interaction between light and matter creates new quantum states known as polaritons in an anharmonic ladder of states. In a phenomenon known as photon blockade, the most anharmonic polariton is used as a two-level system to produce emission with $g^{(2)}(0)<1$. We will investigate how well the emission compares to that of a two-level system by comparing both its coherent and incoherent components as well as its $g^{(2)}(0)$.\n", "\n", "In the version we simulate here, the Jaynes-Cummings system is driven by a continuous-mode coherent state, whose dipolar interaction with the system is represented by the following Hamiltonain\n", "\n", "$$H =\\hbar \\omega_a a^\\dagger a + \\hbar \\left(\\omega_a+\\Delta\\right) \\sigma^\\dagger \\sigma+ \\hbar g\\left(a^\\dagger\\sigma +a\\sigma^\\dagger\\right) + \\frac{\\hbar\\Omega(t)}{2}\\left( a\\textrm{e}^{-i\\omega_dt} + a^\\dagger \\textrm{e}^{i\\omega_dt}\\right),$$\n", "\n", "where additionally $\\omega_a$ is the cavity's resonant frequency and $\\Delta$ is the cavity-atom detuning. We will investigate for finite $\\Delta$ because this increases the anharmonicity of the Jaynes-Cummings ladder. The time-dependence can additionally be removed to simplify the simulation by a rotating frame transformation in a very similar manner as before." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Setup the JC system properties" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# truncate size of cavity's Fock space\n", "N = 15\n", "\n", "# setup system operators\n", "sm = tensor(destroy(2), qeye(N))\n", "a = tensor(qeye(2), destroy(N))\n", "\n", "# define system parameters, barely into strong coupling regime\n", "kappa = 1\n", "g = 0.6 * kappa\n", "detuning = 3 * g # cavity-atom detuning\n", "delta_s = detuning/2 + np.sqrt(detuning ** 2 / 4 + g ** 2)\n", "\n", "# we only consider cavities in the good-emitter limit, where \n", "# the atomic decay is irrelevant\n", "c_op = [np.sqrt(kappa)*a]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Effective polaritonic two-level system\n", "\n", "In the ideal scenario, the most anharmonic polariton and the ground state form an ideal two-level system with effective emission rate of\n", "\n", "$$\\Gamma_\\mathrm{eff}= \\frac{\\kappa}{2}+2\\,\\textrm{Im} \\left\\{\\sqrt{ g^2-\\left( \\frac{\\kappa}{4}+\\frac{\\textbf{i}\\Delta}{2} \\right)^2 }\\right\\}.$$" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [], "source": [ "effective_gamma = kappa / 2 + 2 * np.imag(\n", " np.sqrt(g ** 2 - (kappa / 4 + 1j * detuning / 2) ** 2))\n", "\n", "# set driving strength based on the effective polariton's \n", "# emission rate (driving strength goes as sqrt{gamma})\n", "Om = 0.4 * np.sqrt(effective_gamma)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Define reference system for homodyne interference\n", "\n", "For the purposes of optimally homodyning the JC output, we wish to transmit light through a bare cavity (no atom involved) and calculate its coherent amplitude. (This of course could easily be analytically calculated but QuTiP certainly is trivially capable of such a calculation.)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# reference cavity operator\n", "a_r = destroy(N)\n", "c_op_r = [np.sqrt(kappa)*a_r]\n", "\n", "# reference cavity Hamiltonian, no atom coupling\n", "H_c = Om * (a_r + a_r.dag()) + delta_s * a_r.dag() * a_r\n", "\n", "# solve for coherent state amplitude at driving strength Om\n", "rho_ss_c = steadystate(H_c, c_op_r)\n", "alpha = -expect(rho_ss_c, a_r)\n", "alpha_c = alpha.conjugate()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calculate JC emission\n", "\n", "The steady-state emitted flux from the JC system is given by $T=\\kappa\\langle a^\\dagger a \\rangle$, however with an additional homodyne interference it is $T=\\langle b^\\dagger b \\rangle$, where the operator $b=\\sqrt{\\kappa}/2\\, a + \\beta$ is a new operator representing the interference between the JC emssion and a coherent state of amplitude $\\beta$.\n", "\n", "The interference present in the operator $b$ now allows for the alteration of the measured portion of the coherently scattered light, though it leaves the incoherent portion unchanged since the incident flux has only a coherent portion. We're interested in studying the optimal homodyne interference to allow the JC emission to match the TLS emission as closely as possible. This optimum is determined from the above reference cavity, such that $\\beta=-\\sqrt{\\kappa}/2\\langle a_\\textrm{ref} \\rangle$." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def calculate_rho_ss(delta_scan):\n", " H = Om * (a + a.dag()) + g * (sm.dag() * a + sm * a.dag()) + \\\n", " delta_scan * (\n", " sm.dag() * sm + a.dag() * a) - detuning * sm.dag() * sm\n", " return steadystate(H, c_op)\n", "\n", "\n", "delta_list = np.linspace(-6 * g, 9 * g, 200)\n", "rho_ss = parfor(calculate_rho_ss, delta_list)\n", "\n", "# calculate JC emission\n", "I = expect(a.dag()*a, rho_ss)\n", "\n", "# calculate JC emission homodyned with optimal state beta\n", "I_int = expect((a.dag() + alpha_c) * (a + alpha), rho_ss)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualize the emitted flux with and without interference\n", "\n", "The dashed black line shows the intensity without interference and the violet line shows the intensity with interference. The vertical gray line indicates the spectral position of the anharmonic polariton. Note its narrower linewidth due to the slower effective decay rate (more atom-like since we're in the good-emitter limit)." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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72uN62rRpWrdunZ5++mm9/PLLWr58ucrKytTY2Kj8/Hwdd9xxmj17ti6//HJl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\nUTiSQhPQtda4ivyUHPBTcsBHy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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 326, "width": 496 } }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,5))\n", "\n", "plt.plot(delta_list/g, I/effective_gamma,\n", " 'k', linestyle='dashed', label='JC')\n", "plt.plot(delta_list/g, I_int/effective_gamma,\n", " 'blueviolet', label='JC w/ interference')\n", "plt.vlines(delta_s/g, 0, 0.7, 'gray')\n", "plt.xlim(-6, 9)\n", "plt.ylim(0, 0.7)\n", "plt.xlabel('Detuning [g]')\n", "plt.ylabel('Noramlized flux [$\\Gamma_\\mathrm{eff}$]')\n", "plt.legend(loc=1);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calculate coherent/incoherent portions of emission from JC system and its $g^{(2)}(0)$\n", "\n", "We note that\n", "\n", "$$g^{(2)}(0)=\\frac{\\langle a^\\dagger a^\\dagger a a \\rangle}{\\langle a^\\dagger a \\rangle^2}.$$" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true }, "outputs": [], "source": [ "Om_list = kappa*np.logspace(-2, 1, 300)*np.sqrt(effective_gamma)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def calculate_rho_ss(Om):\n", " H = Om * (a + a.dag()) + g * (sm.dag() * a + sm * a.dag()) + \\\n", " delta_s*(sm.dag()*sm + a.dag()*a) - detuning*sm.dag()*sm\n", " return steadystate(H, c_op)\n", "\n", "rho_ss = parfor(calculate_rho_ss, Om_list)\n", "\n", "# decompose emission again into incoherent and coherent portions\n", "I_c = expect(a.dag(), rho_ss)*expect(a, rho_ss)\n", "I_inc = expect(a.dag()*a, rho_ss) - I_c\n", "\n", "# additionally calculate g^(2)(0)\n", "g20 = expect(a.dag()*a.dag()*a*a, rho_ss)/expect(a.dag()*a, rho_ss)**2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualize the results\n", "\n", "The dashed black line in the top figure represents the coherent portion of the emission and can clearly be seen to dominate the emission for large driving strengths. Here, the emission significantly deviates from that of a two-level system, which saturates by these driving strengths. The lack of saturation for the JC system occurs due to the harmonic ladder above the anharmonic polariton. Additionally, the $g^{(2)}(0)$ values are all quite large relative to the ideal TLS value of zero (bottom plot)." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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zDrvvvnvRz5mHIiDXUwOaaRswIOsQ9eweEZ8HBgEbgQXArJRSdbaxJEmSJEm1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\nR3/8Y53l9eXfbvRojUuiyrzq8cf10R/+4Dl+slY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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 499, "width": 513 } }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,8))\n", "\n", "plt.subplot(211)\n", "plt.semilogx(Om_list/np.sqrt(effective_gamma), abs(I_c)/kappa,\n", " 'k', linestyle='dashed', label='JC $I_\\mathrm{c}$')\n", "plt.semilogx(Om_list/np.sqrt(effective_gamma), abs(I_inc)/kappa,\n", " 'r', linestyle='dashed', label='JC $I_\\mathrm{inc}$')\n", "plt.xlabel(r'Driving strength [$\\Gamma_\\mathrm{eff}$]')\n", "plt.ylabel('Normalized Flux [$\\kappa$]')\n", "plt.legend(loc=2)\n", "\n", "plt.subplot(212)\n", "plt.loglog(Om_list/np.sqrt(effective_gamma), g20,\n", " 'k', linestyle='dashed')\n", "lim = (1e-4, 2e0)\n", "plt.ylim(lim)\n", "plt.xlabel(r'Driving strength [$\\Gamma_\\mathrm{eff}$]')\n", "plt.ylabel('$g^{(2)}(0)$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calculate homodyned JC emission\n", "\n", "Now we recalculate the coherent and incoherent portions as well as the $g^{(2)}(0)$ for the homodyned JC emission, but use the operator $b$ instead of $\\sqrt{\\kappa}/2\\,a$. Thus\n", "\n", "$$g^{(2)}(0)=\\frac{\\langle b^\\dagger b^\\dagger b b \\rangle}{\\langle b^\\dagger b \\rangle^2}.$$" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def calculate_rho_ss_c(Om):\n", " H_c = Om * (a_r + a_r.dag()) + delta_s * a_r.dag() * a_r\n", " return steadystate(H_c, c_op_r)\n", "\n", "rho_ss_c = parfor(calculate_rho_ss_c, Om_list)\n", "\n", "# calculate list of interference values for all driving strengths\n", "alpha_list = -expect(rho_ss_c, a_r)\n", "alpha_c_list = alpha_list.conjugate()\n", "\n", "# decompose emission for all driving strengths\n", "g20_int = []\n", "I_c_int = []\n", "I_inc_int = []\n", "for i, rho in enumerate(rho_ss):\n", " g20_int.append(\n", " expect((a.dag() + alpha_c_list[i]) * \n", " (a.dag() + alpha_c_list[i]) * \n", " (a + alpha_list[i]) * \n", " (a + alpha_list[i]),\n", " rho) /\n", " expect((a.dag() + alpha_c_list[i]) * \n", " (a + alpha_list[i]),\n", " rho)**2\n", " )\n", " I_c_int.append(expect(a.dag() + alpha_c_list[i], rho) * \n", " expect(a + alpha_list[i], rho))\n", " I_inc_int.append(expect(\n", " (a.dag() + alpha_c_list[i]) * \n", " (a + alpha_list[i]), rho) - I_c_int[-1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calculate the results\n", "\n", "The dashed red and blue lines, which represent the TLS decomposition are now matched well by the JC decomposition with optimal homodyne interference (red and blue). The dashed black line is shown again as a reminder of the JC system's coherent emission without interference, which does not saturate for large driving strengths. Additionally, with the interference the $g^{(2)}(0)$ value improves by many orders of magnitude." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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0IiIi4i9Hjx6lcePGnDhxgvbt21d+AIcPw6RJ8NxzcOyYWzdwIFx+eeXHIiJB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g7qvwXqA+OBeUBXoCcwHzjae78xeNvmwGJgmfe+RYF2+gH9gr82BE4I3nZqcN867/2te+mLpgaI\niMS57777jiuvvJJff/0VgP79+/Pkk0/StGnTiLdfuRKGDoX//CdcT+/MM+Gf/7Tp9BXKa6/ZhHWA\nN9+E886zuQxDh9q+s86y4ICUig0bLIW4WbPwvkAAPv4Yhg2DL7+0fc7BaafZtIGePStIQEkkgUyc\nCFdcYUG85GQb/N9zT8LVUY0LsTA1QIGAfJxzTYD7gL5AXeAPYCwwxHu/Od/tmmOD+6Xe+5YF2rgX\nuBco+MKG3uTd7hOhHwoEiIjEqdWrV3PHHXcwYsQIAJo3b84zzzzDKaecAsCCBZCdbSfIwQq/hQIA\noVkDZ51lAYBDD43GMyihDz6A/v1tovuTT1p6wxNPWN462Np5U6ZEt49x5vbbLRtg4ECLt7Rqtev1\nv/5qb8Wbb4aDTB06WEDg3HMhNbX8+ywiYevWWRbAG2/Y7x072nKxnTtHt1+y7xQIkIgUCBARiT85\nOTk8/fTTDB48mIyMDCpXrsytt97KXXfdRdWqVZk3Dx54AN56y87GvvaaBQBeeskCAM5ZAOAf/6ig\nAQCwyel9+th8hrvuskmtb71lGQFg0Y9ffqkAxQ0qliuvtEBSIGBnEc8/384itmmz6+3WrrVq4889\nB2vW2L769eHqq62NBg3Kv+8iicx7G/zfeKNl9qSlwZAh9ntKSrR7JyWhQIBEpECAiEh8mTRpEtde\ney1z584F4NRTT2XYsGG0bt2aOXMsADB6tH3pS06Gtm1tyb9QAGDAAAsAhLIEKqQtW6ywwYYNMGgQ\nvPgifPEFnHiiPfGmTW2SunJcy8SCBVZ7ceRIS8ZISgoHBNq23fW2WVnw9ts2beDnn21f5coWr7nh\nBssWEJGyNX8+XHutFYAFKwb7wgtW30MqvlgIBCjkLiIiUsYmTpzI3Llzad26NR999BEffPABmZmt\nOftsG9y/9ZYFAA46yAZoc+dCTg6cfTbMmmWDsgodBAArV//ii5ZrPnw4fPUV9O1rQYA6deB//1MQ\noAy1bQuvvmoBgUGD7O9s5Eho3x4uuMAGHSGpqXDRRTBzJkyebMUoc3IsS6VjRxuQTJhgAQURKV1b\nt1qd1EMPtSBA7dr2v/vFFwoCSOlSRkAMUkaAiEh8ycjI4KWXXuLqq69m4cJU7r/fauF5b+mdbdrY\n8m45OZYBcPbZlgFw0EHR7nkZmTrV5j/k5VmAYP58WzpQys2SJZYh8OqrkJtrgYFzzrHaEwceuPvt\nFy2y1QZeftkGKmC1Bq6/3hZ7qF69XLsvEne8t8+Fm2+22jAAl11m/6f16kW3b1L6YiEjQIGAGKRA\ngIhI/Fm0yKbF5w8AtG1rZ2hDAYBzzrEAQPv20e5tGZo2DXr0sNFntWoWBGjcONq9SlhLl9pA45VX\n7C15+WW49NLCb795swUPnnrKgglgsZxBgyyNuXnz8ui1SHyZM8f+f0IreBxxBDz7LHTpEt1+SdlR\nIEAiUiBARCT+/PKLpVWHMgAWLNj1TOw998R5AABssetu3eyJp6fbt98DDoh2rwRYtsxmbNx/f9GK\nkOXl2fSAJ56A//7X9iUl2YIQN9wA3btr+UGRvVm7Fu6914p55uXZLKmHH7ZMgOTkaPdOypICARKR\nAgEiIvFn6VKbd/3dd+EAwLnnWgCgXbto964c/Pyznd7KyYEqVWD2bGjRItq9klIwY4YtPzh6tL29\nYGc0b7jBCl2q9IPIrrZvtyDa0KGQkWGD/ssvt0Bc3brR7p2UBwUCJCIFAkREYp/3fucH+Z4sWQIP\nPWSF1kIBgPPOswBApLnYcel//7MFr7Ozbf2rX3/dfe06qfBWrbKsguHDYf1629eoEfz973DFFbDf\nftHtn0i0BQK2HODdd4frAJx6KjzySBzXhJGIYiEQoFUDREREisF7z7hx4+jQoQPLli0r9HZLlsDf\n/mZ1AF56yb4AXnihrQgwcmQCBQGmTYNOnSwIkJpqpegVBIhLjRrBfffB8uX2N3/IIRYcuOceWx1y\n0CDLHhBJNN7Dhx9aPHTgQAsCHH44TJoEH3ygIIBEhwIBIiIiRTRz5kx69epF//79mTVrFk8++eRu\nt1myxAY8kQIAr7+++5rtcW3SJJssnpNjmQAzZiRAIYTEMXSoJXcUVKWKzXH+9Vdb/uyUUyAz0woR\nHnGEzRB55RVLjxaJZ97b/0C3bnDaaTZDqkkTGDHCSqb06hXtHkoiUyBARERkL1auXMkll1zCEUcc\nweTJk6lTpw533fU027Y9QlaW3Wbx4nAA4OWXLQBw0UUJEgBYvhyuvJKdLwbA+PFwwglWAStUGPDg\ng6PXRylV06fDnXdChw5w5plWDLMg5+D44+1M6Pz5cOONtib69OkWKNh/f6sjMHdu+fdfpKz997+2\nSuoJJ1hiVP36Vhdg4UL7bEjSKEyiTDUCYpBqBIiIxIZNmzbxyCOP8OSTT7Jjxw5SUlI4//zr2LLl\nbsaOrY33lgq9dKmd4cnLsy93F1xg6dAJkQG/cCH07g0rVsDtt9tp4jfesG+63kOtWlYYUEsExpXV\nq+2tfuEFO9sPtmLAP/9pq2MUZscOGDPG6ghMmxbe37OnxZL691dxQam4vIevvrK6MJMm2b7ate3Q\neM01FhMVgdioEaBAQAxSIEBEJLp27NjBM888w8MPP8zGjRsB6N37TFJSHuGzz1rhPVSqBK1b2zg4\nFAC48EIrApUQAQCAWbOgTx9Ys8ZyXz/+GEaNsupwYKfA5s61NbEkLq1aBf/6Fzz/fDggcPrptiTa\n4Yfv+b4//WT3e/NN2LbN9tWrZ/9Hl1xiNQZEKoJAwOb6P/xwOMBVowbcdJNlvdSsGd3+SexRIEAi\nUiBARCR6xo0bx7XXXsvvwZLOnTr1JC1tKN9+2xWwAEDz5jYVIBCwZZ8uuCDBAgAAP/wAffvCxo2W\nETBuHDz+uI0AwSbCzp0L1apFt59SLlatgkcftTP9oYDAX/5ifw6dOu35vps3WzBg+HBbYCLkyCPh\n0kvhnHMssUQk1uTm2rKZQ4da4hPY6hjXX2/x0Nq1o9s/iV0KBEhECgSIiETPhAkTOP3002nVqgPp\n6UP59dcTAUdqqs1pXrzYbpeSYtWfb7/dMgMSyqRJ0K8fbN1qo72337ZFsEeOtOtbt7ZvxcrxTjir\nV4cDAjt22L7TToN33rFFI/bEeyug9sorlliyZYvtT0uzOgSXXmpTCDS3WqJt40YrBvvMM1YiBSz2\necstVitGUwBkbxQIkIgUCBARiZ5AwNOlyyfMmNEXSKJqVUtXDq0UWKWKjXlvucW++CWcESPsm25u\nLpx7Lrz6qmUEfPONXd+9u1XJ0mgtoa1ZYwGB556DY4+FTz4p3v23b4exYy0o8OWX4f3Nm1v5ifPO\nS6AlOCVmzJsHTz1lh8HQqhdt21pA+IILFPuUolMgQCJSIEBEJLruuce+7NWsaes9g833vOYaS/ms\nXz+6/YsK7+H++8Op/7fcAv/4h1WGW7LE9p1/vhUKFAlas8YSR1q12vc2liyxgderr4bPvoJNOTjv\nPJs6sP/+Je+rSCR5efDZZ/D00/Dpp+H9ffrY58FJJynuKcWnQIBEpECAiEh05OVZRfMHH9x1vucN\nN9h8z4Sdp5yTY2kQr71m33iffNKmBHTsaDmyAIMHh4MEImUgELDsgFGj4L33wlMHnLMpA+edZ1MI\nNC9bSsOKFbYU7Cuv2M9gGWEXXQTXXQcHHRTd/knFpkCARKRAgIhI+dq+3ca4jz8OixbZvv33t5Pe\nf/ub5nsye7ZVbgOrjFW3rk0HyMqywMDrr1s2gEg5ycwML1Lx4Yf2pwhWu+Okk+Dss+GUU1StXYon\nNxc++ghefNHO/gcCtr91a/ssGDRIi6BI6VAgQCJSIEBEpPR88803vP322zz55JM7P3hD1q6FZ5+1\nbcMG29eyJdxxh5312Vtxs4Ty0UdWLOHbb21NLO9tQuykSdCjR7R7J3EiK8uWEizOYGvzZqsnMGqU\n/TmGBm8pKdCrF/Tvb0saNmxYNn2Wis17mD7dVq4YPdo+F8AOb2ecYQEAFamU0qZAgESkQICISMl4\n75k0aRJDhw5l0qRJAIwY8REXXXQyAAsWwGOP2bzj0JnELl3g1ltt0JCcHK2ex7BAAP76V8vJBpsz\n8cMP0KJFdPslceWVV+Daa+Hii21KTnGX5Fy92lYoeP99q1kZCgo4B9262f93//4lq1kg8WHRIhv8\nv/EGLFwY3t+unQ3+L7rIDnMiZUGBAIlIgQARkX2Tl5fH2LFjGTp0KDNmzACgUqUa5ObewKWX3sAl\nl9Tm3/+GCRPsLBDYVPdbbrGT2i5qH8cxbtMmmxrw22/2e9euNspSiWwpZdddZ0XZwP4fTzsNbr4Z\njjmm+P+f69bBBx9YtsDnn4eDfgCHHmpt9+0LRx1l2QMS/xYssCDR++9bFkBIgwa2CMoFF1gRSn0W\nSFlTIEAiUiBARKR4srKyGDlyJP/6179YGDy1k5xcj7y8G4CrqFy5NnXrwqpVdvvUVBg4EG680c7+\nyB78+KPlxW7bZr9fd50VCxQpI7Nnw7BhdqY2NHjv3NlmpAwYsG+D9owMm/M9dqzNcgkVGgRbEaR3\nbwsKnHgiNGtWOs9Dos97+PXX8OD/f/8LX5eebqn/F1xgU0gqVYpePyXxKBAgESkQICJSNFu2bOGF\nF15g2LBhrAqO8pOSWhAI3ApcTLVqVQBbvgxs3vHf/25bgwZR6nRF8sQTdjo2ELD5Em++aVXYRMrB\nmjUwfLjV8Fi/3vY1aWLLeF522b6nbWdlweTJ8MkntizcvHm7Xt+unQUE+va1TISELxZawWzdarUi\nPvnEgj/LloWvq1nTssDOOANOOAGqVo1ePyWxKRAgESkQICKyd9u2baN58+asD40QOAy4AxhA3bqV\n2LTJlgMESwO+9lorbK8vfkWQmWkjof/+136vVcuKBLZvH91+SULascOyAx5/PDxoT021gN5jj5W8\n/aVLLSDw2WfwxReWPRBSqZLVDzn2WEuMOfpoqFat5I8ppScQsDP9n39ug/+vv4bs7PD19etDv342\n+D/uOM1oktigQIBEpECAiEjRtGlzIb/9thy4E+dOpE4dt7P6f1KSVQq/7jr7Eq85nxFkZ8Mff0Dz\n5uF906dDnz5Wih2seMLnn0NaWlS6KBISCNhg/ZlnbMB3220wdGjpPkZODnz3XTgw8NNP4YKDYIGB\nzp3t3+Koo6wA4f77l24fZM8CAZs+MnkyfPUVTJkCf/4Zvt45K2Ny0km2de6siv8SexQIkIgUCBAR\nKZrHHsviH/9IJSkpPIW9dm2r+Hz11Zrru0e//QbnnGMD/pkzoXp1+Oc/4YEHbGJtUhL86182NUAk\nxixaZCn7Zb0k4ObNMHWqDTqnTLF/lVCmUUiTJhYQ6NYNjjgCOna0fycpHRkZFp/8/nuYNs2Sk3Ym\nggU1aWJn+086yVL+69aNTl9FikqBAIlIgQARkcJlZ8P48fDii5bGG6L0/2J44w246iqbTNu8ua23\ndsUVNsoB+xY9ZQocfHBUuykSazIybCD63Xe2TZsWTp7Jr00bqz5/+OF2eeihVpdEmUl7lpEBs2bB\nL7/Y4ej77+3sf8GvxKGBf8+etrVooddWKhYFAiQiBQJERHa3aBH85z/w6quwdq3tS0uz2nVXXGFp\nuvoiuBebN1u0ZORI+/2vf7V5EzfdFC7PfvLJFmlRCW2RvQoErG7B999bYGDmTJuvnn+OekidOhZb\nO+gguzz4YGjbFho3TrzU9cxMWLgQ5s+HOXNs4P/LL3acLyglxbIsjjrKUv6POgpattTxXio2BQIk\nIgUCRCTRrF27lhEjRjBy5JtMnPgVDRvWBuzL4vjx8NJLu579P/hgG/xfcIFNBZAi+PhjuPxyWLkS\nqlSBRx6B0aPt9CbYt+3hw60cu0icmTfPigsOGgT9+5dtyYvsbBvczpxpNQZmzrSz2pEyB8D60rIl\ntG4NrVrZ1qwZNG1qZ77r1Kl4g17vYcMGq9gf2pYsgQULbPC/bNnuZ/nBDkMHH+VSxT4AACAASURB\nVAwdOtjgv2tXy6pQiRKJNwoESEQKBIhIIggEAkyaNIkXX/wP48aNIzc3B4BLL32eyy67ghEj4O23\nw1+eQ2f/L7/c5uJWtC/GUbNxI9xwA7z+uv3etauNhO69d9dF2idOtBGHSBy67TZ49FH7uXZtuPBC\nuOQSG3CWx7HEe6vLOWeOBQVmz7aff/stnOFUmCpVLCDQtKlNL6hXz7b69cM/16oFNWrYVr26rfZZ\n2v3fts2Ox5s22eXGjbbEY8Ft1SpYvhy2by+8veRkC3i0bWvLNR52mL0X7dqpqr8kBgUCJCIFAkQk\nnv3xxx+MGDGC4cP/w4oVS4J7k4CLgVupVetANm0Kfy527gwDB+rs/z4ZPx6uvBJWr7ZIyp132oD/\nm2/s+pQUePJJqxcgEsc2bYK33rLsolApDLCzzxdeCOedZwPtaMjIsJT4334LX65YAb//bpdbthS/\nzfR0CwqkpdlSi/m3ypUt+BH6mhm6DAQsNpiVZdlYoW3HDutDwSKJe1OzpmU2NGsGBxxg5UjatoUD\nD7QMiJSU4j8vkXihQIBEpECAiMSbrVu3MnbsWF55ZSRTpkzC+9B6XO2Bh6lc+USys8O5n40a2cB/\n4EDVq9tnY8ZYCgVA9+5WzvzZZyE31/YdfrgFBfbbL3p9FImCmTPh5Zct4yi03KhzVi7jwgvhzDNt\nEBsrtmyxoMDvv1v2wLp1u19u2RLeMjIip92XVJUqlnlQs6Zd1qplWQkNGuy6NWxoA/9Yeg1FYo0C\nARKRAgEiEk9++mk23bp1ISsrlCdaA/gHzl1AUlID8vLsMzAtzTLWBw6E3r1Vq67EsrLgmGMsCDBm\njOUlg50S/Pe/4Zprots/kSjLzoZPP7VFNCZMCM+USUuDpUttUFsRBQK2IMiWLeEz/Pm3/IUMQ9Mi\nnLMtNTWcRZCWFt5q1FDKvkhpUiBAIlIgQETiyfbteaSntwHOAS4lKakVgUD4c++YY+Cii2DAAJ1B\nKlVbt9qL+umn4X0nn2xLBWp9RZFdbNoE771nQYHMTFsBQESkrCgQIBEpECAi8SA7Gz7/3NJvx4zx\nZGWFP+u6drWs9QEDrAiWlKJAwAoB/utf4VN/++8PY8fCkUdGt28iFUBWlp0RFxEpK7EQCFDipYiI\nlJrNm+GTT6xG3ccf5y9y5ejUyQb/f/2rFY2SMvDyy3DTTeEXPiUFhgyxIoEiUiQKAohIIlAgQERE\niiQQCPDDDz/w6qvv0rTpodxzz0DAlqWfMAHGjYOvvoKcnPB9Dj00PPhv0yZKHU8En30Gl11mbwbY\nZN/TT4cRI2xyr4iUmdtvh3nz4LTT4NRTrVieiEis09SAGKSpASISK7Zu3crEiV/w+usfMmnSR2zd\nuhqAatUu4I47RjJ+PEyfHr59UhL06AH9+tk4tGXLKHU8HuXlwciR0LGjbQDTplkAYPbs8O26dYPR\no61st4iUKe/tOLd0aXjfkUfCX/5igYHDDgsX5BMRCYmFqQEKBMQgBQJEJJoWL17MmDEfMWrUh8ye\nPZlAIBuoBfQBzgT6AuGqflWqwIkn2sD/1FO1Gl2py821gf1DD8HcuXDCCZbqf9VVdhoypG1bePNN\nWyZQRMrNypXw4YfwwQcwaZIVGwxp2tQCAiedBD17QrVqUeumiMQQBQIkIgUCRKS8ZWfnMGjQPXz6\n6YesWzcHcEBn4CTgLOAQIGnn7Rs1gr597cz/8cerCH2ZyMyE116zon9Llti+evXs9OLateHbNW0K\nTz9tkRgRiapt2ywY8MEHFhxYvTp8XUoKHHuszeRJSiq8DRGJfwoESEQKBIhIeQsEICXleAKB1tiZ\n/z5AeG55Soql/Pfta9uhhyrdtcxkZMALL8Bjj4VHEfXqWWbAxo3h27VqZQGAk06KTj9FZI8CAZgx\nwwICEyfCDz9A9+7w3/9Gu2ciEm0KBEhECgSISFnz3k4yf/VVePvjj11v07y5jTH79oXjjoPq1aPS\n1cSxaBE89xy88ootag5Qty5s3WrrmYW0awfDh1uesYhUGBs3WjLPgQdGuyciEm0KBEhECgSISEkE\nAgFmz55LSko12rVrBtjAf/58+OYb+PprG/gvX77r/erVswF/aGvbVmf9y81jj8Gtt9obBVCzpi0B\nGPrdOatA9tRT0LVr9PopIuXq669hwQKbUtCqlY7JIvEiFgIBWj5QRKSCy8nJ4dtvZzJ69NdMnvw1\nixZNJSdnBwcf/CTnn/83vvkGvvsO/vxz1/vVqWNfLo87Dnr1goMO0pfMqOnSxV78KlVg+3bYvNn2\np6bCWWfBE0+oCqNIAnr5ZVsFFKBxYzj6aFsY5KijoFMnSEuLbv9EpOJSRkAMUkaAiBTGe8+yZSsY\nP34aEyf+wM8//8CqVT/ifWPgCKAL0B04HEjZ5b6NGtn81KOPtsH/YYepYFXUTZoE//wnfP+9TSgO\nqV8fbr4ZbrlFb5JIAhs5EsaNs7oC69fvel1KChx+eDgw0K2brRqqgK5I7IuFjAAFAmKQAgEiEsmo\nUd9z8cX9yMlJxQb9RwYvOwO1d7ltUpLnsMMcRx8dHvw3a6YviDHhf/+DBx6ATz6x9P+QSpUsQvPg\ngzYNQEQkKBCw1UK//94yvL7/HmbPDs8eCvnuOwsKiEhsUyBAIlIgQEQA8vJg4UL45RfbpkzJ5Ntv\ntwD1d7tt/fqWXX7kkTbo79IFatTYvU0pB4GAlQdv1szSMMAKNNx/P3z88a6V/8Em/l5/Pfz97zr7\nLyJFtnkzTJ8eDgzMnGlFYDVdQCT2KRAgESkQIBLfMjMzmT59Ad988xt33HEGYGPDX3+1AX/o8n//\ns6XkC6pVy9O1q+OII+CII2zw37ixzvZHVW6ufRt//3149134/XcYNMgKM0yevHuBhvr1oX9/uOce\naNIkKl0WkfjiffE+B/Ly4LrrrD7MIYfYsrB16pRd/0QkTIEAiUiBAJH4kJmZxXffzefLL2fz44+z\nmT9/DqtWrSIzswpwIHAQ3btfyeLFKaxaFbmNAw6ADh1sPn+HDjbwb95cg/6YsHo1fPqppfhPnBhe\n8q8w++0Hp58Od98NLVqUTx9FRAqxcKGtDpNf48YWEDjkEGjf3pY6PPBAO3zpc0ek9CgQIBEpECBS\ncZ166n38/POvrF+fRVZWZaAl0AZoDxwE1I14vypV7ItXaMDfoYN9GatdO+LNJRoyM2HqVFt78bPP\nYMaMvd+naVM45RS46SZo06bs+ygiUkRr18KoUTBrlm2zZ9uiJZHUrg0nnghvvVW+fRSJVwoESEQK\nBIjEvi1bYNEi+O23Xbevv16H9/UKvV9aWh4HHug4/PAkDjrIUjLbt7fp5MnJ5fgEpPjmzrU3bE9S\nUiyac8EFcPnlULVq+fRNRKSEAgGrMTBrlk1Nmz8/vG3ZAqedBhMmFL294k5VEEkkCgRIRAoEiJSv\n3Nw85sxZyfTpy5g1aykLFixjyZJ1rFmTxXnn3UDbtu1YtgyWL4dly2DpUli3rvD2kpIC1KuXTfv2\nKRx2WDKtW9tg/6CDrHacvhhVEMuXw5tvWtr/rFmwYcPut0lKsihOr15w2WW2fpeISBzx3mZC7dgB\nLVsW/X7vvANXXGEzoVq2tMv8W5MmkJ5edv0WiWUKBEhECgSIlJ2HHvqEjz76kT/+2MGGDdls3+7J\ny6sCNAGaAQcEL6vtsZ20NCv23rr17lvTpjq7H9MCAUvn+Okn6NvXlldYuBDeew+mTLH82FWrrABg\nQcnJ9u31qKNg4EDLlVWlfxGR3Tz6KNx2255vU7u2HVKbNIGzz7bDqkgiUCAgxjjnmgD3AX2BOsAq\nYBwwxHu/lypQpdeOAgEie7dx4zbmz19L3brVadNmP3JzYf16O1O/dq2N4/74Y/dt6dJsvK+81/Yr\nVcqmVq0sDjywMocdlsoBB9iJ39Bl48aJPf4bPHgwgwcPjnY39sx7q94/d64twD13rq21NWsWZGfb\nbWrUgG3brHx2JOnpVimrZ08491yr1igiFUKFOE7FMe9hzRqbbpB/W7zYMutWrgwfigH+8Q+4776i\ntz9nDqxYAQ0b2rbffgrCS8WhQEAMcc61Ar4F6mGD9nlAV+A4YD7Q3Xv/Z+EtlF47CgRIIvvhh+VM\nnjyXpUvXs2RJBqtW7WDDhlwyMjw7diSRk5OK91WA2kB90tMPIjW17m6rs+1JcnIm6emZ1KkToFmz\nSrRvX5X27SvRvHl4sF+rllL498Q5F5vHqFGjbAm/n36y1P5IZ/ULU726LclwxBGWKXDqqZrjL1KB\nxexxSgALFKxbZ/Ha33+3LLuDDy76/e+4Ax55JPx7UhLUq2dBgQYNoG5dCw6ELo891oryisQCBQJi\niHPuM6APcK33/tl8+x8DbgRe8N5fVR7tKBAgFdW2bVmsWpXBsmUbWbHiT37/fSPNmjWjW7f2bNxo\nS6lv3Lj7ln//vHmbyMpKAmoU67GTkuzDvn59+yLQqJGdtQ9tod8bNYJqe876lyKI6hfs1attoD9n\njp3lX7jQTgutXw9bt9q3yz2pUsX+ENq0gc6d7Wz/scdC5b1niohIxaFAQHx74QWrQ7BmjX0srF+/\n59s//TRcc03R2//qKysCXKuWbTVrhn+uVUsfGVIyCgTEiOBZ/IXAEu99qwLXVQNWAx5o4L0vZGGV\nUm1HgQApF4GAJzs7j7S0SoCNn3JybPmgjAzbtmzZ9XL06P8xdepMcnIqkZdXiUCgMt6nAlWA6sGt\nRvCyJFWAAiQnbyMtLZP09Bxq1/Y0aJDMAQdUpm3bqhx4YCoNGjjq1bPBf+3aSgksTyX+gp2TY8X3\n1q+3b3HLl1uZ6gUL7NTQ2rWweXM413PjRkvhz59HuifJyZb236CBVanq0gV697a5/ZUq7Xu/RaTC\nUCAgseTkWIbB6tX2sRL6iFm/3n4+/3zo0aPo7V1yCbz2WuHXV6mya3Dgnntstdii2rDBStZUq2Z1\nh5SFmFhiIRCA9z7hN2AQEACGF3L9Z8Hre5VTO97eGilL9957b7S7ENGOHTl+9eoMv2DBev/jj7/7\nOXPW+61bvd+wwfs//vB+8WLv5871/uefvZ82zfspU7z/7DPvx471/owz7vXnnTffN2jwtq9d+21f\nvfoYX6XKu75y5XE+OfkDn5T0qYdJHr72MN3DLJ+Sss43aOB99ereJyd7b+GA0tryfFLS3b5FC+87\nd/b++OO9HzDA+8sv9/72271/5BHvX3zR+3fe8f6LL7yfMcP7JUu837TJ+7y8fX8Ny/K9Le22S6O9\nkraxL/cH7E3KzAzvzMuzP9SffvL+gw+8f+EF74cM8f6aa7w/5xzvTzjB++bNvU9KKvkfV6VK3teo\n4X2zZt537+79xRd7P2yY91Onep+VVaLXI5bE6nFqX8Xi84lGn8r6MePtOLWv99V3qbIXi//TJRV6\nTq++6v1ll3l/5pne9+5t32Nat/Z+v/3sI6jgx9JbbxXvcc4/P3zf5GTva9b0fv/9vW/XzvtOnbzv\n0cP7Pn28P/107w8++F7/7bfFa3/ZMu/nz/d+xQrv16/3futW77OzvQ8Einb/RPsuVdJ2invffOO9\nqI2BlREAOOceBW4GbvbeD4tw/TPA1cBV3vsXyqEdZQSUUG5ugOzsPLKz80hKctSokUogYPXAcnJs\nq1XL8ccfntzc8L6cHPjll7VMnbqYzMw8MjPzyM4OkJnpyc4OkJMTIDs79DPk5noOOKAJffseuksb\noS3UdnY2ZGVBZibMmLGS335bhPfJWNG6SkBKcEuNsBXn7KXDjiv7LiXFotzVq9sJ1YKXGRlbWL16\nDbVrJ7Pffik0aFCZ/fdPpWnTquy/fwo1a7qdt69aFZKTy/+MTFmeBSrttkujvYht5OWFz55XqWJ/\njKG0jtC2dSts3Yo74wz888/b73PmwC+/WFrI9u32h5udbVtenrWTl4cLBOwvLTnZTmPk5e09Jb8o\nkpPtj7Bq1XA56ebN2bkGY8eOtu5UglRqjLczmrH4fKLRp7J+zApznCrj+8bi31u8icfXuCjPyXv7\niNy8GTZtsq1NG5uaWFSXX24lbbZutY/avfSKd97xnHVW0dsfMADefTdCSw5SU21qQ/7LZ5+18jjh\n2+35dRg1CubPD98/JcW2SpV2/7lSJUvMa9SoaG2DfU3Jy9u1ncI++kvr77A8j1OxkBGg/EhTM3i5\nuZDrQ/trlVM7AFzUeyx5eRDw4AOeQIGfPZDnPY33r8cxx7bDe0sx8j6AD7idv9s+uy8Bz+xZq/l5\nxjwCuPB+b2niAN67XWKcDerX5+hg+z7P4wm3mf9xQo87f+5q5s1fHGzL2gv4JAj+7HF478A7vE+i\nevW6HHTwAfZcsX/6QJ4jLw/yArYF8rztC8C6tVvZsnUTkIwnCUjGYe1C8s4tfF1o3+4Ob7waF3Hg\n3GznT5GvD1+3aQ78+unKQq+PpBEt99BuLpCLY2vw9wBpqZCaApUreyqneFJTPakpASqn2O9pqVA1\nzfPSVBjY6RvWrVxJWmqAKqmQnuapVhWqV4Ea1Ry1ajhqpztq10yibu1katRJpWrDGqRV9qSlelKS\nA4U+X8A+sTZujLAfK4cZiHD/SZOCT2UvbQcClv4dab32SLy3AWPduuz8QwxVf3/33fDveXnhnzdt\nslLF+feFLnNzg4kMwUFtbq7l7DVsuOtA99Zbw/9coS10/YYNtjxBwcfNN4jeZQPo3n3360M/579/\nXl543kboHzSkpDmFV165b/eLVG0/KSn8qZ2WZu9RtWoWSapWzXIp99/fKjM2b27fnlq3VmE+ERGp\nEJyzRWXS063+0L548UXbwE4aBWPzZGTYV6EdO8Jb//7QtWvx2m/QwD5ad+wIx/WzsuxjOzPTtvz2\nHozY1ZgxMH580W///vv2PIrqootg3Lhd9zlnXy+Sk3fdAD7+GE4+uejt3347TJ26ezsnn2xfYwo+\nxs03w5FHFr3911+3MkZJSZG3WKCMAMA59yKW1j/Ie/9KhOsfBO4E7vTeP1Lw+jJoR2+KiIiIiIhI\nHItmRkCMxCOiLnSmvmYh14f2byqndkRERERERETKhKYGmHnBywMLub5N8HJBebQTzciQiIiIiIiI\nxDdNDQCccy2B34AlQGuf70VxzlUHVmFT8ut773eUdTsiIiIiIiIiZUVTAwDv/WJgItAC+HuBq4cA\nVYGRocG7c66Sc65dcOC/z+2IiIiIiIiIlDdlBAQFB/XfAvWB8Viaf1egJ1YL/Wjv/cbgbZsDi4Fl\n3vsW+9qOiIiIiIiISHlTICAf51wT4D6gL1AX+AMYCwzx3m/Od7vmWCBgqfe+5b62IyIiIiIiIlLe\nFAgQERERERERSSCqESAiIiIiIiKSQBQIiBPOuTudc9Odc5udc2udcxOccwdHu18iIgDOuf8LHpd+\nd84FnHMDo90nEREA59zVzrklzrkdzrkfnXM9ot0nEZGQsvoOpUBA/DgWeAboBvQCcoEvnHO1o9or\nERGTDvwKXA/swJZSFRGJKufc2cATwANAR6zg8yfOuaZR7ZiISFiZfIdSjYA45ZxLBzYDp3vvP4p2\nf0REQpxzGcDfvfevR7svIpLYnHPTgJ+991fk27cAeNd7f1f0eiYisrvS/A6ljID4VQN7f7VUoYiI\niEgBzrnKQCdgYoGrJgJHl3+PRETKjwIB8etJ4Cfgu2h3RERERCQG7QckA2sK7F8LNCz/7oiIlB8F\nAioY59z5zrmMfFv3CLd5HItkn+k190NEylFRjlEiIiIiEl0KBJQB59xZzrmnnXNfO+e2BKs7jtzL\nfZo4515xzv3hnMsMVq8d5pyrVeCm44EO+bYZBdoZBpwN9PLeLy29ZyUi8SKaxygRkeIo4+PVeiAP\naFBgfwNgVSk+DRGJY2V8nCozlcrrgRLMPcBhQAbwO9COPVR3dM61wqrU1gPGAfOArlhlyL7Oue7e\n+z8BvPdbga2FtPMkMAA4znu/oNSejYjEm6gco0RE9kFZHq+ynXMzgBOA9/I10wd4p/SfiojEqTI7\nTpUlZQSUjRuANt77msBVRbj9c9gfwrXe+zO893d573sDw4ADgQf31oBz7lngYuB8YLNzrmFwS9/X\nJyEicSsax6h051xH51xH7LOnWfB3LdElIntS1serx4GLnXOXOefaB0+qNASeL72nICJxrkyPU2X1\nHUrLB5Yx51xP4EvgDe/9RRGubwUsBJZ471sVuK4asBqLKDXw3m/fw+MEgrdzBa4a7L2/r0RPQkTi\nVjkeo0KPA7seq17z3l9awqchIgmgrI5XzrmrgNuARsAs4Ebv/dSyeh4iEr/K4jhVVt+hlBEQfccF\nLwsuXRNKsf0GSAeO2lMj3vsk731y8DL/piCAiJREaR2jJuc7LuU/VikIICKlZZ+OV9774d77Ft77\nNO/9kQoCiEgZKvZxqqy+QykQEH0HBi8Lm9O/MHjZphz6IiJSkI5RIlJR6HglIrEuZo5TCgREX83g\n5eZCrg/tL7cKkiIi+egYJSIVhY5XIhLrYuY4pUCAiIiIiIiISAJRICD6QlGfmoVcH9q/qRz6IiJS\nkI5RIlJR6HglIrEuZo5TCgRE37zg5YGFXB+aH1LYPBIRkbKkY5SIVBQ6XolIrIuZ45QCAdH3VfCy\nj3Nul6X/nHPVge7ANuD78u6YiAg6RolIxaHjlYjEupg5TikQEGXe+8XY8hEtgL8XuHoIUBUY6b3f\nUd59ExHRMUpEKgodr0Qk1sXSccp578v6MRKOc64f0C/4a0PgBGAxEFqXdp33/tZ8t28JfAvUB8Zj\nKSNdgZ7AfOBo7/3Gcum8iMQ9HaNEpKLQ8UpEYl1FPU4pEFAGnHP3AvcCBV/cUPrHUu99ywL3aQLc\nB/QF6gJ/AGOBId77wpaXEBEpNh2jRKSi0PFKRGJdRT1OKRAgIiIiIiIikkBUI0BEREREREQkgSgQ\nICIiIiIiIpJAFAgQERERERERSSAKBIiIiIiIiIgkEAUCRERERERERBKIAgEiIiIiIiIiCUSBABER\nEREREZEEokCAiIiIiIiISAJRIEBEREREREQkgSgQICIiIiIiIpJAFAgQERERERERSSAKBIiIiIiI\niIgkEAUCRERERERERBKIAgEiIiIiIiIiCUSBABEREREREZEEokCAiIhICTnnmjvnAs65V2OhHSk/\npfmeOed6BtsKbXNLo4/72Jf9CvQlEK2+iIhI6asU7Q6IiIiUlwiDmWxgC7ACmAm8B0z03u/roMeX\noHtl0U65cc41BxYDI7z3l0S3N6WnGM+rNN+zycFtfb5+nA7cAnQG0oA/gWlAAEgBGgCHAMnA/t77\nVSXswzZgcPDnS4ADStieiIjEEAUCREQk0XhgSPDnZKAWNoC6ELgM+NE5d773fmEx2vwdaAdsLmHf\nSqudaPAFLuNFNJ7XZO/9fbt0wvvxwHjn3OXA88Bz3vt/5r+Nc64l8DnQFChRIMB7vwO4L9huLxQI\nEBGJKwoEiIhIwik4yAJwztUHngYGAF84547w3q8rYnu5wIJS6FeptBMlrsBlvIi155UdvMwteIX3\nfrFz7gGgGfBDufZKREQqFNUIEBERAbz3a4FzsJTspsBdoevyzwN3zrV1zr3tnFvrnMtzzv1fpHni\nzrmjgvveL+wxnXNznXOZzrlaBR+nkMdu7pwb7Zxb75zb4Zyb7pw7pZC2nXPueufcnOBtf3fOPe2c\nq+mcW+qcW1LU18Y59xfn3CTn3Kpgf1c65yY7564KXj8YS58HGFhgbvnAIryGx+Z7rK7OuXedc6ud\nc1nOueXOueedc40i9KvYr01xXpeiPK8I/SnS+1OGvkZn70VEZC+UESAiIhLkvffBM6o9saDAjQVu\n0gr4HpgPjASqYDUGdjaRr63vnXPzgZOdc3W893/mb8g51wU4EHjXe7+pYFcidK8ZNid8ETACqAuc\njaWLH++9n1zg9s8CVwIrgReAHOAvQBfs8z+bIsiXir4KGI/NW68PdAAuBoYDXwE1geuBn4Fx+Zr4\nqUCTkV7DzcHHuhR4EdgBTMBqN7QFBgGnOeeO8t6viNDN4rw2xXldivO8mhejD2VpMflqC4iIiESi\nQICIiMiupgJ5QH3nXHPv/dJ81/UAHvLe35P/DsGCcpGMAB4CzsUGoPkNzHebougJ3Ou9vz/f444C\nPgVuxTIZQvuPwQa784Gu3vstwf13AV8AjYH8z2tPrgCygA7e+10GmM65OgDe+ynOuaUEB8yRpl7k\nU9hr2BYLOCwGjs1f7C44R30i8CRwRoQ2e1KE16a4r0sxn1eR+lDWgoUui/o3JSIiCUpTA0RERPLx\n3mcDG4K/7lfg6tWECw0WxUisqvsuaeTOucpYxsEa4JMitrUUeKBAXydiZ82PLHDb0OM9GBrsBm+f\nA9xZxMfLL4/Ic9LzZzkUdQ59Ya/hVdgJiusLVrz33n8JfIBlBaRHuO9Sivba7MvrUtTnVdQ+iIiI\nRJ0yAkRERHYXGvwVTNH/JThoLBLv/Urn3CSgj3Ouvfc+tC78aUBt4PFiLFX4s/c+0pSBFUDXAvsO\nD/Z9aoTbT8MG9kX1BvAYMMc5Nxr4L/BNUQspRlDYa9gteNnTOVfw+YBNR0jGplPMLHBdUV+b0nxd\nCirO+yMiIhJVCgSIiIjk45xLA+oEfy042F29D02+BvTBzkbfEdxX3GkBAAXrCITksnuGX83g5ZqC\nN/be5znnNhTcXxjv/TDn3HrgauA64AbAO+emALd672cUta2gwl7DusHLW/fUHSBSRkBRX5tSe11K\n0AcREZGo0weTiIjIrnpgZ57XeO+XF7huX9aSH4sVFLwgWLG+PnASdgZ5Vsm6WqhQ2nvDglc455IJ\nD7qLxHs/0nvfLXi/U4CXgf8DPnPOFZw+sdfmCtm/OXhdDe99UiFbsvf+62I+Xn6l+rqIiIhUVAoE\niIiIBDnnkoC7g7+OKo02vfeZwBisEF0f4Dws0FCWBd1mYtMbekS47qjgwvkdjAAAIABJREFU4xeb\n936z9/4T7/3lWKZDHSwgAOG0+n1qG/gO6/P/7e2GJbAvr0tJn1fMcc6lO+eGOedud859Wtg+ERGJ\nXwoEiIiIAMEz9aOBY4FlWLX/0vJa8PKi4JYDvFmK7Rf0evDybudcjdDOYJHCYj0v59xxhVzVIHi5\nLXi5MXjZrDjt5/MM9roMc861idCPysGq/yWxL69LSZ9XLLoMWIItn/jxHvaJiEicUo0AERFJNM45\ndy92ZjgJqAUcjJ0lTsGKxp1foCJ+iXjvv3XO/QYMCD7GhIJL8ZXQLpXtvff/dc69CFwOzHbOvY8N\nsk/DBrZ/YKsZFMVY51wG8D0WIHHAMcARwI/Ysnt477c6574HjnHOvQEsxM6mjy/KFAjv/Xzn3KXA\nK8E+fxpsIwU4IPiYa4CDitjvkJ2vzb68LiV9XgX7UArSgpeRaiUUVW1gqfd+E/DUHvaJiEicUiBA\nREQSjQfuDf6cjc0bX4adtX8vuORbWRgB3B98/NKcFuCJPO/+KmAecEVwW4/VK7gbWAmsLWL7twMn\nAp2Ak4FMbKm824Dh3vv8lfYvBIYBfYFzg/uWA0UaMHvv33TO/QLcDBwHnABsxQboY4C3i9jnnU2y\n+2uzL69LSZ5XYe9PsTjn/gLcggVgPHCLc+4ErPjimd777RHuMwBoi61c0A0rVnkkFvTq4ZxriK0I\n0bPgPu/9bstFiohI/HCRV7oRERGReBRMu58PvOW9Pz/a/YkVsfC6OOd6Al8CQ7z3Q0rY1pHAU8Ei\njzjnrgcaee/vCGbEeO/9ffluv9u+fNdNBo7x3sdNnQQRkUSnGgEiIiJxyDnXIFj8MP++qsATwV/H\nln+voq+CvC73OucCzrm5JWjjXCDDOXe6c+50LJMj/3SUSNMVdu5zzu0X7EOAsi3gKCIiUaCpASIi\nIvHpRuBc59xXWPp4Q6A3sD/wsff+3Wh2Lopi+XVZAgwhPJWgJHUk8oBN3vvx+3j/bQX6IiIicUSB\nABERkfg0ETgMm2dfByuKtwA78/3EHu4X72L2dfHeL8MG36XhdeAT51ya9z4zmAVxqff+JezMf8EB\n/i77vPc7SrEvIiISY1QjQERERCQOBYsJ9gN+BSoDbwBdgfuwk0H/8d4/55w7GRv079wXpS6LiEg5\nUSBAREREREREJIGoWKCIiIiIiIhIAlEgQERERERERCSBKBAgIiIiIiIikkAUCBARERERERFJIAoE\niIiIiIiIiCQQBQJEREREREREEogCASIiIiIiIiIJRIEAERERERERkQSiQICIiIiIiIhIAlEgQERE\nRERERCSBKBAgIiIiIiIikkAUCBARERERERFJIAoEiIiIiIiIiCQQBQJEREREREREEogCASIiIiIi\nIiIJpFK0OyC7c875aPdBREREREREyo733kXrsZURICIiIiIiIpJAlBEQw7xXYkBZcs7F3Wsci88p\nGn0qy8cs7bZLo72StrEv94/Fv7V4FG+vcyw+n3g7RpVF+9E+Tu3rfWPx7y3exONrHIvPKd6OU7F4\njCppO8W9r3NRSwTYSRkBIiIiIiIiIglEgQARERERERGRBJI8ePDgaPdBChgyZMhgAL03Za9nz57R\n7kKpi8XnFI0+leVjlnbbpdFeSdso7v2HDBmiY1Q5icX/6ZKIxecTb8eosmg/2sepfbmvjlPlIxb/\np0sqFp9TvB2nYvEYVdJ2inPfIUOGADB48OAh+/yAJeRibQ6MhFcN0HsjIrEqFudQiojkp+OUiMSq\nUI0ArRogIiIiIiIiIuVCgQARERERERGRBKJAgIiIFNu9994b7S6IiOyRjlMiIoVTjYAYpBoBIiIi\nIiIi8Uk1AkRERERERESkXCkQICIiIiIiIpJAFAgQERERERERSSAKBIiIiIiIiIgkEAUCRERERERE\nRBKIAgEiIiIiIiIiCUSBgDLinLvaObfEObfDOfejc65HtPskIiIiIiIiokBAGXDOnQ08ATwAdAS+\nBT5xzjWNasdEREREREQk4TnvfbT7EHecc9OAn733V+TbtwB413t/VxHu7wH03oiIiIiIiMQX5xwA\n3nsXrT4oI6CUOecqA52AiQWumggcXf49EhEREREREQmrFO0OxKH9gGRgTYH9a4GG5d8dERERERGT\nm5tLXl4egUBg51bw9/z76tatS9WqVaPdbREpZQoEiIiIiIjEkOzsbP7880/+/PNPNm/eTEZGBlu2\nbGHLli07fw5dXnnllXTs2LHIbZ955plMmDChyLd/7733OOOMM4p8+7POOosJEyaQmpq6c6tcuXKh\nP99999306FH0mtrz5s0jIyODqlWrkp6eTtWqValatSpVqlQhOTm5yO2IJLqEDAQ4584CjsUK+XUA\nqgFveu8v3MN9mgD3AX2BOsAqYBwwxHu/Kd9N1wN5QIMCTTQI3kdEREREJKKzzz6bMWPGFPn2vXr1\nKlYgID09ncqVK5OUlLTLlpycHHFfampqsfqfl5dHTk4OOTk5bN26da+3v/zyy4vV/l133cXYsWMj\nXpeamrozQBDa/v3vf3PccccVuf358+ezfft20tPTqVat2s52KlVKyGGTxLFE/Yu+BzgMyAB+B9oB\nhVbmc861wir/18MG//OArsD1QF/nXHfv/Z8A3vts59wM4ATgvXzN9AHeKf2nIiIiIiLRkpGRwfLl\ny3fbVq1axapVq3jooYc4/fTTi9xe1apVSU5Opk6dOtSpU4datWpRvXp1atSoQY0aNXb7uVOnTsXq\n76hRo4r7FIvlvffeIycnh6ysrJ1bdnZ2xJ+zsrLo3Llzsdpv2bIlnTt3Zvv27bttoTY3bty48/Y7\nduwoVvs333wzH3300W77K1euvDMokD9AMHToULp161bk9pcuXUpubu4uwQplMkg0JGog4AZghfd+\nkXPuWOCrvdz+OSwIcK33/tnQTufcY8CNwIPAVflu/zgw0jn3AxZAuBKrD/D/7N15fFX1nf/x1zcb\nSQhZ2VVQREEUt6KgKKBs2taOre2MXay1dnesdrHVqUqw2vbXWut0tXWcbmM7bXVqa11QkKWKuG9V\ncFdAdrKRfbnf3x+BlJ0Ektyb5PV8PM7j3nvOud/zIYkx532/yy2d90+QJElSd/vlL3/Jn//857Yb\n/u1vOnfnrbfe6lD7t9xyC7fddhtpaT1zTu+0tLS2rv9d4cYbb9zt/hgjDQ0N1NTUUFNTQ21tLdXV\n1YwePbpD7R922GEce+yxbe3U1NRQXV1NY2MjjY2Nu3y/29PrYXuf/exneeCBHecUz87O3iEY2D5o\nuO666zoU9qxbt44QQtuwiZ76c6Su1yeDgBjjou1e7nXJhq29AWYCb24fAmw1B/gs8LEQwldijLVb\n2/9jCKGE1p4Hw4AXgHfHGFd10j9BkiRJSfDaa69x9913t73Ozs5mxIgRbdvIkSM55JBDOOiggxg6\ndCiHHnpoh9rvqhvo3i6EQHZ2NtnZ2ZSUlOx3Oz/60Y922RdjpL6+fpdwoKamhuOOO65D7Q8dOpRR\no0a1tVFbW0t9fT319fVs3rx5l/OvuOKKDrX/kY98hIUL//kZZ05Ozi7hwvbbtddey7hx49rd/muv\nvUZjY+MOc0BsP+fDtmXxlPr6ZBDQQdsGFe28HCAxxuoQwiO0BgWTgIe2O/Yz4GfdUqEkSZL2qaGh\ngVdeeYWXXnqJ5cuX89JLLzFz5kw+/elPt7uND3/4w0yYMKHtxn/gwIHe/PRyIQRycnLIyclh4MCB\nB9TWr3/96x1exxipq6vbbchQU1PDMccc06H28/PzGTRoUFuviLq6Ourq6ti0adNuz//iF7/YofYv\nvPBCli5dusfj208G2a9fP+666y4mTJjQ7va/973vsXLlSjIzM8nIyCAzM3Ovz8855xyGDNl5arY9\nW758OXV1dTvMi7H94877Bg4cSGZmZrvb70kMAvZtzNbHV/Zw/FVag4Aj2C4IkCRJUnLEGFm1ahXP\nPfcczz//PM899xzPPfccr732GolEYodzMzIyOhQEHHPMMR2+OZP2JITQtvLBoEGDDri9u+66q+15\nIpGgrq5uh2Bh56BhzJgxe2ltV4ceeihlZWU7zPOwbWtqamobQrFlyxag9b/FjvjTn/7EE0880e7z\nH3300Q4FARdeeGGH2l+2bBkTJ05s9/mTJ0/miSeeIIRACIG0tLTdPk8FBgH7VrD1sXIPx7ftL+zs\nC+/th2TOnDmUlpZ29iUlSZJ6tAceeIDzzz9/t2P309LSGD16NOPGjeOoo45i3LhxHZ6sTuop0tLS\n2oYAdJbbb799j8cSicQuk0EOHjy4Q+1fccUVrF27lqamJpqbm9tWoNjT846EAABjxoyhubmZlpYW\nEonEDo+725eVldWh9hsbG2lqaurQe5LFICCFdTRBkyRJ6uuGDRtGeXk5JSUlHHfccW3bsccey1FH\nHUV2dnayS5R6pbS0tLZ5GvbXhz70oU6saFe//e1vu7T9pUuXkkgkiDG2bdu/3va8uLi4S+toD4OA\nfdv2iX/BHo5v21/RDbVIkiT1CTFG3nzzTVasWMG73/3udr/vqKOOYvXq1QwfPjxluuBK6ht60nwC\nBgH7tmLr454G0Byx9XFPcwhIkiRpH+rr63nqqadYunQpjz76KEuXLmX9+vVkZWWxZcuWdnfRzcjI\n4KCDDuriaiWpZzMI2Ldt62/MDCGEuF1//RDCAGAyUAMsS0ZxkiRJPdHq1avbbvgfffRRnn766V3G\n1paUlHDKKadQXl7e4bHAkqQ9MwjYhxjjGyGEB4BZwCXAj7c7PBfIBW6JMdZ19rW3787m5ICSJKm3\nmDp1KkuWLNlhXwiB8ePHc8opp3Dqqady6qmnMnr0aLv3S+oVSktLmTt3brLLaBP64oR0IYRzgXO3\nvhxK603+G8DDW/dtjDFesd35o4ClwGDgL7QOF5gITANeBk6NMe46Ne3+1xfByQIlSVLv9PGPf5y/\n/OUvTJo0qe2m/+STT6agYE9TMklS77Et4IwxJi3p7KtBwBxgDrDzP37bN+KtGOOond5zMHAdcBZQ\nAqwB/gzMjTHuaWnB/a3PIECSJPValZWVDBgwgLS0tGSXIkndziBAu2UQIEmSUlmMkX/84x/Mnz+f\nBQsWcPrpp/P1r3892WVJUo+QCkGAMWwKCyG0bc4PIEmSkuntt9/mtttu4yMf+QhDhw7l2GOP5ctf\n/jL33HMP99xzT7LLk6SUVlpa2nZvlwrsEZCC7BEgSZKSbdOmTSxcuJAFCxYwf/58Xn/99R2ODx8+\nnOnTpzN9+nTOPPNMDjnkkCRVKkk9Syr0CHDVAEmSJO1gzZo1HHzwwTt8KFFQUMAZZ5zRdvM/duzY\nlPlkS5LUMfYISEH2CJAkScl2zDHHMGTIEKZPn86MGTM48cQTycjwMyRJOlCp0CPAICAFGQRIkqRk\nSyQSzuovSV0gFYIAf7tLkiT1Uk1NTfz973/n6quv5sknn+zQew0BJKn38jd8CnPVAEmS1FFvvfUW\nP//5z/nABz7AwIEDmTJlCjfccAN33nlnskuTpD7LVQO0Tw4NkCRJ7VVbW8vixYuZN28e999/Py+/\n/PIOx8eMGcPs2bP513/9VyZPnpykKiVJ26TC0ABnfJEkSeqBXnrpJS6//HKWLFlCQ0ND2/78/Hym\nT5/O7NmzmT17NoceemjyipQkpSR7BKQgewRIkqR9Wbt2LcOHDwdgwoQJbTf+kyZNIjMzM8nVSZL2\nJBV6BBgEpCCDAEmS1B533303kyZNYtCgQckuRZLUTgYB2i2DAEmS+p533nmHkpISsrOzk12KJKkL\npUIQ4KoBKcxVAyRJ6r3q6+t58MEH+epXv8r48eM5+OCDWbhwYbLLkiR1AVcN0D7ZI0CSpN4nxsiK\nFSuYN28e8+bNY/HixdTV1bUd79+/PzfddBOf+cxnklilJKmrpUKPAFcNkCRJ6iKVlZU8+OCDbTf/\nq1at2uH48ccf3zbJ3+TJk8nKykpSpZKkvsQgQJIkqYvcf//9nH/++W2vBw0axKxZs5g9ezYzZ85k\n6NChSaxOktRXOTQgBTk0QJKk3mHz5s2cd955bTf/J5xwAmlpTtEkSX1ZKgwNMAhIQQYBkiRJktQ7\npUIQYCQtSZK0F01NTTz88MPMnTuXKVOmUF5enuySJEk6IM4RIEmStJ0YI//4xz9YsGAB8+fPZ/Hi\nxVRXV7cdX7RoEe9///uTWKEkSQfGICCFbb/G5Jw5cygtLU1eMZIk9WIrV65su/FfsGAB69ev3+H4\nUUcdxfTp05kxYwZnnHFGkqqUJPVUpaWlzJ07N9lltHGOgBTkHAGSJHWfuXPn7hK2Dx8+vO3Gf/r0\n6Rx00EHJKU6S1OukwhwB9giQJEl92gknnEB+fj7Tpk1jxowZzJgxg7Fjx+7QM0+SpN7EHgEpyB4B\nkiR1n6amJkIIZGT4+YgkqWvVVybIKUwH7BEgSZJ0QFauXMmiRYtYtGgRGzZs4G9/+1u735uZmdmF\nlUmS1KqxNsGdX9iY7DIAgwBJktTDNDc38/zzz/PII4+wdOlSHnnkEVatWrXDOZs2bWLgwIFJqlCS\npB01N0T+/MVNrHmuMdmlAAYBkiSpB1iwYAFLlizhkUce4bHHHtthOT+AgoICpkyZwrRp05g2bRpF\nRUVJqlSSpB011ia467JNrFzWQG5JWrLLAZwjICU5R4AkSTs66aSTePLJJ9tejxo1ismTJ7dt48aN\nIy0tNf64kiRpm7qKFu78/CbWvtBIbnEaH7p1EEPG9gOSO0eAQUAKMgiQJGlHP/zhD3nrrbfabvyH\nDh2a7JIkSdqrqrXN3PHZjWx+o5mCg9L50C8GUTQyMyWWDzQISEHbgoDtzZkzZ5c1jiVJ6knq6up4\n5plnePzxxznhhBOYOnVqskuSJKlLrHm+gT9fuonazQkGHpHJq6N/yrdv/OYO5xgEaAf2CJAk9XS1\ntbU8//zzPP30023bCy+8QHNzMwCf//zn+elPf5rkKiVJ6nwv/a2G+68to6URRkzsx/tuKiGnIL3t\neCr0CHCyQEmSdMBWrlzJHXfcwdNPP80zzzzDihUrSCQSO5yTlpbG+PHjmThxIrNmzUpSpZIkdY2W\npsiSmyt58tdbADjuX/sz/aoi0jOTdr+/R/YISEH2CJAk9TQLFy7kzDPPbHudnp7O0UcfzQknnNC2\nnXjiieTl5SWxSkmSusaWdc389aubWfNsIyEdzvx6ISd8OK/t0//tpUKPAIOAFGQQIElKtsrKSgoK\nCtp9fkVFBVdddVXbDf8xxxxDdnZ2F1YoSVJqePOReu65cjN15QnyhqRzzvdKOPjEfns83yBAu2UQ\nIEnqLps2bWLFihUsX76cF198kRdeeIF//OMftLS0sHHjxt1+kiFJkiDREln6syoe/XkVRDh0cjbv\n+XYxucXpe31fKgQBzhEgSVIfEGPkb3/7GytWrGjbXn75ZTZv3rzb8wcMGEB5eTnFxcXdXKkkSamv\nelML91y5mZXLGghpMPnf85n06XxCWs8I0O0RkILsESBJ6gpDhw5l/fr1O+zLy8tj7NixjBkzhqOP\nPprx48czfvx4RowYYW8ASZJ24/XFddx/TRm1ZQlyi9N47/dKGDmx/cPh7BEgSZLarbGxkbfeeovX\nXnuN119/nfPPP59Bgwa1+/0XXHABDQ0NjB07tm0bNmyYN/ySJLVDU32Cxd+v5JnfVwMwYlI/3vOt\nEvIG730oQCqyR0AKskeAJPVNdXV1rFy5krfffnu32+rVq3dYkm/+/PlMnz49iRVLktQ3bHylkb99\nbTObXmsmLQNO/2IBJ31iwH4NBbBHgCRJavPBD36Qe++9d4/H09LSGDlyJIcffjijR4+mpKSkG6uT\nJKnviTHy9O3VLL6pgpZGKDo0g3O+W8KQcVnJLu2AGARIknQAEokEGzduZM2aNbzzzjusWbOm7fnH\nPvYxpk6d2u62jjjiCEaNGsXIkSMZMWIEI0eO3GEbMWIEWVk9+w8PSZJ6ii3rm7n/mnLeWloPwLEf\n7M8ZXyskKzctyZUdOIcGpKBtQwO2N2fOHEpLS5NQjSRpmzvuuIO//vWvbNiwgY0bN7JhwwbWrVtH\nc3Pzbs+/8cYb+cpXvtLNVUqSpAO1/N5a5l9fTn1VguyCNGaXFnHkzNz9bq+0tJS5c+fusC+ZQwMM\nAlKQcwRIUuepq6tj8+bNlJWV7bJNnDixQ5/YX3PNNVx//fW77C8pKWH48OEcdNBBDB8+vO35aaed\nxjHHHNOZ/xxJktSF6ipbmH99BSvuqwVg1OnZzL6umLxBnTchoHMESJLUif73f/+Xn/3sZzvc7NfX\n1+/x/CuvvLJDQcC5557LqFGjGDx4cNs2ZMgQsrPbv2SQJElKTW8+Usf915RTvaGFzJzAGV8r5NgP\n9u+Vq+sYBEiSus1LL73Eww8/TE1NTdu2ZcsWqqqqqKyspLKycofnn/rUp/jOd77T7vY3bNjAkiVL\ndtiXlZVFSUkJJSUlFBcX77BNmTKlQ/W/613v4l3veleH3iNJklJbU12CxTf9c1nA4cdl8e5vF1M0\nIjPJlXUdgwBJ6sVijB1KsV988UUWLFhAfX09dXV11NXV7fF5XV0d55xzDldeeWW721+0aBGXXHJJ\nu8/fvHlzu8+F1k/sx48fT3FxcduNf05OTq9M8iVJ0oFb+0ID91xVRvlbrcsCTv5CASd/cgBpGb37\nbweDAEnajUQi0TYBXEdmaV+3bh3Lly+nubmZpqYmmpubd9m23z9mzBhmzJjR7vbvu+8+brzxRhob\nG2loaKCxsXGX59u//sQnPsF//dd/tbv9Rx99lMsuu6zd5x955JHtPhfgmGOO4eKLL6Z///7k5eW1\nPRYUFLRt+fn5OzzviBEjRjBixIgOvUeSJPU9LU2RR39exbJbq4gtUHJ4Bu/5TglDjuobq/MYBKSw\nV155ZYcJA/f0vKCggOHDh7e73fLyclatWrXbtnb3uqioiJEjR7a7/U2bNvHmm2/utebtnw8cOJDR\no0e3u/3169fzyiuvtLv9IUOGcNRRR7W7/TVr1vDiiy+2u/3hw4dz7LHHtrv9VatW8eyzz+62zUQi\nQYyxbUskEowcOZKJEye2u/1XXnmFhQsX7tLO9q+33z9u3DjOPvvsdrf/zDPPcOedd7a7/ZNOOomP\nfvSj7W5/8eLF/PjHPyaRSNDS0rLPx7POOourr7663e3/8Y9/5Itf/GLb+3fXZnNzc9v35sILL+RX\nv/pVu9u///77ueiii9p9/oUXXtihIGDDhg089NBD7T6/sbGx3edC6436pZdeSnZ2Njk5OeTk5Ozx\neU5OTod+9wBMmTKlw93xJUmSOtPmN5q496rNrHuxCQJMuDCP079YSEa/3t0LYHsGASlszJgx7Trv\nggsu4De/+U2727377ru58MIL231+R9u/9957u7T9efPmdWn78+fP79L2Fy5c2OH2OxIELFu2jM99\n7nMdar8jQcALL7zADTfc0KH2OxIEvP3229xxxx3tPv+www5r97kADQ0NrF+/vl3nZmZmdrhL+fDh\nw5k2bRoZGRltW2Zm5g6vt9/fke8twMyZM5k/fz5ZWVltW79+/fb4OiOjY7/mJ02axKRJkzr0HkmS\npJ4gJiJP/66aJT+opLkhkj8snbNvKGbEyX1v0l+DgBR2xBFHAOxwI7K758OGDetQu0VFRYwfP36H\nfTvf7Gz/+pBDDulQ+yUlJUyYMGG3be3u+eGHH96h9gcPHsxpp53W7vbHjh3bofaHDRu2wye0+2p/\n56/lvhx88MG8973v3W2baWlphBAIIbQ9P+mkkzrU/pFHHsmnP/3pXdrZedu2v6MTnx1//PFcd911\n7W6/I70xoPUT4z/84Q+kp6eTlpa2z8chQ4Z0qP3zzjuPGTNm7LXdjIyMtvo7atasWcyaNavD72uv\nbUvTSZIkqf2q1jZz3zVlrFzWAMDR/5LL9CuL6DcgLcmVJUdwrfrUE0KIsGsXfUmSJElS+8UYWX5P\nLfNvKKdhSySnKI1Z1xZx5MzcpNW07cOmGGPSxiLYI0CSJEmS1OvUVbTw4DfLeXleHQCHT81m1txi\n8gamJ7my5DMIkCRJkiT1Km8sqeP+OWXUbEyQmRM48+uFjD+vv0sKb2UQIEmSJEnqFRqqEyz6XgXP\n31kDwEEnZHH2DSUUjfDWd3t+NSRJkiRJPd7Kx+u57+oyqta0kJ4Jp11awIQLB5CWbi+AnRkESJIk\nSZJ6rKa6BEturuTp26sBGDIuk3d/q4SBozOTXFnqMgiQJEmSJPVI7zzbwH3fKKP87WbSMmDSZ/KZ\n9Ol80jPtBbA3fXPRxB5i+zXZS0tLk12OJEmSJKWE5sbIkh9U8PuPb6D87WYGjs7go7cPYfIXClIy\nBCgtLW27t0sFwbXqU08IIULrmpeSJEmSpH9av7yRe/+jjE2vNkGAky8awORLCsjolxo32fuyLQyI\nMSatYIcGSJIkSZJSXktT5LHbqnj0lioSzVA4IoN331DMQSf0S3ZpPY5BgCRJkiQppW16vYn7/mMz\n615sAuCEj+Qx5fICsnId7b4/DAIkSZIkSSkp0RJ56rdb+PsPK2lphPxh6Zz1zWJGTspOdmk9mkGA\nJEmSJCnllK9s5r6rN/PO040AjH9/f874WiH9BtgL4EAZBEiSJEmSUkaMkWf/UMPi71fQVBfpPzCN\n2aXFHD4tJ9ml9RoGAZIkSZKklFC1tpn7ry3j7UcbABh7di4zvlFITmF6kivrXQwCJEmSJElJFWPk\nxb/WsuDb5TRWR3IK05h5TRFjZucmu7ReySBAkiRJkpQ01ZtaeHBuGa8trAdg9BnZzJpTTP+B9gLo\nKgYBkiRJkqSkeHleLQ9+s5y6igRZeYHpVxVx9PtyCSEku7RezSBAkiRJktSt6ipamH9DBSvuqwVg\n5Cn9OOu6YvKHeYvaHfwqS5IkSZK6zeuL65g3p4yaTQkycwJTv1K14unEAAAgAElEQVTI8f/W314A\n3cggQJIkSZLU5Rq2JFj43Qpe+HMNAAedmMXZ15dQNMLb0u7mV1ySJEmS1KXefKSeedeWsWV9C+lZ\ncPplhbzrY3mkpdsLIBkMAiRJkiRJXaKhOsGiGyt4/o7WXgBDj8ni7BuKGXh4ZpIr69sMArpICGEK\n8FXgRGA4cFGM8dfJrUqSJEmSusdbj7b2Aqha20J6Jky+pICTPjGAtAx7ASSbQUDX6Q88D/wa+A0Q\nk1uOJEmSJHW9xprWXgDP/am1F8CQcZm8+1slDBxtL4BUEWL0/rSrhRC2AJfEGH/TzvMjgN8bSZIk\nST3J28vquf/aMqrWtJCWAZO/UMDJn7QXwPa2rY4QY0zaF8UeAZIkSZKkA9JYm2Dx9yt49g//7AVw\n9vXFDDoyK8mVaXcMAiRJkiRJ+23l4/Xcf00Zle+09gI49fP5nPzJfNIz7QWQqgwCDlAI4aPALdvt\nOivG+Eiy6pEkSZKk7tBYm2DJzZU887tqAAaPzeTsG4oZPMZeAKmuTwQBIYQPAlOB44HjgDzg9hjj\nBXt5z8HAdcBZQDGwFrgLmBtjrNju1L8Aj273ek3nVi9JkiRJqWXVE/Xcd00ZlatbewFM+kw+kz5t\nL4Ceok8EAcDVwLHAFmA1MJa9zOIfQjgcWAoMovXmfwUwEbgMOCuEMDnGWAYQY6wGqru0ekmSJElK\nAY21Cf7+n5U8fXvrLdCgIzM5+1vFDBlrL4CepK8EAZcDq2KMr4cQpgIL93H+T2kNAS6NMf5k284Q\nwveBLwE3AJ/fWwMhhP7AEVtfpgEjQwjHA5tjjKv2758hSZIkScmx+qkG7ru6jIpVzYR0mPTpfE75\nrL0AeqI+t3xgCGEa8BDwPzHGj+/m+OHAq8CbMcbDdzqWB6yjtTfBkBhjbTuuw9bzt/3X8asY4yf3\nUaPLB0qSJElKCU11Cf7+w0qe+p9qiDDwiEzefUMxQ8bZC2B/uHxgajpj6+MDOx+IMVaHEB4BZgKT\n+OeN/i5ijIto7QkgSZIkST3S6qcbuP+aMsrf3toL4FP5nPI5ewH0dAYBuxqz9fGVPRx/ldYg4Aj2\nEgRIkiRJUk/VVJ/g4R9V8uRvtvYCGJ3B2deXMPQYewH0BgYBuyrY+li5h+Pb9hd2Qy2SJEmS1K3e\nebZ1LoDyt5oJaXDyxQM49QsFZGTZC6C3sOt6Cgsh7HErLS1NdnmSJEmSepGm+gSLbqzg9x/fQPlb\nzZSMyuCjtw9myuWFhgAdVFpausd7uVRgj4BdbfvEv2APx7ftr+jqQpwsUJIkSVJ3WPN8A/d9o4yy\nN//ZC2DyFwrI6JcaN649TWlp6R4/vE2FMMAgYFcrtj6O2cPxbUsC7mkOAUmSJEnqEZobIo/8tJIn\nfrmFmIDiwzI4+4Zihh/bL9mlqQsZBOxq4dbHmSGEELf7WD6EMACYDNQAy5JRnCRJkiR1hneebV0R\noOzNZghw0kUDmHxJPpnZjiDv7fwO7yTG+AatSwceBlyy0+G5QC7w2xhjXVfX4pwAkiRJkjpbU12C\nhd8r53cXbKDszWaKD8vgI78dzLSvFBoCdJHt5wxIBaEvjEMPIZwLnLv15VBgFvAG8PDWfRtjjFds\nd/4oYCkwGPgLrcMFJgLTgJeBU2OM5V1YbwTnCJAkSZLUuVY9Wc/915ZTsbJ1LoCTLnIugO62LQyI\nMSbti95XgoA5wBxg53/sti/8WzHGUTu952DgOuAsoARYA/wZmBtj3NPSgp1Vr0GAJEmSpE7TWJtg\nyc2VPPO7agAGjs7grG8WM2y8cwF0N4MA7ZZBgCRJkqTO8vZj9cybU0bl6hZCOkz6VD6TPpvvkoBJ\nkgpBgJMFSpIkSVIv1FCdYPH3K3juTzUADBqTydnXFzPkqKwkV6ZkcyaIFOZkgZIkSZL2x5uP1PHL\nc9fx3J9qSMuAyf+ezwX/O8QQIEmcLFD75NAASZIkSfujvirBou9V8MKfW3sBDBnX2gtg0JEGAKnC\noQGSJEmSpE7x+uI6HriunOr1LaRnwuRLCjjpEwNIy0iNT6GVOgwCJEmSJKkHq6ts4aHvVPDS3bUA\nDDsui7OvK6bk8MwkV6ZUZRAgSZIkST3UqwtqefCb5dRsSpDRL3Dapfm864IBpKXbC0B75mSBKczJ\nAiVJkiTtTm15C3dfsZm7LttMzaYEB52YxYV3DuGkT+QbAqQgJwvUPjlZoCRJkqQ9eXleLfNvKKe2\nLEFmTmDK5QWc8OE8Qlpq3GRq75wsUJIkSZLULjWbWph/QzmvPFgHwIiT+zF7bjGFh3hbp47xJ0aS\nJEmSUliMkeX31LLg2xXUVybIzA1M+0ohx32ov70AtF8MAiRJkiQpRVVvaOGB68p4fVE9ACNPae0F\nUDDcWzntP396JEmSJCnFxBh58S+1PPTdchqqIll5gTOuKGT8B/qnzIRz6rlcNSCFuWqAJEmS1PdU\nrW3mzi9s4r6ry2ioiow6PZtP3jWUY8/LMwTooVw1QPvkqgGSJElS3xMTkWf/WM3imyppqo30yw+c\n+fUijn5fbsrcQOrAuWqAJEmSJImyt5qYN6ec1U81AHDEjBxmXF1E3sD0JFem3sggQJIkSZKSJNEc\neeI3W1j6kyqaGyK5JWnMuLqIMTNzk12aejGDAEmSJElKgg0rGrn/2jLWv9QEwNH/kssZXyskp8Be\nAOpaBgGSJEmS1I2aGyPLfl7FY7dVkWiG/GHpzCot4rDJOckuTX2EQYAkSZIkdZM1zzVw/zVlbH6j\nGYATPpLHlMsKyOrvgm7qPgYBkiRJktTFGmsTPPyjSp76n2qIUHRoBmddV8zBJ/ZLdmnqg4ydUti2\ndSZDCJSWlia7HEmSJEn74e1l9fzqA+t46rfVhDSYePEAPnHnUEOAPqS0tLTt3i4VBNeqTz0hhAjg\n90aSJEnqueqrEiy6sYIX/q8GgMFjMznrumKGjMtKcmVKpm1hQIwxaamAQwMkSZIkqZO9+lAdD36z\njJqNCdIz4dTPF3DSRQNIz0yNT4TVtxkESJIkSVInqdncwkPfLmfF/XUADD8ui7OuK6bk8MwkVyb9\nk0GAJEmSJB2gGCPL76nloe9UUFeRIDMnMOXyAo4/P4+0dHsBKLUYBEiSJEnSAaha28yD3yznjSX1\nAIyc1I/Zc4spOMjbLaUmfzIlSZIkaT/EROS5P9Ww+KYKGmsi/fIDZ1xRyDHn9k+Z2eGl3TEIkCRJ\nkqQOKn+7iXlzyln1ZAMAR0zPYcbVReQNSk9yZdK+GQRIkiRJUjslmiNP/nYLj/y4iuaGSG5xGjO+\nUcSRs3LsBaAeIy3ZBWjPQghtW2lpabLLkSRJkvq0ja80cvtH17P4+5U0N0SOfl8un/zrUMbMzjUE\n0F6Vlpa23dulghBjTHYN2kkIIULrzKOSJEmSkqu5IfLoz6t4/L+rSDTDgKHpzJpTxKjTc5Jdmnqg\nbWFAjDFpqYBDAyRJkiRpD1Y/1cC80jLK3myGAMefn8fULxWQ1d/O1eq5DAIkSZIkaScNWxIs/kEF\nz/2xBoCSURnMKi3m4BP7Jbky6cAZBEiSJEnSdl59qI7515dTvaGFtAyY+Kl8Jn0mn4ys1BjfLR0o\ngwBJkiRJAqo3tbDgW+W88kAdAMOOy2J2aRGDjshKcmVS5zIIkCRJktSnxRh54f9qWPT9ChqqIpk5\ngSmXF3D8+XmkpdsLQL2PQYAkSZKkPqt8ZRMPlJaz8vEGAEadns3Ma4vIH+atknovf7olSZIk9TmJ\n5sgTv97C0p9W0dwQySlKY/pVhYw9Ozdl1nqXuopBgCRJkqQ+Zf1Ljdw/p4wNy5sAOPp9uUy7opDc\novQkVyZ1D4MASZIkSX1CU12CR35SxZO/2UJMQMFB6cy8tpjDJmcnuzSpWxkESJIkSer13l5Wz7zS\nMipXtxDSYMKFeUy+pICs3LRklyZ1O3/qU1gIoW0rLS1NdjmSJElSj1NX2cJ9V5fxx09tpHJ1C4OO\nzOSjtw/mjCuKDAHUbUpLS9vu7VJBiDEmuwbtJIQQoXUZE0mSJEkdF2Pk5Xl1LPhWObVlCdKz4NTP\nFXDSRQNIz0yNmzH1TdvCgBhj0n4QHRogSZIkqVfZsq6ZB68v5/VF9QAcPKEfs+cUUXxYZpIrk1KD\nQYAkSZKkXiEmIs/+sZolP6iksSaSlReY9pVCjj2vPyHNXgDSNgYBkiRJknq8za83Ma+0jHeeaQTg\niOk5zPhGEXmDXRJQ2lmXBwEhhOOB2cBxwGFAIRCACuAN4CngwRjj811diyRJkqTepaUp8th/VbHs\nF1W0NEH/gWnM+EYRR87MTXZpUsrqkskCQwjpwIXA14FBwMPAK0A5sJnW1QqKt27jgFOBlcD3gV/F\nPj5LnpMFSpIkSfu2+ukGHryujE2vNQNw7Af7M/XLhWTnuxqAUlcqTBbY6UFACGEM8BvgJeBHwLMx\nxsQ+3pMBnAx8idZeAx+JMb7SqYX1IAYBkiRJ0p7VVyVYcnMFz/2xBoCikRnMmlPEiJOzk1yZtG+9\nLggIIUwCrga+EGNcuZ9tjAF+DPxHjPGJTiuuBzEIkCRJknYVY+SVB+tY8O1yajYmSMuAiRfnM+kz\n+WT0czJA9QypEAR02hwBW4cDzATOjTE27287McaXQwjnAP8B9MkgQJIkSdKOqtY2M//6cl5f3Lok\n4PDjs5hdWszA0S4JKHVUl8wRoANjjwBJkiSpVaIl8szvqvn7DytpqmtdEnDqlwo57kMuCaieqVf1\nCNibEEImrasFpANbYow13XFdSZIkST3X+uWNPFBaxroXmwA4clYO0690SUDpQHVJELD1xv9i4EPA\nu4D87Q7HEEIF8CxwB3DrgQwlkCRJktS7NNYmWPqzKp78zRZiCwwYms6Mq4sYPS0n2aVJvUJXrBow\nGFgAjAFWAGuBmq1bJtB/6zYaOBh4ETgrxvhOpxbSgzk0QJIkSX3Vmw/X8eA3y6l8p4WQBid+JI/T\nLi0gq79LAqp3SIWhAV0RBPya1gDglhhj+T7OPRy4FDg4xvjBTi2kBzMIkCRJUl9Ts6mFhd+tYPm9\ntQAMGpPJ7NIiho3vl+TKpM6VCkFAVwwN2BRj/HZ7Towxvg5cHkK4tQvqkCRJkpTiYoy88H81LP5+\nJfVVCTKyA5MvyWfCBQNIy3AyQKkrdEX/mv35r3VLp1fRC4QQ2rbS0tJklyNJkiR1qrI3m/jDRRuZ\nN6ec+qoEh07O5qK7hnLyRfmGAOpVSktL2+7tUkFXDA24E7gT+N8YY6Id538MOD/G+N5OLaQHc2iA\nJEmSerPmxsjjt1Wx7BdVtDRBbnEaZ15ZyNizc1PmRknqKqkwNKArgoAxtE4WmAE8BqwEqoBGYNvF\nioARwERaJw6cFmN8rlML6cEMAiRJktRbrX6qgXmlZZS92bpw2PgP9GfqVwrIKXBJQPUNvTIIAAgh\nFABfo3X5wNG7OSUCzwD3AD+LMa7r9CJ6MIMASZIk9Tb1lQkW31zB83+qAaDo0AxmzynikJOyk1yZ\n1L16bRCwwwVCGACMBPKBFmAjsD7GWNOlF+7BDAIkSZLUW8QYeXleHQu+XU7t5gRpGTDxU/lM+nQ+\nGf0cBqC+p08EAeo4gwBJkiT1BpVrmpl/fTlvLKkH4KATs5g1p5iBh2cmuTIpeVIhCOi05QNDCOnA\nBTHGX3VCWwG4NMb4wwMuTJIkSVK3SjRHnv5dNQ//qJKmuki/AYGpXy7k2PP6E9LsBSAlW6cFATHG\nlhBCVQjhZuDKGGP9/rQTQigCbgV+3lm1SZIkSeoea19o4IHrytmwvAmAMbNzOPPKIvIGORmglCo6\nLQgAiDH+XwhhM7A4hHA78NsYY3l73htCGA5cBpwNXBxjfKIza5MkSZLUdRq2JPj7jyp55vfVECF/\nWDozri7i8Kk5yS5N0k46NQgAiDEuDiHMBP4DeC2E8CawFHgBqNi6pQHFQAkwDpgCDAV+DEyKMdZ2\ndl2SJEmSOl+MkVceqGPBd8qp2ZggpMOEjw/g1M/nk5WbluzyJO1Gl04WGELoD7wHmAkcDxwKFNC6\nfGAF8CbwMHA/8PcYY0OXFdODOFmgJEmSeoKK1c3Mv6GcN//eOip42HFZzLq2iMFjspJcmZS6UmGy\nQFcNSEEGAZIkSUplLU2RJ3+9haW3VNFcH+mXH5hyeSHHfdDJAKV9SYUgoNOHBkiSJEnqvVY/3cCD\n15Wx6bVmAI56Ty5nXFFI/4FOBij1FAYBkiRJkvaprrKFxd+v5IX/qwGgcEQGM68u4tBTs5NcmaSO\nMgiQJEmStEcxRl78ay2LbqygrjxBWgZM/FQ+kz6dT0Y/hwFIPZFBgCRJkqTdKnuziQe/Wc7Kx1vn\n9D7kpH7MvKaIklGZSa5M0oEwCJAkSZK0g+aGyLJbq3j8tipamiCnKI1pXy3k6Pfltk10Jqnn6pIg\nIIRQBGQBG2OMia64RqoLIVwFfAA4EmgAlgFXxRhfTGphkiRJ0l68vayeB79ZTvnbrZMBjn9/f6Z+\npYCcQicDlHqLTls+MITwQeDjwCigEagFioA6YAnw0xjja51ysR4ghHA/8HvgCSANuA44BRgXYyzf\nx3tdPlCSJEndqmZTCwu/V8Hye2oBKBmVwaw5xRz8rn5JrkzqXVJh+cADDgJCCIcB1wOLgHtijGt2\nOp4OnAj8G1ATY5xzQBfsoUII/YFK4F9ijPfs41yDAEmSJHWLmIg8f2cNi39QQUNVJKNf4JTP5XPS\nJwaQnukwAKmzpUIQcEBDA0III2i9wf94jLFld+ds3f8E8EQIYVQI4csxxpsO5Lo9VD6tPQP22htA\nkiRJ6i4bX2nkgevKWfNsIwCHnZbNjG8UUXiIU4lJvdkB9QgIIeTEGOs6+J7sGGP9fl+0hwoh/BE4\nHJgQ9/FFt0eAJEmSulJjbYJHb6niyd9sIdEM/QemceaVRYyZneNkgFIX6/E9ArYPAUIIw4FTgVdj\njM9t3TcSGAb8I8ZYvfU9vSoECCF8FLhlu11nxRgf2emcm2j92py2rxBAkiRJ6ioxRl5bWM9D3y6n\nam0LBDjhw3mc/sUC+g1IS3Z5krpJp0wWGEKYAtwH5Gzd9f0Y4xUhhH7Au4E7YoxJm2Z060SGU4Hj\ngeOAPOD2GOMFe3nPwbRO8HcWUAysBe4C5sYYK7Y7Lw8YvN1b12wfdoQQfgD8K3BGjPGVdtZrjwBJ\nkiR1qorVzTz07XJeX9z6p+rgozKZdW0Rw8Y7GaDUnVKhR0BnBQEPAL8AHgAOBq4C3okxXhlCGErr\nzXHSIsYQwrPAscAW4B1gLPA/McaP7+H8w4GlwCBab/5XABOBM4CXgckxxrJ2XPc/gQ/RGgK83IF6\nDQIkSZLUKZobI0/+aguP/qKK5vpIVl7g9C8WcPy/5ZGW7jAAqbulQhDQWbOALI0x3rH1+UvABSGE\ni0MIFwH3dtI1DsTlwKoY4+shhKnAwn2c/1NaQ4BLY4w/2bYzhPB94EvADcDn99ZACOEnwMeAc4HK\nrYEIwJYYY83+/TMkSZKk9nt7WT3zbyin7M1mAI56Ty7TvlpI3qCkddaVlAI6q0fAl2OMN4UQRsUY\n39hu/3uAIcB/JbNHwPZCCNOAh9hDj4CtvQFeBd6MMR6+07E8YB0QgSExxtq9XCex9bydU57SGON1\n+6jRHgGSJEnab9UbW1j0vQqW39v652rxYRnMuLqIkROzk1yZpN7UI+CREMK3ga+HEE6NMS4DiDHe\ns/UT+OpOuk53OGPr4wM7H4gxVocQHgFmApNoDRR2K1WCD0mSJPUdiebIs3+o5u8/qqSxOpKRHTjl\ns/lMuHAAGVkOA5DUqlOCgBjjYyGEF4Dfxxif3+nY4hDC8Z1xnW4yZuvjnib2e5XWIOAI9hIESJIk\nSd1pzfMNPPjNcjYsbwLg8KnZnHlVEYUHd9Znf5J6iwP61DqEcEQI4QiAGGPtziHANjsNF3jvgVyz\nGxRsfazcw/Ft+wu7upAQwh630tLSrr68JEmSeoC6yhbmzS3j9o9uYMPyJvKHpfP+Hw3kAz8ZZAgg\nJUlpaeke7+VSwQH9ZogxvhpC+EIIYSLwuxhjYk/nbp0s71LgDwdyzb7EOQIkSZK0JzERefGvtSz6\nfgV15QnSMuCkCwcw6bP5ZOU6SlVKptLS0j1+eJsKYcABR4Qxxp+GEGYAd4UQ3gGeADYA9UARMAKY\nTOske9fFGNcd6DW72LZP/Av2cHzb/opuqEWSJEnaxcZXGnnw+nLeeboRgENO6seMq4sYeHhmkiuT\n1BN01hwB84H5IYTxwHRgHJAHbASWAxfHGMs741rdYMXWxzF7OH7E1sc9zSEgSZIkdYnG2gRLf1rF\nk7/dQmyB3OI0zvhaIUe9JzclPmWU1DN0ap+hGOMLMcabY4xfjTF+LsZ4TYzxd8C/hhD+JYRQ3JnX\n6yILtz7ODDv9Ng0hDKC1d0MNsKyrC3FOAEmSJEHrkNGXH6zltnPW8cSvthATcMKH87j4b8MY997+\nhgBSitt+zoBUELpjHHoI4U7gfbQGDy8BS7Zui7t7qEAIYRqts/3/T4zx43s4535gFvDFGOOPt9t/\nE3A5cEuM8QtdWGME5wiQJEkSlK9sYsG3Knjz4XoAhh6dycxrixl6dFaSK5O0P7aFATHGpKUC3RUE\nfBYoBp4BTgOmAhOAfsBr/DMYeKArgoEQwrnAuVtfDqX1Jv8N4OGt+zbGGK/Y7vxRwFJgMPAXWocL\nTASmAS8Dp3blUAeDAEmSJDXVJVh26xae+GUVLU3QLz8w5bJCjv1gf9LSU+NTRUkd15eCgB/EGL+0\n075sWgOBnwGbgWOBAFwRY/zPTr7+HGAOsPM/dtsX/q0Y46id3nMwcB1wFlACrAH+DMyNMe5pacHO\nqtcgQJIkqY+KMfLq/DoWfreCqrUtABxzbi5TLi+k/8D0JFcn6UD1pSDgf2KMH9vDsZHAJ4DvAu8B\nvgNcEmOc1+WFpSiDAEmSpL6p7K3WYQBvLW0dBjB4bCYzvlHEQSf0S3JlkjpLKgQB3bXA6GshhN+H\nEPJ2PhBjfBvIjTHWxRjvAE4HLu6mulKakwVKkiT1DY21CZbcXMEvz13HW0vr6ZcfmHF1IRf8YYgh\ngNQL9NXJArOAB4CxwO+A+4DHYoxVIYRBwH/HGM/Z7vzvbT9mv6+xR4AkSVLfEGPklQdbhwFsWdc6\nDGD8+/sz5UsF5BY7DEDqjVKhR0BGd1wkxtgYQjgb+H/ApbTOvE8IYQuQC3x+27khhBygqTvqkiRJ\nkpJl8xtNLPhWOW8vawBgyLjWYQDDj7MHgKSu1S09Ana4YAiHAOfR2jugAvhTjPGprcfeB/wJeDDG\n+N5uLSyF2CNAkiSp92qsTfDoLVU8+ZstJJohOz+N0y8rcDUAqY9IhR4B3R4E7M3WYQI/Au6KMf5v\nsutJFoMASZKk3ifGyMvz6lj4vQqq17dAgGPP68/plxWQW+QwAKmvMAjQbhkESJIk9S6bX29i/rfK\nWflY6zCAoUdnMuPqIoaNdxiA1NekQhDQXasGaD+4aoAkSVLP1liTYNGNFfzqvHWsfKyB7II0Zs0p\n4qO/G2IIIPUhfXLVAHWMPQIkSZJ6thgjK+6rZdGNlVRvaB0GcNyH+nP6FwvIKXQYgNSXpUKPgG5Z\nNUCSJEnqKza91sT8G8pZ9UTrMIBhx2Yx4z+KGHpMVpIrk6RWBgGSJElSJ6ivSrD0p5U8/ftqYgvk\nFKUx5fICxr+/PyEtNboDSxIYBEiSJEkHJNESeeHPNfz9PyupK08Q0uD48/M47dJ8cgocBiAp9RgE\nSJIkSftp9dMNLPh2ORuWNwFw8IR+TL+ykMFjHQYgKXW5akAKc9UASZKk1LRlfTN/+/pmfv/xDWxY\n3sSAoemcc2MJ5/9ykCGApF24aoD2yVUDJEmSUlNzQ+TJX29h2a1VNNVF0rPg5E/mM/HiAWTm+Bmb\npH1z1QBJkiSpB4gx8trCehZ+t5zK1S0AHDkzh2lfLaTgIP+kltSz+FtLkiRJ2ovNrzex4DvlvP1o\n63KAA0dncOZVRYycmJ3kyiRp/xgESJIkSbtRX5Vg6c8qeeb31SSaoV9+4LRLCjj+3/JIy0iNcb6S\ntD8MAiRJkqTtJFoi//hzDX//YSW1ZQkIcNyH+nPapQXkFrscoKSezyBAkiRJ2uqdZ1qXA1z/Uuty\ngAedmMX0q4oYcpQrAUjqPZzaNIW5fKAkSVL32LKumXuu3MzvLtjA+peayBuSznu/W8yHfz3YEEDS\nAXP5QO2TywdKkiR1j6a6BI//cguP//cWmutblwM86RP5TPzUALJy/cxMUudz+UBJkiQpCWIisvze\nWpb8oJIt6/+5HODULxdSeIh/Ikvq3fwtJ0mSpD7lnWcbWPjdCtY+3wjA4KMyOfPrhRwyweUAJfUN\nBgGSJEnqE6rWNrPkB5Usv7cWgP4D0zj9sgKOfl9/0tJTY9yuJHUHgwBJkiT1ao21CR7/7y088cst\nNDdsNw/AxQPI6u88AJL6HoMASZIk9UoxEXnx7lqW3FxBzcYEAGPPymHKlwopOMg/gyX1Xf4GlCRJ\nUq+z+ukGFv6/cta92ATA0GOyOONrhRx8Yr8kVyZJyWcQIEmSpF6j8p1mFt9Uwcvz6gDIG5zOlMsL\nGPfeXEKa8wBIEoCDolJYCKFtKy0tTXY5kiRJKau+KsHimyq47Zy1vDyvjozswCmfy+fivw3l6Pf1\nNwSQlFSlpaVt93apIMQYk12DdhJCiAB+byRJkvaupSny7B+qefSWKuoqWucBOOo9uUy5vID8YXZ+\nlZR6toUBMcakpQL+dpQkSVKPE2Pk1fl1LP5BJRUrmwE4eEI/zvhqIUOPyUpydZKU2gwCJEmS1KOs\neb6BRd+r4J1nGgEoPiyDqV8u5PBp2SnT7VaSUplBgCRJknqEilXNLLn5nxMB5hanceoXCjj2vP6k\nZxoASFJ7GQRIkiQppdVVtrDsF1U8fXs1iWbI6BeY8PE8TkfMYNUAACAASURBVL44n355zn0tSR1l\nECBJkqSU1NwYeeb31Sz7eRX1VQkIcPS/5HLavzsRoCQdCH+DSpIkKaXEGHl5Xh1Lbq6gcnULACMm\n9WPaVwoZcpQTAUrSgTIIkCRJUspY9UQ9i39QydrnWycCHDg6g6lfKeSw05wIUJI6i0GAJEmSkm7D\nikaW3FzJmw/XA9B/YBqn/XsBx5zbn7QMAwBJ6kwGAZIkSUqailXNPPzjSpbfWwsRsvoHTv7kAN51\nwQCycp0IUJK6gkGAJEmSul3N5hYe/XkVz/2xdSWA9Ew4/sN5TPp0PrlF6ckuT5J6NWPWFBZCaNtK\nS0uTXY4kSdIBa6hO8PCPK7n1rLU887tqEi1w9PtyufieYZz5tSJDAEm9Umlpadu9XSoIMcZk16Cd\nhBAitM6YK0mS1Bs0N0ae+0M1j/6iirryBACHT83m9MsKGHSkKwFI6ju2hQExxqSlAg4NkCRJUpdJ\ntESW31PLIz+ppPKd1qUAhx+fxdQvF3Lwif2SXJ0k9U0GAZIkSep0MUbeWFLPkpsr2fRqE9C6FODp\nlxVy+DSXApSkZDIIkCRJUqda9WQ9D/+oitVPNQAwYGg6p/17AePOySUt3QBAkpLNIECSJEmdYu0L\nDTz8oyreWloPQHZBGpM+k88J5+eR0c8AQJJShUGAJEmSDsiGFY088pNKXlvYGgBk9Q9MuHAAEy4Y\nQL8BLlIlSanGIECSJEn7ZfMbTTzyk0penlcHQGZO4MSP5HHSRQPIKXQZQElKVQYBkiRJ6pCKVc0s\nvaWSl+6uJSYgPROO/7c8Jn4qn/4DDQAkKdUZBEiSJKldtqxr5tGfV/HCn2tINENaBhx7Xn8mfSaf\n/GH+WSlJPYW/sSVJkrRX1RtaePy/q3j2j9W0NEJIg6Pfl8upny+g8BD/nJSknsbf3JIkSdqtLeub\nefy2LTx3R2sAADBmdg6Tv1BAyeGZyS1OkrTfDAIkSZK0gy3rmnnsti08f+c/A4AjZuRw6ufyGTw2\nK7nFSZIOmEGAJEmSAKha2xoAvHBnNS1NrfuOnJXDKZ/NZ/AYAwBJ6i0MAiRJkvq4qrXNLLu1ihf+\nr3USQELrEIBTPpfPoCMMACSptzEIkCRJ6qMq1zTz2K3/XAWAAGPPzuWUz+YzcLRzAEhSb2UQIEmS\n1MeUr2zi8du28I+//DMAOOrduUz6bD4DnQRQknq9tGQXoD0LIbRtpaWlyS5HkiT1cBtebuTuKzZz\n23vX8fydNcQEHPWeXD75l6G897slhgCS1EVKS0vb7u1SQYgxJrsG7SSEEAH83kiSpM7wzjMNLLu1\nijeW1AOQlgFHn9Ofky8eQPGh3vxLUnfaFgbEGJOWCjg0QJIkqReKMfLW0gYeu7WKVU82AJCRHTju\ng/2ZcOEA8of5Z6Ak9VX+H0CSJKkXiYnIqwvqWHZrFetfal0DsN+AwAkfHsC7PpZHbnF6kiuUJCWb\nQYAkSVIv0NIUWf7/27vzMKnKM///77t63+huQEAQQdAgaGw14gIqMEYFJ7gvcSfLZH6OyWSbZAzx\nGxpnYubKZJ3E0UnmFxc0OqP5ukfEDVyQiLgvoGERZYemoZveu+7vH6eqqO6uxm7o6qqu+ryuq65T\ndZ5znnOfU82hnvs85zl/buAv/72bmrVtABQPDnHCtWUce2kpBWUaGkpERAJKBIiIiIgMYM31Yd56\noJ4Vd9dTt7kdgEEjc5j8pTI+e0EJeYVKAIiISEdKBIiIiIgMQLs3tfHaPfW8+UA9LfXBAMNDxuVy\n4lcGMfGcYnLy0mNkahERST9KBIiIiIgMIFtWtvDqHXWsXNhAOLgDgNGTC5g8p4xxpxViISUARERk\n35QIEBEREUlz7s66l5pYfkcdHy0LngBgOXDkrGImX1vGiKPzUxyhiIgMJEoEiIiIiKSpthZn5Z8b\nWH5nHds/DJ4AkFdkHHNxCZ+7qozyUfopJyIivaf/PURERETSTENNO289sIfX7q1jz7YwAKXDcjj+\nylKqLi6lsFwDAIqIyP5TIkBEREQkTWx5r4XX/ljH+39uoL0lmDf0iDwmzynTAIAiItJnlAgQERER\nSaH2VufDpxt57Y91bHg90vo3GD+tkOOuKGPslALMlAAQEZG+o0SAiIiISArs2dHOWw/U88b/7KF+\nazsA+aXGZy8s4bgvllF5qH6miYhIcuh/GBEREZF+tPndFl67p46VTzTQHoz/x5BxuRx3RRlHnVtM\nfrHu/xcRkeRSIkBEREQkydqanQ+eauD1e+vZ+Obe7v+Hzwi6/485Wd3/RUSk/ygRkARmdj3wNWBs\nZNa7wL+6+59TFpSIiIj0u5p1rbx5/x7efXgPjbXB6P8FZcZnLyzluC+WUjFaP8VERKT/mbunOoaM\nY2bnAs3Ah0AImAN8H5js7m/2YH0H0HcjIiIy8LS3Oh8+08ib99ez/i/NsfnDJuZRdUkpk76g7v8i\nItks2gPM3VPWFUyJgH5iZjuAG9z99z1YVokAERGRAab2kzbeur+etx/cQ0NNcPU/t9CYOKuYqktL\nGHF0vrr/i4hIWiQC1B8tycwsB7gEKASeT3E4IiIi0ofamoOr/28/WM9Hy5ohksMfenguVZeWMukL\nJRQO0tV/ERFJL0oEJImZfRZ4GSgAGoFL3X1VaqMSERGRvrDl/RbefnAP7z/WQNPu4Op/Tj5MOKuY\nqktLGXWcrv6LiEj60q0BB8DMrgRui5s1091fipTlAaOBcoIeAd8AZrj7qz2oV7cGiIiIpJnG2nbe\nf7yBtx/cw9aVrbH5wyflcfQFJUw8p5ii8pwURigiIgNBOtwakPGJADO7GJgGHAtUAaXAPe5+9T7W\nOQS4CZgJDAY2AQ8B8929Nm65UmBY3Kob3b2pmzqfAj5x9y/1IGYlAkRERNJAuM1Z93IT7z68hw+f\naaQ90v4vHBRi0heKOfrCEoYfmZ/aIEVEZEBJh0RANtwacCNwDFAHfAIcSewOvq7MbDywFDiIoPG/\nEjgJ+CYw08ymunsNgLvXA/U9jCOH4AkCIiIiksbcnS3vtfLeo3t4/88NsYH/MBg7tZDPXlDC4TOK\nyC1Q138RERmYsiER8C3gY3dfbWbTgOc+Zfn/JEgCfMPdb4nONLOfA98Gfgxct68KzOzfgMcIEg9l\nwBUEvRJm7u9OiIiISHLt2tjG+4838N6je9ixpi02v3JsLkfNLuaoc0sYdHA2/HQSEZFMl/G3BsQz\ns+nAs8Dd7n5NgvLxwIfAWncf36msFNhM0JtguLs37GM7twMzgBHALuBN4N/d/akexqlbA0RERPpB\n0+4wHzzVwHuPNvDxq82x+cWDQxw5s5hJs4v12D8REelTujUg/cyITBd1LnD3ejN7CTgTOJkgoZBQ\nT8YBEBERkdRo2RPmr881svKJBta+1EQ4cvE/t8A4fEYhk2aXMHZKITl5avyLiEhmUiKgowmR6Qfd\nlH9IkAg4gn0kAkRERCS9tDSEWfN8EysXNrD2hSbamoNedxaCQ08qYNIXivnM54spKNNwPiIikvmU\nCOioPDLd1U15dH5FP8Syz26I8+bNo7q6uj/CEBERGZBam8Kse6mJlU80sHpJE62NkVvuDA75XAET\nZhbxmTOLKR2qR/6JiEjfqq6uZv78+akOo1tKBKQxjREgIiLSO811Yda80MgHTzey9oW4xj9wcFU+\nR84sZsJZRZQN108gERFJnurq6m4v3KbDuDP6X7Cj6BX/8m7Ko/Nr+yEWERER6YE9O9r563ONfPhM\nIx+9vPeef4Dhk/KYMLOYI88upnyUfvYMNOnwY1lEpKcG0oVc/Y/Y0crIdEI35UdEpt2NISAiIiL9\noPbjNv66OGj8b3itGQ8H8y0Eo08o4IjPF3HEGUV63J+IiEgC+t+xo+ci0zPNzDwupWNmZcBUYA+w\nLBXBiYiIZKv2VmfjG82sXtLEmucb2bFm72X/nDwYM7WQIz5fxOEziigerHv+M81AusomItlnIPZe\nUiIgjruvMbNFwFnA9cBv44rnA8XAbe7e2B/xxP9BaXBAERHJNo217ax9sYnVS5pY+1Ijzbv3NgYL\nyozDphZy+N8UM+70QgpKNdq/iIikr3QbPNAyPcNqZucD50c+jiBo5K8BXozM2+bu34tbfhywFBgG\nPExwu8BJwHRgFTDF3XcmOWYHZb9FRCS7hNudLe+1sG5pE2tfbGLjmy2xLv8Agw/LZdzpRYyfVsio\n4wrIyRt4V2Ckd6IXRfSbSETSWW/PVXHLp+w/smxIBMwD5gGddzR60Ne5+7hO6xwC3ATMBIYAG4EH\ngfnu3t2jBfuMEgEiIpIt6ja3BQ3/l5r4aFkzTbv2tvxDucH9/uOnFTFuWiGVh+alMFJJBSUCRGQg\nUCJA+oQSASIikqlaGsJ8sqKZdUubWPdSU4d7/QHKR+UwdkohY6cUMuYUdfnPdkoEiMhAMBATARoj\nII1pjAARERnoWhvDbHijhY9faWL9K81sfrelw+P98oqNMScVMGZKIYdNKaTi0NwBOeiSiIjIvmiM\nAPlU6hEgIiIDVVuzs/HNZta/0sz6V5rY9FbHhr+FYMRR+Yw5pZCxUwoYWaV7/aV76hEgIgOBegSI\niIhIVmnc1c7G11v45PVmNrzezOZ3WmhviVvAYPikPEZPLuTQEws45HMF6u4vIiKSYkoEiIiISI+4\nO7Uft7Mh0ujf8HozO1a3dVnuoAl5HHpiAYeeWMghnyugcJAa/iIiIulEiQARERFJqLkuzKZ3Wtj8\ndgub3m5m41stNOwId1gmt8AY8dl8Rh2bzyHHB139C8vV8BcREUlnSgSIiIgI7a3OtlWtbHqnmU1v\ntbDp7RZq1na92l9UGWLUcQWMOi6fUccVMHxSPrn5usdfJJ3NmTOHu+66i2nTpvHcc88lXKatrY17\n772XRx99lOXLl7Nt2zba29sZOnQoxx13HOeccw6XX3455eXl/Ry9iCSDEgFpTE8NEBGRZGhpCLN1\nZStbV7Ww9f1Wtq5sYfuHrbS3dlwuJw+GTczn4KPzOfiYfEYcnU/lGI3qLzJQdfdvd9myZVx11VWs\nWbMmtlxRURFFRUVs3LiRDRs28NhjjzF37lxuvfVWLrvssv4MWyQjpNtTA5QISGMaIVdERA7Unh3t\nbF0ZNPi3vN/C1lWt7PyoDRL8FzP4sFxGRBr9Bx+dz7Aj8zWiv0iGW7RoEeeddx7Nzc0ccsgh/PCH\nP+S8885jxIgRADQ2NrJ48WL++7//mwcffJAnn3xSiQCR/VBdXR27sJsOCXUlAkRERDJAS0OYHatb\n2bG6je2rW9n+1+BK/55t4S7LhnJh6OF5DDsyn2FH5jF8Yj4HTcjTaP4iWWbjxo1cccUVNDc3M3ny\nZBYuXEhlZWWHZYqKipg1axazZs1i8eLFLFq0KEXRikhfUiJARERkAOnc4N/x11a2r25l98b2hMvn\nFVvQ2D8yn2ETg8b/0MPzdKVfRPjJT35CTU0NZWVlPPDAA12SAJ1Nnz6d6dOn909wIpJUSgSIiIik\nmXC7s3tTOzs/amPn+lZ2rmtj5/o2duyjwR/KhcGH5TF0fC5DDs9jyPg8hk3Io+KQXCykRr+IdNTS\n0sLtt98OwNVXX83o0aNTHJGI9CclAkRERFLAw07dlnZ2rm8LGvwftUambez6pK3LwH1RiRr8Q8fn\nUXloLqFcNfhFpGeWL19OQ0MDZsa5556b6nBEpJ8pEZDG9NQAEZGBy93ZsyPM7g1t7NrQzu6Nbeza\n0MaujXvft7d0v37psBwqD82lckwuFWNyqTw0lyHj8qgYnatu/SJywN5///3Y+6qqqhRGIpId9NQA\n6TE9NUBEJH21NISp39JO3dZ26ja3U7+lnd2b9jb0d29sp6153+fx4sEhKsfkRl55wfTQXCoOzSW/\nWAP3iUjy7NixI/Z+8ODBKYxEJDvoqQEiIiJpLNzmNNSG2bO9nT3b2qnbEmnobw3e129po25rO827\nPz1ZW1QRYtDIHMpH5VI+KpdBo3IoHxl5PzJHjX2RftLbH929vRjTk/p1gUdE0okSASIikvHaW53G\nnWH27GinYUc7e3YE7/dsb6dhR3R+mIYd7TTsDEMPfq/n5Afd98tG5FI2LIfS4TkMGpHTocGfX6KG\nvoikp6FDh8be79ixgxEjRqQwGhHpb0oEiIjIgNLe6jTWhmmsbaepNhy83xWOvW/aFXyOljfUBPN7\nzIIu+8VDcigZGqJseC5lI3KCRv/woMFfNjyHoopQWnTtE5FPl+yr8QPxav/EiRNj7998800lAkSy\njBIBIiLSr9panOa6MC31YZrrnOb6MM114WBa7zTvjryPltWHad4dafDXhmlt6P0PbgsF3fSjjfuS\nITnB+yGd5g3NobgipNH3RSTjTZ48mZKSEvbs2cMjjzzC2WefneqQRKQfKREgIiLdcnfampyWBqe1\n0WltCAfvG5zWxr3vWxrCkfJO7/dEG/kea+zva6T8nrAcKCoPUVgeoqgieBWW5+x9XxGiqHzv++LK\nHIoqQ4Ry1LgXEYnKy8tjzpw53HLLLSxYsIAbbriB0aNHf+p67q7eUCIZQIkAEZEBwN0JtwXd4ttb\nnfaW4H241WlrCRrrbc2RV/z7+M9NTmtk2h63TmtTgvWagoZ/S4P36H753gjlQkFpiPxSo6AsREFp\nKJiW2d73pXvf55eGKBxkscZ+QZnpR6iISB+44YYbuPfee6mpqeHiiy9m4cKFVFZWdrv8s88+y1NP\nPcVPfvKTfoxSRJJBiYA0Fv9Dd968ebHHTYhI9zzseBjC4b3vPQzeDuGwB9M2J9wO4fagcR373GUK\n3u60twXLeltP1kk8DRrvTrh17/v2Du/3fo427jsvmyq5hUZekZFfbOQVh8grjn4OkVdk5BVHyopC\nkWXi33dt4OcWqiEvIpIORo0axT333MP555/P8uXLqaqqYu7cuZx//vmxMQMaGhpYsmQJv//973no\noYeYM2dOaoMWGaCqq6uZP39+qsOIsYE4uEmmMzMHWP9KI919PR3me/fzusyPLbzvujrM94TF+6jD\n911vojp6E0/czB7tc6LjkygG4gb76Uk8Pdxu120HjVM8Mj8yDd573Pu4snBkvei8cMfvx8NxZdCx\n/mRuj7jlfe8y3t5NYzzyORxpmHcsi18nrizagO9UR/zncPvez5kslAs5eRa88iPv842cPMgtMHIL\nQ+TkQ16hRT7HT0PkFtBxfkEo8j4yP27ZvEKLNfjVpV5EUiWaNNTv1QMzZ84c7rrrLmbMmMEzzzzT\npXzp0qVcffXVrF27NjavqKiIvLw8du/eHZt30EEHcdttt3HBBRf0S9wiA0Vvz1Vxy6fsR5Z6BKSx\n+760LdUhiAxIlgNmEMoxLETcywjlQCjXCOUG5cE0Mi8HLDLNyTUsbn5vphZdP7qNHGIN9r2N972N\n+VCukZtvhPKITPd+ji2fG8QvIiLSWy0tweAsRUVFCcunTJnCqlWr+OMf/8ijjz7KihUr2LZtGy0t\nLYwePZrjjjuO2bNnc/nll1NcXNyfoYtIkigRkMYOOaEAgA4//eM+dOhZawnKu13PelZXN3V0u2yH\n+V0bLJ+6Xnd1dVuH7bPehOv1ZJ+t68ye7XOCchKUEzTozIJ5FnkR+5y4LJgGDdvYti3SwLVgAxb5\nHKuL6Of93d7exmdPt0eXBnjwPhRpnFtOZL1EjfVIWSgn2GAoh4RlZkFju0MDP+69iIiI7LVlyxYA\nhg4d2u0yubm5XHPNNVxzzTX9FZaIpJASAWns8juGpToEERERERnAGhsbefXVVwGoqqpKcTQiki5C\nqQ5ARERERET63rZt27j22mupq6sjNzeXCy+8MNUhiUiaUI8AEREREZEMsnTpUmbPns3OnTuB4Ja6\nG2+8kTFjxqQ4MhFJF0oEiIiIiIhkkNbWVmpra6moqKCqqorrrruOSy+9NNVhiUga0eMD01D08YH6\nbkRERCSb6fGBIjIQDMTHB2qMgDQWjOYevKqrq1MdjoiIiIiIiOyH6urqWNsuHahHQBpSjwARERER\n9QgQkYFBPQJEREREREREJK0pESAiIiIiIiKSRZQIEBEREREREckiSgSIiIiIiIiIZBElAkRERERE\nRESyiBIBIiIiIiIiIllEiQARERERERGRLKJEgIiIiIiIiEgWUSJAREREREREJIsoESAiIiIiIhlv\n7NixhEIhlixZkupQkubDDz/ki1/8IiNGjCAnJ4dQKMSXvvSlVIclaUiJgDRmZrFXdXV1qsMRERER\nkQFozpw5hEIhZsyY0e0ybW1tLFiwgEsvvZTDDjuM0tJSioqKGD16NOeeey633XYbu3bt6seo9y0c\nDnPQQQeRm5tLTU1Nj9eL/rbuK7t27aK6upr58+f3WZ37q6amhtNOO43//d//Zfv27QwZMoQRI0ZQ\nUVGR6tAEqK6u7vO/vwORm+oApHvunuoQRERERCRDdNcAWbZsGVdddRVr1qyJLVdUVERRUREbN25k\nw4YNPPbYY8ydO5dbb72Vyy67rD/DTujll19mx44dTJ06lcGDB/doncMPP5zi4mKKi4v7LI6dO3dy\n0003YWbMmzevz+rdH/feey9bt25lwoQJLF68mOHDh6c0Humouro6dnE3HZIB6hEgIiIiIpKlFi1a\nxIwZM1izZg2HHHIIt956Kxs2bKC+vp6amhrq6+t5/PHHueCCC6itreXJJ59MdcgAPPbYYwB84Qtf\n6PE6Tz/9NO+99x4nnHBCn8WRDg26qHfffReA2bNnKwkgn0o9AkREREREstDGjRu54ooraG5uZvLk\nySxcuJDKysoOyxQVFTFr1ixmzZrF4sWLWbRoUYqi7eixxx7DzHqVCEiGdOrB29jYCEBJSUmKI5GB\nQD0CRERERESy0E9+8hNqamooKyvjgQce6JIE6Gz69OncfPPNPap7wYIFhEIhTjzxxC5l27dvJxQK\nEQqFOOecc7qUr1q1ilAoRFFRES0tLV3KP/roI959913GjBnDUUcd1aN4oPvBAu+4444OYyg8+uij\nzJgxg4qKCkpLSznllFO47777utQ3ffp0xo0bBwQJgeg+RV+Jxg1Yt24d3/jGN5gwYQLFxcWUlZXx\nuc99jp/+9Kc0NDQkjDta30cffcT777/Ptddey+jRo8nLy+OCCy5g+vTphEIh7rzzTgDmz5/fIY7+\niCHetm3b+MEPfsBnP/tZSktLKSkp4eijj+bGG29k586dCeuPfjfPP/88NTU1fOc73+Gwww6joKCA\nUaNG8bWvfY3NmzcnXDfq448/5rvf/S5HH300ZWVllJWVMWnSJL761a+yePHihOvU19dz8803M3ny\nZMrLyyksLOSII47gm9/8Jp988sk+tzfgubteafYCPPhqRERERLKXfhP1jWuvvdbNzGfMmBGb19zc\n7CUlJW5mfv311/f5NtevX+9m5nl5eV5XV9eh7E9/+pObmZuZV1RUeHt7e4fy//qv/3Iz8+nTpyes\n+7e//a2bmX/961/vVUxjxozxUCjkS5Ys6TD/9ttvj23vpptucjPz3Nxcr6ys9FAoFIv1V7/6VYf1\nLrzwQh82bFis/OCDD+7w+vnPf95lvwsLC93MPBQKeWlpqRcUFMTWP+aYY3zLli1d4o4uv2DBAi8u\nLnYz8/Lyci8uLvYLLrjAL7zwQj/44IO9qKjIzcxLS0s7xNEfMUS98MILPnjw4NjyhYWFseXNzA89\n9FBftWpVt9/N3Xff7WPGjIntR3SfzMwPO+ww37lzZ8Lv9oEHHuiwbHFxsQ8ZMsRzcnLczHzs2LFd\n1nnvvfdi2zIzz8/P97Kysth3PnjwYH/ppZcSbq+z3p6r4pZPXZszlRvXq5svRf/piYiIiCgR0EcS\nJQJ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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 499, "width": 513 } }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,8))\n", "\n", "plt.subplot(211)\n", "plt.semilogx(Om_list_TLS, abs(I_c_TLS),\n", " linestyle='dashed', label='TLS $I_\\mathrm{c}$')\n", "plt.semilogx(Om_list_TLS, abs(I_inc_TLS), 'r', \n", " linestyle='dashed', label='TLS $I_\\mathrm{inc}$')\n", "plt.semilogx(Om_list/np.sqrt(effective_gamma),\n", " abs(I_c/effective_gamma), 'k', linestyle='dashed', \n", " label='JC $I_\\mathrm{c}$')\n", "plt.semilogx(Om_list/np.sqrt(effective_gamma),\n", " abs(I_inc/effective_gamma), \n", " 'r', label='JC $I_\\mathrm{inc}$')\n", "plt.semilogx(Om_list/np.sqrt(effective_gamma),\n", " abs(I_c_int/effective_gamma),\n", " 'b', label='JC w/ homodyne $I_\\mathrm{c}$')\n", "plt.semilogx(Om_list/np.sqrt(effective_gamma),\n", " abs(I_inc_int/effective_gamma),\n", " 'r')\n", "plt.ylim(5e-4, 0.6)\n", "plt.xlabel(r'Driving strength [$\\Gamma_\\mathrm{eff}$]')\n", "plt.ylabel('Normalized flux [$\\Gamma_\\mathrm{eff}$]')\n", "plt.legend(loc=2)\n", "\n", "plt.subplot(212)\n", "plt.loglog(Om_list/np.sqrt(effective_gamma), g20,\n", " 'k', linestyle='dashed', label='JC')\n", "plt.loglog(Om_list/np.sqrt(effective_gamma), g20_int,\n", " 'blueviolet', label='JC w/ interference')\n", "plt.ylim(lim)\n", "plt.xlabel(r'Driving strength [$\\Gamma_\\mathrm{eff}$]')\n", "plt.ylabel(r'$g^{(2)}(0)$')\n", "plt.legend(loc=4);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Second-order coherence with delay\n", "\n", "We additionally consider the second-order coherence as a function of time delay, i.e.\n", "\n", "$$g^{(2)}(\\tau)=\\lim_{t\\rightarrow\\infty}\\frac{\\langle b^\\dagger(t)b^\\dagger(t+\\tau)b(t+\\tau)b(t)\\rangle}{\\langle b^\\dagger(t)b(t)\\rangle^2},$$\n", "\n", "and show how it is calculated in the context of homodyne interference." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# first calculate the steady state\n", "H = Om * (a + a.dag()) + g * (sm.dag() * a + sm * a.dag()) + \\\n", " delta_s * (sm.dag() * sm + a.dag() * a) - \\\n", " detuning * sm.dag() * sm\n", "rho0 = steadystate(H, c_op)\n", "\n", "taulist = np.linspace(0, 5/effective_gamma, 1000)\n", "\n", "# next evolve the states according the quantum regression theorem\n", "\n", "# ...with the b operator\n", "corr_vec_int = expect(\n", " (a.dag() + alpha.conjugate()) * (a + alpha),\n", " mesolve(\n", " H, (a + alpha) * rho0 * (a.dag() + alpha.conjugate()),\n", " taulist, c_op, [],\n", " options=Options(atol=1e-13, rtol=1e-11)\n", " ).states\n", ")\n", "n_int = expect(rho0, (a.dag() + alpha.conjugate()) * (a + alpha))\n", "\n", "# ...with the a operator\n", "corr_vec = expect(\n", " a.dag() * a ,\n", " mesolve(\n", " H, a * rho0 * a.dag(),\n", " taulist, c_op, [],\n", " options=Options(atol=1e-12, rtol=1e-10)\n", " ).states\n", ")\n", "n = expect(rho0, a.dag() * a)\n", "\n", "# ...perform the same for the TLS comparison\n", "H_TLS = Om*(sm_TLS + sm_TLS.dag())*np.sqrt(effective_gamma)\n", "c_ops_TLS = [sm_TLS*np.sqrt(effective_gamma)]\n", "rho0_TLS = steadystate(H_TLS, c_ops_TLS)\n", "corr_vec_TLS = expect(\n", " sm_TLS.dag() * sm_TLS,\n", " mesolve(\n", " H_TLS, sm_TLS * rho0_TLS * sm_TLS.dag(),\n", " taulist, c_ops_TLS, []\n", " ).states\n", ")\n", "n_TLS = expect(rho0_TLS, sm_TLS.dag() * sm_TLS)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualize the comparison to TLS correlations\n", "\n", "At a moderate driving strength, the JC correlation (dashed black line) is seen to significantly deviate from that of the TLS (dotted purple line). On the other hand, after the optimal homodyne inteference, the emission correlations (solid purple line) match the ideal correlations very well." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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R3XLaJS6fsCF9v9kVzA96D2MPiFSUDRF3BfOobuoaz7xe2dB1S7ET65/PhS5E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ph8Dup9M+b97YHVd7xxMIOGEL4OXAS8BOwdYxzw80MI/f7MnTt3MGUohy1/pYs7v1UPEaZsXMTC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\neSBfg3pl5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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 329, "width": 501 } }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,5))\n", "\n", "l1, = plt.plot(taulist*effective_gamma, corr_vec_TLS/n_TLS**2,\n", " 'blueviolet', linestyle='dotted', label='TLS')\n", "plt.plot(taulist*effective_gamma, corr_vec/n**2,\n", " 'k', linestyle='dashed', label='JC')\n", "plt.plot(taulist*effective_gamma, corr_vec_int/n_int**2,\n", " 'blueviolet', label='JC w/ interference')\n", "plt.xlabel('$\\\\tau$ [$1/\\Gamma_\\mathrm{eff}$]')\n", "plt.ylabel('$g^{(2)}(\\\\tau)$')\n", "plt.legend(loc=2);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Versions" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
SoftwareVersion
QuTiP4.3.0.dev0+0f58c6f
Numpy1.9.2
SciPy0.18.1
matplotlib1.4.3
Cython0.24.1
Number of CPUs8
BLAS InfoINTEL MKL
IPython4.2.0
Python3.4.3 (default, Nov 17 2016, 01:08:31) \n", "[GCC 4.8.4]
OSposix [linux]
Fri Aug 04 15:25:33 2017 PDT
" ], "text/plain": [ "" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from qutip.ipynbtools import version_table\n", "\n", "version_table()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 }