{ "metadata": { "name": "", "signature": "sha256:9f9a5106424390ebd841fa896683a717c59ae586d33dfb6d761110533fe41619" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# QuTiP lecture: The Dicke model \n", "\n", "Author: J. R. Johansson (robert@riken.jp), http://dml.riken.jp/~rob/\n", "\n", "The latest version of this [IPython notebook](http://ipython.org/ipython-doc/dev/interactive/htmlnotebook.html) lecture is available at [http://github.com/jrjohansson/qutip-lectures](http://github.com/jrjohansson/qutip-lectures).\n", "\n", "The other notebooks in this lecture series are indexed at [http://jrjohansson.github.com](http://jrjohansson.github.com)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "from qutip import *" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction\n", "\n", "The Dicke Hamiltonian consists of a cavity mode and $N$ spin-1/2 coupled to the cavity:\n", "\n", "
\n", "$\\displaystyle H_D = \\omega_0 \\sum_{i=1}^N \\sigma_z^{(i)} + \\omega a^\\dagger a + \\sum_{i}^N \\frac{\\lambda}{\\sqrt{N}}(a + a^\\dagger)(\\sigma_+^{(i)}+\\sigma_-^{(i)})$\n", "\n", "$\\displaystyle H_D = \\omega_0 J_z + \\omega a^\\dagger a + \\frac{\\lambda}{\\sqrt{N}}(a + a^\\dagger)(J_+ + J_-)$\n", "
\n", " \n", "where $J_z$ and $J_\\pm$ are the collective angular momentum operators for a pseudospin of length $j=N/2$ :\n", "\n", "
\n", "$\\displaystyle J_z = \\sum_{i=1}^N \\sigma_z^{(i)}$\n", "\n", "$\\displaystyle J_\\pm = \\sum_{i=1}^N \\sigma_\\pm^{(i)}$\n", "
\n", "\n", "### References\n", "\n", " * [R.H. Dicke, Phys. Rev. 93, 99\u2013110 (1954)](http://dx.doi.org/10.1103/PhysRev.93.99)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Setup problem in QuTiP" ] }, { "cell_type": "code", "collapsed": false, "input": [ "w = 1.0\n", "w0 = 1.0\n", "\n", "g = 1.0\n", "gc = sqrt(w * w0)/2 # critical coupling strength\n", "\n", "kappa = 0.05 \n", "gamma = 0.15" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "M = 16\n", "N = 4\n", "j = N/2.0\n", "n = 2*j + 1\n", "\n", "a = tensor(destroy(M), qeye(n))\n", "Jp = tensor(qeye(M), jmat(j, '+'))\n", "Jm = tensor(qeye(M), jmat(j, '-'))\n", "Jz = tensor(qeye(M), jmat(j, 'z'))\n", "\n", "H0 = w * a.dag() * a + w0 * Jz\n", "H1 = 1.0 / sqrt(N) * (a + a.dag()) * (Jp + Jm)\n", "H = H0 + g * H1\n", "\n", "H" ], "language": "python", "metadata": {}, "outputs": [ { "latex": [ "Quantum object: dims = [[16, 5], [16, 5]], shape = [80, 80], type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}2.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 1.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & -1.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & -2.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\\\vdots & \\vdots & \\vdots & \\vdots & \\vdots & \\ddots & \\vdots & \\vdots & \\vdots & \\vdots & \\vdots\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 17.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 16.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 15.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 14.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 13.0\\\\\\end{array}\\right)\\end{equation*}" ], "metadata": {}, "output_type": "pyout", "prompt_number": 4, "text": [ "Quantum object: dims = [[16, 5], [16, 5]], shape = [80, 80], type = oper, isherm = True\n", "Qobj data =\n", "[[ 2. 0. 0. ..., 0. 0. 0.]\n", " [ 0. 1. 0. ..., 0. 0. 0.]\n", " [ 0. 0. 0. ..., 0. 0. 0.]\n", " ..., \n", " [ 0. 0. 0. ..., 15. 0. 0.]\n", " [ 0. 0. 0. ..., 0. 14. 0.]\n", " [ 0. 0. 0. ..., 0. 0. 13.]]" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Structure of the Hamiltonian" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(1, 1, figsize=(10,10))\n", "hinton(H, ax=ax);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Find the ground state as a function of cavity-spin interaction strength" ] }, { "cell_type": "code", "collapsed": false, "input": [ "g_vec = np.linspace(0.01, 1.0, 20)\n", "\n", "# Ground state and steady state for the Hamiltonian: H = H0 + g * H1\n", "psi_gnd_list = [(H0 + g * H1).groundstate()[1] for g in g_vec]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Cavity ground state occupation probability" ] }, { "cell_type": "code", "collapsed": false, "input": [ "n_gnd_vec = expect(a.dag() * a, psi_gnd_list) \n", "Jz_gnd_vec = expect(Jz, psi_gnd_list) " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = plt.subplots(1, 2, sharex=True, figsize=(12,4))\n", "\n", "axes[0].plot(g_vec, n_gnd_vec, 'b', linewidth=2, label=\"cavity occupation\")\n", "axes[0].set_ylim(0, max(n_gnd_vec))\n", "axes[0].set_ylabel(\"Cavity gnd occ. prob.\", fontsize=16)\n", "axes[0].set_xlabel(\"interaction strength\", fontsize=16)\n", "\n", "axes[1].plot(g_vec, Jz_gnd_vec, 'b', linewidth=2, label=\"cavity occupation\")\n", "axes[1].set_ylim(-j, j)\n", "axes[1].set_ylabel(r\"$\\langle J_z\\rangle$\", fontsize=16)\n", "axes[1].set_xlabel(\"interaction strength\", fontsize=16)\n", "\n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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w8HDCw8PZt28fH3zwAZMnT6Z3794MGjSI8uXLF1P0IiJSGjmUXI0aNYonnniC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\niZJx8fY2PDc7uwLZ2V33iLiftob9uTMcOrk6d+4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"text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Cavity Wigner function and Fock distribution as a function of coupling strength" ] }, { "cell_type": "code", "collapsed": false, "input": [ "psi_gnd_sublist = psi_gnd_list[::4]\n", "\n", "xvec = np.linspace(-7,7,200)\n", "\n", "fig_grid = (3, len(psi_gnd_sublist))\n", "fig = plt.figure(figsize=(3*len(psi_gnd_sublist),9))\n", "\n", "for idx, psi_gnd in enumerate(psi_gnd_sublist):\n", "\n", " # trace out the cavity density matrix\n", " rho_gnd_cavity = ptrace(psi_gnd, 0)\n", " \n", " # calculate its wigner function\n", " W = wigner(rho_gnd_cavity, xvec, xvec)\n", " \n", " # plot its wigner function\n", " ax = plt.subplot2grid(fig_grid, (0, idx))\n", " ax.contourf(xvec, xvec, W, 100)\n", "\n", " # plot its fock-state distribution\n", " ax = plt.subplot2grid(fig_grid, (1, idx))\n", " ax.bar(arange(0, M), real(rho_gnd_cavity.diag()), color=\"blue\", alpha=0.6)\n", " ax.set_ylim(0, 1)\n", " ax.set_xlim(0, M) \n", " \n", "# plot the cavity occupation probability in the ground state\n", "ax = plt.subplot2grid(fig_grid, (2, 0), colspan=fig_grid[1])\n", "ax.plot(g_vec, n_gnd_vec, 'r', linewidth=2, label=\"cavity occupation\")\n", "ax.set_xlim(0, max(g_vec))\n", "ax.set_ylim(0, max(n_gnd_vec)*1.2)\n", "ax.set_ylabel(\"Cavity gnd occ. prob.\", fontsize=16)\n", "ax.set_xlabel(\"interaction strength\", fontsize=16)\n", "\n", "for g in g_vec[::4]:\n", " ax.plot([g,g],[0,max(n_gnd_vec)*1.2], 'b:', linewidth=2.5)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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k1kmZFip3jspCBgmlAEwgKUYAn4XI7SSAY8A5cySwcYu5jRGI3K4C21vmMDs0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\nO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"text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Entropy/Entanglement between spins and cavity" ] }, { "cell_type": "code", "collapsed": false, "input": [ "entropy_tot = zeros(shape(g_vec))\n", "entropy_cavity = zeros(shape(g_vec))\n", "entropy_spin = zeros(shape(g_vec))\n", "\n", "for idx, psi_gnd in enumerate(psi_gnd_list):\n", "\n", " rho_gnd_cavity = ptrace(psi_gnd, 0)\n", " rho_gnd_spin = ptrace(psi_gnd, 1)\n", " \n", " entropy_tot[idx] = entropy_vn(psi_gnd, 2)\n", " entropy_cavity[idx] = entropy_vn(rho_gnd_cavity, 2)\n", " entropy_spin[idx] = entropy_vn(rho_gnd_spin, 2)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 14 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = plt.subplots(1, 1, figsize=(12,6))\n", "axes.plot(g_vec, entropy_tot, 'k', g_vec, entropy_cavity, 'b', g_vec, entropy_spin, 'r--')\n", "\n", "axes.set_ylim(0, 1.5)\n", "axes.set_ylabel(\"Entropy of subsystems\", fontsize=16)\n", "axes.set_xlabel(\"interaction strength\", fontsize=16)\n", "\n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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LCyuHuL9h5QoAgLKxmC36d+/F+tw0Wv9d46RatYxOBAAVg10fC+zYsaNcXFy0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\njgYAAOyIcgUANpKUJP31r1LT5g5KT5c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"text": [ "" ] } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Entropy as a function interaction strength for increasing N\n", "\n", "### References\n", "\n", "* [Lambert et al., Phys. Rev. Lett. 92, 073602 (2004)](http://dx.doi.org/10.1103/PhysRevLett.92.073602)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def calulcate_entropy(M, N, g_vec):\n", " \n", " j = N/2.0\n", " n = 2*j + 1\n", "\n", " # setup the hamiltonian for the requested hilbert space sizes\n", " a = tensor(destroy(M), qeye(n))\n", " Jp = tensor(qeye(M), jmat(j, '+'))\n", " Jm = tensor(qeye(M), jmat(j, '-'))\n", " Jz = tensor(qeye(M), jmat(j, 'z'))\n", "\n", " H0 = w * a.dag() * a + w0 * Jz\n", " H1 = 1.0 / sqrt(N) * (a + a.dag()) * (Jp + Jm)\n", "\n", " # Ground state and steady state for the Hamiltonian: H = H0 + g * H1\n", " psi_gnd_list = [(H0 + g * H1).groundstate()[1] for g in g_vec]\n", " \n", " entropy_cavity = zeros(shape(g_vec))\n", " entropy_spin = zeros(shape(g_vec))\n", "\n", " for idx, psi_gnd in enumerate(psi_gnd_list):\n", "\n", " rho_gnd_cavity = ptrace(psi_gnd, 0)\n", " rho_gnd_spin = ptrace(psi_gnd, 1)\n", " \n", " entropy_cavity[idx] = entropy_vn(rho_gnd_cavity, 2)\n", " entropy_spin[idx] = entropy_vn(rho_gnd_spin, 2)\n", " \n", " return entropy_cavity, entropy_spin" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 16 }, { "cell_type": "code", "collapsed": false, "input": [ "g_vec = np.linspace(0.2, 0.8, 60)\n", "N_vec = [4, 8, 12, 16, 24, 32]\n", "MM = 25\n", "\n", "fig, axes = plt.subplots(1, 1, figsize=(12,6))\n", "\n", "for NN in N_vec:\n", " \n", " entropy_cavity, entropy_spin = calulcate_entropy(MM, NN, g_vec)\n", " \n", " axes.plot(g_vec, entropy_cavity, 'b', label=\"N = %d\" % NN)\n", " axes.plot(g_vec, entropy_spin, 'r--')\n", "\n", "axes.set_ylim(0, 1.75)\n", "axes.set_ylabel(\"Entropy of subsystems\", fontsize=16)\n", "axes.set_xlabel(\"interaction strength\", fontsize=16)\n", "axes.legend()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 17, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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O+bVvvw2pqbBmjWFu3MqKX5e5JB08TrNbG/l7s7unDn/8G1W+Hk3U0i24DWls/GDES01y\nIcOTRPtv8uESQogXw6lT+l0bg4NzXirPb8ByNgSU4+sLHbCwME58/6Z0iuH943mYasGGDWmT++PT\nd1By5jju7DyDd5ui+ROUeClJLmR4z/0W7IMHD8bBwQEPD49M2x0/fhwzMzM2bdqUT5EJIYQoCKtX\n6zeGyWmSfX75UdzWTWTCUpd8S7IBNCYavlthQVgYfP552vMNpnYi4o9T9OxblF278i8uIUThk+8z\n2gEBAVhaWjJw4EDOnTuXbpvU1FTatm2Lubk5gwYNomfPnmnayLc4IYR4/iUnQ/nycOgQuLhk/7p7\nl+6S6FGPm+O/o9GX3Y0XYCZu34aGDeGrr+DNN9OeP3gQXntNf752bX374sVBq9VXLBEiryQXMjxD\nz2jn+//qzZs358aNG5m2+e6773j99dc5fvx4/gQlhBCiQPitCqVOZWtcXErl6LrgNiNJqN8PbQEl\n2QCOjvp15W+/mUTgV3voXPQvity/TYmHdygZf5u9pgOJTprA8OFQsSK4usK9e/Dq5a/wqhFNuU/f\nosqr+bMNtBCiYBS68n63bt1iy5YtjBo1CqBAdxASQghhXFZTP+TTqj/n6JqgnwNxun2YRjumGimq\nrKWmwuzZMGQIDHI/ToVLe4i6nYrq3AXdxEnoNvzMO+dHkZQEp09DYiIMa3aJY8eg94YeKFMzLHp2\n4KJFffzfWEj01fsF9lyEEMZT6H68ev/9959u0amUkp9EhBDiBfUg+D6uEXvh8xU5um7pClOa919I\nd9sSRoosc6GhMHCg/ibI48ehUiUvwveXRbVuzfXwitRb9Ow6klq1wO+PR5g36oD/mfG0+PkdXDp9\nRWrS50R8vRezxavQVJ/CW52D6TnMlo4dIZ92hxZCGFmBVB25ceMGXbt2TXeNduXKlZ8m1/fu3cPc\n3JylS5fSrVu3Z9ppNBqmTv3/bIZWq0Wr1Ro1biGEEIbj32cRRQ4H0DT0p2xfc/myvgRgSAhYWhox\nuHQoneKnHxN5f0Jxxo2Djz4CU9P/n488fpMEr9aENu9Piz2foTF59hfZML8QUtt1ILReT7wDvsDE\n7P8/KsdGxvPzNnNWrYKrV6FfP33Zwtq18+nJieeSrNE2vP+9pn5+fvj5+T19fPr06c9Peb/MEu1/\nGjRoEF27dqVHjx5pzsmHSwghnm/nLRuR8Mk06k/umO1r3noLqlaFzz4zYmDpiAmJ5pJ2FMFxjnjs\nnY+nZ/rtos7eJrZhG27V7UaLA1+kSbbvB90jon43Hr7iTP2zKyhWsliaPq5e1VdiWbkSXq93nYnT\ni+PgWcYYT0s85yQXMrznvrxf3759adq0KUFBQVSoUIEVK1awePFiFi9enN+hCCGEKCAhOy5j9yQc\nz4/bZv+aENi2zfi7P/7bKZ+/iK9WmyRbR16/OivDJBvAvpYjtoF+xATdYfx7T/j338uvVLejSuhe\nTJITCKg6mJiYtH1UrQozZ0JQEDRL8cOsrgf+r31LSkKKYZ+YEEbm5OSEg4MD8fHxTx9btmwZLVu2\nNOg4ycnJvP766zg7O2NiYoK/v3+aNqdOncLb2xsrKyscHR1ZsGCBQWPISL4n2j/99BMREREkJSUR\nHh7O4MGDGTFiBCNGjEjTduXKlenOZgshhHi+bd6iYW/HrzErnv1bhWbPhlGjwNraiIH9Q0JMAn71\nPqTMxLeJnLmcFmfmUyIb68JfqW6H9tpyDpwyZ+RI0OmePV/CtgQNr//MgS6z8PKCsLD0+7GwgNe3\nDyJ22wGs/P/gmk09zv1w0ADPTIj8o9PpmD9/vtHH8fb2Zu3atTg6OqYppHHv3j06duzIqFGjiI6O\n5tq1a7Rr187oMUEhrDoihBDixZaaCt/sqE7tWX2zfU3EmSgCNkbw/vtGDOwfAgNhoetCit0Jo9jl\nQOpNzNlfytbWsHu3fk35229Dyr8mo02LmjJteQWGDYOmTfWVSTJSuVMN6tz7i/vDJ1L6nV78VfM9\n7t7N+XMSIr9pNBrGjRvH3LlziY2NNdo4RYoUYcyYMXh5eWH6zxsn/jZv3jw6dOhA3759KVKkCBYW\nFtSoUcNo8fyTJNpCCCHyla8vlC4N7jkoIX317S9YVPUb7OyMF9f/fPMNtGkD9l9+QOOwX7Ct+kqu\n+rGygj//1G9U06+ffnOef3v/fZg/H9q3h507M+5LY6Kh6fw+WIRd4op7T9zc4Icf9F9ahCjM6tev\nj1arZe7cudlqb21tjY2NTbqHj49PrmI4evQoNjY2eHl54eDgQLdu3QgPD89VXzklibYQQoh8tWqV\n/qbG7Lp7/g61zq7BdemHxgvqb0uW6I9jx2DgINM0NzPmlLk5bN0KSfEprPacR0JMQpo2PXvC5s36\nme8tk09k2p9VuZKM/lnL3r2wfj00bqwvMShEYaXRaJgxYwbfffcd9+7dy7J9TEwMDx48SPcYP358\nrmIIDw9n1apVLFiwgLCwMJydnenbN/u/qOWFJNpCCCHyzaNH8Mcf+hne7LowZB5n3fsZvfLGoUP6\naiZbt4Kzs+H6LV4cft6oqBl7mMtOHYg8cStNm6ZN4cCOh3jO6oOf9xSULvPqBh4e4O8P770H3brB\n8GGK6OvG+2lePL80mrwfeeXm5kaXLl2e7pOS38zNzenRowf16tWjWLFiTJ06lUOHDvHo0SOjjy2J\nthBCiHyz6ZdUWrTQLx3Jjuir96l9fClVFuduJiu7bp+O5IMeoaxcqa/6YWhFLYrQIPgnYuq2wqxR\nXY5O3JymTZW6JTE/cwi7EzvZZvc2njWTqFQJypXTb/d+y7QCMSY2PNSUJF5jTpJJMd58y5QHt59w\netkJEiq7MtX9N9auhchIwz8H8XxSKu+HIUyfPp2lS5dy61baL5r/ZGlpiZWVVbrHrFmzcjV2rVq1\ncnWdIUiiLYQQIt+4jevABw0OZLv92aELOF+1B+WaVDRaTEmPk7jr3ZMvam2kc2ejDYNZcTO0+6Zw\ne9HvlJn7IftrjiQ+Wr+UJCEmgUNjNhDm3Z8PTBdQPCGGJTc7sXX5XY4e1d8sWez8KQi+BuE3Ieou\nxD6EhESepBbnmK4BF6b+wpuXP8N2WA96Vj1LcHE3/D3HcnTSVmLDZLZbFCwXFxd69+6dZQWSx48f\n8+jRo3SPCRMmZHhdYmIiCQkJaf4d9Puy/P777wQGBpKcnMzMmTNp3rw5VlZWhnlymch1oq2U4v79\n+4aMRQghxAvs5oEbOMecpsmYBtlq//AhTDjblwrLpmbdOA+ONBpDnJUDrXaMM+o4/+Mxoimlrp0m\nqkg5PN1TWF71K+Jsy1Ns3QoS3xzMH+GetIrZRHzN+sR17sW5c1CmDNi5lsa6si0ly5fEvLQFxUoW\nw7SYGRoTDRoNtJ3mRcV7pzGvV5Mt8W243HAgOntHiny/AJNK5Tln1ZQ/OvwHPz9ITMyXpyrEM6ZM\nmUJ8fLxRlo9Ur14dc3NzIiIiaN++PRYWFoT9XTuzZcuWfPnll3Tu3BkHBwdCQkJYv369wWNIT7Z2\nhlyyZAmxsbF8/PHHAJw7d44OHToQGRlJnTp12L59O46OjkYP9p9kNyQhhHi++LX5HM2dSFqc+0+2\n2s+aBefPw9q1xospYOBSym6cR+lrRylZvqTxBvqH+/f1NzLG+Cyh1K2LTDH7gjHDE5m2wBaTf01/\n7d/1hAHDS9CtG/j4QImsy3gDcHljIMGjv2ah53K+X1YER+sELi0/xPnDj1gY3p1r1/Q3X44eDS4u\nBn+KIp9ILmR4BbIz5MKFCylevPjT//7www+xsbHh22+/JTY2lsmTJ+d4YCGEEC8PpVNU2r8auw8G\nZqt9XJy+zN6nnxovpvPLjlBj7SQ0mzfnS5J95Qr07q1PbI8cgWZLBvJu0jxOXbZgz0lbOnZMu7ba\nu30JAgP1yXm9epnX2/6nGr1r0+HOalp3KEKDBrBkdXFqf9CKgb9159gxOHECTE2hUSPo3Bl819xE\nl6LLumMhRI5kK9EODQ3F1dUV0Jdd8ff3Z/bs2YwZM4YZM2awa9cuowYphBDi+XZ+6WGUxoSabzfM\nVvulS6F5c6hZ0zjx3L4Nqz8+x/VJy6ncsbpxBvmHX38FLy9o0ACuX4d166Blx+KYmJlQuTIEBOhL\n9bX1vMuxqdufudbaWj8D/tln+nrbcz9PIDUp6wLaZmbw8cf6aiqbNkGzZnDxov6cs7N+hjwsTF9e\nMGnMOMLMq+P36rfEhqazL7wQIleylWjrdDpM/v4968AB/U0s/9unvnz58kRFRRkpPCGEEC+Co7+E\nEtz+3WzVpU5IgDlzYNIk48SSlARvvAEW7w+j4cyuxhnkb8nxyfjV/ZCDo9excyeMGwc2NmnbmZnB\n9OmwenYkZb94h/0e7/Ak+skzbfr109fMLrFyEefsW3PrcAZ7t/9LtWr6TYLeegu6No9hT7s5JD1O\nAvR1vgcPhnb3f+LRd6socuYYytmZ/TVHcuW3c3l+/kK87LKVaFepUoVt27YBsHHjRpo2bYq5uTkA\nkZGR2NraGi9CIYQQz7WEBPjkdF9c//NuttrvmbCXTtWCqVPHOPF88AHY2oKxVz1GnrjFJUct5reu\nMOVwR+rVy/qaum/XwuraGcweRnOrbH1Ozdn7zPlKlWDkpbE8aNqJol71OfhO9m7oMjGBkSNh/55E\nSgX6E2pXl9PzfJ+e15ho8BjRFK8b60k8dRGdY1lu9/sQbQvFr7/KDpRC5JrKhnXr1ikTExNla2ur\nNBqN+vXXX5+eGzFihGrfvn12ujGobIYuhBCigG3cqFTr1tlrmxSXpMJNK6mziw8ZJZbly5WqXl2p\nmBijdP/USZ+/1G0TR+Xb9guVmpya4+t1qTp16MNf1A2zyuqQfTd1LjBtHxfXnVJXi7qqA5X6qpgb\nD3LW97hfVbhpRXWwQm8VcSw83XZJSfr3rkkTpapUUWrpUqUSE3P8VIQRSS5keBm9prl9rbM1o92v\nXz/8/f2ZOHEifn5+9OzZ8+k5e3t7xowZY5QvAUIIIZ5/Odly/eiYdUSVrILH8CYGj+PYER0TJui3\nOy9VyuDdA6DTwbbXllNuQn9uzVqLdvenmJjlvJKuxkRDk69fxzH6EhGvj6VVGxOGDoV/7vXh2q8O\nZW+dIKXkK/ziMZ3t27O3uYjGREOTOT2xvX2JJKdqFG3kyYJPb6cp+VekCPTqBQcPwrJl8Msv+hs5\nN4w7Qfy9+Bw/JyFeRtkq71cYSUkbIYQo/G7fBldXuHkTLCwyb5ualEqYpSuxPkvwfF9r0Djunr/D\n3brtuL5sH50HvmLQvv8nOhoGDgSLiKt8u8ScMvXLGazvmBj46it9wjt6NIwfD//ca2PXjlTe/8iU\ncuX069tzsuzmxvG7jP28NBcvwvz50KlTxm2PH4cHvYbjGbaVi23GUmfpaEpVNNK3FpElyYUMz9Dl\n/XKUaIeHhxMeHv7Mbjv/06pVqxwPnhfy4RJCiMJv3jw4dw5Wrsy67aExG7D8cSEeMQHZumkyu5Lj\nk7lYpjXRtVvScv90g/X7TydO6G+wfO01mD1bPxtsDGFh+uoju3fDsp5/0n5OG4qY6wdLSdEn4tOn\nQ9u28PnnUDEHG2ru2AFjx+q/GH3zTeb1tYO3XOD2B7NwvfEnZ5uOotbysbxS3S6Pz07klORChlcg\niXZISAj9+vXj2LFjGQaVms93SsiHSwghCr/fbYdQeumXNOvpkGk7nQ4uWjYg4dOZ1P+sg0Fj8Gsx\nFYtLx6kXsS1XyzgyoxQsWaJPfhct0ifb+eHM0URSO3XB5nE4dz+cRcMvuj/9cvLokb5036EFJ5hc\n8zfqbJyQ7VnnxET9l6Ovv4Zv22yjx8JWmNuZZ9g+zC+E66N9eBR8h33v/s5HH0E5w03kiyxILmR4\nBZJot2rViqCgICZMmED16tUpWrRomjZarTbHg+eFfLiEEKJwC9p4Bos3u1M24XqWCe6ff4LPx3fZ\nd9bOoLPZ17ZdolQ3b5KPnTHoUg7Qb8KzrOOvzL/5Or9t0lDd+OW404x/8stdlPr8Y+KLWaObNhPP\nsS2evn6RJyO41vczqgdv52LPyTT5cQRFLbI31R4eqiPUewBOtw4QPvZrGs/pmen7citcx9ffmPDj\nj/D66/racgXMAAAgAElEQVT63VWrGuJZiswU9lzIycmJJ0+ecP369afV6pYtW8a6devw9fXN4urs\nO3LkCJMnT+bUqVOYmpqi1WpZsGBBml3Lk5KSqF27No8fPyY8PDzdvgpkZ8jjx48zf/583nvvPdq1\na4dWq01zCCGEEP8UOXs1wY0HZGsW+dtv4e2PSxs0ydbpILb/O1zoOdXgSTaAn9enNDk4l8P7nuR7\nkg36mxrrf9aByg/P8LDnYEpNGMnsSotYu1ZfK7xMvbI0u7KCBz/vwcJ3G7ds3Dj88SaULutkoUIl\nE5qFruPenB+xXTSTiyUbcXzmzgyvLVfBhHnz9LtflikDTZvqd8E8uysy3fbi5aHT6Zg/f75Rx4iJ\niWHkyJGEhoYSGhqKlZUVgwYNStNuzpw52Nvbo9EY7s+ZrGRrRrtatWrMnTuXbt265UdM2VLYv8UJ\nIcTLLDk+mQdWFYj/cz9O7apl2vbCBWjTBm7cgGLFDBfDsmWwd/551p50xbSoqeE6Bvy6fk353cux\nORfAK9WMc3NlTulSdOzelsTchcW5dAneew+GD9fXDAc4+dVudF98yWdum5kyzxovr+z3e/jDn7H/\nYSY7SvbBrFsnnMolc7FkY27f1t/weueO/p/NQ9fwZdxYIkzKs0YzkKEpP3BfU5ozzt251uMTbF/R\nYGPD08PRKo5qNc0oVtKAb/xLpLDnQs7OzowcORIfHx9CQkIoVaqUUWa0/+3UqVNotVoePnz49LHr\n16/TuXNn5s2bx7Bhw/JtRtssO40mTpzI7NmzadWqFZaWljkeRAghxMvl9KxdlLCojEcWSTboZ7NH\njzZskn3nDnz6KezZ445p2tWOeXJg2Cqq/LkAk4MHCk2SDWBiZkKHV4vT4VUIDNTf0FilCvTtoxjX\n8zr1JrYjdXw7+q6BAQPAwUG/eU+PHvqdKf/pwQPYswdCfvSn/+6BNEyNIBobTGPuM2dVaYqWMMOz\nk35L+Tp1wNFR35+DbR9UfCcswx4w8OYD7oW4cuuXw7QJWkHDBb+zq85ETrp340GsCQ8eQKOLP/NZ\n5GiuFqtCVJnaJNesjVWz2lToXhf7mnJz5Yugfv36aLVa5s6dy8yZM7Nsb21tneGM88SJExk/fnyW\nfezfvx93d/dnHnvvvff46quvKF68ePYCN5BsVx356KOPWL16NY0bN8Ymnf1jV69ebfDgMlPYv8UJ\nIcTL7K/KwyjapD7e60Zk2u7uXf0W4VeuQOnShhu/Xz8oX15/U6AhHZ62C5eZb/H4Dz8qd6ph2M6N\nIDIS1n9xnbcWNeSaQ1OKTfiQ2u95o1MatmzRJ+NhYTC5VxDVvR3wO2PNzp36SjHNm0N37we0qRVF\nhRaVn1Y3SU2FDRv01U3KltX/s0WLzONITUrl2KTNlFr0FceKecO8efTrB0WLQkJMAte3X+Te3kB0\npwMpeSOQjYmvsdJqDLVr88xRsyaYGvbHiedaYc+FnJ2dWb58OQ4ODnh5eREcHMzmzZuNOqN99uxZ\nWrZsydatW/H6+2eb33//nWXLlrF9+3b8/PwYMGBAvs1oZyvRXrlyJUOGDMHExAQHB4dnboZUSqHR\naLh+/XqOB8+Lwv7hEkKIl1V0NFRxTiXkairW9plPJ2/qvZHA5JpM3+RhsPF37tTPkJ87l3Xt7pzY\nvx+Gv3aXX7+9ifsAI+0PbyTx9+I5MWY1FX79hgQzS+73H0ult1oQtu4AlzYHUSzyOp3Zzk67ART7\neAyd3nOhRInM+0xJgfXr4bdJJ5n2+GNMv5hBrdHNMr1G6RR+O+L54lsLrlzRz6gPHpx2AyGl9Jvz\nBAb+/zh9GsaEjaOBTTAJTVtR9s2WVOnuhsbUsJVknifZyYUMsRw5t+nW/xLtVq1a0b9/fxwdHXF1\ndWXt2rVGSbSDg4PRarXMnj2bN998E4C4uDg8PT35888/qVKlSr4n2tnaT7JSpUrqtddeUw8eZH+L\nV2PLZuhCCCHy2aJFSvXqlXW7hNgEddvEUV3ZdM5gY8c91ilnZ6X+/NNgXSqllDp9WqnSpZXas8ew\n/ea3J3Gp6pfa09VhGqv3+FZ1LbFbLWizWYXtv64ijoUr38YT1F2NnTpc5lV1ZoG/0qXqsuwzKS5J\n7R+0QoWaOasTtm3Uqa/3Zeu648eV6t1bKRsbpd55R6mrfjezvOb2mUh18N31yr/6UHXDzEVFaUqr\ngxV6qbUzrqmgIKV0WQ/7QinsuZCTk5Pau3evUkqp4OBgVbJkSTV9+nSl1WozvMbCwkJZWlqme3z1\n1VcZXnfjxg3l5OSkFi9e/Mzjp0+fVkWKFFGOjo7K0dFR2draKlNTU+Xo6KhCQ0PT9JPRa5rb1zpb\nV5mbm6u//vorVwMYS2H/cAkhxMuqUSOltm/Pul3AsFXqhG1bg469r9Enamn9HwzaZ3CwUmXLKvXL\nLwbtNl/Fxyv13XdKVaig1Moqn6sTX+5S168kKh8fpVxdlXJxUWrmTKVCQ5V6fOex8u/9H3WoRCvV\nsE6SWrNGqSdPsh4jKS5J7R+4VF0tVlNdKeamfp54Sj16lPV1N28qNWP8IxVpUkadeKWtOjr5D5Wa\nlJKt53XzUKgKGPqjGtXrnipfXv8+9e+v1PLlSoWFZauL51phz4X+mWgrpdSwYcOUra1tpol2bty8\neVNVrlxZzZ07N825lJQUdefOnafHpk2bVNmyZdWdO3dUampqmvYFkmi3adNGfffdd7kawFgK+4dL\nCCFeRpcvK+XoqFRycubtdKk6damEpzo2fYfhxt54RkVpSquoc7cN1mdEhFKVKyv1g2Fz93zz8KFS\nPj7696R7d6WOHUvbRqfTPz56tFKOtolqf+nX1IERq9XDyMdq2zal2rXTzzoPHaqUv79S6eQmz/aX\nqlOnvt6nBna5r2xtlRozRv+5yEpCzBN1YPgqdcG8vrphVln5dp+nYm5k/5d0nU6pq1eVWrxYP1Ne\n1vaJCizRSO1rPEGdWRigkp9k8aF8DhX2XOjfiXZ4eLgqXry4atmypUHHmTZtmtJoNM/MfltZWaXb\n1tfXV1WoUCHDvgydaGdrjfbly5d54403+OSTT+jYsWO6N0OamOTvGilZoy2EEIXPp5/qazjPnZt5\nuzPf+mH1ySic4y4YZLfG1KRULtk2JbrHULxXD8tzfwAx1x+wpsl/iB39KZ9Neb7WAceGxrBroh/v\n/vUqrVrp35datbK+LuFRMqenbsZs7Y9UvXeIc1V7UvK9t7Dp4sWGn01YvRra31lF1xrBVPpsAM7t\nM68qExYGixfrSy16esI7o3R07qQyLbeodIoLK44S+/l3HL1dieDBX/Luu/obIXMiNVnHxZVHub96\nO46ntmOfEMblCu1I6d6TmlNex+4FKGoiuZDhFcjNkFkl0bIFuxBCiNRkHVPsf6CP7wg8PDMvDbG/\nfD/w9sZ7/UiDjO3/xkKsd2/E476/QRL3+HvxBFdux4PK9fA+9a1BN9IxpnuX7nJ+yDfUOrKYc1V6\n4Lh1CdVr5C72O2ciuTRpLeX2rua8SS32DVlHz55gd+cC93yWU/PMeqJKOHG/0wDcP++TaanDxET4\n5Rc49KUfE68M4lq7UdSaPwTbqpmXR4y4pVi8RMOSJeDmBsOGQffukJsKbZEnbnF1wZ9cP3mfMTc/\nwc0NOnWCzp31XwLycQ8Tg5FcyPAKJNGeNm1alkFNnTo1x4PnhXy4hBCicDnpsxeLaeOoEX8603bB\nwdC6cRyXrphibpv3mraRJ25RpKEnsVv349LFNc/9Jccnc9r5NZLNrWlydbVBEndjizp7m4uDfKh9\n+kfOufam8g/jKd/c2WD9B52K49c/LfjtN301kFdfhVe7pmJ9fA+6VatxC93Bp62P0XpUNTp3zjwR\nvrjqONEz/4N7yBbOO3ejxLD+1P6gFWbFMv5ylpgIv/0GK1fCqVOwwuULqoxoTc1BjXL1JSgxEfz9\nYccO2L4d4uPh3YZHaV3rHh5jW1HCNouSK4WE5EKGVyCJtiENHjyY7du3Y29vz7lz59KcX7duHT4+\nPiilsLKy4vvvv6dWOr93yYdLCCEKlwOVB5Jauy4tfn8/03ZjxujL7n31lWHGfbPrQzpaBtD/p855\n7kvpFAervk2xR/fwvLH5ae3owkopWL0a4kaNw61GKtWXjsOxnuG3m/+nkBB90vvbb/D2mfdxqxAL\nnbsQVKUz6zcV5+RJaNdOP/PcubN+B8j03A+6x7lP1lB6z08sNHufom/3o18/aNgw89nlsOupXBs+\nGyf/H1EaE8Javk31zwdQpn7un3dQEFyYvY3Km+ZQOfY0lxxbktSuK9U/6oJ9Lcdc92tskgsZXoEn\n2o8fP+b+/fuUKVPmmXra2RUQEIClpSUDBw5MN9E+fPgwNWvWpFSpUuzcuZNp06Zx5MiRtIHLh0sI\nIQqNRxGP0JWrQPKFK9jVtM+wXUwMVK6sr3FdzgD54JYtMH68vs6yITZ82/3GEsrvWIJT6H7M7czz\n3qERRUTAiBEQHg4/rlR41sn/tQ8RR8O5OnsT1nt/o9Kjc1yo2JGE9q8SVK0ru/aXIHRvMCuKjuBR\nq1ep8lF3yjWpmG4/V4IUP23QsH69vj53v376wzWTHyiUTnF+6WEefPsjHkG/crjcGzycs5ju3cmy\nBnhmHgTf5+LXf2Ky/Q9cb+5mYrVNlH2zJd266de5F6YlJpILGV6B1NFWSqmtW7cqT09PpdFolImJ\niTp58qRSSqnBgwerdevW5egOzOvXryt3d/cs20VHR6ty5cqley4HoQshhDCy/YNXqqMOXbNsN3eu\nUv36GWbMhw/15er27TNMf/7+SrmUjlXhR7Ku51yQdDql1qxRyt5eqSlTlEpMLOiI9O4ERir/PovU\n0dKdVTnLGNW8uVLTJiWpNYP2qv2V31L3NK+oiyXqqH3a6erSpovp1rzW6ZQ6eVKpjz5SqnKZeHXS\nopny7eSjbh3JvFZf3N04tW3WOdW2rVK2tkqNGKHU/v1KpWSvSmCGEh8lqr07k9TYsfrqMxUq6Kuz\n7NihVHxsUt46NwDJhQwvo9c0t691tma0N2/eTM+ePWndujXt2rVj/PjxnDhxgrp16/L5558TEBDA\nrl27sp3c37hxg65du6Y7o/1Pc+fO5cqVKyxZsiTNOfkWJ4QQhccZay0Jw8fQ2KdHhm1SUsDFRb/k\noH79vI85diw8fKhft5tXkZH6mJYvhw4d8t6fsUSdvc2M96Pxv1uTVaugbt2Cjih9T578fw30jh36\n/+7a6jEdby2j+N0wjkZUYmXJsXTtCu3b67dwt7R8to/UZB3n/rOfh4vX4x70G+FWNXmgfY1K73TF\nuV3VDMcOD4c1a2DjRrhzBybX3UZj72LUGqPN01IgpeDSJfjjD9iz9QkbD1fgWunGJLTqjMuYzhnO\n1huT5EKGVyAz2p6enmrw4MFKKaWSk5OVRqN5OqP9+++/qzJlyuQou8/OjPa+ffuUq6urio6OTvd8\nNkMXQghhZCEhSrUrdUQlxCZk2s5v8l9qrNtug4x57JhSDg5K3buX976SkpRq1kypadPy3pex6FJ1\n6uC761WUxl5tabdQJWT+Uhc6V64otXzydXX8lXbqIZbqlLVWbW3uo77se1a18NYpCwulvL2VWjNo\nrzq/4qhKSXx2KjohNkEd/Wyr8q8xTP1oPlJVrarUBx8otXdv5jP6V68qta3XKnXOoqG6p3lF7a/y\ntjoy+Q/1JCbvL+CDkGh1YMwGFeA8QN3V2KmgYu5qh/dXyt8/6zryhiK5kOFl9Jrm9rXO1ox28eLF\n+eOPP2jbti0pKSkULVr06Yy2v78/7dq1IzExMdvJfVYz2mfPnqVHjx7s3LmTKlWqpNvm35VOtFot\nWq022zEIIYQwjBkzICoKFi7MvN3Zkl7EjfiQJnN65mm81KRUdjm+xeMZ8+j1bsbrwbPro4/0M5Xb\ntkE+bwmRLXcvRHGt3Sjs7l8mafGP1HyrQUGHlCdxUXFcWOhLwqYdVAraxQGzlmzusoyyZaHGkR9p\ndeZr7JNvcblsK1K0bXEa1pYKLSo/vV4pOH1a/35t2wZXr0LbttCnYQjena2wcy2d7rgRR8O56vM7\npfb+hlPsWSZ0v0Sb/o506JB2Nj2nUpNSubT6OOf/DMfn+hvcuKG/IbRTJ/0vJPZ5/5imS2a0De9/\nr6mfnx9+fn5PH58+fbrxZrRLly79dB32v2e0V61aleE66oxkNqMdGhqqXFxc1OHDhzPtI5uhCyGE\nMCKdTr9999Gjmbc7v+KoCjNzSjNTmRv+by5WZ0o2U7rUdBb55tCeL4+qahWfqPv389yVUQSM+13d\nMXFQvo0+UU8eZGMf9OfQjctP1IoVSr35plJlyihVqZJSfbrFqXkN16k/y7yt7pg4qJYVg9XIkUpt\n2KDUrVvPXh8ZqdSKFUqt9PhaxVBSnbVsonzbfqEurjmR4eftzvkotXixftfLkiX1u2Z+/73+1xlD\nuHVLqaVLlXr1VX3/Hzn/pnwbfaJOzd2b5S8/OSG5kOFl9Jrm9rXO1lX9+vVTHh4eKjo6WqWkpDxN\ntJ88eaIaNGighg4dmu0B+/Tpo8qUKaOKFCmiypcvr5YvX65++OEH9cPf+9sOGTJE2draKk9PT+Xp\n6akaNGiQfuDy4RJCiAJ34IBSNWqodG9s+6eDFfso3+7z8jxedPB9FaWxV5c3nM5zX8F/XFR3NXbq\nwvozee7L0B4+VKpXL6VGltuqzi07UtDh5BudTqlLl5RauFCplR5z1X2NrQouWkPtrDJaLdD+pnq1\njFK2tvobEwe9lar8B/+oru++8vRLV0Jsgjrx1W7lV3uMCi7qqh5orNWH3sfVN98odeZM+tvH37+v\n1Nq1Sg0YoFRL2zMqpEhV5efxrjo6+Q/1KPJRnp9TUpJSJ1efV/uaT1FnLRurWKzUsdIdlW/3b9Tl\nvTez/H8nM4U9F6pUqZKyt7dXcXFxTx9bunSp0mq1Bh3nwoULql69esrGxkaVKlVKNW3aVAUEBDw9\n7+Pjo9zd3ZWVlZVydnZWc+bMybCvAkm0Q0JCVOnSpZW9vb16++23lUajUb169VLVq1dXjo6O6ubN\n/L9Du7B/uIQQ4mUwbJhSX32VeZtbR8JUtMZGxYTF5nk8P493lL/bqDz38yjykQou6qr2D1ya574M\nLSREKXd3pYYOVSo+vqCjKVipyanq0vpTyrfzHHWsdEcVQyn1ZgV/1bOnUoP6xKuNZceqmybl1W0T\nR3Ww/BvKr+cCdWlj4NNqI7dPR6iNP8arYcOUqlJFqVdeUapHD30if2VXSJpfRZ6O1/4rdcpa+/d6\n8pZqS5/16vTprL9QZseDkGh1aNyvyr/GcPWaw0FVtqxSb7+t1Pr1SkVF5ayvwp4LVapUSdnZ2akv\nv/zy6WPGSLRjYmJUSEiI0ul0SqfTqQULFigHB4en5318fNTp06dVamqqCgoKUpUqVVIbNmxIty9D\nJ9rZrqMdHh7OtGnT2LlzJ1FRUdjZ2dGhQwdmzJhBhQoVcr5mJY9kXZIQQhSsJw8SaOoUwR8XKlO+\nfMbtdnl/QfFHd2lx+ts8jRf0cyC2fdphGnQxy627M6N0isNOfUktbkHzK8vzFJOh+flBnz4waRK8\n+27hqtlcGKQmpXL+nCLgsBkHDkBAAICibo143gifR8nHEegePWKw6VoaN4ZGjfRHw4ZgZwc3b4Kv\nL/jvTWHSuppY6B4SXE5LSjMtDq82ocqr7pgW/f8OlY8jH3FxkR/HzxTh28sdePRIv/a6ZUto3lxf\nRScv75FS+p1S9+yB3bv173+FCvC51WzsvapQdbB3hmvOofDnQs7OzowcORIfHx9CQkIoVaoUy5Yt\nY926dfj6+hplzJSUFBYvXsyyZcs4fTr9XWrHjh2LUooFCxakOVfgG9YUFoX9wyWEEC+6Q2M2UGzd\nCurd351hm7g4cK6YylHfeJxrWeV6LKVgXK3ddGpwl9Yr3sx1PwB+PRbgsPNHnG4eLFRbbW+YHsTY\nRdVZtw7atCnoaJ4PSsGNGxCwX1Fx9mgqXPPDLimSy7ZNCCvvxVXbRuzWteH0GQ3dLPYysuhyUuo2\n4pVOjajyuif3zt/mxkpf1P79lAs7jC5Zx4iWV2jcGJo0gcaN9Qn6/4SE6BNif3/Yvx8+eDidpjYX\nSW7sTZne3lTp7oaJWe7vqE1JgTNn4NH0eVgc20f1qANEFStPRDUtRdtqcfm4B/aO/++/sOdCzs7O\nLFu2jEWLFlGzZk1mzpyZZaJtbW2NJoNvLxMnTmT8+PEZjmdtbU1cXBxly5Zl3759uLi4pGmjlKJu\n3bqMGjWK4cOHpzlfIIl2q1atWLRoETVq1Ehz7sqVK4wcOZJ9+/blePC8KOwfLiGEeNEdL92RpDf6\n47Uo48R30SL9bN3vv+dtrJ9+gjlz4PhxMDXNun1GDh5QXGn3Dq13jKOitnLWF+SD5PhkDjX+APsr\nBzA7fYKqrmYFHdJz7d6lu1xbfZAn+w5jeu0KHZ9sopKTBleneCrHnsY10pcGEZtxTrjEDQs3jjd9\nH9MB/ahbF0pbxHPykjmHD8Phw3DsGDg4QGf3UF4rtgOHV5vg0t0ds+JmKAVhB8MIX+WL8t9P+RsB\nWKfc42ppL871n43bGzWpWxdysYn2UykJKVz5+QxRP/uhO3OWHo9WUa68Bq0WtFro1atw50LOzs4s\nX74cBwcHvLy8CA4OZvPmzUad0Y6Pj2f69Ons2bOHkydPpknap06dytatWzl27BhFiqStq14gibaJ\niQlHjhyhYcOGac6dOHGChg0botPpcjx4XkiiLYQQBef2qQiK13ejaNStDLcq1+mgRg1Ytgy8vXM/\n1uPH+n42bgQvr9z3c+cO1KsHixdD586578eQooOjudHwDVJNi1Ht5E+UqliqoEN64SQnw/nzcOTI\n/w/rm+f5vsh7RNq6EVG6NgdsunHkugM3b4KHB9SpA23tTlPNJZWkau4E/3WDMmvnUDb0MKWTbnK9\nZG1inOuS2LYLZQa2xdUVzMwgKjCSa6sOsO2hN9tPOHDtmv4z17AhNGgAjStHUb5OaTQmuVtvkpqq\nn/H289Mf27ZlnQsZYvlRbtOt/yXarVq1on///jg6OuLq6sratWuNlmiDftbaysqKQ4cOUatWraeP\nL1y4kG+++YaAgADKli2b7rWGTrTz/LU5JCQEy7wWoBRCCPFcuTx5HaZVetA8gyQb9DsCWlnp17Lm\nxRdf6NfE5iXJTknRr30eNKjwJNnBWy9SpGc3Hnq+RvODs55ZGywMp0gRfeJcpw6MGqV/LDrcmZBV\nn2Dx1xHqnP+NN6LHE2dihb/LEPxqTUWjgds7TuJ28TsqJ1zFonhVosrV5WaXkYS1bYfpvTuoI8e5\ncvAuY/7Q70bp4QF165ahbt036FU1hinzEnmiK8axY/qZ8bVrFJ47WnBPd58bdg2Ic2uIhbYBzr0a\nZLoO+59MTfWJe716+vrv2UmiC8uc5PTp06lbty4fffRRpu0sLS0zXDoyadIkJkyYkOVYqamp6HQ6\nzM3//+fTihUr8PHxYf/+/Rkm2caQYaK9cuVKVqxY8fS/R4wYgZXVs+vr4uPjOX/+PK1btzZehEII\nIQoVpVOU27uK+DmLMm03axZ8/HHeZtSuXIGlSyGD/c2ybdIk/U/406blrR9D2bE5ieqvv0r4oMlo\nl75V0OG8dGwrWGD7WQf4rAOg/0zH+oVgczyOknfhxAlYe3UodmWGUtczlYYJ/lS+c4SSZy+zNqgZ\nm260wNa2BR4e8Ko3VKkCJWPDuZXiQEBAUWI/W0rVO1OJLFGDEuU9aVbTg45N3bGadZDkx/Gk/nYc\n9h/DdP48kqdfpErFMOo1MqN+ffD0hNq1jbfJTUFxcXGhd+/ezJ8//5lZ5n97/Phxjvv+66+/sLOz\nw8PDg7i4OD777DOqV6/+dNPDdevWMWnSJHx9fXFycsrtU8iVDBNtjUaD6T8WwpmYmGDyry2zXnnl\nFUaPHs0nn3xivAiFEEIUKqePJbPPvC8fjmqWYZszi4/S+OoVXn99QK7HUQp+6fMbE8d1o0yZtGsp\ns2vLFtiwAU6ezNv6bkNQSr/W/Ntvi/L77tM0a2VRsAEJADQmGiq1cqFSK+j492M6nf6L3okTpiRu\nfEjVqztweXSGqkX2MqJMXWKc6nDdqSs3cWXXLhj952i6xv3FzWIu3HXw4HCLiTyxtCOBErxy7SSm\nfluY9PkotpbojYdHeTwavobHEKjpqvi5qI6LQfp7ELZvh8BAcCpyi6W6ITx2qU2R+rWx8apJUZsS\nPAq6TdzlcA6U71Ogr1luTJkyhTVr1mQ4Y51bMTExvPfee9y8eRNLS0u0Wi1bt259en7y5MlER0fT\noMH/d1UdMGAAixZlPllgCNlao63Vavn+++9xdXU1ekDZJWu0hRCiYIwZA7a2mc8OH7PvTEK77niv\nTXtXf3YdnbKN0rPHUf7+WYpa5u6Osoij4QR5D6X4X9tp0rxgbzJMSIDhw/Xrhbds0ZdxE8+XlIQU\nQrZfImrXaVKOn2ZbSgeWhrWnVCn90hT3GimUSQ6jfPghSoWcwSr0HEOKriU4tjTVq4OrK5QrB8WK\ngcXta1yOr8i5y0WYeuY1PE0CCbNy546tK7dtXQk1cSYpKoaWYauwS71DWSJw4A57ac0PFuNIrtuI\nPQElJBcysEJV3u/+/fu88krua5nmhSTaQgiR/5KS9InC0aNQOYOiHZc3BlKqXydsH4RQrGSxXI2T\nEJPAndLu3J32H+pPap+rPlISUrjg0IoHjTui3TUxV30YyqNH8OqrYG0Nq1eDhUxkvzB0Orh+HU6f\n/v8x1Lcf2sRd3LCuw0OXOiiPWsS51OKunSuBZ3QEHnjM4ovNqKi7wU3Kcwd7zmjq8rC4PfeLlaVe\n6jHcEk4xnCVcM/egWhUdHnWL4FIpGcvEaJJUEYLuvcL3P5hILmRgBZJoL1myhNjYWD7++GMAzp07\nRyUfBKwAACAASURBVIcOHYiMjKROnTps374dR0fHHA+eF5JoCyFE/tu8GebN09cQzsjBSn1J9qiH\ndtu4XI/j2/ZLzM8fo1Hk5lz34aedRsmzB/CM2p2n2sZ5FX31PnM67uN+qzf4/vuCX74i8kfEqduc\nWHqah/vPYB1+liqPA+mvVhPNK9Q0vUxFm0dUqKihYnkdpYs/osjtcFT4TcZZL+fKFf2XsWrV9F9s\nrUsk4h7+JzeKVOXMIxd8jrWgWvIFrIiTXMjACiTRrlWrFsOGDeO9994DoG3btkRGRjJ8+HAWLFhA\ny5YtWbp0aY4HzwtJtIUQIv+9+ip06QJDh6Z/PnRvMBZtm1DsZghWZXO3QU3E0XCKN/Hk8b7jua51\nfWa+P2U+7AMnT+HgWSZXfRhC5IlbxDVrR7hnV7SHZ8lOjy+wB9eiCV57hLg9hyh14RCfJ4zjcuVO\n1K8P7u7g5qbfSfLRI/3NvWfP6tdiBwbCXw8boKxK8dC5Fqa1PbBt7kbxujUJf2DJlStw68xdOm0a\nQukHVyibdIO7ZmW4bVmVhjF7JBcyMI1GQ+nSivLlwf2VSIZGzCCyXhf6rOlivPJ+oaGhT9dnx8TE\n4O/vz++//07nzp2xs7PLVqkVIYQQz7cbV5I4EFCEtWszzhZPTvwFW6+RaHOZZAMcHLKC0s3eQZvL\nJDv6xkNKfzSAsGkraVCASXbovmto2rflZuvhtNwpf0++SJSCoCA4dAj48UdaHPXBPikcU5uG4NaU\n1I/Gs2xAU2wqpX99/frP9nXn1GbCt5+Fw2cx8duH6YYFOD65QnenKFxqWeDuXpqQb7Zi7g7/Ze++\no6K43j+OvwGlKIodVFQsqNgLdkXsxhhrjCUae43GFkuMxq7RNKOJvfee2LEDNsReERvSq0hRkLbz\n+2N+X5WAugssoD6vcziRnZk7d5OT9cPlzvNoSiWiufQEznjCzOOZ8XY/OTdvgp8fhHgYoxyoQnRC\n2rbAgZYr2nny5GHfvn00b96cgwcP0qVLFyIiIsiVKxeurq60bt2aly9fpnkSaSEr2kIIkbmc7b8n\n2rwoXzinXgc3IACqVFa4fzeRQmmsEnL6NPTrq+BxK5FcFrqPoSjQsYNCyzwX+W5r/TTNISPc33OL\nPF+15UGPn3DYMjTL5iEyjve9WA6fNsPJCc6ehbx5oWFD+Lz0XWpVjqNc56rkMM24B24T45J47G3E\n7dsk+wp5/Bw36hFauDIN/XZJFspgWdKwply5chw8eJDmzZuzY8cOGjZs+KoIeGBgIAUKFND5xkII\nIT4cz4OeU+3qOmJcr7z1nN9/h2/6GqQ5ZCcmqhVNfvvdIE0hG+CvvyAwyIBhe7IuZF84m0S+7r3w\nGvk7Dn92z7J5iPSJi4rj9rIzRO88TInbR7hhUBO37lvp0QOWLYPXPU8q6eX+OUyMKF9e3afdpcsb\n84oxw/vwNjSnb8PSXXq5t8g4Wq1ob926lT59+pAvXz6ePXvGrl276Nq1KwDDhg3jyZMnODk56X2y\nb5IVbSGEyDyuPZdh7HKM+gH/pHo8PFxt2nHjRtrL1i1erJa9O3EibU1url+HVq3gwgV1Llnh+HHo\n1Qs2r4yhTee3d80U2dOTJ+CyPZCKi4ZSMdgFH/PKPK37GUX6fkbFXrWy9KHa1EgWynhZsqLdq1cv\nSpYsiZubG3Xr1sXBweHVsSJFitChQwedbyyEEOLDoEnUUHzvYqIXLHvrOX/9pT4omdaQHRwMs2eD\ns3PaQvaLF2qL9T//zLqQvWeP2uJ7715o0kRC9odAUcDNTf1vd/gwhIXB560KYtutJ0nfraOqbdaU\nMNZW/vz5M7z5y6cuf/78GTqeVivaiqJku/+Q8lOcEEJkjstzj5JnzkTKv7iOgWHKvwtevIDSpeHM\nGahQIW33GN4zgtzF8/Hrr2m7fkzPYCJNLVm3Lm3Xp9fatTB1qtrVr2bNrJmD0I6iUbi/8zqBf2xn\nfMB4YsyL0L27Wk2nVi0wzF6L1noVGal2v/T0fP1V3P0f5nj35rlhXoLMyxFVpBxJNuVIauJI/vaN\n1HbzeVMf72Wsgp+/AT4+4Ov7+qvi+bW0f/A7ReJ8yUkCwTmteWZWnOMl+nOviAP544MxMUrCq2hD\nnj+HsFAN/j4agsMMaWV0ikWJIwnLUZTQHFaEGFgRqFhh8+IO+QjH1DCRnKZG5MyXi6SCllxpN408\n5SyxsoLCBTUYR4dh4OtD7D1v4h/6ovj64htvxdLcE/D3h6Ag9f0ULw6O5pf5Mmw5SVbFMbQuhmnZ\n4uSpUIyC9qWxrFhAf+X9SpQoweDBgxk0aBDFXm9KylIStIUQInPMqr2PRvWTaPF3l1SPn+i+ijte\nuRjt/nWaxr++2BWz8cMpFnaLPBa6p5xz327FYs3v2IRewjxP5i8KbRl7mR//sefYMXU/rcieHh++\nh8/C7ZS8sJ0cmnge1+lB4bljqORYRMou/ocmUUPw9UCCzj7k+bUHJHk+5FZSJVbHf8PDh2qNb1tb\n9bdHjXNdpZLhPfJWL41VwzIUqlQk1R/I/yfaP4rQ6/5E3PHnSVIJPDQV8PMDf39e/XNy2Pd0M9hF\neC5ronMX5YVpQV6a5sXHojrxhiYUin7CC5P87MrdnwDfJEJCDYiKMcLCOJbmxmcZ9fJXQo0sCaUI\ngRpL/OKL0IYjGBspGOcywjSfCUYFC6AULsyTz0dilD8vGg0YBvlT+OpRjAN9yBHij1m4P3mjA9hr\n2JUpMT/pL2j369ePnTt3kpCQQPv27Rk2bBht2qStU1dGkaAthBD65+kJDg7g7Q2mpimPxz+PJyxf\nWSLX/YNdH/uUJ7xHQkwC3gVqEDpqFg1+6arz9d6nHpG7ZX2ebj1GhR6Zu5SsaBRcms2ghNtOTG5d\nwbq8bBfJbp48gR07IM+i2XQJWYZn9e4U/LYHlfvXfWcYFG+nKOoq8MOH8OABGDgdoYLbBizCH2MV\n8xhTJZYAk9IcsJuET9M+lC6tdpEtU0b9zVcuLf43iYuKI+R6AM9u+/P8QQAJXv4o/gG45uvA6cQm\nBASogRzUlejRSb9RLfEqsRZFeZmrAImKIYqBIfFGZpjHhJI3wodbBlVZxghCnxoQHp0TY8NE8hk9\np6nJefq9XMlTg0KEKIUJSCxMmEFh2uCEJqcpprmN8K3Qku/O99JvC/aIiAg2btzIihUr8PDwoHTp\n0gwePJiBAwdSuHBhnW+cXhK0hRBC/0aOVNuGz5mT+vEz/deSe/82aj1NWz1f589/Ibf7KeyDD+sc\nfOKfx/PQshGhbfvQdM93abp/WikaBecm0yh+dT/5L5+gcOUimXp/8XaRkbB1K2zapAbBrl3h6/aR\nNGxtjpGxtOXUtyi/KALPe+H1LB93X5Ti8WN4/FhtU//kCcw2nE47DhOVvxQvrUphUKoUphVKkbtZ\nXYrbFyVfPu2e01AUtflPQABEuV4n/uotEn0CMQgKJGdYILmiAvkz94/sjmpNUhIULap+WVlBx2fr\nsdIEEF/AioScphjFPMdIk4DJyyiMIsIwehrKZexZwwDCnxkSHmNCXEIO/QbtN505c4YVK1awZ88e\nFEWhY8eODBs2jGbNmuk8gbSSoC2EEPoVEaGuQN2+ra4a/VdSfBLe5pWJ/HkZNcfp/vkfcNEXkwY1\neX7cjVItdH+C0bnOBMx8PakbsC9TVycVjYJL4x8peu0QBa+eoJBd5i82ieQUjcLdDZe4s8yFoQ8m\n0LIlDBgALVtCzrRVihR6oNFAyN0wwtweEnXLm/gH3hj4emMW4sN6s2FsDv8cgFKloGRJ9Z9NY45Q\n3DSM3OWtKVDNmiK1rDErYKbTfZ8/V1fhAwPVr1xOezG/647R02BMI4Mxfx5E/rggBhisxz1faywt\n1UD+v39WzPmIoQvLZV7QTkpKYt++fSxcuBB3d3fMzMyIjY2ldu3abNy48VUXSX2SoC2EEPr1xx/g\n7g7btqV+/ML3e8iz/BcqR11IU9A9b/0V8baVcTw9XedrT28JwKZfUyzuXKBA+UI6X59WigJHHedT\n2n0Hha6foGCFzLu3SCnSJ5LrE7dgtW8lponReLUcgt26iVhaybaQD1VEhLpV7X9fVkfWUezuCXJH\n+JH/hR+Wif68MDDnx9Lb8LNrRYkSYG2tfhUvDiWN/ClikwuLUvl0/lzSaODpU7UKUlCQ+hUcDEl3\n7jFpnZ3+g7aPjw+rVq1i7dq1BAUF0apVK0aMGEG7du04ffo0Y8eOxczMjEuXLuk8EV1J0BZCCP1J\nStBQobzC5m1G1E+l94uiwPqiP1BpYAPqzdW9xOvhw7B42F3+vVkG03ypbP5+h8BAtTrEjk3xOLQ0\n1vneaaUoMGkSeB64z7r9BSmQzUu/fawURf0B8OngyTS6tZy7xVth8t1Qaoxrnu3qXIuMp2gUnnqG\n4f8sF95hufHzUx+i9PVVt5GMutKXZpH7MCaO0BxFiTArxguLYjg3m4lRFTuKFlWbDdWoAQV1+F84\nrblTq6C9f/9+VqxYwdGjR8mXLx/9+/dn2LBhlC1bNtl5x48fp127diQkJOg8EV1J0BZCCP25OGUf\nMcs30ix8T6rHjx2DsWPh1i3dy6HFxkLlyrB0KbRtq9u1SUnQurX6gOZ03RfC00xRYMIEOHVKbagj\nDZEzX2QkbNkCK1eqe3Nnt3Sh1aiKFK5imdVTE9nQi5AXhN0KJMIjkBcPArhZsBmPoosQGKiulIeH\n6/b5pdeGNZ06daJOnTqsWbOGHj16YGJikup5ZcqU4euv01beSQghRPZhvOxPEnsNeuvx+fNh8uS0\n1RyePx9q19Y9ZP/vWo1GrVmdWRQFxo8HFxcJ2VnByzOeRUuN2bQJWrSAX3+F5s3B0LBpVk9NZGO5\ni+Qmd4tyr57/aPjGMUVRP4MOHdDwRUf9/hZEqxXtK1euULt2bb1ORFeyoi2EEPpxf/dN8nT/jIKR\nXhibp9ya4eamdmF88ED3B83u34eGDdVW7ak9YPkuZ87AV1/BlSvqr34zg6JRGDvOgLNn1fbqGdw0\nTrzD7TUXiZrxG0pQCPvHOTNqlLoPV4iMcGzuJfL/OoU6z7SrmJTW3KlVjE8tZN+5c4c9e/YQEBCg\n802FEEJkX0E/LsGz2fBUQzaoq8oTJugeshUFvv0WpkzRPWSH3w9ja+ddrFmTuSHbteZo8u/fwIkT\nErIzQ1J8Em6T/uFm3sbkG9qdhDqNqOZ9gAULJGSLjNV8fE0snz/i5soLer2PViva3377LUlJSSxf\nvhyAvXv38tVXX6HRaMibNy/Hjx+nTp06ep3of8mKthBCZLynnmEY2dmSeNuTQpVS1oa+fUuhZSsD\nvLzATLcKW5wfu5M7W27Qz3+uTiFd0ShcKtqBmJIVcbz0i243TSNFo+BaYxQFH1+ixJ2jWJTKlyn3\n/VTFxMD69VBpQjsKGTwlavB46s7vQg5TrXa4CpEmLl/9jcnZk9QP2Pvec/W6ou3k5ESDBg1efT99\n+nTat2/P9evXqVu3LjNnztT5xkIIIbKfvUuDOFFzYqohGyC80wCWtD6gc8iO8oui9OJx1Jvxmc4r\n4a5dFpHrRQgNT8/V7cI00iRqOFPtWwo+vkyJu8ckZOtRUJC6375UKXVrjun2DVSOcqPhH19JyBZ6\nZ/93f8oGneXxEU+93UOrFe1cuXLh5OSEg4MDvr6+lCpVigsXLlCvXj0OHjzIgAEDCAkJ0dskUyMr\n2kIIkbESEtQ2yQcOqKWv/stz5w3y92yDqfd98lrn1Wls59rjMIqOoMn9tTpdd3fjZQr3a0fsKTdK\nOpbR6dq00CRqOFv9W/L73KCUh5PO71Nox+dBHD//YcL27ep+/7FjwdY2q2clPkXOzWZiGOiHw71V\n7zxPryvauXLlIjo6GgBXV1fy5MnzaqtI7ty5Xx3TxoABA7C0tKRq1apvPee7777D1taW6tWrc+3a\nNa3HFkIIkXZ796pBO7WQDRD17WQ8Ov+oc/j03HmDytc2Y7dvgU7XRflFkXtgDx6O+TtTQraiwA+D\nQkkIfiohW098Xb1wtRvCczt7LPIqeHqqZR4lZIusUnX5t9x/YkxggH4Wb7UK2jVr1uTvv//m9u3b\n/P3337Rq1QrD/6/p9OTJE4oWLar1Dfv374+Tk9Nbjx8+fJiHDx/y4MEDVq5cyfDhw7UeWwghRNr9\n+SeMHp36sau/nKRIxAMarB+q05iaRA1xg0bg0WuOTq3KFQVmDA/mes1+NPi9m073TAtFge++A5d7\nltR5vFNCdgbzPvmQs+UHkNvRHk3BIlh5ODP/ZwMKS/d6kcUKVijEjcF/s3iJfrqJahW0582bh5ub\nG9WqVePevXtMmzbt1bF//vmHunXran3DJk2akP8dj27v37+fvn37AlCvXj0iIiIIDg7WenwhhBC6\nu3RJ7arWsWPKY5pEDWbTJ+I/ct5bK5G8zYbVCZzM343G699ekzs1a9fCCW9bWrvov2C2oqhbFy5e\nhKNHIa9k7Axz/z7sqjUf81b1SSxWEsNHD3E8O0e6aopsZdw4WLUKoqIyfmytnjSoU6cOPj4+3Lt3\nD1tbWywsLF4dGzJkCOXLl8+wCfn7+1OiRIlX31tbW+Pn54elpXR+EkIIfVnyRyIjR+bAyCjlsd2b\nYgkv0Jmhv+m2shwWBpOnm+DkNAZDHZ5ru3NHbYbj6qp7ZRNdKQp8/z2cPas2o3njrzeRDh4eMHeu\n+oPLjF5dyfHPcBzloVKRTZUuDa1aqWF7/PiMHVvrjz5zc3Ps7e1TvN6+ffsMnRCQYrO5gUHqy/kz\nZsx49WdHR0ccHR0zfC5CCPGxC74eyMwdjcm36B6QvCRIXBxMnp2btZunYqBjA7Vx46BnT6hZU/tr\nYmKge3dYsADs7HS7n64UjcKqHic5/bAlJ05APsmB6Xb3LsyeDSdPwpgx6v7rvHkzbjFOCH2ZMAE6\ndIBRo8DYGJydnXF2dk73uFoH7fv37zNnzhwuXLiAv78/1tbWNGjQgGnTplGuXLl0T+R/ihcvjq+v\n76vv/fz8KP6WzgZvBm0hhBBp4zF6OYYVW1O6SMq6e8uXq4FX13WMAwfg3Dm4eVO368aMgerVoX9/\n3a7TlaJRcGk0habXj9D1wQUKFNDz0vlHzu/sEx4MnM+wp/MYMKEgK1dCnjxZPSshtFerlvpZt3N9\nDL2H5EqxgJvWUtZarU84OztTvXp1Dh06RIMGDRgxYgT16tXjwIEDVK1aNUMS//906NCBjRs3AuDm\n5ka+fPlk24gQQujJy4iXVDq7guILvktxLDIS5s2Dn3/Wbcxnz2D4cFizBnLn1v6686N3UHnPLJYv\nh7f8IjNDKBoFF4dpFLt+iELXT1DQWkJ2WoXcDsG5xmhyOdTGwNIS9+vGTJokIVt8mGZ3vkrd7+qh\nSdRk2Jha1dGuXbs2JiYmHDt2DHNz81evR0dH07p1a+Lj47ly5YpWN+zZsycuLi6EhYVhaWnJzJkz\nSUhIAGDoUPVp9pEjR+Lk5ETu3LlZt24dtWrVSjlxqaMthBDp5tzxd8zcXakX+G+KY1OmQGAgrFun\n25j7q0/jRuVeTNuq/d6PJ8cfkLtNI8I2OWH3dcrP/Ix0uukMrC/uJv+10zpVQhGvRfpEcvXr36h+\n7m9uVeuN3eYfKVIl9SZHQnwoFI2Cp3ktoifOoc6Mz5MdS2vu1Cpom5mZsX37djqm8jj6v//+S48e\nPXj58qXON08PCdpCCJE+UX5RxJW0JWLPSWw7V0l2LPBqIL2b+bP+tj1vPJ/+Xu4zDmM1dyQFfG9i\nbmX+/guAFyEvCChZn8Au3+KwdZgub0FnTu0WY3tyOXmvnKZwFfltqa5iY+Hvv8Fp7hVmFFyCzfoZ\nWDe2yeppCZFhzo/aRq5Ny6kR4ZLsdb02rClevDjx8fGpHouPj8fa2lrnGwshhMhaa359xvFaE1OE\nbIAHPX9imt0unUJ2pHcE1nOG8vTn1VqHbEWjcL3eUIKL16LJZt1qdOtq3jz45X5H8l4+JSFbRwkJ\nsHKl2ljm/HlYfK42jR+ul5AtPjp1f+lGoefe3F7tliHjabWivWrVKhYtWsSxY8eSPZjo5+dH69at\nGT9+PAMHDsyQCWlLVrSFECLtQkOhYkW4fFktbfWmh/vvYtHJEePHnljYvL3vwX+dKT8QxdgEh9tL\ntb7mRJ8NlNj9OyV8L5CrUC6tr9PVggXqFpjTp0GHHmufPEWjsHdLLD/MzkWJEuoPK/XqZfWshNAv\nly+XYHLBmfr+e169ltbc+daqI3369HlVVk9RFKKioihbtiz169fH0tKSoKAg3NzcsLS0xMXFJdOD\nthBCiLSbN08tvfffkA3wdMhk/L6YjKMOIfvSrCPYeJ0in7f2ZUbc3GDIkc6cPtZMryH7l1/UBzOd\nnSVk6+LG0nMYTRxPWJ62LN00g5Yts3pGQmQO+6UDWFY6jAKeCuUrpO/J7LeuaNvY2CSrX/2uFG9g\nYICXl1e6JqIrWdEWQoi08fFRa1vfuQNWVsmPXV9yhkJj+1A43BOTvCZajRcZCSPLOTFmsim1xztq\ndU1ICNjbq/t9v/hCxzegg4UL1SYUzs7wlkqx4j+8Tz4k4JvJlAx258mguTT462sMc+hYRF2ID9z0\n6RAUBCtWqN/r9WHI7EiCthBCpM3AgWBpqa5qv0lRwC1/WzQ9e9NoWW+txxs0CHLkUGtuayMxEdq0\ngfr11e6B+uLcbiHn3XPQ98Y4CdlaeBqmcKPNRKpfW8etVuOpt20MZlJfXHyiQkOhQgW1CZOVlZ4f\nhhRCCPFxeHjKB/d//JkwIeWxPXtgUoltNFjSS+vxjh5VW5cvXKj9HKZNA0NDmDVL+2t05dxuITYn\nVtHfqbuE7PeIi4PffoOKdgY8KVgbza27OB79QUK2+KQVLqxur1uyJH3jaLWi7ePj896BSpYsmb6Z\n6EhWtIUQQncXrLsRV9UexyOTkr2ekACVK6tbOVq10m6syEioWlXd/6ztNS6/XWbwosqcu2pGYT2V\nsP5fyDY570xRe0nZb6MosGsXTJ4MVapkTtt7IT4kjx6pD/96eUHevBn8MOSbbGxsUn39f2HXwMCA\npKQknW8uhBAi83hsvoJN4Hksrm9IcWzVKrCx0T4wA0yYAG3ban/Nk+MPqDShHXvWOVG4sH6a0kjI\n1s7VbZ58u7gCcXGwejU0b57VMxIi+ylbFlo0V9jyW3Cax9AqaK9duzbFa0+fPuXQoUN4eXkxderU\nNE9ACCFE5ngxZgqhX03F4T8VPqKjYfZsOHxY+7Euzz9O4d0PmfRkuHb3DnlBfIeu+HSfiUNf/YTs\nP2Y/p6aLs4Tsd/A/741Pj4mUDLjAd0tu0n1oPgxlE6kQbzWt6100ffqm+fp0PwzZu3dvbGxsmDNn\nTnqG0ZlsHRFCCO1d+8OZAhMHUvSZB8bmxsmOzZgBDx/C5s3ajRXlF0WUTVWCZq7E/sc27z1f0Sic\nK/cNGBjQ6MEGDAzTVy4rNVJd5N1ehLzg0pcLqHb2b246jKLu7ol6LakoxMdkw6p4+g0xyZqqI05O\nTvTv35/AwMD0DKMzCdpCCKEdRYEbFk140XsYjZZ+nexY4CU/PBoOpMy9w9iUNdJqPNdKwzBISqSJ\n52qtznfpsRSrfSv01pRGQvbbKYraLr36jE54WTeh9I4FFKunQ7tPIQSgh4Y12goNDeXly5fpHUYI\nIYSe7N8Pq4quZf/issleVzQKPh2+xbBRA61D9tWFJyh7/zDmj29pdb7bBYVH++5gc3CPhOxM5u4O\no0eD8ctyLFmynUbDG2X1lIT45GgVtF1dXVO8Fh8fz61bt5g/fz5NmjTJ8IkJIYRIv6Qk+PFHmP+r\nLYb/+cR3m7CHIuEPsN6/U6uxwh88pciUgQTOWIl9SYv3nh8aCl91N+CvHX9TqkVaZv9u24eeZtVJ\nR5xdDCRkvyEgAH74QS27OHcufPONBYaGErKFyApabR0xfMeTEk2bNmXz5s0Uz+RPOdk6IoQQ77dp\nEyxbBufOwRvNfonwesbLcpUJXbqbqkMbvnccRYF+bQJpr+yn2/Gh7z0/Lg5atoSmTUEfj/A4f7YA\nm5OrMb7mTrHK2reK/5jFhseydk4AP20oy5AhMGUK5MmT1bMS4uOg186Qzs7OKV4zNTWlVKlSFC1a\nVOebZgQJ2kII8W7x8VCxIqxfDw4OyY+5VhiMYmJC05t/aTXWokWwdSucPQvGxu8+V1Ggf3+1msmu\nXWRoVQtFo+DSYhYlz2/D7NxJqS6C+u/EbdJerBd9z+XSX1HdaQFlymT1rIT4uOh1j7ajo6POAwsh\nhMhaq1apLYT/G7JPn4Z/Qx2YfbOjVuNcuqS2a7948f0hG+CX+YncupUDV1c9hOyGP1D8+iHyXHGh\ncBXLjBv8A/Vw3x2i+n9HoZgQwn5eQ+fxUhBbiOxEq4/A0NBQvL29X32vKArLly9n1KhRHDhwQG+T\nE0IIkTYvQl5gMWEI82YlJns9NhaGDIEW6/uQ1zrve8eJjITu3WHpUihd+v33vfjDv9jP6sD+/ZA7\nd1pnn5KiwH6HX7C8eZwCN05/8iE7IgIONZiDRedmRLfoTOmIa9SUkC1EtqNV0B4wYAALFix49f2c\nOXMYMWIEW7dupWPHjmzfvl1vExRCCKG7S30WU6ZQJDXrJP/F5axZUKsWdOjw/jEUjcLggRo++wy+\n/PL959/bdo2yCwZjtXJWhj6cqNHA8OGwKrYPxTxOUrBCoYwb/AOTlKR2cqxYEW5btsDw7h2a7hpJ\nDtN0FxETQuiBVnu0ixUrxuLFi/nyyy9RFAVra2v69evH3Llz+e6777h48SIXL17MjPm+Inu0hRAi\ndc8ehaOxLU/UkfOUblP+1evXr0Pr1nDrFlhqsSDs2ms5fsc96OL7J6am7z43+Hogifb18Bn9Ow1+\n0yKVaykxEQYOhCdP4ODBT/vhvgsXYNQoMDGBJUvUH5iEEJkjrblTqxXt8PBwrKysALh9+zaBot2H\n3wAAIABJREFUgYH069cPgI4dO3Lv3j2dbyyEEEI/bnaZwZ0KXZKF7MREGDQIFizQLmR77rxBpe3T\naLD52/eG7NjwWMIad+SB45AMDdkJCfD112q5uiNHPt2QHXwjiAG94+nWDcaOVR9IlZAtxIdBq6Bd\nsGBBfH19ATh9+jTFihXD1tYWgISEBDQajf5mKIQQQmu3Vl6g4u1dVD34c7LXnXsso23CAf5/jeSd\nngc9x7j3V3gOW5QsrKdGo4GNrTcTUbg8TY/9mI6ZJxcXHc9XX2p48QIOHIBcn2C38Pjn8Ti3/5Uc\nNatQV7mIh4f6g4dBxnewF0LoiVabulq2bMnMmTN5+vQpv/76K506dXp1zNPTk1KlSultgkIIIbQT\nFwd7p9+g1eglNCxb4NXrPs6Pqbl3GrbH3d4b0hSNwvWGw1FsGtPkP+3aUzNzJhzPOYhTN/thYJgx\nCTA2PJbbFbrQqlQ3Bp0foFWlk4/N5blHKTBrNLktyhJ99ALDWtlm9ZSEEGmg1R7toKAg+vTpg5ub\nG3Xq1GHHjh0ULlwYgDp16lC7dm2WL1+u98m+SfZoCyFEctOnq/uw//339aqnolG4WrgN0fVa4Hh4\n0nvHODl6P6VW/EBRH3dyF3l32ZBt29QOhBcvarcdRRsvQl7gWbEDsXmtqHdvwyf3kN+T288Jat2H\noqG3CP5hEXVntc/qKQkh0HPDmneJjIzEzMwM40xecpCgLYQQr92+Dc2aqUH7zYof54ZupOCmPyj3\n1J0cZjnfOcbdu9DcIRGXXSFUaFbsnee6uamVS06ehKpVM+IdQJRfFE8qtSPSqgINb6/EyNgoYwb+\nAMTGqvvn/1qisK7ZRlqt7o5pvvdsjhdCZBq9Pgz5LhYWFpkesoUQQryWlKQ+6Dh3bvKQHXonhPKr\nJqCsXP3ekB0To9bLnrsgx3tDto8PdOkCa9dmXMgOf/AU34otiShZjUZ3V30yIVtR4J9/oFIl8PCA\na9cN+GJ3XwnZQnwkMrBnlxBCiKywZAmYmqph+03zfojmTIsZ2PWu/d4xxoyBatVgwIB3nxcdEI1n\ntS+ZOiKc9hm0q8HXF9p/ruBVpztNbv6NYY5P46+m+1eiadMGpk6FNWtgxw4oUSKrZyWEyEifxqeZ\nEEJ8pHxdvbjw0xFWrUre7vzIEdh/pyxt9w1/7xjbtoGzMyxf/u6KFgkxCXjU7ImJVX6GT8mf/skD\n9+5B48bQZUgh2p8en2EPVGZn0QHRuNSdgEndanzROo7r16G5NHUU4qMkQVsIIT5QikYhpPMQhje6\nie0bRSmeP1c7Ka5Y8f6yeA8P32fWyBB27Hh3nWpNooaLVQdioGhocHVphgTiy5fVfeUzZ8L336d7\nuGxP0SicG7GFFyUqYvgsjFw33Bj1vQk5372rRwjxAXtr0N6/fz8RERGZORchhBA6ODdkA7lin9L4\nn/HJXh87Vg2wLVu++/qnnmHk7PgZK3qcpmbNt5+naBTO1B1P3tDHVL67m5y50p8MT5yAdu3UHwa0\nqe39ofPY68HN/A4UWP87oct20+TBOgpXyaBSLUKIbOutQbtTp07cv39fPcnQEHd39wy5oZOTExUr\nVsTW1pYFCxakOB4WFkbbtm2pUaMGVapUYf369RlyXyGE+JiE3g6mwtqJGKxZk6wE3ubNcOYMLF78\n7uvjouPxrdsVL/uvcPi7+zvP3TrEmaIeJyl54wC5CqW/c8yF8bu53+F7du9WK5d8zMLDYcQIGDJY\nIbLDN5SPcKfqkAZZPS0hRCZ5a9DOkydPhq9oJyUlMXLkSJycnLh79y7btm3Dw8Mj2Tl//fUXNWvW\n5Pr16zg7OzN+/HgSExMzdB5CCPGhe/jZKO7UG0DFnq+Xoh8d9CBh8HB27nz3NhBFo+BeexgvcxfA\n4czcd95n5UqYdqoZeW5dIF/p9O/Ldv16BTaLRtNiXW8cHNI9XLaVlKTuebezU/fO73tQCYdNgz+Z\naipCCNVbOwHUrl2bYcOG4fD/n4SzZ89+1aQmNWvXrn3vzdzd3SlXrhw2NjYA9OjRg3379mFnZ/fq\nnKJFi3Lz5k0AoqKiKFiwIDlyfFoNC4QQ4l0ObXyKRXgE9W5Mf/Xai5AXaL7sRrnuY6hW7d3Xu3zx\nK1Z+17B+fOadFT5271b3T7u4QNFy725e8z6KRsGl9VxKu6wj/rgrFZqXTdd42dl510RGjsmBuTkc\nOwbVq2f1jIQQWeWtCXbp0qWMGzcOFxcXQA3JqdXLVhQFg/f19P1//v7+lHijdpG1tTUXL15Mds7g\nwYNp3rw5xYoVIzo6mp07d2o1thBCfAoiImDolIJsPXIMs9dd1rnaaCSGxWrSeN3Ad16/fz/cOqOh\n/+n9mFuZv/W8EyfULQ/HjkG5cumbsyZRwxn7sRT1dMb00lksaxRN34DZVPD1QB50nYRXUC6+X7Wc\nnj3fXcVFCPHxe2vQrlixIocPHwbUPdr79++nXr166bqZNoF83rx51KhRA2dnZx49ekSrVq24ceMG\ned71e1AhhPhETJwI7duTbNvF2YHrKOZzESsf93dWA7lxQ621ffDEJIrVffs93C8q9OplwO7dUKNG\n+uabkADDesfwRXA8Ne65YFEqX/oGzIbin8dzvsdiqh7+mcS6g+h89kfMP86fJYQQOtJqT8apU6eo\nVKlSum9WvHhxfH19X33v6+uLtbV1snPOnz/Pjz/+CEDZsmUpXbo0np6e2NvbpxhvxowZr/7s6OiI\no6NjuucohBDZlbOzWh/79u3Xrz3Y70HFdROJ+MeZ3JZvX6EOClIfPFyyBOq+I2Q/OuhBzs59Wbfd\nFQeH9HUnfPECunUDIyNzWj9a9t5Sgx+iy/OPU2DGKHJblCHqyHkc25TP6ikJITKAs7Mzzs7O6R7H\nQNGhcfutW7dwdXUlPDycAgUK4OjoSOXKlbW+WWJiIhUqVODkyZMUK1aMunXrsm3btmR7tMeNG4eF\nhQXTp08nODiY2rVrc/PmTQoUKJBsrLT2nBdCiA9RbKzaufG3315X6nj+HBrVfsn8bldpN6fhW699\n+RIcHaFtW3hjfSIF/ws+0KQxXgPn0nhFn3TNNygIvvgCKleGVav46GpFP34M48aB/Zk/aDWsLHVn\nf/FJNNsR4lOV1typVdBOTEykb9++bNu2LcWxXr16sWHDBoyMtHuS+siRI4wZM4akpCQGDhzIDz/8\nwIoVKwAYOnQoYWFh9O/fHx8fHzQaDT/88AO9evVKOXEJ2kKIT8iaL49wWnFk8x4zABQFvvlGDbDv\nehZd0SgM+zKMSOPCbNv29j3DYR6hRNVogs9nw3D8d0y65nrnjrq9pV8/+Omnj2uf8vPnMH++WlHk\n++/VmuWm6Vv4F0J8APQatKdNm8aCBQuYPn06vXv3xtLSkqCgILZs2cLMmTOZPHkys2bNStPE00qC\nthDiU+E+4zAlZg8hx82rFK5cBIDVq+HPP+HixXd3f3RuMRuDq5epG7APM7PUz4kOiMbXtjnBNdrQ\n7NycdM316i8nufHTHnKsXEqf9C2KZyuKRmHbdgMmTVL3xy9YAP/Z+SiE+IjpNWiXLl2afv36MX36\n9BTHZs2axbp16/Dy8tL55ukhQVsI8SnwcfHCrFl9Av/eS7XhjQD1ocaWLdXGNBUrvv3aC+N2UXLx\neHJcvvjWSh8vX8Jv9ttorHHB4faydG1/ODNgHRXXT8b/9x3UGOOY5nGym3vbrhE37DuWWM6l31oH\nGjfO6hkJITJbWnPn2wuoviEgIIBGjRqleqxBgwb4+/vrfGMhhBDvFhsey4vPunK305RXITvKP5r+\nXSJZtOjdIfvuxsvYLhpB9KZ9bw3ZsbHqfu/bVXvS+GbaQ7aiUXBuMo2Sm+YQfdDlownZYffCcKk0\njIK92xLVoQ8rbjeSkC2E0IlWQbto0aKcPXs21WMXLlygWLFiGTopIYT41CkKXK4/kmeFyuOw+zv1\nNY3C7QaDmWPxC19//fZrAy/5kb9/Jx5NWpWsc+SbYmLUfdRFisCmTWCUI20hOy4qjvNlelPw+gly\n3XCjTLt3pP8PROLLRFy6/YVSqRIYm5Dz4T2abBoiXR2FEDrTKmj37t2buXPnMmvWLB4/fkxsbCyP\nHz9m3rx5zJkzhz4f00Y8IYTIBtYuj8fraV6qua9+tdJ85uvlFAy9R7MTP771utBQ+KvjcTzbjqbe\n/E6pnvP8OXz+ubrHeMMGSGvz3adPoV1bDf65ylHO+xSFK729e/CH4sQJaFg7jsQzF4jce4qm1//M\nkNbzQohPk1Z7tBMSEujbty/bt29Pcaxnz56sX7+enJlcu0n2aAshPlaXLkG7dnD2LFSooL7mseUq\nhfq05cXRc9i0sk31uogIaN5cLeM3b17qY0cHRDO0YxBm1WxZuRK0LBiVwsOH6hw7dYKffwZDrZZt\nsq8HD9QqIrduwa+/QufOH1e1FCFE+uj1Ycj/uX37drI62k2bNtWpjnZGkqAthPgYhYWBvb1aL7tr\nV/W1kJtBvKzdEL+RP9Pwj69Sve7FC2jdGmrXVquRpBYSo/yieFLpM/zLONDm6vw0h+Nz59S5zZwJ\nQ4embYzsIjJCYc5cA9atgwkTYPRoKdcnhEgpU4J2diJBWwjxsUlKUleJq1eHhQvV154/h+V2i6ht\nG02zU9NSve7lS3W/dcmSatm/1AJ0pHcEvpXb8tSmNk2uL8EwR9pS9o6tSYwcbcSmTerK+YcqKT6J\nc4PWYrx9E6t7OzNnniFWVlk9KyFEdiVBWwghPnDTp2lwPWvI8ePqvumEBLUqiHVxhZUrSbUqSEJM\nAiM6+BFVsDRbt6a+FSTC6xkBVVoTatsQh6uL0lRdJCk+iTOOUwm49ZTKZ1dSvXpa3mH2cP1PF0wn\njyHO2Bzjvxdh17t2Vk9JCJHNSdAWQogPmPv0Q4QvXE3NJ/9gaalWHRk8GAIDYd++1B9YTIpP4qJt\nb2KTjGnyeAPGxinPeRoYT0jZBgTbOdL00q9pCtmR3hHcr9OLHAmxlDi/k0J2H+ZDj76uXvj1mkCJ\noMv4jFpIg9+6Sdt0IYRW0po70/isuRBCiIzi4/yY0rMHYLZMDdkAs2fD9evg7Jx6yFY0CueqDSNP\nVDA1Hx1KNWSHhUHLz4wZ0ulPhm9ulKZQ+eigB4ZdOhJj15aGF34jZ67MffA9I0RHq23TvZfcYnDd\n6hS8uQnrAm9pkymEEBnoA39OXAghPmyx4bHEtOvK3S4/UnVoQwDWrUxgwwY4dAjMzVNeo2gUXO3H\nkd//NrYe+zFLJTSGhKgVSNq1g+FbGqcpZJ/+4zoWHRzw6/0DTW8s/uBCdlISrFqlVm7x84OF9zrg\neHJaqv++hBBCH2TriBBCZBFFo3C2wgAME+Jo+HgLBoYGXJ7jhDJrFha3zlG+Qurh2NnhJ6wuH8Dq\nzqlUazwHBUGLFq8rg+hapk6jgTlzYO2KBA4suEvV3h/ehuxjThq+n2hI/vxqBRd7+6yekRDiQ6bX\nFuwNGjRg48aNxMXF6XwDIYQQqTs87jhWvpeo4b4KA0MDPLZcpdRP32C65Ne3huxffoFDDytQ8NLR\nVEP2g3tJNGoEPXvCrFm6h+zoaDWgOznBhcs5P7iQ/XD/XS4VacelPouZNUvdeiMhWwiRVbQK2iYm\nJvTr149ixYoxduxY7t27p+95CSHER83FBfpvaYWBiwu5i+TG7+wT8n3zBY8mrHi1heS/li1Tv0a7\nf03hykVSHL+95iJJVaszbdwLpk7VfU4PH0L9+lC4MJw+DUWL6j5GVgm9E4Jr5eFYdHIkplFrJniN\noFMnaTojhMhaWgVtZ2dn7t69S9++fdm4cSOVKlXC0dGR7du3k5CQoO85CiHER+XaNejWDbZtN6Bc\nvYI8exROfIu23O86hfoLOqd6zaZNarfHEyfU1un/5f7TQawGtyfqh5/p921unefkPv8kn9d/ysiR\nsGIFmJjoPESWeBmj4fRnCzCsWgnFxJQcD+7R9J8xGJun8nSoEEJkMq0fhqxYsSK///47/v7+bNiw\ngcTERHr16oW1tTWTJk3i8ePH+pynEEJ8FO7fh88/h+XL1X3UsbGwvO2/+NToSNOd36Z6zYoVMHky\nHDsGZcqkPH6mz0pKzR1M0KqD1J3VXqf5KBoF53YLKTm1D9t+9mb48A9jFVhRYPt2qFjJkEDvBKKP\nXqDp1T/IX7ZAVk9NCCFeSfPDkFevXmXs2LGcOXNGHcjAgM6dO/PXX39hlQntteRhSCHEh8bPDxo3\nhmnTYOBAtSrGV1+pq8ebNykYGqVMuCc//53frrdgiWt1ypZNfkxRwLnZTMqc24Ry+Ag2rWx1mk+E\n1zM8G/YnT5Q/+U7tpVi9Eul5e5nG1RUmTlQb+vz+OzRtmtUzEkJ87PT6MOT/xMTEsGbNGurUqYO9\nvT0hISEsWrQIPz8/li9fzvnz5+nVq5fOkxBCiI9d+IOneFTqwtiBUQwcqIbk8eMhPBzWrSNFyFY0\nCs71JlHq5BrW7C+cImQnJMCgQeDkW5lc187pHLLvrHMnunwtXlrZUDbw7AcRsj3PP6VDB/jmGxg1\nCi5dkpAthMjetFrRvnnzJitWrGDLli3ExMTQsWNHhg8fTvPmzZOdd+DAAb788stMqU4iK9pCiA/F\n86DnPCnXgrDKjjheXICiwNSpcOCAujqbL1/y85PikzhXfTgFfa9T9NoRCtgWTD7ec3UlHGDnztRr\nbb+NosCff0Lsj3No9m0l6i/sks53p39BVwO432s6ZR4cZc+8+wwdbYqpaVbPSgjxKdFrZ8gaNWq8\nqjgyZMgQir7lUfSyZcvSsGHqT8sLIcSnKC4qDs/KnYkpXpWmF35G0SjMGhnC4QuWnDqVMmTHP4/n\nil1vzF88peT9k+QplifZ8ZAQdY931arq3u2cOvSQefYMBgxQt7DsuDU11f3e2UmUXxRXeyyk2vll\naOoMwvzhDUaXloQthPhwaLWivWfPHjp16oSRkVFmzEkrsqIthMjukuKTcC/TAwNFQ53HOzDMaYRr\nrTHg/YSqj/ZR4D/P7cXEwNymx/jCfzk17m7FNF/yUPnwXiJt2+egVy/dG9G4u0P37tChAyxcmL2r\nisTHw5ExR2mwoi/3S7el9KZZFG9QMqunJYT4hOl1j3bXrl2ThezQ0FCdbySEEJ8SRYHV7fZiEvOM\nmh5bMTAy5EzVERR8dJEa1zekCNkREdC6NfhVao29954UIfvOOneoUpmpIyN0akSjaBRWzfCnfXu1\nQ+Kff2bfkK0o6laYSpVg750KROw4RuOH6yVkCyE+WFo/DOns7IyDgwOmpqZYWlpiampK06ZNcXFx\n0ef8hBDigzRlCqyJ/BLb+4fIYZqDc5UGY+F3m5Iex7AolXy/SHAwODpC7drqg5E5ciZP0edGbMFy\n4OeET/6FfmP+s9fkHSK8nnHRugvl/hyJmxt0ycbbsU+dUpvlLFigbonZ4GJD+S+rZfW0hBAiXbTa\nOrJr1y569OhB+fLl+fLLL7G0tCQ4OJhdu3bx8OFDtm3bRrdu3TJjvq/I1hEhRHb166+wdq36oGP+\nfAoXKvQjd7gPth4HMLdK/uSitze0agVffw0//ZR8pTrxZSJnG0+m9I1/iNv+L+W7VtV6DnfWuZN3\nSHceV/6C+q6/YJI3ey5j391wiYUr83E22JbZs9XtLYY61cMSQgj9S2vu1Cpo29nZUa5cOfbt24fh\nG5+ASUlJdOzYkUePHuHh4aHzzdNDgrYQIjtat07dP332LFhZQZ8+UPnOTsadak+uQrmSnfv48D3G\n9I+kxZR6jB6dfJynYQr37TpirHlJGfftWjdi0SRqcO38B5UPLeDR98uzbVWRRwc9CBk2jdKBF7jy\n7Vpa/9ZGpwc7hRAiM+l1j7aXlxcjRoxIFrIBjIyMGD58OF5eXjrfWAghPjZ7trxkyhS1g2ORItCj\nB0RFwffuX6UI2bdWnCf3F82Y0OVRipB98ybUrWfApTZTqe5/WOuQ7eMDo+teIL/rv8SecsuWIdv/\ngg9nyg8gb4emxFevi0XIAz5fLCFbCPFx0ipolytXjpCQkFSPhYWFYWurW6MEIYT42Jzpu5oS/Vty\n5LBCqVLQrZvaVGbvXlLUfD47aD1WwzvhM30tTZYlb/K1e7famn32bPhuc11ymL6/CquiwJYtYG8P\nxb9qRJWnrpR0zF61+0JDYeLIGJTGjUkqUgxjr/s0PTQRs4K53n+xEEJ8oLSqoz137lxGjx6NnZ0d\ndevWffX6xYsXmT59On/99ZfeJiiEENmdc7uFlD2+jKTDx7CyM6BzZ8iVC7ZuBWPj1+clxSdxtvFk\nbK79Q9R+F+q0t3t9LEndo71lCxw9CrVqaXfv8HAYPhxu31avq1kTQIe6f3oWFaVWO/n7b+jVKxc5\nH9/HsZTUwhZCfBq02qPdpEkTHj58SHBwMCVLlsTS0pKgoCB8fX2xtLR8taKtKAoGBga4urrqf+Ky\nR1sIkcUUjYJLg8lY3zhI7rPHsLDJj1vVQfxTZz5/7C1FjjeWMqKiYOZnbvTymErpizuSdXuM9I7g\n5+7XcDNrxs6dULiwdvc/s9mbXj+U4ssvYd48MDPL4DeYDjExsHQp/PILfPYZzJgBNjZZPSshhEgb\nve7RNjIyomLFijg4OGBjY4OZmRmlS5fGwcGBChUqYGhoiKGhIUZGRu9tauPk5ETFihWxtbVlwYIF\nqZ7j7OxMzZo1qVKlCo6Ojjq/KSGE0LekRIUzlYZQ6I4zBW65ksMsJ49Kt8Q4V04W7SqeLGQ/fgwN\nG0JMtfpUCzqeLGQ/OuhBuG1dWiQ6ceyYdiE7NjwWlxqjKdmvGRuWx/LHH9knZMeGx+LSeRHHCvbg\n4kW1bN/69RKyhRCfJq1WtDNKUlISFSpU4MSJExQvXpw6deqwbds27Oxe//o0IiKCRo0acfToUayt\nrQkLC6NQoUIpJy4r2kKILBIXp5bjq+uxgREnuhDk7oPJl+151PAbmp6egYHh660bLi5qybqffoIR\nI5KPc3HKPsr8PBjPAQtpvLqfVvf22HIV4wG9CbaqRqXTS8lXRrsHJfUtLiqOi4NWUX7PfJ5Y1iX/\nohlU+Kp6Vk9LCCEyhF5XtDOKu7s75cqVw8bGhpw5c9KjRw/27duX7JytW7fStWtXrK2tAVIN2UII\nkVWeP4f27dU/j77aF8/1F7Do3AzvgbNwdJmZLGSvWgVffQWbNycP2fHP43GuOxHrhaMIWXNQq5Cd\nFJ+Ec5t5FOrTluAh02jovT1bhOz4eDg1cAthBWwxdXHi2Yb91A/4R0K2EEKgQ9AOCAhg/Pjx2Nvb\nU6ZMGerUqcOECRMICgrS+mb+/v6UKFHi1ffW1tb4+/snO+fBgweEh4fTrFkz7O3t2bRpk9bjCyGE\nPj19qlYEsbGBHTvULRGbfvYnYPEeGi/v8+q8xJeJnK45jjOznTlzBlq2fD3Go0fwdYPH5PDzwvTO\nVSr3r5viPv917x50ahSK4bUrJFy4QsMlPTP+zekoMVGtGV6xIpy7YsqzFbuoG3wQu961s3pqQgiR\nbWhVdeT+/fs0btz41baOcuXKERQUxJ9//snGjRs5e/asViX+DAze/yR8QkICV69e5eTJk8TExNCg\nQQPq168vJQSFEFnK30+hdRsDvvgC5syBiRPh0CE4eKU/5cq9Pi/SO4IHtbuTB1hy5ScsSr0+tm0b\nfPcdTJtWkUajdvG+j8SEBLUl+Z9/wsyZVjQetifLuyYmJanVVGbNghIlYONGaNy4a9ZOSgghsimt\ngvakSZOwsLDA3d0dmzeeaPH29qZVq1ZMnDiRf/75573jFC9eHF9f31ff+/r6vtoi8j8lSpSgUKFC\nmJmZYWZmhoODAzdu3Eg1aM+YMePVnx0dHeXBSSGEXngdvU9YxwEM/vEIg8bmoWtXiI6GCxcgf/7k\n5ykdOvDCrg2N3H57VQP7+XM1YJ87pzazUUvwvdvlyzBwIFhbw5UrULKknt6clhJfJnJu4j6GHe1M\noSKGrFwJzZpl7ZyEEEJfnJ2dcXZ2Tv9AihYsLCyUrVu3pnps69atioWFhTbDKAkJCUqZMmUULy8v\nJS4uTqlevbpy9+7dZOd4eHgoLVq0UBITE5UXL14oVapUUe7cuZNiLC2nLoQQ6eKx9aoSaFhUcf1m\nleL7JFGpUUNRBgxQlLi45Oe5jt6thBoUUly/WZXs9duHnigVKihK//6KEh39/vu9CH2h7G2+RLEq\nkqRs2aIoGk0Gvpk0iH8Rr7j2W6M8yVFWuWbhoDjvDM7yOQkhRGZLa+7U6peQ8fHx5MmTJ9Vj5ubm\nxMfHaxXqc+TIwV9//UWbNm2oVKkS3bt3x87OjhUrVrBixQoAKlasSNu2balWrRr16tVj8ODBVKpU\nSavxhRAiI1384V8Kft0Gr3FLKNS6Fi/KVaNfh3BWr37diCYmBgYNguV7CvN0+wmabBgE/H+N7a6L\nsWxvz4IR3qxdC+bm777ftd9PE1q0GpaPznPzYiy9evHe7SX6EhcVh+vXKwiyKE/ufVt59usaakS4\n0LRbkSybkxBCfGi0Ku/XoEED8ubNy5EjRzB8Y4OgRqOhffv2REREcP78eb1O9L+kvJ8QQl80GnBp\nPpPyZ9cQuWYP0Z4BlP15EA/GL6fBL6/3I9+5o1YVqV1bbc7yvyD91DOMRw79MX8eRO4D2ynVvOw7\n7xfpHcGNNhMp9/AIflOWUnfWF/p8e+/08iWsXg33p2+hj+FmTOdMo+rQhlk2HyGEyA7Smju12qM9\nffp0Pv/8c+zs7OjevTtFixYlKCiInTt38uDBAw4dOqTzjYUQIjuKjIQ+fcA+sByVr7oT+uNmyh/+\ng+C1h2nQrw4AigJr18LkyfDrr9C37+vrr/3hjOWEPsTU6kmNU3swNjd+y51Ux5c9pMpIR6j4BeZe\nt6lbwkKP7+7tYmJgxQq1k6O9PUw70os6db/OkrkIIcTHQuuGNU5OTkydOpVr1669arXUQUv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lZ6JvbDIimWcYkd36/HpYwzkZGWhHvIEPjXv/63a+KlU5fY8uJ4/H75hgSnclx+50Pqv930nndV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\n5HZjFxUVRWhoKGFhY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"text": [ "" ] } ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Dissipative cavity: steady state instead of the ground state" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# average number thermal photons in the bath coupling to the resonator\n", "n_th = 0.25\n", "\n", "c_ops = [sqrt(kappa * (n_th + 1)) * a, sqrt(kappa * n_th) * a.dag()]\n", "#c_ops = [sqrt(kappa) * a, sqrt(gamma) * Jm]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 18 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Find the ground state as a function of cavity-spin interaction strength" ] }, { "cell_type": "code", "collapsed": false, "input": [ "g_vec = np.linspace(0.01, 1.0, 20)\n", "\n", "# Ground state for the Hamiltonian: H = H0 + g * H1\n", "rho_ss_list = [steadystate(H0 + g * H1, c_ops) for g in g_vec]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 19 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Cavity ground state occupation probability" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# calculate the expectation value of the number of photons in the cavity\n", "n_ss_vec = expect(a.dag() * a, rho_ss_list)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 20 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = plt.subplots(1, 1, sharex=True, figsize=(8,4))\n", "\n", "axes.plot(g_vec, n_gnd_vec,'b', linewidth=2, label=\"cavity groundstate\")\n", "axes.plot(g_vec, n_ss_vec, 'r', linewidth=2, label=\"cavity steadystate\")\n", "axes.set_ylim(0, max(n_ss_vec))\n", "axes.set_ylabel(\"Cavity occ. prob.\", fontsize=16)\n", "axes.set_xlabel(\"interaction strength\", fontsize=16)\n", "axes.legend(loc=0)\n", "\n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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z4eXlhQsXLuR4/vz58/Dy8tK4+CUREREVg8REoHdvGWxsbIBffsk32Hz7rexn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\npJxWVqXK/3wVK8qQkl+AsbbmhHilhEol5zjctQv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"text": [ "" ] } ], "prompt_number": 21 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Cavity Wigner function and Fock distribution as a function of coupling strength" ] }, { "cell_type": "code", "collapsed": false, "input": [ "rho_ss_sublist = rho_ss_list[::4]\n", "\n", "xvec = np.linspace(-6,6,200)\n", "\n", "fig_grid = (3, len(rho_ss_sublist))\n", "fig = plt.figure(figsize=(3*len(rho_ss_sublist),9))\n", "\n", "for idx, rho_ss in enumerate(rho_ss_sublist):\n", "\n", " # trace out the cavity density matrix\n", " rho_ss_cavity = ptrace(rho_ss, 0)\n", " \n", " # calculate its wigner function\n", " W = wigner(rho_ss_cavity, xvec, xvec)\n", " \n", " # plot its wigner function\n", " ax = plt.subplot2grid(fig_grid, (0, idx))\n", " ax.contourf(xvec, xvec, W, 100)\n", "\n", " # plot its fock-state distribution\n", " ax = plt.subplot2grid(fig_grid, (1, idx))\n", " ax.bar(arange(0, M), real(rho_ss_cavity.diag()), color=\"blue\", alpha=0.6)\n", " ax.set_ylim(0, 1)\n", " \n", "# plot the cavity occupation probability in the ground state\n", "ax = plt.subplot2grid(fig_grid, (2, 0), colspan=fig_grid[1])\n", "ax.plot(g_vec, n_gnd_vec,'b', linewidth=2, label=\"cavity groundstate\")\n", "ax.plot(g_vec, n_ss_vec, 'r', linewidth=2, label=\"cavity steadystate\")\n", "ax.set_xlim(0, max(g_vec))\n", "ax.set_ylim(0, max(n_ss_vec)*1.2)\n", "ax.set_ylabel(\"Cavity gnd occ. prob.\", fontsize=16)\n", "ax.set_xlabel(\"interaction strength\", fontsize=16)\n", "\n", "for g in g_vec[::4]:\n", " ax.plot([g,g],[0,max(n_ss_vec)*1.2], 'b:', linewidth=5)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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LQeAhZW1ymXp61fwQzsN0xo7MHbL+cxNA/qY6Zk7NAQfClwRlROMeFkby4Ya7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\n4+PTqJAODg4oLCyUX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"text": [ "" ] } ], "prompt_number": 23 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Entropy" ] }, { "cell_type": "code", "collapsed": false, "input": [ "entropy_tot = zeros(shape(g_vec))\n", "entropy_cavity = zeros(shape(g_vec))\n", "entropy_spin = zeros(shape(g_vec))\n", "\n", "for idx, rho_ss in enumerate(rho_ss_list):\n", "\n", " rho_gnd_cavity = ptrace(rho_ss, 0)\n", " rho_gnd_spin = ptrace(rho_ss, 1)\n", " \n", " entropy_tot[idx] = entropy_vn(rho_ss, 2)\n", " entropy_cavity[idx] = entropy_vn(rho_gnd_cavity, 2)\n", " entropy_spin[idx] = entropy_vn(rho_gnd_spin, 2)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 24 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = plt.subplots(1, 1, figsize=(12,6))\n", "\n", "axes.plot(g_vec, entropy_tot, 'k', label=\"total\")\n", "axes.plot(g_vec, entropy_cavity, 'b', label=\"cavity\")\n", "axes.plot(g_vec, entropy_spin, 'r--', label=\"spin\")\n", "\n", "axes.set_ylabel(\"Entropy of subsystems\", fontsize=16)\n", "axes.set_xlabel(\"interaction strength\", fontsize=16)\n", "axes.legend(loc=0)\n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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5cyf169c3uiwRERHJRpELV+fPnze6BBGRe2I2m9mwYQMTJ05kz549vPzyy/z5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\n", "text": [ "" ] } ], "prompt_number": 25 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Software versions" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from qutip.ipynbtools import version_table\n", "\n", "version_table()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
SoftwareVersion
SciPy0.13.3
Numpy1.8.1
QuTiP3.0.0.dev-5a88aa8
IPython2.0.0
Python3.4.1 (default, Jun 9 2014, 17:34:49) \n", "[GCC 4.8.3]
Cython0.20.1post0
OSposix [linux]
matplotlib1.3.1
Thu Jun 26 14:33:44 2014 JST
" ], "metadata": {}, "output_type": "pyout", "prompt_number": 26, "text": [ "" ] } ], "prompt_number": 26 } ], "metadata": {} } ] }