{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# QuTiP Lecture: Pulse-wise two-photon interference of emission from a two-level system" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "K.A. Fischer, Stanford University\n", "\n", "This Jupyter notebook demonstrates how to simulate the two-photon interference between two potentially identical two-level systems, using QuTiP: The Quantum Toolbox in Python. The purpose is to help characterize the quality of a two-level system as a single-photon source and the capability of two such sources to interfere; ideal pulsed single-photon sources have both zero second-order coherence and complete first-order coherence, and the sources must match in spatio-temporal overlap to be indistinguishable. In this notebook, we will assume the spatial modes are comparable so we can focus on temporal effects. This notebook closely follows an example from my simulation paper, Dynamical modeling of pulsed two-photon interference, published as New J. Phys. 18 113053 (2016).\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\n", "\n", "from scipy.interpolate import interp2d" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from qutip import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction\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", "$$ H =\\hbar \\omega_0 \\sigma^\\dagger \\sigma + \\frac{\\hbar\\Omega(t)}{2}\\left( \\sigma\\textrm{e}^{-i\\omega_dt} + \\sigma^\\dagger \\textrm{e}^{i\\omega_dt}\\right),$$\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 $\\Omega(t)$ 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", "$$ H_r =\\frac{\\hbar\\Omega(t)}{2}\\left( \\sigma+ \\sigma^\\dagger \\right).$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Problem parameters\n", "\n", "We will explore emission from the two-level system under two different regimes: under excitation by a short pulse which gives rise to an exponential wavepacket and under excitation by a long pulse which gives rise to a Gaussian wavepacket. (Short and long are relative to the spontaneous emission time of the atomic transition.) In both cases, the driving strengths are chosen such that the expected number of photodetections is unity, i.e.\n", "\n", "$$ \\gamma\\int \\langle \\sigma^\\dagger (t) \\sigma(t)\\rangle=1 .$$\n", "\n", "As a result, we can compare the statistics of the emission directly and the normalizations become trivial.\n", "\n", "Note, we use units where $\\hbar=1$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# shared parameters\n", "gamma = 1 # decay rate\n", "tlist = np.linspace(0, 13, 300)\n", "taulist = tlist\n", "\n", "# parameters for TLS with exponential shape wavepacket (short pulse)\n", "tp_e = 0.060 # Gaussian pulse parameter\n", "Om_e = 19.40 # driving strength\n", "t_offset_e = 0.405\n", "pulse_shape_e = Om_e/2 * np.exp(-(tlist - t_offset_e) ** 2 /\n", " (2 * tp_e ** 2))\n", "\n", "# parameters for TLS with Gaussian shape wavepacket (long pulse)\n", "tp_G = 2.000 # Gaussian pulse parameter\n", "Om_G = 0.702 # driving strength\n", "t_offset_G = 5\n", "pulse_shape_G = Om_G/2 * np.exp(-(tlist - t_offset_G) ** 2 /\n", " (2 * tp_G ** 2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Setup the operators, Hamiltonian, and initial state" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# initial state\n", "psi0 = fock(2, 0) # ground state\n", "\n", "# operators\n", "sm = destroy(2) # atomic lowering operator\n", "n = [sm.dag()*sm] # number operator\n", "\n", "# Hamiltonian\n", "H_I = sm + sm.dag()\n", "H_e = [[H_I, pulse_shape_e]]\n", "H_G = [[H_I, pulse_shape_G]]\n", "\n", "# collapse operator that describes dissipation\n", "c_ops = [np.sqrt(gamma) * sm] # represents spontaneous emission" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculate the emission flux\n", "\n", "We evolve the system with the Lindblad master equation solver, and we request that the expectation values of the number operator $\\hat{n}=\\sigma^{\\dagger} \\sigma$ are returned by the solver. If the probability of two photodetections were negligible over the course of the pulse, then $\\langle \\hat{n}(t) \\rangle$ would be the probability density of a detection occuring on an ideal detector at time $t$." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "n_e = mesolve(H_e, psi0, tlist, c_ops, n).expect[0]\n", "n_G = mesolve(H_G, psi0, tlist, c_ops, n).expect[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualize the emission flux\n", "\n", "We plot the emission flux from two different three-level systems. The system labelled 'exponential wavepacket' was excited with a short pulse, while the system labelled 'Gaussian wavepacket' was excited with a long pulse." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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UVKxcuRI33ngjTpw4gQ0bNuCyyy5DdHQ0OnTogHnz5uHPP/9EixYtsGvXLhw4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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 338, "width": 495 } }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8,5))\n", "ax.plot(tlist, n_e, 'r', label=\"exponential wavepacket\")\n", "ax.plot(tlist, n_G, 'b', label=\"Gaussian wavepacket\")\n", "ax.legend()\n", "ax.set_xlim(0, 13)\n", "ax.set_ylim(0, 1)\n", "ax.set_xlabel('Time, $t$ [$1/\\gamma$]')\n", "ax.set_ylabel('Emission flux [$\\gamma$]')\n", "ax.set_title('TLS emission shapes');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculate the correlators involved in two-photon interference\n", "\n", "When two indistinguishable photons impinge on two ports of a beamsplitter at the same time, they exit together. Such a configuration, with intensity detectors at each output, is known as a Hong-Ou-Mandel interferometer. This interferometer measures two-photon interference in the pulse-wise cross-correlation of the detection records of its photon counters.\n", "\n", "If each of the two interfering wavepackets has unity average photon number, then the formula for this normalized cross-correlation is\n", "\n", "$$ g^{(2)}_\\textrm{HOM}[0] = \\frac{1}{4}\\left(g^{(2)}_{aa}[0] + g^{(2)}_{bb}[0])\\right) + \\frac{1}{2}\\left(1-\\textrm{Re}\\iint \\mathop{\\textrm{d} t} \\mathop{\\textrm{d} t'} \\left[G^{(1)}_a(t,t')\\right]^*G^{(1)}_b(t,t')\\right) ,$$\n", "\n", "where $a$ and $b$ label the wavepackets, $g^{(2)}_{aa(bb)}[0]$ are the sources' measured degrees of second-order coherence, and $G^{(1)}_{a(b)}(t,t')$ are the sources' first-order optical coherences. Specifically\n", "\n", "$$ G^{(1)}_{a(b)}(t,t') = \\gamma \\langle \\sigma_{a(b)}^\\dagger(t) \\sigma_{a(b)}(t') \\rangle,$$\n", "\n", "which we will calculate in this notebook with the master equation solver and quantum regression theorem. Importantly, if $g^{(2)}_\\textrm{HOM}[0]=0$ then the photons always exit an output port of the beamsplitter together. Note: for the sources in question $g^{(2)}_{aa(bb)}[0]$ was calculated in the QuTiP example, Pulse-wise second-order optical coherences of emission from a two-level system." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# specify relevant operators to calculate the correlation\n", "# \n", "a_op = sm.dag()\n", "b_op = sm\n", "\n", "# calculate two-time correlations\n", "G1_t_tau_e = correlation_2op_2t(H_e, psi0, tlist, taulist, c_ops,\n", " a_op, b_op, reverse=True)\n", "G1_t_tau_e_r = correlation_2op_2t(H_e, psi0, tlist, taulist, c_ops,\n", " a_op, b_op)\n", "G1_t_tau_G = correlation_2op_2t(H_G, psi0, tlist, taulist, c_ops,\n", " a_op, b_op, reverse=True)\n", "G1_t_tau_G_r = correlation_2op_2t(H_G, psi0, tlist, taulist, c_ops,\n", " a_op, b_op)\n", "\n", "# g^(2)[0] values calculated for the sources in question in the\n", "# notebook 'Pulse-wise second-order optical coherences of emission\n", "# from a two-level system'\n", "g20_e = 0.03\n", "g20_G = 0.44" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Interpolate these functions, in preparation for time delays" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "t_delay_list = np.linspace(-5, 0, 50)\n", "TAULIST, TLIST = np.meshgrid(taulist, tlist)\n", "\n", "c1_e = interp2d(taulist, tlist, np.real(G1_t_tau_e))\n", "c1_e_f = lambda tau, t: c1_e(tau, t)\n", "\n", "c2_e = interp2d(taulist, tlist, np.real(G1_t_tau_e_r))\n", "c2_e_f = lambda tau, t: c2_e(tau, t)\n", "\n", "c1_G = interp2d(taulist, tlist, np.real(G1_t_tau_G))\n", "c1_G_f = lambda tau, t: c1_G(tau, t)\n", "\n", "c2_G = interp2d(taulist, tlist, np.real(G1_t_tau_G_r))\n", "c2_G_f = lambda tau, t: c2_G(tau, t)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculate measured degrees of HOM cross-correlation" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# two delayed exponential wavepackets interfere\n", "\n", "def g2HOM_exponential(t_delay):\n", " corr_e = np.array(\n", " [[c1_e_f(tau, t)[0] * c2_e_f(tau, t - t_delay)[0] \n", " for tau in taulist]\n", " for t in tlist]\n", " )\n", " return g20_e/2 + 1/2*abs(1 -\n", " 2 * np.trapz(np.trapz(corr_e, TLIST, axis=0), taulist)\n", " )\n", "\n", "g2HOM_e = parallel_map(g2HOM_exponential, t_delay_list)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# two delayed Gaussian wavepackets interfere\n", "\n", "def g2HOM_Gaussian(t_delay):\n", " corr_G = np.array(\n", " [[c1_G_f(tau, t)[0] * c2_G_f(tau, t - t_delay)[0] \n", " for tau in taulist]\n", " for t in tlist]\n", " )\n", " return g20_G/2 + 1/2*abs(1 -\n", " 2 * np.trapz(np.trapz(corr_G, TLIST, axis=0), taulist)\n", " )\n", " \n", "g2HOM_G = parallel_map(g2HOM_Gaussian, t_delay_list)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# a delayed Gaussian wavepacket interferes with an exponential\n", "# wavepacket\n", "\n", "def g2HOM_Gaussian_exp(t_delay):\n", " corr_Ge = np.array(\n", " [[c1_e_f(tau, t)[0] * c2_G_f(tau, t - t_delay)[0] \n", " for tau in taulist]\n", " for t in tlist]\n", " )\n", " return (g20_e + g20_G)/4 + 1/2*abs(1 -\n", " 2 * np.trapz(np.trapz(corr_Ge, TLIST, axis=0), taulist)\n", " )\n", " \n", "g2HOM_Ge = parallel_map(g2HOM_Gaussian_exp, t_delay_list + 5.45)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualize the two-photon interference visibilities\n", "\n", "Here, the exponential wavepackets show good HOM interference visibility at zero delay, dipping down to almost zero (red). Meanwhile, in the case of the Gaussian wavepackets, the significant probability of re-excitation (due to $g^{(2)}_{aa}[0]=0.44$) partially destroys the HOM interference (blue); the HOM dip at zero delay still is below the nonclassical threshold (dashed line). However, if the Gaussian and exponential wavepackets, each generated by two-level systems, are interfered with one-another then the HOM interference is not below the nonclassical threshold (purple). This is a result of the re-excitation action that scrambles the phase of the first-order coherence." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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0YP9o/oNpadTR8fi3DDi0J8cODcUbVJIufV0gR6lnCOEd/CAd8KpRs9PmJ3tD\nzXYnOl72UTzovwm/cKzBTzov4j3T7hZ63nawCT9JXRh9xkC8k5p7gC8GL4HplLU80s26nUIIn+DP\nir8QryoYH8zfiaZtGrI/smM/vIRtKn6xMxnvabq97WC0TfbAmwS8iG+zGvzEchPwhRDCIz34XoXI\ntV7OfSpXGiGEWrx9/wN46eM4UtskudySEMJ++I2fB/CL3Rr85P0RXsPhKLyX40Ly1nXmezkPwdvB\nHYe3j74T/70H4dXspuM9kx9HqjlFMv0uk8+2XPDS6V2AI/FHL87HH7czDw8QTsJL5tLX+xn+P7gR\n+DCaPATfLk/izTK2T1+vG+KqoQEPAP6UY9ls2+BK/ML1IbyUMuDbdAZevXeHEMJl3chTvB2Lfdzp\nah/JNq/L40mutIM/13lH4FC8FtAc/LdvxUsmf4s/z/jyxGp348fvPwDv4UHmUPzRWg8De4cQ/ifH\nd8kl17lpPrAt/jzx16PPHYjve1cCG4cQXulOmt3KWAiteEdbJ+K1qZbhAeajwI4hhIdyfV7wfhA2\nAH6El+guBkbix/fX8BoAO4YQ0kvsMv5+IYQ6vL3w9fjj5trw4OLBKJ3fZVs3LZ2FpEoJH47SzbV8\nocdBQgh/wNvKP4YHQ3Gts5PwAL6nx+u4Zl8gcy2/5PxcvYAfiJci/xvfzwK+jY4IIcRVrrvK57P4\nTef4O3XZn0ZPj6khhGvw55rH33MJfjPxsBDCiVlWK/i7FnruyJRe8OZHh+P71Cjgqah2Uk/OjeDN\nYC6Nvt8g/Bg5mdQj5c4CzsRrBXxM6nnrH+O1Sr4YQkivFSklYiEU5XguIr3IzG7HSwrODyFcWOLs\niIiIVBzzfk5m4W2P9wghPN3FKlJGzGwn4BlgeghhrRJnR6RXqSRdRERERPqDg4ERwKcK0EWknPW7\nIN3MVos6TZhpZk1mNs3MrrQ8exA2s6PMrK2LoTcfQyMiIiIi3RB1jnV+9PaarAuKiJSBgaXOwIpk\nZmvjbaMm4G323scfX3ES3tvydsF7nczln3TuMTK2A95e5fGiZFhERERECmZmv8fb966Ct7/9gN5/\nGoGISI/0qyAdPyhPAE4IIVwXTzSzXwGnAD8DcnYAE0J4G3g70zwzezl6eWOm+SI9ULQOwURERPqR\nlfAAfQHewdlpwR8bJpVH10HSb/SbjuOiUvSP8EcdrZ02bzj+vNEArBT8GaHdTf8LePD+GbBG6C8b\nVkRERERR3runAAAgAElEQVRERIqmP7VJ3zkad+ooJITQgD9maxj+iI9CxI9uuEUBuoiIiIiIiBSi\nPwXp60fjD7PM/ygar9vdhM1sCHAY0ALc3P2siYiIiIiIiPSvIH1UNF6UZX48Pa9e3tMcEKX/ZAjh\n8wLWFxEREREREel3Hcf1lriq+w35rmBmqhIvIiIiIiLSx4UQrDvL96eS9LikfFSW+fH0hd1J1Mw2\nBrYF/oMevSYiIiIiIiI90J9K0t+PxutnmR+3Rc/WZj2bHnUYpz7mepeZaRtLn6B9WfoC7cfSV2hf\nlr5A+3HvM+tWAXpqvf7yw5jZWsDHwDRgnWRAbWYjgFn4I9gmhhCW5plmDTATGA6s2Z326HF19/6y\n/UtFBx/pK7QvS1+g/Vj6Cu3L0hdoP+59cZCu6u5ZhBCm4o9fWxM4Lm32BcBQ4I44QDezgWa2QRTc\nZ/NtvKO5J9RhnIiIiIiIiPRUvylJh/bS9JeAicDDeBX4rYGdgA+AL4cQ6qJlpwBTgU9DCGtmSe9F\nYDtgrxDCY93Mi0rSVwDdIZS+Qvuy9AXaj6Wv0L4sfYH2496nkvQ8RKXpXwJux4PzU/GS9auAbeIA\nPX21TGmZ2YZ4gK4O40RERERERKQo+lVJejlRSfqKoTuE0ldoX5a+QPux9BXal6Uv0H7c+1SSLiIi\nIiIiIlLhFKRLn3beeeeVOgsiRaF9WfoC7cfSV2hflr5A+3H5UnX3ElF1dxERERERkb5L1d1FRERE\nREREKpyCdBEREREREZEyoSBdREREREREpEwoSBcREREREREpEwrSRURERERERMqEgnQRERERERGR\nMqEgXURERERERKRMKEgXERERERERKRMK0kVERERERETKhIJ0ERERERERkTKhIF1ERERERESkTChI\nFxERERERESkTCtJFREREREREyoSCdBEREREREZEyoSBdREREREREpEwoSBcREREREREpEwrSRURE\nRERERMqEgnQRERERERGRMqEgXURERERERKRMKEgXERERERERKRMK0kVERERERETKhIJ0ERERERER\nkTKhIF1ERERERESkTChIFxERERERESkTCtJFREREREREyoSCdBEREREREZEyoSC9xC65BObNK3Uu\nREREREREpKdaWuCBB2CnnQpPw0IIRcuQ5M/Mog0fGDwYDjkETjwRNtustPkSERERERGR7lmwAG6+\nGa67DmbMiKcaACEE605aKkkvsT33hGXL4LbbYPPNYYcd4I9/9DswIiIiIiIiUr7eeQeOPRZWWw1+\n9CMP0NddF665pvA0VZJeInFJegiBjz/2Oy633gqLF/v8yZPhuOPg6KNh3LhS5lRERERERERira3w\n6KMeiD/zTGr67rt77ejddoOqKjArrCRdQXqJJIP0WH09/Pa38Otfw4cf+rQhQ+C734VTToG11y5J\nVkVERERERPq9JUvg9tvhiivgk0982rBhcNRRcMIJsP76HZdXkF5hMgXpsbY2ePppuPpqePLJeHnY\nbz84/XTYZpsVmlUREREREZF+a84cr/n8m99Aba1PW3NNLzX/zndg1KjM6ylIrzC5gvSkd9/1OzV3\n3gnLl/u07bbzYH2vvWDAgF7PqoiIiIiISL/z/vsei/3ud9Dc7NO22grOOAP23bfrWExBeoXJN0iP\nzZzp1eD/939h4UKftu66cOqpcOSRXi1eREREREREChcCvPgi/PKX8Mgjqel77+3B+XbbeS3nfChI\nrzDdDdJj9fXewdyVV8Knn/q0CRO8zfoPf5i9qoWIiIiIiIhkFgI89hj87Gfwj3/4tMGDvUD01FM7\ntzfPh4L0ClNokB5raYH774df/ALeeMOnjRoFxx8PJ53kgbuIiIiIiIhk19oK990Hl14K//d/Pm3s\nWH/S1vHHw8SJhaetIL3C9DRIj4UAf/kLXHIJPPecTxsyxJ/Vd/rp/rw+ERERERERSVm2DO64Ay67\nDD7+2KdNmuQx1DHHwPDhPf8MBekVplhBetJLL3mw/thj/n7QIK+e8aMfwTrrFO1jREREREREKlJj\nI9x8s7c5/+wzn7bWWh4zHXmkV3EvFgXpFaY3gvTYW2/5HaF77/WS9qoqOOAAOPdc2HDDon+ciIiI\niIhIWauv98eo/epXMH++T9t4Y/jxjz1WGjiw+J+pIL3C9GaQHvvwQ7j8cn9kQEuL90J40EEerG+w\nQa99rIiIiIiISFloaPDg/Be/SD3jfKut4JxzYM89vUCztyhIrzArIkiPzZjhHSHccos/a72qCg4+\n2IP19dbr9Y8XERERERFZoRobU8F5XHL+5S/D+efDrrvm/xi1nlCQXmFWZJAe+/RTD9ZvvTUVrB96\nKPz0p/7MdRERERERkUrW2AjXXw8//znMm+fTttkGLrgAvvrVFROcxxSkV5hSBOmxTz/15//ddptX\ng6+qgsMO82BdHcyJiIiIiEilWbIE/vd/vbnv3Lk+bautPDjfbbcVG5zHFKRXmFIG6bFp07w3+Ntv\n92B9wAD47ne9Grwe3SYiIiIiIuVu2TJv1nvhhTB7tk/bcksPznffvTTBeUxBeoUphyA9NnWql6z/\n9rfQ2uqPHTj+eDj7bBg3rtS5ExERERER6aitDe65xwsYp071aVts4cH5179e2uA8piC9wpRTkB77\n4APfye+919+PGAGnnw6nnOKvRURERERESikEePRR7539nXd82gYbwMUXw377lUdwHlOQXmHKMUiP\nvfmmPy/wqaf8/YQJ/v4HP4CamtLmTURERERE+qfnn/e45KWX/P3kyd5b+xFH9M5zzntKQXqFKecg\nPfb8817l/eWX/f3kyV595IgjvP26iIiIiIhIb/vnPz0uiQsRx4/3kvRyL0RUkF5hKiFIB69O8sgj\n/id4912ftskm/rzBUvWSKCIiIiIifd+MGR6H3Hmnvx8xAk47DU49tTKa4ypIrzCVEqTHWlu9Y4af\n/MQf4Qaw664erG+2WWnzJiIiIiIifceiRXDppXDVVdDcDNXVcNxxXtV9/PhS5y5/CtIrTKUF6bGm\nJrj2Wu+YYdEiL0k/8ki46CI9tk1ERERERAq3fLk/6/zCC2H+fJ924IH+2Oi11ipt3gqhIL3CVGqQ\nHqut9UD9uuv8zzRkiFc7OfNMGDmy1LkTEREREZFKEQI89BD86Efw0Uc+bfvt4Ze/hK22Km3eekJB\neoWp9CA99skn3onDfff5+wkTvIfFY48tzx4WRURERESkfLz6qrcz/9vf/P1668Hll8M++1R+/1cK\n0itMXwnSYy+/7M9Ujx+HsPHG3oZk111Lmy8RERERESk/M2fCWWfBHXf4+/Hj/UlSxxwDgwaVNm/F\noiC9wvS1IB28msqDD8IZZ8DUqT5tn33gV7+Ctdcubd5E+rMQAqEtQIDQFlJDCB3et89PXz7X+wzz\n8n6dlk6uaQWPIecy8fbJOS2ZRhFet6efx7xkXrLOa/+hMy+Tc71Cl0n7zK7m5ZThssWSRSeWe3r7\ntEzLpS+TY71uLZPhfV7LZnudIY28X6elmWtaPvN6PK6yLqdZVRevk8tHr9Pn5fM+Htqnx0MyfyKy\nwjU1wRVXeDvzxkYYPBhOOcUD9lGjSp274lKQXmH6YpAea272UvSLL4aGBu+N8dRTvTfGSnhUgpRe\nW2sbbS3RsNzHrctbO03r1hClGVpDp2nt01sT81vTpiXWD22p6enLdJqf6XVbaH+faVr7++TQGjpP\ny3MQEZEM0oP3PIaqAVWdpw/IMD/HtKoBVTlfJ8dU0Xn6wKqMy1YNzPB6YFX78p2mJYcBGabFw6DU\n6wGDBmScZgNMNz2kS3GB3mmnwfTpPm2//fxpUZXYKVw+FKRXmL4cpMdmzfLA/Pbb/f3KK8Nll8Hh\nh0NVVUmz1i+FEGhd1kprcystTS20NLd0ft3cklom0+scQ9uyttT75a20LW9rf926LHqf9jrbOO8S\nOMlfhpKkjKVM3Smx6qLkK+frtHRyTevxOP7+3ShV7DQtSiOvUtF8XpMjrfR5yfxnmdf+M/d2CXLa\nctnWzzgvg4znwGyl8/mU+meaVuQaBQXVdMinZkU3Xne7Nkie84o2Tqsxk3eNmi5q4HSo9dNVjZ9M\n6+jmZa+KA/cBgwZQNSjDuHpAp9cDqlPLDKiO3ldXtb/uMMTLDPbxwMEDGTA4GkfT49cDa1Lzkq8H\nDB7gNz9khXvnHTj5ZHjmGX+/ySZw9dWwyy6lzVdvU5BeYfpDkB579VU48UR45RV/v9VW/qfcZpvS\n5quU4oB5+ZLlOYeWpS0sX5p53LK0hZam6H1TS5dDa3Nrqb92t7Sf2HPdxR/QcV5XpQPJEoT0EoZM\npRPJUokux1EpSVclJN0qaclRWtMeMKdPSx/iwFdERNplbQaUNrS1trUvk62WU7xM3jWlcrxOLp+r\nllaHGl9dvG5raSO0hI611NJrlmWpfdZVbbb4Bnsl3fioGljFwJqBXQ9DUuNBQwZlHQ8amnsYWDOw\nX5+Ha2vh3HP9sWptbTB2rD+6ub90Mq0gvcL0pyAd/E95993+WIWZM33akUd6z40rrVTavHWldXkr\ny+qX0VzfzLL6ZSxr8KG5vrn9dfqwvGE5yxqXsbwx+7gUJ7SqQVWd7iqn32FO3p1Of90+zjYk75Bn\nuGPe6XWWcXuJq4iIiJS90BY61oyLgvn0mnWZatW1v07Uvss6NHd8HdcEbF3W2rFWYHKcVnuwFAYO\nGUj1sGoGDRuUfTy8OjWMqO74fng1g0cMbp83eORgD/7L+FqptRVuuslr1dbVwYAB8MMf+lOgxo4t\nde5WHAXpFaa/Bemxhga49FJ/5uGyZd45xM9+Bj/4gf95iymEwLKGZTQtbKJpYRPNi5ppWpR53Lyo\nmebF0VDv42X1y2he3NxrB/QB1QP8DuuQgZnvvkZ3abu6g9t+pzcxDBoyqP31gMFe7Wvg4P59J1dE\nRET6txACbcvb2gP39hqHSzvXQGyvqZijVmOy1mOuWpG9wQYYg0cOZvCIwQweObg9eG8fRg2mZlRN\n5vHomvahN6r/v/aaB+Svv+7v//u/vb+qTTYp+keVPQXpFaa/Bumxjz+GE06AJ5/095tvDr/5TeYq\n8C3NLSxdsNSH2qXtr5fULmHpgqU01TX5sLCJpXVL2183LWyiraWtx3m1Kksd/EYM7nx3M/39MB/n\nvFs6rJqqgWoTJSIiItKXhbbgQXyO2pXLGrPUykyvuRnV7Gxe3Fy0ZozVI6oZMmYINWM8aG9/PaaG\nIWOHtA9Dxw1NvR83hOrh1Z1K8mtrveT8ppu8k7hVV/XgfP/9qfjnnRdKQXqF6a9BemgLLF2wlMa5\njTTMbeT5x5dw981LaK5bwlCWsOnaS1h/8hJaFi+hcV4jSxcsZXnj8oI/b9DQQe13CpN3EDPdVexw\n93FE6vXAIeVdnUhERERE+pfWZa2dan/GQ4cao4ub22uNtk+PCrOaFjUV3Flv1cAqD97HD2XI+KHM\nbRjKa/8ayoLmoTRVDWWnPYZyyDHDGDd5KMMmDmPYxGEMqC5ytdkKoCA9T2a2GnAhsDswFpgFPARc\nEEJY2M20/hs4HtgWGA3UAu8AV4cQnuhi3T4TpIe2wJLaJTTMaqB+Vj0NsxtonNNI49xGGuc00jCn\nof1147xGQmv3vnN8EIjv3HV4PcZf14yJ7vyNrunwuj8eDEREREREuhLaAs2LmzvURI1fL61L1V5t\nWtDUXoM1rtm6fEn3C9FqRtcwbCUP2IevNJyhE4cyfKXhDFvJ3w9fZTgjVhnB8JWH95lreAXpeTCz\ntYGXgAl4YP4+sDWwM/ABsF0IYUGeaf0cOB34D/AEMB+YCHwR+EsI4awu1i/7ID2EQNPCJhZ/tpjF\nny2m/vN6H8+qp3F2owfksxpomN3QrWrlNWNqGDbB/6BDxw9l6IShDB0/lIa2ofzhUb8Lt4ShrLPp\nUC6/Zihb79C5Oo2IiIiIiJRG7ZwWLjhrKff9dglDwhImjV7CofsuYcPVGz2gn7+UxnmNLJnntWMb\n53avoG7IuCEesK8ynOErewA/ctWRjFh1BCNXG8nI1UYyfOXhZf9IPQXpeTCzp4CvAieEEK5LTP8V\ncApwQwjhf/JI5xjgBuB24NgQQkva/IHp0zKkUfIgvbm+mUWfLmLRjEUs/HQhi/+zuD0gj4PyfO+S\n1YyuSd39WiV1R2zYxGEdX3dR1SUEuO8+OOUU7wW+qsof33bRRTB8eLG+uYiIiIiIdFcI8Mc/+vX5\n7Nne8fOJJ3qv7SNH5lgv2eR1TqrWbfy6YXZDe63cxjmNeT0FyQYYw1ce3h60j1h1BKMmj2LU6qMY\ntcYoRq8xmmETh5W042QF6V2IStE/AqaFENZOmzccmI23ylgphLAkRzqD8dLzRmDdroLxHOn0epDe\ntKiJuql11E2tY+G0hSyasYhFn3pAvmjGIprqmrpMo3p4dYcdf8SqIxgxaUR7VZT47tagIYOKmvf6\nev+zX3WVP75t9dXhuutgzz2L+jEiIiIiIpKHTz+F446Dxx7z99tu688/33TT4n5OW2sbS+YtoWF2\nQ3vN3fpZ9dTPrKf+s/r2AsXGuY1dpjVg8AAP3NeIhtVHMXrKaMasNYYxa45hxKQRvRrEK0jvgpkd\nDdxIltLyRCn7riGEZ3KksyfwJ+BK4Ey8bfsmQBPwSgjhH3nmp8dBeltrG4tmLKLuk7r2YDw5dBWE\nD6wZ2H6nadQaoxg1eRQjJ49k5Koj2wPzwSMHF5y/YnjzTTj2WHjjDX//rW/B1VfDpEklzZaIiIiI\nSL/Q0gLXXAPnnguNjV5ifvnlfo1eVcLa5i3NLTTMavCg/XMP3BfNWMTiGYvbCyWX1i7NmcaAwQNS\nQXv6sPYYqodV9yiPhQbpA3v0qZVl/Wj8YZb5H+FB+rpA1iAd2DIaNwNvARsnZ5rZC8C3QgjzC89q\nSgiBhlkN1H5YS+1HtdR+WMuCjxZQ+2EtdZ/U0bos++MXBg0dxJi1xjB6zdE+rDE6dQdpjdEMnTC0\n7Nt6f/GL8I9/wLXXwk9+4tVrnn4aLrsMvv/90h4YRERERET6sjfe8GD8zTf9/be/7QVmq6xS2nwB\nDBw8kNFTRjN6yuisyyxrWOa1iaPmvYs+XcTC6QtZOG0hdVPraJzbSO0HtdR+UJtx/ZGrjWTsumMZ\nt9649vG49cYxZs0xvdq5XX8qSb8ROBo4OoRwa4b5PwPOBs4OIVyeI53rge8DrcC/gB/iwfpawC+B\nrwHPhxB27iI/HUrS21raWPDJAua9N4/5/57PvPfmMe+9edR+WJvzEWQjJo1g7DpjPRhfq+NdoGET\nh5V9EN4dM2bA8cfDI4/4+223hRtvhE02KW2+RERERET6koYG+OlPvQS9Lzc9XdawjLppqebBcY3k\nBR8voG5qHW3LM3eObVXG6DVHM2HDCYzfcDwTNprAhI0mMH6D8R1qIqskfcWJy26XA3uHEGZE7981\ns33xXuJ3NLNt8qn6niuI3pEd2ZmdGTJuiN+1WXccY9cby7h1/Q7O2HXGUj28Z1UwKsnqq8PDD8MD\nD8AJJ8DLL8Pmm8OZZ/pBpKam1DkUEREREalsTzwBP/iBF5BVVcGpp8IFF/TNTpyrh1ez0hdWYqUv\nrNRpXluLNy2u/bC2vVbzgg8XUPtRLQunL/Qmx5/UccOjN/A8zxc1X/0pSF8UjUdlmR9P7+pZ6fH8\nfyYCdABCCEujtu3fw6vFdxmkn8/5qQysMcrvwCTvxqw/niFjh3SVTL9hBvvvD7vuCj/+MVx/PVxy\niQfut97qpesiIiIiItI9CxbAySfDHXf4+y228FqrX/xiafNVKlUDq9prKK+z+zod5rU0t7Dg4wXM\n//d8dvr3Tsx/z2tCz/9gPq3NqebIyVivO/pTkP5+NF4/y/x1o3G2Nuvp6WQL5uPpeUXW+96xL+M3\nHM/4Dcb3uGOC/mTUKK9yc+ih8N3vwvvvw3bbwUknwcUXw7Bhpc6hiIiIiEhluP9+77l9zhyvnXrR\nRR6wD+xP0WI3DBw8kIkbT2TixhM7TG9rbWPhtIXedPnf8zj/rPMLSr8/tUlfC/gYmAasExJf3MxG\nALPwR7BNDCFk7QbQzFaP0pgBrBXSNqCZPQHsBhwYQrgvRzolf056X9HUBBdeCD//ObS2wlprwc03\nw845ewUQEREREenf5szxPp/++Ed/v/32cMstsO66udeT/BTaJr3f9I0dQpgKPA2sCRyXNvsCYChw\nRxygm9lAM9sgCu6T6cwAHgHWAE5KzjOzr+EBeh3wZG98D+mspsarvL/6qj+ncepU2GUXb0uzeHGp\ncyciIiIiUl5CgDvvhI028gB9+HCvpfrccwrQy0G/KUmH9tL0l4CJwMN41fWtgZ3wDt++HEKoi5ad\nAkwFPg0hrJmWzqpROpOBv+K9u68JfBPv9f2gEMKDXeRFJem9YNkyf27jRRfB8uWw2mpwww3w9a+X\nOmciIiIiIqX32Wf+KOPHH/f3X/uatz1fY43S5qsvKrQkvV8F6QBmthpwIbA7MA6YCTwIXBBCWJRY\nbgoepE8PIayVIZ3xwLnA3sAqeMd0LwKXhhBezyMfCtJ70b/+5W3VX33V3x9xhD/TcXT2xyiKiIiI\niPRZIXhHy6ee6rVNR4+GK66Ao47yzpml+BSkVxgF6b2vtRWuugp+8hNvt77qqt7GZrfdSp0zERER\nEZEVZ+ZMOOaYVOn5PvvAb34DkyaVNl99nYL0CqMgfcX58EM48kj4R/RAvGOPhV/+EkaMKG2+RERE\nRER6Uwhwzz3eOVxdnZeeX3stHHKISs9XBHUcJ5LFeuvB3/7mbdWrq73NzaabescYIiIiIiJ90dy5\n8K1v+SOL6+q8j6Z//cvfK0AvbwrSpV8YMADOPBPeeAM23xymT/dHtJ18MixZUurciYiIiIgUzwMP\nwCab+HjECH888aOPqnp7pVB19xJRdffSWb7cH9l28cXQ0uIl7b/9LWyzTalzJiIiIiJSuLo6OOEE\nuOsuf7/LLt5ZnHpuLw1VdxfJ06BBcN553kZ94429zfp228HZZ/sj3EREREREKs2TT3rp+V13wZAh\n8Otfw5//rAC9EilIl35riy28+vuPfuTvL7vMS9Pfe6+0+RIRERERydeSJV56vsce3ov7l78Mb7/t\nncVVKdqrSKruXiKq7l5eXnoJDjsMpk2Dmhr4+c/9wKZONURERESkXL35pncE9/77Xlv0wgvhjDO8\nPyYpPT2CrcIoSC8/9fVw0klw223+frfdvA2POtgQERERkXLS2gq/+AX89Kfex9KGG3o19803L3XO\nJElBeoVRkF6+HngAjjkGFiyAsWPhpptgv/1KnSsREREREX9K0RFHwIsv+vsTTvBHDQ8ZUtJsSQbq\nOE6kSPbbD955x0vSFyyA/feH73wHFi8udc5EREREpL8KAe64Azbd1AP0lVf2zuKuuUYBel+jIF0k\ng0mT4Ikn/KBXUwO33w6bbQZ//3upcyYiIiIi/c2CBXDQQV6CXl8P++6bKlSSvkdBukgWZl596I03\nPECfNg122ME75GhtLXXuRERERKQ/eOEF+K//gnvvheHDvc+k+++H8eNLnTPpLQrSRbqw0Ubwyitw\n5pnQ1ubPWN9lF/jPf0qdMxERERHpq1pa/Lpz553hs8/8UcFvveXNMPUEor5NHceViDqOq0x/+Qsc\nfjjMng1jxsDNN6tTOREREREprk8/9Uer/f3vHpD/+McesA8aVOqcSXeod/cKoyC9cs2bB0cdBY8/\n7u+//3244goYOrSk2RIRERGRPuC++/xJQ4sWeT9Jd97ppelSedS7u8gKMmECPPooXHUVVFfDDTfA\nllt65x0iIiIiIoVobIRjj4UDDvAAfe+94e23FaD3RypJLxGVpPcNb73lPW1+8AEMHgy/+hX88Idq\nJyQiIiIi+Xv7bb+mfP99XVP2JSpJFymBzTbz3t+/9z1obobjj/dHYixYUOqciYiIiEi5CwGuvRa2\n2soD9I02gldfheOOU4Den6kkvURUkt733HuvV1FatAgmT4Y//AG23bbUuRIRERGRcrRwoRf0PPCA\nv1c/R32POo6rMArS+6bp072q0iuvwMCBcMklcNppUKU6KyIiIiISefVVOPBAv3YcORJuuQW+9a1S\n50qKTdXdRcrAlCnwwgsemLe0+LPV994b5s8vdc5EREREpNRC8M6Hv/IVD9C/9CX45z8VoEtHKkkv\nEZWk932PPAJHHgl1dbDaanDPPX5AFhEREZH+Z8EC+O534eGH/f2JJ8LPf+4dxUnfpJJ0kTKz117e\n+/u228Jnn8FOO8Fll0FbW6lzJiIiIiIr0j/+AZtv7gH66NHeDv3qqxWgS2YK0kV60eqrw/PPe7X3\n1lY4+2z4xjdg3rxS50xEREREelsI/ji17beHGTO8F/d//tOfBiSSjaq7l4iqu/c/jz8ORxwBtbUw\naZL3/q7q7yIiIiJ9U12dN3185BF/f8opXquyurq0+ZIVR727VxgF6f3TZ5/BwQfD3/4GAwbA5ZfD\nqafqOZgiIiIifckbb3hncNOnw5gxcPvt3pmw9C9qky5SAVZbDZ59Fs44w6u/n366H8AXLSp1zkRE\nRESkp0KAG2+EL3851Xv7m28qQJfuUUl6iagkXR56yKtALV4M66wD998Pm25a6lyJiIiISCGWLIEf\n/ADuuMPf/+AH/rg1dQ7Xf6m6e4VRkC4AH3/sJelvvw01NXD99XDUUaXOlYiIiIh0x4cfwv77w7vv\nwtChcMMNcNhhpc6VlJqqu4tUoHXWgZdfhu98B5qafHzMMbB0aalzJiIiIiL5+OMfvVr7u+/C+uvD\nq68qQJeeUZAuUmJDhsCtt8Itt3hp+s03w3bbwdSppc6ZiIiIiGSzfLn32P7tb0N9PRxwALz2Gmy8\ncalzJpVO1d1LRNXdJZO33vLq7598AqNGwZ13wp57ljpXIiIiIpI0c6YH5y+9BAMH+rPQTzhBT+yR\njsPG7BIAACAASURBVFTdXaQP2GwzeP11+OY3vcf3vfaC886DtrZS50xEREREAF58Eb74RQ/QV1sN\nXngBTjxRAboUj4J0kTIzejQ88ABceilUVcGFF3qwXldX6pyJiIiI9F8hwDXXwC67wJw5sPPO/jz0\nbbctdc6kr1F19xJRdXfJx5//DAcdBAsWwFprwYMP6jFtIiIiIivakiVw7LFw113+/owz4JJLvKq7\nSDZ6BFuFUZAu+Zo+3R/p8eab3snczTfDIYeUOlciIiIi/cPUqbDffv7I3GHD4LbbvD26SFfUJl2k\nj5oyBf72N39++tKlcOihcPLJ3qOoiIiIiPSeJ56ALbbwAH299eCVVxSgS+9TkC5SAeLHtP3mNzBo\nEFx9Ney6K8yeXeqciYiIiPQ9bW1w0UXwjW/AwoWw997+/HM9Xk1WBFV3LxFVd5dCvfSSP6Zt1iyY\nNAnuvx+22abUuRIRERHpGxYtgsMPh0ce8R7bL7oIzj7bO/QV6Q61Sa8wCtKlJ2bPhgMO8EeAVFd7\nCfv3vlfqXImIiIhUtg8+gH328fGYMXD33bD77qXOlVQqtUkX6UdWXhn++lc44QRYtgyOPhqOO07t\n1EVEREQK9eijsNVWHqB/4Qvw+usK0KU0FKSLVKhBg/xZnbfemipN33VXmDu31DkTERERqRxtbXDx\nxd7ufPFi7xju5Zf98bcipaDq7iWi6u5STK+84o8GmTkTJk/256lvsUWpcyUiIiJS3hoa4Mgj4YEH\nvP35z34GZ53lr0V6Sm3SK4yCdCm2WbP8eeovvww1NXDTTXDYYaXOlYiIiEh5+uQT+OY34d13YeRI\nb3/+jW+UOlfSl6hNukg/t8oq8Oyz3j69qcl7JT3tNGhpKXXORERERMrL00/Dllt6gL7BBv54NQXo\nUi4UpIv0IYMHw403wvXXw8CBcMUV3uFJbW2pcyYiIiJSeiHAL38Je+wBdXXeDv2VV2D99UudM5EU\nVXcvEVV3l9724ov+PPW5c73jkz/9CTbeuNS5EhERESmNpiY45hi4805/f+65cN55ev659B61Sa8w\nCtJlRfjPf7yt1ZtvwogR3tZqzz1LnSsRERGRFWvWLL8mevVVGDYMfvc773RXpDepTbqIdDJ5speo\nH3gg1Nd7la7LL/eqXiIiIiL9weuvw5e+5AH6GmvASy8pQJfypiBdpI8bOhTuucef/xmCP1bk8MNh\n6dJS50xERESkd91zD2y/vT+mdvvt4bXXYNNNS50rkdwUpIv0A2Zwzjnw0ENexeuuu2DHHf2EJSIi\nItLXtLX5tc8hh6Taov/lLzBhQqlzJtI1tUkvEbVJl1J55x2v9j59Okya5IH7lluWOlciIiIixVFf\nD4cd5p3mDhgAV14Jxx/vhRYiK5I6jqswCtKllObN857fX3jBH9t2661+p1lERESkkk2b5oUR774L\nY8bAvffCrruWOlfSX6njOBHJ24QJ8Oc/w/e/D83NcOih8OMfe9UwERERkUr0wgteO/Ddd2GDDfz5\n5wrQpRIpSBfpp6qr4frr4brrvCrYpZd66XpjY6lzJiIiItI9t97qAXltLeyxB/zjH7DuuqXOlUhh\nFKSL9GNm8MMfwpNPwujR8OCD8JWv+PPVRURERMpdayuccQZ873uwfDmceio88giMGlXqnIkUTm3S\nS0Rt0qXcfPAB7LknfPwxrLwyPPwwbLVVqXMlIiIikll9vfep8+ijMHCg1xA8+uhS50okRR3HVRgF\n6VKOFizwKu/PPgs1NXD77XDggaXOlYiIiEhHn34Ke+3lT60ZOxbuvx922qnUuRLpSB3HiUiPjR0L\nTz3lzxJtaoKDDoLzzwfdSxIREZFy8dJLXtvvnXdg/fW9gzgF6NKXKEgXkQ4GDYIbbvBnilZVwQUX\nwMEHw9Klpc6ZiIiI9Hd33gk77wxz58JXv+odxK2zTqlzJVJcCtJFpBMzOPlk+NOfYMQI+MMfYMcd\nYdasUudMRERE+qO2NjjnHDj8cFi2zDu+ffxx7/hWpK9Rm/QSaW+T/sEH3vi3pgaGDPHxwIEeJYmU\ngXff9TZf06fDaqt5j6mbbVbqXImIiEh/sWQJHHGEtzsfMACuvhqOO67UuRJJaGvztqJNTV79NHpt\nm2wCqOO4itEepGeaWVWVCtjj4H3IEBg6NPU6OQwd2nkYNizztGHDYPhwH9fU6GaA5GXuXNh3X28D\nNmyYl6x/4xulzpWIiIj0dbNmwT77wGuvwciRcN998LWvlTpXUjGWL4fGRmho8HFjo9/1icddDUuX\n5h7ioHz58owfH0daCtIrRHuQvs46He+6LF3qd2JWhKqqzsH7iBE+Tr5OnzZyZGocD/EyAwasmLzL\nCtfU5M8gvftu33WuvBJOOEH3eURERKR3vPOOFwr85z8wZQo89hhstFGpcyW9JgSPhRYv9ufrLV7c\n8XV9vQ8NDT7Er5PT4iEOyLMEz70ivZC1pgZ7773oqylIz8nMVgMuBHYHxgKzgIeAC0IIC/NMYzqw\nepbZc0IIq+SRRvZHsLW0dAzasw3JuzuZ7vwk7xDFO2o8NDR4g55iGz48FbiPHg2jRqWG5PvRo30Y\nM8aH+PWQIcXPkxRNCHDhhd7jO3h7sKuv9hYaIiIiIsXyxBP+GNj6eth2W3joIZg4sdS5kpxaWmDh\nQh/q6nyI3y9cCIsWpYb093FA3tpa3DxVVaVqEacPmWojJ4dMtZcz1WquqYHq6owlV3pOeh7MbG3g\nJWACHpi/D2wN7Ax8AGwXQliQRzrTgZHAVRlmN4QQrsgjjdI/J72lpXPgnn43Kv0OVXwHK9udrZ4a\nPLhj0D52LIwb50O21+PH+59GVpi77oLvftfv8+y+u1d/Hzmy1LkSERGRvuDaa+Gkk7xy6UEHwW23\neRwkK0hLC9TWpoYFC7K/joPxurrixAI1NR1r7CZr8cZDrhq/yaa9w4Z5bFHCap8K0vNgZk8BXwVO\nCCFcl5j+K+AU4IYQwv/kkc50oC2EsFYP8lL6IL3Y2to8kF+8OPedsuQdteRdtrq6wkv3hwyBCRM8\nYJ8wofPrCRNgpZVSw7Bhxf3u/dDf/w7f/CbMnw+bbAKPPgprrFHqXImIiEilammBU0+FX//a3597\nrtfeU9O6Hlq+HObNgzlzvKOhOXP8/fz5Hcfx67q6wj7HrHNt2bjwLVft2lGjUoF4dXVxv3uJKUjv\nQlSK/hEwLYSwdtq84cBsvB+3lUIIS7pIazoK0osvboeSvCO3YEHuu3fz5/vQ3eB+2LCOQXs8TJoE\nq6ySGlZayR8cLhlNneptxd5/3zfVww/D1luXOlciIiJSaerrvdT88cc9TrvlFjjssFLnqoyF4NfK\nM2d673rJYc6cjkNtbffSNvNaq+PHd12rNRmMjxzp1culnYL0LpjZ0cCNZCktT5Sy7xpCeKaLtKYD\n1cCZeNv0RuBt4IUQQl69vilIL6IQvAQ/053A+HV81zAeNzfnl7aZl8LHQfuqq/pzyNKHUaP67W3e\nhQvhW9+Cv/7Vayj97nfw7W+XOlciIiJSKWbMgD339I7ixo3z9udf+Uqpc1VCzc3w+efw2Wcdh88/\nTwXls2d373p2/PhUodTEiR1rm6bXRB07Vp1BF4mC9C6Y2S+A04DTQghXZph/LfBD4H9CCDd0kdY0\nIFPF3mnAd0IIL+SRHwXppRKCV8lPBu1z5vjBbtas1MFv5kyfn89vNGxYKmCfPBlWX93rfsfD5Mne\nJqaPWr7cO5G7+WZ/f9llcOaZ/fa+hYiIiOTpjTc8QJ89G9Zf33twX3vtrterWG1tfn356acdhxkz\nUsH4vHn5pTVyZMdaoJMmwcor+zBxYiooHz9eQXeJFBqk96c+mUdF40VZ5sfTR+eR1m3AC8C/gHpg\nbeB44FjgCTPbNoTwfz3Iq/Qms1Q7mPXWy71sS4sfSOPAPdNdzf/8xzve++ADH7J95sorp4L2KVP+\nn707j7O5bv84/vrY961EkrK3iBaVpSTSnigVpWgVpV2lXwktlJIiWaK0EcouUbpRlijRnbJTIftu\nxoyZz++Py9wzZJnlnPM9Z+b9fDzOY+Z8z5nv99J9M+f6fq7PdUGlSvZbqFIlS+JjuEV63rwwaJD9\n53z6aXj2WVi5Et59V7sFRERE5MjGj4dWrWwQUcOG8OWXVjUd07y38vKVK21f4KpVsHr1ocn48VbA\nc+e2hPvwys1TTjk0KVePpWwrdrOCAHnvux926DegvXNuD7Za3xW4KT3nchlYaszoqntGzq3zZ+H8\n3ltDvLRJ+9q1uFdeOfQ9KfuE5s498mkqV05N2lMS+GrV7OsRRtNF43+fTp0s9NatYfBg+100cqTd\nDwnF+TNC59f5dX6dX+fX+XX+6D8/eNq0sZv96ekZFm3x+/feOzQhX7nymF3O03X2pCT7PPnXXzH/\nv6/Onzk5KUlPWSk/QrpwyPF0zUo/igFYkn5pFs4hsSZtJ8saNVKPp03S02PlSnsc6fwVKljCXq2a\n1YIdrwIgQDffbDd6mzaFqVNtT9mkSfZHEBEREUmre3d4/vkY3iLX/giDoYoVO3ThpWLF1GrKtJ8V\nJVvo2rUr3bp1C+k5c9Ke9HuBwcAg7/2DR3g9pXFcY+/9d5m8RnFgOxDvvT/m4G7tSZdDxMXBmjWp\nd2BXrYIVK2D5cvv+wIEj/1y+fJa0n3VW6uPss6FKlcDrzFevhmuvtc7vZcvaiLYLLgg0JBEREQnQ\nnj1w++0wYYJ9hBk6FO64I+CgUqodlyyxx2+/pX6/bdvRf65sWVs0qVLl35WQpUrF8F0HCSU1jjsO\n51wlYAXW3K2KT/MHd84VBTZgI9hO8t7HZfIaVwFfAUu898e8TaYkXdItMdES+GXLbM/7smWpj3Xr\njvwzefLYL46UxP2cc6BmTfvFEcHGIdu328r6d99BoUIwfLitsIuIiEjOsn493HAD/Pyz5bBjxkCD\nBhEOYvNmWLzYHmmT8Z1HaVlVtGhqBWPaR9WqtlouchxK0tPBOTcFuBJ4xHvfL83x3sBjwADvfYeD\nx/IAVYAE7/2qNO89A/jLe7/3sHOfDkzDmsg9573veZxYlKRL1u3ZY0vVh9/5Xb36yF3pCxVKTdhr\n1bLHOeccedN4iCQkwAMPwLBhdlO5Tx945JGwXU5ERESizK+/wnXX2TbrypVtFnpYd+4lJtpixqJF\n9li82L5u2HDk95cqZZWIaSsTzzrLmrNpRVyyQEl6OhxcTZ8NnASMA/4ALgYaAkuBet777Qffezqw\nCljrva+Y5hxdsX3nM4A/Se3ufh2QH5gENPfeH6U++X/nUZIu4bNvn626L1kC//2v/XZctMga2x3J\n6afD+edD7dpWk37BBTaoNES8h5dfhi5d7HnHjvDWW5oGIiIikt1NnQotWlgvtXr1YNw4mwgWMgkJ\n9jlnwQJ7/PyzffZJSPj3e4sUsYWKmjVtkSIlGS9dWsm4hIWS9HRyzpUHugNXAycA64ExQDfv/c40\n7zsdS9LXeO8rpTneAHgQOA8oCxTG9qH/Anzsvf8knXEoSZfI27o1tcwr5e7yb78deRRIxYqWtKdN\n3EukZ0Lh0X36Kdxzj/3ebNoUPvtM00NERESyqyFDoF07a1Z+223w4YdQoEAWTpiYaJ9bFiywAesL\nFthnmiMl5BUrplYN1qpliXnFipArVxYCEMkYJekxRkm6RI0DB2zV/eefU+9CL1xozewOV60a1K2b\n+jj77Awvh8+cCc2a2X71Cy+05jFlyoTozyIiIiKB8x5eeCF10M2zz9r3Gc6PN2yAOXNSHz/9BPHx\nh77HOft8knZhoVYt7RmXqKAkPcYoSZeoduCA7XVPSdp/+gl++eXfvxiLFoWLLkpN2uvUsX1dx/HH\nH9b5ffVqq7SfPBnOPDM8fxQRERGJnP37rWrus8/sPn7//tab5rgSE+2zRtqkfO3af7+vatXUZLx2\nbTjvPCXkErWUpMcYJekScxITrTw+7S/PNWv+/b4zz4SGDeGyy+xRtuwRT7dxo5W8//ijVdGPHWtv\nFxERkdi0fTs0bw4zZtj275Ej4ZprjvLm+HiYO9fe/J//2PdHWgy4+GLbzF63rn1fsmS4/xgiIaMk\nPcYoSZds4fAytAUL/r2/vXr1Q5P2cuX+99K+fTYvddw4m5f6wQf2XERERGLL6tVWJffHH/arftIk\nOPfcNG+Ii7PPCilJ+bx5//7MkLKtLiUpP+ssdZmVmKYkPcYoSZdsKSEB5s9P/QX8ww+WiadVtSpc\nfjlceSU0bkxS0RI8+SS8/ba9/Mor0LmzmqyKiIjEivnz4frrYdMmqFHDtrGdevIBe2HqVPj2W0vK\nD2/wVrOm3cBv2BAuvdS6rItkI0rSY4ySdMkREhJsP/t//mOJ+/ffw969qa/nymWla1deyds72vD4\nO6fjveO++2wPW968gUUuIiIi6TB+PLRqZffkr6gfx+hbRlB85kRLzHfuTH2jc9bQLaW67tJLQzru\nVSQaKUmPMUrSJUdKTLQu8t98Y3fWZ8+2JnUHjS10O7fvH0pcUn6uahDHyAkF1QtGREQkSvV7cz+P\nPp2P5GRH26JfMGh3S/KS+nudqlWtcq5JE2jQQPvJJcdRkh5jlKSLALt3w3ffWcI+dSosX848LuIG\nJrCZk6hV4A8m3z+Wcrc3tC7ymm0qIiISrL//JnncBJ5+4yTeXHMzAN15ged5GVe8ODRubIn5lVfa\nXHKRHExJeoxRki5yBKtXw7RprPryF66Z+jjLfFVO5U8mcy01ymyxDW833ABXXAGFCwcdrYiISPbn\nvVXBTZgA48cTv3AJd/ERo7iVPCQypHIP7mqdDFddBRdeCHnyBB2xSNRQkh5jlKSLHNvWDQk0vWIf\ns5eUoLjbxZe+GY34zl4sUMDu1DdtarNe1GhGREQkdBITYfp0GDMGJk6EdesA2Eopbsw1gR+S61Gs\nYAJffrSXxi1Uwi5yNErSY4ySdJHji4uDu+6C0aMhb55khjabQOs/X7Xh6ily54ZGjeDWWy1hVxMa\nERGRjDtwwLagjRwJX34J27alvlauHKsa3sO1M59h6d9FKF/eOrifc05w4YrEAiXpMUZJukj6JCdD\np07Qu7c9f/lleO7uDbjJk+xDxLRpqc3n8uSxUvhbb4VmzdSgRkRE5FiSkmz6ysiR8MUXsGVL6mtn\nngm33AI33sj8A+dx/Q2OTZtsatrkyXDKKcGFLRIrlKTHGCXpIhnzzjvw2GO2Ne6QEW3btsHYsfD5\n5zbuJSnJfiBvXmtak7LCXrRooPGLiIhEheRk+OEHGDHCStU2bUp9rXp1uO02+9159tmAjVhr2dKq\n25o0sR/R5BWR9FGSHmOUpItk3JgxcPvtEB8PV19tN/4Pyb23bLE3jRxpe+mSk+14oUJw883Qpg1c\nfrm6xIuISM6zahV89JE9Vq9OPV6lSmpifs45Ns/8oP79oWNH+3V6990wcODBG+Qiki5K0mOMknSR\nzJk71xq8b9kC550HkybByScf4Y2bNlnC/umnMGtW6vEKFeDOOy1hr1o1YnGLiIhE3O7dMGoUDBsG\nM2emHi9fHu64w5Lzc889JDEHS8o7d4bXX7fnXbtCly7/epuIHIeS9BijJF0k81asgGuusa8VKsBX\nX8FZZx3jB1JWD4YNgzVrUo/XrQtt29rqQYkSYY5aREQkApKSrAHcsGG2zzwuzo4XLHhoVVnu3Ef8\n8f377VfjiBHW6mXwYHsuIhmnJD3GKEkXyZrNm20C29y5ll+PGwcNGhznh5KTbVX9ww9tZWHvXjue\nP78l6h06wMUXa6lARERizz//wJAhMGgQ/Pln6vEGDSwxb9HiuJvJt2+3Ni4zZth2stGjrb2LiGSO\nkvQYoyRdJOv27bM96uPGQb58tlh+223p/OG9e607/Icf2opDyt/Fc8+1ZP3226Fw4XCFLiIiknXe\nWxl7//72Oy1l2knFijbD9K67oFKldJ1q7Vq49lpYssS2kU2ebL8SRSTzlKTHGCXpIqGRlGRd3/v1\ns+e9esGTT2ZwMXzVKuuGM2QIbN1qx4oVsw837dsfp5ZeREQkwnbuhI8/hvfes6warClq06Z2o7lx\n4ww1Sf3lF0vQN2ywpu6TJ9t2MhHJGiXpMUZJukjoeA9vvmnz1AEefhj69Dnqdruji4+32r733oPZ\ns1OPX3aZfehp3lxtbUVEJDiLFtmq+aefpm7ZKlsW7r/fHqeemuFTfv21VcLv2QMNG1rPVbVpEQkN\nJekxRkm6SOh9/rktfickQLNm9hmmUKFMnmzRIkvWP/kk9YNQ+fLw+OP2QUhz10VEJBK8t0y6Vy8b\nL5ri8sut2qtZs0zfQP7gA/uVlpRku7yGDrU2LSISGkrSY4ySdJHwmDkTbrwRduyAOnVg/HgoXToL\nJ9y1y0oK+/WDP/6wY8WLw4MPwiOPQLlyIYlbRETkEImJ1mK9Vy/49Vc7VqSIDSxv3x7OPDPTp/Ye\nune30WoAzz4Lr7ySoQp5EUkHJekxRkm6SPgsWWIj2v78E6pUsRFtVapk8aTJyTaUvVev1LnrefNC\n69bw1FPaty4iIqGxa5fNPevTB/7+246dfDI8+ii0a5flWvTERMvxhwyxpLxfP3suIqGnJD3GKEkX\nCa8NG+C662DhQjjxRJg40aarhcS8eZasf/llalf466+3TfGXXqoRbiIiknHr18Pbb8OAAZaog90A\nfuopq0UPQR367t1wyy1WPV+woC3UN22a5dOKyFEoSY8xStJFwi/sH0ZWrIDevW1TX3y8HatXz2oI\nGzVSsi4iIsf399/w6qu2tJ2QYMcuu8xu/F5zTchq0NPevC5dGiZMCOHNaxE5IiXpMUZJukhkJCba\n9vGhQ+1zTt++1qg9pDZvhnfftZNv22bHLr3UkvWGDUN8MRERyRbWr4cePWDQIEvOnYObb7bk/KKL\nQnqp33+3fH/tWtv+NWUKVK4c0kuIyBEoSY8xStJFIufwBjnPPGOLFiFvkLN7t23u69ULtm+3Yw0b\nQrdu0KBBiC8mIiIx6Z9/oGdPK2vfv9+S81tvhS5dwtLfZNYsqyILWUNVEUk3JekxRkm6SOQNHQoP\nPBCBUTO7dsE779jw9h077Fjjxpas168fhguKiEjU27gRXn/d5pynbJFq0QJefBFq1AjLJUeOhDvv\ntIX6G2+Ezz7LwmhSEckwJekxRkm6SDC+/to+E+3ZY4vcY8ZkuVHu0e3YYU2AevdObQJ05ZXw0ksh\nL2UUEZEotXUrvPaaVVrFxdmx5s2tvKtmzbBc0nv71fPUU/b8oYfs11Hu3GG5nIgchZL0GKMkXSQ4\nCxfCtddaxeHZZ9uItlNPDeMFt2+Ht96ycTq7d9uxVq1sL+Jpp4XxwiIiEpj9+61fyUsvpVZVNW1q\nyfl554XtsklJ8MQTVtAFtnj/1FPqZSoSBCXpMUZJukiw1q61Jjq//w7lysHkyVCrVpgvunWr7Vfv\n08c+vOXPD489Bp07Q/HiYb64iIhEhPfwxRfWAGXVKjt2xRV2Y7Z27bBeOi4OWre2CaH58sGwYdCy\nZVgvKSLHoCQ9xihJFwne9u3QrBnMnAlFi9pnqiZNInDhtWvhuedscyBYB59u3eD++yFPnggEICIi\nYfHjj7aM/cMP9vzMM+GNN+yucJiXsrdssYX6OXNsG9fYsTbJTUSCk9kkPdS9jUVEYkbJkrZH/bbb\nrAr92mvhww8jcOHTToNPP4V586yR3ObNNheuZk2YNMlWYUREJHasXWsdSS++2BL00qWtQdzixfbL\nJcwJ+sqVUK+eJeinngrff68EXSSWKUkXkRytQAFb0O7UCQ4cgLvvtnFtEcmTL7rIZuOMHg2VKlnt\n/fXXW3O5xYsjEICIiGTJ7t22Zal6dRg+3LYxPfssLF8O7dtHpDrqxx+hbl275Lnnwty51m9FRGKX\nyt0DonJ3kejz7rvQsaMl6PfeC++9B3nzRujihzcYyp0bHn3UyuCLFIlQECIiki7e28bvRx6B9evt\nWAANQcePtz3ncXFw1VUwapRt3xKR6KA96TFGSbpIdBo71j5nxcfD1VfbjNmIfuDZutU6//bvD8nJ\nVrfYt68NuBURkeCtWQMPP2zbk8Cqot55x0rdI6h/f7uxnJwM99wDAwZE8MayiKSL9qSLiIRAs2bw\n3Xdw4okwZYrt6duwIYIBnHCCJeXz5sH558Nff1lQzZrZ9yIiEozERJtndvbZlqAXK2YVULNnRzRB\nT062xvEPPWTfd+0K77+vBF0kO9FKekC0ki4S3VassGa8K1ZAhQo2S/2ssyIcxIED9gHw+edhzx4o\nXNjK4Tt2VBd4EZFImjMH2rWDX3+157fdBm+9BSefHNEw9u+Htm1hxAj7NTB4sD0XkeikcvcYoyRd\nJPpt3mzjbObODXiczbp1tj/9iy/s+bnnwsCBVmIpIiLhs327NYIbNMieV6pkdeZXXRVIKM2bw4wZ\ntg1r9GjrMyoi0Uvl7iIiIVa6NHz7rW0H37HDPgyljDaPqFNOsU9jEydaQ6JffoE6dWxFfe/eAAIS\nEckBRo6EM86wBD1vXnjuOfjvfwNJ0NessYmdM2bY4v3MmUrQRbIzJekiIsdQqJAtYHfsCAkJcMcd\n0LNnQKPMr7sOfvsNnn4acuWCfv2gVi3bDykiIqGxbZt1EL3tNti0CS691G6OvvIKFCwY8XB++snu\ny/7+u22HnzvXCqpEJPtSki4ichy5c8Pbb0Pv3uCcjcRt3962jEdc4cLw2mv2qa1mTVi50j5Adu5s\nmxVFRCTzpkyBGjVs03ehQjaL8z//CaApiZk0CRo0gI0boVEj+P5765MiItmb9qQHRHvSRWLT6NHQ\nurXlw9deC59/HuAY8/37ra3v669bi9+aNeHjj+2riIik35490KmTzTEDqFcPhg2DKlUCC2nAgNQO\n7nfdZU3i8uULLBwRyQTtSRcRiYAWLWD6dJuUNnlyACPa0sqfH3r0sM2JlSvD4sVQu7attCclWY+i\n3AAAIABJREFUBRSUiEiMmT3b6sdTBo337Gn/rgaUoCcnW6+69u3t+y5d4MMPlaCL5CRaSQ+IVtJF\nYtvy5TaibeXKAEe0pXX4KlD9+rYKVLlygEGJiESxKKxGOnzE2sCBcM89gYUjIlmkEWwxRkm6SOxL\nO6KteHEb0dawYcBBTZkC994L69fb/vU334QHHrDN9CIiYn791fYuLV5sjTifeQZefNEqlAKybRs0\nawazZmnEmkh2oSQ9xihJF8ke4uKs4/uYMVYl+cEH9jxQ27bBww/D8OH2/JZb4P33oVixYOMSEQma\n9zB0qP0bGR9v1UYffWR70AO0erVVZy1dalM3J02y4R0iEtu0J11EJAAFC8KoUfDYY5CYaAszL78c\n0Ii2FKVK2UD34cNtOWbUKNurvnhxgEGJiARs716rJb/vPkvQ773XRqsFnKDPm2cj1pYuhXPOseos\nJegiOZtW0gOilXSR7OeddyxZ994+Bw4cGAWNfpYts5X0xYuhQAF4911tcBSRnOf33+3fwt9+Sx2t\ndtddQUfFl19a9VV8vJW2jxqloieR7EQr6SIiAXvkEduXXqiQdeK95hrYsSPgoKpVs2WZe+9NXTm6\n+27Yty/gwEREImT4cLjwQkvQzzgDfvwx8ATde+jd2yaGxMfb4v7EiUrQRcRoJT0gWkkXyb4WLIDr\nr4eNG63j++TJcNppQUeFdXtv39420teoYV2JqlcPOioRkfCIj4cnnrBVc4BWrWDQIChSJNCwDhyw\nqqt337XnPXpY3zr19xTJftQ4LsYoSRfJ3tasgeuugyVLoGxZmDDBtoUH7tdfreRz6VL7oPr++3Db\nbUFHJSISWqtW2b91P/9s+47efhvatQs8E96zx+4VTJxoYQ0bBi1bBhqSiISRyt1FRKLI6afDDz9A\no0bwzz9w2WUwfnzQUWFdiebPt0+Fe/bY14cegoSEoCMTEQmN8ePh/PMtQa9YEebMgQcfDDxBX78e\nGjSwBL1UKfj2WyXoInJkStJFRMKkRAn46itrIrdvn82/7ds36Kiwju+ffWa1lvnyQf/+1rFo69ag\nIxMRyTzvoWdPuPFG2LnT/tH9+WdL2AP266/WwX3hQpv6NncuXHJJ0FGJSLRSki4iEkb58tlI3u7d\n7fPjI4/YXsSkpIADcw46dIDvv4eTT4YZM+Dii60MXkQk1uzfb00xO3e2f9969LDW6SVKBB0Z06ZZ\nQv7XXzbtbc4cqFo16KhEJJppT3pAtCddJOf55BObfpaYCDfcYIvZAfcvMn//DU2b2hJPiRLWUK5x\n46CjEhFJny1b4KabYNYsG6/xySfQvHnQUQHWp65DB7sxe8st8NFHNg1TRHIG7UkXEYlyrVvbikrJ\nktZIrkEDWLcu6KiA8uVh5kwrDd2xA666yj5ZiohEu99/tyqgWbOgXDn7GgUJenIyPPWU9apLSrIF\n/hEjlKCLSPooSRcRiaDLLrO9iFWq2ML1RRfZ18AVKQJffAFPP22fKNu1s9FFgdfli4gcxbRpULeu\ndXI//3ybfx4F+8/37oWbb4Y334Q8eWDIEHj1VcilT90ikk4qdw+Iyt1FcratW22xZ9YsKFwYhg+3\nEvioMHSoJekHDtjA988+s2ZzIiLRYsAAePhhu5F4001WR164cNBRsWGD/Vv+00+2e+jLL+Hyy4OO\nSkSConJ3EZEYcsIJtgjUurWtujRrZmN8o+K+3T33WHClStmsoPr14c8/g45KRMSS8sceg/bt7ftn\nn4VRo6IiQV+82Crvf/oJKlWyBnFK0EUkM7SSHhCtpIsIWFL+8svQpYs9f+gh6NPHSiQDt3y5raQv\nWwZlysCkSXDBBUFHJSI51b59cOut9m9R3rzWO6Nt26CjAmDyZLjtNtizxzq4jx0LpUsHHZWIBC2z\nK+lK0gOiJF1E0ho+3D5rJiTANddYg6FixYKOCti+HVq0gOnTreR9wgTbWC8iEkk7dthNwx9+sCqf\nMWOs+2YUePddG6+ZnAytWtmOITWIExFQubuISExr1cry4BNPhK++spm6a9cGHRXWiv6rr2yJaPdu\nuPpqK4EXEYmUjRuhYUNL0E891b5GQYJ+4AA8+qhtjU9OtoqoTz9Vgi4iWaeV9IBoJV1EjmTlSrju\nOli6FE46CcaNgzp1go4K2/vZoYOVl+bJA8OGwe23Bx2ViGR3a9dCkya2/aZaNeuXUaFC0FGxcye0\nbAlTpljl/fvvw113BR2ViEQbraSLiGQDlStbs6ErroBNm2zx6LPPgo4KyJ3buik/84wtH7VuDf37\nBx2ViGRnf/xhZUXLl8O559o4jChI0Fevtn3nU6ZY9dP06UrQRSS0lKSLiESZkiWtCVGHDrB/P9xx\nh5VRJicHHJhz0LOnPby3LnevvBIlLelFJFv56Se49FL4+29L1L/7zsqLAvb993DRRbBkCZx1Fsyb\nZ+GJiIRSjkvSnXPlnXNDnXPrnXPxzrnVzrm3nHMlsnDO1s655IOPe0MZr4jkTHnzWjOivn0hVy54\n6SUrrdy3L+jIsNX0gQMtaX/+eejUSYm6iITOjBk2u2zLFuuk+fXXNnQ8YB99BI0bW1hXXw2zZ9uo\nNRGRUMtRSbpzrjLwE9AWmAv0BlYBjwJznHOlMnHOU4F+wJ6Dh/RJVURC5uGHbVW9WDEbBXzZZbB+\nfdBRAQ88YC3p8+SBN9+E+++3fesiIlkxcaJlwLt3W8PKsWOhUKFAQ0pOhs6doU0bm8Dx6KM26KJ4\n8UDDEpFsLEcl6UB/oDTQ0Xt/k/f+Oe99Y+AtoDrwSkZO5qwTwAfAZmBAqIMVEQG46irbp16xIixY\nYKWWCxcGHRX2AXr8eChYEIYMsef79wcdlYjEqs8+g+bNIT4e2rWzVun58gUa0t69NoWyZ09rzfHe\ne9Cnj92fFBEJlxyTpB9cRW8CrPbev3vYyy8C+4DWzrmM3K59BLgcuPvgz4uIhEXavY/r1tnXMWOC\njgorRZ061ZaUvvgCbrnFlppERDLik0+sIeWBA/Dss5YN584daEh//23b4seMsWr7KVPgwQcDDUlE\ncogck6RjyTTA1MNf8N7vAX4ACgPpGnbknDsT6An08d5/H6ogRUSOpnRp+OYbK7nctw9uuglefjkK\ntoOnNHUqVcpqQO+4wz5oi4ikx6hR9g+b99aMskcP63kRoLlz4cILrWqpShV7fsUVgYYkIjlITkrS\nqx/8uuwory8/+LXq8U7knMsDfAysAZ7LcmQiIumUPz988AG89pp9hn3hBWjVKgoayp13nq2oFysG\no0fbB27tUReR4xk3Dm6/3TZ+d+0KzwX/seqjj2z85T//WP+6uXOhevXj/piISMjkpCQ9pb3HzqO8\nnnI8Pe1DuwDnAm2999qAKSIR5Rw8/bQtWhctCp9/biWZf/0VcGAXXGD1oIUL297SBx6IgrlxIhK1\nvvrKtsgcOGBTI7p0CTScpCQbVtGmjbXXeOghayx/wgmBhiUiOVBOStJDwjl3MdAZ6OW9nxd0PCKS\nc113na3wVK4MP/9spZlz5gQcVN26MGmSNZMbOhQ6doyCenwRiTrffmt7dhITrV16wCXuO3fCDTfA\nG29YU7gBA6BfPxuHKSISaTkpSU9ZKT/awIyU4zuOdoKDZe4fAUuxZnNHfFtGgnLOHfXRtWvXjJxK\nRHKgs86CH3+02b0bN1qJ5rBhAQd12WXW9T1/fujfH558Uom6iKSaNQuaNrUu7g8+CG+9FWiCvnw5\n1KljC/snnGC9P9q1CywcEYkxXbt2PWo+l1nO55APTs65e4HBwCDv/b96czrnvsa6vzf23n93lHOU\nALal85Jve+8fP0Y8HiCn/PcXkfBKTLRcuG9fe/7EE/D66wE3R540ycYpJSbakOFXXgm8GZSIBGze\nPOvAtmcPtG1r4xtzBbdmNG0a3Hor7NgBNWrY/cWKFQMLR0SymZRE3XufsYXcnJIkOucqASuA1UAV\nn+YP7pwrCmwAPHCS9z7uKOcoAPQ9+L7DXQCcB8zCVtqnee9HHSMeJekiEnKDB0OHDrbF8+qrYfhw\nGx0UmDFjbM9pUhJ0726d7kQkZ/r5Z2jUyGrLW7WCjz8O7E6i93ZT84kn7J+nG2+0cIoWDSQcEcmm\nlKSng3NuCnAl8Ij3vl+a472Bx4AB3vsOB4/lAaoACd77Vek4d1esodx93vuh6Xi/knQRCYuZM+Hm\nm2HLFutIPHYsnHFGgAGNGGFj2ZKTbXm/U6cAgxGRQPz6q7VK37rV9qJ//rlt/g5ASlO4IUPs+f/9\nn91DDHBBX0Syqcwm6Tntn6MOwCbgHefcGOdcD+fcdCxBXwr8X5r3lgeWAN9GPkwRkcxr0ADmz4ea\nNWHpUrjoIusEH5iWLa2JHFhb+v79AwxGRCJuxQorcd+61TpeDh8eWIK+bp21zRgyBAoUsFBeflkJ\nuohElxz1T9LBFfHawIfAxcATQEWgD1DHe7/9SD+W3tNn4L0iImF1+ukwe7ZVmu/ebT2auncPcCJa\nmzbWLhms4/v48QEFIiIRtWULXHMNbNpkifro0ZAvXyCh/PAD1K5t2+IrVLDnLVsGEoqIyDHlqHL3\naKJydxGJBO+twrxzZ/v+xhvho4+gWLGAAureHV580Ua0zZhhc+NEJHuKi7PRE3PmwHnn2d/5gDZ9\nDxxo9wcTE63q/vPPoXTpQEIRkRxEe9JjjJJ0EYmkKVOsT9OOHbY/fexY268ecd7DPffAhx/CSSfZ\noHe1UhbJfpKTrW36F1/Aqafa3/Vy5SIexv79lpwPHmzPH3sMevUKrNpeRHIYJekxRkm6iETaihXQ\nrBn89putpH/6KVx/fQCBJCbavtRp0+xOwezZUKpUAIGISNg8+ST07g3Fi1td+dlnRzyE9euhRQtb\nyC9QAAYNgjvvjHgYIpKDRVWS7pw7BQjVPcpE7/36EJ0raihJF5EgpIwm/uILG1nerZt1No5406Rd\nu+CSS6zjc4MGMHUq5M8f4SBEJCz69oVHHoG8ea2Mp1GjiIcwZ45NudiwwRbyx4yBCy6IeBgiksNF\nW5L+BzAnRKer570PoigzrJSki0hQvIcePeD55+37Zs1g2LAA9qn//TfUqWPtllu2tKV9tVgWiW3j\nxkHz5vaPy0cfRXzp2nt4/30bsZaYaJ3cR4603TUiIpEWbUn6HO993RCda773Ptt1FlKSLiJB++or\n26e+cydUqwZffhlAReqiRXDppdaC/tln7e6BiMSmH3+Ehg2tYVz37vDCCxG9fFycJecffGDPH3kE\n3njDFvRFRIIQbXPSR4TwXJ+F8FwiInLQNdfYPPVzzoFly2ye+vDhEQ6iVi0byZQ7N/TsaS2YRST2\nrFplTS7i4qw55PPPR/zy9etbgl6ggFUHvf22EnQRiU0RbRznnMsLlAByA7u993sjdvEoo5V0EYkW\ne/fCgw/CJ5/Y844dbfUpoqOMhw6Fe++1cvcJE+DaayN4cRHJkq1bLUNeuhSuvBImToxodjxpErRu\nbdMrKle2nhu1akXs8iIiRxVtK+mAJeXOuQedc98653YA+4GNwHpgl3Nu68HX2jvnNAxDRCQAhQvb\n1tF337XP1X372hzhdesiGMQ991hpbMrYpp9+iuDFRSTT4uOtscXSpVCzJowaFbEEPSkJunSxBfwd\nO6BpU1iwQAm6iMS+sK2kO+dOAr4FqgN/ABuAvQcfeYHCBx9VgPLAb8DV3vtIfiwMjFbSRSQazZ0L\nt9xiPd1OOglGjLCEPSK8hzZt4OOP4ZRTLFEvUyZCFxeRDPPeKmA++MD+zs6dC+XLR+TSW7bAHXfY\nYIhcueDll+GZZ9R7UkSiS1Q1jjsY0DAsOR/gvd9+nPdWBjoC5b33LcISUJRRki4i0WrzZmso9+23\n9oG3Rw/o1MlGtoVdQoKNa/rhB2vL/M03kEeFViJRaeBA2ytTsKD9nT3vvIhcdv58m3/+559QurT1\n0mjcOCKXFhHJkGgsd9/ive9xvAQdwHu/0nv/GHDc94qISHiVLg1ffw3PPWfV5888AzfdZF3gwy5f\nPiuXLVsWZsywi4tI9Jk71xpYAAwaFJEE3Xu7L3DJJZag16kDP/+sBF1Esp9wJumZWXPZHfIoREQk\nw3LnhldesZHHxYvD2LFw/vkR2ip+8snW8T1PHujd22ruRSR6bNwIN99sg8gfecS6toXZ7t1W3v7g\ng1Zw89BDdh8vQtX1IiIRFc4k/TTn3O3OuXRdwznXGqgWxnhERCSDUhoxnXeejTiqVw/69bMVrbCq\nXx/69LHv770Xfv01zBcUkXRJTLTmjuvXw6WX2iiIMFu0CGrXtrL2woXh00/t36GITqAQEYmgcO5J\nr441jssDzAP+BHYBCUDKRUsCFYCLsSZyDb33i8ISUJTRnnQRiSXx8fDkk9C/vz2/+WYYMsRW2cPG\ne2jb1lrPV65sG1FLlgzjBUXkuB57zAaQn3yy1ZqXLRu2S3kPgwfbYv3+/XDOObYbpnr1sF1SRCSk\noq5xHIBzrjjwNHAL1sX9cB5YCEwC3vPe/xO2YKKMknQRiUUjR8J991npaaVK9vyCC8J4wbg4W77/\n5RebnT5hgto3iwTl00+ttD1vXqs1r1s3bJfavRvatbPVc4D777d7AwULhu2SIiIhF1VJunOusPd+\n72HHigKnAcWAJGAzsPHw96XnXNmBknQRiVUrVli168KFVm765pu2PzRs3d/XrLE7Adu2wYsvQteu\nYbqQiBzVokWWlMfFWUlN+/ZhvdQtt8Dy5VbePnCg7UcXEYk10Zakz/be1wvRuX703l8UinNFEyXp\nIhLLIl7+Pm0aXH21tZufMAGuvz5MFxKRf9m2zTaFr14Nd99tf9nDcFdO5e0ikt1EW5L+I9CCzHV4\nT+EP/vwY7/35IQksiihJF5Hs4PDy988/t8/yYdGzJ3TubHcC5s+HqlXDdCER+Z+kJLspNmWKVbTM\nmhWWmvOdO21xXuXtIpKdRFuS3htrChcK27z3T4boXFFDSbqIZBdpy9/z5LHRbU89FYat497bkv2Y\nMVCjBsyZA0WKhPgiInKILl3gpZfghBNsBuNpp4X8EnPmWDn76tUqbxeR7CWqknQ5PiXpIpKdxMfD\ns8/ayhdAo0bWlP2UU0J8oV274OKL4Y8/oGVL+OyzMG6GF8nhJk6EG26wO25ffw1XXBHS0yclQY8e\n1mYiKclGPQ4frvJ2Eck+MpukR1WLXOfcVUHHICIiGVeggI01nzQJSpeG6dOhVi0YNy7EFypWzFbS\nixSBESPsToCIhN6GDbb/HKw8JsQJ+p9/wuWXwwsvWIL+1FO2oq4EXUQkypJ0oFnQAYiISOZdey0s\nXgxXXQVbt0KzZrbPdN++EF7kjDOgb1/7/uGHYeXKEJ5cREhOhrZtYcsWaNIEnn46pKcfPdpu4s2a\nZWPWp06FXr0gf/6QXkZEJGZFW5Lezjm33Dn3nnPuJudcibQvOufUJUhEJMqVLQuTJ8Nbb9mItgED\nrJncokUhvEibNrYRfs8e27yamBjCk4vkcO+8Y5nzCSfAhx+GrMHE3r3WaPKWW2DHDutHt3ix3QcQ\nEZFUUbUn3Tl3I3ARkBtoApwD/AJMA74FrvHedwouwtDRnnQRyQkWLoTbb7ct5Pnyweuv23ilkGwj\n374dataEv/+2mtnu3UNwUpEcbvFiuPBCSEiwrSXNQlPk+PPP0KoVLFtmK+ZvvgkdOqilhIhkb9mm\ncZxzrjxwGTARyAM0Aq44+Djde587wPBCRkm6iOQUe/fCE0/AoEH2/Morbcxy+fIhOPmMGbax1Tn7\n/pJLQnBSkRwqLs4S9N9+gwcesDbrWXTggN2c69rVCl7OPtuaw51zTtbDFRGJdtkmSU/hnLse2O69\n/yHNsXe99w8FGFbIKEkXkZxmzBgrdd22DUqUgH79bJU9yytpzz1nLaJPOw1++cVOLiIZ17Gj/cWs\nXt3GrRUunKXTLVtmO1PmzrXnDz1ke881+1xEcopsl6QDOOcqAnWBcd77vc65a7z3XwUdVygoSReR\nnGjDBkvUJ0+25y1awHvvwYknZuGkCQlQvz4sWGBZ/6efhiRWkRxl8mS47jrIm9ey6vPPz/SpkpOh\nf3/rNxcXZ6MYhw61KhoRkZwkWybpKZxzzYD13vsfg44lVJSki0hO5b2Vuz/+uPV9K1MGBg+2ccyZ\ntmyZDVnetw8++cSayYlI+mzcaP0dNm2C117LUjf3v/6Ce+6Bb76x561bWx+6kiVDFKuISAzJVkm6\ncy43UBmoBlQ9+GgIfOW9fzLA0EJGSbqI5HSrV9uUp5kz7fk991hH+GLFMnnCIUNsmb5oUWslX7Fi\nqEIVyb68tzbrkydDo0YwbVqmurl7Dx9/bI0hd+60xvADB8LNN4chZhGRGJEtknTn3ETgDOA0YCuw\nPM1jBfC79/6/wUUYOkrSRUSsLLZPH9tWvn+/bSv/8ENo2DATJ/Pe6ue//BLq1bNGcnnyhDhikWym\nXz/bi16ypHV2z0RHx02boF07GDvWnjdtao0iy5QJcawiIjEmuyTpm4DxwKDsVNp+JErSRURSLVkC\nd91lvarAcoZXX4UiRTJ4om3brGx33Tro1g26dAl5rCLZxm+/wQUX2B2y0aMzvOztvf3YQw/B5s1W\nBfP229YsTqPVRESyT5LeFXgTuByoDnhgHfCN936zc+4Z7/1rAYYYMkrSRUQOlZhoiflLL0FSkq2q\nDxqUiWZT06fDFVdYye6sWVC3bljiFYlp8fFw0UXw669w773w/vsZ+vH16y05T1k9b9QIPvgAKlQI\nQ6wiIjEquyTphbz3+w47Vg5L2ssBT3jvTw4kuBBTki4icmQLF1rOsHChPW/bFt58E0qVysBJnn7a\nZj1VqmQlvFkcJSWS7XTqBG+8AVWrws8/p7tsxXvr1P7kk7b3vGhR+6t2//2Z2souIpKtZYsk/Xic\ncwO89w8GHUcoKEkXETm6xETo3RtefNEqccuUgXffzUA1bkKCrRIuWgRPPGFZvoiY+fOhTh37fs4c\n+7uSDqtWWTI+fbo9v+46GDAgU9vYRURyhGyTpDv7k1wGlOawRnHOuRpqHCciknMsXWpJwaxZ9vzm\nm63PVdmy6fjhBQvg4ovt+7lz4cILwxanSMxITITata3C5MknbTX9OJKSbIza88/blMMTT7TnLVtq\n77mIyLFkNkmPqsIk51wJYCYwEhgELHbOzXbO1QDILgm6iIikT/Xq8J//QP/+Vo37xRdw5pnWAf64\n9zhr17ZV9ORkG82WmBiBiEWiXK9elqBXqgTdux/37b/9BvXr21+lffvg9tut0WOrVkrQRUTCJSxJ\nunOupHOujHMuo+d/FnjBe3+S974kcDYwB5junKsf8kBFRCTq5coF7dtbsnDNNbBjB9x9NzRpYivt\nx9StW+q+9F69IhKvSNRaujQ1MR84EAoVOupb9+2DF16A886DefPglFNgwgT49FMoXTpC8YqI5FAh\nK3d3zrUA7gIqAQnAPqAkEIetjvf33q84zjk6ee//9SnKOXcm8AFwjfd+e0gCDpjK3UVEMs57SxIe\newy2boW8ea1H3HPPHSPf+PZb6/aeP7/tUa9ePaIxi0SF5GRo2ND2jtx9t3V/O4qJE20M4po19rxd\nO3jtNShePCKRiohkG4HtSXfOVQReBv4DTPLerz/s9dzA+cBtwF7v/YvHONc93vsj/tZwzlUHbvXe\nv5SlgKOEknQRkczbsgU6d06dGnX66bZH9oYbjvID99xj86EuvdTq59WGWnKagQPhwQetC+OSJUcc\nl7B2LTz6KIwbZ89r1oT33oN69SIcq4hINhHInnTnXAUs+b7Lez/48AT9YEBJ3vv53vungGHOuSeO\nccqTjvaC934ptiovIiI53IknwuDBMHs21KplK35Nm8KNN6au/h3ijTcsOZk1y4avi+Qk69ZZyQlA\n377/StATEqBHD+v3MG6cjVV76y346Scl6CIiQcjqUsJm731P731Set7svV8F9D/GW3Y55y4/xut7\nMxSdiIhka3XrWhP3Pn0ssRg/Hs46C1591Ua3/U+pUpacgCUr69YFEq9IxHkPHTrArl12J6tFi0Ne\nnj7dbnQ99xzExVnH9j/+sC0lefIEFLOISA6XpSTde/+/lW3nXDnnXAvnXK00x05zztVxzhVJ8zPx\nxzjlB0B351zTo7x+WlbiFRGR7CdPHivR/eMP6zgdFwf/939WqjttWpo3tmhhS+27d1vSou1GkhOM\nHm13r4oVszEJB0sv16+3Tu2NG9vfnWrV7O/L8OFQrlzAMYuI5HAh2ZTnnGsALMdGpy10zqU0f/sH\nOBnYmZ7zHEz67wb6OOdmOOfaOOfOd87Vcs71APKHIl4REcl+ypWDzz6Db76x3nDLlsGVV9ri4dKl\nWHLy7ruWrIwfD6NGBR2ySHht2wYPP2zfv/YanHIK+/ZZg/eqVS0hL1AAXnnFBiBccUWw4YqIiAlV\n55zngTZACaAGUNY519N7vx8boZbujfIHO8BfBKzEZqUvABYCZx28joiIyFE1bmxN3Hv0sNnqEyZA\njRq22r6t4Cnw+uv2xo4dLYkRya6eego2bYJLLyX5vgf45BO7gfXiizZirXlz6yH33HM2/EBERKJD\nSEawOee6eu+7HnbsXiAZmAxs8N4f94aAc65K2jFtzrliQDVgq/d+dZYDjSLq7i4iEn7//GOznocM\nser2kiWhywvJdPiyCfm+nw5t21rXd5Hs5ptvoEkTyJ+f74cu44k+FZg/31467zzo3dsmsomISPgE\nNoLt4MWf8N73ds5VOtgcLuX4dUAZ4P10Jukvee9fyHJAMUBJuohI5CxaBE8+aSPTAaqensAbf7fi\nhgNf4qZNU52vZC/79kGNGqxe7XmmxmRG/fdMAE4+2Zoq3nWXphCKiERC0En6xUAz4Bmgnvd+bprX\nLgMmeO+LpeM824BPgW+A77z3uw57PXd6O8lHOyXpIiKR5T1MnGgVwMuW2bFGfMub5XpGA2dfAAAg\nAElEQVRz7orRULBgsAGKhMjOR7vw6juF6eMeJ8Hno2BB6NTJBhsULhx0dCIiOUegSfrBAAoBVbz3\ni4/w2iEr7Mc4xyxgDXA5tgI/H0vYpwFzgae996+EJOCAKUkXEQlGYiK89x507erZvt1+Z7Y85790\nG12DatUCDk4kC/btg75dNvPam7nZjs1Cv/NOWz0vXz7g4EREcqDAk/RQcM619N6POPh9NeA1wAON\ngNzAPu99mQBDDBkl6SIiwdq2DV5q9zf9R5cmgfzkzu1p29bRpQtUqBB0dCLpt38/DB5sXdr/+ceO\nNSi7lDfGV+fCC4ONTUQkJ8tskp6lHUnOuarOuaoZ/Jnrj/ZaSoJ+8PtlwFzv/U3AicB1wLLMxioi\nIpJWqVLw1qjyLL/uMe5jMCQnM2SIjaZ69FHYuDHoCEWO7cAB63tYvboNK/jnH6jNfL4u1Jz//FJS\nCbqISIzKUpLuvV8ONHHOtXbOHfNczrmyzrlXgD+P8Z6OR7nOAe/9TOCrrMQrIiJyuArvPsvgAo/w\nuz+DVldsIiEB3nkHKlWCzp01pU2iT3IyjBxpowXvuQfWroWzz0rmy5Mf4kcu4sqXG+DKnBR0mCIi\nkkmhahx3BfAIsA7bR74JiAdKAhWA+sA/QHfv/T/HOM8UoOPB5B/n3DPe+9eyHGAUUrm7iEgU6doV\nunWDc89l8dAFvNA1N+PH20vFi1tn+I4doUSJQKOUHC452ZofduliEwvAbiZ16wat1r1B7mc7wRln\nwOLFkDdvsMGKiEh07El3zp0DNAbKA0WAzcDvwFfe++3p+Pl4IB+wHvgOyA887r1fd/D1a7z32WI1\nXUm6iEgU2bfPkpu//oKBA+GBB5g7F55/PnVsW9Gi0KEDPPYYlC0bbLiSsxw4ACNGQM+e8NtvduyU\nUyxZv/tuyLv1H6hWDXbvhilT4Kqrgg1YRESAKEnSs8o51w3oD1wBNMES/lOA34CpQFXvfdPgIgwd\nJekiIlFm5Ei47TY48USb0VayJADffQcvvwzTp9vb8ue3EuNOnaBixQDjlWwvLs72nPfqBWvW2LHy\n5W2M4AMPpJkaePfd8OGHcP31MGFCQNGKiMjhskuSXsJ7v+OwY2dgCfsVwJXe+2wxyFZJuohIlPEe\nLr8cZsywznF9+hzy8rx5tpI5dqw9z50bWraEZ5+1vcEiobJzp40JfOst2LTJjlWrBs88A61bQ758\nad48fz5cdJGVt//2m3U+FBGRqJAtkvTjcc696r1/Lug4QkFJuohIFFq0CM4/H5yzfb1nnfWvtyxZ\nAq+9Bp9+CklJduyGGyxZr1cvwvFKtrJxI7z9Nrz7LuzaZcfOP98aGDZvbjeGDpGcDPXrw9y58PTT\n9n9MERGJGjGRpDvn2mEN5GZ57zPcL9c5d4H3/qfQRxZ5StJFRKJU+/YwYAA0aQJff20J+xGsXQtv\nvAHvvw/x8Xbswgvh4Yfh1luhQIEIxiwxy3v48Ufo1892XCQk2PHLL7fk/Iorjvp/Qfj4Y7jrLmuS\nsGyZNU4QEZGoEStJ+hdAU2z02xJg5sHHjGN1fc+OlKSLiESpLVusZHjHDqttv/HGY7590yZb/Rww\nIHVc24knwv33w4MPQoUKEYhZYk58PHz+uSXnCxbYMeegaVOryqhT5zgn2L3bBqRv2GD70du0CXfI\nIiKSQbGSpLcDSgELgUuAy4DaWBf3FaQm7VOze9KuJF1EJIq9847tS69Uyfb5pmNZPC7OOnD37QsL\nF9qxXLksx3/4YVsZPeqKqOQYa9faDZ3337f7QQClSsF991kRx+mnp/NEnTtbk4SLLoI5c+z/bCIi\nElViJUl/y3v/+GHHCmDJ+nvAVqAm4IBO3vu3IxZchClJFxGJYomJcO65tgH91VctIUon722LcN++\nMGqUjc8COPNMeOghuOMOzVvPaZKSbDpA//4wfrxtJQc47zzo2NEaEBbMSFvcFSvg7LOtNn7uXLj4\n4rDELSIiWRMrSfon3vvWR3ntNKAt8DpwHdATeMh7/3XEAowgJekiIlHum29sX3rhwrB0qQ2mzqAN\nG2DwYFs53bDBjuXPD82aWXVykyaQJ0+I45aosXQpDBtmW8f//tuO5c0Lt9xi1RV16mSyuuLGGy3b\nb9PGSt1FRCQqxUqS3hWoDtzvvd9zhNdf894/c/D7k4G3vfe3RizACFKSLiISA5o3t33pd94JH32U\n6dMkJsKYMTBwoM1dT/mnv2xZG6nVpo3GuGUX27fbtodhw2xsX4qKFW2c+f332//umTZ1Klx1FRQp\nYs3iTj45yzGLiEh4xEqSng+YCpwBfAZ8Bczz3u9yzpUGhnrvb0jz/l7e+04RCzCClKSLiMSAVats\nDNv+/daC+8ILs3zKP/+0ldVhw2D58tTj559vyfrtt1vjOYkdBw7YIIBhw2DcuNQO7UWKWKf/Nm3g\nkktCsG08KQlq1bI+CT172uB0ERGJWjGRpAM45woCrwHtgZSJn7uBQkB77/37ad73QnaZi344Jeki\nIjHimWfg9dfhyistEwuRlL3rw4bZyuvOnXY8Tx5o1MgW8W+8UQul0Wr/ftsRMXasJeabN9tx56Bx\nY0vMmze33RIh88knVtVx2mlWS58/fwhPLiIioRYzSfr/LuzcqcDN2Kr6DmBUygx051xTYBQwzXt/\nfSABhpmSdBGRGLF1q3V537XLatUbNgz5JeLibIvxsGF2HyClsZhztm+5eXN7VKkS8ktLBuzaBZMn\n29aFyZNhT5qNe9WrW2LeujWcemoYLp6QAGecAatXwwcfQNu2YbiIiIiEUswl6cdysPS9LzDWez8i\nxOcuD3QHrsbGwW0AxgLdvPc70nmO17DRcdWAE4B44C9gAtDXe78xHedQki4iEitefhleeAHq1oUf\nfgjrLLXNm2HCBEsEp02zFdsUNWqkJuznnquRbpGwcaPdQBkzBr79NrWUHazyPOV/j3POCfP/Hu+9\nBx062JiAX3+F3LmP/zMiIhKobJWkh4tzrjIwGyiNJeZ/ABcDlwNLgfre+23pOM9+4CdgCbAJKAzU\nxRL3LQfPs/zoZ1CSLiISU3bvhsqVUzPo6yNT5LVnD0yZYgnixIm2kpuiTBkri2/c2B7pnq8tx7Rn\nD8ycaQn5t9/CokWprzkH9eunJuYVK0YoqH37rIxiwwYYPRpuvjlCFxYRkaxQkp4OzrmvgSZAR+/9\nu2mOvwk8Dgz03rdPx3nyee8TjnD8ZeA54APv/b3HOYeSdBGRWNKnDzz+ONSsCQsXhqALWMYkJFi1\n/ZgxtrKbMtItRaVKqQl7o0ZQunREw4tZ+/dbb4CUpPzHH1Nn24Nt+07pEdC0qd0cibheveDpp+GC\nC2D+fJVQiIjECCXpx3FwFX05sNp7X/mw14oA/wAeKOO935fJa9QCFgJfe++vOc57laSLiMSS+Hio\nWtUGXg8fDi1bBhaK9/D775ZUTp9uyXtK47kUNWvaqu+FF9rjzDNVIQ12c2P+fHvMmwfff289AVLk\nymX/vVJueNSrBwUKBBcvO3faHZht26ys4qqrAgxGREQyQkn6cTjn7gMGcZTV8jSr7Fd476dn8hrP\nY/vdO3vvXzvOe5Wki4jEmvfft0HXVarAkiWQN2/QEQE2mevnn1NXg7//3u4ppFWokI15u/BCqF3b\nvlapkr0XZbduhQUL7JGSmK9f/+/3nX12alJ+2WVQvHjkYz2qLl3gpZegQQP4z3+y9/9gIiLZjJL0\n43DO9QKeBJ703r91hNf7AR2wMXAD03nOp4AiQHFsP/rFwIfAQ977xOP8rJJ0EZFYc+CAzU1fvhwG\nDbKEPQrFx1sJ948/piaoa9b8+30lSlgzuqpVoVo1+1q1qiXvhQpFPOxMSUqCv/6CZcvsf5aUx++/\nWyP0wxUrZjcpUm5UXHIJlC0b+bjTZdMmW0Xfu9fuvNSvH3REIiKSAZlN0vOEJZrolHJffOdRXk85\nXiID53wSSLs77QdgxPESdBERiVF58tiqZsuW0K2bzawOtBb6yAoUsElxaafFbd4MP/1kCXtK4r5h\ng+V+33//73OUL5+avJ92Gpx0ku3HLlMm9ftw/9GTkmw1fONGe2zaZF/Xr7dEfNkyWLny0I7raRUs\naNUDKQl57dr2Z4pwO4HM69nTEvTrrlOCLiKSg+SklfRBwH3Afd77oUd4/RWgM+koVT/Cz5YG6gM9\ngSpAW+/9J8f5meP+h3/xxRfp2rVrRkIREZFwS062zG/RIujd25rJxaj16+GPP1JXoVO+rlx5aPO0\noylWLDVhL1nSkvbDH/nzp36fK5c1aouPt0fa71Mee/akJuRbtqTOjD+Wk08+tBKgWrXUR55YXY74\n6y/7w+zfb40Kzz036IhEROQIunbtSrdu3Y75HpW7H0U4yt2PcI4KwDJgp/f+mP1fVe4uIhLDJk2y\nMWwnngirVkHRokFHFFIHDsDatamJ+99/p65ip/2aGIG6sRNO+PcqftmyVpKfUpqfzf7zm/vvtx4I\nt90GI0YEHY2IiGSC9qQfh3PuXmAwMMh7/+ARXk9pHNfYe/9dFq6zEKgJlPPebzzG+5Ski4jEKu9t\nM/Ps2dC9O7zwQtARRZz3sGNHasK+Y8eRV8bTrpgnJR15hT3to1Ch1KT8xBOjpjdfZC1bZr0PwBoU\nVqsWbDwiIpIpStKPwzlXCVgBrAaq+DR/cOdcUWADNoLtJO993JHPkq7rbAROAIp77/ce431K0kVE\nYtnMmdYKvFgxW00/4YSgI5LsolUrWz2/7z4YPDjoaEREJJMym6THSuuULPPerwKmAhWBhw57uRtQ\nCPg4JUF3zuVxzp1xMLn/H+dcVefcv4azOOdyHdzXXhr45lgJuoiIZAMNGtjM6l274LUMtTIRObpF\niyxBz5fPxq+JiEiOk2NW0uF/q+mzgZOAccAf2Ni0hsBSoJ73fvvB954OrALWeu8rpjnHY0APYBaw\nBtiKdXi/DLsBsBa43Hu/5jixaCVdRCTW/fSTtQwvUMC6rZUrF3REEuuuv956Hjz2GLz1rxY6IiIS\nQ1Tunk7OufJAd+BqrCx9PTAG6Oa935nmfadjSfoa732lNMfPBh4ELgHKYyPbdmMJ/wSgr/d+Tzri\nUJIuIpIdtGgBX3wB7dtD//5BRyOx7IcfrNdB4cK2heKkk4KOSEREskBJeoxRki4ikk38/jvUqGHz\nxZYuhUqVjv8zIkfSsCHMmAHPPw8vvRR0NCIikkXaky4iIhKEM8+E1q1tbtnrrwcdjcSq77+3BL1E\nCXjqqaCjERGRAClJFxERyarOncE5+OAD2LAh6GgkFvXoYV8ffhiK/6s/rYiI5CBK0kVERLLqjDOg\neXNISFCzL8m4RYtg8mQoWBAeeSToaEREJGBK0kVEREKhc2f7+t57sH17sLFIbOnZ077efz+ULh1s\nLCIiEjgl6SIiIqFQuzY0aQJ79kC/fkFHI7FixQoYORLy5NFedBERAZSki4iIhE7Kavrbb8PevcHG\nIrGhVy9IToY774RTTw06GhERiQJK0kVEREKlYUO4+GLYuhXefz/oaCTarV8PH35oTQefeSboaERE\nJEooSRcREQkV51JX0994wxrJiRxN7972/5GbboLq1YOORkREooTz3gcdQ47knPMA+u8vIpLNJCfD\nOefAkiUwdCjcfXfQEUk02rYNKlSwbRELFsAFFwQdkYiIhJhzDgDvvcvIz2klXUREJJRy5UpdTe/Z\nE5KSgo1HolO/fpagX3mlEnQRETmEVtIDopV0EZFs7MABqFoV1qyBUaOgRYugI5JosncvnHaa9S74\n7jvrZSAiItmOVtJFRESiRZ480KmTfd+jB+iGrKQ1eLAl6HXqwGWXBR2NiIhEGa2kB0Qr6SIi2Vxc\nHJx+OmzaBF9/bWXNIvv3Q+XKsG4djBsHTZsGHZGIiISJVtJFRESiScGC8Pjj9n2PHsHGItHjk08s\nQT/7bLj++qCjERGRKKSV9IBoJV1EJAfYudM6eO/aBbNnQ926QUckQUpKgjPPhOXL4eOPoXXroCMS\nEZEw0kq6iIhItCleHB5+2L7Xarp8+aUl6KefDi1bBh2NiIhEKa2kB0Qr6SIiOcSmTdbJOz4efv0V\natQIOiIJgvc2am3hQujfH9q3DzoiEREJM62ki4iIRKOTToL77rPve/YMNhYJztSplqCXKQN33x10\nNCIiEsWUpIuIiITbU0/ZWLYRI2DVqqCjkf9n777Do6j2/4G/z2x6LxBC0RSBAJfeW0hAA6I0wYog\nXVSQ4v2pX7kqAQW5NlBBr/SiKCgIolIsJKBBKdJE6YYAoQTSICH9/P5YZsxmd9MImc3u+/U88+xm\nzpwzn53lCfnMOXOOHtTHHaZOBdzc9I2FiIhsGpN0IiKi2y0kBBg61Dhx2Pvv6x0NVbe9e4H4eOMc\nBRzmTkREZWCSTkREVB3U5diWLgWuXdM3FqpeH3xgfB0zBvDx0TcWIiKyeUzSiYiIqkPr1kBkpDFB\nX7lS72iouly+bHzMQQhgwgS9oyEiohqASToREVF1mTTJ+PrBB0BRkb6xUPVYuBDIywP69wfCw/WO\nhoiIagAuwaYTLsFGROSACgqAsDDg3DlgyxagTx+9I6LbKT/fuCZ6cjLw/ffAPffoHREREVUjLsFG\nRERk65ycgGeeMb5Xn1Mm+7V+vTFBb9oUuPtuvaMhIqIagkk6ERFRdRo3DnB1Bb79FjhxQu9o6HZS\nZ/KfNMn4TDoREVE5MEknIiKqTrVqGZdjA4AFC/SNhW6fffuAhATjsmvDh+sdDRER1SBM0omIiKrb\ns88aX5ct43Js9qr4smuenvrGQkRENQqTdCIiourWpo1xObbMTC7HZo8uXwY++4zLrhERUaUwSSci\nItKD2pvO5djsD5ddIyKiW8Al2HTCJdiIiBxcfr4xgTt3Dti6FejdW++IqCpw2TUiIrqJS7ARERHV\nJM7OwNNPG9+rs4BTzcdl14iI6BYxSSciItILl2OzP1x2jYiIbhGTdCIiIr3Urs3l2OxJ8WXXhg3T\nOxoiIqqhmKQTERHpicux2Y/iy655eekbCxER1VhM0omIiPTUpg3QvTuXY6vpuOwaERFVESbpRERE\neps0yfjK5dhqLi67RkREVYRLsOmES7AREZEmPx8ICwPOn+dybDURl10jIiILuAQbERFRTeXsDDzz\njPE9l2OrebjsGhERVSEm6URERLZAXY7tu++Akyf1joYqgsuuERFRFWKSTkREZAtq1wYeewyQEvjo\nI72jofI6eJDLrhERUZVikk5ERGQrnnrK+LpqlXESMrJ9ixcbX4cP57JrRERUJZikExER2YqOHYF/\n/QtISQG++UbvaKgsOTnAp58a348Zo28sRERkN5ikExER2Qoh/kn2lizRNxYq24YNQFoa0LYt0Lq1\n3tEQEZGdYJJORERkS4YNM872vmWLcUk2sl3qjRT2ohMRURVikk5ERGRLatcGBgwAioqAFSv0joas\nSUwEfvjBOCP/Y4/pHQ0REdkRJulERES2Ru2ZXbrUmKyT7Vm+3Pg6ZAjg769rKEREZF+YpBMREdma\n3r2BBg2AU6eAHTv0joZKKiwEli0zvudQdyIiqmJM0omIiGyNwQCMHGl8zwnkbM+PPwJJSUBYGBAd\nrXc0RERkZ5ikExER2aJRo4yvX34JZGToGwuZUm+cjBoFKPxTioiIqhb/ZyEiIrJF4eFAz57Gtbg/\n+0zvaEh19apx6TUh/hntQEREVIWYpBMREdkqrpluez79FMjLA/r0Ae64Q+9oiIjIDjFJJyIislWD\nBwO+vsDevcChQ3pHQ1JybXQiIrrtmKQTERHZKnd3YOhQ4/ulS/WNhYB9+4w3SwIDgf799Y6GiIjs\nFJN0IiIiW6b22K5aBeTm6huLo1N70YcPB1xd9Y2FiIjsFpN0IiIiW9a2LdCqFZCaCmzcqHc0jis7\nG1i92vieQ92JiOg2YpJORERky4TgBHK2YP16IDMT6NgRaN5c72iIiMiOMUknIiKydUOHAi4uwPff\nA0lJekfjmNQbJKNH6xsHERHZPSbpREREti4wEHjgAePs4suX6x2N4zl1CoiLM07k9+ijekdDRER2\njkk6ERFRTaAOeV+2DCgq0jcWR6POrP/QQ8Yl8YiIiG4jJulEREQ1wd13AyEhQGIisH273tE4jsLC\nf0YvcMI4IiKqBkzSiYiIagJFAUaNMr7nBHLVZ+tWIDkZaNgQiIzUOxoiInIATNKJiIhqipEjjbO9\nr18PpKXpHY1jKD5hnBD6xkJERA6BSToREVFNERIC3HMPkJsLfPqp3tHYv8uXga+/No5iGDFC72iI\niMhBOFySLoRoIIRYKoRIFkLkCCH+FkLMFUL4lbN+gBBirBDiKyHESSFEthAiXQixUwgxWgjeZici\nottIXQJs1Sp943AEa9YABQVA375AvXp6R0NERA5CSCn1jqHaCCHuApAAoDaADQCOAugEoCeAYwC6\nSSlTy2jjKQAfAkgGsB1AEoBgAIMB+AJYJ6V8qByxSABwpOtPRERVIDsbqFMHuH4dOHkSuOsuvSOy\nX127Art2AatXA489pnc0RERUw6j9t1LKCnXkOlpP+ocwJujPSikHSymnSSnvBjAXQASAWeVo4xiA\n/lLKBlLK4VLK/0gpxwBoAuAsgCFCiMG36wMQEZGD8/AABg40vv/8c31jsWeJicYE3cMDGDBA72iI\niMiBOEySfrMXPQbA31LKBSWKpwPIBjBMCOFRWjtSyu1Sym8t7L8E4H83f4yqgpCJiIgsU3t1V68G\nOCLr9lBvgAwYAHh66hsLERE5FIdJ0mEc0g4A20oWSCmvA/gFgCeAzrdwjoISr0RERFWvd28gMBD4\n80/g8GG9o7FPn31mfOUwdyIiqmaOlKRH3Hw9bqX8xM3XRpVpXAjhBOCJmz9uqUwbRERE5eLsDDz4\noPG9mkxS1TlyBDh0CPD3B+69V+9oiIjIwThSku578zXDSrm6v1yzvFswB8C/AHwrpfy+km0QERGV\nj9rD+/nnHPJe1dQbH0OGAC4u+sZCREQOx5GS9NtGCDEJwHMA/gIwXOdwiIjIEURGAvXrGyc4+/VX\nvaOxH1JyqDsREenKkZJ0tafc10q5uj+9Io0KISYCmAfgCICeUsqK1re6xcbGVqQpIiJyJIoCPPqo\n8f3q1frGYk/27AFOnwbq1gWiOA8sERGVLjY21mo+V1mOlKQfvfkaYaVcfRbd2jPrZoQQUwC8D+Aw\njAn65YoGJaW0ujFJJyKiUqk9vWvXAgWcs7RKqDc8HnkEMBj0jYWIiGxebGys1XyushwpSd9+8zVG\nlLitIYTwBtANQBaAco0ZFEK8COBdAPthTNCvVGGsREREZWvbFmjUCLh8Gdi+vezjqXSFhcCaNcb3\nHOpOREQ6cZgkXUp5Gsbl18IATChRPAOAB4BVUsobgHG2diFEEyFEeMm2hBCvAHgDwF4Ad0spU29r\n8ERERJYI8U8yyVneb118PHDxInDXXUCHDnpHQ0REDkrcSjd8TXMz4U4AEARgI4xD4DsBiAZwDEBX\nKWXazWNDAZwGcEZKGVasjREAlgEoBPABgEwLp/pbSrmijFgkgHIPg7iVZxqIiGyVI/0fdNscPQo0\nbQr4+ACXLgFubnpHVHONGwcsXgz85z/A66/rHQ0REdVwag4npaxQMudQSToACCEaAJgJ4F4AgQCS\nAXwFYIaUMqPYcaEwJumJUsrwYvunA5gOQAKwdrHjpJS9yoiDSToROTxH+z/otmnbFti/H1i/Hnjg\nAb2jqZlyc42TxaWlAX/8AfzrX3pHRERENRyT9Bqmskk6vy8isgf8nVbF3noLeOEF4KGHjJPIUcV9\n/TUwcCDQsiVw8KDe0RARkR2obJLuMM+kExER2S11KbZNm4Br1/SNpabi2uhERGQjmKQTERHVdHfc\nAURGAjk5wIYNekdT82RlGXvSgX9ueBAREemESToREZE94Czvlff110B2NtClCxAaqnc0RETk4Jik\nExER2YMHHwQMBmDbNiAlRe9oapbVq42vQ4fqGwcRERGYpBMREdmH2rWB3r2BwkLgyy/1jqbmSE0F\ntm4FFMU48R4REZHOmKQTERHZCw55r7h164D8fODuu4E6dfSOhoiIiEk6ERGR3Rg0CHBzA3buBM6e\n1TuamoGzuhMRkY1hkk5ERGQvvL2Bfv2M79es0TeWmiA5GYiLA1xdgcGD9Y6GiIgIAJN0IiLdhIaG\nQlEUxMfHV1mbsbGxUBQFo0aNqrI2qYZRJz9TJ0Mj69asAaQE7rsP8PXVOxoiIiIATNLJzimKUqmt\nZ8+eeodONdiBAwcQGxuLFStWlHmsEAJCiCqP4Xa0STVE376Ajw+wfz9w7Jje0dg2DnUnIiIb5KR3\nAES3U506dSwmK1evXkV+fj7c3Nzg5+dnVh4YGFgd4ZGdOnDgAGbOnIno6GiMGDHC6nENGzaEh4cH\nPDw8qjE6sntubsah28uXG5PQ2Fi9I7JNJ08Ce/YAXl7/PCJARERkA5ikk127cOGCxf3R0dHYsWMH\nHn30USxdurSaoyIy+uGHH/QOgezVY48Zk/S1a5mkW/PFF8bXQYMAd3d9YyEiIiqGw92JiIjsTc+e\ngJ8f8NdfwPHjekdjmzZsML4OGaJvHERERCUwSSe66ezZs1AUBc7Ozrh27ZpZeYsWLaAoCnx8fFBU\nVGRWXrduXSiKgh07dpiVnTp1CuPHj0d4eDjc3Nzg7++PqKgoLFmyxGJbFbFp0yYMHDgQwcHBcHFx\nQVBQEAYMGIBt27aZHbtw4UIoigJ3d3ccOXLEYnvjx4+HoigICQlBZmamtr/4hGRSSsydOxetWrWC\np6cnAgMDMXDgQOzZs6fUWDMzMxEbG4tWrVrBy8sLXl5eaNmyJWJjY03OVVzJidBWrFiBTp06wdvb\nGz4+PujVq1eZPdJ5eXmYP38+IiMjERAQAFdXV4SEhGDMmDE4evSoxTojR46EollgIG0AACAASURB\nVCiYMWMGioqKMG/ePLRq1QoeHh4ICAhA//79sW/fPrN6iqJg9OjRAIC4uDiz+Q6KTxJX2sRxO3bs\nwOTJk9GpUyfUq1dP+2779u2LdevWlfp5ieDs/M8Q7q++0jcWW3T+PLB7t7EHvXdvvaMhIiIyJaXk\npsMGQBovf/lU9HgqXVRUlBRCyFGjRpnsDw8Pl4qiyM2bN5vsv3LlihRCSCGEVBRF7tmzx6T82LFj\nUggh3d3dZW5urknZpk2bpJubm1bX399furq6au3FxMTIrKysCn+GvLw8+fjjj5vE5efnJxVF0fa9\n+OKLZvX69+8vhRCydevWMi8vzyxWIYQ0GAxy+/btJmXTp0+XQgg5YsQI+cADD0ghhHRxcZH+/v7a\nOZ2cnOSaNWssxnvixAkZEhKixebl5SW9vLy0n0NCQuSJEyfM6qnnHTlypBwzZowUQkhnZ2eTz2ow\nGOS6dessnjc5OVm2atVKO4+Tk5P09fXV6rq7u8v169eb1RsxYoQUQsiXX35Z9unTRwohpKurq/Tx\n8TGpu2vXLpN6wcHB0s/PT7s+devWNdmKHx8SEiIVRZHx8fEmbVy7ds3ke/X19TX7bsePH2/x86rX\nq+S/bVvD32nVYN06KQEpO3XSOxLbM3++8doMGqR3JEREZMeK/b1ToVyRPelExfTo0QNSSrOeTbV3\n3Nvb22K5+nPHjh3h4uKi7T916hQeffRR5ObmIjo6GkePHkVqaioyMzPx8ccfw9XVFT/88AMmT55c\n4VhfeOEFrF69Go0aNcIXX3yB69evIy0tDRkZGfjwww/h7e2NN998E59//rlJvSVLliAoKAgHDx7E\nyy+/rO1PSUnB2LFjAQBTp05FdHS0xfNu3LgRmzZtwty5c5GZmYnU1FScOHECMTExKCwsxKhRo3D6\n9GmTOnl5eRgyZAiSkpJw55134vvvv8e1a9dw7do1/PDDD7jzzjuRlJSEBx54AHl5eVbPu3r1avzv\nf/9DZmYm0tLScOrUKfTo0QNFRUV49tlnUVhYaFInPz8fAwcOxKFDh3DPPfdg165dyMnJQXp6Os6f\nP48pU6YgJycHw4cPN4tZtWDBAuzbtw9r167F9evXkZGRgQMHDqB58+bIyckx++4uXLiAefPmAQC6\ndeuG5ORkk61z584mxxt/f5syGAx46KGHsGHDBly9ehXp6elIS0tDamoq5s+fDy8vLyxcuBBffvml\nxZiJAAB9+hgnkfvtN+N64PQPdXTBAw/oGwcREZElFc3qubEn3R5Y60lftmyZFELILl26mOyfPHmy\n1qsqhJD9+/c3KVd7tF999VWT/aNHj5ZCCNmoUSN548YNszgWLlyo9ZaePHmy3PEfP35cCiFknTp1\n5Llz5ywe8/nnn0shhGzevLlZWfEec7UXd9CgQVIIIVu2bGnWwy7lPz20Qgg5e/Zss/KcnBzZpEkT\nKYSQY8eONSlbuXKl1hN95MgRs7pHjhyRLi4uUgghly5davW8q1evNqubnJwsXVxcpKIocseOHSZl\nixYtkkIIGRUVJQsKCixcJSmfeuopKYSQEydONNmv9qQriiJ/+eUXs3r79u3TypOSkkzK1H9HPXv2\ntHhOlTqyoGRPellWrVpltX32pJOJgQONPcYffqh3JLYjNVVKg8G4Xb2qdzRERGTHwJ50KpMQtrPZ\nqB49egAA9u3bh+zsbG1/fHw8hBCYMGECfH198csvv5j0gKo96VFRUdo+KaX27PDUqVPh5uZmdr6x\nY8eifv36kFJWqFd05cqVAIBHHnkE9evXt3jMkCFD4OLigj///BMXL140KevXrx+efPJJFBUV4Ykn\nnsDcuXOxceNGuLq64pNPPoGzs7PVc3t6emLKlClm+11dXfHvf/8bALB+/XqTMvWzDRw4EM2aNTOr\n26xZMzz44IMAgLVr11o8b0hICB6zsJZx3bp10bFjR0gpzZ6zV9cpnzx5MgwGg8V2hw4dCsD6TOuR\nkZHo2rWr2f62bdtq35215/tvl343nzX+7bffLPbEE2nUnmI+l/6Pb74BCguB6GggIEDvaIiIiMww\nSScqJjw8HPXq1UN+fj4SEhIAAOnp6Th06BCaNGmC4OBgREZGIi0tDQcPHgQAnD59GufPn4eLi4tJ\nMnf69GlkZmZCCIGePXtaPJ8QQhtWvn///nLHqca2fPlyBAcHW9waNGiAgoICSClx9uxZszbeffdd\nNGzYEElJSVpy/dprr6FFixalnrt9+/Zwt7JckXqTIj09HX///be2//fffwcAq9cBAHr16gXA+nVo\n37691brqjYq0tDRtX0FBAXbv3g0AGDdunNXrNHjwYABAUlKSxbY7dOhQofNWlYKCAixZsgT33nsv\n6tatC1dXV23yuYCbiUVOTs5tOTfZkX79AIMB2L4d4L8VI/WGxaBB+sZBRERkBZN0R2Ic9Ggbmw1T\nk2a1d3znzp2QUmr71URULVdf27VrZ9JbnpKSor231ttdvKz48WVR13+/du0aUlJSrG5SSgghcOPG\nDbM2PDw8sGDBAu3nLl264P/9v/9X5rlL+yz16tXT3l+5ckV7r3628lyHq1evWiz39va2Wle97vn5\n+dq+1NRU7ee0tDSr1yg1NRWAMeGtivNWhevXryMqKgrjxo3Dtm3bcPnyZTg7OyMoKEi7uaDKysqq\n0nOTnQkMBHr0AAoKgG+/1Tsa/WVnA1u2GN8zSSciIhvFJJ2oBHXIuzpZXMmh7Gqybq3cEmsJYGWp\ny7bNmzcPhYWFZW7qZyppyZIl2vvjx4+bDYuvalV9HUqjXiMhBPbv31/q9SkqKjKbdE5Pr732Gnbt\n2oXatWtj5cqVuHTpEq5fv46LFy8iOTkZ586d047lcHcqkzrkXV0X3JFt2wbcuAF06AA0aKB3NERE\nRBYxSScqQU22d+/ejZycHO15dDU5b9OmDby8vLBz504A1pP0oKAg7f2ZM2esnk9NuGrXrl3uGOvU\nqVNmu2X59NNPsXbtWjg5OSEiIgJXr17V1vcuTXIps0QXLyv+edT35bkOgYGBZcZQHoGBgVAUpczz\n2qIvvvgCAPDBBx9g2LBhqFWrlkn57b6ZQnZG7THevNmYoDoy9UYFZ3UnIiIbxiSdqISIiAjUrl0b\neXl52LZtG/bv34/GjRtrSbeiKOjWrRuuXLmC7777DmfOnIGTkxO6detm0k54eDh8fX0hpcT27dst\nnquoqAhxcXEAjBORlZf67PsWddhmBZ09exYTJ04EAEyfPh0bNmyAu7s7tmzZgo8++qjUunv37rU4\nfB7454aFn58fQkNDtf3t2rUDAKvXAQB++uknABW7DqVxdnZGhw4dIKXE5s2bq6TN8lJvDlS2l/vc\nuXMQQqBNmzYWy61Nckdk0R13AO3aGYd6f/+93tHop6AA2LTJ+J5D3YmIyIYxSSeyICoqClJKzJo1\nC0VFRWZrhqs/z5gxA8A/veslDRkyBADw3nvvWUxsFy9ejOTkZCiKgoceeqjc8T3xxBMQQuCvv/7C\nwoULSz02PT3d5GcpJUaOHImMjAx06dIF06ZNQ0REBP773/8CAJ5//nmcOHHCanvXr1/He++9Z7Y/\nNzcX7777LgBoM7Wr1J83b96MAwcOmNU9cuSINgP8ww8/XOrnqYiRI0cCME6wd+jQoVKPLXmdboWP\nj88ttane3LEU8/Xr1zFr1qxbio8cEGd5B3bsAFJTgYgIoGlTvaMhIiKyikk6kQXqM9x79uwBYD6U\nXf3ZWrlq2rRp8PT0RHJyMu6//34cP34cgDGhXbRoESZNmgQAGDNmDMLCwsodX9OmTTF16lQAwDPP\nPINp06bh/PnzWnlmZia+++47PPbYY2bJ/9y5c7F9+3Z4eXlh1apVEDeXxJs4cSLuueceZGdnY/jw\n4Vaf0fb19cUrr7yC999/X3vG/PTp0xg4cCCOHj0Kd3d3/N///Z9JnUceeQQtW7YEAAwaNAg//vij\nVvbjjz/ivvvuQ0FBAZo3b47HH3+83NehLGPGjEHnzp2Rk5ODXr16YfHixbh27ZpWnpycjBUrViAy\nMtLijYfKat68OQDjzQd1hnlrhIUlCXv37g0AeO6557S5DwDjv7e7775bm+yOqNzUJH3TJmOPsiNS\nb1BwqDsREdk4JulEFpRMukv2pLdr185kGTJrSXp4eDg+++wzuLm5IS4uDk2aNIG/vz+8vb0xfvx4\n5OXl4Z577sG8efMqHOObb76Jp59+GkVFRZgzZw7uuOMO+Pr6ws/PD35+fujXrx/WrFmjTaAGAH/8\n8QemTZsGAHjnnXcQHh5u0uby5cvh7++P3bt34/XXX7d43oEDB2LAgAGYMmUKfHx84O/vj4YNG2Lb\ntm1wcnLCsmXLzG44ODs7Y926dQgJCUFSUhJiYmLg6ekJT09PxMTE4OzZswgJCcH69etLXaO9opyc\nnLBx40Z069YNqampePLJJ+Hn54fAwEB4enqiQYMGGDVqFBISErQh6lWhYcOG6NGjBwoKCtC5c2cE\nBgYiNDQUYWFh+O2330yOtTQk/vXXX0etWrVw9uxZREdHw93dHV5eXujUqROOHDmCzz77zGpdIoua\nNgUaNwauXgV+/lnvaKqflHwenYiIagwm6eSQhBAWezBVLVq0QEBAAIQQaNSokcmSV4Ax6VSfQTcY\nDOjevbvVtvr164fDhw9j3LhxCAsLQ05ODry8vBAZGYlFixZh69atVtcdL42iKFiwYAF+/vlnDBs2\nDKGhocjPz0deXh5CQ0MxcOBALFiwQBtGnp+fj+HDhyM/Px/9+vXDuHHjzNqsV6+etizb7NmzsXfv\nXovn/eKLL/Duu++iWbNmKCgoQEBAAPr374+EhASrw9XvuusuHDx4EK+++ipatGihrfndokULvPrq\nqzh06BAaNmxoVq+s76qsY2rXro34+Hh8+umnuO+++1CnTh1kZWXBYDCgadOmGDFiBNauXYsXX3yx\nSs+7fv16PPPMMwgPD0d2djbOnj2LpKQk5Obmllk/LCwMu3fvxrBhw1CnTh1IKREQEIBhw4Zhz549\nuOeee7T6FYmJHJgQ/zyH7YhD3vftA86dA+rVA9q31zsaIiKiUgn2xOhDCCGB8veEqX908/sivcTG\nxmLmzJkYOXIkli5dqnc4VMPxd5oOfv0V6NIFuPNOIDHRmLg7iv/8B5g9G3jmGeDmjUgiIqLbrdjf\nOxX6T5c96URERI6gY0egbl0gKQnYv1/vaKoXn0cnIqIahEk6ERGRI1AUxxzyfuwY8NdfgL8/YGX+\nECIiIlvCJJ2IiMhROOJSbOqEcf36AVU4MSUREdHtwiSdiMqFE5IR2YGoKMDXFzhyBDhxQu9oqod6\nQ0IdRUBERGTjOHGcTjhxHBE5Mv5O09GwYcCnnwJvvgk8/7ze0dxe588DDRoAbm7AlSuAp6feERER\nkQPhxHFERERUNkca8r5xo/G1Tx8m6EREVGMwSSciInIk995r7FnetQu4cEHvaG4vzupOREQ1EJN0\nIiIiR+LpCcTEGN+rPc32KC0NiIsDDAbjpHFEREQ1BJN0IiIiR6P2LKszn9ujb78FCgqAHj2AwEC9\noyEiIio3JulERESOpn9/47rpP/0EZGToHc3twaHuRERUQzFJJyIicjS1ahl7mPPzjT3O9ubGDWDL\nFuN7Lr1GREQ1DJN0IiIiR6Qmr/Y4y/u2bUB2NtCuHXDHHXpHQ0REVCFM0omIiByRmqRv3Qrk5ekb\nS1X75hvjK3vRiYioBmKSTkRE5IhCQoBmzYBr14CEBL2jqTpSAps3G9/fd5++sRAREVUCk3QiIiJH\n1bev8VVNau3BH38A588DdeoArVvrHQ0REVGFMUknIiJyVPaYpKuf5d57jTPYExER1TD834uI7FZs\nbCwURcGoUaP0DoXINnXvDnh6AocPG3uf7YE6q7t6A4KIiKiGYZJOdk1RlEptPXv21Dv0Crl48SJm\nz56NXr16oX79+nBzc4OnpydCQkIwYMAAvPfee7hw4YLeYepGCKF3CES2ydUVuPtu43s1ua3Jrl0D\nfv7Z2IMeE6N3NERERJXipHcARLdTnTp1LCZoV69eRX5+Ptzc3ODn52dWHhgYWB3h3TIpJWbPno3X\nX38dubm5AIwJqZeXFxRFwblz53D27Fl88803eOGFFzB+/Hi8//77OkddfWrXro0mTZqgbt26eodC\nZLvuvRf4+mvjMPExY/SO5tb8+KNx7fcuXYCAAL2jISIiqhQhpdQ7BockhJCAMckq5/GoyPFUuujo\naOzYsQMjR47E0qVL9Q6n0kaOHImVK1cCAGJiYjBlyhT06NEDnp6eAIDc3FwkJCRg3bp1WL58OVxc\nXJCamqpnyEQA+DvNpiQmAmFhgI8PcOUK4Oysd0SVN348sHAhMHMm8MorekdDREQOrtjfOxUa1snh\n7kQ11IIFC7By5UoIIfDGG29g69at6Nu3r5agA4Crqyt69uyJ+fPn4/Tp0xgyZIiOERORTQoNBZo0\nATIzgV279I6m8oovvcbn0YmIqAZjkk5009mzZ6EoCpydnXHt2jWz8hYtWkBRFPj4+KCoqMisvG7d\nulAUBTt27DArO3XqFMaPH4/w8HC4ubnB398fUVFRWLJkicW2ypKdnY3Y2FgAwJAhQ/Diiy+WWSco\nKAiLFi0y219UVITNmzdj/PjxaNeuHerUqQMXFxfUq1cPgwcPxvbt2622GRoaCkVREB8fb/UY9Tn/\npKQks7KNGzfivvvuQ506deDs7IyAgABERERg6NChWLt2rdnxly9fxvPPP4/mzZvD09MTbm5uuOOO\nO9C1a1dMnz7d7BylTRx37tw5vP3227j33nvRqFEjeHh4wMfHB23atEFsbCwyMjIsfp64uDgoioKw\nsDAAwC+//IJ+/fqhVq1acHd3R+vWrbFgwQKr14PIJtnDLO9//gmcPQsEBQFt2+odDRERUeVJKbnp\nsAGQxstfPhU9nkoXFRUlhRBy1KhRJvvDw8Oloihy8+bNJvuvXLkihRBSCCEVRZF79uwxKT927JgU\nQkh3d3eZm5trUrZp0ybp5uam1fX395eurq5aezExMTIrK6tC8a9atUpr78CBAxWqW9Lhw4dNPpuf\nn5/09vaWiqJo+9944w2LdUNCQqSiKDI+Pt5q+2q7Z86cMdk/bdo0k/P6+vpKDw8P7bzBwcEmxycm\nJsq6detqdZydnWVgYKA0GAzavv/9738mdaZPn27xe5ZSyiFDhmj13NzcZK1ataSTk5O2r2HDhvLc\nuXNm9bZv3y6FEDIsLEwuW7ZMGgwGaTAYpL+/v8k1mzJlitVrQvydZnO2bZMSkLJ1a70jqby33zZ+\nhuHD9Y6EiIhISmny906FckX2pBMV06NHD0gpzXqG1d5xb29vi+Xqzx07doSLi4u2/9SpU3j00UeR\nm5uL6OhoHD16FKmpqcjMzMTHH38MV1dX/PDDD5g8eXKF4oyLiwNg7L1v1apVRT+mCVdXV4wZMwbb\ntm1DRkYG0tLSkJmZiYsXL+K1116DwWDAf/7zH+zevdtifVmJZ4oTExMxZ84cCCEwbdo0pKSkID09\nHVlZWbh06RK+/PJL9OvXz6TOjBkzcPHiRTRq1Ag7d+5EXl4erly5ghs3buDw4cN45ZVXKjRBXLNm\nzfDBBx/gxIkTuHHjBlJSUpCTk4O4uDh06NBBG/1gzeXLl/HUU09hwoQJuHDhAlJTU5Gamopnn30W\nAPD+++/jzz//rPC1IdJFZCTg4QEcOADU1JUgiq+PTkREVJNVNKvnxp50e2CtJ33ZsmVSCCG7dOli\nsn/y5MlSCCFffvllKYSQ/fv3Nyl//PHHpRBCvvrqqyb7R48eLYUQslGjRvLGjRtmcSxcuFDrST55\n8mS54+/atasUQsi+ffuWu05lvfbaa1Z7o0NCQqQQosI96WvWrJFCCNmsWbNyx9G0aVMphJBr164t\nd53SetJLk5qaKoOCgqSiKDIxMdGkTO1JF0LIJ5980mL9li1bSiGEnDlzZoXO60j4O80G3X+/sSd6\n6VK9I6m4a9ekdHGRUggpU1L0joaIiEhKyZ50KgchbGezVT169AAA7Nu3D9nZ2dr++Ph4CCEwYcIE\n+Pr64pdffjHpQVZ70qOiorR9UkqsW7cOADB16lS4ubmZnW/s2LGoX78+pJT48ssvyx2nOkO7v7+/\n1WPuv/9+BAcHm2x169a1+Kx3adQe7YSEhArVK42vry8AICMjAzdu3ChXHR8fHwBAcnJylcVhjb+/\nP7p06QIppdXPLYTASy+9ZLFs4MCBAIAjR47cthiJqlxNfi79p5+AvDygY0egVi29oyEiIrolTNKJ\nigkPD0e9evWQn5+vJWfp6ek4dOgQmjRpguDgYERGRiItLQ0HDx4EAJw+fRrnz5+Hi4sLunbtqrV1\n+vRpZGZmQgiBnj17WjyfEALR0dEAgP3791fpZ0lNTUVKSoq2Xb58GZcuXUJOTo7ZsTdu3MDcuXMR\nHR2NoKAgODs7axO+tb05AVNVJsedOnVCQEAAkpOT0aVLFyxatAiJiYml1rn//vsBAC+++CImTpyI\nuLg4i5+lInbv3o3Ro0ejSZMm2try6vb1118DAC5YGfobEBCA0NBQi2X16tUDAKSlpd1SfETVSk3S\nv/8eKCjQN5aK4qzuRERkR5ikOxDjOEbb2GyZmjSrveM7d+6ElFLbr/aWq+Xqa7t27Ux6y1NSUrT3\n9evXt3o+taz48WUJCAgAUHoSuGvXLhQWFmqbmjiWdOHCBbRu3Rr//ve/sWPHDly9ehXu7u4ICgpC\ncHAwateuDQDIysoqd3xl8fPzw6pVq+Dv749Dhw5pM9/XrVsXI0eOtDhD/osvvogBAwYgLy8PH374\nIXr16gVvb29069YNb7/9ttXZ2K15++230blzZyxfvhwnTpxAXl4eAgICtFEH6ndp7XN7e3tbbVut\nm5+fX6GYiHQVHg40bgykpwO//aZ3NOUnJbBli/E9k3QiIrIDTNKJSlCHvKuJYsmh7Gqybq3cklvt\n8S2pWbNmAIDDhw/fcltTpkzBiRMncNddd2H9+vXaxHYXL15EcnIydt2mdZP79u2Lv//+GwsXLsTD\nDz+M+vXr4/Lly1i5ciWio6PNJm1zcXHBhg0bsGvXLrzwwgvo3LkzDAaD9nPjxo1x6NChcp37yJEj\nePHFFyGEwLPPPosjR44gNzcXV65cQXJyMpKTk7U15aWt31Uiqko1ccj7sWNAYqJxmHv79npHQ0RE\ndMuYpBOVoCbbu3fvRk5OjvY8upqct2nTBl5eXti5cycA60l6UFCQ9v7MmTNWz3fu3DkA0Hqsy0ON\nJTk5GQcOHCh3vZLy8vKwceNGCCHw6aefYtCgQdrz4qqLFy9are/k5ATA+k2Isnq3fXx8MHbsWHz+\n+ec4e/Ys/vjjD4wbNw4AsGjRInz33XdmdTp16oQ5c+YgISEBqamp+Oyzz3DnnXciJSUFY8eOLfV8\nqnXr1kFKiT59+uC9995DkyZNIEpMlnDp0qVytUVkV9SZ0WtSkq7G2rs3oPDPGiIiqvn4vxlRCRER\nEahduzby8vKwbds27N+/H40bN9aSbkVR0K1bN1y5cgXfffcdzpw5AycnJ3Tr1s2knfDwcPj6+kJK\nie3bt1s8V1FRkbacmvrsd3kMHjwYtWrVgpQSs2bNqtwHBXDlyhXk5eUBMN58sOSHH36wWt/Pzw8A\ncPbsWYvle/bsqVA8TZs2xccff4zOnTsDgNlSdyV5eHjgkUcewcKFCwEAv//+e7kmolNvjFj7zFlZ\nWfj1118rEjqRfYiKAtzcgN9/B0q5QWdT+Dw6ERHZGSbpRBZERUVpCXBRUZHWc61Sf54xYwaAf3rX\nS1KHTL/33nsWk8fFixcjOTkZiqLgoYceKnd87u7uiI2NBWDsFZ4zZ0656xZX/LlqS0PFL1y4gA8+\n+MBq/ZYtWwIANm7caFYmpcR///tfi/XKelZbfaZbvYFQ8r2146WUpR6nUm8uWBseP2vWLFy/fr3M\ndojsjrs7oE50uXWrvrGUR1YWEB9vXDakTx+9oyEiIqoSTNKJLFCfS1d7gksOZVd/tlaumjZtGjw9\nPZGcnIz7778fx48fBwDk5uZi0aJFmDRpEgBgzJgxCAsLq1CMzzzzDEaMGKGdp3fv3vjuu+9w7do1\n7Zj8/Hzs3bsXkydPxqVLl8yGdHt7e2tLjY0ePVqbsb6oqAg//vhjqc/ZA8DDDz8MAPj222/x5ptv\nasvWJSYm4rHHHsPvv/9usd6HH36IPn364LPPPjMZTp+eno7Zs2cjLi4OQgj0KfZHd/PmzfGf//wH\ne/fu1RJxKSV2796NZ599FgDQoUMHs+H6lsTExGhxz5kzR7uBkpKSgueffx5z5sxBYGBgme0Q2aWa\n9Fz69u3Gpdfatwcq8MgQERGRTavowurcqmbDPwvbl0tFj6fSRUVFSSGEHDVqlMXyQ4cOSSGEtl24\ncMGkPC8vT3p4eGjl33zzjdVzbdq0Sbq7u2vH+vn5SWdnZ+3nmJgYmZ2dXenPMmvWLJP2hRDS29tb\nBgQESIPBoO1zdXWVkydPlhkZGSb1f/vtN5PP4unpqbVXq1YtuXHjRimEkIqiWDz/kCFDtLqKokg/\nPz+tne+//14rO3PmjFZn3rx5JvF6enpq9dR2nnrqKZPzFC83GAwyICDA5DoGBQXJw4cPm9SZPn26\n1e+5eNxCCOnv76+9HzdunBw5cqQUQsgZM2aY1Nu+fbsUQsiwsDCr38myZcukEEL27NnT6jGOjr/T\nbNiJE8aFOPz9pSwo0Dua0k2YYIz11Vf1joSIiMhMsb93KpQrsiedHJIQwqxXubgWLVogICAAQgg0\natQIwcHBJuXOzs7aM+gGgwHdu3e32la/fv1w+PBhjBs3DmFhYcjJyYGXlxciIyOxaNEibN26Fe7u\n7pX+LNOmTcPp06fx+uuvo1evXto673l5ebjjjjswYMAAzJ07F+fOncO8owDPdgAAIABJREFUefPg\n4+NjUr9jx47YtWsXBg0ahICAABQWFiI4OBhPPfUUDhw4gFatWpV6/s8++wyzZs1CREQEXFxc4Orq\nigcffBC//vor7rnnHgAwu9ZDhw7FokWL8Mgjj6BZs2ZwdXVFdnY26tWrh4EDB+Lrr7/GRx99ZFJn\n48aNeOmll9C9e3c0aNAA2dnZcHNzQ6tWrfDSSy/hyJEjaN68uUmd0r7nNWvWYM6cOWjatClcXV0h\nhEBkZCRWrlypPeNuqW5p/24qcgyRzWrY0LilpQG7d+sdjXVS8nl0IiKyS0JyeSFdCCGM3enlvP7q\nH/38vojIHvB3mo179llg/nzglVeAmTP1jsay48eBiAggIAC4fBkwGPSOiIiIyESxv3cq1IPDnnQi\nIiIyVROeSy++9BoTdCIisiMOl6QLIRoIIZYKIZKFEDlCiL+FEHOFEH4VaONBIcQHQoidQohMIUSR\nEGLV7YybiIio2kRHA66uwN69xl5qW8Sh7kREZKccKkkXQtwFYB+AkQB+BfAugNMAJgPYJYQIKGdT\nLwOYAKAlgHM393HMJhER2QcPD2OiDtjmUmzZ2UBcnPE9l14jIiI741BJOoAPAdQG8KyUcrCUcpqU\n8m4AcwFEAJhVznamAGgkpfQF8PTtCZWIiEhHag/1li36xmFJfDyQmwu0awfUqaN3NERERFXKYZL0\nm73oMQD+llIuKFE8HUA2gGFCCI+y2pJSxkkpT6lNV22kRERENkBN0rduBQoL9Y2lJA51JyIiO+Yw\nSTqAnjdft5UskFJeB/ALAE8AnaszKCIiIpvUqBEQFgZcvWp8Nt2WqEn6vffqGwcREdFt4EhJesTN\n1+NWyk/cfG1UDbEQERHZNiFsc5b3kyeNm58f0KmT3tEQERFVOUdK0n1vvmZYKVf3l3uWdyIiIrtm\ni0l68aXXnJz0jYWIiOg2cKQknYiIiCqiZ0/AxQXYs8c47N0WqLPNc6g7ERHZKUdK0tWecl8r5er+\n9GqIRSOEsLrFxsZWZyhERESmPD2Bbt0AKYGfftI7GiAv75+l13r31jUUIiIiAIiNjbWaz1WWIyXp\nR2++RlgpV59Ft/bM+m0hpbS6MUknIiLdqcnw99/rGwcA/PorkJUFNGsG1K+vdzRERESIjY21ms9V\nliMl6dtvvsaIErc1hBDeALoByALwa3UHRkREZLNiYoyv27YZe9T1tO3mAi1qTERERHbIYZJ0KeVp\nGJdfCwMwoUTxDAAeAFZJKW8AgBDCSQjRRAgRXr2REhER2ZA2bYDAQODMGeOs6npSe/OZpBMRkR0T\nt9INX9PcTLgTAAQB2AjjEPhOAKIBHAPQVUqZdvPYUACnAZyRUoaVaGcQgEE3fwwG0PvmsT/f3Jci\npXy+jFgkgHIPg1A7/x3p+yIi+8XfaTXMo48Ca9YA8+cDE0re564mqalA7dqAwWB87+WlTxxERETl\nVOzvnQo9oO4wPemA1pveHsByGJPz52DsWZ8HoLOaoJesZmFfKwBPABgOIObmMWE39z0BYEhVx05E\nRKQbtedaz+fSf/oJKCoCunZlgk5ERHbN4RYYlVKeAzC6HMclwspNDCnlDBiHyBMREdk/NUnfvh3I\nzwecnas/BvUGAWd1JyIiO+dQPelERLYqMTERiqJAUar213J0dDQURcGKFSuqtF1yMHfeCUREAJmZ\nwO7d1X9+KTlpHBEROQwm6eRwUlNT8cYbbyAyMhLBwcFwcXFBnTp10L17d7zxxhtITU3VO0SyMxs2\nbEBsbCzi4+PLPPZW1tS8Xe3+9ttvGDx4MIKCguDq6oqQkBDExMTgo48+QlqapaeEyC7pOeT91Ckg\nMRHw9wfatq3+8xMREVUjhxvuTo5t9erVmDBhAjIyMgAABoMBvr6+SE1NRUJCAhISEvDWW29hwYIF\neOyxx3SOluzFhg0bsHLlSiiKgqioKIvHuLi4ICIi4rYl6ZW1du1aDB06FEVFRRBCwNvbGykpKTh7\n9ix+/PFHeHh4YMSIEXqHSdUhJsY4cdz33wOxsdV7bvXGwD33GCeOIyIismPsSSeH8fHHH2PYsGHI\nyMhA+/btsXnzZty4cQNXrlxBTk4OtmzZgg4dOiA9PR3Dhg3DwoUL9Q6ZHEi9evXw119/4c8//9Q7\nFE1ubi6efvppFBUVoUuXLvjrr7+Qnp6OrKws7NmzB1OmTIGPj4/eYVJ1iY4GnJyA334Dbt7orDZc\neo2IiBwIk3RyCPv378ekSZMAAIMGDcKuXbvQp08fODkZB5MYDAb07t0bCQkJGDhwIKSUmDRpEg4e\nPKhn2GRnatpyYwcOHEBaWhqEEFi+fDkaN24MwDh0vl27dnj33XfxwAMP6BwlVRsfH6BzZ6Cw0DiB\nXHUpKAB+/NH4nkk6ERE5ACbp5BBefvll5Ofno379+li5ciUMVoZLGgwGrFixAnXr1kVeXh5eeeUV\ns2NCQ0OhKAp27NiB1NRUPPfccwgLC4Orqyvq16+PJ598EhcvXiw1nsTERDz77LOIiIiAh4cHvL29\n0a5dO7z55pvIzs6u9OfMy8vD/PnzERkZiYCAAO354TFjxuDo0aNmxw8dOhSKoiAiIgI3btwwK8/N\nzUXLli2hKAoGDRpkUlZ8QrK0tDRMnToV4eHhcHNzQ4MGDTB+/Pgyr8OpU6cwfvx4rZ6/vz+ioqKw\nZMkSFBUVWayjnnflypW4ceMGYmNjERERAXd3dwQFBeGxxx7DyZMnSz1vSkoKXnrpJbRo0QJeXl7w\n9PRE8+bN8fLLL1t9xroy33tcXJwWKwDMmDFDmxyu5CRxpU0cl5eXhy+++AJPPPEEWrVqhVq1asHN\nzQ0hISEYNmwYfv/991I/b2U5F5vBu06dOrflHFTD6PFc+p49xgnrGjUCQkOr77xERER6kVJy02GD\ncW11WV4VPZ7+cfbsWSmEkEIIOWfOnHLVmT17thRCSEVR5Llz50zKQkJCpKIo8pNPPpEhISFSCCG9\nvLyku7u7dp6wsDCZlpZmse1169ZJNzc3rX0vLy/p6uqq1W3ZsqW8dOlShT9ncnKybNWqldaOk5OT\n9PX1lYqiSCGEdHd3l+vXrzepk56eLu+44w4phJBPP/20WZv//ve/pRBCBgcHy5SUFJOyqKgoKYSQ\n77zzjrzrrrukEEJ6enpKb29vLYagoCD5119/WYx306ZNJtfB39/f5DrExMTIrKwss3rqed9//33Z\npk0b7bN5enpqdQMDA+WpU6csnnfnzp0yICBAO6+bm5v08PDQ6t55553y2LFjZvUq870nJCTI4OBg\n7RgvLy9Zt25dk031999/azFZulbqOQwGgwwMDJQeHh7ad+vs7CxXrVpl8fOq12vFihUWy0tTWFgo\nQ0NDpRBCvvHGGxWuXxr+Tquhdu2SEpCyYcPqO+eMGcZzPvNM9Z2TiIioChT7e6diuWJFK3Bjkl7T\nfPLJJ1ryc/To0XLV+fPPP7WkaPXq1SZlaoLm7+8v27ZtK3/99VcppZQFBQXy66+/lv7+/lIIIV94\n4QWzdnfv3i2dnZ2li4uLfOWVV2RycrKUUsqioiK5a9cu2aFDBymEkH369KnQZ8zLy9PqxsTEyF9/\n/VUWFBRIKaW8cOGCnDp1qpZEl0xef/rpJy3Z++6777T9cXFxUlEUqSiK/Oabb8zOqSZ/fn5+Mjg4\nWH777bdaWXx8vAwPD5dCCNm8eXOZn59vUvfkyZNaUt2zZ095/PhxKaWUubm5cuHChVryPnbsWKvn\n9ff3l+Hh4XLbtm2yqKhISmlMwNWbDg8//LBZ3cTEROnn5ycVRZETJkwwuRZ//PGH7NOnjxRCyH/9\n61+ysLDQpO6tfO8jR46UQgg5Y8YMszJVaUl6XFycnDJlivz555/ljRs3tP1JSUnad+vu7i6TkpKs\nXq/KJOlSSrlmzRrtRoClfweVxd9pNVR+vpS+vsY/H/7+u3rO2a2b8XxffVU95yMiIqoiTNJr2MYk\nvfpMmzZNS2LKq7CwULq4uEghhHz11VdNytRkrW7dujI1NdWs7jvvvCOFEDI8PNysrFu3blIIIRcu\nXGjxvKmpqbJevXpSCCH37t1b7ngXLVokhRAyKipKS85Leuqpp6QQQk6cONGsrGSPeUZGhvY5n3zy\nSYvtqcmfwWCQv/zyi1n5sWPHtJ7xTz75xKRs9OjRUgghGzVqZJJ0qhYuXKglrCdPnrR4Xks3HKQ0\njlRQv++8vDyTsscff1wKIeS0adMsfqa8vDxtNMKXX35pUnYr3/uIESNuKUkvy5gxY6y2fytJenJy\nsmzdurV2w8rNzU1u2bKlwu1Ywt9pNdgDDxj/fLDye6xKZWRIaTAYt/T0238+IiKiKlTZJJ3PpJPd\nU9c99/f3L3cdRVG0469evWrxmCeffNJim+qz24mJiSbPeZ86dQoJCQnw9/fH6NGjLbbp7++Pe++9\nFwDwfQWe+VyxYgUAYPLkyVaftx86dCgA4IcffjArmz17Nlq0aIFLly5h3LhxmDhxIpKSktCwYUPM\nnTu31HNHRkaia9euZvsbN26MBx98EADw5ZdfavullFi3bh0AYOrUqXBzczOrO3bsWNSvXx9SSpO6\nxT344IMIDw832z9gwAAAxufpiz+bnp2djS+++AIGgwFTp0612KazszOGDBkCwPJ1Air+vVeHfv36\nAQASEhKqrM3s7Gz06dMHBw8exJgxY7BgwQLk5uZi0KBB2Lp1q8U6jRs3hqIo+Oqrr6osDrJBvXsb\nX7dtu/3nioszTlTXqRPg63v7z0dERGQDuE46USV16NDB4v569epp79PT0+Hu7g7gnwTq2rVrqF+/\nvtV2r1+/DgA4e/ZsueIoKCjA7t27AQDjxo3D008/bfG4wsJCAEBSUpJZmYuLCz755BN07NgRGzdu\nBAA4OTlh1apV8PDwKPX80dHRVsuioqKwevVq7N+/X9t3+vRpZGZmQgiBnj17WqwnhEB0dDQ+/fRT\nk7rFWbv+Tk5OCAoKQkpKCtLT07X9+/btQ35+PoQQaN68udWY1QTb0nUq7bzWvveqkpqaigULFmDz\n5s04duwYMjIyzCbXS05OrrLzxcbG4o8//kCbNm3w8ccfQ1EUZGRkYNq0aRg0aBA2bNiAPn36aMcX\nFRXhwoULEEKgRYsWVRYH2SB18rgffzQm0Ldz3XL1RoB6Y4CIiMgBMEknuxcYGAgAVmfttqSoqEg7\nPiAgwOIx3t7eFvcX7xnOz8/X3l+4cAGAMalOSUkp9fxCiHL3xqampmrnKc9nzMnJsbi/RYsWmDp1\nKubMmQMAeO6559CpU6cy2yvthoOauBb/vMXfl1ZXLbN2raxdf8D4HUgpLV5/KeUtXf+Kfu9V4c8/\n/0SvXr1w+fJlLT5vb2+4u7tDCIG8vDykpqYiKyurSs6Xm5uLRYsWAQBeeeUVbcb5//u//0NaWhre\neusts0T9999/R1ZWFho2bIiGDRtWSRxko+66CwgLA/7+G/j9d8DKjasqwfXRiYjIAXG4O9m9pk2b\nAjAmHpaWIbPk6NGjWqLVrFmzKolD7fVs3bo1CgsLy9yWLl1aoXaFENi/f3+pbRYVFWk96iVdv34d\na9eu1X5OSEhQ50+4bazdMLgd1Ovk5+dXruv/008/VVtsZRk1ahQuX76Mdu3aYevWrbh27RrS09Nx\n4cIFJCcna99bVX1fp06dQkZGBoQQ6N69u0nZf//7Xzz55JNmQ9/VRy6GDx9eJTGQjauOIe9JScDx\n48b12Tt2vH3nISIisjFM0snuRUdHQwgBKSU2bNhQrjrqcYqioEePHlUSR3BwMIDyD2Mvr8DAQK2n\n88yZM5VuZ+rUqTh9+jTuvPNO+Pj44Oeff8abb75ZZr3z589bLVOHX9euXVvbFxQUpL0vLd5z586Z\n1b0V6vXPzMxEZmZmlbRZHZKSkrBnzx44OTnh66+/RkxMjNkjCGWtR19R165d095bWrf9o48+wiOP\nPKIl6osWLcLixYvh4+ODiRMnVmksZKOqY710te1evQAnDvwjIiLHwSSd7F79+vXRt29fAMD8+fNN\nEhBLMjMzMX/+fADAfffdZ/Ks8a3o0qULAOPwdPUZ8qrg7OyMDh06QEqJzZs3V6qNTZs2YcmSJTAY\nDFi1ahXef/99AMD06dNx8ODBUuvGx8eXWda2bVttX3h4OHx9fSGlxPbt2y3WKyoqQlxcnFndW9G+\nfXsYDAYUFRVhy5YtVdJmeamJbmV6uovfrKhbt67FY6xNcldZYWFhAIzxWhpRIITAqlWrcN999yE3\nNxfjx49Hbm4uZs2aVaEJGqkG69ULUBQgIQG4OY9GlVN76TnUnYiIHAyTdHIIM2fOhLOzM5KTk/HE\nE0+goKDA4nEFBQUYMWIELl68CBcXF8ycObPKYoiIiEDnzp0hpcQLL7xgNQbAOLN2Xl5eudseOXIk\nAGD58uU4dOhQqccWn0wNAC5fvoyxY8cCMD6HHhkZiSeeeAKDBw9GXl4ehg0bVmos8fHx2LVrl9n+\nEydOaDOzP/TQQyZl6gzq7733nsVnvxcvXozk5GQoimJWt7K8vLy02eZfffVVbYI+SwoKCqrs+W4A\n8PHxAVCxeRFUfn5+AIBLly5ZfJb+8OHDWL169a0FWEJQUBC6desGAHj55ZeRkZFhdoyTkxNWrlwJ\n32Izbrdv375K4yAb5u9vfBY9Px8o5UZdpRUVGSemA5ikExGRw2GSTg6hbdu22lJiGzduRNeuXbF1\n61btufOCggJs27YN3bp1w8aNGyGEwLx589C6dWuL7QkhKhXH+++/D1dXV+zYsQN33303fvnlF+1Z\n6cLCQhw4cADTp0/HXXfdVaEhzGPGjEHnzp2Rk5ODXr16YfHixSYjBpKTk7FixQpERkbivffeM6k7\nduxYpKSkoGXLlnj99de1/R9//DGCg4Nx5MgRvPTSS1bP7ePjg8GDB5v04u/cuRN9+/ZFXl4emjdv\njocfftikzrRp0+Dp6Ynk5GTcf//9OH78OIB/JiybNGmS9rnUXt2KsvQdzZkzBwEBATh+/LjZvwEp\nJY4ePYq33noLERER2Lt3b7naLA91NvktW7ZUeGh606ZN0aBBAxQVFeGRRx7BqVOnABgnp1u/fj1i\nYmJKnUSvst566y24uLjg+PHj6NKlC7Zs2aLNZ5CVlYUvvvgC3bt3R0ZGhjZSYODAgUhMTKzyWMhG\n3c4h7/v3A1evAqGhACciJCIiR1PRhdW5Vc2Gfxa2L5eKHk+WrVq1Svr5+UkhhBRCSEVRZEBAgDQY\nDNo+Pz8/+cknn1htIyQkRAohZHx8vNVj1LbOnDljVrZ582aTGFxdXWVgYKB0cnIyiSspKalCn+3y\n5cuye/fuZp/Nw8PDZN/MmTO1OgsXLpRCCOnm5iYPHz5s1ua3336r1du+fbtJWVRUlBRCyHfeeUc2\nbNhQCiGku7u79PLy0s5Xp04d+ddff1mMd9OmTdLd3d3kujs7O2s/x8TEyOzsbLN66nlXrFhh9VqU\n9h3t2bNH1q9fXzuPs7OzDAwMlC4uLibXaceOHeVuU2Xte79y5YoMDAzU2g4ODpYhISEyNDRUO+bv\nv//Wykv66quvTP6Nent7a/GGhobKTz75RAohZNj/b+/O46Oq7/2Pvz5ZIEACYZVNIYji1rqACijX\nII2tuFup6xVwoT9sL0tvreKOtSjXtoJ6q4gLarVelSrS28qVgizVVkRp0Qooi1CigIRFAmHL5/fH\nmYmTyUzIZJtJ8n4+HvM4yTnf8z2fM3MeeeQz3y0vr1rvVzyzZs3yNm3alF23WbNm3q5dO09LSyuL\n9aKLLvJPPvnE8/Ly3Mz82GOP9W3bth2ybv1NawQWLHAH92OPrf26J00K6r7xxtqvW0REpJ5E/L+T\nUK6olnRpUq655hpWr17NL37xC84880w6duxIcXExHTp04IwzzuC+++5j9erVXH311XHrMLMqtajG\nK/O9732PVatWcccdd9C3b19atGjBzp07adu2LWeccQYTJkxg6dKlHH744QndW8eOHVmwYAEvvPAC\nQ4cO5bDDDqO4uJj09HSOPfZYhg8fzssvv8wtt9wCBDN4/+d//idmxn333Rdz7fChQ4cyatQo3J0R\nI0bEnHCtQ4cOvPfee4wbN44uXbpw4MABunXrxqhRo1i2bBnHHHNMzHjPP/98li9fzo033kheXh4l\nJSVkZ2czaNAgpk+fzpw5c2KuNV6V97+yMv369WPFihVMnjyZgQMH0rp1a3bu3El2djannnoqY8eO\nZcGCBQwaNCjh64bLRWvfvj3z58/n0ksv5bDDDmPr1q1s2LAh7lrs0S6++GLmzZtHQUEBrVu35uDB\ng+Tl5XHzzTfz4Ycf0r1790rjqW4PgAsvvJBPPvmEW265hRNPPJGsrCz27NlDz549GT58OAsWLOD1\n11/nmGOO4fXXX6dVq1asXLmSSy65JKHhGtJA9e8P2dnwyScQmjuh1mjpNRERacLM63iJJYnNzILm\n9Cq+/+F/svV5SarIz89n4cKFzJgxg2uvvTbZ4UgDo79pjcQFF8Af/gDPPAOhuTFqrLgY2rULxrt/\n9VXws4iISAMU8f9OQi0makkXERGR6gm3dNfmeukLF8K+fdCvnxJ0ERFpkpSki4iISPWcc06wnTs3\nmJG9Nqiru4iINHFK0kVERKR6+vSB7t1hyxY4xPKPVRZO0sNfAIiIiDQxStJFpFpqMiGZiDQSZrXb\n5b2wED76CFq1ggEDal6fiIhIA6QkXUSqZf78+Rw8eFCTxok0deEW79pYL33u3GCbnw/NmtW8PhER\nkQYoI9kBSP2ZaBOTHUKZu/3uZIcgIiK1YciQYLtoEezcCa1bV7+uP/4x2Go8uoiINGFqSRcREZHq\n69gxaPneuxeeeKL69WzYADNnQno6XHRRrYUnIiLS0Gid9CTROuki0pTpb1oj88c/wnnnQdeusGYN\nNG+eeB0/+Qk89BBceSW8+GLtxygiIlLPtE66iEgTMGLECNLS0pg4MXWGr4hw7rlwwgnBxG8vvJD4\n+UVF37TC/+xntRubiIhIA6MkXURS0urVq7njjjs444wz6NKlC82bNycnJ4fevXszbNgwnnzySbZt\n25bsMJNGM+tLSjH7Jrl+8MHE10x/7DEoLg4moTvppNqPT0REpAFRki4iKWX//v2MGTOGPn36MGnS\nJN599102b95Mq1atMDPWrl3LzJkzGTVqFIcffjgPPPBAskOuV127duWYY46hQ4cOyQ5FpLwrroDD\nD4cVK2D27Kqft2cPTJ0a/HzLLXUTm4iISAOiMelJojHpIhXt37+fc889l3nz5mFmDBs2jNGjRzNg\nwACahZZj+vrrr1m8eDEvvvgiL7/8MscffzwffPBBkiOXROlvWiM1ZQqMHw8DB8Jf/lK1cx5/HEaP\nhr59YcmSoFVeRESkEajumHQl6UmiJF2koptvvplf/epXpKen89xzz3HllVdWWn7NmjU88sgjPPTQ\nQ/UUodQW/U1rpHbtgiOOgG3bgiXZzjyz8vIHD0KfPrB6Nbz8MgwbVj9xioiI1ANNHCfSRK1evZof\n/vCH9OrVi6ysLNq2bctZZ53FU089RWmccaH5+fmkpaXx3HPPsWfPHu655x769OlDixYt6NSpE1de\neSWfffZZpdfdsmULEyZM4Fvf+hbZ2dm0atWKE044gTvuuKNaY8U3btzIww8/DMD48eMPmaAD9OrV\nK2aCvm/fPl555RWuvfZaTjzxRDp06EBWVhY9evTgmmuuqbTlPS0tjbS0NNavXx/z+Lp168rKRCst\nLWXGjBkMHjyY9u3bk5mZSceOHTn++OO5/vrrmTNnToVz1q5dy+jRozn66KNp0aIFLVu2pEePHuTn\n5/PAAw+wdevWcuUrmzhu1apV3HvvvZx99tnk5eWRlZVFbm4uAwYM4Ne//jUlJSUx72nGjBmkpaUx\nePBgAGbPns3gwYPJzc0lOzubAQMG8NJLL8V9z0TKZGfDj34U/Dx58qHLz5wZJOhHHgmXXlq3sYmI\niDQU7q5XEl6AB29/1SRaXpqG2bNne1ZWlpuZp6Wledu2bb158+ZuZm5mXlBQ4MXFxRXOO+uss9zM\n/OGHH/aTTz7ZzcxbtGjhrVq1Kju3ffv2vnr16pjXXbRokbdr167sullZWd6yZcuyc4844ghfuXJl\nQvfy85//3M3Mmzdv7ps3b67W+xE2e/bssljS09O9ffv23rJlS09LS3Mz88zMTH/++edjnhu+p88/\n/zzm8bVr15aViXbVVVeVXTf8eWRlZZVdt3///uXKL1261HNycsrKN2/e3Nu1a1dW3sx8zpw55c4Z\nPny4m5lPnDixwvX79u1bVlfLli29Q4cOnp6eXlbXqaee6l9//XWF85555hk3M8/Pz/d7773Xzcwz\nMjK8bdu25WKZMmVK3Pc8Ufqb1oht2uSeleUO7h99FL9caal7375Bucceq7/4RERE6knE/zsJ5Ypq\nSRdpoFavXs0VV1zB3r17yc/PZ8WKFRQVFbFz506mTZtG8+bNmTt3LmPHjo1bx913382OHTuYM2cO\nxcXF7Nq1i4ULF9K9e3eKioqYMGFChXM+//xzLrjgArZv385NN93Ep59+yp49eyguLmb58uWcc845\nbNiwgUsvvTRuS34sb7/9NgD9+vWjY8eOCb8fkXJychg7diyLFi1i165dfPXVVxQXF7Nu3TrGjRvH\ngQMHGDVqFBs2bKjRdSItXLiQ3/3ud2RkZDBlyhR27txJUVERe/bsYePGjcyYMYNBgwaVO+enP/0p\nu3bton///nzwwQeUlJSwdetWiouLWbJkCePHj6dNmzZVjqF///489dRTrFu3juLiYrZs2cLu3bt5\n4403OProo3n//fe59dZb456/bNky7r33Xu677z62bt1KUVERX3zxBZdddhkAEyZMaNIz6ksVdeoE\n110X/Pzgg/HLzZsHS5cG5YcPr5/YREREGoJEs3q91JIuqeG6666XPlj/AAAe90lEQVRzM/OjjjrK\n9+zZU+H4E088Udaq+tlnn5U7Fm5Jb9WqVczW8pkzZ5a1ru/bt6/csauvvtrNzG+77baYce3bt89P\nPPFENzN/9dVXq3w/Xbt2dTPz0aNHV/mc6rr++uvjtkZXtyV98uTJbmY+dOjQKsfRokULT0tL8/fe\ne6/K51TWkl6ZtWvXemZmpmdnZ/vu3bvLHQu3pJuZT5o0qcK5e/bs8U6dOrmZ+XPPPZfQdePR37RG\nbvVq97Q094wM9/XrY5cpKAha0e+7r35jExERqSeoJV2k6XB3Zs6cCQTjt7OysiqUueGGG+jWrRvu\nzquvvhqznssuu4xevXpV2H/hhRcCsHfv3nJj03fv3s0rr7xCeno648ePj1lnZmYm3//+9wGYO3du\nle+pqKgIgLZt28Yt8+1vf5vOnTuXe3Xp0oV33323ytcBOP/88wF45513EjqvMuEW782bN4e/iDuk\n1q1b4+4UFhbWWhzx9OzZk+OOO47i4mKWLVsWs0yLFi0YN25chf1ZWVl897vfBeDjjz+u0zilkejV\nK5gE7sCBYMb3aB9+CG+9Ba1awU031X98IiIiKUxJukgDtGbNGnbu3ImZlU32Fc3MyM/PB+DDDz+M\nWebUU0+NuT8jI4NOnToBsH379rL9S5cuZf/+/ZSWlnLCCSdUSJjDr1/+8pcAcSdfq64tW7aUe23e\nvJlNmzaxf//+CmWLior4+c9/zsCBA2nfvj0ZGRllE75dGpqgqjaT4yFDhtCsWTOWLl1Kfn4+L7zw\nAl988UWl55x33nkAXHvttUyYMIG//e1vHDhwoEZxvPXWW1x55ZUceeSRtGzZsuye09LS+Mc//gEQ\nN67jjjuOFi1axDzWtWtXAHV3l6r72c+C7RNPBLO9R/qv/wq2o0ZBJV/MiYiINEUZyQ5ARBK3ZcuW\nsp+7desWt1z4WGT5SDk5OXHPzcrKwt3LJcDh5M7d49YZZmbs2bOn0jKR2rVrxxdffFFpEhiZXB48\neJDMzMyypS0i/fOf/+Tss89m8+bNZbHk5OTQokULzIx9+/ZRVFREcXFxleM7lN69e/PYY4/x4x//\nmEWLFrFo0SIAevTowbnnnsuoUaM46aSTyp3z4IMPsnLlSt555x0mT57M5MmTad68OQMHDmTYsGGM\nGDEiZi+JeMaMGcOjjz5ads+ZmZlls8wDbN26lf3798e970M9D0DML0REYjrlFPjOd2DuXHjsMbjt\ntmD/2rXBcmsZGcGa6iIiIlKOWtJFGrh4y2rVhfBEcLm5uRw8e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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 338, "width": 500 } }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8,5))\n", "ax.plot(np.concatenate([t_delay_list, -t_delay_list[-2::-1]]),\n", " np.concatenate([g2HOM_e, g2HOM_e[-2::-1]]), 'r',\n", " label=\"Two exponential\")\n", "ax.plot(np.concatenate([t_delay_list, -t_delay_list[-2::-1]]),\n", " np.concatenate([g2HOM_G, g2HOM_G[-2::-1]]), 'b',\n", " label=\"Two Gaussian\")\n", "ax.plot(np.concatenate([t_delay_list, -t_delay_list[-2::-1]]),\n", " np.concatenate([g2HOM_Ge, g2HOM_Ge[-2::-1]]), 'purple',\n", " label=\"One exponential &\\n one Gaussian\")\n", "ax.legend(loc=3)\n", "ax.set_xlim(-5, 5)\n", "ax.axhline(y=0.5, color='k', linestyle='dashed')\n", "ax.set_xlabel('Wavepacket delay [$1/\\gamma$]')\n", "ax.set_ylabel('$g^{(2)}_{HOM}[0]$')\n", "ax.set_title('Two-photon interference visibilities for '+\n", " 'delayed wavepackets');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Versions" ] }, { "cell_type": "code", "execution_count": 14, "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 Nov 17 11:23:19 2017 PST
" ], "text/plain": [ "" ] }, "execution_count": 14, "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" }, "name": "G2(t,tau) Kevin Fischer" }, "nbformat": 4, "nbformat_minor": 0 }