diff --git a/3_qcvv/blochSphere.png b/3_qcvv/blochSphere.png new file mode 100644 index 000000000..5617308d7 Binary files /dev/null and b/3_qcvv/blochSphere.png differ diff --git a/3_qcvv/exampleCircuit.png b/3_qcvv/exampleCircuit.png new file mode 100644 index 000000000..7b2232096 Binary files /dev/null and b/3_qcvv/exampleCircuit.png differ diff --git a/3_qcvv/wigner_functions.ipynb b/3_qcvv/wigner_functions.ipynb new file mode 100644 index 000000000..755046611 --- /dev/null +++ b/3_qcvv/wigner_functions.ipynb @@ -0,0 +1,725 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Wigner Funcitons\n", + "---\n", + "### Contributers\n", + "Russell P. Rundle$^{1,2}$, Todd Tilma$^{1,3}$, Vincent M. Dwyer$^{1,2}$, Mark J. Everitt (m.j.everitt@physics.org)$^{1}$\n", + "\n", + "1 Quantum Systems Engineering Research Group, Physics Dpartment, Loughborough University, UK\n", + "\n", + "2 Wolfson School, Loughborough University, UK\n", + "\n", + "3 Tokyo Institute of Technology, Japan\n", + "\n", + "## Introduction\n", + "\n", + "In this notebook we demonstrate how to create Wigner functions by either using the full state or by measuring points in phase space. We will show the different methods which can be used by inputting an arbitrary state or just measuring the state on both the simulators and the IBM Quantum Experience.\n", + "The spin Wigner function presented here is based on work from [*T Tilma, MJ Everitt, JH Samson, WJ Munro, K Nemoto, Phys. Rev. Lett. 117, 180401*](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.117.180401) and can be calculated analytically as\n", + "\n", + "$W(\\boldsymbol{\\Omega}) = \\mathrm{Tr}\\left[\\hat{\\rho} \\; \\hat{U}(\\boldsymbol{\\Omega}) \\hat{\\Pi} \\hat{U}^\\dagger(\\boldsymbol{\\Omega})\\right]$\n", + "\n", + "Where $\\hat{U}$ is the rotation by the Euler angles and $\\hat{\\Pi}$ is the parity, such that\n", + "\n", + "$\\hat{\\Pi} = \\frac{1}{2} \n", + "\\begin{pmatrix}\n", + "1+\\sqrt{3} & 0\\\\\n", + "0 & 1-\\sqrt{3}\n", + "\\end{pmatrix}$ \n", + "\n", + "for one qubit. The Hilbert space for a single qubit is spanned by the Euler angles where $\\theta$ (the elevation) and $\\phi$ (the azimuth) thus the full Wigner function for $n$ qubits is given by $2n$ degrees of freedom. \n", + "\n", + "When there is more than one qubit, we take the kronecker tensor product of the $\\hat{U}$s and $\\hat{\\Pi}$. In the following examples, various methods of extracting information from 2 entangled qubits from four degrees of freedom are shown.\n", + "These methods include taking an the equal angle slice, where we set the angles $\\theta_0 = \\theta_1 = \\theta$ and $\\phi_0 = \\phi_1 = \\phi$. We can also set some angles to be constant values as we plot the remaining angles against each other, an example of this can be seen when plotting the plaquettes where we set $\\phi_0=\\phi_1=0$ and we plot $\\theta_0$ against $\\theta_1$. Finally we show how we can simplify the Wigner function by just taking a 2 dimensional curve around the function, this is shown when we look at the equal angle equatorial slice where we take $\\theta_i=\\theta=\\pi/2$ for all $\\theta$s and $\\phi_i=\\phi$ for all values of $\\phi$ where $0\\leq\\phi<2\\pi$.\n", + "With this visualisation methods we show how these points in phase space can be measured directly by using the Wigner function tomography module and it works by using the u3 gates to rotate to points in phase space. Below is an example for measing points for a Bell-state, the first two gates create the Bell-state and the two u3 are example rotations to a point in phase space.\n", + "\n", + "\n", + "# Wigner Functions for Arbitrary States\n", + "\n", + "first we will look at the Wigner function tomography module and show how we can create the spin Wigner function on a Bloch sphere for an arbitrary state. All that is necessary is to input a density matrix or state vector for a known state and then set the desired resolution for the plot (if no resolution is set, the mesh of the sphere will default to 100x100)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Checking the version of PYTHON\n", + "import sys\n", + "if sys.version_info < (3,0):\n", + " raise Exception('Please use Python version 3 or greater.')\n", + "import numpy as np\n", + "\n", + "# importing the QISKit\n", + "sys.path.append('../..')\n", + "from qiskit import QuantumCircuit, QuantumProgram\n", + "import Qconfig\n", + "\n", + "# import tomography library\n", + "import qiskit.tools.qcvv.tomography as tomo\n", + "\n", + "#visualization packages\n", + "from qiskit.tools.visualization import plot_wigner_function, plot_wigner_data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Wigner Function for an entangled Bell-state\n", + "We begin by creating the density matrix for a Bell-state (note that the matrices and state vectors need to be created in numpy matrix format), $\\left(|00\\rangle+|11\\rangle\\right)/\\sqrt{2}$, which is given by\n", + "\n", + "$\n", + "\\frac{1}{2}\n", + "\\begin{pmatrix}\n", + "1 & 0 & 0 & 1 \\\\\n", + "0 & 0 & 0 & 0 \\\\\n", + "0 & 0 & 0 & 0 \\\\\n", + "1 & 0 & 0 & 1\n", + "\\end{pmatrix}\n", + "$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 0.5 0. 0. 0.5]\n", + " [ 0. 0. 0. 0. ]\n", + " [ 0. 0. 0. 0. ]\n", + " [ 0.5 0. 0. 0.5]]\n" + ] + } + ], + "source": [ + "density_matrix = np.matrix([[0.5, 0, 0, 0.5],[0, 0, 0, 0],[0, 0, 0, 0],[0.5, 0, 0, 0.5]])\n", + "print(density_matrix)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This density matrix can then be put into wigner_function which plots the Bloch sphere Wigner function for the equal angle slice, i.e. where $\\theta_0 = \\theta_1 = \\theta$ and $\\phi_0 = \\phi_1 = \\phi$" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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v/MIvyMzujGTyPwBsg0lOphDQPrjrF7mW00gmPwggjkQijgcffLju/a6G9nOy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\nPRdy3+FYrlZgueDT6cDvB1Uhp37xf92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oiypaT64IbUuhQXK06PWRaLAdLNup4oInjqBo\n4/NK2oVH+Xtlu1qUl8SFIKxlz2qzw3R8G7ufpepu2Xl+Edbuolw40Z5wmrdTX20hR4nyVOohguAk\n04Ca++/wEr9tdkmlyluj5UKLlThhdvjRRSqFSDaNNQPA6YnicxZ3sXRdrOJD8G3mKCJYFIqn74d9\ngATaKWSYyWREZNUMycmykXeD0eojDNetMyOLKOG92JgjwTCNYBFNPgULSixz52QhQqzchNNhzx/2\nVTXbLFpgBZyuFdAOEo2sInHFRwXGYJwuXjYhwtpoepIIzOhBao+z40asx7RtHFq4dbF96XvKHTZe\nyoGXlwCC/eOjIClfybWOJ9TTvWsZ7DG/AcHPjMJzrlGJytqPQ3NBuuBiL6zMQ9ZqoxGGPAmeQokZ\nf3kGwMtQcx8Odz9phGrY+krKQNjb2JNE29s4oHBgqfAhL1bKXSxDB3QF+LA/V+Sk8nIk7TPKMJ1O\ny5Q6NWWhowYrvbUW4mQxWtnJWr/euFgUXaA/38WJ7zQxrD1BbAb6H32puQuXolCp/WOKgCaEdhEI\nCVZLNFo0XUoy+TKMyCHBQxcXcoC4COlm7fD7Se8Tn0+QT+zM1xNZBN0ontfF28iZojwsoNgZs+HT\n8FDuFvXZzscKuydKhQ4J29niBUbBlu1jVxJC5LicLPuY3M0isZeDCT3yuRIpeR4AslCZj8LDr5tD\nub5o2Wy4i0W2MnfCeOyOU0qQ2evpX5SFPTG0PeUO7174b4YLf4KS4NtvlGE2m5XJoWuGVHy3EZHF\naGWRBZhi1aXPF/aF+jxMzSweKqRSDpXmYNX6pDuDYP4Tp0Y/Ykf4J5mchql0zetW8ZAgz6sKy8Xi\nyx7bl+DhRMCUFeDiK8v2yUH/XEkg2e8BhQ/DwoQRq80urdDhuKftOWHih+eH5WDCgjbcdbJzuFxh\ny0qx5z/k7hdPjOcjDwEjbMkxy0DXzyKxdQYq83F4MX9yae5e0egSGzu06IKLJDsHi9bz+5BjxOP6\nnBWNFudh8S6GhQ2jUaCvrxtTUymUD2z0IlhXrz1EViaTEZFVM0Rk2Ui4kNHK4UIKFdKUG+4yPPyk\nGIcWMvyCbec8hZ3gbeG10K+RfQGv5jiT5TephIkJ/UalUlBzr4KpCdSDoIPF7/thiovaVd95iJDC\nfRQajLHj88Kk9LiDHZdEXSfbBtChQjoW5XjR95aHMfnjiLUuwu4j0OKNh/r4uri1b6nj8DCyq81e\n51nblM+5M7hCiC73ylUlns9lSCFFKlaaZvcz0KMPTyGS/YS7GzxsWEnoMOwYtH4R4UcSUy59NzRU\nSdgQ0J/BgH/r92/8zw5951v7Dyknl8uJyKopjQ8XKqXuVEr9WCl1TCn1Dsf6A0qpl5VS3/Nvj1W6\nb7WIyGK0qpO1c2cw4d09QNKuDj6D4InSvgguNeVzrqphbMw93U4Y6r9ugBFXXFDFHfc8/4ruE2wZ\nCOZr8RIQfIqdHhjXjAQLr8VFYotElH2Bo77Q83HBF0WxKLKn1aGbnZfFxZPHHlMOl70NPwGG5Wa5\nRFwHigWW7fbxvK1K4NPwEHzuwrxjmVeKp8K8VDVeh9I97zQ6sx8LF0EEia1SeVjltqlCdLkE1bp1\nJoQeFpkEjOjSx+ChbpsOR3v75GXl83n09fU1uhttAs+vrNetTA+U6gDwxwAOA7gKwP1Kqascm37D\n87zr/NvvVblvxUi4kNGqTta6dbqaczxuKjxHoyaPNpGIYG5uEiZMaIcH+bLtUlUbNqwWOrm7RhaW\n2t5ergA7POg/Vl9ZiWLnioSH/ZhCWbxmFq+91AkTtqN1cRSXMKDXSuErOxQJ/zh8RCHV4UrDCC9e\nGwtsP57/FYOp7g+ECxs7RNdhtdNjV4FSnmPFC6bykKj9HHbOF9/WLglRrlq8XV+L54F5COZs8dAh\n3St2TzcKwep6WpmMslLomAAqNdqwVOiQtik1uq2US4bi8gyuTemcUDqKOQhTlNRFe+ZlZbNZ9Pe7\n8z2FhdDwcOEuAMc8z3sRAJRSTwL4RQA/rPO+TsTJYrSqkwUEQ4UTE9rNojSPubkMzEWdJ1LbroEN\nCYWw9cDS/qBqn4ul/nIKJiRCblQ/u3FHi9yoXgTDitypAowj1WMdg4RUN4wo4+FDngdG63ioj8Sa\n7ZjxY3C3iifrh4UOuWqw3ayI1QbWxt0tvg9tE2XrXe4X39Z2T10hRPuzt0cdunLFXHMcUnvWuuej\nDWkAyIx/T5XOp6Ay/7fjeVBZ2JA7WOVGHFYyqjFkGxJdmzYVa7d168w25Hi5CQvRJKxtWp98Pi8i\nq2Y0xQTR6wG8xB6P+G02e5RS31dKfVEpdXWV+1aMOFmMVhRZd92lQ4WU8E4jiQYGdJ2sbBaIxWLI\nZOgCQtCX1S5E2mGtXyz21Ccuyj1X+HQ6umq1G7qgBChKdh9EcViPhwFtl4onjfP13CWyxQtPbu9h\ny3yEHx9ZSMvkSNFr5I/J5eLH5205q42PLqT1EQRHGroseb4f5TC5Co5SH8h94u3c8eCuGLXbSfKu\nUYdwtFUzz6hdi8tVjZ6PmqT3IQ2T+6agSzt8EF7s7eZQ5ZLcs9nwUYnl9iszmjCSTftdCD938UGN\nrqcMhgsr+d3TnwF+7mhdstksVqxY0ehutA2lzsm1wPMwpJR6mjUlPc9LVnmY7wC4yPO8aaXULwD4\nRwBbatZJhogsRiuGC9etA44d0+dgSnanUCEXXeaiQidGKt8wAV0zyw7D8ZNnudpWLUg0CvU7zwNY\nBZNz4hJYPAmdwiQ8OZ0LmzS0iOJT57hKK2Shw31caHWxY3DxROFBoDjsyJftgqMxaBeGjq9YOxfc\nLmfJ5Sq5QoMkhmyBxUN1JOTAtumw9oe1bJd8IHGl4BZfgHs6Hj6qEGw/fgzF7nnIkF4HCa55mH/p\nL0Nl/l940d/Su4aJKE6ZkF9hXaltuAMW8pzlwoY8V4uzenUEZ85w4QkU/7GhAqRxmO9W60+xk8vl\nMGCP7hQWhFL1mTuWk8lg3PO860tscgLARvZ4g99WwPO8Sbb8BaXUnyilhirZt1pEZDFaUWQBRkzx\nP7oDAzpPKyi0SGBNwoyeAvRJlZYbHUGmUY0UPls8geubf4VRRz4PM0qQQm72SELuWJEbxKu/kzNF\nQqgH5v3jgscWWD0wYs12sPgUOj1sf+5CpWBEGcAveEZo8Bwsei3cUYuxZS6kwkQWrY8iKFz4PjRy\nj7tXtkMWJq64U0afu+2C2tPxlJvn0J5LkZYBI8BIuHERyUtZkEgkwTsP/ackgg0r/x+MnPtN91PT\nF67UFafUNpWIrsAXu9jJChNUrm0A7UB4hbdzELq8CxAUXXMI0vp5Wfl8HoODg43uRtuwBCKrHE8B\n2KKUugRaIN0H4AG+gVJqHYBTnud5Sqld0F/ks9CuQ8l9q0VEFqPVwoVvfGMwVDg2FnSyBga0y6Wh\n8NMMW+a5MB0wJ9Cw5HJ7udpaRrz+UjlKbRdemJSgUCG/RuURQWR8HOrmPwGwFibZncKFdtFRO08q\nzR5zUZVB0MHiYR3u9ABaHPEQHhdsPBTInS0uqGhfD+bib4cNuQijzyjqt/PwJk8q50LHdstcQobm\nByTRRYnQrvBgxNqPixourmDty4WbnZzvSoYvJbp47Sy7jhYdjwsaym2j91jBJMHr24kTHX51jhJJ\n65VM18LFUrnQYsh6HhK0ofpZ9nyebv1WbmBJL/Q5hOYy7ECri6xcLoeVK1eW31Aoy1I4WeXwPC+r\nlHoLgC9Bf0H/wvO8HyilHvHX/ymAewH8mlIqC33hu8/zPA+Ac9/F9EdEFqPVRNa6dTpEODam74eG\ndB4WoAUWjS7s7QWmpgATUqLRhbywIMETcsNGFbZGwiu/iAQvKBfC5F9xN4sS310Ci0YUksDi7Vxg\nUU4W2HogGPrrgXGwqK0D+udIx3aFIikZ3oNxquyQIT0vPSf9xGn7MJfK9Zi38ZCjLRzpOTMh+5JQ\nscOHtqCyRwTybexwImHnf3FcIw6VY9nlblHIkP5M0Gvgx34Zau4D8OKPoyoqLQNRyfoFiC4gWLi0\nuIipy8VqX/L5PFatWtXobrQFzSCyAB0CBPAFq+1P2fLHAXy80n0XQxO8Hc1DK4YLqTZWPK5PlHz6\nMz7aMCiW7GR3WMulRnHU6p+rq/RA9XieO7HeJbBSKaDnio8hWK6BFxDlAovnXeVQHDIkZ4sXanQJ\nLCpLQGKABBZ3sLio6gxZtvOxYD3mIcMoe740gk4Vz8lyiawwd5Lcrwx7DARzlyjPzE5Op+PzfV1u\nlktIcSfLnm6HH9sVPgwbcWh/X7jIst8D29HiCfEdACaxNvY+nMq82/FcS0Q2W/bCVmnYsIJQDPR3\nmP6MtX7yez6fl5ysGtEsIquZkLeD0UpO1kc+chTj49qxon+hAwP6Nj0dFBnB0eK8JAO5WpWMKqxn\nrazaYf/JL05t6YcpwcDLH9CF1i46SgInAeMEkpvFQ5ZcYPEyCjn2mAs2eu9JYKVClvnx4e/DHS0g\nWGOMCwRyLO18LC6sctZ9mNtliy8uhui1kpPGa16R+OKimo9YzFjHs3OjXInxfISinafFCQsf2vMx\n2tPuRBGcfkfBCFdKjM+AHK/Tp5U2f5aScm5YCSoPG5Y7J8RhcjlbF8/z0NMTNoWXUA0isoppdJZz\nU9FKTlY0qgUVr3dI9bFohgiqnaUh8QAEHSSXsJxB8KvRGiGDUqWFAKCn5zdhBBQJJ4LaemGcLsCI\nMtqGhBXlcdHx6CQdY+t4vSqqwxWHrpNFx6D3udta5p8Xr4FlV5wHglPtdCEobqL+fYwt8+95l3Wz\na2jZtbMoD4u+Q7wGFi13sdcSsfblOYB8PS3z7yb/3rmEn6udUyopntfMsl0znk/GK8JzaBqeeQDz\nUOf/rxLPtQjK1d7yCbuw8eT3UtsQsVhY5XP7HEC/DzPCsBXxPA+e56G7u7v8xkJF2N+5Wt9ajRbs\ncv1oJScL0IJqetrk1lIeFo0qJIcrHudhAKpIDpS+iLUW5QTWxRe/BcAQtOXAnSq70Ci5VIDJ26LE\ndnJ0uDiKwLyntD1QPJKPcqq4kAJrB4IVz+0crAyC7hVgQoS8sju5Y0BwgmnqF825RKE9eg3cmbIn\nV+aOkP3doJkCeCJ8xlq2XShKlrfrb/ERfXZCfsZahrWNHVakvpcbfchdLHrdWRjByEO9vACqYvtP\n6vuFXgEqDVVVUPm9kppY5fK1Kq+V1frkcvqz7ehoj9fTaMTJKkbeDkarOFlHP/ABHcSyRhVOTJj6\nWDzp3bhZnQDGocNLPOk9LCywVCeeSqfUqZziUCFVdScHyw4L0mPKkaLSDFl/X8rDsQUWF2H2dDYe\ntJhKwYgqLjiyKBZbPAcrAjPikxwqwHx2dsiQnC4Kx/HcrBSC5SJcCe+0zOui8VwuEjo8jEbLJHzs\n2lm0TOKHh525YCLhRaLUTo6n0Ku9zIWZS2iVgpebAILijAtQIBg+5K+dxFkK6szb4G30J5Je7JWm\n0nBgGdHFKU5wr1Rw8bC4KzxY6fvdfGSzWUQirfenslkRkVWMvB2MVnKyOrOzSKW6C9Pn0KTQAwO6\nLhYlvVOh6KmpFIrnJbNHErqg9pBpQBqKO0nbTnrfu/e/AbgAWgD1IuhakcCiY8VZewb6AkMjAPsR\nnLeNJ7+nodQq0IXY88yoQqW6C22xWNTvlxZB0ajnV+OP+3WKbMFpX9hpPRdy1EYvPMaWKaGcQn7c\nYSMxZYss/pz8cRRBIQf23nDnio8ypGPzaW1c7hT1k9fh4tvwfV25WnZSfCUXfhJK5Wpn0chQei7u\n7lE/ugBMoHPst5Fe99/NU9gzDCwil6reUFe16x12PuiHcUNbn3Q6LSKrhojIKkbeDkarOFkAkI93\nIx5HYVJoDj+Px+OmrIMJJwHmJDoJd/5VM4oqN2GlGswyDxFyJ4sLLBpdSI4UYKrAk8DildcBLaD6\n4HnzUKoP8XhwWpZs1kNXlw4v5XK6rasLSKU8dHQo5HL64h6Pd2B+Xu8bi3UVjkHiSzNf9Nzms6SQ\nIYkgwIgsEl8kYPgoPgp9zaI6SFxE2WMOCVQeCgVMAnxYgVKXQ8XbKCGdJ7xz8QMEhbcrYT8MLq54\nKQku1Oi3wQeA0PPqGlqZzHjpjPJKE0ta4kqVgJk9onXOF5z5+XkJFdYQpSorDbecaIVf8pIRi8Wg\nlILn2ReN5iOS0k4WUFwTi4jHdX6WxlUfizsYFU++6WAhhUlrhbnAukZUHjnyHgTnJ4S/zPubgMmn\nopyrOMzFlAQWhQ0BwEMiEUEq5SGR6EIqBV9QUZ6OFljxuOf3S/nuFTmMHqJRhWhUt5lrqsL8vBFf\nJGBSKd13pfSxPW8eRiDyvKw5mJAniRcewswiKKpyMOKHRtaFOVlcMPGQInex+Lb0naKCquRK8WXq\nAw8RkhjkIURXGw9BctHFE9mrwa7TxavP06jCLIJiS/l9p2l3UlA//XV4Vx4NCqrwSQNLb1ND7FBh\nOPxz7of+I8ZpH1EyPz+PaEsI2tZAnKxi5O2w6OzsxPz8fPkNG8TRt79dW1ebNwMozsU6dsyECUdG\nzLIOAVRSgLT1CCvb8OijvwbgFdAii9fDAoKOlh0uTEBfTGkkYAZK9RUEkcHDihUK8/MeaH7Z3l4U\nxBRd7ONx3RaNAl1dHmZm9Hb6D7TePxpV6OjwAssAMDOjjxOPG7Gjv552gj2JKy6o7FFxFOahfcm5\nAYLOli2m7Pwqel4SRlm2nh/PLt1gC6wIW+9KeOd1tSjBPme1cbfK5VyV+wPgSo63C5LCWib4dEiU\ny5aGnpnDgie3L8blWtIrWJiY6kE7lG4AtMiKxRZfr0/QiMgqRt4Oi66urqYWWQD0VXt6GtGoTkil\n+ljHjpmcrPHxYNK7UjE/3wcoP3VGs8ILehZfOItDhZugBROJKXv6HH4ccq/ocT/oIk9OVTxunCfP\n89Dbq3PhqFi0scnJtVIFUdXTo08+qRR8QaZ8N8vz2/VxTbkehVQq7z/W4mdmRm+jHTPjqKVS5Fzx\nPCwKH/I2LnbIFeJ5WS7Hys4Jsx0rD0FRR+KHhxL5KEM6vu1m8Xpa9qhH12hC1yhFcpm4I8UdL3oN\npQqW2k4WP66dBK8QzM+i1zAJ9fwb4F3z19UJKtcow6a6YrXSuaIyRGTVFhFZxcjbYdESye9+Vvu0\nn4vFQ4UTE8UCy9dkPpXOS+iiGU6ydrFKjbv4Kq9fxetf8VAghQkpFyuOWCyOTCYHpbr8WmQehoZQ\ncJc0+sI6NGSE0/w8oNP6PHR1mfddizAtqsjxmp/3Cm4WXwZUQUz19prQ9cyMh56eoECg7WIxffH3\nvJif+xVlgprEF4X0gGCuFLlX5CiFORQUFiP4e0F5a7Zg4c/DhZVLbIUJMLrnk2nbThe5VaVCiWGJ\n8GFOFh9xyEs7UBI8EHS5SHRR2PBlc7hq87BKhRabinLFSpufdDrdUrm4zY6IrGLk7bBo5h/c0de/\nXiuoDRswm4oURhWSewWYsg40qpAu9HrKjEqqvfMcLU5rnEjp+vSBD/whTCFR1z9VPjm0qYuVSESQ\nzQKJRKRQ7HXVKi2guJPFL8wknEhM6T54gXXZrIeeHn2MYD6WKpyUOjo8X0yh8DwkjrWjZQSXaUPg\n+SYL6TNcjNhhwAjcYioLI3AI26mCtY5OIbwmlz2y0B5t6EqAt4UVh4soe53tVvESDi4nyyYs/9JO\nhCcRZSfW25CwnId69pfh7f5s8SbVFrMqlavV5CMWm510Oo1EIlF+Q6FiRGQFkbfDoiWcrOlpdA/N\nYnw6WKXYLkBKF+jgl941khAIdzCaZXhzWF6NDlEV18UiAUVOFSW3k5NFNbEAoAdKmRwn7U5pd2LV\nKiO0SLhqTN5UNouCo9XVpV0s6ks8bkKHOufKiKP5eS2sSFRNT5t10agWU729YAMxVEGEkTjIZnX4\nkAsv/XwRZLM0slF/zp43y15zV+GYGi7G7HAad7uojbaxE+D5/nzKnlJiiye9EyQSw0YkcleLfzds\n58qeesf+HpUrWGq7WjxZ335f6HgK+vs1Yb4wdP//s/euQZJc53XgufXu9xPTPZjBQ8ZLxEPgS4QJ\nkLHSWnKYjA0r9EOUbQVDu2tHwxuSwitTu6Soh2VJS3Mdomyt7JWA1SpCK9mWGKQYphiUHZKCpChS\nkgECfIACRVIAMZghBuD0dM90ddcrK+/+uPnl/e6X92ZV9WM6u5EnoqOy8lVZ2VWZp853vnO7wv9Y\nq9llRJhk2XAU6arVSp61T/T7fbTKdrhDQ6lkZVGeDoFCk6zLlw2TWl9H3JpOuwqpPEhRDZxg0fLB\nYA9uvk3RlalR3YpWmZClwt/+7V8CcB6WWHGDO/muzLA3SjWh9SBR/XSqXi0s2Bvv6qpKS4YzM3Sf\n9ClabjmRDPBmG+2sY9Qse0GiXDPyYpntzE2cOJYlWDaR/do1na5LZC4JsUYUWdXLDKTNfVucXJH6\nkn1PfvJFpvcuLOkgkspLhD7SJXOuOIn3ESu5jHu+eC4Yn+czu/tIl3yvIZBCxgdHp++PhvXA25+H\nEQAAIABJREFUKVjSaUzw6hP/A/R3f8zuanU1/6XGNb/fsDvZ1g16nePBYDDA/Pz86BVLjIWSZGVR\nng6BIpcLAZg78ewsKu3roCRmKhdSmZCG2iGiZYbVoZtgF7bLcNzYhsMYHHo45mvJbXyIASyyaQNL\ntlZhB4GWqLJl5oa4tFRHq2VFBqNamfgFOqekVAFmut1WmJ3VaLcVZmaoY9CqIoOBUbRkREOzaQjb\nzIwtF9Jz2rZatdPttiU2fAzb3UR4lKoWwEuGJJIoRJEhM72eORCteb6TVcrcR5nwLhWqWmAZxTbw\nkiWtT+tIQiUVIlK6evArVnScRKz4YNwEWS70lQ1HKVkc9N4otFSmwnP0k2PfRjA4aFTcOidkeaXF\nERg/umFcSNX7uOJbDo7BYFAODn2IKElWFuXpECg8yWq3ge1txHfeDbTtdZdXIXg+lmt65xEOHNL0\nXjSVi1/E48w0LxX+0R/9MoBbkuXzyJYJp9L9zc210hyrVgtpHANAFRvX3E4lQw5eTgTI+G5M7ERw\nDOFyc7IAu6+ZGas4UflQgke3kaJlwk5lmRSYnjbhp3wZNcwaAkckjZf6fPCV8eRyMr1z4gVkOw59\n6hUnKVOwPwB49yIfR1GSLu7fovX4slGqlg+cdPFSaUjJ4u97wLahdP5EGR9VNgTs3YkzfsCSrTG8\nWvyzkHezCxGvTmc/cS5Fu16Mj+FwiLm50KDYJSZFSbKyKE+HQFHLhY+94Q1GrlpdzShZPIB0dtYS\nLPfDzi+EMlyQUET/VR7BmneWm/vSTbDkCrC+LBvPoJQptdINaXUVKSFZWUFaMuS5WESmiHBJZQsw\n+7ADdvvCR41nyxyra3An0P/MEGOzDu8wBKThHbiWNLL5iBeRq2ZT4fp1+1q1msJwaD7rWksFS3qy\nQkoWJ2k04LRP7aLn1CE4BUOWfGSLHolQkdJF2/qS3XlQ6ShiNY4ZnkDvndQ8HkTKw08JnGQ1kuPv\nQ/3hG6F/4CvurrlKJUkVzZvEIM8WE4Ei+8Aov9ZopSt0vSCcXCVrOBxill9ASxwIJcnKojwdAoVW\nsuhiQMmjsAGkNM0VLEKYbHEUkWCNXrden8PqqiFG6+vAs8/OwJYDpSQ0i7m5euqPMvliKn0uiVO3\nq5zYBq5o7e5a9YqD7p1ULmy1jKGd/nWDRHjhapbWOs3RAhTabTcfi0qGUuGKIuPJsmZ3q6QRuaLH\n4VCnfrLh0HQ3kmpnS4g+Txb5r/qwpESqVXk5WZHYhj+vwRKpLqwKRZCfSZ65JcuEpGrxY6d1Zblw\n3G5DrmqROgX4Yx0UsoSLPFo9V8nyqVjUChxCrWY/XOvrzj6uJ6MBEFkKqVgysNd/Mwydl10YssV9\nnSd/DMMoikqSdcgoSZaL8nQIFFXJAmDkjShK79B00ZQJ7+22VVToum0GH/bl2pxUqT+bkfWJTzwO\n4LZkrlsqrNdbjnJFahUArK3ZaX7/WlvTGUWr1aKuQzKUuyXAZhNpojsdG4WPRlGMZtPmYVkvloEN\nJLWKEnm9zOvYPKZr18gc756DKLLESi7v9QzRsqVD95HIFnUlWuJD/iqpUtFzSaRItTK5Y64ZXipB\nvhIiqVehRwIvJRKkCV6WD6Vni85rKKwUyBI0WocrW3Tsih0jEdQm1G+/Bvqdz5rZlLMCuIF2BFla\n9KHVyjXRy25buvFx1YrWCROukKLM0QnMPxmI47g0vh8iSiUri/J0CBSWZG1vGwbQapnppM1bDgbN\nze58fhbXcXwEqw87juC4oJsgN0APhR+JpB7/RXNxEU48w+qqIUDdrts1zxUtwBCrmRkTv2BJlUK7\nrTE7awzyFN8A2LysTscMBE1qliFoZj1St2h/VD6UhveZGSJz5lis4V2x9+12EhKRI1+WGZDakqnp\naYWtrXHM3i1YX1HIv8XVJ1kijDzrUanQNh4Y+LoNQ5CZWpxQcRO9DzLiYVQCPIGrVzLKgeDLY2ND\n7YQUk3FUrpzl0pPnw6iSobt8VHlQYpS3r7gYDodYoDC7EgdGSbKyKE+HQBHLhY/dcYeZIILFSoWE\nNlPuwxlZIQUrdFMqmsoVTnv/2tfeB+A+AAuwsQ3GjzU1VXGI0+Kidp6TekVeKkCn6hZfj3cdSiN8\nq0XD3RgSFUXaGceQohvkczds1ICG4eGQ63E/li0Vkh/L9WVNTytcvWrJQ6+nMT3tKl4u7Ochiuj7\nwMuGEZsnIaMVgHwSxklXF5ZA0XzZfQhkP6+8A5Jel8gXLxfSsfnKhSHSJREiW/R+uIfNY4CnL638\n5UMsn8vPI7xaMSqoeMp7PgWLwoo5DtZ1eLLHOyVEUVSSrENESbKyKE+HQCGVLLpCrq8D58+b6eST\nLIfPCSlYJvGdnoUIVtHKiHRTlgqAJVhaU5jl34I1uQPUJalUJf3SU5mQCAu/thLR4qVBX1chndOV\nFe0MmcOJDpD1YNVqcMJGAZuNRb6vrHplyoXk2bJRDTop85AfC8l8lS4HrCFelgmtn1olj3mkopLs\nky4VMYA5mJssbVcTj+62+V2F4zwCljiNKiXy4Xd8nZGyXBjnPJcIDbcjvWoSSWbWr52B/t/23EW8\nbNj2eJxGeLViVNLPpq/sx31aecgSrlA+lu/8jGogKC7iOMbS0tJxH8apQUmysihPh0ARlSwAXtM7\nXVwvX86WCnljkv3QV2DJk1QDikCqOPIS3unRTJvzMAtTJlwCqVj1ehOzs3A6CQFgfd2QIrp/ca9W\nt6tSogQYv1a7be0v3Ag/O4ukHEfTLtEiRckGkQJu2Cg99xvbJSnT2s3HkmUiUzK06/M4Cf4oFSxZ\nigyD1CzAmtzJr0X+rQ7M/6LH5gPu2Im+zj/+GCJhcjrvOAm8hBgj36Mlt83bPydYlJ0VSpOnTsPr\nwGyiWPlIFX1YAdc0SBjDq0Ueq8uXw+b3UQZ5+z5CZcPdZJ0BiMhubJwNHlORMRwOS5J1yCgCyVJK\n/T0AvwLz5fwNrfX7xfIfAvBumC/pDoD/RWv9hWTZN5J5QwCR1vqNBzmWApyOYqGQShaQbePe3gZm\nzbA6/HrNP+By2ipZoRtVnheDyjlHhbzgUVouy05mutP5AICHYEqFfqyvu6oflQMl0SKzu7nHmZtk\nkv+KmRkbQkpkzBAwCiB1X5N8U5bk6KQUqLzPCaFuQiJdklxdY2MRm+V2/3w9M1RP8BRhepqO07eU\nTPE+dSiCvZTIEmENhnR1YX1YVAqchi0Rcp8Wz8PiKhUvIZKvr8/Wk48U7ZAHGfcwrprFTfD0funE\nSUN+P5nXgQ3RRRosHAQ3t3u8WFzBIkhje57KBdiYhzAm9WedLJRK1uGiCEqWUqoK4N8D+F4AFwE8\noZT6qNb6r9hqzwP477TWW0qptwF4HOYmQvhurbWnyD45SpIlUEgla5ulRs/O2nbubtaLxTehC254\n7EKJeRyvIT50cwt1OdH0HbBmdzMo9NycGeCZ+6IAQ7bopsQ7CaXZHTAlQVKpfKKC1lbNIqJrPj4m\n+oHKj7OzQKfjerHkc7c0aLsJd3fjdDnPwaLhdKhkOBhoNBrmeaMB9HpxEnLqHvfMTFbZ8pOq5AwP\ntXhOcQ/cV+UzxueV/vg6IbXKF98AZAmMCkxzVYxnbEmPlhyiJw+kTPFSoYZLsHhWGM/NMsRQ/Ysm\n9GNLWRWLf799IJuAIF3kJKDvus83TxiVmzUY7LBn/Ht2Hf4Ih5OPOI6x4stiKbEvFIFkAXgTgK9r\nrZ8DAKXU7wL4PgApydJaf5at/xcw47AdCY7/dBQMhVWyAHN1pNpVu43ZxWUAtiO83TYX3e1tuwmf\nHg9FKBv61IcZsZzWGWBUV+HqqkuiqGwH6IRouWZ3Tr6sB8vMW1tzs6EGg3B5yZjhzXSI2NAjqVQ8\n2d3Mc8cvtGMVJu8+EZZ8qpbZv+ksjCIyu/sT5ccFjYvY7ZJiFYlHH5nipULajitieWRLkiqubnG1\nqyEeZcdhCPL1eOfhqFIikS0qFVKOlw+kvL0CYMktDfq8WNwg72FOV7tGdgyRKq52kp2AI+zV4spV\nSD0GjCrXwUnuLAQMyVqUA3KX2DduEMlaVUo9yZ4/rrV+nD0/B+BF9vwiXJVK4h8D+EP2XAP4Y6XU\nEMBjYt8ToyRZAkVTsh7b2sqaithFOc+LRRdW15d1GCRq1I3rIPARLJo3I5ZTCWkeRLCUmk9CRlMu\nmhi8bUehIaVc3dKMVFEOFgAouBlZ9p7Xahkv1eysKRv2esC5c6RmWW+WeX1XzaKhc8iLZY3tBvT/\nNBEPSNZxuw7p40Aki8iVJXVuydB3M97dNYrXflGrKUSRLA/KzCx+ieFkiubPAtiDLQlSCVFGPdBz\nYH9eLalayWDSGiYb11D6sipsPs8R4wnwfXhL7uvrdjrUUZh8mftRBY1a9n82qizY7YYVLNt5SKRq\nVImQy6MnN+0dMN+9aaqTlzgwbhDJunJQnxRBKfXdMCTrLWz2W7TWl5RSZwD8kVLqK1rrP93va5Qk\nS6CQSla7nekqpNmEWs1fHhwv7b0I6lUIsjxIahXdaD4E4I2w0Q0uqVxfN5ENdPNZXzfEpFZzKzOk\nYi0u2hIhZVnNzFAOlo11sJ2FZn8hbm66B830qDKdr7uQzzcRDW4HISmVRL5on3RDpefyvt3tGmWL\nHwMndBJZk70vCBTIerJI6Qj5rwB7GSLiPm4JcZyS5CTQmHwwaS3mhwZCp/fWczsKOXiMQ45Xqx/Z\njkIbPWJBZUFfRINUsMJdh6OIVhfmPZ3czkKtNbTWmJqaGr1yibFRgHLhJdgBbAFTCrwkV1JKfQeA\n3wDwNq31Js3XWl9KHl9RSn0EpvxYkqzDQiFJlryKkiTDKgr0a9TXeJTtNDrMqAbfOHGTgjrVJGKx\nDs2bh41ruBm8TGhIlSv+1WoKq6tWreK5WDwbi86dLRtqj6hgzfDNpiFEpF7t7gK33moUIvJmAVbB\notIfKVh0H5UqFZGccDaWOS+Dgc4sI9Iky4aShEmCFyojUnmQ9k8eLZrv92gBlkRR3ANgSVWILIX8\nVrScj2cojfG+574heOg5ESnu0Zrks0wqlVSwZAI8Hb+9rqgfegb6P9xvV+Mdhdvb1ndF83myu4cU\n0VBaV674v/++QeQBS7i0jmFJlfRi8XltuCqWwUnuLFRKoVIpypBiJx+VSv5ABTcITwC4Syn1bTDk\n6h8A+Ed8BaXUrQB+H8A7tdZfZfNnAFS01jvJ9N8F8PMHOZiSZAkUrVwIwFx46Y7LxszhQ+jw8iCQ\np2ZxHLaCNc6guxIh/1U2qsFPuohgLWFqyhI16g3gnfDnz7sBpFFEvilDHHyEi7xY1htr1SZe1hsM\nst2AgCnXzc7aMRA7HWNsN8/NOIUAMD1tFZIQuaL509OumkWJ7uTXAsJeMKtSuUny09MKe3s6GFBK\n+5Oki46BhuSx5T8fpB8rpFTllQr5+nnPx0GoFCgHk/atT+qVJFtg2/AvXj9ZLxnLkLoypB+L5gOZ\n5Ve3zWvQD6orV7KCV7frLx36FKxsaZGysYbsb5f9EWgonZPtx+r3+1AqpMiW2A+KYHzXWkdKqR8F\n8F9hbnK/qbX+slLqnybLfx3AzwJYAfB/J58BimpYA/CRZF4NwH/UWv+XgxxPSbIECkey6JctXXDp\nVy1jVNzczktlrhcLKF7YaAj+qAYLPiYe5WNZyC/5+fNWkVpby3YXWp+VJVxyvEJKeedEyqhZ1psF\nkLpkSFSvZ9en16ebYie5T0ljOw0OrVnNjlSpkNmd9m1fS2ded1QW1t6eHZKHd2OOM2SL2a6aqlw2\nuJQeJQGS86mUOA174w55/vi++KDNlEXFHyNYVYvmSxWLe7S46X1ccG+WT82S6MMZ729UjMPsLPa6\nYQLZbo/fUegbv3Bri84zkSrfsfMfOoS+Z97JQr/fRzWvtbbExCgCyQIArfXHAXxczPt1Nv1PAPwT\nz3bPAXjwMI+lAKejWKhWq6hWqxgOC3QBIXc7+bLYVXVy9eokg1/siWgZLC3V0zIhmd75jYVXXNxB\noN2OQm5sX1ggYkXp7q6SQfMpOV5rnYwbaObPz7tGd1Kz+ADSRH52ku55Pt+MB64zpGswcMlSqGS4\nuZklC7JsSLvlJIp7sqQ/S5Iu/jXZywhY0uROzylzjZOqUX4rAmVkteCWDvMg9zUOiZqUdPFOQ8Ad\nYoerXonB//z5bOtvyKuVgPuwQsuJQPlKh6MiHAy2kB9C2oX1Y51s9Hq9kmQdAU7nvWf/KE+HB41G\nA51OQUaXp3qgR8GqsK6mENk6PfCVCr8A4DVQyrZgc/WOohuiyHQJymF06GZDPisKIl1fzw60bQzw\nZlBonj9FpUK+7mBg87N83flEvng2liVX5iZtBp+2+yays71tIxxk6Ohg4BIdrrqFy4b5kF4sasQi\nctVsVrC3Z/43VGq0HYeSQFEoKZ8H8VzOJ0LmKxn6tufT1NHn82RFnsdJPVmh+TxHi0PB6TCkXwQ0\nLUhX3DInu+2JROQlQ8Dvg6HSoY9wWTUr1E1IuVi+ciGS9xGfWD8WYEhW7XReLI8NRVGyioTydHjQ\nbDYLQbIe+9KXzARdIbkvK/k5u72dn/Lumy426CY35ZkHWBUjhukodE3vPA/Lki0KBvV3FLZabkwD\nYNZrtZBELdhH8mgtL1tvljG6m+eNhnlOYaS+7kIiOJ2Om41FXYRmv+aRSJb0aZEPy0zb9zQ9bcyn\ngH2kTkL+2qOH0BmNRsNNlKdzMBySZ4w+dNy7M6ojkMrAM3C9Xb7MLOnh4onwRMjyyFBonlSxRnUa\nypIhPz4e52A9g+rB34L+wg+7u1xcRDxrPs/b2yYbnkgU8S/fQM+ANb/nqVx8SJ0srmO8dPeTn41F\n6PV6qNd9DTcl9ouSZGVRng4PCtdhyOWQbleUDc3dM8+LNV6Mg8QMfJ1ERwcqBdbhV61kACnlY5mx\nCHmeIHUY8uFkzp1zM7L4zajVMiW/blelEQ4U28BBKe9Evjjx4SUYImStliUiSg/R6bmEgncTut2F\n5qa9vR1n1iXSZc3NcbqMfhdIMue78UrSRfvd24udOArf+IiA6UYMwcZI0A1sAfazxG/QNbgql6w3\nhqIcZmBu9pOUCgGXpElVa0xpLxeSbNH+CXwooJ6rZHnA+10k+O8tCaly+WIeoggYDPaQJVa+LkMC\nLxWe/HJhv98v3rX+hKMkWVmUp8ODwpjfky7CFPxuye7qeb6sk/GB9/2aHMImuftIVx2jbrC8m5A/\n5yGt6+tZFUs+3nIuxl63gqnmEP2ognrVPC7VrgO1GfSjCqaayfA3UYS4Wk+fD7W9sU8149RbpZP/\nX1+b9+4qWkjnAW6qPJGhLOmyZncZ30AfZx7T4PNi5T2XHqybbqrg+vXYmUflQnpsNqvo92lYIOnP\nokcyvQOj87F86/pQQVbV4onwPiVGDhxdhatmjZP+zofyCf2YobEWxWc3kVgPg1RxkHLF/VjZUSCo\nqzCG+z54qTAb33CSS4WAUbIKc60/JShJVhbl6fCgcL9u5OB57E54Y8qDRz04dB5k2XAW1vA+j3p9\nLl16/rw1uxNBIhJF50NmYfHOQjK60+k26pZ7NI1aDK2Tx2RePdoz9+VOB5idhWonasDMDCpDw4J0\nILG0rs3NlshXH40MgaKbYhTZaAlSi6Sy1e3q9GWISPm8vdyTNUnpkH81aNqSKvPYZxymn+EzecoV\nLZfrTGH054+M8DzkNA9c1corHRLG9WtxkkKQQ+4YX1Z8/lYAhjjNsx8S9P/mJcLFxSyZCpUOuQGe\n/6ig9QcDnovlO1fbMKQq1FV4IxXuo0O/30erAKFOpwklycqiPB0eFIpkdbu2s1AMudGv2eEgxiFY\nSlXGNjwfH3yxDa3kT+ZnLQGw5UGAm91JyVPpIMzGk5VVrohw+dBqAdDAdCuGbic1Pc5KdnehOh3o\nRIlQpiUQutmETu6SOorMdr2eZUXESGhfSf2uXrXvv17V2Osqz1A6ZhBoX4chJ1SybBgiU7x7UWZ9\nUZzDOFEO9HqLiyo1w1siNok/ixOlkEF+CqZk6CNgOjBNKpZUtfgA0mSE5yGlPoTS3/m0jHQYJNtl\nldvr7YpDrmQVcVTpMC87i1SsbhfY2Rmw4+GlQTK6S0a+C3Oeu+D/u5OuYgHAYDAoh9Q5ApQky0V5\nOjwojITMuwo5C2CJg/m5WJNgHtnBYX2gm9tRgDxZoXwsuuFRh9a5dNg3eQ6IaNG82VkKHzWki4JI\nZfgone6pah+IAG3i3M1jqwVNd7N2G2pmBjoZb0e122Y6YSmq1wM6HWhiLbu7Rs2amTH7GghPCzGg\nhKno5OI/3dKIEqJC74cPpSN9WGR2z8YpWB/W7q71XUnOJ0kUbSPDR/k2/T4FkmZfkzof8xUs3ziH\nkmRJcsURKh1SNhapXD6ME0aZZ4Dn4HENeSXDCMDAIVU8YoTmhQZ356Rqezvrt6K+mFACvBs6Ko+R\nDPBtuOSVSNY45viTgcFggKWlpeM+jFOFUsnKojwdHhRKyQKyBCvBwT7MklRxjNvGHvK3SPhKKOO8\nDt3QZD5WHTKA1Ac3psE/7i4RrrkZ47OqRH3EtYZbZyH2IHdg2giBXg+60zEkjKtXzSbU7m7KZHSz\naclUr2fUoxChT9aLKxVza2/asqk1uses29AlOVrHmbKhb2zCUA6WfO4jYdbr5T7n8zhqtUqyD0mq\n+PiGRKDk52Uao7sNeZdhB/7xDkdh3G7EkFpGz33krSLWsbhyxZAjIlakZMmuwu3tcMo7kSpeRiQV\nK1RaNISLVCwfuIp1sscqlBgMBpjNC4ItMTFKkpVFeTo8KIySRVdPuhBEkf3JOyqCm2F9Pa91Ow9H\nGchKpuLQuIW+1HciWOZCPzdnSBBFN8hSIQCsren0VHHju7S5AcZnhQioRH1zC6Tzz4xbKiE/6S2S\najjVql2fmE+v53ix0m21dtchpsNJGElSiZRU6XVQT+SqStO8OZky0mz6iRTtKo79CtdhoNk06fdk\nhpf+rGazip0dGW/A1S1ZyySSQp2EQFbVoulJ1S1eKpRdhvL5uCoWQf6gID9WNdmvjXJYWfnn+Nzn\nfhlA9sZEkQy+0iFF540iXBKmmxDJcbSRLQ9Kkzt9Qair0Jzj01AqBMzYhXNzc6NXLDE2SpKVRXk6\nPCiUkkU3+DGM78eLgw4UTec8FN9AN0bqOjQyP6VZcJCCRUPj8C5DIl28g7DbhWmR29qyahQrEeJb\n33IkglS1op1yclStmmlehyOyRS8IIEkhNdMJkdI+YxgRs0bD7nPa3Fl9w+jwjCyfB2t62iVg1udl\nD5cjT8miGAffbxLfQNRUOowin88qlJvlQx4Bk6CmjVDcQ54i5Zs/KjOLI1QyJB+YVY/G8WPROpxY\n8dJhu+0nXVtb/HilYkVKlg/kx+rgpA+h48NwOMSMb8DREvtGSbKyKE+HB4UiWbJUyBzIPPF9nA+2\n1uP8EicSIy+8h3mRlTce33GFxi+chSxRkg+Ln4PVVZdM0Xr8cWmmhxgNTEfXoWvCvCJKhKrbNSSI\ndsj+L2mJkKtYNE1MJ/Fjxdy9TIoWrUPxDpWKo3QBcNr6Kj1DLOrJvArz7nJ1y2R5aea/ck3sfB6t\nwweqpsM2L09hq8oZ55AfIp/nU8ysCT7kz5LqVjt5LgmMLB0SeJnO58OSREzuV6pYB0GoRO6+Nnmv\nuCeLq1g+0HJOqohoXbzomuDt55+b3CnJnR+fjGugzzdlYnVw0hPeJYbDIebnR9sOSkyGkmS5KE+H\nB4UqFxL4nVEoWQf7UI8iT0dpdJcgIiFLiKRizcCWeJCa3qUHhiIcFhZs6ZCXCpcXY/SjCqBNaRBI\nSBTgLRE6LKLbtcmhRJg4udrdhSbzupQednehEiIV8+5CoWil8wErBZGixaWhhLgROKGiXcaMvx5m\n2juhWuXmdnu4RMpWVlRaJqTTWKvZ/xUNDeRmYe2JeTTNlSuIdegYfJ9XGddApcJkHMGgt1B2GY6b\nmTWOOgZwEkieLCCrZnGVi0qENI8nvfs6C7e26BriU9UoqsH3gaDy4OlJeJcoSdbho1SysihPhweF\nIVmEAMEaB+P5sWZwY7qG8jquJLjpfSb5oxtiF77hdMyfTm/cvMuwVgNuu027bfC0oNu1JcKkXUtf\nuWJkmeTkpSGissuQl/8GA9dhn5jf9eXLdj0iUsmBpLdgrmglNb+4Ws1mKkjs7qKSSEQzM/brTGVD\n3+hQvMtQxkPIjxd9FXym9ryxdfn6nY6bVTY3V8HOzihV1TcWIWAJk5wnCRhfTsSLug0nhSwRTtJl\nCGR/yNRAxIXIlSwRSk8WV7WodCgJl9zOqlhEovJM7qRikdEdsCqWeX6aVCygJFlHgZJkZVGeDg8K\nUy7M8WJNSrZchDoLQ6oW3VDq2H8o6ajyCc/EItWqDnOD5J6sPoBVANUksT2bEbayoqGUO8+ZjiLU\nyWfFWZfsIuz1wmpWr2dJGVipkP/PEj8WbaOjKOtMT9iIvnLFHWeHKWMAuEQENJuIBwNby0seK42G\n04XIdg8g67/iKRIy0kHOd0NItTNvddWSJpn6ztfzZXiZY6rALR1KgpU35I4c45AvGzWodF4gKVex\nkLOeb598Hf7DguYPYD7bViHiJUAJIlQ2lNYuIxO8z+je6ezAEqzrcNVhaXKnYyST+1ZyfKfL7M4x\nHA6xmDOsUYnJUZKsLMrT4UEhlaxDI1ihDKoigEc1yMysIcxFfx785mR9Vtr5cmvNM7OsupXJDWJq\nllMilF44MsDw+ZyEATYLSw7ozT9PInzU2R8fwJDiIZCY3jlD6fWsVCVAfi36DBNp8mVjhcItRyFf\n3TJEYnFRiW7CEHyKFT0uwv4YCOVlydfwdRtK4zpgCZYMJJWlQ1KtyKc1qsFDlgpllIN7vJxcyRIh\n/X9kCZCb4PmlgOZ1Ol0Y4iR/LJKSxUkVgXuy6NydjjEKQxgOh2VO1iGjJFlZlKfDg8IfrHYEAAAg\nAElEQVQoWUD+4HIR3RT8yC8Vhm4U4w4MTSbhowAdGyloWU/WTTdVkiFzXC+WDCOVKlalzRS8hODo\nK1eAWg36pZfMc+61AqB3dtwSYbMZDIelKAfN2/K4sb3VQkwjQtM8wN9hWK1aJkPzrRPd7l8gqtt5\nUhDj4JsS55NKFqlWozKwfPvc2XGXrawobG5qNBqaccbQJWicbkMZdMpLhkqsI0kV7zbczzAIIX8W\nP7Zxgk4tKNNKerIuXnR9WbK70JKrGFNT/HxR6CgZ3bmSRfPI5F6FS65sWfE0qlgAEMdxqWQdAUqS\n5aI8HR4UhmQdknrlbpoXQkqQitJRw5eVJV+fcoaqyV/4JiaJVrUKLC0MEaNimVcUQW9vQ9EVgdRC\nqWoRmCGeyJbmGWayrEgqFJeLiJyRv4vmAXY7Il28u5DCTCnGgclxWuvMthWmcg0r5v1xTz2Z4Tmh\nkl2G/JDlfPp6EAFjb9cBLefL+DYAMDdXRbudnA/tI1bSg8W7Dn0ELER6JmngyCNdclkovmHUduZL\nycuAXGXlhEuCL6OPH8U0uCVCwP2uc6M7v8aRejWAJV9GzTutBAswStbKyspxH8apQqlkZVGeDg8K\nWS704coVoHWzdxGpWO6mPsI0D3Px9aGF8VStg2RkkWclFNnAS4ZULnTllnPn3CBSgvNl73ZRabUM\nudraSmfrKPL73igug0gX2w/5sQAA7Xaa7u6ExwpypZMxDc2L6mxEg1C0Yv6altXYY/AYqzSxpynX\nl3Xc4L9ZbH6Wj5jkhZNy75Wv63DXswzw+7JCpIhKgrJ0SKpVFfuLduCfaQXfZZe8VfSx4eVDOWA0\nx8WLwGBAnxVOnnjXoK9ESGSKOggB20lIw1adbsRxjOXl5eM+jFOFSiU0lNOrFyXJ8qAwJOuAXqzw\npr7xAEfhsKIcuBE4hnvh54oWJ10ttqwDcxM2vOTcObs1GeF5mfDcuSTxPQL05ctGufL5rxIVSieB\npKAuQrqzUaI7oddzyVavl45jCE6ohPk9nceiG3S1mh3Ch9QofsXi4VPEXHxD87DaoEoIV7Npv+o+\n1YpXIfuiY7/ZdBUon7rly8wKdR/yKihguw/tZ1Qhv1xI6tYcLJHwDbEz6vPK/Vj0pkPkbyie+743\nkyhgGkDf8WQRsSKi5cvD4jEPnY6vXM/DRQdw/WV8TEIqD3bZsuuwxvfTrWIBRgUuuwsPF6WSlUV5\nOjwoTLnQhytXnOTC5dk+Lnt8WT4+NjdXx84OvzDHYppKMfvFJOOahfr/Y1hCRd2F5MnybZMtG9pB\no1l0QNecEM2VKsDIfbWaiVkg0DJeIqQuQkqBJyQDQacvJNPdhaIV0zaAS5DoNUnRoos/V62Sz2Vc\nrbrykFTDfGPqNMb/qvNdT/J7w/VacTKm0nIWLV9eVrh6VSc5W0iWTaHX4wpK3tiDvvm+JHnfcz62\nofR1jfM6fFnoM0+fS19XLQ3fk/k6O+nunHBxX5brvSKViqZbbFqqWRR/wqMaujDkivZ3+suEhDiO\ny8T3I0BJslyUp8ODQpMsD7jBnUpmo7OxYvj9WeMQJfrlf1SdikPYskcf5qZId297F+cJ7r4vdrUK\nk4qfGNt5fpXmcdjcjzVOiVCmv/P16IXB/Fhc5iHCRNJEr+cqWjykFMmg0kQM+edSGOfjet2+fqVi\nCB1LIq1X7bRNd7e7Cw2r4/PX+yIZSOlaXVW4ciXr1ZIhpXJ7Oy0VLJ8Hax72x4D0bPkCS+k1eU7W\nJMP4TKJQccTw+wazHYa8TEiki3uviFh1OiHvFeEKLJEi0DiEtIyCRquw5UFL1l4tBAsoUNXilKAo\nSpZS6u8B+BWYD/lvaK3fL5arZPnbYXwI/6PW+qlxtp0UBTgdxcOJ+uIln2gqk/nIlVt1HJcMjRpa\n5zBIFTe78/BRimkgkzutJ5UsHvpIAaQ6ycryqHlRZMYnpKtAKIeMfFrS/C5LhJJskSmdlCX+XIRS\nad/ozvQagBskJVsE+eeTVCvZJdXrAfV6dsBpAI1GM7Mbn5mdr8P5HSmEPq+V2cYs9w2twy/A5MvK\nlhXzFKkQKfLFNtB78REvCVk6JH8W5WXx55P6ssJE7OLFbHwDJ118viFWgHkv5LvjQ+CQQtUQz4lk\n8XPXhSRXwKuDYAFAFEVQSkGpyTpAS+SjCCRLKVUF8O8BfC+AiwCeUEp9VGv9V2y1twG4K/l7CMCv\nAXhozG0nQkmyPCickjWGFyu0Cs0fHeeQR6ryQkgPY2Bo8mlVYf1X5IOhINIqbOr7FACN9XXFvtBu\nTpaTmRVFWT3Bo1zpdttM7+yYEiJPdc/Lx6LIBjK/00n3xTnQ9r4uQintSFWL+7DouPgxpW84Wc4N\n8JQiPzcnz8S+cdNNCt/6VtbfReSKm9tpOeeWfhO8OU6l5qB1SK3ini0OGdswilzxIXb4dnIdH6RP\ni15/kjgIuy6VCYlc0ef3pZdiuNlV9D+VihVXVbfYMv5DZhO2i9CMRWiVrMGrhmABwGAwcLpwSxwO\nikCyALwJwNe11s8BgFLqdwF8HwBOlL4PwP+nzVAef6GUWlRKnQVw+xjbToTjPx0FRKVSQb1ex0CG\nBhUJ7JMcMriHje+8VOhTp2LPvMME7yik0qA0vNMx8DKhNb1L8NIh3bzna3tAZBboxHsFID0Z+vJl\nKJ5/xZbxEqIT2cCJDR/nELDmd9k5yBUt7pdqNqE3N92hc2ZmTGfhzIwTOhqTgZ6zGRYH4ezXR7IY\nKkPzuW40LKnzmdnNOr4YBv4WwqqVq3SFVCtgZaWC7W3z/85XFmS6u4JrfieM8lEBhpSMUrfGDVOl\nz6oWj6NBJcF2G9C6i3q9hcFgkAifVNaj/yOV+nbF/A4M6eLb0Ml/BdZ/1Wfr74KTtFcTwQKAfr9f\nkqwjQEFI1jkAL7LnF2HUqlHrnBtz24lw/KejoGg0GsUhWfSp3d42ktSVK9nxZBAmVaurXMXiZblQ\nbEJeIOlBhtYZF1zZAuyN0a+acYKl5f2N10p5XIOHTKUmd64K8eWALRHyc8/VKyATPkrrpNRVlgZp\nfRq/sFq185JhdFIwohY3Gvb9xHHWI8beh04N8Jb51BkJC5GsvJwsIOu54stlAGq1agJJiVD5CBef\nF0V5ZUMVmAbyP78tZD+/+wkjHTVItG/9IdxLbgM7OwPMzVm1aTCgnAbyIgJWmQJcAkXzSfGLYQkV\nLeNlQiJVbkTDq41gAUCv10OtAGzgNKIyUQPUvrCqlHqSPX9ca/34Ub/oflF+ygJoNBrY9cVk32jQ\nkC6AZxA+A8kj+DQRLNeXxQeEJg9USNW6UZAKFt14iOj2YUsi/NiMH2ttDVhbs++xVgN0N7Jho4MB\nUK+b0h3r+NPyxIXysbhPK3nukC0xOHQaNDqqXMjmp2nvxDR4rAMncTL1ndDtIp6ezsZA8OmcpPhJ\nUavlB5OurVkTvCRUpqswP8w0bE4ftxNQlu/G9d+QQT7kz/IRKv5a8nW5P4w/mpO3s7MHW8bj74OI\nklTceMaVVLmIZPEy4TasetWHJWPxq5JgAUC32y1J1lFA6wMO+zYWrmit35iz/BKAW9jz88m8cdap\nj7HtRCg/ZQEUzvzO245qNcOcVldNinmC8UqF4xApTnjIUOxb9yBD60jfFU1zBYtUtQGbB5gbhTW7\nr63Z6fPn7TiF0NoMlVNPbjiDQVa5AoLmdz0cQsl8LFki5CeXEzQgWy7kBAxwSFdcrdp90RA77bYt\nJfqkIp8Pi6+XdBl6IcY/JB+i5G2+rsBx7k2yPOjvJLTPaf3lZYVr12RuFu8mpGP2lQm5giV9XNOw\nZMU3liHg+rPySkn7Mb8TaPxDAPh3sESqD1MKp2MkwjQrntNnkatZvBxI++b+KzonZHQ339lXK8EC\nTLmwXpejTJQ4MG4MyRqFJwDcpZT6NhiC9A8A/COxzkcB/GjiuXoIwDWt9UtKqW+Nse1EKElWAIUz\nv/uwvQ2sngGQvdcDpqJIng9ap16fw2CwAz/ZouDPkAGecnYkaHlebtA44AnvlI3Fyya0vIFvfWsI\ncyO1XYUcqUrCTkzqveLqFRtiJ83DqtXSPCw9HALDYTaMlGdoyfEGmWwYc0M8wado+QJJedkwyc1y\nhtHhbEUkxqeQqhb/XCc3meHUdHohkATIH+EQjmgw01mlx1diPHPGjGXI4SpcPmXKN+CyXI/vMy+U\nlPuz6P8zSelwnFBSX04WgQgWefKuwJK8bnJcnETRPF4OpNJfna3Th1G7WnAT3G1cy6uZYAGGZJ2I\na/xJQwFIltY6Ukr9KID/CvOr4ze11l9WSv3TZPmvA/g4THzD12GMnv9T3rYHOZ6SZAVQCCWLut9o\nulZLiNVqrvGdwjglwbKPnFRR6dCnVPn8K0cFUs1IzeI+LMBV14YA/hrAfVkPFhjh8tVQCWR+v3LF\nlhSlXyvpOFStFvS1a8nhBMgWktJjQpT0YAAlSRN5tLrinMpA0uR4dLUKJZfxBHk+PA+Bq1tkmp+a\nSudrD8lS9Tp0bbxf9Tw81BxONs5hlDHeVyb0qVv5vitgsm5AiQpc8/uomIhxPFeheSH/1hbMZ34L\ntuNvAEuOiBRRtARgU9lpXfq/bcKSKalmWfUKKAkWYEhWIa7xpw0FIFnmMPTHYYgUn/frbFoD+JFx\ntz0ISpIVQKF+5fCbMk/erNVQaV/H6up8WqmKIkOu5BB8gMncsY10Pi8WL7fcCE8WDavDuw35WIWA\nVbRofds6f/myWyok4/uZ1URd4CqWMKtpCiiNInPLk5EOfNvE7K5aLWhSljjZEsZ4Wq7ZyecerfTd\na22IGItv0NWqQ6A1J1TJfhS/OezuIq5WoYhtshJganbPKxsmUJG5CTebLtuhzUJD5EjUatpbGvSP\nVejvOqTpxcUqtrfl59AXTpo3dqEkZwqmdOj78eBTxcaBL85hXGyBIhSs55CIFPkQuzC+Kq5KUTzF\ndTa/yvZ1na1r3lNJriz6/T6mCjbG56lBAUhWkVCSrAAK8StHml+4L4t1ko3jxcoSLDkd8mrxUiEf\nB00+P2heFt3cKAeLFCu6+07BesDIt+UOqaN19pTpKLJvnCIZXFnPr3iR7ypAtkBlRAIZ4eEqWqBy\nIZBVtMDM7nTg09OZ5Ph0GzLIyxJgterO8312aTn78aDJk8K8KY2WW24kEhRSqugQb7rJDp0jUa0C\nq6uVdHno94slXD5CNkpp8nUY7ollecb3/aa6j7M8hFdgv0NTMMRIKlqccHHl6hW23gxsqbDN9mHH\nCC0Jlot+v49pWVovcXAURMkqEkqSFUBhlCyfOZuPh9dqpT/Kff5twBAsinDQmsoGvMOQj1tIxIGX\nCn03z2Fg/n7AS4I8nFS+njXAb2z8Kp577t8lyzQrGyporf15S6RgiXnOI5/mJncP2QJg1C1eoiOI\n/KxMgKgsGUqzPGDIUrVqb+GyK5FIliRV0rPlG+cQsOSKkayKiIGwSpbf+D5KtfKb3LPbmGiHLFmh\n/yP//46nNvkIFfdnjSJG1GFYR7bDkN9E8vbjCyel53VYtWkKtqRHqtQsjEeL5nHliroEKbj3CiwZ\no+9OjJJchTEYDEqSdRQoSVYGJckKoBBKFoF/aPlNMODL4ryMFKzw0DpykGi5HLDlGJp/UNWKkyh+\nF66Kdfh09vU0ldC08sxjNzdezqP1oiTegalbipcJQ12DwjQf06i9nIiFIiCaTcSUKg8YhiHKjDph\nHamfi0z3chBomZ1F4LENVILkXVRHVCJpNCyX8w2dww7HWZbXdcjnpR2jKTRMhyEf0LzimTcppEI7\nKWR0gwT3vpE5ncgWT2/fgiVTM7CqF30PG8hGMzRgSNmrK719PxgMBpg7xNEPSiQoSVYGJckKoAhK\n1qPvfCce+0//yTyhTCYKIk264HD+vEOq+DQNpeOKJtyLRaRqlKo1KvZhP6SL+6/ol7dv/3ywaLNs\nY+N3AACXLmm89rUKL79szf4OKLIByHqvkM3Iire3oWq1tMMwXUbgYaZsu5RQ0bpJh2G6f65oUfch\n2396XICNb+Bp7p4k0DiKoCTxAvNhsX058Ch2ms8Tqly1al77zJkKrl2jcp99vbyvSaPh7zr0lQM5\n4fKRrWZzGr0elf9496HM0pq0dEfkTTZ5jNoPZWZxjCJYHN8DQ6RIuaX8qjoMeWonz1swBGsIN6aB\nlxEbybrdklyNiTiOMTvrHz2ixAFQkqwMSpIVQBFIVgbttssmWq3Eb3TGufcvLprPOYWQErpdYGqq\nlQw0SzeIEIHioaB8vszG2q+ixc8vRUf4yoX0+vVknt3uK1/p4+1vbyYcgykd3IeltXVu+bxXFN8g\nzVzMYwW5rU+l4ss4UZHdiOTR4sfAFa3E56W5esVJFttGy7IgYye60bDr8uPxdBfycqEWSleDCaej\n4hp81UkOWxqsYHOTUt+z5bSw+hUKJzXbZcGN8Z5xfwD4Ix7GIWqjAknztqvBkCTe2UvxDDTgM5UM\neSCp9GkRSnI1KYbDYUmyjgolyXJQkqwAClMu5C3/pIiQmpVgcdGscvmy67/izW8+a5ctRfBSIM/J\nGie4dNLyCidScrgceXfmvi9SsX4vXbqx8RN4+eVfTU6FdsuGSG55UQQMBmnJTJYJUySkR8t1AJds\nsXUh16GSIY/dINIURbYrUCpQMzN2G5pXq2WN7nw5gX9Oh0O7n0bDb3bn+zrATSaPcI0qAYa2J4Ky\nsGBUM7Nsv6by0LahINJR4INPcyVtv75EKhGS54pI1hD2+8hzsGj5ZrqHkljtH1EUleXCo0CpZGVQ\nkqwACqdkSV8W5WUlxIv7r2TZkMAJmC0bUgs5kCVYZMjlHYajBtWdBCE/GB8sesjmZbOczGkhguX6\nsZxbLBuHkspjGRO83SF0Uu5TnCjJMQujyFWJZKdg8jxO5unQcDpS+QqRMZqWfiyZ8g7r7QIAhG4m\ntH+uXolyoWIewLxyHsfqqu00HD10zuhUeDstSRNXjuYA7MAQn7wuQp4A3xX7DBE6lbN83PR3DVed\npYwsMrpTd2GXPaf8LEKpWB0W4jjGwsLCcR/G6UNJsjIoSVYAhVKyCJw9MYWLNxvyaUmwshEOXIGa\ndNxCUqIm/SUv77S8PCgN8Q1wYrWx8dHM3gyhsr6slI9obYaE5xgMvPPzTO8O2aJljHhlnrMyn+aq\nFL/wVKvQfBuCr8OQ9lmtmjwsWu6OpJw5Lw58HYWASbOXy+Ug02zfjUY1eXQPzTctD988jkqKD29r\nwIfUkcPsyGnAqrQhxWpUVMRRgcqFXK2i2AX6PpXm9aNEFEWYT0ZRKHGIKElWBiXJCqAwJAsIppUD\nALpdLK/O4sqVSiaIfH3dEKvZWcvPtKaLOKVKA/7kdzICh8qIVCY8aGgpJ1ZyXzbpemPj096tyfyu\ntXYFH8AGdEKoVnQhYCU/aYo3h2OPh5Mt3Rbda2xZLFUpwGW7lLHF/4dJarvudq26lSxKS4xJl2Fq\nUuevww3unPyx40vBt0sUrDzjO39erU8nb8ueV/418cc5IAM+dM7Kikr9We46+ykT7pc08fLfQRAq\nT3JSTz8eBgC2BZEqb/o3CnEcY3Fx8bgP4/ShJFkZlCQrgKKUCx9929vw2Kc/bW7U7XYwzmF21lQP\nL1+209/4hkuw2Iaw3UwDGIPtdbGclwnBpkcpV+OqW7y70OfF4mb4MJG7775/hsuX/y+cO+d2GarV\nVUOspIeJyoHiOREt5fFbyXWIlCgebErzuR/Lp0hRVENC5hQ3uPNp6oAM+bEYu6F19PR0dqxCIB1K\nRx3hD4dKJZT0np3HwXOzfMTqppsUrl71fZ7GJUSyHDjpUFHjkr28siMnWrpUqAqA4XCIpaWl4z6M\n0wetsxmAr3KUJCuAopCsILpd48s6fx79yNxw2m1LqkJlw6mpCjodwN8hSEPYdOAqWIDrxQqZ3ceN\ncuCxDTzGge/frrex8VTu3qJII4oUBgNDMpfuCISRgt3ukq5D3/Jkp6EXczOyaJgj2WEoCRdgVCZe\nQgQr2cGUF52yJIEzFhsc5R4ThCLle2+9no2AmJ31erK0LGGy59WWeziAIVchyBwsd9lkzw3GGRw6\n5MniatUo4tSEHXSZB5HuF/zNlJfcIqAkWUeEUsnKoPzGB1CocqHsAqMP8eysIVrr80FSxS1cRMBc\ngkWqFe80lPEOvMuPIhwOWiYMuadp/DUzWPTGxl+N3NPly8BgkBbYsLXbwNIMI4E8xgGwpUFfhyF/\n5POlr0pO+5aJ7egMKsrK4utTmVC8dtxsupTB56MiRuIrG4rpdP98eY4nix9PBWRmz760mdaZ6bU1\nhZdfzuZjjTK5+wb+dkErzCDrz+JjGUIsG3e/k6wb2kaWCmswhvsSx404jrG8vHzch3H6UJKsDEqS\nFUDhlKwQIQDQqMVYXa3gyhV7jyRCtbpqVC0iYZaAUcmQ/qQnK4YhOtx/REqVLB3K+XngqlVFPCeC\nRTf68f4Hly7FePnlCs6fV4ii5AZNo0UjudWtrEBvbmY3lsZ2BNQsXxmRr0PJ7KQqsefOLbhWM8s4\nyWk2DdGRxF6WDHkOFiXDc4YSysPix8siJQA473sSjN8R6C8D8kR+UsNC20i1TCkVIGGTECSfokVD\n6YRw0DT4GBsbtx1g+xKHhTiOsbKyctyHcfpQkqwMbkQrzYlEkZSsR1/3OrcOyD/EicrVbluCxcUI\nf+chj0Lg5new6RZcJavuWQ8IK1J5IFImvTbuMWxs/PVYe3vwwR8HYMqGWuv0kScaacCRRzLPRUAp\nreOoXnw6iuwg0USYQs99ZI3UrcTMrikOghMlvq5vOWAJG71O8qeHw/QvD1q+Bt+f+KPjzItwoIqm\n1vavUjF/tCy0/fIyRTL4ydLCQpWVgSvsLw+0zgy948A2CvnRDxL7MeaXv2mLgjLx/QghrymH/XfC\nUH7rAyickgUY9iTVrO3thGiZ4/WNI93tWjN8twvmyaIbMClW5MmSw+xIRQuw5Go/pcOQ2Z1S3WNs\nbLw00R4vXtRYW1NYW3NDSaXkkbk1BozxXLnKszHL7dIOROmpkhcHUsTk65Nhnkg+347nZyVMJZ6e\ndtU0ej0On8IV8mH5SqWEZL0q2/+oHKxxSoR83rgeLouQL0uuwx8lfOQqbx95BMu3LIb5vJeX26JA\na42ZmZnRK5aYDKWSlUH5rQ+gSEoWAMOSiDVxosV+jZGCVau5qtbqqg0pNRjA/rIfwPqwfJ6sUAJ8\nCKM6C/ndkqe+0/MhNjauY1JcuqTx4IOA1gpRlNzokuFqiBSl6lWihvjIUwacbPFOQlhCFYtumkyX\noVSTeBQDm5e+HliYKGMezjbSPyajJxixcgaI9vnO+PvKMb7TetW6/weIz5OVha80mF1nVBky/R+z\nfbqfpbwAUTnPN7TOfhDqMKzCdBW+5hBeo8RBEcfmGlWvZ8ONSxwQJcnKoCRZAdTr9cT7sZ+ywBEi\niizZSpSsvdkz6T2W32tbLevHok1MhukctN6BLRWSJ2sLbrr7EK6iBdiuQJ7GPglkJyFhP2VHi/Pn\nfxwXL/5brK1prK8rDLWyt1ytoZWrbo1quM/Ao+hk/FZ8PZ9/S4xP6Mxn82Ia21CuL83sMpA0ZMzn\nxvcR5cNJMZknK3SmQ/+NUdtJTPpdHTWo9CgFbBIc7PNd4vAQRRGUUsEO5BIHQEmyMihJVgBKKTQa\nDfRk1tEx4dGzZ/FYp2NvvsScbr8d07U+ttFwCBaRKu7JItKlNaVMA6ZERwQLyXyKVZBdhiGDu7yB\nhNSsGPbGxmMc6HkFGxuyK2x8GHVDpaVDaG3u9uvrwOXLKWHOXFp96fDw3Fpl8wHN4/NDREeWED1N\nDOnrcRO9j7lw8hUiUD6FiyPQfSgvkNpD1qoiFF6CTrs87DNnKrhyhf7f/jKijfcKlSF9qtV+MU7Z\nbxTBGnVDoc/ViJNW4oZhMBigUintyEeCkmRlUJKsHBSJZKWo1Vzj1fY2sLjoKFmtlhlGh4Y3BAy5\nkvlZtluqy55T6aTP5vmUK94ROK46wgeE5vMoD2uQ3WQC/OEfxjh3roKVFUO0zp8/Y15xcxP8BGlG\nalJqxWMehArl3GYlqeLz8+DzZMn5nrR5r/JERnm5vY9YcZP93JzjHfMeW065kLapXtvCcMGkZXMC\nNI7oO+74h8vLlUAIqQR/0VlkvYNynXFUqcNSr61JvywVFge9Xs/xFZY4RJQkK4OSZOWgaOb3R6em\n8Bg94QYsWFJF4EoWt3KtrgIvvUTDegxgCVYV1sROZIcULd5lSPMHyCpR4yJbMtzYmGDzAB555F2I\non+Tjmc4GGg0iHBobQgWBX6Szwku2Uqfe0gI1zYULxV6LipEjjSQYRQx238axcBXkKZ5QcjimZkM\nCVOidKh9SlVAsRrb+M6gtC8z63AIDO0n/z7I95MXPjoJwRplah83vkHuo7yhFwndbrckWUeJkmQ5\nKElWDgpnfgcMmyJf1vnz6WxOsAi1mh0Ymu7TVsnqwCpLlGzNS4jkxyKSVWV/A/jJ1yiixcuFFhsb\nh0dmX3ghxtpaBSsrJgW+QcZxGsaGhtsBgJUVo3LB7/rxdhGy5bL7UCGgPPF5PhN7tWr3B5shJdPf\ntXV9m0ee7SWzt/ix0vokNR2RF2VUMGl2fT1iXX/JrlLRaDSm0O+PY1bnwaT8szeuz+ugqGJj43VH\ntO8S+0Gv1ytN70eFUsnKoCxM56BoSlYK6ctqtzOh8AQa+QWwBEupCkxpBbBRCqRe0Z2yz56TCd6H\nCttm1K9D38ftcH9R9vvvQhRpvPwyANisLA1DUrT4BSufA7BD5WC0tuEoQqHl3JQeImE854r2Nyof\nRizX7C83U0brbKYXew+hP29+1j6xvwGgZTCp778z8j82xvJJEQf2qVBeYouHkmQdIYhkHeXfAaCU\nWlZK/ZFS6mvJY2ZsJaXULUqpTyil/kop9WWl1D9jy35OKXVJKfX55O/to16zvEgg078AACAASURB\nVALkoIhK1qMvv2xj3GVuFoxy5XskVcuu3oFbKpxBlizRo/RhEbHi5cL9kaXDVLEIL7xgAkkvXtRu\nAiYZ1Go1l1wlpEprHewmHefW7YCID1w9JiUrYj1vpyIEyfFsM5LwiLJgGlC6j4sbJ3F0TBQ0mucj\n5uvkZWHlYfztxgkoPSzklSRJLSzLUkVDv98v5LX9VKDgJAvAewD8idb6LgB/kjyXiAC8S2t9L4C/\nDeBHlFL3suX/Rmv92uTv46NesCwX5qCwShZ3s8/OpsyJfwapfNhu+0qFgCFVXdgbEpVeuDmdfFf8\nOeAa4QnjZmjZG+DGxvwY20yOl156Fy5d+gDW1hSudqewvLZmFrz8MjT3Y7EcLQCp2T197rmr8zJi\niBT5lvFyII9syChrQDiqgcqG/HMZKgH6PFkB1c3r3wo9J6T7sv9Pdygc/2b0ynkmeenJsqfIR3XH\nGfA55MsadzvfhX2cz3ulLBUWECXJOkIUv1z4fQC+K5n+LQCfBPBuvoLW+iUALyXTO0qpZwGcAzB6\nIF0PSiUrB0UlWY9+6lPujG4XtZo7jjQpWHyeW1LkAZpSuaJSISdcfWTHGayKdcYtHz2LjY2MSnuo\nuHhRo9PRiCJAN5vQtZpDsJAQLw0zriFNOz4nPk8ohr6i1bhN/0HQ8DVyHzlD3diDcH9BOqW+KMqG\nnx4SuFDIh9LJKToCAM6cUahWNapVjUrF/mU9WV4tL0He5cu33ST/mVFlSd98acYvVawiYjAYYIqN\neFDikHH0StaqUupJ9jdJ29RaQqIA4DKAtbyVlVK3A3gdgL9ks39MKfVFpdRv+sqNEqWSlYNC/9oh\nNUsgigyZunLFdhzOzrrG+FoNGAxasESrC1epAnvui3IAe4zFNqOJ1sbGW0euc1B8+tNDfMd31JJh\ndljZMCFMKopS0qWHQ6Tdh1EEXa1C8eiCSV54DDKTGXLHt4/AcD6ZfY2Zd5WBJGg5rzH2PgPw52Ad\nBkLE57D224OfRBG5Cn3WzXobG288hGMpcdjo9/uYm5s77sM4nbgxStYVrXXwy6WU+mMA655FP8Wf\naK21Uip4wVBKzQL4MID/VWtNqdy/BuAXYL7kvwDgAwD+57yDLUlWDoqqZAHAox/+MB579FHzJMnN\nIjWLCJUsHYbRgi0XVsV8inTgvqz93in/Ghsb37XPbSfDXXe9Gy+88EtYWQHW1iqocLllbQ365ZfT\nrj5VrRrCBVjDOxGyQImNno/q0xupo/jIHB/rkDOURiO3M3Bk8StU+hszjDTjCwOASv535MZ2yu9X\nqaIfG/Qd6CNsZh/nBlKBOwh7iSJhMBiU4xYeFQpQLtRaf09omVLqZaXUWa31S0qpswBeCaxXhyFY\n/0Fr/fts3y+zdf4fAB8bdTxluTAHhVayADz6WJKa1WqhUTOKEnEFitGKIls6BGwChB+hLkH+MeFd\nhyHC5Zt34wgW4bOfHeKFFzReeEEjXrnJlAjX1kCR5JoM74A5cUnZkHcWgpcY2foZMzs9T8qSExvl\nA8jsR2t/F+GEFzZnH+PCV45MmgW01mn5z/z5xyTML/+569jSo2/bccp5IfjoMp83SQiqTLA31LtU\nsYqLKIowG2rHLnEwFN/4/lEAP5xM/zCA/yxXUGa8pf8XwLNa618Wy86yp98P4JlRL1iSrBwUWclK\nsb4ORBFiVDIh5N2uUba6XZd0WfChPsbxKPC4hjzIm9SNJ1gAsLLybly6pDEYaOzs6DTCQfPuwpUV\np7NQM/JFSpcGbJZVMs1Lj8Dkt3mCr6Mx6CYKRC549xsiYp4L1UHG5+SeLLlP+95GeZrcdfy+rhBG\nlQzbY+zjMHEjuxtL7AfD4bAkWUeF4pOs9wP4XqXU1wB8T/IcSqmblVLUKfgIgHcC+O89UQ3/Win1\nJaXUFwF8N4AfH/WCZbkwB0VXsgDg0X/5L/HYr/4qKlEf3W4jLRleueI+bm8bokWerZ0dIOspoY7B\nBtyhdvrJYweTmnk3Ns4CODtyvaPCxz4W44EHKlhZAXSradPeazXgzBlgc9OWBgHj11pYgL52zTyn\nDkTySUXZqIVxyoa0Hn90lo1BdPK0HwDBC5CrsQT2kbz+QahI6C345m9u+tWiyfheHsEK7Yh/5id5\nMZ72HrrQk4r10AT7LXGjMRwOS0/WUaLA3YVa600Af8cz/5sA3p5M/xkCl0qt9Tsnfc3yJ1cOToSS\nBeDRH/sxXG030u5BPrQhKVny0QaM8qBRn4+E35SqY0wD9GveEKzjxQMPvAcvvKBx6ZLGVncKenoa\nutkEVlbSrsO0VJgoXDrxbjn6R62WmuOlelVptYIFrHGKY3Kb/WJc3SeznHcril+NXJFy9n/AX5Ur\nK+bSsz8Rzfcuxjl78kdFDKu65pUIfctC65cdhUXHcDjE/PzRxMe86hHH5gZzlH8nDCXJysFJULII\nP/mTj+LyZTMtM0pnZ22kFhEt88t8CubGMwX7USDSVUd2EOiheM7Bh90BNjZyO2NvKL70pXfjhRdM\npAPW1oCbb4aennZJFZUQyXeVKFo0nUZAECsgRYzKiNKvRcP4jHF84zmU8udNirH3MSIZ3k8nw3TT\nIW3at8fR+/C/m4Mgj2DlKVjSj1WqWCcBpZJ1hCh+ufCGoywX5uCkKFmEX/mVR/GDP2jM8K2W68Pi\n3qx2G1CqBa0HsESLgke5ujVk8+QvdH9cw8aGP1riuHHpksa5c0awahCZqlYBUrWuXXNztIgwVatQ\nMzPQ7TbU7Cw0pbvu7kK1WoijyD+483CYGdiZkA4KHRprcIL3NY5C5kWgazB3O4/sFFaixnkXbmkv\nu6/9kKdJTOt5mHQwaA3g5PwoezVjOBxikXcDlTg8FKC7sGgolawcnDSSBQC/93tG0aLPea3mHX0n\nAd1IBjAmeBqnkEBky9d1yENIjSH+qANGD4Kvfe09+Ju/MWMa9hdWrYK1sgI0m2a6Wk3HHnJULTLD\ns3JhqmwBaTchEChk8fVqNagkhoG/RuAf5O7Hs+9xkGpAjhmdrzDeXh0tyW39y66rR66SWXcS9Ps9\nZEcd2IF7lvhOdzEefCQtEtO+dRQ2Nr5zzNcocZwoSdYRo1SyHJRKVg5OUrmQ41OfehT33GMUrcSv\nnQ6pQyVtrWNYg3sdxtTuU1bqsESL/1mVa2Oj+OnJnU4HTzwR48yZChYWFOo332zI1SuvmJOTKFrY\n3DREaGUFmqYBq2zRl1y201GoKY9/YBilOClYMjYK+1avcneq3cd09viKVHDcR+/sUc4x3344gfJ9\nVn2anNwXZWGFfFbjKlg8R0tjY+MtY25X4rhRkqwjRKlkZVCSrBycVJIFAH/91yaodGHhMbTbRqDh\nviylKuLmx9Wq8QTOjQ3AVb6Kia2tLTz77LN4+OH34rnn3oeVlQru+VtNN38gIVO62QS6XUOo+HS1\nmpItANnwUrj+KwVkkt1TQjUcZgiVQw9YOdH9F41vqh5FjeSYiZNCe6bCR5Cd3twMKU7Z6dFEb1x6\nqWHJVTfwyDFORyFQmt1PFuI4xtJScVX3E42SZGVQkqwcnMRyocS1a4/i8mXr0+LcYDAAjFLFh86h\nm43sHiTiVcHGxrill+PHxYsX8corr+Dhhx8GADzzzHtx5sy/wvx8DWdvvtlZV1+9Ct1smrEMNzeN\nurWwAFy7BrRa0N2uJUd8kGkAshuRDxItAz8dgsNT5eVg0SKAaqTle5/EKdeTNWKf+4/YOqhZneMg\nPixJ9EIKGGBLhVLFevM4B1miIBgOh1gNDEtW4oAoSVYGJcnKwUlWsji+7dseTaefecYQrsEghj+G\noeqZHmBj4/kjP87Dxle+8hXUajW8/vWvd+b/+Z/HWF5WWF5WaExPA9PTwMyMkfg6HeheL02EVwD0\nzIz1aSUXkJCSpapV6F4vjYHIgJvlwBQysNs6I15easCJj4eEyY7GkRlYgf3JbRxFacxBCPdp/0ox\nHJqucA7zPG9HO3ztwHQexlWwUJYJTyBKJesIUZKsDEqSlYPToGRJfP/3P+o8f/zx9yRTQ5ibSwcb\nGx+90Yd1qNBa4+mnn8att97q/cXa6fwUvvrV/wMLC8DNNy9iqnkNIAULML6smRmoVsv1ZUURsLAA\nvbvrjnEIo/Olt/Cka9Dny0oJFSdHfNgeWk+QOLmf3PcPuGRJqG/AuF4rBFlR6owassIhH2g6Q67y\nOwlpP/R49aq/lSCO84497z1JguVbN+THkjcN2rYsE55EaK3LsQuPCiXJyqAkWTk4jSRLYmPj/cd9\nCIeKKIrwxBNP4LWvfS2mpsKG/C9+8aewvPyLWF6uYOrsWaNcvfSSUbW6XehuF+j1TMkwSXlPVadE\n4dTdrol1SHxbBKc8GEWp6sVLiD6khG04ROwp06VerV7P5HwBQW9VUIEiMPImy4XBbC/fMbGNeSKF\nj3zxuC2+nE+7R5J9DftefKRJ5lbtIXzGeQhpX8zXMMSKb8tLheY1Njb+dmDfJYoK6q6dTr4/JY4A\nJclyUJKsHNTrdVQqFcSyXlGikNjb28NTTz2Fhx9+GJUxylmf/ORPY2HhF3HrrXWsN5uGYHU6UMvL\nhhBtbpoyYq1mfFmDQVoKVM2m8WH1esYg32wahQvIqk++fKnkUUURYmmCZ14sJ1MrQIxS5JT9+L7S\nY1J+OjVK44rn5+2+xvhqBOLA/K+d8+JbW74Xa9NR+faWPO6xeTFsh6E0u8cwcSakng2RPRvmeVkm\nPJmga3m97hvdosSBUSpZGZQkawQajQa6JzDK/9WGzc1NfPWrX8Vb3/rWiQY8fvJJs+78/SuYviVR\nqDY3jVLU7Zqy3bVr5nm1asgWkJrgHZpC5T7mp1LJn9RYAADUZcgIFQWUOp6vKMoqVqzLUdHrhUzy\nIfM6nSe+XJBT7SkxqmvXoJeX0/lRlO0CzPsX+JUrgzi2qpdvPjsyWuLbS2A61LDB19FifgypYm1s\nPBLYT4miI4qisX6AldgnSpKVQUmyRqAkWcXHhQsXsLW1hTe/+c0TESwAuHTpZ7C8/PNYXq7gjlsa\nwNwc0OkYE/zyMvTVq14TPEE3m7Y8SI0SzNyeHo3MnwLzZzHPVLoWJ160Xsjw7svX8iyv7OwgToYT\n8ZGnkZBKGCzBAsLlQprmg0Lz5Xwfdtfch6Wdx2SuOLgdZDGJAj3K7E5lxMPsiixxo9Hv90uSdZQo\nSVYGJckagdPSYXha8eyzz6LVauHBBx/c9z6+9KWfxfz8z6PRqOH8zWeNCR4Arl6FnpszWRfNpo14\nQEJMqlXjy1pYMB4uJCrW/LzpUGTQolvQ8Wf5TOo5xAtgqpfPQC/3Scv5sEEcoX14ngNAzDuzBtnd\n7RdXrxpS5CsvTlJyzCKPbPEfUJxoDWAT5e3273jH/Qc5kBLHjF6vV5Kso0RJsjIoSdYIlCSrmIjj\nGE8//TRuv/12rFBX4AHwmc/8LICfB6BwfqEJPT8PHUXGewUYwjU/b8jWtWvQWhsixnxZCoyUUNkv\nlBAPWCJFZbjhMN0+NcH3+4iTBgxHsUpUMm6C93m26BjT+TLfSx6bJ8k+sy1bHCI/rlLlvM3MtvIx\nNG1GKQDcsh+tyP1XslzIX7gLa3YPDaEjs7LMPm655To+/OEPo9VqYWlpCa95zWtw2223lTftE4Ru\nt4vamCMrlNgnSpLloPy0jcCrocPwpKHf7+PJJ5/EG97whkMlwZ/5zM+i0fiXmH/jLObONwyh2ty0\n5cNm05Ct6WmoxOieKfsl5ndNHYjVKlQUpWRLNZv21i68VIpM9IAtFwLeCAaw+SlhkmSJEuNHlRPz\nTgpnRrQNIxW81MjLfi6hcuMZzHQ21kG8MABgayu7bbIH8Zx3C2pYszuZ3Pc86xFkd+EQMniUfFhR\nFOGll17ChQsX8Gd/9mf45Cc/iYWFBdx66624//770aJR2UsUEr1erzS9HyVKJSuDkmSNQKlkFQvt\ndhuf//zn8cgjj6QDLR8mPvGJf4H5+Z/DrbfWsTo3l45rqJaXTffgYAA9GABCvUrpAl1gmILFc6t4\nGTHjvwIyxMlRx0JlPUm2EPZyBQmZb7/yeUKKYjbs0nDIfVbOprlK1ehYh+w8S4xoRz4fliRjeaXC\nPlsnQjYnyxAubnSv1Wq45ZZbcMstt+Dhhx/G9vY2Lly4gOeffx6f//znMTs7i5tuugn3338/1tbW\ncl67xHGg3++XP5yPEiXJyqAkWSNQfiGLg29961v4+te/PnEH4aT4zd8c4od+qILqt89i6azxaMWv\nvGIuHoxw6WvXoBsNICkdxlFkxyzkkQ6AuzyZp2EiHBSAmIz1RGpICQMsCeOEfxRxCs0/hHIhJzKh\nTkFDnnQyRqF/OWB9WKNg1s8zvvvmy3XkuIW+AaFdFSuvk1AphaWlJSwtLeHBBx9Er9fDxYsX8cIL\nL+DjH/84qtUqFhcXcccdd+Cee+4py1QFQEmyjhglycqg/NaPQPmFLAa+8Y1vYGdnZ18dhJNiZeUX\n8JnP/Azm5yvAzbNYXG8AjYbJ0ZqeRnz1KhBFqeFdN5uGAO3ummkiV8nFJq5WoWioniTclMDVLM0C\nEhVt12waIofEs0WfRw8xUv0+Ygpg5f4sH4kKqFcZo7tnW5G1yqZ95MtPyPLUK0CzBHgzp9PhBvVQ\nZ+GuWEeWCvk+pOE9gkuwImxsPIxJ0Gw2cccdd+COO+5AHMd45ZVXcOHCBTzzzDP4i7/4C8zPz+Ps\n2bN44IEHsLCwMNG+SxwO+v1+WdI9SpQkK4OSZI1AWS48Xmit8eyzz2JmZgYPPPDADXvdnZ1fwEc+\n8tP43u+t4L77apiam4Pa3TUKU7MJnD1ryJbWwE03Adevm+ONIuPfAoxRnsgVmILFSSLzbqXbs2U0\njiJBe0qD3u5E/uPAZ14PbZ+Xk5VMh83u2Wn+dtztfHlYZt6VK6HcKg6evi7nd9i0RKib0N3HpARL\nolKpYH19Hevr63jTm96EdruNCxcu4Bvf+AY+9KEPodVqYXl5Gd/+7d9emudvIPr9fu5IECUOASXJ\nclCSrBEolazjQxzHeOqpp3DnnXdicXHxhr/+YPCL+Mu//Gn0egr33DOF1fV1S7I2N1NlC1evGoWp\n0QD29oAzZ6CT0FIgISfNpjG2AzYCAgmFMC5ws7IkNdPTLiHyKFm8jEhKl3cbNl3pdBDPzmbXlUoW\nv/kn01Hfb3Z3PVfZeXKa+7Hk8uw83llIrzkUy/JKhV02j5MrUrGsknUUw+XMzs7i3nvvxb333oso\nivDNb34zY56/7bbbcN9995VKyxFiMBgcy7XkVYNSycqgJFkjUCpZxwPqIHzjG994rER3c/MX8aEP\nvRfveEcF3VtaOH/zOvRgANVoGHJz/Tr00hLU9DRw/XpaGtRLS1C9HuJGA6rfh6bxD7UGGo3UAJ/G\nMPi6/Wgej2DgZUAiQIHSoU5+sQfLgaMM9YH1Q8SICNf2ts278o1hSIM/m2U8dNTd5/XrvtwsDUOW\nqDQoIxpoXpc90ryQ0Z0IVnxDxiOs1Wq49dZbceutt+KRRx7B1tZWap5/+umnU/P8Aw88gDNnzhz5\n8byaMBgMMJv8uChxBCg4yVJKLQP4PQC3A/gGgHdorbc8630DxocwBBBprd84yfYcJckagVLJuvHY\n2dnBF77whSPrIJwUS0vvwwc/+F78/b+vUK0qrJ07B721ZS4oWhvCdf069Nyc8VBdu+aYzjUSQtRo\nmPIhjPqkej2Ts0VEjLahaAf22UtphKcMyNcDV7VySBjACFSgtCifx0m/Yqij0NdN6F+e7Szk4xLy\n5TblnXZEF3CZmbUnnnMlK0S0ADtWYYyNjTfhRkMpheXlZSwvL+O1r30tut1uap7/2Mc+hlqthsXF\nRdx111246667SvP8ARFFUUmyjhJxnNolCor3APgTrfX7lVLvSZ6/O7Dud2utrxxgewAlyRqJkmTd\nWLzyyit4/vnnj7yDcFIsLb0Pn/400Ou9F3fcoXDLLSuoJyVCff26IVvNpjHCVypQe3tG6aKoh14P\nOooQc3KV7JuCTVO/1NQU0O+75IfKi7I0KD1bfHpqypjlA12J8JQW84zvMp3CTPvM7C5R8i9HcDkp\nWnGsk89AG1nklQZpXqiLsA9DrqL07zgIlg+tVgt33nkn7rzzTsc8/4UvfAF//ud/jrm5OZw7dw4P\nPPAA5pIhkkqMj+FwWJKso0aBlSwA3wfgu5Lp3wLwSYwgSQfdviRZI1CWC28cnn/+eezt7eGhhx4q\nFMHi+G//7X3Y3X0vej2Ns2dnsXjeeLLQbCK+ds0Y4KenjbJ17Vrq06KuQyfCgfm0eNch93DFXK3q\n911C1WiYAajj2HYVCv+V9myTTnvCRSF+VPD1h8kQOpwY9Rl3IWLV62U7CqmEyOfxfRExu36dlxfH\n6SLkyhbNz+silASrf0NKhPuBNM/v7OzgxRdfxPPPP48PfvCDmJqawtLSEu69917ccsstpXl+DAyH\nw5KcHiUKXi4EsKa1fimZvgwgFGanAfyxUmoI4DGt9eMTbp+iJFkjUJKso4fWGs888wyWlpZw3333\nHffhjMSXv/w+dLs/iXZb4847gYXFRaNkTU2ZjsDr1w1ZuekmkwA/PQ29t5cqT7rRMGoWEnJF3YiJ\ngqVgSn1ORlajYYkXEZ9GI0O+Mob3RsPsl9iMLzOLEyt5o06eb18HiB66JMquGkWGKI1bQuQZWf2+\nm+xu1uGG9hhZgzuRqg4sdeVZWL5cLPJwFZtg+TA3N+eY5y9duoQLFy7gU5/6FOI4Ts3z9957b2me\nDyCO45JkHTFuwA/kVaXUk+z544wEQSn1xwDWPdv9FH+itdZKqdDBvkVrfUkpdQbAHymlvqK1/tMJ\ntk9RkqwRKMuFR4vhcIinnnoK99xzD+bn54/7cMbG3/zNv8LVq+9Gr6dwxx0VLC2toD7dMWRrehqY\nmjJqVqNhSofVqiVY/b7JxKL509N2gGlStxI1K410oNIeV6LoB0CzaS9sHqVK9fvQs7NAv+8SKl+n\novi8Wx9WiFhZpYrm953uQ7uNLCHy8qAkYf0+H2Cb/zLmAzbLBHhZIvSpWBGAHoDugWMajhO1Wg23\n3XYbbrvtNrzlLW/B1atXg+b5m2666bgPtzCIouhEXWdOIsaLFz4QrpAR3Qet9feElimlXlZKndVa\nv6SUOgvglcA+LiWPryilPgLgTQD+FMBY23OUJGsESpJ1dOj1enjyySfx0EMPnUhD79bW/4nf+Z2f\nwNveVsUddwBnz7awuL5uyFWlYgaXjiKjbCWeLOzuQk9Pm8BS3mVYr6fmdz09bdWt2VmoRN1KS4f1\nerZ0SJ2EgdIfRUzoVguKBq9milgK4cmiUYBCUQ2djvsolxOx4sSLpg250rh2jS+jKbpUkx9rFy5x\n2hWPfGxCWS6kTsIBjHr1epwmKKWwsrKClZUVvO51r0O328WLL76IF154AX/wB3+Aer2emufvvvvu\nV3VZcTgclhEORwjq/S0wPgrghwG8P3n8z3IFpdQMgIrWeieZ/rsAfn7c7SVO3p3tBqMsFx4Nrl+/\nji996Ut45JHwsCUnAbfc8kt45hlgb+9/x+6uxtmzCktLC5haZ76sqSnj1UrKiHpvz6hP3a4ZbHpv\nD6hUDLki0jU1BfR6pnRIn0HedUilQ0qJTwa9dQz0PvLUaFhP2NSUIXDdLuKZmew2AIYJh+Heq729\nrOfKp3S5UQ5mXl6JMI55NyEN1EzrR+KRl/7o0t5n8/vIerBOH8HyodVqpd2IcRzj5ZdfxoULF/D0\n00/js5/9LObn51Pz/KvNBF6SrKNHwUnW+wF8UCn1jwG8AOAdAKCUuhnAb2it3w7js/pI0tleA/Af\ntdb/JW/7PJQkawRKJevwcfnyZbz44osnnmBxPPfcv8aLL/4EHnhAYX1dYXm5ivX1ZVQaDTOgdKVi\ngkuvXzcEam/PkBzyagFG1aKUd8CWFhPlgUp+CkbN0lNTdp2EZAFW1fKWAaUxnl47IVndnhuZsbcX\nJ48+tcnfcUikqdPJbuPrLKRyYbtNEhjvJpReLJ7oLo3upGL1YRUsIljtE+W/OixUKhWcPXsWZ8+e\nxUMPPYSdnZ20rPi7v/u7mJ6exvLyMu69916cP3/+1KtccRyXJOsIUXQlS2u9CeDveOZ/E8Dbk+nn\nADw4yfZ5KEnWCJRK1uHi61//OqIownd+53ce96EcOgaDX8JTTwHnz78Ld95ZQacTY2lpGq0W0Fo3\nBIuM5KRO6UYDsdY2PJSHiEaRKS1WKrZkSKSKyFK9bomW8G2lZIvFQTieLkbM4oq5FPR67iWSyoU+\nH5bZNZUDaT2dlg5l2XA4BAYDsz6VCIdDzUgbKVd0DNRN2IElV9wEr2EJFydXBCoPfgdKGMzNzeG+\n++7Dfffdh8FgkJrnP/GJT0BrjcXFxTR5/jT+wBwOh1hZWTnuwzjVCIy69apFSbJGoCRZhwOtNb74\nxS/izJkzOHv27HEfzpHi4sUP4PLlf47XvEZhdVVjfV1hfr6GmaUVqOlpkxif+LJ0qwXV6Vgj/NSU\neV6pGMWKSobJcjQaDvFKiRJ1EXY6KaFSw6GJdki8WEBigk9UK650+XKtAEuieEchkaKdnTh9TqoV\nzeP74iVCHkg6HMpUd1kKpD9eKiQSJT1YxNR0Mr0HYBcbG6ePzB8W6vU6br/9dtx+++1461vfis3N\nTVy4cAHPPfccPve5z2Fubg5nzpzBAw88gNXV1eM+3ENBHMdYXl4+7sM41Shm+M7xoSRZI3Aaf83d\naAyHQzzxxBO4//77T7UH5PHHN5MpDeC9AGbwrne9F3fcAayuAnNzMWZmmpiba2JqZTolSKkRfmrK\ndAk2m4grFUO2mKqFRsNskxApPT3tjoNYr1uyBaSkDHDLhUSy+rEhWY2aRi+pvHEyBVhSxEuERKh4\nOTBvPW56N52DGgOWuRXHgNbSyE5Gd65iIZkmgtWF6RSkIsUAptQY4efOWxKj0gAAIABJREFUPW9q\nmB/+cHpg3/yH/xAl/FBKYXV1Faurq3j961+PTqeTmuc/+tGPol6vY2lpKfV6ndSyYlkuPFoUvVx4\nHChJ1giUJOtg6Ha7ePLJJ/HmN78ZVZkmfgrw+OP3Avg4AE4e6TJzHR/4wHvw/d//PrzmNQrnzgHr\n60C3qzEzozA1tYBqVaPW6puheZKyYZyY4UmxSqMeANOlmNwkKN4hVbMSsuVTsHj+VVw1X/t+l0iQ\nShWonR042Nkx63BPFpUQeyxlgYiUj3iR5+raNdf0bvxZ0tguVSzux/J1EA5hDe57+Lk37JjOzDhp\n0x8MzF8U4ebf/31gOMQ3f+AHUCIfU1NTuPvuu3H33XcjjmNcvnwZFy5cwOc+9zl85jOfObHmea31\niTrek4iSZLlQEwaHvSqVwB/5kR9BVOwU20Jie3sbX/7yl0+VwZ3w+OMX4F5O6KsxzebFbNkMfvAH\nfwZ3361w883A/DwwPa0wN6cxPW0u/jMzCjVtjO6q0zEKVb9vlSoiVZX/v713j47qPO9/v3uuuiAQ\nSAghgQHZEhcLhGvHJThO/VtNenLpaur+0iZN1q+/JM3BbU66stLTk0uT1CZpTrn4Ro1rIxobJ8bH\nNhI3GzvYlmNjwI4RFyPuCBAEBAbZCCGJue/zx55H+9nv7BmNQKM9mnk+a2nN7He/e+93dJn56Hme\n990uo53qu3gkSxlNjC1KSZGrvr4Y/H4NfX3m+GmldZ7uS9ZOz7u79YE0I9VY0T4SqljMfN7bqyMc\n1tHbS3IXhDVKRQXvASRGsUisKDVIMwgD8eP68MCfjjGiV5GIceFw2BDPQMDYpjBb/HnnF78IYej0\n9PQMFM9/+OGHKCoqQllZGW699VZMmTLF6eElRdd1rF69GpFIJCf/4VNw5Kav8zVNb8nwNcqB3anW\nyco2RLLS4Pvf/z76+/sH7ygM0NnZic7OTtxxx6j5W0iLxsbDbIuvqs3/NAqVbd3S/s1vPoBJkzRU\nViIuWRqKioCiIh2U6SsqMo7xuAxB0YNBU6pYBEuLV5nHKPUY3xf1GrWEJFJFRaZUUVSK6qGMfvaS\nRZEsq2TZCxVg1l+RSPX2mnVbdP3eXj0ewVLlissU7e+PPw/ClCzEH/sB9OOBr0xOECiEw0b4jKQr\nFAI8HuMxFDLbAwEgEkHnl74EYehQ8fzp06fR0dEBABg3bhxmzJiB2bNnZ1UmIBKJ4KmnnsraW3YN\nM45J1usZvkaFSFbu8cMf/hDd3d1OD2PUcOzYMQBAXV2dwyMZPqxyxUWkMEm7DjOqxSNaiLfH8LWv\nLcakSRrKyzWUlBhiFV8s3uhVpMMspdItj+GwDr9fQyRinDsQ0C0iZWwbx5JU0T4SKr/ffE5LNZBA\nESRivJ3E6aOPrELF96my1dcXi/tNmH1P6B+Xq7DOEgSMmix6fg3WKFYAwDU88H/NMXYHg2ZukoSK\nyxVgyBcXK5KtggKzXyiEzj8d0uxsgaHruqV4/sqVKxgzZgwqKytRX1/v+Ky+QCCAZ599FlF1dkdu\n4ohkNWia/lqGr1E5yiRLarLSQGYYpoeu6/jggw8wefJkTJo06H0zRwWNjXvYlvp7oMMUhQIk/g/S\nC6uEAYZcGO3PPfdTAMCXvvTvmDTJqNcqLERctIz0oa7rA2JlLn+lIxIxJCoQr6tyuw2Zou2iIm1g\nMVASqfhtFAe8w4guUVTKaOO1VwCPSCVGtMzz6PF1rhL30XjMWi0q5FJTgRH22Meeq4LVh/vvvxta\nJC5rwaC59hfJFd09gIuVGtHyeCxyBY8H8PlQ9c476Lz7bghDJ1nxfEdHBzZu3Ai/3z9QPH/LLbeM\nePF8KBQatQX7owmpybIikpUG2RTyzlYikQhaW1sxb948FBUVDX7AKMAqWDrMyIoqWzwqUwjr20wy\nCesDpRs3bfpXAMCnP/0LzJhhpA7LyiiypcGYcGimEkm6KPoUDhv9aI2rYFBHMGgKUzBoHBsKmWtS\nmdEta2G7GsmiLDlJFr99jjnLkPrEX5klLUhLQ6grttPMQPpeUJqQpwwpahUA0I3vfe9PBq7j8xnp\nUV9xfKX7SNhckoLShIDxSMXvgQAGwnvhsCloXLQAVB08CASD6Pyj3F8dPpPw4vloNIoPP/wQp0+f\nRmtrK7Zv346xY8di6tSpqK+vRzEtK5JBAoFAPtRiOYoOWSdLRSQrDSSSlZr+/n7s2bMHCxcuzIn/\nFBsb340/88M+Q05y4FXaKbKlChUtmsl/j7iYGdfZtu1fsS1+n/cvfvGXcdEyolKFhUbkiiJYPI1o\nRIt0uN3GNSMRHf39ZhQpGNQHZImWaFAli8br92sW0eKLjYZC+sBxPGplFrLriMVM6QoEdOi63Qrt\nfKV2Kn7ngkXrXPXib//2NgCG/5DE+XxmECp+S0b4fF54is2fhxaLmpGtUAigD/FQyJAtj8e4FVE4\nbMxCMO9MbZzQ40FVWxsQDotsDQNutxtVVVWoqqrCJz/5SVy5cmWgeL6trQ3FxcUoKysbWHk+EwSD\nwVF5j9TRRl7WFKVAfuPSQCJZyfn4449x5MgRfOpTn3J6KDeMKVcEyRT/+ccG2Q8YwqDDlCo6hmRD\nlbdAvC020L5ly48A+HHLLf+GKVOMui0SLZ/PiFxFImYq0bw1obH90UcxFBaa0a3ubh1+f6Jk8WgX\n/ZrzZRhIuK5dM6JgpmRR38QZiiR3uk4SaaT5DOjxGhJnDRrF7f/jf8wcGEuALeBOQhWJGBE2qmOn\ndsLI/LnhKyiEFotCH1NiSlc8LWhZ0Ist8wC323jucgETJgCxGKr+8Ad0Tp0KYfgYN24c5s6di7lz\n5yIUCg0Uz7/xxhvQNA3jxo1DTU0NZs+eDa9X/Wfm+giFQsN2LiE5ki60IpKVBiJZ9pw9exaXLl3C\nwoULnR7KDdPY+A6S/zmwBaESold8vypPasSL9nGpIqxRLWprb/83tLcbW1VVD2DKFKCsTBuQLZ/P\nWD09viyWcdUgRbXM6BbJVTBoiBqXK8AqVrwuS114lB4pAnbtmhHBIrGKRIIwUoL02vnMwRDbdy3+\nOvvi7RfxiU8Ytaw8excImK/L6zVl0us1Cve5L5FsUQDLuB+3e0C6PHHpGlgzrK/PiF5RVIsiXB6P\nOUsxEgFcLlSdO2ekEGtqIAwvPp8PM2bMwIwZM6DrOrq6unDmzBkcO3YMu3btQklJyUDx/I2s1h4I\nBOS9PMPIYqSJiGSlgaQLEzly5Ai8Xi9uu+02p4dyQxhyRfC10OhPQw1+0+w4r80+HtlKFvFSo1r0\nps8FjEtZcGC7s/Nn6Ow0j7n55p+gtFQbkC0SLZKuUEhHYaE2kPJzuaxrWgWDMfh8GkIh69IOXLgS\nJQuWcyRGrQIwo1WUCiSRotShEbmaMmUq/P4S47vgu8mSDqSsDkkTeREXKVo1noITlBmMRg0BA8xI\nFy2dBbgHgln+4mJjRzAI0AKVtPQDXTQuWXC7gfJyVPX1oXME6ofyFU3TMHHiREycOBG33347+vv7\nB4rnN2zYMFA8X1dXh5tvvnlI5QmhUEjey0cAkSwrIllpIH+YJrFYDHv37sW0adNG/f3MrIKlQsKV\nrFCWZIv/Cakz6NQIFgmTXbSLBIxKR71KH9omUfHhxImfs7b/BxUVhSgtNQSCIlhmOlG3FMADxqPP\npw9Es+xWbVfbjLRhNP76aexhmBEqHqniUtWH4uLJAErg9Rpi1dubKEp+vzV65fNZBcsYk3WbxItS\ni36/cV46Z1+fKV0ej1n7DmiIRLyA5oUnvs/tcpGNGRf2+40FTVl9V5URvkPnuHEQMktRURFmzpyJ\nmTNnIhqN4vz58zhz5gzef//9hOL5wSbchMNhFBQUpOwj3Bg6rP+qCiJZaSEhZoNwOIzW1lbcdttt\no/7NqrHxLaVFlSkSDbvoFodqe+zSiKqI0aKagCFVqmyl6sfFTVf6A8BSXLzoxcWLdE4PgL+HxzN+\nIMrldlN0i5Zd0ONRIatk8XsNRiJRWGWKxhpm29dgLWbvg7XIfwyAMejri8HjcQ3cjofLUDBopgf9\nfmsECrBGtOjPkVZr4NJFEbBg0Hi9V68abdGomWrs77eu5EBfRUUAPF64PTquxfzwFAFej25cSNNM\n24s/r7p6FZ0lJRBGBrfbjSlTpmDKlClYuHAhuru7cebMGXR0dGD//v0oLi5GeXk5br31VlRVVSUc\nHwqFUFioLqkiDDcSybIikpUGEskC+vr6sHfv3pyYQZgoWIB14nGy10fC5UHiWwlPI0LZTyLG/9zs\nUoi8H49+8T6UTqSIFz8nTzUGADTGl4dyg9+woLubn//e+Pld7DXQPvqeUGozHH8eAXA6fgxdn699\n6IO53IWXncc7sHgq4EEkYkoXyRGJFwmX12s8J2ki2SLR6u01a9kBa2rR6zW+KAhFa1D6/aZY+XzG\neqQAcOECtWsoKKCAlgaPxzvw6vTS8dCgD+Qrq8JhdPJ1LYQRo7S0FKWlpZg3bx5CoRDOnj2L06dP\n47XXXoOmaSgtLcWMGTMwZ84ceDwehMNhjB071ulh5zSyhEMiIllpkO+RrI8++ghHjx7F3XffPepv\nSWEvWCpckOyEK5Jif5g9V6NjdinIkE1bGImipQqal/V1KfvoXOraVHapz2b2nM5J16L+/Pxu1u6G\n8ZaqseNcMAXSA/Mt1xMfB507DFO6XPGJfa4BwQKstVYDry5oRroAa1SL0oXUxuWLZiP6fNYbWwcC\nRoE8j2gVFJg18ADw8ceAx+OFz+eFqx/w+TR4WR6zChDRchifz4eamhrU1NRA13VcunQJZ86cwZEj\nRwaK50OhEKqrq50eas4zuj8hhh+RrDTIZ8k6c+YMLl++jIULF+aJYKkMJlyxFPt45AuwpiBTtdFa\nUYApNHbbJGJRWKWMoNouGiPJEBcxj9Kf90tGFMbrpdfnVdrd8XNEbZ7z1xmxjCMaNb6HRsTJg0jE\nKLTn9VrhsNlGEkR+Q7MNKY3Y32+mENUUY188u+l2G+fi5TyBgClZmmbsp2iXGcQ1Ilw9/V54fEBZ\n0Xh89FHnIN83YSTQNA0VFRWoqKjAHXfcgb6+Phw9ehStra0jsuhpviPpQisiWWmQr+nCQ4cOobCw\nEA0NDU4P5Ya5PsFSSSVcfJ8qKXaRpFRtLqVN7UPbPIoVirer0kVRsBhM0aEx0q1rVOGj1+JWHtWU\nILXxejE6pwZTqoBEmePRNho37xeLy5YROdM0M6JFchUIGOlCv98QIR7NUlOI5uxCa6qQoDotwBAq\nHtni0O2HKOXIz1FWViWilaW0tbXhc5/7HF566SWnh5LTyBIOiYhkpUG+RbJisRj27NmDm2++GePH\nj3d6ODdMY+M2pJai6yGVcPGIEhcTihS5lbaY0qZKjnqckWoz+sWUdvqTDrF2nm6Mskf1/Opriil9\n6XVysdJgRrJ4mtAOLpZ8rDQnyQVrRYeRbjRly+hv3CnHGAtFuUiueISLpxntxApITBVSLRif19HT\nY0S8KOpFhfp2TJxYhUuXRLSyhf7+fjQ1NeHuu+/GK6+8Ak1z5L7JeYVIlhWRrDTIp0hWKBRCa2sr\nbr/99px43YZg2UHCMBxvCekIl51s8XY7AVOjXSQigDV9GFGeq+ek/nQsT9fxMaa6r1uMnZce+UxH\nilzRdXk9lt0Y+VsPvS51fMllk1KKxr0Rjf3815VHtOyiUSRjdndZofW6qD6L0obqhNpgEOjuNp5T\niZaRnqyC2y2i5TQkWAsWLBgohhcyi0SyEhHJSoN8iWT19vZi3759uOuuu3LiDamxcTusERmVTLwd\nqDVadtcgadBhCg71jyrb1EY/Dy4ePAJE+3i0Sb0eHRtR9tE5VFlU5cbD9gGJsya5VPFjKBKm1ozR\ndU1RMvpTvRmXSzthi4BLWzAYRTDogdttjI8L1LVryVOAgH1Ei9KPJFqBgBnBoqgYiRXVbtG6Xy5X\nFTRNRMspAoEAmpubcfvtt+N3v/tdTryfjRZEsqyIZKVBLkR0BuPSpUs4ceJETswgBEiwiMFmCGaC\nVG81diLF5YxPhHYr5+Liw+WKR6801pdEjEsOyRhPz6lRI7XGjJZ44DMJ1dfDZctuZqUapePjpO2Y\n0ofOywvn+Tj5OmVUOO+JP0YQDLrhdrsTxIpHqyhipeLxGJEql8uabnS5jC++lhcVxLtcQGcn9a/C\n5MkiWiNNIBDAunXrMHfuXLzzzjsiWCNMNkuWpmkTALwAYDqADgB/o+v6ZaXPzHgfogbAv+m6/qim\naQ8A+D8BXIrv+1dd119JdU2RrDTI9UhWR0cHrl69igULFuSgYCVDLfZ2YnUXuzSjOhNQnfHHBc1u\nNiBJmgaryHBIZnjUS132gcRKjYgNrBiljJskjEuaXeqUR954RI+/Jh5V46/TrMsyzmM3CYCPgc9W\ndCMYNK7tdrsSpIvqt65cMWqveERLXRaOr9V18aK9hAFGdEsYWYLBIJqamjB79my8++67IlgjzChY\nJ+tHAFp0XV+iadqP4ts/5B10XT8KYD4AaJrmBnAOwAbW5RFd1x9M94IiWWmQq5EsXddx6NAhlJSU\nYO7cuU4PZxhRpThk28uKXT3SSL5dqGlGtXhere2iyI56HEWy+Hk0WCNcXOj4fl4XZZc+VKNPdD3A\nPopFMw15f368uTCp9Vxu5TkXQHW2Ik9Zqmt4BQeeR6PmPkO6XPGlHGJwu13o60ueSqT7RXd1GeLk\n95tpQnqMxYwvWiKC7jt9/rxEs0aKUCiEpqYm1NbWYteuXaN+0eTRSpb/m/4lAPfEnz8D4C0okqXw\npwBO6Lp++novKJKVBrkYyaIZhLW1tRiXQ/dga2x836ZVvYUNMZh8OSFedtEtPnYuWzySlSzdqCnt\n/Djaz6WLn8dOiGifutwEn83IU5n8g45qryjKpp6bH8+jXOq1eAqUaseoD6U01eUnYLlmNKoNiJdx\nyx2XZTZid7chSTSjkJ6TQAHmkhCULiQRA6zRrQsXqnDbbSJamSQcDqOpqQnTp0/H7t27RbAcYoQK\n38s1TWtl2426rjemeewkXdfPx59fADBpkP5fBfD/KW3/pGna3wFoBfB/q+lGFZGsNMg1yaIZhJ/4\nxCfgpTnweQm/XQ0xWK2WmuLK5FtKsiJ6EibAGuUCEiNWuk072H7aB1iPs0vXEepaW3aF94D1e2S3\nBhcV/tvVodlFsmi5C/46wqxPhD2PInFdMLvV6gHgWnwhVBciEZI247nbbdwfmguYphkS5nYbz0mm\n1DQjRbdiI/Cpk8+QYFVXV2Pfvn1wu+3+ORJGihH4de/Sdf2OZDs1TXsDQKXNrp/wDV3XdU3Tkgbe\nNE3zAfgLAD9mzU8A+AWMN6xfAHgIwLdSDVYkKw1ySbKuXr2K/fv346677nJ6KMNOY+N+AAVIjFrx\nGyxz7N4O1FotgosG35dqFfjhQj2fnWzZYSdPYG12KUo7cVKPVSNLdoXuJEO0Ty3259LFj7VbhoLL\nER+PWkzPxYynPnkfuqeiy6afigvBYDA+o9CIwLndxsKo9DlOEqbrRoSL7iPNBSsWA/bulWhWJohE\nImhubsakSZPQ1tYGj12+VxhRnP6fQtf1zyTbp2nah5qmTdZ1/bymaZMBXExxqs8D2KPr+ofs3APP\nNU1bDeDlwcYjv5Fp4HK54PV6EQ6HB++cxXz44Yc4ffp0TgqWiZ1gAYAfiX/+tG+oNVuxJM+JkRAv\nfk67AnNNeVTHkGyJCNqn1oTZreNlF8XiqUJKRdrVcoFtJytyt0sP8nOo6U1+TAzmfSRJ0jSlD6ef\nnUOzeQSMdbliA0tEGPdbNOWKolu0rhaParndwG232VxWuG4ikQjWr1+PsrIyHDx4MM+j8tnBKFgn\nazOA/w1gSfxxU4q+fwslVUiCFt+8F8CBwS4okpUmfr9/VEvWyZMnEQgEcOeddzo9lIxgRLGuF4pU\n2knYYOnDdIVquFecT/d6ydKK6jFcjOxmBhJ20SM1DamztsEK+NXlKVRp49EoWlCVZijyWYRUFG8n\nSFzcAuy52penMnkEjt4mjRseRqNGTRegIRAwo2Fut2tAuHiEi6Jcr7xShS98QaJZw0E0GsWGDRsw\nduxYHD58OKeyDaOdLJesJQBe1DTt7wGcBvA3AKBpWhWA/9Z1/Qvx7WIAnwVwn3L8Mk3T5sN4I+uw\n2Z+ASFaa+P1+9NLiOqMIXdfR1taGsrIy1NTUOD2cDFLIntOfua48AsA1mzZ+DJT9Hps2Lhl24p1s\n2vhIzrtJJlHp9ldlSE0X8teoCpVaTG+3MCo/js8e5NEmqrdS18+i/5f5SvHq4qk6rEXwEXYuipip\nMsWL8TWlPz3SfSCpzfwdoxmFfBUUki6jAB7CMECCVVRUhKNHj+bs7O/RSLZHsnRd/wjGjEG1vRPA\nF9h2H4Aym37/a6jXFMlKk9H4n1I0GsXu3bsxa9YsjB071unhZIzGxna2lepPPAYjbQjYR3V4W5Kb\n0yWcT01/qUXoHDUlp14/k6RaIkKFR7PUdcSSvQa6RqrZjepSEtQeUfrxKBZP+fHxkADxm2RTm5oW\nVEWKi5MqUhTR4iJm9xoRH8tVcNGLRDREIm4Eg3wMxnOpx75xotEoNm7cCL/fj2PHjqHAbhVZwVGy\nfJ2sEUckK01Gm2QFAgG0trZiwYIFeVAMWgzzw/dq/PFGo0Z2KURVzPhSBnaoxdqcwYrnkx13oySL\ncNmlFe1SgfwYu3PZ3eOQnx+wigtPLZLYcMkjaeKLpNLMRCh9Aes9HfnxvN5qMK4hUdaSbSdbZoO+\njyTixhifeqoK3/qWpAyvh1gshs2bN8Pj8eD48eMoKipyekiCDVm+TtaIk+ufvsPGaApJX7lyBW1t\nbfjUpz7l9FBGCJ4WHAP7JQP0JG20zSNXQ3mbsJuNOFgqEkg9M1BdTT3ZOYYDtRh+sBoqu2MGO5c6\nk5GWYlAL5FNdm8SGit01pZ1HxOxEiuRLFSQtRZsddj8zLlJ8iQ/a7gGAeB2XhLOuB13XsXnzZui6\njuPHj6O4uNjpIQk2ZHu60AlEstJktESyzp8/j7Nnz+aRYF0v6oelz6bdTsbsjh3qoqbJJCxZkTqQ\nPHo0nKQSLh5xsjtG7W+XFkSSPnxdLl1pI/mxq/fit+hRJUmNqLlgP/7B6GfjV9OKUJ6rqUe7CJr8\nnz9UdF3HSy+9hGg0ihMnTqCkpMTpIQkpEMmyIpKVJqNBso4fP45oNIpPfOITTg9lxGhs7AVQAuuH\nNI9kXbU7bAikEix67k2yn9rsZt8BqWu27EQLsKbK+DWGm8FWngcSU4vUph5H+wfbx6/Dz6cKl3pz\n7GQzPNX6q2RCxqUIKdrV89utLyaRquFE13Vs2bIFwWAQJ06cyKm7U+Qi6czHzjdEstIkm9OFuq7j\ngw8+QGVlJSor7Ra6zRfs1sgqglWU1LRhsrSiKm38/HZtXErSXepDnV2XTppRXfsqk0tDJDtnOtKV\n6jh1Hy9QV89H7TwSlUy61DRfOpEr+lmmE+lKFoWiaJddFAuwRr00NDYuwqJFT6UxtvxG13W88sor\n6Ovrw4kTJzB+/HinhySkgUSyrIhkpUm2RrIikQhaW1sxd+5cqVMYwOmUjCc+Br72UqoIVzIx4VGr\nZFEx9fhski6eYlSXYbATLh5ponYuWnbfLzXSxY9Xa74G20/PU0W/AOv6XKpQ2aFG2/57kP6Crut4\n9dVX0dPTg/b2dpSVJcymF7IQqclKRCQrTbIxknXt2jXs2bMHCxYsyOP7df0AwJOwpglj7Iuns9QI\nFo9spdMXSn8k2YdB9vNZh2p/XtvE96kz8vgxdqlFJ4vn7caRjnAlS1GqYplqsdR0SFZfJmQDuq5j\n69at6O7uxrFjx1BRUeH0kIQhIEs4WBHJSpNsi2R1d3fj4MGDOX6LnHzBrjA6WUSL7xuKQOkY+ShX\nMuFSSXbLHvU8XI5SRbbomGTLSSSLYKnHJ9ufKgKW7FgeHfsqgFchJKLrOl5//XV89NFHOHr0KCZP\nnuz0kIQhwP/NFAxEstIkmyTr3LlzuHDhggjWkElWTA6YK8aninIlawOQEMVS+wOJ0S0uCXyGnSpd\ndn35+egYu/7UZredrGB8uEg3rQiYtVV2MmRXVM/3q6+X96U+XmU7FZLKc4qWlhZcvHgRhw8fRnV1\ntdPDEa4DSRdaEclKk2xJFx47dgyapuH22293eihZwjQAY5E6XZhsG/FHSg+qtU1DDXxziePrZ6lp\nQbsUZUw53sW2VeEiqPZLPYddIT0/Tj0v75vJpSKGGuUabDFUuwhYMugWO+q1k9Vp2bUl6yu1kMNB\nS0sLOjs7cejQIdx0001OD0e4DqQmKxGRrDRxWrJ0Xce+fftQXV0tNQoJpIpQpUMyoaJbdnBBIyEb\nTJz4fnWMHljfjrhg8bcoEiE322eX8qNjk8mVGv2yW5eKY5dapGOHi2Tnup4oUioZs5swMNxRab6W\nFr+WXbrRBUBWfFf53e9+h3PnzqGtrQ0zZsxwejjCDSCSZUUkK02cTBfSDMKGhgYUFhYOfkBekqyQ\neQxMAaKVxpNth2EvS3wGG90Dz4VEkfIqx/JCelXE+AewKj00Ng7JkRpxG2zZBC5otE3X5P35eZKt\n6zVSRfT8OnZj4t+bZD93b5J2wFg8NtmaXeo5ad9Q/8lKNq4vJGnPX95++22cOXMGH3zwAW655Ran\nhyPcICJZVkSy0sSpSFZ/fz/27NmDhQsXwuWSWhGViRNLASzB1auLEYkAug5Eo4DxQWwXdeLY1fgk\ni2ilI2p0rCpNXmW/msIEEmuqXGw/rRpO1+LpQ7Uo3i4ipinHgO1PJU52gjMSwmVXy5UsUpks6hZO\n0g4Yryedtz5+fBCpi+jt2u3/IVq06IM0rp0fvPPOOzh16hT27NmDmTNnOj0c4QaRdGEiIllp4kQk\n6+OPP8aRI0fkFjkpuPfe+7BhwyoAgNsNRCzLDavSpEoV3WCWCxnWEO8wAAAgAElEQVS9TZDQ0PNU\nuGCu+q6mFbkYkShRuhBIlDQ3rOtrccHwwCprgFW6eBQo1WxFwF6SUhXPU/tIC1eyc9pdUx0vfT85\n1If/oiSTsev9x4rORzea5te+eJ3nzD22b9+O9vZ2tLa24tZbb3V6OMIwIZJlRSQrTUZasv7whz+g\nq6sLCxcuHNHrjlZIsDQNKC8HADfCYSAa9UDXjX2RCEW5IrCKDb8XHoen9Hghe9Tm0S5Np8GQL96P\nPvRJlNTzcrlywxr94uMikgmgKll2yx3wwvHBiuftpAusD0XQRmKZiFTnVaXK7vujLiqaDPWelHav\nvzDFvsGOzV927tyJ48eP47333sO8efOcHo4wTNgVOuQ7IllpMpLpwsOHD8Pn8+G2224bsWuOZubP\nB06eNCWKhEpjn2uaxrfVgmgSCZolRrLDo1mpIloFynHqsXQdP8y3IS49JHou5XiKavHr8khYLP5c\nrRuj8wL2MqJGrnjxvBohUoVETdvxY0d6tqIdg6WF7QRV/bl6kZ4UuWCkEe3OzfvQ78c9aZwz93nv\nvfdw5MgR7Ny5E3/0R3/k9HCEYeZGpiDlIiJZaTISkhWLxbBv3z5MmzZNbiMxRGpq7kd7++J4pMrA\n7eY1WsZ2aSkQibig674BGUuMcAHWaA5BvwPJJIxDkU+SKPqi83pgjWbRfr/Sn/arESkqwufj4bVX\nPEKXCjqPnZSp0qRGs9RZi7w92ZpW6rWHG7sZmLrN81Tfm1T1XKkK6lXoHIH4YxcWLUr3vpa5yfvv\nv49Dhw7hnXfeyasb2ecTki60IpKVJplOF4bDYbS2tuK2225DQUHB4AcIA8yYcR9OnTLqsiZNAmIx\nQ5zoUf3i4qVpgMdD2+YHq8fji9d3RZBapqgeC7CKlypVXtYO9sjXfKK0ohrBUiNZJDeU8iRJ4zVo\n6srnap2XWseULHWovlawfXYLpNodx9OJQGLUbCQK5wfrw/sOJmCAfdQqO9bSy1Z27dqFAwcO4M03\n38SCBQucHo6QAaTwPRGRrDTJpGT19fVh7969uOuuu6BpUrtxPcyfD/T3myLlchmS5XKZX/StpUeP\nhyJblGZ0QdddCAZ5Ab3dB24hrNEmXktF0SW7iBRBs9v4sR6lja7Nl43g6UF+rSjrQ22DrRvFJY7O\nS8/tCuHB9vM1uWg/T1Pa1XjxMelIX9CGg8EK59W+an/1bTLZ3yilDu3Ond+TV/bs2YP9+/fjjTfe\nwN133+30cIQMIpJlRSQrTXw+HzRNg64Pb8a5q6sLx48fx9133z3s5843Fi68H9u3L7aIFWA8lpfb\nR7aCQUO2iHDYSCsSBQVGZCMS8QwcY/82oooXhz6USZCoj0dpI9TieH6bHd6uzjLkKUg+K1Gt6wKs\nETAuRXZ1XVyYkhW2q+txJavlUiNgakF+KvkZTtKJdgHm7X7ssHv7THaeHixalJ9r3O3duxd79+7F\nq6++invuucfp4QgZRCJZiYhkDQGfz4dgMDh4xzQ5ffo0rly5gk9+8pMiWDfIlSv3Ydy4VaisNGTK\nmFloPkYiQChkCJfHY/Shx3DYeD52bKKIRaNAIJB4Pb/fECSjj130g4sSRaHCMNKGNOOQz2akP0VK\nT9I57NKKPBXIa69ItCJKf06y+wHy15Asjacu8WDXN1n0i6cISVz49yjZfQ2dXCZisNmH6mxUwH41\n+fydPffBBx9gz549eOmll/DZz37W6eEII4BIlhVZ3XIIDFfxu67rOHjwIHRdl+nLw8yXv3w/3G4j\nGuVymY/qV3k5UFFhPE6aBEyYYIgWSRh9AcZjWZn5NW6cyxL9cruNaJfH44ex9lYhzA9oqq8qiLf7\nWFth/MvP2vzsyx3v74NZK+RhfT2sn0c5B/V3s/NorJ1m0LnZedUvX7wfbWvsi4+Bb6vt/Bo8IscF\nhvaDHYMk22CvIdOoKeF0CClfRg1XPkax2tra0NraivXr1+Pzn/+808MRRohYhr9uBE3T/lrTtIOa\npsU0TbsjRb/PaZp2VNO0dk3TfsTaJ2ia9rqmacfjj+MHu6ZI1hAYjrqsWCyG3bt3o6qqCtOnT7/x\nQQkDXLlyHwDgf/7P+wdqsOhx4kSgshKoqjLkigsViReJlctl1GqVlppixcWLvqhPYSEwZoyLiRkJ\nTxGs0kVmVgCrCHlhihUXI96HZItLEAlQARIlh768MKNHPmWfz6ZN/XIhUdjoK5VwAVYpU2WMnw/K\nccm2VeHiYxsJVOkaTLw0ALfCnF2YPxw8eBC///3v8eKLL+Iv/uIvnB6OMEKo97LINskCcADAXwHY\nlqyDpmluAI8D+DyAOQD+VtO0OfHdPwLQout6LYCW+HZKJF04BG5UskKhEFpbW3HHHXc4ei/EXObt\nt+/D9763Cjt3minCYNCYUUiZXrfbkKFIxIxWUQE8/7JjzBj7PlTbVVxMtV68hssDU6bUE1NNFs1a\n88N8KwnDTD/x9J5dHRediy/7QNdyK8/BtmMwb/tD8EU4aeakWgdGBe4xpZ3Or65qD6W/BjON6LE5\nXle2+evnKU4i0+nEZKg/Ay6GxirmixYN+s9uTnH48GG8++67eO655/BXf/VXTg9HGGGyOV2o6/ph\nAINNMLsTQLuu6yfjfZ8H8CUAh+KP98T7PQPgLQA/THUykawhcCPpwt7eXuzbt09mEI4Q3/nO/Vi5\ncrGl7orWzaL1smgl+FDI2K8SiwFF8TvvpJKvoiLzeHU/rcYRibgGVqA3oEgUYMgU/W6RcOmwChav\nw6I2EimNPed1XKpc8cGpt5fh8sT/AVDlh0j1VsprrGic1JaszizZYqfqyvhcatR6MDUV6cTa0/ya\nASxaNNmBMTjH0aNHsWPHDvz617/GV77yFaeHI4wwncDWfwPKM3yZAk3TWtl2o67rjcN4/moAf2Db\nZwH8cfz5JF3Xz8efXwAwabCTiWQNgeuNPl26dAknTpyQexCOECtWGNGs737XEK1YzKi94qJEES6K\naHnZGpNjxhiPkYhR9G4nVmPHGueg8/l8xjZgpA/DYS5YxqPh6K6BWY1GO9VD0UW4cNlFn9QFTPmx\nYPvs5IqLFZ1TLYRPEsIbQJUzmo1Ij/wejYAhbBSRo2NUYaI+/Px6kr52AuVij3azNJP1JzLxv3f+\n3ez4+PHjeOedd/CrX/0KX//6150ejuAAuq5/zukxaJr2BoBKm10/0XV903BdR9d1XdO0QWesiWQN\ngeuJZJ06dQp9fX2y+N4Is2LFfVj12GP4r0d/jAf+3/8YECCVYNCQoaIic2YhF6uCAnN24dixhjyF\nw1bxojquoiJTvDgFBcYXn5hqSJ0R3TLajT/FSITfR1G9pyLdC5HLChctVa744qaAKTIutp3uPffU\n2Yj8rcMuYqQWtgOJqUe+5pcX1vNosL5uPvuSn0tdnT1ZFEtd14sz3KlGQ7DyKYrV3t6Ot99+G6tW\nrcI3vvENp4cj5DG6rn/mBk9xDsBUtj0l3gYAH2qaNlnX9fOapk1GGnd8F8kaAkOJZNEMwnHjxqG+\nvj6DoxKScd8//RNWPfYYtFgUPp813TV2rPEYChlfsZghUx6PVax4VCsUMtfQ8noN2eLpRC5yPIpF\n7RQ18/utwkV1YUZkzRVfld74XYtGeboNSB5p4ouRqlEfNf2oRraAwQu5+fdPTTGqfXj9FqUI+bh5\nxInvs4tw0fjB+nARUsUt2Vg4djfL5mMjrke48k+wTp06hbfeegsrV67Et7/9baeHIwg3yi4AtZqm\nzYAhV18F8LX4vs0A/jeAJfHHQSNjIllDIN1IFs0grKurw7hx4zI8KmEw7v/pT7H43/8d/v4e+F0u\noMAHuDzQPWaOMBQy5aq01GijiFayOqtoNDFyVVRkbnPpIj8n6aL0Iv1KkXRFo6Z0hcOAMdEFANyI\nRNTFQMNIni4ErDKlFqwD5grlfMV59VxqNI238TqwMBLrtvj5/DAL6tWbWfN0IW1HUmzzMamRNbXu\njL/Fqfu4ZA62Knw6wpV/gtXR0YGWlhY88sgj+Md//EenhyMIKdE07V4AjwGYCGCLpmn7dF3/PzRN\nqwLw37quf0HX9Yimad8FsBXGm9pTuq4fjJ9iCYAXNU37ewCnAfzNoNcc4iKYeb1i5vPPP4/f/e53\nKfsEg0G0trbizjvvhNc7lJvJCpli1WOPAQcOYHFjo2E3Hs/Ao+7xGrLjMSQkHHMPRLVIsOg5TwdS\nXRWJFq/JIpGi2/sAZsSM+rhc5nNq93hM2eIpSXqkfYZsAYYEkDjwfCiXCd7Ob/+j3g+RUBfb5XJm\nd36erksW4eLbdvVhtK2mL+0K9e1SnKkK+u1IFbFLR6aS9ZmZV4J15swZvPbaa1i+fDn++Z//2enh\nCFZkdlWWIJI1BDZs2IDf/va3Sff39PSgra0Nd9111wiOSkiHVfcZa2hZRKu/37Ad2i4oAFyuAdGi\ngna7m0zbSRS1kzCRRFEdF49scSGLxaxtPDpmipV5Lt5u7OMf+hFYl07gqTvej++LKO2ciE0fO7FS\njw3BGglKJVpqX3WbR7lcsIpjsn7qtdLtzxmacC1adE8a/XODP/zhD9i6dSt++ctf4kc/GnSpIGHk\nEcnKEkSyhsCWLVuwefNm230ffvghTp8+jT/+4z+WW+RkKavuuw84cgQAsHjzZqtc0XOKcvX2Gu0e\nD3SX2xLZonQeFyt6pLorwBAhkiuSMWqj4wl63t+f2Eb9VcHiy05Qm65THRdg/LlSJ1WwkskRj0ap\nkqGKlt3xIZhpQ3qBLuW5erwLRgRNs9nWbPqnalOvk2z8nGSyxc+R7FhKEQ46kztnOHfuHF599VU8\n8MAD+NnPfub0cAR7RLKyBJGsIfD666+jqakpof3EiRMIBoOYM2eOzVFCNrHqT/5k4LlFtHw+M7IV\nj2ihoMCodC8shO5yQ4vEP4w9HoQjmiWqRfBoFq/V4v3oUZUltQ8/PtkxvE29x2IgoEoSHcSFQU0P\nqsIRsXmuRrv48gvJ0pZ82y6lp4oWYC9Mqdr4udXXwc9rJ2epzs/hY84/wTp//jxeeeUV/PjHP8Yv\nfvELp4cjJEckK0sQyRoC27Ztw9q1awe2dV1HW1sbysvLUVVV5eDIhKFCsrX42WeNBhItLl30nEJU\n9BWPcIUjmm26EDBTiWotFk/zqXVXgwmW+sjPxwVLXWLCXJOLQwNJFp2ya7Or9dKQWszUfep6WKrw\nJItoQWkD7IWM97NrH2wfMdh6YfUAruWVYF24cAFbtmzBv/zLv2DJkiVOD0dIjUhWliCSNQTee+89\nPP300wCMlExrayvmzJmDkpISh0cmXA+rJhkfkIu3b7emDnlki7fx52QtXq/x5fMhGtMs9Vh8lqGa\nGqRtLkeUSlSL4lM90nOeoqQ/abWeCwBbl4vgMnHN5ruULK2oRsBUAXMpfd3KfsD8HODnSpY65P1h\n0+ZS2u3620WnSOzsjgESJdFcjmXRorE258tNLl68iJdeegnf+9738NBDDzk9HGFwRLKyBJGsIbB3\n7148+eSTCAQCaG1txYIFC+DxeAY/UMhaSLQAYPHOnaa9+P3Gl89npg7Jnnj9Fn3xmaR+/0Cki9dj\ncbmitblUaaIied6WrmDxKBpPJ3KxUm8f1NfHt+wiO+Ek+9VID4mKujwEFyn+3GWzH0iUJVWUkkW1\n7M7F+6njtPsMShXZcgGoHdjKJ8G6dOkSNm/ejO985zv4z//8T6eHI6SHSFaWIJI1BA4dOoSf//zn\nOHDggMwgzDFWTZoEdHRg8YEDRh2W32+NYFHFOy3vzovlaXogTzXSOWIxwOdDOGK856mzCe1ShMnq\nr+wiYuoxvHCe4CLFi+dV4VJrugAgGuXioUZ1uCzxg91IlJ8A24ck+zW2zfu4lH68j10/tT1Zf7t9\n6n465+0AgEWLkFd89NFH2LRpE7797W/jiSeecHo4QvqIZGUJIllD4LHHHsOTTz4p9yDMUVZdM9Nl\niw8dMoSJZupRVItHsWjZd0oZ8tmJFL7y+cz9tA0MSBeJE6/fonb+aBeJInnibapk9fYm3w4qrsFe\nfsIaXYAqXEBi9IqLltqXBImnDemC1NaP5BEusH3XYBUq6qsKWLJ2dfwcNep1+8BWvgnWxx9/jI0b\nN+Ib3/gGVq9e7fRwhKEhkpUlSK5rCHR0dODw4cPo6OhAVVUVGhoaUFZW5vSwhGHivsJCAHHZ+vhj\no5GkKhq1ruFAle0FBWZ+jmTq6tWBlOFAOy353t8PeL3wxve7XNrACvK8SJ6681vyANbaKyoF5FEs\nug0QYAhVqm2e6Q4GrRlPes7FKxp1I/lNlwHr24kHietZRdhzABgDa/quBIlCVAxDqjSlTe3nirf3\nK20AUART6LhEFcYfVWkDgLvjj5fzTq4AoLu7G5s2bcLXvvY1ESxBuAEkkjVEgsEg1qxZg//6r//C\nwYMH4fV6UVVVhXnz5qGiosLp4QnDxKrDhweeL+7sNCNUJFeUEiwsNLbJWHiki1KG3Ga8XrON2unc\nAKJxibErjuepQpIfimJZa6vsFz9NXOLB2scuXaiet7fX+nICAXWNLBU1EkWhNpI1O/nh0kPCpEa5\nXAB6bfoB1oiaKlz9Sru6TwNgRKoXLbps83pynytXrmD9+vX48pe/jOeee87p4QjXh0SysgSRrBsg\nEolg7dq1WLlyJfbt2we3243Jkydj7ty5qKyshKbJ7/loh2Rr8bFjRoPdUg9utzGljxfCFxWZ9VoU\nluLSpQoWnY/w+RCF2yI+djMSqS1VWtBuGwB6eqzbdvVcV6/an4eGqp43krBWhF1dFBcmF4A+JMqS\nXeqPz37k7XbHq9dRrw+bfZ8F8BGA/BWsnp4eNDc340tf+hLWrVvn9HCE60c+fLIEkaxhIhqNorm5\nGY8++ihaW1uhaRoqKytRX1+P6upqEa5Rzip2z8rFPT2W6NNAJEu5LyKAxFmIvF7LTrDonPxRqePi\nMmS3yCmQKD+qUNm12YmYKl5XrpjP/X7rNmBNLxLRqDqjz672yq5uil/cBVOoNKUN8XYgeeTKbh+d\n67MDPRYtak98AXnC1atX0dzcjC984QvYsGGD08MRbgz5wMkSRLIyQCwWw8svv4xHHnkEO3fuRCwW\nQ2VlJebMmYNp06aJcI1iLLJ14UKiWKmC5XIlpg15obydYHEZozYqkorXjdmlFSmIlI5Q9ffbF9Gr\nJIuI0ZBVyVL7ezxAby+lFO1SerztGqwRKiAxSkWiRfB9yUSr16YvANwL4EMA+S1XANDX14d169bh\nM5/5DLZs2eL0cIQbRz5ksgSRrAyj6zpef/11PPTQQ9i2bRsikQgqKiowe/Zs1NTUiHCNUlax//QX\nBwLWyBbJld16WmqEq6jI3Aasi6Kq7dSXtgFEPf6BJp5O5Fm7yzaZL4o4UT+7KBaQPNrFM5vd3eZz\nj8fcVvvQr7rHAwQCdouJUo1VOpLUC2sxPO27ikSZUqNd9w6Ma9GiHch3+vr60NTUhE9/+tPYunWr\nvCflBvJDzBJEskYQXdexfft2LFu2DG+++SaCwSAmTpyImTNnora2Fi6Xa/CTCFmFRbYuX06MUNml\nFfnq8YB1SQg+E5GiV16vrWANtNE2gCBM6SKBopQfFy+11oqLEkftZ1e3pUrVRx9Zt/l5+Od3by/d\nW9H4vXe7gWiUUnjqZ4RdRKuXbQPWGitVzP5X/PE8AJEror+/H01NTfjkJz+JlpYWEazcQX6QWYJI\nloPs2rULS5cuxdatW9Hf34/y8nLU1dVh5syZcLvdg59AyBpWbdhgCQctDoeNFKHLZXx5vYZF8LQi\nYF+zRe08lRhPE1rW27JZf2tgAdU4usebIEZ2QmWXYrRrtzt2sKJ6Gg4/lj7LqY1+3TVNjXLxyBYZ\nH29TRYuOAYAemHIFLFqUeHP3fCYQCODFF1/EHXfcgW3btolg5Rbyw8wSRLKyhP3792PJkiV45ZVX\ncPXqVZSVleGWW27BrFmz4OULGAlZz6rf/MZ4Ep8GuDhZBIvW2VIL5wHDOigqpqYUPR77Ba/GKrd6\nYSlG3WVKO0lRqkJ5wk6qurutUSpaUkxt49sulxHh4v87aJqZyqTPd9p/5UoUPEJlRLmSpQJ7BvoZ\n2/8U3z4NQOTKjkAggHXr1qGhoQE7d+4Uwco95AeaJYhkZSHHjh3DkiVLsGnTJnR3d2P8+PG4+eab\nceutt4pwjTJWKQs5LiaLoCgX1W+RNHk8hnGQYPnj6T/6uaeakcjFi/qPG5cwpnBB4g3N7SJZyVKI\naru6TcPq6koUra4uc3IlPXL50jTzOaUdAbMtGFTX1eKRKx61kpsYJyMYDGLdunWYM2cOfv/730uZ\nQm4ikpUliGRlOR0dHVi6dCmam5vR1dWF0tJSzJgxA/X19SigiIgwKkgQLsBc0BQwhYtEyu837UJd\ng4va6ByqTNG+0tLEdjXiBaAv4k9oAxKL2gEzcpWsH31mc8miNjpWFa1Ll8yXQkGVrq7ENrcbuHIl\nBOBnCWNYtOh7tq9BMAmFQli3bh1qa2uxe/duEazcRSQrSxDJGkV0dnZi+fLleOGFF3DhwgWMGzcO\n06ZNw7x581BIH9TCqMAiXHETWazrhkWQaBUVmTVdasSLrzLP04c8dESCxdsAYMKExAGVllpSioSd\nZJH88HZq45/ZqlCRKFGEil4aPydvc7mAixfN48aPv3/g3KdOBUSqhkg4HMa6deswffp0fPDBByJY\nuY1IVpYgkjVK6erqwoMPPoi1a9fi3LlzKCkpwU033YSGhgYUFxc7PTxhiKx6+mlrQ1yaFtPdo+0k\ny+02vugmhm63NXQ0ZoxVsNQolp2QKdilFlV54m2AdQYhF6pUkgVYRWvWLFOo9u0z+3z2s/fZjlNI\nTTgcRlNTE6ZMmYL9+/fDo4q3kGuIZGUJIlk5QHd3Nx599FH8+te/RkdHB4qLizF16lTMnz8fJSWJ\nH5JC9rPK7pYmcRFa3NNjFi+5XKYgqWEg3k7wKBZZT6qbnNtEva6G/LALgtjVW128mBjJAqyidc89\nhlBxmQKAiRNFqIaDSCSCpqYmTJo0aeB+q0LOI5KVJYhk5Ri9vb1YuXIlnnrqKZw4cQKFhYWYMmUK\nGhoaUJokWiGMHla9/npiY2UlAGDx2bOmaNkJlqYZ7XyKn8tlnz4kyssTmvTS8bZduWTRqS9eNJ5/\n9av3W/qqQnXunAhVJohEImhubkZZWRkOHz4MH1tTTchpRLKyBJGsHObatWtYtWoVVq9ejSNHjqCg\noABVVVVoaGhAWarohTDqWNXWZm2YMsW+4/TpAIDFO3eabapIJYt8ERUVQCyG+3/wA0vzmV57WSOh\n2rJFRGokofupjhs3DseOHRPByi9EsrIEkaw8IRgMYs2aNXjiiSdw4MABeL1eVFVVYd68eaioqHB6\neMIIskqdiXjLLck7z5qV2FZfb9m878c/HoZRCcNJNBrF+vXrMWbMGBw/fhx+v/3sUSFnEcnKEkSy\n8pBIJIK1a9di5cqV2LdvH9xuNyZPnoy5c+eisrJSFiYUhFFMNBrFxo0b4ff70d7eLjOP8xN5E88S\nRLLynFgshqamJqxYsQK7du2CpmmorKxEfX09qqurRbgEYRQRi8WwceNGuN1unDhxQmYa5y/yxp0l\niGQJA+i6jpdffhkPP/wwdu7ciVgshsrKSsyZMwfTpk0T4RKELEbXdWzcuBEAcOLECZlZnN/Im3WW\nIJIl2KLrOt544w08+OCD2LZtGyKRCCoqKjB79mzU1NSIcAlCFqHrOjZv3oxIJIKTJ09irM2q/kJe\nIW/QWYJIljAouq5j+/btWLZsGd58800Eg0FMnDgRM2fORG1trawcLQgOQhHoQCCAEydOYPx4+yU2\nhLxCJCtLEMkShsyuXbuwdOlSvPbaa+jr60N5eTnq6upQV1cnK0kLwgii6zq2bNmC/v5+tLe3y9Is\nAiGSlSWIZAk3RFtbG5YuXYqXX34ZV69exYQJE1BbW4tZs2bJytKCkEF0Xcerr76Knp4etLe3Y+LE\niU4PScgeRLKyBJEsYdg4duwYlixZgk2bNuHy5cuYMGECampqUF9fL8IlCMOIruv47W9/i+7ubhw7\ndgyV8VX/BSGOSFaWIJIlZISOjg4sW7YMTU1N6OrqQmlpKWbMmIH6+noUFBQ4PTxBGLXouo7XXnsN\nXV1dOHr0KKqrq50ekpB9iGRlCSJZQsbp7OzE8uXL8cILL+DChQsYN24cpk2bhnnz5slCiYIwRF5/\n/XV8+OGHOHLkCKZOner0cITsRCQrSxDJEkaUrq4uPPTQQ1i7di3Onj2LkpIS3HTTTWhoaJCFEwVh\nEFpaWtDZ2YlDhw5hevw+lIJgg0hWliCSJThGd3c3VqxYgWeeeQYdHR0oLi7G1KlTMX/+fFlIURAU\n3nzzTZw9exYHDx5ETU2N08MRshuRrCxBJEvICnp7e7Fy5Uo8/fTTA/dbmzJlChoaGlBaWur08ATB\nUd566y2cPn0a+/fvR11dndPDEbIfkawsQSRLyDquXbuGxsZGNDY24siRIygoKEBVVRUaGhpkHSAh\n79i2bRtOnjyJffv2Yfbs2U4PRxgdiGRlCSJZQlYTDAaxZs0aPPnkk2hra4PX60VVVRXmzZuHiooK\np4cnCBll+/btOH78OHbv3o25c+c6PRxh9CCSlSWIZAmjhkgkgrVr1+Lxxx/H3r174Xa7MXnyZMyd\nOxeVlZVyP0Uhp9i5cyeOHj2K999/H/Pnz3d6OMLoQt4MswSRLGFUEovF0NTUhBUrVmDXrl3QNA2V\nlZWor69HdXW1CJcwqnn33Xdx+PBhvPvuu7jjjjucHo4w+pA3wCxBJEsY9dANch955BHs2LEDsVgM\nlZWVmDNnDqZNmybCJYwqfv/73+PgwYN45513sGDBAqeHI4xO5E0vSxDJEnIKXdfR0tKC5cuXY9u2\nbYhEIqioqMDs2bNRU1MjwiVkNbt27UJbWxveeust3HXXXcYrnfgAAAvHSURBVE4PRxi9yBtdliCS\nJeQsuq5jx44dWLZsGVpaWhAMBjFx4kTMnDkTtbW1cLlcTg9REAbYvXs39u3bhzfeeAP33HOP08MR\nRjciWVmCSJaQN+zatQtLly7Fa6+9hr6+PpSXl6Ourg51dXXweDxOD0/IY/bu3Ys9e/bgt7/9LT7z\nmc84PRxh9COSlSWIZAl5SVtbG5YuXYotW7agp6cHEyZMQG1tLWbNmgWv1+v08IQ84oMPPkBrayte\nfvllfO5zn3N6OEJuIJKVJYhkCXnPsWPHsGTJEmzatAmXL1/GhAkTUFNTg/r6ehEuIaPs378fu3bt\nwsaNG/Hnf/7nTg9HyB1EsrIEkSxBYHR0dGDZsmVobm7GpUuXUFpaihkzZqC+vh4FBQVOD0/IIQ4e\nPIh3330Xzc3N+Mu//EunhyPkFiJZWYJIliAkobOzEw8++CCef/55XLhwAePGjcO0adMwb948FBYW\nOj08YRRz6NAh7Ny5E88//zz++q//2unhCLmHSFaWIJIlCGnQ1dWFhx56CGvXrsXZs2dRUlKCm266\nCQ0NDSguLnZ6eMIo4siRI9i+fTt+85vf4Gtf+5rTwxFyE5GsLEEkSxCGSHd3N1asWIFnnnkGHR0d\nKC4uxtSpUzF//nyUlJQ4PTwhizl27Bi2bduGp59+Gn/3d3/n9HCE3EUkK0sQyRKEG6C3txcrV67E\n008/jfb2dhQWFmLKlCloaGhAaWmp08MTsoj29na89dZbWL16Nb71rW85PRwhtxHJyhJEsgRhmLh2\n7RoaGxuxevVqHD58GH6/H9XV1WhoaEBZWZnTwxMc5OTJk3jzzTfx+OOP4x/+4R+cHo6Q+4hkZQki\nWYKQAUKhENasWYMnnngCbW1t8Hq9mDx5MhoaGlBRUeH08IQR5NSpU2hpacGKFSvw3e9+1+nhCPmB\nSFaWIJIlCBkmEongueeew8qVK7F371643W5MnjwZc+fORWVlpdxPMYc5c+YMXnvtNTz44IP4/ve/\n7/RwhPxB3lSyBJEsQRhBYrEYmpub8eijj2LXrl3QNA2TJk1CfX09pkyZIsKVQ5Bg/cd//Ad+8IMf\nOD0cIb+QN5IsQSRLEBxC13W8/PLLeOSRR7Bjxw7EYjFUVlZizpw5mDZtmgjXKObcuXN49dVX8fOf\n/xw/+clPnB6OkH/Im0eWIJIlCFmArutoaWnBgw8+iLfffhuRSAQVFRWYPXs2ampqRLhGEefPn8cr\nr7yCn/70p3jggQecHo6Qn8gbRpYgkiUIWciOHTuwdOlStLS0IBgMYuLEiZg5cyZqa2vhcrmcHp6Q\nhAsXLmDLli344Q9/iF/+8pdOD0fIX0SysgSRLEHIcnbv3o0lS5Zg69at6OvrQ3l5Oerq6lBXVweP\nx+P08IQ4Fy9exEsvvYTvf//7WL58udPDEfIbkawsQSRLEEYRbW1tWLp0KbZs2YKenh5MmDABtbW1\nmDVrFrxer9PDy1suXbqEzZs347vf/S4effRRp4cjCCJZWYJIliCMUo4fP44lS5Zg48aNuHz5MiZM\nmICamhrU19eLcI0gXV1d2Lx5MxYtWoTHH3/c6eEIAiCSlTWIZAlCDnD69GksW7YMTU1NuHTpEkpL\nSzFjxgzU19ejoKDA6eHlLB9//DE2btyIb37zm2hsbHR6OIJAiGRlCSJZgpBjnD9/HsuXL8cLL7yA\n8+fPY+zYsZg+fTrmzZuHwsJCp4eXM1y+fBkbNmzA17/+daxZs8bp4QgCRyQrSxDJEoQcpqurCw8/\n/DCeffZZnD17FiUlJbjpppvQ0NCA4uJip4c3aunu7sb69evxla98Bc8++6zTwxEEFZGsLEEkSxDy\nhCtXruDRRx/Fr3/9a5w6dQrFxcWYOnUq5s+fj5KSEqeHN2ro6elBc3Mz7r33XrzwwgtOD0cQ7BDJ\nyhJEsgQhD+nr68Pjjz+OX/3qV2hvb0dhYSGqq6sxf/58lJaWOj28rOXq1atobm7GF7/4Raxfv97p\n4QhCMkSysgSRLEHIcwKBAFatWoXVq1fj8OHD8Pv9qK6uRkNDA8rKypweXtbQ29uLpqYm/Nmf/Rle\neuklp4cjCKkQycoSRLIEQRggFAphzZo1eOKJJ9DW1gav14vJkyejoaEBFRUVTg/PMfr6+tDU1IR7\n7rkHr776qtzmSMh25Bc0SxDJEgTBlkgkgueeew4rV67E3r174Xa7UVlZiXnz5qGysjJvRKO/vx/r\n1q3DXXfdhTfeeCNvXrcwqpFf0ixBJEsQhEGJxWJobm7GihUr8P777wMAKisrUV9fjylTpuSseAQC\nAbz44ou488478dZbb+Xs6xRyDvlFzRJEsgRBGBK6rmPLli14+OGHsXPnTkSjUUyaNAm33norpk2b\nljMiEggEsG7dOsyfPx87duzImdcl5AXyy5oliGQJgnDd6LqOlpYWPPjgg3j77bcRDocxadIkzJo1\nCzU1NXC5XE4P8boIBoNYt24d6uvr8d5774lgCaMN+YXNEkSyBEEYNnbs2IGlS5eipaUFwWAQ5eXl\nmDVrFmpra0eNcJFgzZo1C7t27Ro14xYEhkhWliCSJQhCRti9ezeWLFmCrVu3oq+vD+Xl5airq0Nd\nXR08Ho/Tw7MlFAph3bp1uPnmm7F3714RLGG0IpKVJYhkCYKQcQ4cOIAlS5Zgy5Yt6OnpwYQJE1Bb\nW4tZs2bB6/U6PTwAQDgcRlNTE6ZOnYr9+/fD7XY7PSRBuF5EsrIEkSxBEEaU48ePY8mSJdi0aRM+\n/vhjTJgwATU1Naivr3dMuCKRCJqamlBZWYkDBw5kjfgJwnUikpUliGQJguAYp0+fxrJly9DU1IRL\nly6htLQUM2bMQH19PQoKCkZkDJFIBM3NzSgvL8fhw4dFsIRcQCQrSxDJEgQhKzh//jyWL1+OF154\nAefPn8fYsWMxffp0zJs3D4WFhRm5ZjQaRXNzM8aPH48jR47A5/Nl5DqCMMKIZGUJIlmCIGQdXV1d\nePjhh/Hss8/i7NmzKCkpwU033YSGhgYUFxcPyzWi0SjWr1+PkpISHDt2DH6/f1jOKwhZgEhWliCS\nJQhCVnPlyhWsWLECzzzzDE6dOoXi4mJMnToV8+fPR0lJyXWdMxqNYsOGDSgsLER7e/uIpSYFYYQQ\nycoSRLIEQRg19PX14fHHH8evfvUrtLe3o7CwENXV1Zg/fz5KS0vTOkcsFsOGDRvg8/nQ3t6OoqKi\nDI9aEEYckawsQSRLEIRRSSAQwOrVq7Fq1SocPnwYfr8f1dXVaGhoQFlZme0xuq5j48aN0DQNJ0+e\nHLbUoyBkGSJZWYJIliAIo55QKIQ1a9bgySefxP79++H1ejF58mQ0NDSgoqICgCFYmzZtQiwWw8mT\nJ6871SgIowCRrCxBJEsQhJwiEong+eefx2OPPYY9e/bA7XajsrISfX19iMViOHHiRNqpRUEYpYhk\nZQkiWYIg5CyxWAzNzc146KGHcPToUZw8eRLjx493eliCkGlEsrIEkSxBEARByC1EsrIEufupIAiC\nIAhCBhDJEgRBEARByAAiWYIgCIIgCBlAJEsQBEEQBCEDiGQJgiAIgiBkAJEsQRAEQRCEDCCSJQiC\nIAiCkAFEsgRBEARBEDKASJYgCIIgCEIGEMkSBEEQBEHIACJZgiAIgiAIGUAkSxAEQRAEIQOIZAmC\nIAiCIGQAkSxBEARBEIQMIJIlCIIgCIKQAUSyBEEQBEEQMoBIliAIgiAIQgYQyRIEQRAEQcgAIlmC\nIAiCIAgZQCRLEARBEAQhA4hkCYIgCIIgZACRLEEQBEEQhAwgkiUIgiAIgpABRLIEQRAEQRAygEiW\nIAiCIAhCBhDJEgRBEARByAAiWYIgCIIgCBlAJEsQBEEQBCEDeIbYX8vIKARBEARBEHIMiWQJgiAI\ngiBkAJEsQRAEQRCEDCCSJQiCIAiCkAFEsgRBEARBEDKASJYgCIIgCEIGEMkSBEEQBEHIACJZgiAI\ngiAIGUAkSxAEQRAEIQOIZAmCIAiCIGQAkSxBEARBEIQM8P8DfOKyIn5LLA4AAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_wigner_function(density_matrix, res=200)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If it is desired to calculate the analytic expression for the Wigner function, we can import the sympy package and run the Wigner function calculations symbolically. The below code is almost identical to the code in the Wigner function tomography module but edited to work with symbolics rather than run through the points in the mesh of the sphere." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.5 \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) + 0.5 \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) + 0.375 e^{2.0 i \\phi_{0}} e^{2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{0} \\right )} \\sin{\\left (2 \\theta_{1} \\right )} + 0.375 e^{- 2.0 i \\phi_{0}} e^{- 2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{0} \\right )} \\sin{\\left (2 \\theta_{1} \\right )}\n" + ] + } + ], + "source": [ + "import sympy as sym\n", + "from sympy.physics.quantum import TensorProduct\n", + "\n", + "num = int(np.log2(len(density_matrix)))\n", + "harr = sym.sqrt(3)\n", + "Delta_su2 = sym.zeros(2) \n", + "Delta = sym.ones(1)\n", + "for qubit in range(num):\n", + " phi = sym.Indexed('phi', qubit)\n", + " theta = sym.Indexed('theta', qubit)\n", + " costheta = harr*sym.cos(2*theta)\n", + " sintheta = harr*sym.sin(2*theta)\n", + " Delta_su2[0,0] = (1+costheta)/2\n", + " Delta_su2[0,1] = -(sym.exp(2j*phi)*sintheta)/2\n", + " Delta_su2[1,0] = -(sym.exp(-2j*phi)*sintheta)/2\n", + " Delta_su2[1,1] = (1-costheta)/2\n", + " Delta = TensorProduct(Delta,Delta_su2)\n", + "W = sym.trace(density_matrix*Delta)\n", + "print(sym.latex(W))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "pasting this result into a latex environment returns the Wigner function" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$W = 0.5 \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) + 0.5 \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) + 0.375 e^{2.0 i \\phi_{0}} e^{2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{0} \\right )} \\sin{\\left (2 \\theta_{1} \\right )} + 0.375 e^{- 2.0 i \\phi_{0}} e^{- 2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{0} \\right )} \\sin{\\left (2 \\theta_{1} \\right )}$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Wigner function using State tomography\n", + "\n", + "We can create the density matrix for a given state by using the state tomography module, more information for the tomography module can be found in the [quantum state tomography tutorial](https://github.com/QISKit/qiskit-tutorial/blob/master/3_qcvv/state_tomography.ipynb). First creating an entangled Bell-state with the following set of gates and then taking the state tomography, we can create the spin Wigner function for the measured tomography" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Q_program = QuantumProgram()\n", + "#Q_program.set_api(Qconfig.APItoken, Qconfig.config['url'])\n", + "\n", + "number_of_qubits = 2\n", + "backend = 'local_qasm_simulator'\n", + "shots = 1024\n", + "bell_qubits = [0, 1]\n", + "qr = Q_program.create_quantum_register('qr',2)\n", + "cr = Q_program.create_classical_register('cr',2)\n", + "bell = Q_program.create_circuit('bell', [qr], [cr])\n", + "bell.h(qr[0])\n", + "bell.cx(qr[0],qr[1])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The above code generates the circuits needed to create the Bell-state and below we show how to then build the density matrix for the state using the tomography module. The density matrix created can then be put into the Wigner fucntion visualisation module " + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + ">> created state tomography circuits for \"bell\"\n" + ] + }, + { + "data": { + "image/png": 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4qKZ9XCzt52R1Wst8ZCAPjQFmdCA5XvSjS9sCRjSn2H6rEIvpMGEiYQRRIqFv\n8bgRViS41q8PCiwSS0NDbnE1NGTauNO1dm3w2Y6NGVeMMKLLFTbkDha5Wv3sMb0G9gTTq2BcLe7s\npcCn6BGhVX/m5+cLnz9hoaQBvKzO5/i3oVJrlVL/x/O8DSU2+TVoAaYAfMfzvAHP89YB2ADgWaXU\n8wDged5j/rYispqNr33ta7jvvvtw0UUX4bbbbpPaVz7J5Bz0v/PtIVvYVblhPebr8+AX9scfP4J9\n+5pHaLVT4rsOE3LHiqa8odefu1G2sAJMIjit52JCJ67HYjEkEsD0dFBA0TKJK8AIKFo3PW2Otn69\nvifhReJq7dqguBodNe0cfg67bXAwAhorlM0CU1MksihsSOKKnjP89nPQIopGIfISFil2T1CuGwkv\nCR8uBel0WlI5akLd89qGPM97gj1OKqWSVex/AYBj7PGI3+Zqv37BvfQRkVVDMpkM3va2t+ETn/gE\ndu/ejfX0i7/M0cUqgeqmMKFtciW34i7GM88cwYYNQHd348VWu4gsI7B4JXdaJuFF71U3a+NhQhJd\nFCYcAomyWCyGTIYqvhvRQ3P0Ug4WYAQUF1yAEV1A0M2i49luFm/ngoufHzDtQ9b/Zmrv64sX+pjN\nApnMFIKOVgamzhaVdKA2IFiUlV4bml7IDrnkRGjVmXQ6ja6urkZ3o8XxUPmMCQtmTCl1bb1PUitE\nZNWI559/HsPDw5iensbdd9+N7u7u8ju1OWZIumuyXv6YxBddiIgI3F9Yc8HPZvWFMpXSF8PpaWBo\n6AhmZhortNohXGgS3QFTioDny/Ekd553RcKBQ4ntpmZWLKbf68HBmFNUcRcL0O8xsWGDvidxxd0s\nEl22m0ViicKItptFYizM5eLt1M9s1rTHYn3IZgGlyNU6i+KQIa+zReHySX+ZBGoKZgQnH82ZltGH\ndSSdTsvv9qJZEpG1WI4D4NW/1/ttsZD2RSEiqwb8/d//PV7/+tdjy5Yt2LlzZ1tcYBdLMvktf4ny\nDstZyLYAs+H70wUpg2hU51BEo/qCl0joi/HGjUfw3HONE1rt4WRRKQbuZAHFAxJoWyBYE4oLL4Pn\nDRRE1cBA0GEaGDAuFs/LArRI4snv9jqeEO9yp0q5VqXys2zRRQLLdrrI0TpzBtCvxyqYsg0URkzA\nJLp3+uv7YdwsKszKk68pvEphcnG16kEmkxGRVROaXmR9AcAb/Jyr6wG8qJQ66XneGQCbPc+7BFpc\n3Qvg/sXk57QCAAAgAElEQVSeTETWIpiensbDDz+Mr3zlKzh48CCG7LjCMsSIK0ALrLAvXJjoyrF1\nrtFdQVKp4CgxcrRSKeD664/gu99tjNBqdaFtXCzKDeIjAW2HkY/6BIqdLFOOo6+v+H2nMODAQNGq\nQIgQcIcPXW4WDxPyECLtw0s58H04YY7WyIhpJ2HF2887L+K3R5BKxVgYkZdyOOc/pnYaXUjh8X4Y\ncUXJ2PSaS55WPUin01i1alX5DYUSNN7J8jzvHwDsh87dGgHwLvhfIqXUxwF8EXpk4bPQJRx+y1+X\n9TzvDQC+DP0k/kYp9ZPF9kdE1gL5wQ9+gOHhYfT19eGuu+6SUSmgC7M9YjYH95cuH9LewdbRxZzf\n+PHMa86FVjarL6zZLHDo0BF87nNLL7Ra2cnS5RrIhaIkd1fZBapqDhinix5TVXbax8T6uItF93wk\nIV9njzK0710iiUKFo6NGgHFxZbtZYaUcXPlZvJ0E1tiYvuftqRQ/P4URSVwBRpSSsDrF2il3ixzb\nGQQn0aaphVIitGpINptFgj5cwiJobEFXpdR9ZdYrAI+ErPsitAirGSKyqiSfz+NDH/oQHn30Uezc\nuRMbN25sdJeagvApQcKEVKXkrHu60Ohj8IRnPnqMHC7ubgiVQu4VEBRXvF4Zx55eh8QDCu3d3X0B\n4UTvC7VRjpVLVPF1QDA3yx5paIsk+nzY4UC7MCk/Hhdd5UKFtA8XXPz8XHBpBmEEVBq6/IOrnXK3\nMtDvxQxM/TGOCK1aISKrFjTeyWo2RGRVwenTp3H//ffjF7/4Be68806pfeVjRg8uhA7rnqDK2Bxb\ncOVAye8UJgSMwKIClq997RF88pNL62a1arjQuFgxBCdytt8fElY8J4u/XzrR3fN0UjsJIxJVPAw4\nMBAs3WCLKg7VzHKJKn5ce5QhEKydFZabZR+zXKgQ0PcjI/q4JLh4u9k+hlQKfgiRcrIGwCeLLp68\nOgP9XqT9NhrdOQPznojQqgX5fF5E1qLxEMzfFERkVchXv/pV3H///bj44otx2223yRxXWIy40uLI\nLPPXspTzFS9q407F9HQwr4cnw7/rXUfw6KNLJ7RaVWSZsgKuRHcSVS4nC9DvibnQe56Z/NzOrbIh\nsWXD3S+65wnv9nFdowwBEz4kwupm0TpO2DoSULydBL9dbyuVMqJL92kAmUweRlyRsuM5bx0w4cVB\naGFFIw0Jer1FaC2WbDYrf5wXjThZNiKyypBOp/HWt74Vf/u3f4vdu3fjggsuaHSXmgJdWDSCSpLT\nK8PO3XKN8knBTEAMAB0FB0SXbjDuFb+Akvj62MeO4Hd+Z2mEViuKrKCLRWLL5WIBZj5JwNR24uvK\nCydXTpYtquzRh9QWlpflqpnlyssCiutmEaVEFy/ZYOdmUXs8HnS0UikjyNavh+9mAdPTEUxNkZgd\nAiW0a+HFxVXKb6OSDvRad0ALL0KE1mLI5/MismqCGBAcEVkleO655zA8PIzZ2VncddddMrzXJ5mk\nH/zShUI1rsR3O0TouojPgSe2F0NJwRq6cA4MmIsqEJzzbilpRZHldrGo3R49SFDbIEh0eV7MT/LW\nkHAiV4fnZFEbhQhLiSo6DokqO7xYKkRI6+1cKqC6kYa0zs7NikZ1O4VFeaiQn4vnZ+n+R5BKxZHJ\n0ETRVB2ei6tu6MR4Pp3RNILvA33PZkRoLRBxsmqBOFk2IjlD+Lu/+zvs2LED/f39OHDggAgsn2Qy\nbLRgGGHbcgeMxFoEJpTYidIizrwftmtF+ViAvrDScgR5HHnTm6ro+8JpNZGlXawOBEcTUniQv4cJ\nmLpZFNIaLKylEOF558UKiedc5PJEdxJPtghev16vo21sNmzQooVunKEhLXboZlPJOlclFjqXvR8/\nnr3f+vVmHxKC9BqsXavvaZ9YLAL9utOoTPv3ph9meiISw/Re9cO8L1r0hg9EEcLI5/MYcH3ghCqx\nR4TX+tZaiJNlMTU1hcOHD+PrX/+61L6y0ALLVc27FC5RRkKKjgdrmwyCw9VdzAGIBwTWxEQwido1\n8jBgc9WRVhNZ5sJtX9y5g8XLativo64vRKEyPgIQKJ3MbocPbex9ea0sIFjJ3Xaywupl0TqgtJPl\nGk0YVvEd0MKK8rKA4rwtcvAohBiPmxDi9HQE09M9MNU/qIZWCvr1PocgKej37ByK3w9xtKoll8th\ncHCw/IZCCcTJshGRxXjiiSdw6NAh9Pf3484775TaV0XE4c7BqiRsyHF9CdMwgooMVhJadqI8QGKA\n51/xizUXWIULvj8Hz5EHHsBDn/lMlX2ujlYSWdrFisO8xjzR3a7kTlCSO1UrD0IOFh9ZSJAoChNV\n5USXnbfFRZddFd4VPuSia7GjDOmYvB+uhHjKwwKM0DLiSvfDJO/3QClKcI/A1Bjj+YgcchYn/e2p\n9pbkaFWDiKxaICLLRkQWtE38wQ9+EO95z3uwc+dOXHrppY3uUtORTNIkv+UgEVTqi8a34eFBvp++\nSJh2Co/QOu1kkXsFmAR3urdHHOajnYhQpdI600oiS7/mvB5Wqe16USy0dehwcNBkH3ADmIqDhpnC\nPMndNc2Ovc3YmLswKRBe0sHlVgFBp8slyDhhBUmB0sKKjkuvAX38eEI85XNFoyQOYwjWs81Af+Yt\nxVr4fsz5txx0WQh6L0RoVUo+n8fKlSsb3Y02QLKQOCKyALzvfe/DkSNHcOedd6Kvr6/R3Wk6kkma\n0BaojWsFmC8iF1VhFd1twYXC8sCAudDZ1cLtkg6RbLpgbR05eBAPfe1rVT6XyolEIlBKNb3YSibH\nYBwqElqU90N5PvZ7PoCw+lg8dMeXOVwYDQ1pUcUFDZ+/0JUIz90qe3QhhRYjWf2HIG0l8a8e8P8o\n+B+aWZgyE2GFSAlXwrtrnUtYkYtFzhU/J01sToKL9pmejmFujvJQ7Kq6NPLzNMz3hBcuJSGsp/ER\noVWefD4v0+osGnGybERkAdi3bx+OHj0qta8cJJNkn1crrkphjyokYUWvP3e2yOmKsXXdhXUTE7HC\nBZdcrYmJ4Gg0cgcA6KtZIElruUMXcUqidsGTrnNWu07a5oLKDg9yQUThQy5+7ZIMdpV+vt7F0BDQ\n6buseUtUdab8BHC7GqpPT3YSyALIZpFOBF2MSuplcSeL6rJRn1x5WYAWgtPTRozRduvXm3bzGkQw\nN0fvyxw7Cr3IVKA0BfPe8JG3eegwYhrJ5DkcPizhsDCUUvInuyaIyOLIlQZAf3+/CCwHyeRqfylT\ncruFwf9p8wmH6T4Nd25WCtpF0RcU18g1W3TRcv9AylSztLOna0yrOFlmEmiim7W7vhN0kSbhW/zZ\n4FXXSUDY4cNSoimsvhZQOh8LACLTvqgilWKfiCwm2pGdqHN6PLBpfqBYdPGEd7s+Fz9sWPkG7nLR\nOtL9rm7r6X/shHiC3F36A0Lh/BhIWBnhPInqBqwsP/L5PHp6espvKJRAnCwbEVkAurq6Gt2FpiOZ\nXOcvVeNg5axlHv7jE0LbowupnSpgU9KvnYcFmNIOMXievoBQMUhaJnFlV39HIqGvfv6V7MjGjXjo\nueeqeH7thTtUCASnzOFFR+l9MmGnvj59UQobVcgFlwsuqOzQoS2o+hN5TE4HhV9ndlYvkDqxT0SK\nJsTJCoguKwkrMlFadPGCo7ZbZRcjtQuV8rwsEll8aigqRcKnGyoWWvzF7kQwAZ5qagHme5gTNyuE\nfF7/6evslClhFo+ILI6ILMgXy00cZpQS3WoN/zJS0UVqswst8pChblNqFtms+edpuxrcySpsQIWZ\nRkfrGjIkJ6u5oVAhCROqjeWCl3GgkYXFn4lKktxpHbk4nHKhw/5EXjdOoziZCygWVeVEF99/bCz4\nIbLihZGJcTMMIxrFbLS/aFMeIuThQ16+ISx8SDmEfD2FEIniEg96AEiwvANN0k1/ZHL+NjkAkyK0\nHGSzWXie1wLOc7PjQRLfg4jIgogsm2RyE2ovqsK+eBTCiKM4GZ4qy/Mq5OR0BUWXnffD2wJw28u2\nXWpIa/xY26FCGzuMa38mOgqTIhO25uGCy/Vyu4qR2uv7E35ouUg1QwsjXnyqlFPlikG6SsC71tlP\nFH4+Fwn1RBzjE+Yz7hJd/DQkMO3wIWBGxnLBxbtuhBZNMwWYCvE5mEEJQNDRIsGVEqFlkclkJGWk\nZoiTxRGRBQkXcpLJq2BKJNCPMrkXdjhwoYQlvPN1lE/CJ8TlpQO0OOB5PxQq5KGa0At4KgXE4zii\nFB6qgyDyPK8FnCwSqTRSLQITKnS9v2bqHBsSFc76ZD6lCpLy9pLTIE1MFNtbYett0TQxEfywuASZ\nXXTLXk84RNfKgTzy/mfZFT50CSsePqT1fD5Ou6yFWUdCi5Lh8zBFSwkerueCTEKHNvPz8+joEHGw\neCQny0ZEFkRkEVpgcUhcUdiQ4PlWC4VytLhTQssZFLssaRhHyyTCT0zECiPWyBWh5bD8rELYcGJC\nXyxztQ+FNruTZQqQ8osyz8uiEYVuxeN5kSJhZUP5WK6wH+0XFjpcOcAEtV3DwW4Py8fiSocnPPH9\nuRIsJaoAd7VSPuUAW2+7d7wrdl7WyEjwNdqwwXw0XeFDetpTU3GYcCFBIw3H/HW8LAf9aUrA5D8K\ngIis2iEiy0ZEFiRcaKCCoy7HqsNaXswPNAkmgosrIJibRYIrhqDjpZ0uPlKNX2O5G0Jiqyc+HWyk\n6o91ElnN72RxgRuWiwUEE6iD4tqeZDksAZ6mOSoXOiyK6NlCirfZhOVj0WNeL8GR6F7WyeKzQQNm\nuCElX42OIlKw8oqT5HmXuHDipUZoeigOrxk2PW3W9/VFMDXFw4QkugAjrlIwVeA5aUhZB0MqlZIZ\nPmqGiCyOiCyIkwUAyeQN/hL92yUngZwsm4U6WXy+QjoOYBLfASOmeJsrJ8scxxZVdB8IQSWsypYU\n01qW4UL+Q+iyomh9cZ5KLKZrCZEo4MndhSPGS4cOucvlhESVbYHR+8ffR7vqLMFFlysTn4uqUvsD\n4fsDwdChH4buSY3r+wH9IpwYDb6OPHzIp//hpRtotCU9PXrK5HRNTABTU3REeiEHoYuR8pxF7nbZ\ng1lmRGhBO1kismqBJL7biMiCHgkWjUaRrXPtpGYlmTzoL83AuBURhLtVC3V+eDV3/kXMwDhVXHTx\nUg60HZ9mx4QHx8bMxZyHDKkwaSjxOI787Gd46JJLFvic3DS/yAKCE0KnoIfsnYWpXUbvEf0JiQN4\nuOgoVOzVNViThJerdhaH3qPOsM+cS1zZ68slwPPvd7n6WVXmYwVCh7ZlF4+XdLJsJ5bnZAHBEYZ2\n+HDdOl1Da2oqD1NHjkOJ750wOVtp6O9St38vYcN0Oi0RjZohThZHRJZPZ2fnshVZGvqhzSH8R5fX\nuqoFFHbktbIAEyLkbSmYOkCdhbaxsZ5AfgvgXs5m4U4MqtNchs2Sk6Ur9k9Bv3dcHFNezlnWFgGg\nYMSVgha6vO2PkcloMXzsGHDsWCf0z0iHf9+DP/zDN5WsAF/O5QIQdLJcKtl2uuxtSokuPltzmJNV\nbiJDOx/LtZ49yc6hIaSz5o8FDxGSbuTJ7rSOngqH8g3pT0TwYz0IM5ChE6a0QwpabM3BjNoFKD1g\nubtZ6XQa8SWY07T9kZwsGxFZPl1dXZidnW10N5acZPIVoPyM8OH6JIYot4PW2xMFlyKPoFPFsXOt\neE5WjLXFrO3MCEPA5P3Qsj1aLZ/oR+ToUXOIMFekBjTCyUomPej3hwuqObidR963CMz7E2HrojCC\nm4QW/8mgZRJYUQDj+MAH/i+YaXqi0O/dGvzHf9zr7DcXXZhwiCoackfLLtFll1uwqWRkIafU+nKi\nKmR9ZyKBlXFgPNUTcKqoZAPvOn00eTdoHz59FLUnEhFMTPRhbm4KQah4by/Md4pULdXTkrBhJpNB\nd3d3+Q2FCmi8yPI873YAH4buzCeUUu+31v8hgAf8h1EAlwM4Tyk17nneUeh/pjkAWaXUtYvpi4gs\nn+VoFWuBRVDule1WcWcrb7VXCg8TcngCPF/Pxd4MTGFFvp/OOeGiiqDwoZ2AHUnNmkQX2sm+uNYI\nz/MKVaTrRTKpAMxDT74HlC+xESb6uLCyw7h2G/1kcHcryto99jjFHo/hzjv/BFp4dQNYh5mZezA9\nbfRIocI6F8IuuOhy1c4qN+qQbxNWP6uSfCyeAO9aT+elWKkPjZyMx/Wcj/bTdTlZrpwsjnGzaMTo\nDNw10OZgBFcGEjbUZDIZ9PaWGvwhVEYEwd/qpcfzvA4AfwngFgAjAL7ned4XlFI/pW2UUh8A8AF/\n+7sB/K5Sik/xcEApVZOLg4gsn+WZ/N4LfSGkiynl4rh+bMMS4BcKOSecDEyCbpjomoOd9E6JwySq\nzDQkwbBUoZGuXqlU3eYwrJeTlUzOoditAszrWam4UtCvp3Ls4xJd1JZBMF8rAi3yeMJrFEZckftF\nIcVZkOjq7f1v6At8D9TMqwv5SwXs5PYweMzMJZjoOKS4XaFFPloiLB+LPjdh66nvtuiyz2+JLkqC\np7INYeFDgr8UdhQUiGFujn9PO2FGDJOgAoL5WTSh9PING6bTaaxZs6bR3WgTGu5k7QTwrFLqeQDw\nPO8xAL8G4Kch298H4B/q1RkRWT7LzclKJl/NHlFIzv5ycHHDJ2wmEUZhpmpx1cbirhadh/KwaFty\ntUw/SWBRcjCFnrjDlUr5JRzWsgs4V2PZLI58+9t4aNeuBTwXN7UUWckkOdckrDwUCyOXWOLrXG30\n3kWs9hxrz8PtctGyxx7Tz0neb8/ChBwpVMxFVxr6PY3C6/0wdJ5YAuqpHcGuusRWWKjXro3lCi1W\n42IB4U4ZESaqXDYrW9/jt0+HjJIFwsOHlJNlV4TXVSpiUIrnLtqQqIrAFCk184kuR6GVzWaRKDlC\nRqiMJcnJGvI87wn2OKmUSrLHFwA4xh6PALjedSDP83oA3A7gDaxZAfhPz/NyAI5Yx64aEVk+y0lk\naYFFLhZdvGlotx0qtOHbVDvK0CWoeLsturqt9QAPL3perCCwiLBaWYGIESVCk3VQBxYrspLJF2FE\nFReyCsXCNuw8lbRzoVzpcVziK4+gO0nOFrlcQNDZ8qBDnRHo0Ys0urEb3tZT0J/PIahvXhCe3A6E\n52qRa0Ql1qktRPCUnCKAiypX6JDW02fJcqqK6jNY57DDg675HOmeQov08aXcQ55yptf1QKlZBMud\nkMPFw2L8TwuFD+sxT2lzk8vlRGTVjLqLrLHF5kkx7gbwX1aocK9S6rjneasBfNXzvJ8ppf7PQk8g\nIstneYUL+VxmgMlxck0EXa5eVi2gEg4EL/PAk3Xp4qCFllJT6O7uK+xVboRh4AHP6wFqHjZciMhK\nJmdRnKhuCyzn2ULWh7Vzwo5vCym+re1icXFF+9ghRc9fF4VxuniIk+dxUbmBWXg3jgLoh/rcoLFt\nwnKt7AR5l0vFRZfLyQqrBErYowpLOWFhM2WXcdL4VDouwcUjm3Z3qSJ8NksV4adRXGiWqsLT5OAU\nOqQk+OU3ibSIrFrRFKMLjwO4kD1e77e5uBdWqFApddy/P+153j9Dhx9FZC2W5SKyksnXQ1/E5lir\n/ZjgX5alSIolUcUFFaD7Rj+AvE9amFGdJkDf84hSICfLrgROO9ttNaAakZVMTqAyB6GcaPJKrKvk\nOHz/vNXOhRQPJ3LsdjoGuVok3GxniyfL07kyMKGsGXiHJgD0Qn2SOaCpVPlcLdoOWFgCfDnRxd3Q\neDx8VCLZTRTXpgv6xAQ6/eWBgZ6SoolONzRkDsvXJxLBJHpdEX4IwCSMSzXjr+XfL8qzI7GVwnJL\ngs/lcujvd8/LKVRLw4uRfg/AZs/zLoEWV/cCuN/eyPO8FQBuBPBq1tYLIKKUmvKXbwXwJ4vpjIgs\nn+UTLuwH/VvV8EmgbXgifAeqz79yHddu67DubbgbQm7XdOExj/aRqOKVtAG9PDYGXDSE4HDDuJWj\nVUMqEVnJ5FmYkYGAybWi12KxYopvX+p4pVAoFl62iOLb2qFDHlKkG4kuytUidyvLlklwZaFfj3kA\nKXiv7QbQi0RiDab+56/MqcMqxPP31Q4N2qKLqxkgXHSFJcDTen5c13yH1K+xMT1UkImuMGONhwfp\nKYSFD0lwjY3xivDEIIyTRfA5ENOF++XkZonIqhWNd7KUUlnP894A4Mt+Z/5GKfUTz/Me9td/3N/0\nFQC+opSaYbuvAfDPfp3DKIC/V0r9f4vpj4gsn+UgspLJt/hLVKaBF/0kJyvHtuH3QPjotcVg52fR\npLbUL9vV4v+SzJeZ/uED4aHCfLzH7G2LqhrnZpUq4ZBMnkHwdeXihf9AlRJHlbhRnIXmh7nOY4cR\neWjRDh161n5cZPGBFORm5dkyDzFmoT+v8wDmMT09C+9NvRgcvArjb/5xcbd5IVKgfK5VufVAuAKy\nSznwUZKVOmXZLCID+jPKyzWUM9dIVNFpaR/aJhaLABhAJkNfBNvJ6kRwbkMabbi83KxcLocVK1Y0\nuhttQONFFgAopb4I4ItW28etx58C8Cmr7XkAW2vZFxFZPssjXEjzmpHAiMO4VRw+ETTduyaKrhdh\nX1L3CEM+qpBHbniosCC2qNr30JAuYMmTomuIy8lKJscQFCP0nCqx1+l1p7ILLux2/j65xJdLQLm2\nKyfQuEi0Ry3m2T0/Bxdj9vvNRybaIisLLbS6Aczh3LlZeO9aB/U7T+pdS1WI5+81Vy+u5KZSSfZA\nefXjCh3aLpcjCT9SSHLvKToknTab1TdetYK2o/ChS3AVJ8HzP/DkZlHNLC2yloubJSKrljReZDUT\nIrJ82t3JSib/zF8ih4iKjNr/Vml+wBz0jy65V3wfV4J8JdhzF9rzGPI6WYBxsfioQzOXoeeZYqTc\niApbjmTTJqGFiyo+k3SNsEVWMnnS2sLlWNliSyEoeuwwq/0e2AIpTJDx99PZe5QXXnabXfoBcLtb\n9ohEuqcyIVF/GxJWtD2fuJxGLZJYSMP72GYAK6Ee/FpQUIWJLh4a5HYQYYcdXaMSuaIPO0dYGQf7\nHA6ni48qHBsLCi5ax3P47coTXHBlMvT7ZifBz8A4WTSal4cOa/vno1nJ5XIYHGx/MVl/msPJaiZE\nZPm0v5PVD52HlYb+Ee1AUHARMQQrv9MFeQ7FOTjV5Gi5wnxhFd/dIUF9QaC8Cb3f2Fgw7aWiEYZ2\nXlYdKr9HIhFks1kkkzTdi2t2ev7clOOxC1tEVbKtXaiUxBfvTyVJ96UcrVJJ87zNntNRsXsST7zP\nHQi6WpSjlYf5k0CfozS8T18PYDXUr3/WnIKHDisJCy7ExaKRjWFV4HmF0bBj8H6s7SlaXS4JfsMG\n8/9h/fpgybDiJHhbPNEXxHazUsvCzcrn81i5cmWju9EmNDzxvakQkeXTzk5WMvkxf4kuRr3QgoW7\nWDRsHghejCkvii5sSxEuJFwJ8sHlShyswrIdKiRx5bcf+Yd/wEP33VeTnv/TP2URDAkSPETmCtVy\nZ4dTrlZV2Lb8HC5RZoeGldXOKedwuYRYuWR5nhxP6ylvi/rDXS+aJ5GEF22TZbc0vM/eBnXH58xh\nubPFk5jCBFWpBHgSXKVGptqiqsr6XJHUrN+sxZbrPwDtQsV2XetJcBUnwdOfFQpX03e/G8GSDssj\nNyuXy4nIqgniZNmIyPJpZ5Fl6AQwBjOcm2PPT0jOhyu0xB/XSnDRP2j+OAEj9MjFMmFDXWyxJ1DC\ngS9TRGf9ev96SNdNfgGtcS4WAOZe2SMnuVvFE79pG1dYsJSIItGRQ7Fw4i6kvZ/9Xtptrj6ECbpK\nceVthQ2kIGFIoUM+MpH6wEUYd7UopJ2C96U7AQxCHfhE8ZQ9hC2oSjld0Wh5J6xU6BAIT4C3hVtI\n6NCu9E7w0CAv5cCdLpME3wngnNUBCiPOIZgUvzxGGoqTVUtEZHFEZPm0a7jwn//5CAYHgXPnaCRh\nJ4rnDaQCkJQISyMP6+lY2QVIiUrChh3QYY/+gGNF19DRUX2toogNpcZcNIDgBTVseYFoccX/yZFA\nJHFFosflXtlwwcXDcMrRRoVkwfbh56pkuh17O9d8hq511bpb9pQ9dj/4Yx46pHCh7XpROz8ed7VS\n8L5xH9Suvy0e5OAaUUpiJ6wCPA8JhokuLtzCCp7ymB8pJMpSHxgo9KNzIIq0Y3ocqvRORqwrhcwu\nDxZMgu+ASYTn3y16PvTng6bnaW83SyklxUhrgjhZNhI89WlXkQXQDzAlFvMfTLqnUCEN56acLZvF\nfFzCqsWXDwkGR0G5RRhd93hBbsAyL8JCQNnsoouRJpOnYC5cJGZJ5HSyNnu96zGNAKP3o4Ots9vs\n9eT40HHAtrNvpbDrWnH48aqF52jZZSwoxKrY+ry1TocDi3Oy6DFVzafbJIBxeN9+EN63/0ewKxQ+\nppsLyrUKK3rK14dtQ6Xb+Xp72T4GqaGJCXQiXRBVYTogkdAfYT6jDy/jtX49H31Ln4sEtGvVz26A\nfn/j/i0GytdKJm33qz1QSkEphZ6e4jw4oVpIZNXz1lqIk+XTjuHCxx8/goEBGl3EhRWNHKL8C8C4\nIXkY0WU7MvV0tviXx66NZW8zDbogRKNBgUXuFW+n5fzASkRGR4MuQ00crDEEJ7d2jaDkzpSdeG7f\nh+Vf0ToeIqR19P7x15Em/aVlOLYh6FguN8vuVzW10yop/2DX0rLdL/v52/3hIUSep0W5WkBhFOK3\nXw91+XvdojqVCi9UCpQN6QW2CTtOuVGLgDM82RNNYzbbWdjFLv/Fc7ZIbI2NlfrvsApagNqfBfre\nUbV9Si1oXzeL6tnFYi5nXage8W44IrJ82lFkAVxDkFuSgnGV7Kl0+MWSl26ottJ7tVAoM4xIyLLZ\nxxZYRKCEA38eNRFX5F5xRwnWY/46wnrMp6lxhRGBoDjjdbLsUYYuQWUf3z6mSwCRoHGFG/m8hIRd\noc8O3WIAACAASURBVN7+rFRSnd4WbXnHPdXWos9jFsWjEaNsmYcM89CTUCsA8/CeeTPU5f93UGzb\nasR2tioRXeVGJSYSxSUlyoUf2fqegQEMDUWKkuBJdFH40FXKgQSXfhoxzM1xZ9nlFMShHeQYu7Wn\nyMpms4hERBjUBgkX2ojI8mm3cOGPf3yk8OObzeqaUkqdQ/ALwPOw+IW51JeEX+zrJb7C8rLcP4RV\njTAEauxe2SE7eyRfxNqGXjueR1VOcJFrZe9DCeJ0z4UJF8x2PSsb12jEMIHGt6N+2AVI+Xqgurwt\n10wDPNGf7klkdaBYaHHXlYcbc/69B++Z16O/fxAvrnlUb8YLToW5XEQluVilRBkRdowSsw/0xPNI\nJCIFQRU2qpAOxRPfAfN4bo4+r2HJ7GloV4tqaOnfiXZMgM9kMvCnURFqgogsjsh3n3ZzsuwaUUrR\nRYK7V5SHRf9Q7fBgGhRmqS2ljmfnZZEIpI/qZGDraNRcRCoSWHYuFh+2VSFBgcXzp2IICi96HEcw\nbyrOlvnjCEweDM+x4rlYEaudbwcY4dFpbWcv8/wt243jIqvDOra9bJ8Xjv1clLqolZrCh1w2O8md\niykqYkrtaegq8bPQn6cXAUxhcnIMXS+8q/j01eZquT47tI6O4crXKpfPVUG+F+Va8VkNeC4WX8fz\ntTS85hx9Zgp7Ihiy74Q7hN/6pFIpdHSIMKgNkpNlIyLLp52crP/+7yMAjLjQ1wn6IaUyCVQLh0QX\nfXg7/TY7J2upQgV8hCMcy8VtPP+KHtvtRU4WDxVVMapIJ//S3Ir0mtoCJc62oXZbPNnJ7TF/Hy6O\n+LYRBMVcqXZbPNk3l7iyxZK9nSvXzHbtgOCx+ByFYUVIXVBokOdh2YnwJKgUip0qSo6fh/4s03Q8\nNGI2Df05m0I6fRbeLx8tLajKiS4upkodo5ok+hL9CEwTZWELrrD169ZF/JIONvZ73Q2TBK/b2i0B\nPpVKIVrjuUuXNyKyOCKyfDo7O9vGMl671uRpUHkgz7OdBvoVpgs0oC9AJK74BZWodXjQ9YUJ+0i6\nRde5c6ZPFTlZi0BfXEjMxK1bN4rFFb840Y1PE8SH0HOxxR+TkIsjKGBcosoltko5V1zM8XPb4gps\nme5dITwupuzRh+V+asK+e9zJyjseu5ysnNVGE0uTuKKRh7MAzgI4A+/ke/QhK3GxqllfSlBV6pSF\nbFPapdIV4F3rudNlPl+DMCMNadQhYD57nWzb9iKdTkvSe83gf6zqdWstRL77eJ6HaDSKTCas1EBr\nMDWlXSz++x32O2/yVmLQI/aA0iKnHjlYfGod+9w0GTR/3M8eB90s13KAReRiJZOTMAIqZt1THhMX\nK4AWA1zA8m1yju1pH8q94kIm5x+LppUJq2MVlkOVtc7DRyeWGzXqOp+LsEry5DZ1oDj3KszR4nla\nPNGf56ABwc9MFmZyaXJfKUeLzwPJxVgv9Gc/A+/ko1Dn/XGwG/YUTDbVJMgTruR2oPSoRSbYeobi\nmE0Vf0/5qEIX3OEKfkdoyi1bYFPFd8CMSKaE+PZhfn6+7dJFGkv7CfHFICKL0dXV1fIiiwoOUk0c\n+mGdmrJzsugix6s/8/Bgs/xjCPvCuttr7fonk6ehLzbcJbJdHXKKctY6l5AisUAXLZqMm7/ednkH\nKtxKQssO7xH8OK5juo7Py0DYow5dCfOl1tmjAsP6Rf0OS8638axtKJzIz0WJ8NTGt+PhR3r/PHaj\nMgUd8M78T6i+3y8tqCodTQiUPk5YFXpaPzpqZocO2k+FBHjALarosCS8qEI8T4TX4fQezM2FzXpA\nQgswI5JNyLBdEuDT6bSIrJpBjrpAiMhidHV1YTrc9mkJSFyR0DLFOTtgat/QP9FOmH+wHTClFII/\nqEHCcrNqXUOrVE4WPZ6E5+l//YsOFTo2TCbPwggsujhT+I+PEiRR1Ymg4xJH0C1UbD/al68j94W7\nYzno8gN0TMCUa7Cr5rvCeITLZXK9Z1xw2eLLxjUq0SWoOipYtoVUGLaAcvVRQf+0katFLho9BtuP\nTzo9DSALb+r9UHhL8LQLdbH4Ni5RlkoFkyfpS8tFFc/nIpXE1vPRhIQ9qtDlYgW3sUPJNhT6ppDr\nUs1fWn/S6TTiiyxGLHDEyeKIyGK0+r+Z3l4TKkwkzAwdozSVHuLQcxcC+uI8CS0MbFEVJrrCKPeD\nGxbC4pAIjJfYtrx7VbXACtlBCyzKs7IrrfMRgSQquMNEjhNgHCgSHvRjzsUXPVYwzgHlFdllG3jY\nj4ff+DlIqBH2cSL+NnabS/zYlKqxVcrlomUeNuSOV7WhaHsqHfs4vMgpiTA7t4teIw9aOFCCPOBN\nfQCq7w/N6bgYKlXmodTFutR0PvY2pJjCQoepFFbGgfFUcZVy7mLF4+6ULr7NXGHAcb+1Fb0+dj29\n9goZZjIZEVk1g3KyBEJeDUarjzBcu9Y4WfR7X2zMkXBIIeikcIEFxzJvcyXFh2FfrPmFvNR5XOct\nzaLdrEDOVj+04KGkX3Kq7ClyuNMVs7YhMWa7YLTMk9ltmz1mHTcG7WhRG+VuAcGQJax9yCHrsNrt\nkY4Rdh9xtNlJ8nZSfBRBNwQIfj7sBHnX+mp/jrgwo7IOfFoeXsaBHqcRLFRKow7pRk7NJLyp/x2e\nx0cF6EqtryZBPpVyF70qcwwKB/KJ0V3b8O0AO/pIie9hLlY3uzcDZdpllGE6nZYpdWpKudGBi721\nFuJkMVrZydq4MZjwzv/BFgstquTMHY+U/zgFM3eh7XBVkiRdCQv5ougJod1icJFYicfJZAb6gkLC\nh9e14mFCEho9rJ2HCXkYkY7FnZ0sjLCiROwYexyz2viUSHRFdYUHSzlJgHEobUfJFX4r5VyVwuVg\nceeJh1xdk1sD1VWL9xB0tex5EXnelp04z+dGJAdsEkAG3txHoLrfqDcNc7Cy2fAEef5l5PVEwpyw\nMEFmrw9xzeyw4Nq13MkOdq/0nw/7e0ZJ8PT5q3QwRPOTzWZlcuiaIRXfbURkMVpZZAHmGuD+veB5\nOFQLi3KyZhC86FDojlPNj6rLraoWe2Shm0UlujvsrmQyCzOKkCped1r3PAHdHmFIQoovK7Y9ofzz\n8GlzePiOhFqYwLLn9qNtYmxdmu1P58wg6BpxoWMLLbudzsVHPtrhSlvguLBzvrjYAyo7hi3A7NCj\nZ21rT82Thf75m4f5GUzDjEKkkYqnEUn9JfLxR/Qmrhwqm0pztUrla5FDVkZ0RRM9hVPYeViA0XPR\nqNt0i0aB886L4cwZHj614UKL19VrD5GVyWREZNUMEVk2IrIYrRwuXLtWRxtGR/WP6uhocZHO4I9i\nJ4AJGKfFzuMBih0tolRh0mp+eO3E7Wo4h/ApQSqAXpiJiUJ81Tv3CphK19ytcuVk2SP9uKiiEYPK\nOgaF7oBikZRD8XyBpRwsoDgPi7+WNHLRdoJ4gjrgFiC24OJOlGsKHztsxxPwlXXcDse2fJn6YifP\nU19LOVv2qEbucpGocu3vsXvKVwN0Ha08lDqFbvURzHlvLN6VRFCpnB5e+Nb1r4CLtbBt+DFCIBfL\nJajI0SJ3i8RYsTALCx2SHU6TyrfPXIa5XE5EVk0RkcWRnCxGqzpZe/boUCHNPev68+t5vPgoJa7y\ni3JY/lWjqS4JnhgdLQ6TFHA4WN4zu1AssOi16nQ8tvOwutkyYPKxaDoSu6I7z8siYUX7RNi+cLTZ\nhUZh9YffeHvOsZ6LySg7bgc7T4d1Plduln3j7w9vV9Y2PK8LCAo0oPKfKJ7kzqvFg7XnrPX2VDyu\nPK15ADNIpc6h1/uL8t2gPK0wMcTXl9qGnK4yx+mMFjt+a9cGy7eEub30JywapWLFgDv5vQO6QCmn\nffKy8vk8+vr6Gt2NNqE5ipF6nne753k/9zzvWc/z3uJYv9/zvBc9z/uhf3tnpftWizhZjFZ1soaG\ndB0cXrKByjgAWnidOzcLM5KQ52S55i4EzIc5hcovdIuh3MhCTnXir3CdssUVCawvrUYwyd12sFzF\nR0n40GM+xQ2FnTrZtnYuVpwt83Bijq2jZcolAozTYjtY/D3igxpUSJudfM4dHFeOFG0XVjuLu1w5\nx3r73nbG7LpervClTSlni5+DFyItlWtmf855La0pzM56Jge8EipwnyoKC9o5Xxad0Tzicd33UmHB\nUsnxAOB5A1BqCuHfr17o3472ysvKZrPo77fFpbBwGvvn3PO8DgB/CeAWACMAvud53heUUj+1Nn1c\nKXXXAvetGHGyGK3qZNGPJx9ROD1tRn9rscUv3PQ8+fMNG+3X/B+RqvOy2A7eX8/BjCQkpynht/XD\n7WiRA9UNI87IqQLMqMNedgzuAvWy5TiCjhYfzciFG/UB7DH8ti52fKoRxZ0ssMfcreJOGNg57f66\nnKmodV6+Da2n83HXiw8YoG3DnC847ktNfWWvc7lW1K6se9vJonkPZ2FGHU7Bm3uP+9SVOlTltinn\nYFUwapF+D/hoQoJGFUaj7vWGsAEmvY5tWpt8Pi8iq2Y0xQTROwE8q5R6XimVBvAYgF+r8AksZl8n\n4mQxWlFkHTqkQ4UUGqAQWSKh3S2a/3hqCijOyaIkaH5xdOVgNQrqlz2dTmWsXetoLAoV0pxtnXCX\nYyCXigsQPsKQ3Cae8G6LF+7scLHLj8XrX1H+EI0CJDeGctg64E6Ad+VhzVn95i4W7wcJG9tR4u08\nyZ3/2Lnyy/g67kTxQRHUbjtlPIeLYx8bqGwEIj+unS8WRfFURREYhxHQQosS4afgTf0vqO7fM4cu\nlUNFy2G5WIQrJ4g7WGVytaLR8N8uPqixlMsFAJlM2EWMfyY6YIoat35eVjabxYoVKxrdjbbBhJ7r\ng1IY8jzvCdaUVEol2eMLABxjj0cAXO841G7P834E4DiAP1BK/aSKfStGRBajFcOFQ0PA0aPB0g3R\nqHGyTOkdXvySl2+Y8W9hYUOgeKThUhD2RV1gqBBAHhFz1GgU3u//N4BV/jH74RZYvHwDT3incCEJ\nG1qmduorF16FXiFY64ontPNwIdhxAVP5HSgOd9kjC4FgiJAnpEegBRsXejznwSWS+LooTH4TFy1c\njNmlGvjzcYmrHExoDgiGCW0BxEOHYeUqgGBVeDomb+dlH7gQ5pNc8z5N++tfhDf3IVOsNEwAcUq5\nV7Se35c7Rsg5KxVU9q7BUg/kGFACPEEFSCn5vRPATMtPsZPL5TDgKvoqVI3n1X5qM5tMBmNKqWsX\neZgfALhIKTXted7LAfwLgM2L710xIrIYrSiyAP0neGwsmG8xMKDFF63TkJCagf6RnGbttExOFrdm\nlzosMAd3+QZ3P1wXE/t6FMjLikbh/dpXYIQVD8fxPCzuWNmuFQkKSpRPW33mgocv0z50kcqy/eYR\ndLPoDbVDZim2jgps2qM0eRs5NryMB7lXds0oO7mUCyfblaJj0WfF3g7WYzqWa1RhqXV0HD7ysJIc\nLV7h3bOWSRySa0jtHntOGXYM2icDYApABBtW/i8cHf8jRz/KUMlE5dWKLsd8cWGCyrUNLZupW2nS\naA7lZHFaPy8rn89jcLB1RWKzsQQiqxzHAVzIHq/32woopSbZ8hc9z/srz/OGKtm3WkRkMVotXPjQ\nQzpUSDkYfDTdxIQWWEeP6seeF4NSlPTOxRMXVfWeKmMxJRs4VJjUTTZrQoV21KZzbAzeniSANTDh\nQZ575RqxZ0+hQ4m/fAqcXpgLMg/Z2QKL9qUCplywUQFU7mzZZRt4mJAcrrAQIRdW1J5HMLRpO1Eu\nkWW322LKdrVIBNluFe1LDh8QFFdA8KJtLwPFQssVLuSOFcEdKgW3q2WLBf6eZ9j2EQCTeOEFD+hD\n6WzyWpUGqMLBsuHlG/j2bv1WLtTDi5JSiZfWFlm5XA4rV65sdDfagqVwsirgewA2e553CbRAuhfA\n/XwDz/PWAjillFKe5+2E/uCfha5rVHLfamn8y9FEtJrIWrtWhwVHR3WocGDAFC+nuQsBXv2d18KK\nwRQWtEemtS6lco4Na2BcLJfAyiEosGIwApGKhJKjRWKLX+hj7N4lsOgYlJdEowcpN4uPPORii8KL\nERgnzM7J4tPt8GW+PQ+9cZFlh+zsbWwxY1+Q7VytLpiwJHe3uGPlElF2ErztcHHB5MrRIgHGt6Nj\nR6xlPkG0K1RK4VwuCqdBVeG9qfdCxf8EC6JUmLGS0GKJY5QSXYCpj+WuCj8Afa3hNP8AmIWSz+ex\natWqRnejLWgGkaWUynqe9wYAX4b+Yv+NUuonnuc97K//OIB7APyO53lZ6AvhvUopBcC572L6IyKL\n0YrhQqqNRXlYfAodSnpPpeC7WARdOAB3Lpad5FqPRHjKZao/3AToesnHYQQWjeqzBRbVvIojGCYk\nkUTrMjBV4YGgqOECiAuMXpicLLqo07Kd32Xnetkihx8/BfN1pj7D35fyqMjZ4mFC7na5EssJ/vpw\n0UTHVtb+XJTQMq82H7EeuxLggaAI4wVUlaPdPq8r0d9VGT5sWiFyt+hYXIDOgxytC2LvxvHMu7Eg\nyhUqrfAYUTZVTrnk9jDKn55+H3jld/5b0prk83nJyaoRzSCyAB0CBPBFq+3jbPmjAD5a6b6LoQle\njuahlZysj3zkCMbGtHtF/0LJyZqYKP6za+DV3WmEIc+/sgVW62LnZWl4aYZuGEFFF2ousChnigRZ\nzmoPE1hA0E0ip4q7ZCSe7NGCQLGo4kIhxc5FF3++PR/gMMe2s0OCUXY8WPvxzwDlJdniiz8/Be1a\n8ZIIPOnfzv2i83HRxl8fWMeBtWwnwXew7TkkwFyV4Hno0LPa6Hj2SEgutDKF5RMnPOA8LJ5yyfH2\ntiFUI6ZKhw1d4WMOjTBsbZRS6O0tP4WXUJ5mEVnNRPt6wAuglZysaFSLKhrhTcVHJyZMfSxe/d3z\neM2ksDpYvGRCrQRWPfI1zDHDxKRrubf3bQjWuOKiKI5gfSz60aU2wNS/onbugvWybXoQrDVF9bQo\nwb7H35aS5un8vC9URT7CHtM6XhuLzsnreZHwofa4tczPZdfFItFHN9d6fuHl25NQ6mLr+YW6y9ov\nwvYBil0ne5m7V652++eMH88WYK6yD7wCPFBcO4vDK8Kn4Z35Y8fxakCltbfKUMrJ4uv6+krklwEw\nrz3VhGvtyu9KKSil0NPTU35joSL4gIt63FqNFuxy/WglJwsw4UHKuyUn69lntcB69lndTgVKNTwX\nK0xIlWqvJnRYX4HFKSewLr74DwAMQQ9Ld40k7EYwPAhocUUOBi2nobOdCRIJlJvF86kI7iqRW9LL\n9rcFCRCsGk85WLa7xduonXKvaBt6LvRVJ+fBVboBKBYqEQTDZNyx42Ug7ER4V1iQP0c+STQPG9qh\nyxzb3na1eO0re9JpwIQVeVtYXhZtT8/RVTuL1tG2pho8sIi/8JWGqqpwuioJG5YvRNr+5HL6/e3o\nWD7PuZ6Ik1WMvByMVnGyjrzvfchDi6dEwowcolDhwIAp22CS3gF9MTwFfSGmxlr+uCxUVM2hsvlK\nciHLBlfZBn2/AsHwIBdV1Mbzr6iNxBNd9BMICgbaph/AnO8Y6pIJSuUQi0WQyeThefqfslIRxGJ6\n/0wmB8/r8tv1eT3P8/Pn7BGE/LM5799z0TUHI3h4nhUPC9J66nuWLfPnxF0eEhKU/A+2PsqWeZiP\nH89OeLdDhHkExRgQFD4xa1sumuz8MpfQAlvmJR3svCxaz4UXn6iaipPyUg78NZqHd/LNUJf4aR+V\nXGnqfDWy//kXJ7hXCh/J6woPUri79chms4hEJKBTK0RkFSMvB6OVnKzI9CRSqf5C0VF7VCFPeo/H\nKfF9EtrlIIE1x45YTmw1449oUGi5Sgtls8CePe+AHlFI4TKXwKJjxa027mCRU0U5bVpgeV4flMqg\nu7sf5kKsAHQgm1VIJPSPeC6n0NER8full6NRhfl5LQw6OoD5eQXPiyEa1YIgk7FFjz2qUFlttujh\n4ssWU7zoZpjIsgWTB1ONHgjWx+rylzPWPnyUIR2zC1q4uPK3MgiKJVdZB+qnvd7lXtmiCwgXV7we\nFz9mWII9HaMTwCR6T/0eZtb8b7NZJQlQNbwqLeZQwX3Dfg9ctbJal3Q6LSKrhojIKkZeDkarOFkA\nkE/0Iw7jYAHuuWZpeh0NF1j0wzKJ4A8qLbdOKYewUKF5HfphxFMCQbFlFxnthRGUNMcgOVXUbvJW\nuru7kEoB3d0xdHVx4aOFFOXTZrPKr2fmIZvVYiWV0hf+3l4PqZTyl/X20SgwM6MQi2nxlUrRBb6L\nnYNEMne06AUgt4iXbYj56/loQ2BhF01ensJO+idnww4TcrHVAS1meJsdwqRl7rhx18puo+cNax3g\nFlq8xIMtyEiE8uPRd4NPucMT4SOYnX3RWEgLGebXUlcoXiurNZmfn5dQYQ3xvNJl45YjrfSNrjux\nWMwP17iSYpuLyPQkpqe1jc+nz+G1D+NxLrB4AVLKEbKrukesbStlIQUJa7O9UvbIMQ1d3w4dei+0\nQCL3CtDiiR+PHCqaSoc7VgAJLM/rLzhMgBZQ8/MKK1YA8/NaQAWdLA/xuPL7QuIK6OrSrlYi4aGj\nQ7dFo4D+rfcwP2/EV3FSt3artCjj4oqeD13Y4zCCiu9vC4csgkKHO1xAsStF8GOQYOPb8s8QjX5M\nI5iTZedpkTtGoUn6XJF7ZudJ0XJYAVObSIl1gLtAqR0upOcLGNeORuxq1y7y7P9AfksyKKgqHTVo\nUz6BqmIWHiqk4tjtJ0bm5+cRbSlh29yIk1WMvBwWnZ2dmJ+fL79hgzjypjfpX8tNm4Dp4KhCqvBO\nYcKRETNx9Nwc4HasgHDXql42eiUCyzVtipuwKXQeeeRNAF4KnexOIoqElu1ocXFCblYvYrEYMpkc\nurvjBYGlf0S0GF+xQrtQNL9sIoGCmKKLclcXhQeBeFxhelq30XG0y+UhGlWYnlbo6vIK55qZATo6\nyBEzbVrQGTGknS4SXjwfi7/WL/r3PC+LCyrPuifo+djuFZ0rHbKehBcvD2ILujzcDpbtepH75kqY\nt12oSkUXUFzewW6zp9sBgmFWgJdzANJgM3YYeHJ7eN2E8ts0xRWsfUKG8/PziMVqMQuFAIjIciEv\nh0VXV1dTiywABRUVj+scsoEBfaNRhamUmcuQQok6AZsOECa2OJEKtqk3YRdH95Q6xaHCS2FEkysP\niztaVJJBP47FepDJ6Iv34GAEqRQC4gdQSCT06zs0pFso2tzVZUKCJKoSCfg5V/AFmYf5eYWODi2+\ncjkTLiTxNTOTR28v0NGhL+ozM7SNEUHZrMLsrEIsFis4sLlc1E+k56+hXUmeBIo9GTItEzzPiyf6\n8/W8fhW5Oq4wIRxtPGE+iuLRq3aivC3O7Pwt262qNj+LFyglJ4uEHm1D56Sbx5a7AEzC+/FvQW37\ndOXD/LLZ4lGGS3i1Wq4XRhFZtUVEVjHycli0RPL79DSwdi2mR42TBZik97GxYI2syko4hLlW9ar4\nvlDcIwzdeVmUgwWYECCJrRxr57lYcfT1RZBKKXR3RwqhwFWrwAQWQBfWoSH9Oq9YYQYZcAdrZkbv\nq3OwjOOVSqnCdZYv03ZAMFyYSqnA42zWiC4q8aNHo+u24PvNK8wDwWR2LqxiCHcoKGRH57Dzseyp\nZ1ylG6hKvp0Ab7fRvuRc8XytGIIOlr09z9/icxuWE1o8P8vO1eKuFhAUlXai/ry/TK4hKi+3vtjQ\n4uJ2XQT8N6W1SKfTLZWL2+yIyCpGXg6LZv7CHXngAa2g1q9HGp2FUYWJRLBkAx9VSAIrHgcymUpy\nscq5Vo3My6hcYL3vfR+GDhOSiLKhopy9IBEZi3X54T79Gvb26uVVq+j1NCKHCy4STtrR8pDNouAq\n0To9ylC7XPPzPB/LA+XdRqPKF1MonGfG1zxcvE1PB5Pk6fgAMDtL20f8tihyOX2CoLvluhpTBfow\nJ8t2Fsl9CtuOixBbbKXZei627ER2O5zIj+UKOXJBReFScqYAt+giXDW0aF9y7PjIQ9d3gVy+eXhP\nPgi175+LN6GrULC+SnC97XKFUUnoUQglnU6ju7uS8jFCpYjICiIvh0XTO1na+kBndhajE8EqxVQz\nCwi6V0EnK0wktVKOhS22IshmzfVK35OLRblXPGQYLDrqeT1sRIzCqlXA/HzQqaL7RALQ+oknpcPf\nB+jqUn4Olm6Pxz1kMibPKpUy4iiV0sJKhxKVn2ul13V0aKeKCy4dQrTbdPuLLxr3DAj2ge61YKPX\njudlAVoc8HCYeT3Cku/NfrDWc+FF91GY+f5oWxJWXERRH8mx4nlldLwOaxu+zq6rZRcUdZVhKAUX\nXlxYuY7D3cF5ABPmDaV7W1TF48WCiuLPRDnRJVe1BZNOpxGX4XA1Q5ysYuTlsGhqkUVxwLVrkY/3\nBOYq5KUauKianta7TU1lEBRSzTxSqHzR0f+fvXcNkuQ6rwPPraquqn5Ov2a6B5gBIA/BB4ARIIoi\nRICMNdcSZWkjzFXI5lpWSLLDjoIV0oZXS++SokSZK8syrbXstS3KAiTZq3Wsl2KQZvBhyg6JQUkW\nITIAAnyAAiWBBDCYwcwA8+jpru6uR1be/XHzy/vdL+/NqurHdHZPnoiOfGdlV2dXnjrfuefLU7L+\nw3/4VQCnYckVLxNSqdC0uJmcVEz102nZb3raPoCXl00Jb3nZEKR2mytZXNFyiQ+pS0ZZ1M4+Rs1C\nqmJZ8uVGO3BsbuqkNKicdbSv8XWp9P2g3C16vVqtgsHAHKs1J1Q0wpCXy8Dm5e9Kiqf0Xvn8WHzq\nG4UoiRWZ3rts+4AdRyVErmpJE7zP7D6qKT6vgbQSx4KtI+M7J589VH7/f0D8Pf/Znl4SKIlxS4sB\n7EXfaQOPif8Iod/vY27O7/EsMT5KkpVF+XYIFLlcCMA8sWdmUGmvgwzg5MWiMiGVB4lomZve8mMZ\nQQAAIABJREFU15eQlwr3G6Hyim+/YesHMKVAmjeqjCVbywiXCauwowYNmVledj1sRrUypnVaT0oV\n3z49rbG5aaambGtUKwOdjCDkIxKNiZ1GE1K5kMqHVGI0RncqF7qREZQuQmVEn3K1zp6L5nmsmN2H\nSJf5uw8GdUa4JJnqwU11l9M4sG0CZsSqVKj4vUZNtnmZEPD7tXxKF0GqWpwgSqP8MFM8wddAWrP9\nNWykA/2+Ej0AXWjN1CwJXjb0YZQRick58iqGNsYljPEqjlL1LpJnczz0+/2yOfQeoiRZWZRvh0Dh\nSRZJU69/PdD2B5A2mybKAchLcc6bP1wqF49t+N3f/VUAdybbeQgpKVrW9H78eAXNpk7KdsDSklWf\nzPPNPFzJk0VTDlpHAgXllEURESBzzkYjGzhK52o0rNJF5cNQVJvWtoxozmu33Ui81nwbvS9JizZ0\nOoY8dLs6HdEYBilTIVAroh5cwzngZkkRoZLb+DFEqEjFCildnHTVkR21OI6q5ZZ8w5D+LB6fIUuZ\nmm3vIVXkhpUN+TZJqOjmGsGrNSpZCmVmXb++E8J0eI3vg8EAs7Ozw3csMRJKkpVF+XYIFLVc+Oh3\nfqchVyS7rK0BtUUA2QBSIlj8C7JSFfbgDvmvbga54o1+rQo1GiTBmgNXIcwDZhk2jgHJPBEsc/zk\n5ATm5+0DaXWViI59e02ZhZcM7fZ22yVcJDjQOcz7blUtKheS98pcq07+blLpMlOjQrr+K2l4d71W\nllwBllTZh67C+rr9fUyQqpnvds2LW0VLZmfJ0XU+Pxa9v9L8zgkVLwf61CsCJ0sTYuqDDCr17StJ\nl2+0ISddfIQhPOs0supsn+1ThyFYHahPvQn6h7/hnoqXDX0GeNMeILyd9kklSruaBsGMGj5K+4UJ\n2rCS4eFVsgaDAWb4B2iJXaEkWVmUb4dAoZUs+jCg2iBcszuFkQJZ47tFKLbhsKhXHDEmJqawumqI\njnluEaki9cpCqemEXFm1an7eKkyrq9mSIZEiu84SLBlrBFBcg1WSqlWNbjerXnFBg8JGKfF9czNO\n1CyZj+W+VhQBN27oXLM7lQ67Xboe8mfZ342IHZUQo4gTXx7RMMHW8SkfTUjql1SrJsS+FQBTMGVF\nrmJx8gW2L035Ppx8+TK2fOVCPpWlRV425OVBIBtKyj1aRKz4/xBFOSRq1jDCREOBQ2g27Q3Hb1QA\n6x3zxZCTJd+DTgb25j8M5f/cJgzZ4l/QDk/rrRCiKCpJ1h6jJFkuyrdDoKhKFgDDmtjT3Y5gswSL\nxzbQl2Ga7/d58jahyOQKyCNYBHrefO5z/x7AXcna6eTHqFom+8psIUJGy0tL9r1011Mp0T6Mm03j\nnVpeNuvIR0XPR1fNAvp9Gz7a6cTM7K7S7Ctrfuf5WObcm5s8L4vUMUPEzL7mWNfsbt8l+s5A5Kpa\n5aQq8NaCyBapQkSwfKUxwH6M0N+ESoN9WIWLkyt4lvk9Sa81CVs6JOKWp5qQAhbBb5CXxCrU9DkE\njay3i183GeDpGqlk2IH692+A/jvPmtWcUM3P+0cc8qkPzWauiV52QaAHH1e3+D7DEfo/PLwqFgDE\ncVwa3/cQpZKVRfl2CBSWZK2tuaXC5NuXbAbtU6/cm54eCnsxamj01jcuSIEYBt8ow5i97kB40ugb\nqf+b6fIyEiXLkJb5eRsiylUpIRSg2TTmdk64mk1Dkmjb5ibSBtFEqsiL1WhwsmTjGky6uy0FNpu2\nnGhLg+6Dn4Jn6Vz8QUqKFylWg4FOrDtkwqez2MiHPNRq1YRo5XmzKMQUyMZDcIWLsrGmYAkTZ3k+\nD5a51uzrUSmO4h2450ua333Xy4kSV7BCow3lNfgS4vNys3oAbrh1fY5RyoI526V66QMRqtEUrHE/\nG/LaFhUbg8EAxyjMrsSuUZKsLMq3Q6CI5cJHz5wxM81mplRIsDlYvpGFhJs1knCnGBbdEHu3RxHw\nF3/xL2D6FM7BGt5noFQjbTtED6H5eZ3xZHEvFTe7r67a99IdVWgUMNo2PU1hpYZsUUmSfFkU3bC9\n7S7TM5MUKZOPZf+2cjShXH/jhi1/2owut3Qo/Vidjku6pB/MBS8hksGZK1YSPHWdm9+z53RLhkSQ\nSL1qwD9CMaSIcfBUeIp/iOAnVhyh0YbcixXKzQLcEYdgx/SQGsPpDygJF7F8rnL5SBXL1YpRQcXz\ne4yiYMl14+NwGt0loigqSdYeoiRZWZRvh0AhlSxysq6u2g/n5E6W7XNCXixTLtyLi9mvb615Jng5\nxNpeg9b00LsLNnwUoHgK7g2mMiG9P/yzlYgWqVF83cpK9j2lUiK1zLGtdMIjCDl5IjLFje1EwEi9\nonIhGeCJPNH6KKL15pxGobOki0Ybcj8WvbZZb8uSZooc0Ln5iEJZPpQfJ76cLCA7EnHYlJvlafSh\nNMTzHC1uss+7X30meMKwkYeceBG5CpXejZql/s0J6J8R5IRuiB16tWLYMrhPpaL4hmEqV5ZwhdQs\n3/uZNwK12IjjGAsLC8N3LDESSpKVRfl2CBRRyQJgP4zb7YwnSzaDliHS9qaX7XQOI3gJysybh8w0\nrIpl/FiTkxXMz9vRgoTVVZX2C+QkdXUV2N5WjgeLK1qAJSSAeZ8pnLTZtASLpjSCkNQsY/2wYaO0\nTGU+qVK127J1jhxJaNfL7eY6zJT+/r5nOH+9YX3RBwMNpWgkIhnit2E+RjqwpcCZZJnWA9m+ghw+\nX5Zv2bfedwwv73ESFsFVtaTRnZ9jVBM8jWoE/G2HNAwx7AFYB5pJXACv7RO4z2qHXi3qfHDlSvhh\nN8wgbxCb6/X+Degm2wYpWq3WkJDVgmIwGJQka49RBJKllPqrAP4VzD/nb2qtPyi2/wiA98D8E28A\n+Amt9VeSbS8k6wYAIq31m3ZzLQV4O4qFQipZQDYXp90G5o1hM9RCh9/s4bwsvpyXCD+Jm1cisJ4r\n14vFCRahh+3tXwPwILKKlwWJgPQWrqzYEiF/ni0v69SjZTKldComTE/bkNJOx3itjJpFpMp9Temb\nqlZtaClftl4tsx/5sXylQR5ISue9wXoRG/Jlz+++vkvCJIZ/v1DY2vKpO1yFlESKlK8OXF9WB7Y0\n2IQtDfJRhk2xn1Sx5KhEHl7qG3Hoi2QI5Wnx35OHkfLt3JvFS4e86TbA+xkCLJNpZmb0EYUehswV\nLELI2B4iVMODStfY/OH1XoVQKll7iyIoWUqpKoAPAfheAOcBPKGU+qTW+k/Zbs8D+O+01teVUt8P\n4DGYhwjh7VrrK3txPSXJEiikkrXGUqNnZsxdvLwMRFkvFj+EPnBHv+mncfN7GPqMxnK934tlHl5N\nAH8JlH4PzKVRDdaLlS0B0rz0ZXFQSZCrXYRm05AdIl9UDqQA0kZDp+13TKlWerHc0iCZ4bXWzmjC\ndtv87lQaJCWNjOu2ZKjTUNNqFYiiGNPTWVJloyKyU/994uZuEba2qOk0J1EcvsgGiQr8KhalqsOz\nne8nSVMIMkdLLvvKhcO8WXyd7GlI157Nzap8YArxby5mVSxeNvTh1CkzJaUruSFlJtYoye+hfba3\nk+7imd+7DRvfQDfU0SBccRxjiXJXSuwaRSBZAN4M4Dmt9bcAQCn1YQDvBJCSLK3142z/LwA4tV8X\nc/BvR8FQWCULMJ+O7XZqLGrOmzBS7sW6csWOQAPc+cNbIgRclWoAS7BiWB+W/xspebHo4cJ9VGZ9\n1uwu86xs6rsbX6BzjEy8NyFXk/iUsL3tlgZNsntWDQsFkpLfTpLBapVIl+l72O1qhLqISIWMQ66j\nZQoytR8lklzRtjyylEe2JMgQT2nvfEpRE6OGmErkGeL5vM8Ez0co+tADUIfWrwBYTNtjAcgSLsD9\nUuXZfq1jmsOHSsBc5bp0KfvgC5MynxfL9550kp+djjAuBuI4xrwv8K7EjlAQknU7gJfY8nm4KpXE\n3wXwu2xZA/h9pdQAwKNa68d2czEH/3YUDEVTsh69ft0dGgc4H7r8M1h23Rjuy0LOfB6GtVvZa9AD\nexp+hYv8WMDk5DRmZtwsrFrNRjZQ2WRmhoeMapY5ZgkXYEqDgFWtyJ/MIxyobHjbbcbXRGU6UrM4\n0THn0sl5rIrFS4M+3xWtp9uTprTdRjuYab/vlgx9D+PNTaDb3flDstEABgMafSjJlpzSvCRjEwC2\nYEuJVBr0BZXyptE++BLr+WtzFUsa5WVfQ3qdUdrv8C4GpGzRPB1HgwU8f4hT7Eu0j1QxQtaLKqjX\nsn8z+vvyjDaOvEysK05RhCIc8j4L+PUdXtM7YP4Xp0zX9RJ7gJtEspaVUk+y5cd2SoSUUm+HIVlv\nZavfqrW+oJQ6AeD3lFLf0Fr/0U4vtiRZAoVUstpt+0HM7mDZr5A+LMNeLI6QL2svIcsoo75GXqlw\nTqz/OIDvSNabBxEnlcaLZUiU9VUR0bJntinutkRIhnbKyOKtd6i1DmBUpFCVh6tZ24mlTUYmkIJE\npGtqypYCGw2rXpmIBndEIPmx6PVl0KgNOnWvq9MxyhZX1PJGF4aUrCxCihWZ4clnRWZwwH4M0bL0\nNNG8LzNrr8DLk5xYhRpISxM8nSMvLwsAuvbGkwoKLXOVy3emqJJLqqjrwxWPo4TWDQ8hvZ5MQ2VB\nyv86vGVDrTW01picnDzoSzlSuAkk68oQM/oFAKfZ8qlknQOl1LcD+E0A36+1vkrrtdYXkukrSqmP\nw5QfS5K1VygkyZKfouTUZoONnnvOzPsIlq9csHfwBThCrBvngzh0HDe9z8BmYZ2EJV42cJSLf7Wa\nctQqnovFs7HobSZT/Oqq9nixzL4zM4Z0TU8btYpUq9tuQ7JM57XkiQzvslE04I4k5EZ3vp8tGcbp\neUjRqlTcfeRIQZ7DxV+DECojciUtmQNgPVp2SqMOiUw0YRQiIlfA8FGEw9ZLtavBpr54h1ApkatY\nMVvmhCrEOEOlQyJXnAjy+9fGk6j/6WvQv3PWbuLZWWz0sDPSkOAhR5xU+ci+zyBP+9N6rTeyB2ZK\nh9yTZXGYRxYqpVCp7CVZv7VRqeSP5bhJeALA3Uqpb4MhV38TwN/iOyil7gDwnwD8qNb6z9n6aQAV\nrfVGMv8OAL+wm4spSZZA0cqFAMwHL5UQqLXOzIwT1cDngVHVrL0GEa6dfrv1lQUHYp5Aniz6xj+H\n2dmqUyIlwsWN7tL0zqMXfITLerHMMilIMzM6/ZOYmAa/+GD6EtpYiO1taqXjGtvJEA8AG8nzLkS6\nSM2iUmC/r1Gvw0lxpwqIJFuSLBHpmpoyURK9QPWH/i1k4+lu1z0PMIUoIg+UZAR0Iw7zZclS4SR2\n3ydvnAepLB3yZVK4ZMSDj1zxf7wIts1OF2m2SE5pUG6/tmZ+ByJHV65k77lOx/5tuMpFx3DClVXB\niFTx330TpjwoexbyzguHE71eD0qNOniixCgogidLax0ppX4KwH+FeSj9O63115VSfz/Z/usAfh7A\nEoBfS+4BimpYAfDxZF0NwH/UWv+X3VxPSbIECkey6JutHOLGPh25uV1mZHEoVRkSOClxM0sBPAZg\nVGWsB5uNZSF/71OnrCK1suJPeqcpES7Zr9DENrgPNaNmGW8WqVT9vpmvVt39ZbK7Xabyn1lut+Nk\n5KJVqXiqvHkNMw35sUxPRDNP5Ie+rIeM0pTVVa+7ozHpura2fEdZTE0pDAakctHIQ1+vTCBLtqQP\ny3eMD5yYcUN8hKyq5Qsr5epVnjcrDzIBnl+TDwnJIpCBMISZGWx1wuej71wh0IhCH+ECgIsXZVyK\nLHUOYONT5Jecw+3H6vV6qPrbHJTYIYpAsgBAa/0ZAJ8R636dzf89AH/Pc9y3ANy/l9dSgLejWKhW\nq6hWqxjIMesHCRo6SL4s9qka6lE4uhcrhP34/aVHa1zEsMqGe/zx41UntoFGE9L7wHvpckXLlgYl\n4VI4doxyrNw8LAOFqSkTu0DJ8f2+MbhT6ZDUKaNm8b6EWZVKEikyuptIB+vPMq/jRjNI4kbPjatX\ns0qDLAnmjSjk26WCRVOufGWJWEi5Il9WHqkKlRC5usXb74QQIiiy7Oc7bpzSoexxyFvsUNNoCnDt\nmv9ld+ivJVsB0kX3SN6IQh7pIMs2nHCFcR3htPcOTFZeB4edYAFAt9stSdY+oAgkq0go3w4P6vU6\ntrcL0puLSoXEEtgnZ4V9iz74UuFOkNdKx7cvgUqFzwK4GxMTNuCRm96Xl5FGNNRq2ttGB7A+q5UV\nnRrbadvMDB9ZqFKVyDcCkFQrKh1Wq/4HGs/GarctkQIArc2Dut2mXCyz3qpW1s9FIwhJeZJho5xQ\nyWcJnVdOJSypcoNNqQw5P1/B1lbs3WaJGx9JSBcoyY/P7A5YEkWkiu8jU9oh1pOqRZ4smkpVS059\nyGu9I988X1NpAlOASKGmeVE67MH4Q30JD7xkCIS9WKH0d6tmhRpC81wsWS4EzPs3OLR+LMCQrFqx\nPyAPHYqiZBUJ5dvhQaPRKATJevTZZ80MfYLyIUXJPM8pBQ6SbO1G+fJ5OybZel+psA/j3TLZWLWa\nIU6cIFmypb0jCql0SDENgNu5hI9GpPY55NFaXLQj/njPw2pVo9sFKhWjcpkSpDknlezsaEJL4gBg\nY8NeR9bs7q4nHxaQTXyn35+PWqRr4K+9W9DvTCoX+bNsvIRPRSLCFRpZSP4rTqoAfxlOlhulIR7I\nNmuW8K2XIaXj9DGUye88zsH+E6p7/2/or/9t9zQzM4hnTOmb+sCT2EWkSIpfBFKpfIQMcNvt+LEO\nvydL4mioWIAhWRMTo37JKzEKSpKVRfl2eFC4EYb8idjpiLKhcTi7WVh7QbBm4Obh7Bdiz7yPVPna\n6hhpanVVORWW1VU5uhC4/XZbDpyZcUcNNpum5NfpqHTbsWPZkYVc1SLSRcdzJajRMGoWLxEqPUBP\nkA5ZGrRZWeahvbYWZ/YlPxY9bDudOCU1Mug0z4clSRdNNzdj8NtflgeJUPFG2hJ0PDWgBiYRRb7G\niJw4zcDkZcntfErzk8m+RKZ2MjpMjjgk+H4vGe8Q2peTLQ2rjhEoHFWY3wPg41182/iUQ6pcvpiH\nKAK2tzvIqlh8mXxY9DtvwpKsw0+0er1e8T7rDzlKkpVF+XZ4UBjzu+nLYpf505KZaG7OTb2fHjX+\nBKAS4gA25d1HuppwlY4seNscvlyrWaWKh5LK/rs0PbkSoxdVMKG76KGOCd1FjDpmsQ6ggR7qaUCk\n7nQQNyZRV/3kau0fp16LoaMIUIDu94EIiBsmo4eXBn2qFYFIlszFonY6Zt59H+g87XZW0ZLlyFAe\nlpwuL1ewseGWCenc5M2ana2kYac2rFSWBSmWga8LjTr0lQxD7XpC/Q4p1kGCG+JJxfIZ4V1fnl0e\nFudA4KZ8C65g+TAOqfJt436s7Dm4gsWVOCoXbrOpxWEuFQJGySrMZ/0RQUmysijfDg8K9+2G3NiE\nAMHav5u7ifyehuMSMHqIjfrahB7MqFv6+yxgctJuP3XKkiheKgSyIy7J8E59t3noKMU+8NIboY6e\niaiMejbLu5M8pLa3gZkZqLVrZnlmBpWueTBpkrYEVGfLPKq1hoIhXSHVqt/XGdVKttPp93Ua3yDj\nf7jaxknWsJGDHPyZJL1XtCxjI1zIcFLAVUV8pIob5EMKmiwZhl532Lphye6h0iGRLD7akED9DGvJ\n1CS/x6u3ATB/X251p783n/pKh6HSHy8LchWLWul0OjwXy0c4yY/l+7/u4eb3N90f9Ho9NAsQ6nSU\nUJKsLMq3w4NCkSwyU8zPZ8hWr2bbQdwcL9ZeqFnD4hl86+swCsMc3HDJVQC2PAjYbCwiTs2mSo3m\nIeVqaSk8uq7ZBKATFardNSyDs4huF6rTgU5OptptIIqgGw3o5KmYEqzNTcuKiK3Q3zNZVv1uqn/U\nodHDRIZ0kR+LkyPah1sJpVoV8mFNTdn8L2mAl4b3vKRw2/JHpSoXjT6kPCL3/KF0eE6qQinvkzDK\nilSFpBFdsWPyQkl5qx0e6zBq30N6bT5P9y8pQzTCMPv5srZmSVS7na0i5pUOOanyBZLyxtDXr8dQ\nit4PUrD6MMRpHVmC2IbtU2jfi8OuYgFAv98vW+rsA0qS5aJ8OzwojITMRxVKX1ayHO5ROC6mER66\nLZOrx3nwjNNOh8D9V9wDQwRrAMB8E181PCvzHvBSoSFXpHIpLC3xDCujTNDxJ5bN6000TDlPr60B\n09PQSY8dzSQC1WhAJ5KX6nSgu11LlrpdoN9PyRc2Nw2RaTTMuSSbEW51nXz419FHrWEefPW6IRz0\nMJ6asoeRakXTTY/YYHldnImQCJEo2SORZ2jRNjK8+1Cv2/yt5KrR7dL9k1cmlOAETEpv3AfF96eS\nch0uERs3gJJI16ieLCJY1cB+hujRrcRD3gnD/FjcCO8LJCXi5RNqtKaapO9/k48q5DfRNmzZsEDx\nNrtAv9/HwoK/qXyJnaFUsrIo3w4PCqVkAftUKpxDmFRx5H2gjkq4dtq3MC/1ffiHIydavvfHGN4N\n4ZqdTozpMp0UsIxFSkGkaG1uQielwlS9iqKUfJEEpbkKRqTL18uGvWZsI9nTTTYXK3YULC6wVatZ\nIkXTmPGELIlyL4Ne1redXs+SLf762V/JrgvFNeTlZknFyjfacFjJkL/2KMgzwfvO6/NnjXZuUrKI\nWBHpkqMKfaSKCBklwPMyIqlY4VGF12FVLB/I7E5K1tEgWIAhWTM5Aw9KjI+SZGVRvh0eFEbJoq+k\nPDacRhYO7/DqNEkmP8beYq8/cH25Wb4keENaFhbMeopu4KVC671yexbSNmmKB0xJEBGyURmMdKmE\nSaSPSE68klJhyjo2Nx0vlkqIk+PPIrIF2JIiwPvdmOnWVtpjjb4EyOpfo+HPveLr8v1SO0e9Diwv\n2zKh9GfNzysnosJ0HxhlZCHfpsU2wJAZKh2OAiJrpG7JUqFMfufLoZwsIEywBsgSM3Pfrqz8b/jS\nl/5P71VSP8K80mEe4fIZ6M1oQsD6qtbhfvnhmVibsEpjj/0M0GqteK/5sGEwGGB2dnb4jiVGRkmy\nsijfDg8KpWTRA37MkYU3PxdrJ30L+b51tk6WCvkw8h6MimVGY1G5kMMa4HW6D71lFDhKb2u9FgPN\nimED16+bkmDS4VlTCNmVK4YAJXKATiLbNR8GSGyiWjXzZI5qNCzZAuxT0cS5m/mESGlffSj5u2su\nDSX3p1Wx/G10fIZ2ipcghEYPyu30L8FvQ4px8BE34pluInwSZ6GkAsVVqWEDIvh23tMwdByly/NR\njKHzDYPGaEnwBKng0v4RDKGz6hH3Y4VKh6RG8e18vS+qIZuNJRUrUrJ8kCrW0cJgMMB0SEkusSOU\nJCuL8u3woFAkS5Ir9jSseEcy7QWmsb8jiEYJAOTlQR5guQD5sJS+NMCMKuSKFpCNZliYNkpGvX3N\neqcIxByS919tbhr/lSwhArZEaFJJzUpStGi/xI8VcyKVrJPqlVNGpG1zrD9jsk4l9+lkw94DnY5V\nUaamTE9CuqQ4zprbpeGdx0WYZTMlQnX8uML6umuG9404zCde9BqT6HZlCZCun+5BHwGbRlb5ItDx\nPOLD59ni56P1oyS/j4phJUPzmleuZIkVqVihOAefykX7nj/vlhjpdrWjCWMYotVGVsUiJYuIFWAU\nQqtkHRUVCzAka25ubviOJcZCSbJclG+HB4UqFxK4xCCUrP25qYnkjFOK2enr8LYrvmuIYT7k52FH\nhxmFyvzu7gON3hMaNVirub0MF+dN7pXJizTvpep0zGPPUyL0Djrg6ynvAQC63VR1SpUpetJ1u1AJ\na4nZ/lLRAmDJlXCya57LIGIhtjqKESoz5YSK1vlM8TtFtWoDV2nZTM06WSbk+xjI/oac4Mu8rLyy\nImGU+5W31/HnVrmqlRx1mAdJrqQZny/b15SjCznp4utlnAMnXOTJ4nj1VT7IQH55JBXLd0O0YX5n\n+jl6KEnW3qNUsrIo3w4PCkOyCAGCNQqWl2W5wFfOkyMLh5X8fOb0cREjv1k0revBlAan4YZJ2g9H\n15NlH3KSXK2saHfEFpGlKDJqFCsR6kuXjPRCJcLkfdfb22b79evmHFzZ6ve95EvzYV6kkiYXkj5y\nuR8rYUZxpRI2xhM2N9NzTjbsQ3SUtPd2O84Y3+Wt71vvKx1KcDGYCBeRq9lZG2QaBle1JNmS6zSy\n4bSyrCjjHoaV+oZdW94oQ9m70Ndax7yxRK54A3PAVbPm511VSxrd+TZudLeEi/63qfmzj1Tx0FGp\nYm3jKHmxCCXJ2nuUJCuL8u3woDDlwhwv1igI785HFkqCw5flg3CvVC3fA5YUrUkxnUm28XysudTX\nIz1ZRsHSafsXWkdoNgFEESZefdUs8BEBokSIbjesZiVxDU6pkNJLaV/esbnTSUccArB1uGTZIWKV\nSrYsSQylXjdlR+5ip3NR+ZGBL9qcrfA2SbJoPf+XoNKhzcWqYH09dtbxKiAdyxUsPm8ytGahNTFg\nSaryyoOTnm2+hHh5Xt/rEIgM5f2/jTLKEPCPrOXtdQy4IiVBRMxXPswzum9sbMH+n7fhKlnS5E7X\n2IH5H1+HLRsePYIFGJI1Lw1wJXaFkmRlUb4dHhRSydoFwQofupOk9v0E5WNNBKZ+T5ZBtiRlM7N0\n6lXKfACQzDVuiRBwSRhgDe6yoTe/n4g0CUUL1ap7rk7HerRMTc593dAXgYTdUOPbRsP83tvbcVqN\ntH0K/acYBnppl3iZKZnbFxasdysPFFJqIEuHc7D9M6V/yufZov3klwGNrALGA0r5KEOZqeUbdTjK\nKEOaz49y4ORKlgiJOEkewLfx/21SrLe3KVw0rzwoiR8nXfT/NcD+WgUOFoPBoMzJ2mOUJCuL8u3w\noDBKFpDPliJ6KPiRH90QIkwh07vcn1Sl/UAspqRiTcN86E9jedmQJ0ClZIr/8NR3Qq2sPPTSAAAg\nAElEQVQGVNqsLEoj965cAWo16IsXzTIRH9q+sWFKhPRkazSy5IirV6Ra0b68DNhsuiqUHGHII9ur\nVcfrZd4KIUd5yonxhPW2TTbMe7jteVb6lCx560vVChi9TCixtKRw9apGva4zzawBeXuHRhvmlQ7p\n/gD80QqAJVGh+1d6qEIY5s/K82b5ESJc58+Hc7K4ipUdXUg+ASJW3PNI5ncqD1Zhy4Qdtg1HUsUC\ngDiOSyVrH1CSLBfl2+FBYUhWiGCNqWq5h+SFkA5rb7Nf4A8rGTrag1EmqjBkqwqgmsQzKO8/tEx9\nr1aB40sDxKhY5SrxYSk6AamFUtUiMDWLUt+d0YakYBGhSliJE8vQaJhzkL/LN4qQWAfL2koVLbov\nGePRPI+BCNvkpF2XHMNJkoxlMNuzZCq8r5lSRAa/bA46J4+SoAR4wtKSwtoajVYMNYjmoMR37tni\nCJGkUUrdMocrhp8c+ZLex0UPwFQ6uhBwH07krfKVAfk2Obpwe3sD7pckPs+VLP4Ztw1bGiTyZVTl\no0qwAKNkLS0tHfRlHCmUSlYW5dvhQSHLhb75K1eA5m3eQ3wqlta+b95zMB++PlDG0DBQRtYw+Pwp\ntE6mu8tSIWBN8LalEGCaPZPxXSL9h+90UCGT+6uvpts19YYk0PtLZIhIF+x5wNrnpKoVESgiXvTk\nTHxYmoJKgVTRAhAMH415iZhc7MR0+IhENnxQ+0hWAcD/nYhwEQFz4SsTEmbhH3UIuARKErW89HfA\nJUhkjA8FlO402oEHknLzuwXdLnxKIgsfXShx/jzQ79P9ycmTVaLylawObPmQjO4xsu//0UMcx1hc\nXDzoyzhS4HbSEgYlyfKgMCRrB4rVaIePMjpQrifCNWxU2DiQpGsA+3DkpKsJS7i2YR6chl+srLhl\nQj6aEGCJ7xGgL10yylXIh9XtmtJgrWaeaLxESGVBQrfrkq1u1+ZkMbVKmt8B2H0oowoIK1q8HMjd\n5LxsKEuGTDoi4sXvacrC4odx47vMuArFNHB1a5i5naNWk/u5hEspBa1JpZJqFW/4zH1Zcr9Roxyo\ndOj7ZwkpVKNEOQyDBtBLVSkysM/PWzKVl4e1tkbeKwkeLtqHWxKlkYW8PNgRx9Eow6NbJiRorcvR\nhXuMUsnKonw7PChMudAHMd57cT7GpUtZ74hP/FpYqOD6df7BLMkWPbT2IqJhGPL8LkSoaJQhXUNV\nTAGfuVgmvtdqADpJiU5Gm1+6ZPxYPOeCq1lUIqRRhAn5SsHT3Ws1Q7aIsciSY6NhHs3cj8XLgoBV\nrTjpovsxua44GWGYQkQ/OM0J6XwTo39xGNV/JVGtaq9qZbKyzDXRBzD5s7inf3a2inabkxd5j/g8\nTnn3kSReXN3aFseOWgKU5UhJtuh+zOtjSGVvI0ZzBZb3MOSEi/uytrdjTE7StfOcq21YJYsHi9Ly\nBKxyRSVCGklI/1OGlB11ggUYJatMfN97lCTLRfl2eFAokjWCmrW8bEuDpOTQcr6aJf1ZNLpvGHZj\neg+VDGV5kP4GFD7qI1guZDBrtQqTip8Y21PGQLlY3I81bHShLBGGepjQC4P5sXiugWyvw0p/ulp1\nXiNdR8fwb93COB/X65ZsTU4aQseCSysDS64bDXN93M5FL5s1vrvT0DpSo5aXFa5csUREKlzck+VT\nvWhq/VkzMGSBjyKcZuskGeLmd4I0vQPZsuIoGOa9ChGufLzwgr9MyL1XRKy2t2kgg/ReEUiR4uyY\nSNUVWGJFahaFja6DPgtuFYIFFKhqcURQFCVLKfVXAfwrmJv8N7XWHxTbVbL9B2BMnn9ba/3UKMeO\niwK8HcVD4f/xPHexJFcc2QQInqQuR/IRdtpaZxR/FpUF63A9WdXkOigbiwJLQwRLo1Yj1cBtnbKy\n4iGYUWT6E0qzO4GHiPr8WN2uW4uUZIvM73wkIC0LRuMY4jm54j0Q5Ta6Fl/3Z8mOul1DtugYRrgm\nkuuleIfkkpKpSyQ8XvuUKHGS5CNcvu8qvjKhv6yYZ373bZfkiv8ePl+WJEz0xYGmE8j6sfhy6Dx5\nyO57/rx/NCHdHnz99jaVgdugkrkNEAXsqEDuy+LKFX+je2wblVxvDYIFAFEUQSklIkRK7BZFIFlK\nqSqADwH4XgDnATyhlPqk1vpP2W7fD+Du5OdBAP8WwIMjHjsWSpLlQaGULCAsRwXuZl+pkKtdBrGY\n9406JLJUh98ATyRoN6Z3/l7X4SpaPZgPfyqvTCfXMQlAY3WVt9JxH2D8rdFRlNUTpHLF1S2KbKAS\nolS2uPKVnMsxv3M/loxzAFzjOmu547ANPvIwIV6psZ3OF/JrEaHiLXiS+XgPTfFctfL0r/b6uDhk\nCx6ORqOBbpeIaV7Z0Ffys70RR2+xwzHKiEJfqbACc++O+uC256QSoRxpePFiDEueAPMFBLCKFf1+\n/P9onW3j668m6/qgFPej2pdwGPr9PiqVcVTMEqOgCCQLwJsBPKe1/hYAKKU+DOCdADhReieA/0eb\nD9UvKKXmlVInAdw1wrFj4eDfjgKiUqlgYmIC/b7PWFo8jJ/0ECJVhJAna7+8WhOwDwNueJcqljW9\nc/Dm0NxUPVfbAiKzUSfeKwA2QuH8eShqoUPwjC4M+rG44gVYPxYnToCraHEVihLjOVmankZMBnrm\nx4qpbMj33dz0jjJMyVWIUCXXxRVbX8Co2SerSrmESqeXIuHbz0e2lpYqWFuLk+0+gkOkZRbuqDeF\nrIKVl6vFMU6LnTx/FidbvkDSfHDju9YdTEw00e/3E+GTSntErDrsR/qvribzvBQIAK+wdT22D5UU\nzft5KxEsAOj1eiXJ2gcUhGTdDuAltnweRq0ats/tIx47Fg7+7Sgo6vV6cUgW3bVkemdu2Zg9REIE\ny+1fmNcn0JzR+mB8IPNs6Byjki/eu5AeUlRGJCWLttPvmNfr0EDL55t8U6TxnedjEamSx0jVSvqx\neAwEH4XI01A7Hat7yNIgMRTqX1it+s3xtG+y7Piw4jjrEeOjDD3qlmLzjUbNuTSCb9Sgr49hiIRx\nVKuUixUH93PX5cU8+NQiXyipPJfscSix056Gw46jGAf+C9axsdHH7KyNVuj3KRiL8uEA66UC3C8a\n12EJF70GLw+SYsVb5lCiu/0fvtUIFgB0u13UCsAGjiIqezoC3YtlpdSTbPkxrfVj+/2iO0V5lwVQ\nr9exudO+I3uJTsefVig+ICR3oHkqE7r2I9m7kJbz+haOgp2oW9KTRaB5Iro9mAekfR3zFhg/1sqK\n68Oq1QDdiWxkg9aAUoZAsYRHZ7Qhi3JIS38EnoGVLKeRDbSd+bF4+TC3XMjWa2Gczy0lAlnZqdNx\niRd/DUqBJ2K1B77Det3ehlyBosu6/XZbTtwS7QVDsRAuhiWuc4SCSXfimeL+LJmbFZKHfa11uE9Q\nXp8G5VaZHoNEigD7u0kSBbae1Cm6B7ihvQP3/aHzEMGidjlHO2w0D51OpyRZ+wGtdx09NAKuaK3f\nlLP9AoDTbPlUsm6UfSZGOHYslHdZAIUzv7fbdqx3rZaqWaOUCt173peuHpqnjKoO/ASKzMF7Balg\nUaxEHy4BGyT+JPPgWlkhAzxw6pRGFCUPNK1Nq5yJCVet4vOA3/ze7UIPBlAyH0uSLe6FovJhqFxI\nIwZpf0a64mrVXge12Gm3/UP5eCgpgcgTJ1bcNC8h+h/SiEO5uw2gz5KoPJBHztc+RxIqTrgWFxVu\n3JC5WbPQWn7h4WorERhfWx2CL7aBHwu4JcQ8gjdKKKkkWgT+ZeJfwxKgHszvRNdP6ybZMpEowH7h\nWGfreQlxDZa40fvUA+9NeKsSLMCUCycmJobvWGI83BySNQxPALhbKfVtMATpbwL4W2KfTwL4qcRz\n9SCAG1rri0qpV0c4diyUJCuAwpnfCfzb19oaMH8CgJ8nrK5azwftMzExhX5/C/mkSj7QuAHeZyTm\nOVaSjMUIP7C4ilWB9WANYPsV8gcNkbA6Ll8mlcIdVWghTOJgvixOrliLndR/1WwaglOrQQ8GwGBg\nmIB8kylDi5MwImWUacUN8QSfolWtZskZLxuS2uXrewhkU+EJtK9Usti6eHYWCn7PlC/awadAcXIm\nByHI89L8iRMmK0vuR+fPjvySzaCBsILlCywNHRvqbJCngkk/Vghx4BoBS7DIZ3cF1jdF67lqReoa\ntb8hYtWHHSCyzqbN5BgqG1oP5q1MsABDsgr7GX+YUQCSpbWOlFI/BeC/wjxQ/p3W+utKqb+fbP91\nAJ+BiW94DibC4e/kHbub6ylJVgCFULI4ISBXN/myGNmSA99WV808J1jcJuSSqmlkS4U0P8rorDyM\nW3LkkQ4+HxZFTvSg9TPQ+tuzHiyYh3y1iqzvCshM9ZUrbv9CwM3TarehajXoGzfMukYjS7boXEzh\n0v0+lCRN1E5HJnzKiIbkenS1CiW38Uh26dfirwVY0/zkpC1jekgWZLhpDqQ45jO056W5y3U+pYuW\n3ebRnCD50uBpe56PSyLP/D5KGOko6/NwHeZ/7DpsOnsHlhwRKSJyhWQd7deBbZXDlSv6fWk0IZnc\nb62Yhjz0er1ifMYfNRSAZJnL0J+BIVJ83a+zeQ3gJ0c9djcoSVYAhfqWw29anrjZbKIebWF1dSq1\nFEWRIVdykBxgMnesAb6HbMI7ES7AXx4cBzv1dJHxnUCKVvaaLl8GVletmlWrmf/xE8uxMyAASDxS\njGClcQ1RZB6PwvzOiZCOIhMDESJbwqsFAKhWHYVLexStuFo1BI95rnS16hBoLVQrDVjiBaSlRkX7\nMRKl+bphD5RkX3nf+4zveahWdSBk1E9CfFlZNM9Lh1FEx0/DfPHk8BndCdKXpWGVq1Ai/Lige3aU\ne16+D9dh1SZStDiRomsl5Yrv24PNwurBfCGhSAZStKzxvSRXFr1eD5MF6/F5ZFAAklUklCQrgEJ8\ny5HGTO7LYiPJpGWIIEcY2qQCngs0jEzRg4P7r2RTZ3iWQ/D1K+RRDTHMt/tY7EsZWjYBPoqY/wr+\nkYWO0V2OHgyNNGT7hshW2ruQwAzumsc68GbQUtGiffk1TE25qhX/5ahkKMuFU1PDCRVtZyRKe9ZN\nTLv3nK8c6CNEy8sK16/7SUa9DqysVHDlSnhUoVmvnamLEAHyKVgUTipHyPJ9QgQrL+NqpyMPQ3gF\n9n9RKlqkXnGy1IdVri7CEq5mMiU1i5Mu8563Wif3+NoPN3q9HqYS72OJPURBlKwioSRZARRGyZIl\nLMCONgQcIhYyu3MFS2t6EErVSqpa3Js1ahPpUREaScjb6viCS+1DvNX6NXzrW7+aLOmUb9RqClpr\nVBR74DPS4/Vl8alcJ03ySMhW8vdQtZolK259y0mGT8HXcRItYx3Yeh1F1p/l82FJyOvh+/H7msqF\n/HcfuH9TMsSHRgL6mkTz1jny30iWAWneRDuMGgKa1xKHky5fKrxvxLDvdWUCfCjx3Qc+yjBE2mqw\nitVkcl2cYM3BeLRoHSlX1JOQyBWpWVQSJHJl2uWU5MqPfr9fkqz9QEmyMihJVgCFULII/CHNs5AC\nvizeHYYIFi8bZstxcr30Z5E3ixvge559h4GTJ34u3mbHd40DcW1mnhLQteZqlnamKcQ/fqpIMXVL\n+cgXzcuehslyzOM1ZD6Wm5th+gnyQFORowUAOrnvUp8YlRKleiVKhik4oaIS5E0YRcXJU8iTlfVd\n+UuL8rwGklBpZElTSMHKa9EjCRb3aeXtN+o2CfqFNKw5nZcHAfNF4yrsSMBpWNWLjzokzxU3xZtB\nIyW5yke/38fs7OxBX8bRQ0myMihJVgBFULIe+eEfxqMf/7hZIOXjyhXjbE88RfHqbV7/Vadjdrt0\nSfqs6VvyOqwyRN+kCXl9C30loVFLhRL84U/n5R4swLbeoddootX6/wAgGWGoEm+W5/T9fkaBAmCN\n6kKxihMTPI0s5PsCkEzVTXyPIlcF6nTso5cTJjqO52158no0ZXsB3viGOIqsD4sRSsfY7vumzglZ\nQr4cEiYIWXXCnOP48Qpu3IiTSxiWb2W3+XsVjmaG55idncDGBhF72rcCqxSFFCwfQspVKKTUtz8p\nWjvJ4YoBvAPW+E7qVQzzP8HDRJswZIoIFn1RuQJLwiZRKlfjIY5jzFCT9hJ7h5JkZVCSrACKQLIy\naLddNtFsorJ2DcCiQ6Tm581z/MqVLCeYnGwmjWZ5yjrBp2rJ4e07ycbyxTjwAFKKjiBCJdf32PH2\nCfzMMwO84x0q4RiiLEMGNK2tSuUDN8HL9T6Dm6d8mDHAE9kis7tH0cqY54RvS/PICE6yaF21mi1T\nMnai6/VsfAPg1u9oO1NHtfiAnGhaUj2qUpWX+A7kt9Ex6laIcOWVCfPIziSsWV7uF4pvGHZOH2Sk\nQyiEtAZDsCiigZLam3Azr2bg5miRJ4uCRQmbJbkaE4PBoCRZ+4WSZDkoSVYAhSkX8jIUPQxJzUow\nM2MWr1wx87yiBbhdX9z735f2zptB5yXA52VjDYM0vnNiJRE701bro+mWVuuncfnyv0neCm3LhsmI\nwTSDOyFaZITnZULpv9JApnSoO+IhzL1aVObjyzx2gzV3VlLR4qxEpr03GtZHxtUnWQbl9+lgYF+7\nXrfz7HjNSdYuRlfRZXJumjdSMHS8j7AdO2ZVs9GJjo94DWvUvBsj+7A0+WH+MioRxsg2bSZvJJEr\nXiLkWVclsdopoigqy4X7gVLJyqAkWQEUUskiNJs2LyshXp2OJVj0Q+sJ/ggH+iYNuGZ3GuXXhkvA\nuDdrN5BxDVxZm2Dz/LWy3iLz/0wEy/VjOY85XlIj8iRN8PaE7khCTrY4q5AKlfxwidxAUqkSpZ4p\nYTZPmQftz4mVzMaSLXeScqHm60Jkis7fY6NNxbXwa65Wa87lhcBHGg5vnYOh28PHKWRDR4HRyBOp\nRiGMSqB86pXcV5Y0uZJFxnYq2ZOKRYSKE/xSsdorxHGMY8eOHfRlHD2UJCuDkmQFUBgli0va/KHO\nTNihCId8ggW4BMYX6zCMTNkh4i7y8oJ4mTCGbQ9SgatmVdmPQav1nzNno/Y65MtK+UjSq1DsbHxa\nwneUKerIkYS83CgVMJkGz0mZR9ECYAgXYNfxvymdU+yPatXkYdFxciRjHjhx4r8bL2sS5OhGVkqs\nVmmkIdg6/zyHLytrWHNon9JlE+BnoTWZ24eVCUcJ0/WV9PYS8nzku6LOBty8TqX40l+1n4iiCHNz\ncwd9GUcPJcnKoCRZARSGZPkgjFaL801cuVLJEKzlZbeE2OkA/T4RIK5akarFy4YUpUB5VeQFIcgy\nIZ/Pazfiy8niryf3NT+t1ue9Z7twQeOBB0xsQ0qwajVDnLh6ZRmma4inMmGohEjHR1Hay1DLxuGD\nQbotlqVFcZ6UcHkYhe507LwcZZiQuZS4cTLEDe7DiJPHn+UY3/noVXGexqTZP9THcBhJ4tuIcJnW\nOtl7JRReOp7CxCGJ1LBS4iivMc42An1xMInthkiVD/ubjTiOMT8/f9CXcfRQkqwMSpIVQFHKhY+8\n/e149E/+xDCkdtu9gdkDsdl0SdXyskl+5wSLHQj7rZl8WWtsO4V+hvobhjCK8sXBzezcHE/kanj0\nwL33/gNcuvSvsbJi1CzKalXLy4ZYBf7pfREPGoDylf8YcSHPFpBkZElliPatVu28DfGyKleyzomN\nqNVyy3UhqYg8W3pqyhIqnvye3MtB8/8eIJz0nl2XPZbmsiRlcVGlJvl8EsXX8W3ynFOw6ta4RGun\nBIuPeNSlQlUADAYDLCwsHPRlHD1onW0bdoujJFkBFIVkBRFFxpd16hS2OuYDXPqyCHx+crKC7W3A\nVZqoROHzYZHCxL1YpGJJ4jXMBC9VrJgdI8NJ7flbradyzkktVxT6fUMyjy/pLKEgcoPk0ZqUASWG\nahHM9B7TqERf02luQpceK7aOt/vRUZTtd8jR7Vo/VsBHlgfNYibimRm/Yif9YcyvRdc2rDdhaNtO\nPVm+7eTFG3+kYR7oOBlEynPhdgJ+jeVHbhFQkqx9QqlkZVD+xwdQqHKhfCDS/MyMIVrzU04IPJ/n\nAxPtyEMewVCHVbTIPCzjHQZif983lWEEyxfj4AOlVRt1q9X606FHXLoE9PvmARlFCq9ereD4EiOR\nWju+q8wjWJINn4E9FNtA875tnHABiLl6xUkU61eYjmRM7r+40XD1Fl+6PK3zlQ3FfErEAtt9oa1y\nv0rFvnY4zsHMG4Uxm481jFCFwuzZlSVTX/hoXs7bTjDuSEJa9rXuEeXYEgeCOI6xuLh40Jdx9FCS\nrAxKkhVAIZUsObItAZUK19ZsBbHZtOvbbUu8rKo1AVs27MFNngZcVYsQ+kY/SowDf2qScuUzu9O1\n0DUOx4ULMS5fruDUKfNQc8zvSNSrpSXoq1fdAxNzvDS+p49MST7yyJbYptmy8wjmviq2LvPBRIZ6\nMKLDc7ASYiWbRafw5WEBNoA0GXG40xIiXQqvuoYN8cPCR/PjDnxZWv7Pcd95RiH2dJzMzJLkapSW\nOvnX1GrdMebxJfYDcRxjaWnpoC/j6KEkWRnstO38kUeRlKxHzp61ownb4lt7MvqQd2vh3mW/wsXJ\nS6iVzrTYJtvhEHZyCxEpC2VvGbRaz410tvvv/2kApmxovE5myh+RlJcFvszWaXMCgE2NmV67ShXN\nyx+5zbcMGPLEvFtxrQadGOdz9/VtR0K25PbEpJ+eNwda/h7U+Jp++DmTn3FS3kPrOCoV83P8uMoN\nI11YUGxbhf3k/obJzxRbHgV7PcIQKL/TFgdl4vs+IvQZuVc/hwzlf30AhVWyeJRA4suqzMyAHja+\nUiF5tZaXzbzxZFE+D2AVK2ppM4ANPSRFi3uyiHTttJ0OYJUswoAtx2i1Lo51tvPnNVZWFFZWNKJI\nIUYFlVrNkCim1ozkuaIpjegTu/hyvFNiRiMQObnxKVUek3t6rVHkl4ronmTb46mprEFfMhpPyc8J\nKOU5WvKaPGXFas2vMvmIVKViDfF8uxx3IOEjan74/hoVzzral0/l/DjwnSsPVZQft8WB1hrT09MH\nfRlHD6WSlUH5Xx9AkZQsALZXjgT7NkZcgkqFND8/b0qJloD1YZQqmu+zdZuwni1qa7PJliWpGjcn\ni85D3qtsSbDVuj7k+CwuXNC4/37jyaLsrFSl0hpKKRPTwPKzQk4au0JbhUiOJIQlVLEwqaeqFJAt\nLybr0nPxkYeAJWu+iAefd4q/DoG/PoSvyufJCu0rttnXylxaMm/fwUrFTz58qfChfXyvYbHT0qDv\nHHmtdfKOk9cg7/sYhuyZoNxW67VjXl+J/UAcm7/TxE1onH7LoSRZGZQkK4CJiQnzYB72lfsgQGwp\nUbK2movpM5Y/a5tNsyuvMpqq4yy03oBVsnzp76RocYJF64HsQ2kcRcv31BzihB6CU6d+GufP/19Y\nWdG4/XaVlgtTgiJS0x0tQ/yNnSXaFvBh5ZroJcHyjTKk9Wxd3Gg4nixv9pWswYXM9/x4eEYP7hKj\npLTT+5v1XvkM8b5597gQgdubEt9+/b/v7v4usXeIoghKKRZuW2LPUJKsDEqSFYBSCvV6HV3fUPoD\nwCMLC3i037dNiIk53XUXpmpmmDknWESqePmQDtOa0qUBoyQRwUKyngeRAi7B6nnWA6OPLhywfSkf\nixSyClqtnY8KiyJTKjx/XmNpSaFOT/qVFeDyZZtNBQyvV2HExy03xNMy30ZIvFcOBInSfL2vnCjL\ngTyXC4JAhUqHvmvLIV4+UjbKyECfCX5pqcKCR/3vLv1ZQtEQYYI1Knb7YB2mXoVer4D2g1sU/X4f\nleHDV0vsBCXJyqAkWTkoEslKUasZ5rS8bObX1oCZGUfJqtXsqEIKNaYRhq5vnkhTny1TyZBnXzXh\npr/TesDtPwi2btjDh+9r0Gr1c/Ybjt/93RgrKxWsrChcuqSxurpoHm2XL3t9Wb5RhZShxUlO5rHO\nVSbCsA+WUTxZQEbt0j5GMxjYsp63nOcvHcazs/a8oWvLI1zJftUb1xEnfd88bRNzQfsMU8AWFyu4\ndi3OrM+C/wVnkI1zAMKRCqH9xt3m24/fXRW0Wq8f8fgS+41ut5u2iCqxxyhJVgYlycpB0czvj0xM\n4FFaEPVB8l0RaJ4TK/JnvfoqZV31Yct+5JGizCzAEiDu0aL13Fc1LvhoRRNI2mrt4DQCDz/8bgD/\nMlW0okhjglhnYirX1SrUYJCu0zzCgS9HkePfAizJ0ADUYJD/SOZkRsQkkFOH7+e0z5F+KaGSpeVE\nWKVJidKhL99qaA9DsT6z7N2PZ2aNQkTG38f/PPSGbnjW5cdDDL8uvn7YwyP0muUDvUjodDolydpP\nlCTLQamZ5qBw5nfASFRRZOp+7OHNCRahVrNKFu1qvfM9ZNuQUAmRRg4S4eKjCanEB+x8ZCFHBa3W\n3pHZF1+M03BSk+agnRGGankZmkYMLi+7EQ6AsyxjHzh45INmpEYmK4H2E54pLYiQnM+Y1VmEgvd6\nZNwD+3F+l33wGPpjG7T3Z9g+/N1z17mBHJOT0rRMcQ7yLzDKCLIQ6Rr1vYpz9q2i1fr2Ec9T4mag\n2+2Wpvf9Ao+8KWCEg1JqUSn1e0qpv0immdh/pdRppdTnlFJ/qpT6ulLqH7BtH1BKXVBKfTn5+YFh\nr1mSrBwUTcnKgGSqTgcy8oVIVbvtzgOAUhWY0gpgvSKkSNHTkhMuMsHDM/XdQqOWCvnr7Q16vXej\n09G4fNl4tHStZn60NuRKsAHtC+NkURlDH7WSKA37IMjbx0PEvMQpcD7K9cpke0nQqEnP+Xi+lvzx\nXfu4ggARstFUL+/Fs9elv07F2TbeuXZLOolg+c6jUH7EFg8lydpHFJxkAXgvgM9qre8G8NlkWSIC\n8G6t9T0AvhvATyql7mHb/6XW+oHk5zPDXrD8BMhBEZWsR1580cY5zMxkSlGkXDNSvXAAACAASURB\nVMmpnDe5V7xUOA03eR2w8QqSUFWQVbV2hr1UsQgXLmhEkcb589o+1Ws1gBKek7JhimQfImQ+OI/R\nURQhUpFYIGjmUSxIlLeXok/BCn3gDCNhIcLEf+h38/w4mhJdF9vFEij3EkLrfRi2r39bHlnKqmD5\nGJV48fs+RLD4tERR0Ov1CvnZfiRQfJL1TgC/ncz/NoD/Mfsr6Ita66eS+Q0AzwK4facvWHqyclBY\nJWt52Uypj06zCXTc+4/Khz6flsE03BiG7WRKRIqPAJTLw3xYIeO727+w1Zobcp6d4eLFd+PChV/B\n0pLCtfYEFldWzIbLlw25oliHhHz5gwVgCSwP7oS1NIeKTL5tmXBS+Vq0HEXh/jR8HwLNS7M7hycC\ngr+ud1Sib9k70tA5UzoXNsEn5dhcHjOMMI2CcXxXwyBbScXI3t++c1fRaj2ww9cssV8oSdY+ovjG\n9xWtNSVdXwKwkrezUuouAN8B4Its9f+slPoxAE/CKF65wY6lkpWDopKsRz77WbuQjDas1Zxc0nSe\ne7Lm5/mzmKISSJUCm8qHCvUU9BGnnZQLn0WrlSmF7ylefFFje9v0uCMPFpEqACbWATBBpQlpzfVl\n5WRpjauVDEOQSuR9kxPf9pxS3x5c0yhwVSj7rjhlzAQrK7aFTqVif8Lv7F7+BqHzDXsNH7kKnYNC\nSEsUDf1+H5O8y0GJvcX+K1nLSqkn2Y8zbEop9ftKqWc8P+/k+2nqwRaAUmoGwMcA/C9aa2qB8m8B\n/CUADwC4COBXhr0dpZKVg0J/2yE1S4CqiFeu2On8fLbloatkdZBVqGiZDPJ1tn8FbiNpifwIh1br\nbcFte4XHHx/g7Nkabr9dY6AVKvW6VYWSEYY68V6lzZyTdji6VjOjCxPsNUFxlCNfeTKnnQ/fnntt\nw75N8mvw9XT0gRNNOl6Fd/FhXA/X+IrX7rxeLnzN0DnoPfa/Zqv1xh1eS4n9RK/Xw+zs7EFfxtHE\nzVGyrmit3xS+BP09oW1KqctKqZNa64tKqZMAXgnsNwFDsP5frfV/Yue+zPb5DQCfHnaxpZKVg6Iq\nWQDwyO/8jh1pmNzUpGbRPU7TtbVh9z3rKO0Y0ZtsmXoLVsW+49xCf4ZWK1ed3TPcffd7cOGCxosv\nGjUrNbNXq0AywpB8WE7JkMgL7xNJJnjh2RrlcS61mMwxHvUJgN/wzv+IOaMIQ68RbBrta0JNx/Af\nfv5E3ePqVYgQyX1GHeRog0lH9XTtlGBRqZy+ROSRq7x/JPpioVB+fy0u+v1+2bdwv1B8T9YnAfx4\nMv/jAD4hd1CmFcBvAXhWa/0vxLaTbPEHATwz7AVLkpWDQitZAB750IfMTK2WaatDvQujyJYO+Xw+\n8p5mMox0VPwZWq2/POYxu8Pjjw9w4YLGhQsavekFUyJcWUmN8NTLUBP5YsZ4wJQSff2KONna7wKX\nzyy/F+f3GuqHgZOv9PV9NHIUE7p/H19pka/3Hz/Oa456HCGUUE/LA7afNbuXKlZxEUURZkb7ICwx\nLopPsj4I4HuVUn8B4HuSZSilblNK0UjBhwH8KID/3hPV8MtKqa8ppb4K4O0AfnrYC5Zft3JQZCUr\nxeqqo2RxUOkwCYUXilYMo1TRt/hJjNckNw+yVHjzCRYALC29Bxcu/DLOngW2t4EJLomQrLK0BFy9\nahUqCiyl+ShKy4dpkCmBhYTutkg1arSmb316LG+x4905TGzG7uNGIyYDnyAhQ7x45ZG25/cPDb1b\ntF62aRp1NCz3X43z1y29WEXHYDAoSdZ+oeDGd631VQB/xbP+ZQA/kMz/MQL/xFrrHx33NUslKwdF\nV7IA4JH3vx9YXka9Fqf5pPT5QaXDmRnb8jCKrMrlgudfcXJZF9NRFCw+gvDkgRAswqc/HSclQw1d\nr9uyYa1mVC0Z21CrQc3P24gHVioEYE30QFr3CsU+SAzTVEY9ftT16XZW7gvuQwpS4PpGQags6CsR\n2h6Gu8G4nqxxCJY8X5/ND+B/h8xyq/VdI75OiYPAYDAoPVn7iWIrWTcdJcnKwaFQsgA88hM/gVeu\nVJyyIIGaQnPCZbZTE2geNOoL6JNNoEPzcoRiBa0WL18fDM6efW/qzbq+WYeu1w2BWlqCbjRspMPS\nkvFoUWAphZgKAsantL3iydii84xSQOPzuyoB8nMEPpCGvob0ZLHync+TtVMsLZmPnp2dIkRwRj0Z\n7cvVKqlahWgwrZdxFrZPYYliYzAYYG5uf+JjbnnEsXng7OfPIUP5iZCDw6BkEd7//kdw6ZKZ555t\nwBItTrhcglWHJVi0bgLZjKxhfiy7/mYZ3EfB175mTPDttjbq1W23QU9NuUSKmeDJCK+SJsicMKXm\neeHR4vN8Wfnc2sLJPaqjKG+d2eCRjAJmeeccoTT5nG0+T5bfT6WD+/DdRvNc5Wl5u4GPYBF4dIkk\nrZygmQy4UsUqPkolax9RfE/WTUfpycrBYVGyCB/60CP4oR8yLaQpo5TQbJoYByodGjLVZ9M+LJki\nojVg60Yzurda/miJg8aLL2qsrACLi8BUo2HJUqNhVK21NSeoNI1zqFahZmagOx2o6Wnozc2Urarp\nacTdrol7oOPoQ6BWs/O0jSW/A56if7WaEqAUPqmHRy7k9VbMQyC2Ifc4z2uFlahRC6B5niu73sf/\nsq+RFxA67HpoO50jb4Sh71wKZSPow4HBYIB5t/1Fib1CwT1ZB4FSycrBYSNZAPCxjxlFiz/rubLl\n3v892KBRrmSBzcvUd1sOtOtMtMN+B4zuBs8//15885ump+FWY96WBZeWgEYDmljpsWPWp0VlQ65y\nUfQDmO7BIiAcJUvEQ9BrErnSbJ/0D5STU7DTcmKqAQVG7o1asxunXDhOVMMw+AhWu81JEClJm/Iq\n2fyWZ3+wfYCwZysS83w/2xy61QpG95QoEEqStc8olSwHpZKVg8NULuT4/OcfwZkzRtGKIvP8JlO8\nvU9JseokU/nNXZYGiWBxxctMW63ipydvb2/jiSdirKxUsLSkgJMnDVm6etVIfES4rl41qtXSEvTV\nq5YUUWyBjHRgbJbHITjcQmzj4KrWOI6icdaPdlLtTtPVu1ek/Kvzzhv+DQeDnRzHt2951nEMCyAl\ncKKm0Gq9ZcTjShw0SpK1jyiVrAxKkpWDw0qyAOCb33wEADA9/WhaJqQoh3YbUGoCWvME95CCQtuy\n/QpbLcBVvoqJ69ev49lnn8VDD70P3/zmL2FxsYJ739AwpcJazUwTMsX7GerpaUOuOh0T4wBkRhsS\n0u0JFBjpGAwcRUslsRAArC+Lxy8k65QsHY44ipGfI30Nj6fK2T4m/MVG/jKhUp2Zv3pVqk15x+WR\npziwPWRoJ8gAUp+hlhOu0INDoywIHC7EcYyFheKq7ocaJcnKoCRZOTiM5UKJzc1HcOmS9WllB2f4\nRwZarxatr6TbWi2ZPVRcnD9/Hq+88goeeughAMA3vvE+nDjxT7G4qLCysuo8HvXly9CNBlSiaKFa\nNeVDwCpZzLMFCNM7/MqUfLx7KYMw0wNwey0GjhtZvcqJTHdojdxnCAHzddqR84Ejh+0wBHlxDKFt\nu42NoFKhVLG+e5fnLXEzMRgMsBxoS1ZilyhJVgYlycrBYVayOO6++5F0/uMffxQm6DyGS56q4oev\n66PVev7mXfAe4Rvf+AZqtRre+EY3ffsLX4ixtKRw7BgwOTUFTE0BGxvA9DTQ6UB3u8an1ekYspQo\nXXpzM2WpsmyokcRQVqvQ3a7ZHvqwYcSF90nUfLswyTvwxUrAVcA4RtGDQnAIGGdUldHUG61dwuV7\nS/IIWXhbnnqVadSJ8QjWKAqWuYZW66ExzluiCCiVrH1ESbIyKElWDo6CkiXxgz/4iLP82GPvTeYG\nMA+XbbRan7zZl7Wn0Frj6aefxh133OH9xtrr/Sy++c1/gsVF4MSJGcw2bgCNBtTiotnh6lWjaC0u\nQl+7Zn1ZibKlWV6LToi40xJbkia6LsASKl8EBFPH0tKjR0kaNvowo0Z5MMo+ofO71+Af6Zj11rtU\nL/s5bNaT5+raNbu/9GH5fVkUEBq+UndZlhMBN65BxjNw0HI5mvAwQmtd9i7cL5QkK4OSZOXgKJIs\niVbrgwd9CXuKKIrwxBNP4IEHHsDkZNiQ/9Wv/iyOHftFzM1VMEsm+JdfNqrW9rYhUoDxa/X7Rp1q\nNKC6XaMeJWRLASZNvdFImYXj10piIABhbveRp+S4SreL2KOipufpdk3Ol3wtz77OfKhcKPZ1lDDp\n7RIIf54Oi5nw+7Dsrn5yFyZYPmwiTJA4emJbDFfBipEtEwKt1oOB1y1RVNDo2qnk/6fEPqAkWQ5K\nkpWDiYkJVCoVxPFetAApsd/Y2trCU089hYceegiVEcpZ/+2//RwWF38RnY7CqZmGIVjJyEIFQF+7\nZtZVq8CNG9aXFUW2tyGQRjGkIwh5Pla3631tIkcqiuxjm3KyPCqXk8WFAAUZ5p+S+wZqccNUrnhu\nzu7D/jWG+7B2h+vXZXQCkF8apGknsMwNir58LN9IQ2O0L8uEhxP0WT4x4etuUWLXKJWsDEqSNQT1\neh2dQxjlf6vh6tWr+PM//3O87W1vGzF2wODJJzXe9CZg8b5jmDptlEt97ZoZWdjpQDUapnw4PW0U\nrBumtKi7XSfeAYBRvYCUbKU+LQCx9Fj5CBXP0OLqk9gvXQ9XeQoa2KWSRWzIR6ZkhIOzySypGzeg\nqbQKIIqyEQ4yaJ5jMNBBkzwpVb5jxIWKZV9Zj28D7IjC0HbfuqzZvSRYhxdRFI30BazEDlGSrAxK\nkjUEJckqPs6dO4fr16/jLW95y1gECwAuXHg/5uZ+AXNzFbzu26rA3JztkZVkZaFWM6VCwJTpGg1D\ntuCOKEyZAZX6fE2ZWUnRCSUFnJiH1FDPiRcnWr5yYGh7Mq2024hnZkxplPun8kqCoW2avFX2PC4x\n8sU2+AJAh5cTLfHKM7vnjXj1ETKJURSsUFxEicOCXq9Xkqz9REmyMihJ1hAclRGGRxXPPvssms0m\n7r///l2c4+cxN/cLqNdruOOOFVQSQoVr16Dn5syHRqMBfeMGdL9vPFHT06mipQDj4ZqetlPybpFB\nnilPQI4/Sya/c+LlG5XoI1sBBLOxAi12fMsAEPORWdn4NAD+OAfJpaRade1a7F0PmL6znrX8bIF5\nX4mRL4fIVQSrYtFDQ+Nd77rHdyElDgm63W5JsvYTJcnKoCRZQ1CSrGIijmM8/fTTuOuuu7C0tLTr\n833xiz8P4BcAaNx1og49N2cIFQ1+uHbNqFjVqiFbgE2CbzSgtTbkS9wvoaR3Bzx8VJAxboKXipMG\noHo9aDL4ewiXGgy864OEK0fJ8h07SsQCz2T1HUfzoe2SYA0GpFo5OmICrmj5CJb0Y8nRhqHE9xin\nT9/Axz72MTSbTSwsLOANb3gD7rzzzvKhfYjQ6XRQGyPUt8QOUJIsB+XdNgS3wgjDw4Zer4cnn3wS\n3/md37mnJPiLX/x5NBr/B+bmJrGwugrU68b8HkVAv2/KgFevQs/NGULV7abkCo2GIVib5iGf+rKm\nppzkdgUglr4nrm7JOAc2n0l8l4GoUhGLIrfpNd8npIBJksWvlbYxUuH6sEKeLH9SF+3vLwOaddev\nW79XHPPz+CIYwNYRiSLSJUv+/FxydKFUseK0bU4URbh48SLOnTuHP/7jP8Yf/MEf4NixY7jjjjtw\n3333ocm7spcoHLrdbml630+USlYGJckaglLJKhba7Ta+/OUv4+GHH4ZSavgBY+KP/ugfYW7uA7jj\njgmszM4a0pSkwOt228Q5kK8KgEqiHPT6ullHhIfumySclOBEPYg6GidUpIilrX7YNsBPjDJRDJ59\nvXEOOaMWnddJrjNmOfmDQXjkbda8buc5IbPbs/4ueq9dNcvnw/K10fEpWXwdH/nZQzZ41CVYAFCr\n1XD69GmcPn0aDz30ENbW1nDu3Dk8//zz+PKXv4yZmRkcP34c9913H1ZWVjK/Y4mDRa/XK7847ydK\nkpVBSbKGoPyHLA5effVVPPfcc2OPIBwXv/VbA/zIj1RQef0kjieKVnztWqpmpcSKSohaQ83NIWa5\nWWg0TEI8RTDAPN5Vt2s1lCR3SwGIq1W33MjJliBefDsQML4jn1AF1asRyoU+U7qZhzM/GGisrYWM\n8QavvuonabQvkavBAEmXAkLeaEIg34vFS4XSVBaBK1l5jZ+VUlhYWMDCwgLuv/9+dLtdnD9/Hi++\n+CI+85nPoFqtYn5+HmfOnMHrXve6skxVAJQka59RkqwMyv/6ISj/IYuBF154ARsbGzsaQTguVlb+\nMb74xfdjbq4C3DaJ5ZMnjTKV/MTXrhlitbgIvbnphJFqIldA+mET1+umpBhFhpQxBYsTJ236HQGA\nJV4AdHIPKnodwEuMVLeLmEIWh5UDA9tzexcm8/wz1J0fNiLQR7iy68wxbpRDu829UpI0bSTTbbFt\nK5l22HZ6TWl4JyWLSoRRLsHyodFo4MyZMzhz5gziOMYrr7yCc+fO4ZlnnsEXvvAFzM3N4eTJkzh7\n9iyOUU/MEjcVvV6vLOnuJ0qSlUFJsoagLBceLLTWePbZZzE9PY2zZ8/etNfd2PjH+NSnfg7f+70V\n1OvAzOws1OYmUK+bn+PHEa+vpyMPsblpW+6QH4vCSBNPVmoc5x9CSSkx3cblnnrdjlJMII3xAPzR\nDaFy4DAlS5i4fQQsZHb3rQ/lZfnysGidGzoaItQD2FGE0rwuy4i8hNhl82GT+7gES6JSqWB1dRWr\nq6t485vfjHa7jXPnzuGFF17ARz/6UTSbTSwuLuL1r399aZ6/iej1ermdIErsAUqS5aAkWUNQKlkH\nhziO8dRTT+E1r3kN5ufnb/rr9/u/iMcf/zlsbiq87nUTWE1Kh2g0gGvXzPTkSeDGjbRECK1tqZCH\nk9brZiSg1k58g240DNEiMsM+oHSinDnKnUfJ0uwepXm+zke4KtvbJjMLQ4zv/OGfzEc9v9nd1wg6\n1BzaN6LQdx5TdgTCCe+cROWVEzuw7zr3YkWwKhYpWHvfLmdmZgb33HMP7rnnHkRRhJdffjljnr/z\nzjtx7733lkrLPqLf7x/IZ8ktg1LJyqAkWUNQKlkHAxpB+KY3velAie7a2i/iYx97H971rgq63RpO\nn16B0hqq0TClv2vXoGdnTTL8jRuIaeRh4rFKvVbUkgdI87UAa1BPiVQSzUDzEqOa2Hm0g1OS5PvS\n+5pTLvQRsFDUAhGutTWed5UtId64YUuJIU8XkKdoxbBq1bDRhduwUQ9dNt+HVbK4B2v/+xHWajXc\ncccduOOOO/Dwww/j+vXrqXn+6aefTs3zZ8+exYkTJ/b9em4l9Pt9zCRfLkrsAwpOspRSiwB+B8Bd\nAF4A8C6t9XXPfi/A+BAGACKt9ZvGOZ6jJFlDUCpZNx8bGxv4yle+sm8jCMfF8vIv4SMfeR/+2l9T\nqFQUTp48gcr6mnFlaw21tWWys4hgra87BCgtFZJqBaM0qUTB0kzl4nAIFW3zKFTe0mGt5idhPsLl\nI17iNQAgTsYr8hGFeXlXVoWS63Vm+40b5pxxLM30shQYiWUiW+S/2hbbNVyjew8uYbPna7W+Czcb\nSiksLi5icXERDzzwADqdTmqe//SnP41arYb5+XncfffduPvuu0vz/C4RRVFJsvYTcZwGMBcU7wXw\nWa31B5VS702W3xPY9+1a6yu7OB5ASbKGoiRZNxevvPIKnn/++X0fQTgulpd/CY8/DnQ678PmpsLp\n0/NonjRNpfX160ClYshWkk2lul3jz+r1HBKVmuDBSoakZrFldLtZwgNPabDXc4kT3z456QScAnDL\nf4HoBwfsfLL/tZn3GddDniu+3X0ZQ67kfjrhsb6WObI0KMkYkDW6azbPRxH2DoRg+dBsNvGa17wG\nr3nNaxzz/Fe+8hX8yZ/8CWZnZ3H77bfj7NmzmJ2dPejLPXQYDAYlydpvFFjJAvBOAH85mf9tAH+A\nISRpt8eXJGsIynLhzcPzzz+Pra0tPPjgg4UiWBxPPfVL2Nx8HzodjZMnm1g83kSl0TAxD+vrpqfh\n8rJRsyoVYGoK2NqCnp6G3tw0ZcbkXCn5qlZNSY+34Em2xeSxIuIlvFgKJtU9JjMvJ2b1OnSv56zT\nPkIW8m/BJV295Atqj/nF+TwRq243q0TxvoW9np+YAToNHwV8rXRoFCEnXVzZom/QpGr5VCwiWD2Y\nSkC/MARLQprnNzY28NJLL+H555/HRz7yEUxOTmJhYQH33HMPTp8+XZrnR8BgMCjJ6X7i5pQLl5VS\nT7Llx7TWj4147IrW+mIyfwlAKMxOA/h9pdQAwKPs/KMen6IkWUNQkqz9h9YazzzzDBYWFnDvvfce\n9OUMxZ/92S+h2/0ZbG5qnDkDLCzMoRLHUFNTRtm6ds2Qq6kpYH09NcLrSgXodg052toypcLpaUuu\n6nWAeiGSN4uTLEG80pR5Rr4ynqt63XiziA35MrP4w1mqZ8m2tXWA1KI8s7vxWbnr+H6+EqFZ76bC\nu7lYMfwGdyJb2/Ab3XmrHHn8AEbBejMOC2ZnZx3z/IULF3Du3Dn84R/+IeI4Ts3z99xzT2meDyCO\n45Jk7TNuwhfkK+SR8kEp9fsAVj2bfpYvaK21Uip0sW/VWl9QSp0A8HtKqW9orf9ojONTlCRrCMpy\n4f5iMBjgqaeewute9zrMzc0d9OWMjBde+Ke4evU96HQUzpxRWFycR3OqZ8qG9Tqwvm7UrIUFU0as\n142iNTVll8mHRVENgN1eqZj19II8kJQS4pkSle7n8VypXg96ZiYtXabwKFlaqCH9AfmwQsTKmt2l\n5wqw3M5XQvQRL5rf3uYhoTRPKe6SbPnULGr+HLN5UrG6ADpotb4bhxW1Wg133nkn7rzzTrz1rW/F\ntWvXgub548ePH/TlFgZRFB2qz5nDiLyI4JsBrfX3hLYppS4rpU5qrS8qpU4CeCVwjgvJ9BWl1McB\nvBnAHwEY6XiOkmQNQUmy9g/dbhdPPvkkHnzwwUNp6N3Y+Gf48If/Id7xjirOnAFOnpzA7OwS6vU6\nNJGtKDItd4jgbG3ZwFI+yjDxaunECM+ztngqPO2bKR3SSMKAiV1Xq8DkpPFpiWyuPON7lPAbtwRo\nt29vu1PAX0J0S4Tc+K6xvp4lZfajep1eKVlHL0QlQWl89xEtl2C1Wg/gKEEphaWlJSwtLeE7vuM7\n0Ol08NJLL+HFF1/Epz71KUxMTKTm+de+9rW3dFlxMBiUEQ77CNnMqoD4JIAfB/DBZPoJuYNSahpA\nRWu9kcy/A8AvjHq8xOF7st1klOXC/cH6+jq+9rWv4eGHHz7oS9kVTp/+53j2WWBz83/H5qbGyZMK\nCwszmFmdMkrW+rotG25umnLi5qYhPFtbhvT0eib9fWrKjj5MSnw88T0lXkkZ0CkdUio8WOAov3e5\n6kUlyOlpqF4Pqt9HPD1t1glP1iDhK5xYbW3lJ7vTvjzKwVci7Pe1OAc/zwDux3Ukpr4SYo8td+CS\nKxPZcNQIlg/NZjMdjRjHMS5fvoxz587h6aefxuOPP465ubnUPH+rmcBLkrX/KDjJ+iCAjyil/i6A\nFwG8CwCUUrcB+E2t9Q/A+Kw+noxsrwH4j1rr/5J3fB5KkjUEpZK197h06RJeeumlQ0+wOM6d+2W8\n9NI/xNmzKiFawMmTxzBRr5swUjLBr69bRSvxZqWkJxlRqBmZImM8gLTkR8RLT01BT0yYfbhqRX4c\nX2CpMLmnClgy7XTdyIyNDfORyYkVV6p8Iw796pWd+sqFcQysr5vX0noDFj4yRUoVqVgdsa0nfgYA\n2ofKf7VXqFQqOHnyJE6ePIkHH3wQGxsbaVnxwx/+MKamprC4uIh77rkHp06dOvIqVxzHJcnaRxRd\nydJaXwXwVzzrXwbwA8n8twDcP87xeShJ1hCUStbe4rnnnkMURfiu7yrmiK7dQOt/jq9+FXj11Xfj\nzJkKOp0YCwsNNBoNzKwmatbEhNl33ZTB9NQUYsraStQrMo7qpNehUzJMmko7fiyxLp3SiEM2wpB7\nrnRyLQAQV8xHQbfrfkQSeXKJFSdc2tk+GOi0dOiOQjSG+E7H7N9uWyLW79P7JwmVNLZzgzv9EMEi\nciVLhX20WvehhMHs7Czuvfde3Hvvvej3+6l5/nOf+xy01pifn0+T54/iF8zBYIClpaWDvowjjUDX\nrVsWJckagpJk7Q201vjqV7+KEydO4OTJkwd9OfuKixd/BZcu/a94wxsUlpc1VlcVogiYmjqGiclJ\n6CiCqtdtuZAb4cn4TtlZnY6Zzs8b49PEBPTkpPF8cQWrXjcK1vZ2an5XcYy42bTbkJjgSeliD1FJ\nluR6l1iZKalcvR6wva2ddYBVqq5dy64j0rW5ac/hLwXGcEuFNGqQh44SwaLlXrK9jVYrOAjplsfE\nxATuuusu3HXXXXjb296Gq1ev4ty5c/jWt76FL33pS5idncWJEydw9uxZLC8vH/Tl7gniOMbi4uJB\nX8aRRjHDdw4OJckagqP4be5mYzAY4IknnsB99913pD0gjz22BqvC/CyAWbz73e9JYh6A2dkY09M1\nzM7WMDXfhKJS3eYm9NaW8WtpDUxOGnWLESLqf0ilRiTlQkXbYL1aKfHiCpYkYwC2+6ac2GgodBOy\nww3udAo+BSyhIjUK4OQpu5/0aw0GVr3q9Sg4n0gTlQqlesVVLJ7uLkcQbgKI8IE7XzQn/8Qn0hd6\n+W/8DZTwQymF5eVlLC8v441vfCO2t7dT8/wnP/lJTExMYGFhIfV6HdayYlku3F8UvVx4EChJ1hCU\nJGt36HQ6ePLJJ/GWt7wFVU8vvsOOxx67H8CnAUyDZbYn0zX8yq/8DH7wB/8J7r5b4fbbgdVVQz6m\npxWmppqoVDSa8xNG2UqIVTw5CbW9bUqFlQqwvW3LfL2eUbXAyFViWqdovRrRbAAAIABJREFUBwWY\ncNLJSVsSZA/FuGr+7XubtmS3sWHmt7bggLxYtB1IvfmOD4sULyJWgCVe/b6Zl7lYhnD5YhhIvYrF\nej6CkHoSUrCoUa8+8OCmyR2LEjIfx4Zs9Xq47ROfAKIIL//QD6FEPiYnJ/Ha174Wr33taxHHMS5d\nuoRz587hS1/6Ej7/+c8fWvO81vpQXe9hREmyXKgxg8NuSSXwJ3/yJxEVu1VAIbG2toavf/3rR8rg\nTnjssZeSOdm4eIot81YvM/jrf/1nU7I1OwtMTyvMzmpMTZkP/6kphWYjxiAGqr2OUbWERwtIfFW9\nXkq8tMzNYutiFkq5ndiVNjdjNBoqLdUBSGMUtrbcj0haz8uANGpwY0On5IpULdqP9yKk+XZbO5EN\nvV4fbrPndjLlJcEYJteKyoL0Q/v1kuM28YHvmzPML4rMC0eRYXj9vpkndpikUr/8fd+HEuNjfX09\nNc9fvnwZU1NTWFpawr333otTp04d9OUFobXGb/zGbyCKoiP5hU/gQJq+PqCU/uw+v8Yy8KW8MNKi\noVSyRkC9Xi9J1ph4+eWX8fLLLx85gvXYY3/Glibhfm/TMIRhiq0norWOj370AwCAH/uxf4SVFYWV\nFY3ZWVK1gMnJ+P9v793DozjP++/v7EErIQsEAiEkMEY24mCBcO24BOLG169J66Zp07Rp0l9yvUnb\nX17SJvldudK3b+I0TW2SNykHn4hxbYlfYpwY1zYS5mgb2/IBG3xAHIwAcUZgDBgEiIPEnuf9Y/be\nuefZmdUKtJrV7v25Ll2788wzM88u0u6H+7mfezAs4WglJUZeVdENiVyqKJOqaNSIUiXysjTAvP1O\n4vc0HDe+RIIJkQoEtGRSuxHY0dHTYwqiGcmy/j+K5IlPDZq1sWif+R5QYjvdI5b28aR3YzUh3eYG\nMIuNqlEsEjCaClQF6wqAXtz/P2uASGIKKBYzRYtCaNGoMejyckO0IhEjsvX668nnJ//iLyBkxvDh\nw1FfX4/6+vpk8vyxY8fQ2mp8vY4YMQKTJk3CtGnTcmomIJYIrRaAYLmKRLKsSCQrA3784x+ju7vb\n7WEMGQ4cOAAAqKurc3kkA4cpV/xPQAdQrGwTFNVS2wCSs69+dT6qqjSMHq2hrAwYNkxHSQmYaOms\nvJVueYxGjchXMGjmUvHtnh49eR6SKZIs2g4EzOd2pRoAs6wCny4kcaL7EXIBo32U7E77enriCbnj\nQsULiqpFRq8qz3lphiCAXtz/gxnG7sR0IDTNjFpFo0YbrzFB0hUOm7Ll91vaTv6P/wHh2tB13ZI8\nf/HiRdxwww2oqqpCfX2966v6gsEgnn766aRs5TmuRLIaNE1/JcvXqJJIVv4hKwwzQ9d1fPjhhxg3\nbhzGju3zvplDgqamD9kW/R5wESERcIpqFdsccwVACZ5//j8AAF/84s8xdiwwdqx5y8OSEkOaAB0l\nJSRYSDzqCAZ1lJaaBT2N+0fryWhRIKAlp/VIpIJBQ6x4lXbaR7lYXKaMdvvpQIAnxRv5VTyiRd9j\nNB4zV4sk6yrMW9xEYc3B4knuJFgkWT342c/mwuvRzUH4fMabRmJl1oSwtvGo1vDhlnwtJO4NWb15\nM07mWfR1sHBKnu/s7MTq1asRCASSyfO33HLLoCfPh8PhIZuwP5SQSJYVkawMyKWQd64SjUbR1taG\nmTNnYtiwYX0fMAQwBItLB01VBZAqVL1sHxF3aKf+Rtv69T8FoGPu3F9g0iQNJSWGcAUChmjpuhHl\nUqNalD9FUS2KVAWDRhSLVgpSVOvqVbOGFd8HOE8XknyZ04bmPhInOifto1wvysECgFiMpttpijAI\nM3pFwkWlF3j+FUWuzuN73/ts8jpFRVrivQgAvgC8SAjUsGHmkkXAjGZFo8aL8XgMwSL5SpTOQFFR\ncnFAdUeHkbM1YwaEa4cnz8diMXzyySc4duwY2tra8M4772D48OGYMGEC6uvrUUqLN7JIMBiUqcIs\no0PqZKmIZGWARLLS09vbi+3bt2POnDl58T/FpqYPEs9UuSaxuppm/1WkChUdo0a1rAK2efNPsXmz\nse+ee36Jykrju3/YMC05lWgIlTWqZQiTnpSvUEhHOMynCfVk1IkkSpUskiGfT1Oqu5v1s8Jh3TYP\niwSMSjOQdAWDeqLAKL1fPcojlyo7wbqCr33NKLzs8ZgSl6hUgURVC/h8QFGRF0VFXsOtigPw+xJR\nLK/XDKuRXPX2Go8+n/E4fLh1irGoCAgGDdkKh3Gywbb4s9APvF4vqqurUV1djU9/+tO4ePFiMnm+\nvb0dpaWlqKioSFaezwahUGhI3iN1qFGQOUVpkN+4DJBIljPnz5/Hvn378JnPfMbtoVw3plwRidVo\n8KtdYXyUOO3nES81EhZHqoQFYUbHjP4vv3wvgAAmTfoPTJyoYeRIDSUlhmgFAjpKSjTEYjrL1TLO\n5klMo3V1xS3Rre5uQ85UyaLt3l7j3IA1x4r2X71qiJo5fYhEuylbFy7QtGRitaNO7wPVrwKswsVX\nDZrTgp/97JTk6+ElJfx+Y7ozEjFuAxkImE4UjVolzOfTUFTkh7/Uh1hcM6YXaYUhyRURjSbKPiTE\nKxw2rK64GIjHUf3xxzhZUwNh4BgxYgRmzJiBGTNmIBwOJ5PnX3vtNWiahhEjRqC2thbTpk2D32/3\n99d/wuHwgJ1LcEamC62IZGWASJY9J06cwNmzZzFnzhy3h3LdNDVtgfnnoP5fLMKe2/3JkGypvyck\nGXYSRqJFH0k8qmVGuo4evQ9Hjxpjqq6+H+PGARUVWiKapScEwxrdikZ1eL06uruNR8CQqu5u4zEQ\nSJWsq1d1XLyIZF/CnBK05mbxqcJw2MwFi0ZJnOwS2alwaAiGZFHeWhhAF26//Q8AmGlSPp/hPvS9\nGAiYqxb9fjNvnSozBAKmIxUVGdJlyJYpXd5SH/RETrAWTiS/+3zGz9WrxmN5uTVx3uNB9alTRlRr\n4kQIA0tRUREmTZqESZMmQdd1dHV14fjx4zhw4AC2bt2KsrKyZPL89VRrDwaD8lmeZaQYaSqyujAD\nfvvb3+L99993exg5xb59++D3+3HzzTe7PZTrwpArgn88qGKkfnQU2bT1dWxRmjb+p+VX2tRt45ib\nbvopysu15CrEkhKaHTOiUkakS0tOBdLfOk0BhkJxlJRoyWgUyRUvKEr7VNmi2ldm1IrfrJkEi5La\nSbAo0d1YHVhTM4FNe5qvnqYAeTvNQtNUIWDKFz0WFRnPdd16PD8fYDrVsGGAFo8lRQqAddqQ/0Sj\nycjWSQr5CVmnt7c3mTx/4sSJZPJ8XV0dbr755n6lJ+zYsSNZVLUAcGV14QxN01dn+Rq3yOrC/ENy\nskzi8Th27NiBiRMnDvn7mZmCZSdLFL3yO+ynBG676Je6j7erbTwKFmdtPqUPiRZFiYrQ2flz1vb/\noqKiBOXlJBa06tB49Hj0hHSZ+VdXrxorF1W5IgmzazOmDWMw3h8aewTWlYIRmPWtaBqwB8XF4wD4\nEAiUAqjAlSvWKBWQTIeyyBcXLGMs1m2SK2r3+cypRSB5F6LkPlqXYaRmeQF4k+IVKGZTiR6PEdWK\nxSwFTatDISOqVVYGIbsMGzYMU6ZMwZQpUxCLxXDq1CkcP34cH3zwQUryfF8LbiKRCIqLi9P2Ea4P\nHeY9GgQDkawMkBCzQSQSQVtbG2677bYh/2HV1PS20uL0H78ITIFS/1x0mDJm96fERU0tYaDKWShN\nPzX/i7b5NRfi3Dk/zp2jtT1FAP4XfL6R8HqNKJexkM6IcoXDuuU5kPoIANFohI2FHkOJ57wcA0Wv\ngjDuP8j/ZkoBlCIYjMHr9SYrLNBUH+VZ8elBaiffoUWAHo9VtqgdMOXKGLd1apHSrQBDrug+2iRX\nPp8RqAI0+Hx+BD1++BJTsFo8ZoQIaTCJFWrVPT04OQir4gQDr9eL8ePHY/z48ZgzZw66u7tx/Phx\ndHZ2YteuXSgtLcXo0aNx6623orq6OuX4cDiMEolCZh2ZLrQikpUBEskCenp6sGPHjrxYQZgqWDqs\nkSiPso+g/6PZLQOnfSRFHC5M9BFE0S4eKQuxfmD9eJ8gTNGKKX2DbDsIoCkx++VN5i0BQHe3D7TQ\n+vLlv4EpRCRodjWtaD+VW+iE8T7Qe8XfEx87poid18cKQfoQi+lJ6SIBIsEi4fL5zAR3TbMmuwNU\nzoHno5k5WsaqQ/POOpQZQTIWS7gTedKZM1bhIqfy+bzwJi4QGzUGHg+gRSNGVCsSwUlaTikMKuXl\n5SgvL8fMmTMRDodx4sQJHDt2DK+88go0TUN5eTkmTZqE6dOnw+fzIRKJYPjw4W4PO6+REg6piGRl\nQKFHss6dO4f9+/fjrrvuQj9z+HKOpqZNiWcUubJ7Pfz/YnYRLv4xogoXFdUErLlZVKYAsEax7Noi\nQMp0odP0YQRWKQyzMUWVRzs5bGHP6ZyqOPHjvGwscdYWTTxqMN8fP8zkf1+iDx1rPDeky5uosuBN\nChZgTvfxhYB2ye6AmSgPWKcG+bEkXZxg0Fip6PUa56WoHwkeYES+fD4viopK4ImS1PmheTyA14tq\njwcne3oguEdRURFqa2tRW1sLXddx9uxZHD9+HPv27Usmz4fDYdTIKtGsM7S/IQYekawMKGTJOn78\nOC5cuIA5c+bkkWABmX8U8H7phMuL1EB5hO3jRG3aVLHikS6+7WXbFDWLsefq2HgUjMbPI15epX8m\nxGB9L+jvI5popwgXl0MaoypaXpiv3bi+IUY+RKOG7JFI0bQftZEE0bQgJbhTpItysSg6Ref2+cxa\npTwJnrh61Zy29HqNH5od50Fcn8+LK+ESeDwlqKgYgXPnTmb4/gnZRNM0VFZWorKyEnfccQd6enqw\nf/9+tLW1DUrR00JHpgutiGRlQKFOF+7duxclJSVoyINijFbBulbSCVeM7VenU7mI0XnsokvUpkam\neJSLCxqPYlEES5UuEp14op2OjbHz0Tno45Gup7Z7YI1SAcb7oE5z0jl9SH3tdG2v0le9tpkHFwp5\nLSlRqlxRkns0akwpUh8e5SLpon1qVKu318ztKi42a5iSYNG1KGDl9/NCqEZbRUW1iFaO0t7ejnvu\nuQfr1q1zeyh5jZRwSEUkKwMKLZIVj8exfft23HzzzRg5cqTbw7lumpreQaoUXW9UThUuvs0/Zrgw\n2YmVKiF0zz7eph4XgRmhiivt9CfNpw1DSI2ccdGh94ZPL3phFTJ+vAYzssYjVzz3zC4qxl8rlzs+\n3cjfR2/ymFjMnKaMxYBQyBgPiRRJEI9wqVOFJEacS5esye+UC8bXdZw9a7RTTli6ouEiWrlFb28v\nmpubcdddd+HFF1+EprlS2aCgEMmyIpKVAYUUyQqHw2hra8Ptt9+eF6/bECw7ocpUutSPDE+afep+\n3odfT83pshMr3o/OycWETx+STZD8cDni46BIFI+o8UenqUPKs6Jr0yMl4PNIF78GXwxgJ1hcIr1I\njZKpAqqew4dQSEcoZIzH5zPfe5IuPlVIGEVK7fcBRlTr0iWz6DvldhUXw7KAAAC6u41HHtXy+arh\n9YpouQ0J1uzZs5PJ8EJ2kUhWKiJZGVAokawrV65g586dmDt3bl58IDU1vQvrl3061GgUYP9x0ddH\nCBcOjtNUY0xpU8WK2uxkTJ3uo+MoN4q3OUHvj4bUCJwqOU41vnjeFW3zY7nY2SXL89WdXhhV4n2w\nSpgqWNRO1/IiGo0gGvUhGDSO4wLV02NKld3/HS5eNCJdTlEtes7zv3iyPOVq0Z+Nx1MNTRPRcotg\nMIiWlhbcfvvteOONN/Li82yokMuSpWnaKADPAbgJxhLpr+q6fkHpMyXRh6gF8B+6rj+iadr9AP5v\nAGcT+/5N1/UX011TJCsD8iGi0xdnz57F4cOH82IFIUCCRTglhXPsXrOak9QfnKYM+bU0pU1nfZ2i\nOFzG+Ph4Oz3nOVo8MT+O1NdG11GFjV8ropybxqMm5dsl4pMQxdk2nZNESYN9NI2Lmt3UKW1bp0Sj\n0SiiUUPW1IgV3ULIWiMrFWNloSFRZqTKOhXp8Vjrl9L0YlFRNcaOFdEabILBIFauXIkZM2bg7bff\nFsEaZHJZsgDcC6BV1/UFmqbdm9j+Me+g6/p+ALMAQNM0L4CPAbzAujys6/oDmV5QJCsD8j2S1dnZ\nicuXL2P27Nl5KFiAvUDxL+S4Qx/CaQowU5yEK135CDWypX5ReBz2eRLn1ZAa0eKoOVk6a6dxeJTj\nvUgdF/8IURPr7UpG8DE6Rbe4bKnTjjy6FYGzlMGyLxr1Iho1xM7r9aTkbdHj5cumeGmauRKRbkKt\ncv68WSBVnYKU7/bBJxQKobm5GdOmTcO7774rgjXIDIE6WV8CcHfi+VMA3oQiWQp/DOCwruvHrvWC\nIlkZkK+RLF3XsXfvXpSVlWHGjBluD2cAISmmL++IU0c4T+/xfSrXI12qcDnlfDkl1nPJ4dEpHnXS\nlPNorF2VG76fS5XG9tH5uWXQR4dapoJHyWg8/Hie7K6uxuRThvS6nMTNrhaYV9nPI2zmPqMmlycx\nBWick+pieZmz8YiVx2NEv0ii1KlFuv1hPG6ucvR4gFOnqjFunESzBoNwOIzm5mZMnjwZW7duHfJF\nk4cqg/Df9NGaprWx7SZd15syPHasruunEs9PAxjbR/+/A/DfStv/1jTtmwDaAPw/6nSjikhWBuRj\nJItWEE6ePBkjRoxwezgDRlPTNptW9QbLRF+5WnZRp3TTikSm0tVXzpcqHzxvihf95O0UJVKjXDzC\npSa1202LkgBSVEmtjaWWm+ByxQVQnV6ka/JpPzUqpkbBVJHkpSwogZ7OQYn/doVUTemKxbyJFYvG\n+Ix7GJpcvGgIFwkVPY9GjeeRiDlNSHIVjwNdXYmRekwBO3OmGg0NIlrZJBKJoLm5GTfddBO2bdsm\nguUSg5T43pXuBtGapr0GoMpm10/5hq7ruqZpjk6oaVoRgL8E8BPW/DiAX8B4qb8A8CCAf0w3WJGs\nDMg3yaIVhJ/61Kfg9/v7PmBIksmful2ull3UK119rEyS5a8VO7lQr6sm7HMZ8sA6DWg35QiYU3T8\nOH5tvnoRsEqNmtTOr0l9+XuiJu5THpqa1M+n/rzKPlWcqE2tfs9ripGMqV++Xhg3s/YiGtUSsmWI\nZSzmta0aH4sZ04o0nUg/JGL0Q+JlN80oDBwkWDU1Ndi5cye8Xm/fBwlZw+2cLF3XP+e0T9O0TzRN\nG6fr+ilN08YBOJPmVH8GYLuu65+wcyefa5q2DMD6vsYjkpUB+SRZly9fxq5duzB37ly3hzLgNDXt\nBkBTu+qfehCp2P0nhldI5zh9U6riwgVhoEg3bZkuOG8XzQJrU6Nfuk273XRmuigWbZN88WlKPhYu\nf+p0oBoV4+UeeBRLLf2gipldFI1WRFK5CbVfzPIYStZsoIie1yJUFNnSdUO+aJqQBIt+duyoxm23\nSTRroIlGo2hpacHYsWPR3t4OX7oiZsKg4LZk9cFaAN8CsCDxuCZN3/8JZaqQBC2x+WUAu/u6oPxG\nZoDH44Hf70ckki63J/f55JNPcOzYsbwULCvqn7kOQ76cok4RmzYVp/8d261S7E9+1/WQrlyEpjyq\nY1DzpuxKPjitgqRtdZWiR3mkc/ESDTQ9yacLubTx47hY2RVP5dOiqljFYI1+eWAVK5WrsEoXVbLn\nxxmvMxr1JCvCU2RL04yaWSRfVLiUR7tuu83mssI1E41GsWrVKlRUVGDPnj15HJUfOgyBOlkLADyv\nadr/AnAMwFcBQNO0agD/R9f1LyS2SwF8HsB3lOMXaZo2C8ZL7bTZn4JIVoYEAoEhLVlHjhxBMBjE\nnXfe6fZQskJT0x6HPZkUGfUr/fi+vuZ61Okwtd4Ucb0rFNOR7npO04qZFFlVk+eBVCGzW0XIc7/U\n999p+pD2cWlTxYqXreARLrWMBK9Cz1dhAtZEfU3py8cBdhzt60nuD4XUY41ViyRcFOXy+Ywol64D\nGzdW40//VKJZA0EsFsMLL7yA4cOHo6OjI69mG4Y6uSxZuq6fg7FiUG0/CeALbLsHQIVNv/+rv9cU\nycqQQCCAK1euuD2MfqPrOtrb21FRUYHa2lq3h5NFSmD+eauRG/5Fn+m0IWGXt8W37cTbqUyD7tCH\nyKZ49ZUIbHdtdXWhXTtgyogaraLzOi2jJyHlKwXpWIpwkWg5iR2tiOR9dJj/LrSPVjaqVen5+Hlx\nVU3pT9tU64vazAURFNkiqUqONiFelBQvXB8kWMOGDcP+/fvzdvX3UGQIRLIGHZGsDBmK/1OKxWLY\ntm0bpk6diuHDh7s9nKzR1HQkw540bRhX2gjertw/xRGnHC4gdSrRSTYGozZZuiR6O0iA1OKo6SrJ\n272vqqT1VaGepgx5bhSPWqm5XBHlHCRbfFqQ53qF2X4nkbKb8oRyLnqNly3nMOpxaYl7K1rPL+lC\n108sFsPq1asRCARw4MABFDtVkRVcI8frZA068mefIUNNsoLBINra2jB79uwCSAYthfmFSNHG6ykY\nqsOoteUkYLw9DHvscrPUc6iik80pRadz9lWXK91UpNO5eCFUNdFdPY7nOwHWKUGKmNFUIa8BRtdQ\nE+Xp30PNr+IRr764qhxnN7Wonou/X1zUrK/9qaeq8a1vyZThtRCPx7F27Vr4fD4cPHgQw4YNc3tI\ngg1Dv5z1wJLv374DxlAKSV+8eBHt7e34zGc+4/ZQBhkdhnDxoLX6nD/ySu9XlX2Zwv+EnKYVeRI2\n4SQgfHswEujT1eXqzzF27XzFolMkjN4bD9un5n1xSaJSD/T+6Ww/YH1fOVy+VPFyarNDlUUSKi97\nVPtdBgBEo56UelxCZui6jrVr10LXdRw8eBClpaVuD0mwQaYLUxHJypChEsk6deoUTpw4UYCCZYed\nLDhFaNTVh055XXZ5XnbRLLVWlLpCzw5VRAb7/4R9CVe6qJRaTsJpxSJs+vCpOV1p4zIFWAWITz3a\nSVJMOcZpujYdJN/pcsD41KDTFKRT9E/oC13XsW7dOsRiMRw+fBhlZWVuD0lIg/yGWxHJypChIFkH\nDx5ELBbDpz71KbeHMmg0NfXAGr1So1Q9Dkdy+vpYcBIsevQ77LeL7PD9PHshXYI4h+cl8WMHmkwi\nXFx+1Cry/Dja7yRddgVUVUHi74+aWO8U8eOJ9HbRLrtIFhza1WR/NWp1LQIn9IWu69iwYQNCoRAO\nHz6cV3enyEeoip1gIpKVIbk8XajrOj788ENUVVWhqsrubgKFzDCkTh3yfCg7MVP7QjmHXRv/su+r\najyhVjK362NX80stx5DtXC673Cs7uVEjXZmUiVDb7WRNva+ik3Sp03yZiA//t+uvKNG/RS87lpec\nUHO3jOdNTf+EefMa+3mtwkPXdbz44ovo6enB4cOHMXLkSLeHJGSARLKsiGRlSK5GsqLRKNra2jBj\nxgzJU0jC5ehauN5pOvqzspM32qb9fUWmnASKC026BPpsRrn6WrHIIzxq/bB0dbl4f7s8LXUK0066\n6Hx2z9VImzqdaBflsmvn50iXa6VGujK9l23hous6XnrpJVy6dAmHDh1CRUVKySIhB5GcrFREsjIk\nFyNZV69exfbt2zF79uwCvl/XvQD+C2ZCtBqt6k8b0vSF0g7lPECq8Djt5/f6A1I/mtLlPnEp4zlL\nan/azrZwqedVpZBHBvsSLqcpSjXC5DRFmCnZmN6TKcOBQtd1bNy4Ed3d3Thw4AAqKyvdHpLQD6SE\ngxWRrAzJtUhWd3c39uzZUwC3yCkE7BLjeWTGSZbUNvUc6vZgl4hwEi4VfmucdOfhryldZIuOccrj\nUvvBpp/dfjWvq699ThGwvwOwAUIquq7j1Vdfxblz57B//36MGzfO7SEJ/cAurl7oiGRlSC5J1scf\nf4zTp0+LYA0IlN9UwtqoGGYm0TAgfYRLzfHiz1WJ4tEqrY++gFVEvA79qc1uO9slIjKpyQU4l27w\nsHYgNVKU7nzqLXHkvnZDgdbWVpw5cwYdHR2oqalxezjCNSDThVZEsjIkV6YLDxw4AE3TcPvtt7s9\nlBxhIoDhMFekkWSo04f0px9DqixxoSJ4CYBM4QnpPC/LScjUdn68h22rwkXQLX/Uc9jValKnI+3E\ni66r9h8o7CJw/NpO/Tl2SfKZfIzxm1ATTjladm3p+kou5EDQ2tqKkydPYu/evbjxxhvdHo5wDUhO\nVioiWRnitmTpuo6dO3eipqZGchQyQq2VlA6nfnTLDjth60uc1GR3VcDUyFYMqR9RJEJets9uyo/O\nnU6u1JIH6T4K7aYW+bmul3Tn6SvXyu6G1Oq/XbppVMCo5j9QaDDvh5lJ4r0G4MwAXj8/eOONN/Dx\nxx+jvb0dkyZNcns4wnUgkmVFJCtD3JwupBWEDQ0NKCkp6fuAgoMkyU4ebkCqAMXYIxekiE1f+pK2\nK1ugipRfOZb22UXPnHKEqI8qDnRtNeKmlnNQX78qaGokhq9W1NlzjhrlsrvOQJAuwsXHpE4rqsSQ\nfnqQl9hwKvmgtvf3P1keh+d/2c/z5D9vvfUWjh8/jg8//BC33HKL28MRrhORLCsiWRniViSrt7cX\n27dvx5w5c+DxXM+Kqvxk3LgyAL/ChQvzoetANArEYoB5rzu7qBKhflF7YV9KrxhW+VFljW8DqRXM\n/cp+NSJG1+b7PGy/B+bNktX8LLUEhMbOwduc5CqdONlJVzaFy+k8ajV5Pg7+2nj/vm7OnelHHx0X\nUrYzmVq0v7fevHlbM7x2/vP222/j6NGj2L59O6ZMmeL2cITrRKYLUxHJyhA3Ilnnz5/Hvn375BY5\nafiLv/gO1q1rhNdrCJaW/C7l0ScVEhH6EuRCxvO0+GM6PDBEik8jqtEymvaLwZwuBNtPP15Yi5Ry\nwfDBKmuAVbp4pO1aCoOmS56n9sESLo7T2J1KV/D3x6m0Cd2Sx64dtf3OAAAgAElEQVR0BqH+zfe3\nRAPdkoePV6YKiXfeeQeHDh1CW1sbbr31VreHIwwQIllWRLIyZLAl66OPPkJXVxfmzJkzqNfNB8aO\nBWIxDyIRD2IxJCNcZpQrCqsM0ZegGsXiSeQ0/aQKFBcpDq0Q9Cv96Hxq0jbvQ+1eWKNffFxgx9mh\nCoidkPDSCX0lz9tJl4pdLtdAf+Ty82cSnbye/K+wzfnUY4od2oV0bNmyBQcPHsR7772HmTNnuj0c\nYYCwS3QodESyMmQwpws7OjpQVFSE2267bdCuOZSZNQs4cACIx4FIxJApgEe1jOfmNo9g8FwkWiUW\ngyFc6pSg08cH/W7EYY1+8elAyuuh83HpoegWYEaxKO+IR73A+nIZU/PGAOcIFm/jRVHpfXBKeLdL\nqufnyiTKpR5zLaSLyPHr8m0nAYo47KN/i74ES4M5jaju58dSxPSPHcZRWLz33nvYt28ftmzZgj/4\ngz9wezjCAOO0VrhQEcnKkMGQrHg8jp07d2LixIlyG4l+Uld3H/btmw8A8HqN6BX9xBI+4vUC5eVA\nNOpBNFqUJsIFmFEkevTAnD6ykylVwKgvj1Dx8wVgjSTROfxKf7DzAOafrFrKgESJ15zKJLpCAmWX\nPE9taqQLbL9dyQdVuPi5+NgHIsrVV5kHuz52eVycKOun4hTRdnqvNZjThhcwb96lNNfNfz744APs\n3bsXb7/9dkHdyL6QkOlCKyJZGZLt6cJIJIK2tjbcdtttKC4u7vsAIcmECd/BRx81wuMxpgrjcUOc\n6FH90RPf95GIEd3y+UiyzC9Kn68oERGLIr1MUT4WbPqpUsWD6WqxzJhyjFfpy6cZSW5oypMiW2rC\nN49uqXlePMIG5TgnSXGaDuyr5IOTdDmJyfV+TKeLdqnTpuq/p1fppxKG87jpP2L9zd0qDLZu3Yrd\nu3fj9ddfx+zZs90ejpAFJPE9FZGsDMmmZPX09GDHjh2YO3cuNE0+oK+F+nrg0iVTpDweQ7I8HvOH\n3lr+WFFhRrKiUQ903YNg0Ix+2X+h0mpDLkbqaj0/a1dliaYB+bE+pY3ORYLE+/EkecBcZchlzO73\nSK0qT9eh89LzvpLkeVQqXRSMj1/dly5nbKALovIFAU5lKgi7KWH+MZkuYhW2aSMKe6pw+/bt2LVr\nF1577TXcddddbg9HyCIiWVYkWzNDioqKsiJAXV1d2LVrF+666y4RrOtkzpz7LFLFf0aPNqJclZXG\n45gxxiNFsrxe4xGwbt9wgwc33OBDcXEAPl8JjLwtEiUv+ymBkXsTgDGlRO0U6fLDkLMATOnwJbYD\nyrmK2Dk8MAWM2n3skRLkSdw87Bh+Pj4eD+uvKe0+5bz8hyJjaptaIsID63tkV+JA7Y80+9SPKbu2\ndNj11ZUfJ+gWPfQTYT+8j91xnEsFO1W4Y8cO7NixAy+99BLuvvtut4cjZBG1OE02fq4HTdP+VtO0\nPZqmxTVNuyNNv3s0TduvadohTdPuZe2jNE17VdO0g4nHkX1dUyJZ/aCoqAihUKjvjhly7NgxXLx4\nEZ/+9Keh6+k+6IW+uHjxOxgxohFVVWYCfCwGhMPWqUKfz/ro9xt9fT5g+HCjLRKxrki0+yf3+YzI\npjGlqOZPAdZVg1HWxy5iBZgiwCNM6nM6H32BU3I+n3LkOWRA6rjUdl7+QY3G2a2YBKyTAumiTnYr\nFJ2q0ve1GtJOlDItHdFXsrw6nnT9OCRavJ/dR2rh5h59+OGH2L59O9atW4fPf/7zbg9HGARyPJK1\nG8BfA2h06qBpmhfAYwA+D+AEgK2apq3VdX0vgHsBtOq6viAhX/cC+HG6C4pk9YNAIDAgkqXrOvbu\n3YvS0lJZvjzAfOUr96G5eX4y+d3nS502JKECTAkLh41+BIlXNGpEtW64gcuaN/ncwBAHr7cIsZhd\nThZgRJPUfCwuYvyjib68uXxwKbKrBs8jQD6lT5y18ShRFOZ0n93KRHqutvPXZbfN+9G4+JQmWBuN\nRX29arFRu3pWdsn0QN8f85lIV3/6cXgZEDOaNW9eBofmGe3t7Whra8OqVavwZ3/2Z24PRxgkclmy\ndF3vANDXrNGdAA7pun4k0fdZAF8CsDfxeHei31MA3oRI1sAxEHlZ8Xgc27dvx80334yRI/uMNAr9\n4OLF7wBoxFe+ch+ef34+NM2QKq/XyL2KxawRrnjcFCtKkqcpQ5KqYcPM6JYKFy/Am3j0sHwuSohX\n87ICSBUhHqmiwqZ9RbIoPwtIFS9+XkqW98I+eqaupnO6TQ8953LIx0ZtdB3+QcYLsTqdV83v4vvs\n6mPZlYxQ+2bykc9ztvrqp17XqdgpMRNADwrtJtJ79uzB+++/j5UrV+Iv/1JuJVQoDFLi+2hN09rY\ndpOu600DeP4aAB+x7RMA/jDxfKyu66cSz08DGNvXyUSy+sH1SlY4HEZbWxvuuOMOV++FmM+89dZ3\n8IMfNGLLFjNKFQrxRHYjwkUCRpGtsjKjD1+RGAymnn/ECPtpRBK00lIgFPIkykQA0Sh9gfNkd45a\ndNQHU3p4hIiLEMkVnxbUlGNVQePt/HxxmGUjoOzj/dUonBr9UoWL1/fichazea5OcfLz0Xunrpqk\nMahtarsqXHYCdj2pqelWJxpR6nnzCkuwOjo68O677+KZZ57BX//1X7s9HGGQGQTJ6tJ1PV0+1WsA\nqmx2/VTX9TUDNQhd13VN0/rM8xHJ6gfXUyvrypUr2Llzp6wgHCS++937sHSpUTeLR6tIsKjUQyRi\nRrdIqngC/LBEHUme16VSVmYIHfXjFBcbX+BUJNWQPVWIAPNPkdoo8kRtmrKfktRpHz13Ejb1vozq\n+bg88Y8Fu2gVkP6jlAsTiQ3dxoaXmeARMTXCRQnzdpE8wF7ICKfb7dgl0PeXvv52+XRoGPPmFVa0\nev/+/di8eTN+97vf4Wtf+5rbwxEGmZPAxv8ARmf5Ml3pduq6/rnrPP/HACaw7fGJNgD4RNO0cbqu\nn9I0bRwyuE+WSFY/uNbo09mzZ3H48GG5B+EgsWSJEc36/vfvw69/PR8+n7G6kHKv6DEcNhLfac1B\ncbEhWpSvRdEsO7GiqUI6H+VvAYaYUTtgRryM8mdehEIkbPTnpwqXKhR29yZE4hj1WPV8XK64WNE1\n1ER4uxtkc9QcMT7FR8LHRc8PI8eM56Sp043Uh68atJMru/28D7XTGLkQ2eV0Ef1ZdKL2dVpZWHj3\n4jt48CDefvtt/OY3v8E3vvENt4cjuICu6/e4PYYBYCuAyZqmTYIhV38H4OuJfWsBfAvAgsRjn5Ex\nrZ+r2gp6Cdxjjz2GXbt29euYo0ePoqenB/X19VkaleBE46OPAgD+4//7T8sqQ1W04nFTmiIRJOtk\n0dQhiVZxceo5VAFTzw8YAhYKmXld/BgSLoCq05MM0MpBeg5YRcgpEsUHpAoTT6jn27xNjQqp04Q8\n4uXUx2k/37aTJf667Lb5OJ3ObVdcVSXdx9j1fsRpAIy/9UKKYh06dAhvvvkmGhsb8e1vf9vt4QhS\nEdcWTdO+DOBRAGMAdAPYqev6n2qaVg3g/+i6/oVEvy8AeATG/+B+q+v6LxPtFQCeB3AjgGMAvqrr\n+vm01xTJypxly5ahra2t744wVhDu2bMHI0aMwIQJE/o+QMgKjY8+ivm/+hVicc0iRjQNSKLF5YiL\nFhXf5wnzNK1IRU/pPGpkSz0/HQOY0S2eUM/bzBwynjtF26qYqM/t5Mou54qfRy2qCps+Tserfeha\n/N6AdgKFRJvdvnTTgXby5SRV1ypbmezn0HimAQDmzcv2jEnucPToUbS2tmLp0qX453/+Z7eHIxiI\nZOUIMl3YDzLNyYrH49i2bRvq6uowYsSILI9K6Iv7/u3fMP9Xv0JJ+JJhRcOKAJ8PMYeVYTfcYDxS\nBIuLUFGRKV48AZ5mkinaBZiRLGqntnDYjG6RjNExsZjZZuRxmX+isaR58fwtdcUg308DUMtH+JX+\nlGBvdy67OlhqIjvPDaNxAcYqSv6cR85oBSXt47erob58FSWXMhp/upw2GjuXNbu6VoSdjDkl09M+\ndZVj4QlWZ2cnWltb8fDDD4tgCYINEsnqB88++yzeeOONtH1CoRDa2tpw5513wu9Xv8wEN2h89FFg\n3z7Mf+IJw4Z8vuRjLFF6IVBk/GpHopplipCeRyLGysFw2L7QKc/JoqlBp0gXQc/DYVO4+JSiGvUy\no2FceOyiV/w5v9ULj1SpUSxCrQNnNz3Izx+BmRNFEuM05ciPVYVMQ6oghZH6H3K1D78ub0+XW5Yu\nutWXbAHOH4PTCkqwjh8/jldeeQWLFy/Gv/zLv7g9HMGKRLJyBJGsfvDCCy/g5Zdfdtx/6dIltLe3\nY+7cuYM4KiETGr/3PQAwRIskq7fXrOHg9wOBAODzJUUrGjW62d1kmmTLm/AL2ia50jRzyo+iV+Gw\nVbrokVY/UlsoZCbjq4JFEmYtH6FKF8/lssvxAsxK9PQcNs8Be4mzEyv1WKfpQf6c9qs3XXYSMWpz\nuqWN3c2b7VZU2u1z2t/Xd5X5ns6bd1cfffOHjz76CBs3bsQvf/lL3HvvvX0fIAw2Ilk5gkhWP9iw\nYQPWrl1ru++TTz7BsWPH8Id/+Idyi5wcpfF73wN27wYAzF+/3pSt4mJTtPx+o+3KFaPd44Hu8aK3\n1xq1AlLzsMJhQ7q4XKk1uki26DlvB6y1udR+dvlcdG4+pWlOK1KeFZBaUZ5v20Wa7PKzVNFyOp7L\nE2BGpei5ejzt54KkRrHsIlg8Skd9I8o2xy66RdKWaWkGFaqFNbyP4/OHjz/+GC+99BLuv/9+/Oxn\nP3N7OII9Ilk5gkhWP3j11VfR3Nyc0n748GGEQiFMnz7dhVEJ/aHxs59NPreIFo9sJeQqKV9FRdA9\nXmhx44tW93hTVisStE1yRZErvrpQlSd6jMetbXYSRuewEyy1eGoopEoShb/iNm2EOvVmF4FShYPn\nOvHzqdenF+RVtvmxvPxCCGYxUvVaagSLn8epjfd3+g6yEzGnvC5aRVg4gnXq1Cm8+OKL+MlPfoJf\n/OIXbg9HcEYkK0cQyeoHmzZtwooVK5Lbuq6jvb0do0ePRnV1tYsjE/oLydb8Z54xGiiSVVJimBGb\nPkxmqvt8RqiqpCQpWk45V5SPpa4u5NN8kYhVnng+llPuFu0HrFLGBYtPN9J2aq0vGohTdMquzS7X\nS52+6+uctI/ExUms+DYc2uzkC8o+p6lFwCpi/Bp8n12SvAZgFoBgQQnW6dOnsWHDBvzrv/4rFixY\n4PZwhPSIZOUIIln94L333sOTTz4JwJiSaWtrw/Tp01FWVubyyIRrobGmBgAwf9MmMyE+EDCnDINB\nM6Ll9Rrt9Jz+bhLypfv8STkiL+OrDFVpcpoeDIWM0ztFu5ymGimviwtVX3W5EnvZ86s275JdLS3A\nOUGe9nmUbb6Skwuaeg0uUYB1qtGuD5cv2LSr1+TnIOzk0m5sAHBb8tm8eYVza6wzZ85g3bp1+MEP\nfoAHH3zQ7eEIfSOSlSOIZPWDHTt24IknnkAwGERbWxtmz54Nn0+qYAxlSLQAYP7bb5tmUlxsTiOy\n1YjJpCySLr6PKCpKrlpUo11qwrtaL4vfE7Gv6UV+Ht5uN4VpV5cLAHp67FYqcvgBXFTUviQ3XmWb\nyw9/rsqROg1oF61S5c1OyKC09Sd6ZXdN3sdMBygkwTp79izWrl2L7373u/j1r3/t9nCEzBDJyhFE\nsvrB3r178fOf/xy7d++WFYR5RmNNDdDZifm7dqVGtbhcsSnD5HNCla6iIiAeh+7zWwSISxEXJ7W+\nFl9tCFinF2m/Kli9vamv7coV8zlfrajmcNndENsqJWpUh0uPKjuq6KgRJjVpPQjze8HunOp57Ppp\nSt+gTbsHZsROFTbC7hqfAgDMm2cX9cpfzp07hzVr1uDb3/42Hn/8cbeHI2SOSFaOIJLVDx599FE8\n8cQTcg/CPKWRhXnmt7cb0kQWQ1EtEiifz4h28XwtvkKRwlf8GAAxj1E7TZ1K5Plb1G73yHO6rl61\n7gNSJUvd5sKVTrLUCvUAEIupUSA1esVPqPb1wpCbdJEjO9Hix9j14+2qlNmdQz0P3wZSx/ep5Fah\nCdb58+exevVq/P3f/z2WLVvm9nCE/iGSlSPIXFc/6OzsREdHBzo7O1FdXY2GhgZUVFS4PSxhgPhO\nonhsYyQCXLhgNJIgxWKplUdJtLhkRaNAT491OxxOloT3Js7pTUwpUsoXYK2nRRXkVcni7bxGF2AI\nFVWrt9u+dMm8nRBg1PIiolFrqQmqo3uVpWnFYlQVPtmivIM+5TkXLX6sl/XholOKVPEqA9AL63dG\nKVKjURqAYYm+qpTdYHMOT6I/kCphAECrUC8UnFwBQHd3N9asWYOvf/3rIliCcB1IJKufhEIhLF++\nHP/1X/+FPXv2wO/3o7q6GjNnzkRlZaXbwxMGiMaDB5PP53/0kbnSkOTK7zcsh0sWYBUuHvUieGSL\nLInODaPiPJA+qgWYESqKbF1VctZ5yQj1fEQwaG3r6Ul9H9Tzkj+a5+CipUavAGt0yQtDdoD0U312\nEa3eDNsAewHj54bSTo9XE8//CAAwb94Z9cUUBBcvXsSqVavwla98Bc/Q6lthqCGRrBxBJOs6iEaj\nWLFiBZYuXYqdO3fC6/Vi3LhxmDFjBqqqqqBp8ns+1CHZmr9vn7U6PK1AJNkCrIJF8kXt9KgKFj8P\nvw1TUREiUc22OKldW7ppQcCIYqmobXb5XKp40XnpJanXiabUirDLbyKZQeJR3aY+sOlHz7lc9di0\nAabQQdnn1H4PgC4AhStYly5dQktLC770pS9h5cqVbg9HuHbkyydHEMkaIGKxGFpaWvDII4+gra0N\nmqahqqoK9fX1qKmpEeEa4jS++27y+fzz503Z0nVj3o1kiQtWPG5diUj76XeBIlhcsGg+kLYDAeg+\n47mTZNlFui5fto5f3QYykyxVovh5fL7U/WrkCwBiMTV36wpMEaI2ujj/O1Gn/jzKsRp7rrbzcyDN\nPpIrg3nz9qa+gALh8uXLaGlpwRe+8AW88MILbg9HuD7kCydHEMnKAvF4HOvXr8fDDz+MLVu2IB6P\no6qqCtOnT8fEiRNFuIYwFtk6ftwUJKoSz8s5qKUefD4zGkZRLdoPWAWLkuepjR4TCVx8WlFdlaiK\nD2AvVOkS5gn1XBcvGo+BgHXbqb8hYjSlyPO57KTKKaLlFOWCso/CblyoeLu6728AGBGrQpYrAOjp\n6cHKlSvxuc99Dhs2bHB7OML1I18yOYJIVpbRdR2vvvoqHnzwQWzatAnRaBSVlZWYNm0aamtrRbiG\nKI3r1iWfz+/tNaXJ4zF/SLx46QcuVBT1om3AWvSUt/t8RtkIInGeiCeQbHK6JY8qQoAZcXLK6SJU\nOVOnCwGgu9t87vOZ22of+lX3+YBgUI1uaQAuw3obHTVKxdsvwxrJon09yjbfT/v+JjmuefPeRKHT\n09OD5uZm/NEf/RE2btwon0n5gfwj5ggiWYOIrut45513sGjRIrz++usIhUIYM2YMpkyZgsmTJ8Pj\n8fR9EiGnsMgWTSPSFGAgYI1GqdEsEik1SZ630yMXLAojUVvAFK1Q3MzrUvO1eLqUmmtFiylV1MhU\nuigZDZcki39X0zQjF6+LF6kQqvF7b9xc2ym/qgfWqBWJFu/Dj7uinONbieenAIhcEb29vWhubsan\nP/1ptLa2imDlD/IPmSOIZLnI1q1bsXDhQmzcuBG9vb0YPXo06urqMGXKFHh5kUsh52lct85iIPNp\nFSKPZPHpRFW8eN4WYE4ZkpVQ7QXaVupvWaYTmcnE4E2ZCuSRJ8JOnoDUSFamx/LjVPmya6Pvdq8X\n6Onh9w1UxQmwRrAuwz5qRf1JroB58/47daAFTDAYxPPPP4877rgDmzZtEsHKL+QfM0cQycoRdu3a\nhQULFuDFF1/E5cuXUVFRgVtuuQVTp06Fn686E3Kexv9OfJknMtTnk2iRZHHBIlGyy+eiH1WwfD5r\nASxqH67crJj1i8XNz1ySIh7Zslt96NTe3W0/XcgDsRTUIzwe4Nw5a4F8TTOPpXb6nu/ujoNHuDQN\niEbVaBZgH9H634nHEwBEruwIBoNYuXIlGhoasGXLFhGs/EP+QXMEkawc5MCBA1iwYAHWrFmD7u5u\njBw5EjfffDNuvfVWEa4hRmPihuLEfC5KHo9ZAoJEiiJaJGZ2guX1WmprJfO8+I3KSeRsbl4e8t+Q\n0pZJiQfi3DnrtrpykYZ1/rxVvDweaxs9nj9vjWSp1yHJAngul10+1jeTx86bt9h+8AJCoRBWrlyJ\n6dOn4/3335c0hfxEJCtHEMnKcTo7O7Fw4UK0tLSgq6sL5eXlmDRpEurr61FMuTvCkCBFuKjEA/07\nknBRVItP/ZF0eb1AaanRxsVLlSkSr/Jya7saBUtwORxIaQPST/E59ePyZCdUfJsez541ZYpEq6sr\nVb6M6FcMwM9SxjBv3vdtX4NgEg6HsXLlSkyePBnbtm0TwcpfRLJyBJGsIcTJkyexePFiPPfcczh9\n+jRGjBiBiRMnYubMmSjhidFCzmMRroS9zI/HTZnyeIwoFt/2eExB8nisBU1JvHikkwSLz9sBwKhR\nqQMaPhy6JzUP0EmeOD6fIUS8D+9Hw+TyRH2p/5kz1oWZtP+TT0z5GjPmvuS5OzoiIlX9JBKJYOXK\nlbjpppvw4YcfimDlNyJZOYJI1hClq6sLDzzwAFasWIGPP/4YZWVluPHGG9HQ0IBS+sIVhgyNv/+9\ntSEhU/ODQVOyNM2MWHH5olwsbigUseKC5fNZ87b4l6wa8UoQKU6dblSjUbwNsK4qpFWLvO3cuVSZ\nAqzyNX26KVS7d5vH3nXXd2zHKaQnEomgubkZ48ePx65du+BTxVvIN0SycgSRrDygu7sbjzzyCH73\nu9+hs7MTpaWlmDBhAmbNmoUym5wcIfdptKu4nRCh+RcumNOKHo8pSKq58HZi5EjzOYWWHAQLADB6\ndErT5aAfdkGQri57ceKCpUazNA344z82hGrnTuv5Ro4UoRoIotEompubMXbs2OT9VoW8RyQrRxDJ\nyjOuXLmCpUuX4re//S0OHz6MkpISjB8/Hg0NDShP92UqDAka33gjtbGqCkCiAr0qXgQlO5WXp2aj\n200fEjb79PKRNh2tkkWnPnPGuPQ3vnGfpa8qVMeOiVBlg2g0ipaWFlRUVKCjowNFtCBCyHdEsnIE\nkaw85urVq2hsbMSyZcuwb98+FBcXo7q6Gg0NDaioqHB7eMIA0tjRYW1IiFcKN90EAJi/ZYtpRDbR\nqiT894Q+KyorgXgc9/3oR5auJ4P2skZCtWaNiNRgQvdTHTFiBA4cOCCCVViIZOUIIlkFQigUwvLl\ny/H4449j9+7d8Pv9qK6uxsyZM1FZWen28IRBpHHECGvDLbc4d546NbWtvt6y+Z2f/GQARiUMJLFY\nDKtWrcINN9yAgwcPIhCwXz0q5C0iWTmCSFYBEo1GsWLFCixduhQ7d+6E1+vFuHHjMGPGDFRVVUlh\nQkEYwsRiMaxevRqBQACHDh2SlceFiXyI5wgiWQVOPB5Hc3MzlixZgq1bt0LTNFRVVaG+vh41NTUi\nXIIwhIjH41i9ejW8Xi8OHz4sK40LF/ngzhFEsoQkuq5j/fr1eOihh7BlyxbE43FUVVVh+vTpmDhx\nogiXIOQwuq5j9erVAIDDhw/LyuLCRj6scwSRLMEWXdfx2muv4YEHHsCmTZsQjUZRWVmJadOmoba2\nVoRLEHIIXdexdu1aRKNRHDlyBMPV+1gKhYZ8QOcIIllCn+i6jnfeeQeLFi3C66+/jlAohDFjxmDK\nlCmYPHmyVI4WBBehCHQwGMThw4cxcqR9iQ2hoBDJyhFEsoR+s3XrVixcuBCvvPIKenp6MHr0aNTV\n1aGurk4qSQvCIKLrOjZs2IDe3l4cOnRISrMIhEhWjiCSJVwX7e3tWLhwIdavX4/Lly9j1KhRmDx5\nMqZOnSqVpQUhi+i6jpdeegmXLl3CoUOHMGbMGLeHJOQOIlk5gkiWMGAcOHAACxYswJo1a3DhwgWM\nGjUKtbW1qK+vF+EShAFE13W8/PLL6O7uxoEDB1DlVHxWKFREsnIEkSwhK3R2dmLRokVobm5GV1cX\nysvLMWnSJNTX16O4uNjt4QnCkEXXdbzyyivo6urC/v37UVNT4/aQhNxDJCtHEMkSss7JkyexePFi\nPPfcczh9+jRGjBiBiRMnYubMmVIoURD6yauvvopPPvkE+/btw4QJE9wejpCbiGTlCCJZwqDS1dWF\nBx98ECtWrMCJEydQVlaGG2+8EQ0NDVI4URD6oLW1FSdPnsTevXtxU+I+lIJgg0hWjiCSJbhGd3c3\nlixZgqeeegqdnZ0oLS3FhAkTMGvWLCmkKAgKr7/+Ok6cOIE9e/agtrbW7eEIuY1IVo4gkiXkBFeu\nXMHSpUvx5JNPJu+3Nn78eDQ0NKC8vNzt4QmCq7z55ps4duwYdu3ahbq6OreHI+Q+Ilk5gkiWkHNc\nvXoVTU1NaGpqwr59+1BcXIzq6mo0NDRIHSCh4Ni0aROOHDmCnTt3Ytq0aW4PRxgaiGTlCCJZQk4T\nCoWwfPlyPPHEE2hvb4ff70d1dTVmzpyJyspKt4cnCFnlnXfewcGDB7Ft2zbMmDHD7eEIQweRrBxB\nJEsYMkSjUaxYsQKPPfYYduzYAa/Xi3HjxmHGjBmoqqqS+ykKecWWLVuwf/9+fPDBB5g1a5bbwxGG\nFvJhmCOIZAlDkng8jubmZixZsgRbt26FpmmoqqpCfX09ampqRLiEIc27776Ljo4OvPvuu7jjjjvc\nHo4w9JAPwBxBJEsY8tANch9++GFs3rwZ8XgcVVVVmD59OiZOnCjCJQwp3n//fezZswdvv/02Zs+e\n7fZwhKGJfOjlCCJZQl6h6zpaW1uxePFibNq0CdFoFJWVlUyEL6gAAAvpSURBVJg2bRpqa2tFuISc\nZuvWrWhvb8ebb76JuXPnuj0cYegiH3Q5gkiWkLfouo7Nmzdj0aJFaG1tRSgUwpgxYzBlyhRMnjwZ\nHo/H7SEKQpJt27Zh586deO2113D33Xe7PRxhaCOSlSOIZAkFw9atW7Fw4UK88sor6OnpwejRo1FX\nV4e6ujr4fD63hycUMDt27MD27dvx8ssv43Of+5zbwxGGPiJZOYJIllCQtLe3Y+HChdiwYQMuXbqE\nUaNGYfLkyZg6dSr8fr/bwxMKiA8//BBtbW1Yv3497rnnHreHI+QHIlk5gkiWUPAcOHAACxYswJo1\na3DhwgWMGjUKtbW1qK+vF+ESssquXbuwdetWrF69Gl/84hfdHo6QP4hk5QgiWYLA6OzsxKJFi9DS\n0oKzZ8+ivLwckyZNQn19PYqLi90enpBH7NmzB++++y5aWlrwV3/1V24PR8gvRLJyBJEsQXDg5MmT\neOCBB/Dss8/i9OnTGDFiBCZOnIiZM2eipKTE7eEJQ5i9e/diy5YtePbZZ/G3f/u3bg9HyD9EsnIE\nkSxByICuri48+OCDWLFiBU6cOIGysjLceOONaGhoQGlpqdvDE4YQ+/btwzvvvIPf//73+PrXv+72\ncIT8RCQrRxDJEoR+0t3djSVLluCpp55CZ2cnSktLMWHCBMyaNQtlZWVuD0/IYQ4cOIBNmzbhySef\nxDe/+U23hyPkLyJZOYJIliBcB1euXMHSpUvx5JNP4tChQygpKcH48ePR0NCA8vJyt4cn5BCHDh3C\nm2++iWXLluEf//Ef3R6OkN+IZOUIIlmCMEBcvXoVTU1NWLZsGTo6OhAIBFBTU4OGhgZUVFS4PTzB\nRY4cOYLXX38djz32GP7pn/7J7eEI+Y9IVo4gkiUIWSAcDmP58uV4/PHH0d7eDr/fj3HjxqGhoQGV\nlZVuD08YRI4ePYrW1lYsWbIE3//+990ejlAYiGTlCCJZgpBlotEonnnmGSxduhQ7duyA1+vFuHHj\nMGPGDFRVVcn9FPOY48eP45VXXsEDDzyAH/7wh24PRygc5EMlRxDJEoRBJB6Po6WlBY888gi2bt0K\nTdMwduxY1NfXY/z48SJceQQJ1n/+53/iRz/6kdvDEQoL+SDJEUSyBMEldF3H+vXr8fDDD2Pz5s2I\nx+OoqqrC9OnTMXHiRBGuIczHH3+Ml156CT//+c/x05/+1O3hCIWHfHjkCCJZgpAD6LqO1tZWPPDA\nA3jrrbcQjUZRWVmJadOmoba2VoRrCHHq1Cm8+OKL+Pd//3fcf//9bg9HKEzkAyNHEMkShBxk8+bN\nWLhwIVpbWxEKhTBmzBhMmTIFkydPhsfjcXt4ggOnT5/Ghg0b8OMf/xi//OUv3R6OULiIZOUIIlmC\nkONs27YNCxYswMaNG9HT04PRo0ejrq4OdXV18Pl8bg9PSHDmzBmsW7cOP/zhD7F48WK3hyMUNiJZ\nOYJIliAMIdrb27Fw4UJs2LABly5dwqhRozB58mRMnToVfr/f7eEVLGfPnsXatWvx/e9/H4888ojb\nwxEEkawcQSRLEIYoBw8exIIFC7B69WpcuHABo0aNQm1tLerr60W4BpGuri6sXbsW8+bNw2OPPeb2\ncAQBEMnKGUSyBCEPOHbsGBYtWoTm5macPXsW5eXlmDRpEurr61FcXOz28PKW8+fPY/Xq1fiHf/gH\nNDU1uT0cQSBEsnIEkSxByDNOnTqFxYsX47nnnsOpU6cwfPhw3HTTTZg5cyZKSkrcHl7ecOHCBbzw\nwgv4xje+geXLl7s9HEHgiGTlCCJZgpDHdHV14aGHHsLTTz+NEydOoKysDDfeeCMaGhpQWlrq9vCG\nLN3d3Vi1ahW+9rWv4emnn3Z7OIKgIpKVI4hkCUKBcPHiRTzyyCP43e9+h6NHj6K0tBQTJkzArFmz\nUFZW5vbwhgyXLl1CS0sLvvzlL+O5555zeziCYIdIVo4gkiUIBUhPTw8ee+wx/OY3v8GhQ4dQUlKC\nmpoazJo1C+Xl5W4PL2e5fPkyWlpa8Od//udYtWqV28MRBCdEsnIEkSxBKHCCwSAaGxuxbNkydHR0\nIBAIoKamBg0NDaioqHB7eDnDlStX0NzcjD/5kz/BunXr3B6OIKRDJCtHEMkSBCFJOBzG8uXL8fjj\nj6O9vR1+vx/jxo1DQ0MDKisr3R6ea/T09KC5uRl33303XnrpJbnNkZDryC9ojiCSJQiCLdFoFM88\n8wyWLl2KHTt2wOv1oqqqCjNnzkRVVVXBiEZvby9WrlyJuXPn4rXXXiuY1y0MaeSXNEcQyRIEoU/i\n8ThaWlqwZMkSfPDBBwCAqqoq1NfXY/z48XkrHsFgEM8//zzuvPNOvPnmm3n7OoW8Q35RcwSRLEEQ\n+oWu69iwYQMeeughbNmyBbFYDGPHjsWtt96KiRMn5o2IBINBrFy5ErNmzcLmzZvz5nUJBYH8suYI\nIlmCIFwzuq6jtbUVDzzwAN566y1EIhGMHTsWU6dORW1tLTwej9tDvCZCoRBWrlyJ+vp6vPfeeyJY\nwlBDfmFzBJEsQRAGjM2bN2PhwoVobW1FKBTC6NGjMXXqVEyePHnICBcJ1tSpU7F169YhM25BYIhk\n5QgiWYIgZIVt27ZhwYIF2LhxI3p6ejB69GjU1dWhrq4OPp/P7eHZEg6HsXLlStx8883YsWOHCJYw\nVBHJyhFEsgRByDq7d+/GggULsGHDBly6dAmjRo3C5MmTMXXqVPj9freHBwCIRCJobm7GhAkTsGvX\nLni9XreHJAjXikhWjiCSJQjCoHLw4EEsWLAAa9aswfnz5zFq1CjU1taivr7eNeGKRqNobm5GVVUV\ndu/enTPiJwjXiEhWjiCSJQiCaxw7dgyLFi1Cc3Mzzp49i/LyckyaNAn19fUoLi4elDFEo1G0tLRg\n9OjR6OjoEMES8gGRrBxBJEsQhJzg1KlTWLx4MZ577jmcOnUKw4cPx0033YSZM2eipKQkK9eMxWJo\naWnByJEjsW/fPhQVFWXlOoIwyIhk5QgiWYIg5BxdXV146KGH8PTTT+PEiRMoKyvDjTfeiIaGBpSW\nlg7INWKxGFatWoWysjIcOHAAgUBgQM4rCDmASFaOIJIlCEJOc/HiRSxZsgRPPfUUjh49itLSUkyY\nMAGzZs1CWVnZNZ0zFovhhRdeQElJCQ4dOjRoU5OCMEiIZOUIIlmCIAwZenp68Nhjj+E3v/kNDh06\nhJKSEtTU1GDWrFkoLy/P6BzxeBwvvPACioqKcOjQIQwbNizLoxaEQUckK0cQyRIEYUgSDAaxbNky\nNDY2oqOjA4FAADU1NWhoaEBFRYXtMbquY/Xq1dA0DUeOHBmwqUdByDFEsnIEkSxBEIY84XAYy5cv\nxxNPPIFdu3bB7/dj3LhxaGhoQGVlJQBDsNasWYN4PI4jR45c81SjIAwBRLJyBJEsQRDyimg0imef\nfRaPPvootm/fDq/Xi6qqKvT09CAej+Pw4cMZTy0KwhBFJCtHEMkSBCFvicfjaGlpwYMPPoj9+/fj\nyJEjGDlypNvDEoRsI5KVI4hkCYIgCEJ+IZKVI8jdTwVBEARBELKASJYgCIIgCEIWEMkSBEEQBEHI\nAiJZgiAIgiAIWUAkSxAEQRAEIQuIZAmCIAiCIGQBkSxBEARBEIQsIJIlCIIgCIKQBUSyBEEQBEEQ\nsoBIliAIgiAIQhYQyRIEQRAEQcgCIlmCIAiCIAhZQCRLEARBEAQhC4hkCYIgCIIgZAGRLEEQBEEQ\nhCwgkiUIgiAIgpAFRLIEQRAEQRCygEiWIAiCIAhCFhDJEgRBEARByAIiWYIgCIIgCFlAJEsQBEEQ\nBCELiGQJgiAIgiBkAZEsQRAEQRCELCCSJQiCIAiCkAVEsgRBEARBELKASJYgCIIgCEIWEMkSBEEQ\nBEHIAiJZgiAIgiAIWcDXz/5aVkYhCIIgCIKQZ0gkSxAEQRAEIQuIZAmCIAiCIGQBkSxBEARBEIQs\nIJIlCIIgCIKQBUSyBEEQBEEQsoBIliAIgiAIQhYQyRIEQRAEQcgCIlmCIAiCIAhZQCRLEARBEAQh\nC4hkCYIgCIIgZIH/HywV/VQ3TpcvAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "bell_tomo_circuits = tomo.build_state_tomography_circuits(Q_program,\n", + " 'bell', bell_qubits,\n", + " qr, cr)\n", + "bell_tomo_result = Q_program.execute(bell_tomo_circuits, backend=backend, shots=shots)\n", + "bell_tomo_data = tomo.state_tomography_data(bell_tomo_result, 'bell', bell_qubits)\n", + "rho_fit_sim = tomo.fit_tomography_data(bell_tomo_data)\n", + "plot_wigner_function(np.matrix(rho_fit_sim),res=200)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "again, using the same code from before, we can calculate the analytic expression for the Wigner function from the generated density matrix, it can be seen that since the density matrix is less sparse, the resulting Wigner function has many more terms" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.493698558640376 \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) + 0.00275286172575906 \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) - \\frac{\\sqrt{3}}{2} \\left(-0.00534735110770023 - 0.00770494561267218 i\\right) \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) e^{2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{1} \\right )} - \\frac{\\sqrt{3}}{2} \\left(-0.00534735110770023 + 0.00770494561267218 i\\right) \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) e^{- 2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{1} \\right )} + 0.00266528247889166 \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) + 0.500883297154973 \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) - \\frac{\\sqrt{3}}{2} \\left(-0.0015149834996068 + 0.000102164609935808 i\\right) \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) e^{2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{1} \\right )} - \\frac{\\sqrt{3}}{2} \\left(-0.0015149834996068 - 0.000102164609935808 i\\right) \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) e^{- 2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{1} \\right )} - \\frac{\\sqrt{3}}{2} \\left(-0.00628509857352323 - 0.000924492486476053 i\\right) \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) e^{2.0 i \\phi_{0}} \\sin{\\left (2 \\theta_{0} \\right )} - \\frac{\\sqrt{3}}{2} \\left(-0.00628509857352323 + 0.000924492486476053 i\\right) \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) e^{- 2.0 i \\phi_{0}} \\sin{\\left (2 \\theta_{0} \\right )} - \\frac{\\sqrt{3}}{2} \\left(-0.000462681165102337 + 0.00867331154973143 i\\right) \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) e^{2.0 i \\phi_{0}} \\sin{\\left (2 \\theta_{0} \\right )} - \\frac{\\sqrt{3}}{2} \\left(-0.000462681165102337 - 0.00867331154973143 i\\right) \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) e^{- 2.0 i \\phi_{0}} \\sin{\\left (2 \\theta_{0} \\right )} + \\frac{3}{4} \\left(0.492697839219187 - 0.0085595434721166 i\\right) e^{2.0 i \\phi_{0}} e^{2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{0} \\right )} \\sin{\\left (2 \\theta_{1} \\right )} + \\frac{3}{4} \\left(0.00247818568149116 + 0.000867188901661959 i\\right) e^{2.0 i \\phi_{0}} e^{- 2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{0} \\right )} \\sin{\\left (2 \\theta_{1} \\right )} + \\frac{3}{4} \\left(0.00247818568149116 - 0.000867188901661959 i\\right) e^{- 2.0 i \\phi_{0}} e^{2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{0} \\right )} \\sin{\\left (2 \\theta_{1} \\right )} + \\frac{3}{4} \\left(0.492697839219187 + 0.0085595434721166 i\\right) e^{- 2.0 i \\phi_{0}} e^{- 2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{0} \\right )} \\sin{\\left (2 \\theta_{1} \\right )}\n" + ] + } + ], + "source": [ + "Delta_su2 = sym.zeros(2) \n", + "Delta = sym.ones(1)\n", + "for qubit in range(num):\n", + " phi = sym.Indexed('phi', qubit)\n", + " theta = sym.Indexed('theta', qubit)\n", + " costheta = harr*sym.cos(2*theta)\n", + " sintheta = harr*sym.sin(2*theta)\n", + " Delta_su2[0,0] = (1+costheta)/2\n", + " Delta_su2[0,1] = -(sym.exp(2j*phi)*sintheta)/2\n", + " Delta_su2[1,0] = -(sym.exp(-2j*phi)*sintheta)/2\n", + " Delta_su2[1,1] = (1-costheta)/2\n", + " Delta = TensorProduct(Delta,Delta_su2)\n", + "W = sym.trace(np.matrix(rho_fit_sim)*Delta)\n", + "print(sym.latex(W))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$W = 0.493698558640376 \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) + 0.00275286172575906 \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) - \\frac{\\sqrt{3}}{2} \\left(-0.00534735110770023 - 0.00770494561267218 i\\right) \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) e^{2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{1} \\right )} - \\frac{\\sqrt{3}}{2} \\left(-0.00534735110770023 + 0.00770494561267218 i\\right) \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) e^{- 2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{1} \\right )} + 0.00266528247889166 \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) + 0.500883297154973 \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) - \\frac{\\sqrt{3}}{2} \\left(-0.0015149834996068 + 0.000102164609935808 i\\right) \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) e^{2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{1} \\right )} - \\frac{\\sqrt{3}}{2} \\left(-0.0015149834996068 - 0.000102164609935808 i\\right) \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) e^{- 2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{1} \\right )} - \\frac{\\sqrt{3}}{2} \\left(-0.00628509857352323 - 0.000924492486476053 i\\right) \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) e^{2.0 i \\phi_{0}} \\sin{\\left (2 \\theta_{0} \\right )} - \\frac{\\sqrt{3}}{2} \\left(-0.00628509857352323 + 0.000924492486476053 i\\right) \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) e^{- 2.0 i \\phi_{0}} \\sin{\\left (2 \\theta_{0} \\right )} - \\frac{\\sqrt{3}}{2} \\left(-0.000462681165102337 + 0.00867331154973143 i\\right) \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) e^{2.0 i \\phi_{0}} \\sin{\\left (2 \\theta_{0} \\right )} - \\frac{\\sqrt{3}}{2} \\left(-0.000462681165102337 - 0.00867331154973143 i\\right) \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) e^{- 2.0 i \\phi_{0}} \\sin{\\left (2 \\theta_{0} \\right )} + \\frac{3}{4} \\left(0.492697839219187 - 0.0085595434721166 i\\right) e^{2.0 i \\phi_{0}} e^{2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{0} \\right )} \\sin{\\left (2 \\theta_{1} \\right )} + \\frac{3}{4} \\left(0.00247818568149116 + 0.000867188901661959 i\\right) e^{2.0 i \\phi_{0}} e^{- 2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{0} \\right )} \\sin{\\left (2 \\theta_{1} \\right )} + \\frac{3}{4} \\left(0.00247818568149116 - 0.000867188901661959 i\\right) e^{- 2.0 i \\phi_{0}} e^{2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{0} \\right )} \\sin{\\left (2 \\theta_{1} \\right )} + \\frac{3}{4} \\left(0.492697839219187 + 0.0085595434721166 i\\right) e^{- 2.0 i \\phi_{0}} e^{- 2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{0} \\right )} \\sin{\\left (2 \\theta_{1} \\right )}$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Experiment" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + ">> created state tomography circuits for \"bell\"\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING:IBMQuantumExperience.IBMQuantumExperience:Got a 502 code response to https://quantumexperience.ng.bluemix.net/api/Jobs?access_token=GwcNFfr1iDZovxtQleJdVmQcahhsWNXd0QIwrkvL872GMIE2R4utDnwvwGUspjgl: 502 Bad Gateway: Registered endpoint failed to handle the request.\n", + "\n", + "WARNING:IBMQuantumExperience.IBMQuantumExperience:Got a 502 code response to https://quantumexperience.ng.bluemix.net/api/Jobs?access_token=GwcNFfr1iDZovxtQleJdVmQcahhsWNXd0QIwrkvL872GMIE2R4utDnwvwGUspjgl: 502 Bad Gateway: Registered endpoint failed to handle the request.\n", + "\n" + ] + } + ], + "source": [ + "Q_program = QuantumProgram()\n", + "Q_program.set_api(Qconfig.APItoken, Qconfig.config['url'])\n", + "\n", + "number_of_qubits = 2\n", + "backend = 'ibmqx5'\n", + "shots = 1024\n", + "bell_qubits = [0, 1]\n", + "qr = Q_program.create_quantum_register('qr',2)\n", + "cr = Q_program.create_classical_register('cr',2)\n", + "bell = Q_program.create_circuit('bell', [qr], [cr])\n", + "bell.h(qr[1])\n", + "bell.cx(qr[1],qr[0])\n", + "\n", + "bell_tomo_circuits = tomo.build_state_tomography_circuits(Q_program,\n", + " 'bell', bell_qubits,\n", + " qr, cr)\n", + "bell_tomo_result = Q_program.execute(bell_tomo_circuits, backend=backend, shots=shots, timeout=300)\n", + "bell_tomo_data = tomo.state_tomography_data(bell_tomo_result, 'bell', bell_qubits)\n", + "rho_fit_ibmqx5 = tomo.fit_tomography_data(bell_tomo_data)\n", + "plot_wigner_function(np.matrix(rho_fit_ibmqx5),res=100)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 0.42449513+0.j 0.04903598-0.03810053j 0.04086913-0.02804089j\n", + " 0.28509530+0.00922257j]\n", + " [ 0.04903598+0.03810053j 0.12420290+0.j -0.03528153+0.00875078j\n", + " 0.05128566-0.04143676j]\n", + " [ 0.04086913+0.02804089j -0.03528153-0.00875078j 0.12430677+0.j\n", + " 0.02853103-0.02387418j]\n", + " [ 0.28509530-0.00922257j 0.05128566+0.04143676j 0.02853103+0.02387418j\n", + " 0.32699520+0.j ]]\n" + ] + } + ], + "source": [ + "print(rho_fit_ibmqx5)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.32699519833677 \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) + 0.124306773174647 \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) - \\frac{\\sqrt{3}}{2} \\left(0.0285310304913017 + 0.0238741788035984 i\\right) \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) e^{2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{1} \\right )} - \\frac{\\sqrt{3}}{2} \\left(0.0285310304913017 - 0.0238741788035984 i\\right) \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) e^{- 2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{1} \\right )} + 0.124202902962916 \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) + 0.424495125525667 \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) - \\frac{\\sqrt{3}}{2} \\left(0.0490359773360699 + 0.0381005337507329 i\\right) \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) e^{2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{1} \\right )} - \\frac{\\sqrt{3}}{2} \\left(0.0490359773360699 - 0.0381005337507329 i\\right) \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) e^{- 2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{1} \\right )} - \\frac{\\sqrt{3}}{2} \\left(0.0512856636758563 + 0.0414367583959388 i\\right) \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) e^{2.0 i \\phi_{0}} \\sin{\\left (2 \\theta_{0} \\right )} - \\frac{\\sqrt{3}}{2} \\left(0.0512856636758563 - 0.0414367583959388 i\\right) \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) e^{- 2.0 i \\phi_{0}} \\sin{\\left (2 \\theta_{0} \\right )} - \\frac{\\sqrt{3}}{2} \\left(0.0408691303527403 + 0.0280408874045363 i\\right) \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) e^{2.0 i \\phi_{0}} \\sin{\\left (2 \\theta_{0} \\right )} - \\frac{\\sqrt{3}}{2} \\left(0.0408691303527403 - 0.0280408874045363 i\\right) \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) e^{- 2.0 i \\phi_{0}} \\sin{\\left (2 \\theta_{0} \\right )} + \\frac{3}{4} \\left(0.285095302985003 - 0.00922257353994807 i\\right) e^{2.0 i \\phi_{0}} e^{2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{0} \\right )} \\sin{\\left (2 \\theta_{1} \\right )} + \\frac{3}{4} \\left(-0.035281529513114 - 0.00875077955598942 i\\right) e^{2.0 i \\phi_{0}} e^{- 2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{0} \\right )} \\sin{\\left (2 \\theta_{1} \\right )} + \\frac{3}{4} \\left(-0.035281529513114 + 0.00875077955598942 i\\right) e^{- 2.0 i \\phi_{0}} e^{2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{0} \\right )} \\sin{\\left (2 \\theta_{1} \\right )} + \\frac{3}{4} \\left(0.285095302985003 + 0.00922257353994807 i\\right) e^{- 2.0 i \\phi_{0}} e^{- 2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{0} \\right )} \\sin{\\left (2 \\theta_{1} \\right )}\n" + ] + } + ], + "source": [ + "Delta_su2 = sym.zeros(2) \n", + "Delta = sym.ones(1)\n", + "for qubit in range(num):\n", + " phi = sym.Indexed('phi', qubit)\n", + " theta = sym.Indexed('theta', qubit)\n", + " costheta = harr*sym.cos(2*theta)\n", + " sintheta = harr*sym.sin(2*theta)\n", + " Delta_su2[0,0] = (1+costheta)/2\n", + " Delta_su2[0,1] = -(sym.exp(2j*phi)*sintheta)/2\n", + " Delta_su2[1,0] = -(sym.exp(-2j*phi)*sintheta)/2\n", + " Delta_su2[1,1] = (1-costheta)/2\n", + " Delta = TensorProduct(Delta,Delta_su2)\n", + "W = sym.trace(np.matrix(rho_fit_ibmqx5)*Delta)\n", + "print(sym.latex(W))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$0.32699519833677 \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) + 0.124306773174647 \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) - \\frac{\\sqrt{3}}{2} \\left(0.0285310304913017 + 0.0238741788035984 i\\right) \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) e^{2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{1} \\right )} - \\frac{\\sqrt{3}}{2} \\left(0.0285310304913017 - 0.0238741788035984 i\\right) \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) e^{- 2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{1} \\right )} + 0.124202902962916 \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) + 0.424495125525667 \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) - \\frac{\\sqrt{3}}{2} \\left(0.0490359773360699 + 0.0381005337507329 i\\right) \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) e^{2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{1} \\right )} - \\frac{\\sqrt{3}}{2} \\left(0.0490359773360699 - 0.0381005337507329 i\\right) \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{0} \\right )} + \\frac{1}{2}\\right) e^{- 2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{1} \\right )} - \\frac{\\sqrt{3}}{2} \\left(0.0512856636758563 + 0.0414367583959388 i\\right) \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) e^{2.0 i \\phi_{0}} \\sin{\\left (2 \\theta_{0} \\right )} - \\frac{\\sqrt{3}}{2} \\left(0.0512856636758563 - 0.0414367583959388 i\\right) \\left(- \\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) e^{- 2.0 i \\phi_{0}} \\sin{\\left (2 \\theta_{0} \\right )} - \\frac{\\sqrt{3}}{2} \\left(0.0408691303527403 + 0.0280408874045363 i\\right) \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) e^{2.0 i \\phi_{0}} \\sin{\\left (2 \\theta_{0} \\right )} - \\frac{\\sqrt{3}}{2} \\left(0.0408691303527403 - 0.0280408874045363 i\\right) \\left(\\frac{\\sqrt{3}}{2} \\cos{\\left (2 \\theta_{1} \\right )} + \\frac{1}{2}\\right) e^{- 2.0 i \\phi_{0}} \\sin{\\left (2 \\theta_{0} \\right )} + \\frac{3}{4} \\left(0.285095302985003 - 0.00922257353994807 i\\right) e^{2.0 i \\phi_{0}} e^{2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{0} \\right )} \\sin{\\left (2 \\theta_{1} \\right )} + \\frac{3}{4} \\left(-0.035281529513114 - 0.00875077955598942 i\\right) e^{2.0 i \\phi_{0}} e^{- 2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{0} \\right )} \\sin{\\left (2 \\theta_{1} \\right )} + \\frac{3}{4} \\left(-0.035281529513114 + 0.00875077955598942 i\\right) e^{- 2.0 i \\phi_{0}} e^{2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{0} \\right )} \\sin{\\left (2 \\theta_{1} \\right )} + \\frac{3}{4} \\left(0.285095302985003 + 0.00922257353994807 i\\right) e^{- 2.0 i \\phi_{0}} e^{- 2.0 i \\phi_{1}} \\sin{\\left (2 \\theta_{0} \\right )} \\sin{\\left (2 \\theta_{1} \\right )}$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Measuring Points in Phase Space\n", + "\n", + "We will now look at how to create the circuits to measure set points in phase space. The following results are based on the figures in [*RP Rundle, PW Mills, T Tilma, JH Samson, MJ Everitt, Phys. Rev. A 96, 022117*](r p rundle prl)\n", + "\n", + "## Plaquette Visualisation\n", + "Staying with the bell state, we will look here at the slice where $\\phi_0=\\phi_1=0$ and we plot $\\theta_0$ against $\\theta_1$" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + ">> created Wigner function circuits for \"bell\"\n", + "COMPLETED\n" + ] + }, + { + "data": { + "image/png": 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OolE1mweV1u109aYEhqHsAfzjH7u0CBTA+vXF7N6tejsvv/yVo+GKBNFonFde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\nV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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "theta1_points = 8\n", + "theta2_points = 8\n", + "number_of_points = theta1_points*theta2_points\n", + "the1 = [0]*number_of_points\n", + "the2 = [0]*number_of_points #initialize theta values\n", + "phis = [[0]*number_of_points]*number_of_qubits #set phi values to 0\n", + "\n", + "point = 0\n", + "for i in range(theta1_points):\n", + " for k in range(theta2_points):\n", + " \n", + " the1[point] = 2*i*np.pi/theta1_points\n", + " the2[point] = 2*k*np.pi/theta2_points #create the values of theta for all points on plot\n", + " point += 1\n", + " \n", + "thetas = np.vstack((the1,the2))\n", + "bell_circuits = tomo.build_wigner_circuits(Q_program, 'bell', phis, thetas, \n", + " bell_qubits, qr, cr)\n", + "bell_result = Q_program.execute(bell_circuits, backend=backend, shots=shots)\n", + "print(bell_result)\n", + "wdata = tomo.wigner_data(bell_result, bell_qubits,\n", + " bell_circuits, shots=shots)\n", + "wdata = np.matrix(wdata)\n", + "wdata = wdata.reshape(theta1_points,theta2_points) \n", + "plot_wigner_data(wdata, method='plaquette')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Curve on a Wigner fucntion\n", + "We can also take a line around phase space and plot a curve. A useful line to take is the equator of the equal angle slice, below we plot this slice also for the Bell-state. When we have an $n$-qubit maximally entangled state of the form $\\left(|0...0\\rangle + |1...1\\rangle\\right)/\\sqrt{2}$, the equatorial slice will show sinusoidal behaviour with frequency $n$." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + ">> created Wigner function circuits for \"bell\"\n" + ] + }, + { + "data": { + "image/png": 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s1o7gaahq7sHpNqzQBDBjq4FqY0ytMWYUeB7YMvkEY8w+Y8zEmsj7gRwvtBtw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\nf6a0MBtgSrMTWZyZwIsV/l0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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "equator_points = 64\n", + "theta = [np.pi/2]*equator_points\n", + "phi = [0]*equator_points\n", + "\n", + "point = 0\n", + "for i in range(equator_points):\n", + " phi[i] = 2*i*np.pi/equator_points\n", + " \n", + "thetas = np.vstack((theta,theta))\n", + "phis = np.vstack((phi,phi))\n", + "bell_eq_circuits = tomo.build_wigner_circuits(Q_program, 'bell', phis, thetas, \n", + " bell_qubits, qr, cr)\n", + "bell_eq_result = Q_program.execute(bell_eq_circuits, backend=backend, shots=shots)\n", + "wdata_eq = tomo.wigner_data(bell_eq_result, bell_qubits,\n", + " bell_eq_circuits, shots=shots)\n", + "plot_wigner_data(wdata_eq, method='curve')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Recreating the equatorial slice of a five qubit GHZ state, $\\left(|00000\\rangle - |11111\\rangle\\right)/\\sqrt{2}$ from the paper, the following gates are needed..." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + ">> created Wigner function circuits for \"ghz\"\n" + ] + }, + { + "data": { + "image/png": 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5vaZDCMhqIfR7HUK1hBahDTRHGoAGU2GPUB6AVQeZeMSvxMJzgozMSxYqmpeA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\nizH6we3VwgAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "Q_program = QuantumProgram()\n", + "number_of_qubits = 5\n", + "backend = 'local_qasm_simulator'\n", + "shots = 1024\n", + "ghz_qubits = [0, 1, 2, 3, 4]\n", + "qr = Q_program.create_quantum_register('qr',5)\n", + "cr = Q_program.create_classical_register('cr',5)\n", + "ghz = Q_program.create_circuit('ghz', [qr], [cr])\n", + "ghz.h(qr[0])\n", + "ghz.h(qr[1])\n", + "ghz.x(qr[2])\n", + "ghz.h(qr[3])\n", + "ghz.h(qr[4])\n", + "ghz.cx(qr[0],qr[2])\n", + "ghz.cx(qr[1],qr[2])\n", + "ghz.cx(qr[3],qr[2])\n", + "ghz.cx(qr[4],qr[2])\n", + "ghz.h(qr[0])\n", + "ghz.h(qr[1])\n", + "ghz.h(qr[2])\n", + "ghz.h(qr[3])\n", + "ghz.h(qr[4])\n", + "\n", + "equator_points = 64\n", + "thetas = [[np.pi/2]*equator_points]*number_of_qubits\n", + "phi = [0]*equator_points\n", + "\n", + "point = 0\n", + "for i in range(equator_points):\n", + " phi[i] = 2*i*np.pi/equator_points\n", + "phis = np.vstack((phi,phi,phi,phi,phi))\n", + "ghz_eq_circuits = tomo.build_wigner_circuits(Q_program, 'ghz', phis, thetas, \n", + " ghz_qubits, qr, cr)\n", + "ghz_eq_result = Q_program.execute(ghz_eq_circuits, backend=backend, shots=shots, timeout = 300)\n", + "wghzdata_eq = tomo.wigner_data(ghz_eq_result, ghz_qubits,\n", + " ghz_eq_circuits, shots=shots)\n", + "plot_wigner_data(wghzdata_eq, method='curve')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Since all the data for the plot is stored within `wghzdata_eq`, we can import matplotlib and go wild with different ways of plotting" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "plt.plot(phi, wghzdata_eq, 'o')\n", + "plt.axis([0, 2*np.pi, -0.6, 0.6])\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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KotTNsWPHKk7T3r17AQDbt2+vOE0XXHCBiqbOQd+oJqEiSWk6QRDgE5/4BP70T/+0a2of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\nQ1a8irZEukdyWa6XlxUpnJKQoqnkaAO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r0nWSLpJc5u5RWrTRH/2fvAwAT9wGuHgid5Dy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\nAzaKLYQk9JiZ+/tjtHX3PXPuaARXutLM/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QDWtdrsjgNo3TH76JMP1iRwvs2FKFZuUqzI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\nBEHQIJIkCIIgCIKg4f8DzssP8lQLzDwAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "density_matrix = np.zeros((32,32))\n", + "density_matrix[0][0] = 0.5\n", + "density_matrix[0][31] = -0.5\n", + "density_matrix[31][0] = -0.5\n", + "density_matrix[31][31] = 0.5\n", + "plot_wigner_function(density_matrix, res=200)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "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": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/README.rst b/README.rst index e3fe7f1e9..621eb117e 100644 --- a/README.rst +++ b/README.rst @@ -193,7 +193,7 @@ Other QISKit projects Contributors (alphabetically) ----------------------------- -Jerry Chow, Antonio Córcoles, Abigail Cross, Andrew Cross, Ismael Faro, Andreas Fuhrer, Jay M. Gambetta, Takashi Imamichi, Antonio Mezzacapo, Ramis Movassagh, Anna Phan, Rudy Raymond, Ninad Sathaye, Kristan Temme, Chris Wood, James Wootton. +Jerry Chow, Antonio Córcoles, Abigail Cross, Andrew Cross, Vincent Dwyer, Mark Everitt, Ismael Faro, Andreas Fuhrer, Jay M. Gambetta, Takashi Imamichi, Antonio Mezzacapo, Ramis Movassagh, Anna Phan, Rudy Raymond, Russell Rundle, Ninad Sathaye, Kristan Temme, Todd Tilma, Chris Wood, James Wootton. In future updates anyone who contributes to the tutorials can include their name here.