{ "metadata": { "name": "Lecture-5-Parametric-Amplifier" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# QuTiP lecture: Evolution and quantum statistics of a quantum parameter amplifier\n", "\n", "Author: J. R. Johansson, robert@riken.jp\n", "\n", "http://dml.riken.jp/~rob/\n", "\n", "Latest version of this ipython notebook lecture is available at: http://github.com/jrjohansson/qutip-lectures" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%pylab inline" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n", "For more information, type 'help(pylab)'.\n" ] } ], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "from qutip import *" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Parameters\n", "----------" ] }, { "cell_type": "code", "collapsed": false, "input": [ "chi = 0.2\n", "N1 = 75\n", "N2 = 75" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Operators and Hamiltonian\n", "-------------------------" ] }, { "cell_type": "code", "collapsed": false, "input": [ "a = tensor(destroy(N1), qeye(N2))\n", "na = tensor(num(N1), qeye(N2)) \n", "b = tensor(qeye(N1), destroy(N2))\n", "nb = tensor(qeye(N1), num(N2)) " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "H = - chi * (a * b + a.dag() * b.dag())" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "# start in the ground (vacuum) state\n", "psi0 = tensor(basis(N1,0), basis(N2,0))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Evolution\n", "---------" ] }, { "cell_type": "code", "collapsed": false, "input": [ "tlist = linspace(0, 10, 100)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "c_ops = []" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "e_ops = []" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "output = mesolve(H, psi0, tlist, c_ops, e_ops)\n", "output" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 10, "text": [ "Odedata object with mesolve data.\n", "---------------------------------\n", "states = True\n", "num_collapse = 0" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Expectation values and standard deviations\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "na_e = zeros(shape(tlist))\n", "na_s = zeros(shape(tlist))\n", "nb_e = zeros(shape(tlist))\n", "nb_s = zeros(shape(tlist))\n", "\n", "for idx, psi in enumerate(output.states):\n", " na_e[idx] = expect(na, psi)\n", " na_s[idx] = expect(na*na, psi)\n", " nb_e[idx] = expect(nb, psi)\n", " nb_s[idx] = expect(nb*nb, psi)\n", "s\n", "# substract the average squared to obtain variances\n", "na_s = na_s - na_e ** 2\n", "nb_s = nb_s - nb_e ** 2" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 11 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = subplots(2, 2, sharex=True, figsize=(8,5))\n", "\n", "line1 = axes[0,0].plot(tlist, na_e, 'r', linewidth=2)\n", "axes[0,0].set_ylabel(r'$\\langle a^\\dagger a \\rangle$', fontsize=18)\n", "\n", "line2 = axes[0,1].plot(tlist, nb_e, 'b', linewidth=2)\n", "\n", "line3 = axes[1,0].plot(tlist, na_s, 'r', linewidth=2)\n", "axes[1,0].set_xlabel('$t$', fontsize=18)\n", "axes[1,0].set_ylabel(r'$Std[a^\\dagger a]$, $Std[b^\\dagger b]$', fontsize=18)\n", "\n", "line4 = axes[1,1].plot(tlist, nb_s, 'b', linewidth=2)\n", "axes[1,1].set_xlabel('$t$', fontsize=18)\n", "\n", "fig.tight_layout()\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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CDJGdLXqw27UTKSM5WXRHbd0KnD4NPPMMCxy1sKgNOtPT05Geno7HHnsMOTk5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\n" } ], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Wigner functions\n", "----------------" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# pick an arbitrary time and calculate the wigner functions for each mode\n", "xvec = linspace(-5,5,200)\n", "t_idx_vec = [0, 10, 20, 30]\n", "\n", "fig, axes = subplots(len(t_idx_vec), 2, sharex=True, sharey=True, figsize=(8,4*len(t_idx_vec)))\n", "\n", "for idx, t_idx in enumerate(t_idx_vec):\n", " psi_a = ptrace(output.states[t_idx], 0)\n", " psi_b = ptrace(output.states[t_idx], 1)\n", " W_a = wigner(psi_a, xvec, xvec)\n", " W_b = wigner(psi_b, xvec, xvec)\n", " \n", " cont1 = axes[idx,0].contourf(xvec, xvec, W_a, 100)\n", " cont2 = axes[idx,1].contourf(xvec, xvec, W_b, 100)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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G6ImgdCdqUFB9j7Mm5LTiXVQ8JZvwnFFwbKizpN3Gkm4331GlEe7lhqFNY14l\nqC+c7pnJdsHax3BTj+OmLSsTUhwmQ65eGfYlPw3rvTmRsnFMu41knqthptPybGdZUn+e3XMx7ILN\nXbgM0OOgdA+MG1R3Qg6/bhdvU3E47c/N2c0N+2tBYM1JGrebGa/FZV6w2r39m30JgV3w9hLUwOO4\nhi+whBSzJM8QnWP1ynZdya72ZlnB3q+CApaUnmc7y+a9m+WsYTo1y/Z/A/vPyXW5w6J0Jy4rqGnF\nK0kt9RWvbdv6sbTylawJesD/ajukbjil/uM93oBK/qnYt7ZG4eIwcM/VMNxDSFJqlg3fIC0lC9h8\nfj0jz26Wzce+a+pzDc/S8CtW5DkNpVuKYYpXiv9SDyjejtLL1z7ua7/aSdP62Hdpkm9P12zSSIVr\nI4iYdVn3Y/YN0SnFu6n+3LpZlvwFbNhZlpJ5dnNsPk4rW2mMwmWAHgale2CylqZ8UsJq2IGVkpOx\nrI+dO+JEOs57+xht2rHbvpOmfIVLSHHYDLt65Rav1DdIt9VfvuHD+letwvfDZFlKlq35fubwbD4e\nJssYhNItTZ4JWfIf47UvP1AcVndSNnu+5mmsH5HUPxkb7uUMkj+c5vuZATV/Ht/nEoWLw2mY4nVW\nsDaV/JfYHCLyFbAxbJbN8/qG6sKGZ/f78KF0S5VnQpb8x3hti2FQPOVrAmve22dI+nak3ZumZ03J\n0bkbbkDNA+ztZSrGYeYbokfc45X6V7HMnq8U79kOyrL7mI7zsZ1lqeDh2f0+0lC6pRuleH1hlVLL\n14TLnobt40Iu++u+STlRtuYbgwJqf00ipDh8RineNE75HlN/Ads5bcjPzbi3aKVkliUKtzyU7lRw\ngyrlD6uUKN/N8EsmtOG3/a9YZHE7PXc47W2mcHHUDFO8Uq5BWkrm2c2yNFyeE1cXDVu29tcksjw+\nSvdApAVVGj2ssh6nOLRSXMS53bU+dsNpf21QQCVCisMvb/FKgwfpDQXHfKXJZdn8HvtrvkND7tfJ\nchEo3QOTdmJVVlhtg8rXWBz8kIj7fL6iNds16OsSIcXRkad4Jf8gncYuYPP4YeTJM1kuG6V7oOwg\n2tLCKuVfcjbc4GY9zuWGdpyA+h4HHCZ5V7Ck9PLNGqbzZtk81pVncHa/J1G4xaJ0p8KoYZWGK+As\naUF3nzurbCUKF0dbnhUs93Fpe76+ArYvxs/iy3NWln3fJ8uTQOlOjWHCKvmXncct4LSfHRROiYAC\nRtYKlpTHEo5qAAAgAElEQVS9imWkZTnvYaW8WU57LHmeFEp3qmQVr+QvXyn9uO+i57F55N3rlbKv\nvSWgOMry5nlasixRtpNH6U6dtClZ8pev/TPuz+WZiPNsiw9lCwyWVrxS/mFaGj/L7nOnbcuwP4dh\njVy63/jGN/Tyyy+rUqnoPe95j37yk5/oxIkTRW7bEZenfKXsAralBX/Qz6X93nGeBzhKsrIs5Rum\nbUVk2f694z4PhjE/6g9+/OMf19///nf99a9/1fvf/349//zzRW4XInc0eEI1b3meJ+2tqOcH4DdM\n1gbteY6SZfd3jLqdGMfIe7oXL16MPn7iiSf0y1/+spANQppB07LkD5I7PWcZ5d7IhBMYTp4sS+Pl\nmSxPq0KO6f74xz/WM888k/LdS9bH58I3jC5vYI1JvMgA4Rzfm+HbrCHPxUk7fpuFPE+n/HnOLN2L\nFy/q+vX+F2389re/raefflqS9Nxzz6lSqejzn/98yrM8lWtDMKxRAlvU78P43MK6lPbAKUOeJ4M8\nz7b8ec4s3d/+9reZv+anP/2pXnnlFf3ud78bZutQuLTr+Yp+TgCT52aPLB8mIy8vv/rqq3rhhRf0\n2muv6f777y9ym1AIggYcDmT5MBn57OWvfOUr6nQ6unjxoi5cuKD/+Z//KXK7AAA4dEbe033jjTeK\n3A4AAA69kfd0AQDAcChdAABKQukCAFASShcAgJJQugAAlITSBQCgJJQuAAAloXQBACgJpQsAQEko\nXQAASkLpAgBQEkoXAICSULoAAJSE0gUAoCSULgAAJaF0AQAoCaULAEBJKF0AAEpC6QIAUBJKFwCA\nklC6AACUhNIFAKAklC4AACWhdAEAKAmlCwBASShdAABKQukCAFASShcAgJJQugAAlGTs0v3+97+v\n+fl53bp1q4jtAQDg0BqrdK9cuaLf/va3eve7313U9gAAcGiNVbpf//rX9d3vfreobQEA4FAbuXRf\neuklnTlzRo899liR2wMAwKF1LOubFy9e1PXr1/u+/txzz+n555/Xb37zm+hr+/v7Kc9yyfr4XPgG\nHHVvhm+zhjwD/fLneW4/vS1T/e1vf9PHPvYx1Wo1SdLVq1f10EMP6fXXX9fq6mr85HNzkr417NMD\nR9A3MwbX6UCegbzS85y5p5vm0Ucf1Y0bN6LPz507pz//+c9aXl4ebfsAADgCCrlON5iAAQBAlpH2\ndF3/+te/ingaAAAONe5IBQBASShdAABKQukCAFASShcAgJJQugAAlITSBQCgJJQuAAAloXQBACgJ\npQsAQEkoXQAASjJjpTsLL4XGNo5v2rdPmo1tnHaz8N9w2rdx2rdPmv5tLHf7KN3CsY3jm/btk2Zj\nG6fdLPw3nPZtnPbtk6Z/GyldAAAOJUoXAICSzO2nvbx9EU/O6+wCuU0wioUgz0B+aXmeaOkCAIAY\ny8sAAJSE0gUAoCSULgAAJaF0AQAoCaULAEBJKF0AAEpC6QIAUBJKFwCAklC6AACUhNIFAKAklC4A\nACWhdAEAKAmlCwBASShdAABKQukCAFASShcAgJJQugAAlITSBQCgJJQuAAAloXQBACgJpQsAQEko\nXQAASkLpAgBQEkoXAICSULoAAJSE0gUAoCSULgAAJaF0AQAoCaULAEBJKF0AAEpC6QIAUBJKFwCA\nklC6AACUhNIFAKAklC4AACWhdAEAKAmlCwBASY5N8snn5uYm+fTAobK/v3/Qm5CJPAP5peV5oqUb\n+FaBz3VJ0lMFPt8ksI3jm/btk4rfxm8W+FyTRJ6ny7RvnzT92ziJ7UvPM8vLAACUhNIFAKAkM1a6\n5w56A3JgG8c37dsnzcY2TrtZ+G847ds47dsnTf82lrt9lG7h2MbxTfv2SbOxjdNuFv4bTvs2Tvv2\nSdO/jZQuAACHEqULAEBJKF0AAEpC6QIAUBJKFwCAklC6AACUhNIFAKAklC4AACWhdAEAKAmlCwBA\nScYu3Xv37unChQt6+umni9geAAAOrbFL98UXX9QjjzzCC1wDADDAWKV79epVvfLKK/rSl76k/f39\norYJAIBD6dg4P/y1r31NL7zwgu7cuZPxqEvWx+c0/a84AZThzfBt1pBnoF/+PI9cui+//LJWV1d1\n4cIF/f73v8945FOj/grgEHML61LaA6cMeQb65c/zyMvLf/zjH/WrX/1K586d0zPPPKNLly7pi1/8\n4qhPBwDAoTe3X8DB2Ndee03f+9739Otf/zr55HNzkr417tMDR8A3p/68CPIM5JWe58Ku0+XsZQAA\nso11IpXx5JNP6sknnyziqQAAOLS4IxUAACWhdAEAKAmlCwBASShdAABKQukCAFASShcAgJJQugAA\nlITSBQCgJJQuAAAloXQBACgJpQsAQEkoXQAASkLpAgBQEkoXAICSULoAAJSE0gUAoCSULgAAJaF0\nAQAoCaULAEBJKF0AAEpC6QIAUBJKFwCAklC6AACUhNIFAKAklC4AACWhdAEAKAmlCwBASShdAABK\nQukCAFCSYwe9AZi06hCP7U1sKwCMa5gsS+R5Oo21p3vlyhV99KMf1Qc/+EE9+uij+uEPf1jUdmFo\n1ZS3sp8DwPiKyCF5nkZj7ekeP35cP/jBD/T444+r0+noQx/6kC5evKjz588XtX3IVFaA3N/DBA0U\nq8wytH8XWS7bWHu6p06d0uOPPy5JajQaOn/+vK5du1bIhiHNNEysB/37gcNgmrJMnstS2DHdy5cv\n6y9/+YueeOIJ5zuXrI/PhW8YXt5QLBX4O+8M+D4T8+jeDN9mDXke3zAFV1SeB2VZireLLA8vf54L\nKd1Op6PPfvazevHFF9VoNJzvPlXErzjC8gS0yKLNet6s4BLY4biFdSntgVOGPI+OLB9e+fM8dune\nvXtXn/nMZ/SFL3xBn/70p8d9OkQGBTQrnIsF/P6tAb8zLbQEFkgaJ8vS+Hkmy9NkrNLd39/Xs88+\nq0ceeURf/epXi9qmIy4roGnhzBPK2oDvdwc8pxtcsy1ZgSWsOOomkedJZVny55nyLdJYpfuHP/xB\nP/vZz/TYY4/pwoULkqTnn39en/zkJwvZuKMnLaC+cKYFc1Ag06T9nAmw/fvs0GaVL2HFUTVs2fry\nXHaWpcF5JsvjGqt0P/KRj2hvb6+obTnCxilbX8CKXF62n98N7TDlS1hxVExrnrOybB5jLIlBejK4\nI9WByxvQrHD6Qln0JQC+0KaVL8WLo2jUsnWL1s3zuFnuqb9c8wzTDNKTQOkeKF+YRi1b+7nynmTl\nO8HCJyu0vvJNCytTMg6rUYbnPFn2PUfa8+XNs83NsnlOBulJoXQPzLCF6wtoWtHmWbJyv+6efJHG\nLuA85UtYcdjlKdxhyjYry+7Pp33dzrNboj7jDNJkeRiU7oEYVLh5y9b3M4OWndO4IaspffKV/OXr\nezxhxWE26vCcNTjnKehBsvKcZZRBmiwPg9It3SiFm1a2btHaP3s8/nAux2btmw+Ww/d3lW9C7lmP\nc8M6aImKsGKWjZNl++cH5XnILEtOnu9az+cOyGkGDdJkeVSUbqnyhtSdbrPC6QTThNK9MdjCgE3b\nsT7uhM+3L8WhzRtY+zFMyTisih6eU4rWl+dRsiw5ec7iDtIUb5Eo3dIMW7i+gKaUrRtME0o7924J\nuzrWx+bnd+QU8KDlrVHDCsySUQt3UNlaRTuJLJvv7R9XvvJ1uStYFO8oKN1SjFO4bkCdsrXDab6V\nFdg09vTcUBDOxfDrUWDt8h209DxM8RJUzLJxh2enbO3cjpLlFcVRMz9vitjkORqmB5Wvb5CmeMdB\n6U7cKIU7IKC+snXDen/4cd3zq2wmOy1J2+HH/1EcXFPA5nftyClf1x1r+yleHDZZl/OMOTzbWZaS\ng7Sb57TyTcuz+bfB5Hlg+W5Z20zxFonSLd2whZsjoObj+5UMpa94Xa3w/bakBxQEVArydL/iwJq9\nXXvvt5NnUjayzoQ2CCqmWZGFOyDLUpxn9/MsvjxvKS5hk2df+e4fV3qbj1K88KF0J2rYkKYVbs6y\ndT+WkiHOYrKzo7hw7dBuS3pbyZM0pJSwulOy+XO6J2ARVMyKrLtCuQFzCzdjtcrks6X0LJunzLvE\nvKVgpWrH+nxbcUfaw3Rf+ZpBOusywbzFyxDtQ+lOzIQK90H1l+0DioNqf09KFrBhvvcf62smN2Ya\n3lKygBfD59pQf1g3NKB4zecEFYeF7y5R9qpUSuHOHfcPz3aG7eJNW8Uy8mTZHCrakXRd/eXrytzr\nHVS8LvLsonRLl7YMJWUW7or8ATUTsm9iVvg40+eN6OK9WCc89dnkwi5d8/G64pBK/rDuSNryFa/k\nP8ZL8WJWDDNAm8e7hbucvXd7SnGxrqi/fM3H9qYMyrOdZfdQkV2+UjxIv2WeRzmL18Xq1SCU7kTk\nvXeqbyp2CtcE0xSvHdBT8pdwVVJjX/P1rhaqu5KkWiP92tpuJ/gHY6dX0d52LQiuCe3bigO7rnhv\n1w6rra94pfSTqwadAQ1Ms7QVKzvvnsK1V6tazns346ZorTxnZVkK8rzTq0hSkOe355IFbFar1pUc\npN8Ot82cODmweM2fjyF6GJRuqQZNxQMK1xdQ+2tVaX5tOwpmZX5XNXVVDY+lLmjXu1U7SxX1VFN3\nqabdvUoU2r3tmlSfS5bv2+EP3e99qkBq8Zr/BnkmZIKKaTDsAG1/bpaU1V+4ZlB+QMnh2ZTtiqKi\nPflAO8pysEXd9CyrIi1JvaWaugrzvFJTb70ZD9OLivd0153Nd1ewEsVryj7PYSOkoXQLNyikvuO4\nsr5mLSmnFe6K+gJqyra51FZNXTXVVlVd1dTTQnhGRdVzJ6leuD07WlBXVfXma9pZqmhjaUW7exVt\n1ptx+W5Ym7luPYlbwCNPyMCscE+OklIHaF/h2qtVbr4f2Fd1pa1ao6vmfDsq2bx53gmXnzbU0s58\nJSjgpbbad5pB+VbnkgO02euVgjJecZ40yrP5t8vOK0P0sCjd0iymfGyHVP3HcE0gzWRsF64V0OZS\nWy2ta0G7amlDC9pJDavNBLSrahjYito6qabaas83VVnbjcu3Wk+GNUvi5Cr7Hwd7mdlFUDFN0gbo\nIVes8hTuA4qG55MPtKOybaqtmnpqajORZUl9eXaz3NSmeqppU031VFNtqat2o6tup6ZeoxkM0mav\n12YXr4lpR9I+Q3QRKN1CFRBSMxW7e7imcB+WN6BNtdXSRhTOuHh7UQHXPAXWDbfZTMhtNYPCVTMM\ne1y+7WpTPZ1M/+PbS1PRtX/un9suVYKKWZd2/Y5ziMheUrYL92F5h+em2jqpdrRidVLtRJYl9eXZ\nzXJPVe1oQRtqqa2mWtrQxnxL7aWm2o2uNnRaqa+gcF3xsGBOrvIeNjIYovOidEvn+0ubMhWbS3Xs\nJWWrcNfWbvYFNCjetpraVE09VbQT7eUOWl4OCndTbZ3USbW1aZXvgnaDDD2sYErOerkTc6mRRFAx\no/IeJjKPdQZo9xCRGZzNnq6ncE8vXUsMz27xmr3ePMvLXVW1GxauGaI31Ir/HZgPfn+0gpXmbcXx\njZaZ0zBE50HpFmackCoZUnsZyi7ch9VXuKf1VhRQ+2OzJGUXb80T0m74+7uqqh0uQ5myDRapeomT\nNmpLXV2T1JNTvFsK9nS3lbwhB0HFoZJ2mMj+WsqKlV24LUWF23r4mprzbT2oa1HJnlZcwBXt6KT1\ncVqWpSDPpnC7qkaFu6CdqHBNWVfnu9ID0qakvZ5VvDsKclxXkOkd6+tbaX9uiUuI8qF0J26EkJqp\n2OzpWmF1C3dNN9TSRvTe7OU21daKNlRRcNZjZWdHte097xZ26/PaXQj2dLuqRVPxptp6S6ejyTo6\nhrSkoHg74VLztpInX3iXmYcJKjBNRhigpXiAtm8us6C4gM2SslW49nuzp2tybU6QzJNlk2NTuk21\ndU0PRoN0ZF5x8Zq7b9j5NUO0FER17CGalStKdyLSLiuQhg7pSvi+FR/D9RWuHdYVU763eprbVjy5\n+u4+I6l+/57qyz016z21l6tBSVvHga/pwXDL4+m6u1TTzlolCKp5XvN7WtbnJqjKE1T7vx9LzDgo\nabd8HHOAdg4RmSVlO7tmtSr5vq3mzqZq23uau6XBWa73dHKhp+bqptoLJ8M942BZ+obvhMqweDe2\na9L2XJDfrXC7T4WPMcvMDNFjo3QLMSiktYzvDwipuQfyA/uJk6aa2kwU7ukosEFA6zf3pFsKziI2\nxdvxbIJ5RZNlaa4unWz11Fzuqbnc1jWd7jtZwxwz2lFFuw9U4qUpc79X3zKzd1nKd90uS8yYJUMM\n0Kes9/VggG4utaO9WVO4Zln5dJjpaHg2Wb6p9CxL8b8ldal+a0/15Q01Vzd1c2FNlbBsK27pSurN\n14LreTsng/w+IP8ycyFD9NFG6ZbGvi53yJCGU3FlfjdRsG7hnta1IKBXFAT0lqQbyt7TNXe9uSFp\nLXjc3LZ0crsnnb2WcewouKa3W62p90A4IZubqqcFNbEs5b4gAjCNspaWXeHfb98AbZaV71c0QLe0\nHi0dn7QOC5nCXd25EQzP1xSUrT1AD8rzcvyY+s6eHl5+S5Xl+NyM3fAobzdacK7Fq1dDD9Fp1+2y\nxOxD6ZbODvGAkN4fvjX2VWt01dJ6dBmPOcniZHgC1Wld08krvaBo/z/FpWuCeiv8ldtKMseZVsPH\nLCso37PSSfVUWd2RFhSeflGVfWlRFNReRXv1erwcboK6Yf2ehqyg+oqc6RjTYJSlZesGGfbJkO4A\nHd5FzhzHtVes7D3dqHCv7AVZNsOzu3KVlmVzq1bz+HcFg/RpbQT5tvSsTJvVq2iZ2R2i7ZtpRJcD\nuv89jm6Z5kXpFi7vZOyEVEoey3X2cu2Q2lPxg9YSVFS4Jqhu8bohVfi76ooL1z5bUVJde2qeDYpd\niifkptrJoN6oB0tSdlDN8GCm4zlZ1+0yHWOWuS9qoPiSP2ngAG2uvW0m3jb7C9fO8s3wY7PnmZbn\nVvjefsx2sHmntaHd5Yo3xxtqqTK/q/l6Nx6iTYnbx3SjeGYtMSMNpTsxgyZjJS91NWE1xZsjpKfN\nSVM7m8GSsgmpWY6yi3fQctSC+grXaNZ76i63o0sQuqqqpY1kUNe2g2Up81xSyrEg338TyhSzziqg\nhvVlM0CHw+18vRsN0HGmNxPZrt/ci3NrBmn3mG5Wns2eqVvM9eC8jdX6DXUXalaOg+t5Tabb1aZ6\n1Xq8d76jeJD2LjGzcjUMSndsWS9u7T7OmYyl/qVl8zUrpJX53egWcCetsFa0kwypCepNJYv3P9Kt\nm1LvHc9WHZMW69LxVv/3tBC8zd0vNeubai+Ym2cElyCYoLbV1EJ1NxlUU7gb7pMyHWNWjLhqZS8t\nL1oPqUoL1fhWjs3wLlPmUNGKNuIVK3uIdor37ra0td2f5yjL/1F8BYEU/7vSCD6uLwSrV2aITuRY\nwYul9BpN6f655KsQucZauTq6KN0Dk1I+ZjK2QlpTN7yt424U0qq6yZCaN7t4b0l3N6Sbt4MZ846S\n+5RVSUvvSL3bUnVbWrb3dM0/HHVJq1L9ZhBUu3CDezuHlxaZoGou/gdnQ/1LzENNx8C0yzixyi4s\na9VqIVzcdW9g01Q7Pku5ozjLVuHeuindeCfeZzR5rkrSO9LS7eBtdVs67i4/31CU6+ByomZ0TDm4\nGU6wouZdYpYKXrk6uoeLKN2DZC9DuZNxyCwtxy9gsBNNyRXtBtfhuiEN35vCvargr/eWkpVWC79+\nR0H56qa0fH/wPnEW5E1JLam5s6nmQjMq3Jp60YsqVOZ34z+H/WcaC0tSmAaDrs9V/11RM1atTLn1\nFe/OTnzSozkktBG/N4V7Q/G+o8mzqf6oxm4H50YeN+dsmOcNh+ja9p6aC8EQXYnu0b4b3e3Ku3Ll\nfaETVq6GNT/uE7z66qv6wAc+oPe97336zne+U8Q2HQGLyQ/dF4K3JmMpfh3cuOSsW8GZ4zsmpObt\nP8nCvaE4rObNfO2mwr3gd4Ki1o7ikzVuKfodte296PV5ffeAna934xOz7OnYFv3jlHXpBTALMg4V\nSX1/982qlbm1atW6RWtT7eAuU/9RMEDbmb4VLCnbhdtVMs83wq+Zj+8oWIJOOwFrblvRTXDse7Pb\nK1eD/rgYzVile+/ePX35y1/Wq6++qn/84x/6+c9/rn/+859FbdshMGSxePYMzR6kCUTie2YyNsVr\nTq7YCUJqlpNNOO943kyAzR7vll3cpnw7ik7aqITTsD0dB3/SjGVhE1Z3uPA+yP0YKMuw52fkYB0q\nSj5Df57nnKHZ/nhrO5lXX57/rWTWe+8E/w4khugd672UKNy+VyELh/5oFc58HH0/338CJI1Vuq+/\n/rre+9736uGHH9bx48f1uc99Ti+99FJR23bkzdfDG5NbhWb2dmvqxpOxYZXvlnM8xxSw+2aCbAe1\n75IEazr2iV7fs7qb/IY96XsDSrniMPAssab81XZfGSh+QZJu8tpb8z4coO2TpqKsOm+GPUQnWM+p\n7XBo97Bf4MR7iMh+QRPJ/QQDjHVM99///rfOnj0bfX7mzBn96U9/ch51yfr4XPh2WOWcfrNk7g2m\nSLklnF2ok+J7eTHk8Wb4NmuOUp4no+/exy7zbeeSoJ6yTzM0xWtX4Na2tOwO0BnI86jy53ms0p2b\ny3hN1chT4/wK4JByC+tS2gOnDHkG+uXP81jLyw899JCuXLkSfX7lyhWdOXNmnKeccQWcaTtgCPZK\nObZirgo2k2/eI1bD6HFCFDCUnUHLWfaNchSegawgv1lp8x1pXjQnNppDPRmvVy+R5zKMVbof/vCH\n9cYbb+jy5cva3d3VL37xC/33f/93Udt25O1tBwGwg2Duf9xVTd36fHzMxb5lWz0MW6imOIxV580u\n5iUFF9hHlwvZQa1L+3VpV5W+7eyGdb7Tc75nL2V5l8C3cnwMTLu7/V9K+Svsllr8gvO1OL9S8pIj\nhbkMRVl13oyaUk71ci5jCl53t38U37Ez/h/13/kqcStIuZ9ggLGWl48dO6Yf/ehH+sQnPqF79+7p\n2Wef1fnz54vatkOgq6HOYPbc1m13ryLNxy+pFz9zVbsLC6rXe8nLc8KbURyvS2vb0p134i3xMa93\nFBWwPRmbG2Q0lDihwvxD0VM1Cmg3689pMjnKXjxQmp7yrQf5jp6mMCdVWGc62S8cYuyqov3wNo1R\njq2PF+vBTS+k4AogH5Nle4A+3lLyRjcLSl7Sp2DPuxdeDGi2qdupSR3r8KHJsP1vVNrLCyLT2DfH\n+NSnPqVPfepTRWzLEbKl6OU+tpRcHjav0PMfRX/pd1RJvAzXTnhPm65qOrnQi29isaE4qC1pcVs6\nE16ru6a4/u1RwFzNcEYpIV1WFNT2srmwIBlQM73vbdeSlxtJ/SduRK9MwgkbmEVbSr6knTVsmte5\nNS/jt63gVbfMt3sVdZdq4UMr6kV7udVo5ap+/17ws+YFSMI8Hf9PMEQrHKJ7St6/zc7zmoLSXV5V\ndDMMLStR5Pt1qa1m9PtN8QbPnTJAs0NbCO5IdZBMQKWgZLcU3zM1/Ave7dTUW6r1vaxeU5vxdGxC\naoJugtoK8qbwNpC+GX4pfFs9ER47WlYcUvNqJasKX96vpraaick42KZKsEfemUsuR/luyD4U7kaF\naWAXbYp95/NtJV8IfjsYSnf3KurN16Isd1VVWyfVVDtYuVruBcOzPUSvBs+zLEk3g7vHZeV5LbwH\ns1qKc2xnuiV16/PqqqYNtRKrVmYA2OlV4tvYbSnjrGfP0joyUboH5q681/dtKy7fXjwdm3IzhdtT\nTetqqbncDl5wflnxnWysgByX9FA9uBdr5k3STUBX5Q3p9uq82mqG/0g0o9fT3TSvq9txpmN7Oarv\nXq1pIzN7v5gmdzT4MsCuUgvZHj7Dlatup6adpUpf4ZpMNeu9YIh2XyEo/Hj5/uCucdXt8NatlijL\nbuGa92uKBuj2wslogN5QKxqkewoGg9RVK5PjvkNF9tXDeXaJj+Z9lyVKtwB5jgO5fwlTlqTuV+p0\nvDNfsQJ6Upvhix601VRldUf1nT3/a2yG9109fkta9p25aC8j1yWdVhDM0wpC+i5pfzkOaVsno5BG\nL2SfNhl7s8dkjFmVdo5GeLjI5LiheOVqK/xaeFx3p1fRxtJKVLQnrfeJIdoMq/YNM+qSbgaluux7\naT/3uG1L0lnFxRuWrztA28XbVjM+njto1SrXoSLWpF2U7sRkLUmF0/G+9VATVBNW8/Hbc9qsN9Vc\na0chMUGtqad1tVRZ2FVteUNz73J+jX2zc1O4vlI2AV1QsnDPSloOjuW2FbzQgRvSHVXUvtPU3o16\nfHN2+7ZzuSZjYNZZK1e+47rOEN2eD3K8qaaq6kVD9DWdls5e08kdJxf2iY1pL2LvnoS1LOld1vt3\nSdtn53VzYS0xQJu97A21/AO0eRtr1YpDRQalWzh3SSrndGx/+f7w/fXg473tmtp7TVXng9OYNsPX\n4aypp7d0Ovi5Zem0NuLXE7DPQt4Ovt93cpNzmVHfMaDT0ubZqq7ptK7pQW1axWtCuqGVZEjN0CAl\nQyplTMZ5LheinDEtUlau9hW/4LsU5GxR0nr43lpi7i3VwsLtRjmuRQu8XVXO7qiuvfhXmMJdVfxC\n9uZ3SP2vamSyvKaodM2K1bpa2lBL1/RglGOzlxsN0PbSsvm4b4Bm1WoUlG6p3EsNwunYXWI2rz3r\n7O1W1nYTr8W5EJ7XHN2s3BRvXfGriywrfrUSKXtJygQ0DKwpXDMVt9XUDa1FBewN6brigNr/NjEZ\nYyakHS4atHIlpS4xO0N0r9FUu9GNhmiT6Wt6MH7KBWn17A3VF/aCnzc5vqF4DzrP8nJ4jsb22Xm1\nF07qmh7UWzqtG1oLD1Ol7OW+reSqm5RcrUoM0MMezz3aKN3SuJcaSNESsy+o18Ov2Xu7d5qqLXXD\nZf8vevMAACAASURBVKgH5eqqKi1LzfpmHFZ7MvZdV9dQMqT1YCK+thzs0QbTcBzWYE83PL6711Rv\nvRmH9G3FITUlbybjfSmejFlaxqzIu3IljTNEV8NrAWzdhZpOn70WnFxlVqPMZUS+PJtLD81hovCQ\n0ebZ4PDQulpR4ZrVq7aa/QO0OUxkD9CmeHMtLQ/6/tHOPaVbiEHTcdYS86JSg2qWpd6WVJ8LXnXT\nmpBtu1rQmm5oVwtqLjTVPNtWc3VT9Zt76ZOxlJiO9+vx8dt1mdIN9nTf0unoY7OsvPl2MzjhYkPB\nm1mKyjz+M8rSMjBtfH9XU87TcIdoSXvVutrVYIhO0w2reGV5Q83ltprLveCVvkzOfHu6UjQ4d+vz\n1gmQcZbj1avg47d0Oh6g18PtdQdoe2k5MUBL/atSrFploXQnIutSA3fKywjq/QpCED5Miidkl7lR\nhbkUoauq2mH51tSNXsartr2X+LlufT68HVxNu6pEZWv2Zjec8r1mytdMxesK/iExy8lvKyjgdWWE\n1DUopEd7MkbZRllitr7fcU6osodoKRhy14Nl5mtS3z8VvfCMjQd1LbiEJ7wRTnu5q8rybpRnX5al\n4PaOwdnJtSjD0d5suGqVKN+9pjYun5benovzuxO+v67ga6kDtBk+WFrOi9KdOHdZ2Q1tSlANc4zG\nmpBvaDU4/qr4vsfB4lRVTbXV0oaaamtBO2ppI3i9zoWguGoLyYLrhje5MHemaeukdS3uycQSc3Dy\nRVC4vcsng39EzLLyuuJlKRPO1JBy/AezJGuJOWWIdg8ZhYeJtKggJ1K0euUWr7lxRnBy06Y2wysW\nzLkbJs++LAfvgzzbJ0iZ4XkzXLUyJfzW3ulgxertueSyshmkzYrVWxpygGZpOQ2lWxh3Oh4jqMb9\nigNq2VNQvLsPVKKXrDDnPZqwbqillja0GV5aZF7D0369THO7N7N3bBevG9Tg85X+ws1aViakOHRy\nDtH2ISMpuGzobd/zxcUb3yJyIbo7VC/K46b1gvf58myuo08ct7UvE9pravPtpvYu15N7tWnLyiMN\n0CwtuyjdUuQM6v7x+AxBe0L22OvVtSlJDyhxW7ngjlXxjTOqYUDtcJrjwWYv2fxsL7wHazAhV/wB\nNUvK9jLydfmXlTtSULiEFLNmnCFawUFV+0SnrFfz2w6KVwp+hSncdnQlb3BdfpDjZJ59WZYU5XnT\nU7zR8Lxu7eGaDJsVK9+ysvdkSNugARoSpVuwMYPqLjNLwYSc8nd4T3VtbNfUXampu1SLCtcsRwVB\n3Y0vKUph30PZFLAp3kRAO3PZhesuK3svK0j+5gAhxSwZNERL0t1giPatXnnNqdc5qZ21inYfqGhj\nfkUtrUflu6CdaJiWNFSe7eJNDM89DS7cvmVl92TIYQZoVq0kSrdE9pnMUhxU5y+mOyEPesrtIKy9\nRlPVlba6SzXVwr1cu3AXFF9kV1U38Uoi0ct5hWE1J2Hs7lXSA7qj/sK13ydCaiOkmBV5h+i0v8+e\n1SvvErOis5H3esEgPV/vJsp3QbvRoSJJfcvLbp7d4m3vBbd3jPZut5Ucnk1ur6v/OG7mipX930IZ\n/y1gULqFGxRUw/zldM+StCZkl33btx3Ft5f7j6RWsnxrja4q88GZjsFvCd4vaNd6ivjFqs09lHf3\nKsFN2XuVZNnapbru+Zp5752KCSkOG9/lgANWr96S9KD6i3dL8UsAhoP0Xj0u33a1mcizL8tSnGeT\nZUnx4Lxdi1eqzGEre3h2v2YfIto3G+ZbsWKAHhalW6ohguor3hXFZxU+oDis5hKjRUn3z6n39kn1\nqielxr7m610tVINw1hr+awJNyUqKw2mXrZmK3YCa32sX7paUXbj28pQdWEKKaTTMEJ22euUUr3mY\n+2IC9iBdV1S+vWpdvUYzd5al4IUVElk2w7mdW3Pzi7eVzLi9h5t6IqS9YsUAPQxKdyKygupbZh6i\neBeUDOu2pFPW05qbXYQFvFevq6e6VJV6Ohn8XCM82NqZi5/XBNM8r1u29ucmwOakKe+S8jhTMTAL\n3CHaXb2y/r7bxWu4L5lnBulFJct3lCyb57Wz7Jatb2j2Fu6wK1YM0Fko3dIMmpBzFK97zoYJ5X8U\nl625NMEuYDk/pzklmLy4pZtWtuZ7HcXFm1m4w07FhBTTJO8Q7R7fXVJf8W7lHKTN0y4ozrLkybOT\nZbNJUn9e3fK1h+qOkrkeWLjuCVUGhTsIpTsxWa+z6wtqytJU2h7vjuKw2uVrPja3kFyInyaVCemO\n9XnalDxUQKXBhUtIMYuyileK/x47xWvybK5vNz9qf9xS/+Bs8jtsnn0FnHt4ltIL1/cLkQelO1Gj\nTMhVeZdb7SnZDatdvlIc0g31T8hp3L1c87WBZSsVV7jAtPIN0b7VK99ho5TidQdpN9v2MO1meV3p\n3FcUs4vWfJ5reDYP9hUuA/SoKN3S5V2a8rHC6itfKS5gN6RvJ58m+vU2X/G64ZRyTMSSv3BtvsIl\npJhmeVavpMHna4TcQXpB/mF63Cyb79v5zTU8SxRu8SjdiRs0IactNQ8IqzzlK/UXsBQvVRmeW0v2\nLTHbx5G9ZWu+mTeg9td8CClmQZ7VK6l/0ExZwTKD9JaCfDWUHKY3lHzJvmGyLPUXrfmat2zNdrvD\nszRc4SILpVuKCRSvFJevL7BSfzgb8rOXudLK11u25uNBAbW/JjEV43DJKt48K1hSdP/1rePBuVFm\nmDZPKetp82bZ/tm+wVnyl63kX60yj5EGFy55zkLplmaU4s3LCqwUB2/HeVjaU9qPs0ObCKd5Ajd4\nw0zE9uMNAopZkzfL0uBB2r0kIcyyGaZNAZuB2v4xHzfziaFZSmbZbJ/5fNzh2f5ZpKF0SzVM8UpD\n7fVGnNAaJrxp9u1P7Ivh00p02IDaPwPMujxZlvIP0r4zoBfjXG5Z1/gOlWUpu2jNdhsU7qRRuqUb\ndUr2MT/nTsu28Ot9QUyTdznJd/nAMAG1nwOYRXnOaB5nkLYLWComy/bXRylb9+fcn8cglO6BGHZK\nlvzl6zs5wy1g++fT+M4uTivNnucxo+zdElIcBmlZlvIN0r7yzXNy1jB5TsukL8vuz1O4RaN0D8wo\nYZXyHe/1XT84zDHirOOuaeH0/Q4CiqMg7VKiUQbpvCadZ4bnSaF0D9SwYZWKCWye7XKNW7Zpzwsc\nBubvdp7lZilZvlL23m/W9cHDbJu7DQZ5LtPIpfuNb3xDL7/8siqVit7znvfoJz/5iU6cOFHkth0R\nWcUrDS5faTIF7Hu+QeGUCCiOtjwrWNJww/QwJ1L6kOVpMj/qD3784x/X3//+d/31r3/V+9//fj3/\n/PNFbtcR01P6X2TfMVvzZnStN9/jRnlzn9f33O52ElIgO8tpeTZ8mSsiy+5zp/3+tO0c9GdDXiPv\n6V68eDH6+IknntAvf/nLQjboaBu01yv5p2Up/U44Nt/JF1mPt2WdQZ2GgOKoSltulrL3fCX/iZCu\ntBOp8uR5lCxL5LkYhRzT/fGPf6xnnnmmiKdCZlglf2Al/5KUa9yCdbchDeEEAlnHY8vIsu/50rYj\nDXkuUmbpXrx4UdevX+/7+re//W09/fTTkqTnnntOlUpFn//851Oe5ZL18bnwDYPlLV8p/XV6i5T3\nxhYENJ83w7dZQ56HN21Zdn9nGrKcX/48z+3v7+e+1Nr105/+VP/3f/+n3/3ud7r//vv7vj83Nyfp\nW6M+PRKGOXvRF9xhDXP3KMI5vm9qjCiWgjwXZdgzkcnz7EnP88jLy6+++qpeeOEFvfbaa97CRdEG\nTcu2sm63SDiB4dm5Ic9Hzcil+5WvfEW7u7vRCVX/9V//pf/93/8tbMOQZtjATvL3AxgPeT5qRi7d\nN954o8jtwEjcwEwqtAQTmLwyCpgsHzTuSHWopAUqT4AJIzA9svJInmcZpXskEEDg8CDPs2zkO1IB\nAIDhULoAAJSE0gUAoCSULgAAJaF0AQAoCaULAEBJKF0AAEpC6QIAUBJKFwCAklC6AACUhNIFAKAk\nlC4AACWhdAEAKAmlCwBASShdAABKQukCAFASShcAgJJQugAAlITSBQCgJJQuAAAloXQBACgJpQsA\nQEkoXQAASkLpAgBQEkoXAICSULoAAJSE0gUAoCSULgAAJRm7dL///e9rfn5et27dKmJ7AAA4tMYq\n3StXrui3v/2t3v3udxe1PQAAHFpjle7Xv/51ffe73y1qWwAAONRGLt2XXnpJZ86c0WOPPVbk9gAA\ncGgdy/rmxYsXdf369b6vP/fcc3r++ef1m9/8Jvra/v5+yrNcsj4+F74BR92b4dusIc9Av/x5nttP\nb8tUf/vb3/Sxj31MtVpNknT16lU99NBDev3117W6uho/+dycpG8N+/TAEfTNjMF1OpBnIK/0PGfu\n6aZ59NFHdePGjejzc+fO6c9//rOWl5dH2z4AAI6AQq7TDSZgAACQZaQ9Xde//vWvIp4GAIBDjTtS\nAQBQEkoXAICSULoAAJSE0gUAoCSULgAAJaF0AQAoCaULAEBJKF0AAEpC6QIAUBJKFwCAksxY6c7C\nS6GxjeOb9u2TZmMbp90s/Dec9m2c9u2Tpn8by90+SrdwbOP4pn37pNnYxmk3C/8Np30bp337pOnf\nRkoXAIBDidIFAKAkc/tpL29fxJPzOrtAbhOMYiHIM5BfWp4nWroAACDG8jIAACWhdAEAKAmlCwBA\nSShdAABKQukCAFASShcAgJJQugAAlITSBQCgJJQuAAAloXQBACgJpQsAQEkoXQAASkLpAgBQEkoX\nAICSULoAAJSE0gUAoCSULgAAJaF0AQAoCaULAEBJKF0AAEpC6QIAUBJKFwCAklC6AACUhNIFAKAk\nlC4AACWhdAEAKAmlCwBASShdAABKQukCAFASShcAgJJQugAAlITSBQCgJJQuAAAloXQBACgJpQsA\nQEkoXQAASkLpAgBQkmOTfPK5ublJPj1wqOzv7x/0JmQiz0B+aXmeaOkGvlXgc12S9FSBzzcJbOP4\npn37pOK38ZsFPtckkefpMu3bJ03/Nk5i+9LzzPIyAAAloXQBACjJjJXuuYPegBzYxvFN+/ZJs7GN\n024W/htO+zZO+/ZJ07+N5W4fpVs4tnF807590mxs47Sbhf+G076N07590vRvI6ULAMChROkCAFAS\nShcAgJJQugAAlITSBQCgJJQuAAAloXQBACgJpQsAQEkoXQAASkLpAgBQkrFL9969e7pw4YKefvrp\nIrYHAIBDa+zSffHFF/XII4/wAtcAAAwwVulevXpVr7zyir70pS9pf3+/qG0CAOBQOjbOD3/ta1/T\nCy+8oDt37mQ86pL18TlN/ytOAGV4M3ybNeQZ6Jc/zyOX7ssvv6zV1VVduHBBv//97zMe+dSovwI4\nxNzCupT2wClDnoF++fM88vLyH//4R/3qV7/SuXPn9Mwzz+jSpUv64he/OOrTAQBw6M3tF3Aw9rXX\nXtP3vvc9/frXv04++dycpG+N+/TAEfDNqT8vgjwDeaXnubDrdDl7GQCAbGOdSGU8+eSTevLJJ4t4\nKgAADi3uSAUAQEkoXQAASkLpAgBQEkoXAICSULoAAJSE0gUAoCSULgAAJaF0AQAoCaULAEBJKF0A\nAEpC6QIAUBJKFwCAklC6AACUhNIFAKAklC4AACWhdAEAKAmlCwBASShdAABKQukCAFASShcAgJJQ\nugAAlITSBQCgJJQuAAAloXQBACjJsYPeAJRhKcdj7kx8KwAUgTzPMkr30MgTxFF/ngAD5ZpUnsny\nQaN0Z9a4oRzndxFcoFhl5ZksHzRKd6aUWbRZ7O0gtMBopiHPZLlslO5MGDWc1RF+pjfk4822EVhg\nsHGKdtg8j5pliTxPDqU71YYJ6CgFm/d58oSXwALppiXL0nB5JstFG+uSoStXruijH/2oPvjBD+rR\nRx/VD3/4w6K264hb0uCQVp23SRr2d+XZfuAoyJuFsrI87O8iy0Uba0/3+PHj+sEPfqDHH39cnU5H\nH/rQh3Tx4kWdP3++qO07YvKGM8tiERsS2sqxDVlT85KYlHE0TVuWJX+eh8myRJ7HN1bpnjp1SqdO\nnZIkNRoNnT9/XteuXaN0h5ZnrzZNnmCOel2f+9xZoU0LLGHFUXPQeU7L2qA85ylg8jyuwo7pXr58\nWX/5y1/0xBNPON+5ZH18LnxDLCtAaeFMC+Y4y0B5ruuzf29aYAlrPm+Gb7OGPKcbtWyLznPea+7H\nzTNZjuXPcyGl2+l09NnPflYvvviiGo2G892nivgVh1BRZet7niKOC5mwpV3XlxZYwpqPW1iX0h44\nZciz37B5zpvltJ8fhp3FtBMezfb4ypcsD5Y/z2OX7t27d/WZz3xGX/jCF/TpT3963Kc7IsYNqPvz\naaEcdVK+43lOt4QHBTarfAkrDpNhynJQltN+rsgsS0EufQU8Spbtn8cgY5Xu/v6+nn32WT3yyCP6\n6le/WtQ2HXJFBdR9vO95RzkRY8vzXG5whw0sxYvDaJjhedjBuag8+9h5ThumGaQnZazS/cMf/qCf\n/exneuyxx3ThwgVJ0vPPP69PfvKThWzc4ZO3cPOWrft87s9N4vKDvIHNW7z2zwGzYtThOe/gPKks\n+4Zqwx6mGaQnZazS/chHPqK9vb2ituWQG6Vw85TtYo7HDGOU4NjlmxZWpmQcFmVnOet3DpKVLbuA\n3WF6nEGaLGfhjlSlyHPcZpiA+sK55HncqPIExzcxE1YcdkUVrq9s08q4yDwPypmvfLMGabI8LEp3\n4kYt3KyyzVm0o/zffcf3fHmm5UFhpXgx6/IU7jhlu+R5jGXYPL9jfzJscZs8Dxqk01awyHIaSnei\nxi3cQWXrPL/9f9N+WvcqLp+O87nJlLeEs6SFlSkZs2zUws07PGcMze7h3WHzbM+779jbMUzWRhmk\nybIPpTsxwxRu1kS86Pma9Xg3mHYgFzy/ymfLeexO+Dwd6/uSE9i8ssKadQ0gMC3GLdwhyjYtzwvJ\nh+XOs8myNESee4pzaq9iUbxFoHQnYpTCzQrogLJ1gzmogF324zrWzy/IX8CFhpWgYhaNUrgpZesr\n2qwsS+l5tktWSubWzfNQw3TWChbFOwxKt3BFFW5GQNPCmVa+UvaSlL0U5U7IHevrbmAzw0rx4jAY\nlOdBhZtjeHazm1W+0uDlZV+e7b1dU8C5ytcM0u7XzGN9xYsslG7pRixcd8/WF860JalB19SvKM5M\nS0G5SkEg06ZjY2D5ShQvZlPRhZujbIcZpNPYeXaXlu2yXVR/+eYapA07z2Q5L0q3UHlDOqhwnYnY\nDqgdTmlwWOspm2KYbKxJ2g4/9gXU/dyUsZQRVntKTiteG8d4MS2KKNwhhuesbCv82qAsS+l5tvd4\n3fya35VavvaVCVkrWBRvHpRuYYos3JSJOC2g9sd166l9xZtmW9IDCkK3oiAvDevzLSUD6/vYW76D\ninfQ0hRBxTQbsnCHybIU53mYLEvJPNcVl3BWfm2Ze7128boo3kEo3YlJm4rt72UU7qhlO2rx2lNx\nz/qa+dwOaZaxi5eg4qCNM0APWbgrnq+5WZaGK17fAL0dPkddg4dnI1fxStmrV3BRuoXIexnNkufj\nIQrXF1DztdTS3Zckzde7mVu2t12TOnP+kLqBlfrD+pb1ZEMVr8GlRJhWBRbusBlOfDxElqUgz74B\nelvS28rOsF3Cm+aL7r9zacXLEJ2F0p2IPCE138tRuC35A/qAkuFckdTYj0K5UN1VrRF8XJ3PLrHe\nXlXdThDWnV4lLmE7pKZ8pf693geVY0r23aM5bwCPdlBRlqwBOmvFyj3G6+TZzvCCgryYfK/JybAS\nRTtf7w6dZUnqdmpxlqtz/QP0DcWD9Fvqz7Bt0/7E/m/klmve4j26KN2xuSEddirOKFw7mCa0JqB9\nQU2GszrfU01dVbSjmvUXvqZ4Su6qFn88X9XuUtCi3aVaVMK99WYcWDukZlKW+qdkI3V5atQJGZik\nPJf7uY+zP07Js29oNvm2h2driJ5f2/ZmWdLAPHfng23eXVpIZDkq4Lfn4vJdV3KQNnyHkTbNn9f3\nWtq+1assR3eIpnRL507FlqzCTQvoA0HZnnyg3Ve0wce7UTDtgBpRUMP3u6qoq5q681W1l06q1+gm\ny9cOqXlvpuShi9c8Sdoys+voBhUHoYAVK1/h+t6HQ7Rdtq35jaGyLCXzbGfZFPDGnZZ26lb5mgFa\nio8Vp523MfTqFUO0D6U7lmH3cgdMxfaSclrhWkE1AW0tbaipzSicTbWjkEpBQKspIZWkni+oqqmm\nXhTYjUZXm283tdcIwyolT+gwU7IpXrs3o7Da7AnZ/HdyC5WgYprlWLHyFa69WmUNz9WVdqJsV7QR\nFa1buoPy7GbZfFxb6kbl21M4SBvbqU8ZMB2aa4jOc3XC0RyiKd1S5JyK3aVkX+GuqS+gpmTt91V1\n///23i9Gkqs8/39m5J3erm4Ps9Ozs2vv+oc34Ih1kM3KSBZSJBTQhjiKEQpI/BHhBpSLCCJAQuIi\nlzEGHIQcEW6QAEVIiAsuTCxnxQoHX4ASSwhFAnNhibW++8e76+ndye5M186sPfO7qHqr3jp1TtWp\n7uqa/vN8pFFXV1dXn53tZ57nvOfUKbSwizYGSTmquKfbRogAO1hKRBtggAECbGIFS4s7aB8LU7Fi\nwS1Ss+ebaM6WkOX3Q6GSg2SUAG2gK1ZlhmsJz2K2a9hIjLaKngdx20XPfaylposBNtBDsDxIgzQ6\n6fCRjR3jMWO8+hpeoFibDNEATXcEqojUdnyMLRV7GK4WqDZbMVyzJKUFuoRd7GIpeW6WpDbQQ6hM\nN8AAm1gBgFSsnRXsXbNcu3AbqeHKr6EwIQMUKpkePAK0OUSkjddiuEeObibhWWu5hw20sIse+oXl\nZZuede92BZvYxEqi6SXsZoN0uxcNH0H1eoWd/C4AxoxmV4WKIdoGTXfslIjUlYrvhbfhikBXsOlM\nyQDQisvNmp1YrLokJSLtoY8+epny1iZWgMWoXTeBKCWbiOE6E7Lr91Rl0QxC6sJnxnKFAG0OEWlt\nlxjuWqzjSNP93HCR7vXakEoVAGxiJTtUhDba6jwSpLEM9IG0gmXjtuWRIXooaLpDUaNIgVJxmoZ7\nP65YBSr7lrCbpOQgKRxHxru0k0bX3VY8WzkWaR+9RLS6l9uOf3TSzhhv2InGdLtIL8fVCdkU7MhC\nnb90TJrEtcaiZ4C2Vawchnvf4hVneDZ7vkVaBrJ6DtHGCjaT8nKq5zD5u5ApT2vj3Y4vFRRN30a2\narUDo3rl+l3Nt7m6oOnWgkukGk+RivHqxSgchntfsp0V7RFsoo0QKzs3EWzvYUHGXo1SUScWxZFW\niP0OsNK5id1WC3300MYgU46yEhtvfztAYUK2lpltUKhkkhgyQOvKlVSslKZ1D1dr935cyYRnbbo9\n9LG0s5Pq2VL27SAEWsBKJ8Sgs4jdVgsDBHGJeiMxX9fMZywDV8Il7K0VLHm1g4ohmiVmE5ruWCmY\ncOEjUknFnUFSUrYZrhhx0uMVs72BdCUaEak5+akTffZCF+h09tBphVhav4Jeq5+Yr6CvD0yu8V0E\nBmtBcUIWoco+wPF7qSJUQuqgaG6Gi5IALc91gFYVK7OkrA1XtCzhuYc+Vm6EqdHKZKcd2LUMYKEF\ndLp76HRCrKyGCFYHiflm/6V58w2PtourV7WE6PkO1zTdWrElY9k/hEhVKpYxXJ2A78fryfMkJd8I\nI7O9hlSY2wDuwD7bWELtYQDrURs6O6n5yjV7rt7uAG30lvtpQm5MqPOVjslBU2DGZQH6GBJdt9ei\n6+mLDDfR8s5NdK7vATcQ6UpCtEvLiD/vcPzYARa2gSPbIVY6IbAaHaJ7uvpyQQDYXWxlq1eVQrTW\nY9l1u/MLTbcyvsnYU6TyaBPp0f3oUoLFPqK+ZCpUbcAi0iMXw0iYfQDXkYrzevw5rpmIrfhz+0jv\np9sDOtjDfetX0G5lTVAuSdjFUvzTwpGjm5FQj9UlVEIOEldp2RKgAXeAPopMWTnoDjIVqx42rIZ7\n/41+Gp7FbPtIQ3SZluUnrnQtHAPuRx/BqntRDZnpPFgM0F7bRLh1JGr/NuwhWsZ2rWszVzXX+dE+\nTXesmAZtiFQezV6uiLQzQNCNVpjShtuzjAMlhvv/kIrzOtKSlBappGS9Ao2s96qT9FbU68UDN5OA\nIEYLpDOeo1Vv6hYq0zGZAvSMZSAfoNW8DAnQa2pWclbXG3nDvYhUz0XDRTYtt5Ax6YVtYAUhsHox\n808YxNfzirZXcBNht42wuwKE8RKwrhC9Ff8OWGL2hqZbGz6lZeNQbbZ6LDc2Xy3SNWwkM4lNA84Z\n7nVEz20lZiAvVClHrapjt9PjOoiMN2y1M0bbjrdWsBnNq3QJdSP+HBFtqVAJaYIaqlYazwC9hN1c\nxaqHDdyP17GyczMy3P+HSMdaz7qnW6ZlMd2d7PELiIx3sNoHkPZw03nRsbYXwzREyxrvpkdq8wXA\nypUfNN2mMcd/BD1jWZWillQGNUUqY7g5w9XpWAvVNabbQdq7Xbe8DqDT2kPvgb4SaVaoAUK0F0Ms\ndgbY2+qkQt1AekmUpPNMidkGx3XJpFFStdLLqXsE6ES/sfkewWY6hnsNqeFehL3EDBTruYNoqMjC\nQnylAlpI/rpsYiUJ0VGQVr3dbjxk9AbyvVz597Jy5Q1NtxJF1+dqSpKxNltdmlLpuNXejW9gECqL\nG+REuiAJ2DRcEW1clroVC/T2HfXRh6PXliUVryM/SUMSdDe+FGG17xRqgOguR2E3iIS6Eb/fVmJO\nYDomk0qFqhWQD9KJdvZzAVpfK9uW+LodT5rS8zKuGc/jUrFLz8vSs5XPNo35cNTOTmsPuw9Ei2xI\noLf1dhc7A+x14gmSEqQrl5iJhqY7Ep5lJwA5AdtKy4ifxzerDjLJczMZC8qIVFKxjPlow43HnY9s\n/wAAIABJREFUdC/3kcxX1Bnz2p04d96JBQvVDv14GNFkjG0gWM0KtY+eGg3aQdAdREvKSdp23Z+z\nUjompEnuLT8EsFetHKVlW4AWDTkDtGnAcXi+fSfSs9lfHNyJNH1MzBdIdQjjuQrRm1iJ2xXaQ3Q7\nPoEeKtIMXbmaT2i6Y8NxQX2RnpVAzGQsIpWUnIh0B1HvVFKxlKCuA7duRAK9htS6zNsM3IpbN7iD\nqNcLpJOwWtE+U6j91VSUPRiilXT8RifNJCOnY5akyBSgtS0mHFetsoMy6dromQAtupPZyXpCZGy4\n1+5ESriFvI2JlnEn0v0JeaGv2iTDTCpEy7KvAdJAndyhrDtIS8xm5WoDHpWrIuZzuIimO1akHGVg\n3q+ymz3MloyBbM83Eam+hEALdSdruCHyX+dEpII23k60bRNqezVNxACGS8eEzAJdy76O+zWztCzb\nCxKWbQF6O2u4OkRrtM5PIKpwJcYbV6syIfpYtJRk0Bpkwn3aVuWm8p430l1owTGuS4pYHPUE586d\nw7ve9S489NBD+MY3vlFHm6aYkjFfHXF0OUqw+LNOxtEhUTJekEsHzNnG8c+t7agEpYV4O/65Hv/c\nBnAZqYhvIx4j0jOe5TNk/w6SPxbSPtfi68m/0baqnO2PFSETh8cQkvRw9YQqx3iuICYXYBCtoaw1\nJwFaPb9tGK5Ny7oHfBmx/vVsZ31ORI/B9l5mJBfQ4T6tXFX5dXgtmznHjGS6b731Fj7/+c/j3Llz\neOWVV/DjH/8Yf/jDH+pq2xThOQZU9DZHOUowRQEgLS1rc4z3i0i14YbIFnNkWx9nFaohVlloXZeh\nzHFdGZcmZDIZZvlH13uRr1450Hf9SvQsVSuTWNs6QBdpOURqvIAK0UD+6gX5mxGTtim0Lg8ZHxRh\nBmbrv72Nof8uzjgjme7LL7+Md77znXjwwQdx6NAhfOITn8Bzzz1XV9uIhaRX6VqRJhaWiBRIRQqk\nwpUfvd92Htf5dSBwilRjXlJByKxjVHjMEJ3DVrVCGqBNTC0DqZ4z4716IQ1duQLSm6H4tI/Uwkhj\nupcvX8YDDzyQPD958iT+53/+xzjqRbV9Kv4hVXCWbwXpjcbcchjmgUxRMMeBvJn1GY8X4p9pg3pO\ncIVHY34GkL1ZSPZQ/+942ZEyR+M2LH3xbTiv2/UyWLMQ4NmzzzLLE6X89TyS6S4sOG7nluEDo3wE\nmVtm2XCBvGG96DpwwqCeE2QtcZNZ/OrO4r+pVvz1PFJ5+cSJE7h4MV3H8+LFizh58uQopyQWduK1\njjO0jG31fNlxO8xxTWmQO5VYsfW6efUPmRP2tuUuPvYx49BjLPnew9Fj2ZHLKBhJNf8mHE435Q5D\nA6XjQZGmAffwViGz2sutxkim+973vhevvvoqXnvtNezu7uInP/kJPvzhD9fVtimiBhdxLSIRIyLI\nGLCtxCPX+SI1WX3h0rLxIyLV90xZlssDlDCTc3ey7dk1AsEuWhhsWQRLoyUTRQMGYAROmRMs28n+\nTvxnuGP5iTFXdtf3OTLud5S8niB/J2RpSnXefUtAd4ZoV293KAOeX0YqL99zzz34zne+gw996EN4\n66238NnPfhanT5+uq22zh14IYguRGMxxlhDYCZcwWA4yIgWyiXSlE2IBSBc4FzHdic577+FowYuy\nPy1iuCLS5NP0XUta2ee7rUjF2nD13Yeif58aerD1dktCBiHNEsJ/BnPuCvfIeLYQ3QcbiL7zR12f\nlOo40bdptC0k2l6Or0bQIdqFDtD3Iu4l28xc/mYg6m2nbfL4HXhpV+ZSE5ORF8d44okn8MQTT9TR\nlhnAIkYbcns72RaxOpJkunZNtFxGiDYGnUV0unt5IcXrropQTyC6Zg+wT2MQw11GdBvfEz1Edxvq\nIFqLWcw8XrN1v5PeCkz+aFjL3wCNlcwAHmasx3ZvIxKSsLWAwVaA3eVWJpimF9gtYbfVQqcVpkYr\nd/sSDW6nIVq3ykT+8hxD9Ofl2GFgWbQc69e83+6gs5hZ2iZzu060Ee61oxK5BGdXbzfjr7cc2wTg\nilRjRr6JHkYsX+btaBwo3GtjsNjOiAFI0/Fuq4XOahitWCM3LOghc6cgvSqNXL9n/vmQRBwgTsUi\nStlejc8Xr2Az6CzmknFWqAF2wqX03yPGa96ZhJBZQCpWGunlqp6v7tXqwCraWemEWJCAa4bo9fgv\nyA0giI1XV6c0oudjh9UwkSNAS9VK30sXgFoI0hgq0hUrfU/fDDTZMmi6Y0P3etW2TsXSy20hiqeJ\nWPPpeCe+q88aNhLRrnRCLIjRyko2q9lWnEB0CVFwx16WErPN3GmoFz8eQyrSVSQilT8Ym1hxJ2Mg\nvWLfNFoRa+m6y/pKY0ImGNFxVz3vIBkuEvlnV12OdNNHDyudm+h09tJb8lluxbmM+EYG8VrKpXqW\nwNxDNkDH2t5eX0QfvYyGdSBISt9bC6mGt5GVo5c0Xd1j2+rRsw9NtxJm+dhVerLtV+81BQpEX+Y2\nknRsjuuKUDewlq7fujrAke0wuxykheVWJFbb9buJ2ep7cIpQHSLdjG8wKCLNJeOthXx7zGScK0eZ\n6+kQclDI3TlKkNCoh4uA1HCBXOVKbiywgs1soG4dQbDajxarkGqVTc/bwIn45vSmnpOrFiQ8i55X\nEQVobcBGgBbz72MtE6CTqpUOz5kb14PVq4rQdA8Sbb56XDd0l5i1UAcIsLS+g87OnnsG4WEky8kt\nu1aZ0oYrjw8gFWkP2F8FNltHjFsbFJSWt5CGgcJkTJMlk4pZrdJ4Vq7aSCpXm8tHECBMqkTmncMy\nIRrIm24H6Q1NtuPxWhN95cG6assDyBiwGaA3sWIN0LnxXG2wOkh730uXVSuabm2MmI6B6EstSbed\nFap5H04RKlpIE7IgvVcx8xuIRNhDsvwbgPSSoI56zzFky1L/X/R8c7WdE6n5k5l0ocd0zfHc0mTM\nchSZdDwrV3GJOdxYQdgdZEJ01OvNxtal9SvoYC89jx6XvYZ0nFf0bupZa7mLrJbjipUE6JtKu9le\nrgrQUlqWzxQd696us2pl7icATXcMFKVjRK9JOpZHLdo2omUTO3mhSjoWoQrRPTHjS4g0+vZ8ujQk\nyAQQmWBhjunGydiWikWkG0qoN99YyYpUtKdNtnIyJmRcjDJcFKNDtFm50gbpCNEDpCXnNgZAC7jP\nNF4g1afcfMSlZzF+fQWC6uHurwJXVnsZ/W6gl/RycwF6A9nKVWFp2XbzUGJC0x0bJZcaiEArCBXI\n3o8TUOumrl6MjFeP0W6rR6hHEaq+aF6XmFeRpOSbD0Q9XEnFV3A/NpQBi1D7t3p5keret+7tJqLV\nt10wx3M5iYocJK7Klf4+GiVmV4iOda1DdMZogcxt/zLGK4FYa1n3dIu0bJSYtx9YxGbrCPro4Qru\nN0J0asDOAK3xLi2zamVC062Mbzou4E1kx4I8erubi5FIRaw2Bqv9aBZkay89p0zIUHcWyaBLzMps\n9ztpSVkEKqLUYt1AD/29XlSKesMQqVlaHkmkhBwEjqsQzOdFIXojft5ewM03VtA+lgZoIXdDhBbQ\ne6AfXaFgM12bloF8iflY9Li9HhnuFdyHPtaSAC093jREt9wBeuTSMgM0QNOtGUnHHiVmoLy3ew0A\nFnCzswIcBZYWI9eyma7MJA5bbfQe6EcTrK7vlZejgEx5WcxWZjNuWnq4r+N+ZcBHogkX1zpZs72G\nSLReIvVhfpMxaZIhS8w+IRrAXjdA/1YPWEamepX/tLgAHQfpYHsPC6uIhosA+3WyFj2L2YZo42bc\no5UQbe3x7vUQbqxkA/QGgNeRD9BbUAGapWVfaLpjZUShxua7d62Dm0CSkE2SBTOwlIg1aA0i893Z\niW6Sjey9MzX78co0cglBPx7j0QnYNNxo/xH0b8UiDRH9YRGz1aVkLdIELUqWlslBUbSKXM0hug3g\njQWESKtXJgO0sWus9tZv9dBr9RGsDrC0HunZV8titmE8J0S0axruFdyP/l4vLSuLjt9Aql9tvIBF\nnubfJ9/S8nxB0x2KYUrM5jfUIVQHe+ig3+5lPjZ7QXsq1k2sYAWbuIkVtFq7CFrRxT1YzfaS5eL3\nMJ6etaNMW67DFYGm5qtKU7dUKr4Ge1nZFClLy2RqGSJEW0mrV/qWMxKa9XzmXSxhCbvYwVI0l6MV\nTbZqr0Za8dGz1rKEZzNQi+HuXesUl5WdvVwdlKsG6PnqFdN0a8dMx2IkljRtE6o86oQMJOO7fcep\ntFijWZHR45KadNW2lKX18pI6YUdCbVsFmunhvmGk4muoIFLfCVQsLZMmGTFE60egsHplGq8gQVoC\ntMzl8NGzmK+Y7S6WsBGvPGWGZykpZwxXV6zMsnJuMiRgHyZigHZB062NIYX6JvJCtSXkawC2FxBu\nHcGVY0sIj7axu5iuKCNGK4l4A73EhrVQbejb9Onysi5JiXALDVdScR8FItWGq6FIyUFRpcTsEaKB\ntGolhvt6/vC9sIP+doDBWhCvPpdWqwIMECJAO76sSGsZsM/rELIBup3r7WaqWEWGaysry6N1LJcB\n2gea7tCMKlRjPWYbZrk5Ps0e0pQ8WIyEtYZ+prQslyO0sJsk4twMSaS38gqN8nJksqnZ7qKVCnQ7\nsBvu60gNVx5zIjV/T1VFSkgTlIVox9iurXr1OoD7kDfeLQCIxnj7AMJuGqR1taqPNS89ay0DcA4X\nRT1oFZ63FrKGK6VlbbzOeRm2GcvUbBE03VqpItQ2EuN1JWQT9YWXlNxe20zEuoSdZJm5ZIUbz2QM\nIFNe1uPDA0QzLnfCpTQRiyi14ZppuLSsLFQR6fwlY9IEVUO01rn+/hplZm24pvEmK1hFFaydY0sY\ntKNer22IaJieLpCWmcVsw712PjyHyD5qjevHwnkZDNA+0HRHYlihOsrMOiFr5NKAY4gvI0KakpVY\ng+4A7cUwKUcBKBWqNlx5HpW5WlmzFYFuIzVaPYare7ZiwKVlZYqUTDIlNy5JvrPGIho6RAN2A5bT\ny+PRKEiHRwNcCZdw5OgmBotiujve5eV8gE61HO61MdgKsr1bm7HajDZnuK55GQzQZdB0a8c0V9sl\nB8vqWCE2XhGmYF6L10Ui0oxY2x2E3ZWk59te1KabnkSXpAbqD8pu3LXW4syZrRaiJOIywy0tK1Ok\nZFLwCdGCZ4g20cYrp9NzObYXsLcWVbEWOwO02rtJmBajLdNzoZa3FrK9Wh2itXa14Yq+vStWDNBF\n0HRHpkioJiJUMyHLc4fxarT2ZUp/B7EJRz3fsLuCxU4k0FY7TsZddzkKQHKz6pw4xWxNobqEaTVc\nipRMK0UhWs/V8DDe28gbLpAP0lsAugvY66RhWgwYGELLgN1sTQ3bQnOh4ep9tu0i5jdA03THQplQ\ntfFCHavGeE1h6lNJ0BWxavNtIxEsAITt+LGbvxA/w9ZC2nRttLZtl0C9DVeL1tdw51ekpEl8Q3SF\n6pX+apu6lvkP9yLS1xqyuu4C2EgNGKioZaBYzy4NW8dw9fW4QHHFigHaBU23FmxC9TFeeU1YRsZ4\n5SUtTI3sy4kUqQEDiXALkRJXkVBNYx3acGHZLoKGSw4Sm5bN13T1qsR4Ba1rfS2sLOPYVttvqCZ0\nS7QMZPWstQxk9WyrUBVqWU5qM1wGaB9ouo3jU5qK91cRq/wdMEUqJix0jHPp5eRMocq+ymYr/06X\n4TIVk0lm2BDtYbw23bq2nQE63vbVsrymNQsMEZ7lhL6Ga2O+DReg6daIr1D1sTbj1eKtINY+0tuL\nAVnRAqlA37A03SbWMnECBQKVxyLDZSomk0xZmXlI45W3muilU7W25VRA1oQBu5aBbGDWn1ekX6/w\nLCdzadmEAdoGTbdWqhivfh0o7fHCeNkUqHn6HUQCNa/31R9vfpw2Wf26l9kC9kQMMBWT2cB1HX7R\nfA0TR5AWnZp35dL6NvVsG27S2PTsCtLy+kiGywDtA023dqqWpuR1jZmSgUSsN5E3V3mub/elv/9a\nnP2CpmtTBYrFChT0bvXJfA2XqZhMGsNWr9TCN75BWrTbQnF4rqplOYd8hhmc5djC8CwH0XDrgKbb\nGC7jBSqlZCBvvjazNWdI+mD2cOW95n4vgcKyv4rhUqRkEhiX8QKZIH2POlUXeQMWDVbVsjRRv7fQ\nbPWjT7VKf4B+3XZeAtB0x4TPZQfDiFX2G+arBSuzH0VgLctpXGhBFxqttEUey8xW76PhkmljlPka\nPqier4RpINvbFXy1bL6vNDjrR9/wbDaI1SofaLpjo0yoQLnx+pzbEKwYMJBNyL5oDVlXk6pLoPoY\n2/kJmSR8jBewDx359HqBTJgGGtBzVS3rfebJXYZLPZvQdMeKS6iAX0r2FauwnBXWTbVd9j9deHN5\nlziB4QRqHmc7npBpwBWkqw4dAbkwDdj1XIuW9bbLbPVrZttpuMNC0x07rlJzUUoG7CUqX/PVx8cU\nCtHEtYBFkdmar9Nwyazho2XAL0hX/aw6tKyf27Tser2qlm2fS4ShTfcrX/kKnn/+eSwtLeEd73gH\nfvCDH+Btb3tbnW2bIUYRqz5OG7LNfM3z+Ywtm+20nVO3z3YsBUrmhSpaBtxB2td8yz637D1mG832\nmce5tGy+xzy26HOJZmF/f39/mDeeP38eH/zgB7G4uIivfvWrAICvf/3r2ZMvLAD455EbOTu4RGO7\n9k9PPzbf1y54zbx4z3V+E5eAXOI030OBjsY/YUgpNgb1bOKrZ1OT+n1VtWw7vw2b3mwTM13HF4Vn\n1/nN980zbj0P3dM9e/Zssv3444/jpz/96bCnmiOKUjJQ3OsFsj1fOV5/yV09YNuiHLZjbBQZre11\nCpTMC8P0euV9QPVZzr74ahmWzx82PLvOT0xqGdP9/ve/j09+8pN1nGoOKCoT+YoVyAu2qFzlMxZc\nJBifMdgqZlv2eYRMC1WDNFAepuV9No34zutw6ct3PgXD87goNN2zZ8/i6tWruf1f+9rX8OSTTwIA\nnnrqKSwtLeFTn/qU4ywvqu1T8c+8Y4pN4yNWfQ45j00QbcuxZVQ1yqpm6zrPvHEh/pk2qOc8VYI0\nUB6m5X0mVceBXecxP9Nsl+85XOeZR/z1PPSYLgD88Ic/xPe+9z384he/wOHDh/Mn5xiQB2WTI1zj\nN0Xl4qoTLly4BDWMOIvORzimOysUaW8StQxQz+NgDGO6586dwzPPPIOXXnrJarjEl6JeL2Dv+QLu\nxZX1OeukqKTlMy5FgZJ5oKzXCxRrGXBXtOpkFD1Ty6MwtOl+4QtfwO7ubjKh6n3vex+++93v1taw\n+aPskgCXYAG7gMomTpXhM25EsyUkj2+QBvz0TC3PEkOb7quvvlpnOwiAcrEC5YIVqiyiUQXf2ZYU\nKJl36tLzQWsZoJ7rgytSTSQ+YgXyovG5fq8qVS9poDgJyUI9kxSa7kRjm9VYRJmgbCKu6zpBipOQ\nYnzNVzgoPVPL44SmOzVUFayNui/EpzgJqU7VMO2Cep5GaLpTR12CrePzCSGjcZB6ppYPApruVONa\nsWac5yeEjAdTb3WbMPU8CdB0Zw4Ki5DZgFqeRRYPugGEEELIvEDTJYQQQhqCpksIIYQ0BE2XEEII\naQiaLiGEENIQNF1CCCGkIWi6hBBCSEPQdAkhhJCGoOkSQgghDUHTJYQQQhqCpksIIYQ0BE2XEEII\naQiaLiGEENIQNF1CCCGkIWi6hBBCSEPQdAkhhJCGoOkSQgghDUHTJYQQQhqCpksIIYQ0BE2XEEII\naQiaLiGEENIQNF1CCCGkIWi6hBBCSEPQdAkhhJCGGNl0v/Wtb2FxcRE3btyooz2EEELIzDKS6V68\neBHnz5/H29/+9rraQwghhMwsI5nul7/8ZXzzm9+sqy2EEELITHPPsG987rnncPLkSTzyyCMlR76o\ntk/FP4TMOxfin2mDeiYkj7+eC0337NmzuHr1am7/U089haeffho///nPk337+/uOs3zAqyGEzBem\nYb3oOnDCoJ4JyeOv50LTPX/+vHX/7373O1y4cAGPPvooAODSpUt47LHH8PLLL2N9fb1ycwkhhJB5\nYKjy8rvf/W5cu3YteX7q1Cn85je/werqam0NI4QQQmaNWq7TXVhYqOM0hBBCyEwz9EQqzR//+Mc6\nTkMIIYTMNFyRihBCCGkImi4hhBDSEDRdQgghpCFouoQQQkhD0HQJIYSQhqDpEkIIIQ1B0yWEEEIa\ngqZLCCGENARNlxBCCGkImi4hhBDSEFNmutNw/1G2cXQmvX3AdLRx0pmG3+Gkt3HS2wdMfhubbR9N\nt3bYxtGZ9PYB09HGSWcafoeT3sZJbx8w+W2k6RJCCCEzCU2XEEIIaYiF/f39/bGdnPfZJcSbMUqx\nFqhnQvxx6XmspksIIYSQFJaXCSGEkIag6RJCCCENQdMlhBBCGoKmSwghhDQETZcQQghpCJouIYQQ\n0hA0XUIIIaQhaLqEEEJIQ9B0CSGEkIag6RJCCCENQdMlhBBCGoKmSwghhDQETZcQQghpCJouIYQQ\n0hA0XUIIIaQhaLqEEEJIQ9B0CSGEkIag6RJCCCENQdMlhBBCGoKmSwghhDQETZcQQghpCJouIYQQ\n0hA0XUIIIaQhaLqEEEJIQ9B0CSGEkIag6RJCCCENQdMlhBBCGoKmSwghhDQETZcQQghpCJouIYQQ\n0hA0XUIIIaQhaLqEEEJIQ9B0CSGEkIag6RJCCCENQdMlhBBCGoKmSwghhDQETZcQQghpiHvGefKF\nhYVxnp6QmWJ/f/+gm1AI9UyIPy49j9V0I/65xnO9COADNZ5vHLCNozPp7QPqb+M/1XiucUI9TxaT\n3j5g8ts4jva59czyMiGEENIQNF1CCCGkIabMdE8ddAM8YBtHZ9LbB0xHGyedafgdTnobJ719wOS3\nsdn20XRrh20cnUlvHzAdbZx0puF3OOltnPT2AZPfRpouIYQQMpPQdAkhhJCGoOkSQgghDUHTJYQQ\nQhqCpksIIYQ0BE2XEEIIaQiaLiGEENIQNF1CCCGkIWi6hBBCSEPQdAkhhJCGGNl033rrLZw5cwZP\nPvlkHe0hhBBCZpaRTffZZ5/Fww8/zBtcE0IIISWMZLqXLl3CCy+8gM997nPY39+vq02EEELITHLP\nKG/+0pe+hGeeeQa3bt0qOOpFtX0Kk3/HCUKa4EL8M21Qz4Tk8dfz0Kb7/PPPY319HWfOnMEvf/nL\ngiM/MOxHEDLDmIb1ouvACYN6JiSPv56HLi//+te/xs9+9jOcOnUKn/zkJ/Hiiy/iM5/5zLCnI4QQ\nQmaehf0aBmNfeukl/Mu//Av+4z/+I3vyhQUA/zzq6QmZA/5p4udFUM+E+OLWc23X6XL2MiGEEFLM\nSBOphPe///14//vfX8epCCGEkJmFK1IRQgghDUHTJYQQQhqCpksIIYQ0BE2XEEIIaQiaLiGEENIQ\nNF1CCCGkIWi6hBBCSEPQdAkhhJCGoOkSQgghDUHTJYQQQhqCpksIIYQ0BE2XEEIIaQiaLiGEENIQ\nNF1CCCGkIWi6hBBCSEPQdAkhhJCGoOkSQgghDXHPQTeA1M1yjee6VeO5CCHVqFPLAPU8GdB0p5q6\nRelzfgqXkPoZt5Zdn0E9Nw1Nd6poQphlmG2gaAkZjknTM7XcBDTdiWcShFkERUuIP5OsZ2q5CWi6\nE0td4ry3wrG3R/wsaTMFS0hKnUbblJ5pwOOCpjtxDCvQKmIc5hxVBEzBEnKwWi46T1UzZpiuE5ru\nxFBVoHUJc9jP8xUuBUvmDWqZuKHpHjhVBFpVnMMmbR9R6bb4iJaCJbMOtUzKoekeGL4i8hFn3ZMz\nql5aIG30FSzFSmYNHw36Gm2denady6XBKgZM8x0Gmm7j1GW2vuepKmCXgHwuFfIVLMVKZoU6zLZp\nLZvnKjNgH/Olln2h6TbKqAIten9d6di3l1smWh/BUqxkWplWLQN5zdWlZdf7iYam2xhlQnIJ1PW+\nYc/nixZYWS+3SHD3gmIls8Uo2htGz3Vq2fZZtxyvmZpkkK4Dmu7YqdNsXeeqo3zlEpjgMmGbYClW\nMquMW891zOEo0zJg17NvmC7TM7VcxEime/HiRXzmM5/B9evXsbCwgL//+7/HP/7jP9bVthlgGIGO\nIs5RylJlpSiXCduESbGSWWSY3qj5noPUMmDXs6llfZzeb9NzkZZt7yEjme6hQ4fw7W9/G+95z3uw\ntbWFxx57DGfPnsXp06frat8UU1WgPmZrvm/YpOzLbctnmKId1nxpvGRaqCM8l2nZ9TlN6LnIgE09\nM0iPykime/z4cRw/fhwA0O12cfr0aVy5coWmO7LhFgl0WPFWxRQjkBetTbBVxMqUTCadcWp5mNeH\npUzPvmGaQXpUahvTfe211/Db3/4Wjz/+uPHKi2r7VPwzy1QR6bBmW3aedkEbhsXHYO8teM0m1nlO\nyRfin2ljnvRcp+H6BmfbZzahZ9drReZL403x13Mtpru1tYWPfexjePbZZ9Htdo1XP1DHR0wJVSY6\nDSNQ135TlIcc7agLU5Q286VYizEN60XXgRPGvOi5rvBcVctAVs/j1jJQrGeb+ZYF6XnTMlBFzyOb\n7t27d/HRj34Un/70p/GRj3xk1NNNMcMabhWBuoxWCdP2P+ozLJTTySHgTY/3WaFYyTQzTsMtC86G\nyQ6jZ5uM3vQxb1/zLQvS1HIRI5nu/v4+PvvZz+Lhhx/GF7/4xbraNIXUabi+ZuswWv2RZtGhCDl2\ny9ifaKfMhEWYZWItGustu6aXkHEzrOEOY7aW4OzSMuCv51Itw9OE5U1ap2YVq8h4zQ+F49j5YiTT\n/dWvfoUf/ehHeOSRR3DmzBkAwNNPP42/+qu/qqVx04Gv4boScZFAC8z2HuNQICtKl0A7xvNt43kX\nWbHq56IfL8G6xDpsSp5voZKDpqrhFu1zaFkfWpeWgVS/pradeg6R6s38d+twDRQbL0BpH5YBAAAg\nAElEQVQ95xnJdP/8z/8ce3t7dbVlChnGcH0TcYlATXHKoynEslKU7WoBOUeRIVcyYKCaWClUchDU\npeeatAxk9VxFy0BWz6Jl03j1cU4tm1WsogoWjbcMrkg1NAcg0DKjLSotl5WmtoxjtpBqRYvWJCPY\nu3G7zaRsipXGSyaNUfTsG549zNZmssNoWR8nWgayehYDlkevIG0bPvIxXiLQdMfKKIZrEahNnL4p\nWR+rMXu3gF2QpgHbSlVWsdJ4yaQzDsO1hGeb2bqCc1kFy9Y8INWoIFoF7HrWWM3XDNL6g1zBGqCW\n3dB0h8JHpMMYrkOgLrMt6/GWjQVtW44xU7GcxyVYZ8lZxKqp03gJqYM6DNczPLvM1seEAbuezaEg\nW7UKcAfmomrWUEGaxlsGTbcyVWYqm8fbROpIxKYQTbN1iRYoHgcyRWkimtDiFK24BKvPLUk5I1Yz\nJQPVJ2SYzJdQSZPUaLhF4blI40CxAcM4Biierax7u2KyZpjWx5YGaRrvsNB0a6FsprI+xmW4RiK2\nCdRmtkXmaybjw8bzNQB3jH3mjEfTbE3BCmZSzo0P2WZEFhmvhkIl46Do8iDbMT6G6xGeywK1z9AR\nUK5n05BN7eowDWQ1Dsu+sRvvfEDTrUSdIi1JxEUCtYlTG/Jh9R5Ytk20eZrvNVOvLRXbZkQK1hKV\nj/FSqGScjFKx0s9LDLcoPJv6NoP0qHpeU9v674OYqBmmXZMlhUItVzVeG/MRomm63gw7jjui4brM\n1jTjw8iLNXncKf6nAcBWS20jFat5XhGoLRW7cKZkwD7GC+O1IuZDqKQJqlSs9HaB4brCsU3PZnDW\nz6toGUj1LDreQta8bfoVCbpeR/z8zfjfmeBrvJr5DdE03ZEoS8VjNFzTbDMC3UG7OwAABPEjALQX\nw1xLw710stNgK4j2xY/YatkN2GW+5mtmuTkxXv07qZKQ51eopE7qqFhVMNxhtAzZjkx2ZD1rExYD\nLtJrEaXGa1KlejX7IZqm60VVkdrQBu1puMfgb7ax0Yoo24shAsRCRSrUHIvRwwABest9DBAAy32E\ne20MtgK7AZtjSb5kylN6ctWoCXn2hUrGTdUALdsjGO59KNQyEJmsmKuvngeINCt6DuNzJXo2tWwL\n0q+7PwJAifHqbWrVhKY7NFXKymYqVl9UU5T3YSiBijgDDBBggDayQjW3NQME6KGfPIZoY7AYm/By\nkDXgrRZwNX5jURnKRc545ZdQdAKWmUldVAnQReO4+jVPw73Psv8wgONwahmAVc9lWpbtAIPEiNvL\nIcLuwG2+mvtQruvEeIHyYSOGaIGmW4qPSM1jy1Ix7CK1Ge5xFAq0t9zPGG1WqLKdLUMFGCRpGEBs\nuG30AITx/kF81gADDBYNweKIW6xFKVnPmHzTJyFzPIg0gStA2153VKyKDPe4sf84suH5uDs4y3b0\naYOcloGsnlPDTfU8QJCcK6dlbb5QbSrr6Qpew0Yms22qZdB0h6JMpOaxFVKxbOvS8hqsAu0t9nPi\nFGFqoQJAC7uZVq1gM/N8B0sAtEjFcvOC7QP2Xq9wH/Kita1iFbcwoiwhz7dQSR2UGart2KIArYaI\nfAxXV6tUeO4d38iZ7Ro2MqFZh2hTy0BWzztYUoYbJqE6/YQA/cVe1nyvHonaJPqUnu7V3EflKa1e\nDTNXY3b1TtMtZNReboVUfBzFhnscOYH20M+ZbQ8bACJh6mRcNA4kKXmANlawiRABdrCUsfI+1tKe\n9DLyvd6rcRsF03jNZewKE7KL+RUqaQKX3l1lZbVbb2ttm4arAnT7+M1ceBaz1UYrWgZQqmddwRKj\n3cFSHKDDJEwHGKCPXj5IX40nXEkF6ziGMF6gepl5fqDpVsanl1tQVhaKZjIWGK5NoGvoZ8RpJuMi\noWbHgNpJOh6grc4XIEAYiVQMejFI2pakZNN4XVU5wZqQ5XdGoZI6GSVAm9sFAdo2hmsa7vHs0JCE\n5x42MtpdwWZGu2Z52aXn6DFbXtYGHAXoaO8G1jJBuo+1bAULyBqvOcPZdX0+Q7QTmm4tlIkUsF4w\nrwVrjuEqwzUTcQ/9RKA9bGTMVgsXyE7CkOcaEWkYB4OBIdIBAvTRUyLtJWLFItKU7DJeoWs8t4rV\nR6ia+REqGQfDBmjPISK9z2K4UWjOh2cxW3O4KB0ysodoHaDDRLFp71aH6U2sYBCfJxOkjwP9q2vA\n8dh4ZYWrjvEIpDOd9XOG6FJouk7Kxn9qEKmtDFVguDoRmwLVZmufhJE3XptIZRZziDY2Mom4l4wl\nDcxzLSNvvCLGbeNRtuV153gQwLFd0jw+AdqgaE6GnjRlGG6q534SnmWfmPCwWpZ9ouVkLBe9xIg3\nsRKfT5n3IrLGK8hwkR42Mn8tmfzbdr1QwHyEaJruyIwgUr2ty1CqpKwNVyfiFWxmRCui7JlCHUQC\nbVkufD8Si3cnTq+DIM3EMoFKm28fawCyIt3AGtawkTVenX7NhLyF/PjuTdkwJ1URUgdjDtBAvmIl\njzJpymK4ulplhmfpBedC9CAs1DIQ6XkQtHMBWs4VVaui3q30ejNo4+0q473XeDSDdebKhLvI4lp5\nbvZMtQyabq3UJFI1q7HIcLVATbM98kaYlnC3UbjaTKsjjyGOdMNEtJkxXGOChkYEHXbb0RgvjqSl\nKUnGplCBtH33oESoJvM5FkTGTcUAbSsr2ypWXZQa7hr6uRCdhGkx2i3YK0eaDtBCpGV0gaATYhC0\nMwE6GR5CtmqlGSwG6B3fiIL21VZ6NyL5bF1adoZowD1kNL8apelaqZqMaxKpkYqzlxHkDdcm1MRs\nxWh3UCzUDoAbSO8StB2ZcKsbIuhcwkbQy4hUJlRZWYz+HWE3iBKyvgWg2QZzPKhQqBwLIgeJI0AL\neo6G9ZKhqGKVLRXnDVeP8fbQT832GlItA+V6lsdWrOVOiOBYar5av5nSssHG4hra3QHCbiv6t+jx\nXfkzt2VsAypEA/axXZP5CtE03ZEoKksNKVJHKnYZbkagIs4bSE1X93ZhbOuEqgOACHYdONHt4+bR\ntGdbdKmCrGSVCFWP73aQlpZrESohPtRRWnZgC9BAacVKNGwabk+F6CQ8X0canM3eLlCsZQBYj45p\nbQOtYyGCTggpWpkGrEmmXnXbaYgWykK0dQi37Lrd+YGmWxv1idSWiosMNyNQMVzd2/UoSSU9XW2+\n8XuOIASO9jMiHaAdX0gUJJO79K8iM757BzUKVX3IHKVjMm5cpWVD17ZhItnvCNBmxarIcNcG/Xx4\nlue+WpZHCbhdpOa7Dqwd6wNBNkDLXGm5pndN9Czju2aZ2RairWO7ArUo0HS9GLG0PKRIdSqW+YdW\nw70Gu0CvIy9SLVYzHeufWKRYj16OjDed5bwWz5QUomgwsCfkWoVKMyVNY6w+BeQnQ3oEaAnMLewm\nc4qthiu92+vIG645P8OmZ1PLRm+4hch4ZegoRDuZ+SxEoXqQr165QrSeIOm8dhegfmm6Fnwvoq9Q\nWhYqiLQXXxIUIFr0Qo/fyusZw72OtLerDVeL1CYGPRlC/wC5NC09Xo0kZOnpWsvMplD1LQHFgAuh\nUEmTlPwNsE2GBEoDtBitrli142UaM4arA7SpYx89a/NdR2q86+lhYrxqfmSmerWGflJn8wrRXaTF\nJvn9ZOZpyC+IlSuabi14lpaB7NhuSSlKi7StzFbGcLGF1HAlEZumWzbj8TpSo9VjurrNCjFeaV16\nWUKQtDsnVLTSf7v0EORa3dISMyF1MkLVylzYBshqxSNAR5cGyUSqfmzGg2jClBiu1rI23WvxZxVd\njaB7tV2kZmvRsjZeXb2SMrO+5CgJ0bCM7WofBRzzNABWriJouuOmqLRcUIpyiTTAIJuKtbFqkRpl\nqbsFlwwdso3pAlahAtFlCL1ABBqgh41EqJl1cBaD9N8tdyWS564Ss9csZv06b3BPXNRctRLMAK0v\n+SsJ0LqsLFpPKlZ6wtR1ZPVszNFw6fmQDgHbiBbpuI7IeK/nj291gSCI2hPGPd0AoTVE99FL/413\nkL86QeubJWYnNN1SfGY6msdZdtlKywa+Im2J+CQVXzd+VJn57jYQxpca3L5j+1Tg3h2gvW2YL5CO\n6+recAtoXQOCU4NYpANDqGEytgugeCzIVmJ2zmLW+Ip2vsVNxoCpXcc0DluAjsZyRdNhEqAzodnU\nsxGgRc9FWgaUnoE0JIjx6oB9Ta7lDZOerS1E99FD0B24S8zyu7lt2SYZaLojYSrOMxnLW41kDCCz\nCk2hSPVlQfrHYri370TW4yzu3AGW7yjzXUdaygKyKTkWbDCIhKrbK5MvZPEMa4lZzqHNV343pWO7\nhIwbz96x1rKlagUg0QUQXQ8rP3qVqUyANq84UIZ793pWy0Bez4mW1b5D0ssVPZta9gzRAQb2ErP8\nLrwqV7Jzvt2Yppth1HKUByXJGEgvWE/vEmQRqa2srBLxrRtZs3V9zW/rJkl6vh4br/RCzT8Erei6\nvyBIS8mygKS+dViIdnodoJiqmYC9EzF7reSAcY3nGkhpGUASmmXGsl4fPcAgb7S6l+swXJeeRcu3\nEIXo5TuRxybGazN0S4iWdvfjm5tENzwJ7SVmW+VKUziuO5/DRTTdcWOO5wLeyVgvVS6vW9OwIdq7\n23mB2tKxNTrExnuo6DPiVBt0QgSBjPlEdxuSmyIkYl0M7ekYyJam5Hc0mzojU0XJUJHGMp4rmHcD\n0jcsaCOMJkNuIxrLNXWtnovhXkIqD5ee5ZYgSbPjcvMhfVmPI0QjSP8GDeIgvYmVzKpVQXcQLfNq\n+/3oSVyVqlbzFagXRz3BuXPn8K53vQsPPfQQvvGNb9TRpiljhF6vQpIxgCQZy3b0mN68ILMcnCFS\nKSmbhquf37bsv6yPuRNP1LBM4NDPW9vZPyy2Py4J+o+SuUJX6aXOJTeQIMQL35nLxuu2roljXoZQ\nVrUCkK1a6RnJxoQpCdCi2UtINevSszy/fSee01H0WUAUonUPHEhCv/73RP/2nWynwdbjL/n9zDMj\nme5bb72Fz3/+8zh37hxeeeUV/PjHP8Yf/vCHuto2/ZhfvIJylKC/3GYyBmA1PxNTpNpsgTRTarHC\n2LYKFZZHo822PzKETCfx/AyNQ8OaoGuGT129MqpWQN5sFTpAA1mtynObnk3jzYVoqOdxiE9CPdKw\nr7e9tDxWs62ng3PQjGS6L7/8Mt75znfiwQcfxKFDh/CJT3wCzz33XF1tmw8KylHmduaWXua2KkXp\nQo0e/zHFa5qtKey75h8BT8M1CboFYrWJlIMeZBqwFWC6O5adpokpPdhuYqCqVjJL2RaOTZ3bCrSZ\nfba/GZbXdIVKDxcB2YocGY6RTPfy5ct44IEHkucnT57E5cuXR27UzKHF2XVs+2L2bC09XcEUZdkx\nQGrQmUsS9PjMtn2/j/kW4uxBlJUBCRmFEXtP+nur9KxLtDZ0r9J6UxJF1dFObdDy/tAcktI4DHe8\nVarZ6LUOw0h9ioWFBY+jXlTbp+IfUoVhvvy1z0cqMHcXyWzHoTgE93W6mmmdhHEh/pk2qGcrh8sP\ncRlwneiJVHLL+LpxToyca/z1PJLpnjhxAhcvXkyeX7x4ESdPnjSO+sAoH0GGRC4dIJOKaVgvug6c\nMKhnQvL463mk8vJ73/tevPrqq3jttdewu7uLn/zkJ/jwhz88yinnC89p9bK6EwCviRw2Ri7mFKzH\n7CLT7src9TyO0YKMwojfH6kAGStEyXdfForJbQfpdtmyq1VYtmzntO/5OS79hluj6FqYX92OZLr3\n3HMPvvOd7+BDH/oQHn74YXz84x/H6dOn62rb7KBrvabRquehEqXgNK4CE9RiW0ZaYrIZr2vE9N7D\nallI19iz2q/bGRptHviI1Fm+do06EzJhFITogUXbVgw933vYT7d6n+UuwGi3kL2Zif4stc/2NwgY\nNUATzcjzRJ944gk88cQTdbRlbgm3AmA5vWXeAAFWsBmvgxrtD9HGTideTNEUi7olXzue8biMrD3J\n+i4uk11G1qzb5pCNefehTtrW5N9RYLxObH+o3vR7KyEHir5DlrCVCifSb6SFFWwm+xJdd5Gujqr1\nFd8d6FAnmgBlm7Vg0zKQGu6y2r7XHG82PwvIGa+EhB0sZd4a7nmGB+Jk5MUxSEGZxDSUgslI8mUW\nE5MvuyyZDsQlKZtY1G35DnXSdKwFKM/NH6BApOb9dY3nO8p4pd25Xq5+LncaKuqsWl9j75bUQZXv\n0S1EE/mMYQ61mIQLXdmxBVGtl0KNddLwa+rZpmX9OtR2u2WpWunPjD9jELQzehXjTR8NLcudhmxX\nNIxlHfXZKEnzisimkHWHXc+BJAFHN4WHerSkY/Om80ZvF4jWXi3DLElZRarPr0Q7CGTZjlSUO1hK\n2iv7w62gsKxOTyXNYy6YmFmFPEtZ5UV6vKpHqatUcr9pJHfx6ecrVzadxb3ddQD4P79/Vc6c9TBR\n0U9Xj0MHSUDQQQGIA8WWZebySBqeDTP1hT3dDGP4zzfN5jbyyXCrlaRj+cLrH9k/QBD1LguEg050\ns4J2CzhxGDgJ4AQiIZ5Atudr27/+tlik6wWfs4rEfPU9U2zJuLAcZfb8eZchMhFYHOS2Y9sSJmWi\nkaycDkCFUXWzP6lclYRoXb0SUzW1rPWsDTcZy12H3djj7Z1O2l5dtRoYf4MKcV5vfBd+l//NB+zp\nDoWZkjXy5VLLx20jUoMsOC5sAVhLn8rNomVbxnVlf4g2BkEbrU68UPoxpDcgkJ9jAK7FdwmSW3jd\nsS+GDvVcBJox3GPxtvwYIu2jp3q12Z9cMh65HDVfaZhMIGZ1SnRtIdxrY7CYVq6C2HDl1vDt+IZ5\nwbH4zmE7yOv5WHyy63EFaju6gcHyHfdfID08tLyKrMFqLRsBWkrLMp4rVSsAsFat9FCRS7u3YVQJ\nyiZF3ip4bXag6Zaiy05lJSn1+pvITrTQ21vqefzlDbcChN0BsIhYlIM4Haci2MBadHcSU6ia68gY\n76HtSKzhjvtC+Uw5WQu+oJfrEmmaktvFyViLtfLCG74GTKMmVSkK1EiDs75Npb5tpapctZdjY40j\ncxg/5kL0sTA123X1WdeR/s3YjrQser7XvtpkMgac6FnCslm56iLSsiNAD5Kb+aW930zVyhy6Eg2L\nVzpD9OyaqS803dpwjAm50vE2rEIdLAfx1z368rewiz7WEilkhKo/Y934DNmvxOrEVnJaV4/riEzY\nItINrBWKtDQZmxp8E0jLUbxciEwgtsqVHtfdSq9IkPBZGKI7IVrr6tzbyOq5g8z9bwv1bE7I0oar\ntbyevr4R9JIAvRHrehMrqoIVa1pXrYC0amUaLatWhdB0a2HIdKxfj7+okoIjUfbQRnRvS7mh9EZc\njw46l9ASMcY9W2jhAqlYy3qUtokcWqhiuOvAzrFUpJHxtnMiTcZ5i0rLul3yO6g8c3k+ylFkWEp0\nmTvOVrmKefOQvXKl71MLpN9zpCXmohDdRw8IgBPdftZszfXOpSds3inIRNqh9WxqeR2Rno8BN4+m\nY8xDBWhh6KrV/EHTHQtxL/TNgnFdXWKOx2CkxKyF2scaWtjFACE24nWMAwywEfSwdqyfXQHVdvs9\nEaverzGTsSlUi+H20Ut6umFsvlqkffSKRWr2dpmMSWMUDRe5jlPId7WoxAxkSsyuEA0gsbebR9s4\noicb6bkf5i02XXruWB51WdliuH30sIG14QK0/D7M0rJse1Wt5m+oiKabY5R0LF8k9X7Z1TW2C0rM\nWqhtDLCJFQCI94XpTQQCZI1XxCbGbrsfrg3TePWkKWW4comQpOJIsL1kLFcMuJJIdbsyIiXkoPD4\nG1AWorfcIRpIbxCfuSHI0X5qvCLqLqIqluu+1jZsczFkjkZsuDud9MoD0XE/1rQEaNG4NUBLG2yl\n5aHGc+enakXT9cInHXuUmIFUqLrXp4V69Uh0dd8yEqHGI7lJTzeDGK+IswXgBuw3uvfp6eqylIzh\nxj3cUAlRp+J+YsBr7lKUfL5tooW1tHwL+egs+32YnWRMmqBI1zFFJWZHiO5fXQOOA8FiGqKD2Ois\niPHqHrVZVi7Ts9a0jOnKpUOqhztQIVkC8yZWEgO2juVKgJZqlc/wVQbqkqY7FoYU6lUAx9OE3F/0\nuy1eGLTRC5RYRaQ7SEVaVMI1V6lpIent7nTyJWVbKk5nMlcU6dCl5flJxmQUbGbqe0VCSYlZb9tC\n9FUAx6Pq1cayujawhMHREGsdI0hr8zXboLFpWS7zi6tVEpB1iDYrVoVjuUA+QJvbhaVlYT4NmKY7\nEq4S85BCldcsZeYikmtiRaw6FbcQ9Vj1JQZ6opWghR2brQg0LUGtxeNRa7lUnIwN3eohvHokP5Zb\ni0gJaQrTjNU8DZ8QLTjKzBuOTw3RjlasioN00AmzepYwbZs0KZjrOXej3q3u2YrRhnGINitWffTQ\n3+tFPfVaArRrdRGgPEDP1t8Dmq6VqunY9b4CoUI97wJ4HcB9sJaZhTYGyKymgWj1p7V4WTkRazsI\nERwdIBgowQKpQFfVCdRsx2QtZWW2LqGahptLxVeRnbFci0hnS3xk0vCcpwGUh2ggLTNfbUVjuceR\nrAG4ho2c8YbILh05QBAZbzBIzVd/3jbsWo4/W4JzejnQmpqTEWl3gLbVcDMVq6sANlBDgKZ+AZpu\nDbgMGvn9Wqj3quf60Sgzm8YbYqC2U5HKSjc99NX1vCEQAMHR6D3BwD5BSS90rpeCE6FK71YEGiLI\nGW6Siq+qVHwVaSqWx1pEOl/JmIzKAYRo/Qgk1St04TRevYyqBGm5hDAIBlGYxgA4Wqzl6BxBTsu2\nEC0zlXXJeYDAXrGyBejbYICuCE13aFxjQSVCBbIzmYF8Qj6OJCGHx5ExXl1qTpeMjEQ60CJVV9vJ\nNb59R5U6u9B5Ks70DJEod7CUmK/VcKUMZUvF5oxlipRMDR4hGsgOEenHeHw3xJFI28p49bKvPWwk\nQTpMJl2FOTUCQBCk4VujtQwgp2dbeA7V1Qg5w9UVq6vIB2ggG6YZoEuh6TopS8dlOIQKuMVqS8iG\n8UbpOCoxi8mKWLVI9TaQituGKVSb2WqBZpLxXjs1XBGlKxWb2xQpmRhE72aJ2SNEA+llQ0BSqUoe\nke43jTdZ01jpdAdLWMEmogU1out6g1ibYp/O2c/I6llrWbbN8Jzp/doM16xYmb3cQhigTWi6IzGi\nUIFsmVnGdeVRMIxXysdRIh4kPV0xRxFpH0gMGAUijVqYF2p6vsAqUKvhSi/3qvFYWFbWUKRkHIwx\nRAN58zGrV0JsvGE3AI4Dg8XsXcR62ICsXtXGAC3sZgJ0P15gowhTy7JPm60Oz1KtGmwFbsPVFSvT\nfGsJ0PMDTbeQuoV6N2+8pihNA072tRB2W+gDCLvtjFgjE873dKMl57IiDYyFJ7QoASRGK+fWZpuM\n94hAt4J0DFfM1lWGKiwrU6RkEvAJ0ZbLAW10HfuB5FKi/tU1tLuDTJAGkOndSs93EyuJAUuAdmk5\nOkdWz/leryM8uwz3dVSoWAlVAvT8VK1ouiNTRaiWe8uaCVmXpF6PTyWlqm6aktvdAcJuG73F7IQL\nESzQSwxYVrTSq1tpcjeqNsSZmZDhEqjNcK/BMxULt9XviiIldVMlRJddDlhQvQLypruNVNdyh55u\nPkiLjrNF4UFisDJMVKZlIFu1Sp+rmcx77Xx4NidB2gzXDNOZ2/fJ765Mv/OrVZpuKQ0KVbiKaIxI\nl5i76rVYrGE3wKAboLfcz0yYSidQZUVaVGI2hRnty5qtU6BbyArT23D1761sgYv5FSlpkrKZzJYy\n85vIf33NISIgP8YbX61gBunBol6HLj+WW0XL8ujU8pbSsq5WiYZt+rWO4xaVlRmgNTTdWqgiVE/j\nBdKerkZMrovEfC9tRYIN4gvwMzOW0UNb9Sb1hCpz0Q0pb2lxAsgL1OzdamGaY7iFhkuRkqYZJUQ7\nysw4lJ5GoytVggTqe+EM0tp8gbT0bGpZXgOKtSyPTrPV4dmsVtkMd6iysma+V5Oj6XpRh1A9xneL\nkLuLiFgt5iuC7aOHIH5sL2bLUrZZj1qwTqMFahJo8knImmyR4c63SEnTlOldazvmzUPRX9OiMV5d\nYtbYtIwjQHcnMWCtZcBPzzktA8VmWzZRqtRwi8rKtxz7bcx2gKbpjoQWopmCfcZ3KxqvRkRqChat\nqGTVjUTW7ubFGXQH0YX6Bhlhymfo6/FGFiiQL0NVScUuZlukpG6GCdHmc8ewUZHxAtmeblGQBnIG\nDPjr2apleRzGbIEhDHeYitXsQ9P1xlVCLjvGTMV6u8B4TUHq5/qemqb5In4u5hs/akIcyTd9y9g2\njVb2FwkUln1ehutKxSbzKVLSFFVDtGPYqMx4zY+zmS+QM2DAU8+mluVRn9dmqGXhWdpsnZNhbpdV\nrFzMfoCm6Y6Mb0I2jy8wXi02jUzVN81XTinv0eISii5h0MeZ7xXxAVmz1c9Nger3eRvusGXl2Rcp\nGQdVQ3RF4wXsX1mt1cwykchqG/HrG+rxsDrepect47lptNKGIrOFZZ/8W6w9XHmDrXoF4zhUOGY2\noelWosxIzWOKhOrZ4wXyYrTt071fLVphA24jtz3Xxir7XWZr7pP3OydNVTVcF/MhUtIkZoge0nhx\nKD+r2QzT8twMz+adg3z17NKy/LOAbDB2BWVnORmoZrisWNmg6VamzoRsTMYAilOy7JekrNOx/lth\nu92XoP+euAweKDbfMtECNRvufIuUjAufEO06zsd4kQZp85S2ISJzGEmbMlBdz/rSHpuei6pZufAM\nDG+4rFhpaLq1MWxC1s9LxKqTsuy3CVa+17aqt3mNnZmOtSZMAzbFKfsqCbToubltNkgzPyIl48TX\neG3Hu4xXUBUsqJe1jm3mK2EayPZ2Ta1qQ4bldf2ZNi2br3uFZ6B40pTeZ267mHXiiZcAAAt9SURB\nVC8t03SHYpiEXNLDzeAQq+AqSwHZmyZoQYp4i3q3+vzmdpnZAgUC1QfRcMmkMWz1CvCuYAH54SOb\n+Zpheku9rtHhWmNbuKLIaM3XM1oGqoVnvc/cNo+bX2i6QzOq8QKVxHoTxf9bNtEKXdhTsIltDEjO\nrV+3mi3gJ1DXPhMKlBw0PlrWxxVVsAqCtDZYV8Uqc2UCyvXsqmBV0jIwfsOdvwA9tOl+5StfwfPP\nP4+lpSW84x3vwA9+8AO87W1vq7NtU8AoxquP8+wFa/M1EzGQFS1Q3Lt14er12gy5skBd+6oIb/5E\nSppgWC0D/hUsRVkVy1WCrppFXeXnoc22bJ+5bR6nmU8tL+zv7+8P88bz58/jgx/8IBYXF/HVr34V\nAPD1r389e/KFBQD/PHIjJ5uispQ5JrTs2L7Xsv9ey3Fyw4RYsDoy6VOYsxqLLhcSbMm50GiB8QjU\nPFYzyyL9JwwpxcaYbz0Xadl8btOuuc/QMpDquUjLrn0mPjOZgQKzBfzCs7mfhhvh1vPQPd2zZ88m\n248//jh++tOfDnuqKadoPKhKSgaKJ2UYE62ANC3LR7k+1qe0bDY78zn6ib4o3jRb/eZhBGr78KJj\nCambKj1eoLyCJcd49IRFz3ooyTafqzY927QMDBeebc+pZRu1jOl+//vfxyc/+ck6TjWlDGu85nOX\nWD14E8ik5rIx4MLzmJSJE6hmtrbnRf/O+RYpaZoqM5qLho4Ae5D2KEO/WYOWAYueq2jZd3+V8EwK\n/yvPnj2Lq1ev5vZ/7Wtfw5NPPgkAeOqpp7C0tIRPfepTjrO8qLZPxT+zSFXjBfzEKsdVEKxgGnEp\ndy37jN61t6nScIu5EP9MG/OuZx/jBfyC9Di1DNSn5ypaNo83oZ6HHtMFgB/+8If43ve+h1/84hc4\nfPhw7vX5GAMyqTLGazvefG4b73Wdz/bZbcs+F6YghSqGSoEOB8d0J5M69VykVx8tA/56HkbL5utF\nr9me295TdvysMoYx3XPnzuGZZ57BSy+9ZDXc+aWsxwuU93r1c1cqNkvPFVKzE9f7bUKqYraufRQo\nmXSqVLBsx7uqWPIaUGkYqRK+eq5ixK7zUsu+DN3Tfeihh7C7u4vV1VUAwPve9z5897vfzZ58LpOx\nUHaxvU9Ktu3zfZ/r2DKqTH4oE6fv+3zeM+uwpzvZVO3x2t5jO4dvD7foc4o4aD3Po5aBsfR0X331\n1aGbMx+YPVYTV0o23+Pq+QL5xIyCY6sySq+36vt93kfIQVK1giXvAfJVLL3Pp1o1qp6LNDWKnqnl\nYeCKVGOnDrHqfXq/+aV3mfAoVE2xNFsyqxRpGRhOz3qfLVDrY+ug6mU81HPd0HQboU6x6v3ma0VC\nKCpN+SboIiFVTdO+7yVkkiirYAH2KpbrvcNoGY7z+77X9tk++33PTT0XQdNtDF+xAm7ztb3fVVp2\nnbsKZeIpe50CJbPKsEFa3iu4DNj2uu38vvjojGbbBDTdxikTKzCcYG2vj4M6jNbnPIRMOqMEafMc\nrvNQz7MGTfdA8BErUE2wQtk5q+IrJoqTzCtVgjTgr+eD0jJAPY8Pmu6BUtV8gfLLBpoUwThKXIRM\nI75aBvz13LRequiZWh4Wmu5EMKxggeGu3RuFcYwNEzIrVNEyUC1Q1w21fBDQdCeKqoIFxmvCo66S\nQ4GSeaUOLQP16ZlanhRouhPJMIIVDvruHhQnISllE6XKoJ5nDZruRDOqYJuE4iSkmFHCdJNQy+OE\npjs1TJoBU5iEDMe4ZykPA/XcFDTdqeQgREtREjIeqOd5gqY7ExQJqIqAKURCDh7qeZah6c48FB4h\nswP1PO0sHnQDCCGEkHmBpksIIYQ0BE2XEEIIaQiaLiGEENIQNF1CCCGkIWi6hBBCSEPQdAkhhJCG\noOkSQgghDUHTJYQQQhqCpksIIYQ0BE2XEEIIaQiaLiGEENIQNF1CCCGkIWi6hBBCSEPQdAkhhJCG\noOkSQgghDTGy6X7rW9/C4uIibty4UUd7CCGEkJllJNO9ePEizp8/j7e//e11tYcQQgiZWUYy3S9/\n+cv45je/WVdbCCGEkJnmnmHf+Nxzz+HkyZN45JFHSo58UW2fin8ImXcuxD/TBvVMSB5/PRea7tmz\nZ3H16tXc/qeeegpPP/00fv7znyf79vf3HWf5gFdDCJkvTMN60XXghEE9E5LHX8+Fpnv+/Hnr/t/9\n7ne4cOECHn30UQDApUuX8Nhjj+Hll1/G+vp65eYSQggh88BQ5eV3v/vduHbtWvL81KlT+M1vfoPV\n1dXaGkYIIYTMGrVcp7uwsFDHaQghhJCZZuiJVJo//vGPdZyGEEIImWm4IhUhhBDSEDRdQgghpCFo\nuoQQQkhD0HQJIYSQhqDpEkIIIQ1B0yWEEEIagqZLCCGENARNlxBCCGkImi4hhBDSEDRdQgghpCGm\nzHSn4f6jbOPoTHr7gOlo46QzDb/DSW/jpLcPmPw2Nts+mm7tsI2jM+ntA6ajjZPONPwOJ72Nk94+\nYPLbSNMlhBBCZhKaLiGEENIQC/v7+/tjOznvs0uIN2OUYi1Qz4T449LzWE2XEEIIISksLxNCCCEN\nQdMlhBBCGmJqTfdb3/oWFhcXcePGjYNuSo6vfOUrOH36NB599FH87d/+Lf7v//7voJuUcO7cObzr\nXe/CQw89hG984xsH3ZwMFy9exF/8xV/gz/7sz/Dud78b//qv/3rQTXLy1ltv4cyZM3jyyScPuikz\nAfVcnUnWMjA9em5ay1NpuhcvXsT58+fx9re//aCbYuUv//Iv8fvf/x7/+7//iz/90z/F008/fdBN\nAhB9uT7/+c/j3LlzeOWVV/DjH/8Yf/jDHw66WQmHDh3Ct7/9bfz+97/Hf//3f+Pf/u3fJqp9mmef\nfRYPP/wwJxfVAPVcnUnXMjA9em5ay1Npul/+8pfxzW9+86Cb4eTs2bNYXIx+tY8//jguXbp0wC2K\nePnll/HOd74TDz74IA4dOoRPfOITeO655w66WQnHjx/He97zHgBAt9vF6dOnceXKlQNuVZ5Lly7h\nhRdewOc+97mJn3E8DVDP1Zl0LQPToeeD0PLUme5zzz2HkydP4pFHHjnopnjx/e9/H3/913990M0A\nAFy+fBkPPPBA8vzkyZO4fPnyAbbIzWuvvYbf/va3ePzxxw+6KTm+9KUv4Zlnnkn+EJPhoZ6HY5q0\nDEyung9Cy/c09kkVOHv2LK5evZrb/9RTT+Hpp5/Gz3/+82TfQfU0XG382te+lowNPPXUU1haWsKn\nPvWppptnZVpKoVtbW/jYxz6GZ599Ft1u96Cbk+H555/H+vo6zpw5g1/+8pcH3ZypgHqun2nRMjC5\nej4oLU+k6Z4/f966/3e/+x0uXLiARx99FEBUGnjsscfw8ssvY319vckmOtso/PCHP8QLL7yAX/zi\nFw21qJwTJ07g4sWLyfOLFy/i5MmTB9iiPHfv3sVHP/pRfPrTn8ZHPvKRg25Ojl//+tf42c9+hhde\neAF37tzBrVu38JnPfAb//u//ftBNm1io5/qZBi0Dk63nA9Py/hTz4IMP7vf7/YNuRo7//M//3H/4\n4Yf333jjjYNuSoa7d+/u/8mf/Mn+hQsX9nd2dvYfffTR/VdeeeWgm5Wwt7e3/3d/93f7X/ziFw+6\nKV788pe/3P+bv/mbg27GzEA9+zPpWt7fny49N6nlqR6UmtQSyxe+8AVsbW3h7NmzOHPmDP7hH/7h\noJsEALjnnnvwne98Bx/60Ifw8MMP4+Mf/zhOnz590M1K+NWvfoUf/ehH+K//+i+cOXMGZ86cwblz\n5w66WYVM6ndwGpnU3+Uk6nnStQxMn56b+v5xGUhCCCGkIaa6p0sIIYRMEzRdQgghpCFouoQQQkhD\n0HQJIYSQhqDpEkIIIQ1B0yWEEEIagqZLCCGENMT/Dx7hNPEy2iP9AAAAAElFTkSuQmCC\n" } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fock-state distribution\n", "-----------------------\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# pick arbitrary times and plot the photon distributions at those times\n", "#t_idx_vec = [0, 10, 20, 30]\n", "t_idx_vec = range(0,len(tlist),25) \n", "\n", "fig, axes = subplots(len(t_idx_vec), 2, sharex=True, sharey=True, figsize=(8,2*len(t_idx_vec)))\n", "\n", "for idx, t_idx in enumerate(t_idx_vec):\n", " psi_a = ptrace(output.states[t_idx], 0)\n", " psi_b = ptrace(output.states[t_idx], 1)\n", " \n", " cont1 = axes[idx,0].bar(range(0, N1), real(psi_a.diag()))\n", " cont2 = axes[idx,1].bar(range(0, N2), real(psi_b.diag()))\n", " \n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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Z668j9alfzvVnwnJmurk1nSKWNeM9NAA3t0K+/uklQHmayWufX9UAAACMQ8ABAADGIeAA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\nY2OjNm7ceLUI++ZA2eIeHAC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} ], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Nonclassical correlations" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# second-order photon correlations\n", "g2_1 = zeros(shape(tlist))\n", "g2_2 = zeros(shape(tlist))\n", "g2_12 = zeros(shape(tlist))\n", "\n", "ad_ad_a_a = a.dag() * a.dag() * a * a\n", "bd_bd_b_b = b.dag() * b.dag() * b * b\n", "ad_a_bd_b = a.dag() * a * b.dag() * b\n", "\n", "cs_rhs = zeros(shape(tlist))\n", "cs_lhs = zeros(shape(tlist))\n", "\n", "for idx, psi in enumerate(output.states):\n", " # g2 correlations\n", " g2_1[idx] = expect(ad_ad_a_a, psi)\n", " g2_2[idx] = expect(bd_bd_b_b, psi)\n", " g2_12[idx] = expect(ad_a_bd_b, psi)\n", " \n", " # cauchy-schwarz \n", " cs_lhs[idx] = expect(ad_a_bd_b, psi)\n", " cs_rhs[idx] = expect(ad_ad_a_a, psi)\n", " \n", "# normalize the correlation functions\n", "g2_1 = g2_1 / (na_e ** 2)\n", "g2_2 = g2_2 / (nb_e ** 2)\n", "g2_12 = g2_12 / (na_e * nb_e)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stderr", "text": [ "-c:24: RuntimeWarning: invalid value encountered in divide\n", "-c:25: RuntimeWarning: invalid value encountered in divide\n", "-c:26: RuntimeWarning: invalid value encountered in divide\n" ] } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Second-order coherence functions: Cauchy-Schwarz inequality\n", "\n", "Walls and Milburn, page 78: Classical states satisfy\n", "\n", "$[g_{12}^{(2)}]^2 \\leq g_{1}^{(2)}g_{2}^{(2)}$\n", "\n", "(variant of the Cauchy-Schwarz inequality)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = subplots(2, 2, figsize=(8,5))\n", "\n", "line1 = axes[0,0].plot(tlist, g2_1, 'r', linewidth=2)\n", "axes[0,0].set_xlabel(\"$t$\", fontsize=18)\n", "axes[0,0].set_ylabel(r'$g_1^{(2)}(t)$', fontsize=18)\n", "axes[0,0].set_ylim(0,3)\n", "\n", "line2 = axes[0,1].plot(tlist, g2_2, 'b', linewidth=2)\n", "axes[0,1].set_xlabel(\"$t$\", fontsize=18)\n", "axes[0,1].set_ylabel(r'$g_2^{(2)}(t)$', fontsize=18)\n", "axes[0,1].set_ylim(0,3)\n", "\n", "line3 = axes[1,0].plot(tlist[10:], g2_12[10:], 'b', linewidth=2)\n", "axes[1,0].set_xlabel(\"$t$\", fontsize=18)\n", "axes[1,0].set_ylabel(r'$g_{12}^{(2)}(t)$', fontsize=18)\n", "\n", "\n", "line4 = axes[1,1].plot(tlist[20:], abs(g2_12[20:])**2, 'b', linewidth=2)\n", "line5 = axes[1,1].plot(tlist, g2_1 * g2_2, 'r', linewidth=2)\n", "axes[1,1].set_xlabel(\"$t$\", fontsize=18)\n", "axes[1,1].set_ylabel(r'$|g_{12}^{(2)}(t)|^2$', fontsize=18)\n", "\n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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9L3x8fJCSkgJvb28YDIZ6BW4pTDpE0pJyn2KuIaLqmLJPPXSY+OXLl/H777+jcePGAIAL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\nbqqSxN2ljgAAAABJRU5ErkJggg==\n" } ], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Clearly the two-mode squeezed state from the parameteric amplifier does not satisfy this inequality, and is therefore not classical." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Cauchy-Schwarz inequality\n", "-------------------------\n", "\n", "Walls and Milburn, page 78: the Cauchy-Schwarz inequality for symmetric modes\n", "\n", "$\\langle a^\\dagger a b^\\dagger b\\rangle \\leq \\langle(a^\\dagger)^2a^2\\rangle$\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = subplots(1, 2, figsize=(12,6))\n", "\n", "line1 = axes[0].plot(tlist, cs_lhs, 'b', tlist, cs_rhs, 'r', linewidth=2)\n", "axes[0].set_xlabel(\"$t$\", fontsize=18)\n", "axes[0].set_title(r'Cauchy-Schwarz inequality', fontsize=18)\n", "\n", "line1 = axes[1].plot(tlist, cs_lhs / (cs_rhs), 'k', linewidth=2)\n", "axes[1].set_xlabel(\"$t$\", fontsize=18)\n", "axes[1].set_title(r'Cauchy-Schwarz ratio inequality', fontsize=18)\n", "\n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stderr", "text": [ "-c:7: RuntimeWarning: invalid value encountered in divide\n" ] }, { "output_type": "display_data", "png": 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1Ll27PTg42Ol4JTFmleXE7wavGa9Z1TzxmpX+VBbFBiyLxaJdu3YpMzNTX375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\nH+sapbcxVOlXAAAAAElFTkSuQmCC\n" } ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Two-mode squeezing correlations\n", "-------------------------------\n", "\n", "The two-mode squeezing can be characterized by the parameter $\\sigma_2$ defined as\n", "\n", "$\\sigma_2 = \\frac{2\\sqrt{\\omega_a\\omega_b}\\left[\\langle a b\\rangle e^{i2\\theta_\\Sigma} + \\langle a^\\dagger b^\\dagger\\rangle e^{-i2\\theta_\\Sigma}\\right]}{\\omega_a\\langle a^\\dagger a + a a^\\dagger \\rangle +\\omega_b\\langle b^\\dagger b + b b^\\dagger \\rangle}$\n", "\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# pre-compute operators outside the loop\n", "op_a_b = a * b\n", "op_ad_bd = a.dag() * b.dag()\n", "op_ad_a_p_a_ad = a.dag() * a + a * a.dag()\n", "op_bd_b_p_b_bd = b.dag() * b + b * b.dag()\n", "\n", "e_a_b = zeros(shape(tlist), dtype=complex)\n", "e_ad_bd = zeros(shape(tlist), dtype=complex)\n", "e_ad_a_p_a_ad = zeros(shape(tlist), dtype=complex)\n", "e_bd_b_p_b_bd = zeros(shape(tlist), dtype=complex)\n", "\n", "for idx, psi in enumerate(output.states):\n", " \n", " e_a_b[idx] = expect(op_a_b, psi)\n", " e_ad_bd[idx] = expect(op_ad_bd, psi)\n", " e_ad_a_p_a_ad[idx] = expect(op_ad_a_p_a_ad, psi)\n", " e_bd_b_p_b_bd[idx] = expect(op_bd_b_p_b_bd, psi)\n", " \n", "# calculate the sigma_2\n", "theta = 3*pi/4\n", "w_a = w_b = 1\n", "sigma2 = 2 * sqrt(w_a * w_b) * (e_a_b * exp(2j * theta) + e_ad_bd * exp(-2j * theta)) / (w_a * e_ad_a_p_a_ad + w_b * e_bd_b_p_b_bd)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 18 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = subplots(1, 1, figsize=(8,4))\n", "\n", "line1 = axes.plot(tlist, real(sigma2), 'b', tlist, imag(sigma2), 'r--', linewidth=2)\n", "axes.set_xlabel(\"$t$\", fontsize=18)\n", "axes.set_ylabel(r'$\\sigma_2(t)$', fontsize=18)\n", "axes.set_ylim(-1, 1)\n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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} ], "prompt_number": 19 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Quantum-classical indicator $\\langle:f^\\dagger f:\\rangle$\n", "---------------------------------------------------------\n", "\n", "Using $\\langle:f^\\dagger f:\\rangle$ we can again show that the output of the parametric amplifier is nonclassical. If we choose\n", "\n", "$f_\\theta = e^{i\\theta}b_- + e^{-i\\theta}b_-^\\dagger + ie^{i\\theta}b_+ -i e^{-i\\theta}b_+^\\dagger$\n", "\n", "we get\n", "\n", "$F_\\theta = \\langle:f_\\theta^\\dagger f_\\theta:\\rangle = 2\\langle a^\\dagger a\\rangle + 2\\langle b^\\dagger b\\rangle + 2i\\left(e^{2i\\theta} \\langle a b\\rangle - e^{-2i\\theta} \\langle a^\\dagger b^\\dagger\\rangle \\right)$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# pre-compute operators outside the loop\n", "op_ad_a = a.dag() * a\n", "op_bd_b = b.dag() * b\n", "op_a_b = a * b\n", "op_ad_bd = a.dag() * b.dag()\n", "\n", "e_ad_a = zeros(shape(tlist), dtype=complex)\n", "e_bd_b = zeros(shape(tlist), dtype=complex)\n", "e_a_b = zeros(shape(tlist), dtype=complex)\n", "e_ad_bd = zeros(shape(tlist), dtype=complex)\n", "\n", "for idx, psi in enumerate(output.states):\n", " \n", " e_ad_a[idx] = expect(op_ad_a, psi)\n", " e_bd_b[idx] = expect(op_bd_b, psi)\n", " e_a_b[idx] = expect(op_a_b, psi)\n", " e_ad_bd[idx] = expect(op_ad_bd, psi)\n", " \n", "# calculate the sigma_2, function of the angle parameter theta\n", "def F_theta(theta):\n", " return 2 * e_ad_a + 2 * e_bd_b + 2j * (exp(2j * theta) * e_a_b - exp(-2j * theta) * e_ad_bd)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 20 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = subplots(1, 1, figsize=(8,3))\n", "\n", "for theta in linspace(0.0, 2*pi, 100):\n", " line1 = axes.plot(tlist, real(F_theta(theta)), 'b', tlist, imag(F_theta(theta)), 'g--', linewidth=2)\n", "\n", "line = axes.plot(tlist, real(F_theta(0)), 'r', linewidth=4)\n", " \n", "axes.set_xlabel(\"$t$\", fontsize=18)\n", "axes.set_ylabel(r'$\\langle:f_\\theta^\\dagger f_\\theta:\\rangle$', fontsize=18)\n", "axes.set_ylim(-2, 5)\n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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nFRUVVCRv9TqaAYc47ZBOK0hlmIsx+nw89JB7+41ExLvvpDEmx5kz4vhwcVAz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\ngg==\n" } ], "prompt_number": 21 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Entanglement: logarithmic negativity\n", "------------------------------------" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Wigner covariance matrix:\n", "\n", "In order to evaluate the logarithmic negativity we first need to construct the Wigner covariance matrix:\n", "\n", "$V_{ij} = \\frac{1}{2}\\langle R_iR_j+R_jR_i \\rangle$\n", "\n", "where \n", "\n", "$R^T = (q_1, p_1, q_2, p_2) = (q_a, p_a, q_b, p_b)$\n", "\n", "is a vector with the quadratures for the two modes $a$ and $b$:\n", "\n", "$q_a = e^{i\\theta_a}a + e^{-i\\theta_a}a^\\dagger$ \n", "\n", "$p_a = -i(e^{i\\theta_a}a - e^{-i\\theta_a}a^\\dagger)$\n", "\n", "and likewise for mode $b$.\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from continous_variables import *\n", "\n", "R_op = correlation_matrix_quadrature(a, b)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 22 }, { "cell_type": "code", "collapsed": false, "input": [ "def plot_covariance_matrix(V, ax):\n", " \"\"\"\n", " Plot a matrix-histogram representation of the supplied Wigner covariance matrix.\n", " \"\"\"\n", " num_elem = 16\n", " xpos,ypos = meshgrid(range(4),range(4))\n", " xpos = xpos.T.flatten()-0.5 \n", " ypos = ypos.T.flatten()-0.5 \n", " zpos = zeros(num_elem) \n", " dx = 0.75*ones(num_elem) \n", " dy = dx.copy() \n", " dz = V.flatten()\n", "\n", " nrm=mpl.colors.Normalize(-0.5,0.5) \n", " colors=cm.jet(nrm((sign(dz)*abs(dz)**0.75))) \n", " \n", " ax.view_init(azim=-40,elev=60)\n", " ax.bar3d(xpos, ypos, zpos, dx, dy, dz, color=colors)\n", " ax.axes.w_xaxis.set_major_locator(IndexLocator(1,-0.5))\n", " ax.axes.w_yaxis.set_major_locator(IndexLocator(1,-0.5))\n", " ax.axes.w_xaxis.set_ticklabels((\"$q_-$\", \"$p_-$\", \"$q_+$\", \"$p_+$\"), fontsize=20)\n", " ax.axes.w_yaxis.set_ticklabels((\"$q_-$\", \"$p_-$\", \"$q_+$\", \"$p_+$\"), fontsize=20)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 23 }, { "cell_type": "code", "collapsed": false, "input": [ "# pick arbitrary times and plot the photon distributions at those times\n", "t_idx_vec = [0, 20, 40]\n", "\n", "fig, axes = subplots(len(t_idx_vec), 1, subplot_kw={'projection':'3d'}, figsize=(6,3*len(t_idx_vec)))\n", "\n", "for idx, t_idx in enumerate(t_idx_vec):\n", " \n", " # calculate the wigner covariance matrix\n", " V = wigner_covariance_matrix(R_op, output.states[idx])\n", "\n", " plot_covariance_matrix(V, axes[idx])\n", " \n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stderr", "text": [ "/usr/local/lib/python2.7/dist-packages/mpl_toolkits/mplot3d/axes3d.py:1482: RuntimeWarning: invalid value encountered in divide\n", " for n in normals])\n" ] }, { "output_type": "display_data", "png": 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AGbKXicpms5017hSNhqC0Wq1focToq67irfx82gVxjCTEqrUcEQnsJ7r1FSeC\nlA4ihBzJiHrSMMJPPWYD27du9fueXFStqqqq0ale3xe/X79+2BA5cd9PZZ1+nUB0yO9EpE7bEf9E\nJSFSJoUIwYkeQbDXIe6jN7QA7ghkxyXRu3Qe4jnYjGgbaMxEZUQ8I+cA+UePcsMNN9AuJ4ct27bV\n+JwSRLVjxw5eeOEFflq0CLvdTi6ibquEMXEskQz0Q9zHXVu2MPLSS+nUqRNz3nyTQYMGAYKo5Dqf\nvBiNd6JqFDUoqC03l/PXO3fuZPAFFzCU0HP4JYj6ig2xeu6I8pOsC7FCP4iY1BMRKcbhKKPQ2gbk\npadTcOwYUFsWrdVq0Wq1JCcnh7QaTTCbGUL9K5xjiFqDmzNEFW/JhTIEKRUixpmDuP8d6vidjcDS\nZiYueuVyRcfy4/0LOcfmIuP0/8vijMOIe90YicqBkFMXIP4WCQghyoHTz2wghGpx9PjjjzN37lwS\nEem7xlTX84UVMXftB3Jycnhl9mwuv7zms+rd9OtNVPEkqGg0EZSc4vN1pO7WrRtGnY5KlyvkCb8Z\nMACRbtmLSFt1A9rTsAfbN31kQqwebwTPxKQUMoDyigrPffGW2CYnJ3t+FupDadTpsLpcJNfzuZan\nX0cQ0dQOxCSbS2wnhypElHQAkU7NBq5F/H2DGZcWkCIQQUmSVIN8tODxbytERFT5iHuYw9lLVC7E\ngqwA8V1IQtSlhiOucU+2b8xaGzqdzpOittvtVFVV1Wlx9NumTSQh/t5bEPewFWfvPawLZmqmT/94\n/fW1/P68U3+yWOTAgQMkJSVxzjnnxHL4HjQaggJhtyMrfrwjgo6dOlG6a1fYEYlcXzmGIKmdiIe7\nLcE/3BIibXcQMVkbEER3DeJLEik0B6yn/eCSk5NJTEysUSDVarW4XK6Qj5uYkICtsrJegpLR+vRL\nNmjdjkhjRXOStXGGlKoQ92YEIjUSKlkKglJ0eAKS/7H4EtUWzqT+zhai8v4OHEak9joDNyEWgzJK\ngJwOdcWvNaHVajGbzbWIytc5omDPHo8isgDYBGylcUalMuT0aWdg38mT3HvnnfzlgQf44ptvaqT+\nZKJ67733uPrqq1WCigRSU1P9TraXX3EF/961i4aWs+VoQJ5kdyBWKa3x/3BLiC/bIcSkokWQ2u2n\n/40GDIgIbefOnX43OpRXoKEiIzMTW4AG4Log7/tUiJgctiGIKlIThIMzYpMSRFG5H6Lu0BABjA6Q\nHKETe33ryM4oAAAgAElEQVTwjaB84U1Uh6hJVG2Iz5RVOYKUDp7+/1zgztP/+sMpYGgIBCXDm6gc\nDofH3FUmqtLSUloh7lFHxAJRjkplosohPu9hQyCXEU4isjeW6mq2bNniIShvrF27lqlTp0Z5hIHR\nqAhKp9P5Jag77riD12bP9lvUDwc5CFIqBH5DRAM9OFNI93V1aAP8AbGKiQWaAytWrPBLUHJq1O12\nhyQ9zWnfnn0FBWGPKRdxX+QJYhviHiqRcpG/kAc4kz7qDlyEcn1uWsBpdfHzk0vpc08vmnVqVu/v\nBANJCu765cVODuJZk8m+G/ExyVYjxlWAqIdkI8Qm3an/+kqBbt26hX1urVbr8aaTiUqn02F1Omv8\n/b3J/jAidZqPqAG3Jf5FPXVBFvwcQFybCVFHHwO8A7Xc0gFKSkpITEwkISEhiiOtG42KoOS+Hl/d\nR/fu3TFotVS63Yo5Rng/3PuB9YjiruP0qyUifded2E8WLYBNmzb5fU8O70MlqI4dO7Jt6dIGjcv7\nHh5EpFzkiCpU93kJQUYHERGTCf/pI6WgBZISE9FLSfzywgqSWycLourYwLMFSVDe4/Amqnxqpv6i\n+ez5ih2aAUMRfXKhTPblEPImnP7gTVRr165Fh/8JT4t4BmWi2olYdHZBRFlnE1FVIr4DBxCLY99o\nNR/hUepvB4NffvmFiy66KDoDDRKNiqAgcD9U2/btKd23T3FLIy1Cht4B+BWxgr2G2JOSN7KBnfn5\nAd+X61D1bfPubUPTrl27Wr1Q4UKLmAjaIia3DYgi73mIsQeasGVjXNnuSXf6OHcjorNIQgug0bBv\n7z5WrVrFLbfewi/PryClTTK97+1Fs/bhEVW4UX6siKousUM4ze5uTttnde6M0+lURFWm1WpZu3Yt\nwcQFbU6/jiJUcDsQQoN4bjy3cyZarULU2K5E/B18/+57gL4XXuj3OMuWLeOee+6J2DjDQbze87AR\nqB/qslGj+OzNNwPmvRt8XoSfn5v4IicQSr51hw4FfL++OpT33kYg7I769++vGEHJ8K4NeEelPRBf\nOnmaquAMKbkQE8pNCCVktCBEEuKeDR48mP379rN8+XL+dNuf+OW5FaS0SaHPvb1Jbx+inWg9Nahg\nxiUbmUaKqAKJHf5Iw3cJqEDUTdPT02vYazWUqDZs2BBSA26r068TiMbznYhr7Eh8eE7KaewChMo4\nBdHDeSF111b3AeNvuKHWzyVJYsuWLfTv31/xsTYEjZKg/OH222/nrTffVKwO5Q/NOVMIjic0Byot\nloDv+1PyyYoo7w33kpKSPM4SAwYMwE74K/664B2V7kVEpsmcEahUIyKrKxHkFYsFgRZqkfrQoUMp\n2F9AXl4et91xG3nP/UJqTgp9xvYmrW1wRKXU/dRwJm3lTVTdCF/iH6rYIRyUAebTvntyTVkJh/Od\n27aFVX9scfpVxJldbzudfkXbZca3rmSkprtJfag8/frd735X673Dhw+TnZ1dbxYl2oiv0SiAQHWo\nPn36oNVqqXK7g5ZGh4osxAPsID5WWTLSAbskUV5eTmpqbbG9vM2Bvw33AtkdpaamokOkFyK1OZ6W\nM04emxGrvxGI3rRYP7ha8JtKBhg+fDgH9h9g6dKl3H7n7Sx75hdSc0VEFQxRKU34snJSVp/KRNWW\n+onKn9jhWiJXWy0DUk4/o7LzgTdRye4HoRLV4YMHad2AccmtJqcQi6Y9iGjqHCK/OaS8a0EB/utK\nwaKAwPWnvLw8LrnkkoYMMyKI9fc8IgjU25Obk0PZwYMRIyg94mE9hrKryoZCh6gNLF++nCuvvLLG\ne/LOpk6nk7KysqDtjgBMBgM2hyPiX1AtQjV5BCEPjwdoAbcfgvJ24e7bty/5W/JZuXIl9953ryCq\ntqn0GduLtBz/RBWsii8ceBPV9tMvf0TlK3ZIR3hABmNO3FCUAS18doBWgqgqLBZFFJzNT7/KECS1\nD5GS7oyyBtO+daVMAteVgsVeoP/QoX7fW7ZsGZMnTw7zyJFDoyQofw+s2+1m+CWX8H/z50e0gG5A\nhN/xRFAg6lCrV6/myiuv9HSOyy4Ssg9XWlpaSEq+lORkbCUlERpxTZhB8ZpXQ6CjZgQl2+7IW5jL\nKVGdTseoUaMoPFDIjz/+yN333M2yp2Wi6kNaTm3ZTqQbRgMRlQmRPpItt85HSPOj6exfDLQL0AMl\nE5Verw+JqCorK3G63Ypeh9xP5+3b2Q5BVOESob+6Uh9CN4gOhL3A+NMuEt5wu93s2bOnQdL+SKFR\nEpQ8yfqmrG688UY+mD8/onWoRMSXvHYLXGyRDfz2229UVVVht9vR6XQex3K5iTFUW8asli2pjiJB\nRarmFQ7kGpS8q668905CQkLAgv7ll19O4cFCvv/+e+4dey/Lnl5GWrs0et3di1O7iylYXBDV65OJ\nSu4B0iEUa3+g4WKHcFECXBqEi4G/rTgCEdXKlSsxEpmUZCqCqCoRLjMHEPe0C8G5osvN/AWcqSud\nS/B1pWBRgdhLbtSoUVit1hqbNO7evZvOnTvH5RYc8TciBaDRaKiqqqKsrAyHw4HZbCY9PZ1LL70U\njUZDdQTP3RyxMo03ZAG78/PRarWkpqaSmpqK2Wz2PJThWB6169gxalGNvIKsvS1lbKAFXG43/Qf0\n5/Dhw6SkpJCQkBBUymnUqFEUHizkyy+/RFOhIe+ZPPI/3kaLJNHqHW0CboNQS16KaOSMFTmBSJ2F\nspKXicpsNuN0OrFYLJ7deGWsXr064huRJiNUdP0R1/ATsA5BXP5QhYhcvwdWIRYHdwBPAL9HWXIC\nQZwZaWmkpqai1WqxWq1UVlaybt06li1bFpf1J2ikERRAYmIiiYmJtSaL1q1aUXrkSMQe2EyEJNVK\nfG16mAGcKioK2CUejuVRp06dWK3A2IKFDlG0j4dN5EQfFFhSq+g/qD/ndDiHr778ivbt2wd9jFGj\nRnG48DDFxcWkp6ej0+lITkqK2Xbi8fC8VgJ9+/YN+ffq2opjy5YtUdvjKRGRlrMi5oEliMVhd8T9\nPYyIlioR38nRiE1TIx0p7EbUn+RNGg0GA3v27OG2224jPT2dp556SthsxZGTOTTSCAoIWOS/+LLL\niGRSSovI5R+J4DnCQQZQZQ0c74QTQXXv3j2qdSGZoOIBQsUHAx8awPCnh1JmLqVnn57079+fwsLC\nkI6VkZFRYz+epkpQNkQdpkMYPnwyvCMql8uFxWJhV5gS84bAjNjSYwAiNb0UWIQgp16ISOnPiE1I\nozEJ7wNuvPFGz/9rNBo6d+7M+vXr0ev1/P3vf2fIkCH88MMPgQ8SAzRaggqUT73lllsoQXwhIwVZ\nKBFPkJuIDx/2P7JQIyhJkjjvvPOwKTO8oBBvBCUjNSeVCyYOZOhTQyjWF3Fez/PoP6A/x48fD/m4\nsaqxuYk9QZUBJoXqIN5EdfLEiaBcJCIBMyJCSgBGAQ8jdu2NZhagAvG9ufbaa2u9t2PHDgYOHMj2\n7dt56KGH2LFjR1DHXLRoEV27dqVz585Mnz691vtFRUWMHj2a3r1706NHD+bPnx/W2BstQcn9UL4Y\nPnw4kkYT0ZV/EiLnG0/QIAq6y5Yt8/t+IAcOb8iSdIvFQllZGR06dMCJmNyiAS2i0BsP0FJ7kZPS\nKpmMrhnojFq2b9vOjBkzQjqmfP9jRVCxtggtAxLNZiwWC1arNSyXfV/odDqqbbaoR1C+cCLk6LFA\nAZCZnu63CXfp0qVcdtll6HQ6brrpJh566KF6j+dyuXjwwQdZtGgR27Zt45NPPmH79u01PjNnzhz6\n9OnDpk2bWLp0KY8++ihOpzPksTdaggL/UZRWq6VlVhalETxvJvEXQYEY17p16/y+J/eY+FPyuVwu\nqqurKSsro7KyEkmSSEhIIDk5GT1ELYrSEF8RlIQglcKVh1j6TB7/d9937PhiJx1zO/H111/z8ssv\nh3RM2TEhFgTlIvYRVDmQnpGB0WhEkiRFiKqwsBA3sa1bWhHinqwYnX8PMHD4cL/vrVixImSBxK+/\n/so555xD+/btMRgM3HTTTXzzzTc1PtOqVSvKy8sBKC8vJyMjIyyXiiZHUADDLrkkogSVjnggQ98t\nKbLIBrZu2eL3PV8HDrfbjdVqpaysjPLyclwuFwkJCSQmJvLvf/+b7j26k9EyAw1Nm6AWjF3Ixnc2\nkexOZvas2VRWVLJ+3fpa22sHA6vVGrPoyUnsCaoE2HeokLFjx3p2xm0oUeXl5ZFAbFsTihA14FhN\ntvuAG/z471mtVqqrq8nICG0f78OHD5Obe6bTMycnp1bpYOzYseTn59O6dWt69erF7Nmzwxp7oyao\nQIqUm266qUkKJbKAgl27Ar4vy0/Ly8spKyvD6XRiMplISkpi8eLFDBg4gIyWGTw++XGMXQ0MeWIw\nxlRj1IQSOoQ8Nx6gQxDUwxMfprysnN07d3Pvvfc26JiyGW+04URM4LGW9BYjhCff/O8bNBqNZ6sM\nX6IKRcyzbt26mKf3SojeBqW+KEcs6q6++upa7/36668MHDgwZOVeMJ9/8cUX6d27N0eOHGHTpk2M\nHz+eioqKkM4DTYCg/N3MkSNH4iKyzgR64q8fKgMoOXWqxs8kScJut1NRUeFxQ5BdEH777TcuueQS\nslpncuvtt1KdaWHAX/oz+rWRnH9LD9Lbp2PMSIxaBGUgfqJSOYJ6/vnnayjwgsWCBQsYMHAAo0aP\noqysDACLxRKTlb6N+PCOLAFGjBhBaUkpRqPRs5+TL1FVV1dTXV0dFFFty8+PmsQ8EGzEzlmmAMhq\n1sxvem3ZsmVcdtllIR+zTZs2NZSqhYWF5OTk1PjMypUrParBTp060aFDB3bu3BnyuRo1QUHtNJ/s\nlZbZvHlE03ypxJ9QIgOwOBweIqqsrKS0tBSr1Yper8doNLJv3z5+97vf0aJNCy4fdTlHpMP0ursn\no+eMpM+9vcnsmoFGe2YaTcxKiFrazUT8RFD+RBL1YcuWLYwYMYLm2c25+U83U55WRv6RfHI75DJy\n5EhKSkpiRlCR9lMMBhXAo48+Wovw/REVEBRRFezZE/MIygENMqptCALVnyRJYvXq1QwbNizkY/bv\n35/du3dTUFCA3W7ns88+q6UQ7Nq1K4sXLwbg+PHj7Ny5k44dO4Z8rlhH9RGH3N/ju6fRoGHDWP3N\nN7SM0HmzENtwx4s1DwiVlhZYu3Yt3bp1w2AwkJSURElJCffffz/f//w91ZXVNDunGd1v7krL3i3R\nJ9T9iCS1SuZEVEYvCt2hJwkiA/lvKjeEBsKxY8eYMGECP//yM9YqK5ndM+l5Zw9a9GyBziAm4qId\nxeR/tpXhlwyPye6tNmJff5IQCs0+ffoE/IxMVG63G6fT6fleW61WtFqtZ98ob5SUltIqskOvE1ZE\nCjUzRuffB0y49lrsdnuN3tDy8nL0ej1JSaHHl3q9njlz5jBq1ChcLhf33HMP3bp1Y968eQCMGzeO\nJ598krvuuotevXrhdruZMWMGzZuH7lHS6AkKoKyszLOnUXJyMjqdjptvvplFPsoTJZGM+NLJbtDx\ngmbA+vXrOf/885k0aRKfffEZ5WXlpLRKpuM1HWjdvxWm1ODX0yltUqK2B5YZokaG9UFz+lVcXExK\nSgpms9kzOdrtdp544gk+++IzKsoqSM1NofPvz6FV/5YYk2rryTK7ZjDs70PZ/3MBOz4MvPNxpGAn\n9hLzSsRklJ5e97fFbrfz17/+lW+/+5buXbrz0UcfYTQa/RKV2+3G5nTGNII6QewEEmUIgrzuuutw\nu91UVVVhMBhwOBysWLGCYcOGhe0cccUVV3DFFVfU+Nm4ceM8/52Zmcm3337bgNELNHqC0mq1pKSk\n1KpHXX311TiIXHpDFkocJr4IKhOYPHkyj096HHO6ibYXt6X/oH4kZoQ3RTXrkI5d2SEGhJnoKQaD\ngYYzm+hVVVUxd+5c5r09j5PFJzGlmWg3oi05g/qTEMS91Wg0pLZOiUm07UCkpGOJMsBcRyQ6b948\nZr48kxNFJzClmcgdnMP6jetp27EtQy4YwocffkhCQoJHfarVatmyZQs6YjvJlSL2jYoFCoCs5s09\nKVG3283Ro0cZMmQIgwYNYuzYsTEaWfBo9AQFYhLxzVPr9XoymjWjtKSE7EidFyGUOC9Cxw8H2cB+\nk5thfx1KapvaWz2ECnNzMxIijRHphyneHM01wLfffsurs16l4FABWp2G3KG5dB0yhNSc0Kd8t9Md\nM4KKdZ2mDEhOrrlTW15eHo8+9ii79+8GIHdoDkOHDiEtV9zbc6/rTNG2Ijb9ZxMdOndgUP9BfPLJ\nJx6iysvLi/l12Ymdgm8PMOiiizz/r9VqadOmDXl5edx0003cfffdLF68mMcff5y2bWM1yrrR6EUS\nELgfatDQoRHvh4o3oUQmoHdKipATiHur10QnstEjSCFaEVt90AAPTngQWwsrF0wYwKjZIznvj93D\nIieIHUE5iQ+CymzVisLCQq655hoyWmZw1bVXUZpUQv8/92X0ayPpcfN5HnICEXVmnZfF8GeGMuCh\n/mw9tIUO57TnmmuvwWKxkJ+fH/PrskPMamD7gD/84Q+1fm4ymWjbti3bt28nOTmZKVOm1Hus+qyN\nQLhS9OnThx49enDxxRc3cPQCTSKCCpRnvf766/lRgTxpIGQBG4ifFT+IfLijWtlNK/RGHVabKypy\nXj2iryMeVGda4MLJQ0hvr0wS1xUjgnITe4I6BWzbvZPuPbqT3jFdiHT6tkRvqn+K0mg0ZHXLJOuZ\nYRTtKGbbf7bTqUsnzBpDxERQwcCCcOgIrQ1WGZQiyNG3TgRCXj5ixAiys7OZNm1avceSrY0WL15M\nmzZtGDBgANdee22NbVFKS0sZP34833//PTk5ORQVFSlyHU0igtJoNH6jqDFjxmAncivyRMQNLo7Q\n8cNBc8DuFqt1paBPNkatNqQjvvz4lFx6uB2xIah4cDI/BaR3TOOymZcwdNKF5AzOCYqcfJHZNYPh\nTw9l0MMDcdisMRV/FCEWqbGYZA8AWRkZfue9vLy8kPqfgrE2+vjjj7n++us9/VCZmcroFpsEQYH/\nKMpoNNIsJYWyCJ5XFkrEC4yIMZXsVy65acxKiJqbhJb4sTvSoCzRu53umHwh44GgSoHcobmY05UZ\nSUaXjJhHhqXErv60m5r1JxmSJLFjxw569uwZ9LGCsTbavXs3p06dYsSIEfTv358PPvgg7LF7o8kQ\nVKA61IALL4yo7ZERCG13oMijGVC861S9nwsWSS2SmiRBaQG3I7Q9tOqCFMMUX6wJqhJIa5+m2PGc\nVicuKbbXZSd2DhL7EZZutX6+fz/t2rULaXv3YKToDoeDDRs28N133/H999/z/PPPs3v37lCG7BdN\nhqAC3eTfjxkTUYJqBlHrEwoWLYDyA8rFjcmtkqNGGvFmGOtyKBdBxbIGFcuJ3HH6ldIyub6PBo2i\nHUUYiO0EZyc2DhJy/WnkyJG13lu6dGnI7uXBWBvl5go3lISEBDIyMhg+fDi//fZbOMOvgSZFUN6r\nBkmSsNlsjB492mOHHwlkInLRyq2zG45swHJYOU+GtNzUqDqax0sNSukUn+SSmuReUOWAUQNavXLT\n0ak9JTH14LMg7mvo3gkNRwHQIjNTkfoTBGdtdN1117F8+XLPLsZr1qyhe/fuDbgKgSah4pOh0Wiw\n2+3Y7XYcDgd6vZ709HTSkpIoq6qKiB2JGZHmO0Hs5Ka+yACcp5SLQ9I6pEWtP0lPfPnxKVqDcrhi\nJjOPZQRVBugVJCeA8sKKmBLUSYRAIhZ/z93AwGHDsFgsHlcNjUaDy+Xi0KFDdOrUKaTjBWNt1LVr\nV0aPHk3Pnj3RarWMHTtWJahQIduhGI1GEhMTPSuMvgMHsmvJkoj5ZRkQW2/EE0E5bMrFdMZEI1pE\nFBrpjeGMxJejuZIE5YpBBOVGRPexlO2XAfokZf3Uqw+Xx9TBpQToGqNz7weeveUWDAYDNpsNjUZD\nQUEBDoeD7t27h2VvVJ+1EcBjjz3GY4891pCh10KTSfGBUO2lpqZiNptrhL+/+/3vUU4yUBtm4qsO\nlQ44JFFIVgp6nSYqQgkjjTeCkmKg4rMjVqmxnAhKAV2msno7e5k9pmlLJ5BT76eURwlioXj55Zdj\nMBhITExEp9Mxfvx47rvvPtLS0hq0Q3G00aQIKlA/1C233EI14qGKBJoTXwSlQ8hvV72yRjGS0pt0\nUalDGYkvkYRbQZGEOwYRlI3YbocOok8wsYWyCTmH0x1TibmN2AgkCoDsrCzPPCdv/Cg32S5ZsoRe\nvXrxn//8JwajCx1NiqDAv9w8OTmZ1ISEiPVDZSHSGJESYoSDDKB0bynf/XkRv83f3OBIwJBujkoE\nZSZ+CEoHuF1K9kFFvwYVD3tBlQDJLZUjKEuRBYnYEW8Voh7bLAbn3g1cOGJErZ/L4oWNGzcyffr0\noBR2wdgbgdi+R6/X8+WXXzZk6H7R5AgqUP71/L59I+bLp0dMAscidPxw0AIYNXIU94+7n8Llh1hw\n/0K2fb4t7PDfnBWdnXXNRHYn5FAQCRVfLFJ8se6BKgdSc5XxhgQo2l6EmdjZi51EKGWjfX4JEUH9\n8Y9/rPXeunXr6NevH1qtliuvvJIXXnihzmPJ9kaLFi1i27ZtfPLJJ2zfvt3v55544glGjx6NJIW6\nhWf9aJIE5Y+krvvd7yLaD6UnvhwlWgB7t29n5syZHD92nDG/G8Pe7/fz3f2L2PV/u0MmqsQWSVGJ\nbBIQqVjlvwqhQ4uoGykFtzM2Kb5YEpSEiDiU8jMEKNlXGlMFXynQLkbndQCXXnpprfdC3d49GHsj\ngNdee40bbriBrKysBow8MFSCOo1bb72VKiLXr5REfDmbZwAnjx+nslJo4t59912Ki4oZeelIdny5\nk0Xjf6BgSUG9xzm1p4RVL69h/+L9USEo7elXPERROmDf4gLKCpVJDkvu6DfqOohtD5QF8fdUyuII\noOJQbCXmDmIjkNgPZLdoUauMIUkSq1atCslhPBh7o8OHD/PNN9/wwAMPAME5ToSKJkdQ4L8O1bx5\nc5LN5ojVoZoj9oaKF2QAFquVlJQUEhMT0ev1mEwmvvjiC44fO86APgPY/O+tLPzL9xxeU/PBrDxe\nxfq3NrLg/oUsn7ICa6GV68dcH7VtMHTERx1KB2gdWpb9/RfynvuFiqMNE8DHYrsNB8R0Mi8HDFpl\nr9p2rDKmAolYbbGxBxjqxyWiqqoKSZJISQk+jRoM2UycOJFp06ah0WiQJCkiKb4m1Qclw/fmS5KE\n0+mkW48eHFu3LiLd35nATsTKP9Y5fxA7qLqAEydOkJ1dc8vG5ORkFi9ezMmTJ7nmmmtYP3cj+Z9u\nI/O8LE5sPoG9wo45wcw1V1zDrFmzyMrKwm6388UXX+Am8queeCEoLXD33XczePBgxv9lPEueXErz\nc5rRd1wfEkOUTVefqqZkb2nUnQdivRdUGUIBqiTsltht8y77s0S7B0tCRFBTb7651nsrV67kwgsv\nDCnCCcbeaP369R6/v6KiIhYuXIjBYKjlMtEQNOkIyul0YrFYKC0txWKxMPrKKyNWh5K3gD8SoeOH\nCg2CpPLy8gJ+Jisri9WrV5Ofn0/r5m0o2ljEgJ4D2LBhA8VFxXz00Uee3LPRaESv0URFKKElPuyO\ndIDNZuOaa67hyKEjfPDBB9hPOFj8159ZMX0V1SV106jT6mT7Vzv54eEf+fHRn7CWWGNSWI81QWlT\nlNPbuZ1unG4pZmnLImIjkChBLDgHDx5cK5KJlL3Rvn372L9/P/v37+eGG27gzTffVJScoIkSFIDF\nYqGyshJJkkhMTCQxMZE777yTSiI3+emJvzTfr7/+Wu/n2rdvz5YtWyg+WcwPP/xAly5d/H4uwRid\nfaHixdFci4i+DQYDGo2GMWPGcPzocebOnUt1YTU/PvITq19Zg7X8TMXM7XZzIO8gS55axncPLGLv\ngr1069idZcuWMfLykTEhqFhG9KeAshMWfnu/4a0OACUFJeiIXWqojNgIJAqA7OxsJEnCYrFgt9s9\nabe1a9dy4YUXhnQ8b3uj7t2788c//tFjbyRbHEUDTTLFJ0kS8+fPp2fPngwcOBCtVotGoyE7O5tB\nF1zAmjVraAF0QNkekWTiSyjREsjfulWx46WmpWE9cUKx4wVCvDia6xDbDPjitttu47bbbmPevHk8\nOflJfpiwmKweWbgcLkp2lyBJEm3btmXWv2bV2BLBbrc3SYLq2rUru5bv4mBeIe0uyqXHLT1CNo4t\n2lnMzq93UbyjGOUE66EjVg4SuxD1p4SEBFwuFw6Hg+nTp+NyuTzuOaEiGHsjGe+99144w64XTTKC\n0mg0XHXVVfzrX//iT3/6Ezt27PCExYt//pnNW7fSundv1iAKj0o12GYSPyk+EI2Eu/PzFTteq9zc\nqERQ8eJoHoigZIwbN47iomKmTJmC5YAF6aTEY48+RnlZOdu3ba+1X4/T6YyJF18sCaoUuP/++yk9\nVcqdd9zJwbxDLBi3kM0fbqk3orIUW9jwziYW3L+QldNW4T7hplu3bii3aUdocBMbBwm5/0l+nnQ6\nHWazmeuuu47NmzezfPlynn/+eUpLI9XpGTk0SYICOPfcc/noo4945plneOaZZ3jggQc8RcEOHTrw\ny4oVLPvlF0zt27MaEfk0VIKejlD4xNLs1A5sBt4DvgPSMzIUO3aL7GxKEV/USMJAfBjGaqmboGRM\nnDiRE8dOcKjwEM8++yw6nX9RgNPhaHIEVQH07dsXnU7HnDlzKC0p5bY/3cbBpYUsuH8hWz7aWoOo\nnHYnO7/ZxQ+PLGbxYz9zcsNJrrniGgoLCzlUeAg9saupVXKmthtNnALcGg0X+eyg261bN1q1asX7\n77/P3r176datm6etJBDqc4/46KOP6NWrFz179mTIkCFs3rxZyUupBY0UCW3gWQZJkliyZAnPPfcc\nvaETSNEAACAASURBVHv35rHHHiPDa+L+4YcfuH/sWIqLiuiAkJCGy+xrgeuAcxs+7KDhAvYCGxAR\nYbPUVH5/001MmjSJFi1aKHaevLw8/jBmDNbqajoiUoiRmHB3ISaB2vuFRhf/B7S57jo+/vhjRY53\n0fDhFK9fH9UaxgrgQUC5vWyDhwt4AThVUoLRWFMo4XK5GD9+PB99/BESEq0HtKLiSCXlB8vR6rT0\n7NmT2bNm079//xq/l5udTevKyojtTFAX9p3+9+4on3c98FvLlmzdtavGzyVJYuTIkaxYsQKdTkdx\ncXGNec0XLpeLLl26eHz7BgwYwCeffEK3bt08n1m1ahXdu3cnLS2NRYsW8eyzz7J69epIXVrTjaC8\nodFouOSSS1iyZAnDhg3jxhtvZMaMGVRVCd/skSNHsu/AAV6fN4/jiYmsQezvFA6zR0soISG2mv8f\nMB34P5OJ7mPGsGb9egqOHuXVV19VlJwAhg8fzrGiImbOmsWRhARWE/59qgvx4mgugecZUQKxiKBc\nxK5RV2xUqKlFTiDSVHPnzqW0pJRbbrqF4s2nSHYl88Ybb1BRXsGK5StqkRNARVVVzCKocmIjkNgN\nDPPjHnHo0CFatWrlidjrIicIzj1i8ODBpKWJ5cwFF1zAoUORnc1UgvKCVqvlhhtu4JdffqF169Zc\neeWVvPPOO9jtogX1T3/6E0dPnmTyP/7BfoOBtRCyLD0VkS+OFE4Ci4GXgI+1WlKGDeObhQs5euoU\nH3zwAV27Rn6XmrFjx3LkxAmefO45z30qRjmiMhE7kUQlsAqYg0iVnnuucrFwRXm5Z+PHaEC2jFJ2\nJ6bgUQaY/ZCTN3Q6HW+99RbFJ4vZvWs3d9xxR8DPlpeX45SkmKUsHUCbKJ9Trj/dcssttd5btmxZ\nSNu7B+Me4Y1//etfXHnllSGMNnSoBOUHBoOB++67j2XLlmGxWBg1ahT//e9/Pf50jz76KMeKirhr\n/Hi2abVs5EyDXn3IQpjGKjkJlQPLgX8CbwMV553HnPfe40RZGd8tWsTw4cPDOu7y5cu5YNAFDLhg\nALt37w7pd7VaLY899hgnTp3ivokT2anTsQEUMeSNtqO5A9iCqNu9Cuxo3ZqH/vEPTpSUMHPmTMXO\nc+c993BCp2Mdoq4QaaKyISL6WJmqliGUn0phxYoVGInNpBYrgUQxov40ZMiQWu+F6r8XSiPvkiVL\nePfdd+t0OVcCKkHVgcTERP72t7+xcOFCtm7dyujRo/n555+RJAm9Xs+MGTM4cvw4l99wA5uArdSv\nLktGTDwNtVSyImpKbyOIaX9uLo+9+CKHTpzg+59+4sorr8TlcoVsP7Jv3z6uvvpqMlpmcMXVV3DK\nXEyJuYS+A/vSf0B/jh0LzZNdq9UyZcoUjhcVcePdd7NVo2ETwRO6P5gg4mpBN6Km8B9EinRZSgoj\nx45lz/79bNu9m0cffdRvaqoheOSRRzh56hT3PPQQO3Q61hN6hB4KrMR2q41TQFZr5ab0VatWxdRB\nQgdRl7gXAK1btqxl3+Z2u9m3b1/AnkV/CMY9AmDz5s2MHTuW//3vfzRrFtlNRVSCCgLNmzdnxowZ\nfPrpp3z99deMGTOGDRs2eJp833//ffbs38/5F13EOmAHgSdQLaKGEo6zuRPYDnwIzAR+bdaMGyZM\n4MDhw2zesYMJEyaQlJREcnIyJpMJq9VKVVUVTmfdmxJWVlZy7733kt0mm159erH56Ga639KN0a+N\npP+f+zFgfD+GPz2UIm0R53Y/lxEjRtSrBvKF0Wjktdde4/CxY1x6/fVs0mjYQni1JPPpexEJteAx\nYBEwA/jSYKD9VVexYs0aDhw7xqxZsxSv2/lCr9czdepUjhcVcfPYsWzTatlAwxc0/mAn+gRVjRAK\nvYEQaAz2s/IPFytXrkRPbJzui4icKKguyPs/+S5Ed+7cSZcuXfz6jgZCMO4RBw8eZMyYMXz44Yec\nc845SlxCnVBVfGFg+/btPP3002g0Gp566ik6d+7seW/fvn3cduutbN68mTaIoqlvN/QmoBswKohz\nyTnmjQhySk5I4Irf/54nn3ySDh061P27koTD4cBqtXp6I+SCqcvl4vnnn+fd99+lpKSEpOwk2l3U\nljYDW2NKDTxtndpbQv7H+VQcqWDEsEv4/PPPw4okioqKuPfuu/n5p5/IQDRFh1KsXw48gjKS4nLg\nN0REatFo6NmnD3/929+46qqrGnTcVatW8cijj2Aymfj0k09p2bJlyMewWq089NBDfPbxxyRLEh1R\nTsZ8AEFSYxU6XiC4EOrRdQi/uJZZWdxx33088sgjYTWQBsJrr73G3ydPRu9y0RHhlBItwtgI9AKC\nr/g0HBIwDfj0q6+44IILMBgMGI1GNBoNc+fOJTM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ByKFDhxg+ZAh3791DhmHzTcfgyj5m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ZLzkQSqmMgvUnLU9Nn8KOgMyhJ37uIkr2Ze8VDbUeMrcuMqaURbyEuoxK/bA3sMTzQlrxLz/KoX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kYG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} ], "prompt_number": 24 }, { "cell_type": "code", "collapsed": false, "input": [ "\"\"\"\n", "Calculate the wigner covariance matrix logarithmic negativity for each time step\n", "\"\"\"\n", "logneg = zeros(shape(tlist))\n", "\n", "for idx, t_idx in enumerate(tlist):\n", " \n", " V = wigner_covariance_matrix(R_op, output.states[idx])\n", " \n", " logneg[idx] = wigner_logarithm_negativity(V)\n", " \n", "fig, axes = subplots(1, 1, figsize=(8,4))\n", "axes.plot(tlist, logneg, 'r')\n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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} ], "prompt_number": 25 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 25 } ], "metadata": {} } ] }