diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..30a9827 --- /dev/null +++ b/.gitignore @@ -0,0 +1,6 @@ + +*.pyc +*checkpoint.ipynb +doc/.DS_Store +.DS_Store +dist/.DS_Store diff --git a/.ipynb_checkpoints/Documentation-checkpoint.ipynb b/.ipynb_checkpoints/Documentation-checkpoint.ipynb new file mode 100644 index 0000000..fd2a1c4 --- /dev/null +++ b/.ipynb_checkpoints/Documentation-checkpoint.ipynb @@ -0,0 +1,439 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# **PYED**: Exact diagonalization for finite quantum systems\n", + "\n", + "Copyright (C) 2017, H. U.R. Strand\n", + "\n", + "The python module `pyed` implements exact diagonalization for finite fermionic many-body quantum systems, together with calculations of several response functions in imagianary time.\n", + "\n", + "The many-body system is defined using `pytriqs` second-quantized operators and the response functions are stored in `pytriqs` Green's function containters.\n", + "\n", + "## Hamiltonians\n", + "\n", + "As an example let us solve the Hubbard atom with Hamiltonian $H = U\\hat{n}_{\\uparrow} \\hat{n}_{\\downarrow} - \\mu ( \\hat{n}_{\\uparrow} + \\hat{n}_{\\downarrow})$, where $\\hat{n}_\\sigma = c^\\dagger_\\sigma c_\\sigma$.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "H = -0.1*c_dag(0,0)*c(0,0) + -0.1*c_dag(1,0)*c(1,0) + 1*c_dag(0,0)*c_dag(1,0)*c(1,0)*c(0,0)\n" + ] + } + ], + "source": [ + "from pytriqs.operators import c, c_dag\n", + "%matplotlib inline\n", + "up, down = 0, 1\n", + "n_up = c_dag(up, 0) * c(up, 0)\n", + "n_down = c_dag(down, 0) * c(down, 0)\n", + "\n", + "U = 1.0\n", + "mu = 0.1\n", + "\n", + "H = U * n_up * n_down - mu * (n_up + n_down)\n", + "\n", + "print 'H =', H" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Thermal equilibrium solution\n", + "\n", + "To solve the thermal equilibrium of the system we can diagonalize $H$ and determine the partition function $\\mathcal{Z}$ (or alternatively the free energy $\\Omega = -\\frac{1}{\\beta} \\ln \\mathcal{Z}$) and the many-body density matrix $\\rho$ using the egenstates $|\\Gamma \\rangle$ and eigenvalues $E_\\Gamma$ of $H$. The partition function $\\mathcal{Z}$ is given by the sum of Boltzman weights\n", + "\n", + "$$\n", + "\\mathcal{Z} = \\sum_\\Gamma e^{-\\beta E_\\Gamma} \\, ,\n", + "$$\n", + "while the many-body density matrix is given by the ket-bra Boltzman weighted sum\n", + "\n", + "$$\n", + "\\rho = \\frac{1}{\\mathcal{Z}} \\sum_\\Gamma e^{-\\beta E_\\gamma} |\\Gamma \\rangle \\langle \\Gamma|\n", + "\\, .\n", + "$$\n", + "\n", + "To accomplish this we pass the Hamiltonian $H$ and a list of unique annihilation opeators used in $H$ together with the inverse temperature $\\beta$ to a `pyed.TriqsExactDiagonalization` class instance:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Hamiltonian diagonalization:\n", + "Density matrix calculation:\n", + "Z = 2.9840296413\n", + "\\Omega = -0.646637307852\n", + "\\rho =\n", + " (0, 0)\t0.27437085133\n", + " (1, 1)\t0.335117314573\n", + " (2, 2)\t0.335117314573\n", + " (3, 3)\t0.0553945195228\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + " 0% | |\r", + "/usr/local/lib/python2.7/dist-packages/scipy/sparse/compressed.py:774: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n", + " SparseEfficiencyWarning)\n", + " 25% |################## |\r", + " 50% |#################################### |\r", + " 75% |###################################################### |\r", + "100% |########################################################################|\r\n", + " 0% | |\r", + " 25% |################## |\r", + " 50% |#################################### |\r", + " 75% |###################################################### |\r", + "100% |########################################################################|\r\n" + ] + } + ], + "source": [ + "beta = 2.0 # inverse temperature\n", + "fundamental_operators = [c(up,0), c(down,0)]\n", + "\n", + "from pyed.TriqsExactDiagonalization import TriqsExactDiagonalization\n", + "ed = TriqsExactDiagonalization(H, fundamental_operators, beta)\n", + "\n", + "print r'Z =', ed.get_partition_function()\n", + "print r'\\Omega =', ed.get_free_energy()\n", + "print r'\\rho ='\n", + "print ed.ed.get_density_matrix()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Thermal expectation values\n", + "\n", + "Using the many-body density matrix we can evaluate the expectation value of any operator $\\mathcal{O}$ by taking the trace\n", + "\n", + "$$\n", + "\\langle \\mathcal{O} \\rangle = \\textrm{Tr} [ \\rho \\mathcal{O} ]\n", + "$$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " = 0.390511834096\n", + " = 0.390511834096\n", + " = 0.0553945195228\n" + ] + } + ], + "source": [ + "print ' =', ed.get_expectation_value(n_up)\n", + "print ' =', ed.get_expectation_value(n_down)\n", + "print ' =', ed.get_expectation_value(n_up * n_down)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Imaginary time single-particle Green's function\n", + "We can also calculate the dynamical fluctuations of the system by computing its response functions. The simples case is the single-particle Green's function, defined as the imaginary time ordered expectation value\n", + "\n", + "$$\n", + " G_{\\sigma \\sigma'}(\\tau) \\equiv\n", + " - \\langle \\mathcal{T} \\, c_{\\sigma}(\\tau) c_{\\sigma'}^\\dagger(0) \\rangle\n", + " =\n", + " - \\frac{1}{\\mathcal{Z}} \\text{Tr}\n", + " \\left[ e^{-\\beta H} c_{\\sigma}(\\tau_1) c_{\\sigma'}^\\dagger(0) \\right]\n", + "$$\n", + "where the imaginary time dependent operators are defined in the Heisenberg picture $c_{\\sigma}(\\tau) \\equiv e^{\\tau H} c_{\\sigma} e^{-\\tau H}$ and $c^\\dagger_{\\sigma}(\\tau) \\equiv e^{\\tau H} c^\\dagger_{\\sigma} e^{-\\tau H}$.\n", + "\n", + "To calculate $G(\\tau)$ we first create `pytriqs.GfImTime` instance to store the result and pass it to our ED solver instance:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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7jzRySdl4vnPHJUTKCxJRjohIQiVLiExw9+pg+DAwIUab2cAJM/spMB1YB6x2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\nAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from pytriqs.gf import GfImTime\n", + "g_tau = GfImTime(name=r'$g$', beta=beta, statistic='Fermion', n_points=50, indices=[1]) \n", + "ed.set_g2_tau(g_tau, c(up,0), c_dag(up,0))\n", + "\n", + "import matplotlib.pyplot as plt\n", + "from pytriqs.plot.mpl_interface import oplot\n", + "\n", + "plt.figure(); oplot(g_tau); plt.savefig('figure_g_tau.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "![Single-particle Green's function](figure_g_tau.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The two-operator response function calculator is more general and can be used to calculate any type of two operator response, e.g., the density-density response function: $\\chi_{\\sigma \\sigma'}(\\tau) \\equiv -\\langle \\hat{n}_\\sigma(\\tau) \\hat{n}_\\sigma' \\rangle$. However for the very simple single-Hubbard-atom system this response function is $\\tau$ independent as seen below:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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Ged5EKekrktrcGCJpkKQLJS3hvau9zMzM8hpzmQ18FrhL0ljgVTKXJfcHfg/8KCL+WrwQ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\nFzMzS52Ti5mZpc7JxczMUufkYmZmqfv/W/+27YrlTU4AAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from pytriqs.gf import GfImTime\n", + "densdens_tau = GfImTime(name=r'$\\langle n(\\tau) n(0) \\rangle$', beta=beta, statistic='Boson', n_points=50, indices=[1]) \n", + "ed.set_g2_tau(densdens_tau, n_up, n_down)\n", + "\n", + "plt.figure(); oplot(densdens_tau); plt.savefig('figure_densdens_tau.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![Density density response function](figure_densdens_tau.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For fermionic two-operator response functions `pyed` can also directly calculate the fourier transformed response function\n", + "\n", + "$$\n", + "G(i \\omega_n) \\equiv \\int_0^\\beta d\\tau \\, e^{i\\omega_n \\tau} G(\\tau)\n", + "$$\n", + "defined on the (fermionic) Matsubara frequencies $i\\omega_n = \\frac{2\\pi}{\\beta}(2n + 1)$. \n", + "\n", + "NB! `pyed` currently lacks support for handling bosonic response functions in frequency." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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gHfBLd19jZl83s3jv5vVAFXCXma0wswdyFK4UipcfgVs+FDx+e/mjmU0goLEiUnCiVBPB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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from pytriqs.gf import GfImFreq\n", + "g_iwn = GfImFreq(name=r'$g$', beta=beta, statistic='Fermion', n_points=10, indices=[1])\n", + "ed.set_g2_iwn(g_iwn, c(up,0), c_dag(up,0))\n", + "\n", + "plt.figure(); oplot(g_iwn); plt.savefig('figure_g_iwn.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![Single-particle Green's function in imaginary frequency](figure_g_iwn.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Four-operator response functions\n", + "\n", + "In `pyed` there is functionality to compute also higher-order response functions (involving more than two operators and more than one time). Currently two- and three- time ordered expectation values are supported solely in imaginary time.\n", + "\n", + "The two-particle Green's function $G^{(4)}(\\tau_1, \\tau_2, \\tau_3)$ is a prominent example\n", + "\n", + "$$\n", + "G^{(4)}_{\\alpha\\bar{\\beta}\\gamma\\bar{\\delta}}(\\tau_1, \\tau_2, \\tau_3) \\equiv\n", + "\\langle \\mathcal{T} \n", + "c_\\alpha(\\tau_1) c^\\dagger_{\\bar{\\beta}} (\\tau_2) \n", + "c_\\gamma(\\tau_3) c^\\dagger_{\\bar{\\delta}} (0) \\rangle\n", + "$$\n", + "\n", + "That easily can be calculated with `pyed` by passing a suitable `pytriqs` container to the ED solver:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pytriqs.gf import Gf\n", + "from pytriqs.gf import MeshImTime, MeshProduct\n", + "\n", + "ntau = 10\n", + "imtime = MeshImTime(beta, 'Fermion', ntau)\n", + "prodmesh = MeshProduct(imtime, imtime, imtime)\n", + "\n", + "g4_tau = Gf(name=r'$G^{(4)}(\\tau_1,\\tau_2,\\tau_3)$', mesh=prodmesh, target_shape=[1, 1, 1, 1])\n", + "ed.set_g4_tau(g4_tau, c(up,0), c_dag(up,0), c(up,0), c_dag(up,0))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To visualize this three dimensional scalar field one have to resort to some cut plane to represent it in a two dimensional plot. So instead of plotting $G^{(4)}$ we here show the special case of a two-time response function correspoding to $G^{(4)}(\\tau_1, 0^-, \\tau_2)$ namely the particle-particle equal time response function\n", + "\n", + "$$\n", + "G_{\\alpha \\beta \\gamma}^{(3)}(\\tau_1, \\tau_2) \\equiv \n", + "\\langle \\mathcal{T} c_{\\alpha}(\\tau_1) c^\\dagger_{\\bar{\\beta}}(\\tau_2) \\hat{n}_\\gamma(0)\\rangle \\equiv \n", + "- \\langle \\mathcal{T} c_{\\alpha}(\\tau_1) c^\\dagger_{\\bar{\\beta}}(\\tau_2) c_{\\gamma}(0^-) c^\\dagger_{\\bar{\\gamma}}(0) \\rangle \\equiv \n", + "- G^{(4)}(\\tau_1, \\tau_2, 0^+)\n", + "\\, ,\n", + "$$\n", + "that can be calculated separately as:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "prodmesh2 = MeshProduct(imtime, imtime)\n", + "g3pp_tau = Gf(name=r'$G^{(3)}(\\tau_1, \\tau_2)$', mesh=prodmesh2, target_shape=[1, 1, 1, 1])\n", + "ed.set_g3_tau(g3pp_tau, c(up,0), c_dag(up,0), c(up,0)*c_dag(up,0))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "To visualize this we use `matplotlib` directly\n" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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JH12ymIsf3spdo0U8ilFnIGOMkvOy9Xz3siJae528sqeVTZ+08uNXq/np6zWc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\ncCfsZHSNjBNrVDHi9mONmCqCHapRXlBs464PWtCpFLx8VSGb24d5q24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ZM71pKjSDmRKp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GCskEen54f/48IaTN2mI+PEZ+eR2Hlo6iv5V+ugBFgYDLly9TVlYmjQ1opu168gakVqvJysqi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\nHfnxSuaWU1VVxbRp0/jggw9adWzKtEZb0Qc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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "from mpl_toolkits.mplot3d import axes3d\n", + "fig = plt.figure(figsize=(3.25*2, 2*2.5))\n", + "ax = fig.add_subplot(1,1,1, projection='3d')\n", + "\n", + "data = g3pp_tau.data[:, :, 0, 0, 0, 0]\n", + "tau = [tau.real for tau in g3pp_tau.mesh.components[0]]\n", + "t1, t2 = np.meshgrid(tau, tau)\n", + "ax.plot_wireframe(t1, t2, data.real)\n", + "ax.view_init(30, 60)\n", + "ax.set_xlabel(r'$\\tau_1$')\n", + "ax.set_ylabel(r'$\\tau_2$')\n", + "plt.tight_layout()\n", + "plt.savefig('figure_g3pp_tau.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![Equal-time two-particle Green's function](figure_g3pp_tau.png)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Anderson.ipynb b/Anderson.ipynb new file mode 100644 index 0000000..c3e64c7 --- /dev/null +++ b/Anderson.ipynb @@ -0,0 +1,422 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Another example: Anderson impurity model" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The calculation takes about an 10 minutes." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Hamiltonian\n", + "\n", + "As an example let us solve the Anderson impurity model local with Hamiltonian $H = U\\hat{n}_{\\uparrow} \\hat{n}_{\\downarrow} - \\mu ( \\hat{n}_{\\uparrow} + \\hat{n}_{\\downarrow})$," + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "H_loc = -0.5*c_dag('dn',0)*c('dn',0) + -0.5*c_dag('up',0)*c('up',0) + 1*c_dag('dn',0)*c_dag('up',0)*c('up',0)*c('dn',0)\n" + ] + } + ], + "source": [ + "from pytriqs.operators import c, c_dag\n", + "up, down = 'up', 'dn'\n", + "n_up = c_dag(up, 0) * c(up, 0)\n", + "n_down = c_dag(down, 0) * c(down, 0)\n", + "\n", + "U = 1\n", + "mu = U/2.\n", + "\n", + "H_loc = U * n_up * n_down - mu * (n_up + n_down)\n", + "\n", + "print 'H_loc =', H_loc" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "with 5 bath sites. Parameters of bath sites in ek and V arrays." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [], + "source": [ + "from itertools import product\n", + "ek = [-2,-1,1,2]\n", + "V = [-1,-2,-2,-1]\n", + "H_hyb=sum(V[i]*(c_dag(s,i+1)*c(s,0)+c_dag(s,0)*c(s,i+1)) for s, i in product(['up','dn'], range(len(ek))))\n", + "H_hyb+=sum(ek[i]*(c_dag(s,i+1)*c(s,i+1)) for s, i in product(['up','dn'], range(len(ek))))" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-1*c_dag('dn',0)*c('dn',4) + -2*c_dag('dn',0)*c('dn',3) + -2*c_dag('dn',0)*c('dn',2) + -1*c_dag('dn',0)*c('dn',1) + -2*c_dag('dn',1)*c('dn',1) + -1*c_dag('dn',1)*c('dn',0) + -1*c_dag('dn',2)*c('dn',2) + -2*c_dag('dn',2)*c('dn',0) + 1*c_dag('dn',3)*c('dn',3) + -2*c_dag('dn',3)*c('dn',0) + 2*c_dag('dn',4)*c('dn',4) + -1*c_dag('dn',4)*c('dn',0) + -1*c_dag('up',0)*c('up',4) + -2*c_dag('up',0)*c('up',3) + -2*c_dag('up',0)*c('up',2) + -1*c_dag('up',0)*c('up',1) + -2*c_dag('up',1)*c('up',1) + -1*c_dag('up',1)*c('up',0) + -1*c_dag('up',2)*c('up',2) + -2*c_dag('up',2)*c('up',0) + 1*c_dag('up',3)*c('up',3) + -2*c_dag('up',3)*c('up',0) + 2*c_dag('up',4)*c('up',4) + -1*c_dag('up',4)*c('up',0)" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "H_hyb" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Thermal equilibrium solution" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 36/36 [00:00<00:00, 285.18it/s]" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Hamiltonian diagonalization:\n", + "Z = 3.94725339567755\n", + "Omega= -10.988298359655117\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "beta = 5.0 # inverse temperature\n", + "fundamental_operators = np.array([[c(up,i), c(down,i)] for i in range(len(ek)+1)]).flatten()\n", + "\n", + "from pyed.TriqsExactDiagonalization import TriqsExactDiagonalization\n", + "ed = TriqsExactDiagonalization(H_loc+H_hyb, fundamental_operators, beta)\n", + "\n", + "print r'Z =', ed.get_partition_function()\n", + "print 'Omega=', ed.get_free_energy()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Thermal expectation values" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " = 0.4999999999999989\n", + " = 0.5\n", + " = 0.23891890902080304\n" + ] + } + ], + "source": [ + "print ' =', ed.get_expectation_value(n_up)\n", + "print ' =', ed.get_expectation_value(n_down)\n", + "print ' =', ed.get_expectation_value(n_up * n_down)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Imaginary time single-particle Green's function" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 60/60 [00:00<00:00, 101.34it/s]\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from pytriqs.gf import GfImTime\n", + "g_tau = GfImTime(name=r'$g$', beta=beta, statistic='Fermion', n_points=60, indices=[1]) \n", + "ed.set_g2_tau(g_tau, c(up,0), c_dag(up,0))\n", + "\n", + "import matplotlib.pyplot as plt\n", + "from pytriqs.plot.mpl_interface import oplot\n", + "plt.figure(); oplot(g_tau); plt.savefig('figure_g_tau.png')" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 1001/1001 [00:10<00:00, 91.83it/s]\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from pytriqs.gf import GfImTime\n", + "densdens_tau = GfImTime(name=r'$\\langle n(\\tau) n(0) \\rangle$', beta=beta, statistic='Boson', n_points=1001, indices=[1]) \n", + "ed.set_g2_tau(densdens_tau, n_up, n_up)\n", + "\n", + "plt.figure(); oplot(densdens_tau); plt.savefig('figure_densdens_tau.png')" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 239/239 [00:00<00:00, 1912.81it/s]\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from pytriqs.gf import GfImFreq\n", + "g_iwn = GfImFreq(name=r'$g$', beta=beta, statistic='Boson', n_points=120, indices=[1])\n", + "ed.set_g2_iwn(g_iwn, n_up, n_down)\n", + "\n", + "plt.figure(); oplot(g_iwn); plt.savefig('figure_g_iwn.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Four-operator response functions" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [], + "source": [ + "from pytriqs.gf import Gf\n", + "from pytriqs.gf import MeshImTime, MeshProduct\n", + "\n", + "ntau = 100\n", + "imtime = MeshImTime(beta, 'Fermion', ntau)" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 5050/5050 [01:34<00:00, 53.32it/s]\n", + "100%|██████████| 4950/4950 [01:32<00:00, 53.81it/s]\n" + ] + } + ], + "source": [ + "prodmesh2 = MeshProduct(imtime, imtime)\n", + "g3pp_tau = Gf(name=r'$G^{(3)}(\\tau_1, \\tau_2)$', mesh=prodmesh2, target_shape=[1, 1, 1, 1])\n", + "ed.set_g3_tau(g3pp_tau, c(up,0), c_dag(up,0), c(up,0)*c_dag(up,0))" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "from mpl_toolkits.mplot3d import axes3d\n", + "fig = plt.figure(figsize=(3.25*2, 2*2.5))\n", + "ax = fig.add_subplot(1,1,1, projection='3d')\n", + "\n", + "data = g3pp_tau.data[:, :, 0, 0, 0, 0]\n", + "tau = [tau.real for tau in g3pp_tau.mesh.components[0]]\n", + "t1, t2 = np.meshgrid(tau, tau)\n", + "ax.plot_wireframe(t1, t2, data.real)\n", + "ax.view_init(30, 60)\n", + "ax.set_xlabel(r'$\\tau_1$')\n", + "ax.set_ylabel(r'$\\tau_2$')\n", + "plt.tight_layout()\n", + "plt.savefig('figure_g3pp_tau.png')" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(54.135,0.5,'$\\\\tau_2$')" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(8,8))\n", + "plt.imshow(data.real)\n", + "# plt.xticks(range(10))\n", + "# plt.yticks(range(10))\n", + "plt.savefig('im_g3pp_tau.png')\n", + "plt.colorbar()\n", + "plt.xlabel(r'$\\tau_1$')\n", + "plt.ylabel(r'$\\tau_2$')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.16" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Documentation.ipynb b/Documentation.ipynb new file mode 100644 index 0000000..1b9f060 --- /dev/null +++ b/Documentation.ipynb @@ -0,0 +1,467 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# **PYED**: Exact diagonalization for finite quantum systems\n", + "\n", + "Copyright (C) 2017, H. U.R. Strand\n", + "\n", + "The python module `pyed` implements exact diagonalization for finite fermionic many-body quantum systems, together with calculations of several response functions in imagianary time.\n", + "\n", + "The many-body system is defined using `pytriqs` second-quantized operators and the response functions are stored in `pytriqs` Green's function containters.\n", + "\n", + "## Hamiltonians\n", + "\n", + "As an example let us solve the Hubbard atom with Hamiltonian $H = U\\hat{n}_{\\uparrow} \\hat{n}_{\\downarrow} - \\mu ( \\hat{n}_{\\uparrow} + \\hat{n}_{\\downarrow})$, where $\\hat{n}_\\sigma = c^\\dagger_\\sigma c_\\sigma$.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import warnings\n", + "warnings.filterwarnings('ignore')" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "H = -0.5*c_dag('down',0)*c('down',0) + -0.5*c_dag('up',0)*c('up',0) + 1*c_dag('down',0)*c_dag('up',0)*c('up',0)*c('down',0)\n" + ] + } + ], + "source": [ + "from pytriqs.operators import c, c_dag\n", + "up, down = 'up', 'down'\n", + "n_up = c_dag(up, 0) * c(up, 0)\n", + "n_down = c_dag(down, 0) * c(down, 0)\n", + "\n", + "U = 1\n", + "mu =-0.5*U\n", + "\n", + "H = U * n_up * n_down + mu * (n_up + n_down)\n", + "\n", + "print 'H =', H" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Thermal equilibrium solution\n", + "\n", + "To solve the thermal equilibrium of the system we can diagonalize $H$ and determine the partition function $\\mathcal{Z}$ (or alternatively the free energy $\\Omega = -\\frac{1}{\\beta} \\ln \\mathcal{Z}$) and the many-body density matrix $\\rho$ using the egenstates $|\\Gamma \\rangle$ and eigenvalues $E_\\Gamma$ of $H$. The partition function $\\mathcal{Z}$ is given by the sum of Boltzman weights\n", + "\n", + "$$\n", + "\\mathcal{Z} = \\sum_\\Gamma e^{-\\beta E_\\Gamma} \\, ,\n", + "$$\n", + "while the many-body density matrix is given by the ket-bra Boltzman weighted sum\n", + "\n", + "$$\n", + "\\rho = \\frac{1}{\\mathcal{Z}} \\sum_\\Gamma e^{-\\beta E_\\gamma} |\\Gamma \\rangle \\langle \\Gamma|\n", + "\\, .\n", + "$$\n", + "\n", + "To accomplish this we pass the Hamiltonian $H$ and a list of unique annihilation opeators used in $H$ together with the inverse temperature $\\beta$ to a `pyed.TriqsExactDiagonalization` class instance:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 4/4 [00:00<00:00, 470.75it/s]" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Hamiltonian diagonalization:\n", + "Z = 2.2706705664732256\n", + "\\Omega = -0.7050187979007294\n", + "\\rho =\n", + " (0, 0)\t0.05960146101105877\n", + " (1, 1)\t0.44039853898894116\n", + " (2, 2)\t0.44039853898894116\n", + " (3, 3)\t0.05960146101105877\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "beta = 4.0 # inverse temperature\n", + "fundamental_operators = [c(up,0), c(down,0)]\n", + "\n", + "from pyed.TriqsExactDiagonalization import TriqsExactDiagonalization\n", + "ed = TriqsExactDiagonalization(H, fundamental_operators, beta)\n", + "\n", + "print r'Z =', ed.get_partition_function()\n", + "print r'\\Omega =', ed.get_free_energy()\n", + "print r'\\rho ='\n", + "print ed.ed.get_density_matrix()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Thermal expectation values\n", + "\n", + "Using the many-body density matrix we can evaluate the expectation value of any operator $\\mathcal{O}$ by taking the trace\n", + "\n", + "$$\n", + "\\langle \\mathcal{O} \\rangle = \\textrm{Tr} [ \\rho \\mathcal{O} ]\n", + "$$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " = 0.5\n", + " = 0.5\n", + " = 0.05960146101105877\n" + ] + } + ], + "source": [ + "print ' =', ed.get_expectation_value(n_up)\n", + "print ' =', ed.get_expectation_value(n_down)\n", + "print ' =', ed.get_expectation_value(n_up * n_down)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Imaginary time single-particle Green's function\n", + "We can also calculate the dynamical fluctuations of the system by computing its response functions. The simples case is the single-particle Green's function, defined as the imaginary time ordered expectation value\n", + "\n", + "$$\n", + " G_{\\sigma \\sigma'}(\\tau) \\equiv\n", + " - \\langle \\mathcal{T} \\, c_{\\sigma}(\\tau) c_{\\sigma'}^\\dagger(0) \\rangle\n", + " =\n", + " - \\frac{1}{\\mathcal{Z}} \\text{Tr}\n", + " \\left[ e^{-\\beta H} c_{\\sigma}(\\tau_1) c_{\\sigma'}^\\dagger(0) \\right]\n", + "$$\n", + "where the imaginary time dependent operators are defined in the Heisenberg picture $c_{\\sigma}(\\tau) \\equiv e^{\\tau H} c_{\\sigma} e^{-\\tau H}$ and $c^\\dagger_{\\sigma}(\\tau) \\equiv e^{\\tau H} c^\\dagger_{\\sigma} e^{-\\tau H}$.\n", + "\n", + "To calculate $G(\\tau)$ we first create `pytriqs.GfImTime` instance to store the result and pass it to our ED solver instance:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 500/500 [00:00<00:00, 1714.22it/s]\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from pytriqs.gf import GfImTime\n", + "g_tau = GfImTime(name=r'$g$', beta=beta, statistic='Fermion', n_points=500, indices=[1]) \n", + "ed.set_g2_tau(g_tau, c(up,0), c_dag(up,0))\n", + "\n", + "import matplotlib.pyplot as plt\n", + "from pytriqs.plot.mpl_interface import oplot\n", + "%matplotlib inline\n", + "\n", + "plt.figure(); oplot(g_tau); plt.savefig('figure_g_tau.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The two-operator response function calculator is more general and can be used to calculate any type of two operator response, e.g., the density-density response function: $\\chi_{\\sigma \\sigma'}(\\tau) \\equiv -\\langle \\hat{n}_\\sigma(\\tau) \\hat{n}_\\sigma' \\rangle$. However for the very simple single-Hubbard-atom system this response function is $\\tau$ independent as seen below:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 1000/1000 [00:00<00:00, 1987.30it/s]\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from pytriqs.gf import GfImTime\n", + "densdens_tau = GfImTime(name=r'$\\langle n(\\tau) n(0) \\rangle$', beta=beta, statistic='Boson', n_points=1000, indices=[1]) \n", + "ed.set_g2_tau(densdens_tau, n_up, n_down)\n", + "\n", + "plt.figure(); oplot(densdens_tau); plt.savefig('figure_densdens_tau.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For fermionic two-operator response functions `pyed` can also directly calculate the fourier transformed response function\n", + "\n", + "$$\n", + "G(i \\omega_n) \\equiv \\int_0^\\beta d\\tau \\, e^{i\\omega_n \\tau} G(\\tau)\n", + "$$\n", + "defined on the (fermionic) Matsubara frequencies $i\\omega_n = \\frac{2\\pi}{\\beta}(2n + 1)$. \n", + "\n", + "NB! `pyed` currently lacks support for handling bosonic response functions in frequency." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 200/200 [00:00<00:00, 22229.13it/s]\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from pytriqs.gf import GfImFreq\n", + "g_iwn = GfImFreq(name=r'$g$', beta=beta, statistic='Fermion', n_points=100, indices=[1])\n", + "ed.set_g2_iwn(g_iwn, c(up,0), c_dag(up,0))\n", + "\n", + "plt.figure(); oplot(g_iwn); plt.savefig('figure_g_iwn.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Four-operator response functions\n", + "\n", + "In `pyed` there is functionality to compute also higher-order response functions (involving more than two operators and more than one time). Currently two- and three- time ordered expectation values are supported solely in imaginary time.\n", + "\n", + "The two-particle Green's function $G^{(4)}(\\tau_1, \\tau_2, \\tau_3)$ is a prominent example\n", + "\n", + "$$\n", + "G^{(4)}_{\\alpha\\bar{\\beta}\\gamma\\bar{\\delta}}(\\tau_1, \\tau_2, \\tau_3) \\equiv\n", + "\\langle \\mathcal{T} \n", + "c_\\alpha(\\tau_1) c^\\dagger_{\\bar{\\beta}} (\\tau_2) \n", + "c_\\gamma(\\tau_3) c^\\dagger_{\\bar{\\delta}} (0) \\rangle\n", + "$$\n", + "\n", + "That easily can be calculated with `pyed` by passing a suitable `pytriqs` container to the ED solver:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 1540/1540 [00:01<00:00, 945.61it/s]\n", + "100%|██████████| 1330/1330 [00:01<00:00, 966.69it/s]\n", + "100%|██████████| 1330/1330 [00:01<00:00, 977.98it/s]\n", + "100%|██████████| 1330/1330 [00:01<00:00, 965.98it/s]\n", + "100%|██████████| 1330/1330 [00:01<00:00, 976.40it/s]\n", + "100%|██████████| 1140/1140 [00:01<00:00, 942.44it/s]\n" + ] + } + ], + "source": [ + "from pytriqs.gf import Gf\n", + "from pytriqs.gf import MeshImTime, MeshProduct\n", + "\n", + "ntau = 20\n", + "imtime = MeshImTime(beta, 'Fermion', ntau)\n", + "prodmesh = MeshProduct(imtime, imtime, imtime)\n", + "\n", + "g4_tau = Gf(name=r'$G^{(4)}(\\tau_1,\\tau_2,\\tau_3)$', mesh=prodmesh, target_shape=[1, 1, 1, 1])\n", + "ed.set_g4_tau(g4_tau, c(up,0), c_dag(up,0), c(up,0), c_dag(up,0))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To visualize this three dimensional scalar field one have to resort to some cut plane to represent it in a two dimensional plot. So instead of plotting $G^{(4)}$ we here show the special case of a two-time response function correspoding to $G^{(4)}(\\tau_1, 0^-, \\tau_2)$ namely the particle-particle equal time response function\n", + "\n", + "$$\n", + "G_{\\alpha \\beta \\gamma}^{(3)}(\\tau_1, \\tau_2) \\equiv \n", + "\\langle \\mathcal{T} c_{\\alpha}(\\tau_1) c^\\dagger_{\\bar{\\beta}}(\\tau_2) \\hat{n}_\\gamma(0)\\rangle \\equiv \n", + "- \\langle \\mathcal{T} c_{\\alpha}(\\tau_1) c^\\dagger_{\\bar{\\beta}}(\\tau_2) c_{\\gamma}(0^-) c^\\dagger_{\\bar{\\gamma}}(0) \\rangle \\equiv \n", + "- G^{(4)}(\\tau_1, \\tau_2, 0^+)\n", + "\\, ,\n", + "$$\n", + "that can be calculated separately as:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 210/210 [00:00<00:00, 1107.79it/s]\n", + "100%|██████████| 190/190 [00:00<00:00, 999.15it/s] \n" + ] + } + ], + "source": [ + "prodmesh2 = MeshProduct(imtime, imtime)\n", + "g3pp_tau = Gf(name=r'$G^{(3)}(\\tau_1, \\tau_2)$', mesh=prodmesh2, target_shape=[1, 1, 1, 1])\n", + "ed.set_g3_tau(g3pp_tau, c(up,0), c_dag(up,0), c(up,0)*c_dag(up,0))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "To visualize this we use `matplotlib` directly\n" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "from mpl_toolkits.mplot3d import axes3d\n", + "fig = plt.figure(figsize=(3.25*2, 2*2.5))\n", + "ax = fig.add_subplot(1,1,1, projection='3d')\n", + "\n", + "data = g3pp_tau.data[:, :, 0, 0, 0, 0]\n", + "tau = [tau.real for tau in g3pp_tau.mesh.components[0]]\n", + "t1, t2 = np.meshgrid(tau, tau)\n", + "ax.plot_wireframe(t1, t2, data.real)\n", + "ax.view_init(30, 60)\n", + "ax.set_xlabel(r'$\\tau_1$')\n", + "ax.set_ylabel(r'$\\tau_2$')\n", + "plt.tight_layout()\n", + "plt.savefig('figure_g3pp_tau.png')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.16" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/LICENSE.txt b/LICENSE.txt index 545c2d7..ea03edd 100644 --- a/LICENSE.txt +++ b/LICENSE.txt @@ -1,13 +1,13 @@ PYED: Exact diagonalization routines for finite quantum systems -Copyright (C) 2017 by H. U.R. Strand +Copyright (C) 2018 by H. U.R. Strand, Ya.V. Zhumagulov PYED is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. - + PYED is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. @@ -15,4 +15,3 @@ PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with TRIQS (in the file COPYING.txt in this directory). If not, see . - diff --git a/MANIFEST b/MANIFEST new file mode 100644 index 0000000..886e2d6 --- /dev/null +++ b/MANIFEST @@ -0,0 +1,8 @@ +# file GENERATED by distutils, do NOT edit +setup.py +pyed/CubeTetras.py +pyed/SparseExactDiagonalization.py +pyed/SparseMatrixFockStates.py +pyed/SquareTriangles.py +pyed/TriqsExactDiagonalization.py +pyed/__init__.py diff --git a/Readme.md b/Readme.md index 374b23b..e9164f4 100644 --- a/Readme.md +++ b/Readme.md @@ -1,6 +1,6 @@ # **PYED**: Exact diagonalization for finite quantum systems -Copyright (C) 2017, H. U.R. Strand +Copyright (C) 2018, H. U.R. Strand The python module `pyed` implements exact diagonalization for finite fermionic many-body quantum systems, together with calculations of several response functions in imagianary time. @@ -8,21 +8,13 @@ The many-body system is defined using `pytriqs` second-quantized operators and t The original purpose of `pyed` is to provide exact solutions to small finite systems, to be used as benchmarks and tests for stochastic many-body solvers. -## Dependencies - -`pyed` requires [the `triqs` library](https://github.com/TRIQS/triqs) to be installed from the `unstable` banch or version `1.5` scheduled for release late 2017. ## Installation -To do: Add `setup_utils` install script - -There is currently no formal installation scripts packed with `pyed`. To use and develop the module simply ammend your `PYTHON_PATH` with the `./pyed/` folder, e.g., add the follwing - ``` -export PYTHON_PATH=${HOME}/path/to/pyed:$PYTHON_PATH +pip install git+https://github.com/yaros72/pyed ``` -in your `.bashrc`, `.bash_profile`, or `.profile` file. ## Documentation diff --git a/dist/pyed-0.0.0.tar.gz b/dist/pyed-0.0.0.tar.gz new file mode 100644 index 0000000..76e93d7 Binary files /dev/null and b/dist/pyed-0.0.0.tar.gz differ diff --git a/doc/.ipynb_checkpoints/Documentation_CPT_2D-checkpoint.ipynb b/doc/.ipynb_checkpoints/Documentation_CPT_2D-checkpoint.ipynb new file mode 100644 index 0000000..26229cd --- /dev/null +++ b/doc/.ipynb_checkpoints/Documentation_CPT_2D-checkpoint.ipynb @@ -0,0 +1,327 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# **PYED+CPT **:Cluster pertrubation theory with exact diagonalization for finite quantum systems\n", + "\n", + "Copyright (C) 2017, H. U.R. Strand, Ya.V. Zhumagulov\n", + "\n", + "The python module `pyed` implements exact diagonalization for finite fermionic many-body quantum systems, together with calculations of several response functions in imagianary time.\n", + "\n", + "The many-body system is defined using `pytriqs` second-quantized operators and the response functions are stored in `pytriqs` Green's function containters.\n", + "\n", + "Cluster pertrubation theory addition to `pyed` allow calculate bandstructure and Fermi surface of several models. \n", + "\n", + "## Hamiltonians\n", + "\n", + " As an example let us solve the Hubbard model with Hamiltonian including only nearest-neighbor hoppings $H = U\\sum_{i}\\hat{n}_{i,\\uparrow} \\hat{n}_{i,\\downarrow} - \\mu\\sum_{i}( \\hat{n}_{i,\\uparrow} + \\hat{n}_{i,\\downarrow}) + t \\sum_{,\\sigma}c^\\dagger_{i,\\sigma} c_{j\\sigma}$, where $\\hat{n}_\\sigma = c^\\dagger_\\sigma c_\\sigma$. \n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "from pytriqs.operators import c, c_dag,n\n", + "from pyed.TriqsExactDiagonalization import TriqsExactDiagonalization\n", + "from pyed.ClusterPertrubationTheory import ClusterPertrubationTheory_2D_Square\n", + "import numpy as np\n", + "import progressbar\n", + "from itertools import product\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Parameters of model: U=8, t=-1, $\\mu$=U/2 and size of exact diagonaliztion cluster will be 2x2" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "t =-1;U=8;mu=U/2\n", + "Lx,Ly=2,2;L=Lx*Ly" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "T=np.zeros((L,L))\n", + "for i in range(L):\n", + " for j in range(L):\n", + " x = i % Lx - j % Ly\n", + " y = i // Lx - j // Ly\n", + " if (x**2+y**2)==1: T[i,j]=t \n", + "H_int = sum(-mu*(n('up', site) + n('dn', site)) + U * n('up', site) * n('dn', site) for site in range(L))\n", + "H_kin = sum(T[st1][st2]*c_dag(sn,st1)*c(sn,st2) for sn, st1,st2 in product((\"dn\", \"up\"), range(L),range(L)) )\n", + "H = H_int +H_kin" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Parameter $\\beta$ will be 200" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Hamiltonian diagonalization:\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + " 0% | |\r", + "/usr/local/lib/python2.7/dist-packages/scipy/sparse/compressed.py:774: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n", + " SparseEfficiencyWarning)\n", + " 4% |## |\r", + " 8% |##### |\r", + " 12% |######## |\r", + " 16% |########### |\r", + " 20% |############## |\r", + " 24% |################# |\r", + " 28% |#################### |\r", + " 32% |####################### |\r", + " 36% |######################### |\r", + " 40% |############################ |\r", + " 44% |############################### |\r", + " 48% |################################## |\r", + " 52% |##################################### |\r", + " 56% |######################################## |\r", + " 60% |########################################### |\r", + " 64% |############################################## |\r", + " 68% |################################################ |\r", + " 72% |################################################### |\r", + " 76% |###################################################### |\r", + " 80% |######################################################### |\r", + " 84% |############################################################ |\r", + " 88% |############################################################### |\r", + " 92% |################################################################## |\r", + " 96% |##################################################################### |\r", + "100% |########################################################################|\r\n" + ] + } + ], + "source": [ + "fundamental_operators = np.array([[c('up',i), c('dn',i)] for i in range(L)]).flatten()\n", + "H=H_int+H_kin\n", + "beta=200;nstates=200\n", + "ed = TriqsExactDiagonalization(H,fundamental_operators, beta,nstates=nstates)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we construct, frequency meshgrid, momentum meshgrid and pertrubation matrix V\n", + "\n", + "Further explation you can find in:\n", + "\n", + "https://www.physique.usherbrooke.ca/pages/sites/default/files/senechal/publis/Senechal2011vn.pdf" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "N=60\n", + "kx = np.linspace(-np.pi, np.pi, N+1);kx = np.delete(kx, 0)\n", + "ky = np.linspace(-np.pi, np.pi,N+1);ky = np.delete(ky, 0)\n", + "kx, ky = np.meshgrid(kx, ky)\n", + "V=np.zeros((N,N,L,L),dtype=np.complex)\n", + "for a,b in product(range(L),range(L)):\n", + " x=a % Lx - b % Ly ; y=a// Lx - b// Ly\n", + " if (y==(Ly-1))&(x==0):V[:,:,a,b]=t*np.exp(1j*Ly*ky);V[:,:,b,a]=t*np.exp(-1j*Ly*ky)\n", + " if (x==(Lx-1))&(y==0):V[:,:,a,b]=t*np.exp(1j*Lx*kx);V[:,:,b,a]=t*np.exp(-1j*Lx*kx)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To apply Cluster Pertrubation Theory to our exact diagonalization we use `ClusterPertrubationTheory_2D_Square` class for 2D Square models" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Calculation green function of full system\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100% |########################################################################|\n", + " 0% | |\r" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Coupling system\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100% |########################################################################|\n", + " 27% |################### |\r" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Reduce mixed representation\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100% |########################################################################|\n" + ] + } + ], + "source": [ + "omega=np.linspace(-10,10,200);\n", + "CPT=ClusterPertrubationTheory_2D_Square(ed,(kx,ky),V,omega,(Lx,Ly))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can calculate Fermi surface" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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K2tV1W2Gk9ek0n+1h0wBT4OE+r/MquI/UunEF7P7VYpHwUNWHw6fazqqynaI3\nP1ugzM4GoWc2yAfKd7dB+B02yGVIAxZINFC7xiwhLU9BLfnUofFLGcBeQTl40wsoj2kclbjVDWir\nwvCtFbNXffN/i6CiKWjNqRb7IwcUC7UlqK3xjIOHPcpfBPW6N70IbF3fCs4r71q35aMdMn2rctYr\n3q6By66XvZVHvez06SqwAfT+P7Slphq0xZR1P/xdbTed7kqThmreDmlEU7DxwV1AaKvGVhqOQihM\nrlWjqOucdy3zkKbOqSD2ihqIfrXaIUUm6jRV0h7SkHrbYYEnNsBWNS/ApQMzoIHxNEAbaCf/WrNQ\nBqTHwZ4V+LWf98co6xxcXGWBuM9seazBDfOndRzaOvEdoF7BOf4t7I/wx1PwkNM4CoNq6x61BRVF\nOa+86k1Q8Vaagbo6eBcNJMrni/OrDdhOTa8gvQu0aWkcQT3nSjs4X1DX36rs7I8DZamMv0XZwttZ\nH1M2SVDaT4CdJwu0KzMOit516MPEAN5/T7U/DoG2wrpR6UFIsUBCQ5miQceuqDVDhGtveMLS3zUq\nAEm3C74zD6idBRtlxwDwALmr2w+7T5Kdlu80b1tUPDfZzia2yMa77n64g/YqI0T2KbBONpqXVsjz\n8uNe65VaMS4BDQQgW32C9Mr2MBirjVE0rxoXQb0C9yL7ww/XrLQV1Ayuw/5QRV3cZ61zqt6NGl7q\nsQwqGpgxe9UvHwB1hvTzDoX6h4c2EBV2X89aXX+t4mGc/epnPvV7gd2Qm3zvy2ydnCtoP7y6YZ79\nHpXkRgm236PnVaucfaDosWCgEgF42Lj61YAMl0fPCCmEAwUHDskQ6XbICwiNi6XyabCRmXC0/gTJ\n3IONqCxuAQFVZfQCxhVTsNHbIQz9dMFLLSkrZAtsuzG4ZUnWe2hgFEMl76DNHNQ3gKHA9TdTeANz\nZkguu/pUvr+yPrFBgq2RVTRwCumspkGY8qhHsDCBmpAsC1oAeWOJkJ9nYX9UTkFFiPWBp/ZHyK1e\n2B9eTaul4TM/XuiQ4CJvgB0hHR/l93Bozv7w0AYGkIuAYqWu+/qjT/2jfOsM7N41aNz3g8sE31V5\nTw962f7Ygfrqb2JFLyfjlT7nd9ujQskHGLClHBDPun8ZWiMcVExha0dPD3DMFimE2gq4NNTSfeyn\nqXwF0EwPhehKTauKJsRP71+bHSGqu1/rM7Cp6csPeAT6ZJuoirLmblMwSPrCUncbXXR5Vd1/IKe2\nMWwSr67s3TjNAAAgAElEQVSzkv6gf/1DbBDOd5IFoIG1ujbxpP146DrV2vC2B10E9WrY5oezTRDt\njwB4TPYHbP6oqMfbX3gKKm5T9ZL9Ydkfyaf2mR/WUVMCtge1h7SHwarLT02f0/kU2h3ObCotK+ic\njfEs9e4jCvy9qjrPu1LYX9sq8XbHbhyYQf3sdwEQ1SKQBGYGNhmwNSvkQMGLg3cT39rDGgCOQrhx\nCcFGZsIhrRlrKTGVT4ONOZWveCUtnwL1pR3i91GXmfabrCMlahtgG1g7ROkQgMvxoENuJoy1yk6q\n2sAs9QZuYHT8BKe8MereW767DRL8mlXqnge01mdIZzWdbA/vT/s86l7vgUxbRb2yO5bAdgo62x8x\nqOiAXWNQ8ab2R2m412Pq/2OX/RH7qfa2R1TW3gpZgVphUE8eu3tDFmd3sDx2JzjPoH4/eJ/Nr6A/\n86O/pKzUdfx+2kMzlWVveicNX3agzt835bjTDK9KjAJClebhxUHa5iUA2ue1lOxfmx3SCu7U8KA2\ntWys3FyDGaAwodYWg40sT5qqliXYqGAmBXTwsjFY4KHNQ0n7IxOYuAL24dL6dFLr30etBwbNv+Yd\ntGVc7RFgtkMU3jLMZ+f0T2uDuObmQWFv1TUGoIE1pJ1fbfN7f5q6mo4ZHj49zytuD2A3X0X49LbG\nZH9UOSmrzCNWCFVGqT6oGEFdXUvFl/LASz3wUh6T/fFLeUywHj71HtSa1pfVdE2A8D+HYmUFBw9s\nACHPWXOrv/TN477sbBKvqjOozzJKvKodvnrOP5bGOReskKt2Sf+ePXxXv81qGXcljXmIx9MNu2vG\nmHVsgK37MEANdCWtdoh+4VDWPvdamqqz9HvNXWmXQhZsVH9E1bLG7Kxlo/erdcN8Qz8Ha/WvZc1j\nkkCcSXjaws73BQ9pOMNaF9dtKvsM2sBQ24B51RnefdK1G/uz8l1hbbaElqWylvEdoHXeheUBU8qq\nvB2EsxUSlDEtIL0AeB6uQKvcbwQO0uwgnrM/tKWiBhS9/XGv3Yd+EavjLPvj7oDtfepdUDGDWkEw\nwLAuub4HzDkAG8Cpur5SMog9ZH3rxayqd6C+kva3ehmBwnmnrn2Q8Uttkty4xX9fsD4WN9Gw3FQj\n8wuEClhaIIqaOAG2pu9pOdCzQUKGiNiPBxN2uddABydXzRDpMQk2u6CDmT1IvaLW7TJ4x9Kg8ccO\nbEVFdx70jeVJVRMEot36oAMdsk22hdBf6+VvGjtoAxO4gRne/TjM2+8LX7xUfmhHTmEjS7JBVDnr\nfC74uIP0CDw6te1eIBDskCugXkE6LMtOXWP41FWyP4LtIZkftaHWboFo9sfN2R+77I+gposPIsaA\nonXOtAH13Zo8K7Qh489/vUN2LwMbjKW6zuW9udMBvm74I6Ceumd1BMjQzsBeqWtvhfTWgm1Svrrd\nVzNIdLu89bG6mT79rXgMqNIe3Gqo3K+BqhE72YdD7DVfDpQZ1pLO14p7PRj38cYj95qrpPWJHdKt\nAckOqepfCCgtBU62v+qOrHeWOAJ7SfScGSKKnT3Mm1PZ3nppJ9CWG8sEbmCCd9/WZz/Yz2iDJGUd\nbBCvmuEADQT42nKyrgBpp6onFe2GfeBw5VFP1ocO06Iu+9Q1NX4RiFOBBBKj/XGvR8j+OG38sv0b\navqOY2l93Kkt1XQdh/i0NJl3BWwtzxT1M1Cvgo4rVT3NY/CeVeH2u9J26/LPgA1cU9fHCcB92U2v\nQWVrHaa6ZSFdd/+9TFU6bnVQN7zseYgm2SGNCo5CUzqf7zvkluwQ7ehJs0NKIWkyziANxInFwXD+\ntab3HZgCjrb5DtQZ2NnDDjtuN4dkiwjILfjIbrEltPuAqm3dJmAB71C5Osi8Pf65fHfPetm0HE5l\npwCjT8MbsMbI8hBI6zzmTa9sjw2kDd4rj9orau9ba0CxuGFN0zOV7Rq/GKifZX9s7I8NpKvzpa+C\negVpbw36Yr1HYg1s2PThXZ+Vp8FDkKi8a6p6Berdd+zewejtGz/PyhLZqWtbF5f+APleNb2wXGLr\nx/4ZFPaVlRurvMouprBfCVtgHyjSmvHRlytzOl/oO0TS+JgPs0NulcwOASDpd66xjPxxjf61V7ka\ncCQZb9U43p0NREukAIELGgy0n4Q9wDtDqC1U9hm05dgapG3dg/+6w1P2G9w63tFA5vsr6w2sA5x1\n3jCM2e5wkPZq2YZ13gDdfcOWfZAxj6/yqXVdYn/UYX/kxi83Z3/4xi8aTPylPPBLfeAlBRJ/LW/B\np9bMD7U9Ko23kz8DdYZ0XZxQB7NNV6HjgQ1bdv8KrlU5uHd/f4BseD1fVNXPQO0hfabi87ShpmlS\n2R7YoGGHZCCfWSFXy2rZshj2kF79bpOSo6yyNdkZeOGGVwIqk/wmDZUIDQ13PHBQOtZiiQQ7RBrL\n3LhYdojmazcms0O4MGoV76AyGhCCilwdBScLZIxrep3bvdnDnu6VfZ0dzDJOEAjDgK5eNvEe2gyy\nzJVgiwND2Tf3vc9M659VWVujFV9MMSc4AwHQfR6cQ5pULc9qOnrVEdIB2hnQpqYF1FlhV0SfWkFd\nm6XpVfGqKzFutXvU93rgpRziV3cF/Ut9hDS9X8qjQ3rpUycLhA68QOs115rxos2PE6Tzha7TLANE\nL1SBtge2/ZxPrI+rpcN4raozqK9C+tKbZ5yaBqBXstXvgK3bpr3Zh369BYRxvr7uZ3bTchvdbuxu\nrmG96RFcfzuvskENhQlvVPCiHT3bMhjj6Qc3WBf9Hd56vWSG+NKYcOeurG/uDjOy2wqgmSKQDVQl\n7YFtrOO4b1rbH7JHWrMqaeOEVKlXrdMaxL/uhGU3nVmGGab0e58mqvwRwS2b18dZ7xy2X18jI+Q7\nZ4MQmm/B6M8pB2cbfwLoMO4h7acnNT0D24F65VF7UAfrYw9qH1gspaHWoahvkgVyF8vjLop6UtaL\n9Lw7PZy6fjwF9QD2ALWH9A4cvr7J/B7Yfr6v0WRk51UrqG1bTkC9AvdYbr2nHcRj/gBulWY2jgBs\ncG/c44GtQLY+UxZquwnIR1M+/R79jvVFfeW3Wta5wFdFv7yajHce9r6qT4Ts6OAJJd7RC/Ab7jhw\n4Bf7HdbpfH61/QUqhMJstzNN7etf23vtmCyRvGEYIJ6L3ZnGkHKkifVB4yUC3cJnEcIO6gzLFjG1\njQhuxrBDzC7xmwsg51l/pJHMD/Cs3YgHMxDhDIyDi3NImy9twwrapKYJs+2R7RAfNNx41OpJG6h9\nQFFUtc+nrnV00nSrB+5FgX0sO2k6y6f2anoFam3wcgZq/xPUjfo8XBDSA9uWo2iFPCuNo+2RLRCv\nqjOoD5QJ1GeQ3sHZ9+6X5/PgjqqaBsQ3wM77qTbDs/dWfrTkm+3uN+xFfqSUrXAnoBiwexbPSmEf\nKJYh0qThjAYcV/71L+F3iP615l/3zRjSXW8eIeCowN5ZIrJ8tkR6pf45KIuSBpCsEPGy1QppsBsZ\nM42XHqiKthQ+l6ed7JAA734gFr9KvIFdKT8uG2QZXIyfGdChLinpWLdX0942uQzqEkFtilpbKAqk\noR61KOqRpieQriOgaJBOaXo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4eaWYjcEyLBD38K4Y9SWBuxHhTkewRlBgKlt/l76domzt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n//Zvl9g1d/Ps01oNfDHVBT22UrMlbDO9CWRLjEIqIoiiOp81I/U0H1hev/nWU+inW3YM3MJzP/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\niBusb3GLW9ziHcQN1re4xS1u8Q7i/wc41oi5BXFnLwAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(6,6))\n", + "CPT.calculation_Fermi_surface()\n", + "plt.imshow(CPT.FS,interpolation='lanczos')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And band structure" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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5t/HrybaluJYHOx+haEb2rxvyM4+f31B3i0+RXEqA3ycJvhYUyfA2/nBNxlpr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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(12,6))\n", + "CPT.calculation_bandstructure()\n", + "plt.imshow(CPT.bandstructure,cmap=plt.cm.jet,interpolation='lanczos', aspect='auto')" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/doc/Anderson.ipynb b/doc/Anderson.ipynb new file mode 100644 index 0000000..0f902eb --- /dev/null +++ b/doc/Anderson.ipynb @@ -0,0 +1,438 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Another example: Anderson impurity model" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The calculation takes about an 10 minutes." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Hamiltonian\n", + "\n", + "As an example let us solve the Anderson impurity model local with Hamiltonian $H = U\\hat{n}_{\\uparrow} \\hat{n}_{\\downarrow} - \\mu ( \\hat{n}_{\\uparrow} + \\hat{n}_{\\downarrow})$," + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "H_loc = -2*c_dag('dn',0)*c('dn',0) + -2*c_dag('up',0)*c('up',0) + 4*c_dag('dn',0)*c_dag('up',0)*c('up',0)*c('dn',0)\n" + ] + } + ], + "source": [ + "from pytriqs.operators import c, c_dag\n", + "up, down = 'up', 'dn'\n", + "n_up = c_dag(up, 0) * c(up, 0)\n", + "n_down = c_dag(down, 0) * c(down, 0)\n", + "\n", + "U = 4\n", + "mu = U/2.\n", + "\n", + "H_loc = U * n_up * n_down - mu * (n_up + n_down)\n", + "\n", + "print 'H_loc =', H_loc" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "with 5 bath sites. Parameters of bath sites in ek and V arrays." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [], + "source": [ + "from itertools import product\n", + "ek = [0]\n", + "V = [-1]\n", + "H_hyb=sum(V[i]*(c_dag(s,i+1)*c(s,0)+c_dag(s,0)*c(s,i+1)) for s, i in product(['up','dn'], range(len(ek))))\n", + "H_hyb+=sum(ek[i]*(c_dag(s,i+1)*c(s,i+1)) for s, i in product(['up','dn'], range(len(ek))))" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-1*c_dag('dn',0)*c('dn',1) + -1*c_dag('dn',1)*c('dn',0) + -1*c_dag('up',0)*c('up',1) + -1*c_dag('up',1)*c('up',0)" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "H_hyb" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Thermal equilibrium solution" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100% |########################################################################|\r" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Hamiltonian diagonalization:\n", + "Z = 1.0\n", + "Omega= -3.236067977499788\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "beta = 50.0 # inverse temperature\n", + "fundamental_operators = np.array([[c(up,i), c(down,i)] for i in range(len(ek)+1)]).flatten()\n", + "\n", + "from pyed.TriqsExactDiagonalization import TriqsExactDiagonalization\n", + "ed = TriqsExactDiagonalization(H_loc+H_hyb, fundamental_operators, beta)\n", + "\n", + "print r'Z =', ed.get_partition_function()\n", + "print 'Omega=', ed.get_free_energy()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Thermal expectation values" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " = 0.4999999999999998\n", + " = 0.4999999999999995\n", + " = 0.13819660112501048\n" + ] + } + ], + "source": [ + "print ' =', ed.get_expectation_value(n_up)\n", + "print ' =', ed.get_expectation_value(n_down)\n", + "print ' =', ed.get_expectation_value(n_up * n_down)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Imaginary time single-particle Green's function" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100% |########################################################################|\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from pytriqs.gf import GfImTime\n", + "g_tau = GfImTime(name=r'$g$', beta=beta, statistic='Fermion', n_points=60, indices=[1]) \n", + "ed.set_g2_tau(g_tau, c(up,0), c_dag(up,0))\n", + "\n", + "import matplotlib.pyplot as plt\n", + "from pytriqs.plot.mpl_interface import oplot\n", + "plt.figure(); oplot(g_tau); plt.savefig('figure_g_tau.png')" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100% |########################################################################|\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from pytriqs.gf import GfImTime\n", + "densdens_tau = GfImTime(name=r'$\\langle n(\\tau) n(0) \\rangle$', beta=beta, statistic='Boson', n_points=1001, indices=[1]) \n", + "ed.set_g2_tau(densdens_tau, n_up, n_up)\n", + "\n", + "plt.figure(); oplot(densdens_tau); plt.savefig('figure_densdens_tau.png')" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100% |########################################################################|\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from pytriqs.gf import GfImFreq\n", + "g_iwn = GfImFreq(name=r'$g$', beta=beta, statistic='Fermion', n_points=120, indices=[1])\n", + "ed.set_g2_iwn(g_iwn, c(up,0), c_dag(up,0))\n", + "\n", + "plt.figure(); oplot(g_iwn); plt.savefig('figure_g_iwn.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Four-operator response functions" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [], + "source": [ + "from pytriqs.gf import Gf\n", + "from pytriqs.gf import MeshImTime, MeshProduct\n", + "\n", + "ntau = 10\n", + "imtime = MeshImTime(beta, 'Fermion', ntau)" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [], + "source": [ + "prodmesh2 = MeshProduct(imtime, imtime)\n", + "g3pp_tau = Gf(name=r'$G^{(3)}(\\tau_1, \\tau_2)$', mesh=prodmesh2, target_shape=[1, 1, 1, 1])\n", + "ed.set_g3_tau(g3pp_tau, c(up,0), c_dag(up,0), c(up,0)*c_dag(up,0))" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "from mpl_toolkits.mplot3d import axes3d\n", + "fig = plt.figure(figsize=(3.25*2, 2*2.5))\n", + "ax = fig.add_subplot(1,1,1, projection='3d')\n", + "\n", + "data = g3pp_tau.data[:, :, 0, 0, 0, 0]\n", + "tau = [tau.real for tau in g3pp_tau.mesh.components[0]]\n", + "t1, t2 = np.meshgrid(tau, tau)\n", + "ax.plot_wireframe(t1, t2, data.real)\n", + "ax.view_init(30, 60)\n", + "ax.set_xlabel(r'$\\tau_1$')\n", + "ax.set_ylabel(r'$\\tau_2$')\n", + "plt.tight_layout()\n", + "plt.savefig('figure_g3pp_tau.png')" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(60.385,0.5,'$\\\\tau_2$')" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(8,8))\n", + "plt.imshow(data.real)\n", + "plt.xticks(range(10))\n", + "plt.yticks(range(10))\n", + "plt.savefig('im_g3pp_tau.png')\n", + "plt.colorbar()\n", + "plt.xlabel(r'$\\tau_1$')\n", + "plt.ylabel(r'$\\tau_2$')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from pytriqs.applications.impurity_solvers.cthyb import Solver\n", + "from pytriqs.gf import *\n", + "\n", + "\n", + "# Construct the impurity solver with the inverse temperature\n", + "# and the structure of the Green's functions\n", + "S = Solver(beta = beta, gf_struct = [ ['up',[0]], ['down',[0]] ], n_l = 100)\n", + "\n", + "# Initialize the non-interacting Green's function S.G0_iw\n", + "for name, g0 in S.G0_iw: g0 << inverse(iOmega_n+inverse(iOmega_n))\n", + "\n", + "# Run the solver. The results will be in S.G_tau, S.G_iw and S.G_l\n", + "S.solve(h_int = U * n_up * n_down, # Local Hamiltonian\n", + " n_cycles = 500000, # Number of QMC cycles\n", + " length_cycle = 200, # Length of one cycle\n", + " n_warmup_cycles = 10000, # Warmup cycles\n", + " measure_G_l = True) # Measure G_l" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.15" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/doc/Documentation.ipynb b/doc/Documentation.ipynb index 66543f4..8f3e67b 100644 --- a/doc/Documentation.ipynb +++ b/doc/Documentation.ipynb @@ -19,27 +19,37 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 23, + "metadata": {}, + "outputs": [], + "source": [ + "import warnings\n", + "warnings.filterwarnings('ignore')" + ] + }, + { + "cell_type": "code", + "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "H = -0.1*C^+(0,0)C(0,0) + -0.1*C^+(1,0)C(1,0) + 1*C^+(0,0)C^+(1,0)C(1,0)C(0,0)\n" + "H = -0.2*c_dag('down',0)*c('down',0) + -0.2*c_dag('up',0)*c('up',0) + 1*c_dag('down',0)*c_dag('up',0)*c('up',0)*c('down',0)\n" ] } ], "source": [ "from pytriqs.operators import c, c_dag\n", - "up, down = 0, 1\n", + "up, down = 'up', 'down'\n", "n_up = c_dag(up, 0) * c(up, 0)\n", "n_down = c_dag(down, 0) * c(down, 0)\n", "\n", - "U = 1.0\n", - "mu = 0.1\n", + "U = 1\n", + "mu =-0.2*U\n", "\n", - "H = U * n_up * n_down - mu * (n_up + n_down)\n", + "H = U * n_up * n_down + mu * (n_up + n_down)\n", "\n", "print 'H =', H" ] @@ -67,25 +77,40 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 25, "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100% |########################################################################|\r" + ] + }, { "name": "stdout", "output_type": "stream", "text": [ - "Z = 2.9840296413\n", - "\\Omega = -0.646637307852\n", + "Hamiltonian diagonalization:\n", + "Z = 2.4900911680955877\n", + "\\Omega = -0.42807983087483964\n", "\\rho =\n", - "[[ 0.27437085 0. 0. 0. ]\n", - " [ 0. 0.33511731 0. 0. ]\n", - " [ 0. 0. 0.33511731 0. ]\n", - " [ 0. 0. 0. 0.05539452]]\n" + " (0, 0)\t0.1804467924204023\n", + " (1, 1)\t0.40159172194678966\n", + " (2, 2)\t0.40159172194678966\n", + " (3, 3)\t0.016369763686018366\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\n" ] } ], "source": [ - "beta = 2.0 # inverse temperature\n", + "beta = 4.0 # inverse temperature\n", "fundamental_operators = [c(up,0), c(down,0)]\n", "\n", "from pyed.TriqsExactDiagonalization import TriqsExactDiagonalization\n", @@ -112,16 +137,16 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - " = 0.390511834096\n", - " = 0.390511834096\n", - " = 0.0553945195228\n" + " = 0.41796148563280805\n", + " = 0.41796148563280805\n", + " = 0.016369763686018366\n" ] } ], @@ -152,30 +177,41 @@ }, { "cell_type": "code", - "execution_count": 4, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100% |########################################################################|\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "from pytriqs.gf import GfImTime\n", - "g_tau = GfImTime(name=r'$g$', beta=beta, statistic='Fermion', n_points=50, indices=[1]) \n", + "g_tau = GfImTime(name=r'$g$', beta=beta, statistic='Fermion', n_points=500, indices=[1]) \n", "ed.set_g2_tau(g_tau, c(up,0), c_dag(up,0))\n", "\n", "import matplotlib.pyplot as plt\n", "from pytriqs.plot.mpl_interface import oplot\n", + "%matplotlib inline\n", "\n", "plt.figure(); oplot(g_tau); plt.savefig('figure_g_tau.png')" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "![Single-particle Green's function](figure_g_tau.png)" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -185,26 +221,37 @@ }, { "cell_type": "code", - "execution_count": 5, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100% |########################################################################|\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "from pytriqs.gf import GfImTime\n", - "densdens_tau = GfImTime(name=r'$\\langle n(\\tau) n(0) \\rangle$', beta=beta, statistic='Boson', n_points=50, indices=[1]) \n", + "densdens_tau = GfImTime(name=r'$\\langle n(\\tau) n(0) \\rangle$', beta=beta, statistic='Boson', n_points=1000, indices=[1]) \n", "ed.set_g2_tau(densdens_tau, n_up, n_down)\n", "\n", "plt.figure(); oplot(densdens_tau); plt.savefig('figure_densdens_tau.png')" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "![Density density response function](figure_densdens_tau.png)" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -221,26 +268,37 @@ }, { "cell_type": "code", - "execution_count": 6, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100% |########################################################################|\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "from pytriqs.gf import GfImFreq\n", - "g_iwn = GfImFreq(name=r'$g$', beta=beta, statistic='Fermion', n_points=10, indices=[1])\n", - "ed.set_g2_iwn(g_iwn, c(up,0), c_dag(up,0))\n", + "g_iwn = GfImFreq(name=r'$g$', beta=beta, statistic='Fermion', n_points=100, indices=[1])\n", + "ed.set_g2_iwn(g_iwn, n_up, n_down)\n", "\n", "plt.figure(); oplot(g_iwn); plt.savefig('figure_g_iwn.png')" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "![Single-particle Green's function in imaginary frequency](figure_g_iwn.png)" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -263,14 +321,14 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "from pytriqs.gf import Gf\n", "from pytriqs.gf import MeshImTime, MeshProduct\n", "\n", - "ntau = 10\n", + "ntau = 20\n", "imtime = MeshImTime(beta, 'Fermion', ntau)\n", "prodmesh = MeshProduct(imtime, imtime, imtime)\n", "\n", @@ -296,10 +354,8 @@ }, { "cell_type": "code", - "execution_count": 8, - "metadata": { - "collapsed": true - }, + "execution_count": 21, + "metadata": {}, "outputs": [], "source": [ "prodmesh2 = MeshProduct(imtime, imtime)\n", @@ -317,9 +373,22 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 22, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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GxsZwOBzY7XYhnJcIQjATgCqOsY3/sfkN9S5Znbpxri9TogUn0UU/Ioc5G1mW8Xq9+P1+Ojo6tLyzxWLRCnLWrVuH2WyO+wK70O3uevYME54g29YnU5ShFNqUZNo4M+rBoFeE5bmWMfomfegkCZCZ8ARwB0LR51EKIEbdATblObT9/sW2XA50TJLhMPHph4/zi4/uojLXwXXlmTx5YpC/v7EMo35h7UZWq5WtW7cyOTlJc3Oz9h6tZA5TnZazGFThHBhQqoPVaFMUBq19hGAukXPlG2OJN9+o1+vXdAS4En2Y8V4IL8RSBTMSiWgtPWr0GAqFsFqtRCIRUlNTKS4uxmQyLdsxL+Z4/UHlc//CI838+H2bAUi3GckoTOVor9IaIgNfeewkEVl57OsdU9jMyiVj2/pkGnqn8AQimhMQwHXlGdhNerauT+Z4v4u/+nkDD310N+/clsczzcO8dmaca8sVq72Ffm6pqanU1NQwODhIS0sLDoeDwsLCRQnnYiLFWOKdjqI+p8FgQJIkYbV3iSAy04tgbn9jf38/AwMD2kVRdQI5V5XqYr8kl4JgJjqCvRhaPyKRiGYE0dLSwuHDhzl06JDW45iRkcGWLVuoqalhy5Yt2Gw2UlNTl1UsF4ta5DM45ef//Ukp8kmyGHhTeQbu6DSSj16Wz7E+F9EfealtHKdXiTArcuxcUaz0YJ4e9mj7tRj13FCZyWvtE9x722bCEZk7f3aEihw7qTaj1pO52BsdSZLIy8ujpKQEgAMHDjA4OLiozyge4QuHw3EJbey281XURiKRi66oTHBhRIQ5D7H5xrlm47Ff8snJSXQ6HQ6H4zx7ix8hmOdnNVo/wuGwNrZMncoiyzJ2ux2Hw0FOTg4bN27EYLi4v1qqI0+6zchr7ZMAJFuUIp9/eboNgOvKM+l3+nn82BB6CQ53O9mYZdMe+49vLeXt9x3iaO8Ur7SNc1Wp4vpzy9YcHjs2RMeYl/s/uIM7HjzMJ3/ZyPWVWTxxbBCXL4TVEH+eODs7m+zsbNra2uju7qaiouKCxu6rYXgwd1v19cqyjN/vFxW1a5CL+1u9QoyNjWkVh+fLN85dSjEYDOftGVsqa7loBhKfw0y0YIZCISYnJ7ViHLfbjSRJWi5t/fr12O32uCOQlWTE5UeSJDKTTMrNoAw6CcY9QQpSzfRM+olEICfZjMWgwxeKYDXquPOyfB4/NqT5x7YMuQGwmw0zLU7AFx9p4sfv38quDSns2pBCXrKZ/ccGeeBDO7nv/dv4+C+OAjL+UIRnmod455bsuE3UdTodZrOZTZs24XK5FmTsvpTB0/EK2nzRaexrVitqDQaDtnQruLgRtzbAxz/+cU6ePInP59OiSHU5NTbnMPeENhgMCY0AV+ILlMjnWIkRXMslyOpUiu7ubpqamhgeHub06dMMDQ2h1+spKChg165d7N69m8rKStavX09ycnJcYrkaPZ7vvv8wb7+vDk8grC25FmUo1a15KYrIvNg2hicQxmxQLgveYFjLdQIY9RLd414AbEY9kx7lZlFGiTg/95sTnBycRidJvH1zNq+fmWB02s++4nS+957NtI96sBh1PHZ0YNnaQxwOB7t27SI3N5cjR47Q1tY2byvTcg6eXo5thdXe2kQIJpCcnMz09PSijcYTvWS61rlYi4oCgQBjY2N0dnZy/Phx6urqOH78OGNjY5hMJoqKisjJyaG8vJyKigrWrVsXd3XmSnOuc9cdCOMJRPjmk63aQOi8ZAvl2XY6oyI47g7ynWfblJARONTtxBl9bIYFgmGZMbcikjaTXvtbus1ISaaNJLOBTz18nI4xDzdvySEsy/zh+BAA11dmc9e7qvEFI9R3TdI17lm2MV2SJJGdnc2+ffswGo0cPHiQvr6+WefGxbAkOx9zhVMMr764ufivACtAUlISLpdr0dsJwTw/q70kq/Y4joyM0N7ezrFjx6irq6OpqYmJiQmsVisbN25kz5497Ny5k7KyMnJzc7W+ubV20Tqv+Xo0Z/nH5hH2R23qHBYD15VnMOwKAPC26kx+3ziEx68I4YH2Sa3IJ9MqsXtDsuYjazPptb9dV57BoW4n//4XlQB84qHjWI06NuU52B9jvP6u7ev4zNXFAPz+6OCyR3yxxu5TU1OzjN1XQzAXsww8tzCot7dXWO1dhAjBRIkw4xXMtexko5KoL+VKLsmqPY7Dw8OcOXOGo0ePUl9fT0tLCy6XC4fDQVlZGXv27GHHjh2UlpaSk5NzlltO7L4TyUpeCNWcJSj+sPe/1gMoy6iq0TrAe3auY2dBMuoq7MHOCUZdio+szSDxn++u1h47OOVj0qtEmzdvySYsQ9PAND963xam/SE+8dBx3lyZSdOAi9PD09p2X3jzRi4vSWf/8WEiLE+EORej0UhVVRVbtmyhq6uLhoYGzbZusSTSOGQ+1NRPW1sbgUBAq6gVXBwIwWRpgrkSEWaiRSeRgpmIL7s65Njv99PZ2cmRI0eor6/n9OnTuN1uUlJSqKqqoqamhm3btlFSUkJWVhZWq3XBQrhWzNcXgi808xn4gmF00ae3m/RU5yZh1Cu/SDIb+NY7yrXHBsIyx6NG7HajRLrdpEncPS92KsOhgW35KVTlJPHE8SGqcpP44W2bGZzy89QJpbo2drwXwIcv28DIdIC6gcUXzC0mFxlr7D42NkZ3d/eii/RWWjBhdjuKWhgkhPPiQAgmSuGAOgJpMSS66AfWdmvJcuz7fEOOI5EIKSkpbN68mZqaGrZu3UpxcTGZmZmYzeYlPe9aXJKN5S9+coh/2t8CgDNanJObbMYbjLA9X2nBONztRJIkbEalcEkngcUwU8Rk0ktaVazNCP5QRFuS1QGPHx/CbtJh0Em8Y0s2TQPTtI962FmQwt1/WU3HmJcki4H9jYNEIjPv5dWlGRSkWnj6jHfRryueateMjAwyMjKw2WzU1dXR3d294PNyNQRTfc7Y/GY4HBbDqy8ChGACKSkpF22EuZZ7JRebw4xEIucdcpyVlcW2bduoqalh8+bNOBwOkpOTE2YAcDGYIsRL24iHx48PUd81yXhUMDfnObAadYy7lZzlsX4XT54YxhANOU8OTmsFQTaTnkBY1gqCzHqJKe9MdFaYYSMckfEFIwxO+blpUzY6CZ6IFvlcVZrOd/+iGqc3xJDLz2tnxrRtdTqJ23bm0Doe4lifc1GvaynjvfLy8ti7dy9+v5/a2lpGRkYW9Hwr3TY0tx1lvopaURi0OgjBJP4l2ZXok1yJCDNR+z/fhS0cDuN0Ount7eXkyZPU19dz+PBhrboxLy+PHTt2sGfPHjZt2sSGDRtIS0ubZQiwVpdNE7Vv9b0Ix0RzX/7dSTrHlKXTNJuBKzem0xWdRrIx08a3njqNP6R8/gc7J3H6FFHMTjKxIc2i7cuiR6uKBTg1NE1Zlg0Z+MRDx9BJcHlJGk+eGCYSPY6bNufw9ZuUJd5/2n8St39m+7dXZ2IxSPziYM+iX+NSioVUY/cdO3bQ39/PoUOHzru6FA6Hl2Xw9GI4l7tQrHAGg0FRUbsKCMEk/iXZlSDRgploA3aYPeS4qamJ+vr6uIYczyXR0fFavBBJksSUbyYSdPpC/OS1bgBSrEauK8/AH81pfu6awuiEkqhXbPuE1ltpN+v5/q2btP2EZbSqWICIDBOeEFW5SfQ7/XzqVye4viKTgSk/h7tnosYP7t3A7g2pDE75ec/99fRNKhGr3aTjTUVW/nhiiJFoYdFCiFcw5y7lWq1Wtm3bRmlpKU1NTTQ3NxMIBM7aLt7+zaV4HF/Ijk9Y7a0eQjCJP8JcCRItaMstOoFAgPHxcbq6ujhx4gRut5vGxkZGRkYwGo0UFhZqBgAVFRWaAUA8d/GJjjDX6gVoZHrmwl+QauHMqCJSqVYjV0ft6wDWp1r515srtLzkuCdI04By45hkNlCabccSNTF4riukiZ1Ogs15SYy6A2xIs3L3u6s4PezmscZB7Ca9tiyr8s2blXaTngkvt/6kjsPdk8iyzE3lSQTDMr8+3Lfg17aU9pD5BEw1dk9LS5uVG4/dLp4l2aV40C5mBqd6norCoJVBCCbx5zBXgot5ZqXf72d0dJSOjg6tx/HEiROMjY1hNpspLi7GZrOxa9cuysvLycvLIykpadmKKNaqYCZi3/e93MnglBKpjUYF027S0zPhpTBdcfKZ8ARIsRqxGpX332rUsXPDjAerToLGPmVSiSM6lUStAXIF4Ycvd0W303PzlhyCYZkIMleXZfBvt1TQ2OfCbtbz7MlR+odGGBgYIBKJUJqdxBUb03GYDTjMBj784GH2nxghP9nI1WUZ/Kq+l0BoYedgIgZIq8bu+/btQ5ZlamtrNWP31ejfXIzYxk5BikQieL1enE7nmr3Zu9gRgsnSlmRXYmblaucw1R5H1QCgsbGRgwcPcvLkSZxOJ3a7XetxnM8AIFFcLNNKVpveCS///Uo3n/j1KSKyzHjUjWdvUSphGdKsRgB+2zDA6HQAU7SNZNwT1Ip8or/i1KDyPUi2KoKpWuPl2iVNkK0mHTdWZwHKAOmxsTGq7B4+utXGsCuAOxDm6RPKFJ/a2lpGR0f50N4CxtwBPnFVETVFafzrn7r4nwYn79+Tz8h0gKebZ0el5yKRAqbX6ykpKWHXrl2Mjo5SX1+Pz+dbtSkni0FdpvV6vZw6dUpY7SUIYb7O0pZkVUFLVOn5SucwVXFUDcddLteyDzleLhLpJLTar20xDEZzgIOuAI+06CgvVARz63oHJ/pd9DmVv3uDEf5h/ynUa2h91yRXlyrGBWk2I9P+MC6/cq7ZTHr8oYhmYjDkkdlXlMLrHU5c3hDNzc0AtA1PMzo2TmpKMp94czXJGaN874VOHmrycOf12yksDCozLMNhClItPNrQz88/sov/7/Fj/LZxlPFQD4XpVn5e28MtW/Mu+FqXkhtc6HZms5nNmzfjcrmor6+nra2N6urqcxq7z8dKRZjzPa9q5K4OkhAzOJcPIZiAxWKZN+G/EAwGA6FQCKPRuMxHpZDICFYdXzY2NsbExMSsIccOh4O0tDQ2bNiwqnMbz0cinYTWUvSqRpQAj7X6eJtBWVbNsBu5tjyDRxoU44C/uqyAH73arbWRvN4+wfb8ZECZPvK5a4v4/548DYBJB90DM20XYRlGJ13oJPCHZX7eqvzeG4IxQyYVOWkAfPTyDbzcNs7hnik+9NPD/OgDO9i+fTvj4+Nc2XqCh085aep38oWr1pNjifDjQxMkWwx0jXtp7HWyLT8xY7riweFwkJqaSlZWFkeOHCE7O5vi4uIFiVmiPWjPRSgUmjUsQpZlbXi1OkpMCGf8iCXZGOK5iK1EBLgc+z/XkOPJycl5hxwXFRWRkZGxLGK5FkVtLbWsxApmilniuRal5zHNZuK68gzNFu+mTVm8Y3M2oegvjvZO0e9UWkzMepndaQGi6U2eb+qna3BU22+2VWLYp8Ok11GQZuFApyLKVqOOP5yYvZz6nXdVoZPgeL+L99xfT+vQNOnp6XzpXZdhMUh8/49HGR0d5cbSJH56x06tdeXuP7dd8LUuJcKMB1mWycrK0ozda2trzzJ2n4+VXpI917axFbXCam/pCMFkaRewi1Eww+HwvAYAPT09hMNhcnJyNAOAdevWkZ6eTnp6ekKi5EQLTyK//Gsl/zMZbSORJEi36DRBdFgM1BSmanZ2NpOBz19doG0XkeGZw2cAMBHBbDaTZlPOgU6XzNM9M9+LPbl6Jr0hZGRKMmy8fZOSw0y3G/nzqVE8gZlzNDfZzA2VWViNenzBELc9UM+fTw2TbDXylzvXUzcUYWBimv7+fsrTdDz6yb2k2YzUdU7QO3F+95+Vdt5Rn081dt+zZ49m7D4xMZGQ40yE2MYWBomK2vgRghkl3gv7agumOuS4p6eH5uZmrcexv78fgHXr1mkGANXV1RQUFJCamqoZAFzMVbgL2fdaiQLnspTjfu3MODu/8wovtiqRpNo7uTUviU5nmMLonMvfNQzgdjmJdoZw4lgDx5uatf0Y9RIDQcVCMCfdQW5uLrro685NNvPMyZkI8/I85SIcjij5zSs3Ku0pfZN+vMEIz7XMPBbgA3vW4Q6E+fC+DWzMsvNgT26mAAAgAElEQVTZh4/x3y+184E9+QTDMvXjZrKzs2ltbWWit42HPrIdg17HfS93nPe1r3SEOVf4TCaTZuze0dFBQ0MDHo/nrO0ulggzFmG1t3SEYEax2WzznvgXItETS2IFZ+6Q47q6OhobG5c05DjRfZ6JLsx5Iy7JHuiYIBiW+doTp3B6g7iila5XFSrOO26Pssz6+PFhnj7Woz1fSkEFhWVVACSZ9QTDMp1j3ujPyg3UdDRSnPaH2JHv0J4zxy5h0kuEIzJWo05z/bmpOhOAH7/SNesYt+cnU53n4PHGQX7+kZ3cvDWX7z/fzg9e7ODyknQebxrHYLKwe/dusrOzGWg7wdvKHPy+YYDu8XN/D+Pxkl0K54oU7XY7O3fuZMOGDTQ2NtLS0jLL2H21cphqkc/5EFZ78SMEM4rD4WBqamrR2yXKgF0dcjw8PMzw8PCsIceqAcDu3bvZtWvXkoYcX6xDnhfCWhXMpaKaqU/5wnzhoUN0RYtzim0B0i0S00FFIEszrfzw8DShsPI6XjkzobWRpFmN7C1K0fKbVqOeiCzj9quCGaYww6Y950u9yu9llGHUU1HXn2/dXMnGTBtdEz7+cf8pgmHlXJIkiQ/tLaBtxM3R3in+/d2b+PINpTzdPETPhJcxT4jXut1IkkROTg779u3jPZuS0Ukydz9z8pyvfTVymOf7TmVkZLBv3z7sdvssY/eLbUl2PoTV3uIRghkl3l7MpS7JLmTIcVJS0qwex+U0AFjr5u5rpZI1XmKX3NVVhd7hGSPzw4NBxoJKYVZpUQG780x4o70g/3ZLJaGwTASQgBdax2aZq8fOt3T6gkz7w5rrj92k53if0mpl1Ev84mSQQFR4eyZ8OH1BHGY9ZoOOH962GQl44vgwn3r4uLZEfNOmbNLtRn5W240kSXz8yiJ+9P7tjLn96CR4uHEmB6jX69mzpYLbd6/j6VMTPPFSHW63OwHv6PIjSRL5+fns3bsXn8/HwYMHcTqdF92S7LlQhTMUCnHo0CFhtXcehGBGcTgcCZ9YEs+Q46ysrISWgq91wbyUxDgcDs8Sx/r6eo4ePaotuaurCkbbzFJpVW4SvdE+S7NBx548kyZ6pdl2vnJDSfT1QMeYV5thaTfrSbEaybIrRT5/OjlCfdeMgF1RkkbnmAeDDnIcZkpTZy4V7aMeJtxBkqOGCOtTLbylKguLUUdDj5Pbf9pA67Abs1HPbbvyeaF1lJ7oMuu15Zk88om9OMw6uiYDfO2xZvzBme/Pp68pxWLU8WyfgePHj3Pq1KklpzxWKio1GAyUl5ezfft2zTs5npvw1cx/hsNhYbV3HoRgRklOTo5rSfZcOUx1yPHg4CCnT5+Oe8jxahcVLZVEitpaLfpRiy6cTudZxVqqOG7YsEHLR0up63l1AG1VwR3NM2YlmUizGbW+Sm8wTFXmTKWzUa9jZ4HS16guvR7tVc5xNWdpNSkXV6NOx9f2t2rbXl+VSVhWjtVu0vO+ypm8mC8UoWPcQ4pl5ncf2LMOXzDCHXvzCYQifPDBBp5tHuZ9e9ajlyR+WderPXZjlp0fvrMQo07ikYZ+bv7vWl5tU6LmjCQTH9xbwJ9ax8ko3kRSUhK1tbX09vbG/VnHa6AeL1arldzcXHJzc89r7H4uVnM5VzU9iK2oFYVBMwjjgihLWZINhUJMT0/PcscJh8PYbDYcDgcZGRkUFhbG1dO4lgdIq/tfi3nG5dx3OBxmenqaqakpXC4XY2NjOJ1OUlNTcTgcFBQUYLfbz3mR/OcnWzkxME2G3cSbKzPxRgXzxqosfnOkH4dZz4Q3xL/9qZMv7jQhoeQawxFZKwgyRgt2mgaUVZQks3JRVT1cM5JMuANhTYy3r0/GYtQRDEWwmfSEIsFZx9Q97p1lMrA9P5mq3CRePD3Ow3du54uPnuTzvznOX19Xwluqs3mkoZ+/vq4Ee1Sos+0G7tydyU/qRvCHIvzVzxt426Yc/uGtZfzVFYX8sq6Xe1/q4Pvv3UpOTg5nzpzh4MGDcUWbqzUE2uFwsHHjRgYHB6mvr2fdunUUFhZe8FhWM8JUC4ZijQ9CoRChUAiDwaAJ6hsVIZhRFhphRiIRTRynp6eZnJwkEAgQCoVwOBxkZWVRUlJywUq1hbKW2z4Svf+LcUlWFUeXy8XU1BRut1LYotoKFhQUoNPpyMvLIyXl/K42Kqpd3deeaGHTOgfeYAQJeFNFBr+o78MQVn6u75nmEZtVW5I92juFL7rcuS7ZzIArwGjU5MAWjSzVffdO+vjUlRv40avKKDAlR2lgJBhAp5OYjtFLq1GHOxBhOmaMmCRJfGDPOv7piVY6xrz89EPb+Jen2/jBC+3sLUrD5QvxeOMg76/JB5QVmHdtzuDRJieF6Tbes2s9P36lk5fbRvn8dRv50N4CfvxKJ6cGXVTmOqisrGR6epra2lqOHTtGeXn5gq3qVkMwVbtM1dg9Ozubzs5Oamtr2bhxI9nZ2ecUntUSTNUlKJa5wvlGt9oTS7JR5sthXmjIcW5uLtXV1aSlpZ1zyPFSSfQXfS0LZiKjV7hw0c9850dDQwMDAwNaIcjcNh+Hw7HoC40qer5QhL/7/Ul8wTA6ncSOghRSrAZ8wQhGvcTbqtL5fctM439skU+KzcjfXFuk/c1siFbFxhgOtAzPrLB84bfNmvBOeoK4gzPvxaevKgTgWP8097/Wrb1Pb63OJt1m5Jf1/ZgNOr7zrmr+4cYy6jonsBh0/PT1LiLRtWFZlrGZ9HziykIOdk5QU5TGk5/dx86CVO56upUXWkawmfTc+2K79rxJSUnacueRI0c4c+bMgm4m421FWcq5NXcsmF6vZ+PGjezatYuRkRHq6+txOp3n3PZiq7CdO4PT7/dr+c43EmtGMJ9++mkqKiooLS3lO9/5zll/f/DBB8nKymL79u1s376dBx54YFH7NxqNnDlzhm9/+9s89dRTZ1381q9fz86dO88acmwymRIaASaalchhroVl0/n2HYvqnhQrjkeOHKG/v3/WEOy5PbDLccMTiLZqGHUSR3unmPKFMOgkDDqJa0rTichg0El85U0byLYrz2fSS7zQOsqUNzoQ2qTngzXrMUbHkhzsnBkWDVCaZaOxV7lhNOgknN4Q4+4AOgmGXH7cgZn3WfWfNegk7nmxk7/7/Sk8gTBmg45bd+Tx0ukxeia8SJLERy4v5IEP7QAJuie8/PAlRQDVvOLte/LJcpi45/kzFKRZuf+D27nnti04fSE8gfBZxUiSJJGdnc2+ffvQ6XTU1tYyNDR03vMgXgFaSrHQuZ5TNXavrKyktbWV48eP4/P5znpcooZPnw912fV8vNGt9taEYIbDYT772c/y1FNP0dzczMMPP6xNS4jltttu4+jRoxw9epSPfexjF9zvvffey2233caOHTu4++67aW5uJj09nerq6gUbACTauCDRrOUIM1GCqc4VnJqamiWOfX3KoOO5N0/LKY7zEQgpr9EXinBtWbrW3gFwVdRxR5LAYtDx3irF5SciQ/eEj85xJeJ0mJXcU3rU+q5txMNdz56Z2U9pOuOeIBLKcu29791ERFb2M+0P0x/jJaC+56GIzDs2Z/PsyRHu+L+j9E36eO/OPPQ6iV8d7tcef2VpBr/9eA16ncS9L3bwyV82MDAVQJIkLEY9n7qqmPquSWo7JpAkiRurc/jj5y7jgzX56CT4wQvtZ33OOp2O4uJidu/ezfDwMIcOHTpnDUK8RT+JjPSSk5PZvXs3OTk5HDlyhLa2tmW5cV3JHs43otXemhDMuro6SktLKSkpwWQycfvtt/P4448veb8VFRV885vf5NChQ9x3331UVlbymc98ZkGJeZVEO+Ukmje6YEYikXl9d0dHR5FlmXXr1p21snAh96SlHvcd/3eUr/+hRfs5FJFJsRiwGnVkJSlWdv5QhO5xL5vXKy0msqwIgt2o17YBaI7Ot1SrYvXRitr8VAtPN89MI7mmNB2dpAyRtpn0lGXbZx3TmcmwNnha1et0m5F+p4//vn0z/U4ft//vEbonvNxQmcnvjw7i9s/cSJbnJPHVG8sAONA+waef6Ofnh4cJhCK8Z+c6cpPNfP/5M9r7kmQ28PW3V/IPby3nYMcETzUNz/temc1mtmzZQllZGU1NTZw8eXKW4w4kdobmUraNjZYNBgO1tbX09/cv+ZyONzpdSIQ593lirfZ6e3vxeDyX9DLtmhDMvr4+CgpmTKPz8/O1u/1YHn30UbZu3cqtt95KT0/PBfd7ww03UFlZiV6vj3sm5ko5wqzF9glIfA5zMftWJ7bMFUe1ZSEvL0/z3S0sLCQpKYmUlJQliWM8NPZN8VjjELUdylJkKBzBatJzeUkaL0XbLyTgS482Mx0t2vGHlUZzTzTXmJWkVGS3DruRAEtU7FSTdE8gzJvL07XnzLSbyLSbiMhgMShLsrH0T8uYomKrVtZeW5bOkZ4p0m1GHrpzB2k2Ix//5TEyk0y4/GH2HxuctY/bd+eTm2ymNMvO7nVm7j84xM3/Xcvh7kk+dXUxDT1OXmkbm7XNB2oKqM5zcNfTrbh8s4UwltTUVGpqakhOTtYcd9TvTLw5zJXKJep0OoqKitizZw9OpxOPx3NeY/dEEW90qgpnT08PgUDgkrbaWxOCuRBuvvlmOjs7OXbsGDfccAMf/vCHF7V9SkpK3EOk17LoJJrVymHOHWcWO7ElEonMEsfq6motJ61eMFbTfF3tmfzy704yOOUjLIPZIHFdeQbDLqWfLzPJRMuwmx++1AkoLSRto16moy4/1blJZNlNmnuP1aRHlmWmo1HfuCdIZe6MAcKjjYMkWw3I0ed3emfEaXdBMjIzFbVqTvUt1VlYjToeOtRPUYaNh+7cwZUb0/l5XR+pVgM/q+2Z9TpNBh2fvrqYpgEXN2xM4u5bSpBlmTt/1kBt+zg5DjP3zFl+1esk/vntlQy7/Pz3i+3nFTA1l7x37168Xi+1tbWMj49ftBHmXEwmE5WVlVgsFjo6Ojh69Ghc/tbxMl+V7GK3N5lMl7TV3poQzPXr18+KGHt7e1m/fv2sx2RkZGA2K8tVH/vYxzh8+PCiniPePsyVINGtJYk8oVdiSfZ84qiOM5s7seVCkeNqma+rXqygeLb+7e8UX1WLQc81pRlEgzzSbUY+fkUBL54e1x7/crtTizCTrQb+9ZZy7W/+UARfKEI0OMSol7QIFuCnB3qZjOYwp/1hrboW4C1VGeglUI+svmsSgHUpFm7ZmsNTTcOMuwMkmQ3c895NfPyKAia9ITrGPDx5fPaszHfvWMf6VAsPHXOytzCZJz6zj7++roTnW0eZ8AY43jfFc6dGZm2zvSCFW3eu42cHe+mfvvC5ZDAYqKioYOvWrXR2dnL69Om4vj9zK10Xu228Im00Gtm5cycFBQWasftK1EksxLj9fKiveW5F7aVktbcmBHPPnj2cPn2ajo4OAoEAv/rVr7jllltmPWZgYED7//79+6mqqlrUc8S7JKuSyJNhLedJl1sw1T7Y/v5+Ojs7GRsb4/Dhw3R3d2viuH379rPGmcXjr7kaX/CpmMhufaqFY1E/V6tRR6rNSGVOkvbzZ68uojRLMUi3m/S8fGZSa/+wmwxcVpKOKVoV+3jjIKeHZ7xZd+ancGJg5gbxhsoMRt1BdDqY9AYZdPm1v9lNeqzR66gE/LxOKehxmPW8f/d6AmGZR48qy686SeLz1xbznXdWAPCV353g57XdhKI3AmqUeXo8yIEuF2ajns9dW8KTn91HTVEaAF/87XF+Wdcza8bm315fis2k52fN/gV/LupEkfT0dIaHhxddWKP2UsZDvMubsdupxu42m42DBw9qxu7nYqmORksVTJh9Mxjbw3mpFAatCcE0GAzce++93HjjjVRVVfHe976XTZs28Y1vfIP9+/cDcM8997Bp0ya2bdvGPffcw4MPPrio5zAajXFHcZeCfV2iWIpgquI4MDBAa2srhw8f5tChQ3R1dREKhcjMzCQ5OZk9e/awadOms2Z9LoWVFMzJGJGciOYOzQYd3eNe3lyRAYAnutS6JVrko9NJ6HUSN2/JBpRl0tYRL2Me5TxRC3Qs0SIgX2gmWgUl/+gPKYYHZoOO776rCp2kzLuMyFDXOdMjaDPqichojy2PFgT9y9Nt5DhMXFacyq8O98+Kjt++OYePXVFIWIZvP9XKrT+po6FHiUzftT2PHLue+2sHtPd4Q7qNBz64gzsv20AgLPOtJ1u45j9f4bvPtNIz4SXdbuLz1xZxcizMkydmR60XQjWMUAtrBgcHF/TZLtXwIN7K3FihlSSJgoKCWcbuo6Oj8267lApZWPqS7HyoohlbUbuWRXPNOP3cdNNN3HTTTbN+961vfUv7/1133cVdd9215OeJp/dKFbTlNCyYb/+JJFEG1QsVHtV7d669oN1uP6eDkt/vZ3Bw8Dx7XRorkXt9pW2cz/z6BJ+6cgOfvaaI8WklR7k9P5mDnZMUpCpuNmdG3HSOeSjLUsRKLfZRq2OD0dLVPpciuNaoUIajIlad56BlcCbC3F2YitmgIxiOaK4/EVm5g44ABzpmlnpNeglvCBwWA1O+EJvz7HSNeXixdYwP/t9RPrBnPd/842meaxnjrdVZ2nafvaaYx44OkGY3Mu4JcvsDh/jLHev48g2lvKc6iXvrnTx3aoTrq7K19+XvbyyjecDFif4p9hSl8X+1Pfz0QDdvqsjivduyKEnV851nWrm2LJMky8K+b7Iso9frKSoqIi8vj9OnT9Pd3U1VVRUOh+Oc262mQ9BcVGN3r9dLS0sLXV1dVFRUkJSUNGvbpQjeUra/0HclVjTXMmsiwlwJliIWl0KEuZKVrKo4xkaO9fX1dHZ2EgwGycrKYtu2bdTU1JzXQeliHvK8UE4OKkuu97/WTcvQNOPRaLM82876FDOHupVIT6eT+FJMhDjmVoTVFS3i2bVBMRMYiOb4LEYdEVnWItPOUS8fu2Km0lxGJsehVMWa9ZKWszQadNhMeiY8IS1fKssyMpAcFaimATeZDjM/et8WRqYD3P1cO1lJJh6qn125bjXp+fhVRZwedvOtmyv56OWFPN44wFt/8Dq+UJiCVKXIR3X/AeV9/8bbK/CHIqRajTz/N1fwySuLONw9ySd/3cx0UGbUFeC/nj/DQoldqlSNAyoqKmhubqapqemcxuirJZjnEy2r1cr27dspKSk5y9h9OSLMeG/6V+O9Wg0u/Ve4COIVjrVukJ7IHKkkSVokGCuOHR0dZ4nj5s2bF2UveDF6yS4WVagiMnzxkSaGppTcYbLFwHUVmZwaUqLCq0vTaRt28+hRJVc/7g4y4QlqOc+awlTyU8wEom+HxajHHTPf0ukLaRWyAP+0v0UzQg9FZK2NJBiO8PZNWdoxAdr4LYNeItlioGPMQ7JZz2XFaTx85w5yUyyMTgdo6J2iqX+2H/Ptu9eT5TDxwKtdfOUtpTz26b1U5CTxQMM0ERlahqZ59uTsHsvS7CQ+fNkGHm3oZ3DKzxevL+WlL13JP7+1BKtBQgZ+cbCH5oGFTRea72KekpJCTU0N6enp1NfX09XVdda5dDEKpkpaWho1NTWkpqbOutlcimCuliXfWkIIZgzxVsoaDIaEVrGtFUGeb6RZS0sLTqcTv99PZmYmW7dujUscz3Xca9F2D2aWsLSlVaDf6ed30eKZZIuBN5VnaAYEFdlJfPqqQk5Gl1Vl4KXTY5rQWYx6vv6WDdr+u8e9sypdrUYd9V0zeckzox46Rt3oJKUaN1a481IsZCXNjAn7r5eUCvVwWGZDmoVAWNbMCwrSrPziw9u5pkzp6fzCI800d/TT3t5OX18fZoNulpNPWXYSP/vILv56t0ObuvL1/SfpGJ09LPoz1xSTk2zmm0+eIhyRsRj13Lw5i39/czo//sA20u1Gvvxok7aP83EuIVCN0ffu3UsgEODgwYOMjY1dcLtEspjKXEmSWLduHfv27SMcDnPs2DH8/oUXRZ1rn/GwmOh0LZu2C8GMweFwxD0Tcy0vycYjmLIs4/F4zpr32dHRgd/vJyMjgy1btrBp0ybS0tIoLCwkPT0do9F44Z0vkNUY8rwcxF4wXDFR397iVNrHFCu7FKuBHQUpmA3KVzTZauCTV20gx6EYEthMep5vHdMKhiwGHVvyklD3/PChPl47M5OHvKw4jZahGVH67l9U4ota7nmDEdpijNetRj1p1pnPaSiaV3UHwuSnWjDoJEZcypzEsbExhvt7+FhFmLIUiSFXgA/9uo0nzwSYcLqoq6vjLaVJs5x8JEniygIzj31yJ1eXZTDlC/HWHxzgU788yqttY8iyTJLZwFdvLKd5wMWvDimzNFUxubY8i//4y82cGXHz3WdPX/D9vpDwGQwGysrK2LZtG93d3TQ0NODxeJbkQRsv8VTmqsbupaWl+Hw+6uvr47qOLYWlLOeuJYRgxjDfxJKFcDEK2mL3f77jV8VxaGholjieOXMGn8+niaMaOcaK48VujXe+fSeCY31TvN4z04zuiUaYBWkWRqeDrEtReomHpvwYdBK5yYpAWo06dJJEVbStJBSO8Hr7hCaYVqOyrK6+Gxl2I9/900ye7/rKTEIRGb2k7OvGqmwsBklbdn2pbUZcbSYdwYisifVf7c0FFLODrlEXOmQmvCH2v3qU8fFxrFYrZWVl/PjDNZgNOtJsJn5SN8xXnp9g2r6ervY23llqpqHHyatREZdlmWSLkZ98YLt2Y3C018lf/byBm+49wC/reri6NJ3LStL5r+fOMDYdmFWYdvnGDD56+QYeru/l+ZbZfZtzWWhBm81mY8eOHWzYsIHGxsZZrWqLYbWWNtWxcZWVlbS0tJzT2D0RLEQwRR/mJcZShkhfKhFmrDi2tbXNEkev10t6eromjlu2bKGoqOi8kWOiBTNRJEqMv/LYKf7faxO0jCii6Y7mB99anUXrsJv8NKUq9n8O9DDs8pMajfQGorlNb9R5IBiW8YcijESjP4tRpxX4AGzLTybNNvOZ7CxIxmrUKa4/Rj3hiIwvJGvtJ6+emTExsBh0THmDOEzK+3uqS2nj0ElwcsRPIKJMKjkynUxZWRk5OTnYbDayHGbet3sdI9MBvvG2MkIRmc/89hS/7DBzTUUOGRaJ/3j6JJFIRCvEkSSJf7mlinBE5k0VmXz33Zuwmw1KW8ndr5LlUAZb/8efT58lfF98cylVuUn842PNjMT0jc5lsQKWkZHB3r170ev1dHZ2LtrfdbXHc801dl/IGLSlnusLjTDVz3ytIgQzhoUOkZ5LoieWJEowZVnG6/Xi9/vp6emhoaFhljimpaWxefPmWeKYkZGxqGXV1TIAWCqJOm61Gf8fn+rG6Q1qObi3VSutFYNO5cLvDyqzL9VxXKeiJuquaK5R7b+MzWGq1nUADT1TfGjPjBtWz7iPrCSlKtakl7T96HUS+SlmLVcK0NfVjtMXIsWsQwLOuJXPW5Zha7QP1KSXeOrEsFatq3LnvnzMBh2Huif5w2f28fnrSni+ZZSPPdrOzqIMTo34uP8PrxMIBLQLZ1l2EnfsK+DRhgGKM2w88okafvPxPVxbnsUfjw8Rjsj8rmGAn7zeiytmzJjJoOM/b92CJxDmq481z6q2jSUeAdPpdKSmplJSUsLk5CR1dXXnnF85l6WI3lLchWKfN9bYXa/XX9DYfTUrbNcSQjBjWErRT6IjwKXuXxVH1fFEFUfVNsxut7Np06azxNFkMi352Ndi71WiBFNt7h/3hPnH/S2aYG7MslGaZWPMrSyxfuaaIo70TNERzWke73fN8oK9oTKT9SlmbUnVYtRpBUQAo+4gPZMzy3Ff+l0z+qhA+YNhjp1qAyAQDFOdDobYK0HKekIRpQXDZtLTPenHpFMKjXYVpGivIxiR+f4LHbNeX7rdxPt2r+epphF6Jrx89toSnvzcZewrTuNPp0Yx6CQeaQe3282pU6e0lojPXltClsOkFflsy0/hP2/dzAtfupJPXFmIToL/rRvijt8P8O4fH+R7f26jrnOCgjQrX72xnFfbxvj5wfkHLizFps5kMlFdXU11dTWtra2cOHECv//c0exSng+W311orrH7wYMH5zV2X6rgiSrZNyDx2uOtxJLsYkQnVhzPnDkzSxzdbjepqamaOG7dupW0tDSSkpKWLI7zsVYFExKTcwlFy0uTLXpebhtn1K34t+okiTeVZ+KOCugNlZm8b/c6TUDH3EFahtza360mPX93fYm239qOiVmCaTHoaOhVIiIJMBCma9yrVMUGI+htSqQYkmFDXjbFmTZt2x9EDd1lZDLsxujxzX4dX7lhIxaDjt83DvGP+08xHhNpfmRfPlaTnntfVMS0IM3Kfe/fzo/evw2HxUD3hI9/OaLj2KSRAweVySJ2k56v3lhOU7+L3xye6efMdpj52xvK+N87diIBpelGLAY997/WxYd+epi9332Jl06PUJ5t59+fPc2pwbO/v/GacsSKgMPhYPfu3WRmZnLo0CE6OzvPeV6v9pLsfJhMJqqqqti8eTPt7e1nGbuvVIS5lpdjQQjmLFJSUtZclexccTx69OgscUxJSaG6uloTx+LiYjIzM2eJYyLN3deqYCbqi60ufTp9Ya4uTccdCKM+1ZvKM7THWQw6/u76EgxRpZKAF1rHtCVds0HP5nXJ2uP/90AvzzTNWMZtSof2EQ8GSYk+//eD20BS2kYCYZlet7LfiKzkNNNtM+eDuuzaO+EjyWwgw25A1eJI9CaiMtfBf91aDcCTJ4Z5x48O8VB9H6GITJrNyAf2rOPp5iFahmZWbK6ryOK5v7mcbIeJYU+Ebz/fz9dqI/y0bpCnX3qdK/LN1BSl8b3n2mYJMMBlJem8f0cWbeNB7rx8Awf//hruvX0rt2zNpW3EQ+uwm2BE5tMPNTLtm50eWa5pJZIkkZuby759+wiFQtTW1mI72GMAACAASURBVDIycnbB0UoNcY5n26SkJHbt2kV+fv4sY/elRphiSfYNyFKKflYihynLMj6fj5GREU0c6+rqaG1tZXp6mpSUFKqqqs4SR3WKy/n2vxYrWRPJcg2n/tyvT8wSjbAsk2ZRvnbVuUobSESGfqeP6pi2ELNRj1Gv0ypVjXqJP7WM4o0W9gS905zunFmCLE6W2N8yE13dcXUlIVnJUVpNekpzU7Th0QDPnJzxI7WadPhDEexRi7xbdyhVsS5/mI4xD1aDTqu+Ve1iU6wGrtiYzmXFqTjMBiqy7dz17Blu/58jNPQ4+fDefOwmPT98sX3We2I3G/nee7YSkZVCp8pcBw8dn+LLL/n40m+PcVl2GLc/zN1/bjvr/fzI7kzKMkz80+Mn8QTC3FCVzTdvruLPX7icZz5/OR+syWdoys8XHzmumb2rn8NyjvfS6/WUlpayY8cO+vr6OHLkCG63+4LbLYSVEtvMzMxZxu4DAwNL6jldaJWsiDAvIeJdkk1EDjNWHHt7e5mYmKCuro6WlhZcLhfJyclUVVWxd+9etm3bRklJyYLEcT7WautHIlmO467vdvJS2zifevg4vmCYcERGlsFh1lGVbeHVMxOaiP3toycJhmXUa5b63P7ohT8QlmdNG3FPTRKQZ76+N24tYH3KTJR4eUkaJr1EOBpB+kMRgmEZh1mPBByKMTGwGvU4vUEy7EpxT130b7nJZoJhmV5ngKiWEoie5ylRm7zPXF2E0xfiyo1p/Me7q5j0BrnjZ438vz+1856d63mmeZiTA7O/U7sLU7linYHnTo3ytbeV8/RfX8b7a/I5Nhrh+3VT2Awyvz3ST13H7GHSBp3EV67OwR8K89XfN2lFPpIkUZRh4+tvr+Sf31HBy6fHZvVnJmoepmpTV1RUxLFjx7RobalFPysltrHG7l6vl6GhoXMauy/XcwvBvIRYrT5MdfzNyMgI7e3tNDY2niWONpuNmpoaTRyzsrLiEsf5WKutH4lmqYI5Ec0/jrqD/OvTbVrBjlmv44pCBycGXIQiMnaTnhMDLu56tg31Y9j/ehMHDtZpOc+bymabhFeWbcSUlKr9/HLbONdtTNF+fq19ghSrkVBExqiXZo0N27zOQewrs5n0TPlCJJmVC97r7UpRiF6CK0rSkCRQDXX6JpRCouRou8v2/GSuKEnjwdperixJY/+n9vCxywv4Y9Mwvznci9mg4wcvnO37+p5yI2ajjm//sYWiDBtfe1sFL/3tVXzj7RWkJ1kBuOPBBj7y0zp+VtvNmRE34XCYwjQL//DWcl5vH+dntd1n7fe23fl8eF8BP6vt4aG6GcODRA6QTk9PnxWtjYyMxH3er8ZyrsFgIDc3l3Xr1tHb28vhw4cXvdImlmTfgCQnJ69IH6bf72d0dFQTx/r6ek6ePInL5cLhcFBRUTFLHLOzsxO6nJHoAdVrkeV4r50xubTHjg3x2walEd5ikLi80K79zayTuanYyCMNg5qQNTkNlFVv1R7z9XduwWaa+bpaDDqtNQSgeXCaUU8IvaQU6Hz5dye1myB/MKJZ34UiMpvykjRxBHji2BCTniBGvQ6dhFZo5A9FyEgyIcuQZlHej/puJ3aTTsutAnz26kImvSEePtSPzaTnC9cV89gnd7NjQxr+UITnWka5/5XOWcukKWaJz1+3kVfPjPOnk0oeMMls4AM1BTz9+cv5wnUlyChGD//6VCs33XuA9z18hrtfHcJhMXB1WQb/8ee2eYt8/v7Gcq4tz+TbT7Xw2pmxuL87ixFaNVqrqanB7XbT39/P5OTkop9zNfOfFovlnMbuF0II5huQlJSUuCLM83maquLY0dFBY2MjBw8e5OTJkzidTk0c9+zZo52oWVlZWCyWswaxigHVK8tyvOexglaYZuaH0epTQn6CY71k25Svn9mk55u37mZHvlLEo5Pg9S4XLv/MZ2I16rlpU7b28x9ODM3av06C0yNejDpIsxmpyLEzFp044vSFNMEMhGVsJgPFGVZt21fbJwjLipjaTHosRqX/0huMYNQpZufVmSZte3cgwk9e7cYfUmd0JnN1aTo/re3VouiiDBsPfHA7//6Xm9BJ8B9/buNN33uV+17qYCxqtvCBmnzKc5K46+nWWZ6wkiTxmWtLuG33ejxB+Pr1BdxRZaQ4WccrndN88bcnePn0GLIMH/m/Izx6pJ9jfU4titbrJP7z1s1szLLzhd8cp8cZTGiEGYvRaCQvL4+8vDza2to4duzYotx2liJ6SxGt2G3nM3a/0PVhoc+91ieaXPq3BIsg3hymSiAQYGpqSpvn6PP5MJlMOBwOHA4Hubm5Z4nhQkj0suZarWRVSUT0vZT9qedBz6CSD9IBRjlEkknHpC+CzWqhtLSIK8Yn+H3jEGaDAYvJyBffXMwd/9dIRIYJT5DDPUouUS8pw6K3rnPwSINizv7dP7Vrw6UtRh078pM50uNELylLrD9+3xauuvsAEVkxS2iN5j/DEcXdJ92mtIvIwEf2rufBg320DLlxWAwUpJk4Oai0sKjXNzXXqpdAkpTWk8eODfLVGzZy9f/P3nmHx1Fe3/8zM9urpJVWvXd3W5ZtejF8HZsAAZuaQEJCIJSEEgKkQH4hBJIQAiQh9NACofdiwDbGBmwVy02W1bus3rb3/f0xuysJG3AFnPg+D4+RNPPubHvP3HvPPafQwpXHZ3P+vzbzTFUPlx+bHXsNz5iViscX4pY3d2LSKrl3TQv3f9TKfKuIPsvOrcuK+N7jNTy4vo3rFhdMeR1vXlJERdsoD1cO8OrlC2nduR27w4lkLWD7QIB3dvTRMujiV6/Xxc6J1ynJsejITtBxTF48L9bs4s4NdhbMDpCi2bf38UBKuVqtlqKiIgYHB6mpqSElJYWcnJwvXe/rJAxpNBMvUFTYPTk5mfb2djZu3Eh+fj5Wq3WP340j9l7/g2EwGKaw3b4ofD4fw8PDtLW1sW3bNpxOJzt27GB8fBy9Xk9hYWEsc4x+0LRa7Teyp3c4A+bXTSry+/2MjIzQ3t7O716q5KKH1lNbW8v4+Dg+Qb4fnZ9tpnU8yPcWZADQNOInEAwxMzIWEoi89orJVQXg01ZZd1WliIDVpA3p2Lx4VjcMIwBahcjpM5PxBmTfSo1SQh1htkZXfHP7xMiJViXh8odiZdlcizyDKQoyUPsDkz8LkbGWyLVZDCoCIfjl/+WjEAWuemEHVz9fK9uRFVl4sqJniksKwIp5acxKNzHq8vPSZeWcPz+DzQNBzn2kij++18zcTDOPfdJB+7Brynk6lcTdK2Yw7PBx2zuNWCwWcnOyMXgGOS7BziuXzuO6xfkALJ1u5RenFnBqqRWlJLKhbYTHN3Th8AYZ8YS5+oUdUzLyvYn9BYEocE1W2wHYuHEjAwMDX/h5PdB5yIPtNhIVdp83bx4DAwNUV1d/7ujdN3FvO9hxJMOcFJIk7fHD7PP5YlmjzWbD4/GgVCoxGo2YTCZSUlLYvn07c+fO/Rqu+sDjcO5hRj0xv4q722AwGPsM2O12nE5nTLvTaDTyUU+QQUeYHX4rF+VnENouGz4vm26lsmOcnojs3Yg7yOObhji+JBUAZ8TEMiptF6dVMOYO8ElE3zU6WjLZ2eSihRk0DTrpt/sIA4uLExFoIBCSxdWj4GBQS7j8Qbb2TFROtEoRmzuAxaDC7nXzSZv8OIVJejpG3DQPuVFKAv5gGN8k8JQEWRJPKQmsbxnh5R+X8WzVLv65voMzH6rm9BnJ2D0Bnqns4coTcmLniaLAraeVcM4jlby5rY/fLCvmKMMQ/ZpsnqnsonaXfJP6w6dquP2MUuZnx6OKPOcZaSauOTmfu1c1My0uxJmzUigrK2NgYIBNmzaxJDONjjmpvLKll8UlVi49duJxXb4gnSMunlxVw5stDn74VA3/ungeRs3ebXsHiywkiiJ5eXmkpaXR2NhIZ2cnJSUlGAyGPZ7/dQDPlwG1RqNh5syZ2Gw2Ghoa0Gg0FBYWTslK9yYOd1A9rABz5cqVXHPNNQSDQS699FJuvvnmPR738ssvs2LFCqqqqpg/f/4+PYYkSbzyyivYbDbKyspwu90xcDQajZ+bKUaztEO5cR8q4s9X0cM8VNd+qDwxQ6EQwWCQnp4ebDYbDocDQRBin4Ps7Gx0Ot2U9zsQkmcO/7K6lVkZJpwRAJybaSbVpGZbBLQKEpQ8t3UElUbuI9rcfnyBUKz/l2hQkRGvpXaXfLxGKW9k0cxNAN6rG2RmmonBxiHG3AHWNg2jVgh4AmHUkhg7NhgKsyA7jg1tEwQUVeTviQa5L7khwooNA8XJMmgORYg/k2dIdSpZr7Y0xcDHLaPU9Tn4/qIMlk5P4p41bbyytQ+NQuRfG7q4sDyNJPOE5vDMdBPnzkvn35XdrJiXjlYhcOGCDC4oT6eifZQ73m2god/JJU9tRqMUKc+O55j8BI6JuJKsaxrigYphFuRaSEkBq9WKxWKhra2NpUljtKYZ+NXrdWTEa5ibGRe73pIUI6fnKVlcVsq1L27fJ9A80Azzs6HRaJg1axZjY2PU1tZiNpspKCg4qJZ3+xt724OMCrsPDAxQU1NDcnIy2dnZX8EVfjPisCnJBoNBrrrqKt59913q6ur4z3/+Q11d3W7H2e127rvvPhYuXLhX67a0tPDHP/6RFStWMGfOHLq7u1m9ejUGg4H8/HzKy8uZO3cuBQUFMVeGPW38h1rt51CWHg91SfZQ23Ad6NrhcBiHw0Fvby8NDQ1UV1ezadMmfD7ZUio9PZ2ysjLmz59PcXExaWlpGAyG3TZTf2QERK0Quf6lugmvSqXISUUW2kdkXdgTcwwUJ6p5bpPMmg2GobJjLJYVapUSd59dGls3GJk3tHsCsR7l+/WD2L0B9CoJnVLkV6/Xx1SEJhtC+4Jhiq36KazYRz7pZNTtRxERdo9mtoFQGK1KQqUQmZ4is3hrex2xa9SqJGzuAPOzzMTrlPxzXQcgy9fdeWYJT1w0m2STGk8gxJkPVfNSTc8UMs91p+RjVCv4/Tv1sfdMEAQW5Sbw2k8WsSAnDpUksmSalZ4xN398r4nT/7mRE+/5mHidLBz/2/c6Y2zbqIDA/HlzuXK2gng1XPnsVnrG3Lu9x6eUWrn33Jns7LPzw6dq9ro8eyjYtXFxcSxcuBCj0UhFRQVdXV1f+6zyvpSCBUEgOTl5irB7IBD42p/DVxGHDWBWVlZSUFBAXl4eKpWK888/n9dff32342655RZuuummvS4VeL1esrOzueOOO9i8eTOZmZnce++9rFix4nPBcU+hUCgOS8cS+Gr8Nr8pwgif5+3Z3t6O3+/HarUyZ84cysvL0Wq1ZGRkYDKZ9irTiM5MCsC42x8TGlBJIicXW2LAZ1SL3Lo4jQheIYkCaxqGY1qwOpVEmllDVsTqa9Dh472dgzJgSgLxOiUOb5Bd4x5EUaDAqmdWuolo9XTQ4YsBgsx8VZCdMMGK7bf78PhDMS9Os1bOLLyBEDqVxLg7QEb8xPEAm3bJTM8wcgZ8yaIMPm0dZUv3hABCWZaZ1y6fz+x0I8NOP79+fScn/HU9f3qvkc4RF/E6FdctzqeyfYyKvqmfZVEUuOvsGWhVIq1DLt64chFrrz+WO74zjQXZ8VR1jOINhmkYdFP+x4+46PFqfvN6HQ+vb+fjdgfJOcXceVo+bp+fHz5ehd29+zjEKSX7B5r7GnuTmQqCQEZGBosWLcLlcn2uKPrexldlzzU5osLuc+bMIRQKUVlZ+aXP4UhJ9iuKnp4eMjMzYz9nZGRQUVEx5Ziamhq6uro47bTTuOuuu/Zq3agTQTQMBgN2u52EhIR9ur5vmgD7vsThnmF+0bV7vV5sNlus7+jz+dBoNJhMJhISEsjJyTloJbFAKIwogMsf4pKjMnh8gzw4r1KIzMs0x/qCKoWI1aDk5KJE3t4xgFoSWNs0zFmzkwEZMAGyE3R0jnrQKERuenUn01ONSIJAgk6JLxhiyOFDrRDRqyT+37IiltxfCcCQw0fP+MQog0YpEqdVxFixNyzO5Q/vtdAw4EQpCZQk66loH8fhDaBWiDh9wVgP0aiRsHuCBEJhBuwyCIVCcF5ZGk9UdHP/ug4euXBiXlQhCty7YjqnP1hFbqKeNLOapzZ28fiGTo4rsHDB/Aympxp5vsHBZd4ABvXEFpRi1nDb6aVc88J27l/bxrWL81k+N43lc9MIhcK8s2Ebj21zUtfnot/upWXQtZu9WJxWQfuYj1PuWcdxBQnEGfQM9fuo9rSgVshSg8vnpvHiph7OfaSS5y8tj4kwHKzYl2xNoVBQXFwcc29xuVx4PJ597g0eKFnoQI2rzWYzhYWFNDQ0IEkSxcXFaLXaLz/5MIvDBjC/LEKhENdffz1PPPHEAa0T9cT8pgHmoRZI/6oMqg/F2lEw9vv9U8DR7XajVqsxmUyYTCYyMjIOmjpS77iHS57eyp/PKmVWusx2DYbDJBvVjLv9uLxB9CoJpy/Ih41DnDkrhXidkgG7D0mQMwKTRt6gXP4QLr+PjhE3giCLEsBE5qdXS2TEGdjWY0OlENGqJL49I5l/behCIQlolNIUP8sw8FbtQOxnrVLC7Q9h1CiweQJoI4Acr1Mw6grQHbEBs7kDMUECZeTf7Hgttb0OEvUSgbDEoMPHfWvbcPoCXLwgnXs/bGdT5zhlWRMqQ4kGFVefkMsf32/mJ8fN4tdLS3hhUzfPb+rhiv9sxWpUM+YN89dVzdx6WsmU1/Vb05M5e84QD61v49gCC/Oz5X6kKArkxSt5+JwSrn+zjc1dYzz1gzKKrAY6R120D7vpHHHRMeyiumOMzlE3K3eOoBRH8IfA3z7VhgygbcjF+Y9V89CFs8lM0O329/2N/el96vV65s6dyyeffBLrDebk5Ow1iB0oYB4I/yKanUaF3YeGhtiyZQsWi4W8vDwUCsV/Tbn2sCnJpqen09U1ITbd3d1NevqEQa7dbqe2tpYTTzyRnJwcNm7cyBlnnEF1dfU+PU40w9zX+DodSw40DhVxZvL6BxswA4EAo6OjuFwuGhsbqaysZPv27YyOjqLT6SgsLGTBggVTBCEOFlgCvL9zkJ5xLz97cQcu34ROrE4lckxeAh82DqOK1Fxvf7eJxgFnTNy8zyGXAqMlwZwEOZuo7XUgMMGKdfmCsVGPu88uRa2URdKd3gDfnpEEgC8QRjOJFasQQRKJEYxAzjBtngBJEZLPxy3yuEpBkh6TRkHPmBdRAH8ojC/SH1RI8jVolRIqSWDQGSTZKJ8/L9PMA+s7eW7TLoxqifvXte/2+lxQnkaRVc8dKxsxaxX89KR8PrzuWO45Z2asPPxMZTdnP1jBg+va2NYzHitZ/3pZMelxWm58pXaK80goFEKllPj7ebNIM2u46rmtjLn9TEs1sWxGMj85Ppc7z5rOB9cewy+/VYQ/BAuyzdy1MMQ7F+ey5dcnUHXzCXx8w3GsvvYY7jlnBkMOLyseqaK6Y//LoZ+N/QWvYDCIWq1m0aJFiKLIxo0b6e/v36vv5sHwozxYIymJiYksXLgQrVY7pUcrCMJhX5I9bACzvLycpqYm2tra8Pl8PPfcc5xxxhmxv5vNZoaGhmhvb6e9vZ1Fixbxxhtv7DNL9kDk8Q7XHuY3XRghGAwyPj5Od3c3dXV1VFVVsWXLFgYGBpAkifT0dMrLy5k3b16MnHWoZ16j/cZhp59b32rEGWG4ahQSJxdbGHD48ARCCAIYNUqufWlHzMarYUgeL4lK550xKwWNQqRnzEM4DGqlGHmMAJIoEIqQghK0SkQBdvQ56IwQiPzBEFqFhM0b7VnCMbnxU641jMywNWqiWrEyYzYchmSTmtIUPdE9eWu3DLRR5TtPIEi6SZ69HHPLj/HrbxXwr+/NwqBWYPcGqeoY54VNu6Y8pkIUufW0EnrGPDy8vh0ApSSybEYyT19Sxs3larRKiaZBJ/esbuGch6s4+s/r+Nnz23h7ex83nFpA77iH37/TMPE8IptunE7Jg9+dgz8Y5opnt8TYxZPjB0dl8cslhaxtGeffrQqCYdhcXYXPOU6SUU1GvJalM1J44ccLiNMq+cGTNbyyeddu6+xPHCi7VhRFcnNzmT9/PoODg1RXV3/pTfzXaeC8p/6nKIoxYfdoj3Z8fPxzVjh84rABTIVCwT/+8Q+WLFlCaWkp5557LtOnT+fWW2/ljTfeOGiPEy3J7s/1Ha4l2UMd+9LDDIVCOBwOdu3aRX19PdXV1dTU1LBr166YXudkxqpOp9sv9aQDjclmze/tHOTJCrlfqVaIHF+QgCTIJBqFKPDX5aX0jnvZNSYDZd2gV36ekY3epFHwk+OyABncop6Xdk8QAbmn+eb2fpz+IBqFiEmt4Bev1gOyNZg3EJwiFjA7w4RKEmKkovs+bGPc7UcR2cQn68pqlSICAnMisnyx8mzkGIc3SLpJgSTAgF2+frNGQXl2HC9eWsbPF+ciAL9f2cwF/6rhjW39Mcm88px4vj0zhUc+6aBrZEKUIBwOU2JR8PfzZ+ELhDhnXhp/WT6Dk4sT2dI9zq1v1nPNC9sxqBW8trWX//fWTmo6xxhzB2Pvc16inr+dO5OWIRc/f6k2lp1Ojh8cnc3NSwqp7g9xf42TmbNlFvzmzZtxu+UbjhyLjhd+XM787Hh++Vodf/mgiVAofEAVl4M1jqJWq5kxYwZFRUXU1dV9obbr16nl+kWPHe3Rzpo16xsxPnOgcVj1MJctW8ayZcum/O62227b47Fr167dr8f4uhxL9mb9w1WN5/MyzKj59eS+YzAYRK/XYzKZSE1NxWAwfOGd89elUuSclNWUphh49FO5XaBRSpi1SsqyzFR2jKMSBOZkmLnx1HzueE/2eBx1B2kd8WHzyJ8XlULkvBlp3PdhO2Hkcu/3F2Zg9wYIAzkWLRvbxhAix55UZGFrj422YXnT7xz1TGF8GjVKUs0aOiJZaDAUxhsIMxKZrYwKIwSCIfRqBT1OD0XJE2LwAO/ukAXRx1x+ShP1SII8ogITTiUKUeAHizIxqBX87p0mem1efv1mA3etauHsOalcuDCLG/+vkDUNg/xhZSMPXjgHmMgUjyuwcNHCTJ6u6GLJ9GTuPGs64XCY1iEXn7YMs75lmPVNw/ynqof/VPUAoP9glGyLjqwELdkJOk6bkcwb2/r4f2/V84tTC1ArRFQKMQasPzgqi7b2dp7fMYCAwF+Wz2JsdITNmzcTn5hEfHIGDm+QK07IQSkJPPJxB1u6xrn//JlfuURdKBTa43lms5kFCxbQ29tLVVUVmZmZZGZmTrlJPJAM82AwbL/ssfdl4uCbHIcVYH4VcSAlWb/f/+UH7mccakA+lBHNjj0ezxRw9Pv9aLVaTCYTiYmJ5Obm7vNd6Ncljefyy++FWiESr1WQatLQM+5BEORrOa4ggcqO8ViWd35ZKn96v5kI5vBppwOnL1rGFTGoFWiUIm5/CEkQ+PGz2/EHQ4TCUGzVU9frIIxMLDJpFfzilHyufL4WgKZBJ+OT7Ls0SjHmVwnwyyUF3PRaPa3DLkRBNq7+tG0sIl6gZtwTQBvpmyYZlAw6/ORYNLQNexh1Bxiw+/BFFIQ8/lDk9Z7Y/JbPSeHN7f20Drm4d0Upb24f4MmNXTy+oYvjCy0sm57MS5t3sbZxiBOLEqeIWNxwagEbWkf45as7eOPKRSToVeQn6clP0nPRoiy6R92c+4jM/l2cpUDUmdll81Pf52DVzsEY2emFTT28sKkndk1KSYixYgkGiNcpeXdHP+uahtCqROyeIN5AB9Cx23tb3THG2Q9VcUmpyKL9+GwcSIb5eedFtV2tViutra1s3LiR4uLiGDnxQHVkDyQ7jfZe/xfiCGB+JsxmMz09PV9+4GficO5hHoqYLEQ/NDTE0NAQer0eo9FIXFwcWVlZqFSqL1/oS+KrAsyrX6glJ0HLDafI2qXRsulx+fF81DzCLxbnccf7LezodeDxBynPktmd0dxXEISYdZcowLo2B06f/JvoCEcUgo7Oi2dbj51Rl/wYSQY1pSkGdvY58AfDMVJQNDz+EOuaRxAFuUSrVYp4AiGMalmZJ6pRm25W0zPupT6i3jPs9DM9VcThCcTUhPISdQw6xtGrFJgirNrqXXKmalQrcPt9vLq1j3PnpcUe3+fzccUCC5e/YuPNymYuLJY4I93A2i4/63bZGHb6UYgCN72yg6d+MI/cBHUMMDVKib8sn8E5j1Ryyxs7+cf5s6ZkIhnxWh767ly+93g1W/pDPPOjPEwGmdEaCIboHffIQL2mhbpeOycWWpieZsIXDOENhPD4AvT2D2KKT6BxwEHTgBO1QuSsOWmkmtXoFGAfGUCnCDO9IBdrvJHuUTe3vrmT2ze4GFK2cNWJuSilfQPA/cmm9gb0FAoFRUVFuFwu6uvr6ezspLi4+IBdTg6k/xkIBNDr9V94TDgc/q8QZz8CmJ8Jg8GwXxnmV9HDPJSADPsvXxcIBGLgaLPZpsgJmkwmLBYLFouFxMTEg37NXzaHebBiffMIH4XhxCIL87PiYhnmt6ZbWdUwTGdEXWbcHeD2lc386ChZaD0qZuANyNkiyJqsneP+GECqFTJL2eOXn0f3mIf7z5/BOY/WAODyBTguP4GdffLnUquUpujKCkBNlw2lKAOmRiFh9wRINspasRsjDNDsBC0OX5DxSCnY6QsSDMuC7cpIKqxXyf3KhgEnCTolNg+clKvnwzYnAw55JOaBde3Mi/PhdsqjOyqVCqvJxJnTE3h9xwiXnzqTRWkmjnI6+faOOhqcJl5v9NAw4OSMBypIMakpMofo1/RxVF48palGrltcwJ/fb+LlzbtYMW+C/Q6yrN6d35nOdS9u57aVzdy1fCaCIKCQRDITdGQm6Dg6P4HrX9zO+zsHOa4wke8tlGe2/X4/W7a4KC+fCcAHOwf4xcu1stTehbMpSnwaygAAIABJREFUSTECuQwPD9PQ0EAAK0fl5vL8JbP59cubeWBdG+ubh/nL8unkJn4xKBxo7Avo6XQ65s2bx9DQEJs3b0atVmOxWPbrcQ8GYO5NhvrfUJI9/CH/IIfZbP5KTKS/aevvbS8wyljt6upix44dVFZWsnXrVoaGhlCr1eTl5U2RE7RarahUqkMq6/dVZJjRh7j2pTr6bN4YuC3IjiNep2RLl0wUm5Nh5PVt/by2VXYH8YfCDDl8U5icP14gb2zRq1Yr5FJs9NVvGnQhTdpcXtnah9U4kY2rP2MevSjCio1cEoFQGJsnQFyk17iuSQbMUBjiIv3VCBGXmk6ZuaiKZFDeQIgEvQp/MIw3smCuUb5SnUKWyBtyBvjDuiEM1swpXq43LCkhTqvkjveaCYXDmM1mjjlqEacUJXDTnBCnFpoRgDSzmk19AW54uZZj7lrPGf/cyIDNQ3GygdvfkVWBPhvLZiRzVqGaN7cP8Ognu5dRlZLI3StmckpJEr9/p4FnKuSe8mfLo6eWWnnmh/MJhMJc8Fg1axtlCzaLxRKTequoqMBtG+XKMhN/O28mXaMuvvNABY9+3E5oD+SigxWf18P8okhMTGTRokUIgkB7ezu9vb37/H040JLs/4p5NBzJMHeL/fXE/G8BzMlf2FAohNPpjPUdowLkBoMBk8lEVlYWer3+S0st3yRpvP2JUCQLA3D7glz/cl2sJKtWiJxYmMDbEaGAY/MTMGuUMdYswNqmYcojA/gASwvNvLR9nAHnBOhNBtRgKMx7OwdjPwsI3PfhxOC9ShKmsGJPLIxnQ9somoj4+u/fbcLpC8bKiP0RdmswLLNig6Ew01ONbOmxx0TWO0cjGbLLg0kZxq2cGHuJ9mF1aiVlWXq29zqo7nFx5qPbOLHIwvllqSzKjcekUXDtybnc+lYjb20f4Ox56QiCQHZ2NsnJySg09dT2yuMz95xiIiGzmA2tI3zaOsKz1T0xZ5Qz/7mRk4qTyEvUkxkh92QlaDkzX4FHaeLuVc3kJepZXJI05X1SKUTuOWcm17ywjdveaUAQBM6aadkts5meZuKly8q54tmtXPHsFm5aUsTFCzMYcfkZFuNoFwVeXttB55gXe9iJ0xsgEIK7PmhmVf0gv15azMyIWMXBjC/qYX5RRJV2rFYrIyMjdHV1UVJSgsm0d9f4daoEHW5xBDA/E0ajcb/GSr4pGeCBrG+32/F6vbHSajgcjjFWo4Lj+/PFOJwBMxwOTxEQz4jXsn2XPSZfp1KInFyUyKuRjNKoUXDHmSWc+WA1Q04fSknWiS1Nlq2cBGRxgVPyDTy7TZ6HvOfDNm5ZMmGenGJSs6ZhKPbzpcdk8tink0Q7IkIDUam9NLMWk0YRA90oPkSBUhshEwWCYbRKiXG3nzTT1P7x2iZZzGDU5SPVpCEsKmiNsHCNeh3gwuUPkhav5ZqT8zj3sRqKkw1s7bbxYeMwWfEazp2XxhmzrMxKM/KXVS2cOi055gqi0WhYWDaH32s6ufzFRh7bHOCJBQZmppu47Lgc3L4gNV1jPFPZzer6QdY0DPJ2bf+Ua9QqIMsij+H87PltXLggg8x4LSpJRK0UUUkyQ3bF3DRGnH5+93Y9bYNppCsC9Gzrw+b2M+7xY3MHGPf4STKq2TXu4c6Vjdz1ftMUtSSVJGDViSTrfJSVmpiVl8q4O8iTGzs555FKzp6TxvWn5JNoOHhklwMl7qjVaqZPn47NZqO+vj7my/tlXIEDzRD39vwjPcz/wtjfkuzhJL4eDodjjNUoODocDsLhMAkJCSQlJcUkrQ5GfJ1asge6djgcxhkBTEkUaB92cfGCdJ6qlIlhClFgUW4ckigQDIXRKiRMGgUXzE/l7x/JpcON7aOcV5YCyCAniiLTkic22u09dm57tyn281G5cTEABsiM13Lh/HQe/qQTkEUMpqUY0CklxoMB1EoRrUrEFpGP/c23Crnu5Tpah91IAhRZ9WztsTPmcGNUwbDNT6Ikg6lFJzHsCrIw20xFxzg9tiCiGEQhCRhUEg5fEH8ESFy+EHFaJcXJBs4vS+O5Tbt4+vtz6Br18PymXfxldSt//6idhTlxbN9l5+8ftvCrpcVTXtPjpmdx2S4XD3zczb2vfsIlJ88gPj4erUrimHwLx+Rb+MeHrfx9bSvXLc7n1FKrLHk34qayrhWfSoPTF2TcHeCpjV18WTxVGRUjqI39TqsUMWuVmLRK8hN1DDn9tA+7iNcpueKEXE4uTkITdDE0OEBxcTGdnZ309HRyUnEhF8w/in+ua+fpik7eq+vn6hPz+O6CzBhx60A+5wfCNp0MtiaTifLycvr6+qiqqiI9PZ2srKzPBawDzRCPlGT/h2N/S7KHOgM8EMCMCpBHwTEqQG40GomPjycrK4vm5maysrI+19T2QOKr0pI9WPFWbT+r6of4brY8wB4tfxZb9dT1OchL0qEQZVWdmq5x5mWaseiUMikmsu/oI6LiUcuv6g65ahEtk4qTxjJ+fnIuf10zUXI9Lj+B17b2x8rAmuh4RCR29jnQKkU0SpFxjwwA/kAItULAGwgT9MvImaIX6XOGaO6XP8/D7iBZFiONo3bSU5Kgr4+SFBOftI7Gxl1UkhATL4jXKcEXZNOuCbusqL7tVSfksLJukLtWtfLUxbM5bYaVhn4HL9T08uZ2+dqf3NhFIBTmzNmpTE81xuT2LlmYzpqdfTzTEGBaUhPp8VqKi4tjmdBVJ+bSPOjk3jUtFCUbOLlYLr0Whbs5+mjZpL1l0MnFT2wiFA5z3zmzSDWr8UUMr6MMWac3wKPrW6nusnNycSK3LCsm0aCOgdvkqGof5cZXdvCn95pweAIsn2ZEFMWYI0dqaioNDQ34u7q46phiFuXG85cPmvjje008saGTG04tZOl0KwL7zwbdnx5mND4LeoIgkJqaOmUMpaioaI/EuwMFvK/KwP2bEP8bz3IfQqfTxVRA9iUONQNsbwHT7/czMjJCe3s727Zto6Kigrq6Omw2G0ajkdLSUhYsWMCsWbPIzc3FYrGgUqkOOagdTiXZf33axeqGYV5tkft79ogkXH6ijlSTmrWNwzHVnOtfrqPf5o0ByWDE0SNaHo3qxK6OlFijwOfwTbweKSY155alxn626JVkWyacHjRKEYc3EBNEB5kVG9V9ddtt2D0B4lXy61DRKPtsZiXoiNcp8IWjvpchNColHn8oJvAedQvZvsuOgMzqPXt2MpIoMOKSn39V9wQJx6yRiUQmjYJrT8plS7ctJvRenGzglqWFrLlmET9fnI8kCjxT2c25j1Sx8E8fceV/tvLvii46Rtz8dL6JUBj+3SySYEmkqqqK7u7uGFP7zu9MY1qqkZ+/VDvFxDoa+Ul6nvpBGaIgcP1L2/GHwuQn6SlNNTI7w8yCnHhOKk7iH8uLOH+6gTUNQ9zw8o49yuiBrEr0+hULWTrdyt8+bOXqV5oYiIz1OLwBanqcfDxq4B/bghx/70Yue2YLjQPOWE/4hpdrWfqPDTxf3U1oP7fV/e1hwuczXSVJorCwkLlz59Ld3U1NTQ0u11RS1VelQ/vfwJI9kmF+Jr6pd0p7ksYLBoOxrNFms+FyuVAoFLFxDqvVuteaqoer3+ahAMwoEL3ZEmBp6yiByPI6lawT+2JNL4GQPA/p8gW5/pW6mBlzXcRw2RmRzpudYcbpC9EVydrUERUa1yTAXNUwxMKcCf3Xu9e0kW/R0h7pIaoVkuwyohTxe4NkmhR02wKMuuTNf9TmwB+CFLOWPpebepv8tZYUCuJ1KoqTVWzqHMcfDFPVEWHFRgDTHwyhlgS8gVCsJ5qbqEcSBZIMKvps3hj7FsA4yYj6zNnJvLi5l7tXt3JSkSUGvga1gh8dk0VBsoErnt3KycWJJBrUbGgdYXW9TGZK0IgUJxuo6hjjuTozPz1hAS3NzVRWVjJt2jSMRiMPXDCb5Q9XcsWzW3jpsgW7vU/5SXqe/P48Ln6ihouf2MS/L5lPjmWq60g4HOb8mWYWTsvhplfrOO/RKh68cA75SbuPiGhVEledmEeiQc2zlV1c/rqLxNXDDNi9sWy/IEnPt2akkq0PkhAa59jZhViTrKxpHOKBdW387p0mEjQCPwl3cm5ZeswZZm/iUIoPaLVa5syZw/DwMFu3bp3iJBIMBv8rrbgORRwBzM+J/Z1JPFQhCAI+n4/u7m5sNhtOpxNBEDAajRiNRnJyctDr9ft9zYcbqE1e+2ADvS+CkBoJbn6jgUuPkmf69CqJY/ITeKZK7ospJYHbvl3E9S/vjFl1bd8llz8dXlkHVqMUuWVpAT97sQ6QmaoAzkko9FHzCIWTNvBtPXZSJpFydnW209FrR0R+nkuK43i0aigmcfe3Krncq1LIhd7aXvkagqEwGoWIPxhmeoqBLT32WNYYzdq8gRBmnRJREOi3yX1NvVrCGwihVUrkJmoZdXgZ9cjXe8vbjZzX6+CceSmkmDT8akkBFz6+mQfWd/CLiKhDNE4uTuK8snReqOnhqR+U8fszSukadbNmRw8f1fdRNyxnOg+v7+DxTzvJTtCRYlSiq6sh26JnXmEmv15azE2v7ODq57ZxefHun6ECq4Envj+Pi5/YFAHNMrImWXVFB+aXlaZgNaq5+rltnPtIJVefmIdOJdE+7KJtyEXbsIuuUfcUTVpJkIlTSQYVlx6bw9lzUqd4Z3q9XhobG+np7ubo0lJOuWwBr9V0cd+aZu5Y2cjfPmzh3LIMVsxL2yNAfzYOFDD35lyLxcLChQvp7u6moqKC3Nxc/H7/1yard7jFEcD8TBwoSB4MoA2Hw7FxDrvdjt1uJxwO4/XKG1pGRgYGg+GgZsOHa0n2UAg6RDNMXwiU4TBPRwg+OrWCeVnmmAKOUhI5tSSJS492xLRke21e2oZdOCKyd7IYuwWdUsTlDzFg97GuzY4zkmGKyEo9W7rGYgbPF5YoebZ+QmQ7JTUZRRsYvR7GvB5On5vNY9VDsc092mMdcQVQKyBadQyEwmhVcnaabp5KJvm0TWboDtq9mLVKkvRK+iKAqYkMafpDIZIMKkoTJN5ulAG2MEnPI5908uinnRxfYOG8slTOnpPCM5U9nDU7hYLPAMNNSwrZ2DbCTa/I0neZ8VrOmG6hPMFHSUkpNV1j/PT5bbh8QZJNagYcPrpGgrzfPgabxmLrbOoc4/peKKqvQq2UUEpCjBWrkkTKc+L5qHGI7zxQwfEFFkLAmNvPiN3NmNuPK7ArlvUD/PE9mWSlkgRyEvUUJxv41jQruYk6chP1qLxjaKUw220a/vx+E3eubKS+z87PTykgySi/ljIrdQYbGnr4/SvV1I0KNA77CCOXrNPMGp7a2Mm/Pu1gXpaZc+al863pyTGG9WfjYPYwvyhEUSQrK4uUlBSam5vp7+//UqWez4t96V9+kxKQ/Y0jgLmHUKvVeL3efXY9j5Y196WBPlmAPFpejQqQG41GkpOTKSgoQJIkqqqqyMjI2Nens1dxuALmocheo+o8oTAsn53CExGmpUElohAFFubE8UH9EIrI9//qE3J4YmMXkTFCPmwcxuEJEkYWBJBEgYx4LY0DTnRKkTvW9jHbqkQSQCGAWS1Q12tDKQn4gmEuXzKXWttOtkWy1Z1DARzeYKyMqlNLCIA9AgC/XVbIDa/W0zzsRS0JZMSr6Rr14PYHsehVdI/6KbLKG2K8VsGoO8DS0kTe3TlE46ALs1ZBvFaJJqIVGwpPqBOZtUpEwYskyKIF585L5fbTi3lpcy+vbO1jbdMwqSY1Cknk9+828cRFs6dsjHq1gruWz+CCx6q57e167lo+I3ZTKYoC87Pj+fcl8znv0SqGHD6e+9F8dCqJIYeP1gEblXWt7LL5qR0VaRyUs8D0OA22UBh/IIQvGMYfDOGLlJQd3iAr6wZIi9OQbFKTZFCSZZLIsCZg0iqJ0ypRKQTeqe1nQ+so09NM3LV8BpnxU0uSnZ3jCILI6bNSOKk4kYfWtfP4hg7e3znAD4/KIjNBy6cto6xrHmLEKas2lSRpOD1XoixNwzmLFyJJIoN2L69t7eWlml388rU6bnu7nuMKEzl/fjrl2fFTCEgH0sPcH+k5lUrFtGnTcLvd9PT0MDY2RlFR0T4xdf+XGLJwBDD3GAaDAZvNdtABM5olTu47RgXIjUYjFouFnJycr8UG51Dahx1KNZ6DAZj+SEYZZbD6Q2EMagmJED3jHuZlmqjpslHTZeO7C6Asy8wH9UOxvpYkCihEkUAohCTAe3WDqCNoqhRhbGwMoyS/tnpFiHS9wOZ+P0oRtGoFy+en8cD6TgwqEV8wjE6txKRVYFJL2LxB7v+oHbNWiSHSPxQE2SMzmpFGdWCtBiUDDn9MiH3I4ScjTovNE0AXyRqLkvVUtI/jjdwUxGkV2D0BqjrG0EfW/6RFVgby+IOYNQocDg8qScAdCPOPjzp49bIyrjkplyuPz2ZV/RAv1PTSa/NS02XjrIc38e0ZVo7KtzArQx63mZ1h5srjc/n72lZOKk5kYapyCqjmJ+m555yZXPbvzdz4yg7+ft4skoxqkoxJLMxPYmRkhJ07d/JivcC7nT5OKbXy29OK95ixdAy7uOyZLfSMublucQHzk+Qb0ry8vCnHnVuWwZvb+vh/b+3kzAc28tvTSjhz9gTxKhQKoVQqCYXC9I57yErQclJRIuubh/n7WpnRrFWKnFiUxMkliRybbyFBr6K/v5/GxkZqajZRWlpKktHAiUWJODwBXt2yi367j9U7B3m/bgCjRsHxBRYWlyRxXIHlaxMAEEWRmTNn4nA4qK6uJi0tjezs7L0C4L0BzP+msu0RwNxDRB1LrFbrPp33WeKMz+eLgaPdbsfj8aBWqzEajZjNZjIyMr4xKv+H0j7sUM9KHsjale2jXP/yTo4vTOCOM0oAWdRbp5KYZ1XySesYp5RYqOmC9+uHWN88QmEkW4uWbsPhcMwDEqCuz0GqXt7Mhwb66O/3IYhyf9EdknjsjFy+93wrNm+IMHD6zGQeWN8Z05qVpe+CxOmU2LxB7JH/chPkLMgfeSyLXsmQ08+gQy6lZppVhEIhRiLszhGXTwY6fygGqvE6+WasqkMudyolgVNLEtnYPhYziP6gXmb0evxyhjk4FkIhCWgR6Bx183RlDz86OhOlJLJ0upWl06009jv4yXO1tA27uG9tO/etbceoUbAgJ56jcuM5tTSJdU1D/PbNep68oGiK9B/AcQUWbl5SxB0rG7nvwxauWzwh5JCQkMBRRx2F17sWRIn/VHWjEAV+vbRoN9DMtuh4/tJyfvr8Nm54uZbvlyVywUzzHt/702elMDfTzI2v7ODGV3awrmmYG04poHXYyZqtwzSM+KkfbIrJEMbplCzKTSBOp2R7j43mQSebOseYk2lGG3l9JUnCarUSUMdx5+s1VA2E6RjzIwqwKDeBn56UzPGFFmp32VldP8iHjbJAgyQKZBgEznb2UJ6bwMw00x7HXw5FBAIBlEolycnJJCYm0t7ezsaNGyksLCQpKekLz91bkBcE4UhJ9r819sdEOhAIEAgE6O7uxufzxRirJpMJk8lESkrK12J0vLdxKMXdv8lzmCMuP+OeAG9uH6A8K46z5qQQDIVRSiLlqSrWdPjojhg/p5vV3PR6Pb84Rc5WXL4Q/f39DI3aYtnmtws0vN7kYcAl/yYvO4vi4nQCG7egEOWS4YDDT7ZZSd2Qj3F3gG09dvQqCU8ghEqSNxaHNxCbW4y6kLRF/C3dkf5oqlnDkNPPp60y+AXDYRK0EunxOnb0OgiEwmyKaMVGx1kiGB8r59o9AZJNGix6FQa1gu4xT2x21BcMo5QEPP4wAgIJBiWFSXoe+riDb8+wkmyauNkrSjbwxEWzWfHoJkpTDJw/P52qjnE2tI3GmLHxOiVOX5BrX2vh8jITcalerEZV7Dtx8aJMmgYcPLiunYIkA6fPSpnyPms0Gu44bw7CSzU8XdFFOBTkN6eV7vaditMpeeyiudz65k6e3NRL95iXezOzp4gLDNh9tA07aRtyMS3VwJDTy1vb+3hre19snTyLhmXTk5mbZWZOhpkcy4SnYzgcZmPbKP/8qI07Vzby0Po2VsxNI+z38FHzKI3Dck97erKW75bA8gV5TMvLiJ2fbNKwMCee6WlGnt7YRduwix57mHvWtAKtqBQis9JNlGXFMSfDxJzMOBL0B+7us6eYDHqSJJGfn096ejoNDQ10dnZSUlLyuT3OIyXZIxEryX5eBINBHA5HLHN0OByx7NJoNJKbm3vIDFMP1ZDw/2oPMwoOczKM/H5lE7mJWoJhWcFnmkWBTiVrnwL8oCyRv33Sy72rZMJIIBRmW/cYOdY4QJ59/Nm3ZvFp7xYGHTJpJ+oK5fAGkCJiB6ta7HiCYUwaBR5/kF+9UY9BrZBZrRFCiD0inq6UBE4oSGBVwzBmjcS4J8jt77UAYFDL5JdothgIhVFLAoFQmDkZJqo7x+mLzIVGnU78wRB6lYherWDA7sMTkK/D5QuiV0moJIGsBC3NgzKD9V8bujCoRAIhMGskbjw1j+88VM3da1r583dKp7yWWQlabjw1n9+908T/lVq5/cxpAHSNutnYOsKG1hHWNg7RMerlV6sGYdUgGqVIRpyWzAQtmfFaCpL0FCTp+eVrO0gyqJiXFRdzUgF5TvqvFx2D7pUt/LtqFz6Pm9+dPVduKYTC2D0Bxt1yWXrpdCsj43ZWt9j5v/s+YUaaiV02D21DrpgWMMil1RyLjqPzEmjodzDs9DHDqubmU7IpL87c4+dGEATKs+O45uQ8nq/qYXXDIA9/LCs7GVUiF5anc+kxOaTHa/H5fDQ1NVFdXU1JSQktYyFe2NTDO7V9uP0hipMN3LqsmGRPJ/Pml1PTOcamzjE+aRnh4Y/bY8L/CXolBUkGCq36yL868pMMxGkPbBvf056i0WiYPXs2o6OjbN++nfj4ePLz83cDxyOAeSSmmEhPFiCPgmM4HI6Nc2RmZsYEyFtbWzGZTPvNOPuyiJZNDzfAPNRjJQeydpTg85tvFXLtS3Vc95I8/qEQIODzMCtRoqpXBh1N2M0tJ6dx08oJYfV6u5qi3AmRa7VS4nsL0rknotzz0uY+zp6TisMbBEHAalSyutmGUggjCSJ5iTr0KonKyHxklHBj9wZI0CvRKES+PUO2EDNrlfiCYbZ0yzdzDm+AOK2CQYcflSSr/MSpBPrdATLjpvbfP2mV+5J9NpkVW5piYHXDMCCr97j9QbRKiTitkgvmp/H7d5sBWUz+45YRQmFoHXbzYeMwF85P44mKHs6dl8r8rLgpj7N8TgofNQ3z19WtHFOQSFGygcx4LZll6ZxTlk4oFOKKf1eztsXG8rmpmDRKukbddI66qWgbnQJk33+yJvb/SlFAFMJo132EUhJQiAIGtcQL20d5c+caJFHE6Q/xeR+FXpuXfvsgJckGls9NI9eiizFik41qxIgoRCAY4vnqHu7+oJHvP9fA9xe5ueqEPAwRTdwhh5f1zcN81DjMJy3D2DwBFKLAvKw4ipP1dA6OU9np4NmqHirbxzhnXhpnzE4lI6+I5yvauPnBKrodIbRKkW/PTOHcsnRmppsQBIFPP+0iXqdEp5JoGXTS0O9AIcJR+QnMy4qjZ8xD84CT17b0xuQaQSaWxanD5DRUk2zSkGRQYVQrSI/XYlAr0Ksl+V+V/G90FjgaLn8YhzeIQhR2mxuNj49n4cKF9PT0UFFRQXZ2Nunp6bHz/5esveAwBcyVK1dyzTXXEAwGufTSS7n55pun/P3BBx/k/vvvR5IkDAYDDz/8MNOmTfvSdUOhEE1NTbS0tLB582Zuv/12fvvb35KRkYHJZCI1NfULBci/KseSQ3FHd6hJP9/U7DXahww4x/j5Aj03rZJBJBwKIAgqFpcksXGXzJLNy85iVrqJla1u1jQMo1GIrGkc4uTiCR9ClUJkcbElBpiNA06ueXEHdo+fcFg2aN7QNoZeKaBViWiUEv84bwZH/eVTgiHZE9PtD+L2hxAFAbVCig3jDzh8mDUKzpqTwoPrO6nd5SDZqIr5aXoDIVQ6CZvHH5PmUytEvIEQZ85M5vXt/dT3O9GrJESI6d/qlLIAg1kbwqRVoJx0QzY73Uhj3zjDblkd6K5VrTJZSSly61uNvH75/CnmyoIg8NtlRSx/ZBO/eKWWF3+8YEovThRFfrM4g0F7K29t7+fZH81nRpp8wxEOhxlx+ukcdVHdMcY/17YhinDWnFTUkkh3by+JScn4g2F8wRC+QJBtPTa6Rj1YdWH+L19PYWYKCQYNcVolZq0C+1AfSWY9aM3c+GoddX0OyrLjWTEvDbVy9++xQhL57sJMchWjvNYa4vFPO3l58y7mZ8XRZ/OyIzLjmmRQcWqplROKLBydZ4mJzHd2duLyhdg+ruSFTT3c+V4Tf3pfrkiEwlCaYuC6OQYKVGNMK4wjNVUGS68/yPqeAHc+UEFjv4MEvZKrT8zlgvKMmMB7IBji7dp+HlzXRuuQC6tRzSklSagkqO/sxx8K83HzMKORWdt9ijVrKbIaePOqRbv9SRAEMjIySE5OpqWlhYqKCkpKSoiLi9trL80jgPk1RTAY5KqrruKDDz4gIyOD8vJyzjjjjCmAeOGFF/KTn/wEgDfeeIPrr7+elStXfuG6Z555Jh0dHRQWFuL3+ykpKeGhhx4iISFhr69NkqTDRoB9T2t/U0Hti2JfM0yfzxdjKNtsNlrb5NJjKOCjrCCN68Mm/vhBG46AgE6n48SUJP6wJipUIG/8pcl61jQM4wmEaB500To0ITWmkkT0qomv1blzU3hxc59s0iwK5Cbq2NZtwx0IoVULaBQiGoVIKBRGKQr4Q2F++1Zj5LmBWiniiGQTMgkHEnRyL8ugluiz+zCoJRzeEE5fCLUks161EVZsYZKO2l4H6sjPSQYlI04/qxqGUUnNEVQaAAAgAElEQVQCQWBrjz0ynhHGolfEzLEBXqjpk30xw7BkWhLnzE3lxZpeXt3WT9eoh2Pu/pQTCy0szIljQU4cmfFaEg0qbj+jlCuf28bfPmzhhlMLp7wHkgC3nJTM9Sv7ufI/W3npsgVYjWoEQcBiUGExqJibGcfxhYlc/MQmVtUP8sRFcxhoG2PBgpIpa4XDYZ7Y0Mmf3muibijIcdYe5ublk5Ii23q1+IYx6FUkJ5t46cfl3PVBM09XdFHRPspfV8yg0GqYstaucQ+bu8ZZtcNOm11AEGRT8NUNQ6gVIqeWJnHZsdnMTDfvEQT8gSCNw3629LlojwgzKEQRSQS3P0TjgJM4nQpNQTqqXcPsaOlkm8vMy1sHGXb6KEpW8YczSzl9ZkoM0H2BEK9v7eWh9e10jbopsuq555wZLJkmSxg6XS6eXD3GG+1+Rl1+pqcaufSYbKalmXB4AzT02Xm6spudvXbidUq+MzuVFJOaMLKAxXu1vbgCcsn3i+bIlUolJSUlOBwO6uvrUalUaLXaL62oHWHJfo1RWVlJQUFBjCZ+/vnn8/rrr08BzMk+cFFFnC+Lp556CrNZZtM9/fTTtLe37xNYggw6fv9+3N3tZXyTM7Wva+0vAsxgMDhlvtXlcqFUKmNErPT0dLZ6BqGhldzsLAxqBWVZSqCNMXeA91o9/DhLRBWZj4yaLrsiKj1GtYTdG4zpxIqCnLXZJ+mVZsRr+dWSfP7wXgv+UBiVJHJMjpH3m8YJhUKoIvJ6YSDVrKJr1Mu7dTJJJqrUE2VpSqKA0xuM/ZydoGPM7Y+Jpdu8ASRRRTBMTCs2I05Lba+DDW1ySVarlDg230jjgJPeiFDBG9sjZtfBMGatckpZtN/ujQnNR51KfrO0kGtPyuGHz2ynoV9eO3rN6WY1C3LiODrfwumzUnj0kw5OKEykfJL0XzgcJl6n5IELZ3PBY9Vc9Z+t/PuSst0yvuJkA09cPI/vP7mJHz69hRvn784oFwSBS47OJjNey89fruWuLUpu1PST2N3NtGnTprQw1EqJ3ywr5rgCC798rY7lD1VyYXkGVqOKLd02arrGYlrAaglmpZu4/LhcZmeYGHf7eWJDJx/sHGRnn4PLj83hO3NSUUVudrZ0j/P29j7e3tbLqCeITiVxamkSp81I4ej8BCRBoHaXjVX1g6zaOcCd78t9aHk0yEFenIJzZim59uyFsf3K4w/yUs0uHvm4nT6blxlpJm7+ViEnFyUhivLn/qPGIe7+oJGGAReFVj3/OH8Wp5QkIQgCg3Yvj33SwUs1PRjUCm5eUhhzVmkZdHL7Ow182jpCukHgwRVzWZi7d/udwWCgrKyMwcFBamtrSUxMJCUl5QtbRUcyzK8penp6yMycaMRnZGRQUVGx23H3338/f/3rX/H5fKxZs+ZL142CJciemPvjWKJQKPB4PPt83t7GEb3Xz1/788yuo7q6n0fE+uwMZrQ3FK9T8OR2J2UFdkRB3tZ6bT4KrLJOrACcWGThndqBmJekKrrGJEWZqo5xbl1WwB8iRJ0Pdg5ySVkC7zeN4w1EADFyvCCIpJjUMSBrGXKRGa+NAWTUEaXX5kGjEPEFQxRZ9QgCdI968AehZVje8GOM0Mh1dI16Ys8v0aDCE5BHWvpsXtyRG4Axtx+FAC5fMMbMPaEggY+a5ednnkQuMWiUPHj+DM5+ZBMJOiWPfncWNV02KtpHWdUwHLMnU0oClz+zhSuOz6Ew2SgLBPiDKASBkhQjfz57Olc/t43fvLGTP589fbf3pzTVyGMXzeOSJzdxxwY/c+d4SDbtPh99SqmVf18ynyue3cItH41xx7I8tm3bRigM9rCGHaNDtA46aRt20TbkjJWwH98gW6ZZjWoW5SYwN9PMvMw4nLuamFZagk43IbN35uxUPmwc4p8ftXHLmztlNxWrnrZhF302LyqFyPw0DUunJXHG/LzYKE80MhO0JOiUMcNSpSSQoFMx5vbTOhbgwTF4q2M9ZdkJ+IIhNrSOMOYOUJYVxx/OnMYx+Qmx16eqfZS/rm6mpnOcdLOany0w85Ol85FEAbcvyOMbOnjk4w58gRDfW5jJlSfkEq9T4fAEuGd1M09t7EKrkvjlkgKKxf69BstoCIKA1WolJSVFZgxv3EhBQQFJSUn/NeC4pzjsAHNv46qrruKqq67i2Wef5fbbb+fJJ5/c63Mnk372Jb6qHuahiEPZwzzYgDnZz3N4eJjh4WGqq6unmF0bjca9IkdFvR4VEdJHFDBnpBppHbDxm3faCIVlQKnsGOO4goTYMXFaJefOS+M/m+SSbVSAfbIjxqbOMYadE1WHXeNeXtwmA5A3IGeY0ePD4TDpcRoGHD6CoTDhMLQNufioKULO0SkYcPjY1mPHGGHYqpUioTDMzzJR1WmjdUxeqz0yghIVV1dIIk6fnJ2aNDLJJ5qF5ifqaBly4Q+G+aBhmBSTfJMgEOaak3ImAFMzVVAjQa/ittOKuOqFHbxdO8D1i/O4YH4awVCY5mEPFW2jvL9zgK3dNv6yqmXKuRadRHbiAJnxWhbmxPHGtj40SpGz5qShlESUkoBSkrP7JIOKO08v5P+zd95xchXk+v+eOWd62957TbLZ9EIQEnoJCAKiIArCtSEqgvXq/aEX5apXLooKKlWUXqWDCSUhpG42m77Zku29zuz0mXPO748zc3aHTSCFING8nw8fZjanz8x5zvu+z/s83/17I194cCv3XDUPUTTobNjxQJTx+Ovllems2jvEt55tIt1hYtQXQWGfvt9Um5HSDBunV2dSmm6lfyLMSzv6GfFHSLEa+WRtDi6rka2905VzxoNR/GGZ4jQr+4f9jPgjbGiLYBBgcXEK3zitjJTIIBkZqTpYqqrK5vYxntzaw+t7BonKKvMK3Nx28UxWzs7BZhKJygo7usZ4ZM0u6gZknt8xOdoiCNo87ZNbe2jo8mCSBN5oHKKh20umw8R/XziD04stjI4MIQDPNfTymzdaGfCGOWdmJt85u5KSdBuKovL3hl5uX9XCsD/CZfPzuPnMCuySwu7dIwf+cRxCyLJMcXExFRUVNDU16WMox8Im8OMQxx1g5ufn09U1xX2+u5v8/PyDLn/FFVdw/fXXH9Y+jtQT81gD5rHMAo+1cMHRRDQaTeo7JmQLE36e0WiUuXPnHtm2ZUUvpQIE4jOOTrPED05O4UdvjZGoUG7YPwZngj8c03qSooGrl04CZiAi0zUWTMowA1GFda2j+vtP1mbx4k7NDiumqCiqqgOmrGpOH/PjIyEFKRbGg1Fe3q2VO1Ehw26kbThAfqqFQETGKolMhGKUlKawpdOrS9i9El9nxB/BbTVSmWXn3f1jROLjLMGogiBoJcFvrCjhpmc0dvBJJSls7/ESU1QEAZ5pmLx5D06Ep12/5ZXpXD4/l79s7ObUijQWF2vqPjW5Tmrz3XzplBIe39LNT15q5MLabE6rymRXWx/9vhijEYHN7WP0ebTtPrm1lye39k7bx9ToGA1y7u83HPTfbSbNwFtWVYZ9EXIcIp+Zl0WGIUCeQ2Tx3FnTFLy+eVo5d77ZysObu3hl1wDfO6eCPFlGEAR293pZ0zzM2uYRtnd7UFSt13f2jCyWV6aRajPxyq4BXt41wDUP1VOSIvHp+QLn1NpYtXeQp+p7aR8J4LJIXLGogMsX5lOdndw33dHj5YH1nbyxP4poEDh3RhqV1gAWqxWfwUnrSJCGbg+v7xlMOu6JcIwHN3TyQoOAIst0vvgOI/4IeSkWblhRypwCtyYxOOzjnnc62NbloTbfxd1XzmVOgVZR8/l8R0UiTLBkzWYztbW1jI+Ps3v3blwuFxUVFbpq2cfVBepw47gDzMWLF9Pc3ExbWxv5+fk8/vjjPProo0nLNDc3U1mpEQ1efvll/fWhxpGWZI9n0s+xNsA+1Jg645pwZXk/AYhQKMTQ0NAR7y8mq0kszwTYWU0G8l0i/3lmIT9+VZuv2zfop98b0kukJlEgx2Umz22m1xNGVeGLf9vOlQvz9O2l2YysaZ4EzPmFbtxGmb/Va0/1XWNBvCFtn7KiYjEaqMrSAHMiFGNegRtvKEp9l5f20SDVWXaG/VFissaoNce9MhNKMwkj6PNmZvDa3mG290zgNItkOSeH3p1mkUBExmgQcFgkXf0HoDrbjtMisbZlFIMAj26ZBLCHt/RwxaI83cYrEd89q4xN7WP8+IV9PPPlhTpjNBFXLC6gadDHI5u7ObUinSvnpmI0GvUH3UhMoX0kwA//vps9fRNcu6yIeYVuYnGd2KisMhEI0j84RMScwnMNfRgEga+vKGV+YQopVgm31YjbatRL0Yqi8teNnfz6H8081jDMry+rpcIpU19fT15eHkVFRfpNPMVm5CcXzuCy+bn81wt7+eFze3CZwPDmBl39qDbfxddXlLKiMoPZeS59DAXg5HJNpeiZbb3cu7aF29/q4va3tIf6kjQbP7mwmkvn5SWVaKOywut7BvnLhk529nhxWSQuqrTwnYsWke2yoKoqPT09vFq/n8FxiQFvmBSrxIW1OczJdzMWjNLvCbG3f4Id3R69rw7QOx7irjWThuSggfxtF8/k0nl5Scd+tHJ8710/JSWFJUuW0Nvby+bNmykqKiIvL+99tnB8xXEHmJIk8Yc//IFzzz0XWZa57rrrqKmp4ZZbbmHRokVcdNFF/OEPf2D16tUYjUZSU1MPqxwLWj/zSEqyCW+5YxX/aoCpqiqBQEAHx4QrS6LvWFxcjM1m+0AywVEJFyhq0mB8otxqNUmAzOzsZH/FN/eN6KzVxM25INVCrydMusNETFa5f8NkBeT0qnSe2z6ZpZklA5UZk0LfO3t8dI1qbMqEx2ZKHMA8oRgWSSAr007ToJ9ARGZPnw+jQWAsECUSkxHjurIJwYNMm8hQQGZmroPX9g6TbtdYsS/sHEAyaKIGQ/4owaiMaBJxx0ULErG6cZjSdBuSQaAyy85XP1HI9U/sBmDEH+WU/1vPgiI3S4o1VmxtnhObSeQXF8/g6oca+OU/WvjZhVVEIpGkTO4/z6uiZciv9SrPzWNe4SSAmyQDVdkOHrl2EV95pIGHNnYxt8DNBbWTSj9er5eOjiC1tTO55qQivvJIA79/az//e2kNi4qTZ0EBDAaBL55cTGpsmLu2Bbn2r/V8+RMl3LBiMV0d7Zq1VUUVnX4D2zrH2dblYVu3h/H4SMZEBFRilGXYuPmscs6emX3A708kprC2eZiXdg7wVtMQoahCmk0i22VhyBehfTTAz19p4vXdg5w9M4slJam83TTMI5u76PeGKUm3ccsF1Zxd7qS/p1MHy7ebhvnT2j4auiOkWWN8bqaZr509m+x0jTzV2D/Bb99oZWPbGClWkWsWZHL92bORVa0S8NCGDp6p7yWmqqysyeaWC2YkWZMl4lDHQg4WB5rDFASB/Px8fQxl27ZtLF269Ij38XGK4w4wAVauXMnKlSuT/nbrrbfqr++8886j2r7b7T5saTz4aHqYxyqDPZbEnESEw+Gk0mo0GsVms+FyuZJcWQ4njlZLNiorev8SJvuPNqOIIChJIxYAz27vxx9OZJgaYKbFb0TRmMJDV8/lcw9u05c/vyYzqaxpkgx4pphHy6rKHfGZzWhMSWLFxhQVbyiGIAik2YyIgoBRFBj2R4lGEkQhbTvm+DmUpBgZCsi6UbTLLFGRaaNzNKSTif6+fYBAOIZVEnXRgkT0eMKIogFVBbdFwjYlm5yT72RX7wTDvgh3r+3grrUdWIwG5uY5qM0ycVqJlRd2DlIgjLMoR9NULSsrQxRFjKKBOz9Ty+X3bOHWt/r582V23pt3WE0if/rcXL708Da+8/QuJFHgrBmanvPUcYfSDDtPfGkxX39sOzc+uZPvnR3kPz5RfMDSf7FL5NGr53D7213cs66dV3cPsKDQTfMg7Ht9m56Rl2faObM6UyP9FKXQvncbXcYi7lvXzjce38ni4i5uOK2Mk0pTkRVNFu/lXf2s2jvERChGqs3IJfPyqDJ7uejkGhx2O6qqsrPXy6o9g7y0c4CfvTLZS81ymviPk4u4+qQictwWxsfHEQwGXtutzVnu7feRn2LhpxfO4NJ5uURCAfbu3cuOFgsvt6u8umcIl0Xi5jPLWZGnkbAk0cCLDb389s1WhiYinF+TzXfOKqcwzTbtuujfv6Oc634/IRVJkqiuriYajZ4oyf4rh8ViIRKJfPCC74mPood5LIk5H2bEYrEkVxa/38/evXtxuVy43W4KCwsxmY5eG/NotWTfW5L1xUuyCTWURMYpoBFGWgb9+oxjIjMNxVR9nKQg1cq5szJ1lqgoaKSVhFSeOU6+SYTpPdmtMc6atRkNBKMK7aNByjIEnBaJIV+Ei+bk8sTWXiLxO31Cts8Yz3YTLikJwPRHZLKdZhxmiXBMYTQQZSDeixwLRsh2mZIyzJk5DpoGfIgGAbc1Ofu889M1XH7/VlAVHrwkj4aucXYMhGka9bGpI+7vKcA9u6IMiWlkewMY96xn8awyZpfkkGoz8cfPzeXyP2/i/73eyZMl+dOYpHazxL1Xzee6v9Xz7Sd3cteVc1lRmTHtxpxmN/HQNQv4wXN7+PWqFjrHgvzX+VUM+6K0jfjZP+Rn/3CAHe0eBlc3MBgfF+kaC9I1FiQvxcIXlxVR4Vaxh4aYXamVDhO/g4FmA19cVsQVi/J5amsPf17XzhcfqifTYSIYVfCFYzjMImfPzOKC2hxOKk3FKBrYunUrkjgpb7ij28vbzSP0ekJYjAYqM+0YRQP7Bn3cv76T+9d3UphqJd1moH0kyHion6I0K7+8ZBYX1ubo380Rv5Hnex0829CL0QBXzUvnxnNrcNtM7N+/n219Qb7+wib2DfiYV+Dmd5+Zw4Ki6Zn3e+PDEEL5oHvHP8OB5VjFCcB8nzhcM+hjXdY8lsSco4kDjXQYDAa9tFpeXk4wGGTevHkf+r4/7JKsL57dGeMi6ImeplEUePTaeVz38A564ySVREnWH4npIuVrmkcQDZogQSimcOPTuylOs+mAaZIMunk0wLwClw5uMUXljcZh5uY7cVmNhGNhej1hXBYjbqtIKKpJqsmKSnGqhY6xEG82ab3QhKVXTFGxmUQd6HzhGC6L5mpiM4mMBqKk2YyMBqIEIgr1XV48wcmqxTeWF3PDk7tR4uSgUa8fAIsIbXu3c3W1gTu2hnmxOcgPzqnhung/edgXoa5znNWNw/yjcZin42INANTvBfaS5TBRmGajMt3EjoEQn39wK19YWoBJEjEaNFasFGfHfvO0Mv7ntSZueGw7Pz6/ijSjTNdAiO3+bsYDcXZsMEowEiPbaeaJuh6e2tqjO76AJuyQbYWlJelUZjkpzbDjtko8ubWHl3YO8NqeQX58fjXLy8tobm6mp6eHWbNm6QzPnvEga5pGWNc6ijd+fROfo8si8dmF+Vy5pID8lMkSeywWY3uvj2cbWnl19wDhmEJNnpNbPzmDC2bn6BJ7MVlhS8cYD7zbycb2UbrGJg+8czTIXW+3sXrvEAUpFlqHA6zfP4IAXLWkgC+dXMR4fyeNO7dhyizm9lV91PUGKUi18pvLazm/JuuQ71tHW5L9d4sTgHmA+CjKk0cSxzqDPZSYOtKR+E9RFH2kIz8/H4fDMa0Ek7imH3Yme/Ti68kl2YTowHvnMiWDQH6KlXuvmsMFd28BoM8Tn20My0iCBqov7hzEajRgNmqAaTOKNPZPEsjMkqZ5ajRAVIGTSlPZ3OHBLAqEZZUhX4Q3m0ZItxuRVS1j6/OEyHe7UQHRYEBW4dSKNDq29OK2SniCMR7Y0B0/XoVUq0Suy0zrcIBAVNFYsfHZSoBvn17CLS83633KzvgICsA7+/oxGSCiQE/fAPao1od0WCQWLFjAYlGkh2ae2NrHyrlhlpRoYJHhMHHerCzOm5XFW00j3PjUbs6emckXlxXRMxZkb/cwTT0j+KIReie0a7yzx8v3n93zgZ/RT1/aN+WdRqCymURd/q4s006m08TePh92k4Hrl5fwqXl5ZDhM1NXVMXfujKRqxtLSND67qIBbX27k649t5/SqDH58fhXZhHl6zXYaJyQ2dwbpef1dAApTrXxmYQHLK9NZWORmU/s4T9T1cN/6Du5b38GpFelcWJvDqC/CX9f76fU1YDeLXDIvl88szKcmzzX1dGgd8vPQxk6e395HKKpwSnkan6x2kGmWCVky2DcwwY5uL5vbx1gdSm7BPF7Xw9tNI2Q4TISjCo0DuzCLcP2yHL5+1qzDtgSTZfmI/XcP53f3rzKbeQIw3yeOxQ3+aOKfkWFO9fScOtLhcrlIT0+ntLT0kMWXP46AOY0lG5nMKAVB0If6EyVP9xQG6IMbuzmpNBV/RMZgMJBtk1jXOsrCIjdGg4AowF+unsel99QRVRR9u4GIglUSiEZUct1mspwmhuOZy1WL83mivpc+r/a+ItNO86AfoyH5urnix5HIDhcWuajr9LJ7MEKGw8TCIgetcck+l1UiFFUQ0ErLC+MkmZiiUu4WqHIZeb5JO+8nto/omeHOMQPzqzIBP6k2o56J3HxGGZvaxvnxi/t49gCs2NOr0rnxjHJ++2Yrc/LdfOXUEi6el0c0GqWpqYnh4WEKi8u5f7uPp+t7uXR+Lp9fUoCsaJZiMUVjxsZkhbFAlHvXtdM2HOBTM53ctHIuqTbTAYGhedDHzU/t5PbVrYwGotx0ZsVBe2xLSlJ54kuLuWN1C09u7eGc361HNAhEZRXJAGVOlW98Io8LFpRQmp4seHFGdSZnVGfSMuTnN6tbWNs8wtr4rKzTCF9YWsANK8pInWLHlbADe3B9B2uaRzBJBi6ak8M1JxVRle2gp6dH6/W57Ly1b4h1rdr2Lp2XyzmztIyxZzxI23CAd1tHaOjSqhJXLSngEykeJHmUgb4eCgoKDus3FovFsFqtH7zgAeJYGUF8nOMEYB4k7HY7wWDwiJxHjhXQHsseJmjH7fF4DjrSkZubi9lsPqJzS5SrP+wf2FHPeMoHZsnqJdlIMsFnav8x3Wbk64/vwigJCAgUpFjoHg/RMx5CEg2YJAP5KRbmF7pYv38cFXh19xD+iCYa4I3ImCUD2U6z3mMrSLFQnGpl2B9hxB/VRNuBgTigJh4OEoCR0J9dWZNNXacXs1FgMJ6lJtR6REErG8uyjM0osG37Lv0c9g6FWVycgmQI4zCLPHbtfFbevQUVGPZH+c2b7YBW2t3UPsbcfBc2k8j/XFTNFx5q4Bf/aNGNt6fGV08tpmnQxx1vtFCV7eC0qgyMRiM1NTVs376dnq4Orq3JRTLk83hdD7kuC986o/yAn9HK2dl8+7F6ntvrweZs50fnVR1wucosB099ZQm/er2ZB9Z3sql9jC+Ux1gc/84N+8I0dHmo7/JQ3znOrl6vbu+WKGObJQOfW1LAXOMAeekxxjv3EbLP1EElElN4p2WEl3f28+a+IYJRhSynidl5LmRFZXPbCH/b1M2zDX2cXpXB6VWZTIRjPLalm30DPtLtJr55ehlXLiog3TEJqG0jQR7bPspb+1sRDQKfXZjPf3yihLy464wvHGNXr5dnG3oJRGQunpvLN04rpTDNxo4dOygsrGJwcDBJGP1Q4mjGSg7FqeTjWKk7mjgBmAeJhCfm4QJmgoRyLADzwyzJJkY6PB4PExMTTExMEAgE6O3txe12U1xcjN1u/9DO41iWuY++JDsJ4gG9Z5lM+tH7lVNECb59Rin3b+imOU4ESneYqM6y0z4aJMNu1E2bYwrkuEz0eSM8vKWHPJeRBNfFLBqQDJOuIiZJIBCVmZvv5M2mUfrjmWbToNZLTNQXEsdckm6leShAn1crD6daRKqyLLQOBfR+3nNb9jMR1PbhskgUllbAuzsBaB2NUJAWQzQIuCwSGQ6TnmEWpFjo9YRQVejzRvnSIzsxigJz810sKU7hwtosnt8xyGmV6ZwzMzPpugqCwP9cPIuOkQA3P72Tp768hPJM7bdkMpmYOXMmHo+Hc9LH8Nekc9eaNkySga8tL532GVmMIrecXUCaBR7Z3E3veIg7Lq/FZpp+o7cYRf7fympm5Dj45evN/FefzONtdYz4I7o8oFEUmJ3n4gtLi1gQN4fOdJppGfRx95o2/rK+E5MI1yyz86mZTrbW1zNACluHNGlDbyhGis3IxXNzubA2h4VFKfps45p170J2Nc/W97J67xAvxXV6LZKBFZXpXLEon6WlabqbTGP/BH9c28bruwcxSwLXnFTItScXk+XUdHNDUZlHN3dzz7p2xgJRzpmZybfOKE8SjZdlGbPZTHV1NT6fj71792K1WqmqqvpAYt3R+FkejrXXx6lSdzRxAjAPEgm1n9zc3MNaLzH68WEwQA+07SMFzMRIRyKDjMVi+khHTk4OFRUVbN++ncrKymNmH/ZxJCzF3kP6SYyRJP4WiBN0zGJCOm+yp5RuN/HnK2dzxp2bCEYVRnwRPlmbze1v7EdRVT0r1RiVEhBBAHq9URKyrJobiUKuy0T7aIiBiYjmNhIHg2uXFfDAhm4duIPxHmtChi8/xULzUIBVe7Qbsy8Uo8IdojbLxM7BCL6Iwp5RFQFwWQVynCamcI5ItRmp7/aAOl14/Qdnl3Pzs3tQZJWLa9I5pyaHzR0eNneM88d3OlDRSrzf/3sjbzWNUJllJz/FQr7bQkmGg1S7ibuunMtlf97M9Y828NRXluC2ao4YoihSXl5OTk4OkrQbz4SF37zRilkycO3JxdM+JwH48uIMakpy+Pkr+/j8g3X89tO1BKIy+4f97B8KaP8f1vRiQ1MG+Ru6vaRYjVy7rIhzZmUxO891wJJuRZaDOy6v5WvLS7j1mTruXdfOA+sFJFEgFO3DIsJplWlcuqiIk8vSkkr5AOGoTF2/TENzO5vbxxHjknnZLjM94yHebR3VSGGCQEmGjUhMoWssiKhSnasAACAASURBVNVo4NOzXXx+UR4zSgsA7UHumfpe7lrTxuBEmFPK07jxzHLm5LunHfdU4HI4HCxatIiBgQG2bNlCYWEhhYWFBwWsY51h/qvFv9fZHkY4nc6PnXjBoYJOLBZLIuWEQiHMZjNOp5OUlBSKiooOCOjHs2PJkUZUVpIAM5goyRq0DDMQ1aTzDpRhmiSDDooGATa1j3PerAxAA9pEb88XlrFPyYaskkAopuVxrUMBfCFtQL59NMTGtjF8YRlLfLuJTCMhOvBEXDpueEhzSBkdG8MmQfuYlokGZSgryKFtOIDbquKLhPXSrCcYwxeK8ZeNkwbYVy7M5e53OpHiGWZwCtCUZ9qozXNS3+WlxxtheWU6yys1709PMMrWTg9v7BvmpV2DvLp7kJcmK72AVuYsSLVSkm5lW5eHz9y7hasWFzAy5CdjbASXI6SZQTuKOXvGGP3eXn75ejPdY0EWl6TqGrFjgSi9wx7Gg1EiGMlwmNndO8HZv1uv70sQID/FSlmGjaWlaZRl2CjLsDO0fzd+dym3r27hr5u6EASoynYcEDC7x4KsaR7m7X1DNAxpDjKqqhKOap9Vbb6LGY4wrkAvquwC0RT/DP08ubWHvzf0MR6MUpgq8p2zKrh0fq7uZZm4Zve928FzDb20Dvknv3NRhb/v8bJ9IMqsvHFMkoGNbWN0jgaZX+jm9stq3lcc/b2gJwgCOTk5ZGRk0NraysaNG5k5c+YBy7RHA5hHqxJ0PMYJwDxIOJ3Oj514wYG2rSjKNCk5g8GAy+XC6XSSlZWF1Wo9JFA5Xk2kjyZispo0C6iTfKaQfsT4yAOgq/yA1tdMzG1KBgG31cjPXm3Rl0u3a+zDiXBMJwudUpHGupZRylJFWsdkfvmP1niJUCuxNXR7UVQwxY/JH9AYrHMyReoHYphEjcH6TKP2MGe2OckXYnSMBjVPS0XTwQ1G5bjLCnxmfi6P1/dhNRpItRnZ3D6un0NUVnSbMmvcSDoRLoukk4vquyfYN+DTdVDdViNnVGdwRnUGZ8/I5FtP7eacmRl8+eRCej1h+iai9IyH6B4Paj1dg0D7SIDbXmuKb91z0M/k4c3dPLx5EtRtJhGHScBlFslyW1hUnIKiqGxoG8UbjPG5JQV856wKvcw5Ndb3Gli5MJ+zZmZyx+pWHljfycu7BvjP86o4szqDbV0e1jSPsKZpmJY4iBWmWji9yMRnT61hcXEKnlCMZ+p7eXJrD7/tDJG2J8xJ9e9SnJ3Glr4odZ3jGOMiC7Ot41x3wclJ8nPeYJQnt/bwt02T6j43XFjGBbOz6fWE2DfgY93udnYOybywox9FhRk5Dv581TxWVKZ/4G/3YNyAhHBAwr/SbDZTVVWF2TwJ4h9VSfZfJU4A5kHi4yrArigK/f39upScoig4HA5cLheFhYXY7fYjJtYcawH2jyMBICqrOgNVVVVCsUlWbKKHmVDYAXSVH9BAVRdOV1TOn5XJzt4JtnV7kRWVWLyJ6A/Lurj75xbl8U7LKDFFe39qRSprW8bY1qU9nCX6jqNDmtD26LgGLEvKM6kf6MNsMuKLRhEEAyCzp99HabqNGTkOdvRo31eXJc6Kjd+nrl5awOP1fYRjCstKU6jIdPCrVZp7yL3rJ4Fp74A/yWnFaZH0BwKbSeSHzzfy+HUL9N5sIk6rSucbK0r4/Zp2anKdXLesEKPRmHSjVFWVu9a08fu39rOswMz3z63GarMTU1RNM1ZR4vq4Mne/1cKWrglOK3Vw+2cX4LSa6OzsRBCEJGs/XyjGT15q5JHNWh/59stqDmj9BZBqM/Hj86uYlevk7jVtfPvJnYgGATlekl9UnMrlC/JYUZVBjt3Anj17WFihZdNZRpHrV5Ry7clF3PtOO0/V9/JKexjah5AM8IlSN98+q4rafBcbNmzQwbJzNMBfN3bxzDaNqHNSaSo/vXAGKyoz9GXMkoH6Tg/ru0IMB2Rmxc2fz6/JTgLdD4r3A6WEf+XAwAB1dXUUFBRQWFioPyCfAMxDjxOAeZA4GsD8sOTrIpFIUmk1EokQDocJh8NkZmZSVlb2ofYQjteS7NFEVFH07HFqOXJqhikI0+cyQSvJjsW1R2UV7GaRn3+yigv+WAdoLNOorBCOaVmqKMDSEq0sNhTQtnNZhZG1LegWYLlOib6JGNnZWdDRS1p6BuDHEWdpjvijmESB65YVcPsbbQQiCrv6fBSlTgKFyyrpvViTKEwKkqvQ741Qnjn54PLA5+dw49O7mQjJ9IyH+NIjO/T1Gvt9ukzf5xbmcM/6Hv6wpp3vnFk27Tp++ROFNA36+e2bbVRk2jnzPdqrgiDwjdPKQIXfv72fR7YO8PNPzT7gzXRZWRq/faOFP73TwRfve5ffXzEXVZ1ut+WwSNx+WQ2fKE/j1pcbueiPm/jlp2ZxerVGQBqaCFM3EGPta01s6/Kwu2+SFZtmM+KPyMiKyqLiFG46s5y5cQePQCCg70tRVLZ2jvPSzn5e2zPIeCCKyyKxsiYLu1liV88477Z5ePfeLczItjPLFWXI3svruwd5s2kYySBwwewcvrisiJm5Tv3YAxGZJ+u6uW99B0MTESrTJP7rvGrOm3N4YyGHGokybWZmJq2trTqbVlGUI97fCZbsidDjaBxLjiTDlGU5ad4xEAhgNBr1kY78/HzMZjNbtmyhuHg6KeLDiH9HwIzJqk6gSc4eDaBq9lyCIEwh8By4JAsagCa0SU2iQCAi818vakP3qiJjFAUadu0FIBDvi0lmDejOnJHB6sZh+uJD/QlGZ0ICL4EVZsmAoqpE4sbXaXaJVJuJ1qGAfhxDExGC8d6ry2JM0oqt7/JQk6uVVUUBFhW5cZgkJkJaSVbLcFUisspnH9hG4lbqDcU4e0YGD23sZnncxmtqCILArRdW0TEa4Ad/38uTGQ7Ks6Z7It5wWimdPX083TCA02rmB+dWTrthC4LATWdVUpBq4ycv7uWLf23g5kVWasoKpm1PEAQunptLjsvMLS828rVHt1OWYSMcU3TZQJPUTW2eiy8uK2J+YQrzC92k2TVJwEc2d3H/ux185t4tLK9M55unl1HqMtDukfnH6028smuAfm8Yq9HAGdWZXFCbw6kV6Uk90K7RAA+va+Kl3cM8OwDPNu9BACqy7Fw2P4+zZmZpxtloWfGjW7p5cEMHo/4oS0tT+fWlszGPtzPjEMqvRxuiKFJVVYXf76exsZFgMEgkEkkq0x5qJNi5HxQnMsx/g3C73QwMDBz2eodC+lFVNUlKbmJiAkEQdCm50tJSbDbbR/5FO14B82jHSvRy65Ts0WgQEBRNZEBgKmtW1gk4JlFIAlmTaNBJQZl2CVlWeDXuS+n1hzCJAq70LGBE9610ulOBTjLj/c5Z2Xb2DPhZt38MQAfGRBSkmGkdDtI6HERAK/deMDuVTIeJrR3jRBS44839mERthMRlTSbyhKIK7+4fQxA0W6upozOfX5zPfes1p5WydCtfPbWYW15qIhxTeLxe+y0YBLj+8V1cPCebsgwbeW4LeW4z+SkWHGaJ311ewxUPbOPrj+/gqS8vnuaQIQgCV8yyYnOl8OCGTsxGAzedWXHAz+byhfnkuC1864kd3LohyFc8zVR4FcYVM/uH/LQOa3qx7SMBIrHJc9w/HMAiGbhkbi6zzCNcce4pByT52EwiXz6lhM8tLuCvGzu5790OLr9niy5rKBnGObUig++dU8npVRnTeqSqqrKty8OTW3t4Zdco4Rjk2zUBfIvdybaeCX75ejO/fL2ZHJeZHJeZtpEAnmCMUyvSuX5FKQvjeq9bt7Z9pAQau93OggULWLt2LXV1deTn5ydZnh1KxGKxI5pTP57jBGAeJD6sDFNV1WkuHYkvWkIMoLKy8rB+LMejMMLHtoepqBgN08utRtGAoAq6z6BxyoiISRKIRVRMkgFvKKqvMzzYT92oBjiyolCRaeOaZen8anU7rePx0RKjlmlkO0R6J2TdlDlxo/rU3Gz2/GO/Xjp8p0XTEE1cOpdFwigKbOkYxxxn2zrNEgZBIMNupHciiqJCKKYQ8kXwhWO8unvSeHhZaQob2sbj2af28w/FM9C5BS5Oiv+7aBBYWZPFra80EwaeuHYu+0dD/GPPEG81j/L0tr4k3VYAt1Uiz22hNN1GfbeHz963hauWFGKWNI1Y0SAgGQx09UZYWpxFtyfCn9a2M+gNs7wqgzF/lPFghPGAxowdD0YZD0RxmiUGJ8L8YiuwtVm7XoImWVeWYefUinSdFVuaYWP/cICfvtTIc9v72J9p4PSJsJ7hTY1Rf4S1LSOsbRpmXesIvrAmH5joPWe7NILRyWVpSWDpCUZ5fnsfT27toXnQr8vgfXJWGtJEH8XFxTQ2NnLTkjzao07uf7eLhh4P/d4wZ87I5PrlpdTmJ8vlybJ8RNyDoympCoKA0Whk6dKl7N+/n02bNlFdXU1a2sEZuVPjRA/zROhxpD1MgImJCdrb25NGOlwuF6mpqRQXFx+xdiNMZmrH4mn0WJJ+jvVYyZE+REwtyQaSAFNAkAWCMQUQMEnaPjyBCHFDEHZub6CpaxIwc7MyyXDZoH4vBlHCabNQnaPdGO0mEW8oxp1vaVZeeXHAXL1PGw9J8Dsi8XETu0nEH5FpGdJYsutaNQ3VQFShOM1Ky1AAu8kAqPFxEFkn+RSmWugaC2GTBBAEHpwyRrKkOIUtnR5icXF1WVH1sq/LIrGkRAPMjtGg5rkZz3DLMmzMynNz4exsnt7Wx3+/0syVi/K4qDabHk+I3rjCUY8nRK8njCgI7B8OJFlaJcWWRv3lsw19PNvQp7+3mzWd2FSbiRSbkeJ0G0HfBDsGIwz6opxe7ubSohAzyg48Y7iwyMSzX13C3zZ28ts3Wrjwrg1cv7yUa5cV0Trs5+2mYdY0jbC9x4OqavO0Z1ZnsqIqg0+Up+P3jvHCti7W9ij8elULd761n/NnZTG/KIX6zjFe3zNEOKYwJ9/Fzy+aycrZ2djNEhMTE7T5DaSkpBDLqOAnbzaxtbcDs6Qp91x9UpEu3vDeONIRjaMZ7UiArSiKVFZWkp+fz969e+nq6qK6ujrJz/RAcQIwT4QeLpfrA+cw3zvS4fP5dHJCWloa2dnZWOJuDh9WJDLYYwGYx2tJNuGJeSTXJKkkG07OMGVZJhDRCDve8TE2b97M8LiiM14Xzp9LQ7gXmjoBcNotepYak1WM0mSPc0aOg5ahAOtatVKrigaSifeJr0iCpbuoyM2allFm52rrbWjTRkEGvWGWlKTQPR7Sgc5pmdSKBbjpjFJufmYvsgpnVaZRkWnnzrfbAfjt2+2YJQEVCEZlPbsEbVQkGgfsmKLys1ebNW3VKaQngE/Pz6VxwMdjdb3MyXdy4ezp5sqSJPGbN/Zzz7p2Pjknh2+dVoqsatvdsXM3ZeUVCKJEJCbzl41dvNE4xJkzMvnfS2p0R4+psW/fPlzuVB7Z6eHedR10e+3caPPS17eZWbNm4XQ6k5Y3igauWpyPPNbNy10Sv3mjld+9tR9ZmZypvGFFKSuqMpid60pipIYm4LRSB185t4pVewa5e20bL+zo5/kd/Qjxz/K6k4v55JycpN92IBzlzY4QP3pnI82DfjIdJm5YXsQcm5dUW4QC18FvtwciNR1KfJhzlDabjYULFzI4OMjWrVvJy8ujuLj4oMd1QrjgROjx3gxTVVWCwaAuJef1elFVddpIh9frZXBwkOzsAzu0H20cy7GVjwLUjkUcjSempvSjnfeId/IBaffOHVgNMaKKBmyZaaksWVLN3fu2YzGFEYIyFpPGtLTGvStNogFPMKJv1ywa9DENVYVcl5lPzcnmwY3dbOuPIBmESdJQ/PADUa1HWp1tZ03LKJ1jQUrSrBSlWVm1b5ixYIwtHR6ynSY6RjVSi8si6UBrFgWWxAk54biwfLZrkpjxzRUlPLChkzAqTYMBrpxidi0AvriS0eIiN6sah+PbnH7dfnB2OS1DAX76cjOlaTZq8pIBSxAEbj5L04a9Z107aTYj/3leFYIgMO4yMDvfpVdaFpekct+7Hdy+qoWvPdrAXVfOxf2e3qeqqpiMIt89u5KlpWl8/9ldfPcfg3z39GKUXbtIS0sjp7CEXX0+6jvHqe/00NDt0asGbqtETFHxh2UqMu187dQSzpyRecCH2e7xEK/s9rJx1QaaBv2IBoGTytLId5vp9YTZ3D7G957dzW/fbOXcWVksK01jR4+Xhzd1MhaMMSPHwa8umcXK2Tl673RwcFAf6SgqKvrQHqKPxp7rYCMlWVlZpKen09bWxsaNG6muriY9Pf2A+z4BmMdJvPbaa9x4443IssyXvvQlfvjDHyb9+x133MF9992HJElkZmbywAMPHBa7NGFhdfPNN1NUVMTJJ5+M1WrF5XK970jH8WwifawzzGPVwzyS/miirxyJKQwPDlBXN0z30OSNZ+H8uYyOjAAtqIDFrBFkEqQfU2JOMxzDMgUwE2MYEVnBLE2+V1QVs2Qg162VuZwmAU9YIw5FZBUV4iQiGZdFIhYHam9IJtelSdilWI2MB6KaEfToZCnYaRYJRmQEFRwmQxIrdk/fBLX5k2B25aI8NrWPsaXDgwqMBya3c/Gf6/S+Zp7bwozsGI0DfiRxelnNKBq449KZXPngNm58ejePX7eAjCli4onlbz6rnGBU5qGNXVhNIjedWTGtfC4IAl8+pYRct4UfPrebK++v497Pz0vymZyagZ1SnsaDVy/gR3/fw8//0UZxmhWUfjrHuzS5PgGqshxcWJNJhuDlsuXzyU+xoKjw8q5+7nq7jRse30FNrpNvnVHOisp0hn0RXt09wMs7B2jo1mZfFxalcMsF1Zxfk03aFOcRTzDK6r2DPLG1hwc3dPLAeq3CcHKJi5XlZj596pxp1ysBQomRjpkzZ+J2T5e5O9w42jnKg4GtKIpUVFSQl5dHY2MjXV1dzJgxI6lMe6jZ7YmS7D85ZFnmhhtuYNWqVRQUFLB48WIuuugiZs2apS8zf/586urqsNls/PGPf+T73/8+TzzxxPtud9WqVdxzzz00NTWRmZnJ8PAwV111FcuXLyc/P/+Qju1YA+ax7jNGo9EPXvAIt/3PEkWYOrLj8XgIBoOYTCacTieyCnk52SxZUsbejd3AfgDMRlGXr5NVksZKJFHAFC/j+sIyVqPIGLG4ObTmRBKJKRilSQaqrGiKQomMc3amiZ3DMt44oLYM+jEbRbzhGA6zSDgmYzOJBKMK/RNhAlEZs6iVUv/j5AKe2dZPT9zI+per9jMRjuEwCjjMhiRWbNNQQB85EdD6g/6IJvu2qMhNXacGDpIBvnpKMY9u6QHguR2TDPGJCPxlUzeFqVbyXBbyUiykWCXS7Cbu/HQNV/+1gZue2cP9V83RM6oEKAqCwI/PryIUlfnT2nYsksgCy4H7zRfW5pDlNHPDY9v57L1b+OPntEyzdcjP+j1exnaG6fa2sH/Yn2R63TEaRDIIrKhI46SMCDMyzSyonYWiKDQ2NlIQJ/yIAlw0J5eVNdm8uLOfO99s5auPNOAwi/jD2jWZkePgK0uyOKXYytLZldOOcdQf4bkGjfDTPhLAaRZZUZXB11eU4VB8OuP9QJEY6fD5fOzZsweHw0FlZeVRcRqOtbSdzWZjwYIFDA0NUV9fT25url6mPWHvdZzE5s2bqaiooKxMG6C+4ooreP7555MA8/TTT9dfn3TSSTz88MMfuN2ysjJuu+02KioqEASBefPmceWVVx7WsX0UgHkspfeOJRh/WIIOB9p2AjCnls4TIzuAPrJTVlamj+xEZQXowWLSfgZThdWNoiFO+EFXg9GWkUmzGXV/zARAApgkTfnHZjIwGohhFg1MhGN6Fum2aj1No0EgpkKmw8TsXCfr28bY0D6OWTIwPBHBYdZ6klajiCAIeIIx+jxhfZ9pNhPpDhMGAbrGw+wb8KGoEIhAuk2ke2zSENppEfXSqtMiYhAEvVd7elU6Q74IHaNB7GaJr51azKb2ceo6Pdx0egm93jBPbNXYsAmbr0RYjZp1WZ570r7sa4/v5IqFuUgGA2aTEUk0IBk0duyn5ubS7w1pZcxiiWj6GJ5gjLFAlLFARGPFxtmxGQ4T7SMBPn3PlqR9ptmClGc6OK8mm7IMO+WZdsoz7HiDUX76ciNvt4zij6YwqySNuro6cnJyktaPygpbO8dZ0zTM203D9MUfOEJRBRUtiz+zOpNT8wTSbZO3RlVV2dQ+xhN1PazaO0hUVllYlML1K0o5b1aWLq3Y1+c9JABxOBwsXryY3t5eNm/eTGlp6RFXXz4q8fTMzEzS0tJob2/Xy7Twr5U9Hkocl4DZ09OTJJFVUFDApk2bDrr8/fffz/nnn/+B2y0vn/Tjm3oDPpwvhSRJxwwY4EQP870RjUaJRqN0dHQQDAYJh8N66Tw7O5uKioqD3lASoxuSYRIMEzOWRlHAP8XWQ/fDDMdItxuTnEgSWVViDtNpljTAlAyMBqI4zBKRmFai9YVj2M0iUVkr0bqtEgUpZixGkZahAHWdHnJcZibC2vr+cAyr0UDzoJ/U+E08QfIxSdp5JcY7DMCQX+brT+zWj/vi2hwejmeNib5gQgUo1WbkmqX53PpqC5GYgqqqega8oCiFearKE1v7SLfASAhuPqOU4jQrvZ4wPZ4QfZ4QvePaa4AtHR62dBxcIzYRr3fEeP1vDUl/c1s1AYbUOCu2OttBfaeHgYkwp1dl8JlylcU1FdPIPQB5KRYevW4Rz2zr5dermrnuSQ/XLitk+fgEvUOjNG5sY2PnBOtatNERoyiwpCSVKxYVcFpVBgWpVta1jPDI5i7uXtvGH4FTSpx8ZomF9hE/T2/ro30kgNsqceXiAj6zMD/JXisRhzMaIggC+fn5ZGVlsW/fPoLBID6fD4dj+nbfLz5K8fSEw0yiTBsIBAiFQh/Ipv1XAtXjEjAPJx5++GHq6upYs2bNYa13pB5ux1rR5nhlsn4YPUxFUfD7/Xr26PP5kCSJaDSK1WqlqKjoA3+8UyMqJ89Y+uM3UwCDIBCMTR6vUdQy0oisYhAmS7L+sIwjzopJKP8krLmMkpZhaiVWBVP8vd1kICKrmM3ae5fFSJ7bQlRWGfVH6POGGfZFcFslAlGFU8tTead1TN+PBpgyRtGgW0htbB/HJAkszrGS6rLzSlww4fkd/TopyRHPpBOOLG6LhMU4KQv49x0DSSSZrnimWp1qICA6+OM7HfztmnmcUZ0x7Vp6glF+8nITb+wb4fOL87l4Xh6yquqaunJcMzYUlblr1W72jSmcX5PFj86vJs2mZaPvjZis8Pu39vPnde209IvckRNkzgEAE8BgELh8YT4Litz890v7uPfdTv4iCvGHolbSrCLnzsrijOpMlr1nrhJgRVUGK6oy2Nc/wc9f3Mn6jgnWtmkygQuLUvj6ilLOnZJNHiiOhKltNBqZMWMGHo+HnTt3kpGRQVlZ2SFv559hz2W1Wpk3bx7vvPMO9fX15OTkUFJS8m9Rnj0uATM/P5+uri79fXd39wF7jKtXr+a2225jzZo1RyT9dCTjCh+FtNXxWpI93G2Hw2EdHBOCDwcSmt+9ezdpaWmHBZYwmWFOVfHRwFM7zqm9QJNkmGbtBVqGmWoz6n/TSrLa98UczzgdZolhXwSzaGDIF8FhEonKURxGDWCdFolQTLMAC0ZFFhW5qe/2MhzXl02xGZEMAqNxgk5CXF00CLhtRm5YUcLG9gZCMZVMu8TpMzJ1wJyV62RT3J2kecjP/7zeoosxuKxGOkeD+jZ/9Y9WXVg9xWqkoVsThHeZDdx28Sw++0A933pKI/gkzjkRbquR/7t0Fj98vpGHt/RQlungqqWFHCjs4y1sCmRzz7p2glGF31xei3SAn5gkGrjprAoWl6Ry85MNfOHhXfzkghlcMi9X71vvHw5orNgujRnbPqL1a0UDiIJAFJXCVCvXzHVRZhpnZnbuNLCMxBTeaRnhpZ39vLlviFBUIdMucVp1Fl9cVkTFAbLJA4Usy0fkg5uQmFuwYAGdnZ1s3LiRqqoqMjMzD2ndf4Y9l6IomEwmlixZopdpq6qqyMiYfJj6OAqVHG0cl4C5ePFimpubaWtrIz8/n8cff5xHH300aZlt27bx1a9+lddee42srKwj2o/D4cDv9+NyuT544Y8ojnVJ9p9V7j0YMcftdn+g4MORlntj8XWmlmRFg4BKPOuammEaBH3kQns/2cNMAK5JEvBFZF3mLlGCdZhFejyKZhYdL8mOTUQxiwaGfREy7Da8oSiWOIAWpFrxhWUGfWE6RkO8uHMQo0HQAdxlkQjGFKwmEZdZItup3aQVFcIxJYkle9snq7nt9Rbeahohpqg8Xd9LQm3vRy80khlnttbmOWjonsAT1EDZaZEY9WsjMi4TZDg0gs81f23gu8/u4U9X1k4zUBZQ+eGKXMa9fm59ZR9Wk8il8/OmXXeDIPCdsyvIcZv5+Sv7uPovW/nz5+aR7jgw2JxSkc5tK1zcs0vhP/++h79u7CLdYWRX74TO8k2xGVlQ6ObTC/JYUJTC7FwnE95xnqtr55mmMD9/e4AZ2XYuHN/HSUUOKiqr2N7n56Ud/by+ZxBvKEaKzcgl8/KYlxplWWU22Yd53zjSWeAEcBkMBkpKSsjJyaGxsZHu7m5mzpz5vg+Ch6rneqCIxWJHta4kSRgMBsrKysjNzWXfvn06m9YaNws40krdxzWOS8CUJIk//OEPnHvuuciyzHXXXUdNTQ233HILixYt4qKLLuJ73/sePp+Pyy+/HICioiJeeOGFw9qPw+HA6/V+rADzX4HJqqoqgUAgSUsXJok55eXlh+zhmTjuI3mancwwJ8FPMgi6iECS8s97MkyjJKCo2lxfAnC1HmaMwrhziFESmAjLFKZY9B7mRDhGntPIgKJiNhrwhjRAHfSFsRlFJrzbJgAAIABJREFUAhEt4wzHFFKsJjoI8ZkFuTxVP6mE09jvIxSViSkSaTZjUibc0BdiccUksLusEoqiPQLYzSJWk8jghAaEuS4z2+JZ5Lv7x0m3a3OlArClY5z2ePaZYtbOb3aek5+srOLHL+7j/97Yz00rCvF4PHoVIGE19+PTc/jx61386O97EFG4eP500XSAq5YUku0y852nd/HZ+7Zw3xfmk+e20DYSoHXIr+vFaq99JE5zb/8EogALi1P4ZG0Oi0pSKU2frr08oaosL3Fw7VnzeWlnP797az+3bw6RuTtM+IV38EbAZhQ5a2YmF87J4eSyNIyigcbGRqQjAL4jZY2+F2gtFgvz5s1jeHh4GjP1vfHPyjDfW85NlGmHh4fZtm0b2dnZ/5Jl2uMSMAFWrlzJypUrk/5266236q9Xr1591Ps4Gnm8Y6X3+nErmx5KRKNRJiYmGB8fp6GhgUgkgtVqxe12fyAx51DiSHVqp5VkwzKigG68nHAUSSyTGBFR42Mmwfh4RkJazxxX9rHEAThB2rGbDFoPM97jdGRYdNKPLyzjsEiEo4o+A+k0axmkI17aPW9WJmuaRwjHFMaDMW5+VnM8GQ9EyXWZk9R6Bvwx6uPempIBLJKBQFRGAc6oSufFXZO6sn+6spY/rGnngQ3dnFKWikGAta1jqMBXHt2pL/fw3igbRraRZRdJNanUZEg8sqWXwPgwZ1Sm4nI6SSnMwWySEAWNFfubK3P55uP1/PD5RrxeLytmlzAW1Fiwm3tiNL7bwVggymggwuw8Fw1dHs7//XpUVddwQBAgP8VKeYaNcnuEpTOLqcpxE5UVfvWPZja3j2OWRJaVpR3wt6YoCp6wygs7+nm7aZixgPagMBKIcVplOvPSYsxOhflzNOb01PU+StWdg5GFMjIySE1N1XVeZ8yYQWpq6oeyz8S6H7YXZkZGBmlpaXR0dLBx40Zmz5592K2Sj3Mct4D5UYTT6fxAebwDRaJseixUMD7uJdmDEXOsViuSJDFz5swjLgMdLI4cMN9D+onEMBgEHTCDUQVJgJiabOWlqGq8X6m9FwVtfcmgCRmY4mKz2liJjN0koajJJdpIXIUnEJFxxklBiVu+0yISjmp/Bw1AwzGFbKeZcEzhP88p55aXm/FHZOo6Pfzs1Wb9nPKcEm83j8a3I8XFFbTjrMiy89mFeTxW14tk0M47Mc945owMLpmbw7xfvINBAIdZJNUi0jEeodKlEgn52e0RGAnKeqb3XHOE55oHgPd39fn5m738/M3e5D/uasYoCjoztibPSeuQH19Y5qy4QHlFll0n2WzatImFC/L139RTX17Co5u7uOONVi64ayPfOK2Ma08uQhQE9vRP8HbTMKt397F3UMuSs5xmLqzNZUVVOstKJ0k/o6OjNDQ0JBFXjiZT/LCBNqHzmpeXx969e7FYLFRVVem90qPNEo/FugaDgdLSUnJyck5kmP9O4XQ68Xq9h73e8QqYR5K9JhSRppbl7HY7brc7iZgTCATYv3//hw6WcBQ9zAOMlViN4mTGGVUwixCLEQe3SdUe05SMMyFDKqvaf8Y4g8UYt/8yx5moRkkDL7tJ1CX3AG3uMqboeqaJ94lwWDRAlRVNMH15ZTrQjEUyUJZh0wUMADLsEr0T2phHYowkcZwui8SiIjeP1Wl9zBF/RFcikpQILW2aYk2qCfxRmcH4MVxba+HMU5bq5z7si9A04OPnr7Uw6Itw7dJ8ClMtKKqKogrIqoqigopmj/b0tl56xkOcViBxybwcguNDnH3qMuxmMVmLNSLzs5cbebahD28oyu2X1eqA+d6KjWgQ+MJJRZw1I5Mfv7CX/1vdwl82dCAIMOyLIggwM8vK1fPTuGRpBTNznAfMQtPS0jjppJP0LG7mzJlHBXzHKjO12+0sXLiQ/v5+3RM3Pz//qOTpjnV2arFYTgDmv1McaUn2454Fvt+2P4iYM9WmLBgM6k4saWlplJSUvC8x51ix5o64h6lMZ8naTKKecQaiCiZJwB/TAHLEP6naY5yiE6tlpRCOl0YTIycqAooK1vhNX0ArNzrMEhFZRYjnlE6LNqeZuJ274j3MxCk54oo/sqrqM5igye8tK0ulJsehl2l3D4T08/OFY2xuH9d7sS6LUbeuUoHvP7UNX1z7NuobJ+LWyn3ZqXa+ekoxNz69BwCrqKIoCoqizWqmWgwsLXbx1y/U8qXHdvNIXR/3fX4OcwsmTaVVVdU/k2tOKuD7z+1ldeMQaU4Pp6WFUKNBBEvyiIjNJPKLS2pYWprKT19q5FN/2sj/XjqbUyvSdWm8SExhb/8E9Z3jbI1rxo7EyUmBiMxpVZmcVpXO8soMguNDRKNRSnLfn4NgMBioqKggNzeXPXv2EAwGj+gB7EhJP4e6niAI5ObmkpmZSXNzM1u2bNHdRo4kjgZsD2XdEyzZf7M4FMeSA4UoisdMvOBY9jCnPoG/l5jj9Xp1k2u3231ExJx/ljTewWJqSVZWVILR6WbRGvhpAJkobcqKqsvggQaEZsmAL/4+Abhy/HwTJdrEIdqMQrysGXcbiWeUiTNwmLWephJfISFQEJUVUm2TPUtFjZdrp5hM33lhPn/YPE7jgJ9hX5T/eGSH/m9PbWwh26Ktm2YxsLknTL7bBESorS6Pz2S24zRLrKhIxWWR8IZivNUtU1U5Smpqqn6DFgSBXIuFB74wny/8pZ6vPbaTh66eT1W2Q/9MEp+LSYQ7LpvFL15v4bG6HnpyROyOXWRnZlBeXj4tC/nUvDxq893c+OQOvvS3bZxfk40hEOLuxq3s6PHqDwyFqVZOrUhnQZGbhUUplGXYk1xHukYPL1O02+0sWrSI9evXs2PHDqqqqg7LROGjykwTrQ2Px8OWLVtob2+nqqrqsMHvo5jh/FdiyMIJwHzfcDqdjI2NHfZ6kiQd07Lpsdh2NBrF4/EQDod1Yo7NZsPlcpGTk3PUxJyPJ2DGS7KiMIURKyRlmPFqqpZpxkuyUUXVhdITYRQN+OLlzTje6ts3xwFPjh9jQiwgodDjMGs9Sz2jNBsIxf4/e+8dZ0ldpf+/6+Z8b3ffzjmHyaGZIQgIAoqCqIvLyuoqopjddWVX19+Kqz8VV1gVs+uKuiqgICIsouQ402k655xzuDnf+v5Rt6q7Z7pnOkwjYc7rNa/p233rU3VD1VPPOc95Tpy4KP1NBvZITBoWHVyhirUZVj9ON6nIsqjpnYEDaSouytJwV1OYuAg1E2ESh0QwBulWHRMuiZ3p1eDyS6ldq0G6KdOpJQ78u94YhcnDHM5dOGXYebpNz8/eu5/3/ryRD/6qmf99/wEKUpYFNPIFU4XIv11VTJpVx3eeHkQw6rg1RcXx48cpLa/AI+oZmPXRNyupYvvnfIrF35/ap1EJUJUZ528PZXMwz8HBPAdp1tOn97fC+ARBQK/XU15ezuDgIOPj41RWViptEqeLl3umpd1ux2KxYDKZqKmpoaSkZFMAv12GuZH35LUW5wDzNGG32xkZGdn0djtdZzwbwhx5jqfL5cLn86HRaLDZbKhUqh0T5rzSbPfk9KRWtRIwRSWl6g/HlZ+1KknkY9JJtna6laO7SIiCEmuoE2xBWT8BwPHEY33isQzxRq2amIjCKOW/R+MiFr1GaRsJReNYDRoC0eXPXyOGGZuVygYCsDg7hTeoRgSKslL5wFvK+Hbj8wD8/sOH+EPzNHcfH0OnUbHgCyvHcN1/n1BUuj0zfn744rhiI5duM/CD5hDfy0ujrq6O0tLSVQ3qOUlG/ue9+3jfzxu56X+b+N/3HyTbYSASiyv+sFNLPsZnl/AveTmYpqZmaJGPzPqwGdQM/eWEAuQAGTY9Jalmrj+UTbHTTFGqCd9IJ2+8+LyNf7hsfcZkPB7HYDCwd+9epU1Cng15Osa0HYa5VQP2eDxOfn6+0gc5Pj5ORUXFKtXverHV9wden5NK4Bxgnja2k5J9pfi9iqJ4imOO3C9ns9nIy8tThDkAi4uLOyLM2cnxXlvvw1xOySotI7CCYcYwJFJ8Wo2kaDXrpF5J7YqULCLoNcuMU+7nD0flFK20hqzj0SVqmvIwY9k1SH6sTiwQicWVnkyAUDSGJh5mYHhMeQ0hzxLhuLSeRSeQl5eHamCeuBjEbtThDy2XBpINajJtkrryigont76piMvvqsETivHhi/I5PrhI05ibRX+Eu4+NKoAvW+R94P4hKb38dBtqFWg1GtQJc3WVIKBVC8x4Qlz3o9rEbM31zwGTToVeoyI/xcxl5Wkka8Loggu8YV8p+dkZpzz/pYnNX3jPhtpVbu2Qx3JVVVWt25e9Vaa41dqnHDIr3rt3L/Pz86eofncizqVkz8UpYbVatyz6eTkmc6wV0Wj0FMccg8GAzWYjJSXltMKcnYydFP2czZSsKK6sYcaxJLJOWrU07NmsV7MUiCQeS59xTBTRapYZp3yRkMeDySpc2VlIKz9OALbMYmNxEZNOrah3Q5EoNp1AW2c3AIGIiE6IoTVYAal1ZHdZETM9cwgsYNVLqVRPMOHWo1fhD0k/C4DdrFd6S51WAxajnrgo7f99R3OZcodoGnOTbNYx4wkRjYuUp5u5+cJ8BmZ9klJXlGqzHq8fl9uNxWpDrdESCIUIhcKk6dUY1CJOi55Uu4nMJAvpDjPJZp3SQuIwSf2asvJVrokGg0E6Oztxzc9QUVGxJZu5lRGPx7d0wT4ZaOWxXB6Ph46ODux2OyUlJacAxlZ7r7eqrl0rUlJSOHr0qDL8uaKiguTk5LOy9sp4PQ6PhnOAedrYqkpWo9EQDod34IhWhyzMWTnKShAEbDYbNpuNkpKSTQlzVq57tu8Md/JOc6uAqQCYWqUoLeOiuMwwwzHUphWTSMJRzNrllKwvFEOvURGNi6v6NGXdicww1YlfLDNaGSCl58nGB/5gGKNapKFJEuoEQlGyrQZS0jIBqb0pLzMVjWH5hseoAX8oikqQ6pnT09PKcSSZDUSRmItJp0aj0SjzN+NinPsaxhUbvQu++YKyZiQW57p9mezLsXFpWQq2FfuT0/lLS0ssLgosLCygUqnIyMggJSUPu92+4Rsy+XOLRqOoVCr0ej0HDhxQWicKCwvJzMzc8ndnO/Ma19qn1WrlvPPOY3R0lJqamjX9XrcKmNthmCeHSqWiuLiYzMxMOjs7GRsbo7y8/Kxmjs4B5rk4JV5pKdlwOIzb7SYUCtHY2EgkElGEOZmZmacIMrYSWzGc/2vHVmuYK51+fKFl5alGLdne+SNxxZRAfo5pxWSSBV8Es15NWHHxSdQ0ZWFNgmGqExfRcOKxDKgurw+tCpqaJYAMRaJYDVoKSkrh+RbigopUhwVBu8y0TBpBYY2QmFwSlW5wkq1GyssL8Dwrjc6yGzWrWO73nhnkkVbJZODHzy/X5nVqgY9eXED98BIvDizyn++o4mCe1CISDoeZnZ1laWkJl8ulGOA7HA6KioqUOl9fXx82m23TF1EZYOS2FZVKRXp6OikpKXR3dzM5Oblqzu1mYjs1uvVCEKS0d1paGl1dXYooaDtgtFPnmzz8eWZmhvr6enJzc8nNzVXOl+3cxG4EMF9rPrJwDjBPG3/NPkz5Tl5mj7Iwx263o1KpqKqq2pFao9y28moCzK0Op5YZn0a1bEIg91jKKVpZ8SqLejJt0nsuGa1HE5NHEv2a4RhGrUqp/QUSqtpoVAK42YVFVAIMDgxIv49LgFdasQteagS1liS9hpiYMH8PxzFpVfiCywBpN2qZ9qwwKrCZCCeA327UYrfbiYgqIMbPnuliJiSd4q5glB8+N6RMUnnb7jTqhpeY9oTRaVT8/ZEcWsYlFhv3LdDWNqa4NDkcDhwOB/n5+WumSVNTU3E4HPT29jI1NXVGw/CTY2ULinzjo9Fo2L17N/Pz85w4cYJIJLLpzMd2GOaZQvZ7lcEoLy/vZR8CvZH9CYKg3ID09/dTW1urqH63c46f68M8F6eE1WrF5/NtervNAqYoiopjzlrCnPz8fMxms3KxmJ+f33Z9Z73Y6XmeOxFbTsmuMF/3rwRM1TLjlNmgVi3gD0UxaI3KNr5QDLNeQygqYtQlJpHo1Hj9QXRqgeGJGQxqGB6VBjij1mHRh8ktKIKGHgSNFptBVPoqg9EY6VYd3qCUHg5E49gMWiLiMkgkWQyMJlpBDBoV4VicCVeQWFykadTFBXe8gCdx7F2LcTJM0nMLko389kOH+eR9bdQMLfIPR/P4pzcWcPl3a/GGYlz9nRcU03mHQU1aSh4Wi2XDgKPVaqmqqlKs5nJycsjOzt4UwK3FNmUnnmeffZba2lp27dq14SHL22VRG4m0tDSSk5Pp7e3F7/dveQj0TnvXajQaysvLlTqsyWTa1s3ETrD3V0OcA8zTxFb7KTUazWkZjyzMkdljIBDAaDQqwpzCwsLT3r3tJAt8tQLmllKyK5x+ZIYZTTBMxZRAZpgJYwKDZuWw6CgmrYA7EEITh9EpL2oxxoLLg04toDZYsJtEMrJzoaWXuEqj+MICBCKSr6zMRIMREZtBS4zlC5HDrGOFtzq+UJSWMZd0/LE4R77xvNLPGYhIPqy/b5xMtIsIHC5OY6hxCosQJuhZYtErzYsc6GplMsE2C5P1eENxZhLzN0sK8zf9XsqRnJxMdXU1fX19nDhxgsrKyg21OMhxMtsURRG1Wo3BYKCiooLW1lbS0tIoLCw84wV7JxnmypCNBObm5l7WIdBbqSPKddj+/n6mp6eZnJwkIyNjx24szqVkX4ex2VTQSoYpiiI+n2/VKCuVSqWMskpPT8dgMGxqfRnUzgGmFNttK9EkGKVKkAFT8oAFFOhSC0jPEaXfz0xNMLvox2lSE4qA2WYihgonUcw2CwbtAqG4gFmvIRiRtvEnZmHKPgNef5iMJLMCkMFIDJtJy8pujHlvmIYRl/L4k79tU37Wa1T8w/l5/KVjhv45Px+8II/3Hc3lgUZpFNjuDBP3N05Jr0OI0draijco7WtWn0X9iAvwM7gQSjwHCp0bB7f1Qq1WU15eztLSEi0tLWRmZpKXl7clthmLxXC5pNdvs9k4cuQIg4ODSouH3W5fd42XkwXJ5+ORI0cYGRmhpqaG8vJyUlJSNrztZmOrQCsIAqmpqfj9fubn55U6rNls3vRar7c4B5inia0UrcPhMEtLS3i93lXCHLvdftaEOTIg70R7yE561cLOKXC3Ow9T9pENReOr+zLjcTQqqKk/QTQuEg5KDC0rPZX44BTZaTbmxt1YjHomXaGEa08crRrcgQgWnUpJuQYiUoo1LkinXSAaJxrw4g1IgOUPx5h2h7i3YVw5xp8dG111zEcLkzg+KLlPZTuMfPLSQp7smgUgHvLR3CZ5ygrA58+38L0TAk/3e2idg/9sNzLhlXoq73hyUDEq2JNl5XNXlVKVaVFcic5GOBwOqqurGRwcpL6+nsrKyjOmK8PhsDJjc2lpSREZFRUVKQBRXFxMeno6HR0dihp8Laa1FYa51bqbDHryEGj5+GQjgdOVUF5uhyCQ2KlOp6OiooLFxUVaWlpITU2lsLDwjGtu5D16LdYv4RxgnjHknsq1wCkejys9j7IwR6vVYrVKkxF27dq1I7XGV9rEko2GDGyvFMCMxkRUgtT24Q1F0asFvCGRpYU5mvwSMxNFCUCLyqrg8XoyU53QN4rNbMIXimLSSYbgGhV4gtLw6FA0hl6jxi8DJMtWe9lmnZIK9kfBG9fxg6f7AGnSydM980rfJsCnLi0kGI3zkxeGAfjJjXv56G9aeHFgkd5ZH//0vy+x4JYAV6+K41LZgBnUKoFbn3YzMCcBvAgMLwQQBAlMb79Izzw2vvH8LNUFDg7krs/UthNqtZqSkhLcbjcdHR04nU6loV7Ovsjg6PF4FGGbw+EgLy9POX9kM3e5BcVsNlNdXa20eFRUVJzC5rZSwzxbo72MRiMHDx5kenqauro6CgoKyMrKWndu58vdjrJy26SkJI4cOcLw8LDSLrPSyWmt493Ie3ROJfs6DIvFgsfjISkpadUoK4/Howhz7Hb7KcKcxcXFHRXmvFKchDYTcq1xJ6T+mwXMUCiE2+tDLUBDQwNj00F0grRGarKDTKcVmntQq9XoNQLhhPBGVs0KxCUjA62KcEzEoFHjC8ewGbV4QjH0WjXeUIxsh5FQNI5GJTDnDROJifzouSEA3MEY7qCfJJMGWK5556cY6Z+VgO7C4iT+0j4tGbyr4UR9PSFfELUAmVYtfx4MKVNO7jo2jz8isc1YXCQvyUiSSUvDiIvPXVmMxaDl//tjFyKwYMxhbnYOAMvLcBWw2WwcOHCAnp4eXnjhBYxGI9FoFLPZjMPhICcnB6vVuu53Y73aptzi0dHRwcTEBBUVFcrN7Va+a2dzpqUgCIn+1BR6enqYmJigqqpqzdTnyw2YJ9c/V86w7OrqYmxsjIqKijXVzq/XHkyAV73M6bHHHqO8vJySkhJuv/32U/7+3HPPcfDgQTQaDffff/+G13W73Tz55JO43W5uuOEG3vzmN9Pb20sgEMDpdLJv3z6qq6uprKwkKysLi8Xyst1N7SQL3EnA3Cl7vDOJfuLxOG63m9HRUdrb26mtraWjowNfMIRWrWLv3r3ozTYcCVsfs9Gg1DBFUapxLvkkFpdwtUOr0RCNi9jNkmeqQafBF45hMWgIRWJEY3FmvSFaJ9z8qnaMaFxkwR9hZMG/aqLGTRfk8pE3FCqPz89UMZRghQB9na1MzMyhEsCs1zCuzWE8qCEmwphbEunI76jTouOWi/IAyE0y8IO/26sYoWc5DLxzfyY6tYBGJXD7X/q5v0tSgPsXphgaGjqrn40oigQCASYnJ+nq6qKmpobGxkYF5OLxOE6nk127dpGXl6e0S50pBEFQnheNRonFYorhgdPppLa2lqmpKYWRvlyAebrttFotu3btoqSkhJaWFvr7+8/KOXa2GObKMBqNHDhwgOzsbBoaGtb8XryeAfNV/apjsRgf//jHefzxx8nJyaG6upprr712VaNzXl4eP//5z7njjjs2tOb8/DxXXnklBoOB8847D4vFwqc+9SmuvPLKV4yM+pXkVftKWPtkIA6FQkomwOVyrdui8+h0HzpNEK1Wiz8cU4YVqxDxBhNtJWoVghjDn6hDGvSJFGFiX+ZE3XNsKYAnGOWJzllmPMum5gAOo5ZARALcQ3kODuc7+EGCZaYY1cwvLYt6jmZqMKiiPD0uvU//063BH44RE2HeH+ULD3crrS6H8+3cclEBH7unhUhcZGQxyEMtUirZmqhPygOiHUYdcVFMGLqrKUk10zgq9V1esL+KaHSB+vr6dRnQmUIuT8gGBz6fD4PBgMPhIC0t7ZTafX5+PqOjo9TV1VFRUYHD4TjN6qfGyhYUGRhlNtfV1cXk5KSSvt3s69ipEV1y6lO2rausrCQpKWnT+1q5z+0wzNP1caemppKcnEx/fz/Hjx9fJbB6vfrIwqscMGtraykpKaGoqAiAG264gYceemgVYBYUFABs+CRITk7mpZdeUr5Mt9xyy4bvfk+OnajXwSt/Gsp6sROAGY/H8fv9eDwe2tvblTqy3W4nKSmJ/Pz8U+rPcp9fOBpDrRKIRCL4wlFSTNLzDDoNrlAYtSBgszvQe5do6ewFQEhA4RPdUjrzO0/3E4mJPNU9D4BGpcJp0ZFs0tI94+P9R3MZdwV5oW+BWW+Y2uElBmY9qAWpZumam8YdWz6+9oCNVpcbkPonB+YDif1CXrKRu969m397qJP2SS+Xl6dyQVGSUhO96927+dIjku/sgi/Cgi+sjMj61pP99M/5iYtSKnhgLsD5hQ7SbQaOFCYhCMm4XC7a2tpIT08/42QOWdwm1x9jsRhWqxWHw0FxcTEmk+m028uOOU6nk87OTsxm87rindOtIadpZcDSarXs3buX2dlZGhsbGR8fV9xtNhJb7YncqNJ1pW1de3s7JpPpZTc82Oi2soeu1+uls7MTk8lEWVkZ0Wj0dTmpBF7lgCmfDHLk5ORQU1OzrTVl5385tmrAvlMCF3j11zC3EyvZo9vtVlJywCl1ZDlkFhKLxVb9LRKTLO0khhknN0kCLr1Wqkea9Wp8oRhxVDS6jECYbz0pufQ82CQxObtBizcUwqpX4wnFuPmiPO5rmMBp1tE944NIkPlFF8Sk9Oml+QZeGA0q46xq5jT0zi7bLz7bO4/DqEWdECN94UIb3zjmxh8RCUbipFn1+MPSe7hykglASaqZKytTubdhgkl3iIvufFH522IgwhWVqTzQOElZmpkHb6k+5X2y2+1UV1czMDCwim3K4pylpSVFAb7SAWg7hv6yfdv4+Dj19fWUlpZuqBVjZaxleOB0OjGbzfh8vk0x5622omwWaE0mE4cPH2ZiYoLx8fEt9UNuRym/mbSqxWLh8OHDTE5OUltbS3Jy8llR0r4a41UNmC9H2O32bU0s2SmV7E6mTf9ak1ZOjrXsAddijz6fj6GhISwWi3LRlMUh8gVInoohT8ZQqVTEUaHVqFCrpZFd8tSQ+mEXDSNLeENRnu+XpoJMJZSou9L0tEyH+MdLc/j2M2N8/s1lfOK+VsUO7+n2cTy+INqoVIdUx8OERDWoNUCEQY+gmK4DdEx5SbfpCUel6SD/9/Ej/Oi5YR5pncZm1HD9pQd5dLCOulEvM54Q1/6wVnEomvOE+OmLy56wV39/+WbRYdAQFUXFiP03HziEIMADjZOkmHXrXpjltgi9Xk9DQ4PSKiGL2/LyNucAtJEQBIGcnByFbU5NTVFWVrYpMFjLXk8QBCorK1laWqK5uXlDI69ezhFdsihoZGSEubk5RRS00cHMsVhsUxaEJ2+7meMVBIGsrCxSU1NpamoiEAgo2o3TbfNai1c1YGZnZzM6utynNjY2RnZ29lndx1YZ5lZdgjYSarV6x6ah/DXZ68oePLfbrfTgraVClkOgCbHuAAAgAElEQVQGyGg0SiSy7LkqCAIajQaVSrVKKLIy/OEo4Wicbz81wGIgwl86JYXpQy1TaFc8Pcmo5cbzsvjes8Ncdyiflkd7WJqRTMznpiWmeX6GwFOj8NyQD41KQK3RA0F+2eJh0b98XBqVQHGqiSl3CG8ohkoQmHaFUKsEonGRJJOOYDSOICzXIVFrQIBSh4ZJXwRPWALMbz89qKyrVQt8/qpSJlxBfvriCO8+nM0HL8jjjd9+CX84xvt+cYJbLioAVqzLsi2jzB7dbjeCIGC32yktLVVapgoLCzdt+bbZkP1Zp6amqK+vp7i4mLS0tA1vv7KOurS0pGQV7HY7R48eZWBggJqaGnbt2rXuTMudEP2cLmSWuGfPHubn52lsbCQzM5P8/PwzrrfdlOxWhDtarZb09HSCwSBtbW0kJydTXFz8qvKe3k68qgGzurqa3t5eBgcHyc7O5t577+U3v/nNWd2HzWZjampq09u9WuuML5cC93TsUTb6Xq/2eDJ71Ov1iKLIwMAApaWlazKTWFykb9ZH05iL5jE3L/bPM+uVgOynLwwjAoWpJvpm/dz21jIe75zFHYgy7Qkx6w3z61rJTGByYgKAaKLNZHZBMhGYjZkAqTYZTQhwAIpSjMzqNcRFkbGlIP/xtnJ+VTvOUiCKNxTjR+/Zyz/f386CP4KAZH0XCMeIixCKxLn19+2cGHURF6FnMboKyG0GDR+7uIDb/9KH06LjhsPZfPcZCURTzFqsBg1GrWSk4AnGuPXBDgAMqjhDQ0O4XC78fj9GoxG73U5GRgZlZWWrLn6ZmZm43W7a29tJS0vb0IV8OyEIApmZmYp4Z2pqat3G/0gksqqOGo1GsVqt2O12pY4ai8WUFpSSkhLFUMDhcFBSUnLKhf5stpVsdDt5fykpKRw5ckQB9jM5GW0V9IAN1yHX29ZqtVJaWsrIyAjHjx+ntLT0lJubcwzzFRYajYbvfe97XHXVVcRiMW666SZ27drFF7/4RQ4fPsy1115LXV0d73jHO1hcXOThhx/mtttuo729fcP7sFqt9PX1bfrYXm3imZ1eOxwOEwgEGBsbY2BgYMPscWXtUa4Jr8UeDx48yNjYGA0NDVRVVSFqjbSMu2kaddE05qZl3K2499gNGlzBKBqVQJpVx68+cJDLvn2MC4qS6Zv1k2rWsuQLoVfFsWlimKwCU34pTV0/K7G7xkUdEOb7LdLv2yakLMRbdqfxZNccOrUKVzBKOCZi1quJJVK2ct1RHvlVnmZhT7aNlwYWiMRELvv2MWJxEREYWwoSiYnoNSoisRjvPZLDP7+pmINfe5a4CEa1yO1/kb6bpoTC1xWQbgIcJg0dk57EyDGRWGyZ5aZoQuh0OkpKSs4ozgHppnGlY09VVdWOs02dTsfevXuZmZmhoaGBgoICbDabAo5utxu1Wo3D4VBSxWuB6smGBxaLhfPOO0+xrzt5wPJfg2GuBC61Wk1paSmZmZl0dHQowLQWMO606Ge9kOufgiCQn59Peno63d3diquRnFI+B5ivwLj66qu5+uqrV/3uy1/+svJzdXU1Y2NjW15/uzXMnYhXOhjL7FEW58jsMR6PY7PZKC8v3zB7lGuPKpVK+XfK/kSRgTk/zXNqjo2aqH2ugblg4vUIUJZu4Zq96ezPsbMvx0ZekpG64SU+/OtmJlwhfvq8JORxL0n1yuHBfjyBKI4kA7MBEbVWhdUQJeSL0Dgu9S72JYQ6Nx7O4tf1E1xeaOSJwQAfvTCHJ7vm2Jdj47m+BXpnfIRjklgHpEHOi/6wMrj5PT9rYGghoLwWjVpKzQrARcVJ/PjG/Vxx1zG8oRjl6RZUAorZ+l1vz+eOJ4eom44zshjgf14cpmZAUut+4Q9dJEZhIgC7My0cLkihKsvG0cJlgNhoyOpO2SQgNTV1R9mm3Dvr9/sxGAx0dXWhUqnIzs4mKyuLioqKTbnNnGx4kJ+fT1paGu3t7UxMTCjfyZ1sK1lvu7WAy2KxKNeumpqaNRncdlniVtnpycdsMBjYt28fc3NzSkp5pRjztRSvesDc6Xil1jBfSYC50drj4OAgFotFuTCtpVxVqVRnrD16Q1Faxtw0jS2zR3ei31CvEQhFYU+anjfnCVxz4R6c9mU2FIvFWFxcJFV0kW9TMe2L8ZsGqR7pE/WAn9pFE5PeRUbdy+pVq16NVa8mP9lE26SHWFwComv3ZfDr+olEH2GA/q52QtG4Amrfv2EPH7mnRRENXffDWnyR5fe30GkmFheZ90fITzZy7wcPccVdx5jxhKkfcfFi/4LiRWszaAglthWAziUVgs4A+InERO5MKHgB3liaxBW7Mvj8Q12kWrT84MZDm/pM1wur1crhw4fPOttcq03FZrPhcDgoLy/HaDSysLBAT0+PkkLeTMjAKde7VSoVBoOBQ4cOKerPkpKSbTHMrShWTycWEgSB3NzcU4ZVy0Kf7bDE7RjTrwe2TqeTpKQkBgcHaWpq4siRI1ta/5Uc5wDzDPHXHCK9Xuy0MOd0a6/HHs9Ue5TVseFwWBHnbIQ9iqLI0HyApjEXL/Qt0DvrpX/Wj4gEGiVpZq6qSmV/jp39OXacFi1f/3Mff2ieIooRu7aJyhypTUH+HG02GzqTlahKh8MMSRbJZ/XxHqkeWTe8BMC+bBuTriAH8ux4g1E8oRgXFiXRNukh2axlxhvhG4mUqDz5JKekivgzjXSMS2t88FfNq15PVJTqiwICgiAB6nt+1sBSIIrNoEGrVuEwapnxhNFr1Hzo182Kt+xTndP84kUJFEXgS4/2oU9cL/MdGpK0cZpmpeO4Zn82b6pI5V8f7MSoPbuCjO2yzZVtKrLNpNymkpSUtG6bSkpKijI6rLGxURmEvNljP5ltZmVlKTVTn89Henr6ptaEnTU80Ov17Nu3j9nZWRoaGsjJySEvL29bgLmdOB07lWvFWzGNeDXEOcA8Q9jtdrxe75mfeFK8WoU5J6+9VeXqWuxRviip1WoyMzPXPKF84Sit4x5FnNM05sIVkNijAFj0am48L5tLS53sybatUnzGYjE8Hg8f3mekQGfhJ41evjIPf7s0x540HSFLFu3TAZqaXHRPTyosMNMupUuTTRoW/FEqMiw0jro5WpjEQy1TmHRqpt3SJJJwTESnVnG0MJmne+doHpPccp7pkVKh7/xpIwBLoTgC8A+H03iwbYEUi45JV5C8ZCPd0z4MGhUZNmm/wWicuCjNwgQSdUfItmsQxBiLQenz+EPrLBkJ41eTVsV9Nx+mZdzFF/7YzSVlGXzq4myu/kEtM36Rf/xdGzddkIcIGHU7c1GV2ebQ0JAyjcRqtZ7yvFgshtvtVtSrwWBwwx6yJ4dGo1EmbDQ3N5OVlbUpYwJYnaaVL+w6nY59+/bR3t7O6Ogoer1+UwOwX46JI7L7Tl9fH7W1tUQikVccYMrxWgRLOAeYZ4ztMMydav3YKTCWXXN8Pt8prjlnYo8rWSSszR4NBgPV1dV0dXWxuLhIeXk5k54oTWMuaoYW6Zzy0jPtVYCsyGni8vJU9ufY2J9rp3vay1ce7eH3TVNUZlg5IEaYnp5XmIooithsNgxmK7uL8/h7nZf7Gyf5ZWcEOqNAH0ativ05dm65KJ+HWqYpTTPzzv2ZfPp3bbz//Dz+68kBWsbdiMCUO0gkJk0r8YZiWA0aeme8iIg80zuPJ7j8GbiCUVQCfOKSAu56Zoh9OTYG5/y8KSPE75olpabdqOW+Dx7m4v96EXcwyrgryLGBBdyBCKFonNbxJS6+4znm/NK6XdMBdqUbWJySCrICcKTIyUMtUySbdRSnmnmuTwJqu0mLyWTCZDCAP8B56WqlR9Oi27nTXKVSUVRURGpqKp2dnTidTkVZu/Jzsdvt2O12xdB7u4KQpKSkNU0WNhNrGR6YTCaKiopwu91MTk6ya9euDQ3AfrnUtfKsUbfbTU1NDb29vWuqfXcyznnJnot1w2w24/f7z/zEk+LVUMNciz3KF4czsceTGa5cc1xpDHByBCIx2ie8NLmsHO+bofXhF/AsizcpTTVzy0X57MuxszfHhsO4DM7xeJxUXZTvX5PN154a5wt/7OKhTA3/dFEGOpONubCNlgkvja0uOqemFSOB3CQDWXYDndNeLDo1N+/R8oZiEyUlBTzWMYtJp8YXlhidNnHMX722kn/9QycPtUyjEuD4wALjS0H6Zn3K8Rg0IulWPdfuTee/Xxwhx2FgbCnIb09Iw5ujcRGrQcOBAweI/OlZfIEgVqMef1gaVK1VC0Rj4qqU7VIgygUFNl4YdBOOiXztukquqEjl4NefA+C6fRk82CwPhJa2cSXUu/F4nAcaJ5j2SLXS41PL34/zCjbn07qZEEURr9fL0tISRqOR0dFRhoeHycjIIC0tjeLi4h27uMqKUrfbTVtb25baXk621wuFQtjtdqqqqlhcXKSpqYmsrKwzWgXutKXeyWGz2TCZTBgMBo4fP055eflpR3KdvM/t3LBstP55TiX7OoytTtjYyZTsVizm1qs9ysIKmT3GYjGampoU15y12COwijmuV3uccIU4MbJEy4Sb5jE3XVNeBcgKUoxcUubEKXjIc9p4sCdI64SHXVlWbsqzoyHGzMzMKV6lKVY7n31TCf97YpZne+e58f4xhZEaNCp2Z1l5//m5iZqmjWSz1GrQM+3lXx7s4M46H91uD2+bq1XGbvkT7SYDcxIg/uylZfecuAiji0FUAhzKs2PVa+ic8pJm1WE3aqnIkAQv6TY9Oo2KQGKt8cUgTouO/lkf4ZiIOyywGAxywR0vKGtbtAIZdgN9c5JK9pq9GfzH2yrY99VnAMkwIbhCIPSVaysocpq488kBRhaDfOCXjYwsSDdz339OmpcpIIHpp99YxIFcG9bIIq6FWTwe55rp0s1GNBpVPhOXy0UoFMJisSgWebt371a8R3U63bbMxTcactvLmVLDJ8daqWKTyUR2djaxWAyHw8GRI0fo7+9XDA/WW3erwLedOuTKto7Ozk6lreN0purw+maI241z79oGY7O+sDsNmGeK7dQeo9Eo4XBY+ftG2GMoGqNj0kvj6HLtcdYrpaTVKjiQY+emC/LYn2NjX46NJJNO2efAwAA5Gg9PJtv5bfMUL/VM87GDJg7mJyPqLSyYrLROeGnqdNM+2a/4pzotWgLhOL5wjGv3pPPFt5ZhWif9WJZu4b6bD/Htpwb5xfFRTkzqWPCFaRia5/lEWvN3jRI7DCVUqR84P5efHxvFkvCJjYsiJp0anUa1atYlQCAcw2nWcVW1k6/8qY8Ff4QFf4Rrf1SXeH9E7EY115SaubfNjVol8JY9EkAe+NqzhKJxHmicJN2qJxJb7tkMRqVj0agFbv9zn3KsADVDS8oszA9dmMt1+7J490/rUQnwoYvyE39JwuvdeitIIBBQwNHlcikuQA6Hg+zs7DWt2eTa5vDw8KYAbDshp4bT0tLo7OwkKSmJoqKiVa9VVuKudAKSbxhXpopXZlBUKhVlZWWKuX9KSgrFxcWnvIfbaSvZrn2mwWDgwIEDTE9PU19fT35+/mnrrzstFnqt+sjCOcA8Y2w1rbCTgHlyxONxZXL96djjydusxx7tdjs9PT1UVlauezJPuYM0jS0bA3RMelalQY8UJrE3y0bTmItH22fwhGJcsyed4lQz4XCY2dlZ5XgjkQgmg56Lkz1knJ/C3Y0u/uNFH7aGEK5Eu4hWLVCVYeWGw9lSTTPHTrpNSnF+8/E+7muYoHfWx3++o4ri1NW1rJVtKP2zPoxaFRNuCcynvFGcRomZ3Vidza/qxvnsFSV84rdtXFiUzN3HRvmbg1ncfWyUxlE3/QY/DqMWbyiKIEB9QlHbO+MlEofaxGMVSIuKEAfsRg0XFifzubdX8evWZ4hFRcRwQLpBSbxve7JsfO/ZIeW4f/DcEJ2TUv08GhN5oHGCbIcEUEcKHLx9XwZffKSbaEwkGpemmUTiIlb96ouhbJ49ODioGDusVe+TsxAyoJxpRNfpQh5InJqaSkdHBykpKRQWFu64GER+rUNDQxw/fpy0tDRCodAqJW5ycjKFhYXrtoGsVdu0WCwcOXJEWffk0VwvN8NcC5TS09NJSUmht7eXurq6dVt+tuMQtFEwlFPdr7U4B5gbCJ1ORygU2pTR8U7WMMPhMNFolL6+vlPYo2yOvZ3a465du5iamuLEiROSdN9ipXPSQ/OYm8aEelXuK9SpBfZk2/iHo7nsSwCZ07IMsjeel82bSu38x2MDvOsntdxQruXyfD0OhwOVwcKSyULbpJ+mHhct4xCIzCvruoJRchwGbr2imItLU9BrTr2wmHRqbntrOW8oSeHfH+7i+v+u54MX5pHjMEiAPuaiZ9qntKGUppl5254MytPNfP3PfcTiInFBg14dxaqWwDmUaBHRaVTKsQBcVu7kmZ45pefzT+0zynGIQGmqiev2ZfDNJwZINms5mOcgFI3zbO+8sk0kLiopZJ0Q45lj9YoLkD8sWd/JWdjGERd7c2zMDSySatHxxKfP55HWab7wxy7K0y1cty+Te+vHaRn3cPexUZrH3ERjcQzaU29y5FaQ1NRU2trayMjIOEWcE4lEFGu5oqKiNbMQmw0ZwHaabcpGBzLYBwIBDAYD09PTWK1WDh06tC0zd7kFpbCwkPT0dNrb2zGbzZSVlaHRaLbVv7lVs/e19qfRaKisrMTlctHa2kpqauopTHs7hgd/rVaWV0qcA8wNhGxesBnAPFtOP+uxR7nGsln2eKbaI8CsJ0Tropr6RQdf/2UTQ664chHPtOs5mGtHr1HxaPsMBq2KD5yfx2XlkuAgEokwP7+sXA2Hw2SbzXz/mmy+8cI8v+zw8cS4Cq16nuEFyYFJLQiUZ5h5x/5M9mXbyNaHCM6PMyRk8F/PjvHvD3fzpbeV8+aqU424g5EY7ZMeBud8VGVaqR1c5PsJlmbSqTiQY+fyi1M5kGtn70ltKHc+0c/hwiSODS4Si0PjiNSH6QtJSqTmMYktPnBC8pF9KjEDM0EcSTJquKzcyQNNUxi1ao4UJlOZaUscVxynRccHjubybO88cRH+0jFLbtJy3+BfBoP8pnVZ9RSJibxtb4YyOswbjiktNUkmLVq1iqWE9V1SYnZnOGHn8+EL8/hFjVTPNWrXrikHAgG8Xi8Wi4WhoSEGBgZIT0/H6XSuay13NmIl2+zs7FQY3nbYplxykAFypdFBWVkZRqNRATzZMrGsrGyVDd5GQr5hWNmCYjQaOXz4MOPj49TU1FBWVnZWvGQ3u93p9me32zly5AjDw8McP358lQXgX8tS77UQ5wBzAyG3lqSmpm54m61azMkXAlmcsx57rK+vJzk5WdnPeuxR/rde7TESi9M97aVpzE3zmIvGURcTLok9atUCuzKtvDU9Tp45zluPVJHrXGYHN1+Yx2fub+MT97XylmIj7yiUZkna7XY0Rgses4V2j5+mfjct4xMKy5pwhdBrVLxrfwbX7M1gd5YN00m9gn5/Ktr2dr7zlgzuqnPzmfvbeX7/PB+6IJ+uGS9No9Kxdq4QEuUnG7l6dxrBaJynuucwatW890guF5euPV8xEhOpyLAgiiK1w0scn5DStN/4kzQs+s4nJSNzmRF+8IJc6kdcCEDTmBtPKMYjbRLL9IZiUp+mXNOMxNBrVJwYdSn7i4kiP3p+WHmcYtJx3b5Mpf3jlr06qsqyeLBpCrUAX3xrOV97TDqWUFT6jGWv2Bl3iDuf6GdwXhIq/SSxhkmn5m17MlYxrpUm63LtsbKyErfbTVdXF1ardctzFTcTFouFQ4cOMTw8TF1dHZWVletODVkZMtivnKgi+8ieaR6n7JYjg7U8Omyrg6pXss2cnBwl5ez1erckptkqAG20F1JmxJ2dnUxMTCgDoLdj2r6RbV+L6Vg4B5gbiq3Y423kC3O62qPdbic3N/eUu375hFWpVASDQcUEGVanV9e7a533hSVTgFEpXdk24SGYuMinW/VUZlrwhmL4QlE+cUkhH7wwD5UgMD8/T3d3K1FPJoCiKvzCeUYeHNDwYIebxlk9B3IsDMwv0TM9fpIbTxoHcqWUrTcU5dbfd/D7pilSrXoO5J5qc2Yymdi7/wBPnehhjz2EN2TkwaYphX3pNSr2ZFl5/9Fc9ueuVsSCpIq99cEOPnJPCzeel80/X16MIeF44wtFaR5zEY2LPNIywbQ3qoAiQMIngM8cTeK/ji9y7b4sfn58lDeUpFA/7EKdSNF+7JIC7qkbZ9YbRgTC0Tg1QxJLjYnwi+Ojq9bdlWkhyaTjuT7Js/aSMifvPpSlAGZ+VhqNLW0AGHUarj+YhSiKfOn/ehheCPCmu47hTjDOexom0KgEBEAQ4JtvL6fQKqKJ+llamqG2dlJhXOuZrDscjm0752w2Tmaba4lzTh7TtRLsN+MjuzLk0WGTk5PU1dVRUlKyqRtgWN/w4MCBAzz77LPU19dTVFREZmbmK8rwQB7SPTU1RV1dHQ6HY8uf8znAPBdnDKvVitvt3vY6G2WPK2M99uh0Ounq6lIGzq51AYnG4/RM+xTVau3QktKnp1EJVGZYuP5QltKCkWmXUs6uQIR/f7iLbz01wAs903z0gAkh7EOtVjM2NobWYCZqy6LDF6S5x0PzmOSENOUO8aeOWYqdJj56cT4Hch2npEHluP/Dh/naY7386Plhjg0s8s13VmHWq2kaXa6Tto67FTBP0sP+TBP9C2H84Si3vCGfD12Yj1q19olZlm7htzcf4s4n+vlV7ThPdM6yK93I0LyfwcUIMo4FIiIOg4Yks479uXYeaZ3GoFXhCkRpnZXYXChhQGHRawjH4ugStVStWqDYaWYuAZg/Oza66hiOFiZxQWEydzzZD8CN5+WyJ8vGc33SoOefvDDM4Nxyj29Bdjp+dHC8nVgsykd+06zY9AFMukKKKvZfLsvj4lwdf3dPP6EopIUn0MYc2M/AuE4OuRFeds7Jzc0lKytrxy94K2ubtbW1ZGVlKSpWeXzU6cB+KyEPQZYdp6anpykrK9t0KnqlKEhmm1qtlurqarq7u5mcnNzwIOiXSywkj01zOp00NDSwuLhIRkbGhkwZVsZGAPOcSvZ1HjabbdP2ePF4nFgsxtjY2KbZ43q1R5k9AhQWFuJwOGhpaVHulpf8EcWQvHnMRcu4R5mK4bToSBAjrqhw8uVrKrCvMAaQTcnlutANOX5ytSZ+1e7jM/Mhrj+YiT8Sp2nUTdeUi5gopRoLU0xcXJrCgVw7eUkGfvzCCMcHF+mf8/O+o7lrgiWAUavm/Udz0agEHmya4qrvHUd+yWuBudOkprOzk2DczG96Re56epDjA4vc/o5KMmzLteVwNE77pJu6wXkahhZonZIAadoTZtoTJseu4+bzs9mXl8Qn7mvjgxcV8MeWKfKTjRi1avQaFVfvSuN3JyZ5vF/6zPvHpcHSHZMeptwhRaRz5xOSr6t8KTfp1EpPJ8B1+zJJsy5/xlb9cpsIwLv2Z/L7pknl8Yd/1UTHlLTPQBR6Jxcpc5ponvRxVbmDa0qNfPZPkwRj8HTnJEcycoiJAgadmsOHD6/5Pm80kpKSOHz4ML29vczMzFBVVXXGfr6txMqB1YuLi8qN6NDQEHa7nd27d29KK7CVkL1Zp6enaWhooKioaNP+sTLbjEajLCwsKECye/duZRB0dnY2eXl5O2J4sFVmKg+AjkajNDU1kZGRQUFBwYaPYaP7PccwX8exkZTsWuxRtsbLy8vDbDaf8qVcjz2uTKuuV3uMxUVmw1oG1dnc/ccuOhY6WAhI66gFgYoMC+/Yn6EATrbDQCQu8q0n+vlFzRijC4382xszsBJYZStnstoIWjLpDoQYj7qxGsIs+KP894ujaBL9lB+8MJ/SJA06zzi7S/PIzMxUjqu6IIm7XxrhO08P0jru4ZvvrOJArv2UCSPNY248Cc9Uu0GDCLiDUS4sTub2t1eQYjn1Yr1nzx4mJib428AI5+Xkc+czY7z9h3X8zYFMQuEQTaMueuZDRGWBklXDkXw75xWmUJxm4efHR3mmZ572aT/X7s8GQKsS8IVimHWahA2eQDgax27UcH5REo+0zlA7LS34xUe6AUlMBPDxiwsYWvDzYv8CS4EoX722gl/WSO0nAO5gBLtx+RQz6dT0TC+7Bb3QP8/K26I5b5jLy5083jVHqVPP1y6x85uGGZoBuzpMZWYG5Rkemse9NExF+OT/TRKKxTHrz85pLCss5+fnOXHiBAUFBWRkZGzr4ienV+UbsZWtKpmZmZSXl6NWqxFFkeHhYZqbm6moqNj0NJKtRHp6OsnJyXR3dyuDqs90k7BeL6dcG1SpVCQnJ3PkyBHF83XXrl3rTnR5OVKyJ0c0GlWGbMvDqisrKxMTd8687evZ9OD1+8o3ETabbVVKdqO1xxMnTpCRkaHIzlfOfFwZJ7PHtQDSHYwkUqsSe2weWx6IbNap8YXj5FhUfPbKUi4qS18lolkpAHlLZgDbfi13t/u55YEBPnJBFjnOPMkYoN1F++S00jif7TBwflEKVRkWGkZcPNUzRzQucv3BLLIdBqLRLDo7O1lYWKCiokICeUHgpgvyyE028uX/6+Hv7z5BilnLnC8xoQQoSzdz9e40CcxzpfmUMVHkh88N8+Pnh3jP3Y3c8c4q9mSvFoTERfCo7XRGnLzQNYpRHWchCHcfH0UAyp16bjiYQXVhCvtz7aSeBLrV+Q5+e2KCb/y5jxvvPgGAVq3CF47iD8fon/PhDcV4uHWGcCzOI62SoEenFgjHREqdBqbdQYqcRpomfFxZlcbdx0aUtLDTouOqyjQFMG//cx9HCpcvQh+9p0VJMQNUZVq5tEzHfQ2TaFUw5QkTHpKUuBaNQEZGBilZOhgaQy9KLR8ygf34JQX84vgYsbhUzz2bkZKSwuHDh+np6WFmZua0/bgnh+wEJGcrIpGI4jwgU0IAACAASURBVAR0ulYVQRAoKChQRDQOh2NNg4CzHVqtlt27dzM3N8eJEyfIz89XapBriY1O18t5suFBeXn5ads74OXzoF1rW5VKRUlJiTKsemWbzHrxeq9hCpvMN79ik9OPPfYYn/70p4nFYtx888187nOfW/X3UCjE+973PhoaGkhJSeG+++6joKBgQ2t/97vfpaWlhXg8zpvf/GaSk5OxWCwKQK7HHuV06cq7Vpkxno49xkWRwTk/TWNuXuyfp2fGy0DCPk0lQGmahf05Ng7kSgORcxwGfvbSKHc9PUCKQeC2K3PZlWlVFJLxeByr1YrZamM2oqNrLsTxgUVe6F8gnABHrUpgd5Y1IaCRWGmqdTXgPNo2zW2PdKNWCXzlmgquqEyVxm+NjvN8+zBefSodsxLTW/BLAKlRSQORs+0G/vGyIi4pS8FyGkZUP7zEvzzYwZw3zC1vyGdPlpX6wTkaRpbomgkSSLRROAwqypLUFNoEvBobj7bPkZds5I537mJX1un7/BpGlrj1wQ6mXKHEzcZymlSjEkg2a9GoBD5xSSH/9scurt6Vxp/aZ9BrVISicbIsKsa9cR7/5Hn811ND1A8vMesN8+P37OEPzVP8qX12zf1esyedFJOGn9dIbSq/fKuNhvEA32mKkGHRcOvlBdz22GBiWLSZ+z9UzVf/1MO9DRO8Y4+Tmfkljk9GiSmpa0i16vmHo7m878jODOydnZ2lr69v3bTl6ZyAHA7HltK6oigyMjKisL6Xg22CxB47Ozvxer0YjUZCoZAiNnI4HNhstjOCmyiKyg2xfJ6LosjQ0BDT09OnMLmXXnqJCy64YNPHOjY2RiwWIz8//8xPPina29vJyclZ9b6Kosj4+DjDw8MUFxeTnp6+JugNDAxgNBpXZZVOjng8jk6ne7W1n2wI4V8TgBmLxSgrK+Pxxx8nJyeH6upq7rnnHqqqqpTn/OAHP6ClpYUf/ehH3HvvvTz44IPcd999667529/+locffpjW1lbi8TgZGRm8+93v5sorr1zTH3Mt9jg2Nobb7VZst2Bt9ugNRWkZdyvinOax5YHIAlLP3bv2Z3J+cTJ7sqyrUnAr3VlqBub4do0LTxj+tlzL9UeKGPapaJv00TTmpm3CTSDRUJlm1bE324YvHOP4wCKFKSa+df0uStNOPwx4ZCHAp3/XSve0j7I0M1q1QPe0T2ntyLZpOVyQzIFcBwdybRQ5TTzcOs1XHu1FpxH46rWVSs/myhBFkZHFAA3Di7zYO8Oz/S78keX3sjhZx/4cO9WFKRzMc5DtkGzMFhYW6O7uxm3I4PZnJpn3hfn0Gwv5wAWSujcWF+mf9dGYaJlpHHUzuhg4Zf8XFiWh06gYXgjgMGrRqgU+dFE+N/+qmSsqndQMLnHPTYe45oc1ivL1U/u1/N+omjFXWLHIWxk3VmfRP+Pl+LDEOG/arcOsFfhuYwi9RuDYZ47y3KCbf/xdOxVpZn7/kfP47xeH+FaincVm0OALLQNkkkmLLxQhEoP/ec8uDhY4FXOFnYxwOEx3dzeiKJKTk6N831amV+VpJGfzIunz+RS2WVRUdNYvwCt9cZeWlgiHw1itVnQ6HbOzs+Tm5m56dJgcMnCuNAWRpwBZrVZKS0vRaDRbBszh4WGltWWz0dzcTHFx8Zpp4nA4TFdXF9FodE3VdE9PD0lJSadVGJ8DzOV4RQLmsWPH+NKXvsSf//xnAL7+9a8D8PnPf155zlVXXcWXvvQlzj//fKLRKBkZGczOzq57Mjz99NMkJSWxe/dunn32WR544AG+8Y1vAMu1x5V3k7A2e5yenmZwcJCqqqpVPWfP9MzxVM8crePuVU40JWnmhN+qnf3ZNmqGFrn9L32kmHXc8c4qdmeYVplfy0pbq83OQkxH01SIXx4fZdqzPFpMFtHsy7FzIFdaO9OmV177sYEF/uXBTryhKP/25lL+5sCyLF7u02xMtKE0jroUlx+QmuSv3p3OZWVOdmeamZ8YJhgMUlVVtSqNNzjn57O/b6dzysuN52XziUsK6Z3xSuKc4UXapvy4QxLomLQCu9KNmPR6jg25MOpUfO3aSt64BtDCMjMIoeEXHVGe7l0gx2Eg026gc8qDNyQxyBSzjgO5EjNPs+i59cEO3n80h58fH0MlQEGKSWrVECDbYeT6A5l89N5WLi5JpnvGx5euLuMT97WiUglK2hok1h8X4Z8vL6R70s2jnZJRwV2X6mmcV3F36zJA78+x0TTmJsWs5fl/vohf147x1cd6SbfoSLPpaZvwKCeZIKAIob777l1cVp7KG+58EV84yg8vM+y4ovVkQPH7/cq5k5ube1acgM4UZ5NthkIh5bW4XJJobT02HIvF6O/vx+12U1lZuenRYfKxn8w2QbqRHhkZoby8nJ6eni0B5kaY3nqhOHidRsU7NzdHT0/PKZNaOjo6yMzMPK2p/msZMF8TNczx8XFyc5dTUjk5OdTU1Kz7HI1Gg91uZ35+ft2ROG984xuVn61WK9PT00QikVXPkU+C09Ue09PTsVqttLW1kZmZSU5ODoIg8O2nBuif9XEwz87HLilgf86pTjSiKJJqiJOhzeHLT47zvl80cn2Zjr87mIbWaMUbt0m2cn0uWsYHFWBIMmooSTUxMOfHqoX/uCqPKw8Urfv+nV+UzIO3VPO5P3Rw2yPd/LF5il1ZVjomPav6NDNsUs+knLKd9Yb44sPdPNo2LVniWQ2kVlQwMzNDQ0MD5eXliruIWa/mA0ez+Z8XR/h17Ti/rh1X9p9t03JRkSPBHpMoTjWhSpygA3M+Pvv7Dj5+Xyvvqc7ms29a7qeUJqIEaRx1c2LcQN3APP0LEpiPLQWZcAU5vzCJa/ZmcCDXTo5jeQ5jz7SkRs1Lli4aVZlW2iY8mHRqbAYNWXZR6ZesHVoiGI3z0XtbAdCpBOJxEZtRy6I/gl4tqVrLxHG6wmrUCQC95MIjTNRNQGsf+gRjlV2IvKEoV951jLEladbljDdMTrKRfQlA/dSlhVyzN4N3/rgOTyjKPfUT7M91SG0tahXV1dX09PQwOztLZWXlWVG0yupVuV4HnGK0Lt+cDA8PU15evuMCEHkih9PppLOzU7HtO9PFWBRF/H7/qtej0+lwOBw4nc4zjh1Tq9WUlZXhcrloa2sjPT2dvLy8LY8OW9mCIhspdHR0EAgECIfDm25t2a7o50yfm9PpJCkpSZnUIt/wb2S/r1UfWXiNAOZOh0ql4tixYzz22GNcc80169Ye1wuTycShQ4fo7u6mra2NyspK3n0oi28+3s/wQoBPXlrE4XwHkUiEubk55a4+EolgNpspTrZz+zVl3PHsGPd1e3l4cBJ/WLKVk2uab92droBZbpIEDM1jLj5zfzv//Mgw7xtd5DNv3b/qyx4XE+nKBHscX5KYUMOoi4ZRF8VOE+8+lKUYA6xs35BjT5aNf3mwg39/uIvjgwvc9tZykp1OJgJqfvxUJwNu6F2MMeOTwFyngvwkHdOeKHFR5DOXF/PeIznrnmBFTjP33nSIbz01wC+Oj/J83zxXVKQythSkaczFTIJJm3Rq9mXbuKw8BXtknrx0Jz8+4eLFgUWyHEbeVJG6ah8yQ4wm/r+kJJlJV5B5XwR/OLaKRWvVKpJMWv79qkI+9rsuMs0qFgIiX7tAx78+H8MdiiMACyEBlUaHWhVCoxaIxKA3MUMzLor84viYwh5DURGVIHBpaTLP9C5wzd50br+uiv//0R6axtxkOQxkOwzkJRton/RSN7zEdT+qJRCJ4zBqUKvVVFZWKmKV4uJi0tJOtQ5cL1bOsVxaWsLr9aLX6xWj9ZKSkjUvqjqdjr179ypN8GVlZaSkrO2kdDbDbDZz6NAhRkdHqauro6KiYlUtUFbjLi4uKl6yJpMJh8NBTk4OVqt1S+Iau91OdXU1g4ODW/bCXcteT6/Xs3//fp5//nnq6uooKiralCL55fCDlW8aPB4PHR0d2O12IpHIuT7MV3tkZ2czOrrcND42NkZ2dvaaz8nJyVFSTRs90Q8fPkxLSwvvfe97qa+v57bbbtv0yadWq6mqqmJiYoKGhgauqaqi0lnFrQ918/5fNvKuEg1vLZYuWDqzlYDVSvu0n6Y2N81jI4qHqCExc9GiV/OpSwt5x/7MddsK9uXYeeCWar7wUCd3N81zYvxF3nN+ESOuCE2jLprH3QorTTZp2Z9r528OZGHUqfnpiyMMLwS4/qCBqypT1z2RU6167nzXLv7zL7083DrD452ziKKoeM869AIlDoEbq3M5UpxGRYYFnVrFrCf0/9g77+i2CnuPf7Rty7aG997biRNnBwIBCoQS0gApr4VCKaUFWlpo2YXSsMooJQ/aMh6QAu1jlbBJAxQI2Xvb8oinvKdkWdbWfX/I91pK7MR2nPS1zfcczmlPrOt7Zen+7u/3+w7uet/EY58dZm+LlQeWFhAdFiq27x9yB4q52cqhtgFUchnmfiert5rRD6d/lKfpmZmmIy9eK7FV/X4/hw8f5o6Zctanp/Dq9lZ2NVn43WXFFCdF0TPoZnN9oHv887DZgJgnqVbKJH/WvNgwanucGNR+olV+wuzD4c1KJfpIFWcvnEtaxS5aLQ6sDi8rt3swhnnx+AIBvfMe34gv6OZxUWk8g04vayu6SIhW09zvkMKrRW9YSWozrJEVd84/OTuTV7ea8fmFEFZsbGwsOp0Ok8lEV1cXBQUFo5oW+Hy+kPHqkTmWo5lmjAVRBG8wGDCZTHR3d08oyWSykMlkpKenExsbS0VFBWq1moiICGk1ERUVhcFgCPGSnQqIxvVidNhkkldG6zYhoAktLy8PMTwYjw71RBNHJnLuUVFRzJ07F7PZjNlsxmKxTNjw4N8F/xYFc86cOdTW1tLQ0EBKSgpvvvkmr7/+esjPLFu2jFdffZUFCxbwzjvvcO65507oCxUbG8vHH3/Mww8/zPLly3n55ZdJTEwc9+vFIu10OpHL5ezYsYPIyEieuTiFP+208LdaC/utGsBCXXebdKPNjo3gvMJYKdIqKzaCynYbv3yngic+r8PjF7h2/tHEBJFEs888QGykmrhINfu73ez/MOBNWpCg5eLShBBpR/AxvlmawL0fVPHYZ4fZ3mjhkWWF6CNUAcZfr4NdTX3srO9hf5sNs3WEoOQXBHx+WFoaz8/PzSZFF4bFYqGqqopEVTRqRWCPGxel4aXvlbF6SzPPfNXAwdYBbjk3G6fHz16zlX0tVhp7Ax2vUi6jOCmKK+ekkBuv5eODnWxvtDDk9rOkJE7K1hQhZhj29vbicVcTd3Yyz2/r5Nsv7SI6TCkZmovnDHDL4nT+fqiLcIXA/k4XhUY51T2BcanTr6AoXk9hcQGs3YRfkBOpUWDqsNFlc+H0+JHJAn6v7cP+FioErpoVT4dd4DNTN8VJ0ay8uIDnNzQCAT3r8rIkfvlOBQB1XXZ8fgHbMNlrS10fH+zvoLE3YLzw9JcNRKjkZMWEc/W8UKKHSqWSuj7RZFyr1Ybs6wRBkMarycnJU2IOINrNtbW1sXPnTgoKCk5aYHTwuFhk43o8Hmm3OVGbu8lAzPlsbm6WutyJ7lTF75jD4aC3t1dyCZo2bRo9PT3s3r17XGSjU22CLj6smM1mOjs7JbnRWKuAf9eR7L8F6Qdg7dq13Hrrrfh8Pq677jruvfde7r//fmbPns2yZctwOp1cffXV7N27F6PRyJtvvkl29th7vWNh3bp13HnnnTz55JOceeaZR/17sH5LNDMQ6fbiTUupVGIymaSxxxu7O3j8s1qUCjmXlMZzflE8ZanRIW48wRhwerjvwyr+UdXDOfmx/OabeTT3O4eJOYERa/+wtCNSExhXJunC+KqmB8uQh6umRXHb0hmojvGUKggCq7ea+e8v6wlTysnQqzBbXNjcgY9BpFpGaaKW2ZlGZmcaKU2OxuPz8+uPAue1KNfIb79VRIxWjcfjoaKigrCwMPLy8nD54GBrwAbv69peDrQOSAQXfbhSYtnOSNVRmhwl7S0hUJT/ur2F339RhyFCxWPLi5mfFbhR292iQcKAVHjFLlqlCJB1MozhXFhg4H+2tnFFUQRvm4Z45MwIXq7wEBupYYd5kHsuzKPd6uSVbYEOND9Oy3UL07n7AxMaZeA4IltWLgvY5v3krAxe39lGc78DpVzGL2ZHUNkv8PfDQyzMNvI/V5Xx9Jf1vLCpiW+XJ/HA0kLufq+SDw92AhClUTDo8klfsiSdhl67B5/fz9vXzyY/PnJUK0BBELDb7VgsFnp7e+nt7UWpVJKUlITRaAyY4Z/kXaPD4aCyspLIyEhyc3NP6GYuXo84Xg0eF4uMXPH4Q0NDmEwmoqKiyMnJOWVFxG63YzKZiI6OPu7vDR5/9/f3h7CL4+Li0Gq10ut9Pp8U21dSUjIm2Wg8xJ2xMFlmbvBru7q6qK2tHbW4+/1+KYz7Xwj/OSzZfwaam5u58sorufjii7n22mvZsmUL6enpeDweaX8iFseoqKhRv1Bi9FB7ezulpaXU9nn45ZoKum1u7roglyvnjJ2a3jHgZE+zlTd3t7K7yRryh8mMCR8m5uiGpR0j48rgQlsWp+DJb08nJVYfctzdTf3sqO9hX8sA9X1uggihFMSF8505qczOMJAVO0LOOfK63trdxmOfHkYXruTxS4tJN4azt9nCpqo29rfaMNv80nFz4iIoTYqiodfBgdYB5mToeeLSYhKij01kqWy38Yt3DtHS76QoMRK/IFDTZccvjGRfzkjTUZYcicFvAVs3O/vU/G+lC7kcnF64dk4ir+zs4POfz+emNw6SGK1hU10ft38jh6rOQT4eLmbBUMhlJEVr+Pk52fzu80CmZn5CJKuvnsGNr+9ne6MFhVzGkNtHhl6N2eLm3HwDT/9XGb/5uJp39rYPny9Ud45YLsqHWbEC8MZ1MylL1TP/iY34/AI77z5L+jmfzxeS/eh0OtFqtVJB0Wq1tLW10dbWNu5EkKmA+HlubW2lqKho3N3XWNdjMBjQ6/XHHRcH/94jd5snE4IgYDabaWtrC+muRaMQseA7nU5p/G0wGI5iF4ts2mCGvcViwWQykZCQMKp13c6dOykrK5tUJNtUFExAyuS1Wq0UFxcTFRUlXcvpghnA6YJJoFhu2bKFjRs3smbNGsLDwykvL+fOO+8kNzd3wh8Wq9WKyWQiOzsbdZSBe9438XVtL0uK43nwkgI0SjlVHYMh3aNISglTysmMCafF4sTh8fPTszK5YVHGcW8wr+9s5YnPDhOuFDgnJ5oBNxxst9MzNEzOUUBRfASzMvTMzowhL07Lqi/rWVvRxYIsA49dWnSUk44IUYryaWUXb+5qCzEGCFfJKU7UkqRyMD83nnOnZ6EfHqkKgsD7+zt4+O81aJQKHllWGCIl8fr9VHfY2TMc7RX8PkDA8ehb0xNYmKUjQ+vH67CF2P6FhYXR0dGBTxvLg+t7aLE4KYjXUt1lZ/X3ZnDbuxUoZDJ67COSHBFZMeG0DwTGr+EqORcUxfHo8mIW/X4TXr/A3AwDT19RynV/2cc+s5Uzcowk6zX8ZdikQK8J7LF7h0a63TkZetqsThp7Hfz3ihKKk6JY9twOnF4/3yiM5cGlhZz39BY0Sjnvf78gxIhCTCLR6/Vjft5EHWNMTMyE/EJPFENDQyH6ySN/r8fjCbGX8/l8IfKOyd5sxW5zKrrcicBms1FRERitKxQKKZtTLPjj6QLHMjxoaGiQvH2DH0C2bdvGnDlzJnyNfr+f7du3s2DBggm9TsRoxVa8fxmNRonBfLL9gE8CThfMk4WVK1eiVqtZsGABs2fP5sMPP+TJJ5/k+eefZ9q0aZM6pjiyDA8PJyc3l1e2tfD0lw1EhgUMvUVWZ7C0Y2ZaNAUJkagUcqwOD/d+WMWX1T2cVxDLw8sKjxrnWoY87DFb2Fnfw55mC6Zup+S7GqGEeRnRzMuOZVaGkfwELSpF6I1OEATW7G3nkXW1RGqUPH5pEQuzjVgcHvabrewdHoMGp4zER6lRK+SB4pQQydPfLiHdGIHP56Oqqgqfz0dRUVEIUaWhZ4jb3q2gqmOQc/JjyInTcrB1gAOtI8YLidGBIOsZadEUGFVUt/bx9JYuvH6Ba0vDWFoaL43vgseRPp+PfRXVvHWwn4/rji6Mog3ed2cn4xfgrd1tANz+jRzy47X8+PUDAKQZwnjr+tlc8MxW/AJcUBTHr5bkceXq3dT3DBGjVTPo8knm9wCZeiX4/TQO+Ll3SR5XzU3lutf2sq3Rwv/+oJyZaTpJaqKUQ5RajsXpxxAm45XLUqXrmUh2pd/vp7Gxkd7eXoqLiyelJ5wMRG/Yjo4OcnJy8Hq9ktl6cJalXq+f0izOU9FtulwuqXu0Wq3I5XJ0Oh1+v5++vj7y8/PHlKsdD6N1m4ODg1RUVEjpLQqFgi1btrBgwYIJP1i43W7279/PnDlzJnVuW7duHbU79fv9NDc309raSklJyYTN7P8f4HTBPJWoqKjgmmuu4YYbbuCqq66atDtIU1MT3d3dTJs2jUOdTm5+6yB2l5cV5cncsChjVGlH8Otf3WbmqS/qSYjW8MvzshkYcrOjoYcDbYO0DgQIJQoZ5MZomJmuZ1qqns9N3ayv7WNarJwnV0wnLX5s4oYgCKyv6WXlJ9V0D7rRhyuxOMTjyihKihwu5qGRYZ8c6mTlsK3ew8sK+UZhgKTR0dFBY2MjhYWFWP1qyY1nT7OFuqDoq9zYCOZnG5meHEmOTobGN3QU29OliODBz5rY1Wxl6bQE7v9mPlq1ghaLc/i4gf9qu+zSBzlCJWPII6CQy9Ao5ZSnRbOprp/Xf1DO+tpeXtrchF+AlRcXUJgYyXde3g0ExqdGrZp+eyDaKzpMxYDTI+01jREqlpTEs89spbJjkNy4CA53DxGtUTDg8nHPOUlcvaiQ77y8iwOtNp5flkI0Q9y0rh+bB66ZaWBNRSCkOsMYzt9vnj/hz1MwBgYGMJlMJCcnS1rgkwFxXycWFJvNhtvtJjo6mqysrCl3AxoLU7VTDdZz9vf3Y7PZUKvVUvd45PU4nU6qqqpQKpVjMpbH8ztHMzwQC1JBQQHV1dWTGqs6HA5MJhPl5eUTfq3X62X37t3MmzdvzJ8ZGgp8Z08W+esk4nTBPNWw2Wxcf/31REZG8sQTT0w6pLW/v5+qqiry8vIgLKBz3NbQz/KyRH79zXzCVUd/+e1uLwdbB9hZ38vXNT2Yup3SHytSJWN6cqREzilJjgo5xsjOsZYIpcD930hjyaxcABweHxVtNqnY7GsZkCQuIokmSafh9m/kcHZebIjp+5Fo7nNw+7sVHGqzcUV5MheVxHOo3cbuxj72NFsYGCYTRWmUlKVGU56mw+fz8pcdbbi8fq4sUnFWilK6UYnju2A4PT4e/fQw7+xtI0wpR62US6xYrVohefDa3T7+vNXMGSkq9nV5mZdl5MuaXnThARbtBzfO5f397by+sxWX189jy4twe/1SYkm4Si51uwDJOg3Ly5J4f387bVYXPzkrk5sXZ/GD1/ayvdHC3RfkogtXce+HpkBHmi5neabAI7uh1S5w3awY2obg06peifwUppQRF6XhhwszuGJW8gQ+QaNDJJTY7fZxyxfGc8wj5SpilqW4Tw1+ECwuLh4zuWOqEdxtjpfBO1p4tajnNBgMREZGjstPVnT4mqg+9sjjHGmvJz4IWCwWzjrrrAkXZJvNRkNDA9OnT5/w+TidTioqKpg1a9Yxz1kmk52UaLiTjNMF858Bv9/PH/7wB9544w1Wr149boP3I+F2uzl06BDR0dFkZmXz/MYmntvQSG68lqcuLyZMpWRPcz876rrZ12qjod8tdTcZehXFiZHU97up7rRzfmEsDy8rGjObUoSpw8bP3z5Im8VFnlGJWhNGVZBPbFZMBDPTdBJ7NSs2grWHulj5STUqxdg+sQC9djd7zVZ2NVlYV9FF1+DIODTNEM7M1GhSNC5SNC6mZ8YxZLdjt9vRaDT41ZE8vcPK7pZBlhTHs3JpvqTZtDoCmtLRxsGi487i/Bh+enYWBQkjLNO3d7ex8pNqzi+M5UCLhcfOUHPDPxx4fQJ+4NcX5bG5vp+Nh3vx+ATJeF1ESVIUFxTFserLQCZmfKSal6+ewU1vHKDF4uSuC3K5Zl4qV7y4k4oOOzfPjqbc6OHXW5y0DgbeT2O4gj7HyMg2LlJNn92DUiHjL9fOlMbtU42+vj5qamqkZI6JYLR4qyP3j2PBZrNhMpmIj48PsVs72ThWtykWfLEj9ng8IQX/RMKrgz14CwoKJm1EP1q3uWHDBpRKJbm5uRMaf1osFmlsOlHY7XZqa2uZMWPGMc9XLpdPioz0T8bpgvnPxObNm7npppv4zW9+w5IlSyY9oq2vr8disVBSUsKW+n7u/bgWu8uHN6gLKU4IpzzdwOxMI2WpOml36RcEXtlqZtUX9STrNaxaUUpx0ohLidfvp6bTLpGJ9pqttFmd0r9HKOGSafGcXZBAWWr0UXpHEY29Q9y2JuATe/W8VH5xbjZmSeJiZY/ZSnNfQFOpUsgoSYoiLlLNlvp+vH4/N8zSMzvGi9frRaVSYbfbyc7OJiVlhCXsFwRe2tzEM181EB2mpDxNR1O/g7ruwAhI9MudmaZjRpqO8jQdYSo5D35Sw9qKLuZm6EPCpkUP10U5RjpsLp68JJtLVx8kWhPYGx6JbxTGkm4MZ/WWgMzkiUuLWZwfw9zHNwbeK7UCn19AKQe728+PZ2iZF+fjvi1u2u1+zsiMZsAtcLBt9FzVF5YmsLCsgFmPbSQqTMXG284Y34dkkvB4PNTU1ODz+SgsLBz1BhcsjxLHkWK81WT2qRB4oKyvr6e/v/+U71RbW1sxm81SgLLFYgEIIeicjM5ITHw5kXzR4G5TLpezbds2Zs+ejclkwu/3jzvwu7e3l56eHgoKCiZ8DlaryJeDXgAAIABJREFUFbPZTGlp6Zg/4/f7USqVU7qXPkU4XTD/2ejq6uJ73/seM2bM4L777puQFi54NNTV1cXAwABRUVHItAYeXN9DXa+TC4vjeHhZIVr1sY+712zltjUV9NrdfHtmEtFhSva12jjQOsDQMIM1Pkod6B6HfWIrOwZ5/NNaNAqB+85L5eLZuWN+0YfcPvaaLfxxfSP7WwckM3IIONiI+8zi+DCSNR4cdlsgaNsNL1f4ONjlYklRLA8uKyJSo8TlclFRUYEmXItLG8/+1pGRcK99xM83wxjOJdMTmJ2upzQ5etRx8AjzthaVIrA/XZwfw+//Ucer21owRCgZdI2QqmQEPuTTkiM52DYoXcuaH8+m1eLk528fAuDZ70yjKCGCc54OeBZfW6JhZ4eHit5AsZ2WpMXi9GHuDzyAqOQyylKjqe4cxOby8d4Ns3F7Bb67ejd+AVaU6LgwxcONnw+RGB3G57dMjsU4UXR1dVFXV0deXh5Go/GocaQYb2UwGCZtLzcarFYrVVVVJCUlTToR5HgQBEEyPBAJR6LhgVarHXeRmQp4PB5qa2txuVwUFRVNehwudviNjY3Mnz8fmUxGd3e3NDEIfsgcDZ2dndhsNnJzcyf8u3t7e+nu7qawsHDMnzldMENxumBOEF6vl5UrV7J161ZefvnlMfcZ4hdB3Af5fL6Q0ZBcLqeiooLY2FiSU9N45qsGVm81U5wUyaoVpaQZQvelwU4/e8xWdjdbqA8i0eTHa5mdoZcYt8k6zVFftJrOQX7xziEaex1cVhjOfctnoVGr6BxwhUg7qjoGpbFtQnRgrCiXybhxQRIXZqmxWq0hN99gbarPL/Di5ib+tL6RRJ2Gq+ak0Gf3sGd4vOoZPm6aIXyEFRuv5S87Wvl7RRfzMvU8tvzYmk27y8tnld3891f1dA+6pYxOCGRK6sPV/PCMdB7/7DAzUqMxddh49hwNf6pUsLc1QBC64cx00vVq7v34MAB3zVZjjFBw14ZA51yaGEmzxcGAM/AAIgOmp0RLodRvXFdOWaqOs5/aTPegm+13LiIqTMmcxzbg9Prx+QXy4sKp7XaQplOx7udnnPSRpeg+1dPTQ3t7OxAIjzYajSc8jhwPxEQQm81GcXHxpHf+IkbzxxUNAgwGg5RnKXabLS0t5OfnSwEBpwLiODw1NfW4xQ0C94VgRi4gGR7o9Xppt+n1eqmpqcFut1NSUjKmdV1bWxsul4usrKwJn/t4iu3pghmK0wVzEhAEgU8++YRf/epXrFq1irlz53Lw4EFiY2OxWq0hoy7RDWi0EZnokTo0NERJSQkb66386gMTggArl+aTEKVhb0vAe3Vfy0g3JpJoZqRG0z7g4v197aQYwlm1ooSixGMbSQ84Pdz1XkAXGqWGMJWKbvuIr+30lACJpjQpgqwo8DlsHG7v49m9DuqsAt8s0HHPhbkYdVFHibUbex1S4d1a30f7sKZSLgvsCMvT9RTGKAkbbKesICvEivBYms12q1MaBe8xW6npHJTMDPQRgYQRMTg6Ozac3LhIfvutImY/toHpKVG0Wpx8/tPZ/PjVHdT0+yUyUrJWRps98L/z47XU99glWU5StIYF2Ube39+OXwjITsz9TtQKOW6fn3U3zyfdGM7C323E4vBy6NeLkctkzPzt12iUcq6Zn8rLm5txePzkGFQ8cEbElBFzRBwr3kpM7zGbzadU/A9I1onjLSIijmUQMB7DA5ExGhERMabZ/MmASL4aHBykqKhIKm5iRyxez8DAACqVKkSCE7x/HU2C0t/fj8lkIikpiYyMjKMmAs3NzchkspB0p/FiPMXW7/ejUqlO2Xs5hThdMP+/wGazsWPHDj755BNee+01tFotBQUFPPXUU8TGxo6LeReMrq4u6uvrKSoqwuZX88s1AeapiAxjeJBWUxcSlwWwu9nC7Wsq6R/ycM+SXK4oH8lUtDm97G8ZIdEEj20h0JFdmBfNt2elkqDxMDgwUvCDb74yhZI/fNXAS1uayY3T8tjyQhweP/vMVvYcYd2nC1cyM1VHUWIkO5os7G62sijXyKPfKsKoVeP1ejGZTMjlcgoLC0NuGoe77dzy9kEaeh1kGMNxenxSFmi4SkHZMCu2PE1HWWo0kRolW+r7+NlbB3F4/ESq5ZxXGMcd52Vx5qpt5BhV2JxefrtQzX/v91Pf72HIC8YIJX1DIx60RYmRFCZE8t7+gCH7+zfMITdeS+lD6wF498ez+WB/B69uD6TK/PnqGczLMjDnsQ24vH6euKyYPc1W/rqjRTqmjIDp+q3nZnNepoaamhqys7MnpWkT5RDB9nLBN9+x7PJEgowYo3WqzA58Ph+1tbUMDQ2N+aAg7h3F/7xe74QNAo6EIAi0tbVhNptPebfZ398vkZHkcrnUEYvXI3bEx0LwblPcbwqCQF1dnaS9DXZ6amhoQKPRkJw8cdb1eIrtv2gWJpwumP8/IAgCF110EUVFRSxcuJCZM2fyu9/9jp6eHp599tkJRwWJGBoakjI24xOTWflJNR8c6KQ0KYqnryiV9I9joc/u5u73TWyq66MsNZqc2AgOtdkkjaJcBgUJARJNWUoUuXo5nT39PLK+k7ZBP0vSZdy0KJ242JhRd1siK/ajAx18VdMrjUAhYN0n7ktnpulCLPYEQeDNXW08/tmIrd78LIN0Y6tpaMavT6eqN3D8/S0DIU5CURol35mdwgVFcRQkalGOccN58GMTb+3pQABiw2T8vFzD/VucGCMUuH2gUcpD9qVlsXIEpZoDHYGd5OUzkrhsZiJX/XkvAJ//fAExWhXlj24AYP0vFhIfpWH6w+vx+gUUMhmFiVoq2kes8MKUcpxeP9FhCn5/ealU0EV4PB7Jb/h42ZNityUWE4fDEWKXN5GHMlEGIjrMnCoZCIyMLNPT0zEajRKDVTRcD+62ppKJ6XQ6qaysJDw8nLy8vJPSIQXzEvr7+yULTZ/Ph9vtpqSkZNL3g9G6TdGByGg0Sn63tbW16HS6SUldxhNafbpghuJ0wZwCCILAa6+9xjPPPMMLL7xAcXHxpI7j8/morq7G6/VSXFzM59W9/PqjatQKOY9fWsSi3ND4MrfPj6ndNmIOYLZIRUEmg7LkKM7MjaEkMYL0CB8ex+BRVmwabRRPrTfz7r4O8vVynlxRQnZSDPU9QxIx50hWbEG8ll67h/YBFxcUxfHIssIxI8lEVHUMctuaChp7hzivMJa4KDX7zANUB41X8+K1lKfrpIivmk4b931UjdPj41dL8rhsRpIUqXTkbuv1Gj8bWzy4fUd/pDVKOUuK49nfasXq8CIIAht/uZAnPtzDXw6OFLxUQxgtw6SerXcETPgX/G4TADefncmhNhvra3tHPf5r359JYWIkZY98TV68lg9unDvq+yAIAu3t7TQ3N4eMSj0eT4j+Uey2xGIyFfFWg4ODVFZWnhIZSLBBQF9fH729gfctOTlZijA72Tfhqe42gzWq/f39kmQluCMW39OBgQGqqqqIjY2dtI3hWBKUpqYm2traKBwOd4+Li5tUhmlNTQ0Gg+GYyTCnC2YoThfMKcT+/fu59tpr+dnPfsZ//dd/TfqG1N7eTlNTE6WlpfS45Nz6t0PUdtn5wYI0Zqbq2D+cCnKozSZpCdMMYZK9nt/r4dmNZmwuH1cVqjg3M3QsdOQC3+Hx8cKGRlZvNSMIAiqFDOewzkVkxYpj0JKkKNRKOT6/wAsbG3l2QyNphnCeGmV/6vML1HQNSoV3V7OFzoHAeFUuC5BoFmQZKEuJQuvsRuF3U1xcHNJpdNlc3PluBTuarJyZHsHVRUoUPhcOeQRmp5rafj+HOoakYGcIjFvdPoFBl48ItYJZ6TpeuLKMK1fvpsXiJEwp57OfL+D5jY0881UDCuCJS7J44HMzA8NxXNfOT2VXk4VDQR1kVkw4Db0OVAoZH9w4hx2NFlZ+UoMMePqKUs7Jj2Xaw+spS4nmjR+OLQaHwJ6vsrJSugkqFIoQ/ePJ0r2JMhBR2nSixJzg4wY7AgUbBIiksL6+Pmprayc9lp4snE4nJpNJStYZb7d5pEeu3++X/kYGg+G4jFy/3y8ZPBQWFk7aNH+0blP093U4HBQXF0+qYFZWVko5qMf63Wq1+pSN8qcQpwvm8bBu3TpuueUWfD4f119/PXfffXfIv7tcLq655hp2795NTEwMb7311qSNCMaCxWLhhz/8IbGxsTz22GOTprmLfpNpaWkY4hJ45O+1vLsvwHxUyKAkOXp4vBpJdrQMpcceYi0nqLU8tbWPHc02LpmWwP0X50tylW5bgBW7b7h7NAWxYkXv1RnxKn69bBqFSdHHLPw7G/u5473A/vTWc7MpiNeyryXA5A0er4oyl/I0HXaXj5e3NB9lqydKIsSYNlE64PH5ebdBxrrDQ2iUcsJUcsm+L1KjYEaqDsuQh6Y+BzaXl/suymNGqo4VL+4CIDpMyZs/nMUd71bSMeAkNlLNezfM5Q9f1fPcxibCVTLmJSrZ3+2jf1izKQNy4yKo7R5CrZDx1S8WEq5SUP7oBvQRSrbcvgifX2Daw+ul92xpaQIfH+pkQZaBl68eEYOP1hGL8VZOp5PBwcFjRj+dDIjEnLS0NJKTkyf8cDdatxUZGSk9mI3FyPV4PFRXV+P3+8fUi54MBHf2eXl5oxYYkUQljozlcvmUeOQODg5iMpkk8/rJdGtjdZvbtm3D6/VSUFAw4bHsgQMHyMrKOubY2O/3o9FoThfMYfzbFEyfz0d+fj6ff/45qampzJkzhzfeeCNkPPrss89y4MABnn/+ed58803ee+893nrrrSk/F7/fz1NPPcW7777Ln//850kx2CBwTSaTCZlMRmFhIe/s6+DRdbVo1XJ+MU9HeliAhXpk0oV0HkKgC/zT140YIlSUJkdR1z1EiyUwdtQo5UxLjpI6yBmpAXOARz89zN/2tJGrl/PkZcXkp44+sukYCLBXt9T38Wllt5RTCYFA6+DONFkXmljR1DfE7WsqqWi3saIsju9Pj5L0nBa7i05vON1CFJXdLg62DUqm56Lbz9l5Mdy8eMTt51cfmNhc10f3oJtHv1VEQUIkl/3PTsKUcvyCgEIuJypMgcPtQxeuojgpig2He3EO2+FFhymJi5BT1+dGrQgQLsKHC7M+XMWWO87E6vCw4HebSIrW8MWtCxly+5j92AYKhmPHRGP38wpiePCCtJB4q2OxPQcGBqisrJwwq/RE4fP5qKmpkbSEx3q4OxFHoNEgPhydiNXcZCB2m2q1mvT0dGw2m2TiIJKoDAbDlI+MBUGgubmZ9vb2E2ItC4KA3+9HLpejUCjYu3cvubm51NcHHKqO93cMxt69eykoKBhTsgL/slmYcLpgHhtbt25l5cqVfPrppwA8+uijANxzzz3Sz1x44YWsXLmSBQsW4PV6SUxMpLu7+6R9GL7++mt+9rOf8dBDD3H++edP+PUiqaCpqYm+vj5UKhU9HjV/2uekzebl5rMz+fGizBDG7JDbx4HWAWkMur9lAJtrhA1anBjJxaXxlKfrKUqKQj2GVdvaQ53c/1EVMvzceVYil84voLbbHrLXbLcGCna4KlB4FXI52xv7SYjS8NSKEspSj85PDO5Mevr6eb3CzmdNPuK1SmamRdPU76ama2SvWRCvpTxDT/lw8Y3UKFn5SfVRms0736tkV5OFjgEXz1xRSkKUhv96eTdKuYy8eC0tFic258j7kKIPQ62Q09Q3RIYxgo9+MpdPK7u4bU0lsWHw2MWZPPhlB839TiLUcjbffiYDDi9nr9pCVkw4T1xawqa6Xp7+qiFEByqXwQ9KVHyzKCZk/3g8BBevI8fSJxs9PT3U1taGFK9gR6CBgYETdgQaDW63m6qqKuRy+aSNzceLI0OfxT1xYmIiKSkpU2ricCyIkWVarXbS0hex2/T7/ezZs4dZs2ahVqulEOjMzMxxTQ3Gk8F5umCG4t+mYL7zzjusW7eOl156CYC//OUvbN++nT/+8Y/Sz5SWlrJu3TpSU1MByMnJYfv27ZOO7hkPOjo6uPLKK1mwYAF33333MZ9aPR5PCDNSHHPp9XqUSiUNDQ1kZ2cTqY/hNx9Xs7aii4XZBi4sjqe2K1DMqjoG8Q1/BnLjtFKHl2EM5+mv6tneaOFb0wOm78cyVre7vXxe2c1TX9TRY/eglCHZ98VFqofJOYEiFuyRur/Fyu3vVtI54OKWc7K4clYCA8MF0mq14vP7saClcVBBTb+XA22DUuEFyI6N4IKiOGan60mP9GOurz2qCxEEgff2d/BIkGbzw4Md7DVb6bK5OTc/hsM9QxJRSQYUJmo53D0k+ci+/L0yPj7UyTt72pmRGs1r15bzwf4O7vnARF68lt8u0nKo08kDmwaAQIGdmRbNxwe7JPcgEXoNfGeannnZsczITkBzAsVOtF3Lzc09JhljKiEIAhaLherqajweDwqFIsQRaDxyiBNBR0cHDQ0N5OfnT2oXNxqCWcb9/f2jhj67XC5MJhMajYb8/PxTpjUMNloYazw8Gnw+n3Rv6O/vx+v1otfrpXMXXY9qampwOBzH3VFv3bqVefPmHfNv++9eMP/l1KX/7khMTOSzzz7j3nvvZcWKFbz44ovExsaG2HyJomYxh0+v15OamnrUaCUmJobKykrCLBYeX17I7Aw9j35ay5b6ftQKGTNSdVx/Rnpgt5kafVR+5kvfm8FzGxp5bkMjB9sGWLWilLz4wN5MHK+KxgPVHXap8IqJH/HhMh64OJezikYfGwqCQI5ewR8uTuaJ9S38/ot6Pt3fxCVFBrpcCkw9ag60DjDoChQyca957Xw9mcZwXtrSzM4mC+Z+J9ctDEgy4g3RVFZW0tfXR15enuSEsrwsEUO4kof+XstP3zqIQgYiQXZzXT/ZcSNjplvOyeLHizI5+6nNWB0elHIZ17y6l4KEgLxClH64fYHxbJhSTossjq9am6VjtFqctA6PsnUauGFuHEnGaG79oI75OXH8/Jtj+3FOBHFxceh0OiorK+np6SE/P3/KGYqjFROtVktKSgo+n4/29nYyMjJOmYYxMTERg8GAyWSis7NzUsVrNNN1cVVRWFg46k0/LCyMGTNm0N7ezs6dO6e0YB8LMpmM1NRUYmNjMZlMdHR0kJ+ff1SHHUw66u/vRxAEqctPS0uTOkO/34/X60Uul6NUKikpKaGvr4+9e/eSnJw8JiNaJBKNhQk2X/+S+I8tmCkpKZjNZun/t7S0kJKSMurPpKamSjZip+ILolQqefDBB3n66adZtGgRaWlpdHR08OKLLxIfH09iYuK4bowqlYrp06fT3NzMnj17+FZpKdOSZ3HzWwfptbs5tyCWq+eNnY2okMu4eXEWM9N03P5uBSte3ElxYhRdg66Q8er0lGh+dOZI4Y0OU7Gusotff1jF7R/U8sseK99ZVHyUVtDpdOJWhNPiVJMeq6PJNsChHheHNvYAATedi0sTmJmmY1b60XvNhTlGXtzUxB+/buBA6wC/v7yY0uRoysrKqGts5vXPd2BVx3KoY4h9LQMSozVMJcfp8Us+sW9cX063zc0Nw+HQBm3gxuL2+fEJcPn0RAZdXj462AkEWMLv7Gljzd7ADvJgm41fvFOBcvjUYjTwneJw1rfLqOgYQqFUsXRuPrVdAQZt5HEkNROFWq2mrKyM1tZWdu7cSVFRETrd0ePt8WIsg4CxikliYiKVlZV0d3efUPbkRKDRaCgrK6O9vZ1du3YdVwYiFhOxQMKI6fpoD5tjQSaTkZycjNFolAp2Xl7eKbGCEwt2R0cHu3btIiMjA4VCMSrpKDMzc8xzEs0N/H4/giCgUCgwGo3MmzePuro6duzYQXFx8aQ0oaKBwr8r/mNHsl6vl/z8fL744gtSUlKYM2cOr7/+ekjszZ/+9CcOHjwokX7effdd3n777ZN6XqLRQXd3NzNnziQ7O5t169Zx6aWX8qMf/WjSoy6LxYLJZAp8ubU67v2wii+rezi/MGDgHhz9Je419zRbAnvN1oEQgk6yLowr5yQzN9NwzAiquk4rt62ppKbHyTnJcEWhGqcyiuYhFTV9Xg60D0rm5GFKOdNSoskwhLOxro/uQRc3LsrkprMypUiusbC72cJt71TQO+ShPE2Hy+OjMojJm6FXMycrhlnpesrTdaTqw7j8f3ZJu8/bzssmMyaCnw0bq//+8mIuKklg9mMbGHL7uHxmElkxEbywsRFb0PugkYPLD1l6BbcvTmNIUHPHBzWcXxTLLbO0bKnt4LfbXcgJFOGLSuL5644WfrAgjTvOn7j59Xhgt9uprKyU9HzjuXkdyfacjEGAmD3Z1tZGUVHRpCURk4FoOiDu+RQKxVGm62IxEQk6U1HgBEGQAtDz8vJO6qoGkGzzxL+Ty+VCrVaTk5NDbGzsCbFpgyUoIqksJiaGnJwc6Z6zZcuWY4ZWi7VkKu0cTyFO7zCPh7Vr13Lrrbfi8/m47rrruPfee7n//vuZPXs2y5Ytw+l0cvXVV7N3716MRiNvvvmmJGE4mbDZbCFPdw6Hg5/+9KcMDQ3xzDPPTNp5JThjMysri7/saOWpL+pJ0mn4dnkyXTZ3yF5TNAcQ2atlKdF8cKCDFzY2kROnZdWKEnLiAiPaYOG5xWLBZrPhlylo94TzZsUgFZ0O5IAYnBWjVUn70plpuhBCkd3t5eG1tXxwoIM5GXqeuDTUXF0QBJr6Rnxo9zRbaegdMZaPDlNyybQEFmYbmZ4cSUdznSRLEG+U17yyhzark7bhTnlGajT7WgL7x5vPzsTjE/ifTU0hH3i1Atw+iFDJGPIIFCVoMXXauWpOCvdelM/fK7q4bU0Fl89I4qFlhXy0p5G7Pm5gcXYULTYfh4ejyG45J4sbFmVO6m84Hvj9fhoaGujv7z9qLzXa32kq2Z5iwY6JiZm0AH+iEK+poaGB7u5u1Gr1UTvVk9n1irtNlUo16qh0MhCj1cQCabPZ0Gg0GAyGkD2xyB7OysoiISHhhKLDYESCIro9tbe3U1xcjE6nY+vWracL5n9ywfxXgiAIvPzyyzz33HO8+OKLx4zYOd5xxJtpaWkpFZ0ObltTSafNhVIuY2ZqNOXDnZg4Xj0Sm+v6uOu9SobcPn46z8isGB8OhwOvIowWl4Y6q0BFp4OK9qAUkyg1vXYPcgR+OMvITy+cdtyb6fv723lobQ1hKgU/PiMdAaQiKToUiT605ek6ZqZGU9E+yO+/qMMQoeKJS4uZmxkQWYudgDiuvHL1bnrtbsz9TpYUx7GusjvkdwcTdS7Oj+InZ2Xy8BdmtjZY+OlZmbh9fl7cHNhZXj4jgYeWFbNmbxu//qia789P5ZZzsnn26wZe2mImLkKOzeVnOMiEF66cfpQL08mAOFWIj49HqVSOaRAw1UXN7/fT2NgoeZlOtV5UZLCK41W73S5dU3h4OM3Nzeh0upDu6GTjRLtNQRCw2+1SgQy+JoPBcExrQ5G44/F4pJH5ZK/hyG5TfACKiIjAZrMxf/78Y75eJpOdssi0KcbpgjnVOJ7RwSuvvMIdd9wh7UJvvvlmrr/++ik9hz179nDddddx2223cdlll016X9Db20tNTU0gSFYTya1/O8SuZitLpyXwmyDTAhFHuph0D3p47pCPun4v6YbAF7RZzH5UyJg2bJQQ+C8QPt3S75CM4s/PVPPIillERhz95bY5vVL49Oa6Pg612aQPXqpew6x0Q6BApunIjg01lgcwddi4fU0ljb1D3Lgog5vOzkQplzNot/PZ9oO0eyL4634rgy6vRPwJJgEtzNDym2/mceFz+wD4/eUlXFQSz/f+vIc9Ziv3XJjH1fNS+fnbB/lHVQ9yGfzkrExaLE7e399BYpSGHrtbeliI0apYmK4lUWlnyaw8itJPnmtNsAxHNKbw+XwolUoKCwsDxvinaMc0MDCAyWQiOTmZ1NSxd+XHw2ipJMHRd1qt9qgkHLPZTHt7+ykfD7tcLqqqqlAqlcfsNkfzldVqtVIHeeQ1jQfidzo9PX1S5hIwtuFBQ0MD9fX1lJWVjcnGFovtqZQ4TSFOF8ypxHiMDl555RV27doVIk05Gejr6+Paa68lPT2dhx9+eNIfUKfTyaFDh4iJiSE9I4MXNzXzx68byDRG8OglOcQo3RIj14+cHn8EjYNyqno97G+1SWkjAFq1givKkzivMI6S5Cg0ytFHYG6fn1X/qOPV7S1kRMl4YnkhsUZ9IIqreSSOSwAUMhlFSZFMS4mmqXeILfX9TE+J5veXF5OiP7ZW0e728tDaGj480EmyLoxUvQZTx6C0g5TLQCkDuVzGM9/KotEGv/2sXnr97HQdu5oDEVjPf3c6Z+XFsOJ/dlLZMcjDywqYm2Hgng9M7G62Ss49IlL1YSwpjqfV4uTvlV08fEkBl81MxuFwSO93VlbWlBSuYDKL6Ps7mkGAOLo7VcxOEWKUld1uH3dcmUiwC9Y/TiaVROyOjEYjWVlZ/5RuU5T7+P3+EKcjl8slEakMBsOUeP9C4L0TIwCLioombWV4ZLdpt9uprq6WDBBGc136F87ChNMFc2oxHqODU1UwIfDhfPzxx1m7di2rV68+iuE7keMcPnwYi8VCbGwsW+v7+MMuGy4ffKtIh0YTRkWXg0Ntg5KMIt0YCHMW949tVid3v2/C6fHzwNIClk4bu4Py+QVqu+y8uauV9/a1SwHRABFqBTNSo6XjTk+NDul011V2DZsjyHhoWQEXFIU6vliGPJLUZXezhYp2G57hQiYDSmIVnJ+vZ35OHHd8VM+g002YWs0/bj2D/93RwiPragG458JcVn1RJ/njvvb9mWg1Cn78v/vptXuIDlNKjFuAgvgIkvXhfF3bi1+A689I55fn5fDbdTX8dUcrf7yilHOH7fyOtV8cD0SDAFGnOhGDAJfLRUVFRQg55lRBTCHJyMg4Ku1CdAUSiz4EcjrFAnl8RHryAAAgAElEQVQiHUtw8kpRUdGk00AmCp/PR3d3N3V1dXi9XtRqtfR3MhgMJ33P19/fT3V1NcnJyaSlpZ1wt2mz2Whra6O0tJSOjg7JkjIxMVE69n9CwfyPlZVMFK2trSGWdampqWzfvv2on1uzZg0bNmwgPz+fVatWTdrm7niQy+Xcc889zJ07l8svv5xHH32Uc845Z1yvHS3pQqVS0draynmleZw/V88d75l4+5AFGVZKkqP47pwUZqUH7PBiI0NvYDlxWtb8eDa3r6nkzvcq2dlk4Z4LcwlTKXB4fBxsHZC6x30tVolxG6NV4fMLWBxe5iQqWfXdWRijxrbdWlIcT0lSFLevqeDWv1VwybQe5mbqOdBqY0+zhbqeAKlGIYPMaBlLsjSUp+tJj9fz+/UtHOoYZHpWGPlp8QiyRpRKNUq81NbW4vaOXNOy6YnIBIHfflYHwA9e20twqElRYiQXFMWztqKT3c1WfnFeLmflxfCztw7yRXUPL21uxu31Y3EEOnB9xMix5XI5OTk5WCwW9u3bR1ZWaDB2MIL3WqKnbFhYGHq9nqSkJAoKCibUNWk0GmbOnInZbGbXrl2Tlg5MBkajkVmzZlFTU0NHRwexsbEMDg6GFP3Y2FhycnKm1BBAJpORmZlJbGwslZWVxMXFjRqsfKIYTbai0+nIzc3F4/FgNpuJjY09ZeYSBoOBOXPmUF9fz+7duykqKprwLlkQBKxWq5QeExcXhyAIJCYmEhMTQ3V1NW1tbZSUlPyrEn0mjNMd5jgxHmeg3t5eIiMj0Wg0vPDCC7z11lt8+eWXJ/3cWltbueqqq1i8eDG33XbbUansxzI8CH6CdzgcHDx4kMTERJJSUnjyH/X8ZXsLBQlaVq0oJTNm7GIG4PX7efzTw/zvzlYMESriItXU9wxJuzyRcVsepKv0+gWe/rKe1VvNpEXKePxbBczIOTpvz+cXqO4cZI/Zyq4mCxsP9+IY9nUNU0CeQU5pQgRzMg3My0tCHxVq5u32+ln1RWAUXJAQSe+gG5kM0gzh3LlAxzOb2tjSFugag/eZIpJ1GuxuH1aHlzd/OIvpKdFc++pedjRZ+Ou1MylP13Pr3w7xmambi0ri+XtFFwq5DJ9f4JOfziUr5uiblcfjoaqqSvL+lcvloxoEiJ3WkZ6yJ4JTFd11ZJC1zWZDJpPhcrnIyMggPT39lI1Kxe6+r6/vhMlIbrc7ROJxPNmK2+0OyTY9lV2Y1WqlqqpK+luP9X4HmzmIzkCjdfrBpKDe3l7JlD8lJQW1Wn3KHJCmGKdHslOJ8Yxkg+Hz+aQA3FMBj8fDXXfdRWVlJTfccAO7du1ixowZGI1GqSsR47qONYrz+/2S5VlxcTGbG6zc/X4lXp/AQ8sKWVIcajnX2Otgj9ki7SCbhu3lILAnXJwXw7fLk5mRpjvKSSgYX9f0cM8HJpxuLz+dF8N3FhVzqM02fFwL+4KSTGLCZOQZFOi1GjY1O/AJ8JuLC1g2ffROLRjra3q4+30TA04vSrkMpRxp9AogB65bmE6KPowH1tYA8LvLivntulppZ/vRTXPIiYvkv17axcE2G+/fMIf8hEiu/+s+ttT384MFaexo7JfConfcdSaRmqOvXTQIMJvN9Pf3S7KB4LHdySTo+P1+6urqGBgYmLIuQRCEEDKLyMoVrysqKkoqmKLN3MkKbB4LIhkpMTGR9PT0cb3HwRpI0StXJOhMRIrT2dlJfX39KbUyhJGHhd7eXmk0LX7+xIcZcf8tXtdoo3BxTCuTySQXLZ/PR21tLQMDA8yfP//feiR7umCOE+MxOmhvb5f2M++99x6PP/4427ZtO+nntmnTJj7//HM2b95MXV0dERERXHDBBfzoRz+adPcgkhZKSkqw+VX88p0KDrQO8K3piWTHRgSMDcxWqYjow4d1lek6ZqXpMGpV3P2+iX0tA3xndjJ3XZA7JhEIoGfQzVfVPfzx6wa6B92SrEMGpETKKIxVMTM1mvm58eSnjIi0Owac3PFuJbubrSwvS+S+i0I9b8WMTXEkvKfZSqdtxItWo5Tzw4XptFgcfHSgk5hwOc99MxaZIZUVL+0BYP+9Z9M/5OHc/96CX4Bz8mN4dHkRV/15D3XdQ3x3djLVnQFvXvELkh0bQUlSFEWJkVy7IB0YMQgQ94+A9CCj0WioqamZkOHAVKG/v5+qqqpjjofHgs/nC+mKXS6XxGA1GAxjxnZBaGDziSRyTAbiw4LVaqW4uDgkgSNYq3osDeRkcSpN5IPh8XgkH15AiowTr2si5zFW5ubJ1ryeRJwumFON4xkd3HPPPXz44YcolUqMRiPPPffcpPWSE8Frr72GVqvljDPOIDExkaqqKq6++mq+//3vc+211076y2232zl06BCpqanEJSbx1D/qeG17CxAYUc7NNATIP+k6smKOvjF6fH5p3FqUGMmqFaWkG8Ml44HdzdZAdxrUmSplEK2GPhcYNbDy/FTOm5l7zALi9ft57utGnt/YREZMOD9cmE73oJs9zQFpitiZJkZrmJWuY1a6nic+O4zXL+D1C6QbwylLieaTQ53kxGp5dlkKGw418dD2gDb1wH2LAZjxyHrcvoChg1IukwhLYt5oq8VBr93D+l8sIC5SIwnPx2sQIIY1W63WU74XEnMngWPexEezzQsOSZ7MOTscDiorK9HpdGRnZ5/SLEVRqxobG4tGozlK12kwGKSueKohdpsnK7IsmExlsVhCrPMGBgbo6emRpEaTwZHdphgefbpgjuA/umD+K8Fut3PjjTciCAKrVq2a9L7myIzNv1f28MAn1SjkMh5bXsTi/OMLtD83dfGrD6rw+AUKhqOzxM40UgW5egXTkyKYnWlkTk4Cuigtmw73cud7lTjcXm6aY+T6b4xudGAZ8khj2/U1vdQHOf7kxkUwK10vWeIl60Zu5mWPrAcBzi2IZX/rAJ0DLpBBWXIUr/9wNpuq2vjx29Wo5XBhSQJ7zFbJTF3Mv3R5AzvULbefiS5cycV/2kZjn5M3vmU8IYOAvr4+qquryc7OJiHh5Gk2R4M4WSgoKMBgMEi7utG64hNlsAYjmM1aXFw8aTer8UDUQIrXNTQ0JN34CwoKMBqNp6zDF7tN8XefyPvpcrlC9qoimUochx9ZyMTosMjIyBNiTYuSme3bt7NkyZJj5mX+P8bpgvnPxHXXXcfHH39MfHw8hw4dOurfBUHglltuYe3atURERPDKK69QXl4+pefg9/t54YUXWL16NS+99BJ5eXmTOo44OmtpaaG0tJRel5xfvHMIU8cg1y9M5+fnZqEMKgaDLi/7JHmHlQOtA1JxAUjSylhepGNBbhzTMuPHjLfqHHBxx7sV7Gq2sihVyaOXz2TIr5COu7vZQv0wM1Y0SyhMiGRvixVTxyAXFsfx4NJQn1zxekoeWg/AjYsyuGZeGite3Emb1UW4Sk55up59QZ1ptFrG3Cwj/6juRSmXsedXZzHo8HD2f2/F4xMojlFwXbGSJ3Z76HH42f7LucccRY4HHo9HIokUFhaesqd2h8NBV1cXTU1NCIIQQjrS6XQnfdd4MshIR2og3W43UVFRIbpOmUwmSTHS0tImLfyfLCbTbR65V52MxaHoAdza2npcA/vg11gsFrZs2cLGjRvZtm0bcrmchQsXct99952y1JopxumC+c/Ehg0biIyM5Jprrhm1YK5du5Y//OEPrF27lu3bt3PLLbeMKlOZCuzcuVNyJlq2bNmkbwQ2m42KigoyMzMxxMbx6KeHeXt3GzPTorlkWgKHu4fY02wNCXROj5JRFKcOMGOzYvnQNMCr21soSYriqRUlpBnG1iH6/AKmDhvPfNXApro+KV0EIEoTCJAuTw+ERU9LGTFL8AsCL29u5pmvGkjWa3jyshKmpYy4vXh8fsoe+RqA+Zl6/ALsarZIx1bIoDAxkor2QVJ0Gv76nRxqag9zw5duIlQynvuGFr/fz81fOnB6BVRKOeEqBS6vH6/Pz757F0/q/T0SwTu+4uLiKXesEWUrYiERZSviDddisdDd3X3SO74jIY6mLRbLpLSqYg5ksPFBMNvzWGNjrzcgM3I6nRQXF59Sm7djdZsi2z24QE7lXtXhcGAymQgLCzsqLk0QBPr6+ti0aRObNm1ix44dqFQqzjzzTBYvXswZZ5xBdHT0v3pKyemC+c9GY2MjS5cuHbVg3nDDDSxevJjvfve7QGBvtH79+qNE3VOF3t5errnmGvLz81m5cuWkiQZer5eKigopRPejgx088EktTq8fpRzy9HJK4sOYnWFgfn4icfqj9z9fVHdz7wdVCAI8vKyQ84sCbEHnsGZz9zA5J1izqQ9XMeT24vMLXFESxV2XzECtOna3s9ds5fZ3K+i2ublxUQY5cRHsNQ+ws8mCqSPAYJUBxUlRDLl9NPUNsSDLQKvVSWNvYKeaqVNw/zw1bh/c+IUDnVrG179ciFqtZvZjG5ABT1xazIN/r6FzINCh7r7n7Em9t2PBbrdTUVFxwl3XWHZswX6lRx7bZrNRWVl5wvZ2k4HFYpEkC8fq+MbSQJ6I8YFoM5eZmRkizj8V6OzspK6ujtTUVORyubQDFx9mxL3qVO96BUGgvb2dm266ieXLl6PX69m4cSM7d+4kIiJCKpALFy48ZfrdU4jTBfOfjWMVzKVLl3L33Xdz5plnAnDeeefx+OOPM3v27JN2Pj6fj0ceeYQvv/yS1atXT5gRCSNMT7PZzMDAABEREQwqInlss4X2AQ8/OTuTGxcdP5Krpd/BLX8LjHWLEiNRymWYgiK5cuO0zEoPEIrK0/Qk6wL+rHe+W8n2RgsLk5U8/u2ZxOiO7nwEQaC5P0Aq2lbfzxfV3ZJmU6OQUZIcxR5zIJnkgaUFrJiZxC1v7eeLmn6W5ISxNF3gD/u9VPX50KrkvH/jHLRhKhb+bhNxEQp+MkODVR3HM183IQgjX4pwlZwzcow8c8W0Cb+vx8NkJCDBvrL9/f14PJ4QBut47dhEe7uhoaFT3nX5fD5qampwuVwUFRWh0WiOiiM7GdFdMGJq7vV6KSoqOqkeqUearw8ODkoOQfn5+RgMhpOqle3s7GTjxo1s2rSJAwcO0N3djVar5YEHHuDCCy+ccgP9/4c47fRzGqFQKBTcf//9zJs3j+XLl/PEE09w1llnjfnzx4qCysrKAqCmpoayzAQ+LCviwbXV/OnrRvaarTx+aTEx2tCRUqvFKdnW7W62SvtHU8cgESo5l81IYnF+DDPSdOhH0WzGRWp46XszeGFjI89uaOTbL+7it0tzmJ2fQnWHnT1myzDz1krPoBsIpJnMywzcbDYe7kUfoeYH81PZY64EwNrZwrZtTVgGfAhAYqyBxWcWMKjv5K73TDi8fpa/sIs5mQHJQ8+Qjwe2DAFNQCDH89ffzGdWup40w8nTTcrlcvLy8ujr62Pv3r2j7rqONMgP9pVNTk6eNOtWFNv39vayZ8+ek8bqHOt3Z2ZmYjab2bJlCyqVSoruio+PJy8v76Ttd1UqFSUlJXR3d7N79+4pve7gxBVRryrui7OzsyXz9a6urikngImj/g0bNrB582b27t2LwWBg0aJFXHnllTzzzDOEh4ezZs0aHnjgAUpLS8nPz5+S3/2vjtMd5knE/6eR7JEwm81ceeWVLFmyhFtuuQW5XI7P52NwcFC64Y6H6el2u6moqCAyMpLs7Gze+7/2zjysqnpt/58NG5B5FJBZkRkRBZxSQE8e39SylLeyHE5lWR3fTE8dT4NlnjdNMyujbDDTX52OvsdOZWmWaR4FFWVwABwQGQSZZZB5D+v3B64VWxA300Z0fa7L60r2cq+1bbvu9X2+z3PfJ0v435+ysLNQsmSSL7VNakkkS6+2iNj1+4+lV5t4Y9d5FAp4c0YgfwjoeKC7QaXh/5IL+eBADg0qLcZGIPYUudkOkEZHRnq1pJlor620krNLeOtgKSX1v3+NNz4YRHSAC099fYrE7Cs8M8GboEHWbDteyOGcyjbntrdQ8vq0AEJdLJgcfxwXK2P2Lr7LoK30rV1jHB0dqa6u1llpib96Y75PPLdSqSQgIKDHm4Dam4EUjTesrKy4fPlyn7jlNDc3S2M3rXNV9aV1Z67o4mRlZSWVWDtqEhNHfsRM186udAVBID8/n0OHDpGYmMjJkydxcnIiOjqa2NhYRo8efcOqQWVlZX+erewMckm2r+lIMHft2kV8fLzU9PPcc89x7Ngxg15feXk5jz/+OAUFBQiCgJeXF6+++mqb7sGbIQiClH8YGhpKTpWKJTsyuHSlAYGWLMxIbztGetoR4WXLUGfLNpFclyobWLojg4yiq8wf7cGSu32lQOmqehUp1+Y1U/KrySy6KpVuLUyMqFdpGWpnxOoHQgnxdGzXIEDc0zIxt+LVXdn8dr4cgDfvbfFjfefXC5TX/Z6+ojRSoNYKBLta8ecYH3ZllLI7vRRzEyN2PBnFYCcLglf+ho+dCSvGmBISEtKrZSsxULi1kGi1WlQqFb6+vgwaNMhgNzVxrys/P7/bhgPiSkv8XOIM5PXOQK0pKiqSRl8M3ZGpr1NP60iy1ukkokB2xcVJTJy52WpTzCMVm3ROnTqFm5sb0dHRxMTEEBUV1V8juHoTWTD7ktmzZ3PgwAHKy8txcXHhjTfeQKVquSGL85GLFi1iz549WFhY8MUXX/Tq/mVrRIFWKpWMGTMGQRBISEhgw4YNhIWFdfl9xfnBgIAATCxsWLojncSLlUz0d2TVjKAOrfGgxe/17b0tXrSe9gMY5mbDudJasst0R0dEN6FwT1uszIzZeCCbjxMLcDSDp0KNCXSx1FlpiUKiFVqSUn7OKOHjhHydc4sduPeEDGTOKE9S86t5Z182T97lxZI/+HKupJYHPjmO0kiBibERy6f68fL3Zxnmbs2mBwPIyMjo0XGE9gKFxVJk66YPsSHIxcVFb5u3nqKhoYGMjAzs7e31js+6fgayoaFBWmm1l215IxobG8nMzOyT5JX2Vtnt7RdfL5A9gbjaLC8vx9/fHzc3N2l/WxRI8bsoriBHjhzZX+3qDIksmDLtU1/fIkCtB4wzMzOZN28eCxYsYO7cuV2+8TY1NZGeno69vT0+Pj784/hl3t57ARcbM9bP0h3vgN9FLPXaXGXqpWqKa363rgse1JIMIo6OmBobSZ2eoiuLubk5BU0DWJtQRnWDmsfCbfife8LRCArSL9dI+5ppl6p1YrkAHCxNqKxTYWdhQmW9iviHhjEpwIkP/5PDh//J5S9/GMITd3lzsrCa2Z+nMtHfkdomDcfzWroxR3nbsWX+CDQaDWfPnkWr1RIUFNTpUmV7JTt9A4XFiLba2lpCQkIM2pQjrmYqKioICQlpM7QuWueJAtl6BrK7frniDOHly5cNHhStVqvJycnh8uXLmJqaolAodHxYe/P/gVar5R//+AerV6/G29ubK1euMHjwYEkgw8PD+6sBel8iC6ZM56itreXJJ5/E3Nyct99+u8vhs+IcXU1NDaGhoZwpbWDpNxmU1zbzlz/4EjLIitRLNaRcM1UXRczZ2vSaM0+LK88HB3I4U1zL7BEDeSjInNqa6g69Si9V1l8r69ZibQJNWrjmPcBgRwtpb9NmgJI/bz8NwMGl4/jgQA7/Si0CYN3MYKaGurD2lwtsOXqJ16cF8FCEG7tOl/Dit5n4DbRAaazgbHEdAjAt1Jm3Z+r6Cefl5REUFNSh5VjrZIiqqiqpg7U7QiKOQhja2BtaEjHOnDmDm5sbFhYWbazz9JmB7CpiULSjoyM+Pj69Yq3XnlG5uCIuKSnB0tKy1xqQtFotZ86ckfYgz507h5+fH1FRURw9ehRTU1M++ugjgzVi3abIgtmfuJkz0IEDB5gxY4bUnTpz5kxee+21Hr8OrVbLhx9+yFdffcXmzZul83WFsrIyLly4QFBQEJha8rfvMjl44Yr0+hCn30VspKct7nYDdLxKSysq+eeZJvZfUhPsYs66B4Lwcf5dhMpqm6R9zZT8Ks6V/G6YIADmSpgf6cycu/xwaNWxe7KgmtmbW4zV05fHYqRQMO7tQ1Q1qLE0M+atGUHsySxlV3opo7xtKa1tluYyjRW07Md62eHrZMHkoIGYGOveoOvr68nIyJCyFxUKhc6sYHV1tU4yhGi+3hOITVjm5ua92kEq0vpziStjY2NjhgwZgpOTk8H2ylqvdLsb3QUtn0sUR3G2s7XNXOsSZ0+byGs0GjIyMiSBvHDhAoGBgcTExBAbG0tISIjOQ8GuXbs4c+YML7zwQrfOe4cjC2Z/4mbOQAcOHGDdunX8+OOPBrmew4cP88wzz7B8+XLuueeeLpfNGhoaSE9Px9nZGQ9PTzYezGPjoVw87Aaw4cFheNsqpRuTmNV5fafnTxklvPbDOYwUCu4Pd6W2SU1KfjX51wzbByiNGO7R0nUb4WXLcA8bzhXX8pdvMqioa2Z+mDWLp/5epkrOq2Le1jRMjY048UoMWkFg/LpEqhpUWJkZS2YJ0NJUNMrHHqUR/HqugmdjfFgUc/OHiIaGBs6ePSuN4rT29ezJWcH2aF2qDAkJ6VGXno5mIO3s7FAqldKDkp+fH05ON/ca7knE6K7OGi10lG8pfq6bIZrIW1tb4+vrq/fDilqt5vTp05JA5ubmEhwcLAmkmJUq06vIgtnf6Kir1tCCCS0rxDlz5hAWFsby5cu7vC+i1Wo5f/48jY2N+Pj4cDirlDd/K6K2WcufQs25f7hLm6xOMTBaXD0ez6uSDNvNlArGDHYgyrtFIIMGWUsdta2pqlfx0vdn+E9WBREuxqyNG84gR1sOXahg4denGKA0Ysxge1Jb7W06WphgPUBJ7jUxXjcrmKkhLmxKzGP9vou8PMWPOaM9dM4jdrC2Fn4xOkmhUFBUVERAQACOjo5d+vvrKrW1tWRkZDBo0CA8PT279NDTujO3M36lzc3NZGZmMmDAAIOsdFsjGi3U1dURHBzcbhm4PaNyURzbMyrXl9YPKzdKAlGpVJw8eVIyCigoKCAsLEzag/Tz85MF0vDIgtnfuJlgzpo1Cw8PD9zc3Fi3bp1OFmdvodFoeOONN0hISODzzz/v1PC02Frf2vhArVa3JLPbOLFybx5Hc6q4f7grf53sy4WyepLzq9rEcg2yNSPCy47h7tYk51fzc2YZIz1tWTcrGFebjvfEBEHg04Q8PjiQwwBjcLc1I7eyWYrm8nE0J8LLjh9Pl9Ck1kphzzM/OcbZkjrMTYxYeW8gWSW1fJqYz5r7A5k+zFUaOm/deNR6FKL1Da+pqYmMjAxp5WHIm6EY7tvQ0EBISEiHJVJxBrJ1JJk4A9kVv1JBECgsLKSgoKBXvHBvxpUrVzh//jze3t7Y2dm1Ef7WPqw9Lej19fUcOHCAX3/9lddff50zZ86QkJBAYmIixcXFhIWFERMTw8SJExkyZEh/92G9HZAFs7/RkWCK5UorKyt2797N4sWLycrKMsh1CYLA7t27eemll1i/fj3jxo1r9zi1Wq3TyKJWq7GxsZGe2s3Nzamvryc9PR13d3dcB7nx8aE8Nh7Mxfja3CPo2uJFeNnpxHIB7Eov4fUfz2GmNOKt+4OYMFR35VZZ33xtZdoS+5VZVIum1ffcw9qYgqsaPO0H8PP/jAVg5Kr/0KjWkrE8FoVCwdwtqaTkVxMyyJqMoqs4W5lQWqvihVGWBNlqOj0KIcZXlZWVERoa2uWGqq5SXl5OVlaWTpm0tdtM6xzIjmYgu4LYlGOocOzWK/6KigoqKiowMjLC3d0dJyenbhuV34ympiaSk5M5ePAghw4d4uTJk0yYMIGZM2cSGxvbYyksMj2KbI13O9H66Xzq1Kk8++yzlJeXG2SPSKFQMG3aNEJCQnj00UeZMWMGzz77LEVFRVy9ehWFQtHGIMDLy6vd1YylpSWRkZGcPXuWqqoqnpkQxAhPW57/VzpGWoGXp/jxYIRbh9czLdSFYFdrln6TzsKvTzE70p1QN2tOFNToRH6ZGhsR5m7Ngru8iPCyZchAC1bvucC+cy2mBQOUv/8b0WgFTK7lXKrVamobWlyJ4nzUGKuMOFXeUg4OGerN6KGdtyhTKBQtKS/29pw8eVIy9TYUTk5OWFpacvr0aXJyclAqlTpuM63t2HoaS0tLIiIiuHjxIikpKV1KIOmI1itj0YdVXPF7e3sTGhpKeXk52dnZ2NnZ9bhYNjQ0cPz4cRITE0lISKCqqorIyEiio6N56qmnqKmp4amnnqKoqAgfH58ePbeMYZFXmLcQHa0wi4uLcXFxQaFQcOzYMeLi4sjLyzPYk6ogCFy8eJH9+/ezfv16rl69irOzM4sXL2bSpEldykoUOwtDQkKo05rwl28ySL1UzcORbiz741Apruv668guryc5r4pjuVX8J6tcMla3MDWSAqMjvGwZ5maDqdKozZ9/6bsz7DxdglIB66d7ER3iycg1iZgawyujzTl3RcO/s1TUq3//uluYGjHQyozvnx7V5j07i5h1KQ6+99b+3o1mILVaLXV1dYSEhBg8dUJMIPHy8mLQoEFd+v525A50o9QVaFn5nTlzBjMzM/z8/Lq8J19fX8+xY8c4ePAghw8fpq6ujqioKGkPsr3PpVarSUxMJCamZ5NsZHoMuSTbn7iZM1B8fDwbN25EqVRibm7eYWm0N1iyZAk5OTlMmDCBu+66i8zMTOLj4/nkk0+6tZcqZmx6e3vj5OzCht9y+PxwPsGDrHg3LhRXGzPOFNdKhu2p+dVUNbT8vThZmRLhZYuZ0ohfMsuwMDVmzQPB3OXbsV3a/x3PZ8VP2ZgagUoLQfaQeZ1trLECNAK8ds1Y3XegRRs7v+7QOpQ7ODi4R4Tr+pK4RqOR3Gaun4Hsy9gutVrNuXPn0Gg0BAUF3bRjWBAEHVMHMZZMH1OH9t6rsyMgtbW1HD16lEOHDnHkyBEaGxsZNWqU1MXq7NLenVIAACAASURBVOwsl1j7P7JgyvQup0+fZv78+Tz77LPMnj27yzcNtVpNZmYmJiYm+Pv7858Llbz8/RmaNVq0WmjWtKwgvRzMpbnNCC9bvOx/97q9WF7Hkh0ZXCitY+EEb/4cMxhjI4VOua6kvJKThdXsuySQVqqW5jVFzJQKVkwLJMLLlnlb0yivbebUq7Hd+0u6CWIna1eEq7s5kK2js4KDgw3uLyr6svr7++t0ELfnenQjs4quIo6A2Nra4u3tLYm2KM5HjhwhISGBw4cPo9FoGD16NBMnTiQ6OhpHR8c7RiD37NnD4sWL0Wg0Ugh9a5qampg3bx4pKSk4Ojqyffv2/lp2lgVTpveprq7miSeewN7enjVr1nTZyUVsxy8qKiI0NJTKZgXP/PMUF8rqifFz5LV7/Bhk1/G+V4NKw5s/neffJ4oJcx3A3CBT8isbyKk15kK1QFZFE9e0FwC/gRY8E+1Ddnk9H/4nFyPgnWme/HGkL9HrE6lt0pD2cu+X0MROVlG4brTi0mcGsiuIpt7XC5chaGxsJCMjAxMTE6ysrNq1z+utBinRQ3nJkiUsWLCA/Px8jhw5AsC4ceOIjY1lwoQJvZpFeSuj0Wjw9/dn7969eHh4EBUVxT//+U+Cg4OlYz766CNOnTrFxx9/zLZt2/j222/Zvn17H151l5EF83bm0qVLzJs3j5KSEhQKBU899RSLFy/WOUYQBBYvXszu3buxsLBgy5YtjBw5ssevRavV8t5777Fjxw42b96Ml5dXl99LtFgbMmQIdg5OrN17ga+PFxLuYcM7s0IYdF3HrFarlUyvLxZVkF7SSGIxZJSppC+raNourk4zi6+y4bccnhjnyV/uHkp1g4qxbydgYqRAIwg8FGzJruwmNFqB43+7cV5oTyMKV2BgIPb29m1mO/WdgewK4uiLlZUVQ4cO7dUu0vZsAY2MjGhubiYoKKhXRVsQBCorK0lMTOTQoUMkJSVhaWlJVlYW//Vf/8XatWtxcHC4IwXyeo4cOcKKFSv4+eefAVi9ejUAL730knTMlClTWLFiBWPHjkWtVuPq6kpZWVl//PuTu2RvZ5RKJe+88w4jR47k6tWrREREMHnyZJ2nv59++omsrCyysrJISkrimWeeISkpqcevxcjIiKVLlxIZGcmDDz7IypUrmTx5cpf+0dja2hIREUF6ejpVVVW8PGUoEV52vPbDWWZ9mszqGQGEOCiorKzk/OVKMsubya1Tcu6Kmss1LXub5ibGhHvYkHelgcp6FY+N9eR/YodgbNRyPelFNQBYDWj5+qs0LdLq52KJt4MF/8woBcBmgOGG7QVBwNLSEldXV06dOtVy/mv7j25ubr3u9mJmZsaIESPIz88nOTm5R+PKWu+tVlZW6tgCenh4SLaAtbW1ZGZmUltb22PJK4IgUF5eLiV5JCcnY2pqyvjx45k2bRqrVq3C2tqa5uZm3njjDZYuXcrWrVu7fd7bgcLCQjw9PaXfe3h4tLl/tD5GqVRia2tLRUWFwR2eDIUsmP2UQYMGSWHT1tbWBAUFUVhYqCOY33//PfPmzUOhUDBmzBiqqqooKirqtZDq6OhofvnlFx599FGSkpJ46aWXulQmNDExITw8nNzcXJKTkxnm5saaux1Zc6icZ7el42WrpKZZoLKhxdjAzhwivGyZO6ZlbzPQ1QqlkRH1zRr+vvs8nybkc7KghrUzgxloZUb9Nes7G7OW0mezuuX39U0aFAjYDFBS06hGiZaCggLc3d17/Im5oxnI8PBwysrKqK6uxtXVtVcMy9tDoVDg7e2Nvb09p0+fxsPDo0ufXdxbFcvHcPNxIwArKysiIyPJzs4mNTWVkJCQTn92QRAoKSmRRjyOHz+OlZUV48ePZ+bMmbz99tvtWgWamZmxatUq6urqOnU+mTsLWTBvA3Jzc0lLS2P06NE6P2/vCbGwsLDXBBPA1dWVn3/+meXLlzNr1iw2bdrUqeSM663YAC5cuMBgb2++eXoMb+3N4d8ninC0NOEvf/Amxt8JX6f2m0AsTI1ZfX8QUT52/O/u88z6NJm3Hwim9pqDUNqlKg5fvMKx3JaGmdwrDdQ1a7jL1wHfgRZM8nOkprKAysrKLkV2taa9RhZxBtLX17dNI4utrS1XrlwhLS3N4OkjNjY2REVFce7cOcnMvKNOVtGoXNxbhd+Nyn18fDrlm2tkZISfn5/02W8WliwIAsXFxRw8eJDExERSUlKwtbUlOjqahx56iHfffbdN5FhH9GYIeH/D3d2dS5cuSb8XHx7bO8bDw0OqJBh6H9yQyILZz6mtrWXWrFm89957BrceuxFKpZJVq1axc+dO7r33XjZs2MCoUaPaHCeGJIsCWVtbK1mxtS5DihmbWq2Wv98bQKS3LSt3nWdrUgHD3G0YOrDjm9y0UGeMgLd/zeaxL09ImxU/ppfiaT+ACC9bDmRVED3UgY2zw3TFd1AwRUVFJCcnd8rerfUMpBgoLDayBAYG6hXf5eDgQEREBJmZmVRUVODv728wWz1jY2OCg4MpLS0lOTmZgIAAHBxaxnXaMyq3t7fHyckJX1/fHslidHBwkAwuzp49S2hoKI6OjlJzmCiQJ06cwNHRkejoaObMmUN8fLzBVuS3CjfrZN2yZQsvvviiJHaLFi1iwYIFN33fqKgosrKyyMnJwd3dnW3btvH111/rHHPfffexdetWxo4dy44dO5g0aVJ/3L/UG7nppx+jUqmYPn06U6ZMYenSpW1eX7hwIbGxscyePRuAgIAADhw40KsrzOvJzs7m0Ucf5aGHHmL+/PkcO3YMW1tbyb7M0tJSWo3caOAcrhkWZGdLGZt5Vc08/68M8q7U8z+xg3lyvLc0J1nXpOZEQQ3JeVWk5FdxqvCqNJpibWbM1Wsl2ZXTA4gb6UZSTiWPfXmCWSMG8fd7A9s9f11dnWRk3t74x/X7dBqNpsdyIAVB4NKlSxQXF/fo3qK+VFdXk5GRgULR4oQkGpX3RvPR9QiCwOeff867774rbTu4uLgQHR1NTEwMo0ePNvg4zK2EPp2sW7ZsITk5mfj4+E6//+7du3n++efRaDQ8/vjjvPLKK7z22mtERkZy33330djYyNy5c0lLS8PBwYFt27YxZMiQnvyIhkLukr2dEQSB+fPn4+DgwHvvvdfuMbt27SI+Pp7du3eTlJTEc889x7Fjxwx2jY2NjRw7dox9+/bx+eefo1AoGDZsGEuXLiU8PBxzc/NOP42KnqiBgYGYWljz+o/n2J1RSoSXLUMHWpJZdFXyjjVWKAgeZMVILzsivW2J8LTD1lzJA58c53xpHfYWJrwXF0J1o5rn/i+deaM9+NsUvxueW5xbVKlUDB06VHKb6coMZFcQTR6645KjD2J3rlgWNzU1xd7ensbGRq5evcqwYcM6VebsDGL4uNikI+6lDh8+nF9//ZW7776blStX3tEi2Rp9Olm7I5h3EHKX7O1MYmIiX375JcOGDSM8PByAVatWkZ+fD7S4A02dOpXdu3czdOhQLCws+OKLLwx6jX/6059wdHRkwoQJHD16lF9++YUPP/xQGj7vCk5OTlhZWXH69GkGDhzI2geCiPS2Y9WeLFLyqwl0seTJ8V5EeNkR7mGDpVnbr7i9RcuemoWpMY99eYIxg+0B2j1WRJyBVCgU1NTUcPToUZydnXF1dWXIkCE9Uoa8GdbW1kRGRkp7i93dVwVdo/LKykopoUTsYL0+eaW6uppTp071mGhrtVqysrIkgczMzMTb25uYmBiWLFnCiBEjpM+o0Wh455132Lp1K08++WS3znu7oE8nK8A333zDwYMH8ff3591339X5MzL6I68wb2EOHjxIdLTh5gANQVpaGo8//jjPP/88cXFxXb7hijdaMbbqTGk9f/kmk5KaJl6425e5o2/smvPI5hROFNTw059Hs+7XbMmM/cW7fXlsXMsMaXszkOLq0dbWVtpXdXV17XLWZHcoKioiLy+PoKCgdjMXb4S4bywKZOtoMnt7e70SSjprbdcarVbL2bNnpSzIc+fOMXToUMmHdfjw4QbNzuzv7Nixgz179rBp0yYAvvzyS5KSknRWkxUVFVhZWWFmZsYnn3zC9u3b2b9/f19d8q2KXJLtrwiCQFlZGXfffTdTp07lrbfe6pH31cfs4MCBA8yYMYPBgwcDMHPmTF577bUeOb9IZWUljz32GG5ubrz55pvSHF5XKCkpIScnh+DgYAQTc17ZeZb958q5O9CJ/70vEJsBv9/MBUHgcnUj87emcbm6CU/7AVyqbATASAHrpnrgYdaks8oSRaS9ZhsxGPtmDj29hRiV5uzsfMPIqNbjK5WVldTX1+tlVK4PorWdaLTQHhqNhszMTA4dOkRiYiJZWVkEBARIAhkaGnpHCOTjjz/Ojz/+iLOzc7vhCl01GdGnJNsajUaDg4OD1M0sIyELZn9EEATpBpaRkcGECROIjIxk69at3W7WKSoqoqioSMfs4LvvvtNpEDhw4ADr1q3jxx9/7Na5boZWq+Xtt9/mhx9+YPPmzXh4eHT5vUThGDRoEO7u7vy/pALW77vIIFszXpw8lCt1KpLzq0jOq6K4pkn6c6M9zBlqC4MtNQS4WDLQ0aFLIiKKdmdXez2BVqvlwoULUvqIiYlJG6NycXylp3xYW9PQ0EB6ejpHjx5l4cKFGBsbc/r0aUkgc3JyCAwMlMKSg4KCDBqgfatw8OBBrKysmDdvXruCuXv3bj744AOp32Dx4sV6mYyo1Wr8/f3Zt28f7u7uREVF8fXXX+sEIrSevf72229Zs2YNR48e7bkPd3sg72H2N1qL5TfffMOpU6dYtGgRTk5O3HPPPezduxcnJ6cu3/D0MTswFEZGRixbtoxRo0YRFxfHqlWrmDRpUpfey8LCgoiICM6dO0dGRgZzooIIc7fhL99ksvhf6QgCOJgbE+I8gCleRuzMaqCqCf7+R48eEREXFxdsbGyk1V5PudToi7OzM4WFhSQkJGBqaip1Hfv7+3epsaozmJiYIAgCR48e5cMPP8Tc3JyRI0cSExPD2rVrDToKcysTHR1Nbm7uDV/vqsmIUqkkPj6eKVOmSJ2sISEhOp2sGzZsYOfOnSiVShwcHNiyZUvPfrg7CHmFeQvyxRdfkJqaSlhYGHPnzmXAgAHk5ubi4+ODVqvtkRtQbm4u0dHRpKen68wWHjhwgFmzZuHh4YGbmxvr1q3rVnyXPly+fJlHHnmE6OhoXnzxxW6V6C5fvkx+fj6enp6UVtezYl8RWZUaxnuasWySF27Ojkz7pHeSSK7fV+2NEq3ondvefKelpSXZ2dlYW1vj6+vbK0KlUqlIS0uT9iCLiooYPnw40dHR2NnZsXr1apYuXcqcOXN6/Nz9nY7ybqdPn87f/vY3xo8fD8Af/vAH1qxZQ2RkpKEv805FXmH2R+rq6jh27Bj3338/d999N8bGxlRUVFBeXo6Pjw9GRkY6K9Gu0JHZwciRI8nLy8PKyordu3dz//33k5WV1d2P1SFubm7s3buXl156iQcffJDPPvtMGpLXh/a8SrOysnBxcWHbk6PYeqyY+P/ksHhXIe/G2aPSaCVf2Z7EyMiIgIAASktLSUlJ0TtvsSNaG5VXVlaiVqul8RU3N7c2850jRowgNzeXlJQUQkNDu5300dTUREpKCgkJCSQmJlJaWkp4eDgxMTFs3LiRwYMH63wXp0yZwpo1a2hubpZHP2RuO+QV5i3Ik08+iZOTk7SBr1Kp2LBhA/n5+d2K0BLfqyOzg+vx8fEhOTnZIGbKgiDw73//m5UrVxIfH09ERES7x4lWbK1nIO3s7KRfpqamqNVqzpw5g7GxMQEBARzPr+HFf2dS36xGrRUwMTYiuReTSMS9PScnJ3x8fPR+wFGr1ToZl62Nyu3t7fUWoaqqKs6ePcvgwYM7tJa7nsbGRo4fPy55sV65coWIiAipScfQ5ebbiY5WmLeCycgdjtz0058pLS3F2dlZ52cff/wx/v7+Xd7r08fsoLi4GBcXFxQKBceOHSMuLo68vDyD3iTPnz/PnDlzmDNnDo8//jiXLl2ivr4ehUKhY8UmCuSNZhGvz9is0xjzwr8zOZ5XhZ25ksMvTujVz6HVasnOzqa2tpaQkJB2xa6jEGh7e/tulXVVKhVnzpxBqVQSEBDQbqm7oaGBY8eOSU06NTU1REVFER0dzcSJE3Fzc7tjBPJmnazd7SDvSDD72mRERhbMfknrPcrs7GyKioqor6/n+PHjNDY2EhkZyYwZM7r03gkJCUyYMIFhw4ZJ57je7CA+Pp6NGzeiVCoxNzdn/fr1jBs3rmc+nB4IgkBeXh579+5l7dq1NDY24urqyvPPP09MTEyXrNhqamrIzMxk8ODBOA4cyBeHL+FuN4CpofqvvLpDWVkZFy5cIDAwEEtLSx2B7KkQ6BshCAKFhYV89tlnTJs2jZCQEJKSkjh48CBHjhyhvr6eqKgoYmNjiY2NlR6W7kRu1snanQ7y2bNnc+DAAcrLy3FxceGNN95ApWqJo3v66acRBIFFixaxZ88eyWRE3r80KLJg9nd2797NsmXLeOSRR3j44YdxcHAw+NiCoZk/fz5XrlwhOjqaCRMmkJqayubNm9m0aRP+/v5dfl+VSkVGRgbm5ub4+fkZrHOzqamJyspKysvLKS0txcTEhEGDBkkC2ds+rLW1tRw5coSff/6ZH374AWNjY6ZPn05sbCwxMTEMHDjwjhXI9uhoFWiokSuZPkEWzNuBpKQkdu7cycMPP8ywYcP6+nL6hOTkZBYsWMBf//pXZsyY0eUbvLh6LSsrY9iwYb2SatHY2Kjjw2piYiKtIK2trcnLy6OmpoaQkJBuGTa0hyAI1NTUcPjwYRISEjhy5AiCIDBmzBhiY2OJiorizTffpLS0lE2bNt3QbOBO5maCaegOchmDIQtmf6Z1J2xtbS0qlapPbnCNjY1ER0fT1NSEWq0mLi6ON954Q+eYpqYm5s2bR0pKCo6Ojmzfvh0fH58evY6Kigrmz5+Pr68vK1eu7NbeXmVlJWfPnsXPz69bzUyCILQRSDMzM2n/0cbGpt2VbEVFBefPn9eJzOrq+auqqqQGnSNHjqBUKhk7diwTJ05k/Pjx2NnZtXnA+O6774iKimqTbSjTsWDW1NRgZGQkdZAvXry41zvIZQyGLJi3A90dIemJ89fV1WFlZYVKpWL8+PG8//77jBkzRjrmo48+4tSpU3z88cds27aNb7/9lu3bt/f4tWg0GlavXs3evXvZvHlztzoIm5ubpRlUX19fvf6OBUGgvr5e2n/U10KvPRobG8nIyMDOzo4hQ4boff6KigoSExM5dOgQx48fx8TEhPHjxxMbG8tdd92FjY2NXGLtBh0J5vUYsoNcpteR5zBvB/r65qdQKLCysgJa9gFVKlWba/r+++9ZsWIFAHFxcSxatKhXhN7Y2JhXX32V0aNH88ADD7B27doum9ObmpoyYsQILl68SGpqKqGhoW1KpO0ZlYs+rN7e3t3yYR0wYAAjR4686flLS0t1BNLCwoIJEyYwY8YM1qxZg7W1dZfO3x/Rxwu5q56s+nB9B7lWq8XR0bFH3lumfyALpsxN0Wg0REREcOHCBf785z8zevRonddbRwwplUpsbW2pqKjotSfvyZMns3v3bh555BGOHz/OkiVLutTEo1Ao8PX1paKigtTUVAICAjAxMdExKre0tMTe3p4hQ4ZgaWnZow8B4vmvXLnCihUrGDVqFGPHjuXgwYMkJiaSkpKCtbU1EyZM4L//+79Zv369wcOjbyWUSiXvvPOOjhfy5MmTdawdf/rpJ7KyssjKyiIpKYlnnnlGL09W0O1k9fDwaNPJumPHDp0O8m3btvX5A62MYZFLsjJ6U1VVxQMPPMAHH3xAaGio9PPQ0FD27NkjGaj7+vqSlJTU66Wq5uZmXnzxRS5evMjHH3/c6T1erVYrGZVXVFRQXV2Nubk5np6evWJUfj2CIHD58mUOHjwo/RIEgblz5zJp0iTGjBnTbaee25kZM2awaNEiJk+eLP1MNgCQ6SJ6/UOXXZFl9MbOzo6JEyeyZ88enZ+7u7tz6dIl4HebOkOUqkxNTXnvvfd49NFHmTZtGidPnuzweK1WS1VVFTk5OaSmppKUlERBQQGmpqYEBwcTExODo6MjZWVlmJqa9rhYil26X331FU8//TTjxo3jmWeeobCwkCeeeIKMjAwWLFhAYmIigYGBslh2QG5uLmlpaR1WO6AlULmwsNDQlydzmyKXZGU6pKysTBqNaGhoYO/evSxbtkznmPvuu4+tW7cyduxYduzYwaRJkwxWqlIoFDz88MMMHz6cuXPnsmDBAubOnYtCoUCtVlNTUyMZBahUKmxsbLC3tyc4OLjdsRJ/f3/JC7a7cV1arZbc3FzJqPz06dO4ubkRHR3NwoULiYqKauP+8+qrrxIdHX1HZER2lY68kGVkehO5JCvTIadOnWL+/PloNBq0Wi0PPvggr732mk58UGNjI3PnziUtLQ0HBwe2bdvGkCFDDH6tJSUlzJ49m8bGRurq6vD19eWVV16Rulg7M/coZmy6urri6emp1wOAmE2ZkJBAQkICGRkZeHl5ST6sI0eONHjI9O3GzbyQ5ZKsTBeRx0pk7gx27drFW2+9RXNzM2PGjKGxsZHTp0/z6aefdku4NRoN58+fR6VSERwc3Ma2TqvVcu7cOUkgz5w5w5AhQySBDA8P73Gru1sdfTpZu+rJqo8XsuzJKtNFZMGUuTMoKSnB1NRUp+knKSmJp556ildeeYVp06Z1q0RcVFTEyy+/zNNPP42VlZXUxXr+/Hn8/Pwko/Jhw4bd8aXUoqIiioqKdDpZv/vuO51O1q5azOnjhSx7ssp0EVkwZe5sysrKmDt3LqGhoSxfvrzT5VCNRkN6erqU5HHkyBG8vLyYP38+sbGxhISEGMyTtr/SXier7Mkqcwsid8nKGJ7GxkZGjRrF8OHDCQkJ4fXXX29zzJYtWxg4cCDh4eGEh4ezadOmXrmWgQMHsmvXLiwtLXnggQcoLi7u8Hi1Wk1qairvv/8+Dz74IOPGjeO9997DysqK1atXk52dTXBwMCdOnDCogXt/5UadrABHjhxh+PDh3HPPPWRkZPTB1cnIdB55hSnTo+hjpbdlyxaSk5OJj4832HX99NNPLFu2jHfeeYe77roLaGkgOXHihLQHWVBQQFhYmLQH2Z4oCoLADz/8wLRp0+748mtH1NbWEhMTwyuvvMLMmTN1XpM9WWVuQWRrPBnDo4+VXl9wzz33EBwczOzZs7G1tUWj0VBcXMzw4cOJiYkhPj5eL09XhULBfffdZ6Cr7p+oVCpmzZrFo48+2kYsAZ1RkKlTp/Lss89SXl4ue7LK3PLINSWZHkej0RAeHo6zszOTJ09utyT3zTffEBYWRlxcnGR60Nt4e3uzf/9+wsLC+PTTTzl58iRffvklCxYs0NuAvb+jT8m8qamJhx56iKFDhzJ69Ghyc3P1fn9BEHjiiScICgpqd+wDWjxZxcqWoTxZ09PTqaurk65RRqYryCVZmV7jRlZ6FRUVWFlZYWZmxieffML27dvZv39/H17pnUNvp8/o08kaHx+v48m6fv16xo0b16Of8/z58/zwww/89ttv5ObmYm5uzqeffsqIESOAFltFU1PTPk8DkrllkLtkZfqelStXYmFhwQsvvNDu6xqNBgcHB6qrqw18ZTL19fWMHz+ejRs36lQBpkyZwooVKxg7dixqtRpXV1fKysr6hbCIArhhwwZOnz5NSUkJo0aN4tVXXwUgMTGR9evXExwczN///ne0Wq3cvCUDcpesTF9QVlZGVVUVgGSlFxgYqHNMUVGR9N87d+4kKCjIoNd4p3OzkvmN0mf6A6KoP/fcc3z22WfMmjULCwsLoKULOjg4mLfeektqMpLFUqYzyE0/Mj1KUVFRGyu96dOn61jpbdiwgZ07d6JUKnFwcGDLli19fdl3FMbGxpw4cUIqmaenp+uUzG8XVCoV+fn5ki2eUqmUbBItLCwoLCzE3d29j69Spj8hl2RlZO5g2iuZ9+eSrIhYmv3rX//KsGHDuP/++7G2tpZKsKtXr8bIyIiFCxdiZ2fX15cr0/fIJVkZmf5Gbxs/6FMyF9NnAIOnz/QU4kJg2rRpbN26lYULF0rzn2lpafzyyy+kpqaSnZ3dx1cq05+QV5gytwwajYbIyEjc3d3b2KY1NTUxb948UlJScHR0ZPv27fj4+PTNhfYivW380J/SZ3oCrVZLcXExbm5u0s8aGxtRKpV3nDG+TIfIxgUy/Yv333+foKAgampq2rz2+eefY29vz4ULF9i2bRvLli3Te9ShP9Hbxg9hYWGkpaW1+fnKlSul/x4wYAD/+te/euycfYmRkZGOWAJSDqpWq5WOkZHRB/mbInNLUFBQwK5du1iwYEG7r3///ffMnz8fgLi4OPbt23fbDqDfqsYPtxtGRkayWMp0CvnbInNL8Pzzz7N27dob3sD686hDZxG7WAsKCjh27Bjp6ek6r997773k5uZy6tQpJk+eLD1IyMjI9C6yYMr0OT/++CPOzs5ERET09aXcUtjZ2TFx4kT27Nmj83NHR0fMzMwAWLBgASkpKX1xeTIydxyyYMr0OYmJiezcuRMfHx8efvhh9u/fz5w5c3SOcXd3l0qParWa6urqXvcfvREajYYRI0Ywffr0Nq91x4cVZOMHGZlbGVkwZfqc1atXU1BQQG5uLtu2bWPSpEl89dVXOsfcSqMOYnNSe7RuTlqyZAnLli3r1HsXFRUxceJEwsLCiIqKYvLkyZLxw86dOwHYsGEDISEhDB8+nA0bNsjGDzIyhkIQhM78kpHpVX777Tdh2rRpgiAIwvLly4Xvv/9eEARBaGhoEOLi4gRfX18hKipKyM7O7pPru3TpkjBp0iRh37590nW25o9/Fapp2gAAAQdJREFU/KNw+PBhQRAEQaVSCY6OjoJWqzX0ZcrIyHQOvTRQnsOUkekEcXFxvPTSS1y9epV169a1mRcNDQ1lz549eHh4AODr60tSUpKc9Sgjc2sjO/3IyPQkcnOSjMydjSyYMjJ60t+ak2RkZHoWWTBlZPSkvzUnycjI9CyyNZ6MTDdp7cP6xBNPMHfuXIYOHSr5sMrIyNwedLbpR0ZGRkZG5o5ELsnKyMjIyMjogSyYMjIyMjIyeiALpoyMjIyMjB7IgikjIyMjI6MHsmDKyMjIyMjogSyYMjIyMjIyeiALpoyMjIyMjB7IgikjIyMjI6MHsmDKyMjIyMjogSyYMjIyMjIyevD/AfktuNNvz87AAAAAAElFTkSuQmCC\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "import numpy as np\n", "from mpl_toolkits.mplot3d import axes3d\n", @@ -338,11 +407,11 @@ ] }, { - "cell_type": "markdown", + "cell_type": "code", + "execution_count": null, "metadata": {}, - "source": [ - "![Equal-time two-particle Green's function](figure_g3pp_tau.png)" - ] + "outputs": [], + "source": [] } ], "metadata": { @@ -361,7 +430,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", - "version": "2.7.13" + "version": "2.7.15" } }, "nbformat": 4, diff --git a/doc/figure_densdens_tau.png b/doc/figure_densdens_tau.png deleted file mode 100644 index 9b66061..0000000 Binary files a/doc/figure_densdens_tau.png and /dev/null differ diff --git a/doc/figure_g3pp_tau.png b/doc/figure_g3pp_tau.png deleted file mode 100644 index 6d324d4..0000000 Binary files a/doc/figure_g3pp_tau.png and /dev/null differ diff --git a/doc/figure_g_iwn.png b/doc/figure_g_iwn.png deleted file mode 100644 index 3947684..0000000 Binary files a/doc/figure_g_iwn.png and /dev/null differ diff --git a/doc/figure_g_tau.png b/doc/figure_g_tau.png deleted file mode 100644 index 6a8741e..0000000 Binary files a/doc/figure_g_tau.png and /dev/null differ diff --git a/pyed/CubeTetras.py b/pyed/CubeTetras.py index 36c6bcb..b80796d 100644 --- a/pyed/CubeTetras.py +++ b/pyed/CubeTetras.py @@ -1,5 +1,5 @@ -""" +""" Helper routines for the equal time imaginary time cube and its sub tetrahedrons. @@ -11,23 +11,29 @@ import itertools import numpy as np +# ---------------------------------------------------------------------- +def Idxs(integer_index_list): + from pytriqs.gf import Idx + return tuple( Idx(i) for i in integer_index_list ) + # ---------------------------------------------------------------------- def zero_outer_planes_and_equal_times(g4_tau): + from pytriqs.gf import Idx beta = g4_tau.mesh.components[0].beta - + for idxs, (t1, t2, t3) in enumerate_tau3(g4_tau): if t1 == t2 or t2 == t3 or t1 == t3 or \ t1 == 0 or t1 == beta or \ t2 == 0 or t2 == beta or \ t3 == 0 or t3 == beta: - g4_tau[list(idxs)][:] = 0.0 + g4_tau[Idxs(idxs)] = 0.0 # ---------------------------------------------------------------------- def enumerate_tau3(g4_tau, make_real=True, beta=None): from pytriqs.gf import MeshImTime, MeshProduct - + assert( type(g4_tau.mesh) == MeshProduct ) for mesh in g4_tau.mesh.components: @@ -40,13 +46,13 @@ def enumerate_tau3(g4_tau, make_real=True, beta=None): yield (i1, i2, i3), (t1.real, t2.real, t3.real) else: yield (i1, i2, i3), (t1, t2, t3) - + # ---------------------------------------------------------------------- class CubeTetrasBase(object): """ Base class with definition of the equal time tetrahedrons in three fermionic imaginary times. """ - + def get_tetra_list(self): tetra_list = [ @@ -57,17 +63,17 @@ def get_tetra_list(self): (lambda x,y,z : x >= z and z >= y, [0, 2, 1], -1), (lambda x,y,z : z >= x and x >= y, [2, 0, 1], +1), ] - + return tetra_list # ---------------------------------------------------------------------- class CubeTetras(CubeTetrasBase): """ Helper class for two-particle Green's function. - + Looping over all tetrahedrons in the imaginary time cube. \tau_1, \tau_2, \tau_3 \in [0, \beta) """ - + # ------------------------------------------------------------------ def __init__(self, tau): @@ -79,21 +85,21 @@ def __init__(self, tau): def __iter__(self): for tidx in xrange(6): - + func, perm, perm_sign = self.tetra_list[tidx] - + index = [] for n1, n2, n3 in itertools.product( range(self.ntau), repeat=3): if func(n1, n2, n3): index.append((n1, n2, n3)) index = np.array(index).T - + i1, i2, i3 = index t1, t2, t3 = self.tau[i1], self.tau[i2], self.tau[i3] taus = np.vstack([t1, t2, t3]) - + yield list(index), taus, perm, perm_sign # ---------------------------------------------------------------------- @@ -101,16 +107,16 @@ class CubeTetrasMesh(CubeTetrasBase): """ Helper class for Triqs two-particle Green's function in imaginary time. - + Looping over all tetrahedrons in the imaginary time cube. \tau_1, \tau_2, \tau_3 \in [0, \beta) """ - + # ------------------------------------------------------------------ def __init__(self, g4_tau): self.g4_tau = g4_tau self.tetra_list = self.get_tetra_list() - + # ------------------------------------------------------------------ def __iter__(self): @@ -120,7 +126,7 @@ def __iter__(self): tetra_tau = [ [] for n in xrange(6) ] for idxs, taus in enumerate_tau3(self.g4_tau): - + for tidx, tetra in enumerate(self.tetra_list): func, perm, perm_sign = tetra @@ -133,5 +139,5 @@ def __iter__(self): func, perm, perm_sign = self.tetra_list[tidx] yield tetra_idx[tidx], tetra_tau[tidx], perm, perm_sign - + # ---------------------------------------------------------------------- diff --git a/pyed/SparseExactDiagonalization.py b/pyed/SparseExactDiagonalization.py index 6a5b4f0..ad14be4 100644 --- a/pyed/SparseExactDiagonalization.py +++ b/pyed/SparseExactDiagonalization.py @@ -9,6 +9,7 @@ import time import itertools +import progressbar import numpy as np from scipy.linalg import expm @@ -16,7 +17,9 @@ from scipy.sparse.linalg import eigs as eigs_sparse from scipy.sparse.linalg import eigsh as eigsh_sparse - +from scipy.sparse import csr_matrix +from scipy.sparse import diags +from tqdm import tqdm # ---------------------------------------------------------------------- from CubeTetras import CubeTetras @@ -24,50 +27,35 @@ # ---------------------------------------------------------------------- class SparseExactDiagonalization(object): - """ Exact diagonalization and one- and two- particle Green's + """ Exact diagonalization and one- and two- particle Green's function calculator. """ # ------------------------------------------------------------------ - def __init__(self, H, beta, - nstates=None, hermitian=True, - v0=None, tol=0): - - self.v0 = v0 - self.tol = tol - - self.nstates = nstates - self.hermitian = hermitian - + def __init__(self, H,blocks, beta): self.H = H + self.blocks=blocks self.beta = beta self._diagonalize_hamiltonian() self._calculate_partition_function() - self._calculate_density_matrix() - + # self._calculate_density_matrix() + # ------------------------------------------------------------------ def _diagonalize_hamiltonian(self): - - if self.nstates is None: - if self.hermitian: - self.E, self.U = np.linalg.eigh(self.H.todense()) - else: - self.E, self.U = np.linalg.eig(self.H.todense()) - else: - if self.hermitian: - t = time.time() - self.E, self.U = eigsh_sparse( - self.H, k=self.nstates, which='SA', - v0=self.v0, tol=self.tol, ncv=self.nstates*8+1) - print 'ED:', time.time() - t, ' s' - else: - self.E, self.U = eigs_sparse( - self.H, k=self.nstates, which='SR', - v0=self.v0, tol=self.tol) - - self.U = np.mat(self.U) + self.U=csr_matrix(self.H.shape,dtype=np.float) + self.E=np.zeros(self.H.shape[0]) + print 'Hamiltonian diagonalization:' + # bar = progressbar.ProgressBar() + for i in tqdm(range(len(self.blocks))): + block=self.blocks[i] + X,Y=np.meshgrid(block,block) + E,U=np.linalg.eigh(self.H[X,Y].todense()) + self.E[block]=E + self.U[Y,X]=U + del X,Y + self.E=np.array(self.E) self.E0 = np.min(self.E) - self.E = self.E - self.E0 + self.E = self.E-self.E0 # ------------------------------------------------------------------ def _calculate_partition_function(self): @@ -78,67 +66,49 @@ def _calculate_partition_function(self): # ------------------------------------------------------------------ def _calculate_density_matrix(self): - exp_bE = np.exp(-self.beta * self.E) / self.Z - self.rho = np.einsum('ij,j,jk->ik', self.U, exp_bE, self.U.H) + exp_bE = (np.exp(-self.beta * self.E) / self.Z)[:,None] + self.rho=self.U.getH().multiply(exp_bE)*self.U # ------------------------------------------------------------------ def _operators_to_eigenbasis(self, op_vec): dop_vec = [] for op in op_vec: - dop = np.mat(self.U).H * op.todense() * np.mat(self.U) + dop = self.U.getH() * op * self.U dop_vec.append(dop) return dop_vec - - # ------------------------------------------------------------------ - def get_expectation_value_sparse(self, operator): - - exp_val = 0.0 - for idx in xrange(self.E.size): - vec = self.U[:, idx] - dot_prod = np.dot(vec.H, operator * vec)[0,0] # - exp_val += np.exp(-self.beta * self.E[idx]) * dot_prod - - exp_val /= self.Z - - return exp_val - - # ------------------------------------------------------------------ - def get_expectation_value_dense(self, operator): - - if not hasattr(self, 'rho'): self._calculate_density_matrix() - return np.sum(np.diag(operator * self.rho)) # ------------------------------------------------------------------ def get_expectation_value(self, operator): - - if self.nstates is None: - return self.get_expectation_value_dense(operator) - else: - return self.get_expectation_value_sparse(operator) - + op=self._operators_to_eigenbasis([operator])[0] + return (op.diagonal()*np.exp(-self.beta * self.E)).sum()/self.Z # ------------------------------------------------------------------ def get_free_energy(self): - r""" Free energy using ground state energy shift + r""" U(1) energy using ground state energy shift Z = \sum_n e^{-\beta E_n} \Omega = -1/\beta \ln Z Z = e^{-\beta E_0} x \sum_n e^{-\beta (E_n - E_0)} = e^{-beta E_0} Z' \Omega = -1/\beta ( \ln Z' - \beta E_0 ) """ - + Omega = -1./self.beta * (np.log(self.Z) - self.beta * self.E0) return Omega - + # ------------------------------------------------------------------ def get_partition_function(self): return self.Z # ------------------------------------------------------------------ def get_density_matrix(self): - return self.rho + try: + return self.rho + except: + self._calculate_density_matrix() + return self.rho + # ------------------------------------------------------------------ def get_eigen_values(self): @@ -151,13 +121,13 @@ def get_eigen_vectors(self): # ------------------------------------------------------------------ def get_ground_state_energy(self): return self.E0 - + # ------------------------------------------------------------------ def get_g2_dissconnected_tau_tetra(self, tau, tau_g, g): g = np.squeeze(g) # fix for now throwing orb idx g = g.real - + N = len(tau) G4 = np.zeros((N, N, N), dtype=np.complex) @@ -181,7 +151,7 @@ def get_g2_dissconnected_tau(self, tau, tau_g, g): g = np.squeeze(g) # fix for now throwing orb idx g = g.real - + N = len(tau) G4 = np.zeros((N, N, N), dtype=np.complex) @@ -195,12 +165,12 @@ def gint(t_in): t1, t2, t3 = np.meshgrid(tau, tau, tau, indexing='ij') G4 = gint(t1-t2)*gint(t3) - gint(t1)*gint(t3-t2) - + return G4 - + # ------------------------------------------------------------------ def get_g2_tau(self, tau, ops): - + N = len(tau) G4 = np.zeros((N, N, N), dtype=np.complex) ops = np.array(ops) @@ -209,16 +179,16 @@ def get_g2_tau(self, tau, ops): idx, taus, perm, perm_sign = tetra print 'Tetra:', tidx - + # do not permute the last operator ops_perm = ops[perm + [3]] taus_perm = taus[perm] # permute the times - + G4[idx] = self.get_timeordered_three_tau_greens_function( taus_perm, ops_perm) * perm_sign - + return G4 - + # ------------------------------------------------------------------ def get_timeordered_two_tau_greens_function(self, taus, ops): @@ -227,8 +197,8 @@ def get_timeordered_two_tau_greens_function(self, taus, ops): ops = [O1, O2, O3] Returns: - G^{(4)}(t1, t2) = -1/Z < O1(t1) O2(t2) O3(0) > - + G^{(4)}(t1, t2) = -1/Z < O1(t1) O2(t2) O3(0) > + """ Nop = 3 @@ -247,18 +217,17 @@ def get_timeordered_two_tau_greens_function(self, taus, ops): assert( (t1 >= t2).all() ) assert( (t2 >= 0).all() ) - et_a = np.exp((-self.beta + t1)*E) - et_b = np.exp((t2-t1)*E) - et_c = np.exp((-t2)*E) dops = self._operators_to_eigenbasis(ops) op1, op2, op3 = dops - G = np.einsum('ta,tb,tc,ab,bc,ca->t', et_a, et_b, et_c, op1, op2, op3) - - G /= self.Z + for i in tqdm(range(len(G))): + et_a = np.exp((-self.beta + t1[i])*E).flatten()[:,None] + et_b = np.exp((t2[i]-t1[i])*E).flatten()[:,None] + et_c = np.exp((-t2[i])*E).flatten()[:,None] + G[i] = (op1.multiply(et_a)*op2.multiply(et_b)*op3.multiply(et_c)).diagonal().sum() + G /= self.Z return G - # ------------------------------------------------------------------ def get_timeordered_three_tau_greens_function(self, taus, ops): @@ -267,8 +236,8 @@ def get_timeordered_three_tau_greens_function(self, taus, ops): ops = [O1, O2, O3, O4] Returns: - G^{(4)}(t1, t2, t3) = -1/Z < O1(t1) O2(t2) O3(t3) O4(0) > - + G^{(4)}(t1, t2, t3) = -1/Z < O1(t1) O2(t2) O3(t3) O4(0) > + """ assert( taus.shape[0] == 3 ) @@ -287,27 +256,17 @@ def get_timeordered_three_tau_greens_function(self, taus, ops): assert( (t2 >= t3).all() ) assert( (t3 >= 0).all() ) - et_a = np.exp((-self.beta + t1)*E) - et_b = np.exp((t2-t1)*E) - et_c = np.exp((t3-t2)*E) - et_d = np.exp((-t3)*E) - dops = self._operators_to_eigenbasis(ops) op1, op2, op3, op4 = dops + for i in tqdm(range(len(G))): + et_a = np.exp((-self.beta + t1[i])*E).flatten()[:,None] + et_b = np.exp((t2[i]-t1[i])*E).flatten()[:,None] + et_c = np.exp((t3[i]-t2[i])*E).flatten()[:,None] + et_d = np.exp((-t3[i])*E).flatten()[:,None] + G[i]=(op1.multiply(et_a)*op2.multiply(et_b)*op3.multiply(et_c)*op4.multiply(et_d)).diagonal().sum() - if True: - q_tac = np.einsum('tb,ab,bc->tac', et_b, op1, op2) - q_tca = np.einsum('td,cd,da->tca', et_d, op3, op4) - G = np.einsum('ta,tc,tac,tca->t', et_a, et_c, q_tac, q_tca) - else: - # Not efficient... - G = np.einsum( - 'ta,tb,tc,td,ab,bc,cd,da->t', - et_a, et_b, et_c, et_d, op1, op2, op3, op4) - - G /= self.Z + G /= self.Z return G - # ------------------------------------------------------------------ def get_tau_greens_function_component(self, tau, op1, op2): @@ -317,55 +276,47 @@ def get_tau_greens_function_component(self, tau, op1, op2): """ G = np.zeros((len(tau)), dtype=np.complex) - op1_eig, op2_eig = self._operators_to_eigenbasis([op1, op2]) - - et_p = np.exp((-self.beta + tau[:,None])*self.E[None,:]) - et_m = np.exp(-tau[:,None]*self.E[None,:]) - - G = -np.einsum('tn,tm,nm,mn->t', et_p, et_m, op1_eig, op2_eig) - - G /= self.Z + # bar = progressbar.ProgressBar() + for i in tqdm(range(len(tau))): + et_p = np.exp((-self.beta + tau[i])*self.E)[:,None] + et_m = np.exp(- tau[i]*self.E)[:,None] + G[i] = - (op1_eig.multiply(et_p)*op2_eig.multiply(et_m)).diagonal().sum() + G /= self.Z return G # ------------------------------------------------------------------ def get_frequency_greens_function_component(self, iwn, op1, op2, xi): - + r""" Returns: G^{(2)}(i\omega_n) = -1/Z < O_1(i\omega_n) O_2(-i\omega_n) > """ - # -- Components of the Lehman expression - dE = - self.E[:, None] + self.E[None, :] - exp_bE = np.exp(-self.beta * self.E) - M = exp_bE[:, None] - xi * exp_bE[None, :] - - inv_freq = iwn[:, None, None] - dE[None, :, :] - nonzero_idx = np.nonzero(inv_freq) - # -- Only eval for non-zero values - freq = np.zeros_like(inv_freq) - freq[nonzero_idx] = inv_freq[nonzero_idx]**(-1) - op1_eig, op2_eig = self._operators_to_eigenbasis([op1, op2]) # -- Compute Lehman sum for all operator combinations G = np.zeros((len(iwn)), dtype=np.complex) - G = np.einsum('nm,mn,nm,znm->z', op1_eig, op2_eig, M, freq) + op=(op1_eig.getH().multiply(op2_eig)).tocoo() + M=(np.exp(-self.beta*self.E[op.row])-xi*np.exp(-self.beta*self.E[op.col]))*op.data + E=(self.E[op.row]-self.E[op.col]) + # bar = progressbar.ProgressBar() + for i in tqdm(range(len(iwn))): + G[i]=np.sum(M/(iwn[i]-E)) G /= self.Z - return G - + return G + # ------------------------------------------------------------------ def get_high_frequency_tail_coeff_component( self, op1, op2, xi, Norder=3): - - r""" The high frequency tail corrections can be derived + + r""" The high frequency tail corrections can be derived directly from the imaginary time expression for the Green's function - + G(t) = -1/Z Tr[e^{-\beta H} e^{tH} b e^{-tH} b^+] - and the observation that the high frequency components of the + and the observation that the high frequency components of the Matsubara Green's function G(i\omega_n) can be obtained by partial integration in @@ -383,39 +334,39 @@ def get_high_frequency_tail_coeff_component( Using this the high frequency coefficients c_k takes the form - c_k = (-1)^(k-1) (\xi G^{(k-1)}(\beta^-) - G^{(k-1)}(0^+)) + c_k = (-1)^(k-1) (\xi G^{(k-1)}(\beta^-) - G^{(k-1)}(0^+)) = (-1)^k < [ [[ H , b ]]^{(k-1)} , b^+ ]_{-\xi} > """ def xi_commutator(A, B, xi): return A * B - xi * B * A - + def commutator(A, B): return A * B - B * A H = self.H - + Gc = np.zeros((Norder), dtype=np.complex) ba, bc = op1, op2 Hba = ba for order in xrange(Norder): - tail_op = xi_commutator(Hba, bc, xi) + tail_op = xi_commutator(Hba, bc, xi) Gc[order] = (-1.)**(order) * \ self.get_expectation_value(tail_op) Hba = commutator(H, Hba) - - return Gc + + return Gc # ------------------------------------------------------------------ def get_high_frequency_tail(self, iwn, Gc, start_order=-1): - """ from the high frequency coefficients Gc calculate the + """ from the high frequency coefficients Gc calculate the Matsubara Green's function tail G(i\omega_n) = \sum_k Gc[k] / (i\omega_n)^k """ - + Nop = Gc.shape[-1] Nw = len(iwn) G = np.zeros((Nw, Nop, Nop), dtype=np.complex) @@ -424,8 +375,28 @@ def get_high_frequency_tail(self, iwn, Gc, start_order=-1): G[iwn_idx, :, :] += \ iwn[iwn_idx, None, None]**(-idx+start_order) * gc[None, :, :] - return G + return G - # ------------------------------------------------------------------ + # ------------------------------------------------------------------ + def get_real_frequency_greens_function_component(self, w, op1, op2, eta): + + r""" + Returns: + G^{(2)}(i\omega_n) = -1/Z < O_1(i\omega_n) O_2(-i\omega_n) > + """ + + op1_eig, op2_eig = self._operators_to_eigenbasis([op1, op2]) + + # -- Compute Lehman sum for all operator combinations + G = np.zeros((len(w)), dtype=np.complex) + op=(op1_eig.getH().multiply(op2_eig)).tocoo() + M=(np.exp(-self.beta*self.E[op.row])+np.exp(-self.beta*self.E[op.col]))*op.data + E=(self.E[op.row]-self.E[op.col]) + # bar = progressbar.ProgressBar() + for i in tqdm(range(len(w))): + G[i]=np.sum(M/(w[i]+1j*eta-E)) + G /= self.Z + + return G # ---------------------------------------------------------------------- diff --git a/pyed/SparseMatrixFockStates.py b/pyed/SparseMatrixFockStates.py index 6b69f3e..24cc0dc 100644 --- a/pyed/SparseMatrixFockStates.py +++ b/pyed/SparseMatrixFockStates.py @@ -4,6 +4,7 @@ and annihilation operators for a finite Fock space. Author: Hugo U. R. Strand (2017), hugo.strand@gmail.com + Yaroslav Zhumagulov (2017), yaroslav.zhumagulov@gmail.com """ # ---------------------------------------------------------------------- @@ -15,10 +16,10 @@ # ---------------------------------------------------------------------- class SparseMatrixRepresentation(object): - """ Generator for sparse matrix representations of - Triqs operator expressions, given a set of fundamental + """ Generator for sparse matrix representations of + Triqs operator expressions, given a set of fundamental creation operators. """ - + # ------------------------------------------------------------------ def __init__(self, fundamental_operators): @@ -43,52 +44,77 @@ def __init__(self, fundamental_operators): assert len(operator_labels_set) == len(self.operator_labels), \ "ERROR: Repeated operators in fundamental_operators!" - + self.operator_labels = [ (dag, list(idx)) for dag, idx in self.operator_labels ] self.nfermions = len(self.operator_labels) self.sparse_operators = \ SparseMatrixCreationOperators(self.nfermions) - + self.blocks=self.sparse_operators.blocks # ------------------------------------------------------------------ def sparse_matrix(self, triqs_operator_expression): """ Convert a general Triqs operator expression to a sparse matrix representation. """ - + matrix_rep = 0.0 * self.sparse_operators.I - + for term, coef in triqs_operator_expression: product = coef * self.sparse_operators.I - + for fact in term: dagger, idx = fact oidx = self.operator_labels.index((False, idx)) - op = self.sparse_operators.c_dag[oidx] - if not dagger: op = op.getH() + if not dagger: op = op.getH() product = product * op matrix_rep = matrix_rep + product - + return matrix_rep - + # ---------------------------------------------------------------------- class SparseMatrixCreationOperators: - """ Generator of sparse matrix representation of fermionic + """ Generator of sparse matrix representation of fermionic creation operators, for finite number of fermions. """ - + # ------------------------------------------------------------------ def __init__(self, nfermions): self.nfermions = nfermions self.nstates = 2**nfermions + # -- Make python based fock states + self.numbers = np.arange(self.nstates, dtype=np.uint32) + tmp = self.numbers.flatten().view(np.uint8).reshape((self.nstates, 4)) + tmp = np.fliplr(tmp) + self.states = np.unpackbits(tmp, axis=1) + + + + raw_states=self.states[:,-self.nfermions:] + states_up=raw_states[:,::2] + states_down=raw_states[:,1::2] + indexes_const=[] + self.blocks=[] + + for n_up in range(self.nfermions/2+1): + for n_down in range(self.nfermions/2+1): + indexes=np.where((np.sum(states_up,axis=1)==n_up)&(np.sum(states_down,axis=1)==n_down))[0] + indexes_const.append(indexes) + self.permutation=np.zeros(self.nstates) + self.permutation[np.concatenate(indexes_const,axis=0)]=np.arange(self.nstates) + self.permutation=np.array(self.permutation,dtype=np.int) + for n_up in range(self.nfermions/2+1): + for n_down in range(self.nfermions/2+1): + indexes=np.where((np.sum(states_up,axis=1)==n_up)&(np.sum(states_down,axis=1)==n_down))[0].flatten() + self.blocks.append(self.permutation[indexes]) + self.c_dag = [] for fidx in xrange(nfermions): c_dag_fidx = self._build_creation_operator(fidx) @@ -96,27 +122,22 @@ def __init__(self, nfermions): self.I = sparse.eye( self.nstates, self.nstates, dtype=np.float, format='csr') - + + + # ------------------------------------------------------------------ def _build_creation_operator(self, orbidx): nstates = self.nstates - - # -- Make python based fock states - numbers = np.arange(nstates, dtype=np.uint32) - tmp = numbers.flatten().view(np.uint8).reshape((nstates, 4)) - tmp = np.fliplr(tmp) - states = np.unpackbits(tmp, axis=1) - # -- Apply creation operator - orbocc = states[:, -1 - orbidx] - rightstates = states[:, -1 - orbidx:] + orbocc = self.states[:, -1 - orbidx] + rightstates = self.states[:, -1 - orbidx:] - states_new = np.copy(states) + states_new = np.copy(self.states) states_new[:, -1 - orbidx] = 1 # -- collect sign sign = 1 - 2*np.array( - np.mod(np.sum(rightstates[:, 1:], axis=1), 2), + np.mod(np.sum(rightstates[:, 1:], axis=1), 2), dtype=np.float64) # -- Transform back to uint16 @@ -126,8 +147,10 @@ def _build_creation_operator(self, orbidx): # -- Collect non-zero elements idx = orbocc == 0 - I = numbers_new[idx] - J = numbers[idx] + + I = self.permutation[numbers_new[idx]] + J = self.permutation[self.numbers[idx]] + D = sign[idx] # -- Build sparse matrix repr. @@ -137,4 +160,3 @@ def _build_creation_operator(self, orbidx): return cdagger # ---------------------------------------------------------------------- - diff --git a/pyed/TriqsExactDiagonalization.py b/pyed/TriqsExactDiagonalization.py index a4d5e06..03b1eaf 100644 --- a/pyed/TriqsExactDiagonalization.py +++ b/pyed/TriqsExactDiagonalization.py @@ -1,5 +1,5 @@ -""" +""" Exact diagonalization and single- and two-particle Green's function calculator for Triqs operator expressions. Author: Hugo U. R. Strand (2017), hugo.strand@gmail.com @@ -12,27 +12,42 @@ # ---------------------------------------------------------------------- -from pytriqs.gf import MeshImTime, MeshProduct - +from pytriqs.gf import MeshImTime, MeshProduct, Idx +from pytriqs.operators import dagger +from pytriqs.utility import mpi +from pytriqs.operators import c, c_dag,dagger # ---------------------------------------------------------------------- -from pyed.CubeTetras import CubeTetrasMesh, enumerate_tau3 +from pyed.CubeTetras import CubeTetrasMesh, enumerate_tau3, Idxs from pyed.SquareTriangles import SquareTrianglesMesh, enumerate_tau2 from pyed.SparseExactDiagonalization import SparseExactDiagonalization from pyed.SparseMatrixFockStates import SparseMatrixRepresentation +# ---------------------------------------------------------------------- +def mpi_op_comb(op_list, repeat=2): + + work_list = list(itertools.product(enumerate(op_list), repeat=repeat)) + work_list = mpi.slice_array(np.array(work_list)) + + return work_list + +# ---------------------------------------------------------------------- +def mpi_all_reduce_g(g): + + g << mpi.all_reduce(mpi.world, g, lambda x, y : x + y) + + return g + # ---------------------------------------------------------------------- class TriqsExactDiagonalization(object): - + """ Exact diagonalization for Triqs operator expressions. """ # ------------------------------------------------------------------ def __init__(self, H, fundamental_operators, beta): - self.beta = beta self.rep = SparseMatrixRepresentation(fundamental_operators) - self.ed = SparseExactDiagonalization( - self.rep.sparse_matrix(H), beta) + self.ed = SparseExactDiagonalization(self.rep.sparse_matrix(H), self.rep.blocks,beta) # ------------------------------------------------------------------ def get_expectation_value(self, op): @@ -47,41 +62,63 @@ def get_density_matrix(self): return self.ed.get_density_matrix() def get_ground_state_energy(self): return self.ed.get_ground_state_energy() - + # ------------------------------------------------------------------ def set_g2_tau(self, g_tau, op1, op2): assert( type(g_tau.mesh) == MeshImTime ) assert( self.beta == g_tau.mesh.beta ) - assert( g_tau.target_shape == (1, 1) ) - + + op1_mat = self.rep.sparse_matrix(op1) - op2_mat = self.rep.sparse_matrix(op2) + op2_mat = self.rep.sparse_matrix(op2) + + tau = np.array([tau.value for tau in g_tau.mesh]) - tau = np.array([tau for tau in g_tau.mesh]) - - g_tau.data[:, 0, 0] = \ - self.ed.get_tau_greens_function_component( + g_tau.data[:,0,0] = self.ed.get_tau_greens_function_component( tau, op1_mat, op2_mat) - self.set_tail(g_tau, op1_mat, op2_mat) - + #self.set_tail(g_tau, op1_mat, op2_mat) + + # ------------------------------------------------------------------ + def set_g2_tau_matrix(self, g_tau, op_list): + + assert( g_tau.target_shape == tuple([len(op_list)]*2) ) + + for (i1, o1), (i2, o2) in mpi_op_comb(op_list, repeat=2): + self.set_g2_tau(g_tau[i1, i2], o1, dagger(o2)) + + g_tau = mpi_all_reduce_g(g_tau) + + return g_tau + # ------------------------------------------------------------------ def set_g2_iwn(self, g_iwn, op1, op2): assert( self.beta == g_iwn.mesh.beta ) - assert( g_iwn.target_shape == (1, 1) ) - + + op1_mat = self.rep.sparse_matrix(op1) - op2_mat = self.rep.sparse_matrix(op2) + op2_mat = self.rep.sparse_matrix(op2) - iwn = np.array([iwn for iwn in g_iwn.mesh]) - - g_iwn.data[:, 0, 0] = \ - self.ed.get_frequency_greens_function_component( + iwn = np.array([iwn.value for iwn in g_iwn.mesh]) + + g_iwn.data[:,0,0] = self.ed.get_frequency_greens_function_component( iwn, op1_mat, op2_mat, self.xi(g_iwn.mesh)) - self.set_tail(g_iwn, op1_mat, op2_mat) + #self.set_tail(g_iwn, op1_mat, op2_mat) + + # ------------------------------------------------------------------ + def set_g2_iwn_matrix(self, g_iwn, op_list): + + assert( g_iwn.target_shape == tuple([len(op_list)]*2) ) + + for (i1, o1), (i2, o2) in mpi_op_comb(op_list, repeat=2): + self.set_g2_iwn(g_iwn[i1, i2], o1, dagger(o2)) + + g_iw = mpi_all_reduce_g(g_iwn) + + return g_iwn # ------------------------------------------------------------------ def set_tail(self, g, op1_mat, op2_mat): @@ -92,7 +129,7 @@ def set_tail(self, g, op1_mat, op2_mat): op1_mat, op2_mat, self.xi(g.mesh), Norder=tail.order_max) for idx in xrange(tail.order_max): - tail[idx+1][:] = raw_tail[idx] + tail[idx+1] = raw_tail[idx] # ------------------------------------------------------------------ def xi(self, mesh): @@ -102,14 +139,11 @@ def xi(self, mesh): # ------------------------------------------------------------------ def set_g3_tau(self, g3_tau, op1, op2, op3): - - assert( g3_tau.target_shape == (1,1,1,1) ) - op1_mat = self.rep.sparse_matrix(op1) - op2_mat = self.rep.sparse_matrix(op2) - op3_mat = self.rep.sparse_matrix(op3) - ops_mat = np.array([op1_mat, op2_mat, op3_mat]) + + ops = [op1, op2, op3] + ops_mat = np.array([self.rep.sparse_matrix(op) for op in ops]) for idxs, taus, perm, perm_sign in SquareTrianglesMesh(g3_tau): @@ -120,29 +154,37 @@ def set_g3_tau(self, g3_tau, op1, op2, op3): taus_perm, ops_perm_mat) for idx, d in zip(idxs, data): - g3_tau[list(idx)][:] = perm_sign * d + g3_tau[Idxs(idx)] = perm_sign * d # ------------------------------------------------------------------ def set_g40_tau(self, g40_tau, g_tau): assert( type(g_tau.mesh) == MeshImTime ) - #assert( g_tau.target_shape == g40_tau.target_shape ) - for (i1, i2, i3), (t1, t2, t3) in enumerate_tau3(g40_tau): - g40_tau[[i1, i2, i3]][:] = \ - g_tau(t1-t2)*g_tau(t3) - g_tau(t1)*g_tau(t3-t2) - + assert( g_tau.target_shape == (1, 1, 1, 1) ) + + for t1, t2, t3 in g40_tau.mesh: + g40_tau[t1, t2, t3] = g_tau(t1-t2) * g_tau(t3.value) - g_tau(t1.value) * g_tau(t3-t2) + + # ------------------------------------------------------------------ + def set_g40_tau_matrix(self, g40_tau, g_tau): + + assert( type(g_tau.mesh) == MeshImTime ) + assert( g_tau.target_shape == g40_tau.target_shape[:2] ) + assert( g_tau.target_shape == g40_tau.target_shape[2:] ) + + for t1, t2, t3 in g40_tau.mesh: + g40_tau[t1, t2, t3] *= 0. + g40_tau[t1, t2, t3] += np.einsum('ba,dc->abcd', g_tau(t1-t2), g_tau(t3.value)) + g40_tau[t1, t2, t3] -= np.einsum('da,bc->abcd', g_tau(t1.value), g_tau(t3-t2)) + # ------------------------------------------------------------------ def set_g4_tau(self, g4_tau, op1, op2, op3, op4): - - assert( g4_tau.target_shape == (1,1,1,1) ) - op1_mat = self.rep.sparse_matrix(op1) - op2_mat = self.rep.sparse_matrix(op2) - op3_mat = self.rep.sparse_matrix(op3) - op4_mat = self.rep.sparse_matrix(op4) - ops_mat = np.array([op1_mat, op2_mat, op3_mat, op4_mat]) + + ops = [op1, op2, op3, op4] + ops_mat = np.array([self.rep.sparse_matrix(op) for op in ops]) for idxs, taus, perm, perm_sign in CubeTetrasMesh(g4_tau): @@ -153,8 +195,20 @@ def set_g4_tau(self, g4_tau, op1, op2, op3, op4): taus_perm, ops_perm_mat) for idx, d in zip(idxs, data): - g4_tau[list(idx)][:] = perm_sign * d + g4_tau[Idxs(idx)] = perm_sign * d # ------------------------------------------------------------------ - + def set_g4_tau_matrix(self, g4_tau, op_list): + + assert( g4_tau.target_shape == tuple([len(op_list)]*4) ) + + for (i1, o1), (i2, o2), (i3, o3), (i4, o4) in \ + mpi_op_comb(op_list, repeat=4): + + self.set_g4_tau(g4_tau[i1, i2, i3, i4], o1, dagger(o2), o3, dagger(o4)) + + g4_tau = mpi_all_reduce_g(g4_tau) + + return g4_tau + # ---------------------------------------------------------------------- diff --git a/setup.py b/setup.py new file mode 100644 index 0000000..d599605 --- /dev/null +++ b/setup.py @@ -0,0 +1,8 @@ +from distutils.core import setup + +setup( + name='pyed', + packages=['pyed',], + license=open('LICENSE.txt').read(), + long_description=open('Readme.md').read(), +)