{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Electronic structure calculations\n", "=================================\n", "\n", "*This is a part in the tutorial series. Read the previous tutorials to understand all material presented here.\n", "The initial setup and other issues described in earlier parts will not be repeated.*\n", "\n", "Electronic structure is a fundamental property of any crystal. The determination of the electronic structure is a first step in any quantum mechanical calculation. The description of the methods used by the Quantum Espresso package and the DFT approach are discussed in many review papers and textbooks (e.g. [M. Payne](http://dx.doi.org/10.1103/RevModPhys.64.1045)). Review of this paper or some other handbook on DFT calculations is *highly recommended* before starting any serious computational projects.\n", "\n", "To continue skip over the initial setup to the second cell below." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Import the basic libraries\n", "\n", "# ASE system\n", "import ase\n", "from ase import Atom, Atoms\n", "from ase import io\n", "from ase.lattice.spacegroup import crystal\n", "from __future__ import division\n", "\n", "# Spacegroup/symmetry library\n", "from pyspglib import spglib\n", "\n", "# iPython utility function\n", "from IPython.core.display import Image\n", "\n", "# Import the tools from the qe-util package\n", "from qeutil import RemoteQE\n", "from qeutil.analyzers import plot_bands\n", "\n", "# Access info\n", "import host" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Preparations\n", "--------------------\n", "\n", "To start any calculation we need to create a crystal and the calculator (see earlier tutorials for details). We will use a cubic, zinc-blende (F-43m) SiC crystal again, with a lattice constant determined in our first tutorial.\n", "\n", "The Quantum Espresso calculator will use a denser Brillouin zone grid (kpts: 8x8x8) than in previous examples to better reproduce and sample the electronic configuration in the crystal." ] }, { "cell_type": "code", "collapsed": false, "input": [ "qe=RemoteQE(label='SiC-elec', # A name for the project\n", " kpts=[8,8,8], # Dense k-space grid\n", " xc='pz', # Exchange functional type in the name of the pseudopotentials\n", " pp_type='vbc', # Variant of the pseudopotential\n", " pp_format='UPF', # Format of the pseudopotential files\n", " ecutwfc=70, # Energy cut-off\n", " pseudo_dir='../../pspot',\n", " use_symmetry=True,\n", " procs=8) # Use 8 cores for the calculation\n", "\n", "\n", "print qe.directory" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "calc/SiC-elec.Quqnj_\n" ] } ], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "a=4.3366\n", "cryst = crystal(['Si', 'C'],\n", " [(0, 0, 0), (0.25, 0.25, 0.25)],\n", " spacegroup=216,\n", " cellpar=[a, a, a, 90, 90, 90])\n", "\n", "# Assign the calculator to our system\n", "cryst.set_calculator(qe)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Structure check\n", "---------------\n", "Run the calculation to get stress tensor (Voigt notation in GPa), to make sure our structure is reasonably close to the equilibrium lattice constant. \n", "\n", "**Note:** The change in k-space sampling influenced the equilibrium lattice constant, and the stress is not close to zero any more. In fact the equilibrium lattice constant for a 8x8x8 k-space sampling is A=4.3341 A. To keep the structure at P=0 we change the lattice constant to the appropriate value. Note how the calculation was automatically re-done after we have changed the lattice constant. The `scale_atoms=True` makes all atoms move with the unit cell - otherwise the positions of atoms in Cartesian coordinates will stay the same and we would destroy the structure!" ] }, { "cell_type": "code", "collapsed": false, "input": [ "print \"Stress tensor before and after change (Voigt notation, GPa):\\n\", cryst.get_stress()/ase.units.GPa\n", "\n", "a=4.3341\n", "cryst.set_cell([a,a,a],scale_atoms=True)\n", "\n", "print cryst.get_stress()/ase.units.GPa" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Stress tensor before and after change (Voigt notation, GPa):\n", "[ 0.381 0.381 0.381 0. -0. -0. ]" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n", "[-0.007 -0.007 -0.007 0. -0. -0. ]" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Electronic structure\n", "--------------------\n", "\n", "The electronic structure calculation provides two main results:\n", "\n", "* The band structure\n", "* Density of states function\n", "\n", "The band structure is calculated along some path in the Brillouin zone which must be specified before the start of the calculation. It is specified with the parameter `qpath` to the calculator. The `points` parameter specifies how many data points should be calculated along the path. For the DOS calculation we need to specify the grid for the reciprocal space integration (`nkdos`). Additionally we need to specify number of bands included in the calculation (`nbnd` parameter), since otherwise the unoccupied levels *will not be included*. If we want to obtain information about band gap and the shape of excited levels we need to include them in the calculation. The default value for the insulator is equal to number of valence bands (number of electrons/2) and for metal it is larger by 20% (minimum 4 levels).\n", "\n", "The reciprocal space points are specified in *Cartesian* coordinates in units of $2\\pi/a$ (the same rule as for the phonons). You can find the coordinates of special points in the Brillouin zone using the [Bilbao Crystallographic Server](http://www.cryst.ehu.es/cryst/get_kvec.html) (the correct coordinates are in the \"Conventional basis\" column of the table.)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Several special points in the FCC lattice\n", "G1=[0,0,0]\n", "G2=[1,1,1]\n", "X=[0,1,0]\n", "L=[1/2,1/2,1/2]\n", "W=[1/2,1/4,3/4]\n", "K=[sqrt(1/2),sqrt(1/2),0]\n", "M=[1,1,0]\n", "\n", "\n", "# Set the path along which we would like to plot the electronic structure\n", "qpath=array([G1,X,G2,L])\n", "\n", "# Name the special points for plotting\n", "qpname=[u'\u0393','X',u'\u0393','L']\n", "\n", "\n", "qe.set(nbnd=8) # Increase the number of bands to include excited states \n", "qe.set(qpath=qpath) # Define the path for the band structure calculation\n", "qe.set(points=100) # Set number of points along the path\n", "qe.set(nkdos=[15,15,15]) # Set the grid for reciprocal space integration of states \n", "\n", "# execute the calculation of band structure and electronic dos\n", "qe.calculate(cryst,properties=['bands','edos'])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Analysing the results\n", "---------------------\n", "\n", "After the calculation the results are imported into the `results` dictionary of the calculator and can be easily for analysis. Let us first check the band gap in the crystal. The Highest Occupied Level (HOL) and Lowest Unoccupied Level (LUL) entries in the results dictionary contain energies of the lower and upper limit of the band gap.\n", "\n", "It is a well-known fact that the DFT procedure strongly underestimates the band gap in most of the materials. Thus it is not surprising that the result we have obtained is also substantially lower then the experimental value (2.36 eV)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Print the position and size of the band gap\n", "print \"Highest Ocupied Level (HOL): %(HOL)8.2f eV \\nLowest Unocupied Level (LUL): %(LUL)8.2f eV\" % qe.results\n", "print \"Band gap: %.2f eV\" % (qe.results['LUL'] - qe.results['HOL'])" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Highest Ocupied Level (HOL): 9.48 eV \n", "Lowest Unocupied Level (LUL): 10.83 eV\n", "Band gap: 1.35 eV\n" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Density of States (DOS) function is imported into the `edos` entry of the `results` dictionary and can be easily plotted and further analyzed. Here, we will plot the function and mark the band gap with a gray band. \n", "\n", "**Note:** The Fermi energy level (HOL in the insulator at T=0K) is *not at zero*. The absolute value of energy has no physical meaning and the Quantum Espresso programs do not move this energy to zero - as is sometimes customary." ] }, { "cell_type": "code", "collapsed": false, "input": [ "figsize(9,5)\n", "plot(qe.results['edos'][0],qe.results['edos'][1])\n", "axvspan(qe.results['HOL'], qe.results['LUL'], alpha=0.15, color='k'); # Mark the band gap with the gray rectangle\n", "title('Electronic DOS')\n", "xlabel('Energy (eV)')\n", "ylabel('DOS (a.u.)');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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k/HzndFY4Z8VYvTvYtmvXDgDg6emJuXPnWnzDycnJCAsLq7z+xIkTsWnTJkRG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\njWWUvN3+kSNAVJTzulN//zvwwQd1b0r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"text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Band structure\n", "--------------\n", "\n", "The band structure can be plotted \"by hand\" easily enough but doing it in this way is fairly involved. The results are imported into the `bands` and `bands_kpt` entries of the dictionary. However, the `QE-util` library provides a utility function for creating a \"standard\" band structure plot. The function needs on input the `results` dictionary from the calculation as well as specification of the special points along the path as well as their names. The return value of the function is a pair of handles to sub-plots of the figure, which provides the simple way to further customize the figure (as is shown below)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "figsize(12,7)\n", "ax1,ax2=plot_bands(qe.results, qpath=qpath, qpname=qpname, label='DFT calc.')\n", "ax2.legend();\n", "ax2.set_xlabel('Wave vector')\n", "ax2.set_ylabel('Energy (eV)')\n", "ax2.set_title('$\\\\beta$-SiC band structure')\n", "ax1.set_xlabel('DOS (a.u.)');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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YkcF6zZqm/2x6Okt5fv450KsXMHWqeT8v7JMcXyIv2SeEVjncSHpERAS6dOmC\nxo0bw9/fH99++y0A4M6dO+jevTvq1auHHj16ICEhQa0u2qX0dODpp7mS5NtvA5cvS4AuHs3fnyPj\nhlz1+fNNzzcvVYqVXy5d4kXh448D//0vcOuWdfsshBBCWENxxbCqjaTfvHkTN2/eRPPmzZGSkoIn\nnngC69atw6JFi+Dh4YFJkyZh5syZiI+Px4wZM3J3Wq62C+XAAaYdlCjB3PNWrdTukbbJfpa/f//l\nXRi9HvjlF6ZMmSMmhqPqK1YA48YBEyYArq7W6avQLjm+RF6yTwityrtvFiWGNYdqI+lVqlRB8+bN\nAQAuLi5o2LAhIiMjsWHDBgwfPhwAMHz4cKxbt06tLtoNvR544w3mCXfqxFx0CdBFYTVowLrq//kP\n96fPPuMdGlN5eXEk/vhxjq77+QFz5wL371uvz0IIIYSlFFcMq4mJo9euXUNQUBDatGmDmJgYeHl5\nAQC8vLwQExOjcu9sW1gYUKsWl3FfuRLYuJEj6UIUhZMT8OabwKlTnFz6xBMs3WiO2rWB334Dduxg\n6UY/P2DBAvMCfiGEEEJN1oxhVQ/SU1JSMGDAAHzzzTdwzXPPW6fTQafTqdQz2/fVV0DdukD58kB0\nNDBokNo9si0BAQFqd0HzvL1ZW3/KFOCll4DXXgPi483bRpMmwF9/AevX8yKyXj3WZ8/IsE6fhTbI\n8SWEsHXWjmFVHVPNyMjAgAEDMGzYMPTr1w8Arzxu3ryJKlWqIDo6Gp6envn+bM7yXZ07d0bnzp2L\noce2ISmJk0NPngQCAoBPP1W7R7ZJSsSZRqcDBg4EevZkzf1GjYA5c4CXX+b/maplS2DzZo6qf/op\n89Y/+ggYPpyTT4V9keNL7NmzB3v27FG7G0I8wJR9sygxrKlUmziqKAqGDx+OSpUqYd68ednfnzRp\nEipVqoQPPvgAM2bMQEJCgkwcNcOGDcDgwRw937XL/El9QhTV0aMcUa9UifX3C7sPHjwITJvGiaof\nfsiKRKVLW7avQgjtkHO70Kq8+2ZRYlizXletIP3AgQPo1KkTmjZtmn07YPr06WjdujUGDhyI8PBw\n+Pr6YvXq1ahQoULuTsuB/IDMTI5mrlsHDB0KLF7MvGEh1JCZyfzyzz5jffVPPy18BZfDh7mdM2dY\nCWbsWMDFxaLdFUJogJzbhVbl3TeLEsOa9bqymJHtO3GCqQbp6QzSu3VTu0dCUEwMVx395x9g1ixg\nyBDzUmD0QngqAAAgAElEQVRyOnkSmDGDi2+99RZrr1eqZNHuCmH3MjOB27dZ5SsxEUhJYbt7l4/3\n73M+iKGlpwNZWflvS6fjYJDhMb+W9/9y/kzeNm6cnNuFNqkVd0qQbuP++1/gm2+4yMymTUCZMmr3\nSIgHHTrExbNcXIB581gNprAuXGDAv3Yt89XHjwd8fS3WVSFs2u3bLG0aFgZcvcoWFsbiAbGxnLPk\n7g5UrsxHFxfgscf46OLCc0jJkmylSvHR2fnBi2tFMTa9no9ZWcZ/52wFfS9v+/57ObcLbZIg3QwS\npAPXrzMwv3GDy7T/f1lOYUGBgYEyuc2CsrJYCvTTT3nn54svgOrVC7+9GzeAr78GFi3i3aMJE4C2\nbS3XX2FdcnwVjaIw+D51CggONrbkZFZIql2brVYtturVAU9PBubOzmr3Pn9ybhdaJUG6GRz9QJ41\ny1hFY8cOfvAKy3P0/cxakpKA6dOBn3/miqMTJwLlyhV+e8nJDP6/+QaoUoV3l/r14wig0C45vsxj\nCMp372bK1549vPBt1Qpo3tzYfH0Ln1KmNtknhFZJkG4GRz2Q4+I4Ynj2LCfSffih2j2yb466nxWX\na9eADz5gFZeAAFZvKcpCW1lZrLX+zTfA5cucYDp2bNFG64X1yPH1aJmZwP79TO3asIH54V26AJ07\ns/n52W5Anh/ZJ4RWSZBuBkc8kBctAl5/HahalSMptWqp3SP754j7mRqOHePk0shIpsAMGFD0wCM0\nFPjhB66y26UL8MYbQNeuUvFIS+T4yl96OrBtGxf4+vtvjoy/8ALvDjVqZF9BeV6yTwitkiDdDI50\nICclAb16sQzd+PGcdCeKhyPtZ2pTFGD7dt4dKlGC6TBduxY9IElOBn77DfjpJyAhgXM3hg9nrq5Q\nlxxfuYWGcjDmt9+4UvRLLzEwr1lT7Z4VH9knhFZJkG4GRzmQV64ERo3iwkTbtwNNm6rdI8fiKPuZ\nluj1wOrVnFzq5QUEBlomWAeAoCCuH7BiBdC4Meu3v/ACjy9R/OT4YsnD5cs5p+LGDe6TI0YwSHdE\nsk8IrZIg3Qz2fiDfuwf07g3s3QuMGQP8+KPcpleDVJ8wz61bzC/fvx84cICl3/JydWWA7O/P1rgx\nVyTNu5JoZiawahXnXlSuzGC9WzfLBOtpaSxXunQpU8c6d+ZCYH37Am5uRd++MI0jH1/h4cD8+Rw5\n79SJcyd69NBu1ZXiYu/ndmG7JEg3gz0fyKtXcyTlsceAzZs5c18IrUpMZBnElSuBmzeB9u2Bjh3Z\n6td/8OIyPp4Tn0NDjY/h4Xz+M8+w1a1rDMazsoDffwemTQMqVuRE0759LXfRmpjICXmrVwP79jF/\nvU8fppjJhFNhaUeOMGVxxw5+zr/9tswvysmez+3CtkmQbgZ7PJCTkhgcHDgAvPIKb3/K6LnQqqQk\nVlH59lve9Rk/nulYhRkJTEgAdu4EtmwBtm7lAiq9ewODBjHod3JisP7XX8DMmUwRmDgRGDr0wRH4\nooiP50S9LVs4cc/HB3j2WV44tG4tC4WJwlEUYNcu3hUKD+exMnKk3LXJjz2e24V9kCDdDPZ2IC9a\nxOoTFSpw9Pzxx9XukRD5S0nhbfp587gg0ZQpXDjFUhSFI+zr13N0PikJGDyYrUULPmfPHq4VcPo0\n8M47TBXw8LBcHwCm2xw9yuNx2zbg/HnWoG7fHujQgY+yPoF4GEXhvvPZZ1wF9OOPgSFDilZm1N7Z\n27ld2A8J0s1gLwdyXBxvq588Cbz1FkcmZfRcaFVICCtONGvG9JMGDaz/mqGhDNZXreLiRCNH8k5T\n1arsz7x5wLp1nAD69tvWu8BNSWGpyEOHmHd/5AhH/Bs1Yl59o0bMrffxAapVA8qWtU4/hPYpCu8I\nBQRwftEnn/C4cfR8c1PYy7ld2B8J0s1gDwfyF19wMly1ahyta9xY7R4JkT9FYfrV5MkMiocOVacP\nhw/zrtOffzKHfeRIpoglJgILFwILFgDe3rzg7d/fuukpigJERQHnznHk/9w5jrZHRvL7Zcsyp71q\nVS7D7uaWu7m4cN7JY4/xaxcX5txXrsw7avZcC9ueHTrEMqKxsRxB799fBl7MYQ/ndmGfJEg3gy0f\nyKGhDCwiI5kq8OmnavdIFMSRq08Y3L3LVKyTJ4E//uCIsdru3mWg/uuvwL//su75mDGsff733wzW\ng4KYWjB6NNNUipOiAHfuMFiPiuJFRFJS7se7d9lSUoyPt2+zQs79+0ClSkyn8fPLPVpfr5795Mbb\n0/EVEsJ0ltOngalTgWHDJK2lMGz53C7smwTpZrDFAzkzkwHDsmVAy5bAxo2S06p1trifWdKFCxwJ\nbNUK+P57jvpqzcWLwC+/AEuWMJAdO5Z9jo7mqPuiRRydHjWKZRYrV1a7x4+WlsaAPSaGv9+5c8YR\n+7AwXnT07MmSfa1b224waA/HV0QE01m2buUI+uuv289FlBrsYZ8Q9kmCdDPY2oG8fDk/vBWFt+UH\nDVK7R8IUtrafWdLJk7zjM20aA1+tS0/nZNOffwaCg5m3PnYsyznu3MlgffNmTvocMoQrObq6qt1r\n86WmMid++3ZOSrx+nYs9DRzI38mS1W6szZaPr6QkVhr68Ud+tn/wgVRrsQRb3ieEfZMg3Qy2ciBf\nuQI89xxvyQ8bxhE/Wx31ckS2sp9Z2v79wIABDHj79VO7N+a7coXH2qJFnNz66qscXc/MZE30lStZ\nE71nT37/2WdtN8C6eZPB+rJlvDh5+WXesWvWTO2ePZotHl+ZmcD//seUlmeeYd65t7favbIftrhP\nCMcgQboZtH4gp6czR/a337iq4tq1QJ06avdKmEvr+5k1bNvGC8oVK4Cnn1a7N0WTns4c9Z9/Bk6d\nYgA7ZgzQpAnTSdauZdu/nyPsL7wAPP884OWlds8LJywMWLzYmOLzzjv8nUuVUrtn+bOl40tRWD//\n/fc5GXjOHGNJUGE5trRPCMciQboZtHwgz57N0lslSnDERVJbbJeW9zNrWLMGePNNBq7t26vdG8sK\nC2Pw+uuvrLoyZgxrr7u6MnVhyxb+3lu3MkWmVy+21q1tr3ReVhbwzz8MJC9eBN57j7+v1uYU2Mrx\ndeYM/4bh4cDcubzzItV3rMNW9gnheNTaN6U4lIVs2MARuI8+YjWMhAQJ0G1dQECA2l0oNr/9xjrj\n27bZX4AOcOn1adOYwx0QwKDc25uVYU6eZB3rVatYOm/WLE7efO01HtNDhjB95upVjqhqnbMzUzF2\n7OAqrQcO8PcPDGTVGa3Q+vEVE8N94OmnmbZ45gxXwpUAXQhRXGQkvYhCQngSP3+eH+RLl9pufqtw\nTH/9xdriO3dqo8RicYmJYVrPokUcTR8+nK12beNzbtzghcuuXWylS3OiZpcuQKdOXLzIFoK2ixd5\n8bFuHdNg3n0XKF9e7V5p0717XA9g3jzuD598wlr3wvq0dG4XIidJdzGDFg7k8+dZQeLkSeYmrl4t\neefC9mzbxv1461bHzbFVFE66XLyYQXvdusB//vNgyUZF4STwXbuA3buZy16qFBdWevJJ5rX7+2s7\nPebKFd5R2LIFmDCBAbvW0mDUotdzAu4nn/Bu0vTpuS/YhPVp4dwuRH4kSDeDmgfypUscXTlyhCfk\nX39l3XMhbM2BA5wsuW4dA0wBZGSwvOHy5caSjS+/DPTt++AdMkUBLl/m39HQoqOBJ54A2rYF2rTh\nY5Uq6vwuD/Pvv0x/2bMHmDSJKXply6rdK/Xs3MlJoWXLMu+8XTu1e+SYJEgXWiVBuhnU+GMFB3NS\n3ZEjQP36DM7lg1zYqlOnmLe8fDnQvbvavdGmlBTWXjeUbHzqKeDFF5nWVlD6w507wLFj/Jw4epSt\nXDleyLdsyQC+ZUvtLKoUEsJg/ehRYPJk1pZ3pMV4Dh/mSqE3bgBffMH31xbSl+yVBOlCqyRIN0Nx\n/rHWrwcmTuSImb8/8N13zEUVwladP8+86gULOJIuHi0xkasE//knR13btePoep8+gK9vwT+nKKws\nc+KEsZ06Bbi4ML0oZ6tZU70A8dQpTqgNDubk99GjtVu60RJOn2Zay+nT/L2HDzdvDYvUVP7s6dO8\nK3HjBhAfz/0kORm4e5eTjxUld9PpOK+hTBmO2pcrxzs0Varw/a9dm7X9GzcGKlSw3u+vVRKkC62S\nIN0M1v5jpaezlOI337CesiGgqVvXai8pNCgwMBCBgYFqd8Oibtxgvu3nnzMXXZgvJYU53Zs2MSWm\ncmUG6717M73lUcGtXg9cuwYEBTEoDgpiu3uXNdybNjW2xo2LdyL60aMMWs+cAcaPZ3UTa00wVeP4\nOnWKK4Xu3Qt8+CF/v4LuHCQkcO7BoUO843D1Kicb373L99DJiYF2+fK8s+Lmxq8rVgQ8PPhvZ2c+\nz/CYlcVAPiHBGNAnJvI8k5DAfSstjc9zcmIQX6kSUKMGzz+tWgHduvFurj2SIF1olQTpZrDWH+vg\nQd76PHCAJ9qXXmKg7ogjGsL+Thjx8ZzgOHw47w6JotPrgePHOcq+eTPnrLRvz+ovXbtyhNzUEdq4\nOAbHISEcoQ0J4V0PDw8G6/7+bA0bcrTV1dV6v1dQEOusb90KjBrFgL1GDcu+RnEdX4rCCdKzZ7PK\nzfjxwOuv824GwFVE9+3jc44f53Nu3eJgTalSDLq9vfl3N6QtNWvGANpa0tP5Hhw7xv3g0iUgIsJ4\nkaDTsf9VqjBgb9OGaWutWjG4t1X29pkr7IcE6Waw5B8rPJwjK7//znxSf38G6lLjXNjTCSM1FejR\ngznRX30lebfWcucOAz5DycYbNxg4tWnDhZHatDFvRdOsLI66h4YCZ8/y8fx5BpIVKxoD9gYNgHr1\n2GrUsFygdv068PXXwJIlDAKHD+d+ZE5qSEGsfXylpDA96auv+O+JE/k7GEpqBgXxb5uczJHuSpWY\nbvL447zA6tnTGMhriV4PnDvHtKtjx7hfhIdzRF6vZ59r1GA51Q4duChXw4Zq99o09vSZK+yLBOlm\nKOof69Qpjqr88w9vM3p5AQMGcOKQpUbNFYUniZs3jS0xkaNiVaoYmyNN0rI19nLCyMpiOcGSJVli\n0JZH2mzNrVvGCaTHjrG5uTGVxd/fOELeoIF5nwV6PQPo8+eNQbuhxcezHKyfHx8NrXZt1nUvTK55\nfDwHMpYuZdrHyy8zXapZs8Jf8Fnj+EpPZxC+fDnTkapW5R2H2Fi29HT+natVY2pRp07A88/bT/nc\nS5d49+PgQV7QRUTwIgTguc3bm793hw5cObVmTXX7m5e9fOYK+yNBuhnM/WOdOsUVFXfv5kns/n1O\n9howgMs9W6JE2q1bzF08dIgfkMHBDNSrVjUG5G5uvCi4eZOl2mJi+L1u3ZjT2qsXR3OENtjDCUNR\nuJLo+fPMoy5dWu0eOTa9npPQc46Mnz3L+uVeXgykczYfH46KVq3KiyxTpKTwc+7KFQbUV64YW1QU\n4OnJ4MzQvL0ZtFavzubl9fBa75cusZ740qV8XrduxgWezLlLYInj6+ZNTu7fvJmfuTdu8Pt6PS8e\nKlQwjo4//TQDUy2OjluTXs/1PLZv50Xi+fPcD+7e5QV7+fLcx+rX592ezp3NS9OyJHv4zBX2SYJ0\nM+T3x9LrefLYu5dB+fnzrKoQHc2RRE9PfvD07QuMGFH0fML793nLdNMmLr8dE8NJYx06sLVs+egJ\nV4oCREZy5GfjRm6vSRNjH8054QnLs4cTxpdfcgR03z5ZYVLLMjI46nn1au4WEcEWG8u7cN7euS/8\nDa1yZV7ge3hwEmNBQXZmJj9zwsM5En/9OrcfGckWFcWUHQ8PfmZ6eRkfPTyYYmNoFSrwcy84mKUM\nDxxgsN+6tTH1pm5djujnV4P9YceXXs9+XLvGi4ugIF7MXL/Ov0ViIlO4DEqV4u/fqhVTWnr1sp/R\ncWvJzOQdnj17WHXowgW+/8nJ/PuXLs33uUYNvocNGgDNm/M85+lpnT7Zw2eusE8SpJtBp9OhZEkF\nen3u8lYAb2VWqsSRcn9/1jR+5hnL3OK/do2jkRs3Muh5/HFWdOjZ0zIrDaam8iLjzz/ZBg3iAht+\nfkXvuzCfrVd3WbwYmDqVd3aqVVO7N6IoMjM5ahwRkTuFznBXLi6Od+ni4hjAli/PINrNLXd77DF+\nRhpKAJYpwxH6nFVIDKl6huojSUlsKSlsd+8C9+6xpaYyhSQ9nYGdYTuGz2S93jiqnbdlZWXC2bnE\nA2UKCzojlSzJwRVD4Ni1K+uaN2okKVyWFhXFFXWPHePdnuvXebc4OZkXlDod9x0XF14UenryLoyP\nj/HRUFLSnBRSCdKLR1YWBxrv3WM1IcMxnJ7O99ecr/P+OzXVuO2RI3kHyx5IkG4GnU6HoUMVlCxp\nPMEA/AAxjA5FR3P0p2FDBtBNmvCxUSPTl8FOSuIow/btbImJnDRlCMwLWtDEEmJiWJP9xx95+3HS\nJI4SCWGKrVt5N2bPHo6ACe1RFJ7UDCfJMmUYhBY14MzKMtbsTkrK/Xj/PltqqvFkmpHBQDory9gA\nBmJOTsagukSJB1vJksZHw2sbft4QoKenG4OBjAxjYJ+VxQuF0qWNzc2Ndwtq1+Ydg3LlmFNuzUo2\nwjyZmZy4GhTEtKpr13gXJjaW+13O91qv58/odDxPOzsb9xfDBZ2hOTsDN25IkF5Y9+8zbrh5k495\nW87vJycb6/SXKcM7USVL8jHv1w/7v7xflyzJ7Rq23bat/QwySpBuBlP+WJmZzE88d44jAWfO8PHC\nBY7E1KrF5uvLZrgNHBnJn4uM5IdPmzYMzHv04GSv4h6xSUkBFi7kUtVPPAHMmiX12sXDnTjB3Nt1\n61gOUKgjNdWYRpAzP/zaNWM97BIljCdJQ9BctixHKF1djRPNvbzYqlThXZEaNThi6ekpo8hCu/R6\n3t2JjTXe7YmPZzOMwOZsX38tQXpOd+8+OuA2tLQ042eE4fMiv1alCu+0yeeGeSRIN0NR/liGYDws\njCfLsDC2kiV50jOc/AyLR1izFq45UlNZs332bGDYMGDKFF5sCJHTlSushb5gAdCvn9q9cSz37jE3\ne+9etpMneeeuUSOODBuqrNSqxRHj0qUfPFHq9dxOcjLbrVu5T8TR0UxFMAwmJCZyxLlGDaYYeHuz\n+fgYm7u7lNwUtsGe012ysjjPIi7O2Awpavm1mBjGKwUF2nm/V768HOfWJEG6Gez5QH6U2FiuCLhm\nDeu5v/mm6VUfhH27dYsj5++9x8VahPWlpnLy+MqVTInz92d62lNP8b2wdppGaqoxYA8PN040DQ83\nTg5VFOYH+/gY7xzmbJUry8ldaINWz+2KkntUOzbW+HjrFoPv27d5gW2Yi5FzTsaxY+a93oIFwH/+\nw88POTa1QYJ0M2j1QC5OoaHAhAkcVVuwgPV+heNKTmYpvB49gM8/V7s39k2v50IyK1Ywpejxx1k3\nvH9/685TKayEhNzVXAx3EA2PGRm5R/rr1DFWZ6leXYIEUXy0dG6/fJkLYIWE8A6WTpe72pHhsXJl\n3tWuVIl33p2dc8/nMDympXG7+U2UzlkEQ6fjpOiiFqIQliVBuhmK+sfKyOBBZxh1unGDOaD16/PE\nVK2abZyYFAX46y/g3Xd5UM+aJWUbLclWqrukpbHOvq8v8PPPtrHv2qLkZK68OX8+88ZHjOAiUbZe\nOSchIXfO/OXLLGd74QJz5w0Be4MGTN1p2JD/LmrNfUsfXxkZfMw74VXYDq0E6Zcv55771agR70S5\nujJVzTCZ2fC1oXpShQq8UK9Ykedi2f/shwTpZjD1j3XvHuul5104JDqaV8He3szlrFGDJ2DDin0p\nKTxAO3Zk/nerVto+2FJSgGnTgEWLWHLvtdfkKtwStHLCeJisLI7iZmQAq1erswCJvbtyhZWWli7l\nxfD48VwLQcufCZaSmMjPxAsXgH//5UR8wxoUPj4M2OvXZwBveDR1QTZTj6+0NN4JyDn6Hx7+YA5v\nWhrfk5wjk87ODJgqV2bz9DQu5mS4e1C7NgMsoT6tfebevWtMbYmPZ5UkQ1nSnOVJk5N5rCQk8HkX\nLvDnt23j3U1h+yRIN4NOp8OuXQru3kV2S07miPi1a8bbuklJHPHx9ze2xo15cnlYMGM4MW3ZwpX1\nnJwYrA8dytFKrTp7ljnq9+4BP/zABZVE4WnthJGXYTXRc+e4r5qzrLx4tLNngS++AP75Bxg9mseW\nj4/avdKG9HSOtv/7rzGAv3CBTVFyT2L19mZgXK4cy98aWseO7fHPP4dyfY7Hx/NzPGe7fZtpN4Zq\nXLVqcfuenqx+Y2iPPZb7wklROPHuzh3mDRvyh2NieH4w3Dm4epXHjuFOQc4m6T7FS+ufuY8SHMy7\nmhkZ3O+/+kpSUe2FBOlm0Ol06NRJyf6wd3Fhq1GDIyS+vnz08ip6mSFF4apsy5ZxpLJ5cy4w1KOH\nNj+8FYV9/eADYMAA5iebs5iEMNL6CSMwENiwgbXQZSTQck6f5nGzbx/nfbz5ptTpNpWiMNA2pBIa\nWlwccgXjd+8Chw8fRrdu7XIF7xUq5L7DWaMGP8eteYdIURi4X7jAC15DO3uWo/NNm+Zu/v6mr7Uh\nzKP1z9xH2bGDQfr777Nksq8v0+EqV5aSh7ZOgnQzqPXHSk8HVq1i7neJEpxUMnCgNqur3LkDfPQR\ng7jZs5kSocWLCi3T8gnju+9YkvPAAZmHYCkhIcCnn/Ki/P33WSFHgjHr0fLxZXDrFveLkBBevJ0+\nzWC+Zk0O2LRoYXysXFnt3to+W9gnHuXkSWD9euDUKV6gRkXx7ryXl/HC082NpXJHjFC7t8JUEqSb\nQe0DWVGYXjB7Nm+Vvvce8Oqr2kw3OHqUwUaFCpzw5u+vdo9sh9r7WUEWLuTcg717eetfFM3VqwzO\n//kHmDyZx0vZsmr3yv5p9fh6lPR0pvcEB7MFBfGxXLncQXuLFhxJlRFU09nqPvEoaWlcGPH06dzf\nT0yUu6C2QoJ0M2jpQD52DPjsMx58U6bwylhrI+uZmaz6ERjIEfXAQEmBMYUWq7v89htTmXbv5nwL\nUXg3bzKtZeVKYNw4prZIWkvx0eLxVViKwjz3oCBj0B4UxHlRTZsycG/eHGjWjPOi5CIwf1o6t1va\n0aOsfa7XAyNHckKzmxsXIXJz4107b28uVCS0R4J0M2jxQD5yBPjkE05cDQwEhgzRXoWVW7e4ANLf\nf3NC3IgRMspjS/74g8Hkzp2c1CYKJyUFmDOHd5aGDwc+/FBSFYR13L7NARzDqHtwMCfc+voyYM+Z\n5+7jI5/HWjy3W5KicIDln394AbdgwYPP0eslNVWLJEg3g5YP5N27GQgnJTEQeOYZtXv0oBMngHfe\n4Qj7V18xN05o2/r1LK25fTtP6sJ8mZksUxoQwFKKX3zB3GIhipMhXSZnrvvZs0x9aNyYzd+f5S0b\nNuToqqME71o+t1vDyZNAr168QHvhBZZ+9vVlGdOSJYFSpR58dJR9QWskSDeD1g9kReGEzYkTmTM8\nZw7QpInavcpNr+ck2A8/5Cz0mTNzL94gtGPzZt712LKF75Uwj6IAW7fyePTw4PEo5UmF1sTHG9fz\nCA1lPfrz5zng06CBsSZ9vXr8rK5bl1XN7InWz+3WkJHBu6M7dhjXAYiP5/fT0x98dHJisJ6Wxs82\ngHdYn3+egw/COhwySB81ahQ2bdoET09PnDlzBgDzFH/55RdU/v/7z9OnT8czeYajbeVATk8HfvyR\nea/9+nHBIa3lm92/zyohc+awDvyUKaYvRiKsb80a4I03eNHXtq3avbE9Z85wYnd4OCd69+kjt5KF\nbUlI4Mj7+fPGBfcuXuSqmBUrckGmvM3Xlylctrav28q5XS2KwgXs0tMZpP/3v1wF2WDOnPxH33M+\nli3L/cPFhXnwpUrZ3n6ihrz7ZmHjV7NfV80gff/+/XBxccErr7yS/UtOnToVrq6umDBhQoE/Z2sH\ncnw8b60vXszqEePG8cDQkthYVgz5/Xf27913Zda52pYs4Z2OTZtYKUKYLjaWF5xr1/Lx9de1N6Fb\niKLQ61ni78oV46JMhq+vXeMAjI8PU7pq1jTWn69enc1QClBLAZqtndu1ICkJ2LWLRSzS0vIffTc8\npqczrSoy0rhegV6PXGvO5FxwrEwZ7h9paWypqcbR+7xvkylvm7MzY5/y5YFff7WtAcG8+2Zh41dz\nqbqI+JNPPolr16498H17O0jd3XmF++qrXFJ84ULg22+B7t3V7pmRpyfw/fe8Mp82DfDzY63ot95y\n3FrRalafmD+fI7+7dvFWtzBNairvDM2eDbzyCmtau7ur3SuRH3uq7qIGJydjAJ5fmkNKinH17evX\nGdDv2cMAzbCaq6Lw7m7OZljJtXJl42qulSqxIli5ctoK6gUvtPr1YwP4niYns1BEYiKD+KQk49c5\nv3f3Lv8dG8t28yZ/tjhERdlWkJ5XccWvquekX7t2DX379s11JbJo0SKUL18eLVu2xNy5c1EhT71A\nW77aVhRWV3n3XeDxx4G5c7U5ee3cOVap2b+fJf/GjnW8YF2N/UxReNdlyRLmKGpx39AiRWFq0KRJ\nnFg7e7bMsdA6W/4ctweKwkA+JobBmaHFxLAqTVwcA724OP47IYGTrytUMDYXF5YtNTQXF6ZTlCvH\nR0PLm3JRsiRHVZ2cGPQ7ObG1ayf7hKmCg3mOuHyZF2GGQPvWLS626OHB98hQ4jFnucfy5fl+5Rw1\nN7ScKwAbRtNlsmr+n1eFiV/Nfl2tBemxsbHZ+TxTpkxBdHQ0Fi5cmOtn7OHD/f59BhLffssR6/fe\n0+bt+OBgjqwfPAi8/Tabo4xMFvd+lpXFyY3//MOmtfkLWnXyJO8AJSYC8+bJ5ClbYQ+f444mLY3B\nenw8j7fkZLaUFOPX9+8/2HKmXRi+VhSmWuRsR4/KPmGKQ4c4cj5kiLEijJcX74JUrsxAW1iWKUG6\nKcEKS4gAACAASURBVPGruVRNd8mPp6dn9tdjxoxB3759831eztuknTt3RufOna3cM8sqW5arHA4d\nypSS334DfvoJ6NBB7Z7l1rw58NdfnLQ0cyYnJY0ezaCoWjW1e2c/kpK40NTdu1xJtGJFtXukfZGR\nLHe6bRsXFBs5UntrEwhhT0qXZjDo5WWZ7e3Zswd79uzJ/vfRo5bZrr37808WFJg6Ve2e2K+8+6Yp\nTI1fzaG5kfTo6GhUrVoVADBv3jwcP34cK1asyPUz9jYCoyg86N59F3j2WQbDWg3SwsOZorN0KdC7\nN+utt2mjdq+so7j2sytXgOeeA556ivnUWryjoiV373KOx7ffcp7Hhx/KJGdbZG+f46LoZJ8wzZYt\nwEsv8VxRubJx/oDha8O/q1XjBOG6dWUAo6hMGUk3JX41+3XVDNKHDBmCvXv3Ii4uDl5eXpg6dSr2\n7NmD4OBg6HQ61KpVCz/99BO88ly22+uBnJjIVUv//JOB8JAh2p2kc+cOZ2d//z1vsb3zDj80SpdW\nu2eWUxz72a5dHEEPCODIiCiYXs87Th9/DHTsCEyfztu8wjbZ6+e4KDzZJ0yXlcW0o5xzB27dMn79\n9dfG586bx0FAUXh5983Cxq9mv67aI+mFYe8H8rFjwJgxLJn1ww8so6VVWVksETh/PmtSv/IK0w4a\nNlS7Z0VnzeoTigJ89x0nia5cCXTpYpWXsRt793LeRokSPOG0a6d2j0RRSXUXkZe9n9uLi6IA7dsD\nR47w3+XLs+xmtWqsqJJzIm9+9dRLleLcgeRk4wRfZ+fcXxsemzYFnn5a3d+3ODjkYkaF5QgHcno6\nJ5bOm8dR1jff1P7tqgsXuOz6kiVcaXXUKGDgQElFyCs6mnn9sbFc9dXPT+0eadeFC6wudPo08OWX\nwODB2r27JIQoGkc4txc3ReGIe2Qkyx7euZO7bnp+tdQjInjX0pzXsHcSpJvBkQ7kf/9l3m1GBuur\nN2qkdo8eLTOTy7D/+ivTOXr2BAYNAnr14oRZR7Z6NVODXn+dqU2Sf56/W7eMi2tNmsS/WZkyavdK\nCGFNjnRu1wK9nvXyr1xhKcfLl/n1/v28W7lundo91A4J0s3gaAeyXs/KL59+yqoqEyfaTnB36xar\nw6xeDZw6xcmmAwcCPXo4VtAVH8/ylSdPctJt69Zq90ib7t3j5NmvvmKu/pQpnAAlhLB/jnZuLw4Z\nGSz4YAjCDYH45ctAWBiLVPj5sXKbnx9bixayzkReEqSbwVEP5OvXOaoeF8dR6mbN1O6ReW7e5IIz\nq1cDQUHMw+7Th4G7vZZzNNwBmTYNePFFYMYMqWGbn8xMpkkFBHAE58sv5SQhhKNx1HN7UWRmMoUy\nPJxpKhERwLVrxkA8IoLn17yBuJ8fULu2nI9MJUG6GRz5QFYUYPFi5um+8QYrXZQqpXavzHfnDlNi\nNm7kY61aHF3v0oW14m19dVNDWc2PP2YFkhkzuMKsyE1RuA9MnswR81mz7LekpxDi4Rz53J4fReGg\nXM4APO/XMTEsuejtzebjw1a3LoNyX1/7qrqmFgnSzSAHMieAvP46r5gXL7btADAzkyuo7dgB7N7N\nUfbmzblyZMeOTA0p4sq6hVKY6hOKwt/j44/5e82cCXTvbp3+2br9+4GPPuIF24wZvKsik0Idh1R3\nEXk54rk9Pp5pJ/m169c5j8vHxxiEGwJxw9fVq9tO+qstkyDdDI54IOdHUTgD+733jBMRbXFUPa+7\ndxm0794NHDzIXPbq1TnC2qYN8MQTQOPGgIuLdfthzn524wbTNRYtYq79xx9zsqyTk3X7aIuCg/n3\nOXuWk0OHDtV+5SJhefI5LvKy530iKoqffWfPGtulS5xzVqtW/s3X1/rnOWEaCdLNYM8HcmFERQGv\nvcZbX4sXc9KHPcnM5Afa0aNsQUGselO1KtCkCeDvz6o3deqwVapkmRHZR+1n0dHAnj3AsmWsRztw\nIMtOtmolI8L5uXSJOee7dnEE/bXX5DasI5PPcZGXvewTWVk8Tx08CBw+zHb3Lu94N25sbPXqceKm\nnC+0T4J0M9jLgWxJisJg8f33WVP9o4/sY1S9IJmZnBQTGspFlM6f50SZK1f4t6hdmyMRVasCVarw\nsWpVwMuLCzsY2sOCRMN+du8ecPs2J74eP85R/oMHgaQkLhgxaBDQv79MwClIWBjw2WfAhg1c9e7d\nd2V0SMjnuHiQre8TGzZwcbp//uF5p2NHToRv354TNSUYt10SpJvB1g9ka4qKYgWYyEiOqttaBRhL\nuHOHwfr16xztvnmTj9HRnGSTlAQkJrI5OQGursbV1gzN2RkIDY1A2bLe0Os5qbFyZY6EdOjAD936\n9eVD92Fu3AA+/xz44w9eOE6YALi7q90roRXyOS7yssV94s4dLkq3aBHPKZMmAc88A9SooXbPhCVJ\nkG4GWzyQi5OiMD964kRg3DhWzpCJJQ9SFCA1lUF7RkbulpUFNGvmg5SUcJQrJ8G4OW7c4ITZFSuA\nsWN5d0dqnYu85HNc5GUL+4Rez7TLPXuAffuYyvLMM8DIkcDTT8v8Gnul1r5ZothfUVidTgeMGMEP\njLFjgbZtOarepInaPdMWnY4z5wtaBTUgYJTNl4IsTuHhrNKyahUwejRw7hzTi4TIT0BAgNpdEMJk\nej3X+fj8cw7k9OjBu9YrVsgdQmE9MpJu5xSFCx9NngyMH8/66jKqLizp2jUG53/8wYvC995japAQ\nQphDi+f2rCwuwPf555xL8+mnwLPPyt1VR6PWvikF4uycTsdRzVOngAMHOKoeEqJ2r4Q9OH8eGD6c\nJTErVgQuXGCwLgG6EMLWZWayGEOjRsB33wHz5rGKV+/eEqCL4iNBuoPw9ga2bOEEvm7dWG0jI0Pt\nXglbdOIEMGAA0LkzJ89euQJ8+aXknQsh7MO+fSy68MsvwA8/cICrRw8JzkXxk3QXBxQRwVy6mzeZ\nCmNvddWF5RlWUp09myPoEycCY8ZI2UkhhOWofW6PjeVn265dwNdfs7SuBOYCkHQXUYy8vYHNm5mj\n3rMnV39MTVW7V0KLMjM5Merxx4H//hf4z384cj5unAToQgj7kJUF/PgjF8bz9OSk9wEDJEAX6pMg\n3UEZKsCcPs2R0RYtWEpKGAUGBqrdBdUkJXEkyc8P+Pln4IsvuGjU8OH2vUiWKD6OfHwJ7QgK4roX\ny5cDO3fybqGrq9q9EoIk3UVAUYA//+To6KBBxlnsjs4R97Nr14D581mys3t3LkDUurXavRL2yBGP\nL/FwxblPKAoHIKZM4boOw4dzcTsh8iPpLkI1Oh3w0ktAaChXTGvcGPj7b7V7JYqLogCHDgEDB7JS\ni5MTR5dWrZIAXQhhf+7d4+JD8+dzUujIkRKgC22SkXTxgF27gNdf5+z2b78FqlZVu0fqsPf9LC0N\n+P13vscJCcA77wCjRsmtXlE87P34EuYrjn3i4EHgjTd4fvvxR8iCdcIkMpIuNKNrV+aq168PNG3K\nElRZWWr3SlhKVBQX5KhZk3mYU6cCFy9yIrEE6EIIe3T4MMsoDh3KCi5Ll0qALrRPRtLFQ509y1H1\n+/eBBQscK/3BnvYzRWHt3++/ZynFwYM5ct6wodo9E47Kno4vYRnW2CdiY4HXXuOCfp98IpPfReHI\nSLrQpMaNGdyNHw/068dl3+Pi1O5V8QgICFC7C0WWksI7IU2a8GKrUydODl2wQAJ0oS57OL6Etm3f\nzsplDRvybuHYsRKgC9siI+nCZImJQEAA62ZPncoPvBIl1O6VyE9oKIPzlSuBLl2At97io9T9FUJo\nlaXO7RkZwEcfcfL70qX87BOiKNSKOyVIF2YLCWG5xtu3gblzmecn1JeWBqxZw+D86lVeRI0dC1Sv\nrnbPhBDi0Sxxbg8PZylhDw+Wkq1UyTJ9E45NgnQzSJCuPkUBNmwA3n8fqFsXmDMHaNRI7V45pqtX\nWe930SKmtbz5JtC3L1CypNo9E0II0xX13L5pEytUvf8+8N57UlZRWI7kpAubotMBzz/PiaU9ewKd\nO7OsVXS02j1zDJmZvEjq1Qto04a3d/fv56TQ/v0lQBdCOJYffwRefRX46y9Wb5EAXdgD2Y1FkZQq\nxUml//4LlCvHiaaTJjEVRljezZtcEbZ2bWD6dGDIEN7enTsXqFdP7d4JIUTxW74cmDGDRQ46dFC7\nN0JYjgTpwiIqVmSgGBICJCWxxnpgIL+2VYGBgWp3AQBTi/buZZ5lw4YMytevZ93fV14BypZVu4dC\nmE8rx5ewbcePA+++C2zcCNSpo3ZvhLAsyUkXVnH1KivAbNkCvP02W8WKavfKPGrvZ8nJwLJlLJeY\nlcVc81deAcqXV61LQliM2seX0B5z9onQUI6gL1nCu4ujRlm5c8KhSU66sCu1a/PDc98+1uX28+Nk\nnqgotXumff/+y+o5NWsCO3cC334LnDvHxYckQBdCOLpVq1hWsUQJlpkdOVLtHglhHRKkC6tq0AD4\n9Vfg9GlOdvT35+Se8+fV7pm2ZGUBf/8NdO/OSbhubvybrVkDdO0q9c2FEAJgJbFJkziA8dlnwFNP\nyeejsF+S7iKKVVwcMH8+8NNPDNjfeovlArW4KFJx7GcJCbyI+e471vV95x1g4ECgdGmrvqwQqpPP\ncZHXw/YJvZ7B+ebNwLZtgLd3MXdOODSpk24G+XC3fYaFd777Drhxg+UbR44EqlRRu2dG1tzPzp7l\n775qFfDss0xvadPGKi8lhCbJ57jIq6B9IiMDGD0auHyZE0RtbX6TsH2Sky4cSunSwMsvA4cOAevW\n8cO3YUMGrL//Dty/r3YPgYCAAItuLyuLv2u3bsDTTwNeXsw1X75cAnTheCx9fAn7deQIcOAA14GQ\nAF04EhlJF5px9y6D2KVLWVZrwABg8GCgUyfbXpzn1i2uBvrDD0DVqkxpGTCANeaFEEJQ3nN7bCzw\n55+88/j33yw/K4QaJN3FDBKk27/ISGDFCn5AX77MEfZ+/bi6qYuL2r17NEUB9uxh7v22bez7W28B\nLVuq3TMhhNCmnOf2bduYAtmtG9fdaN4c6NNH5Q4KhyVBuhkkSHcskZFcvGfdOt72bN+eFU+6dgVa\ntACcndXuoVFEBNN1fvmFk2Ffew0YNgyoUEHtngkhhLbpdDqkpSn45BOWVly2jNWuhFCbBOlmkCDd\ncSUkALt3A7t2sUVFMR2mUyeOUrdowfKFxenmTeCPPxicnz/PUfNRo3gxIaXBhBDCNDqdDs2aKfDx\nARYuBCpXVrtHQpAE6WaQIF0Y3LzJtJIDB4CTJ4GQEKBGDeCJJ3h7tF49LqRUpw5QtqxlXjMx0TiR\nae9e4MwZlpEcNIh1ziXXXAghzKfT6bBkiYJhw2SAQ2iLBOlmkCBdFCQzk6PZhoD90iXmtIeFcVSm\ndm1WVfHyAjw92Tw8GMCXLm1sJUsC8+YtRu/eIxAby8mfUVHAsWPAlSscte/QAejYkSvflSmj9m8u\nhG0JDAxEYGCg2t0QGiLndqFVEqSbQafT4ciRI2p3Q9iQrCwgJqY0oqJKIz6+BO7cKYn4eLaEhBJI\nS3NCRoYO6el8zMhwwpUrx9GlSxO4u2dktwYN7qJ+/XsoWdLmDhshNKVt27byOS5ykX1CaFXbtm1V\nCdI1uM6jadzd3dXugrAxHh5A48YAoABI//9WsPr1O+PHHy/k+W6p/29CiKKSz3GRl+wTQhjJYkZC\nCCGEEEJojATpQgghhBBCaIwE6UIIIYQQQmiMqkH6qFGj4OXlhSZNmmR/786dO+jevTvq1auHHj16\nICEhQcUeCkf29ttvq90FIeyWHF9CCFtVXPGrqkH6yJEjsXXr1lzfmzFjBrp3746LFy+iW7dumDFj\nhkq9E47unXfeUbsLQtgtOb6EELaquOJXVYP0J5988oGZ3Bs2bMDw4cMBAMOHD8e6devU6JoQQggh\nhBAPKK74VXM56TExMfDy8gIAeHl5ISYmRuUeCSGEEEIIUTBrxK8mB+mpqalIS0sr8guaQ6fTQSdr\nAwshhBBCCBthqfi1wMWM9Ho91q1bh5UrV+LQoUPQ6/VQFAXOzs5o164d/vOf/2PvvsOjqNo2gN8p\ntNClkwChh96LBQSkCYJiAcGChdfe4FX041UTGzZUBEHFggVEKaIoFroUKaFK7yUECIQa0jc73x+3\nyyaQkCzZ3ZndvX/Xda5NKNmTZM7MM2ee85y7cMstt7g9iK5SpQqOHTuGqlWr4ujRo6hcuXKu/278\n+PEXPm7fvj06dOjg1n6IiIiI56xevRpr1qwxuxsil7iSY7Og8asrgow89jnt3LkzOnXqhP79+6Nl\ny5YoVqwYACA9PR0bNmzAnDlzsHz5cixdurRQHThw4AD69euHzZs3AwBGjhyJChUq4Pnnn8dbb72F\nM2fOXJJ8HxQUhJ07L94JUsS9xo8fr8VtIh6i8SUXa9iwoa7tYkkNGzbExeHylcSvrsozSM/IyEDR\nopff/jw9Pf1C8H4lBg8ejL/++guJiYmoUqUKXn31Vdx8880YOHAgDh06hMjISEyfPh3lypXL2WkF\n6eIFumCIeI7Gl1xMx4RY1cVB+pXGr67KM0jv06cPhgwZgltuuQWlSpUq1Ju4m4J08QZdMEQ8R+NL\nLqZjQqwqt5l0b8gzJ/2hhx7C999/j+HDh6Nr164YPHgw+vbtm+/suresWFEClSrZUKlSFkqXtiM0\nz+9EREQKy24HsrIAuz0INhtf+TlgGEGw23N+bBjZG/9PRgaQkhKMU6dCAQxAbGxxFCtmIDTUQJEi\nQPHidpQta0epUnYEW672mHiDYQCqFyFCec6kOyQnJ+OXX37B999/j5UrV6JPnz4YPHgwevbs6a0+\nXoKLVe3Z/wQAv42QEAPFitlRurQNlStnIirqPFq2TEK7dmdRpow9ty8nkquOHTti1apVZndDJE+G\nwaA3KSkU58+H4Pz5UCQlheD8+RCkpIQgNTUEqanB/34cjLS0EKSnByMjIwjp6cH/fhyMzMygfxs/\nttnYsrLYbLYgGEYQQkIMhIQYCA42EBwMhIYaCAoy/u1L0L+BfBAMAxf+r70Qp92gILbQUAOhoXYU\nLWqgePEslChhR9myNpQrl4kKFTJRuXIGqlVLR2RkKiIjU2GRuSRxUceOHRESYkdYWBbCwrJQsmTW\nvx/bsWZNWQDAe+/tRI0aaShXLhOlS2cpoBev6Nixoykz6fkG6dlt2rQJQ4cOxebNm5GVleXJfl1W\nUFDQhR9WZiZw5gxw4ACwbBkQGwvs2gUcOQKcPs2ZG4AXs5AQ4KqrgKgooEsXYPBgoFEj074Nsbjs\nx5mItxgGz11xcTyPHTvGdvQoX0+cAE6eBBIT2YoUAcqXB8qVc7ayZYEyZYBSpZytZEm24sWBEiX4\n6mjFigFFizpfixYFQkP5tUND2UJC2L/Dh4G//2bbuBHYvh1ISwMaNuT/c/S9WDGgXTuea9u1A6pX\nBypWZF+Dgzm+bDYDiYlAQgK/t61bgfnzgaVLgfr1gfbtgdat+T0dP87vPTHR+XryJHD2LJCUBKSm\nAunp/PkFB/P9S5UCKlQAqlUDIiOBBg2A5s35dStWNPO3LLkJCgpCRoaB8+eBc+f4e3W83nMPf+/N\nmwPJyfz9p6Tw91uxIlCp0qWtQgW2q65yvpYqpZl6cZ1Z8UC+QfqxY8cwffp0fP/99zh69CgGDRqE\nwYMHo0WLFt7q4yVc+WElJAArVgALFwLz5jGYL1WKwX1yMi8+1aoBHTsC990H9O4NPWYVAEBMTAxi\nYmLM7ob4oaQkYO9eYM8evu7dCxw8yOD20CEGxDVqAOHhQNWqPEdVrcpWubIzMKlQgUG2Jx04APz+\nOwPnv/9mYHTNNWwtWjAo/+UX4LffgG7dgFtvBTp3BmrWvPzXvdz4Sk8HVq5kwD5jBlC6NPDUU8Cg\nQfl/vykpwI4dwLZtnLDZs4c/02PHgFOngPPnef4PCgLCwnjTUK0aULcu0LQprwUdOvA6Id7laiCU\nkeG8acutnTrFG7nsrxkZOYP27B9XrMhWtizQti1Qu7YHv1nxKZYL0idNmoTvv/8eO3bswG233YbB\ngwfj6quvtsTmQoX5YZ07xwvO7Nm8qNSowQvA8eM8kRsGZ1y6dQMefZSzOCIirjIMzn5v28bZZsfr\njh0M0uvUAerVY3BYty7POzVqsJUta16/09MZkP/+O9upU0CvXjwnXnst+3z2LDB+PPDpp0CVKpzg\nGDzYM7PTdjvw55/Ahx9y5v6hh4BHHuHM/JWy2YAtW4C1a4F//gF27uT5PyGBvxubjTdKZcrw+6tT\nhwF8+/bA9ddrFt5TvBEIpaXxmL44gHd8/M47zn+7dKnz5lgz8IHNckH6/fffjyFDhqBbt24IcTzn\ntAh3/bDS0jjDPmsWg/arr+Zj2Z07geXL+ai5RAmemB98ELjzTmiBqohcwmZjEL5xI9umTWxBQUCT\nJkyra9yYr1FRnCG30gU/MxNYsAD4/nvOikdFATfeyNa6tfPpYmIi8MEHwCefAP37AyNGAM2aea+f\nO3bw5uD774GHHwb+7/84yeJuKSnAqlXA6tUM4nfvBuLjnTOxwcF836pVnQF8hw5A166ckZUrY4UU\nw88/5xgoUiRnqhnA33eVKs5Xx9qHzp2B224zr8/ieZYL0h3sdjumTp2K/fv34+WXX8ahQ4dw7Ngx\ntG/f3lt9vIQnfljJyXys+sUXPCHfcw/bokXAlCnA5s28EDdsyFmjp57y/GNmEbEewwD27QPWrGGL\njWVgHhEBtGrFFJCWLflataq1gvHsDIMzhVOnAj/+yHPboEHA7bdfOkt9/Djw7rs8P95xB/DCC+am\nAsTHA6NGMR3m9deBoUOdOfOelpHB3/mKFcCGDbxeHD7sXAMVEuIM4OvWZQ51x44M5ApZMtnvWSFI\nz8v5886gvVMnz77XuXOeufmUK2fZIP2RRx5BcHAwFi1ahB07duDUqVPo2bMn1q5d660+XsLTP6yd\nO3kxmjyZj3f/+1/guus40zR2LPDXX5xpadCAgfzw4cxtFBH/k5HBYGz5cgZmK1Zwlq1DBz5la9cO\naNPG3BQVVyQkAF99xRnD4sWBe+9lcJ5bDnl6OjBuHPD223yS+PzzTMexithY4JlnuGj0gw+YimKm\njAzOwDsC+D17eENx+jSfVmRPoaldmzPwbdvy+lKY9B1/YeUgPbsZMzgW9u/P+ee1arFFRrLVrOlc\n2+C4Wc/v26tShYutxVosG6S3atUKGzZsuPAKAC1atMCmTZu80sHceOuHlZwMfP01T/7lyzNYv+02\nprysWMHctUWL+O+iopjD/uijSokR8WWOmdLFi4ElS5jyULcub9ivvZYBVX6LIq3GMDjJ8MknPGfd\neivwn//wRiO3mX7DAH79leksUVHAe+9xUsKKDINB07PPAn37csbfios+09K48Hb1aqZCZQ/g09P5\neyhZkosYa9Zk7n/z5rwJbNcOAVFW0leC9Owc6xu2b+fi7wMH2A4eZAO42PvgQf5+T5xgGq34FssG\n6R06dMDff/+Ntm3bYsOGDThx4gR69ux5IWA3g7d/WFlZzFF77z3mqf/vf5xBL1KEf79iBR+5LlnC\n2ZJWrXhxGzRIlWJ8maq7BAa7nXnH8+ezrVrF8n9dujDH+LrrfDdNITWV6Sxjx/Jc9PjjXOBZpkze\n/2f7ds5OHzrECYrevT3TN3ePr7Nn2e+lS/mkwNMpCe7kOAYdZS137mQKTWIi0yzsdk7+lCrFRavh\n4cyFb9KEgXybNv6RC++LQfrlGAYn8Y4cYToZwKpIbdowTmjZkr9HX3kKF8gsG6RPmTIF06dPx7p1\n6zB06FDMnDkTr7/+OgYOHOitPl7CzIG8dCnwyit8zPW///FRsSNYB7gAdcwYzpaEhgLduzOAb9nS\nlO5KIfjbBUOcjh5lxZB58zjDXL480KMHx+v11/NzX5aQAEycyJnzdu2Yktet2+Xz4zMymNby4YfA\niy8yoM9+bnM3T42vOXNY/WXIEJ57/WHt0LlzLEm5YQNvovbtY+B38iSDQJuNv9vixXkDVqECc+Jr\n1GAQ6Fi0XL++tWfk/f2ce+oUb8I2bGDbuJGz7sHBXNNSo0ber5e7sRbPs2yQDgDbt2/HwoULAQA3\n3HADGpm8A5AVBvKyZQzW9+7lBW3o0JxpLjYbMGEC2549PGneeSf/jz/MeAQCKxxn4h42G2fIf/+d\npVcPHGBA3qsXg/NatczuoXscOsR0j6lT+STv6aeZrpKf2FhWsKpZE/j4Y+/knXtyfCUmMvVw2zZg\n+nTOOPszm42Vb9av54ZQ+/czleb4cabTnD/Pm7DsGz2FhXEGt3x5Z1AfHs6gMCKCx0JkpHefIgXi\nOdcw+BTo8GG2uLhLX+PiuJ6hWTNn+lPr1qzvX6aMdRen+xPLBelJSUkonc/y4oL8G0+w0kBevpxB\n+okTwJtvAv36XTpgEhOB6Gjghx94Jx0VxXSYBx5QOoyVWek4E9edPs2g/NdfgT/+YCDuKCt49dX+\ntXZk717grbdYpWXYMJ5fqlTJ//+lpAAvv8wKVu+/z1QYb13wPT2+DINrip57juk+d93lsbfyGSkp\nvHHZuZOTR3Fxzl1sT5/mjH1yMgN6m41pNgCvU44daB271JYsydzqsDDnrralS/PzsDB+7Njltlgx\n5/8LC+P/c+xim/21RQudc3Pj2IV440beUMfGcl1DQgLXOjg2YapUyflxmTI5W+nSuX8eFqYgvyAs\nF6R3794dDRs2xM0334y2bdviqn+nf0+dOoXY2Fj89NNP2L17NxYsWODVDgPWC54Mg7NzL7zAmYl3\n3mHeWW5iYxnUL17MgdGtG/DGG9o0yYqsdpxJ/vbsAX7+mWtI1q9n6kq/flxQGB5udu/cb+9ePp37\n7Tempzz1FGdFC2L1aq6taduWKS6VKnm2rxfz1vjatIllJXv14rqiYsU8/pZ+w27nbHxcHNNrobcZ\nggAAIABJREFUHAG9I6hPSuIs/fnzvAFITWWAn5nJZrM5g/3szTCcVU6yHwJ2u865rkpP50SgY+dV\nx8fnzvH3c+6cs2X/PCmJM/g2G5+WlC+fe7vqqkv/LCIi8DICLBekA8CiRYvw3XffYcWKFThy5AgA\noHr16rjuuutw1113oYtJdYKsGjxlZQHffsuZqbZt+di5bt3c/63dDnz2GRdm7drFO9+77wZiYpR7\nZhVWPc7EyW4H1q0DfvqJwXliIjfZ6dcPuOEG/y2Nevgw8NprwMyZDMyfeabgi88yMzkx8PHHTMe7\n/XbP9jUv3hxfZ84A99/PQHPGDN+rzhModM71vowM3nBd3E6duvTPEhO5uBngBEGdOub23ZssGaRb\nldUHcmoqH6++9x4fPf/vf5ffmCAxEXjpJabDnDnD2rkjR3Lhk9JhzKPqLtaUmcm9CmbPZmBeujRw\n883ALbewbrk/j5njx5lW9/XXLKE4cmTBZ84BTgjcfTdnwb780tza3N4eX4bBRf3vvccdS1WL2nqs\nfm0PdAcOODcxe/pprrPLq4yrv1GQ7gJfGchHjnBXvHnzgNGjWQkmvwBixQoG7MuWMUevVy/Oevn7\nwieRy0lJ4TiaPZs55nXrstb3LbcUbGGkr0tOZs742LG8eR81iovGCsowgE8/ZardK68Ajz0WGBfW\n3CxcyJ/hm29yXZBYh69c2wOZYXBdw4wZXMuydy8XaU+caHbPPEtBugt8bSCvWcO7zqwsPl5u1y7/\n/+OoDjN+PMttVakC3HcfZ+WtuFGHiLudPQvMncvFkPPns7awIzCPiDC7d96RlcWa39HRrNc+erTr\nj5hPn+as+969wLRpgXFTk58dO4CbbuLx9NZb/v30xZf42rU9EBkGc9rj44FJk7ieBeC5yp/HkVnH\nph//SK2jfXvmcT3xBPNlH32U+V6XExrKwH7PHuaf3ngjc0jLlGHN9alTnSvvRfzF8ePcrr5PH5YB\nnDaNiz737uVOmU88ETgB+h9/cKx//TUwaxZTNFwN0Feu5KYp4eEsQakAnaKiuHB29WruIp2cbHaP\nRHzDtGlcaNq+PTfgqlYt/z0Y5MrlG6SPGDECW7du9UZf/FpQENNdtm9nuanGjYHJkwsWaFevzvzR\nM2cYqJQrx1n1kiU5G7R+vce7L+Ixhw5xNub667nZyvz5HCuHD7NKy/33c2F1oNixgzcpTz3FzXj+\n+ot5n66w25nOMWAAMG4cf76qapJThQo81sqX5+6k8fFm90jE+u68kxMHV13FtnYtU8gUpHtGvuku\nn332Gb766itkZmbigQcewODBg1HW5D1s/eGR2Lp1zAstUoS5oq7mnDvSYSZOBHbv5oXmjjtYHaZq\nVY90WcRttm9nGsvs2VyM1L8/Uw+6d/ePHSKvxOnTwKuvskLUqFF8anAlu0MeP87FoWlpwHffBc6T\nhytlGNxp9ZNPWFff5L36Apo/XNsDRWoq18tNmcL9FYoUYQZA9lanDtMT/YFpx6ZRQNu3bzeef/55\no0aNGsbgwYONRYsWFfS/up0L3ba0rCzDmDjRMCpWNIwXXzSM1NQr+zonTxrGU08ZRuXKrD4bGWkY\nMTGGkZzs3v4GmujoaLO74Deysgxj9WrDeOEFw2jY0DAiIgzjyScNY9Eiw8jMNLt35rLZDOPjjzl+\nH3rIMBISrvxrLVliGOHhPJ9Y/edqtfH19deGUaWKYaxYYXZPApe/XNsDSVCQo+p97s1f4hCzjs0C\nLRzNysrCL7/8gsmTJ+Pw4cMYOHAgli9fjrCwMPzwww8ev5G4mL/dbR85wvzzTZs4q96165V/ra1b\nOZv+xx/Ms2zShDP2//mPf+2w6A3+dpx5W0ZGzlKJZcuyVOKtt3IfAT0eda5VKVWKaSktW17Z13Gk\nt3z0ER9F9+zp3n56ghXH1x9/MNXq88/5dEe8y4rHhORtzBju6DtuHPDkk2b3xrMsW91l+PDh+OWX\nX9CtWzcMGzYM7du3v/B3DRs2xM6dOz3eyYv560CeM4cX7BtuYC3fwu7otWQJH0ctXcqV1y1bciDd\nc49/r8J2F389zjzpzBkGOnPm8DUqio87b74ZaNjQ7N5ZR0IC8PzzwIIF3PTszjuv/KblxAmO6ZQU\nLurylZ1VrTq+1q5lgB4TAzz0kNm9CSxWPSYkd+3aserWxIn+H1NYtrpL8+bNsWnTJkyaNClHgA4A\nq1ev9ljHAlH//pwJL10aaNaMM5CF0aULF0alpnKjpBIlOKNerBjQsSNzyVQhRgpr3z7OpHTvzp0c\np07l06CtWzlTPHKkAnQHm42LOJs2BSpXZm7+4MFXHqCvWMGLZMuWXFTuKwG6lbVty4mNd97hrq6K\nGUVyN24c66WHhHAiRtwv35n0devWIeiiK0jZsmVRq1YthJqUPxEId9srVnCjjRYtWCu9ShX3fF27\nnYNq7FjOGBkG3+PBBzlrpJQYp0A4zq5EZiaPz7lzubHQ6dOsRnLzzQzUS5Y0u4fWtGIFU88qVWJa\nSmHKIRoG8MEHXPD45ZcsU+lrrD6+jh3jZnLdu/OxvtKzPM/qx4Rcau9eoF49Phl8803/HSeWTXfp\n2LEj1q1bh+bNmwMANm/ejCZNmuDs2bP4+OOP0atXL690NLtAGcipqdwdcPJk7jY4ZIh7B4Ddztn6\njz5iDeWMDM54DhrEHPly5dz3Xr4oUI6zgjh8GPjzT7b583lS7tuXrU0b/3/UWRgnTvAC9uefHMcD\nBxZuHJ89y7KUhw8D06cDkZFu66pX+cL4On2ax3ijRty4JSTE7B75N184JiQnu50lpf/v/4ChQ83u\njedYNt2levXq2LhxI9atW4d169Zh48aNqFOnDubPn4+RI0d6o48Bq0QJ7oY3dy5nzAYM4OyOuwQH\ncyOPxYt5QzBvHksmffABSzpWr85gYMsW972nL4mOjja7C6ZJTWW+9HPPMfWqRQsG5336cEvo2Fjm\n7LZrpwA9L3a7s7xquXJMbRk0qHAB+saNvCmqXh1Ytsx3A3TAN8ZX+fI8Lx46xN9derrZPRKxluBg\npjiOGMHX7duVIuZO+c6kN2nS5JLNjBx/1rJlS2zcuNGjHcxNIN5tZ2SwhvLnnzOnddAgz77f7t2c\n9fv1V87YhYUBrVuz/vLQoYFby9pf2e0MAOfPZ3C+ahXQvDnQowd3u23bVrOIrtiwgTsLBwdzp+AW\nLQr/Nb/4AnjhBeaBDh5c+K8nBZeezieZ58+zvr9SujwjEK/t/sBuZ/Wu8+f5+fz5TBPzJ5ZNdxk4\ncCAqVKiAO++8E4ZhYPr06Thx4gSmTJmC6667DrGxsd7q6wWBPJDXrGGQ3KwZNzOqVMnz75mSAnz2\nGStHbNrEC1Z4OHeIHDaMC1TFt9jtwObNrAC0ZAkXylWuzKC8e3f+TsuUMbmTPigpCXj5Zc4ovfkm\nn0QV9klDSgqrPq1eDcycqc12zGKz8Xy3Zw/w228aH54QyNd2X7Z8OXdBnz4dqFHDO3GJt1k2SE9N\nTcWECROwYsUKAMC1116Lxx57DMWLF0dycjJKly7tlY5mF+gDOTUVeOklBgKffOL9VdXr1zOPffFi\nPgYODmaaTM+evIFo29a7/ZH8ZWTw97Z8OduyZUDFigzGHa1aNZM76cMMA5g1C3jmGY6Dt992z4Vq\n927g9tt5U/7pp5rBNZvdzhumtWtZYrSwZXIlp0C/tvuqxYtZ6GLDBv9dy2bJIN1ms6FHjx5YvHix\nN/uULw1kWr6cG2907cpqLSbcL8FuZ0rMN9+w3N6xY0yLiIwEOnUC7rqL/VPesncdO8aZ19Wr+XtZ\nuxaoXx+49lrguuv4u1G5PvfYt4+B28GDvGnu1Mk9X3fWLKbMvPoq8PDD/ls1wdcYBvDss8DChXys\n74+zhmbRtd13DR/O9Rtjx3KvF3+75lsySAeAG264AbNmzUI5C90eaSA7JSVxcCxaxED5uuvM7Y/N\nxoWuP/zA4PDwYQbylSpxNrBnT27cUrOmuf30J6dOcQZj/Xou6Fy9msdF+/ZAhw7A1VezlS1rdk/9\nS0YGNx177z0usB0+HCha1D1f9/nngZ9+YrlUPZmyHsNgWtOsWQzW9RTKPXRt912GwfPV66/zaf9/\n/sO1c7Vqmd0z97BskN6/f39s2LABPXr0QMl/n7UGBQVh3LhxXulgbjSQLzVnDmfbhg5l2cZixczu\nkVNsLHPVliwBdu0Czp0DihQBqlblpi5durByTf36Zvc0p5iYGMTExJjdjQvsdmD/fuaSb97MhZ7r\n1wMnT3Izm1atWG2lfXv+LDXz6jlLlwKPPMI0r48+cl+Vlbg4XtgqVAC+/tq/0ymsNr6uxOjRwFdf\ncbG1Jh4KT9d23+cI1v/zH17rARa7eOopc/tVWJYN0r/66iv+w3+v+IZhICgoCENNLIipgZy748c5\nMOLimK9u1QVmaWnA77+zrV3LdIGzZ/l4rFw53nk3a8bUjF69zLsTN+s4y8jgBhE7d7Lt2MHdO7dt\nY/DWtClbq1asuFOvnv89WrSqEye4g+qCBbzwDBjgvpuhP//kTfbw4ZyZ9/ffqb+cx8eOZcWdRYt8\nuySmFfjLMRHI7HZnJbBbbwWSk/lksGtXc/tVWJYN0gEgJSUFhw4dQlRhtshzIw3kvBkGK7GMGsXH\nTr6Sy2qzMU1jwQK+7tzJvOqUFPa/ZElWH4mM5IZLjRuzXnSrVp4rB+mp4ywrC0hIYCrQgQOcHd+3\nj6/79/Mmq0YNfp9RUc7vt2lTpayYxW7npmKjRnGdxSuvuG8NSFYW886/+AL47jugc2f3fF2r86fz\n+IQJwDvvMFCvW9fs3vgufzomAtk//zAN8KefmAp27bXO1qCBb8QkF7NskD5nzhw899xzSE9Px4ED\nB7BhwwZER0djzpw53urjJTSQ87djB+v6RkTw4u+ri5vsdm6mtHQpUzt27ADi45mHnZLivGsvUYJB\nU/nyDOarV+f3Xq0aP65RgzPyVasWfIayoMdZZiafBJw543xNTOSTjRMn+Hr8OHDkCPuekMA0hvBw\n3nTUqQPUru1sdeq4J7dZ3GPzZi7gzMzkwtBWrdz3tY8dY9BvGAzQq1Z139e2On87j0+axImRBQsY\niIjr/O2YCHRZWbx+L1jAAhNLlvDPP/oIePxxU7vmMrOOzdD8/kFMTAxWr16Nrv8+q2jVqhX27dvn\n8Y5J4URFcUOal15ivvLkyVy06WuCg7mpTvPmuf99SgpTZv75xzkLffQoA/pFi7iAJT2dAVZWVs6v\nGxzMAD80lHf2wcHOVwby8YiMZP58aChfg4P5nqmpbCkpTE8pW5apOo7XihV5s1CpEvteqRKD8vBw\n3jgoCLe+8+c5wz15MvDaa0wlc+eGTosXc3OwYcO4CFGbRfm2hx7ieaJbNwYlFnnwLOIxmZncN+DQ\nIWeLi+OEVGKis2VlcWIqKoqfa4+Bgss3SC9SpMgllV2C/T1Z0k8ULcp6zb16sVTjkCGc6fGnADEs\njOkBBU0RSEnhLHxiIl9Pn+bMt83GYDszkx+npQHR0d+hS5dncfIkF2ceOcKZ8q5duQtnjx4MvsPC\nfPPxneTOMIDZs1nzvEsXzgRVqeK+r5+VxQWHEyeyIlOPHu772mKuBx5wBurz5wNNmpjdIxH3OHuW\nmxlu3OhsO3bwiXWtWlw4XbMmr8XVq/PaWLEim66RVy7fIL1JkyaYOnUqbDYbdu/ejXHjxuGaa67x\nRt/ETbp144B64AHmhE2bxsWGgSgsjC0iIv9/a7efx8XFJw4eZCWd6dOB//6Xu64++iiDdp2EfN/e\nvcCTT3KtwLff8vfrTgkJwD338OnOunW8mAWq6Ohos7vgEffey0C9e3fWjW7WzOweiVxeVhZTMR0p\nmUeO5Gx79zJls1kzoEULlvZ9+GF+HhZmdu/9W7456cnJyXjjjTcwb948AECvXr3w0ksvobinVusV\ngPLWroxhMBfs1VdZkeCuu8zukW87cwb4+Wfg/ff5+ciRLJ8Xmu+tr1hNWhoX/o0b596a59ktXMgA\n7v77gZgYHSf+7vvveRz98QcDG8mfru3eYRh8iuwoIZqUxBnviAhOHISH89XRIiO5IDqQU/Isu3DU\nijSQC2fTJm4o1L49qxKUKmV2j3ybYfBC/PbbnIH973+Zv2zifay4YO5c4OmnGUh98IH7613bbKwG\n8+WXrH3evbt7v75Y14wZfDLzxx9cGySXp2u7Z+zezXPb9u2cKT98mHupREXx3HT99dbaW8WKLBuk\n79y5E2PGjMGBAwdgs9n4n4KCsGjRIq90MDcayIWXnMyLx8qV3B00r4WZ4prVq5n3v20bS1DdfLPS\nYKzqwAHmnW/bBowfz7Ub7nb4MNeCFC/O9Bl35raLb5g1i5UsfvuN+xpI3nRtd7+vvuLE0dNPM901\nIoIz5Zqcc41lg/TmzZvj0UcfRevWrRHy77OOoKAgtGnTxisdzI0Gsvt8+y0wYgTwxhuc/VVA6R7z\n5zMArFaNqUVNm5rdI3FITXWmtowYATz7rGdmkX7+mXmbTz/NzTy03j5wzZ7NHWp/+437O0judG13\nn40bOXu+aBHLHyrlqnAsG6S3adMG69at81Z/CkQD2b127AAGDmQlgk8/VXkkd7HZWFf71VeZq/7a\nayzPKOYwDG6uMWIE0LYtMGaMZ3azTU1l4P/bb6x9fvXV7n8P8T0//8wyjXPn8viTS+naXjhZWSxs\nMHYsF3s+/jhvDsuXN7tnvs+sYzPfuZ1+/fphwoQJOHr0KE6dOnWhif+IimKaRpkynOXZuNHsHllD\nzMWlXVwUGgo88QTzAG02zqbPnu2evolrtm9nOsuLLwKff85cYU8E6Fu2cK3HqVMcRwrQ81bY8eVr\nbr6Zx17fvkBsrNm9EX/yzz98WhcZyaeEjz3GfUP+7/8UoPu6fGfSIyMjEZRLDsT+/fs91inH+5Yp\nUwYhISEoUqQI1qxZc+HvdLftOd99x8fzo0dzk5VATn9x93G2bBl/ps2ascpOIO0uaZZTp/gkY+pU\nBuiPPcZNqdzNMPjU5OWXgXffBYYODeyxUxCBeh7/9VfgwQc549mhg9m9sZZAPSauRHo6d7n97DPW\nMB8yhBXblFrpGbkdm5eLU932vlat7lK7dm2sW7cOV1111SV/p4HsWTt2AHfcwWoEH38cuAtMPHGc\npaUx7eWzz4C33mI5PgVz7mezMXXr1VeBW2/la6VKnnmvhAQGXceO8SZXW8IXTCCfx3/7DbjvPgbq\nHTua3RvrCORjwhU//si0vaZNWTK2UyetefG03I7Ny8Wp7pLnr/Wdd9658PGMGTNy/N2oUaM81qHs\nNFjN4Uh/KVKEj+63bjW7R/6jeHEu0p03j+Uvb7yR2yiL+/z5JxdJzZ7N7dk//thzAfovv/BmtmVL\n4O+/FaBLwfTpw3Kc/fuzwpaIKyZM4MZ6s2ezfKICdPN4Ok7N81c7bdq0Cx+PHj06x9/9/vvvnuvR\nv4KCgtC9e3e0bdsWn332mcffT3IKC2Nd55EjuTX61Klm98i/tGwJrFoFXHcdy7J99RVTJuTK/fMP\n0Ls31wG8+SYr7Hhqt8fkZFZueeop5re//rr7Nz8S/3bjjcA33zBXfcUKs3sjvmD/fs6iFynCdMmM\nDLN7FNi8Eada9v5rxYoV2LBhA37//XdMmDABy5YtM7tLAem++7hT4iuvMJ83Pd3sHvmPIkWYJ71g\nAVfj9+vHLZjFNYcPM22oRw8uytu6lTOUnkoj+vtvoFUrpi5t3MgbLZEr0bs3MGUKMGAA16yIZJeZ\nySot8+bxfFanDp/A9OjBmfSSJc3uYWDzRpxq2Y2pq1WrBgCoVKkSBgwYgDVr1qBTp04X/j57ZYAu\nXbqgS5cuXu5h4GjenNUIHniAuW+eqoxhNdHR0V55nxYtgDVrmAbTsiU3Qbr7buWq5+fsWVYy+OQT\nzmrv2gWULeu590tPB6Kj+dRjwgTgtts8916BwFvjy+p69uRahttu47n1+uvN7pH3LFmyBEuWLDG7\nG5bVpQs3XXOk63XowFKe4nkFOTbzi1PdIc+FoyEhIQgLCwMApKamokSJEhf+LjU19cLuo56QkpKC\nrKwslC5dGsnJyejZsyeio6PRs2dPdlqLS0xhGNwc4e23gcmTmVcp7rV+PZ9eREZy4eO/5wDJJiWF\nQfK77/IYfO01oEYNz77n+vXAvfcC9evz91K5smffTwLP4sXcT+GHH4CuXc3ujTl0bc+peHEgMTFw\nizdYycXHZn5xqrvkme6SlZWFpKQkJCUlwWazXfjY8bknJSQkoFOnTmjZsiU6dOiAm266ye3fuLgu\nKIgrymfN4qYc0dHcPEHcp3VrYO1azq63aMEdYXXNosxMzprXr898/iVLOKvtyQA9M5OpXr17Ay+8\nwHxQBejiCV27ciZ90CCmGIrUq6djwaq8FadatgTj5ehu23zHjgF33sk7/alTgQoVzO6R/3HMqteq\nxeA0PNzsHpnDZuMx9tprQN26XKTZrp3n33fdOqZ4Va/OkpkREZ5/T5Fly5j68u233IArkOjantNf\nf3E38Hvv5R4MpUub3aPAZdkdR0VyU7UqFzw2a8ZdSteuNbtH/scxq966NXPVJ0wIrCcXmZmsMNSw\nIWfMP/+c5RU9HaCnpXGnvj59gGefZU1rBejiLZ06AT/9BNxzDzB3rtm9ETNdfz2weTNw/DjQti0w\ncSLPRzt2BNa1IJBpJl0KbeZM4NFHtUupJ23bxsWRmZnMiW7RwuweeU5GBisYjB7NmfOXXwY6d/bO\ne69YwY2JHLvCVqninfcVudiaNaz4NGkSyzQGAl3b8zZ1Kjdl27XL+Wf6UXmPZtLFZ91+O7B8OcsI\nDhvGmUh/kL2CkNkaN+ajz2HDWH5r5EjW6vYnjmottWvzxm/KFD6t8UaAfvo08Mgj3Gl39GjmBitA\n9ywrjS8rat+es6YPP8x1QBLY7rqLVdYcKVDly/PPxo9XsO7PNJMubnP+PHN49+3jRcXXyzRa9ThL\nSOAC3r/+Yn72vff69o5zhw/zBm/yZG7w8uyzTO/xBsNgNY0RIzhb+eabQLly3nnvQGfV8WU1mzZx\n4fLYsVxU6s90TBSMYQA7dwIdO3JyIyUFyFaATzxAM+ni80qVYsAzeDDruc6fb3aP/FOVKnz0OXMm\nH4W3bcvybb7EMPj0ZcgQ1uHPyuJC2SlTvBeg793L4Gf0aN5UfvyxAnSxnhYteC4dPpw7lEpgS0ri\nebJRI6BJEyA+XgG6P9NMunjEkiUM1p96iqXrfDFP3ReOM8NgasYLLzCP+o03gKZNze5V3s6f5w3G\nxIlAaip3sR06lI9uvSU1lWk148czbWj4cO7+Kt7lC+PLSnbsYKrbSy+xBK4/CqRjwjCAc+eAEydy\nb6dOAWfOcKbc8Xr6NNNJixXjRNjvv/vmtdUXmXVsKkgXjzl8mPnq1apxIWCZMmb3yDW+dJylpXGh\n43vvcWb9+eets1293c4FmVOmOHdUfPxxoFs376bpGAYwZw7wzDOsSPTee76fkuXLfGl8WcXevcAN\nN/DG8umnze6N+/nyMWG3M7DOK+i+uCUmsoRxpUo5W8WKfK1QgU/2ypbN+VqhggJzMyhId4EvD+RA\nk57OoGjRImD2bC6A9BW+eJylpfGG6N13mRbz/PPATTeZk7O+YwcD86lTgbAwlpS76y7P7w6am507\nGdQcPMgZ9O7dvd8HyckXx5cVHDzIQH3YMD5B8ydWPybOnAH27+e6q4tfDx7kee7ioDuvVrEig3Tx\nDWYdm6Fef0cJKMWKMdf3q684gzpxIito+ILo6Gizu+Cy4sVZDWLYMOZZv/oq8MQTXHA2aBBnkD01\nC2OzAX//zdrOc+cCJ08y5/zHH5lnbsbsz+nT3ATpm29Y+/zJJ4GiRb3fD7mUL44vK6hVi4vGu3fn\ngsFXXtHMqjulpADbt7Ps7bZtwJ49zmA8M5PVp+rU4WujRtxPoU4dIDKSQbqIO2kmXbxm/XrupHfb\nbcBbbwGhukX0ii1bgO+/56Jew2CwfuONDJxLlbryr5uWxo021q5l0DBvHi9cffoAffty06GQEPd9\nH67IyOAN4ejRwK23MpBRSUXxJ8ePM0e9e3dgzBj/CNTNuLanp/Np39KlnGSIiwMaNOBT30aN+LEj\nKK9Y0T9+zuI6pbu4QEG67zp5kikP6ekMHBU4eY9h8Ebphx+4sHfLFs7+tGnDVqcOt53O3rKyGAwk\nJPD1+HFg924G5jt38gLWti1wzTWslFK9uvnf4+zZTPOpX59pP02amNsnEU85dYo3xc2aAZ98Yt5N\nsbuYcW2fNAn43//4xO3aaxmYawJJLqYg3QUK0n1bVhZnNidPBqZPB66+2uweBabMTGDrVmDdOrZD\nh1jeK3sLCeGNVOXKzla7NgPz5s2tVfpr4UJg1CjO8I8Zw1lGEX+XlMQa/5UrA99+69uVisy4th87\nxlTMzp2BDz9UyorkTkG6CxSk+4dffuEW7NHRLMWnx4hyJVau5EzY4cPMwR840Lc3dxJxVVqac63P\n9OnWunl2hVnX9qQkVpxatYoz6126eL0LYnEK0l2gIN1/7NnDHPXmzYFPP9UshhRcbCyfyGzezBu9\ne+/VY2oJXJmZHAMJCcDPPzNdzdeYfW3/+WcutL/6aqa/NGxoWlfEYrTjqASkevU4Ewpwi+Ndu8zt\nT3YxMTFmd0EuYhhcpNqzJ2/uevfmMfPAAwrQfY3Gl3sVKcKSp/Xrcw+CEyfM7pHvuflmlo5t3Zr7\nTAwbxrU7ImbRTLpYgmFwJv2ll/h6661m90jHmZUYBnfXe+MNBh8vvADcfbfKKfoyjS/PMAyeR2fM\nYMUlX9qwy0rHxOnTzFGfNImTSY89xuuSzjmBSekuLrDSQBb3io1lbqWjTKOZi6B0nJkvJYWL4T78\nkMfCqFHcxdbXq1iIxpenffghF1D/8YfvVDiy4jGRmcmdiidO5EL7YcOAhx4CatY0u2fsBv6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/iSiwXSMTFjBrBlC/Dqq/z8+ed5vRJrUpDugkAayOIawwDmzAFGjmQlk5deYp71lcxM6DjLXXw8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\n0qULunTp4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