GPR propagation TMz mode 2D with GPML boundary condition

2DGPRTMzmode_pml.ipynb

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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from SimPEG import *\n",
      "from scipy.constants import mu_0, epsilon_0\n",
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from SimPEG.Utils import mkvc, sdiag, sdInv, speye"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cs = 1.0*1e-2\n",
      "hx = np.ones(200)*cs\n",
      "hy = np.ones(200)*cs\n",
      "mesh = Mesh.TensorMesh([hx, hy], 'CC')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data[mesh, mesh] = 1."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "2D Geo Penetrating Radar (GPR) modeling: $TM^z$ mode with Generalized PML (GPML) boundary "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a href=\"http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=1429022&url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel5%2F9769%2F30810%2F01429022.pdf%3Farnumber%3D1429022\"> \n",
      "Generalized Perfectly Mached Layer for the Absorption of Propagating and Evanescent Waves in Losless and Lossy Media (Fand and Zhonghua, 1996)\n",
      "</a>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Maxwell's equations in time domain:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$ \\nabla_s \\times \\vec{E} = -\\imath\\omega\\mu^{'}\\vec{H}$\n",
      "\n",
      "$ \\nabla_s \\times \\vec{H} -\\imath\\omega\\epsilon^{'}\\vec{E} = 0 $\n",
      "\n",
      "where\n",
      "\n",
      "$\\mu^{'} = \\mu + \\frac{\\sigma_0^{*}}{\\imath\\omega}$\n",
      "\n",
      "$\\epsilon^{'} = \\epsilon + \\frac{\\sigma_0}{\\imath\\omega}$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\nabla_s = \\hat{u}_x\\frac{1}{s_x}\\frac{\\partial}{\\partial x}+\\hat{u}_y\\frac{1}{s_y}\\frac{\\partial}{\\partial y}\n",
      "+\\hat{u}_z\\frac{1}{s_z}\\frac{\\partial}{\\partial z}$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "where"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$s_x (x) = s_{x0}(x)(1+\\frac{\\sigma_x(x)}{\\imath\\omega\\epsilon})$\n",
      "\n",
      "$s_y (y) = s_{y0}(y)(1+\\frac{\\sigma_y(y)}{\\imath\\omega\\epsilon})$\n",
      "\n",
      "$s_z (z) = s_{z0}(z)(1+\\frac{\\sigma_z(z)}{\\imath\\omega\\epsilon})$"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "In time domain assuming $TE^z$ mode ($h_x$, $h_y$, $e_z$):"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$-\\frac{\\partial h_x^{n}}{\\partial y} = s_{y0}[\\epsilon\\triangle t^{-1}(e_{zy}^{n+1/2}-e_{zy}^{n-1/2}) \n",
      "                                 + (\\sigma_0+\\sigma_y)e_{zy}^{n-1/2}\n",
      "                                 + \\epsilon^{-1}\\sigma_0\\sigma_ye_{zy}^{I \\ n}\n",
      "]$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\frac{\\partial h_y^{n}}{\\partial x} = s_{x0}[\\epsilon\\triangle t^{-1}(e_{zx}^{n+1/2}-e_{zx}^{n-1/2}) \n",
      "                                 + (\\sigma_0+\\sigma_x)e_{zx}^{n-1/2}\n",
      "                                 + \\epsilon^{-1}\\sigma_0\\sigma_xe_{zx}^{I \\ n}\n",
      "]$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "where $e_{zx}^{I \\ n} = e_{zx}^{I \\ n-1}+\\triangle t e_{zx}^{n-1/2}$ and $e_{zy}^{I \\ n} = e_{zy}^{I \\ n-1}+\\triangle t e_{zy}^{n-1/2}$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\mathbf{Curl}^{vec}\\mathbf{h}^{n} = \\triangle t^{-1}\\mathbf{S}_{\\epsilon}(\\mathbf{e}_d^{n+1/2}-\\mathbf{e}_d^{n-1/2})\n",
      "                                     +\\mathbf{S}_{\\sigma}\\mathbf{e}_d^{n-1/2} + \\mathbf{S}_{\\epsilon^{-1}\\sigma}\\mathbf{e}_d^{I \\ n}\n",
      "$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\n",
      "\\mathbf{e}_d =\n",
      "\\begin{bmatrix}\n",
      "    \\mathbf{e_{zy}} &  \\\\[0.3em]\n",
      "    \\mathbf{e_{zx}}\n",
      "\\end{bmatrix}\n",
      "$\n",
      ",\n",
      "$\n",
      "\\mathbf{e} = [\\mathbf{I}^{cc}, \\mathbf{I}^{cc}]\n",
      "\\begin{bmatrix}\n",
      "    \\mathbf{e_{zy}} &  \\\\[0.3em]\n",
      "    \\mathbf{e_{zx}}\n",
      "\\end{bmatrix} = \\mathbf{e_{zy}}+\\mathbf{e_{zx}}\n",
      "$\n",
      "and \n",
      "$\n",
      "\\mathbf{S}_{\\epsilon} =\n",
      "\\begin{bmatrix}\n",
      "    \\mathbf{diag}(\\epsilon s_{y0}) & 0 \\\\[0.3em]\n",
      "    0 & \\mathbf{diag}(\\epsilon s_{x0})\n",
      "\\end{bmatrix}\n",
      "$\n",
      "\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\n",
      "\\mathbf{S}_{\\sigma} =\n",
      "\\begin{bmatrix}\n",
      "    \\mathbf{diag}((\\sigma_0+\\sigma_y) s_{y0}) & 0 \\\\[0.3em]\n",
      "    0 & \\mathbf{diag}((\\sigma_0+\\sigma_x)s_{x0})\n",
      "\\end{bmatrix}\n",
      "$\n",
      ", and\n",
      "$\n",
      "\\mathbf{S}_{\\epsilon^{-1}\\sigma} =\n",
      "\\begin{bmatrix}\n",
      "    \\mathbf{diag}(\\epsilon^{-1}(\\sigma_0\\sigma_ys_{y0}) & 0 \\\\[0.3em]\n",
      "    0 & \\mathbf{diag}(\\epsilon^{-1}(\\sigma_0\\sigma_xs_{x0})\n",
      "\\end{bmatrix}\n",
      "$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Seps = sp.block_diag([sdiag(epsilon*sy0), sdiag(epsilon*sx0)])\n",
      "# SepsI = sp.block_diag([sdiag(1./(epsilon*sy0)), sdiag(1./(epsilon*sx0))])\n",
      "# Sepsisig = sp.block_diag([sdiag(sig0*sigy*(1./epsilon)*sy0), sdiag(sig0*sigx*(1./epsilon)*sx0)])\n",
      "# Ssig = sp.block_diag([sdiag((sigy+sig0)*sy0), sdiag((sigx+sig0)*sx0)])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 62
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\frac{\\partial e_z^{n+1/2}}{\\partial y} = -s_{y0}[\\mu\\triangle t^{-1}(h_{x}^{n+1}-h_{x}^{n}) \n",
      "                                 + (\\sigma_0^{*}+\\sigma_y^{*})h_{x}^{n-1/2}\n",
      "                                 + \\mu^{-1}\\sigma_0^{*}\\sigma_y^{*}h_{x}^{I \\ n+1/2}\n",
      "]$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$-\\frac{\\partial e_z^{n+1/2}}{\\partial x} = -s_{x0}[\\mu\\triangle t^{-1}(h_{y}^{n+1}-h_{y}^{n}) \n",
      "                                 + (\\sigma_0^{*}+\\sigma_x^{*})h_{y}^{n-1/2}\n",
      "                                 + \\mu^{-1}\\sigma_0^{*}\\sigma_x^{*}h_{y}^{I \\ n+1/2}\n",
      "]$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "where $h_{y}^{I \\ n+1/2} = h_{y}^{I \\ n-1/2}+\\triangle t h_{y}^{n}$ and $h_x^{I \\ n+1/2} = h_{x}^{I \\ n-1/2}+\\triangle t h_{x}^{n}$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\mathbf{Curl}^T\\mathbf{e} = -\\triangle t^{-1}\\mathbf{M}^e_{s\\mu}(\\mathbf{h}^{n+1}-\\mathbf{h}^{n})\n",
      "                             -\\mathbf{M}^e_{s\\sigma^{*}}\\mathbf{h}^{n} - \\mathbf{M}^e_{s\\mu^{-1}\\sigma^{*}} \\mathbf{h}^{I \\ n+1/2}\n",
      "$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\n",
      "\\mathbf{M}^e_{s\\mu} = \\mathbf{diag}\n",
      "(\\mathbf{A}^{e \\ T}_{c \\ vec}\n",
      "\\begin{bmatrix}\n",
      "   \\mu s_{y0} \\\\[0.3em]\n",
      "   \\mu s_{x0}\n",
      "\\end{bmatrix}\n",
      ")\n",
      "$\n",
      ",\n",
      "$\n",
      "\\mathbf{M}^e_{s\\sigma^{*}} = \\mathbf{diag}\n",
      "(\\mathbf{A}^{e \\ T}_{c \\ vec}\n",
      "\\begin{bmatrix}\n",
      "   (\\sigma^{*}_0+\\sigma^{*}_y) s_{y0} \\\\[0.3em]\n",
      "   (\\sigma^{*}_0+\\sigma^{*}_x) s_{x0}\n",
      "\\end{bmatrix}\n",
      ")\n",
      "$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\n",
      "\\mathbf{M}^e_{s\\mu^{-1}\\sigma^{*}} = \\mathbf{diag}\n",
      "(\\mathbf{A}^{e \\ T}_{c \\ vec}\n",
      "\\begin{bmatrix}\n",
      "   \\mu^{-1} \\sigma^{*}_0\\sigma^{*}_y s_{y0} \\\\[0.3em]\n",
      "   \\mu^{-1} \\sigma^{*}_0\\sigma^{*}_x s_{x0}\n",
      "\\end{bmatrix}\n",
      ")\n",
      "$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Mesmuisigs = sdiag(mesh.aveE2CCV.T*np.r_[sigs*sigy/epsilon*sy0, sigs*sigx/epsilon*sx0])\n",
      "# Messigs = sdiag(mesh.aveE2CCV.T*np.r_[(sigs+sigy*mu/epsilon)*sy0, (sigs+sigx*mu/epsilon)*sx0])\n",
      "# Mesmu = sdiag(mesh.aveE2CCV.T*np.r_[mu*sy0, mu*sx0])\n",
      "# MesmuI = sdInv(Mesmu)\n",
      "# Icc = sp.hstack((speye(mesh.nC), speye(mesh.nC)))\n",
      "# curl = mesh.edgeCurl\n",
      "# curlvec = sp.block_diag((curl[:,:mesh.nEx], curl[:,mesh.nEx:]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 63
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Discretize the system:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\mathbf{Curl}^{vec}\\mathbf{h}^{n} = \\triangle t^{-1}\\mathbf{S}_{\\epsilon}(\\mathbf{e}_d^{n+1/2}-\\mathbf{e}_d^{n-1/2})\n",
      "                                     +\\mathbf{S}_{\\sigma}\\mathbf{e}_d^{n-1/2} + \\mathbf{S}_{\\epsilon^{-1}\\sigma}\\mathbf{e}_d^{I \\ n} + \\mathbf{j}_e\n",
      "$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\triangle t^{-1}\\mathbf{S}_{\\epsilon}(\\mathbf{e}_d^{n+1/2}-\\mathbf{e}_d^{n-1/2}) = \\mathbf{Curl}^{vec}\\mathbf{h}^{n} \n",
      "                                     -\\mathbf{S}_{\\sigma}\\mathbf{e}_d^{n-1/2} - \\mathbf{S}_{\\epsilon^{-1}\\sigma}\\mathbf{e}_d^{I \\ n} - \\mathbf{j}_e\n",
      "$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\mathbf{e}_d^{n+1/2} = \\mathbf{e}_d^{n-1/2} + \\triangle t\\mathbf{S}^{-1}_{\\epsilon}[\\mathbf{Curl}^{vec}\\mathbf{h}^{n} \n",
      "                                     -\\mathbf{S}_{\\sigma}\\mathbf{e}_d^{n-1/2} - \\mathbf{S}_{\\epsilon^{-1}\\sigma}\\mathbf{e}_d^{I \\ n} - \\mathbf{j}_e]\n",
      "$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\mathbf{Curl}^T\\mathbf{e} = -\\triangle t^{-1}\\mathbf{M}^e_{s\\mu}(\\mathbf{h}^{n+1}-\\mathbf{h}^{n})\n",
      "                             -\\mathbf{M}^e_{s\\sigma^{*}}\\mathbf{h}^{n} - \\mathbf{M}^e_{s\\mu^{-1}\\sigma^{*}} \\mathbf{h}^{I \\ n+1/2} - \\mathbf{j}_m\n",
      "$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$-\\triangle t^{-1}\\mathbf{M}^e_{s\\mu}(\\mathbf{h}^{n+1}-\\mathbf{h}^{n}) = \\mathbf{Curl}^T\\mathbf{e} + \\mathbf{M}^e_{s\\sigma^{*}}\\mathbf{h}^{n} + \\mathbf{M}^e_{s\\mu^{-1}\\sigma^{*}} \\mathbf{h}^{I \\ n+1/2} + \\mathbf{j}_m                          \n",
      "$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\mathbf{h}^{n+1} = \\mathbf{h}^{n}-\\triangle t(\\mathbf{M}^e_{s\\mu})^{-1}[\\mathbf{Curl}^T\\mathbf{e} + \\mathbf{M}^e_{s\\sigma^{*}}\\mathbf{h}^{n} + \\mathbf{M}^e_{s\\mu^{-1}\\sigma^{*}} \\mathbf{h}^{I \\ n+1/2} + \\mathbf{j}_m        ]                  \n",
      "$"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Some useful properties:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$s_{x0}(x) = 1+s_m(\\frac{x}{\\delta_x})^2$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\sigma_x(x) = \\sigma_m sin^2(\\frac{\\pi x}{2\\delta_x})$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\sigma_m = \\frac{\\epsilon c \\delta^{-1}}{1+s_m(1/3+2/\\pi^2)}log(R_{th})$"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "First compute:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$ \\mathbf{e}_d^{I \\ n} = \\mathbf{e}_d^{I \\ n-1} + \\triangle t \\mathbf{e}_d^{n-1/2} $"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\mathbf{e}_d^{n+1/2} = \\mathbf{e}_d^{n-1/2} + \\triangle t\\mathbf{S}^{-1}_{\\epsilon}[\\mathbf{Curl}^{vec}\\mathbf{h}^{n} \n",
      "                                     -\\mathbf{S}_{\\sigma}\\mathbf{e}_d^{n-1/2} - \\mathbf{S}_{\\epsilon^{-1}\\sigma}\\mathbf{e}_d^{I \\ n} - \\mathbf{j}_e]\n",
      "$"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Then we compute:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$ \\mathbf{h}^{I \\ n+1/2} = \\mathbf{h}^{I \\ n-1/2} + \\triangle t \\mathbf{h}^{n} $"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\mathbf{h}^{n+1} = \\mathbf{h}^{n}-\\triangle t(\\mathbf{M}^e_{s\\mu})^{-1}[\\mathbf{Curl}^T\\mathbf{e} + \\mathbf{M}^e_{s\\sigma^{*}}\\mathbf{h}^{n} + \\mathbf{M}^e_{s\\mu^{-1}\\sigma^{*}} \\mathbf{h}^{I \\ n+1/2} + \\mathbf{j}_m        ]                  \n",
      "$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "npad = 20\n",
      "ax = mesh.vectorCCx[-npad]\n",
      "ay = mesh.vectorCCy[-npad]\n",
      "indy = np.logical_or(mesh.gridCC[:,1]<=-ay, mesh.gridCC[:,1]>=ay)\n",
      "indx = np.logical_or(mesh.gridCC[:,0]<=-ax, mesh.gridCC[:,0]>=ax)\n",
      "tempx = zeros_like(mesh.gridCC[:,0])\n",
      "tempx[indx] = (abs(mesh.gridCC[:,0][indx])-ax)**2\n",
      "tempx[indx] = tempx[indx]-tempx[indx].min()\n",
      "tempx[indx] = tempx[indx]/tempx[indx].max()\n",
      "tempy = zeros_like(mesh.gridCC[:,1])\n",
      "tempy[indy] = (abs(mesh.gridCC[:,1][indy])-ay)**2\n",
      "tempy[indy] = tempy[indy]-tempy[indy].min()\n",
      "tempy[indy] = tempy[indy]/tempy[indy].max()\n",
      "tempx[tempx>1.] = 1.\n",
      "tempy[tempy>1.] = 1."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Lx = mesh.hx[-npad:].sum()\n",
      "Ly = mesh.hy[-npad:].sum()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sighalf = 1e-3\n",
      "mu = mu_0*np.ones(mesh.nC)\n",
      "epsilon = epsilon_0*np.ones(mesh.nC)*1.\n",
      "epsilon[mesh.gridCC[:,1]<0.5] = epsilon_0*2.\n",
      "sig0 = sighalf*np.ones(mesh.nC)\n",
      "sigs = 0.\n",
      "c = 1/np.sqrt(mu*epsilon)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 41
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fmain = 3e9\n",
      "lamda = c.min()/fmain\n",
      "sm = lamda/(2*hx.min())-1\n",
      "sm = 3.\n",
      "Rth = 1e-8\n",
      "sigm = -(epsilon.max()*c.max()/(0.5*(Lx+Ly)))/(1.+sm*(1./3+2./(np.pi**2)))*np.log(Rth)\n",
      "print ('>> sm: %5.2e, lamda: %5.2e, sigm: %5.2e') % (sm, lamda, sigm)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ">> sm: 3.00e+00, lamda: 7.07e-02, sigm: 1.87e-01\n"
       ]
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sigx = sigm*np.sin(0.5*np.pi*np.sqrt(tempx))**2\n",
      "sigy = sigm*np.sin(0.5*np.pi*np.sqrt(tempy))**2\n",
      "sx0 = 1.+sm*tempx\n",
      "sy0 = 1.+sm*tempy"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 43
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(mesh.vectorCCx, sigx.reshape((mesh.nCx, mesh.nCy), order='F')[:,0])\n",
      "plt.plot(mesh.vectorCCx, sx0.reshape((mesh.nCx, mesh.nCy), order='F')[:,0])\n",
      "plt.plot(mesh.vectorCCx, (sigx*sx0).reshape((mesh.nCx, mesh.nCy), order='F')[:,0])\n",
      "plt.legend(('$\\sigma_x$', '$s_{x0}$', '$\\sigma_xs_{x0}$'), fontsize = 16)\n",
      "plt.xlabel('x')\n",
      "plt.grid(True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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X3NxcMjMzAUhOTiYrK6vpllyNB2FML6/PXU9+eT5L31xKSd25L11JQQlA2C4f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\nY2cNxgp0JysAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10be0748>"
       ]
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Seps = sp.block_diag([sdiag(epsilon*sy0), sdiag(epsilon*sx0)])\n",
      "SepsI = sp.block_diag([sdiag(1./(epsilon*sy0)), sdiag(1./(epsilon*sx0))])\n",
      "Sepsisig = sp.block_diag([sdiag(sig0*sigy*(1./epsilon)*sy0), sdiag(sig0*sigx*(1./epsilon)*sx0)])\n",
      "Ssig = sp.block_diag([sdiag((sigy+sig0)*sy0), sdiag((sigx+sig0)*sx0)])\n",
      "Mesmuisigs = sdiag(mesh.aveE2CCV.T*np.r_[sigs*sigy/epsilon*sy0, sigs*sigx/epsilon*sx0])\n",
      "Messigs = sdiag(mesh.aveE2CCV.T*np.r_[(sigs+sigy*mu/epsilon)*sy0, (sigs+sigx*mu/epsilon)*sx0])\n",
      "Mesmu = sdiag(mesh.aveE2CCV.T*np.r_[mu*sy0, mu*sx0])\n",
      "MesmuI = sdInv(Mesmu)\n",
      "Icc = sp.hstack((speye(mesh.nC), speye(mesh.nC)))\n",
      "curl = mesh.edgeCurl\n",
      "curlvec = sp.block_diag((curl[:,:mesh.nEx], curl[:,mesh.nEx:]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 44
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = plt.subplots(1,3, figsize = (15, 6))\n",
      "dat = mesh.plotImage(sigx, ax = ax[0])\n",
      "plt.colorbar(dat[0], ax = ax[0], orientation='horizontal')\n",
      "dat = mesh.plotImage(sigy, ax = ax[1])\n",
      "plt.colorbar(dat[0], ax = ax[1], orientation='horizontal')\n",
      "dat = mesh.plotImage(epsilon, ax = ax[2])\n",
      "plt.colorbar(dat[0], ax = ax[2], orientation='horizontal')\n",
      "ax[0].set_title(\"$\\sigma_x$\", fontsize = 18)\n",
      "ax[1].set_title(\"$\\sigma_y$\", fontsize = 18)\n",
      "ax[2].set_title(\"$\\epsilon$\", fontsize = 18)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 45,
       "text": [
        "<matplotlib.text.Text at 0x122def98>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10badac8>"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def ricker(fpeak, t, tlag):\n",
      "    \"\"\"\n",
      "        Generating Ricker Wavelet\n",
      "        \n",
      "        .. math ::\n",
      "            \n",
      "    \"\"\"\n",
      "#     return (1-2*np.pi**2*fpeak**2*(t-tlag)**2)*np.exp(-np.pi**2*fpeak**2*(t-tlag)**2)\n",
      "    return np.exp(-2*fpeak**2*(t-tlag)**2)*np.cos(np.pi*fpeak*(t-tlag))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 46
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dt = 1e-11\n",
      "fmain = 3e9\n",
      "time = np.arange(700)*dt\n",
      "wave = ricker(fmain, time, 50*dt)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 47
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(time, wave, '.-')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 48,
       "text": [
        "[<matplotlib.lines.Line2D at 0x118a05c0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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kyq0rca9I8+iXLIGHH4Z/+7fyv7NjB0yYADt3Vl2tJDVUPebRPw1MB6YAg4BPEh7GdnYc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\nJElSsvx/NFfbA4IYhLIAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x103ed470>"
       ]
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Put Jx source\n",
      "# txind = Utils.closestPoints(mesh, [0., 0.], gridLoc='Ex')\n",
      "# q = np.zeros(mesh.nE)\n",
      "# q[txind] = 1.\n",
      "# q = Utils.sdiag(1/mesh.edge)*q\n",
      "# Put Mz source\n",
      "txind = Utils.closestPoints(mesh, [0., 0.], gridLoc='CC')\n",
      "q = np.zeros(mesh.nC)\n",
      "q[txind] = 1.\n",
      "Px = mesh.getInterpolationMat(mesh.gridCC, 'Ex')\n",
      "Py = mesh.getInterpolationMat(mesh.gridCC, 'Ey')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 49
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "First compute:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$ \\mathbf{e}_d^{I \\ n} = \\mathbf{e}_d^{I \\ n-1} + \\triangle t \\mathbf{e}_d^{n-1/2} $"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\mathbf{e}_d^{n+1/2} = \\mathbf{e}_d^{n-1/2} + \\triangle t\\mathbf{S}^{-1}_{\\epsilon}[\\mathbf{Curl}^{vec}\\mathbf{h}^{n} \n",
      "                                     -\\mathbf{S}_{\\sigma}\\mathbf{e}_d^{n-1/2} - \\mathbf{S}_{\\epsilon^{-1}\\sigma}\\mathbf{e}_d^{I \\ n} - \\mathbf{j}_e]\n",
      "$"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Then compute:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$ \\mathbf{h}^{I \\ n+1/2} = \\mathbf{h}^{I \\ n-1/2} + \\triangle t \\mathbf{h}^{n} $"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\mathbf{h}^{n+1} = \\mathbf{h}^{n}-\\triangle t(\\mathbf{M}^e_{s\\mu})^{-1}[\\mathbf{Curl}^T\\mathbf{e} + \\mathbf{M}^e_{s\\sigma^{*}}\\mathbf{h}^{n} + \\mathbf{M}^e_{s\\mu^{-1}\\sigma^{*}} \\mathbf{h}^{I \\ n+1/2} + \\mathbf{j}_m        ]                  \n",
      "$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "h0 = np.zeros(mesh.nE)\n",
      "h1 = np.zeros(mesh.nE)\n",
      "hI0 = np.zeros(mesh.nE)\n",
      "hI1 = np.zeros(mesh.nE)\n",
      "hx = np.zeros((mesh.nC, time.size))\n",
      "hy = np.zeros((mesh.nC, time.size))\n",
      "\n",
      "ed0 = np.zeros(2*mesh.nC)\n",
      "ed1 = np.zeros(2*mesh.nC)\n",
      "eId0 = np.zeros(2*mesh.nC)\n",
      "eId1 = np.zeros(2*mesh.nC)\n",
      "e = np.zeros((mesh.nC, time.size))\n",
      "\n",
      "for i in range (time.size):\n",
      "    \n",
      "    je = np.r_[q, q]*0.5*wave[i] \n",
      "    eId0 = eId1.copy()\n",
      "    eId1 = eId0 + dt*ed0\n",
      "    ed1 = ed0 + SepsI*dt*(curlvec*(h1) - Ssig*ed0 - Sepsisig*eId1-je)\n",
      "    ed0 = ed1.copy()\n",
      "    e[:,i] = Icc*ed1\n",
      "\n",
      "    hI0 = hI1.copy()\n",
      "    hI1 = hI0 + dt*h0\n",
      "    h1 = h0 - MesmuI*dt*(curl.T*(Icc*ed0)+Messigs*h0+Mesmuisigs*hI1)\n",
      "#     hd1 = hd0 - SmuI*dt*(curlvec*e0+Ssig*hd0+Smuisig*hId1)    \n",
      "    hx[:,i] = Px*h1\n",
      "    hy[:,i] = Py*h1\n",
      "    h0 = h1.copy()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 56
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "icount = 500\n",
      "extent = [mesh.vectorCCx.min(), mesh.vectorCCx.max(), mesh.vectorCCy.min(), mesh.vectorCCy.max()]\n",
      "plt.imshow(np.flipud(e[:,icount].reshape((mesh.nCx, mesh.nCy), order = 'F').T), cmap = 'RdBu', extent=extent)    \n",
      "# plt.imshow(np.flipud(c.reshape((mesh.nCx, mesh.nCy), order = 'F').T), cmap = 'jet', extent=extent, alpha=0.2)    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 65,
       "text": [
        "<matplotlib.image.AxesImage at 0x1a5c2c88>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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OB1IfK9W6OFgiSHQ/HzZPhZvbdDjP96UthFvt8F9b6fvubav5Lcp4vAwA0QXZ\nXbk5IFZaH9c8cyFEcyKEGNs0nEwIIfIMUWMek53DPx8sdxwcxqx6BwytwzcO3zSEbo97IAJC0zV0\n7TxuIO87baLzVoRrANBpI9/L3PwxawLfh4QRV/hdaxH9ha+SlfvxFzq+xRO1hdp7KufjxmPv8Z3p\nEZqaUMegv+A61BhMlNvTkO4uOBy4wfYJPn3b4ro8/76MOyxDCDTOs2scjQ8UVkdEhq5D3Ciz9A/I\nZfkDuY0fnbyDM+E7kWFx6viCbgxHMIBd41nXLUqE2gdCiCkRfVXS7EraXT14KYDBBR9u6dlug7H5\n94E/Bf4c+C9u+P7fBS6B/7N7/ZcfdrnuyQdQ0AO3EJzHVS3Vckd9ucFtNtDUhOCpWs+ybDnb1FyU\nsXiNC3T2Rn2YpDP8QEbPsMLd5WjMH4qM2vF7b0oZgCDWdm27MdiAd3jinopl1XK+abjcNZRtzHWK\na/DbDfXlhnq9oy1rvNsT6vsUhh8+Zj5Uc9DAfwv8e8AXwP8G/M/An1w57p8B/+EHXivKYK915IzW\niI4uHV+31Ksa13qS+QWTizN0tcFbx7Z2PF+VXGwbCPD5UYvzSQSEuox5+Gwa6x72bqbuOnxvEXrj\ngfwaTuRe3l1+EPtgemDotV0fs6ZXOzAJkrV4H1jVLc9XFb8635InmsfTFNe2hGZHe3HG9sUFu1cb\nbGHwrSPu2VCRZR+7SD/ALP1QcPh94F8Bf9n9/38E/iOug8Ot90rP2g5l6UThGsfuoqTeNCijmH/z\nnHS9xGU1F7uGv3qx4eWyom09v/1oivMBaWvCdkWotqhiBtm0A90urBVB/Pftd7/nHj5cRh6p70kk\nBILqFp1+8fF+yJqOSZDJMSEELsuWf/Niw7/+ZsUst3y6yHFtAtsV1fNvWP3yjPXXa/KTHF+38Xza\ndJr0D4NzeAb8cvT/XwF/cOWYAPwR8C+J2sUfA//vh1w09MgoGoxFbAKiaMuG7csdly931LuW2Wff\nUFxe0C5qXq0r/urLJavzLU3V8uLzE3yAUG7w5y8I1RYQ1OxkMFU+RmDJvfw6S+8x6fdWxDHmd1vc\nxUtEG9T0hHAivNo2/MUXl3z55SX5LOMXD6c0TYJbL1n95de8+vMz1i+2nARoqy5zmZguBb7q9v18\n2KL2oeDwLjPn/wA+A7bAfwD8T8AvbjrwH/6jfzy8/7t/9Af83T+6ijNjURGFuzRuILRVw/mLLX+6\nrJjtatJ+hS6zAAAgAElEQVQ/+5KT5y9pHpdcXJR8/RdfcfHLf03509/mr/7GI5w/wZ9/Q/2rvwLf\nkiYp4v1QiIQunHWoSSASryt8R27NcJ08E3XnIwi/U7nWXn2bfgcahMS9EXKFxwqqTyRkIwG5XdE8\n/xrferJijnz6t/nr8y2/+ovnfPHnf8bs4RPOfnJMVae0Z694/qdf8Kd/vWRVO/6tr9c82lRxwdS2\nK6Gg37io/bN//i/4Z//8X7z19j8UHL4gTvxePiNqD2NZjd7/U+C/B06As6sn+wd//Pff8bJ9tJx0\neRciQHjn2TSOV7Vj7Tw/e7mlWa4JbY1znmq7o7x8yfbihFerMrqJ6KLT2obQVNAVCBlcmjGiin3R\n29vb2PJGCYEhWovR33tg+HbSb6gbI6yE18Qb3Pa1w6ERc3Wnpo9EZGiqbst15NEaF3i1rthcvKK8\nfEEymeNaT2gb2tWayxcbvto2bFrPb2ybmMOELqpv2MT2eo7q6sL7X/3X/82Nx32ot+J/B34L+BxI\ngL9HJCTH8ph9z/x+9/4aMHwrGfupuwkkwyXiXwUoFRspUVBkhnxWkM5PscWCEGDXBFg8IHn0BDNf\nRHOiqaDZdSnjRslfDpK+fAcyDOgwxGK85sDv9r5+0PK6EOtRO/aq2HdKTkaSsB9H4kOsm9mUUJeA\nYGZzksdPkOPHbJvozrT5jHR+SjadUGSGVEUPhyiJ+4N6vtr3e1Ju964/VHNogf8c+F+Inov/gUhG\n/qfd9/8E+I+B/6w7dgv8Jx94zZF0oY/OEbyLeSGN8DDVHFnN0WmBneZkieXhkebZTx9hrWZ6csTR\nNKV0gfboKdnPKjj/ZqicJbtlJI+SYkguG5S6eZPWR5EbAmV61xccvr93YYwkcODkH9yFYd+c46b9\nLrSHeCOdKRHXYnFVrMFaRq1WFVNUMYHFQ5rTn7BpPPPC8vDTB6hEc/JgzsOTgiK1mCJj/mDCp7nh\nvPakeSyUE4Z9FbcntxEE9U+711j+yej9f9e9blmij1h826llNUor5ouUnyWa0wcFT37nKemjU+os\n56cPLH/4u0959ZNTitzwswcTah+4UFOOHvycdHKM2pwj9Q62y1iclwDJZED8OMY+9u7FmwZzrx10\nKvI9HrxBwuHbAUivuIUHbYKPDhD7FABdOvp6C7sVlKtoBRw/whfH1JNTLmXCpnR8dpzz+3/zCauf\nnbKYJPzm4yl5JtjTEx79jWf8xq8uefViS3GUooyCth3iJG5rAbu7EZLd9laaCl9tCVUV3ZefzJhr\n4fS3n/Dw9/8W9ulPsfmEz0WT/84jqtZhtZDoWDzkm52nzApOJglTk2GW3xA2F+CXqC4hR7B5F30W\nI98/av3LGM0SX0MnX3lPZ2Peo8QbpG+fPtMSh7b4dxRCHYZdvhIjcdsKqTaE7ZLQ1kg+wy0es8lO\nOfMJF9uW1gd+cTrhp0c5rfdYpXgwSUjygH70Kaf/9u/Rbkqmf/IVogVtFaGtoSkRVxOMvZVnu5vg\nEADp6lVUW/xmhasqdGaZ//SI6dNjjv/23yT/vb+De/hTlMl4pBxPUo32Lqbe0gnfbD0vtjXnZctu\nYnmWHjGftki9I1RbQrlBdIIoRSAdyJ7IQH+kiTlexYb4q5GtPLjDuMeGN8nQPle1hPExH1tjGAUj\neYe4BtXsCNUmkt82wU9P2KQnfFUbvlyVtD7wsLD8ZJaQ+zIuBaLxRmO0xh0/Jftbf8ATCaSz/4vt\ni8tYfbsu43htK8RmXfLaD5O7CQ50NTJdTSjXuNUKV9bYIqV4eMTx7/0O9nf/kPrRb7FVBQJMqUjW\nXyLL5zHz7ye/oE4nfLUOnO1qaudJj3OyyQOytoTL5xHZ6w1KKYIlujhVjMYMqI+b7GXwVnCoFveg\ndB9/8WYZt1OXbWlPRo4+/1iXH22C6gsvSbNDqg2+qWLA0+yUevKQM5fyy+WO55uaeWJYZJqHaod+\n8efQlDA9pV48Y6enrKSgePI7pNby0CrO/58/w5UxNb3frpByiyQTbiOXxZ0FB7yPxXN3G9x2jW9a\n7DRn8Zufkf3u32H96Ld53lga33KSamy5xP/l/031F3+Csgl5CMyf/h6zRPNq23C2a/jKaiYm4eHi\nKRYI63NCXSE9kdT9E7qs1IMP+1YfrTvf2P02qMP3gPBeMopRGUTCqK1vNynMzcBQRmCodlEbnSxo\n50+4JOOrdc3LbYPzgVmqObJgvv5XlP/yf8VvN9jPfgPz2xlhMeFV6TgXxZMHv2D6N2qmmy3bX36B\nr1vcZoOuduAbCF35xg+Ii7mT4CBdMs5Ql/jtkrDbAJAcLUh++ls0j36LL0rFL5clhVXMlCMsz6h+\n+Vec/8lfoRKLPjplcvpTnk5O2LUJF7uWde14vnPYacbx4ilaBDYXhKZCer4BwHQAQRfGfZsA0Q/U\nITPQvdyK3JQt6iNkihpnLD8AhnoTS9YpBZMj3OwJl2rCi61jVTmsCMdFwqfThLlb0/z1n3LxZ39J\nu94w95riyW/i8sdc7OCiamnnKT9/9AvSz35Fc7nClyV+tyVUm5gw2YxI7feUu5lDMnQBJNUOt9nS\n7CpQiuzBMfrpz3nlLH9xXvLFsmRTu1gJqFzTLi+oVzvq1Zb27AX68kse2pbPj3I+maUYJVxWjuc7\nzwUZbvYYikUMSW2jWkhbIW0Ty+Z9rDRk/UD+3rIX/ZhlFOPwsczCvmSBa5Cmc1s2dYxxKOb42SMu\nVcGL0nNeOkTg0TThZ8c5j7OAvvwSd/acZrWmXu1wqyVhtyK4uJv4y2XF/3e25aVLkSefk56eIFrw\nVUUod10g34c/2x0FBw++JdRb/G5DaB2myLGPPsEdP+OLteOXlyXLqgUBHVxXotyjrEZbg69r/Kuv\nydZf8yRp+GyRclpYAnCxa3lVBlZqQjt9CMVRjMLsqiLT1nuA4HC1eP9nGnMJI2DobZkfxI7COywH\nQHsDQNyCydaPg0FjaCuk7QrcagPFAjd7xEpPOavgvGxxIXCcWz5bpDzNA/nmG/zLL3BVFbOoWxNz\njjQ12rcogU3T8uVlxVebhmb2GHV8ikpTQkfQh6aKnpEPfKY7aVbQhzvXJb6qIATsfIZ68JS1nvLl\nes3ZtqFINJlRJFSIb9BZSvbgCJNadJoQNheoF39NHgIP5k/QkxwRWFeOi7LFaoskUyaTgFEKqbdd\nx1d74lvbgyIm7+3mPAjw7GMZRqpwGPEP99zDu8s4EKqXMPpuOO79LzHODymdVhuBoUa8i7UxkwKX\nH7G1cy5q4bxsaVxgmmgeFZZTXZEtv4GXv8Qvz9BWk50eYYoSk2cIDktDZvIYYryt+dWy4vOnc6bH\nj9HFl1BtCXUdtZSuSNOHeLTuHjj0CTLaBqqS0NQoa7BHC8LiMWc1vNjU1K3nwSRhnmpScQgBM58x\nVRqVZuhpEatknX2FtA2pdxwvnhGKHEEoG8+ycmgxiJ1S5DFVOPU2ahCMAcIMq0aQgAzM+BsfpPsr\nN/y9wT4eQOJDGu/XUG5sr3HbX23/q9+/5fQjjUS6jE7SVoiLVa+DUgSb02YLSjvjslEsK4cLgWli\nOC0MJ6oiW34F3/wb/MULQlOhp3OKZxZXRnBQAklomaeaaWJ4ua55sam5aAsmi0eYxQJ3Fvdo0FRI\ncHF/0AeA3t0DB2LwU2iqSPAEj8oz9PED2tlDnm8aLnYt1igeFAlHVrBNjQiYxSnm6AGSFfFM21V0\n/zQ1KgRSUZwsniFFynnpqF1gXTuUaMRMyLPYYNLsIDhk0CDCCCDkWwDE/pmu9+Lrfn+PDt9O3rQn\n5aZj3302XQMG1yKujkWZg4vl7kxOm80jMDjNsvY4H5hYzVGmOdY1+eob+Obf4F5+Qah2qLRAjh6S\nHElMAuM9KIVpKxZF4OEk4Zt1xbJseLVteVwck8xPCOuLWP1tiJT0IO8f73D3wKHXHJoa39QIAT2Z\nxg0rdsY36w1l61nkhkfThLk06HoLIqijUySfIWkBTYkLHsptBAkRtLGk2nIyf4LKEy4rR+MCm8aj\nxICJIaxaFNJsYyisq2/QIKTb1g37wfk6TYErY3Lsix9/1v/mHhy+vYzbTUZ/RrEPg9wEENc1iT0w\ndFnJe2BwHTB0kbVtOqOyU9besGkczgcyq5gnmiPdkK1fRlPi7GvCZglKI2mOPn4ESR6Dm3brmI6+\n3jEpKh5PE361tJxtal7tGsrJnGR2isq+jvxEW99KGPWdBAcJvkPIFtEaPV/gZw+4bISzXYNWwoMi\n4WFhyP1FDFfVBlXMYXoMJovBTeWWsF3j24ZQbvEXL9DWkgicLJ6ixLCsYxm9beMR0YidkikVAaLe\nRA3C14S2Gzr9PgzpE26MzYEwGpQjuVqT82DMyv7393zD+0m/H2UMCEM7j4OhXqNNjDe8sQcGCYE+\nObG4FnEx2znK4G2Oy+ZUZsLaadZNzFmaGcUsVRxpR7J6gZz9Cn/xHL9bx0ukOWq6iOM0ncYiz8l5\nBIh6S9pseJAXPMgTLncNF2XLmoLZ7AQ1meE3S0LbQtvGzYMf0Gx3EBx8V1k7oqNKU/TihLo45rxs\nWTeOosu5d5IIyWYbt2BrgxQLfL4gKButzekRUq4j2DRdKPb5N6gQ95+fHn+KEsWq9jQdQIACMyHL\nY6CL6jkI3xDagChD0CbGnnQg0ae9Z9gjcUOOgYNnvEHLuHdWfIC8JhryjUA7BoW9N2rvkQhdGcYI\nCuLbeLwyeFvgszmVKVg7xabxuBBItTC1imMbMJdfR43h/OsIDKKQfIqaLpDpESGdEtIZ4FHBI20D\nTYmt1xwXD3gyS/hyXbJtYpzEw3xOMpkju+1QXPpDtcy7Bw5An7FXBCQvYHpClcx5tWxoWs+DIuFB\nYcmaJWzOCU0N2ZSQTvDJJAaiuCYWJJ2dIEh0idYVfruGEFAEdPAcHz9DJZZ1E6h9YNd4QlAEW1BM\nYjo5qdZx5fDNwQ6IawDxLjIOgropcKc/5j7py9ulb6c3teO3kLcBQ1CakE7x+ZydZKxbYdsGfIBU\nCzOrWBiPufiC8OpXERi2awig8gkqnyLTBVJM8SYlJFk8b1KDWUG1g80FSX7Jw2LBUWZY145l7anz\ngqRYIMkZodOspSsyjXo/V/udAweB/dZUpVDZhDA5YoPlstwhwHFhOc016XYTt8Z6jyQZ3mYEk8SF\nRGmCyZDZMUqb+P1mGc2L3Rb4BqUEDcxnjzBpzrpVVG0sirMWAZOST05RolD1dhgoIQSErs6A0nHQ\nDCHY3Y7KgwjIG+IYDjSNKwP7HhjeTW5spzfEjBy0tQzgcRj16MB1wODbuDNYhKATfJITimN2WDYN\nlC6Og9wqpjYwCSXm4gXh/Av8+Tf47QZBkLxAihlqMkeKGcHkcf+PaNCKYDOUTeOdlWtsdcnR4oQH\nRcqu2bGqWsrZhGlxhKRFZ8F+eEHiOwcO9HyDc6BMjFHPZyxrx6Zx5NbwZJoyoUJ2l9GtYxNIMtBJ\nt5o4QAjKQlIgyoBJUErHwqTVFl+VcP4ChaCDo5g8RNkpG1FUjkhUihDEkBenoAyq2kBPSLmms0k7\nArUDiKhFjHiF3m15gwob/78nvt6sBl/ZmPXrJKNyiG885o1m3Pi3ewA5CGzyPoKBbzt3to8b8XSC\nTyb4fMEuKLYt1D6ggMQqJiqQtRv0+iXh8mv82XNCuUVEkCRDTY+Q2RGSTQkmJWjb3WoAVPx/kiPG\n4ncbZLtkMqt41Hkt1k3L1qf4bIrOJ1HD8O7XjHMYqgNFVBRjIZ/S2IJNFWg9ceNKakjqM2S7im6d\nbAImIygTtYY+aazWBMliHkpRCNGc8EqgrghNhb98hQoB4z351KGSOUYZqrYjKlsIRpGnc7QyqGqN\ndAVyohbhkWCumBmd+2vIzcB+Ul8hv/Yy4h1uBIBRwMvVmozvG5j1Q5RxPYabApxed/xNwHAtm9Y+\nIvXG+AXXdl6ALjJWmTiZkwkunbILhl0b+SklkBpFLo60WWE2rwgX3xCWr7o9FhqxCaqYIdMF5HNC\nkscx2hOe3hNU5DGCSRCTgF8StktsteQoO6VIdFyo2kBrc0w2iWb0kDru/fv9DoJDjEADkCSDYk6l\nc9Z1VOfnmWGeKsxyTSjjhqyhWI2KNqi4WNkqiMQIR20iincJQZWoSBJ1sRRheQYhchDZ1KPSGSZJ\n2bUB56FsA0EbMjvBiEI12xhm7Wr6UO+xmUEXURm6nYISALliGx9wklcG+BtBYvTba67QXjpN5Ifq\n/Rhnb7pmUr3m/U3niG+uf3djij1hX0quB4V+MXKRVxhiBwSUjWaqLWhtThkMZetxHowSMi1kocHW\nS/TmjHD5grB8FXdlKgU2jRxDMYN8FoHBpMMYHbKcdbsrg0nApHGFKbfo3SWLk4fMU8PZrqZsPHWa\nkKUFsl3tF9IPWBTuFjhAnNQ+IrfKcnw2o8SyrkuMEk5yy0RaVLmMuymTNPqLTULcEOP2Ze/oagcA\nwRDdpAIiCqUNYbeGaheReHMZr+kd6bRF50cok1I5ofWBykVNJDE5Vmm0MlBvu0i5DiBCiH5opZHO\nxIhAARJUFxgRroPEwfgeqcfX5s7VQf+uA+Oqv/81E/NW5Wrsweiab7zs69BBrry9Grswfjv6/6Ah\n7EPgIezJvL48QXCdlq9jXg+b42xBq1PqoCmdxwewWkhVIAsVprpErV8RlmeEzUXc/q8UkhZIPkXy\nKWSTPTBou7/H4CLpriO3ho6msdiEsF3BbslEHEep5rIUSueplSWkBRjL283Qt8sdA4fQTbAASiFp\njrM5WydUrSczipPMYJt1TMPlHWLTSDaqTrV3bTdRfZf0sxscSkcAYQQOxuCVjptZ2iYCRPBIcBjf\nkufHaJ1TiaIJULtY0SioFJtojDJQb2LEnG+JUZVxVQhKI6KHezjwnYs/HMTjTpbxG3ntHHjzDLvh\nvK+VmwKF3leugs5VEpYrk/dt9/cmQBj9/sbn7NtOHYBCH0czgEK/RwFikJtJCLbA2ZxGLHUQGh81\nzlQLqXgSX2J2l8jmjLA6i2OxqUHHACc1mUd+IcmjVquTwbSNt+ajSRHiWA0SvxebIUkaq2NtV9h6\nzSLNSbSibgONJJBOIscGgP8g3uFugUOvKgUf1fMkp9UJu9bThkCRaOapRu9WhDJGRWLTTl3r+AbX\nxGCVa/H1ESAwyZD3T7RGSSyeE+oykqCdyiatQ7uWrDhG2wmVMjQeXIDKR/aaxKCURje7GGvRB8l0\n4BRBQA9kJUIXOKX2hNRVsmzgJMYN02sS42Cqa433poa94ZjRdT4KNtxwP28Fq5s8Ojdd5E3n68nG\ncUBT/J0caAp+ry1ITwpmOJPjbU5NtPVdiOUirBYSPLbZoLbnyOY8agu7dResZ5EkRYopUswJpvOc\naTviGUbPGEJcyFQTiXOlo1lhsxiWXW5QuwumWUFuYtX4Co23OcamUWvulbD3zHp1t8ABgAC+W3lt\nRiOWso0IOUs0UyuoixW+qRBtwGYEHW21fkXo3aDxdGG/6ogi9IVBIJohhcRjdyZu9HINYbdBOYeE\nmBcwKY4x+YJKW+oOIGoXcEpI7AS0RWkL9W4gK/s6AxJ8JC37yEo1XskEJOy9Hm8a+De6Qq823Xus\nIbedlu69z/MGF+TBuV93fjnQ0EY/iqAwaAu9C7BDMq0j6WgjKLQ6ofbRlAyAVpAoyHDI7hK1PYft\nJWFzGTVO7xGbIEmGZAUqn+JtvvdKKH3lfkbux26sSh+ObRKwGWISQr1DVSsmE6GwinXjqNpAqzUm\nSTperV9Mf53AAUG0ISQFrUpoPGglzFJDoQNslrFR8wmkORhLUIK07SHfMJyyJ2+gr1AczL4xRSSq\nddoQyi2h7dLhr85RrkX5FlxDmi/QJqdG0fpIVlYh4FVCklmUMkhjUE23xz+46B7roz6VRoKOK8Oo\nlHpMbc4+kOqa//qKfXljcM9rJtcPMWbi2wQnvREQ9ue6ERT6ieO6eIV+HAggOq7qJo3xC0lB7RWN\nD7EAs4ARIRGPdSWyu0TvLgmbixjY1NQQBGUTSHMknyDpBK/TaJpo25kSPc8S2EfOjp7Nt+Bagu3q\nwiZ5NC12a8J2TfEwbuLaNo7aeRqtyUwGqiR8YMKXOwUOwwqqJBIzaU4thrptSbRiYRVqd0noos4k\nyQg2ix0RiBulXjuxxrrziIPoipGIdCXOtR62itM2+O0K5R3KNdBWmHyOTme0Jo3aQwg0PuARrJ1g\ntI3JRfukMQNItMNgDV6iJqEUY5t4H0jV3/prJsbVZ3yTj/9dJuLHSIP3XvItSLYbApj6cxyQjX20\nYw8KSkduQScEmxNsSqtTGs9IWxASBTa0SLlClZeoakXYLPHlFpomjlGTImkWN/p1pGOwaZek2FwB\n65uJ2N7ECRDBpOPQRAS/XaPrNTM74UIrWg8tkTCV94yKHMudAoexiE3wJqNG0/o6+pQ1qHKJ63P1\n2Sy6MLsYhsGkgH3H9Crk4DcfkZSioj1o4vEiClEaMUkcBB0P4cuYBEZc5CFC2yDpFGUzWmUjOPhA\nI4KXBJNYtE669GEVuHofm++bGP/QaRIo3XX0CCT6Qqm9yRE/vT5xxrEAHxI+/LHS4b1J3qQR3BgS\nvNeMBi1h5KqVfmUeQKF730esqq6vO20h2BxvMpogMSAyBEQEq8AGh25KpFqjylicxpdrQhU1QjEG\nkhSVFjH4zkTeKxizL614QIL2buyxJ0qBdNpMH9AkiqATJMnj4lVtUdWazBZYJfgArXTchOqm9ge4\nM+8OOHQqkoQQV3Gb4pSh8YGAkBshNyCbTdyy2ndKHxU5uKNGIcswqHMDebNncbrDVCSEUAQ6gNAm\nTljd1dZ0jlBX4EO3O69GuxpJJqhkgjYpbRBciHxEQPA6RYtGmQRpqnjPY5AYezb8WHvR+67u/fJX\nJpLclJj2Jo7ibavwR01Nd/NKefj9a3gVtZ9coTcPB95o1K+h1zbdPnDuKijICBR0QrAZXic4ZXDE\nCddrC0YCxtWoeoPUG6Rcx5J21S4SgBBX9s6UGLQFbUfEY3efYVSYKHQgL4EQ1GG7D8Soj9qG6TRP\nbWLMRL0lSwOJFgIBT9R4lf7wqX13wAH2g6ULXmpR1C5OjNwYck1kh71DWUuwaZdjoY9vcANZHgaU\n7qtmh+5/N62wQtAakb0nI07WaJfSVN1+j5ZQ9XkeGlS3v1/SCaJTjE5pEUIItEHwyqJFo5VFTBPz\nDbZ1DL3uVV3vENxwzSEIp/v/AXmpugkzSjQjjIDjmmbxNnPhI2oMb7v2TQTrGBCugUH3T7evpY+k\nHQKZBlAYg77pog87dV8nODF4UR2IgxJBS0C5Gu2qCAxVfA35Gl0b4xdMAjZBbBrNWZMSdHcNddWM\n6G969BqSgESeaehZH2N7RFuC6sZ1ksZ9Q9WGdBFIjaZ24ERFbVnr91UYBrlb4ECIJIsogja0RIJI\nS9QcEt90aeoDYlOwSewUIpknfdLNUVFTDiYPXGvR0eSLG2HixJSeNNQmqpF1BIjQZanCd0EsbY1y\nNcrm+GSC6lYljyKEgEMRVIKIQWuLmDp6NNqmA4kR60wA5zv3vN4DRgcWob9f6UrACTEmJDbAXsUG\nDvIZ3NjUnRr+seRNDPoQe6IO9KGxF2n4bLzy/v/svUmMJUma3/cz8/WtsWVERq61dFfNcNgkZ8TZ\nMDyMIJCCJAKkbrqJ0kHQhdBJBwECJIDQQQJIQBgJEAhIh7npKAy0QKIIYUhgpFa3unu6qruWrMqq\n3DMyMra3+fPNTAczc/f34kVkZCyVGVnxAZnxdnc3N/vb9/2/v31mM1miAoPSHax2291u185TsMrD\nUnhmZykcrSWQaKTO8YrcrLy1m9KQTUxqu8jNsT0zoxtQiCpBU70JkncMv6BnX29er9W9aF3WZd9s\nSlNGLRQCPZ0QoYj9gEIpSkSd+ixLzoIQlwwcqDuVF1AIidLge4KWrxH5xMzcmAUtVUjhSCdVu5Lu\nZomKbzDPjM2FHk0dgZuthTDcQMUL+GbWzzOT7iwLsF6ELHIIzYAXYQsZtCi9ACU8NCbcEKL+HemF\nFiRMqGHYdAcSdhCUynovotZl2FRoLaZp5vTrTqIBIRwgHkXQznXmc7NmW9I4v+ZHbJZm5vPuv6YX\nZECzSj/qOU/BfVE0OAXpm0HrR2g/MOI44VFq49FJAVJopC7wlNtzIkFmY8gSAwoO/IVA+EHlMZgZ\nO6wk+RW/MN+WM2Fgk3sAgagl3EJSyeqVJaut5kKGkQkxswSvzIhkxEQISi1QNvx03zlMuJ/MLhE4\nNBrUrYTDQ2tNIAWRxG4ckpoy4IG5+VUtBddQglmvYW7mFI3XmjuouXddZ9PuJ4QhC4VluYXnmzUZ\nRW70GJaTEG7tfzFFB1NE2DLxrQyN9wA1SHgGJIQXWtGWAZxK3VmJdKxWogo7BCg5m+WoAKIZmzfD\nqsOubgUc1Uvn6UHImUPqRefQJOvcHw3QvOY6VDgMCO53ZEXqusVLuprRAwMKGO9KoC0oqBoU8sTs\nul5MIZ+is9SAvp3BhW+ETfg2fJWBDSO8BcAwC2qL91pthBjChonOlXH3vEGaCs8zKdNsTBB08IRA\naSPM0sJDysIeVZ8GGy4TOFC7xZ5J1yg7qHwpCdHILKEoC+s1BCADO2AsKVXFm00ysomqsySZYYiZ\nea12baVNbFgdgvJqL8LzEXlWVavSqoDULvgqM7vvRYoOYkTQMmv1vagiwEoEQnhIzzPKujIwnoP7\nfpk3GPcFQKEsGFTg4ADDzNY1idccqI3w6VDDy7lGOIMdm/loDCA70GuwrnmEOoxYsOrQhVqujkZF\nBrrZ3MzoqjEveICHssVhpxYYDCC4lLPOs1qsZoEBP7QaGneMptq1CXqzk9AsMMwDsfNkHaA7XsyI\n5QCbQbMeSmGAzA9KpAyq/mPCihPekyPscoGDM8s5KBtbBx6EsjQIr0rDAXihQXEhcBpzcQqlWAUQ\nTczdutwAACAASURBVPBoAgRUS7FdulMLz6Y8fYPsdqmvLnLjRfilyUwUKbrI0IWJU0VgQiETbmBq\nSyARXmRDjRJRhLaeQAEqr357xptQCigRzfCirNdwiCqmdyDCYpKvGQK87rTzSmvyPA1vAGo3uskn\nzIPBjGjNkbM2g2RDB0cEapspUA74rAPpPAVRZgYQ7CY0BhhMBskAvCGBhQwsKFhgqH7frwRNFWHd\nvM4ZYHh9L6xaT+Q8Cs/0b+H7ZrPnPCUQCt8e1vBY3sx+GqexSwcOwpOmI3s+pZ3WQykIBIYUVJaM\n9EMQlrFVtcup3Q3EIvgJJkRHdukZj6OelTXuqS0qKyRaGSJKSB+pclOjsgKJzJYYM+pKXUxNDFyk\n1l20IZE01ax15U34yNC3HkNhsyJGnalVXhUiacbgQAUW0AAGIexLC/gJ0QQIODTbC2HDgVfZAve5\nOTia8bBufFY3QIL6/RngsguVZgDBudyNAevazyUOzVysbZhneB1RpohsWu03oYsMnefG21SNEMKv\nvQ9kYEOJhrfQbKsZXuGoMOKoNlN13Q8h7GJd5yVSCfSEH6L0CFFm+Cj8KpuDlWWfLdt06cDBmAAZ\noJVECk3oSQKhbBENgQgilFU3CnTNXp/RNT7sRbgwxaQYtTDKRl2lGk24oZVvwgTrPWg7eJ0ngR8g\ny7wCB/MvNGy6c4st463MnQcZIGWA8EweXJSFBQhlwhhVInRhPJUqJm8Mtkpaa4m1eeKv4R01zQCh\nOLkfoRcEKvODXzc+PCMDd0eRxstxA8bF9NI3E4D0zKD1AvNcSOtRi3qy1dqWeHMl5HMDCrkFhzI3\noUOZ17Jj6SF8Awxaeignea6OX1cab/aD+QY4GTBYgvYoLsJpNLCkpPQNKam1UeZidmUrlEY1ShGc\nxS4nOEgPZQeKQBNIbQZXnuJWYgpXg68SkTQG8qG4d85tPib8qFJmNNb/NzpEM7wwHaeouAjK3HQ4\nm+bUZYlGWw7BrMATdo9FAwwh2rqwWpowSTom2s6I2g4GKX3QkUl7ud+3jw0YlZXWw8X0wrn02Ety\ng3OGY5ltJ3EaV7V5nJnXqMEIZryXGYAVDYKvIhl9syjKLXUWRqTmPBopqLwn0SCEjWQ9awCEBQVV\nmphea9yKXCpy0a89Btf+ldve7Df1NYoZz+GodtGz1z9vVV91k5Gd5KyHJILIpNSL3HgOHhTWS5pV\nYZ7OLhc4NERQpTbgIIXAR5uiKkVhbqyrwyAEQuk6UzETTzds5qUmQXnsyRjpwMIbYGN76WYDVcei\nyoKD9EwhD2VdV61MRkIbsBBejvBSdGHYdWGBQnthxb4rIaly6E4tiZlVhBdSKeucPr/iJnT9nhsQ\nDe9CzLv+zXZyIPI65mTpzecOV2dAoKnZkLUeRUq08O1zVwOjBoTak6nXTQgHki58sGRu/Ti3AGor\nNWMB3bPHdWlPBwTSr8+n6S0sutyTAMPrtJ3zKJr9WPpGiSkkFDlSl9TrO0XlQZ3FLgc4NGJTjREj\nacyYEkLgUSKKzNxkK3Chko82yCyYA4eTAsGRJ0YlF1gAEtrOeqY+gwUI6VlA8OpiInbwuvJ1Nr9m\nKwGZGU/LFFHU4KC9wEhkZR1bi2pw2YFmhVZ4zcFfk5Z6kTZgPgSZCQGa7XlCa86uM6GKOU89BwxN\nBWrtKciZ7zS1G3UpN410npFLG7usTllzPK44bK17wYKCFStZYKhBofF6A4wWXmqzjc5kuvZe3bXO\n3BfM0n7P8i6FuV7pm/cUwrTZ/G++2zoHa0Ja5tkk5TxUvQWYcwNdzGWJLqNKPTq9dNbzMl4EHL4B\nTgorjLpSy2oga9koQaZUDRwzM3kGwoKeMm6xS5c6JZxZhdckx7yZAWdidgDPXrIlAC33oJkFBD0D\nGEeRhNXVLWiRuTaYJ+tmxGTNQW8fS9EYhI4kdYetwQBUo/3crlMF6MJyC4ZUnAFh1bgm6ZnfrfgL\nOQMI2q2MtW14NPt/UlA44QDVGiejrprQvu7SmTPejJPr69LoZGi078wpHh0uL7JLBA7WBGaGsffB\nk3WOWmsNvl/faNFA3PrL5t+51zFoehHuWI13RaPCk2djam3dV1WCdB3drc6sFwsZb8K6zMKETpR1\nhxY2HnYA0QQKhHfYdYc6DGkKwmDGS6ueV3/n3mu8PWNzPMUhcrNi1RuegKbxOTEbvrisgQt5HBjY\nPSSq4q8qr7yvqoS8BTrd7AfSenSON5jzECrvxYrJ3P07+p6fcJI5RSq9umeVTsfwFI53EW5CKTIk\nZk9Xja48x7N4MZcPHDA3yuWsnZDMxY/Sq1lkY3NZCgsur9VmbrHTidN39XnOn7c5BVlpDLQjwLTd\nA0F5ZgDImjwUWqGVsh28MWNKBxSywdyb2a8CCOHZdSBz7LpszNhV2zgA0YtTlaeOpY9yxZuzY2Pw\nqjqkqdWtiuZiNFP/wmYf3AK1auWt3YndueDucF5j0hBusyExmxZt1hVtks7zV3SevMJRJoSbaYxV\n95/Ky8ELTDht64FUn25Ojqe0SwkOZtmy8R7cApmKYGtq2iv33PzTEvQZc7/GXEx4vNrPxaDz5JW2\nbnIV6rjzUsqEG1qB9kAou+BGgWwqA80CNKGU/ZGy1vpXsbs/MzMKy0u4NRgV296M76WsQWGBtqH2\nvE7TZE0PbrYdm6soa1JUVx6CAUNVhQYVGMyRqpWaUrttAKyqwXlIMzxGI/tRgSWvBIYTi5helYk4\noVUTyjwvhKjDHutpSrTF4KNB7XXsEoKDJdqw4aIQeFbUAsKkoKq6fK5DXjDCa3UsUDQ7lD7U+bTx\nJKAGCctMC6HQ+HbQlLWE1nky88o7DVBajiO3QGBXkwqvQVhKG364wVETmDOfWRgOnKbTNWY8J4tu\n8io0QaEmTJteA9RZiKbAa6GGQIjZ8KC6xnqFZEWEVqDQDB9mr/HkgDDXDxrZtXOzKt0qLFdir8O2\nV929nOdw+kNdQnAw5q7ZTLy2SCjYGFtWN3nxqkt3w+db7iQk5dxnKqJO1TfjmBljVm05O0PVLqG5\nMK2lJSoNX6HnBpFuDJKmy18rDR1QWK6iEePX+2ZIA0729ZoHkCYVC1SpxeYJnqTDz3AXUC2Wgip9\nW8/4UIOEW3Y9S5S6v01AmC3G2wCzOdCbee5AoTGQF9eYPElfwN73Zj84xqN81fvuarRCY0l1m84U\n9py0C42FWfCnbRgl0bakxxk8vIZdTnAQ9XJeKUBqV+eBSklnZKdzA7kiv86bjLSm64HwKpdyXkzl\nyoCZ92wHEnaG0Fai7WJvm1FoahQq11xrtDgm/ehiWIHxEmbSjDar0gQJqDyQmetpDsrDDdE4buM1\nl1K2JJ6YGfQ07ksjHJz5PXcJTXBqaiNEPWvOA4IU7qJnPKCmlN40zUkVjc3zPsP0fFz44TQNC0DL\nLQMQVVZONc67AYpnWH11+cChmfLCdWfnnjr5cpOBPyNxdNobP/+9Y9Jg7qbOr5SuO7MdZBIMiWk5\niapDaJuObMSlNLwjOxhn2mGeAxCzDw6DwaLZThyDDQvabQaUFwz+ma/oxu83+I4qpm6EAzN9oqGu\nhNmwYcEgbGoTXgkKM+8f89nXnXyqyeQVb8yToE0CVTf1oVTeBtBIs7+eXT5wcIgPdaZCYwg6aGQq\nbGvo5vdOGS8f+dYJ3M75h8e640f9XnNGxNxpbdBC63omPuRBwIxbLmYG5NxAnX88P8DPURNy5Gsz\ng7cxwKvQSzSAAGr9AfU9b7bTjIdxNDi/+rQXezDfmTXbpXkKLjyqgN4UwT08HdZe6uvYJQQHaBIt\nZmJtzIKV8MdZHase8WOcPj57nc4yH3I0j39Sa4QATVFFw73VUMfr7oAWQPQiV57550ecszt88/Fr\nv9f0NBZc93xGRDQ8gfmB78KfCgjq114NCCexI0DyQm2+4eZft+810pnVsny7wP/sTENt5wEO/wbw\nX2NqZvz3wH+14DN/AvybwAT494Cfn/5wzt1shhVUYcXMzDIv6Flk59maJ7JmHN4cLK+L7HNAUX1d\no50PWQGBV3kNVQHdQ/G+9SxmztN1wsZr86coxAnfEwveq1+b5TgaXoI7AcczzQmpZn7nqNj9RNZo\n/+9Cw3CUvUqboGm8P9vXD6tVzwaSZwUHD/hvgb8NPAF+AvwZ8FnjM/8W8EPgI+APgP8O+MMzHheo\n55iZjMR8J3yD9/nV5s5b1H9PZfMz8tyg1nZTlLlOPxNju88s+Fz92oLzP+6cDr10CD1mXzuUPVjw\nuYX6i7OYBQXXf75TT+E1bZ5gnycqm5wDTbg73fWcFRx+H/gK+NY+/x+Bv88sOPw94E/t4x8Dy8B1\nYOuMx15oYiFx9pbbfGr01HoCa4cGjJXRzr0+s11aMyduPZAZ8DgyZG+GJ83Z/HjT867//Ky/cMcm\ncQ5gMHMWs6B8LrzKRdkCr+CYtlAalwg9tZ0VHG4BjxrPH2O8g1d95jYXBA4wP+tcIlu4uOkcBsRR\nYHMUjjqV4esc9oT5+0PnddS1XRjIL+BXLiq1/dbYmwkrTgq182e38Hv/6B//SfX4j//oD/jjP5rH\nmRMeTOu31TE8hbnOfN6zJkcPQNE87kntFMDwXRI+b5JHeMvsz//ix/z5X/z4lZ87Kzg8Ae40nt/B\neAbHfea2fe2Q/Wf/8X90gkMe36G0PmPJ3bfW5gbrhYdPFwBG37W9Ux7Bgvn1GPCWM9g7+7n5ife/\n+Cf/zeLfeP2TnLGfYojG94EQ+HcwhGTT/gz4d+3jPwT2OaeQQlf/xNxgaQ4i8Z1OUN+ZzVRwavz7\nXtqCdningMHaoTBslpycz1ecvKjtYjur51AA/xD43zH8x/+AISP/Q/v+PwX+V0zG4itgDPz7Zzvk\nbApOuxDCMf7NDQkqYGgw+It+7tKCx4JrWnSZl90DaNprZ00umb1qQM8AhANBTSV5X/ylU53Keegc\n/jf7r2n/dO75PzyH49Rm006V59DUNrg1//OE3qHdaaofqz/3TtgJAaNpbxN4vI7q9J2zo3iRudeq\n7IqyGSfT/53ncJjNeTOpzDdkuuLMTKl2YQqaQO1uOzsi7jq5HeN1XBp7xfmf2ntybbPo7wmOe+TJ\nXNmMVdqLuRBZa9Al9cIz40kfrhD+5jyH79bmVI91WGFy+bryHAyEiLOKSl+lWHsnTJ9iTApwO3cL\nZv82f/fKXm1Hds85kJ3P8FT1Lups1oyQzT5ZXNv01XYJFUOAdvWcNKYMiLALUJipJnSIwHHA0lyY\ndWWntAa3c2jp8lXa8MR2XEpXLPBahas/WpfhB6rqaMYcF3E2UvZygkOjwbRugAPUFXEs71Bp9vXc\n9xbelHcgfXdlb7edMAU9U1rQke9OIO36sjZ7kSDM5xXShtnnA86XEBzs0lTM5RdKUyJMmW4XVpSF\n/ay8AC/hCkCu7A1as3Bs6YoQY8vi1RsFH+LeTmGXDxw0phw5yjoE2noOtrJwUdR1CAV1YwqzIak4\no6t1ZVd2YjtOHn7Sn9AuWLAZuQocbD1NuwM4bhdxiw5n1TjAZQQHjNzD+QNaY3bblr6pi9jYr8AQ\nvPO8A++mQObK3j07VPmp0Ze1Nv28LEx2otpR3PE/6sz9/FKCA1pXbVQqKJF2h2VhQooZrYOgvsxG\nY59XaHAVYlxZ0867P8yoPS1PpjH7VKjSTIbSAz9ACQ+jetDM1pQ8nV0OcJhJxZjcrrSJSgWGc/BD\ns9+h2ydRWd7BsruO4T0kjjrR8Y9Lh16Bw5U17Yj+8DoDdUF/M2K/RsVsrep9Pz0P7YcoZF2vVs1V\nVz9FiHM5wMENZGFVC1qZ3SuE0TmUSPBDs3GLIyRLuwBrriDt4WIZRzXY/Oeu7MpOa4uyB8dlFObC\nB1eLozHAhSqhyI0X7QVoyzmYb2sWb73wenZJwMFZLRuVwtToVxoKLdB+BH4AWqOLHKFK61aJxhZn\nTlI512gLFatXeforO2+b09y80nTFnQkx348LyDPjIfgBpfAotQukrXLyexFWzJtSSK2s52DAoZQ+\nIowsOKRgd1jWTYbXfHlBo82FG1d2ZRdhr6o8fqgITa0GrlYeC2kAo8zReYrWCuEHlEgKZdDBLC34\nvqYybbwltUKhSUtFoSUijE2DZBmUmd1nsRmrnZRjuHzNcmVvuy3oeycueGPXTtjFVUKZncV1npq+\n6ofkCAMOaCSq6vtnsUs3CrRShk8ocqRlcfNSkWkgiAwBmadQWHAQzOy6LZzsFKuSPO2CoysAubLj\nbGbgvw4ZWJfbN33VZdek7ceYTESeofPc7FPhhxRICrvOSEK1AfFZ7HL2cK0QqjAIiSZTkCkJQWw0\n5mUBRYYoC8sxiMb+mRdgV0BxZXBh/aDe/s+uqSgLE1aUuZkMg5hCexRuLsSMj+9HKtOZ2wm5LKHM\nTSMAhVLkCFTQQni+EYaUuSFt0HWsNp+xqPYTPANoXAmqrqxpZyWym7VJqLU62m19B1b8lBo1sB8a\ncEBSal3tOo86e7+8RODQGMDKgIOHQghBXmqmpUBHHUQYG88hT43eQSuDvNKrF2A11WNHyheuiMkr\nO42dEBwWcmCNUMRVNQMrj/YAaULiMjdhhSogCCHskCFR2mTwPGFEUvXWA/O7wJ3MLhE4WLN7A4oi\nx9MlnjCLr5ISVNBGxG1Ao/MpFClVMQzpkFcvnu0PVSc+QWNeAciVLbSTEo3OFtXTcGlM3eAb7JqK\nMkNlU5O1i1oUMiBVUGrwhEbq0qYy4Sw1VC8XOAhh8r1agcrx0fhSoDQkhSITPqLVAQQ6ywzvUGUs\nPPvPrYWvl8GevnDRFThc2QI71aRh+6NoPtfW65U244bxmvMMnSbmY1GbTEumhUJr8NAIlTfCitP3\n0csFDq66rtZQ5PgoQs9cQpIrkhJEq4fwPHSRIXKjdxBN9G0Iqeq1F+cwyK+8iO+5nVcfsirHavd0\nM7EhPeNElAWiSCFPzXKBqMNUC9LCgIGnS5Opq8oWnN4uDzg4MkYItFZQZHgqJ5RmEVZSKJICVNgB\nPzKNk6eIIjdAICUI45rVO03D+QHEOYHMlV1OO/Pk0Ow/RvwkaIYU0jwvc8hTdFki/BAVdZgqQVaa\npd0eClFkhnerfvd0dnnAYc50niLyKSElvhSkpWJSgo77RgylNDjeQSlTRUc2GF9TU+5NXsKVvZN2\nDhPETIFkJ4ASpspZkZl+rUpE3EaHHZJSkCuNlOBpMylWIqgz7Cx2qcChKkGvFDrPIUsIdEHkSbJS\ncZApyriPaHdNSjibQj41MRgamryD0g3C5vSkzZXG4cpm7DQeRFO5X22xYHY919JDS2lXWhaQT9Fp\ngtYa2epSRF1GuREC+hICFKLMZzdJPqVd2p6tixyRTvBVTuBBqTTDtGBSgugsgfRQeQZpYohJrW3G\nwu497OpMaktKusJzp8lTX2kdrgxO1w+qVZeuH+q6khnYUNizGboMsgSdpQjPR7R7TAoY5QUaiDyJ\nTwlFaiTW3tn22b584GBzvkIrKKYEOiP2TB53lJUMM00ZdiGMrcx6aggctwu09GqAqEKLc+IdvuvN\nYa/sLbDzkNIbXSPATHEX11dd+r7MEPnUKCP9ABX1GBeaJFdIBJEnCHRpFmQ5z0GcTuMAlw0chG1E\nIdBlgU4TgjKjFUh8KZjkJYO0pIx7ld4BF1qUuf0Nb6ZS9axLd9rzulzNeGUXZOeRsdINdWMzw+ZC\niiwx3EPcQbeWGeUGHHxPEFIgsolZyg31coHvBTggap251pAmeFlCW2piz+R6d6c5WdBFtJdMSjM3\nrphZwq3RUprUULW4xd4IbX7/KiV5Zae3s/edalsaIWxfdV5Dbie6FCEkot0nCzrsZ4pcKSJPEKoc\n0rFZeOh+4wz9+ZKBAyalI81GXSpNIBkS64xu5FMqzW5SMC49VNwzKc0ihzSZCy186g1DDM9w2l2B\nDp/fOf3OlV0OO9OttsUXhLD9z4UULoUZGM/B8g0iS8xk5wfQ6jNWkv1pQak0kS8JdYZIJ5DnzIQq\np7TLBQ4uW2GJFp1NIRkQlgm90EMKwWBacJCVFGEXorbxMPIpIp8atWTFOzRiPPPjDXXamU7yChu+\nN3ZGjqnivt2KS/uiE+1VupwSUUyNB6xKiNqUrT4HackwNdWn274kKDNIJ2bNRXMl5yntEoKDqEQh\nusghGRLkEzqhJPQE46xgf1qY0KKzZIAkT21okWEkqZYBbtTcu8CTvsDfvrJLbYe6RjO9LtHSAkZp\nsxT51HjOnT5Z2GN3WjLJS0JP0g4Efp6gpyPDWUjPSq6/L+AApnE836RpyhI1HuAlA3qBoB14pKVi\ne5wxEiGqZQRRusjR0wkin9qGk2aHLBvPnUdJrSNO9orDeNesORuf+daa33IhhWjs5Wr6p2dS7kWG\nTifoPEMEIbq9RCJjticZeanphh5tUSKnQ1QyMZkKeTZggEsIDhoBnm88Aq3QyQgx3qOjU1ZaAUpr\n9pKcvWlJ6rfQUdugbzpB5InNWgjDO7gGdFJVzkbg1HYFCu+8nVPautqztZnCFBK8ABCmaEueQDox\nwqiwTR502EsK9hPTl/uRT1yMYbxvF2RZTc8Zs2iXDhwAc+FeYHa7SibowQ5ROmC1FRD7HoO0YD8p\nyMI+orOMCAJ0YeIxR0xqIdDNhVjfhV3t7n057cJT1ZrZLIVV8aKN/N96DXg+orNEHi+xMy0YpAWB\nFPRCjzCfQDKosxleYPm105/75QMHIUB4CLtPhcoy1MEe/mSXldijH/ukhWJrnLFXSPKob4hJVaKn\nY0SRIpTNWgi/QUyqc/Yemufc2IjkQvmNK7sQq2b08xW5zez0XvHidTZNNEIKyhwRtQwRWfq8GGVM\nc0U38liOPbzkAD06qHbAMurI71lYUa1t9zzwPSgVxXCAONhmyS9Zb4cIYH+as5eUTP02tPsI6UE2\nReQTU2ILZgrP1mXA4Xw6gM1aXO1/8Q6Zdf/PO13d7HuVxF9AmSHzxKTiERD3SMMee9OSvSRHCFhr\nBbTLCWKwQzkeopVCBIHxrL9vnANgkDGIkEFkQovREL23RZwesNEJaYc+k6xke5IxEjGqvYKIWlDk\nhqOw2nMtpAktKlZ3wYY3Z7JFac2rsOJS2fwAO3cdi1uajSEi7eJAoRUiT9HTMRQ5IozQnWUmXpsX\n45xhWhAHHmvtgCjdRw+2UcnYbDHtB7MT3yntEoKDLbYZRKbBhEeRpOQ723gHz1lvB6y2Agql2Znk\n7GWQBm2Iuyaem04QWWKLz2Ll1Bapm6XAz60DLJCwXq3BuBzmao66x+bBef04IOoMBdRegzByaVFM\n0enYcGRxhyzssp8LdpKMvFSsxD7XWj7BaIdyfxeVZQjPhNzfy2xFJYTyA0QYI4IAlRdkO3vw8jHL\nXs5GNyDwBMO0YHucMyJGd1YgiIy0NB0hiqmRTgsnp3YN2SjPdb4nXnsneu71K3uLrHE/nCjpAsBc\nNz1V7bguo78xiwpTSMeQpeCH0F5h4rXZHhsdT+BJNrsRfZHC3nPy/QNUYXa/wg+tR/x9EkE5Ezad\nGcXIMEJrTXYwoNh6Qjx5yWbbZyn2SUvFy0nGXuGRxUuIVtcgdTI23kOZm/vfTPtoLsB7qE58DoRc\n2HEFEG+NHbofF+HlWfGdi2KrAsg2S1EWhmtIxraoS4e8tcSBCtgeZyRZSS/yudGLCMfbFC+fUYxG\nAMgwRARRLfL7XomgoGJ0RdhCtlpIT1IkU9KtLeTLB1yLYL0d4gnBXlLwYlIw1CG6swx+gM4SRDZB\nlPV6i3oxVj2tX8wmOKJWelZS2Qs4zJW9vlVhhK7v0QX0AT0zQVBl4Op9MM0aCZ0l4Pnodp+xiHkx\nKdhJzOria+2AtUggdx6Tv3yJSjPwjDeNH9bhyRnskoKDFTEFMV6rhRcFqKIk2d4lf/QVS2rCZsen\nF/lMC0NM7iufonMN0e6b5d7JCLLEVqcWdRYE6kIwF2FVCfxGx7vKaLwd1tzuvir+czH9QFSqXF1P\nTgiEUohsgp6OTEGjuEPZvcaAiO1xzjgv6IQeN7oB/XJE+exb0p1dVFEiwwgRdywXd/ahfTnBAdBC\nIsII2ergtVoIIcgORkyfPMTbecD1SLPeCRDAzjjj2ahgoEN0exkRROhsirTeg3arNcUs2poNcS6g\niRYBxJW9HTYDDOcP2lrI2YnHeQ1Smr20yxSZT9BpgvADdHuJERHPxwUvxilKwbVOyGbHw9t/SPb8\nKflgbOa3yJL0Ta/hDOB2KcGh2sEqjJGdHl63jxcGlGnG+Ok2+aN7rIiUW72QpVZAWuqKe1BLm3i9\nZXRRmDRROqkLwcgGOXlRnoMjVDUXuKbjyk5t1VobqLdRvKDjCKrUJWD2wMwSdDJC5xmy00cvbXKg\nQ16MMyZ5SS/yuNULWZM5xYPPmTx7QZlmeFGAbHcgbFkR1ffWcxB1aBG28bo9/E4MGqa7Q6YP7uPv\nPGQ9KNhoh0jg5Tjj6TDjoAyM7iEMTS2+PEGUma2+Y7gM3WiWCwsvHEgs8hyuUp3fjS302o65L+dx\nyKo/adPPGlyDKFMTUmRTk4VrLzNQIU9HJuuGhvVOyGYMwd5D0kffku4OAPDbLbxeD6K2XRZwdruk\n4IAVMPkQtfF6fcJ+Fy/0KSZTxo+fUzz6kuVyxM2ez7L1HrbGGduppuhtILrLgDaeQzoxANHcdNdV\nm7qYs2emPt18Oa+LUOFd2awdpWFokoUXdf91k/A0JLgoc5NBSydQlojOEqq7zk4u2RplJEVJP/a5\n2Q1ZFVPKR/cYP3pOkaTIwMfrdJGtLiKM6qzHGe3SgoMJsjxEFON1+/hLy/jtFrpUJNv7TB/cJ9h9\nzIafs9kNCaRgd5LzZJhxoCJUZ81wD3kG2dgU03DCKCktql/guQMzAOH+VgDRfP/Kzt0WaRjEzJsX\nd/8FQIPj0mWlazBeQ4jurjEg5tm4YGeSIRFsdCI2I0W0/4TpN/dItvfRShF0YrxeH9HqmkzFlvaH\nggAAIABJREFUOS3wu7zgIDCr1/wIWj38/jLRchcZBuTjKZNHzyge3qOf7nGj47HSCshKxbNRxtNx\nQdpaRbeXzM3JppBZ72Fm67wLbp4ZAHCimEaa80Jy7FdWtXWTfKT5uPm5izBpNlhy9SGL3BSGzabm\n7fYSWWuN54ni2SglKRRLsc+NjsdyMaB89CXjh0/IRgky8An7XfzeEkQdtDz7mor6LE9vq8A/A74E\n/g9g+YjPfQv8Evg58P+e4XjWGi65EKbOXtTBW1ohWlsi6LbQSjN5sUfyzdf4Lx+y4aXc7EfEgcfB\nNOfRYMq+jig7awi7YpM0scVgXJVqeTGZisrmMhVVGDMHClfYcM42L3DStZt/5OfO13SVGcN4q8XU\n7K9S5ogwRnWvMRAtngxzdic5gSfY7IVshgXR3hOS+/eYvNhDFyVBp0WwvIzsLZn1Q+dYhuAsvf8/\nwYDDx8A/t88XmQb+VeB3gN8/w/HsrzXlx7YmQ9hC9lYIVq8Rr/TwQp9sPGX86Bn5g3t0xy+42ZZc\na4cUSvNsmPJ0mDMJl1HtFaO2bNZ7UOp4wvBcba6zzkQa7lrnO/SVnc7m1Knu4YUrIufOwXksSplF\ngOnEbHEnPXR7mWlrlWejnKfDlKxUrLYCbrY9ltJdiofGa8it1xCv9PBX1kxJxGAujXlGOws4/D3g\nT+3jPwX+7WM+e66tLZq19qQHQQztPv7KOq2NFcJ+GxQkLw+YfPM18tnXXNMj7i5FdCOPg6Tg2/2E\n7UyStpbRcc+ATpYgsqShnLSLvL6rATmjyGuGF3r2M1d2cptprwX6kgtSQR5xMtZrcCRkZqo8ZYnp\nb1GHvLPKy9zj2/0p+0lOK/C43Y+5Lqd4W9+Q3P+SydYeqtAEvRbxtWX85TVE3EV7jm9oXuvp7Szg\ncB3Yso+37PNFpoH/E/gp8B+c4XiLTUi0Z7IWcnmNaH2DaLWPFwcUk5TxoxdM739Je/8Jd3oBN7oR\nnhS8GGU8GWaM/SVUZ83ukGXq/gu3Eal1/7R8UxWcFnTcq633Xs8OZRzenPBMN3bMRpXGS00nxmv1\nI1RnlUm0ypNhzvNRhgaud0Pu9AJ64xdk979g9OA5+WiKF3m0ri3jr64j+ys2hekzQ2ifMdviv+L9\nfwZsLnj9P52/bo6Gqb8FPAPW7e99DvzLRR/8R//4T6rHf/xHf8Af/9EfHHNqCrR1/a2UWnaW8Neu\n077+kuxgzDgtSPdGjO9/S7j+a/r9a3ywssFOkvNimPFokNCPPcJ2l35nFaG2zY3KE6T0URXKi8Nc\n1Xdmc535Chxe394K3UjjPqoCWRiNDUVq1k90lkmiJZ4Ocx7sTxilBevdkPeWY1aybdTDXzO+/zXJ\nzgCEIFru0tlcwV9dh7hniPmqqhkcV1H9z//ix/z5X/z4JGd8avscwyU8B24A/xfwm6/4zn8OjIB/\nsuA9nT27d7Ijuy3JXYl5gVnJlo5g/znZN58x+OIrht88Id2fEPRarPzWD+j9wd8i+eEf8tnQ4xfP\nBmSl4v3lFn/lWotbfkJrtAXjPVOrr9VHRR20H+MUk0KXb0jR2AijZl4+7+I075DNk8lvUjsiBDO7\nrOVTRDZGJENT27TVJ+1d55nu8dnOlK92xnhS8Nev9/mtvqb36OeMf/Iv2fvlF0z3R4TdmP77N1n6\nqx8T/eBH6OXrqLBryUhtuAxdnngiCW98BAsa5ixhxZ8B/8A+/gfA/7TgM22gZx93gH8d+OQMxzSm\nVaNIho0hPR8dxNBZwlu7TnvzGvHaEl4UkI2mDB88ZfrV57R3H/D+csStpRghBFvjjMfDnD3aFJ01\niLpQFuh0ZDfCyakXx7zJ8AKqcmIz135lC22+rd6YqExYzYzlGVRuw4mx2XclNP3uQPZ4Msp5NkxR\nGm70Yt5bjugOn5Dd/5zRN49JBxNDQq71ad9cw1/bRLd6ZgJrFCw6r35xFnD4L4G/g0ll/mv2OcBN\n4H+xjzcxIcQvgB8D/zMm7XkOphv/hOUeQnTUwVvZINzYpHV9jXCpDcB0Z8Do6/uU9z9hNd3mw+WI\ntXbAtFA8HaY8nZQMvS6qtwaB2UZPZBPDP5RFdRz9xlxUURPpLpNxZceYnmuvNwQMzeX5qkTkab3Z\nrR+gu6uMgz7PEsXjg5RxVrDSCvhwNWat2EU/+BXjr74yqctSE/Xapl9v3ECubqCjLtpVmq4u/XzU\nna/iHI6zXeBvL3j9KfB37eP7wG+f4RivMDcraMy6CA+CFqKzjLe2STwckg1GFJOUbJgwfrJN+Nmv\nWV69xu0Pfp/BckxaKKN9OJjS9lsEcZ9uJ0UMd4xazfMRQjTCGIlGmUN+5wNULHx4paZs2Ezo9SZ5\nBtdnrLepSrPfZZ6YeiJSotvLJOESW5nk4UHCbpLRCjw+WGlxNy4JH37G8PPPGD16TjnNCDoRrfVl\nWpvX8a7dhPayydRJN4zNZCnOqRbqWcDhzZolXXQTIIREewEq7CD6awQbQ9rDAcU4oUxzskHC4P4T\nwpW/pLO0wYcrHzHKY+7vTtgeZ7R8j1iGBPEqcZHCZGDSm1bvoP3oLQAIZ02g0Mxu9Pl9Aop5wHzT\nxCMcAgbtgGEC2cT011aPrLXCyzLg4SBja5QhhOBmP+KHyyH9g69JPv+E4dcPSffGSN+z4cQ64fUb\nyOVr6LBtvQZxIeHm5ZVPN1HSLn12s7v2Q2gv4a1cJ7pxg/bmNaKVLkJA8nLAwWdfU3z+M9byXT7o\n+VzvRigNz0Ypj0YFuzom71wz6aGyNNqHPEEUWaV/qEjRt6QzzlYumv/3LtnctR267jdtDWBwRHaZ\nWxJyYnmGFnl7lT3aPB6VPB0YsdO1TsCHSyEbakB57+cMPr/HZGsPrTXRUsfwaDduIFevQ6tvODbp\nU6fSzpeHuryegzOtQSjQEmEBQngBOmwh+6v46U3i0Zh8PKFIMpKdEaMnL4l+9StWVq5x44e/x6jf\nJclLdiY5jw5SWr5HtLLMcidHKoXOpwiR4FZsahHazvg2eBAL7FBWo/rvktub0yic1GaBQdvt7Mx+\nKTrPEH5I2VllFC7zZKh4eJAyygr6kc/7/Yjb/hTxzc8YfvoJo4dbFNOceLlNe3OF+MYm3vpN5NI6\nKmyb8gJCNGqeatsXz8cuPziA7fdO92B3F/ZCVNhFLK0TbE5oJxOKSUqRpGSjjIOvnxD2f0K33efu\nrR+RLMdMC8VekvH1HrQCj3hlk5ZWyNFLKDIDEHZ20n6tRnurAKK536Kzo2bVt1kzcZJ1LRe0E9Vp\nrVI/OmAoc+NxZglYYNCdVdLuJs+GBff3El5OMlq+5O5SzPutkvaLe0z+8v9h/94jslGKH/u0NpZo\n39okunELubyBCjtoP6rrNtgCNQYkzq+A0OUGB+s1GKfK3hDrPWgrjKK9hFy9TpxOUMmYfJxQprtM\ndifs/PoBsvsTeu0eH659RKbafLE9ZnuU8aU3JvIFd3ubRLpEDF8aprnRCd9KgJhhrY8Z/MdWOTof\ntvuV9qpBfVz8fJFVmk5hNTDIw8BQpMajaC2RL9/m2ajk3u6ErWFKIAXvrbT4qC9YGT5h+umPefnp\nN0y2R8hA0rrWp3trnfjmTeTaJrqzjA5bpn9DAxDOv6rY5QYHaPQd10guqyCscrKF6K4gr6VESUJv\nMqVIUsZbQybbQ/Z/9RWy02flt2N+2H+ftGjx1c6E58OU0BNI0eFW6xotrdDjPQMQgsq9fSsBwtmh\nwdMY9G+D13Bi8uxtDieaHIOr6OQ4hinkU/N+e5msd51nE8WXOwnPBilCCO4stfhoyWdt8ozs1z9h\n75dfMH52AEC83KF7e5341h289VuI3io6bJuVyK5S9QV5DfAugIMFBeEWMDruAarwgrCL6F8j2Mxo\nTROKJEWlBdP9hNGTHbxPfs1y3GbtRzEfr94mKxUP9hMeHUwJPIlcidmM12hrYLKHztPZTKL/lnMQ\nlV2StRpvSZjwajuafCRL0PnUvNdeIm2vs5UF3NtLeHiQUGrNrX7Mx2sxG9kL1Jc/Z/DLTxg+fIEq\nFNFSTO/2NVq3bxHcuINY2kCHZnGVdiBU1bt0IHG+V/cOgANWn2RnIW28B4FES2EWTfkhxD3E0gbB\nzSmdNKWc5qhyi2w4ZfTwOX7rU/qtNhu/EfLx6jpZqXg8mPL4YIonBGI55Hq8QguQk/0aICxSXx6A\nmLOTzMjn6a6eyAO4jMAwG0roPDVahlafaWuN7TLi6/2UB/sJWanZ7IZ8tNpis9xDfvsJw0//ksH9\np+RJRtiN6N5ao3P3FtHNu8jlDaOEDGK7JBuEcl6g8xrOv6+9G+BQNYwDB7s5jS3ioT0ftFnW7a1u\nEmUp3SylzHJ0+ZJsNGVw/zEyDumFITd/+Ltka8vkSrM9znh0kCAFsNQEiD3I0hl2uFKqvRU6iJPa\nCQbiuY7VyzDwX2XzAidlsxKOfJwipGeAIV5lu4z5ZpDxYD9hnJWsd0I+WmtzSwwIH3zC6JOfMfjq\nAelggh8HdDaX6b1/k+j2XeTaDcMzBK161WWlaSgbXMP5A8Q7Ag4Y5EajhTKNBght16ZZcRRhGzor\nyPWCuMhQaYbKckbP9kn3xwy+/Bbp+/SCkPc+/JsUa22U0uwmRkEpoAKINsBkz8SW7sbo2HoQVigl\ndO36XWp7Fwb0OdlMjQ8XSmSVjoEiM++3lpjGK2yrmG+GOd/uTxllJautgI/X2rwXJLQe/ZrJL/8/\nBp9/TbIzRPoe7fU+vfdu0LrzHt76beitosOOqdUgzZYGdTjhFledf0gB7xI4AC7Pq1GYG2fDC7BF\nY0OIusi+xlcFrWxKmeWoUjHeOiB5OYTPvkb6kl4Y8oM7v41abfHlLuwkOQ8Ppua3liKut9ZoC9Cj\nXUNSutgPbZfPmhqUGlUXp3nrvQhn3+V5XhbgEbZLNbZNbEiiTVYiM25/e5lpa40XZcQ3g5yH+1OG\nacFy7PPxWpsftHK6Tz9j8sufsP+rLxlvHSCEyUz07m7Sfu8O3uZdxNI1VNQ1E04FDK6fqSo7Z+wq\nrDjeqlqAjrk1LxuAEKaB/RBNB7G0jp9ndPICXZToQjF+ccDkxQDx6T08T9D1fX64+SP0aozehd0k\n58H+FKVBL0fc6GwQC4kYW5KycvdAB2G1uYjxXjRCWZR/q+07SmM6e2skz8eZq+Ak5oAhrdSzOk+N\njqG9Qtq+xlYR8M1BxoODhFFashT7fLza4jd6mt7zz5n84v9m75PPGT/fB62J17r07m7Q+eAu/ub7\niOUNU6HMSfabwDC/HPuCPNN3CxzAuHl2xjZm3D8hzCYiWvrgtyDSiLWb+ErRLktUUaCKksn2kNGz\nA+BLhNR0f0/y0eZfQay2+MJ6EA/2DdusVlvc7t8iEh5itGOUlHafTa3b6CBCy3rFnJbuBh8efK6Y\n7YVtonNie0Xa8LXJr7c5DWmsbvtF1ybqCk5ApXosUlOxPE/QRYGwlZyy3ibPpnB/b8rDgynjrDQe\nw2qL3+jB0ssvmPzsX7Dzi88ZPdlFlZrWWpfenQ06798huPUhcv0WKu6h/Rbas3toNtKWjmeovYiL\nsXcPHKyZdGYTXd0b0rh+fgwxeGs3icoSyhKtFEopku0Rwyf76PILNoDu75Z8dPOvIb0OX+xM2Bql\n3N+dkJcKpTvc7t8kFhI53kGnE0hGZmsz1YYgtmGGb09DAgpRCVcAISpQOL6jvgV2adKMr7aFgFzV\nfpCz3oKQoAoTRhRTE0ZkCVopRNSi7KyS92/xeFRwb2disxKKtU7Ix2ttPu4o+i8+I/npP+fFT79g\n9NismYhXO/TubtD98C7R7Q/x1m+h4iVDQHqNGg2Vx1DWwHDB9m6Cg90YtwYIxz8wS1ACKu4j128R\nakVXuVn9Ocn2iNHzAeLn99BK0P6bJT+4/SP89S6BFDwbpjzcn5KVmrTocKu7Tt8LCMYvIRkZkChz\npCrRqkQFtiCHlKAFWgvjKooG+ttNVnVjUdf5g8QxYcMbG/jf5Tm5mhz2mWv7mR223b4SbtMZbe5l\nMUXkU3Q6tqlKD9HuUXTWGEVrPD3I+XJnzLNhSqk1m72Ij9fafBCldJ5+xvhn/4Ltn33B8PFeFUr0\n39ug9+Fdojsf4m3cQcVmQZX27IIqreuqTjZsrc/5YgHi3QQHOAwQdivMSmrtJNZhC6UVcu0m0UwH\ntQBhQ4yVUtNJU95//28Qrq8QepKH+1OeHEzJSkWSt7nT7bHaDYj8XVNuLk/RaoBUBajShBmerfVn\nO55WhlyqPAnqoaDFfHGZJgF1WjtGCPU2eCsXIIk+vHq20Y6N9RkaCwZ212v3vslG2JqP6QSK3HBX\n7WWy9ir7tHm8n/PV7oQX4xQpJLf7MR+ttrgjR8QPP2X8ix+z+8vPGT2ZBYbuh+8T3f0Qee0WqrVk\nMhMy4BAwKOM5fFfAAO8yOABuebUBCN0YfK50lzA3IuwAILUm1KaenbHnTHfGjLcGaH0PVSg6RcHt\nD/4G4foGoSf5di/h5TijVJAUEXd6IRutddp+hBy+NOXAkiHkKSLqQFjaMCMwndDzQBvvQlDWLqQ9\ny3qmE/axObPDIDGXznqdON+RbMe25TmAxnlzD81zWkBs1h7CPLgebistvLoytHPlLbcg8gSmY7NG\nQmsI2+juKkm0zMsi4NHIENUvJxmxL7m71LICp12Cbz9h/Mufsv/pl4ye7aNVExjeI75rQgndXUVH\nnZn6DDXBbbMTzAHaBdu7DQ5AXSmqqTdwIYYFCKeB6IIHxML1NYGUWyS7I5LtAeivUEVBN0vZ/MFv\nE6xsEvkd7u9OOJjm5EqR5BHTpZAb8Qq9pRB//BKmQ7M3QWlj1qhtXUeX0fDBk2jl1bOD4yPQ9myt\nt+NWhTbGQSXEqjXki8f6sZmBVwzccxnXp/2Ro/L4Bjyb1zW7FdwiUGgCiqxTk/MpyjIzYqZsYu5d\nYcq6EXUpOmuM/R5bmeTBQcbTwZRhVtIJPD5YbfPDvsd6+gz57SeMPvk5B59/zWTLrJdoXevRf2+D\nzgcGGOT6LXRvzZZ7C+eAYT6c+G4zSe8+OIBpWFRFBjqbBYgQQqALUggiIRBSIqRE+i+YvBySvByi\nivuoaUY3SVj/zd/B798hlG2zCcm04OFBQlKUJEsxN9o9VroerSCG8a7ZC3E6Msu/oxYibKP9uBa4\neBK0NCTXXMeovCCXGm2EB1o0AMS8wuyA0vWfI8fnqwbud8FFHNHxZzQiovGnsW1A9Qn3xEqL3WNX\npAcqgrHalq4ZQhQ5FNM6hMjtDmhhjO6sMI2W2Bcdno81DwcJW6OMvFQsxz7vr7T4QUezOn6MuveX\nDD79JcOvHpDsDkFK2qsdenfW6X7wPuHdD/CuHeUxuMmh/ldnua7A4ZzNIi+cACBMB/I8j0hI8Dyk\n7yP850xeDJjujVBffEuRTFmajln9q79LsPIeLS/m20HO1ijl+TAlyRXDXsTtXouNVkjHj5HjHYTz\nIorMhBphx1Sc8kK0FyCEZ7wILesS46qsrgFdVl4NTr9BY8a0g2a2jmADLOYBo2mvNf5P8uHX6MgL\nRWJN96gOrdxb5l42v6OrAbQ4ZWy0LvMhhMaui7C6BbKxAfKyMJ9r91GdNcZBj+0i4Mmo4Mlgyl6S\nI4Rgsxvx/nLEe1FOf/8B+ec/Z/DJrxh++4TsIEH4nvUYrtN+/w7RrQ/w1m+j2ssNYJBzwFCHmG8C\nGOB7Aw7WtDoBQJiNeZWQyA1J6HlIz0P45u/kxT7ZcMrBV08okynL4wH9H/0eH938DbprfTqhx+OD\nKbtJziQvGaYho+WY2911Ol5IFLSQkz2TzZgMDdFVTM3S8qiN9tx+hx7C89DaA1kiVIOYQtv9PHUN\nFNoJdcwVzbrXtiy6aHgQ7vrnxtZrdcDj8OG1fmuOGxCN1513VAGDU7Y1PAQNzXKB1evuM9LJ2b3G\nY/MZYTeYMVsh2hqPeWqOF7bMUuvWMuNwhScjI6N/PspI8pJWILnZj/mgH3DbmxBvfUny6U85+NWX\nDB+9oJhk+HFAa71P7+51uu/fxb/9Id7aTUs+tmdCCd4iYIDvGzjAyQBCBhAKlJRIKQmkpBv4eGGA\nDH3Gz3bJhikH374gHyesjQZ0/vqA93/wO/RWVukGbb7Zn7Izyfl2P2GQFQymLW71uqx327TDNt54\nBzE5QKcJpFNEGCHyDipsI8KWyWp4gS3q4YNUxoOQhQEKVcu1bX7WEJrSXFcNFPVfPXOxwj5cRGwu\n6oivIEBPZAvQZEGqsvaCDmcZzHkrUNpmeCxQzp+jFS45oEV6BhzACNVKJ2RKkPkEPR2js6n5PT+E\ndp+ys8Y0XuFl7vNkZ8qjg4SdSY5GsxIHvLcc84Oez4YewDe/YPLLH7Pz628ZPz9AFYqwE5lFVO/d\noH33Dv7me1bg1LcLqYIZYBBvETDA9xEcrAn9Kg7C6CCIQVwTBEGICGNkFOKFAaPH2yT7CaNn+6g0\nIxtM6O+9ZO03/xXi1ffpRx3u76c8OZiyNcwYTEu2JyHvL7e42bvGctQjau0a4dRoHzUeItIEEcaI\nVsektMKWEWtJ33Ry6YH2qZh0VZjO5PQZWkFpMzJCYpaSOjJTNgZdXUVJL5z9DwPEeegt9Hya8iQa\nhgaRKJrFTCpwbPyWkDZNbJWwMmjsG2GFZmUONgMhswk6GaGyKbrIEX6A6Cyhu2ukrVUGos2zUc43\neyO2RimTvCT2PW70Yz5cjrkbF/QH31J88TOGn/6S/a8eM9mZAJq436Jza43eezdp3b2Lt/meKfEW\nuaXXiziGOWB4w/b9BIdKA3EUQNjBVC3BFgjh4Umflh8iwxAvCpCPXzDdGZPsJRS/fkB6MGZpb4fO\nb/02P7z7I9ZurrPeDrm3M2ZnkvFgL2F/mrM1jrjTj7jZucFSZxW/9QJvskc53EeNDxDTMSJsIVod\nRNS1IBGBF6GlFeh4viEulVXNqcLyE9bD0ApRmIHkQEE01X4VmWkH7MxAFfVgc03m2u20tmh7unmw\ncanmpu6iWcwEqhSungsZml5CBaSIeqCVaaVVEOnYgEKaoIsMEUR4/VV0Z4Wyu8FAtHg2Lng8GPFk\nmLI3yREC1tohH662+XA5Zq3cw3/0a5LPfs7+r+8xeviCbJQhQ0m80qV365qpx3D7Lt7GnXoRVdCy\ntR9PAAxvGCC+n+AAdUdkPsTQVCs5G1JrjUT0BZ7nE4URMorx2xHDRy9Itg/IJzmDh9vkk5T+3gHd\n3W3WPvxrtFbfYynu881ewrNRyigt+XYvYS8p2O6G3OqFrLdustRdR0bPTSGZZGDc3HSCCAaIuI1s\nddFB2xQW9SMDXJ5na1Womo9wBGYFGrVrWi38EmXdDhU3YT2NJvEnSts28589han6mKJaFNdILzaW\nts9oONznhKVYpRWPSd8CgwsZaq/BHa/aei6fIvMEPR2hkzEqN1sMCM/HW7qGai9T9K8zJGJ7Ck9H\nCc+GKXtJTlZq+rFvSMeVmFthQXf/HvrbTxl89isGXz1i8mKfIi0IOj6t9SW6tzdo375FePMu3toN\ndHcVFXfBj6raj4uUj3Uo8ea9Bvg+g4OzYzkIqy2Qnl0dJ0B6eF6ADGNk3MJvxwSdbSZbe2SDCcn2\nAWWakQ/GdF6+pPXD3+T927/JyuYmj4chDw+mvJzk7E4yRmnBTpJzvRNysxey0r5Bv3sNf/QSMdmH\nZATZFJ0m6PEAwhYibludRMvsW+CF9Yzp+9U11UDRAIx5sNCN/D8lqAWx/gJycO6NVzWw/VN7CnWB\nnGb4MpuqrIRfcj7D4NnnspFxsN9X2ugTXOYhT4wIbTpBZYlRNmqNCCJEq4tuL1H0NhjogL3M49m4\n4PkoY2eSMS0UkS+51Ym4uxxzpxeyNH1B8OBL0q8+Z/z114wfbTHdN2FEa6VD+/oy3dvrRDdvE9yw\nFZzay4Z49MPZxVsVMKi3EhjgChyMzQOE1jWP11jurbGpTukh/IAgCPFaLWSrg9+OmTzfId0bkQ8T\nDu4/JT0Y0dvZobP7grX3f4vW8i1W1rs8nYQ8HZiZaWuUsZ/k7CQ519ohN7oxy61Neu1VwukBYrwH\n05EFiH10MkT4IURtZNyG0ICE9i2BaUMh7XtoQkM4qobr2gg7Zv/pGdCoBrJy2YFmgzWyBsfa3Oeq\n8V//mK5I00Yo09xFXcraM3DAYE+mGkxlYSTOdlEUWYKeTtDpxOxiXZZGsxJGZrv6zjJ5a5mhDjko\nQp6NcrYnRumaFApfCtY7ITd7ETe7PhtM6Lz8mvLBZ4zufcno28fVJOCFnt1wZpX2rU3im7fwrt1E\nLK2jW/2G2M3WY6DR5o0U9VGrdd+kXYGDs4rwsmlAhZnihInVK4AQlkgSHsLzkUFEHLXx2h2CTovJ\n85ck2wdk45TJ1h7FOCHb3aOz/YLWhx9z68YPWOpssBbFPBsHbI0y9pKcJ4OUl+OM7UnIejtko91m\nJYroRn2ifIKc7CEmA0gn6OnECHQmgdn0N4gRUct4FhYohB8a0qsaXL710OvqVNqpAWfCEtdJZwHj\n0Ay/SIbszKZTaxCY80iqv7ImDO16kyo8cMRwgx8R1QxbIsrcbHZcmrCBLIHU7ENJnpqdpbQGP0C0\nutDqozrLpGGXEREHRcDWJGd7MmFnbDwFASzHPte7ITc6Ptf9jN50C+/510y//pLxN98wfrZDNpig\nlSboxLSu9c1OVDdvEG7eRK5uInorRvHoxzb8aRZq0dDwGmaVm1fg8JaavUFC2PJyzZslZ3kIL6hi\nXbwQL4iRcRuv08bvdvA7L0he7JEdTMiHCYPkOen+iM72C9ofPKP/3ke0r91ltb/CervF02HAi0nG\nQZLz5GDKzjhnq+VzrR2y3umwEnboBj3izoQgHcB4H5FOTOotS0EMzSAIQghjhB9DZIACP0L7gdkF\nzIUfQoLwjctux7eo0qLarB+ouADbiZsd2PEAmsWznaABAPYFB7DVYG94CxUB6j5DBUzL0EbAAAAO\n30lEQVTCgpZQReUhGAHZFNLEAsMUnac2bFDGswtjdNhGdJYo4j5Tv8NIxuzngu1JzsvxmN0kJ8mN\nqKwX+6y3Q252A66HBUvZS4LnTyge3mN4/x6jR1tMd4eovEAGPmG/TWt9mfaNDeIbm/gbt4y30K71\nCzXx2PByGuTjoRWhb5mdgWE6d9PZs3tv+hyMVWk+x9jX8W0107kbbrc7k9kYPdih3Nsif/Gc6fPn\nJFs7THcOSAdTdFnityNa15bo3LlB64Mf4N/9iHz1Nvtel+3c58kwY3ucM0wLSq2JPEkv8llrB6y3\nQ1ZaHiu+IswGREWCTAbo8YFdKZiiyxIQCM9D2NQrQQyBITEJQgMWXmDSo54l9SrQmOMUqqjALARz\ndTorO84NnvstXVXoangUje9Xawnc6sOyAJUbOXOZmR2j8hQswaizKTpL0coONOmZ6wvbiHYf3Vki\n9VpkYY/90mNvqtie5OxMMgZpwbRQSKAT+Wx0Qm52QzbCkhU1Jjx4SvnoHsk3XzF++ITkxT75OEN4\ngrAbE6/1aW2sEW9eJ7y+iVy5jly6hgq76DC2KVRZgdyhmo9vGTCENz6CBVhwBQ5H2SKAaKQBa5Cw\nlYHKzEhvJwcGJHaek714zuT5NsmLPaa7Q8ppBlIQdmLaGyu079wgfu9D/DsfU6zdZY+YrSk8Hxds\nTzIOpgV5qfGloB16LMcB1zshKy2f5dijqzPCfISfjZDTIXp8YJSX2dTyChjvwPMRfmiEVkEEYYSW\noVlI5Idmbw/nWXierXLcuF4a12sa5zUasg5DxP/f3rn8RpKkBfwXEfmohx9tu9327vZo0AqQ4AaH\nBcGBuYBYDsA/gThwZ0HwB6A9IsR9b9xASCwSy4EVYsUixM4iDsvurFhmepixe9y2y/XKR0Rw+CKz\nssp2t6fbr+6On5TOrKq0KyKd8cUX3ytXtBF8cMW6GmUtPlxHqhJsKUuHqhBBUBX4qpKQZuekCdpA\nmqNyEQiuv4HNhpTZOhPd42ReczyrOZyUHM9rJuXiem70Eh4OUvaHGfs9z5YqyE4+pv7oRxQf/pjp\nhx8zPXhGeTbDWU+Sp+Tba/R3txjsPyTb28fs7KM3H0LH6NitEL2UVdlkVi4JhvthfIzC4WXoCohW\nJW5y/jXniobYClWXokVMTrDHh9ijA4qDT5keHFE8G1GOptiyRmkla9bdBwwf79N798uk7/wMdudd\nTvWAzwr4dFpzOK4kFLus8UCeaDbyhK1+yu4w40EvYTMzDI0lq8aY+Rm6HMPkFD8dy9Kj1Spk5lYm\nEYFhkiAsMlSSo5JU4idMGjSKRGIqdLL8uLduvERg+YGuLFnhl5KHXAgFb4SCq8FW+LoWQVCV+Gou\nr61svmm3NpCIRqQGazDcwOXr2HydKl1j4hNGheOkqHk6KXg2qxgVlqISN2o/NeG6pXxhmPIwV2zp\nOeboQ+onHzD/3w+YfPQJs8NjqrMZznl0asjWB+Rb6wz2d+g92sM83MNsPUKtbctzK1NJwfdad+6H\nrmBY1Hy8b4IBonB4NS7VIpaFRKMay4wnwTZMTnHHh9RHn1I8fcrs8Bnz4zHVeIYrK5TRJIMeve0N\nhl/cpff4HZLHP41/+C7zwUNObMrTacXhpOTptGQ0r5nXVjJHjWaYJWz2Erb6Cdu9lI3csJ4phgb0\n/BQ1P0MX49bH7+diq/C2DtqFX/IUqCAMMEkYjGGvxVDYHisTIjCR9wLeLWwXjWfEu4Vr1VsrA96K\ncJDyfI26DW32pBaDr8qCZtAfivsxG+J6G7j+JlOrGFeeUWF5Nq9FGMxrxqWlqC3WefLEiJYQhOmj\nYcpWYunPj9FHH1I/+SHzJx8x+b9D5ken1JM5rrboNCFd65NtrjF4tEX+aJdkZx+z9QjWHkA+DKXc\nsmDw7d4Dq9qC41xxmXtEFA6vStAeuoVXVmfSdvZsZsjmeQbFGDc5xZ0cUR8/pXr2GcXRKcXJmHo6\nw5Y1KDB5Rra5Rn93m3xvj2TvS/DwMXZzn3m+yWltOJ5bns0qjkNiV2k9znuMVvQSzSA1rGWG9Txh\nM9MMDPQT6BvIfI2upqhigq6CMa9R20sx6PkwYMUw2dzg3ZiH7qOE1cV3UBvg1LzsejW8CKHmugUh\nQCJajMp6kOWQ9HBZX8LI0wGlTplZmNUws3BaOc6KmrPSMi0t89pRO49SikyrVkvY7ovgfJA4+uUI\nMzqAo4+xB08oDsQuVI7G2HmJD5pCOuiRba6R72ySbu+Qbj1CP9hBDR9ATyJWG7vNuf97G8y1HE8i\nXb9/ggGicLg+lqoyaVhacnQjDMNN0ljYq3lwP45wZ8fY02Pq0Qn16QnlaEw9kWdoeO/RiSHp98g2\nN8h2tkh3dlFbe/jNXerBNkW+wUTlnFWeSek4Ky3jomZuZYAQhEVmNLnR9BNNPw17Az3jSfFk2pEp\nSJTDNBWV6xAvYCuZ2RvVv539nWgCSwPhgmsUBKfSi72EfieidZhEZt0kk7W6yXAmpfKaykPpNCWK\nwsGsVsxqL3UyakdRO0rrsE6eqJ4oRZ5oEYpZwjDToj1Rkhcj0ukxavQZ/viA+uiQ4uiY8nSEncyw\nlSzxdJqQDnuk62ukm5uYzQckG1vojS3Jt8gGUtPBZFLFS4daEnD+Wvim7N/9FgoNUThcK82MqYOn\nqpsBqZcFRKti12KBb33yE5idYccj7NkIOw7Hsxm2kAftKCU3bdLPMWvrJOsb6M0t1MaO5AH0N6jS\nAaXpM1cZU6eYVY65dVQWiiAsmntUK0i0IjWKRGsyDWkQIInyJMpjcBjCXnk0HoPsO9UjJLoSLsjq\nhMan0ajaEkEim22OPVh0u9UoKqcoraN0nsp6aueonKe2HuuD3QEvbU80qYZeIkJvYDw9KnI7I62m\nmNmZBJCNjrCjY+rRKXY8lutb1aIlGC2Ztv2eXN+1dcz6JnptQ2Ij8jVU3l8kShlD64JtJ4CupkDH\n5dsNEb/fROFwIzTq9iJ5qQm5PlechM5yw9ngpivwRdAoyilucoabTbCzGW42w5VioVfeyp8zWpK+\n+gNUfw093ID+OvRlb7M+lcmoVEatUyqVUGIow6Crncd68N438Y9AqKekVEitUGj5KukGikQrWQF0\nzwvHl60qPCKUnJfj5rmv1ssySI7D5817KFzXvYlvvy8NQi3TigxL5msSV5L6isSWmGomhXSmI6n+\nPTnFzSayFSXeWhnHSqOSFJ3l6H4f0+uhB2uo4ToqH0AuKfMkUnxnkcPR0RS6Qp+OVwJ4nYRCQxQO\nN8mFPv1uNGDnnG4KcrDaq6C+U4r/XuwAUuehsQe4qhALvguCIlSpUkkaUsn7EiWZS5q3zxeh1Van\n1GhqNFbJTO3CZkO5NBcGajOYgTbGacnGEHbPc2p2h8VirC/+plr6fdXmexkl1nzjPTroGgZL4h0J\nssnyRwKgVDltNTFfyOYKSb/G1rIE8nSMmxk6zSVQLO+JEMh6Elad9mSpo9OQ4blw456Ly2hjE3zI\nE+ksG+5ZCPRVuEw4xAjJ62C19kEniahRxOXJ33RGRSezsKnRkPRQfddx8dUS9VcVEgFobcgVqOTY\nLlxkvq7wtkYVs3Z2VGmKTnNMkpElqbjbTCrxDc2smIhhzSmN8wpRkJXM+hAWE4Lr9q4Z5ZdflE53\nF3WcmqVIs0TRoZqVUR7tPbhqsQSzIQDKVovXrbuzxFkpfOOb4jfaoPtDsXGYJoJVYjwwCaSZuG6T\ntO1366Ztsj3b6M1OP5r8klYgdAKXXjMt4fMQhcO1s2yZV23Ks/javW+mzcXAEsOmDzkcgE+XjFwq\nBAu1lYKcC+7A4I4MAUSNO1A16dFai8BwTgqlKi01HbSUoGu0D5TGNEVSOrEcPpy7GCyd5dILC7V0\nVO0mNLs5dnbJ5aeaWgZNIlIdZn3bZJMuPAHeO3GpppmEi2vd1qlQITYDrYMHJNTjaBO3Qgr+UqxG\nEF9L/fGLQd/YEZa6dvdRjbdBFA43zYqlWrU/nzOwmoxEkAHRqORt9aPwTItVAdJNmOp+dzAe+ib2\nYKk9wbDmLI0A67ayNbR223ZBjy4eLB2jXUtYk3d+bXXw+dbTkbTfqXQ3IA2WbDptWHvXrdwti3dB\nHsdqSy8c8Kttf7uIwuEueNmZp8lW7P52xxgmk12nJkXnxvarN3qzHFlu2J0MBr86YEOFvq52snrO\nUh7IUv2Jiwd/99ve5gH/eYjC4XXn3GBYKe0G57SF5wqmW1eZXzSYVz7rhChHbpYoHN4GPteA8rcr\nG+AFwiFyV0ThEFlBnZusI28nUUeLRCIXEoVDJBK5kCgcboFvf+e7d92EGyX2780kCodb4E2/uWL/\n3kyicIhEIhcShUMkErmQ++S0+ifg1+66EZHIW8i3gffuuhGRSCQSiUQikUgkErkS28C3gB8C/wA8\nuOS8nwD/CXwP+Ldbadmr8ZvAD4AfAV+75Jw/D59/H/iFW2rXdfGi/r0HnCL/r+8Bf3prLYu8MXwd\n+MNw/DXgzy45738QQfI6YIAPgJ9CkqrfB35u5ZzfAr4Zjn8J+Nfbatw1cJX+vQf87a226g6Jrsyb\n4beBb4TjbwC/+5xz75PH6Hl8BRk8PwEq4K+A31k5p9vv7yIa094tte9VuUr/4PX5f70yUTjcDHvA\nQTg+4PIB4oF/BP4d+L1baNer8CXgo87rJ+G9F53z+IbbdV1cpX8e+BVkyfRN4Odvp2l3Q0zZfnm+\nBexf8P6frLx+XvWUXwU+AXbD3/sB8M/X1cBr5qpVHlZn1tel7NJV2vkfwDvAFPgq8DfAz95ko+6S\nKBxenl9/zmcHiOD4FPgCcHjJeZ+E/VPgrxHV9r4Kh4+RgdHwDjK7Pu+cx+G914Gr9O+sc/z3wF8i\nNqNnN9u0yJvE11lYu/+Iiw2SA2A9HA+BfwF+4+ab9tIkwI8Rg13Giw2Sv8zrZZC8Sv/2WGhGX0Hs\nE5HI52IbsSWsujK/CPxdOP4ycgO+D/wX8Me33MaX4avAfyOGu6a9vx+2hr8In38f+MVbbd2r86L+\n/QHyv3of+A4iACORSCQSiUQikUgkEolEIpFIJBKJRCKRSCQSiUQikUgkch/5fwFaMrI6tWr4AAAA\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x12eff9b0>"
       ]
      }
     ],
     "prompt_number": 65
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from JSAnimation import IPython_display\n",
      "from matplotlib import animation\n",
      "extent = [mesh.vectorCCx.min(), mesh.vectorCCx.max(), mesh.vectorCCy.min(), mesh.vectorCCy.max()]\n",
      "fig, ax = plt.subplots(1,3, figsize = (24, 8))\n",
      "for i in range(3):\n",
      "    ax[i].set_xlabel('x (m)', fontsize = 16)\n",
      "    ax[i].set_ylabel('y (m)', fontsize = 16)\n",
      "    ax[i].set_xlim(extent[:2])\n",
      "    ax[i].set_ylim(extent[2:])\n",
      "ax[0].set_title('$e_z$', fontsize = 20)\n",
      "ax[1].set_title('$h_x$', fontsize = 20)\n",
      "ax[2].set_title('$h_y$', fontsize = 20)\n",
      "nskip = 40\n",
      "def animate(i_id):\n",
      "    icount = i_id*nskip\n",
      "    frame1 = ax[0].imshow(np.flipud(e[:,icount].reshape((mesh.nCx, mesh.nCy), order = 'F').T), cmap = 'RdBu', extent=extent)    \n",
      "    frame2 = ax[1].imshow(np.flipud(hx[:,icount].reshape((mesh.nCx, mesh.nCy), order = 'F').T), cmap = 'RdBu', extent=extent)\n",
      "    frame3 = ax[2].imshow(np.flipud(hy[:,icount].reshape((mesh.nCx, mesh.nCy), order = 'F').T), cmap = 'RdBu', extent=extent)    \n",
      "    for i in range(3):\n",
      "        ax[i].imshow(np.flipud(c.reshape((mesh.nCx, mesh.nCy), order = 'F').T), cmap = 'jet', extent=extent, alpha=0.2)    \n",
      "    return frame1, frame2, frame3\n",
      "animation.FuncAnimation(fig, animate, frames=16, interval=40, blit=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "\n",
        "<script language=\"javascript\">\n",
        "  /* Define the Animation class */\n",
        "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
        "    this.img_id = img_id;\n",
        "    this.slider_id = slider_id;\n",
        "    this.loop_select_id = loop_select_id;\n",
        "    this.interval = interval;\n",
        "    this.current_frame = 0;\n",
        "    this.direction = 0;\n",
        "    this.timer = null;\n",
        "    this.frames = new Array(frames.length);\n",
        "\n",
        "    for (var i=0; i<frames.length; i++)\n",
        "    {\n",
        "     this.frames[i] = new Image();\n",
        "     this.frames[i].src = frames[i];\n",
        "    }\n",
        "    document.getElementById(this.slider_id).max = this.frames.length - 1;\n",
        "    this.set_frame(this.current_frame);\n",
        "  }\n",
        "\n",
        "  Animation.prototype.get_loop_state = function(){\n",
        "    var button_group = document[this.loop_select_id].state;\n",
        "    for (var i = 0; i < button_group.length; i++) {\n",
        "        var button = button_group[i];\n",
        "        if (button.checked) {\n",
        "            return button.value;\n",
        "        }\n",
        "    }\n",
        "    return undefined;\n",
        "  }\n",
        "\n",
        "  Animation.prototype.set_frame = function(frame){\n",
        "    this.current_frame = frame;\n",
        "    document.getElementById(this.img_id).src = this.frames[this.current_frame].src;\n",
        "    document.getElementById(this.slider_id).value = this.current_frame;\n",
        "  }\n",
        "\n",
        "  Animation.prototype.next_frame = function()\n",
        "  {\n",
        "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
        "  }\n",
        "\n",
        "  Animation.prototype.previous_frame = function()\n",
        "  {\n",
        "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
        "  }\n",
        "\n",
        "  Animation.prototype.first_frame = function()\n",
        "  {\n",
        "    this.set_frame(0);\n",
        "  }\n",
        "\n",
        "  Animation.prototype.last_frame = function()\n",
        "  {\n",
        "    this.set_frame(this.frames.length - 1);\n",
        "  } \n",
        "\n",
        "  Animation.prototype.slower = function()\n",
        "  {\n",
        "    this.interval /= 0.7;\n",
        "    if(this.direction > 0){this.play_animation();}\n",
        "    else if(this.direction < 0){this.reverse_animation();}\n",
        "  }\n",
        "\n",
        "  Animation.prototype.faster = function()\n",
        "  {\n",
        "    this.interval *= 0.7;\n",
        "    if(this.direction > 0){this.play_animation();}\n",
        "    else if(this.direction < 0){this.reverse_animation();}\n",
        "  }\n",
        "\n",
        "  Animation.prototype.anim_step_forward = function()\n",
        "  {\n",
        "    this.current_frame += 1;\n",
        "    if(this.current_frame < this.frames.length){\n",
        "      this.set_frame(this.current_frame);\n",
        "    }else{\n",
        "      var loop_state = this.get_loop_state();\n",
        "      if(loop_state == \"loop\"){\n",
        "        this.first_frame();\n",
        "      }else if(loop_state == \"reflect\"){\n",
        "        this.last_frame();\n",
        "        this.reverse_animation();\n",
        "      }else{\n",
        "        this.pause_animation();\n",
        "        this.last_frame();\n",
        "      }\n",
        "    }\n",
        "  }\n",
        "\n",
        "  Animation.prototype.anim_step_reverse = function()\n",
        "  {\n",
        "    this.current_frame -= 1;\n",
        "    if(this.current_frame >= 0){\n",
        "      this.set_frame(this.current_frame);\n",
        "    }else{\n",
        "      var loop_state = this.get_loop_state();\n",
        "      if(loop_state == \"loop\"){\n",
        "        this.last_frame();\n",
        "      }else if(loop_state == \"reflect\"){\n",
        "        this.first_frame();\n",
        "        this.play_animation();\n",
        "      }else{\n",
        "        this.pause_animation();\n",
        "        this.first_frame();\n",
        "      }\n",
        "    }\n",
        "  }\n",
        "\n",
        "  Animation.prototype.pause_animation = function()\n",
        "  {\n",
        "    this.direction = 0;\n",
        "    if (this.timer){\n",
        "      clearInterval(this.timer);\n",
        "      this.timer = null;\n",
        "    }\n",
        "  }\n",
        "\n",
        "  Animation.prototype.play_animation = function()\n",
        "  {\n",
        "    this.pause_animation();\n",
        "    this.direction = 1;\n",
        "    var t = this;\n",
        "    if (!this.timer) this.timer = setInterval(function(){t.anim_step_forward();}, this.interval);\n",
        "  }\n",
        "\n",
        "  Animation.prototype.reverse_animation = function()\n",
        "  {\n",
        "    this.pause_animation();\n",
        "    this.direction = -1;\n",
        "    var t = this;\n",
        "    if (!this.timer) this.timer = setInterval(function(){t.anim_step_reverse();}, this.interval);\n",
        "  }\n",
        "</script>\n",
        "\n",
        "<div class=\"animation\" align=\"center\">\n",
        "    <img id=\"_anim_imgPSNFFGOHXPJZQGDC\">\n",
        "    <br>\n",
        "    <input id=\"_anim_sliderPSNFFGOHXPJZQGDC\" type=\"range\" style=\"width:350px\" name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\" onchange=\"animPSNFFGOHXPJZQGDC.set_frame(parseInt(this.value));\"></input>\n",
        "    <br>\n",
        "    <button onclick=\"animPSNFFGOHXPJZQGDC.slower()\">&#8211;</button>\n",
        "    <button onclick=\"animPSNFFGOHXPJZQGDC.first_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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        "    <button onclick=\"animPSNFFGOHXPJZQGDC.reverse_animation()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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        "\"></button>\n",
        "    <button onclick=\"animPSNFFGOHXPJZQGDC.play_animation()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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        "\"></button>\n",
        "    <button onclick=\"animPSNFFGOHXPJZQGDC.next_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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        "\"></button>\n",
        "    <button onclick=\"animPSNFFGOHXPJZQGDC.last_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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        "\"></button>\n",
        "    <button onclick=\"animPSNFFGOHXPJZQGDC.faster()\">+</button>\n",
        "  <form action=\"#n\" name=\"_anim_loop_selectPSNFFGOHXPJZQGDC\" class=\"anim_control\">\n",
        "    <input type=\"radio\" name=\"state\" value=\"once\" > Once </input>\n",
        "    <input type=\"radio\" name=\"state\" value=\"loop\" checked> Loop </input>\n",
        "    <input type=\"radio\" name=\"state\" value=\"reflect\" > Reflect </input>\n",
        "  </form>\n",
        "</div>\n",
        "\n",
        "\n",
        "<script language=\"javascript\">\n",
        "  /* Instantiate the Animation class. */\n",
        "  /* The IDs given should match those used in the template above. */\n",
        "  (function() {\n",
        "    var img_id = \"_anim_imgPSNFFGOHXPJZQGDC\";\n",
        "    var slider_id = \"_anim_sliderPSNFFGOHXPJZQGDC\";\n",
        "    var loop_select_id = \"_anim_loop_selectPSNFFGOHXPJZQGDC\";\n",
        "    var frames = new Array(0);\n",
        "    \n",
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