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{
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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 8: Variable-Reluctance Machines and Stepping Motors"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.1, Page number: 411"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "%matplotlib inline\n",
      "from numpy import *\n",
      "from math import *\n",
      "from matplotlib import *\n",
      "from pylab import *\n",
      "\n",
      "#Variable declaration:\n",
      "R=0.038                               #m\n",
      "a=b=pi/3                            #rad\n",
      "g=2.54*10**-4                       #m\n",
      "D=0.13                              #m\n",
      "N=100                               #turns in both poles\n",
      "uo=4*pi*10**-7                      #permeability of free space()\n",
      "i1=5                                #coil current (A)\n",
      "\n",
      "\n",
      "#Calculation:\n",
      "Lm=N**2*uo*a*R*D/(2*g)\n",
      "#x=symbols('x')\n",
      "subplot(2,1,1)\n",
      "x=linspace(-180,-120,100)\n",
      "L=-(Lm/60)*x-2*Lm\n",
      "plot(x,L,'b')\n",
      "#grid()\n",
      "\n",
      "x=linspace(-60,0,100)\n",
      "L=(Lm/60)*x+Lm\n",
      "plot(x,L,'b')\n",
      "grid()\n",
      "\n",
      "x=linspace(0,60,100)\n",
      "L=-(Lm/60)*x+Lm\n",
      "plot(x,L,'b')\n",
      "grid()\n",
      "\n",
      "\n",
      "x=linspace(120,180,100)\n",
      "L=(Lm/60)*x-2*Lm\n",
      "plot(x,L)\n",
      "annotate('Lm=0.128 H',xy=(-150,0.10))\n",
      "annotate('Lmax',xy=(0,Lm+0.005))\n",
      "ylabel('L11(theta)')\n",
      "xlabel('theta')\n",
      "grid()\n",
      "\n",
      "#part(b)\n",
      "subplot(2,1,2)\n",
      "x1=linspace(-180,-120,100)\n",
      "x2=linspace(-150,-90,100)\n",
      "i1=5\n",
      "i2=4\n",
      "Tm1=(Lm/(2*pi/3))*i1**2\n",
      "Tm2=(Lm/(2*pi/3))*i2**2\n",
      "dll=np.ones(100)\n",
      "plot(x1,-Tm1*np.array(dll),'g')\n",
      "plot(x2,Tm2*np.array(dll),'b--')\n",
      "\n",
      "x1=linspace(-60,0,100)\n",
      "x2=linspace(-90,-30,100)\n",
      "Tm1=(Lm/(2*pi/3))*i1**2\n",
      "Tm2=(Lm/(2*pi/3))*i2**2\n",
      "dll=np.ones(100)\n",
      "plot(x1,Tm1*np.array(dll),'g')\n",
      "plot(x2,-Tm2*np.array(dll),'b--')\n",
      "\n",
      "x1=linspace(0,60,100)\n",
      "x2=linspace(30,90,100)\n",
      "Tm1=(Lm/(2*pi/3))*i1**2\n",
      "Tm2=(Lm/(2*pi/3))*i2**2\n",
      "dll=np.ones(100)\n",
      "plot(x1,-Tm1*np.array(dll),'g')\n",
      "plot(x2,Tm2*np.array(dll),'b--')\n",
      "\n",
      "x1=linspace(120,180,100)\n",
      "x2=linspace(90,150,100)\n",
      "Tm1=(Lm/(2*pi/3))*i1**2\n",
      "Tm2=(Lm/(2*pi/3))*i2**2\n",
      "dll=np.ones(100)\n",
      "plot(x1,Tm1*np.array(dll),'g')\n",
      "plot(x2,-Tm2*np.array(dll),'b--')\n",
      "grid()\n",
      "ylim(-3,3)\n",
      "annotate('___ i1=I1, i2=0', xy=(110,2.6))\n",
      "annotate('---- i1=0, i2=I2', xy=(110,2.2))\n",
      "ylabel('Torque [N.m]')\n",
      "xlabel('thetam [degrees]')\n",
      "\n",
      "#Results:\n",
      "print \"Lm =\",Lm,\"H\"\n",
      "print \"(c)The peak torque =\",round(Tm1,2),\"N.m\"\n",
      "print \"\\t(i)  The net torque, (at thetam=0) =\", 0, \"N.m\"\n",
      "print \"\\t(ii) The net torque, (at thetam=45 deg.) =\", 0, \"N.m\"\n",
      "print \"\\t(iii)The net torque, (at thetam=75 deg) =\", round(Tm1,2), \"N.m\"\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Lm = 0.127968099059 H\n",
        "(c)The peak torque = 1.53 N.m\n",
        "\t(i)  The net torque, (at thetam=0) = 0 N.m\n",
        "\t(ii) The net torque, (at thetam=45 deg.) = 0 N.m\n",
        "\t(iii)The net torque, (at thetam=75 deg) = 1.53 N.m\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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O121sbG5GRUXNJIRg3bp1EevWrYtQnPPVV19F29jY3HRzc7uUmprqpdifkZHh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\nfdjo4+BtxUEIEYWGhsa2bt364YoVK76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jJ9/KU3mbPXv2HEtLy3xFGcbHxwfV5czVlpCQ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\nEEIoIlg4EEIIRQQLB0IIoYj8DRLhonoh4yhPAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x2cad490>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.3, Page number: 424"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "%matplotlib inline\n",
      "from sympy import *\n",
      "from math import *\n",
      "from matplotlib.pyplot import *\n",
      "\n",
      "#Variable declaration:\n",
      "n1=4000                             #r/min\n",
      "R=0.038                             #m\n",
      "a=b=pi/3                            #rad\n",
      "g=2.54*10**-4                       #m\n",
      "D=0.13                              #m\n",
      "N=100                               #turns in both poles\n",
      "uo=4*pi*10**-7                      #permeability of free space(H/m)\n",
      "Ll=0.005                            #H\n",
      "Vo=100                              #phase voltage applied to phase 1.(V)\n",
      "\n",
      "\n",
      "#Calculation:\n",
      "wm=n1*pi/30\n",
      "Lm=N**2*uo*a*R*D/(2*g)\n",
      "thetam=symbols('thetam')\n",
      "t=symbols('t')\n",
      "#for part (a):\n",
      "#for -60<=thetam<=0deg,\n",
      "L11=Ll+(Lm/(pi/3))*(thetam+pi/3)\n",
      "L111=diff(L11,thetam)\n",
      "R1=L111*wm\n",
      "#which is nuch greater than resistance R=1.5 ohm\n",
      "thetam=-pi/3+wm*t\n",
      "i1=Vo*t/(float(round(Ll,3))+float(Lm/(pi/3))*thetam+float(Lm/(pi/3))*pi/3)\n",
      "\n",
      "#for part (b):\n",
      "V2=-200                                     #applied voltage(V)\n",
      "thetam2=symbols('thetam2')\n",
      "L12=Ll+(Lm/(pi/3))*(pi/3-thetam2)\n",
      "L112=diff(L12,thetam2)\n",
      "to=2.5*10**-3                                     #ms\n",
      "thetam2=float(-pi/3+wm*to)\n",
      "i1=Vo*t/(float(round(Ll,3))+float(Lm/(pi/3))*thetam+float(Lm/(pi/3))*pi/3)\n",
      "i2=(0.25-200*(t-to))/(0.005+51.1*(5*10**-3-t))\n",
      "\n",
      "\n",
      "#Results:\n",
      "print \"i1 =\",i1,\"\\t, (where round(16.2934044186179*pi,2) = 51.1 )\"\n",
      "print \"\\ni2 =\",i2,\"\\n\"\n",
      "\n",
      "\n",
      "#Calculations & Results:\n",
      "#for part (c):\n",
      "Lleak=0.005\n",
      "Posintegral=0\n",
      "integral=0\n",
      "N1=500\n",
      "tmax=3.75*10**-3\n",
      "t=[0]*503\n",
      "thet=[0]*503\n",
      "Torque=[0]*503\n",
      "deltat = tmax/N1\n",
      "thetm=[0]*503\n",
      "i=[0]*503\n",
      "for n in range(1,N1+2,1):\n",
      "    t[n-1]=tmax*(n-1)/N1\n",
      "    thetm[n-1]=-(pi/3)+(400*pi/3)*t[n-1]\n",
      "    if (thetm[n-1]<=0):\n",
      "        i[n-1]=100*t[n-1]/(0.005+51.1*t[n-1])\n",
      "        dld1d1theta = 0.122\n",
      "        Torque[n-1]=0.5*i[n-1]**2*dld1d1theta\n",
      "        Posintegral=Posintegral+Torque[n-1]*deltat\n",
      "        integral=Posintegral\n",
      "    else:\n",
      "        i[n-1]=(0.25-200*(t[n-1]-2.5*10**-3))/(0.005+51.1*(5*10**-3-t[n-1]))\n",
      "        dld11dtheta = -0.122\n",
      "        Torque[n-1] = 0.5*i[n-1]**2*dld11dtheta\n",
      "        integral = integral + Torque[n-1]*deltat\n",
      "\n",
      "print \"\\nPositve torque integral =\",Posintegral, \"[N-m-sec]\"\n",
      "print \"\\nTorque integral=\",integral,\"[N-m-sec]\\n\"\n",
      "\n",
      "plot(1000*np.array(t),i)\n",
      "xlabel('time [msec]')\n",
      "ylabel('Phase current [A]')\n",
      "title('(a) phase-1 current profile')\n",
      "grid()\n",
      "show()\n",
      "plot(1000*np.array(t),Torque)\n",
      "xlabel('time [msec]')\n",
      "ylabel('Torque [N-m]')\n",
      "title('(b) torque profile')\n",
      "grid()\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "i1 = 100*t/(51.1872396234976*t + 0.005) \t, (where round(16.2934044186179*pi,2) = 51.1 )\n",
        "\n",
        "i2 = (-200*t + 0.75)/(-51.1*t + 0.2605) \n",
        "\n",
        "\n",
        "Positve torque integral = 0.000456384094483 [N-m-sec]\n",
        "\n",
        "Torque integral= 0.000335463884625 [N-m-sec]\n",
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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dUQoZAcrJtcaSc9kytmn45k3V5KmOVMqzIWrskuVzcjy+5ecDV6/SaCRCGgsT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\nV1DFQAgh5BVUMRBCCHnF/wGN24SgosJe8AAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3e4b1d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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RDV3XvFYqlaipamsaarXa6qeffnorLS3N+5NPPvksPT29RW5ubrOAgIAkUw+6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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3a66fd0>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.4, Page number: 433"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "%matplotlib inline\n",
<<<<<<< HEAD
      "from matplotlib.pyplot import *\n",
=======
>>>>>>> 0ee873700378b995b441b1be6652178f741aea5b
      "\n",
      "#Variavle declaration:\n",
      "rpm=2500                        #rpm of motor\n",
      "\n",
      "\n",
      "#Calculations & Results:\n",
      "#For part (a):\n",
      "theta=[0]*12\n",
      "i=[0]*102\n",
      "lambda1=[0]*102\n",
      "for m in range(1,11,1):\n",
      "    theta[m-1]=10*(m-1)\n",
      "    for n in range(1,102,1):\n",
      "        i[n-1]=30*(n-1)/100\n",
      "        lambda1[n-1]=i[n-1]*(0.005+0.09*((90-theta[m-1])/90))*(8/(i[n-1]+8))\n",
      "\n",
      "    \n",
      "    plot(i,lambda1,'.')\n",
      "    \n",
      "    if m==1:\n",
      "        hold(True)\n",
      "        \n",
      "xlabel('current [A]')\n",
      "ylabel('Lambda [Wb]')\n",
      "title('Family of lambda-i curves as theta_m varies from 0 to 90 degrees')    \n",
      "annotate('theta_m=0 deg',xy=(6,0.03))\n",
      "annotate('theta_m=0 deg',xy=(8,0.5))\n",
      "\n",
      "\n",
      "#for part (b):\n",
      "lambdamax=25*(0.005+0.09*(8/(25+8)))\n",
      "AreaWnet=0\n",
      "AreaWrec=0\n",
      "deli=0.25\n",
      "for n in range(1,102,1):\n",
      "    i[n-1]=25*(n-1)/100\n",
      "    AreaWnet=AreaWnet + deli*i[n-1]*(0.09)*(8/(i[n-1]+8))\n",
      "    AreaWrec=AreaWrec + deli*(lambdamax-i[n-1]*(0.005+0.09*(8/(i[n-1]+8))))\n",
      "\n",
      "Ratio=(AreaWnet+AreaWrec)/AreaWnet\n",
      "print \"part (b): Ratio =\", round(Ratio,2)\n",
      "\n",
      "#for part(b):\n",
      "rps=rpm/60\n",
      "T=1/rps\n",
      "Pphase=2*AreaWnet/T\n",
      "Ptot=2*Pphase\n",
      "print \"part (c): AreaWnet =\", round(AreaWnet,2),\"Joules\"\n",
      "print \"Pphase =\",round(Pphase),\"W\",\"\\tPtot =\",round(Ptot),\"W\\n\"\n",
      "plot(AreaWrec=0.7,AreaWnet=25)\n",
      "grid()\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "part (b): Ratio = 1.55\n",
        "part (c): AreaWnet = 9.91 Joules\n",
        "Pphase = 825.0 W \tPtot = 1651.0 W\n",
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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g0KFDZmhda5gW2iQW17SFgZvmRpwqhqikKIjZGwPVT6u1cZecshz47dZvcK7k\nHKTdToPiqmIAaIm7ODk4adezFmaBKFgEp+echoOig9plfjc+8Lvx4YDoQJtlBDXI4kEAAIBMJoPY\n2Fj43//+BwAa4dm6dSukpqYyPsaLL74IW7ZsgWHDhpmqmXpZtWoVeHh4wKpVq2DTpk0gl8th48aN\ntPu88cYbEBsbC1OmTDFTKzVERem2apALzTCYZpBZMu5iTths8SDhQQAAwIwZM+DYsWMgFAph/Pjx\nMGHCBFi3bh14eHhAfn4+DBs2DJKTkwEA4MqVK7B8+XJQKBTg4eEBSUlJ8Oeff8Ibb7wBPj4+4OTk\nBJmZmbB582Y4fvw4KJVKiIiIgB07dlB+flRUFAwdOhTOnz8PCoUCdu/eDZ9//jncuHEDpk+fDuvX\nr2fUj4EDB8K5c+egZ8+eUF5eDlFRUXDz5s022y1duhTS09PB19cXunTpAvPnz4epU6fq7JuXlxdc\nunQJFixYAHZ2djBu3Dg4efKkVqTbA9GlplK1zLSJEgOYYUiQn+gmY7NrzNiwWXgAwzCTvdLS0l4T\nCoU3AwMDb23cuHE1+f2MjIyoHj161ISFhV0LCwu7tn79+g/J22iaaLtkZGRYugkYhmGYTCbDBg0a\npF3PyMjAXFxcsLKyMqy5uRkbPXo09ueff2KNjY3Y6NGjsUePHmEYhmEpKSnY/PnzMQzDsKioKOzK\nlSvaYxw7dky7PGfOHCw1NZXy86OiorD3338fwzAM+/rrr7FevXph5eXlWENDA9a7d2+sqqoKwzAM\nGzt2LBYWFtbmdfbsWQzDMIzP52uP2dzc3God59ChQ9j48eOx5uZm7MGDBxifz8cOHTpE27eQkBAs\nKysLwzAMe//997HBgwczOneLFmFYZCSGRUdjmFyuWQbQvOLiMEwk0vyfjbDl2lx0bBEW+XMkFp0c\njY35cQwG6wCDdYAJNgu0y6IDIiw6ORqDdYCFJ4Zj43aP0y7L5DJMdECEyZWtv2i29M9UPHt2mvQZ\nb+jLZON41Gq13dKlS79LT08f5+PjUxYeHn5p0qRJx4KCgv4ibhcZGXnu2LFjk0zVDgQzMB1W5YgR\nI8Db2xsAAMLCwkAmk4GLiwvcuHEDxo0bBwAAarVauw35ONeuXYPPPvsM6uvroaqqCkJCQmDixImU\nbZg0SXMZDBo0CAYNGgQ9e/YEAIC+ffvCvXv3wNXVFf744w/GfeJwOMDhtP3Bd/78eYiPjwcOhwO9\nevWCl17vaaOTAAAgAElEQVR6CQAACgsLdfatpqYGFAoFjBw5EgAA4uPj4fjx45SfS5WRRo7dJCUh\n6waH6VgY4vgXoptM34BKaxrj0hkwmfDk5OSMCAwMvB0QECADAJgxY0bK0aNH48jCg7HVFDQTbM4a\n6tq1q3bZzs4OmpqaAAAgJCQEMjMzde6DP+ifPn0KP/zwA1y5cgV8fHzgk08+gadPnzL6PC6X2+qz\nuVwuqNVqAAAYO3YsKBSKNvtu3boVXnrpJa2LzcvLCx4+fAienp46P0uX0FL1jZyggO9LPHeGTJLG\ndtEx56h+qnRlcaq4VZDf0MGVumDzvWfrmEx4ysrKfHx9fUvx9d69e9/Pzs4eSdyGw+FgmZmZEaGh\noXk+Pj5lW7ZsWREcHFxAPta8efMgICAAAAD4fD6EhYVpLxq8tDla79j64MGDoa6urk2peOI6h8OB\n8vJyuHfvHmRlZcGoUaMgPT0d7t+/D/PmzQMejwd//PEH1NbWQlhYGAAA3LhxA65fvw4HDx6EadOm\nUX4+8fNyc3NbrRMf/Hish6o/zz33HKxduxZ27NgBu3btgqFDh7ZKC5ZKpeDm5gb79++HuXPnwq+/\n/gpnzpyBWbNmgVAohHv37sEPP/wAS5YsAZVKBXv37oWAgADg8XiQk5MD9fX18N///rfN91NUFPUs\nUUAKbm4AAFHPKjxLYft2gCNHooDP12y/ZAkAn9+x82Ut6xM/nwj3a++D92Bv8OzuCblZudDVviuc\n+vCUxpJ5ll3hFaJRaGGdEJwbnKGyayWEe4dDgksCAAA4d3GGxNhEyM3KhSWCJVqhWSJYArlZuazp\nryXXpVIpJCUlAQBon5esxVQ+vF9++WXqwoULd+Lre/bsmb106dJvidvU1tbynjx54oRhGPz222/R\n/fv3LyIfB1CMx2zEx8djgwYNwlatWoVJpVIsNjZW+97SpUuxXbt2YRiGYbm5udgLL7yAhYaGYiEh\nIdh///tfDMM0sROhUIg999xzmFKpxObMmYP169cPGzNmDDZ//nzsk08+ofxsYnyI/Nnk2BEdjx8/\nxl5++WWsf//+2Pjx4zE5RQBl6dKlmFAoxMaPH49NmDABO3ToEG3fsrOzsSFDhmBhYWHYO++8g/Xs\nOQYLDc3Qxm6iozVxm/BwDJPJ2B27YYqh16YhMRliHEaulOuMyRgbNt17pgBYHOMxWVZbVlbWqHXr\n1q07efLkawAAGzZsWMPlcptXr169iWqfPn363L1y5cowNze3Kvx/tp7VRvw1bmvYUt+ePHkC777b\nHYqKAB4+3AgKxd/w4EEcAESBSKRxnVmLC40pdOePaXYZ04GXlsgos6XrUxdszmozmfA0NTXZC4XC\nwrNnz77s7e39YMSIETn79u2bSYzx/P333z09PT0rOBwOlpOTM2LatGkHZDJZQKsG2rjwINgNHrup\nqTkAt25tgCdPmgAgADw9k6Ciwl077sZWxIYOJjEZ8jgZfTEZhOlgs/CYLMZjb2/f9N133y199dVX\nT6nVarsFCxb8GBQU9NeOHTsWAwAsXrx4xy+//PKP7du3v2lvb9/k5ORUn5KSMsNU7UGwg6VLl8IF\nPPL+jGXLlsHcuXMt1CJ6Wqo/TwMvr2nw5EnnGXdDrl1mSHYZOaMMZZchANAAUotjy+a+NfaNXDMt\nPp66+rM19k8fRLEpzSuF/O75AGCblowtnj8indLiQSCsBbpxNxJJ69iNLcxpw3TMjFudG0B3QJYM\nwuggiwfRKWE67YCtuNE6Gp+xJksGoQFZPAgEy2jPzJ3WiCniMwiEsUDTIlgY8gBKW4JNfSNOQVBd\nbZxpB9jUP4DW5f8LKgu05f7Jo/+ZlvhnW/+MjdX3j3hRz5vX+gIXiy3cOHqQxYOwWTpD7IbKhUa0\nalB8xoohZ7usWqX7ohYIACorW/apqLBcmxmAYjwIm4VuvhtrdaORXWhUgzVRfIbl0AmKpyeATNZW\nXEQijaDouqhdXFrm2Dh9GiA+HjhpaSjGg0CYGvK9THSnWXPshsqqoSugieIzLIF4UVIJCm6h4IJC\ntF7IVWbj41vWiRc1fhz8ApdIAFxdzdbNdmPpmj36XoBqtVkt5u4bca4bvFaaKWummbJ/VPXOvL7w\n0tY3M3VdM1u+NjHMiP0jTro0dy71BEwCQcuyl1dLcT9ysb9x46gL/7XjogYW12pDFg/CqiH+oHRw\n0PwP/3FoTbEbplloulxoyLIxA1SWi0TSOkWSHGshmt1EdxjZBCcGHfF9dV3E1nRR04BiPAirgypp\nIC4OoEsX63GnUbnQ0HgaM0InKEwC+SIRgELRUt6CHGvBP8MCkzGxeRwPEh6E1WHNSQN0WWh4YgAb\nKjfbFIZkhrUnkI9/Bstm+mOz8Fjc16fvBSjGY7UYq29EFzqb5r5h0j9irEaulGORP0fqjNcQ56Nh\nC1Z3bVLFWsaMaR38exZ3ySDHWoixFboLzdTBQyMBKMaDQBgO0YVuDWNwUBaamSBbMlSxFqrMMKEQ\n4NQp+swwqguNbRedlYFcbQhWQnymqFStPRtsdKchF5oJYZKSTBdrIQfy8ZH9LHCHmRI2u9qQ8CBY\nCTGOw8akATSQ08jQBfknT6a2ZIgBPvw4LIu1WAokPB3A1oXHlucEaW/f2G7ltLFqzl8ACLDdLDSj\nX5uGBvmZWjKW7h/LYLPwoBgPwmLQuejj4jTPHEv/YDVGLbRODV3BPHLWGEBbcSFbL8RlNgb4EIxA\nFg/CYhDdaeQftmyxcqKSopALTR9MLRmya4xqelf8mJb+1WHlsNniQcKDMCt07jT8fUs+b8ixm/hD\n8TbnQjMKVJYM3fiXThrktxRIeDqArQuPLfuZdfWNjUkDdBUEEmMTKbPQbPncAQBIJ06EKIXCeJYM\ny8TF1s8fm4UHxXgQJoeqnlpSEjssG7rYTaeL1xBPVmkpQH5+y/+pYjJ0dcdQHAahA2TxIEwOG6wc\nlP5MgGnqspVaMggNyOJBdGqIBXotZeUQqz13ygoCVDEZumrKyJJBmAhk8VgYW/Qz4884pVIKp05F\naf9nSStH1ayC9DvpRq0gwOpzR840o7JkaApeSnNz2ds/I8Dq82cEkMWD6FSQa6sdOGCeH8d0c9rE\nCeO0yQI2NY8N0xkuqSwZ/H3irwJkySBMDLJ4EEaBDVUHiGNuyNUETs85bRsxGzpLhmk5GRST6RQg\niwdh81iq6gDRynGw06TMUVUTsFroRv8zneESAFkynQhxYaGlm0ALsngsjDX7mfVZOabqG1UqdJww\nDrrYdTGb0Jj03FGJjRkLY1rztckEa+yfuLAQipRKcOJywdPBAWQNDW2WJcHBMDk/H84991zntHhO\nnjz52rJly75Sq9V2Cxcu/O/q1as36dru0qVL4aNHj7544MCBaVOmTDlsyjYhjIelrBxi7IY47iZp\ncpL1WjZ0hevoxswAoHlibACmglKkVMK56moAABA4OEClStVmWVxYCE5crsX6wgSTWTxqtdpOKBQW\npqenj/Px8SkLDw+/tG/fvplBQUF/kbcbP378GScnp/o33njj56lTpx5q1UAbt3isCfKzkTisw5Sx\nHJsqY2PI3DJozIzV0i4LRY+giAQCUKjVkFZVBeE8HrjY20O6XN5m+XRoKAAAuDo4dD6LJycnZ0Rg\nYODtgIAAGQDAjBkzUo4ePRpHFp5vv/32rX/84x+/XLp0KdxUbUEYB30zgRoTulk8JVMl1lMJ2tBZ\nMvF90ZgZ1kEUE0lwMKwqLtYpLoZYKHSCkigUarenW+bbsz90b7IWlpWV+fj6+pbi6717976fnZ09\nkrzN0aNH437//feXLl26FM7hcHSaNvPmzYOAgAAAAODz+RAWFqb1zUqlUgAAq13/6quvrKY/mji2\nFIRCgMTEKODzAZYskUJuru7t8WVDPk/rTpMBuHVzA/DSuNMSXBIgNytXKzaW/D4o+7dli7bGmfRZ\n2ZkoAACxGKRKpWb7Z8kA0vR0AKEQop5NwSxNSADAx88cOMDO/tnIur7+iQsLIef8eejK4UBQRATI\nGhpAeeUK1Dc3Q37//gAAMDk5GaqbmiAvMBAAAFzy86GmqQkgLAzEhYWgvHIFoK4OwseO1YhIRgYI\nnZzAd+RISJfLQVhUBAlqNTwfGQniwkJIKC8HAABXLy9IFArhz3PnQFVaCkdmzwa+vT1IpVJYAgD8\nkBAAAFhSWQm5lZUQFRUFSyorYdkXXwAAaJ+XbMVkrrZDhw5NPXny5Gs7d+5cBACQnJw8Ozs7e+S3\n3377Fr6NSCQ6uGLFii0jR47MnjdvXlJsbGxqZ3O1sT3ASfzBvn17+zw+7e0b1YBPtrrTWvWPBckA\nxobt16ah4BaL8soVraC0x/3l5eAA5SqV1q0VX1Cg0/2Fu7wsZaGwOZ3aZMKTlZU1at26detOnjz5\nGgDAhg0b1nC53GZigkHfvn3v4F/Mo0ePPJycnOp37ty5aNKkSce0DbRx4WE75DlzTOnxIY7DMXeG\nWrthWhkAxWcsAlVsxRjxlIMhIbCyuFgrGtVNTax0eXVK4WlqarIXCoWFZ8+efdnb2/vBiBEjcnQl\nF+C88cYbP8fGxqaSs9qQ8Jgfcw0GpUsaYOWAT7o5aFAygNmhi7XUqtVwoaYGADoWoGejoDCFzcJj\nsm/Q3t6+6bvvvlv66quvnlKr1XYLFiz4MSgo6K8dO3YsBgBYvHjxDlN9tjXBRneGsdKkdfWtPUkD\nrIDGhSaFZ7EaG00GYMu1SWW9EMVFXFgIFSqV1pLxejb/Bl2APqG8XBtboRKXA89iKeRlRMegtXgO\nHTo09ZnFQamajo6OypiYmN9M0jqwfYuHLTc3kZgY46RJ6+ob1VTSrLFw2uFCk86dC1FHjtisVWPO\na9MQ1xhdrIXoDsOPT7ZW2HjvGRM2Wzy0wuPu7v6YGG8hg2EY5/z582OLi4v7maR1YPvCwwbIz1r8\nf8byFFlV0gA5qIVcaEbD2K4xuliLtbjDTInVCs+sWbP27t27dxbdAZhs0xGQ8JgeUycQsD5pgC6o\nhb+PxIYxTFxjIoGgjWsMt15sLdZiKaxWeNiArQuPpcx9UyYQ4BaO8rYSTn14ip1JA1Sxm3ZMkWrr\nrhq6/lnCNWbO/tkCbBYeRmdVqVQ6/vDDD0v+/PPP5zkcDjZ27Njzb7755vZu3bo9NXUDEabBlHXW\ntIM/y1iUNMC0Fpqlpki1AohiQ+UaoxuFT3aNSYKDWwkMCuR3HhhZPCKR6GCPHj1qZ8+enYxhGEci\nkcTX1NS4HDx4UGTyBtq4xWMpjJVAgEM32ycrxAalPzOCqSWDXGPsh80WDyPhCQ4OLigoKAjW9z9T\ngITHeHSkCoE+WBHHYZqR1sljN4a4ychBfku4xhDtg83Cw+gqGTp06NWLFy+OHj169EUATVWCYcOG\nXTFt0zoH5vQzE71LK1d2PImAahI2fHoCs/vQyVVMqaZ7NtLEaNYUIzDETdacmwuV/frpLFBpC64x\nazp/tgat8AwePPh/AJoqBGPGjLng6+tbyuFwsHv37vkJhUJ2T3GHaAPxOYyPeewIxHlx4oRxIAoW\nWdbKeTZosLNWeKazZIhVkpkMrkwUCuHP6mrYLRBQDqhEIAyF1tVWUlLiDwA6zTUOh4P5+/uXmLBt\n2s9BrjbDMPb4HNaUuDFCRpqtwMSSQW6yzgmbXW20wvPOO+98PWbMmAtjxoy54OPjU2bGdmlBwmM4\nxh6fQ4zj4NaNWbLV2hO7sUHBMXbAHwlM54DNwkN7BQYGBt4+cuTI5FWrVm3GMIwTERGRiQtRaGho\nHpfLbTZXQ20VU/qZjeFao4rjMJmEzWh9a2/sxkyY8twZEpPRZ8m0101m6zEQW+8fm6EVnrfeeuvb\nt95661sAzaRtFy9eHJ2ZmRmxbdu2dysrKwW1tbU9zNNMBFOMnblmsThOJ4vdkMvJGBKTsYWAP6Jz\noDedGsMwzvXr14dkZmZGZGZmRhQUFAR7eHg8ioiIyFy7du0nJm8gcrW1C2O41yw2JqcTxG6YlpNB\nMRlER2Gzq41WeMaPH3+mtra2R1hYWO7IkSOzR48efXHgwIE3qaaoNkkDkfC0C2MMDLXYmByiatpI\n7IZsyTAtJ4PviwQGQUWhuBCURUrgOnHBwdMBGmQNwHXiQrAkGIpXFcPAnQNZKzy0V3Tfvn3v5OXl\nhd66dau/m5tblUAgqBQIBJUeHh6PzNVAW8cYfmZju9ecHDQxFOKYHEPQ2zdy0gBLYjdMoeofVXym\nPeVkACzvKrP1GAib+kclIroEBd9OXauGmguaa8tB4ACqSpX2WKoKlSW7oxda4cEnbaupqXHJysoa\ndfHixdHffffd0kePHnmEhITc2L17d4J5momgo6MDQ8lp0iatrUblThOLNeJjpbEbKrEhxmfIrjLi\nMjk+g7ANmAqKskgJ1ec0ljBRRHQJinY7L821xQvngb2LPcjT5cAL54EwUQgF8QUW6C1zGJXMaWho\n6JqTkzMiMzMz4sKFC2OysrJGeXp6VuTn5w8yeQORq00vHXWvkdOk6TLVOoyNuNPoXGhEt5kuSwZh\n3RDFhGyFkAUlf3K+XkERiASgVqihKq2qjYgQl0NPh0JBfIF2u5CDIVC8shiEiUJtu4SJQrDn20NT\ndRM4uDqw1tVGKzzvvvvutszMzIiioqIBzz333DU8nXr06NEX+Xx+tVkaiISnDcYYGGrWBAKqORis\nwJ1GhMqqoUsGQGJjPTAVFKKLSyAStLZCDBQU/PPJIkJcxgWFuE6H1SYXfP311+88//zzf4aGhubZ\n29s3mbFdWmxdeAzxMxsjc82kCQTPhEaqVELUqVOtB3yyPEON6SyZXg4OUH7pEoSPHWuzyQBsioF0\nBCpBuaK8AhFBEe0WFAcvB1CVq3RaIYYKiilgs/DQ9njatGkHevXq9ZBum4cPH/bStw3CuBg6MFRf\nUU+jQTfgk4Xz3dAlA5BnyQRoGaw599YtOBIayppkgM4OVTyFKCjEOEkd1EHV3apWggIAbeIkZEEh\nurjs+fYQLAmmFZSQAy3XBdVyZ4PW4hk6dOjVq1evDqU7AJNtOoKtWzyGUF1tWM01c1g51jJ9NF0y\nAJNZMm3FqrEGmAboKeMpDC0UsqAQ3Vp4O0xpoRgbNls8tMJjZ2endnJyqqc7QI8ePWrLysp8jN6y\nZyDh0UCO6xjy/I7ZG2O6op5E/x8L3WmGJgNUNzXZnAuNjdCNSelogN7WBIUpVis8bMDWhYepH92Q\nuA45TRr/n1msHL4F5uMhN8/EyQCW7p+pMUb/9A1y1DcmxRgBeipBsfXzx2bhsS2Jt2EMiesQ66yJ\nU8VwQHTAuKnSxFhOXJxGEVlk5VDVO0NjaIwLXTaYvkGOTMak4NszCdCjGIp1gCwelmKMlGmju9bI\njYqP73h9HiNCdqeh+IxxYRK8b5MNRoivGDomBWEYbLZ4kPCwFENTponute0TtsPKMyuN51ojNyox\n0eJJA3TutEShEMVn2olBsRaa4L2+QY5IYEyHzQhPRUWF59OnT7vh635+fvdM0ioCti48VH5mQ6sR\nGL0KgZ44Dh2m8qEzzUgztdhYa4yAqbjku+TDoBpNcRJDg/dsFhRrPX9MYbPwMLoqjh07Nmn58uVb\nHzx44O3p6VlRUlLiHxQU9NeNGzeQE9VEkMuWMYVY4DMx1sDZ34iwII7DdK4a5E5rwdC4C9dJU8SU\nF84Dx2ZHgCugN9Ziz7dvFU8hryMQZBhZPEOGDLn++++/vzR+/Pgz165dey4jI+PFPXv2zPnpp5/m\n0+138uTJ15YtW/aVWq22W7hw4X9Xr169ifj+0aNH4z7++ONPuVxuM5fLbf7iiy9WvvTSS7+3aqCN\nWzxEDE2ZNrp7rQNWjrFA5WnaD1FsDI274MdBsRbrh80WDyPhGTZs2JUrV64MCw0Nzbt69epQOzs7\n9ZAhQ65fv359CNU+arXaTigUFqanp4/z8fEpCw8Pv7Rv376ZQUFBf+HbPHnypHv37t2fAAD873//\nG/z666//evv27cBWDexEwmNoXMfo7jULjclh6kLDt+2MYsPYkjEw7oKwHdgsPIyuNFdXV3ldXR1v\n7Nix52fNmrXX09OzwtnZWUG3T05OzojAwMDbAQEBMgCAGTNmpBw9ejSOKDy46AAAKBQK5844zw/R\nz8w0ZZo8PqfD7jW6eXE6UOKmvT709rjQ2JD+bMoYQXvLvwC0TkmmK+tCdoVRucVsPQZi6/1jM4yE\n58iRI5MdHR2V27Zte3fv3r2zamtre+ib9rqsrMzH19e3FF/v3bv3/ezs7JG6jr1mzZoNDx8+7HX6\n9OlXdB1r3rx5EBAQAAAAfD4fwsLCtBeMVCoFALDa9dzcXO26RAIwebIUVqwA4POp98+5kAN5jnkA\nADB542RYEbECnLs4Q2JsIuRm5bbZXu96Tg5E5WmOJ508GWDFCohydgZITARprgHHY7guLiyEnPPn\noSuHA6fmztVMkpabC0InJziVkAAri4shobwc7mZlwQGWnC9TrfeS9NIWrgz4KADci9yh+lw15EIu\n2LvYa4P8+W750ARNMDZ8LAgThbDr1V1QB3UwNnwshBwMgZS5KeC7whe6+XeDkAMhrT6PvM6m/qP1\njq9LpVJISkoCANA+L9mKydKpDx06NPXkyZOv7dy5cxEAQHJy8uzs7OyR33777Vu6tj9//vzYhQsX\n/rewsFDYqoE27mozJK5jlPE5ForjdPb0Z6ZjYWwtgwxhfqzW1ebs7KzgcDg6n/ocDgerra3tQbWv\nj49PWWlpqS++Xlpa6tu7d+/7VNuPHTv2fFNTk/3jx4/d3d3dHzNpvC1ALuRMFdcxegKBGbPVmM7O\naYsVBMgxGcqZJkmVkfF9UQYZwhahFR6FQuEMAPDhhx/+n7e394PZs2cnAwDs3bt31oMHD7zp9h0+\nfPjlW7du9ZfJZAHe3t4P9u/fP33fvn0zidsUFxf369u37x0Oh4PhFa47k+gAACiVUgCI0hvXIZa/\nWXlmpWEJBEQr59lD35RTFUif+dBtNf0Z7x8A85gMMV2ZzpIBsHz5F2L/bBFb7x+bYTyOh5jB9uab\nb24fMmTI9fXr139EeWB7+6bvvvtu6auvvnpKrVbbLViw4MegoKC/duzYsRgAYPHixTsOHTo0dffu\n3QkODg4qZ2dnRUpKyoyOd8m6+OgjgN279RsbRhmfYyYrB7dwlMXFcOr55zWxG9AtNtZq4RSKC+F2\nzm1w83YziSWDQNgyjGI8o0ePvvivf/3r+5kzZ+4DAEhJSZnx/fff/yszMzPC5A20sRiPoWN1qp9W\nt7+ytBlrq3WG2A3dOBmmMRkEwhQUFopBqSwCLtcJgoMlUFy8CgYO3MnaGA8j4bl7926fd95552tc\naMaMGXPh66+/fgdPlTZpA21MeJiO1SGnTBsUyzFjbbWo3Fyd89uYo3SNMTF0nAy+Lxobg+goRBFx\ncPCEhgZZK0HR9Z5aXQs1NRcAAEAgEIFKVQHPPXfOuoXHktia8JBrsOXm6vYzG2VQqKEF3xhCtHJU\nGAbpcnkrd1pCeTlMfPllo36mKTBkxD+eujz7yGybFRdbj4GYo39UIkInKEQRcXAQgEpVCQAtglJd\nfa7New4OXqBSlQOPFw6hoaehoCAeQkPTWCs8jO6Y4uLifsuWLfvq4sWLozkcDhYREZG5bdu2d/v2\n7XvH1A20NZjWYDM4pkN0r23fDrBypdEsHLqaaXHu7lq3Gh67kVZWdvgzTQWV2JBjMgXxBdp1stss\nYF2AzYoOojWGWCHBwRJQKosohKJlubBQTBIULwAA4PHCwd7eBeTydODxwkEoTISCgnid74WEHITi\n4pUgFCaCvT0fgoMlAOBq5m+JOYwsnpEjR2YvXbr0uxkzZqQAAOzfv3/6t99++5auAaFGb6ANWDxM\n4zpGSZk2tO4Ok0MT3Gnkmmlsd6mRXWitSvyTLBk0TqbzwFRQDLFCBAIRqNUKqKpKayMUxGXcQsG3\nI4oI3kZcUJqaqrXr5PfIsHkcD+MioeS6bKGhoXl5eXmhJmvZM2xBeJhqgcHuNRMOBqVyp1lDzTSm\nyQAoAcA2MK1bq8WVRSca5PfwdpGFgrhMFhRdImIIVis8VVVVbhiGcTZv3ryKz+dX41lt+/fvny6X\ny103btz4vskbaAPCQxdqIfqZDa5IYMKinkQrJ87dHbpwuYyFxtwxAqZWDTkZwFCxQTEQ88BUUPLz\nJ+t1axEFJTcXIDycmaAYywoxJ1YrPAEBATJdlQswDONwOBzs7t27fUzaOrAN4amupo7rTPx8Iii8\nFR1zrxk5iYDOymmPZWOW4K0FrRq2PJhNhan7Z2xBaa9bq6hICAkJpxgJiqVFxBCsVnjYgC0IDx0G\nudfIQSP8fyywcswBXWKAsa0aRMegi6EYW1Dwz7OEW4uNWL3wNDU12Z84cWJCSUmJf1NTkz1u8bz3\n3ntfmryBVio8TBMKDHKvGTmBgJytFl9QwKqkAUMTAxCmwxhBeWMLCqI1bBYeRndnbGxsqqOjo3Lw\n4MH/43K5zaZulC3AtPjnEsES7ZQGtKJDVWeNrsAbDVSVBsSFhSAJDjZK0kBHXDVUVg253hlZbMxZ\ndsbWXW179kyEwYMV7RKU9qQG49szEZSQkJYbiGq5vdj6+WMzjJ4qZWVlPnSzjSLaQjWpG7kigXMX\nZ2buNSPXWaMq3GnJGmpMx9bg26IaZ4bB1Fp5+rQUqqvztfsYMtaELigPYBpBQbAfRq62FStWbBk/\nfvyZV1999ZQZ2tQKa3W1USUUGJwybYQEAn2VBswdx0EuNNOhq3ZXR1KIDc3yQi4wy8FmVxsj4Tl8\n+PCU2bNnJzc3N3MdHBxUAPrn4zFaA61EeIwe0zFBAgEbkgbQ2BrjQmW96Krd1d4xKeTR8EhQrAur\nF56AgADZsWPHJg0aNCjf3DEeaxEepvF+cpVpSj+zERIILJ00gPfNVrPQzBUjMCwzrOPWyp9/5tp0\nDAgBGV0AACAASURBVMTWYzxsFh5Gd7efn9+9kJCQGyixgBqqmA5A27gOI/ca3QEZQozjGDNpQB+4\n0BQri+H5U8+3nquGEK/RN/lZZ8IQ11hhoRi4XM11wqR2F1FgqOIp5PcQCFPAyOKZO3furrt37/aJ\njo5O69KlSyOAxhJB6dQt0A0SZRzXMUKBT2MN/uwIuVG5WqFBLrTWGNs1hh8TpRcjyFi9xdOnT5+7\nffr0udvY2NilsbGxCz6Ox9SNsyb4fGpvGONK08TMtZUrDXKv0VWMNiVEdxrHQXOtd9YsNDrXGHW1\n4pYsMWNlhiEQbAVVLugATBMK6GYPbeVnNjBzzVJWDlXsxj3OHbhduFCeUA4vT2T/fDyGQjx3RLEx\nZNAkGwP5th4DsfX+Wb3FU1FR4bl58+ZVBQUFwUql0hFAIwi///77S6ZtHruhGyTKOK6zZQvAunUd\ncq+Zy8ohpz9TxW6CkoLAnm8PlVL2zsdjCGRL5vbtXHBz89ZhybR/0CQ5toJiLQhbhtGTadasWXun\nT5++//jx4xN37NixOCkpaZ5AILCtp4oB0MX/ix4XaeM64lQxpfBEKRQddq85cTUj+cN5PEgKCjKZ\nlUMUGn0VBADAKn9NtifIHxhYCVVVeW2C/LbiGrPG89cebL1/bIaRq23o0KFXr169OpQ4L8/w4cMv\nX758ebjJG8hiVxtdQgHj8ToGuNfIadL4/0xt5WAqDOTpcqtNf6aCyk1maJAfBfYRbIDNrjYuk43w\nTDYvL6/y48ePT7x69epQuVzO3nlVzQSeUKBLKyRTJSAKFrUVHbFYM0YnJgaguhqkS5Zoxum0I6aD\nu9bSqqpAXFioLXFjLNEpFBdCblQuXI+5DvUF9VB9rhqq0qqA250LApEAQk+Hgj3fXpsoQCU6UqnU\nKO0xBYWFYsjNjYLr12Ogvr4AqqvPQVVVGtTXFwNAS5CfaMkMG5YFAoEIQkNPQ0jIQZDJIiE09DTY\n2/O1rjFbEh02nz9jYOv9YzOMnlQffPDBZ9XV1fytW7cuf+utt76tra3tsW3btndN3Tg2QpVQQI7p\n8LvxdbvXyIGhJUsYudeIVo4DR/MjBq+tZmz0xW6sBebZZS0xmfaMfwkIWGdTQoNAmAuDs9q2bdv2\n7rvvvrvNyO1pA9tcbVQFBRiP1TEwc82U5W7ISQMF8QVWOe6GHJ+hGtVPzi4jiw0CwRbEYjEUFRWB\nk5MTSCQSWLVqlXbd09MTZDJZm2V8u507d7LW1Waw8Pj6+paWlpb6Grk9bWCb8FDpBuOYDl1giICp\ny93Q1UwTJgqtJnZDF5+hSl1GMRmEuSAKhz6h0LVdbW0tXLiguaZFIhFUVFTAuWe/fAUCAVRWVrZZ\nJm6HhMdA2CY8VLpBN1aHbsAP1VgCooWDp0cbM4GAWF2AXDONbVNDM880a12fDN/XVKP6bX0cSGfv\nX0dFQyKRwOTJk9slFOT3vLy8oLy8HMLDw+H06dMQHx8PaWlpEB4eDi4uLpCent5mmbgdW4WH3T9n\nWQixQgHjsTpMZ4UjQEyRNtYcOVTVBdjoTqOyZOjmhdHlMrOW1GWE6aByVymVSggKCqIUlKKiIr2i\nIRaLKUVDLBaD07MxF3RCkZiYCPHx8Tq3O3jwIKxcuRISExOBz+eDRCIBsVgMic/Gb+haxrdzdWVv\n/hetxePs7KygKo1TX1/vpFar7UzWsmewzeIhYuy4DtG9tn3AgA7PkUM33w1eXcAaxIZppWXkMrN9\nqKwQU7irFApFu6wLXe/hbdYnFNXV1ZTvGQqb06kBwzCTvdLS0l4TCoU3AwMDb23cuHE1+f3k5ORZ\nQ4YMyRs8ePD1iIiIC3l5eUPI22iaaDkWLcKwyEgMi47GMLm89XvRydEYrAMsPDEckyvl1DvKZBgm\nErU9AInIa9cwyMjAICMDE+Xnd7jt1yKvYRmQgWVABpYvysfyovOwDMjALodfxlRyVYeP31Fu3lyE\nXbsWieXlRWMqlRy7di0Sy8gALCMDsD//9MIyMgC7fDkcUyplWH6+CFOpNN+fSiVvtY6wThYtWoRF\nRkZi0dHR2Ny5c3Uuy+XyVtuNGTMGAwAMADCBQKBdFolEWGRkpM73vLy8MADAwsPDMblcjkVHR2vX\nx40bp3NZLpdjcrkcE4lEtMsYhtG+Z0mePTtN+ow39GWyAzc1Ndn169fv9t27dwMaGxsdQkNDcwsK\nCoKI22RmZo6urq52wZ6J1MiRI7PaNNDCwhMZqfmWADTaQUSulGOiA6K2oqNvRwIZGRna5ei8PAwy\nMrDwy5cxucowYbi56CZ2LfIalhedh+WOy20lNCq5CssX5ZtNdIh907aPIDZXr47RCk1+vgjLy4um\nFBs2oqt/tgTT/hGFgSwUdIJCJRR0gkIUEbJQUAmKTCbTKRSpqamsFQ1j0CmFJzMzc/Srr756El/f\nsGHD+xs2bHifavuqqipXHx+f+20aaGHhiY7WfEvh4XoNFoN2nLB7NxZ57RoWnZeHyZRKTJSfb7Do\nYFhrK+d63HWzCg0Z/MFFJTZEq0alkludJWPrwjNhwgRGgkK0QugsD7KgMLU8iNsRRaSjloetnz82\nC4/JnPtlZWU+vr6+pfh6796972dnZ4+k2v7HH39cEBMT85uu9+bNmwcBAQEAAMDn8yEsLEybjYKP\nPjbV+pIlUqivBzhyJAr4fICJn0+E+7X3wXuwN0imSiA3K1f3/hIJgFgM0oQEgNxcyuPfb2iAPKkU\nICwMVhYXw5LKSsitrGxXe0u3lMJgxWDgOnHhiuIK1EEdjA0fC0FJQfBn7p9Qmdu+43V0vbR0Cwwe\nrAA3Nyc4e1YBd+/mQGBgHgAA5Oe7QVMTwNixmvhMSspc8PVdoY3PVFYugcpK6u+LTetRUVGsag/T\n9S1btoBCoQAnJydobm6G8vJy8Pb2BolEArNnz4b79++Dt7d3q9gIXRDdzc0NADSB8YSEBFi/fr12\nvbm5GSorK1vFP4RCoTaWMXnyZFixYgU8//zzIBaLISEhAQAAXF1dITExEXJzc2HJkiXg7Ozcah2P\nfSxZsgRyn91ffD6/1fqBAwds8vxRrUulUkhKSgIA0D4vWYupFO2XX36ZunDhwp34+p49e2YvXbr0\nW13b/v777y8GBQUVVFVVuZLfAwtbPGQif47EYB1gsA4w0QGCC40uGERg0c2bWgtHrlIZxb3GBivH\nllxo1gqVRWJonIRpbITKlaUvNoIwLcBii8dkB7548eIooqvt888/X6MrwSAvL29Iv379bt+6dStQ\nZwNZJjyUCQUMYzrkBILU9PR2u9eIcRyVXGWxpAF9LrQdO4RW6UJjiiVcNXTxFEMEhc6tlZKSYhVB\ndENBrjYbFB6VSmXft2/f4rt37wY0NDR00ZVcUFJS4tevX7/bFy9eHEXZQAsID53xQplQwDCmQ7Zw\nDLn4ydlq5koaaG8WWnp6qknbY2mM+eBiGqCni6cwFRSmcRJbfzDbev/YLDwmnYE0LS0tetmyZV+p\n1Wq7BQsW/LhmzZoNO3bsWAwAsHjx4h0LFy7876+//vq6n5/fPQAABwcHVU5OzgjiMSwxjoeqHhst\nNKVwjDE+h256AlOOw2FakgaNp2EG1TgUpmNN6EayEwcb4p+la5xIR8aGIKwHNo/jQVNf64A43jN4\ntRhkda2rTmthOPc1ufyNIRUIiCVuTD34k+lATnxbJDbMy6tQlVBhWhqFPJIdCQqCCjYLj8VNLn0v\nsICrTS5vGe9JmUyAYYzjOnQJBFTmviXjOEwHcurD1lwZZPdXaGhou8ekdDRAb05s7fyRsfX+AYtd\nbeyolcIyiPXYnBye1VryDofEWNL81jRzX3fUvUaeZjpYEmyyitHkIpxU0ziT56OxRejK0BPdYbi1\nkpeX166aXPhn6HKHHSD4dMnrBwyYEh2BYCvI1aYH2qrTNHEdQ9xr5ozj0MVuhMJEm3ehGRJrIbrD\nDK3JhUCYCza72pDwPINhuIbxhjHXr7d7/hxTx3GYxm5sUWzIlowhsRa64D0CwTbYLDwW9/Xpe4GZ\nYjzEcE2ftxdhkT9HYtHJ0W3TpiniOuSBoXKVitH4nN0TdlPWVusohhbhNBbm9qEzHeNiaKzF0v0z\nN6h/1g2gGA/7IYZrugwu0k53IE4Vt57ugCKuU6RUal1r4sJCOBASwsi91nC/AarzWqwcfAZQY1g5\nSmWRdt6awkKxzcRumLjJyCVevLw08/Z0NNaCQCCMgKWVT98LzGTxEDPZaKc7IG5IwNDSN8bOViNa\nObm546y6CCcO2ZIxpPw92ZJBIGwdYLHFg2I8OmiVUPD2KkYxneqmJkZTU5MnZ8P/1xErhyp24+4e\nB1xuF6tJEmAa8KeaoAuNcUEgWkAxHiuweCihGatDjuswgVzuxhh+ZqrYjaUtG319M9SSYcMYFwyz\n/RgB6p91Ayy2eDptjIdxFhvNWB1dcR1dEK0cjoPmBwgvnAfCRCFU5la2u+3tGXfDNohWDTkmQzUW\nhmzJAAAa44Lo9BCfYZ6eADJZy/Ns1SpLt46eTutqI9dj488RQ9FjHaVxaMbqME2ZNkaatDWNu2E6\nCJOcuozvi9KVEdYK+QftqlW6xUGXULR3u9pagGe3EggEAM9GBIBIBFBRAXDuHHtdbZ1WeIj12E6f\nBph8JEqbySYKFrXOZCNgSEWC6zHXoSqtqkODQXNzo7QZamwcd0NlydANwtRlySAQ5kSf1dARMWgR\nAM06URx0C0X7tvPyAigv1zzDXFwA0tNbnmfx8QBpaewVHov7+vS9wEQxHnJyGjGT7en8uZTzIpDn\n06GCWGtNKVNSTltAWauNNAaHjZOpUY2TwWMyQqHQprPLbD1GwMb+EacsmTu39W1K9R7VdiNGZGBj\nxrSEcAWC1uFcYniX+B7ddl5eWKvZUYizpYwbp3vZ0O1kspZnGPl5JpezO8Zj8QbobaC50qmJ8+zQ\nJBQwTZsmJxFQQXVzExMGcJGxtNjQJQMQEwBwcUlN1czHYwuThumCjQ9mY2Ls/pHnuWqvUERHY0YW\nioxWQmFsMcCw1oJAtWzodvpAwmMFwtMKmkndqCoSGKOaNN0YHEvBdPS/LVkyCN0YIhTE94iiYQyL\nwhxWg7HFwJwg4WGh8Cw6RlMWh3AlMU2ZNsasoEQr5/r1OLNZOExLzdClNSOsB0PcVXK5YUJBfM8Y\nbihbFgpjw2bh6VTJBcRAYu2UKLhQRkgmOMPXmV/NtMq0oQkEe/ZMhMGDFcDlOgGGqUAuTzdL0oA5\nkgGkUilERUWZrA+Whg39owqOdywbSrPu4iKFmpoo7XsKRUtCDjGYrTuw3fa9gwcBVq5sSRAlJozi\nfSEvk7czZg4KG86fKUEDSFli8bQy2ZeTyuJQxHXoYjpMEwjo2Lkz1GxWDlNLxlguNBQDYY6h8Q9T\nuquGDcto9V5H4xVsw9avT2CxxWPxBuhtoBGFp5XJXk5IJiC/SbhL6KpMM00gIEKXrWZqt5q+ZAAm\nFZkR7YOpoBga/zCXuwphfSDhYYnw0N5IBsR1DEkgMGe2Gjl2g5IBjIexBcXQ+AeKayCoQMLDEuFh\nCt1YHUPca3TZasZPWaXOQjO3JWONroz2CUqG0QTF0DRcU2KN56892Hr/2Cw8napWmzi1pSzOr797\nQtdimc5ibU5cLgAAhPN4kCgUtjqGskipLX9TvLIYQg7on3OHOC+Ou3uctsyNsZIHqBIFyHPQoLll\nWqAKyhMD72Ix9YjyZ1+ttoRffHzLOl1AXSKhDqITTw15nWoZgbBKLK18+l5gzOSCnyMxWAcYrAMs\nP5jkLCdAF9dh6l4z5Zic9g7k7CzuNKbWCl1Q3tgWCgJhKYDFFo/Np1MTf9mqpsVAekkahHuHw4Vf\nXMDhdEsOqPjvv7U12CTBwdraa4bOn0OsrWaMeXHo0p+J89N0hvpnTKwVuvpXdKnBTFN+bfSrRdgQ\nKJ3aghYP8Zdt3HRCJhvpZylVXIdp5pqh2WpM/cxUVg2bB3J2xIduSmvFWHETW48RoP5ZN8Bii8fm\nYzzE6XSS/sMHPv+Zg7wbtHKWU8V1uE6a/+Pz51BBjOMUFoohOFjSoakKyFMLEOeq0Tc/jbVAV0Ke\napCjWNz6nBoaTwFAcRMEwlLYvKuN6ahnqqmrm6qbKF1rxDlyjFF1gM6dlpiYaLXz0xjiGqMr+Y4f\nE7m/EAhq2Oxqs3nhaQXDaUfJcR2qWI4x4jh0GWnESdLYLjZ085pMnkydGYaLC7nUCtF6wY+PxAWB\nYA6bhcfivj59L+hgjIdYDFQ1tmU036LvvqMcJMo0rmOMqgOhoaFWm5Gmv1x9Bu3oerrMMGvA1mME\nqH/WDbA4xsM1paidPHnytYEDB97s37//rU2bNq0mv3/z5s2Bo0ePvtitW7enW7duXW6KNhQ9LoJz\nJecg7XYaXK8r1vwzPByKRo6Ec9XVkFZVBeLCwlb70MV1CgvFkJsbBdevx8CAAdtBIBC1y7UmFosh\nKioKYmJioLq6Grp27fqsSeGQlZUFIpEITp8+Df7+/nDgwAGLWzpisWaa8JgYgHnzWparqzUWzrlz\nGiuluOWrhdBQzbJQqLFSJBKNK+30aY0lgy/7+2tiK3gX8bEryKpBIGwcUylaU1OTXb9+/W7fvXs3\noLGx0SE0NDS3oKAgiLhNRUWF4NKlS8M/+OCD/9uyZctyXceBDlo8xJlFqx+2/MQmF/9kWpGAXPKG\nCWyqJqC7fYZNvMW0/hcCgTA/wGKLx2RZbTk5OSMCAwNvBwQEyAAAZsyYkXL06NG4oKCgv/BtBAJB\npUAgqDxx4sQEY30uOYwjmSoBcaoYEmMTwaVby3BwibNzq2QCGUVFAmICQXCwBLhcTUoVjxcOQmEi\nozYVFRW1mmYAwPLVBFpNEUEzWp84Qp8Y5Nc38h5liSEQCCpMJjxlZWU+vr6+pfh6796972dnZ480\n5Fjz5s2DgIAAAADg8/kQFhamnUdDKpUCAGjXc3KkkJcHABAFYjHAkiW5sESwBPjd+CAuLISc8+eh\nK4cDp+bOhQMhIdr93ZzcAACgSFgE6gQ1hIBGeM6fzwGFIg/CwjQiVFm5BEpL62H27CNgb89v8/n4\nukQigaKiIlAqlaBWqwFAIzbLly+H7du3w5EjR4DP58NXX31F2x9jrovFmu+na1cAB4eoZ2IjBTc3\nzfcVHg6QkCCF9etb1pcvl8L27QBHjmiON3myFFasAODzNetLlkghN1f35+HLpuqPpddR/6x73db6\nJ5VKISkpCQBA+7xkKybLajt06NDUkydPvrZz585FAADJycmzs7OzR3777bdvkbf95JNP1jo7OyuW\nL1++tU0D25nVFhPTkhl1+jQAf1XLT/uoTz+FcwoFALSd1I0qbfr69Rioqkprd5p0VFSU1sqJi4uD\nLl266EyFlhp5Miqm2WXEjDK60fodibcYu29sA/XPujFF/4j1ICVTJbDqzCrtumd3T5BVy9osm2q7\nnZN2AsbSrDaTWTw+Pj5lpaWlvvh6aWmpb+/eve+b6vNwiIMG+XxoiYADgNP06QD+/hDO48FH27iQ\nezu3Vcq0LvfagAHbobh4pd40aboBn0lJSZRJAsa48KncZnQDL8liQ1eg0lBs+aEFgPrHNogPfaYP\n76QjSUYVg9qGWrhQekHbnoonFXCuRPP8ETgJoLK+ss2yqbZjMyYTnuHDh1++detWf5lMFuDt7f1g\n//790/ft2zdT17bGVOVV58VQEVME8Sc0FwWf8LSVTJwI4vJySBQKQXY7XxvTKRQXtqoyTaxCUFy8\nEkJC9D+FiXEcsVgMEonEZAM+yXEsgrYaHJNBIIyFIQJgjO3wDFYA8z/k8e28uj+L4XqHQ2JsIsQf\niteuu3RzgfQ76W2WTbkdWzHpANK0tLToZcuWfaVWq+0WLFjw45o1azbs2LFjMQDA4sWLd5SXl3uF\nh4dfqq2t7cHlcpt5PF5dQUFBsLOzs0LbwHa62qKSorQXgShYBAfGJ+r0G12PuQ5VaVXAC+dB6OlQ\ng9xrRCtHpfr/9s48qqlr3+PfgEgFcgkok2DBKxWZTFDBAZUgoEIVrBq1qHWm15Znfe1y6GvXqp0s\nbZeP0tq6nFqwtkUpr632iqXUoKgXUQQHaEV6SRUFRAElijLt90dMOMQkhJCQk3P3Z62zyMnZOdk7\nm+xvfsPeuw15eXm9nvCpr7mvzapRX/CSTRMvqauGnWgTBvVBvrOqEw+9HvZaAOZkzulxwJYESPQa\n2HtTTt4qR05ljs5BOXdpLhKzE5FTmQO/Zj8MEw7rsZy+9wsdGoosSRY2/LoBu2bvguApAZoeNqmS\nm5SfvfpjU5VzGuTEWlcb51YuiPsmTvVPkLs0Fxv/0rzqtHpMR1/3mraVBnTFcXShbfBSt2q0xWfU\nl5Bh0xwYSx2Y9cWU7TOl1cB0B+ka5B1rHHHX467Ga8YUAGOVU35u+g7eLzi+gMlTJxtVDARPsecL\nyOaVCzgnPOr/BOLSUhxvUrjUtn9ui/D6QRqXwmEuf+PiItHqXmMmDRh7WRtDrBo2CQ1Fgb4Whbms\nBnd7d9Ter+3VIG9KATBWOUp3qPD0AX2Ehzlg/+CaBFtZl6kQd+0achoaEMrn44tXrSA/ofgF5yJx\n6RbX0eZeU08aSExMNOreN9rExlKsGq5hjKwkfS0Kc1kNTHeQss09DfJUACwPKjx9QB/hEYu73FCX\nXcQIrH98IpGg6dtvVRNFr8WXq+I6dnt34FFHpWpiKACN2xgwLRxjrBKt7kITi/Nx4YIYgO4UZ0vE\n3K42QywPpmj0KBTl9YCPcSyK/rQa9BUHc/efqeF6+6jw9AF9hIc5d+eUYxxs8pgTebq+ZMy4zmVZ\ntF6utbi4OJWFY6g7TZcL7a+/8lFUJOaM2DAx1hfbUCtEm7tKl6AwRaNHoTiWh9BJxrEo1MuxAa4P\nzFxvHxWePqCP8CzPTsKRMxUQBtjh+5k74Liua/TWtsWBrsw1pnttx44dBrnTqAutZ/QVlF5ZIXq4\nq3QJijGyktgiHJT/bKjw9AG9XG2MFOrhYdvxtEe4KotNFt01X8d2++cYFF7fY+aaunvNkLXUmO4/\nrrnQesLYgtIrK0QPd1VPsQwKhQtQ4ekDernaGCnUA8d+gVP3upbFeXNDhyquY/XFq7grPwHgSfda\nX+fkqMdutG1qpn4rSzL3ey0oMkAS13dBMdQKMTWW1HeGQNtn2bBZeEy2ckF/8sMxV1QWumCklyMS\nxig+51A+H7v8/ODwLVRxnfJr9gA0ryzNXHkgISFBlUigS3R0rfCsvnQPm1cJMMRC0TWzWzl722+w\nn87Z1uqCwlxJXPkeymsHJV0foPq5tscUCoWdcMLiYfq1mhYvRtLrr6u2O2DS3t6kylx76aWNWtOk\ndVk5+sZu2OhG05blZWyXl74WCnVrUSimg80WDzeEh5HWdiVgL1pkHapkgj/rXuq2n44ynmNomjTb\nYze6Uoi1ZXlRQaFQuAcVnj6gTXi6Lf//ziXIrlyE3ahReEdtkmjb/7ysMW1a3zRpQ2M3+mKIn1mX\na0zX5EVtWV6mEhSu+9Bp+ywbrrePzcJjsTEe5orMLos7UO/pCTQ3Y2GnDbwB8EP5j+M6XTuGpqba\nobJS3GOaNBtiN/qKi67VcdVXrFWW70sMhUKhUPqKxVo8w15KQnVLBRzt7BCy/F3k329GKJ+P3QO+\ngPzyJTiMckagMBNA14oE0dFz9EqT1uZOM3Xshik2uuIuulxjuiYvUiiU/xzYbPFYrPBM3iPGqRuK\ngfjTkzvgfDcYo5wdYPXeum4p02lpAr3SpJlWTltb1z42xo7d6GvJ6CsudPIihULRBJuFx8rcFTCU\nN779E9J04OT3jph4XwTPs21o/qURD8o6AXSlTCvTpHNycmBvbw+JRILc3Fxs3CiAWKzIS2hq6nLd\n5eQA9vaK5WxycwFvb4U7rS+ik3Q4CeJ0MeK+iUN5fTmO/3UcOZU5SDqchKJTRarzPxv+BKBwkxWu\nLoQkQILcpbmqVOM5PnOwsGUhvAXeOCg5iNLCUsyePVvlGtNHdDIyMlBTU2N4Y3oBc097Jg0NDYiJ\nicHIkSMxffp0ND1ePVwXy5cvR3Z2tpFr2De0tY8r0PZRTIXFCk9MuzfEMiD88l0MrLoCQBHXGTvr\nB7i4SFTL4KhvQX3w4EEIBIJuQqO+LXR6eu/FhikuSgtEk9gwxWXX7F2wHWCrOmeKjVJclGIieEqA\n1IhUpO9O79Pnlp6ejps3b/bpHn0lJSUFMTExqKioQFRUFFJSUnp8DY/HA4/Hyh9vFAqll1isqy3p\nk09QAcDO1hYfjDsNecUVOIxyxmc73FFZKVPNzwGgSpPeuFGg0Z1m6JpphsRk+uImW7RoEQ4dOgQ/\nPz/ExMTg2WefxZYtWzBkyBBcvnwZY8eOxf79+wEAxcXFeO211yCXyzFkyBCkp6fj5MmTWLFiBTw9\nPWFnZ4fTp0/jo48+ws8//4yWlhZMmjQJO3fu1Pr+YrEYY8aMQUFBAeRyOfbt24etW7eirKwMCxcu\nxLvvvqvX5zZq1CgcP34cbm5uqK2thVgsxh9//PFEueTkZOTl5WHYsGEYOHAgVq5ciXnz5mlsm7u7\nO86ePYtVq1bB2toa0dHROHr0KC5duqRXnSgUrsFmVxsIIaw+FFV8koizZwmkUgKplOw/GUqkUhCp\nFCQ01IUAIACIRCLp/poIQgDFkZBAiERCSGOjxttrZc2hNSTiqwgSuz+WhO8NJ9gCgi0g7h+7E2wB\nCd0VShpbGkns/ljVuaxRRiQHJaSxpZdvpoZMJiNBQUGqc6lUShwdHcmNGzdIZ2cnmThxIjl58iRp\nbW0lEydOJLdv3yaEEJKZmUlWrlxJCCFELBaT4uJi1T0aGhpUj5cuXUoOHz6s9f3FYjHZvHkzIYSQ\ntLQ04uHhQWpra8mjR4+Il5eX6l5TpkwhIpHoieO3334jhBAiEAhU9+zs7Ox2riQ7O5vExMSQfNNF\nagAAEQxJREFUzs5OcvPmTSIQCEh2drbOtgUGBpLCwkJCCCGbN28mwcHB+n60FArneDx2mn0M13RY\nbDr1nA9aMedPwNbeGn5pTpC3KeI6zs6OABQJBIpJoV1JAzY2itcq3Wn6WDbqyQAVdyo0pi7rWv5F\nPT2ZSW/mEhANll9YWBiGDh0KABCJRJDJZHB0dERZWRmio6MBAB0dHaoy6vc5duwYPv74Yzx48AAN\nDQ0IDAzErFmztNYhPj4eABAUFISgoCC4ubkBAP7+97/j2rVrcHJywokTJ/RumzYXWkFBARITE8Hj\n8eDh4YFp06YBAK5cuaKxbXfv3oVcLsf48eMBAImJifj55591vndf4fo8ENo+LahP7tu4kTGp0BWQ\nyXq+1h/lWIzFCs/k24Mgv9AKoAMpzz+Fa04ucHZ2xM6de7rNz2HO90lIUCQN9ORO0+ZCSzqcBDub\nxzEjDWKjay6MqbC1tVU9tra2Rnt7OwAgMDAQp0+f1vga5UD/8OFDvPzyyyguLoanpyfefvttPHz4\nUK/3s7Ky6vbeVlZW6OjoAABMmTIFcrkccrkcDg4OqjLbtm3DtGnTVC42d3d31NTUwNXVVeN7aRJa\nbW1TT1DQ9tr/GPQdHHUNbJ2dwJYt7BhETVGupQXw9+/9/dQn9926xZhU6ALU1/d8rT/KsRiLER71\n79FAe2sAioSC+oFNOHuqHkAeIiOv4umnDyIxUVFOPWlAm+BoExumVdPTxEtD6M0vLj6fj+bmZp1l\neDwe/Pz8UF9fj8LCQkyYMAFtbW24evUqAgICwOfzce/ePQBQiczgwYMhl8uRlZWFBQsWGNwWJQUF\nBTqvx8fHIyMjA5s2bUJGRgbmzJnzRJmpU6di586dWLZsGerq6iCVSrF48eIe21ZUVISwsDBkZmbq\nX+Fuy2DoP5iJ2TSIGjo46hjYxGwaRE1QTgwAVVW9v5+7YkxAaKjiV2xiYte5o2NX8FjXtf4qx1bM\n7evr6cDjGI/7mjUEyyMIFseShIWNpPziKnJyfygpPTeDzJgRTQCQ0NBQEh7eporjKGM4mmI5zFhN\nY0sjifgqQmO8xljxGWORmJhIgoKCyMaNG0l+fj6ZPXu26lpycjLJyMgghBBSWlpKpk6dSoRCIQkM\nDCR79uwhhChiJ35+fiQkJIS0tLSQN998k4wYMYKEh4eTlStXkrffflv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       "text": [
        "<matplotlib.figure.Figure at 0x315dc10>"
       ]
      }
     ],
     "prompt_number": 16
    }
   ],
   "metadata": {}
  }
 ]
}