2014_07_18b_pymc_nonlinear_model_example.ipynb

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   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pymc as pm\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt, seaborn as sns\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# From [StackOverflow](http://stackoverflow.com/questions/24804298/fit-a-function-to-data-observations-pymcmc-pymc)\n",
      "\n",
      "> I am trying to fit some data with a Gaussian (and more complex) function(s). I have created a small example below.\n",
      "\n",
      "> My first question is, am I doing it right?\n",
      "\n",
      "Yes!  You need to include a burn-in period, which you know.  I like to throw out the first half of my samples.  You don't need to do any thinning, but sometimes it will make your post-MCMC work faster to process and smaller to store.\n",
      "\n",
      "The only other thing I advise is to set a random seed, so that your results are \"reproducible\": `np.random.seed(12345)` will do the trick.\n",
      "\n",
      "Oh, and if I was really giving too much advice, I'd say `import seaborn` to make the `matplotlib` results a little more beautiful.\n",
      "\n",
      "> My second question is, how do I add an error in the x-direction, i.e. in the x-position of the observations/data?\n",
      "\n",
      "One way is to include a latent variable for each error.  This works in your example, but will not be feasible if you have many more observations.  I'll give a little example to get you started down this road.\n",
      "\n",
      "> It is very hard to find nice guides on how to do this kind of regression in PyMC. Perhaps because its easier to use some least squares, or similar approach, I however have many parameters in the end and need to see how well we can constrain them and compare different models, pyMC seemed like the good choice for that.\n",
      "\n",
      "Someone should write a book!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# set random seed for reproducibility\n",
      "np.random.seed(12345)\n",
      "\n",
      "x = np.arange(5,400,10)*1e3\n",
      "\n",
      "# Parameters for gaussian\n",
      "amp_true = 0.2\n",
      "size_true = 1.8\n",
      "ps_true = 0.1\n",
      "\n",
      "# Gaussian function\n",
      "gauss = lambda x,amp,size,ps: amp*np.exp(-1*(np.pi**2/(3600.*180.)*size*x)**2/(4.*np.log(2.)))+ps\n",
      "f_true = gauss(x=x,amp=amp_true, size=size_true, ps=ps_true )\n",
      "\n",
      "# add noise to the data points\n",
      "noise = np.random.normal(size=len(x)) * .02 \n",
      "f = f_true + noise \n",
      "f_error = np.ones_like(f_true)*0.05*f.max()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# define the model/function to be fitted.\n",
      "def model(x, f): \n",
      "    amp = pm.Uniform('amp', 0.05, 0.4, value= 0.15)\n",
      "    size = pm.Uniform('size', 0.5, 2.5, value= 1.0)\n",
      "    ps = pm.Normal('ps', 0.13, 40, value=0.15)\n",
      "\n",
      "    @pm.deterministic(plot=False)\n",
      "    def gauss(x=x, amp=amp, size=size, ps=ps):\n",
      "        e = -1*(np.pi**2*size*x/(3600.*180.))**2/(4.*np.log(2.))\n",
      "        return amp*np.exp(e)+ps\n",
      "    y = pm.Normal('y', mu=gauss, tau=1.0/f_error**2, value=f, observed=True)\n",
      "    return locals()\n",
      "\n",
      "MDL = pm.MCMC(model(x,f))\n",
      "MDL.sample(20000, 10000, 1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--------         21%                  ] 4219 of 20000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------- 42%                  ] 8515 of 20000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------60%--                ] 12051 of 20000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------76%---------         ] 15300 of 20000 complete in 2.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------92%---------------   ] 18576 of 20000 complete in 2.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 20000 of 20000 complete in 2.7 sec"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# extract and plot results\n",
      "y_min = MDL.stats()['gauss']['quantiles'][2.5]\n",
      "y_max = MDL.stats()['gauss']['quantiles'][97.5]\n",
      "y_fit = MDL.stats()['gauss']['mean']\n",
      "plt.plot(x,f_true,'b', marker='None', ls='-', lw=1, label='True')\n",
      "plt.errorbar(x,f,yerr=f_error, color='r', marker='.', ls='None', label='Observed')\n",
      "plt.plot(x,y_fit,'k', marker='+', ls='None', ms=5, mew=1, label='Fit')\n",
      "plt.fill_between(x, y_min, y_max, color='0.5', alpha=0.5)\n",
      "plt.legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "<matplotlib.legend.Legend at 0x1ae81978>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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qyhbaPA90UUp9ArwOTGtFb6NTeeABG2PcK6lJ6YYrNZWVDz8Stl7Tw05Op4MN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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x18f11fd0>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pm.Matplot.plot(MDL)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Plotting amp\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " size\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " ps\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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5w3ehX/DkcDjICmOap0QHX8keWWzEwG787LyxvL10C9v3V8XtPCce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\ndx+FbdPrGZrUKlVnvs4HNmbm9og4A7i8XEZEHAv8DnBqZu6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       "text": [
        "<matplotlib.figure.Figure at 0x18f577b8>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ZT4EhuKqtaQxqsVq4fAsiO0jOlfNIzpX9YgmuPABKqbOAUq31bKWUG4hvvZV4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\nooiTJjt7wsdMbDe066Nx/EGD2FTZwAU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       "text": [
        "<matplotlib.figure.Figure at 0x1b34d898>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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+9ANefn+Vp9O0Ipd/6hBxUxvrGrl75gLmfLzO/UJJ3lC+kvepDt2XqFtzEvA8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\nkiRJkiRJkiSpFf4fCBSj6tPQmjAAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1ba54828>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is a way to include error in `x`:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# add noise to observed x values\n",
      "x_obs = pm.rnormal(mu=x, tau=(1e4)**-2)\n",
      "\n",
      "# define the model/function to be fitted.\n",
      "def model(x_obs, f): \n",
      "    amp = pm.Uniform('amp', 0.05, 0.4, value= 0.15)\n",
      "    size = pm.Uniform('size', 0.5, 2.5, value= 1.0)\n",
      "    ps = pm.Normal('ps', 0.13, 40, value=0.15)\n",
      "    \n",
      "    x_pred = pm.Normal('x', mu=x_obs, tau=(1e4)**-2) # this allows error in x_obs\n",
      "\n",
      "    @pm.deterministic(plot=False)\n",
      "    def gauss(x=x_pred, amp=amp, size=size, ps=ps):\n",
      "        e = -1*(np.pi**2*size*x/(3600.*180.))**2/(4.*np.log(2.))\n",
      "        return amp*np.exp(e)+ps\n",
      "    y = pm.Normal('y', mu=gauss, tau=1.0/f_error**2, value=f, observed=True)\n",
      "    return locals()\n",
      "\n",
      "MDL = pm.MCMC(model(x_obs, f))\n",
      "MDL.use_step_method(pm.AdaptiveMetropolis, MDL.x_pred) # use AdaptiveMetropolis to \"learn\" how to step\n",
      "MDL.sample(200000, 100000, 10)  # run chain longer since there are more dimensions"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  1%                  ] 2432 of 200000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
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       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-                 3%                  ] 6373 of 200000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
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        "\r",
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       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
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       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                6%                  ] 12410 of 200000 complete in 3.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                6%                  ] 13979 of 200000 complete in 3.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               7%                  ] 15822 of 200000 complete in 4.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               8%                  ] 17627 of 200000 complete in 4.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               9%                  ] 19714 of 200000 complete in 5.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             10%                  ] 21723 of 200000 complete in 5.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             11%                  ] 23678 of 200000 complete in 6.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             12%                  ] 25784 of 200000 complete in 6.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----            13%                  ] 27559 of 200000 complete in 7.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
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       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
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        "\r",
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       ]
      },
      {
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        "\r",
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       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
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       ]
      },
      {
       "output_type": "stream",
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        "\r",
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       ]
      },
      {
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        "\r",
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      },
      {
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        "\r",
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      },
      {
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      {
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        "\r",
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      },
      {
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        "\r",
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      },
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        "\r",
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        "\r",
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      },
      {
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        "\r",
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      {
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        "\r",
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      {
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      },
      {
       "output_type": "stream",
       "stream": "stdout",
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     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# extract and plot results\n",
      "y_min = MDL.stats()['gauss']['quantiles'][2.5]\n",
      "y_max = MDL.stats()['gauss']['quantiles'][97.5]\n",
      "y_fit = MDL.stats()['gauss']['mean']\n",
      "x_fit = MDL.x_pred.trace().mean(0)\n",
      "plt.plot(x,f_true,'b', marker='.', ls='-', lw=1, label='True')\n",
      "plt.errorbar(x_obs, f, yerr=f_error, color='r', marker='.', ls='None', label='Observed')\n",
      "plt.plot(x_fit,y_fit,'k', marker='+', ls='None', ms=5, mew=1, label='Fit')\n",
      "plt.fill_between(x_fit, y_min, y_max, color='0.5', alpha=0.5)\n",
      "plt.legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "<matplotlib.legend.Legend at 0x1ba70400>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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TWIgF1Gz7DNOU6SUhEoH8TxZkZQXf571yyTeN99QFN/uVsyxZ90GIRCLBQbBq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\nQgghhBBCCCGEEEIIIYQQ0fH/AXxaolRRymo8AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1b8e4d30>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pm.Matplot.plot(MDL)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Plotting size\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " amp\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " ps\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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2C3UQEZdyXgCVZpmYGfTpkrKIicAvvu971EZNbUPC0/gTKflt//iEa+5/n+11\nDXyzagsPvPBl3O+NJwE+uAfq1icWJFCy3LVm4zYlTmfWLOB6/895QD2wt7U2MD4/BzgS2BeYZ62t\nt9ZWAkuBscAk4GX/sS/7jxURiYvjhvByoQPqnmcXRd3v9Xq56M/Rc7DCvi/B42t3NHLXrM8SXpD0\no68SW0R0SZILnuaa6x/+CIBzfziaof0LYxwt7WWtrQYwxhTiC6Z+C9wZdEgVUAwUAVsjbK8M2Zbz\nAvk0GhpyB7WXczkugEo7T/oXcIzmq5VbuG7mh0m9d21Z4km5yazmHk8O1OoNznlsiNM8+OJXXH7a\nXtkuRodgjBkCzAbutdY+ZYy5PWh3EVCBL0gKjmgLw2wPbIuqpKQ7nTrlp6LoUZWWpi8Av+GGG9J2\n7nDaU5cunTtBkvN5OnfOT/nnmM52iSQd7ZWNeqRLNuviuADquQw8muK7LM8OWh/mES5OEs8Q3t/n\nfJ2BkrRPNhPdp//rs+xdvIMwxvQHXgWmWmsDC4p9aow51Fr7FnAM8DrwEXCLMaYr0A0YjS/BfB5w\nLPCx/9iY3cJbMpAfWFpaSFmZcx7d1B7trcuO+uSHxOvrG1P6OeZKu+RKPSD7dXFcAPVtO9baiVe6\nn8EmIhlxLb5ht+uNMYFcqEuBu/1J4l8Cz/hn4d0NvIMvV+paa22dMeY+4FFjzDtAHXBm5qsgIm7l\nuAAq3TzATY/Oz3YxHE3PMRM3sNZeii9gCnVYmGMfBB4M2bYdOC0thXMw5dS4i9rLuTpeAJULWepp\npvhJJHfpRuwuai/niiuAMsZMBG6z1k4O2b4vvnVXPMBa4CxrrfOW8JYOST1pIiKSLjHXgTLGXAXM\nxLfSb/B2D/AAcLa19mB8yZrD01HIVKrYpvgultocWcsonQ90FhGRji2eHqilwEnA4yHbDbAJuNwY\nMwZ4yVr7TYrLl3I1tbkRHKRTroQdn6Xxwc4ibpXpnJpHn3qWuiRn022p2NZBVueKTDlQzhUzgLLW\nzjbGDAuzqy++RyNcCHwLvGiMmR80ndiRlAMlIh1Zpm/E73z+HU3FeyT35uLS1BbGhRQ4OVd7HuWy\nCVhqrf3GWtuA71EI+6SmWOnz7brcWP9CREREsqc9AdQyoKcxZqT/9cH4FqdztPlfbch2EURERMTl\nElnGwAtgjDkD6GmtnWmM+SXwpD+hfJ61dk46CikiIqmhnBp3UXs5V1wBlLV2Bb58J6y1TwVtnwtM\nTEvJRETVSxeRAAAgAElEQVQk5XQjdhe1l3O1ZwhPREREpENSACUiIiKSIAVQIiIdyIwZ05vzasT5\n1F7O1eGehSci0pEpp8Zd1F7OpR4oERERkQQpgBIRERFJkAIoEZEORDk17qL2ci7lQImIdCDKqXEX\ntZdzqQdKREREJEEKoEREREQSpABKRKQDUU6Nu6i9nEs5UCIiHYhyatxF7eVc6oESERERSZACKBER\nEZEEaQhPRKQDCeTT5PrQUMXWrTzxz2eTem9Bt66cfMIPU1yi5HSU9nIjBVAiIh1IR7kR1/famzeW\nJ/dez5bFnHxCasuTrI7SXm6kITwRERGRBCmAEhEREUmQAigRkQ5E6wq5i9rLuZQDJSLSgSinxl3U\nXs6lHigRERGRBCmAEhEREUlQXAGUMWaiMWZulP0PGGNuTV2xREQkHZRT4y5qL+eKmQNljLkK+Cmw\nLcL+84ExwJspLZmIiKSccmrcRe3lXPH0QC0FTgI8oTuMMQcC+wH3h9svIiIikotiBlDW2tlAQ+h2\nY8xA4HrgIhQ8iYiISAfSnmUMTgH6Av8FBgDdjTFfWWsfS0nJREQk5fRsNXdRezlX0gGUtfYe4B4A\nY8zPgd2SCZ7Gm1I+tWXJFkNERBKgG7G7qL2cK5FlDLwAxpgzjDFTIu1PVJdOWklBUqtHN60PKyIi\n6RXXncZauwI40P/zU2H2P5raYokkb9jAIr5YvjnbxRARkRym7h/JOZrRIBKZ1hVyF7WXc+X8WMdu\nO/fi61UV2S5GWp19zG48MudrAA7YYwDvf7E+yyXKrqTGkkU6COXUuIvay7my3gPl9ab3dlfYvUta\nz+80fYq7xTxmSL+eGShJ9uTndYw+qFGDi7NdBBGRDiurAZTJwA0g3vBsaP9C+pcURD3mhrP3bX+B\n4nTw2IEcvd/OXHzSnik/94+P2CXl53SSbl3ys12EjNh7l9KUn/N7+w5J+TlFRHJRVgOo/Pw8PJ7Y\nvQXtmlUVo4era+d8bjh7X244Z1+OmzQs6rFDBxQmX44EHTFhMKcdPorxppSuCQQEmQhKna6ga+vv\nyxlhAsbDxu2UsutNOW53Tp08Mu7jx+/Sl71N8sHPYeMHAbDrzr2SPod0XMqpcRe1l3NlPQcqniG8\noh5dqK5tsxh6fOePsf++Kw4NKktSl2h2ycljufvZz5N676QxA5i3uCV3KTiwTGRAao/hvRO/9tid\nmPf5dwm/z6lC2/GofYfwwZfrWb6uqnnbwD49Una9kYOK6dergFlzv03ZOaP52fcMJx40nKIeHWt4\nWlJDOTXuovZyroz2QB21385ttjU1xY5a4umlCthjeG9+/eNxLRsymFE8bpe+Sb93z5F9UlKGRD6r\nAG8HSLvu0ql1L95h41PXA5WoWD2d4ew+rKT5Z4/HEzN42ivJ71OsYexQN587ManriIi4XdaTyEcN\njjwMsc+uvmGO0JCgf+/uEd9zwkHDGT2spRdmYN/U9TQA/PzoXaPuL05Dr0CsmGji6P7tOn+a8/hT\nZtKYATGP2WNE+MAhtIqdO2UnT2pgn+4MG1CU8FILe42MHZxPu3ASA/v4/m2cdGj8Q4rBDgkZ2hxU\nGvnfT6f8PHZK8b8vERG3yGgAFe5GHanXZrede3HK5FGMGlTMlON2b7XvitP2iniN0BtTpxTPyDp0\n3CAeunpy8+tdh7QOANMTi0SvQyI5UgC7DC5OaqgvUb8+Y3xKz5cLN+tAD+H+e8QOBhNVUtiVW6bs\nz8O/OZwh/XqySxL5cPl5eVx+esu/rz/8Yr8oR7sk8pZWlFPjLmov58psABXmF26/XpGHDPr1KuDa\nn01g5/6tk7f7RnlPe1ZRjDexN3iYLDR4SdWyDMHVSPWssk75eVxx+rjYBwKT9hzAA78+LK5jdxlc\nzPf3a5nFNXpoCQ9dPZmHf3N4MsVso12fbDva5YqgIeE//d8B7SlFswm7pn4GXaih/WNPeijs3rnN\ntp4FLdtCh4THjIgceCcTsEnmTZ16ufJqXETt5VxZ7YFKRS9IXsgveE9IBDVsoO8msk+YG1boOjqh\ns7fi0d3/nsAz/ZK9T0fLXfrVqZF73OJ12/n7t9k2eW/fbK5jDhjWZt8vjh3N3ZcezC+OHU2n/Mhf\nk8CQEcA1P53A6Ye3nvGWTE5WJF07xxtIprZnJDiALY0WvMchmU+jpLArpf7cpOEDUzsTNDhYCugc\npb0PHz+4zbY//HI/Ljl5bFL/fkRE3Cqjv/GC76W/+/k+Uf9CjnTjDV0k0eOh1f0y9G17jujDb8/a\nhyH9etCti+XdReua912VgiGmYQMKOWKfwfQt9t3g0rEw6OAULHzZr6Rt3thPjzKccuhIdh5c0maf\nF2/Ym2vf4m6Ub61tfj20fyHrNtW0u3yxdO6UF3d+Wc+C1OahjRhYlLJzhX4/Q76+Yd0x9UA8wEUn\n7YkZksDSBXFEazuHab+d+vbghIOGh/0DJ7gHKvBVH1zak8GlPXlz4dr4yyYi4nIZDaCOO2gEr3+8\nmotO2pPhMW5KB4YkDN8yZSLXzfyQX/xgdKvtnfLzaGxqjHgej8fDiJ181/rxEaOaA6ih/Quj9qwk\nYuROLT1ZcUwqDCu0Jy2VD3QbXBo+APN4PAn3GvzmJ3vz5YotbNhSQ1XNDk46dCRH7TuEHmGCrVT6\n4YHD4jrO6/XygwOG8t8PVrb7mpPHD+LIfQantBctuJ3vv/JQwMP5d74Z9thJYwZw8F47Nb+nPWtH\nhRrav5BTJ4+krr6RD7/c0Gqfx+PhhIOGt3nPr388rsOs8p7LAvk0GhZyB7WXc2U0gBo5uBcPXT05\n5g1p6olj2Ge3fq22DezTo1UuzW/P2ofX5q+mW5d83lwY3xpG3bt1ZtSgYpau3Ur39izOCZSWFFC2\nZXubR8WcccQuPPzfrxI+X5/irhwzcWfmfLgq6nFHT9yZl/3HHL3fzvTqGbu3Zb/Rvs+yX0lB81Bj\nTFECwYPGDmz1uihNj8vpXdSVzZV1ABwzcWcWLimP+Z5O+Xlhg8K8oBt/vKu7/+z7LTMuLzt1bNyP\nBbrxF/txw8MfNb8+Yu/BvP7JGqB1z2qsmYC//OHuUfe3R+fOeew+rHdcn2mwVuuTKZZyJd2I3UXt\n5VwZX8YgXPB01tG7tlptPJ7ejBE7FXHe8XvQKd6AoE05knpbs1unHsSph41k4u6tlxA4aOxApl04\nKex7Zl51WKvX9/7qkOafhw0o4tTJoyJe76zv78qU43anNOhZd6cdPorv+dfW+v5+Qzhyn7b5Ka3K\nfN7+3Bh1VlWLbM+v6ldSwHU/26f5dTy9hf1LCrjo1PDJ8T8/ejd2H1bCrefvz/iQnpx4VrofO7Jv\nxF7T0K9S6LMGgycaZDLoCM0HTDW3LH8hIpIOWV8HCuCwcYO457JDYh+YAqlaNLJ/7+4cs//QVj0b\nASWFXcO+Jz+v9cedyPDZYeMHccAeAyLegU8/fBfOPNKE3Reoscfjidn716fIV/Z4erbSaf/d+0f8\nHIONG9WyDMZlp+0Vcd2v/r27c+WPx9M/TC7Y5aeP4/qz9wnzrsQcP2lY2Ee6BH9Hwn1fgo0clLp8\nq3CKArPukvlnEPLdOePI3H6moohINI4IoAL29/fmDEpgvZ/QGUPx/oWfrdGHfnGu9Bwp1yTd5b72\nZ/tw9jG7sWeEBSlTmQ+UCpecMrb553Alu+5nE2Kew+Px9QAGO3b/oRGPv+uiSWF7GU88eATHTGz9\nvjHDe7d6QG+sT2/SmIExjojfwL6tg8WCrvnNExKa/5BoR3MeELKWVToWkZXU07pC7qL2ci5HzTue\nctzu/PyY3RKYrg7jTWnMvKFsyvN4aPJ6m4PCYQMK2bhle/P+c47ZjS1Vdc2vLzt1LxZ9u4kBkVZb\nT+aGF8dYy/GThtHY5KWksCuH7NX2MSeB2Xfdk5yqftDYgbz7+bqoxwzq24MfH7kL/3x9KZP3bjsc\nGVqLeHrJRg5KfG2iWOtWFfeM3TMWcHnIeluZDEAPGbsT35VV89oCX/7V3ZcezF3/+qzVMWOG92a3\nnXvx9aqKmOeLVfJTJ4/inRhtLNmnnBp3UXs5l6MCKI/Hk1DwBGGWNYj1az7DeRuBZRYCeTGhs/QO\nDglWxo7sw9gozzHbxR8QTNoz/pWs46nyiQePiLr/5nMnUl3bENeq5zf9cj8qqne0Pv9BwyMGUMdP\nGsZ/5q3gyH0Gs8ew3vzhly15Wreevz81/gdJhy4oGjrRINOKunemsqY+rhyqgFjxU6Dn7+wftD+B\nPC/Pw76j+zUHUPl5eW1X6s/P41enjYs4EzCa0Lr0LOjMDw4Yykvvt38GpIiI0zkqgMqoOHsC9hvd\nj4++2pj0ZZqXWfBfrr3rRA0q7cmfLzmIwjQvGxCqS+d8usQZ3A4q7cmgBGbcH3/QcPYd3Z+d+rTt\ndQvOWdpjeO/mYAvCLf2QXO9OIOi++OQ92RS0xlUsfzzvACq21dG9W/xtEa2EPzpkBH2Ku/HQ1ZPp\n16+IsrKquM+bsChrp0XS9uN21nCuiEgm5WwAtfuwkrA3q+EDi/j2u0p27h/f4pTJrhV13c8msHxd\nJf+bv5qyisbmsjQlu1BUkISXDXDAbKnguPF7+w5h92ElPPPmMk48eDh5Hk9ceW95Hg8nHjyiOYAK\n1d7b+fhdEltnqXu3Tu1eDgN8kw62VNWxUx/fZ5DWwMR/7kS+EpP3HsTcT9YyKGQ9sXClzMbMPGPM\nROA2a+1kY8x44AVgiX/3DGvtLGPMFOA8oAG42Vr7kjGmAHgCKAWqgJ9baxNb18GFtK6Qu6i9nCtn\nA6grfxx+lfFTDhvJqMHFjI/wEONQxf48m0QfZDtyUDEjBxXz6serE3pfKvzlkoNoavLyq7/Oy/i1\nIwme/fjjI3yzt8aOjK8NknHKYSOp2FYX+8AMKynq1mbbtT+dwMKl5Yw3iX8ek/YcwLxF65vX+goV\nOqSdTGj2s+/typlH7tJmFmm4OC+R4cxUMMZcBfwU2ObfNAGYbq2dHnTMAOBi/74C4F1jzP+AC4DP\nrLV/MMacDvwWuCyT5c8G3YjdRe3lXK4PoPqEuSFF06VzPvuN7h9x/0Un7cnLH65i6dqtAPTs1pk7\npx4Y9qGrifHdbY6bNIxPl5RzwB6Ry9BeoQs+OqADqnmGVrT8rkRFW7w92iy6WOdJpzPDTP3vU9yN\nIyZEX8Mrkl/+YHdOPGgEvYviT2yH1j1F8dQ/NHjyv7PNlsMnDGbWm98CvocwD+zdnRfTO4FoKXAS\n8Lj/9QTAGGNOwNcLdRmwHzDPWlsP1BtjlgJjgUnAn/zvexn4XVpLKiI5Ja7xKWPMRGPM3DDbzzDG\nfGCMedcYc58xJuNJEUU9urSaUt7em+HeppRrfzaheQ2ingWd6V3ULeaq0fEaNqCIh39zOFOO2yMl\n54tHOp7Pl6jOnfK5/8rDuDRo2YH2Cu1d6eaCh9nGu5p5IvoUd4t72C+QeD8xqMcqz+Nh3Ki+nHJY\n2zWsogl3yeBJIHsM603vBP/ASZS1dja+YbmAD4ErrbWHAsuAG4BCYGvQMVVAMVAEVIZsExGJS8w7\nTpgu8sD2AuAmYIy1ttYY8yTwQ3z5BxkVz4KLibr6J3vz/uL1HDAm/tlu4Zx++C7c+9yimKuEdwSd\nk1w1PiL/DXzahZMoq9ge9uHH2dKrZ5c2a0s5wcFjB/oDm5Z/Mx6Pp9V6Wi73nLU2ECw9B9wDvI0v\niAooBCrwBU+FIduiKinpTqcU/TEVTWlp5Aett9eNN94IwA033JC2awTrlJ/HjtiHOUp+p7ywbZDO\ndokkHe2VjXqkSzbrEs+f7KFd5AG1wAHW2sC0pU7AdrLEDOmFXV2Rsr94+/UqCPtA1URN2LU0ruf/\nSfJKCrumJYhuj2kXTnJEm+fnh+RAeTz0KU5vr1CWvWyMucRa+zFwJDAf+Ai4xRjTFegGjAYWA/OA\nY4GPgWPwBVpRbdlSk65yNystLUzrDMxATk1aZ3n6lZYW0tDYlPbrpFpjQ1Obzyfd7RJJqtsrW/VI\nh2zXJWYAZa2dbYwZFma7FygDMMZcDPSw1r6W8hLG6aozxlNT1+CoXoiAbN9IHTCClxap+ljT0T7Z\nbvOAoQMKmbTnAPbdLfU5dw6pYkDgW/5/wL3GmHpgHXCetXabMeZu4B18aQvXWmvrjDH3AY8aY94B\n6oAzs1FwEXGndiWNGGPygNuBUcDJ8bxHXYeZ4/H4gqfuPbrELKvT6xJOj+5dU9LNXlLSPe31v+/q\nw6mpbUjoOqkq02/OnpiS8wT8cNJwPrVl9O9XFDVQzNR3ylq7AjjQ//NnwEFhjnkQeDBk23bgtAwU\nUURyUHuzbu/HN5T3I3+PVEzqOswgf4tUV++IWlZX1CVIfp6HxiYv27e3rVcydanYUkNZ5/Q+FrKr\nB7oWdIq7bE5uk5MOHs5JBw+nvHxb1OOcWv6OTusKuYvay7kSCaC84Jt5B/TEl1vwC3x5A28YYwD+\nYq19PtWFlOTsObIPn3+7KaGHM3ckU08cw/xvNrJTqT4f6Th0I3YXtZdzxRVAhXSRPxW0K/3TUSRp\n5x+/B0vWbGXMiN7ZLkpKpSqna5/d+mX9eXoiIuJOzl84R5JW0LVTSheudIrAquYOS2IWv4m792er\nA1eBFxFJJQVQ4jpTTxzDw//9mkPG7pTtokgY5x+fuUViJXHKqXEXtZdzKYAS15mwaz8m7KqhN5Fk\n6EbsLmov50rv1CMRERGRHKQASkRERCRBCqBERDqQGTOmN+fViPOpvZxLOVAiIh2IcmrcRe3lXOqB\nEhEREUmQAigRERGRBCmAEhHpQJRT4y5qL+dSDpSISAeinBp3UXs5V0YDKI9HD98QkciMMd2ttTXZ\nLoeISCzqgRIRJ7nFGAMwy1r7XrYLIyISiXKgRMQxrLW/Au4FbjfGvGSM+Um2y5RrlFPjLmov51IP\nlIg4hjHmUWA9MMVa+5Ux5k7gH1kuVk5RTo27qL2cSwGUiDjJE8BKYIgxpre19spsF0hEJBwN4YmI\nk/wcWAbMBc7LcllERCJSD5SIOEkdMN7/szebBclVgXwaDQ25g9rLuTISQBlj8oAZwFh8vyDPtdZ+\nm4lrJ8IY0xl4GBgKdAVuBr4CHgGagMXAhdZarzFmCr6/kBuAm621LxljCvANQZQCVcDPrbXlGa9I\nEGNMP2ABcAS+OjyCC+tijLkGOA7oDPwVmIfL6uL/d/AgYPzlngI0urAeE4HbrLWTjTGj2lt+Y8z+\nwJ/9x74DTMD3u+mqDFetQ9CN2F3UXs6VqSG8E4Eu1toDgd8A0zJ03UT9BCiz1h4CHI1vNtA04Fr/\nNg9wgjFmAHAxcCDwfeBWY0wX4ALgM/+xjwG/zUIdmvkDwvuBanxln44L62KMOQw4wP/9OQwYgTvb\n5XtAD2vtQcAfgD/isnoYY64CZuL7AwNS8536G3CG/3M5DvgBviDqT5mplYhI4jIVQE0CXgaw1n4I\n7JOh6yZqFnC9/+c8oB7Y21r7tn/bHOBIYF9gnrW23lpbCSzF17vWXE///4/MVMEjuAO4D1jnf+3W\nunwPWGSMeR54AfgPMMGFddkOFBtjPEAxsAP31WMpcBK+YAna+Z0yxhTi++NquX/7WuAta+051tpz\n0l8dEZHkZCqAKgIqg143+oczHMVaW22t3eb/pT4L31/IweWswnfjKwK2RtheGbItK4wxZ+PrTXvV\nv8lDy00PXFQXfEM+E4BTgP8DnsSddZkHdAO+xtczeDcuq4e1dja+obaA9pY/9HdDb+AIY8wvjTG/\nSG3pBbSukNuovZwrU0nklUBh0Os8a21Thq6dEGPMEGA2cK+19iljzO1Bu4uACtrWpzDM9sC2bDkH\n8BpjjgTGAY/iC0QC3FSXcuAra20DYI0xtcCgoP1uqctV+HpmrjPGDMY306xz0H631CNY8L/jZMof\neuz7QD6+XitJA+XUuIvay7ky1Qs0DzgWwJ8w+nmGrpsQY0x/4FXgKmvtI/7NnxpjDvX/fAzwNvAR\ncLAxpqsxphgYjS+BtrmeQcdmhbX2UGvtYdbaycBC4CzgZTfWBXgXX04axpidgO7A6y6sSw9aelu2\n4PsDxpXfryDtKr+1tgrYYYwZ4R/aPBJfkv1AfL2OIiKOlKkeqOeAo4wx8/yvnZrbcC2+YYXrjTGB\nXKhLgbv9SbBfAs/4ZxndjW/GUB6+JNo6Y8x9wKPGmHfwzTY8M/NViMgLXAHMdFtd/DO4DjHGfOQv\n41RgBe6ryx3A3/3l6Axcg2+GpNvqAS1LDKTiO/V/+FYbzwe2AR9ba582xvw1g/UREUmIJ/YhIiKZ\nYYz5C77h2deAQ6y1TvojhI0bK9O+NlVpaSFlZVVpO38m1xUqLS3khHP/SFPxHmk5/4vTTwTgh5c/\nn9LzerYs5qE/XdJqW7rbJZJUt1e26pEOmahLv35FEeMkLaQpIk5yJXAUvt6os7NblNyknBp3UXs5\nlwIoEXGSB/z/7wWcD/wwi2URv6am5Ob8NDU1gVcLyktuUgAlIo4RvPaTMebP2SyL+JSVlTHl6jvp\n0WunhN+bl+eBHoNaTTUVyRUKoETEMYwxN/l/7ATsnM2y5KpEc2qampro1mcUXfuMTGexJAI9C8+5\nFECJiJM86P9/A/BdNguSq3Qjdhe1l3MpgBIRJ/krsBpfADXGGLPQWqs7iIg4jgIoEXGSL621VwMY\nY+601l6Z7QJJx9PQqZhrbnuw1bauXfKp29EY87012yr4/RW/oKSkd7qKJw6hAEpEnKSLMebX+JYx\n0O+nNFBOTWz5hUPYELpxR3zvralbzvbt2ykpSU1Z1F7OpV9QIuIkvwZ2AUqste9luzC5SDdid1F7\nOVemnoUnIhKPu/E94qaHMeb+bBdGRCQSBVAi4iQNwBpr7f+A+mwXRkQkEgVQIuIkK4DDjTFPARVZ\nLktOmjFjenNejTif2su5lAMlIk5SCRwJ5FlrK7NdmFyknBp3UXs5lwIoEXGS04HuQLUxxmutfTjb\nBRIRCUcBlIg4gjHmIeBmYDiwPMvFERGJSjlQIuIUXay1bwGHWmvf8v8sKaacGndRezlXRnug6usb\nvFu21GTykmlTUtId1cV5cqUuuVIPgH79ijxxHjrAGHMEMNAYczjgsda+nsaidUjKqXEXtZdzZTSA\n6tQpP5OXSyvVxZlypS65Uo8E/QMYDDwFDMlyWUREolIOlIg4grX2kWyXQUQkXsqBEhHpQJRT4y5q\nL+dSD5SISAeinBp3UXs5l3qgRERERBKkAEpEREQkQQqgREQ6EOXUuIvay7niyoEyxkwEbrPWTg7Z\nfhzwO3xPUH/YWvtg6osoIiKpopwad1F7OVfMHihjzFXATKBryPbOwHTgKOBQ4DxjTL9UFWzz5k08\n/vjfU3U6ERERkZSJpwdqKXAS8HjI9tHAUmvtVgBjzLvAIcAzyRRk8eJFPPfcLAoKChg0aAiTJx/B\n6tWrWLjwEz744D2qq6t5//13eeqp2cycOYMdO+qpqtrKT35yNiNGjASgvr6eO++8laKiYlauXMHF\nF/+KgoLuPPDAvRQUFOD1epk69VLuuOMWiop6sWXLZi666DLuv/9eAMaOHcd//vMcw4eP4Ac/OIG9\n9hqXTFVEREQkx8UMoKy1s40xw8LsKgK2Br2uAoqTLUhFxWbq6uqYNOkQRo0a1bx93Li9GT16D266\n6XdMm3YPCxZ8jLXfMHr0Hni9Tcyf/1FzANXY2Mixxx5HTU0N5eVlLF78OWvWrObEE09m993H8PXX\nX/HKK/9l//0ncdRRR7No0Wf8619P4vF4OPXUM9hlF8Ps2f/i2mtvSLYaIiKOFsin0dCQO6i9nKs9\n60BtBQqDXhcCW6K9YdiwYaxYsSLsvrFjRzNu3B58+eWX3H77zUyfPp1u3TrTu3d3rrjid0yd+n/s\ntdeevPXWZsaOHcPVV1/NsmXL2LhxI6WlvmJ8/vlyXnjhWc466yz23HN3Cgu70akTlJT0oLS0kEWL\nttGjRxcKCwsoLS2kuLiAgoIu1NZ2ZtiwgZSWFlJS0qv5fLHEe5wbqC7Okyv1EGfRjdhd1F7O1Z4A\n6mtgF2NMCVCNb/jujlhvKiurCrt9+fLvePrpJxg8eAhjx+7N5s3V1NbWc9ttd7J69VqeffZ5nnnm\nOc488yzWr3+B6667nvLyMi666FfN56yv97B581bmzPkf5eVl7NjRxNFHn8ADD8ygZ89CunXrxjnn\nTGHatNtYsGAhlZWVTJlyAffffy+bNlXTuXMV9fWNEcsYrLS0MK7j3EB1cZ5cqYeISK5KJIDyAhhj\nzgB6WmtnGmMuB17Bl4z+kLV2XbIF2WuvcW1yjiINpUXavvPOw5g+/Z4222+44eZWr3/3uz9EPN89\n99wfV3lFxBmCZwkbY0YBjwBNwGLgQmut1xgzBTgP34zhm621LxljCoAngFJ8KQg/t9aWZ6USIuI6\ncQVQ1toVwIH+n58K2v4i8GJaSiYiEoN/lvBPgW3+TdOBa621bxtj7gNOMMZ8AFwMTAAKgHeNMf8D\nLgA+s9b+wRhzOvBb4LKMVyLDlFPjLmov59Kz8ETEzUJnCe9trX3b//Mc4HtAIzDPWlsP1BtjlgJj\ngUnAn/zHvoxvTbucpxuxu6i9nEsrkYuIa1lrZ+MblgvwBP0cmBkcacZwEVAZsk1EJC7qgRKRXNIU\n9HMRUIEvSAqdMRy6PbAtqpKS7nTqlJ+akkbhpBmYjY3VeFrFpRKVx0OfPj0d1YahnFy2RGWzLgqg\nRCSXfGqMOdRa+xZwDPA68BFwizGmK9AN3yLAi4F5wLHAx/5j3w5/yhZbttSkq9zN0j0DM9GcmvLy\nbXh9c4gkHl4vmzZto2vX1LRhqnOgcmmGb7brogBKRHJB4A5/BTDTGNMF+BJ4xj8L727gHXxpC9da\na+v8SeaPGmPeAeqAM7NR8ExTTo27qL2cSwGUiLhayCzhJcBhYY55EHgwZNt24LT0l1BEcpGSyEVE\nRF7xZFMAABRfSURBVEQSpABKRKQDmTFjenNejTif2su5NIQnItKBKKfGXdRezqUeKBEREZEEKYAS\nERERSZACKBGRDkQ5Ne6i9nIu5UCJiHQgyqlxF7WXc6kHSkRERCRBCqBEREREEqQASkSkA1FOjbuo\nvZxLOVAiIh2IcmrcRe3lXFEDKGNMHjADGIvvYZvnWmu/Ddr/I+BafA/yfNha+7c0llVERETEEWIN\n4Z0IdLHWHgj8BpgWsn86cBQwCbjCGFOc+iKKiIiIOEusAGoS8DKAtfZDYJ+Q/fVAL6AA8ODriRIR\nEYdSTo27qL2cK1YOVBFQGfS60RiTZ61t8r+eBiwAqoFnrbWVoScQERHnUE6Nu6i9nCtWD1QlUBh8\nfCB4MsbsDFwEDAWGAf2NMaeko5AiIiIiThKrB2oecBwwyxizP/B50L5uQCNQZ61tMsZsxDecF1Vp\naWGsQ1xDdXGmXKlLrtRDRCQXxQqgngOOMsbM878+xxhzBtDTWjvTGPMo8J4xphZYCjwS64JlZVXt\nKa9jlJYWqi4OlCt1yZV6iPME8mk0NOQOai/nihpAWWu9wAWhm4P23wXclYZyiYhIGuhG7C5qL+fS\nSuQiIiIiCVIAJSIiIpIgBVAiIh2I1hVyF7WXc+lZeCIiHYhyatxF7eVc6oESERERSZACKBEREZEE\nKYASEelAlFPjLmov51IOlIhIB6KcGndRezmXeqBEREREEqQASkRERCRBCqBERDoQ5dS4i9rLuZQD\nJSLSgSinxl3UXs6lHigRERGRBCmAEhEREUmQAigRkQ5EOTXuovZyLuVAiYh0IMqpcRe1l3OpB0pE\nREQkQQqgRERERBIUdQjPGJMHzADGAnXAudbab4P27wtMAzzAWuAsa+2O9BVXRETaI5BPo6Ehd1B7\nOVesHKgTgS7W2gONMRPxBUsnAhhjPMADwMnW2mXGmCnAcOCbdBZYRESSpxuxu6i9nCvWEN4k4GUA\na+2HwD5B+wywCbjcGPMm0Mtaq+BJREREcl6sAKoIqAx63egf1gPoCxwI3AMcCRxhjJmc+iKKiIiI\nOEusIbxKoDDodZ61tsn/8yZgaaDXyRjzMr4eqrnRTlhaWhhtt6uoLs6UK3XJlXqIsyinxl3UXs4V\nK4CaBxwHzDLG7A98HrRvGdDTGDPSn1h+MPBgrAuWlVUlW1ZHKS0tVF0cKFfqkiv1EOfRjdhd1F7O\nFSuAeg44yhgzz//6HGPMGUBPa+1MY8wvgSf9CeXzrLVz0llYERERESeIGkBZa73ABaGbg/bPBSam\noVwiIiIijqWFNEVEOhA9W81d1F7OlZVn4U2YMAaABQsWZ+PyIiIdlnJq3EXt5Vx6mLCIiEiKePK7\n8NTsOfQsTHwWrdcL3zt0IiOGD0t5uST1FECJiIikSEGvQXyxDdiW+Hu93ib6fPa5AiiXUA6UiEgH\nopwad1F7OZd6oEREOhDl1LiL2su51AMlIiIikiAFUCIiIiIJUgAlItKBKKfGXdRezqUcKBGRDkQ5\nNe6i9nIu9UCJiIiIJEgBlIiIiEiCFECJiHQgyqlxF7WXcykHSkSkA1FOjbuovZxLAZSI5BxjzCfA\nVv/LZcCtwCNAE7AYuNBa6zXGTAHOAxqAm621L2WhuCLiQgqgRCSnGGO6AVhrJwdt+w9wrbX2bWPM\nfcAJxpgPgIuBCUAB8K4x5n/W2h3ZKLeIuIsCKBHJNXsB3Y0xr+D7HXcdsLe19m3//jnA94BGYJ61\nth6oN8YsBcYC87NQ5owJ5NNoaMgd1F7OFTWAMsbkATPw/VKpA8611n4b5rgHgE3W2msSufiECWMA\nWLBgcSJvExGJphq4w1r7kDFmF+DlkP1VQDFQRMswX/D2nKYbsbuovZwrVg/UiUAXa+2BxpiJwDT/\ntmbGmPOBMcCbaSmhiEhiLLAUwFq7xBizCRgftL8IqAAqgcKg7YXAlmgnLinpTqdO+aktbRilpYWx\nD8qQxsZqPHiyXYwOo7Bnt7S3v5O+X+2VzbrECqAm4f/rzVr7oTFmn+CdxpgDgf2A+4Hd0lJCEZHE\nnIOv1/xCY8xO+AKjV40xh1pr3wKOAV4HPgJuMcZ0BboBo/ElmEe0ZUtNWgsOvhtCWVlV2q8Tr/Ly\nbXjxZrsYHUbVttq0tr/Tvl/tke26xFoHqgjfX2kBjf5hPYwxA4HrgYtAf56IiGM8BBQZY94GnsYX\nUF0G3GiMeQ/fH47PWGs3AHcD7+ALqK7tCAnkWlfIXdRezhWrByq0izvPWtvk//kUoC/wX2AAvqTN\nr6y1j0U7YWlpIXl5njbb3Mit5Q5HdXGeXKlHpllrG4Cfhdl1WJhjHwQeTHeZnEQ5Ne6i9nKuWAHU\nPOA4YJYxZn/g88AOa+09wD0AxpifA7vFCp4AysqqaGryttnmNtnuOkwl1cV5cqUe4gzr1m/g1bnv\nJJXLVFW1FTzpz/sScZtYAdRzwFHGmHn+1+cYY84AelprZ4Ycq0FyEREH+mj+J7zxbSH5nTon8e4S\nuvdOeZFEXC9qAGWt9QIXhG4Oc9yjqSyUiIikxz5FCwGYXzkuyyWReGgdKOfSQpoiIh2IAid3UeDk\nXLFm4YmIiIhICMcEUBMmjGlemVxERETEyRwTQImISPrtU7SwOQ9KnE/rQDmXcqBERDoQ5UC5i3Kg\nnEs9UCIiIiIJclwApVwoERERcTrHBVAiIpI+yoFyF+VAOZdyoEREOhDlQLmLcqCcSz1QIiIiIglS\nACUiIiKSIAVQIiIdiHKg3EU5UM7l6ByowGy8BQsWZ7kkIiK5QTlQ7qIcKOdSD5SIiIhIghRAiYiI\niCRIAZSISAeiHCh3UQ6Uczk6ByqY8qFERNpPOVDuohwo54oaQBlj8oAZwFigDjjXWvtt0P4zgEuB\nBmARMNVa601fcUVERESyL9YQ3olAF2vtgcBvgGmBHcaYAuAm4DBr7UFAMfDDdBVURERExCliBVCT\ngJcBrLUfAvsE7asFDrDW1vpfdwK2p7yEIiKSMsqBchflQDlXrByoIqAy6HWjMSbPWtvkH6orAzDG\nXAz0sNa+lqZyiohICigHyl2UA+VcsQKoSqAw6HWetbYp8MKfI3U7MAo4OfXFa0vJ5CIiIpJtsQKo\necBxwCxjzP7A5yH778c3lPejeJPHS0sLycvzJLQt0v5sc0IZUkV1cZ5cqYeISC6KFUA9BxxljJnn\nf32Of+ZdT2A+8AvgbeANYwzw/+3dfYxcVRnH8e/O0hYoy4KyILWIKDyEBNC4vAlSahB8iY2C/AOa\nBtSiIIQECEixaJQIWiS8+QJbSiGmmkC04UVeIqjQQqQ2GopaHkEhljawbsqyLS3bffGPc6e9u3tn\nZmd25s69O7/PP7tz7tyZ59xzZ+4z55yZw63uvqrcA/b2DjAyMlpVWantzdTV1dH0GOpFdcme6VIP\nyZ7i/CcN5eVDcf6ThvKyp2wCFfUqXTS+OPZ/e90jqoKG80REqqPEKcvaWPWnV3hw9S2xsvBdr+eu\nvCV5l5gTj3wPlyxa2KDYZLzc/JCmiIjIdNbW1sasgz5S+/7tb9QxGqlES7mIiIiIVGlaJFDd3Ufv\nGs4TEZHS9DtQ+aL2yi4N4YmItBDNgcoXtVd2TYseKBEREZE0TbsESsN5IiIi0mjTLoESEZHSNKcm\nX9Re2TVt50DpN6JERCbSnJp8UXtll3qgRERERKqkBEpERESkSi2RQGliuYhIoDk1+aL2yq5pOwcq\nieZFiUir05yafFF7ZVdL9EAlUa+UiIiI1KplE6giJVIiIiJSrZZPoOKUTInIdKc5Nfmi9squlpoD\nNVnxuVKaNyUi04nm1OSL2iu71AMlIiIiUiUlUFXQEJ+IiIhAhSE8MysAPwOOBd4Fvu7ur8S2LwCW\nAEPAcndf1sBYRWSKJjskraHr7LlrxUqe/XtvTfsODY8wo+sYgF3zaTQ0lA9qr+yqNAfqi8BMdz/Z\nzE4EfhKVYWYzgJuB44B3gDVm9qC7v9nIgLOgu/toCoU21q5drwuN7NLIc2Gqj53Uczq+LD7nr57P\nLfUxTDuF9x5T074zY//rQpwvaq/sqpRAnQI8BuDufzaz42LbjgJedvd+ADNbDcwDHmhEoFmnieet\noZako97nQ1IMaT6vzmsRkcoJ1L7A27Hbw2ZWcPeRaFt/bNsA0FnuwTZuXE1392w2bVo9prxSWS37\n1Lts4va2Se1TrU2bXgdgzpz3V71vrQoFGBmpPtYsmmpd4se/+H9RKKv9vDn44LcqPHa8rJ85c+bE\nyiq9FkrfrzGvi0rxp3sOiwi88K83ufqGnrL3mTlzDwYHhyaUH3LAXlyy6CuNCm1aqpRAvQ10xG4X\nkycIyVN8WwewpdyDzZ07N/p7SMK28mW17FPvsqk8TpKNGzdG959bdt/i/XbfZ+6Yfcttr1dZpfjT\niCHpeCXFkBRvpX13P0/9z7m8n7tTKRvfjtJ8mlOTL9W0187OY6g4S24n0DaxeO+B16qOrdVVSqDW\nAAuA+83sJOCF2LYNwBFmtj+wjTB8t7Tcg736KvT2DtQebYZ0dXXUoS7FDrtKjzO+Yy/e2ZfU8TdA\nd/cpY0rWrn2xZFmh0MbIyOiusuTnKx9/8bF3D+/sjqs49FMqhnL1i++bfLzGHofS7VJp32ypz/mV\nBZ0ceGCzY5A4JU75ovbKrkoJ1G+BM8xsTXT7AjM7F9jH3XvM7HLgccLPIdzt7psbGKtUIUvzVOKx\nVBtXluohIiJSVDaBcvdR4KLxxbHtDwMPNyAuaYBiMhKfhLxu3Yt16e1QoiMiIq1ES7m0ICU7Iq1L\nc6DyRe2VXUqgRERaiC7E+aL2yi4t5SIiIiJSJfVAiYiItLiNfTu49kd317Tvnu2DLLly/HTp6U8J\nlIi0rErrfU5HmlOTL2m113DHkWwerW3f2QMb6htMTiiBEpFWVnK9z+lKiVO+qL2ySwmUiLSycut9\n1t0dy37Ja2+8U/Y+M2e2Mzg4PKG8f+t26OxqVGgiUiUlUCLSysqt91l3W7bupK/98PJ3GgbaE8rL\nrjQq0jzbhmax5KblNe27faCPH3/3CgqF/H2nTQmUiLSycut91t3wu1sZ6Vtf9j7texQYHmpYCJxw\nWOjdev4/SVlafTW6LkWVjmk9pFWX8erdXo2qx3/fqG2/7VsHOPu8C2hLWJ+vktHRYZZe/z2OOLzC\nhxIREakvMzvbzO6J/j/JzB5pdkwikg/qgRKRVjZhvc9mBiMiIiIiIiIiIiIiIiIiIiIiIiIiIiIi\nIiIZVMMvL1Qv7+tNmdkMYDlwKDALuB74J7ACGAFeBL7l7jWuJJQ+MzsQWAecTqjDCnJWFzO7BlgA\nzADuANaQz3oUgGWAEWJfRPg5xRXkpC7RMig3uvsnzexwEmI3s0XAhcAQcL27t/xPBsSP27jyc4HL\nCMdqPXBxltsfStcltv0uoM/dr0k3suqUaZPjCUv9tAGvAwvdfbAJIU5ambqcBSwGRoHl7v6LZsQ3\nGUnXX3d/KLZ9AbCE8FpZ7u7L0ootrZ/+3LXeFPBtwkmYJ18Get19HvAZ4KeEOiyOytqALzQxvqpE\nJ+SdwDZC7DeTs7qY2Xzg49E5NR/4EPltkzOB2e7+CeD7wA/JUV3M7Cqgh/DmBgnnk5m9D7gUOBn4\nNHCDmc1sRrxZkXDciuV7AT8A5kfnRCfw+fQjnLxSdYlt/wZwNOGCnVll2qQNuAs4391PBZ4EDks/\nwsmr0CY3A2cQljK6wsyy/Dv346+/dxQ3RNeyYl1OAy6MOgdSkVYCNWa9KaCh6001wP3AddH/BWAn\n8DF3fzoqexT4VDMCq9FS4OfA5uh2HutyJrDezFYBDwEPAt05rAfAdqAzepPuBAbJV11eBs5md492\n0vl0PLDG3Xe6+9vRPsemHmm2jD9uRTsIHw52RLf3IJwjWVaqLpjZycAJhA9tqYx6TEGpehjQB1xu\nZn8E9nP3l9INrWol24RwDdsP2CvanuXEdvz1dyi27SjgZXfvd/edwGpgXlqBpZVAJa43ldJzT5m7\nb3P3rWbWQWjM7zD22G0lJytVmdn5hGz+iaiojbEvsLzUpQvoBs4BvgmsJJ/1gDD0uCewgXCRuY0c\n1cXdf8PYN7V47AOE2PcF+hPKW1bCcSuWj7p7L4CZXUronfx92vFVo1RdzOxgwsXvErKfPJWsB3AA\noff0dsIHgtPNLHGoMivK1AVCD/c6whD7Q9GHmkxKuP5eG9vc1PeVtJKYVNebagQzOwR4CrjP3X9F\nmN9R1AG81ZTAqncB4ZeX/wB8FLiXkIwU5aUu/wOecPchd3fCp/b4Cycv9QC4itA7cyShTe4jzOsq\nylNdYOxrY19C7OPfAzqALWkGlSdmVjCzmwhzFL/U7Him4BxC8vE74GrgPDNb2NyQatJH6Ol4yd2H\nCCMqeRtJAcDMPkBIaA8FPggcZGbnNDWoCsZdf38d29RPE99X0kqg1gCfg7DeFPBCSs9bF2Z2EPAE\ncJW7r4iK/2pmp0X/fxZ4OmnfrHH309x9fjSp8G/AQuCxHNZlNWE8HDObA+wNPJnDegDMZncP7RbC\nkE0uz69IUuzPA6ea2axovsVRhE+/kuxOwtyVs2JDebnj7re7+3HR+82NwEp3v6/ZcdXg38A+Zvbh\n6Pap5Pf83ZPwJZV3o46MNwnDeZlU4vpbtAE4wsz2j+ZUzgOeSyu2tNbCy/t6U4sJvRvXmVlxLPYy\n4Lao0f4BPNCs4KZoFLgC6MlTXdz9ETObZ2bPEz4IXAy8Ss7qEVkK3GNmzxB6nq4hdK/nrS7FeRQT\nzqfoW3i3Ac8Q2mtx1r/BlKJR2PXNu32AvwBfJSSeT5kZwK3uvqppEU7emLq4e0/S9hyYUA8z+xqw\nMpqruMbdH21qhJOXVJd7gWfNbAdhrtSKJsZXSdL1t4cwtN1jZpcDjxPeV+52980lHkdERERERERE\nREREREREREREREREREREREREREREREREREREREREREREpDX9H1bH3EgKH1bkAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1b8e4898>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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WzgLHwcp2a7d0vhnXNjR3eeJ7ERHxiJRwXw2U+D3Psda2feMaY3KMMX8EjgfO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\nvG6tbUxHuUUkOyn4EpHu4ECgyBjzXzzfezcAB1t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gXDr1PSml740w5oWUOccGet1X/W3H\n5m+gAGwfh2869CMibgB+k/nzI66iGBpaBfwPxTeDxvabaJ3UP4F8kGLC7Q4yzCUi/gq4iOLDxYeB\nfWSYS0ScCnyGYhhrJfBJim8EZZNLRJwN3JFSuiAiXkuH2CPiMopvO9aA61JKd1YWcItO71EUQwtr\nU0o7mrZ7APhg4/2r9RysD0tUqkwunc7Bqq+0dMsDeKT+r/lDyScp5t+MXV9TIpcbKCZz/xbz+563\nNxUBlSiTS0rprqb9572GqlTmHEsp/ds4vu4lSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIk\naUn8P8ooklRW1bNSAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1ee265c0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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QBVdRjpK3qD3dQ8GZiLQLxpjrgB8Au4ObRgF3W2vvDjumN3BlcF8+8IEx5k1g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\n+tNfHmfBV2XxD4zC7/eTXdTf4RKJeJeCMxERicv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       "text": [
        "<matplotlib.figure.Figure at 0x1b5626d8>"
       ]
      }
     ],
     "prompt_number": 8
    }
   ],
   "metadata": {}
  }
 ]
}