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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Figure 2\n",
      "\n",
      "In this notebook, we analyze the accuracy of the diffusion tensor model (DTM). \n",
      "\n",
      "We start by importing the necessary modules: "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import nibabel as ni\n",
      "import osmosis.model.analysis as oza\n",
      "import osmosis.model.dti as dti\n",
      "import osmosis.viz.mpl as mpl"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We set the path to point to where the data is installed: "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import os\n",
      "import osmosis as oz\n",
      "import osmosis.io as oio\n",
      "oio.data_path = os.path.join(oz.__path__[0], 'data')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We create strings that point to the data for this subject:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "subject = 'SUB1'\n",
      "data_1k_1, data_1k_2 = oio.get_dwi_data(1000, subject)\n",
      "data_2k_1, data_2k_2 = oio.get_dwi_data(2000, subject)\n",
      "data_4k_1, data_4k_2 = oio.get_dwi_data(4000, subject)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We will only analyze data within a white-matter masked region. Here, we load this mask and generate a masking array:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wm_mask = np.zeros(ni.load(data_1k_1[0]).shape[:3])\n",
      "wm_nifti = ni.load(oio.data_path + '/%s/%s_wm_mask.nii.gz'%(subject, subject)).get_data()\n",
      "wm_mask[np.where(wm_nifti==1)] = 1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We generate the model class instances, which will be used to analyze accuracy. Model parameters are not saved to file: "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "TM_1k_1 = dti.TensorModel(*data_1k_1, mask=wm_mask, params_file='temp')\n",
      "TM_1k_2 = dti.TensorModel(*data_1k_2, mask=wm_mask, params_file='temp')\n",
      "TM_2k_1 = dti.TensorModel(*data_2k_1, mask=wm_mask, params_file='temp')\n",
      "TM_2k_2 = dti.TensorModel(*data_2k_2, mask=wm_mask, params_file='temp')\n",
      "TM_4k_1 = dti.TensorModel(*data_4k_1, mask=wm_mask, params_file='temp')\n",
      "TM_4k_2 = dti.TensorModel(*data_4k_2, mask=wm_mask, params_file='temp')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b1000_1.bvals\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b1000_1.bvecs\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b1000_2.bvals\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b1000_2.bvecs\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_1.bvals\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_1.bvecs\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_2.bvals\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_2.bvecs\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b4000_1.bvals\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b4000_1.bvecs\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b4000_2.bvals\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b4000_2.bvecs\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We calculate relative RMSE, based on average from cross-prediction between the models fit on each data-set in each b value:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rrmse_1k = oza.cross_predict(TM_1k_1, TM_1k_2)\n",
      "rrmse_2k = oza.cross_predict(TM_2k_1, TM_2k_2)\n",
      "rrmse_4k = oza.cross_predict(TM_4k_1, TM_4k_2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b1000_1.nii.gz\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b1000_2.nii.gz"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Predicting signal from TensorModel"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Fitting TensorModel params using dipy"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Predicting signal from TensorModel"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Fitting TensorModel params using dipy"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_1.nii.gz"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_2.nii.gz"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Predicting signal from TensorModel"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Fitting TensorModel params using dipy"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Predicting signal from TensorModel"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Fitting TensorModel params using dipy"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b4000_1.nii.gz"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b4000_2.nii.gz"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Predicting signal from TensorModel"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Fitting TensorModel params using dipy"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Predicting signal from TensorModel"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Fitting TensorModel params using dipy"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We generate a figure that shows the distribution of the rRMSE measure across the voxels in the white-matter:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Gray-scale color choices, based on http://colorbrewer2.org\n",
      "fig = mpl.probability_hist(rrmse_1k[np.isfinite(rrmse_1k)], label='b=%s'%str(1000), color=[0.8, 0.8, 0.8])\n",
      "fig = mpl.probability_hist(rrmse_2k[np.isfinite(rrmse_2k)], fig=fig, label='b=%s'%str(2000), color=[0.59, 0.59, 0.59])\n",
      "fig = mpl.probability_hist(rrmse_4k[np.isfinite(rrmse_4k)], fig=fig, label='b=%s'%str(4000), color=[0.32, 0.32, 0.32])\n",
      "ax = fig.axes[0]\n",
      "ax.set_xlim([0.6, 1.4])\n",
      "fig.axes[0].plot([1,1], [ax.get_ylim()[0], ax.get_ylim()[1]], '--k')\n",
      "fig.axes[0].plot([1/np.sqrt(2),1/np.sqrt(2)], [ax.get_ylim()[0], ax.get_ylim()[1]], '--k')\n",
      "\n",
      "plt.legend()\n",
      "fig.savefig('figures/Figure2_histogram.svg')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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QKpUh39JOS0uDx+PB9OnTcfToUeoiISTMUNEG4HQ64XA4IJfLoVarQ7poCwQC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\nmZn4r//6L+44BAIdaxKsJvq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l5z333IP6+npkZGSgrKwML730UqBj+pSzrKyM+0hXVVWF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\nIYSEkP8Phv3yeYV9DRMAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x109064110>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We also print to the notebook the proportion of voxels with rRMSE that is adequate (smaller than 1):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for this in [rrmse_1k,rrmse_2k, rrmse_4k]:\n",
      "    isfin = this[np.isfinite(this)]\n",
      "    print \"The proportion of voxels with rRMSE<1.0 is %s\"%(100 * len(np.where(isfin<1)[0])/float(len(isfin)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The proportion of voxels with rRMSE<1.0 is 98.0485232068\n",
        "The proportion of voxels with rRMSE<1.0 is 98.8458674609\n",
        "The proportion of voxels with rRMSE<1.0 is 97.4280218416\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We examine a particular voxel. This is used to demonstrate how rRMSE is calculated: "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Look at the same corpus callosum voxel as in Figure 1: \n",
      "vox_idx = (40, 73, 32)  # This doesn't make sense in HT's brain."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "First, we scatter-plot data-to-data reliability in this voxel: "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, axes = plt.subplots(1,3,squeeze=True)\n",
      "axes[0].set_ylabel(r'$\\frac{S}{S_0}$')\n",
      "for ax, models in zip(axes,([TM_1k_1,TM_1k_2],[TM_2k_1, TM_2k_2],[TM_4k_1, TM_4k_2])):\n",
      "    ax.scatter(models[0].relative_signal[vox_idx], models[1].relative_signal[vox_idx], \n",
      "               color=[0.5, 0.5, 0.5])\n",
      "    ax.grid()\n",
      "    ax.set_xlim([0,1])\n",
      "    ax.set_ylim([0,1])\n",
      "    ax.set_aspect('equal')\n",
      "    ax.set_xlabel(r'$\\frac{S}{S_0}$')\n",
      "    \n",
      "fig.set_size_inches([10,10])\n",
      "\n",
      "fig.savefig('figures/Figure2_scatter_self.svg')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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YDAbxfyNGjMDs2bPt/p7sRQ7zUQ4ydAbFxcX44YcfJA3ho6KisGTJklZdh2VZ\nXL58GWVlZQgMDMSYMWOstj+TkpIQHx/fYtymRqPB5s2bmz2H4zj88MMPKC8vB8/zNueuQqGAq6sr\n3NzcoNVqUVdXZ3VPm8tYTUhIwOXLl6FUKsHzPF588UX07du3WbmeFnKYj3KQ4VlAq9Vi165dqKmp\ngSAImDFjBoYOHYqDBw8iMzMTABAeHo6lS5c220+4MT/++KP4XgsDBw7Eiy++aPP8wsJCFBUVwcPD\nA+Hh4bIsoUNi3gjt4tSpU0hOThZX+FOnTpU0urZgzyTz8PDAyy+/LDlWVVWF7du3i6strVYruTbL\nsrh58yamTZvW7LUvXbqEixcvQqlUwmw244UXXpAEZHt4eECr1dp8ryAIcHJywjvvvIMHDx6goqIC\nffr0kfRpJXRNMjIyJLX+OI6z6WFtDp7nsWvXLjHZJi0tDbm5uVi2bJnkR3/kyJEoKysTm8zbgqIo\nu7wBNE1j3bp1yMrKQk1NDc6fP4/KykqJnvE8D6PRiD/84Q+orKzEnj17UFZWJrkOx3FW3UmAhp6q\nV65cAcdxomF4+PBhfPTRRzZDFQiEjmLv3r0wGo3i67Nnz6KwsBBZWVmirmZlZSExMRFTpkyx65q2\nvHVNefCuX7+Os2fPiq+jo6OxcOFCWRpwbYHEvHUwcthDb60MOTk5SE5OBsuyqKurA8uy+PXXXyXe\nKaBhdW95cN29exc5OTlNGnNPypCeni55uNraAhIEoVnjsLy8HBcvXhQfVBzH4fjx45KH1uLFi+Hs\n7GzVioimaURHRwNoyGQdNGgQJk2aRAy3TqAzdEKlUll5yBpv09gjQ3FxsSTZhuM4ZGZmWukBRVHI\nzc2VPAQYhkFQUBAYhoFKpYKrq6tk27+58ZVKJSIiIhATE4MNGzbA19fX6hxLjUJ3d3ebW7FN6Y5O\npxO/l8ZxoCaTqekvgvDU6YrPidbAcZwYZ9yY3NxcUb+ys7PBcRxycnLsvu6gQYMkem1pMWdrfEuh\nd8vfo0ePUFBQIDlPDvehrRDPGwE6na7F1QhFUZgyZQpUKhW2bdsmunoHDhxoV2yaPat8lmWxdetW\nxMbG2mwTVFlZCaVSKdlaUigUqKqqgkqlAgD07NkT7777Lo4cOQIPDw8UFBTA1dUVU6dOhaura4sy\nELomMTExuHz5MoxGI8xmMxiGwYwZM1p1jcaLCwsURVkdr6+vF+upNT5vxIgR8PPzA8uyCAgIaFP9\nQLVajcGAmDZKAAAgAElEQVSDB0s8BhYuX76M2NhYCIIAmqYletBU0o+vr6+V/DRNE10gPFWUSiVU\nKpWVV8zT0xN6vV5cvFtiou1l5MiRqKurw7Vr16BQKDBu3DjExMRYnVdTU2P1/LA8K7oLxHjrYBxd\nrbktMvj7+7e4HcowDIYPH46//e1vkofB/fv3MWzYMAQHBzcrQ1RUFNRqtVgahGEYDBgwAHfv3hUV\n2ZIZevDgQURERGDp0qUSBfTx8bHy2FEUZZWVqlKp8NJLL9n9+QlPl87QCZVKhY0bN+LWrVuoqalB\nnz590Lt3bysZMjMzcfbsWdTX1yMmJgYTJ04UPVP+/v5wdnYGy7IQBAEKhQJeXl5WcZUMw0ChUFgZ\nRT169GiyzVVrvoP+/fvbNN4smXUeHh7w9vZGWVmZqA/Ozs424928vb0xa9YsnDp1SqxBt3z58k7p\nMEJomq74nGgNFEVh8eLFOHDggBiK079/f0ydOhXbt29HdXU1oqKi4OzsjKlTp7bquhMnTsTEiROb\nPc/V1VWsv2iB53kr/ZTDfWgrstDguLg4REdHIzIyEp9++qnNcxISEjB06FAMHDiwS3/hcsTf3x/T\npk2DUqkEwzBwdnaGs7Oz+APPMAwmTpzY5GqmcVxDU6jVamzYsAHPPfcc+vbti+nTp2POnDk2t085\njkNGRoZVWQ83NzcsWLAANE2L21PLly/vlh0SiE60HpVKhTFjxiA2NlZiuFkoLCwU20dVVFTgypUr\nuHDhgvh/hmGwbt06REVFQaPRwNPTE9HR0VaJCRRFYc6cOWAYRpyLvXr1kpTlaA8eHh6IioqSHGMY\nBmFhYQAavApms1lccPXo0QNr1qxpUg+GDRuGDz74AK+99href/99hISEdIicnQ3Ria5Fnz598NZb\nb2HhwoV45ZVXMH/+fLi6uuLNN9/E0qVLsWTJEmzatKnJxLT2QFEUVq9eLXYXUavVWLp0abeq5enw\nbFOz2Yy+ffvi3LlzCAoKwogRI7Bv3z7069dPPEev12PcuHE4ffo0goODodVqbQYDyyGLSA690toq\nQ319Paqrq6HRaFBTU4MrV67AaDQiOjoaAwYMgCAI+Mc//iFxPTMMgzfeeAOenp5tkuGrr75CeXm5\n1XGapq2SESywLIuqqipoNJoms5TkcB/aOh+JTjwdGTiOw+XLlyXHXV1d8f7770uOWQKdWZaFUqmE\nm5sbNm7caFV2pLCwUCzL0bdv32a9Wa39Durr67F//34xHmj48OGYOXMmKIrCoUOH8PDhQ3HhwzAM\nnn/+eYwbN67Za8rhPhCdaMAR94LjOCQkJCA/P19sCzh9+vROlaExnfUdmM3mJsN2urJOOHzb9Nq1\na4iIiEBoaCgAYNmyZTh69KhEKffu3YsXX3xR3Jp7Fmu6tIX6+nowDGN3do2Tk5P4gHJ1dbVSbMtq\nZvfu3aiqqoJSqcTChQutDDdb5OfnIzU1FU5OThg2bJi42nrppZfwzTffWJ0vCAKCgoKsjnMcB4VC\nIY5pKQrcnTLniE48HSxdCBr/UNqaN+fOnRO9bWazGVVVVXjw4AGGDh0qOS8wMLDdzeSbwsnJCatX\nr0Z9fb3YvcFCUVGRVaZ2YWFhh8sgCIJsMvOITrQPQRCwd+9e5OXlgeM45OfnQ6vVYsqUKZ3626nT\n6aDT6Tq13253ejY0xuHGW0FBgSTjLzg4GElJSZJz0tPTwbIsJk+eDKPRiHfffdeqFIWFNWvWiAru\n4eGBIUOGiJa1JbPkab+20FnjPfl6wIAB+Pzzz3Hv3j0olUr88Y9/RFRUVIdd/7333kNdXR1+//13\nlJSUiD+gjc+fNGmS+DogIACHDh3C48ePQVEUkpKS8MYbb+D69esAAD8/P5SWlorZcKGhoZgxYwbu\n3bsnXs9sNuOvf/0rsrOzERYWhpiYGFy/fh1FRUUIDw/HqFGjREP1yfE76/v/4osvkJycLM6/tkJ0\n4um8NhgM2LdvH+rr6xEaGgqGYaDRaCSr74SEBKSnp4vbrtnZ2VAqlWKh6s6W/8qVK1b/LysrA8Mw\n4HlelM+e69mrExUVFcjNzUVlZSVKS0sxefJkLF68uE3yE52Qh06YTCbRcLP8zkZFRaGgoECsm2bv\n9fbu3Yvk5GRERUVh7NixYnealt7fo0cPnDlzBjk5OeB5Hps2beq0z9/Ua3t1oiNfd5ROOHzb9PDh\nw4iLi8O2bdsAALt370ZSUhK+/PJL8Zy33noLt27dQnx8PKqrqzFmzBicPHkSkZGRkmvJwR3uaHie\nx+eff261tblp0ya79vvT09Px4MEDuLi4YPTo0Xa1qGqJf/7zn5I2JgqFAs8//7wYdGowGMRYJJVK\nhQULFlgVEY2Pj8fVq1dtFjEFGj7jnDlznkqD+bbS1vlIdOLpodfrcfXqVdTW1mLgwIGIiIiwOmf/\n/v3IyMgQ5xrDMHj99ddl48kxGo344YcfUF1dDUEQ4O/vj9WrV9td6LQ5WJbF559/jpqaGvGYWq3G\ne++9J2Z0tweiE45Br9fj66+/tspQdnd3R11dHUJCQjB37lyo1epmr5Oamor9+/dLjr3wwgsYNmxY\ns+8zGAz48ssvJePTNI0//OEPre6/W1tbi7q6Ori5ucnGM9weuuy2aVBQEPLy8sTXeXl5VpmLvXr1\ngo+PjxhIP3HiRNy5c8dKKeVA41W8IzCZTHj48KFklapQKFBUVNSi8Xbr1i3ExcWJrUeSk5Px5ptv\ntqmsQOPvobq6WvI/nuclKeRubm54/fXXxW0anudx5coV5ObmwtfXFxMmTEBmZmaThhvQ8NDJysoS\njTdH34f2QHTi6cng4eGBmTNnNnvuokWLcOLECWRkZMDFxQVz5syxMtyqqqqQkpICQRDQr1+/Fhc5\nHfkdaDQabNq0CcXFxVAqlejZs6dd2aP2yGDp9NAYQRBQWlrq0JqIRCfah7u7OwICAlBUVCSGnqSn\np4ven0ePHsFoNOLVV19t9jq//vqr1bGzZ8+2aLzZKvOUk5ODyspKu403QRBw7tw5JCUliVUGXnnl\nlXY5GOTw29RWHG68DR8+HOnp6cjOzkZgYCAOHDiAffv2Sc6ZP38+3nrrLZjNZtTV1SEpKanFtjPd\ngdraWly4cAHl5eUICQnBuHHjWty/d3Z2trLieZ632c+Q53lotVrQNA1PT09cuHBBjPWxFAVNTk4G\nwzBIT0+Hm5sbJk+e3KreiHfv3rXK1lMqlWLB3MZYVlE///wz0tLSwLIsHj9+jLS0NHh5eaGoqKjJ\nFYpCoeg2mUREJzqXgoICnDp1CtXV1YiMjMT06dOxaNGiJs/X6XTYunUrOI6DIAi4cOEC1q9f36me\nOZqmrYyXjsDFxcVqkWQ2m59KRmBrIDrRPiiKwqpVqxAfH4+CggLQNC0pjms2m5Gfn4+6urpmPay2\nWsJZSuZYFt+W3+jGXjEvLy+rRQHP83bFS1tIS0vD9evXxfF0Oh0OHTqEtWvX2n2N7oTDjTeapvHV\nV19hxowZMJvNWLduHfr164ctW7YAADZs2IDo6GjMnDkTgwYNgkKhwGuvvYb+/fs7WHLbdJQVz3Ec\nvv/+e+j1epjNZuTk5KCoqKjF+mU0TWPTpk349ddfReUZOHCgVfC/yWTCzp07YTAYwPM8evfubfWj\nLQgCHj16hNLSUtEbl5aWhk2bNsHZ2blZORrv9z+ptBEREU2WK6iursajR49EBTWbzdDr9Zg4cSJy\nc3NRX19v0wOn0WgwduxYq/G7IkQnOk8GnU6Hf/3rX+JD6fbt26ipqWmyVyIAXLhwQdJf1Gw24+zZ\ns1i+fHmrx+9M7JHBzc0NY8aMQVJSkvgwHjZsWKcGmNuC6ET7cXJywqxZswA0GEJFRUViLKeFlpwD\nMTExVrGGISEh+Oabb1BWVib2z1UqlXj++ecxfvx4lJeXQ6/XY8aMGTh9+rRo4H300UctbtM2prCw\nUGI8CoKAkpISu99vCznoZVtxeMxbR9KdYhkyMzNx4MABiXIplUps3rzZLjdzQUEBzp8/D71ej4CA\nAMycOVOy/Xnw4EGkpqZKyg34+/ujuLhY0tyb53mJ8cUwDGbPno0hQ4bY9Tn+/ve/W/VcHDVqVJNb\nV0ajEf/85z8lBppKpcKSJUsQGBiI5ORkxMfHSwqkKhQKbN682eHegSeRw3yUgwxy5tq1azhz5ozV\nfPp//+//NfkeW82xvb29sWzZMtnExbWX7OxslJaWwsfHB+Hh4R12XTnMRznI4Gg4jsO2bdtQUVEB\njuPEIuz2lA75+eefcf/+fQANjeVLS0tt1vpkGAbR0dF4+PCh2It69uzZ6NWrF9zc3KxK77REcnIy\nTp06JTHgfHx8xMSHrkpb52PLgRKEVvFkJlFbaSpN356bfOHCBZw7dw65ubmoqKjAw4cP8f3330sm\nfXFxsVW5AY1Gg1GjRsHT0xP+/v42eyjaK0NCQgKKiopsutlttTOx4OrqioCAAHEFSFEUGIZBcHAw\nnJ2dMWbMGIwbNw40TUOlUoGmacyfP9/KcLN1HwwGA9LS0lBcXNyi/ISOo6N04mnIQNO0VbxYS96H\n6Ohoq4K4er0eW7ZswcWLF1s1fmfSGhlCQ0MxcuTIDjXcCP/G0fOBpmlERERg4sSJGDZsGF544QVM\nmzbNrvcuWrQIf/7zn/HnP/8Z8+fPlyS3NIZlWdy/f1/Si/rUqVPQaDRwcnKy+zuor69HRUUF+vfv\nj969e4sF2tVqdbMecntw9H1oDw7fNiXYplevXlCpVGBZFjzPizEu9njdamtrkZeXJ3oTLAkCeXl5\n4o+xn58fKisrRQOOpmn4+/tjwoQJmDJlinitmJgYpKSkiNumSqXS7gDg8vJy0DQt8R42rtFmC4qi\nsHLlSsTFxSE/Px9eXl6YPXu2JA5j8uTJGDBgAPR6PXx9fe2Km0hLS8OhQ4fEVi3Dhg1rMXCd0P3p\n378/EhISJG3bWmq9M3z4cBgMBkn2s0XXLl26hP79+3cbDxyh+8IwDCZMmNCua6jV6iYX8xRFWbWR\ne7IXdUvcuXMHJ06cEJ89y5cvx/PPP4/a2loEBga2OlO1O0G2TWWM0WjE6dOnUV5ejl69emHatGl2\ntYIymUz4/PPPJUrj5OSEZcuWiS12niw3EBgYiFWrVlmVGzCbzUhMTMTjx4+h0Wgwffp0sZGwyWTC\n0aNHUVxcDC8vL8yfP19iSJWUlGD79u0S75tarcaHH37YqSnegiDgb3/7m0QOhmGwevXqpxL0bUEO\n81EOMsid6upq/P777zAajYiKirI7Tkqn0+Hbb7+VzCuVSoUXX3xRlhmOckAO81EOMnQnrly5IsY2\nm81mUBQFmqahVqtRXV0teQ6pVCq8//77dj3HdDodvvnmG0kIjVqtxgcffNCmwrvV1dU4e/asmAA4\nadKkDimv0166bKkQQtNoNBqxOGZr6NGjB/r06SOW11AqldBoNJJUf1dXV8yePVssx9G/f38cO3YM\nqampoGkas2fPxoABA6BUKhEbG4vY2FjJGDzPY+fOnaioqADP86iqqsL27dvxzjvviLEMPXv2xKRJ\nk3D+/HnQNA1BELB8+fIONdyKiopw5MgRGI1G9OrVCwsWLLBKpqitrbXZ0F6n0z1V443QNXBxcZF4\nm+1Fo9FYbbnyPA9fX9+OEo1AkD1jx45FcHAwioqKxDhphmHQr18/PH78GEeOHIFCoQBFUVi2bJnd\nvahLS0utyotwHIeqqqpWVxZgWRbbtm0TE/SKiopQXFyMVatWteo6coIYbx2MHOrGJCQkYOnSpbh0\n6RLy8vLg4+ODyZMnS1YZx48fF4NOAeC3335DWVkZgIYYg0OHDsHFxUX01D2JXq+XbLsKggCO41BY\nWIjQ0FAkJCRgwoQJ0Ol0UCqVoCgKsbGxHdoU22g0YufOneK27OPHj7Fnzx6sX79ech/UajXUajVM\nJpP4XkEQ0LNnzw6ThdA0na0T6enpYm/SmJgYTJo0CRcvXmxWBkvZHJPJBGdnZ/j4+LS4KqdpGsuX\nL8e+ffvA8zwEQcALL7wADw8Pq3Pl8rvgaBkIDXTkvRAEASkpKcjKyoK7uztGjRplVzJAR8oQEhJi\n87d9wIABiIyMRFVVFdzc3CQ61dL4np6eEq8d0GC8VVdXw93dHdXV1bh27RpMJhOioqKa9Xbn5eWh\nurpafF5ZOk3ExcV12fAZYrx1YVJSUnDy5EnU19cjLCwMixYtElOvG7fMeZKioiLcv39fst1jMdwa\nc+nSpSaNN0t7nsZYVlwW4uPjkZycLK6cTp8+LfbT64hq7bm5uVbjFxUVWWW3Wmoc/fjjj2IM4cyZ\nM+Hn59duGQjyIj8/Hz/99JM4t69evQpBEJrdZjGZTNixYwd0Oh14ngdFUXB1dcXatWtFQ8xkMuH6\n9euora1F3759Rb3o3bs3PvjgAxgMBri6urY6g45AaC+JiYm4cuUKWJaFUqnE3bt38frrr9vt4Xra\nODk5tanUjJ+fH0JDQ/H48WPJ8RMnTuDll1/Gli1bUFVVBZ7ncefOHUybNg0jRozoKLFlD4l566IU\nFhZix44domGkVCoRHh6OFStWwGw2i25qW6Snp+Pw4cNWRs6ThISENFtx+5dffsHDhw/BsixomkZQ\nUBBeeeUVcdwvvvgClZWVkvdYKmNv3LixVTV+mvochw4dskqI+Pjjj20+rM1mM4xGI1xcXDrlISuH\n+SgHGZ42giAgPj4eN2/eBMuyVqt1jUbTbLHWAwcOIDU11ep7Cg4Oxrp161BdXY1vvvkGNTU1YvJQ\nVFSUWC5kxIgRmDx5cpP6Vl5ejkOHDqG8vBxeXl5YvHjxM5vQIIf5KAcZOgqe5/HJJ59IFtJOTk6Y\nP3++bGvctYa4uDirunIuLi6YPHkyTp8+bRUP99FHH9m8Dsuy+Pbbb2EwGGA2m0HTNHr37i2LbdNO\nj3mz1G0hOIasrCyJwprNZmRmZuLrr7+GVquFSqXCwoULrXqEAoC/v7/VZLFkYTZm+PDhzcqwYMEC\n9O7dG4WFhfDx8cGIESMkDzC1Wm1lvAmCgKqqKly/fh0TJkxAdXU1bt68ibq6OkRGRooNwe0hPDwc\nPj4+KC0tFWsVjRkzpkkvi1KptLmlRejaXL58GdeuXbNZlgZAix6IkpISmz+eWq0WQEN9qcZxkxzH\nISUlRTzv6tWrYhmbJ2FZFjt27BC37EtKSrBz5068++67svGMELoulu36J2lKFzoKlmXFbg0+Pj6Y\nNm3aU8n8DAoKAsMw4udRKBTw9/cXd1Aa01z7RIZhsH79epw7dw5arVZMWOjKtLnOW3dZuXQ0nVU3\nxtnZ2cpI4Xke5eXlyM7ORl1dHQ4fPoyKigqr92o0GixbtkwM7Pfw8MCrr76KgIAA8ZyxY8fabGHV\nGEv19blz52L06NFide2qqiqcP38eM2fOtPmAMpvNqK6uRk1NDb777jskJibi8uXL2L17tyQOryWU\nSiVeffVVTJ06FWPGjMGiRYswefJkAF27fk9342nfC0spG1vQNI3Y2NhmZfDz87PpNbNkTtfX1ze7\nUGVZFg8ePLD5P61WC5ZlkZ2dLR7jOM5mmMLThuiEfOioe0HTNMLCwqyeBU2Fu3SEDIIgYPfu3bh5\n8yby8/Nx9+5dbN++vVnjqa3jDxw4EIMHD4ZSqQRN0/Dy8sLChQsRGRkp+cw0TaNfv37NXsvFxQXz\n5s3D2rVrMXXqVNA03aV1olnP26+//ophw4a1KrC7pKQE9+7dQ0xMDAkIf4rExMTg6tWrYvsshUJh\npTwURaGgoMBmvEFYWBg+/PBDmM1mUQlef/116PV67NmzB0lJSbh69SomTpyI559/3i6ZLLXUeJ5H\nXl4e/vSnP2HdunU4cuQISktLJd0cIiMjkZycLEkl5zgOZ86cwcCBA+3+HmiaxqhRo+w+n9D9eDK7\nmKIoeHt7IyQkBAMHDkRYWJjVj7Ql8NnV1RVz5sxBfn6+JKGl8XX79u2Ly5cvN/twasrroFarrTwE\nZrO5Q2I+CQQAWLp0KU6ePIns7GxoNBrMnTu3xWbtWVlZ+P3338FxHEaOHNmq5u4GgwGFhYWiPlgW\n7AUFBa3aObEHiqIwZ84cTJ48GSzLws3NTYxJXblyJX799VdUV1cjKiqqyyYetJVmY95++eUXjB8/\nHrt370Z5eTlefPFFDB06FIDtbTYAOHXqFKKjo5GWltbpX2Z3imWwB5Zlce/ePdTU1CA0NBQ7duyw\nqu320ksvwdvbGzzPw8PDo8UyHTt27EBeXp74PTIMg6VLlyIiIqLZ9z148ACHDh2SHFOpVNi8eTMo\nisLRo0eRmpoKhmEwdepUDBs2DImJiVYP1ebiFroacpiPcpDhaVNcXIwffvhBnPsMw2DDhg1NFm9+\n9OgRfv75ZwiCAJqmsWLFCqSkpODq1auS8xrPxfv37+PIkSPiGAqFQuyCQtM01q5d2+Ri9ejRo3jw\n4AFYlgXDMOjfvz8WLFjQUR+/SyGH+SgHGRzJ/fv3cezYMbHwulqtxhtvvAGNRmPX+ysrK/HVV19J\nFjMMw2DRokUICgoCy7Lw8PCwKqNDsM1TiXnz8fGBh4cH4uPjceLECfz6669W59jyziUkJEi24AhP\nB4ZhMGzYMPH13LlzcfLkSVAUBYqiEBYWhitXriAnJwcURcHX1xerV69udtVfVFQkmUgsy6KgoKBZ\n462mpgZHjhyxOs7zPHQ6HXr27GmzXl1kZCQuX74s6aXa0lYtofsiCAKuXLmCGzduiI2tm2ulZsHf\n3x8bN25ESkoKKIpCTExMk54Eo9GIn3/+WZxzHMdhz549NmNDLYZaRUUFfvvtN4leKBQK9OvXD35+\nfhgwYECzXT7mzZuHiIgI5OTkiKUcCARHER8fL85/QRBQV1eHW7du2b3D4ubmhl69eiEvL0804FiW\nxYEDB8TFjIeHB1555RXZ9ZvuTjRrGjs7O2Pz5s14++23AdiOc6utrYVCocDnn3+O//zP/0RAQADW\nrl2LWbNmPR2JZY4j99CHDBmCdevWwcfHB4sXL0ZAQABycnLAcRxYlkVJSQni4uKavcaTqy+GYZot\niJiVlYU9e/ZYxQRlZ2fDbDY3u5oLDAzE4sWL4enpCRcXFwwaNAhz5syx45O2TFeOZehu2Hsvrl69\nisTEROj1epSXl+P48eNIT0+3671eXl4YP348xo0bZ9Nws8hQWlpq5RFoqo8wRVE4efIkvvzyS5SU\nlEh2GjiOQ48ePTB+/PgW27MJgoCDBw/i9u3buHjxIr766isYDAa7PldHQnRCPjjyXlgMN0scJs/z\nkoz9lqAoSsyYflJvBEEAy7Ki/jaHHOajHGRoK8163oYPHy5mHN6/fx9FRUVW59jjnetqVFVVobS0\nFG5ubl0upd/f318sWHj9+nWJa9tsNqOwsLDZ9y9cuBA//vij6MoNDAzEoEGDbJ6bk5ODffv2NRks\nPmnSpBYzkKKiohAVFdXCpyI8CyQnJ0vmEsuyuHPnToe2mvLw8LBaaJjNZvTs2dMqg75Hjx64efOm\nzetYvAunT5/G7du3QVEUJkyYgMGDB6OwsBDOzs4ICgoCRVG4desWCgoKxA4nLMviyJEjWL16dYd9\nLgLBXgYNGoQbN26Iry1b+fYiCAL2798PrVbb5HafpeYm4elhd6mQgQMH2gwkt8c715XIyMjAgQMH\nxIa6I0eOxLRp0+x+vxzSjy0y+Pn5ITMzUxKn01LrnuDgYLz11lvIz8+HWq1GaGiouLoyGAwoLi6G\nRqNBQEAAkpKSrAw3SzPiVatWtbvpcXuQw30gNGDvvbCVmdxR9fiGDh2KY8eOoaqqCuHh4cjMzBSN\ntTlz5sBsNksMN5qm0b9/f1y+fNnqWhRFISAgQCxzY9GB8+fP48KFC2LWdVhYGJYtW4bi4mJJazpB\nEBySbUp0Qj448l5MnToVSqVSrHc5ffp0BAUF2f1+g8GAoqKiZhN4LElDzSGH+SgHGdpKuzss2OOd\n6ypYtjcaGyTXr19Hv379ukQPzPr6epw6dQo5OTnQaDQYMGAANBoNTCYTKIqCi4uLXUkkGo3GKu06\nPT0dP/30k5ioMnjwYJvv9fLywvLly1tUXALhSWJjY7Fv3z7xoeDk5ISxY8e2+7omkwlbtmxBbW0t\nBEEAwzAYPHgwIiIi4OfnB2dnZ/zjH/+QvEcQBLGEyJML0iFDhmDu3LnYsmWL5LeicdY00BBS8ODB\nA/j7+0tqVVniTwmEjkYQBOh0OigUCri7u9sMB1AoFJgyZYrYz7eyshLl5eXw9PRsd5IBRVFwcnIC\nwzCYN2+eKNNvv/2Ga9eugaIojB8/HiNHjmzXOIR2GG+2Mk2b8s51Ferq6myW22hNA3NH9g/cv38/\ncnNzkZGRgdDQUOTl5cHJyQkKhQKxsbF4+PAhtmzZAl9fX8yfP9/u5r6CIODQoUOSB9WdO3cwdepU\npKeni98ZwzCYMmUKvL29Hd5H0dHjE/6NrXshCAKSkpJw9+5dqNVqTJkyBeHh4VizZg3u3LkDpVKJ\n4cOHd8gi4MGDB0hLS5NsW969exdz5swBRVEoKyuzemjRNA03NzcMHToUt27dkhyvqKgQt0abg+M4\n6HQ6jBs3DkePHoWzs7OY3Td//vx2f67WQnRCPjyNe1FXV4ddu3ahrKwMgiAgJCQEy5cvb7JH7/nz\n51FeXo60tDRQFAV3d3esWbOmxSSDJxMWFAoFNBoNFi1aJO5YBQQEiF7za9eu4dKlS+Lz49y5c3B2\ndkZ5ebnD52NX1gnS27QRKpUKarUa1dXV4jGe57tED8z6+nrk5ORYGdX19fWgKApnzpwRq3GbTCb8\n8MMPePvtt1tsvg00POxsGbUqlQorV67Eb7/9Jm4TmUwm5OTkdOhnI3Q/Ll68KMk0/te//oXXXnsN\nQUFBrdrCsQdBEKy8ZyzL4rvvvsPq1attLmJ4noePjw9eeOEFjB07FvHx8eJCJScnB7t27cL8+fNR\nWLKjyxsAACAASURBVFgIs9kMiqJE3bOMRdM0AgMDxcVTTEwMWJaFr6+vXXpHIDSHpb4n0DBfT58+\njZKSEtEDnJubi0uXLomFy58kNTUVOp1O/G2vqKjA8ePHsWTJkmZ7AVMUhRUrViAxMRH5+fnw9fVF\nbGxsk+0O7969axXLeu/ePQQGBrbpcxMaIL8gjaAoCitXrsTu3bvFGJhp06bZXWzYstL++9//DoZh\nMH36dLtKHXQEjZUtNDRU8j9BECTxPIIgoLa2FmVlZXaVdGEYBq6urpIMOUEQ4O/vj549eyI0NBRn\nz57FpUuXxP87uhxCV11NdUds3Yvr169b/aDfv3+/yQdNe+jbty8iIiKsMuq0Wi1++eUXrFq1CsuX\nL8f+/ftFA2zRokVwdXUFAHh7eyM/P1+ygGFZFsXFxdi4cSMePnwIhUKBkJAQHDp0SGyWPWbMGPTp\n0wcAMHHiRJw+fRqPHj2CWq3GrFmz7KqC35EQnZAP7bkX9fX1+Omnn5CRkSEeEwQBTk5Okt95juNQ\nUFDQ5HUCAgJQWloqvuZ5Hqmpqfjkk08QGhqKl156yaqslFarhVarhZeXl7jt2hK2SlOpVCpZzEc5\nyNBWiPH2BIGBgdi8eTMqKyvRo0ePVjVPP3nyJFJSUsBxHOrq6nDs2DG4ubl1eNVpWyiVSowYMQK3\nbt2ySiKwBFA39j5YCpRayiRkZmbiyJEjqK6uRmBgIJYuXSo+vO7cuSM2sbckJEyfPl00avV6Pa5d\nuyZ5uF29ehUjRoxoVeVuwrPDk9uUltqETwMPDw+sW7cOO3fuRE1NjXi8cUZcaGgo/vjHP8JoNMLV\n1RUZGRk4ceIEXF1dMWrUKCvZLHrg5eWFcePGicfffvttGI1GqNVqyUPr5MmTuHfvHjiOg9FoxL59\n+7B+/fou4dUnyItTp04hKyvLyptsq9yHXq9vshSOxQP85K6KIAjIzc3FsWPHsGTJEvH4tWvXcPbs\nWTHRZ9KkSZK53xRTpkzBv/71L7EoMMMwdteUIzQNKYFsA5qm4e3t3SrDDWhwQz9+/Fh8zXGc3XWq\nOoIZM2Zg1qxZoCgK/v7+UCgUUCgUCAoKQkREhJjNR9M0VCoVvv32W3zyySc4efIk9u/fD6PRCLPZ\njPz8fOzZswdAQzmQU6dOSYy3vn37SprWm0wmKzd7Tk6OVbuhzqQr1+/pbti6F+PHjxfno+UHvakk\nmI4gOTlZnMONsSxQgIZFjoeHB65fv47Dhw/j5s2bSExMxGeffQZvb2/JVifDMBgyZIjV9SyB4k96\nG44fPy55SHIch7S0tI74aHZDdEI+tOdeZGVlNdtrtzEGg0Eyz/Ly8vD111/js88+Q1xcHAICAsAw\njNXvt9lsloS/mEwmnD17VnRMcByHhIQEVFZWtihDUFAQ1q9fjwkTJmDChAnYsGEDfHx8ZDEf5SBD\nWyGetw7kSWNPqVS2GNTckVAUhaFDh6KyshKTJk0Cy7Iwm81if8UbN24gKSkJFRUVqKqqAtCgpLdv\n35ZcRxAElJSUgGVZZGRkSDx5PM8jMzNTcr6tWnj2pIoTug8cx0GpVNrtPRs5ciScnJyQkpICZ2dn\nTJw4scVit/ZiiUFr7N0zmUygadrKO2Erm/XChQtW3uvc3FwMGDAAtbW1UKvVmDBhQqvkffLhqFAo\nbJZGITzbGAwGPHz4EADQv39/m0XOnwxhaQ5BEEQDS6/X48cffxTndmFhIfr06YM1a9bg9u3buH37\ntlWdQwtGoxFKpVKyAFEqlTAYDHYlvvn5+SE2NtYume2F4zixPWRYWNgz19WJGG8dyKxZs0TvlaWO\nTuP2VZ2FZR+fYRjxAaFQKFBVVWVT6RsHvlpQKBSgaRouLi5WrvUnjVSVSoWXX34ZBw4cgNFohEaj\nwV/+8pcOq9HVFrpyLENXorq6Gvv27UNBQQEUCgWmTp2K0aNHi//X6XRwd3dHSkoKoqKiQNM0iouL\nsXfvXlRVVUGtVmPp0qU2Df36+nqkpaWB4ziEh4e3uAVfX1+PgwcPIjMzUyxJMGnSJFAUhVmzZiEl\nJUVyPk3TCA8Pt7qOLa+G2WyGTqfD2rVr7f1qJLz++uuIi4sDy7JQKBRQq9WdFg9rgeiEfLB1L7Ra\nLb7//nvxtzYhIQGvvfYavLy8JOfNnTsXO3fuFLsZAA1zWaFQwMXFBXq9XjzXUpMQaPDYNSYkJAS5\nubno2bMnpk2bhuzsbBgMBnGb1VLqAwA8PT2ttml5nrdrgS4IAjiOs1qstGc+siyL77//HjqdTnx+\nLVy4sFXFhtsrg6Mhxls7YFkWVVVV0Gg0oGkakZGRWLt2LdLT0+Hk5IQhQ4a0euu1KQRBgMFgAMMw\nLXYtaIqMjAybhRUpikKPHj1QW1srGp7Tpk0TPXnXrl0Tg7ApirLZwiooKAibN28W3094Nvj5559R\nWFgoJsWcP38efn5+CA8PR05Ojrj9TlEUPD098corr2DXrl1i7FlNTQ327duHd999VzKva2trsXXr\nVphMJvFh8uqrr8Lf379JWU6ePIns7Gwxu/T333+Hr68v+vbti/Pnz8PFxQVGoxEMw4DnecydO9em\nZyM6OhoPHz60eli1p0/jsGHD4ObmhtTUVLi4uGDkyJFt1mNC9yQ+Ph719fXivDObzYiPj5fEnQEN\niQabNm1CZmYmFAqFON/DwsJgNpuxa9cuUW9iY2PFEjkqlcrKM24JrVEqldiwYQPS0tJQX1+PsLAw\niUdNpVKJST0WY2nJkiUtzuGsrCwcPHgQdXV1cHV1xYoVK5rVYXu5f/8+dDqdaLzyPI+TJ0+22njr\nysgi5i0uLg7R0dGIjIzEp59+2uR5169fB03T+PnnnztROtukpKTgs88+w7fffov//d//FeMDUlNT\nMXHiRIwePbrDDDeTyYTvvvsOX331Ff7xj3/g+PHjzXayaGof383NzWbgdY8ePbB+/XrMnTsXsbGx\nWLVqFUaMGAGg4eEaEhICLy8v9O/fH+vXr2+2Sb3FcHN0LIGjx28vXUUn8vLyJOVpWJZFbm4uAODY\nsWP4/+ydeXRUVbb/v7emkHmeQxJIQkiADEAIg8xThyEiiAQEQVAGRcVW236+53rdr/vZ2v2W2i0q\nqGFQEEQRmUOYAkgSAoFASAJmnicyj1W3qs7vj/zqdm6qKqkkldwKnM9aLldV7r1nF3V2nX322QPL\nssjOzoZCoUBNTQ2Sk5O1PFsMw6CyspL3XlJSEhobG6FQKMCyLBQKBU6fPt2tLJp+up1lycvLw+HD\nh/Hzzz9zXgWxWIxt27bpjbFbtmwZr0i1piyOodl1ukhISIC/vz8WL16M2bNnC9Kwm+qE6aDru9AY\nXJ3Jy8vT+VtvY2ODsLAwhISEIDQ0FGFhYbC1tYWDgwPeeOMNvP7663j33Xd5XvBRo0bBzs6Oi90s\nLi7GnDlzuDVB01VE86yuaJJ6XnvtNfzhD3/odh3QfJ7Dhw9zxbGbmprw3XffcTran/nY1tam9Tui\nK6a1J4ayTgjueVOpVNi+fTsuXLgAT09PREREIDo6WqvCv0qlwrvvvovf/e53grfgamxsxLFjx3he\nrEOHDuHtt98ekPGOHz+OR48ecYtkeno6vL29eYuPZnHsblFYsGAB16ge6Nh1zZw5E+PGjUNzczM8\nPT3h4ODAKXNJSQkXI0EIQW1tLdzd3Q0unULpG0NJJywsLHhxZJqyMgC0ElaUSiUUCoXO3qJdPWAN\nDQ1a1zU1NXUrS9dYILFYDEtLS9y7d4/3LJVKxZU70IVUKsXKlSvR2NiIjIwMAB3xR4YWtaYYn6Gk\nE30lKCgIxcXFvPdYlkVGRkavit8zDKPToyyRSPDSSy/h9u3baGxsRGVlZa87mIjFYoMrCFRWVmo5\nC5RKJerr6/sdD+3r68t1+9HINdild4RGcOMtJSUF/v7+XG2ymJgYHD9+XEspP/vsMzz77LO4efOm\nAFLyqa6u1gre1ASG9vYMXa1Wo7KyEmq1Gq6urjqLd5aWlmp5N0pKSjjjraysDN999x13dDVlyhSd\nY9nb22P79u3IyckBwzAICAgAy7KIjY1Fa2sr1Go1/Pz8sHLlSpw7dw6pqala4167dk3v8zsjdCyB\n0OP3h6GkE08//TS+//57AP9OUtFkYfr4+HDdPoAOo8jf3x9WVla4cuUK94zx48drJb34+fkhMzOT\nF9PT04/z0qVLsXfvXu6Y1crKChEREUhMTNSqfWhIGyAbGxuD5roh6JqPra2tSE5ORktLCwIDAzFq\n1CijjNUbGYYKQ0knDEHXdzF58mScP39eq6STIRmdhiKVSvtdg7OpqQmZmZlQq9UICgqCnZ2dzuus\nrKx0btQ0R639mY8eHh545plncPr0acjlcowYMQIrVqzo9XOGsk4IbryVlpbymjZ7eXnhxo0bWtcc\nP34cly5dws2bN7vNaNuwYQOn4HZ2dggLC+O+II2LtL+vx40bB5VKhYKCAgAduwC1Wo3bt29DKpUa\n/LwLFy4gPj4ednZ2YBgG5eXlWLRoEdd/NCEhASzLor29HQC48UaMGAEnJydcvnwZtbW1yM3NRXt7\nO/d3hmHg7+/PZYV2J8/58+dhZmYGQggKCgqQn58PGxsbpKWlcfdr/j01z6+pqeFaYBnj3/Nxef3p\np58iLS1Ny1DoLUNJJwoKCjBu3DgMHz4cZmZmKC8vx6+//opZs2Zh2bJl+POf/4zKykr4+flh7Nix\nSE1NhbOzM9avX4/Kykr89ttvvPACzfNnzpyJR48ecZuSBQsWYNGiRd3K4+bmhpCQEFRUVGDy5MkY\nNWoUrl+/zvUz1RzpWlpacv8eQs2ZyMhI7Nq1C/fv3wchBAEBAZg3bx7X3cXd3R0nT57EgwcP4Orq\nivfffx/Dhg0TfI5TnRjY1+7u7khMTATQ8bsrFotRXFyMhE5tnPo73uXLl6FSqTBv3rxe319fX493\n330XSqUSI0aMQEJCAkaPHg17e3ud148fPx5Hjx4FAIwcORKzZ8/mvjdjfJ7g4GDuteZ3ROg5P1g6\nwRCBfctHjx5FXFwcvv76awDAgQMHcOPGDXz22WfcNStXrsTbb7+NyMhIbNiwAUuXLtVpZetqIj1Q\nXLt2DVevXuUKFi5duhQhISE8JeuJS5cuISkpiefBMzMzQ1RUFOdVe/DgAX7++Wet0gXvvPMOTp8+\nzWXjdaa4uBjbtm3DhAkTepTh448/1jqO8vDwQEVFhc7+tUDHwrJ58+Zun9ubf4eBQOjxgb7Px6Gq\nE/r4/vvvkZ+fzxWLDggIwLPPPmtQWRFCCNRqdb+SYNRqNb744gs4ODjAwcEBs2bNMlo8qqF0nY+3\nbt3CuXPntLK43333XVRUVCA2Npb7m1gsho+PD9atW2dUGYRgqOtEXV0dysvLYWVlheHDh/e5sLS+\n76KhoQHffvstGhoauISDzoVwCSEoKSlBY2Mj3N3d9R796yM9PR0nTpyASqVCTU0N/vznP8POzg61\ntbUoLy+Hra1tt328Dx06pFWf0N/fH88//7zeewoLC1FbWwtXV1deSyxTmI+mIENf56PgnjdPT0/e\nOX9xcbHW5ElNTUVMTAyAjnTqs2fPQiqV8lKZB5vp06cjKCgIdXV1cHZ21us67o7Kykotw0sul+P0\n6dMQiURcKQFdSQY5OTm8pvBd0VV7TRfOzs5obm7m9WN0d3dHdXW1XuOttrbWoGdT+sZQ1Ql9XLt2\nDW5ubtxczc7Oxm+//YbAwMAe72UYpt/ZyyKRCGPHjhX8R7ozLMtq6Zfm30eTMauhs5f/ScUUdOLh\nw4c4evQot9gGBQVh2bJlRu0MYmtri+3bt6O1tRVmZma8MBpCCE6cOIGMjAxOhmeeeUbr6FgflZWV\nOHHiBDfPGhsbcfDgQcyePRvHjh3jMlfHjRuHpUuXat2flJSks+h8T8XYfXx8BqXL0JOG4MbbxIkT\nkZ2djYKCAnh4eOCHH37AoUOHeNd0Lgr74osvYunSpSaxSDk5OWkZSb1ZIDw8PJCXl6dlgLEsi5s3\nb2LcuHEYOXIkhg0bxiUNAB1xC7ruAzqMr5iYGIOUhRACJycnrv6PSCTCiBEjEBUVBaCjLRYA3jgM\nw8DZ2bnHZwu9UAo9fn8YyjrRFUII3N3dteJ4Otei6gmlUokLFy5wR/pRUVG99jgYez48ePCA6+U7\nefLkHmu2dR0/ICAAly9f5gw4TaYf0OGBE4lEvHghY9RMpDrRdwghWicgWVlZCAsL6zEWs7i4GL/8\n8gtaWlrg6emJFStWdPtdaCoAdKWoqAgZGRk8GY4dO4bRo0cbZECWlpbyrvP19UVNTQ1+/vln3lxL\nT09HWFgY75i6ubkZly5d0vIQSSQSg43HrvR1Psrlcvzyyy/Iz8+Hubk5li5dqrNe40DKYAoIXipE\nIpFg586dWLhwIYKDg7Fq1SoEBQVh9+7d2L17t9DiDSjTpk3T63qXSCRQq9VI+P9xb51RKBS4f/++\nVtC1g4MDXn31VS6WoSeuXLmCO3fucAopEokwefJkiMViLFmyBNu2bcP69esxbtw4SCQSyGQyWFtb\n9ykwlGI4j5NOMAwDJycn3hzvXDjUEDStqqqqqpCbm4tvvvmGiw0TguzsbBw9ehRlZWUoKyvDyZMn\ncf/+/V49w8nJCWvXroWbmxtsbGwQHh7OeTvGjh0Le3t7SKVSrlj2okWLBuKjDBmE1gmWZbV+hxmG\n6TGZoLGxEQcOHEBtbS3kcjkKCgq42oe9paGhQWutUKlUBpfIsLa21rpfk+TWGV2fq7m5WacHPDAw\n0KD+psbkp59+QnZ2NuRyOerr63H48GFUV1cPqgymgOAxb8bEFOJ7enuGTghBVlYWr/SIVCrFmjVr\nkJeXh+TkZK0fDQ2enp6oqKiASCSCubk5NmzYAHt7e4Nl+Ne//oW6ujree+Hh4Tp3qw0NDZDL5XB0\ndDToGEvoWAKhxwdMYz6aggwnTpxAXl4eV8dq7ty5erM4VSoVKisrIRaL4eLiArVajf/93//lfQaZ\nTIYlS5b0qkOBMefDwYMHeT2MAWD48OHddl/o7fhKpRL37t1Da2srRowYAU9Pz76K22cZBgJTmI99\nleGf//wnz2MslUqxadOmbksnpaen49SpU7xyOppN8vz583s1fnV1Nb766iveSYiNjQ127Nih1/PW\n1taGuLg4VFRUwNnZGe3t7VztuIKCAp1B8xKJhOs/qkEul+Pjjz/mfQ6ZTIYdO3b0uQVkX+YjIQR/\n/etfeSEHEokE8+fPx6RJkwZFBmMzZGPennQYhkFwcDDs7OyQkpICQggmTpyI4cOHc0VOdSESiRAQ\nEIA1a9agvb0dtra2PKMqNzcXZWVlsLW1xdixY3WWRujarkRTjFQXtMYVpa/Y2NjgjTfe4Nph6evp\n2dLSgj179nAxmG5ubli7dq3OHzdDSn0MFLo2L8buKiKRSARprUfRz/PPP4/vvvuOi/FatGhRjzUv\n9f2e9mW+ODs7Y+nSpThx4gSAjhqLGv3QhVqtxr59+7gaoY8ePYKdnR1kMpmWt07TdQQAoqOjtcKB\nzMzMsGbNGhw+fBgsy0IsFmPVqlWD2rsb6FijuvYo7m7depyhnjcjoXE/66rT1le++uorlJeXa72v\n6Y24bds2riBqZ65cuYLr169DqVRCIpHA29sbzz//vJaS5+Tk4MiRI2BZFgzDQCaTYevWrbzki4H4\nXE8KQ9nL0FcaGhpw5MgRVFZWwtLSEitWrIC3t7dB9x45cgQPHz7kxYFNmzYNLS0tuHv3LtcX1Nra\nGtu2bRPsB7u4uJjX4FsqlSImJqbPcTdPEkNdJwghaG1txbBhwwwywFQqFfbu3YuqqiqwLAupVIoZ\nM2bgqaee6tP47e3tuHLlCmpqauDv74+IiAgwDAOWZfHrr7+iuroaXl5emDx5MtcrtbMDQCwWw8nJ\nCVVVVbwY6oULF2L06NE9fi61Wo22tjaYm5sbtIHSJVd/N16pqak4d+4cWJaFRCKBnZ0dNm/erHdT\naOr0dT5S480I/Pbbbzh69ChYloW9vT3WrFnT7wrSQEfW2ffff88tWpqgZhsbG0ycOFFnFW2FQoGP\nPvqI51aWyWRYs2aNziSGkpISZGRkQCqVYsKECTwP282bN3Hu3Dmo1Wp4eHhg9erVgrT1GaoM9YWq\ntxBC8Pnnn6O2tpYbUyaTYfv27Trnalc+//xzPHr0iPdeYGAgVq1ahZs3byI3Nxd2dnaYOXOm4H1B\nS0pKcOPGDRBCEBERQbPpDORJ0wmg4wg8LS0NTU1N8PLyQkBAQJ+ew7IsvvzySzQ2NkKlUkEqlSI0\nNBRRUVH48ssvebrj5+eHqKgo7Nq1SyuxbezYsSgsLIRCoYBarcbIkSPx3HPPGd2brVarERsbi6qq\nKq4x/ciRI7mM4P6gqUlqYWGB8PBwoyT0CAU9NhWIuro6/PTTT9zu5vbt21CpVHjjjTf6nULu6+uL\njRs3IisrCxKJBGFhYT0uggqFAoWFhbxMIYZhuEK/XfHy8tJZ16ewsBDnz5/nglnLy8vx008/Yf36\n9QbJLnQsgdDjP4m0traivr6e90PEMAx+/vlng+aNm5sbamtreZ43T09PMAyDSZMm9SmmRUNfYlGz\ns7PR0NAAT09PXn0qQL/eGGv8gcAUZHgSkUgkmDhxIu+9vnwXubm5aGlp4X6TWZZFamoq/P39tTY9\nubm5kEgksLW1RU1NDe9vDx48wDvvvIMTJ05g5syZWglFxqKsrAyPHj3ijEeWZZGTk4OmpiZYW1v3\naz76+vr2u8gtMLR1ghpv/aS8vFxr4jc3N6Otrc1g74BKpcKNGzdQVlYGFxcXTJ06lTumdHNzg5ub\nG3JycrhuCFOmTNFbKsHS0hIWFhY8a54Q0uuA56KiIt6OTa1Wo6SkpFfPoDxZaDp1dIYQYvDxZlRU\nFCorK9HQ0AC1Wo3hw4dr9V4sKyvDuXPn0NbWhuDgYEydOhWXLl1CXl4erK2tERUVZXCNQ30QQnDk\nyBHk5eVBrVaDYRgsXLjQoKLXFIqhKBQK7kTFELpmhWqorKzU+X5DQwMiIiIQHx/PO4lRKpX4+uuv\n0dLSYvQ6dV3l1VWjVN/noPQOemzaT4qKinDgwAGtxILx48djyZIlPSoGIQSHDh1CXl4eN9mtrKyw\nfft2zhWcnp6OkydPcmOYmZlhy5YtsLe31/nMxsZG/Pjjj6ioqIC1tTWWL1/eKy8BANy5cwdnz57l\nfS4bGxu8+eabvXrOk8yTeER0/fp1XLlyBSqVCiKRCHZ2dhgzZgxGjRql5b3ShSawWiwWw8HBgac/\nNTU1vGMgTZPspqYm7j0zMzNs375dZyyooXQOV9AgFovxH//xH0ZPTHjSeBJ1oisKhQI//PADV4x5\n4sSJiIqK6nGtaG1txc6dO9He3m6Q/G+//TaUSiW++OILXoC/BolEgoCAADz33HN9/izdwbIsdu7c\niaamJhBCIBaL4ezsjM2bN/fZYFSr1cjLy0N7ezu8vb1hY2NjZKkHH3psKhDDhw9HYGAgMjIyeF9A\neno6fHx8EBIS0u399fX1nOEGdBhzTU1N2LNnD7Zs2QKGYXDx4kXeQiKXy3H79m3MnTtX5zNtbGyw\nadOmfn2ukJAQ3L59mxfY+vTTT/frmZTHn2nTpsHT0xP5+flISUlBXV0drly5gsTERKxcubLHeB+R\nSAQXFxfutVwuR1VVFczNzXH//n2eN1ilUmmVulGr1cjNzeXay/WFlpYWnYuLXC4XPNaOMvCo1Wok\nJyejqKgIzs7OmD59ulFjquLi4lBYWMh5w9LS0uDq6tqjZ9fCwgKbNm3C6dOntbpwdIZhGEyYMIGL\nT964cSPOnj2LmpoatLa2cuMqlUo8ePAAarV6QLK3NaVUzpw5g0ePHsHDwwOLFi3qs+GmUqmwf/9+\nnqdx7dq1vBChJwnBi/QOdRiGwfLly7mjIU0bG5ZlUVpa2uP9ulzLQIeXoaqqCgqFAo2NjVp/19cW\nC/h3I9z+IBaLsWHDBjzzzDOIiorC1q1be5VNZwwZ+oPQ4z/J+Pr6QiKRgGVZrrUTy7I4e/Zsr55T\nUVGBTz/9FAcPHsTu3buRlpbW4z0Mw+hciHozHzw9PbXi9mxsbPpVFsEU5qMpyDAUOHr0KBISEvDw\n4UMkJSUhNjaWd9RHCEF8fDw+/PBD/P3vf+cayRtKYWEhcnNzudcsy3JdbnrC0dERzz77bLfGFsMw\nvI29q6srNmzYgAULFvCOaAsKCvRuUkpLS3ssQGwINjY2iImJwfbt27F8+XJeT+Hezse7d++ioqIC\nCoWC+++XX37pl3xDWSeo580IMAwDR0dHnrEmkUgMyjh1cHCAtbW1lgdBJBJBrVYjPz9fq1UO0JGF\nV1lZifj4eLS2tmL06NGYPn26UXdQYrEYo0ePNtrzKE8O7e3tWnPW0ErwGn788Udeok1TU5PWNZq6\nT5qM7GHDhmHUqFF9E/r/Y2dnh+eeew4///wz2tra4OTkhNWrVw9YbBDFdGhtbcXDhw+5uatSqVBf\nX4/i4mIuQP7atWu4desWdxqSkJAAKyurHk9ZNHStmSkWi/WGwOhi2LBh3c5FQghyc3MxZswYAB3G\nYVJSEvLz80EI4Y7pxGIxJk2axFszSkpKcODAAe6zT5kyBXPmzDFYtoGksbFRKzypublZIGmEhxpv\nRmLZsmXYs2cPAgMDudIahgQ4i0QibNy4EZ999hkvLsHS0hIuLi5oaGiAWCzmLYQMw8DCwgKxsbHc\nPRqXeFRUFJc9o1QqUVRUBJVKBW9v70GtiyV0Bo/Q4z/pjBo1CikpKVAqlZwnrrcbga47f0IIt6kB\nOnQnKCgIvr6+yMnJga2tLWbOnKlznmvmQ1VVFRISEiCXyxESEqL3eNXf3x9/+MMfjHakZArz0RRk\nMHUMCbLPzMzkGREsyyIjI8Ng423x4sWoqKjgnmllZdWrFlMikQjR0dG8JvO6PodGtl27dqG2Sf+i\nGwAAIABJREFUtpb3eXx8fLB48WKtNerw4cO8TVZycjICAgIG5Giyt/PRy8sLUqmU+7cXiUT97jwy\nlHWCGm9GwsnJCa+//jrKysogk8m4EgedUSgUOH36NAoLC2FtbY2lS5fCxcUFFhYWsLKy4imY5thm\nxIgRkMlkXGN6iUQCPz8/5Obm8n5QWJbFnTt3uKbycrkcsbGxXD88iUSCl19+mXZKoAwKPj4+iI6O\nxvnz56FQKBAUFMTNTUNxcHDg9SyUSCSYMmUK0tLSIJfLERAQgOjoaEilUl4phvz8fFRXV8PJyYl3\n1F9TU8Pb8BQXF6O9vR2RkZF6ZRCykwNl8LGysoKbmxvKy8s5Q04mk/GMl67H55rNtKE4Ojpi+/bt\nKCgogFgsxsiRI3tdYHbcuHFwd3fH9evXtcIJpFIp/Pz8AHQYml1PdTTrSNfyJUqlUmfP4OrqapOI\nK/P398f06dO5o04XF5cnus82Nd76ASEEhYWFqKurg6urK9LT03H8+HEEBQVh/vz5Wp6Gw4cPc56w\nhoYGxMbGYsGCBWhra9M6EmpoaEBeXh4CAgLw8ssv48SJEygsLASgP91aYywmJCRAqVSitraWu05j\nOK5Zs2Yg/im0ELp+jtDjUzoWmHHjxvX5u3juueewb98+LnZu/PjxmDVrFmbPnq33nvPnz+PmzZvc\n8dCECROwcOFCJCQkQK1W87zbLMsiMTGxW+PNWJjCfDQFGUwdhmGwdu1axMXFoaSkBI6Ojli0aBEv\nYWHBggXYu3cvZ9xJpVLMnDmzV+OkpKTo/C6KioqQkpLC1TbszmhycnJCdHQ03NzccOXKFbAsCycn\nJzz77LNcsoK++p5tbW1a80EikcDCwoJr/6XB2dm5V5/NUPoyH6dPn46pU6dCqVQa5SRpKOsENd76\nwalTp5Ceng7g327qtrY21NbW4ujRo1i3bh28vb2hVCqRkZGhFZSqUCgQFxfHtTfpDCEEJ06c4Ir9\nFhcXcy7y7OxsNDU1QSaTcWnjUqmUVxOrpqZGK8i26w6MQjFlnJycsGPHDtTU1MDc3LzHsgANDQ3c\nUa2GW7duccV9dWXnCV22gmJ6mJmZdZtZ7+7uji1btiArKwsikQjjxo3jiqfX1taitbUVzs7OvTYu\nCgoKcPDgQW7+PnjwgFtD9MEwDCIjI/VuQEaOHKlVioJhGIwZM0Zn+ZCYmBgcOHAAhBCwLAu1Wo3v\nv/8eU6dOxVNPPWUScZ9isZiW7AGt89ZnysvLsXfvXr2N4wFgypQpmD17NmJjY1FbW9vttbqQSqXY\nuHEjqqurcerUKS1l8/Lygr29Pdrb2xEUFISwsDBOuZKTk3Hp0iVuTLFYjJCQEERHR/fyk1L6itD1\npExFht6iUqkQHx/PtW1bsGABgoKCeryvvLwc+/fv58XsmJmZYe3atfDy8kJ1dTW+/vprXk/SmTNn\n9ireiNI/TGE+DoQMhBCcOXMGaWlpEIvFYBgGEydOhEgkgo+Pj0GZ+gcOHOBloQJAQEBAv05LioqK\ncPPmTWRlZXG1FydNmoQFCxaAYRg0Nzfj7t27UCqVGD16NFxdXSGXy3HhwgWkpaVxhqRUKkVUVBTC\nw8P7LAtFN7TO2yDT3NzcbTyMSCSCTCZDamoqqqureRWuDUWtVkMmk+mtMVRaWgqRSIQXX3xR62+T\nJk1CWVkZMjIywDAMPD09sXDhwl7LQKEMNvHx8bhz5w5nZB07dgyWlpY9Nrh3dHTU0kmGYbhjH2dn\nZ2zYsAGXL1/mEhZo1wSKMcjJyeGMII3B8+uvvwLoMHzmzp3b4/G8ruSD/nQjuHv3Lk6fPs01cHdw\ncMCWLVu49aSpqQm7du2CXC6HWq3G9evXsWbNGvj6+qK0tJQnD8uyyMrKGnTjjRCC1tZWDBs2jHrb\nukCjcfuIm5ubToOsoKCAK1kQEhKCK1euaF3HMAxGjRrVY5Cqn58f7O3tuf93XZgIISguLtZ6fkJC\nAkQiEZYvX4533nkHb775JjZs2DCo2aZC188RenzKv0lISEBDQwMyMzO7LS6qQVc234MHD3ocRyaT\n4YUXXuCScmxsbLBu3TqYmZlx88HDwwPPP/88Nm7ciIkTJw7aMZApzEdTkOFx5dGjR3o36CzL4sKF\nC7x5r+u7mDRpEm9NkEql/erne+7cOU6PlEolmpqauDAfANi9ezdX0kdzTBoXFwcAWgkYvU3KMISe\n5mN1dTU++eQTfPLJJ/jb3/6Ge/fuGXV8Q2QwZajnrY9YW1tj1apV+PHHH6FQKGBtbY05c+YgPj4e\nERERmDBhArKysvQelYaGhsLBwQEpKSkghMDLy4sr9yGRSBAZGYk5c+ZwmaKbNm3CyZMnkZGRwfuR\n0Ljo9dG5KCKF0htYluXmX38oKytDYmIiN099fX0RExMDhmEgl8shkUh4u+qumxqRSGTwxsPNzQ07\nduwAIQSEECQlJSE+Ph5FRUUIDw+n2daUAcHFxUVnPU4NGgOpu9/q4OBgqNVqTlemTZuGwMBAg2Wo\nra3F1atX0dbWhrFjx2qtPSqVihdSoPG4daa6uhpyuRzz5s3j4qz7mpTRHwghOHDgAC+R79SpU/Dw\n8Oh37+LHBRrz1k8IIVAqlVoLTkpKCuLi4vTKY2trix07dkCtVkOtVnMLpMbFrUvJVSoVYmNj8ejR\nIyiVSkgkEtow24QZqvE9SqUSP/74I3JyckAIQWhoKKKjo/vkpcrNzeWKfmqQyWSIiorCrVu3UF5e\nDqAji0yT9fXw4UP89NNPUCqVEIlEMDc3x9atW3vdr/T06dO4e/cuZ4Sam5vj1VdfpS2uBGSo6oQ+\nCCGoqalBW1sb0tPTcefOHa0ENLFYDC8vL2zYsMEoY+qioaEBX375JRQKBZfAZm9vz0tc07SrcnV1\nBdCR+Hbo0CGtf4tZs2Zh5syZqKurQ1ZWFhiGwdixY7mkjMGgvb0d//jHP3jGpUwmw5IlSzBu3LhB\nk2MwoDFvAqHZlXSmuLhYy03eFU3ygUgk4h2HSiQSbrdhbW3NWzDFYjE2btyIe/fuobm5GT4+PvDx\n8THmx6FQcOHCBeTl5XE/nBkZGXBxccGUKVMMur+8vBxxcXFoamrSmeGs8S7U1NRwYyQmJsLNzQ1N\nTU24efMmbGxsYGdnBzc3N0ydOpUrfWAohBDcvn2be77mWOi3335DWFhYr55FoeiCEIJffvmFyzoV\niURYvXo1LCws0NzcjDNnzqC1tRU+Pj5YtmzZgMpy7949rhYo0OEEaG5uRmBgIHJzczFs2DAsXryY\nM9yAjmQIMzMzrXIi9fX1AAB7e3teBYPBRCaTQSwW84w3Qshj0YjeWFDjzcgkJCRg2LBh3Qaa6qs2\nz7IsDh48yLXZ8vb2xurVq3nHVhKJBOPHj+9RBqFr1wgtg9DjD2UKCgq0gpXz8/MNMt7q6uqwb98+\nXmZ0QUEB11pIQ2NjI++HmWVZ3Lx5E8XFxZzXora2FgUFBWhtbe2z56+zDAEBAX2+v7+Ywnw0BRke\nJ7KysrRCY+Li4rBp0ybY2dnh9ddf17qHEIKWlhakpKQYte1U54bznVm5cqXeexISEjBq1ChkZGTw\nvHO96WHdH7qbjyKRCMuWLcMvv/zCdVUZM2ZMj0lLxpTB1KHGWx9pbm5GQ0MD7O3teccwhBBUVFRo\nKZJYLIalpSVYlkVgYCAWLVqk9cwLFy7wsnyKiopw9epVk+ktR3ky6JrdLBKJDO69+Ntvv/WYITdr\n1izcu3cPVVVV3HsSiQTV1dVacTpqtRoZGRnw9fXV28pKFwzDICwsDOnp6dwzJRKJoAYc5fFCE77S\nmerqavz9738H0FFjbdWqVdzmu7KyEt999x3kcjny8/Ph7OxslCNAhUKhM5jfkMzQRYsWoampiWtS\nP2nSJIwdO7bfMhmD4OBgrtuFjY0NvLy8TKLOnKlAjbc+cOfOHZw5c4Zz6y5fvpzzpEmlUty/f1/r\nHkIIduzY0e3k65qerVQqUVxc3Gv5TGEnIbQMQo8/VKmrq+Pi0DSIRCKDg5V1JdD4+vpCJBKBYRjM\nmzcPkydPhoODA44cOcK7z8rKSmfzeZZlUV5e3ivjDejoIWlra4vs7GwEBwdj/vz5vT5+NRamMB9N\nQYahSnV1Na5evQqFQoHQ0FAEBwfDxcVFZ7ySZuNeUFCAS5cuYcGCBVwAvqZ7wfDhw3HixAl4eHjA\n0dGxX7KVlpbq3DDV19ejqalJb6yaZj688MILYFkWYrF4UNvBGTIfHRwc4ODgIKgMpgo13npJQ0MD\nzpw5w6vn8/PPP+Ott96CmZkZkpKSum1d1R1OTk4oLy/nlF8sFg9YaxIKRRf5+flac9XQVjQ5OTm4\ndOmS3mbZMTEx8Pf3B/DvGlgaVCoVhg8fjurqaq37JRJJnzLMRCIRZsyYgRkzZvT6XgqlpqYGRUVF\nIIQgLi6O8+Dm5+ejvb0d4eHhMDc312onpUGpVCIlJQXjxo2Dra0t2traeH8XiUSoqKjot/EmkUh0\nxldrSvO88sorPSbp9La3KkV4TKbOW1xcHEaPHo2AgAB89NFHWn8/ePAgQkNDERISgmnTpg1IzRdD\nqKur0yoWyDAMCgsL8e233yIzM1PnfY6Ojj0W6p0/fz5sbW25wrz29va8I1O1Wo2EhATs3LkT33zz\nDdfrtCumULtGaBmEHt8YDKZOEEKQnJyMpKQkLePJkB15XV0djhw5orVAAf+ufXj+/Hn89NNPqKqq\nQmVlJe8aTfb0888/j8DAQIjFYkilUkilUnh7e/cY59kTQs8Hocc3FRn6y2DpxPnz57Fz506cOHEC\nJ0+e1Ko7eO3aNTAMw7Wf0odKpcK3336rVSakoKAALMsiNzcXjY2NfZJRg6enJ5ycnLTWJUIIFAoF\nHj58qPM+oeeD0OObigx9xSQ8byqVCtu3b8eFCxfg6emJiIgIREdH81rijBw5ElevXoWtrS3i4uKw\nefNmJCcnD7qs9vb2Wp41tVqNY8eO6W0CDHTs4k6fPt1teypLS0u88sorKCkpAcMw8PLy4inkxYsX\ncfPmTe6H5ODBg7zUb8rjw2DrxMWLF5GSkqIVcyaVSjF79uwePcfFxcXdXqNUKlFVVYWqqipkZmZq\neQokEgnc3Nzg6+sLX19fyOVyVFRUQCqVwt3dfVBjXdrb25GZmQmVSoWAgADY2dkN2tgU/QyWTpSU\nlPR4j2YjvmDBAhQWFnI9ppVKpdbcJoSguroay5Ytw9GjR7m/E0Jw584dZGVlYcuWLX2eZyKRCBs2\nbMD169dx5coVLTn70t2HYvqYhOctJSUF/v7+8PX1hVQqRUxMDI4fP867ZsqUKVyBzcjISJSUlAgh\nKmxtbbFo0SJIJBKYmZlxVbA1CtI1q06DSqXiVbfWh0Qiga+vL3x8fLR2UmlpaVo7QF2ePlM4xxda\nBqHH7y+DrROdNwVAhzfZ19cXK1euNCjLVN+xjEwm09IJXUc8I0aM4AVKm5mZwcfHBx4eHkYx3Ayd\nDy0tLfj8888RFxeH+Ph4fPnll1oxgAM5/kBiCjL0h8HSiZqamm7LPEmlUq7VlZWVFV599VWsWLEC\nK1euxLZt27S81Gq1Gubm5rCwsOCSFzrrRHt7OxITE3stZ1eZZs2apVWEWqVSwc3NTec9Qs8Hocc3\nFRn6ikl43kpLSzF8+HDutZeXF27cuKH3+tjYWJ3ZmoNFeHg4Ro0ahfr6etjb26OoqAi3bt3iXcMw\njFbF7f4Gg3a9XyQS0X5vjylC64RIJEJgYCCXnVlYWIjs7GxYWFhg/PjxWp07/Pz84OXlxbVrE4lE\nmDt3Lnx9ffHVV191u/uXSqWYPn26SWSSXb9+XavswtmzZ7Fx40YBpaIAg6cT+hIRLCwsYGdnh9DQ\nUERERHDvy2QyjBo1ins9efJk3Lx5kws/MDMzQ0NDAwgheteA7k5tDIUQonUEKxaLUVFRAU9Pz34/\nn2JamITx1psf7cuXL2PPnj24fv26zr9v2LCB29XY2dkhLCyMs64159vGeG1paYmbN28CAKZNmwYr\nKyukpaWhrKwM06dPx9ixY3H27FnI5XL4+PhAKpXC2tqaV1emt+Or1Wpezazi4mI0Nzdzn73z+f2s\nWbOM+nl7+7qrLE/C+J9++inS0tL0el97w2DrREREBFJSUpCdnQ0AXP2nvXv3QiKRwMPDA0qlkouz\nHDVqFHx8fNDU1IS7d+/Cx8cHwcHBYFkW7e3tiI6OhpeXFxISEpCXl8eNX1BQAODfnoeioiJYW1vD\nw8ODJ4+xvyPNez1dn5ycjPz8fJ68NTU13DMGenyqE/oZLJ14+PAh7OzsUFtbC6BjDlhZWeHDDz+E\npaUlPvvsM3z99dfw8fGBv78/HB0dOc9XVVUVampqYG1tjfr6eqjVaty/fx9ZWVl49dVXuedVVFRg\n8uTJADp+xzvXVuvrv/nMmTMhFouRk5MD4N9Z3nfu3EFTU5PJzUmhxx/qOmES7bGSk5Pxpz/9iWuK\n+7e//Q0ikQjvvvsu77p79+5h+fLliIuL47LWOiNk65X29nZcv34dv/76K5YsWYLx48ejpaUF169f\n5ypd96d+Tm1tLXbt2sU72nJzc8OWLVu0rk0wgcKDQssg9PhA/+bjYOlE57/duHEDWVlZGDZsGAoK\nCniFdnWhKZ7ZeSw7OzuMHj0aTz31FHeUumfPHpSVlWnFinp6esLV1RUzZszArVu3UFtbC19f3wFp\nGG/ofEhPT+cFqEskEkyYMAG/+93vBmX8gcQUZDBVnSCEID09ncv+DA8PR2trKyoqKmBlZcX1Lj11\n6hRSU1N59zo5OWHTpk04ePBgt8e0Dg4OqKurAyGE24QPGzYM8+fP10rIkcvlSE1NRUtLC0aOHAk/\nPz+dz2xubsbt27ehUCgwevRo5OXl4ddffwXLshCJRLCyssIrr7yiM1tc6Pkg9PimIkNfdcIkjDel\nUonAwEBcvHgRHh4emDRpEg4dOsQLRC0qKsKcOXNw4MABbsfSFVPomzdQpKWl4cyZM1pxSe+9916/\nG4dTBob+zMeB1gmVSoWTJ08iPT0dIpEIU6ZMwezZs6FQKPD555/rrLdmKF0XjdLSUuzfv583d6VS\nKXx8fJCbm8tl4ml6Mo4bNw5Lly7t8/j9gRCCa9eu4dq1a1xV9+joaKpjRsJUdeL48ePIyMgAy7Lc\n3FyzZg1vE1FTU4PPP/9cp/xdNzKGIpFI8Mc//pEX/qJQKLBr1y40NjZCpVJBKpVi/vz5vKNaoMNw\n+/LLL9He3s71x165ciUUCgVycnJgbW2NqVOnwtzcvNdyUQaPId3bVCKRYOfOnVi4cCFUKhU2bdqE\noKAg7N69GwCwZcsW/M///A/q6uqwbds2AB0//ikpKUKKPagMGzZMyxtBY94eXwZaJy5duoSMjAwu\nGy0xMREPHz6ESqXiHcX3BbVajdbWVmRmZiI8PByenp6IjIxEcnIyxGIxCCFwd3dHXl4eL/MO6EjC\nSUtLw8KFC7U6PQwGDMNwteG6lnegCMtA6URTUxPu37/PxaixLIvCwkJUVFTA3d2du66urk7vQtuT\n4SaRSKBSqXQW9G1tbeUV0s3MzERzczPnqWZZFhcuXNAy3m7dusUZbkCHcXvu3Dm89tprJtMlgTJw\nmITnzVgI5XlTKBRISkpCXV0dqqur8dJLLxn0o08IQWpqKkpKSuDk5ITJkyfr3eGrVCrs27cPlZWV\nXE0sXbsxwDRcwULLIPT4gGl4gvXJ8MUXX6C6utrg51hZWUGlUkGhUIAQwu30CSF622GJRCIsX74c\n1dXVmDVrFmpqatDU1ASZTIa9e/fqLeYrEonwzjvvaCVF9Aeh54PQ45uKDKaoEzU1Ndi9ezfPM2xm\nZobVq1fDx8eHe6+4uBh79uzp9XjW1taYO3cuFwMN/Lvfr1gsxnvvvcdLZEhJScH58+d5+iESifBf\n//VfvHXl3LlzWiVNrKys8NZbbxkkl9DzQejxTUWGIe15G8oolUrExsaipqYGKpUKxcXF8PT0NCjL\n6dixY3jw4AFYloVEIsGDBw+wceNGnRlJYrEYGzZsQHp6OpqamuDt7c37YaFQeoOVlZXBxpu1tTUs\nLCzAsiwmTZoEc3NzVFVVwcvLCzY2Nvj+++91eh7UajV++eUXrn+jo6MjFAoF9u3b163h5u3tbVTD\njULpDnt7e1haWnIZoUDH723XEhtyuRxisbjH3r1dGTNmDEJDQ+Ho6Ih9+/Zp3X/79m1MnDiRe+3n\n54cLFy5wr8ViMfz8/LQcAqNHj8atW7c4XZJIJBg1ahT27t2LkpISmJmZITo6mmvdSHm8oJ63LlRX\nV+PatWuQy+UICQnBmDFjur0+JycHP/74Iy+4WyQSYePGjbCystKqu6OhpaUFn3zyCU+RZTIZnn/+\neXh7e/frM1BMA1P0MmioqqpCbGws1Gq1zuOczvczDMMZZxKJBObm5lxRUi8vL1haWuLhw4c6DTLN\nAhIcHAygI3mhu369QUFBWLZsmSBHppSBx1R1orGxEceOHUNlZSUcHBzwzDPPaLWtyszMxI8//qjz\nmd0ZdSKRCOvXr4e3t7dOb5mtrS127NjBe6+goACnTp1CW1sbRo4ciaVLl+rUiYyMDM5LN2bMGJSV\nlaGsrIynry+99BIt5G7CUM+bEaitrcU333zDGWKaHnYTJkzQe4+uBUutVmP//v1Qq9Xw8/PDM888\no+VJUCqVWjsphmH0eiQoFGPi4uKCV155BdnZ2WhubkZiYqJWdwUNnb1qSqWSl8xQUFAAsVgMW1tb\nBAUFITk5mbeIqdVq3gZGXx9IoMPDt2LFChrHSRl0bGxssH79eq3329vbcerUKeTn5+ts/Qb8O4tU\nH2q1Gvv27cPzzz+v81RF18Lt6+uL7du39yj3mDFjOAcDIQR/+ctftJ5XVFREjbfHkP5VjX3MuHPn\nDs+Dpulh1x3e3t68xUZTx4plWahUKvz222/4+OOPUVFRwbvPxsYGTk5OnDIzDAOJRGKUYoqda9cI\nhdAyCD3+UMDW1hYTJ07ErFmzsGzZMtjY2MDMzAwMw3DdQwxpSK9SqVBbW4u0tDQsWbKE130kNDQU\n2dnZIISguLgYIpFIbzxoW1ubQd9bdnY2fvrpJ5w8eZJXg607hJ4PQo9vKjKYOu3t7bh79y5XG+3g\nwYN48OABWltb9XpHFi5c2GM2MiEEhw8f5tYXzToBdCRMaGqG9geGYbS8cwzD6M02FXo+CD2+qcjQ\nV6jnrRP64na6w8LCAhs3bsSpU6dQX1+vc2FiWRY//PAD3njjDe49hmHwwgsv4MSJEyguLoa1tTWe\neeYZgxZLCsWY1NTU4Pjx49zCIpFIMGbMGNy/f1+r8rtmfutayJRKJZydnbF161ZUVFTA1tYWnp6e\n+PTTT/Hrr79qHSt1PS5QKpXIzMzE3Llz9cp67949nDp1CizLgmEY3L9/H1u3boW9vX2fPz+FAnR4\nhXfv3s3NeZFIxCXodEdZWZler3VnlEolbt++rfU+IQTnz5+Hl5cXL7tV13VA98WKFy9ejBMnTnDd\nHFxcXHilVCiPDzTmrROVlZWIjY3lFFEqlWLGjBl46qmnDH7G7t27tbxsGtnef/99nuLJ5XLs2bOH\nM/rMzMzw0ksv8dLGKUMXU43v6UpcXJxWmyELCwvI5XItg2vZsmW4evUqmpqatBYsiUSCLVu2wMnJ\nCUqlEgqFAg8fPsTZs2cNWtwAwN3dHZs3bwYhBO3t7ZBIJJBKpdzf//Wvf2kdUU2bNg3z5s0z6PkU\nYTFlnThz5gxSU1N7Xa9N1/Pc3d21euLqapmoQSqVIioqCuHh4Vp/I4QgISEBiYmJUKvVXB1EfeEF\nZWVlKCoqgoWFBcaMGUPDEEwcGvNmBFxdXbFu3TpcunQJcrkcoaGhmDRpUq+esWLFCnzzzTdcSrgG\nOzs7rR3TtWvXuCxVoKPkyJkzZ7Bq1ar+fRAKpRfoWkxaW1t1XpucnIytW7eisrISV69eRUFBAVfY\ndNSoUXB0dERiYiIuXrwIhmEgFov1Gm6aUAGVSgW1Wg2pVIqFCxeitbUVBw4cQFVVFQghiIyMxPz5\n8/XGhNI4UYoxaGxs1DLcesou1Vect7W1lbcoa4409T1LpVJprRka7t69i6SkJG6eZ2RkwNLSEvPn\nz9d5vYeHB9dujvL4QmPeujB8+HCsX78emzdvRmRkZK+LdN6/fx+///3vuR2PTCaDubm5ToOsurqa\np8yEEINjeLrDFM7xhZZB6PGHEqGhoQZ3EKipqUFtbS28vLywevVqLF26FE899RSWLFmCFStWoKio\nCAkJCVwWq0Kh4MX3dEYkEmHZsmWYPXs2Zs6ciU2bNsHHxwfHjx9HZWUlZ9TdunULmZmZAKAzrEDT\nhqs7hJ4PQo9vKjKYMgEBATwvr1gsxvDhw3Veq9EXfV66pqYmnjdFLBbjlVdewaRJkyCVSrUyrtVq\nNS5evIj09HStZz18+JC3AVIqlVwP4v4g9HwQenxTkaGvPJGeN5ZlcfLkSfz2228wMzNDVFSUUWvh\nyGQyPPvss2hoaEBrayscHR11pnl7e3sjPz+fU0yxWAwvLy+jyUGhGIKXlxfCw8O1gqZFIhEIIVou\nfc2GhmEYroabhtLSUoPrYI0cORIeHh5c4WnNfcXFxbxFkWVZFBUVYcyYMToz/vrTyotC0TB+/HjU\n1tYiKSmJK0RdXFys5X3z8fFBYWGh3ueIRCItj5xSqeS8ZYGBgfi///s/nTGf58+f19Ipa2trredZ\nWloa4yNThjBPpOftxIkTyMrKglwuR2NjI44ePYrS0lKjPLtztWZbW1u4u7tzhltxcTGuX7+Ou3fv\nQqVSYcqUKfDz84NYLIZEIoG7uzsWLlxoVBmEQmgZhB5/qJGTk6P1HiEEbm5uvJgZlUrVrXfY1tZW\nK8YmMDBQ6z2GYTBnzhzs3r0b165dQ2JiIvbt24e8vDydxp/GaLOzs+O9L5FI9CYrJCeHOGRsAAAU\nb0lEQVQn4x//+Ac++ugjKJVKQWOtTGE+moIMpoxmTmq8u5ruIZr5KBaLERkZibVr12rNOZFIBGdn\nZwQGBmL58uVaJzad9eLWrVtwcXHRm/TTlRkzZsDc3BxSqRQSiQQymQy/+93v+v15hZ4PQo9vKjL0\nlSfS85adnc1TEpVKhZycHKOU6dBHamoqzp07B5VKBbFYjNTUVGzYsAGrVq1CS0sL1Go1rKysaC9F\niiA0NDRovRcUFISnn34au3fvRm1tLYCO451jx47Bzs5OZ2ZccHAw0tLSUFRUxHkWli5diuPHj3OL\nIMMwcHJywp07dyCXy3l9TS9cuKCzFpamTmJ0dDT27t3LeQQdHR11xqXev38fly5d4rzaKSkpkMlk\nmDFjRh//hShPAk1NTXo9x2q1Gubm5pBIJHj66afx7bffct6w4OBgrFixgru2vr4ely9f5jbma9as\ngVwuR2lpKQoLC3WOocny7oqVlRVeffVVZGVlQaVSYdSoUXqLv1OeHJ5Iz1vnuAagYzExVjseXWfo\nhBDExcWBZVmo1WqwLIvKykoubsHS0hLW1tZGM9xM4RxfaBmEHv9xwNbWFjKZTOtYkmVZ3Lt3T+c9\nDMNgzZo1WL16NZ5++mm8+uqrqK6uxurVq2FlZQWRSAR3d3esXbuWZ7hpkMvlcHZ25r0nkUi4IqMu\nLi547bXXsGzZMjz33HPYtGmTzni9jIwMXpxQdnY2FzcnBKYwH01BBlPH0tJSr4eWEILMzEyutEdn\nHjx4gMrKSu71tGnT8NZbb2Hz5s34/e9/D4lEgk8//RTff/89GhsbdcaBMgyDBQsW6Bzb3Nwc48eP\nR0REhNEMN6Hng9Djm4oMfeWJNN66lhXQBFcbQlVVFeLj4xEfH99jb8icnBycPn0aly9f1no+IURv\nRh+FMhgolUo0NzfrXaw0iQC6jKM7d+7oDdZmGAa+vr4ICgqCjY0NAGDEiBF44403MHnyZABAfHw8\nRo4cydtISaVSjBs3Ds888wysrKy4Qr8jRozglVCwsLDA6NGjuZADXZibm2tthmi/VEpPSKVSPP30\n01obfA1VVVU4fvw4rwWVhq5JCObm5nB0dIRYLMbhw4fR3t7e4zrT3Nys8/329nbU1tb2uq8q5fHl\niazzdvfuXZw6dYp3dCqVSvHee+91e19paSn279/PqwO3ceNGrQbGQEdcQ3x8PFiW5R0DaRReKpVi\n69atcHBwMOizUYYeplzTKiUlBfHx8WAYBpaWlpBKpXj06BH3d7FYjJiYGPj7++P8+fNITEzk3S+R\nSLB9+/ZeeQEOHz6M3NxcrjWcpaUlZs2ahWvXrkGlUiEsLAxz5swBwzCcd1omk8HZ2bnXXum6ujp8\n9dVXXJFViUSC9evXD2hoBKVnTFknOtPQ0IB9+/ahvr5e59+7JhDIZDI8/fTTXA/frvzlL3/psX6c\nSCTC7Nmz4enpiREjRnDvJyYm4tKlSxCJRJDJZHjhhRfg4uLS7bMoQwda560X6Kqnowlo7m6RSEhI\n4B3FsCyLhIQExMTEaF178eJF7lq1Wg2xWAwbGxs0NjbC3Nwcy5Yto4YbRRBKS0tx4cIFbhff0NAA\nOzs7SCQSbkNDCEF5eTlKSkp0HpESQvS23dGFQqFAdnY2t4ARQqBQKGBpaanVlBvo2Nz0J/Pa3t4e\n27Ztw71796BWqxEcHAwnJ6c+P4/y5KBUKpGSkgKpVKp3YdV0MNC0e3N1dUVgYKDeZ+qrB9eVK1eu\ngGEYREZGYu7cuSgtLUVCQgKXOMGyLA4dOsTr1kN5Mnkij039/Px4RppYLIa/v3+Pu/vOfU/1vac5\nQ9eVNTRx4kT813/9F9566y34+fn1QXLDMIVzfKFlEHp8U6asrExrQera2k2tVuPy5cu4fv067yhH\nLBZDKpVi7ty5Osvf6EKo78LGxgZPPfUUZsyYgfv37wsigwZTmI+mIIOpQwjBoUOHkJKS0m1YDCEE\nvr6+CAwMBMuyKC4uxl//+leuNZWGmpoa7Ny5U2s96BrzxjAM1Go1lEolWJZFUlISmpqadHbrqa+v\nN8rxqdDzQejxTUWGvvJEGm+Ojo5Ys2YNHB0dYW5ujtGjR/MyhfQRFhamFaMTFham89qgoCBerJBI\nJEJAQED/hadQ+om+o86umxdCiNai4+XlhXXr1mHKlCm9GlMmkyE4OJjTH5FIBHNzc4wcObJXz6FQ\nBpKWlhYUFhbyPNBSqVQrBk4ikcDW1hZZWVm899PS0pCUlASgYwO0f//+Hguva8p/dEYsFqOtrU1n\nGRxzc3Pa8oryZMa89RVCCFJSUpCUlASGYTB16lRERETovFapVOLs2bPIzs7GsGHDsGjRIvj6+nb7\n/La2NsTHx6OyshJubm5YsGABDbIewphqfA8hBB988EG3baUYhuG8AZ3fmzZtWreN47tDrVbj119/\nRUFBAezt7TFnzhxabPQJw1R1QkNLSws++eQTnmdLJpNhyZIlOH/+PBdD6eTkhICAAFy5ckXrGV5e\nXnj22WdBCMEXX3zBC7XRdXxqY2MDuVzOC+exsLDAjh07IJFIcOrUKaSnp3NFs1evXt3jWkIZOvRV\nJ6jxZiKo1Wrs2rWLyygSi8VwcnLC5s2bdda9opg+pjAf9cnQUwC1nZ0dpk6divj4eC7BQCaTYevW\nrVqFcikUQzFlnQA6NjYHDx7kvG8ikQiWlpaYPHkyrK2tYWlpCYlEAi8vL6SlpeHUqVM6nyUSieDi\n4qLVAlFzGqPZOEmlUsybNw+enp44cuQImpqaYGdnh5iYGF5SQmVlJZqbm+Hq6gorKytj/nNQBKav\nOkGtAiPT1zP0yspKNDQ0cIquUqlQW1vLywAcaBmMidAyCD2+qaMp4aEPsViMiIgIrFmzBuPHj0dk\nZGSfDTdT+C6ElkHo8U1FBlOHYRjExMRg8uTJ8Pb2hoeHB9ra2nDp0iWcOnUKN27cwPDhwyESiRAS\nEgJHR0edz1Gr1aioqICzszPXGUEqlSIoKAgbN26ESqWCr68vFi9ejIkTJ8LT0xNvvvkm3n//fbz+\n+uta2aSurq7w8/MzquEm9HwQenxTkaGvPJHZpqaIxiXeFdpxgTIQrFixAnv37tXrfdO8P2LECF7Z\nAgrlcUcikWDu3LlQqVT44IMPOF1QqVQoKChAYWEhfH19IZFIsHXrVty5cwfFxcXIysriHZECHSVr\n1q1bh4qKCtjZ2XGJcXPmzMGIESNw5MgR/PLLL7C3t8fq1au1ClRTKPqgx6Ymglqtxp49e7gm3Zpe\npy+++CI14IYopjAfu5Ph0aNHyMzMREtLC27fvs07ypk9e3avkxIolJ4wdZ3oTGtrKz7++GOt+Ddd\n9dz0xZGam5vjD3/4g9azm5ub8dlnn/GqFVhaWuLNN9/kkhGqq6uRmpoKtVqN8PBwne3oKEMfWudt\niCMSifDCCy/gypUrqKiogLu7O2bOnEkNN8qA4eTkxPX6HD16NC5fvgyWZREeHq43EYdCeVIwNzeH\nra0t6urquMWVEKKz0PPDhw91LsDjx48HAKSnp+PixYtcMWpvb2+t33aFQoHGxkbY29ujoqICe/bs\n4Tx5aWlpWLt2Lby9vY39MSlDFBrzZmT6c4Yuk8kwf/58rFu3DvPmzdPbomUgZTAWQssg9PhDjREj\nRmDjxo3YsmULJk2aZNRNgyl8F0LLIPT4piLDUIJhGKxbtw6urq5cR5DVq1frLLVTV1en8xlz5sxB\nbm4uTp48iYaGBjQ3N+PGjRv48ccftUIWNI3vAeDatWs6C8IbE6Hng9Djm4oMfcUkjLe4uDiMHj0a\nAQEB+Oijj3Re8/rrryMgIAChoaG4c+fOIEtoOGlpaUKLQGUwgfH7C9WJx0sGocc3FRn6gxA6YWdn\nhy1btuD999/H22+/rTf+093dnVcVgGEYuLi4QCQS4f79+1qG2K1btzB27FheMsPs2bO50lCGFITv\nL0LPB6HHNxUZ+orgx6YqlQrbt2/HhQsX4OnpiYiICERHRyMoKIi75syZM8jJyUF2djZu3LiBbdu2\nITk5WUCp9aOvFx6V4ckavz9QnXj8ZBB6fFORoa8IrRM9eaJ9fX0xY8YMXL58GWKxGBYWFli1ahUA\nYNiwYVpxTSzLYunSpRgzZgzq6urg5ubGawcXHh6OwsJCXh9tzRGssRB6Pgg9vqnI0FcEN95SUlLg\n7+/PFR2MiYnB8ePHeUp54sQJrF+/HgAQGRmJ+vp6VFZWwtXVVQiRKZQBheoEhcJnKOjEU089hYiI\nCLS3t8Pa2przxE2ePBlpaWmQy+Vcx4aRI0eCYRi9bRKDg4OhUChw7do1EEIwefJkhIeHD8rnoAwN\nBDfeSktLMXz4cO61l5cXbty40eM1JSUlJrlQde1ZR2V4MsfvD1QnHj8ZhB7fVGToK0NFJ8zMzGBm\nZsZ7z9bWFtu2bUNqaiqUSiXGjBmD9957r8dnhYWF6W2/aAyEng9Cj28qMvQVwY03QwOju2by6LvP\nFLIz9+/fL7QIVAYTGL+vUJ14PGUQenxTkaEvUJ14PGUQenxTkaEvCG68eXp6ori4mHtdXFzMO/vX\ndU1JSYnOdG2h6wdRKMaA6gSFwofqBIXCR/Bs04kTJyI7OxsFBQVQKBT44YcfEB0dzbsmOjoa3377\nLQAgOTkZdnZ2Jnk8RKEYA6oTFAofqhMUCh/BPW8SiQQ7d+7EwoULoVKpsGnTJgQFBWH37t0AgC1b\ntmDRokU4c+YM/P39YWlpib179wosNYUycFCdoFD4UJ2gULpAhiBnz54lgYGBxN/fn3z44Yc6r3nt\ntdeIv78/CQkJIbdv3x50GQ4cOEBCQkLIuHHjyNSpU8ndu3cHdXwNKSkpRCwWk6NHjxp1fENluHz5\nMgkLCyNjxowhM2fOHHQZqqurycKFC0loaCgZM2YM2bt3r1HHf/HFF4mLiwsZO3as3msGei4SQnXC\nkPE1UJ2gOjFYclCdoDpByMDoxJAz3pRKJfHz8yP5+flEoVCQ0NBQkpmZybvm9OnTJCoqihBCSHJy\nMomMjBx0GRITE0l9fT0hpGPiGFMGQ8bXXDd79myyePFi8tNPPxltfENlqKurI8HBwaS4uJgQ0qEg\ngy3Df//3f5M//vGP3PgODg6EZVmjyXD16lVy+/ZtvUo50HOREKoTho6vuY7qBNWJwZCD6gTVCQ0D\noROCx7z1ls71fqRSKVfvpzP66v0MpgxTpkzh2qhERkaipKRkUMcHgM8++wzPPvssnJ2djTZ2b2T4\n/vvvsWLFCi6w2MnJadBlcHd3R2NjIwCgsbERjo6OkEiMFy0wffp02Nvb6/37QM9FgOqEoeMDVCcA\nqhODJQfVCaoTGgZCJ4ac8aarlk9paWmP1xhTKQyRoTOxsbFYtGjRoI5fWlqK48ePY9u2bQCMnxpv\niAzZ2dmora3F7NmzMXHiRHz33XeDLsPLL7+MjIwMeHh4IDQ0FP/85z+NKkNfZDTmXNQ3BtUJqhP6\nZKA6MThyUJ2gOtEfGXuai4InLPQWY9f7GUgZAODy5cvYs2cPrl+/Pqjj79ixAx9++CHXlqXrv8dg\nyMCyLG7fvo2LFy+itbUVU6ZMweTJkxEQEDBoMnzwwQcICwtDQkICcnNzMX/+fNy9exfW1tZGkcEQ\nBnIu9uZ5VCeoTgBUJwZLDqoTVCd6Q2/n4pAz3oxZ72cgZQCAe/fu4eWXX0ZcXFy3LtOBGD81NRUx\nMTEAgEePHuHs2bOQSqVa6fUDKcPw4cPh5OQEc3NzmJubY8aMGbh7967RlNIQGRITE/Gf//mfAAA/\nPz+MGDECDx8+xMSJE40iQ29lNPZc1DUG1QmqE93JQHVicOSgOkF1oq8yGjQX+x2JN8iwLEtGjhxJ\n8vPziVwu7zEQNSkpyeiBqIbIUFhYSPz8/EhSUpJRxzZ0/M5s2LDB6FlEhsiQlZVF5s6dS5RKJWlp\naSFjx44lGRkZgyrDm2++Sf70pz8RQgipqKggnp6epKamxmgyEEJIfn6+QYGoAzEXCaE6Yej4naE6\nQXWC6gQfqhNDSyeGnPFGCCFnzpwho0aNIn5+fuSDDz4ghBCya9cusmvXLu6aV199lfj5+ZGQkBCS\nmpo66DJs2rSJODg4kLCwMBIWFkYiIiIGdfzODIRSGirDP/7xDxIcHEzGjh1L/vnPfw66DNXV1WTJ\nkiUkJCSEjB07lhw8eNCo48fExBB3d3cilUqJl5cXiY2NHfS5SAjVCUPG7wzVCaoTgyEH1QmqE4QM\njE4whNBeIRQKhUKhUChDhSGXbUqhUCgUCoXyJEONNwqFQqFQKJQhBDXeKBQKhUKhUIYQ1HijUCgU\nCoVCGUJQ441CoVAoFAplCDHkivRSBpZbt26hra0Njx49wrBhwxAVFSW0SBSKoFCdoFD4UJ0QHmq8\nUXjs378fH3/8Merr66FWq4UWh0IRHKoTFAofqhPCI/7Tn/70J6GFoJgOYrEYv//979Hc3Ix58+YJ\nLQ6FIjhUJygUPlQnhIfGvFE47t+/j4ULF+LUqVOoqakRWhwKRXCoTlAofKhOmAb02JTCcePGDRQV\nFYFhGKxYsUJocSgUwaE6QaHwoTphGtD2WBQKhUKhUChDCHpsSqFQKBQKhTKEoMemFIhE3dvwDMNA\npVINkjQUivBQnaBQ+FCdMC3osSmFQqFQKBTKEIJ63igAaNFFCqUrVCcoFD5UJ0wHarxRANCiixRK\nV6hOUCh8qE6YDrRILwUALbpIoXSF6gSFwofqhOlAs00ptOgihdIFqhMUCh+qE6YFTVigIDY2Fu7u\n7mAYBm5ubigvLwcATJgwAa6urgJLR6EMPlQnKBQ+VCdMC2q8UbTYs2cPZs2ahby8POoap1BAdYJC\n6QrVCWGhx6b/rx07qAEAhIEgiI2KqH8vVcObIAAumVHQT5PNcamqNTOru1+fAl/wE3DyE29Z3gAA\ngljeAACCiDcAgCDiDQAgiHgDAAgi3gAAgog3AIAg4g0AIIh4AwAIIt4AAIJsVvH9hOVdKAQAAAAA\nSUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x109056fd0>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next, we scatter plot the accuracy of model predictions from one data-set, relative to the data from the other data-set in each b value:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, axes = plt.subplots(1,3,squeeze=True)\n",
      "for ax, models in zip(axes,([TM_1k_1,TM_1k_2],[TM_2k_1, TM_2k_2],[TM_4k_1, TM_4k_2])):\n",
      "    ax.scatter(models[0].relative_signal[vox_idx], models[1].fit[vox_idx]/models[1].S0[vox_idx], \n",
      "               color=[0.5, 0.5, 0.5])\n",
      "    ax.grid()\n",
      "    ax.set_xlim([0,1])\n",
      "    ax.set_ylim([0,1])\n",
      "    ax.set_aspect('equal')\n",
      "    ax.set_xlabel(r'Measured $\\frac{S}{S_0}$')\n",
      "axes[0].set_ylabel(r'Predicted $\\frac{S}{S_0}$')    \n",
      "fig.set_size_inches([10,10])\n",
      "\n",
      "fig.savefig('figures/Figure2_scatter_cross.svg')\n",
      "print rrmse_1k[vox_idx],rrmse_2k[vox_idx], rrmse_4k[vox_idx]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.768360252996 0.76873348285 0.863855189387\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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g9+7diImJwebNm8UyGzZsQHx8PM6ePYva2lqMGzcOx48fR1BQkPTLEEdUAE0n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yAAAC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\nAEGcNwKBQCAQCIQBxP8HW4+9EXp6km4AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10907bbd0>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}