Smoking Cessation Meta-analysis.ipynb

{
 "metadata": {
  "name": "Smoking Cessation Meta-analysis"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The following lines import modules for the analysis and set some display options."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pandas as pd\n",
      "import numpy as np\n",
      "\n",
      "pd.set_option('max_columns', 30)\n",
      "pd.set_option('max_rows', 100)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Import data from Excel spreadsheet:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "outcomes = pd.ExcelFile(\"/Users/fonnescj/Google Drive/Smoking Cessation Data/Smoking Cessation_Study Outcomes Data_41113.xlsx\")\n",
      "interventions = pd.ExcelFile(\"/Users/fonnescj/Google Drive/Smoking Cessation Data/Smoking Cessation Intervention Components Data 42413.xlsx\")\n",
      "\n",
      "_outcomes = outcomes.parse(\"AO Data\", na_values=['NA','NR','','?','UK'])\n",
      "_interventions = interventions.parse(\"Sheet1\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "_outcomes[\"Arm\"] = _outcomes[\"Arm\"].map(unicode.strip)\n",
      "_interventions[\"Arm\"] = _interventions[\"Arm\"].map(unicode.strip)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Check to see if all studies in inteventions dataset are in outcomes dataset:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.all([r in _outcomes['Ref ID'].tolist() for r in _interventions['Ref ID']])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Drop unused columns from outcomes dataset:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "_outcomes = _outcomes.drop(['KQ','Age Min', 'Age Max', 'Ins status', 'Pop specific', 'Unit of Random', \\\n",
      "    'Nicot depend', 'Prior quit', 'Sub/Alcoh abuse', 'Partner smok', 'Employ status', 'Insur Status2', \\\n",
      "    'Mental health', 'Other', 'Intervention Characteristics', 'Intervention Delivery', 'Validation', \\\n",
      "    'N abst', 'vs.', 'OR', '99% CI Low', '99% CI High', 'No. Timepoints', 'No. Arms', 'No. SubG'], 1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Merge intervention components with outcomes, using the reference ID number and arm:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "temp_data = _outcomes.merge(_interventions, on=['Ref ID', 'Arm'], how='outer')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is a sample record from the merged table:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "temp_data.ix[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "Ref ID                                  11\n",
        "Category                               NRT\n",
        "Author                  Coleman, T, et al.\n",
        "Year                                  2012\n",
        "Study N                               1050\n",
        "Country                                 EU\n",
        "Trial type                             RCT\n",
        "Setting                               HOSP\n",
        "Preg status                           PREG\n",
        "Smoking status                        SMKR\n",
        "Outcome                          Cessation\n",
        "Timepoint                         PRENATAL\n",
        "Arm                           Intervention\n",
        "Arm N                                  521\n",
        "Analyzed N                             521\n",
        "Rate %                                 9.4\n",
        "Clinic Reinforcement                     0\n",
        "Counseling                               1\n",
        "Feedback                                 0\n",
        "Groups                                   0\n",
        "Incentives                               0\n",
        "Information                              0\n",
        "NRT                                      1\n",
        "Partner/Household                        0\n",
        "Peer Support                             0\n",
        "Personal Followup                        1\n",
        "Prescription to Quit                     0\n",
        "Quit Contract                            1\n",
        "Quit Guide                               0\n",
        "Usual Care                               0\n",
        "Other                                    0\n",
        "Name: 0, dtype: object"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Test merge to see if it has the correct number of rows:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "len(temp_data)==len(_outcomes)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Function for generating indicator variables from categorical series:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def generate_indicators(series, values=None):\n",
      "    if values is None:\n",
      "        values = series.unique()\n",
      "    print('Unique values: {0}').format(values)\n",
      "    value_dict = dict(zip(values, range(len(values))))\n",
      "    return series.replace(value_dict)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Recode variables of interest:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "temp_data['categories'] = generate_indicators(temp_data.Category)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Unique values: [u'NRT' u'MAT' u'OTH' u'PS' u'COUN' u'MULTI']\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "temp_data['smoking_status'] = generate_indicators(temp_data['Smoking status'], ['QUTR','SMKR + QUTR','SMKR'])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Unique values: ['QUTR', 'SMKR + QUTR', 'SMKR']\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "temp_data['pregnancy_status'] = generate_indicators(temp_data['Preg status'])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Unique values: [u'PREG' u'PPT']\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "temp_data['country'] = generate_indicators(temp_data.Country)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Unique values: [u'EU' u'USA' u'CAN' u'AUS']\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "temp_data['cluster_rct'] = generate_indicators(temp_data['Trial type'])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Unique values: [u'RCT' u'CLUS RCT']\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "temp_data['setting'] = generate_indicators(temp_data.Setting)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Unique values: [u'HOSP' u'CLINIC' u'ACAD' u'MULTI']\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "temp_data['treat'] = (temp_data.Arm!='Control').astype(int)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "temp_data['stage'] = generate_indicators(temp_data.Timepoint)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Unique values: [u'PRENATAL' u'POST 0-3 MOS' u'POST 3-6 MOS' u'POST 6-12 MOS']\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Function to count values of a variable by study:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "counts_of = lambda field: pd.value_counts([temp_data[field].ix[k[0]] for k in temp_data.groupby('Ref ID').groups.values()])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Summary of studies by variable:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for f in ['Country', 'Category', 'Timepoint', 'Outcome', 'Setting', 'Trial type', 'Preg status', 'Smoking status']:\n",
      "    print f\n",
      "    print '='*len(f)\n",
      "    print counts_of(f)\n",
      "    print"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Country\n",
        "=======\n",
        "USA    23\n",
        "EU      4\n",
        "CAN     1\n",
        "AUS     1\n",
        "dtype: int64\n",
        "\n",
        "Category\n",
        "========\n",
        "MULTI    8\n",
        "MAT      6\n",
        "COUN     5\n",
        "OTH      4\n",
        "NRT      3\n",
        "PS       3\n",
        "dtype: int64\n",
        "\n",
        "Timepoint\n",
        "=========\n",
        "PRENATAL         25\n",
        "POST 0-3 MOS      3\n",
        "POST 6-12 MOS     1\n",
        "dtype: int64\n",
        "\n",
        "Outcome\n",
        "=======\n",
        "Cessation     23\n",
        "NO RELAPSE     4\n",
        "BOTH           2\n",
        "dtype: int64\n",
        "\n",
        "Setting\n",
        "=======\n",
        "CLINIC    17\n",
        "HOSP       7\n",
        "ACAD       3\n",
        "MULTI      2\n",
        "dtype: int64\n",
        "\n",
        "Trial type\n",
        "==========\n",
        "RCT         28\n",
        "CLUS RCT     1\n",
        "dtype: int64\n",
        "\n",
        "Preg status\n",
        "===========\n",
        "PREG    27\n",
        "PPT      2\n",
        "dtype: int64\n",
        "\n",
        "Smoking status\n",
        "==============\n",
        "SMKR    23\n",
        "QUTR     4\n",
        "BOTH     2\n",
        "dtype: int64\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This list gives an idea of how often an intervention component appears in the intervention arm (only) of a study across the set of studies:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for f in _interventions.columns[2:]:\n",
      "    occurences = []\n",
      "    for id in set(temp_data['Ref ID']):\n",
      "        for val in temp_data[f].unique():\n",
      "            intervention_list = (temp_data[(temp_data['Ref ID']==id) & (temp_data['Arm']=='Intervention')][f]).tolist()\n",
      "            control_list = (temp_data[(temp_data['Ref ID']==id) & (temp_data['Arm']=='Control')][f]).tolist()\n",
      "            if (val in intervention_list) and (val not in control_list):\n",
      "                occurences.append(val)\n",
      "    print f\n",
      "    print '='*len(f)\n",
      "    print pd.Series(occurences).value_counts()\n",
      "    print"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Clinic Reinforcement\n",
        "====================\n",
        "1    6\n",
        "dtype: int64\n",
        "\n",
        "Counseling"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "==========\n",
        "1    5\n",
        "dtype: int64\n",
        "\n",
        "Feedback"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "========\n",
        "1    3\n",
        "dtype: int64\n",
        "\n",
        "Groups"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "======\n",
        "Series([], dtype: int64)\n",
        "\n",
        "Incentives"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "==========\n",
        "1    3\n",
        "dtype: int64\n",
        "\n",
        "Information"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "===========\n",
        "1    2\n",
        "0    1\n",
        "dtype: int64\n",
        "\n",
        "NRT"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "===\n",
        "1    3\n",
        "dtype: int64\n",
        "\n",
        "Partner/Household"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "=================\n",
        "Series([], dtype: int64)\n",
        "\n",
        "Peer Support"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "============\n",
        "1    6\n",
        "dtype: int64\n",
        "\n",
        "Personal Followup"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "=================\n",
        "1    8\n",
        "dtype: int64\n",
        "\n",
        "Prescription to Quit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "====================\n",
        "1    2\n",
        "dtype: int64\n",
        "\n",
        "Quit Contract"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "=============\n",
        "1    1\n",
        "dtype: int64\n",
        "\n",
        "Quit Guide"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "==========\n",
        "1    9\n",
        "0    1\n",
        "dtype: int64\n",
        "\n",
        "Usual Care"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "==========\n",
        "0    5\n",
        "dtype: int64\n",
        "\n",
        "Other"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "=====\n",
        "1    1\n",
        "dtype: int64\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Drop string variables:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dataset = temp_data.drop(['Smoking status', 'Preg status', 'Country', 'Trial type', 'Setting'], 1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Include only cessation studies:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dataset = dataset[dataset.Outcome=='Cessation']"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The number of unique studies in the meta-analysis:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "len(dataset['Ref ID'].unique())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "24"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Save merged dataset to file for reference:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dataset.to_csv(\"merged_data.csv\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Distribution of control quit rates:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pymc import logit\n",
      "hist(logit((dataset[dataset.treat==0]['Rate %']+1)/100.), bins=10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "(array([ 2,  2,  6, 17,  5,  2,  0,  0,  0,  2]),\n",
        " array([-4.59511985, -3.94551199, -3.29590413, -2.64629627, -1.99668841,\n",
        "       -1.34708054, -0.69747268, -0.04786482,  0.60174304,  1.2513509 ,\n",
        "        1.90095876]),\n",
        " <a list of 10 Patch objects>)"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x113053f50>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Distribution of treatment quit rates"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hist(logit((dataset[dataset.treat>0]['Rate %']+1)/100.), bins=10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "(array([ 1, 11, 12, 10,  3,  2,  1,  1,  1,  1]),\n",
        " array([-3.17805383, -2.61449442, -2.05093501, -1.4873756 , -0.92381619,\n",
        "       -0.36025678,  0.20330263,  0.76686205,  1.33042146,  1.89398087,\n",
        "        2.45754028]),\n",
        " <a list of 10 Patch objects>)"
       ]
      },
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXAAAAD/CAYAAADoiI2GAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x114cadc50>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Notice the long tails on these distributions. We will use **robust random effects** to model both the baseline and treatments."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Meta-analytic Model"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Extract data columns of interest:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "unique_studies = dataset['Ref ID'].unique()\n",
      "study_id = [np.where(unique_studies==i)[0][0] for i in dataset['Ref ID']]\n",
      "\n",
      "treat = np.array(dataset.treat)\n",
      "\n",
      "n = np.array(dataset['Analyzed N'])\n",
      "y = np.array((n*dataset['Rate %']/100.).round(0))\n",
      "\n",
      "stage = np.array(dataset.stage, int)\n",
      "postpartum = np.array((dataset.stage>0).astype(int))\n",
      "\n",
      "dataset = dataset.rename(columns={\"Other\": \"_Other\"})\n",
      "dataset[\"Other\"] = dataset[['_Other','Quit Contract', 'Partner/Household', 'Groups', 'Counseling']].sum(1)\n",
      "\n",
      "#intervention_subset = ['Clinic Reinforcement', 'Counseling', 'Peer Support', 'Personal Followup', 'Quit Guide']\n",
      "intervention_subset = ['Clinic Reinforcement', 'Feedback', 'Incentives', 'Information',\n",
      "    'Peer Support', 'Personal Followup', 'Quit Guide', 'NRT', 'Prescription to Quit', 'Other']\n",
      "factors = dataset[intervention_subset]>0\n",
      "X = np.array(factors).T\n",
      "X.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "(10, 79)"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Check correlation among factors:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.corrcoef(X)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "array([[ 1.        ,  0.14320578, -0.063602  ,  0.17874236,  0.18055019,\n",
        "         0.46547538,  0.2219697 ,  0.22406371,  0.24397502,  0.20597146],\n",
        "       [ 0.14320578,  1.        ,  0.14376528, -0.18946122,  0.0917465 ,\n",
        "         0.00745632,  0.05196984, -0.07752025,  0.21301296, -0.04298712],\n",
        "       [-0.063602  ,  0.14376528,  1.        ,  0.25670713,  0.29225708,\n",
        "        -0.01533983,  0.10965862, -0.08280787, -0.05778856, -0.02839451],\n",
        "       [ 0.17874236, -0.18946122,  0.25670713,  1.        , -0.09751535,\n",
        "         0.17205114, -0.04189274, -0.01464583, -0.01022078,  0.3322053 ],\n",
        "       [ 0.18055019,  0.0917465 ,  0.29225708, -0.09751535,  1.        ,\n",
        "         0.00940074,  0.33392078, -0.09773556, -0.06820604,  0.13195808],\n",
        "       [ 0.46547538,  0.00745632, -0.01533983,  0.17205114,  0.00940074,\n",
        "         1.        ,  0.07907375,  0.27530419,  0.286397  ,  0.07124035],\n",
        "       [ 0.2219697 ,  0.05196984,  0.10965862, -0.04189274,  0.33392078,\n",
        "         0.07907375,  1.        , -0.02701477,  0.24397502, -0.08459542],\n",
        "       [ 0.22406371, -0.07752025, -0.08280787, -0.01464583, -0.09773556,\n",
        "         0.27530419, -0.02701477,  1.        , -0.03721937,  0.07200823],\n",
        "       [ 0.24397502,  0.21301296, -0.05778856, -0.01022078, -0.06820604,\n",
        "         0.286397  ,  0.24397502, -0.03721937,  1.        ,  0.05025189],\n",
        "       [ 0.20597146, -0.04298712, -0.02839451,  0.3322053 ,  0.13195808,\n",
        "         0.07124035, -0.08459542,  0.07200823,  0.05025189,  1.        ]])"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Model Specification \n",
      "\n",
      "Our meta-analysis uses a logistic mixed effects model to characterize quit rates across studies and estimate factors associated with intervention efficacy. Thus, we treat $y_i$, the number of quitters in some study arm $i$, as a binomial random variable:\n",
      "\n",
      "$$y_i \\sim Bin(n_i, p_i)$$\n",
      "\n",
      "where $n_i$ is the number of individuals in the arm and $p_i$ the latent quit probability. This probability, in turn, is modeled as a function of several components:\n",
      "\n",
      "$$\\text{logit}(p_i) = \\mu_{j[i]} + \\theta_{j[i]} \\times I(\\text{treat}_i) + \\alpha \\times \\text{stage}_i + X_i \\beta$$\n",
      "\n",
      "Here, $\\mu_{j[i]}$ is a baseline random effect belonging to the study $j$ corresponding to arm $i$. $X_i$ is a matrix of indicators corresponding to each of the intervention factors included in the analysis:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "factors.columns"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "Index([Clinic Reinforcement, Feedback, Incentives, Information, Peer Support, Personal Followup, Quit Guide, NRT, Prescription to Quit, Other], dtype=object)"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "while $\\beta$ is a vector of associated parameters. $\\alpha$ describes the effect of the pregnancy stage at which the intervention is applied, which can be any of the following:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "_ = generate_indicators(temp_data.Timepoint)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Unique values: [u'PRENATAL' u'POST 0-3 MOS' u'POST 3-6 MOS' u'POST 6-12 MOS']\n"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finally, $\\theta_{j[i]}$ is another random effect, corresponding to generic smoking cessiation treatment effect of study $j$. By \"generic\", we mean the effect with all the factors included in $X$ set to zero. Hence, it includes all unmodeled factors.\n",
      "\n",
      "We used robust random effects for both the baseline mean and treatment effects. This entailed using a Student's T distribution rather than a Gaussian to describe the distribution of effects:\n",
      "\n",
      "$$f(x|\\mu,\\lambda,\\nu) = \\frac{\\Gamma(\\frac{\\nu + 1}{2})}{\\Gamma(\\frac{\\nu}{2})}\n",
      "        \\left(\\frac{\\lambda}{\\pi\\nu}\\right)^{\\frac{1}{2}}\n",
      "        \\left[1+\\frac{\\lambda(x-\\mu)^2}{\\nu}\\right]^{-\\frac{\\nu+1}{2}}$$\n",
      "        \n",
      "The T distribution has heavier tails relative to the Gaussian, which accomodated more extreme random effects, if present."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pymc import Normal, Uniform, Lambda, Categorical, Beta, normal_like\n",
      "from pymc import invlogit, observed, deterministic, Binomial, NoncentralT\n",
      "\n",
      "def meta_analysis():\n",
      "\n",
      "    # Hyperpriors\n",
      "    mu_0 = Normal('mu_0', mu=0, tau=0.01, value=0)\n",
      "    lam_0 = Uniform('lam_0', lower=0, upper=100, value=1)\n",
      "    nu_0 = Uniform('nu_0', lower=0, upper=100, value=10)\n",
      "    \n",
      "    # Study random effects\n",
      "    mu = NoncentralT('mu', mu_0, lam_0, nu_0, size=len(unique_studies))\n",
      "    mu_pred = NoncentralT('mu_pred', mu_0, lam_0, nu_0)\n",
      "    p_pred = Lambda('p_pred', lambda mu=mu_pred: invlogit(mu))\n",
      "    \n",
      "    \"\"\"Intervention factors\"\"\"\n",
      "    # Clinical reinforcement\n",
      "    betas = Normal('betas', 0, 0.001, value=np.zeros(len(X)))\n",
      "    \n",
      "    # Odds ratios\n",
      "    odds_ratios = Lambda('odds_ratios', lambda b=betas: np.exp(b))\n",
      "    \n",
      "    # Postpartum effects\n",
      "    alpha = Normal('alpha', 0, 0.001, value=0)\n",
      "\n",
      "    @deterministic\n",
      "    def p_quit(mu=mu, alpha=alpha, b=betas):\n",
      "        # Model of quit probability\n",
      "        return invlogit(mu[study_id] + alpha*stage + dot(X.T, b))\n",
      "\n",
      "    # Data likelihood (model of number of quitters)\n",
      "    quitters = Binomial('quitters', n=n, p=p_quit, value=y, observed=True) \n",
      "    # Samples from the posterior predictive distribution for GOF evaluation\n",
      "    quitters_pred = Binomial('quitters_pred', n=n.astype(int), p=p_quit, value=y.astype(int))\n",
      "    \n",
      "    return locals()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Instantiate model:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pymc import MCMC, Matplot, AdaptiveMetropolis\n",
      "\n",
      "M = MCMC(meta_analysis())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Run the model in two separate MCMC chains:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "M.sample(500000, 400000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 500000 of 500000 complete in 603.2 sec"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "M.sample(500000, 400000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 500000 of 500000 complete in 589.3 sec"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Results\n",
      "\n",
      "Posterior distribution of the mean of the population baseline quit rate (on the inverse logit scale). Not directly of interest."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Matplot.plot(M.mu_0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Plotting mu_0\n"
       ]
      },
      {
       "output_type": "display_data",
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fJbmIf3z7O1xW1Bot4WCoqr5JG9yfaGsbLyudvNx2riIA1JioCadrwd4L2n//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\nmLOfjY2N2sZFRMSPKCGTVlVVVZkJy+7du6mtraW8vNycLXr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       "text": [
        "<matplotlib.figure.Figure at 0x114cf0e90>"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Posterior distribution of the postpartum effect**, on the logit scale. Covariate values are 0=prenatal, 1=0-3 months postpartum, 2=3-6 months postpartum, 3=6-12 months postpartum. This effect is negative, indicating that the effects of intervention are attenuated with delivery during the postpartum period relative to prenatal, with a linearly-stronger negative effect with the number of months postpartum."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Matplot.plot(M.alpha)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Plotting alpha\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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fzoZta3F7IoPDz3yRa/LwNYPA7cMTprlqGhv1NAzQ1FoBM941Ha5z5k/QnqLm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\npImIiIh4ISVpIiIiIl7o/wHpbrFDvr+ybwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x114cdaf90>"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Treatment factor odds ratios** for the probability of cessation, shown as medians (points) with 95% posterior credible intervals (thin lines) and interquartile ranges (thick lines). The first (`or_treat`) is the generic treatment effect (i.e. other factor covrariates set to zero). \"R-hat\" values are convergence diagnostics which suggest lack of convergence when values greatly exceed one."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Matplot.summary_plot([M.odds_ratios], vline_pos=1, custom_labels=intervention_subset, main=\"Odds Ratios\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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3Z9CgQdy+fZvvv/8enU7Hv//9b4YPH86hQ4dwcXGhb9++nDp1iiVLlpCZmYmf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\nl6lOd8/yy3uW4ObmZvlZr9eTm5tb6jL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       "text": [
        "<matplotlib.figure.Figure at 0x114ca87d0>"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "M.summary(variables=['odds_ratios'])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "odds_ratios:\n",
        " \n",
        "\tMean             SD               MC Error        95% HPD interval\n",
        "\t------------------------------------------------------------------\n",
        "\t1.071            0.194            0.014            [ 0.694  1.449]\n",
        "\t1.65             0.304            0.021            [ 1.095  2.242]\n",
        "\t2.978            0.64             0.044            [ 1.832  4.245]\n",
        "\t1.172            0.167            0.01             [ 0.873  1.539]\n",
        "\t1.115            0.194            0.012            [ 0.767  1.496]\n",
        "\t1.107            0.126            0.006            [ 0.871  1.367]\n",
        "\t1.356            0.207            0.014            [ 0.989  1.792]\n",
        "\t1.328            0.225            0.012            [ 0.902  1.766]\n",
        "\t1.297            0.486            0.036            [ 0.541  2.306]\n",
        "\t0.376            0.063            0.005            [ 0.264  0.503]\n",
        "\t\n",
        "\t\n",
        "\tPosterior quantiles:\n",
        "\t\n",
        "\t2.5             25              50              75             97.5\n",
        "\t |---------------|===============|===============|---------------|\n",
        "\t0.726            0.935           1.058          1.194         1.487\n",
        "\t1.147            1.433           1.622          1.834         2.334\n",
        "\t1.929            2.517           2.914          3.371         4.425\n",
        "\t0.875            1.057           1.159          1.273         1.542\n",
        "\t0.798            0.977           1.096          1.228         1.553\n",
        "\t0.873            1.02            1.103          1.189         1.371\n",
        "\t1.002            1.208           1.336          1.483         1.812\n",
        "\t0.931            1.167           1.313          1.476         1.803\n",
        "\t0.65             0.958           1.2            1.519         2.628\n",
        "\t0.269            0.329           0.371          0.418         0.511\n",
        "\t\n"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Model Diagnostics\n",
      "\n",
      "The plots below are goodness of fit diagnostics for the model that plots data (outcomes from constituent studies, red lines) against histograms of data simulated from the model."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Matplot.gof_plot(M.quitters_pred.trace(), y.tolist(), bins=20, verbose=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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SEydO0NHRMd3hi4jIFZr2hGKz2fj0pz8NgNVqxeVyEQgEaGtrY+nSpQAUFRXh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\nIiISE/8PezkfUD1sqbAAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x12a882210>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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0iNwxdJ8PsulnR2/oPb63+P44VSOJzGwy8cGpszGfn56axL3WO+JYkdwqxj1E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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x114f03e50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x114f689d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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yy1/+EhhYZPvoo49y8uRJfvvb3970u0HL+KMgEbHgjjvu4O9//zvnzp3j7rvv\nxmazkZmZycKFC4GBVdvV1dVcvnyZYDBIbW0t9913H4Zh8Kc//Yk1a9aE9zbq6+vD4/GQlZUFwDPP\nPAMQ3tp+zpw5VFVVxeAqRUamqS0RC+bPn8+HH37IX//6V772ta9x6NAh7rnnnvDvOxyO8Of+8pe/\nEAwGw5vfffXVV1dtMGq326/62q2trRQXF5OSkhKFKxExT0EiYsGkSZOAge3QbTZbeFX8oFAoBEBG\nRgaVlZVkZ2eHt+e+/fbbr9oXbvCzg9LS0igqKiIQCHDp0qUbfSkipmlqS8Si73//+8DAnkqGYdDe\n3s7rr79Of38/3/zmN8Of27FjBxMmTKC2thaAhx56iIqKCoLBIKFQiO9+97vhz/r9fo4cOQLAtGnT\nSExMjOIViYyOtkgRuYn87Gc/Y9OmTaZ/XyQWNLUlchNJSkoa9o2eJ0+evCk3/hPRiERERCzRiERE\nRCxRkIiIiCUKEhERsURBIiIilihIRETEkv8PsRbf1oOMinIAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x129b77a10>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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5dOgQ06dPZ9OmTZw5c4a//e1v8S4rZrq7u/nVr37Fyy+/jN/v5+DBgzQ2Nsa7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\nRERMU4iIiIhp/x9kUbADySrJ9gAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x129bc5310>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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dyJYpoG1Tlho11kVExDCFiKQMPSciYr5lt5w1MDDAt7/9bWZnZ9m8eTP33Xff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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x12a7e7f90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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iYnYKERNTT0REzE4hIiIihilERETEsDnf9kSM095ZYnbaxFEUIjM4NTrB0Lno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\nIiIiYphCREREDFOIiIiIYQoREREx7P8DUA8CKo+ON8UAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x12a839ad0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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tGvPnz6elpSXaZUVFe3s7aWlpJCcnc/XVVzNv3jw+++yzaJcVVS6Xi2PHjgEQ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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x12a9c9490>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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6a+PGjSxbtixR9YiIyAJywxBxOBysWrUKm00P+xURkWvdMB3Onj3Lq6++GluJPPfccwkp\nSmQh0H0iIjcJkeeff56enh5WrVpFMBhMVE0iC4LCQ+QmIfLP//zPjI2N8fTTT3Ps2DGeeuopU2/y\n7rvv0tLSwsTEBNnZ2Tz55JOMjo5SW1tLX18fK1asYOfOnbEVT2NjI01NTVitVkpLS8nKygKgp6eH\nuro6IpEIPp9PV4yJiMyzG4bIHXfcQXJyMgBLly419QYXL17k2LFj1NTUkJSUxPe+9z06Ozv56KOP\nyMzMpKKigrfeeoujR4+ydetWenp6aG5upqqqilAoxN69e/nhD3+IxWLB7/fzrW99C6/Xy/79++ns\n7CQnJ8dUXSILndVi4f0LI6bmpqUmsdJ+R5wrksXohiHicrl47733+MlPfsLKlStNvUFSUhIAly9f\nBmB8fJzU1FTa29t5+eWXASgsLOTll19m69atBAIB8vPzsdlspKWlkZ6eTnd3N3fffTdjY2N4vV4A\nCgoKCAQCChGZN/PdExkai/LKu5+YmnvgEa9CROLihiGyefNmvvzlLzM1NYXT6TT1BklJSTz11FM8\n88wzLF26lIcffpiMjAyGhoZif6fD4WBoaAiAcDhMRkZGbL7b7SYUCmGz2XC5XLFxl8tFKBQyVZNI\nPKgnInKTEDl48CAAo6OjWK1WKioqZvwGw8PD/MM//APf//73SU1N5bXXXuPUqVPTjrFYLDP+e0VE\nZP7dMER2794NwMTEBP/2b/9m6g3OnDlDRkZG7GnA69ev59e//jUOh4PBwUGcTifhcBiHwwFcWWH8\n/pVgwWAQt9t9zcojGAxOW5mIiEji3fDZWefPn6enp4ff/va3DA4OmnqDrKwszp49y8WLF5mYmOD0\n6dM88MAD5Obm0tLSAkBrayt5eXkA5ObmcuLECaLRKP39/fT29uL1enE6nSQnJ9Pd3Y1hGLS1tcXm\niMwHPTtL5CYrkZMnTwKQkpLCo48+auoNUlJSeOyxxzhw4ACRSIScnBz+9E//FK/XS21tLXv27Ild\n4gvg8XgoKiqisrISq9VKWVlZbLurrKyMuro6xsfH8fl8aqrLvFJPROQmIfLFL34x9udPP/2UTz/9\n1NQXUxUWFlJYWDhtLDk5+TN7LMXFxRQXF18z7vF42Ldv34zfX0RE5sYNQ+Sdd96JXVJ75swZ1q9f\nn5CiRERkYbhhiKSnp/P4448D8I//+I/XrCZEFrP5vk9E5FZwwxC5++67qa+vB2DVqlUJKUhkoVB4\niNwkRB599FGGh4dJSUnBMIxE1SQiIgvEDS/x/dnPfsabb76JzWbj9ddfT1RNIiKyQNwwRCYnJ7n7\n7rsBYg9iFJErdJ+IyE22s1JSUvj444/52c9+htVqTVRNIguCeiIiNwgRwzDIzs5mzZo1TE1NTbtn\nREREBG6wnWWxWDh16hSrV69WgIiIyHV95kokEAjw0Ucf8c4777BmzRpA37Eu8vt0n4jIDUKks7OT\nvXv30tDQwNNPP53ImkQWBIWHyA22swYGBujo6Ij9s6OjI5F1iYjIAvCZK5H169czPDwc+6eIiMgf\n+swQ0XOyRG5MPRGRm9wnIiKfTeEhcpM71kVERG5EISIiIqYpRERM0rOzRNQTETFNPRGRBIXI2NgY\nhw4d4re//S0TExOUlZXh8Xiora2lr6+PFStWsHPnTpYtWwZAY2MjTU1NWK1WSktLycrKAqCnp4e6\nujoikQg+n4+SkpJElC8iIp8hIdtZhw4dIjs7m1dffZXq6mruuecejh49SmZmJtXV1WRkZHD06FHg\nSlA0NzdTVVVFeXk5fr8/9oVYfr+f7du3U11dzblz5+js7ExE+SIi8hnmPEQuX77Mr371KzZu3AiA\n1WolJSWF9vZ2NmzYAFy5JyUQCABXntmVn5+PzWYjLS2N9PR0uru7CYfDjI2N4fV6ASgoKIjNEZkP\n6omIJGA7q7+/H7vdjt/v5ze/+Q2ZmZk8+eSTDA0N4XQ6AXA4HAwNDQEQDofJyMiIzXe73YRCIWw2\nGy6XKzbucrkIhUJzXb7IZ1JPRCQBK5HJyUnOnj3LunXr2L9/PxMTE/z3f//3tGMsFstclyEiInNg\nzkPE7XazfPlycnNzSUpKIj8/n/fffx+n08ng4CBwZfXhcDiAKyuMYDAYmx8MBnG73desPILB4LSV\niYiIJN6ch4jT6Yz1Naampujo6GDNmjX4fD5aWloAaG1tJS8vD4Dc3FxOnDhBNBqlv7+f3t5evF4v\nTqeT5ORkuru7MQyDtra22ByR+aCeiEiCLvF95pln8Pv9DA8Ps2rVKrZu3YphGNTW1rJnz57YJb4A\nHo+HoqIiKisrsVqtlJWVxba7ysrKqKurY3x8HJ/PR05OTiLKF7ku9UREEhQif/RHf8Tf//3fXzNe\nUVFx3eOLi4spLi6+Ztzj8bBv37641yciIubosSciImKaQkTEJPVERPTsLBHT1BMR0UpERERmQSEi\nIiKmaTtL5tyF4XH6L0VmPC8SNeagmvjRd6yLKEQkAfovRaj4+ZkZz3tp8+o5qCZ+FB4i2s4SEZFZ\nUIiIiIhp2s4SMWkh90SsFgvvXxiZ8by01CRW2u+Yg4pkoVKIiJi0EMPjqqGxKK+8+8mM5x14xKsQ\nkWm0nSUiIqYpRERExDSFiIhJenaWiHoiIqYt5J6ISLxoJSIiIqYpRERExDSFiIhJ6omIqCciYpp6\nIiIJDJGpqSleeOEF3G43lZWVjI6OUltbS19fHytWrGDnzp0sW7YMgMbGRpqamrBarZSWlpKVlQVA\nT08PdXV1RCIRfD4fJSUliSpfRESuI2HbWY2NjXg8ntjPR48eJTMzk+rqajIyMjh69ChwJSiam5up\nqqqivLwcv9+PYVx5JLjf72f79u1UV1dz7tw5Ojs7E1W+iIhcR0JCJBgMcvr0aTZu3Bgba29vZ8OG\nDQAUFhYSCAQACAQC5OfnY7PZSEtLIz09ne7ubsLhMGNjY3i9XgAKCgpic0Tmg3oiIgnaznrjjTfY\ntm0bo6OjsbGhoSGcTicADoeDoaEhAMLhMBkZGbHj3G43oVAIm82Gy+WKjbtcLkKhUCLKF7ku9URE\nErASOXXqFA6Hg9WrV8e2pf6QxWKZ6zJERGQOzPlK5OOPP6a9vZ2Ojg4mJiYYHR3lRz/6EQ6Hg8HB\nQZxOJ+FwGIfDAVxZYQSDwdj8YDCI2+2+ZuURDAanrUxERCTx5nwlUlJSQn19PX6/n2effZY1a9aw\nc+dOcnNzaWlpAaC1tZW8vDwAcnNzOXHiBNFolP7+fnp7e/F6vTidTpKTk+nu7sYwDNra2mJzROaD\neiIi83ifyGOPPUZtbS179uyJXeIL4PF4KCoqorKyEqvVSllZWWy7q6ysjLq6OsbHx/H5fOTk5MxX\n+SLqiYiQ4BC5//77uf/++wFITk6moqLiuscVFxdTXFx8zbjH42Hfvn1zWqOIiHx+euyJiIiYphAR\nMUk9ERE9O0vEtMXYE7FaLLx/YcTU3LTUJH0/+21IISIin9vQWJRX3v3E1NwDj3gVIrchbWeJiIhp\nChERk9QTEdF2lohpi7EnIvKHtBIRERHTFCIiImKaQkTEJPVERNQTETFNPRERrURERGQWFCIiImKa\nQkTEJPVERNQTETFNPRERrURERGQWFCIiImKaQkTEJPVERBLQExkYGMDv9zM0NITdbqewsJDCwkJG\nR0epra2lr68v9h3ry5YtA6CxsZGmpiasViulpaVkZWUB0NPTQ11dHZFIBJ/PR0lJyVyXL7/nwvA4\n/ZciM54XiRpzUM38U09EJAEhYrPZeOKJJ7j33nsZHh6mvLwcr9dLS0sLmZmZVFRU8NZbb3H06FG2\nbt1KT08Pzc3NVFVVEQqF2Lt3Lz/84Q+xWCz4/X6+9a1v4fV62b9/P52dneTk5Mz1R5D/r/9ShIqf\nn5nxvJc2r56DakTkVjDn21lOp5N7770XALvdjtfrJRQK0d7ezoYNGwAoLCwkEAgAEAgEyM/Px2az\nkZaWRnp6Ot3d3YTDYcbGxvB6vQAUFBTE5oiIyPxIaE+kt7eX8+fPk5mZydDQEE6nEwCHw8HQ0BAA\n4XAYt9sdm+N2uwmFQoTDYVwuV2zc5XIRCoUSWb7INOqJiCTwPpGxsTF+8IMf8MQTT8R6H1dZLJZE\nlSESN+qJiCRoJRKNRqmpqeGrX/0qeXl5wJXVx+DgIHBl9eFwOIArK4xgMBibGwwGcbvd16w8gsHg\ntJWJiIgk3pyHiGEY/PjHP8bj8fDII4/ExnNzc2lpaQGgtbU1Fi65ubmcOHGCaDRKf38/vb29eL1e\nnE4nycnJdHd3YxgGbW1tsTkiIjI/5nw763//939pa2tj1apVPP/88wB885vf5LHHHqO2tpY9e/bE\nLvEF8Hg8FBUVUVlZidVqpaysLLbdVVZWRl1dHePj4/h8Pl2ZJfPqaj9E21qymM15iGRlZfHTn/70\nuq9VVFRcd7y4uJji4uJrxj0eD/v27YtrfSJmKTxEdMe6iIjMgkJERERMU4iImKT7RET0fSIipqkn\nIqKViIiIzIJCRERETFOIiJiknoiIeiIipqknIqKViIiIzIJCRERETFOIiJiknoiIeiIipqknIqIQ\nWXQuDI/Tfyliam4kasS5GllMrBYL718YmfG8tNQkVtrvmIOKJB4UIotM/6UIFT8/Y2ruS5tXx7ka\nWUyGxqK88u4nM5534BGvQuQWpp6IiEnqiYhoJSJimnoiIlqJiIjILChERETENG1niZik71hPDF3V\ndWtbcCHS1dXFG2+8weTkJJs2beLhhx+e75JkkVJ4JIau6rq1LagQmZqaor6+nu9+97u4XC6+853v\nsHbtWjwez3yXlnBm7/fQvR4iEk8LKkTOnDlDeno6aWlpAOTn59Pe3r4oQ8Ts/R6610MWC7PbYKCt\nsJlYUCESCoW46667Yj+7XC7OnDF341w8TU6Z+7/7JRawWCxxrkYSRT2RW5vZbTCA1x7NMLXSX4zh\nYzEMY8Hsb5w8eZL333+fb3/72wD853/+J2fOnGH79u3XHHv8uP7DFhExY9Omz38T7YJaibhcLgYG\nBmI/B4NBXC7XdY+dyUkQERFzFtR9Il/84hfp7e2lv7+faDTKf/3Xf5GbmzvfZYmILFoLajsLrlzi\ne/jw4dglvsXFxfNdkojIorXgQkRERG4dC2o7S0REbi0LqrH+eS3mu9rr6+vp6OjAbrdTU1MDwOjo\nKLW1tfT19bFixQp27tzJsmXL5rnSuTUwMIDf72doaAi73U5hYSGFhYWL8lxEIhFefvllJiYmSEpK\nYv369Tz66KOL8lxcNTU1xQsvvIDb7aaysnLRnotnnnmG5ORklixZgtVqZf/+/TM/F8ZtZnJy0vib\nv/kbo6+vz5iYmDD27NljnD9/fr7LSpiuri7jN7/5jfHcc8/Fxo4cOWK89dZbhmEYxrFjx4w333xz\nvspLmHA4bHzyySeGYRjG0NCQ8dRTTxnnz59flOfCMAxjbGzMMAzDiEQixnPPPWd8+umni/ZcGIZh\nvP3228bBgweNqqoqwzAW538jhmEYZWVlxsjIyLSxmZ6L22476/fvarfZbLG72heL7OxsUlNTp421\nt7ezYcMGAAoLCwkEAvNRWkI5nU7uvfdeAOx2O16vl1AotCjPBcAdd1y5AW5sbIypqSmWLl26aM9F\nMBjk9OnTbNy4MTa2WM8FgPEHbfGZnovbbjvrVr2rfT4NDQ3hdDoBcDgcDA0NzXNFidXb28v58+fJ\nzMxctOdiamqKyspKzp8/z5NPPsldd921aM/FG2+8wbZt2xgdHY2NLdZzYbFY+Nu//VssFgtf//rX\n2bx584zPxW0XInJji+0xK2NjY/zgBz/giSeeuGZfdzGdiyVLlnDgwAH6+/vZv38/991337TXF8u5\nOHXqFA6Hg9WrV/M///M/1z1msZwLgL179/KFL3yBnp4e9u/fzz333DPt9c9zLm67EJnJXe2LhcPh\nYHBwEKfTSTgcxuFwzHdJCRGNRqmpqeGrX/0qeXl5wOI9F1elpaXx0EMP0dXVtSjPxccff0x7ezsd\nHR1MTEwwOjrKj370o0V5LgC+8IUvAODxePjyl7/MmTNnZnwubrueiO5qv1Zubi4tLS0AtLa2xn6h\n3s4Mw+AW8uMIAAADBElEQVTHP/4xHo+HRx55JDa+GM/F8PAwly5dAmBkZITTp0+zatWqRXkuSkpK\nqK+vx+/38+yzz7JmzRp27ty5KM/F+Ph4bEtveHjY9L8Xt+XNhov5rvaDBw/S1dXFyMgIDoeDLVu2\n8Gd/9meL7vLFX//617z00kusWrUqtiT/5je/yX333bfozsXvfvc7/H4/U1NTOJ1O1q9fz8aNGxft\nZa1XdXV18fbbby/aS3z7+/s5cOAAAHfeeSfr16/na1/72ozPxW0ZIiIikhi33XaWiIgkjkJERERM\nU4iIiIhpChERETFNISIiIqbddjcbiiRCS0sLjY2NvPrqq0SjUXbt2sX27ds5deoUY2NjJCcn8+d/\n/uc0NzeTmprKk08+ye9+9zu+853v8Prrr3Pp0iUOHTrE8uXLWbJkCX/913/NgQMH+MY3voHP5+PI\nkSNMTU1htVrZtm0bnZ2d/PSnP2X//v3z/dFFplGIiJh0zz338PHHHzM4OMh9992HxWIhOzubgoIC\n4Mod8y0tLUxMTBCJRGhra+NLX/oShmHwi1/8gtLS0thz3iYnJ3G5XPh8PsbHxxkcHGTnzp3U1dUR\niUTIycmhqalpPj+uyHVpO0vEpHXr1vHee+/xwQcf8MADD/Av//Iv3H///bHXbTZb7Lhf/vKXRCKR\n2BOWL1y4MO1BoVarNfbnO+64A5vNRlVVFVarlaSkpAR9IpGZU4iImHT1l7vT6cRisfD444/T1dUV\nez0ajQKQmZnJ8ePHyc3NjT12e+XKldOe8Xb1WIBPP/0Uu93OCy+8wJ133klfX18iPo6IKdrOEpmF\nbdu2AVeeMWQYBv39/bz++utMTU3xla98JXbc3r17WbJkCW1tbQB87Wtfo7GxkUgkQjQa5a/+6q9i\nx65cuZLLly9z5MgRxsbGWLFiRWI/lMgM6LEnIreI1157jeeee8706yLzQdtZIreI1NTUz/wWzs7O\nztv+gYCyMGklIiIipmklIiIipilERETENIWIiIiYphARERHTFCIiImLa/wNPb3aWU0U60wAAAABJ\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x12ab65490>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x12abc1fd0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x12ad15210>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x12ade6d90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x12ebc1ed0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x12aa8d510>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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RK3IlsiQl8c7JM5f1GhlpydxouyZGFcmXlekhYrfbsdvtANhsNtxuN4FAgLa2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\nEBERkagpREREJGoKERERidr/B+DAC8WtwE26AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x114f02310>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x114de5a50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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TplFbWwtAXV0d06dPB2DKlCns27fv/Fc4DPSciIjY1aDLWbNnz+aOO+5gYGDgopaN3n33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\nERHTFCIiImKaQkRERExTiIiIiGn/HyLCrNUo/fnpAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x12ed58150>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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rpjWNj48blZWVxtjYmDExMWG8/PLLc/7s3XLTVgt1B3p2djZLly6NdRmzOBwO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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x12ef2bcd0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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kKyuLzs5OIpEIAwMDeL1eAIqKiuL7iIjI1JjUnkh3dzdnzpwhJyeHvr4+nE4n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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x12f0037d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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8Zq9befaWnrs1eylERMQUt/LsLT13a/ZSY11ERAxTiEhS0X0iIubScZYkFfVE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\nMUwhIiIihilERETEMIWIiIgY9n+0g758hZlJ5wAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x12f05b2d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x12f1ba390>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x12f293dd0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x12f2e74d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x12f3b3f50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x12f50d590>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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2T04Kkasw+pkgoM8FkYXhUj/kt6e1jD7pDnraPVkpRK7C6GeCgD4XRBYG9UTE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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x12f5e1990>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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6IpKV1BMRMYc5HSIfjIxNe84CSxoKEckwo/eY6P4Sma45HSIPvNQ37TnV3qv5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\nYQoREREx7P8DliNR3Q32iFUAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x12ef45dd0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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6a9DZWSJidgqRKxg8F2b760cNz39+3W3XXYPCQ2aDjpKXa6EQEZFpdJS8XAv1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\nbfsAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x12f6ff6d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x12f85bbd0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x12f92e590>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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Gt771LX74wx/G8r9CRCEiYsY111zDkSNHOHHiBN/+9rdxOBxkZGQwd+5cYPit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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x12f982950>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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QQdtZIiLyKShEREQkagoRSRj6PBER46knIrdlOtx5rp6IiPEUInJb7qQ7z0Xk\nzqHtLBERiZpCRBKGeiIixtN2liQM9UREjKeViIiIRE0rkQQzHa6yEpE7h0IkwSTyVVZ6dpYYSc/c\nGjPlQuTkyZO88sorjIyMsHLlSh555JHJLkmmCIWHGEnP3BozpXoio6OjVFdXU1ZWxr59+2hoaKCz\ns3OyyxIRSVhTaiVy+vRpMjIySE9PB6CwsJDW1lZcLtckVxZ/6m2IyJ1gSoWI3+/nnnvuiXztcDg4\nfXri+/u3MjA8Qmh04r9kZ5ggLSm6t/LThMH/e+vMhOdNh95GtNQTETGeKRwOT5n/NT127Bjvvfce\nX/nKVwD4xS9+wenTp9m0adMNx9bX6xeFiEg0Vq68/Ztyp9RKxOFw0NPTE/na5/PhcDhueuxE3gQR\nEYnOlGqsf/azn6Wrq4vu7m5CoRC//OUvyc/Pn+yyREQS1pTazoKxS3wPHz4cucS3uLh4sksSEUlY\nUy5ERETkzjGltrNEROTOMqUa67fS09ODx+Ohr68Pq9VKUVERRUVFvP7669TX12O1WgF47LHHyM3N\nneRqYysYDPL8888zPDxMUlISS5YsYc2aNQwMDFBZWcmFCxeYM2cO27ZtIzk5ebLLjalbvReJeF7A\n2M26zzzzDE6nk/Ly8oQ8J6764/ciUc+JrVu3kpKSwowZMzCbzbz44osTPi+mxXZWb28vvb293H//\n/fT391NWVsZzzz3Hr371K1JSUlizZs1klxhXQ0NDzJo1i+HhYZ555hl27txJfX09d911F1/+8pd5\n4403uHz5MuvXr5/sUmPuZu/FO++8k5Dnxc9+9jN++9vfMjAwQHl5Oa+99lpCnhNw43vx+uuvJ+Q5\nsXXrVr75zW8ye/bsyNhEz4tpsZ1lt9u5//77AbBarbjdbvx+PwDTICMnbNassefyDA4OMjo6ysyZ\nM2ltbWXZsmUAFBUV4fV6J7PEuLn2vRgZGWHmzJlA4p0XPp+P48ePs2LFishYop4TN3svIPHOiav+\n+O890fNiWmxnXaurq4tz586RlZXFRx99xH//93/T0NBAVlYW//iP/0haWtpklxhzo6OjlJeXc+7c\nOZ544gnuuece+vr6sNvtANhsNvr6+ia5yvi42XsBJNx58corr/D4448zMDAQGUvUc+Jm7wUk3jkB\nYDKZ+Od//mdMJhMPP/wwq1atmvB5MS1WIlcNDg7y7W9/mw0bNpCcnMzDDz9MZWUlL7zwAjNmzOBH\nP/rRZJeFoVgdAAAEW0lEQVQYFzNmzGD//v185zvf4a233uLjj69/0qjJZJqkyuLvZu9Fop0X7777\nLjabjXnz5t3y/7YT5Zy41XuRaOfEVXv27GH//v1s376dI0eO8OGHH173/ds5L6ZNiIRCIQ4cOMDn\nP/95CgoKgLEUNZlMpKam8jd/8zeGPmdrKkhPT2fRokWcPHkSm81Gb28vAIFAAJvNNsnVxdcfvxeJ\ndF6cOnWK1tZWtm7dysGDB/nggw/47ne/m5DnxM3ei8rKyoQ7J666++67AXC5XDz00EOcPn16wufF\ntAiRcDjM9773PVwuF6tXr46MBwIBAEZGRmhpaWHu3LmTVWLc9Pf3c/nyZQAuXrzI8ePHmTt3Lvn5\n+TQ2NgLQ1NQUCdrp7FbvxdV/IIlyXpSUlFBdXY3H4+Gpp55iwYIFbNu2LSHPiZu9F1/96lcT8nfF\n0NBQZEuvv78/6t8V06In8tFHH9Hc3MzcuXPZvXs3MHaytLS0cPbsWSwWCzk5OWzYsGGSK4293t5e\nPB4Po6Oj2O121qxZw8KFC3G73VRWVrJz587IZXvT3a3ei8rKyoQ7L25m7dq1CXdOXOva7azXXnuN\nTz75JKHOib6+Pvbv3w/AXXfdxerVq3nwwQfJysqa0HkxLS7xFRGRyTEttrNERGRyKERERCRqChER\nEYmaQkRERKKmEBERkaiZn3/++ecnuwiRqaKxsZGqqiq+8IUvEAqF+OpXv8qcOXP46U9/SktLCydO\nnCAlJYV///d/5+TJk+Tm5vK73/2O0tJS1qxZQ39/P5WVlZw4cYK2tjYyMzP5xje+gc1m47777uMH\nP/gBbW1tnD17lvnz59PW1sbhw4e5fPkybreb4eFhvv/97+Pz+XC73ZP9dohMj/tEROLpM5/5DKdO\nnaK3t5e//Mu/xGQykZOTw9KlS4Gxpyc0NjYyPDxMMBikubmZv/7rvyYcDvPzn/+cjRs3Rp7hNTIy\ngsPhIC8vD4DNmzcDcODAAQAWLVpEcnIyv/vd7wCYOXMmRUVFka9FJpu2s0QmaPHixfz617/mxIkT\nPPDAA7z++uvMnz8/8n2LxRI57p133iEYDEYe5nf+/PlIgACYzebrfnZnZycHDhwgPT09Dn8TkU9P\nISIyQUlJScDYRxCYTCYeffRRTp48Gfl+KBQCICsri/r6evLz8yN3R99333309PTccOxVLpeLsrIy\n+vr6uHLlCpC4jyiXqUHbWSJRePzxx4GxZwuFw2G6u7v54Q9/yOjoKJ/73Ocix+3Zs4cZM2bQ3NwM\nwBe+8AXq6uoIBoOEQiH+4R/+IXJsIBDgjTfeAODee+8lNTWVU6dO8eabb3L58mUcDgcPPfRQHP+W\nIn+aHnsiMslefvllnn766ds+/je/+Q3nzp3ji1/8YgyrErk92s4SmWRpaWm0trbe1rHDw8O0trbi\ndDpjXJXI7dFKREREoqaViIiIRE0hIiIiUVOIiIhI1BQiIiISNYWIiIhE7f8DijlO/pV4sXwAAAAA\nSUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x12fa50d90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x12fbace90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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006DIx6MQEUOpJyJibro6S0RE4qYQERGRuGk5Sww1Wz0RNchFjGG6EDl16hQv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\nSNz+P8WsRWvHwk82AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x12fc84310>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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zc/H7/XR2dvLdd99x+PBhGhoa+Nvf/hbuoYmMmra2RMbo4YcfBgaetWQYBi0t\nLbz11lv09/fzk5/8JPi5Xbt2MWnSJCorKwG45557KC0tpbe3l0AgwM9//vPgZ30+Hx9++CEAN998\nMwkJCTz55JPAwJtA77nnnkgNT2TE9IgUkevAyy+/zFNPPTXiz3/55Zc0Njby05/+NIxViYyMtrZE\nrgMJCQnU1NSM6LOXLl2ipqYGt9sd5qpERkYrEhERMUUrEhERMUVBIiIipihIRETEFAWJiIiYoiAR\nERFT/g+2XCEmnM8RwQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x12fcdc850>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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ictsyetOgbhiceeqJfDJGv8zKCIWI3LaM3jSoGwbF7Ix+mRXA/sVT217LWSIi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\nAwStMPRGwaPtAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x12fda20d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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PPYRCIf74xz8ybtw4br/9dm644QaKi4u54YYb+P73vz/CfxsiChKRIbnuuuv4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\nFCQiImLK/wEcNC8K2K5oiwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x12ff033d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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IxGr6XdpatGgR9957L729vVEtIe3fv5/KykpSU1N57LHHSEhIIBAIMHXq1MhrvF4vfr8f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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x12ff50d90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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+PwB+v5+CggIsFgvp6elkZGTQ1dVFKBRiaGgIt9sNQGFhYfQcERGZGdM6E+nt\n7eXUqVNkZWUxMDCA3W4HwGazMTAwAEAoFMLpdEbPcTqdBINBQqEQDocjuu5wOAgGg9NZ/i1LMxER\niWXa9okMDQ3xne98h2eeeSY6+7jCZDJNVxligGYiU2M2mXj39DnD56enzeMe620JrEgkeaYlRMLh\nMJWVlXz+858nPz8fGO8+zp49i91uJxQKYbPZgPEOIxAIRM8NBAI4nc6rOo9AIDChMxG5UQwMhfnm\nOx8YPn/3KrdCRGaNpF/OikQifPe738XlcrFq1aroel5eHs3NzQC0tLREwyUvL4/Dhw8TDofp6+uj\nt7cXt9uN3W4nJSWFrq4uIpEIra2t0XNERGRmJL0T+fWvf01raysLFy7kpZdeAuCpp55i9erVVFVV\nsXnz5ugtvgAul4tly5axdetWzGYz5eXl0ctd5eXlVFdXMzw8jMfjITc3N9nlC0TnIbqsJSK/L+kh\nkp2dzQ9/+MNrfm3Lli3XXC8pKaGkpOSqdZfLxY4dOxJan8Sn8BCRWLRjXUREDFOIiIiIYQoRiUv7\nREQkFr1PROLSTEREYlEnIiIihilERETEMIWIxKWZiIjEopmIxKWZyPTSs7dkNrmpQ+SXZ84bOs9s\nMnE5kuBiRK6Tnr0ls8lNHSJfebPL0Hn3Wm9jQ4ErwdWIiNx8NBORuDQTEZFYbupORBJDMxERiUWd\niIiIGKYQERERw3Q5S+LS+0RmF90iLNNp1oVIZ2cn3//+9xkbG2PFihU89thjM13STU/hMbvoFmGZ\nTrMqRC5fvkxNTQ1f//rXcTgcfO1rX2PRokW4XLodVyRR1MnIVMyqEDlx4gQZGRmkp6cDUFBQQFtb\nm0JEJIHUychUzKoQCQaD3HnnndE/OxwOTpw4EfP4TGeKoc9Jv32eofNuVpqJyFSok7m1mCKRyKx5\nwMeRI0d49913+fKXvwzAf/zHf3DixAnKysquOrahQf/giYgYsWLF9W8unlWdiMPhoL+/P/rnQCCA\nw+G45rFT+UsQERFjZtU+kU9+8pP09vbS19dHOBzmP//zP8nLy5vpskREblmz6nIWjN/iu3///ugt\nviUlJTNdkojILWvWhYiIiNw4ZtXlLBERubHMqsH69dKu9sR64YUXSElJYc6cOZjNZnbu3DnTJc0a\nNTU1tLe3Y7VaqaysBODSpUtUVVVx5swZ7r77bjZs2MD8+fNnuNLZ4Vp/nz/60Y9oaGjAarUC8NRT\nT5GbmztZw0sXAAAFIUlEQVSTZc4K/f39+Hw+BgYGsFqtFBcXU1xcPPXfz8hNZmxsLPI3f/M3kTNn\nzkRGR0cjmzdvjpw6dWqmy5rVysvLI+fOnZvpMmalzs7OyG9+85vIiy++GF07cOBA5I033ohEIpHI\noUOHIgcPHpyp8mada/19/su//EvkzTffnMGqZqdQKBT54IMPIpFIJDIwMBB57rnnIqdOnZry7+dN\ndznro7vaLRZLdFe7fDwRjc4MycnJIS0tbcJaW1sbRUVFABQXF+P3+2eitFnpWn+foN9PI+x2O/fd\ndx8AVqsVt9tNMBic8u/nTXc5a6q72iU+k8nE3/3d32EymXj00UdZuXLlTJc0qw0MDGC32wGw2WwM\nDAzMcEWz309+8hMaGxvJysrir/7qr64ZNBJbb28vp06dIisra8q/nzddiEjibd++nTvuuIOenh52\n7tzJvffeS05OzkyXdVMwmUwzXcKs9+ijj/KlL32JS5cuceDAAX7wgx+wfv36mS5r1hgaGuI73/kO\nzzzzzFWzj+v5/bzpLmdNZVe7XJ877rgDAJfLxWc+8xl1dh+TzWbj7NmzAIRCIWw22wxXNLvZbDZM\nJhOpqan86Z/+qX4/pyAcDlNZWcnnP/958vPzgan/ft50IaJd7Yk1PDzMpUuXABgcHOTYsWMsXLhw\nhqua3fLy8mhubgagpaUl+n9eMSYUCgEwNjbG4cOH9ft5nSKRCN/97ndxuVysWrUquj7V38+bcrOh\ndrUnTl9fH7t37wbg9ttvZ+nSpTzyyCMzXNXssXfvXjo7Ozl37hw2m401a9bw2c9+Vrf4GnTl73Nw\ncBC73c6TTz5JZ2cn3d3dWCwWcnJy+LM/+7PoNX2J7b333uMb3/gGCxcujF62euqpp/jUpz41pd/P\nmzJERERketx0l7NERGT6KERERMQwhYiIiBimEBEREcMUIiIiYph2rItMQXNzM/X19bzyyiuEw2E2\nbtxIWVkZR48eZWhoiJSUFP7kT/6EpqYm0tLSePbZZ/ntb3/L1772NV599VUuXLjAvn37WLBgAXPm\nzOEv//Iv2b17N1/84hdZvHgx3/ve94DxTbOrV6/m/fffp6mpCYDly5dz3333UVtbyyc+8Qm+8IUv\nzORfhQigEBGZsnvvvZf333+fs2fP8qlPfQqTyUROTg6FhYXA+C7g5uZmRkdHGRkZobW1lU9/+tNE\nIhF++tOfUlpaGn2+29jYGA6HA4/HA8Dzzz8PEH3M+dGjR3niiScwmUy0tLSQmZlJcXExv/3tb2fg\nJxe5mkJEZIqWLFnCz3/+c4aHh3nooYf40Y9+xObNm6Nft1gs0eN+9rOfMTIyEn0g4OnTpyc8INRs\nNk/43j09Pfzwhz8kPT0dgKVLl+Lz+TCZTPz1X/91sn80kSnTTERkiubNmweMP0rbZDJFd01fEQ6H\nAcjKyqKhoYG8vLzoo8rvueeeCc92u3LsFS6Xi4qKCgYGBrhw4QJvvfUWX//613n55Zd56623kv2j\niUyZOhERA9atWweMP1soEonQ19fHq6++yuXLl/nc5z4XPW779u3MmTOH1tZWAB555BHq6+sZGRkh\nHA7zF3/xF9FjQ6EQb7zxBgB33XUXaWlpfPazn+W1114DxjsbkRuNHnsiMsP27NnDiy++eN3H//KX\nv+TUqVMarMsNQZezRGZYWlradb99c3R0lLa2NpxOZ5KrErk+6kRERMQwdSIiImKYQkRERAxTiIiI\niGEKERERMUwhIiIihv0/tXjnMHMCA5wAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x130025f50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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HyDuhkWmfM3+efkCWiMjNSukQ+X8/fmva56zx3sGn73F/8IEiIqKrs1Kd7hMR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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x130019e90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x13024d590>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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0OvnLv/xLNm/ejNvtXurSROQz0lVdK8uyCpFz586RmppKSkoKAPn5+XR0dNzU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\nzRJUpKBZAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x130322510>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x130374d90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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2mTlvXuS/aGlLZBhmz57NO++8w9/+9je+/vWv88orr3DddddFv+5wOKKv++tf\n/0o4HI4+lfn48eMDHixqt9ujvz958iTHjh1jxowZA77fH/7wB/bs2RMNG5FLiYJEZBjGjRsHnHtU\nvc1m4/bbb6exsTH69UgkAkBWVhZVVVXk5uZGH9V95ZVXDnge3PnXAnz44YeEQiFeffVVPvjgA9ra\n2gD43ve+x4MPPsi+fftG/L2JDJWWtkSG6e677wbOPYvIMAz8fj/PPfcc/f39fOtb34q+bsuWLYwZ\nM4aamhoAbr75ZiorKwmHw0QiEX74wx9GXztnzhzmzJnDv//9b/bt20d6ejr79+/nn//8J+FwmFtu\nuSWxb1LkK9AjUkQuAU888QTr1q37yq//4IMPaGlp0bBdLgla2hK5BEyYMOErf5Ln2bNnqa+vx+v1\njnBVIl+NOhIREYmJOhIREYmJgkRERGKiIBERkZgoSEREJCYKEhERicn/AXPqOt9M4Z6FAAAAAElF\nTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1304ccd50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x1305a1190>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x130675f90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x1306c6790>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x13081ed90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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3200oFALA7XZTVFREeXk5XV1dtLe3R7p8ERGZRMRXIjabDZvNBoDVasXlcuHz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1308f1f10>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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OdpF4uOGGG/jiiy84efIkN998MxaLhaysLObMmQP076jfv38/58+fJxAIUFtb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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1309c2250>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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JFRUVHD9+nI6OjmiXLyIiE4h6iDgcDj772c8CYLfb8Xg8BAIB2traWLZsGQAF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\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x130a22890>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x130b7cc10>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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GZz/7WQCsVisulwufz0d7ezvLli0DoKCgAI/HA4DH4yEvLw+LxUJKSgqpqal0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\niGH/D55ruOTcNfAIAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x130bd3950>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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sjKqqKk6ePEl3dzcATU1NzJ8/n6qqKtasWcOBAwdu5ucWEZEYmDZEzp07x8DAAKmpqVgs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\niIiIRE0hIiIiUVOIiIhI1BQiIiIStf8HfJsx1i8PyqEAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x130c9cb50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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k5+dH7xEREXNMaU2kp6eHU6dOkZGRQV9fH06nEwCHw0FfXx8AoVAIt9sdvcft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\nU4iIiEjMFCIiIhIzhYiIiMTs/wE6PAQpYom9BQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x130dfb1d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x130ecca50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x130fa05d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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cfPPNfPnll5w+fZrbb78dm81GdnY2c+fOBfruhj548CAXLlwgHA5TXV3NXXfd\nhWEYfPTRR6xYsSL6TLienh48Hg85OTkAjBs3DsMw+Pa3vw3AggULWLBgAa+88gp5eXmMHj2a+fPn\n8/XXXw/Pzov8Lzq1JTIEs2bN4pNPPuGzzz7ju9/9Lnv37uWOO+6Ift3hcERf99e//pVwOBx9qN/J\nkycvebCo3W6/5O/evn07K1eu5P33349uC4fD+P1+Jk+ebOVuiQyJgkRkCMaMGQP0PWbcZrNF71bv\nF4lEAMjKyqKiooLc3NzoY8cnT558yfPg+l97MYfDwahR//nveejQIWbNmmXJvoiYpVNbIkP0k5/8\nBOh7FpFhGPj9fl5++WV6e3v5wQ9+EH3d5s2bGTVqFNXV1QDce++9lJeXEw6HiUQi/PjHP46+9sSJ\nE7z77rs4HI7oqS6ATz75hF/84hdx2jORwdEjUkSuAy+88ALr1q275tf/85//pLm5mR/+8IcWViVy\nbXRqS+Q6MH78+Gv+JM8LFy5QV1eH1+u1uCqRa6OORERETFFHIiIipihIRETEFAWJiIiYoiARERFT\nFCQiImLK/wcSUE2J5AJuegAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x130ff2a90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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OKxERETFNISIiIqYpREQi1BMRiZ16IiIR6omIxE4rERERMU0hIiIipmk7SyRC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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1310b6c10>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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kykfewFCIr//8fcP9d97nUhIRw2K+nGWz2bjtttsAsFqtuFwu/H4/7e3tLFmy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\nKYmIiIhhSiIiImLY/wHfjbZ9F6p77gAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x131156dd0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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Kigq6urpob2+PdvkiIjKBqIeIzWbjc5/7HABWqxWXy4XP56O1tZUlS5YAUFBQ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\nP/3lcFUAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x131274390>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x1313dedd0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x1314b0510>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x131501b90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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G1YjISNTr0tb777/P22+/jc1m4/XXX49XTSIiMoz0GiRdXV3ccsstAOGHN0piqN6ay4pZ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\nVBQkIiISlf8H3GCn4rTOeEIAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1315cff90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x131731210>"
       ]
      },
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAZEAAAELCAYAAAAY3LtyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3X9UVOedx/H3OIMRsDOTGUNoMrXNdiCQ1dQ6UNdyiqgk\npyH2jz1u3EP0nAQ2P