ml-finance-python

python scripts for finance machine learning

git clone https://9o.is/git/ml-finance-python.git

notebook.ipynb

(393236B)


      1 {
      2  "cells": [
      3   {
      4    "cell_type": "markdown",
      5    "metadata": {},
      6    "source": [
      7     "# Violations of Regression Models\n",
      8     "By Evgenia \"Jenny\" Nitishinskaya and Delaney Mackenzie\n",
      9     "\n",
     10     "Part of the Quantopian Lecture Series:\n",
     11     "\n",
     12     "* [www.quantopian.com/lectures](https://www.quantopian.com/lectures)\n",
     13     "* [github.com/quantopian/research_public](https://github.com/quantopian/research_public)\n",
     14     "\n",
     15     "---\n",
     16     "\n",
     17     "When using a regression to fit a model to our data, the assumptions of regression analysis must be satisfied in order to ensure good parameter estimates and accurate fit statistics. We would like parameters to be:\n",
     18     "* unbiased (expected value over different samples is the true value)\n",
     19     "* consistent (converging to the true value with many samples), and\n",
     20     "* efficient (minimized variance)\n",
     21     "\n",
     22     "Below we investigate the ways in which these assumptions can be violated and the effect on the parameters and fit statistics. We'll be using single-variable linear equations for the examples, but the same considerations apply to other models. We'll also assume that our model is correctly specified; that is, that the functional form we chose is valid. We discuss model specification errors along with the assumption violations and other problems that they cause in another notebook."
     23    ]
     24   },
     25   {
     26    "cell_type": "markdown",
     27    "metadata": {},
     28    "source": [
     29     "# Focus on the Residuals\n",
     30     "\n",
     31     "Rather than focusing on your model construction, it is possible to gain a huge amount of information from your residuals (errors). Your model may be incredibly complex and impossible to analyze, but as long as you have predictions and observed values, you can compute residuals. Once you have your residuals you can perform many statistical tests.\n",
     32     "\n",
     33     "If your residuals do not follow a given distribution (usually normal, but depends on your model), then you know that something is wrong and you should be concerned with the accuracy of your predictions."
     34    ]
     35   },
     36   {
     37    "cell_type": "markdown",
     38    "metadata": {},
     39    "source": [
     40     "# Residuals not normally-distributed\n",
     41     "\n",
     42     "If the error term is not normally distributed, then our tests of statistical significance will be off. Fortunately, the central limit theorem tells us that, for large enough data samples, the coefficient distributions will be close to normal even if the errors are not. Therefore our analysis will still be valid for large data datasets.\n",
     43     "\n",
     44     "## Testing for normality\n",
     45     "\n",
     46     "A good test for normality is the Jarque-Bera test. It has a python implementation at `statsmodels.stats.stattools.jarque_bera` , we will use it frequently in this notebook.\n",
     47     "\n",
     48     "### Always test for normality!\n",
     49     "\n",
     50     "It's incredibly easy and can save you a ton of time."
     51    ]
     52   },
     53   {
     54    "cell_type": "code",
     55    "execution_count": 1,
     56    "metadata": {
     57     "collapsed": true
     58    },
     59    "outputs": [],
     60    "source": [
     61     "# Import all the libraries we'll be using\n",
     62     "import numpy as np\n",
     63     "import statsmodels.api as sm\n",
     64     "from statsmodels import regression, stats\n",
     65     "import statsmodels\n",
     66     "import matplotlib.pyplot as plt"
     67    ]
     68   },
     69   {
     70    "cell_type": "code",
     71    "execution_count": 2,
     72    "metadata": {
     73     "collapsed": false
     74    },
     75    "outputs": [
     76     {
     77      "name": "stdout",
     78      "output_type": "stream",
     79      "text": [
     80       "0.832710660505\n",
     81       "0.0326186154758\n"
     82      ]
     83     }
     84    ],
     85    "source": [
     86     "residuals = np.random.normal(0, 1, 100)\n",
     87     "\n",
     88     "_, pvalue, _, _ = statsmodels.stats.stattools.jarque_bera(residuals)\n",
     89     "print pvalue\n",
     90     "\n",
     91     "residuals = np.random.poisson(size = 100)\n",
     92     "\n",
     93     "_, pvalue, _, _ = statsmodels.stats.stattools.jarque_bera(residuals)\n",
     94     "print pvalue"
     95    ]
     96   },
     97   {
     98    "cell_type": "markdown",
     99    "metadata": {},
    100    "source": [
    101     "# Heteroskedasticity\n",
    102     "\n",
    103     "Heteroskedasticity means that the variance of the error terms is not constant across observations. Intuitively, this means that the observations are not uniformly distributed along the regression line. It often occurs in cross-sectional data where the differences in the samples we are measuring lead to differences in the variance."
    104    ]
    105   },
    106   {
    107    "cell_type": "code",
    108    "execution_count": 3,
    109    "metadata": {
    110     "collapsed": false
    111    },
    112    "outputs": [
    113     {
    114      "data": {
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7ffe7vOUeThvUqYkmDWun+nWqllqtgDMQmgAAACqx4rTlzj2ctl3zOnpkpL/a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\n",
    116       "text/plain": [
    117        "<matplotlib.figure.Figure at 0x7f52f81bf310>"
    118       ]
    119      },
    120      "metadata": {},
    121      "output_type": "display_data"
    122     }
    123    ],
    124    "source": [
    125     "# Artificially create dataset with constant variance around a line\n",
    126     "xs = np.arange(100)\n",
    127     "y1 = xs + 3*np.random.randn(100)\n",
    128     "\n",
    129     "# Get results of linear regression\n",
    130     "slr1 = regression.linear_model.OLS(y1, sm.add_constant(xs)).fit()\n",
    131     "\n",
    132     "# Construct the fit line\n",
    133     "fit1 = slr1.params[0] + slr1.params[1]*xs\n",
    134     "\n",
    135     "# Plot data and regression line\n",
    136     "plt.scatter(xs, y1)\n",
    137     "plt.plot(xs, fit1)\n",
    138     "plt.title('Homoskedastic errors');\n",
    139     "plt.legend(['Predicted', 'Observed'])\n",
    140     "plt.xlabel('X')\n",
    141     "plt.ylabel('Y');"
    142    ]
    143   },
    144   {
    145    "cell_type": "code",
    146    "execution_count": 4,
    147    "metadata": {
    148     "collapsed": false
    149    },
    150    "outputs": [
    151     {
    152      "data": {
    153       "text/html": [
    154        "<table class=\"simpletable\">\n",
    155        "<caption>OLS Regression Results</caption>\n",
    156        "<tr>\n",
    157        "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th> <td>   0.538</td>\n",
    158        "</tr>\n",
    159        "<tr>\n",
    160        "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.533</td>\n",
    161        "</tr>\n",
    162        "<tr>\n",
    163        "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   114.0</td>\n",
    164        "</tr>\n",
    165        "<tr>\n",
    166        "  <th>Date:</th>             <td>Mon, 21 Sep 2015</td> <th>  Prob (F-statistic):</th> <td>4.15e-18</td>\n",
    167        "</tr>\n",
    168        "<tr>\n",
    169        "  <th>Time:</th>                 <td>14:32:35</td>     <th>  Log-Likelihood:    </th> <td> -481.43</td>\n",
    170        "</tr>\n",
    171        "<tr>\n",
    172        "  <th>No. Observations:</th>      <td>   100</td>      <th>  AIC:               </th> <td>   966.9</td>\n",
    173        "</tr>\n",
    174        "<tr>\n",
    175        "  <th>Df Residuals:</th>          <td>    98</td>      <th>  BIC:               </th> <td>   972.1</td>\n",
    176        "</tr>\n",
    177        "<tr>\n",
    178        "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
    179        "</tr>\n",
    180        "<tr>\n",
    181        "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
    182        "</tr>\n",
    183        "</table>\n",
    184        "<table class=\"simpletable\">\n",
    185        "<tr>\n",
    186        "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n",
    187        "</tr>\n",
    188        "<tr>\n",
    189        "  <th>const</th> <td>   -3.7552</td> <td>    5.981</td> <td>   -0.628</td> <td> 0.532</td> <td>  -15.624     8.114</td>\n",
    190        "</tr>\n",
    191        "<tr>\n",
    192        "  <th>x1</th>    <td>    1.1143</td> <td>    0.104</td> <td>   10.676</td> <td> 0.000</td> <td>    0.907     1.321</td>\n",
    193        "</tr>\n",
    194        "</table>\n",
    195        "<table class=\"simpletable\">\n",
    196        "<tr>\n",
    197        "  <th>Omnibus:</th>       <td>10.027</td> <th>  Durbin-Watson:     </th> <td>   1.986</td>\n",
    198        "</tr>\n",
    199        "<tr>\n",
    200        "  <th>Prob(Omnibus):</th> <td> 0.007</td> <th>  Jarque-Bera (JB):  </th> <td>  15.483</td>\n",
    201        "</tr>\n",
    202        "<tr>\n",
    203        "  <th>Skew:</th>          <td>-0.419</td> <th>  Prob(JB):          </th> <td>0.000434</td>\n",
    204        "</tr>\n",
    205        "<tr>\n",
    206        "  <th>Kurtosis:</th>      <td> 4.736</td> <th>  Cond. No.          </th> <td>    114.</td>\n",
    207        "</tr>\n",
    208        "</table>"
    209       ],
    210       "text/plain": [
    211        "<class 'statsmodels.iolib.summary.Summary'>\n",
    212        "\"\"\"\n",
    213        "                            OLS Regression Results                            \n",
    214        "==============================================================================\n",
    215        "Dep. Variable:                      y   R-squared:                       0.538\n",
    216        "Model:                            OLS   Adj. R-squared:                  0.533\n",
    217        "Method:                 Least Squares   F-statistic:                     114.0\n",
    218        "Date:                Mon, 21 Sep 2015   Prob (F-statistic):           4.15e-18\n",
    219        "Time:                        14:32:35   Log-Likelihood:                -481.43\n",
    220        "No. Observations:                 100   AIC:                             966.9\n",
    221        "Df Residuals:                      98   BIC:                             972.1\n",
    222        "Df Model:                           1                                         \n",
    223        "Covariance Type:            nonrobust                                         \n",
    224        "==============================================================================\n",
    225        "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
    226        "------------------------------------------------------------------------------\n",
    227        "const         -3.7552      5.981     -0.628      0.532       -15.624     8.114\n",
    228        "x1             1.1143      0.104     10.676      0.000         0.907     1.321\n",
    229        "==============================================================================\n",
    230        "Omnibus:                       10.027   Durbin-Watson:                   1.986\n",
    231        "Prob(Omnibus):                  0.007   Jarque-Bera (JB):               15.483\n",
    232        "Skew:                          -0.419   Prob(JB):                     0.000434\n",
    233        "Kurtosis:                       4.736   Cond. No.                         114.\n",
    234        "==============================================================================\n",
    235        "\n",
    236        "Warnings:\n",
    237        "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
    238        "\"\"\""
    239       ]
    240      },
    241      "execution_count": 4,
    242      "metadata": {},
    243      "output_type": "execute_result"
    244     },
    245     {
    246      "data": {
    247       "image/png": 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AEORopw0EFqEJAAAAAPwgNAEAAAQ52mkDgcWaJgAAgCBHO20gsAhNAAAAIYB2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\nAAAAABggNAEAAACAAUITAAAAABj4/8jxxIuqBPKNAAAAAElFTkSuQmCC\n",
    248       "text/plain": [
    249        "<matplotlib.figure.Figure at 0x7f52f81a6050>"
    250       ]
    251      },
    252      "metadata": {},
    253      "output_type": "display_data"
    254     }
    255    ],
    256    "source": [
    257     "# Artificially create dataset with changing variance around a line\n",
    258     "y2 = xs*(1 + .5*np.random.randn(100))\n",
    259     "\n",
    260     "# Perform linear regression\n",
    261     "slr2 = regression.linear_model.OLS(y2, sm.add_constant(xs)).fit()\n",
    262     "fit2 = slr2.params[0] + slr2.params[1]*xs\n",
    263     "\n",
    264     "# Plot data and regression line\n",
    265     "plt.scatter(xs, y2)\n",
    266     "plt.plot(xs, fit2)\n",
    267     "plt.title('Heteroskedastic errors')\n",
    268     "plt.legend(['Predicted', 'Observed'])\n",
    269     "plt.xlabel('X')\n",
    270     "plt.ylabel('Y')\n",
    271     "\n",
    272     "# Print summary of regression results\n",
    273     "slr2.summary()"
    274    ]
    275   },
    276   {
    277    "cell_type": "markdown",
    278    "metadata": {},
    279    "source": [
    280     "###Testing for Heteroskedasticity\n",
    281     "\n",
    282     "You can test for heteroskedasticity using a few tests, we'll use the Breush Pagan test from the statsmodels library. We'll also test for normality, which in this case also picks up the weirdness in the second case. HOWEVER, it is possible to have normally distributed residuals which are also heteroskedastic, so both tests must be performed to be sure."
    283    ]
    284   },
    285   {
    286    "cell_type": "code",
    287    "execution_count": 5,
    288    "metadata": {
    289     "collapsed": false
    290    },
    291    "outputs": [
    292     {
    293      "name": "stdout",
    294      "output_type": "stream",
    295      "text": [
    296       "p-value for residuals1 being normal 0.784522688195\n",
    297       "p-value for residuals2 being normal 0.000434469596894\n",
    298       "p-value for residuals1 being heteroskedastic 0.626386416784\n",
    299       "p-value for residuals2 being heteroskedastic 1.72642319402e-06\n"
    300      ]
    301     }
    302    ],
    303    "source": [
    304     "residuals1 = y1-fit1\n",
    305     "residuals2 = y2-fit2\n",
    306     "\n",
    307     "xs_with_constant = sm.add_constant(xs)\n",
    308     "\n",
    309     "_, jb_pvalue1, _, _ = statsmodels.stats.stattools.jarque_bera(residuals1)\n",
    310     "_, jb_pvalue2, _, _ = statsmodels.stats.stattools.jarque_bera(residuals2)\n",
    311     "print \"p-value for residuals1 being normal\", jb_pvalue1\n",
    312     "print \"p-value for residuals2 being normal\", jb_pvalue2\n",
    313     "\n",
    314     "_, pvalue1, _, _ = stats.diagnostic.het_breushpagan(residuals1, xs_with_constant)\n",
    315     "_, pvalue2, _, _ = stats.diagnostic.het_breushpagan(residuals2, xs_with_constant)\n",
    316     "print \"p-value for residuals1 being heteroskedastic\", pvalue1\n",
    317     "print \"p-value for residuals2 being heteroskedastic\", pvalue2"
    318    ]
    319   },
    320   {
    321    "cell_type": "markdown",
    322    "metadata": {},
    323    "source": [
    324     "###Correcting for Heteroskedasticity"
    325    ]
    326   },
    327   {
    328    "cell_type": "markdown",
    329    "metadata": {},
    330    "source": [
    331     "How does heteroskedasticity affect our analysis? The problematic situation, known as conditional heteroskedasticity, is when the error variance is correlated with the independent variables as it is above. This makes the F-test for regression significance and t-tests for the significances of individual coefficients unreliable. Most often this results in overestimation of the significance of the fit.\n",
    332     "\n",
    333     "The Breusch-Pagan test and the White test can be used to detect conditional heteroskedasticity. If we suspect that this effect is present, we can alter our model to try and correct for it. One method is generalized least squares, which requires a manual alteration of the original equation. Another is computing robust standard errors, which corrects the fit statistics to account for the heteroskedasticity. `statsmodels` can compute robust standard errors; note the difference in the statistics below."
    334    ]
    335   },
    336   {
    337    "cell_type": "code",
    338    "execution_count": 6,
    339    "metadata": {
    340     "collapsed": false
    341    },
    342    "outputs": [
    343     {
    344      "name": "stdout",
    345      "output_type": "stream",
    346      "text": [
    347       "                            OLS Regression Results                            \n",
    348       "==============================================================================\n",
    349       "Dep. Variable:                      y   R-squared:                       0.538\n",
    350       "Model:                            OLS   Adj. R-squared:                  0.533\n",
    351       "Method:                 Least Squares   F-statistic:                     114.0\n",
    352       "Date:                Mon, 21 Sep 2015   Prob (F-statistic):           4.15e-18\n",
    353       "Time:                        14:32:36   Log-Likelihood:                -481.43\n",
    354       "No. Observations:                 100   AIC:                             966.9\n",
    355       "Df Residuals:                      98   BIC:                             972.1\n",
    356       "Df Model:                           1                                         \n",
    357       "Covariance Type:            nonrobust                                         \n",
    358       "==============================================================================\n",
    359       "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
    360       "------------------------------------------------------------------------------\n",
    361       "const         -3.7552      5.981     -0.628      0.532       -15.624     8.114\n",
    362       "x1             1.1143      0.104     10.676      0.000         0.907     1.321\n",
    363       "==============================================================================\n",
    364       "Omnibus:                       10.027   Durbin-Watson:                   1.986\n",
    365       "Prob(Omnibus):                  0.007   Jarque-Bera (JB):               15.483\n",
    366       "Skew:                          -0.419   Prob(JB):                     0.000434\n",
    367       "Kurtosis:                       4.736   Cond. No.                         114.\n",
    368       "==============================================================================\n",
    369       "\n",
    370       "Warnings:\n",
    371       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
    372       "                            OLS Regression Results                            \n",
    373       "==============================================================================\n",
    374       "Dep. Variable:                      y   R-squared:                       0.538\n",
    375       "Model:                            OLS   Adj. R-squared:                  0.533\n",
    376       "Method:                 Least Squares   F-statistic:                     94.33\n",
    377       "Date:                Mon, 21 Sep 2015   Prob (F-statistic):           5.10e-16\n",
    378       "Time:                        14:32:36   Log-Likelihood:                -481.43\n",
    379       "No. Observations:                 100   AIC:                             966.9\n",
    380       "Df Residuals:                      98   BIC:                             972.1\n",
    381       "Df Model:                           1                                         \n",
    382       "Covariance Type:                  HC1                                         \n",
    383       "==============================================================================\n",
    384       "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
    385       "------------------------------------------------------------------------------\n",
    386       "const         -3.7552      3.542     -1.060      0.292       -10.785     3.275\n",
    387       "x1             1.1143      0.115      9.712      0.000         0.887     1.342\n",
    388       "==============================================================================\n",
    389       "Omnibus:                       10.027   Durbin-Watson:                   1.986\n",
    390       "Prob(Omnibus):                  0.007   Jarque-Bera (JB):               15.483\n",
    391       "Skew:                          -0.419   Prob(JB):                     0.000434\n",
    392       "Kurtosis:                       4.736   Cond. No.                         114.\n",
    393       "==============================================================================\n",
    394       "\n",
    395       "Warnings:\n",
    396       "[1] Standard Errors are heteroscedasticity robust (HC1)\n"
    397      ]
    398     }
    399    ],
    400    "source": [
    401     "print slr2.summary()\n",
    402     "print slr2.get_robustcov_results().summary()"
    403    ]
    404   },
    405   {
    406    "cell_type": "markdown",
    407    "metadata": {},
    408    "source": [
    409     "# Serial correlation of errors\n",
    410     "\n",
    411     "A common and serious problem is when errors are correlated across observations (known serial correlation or autocorrelation). This can occur, for instance, when some of the data points are related, or when we use time-series data with periodic fluctuations. If one of the independent variables depends on previous values of the dependent variable - such as when it is equal to the value of the dependent variable in the previous period - or if incorrect model specification leads to autocorrelation, then the coefficient estimates will be inconsistent and therefore invalid. Otherwise, the parameter estimates will be valid, but the fit statistics will be off. For instance, if the correlation is positive, we will have inflated F- and t-statistics, leading us to overestimate the significance of the model.\n",
    412     "\n",
    413     "If the errors are homoskedastic, we can test for autocorrelation using the Durbin-Watson test, which is conveniently reported in the regression summary in `statsmodels`."
    414    ]
    415   },
    416   {
    417    "cell_type": "code",
    418    "execution_count": 7,
    419    "metadata": {
    420     "collapsed": false
    421    },
    422    "outputs": [
    423     {
    424      "data": {
    425       "text/html": [
    426        "<table class=\"simpletable\">\n",
    427        "<caption>OLS Regression Results</caption>\n",
    428        "<tr>\n",
    429        "  <th>Dep. Variable:</th>    <td>Equity(33729 [DAL])</td> <th>  R-squared:         </th> <td>   0.660</td>\n",
    430        "</tr>\n",
    431        "<tr>\n",
    432        "  <th>Model:</th>                    <td>OLS</td>         <th>  Adj. R-squared:    </th> <td>   0.659</td>\n",
    433        "</tr>\n",
    434        "<tr>\n",
    435        "  <th>Method:</th>              <td>Least Squares</td>    <th>  F-statistic:       </th> <td>   486.2</td>\n",
    436        "</tr>\n",
    437        "<tr>\n",
    438        "  <th>Date:</th>              <td>Mon, 21 Sep 2015</td>   <th>  Prob (F-statistic):</th> <td>1.44e-60</td>\n",
    439        "</tr>\n",
    440        "<tr>\n",
    441        "  <th>Time:</th>                  <td>14:32:36</td>       <th>  Log-Likelihood:    </th> <td> -610.08</td>\n",
    442        "</tr>\n",
    443        "<tr>\n",
    444        "  <th>No. Observations:</th>       <td>   252</td>        <th>  AIC:               </th> <td>   1224.</td>\n",
    445        "</tr>\n",
    446        "<tr>\n",
    447        "  <th>Df Residuals:</th>           <td>   250</td>        <th>  BIC:               </th> <td>   1231.</td>\n",
    448        "</tr>\n",
    449        "<tr>\n",
    450        "  <th>Df Model:</th>               <td>     1</td>        <th>                     </th>     <td> </td>   \n",
    451        "</tr>\n",
    452        "<tr>\n",
    453        "  <th>Covariance Type:</th>       <td>nonrobust</td>      <th>                     </th>     <td> </td>   \n",
    454        "</tr>\n",
    455        "</table>\n",
    456        "<table class=\"simpletable\">\n",
    457        "<tr>\n",
    458        "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n",
    459        "</tr>\n",
    460        "<tr>\n",
    461        "  <th>const</th> <td>   31.0620</td> <td>    0.344</td> <td>   90.425</td> <td> 0.000</td> <td>   30.385    31.739</td>\n",
    462        "</tr>\n",
    463        "<tr>\n",
    464        "  <th>x1</th>    <td>    0.0522</td> <td>    0.002</td> <td>   22.050</td> <td> 0.000</td> <td>    0.048     0.057</td>\n",
    465        "</tr>\n",
    466        "</table>\n",
    467        "<table class=\"simpletable\">\n",
    468        "<tr>\n",
    469        "  <th>Omnibus:</th>       <td>30.398</td> <th>  Durbin-Watson:     </th> <td>   0.085</td>\n",
    470        "</tr>\n",
    471        "<tr>\n",
    472        "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  44.557</td>\n",
    473        "</tr>\n",
    474        "<tr>\n",
    475        "  <th>Skew:</th>          <td>-0.748</td> <th>  Prob(JB):          </th> <td>2.11e-10</td>\n",
    476        "</tr>\n",
    477        "<tr>\n",
    478        "  <th>Kurtosis:</th>      <td> 4.417</td> <th>  Cond. No.          </th> <td>    289.</td>\n",
    479        "</tr>\n",
    480        "</table>"
    481       ],
    482       "text/plain": [
    483        "<class 'statsmodels.iolib.summary.Summary'>\n",
    484        "\"\"\"\n",
    485        "                             OLS Regression Results                            \n",
    486        "===============================================================================\n",
    487        "Dep. Variable:     Equity(33729 [DAL])   R-squared:                       0.660\n",
    488        "Model:                             OLS   Adj. R-squared:                  0.659\n",
    489        "Method:                  Least Squares   F-statistic:                     486.2\n",
    490        "Date:                 Mon, 21 Sep 2015   Prob (F-statistic):           1.44e-60\n",
    491        "Time:                         14:32:36   Log-Likelihood:                -610.08\n",
    492        "No. Observations:                  252   AIC:                             1224.\n",
    493        "Df Residuals:                      250   BIC:                             1231.\n",
    494        "Df Model:                            1                                         \n",
    495        "Covariance Type:             nonrobust                                         \n",
    496        "==============================================================================\n",
    497        "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
    498        "------------------------------------------------------------------------------\n",
    499        "const         31.0620      0.344     90.425      0.000        30.385    31.739\n",
    500        "x1             0.0522      0.002     22.050      0.000         0.048     0.057\n",
    501        "==============================================================================\n",
    502        "Omnibus:                       30.398   Durbin-Watson:                   0.085\n",
    503        "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               44.557\n",
    504        "Skew:                          -0.748   Prob(JB):                     2.11e-10\n",
    505        "Kurtosis:                       4.417   Cond. No.                         289.\n",
    506        "==============================================================================\n",
    507        "\n",
    508        "Warnings:\n",
    509        "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
    510        "\"\"\""
    511       ]
    512      },
    513      "execution_count": 7,
    514      "metadata": {},
    515      "output_type": "execute_result"
    516     },
    517     {
    518      "data": {
    519       "image/png": 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11xjxs59BZiacey7s3t3bs5J+SItMRURERHrJ39/bQmVtE7+5/UwslqPnBXna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FzzWjp3qSkQihpbu5QQF60Yhz2cQwOAsLp8r6LmNrfys2isACA0CEVDOHOxSfYom27K6V3YGeOw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\nAADA0v4/HKMExZL9mPcAAAAASUVORK5CYII=\n",
    520       "text/plain": [
    521        "<matplotlib.figure.Figure at 0x7f52f81b1b10>"
    522       ]
    523      },
    524      "metadata": {},
    525      "output_type": "display_data"
    526     }
    527    ],
    528    "source": [
    529     "# Load pricing data for an asset\n",
    530     "start = '2014-01-01'\n",
    531     "end = '2015-01-01'\n",
    532     "y = get_pricing('DAL', fields='price', start_date=start, end_date=end)\n",
    533     "x = np.arange(len(y))\n",
    534     "\n",
    535     "# Regress pricing data against time\n",
    536     "model = regression.linear_model.OLS(y, sm.add_constant(x)).fit()\n",
    537     "\n",
    538     "# Construct the fit line\n",
    539     "prediction = model.params[0] + model.params[1]*x\n",
    540     "\n",
    541     "# Plot pricing data and regression line\n",
    542     "plt.plot(x,y)\n",
    543     "plt.plot(x, prediction, color='r')\n",
    544     "plt.legend(['DAL Price', 'Regression Line'])\n",
    545     "plt.xlabel('Time')\n",
    546     "plt.ylabel('Price')\n",
    547     "\n",
    548     "# Print summary of regression results\n",
    549     "model.summary()"
    550    ]
    551   },
    552   {
    553    "cell_type": "markdown",
    554    "metadata": {},
    555    "source": [
    556     "###Testing for Autocorrelation\n",
    557     "\n",
    558     "We can test for autocorrelation in both our prices and residuals. We'll use the built-in method to do this, which is based on the Ljun-Box test. This test computes the probability that the n-th lagged datapoint is predictive of the current. If no max lag is given, then the function computes a max lag and returns the p-values for all lags up to that one. We can see here that for the 5 most recent datapoints, a significant correlation exists with the current. Therefore we conclude that both the data is autocorrelated.\n",
    559     "\n",
    560     "We also test for normality for fun."
    561    ]
    562   },
    563   {
    564    "cell_type": "code",
    565    "execution_count": 8,
    566    "metadata": {
    567     "collapsed": false
    568    },
    569    "outputs": [
    570     {
    571      "name": "stdout",
    572      "output_type": "stream",
    573      "text": [
    574       "Prices autocorrelation p-values [  9.22951839e-052   6.54325625e-096   1.29666216e-135   1.30651874e-171\n",
    575       "   6.92102050e-204   3.24924533e-232   3.23985200e-257   2.96588565e-279\n",
    576       "   6.50391089e-299   0.00000000e+000   0.00000000e+000   0.00000000e+000\n",
    577       "   0.00000000e+000   0.00000000e+000   0.00000000e+000   0.00000000e+000\n",
    578       "   0.00000000e+000   0.00000000e+000   0.00000000e+000   0.00000000e+000\n",
    579       "   0.00000000e+000   0.00000000e+000   0.00000000e+000   0.00000000e+000\n",
    580       "   0.00000000e+000   0.00000000e+000   0.00000000e+000   0.00000000e+000\n",
    581       "   0.00000000e+000   0.00000000e+000   0.00000000e+000   0.00000000e+000\n",
    582       "   0.00000000e+000   0.00000000e+000   0.00000000e+000   0.00000000e+000\n",
    583       "   0.00000000e+000   0.00000000e+000   0.00000000e+000   0.00000000e+000]\n",
    584       "Residuals autocorrelation p-values [  9.22951839e-052   6.54325625e-096   1.29666216e-135   1.30651874e-171\n",
    585       "   6.92102050e-204   3.24924533e-232   3.23985200e-257   2.96588565e-279\n",
    586       "   6.50391089e-299   0.00000000e+000   0.00000000e+000   0.00000000e+000\n",
    587       "   0.00000000e+000   0.00000000e+000   0.00000000e+000   0.00000000e+000\n",
    588       "   0.00000000e+000   0.00000000e+000   0.00000000e+000   0.00000000e+000\n",
    589       "   0.00000000e+000   0.00000000e+000   0.00000000e+000   0.00000000e+000\n",
    590       "   0.00000000e+000   0.00000000e+000   0.00000000e+000   0.00000000e+000\n",
    591       "   0.00000000e+000   0.00000000e+000   0.00000000e+000   0.00000000e+000\n",
    592       "   0.00000000e+000   0.00000000e+000   0.00000000e+000   0.00000000e+000\n",
    593       "   0.00000000e+000   0.00000000e+000   0.00000000e+000   0.00000000e+000]\n",
    594       "Jarque-Bera p-value that residuals are normally distributed 2.11092237997e-10\n"
    595      ]
    596     }
    597    ],
    598    "source": [
    599     "_, prices_qstats, prices_qstat_pvalues = statsmodels.tsa.stattools.acf(y, qstat=True)\n",
    600     "_, prices_qstats, prices_qstat_pvalues = statsmodels.tsa.stattools.acf(y-prediction, qstat=True)\n",
    601     "\n",
    602     "print 'Prices autocorrelation p-values', prices_qstat_pvalues\n",
    603     "print 'Residuals autocorrelation p-values', prices_qstat_pvalues\n",
    604     "\n",
    605     "_, jb_pvalue, _, _ = statsmodels.stats.stattools.jarque_bera(y-prediction)\n",
    606     "\n",
    607     "print 'Jarque-Bera p-value that residuals are normally distributed', jb_pvalue"
    608    ]
    609   },
    610   {
    611    "cell_type": "markdown",
    612    "metadata": {},
    613    "source": [
    614     "##Newey-West\n",
    615     "\n",
    616     "Newey-West is a method of computing variance which accounts for autocorrelation. A naive variance computation will actually produce inaccurate standard errors with the presence of autocorrelation.\n",
    617     "\n",
    618     "We can attempt to change the regression equation to eliminate serial correlation. A simpler fix is adjusting the standard errors using an appropriate method and using the adjusted values to check for significance. Below we use the Newey-West method from `statsmodels` to compute adjusted standard errors for the coefficients. They are higher than those originally reported by the regression, which is what we expected for positively correlated errors."
    619    ]
    620   },
    621   {
    622    "cell_type": "code",
    623    "execution_count": 9,
    624    "metadata": {
    625     "collapsed": false
    626    },
    627    "outputs": [
    628     {
    629      "name": "stdout",
    630      "output_type": "stream",
    631      "text": [
    632       "Old standard errors: 0.343510916163 0.00236807424591\n",
    633       "Adjusted standard errors: 0.507679344438 0.00511956168035\n"
    634      ]
    635     }
    636    ],
    637    "source": [
    638     "from math import sqrt\n",
    639     "\n",
    640     "# Find the covariance matrix of the coefficients\n",
    641     "cov_mat = stats.sandwich_covariance.cov_hac(model)\n",
    642     "\n",
    643     "# Print the standard errors of each coefficient from the original model and from the adjustment\n",
    644     "print 'Old standard errors:', model.bse[0], model.bse[1]\n",
    645     "print 'Adjusted standard errors:', sqrt(cov_mat[0,0]), sqrt(cov_mat[1,1])"
    646    ]
    647   },
    648   {
    649    "cell_type": "markdown",
    650    "metadata": {
    651     "collapsed": true
    652    },
    653    "source": [
    654     " # Multicollinearity\n",
    655     "\n",
    656     "When using multiple independent variables, it is important to check for multicollinearity; that is, an approximate linear relation between the independent variables, such as\n",
    657     "$$ X_2 \\approx 5 X_1 - X_3 + 4.5 $$\n",
    658     "\n",
    659     "With multicollinearity, it is difficult to identify the independent effect of each variable, since we can change around the coefficients according to the linear relation without changing the model. As with truly unnecessary variables, this will usually not hurt the accuracy of the model, but will cloud our analysis. In particular, the estimated coefficients will have large standard errors. The coefficients will also no longer represent the partial effect of each variable, since with multicollinearity we cannot change one variable while holding the others constant.\n",
    660     "\n",
    661     "High correlation between independent variables is indicative of multicollinearity. However, it is not enough, since we would want to detect correlation between one of the variables and a linear combination of the other variables. If we have high R-squared but low t-statistics on the coefficients (the fit is good but the coefficients are not estimated precisely) we may suspect multicollinearity. To resolve the problem, we can drop one of the independent variables involved in the linear relation.\n",
    662     "\n",
    663     "For instance, using two stock indices as our independent variables is likely to lead to multicollinearity. Below we can see that removing one of them improves the t-statistics without hurting R-squared.\n",
    664     "\n",
    665     "Another important thing to determine here is which variable may be the casual one. If we hypothesize that the market influences both MDY and HPQ, then the market is the variable that we should use in our predictive model."
    666    ]
    667   },
    668   {
    669    "cell_type": "code",
    670    "execution_count": 10,
    671    "metadata": {
    672     "collapsed": false
    673    },
    674    "outputs": [
    675     {
    676      "name": "stdout",
    677      "output_type": "stream",
    678      "text": [
    679       "R-squared: 0.887802860768\n",
    680       "t-statistics of coefficients:\n",
    681       "const   -11.676469\n",
    682       "x1       24.201404\n",
    683       "x2       -5.862084\n",
    684       "dtype: float64\n"
    685      ]
    686     },
    687     {
    688      "data": {
    689       "text/plain": [
    690        "<matplotlib.text.Text at 0x7f52f81a6810>"
    691       ]
    692      },
    693      "execution_count": 10,
    694      "metadata": {},
    695      "output_type": "execute_result"
    696     },
    697     {
    698      "data": {
    699       "image/png": 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8u+kf+A1/yGJoGIBrelTpERERERE5C5TUl/H6zmUkOOJYMv1GosIjmTP0HH7/8m7qaGFs\n8ij2VR1iP4WsKlzHRTmzQxJHQ7MHkwki7D2b3lbaUM7aQ3kAmE1mzCZT63/NWM1WzsueRpQtsktj\nKekRERERETkLbCrdgc/w862Ji4gKDyQD2TGZHCrZSlZKFFNGJbNrxWjsSVX8bdtbzMyaQmR4RK/H\n0dDsJsphxWI2dXuMWmc9D674b2qcdac8p7SxnO9Mub5L4ynpERERERE5C+RXHwRgTPLItmPlNc20\nuLwMS49h/PBEDLeD4Zbp7Het4x873mPJtBt7PY6GJjdRPVjP4/f7eXLdc9Q467h27GWMTxmF3/Dj\nNwz8hh+f38cTa59lb+WBLo+ppEdERERE5Azg8/uwmC2n/PxA9UEiwyNIjUxqO1ZYUg/A8IxYRg2N\nJ8xioulQNum5BSzPX8WCnPMZGpfVazEahkFDs5uU+O5XkN7Y9T7bj+5lesZEvj3xGkymkytG7+z+\niMKaQ3h8HqyWzqfRqZGBiIiIiMgA4/L4+N2bn/O/Xyzjz1/9jfs++g23vHEXv/j0v2h0N510vtPn\n4mhjBSPih56QJBSVBKaHDUuPwWa1kJsdT+GRRm6eeAOGYfBs3qsn7OnTU063D6/PIKqL7ar9hp8d\nR/dS72wAYFvZbl7f+T7JEQn868zb2k14AHITh+P1eymqPdyl+6jSIyIiIiIywKzctZ01rlcxlQQS\nEovJQlJkAnsqD/DIqj/wwIX/RoTV0XZ+qSuw6eiIr7WiLiwNVnpiABg3PIHdRdVYW1I5J3MyXx3Z\nypcHv2LusJm9EndDU9c6t/kNP58VruOdPcspbSgn1hbNLZO/wctb38RsNvPj2d/vsEnByMRhkA/7\nqwrJTRzeaVyq9IiIiIiIDDAbyjZgMhtYysfg3DGblo0XM9m7mPOzZ5JfXcRvVv0Bp8fZdn6ZsxI4\nlvTUNDjZll/B/kO1REeEkxBjB2B8TiIAOwuquG3qYqwWKy9tfYNmT0uvxN3VPXpe3voWz3z1EuVN\nVczInEyTp4WnNrxAnauBWyd/o9NEZlTr5/urCrsUl5IeEREREZEBxOl1sbduJ36XndvOWcR/3Hgx\nyXGRvPN5AcVfDWd29gz2VhXw6JdP4/IGkoyy4yo92/Mruf1XH/MfT6+hsraF3Oy4tmliY4cnYjLB\nzsIqUiITuWbMpdQ66/mscG2vxN6VpOeDfStZuvcTMqPT+MNVD3PvnDt55OKfkpswjPk553NF7kWd\n3ic1Kpno8EglPSIiIiIiZ6INh7fgMdz4KjOJdtg4d0I6T90zn5nj0thXXMd5cVcwM2sKO8v38fiX\nz+D2eSh1VRJnj8Fw23jspY34/QbXXzSSHy6ezL/dOKVt7CiHlWHpMew7WIPH6+PSkRdgNpn58uBX\nvRJ7Q7MHgOhTrOnZcHgLz2/+J3H2GH4274ckRsQDMCw+i19f8lPuPOeWU67jOZ7JZCI3cTjlTVXU\nOes7PV9Jj4iIiIhIP6l3NfJF0QaeWPssD674b7aU7mRl4RoAfJWZOOyBJfjhVgu3XjkWgNc/yeeu\nc5cwPWMi247u5pFVT9LgbSInfiiPvZRHbaOLJQvH892rx3PZrGEkxjpOuOf44Ym4vX72H6olzh7D\nxNQx5FcXUdpQ3uPn6ajSs6+ygCfWPUd4WDj3zf1XUiITe3Sv3LYpbkWdnqtGBiIiIiIifcRv+Cmq\nOcSm0p1sLt1BflURBse6p+2q2A9AvDmDElcEkfZjX9eHpcdw7vg01u8sY3dRLT+Z/S889uUzbC3b\nBUC4J9Ck4PzJGSycm3PKGMaPSGTp6kJ2FlQxbngic4fOZGvZLr48uIHFE67u0fMFkx6bzcDpdWEP\nswFQ2lDOo1/8EZ/fx/+bewc5CUN6dB84PukpZEbmpA7PVaVHRERERKQP+A0/P/v4t9z38W95bcd7\nHKg+yJjkkdw06Vr+67IHeOzS/2BkwjAAUo0xAETYT5wm9s2LRwHwj4/3YbVYuef8/8OElNEAeOvj\nALj6/OEdThEbPzxQYdlVWA3AOZmTCbdY+fLgVz1uX93QFJje9o/CF/j3939JWWMFdc56Hvn8DzS4\nm/iX6d9mavqEHt0jKNi0oaj2UKfnqtIjIiIiItIHShqOUlhziOFx2Vwz9jImpY0hKvzEtsy/WnAP\nZY3lvPzOYeAIEfYTv66PGhLPtNEpbNpbzu7CasYOT+BnF/wr76/9mLXbIjGZXORkxnYYR3yMnfSk\nSHYXVuHzGzisdmZkTGLNoTwOVB8MtIPupmClp8ZVTbO3hV+u/B1xthiONlbwjXFXsGDEnG6P/XWR\n4RFEh0dS3ljV6bmq9IiIiIiI9IE9FQcAWDBiDrOHTD8p4QEwm81kxKTR7AxUTCLtJzcECFZ7Xvt0\nHwBWi5UMewoFh+vISok6qTrUnvHDE2lyejnYuo/P7CEzANjSOlWuu4JJj8vnxmqxUtVcw4Gag1ww\n7FxunLCwR2O3JyUyifKmSvyGv8PzlPSIiIiIiPSBvZWBpGdM0ohOz212ejGbTdjCLSd9Nj4nkfE5\niWzcfZQDh2sBqKr30uLykZsd36VYjt+vByAtKhmAmpbaLl1/Ko3NHswWPz7Dx9ikkfzL9Ju4Ivci\n7pzRta5spys5KhGP30ttJx3clPSIiIiIiPSBvZUHiLA6yIpN7/TcJqeHCFvYKROFG79W7SmpDlRY\nRmbFdSmWtqSnMJD0xNljAKhzNnTp+lOpb3ITFRVIMexhNi4ZOZfvTfsmYZbQrKpJiUwC6HSKm5Ie\nEREREZEQq3XWU9ZYweikHMymzr+CNzu9J63nOd6UUcmMGhLHmm2lHCyrp6Q6MB0uN7trSU9aYgQJ\nMTZ2FlRhGAZRtkjMJnOX9rzpSGOLm8iIQKIW7NwWSqnBpKepssPzlPSIiIiIiIRYcGrb6C5MbQNo\ndno6XJtjMpn45oJAtef1T/dTUuXGbDYxLCOmS+ObTCbG5yRR2+CitLIJs8lMjC2KWlf3Kz2GYdDQ\n7CEimPRYQ5/0pEQFKlZKekRERERE+tneiq4nPX6/QYur40oPwDnj0hiWHsPnmw9TUu1mSGo09vCu\nTyMbPzwBOLauJ9YWTX0Pprc1O734/Qb21r1Q7WH2bo/VVZreJiIiIiLSDwzDoKTh6Al73uytPIDF\nZG7bh6cjTrcXwzh5j56vM5tNfPPiUfgN8Pm7PrUtaNzX1vXE2mNo8Tpxe92nNU5QY0tgip2tNdfp\ni+ltSRHxmDB1WunRPj0iIiIiIr3o04LV/Hnj3xiTNIJbJn+DyuZqCmoPMTx+CLaw8E6vb3Z6gfbb\nVX/d7EkZZCZHcaSikZGnmfQMTYsh0mE9VumxRwNQ62ogJSzxtMaCY+2qw8P94AVHHyQ9VouVBEcc\nR5sqoYPtiVTpERERERHpRVvKdgKwp/IAD3z6OP+z9ll8fh8zMid16fqm1j16OpveBmAxm1iyaDwJ\n0WHMGJN6WnGazSbGDU+grKqZqroWYts6uAWaGeTtOcq+4pouj9fUHIg7LDywZ05fVHoAUqKSqG7u\nuNW2Kj0iIiIiIr3EMAz2VhaQ4IjjBzO/w8cHviA7Np1zs6YyJDazS2M0twQqPV1JegBmjkvDsjCN\nlISI0453Qk4iX+06ytb9lcRFBSo9dc56DMPgty98RXK8gz/eu6BLYwWnt1msrUlPHzQyAEiJTGR3\nxf4Oz1HSIyIiIiLSS8qbKqlz1jMrexqT0sYyKW3saY/R7ApWejqf3tZT54xL469Ld/Hl1iPMmx+o\n9NQ6G2hxeXG6fRwub8Tp8mK3dZ42NLYEpreZLcFKT+gbGUAg6emMpreJiIiIiPSSvZUFAIzpYmvq\n9gQrPZFdrPT0RHZqNDkZsWzeW47NFGi7Vuesp6F1qpphQFFp1/buCV5jCgvE3xdreuBYB7eOKOkR\nEREREeklwf14RiXmdHuMYKXH0QeVHoA5UzLw+gyKil0A1DkbqG9ytX1eUFLXpXEaWxsZYPIBfbmm\nR5UeEREREZE+s7eyAJslnGHx2d0eo6kPKz0Ac6cE1hpt2xOo6NS66mlo8rR9XnCki0lP65oewxz4\nb18lPamRyZ2eo6RHRERERKQXNLtbOFRXwsjEYYSZLd0fJ9i9zdE3lZ60xEhGDYlj5/5GTJhOrvSc\nZtLjI5C02a19s6YnzhGD1dxxgqikR0RERESkF+yrKsTA6NHUNoBmV2v3ti40D+gtc6dk4febsJnt\n1DnrqW8+tkHpwdJ6fD5/p2MEW1Z7jcC1fVXpMZvMXDv2so7P6ZNIRERERLpgw84ySiob+zsMkdNW\nXHuEZfs+BWB0D5oYADS1Vkwi+6jSAzA+JwEAi+EINDJo8mBJLSJxSA1ur5/D5Z3/uWxocWMLt+D2\ntyY9lr5JegAWT7i6w89Dlj66XC5uueUW3G43Ho+HBQsWcPfdd7Nt2zYeeughvF4vFouF//zP/2TS\npK5t1CQiIiJnr7KqJh5+bj3ZqVE8+f/mYzGb+jskkQ75/D7ySrbzwf6V7CzfB8DQ2EzGJY/s0bgt\nrZUeRx9WehJiAlPRzD4bDUY15Y2VhA/dg4kEKJ5JQUkdQ9NjOhyjsdlDlMOK0+PCZgnHbB449ZWQ\nvUmbzcaLL76Iw+HA6/Vy0003sXHjRp544gnuuusu5s6dy6pVq3j88cd56aWXQhWGiIiInCG27KsA\n4NDRRlZuLObimUNP6/qaeicRDis2a/fXUoh0RYOrkU8LVvNR/udUNlcDMDF1NJfnXsT09Ik9/rIf\nrPT0xT49QXFRNkwm8LvDwQ4HXbsCmUJYoGpTcKSOi6Z33JyhscVDUqydFq+zz6a2dVVI00eHI9Dr\n2+Px4PP5iI2NJTk5mYaGBgAaGhpITU0NZQgiIiJyhtiyP5D0WMwm/rZ8LxdMzSK8nQTGMAzqm9xU\n1Law+1ALB+v3s2ZbKXuLa5gzOYOffuecvg5dBgnDMPiscC3Pb/4nLV4nNks4l4yYy+W5F5Idm9Fr\n92l2eQkPM2MN67tKicViJjbKhtdlBTuUmwKVK6evBZPJ6LSZgd9v0Oz0EJUeQ63XNbiSHr/fz3XX\nXUdxcTHf/va3yc3N5e677+amm27isccew+/3849//COUIYiIiMgZwOc32La/guR4B3MmZ/LWZ/k8\n9fpWhmfE0uL0UFHbQkVNCxW1zVTUOnF7fMddXYXZBGEWM1v3V2AYBiaTpsZJ7/L6vPxu7V/46shW\nHFY7t06+nvk5s4kMj+j1ezW3ePqsc9vxEmLslDRZMMWC19IEgM/wkZZkY/+hWuoaXcRGtZ/MNDs9\nGAZEOayUeV1ER0T2ZeidMhmGYYT6Jg0NDdx+++3cfffdPP3009x8881ccsklfPDBB7z22mv89a9/\n7fD6vLy8UIcoIiIi/aik2s2fPyxnak4El0yN4/fvleJ0n/wVJcJmJjbCQmykhdiIsMB/Iy0MSbbx\nYV4tO4tbuGtRGvFRfbcWQgaHHfX7WVa+iix7GlenziPWGh2yez3+Zgl2q5kfLUwL2T3a87fPKilw\n5xOes+OE4+d4ruLzzT6m5ERw7ayEdq+tbvDy+/fKmJzjYH/S22TYU7gla2FfhH2C6dOnt3u8T/5G\niI6OZt68eezYsYNt27bx/PPPA3D55ZfzwAMPdGmMUz3AYJCXlzfonn8wPnN79B70Do432N/FYH/+\n452N76JwxX6gnAXnjWXutCxG5DZSfDQwHd5mtZAc7yApzoE9/MSvLse/i2pPPjuLd2KPy2L65My+\nfoR+cTb+Xuiu3n4XXx3ZyudF6/n+9G8Ra4/hvRWrAPjpgh+QGtX5Zpg94XmthPTkqNN6nt54/tX5\nmzmw91Dbz8M8cXittVxz2XgOHS1iS0E937x8KhNHJJ107f5DNUAZ2Zkp7HMZJMUl9vnvzY4KJSGb\nKFhdXU19fWBXV6fTyZo1axg7dixDhw5lw4YNAKxbt45hw4aFKgQRERE5Q2zZVw7A5NzAl8mM5Chm\nTUhn1oR0po5OISsl+qSE5+tys+MAyD9UG9pg5ay3/vBm/r/Vf2b94c38ffu7lDWUs6tiP+NTRoU+\n4fH6cXv9RNr7vlqZEGvH8IQDYPgsxPmGANDsbeaHi6dgMsEfX9+Kx+s76drG1j167I5AhXbQrOmp\nqKjgvvum963uAAAgAElEQVTuw+/34/f7ueaaa5g9ezYPPfQQDz30EG63G7vdzsMPPxyqEEREROQM\n4PL42FVYzfCMGOKiu/9FaURWLAD7lfRID6wpzuPJdc8RbrESa4tmZcEaGlyBPWouGj475PdvdvZ9\n57aghBg7htuBCTPe2mSi4qKpBBpcTUwZFs9Vs4ezdHUhb6zM51uXjD7h2sbWjnM2WyDpcYTZ+zr8\nDoUs6Rk9ejRvvfXWSccnTpzIP//5z1DdVkRERM4wBw7X4vH6mTjy5CkzpyPCbiUzOYoDh2vx+w3M\n2udHToPH5+GlLW/yYf5n2MJs/OyCf8Xt8/DrVU+2NS84N2tqyONodgb26Inoj0pPjB284Yz3LuKr\nogaizw0DLzS4A0nfLVeMZc32Ul77ZB9zp2SSmRzVdm0w6QmzDcxKz8DZMUhEREQGpbKqZgCyUnq+\nMDw3O44mp5eyqqYejyWDR1lDOQ98+jgf5n9GVkw6j1x8L2OTc5mcNo6p6eMBOH/IOdjCwkMeS39X\negAqSsPBZyXOEUhqGlyBP0+RDit3XDcRj9fPH1/fyvH90BqbA/v5WK1+AOxWJT0iIiIibcprAklP\nanzPW/+ObF3Xoylu0lVrijfy049+Q2HNIS4cfh6PXPLTE/bcWTLtRmZlTeOaMZf0STz9WemJjw4k\nPYfLA01E4iNiANqm9wHMnpjOOeNS2ZZfycq8w23Hg2t6LMGkR5UeERERkWOOtlZ6UhIcPR5rZFZr\nM4PDSnqkY26vmz9vfIX/Wfssfgx+eO53+cHM75z0ZT01KpmfnP8vIW9gENTUWumJ7IdKT3xM4Nm9\nvkAFJymqNelxH6ucmkwm7rxuErZwC8++u4P6pkCFJzi9zRwWaHKgpEdERETkOMFKT0ovVHpyMmMx\nm2B3YTV9sBWhnKHKGyv5j08f55MDXzA0NpPfXnIfFww7t7/DAo5NE+uPSk+YxUxs1LEpfClRgeYg\nx1d6AFISIrj5sjHUN7l5fulOABpbAnGbLMGkZ2A1MlDSIyIiIv3qaHUzCTE2wq2WHo/lsIUxZlgC\ne4trePzlPJxuby9EKGeTXeX7+NnHv+Vg7WEuzpnDry++l8yYvt0E9FT8foOlqwsBGNFatexrwXU9\nAPExETjC7CdUeoIWzc1heEYMH28oZndhddv0NsMU+DOnSo+IiIhIK5/PT2VtS69UeYJ+dttMxg1P\n4IstR/jZU1/S1DrtRiS/qoiHP3uCZk8Ld8y4iTvOuZnwPmhO0FUrNh7iwOE65k3Napuq2dfij0t6\noiPCibZFnlTpAbBYzHz/mgkALF9fRGOzB4fNgtsfqPg41MhAREREJKCq3onPb5CS0HtJT1y0jV/d\neT7zZ2STf7iOx17aiM/n77Xx5cz1yra38Rl+7plzJxePmNvf4ZygxeXlxfd3EW61cNtV4/otjoTo\n45KeyHCiw6NocDe1O110Qk4SSbF21m0vpbbRSaQjHKfXCajSIyIiItKmvLq1c1svJj0A1jAz//bN\nKcwYm8qmveX86e3tWuMzyG0/uocd5XuZkjaOaRkTQ3qvsqom/r58T5enV/p8fp7651ZqGlx848KR\nJMf3vKlHdyXEBpIee7gFm9VCtC0Sj8+Dy+c+6Vyz2cScKZk0Ob1U17uIclhxelyB67WmR0RERCSg\nN5sYfJ3FYuaeW6YzLD2GD9YU8c7nBb1+DzkzGIbB37e9A8C3Ji4K6b0qalq4/+nVvPLRXlZtOtzp\n+W6Pj9+88BWrNh9m9JB4rr9oZEjj60xCdKBCEx0ZmPYXZQvu1XPyFDeAuVMy234cHRGO0xtIehyq\n9IiIiIgEBNtV93alJyjCbuUXt88iIcbGc+/tYP2O0pDcRwa2LWU7ya8uYlbWNHIShobsPjUNTn7+\np9VU1LQAsGlveYfnt7i8/PIv61i/s4zJuUk8fOds7La+79p2vGClJ6Y16YkJjwSObVD6dbnZcaQl\nBv78RkVY25IeTW8TERERaXW0JrRJD0ByvIOfL5lFuNXC43/L0x4+g9COo3sBuCx3Xkjv84fXtnKk\noonrLxpJakIEW/dVnHI9WUOzm58/s4Zt+ZWcOz6NX9w+C0c/JzxwrJFBdEQg6YkOVnrc7Vd6TCZT\nW7UnymGlRUmPiIiIyInKqwP/Ih7qNQwjs+O4+6bpuD0+Hn52PZW1LSG9nwwsxXUlAAyNy+zkzO7b\nfqCSDbvKGJ+TyG1XjWPa6BSanF72FtecdG51vZOfPfUle4truGh6Fj+77ZxeadneG1LiIzCbIDku\n8Gcy2tZxpQfgounZWMPMDEmLbqv0DKSueKCkR0RERPrR0ZpmEmLsWMNC/4XvvInpfO/q8VTXO3n4\n2fW0uLSHz2BRXHeExIh4olqnavU2wzDaNulcsnA8JpOJaWNSANi058Qpbkerm7nvD19ysKyBq88f\nzo+/NQ2LZeB8JU+IsfPwnbO55YqxwHGVnlOs6QHITo3mhf+8jIVzR+D0OrGH2TCbBs4zgZIeERER\n6SfBPXpCObXt666dN4LLzxtGQUkd732hxgaDQYOrkZqWOobEhq7Ks3pbCfuKa5kzOYNRQ+IBmDQy\nCYvZdMK6Hr/f4OfPrKG0qokbLx7FHddNxGw2hSyu7po0Mrltk9Lo4JqedjYoPV50RDgWswmnxzXg\npraBkh4RERHpJ1V1Tvx+IySd207FZDLxrUtGAWhtzyARnNo2JDYjJON7vH5eXLYbi9nErVeObTse\nYbcybngi+YdrqWsMTPk6WFZPaVUTF0zJ5JYrxmIyDbyE5+u6Uuk5ntOrpEdERESkTbCJQUpC3+5J\nkhBjJ8phpbisvk/vK/2juPYIQMgqPcvXFVFa1cQVs4eRkRR1wmdTRydjGLC5tdqz/UAlQNvUtzNB\ndHiwkUHHlZ4gp9eFY4Dt0QPQ/y0iREREZFBatz3QPjo9MTTrLE7FZDIxND2G3YVVuDw+bANkAbmc\nHq/Py583voLT6yLGFkVjdQNH99URY4si2hZFVkw6iRHxxyo9cb1f6Wl2evj7R3tx2ML41iWjT/r8\nnHFpvPj+btbtLOPC6dnsLKgCYHxOYq/HEipRbY0MOq/0GIYRqPRYB16lR0mPiIiI9LlVmw7z7hcF\nZCZHcf7k0Ew76sjQtGh2FlRxqKyBkdlxfX5/6bl9VYV8VrT2hGNraja3/dhhtfPklQ9RXHcEi8lM\nZnRar8fw5sp86pvc3HLFGGKjTv6iPzQtmvSkSPJ2H8Xp9rKzoIqkOEefrmPrqXCLFVuYjcYOurcF\nubwuDIwBOb1NSY+IiIj0qYIjdfz+tS04bGH8x/dmEmG39nkMw9JjgMAaCyU9Z6aKpkDV5KZJ1zIt\nfQJ52zeRPiyTelcjeysP8MXBDSzbt4JDdSVkxKQRZundr71VdS28teoACTE2rpk7ot1zTCYTsyem\n88bKfN77ooC6RjcXTss6I9byHC8mPJL6U+zTc7xGT2DKamSIuuT1hNb0iIiISEjUNrhodnpOOFbf\n5ObXz2/A7fFx903TyE6N7pfYhqQFkp6i0sC6nn98vJfl6w72aMyDZfVs3H20x7FJ11Q0VwMwLC6b\nIXGZDInIYFb2NC4deQF3zLiZGFsUS/d+gtPrCkkTg1eW78Xt8XHTZWOxd7Cp6OxJgXv/89P9wJk1\ntS0oKTKB6pbatvVRpxKsBkWFD7xKlpIeERER6XWGYXDXf6/k539ag99vAIEW1Y+99BXl1c18+9LR\nnDshvd/iGxqs9JTWc6SikZc/3MOz7+7A4/V1e8wnX9vCL/+yjpLKrnW5kp4JVnqSIxNO+swWFs7V\noy/G4w/sxdTbTQyKy+r5ZMNBslOjufic7A7Pzc2OIynW3rYv1IQRZ17Sc82YywJ7EW3+J4ZhnPK8\nYLODaFV6REREZDDw+vxU17vYV1zLl1sD/zr8/LJdbN1fybnj09pd9N2XohxWkuIcHCxrYMXGQwC0\nuLxs3lvRrfFaXF4OOLdiHbGVj9f3rGIkXVPZ3Jr0RJyc9ABcOvICIq2BzoBD4no36Xlh2W78Bnz3\nqnGdbixqMpk4r7XaExdtIzM5qsPzB6JpGROYmj6BHeV7+erI1lOe1xhMemwD7xmV9IiIiEiva3Ed\nq5i8/MEePv2qmLdXHSAzOYqf3DRtQGzIODQtmup6Jx+tO9gWz+ptJd0aa3dRNZbUIsISS/l412Z8\nPn9vhirtKG+qJtYWTXhYeLufR1gd3DhxEUkRCYxKHN7lcTfsLONPb23De4pfw9oGFxt2lTF6aDzn\njEvt0pizJwaqmhNyEs+49TxBt025HovJzItbXsft87R7ToOmt4mIiMhg4nR7235cWtXE/7y6uV8b\nF7Qn2MygttHF/OnZJMU5WL+jFI/39BOWTfmHMNsDi7ibHUVsat2XZaB4c2U+63eU9ncYvcZv+Klq\nriE5suOpYpfnXsgfF/66y5UHp8vLk69tYemXhby5Mr/dc45UBKYvnk4CMz4nkX//9lRuu2pcl84f\niDJi0rgi9yLKm6pYtvfTds8JVnqiwlXpERERkUHA2bp+4byJ6djDA/vg9GfjgvYE1/UALDgnm9mT\n0mlyetm6//SnuG09sq/tx5b4o3y4/kCvxNgbmlo8/HXpTl5fsb+/Q+k1tc56vH4vSe2s5+mJD9YW\nUdvoAuDvH+3lYDsb2AaTntOZpmYymZg/YwhpfbwnVW+7fvyVxNiieHP3h1S31J70uRoZiIiIyKDi\ndAemt6UmRPDgv5zHf35/Vr82LmjP0NYObmmJEYwbnsj5resu1pzmFDeXx0dJc2Dd0oiEoZjCvGwu\n3dH25bi/BeNodnk7OfPMEWxikNJJped0OF1e3li5nwh7GP/+7al4fX5+/4/N+PwnLtw/Uh54nxln\n4NqcnooMj+DbE6/B5XXxyra3T/q80R2odkbbBl5yp6RHREREel1wepvDFsb4nERmjO3a2oe+NDQt\nmgXnZPPdq8djNpsYMzSBhBg7a7eX4vJ0vYvbvoM1EFkDwPemfhMAU8IRHn52PY0t7a996EuHW7+k\nt5xVSU+gXXXSKZoYdMf7awqpa3SzaO4I5s8YwgVTMtlXXEve19qQB5PIrJTBl/QAXDR8NsPjsvm8\naD37qwpP+KyhdS+fKHVvExERkcHA2drIwB4+cPdBt1jM/Phb09oqPGaziQXnZNPY4uHzTYe7PM62\nAxWYI+tIsCUzKimH4fHZhMVXUVJXzuMvbeywqYFhGB22AO4NwS/pLc6zKenp3UpPoMqTT6Q9jGsu\nyAFgUet/g90Hg0oqG4l0WImJbL+BwtnObDbz3WmLAfjrptfwG8d+fze6mzGbzES0ds0bSJT0iIiI\nSK8LVhXsNks/R3J6rjhvOGaziaVfFnY5Gdl8MB+Txce4lBEAXDVqAQZ+4ibuZNO+Mp5buvOU1/5u\n7V944NPHeyX2UwlOx2p2eUOeYPWV4MakvVXpWba6kPomN4suGEFURCCZGTUknqQ4Bxt2lrXt3+Tz\n+SmtbCIzOfKM7cLWG8Ym5zJ7yAzyq4v4omhD2/FGVxOR4RED8t0o6REREZFeF1zTM5ArPe1Jjncw\na0IaBSV17Cqs7vR8n9/gYH0xAONTA0nP3KEzuXDYeTgtVcSPyefdzwv4qJ29ewzDYHvZbvKri074\n1/Ledri8AQC/38Ddjc50A9GxjUl7XulpcXl587NAlWfRBSPajptMpuOaW1QCUF7TgtdnnJF77fS2\nWyZdR7jFyivb3qbF4wQC09sG4sakoKRHREREQuDYmp4zq9IDsHBOYFrTe18WdHrukfIGfI5AcjQq\nKXCdyWTi9unfYmhcFs7oAiIzynj6ja3sLKg64doGdxNNnhYMw6DZ3dLLTxHg8xuUVDa1/fxsmeJW\n2VRNVHgkDqu9x2MFqzzXXDCCKMeJ7dTnTApsarp6a6C5RXc6t52tkiITWDTmEmqcdawp3ohhGDS6\nmwfkeh5Q0iMiIiIhEEx6bGdYpQcCe6oMS49h7fZS9hR1XO3ZXVyOJaYKqymczJi0tuO2sHDunv0v\nRFgdmLN3gr2e37ywgaPVzW3nlDUc28un3h2aTm8VNc0n7Dt0NjQzMAyDiuYqknuhXXWz08ObK/OJ\ndFhZeFyVJ2j00HgSYuys21GK1+dvS3oGY+e29kxKDew7VNpYTovHid/wEzUAO7eBkh4REREJgWAj\nA8cZmPSYTCZuXzQeDINfP7+BippTV2GWH1yOKdzFzLRzMZtO/FqVFp3Cv557G17DQ8LkndS1NPGr\n59a3JR4lDce6ggX3N+ltX2+bfTYkPfWuBtw+D8kRPZ/atmx1IQ3N7Vd5INDcYvakdBpbPGzeWz7o\nO7d9XUpU4NegvLHquI1JB94ePaCkR0RERELAeYY2MgiaMiqF2xdNoLbBxa+fX99WuTre9qN7OOzf\ngdESyZKZ32h3nHMyJ3Pt2Mto8NaSPeMARaV1/P2jvQCUNR5X6XGFptITbFedmRz41/dmZ/+30O6p\nYLvqnq7naXZ6eOuzQJVn0dycU5634JwhALz84R4OHw28z/QzfJPR3hJnj8FqDqOiqYqG1qQnOnxg\nJoRKekRERKTXDYRGBi0eJ+VNVZ2feAoL5+ZwycwhHDhcx/+8uvmEzmd+v59nNryMYZhIqp9NtP3U\na0tunLCQ8SmjqDSKCEsrovBIHQClDRVt5zSEKOkJdm4bmRUPnB2VnvK2JgY9m9629MtCGpo9XDdv\nBJHtVHmCRmbFcdH0LAqO1LH9QCVJsXbstjOvghkKZpOZ5MhEypsq2yo9A3FjUlDSIyIiIiHQ4u7/\nSs9TG17grmW/4LPCtd263mQy8X+vn8z4nERWby3h1Y/3tX1W3lxFRXMVvupUxqWdukoAYDFbuOu8\n24m3x2LN3suRlkAnt9LjprcF/5W8tx2paMRkghFZscDZkfQcqS8FICO6+xvetri8vL0qnyiHlYUd\nVHmCvnPlOMKtgd/LmZradoLkyEQa3E1tHfU0vU1EREQGjbbpbf1U6fH6vGwt243P8PPHDS/y5q4P\nurVHjTXMzM9uO4eUeAevLN/D6m2BLl4l9WUAGM3RjMyO63ScOHsM/z77+2CC+shdgf1eGiswEdjP\nJFSVnsPlDSTHOYiNsgFnS9ITePfHN444XWu2ldDQ7OGq84cTYT91lScoKc7BDReNBNTE4OuCG8QW\nVAdat0dpepuIiIgMFsHpbTZr/1R69lUV4vK6mJYxkaSIBF7d/i7/m/d3fH7faY8VG2XjgSXnYg+3\n8Lu/b6LgSB2HW794+52R5GZ1nvQAjEkeicOfiCm6in1HD+PyusiKTQdCU+lpdnqorneRmRxFhD2Q\nfJ4tSY8tzEZiRHy3x1ix8RAAF88c0uVrvjE/lxsvHtXW0lwCUiKTADhQE6hgqtIjIiIig4bT7cUe\nbsFs7tnO7OsObeJvW9+i9Lj2zl2x/egeAC7OOZ9fXXwPQ+Oy+OTAF/zX6j/h8rpPO47hGbH85Kbp\nuNw+Hn5uPdsPFwFgdscwND26y+NkhOdgMht8sG8VAKMSA1+gQ1HpadtTJiUKR+salDN9nx6/309J\nw1Eyo1NP6pbXVeXVzWzLr2R8TiJpp9GQwGa1cMsVY8lO7fqv92AQ7OBWXBeogkbbVOkRERGRQcLp\n8vV4altRzSGeWPcc7+z5iLve/08eWfUkm0t34Df8nV67/egezCYz45JHkeCI45fzf8Kk1LHklWzn\noZW/o97ZcNrxnDcxnVuvGEtlbQubigowDBNDE1KxhnW9mjU6fjQAeRUbARiZMBQTptAkPeXB9srR\nbUlP8xle6SlvqsTj9/ZoatvKvECVZ/6M7N4Ka1ALVnqCVVRVekRERGTQcLq9nTYxqHc18tqOpWwp\n3XXStDO3183v1/0Vn9/HDeOvYnRiDlvKdvGbz5/i39//Je/vW0Gzu/39c5rdLeRXF5GbMIyIcAcA\nEVYH9839ARcMPZf91UU88OnjVDZ3vPFoexYvyOW+78zAHtNCBDF854oJp3X9uNQcDE84Hn+g2pQZ\nk0ZUeERIprcF21VnJR9X6TnDk57DrU0MsmLSu3W9YRis2HiIcKuFOZMzejO0QSvla63Do8MHZve2\nkK0udLlc3HLLLbjdbjweDwsWLODuu+8G4KWXXuKVV17BYrEwb9487rnnnlCFISIiIv3A6fISHXHq\nf/E1DIOn1r/A5tIdAESFR2KzhNPoaSbWFoXD6uBwfSmXj7yQb064mm9OuJqC6mI+3P8Zq4u/4vnN\n/+Tv299lXGQOqfUZxNiiqW6uJTkygV0V+/EbfiamjTnhnmGWMP713NuIc8Ty7p6PWLrnE7477ZsA\nVDZVYzabSXB0vD7HZDIxYXQ0nj0uJmeNYdrolNN6L6mJkfhqkwlLPgIENjCNtkWFpNJz+LjpbabW\nWYZn+vS2w91sYpB/uJYnXt3M0eomWlw+5k3N6lIDA+lcVHgkjjA7LV4nFrMFW5itv0NqV8iSHpvN\nxosvvojD4cDr9XLTTTexceNGvF4vK1as4N1338VqtVJdffr/yiIiIjIYlFU18ae3trNk4fgzah2B\nYRg43T7s4aeu9Hxa8CWbS3cwNjmXIbEZbCrZjslkIj0qmZqWOsqbqsiOzeDmyde1XZOTMIQfnPsd\nbpl8HZ8WrOaj/M/ZXLebzR881HaOPcxGUkRg/5aJqWNOuq/JZOLGCVfzwb4V7KrYD4DX7+NnnzxK\nk7uZq0cv4Lqxl+OwnnrfnSP1gVbTmd1omZwSH9GW9DjC7MTaoom2RVHaWI7f8HOoroS3dy9nQc4c\nJqSOPu3xT4izvBF7uIXEWHtbhedMn94W7NwWbADRVe+vLqSotJ4hadFkJEVy4yWjQhHeoGQymUiJ\nTORg3RGiwyMxmXq2ji9UQtpH0uEIlJQ9Hg8+n4/Y2Fieeuop7rjjDqzWQHadkNCzjaVERETOVi++\nv5uNu48yIiuWWy4f29/hdJnX58fnN065gWNZQzkvbH6dSKuDf5v1PRIj4rl9+rdOOKfe2YA9zEZ4\nWPhJ18fYo7lu3OUsGnMJ//jiLQ6bKzCZTMTaY8gr2cbh+lLsYTZyE9vvsmW1WMlNHM7uinwa3U0U\n1x6hzlmPCRNv717OppIdPHbZ/adcKF/S0P2WyQ5bGBGeDHz+bWTHZmAymYgOj8QwDJo9LXyc/wWr\nizeyungjMzImccvk68joxn38foOSikay06IxmUxt66uCyY/L66bF6yTOHnPaY/enw/WlhJnDSG1d\nR9IVPp+f9TvLSIix8eTdF/W4uYacLDkqiYN1R4gaoFPbIMRJj9/v57rrrqO4uJhvf/vb5ObmUlRU\nxMaNG/nd736HzWbj3nvvZeLEiaEMQ0RE5IxzsKyeL7cGpkAdLK3v52hOT7BddXuVHp/fxx/Wv4DL\n5+b/nPO9U7YdjrF3XtmymC2MjhrOTdNvaDvm8S1mTXEesfYYwsynrjSNS8llV8V+9lQcYG/lAQB+\nPPt2vijawMaSbeyuyGd8SvvVgO5OsQpKi4umeN8s/u+VlwDHul01uJo40lCGCROjknLYWLKNzaU7\nuHTkPG4Yf+VpdcWqqG3B7fWT2bqnjNlswmGztE1ve3HL66w5lMczC3+DrZ3EciAyDIMj9WWkRyVj\n6eDX9ut2FVVT3+TmivOGKeEJkZTW6mq0bZAmPWazmXfeeYeGhgZuv/121q9fj8/no66ujtdee41t\n27bx4x//mE8//TSUYYiIiJxx/v7RXgwDTCY4WHb6ncb6U7Ca0F6l5509H7GvqoDZ2dM5f8g5vX5v\nq8XKvOGzOj1vXHIuALsq9rP96B6s5jCmpU8kxhbNxpJtfFG0/pRJT3Bj0szo7iU9KQkR5B+OIcIU\nh2EYxyU9jZTUHyUpMoGH5t/NhiNbeHnrW3ywfyWfF63j+vFXkhaVzIHqYnIThzMt49RNFI4c18Qg\nyGELa/u1OVxfRpO7mTpnPSlRXa+a9IeC6oNsKdvFrOxpOL0uMk9zatva7YHmB7Mmdq/5gXQu+Hso\ncrBWeoKio6OZN28eO3bsIDU1lUsvvRSASZMmYTabqampIT6+4w2m8vLy+iLUAWswPv9gfOb26D3o\nHRxvsL+LwfL8R2s9rN56lIwEK9YwEwfLm1i7/ivCw45NtxrI76K8zgNAbX0Z675aj9Uc+Lpx1FXJ\na4feI8oSwYywsWzatKlX7tedd+HxezFj5osD66jzNjLMkcmOrdsDSUhYJKsPbmSqaRRh5pO/KhVU\nFhNliWD39l3ditdwB5LYz9duYvXuRirthyEe1u34ihpnHcMjsti0aRNhwK2pV7PJvovV1Zt5ccsb\nbWPEhkVz57AbT/n86/YG7uFqrCAvL9AZzmT4qG/ykJeXR0VdJQAbtm4k3Z7crefoK2+Wfsz+poO8\nu+sjAMyNxil/zb9+3DAMPs8rw2Y14akrJq+1XfXZqr/+XqhvqgXAVd8yYP9uClnSU11dTVhYGDEx\nMTidTtasWcMPf/hDIiMjWbduHTNnzqSwsBCPx9NpwgMwffr0UIU64OXl5Q265x+Mz9wevQe9g+MN\n9ncxmJ7/2Xd3AEf53jVT2bqvgoPlhSRljCQ3O/D/y4H+LvYV14D5CIXxq3irOomHLw50af3bR7/B\nj8G/nX87U9LH9cq9evIucus+Z29VAQDzRp/H9NGBcS6yFvPuno8hPZzpWVPbzjcMg4rmaurzGxmf\nMqrb9y1pLmDtnu0caYhk96EKLElmwuPBFeWDozA2axTTpx4beyYzudl1A8vzPwcMvijaQEVzNdOm\nTWPTpk1tcdS21LFs3woSI+JpCHeB2csFsyaRkxkLQPwXqygua2D69On8oehVALJyspmSPr5bz9FX\nXnz/XUyYaPY5AZg5ZhrTh5z87tv7vZB/qJa65iNcOC2Lc2cO3D8zvaE//14Y3jyCZe+vYmbuNKbn\n9t977ijhClnSU1FRwX333Yff78fv93PNNddw3nnnMWPGDO6//34WLlyI1Wrl0UcfDVUIIiIi/c7v\n92miYgMAACAASURBVLOzYh9DYzO7tE4FYOv+CsLDzEwbnUJtgwsIrOsJJj0DndPtxZJQhpsWCmsP\n8fKWN7GYLRyuL+XSkRf0WsLTU2NTctuSnqnHffGfM2Qm7+75mBUFq7GawzhQfZADNcUUVB+k1hlY\nXzUkNrPb901NCLTy/mBtEQCGN7CmZk/r2qL2ps1F26K4YfyVABTWHKK0sZzGr+3ts7JwLe/s+ajt\n5/bp8MSWbQwvHsLwuGysDgO3x4fX66P5/2fvvMPjOsu8fZ/pVdKoWb03d8vdjlt6LySkEAIJoYfA\nssvCR1i2wi6wWVhYUmgJECCkkN6b023H3ZYsq/deRzOj6TPn++NoRpbVbbUk731duSLNec857xmP\n5ry/8zzP7wm4QYJuxyAs4qyvYDhEt6uXooRczs/fxrtN+1kx7MonyzIv723E4wsRY9bR3enBnNhP\njFlHjFlPTfMAf375JCBS2+aaeFMcD37if8aNjC4W5mxmxcXFPPXUU2Ne12q13H333XN1WoFAIBAI\nFhWv1r3Dg4cfRUKiID6br2767KSNFQddPhraHawuTESnVZOdorhrfZjqery+EJpkJY0oxZLEy7Vv\nAZBqSeaW1dcu4MxGsyypkKdPvkKyOYHUU+yns+PSyYxN40jHCY50nIi+nmCysTF9DXnxWZyfd84Z\nnzfJZoz+LElAUHG0bR1Uak+mMkiwGZTIzYBncNTrfZ4BAG5YcSVPvnOCsGEQu87BnuaD7Gk+iMWa\nCqzG7vEgS2HlGO7F/bnqcvUQksOkxixhV+4WduVuiW6rbh7gvieOjxr/17ffHXOMTctT2Lhs5vbi\ngpmhVS/uvkeLV44JBAKBQPAR4M36PaglFUWJ+ZzsqeGvx5/h29u+MuH48ro+AFYVKHUW2alKdKjx\nQ+Tg1upsQ2UZJMOQxzfPuZm7Xv8JoXCIOzffhmERNS4sSSogMzaN7dkbR/UWkSSJz6y+lt31e8iK\nSyPPlk1efNas2Tsn20aatl62NZcXDymmAzIyAOkxky/QbUZF9PSfJnoiv+/I3MofawOsKUzi3z+x\nme6hPr732k8I+pTIUI/DHt3H7pn9pqizSbsz0hNprBBsHn4QcMW2XPLTY6moaiDGloRjyI9jyI/Z\nqOXKbXkUZE7ecFbw8UCIHoFAIBAI5ohmexsN9hbWp63iO9u/yj++/EMOd5Tj8g1hmcDa9VhNDwCr\nChU3JJNBS7LN+KGyrT7erxgULI9bS1ZcOv927t/jC/ooTMhd4JmNxqDR89NL/nncbWtSl89ZrYvZ\nqGV1YSLJNhPnrE7jhQ+qRrbpTMToJ0+DtBmVRfyAx04MIyJywG1Hq9IwaFfEU0ayBZWkIsWShM0Y\nS7tfMS9o7O6N7uP0LW7R0xa1Bx8rBFuGHeq2rU5neV4CNnUv69Yt7vokwcIxftctgUAgEAgEZ807\nTR8ARC2Ud+RsJBQOsadl4mLb47U9GPUaCjNGnk5npcQw4PQx6PLN7YRnAW/QR43rBLJfT3FcMQCF\nCbnROgyBwg+/cg7fuLFUifoEtQwHeUi3pkzZ0T5+ONIz4D090mMn3hhHW68S0UlPHrGrjjNYCeEH\nKUxTT3/0dZfPPRuXM2dEIj1p1rGip7VbifRkJE+/f5Hg44sQPQKBQCAQzAGhcIh3G/dj1plYm6r0\nU9mWtREJiXcbPxg1NhgKcqyzgl/u+RPdln0sy49DrR65ReekKmlVzR+Cup5Xat4mIPsIdmdiMnw4\nml4uJImxBlQqFSpZidikTZHaBqemt42kqYXCIew+B/GmuGiPnvRTevREokeS1kfbwCmiJzDaDGGx\n0e7oQi2pSLaMtdVu7XYRY9YRa1k8KZOCxYtIbxMIBAKBYA4o66piwDvIRfk7ogW+8aY4Viwpoqyr\nSnHgcnaxv+0YRzrK8QQUO15NEiTFjV6IZqcoC9amTgcrCxZvI0lPwMuzla+iQY+nKxujTiwzpkKt\nVpEYa8AV0ILeN62GpyPpbYMw7Ilg9zqQZRmbMY62tmHRc0oEJDZSj6Tx0z04BIpuwh1cvJEeWZZp\nc3ayxJKERqUetc0fCNHVN8TS3IQFmp3gw4aI9AgEAoFAMAXugIfX694lHA5Pe589zQcB2JGzadTr\n27OV3//fq//Fz/c+oLhq6cxsSdmKsWcNAC5986h9ctKUFWpD+/zW9QSCYb5773s8+WbNtMa/WL0b\np3+ILPVqCGkx6NVT7yQgyWYi5FcE4lTObQBWnRm1Sj3KvS0S9Yk3xtHa7USvU5MYO+ISFxuN9Pjp\nd498jrwhz6xcw1zg9LkY8rtJG+c96egdIiyL1DbB9BGPYAQCgUAgmILnKl/niYoXsRnjWJe2csrx\noXCIQ+3HsRliKUjIGbVtU0Ypz1W+hlqlZmPGGtamrGT/ITePPF9NKGzFlmyhsr+CYCiIRq3cpjOS\nLWg1Kmpb7eOcbe6obOrnRH0fHm+Qa88tnHTskN/N81WvY9GZSfItAzoxiEjPtFgSb6JmUEkFnI7o\nkSSJeEPsuKLHZoilrWeIjCQLKtVIbVAk0iNpfYQkHxpAlsG3wKJHlmUOtZeRGZvKktNS2NqcionB\nePU8LdF6nun1vhIIxLeRQCAQCARTUDXcNLLL1TOt8dV99Tj9Q1yQvx2VNDqpwqg18NNL/wWAzr4h\nfvbwYU429pMQa+DvP7WWI04/L9a8SVl3JaXDtUAatYrctBjq2wYJBEOzeGWTc6SqG1AKxkNhGbVq\n4gL7/a1HGQp4uHHFldQcUq5ZRHqmR7LNRLAyl/OXryJlnNqV8bAZ46jrb0SWFQeEfrciejSyEX9g\naFRqG0DscGNcSeMHTQAA2W8goPcSDodRqRYm+edkTy3//d79SEiUpq3g0sJdrFqyFEmSaHcoJgZW\ntY39JzrZuHxEELYO1y2JSI9gugjRIxAIBALBJITCIWr6GwHodQ9Ma58DbUrDxA3pq8bdLssybxxo\n4TdPH8fjC7FtdRpf++RqLCYd+p51vFjzJvtajkRFD0B+RhzVzXaaOubPzCAievzBMF19Q6QlTbzA\n3NuoXLMtnIPPr6RPiUjP9Ei2GQm7bBTq1kzp3Abw+v4mQj4dITmMO6TUgkUiPQH3cMTotH+rSHob\nWj9SRPR4zaD3MhRwY9UvjHhoHmwDFHOGw+1lHG4vI826hEsKd9E82A7A23vt1FR+wNdvWMNFm7IB\naO1SRE/mEhHpEUwP8W0kEAgEAsEktAy24wsqVtG9Q4rrVTAc4ncHH8aiN7MtawPZcRnRxaosyxxs\nO4ZBo2dFcvGY48myzM8ePsxbh1sxGTT8w81r2bV2ZP+ixFxsxlgOtB3jC6GboiYIBcMW1rWtdpLm\nwRRt0OWjrm0kfaqp0zmh6AmFQxzvqiQcMHD8hBePLwiAXisiPdMhOV5pVto1MLWpQCgsc/+TZRhy\n/RAHrpCyT0T0uBzKe356BCQa6dH6lWiPLCH7lJofp39owURPxJL6O9u+QliWebnmLfa0HOLBw49G\nx9TUBAAdv3ryOHlpsRRkxtHS7USnVZMUZ5zgyALBaISRgUAgEAgEk1DVWx/9udetiJ76/iZ2N+zh\n2crX+M6r/8U/vPwf/O3Ei3Q6u2lzdNLp6mFNyvKoYDmVpk4nbx1uJS89ll9+61zOXZc56um+SlKx\nOWMtLv8QX3n2Ln594C84fK5Romc+OFrdgyzD0px4AJq7JjZReO7gUcIqH2FHAhUN/fj8QfQ69aia\nEsHELBkWPT0DSn2N2xuYcGxX/xD+QAivS/lsuYKjRY+9X3nPx6S3nWJZjSaAVjIgB4eP4Vs42+qO\nYdGTYk2mICGHOzffxv1X/ic3rriSeGMcMVIyhHRcvDmbYCjMjx46QM+Ah7Ye15i6JYFgMoToEQgE\nAoFgEqr7FNGjVWujoifydHpX7hY2Z6yl29XLY+XP8Y0X/5X/eOvnAKyfILWtqklJkbt0S070Cf/p\n3LjiSi4p3IVapeaN+vfY03yQzCVWNGoVdROIHo8vSFuP68wv9DQOD6e2XbMzH5i4R1AgGOLJg3sB\niJcy6egdorPPLeyqZ0BCrBFJgq5+N/f+7Rif/peXOFrdPe7YSHpjyKeE+1xBRbD0e+xY9RY6ehTh\ndHp6m06jw6DRI2mU9Daj2oR6uDeQy79woqfd2Y3NEItJe4rTnCGG65Zfxs8v+QFDxzcRZ9Xz5U+s\n4lMXldDd7+bvfvYmPn9I1PMIZoQQPQKBQCAQTEJ1bz1mnYnC+BzsXgeBUIAOp7Ig3ZmzmX8454v8\n9pr/5msbb2V1yjIGfU4MGn20IemY4zUroqcoyzbhOU06I7evvZFvbL4dAIfPhVajIicthsYOJ8GQ\nHB0bCsu8sq+RL/3X69zxkzdo7Dh7W2tZljla3U2sRcemFanodepxRU8oLHP/E8cZ0nYAsKto2HLb\nExAmBjNAq1GREGOgoqGPl/c2EgzJ3PP4MbzDaYKn0typ/PvKgWHBEnIjyzL9nsGoXXVCrAGjfqzo\njNVbkXQ+UAcw60zoVAYAnAsU6fEH/fQO9ZNqTR53+57j7bg8AS7cmIVWo+KmC4v44tUrGPIokbAM\nUc8jmAHiMYxAIBAIBKfxTuMHtDo6uDB/O11DvZSmriBGb4GeGvrcA1HRE1msmbRGduZuZmfuZga9\nDgLhIBa9edxjVzcPoNepow1HJ8OiUyJBkSfxBRlx1LbY6R5UFn3Hqnv43bPlNHY4UEkQluH9Y+3k\npMac1fVXNQ/Q7/CxszQDtUoiM9lCU6eTUCiMWq08Lw0Ew/z04UO8X9aMcZ2dnLgsSvMzeJRGQJgY\nzJTkeBO9g14SYw2UFifz2v5m/vJKJZ+/arR4jojPqOgJuvEEvPiCPuL0MVQOelldOH4D21hDDF3a\n3uGfLTgkA0EWLtLT6epBRh7XkjoQDPPUW3VIEly8OQdQrLqv2pFPxhIrj71ezeYVU9t7CwQRxDeS\nQCAQCASncKK7mnv3/xFZlnmzfg8AxYl5BMPKU/dedz8dzi4MGj02Q+yY/SP9UMbD4wvS3OlgaW5C\nVDxMhkWnCCeXX6nbKMhQznei2cPRBz5gf0UnkgTnb8jkk+cV8vX/eYsPTnTw6UtKZnbRp/Hnl04C\ncNHmLACyUmKobR2ks99NepIFrz/Ij/54gMOV3eSUBOiSwpSmLqMwMw6NWkUwFMagE5GembA0J57m\nTif/8oXNpCVZKK/r49l36thRmk5h5khUsCkS6fErURpX0B2t59GhfF5OT22LEDEzAIg3x9CrMTKE\nYmSwEETSRFPHET1/fbWSxg4HF23KjtY8RVhbnMza4vGjQwLBRAjRIxAIBIIoXn/wY/2E3u518Iu9\nD6BCYk3aCg61lwFQlJBL91AfAN1D/XS4ukmPSZmWvfCp1LbaCctQmBk3rfGRSM/QsOjJT1f2e7/C\nCThZkZ/A569aETU5WFWYyOHKbjr7hkhJGD/SJMsyQ54APXYPPQMeegbc9Ng9hMIy1+zMp7nTybGa\nXtYWJ7OqQOkZkzWcRtTc6SDOouc/HthHRUM/a0sScGW8CQ7YkL4anVZNUVYcFQ39GMZJrxJMzK2X\nL+PTl5Sg1Shi8c4bVvNP9+/hl48d5Wff3BkVk9G6rZAGNRpcoRHRIwUVIXS6iUGEqG01EG+yYtIq\n4x3e2asFmwmRiGlazGjRU9HQxxO7a1gSb+LzVy1fiKkJPoKIbySBQCAQAPDW4VZ+/tfDfP2GNZy/\nIWuhpzPvhOUw9+z7A3avg1tWf4Iriy/kldq3Ke+qojgxn/BwE8jq3jr8ocC4T6dPpa3HxXtH27j2\n3ILoQrZ62MSgOHviep5T0Wv0qFXqaPpRdmoMyTYjgYCfr35yLZtXpI4SXptXpHK4spv9Jzq5akf+\nmOPd/aeDHDjZicc3foPT1/c3YzUpBfKfvWxp9PWs4VS8sro+Hnmtmvq2QbavSSd7TSdPVLRzft42\nChJyAFiepzi4iUjPzJAkKfo5AVhVkMSFG7N4bX8zT71Vy/XnF9He4yIYkslIttDa7UIvmXAGh0Z6\n9HiUlLeJIz0jUcgYgwWzVvm3XijRMxLpGYnauL0B/vevh5GBv//UWkyGsQ6IAsGZIESPQCAQCABo\n6XISCsv836NHMOg0nLM6baGnNK88ffIVjnedZG3qCq4ovgBJkrikcBeXFO4CINGkCJXjXZUApE1Q\nfB3hmXfqeGlPI0aDhqu2KwKkumVqE4NTkSQJi9YUFT1ajYpf33UBR48cZv3Ksf8+m5ancN/fjrGv\nfKzo6Rnw8M7RNuIselbmJ5FkM5IUZyQxzkiSzUhD2yAPPl9BR98QO9akk58xEo3KSlEWy8+9qzjZ\nXbw5m8svSOR7r/+BBKONz6y+Njp2WW4CUCMiPbPA7Vcu58DJLv76ahXnrEqjabieZ01hEq3dLnRh\nK3a5jYePPw2Az62856eng0U4Nb3NojNj1SuiZ3ABIz1qSUWyeaQG6cHnTtDZ5+a6cwtYnpewIPMS\nfDQR30gCgUAgABjlFPU/fzmIXreJ9Usnj2Z8VKjorubR8udIMNr42qZbUUlj620STEq/mohtdapl\n8vemo1cRKn97o4aLN+eg16qpbhogzqqfUUNFi86Mwz+yKNWoVROm1cXHGCjOsnGioY/mTgeZS6zR\nsSfqlQL2684r4JqdBWP2XZabwOqiJF7f38zVpwmmpDgjRr0ajy/EtbsK+MxlxXz/jbsJhUN8acPN\nmHQj17MiP4F1JclsWZE67WsUjI/FpOMrn1jFjx86wC8fP8ryXEUErCpM4vn3G4gf2oA1MUSLtxMA\n16AaCJFkm1r0WPVmzHoVsk8drRmbb9qdXSRbEtGolAjX/opOXtnXRG5azFnXpQkEpyNEj0AgEAgA\npcge4M7r1/CrJ4/zoz/s59++uIWVBeM7QS0ktX2N/ObgX0g2J5IXn0WeTfkvxjBzC9tBr4Nf7H0Q\nCYlvbv38hJ3p9RodMXoLDp8iQCay2Y3Q2aeIngGnj1f2NlJanEzvoJdNy2dWC2TRmehwdSPL8rT2\n27IylarmAb5295skxhr47q0bKM6Op7xeqUma7Ol5RrKV264YW0OhUkl8+ROrCIZkLtqUxTOVr1I/\n0MzOnM2UnmbNbdBp+Lcvbpn29QkmZ+uqVDYtT+GDE500tismBsXZNgw6NZ5BPZ9ZfTlSmp5uVy9P\n/C2AzRpGrx0/tfDUmh6LzozJEEQe0jK0AEYGTp8Ll3+I4sQ8AAZdPn752FE0ahXfunndqFQ/gWA2\nEKJHIBAIBMCI6Fm/bAnfi93IDx/8gB88uI8ffHkrxdnxCzy70bzZsIdGeyuN9lb2tx2Nvp5oilcE\n0LAQKk7MxzhcrD0eYTnML/f9gQHvILes/gTFiWPrYE4l0RQ/LdETDIXpHvCQucRCr93Dw69W8ccX\nFUe0dSUzc50y60yE5TCeoHdUA8eJuHxbLnqdmrK6XvYc7+DhV6r49y9tobyuD6NeQ17aWMe56RCp\n82p1dPBY+fPEGWK4dc0nz+hYgukjSRJfvW4VZXW9uDwBrCYtNqsem9WA3elFkqysS1tJKCzz64Hn\nKJjEJOPUhwJWnRmTYQiCWtzB+Y/0nOrcJssy9/7tGHanj89dsZzss7RcFwjGQzQnFQgEAgEAXr9S\n3G7UaVhXsoR/vGU9Pn+If/vtPhraBxd4dqOp6K7BoNFz7xU/5DvbvsJ1yy6jNHUFgXCQ/W1HeaTs\nWf7rnXu467UfIw8bEITCIfrcA6OOc3odz1QkDqe4xeqtmHXjpxAB9No9hMMy+RlxXLEtjyFPALNB\nwzdvKo32HJkup9tWT4VBp+GKbXncdetGirNsHK3upq7VTluPi6W58dOyyp6IcDjM/fv/RDAc5Ivr\nb56wF5FgdkmINXLb5csApb5KkiTirHrsLj/hsPL57h/0EgrLE9bzAMTpR8SERW/GpNcgB3X4w36C\nobGNUOeSqHObNZndB1vYW9bBivwErt45+YMHgeBMEZEegUAgEABKpEeSQDecGnPOqjT+7qa1/O9f\nD/Mvv97LjrXpHKnqIT89lm99et2CzdPuddDm7GR1yjKSzAkkmRNYn74aYLgzvZ36gWaerHiJuv4m\netz9JJsTeK7qdf5a9gz/uuubLEsuomGgZco6ntOJmBlMldoWqedJTTBz/flFFGTEsaYo6YycqEbZ\nVptnVth93oZMqpoHuP+J4wCsOMvC8BdrdlPT18DWrPVsGH7PBfPDxZtzsLv8LMtVhLctRk84LOP2\nhwHo6lc+c5OJHpPOiFpSEZLDWHRmjAYnclD5TLr8Q8QZzywKeCY09ncA8Oo7fTRUD2LUa/j7m9ai\nVs3MBl4gmC4i0iMQCAQCQBE9Bp0a1SmLjvPWZ/LV61Zhd/l49p16WrqcvHW4lZYu54LNs6K7BoDl\nyUVjtkmSRILJxob01WzL2gBAZU8tAAfajiHLMo+WP4csyzxS9iyyLPPlDbdMWMdzOolmZcE5lV11\npJ4nJcGMVqNi66q0M7bejURTXGdQd7F9TToatYqqZiXCtSLvzOuzOpzd/LXsWWL0Fm5fe+MZH0dw\nZqhUEp+6qJjVhUrvpDiLYk/t8igR2u4BJRKYPIGJAYBKUhFjsKJX69CptZgMGhgWPfPdoLS8pRmA\nymovGrWKv7uxlORJBJtAcLaISI9AIBAIAMW9bbzGpJdtzVUaXcow4PTy80eOsPtgC7cOp9vMNxXd\n1QAsSyqcdFxJkuJQVtlTy/r0VdT1NwFwsqeWJype4khHOcuSClmdsnSyw4wixaJEeDJjU/mgvIOi\nLBu2mLE1Q519ygI0JeHsF3FmrXKMMxE9VpOOTctTeP94OzqtetJ6j4lwBzzsaT7Ic1WvEwgFuHPT\nrcRMUyQK5o7I527IG4n0eACmFA5bM9fjDihjTQYNckART31uO5mx82dT3+vpQ0bF/33jErJTYmfc\n6FcgmCki0iMQCAQCALz+IMYJequsLU5mbUky29ekYzZo2H2whdBwLcF8U9FTg16jJy8+e9JxOXEZ\n6DV6KnvrONlTS1gOR53GHit/DoCbVl49rcXWwZNd3PT9F0lUZfGNzbdTZF7DD3+/n7vuew+X2z9m\nfEffSHrb2RKp6Rk6Q1vh8zZkAlCSbUOrmdlt3xf08+1X/pPfHHyYTlcPlxTsYnPG2jOah2B2sVmH\nIz3e4UhPv/L5mCy9DeDW0k/y1Y2fAcCk1yJ7lc9Xm6NjrqY6Lh55EMlvEoJHMG8I0SMQCAQCADy+\n0JQNJXVaNdtLM+h3eDlW0zNPMxth0Oug1dFBSWJetLfHRKhVaooScml1dLC35RAAV5VcyPq0VQCU\npi6nJGl6RdNHqrsZ8gQ4UNHNtuwN1DQp6X1tPUP8+KEDBEPhUeM7+4bQ69TEDS9MzwaLPhLpOTPR\ns644mevOLeBTFxXPeN9jnRX0DPWxOXMt913xn9y+7kaxQF0k2KxKpMflUT57kfS2mfSAMhk0hD1K\n1K7V0TnLM5yYzkE7sjqAWS0Ej2D+EKJHIBAIBMiyPGmk51TOH44cvHGgea6nNYaKHqWeZ1nS2Hqe\n8SgZtqB+r+kAWrWWwoRcbllzLaWpy/nsDOyWu4bT1SoalMaklU3K/wsz4zhW08tvniqLusTJskxn\nn5uUeNOsLOjOJr0NQK1WcdsVy1mRP/N6nv2tih341SUXkTBs4iBYHMSdFunp6ncTH2OIGpFMB6NB\no0R6ZInWOY70/Omlk3zt7t34AyGONDQCkGxKmtNzCgSnIkSPQCAQCPD5Q8gyGHRTL5iKs2ykJ1nY\nV9bBkCcwD7Mb4XhnJQDLkiev54kQqesJy2FKEvPRqbWkWZdw1447SY9JmfZ5u4ZThyob+wmHZaqa\nBjAbtfzwK1vJTYvhpb2NPPdePQCOIT8eX1Cpg5oFRowM5reXSjAc4lD7cRJMNvJsWfN6bsHUjIie\nMKFQmF67Z8rUttMxGbQgq9CFrbQ6OqLCfS74oKGCtnA5hyq7qOxoASA7fvp/gwLB2SJEj0AgEAjw\n+JUeHVOlt4HikHb+hkz8wTDvHWub66lFCckhPmg9gs0QS2F87rT2KYzPiVpRr1xSckbnlWU5Knpc\nngAVDX109A5RnGXDZNDy/ds3EWfV88Az5Rw82TVSz5M4S6JHd+bubWdDRXc1QwEPG9JXixSkRUi0\npscTom+4R89kzm3jodOoUKsk1IEYhvxuBn1z58rYZziOLuckrx09SVO/kkpXkpo+Z+cTCE5HiB6B\nQCAQ4PUpKTKmaYgegHPXZSJJ8PLhE7zdsG9OnxBHaHC34vIPsTVrPSrV9G5fBq2B3DglHW9F8sxr\nWgCc7kC0hxHA02/XAYoxACgWwf/0uY2o1Sr++08H2X9CWdDNVqTHrFVqNM7UyOBMiaS2bUxfM6/n\nFUwPrUaNxajF5Q3RFbGrjp9+PQ8oDzBMBg34hut6BucmxU2WZYKS4hh3vKuS7qFeAEpSM+fkfALB\neAjRIxAIBAK8M4j0ACTGGSkukWiNfYV79/+Rwx3lczk9AE44FbGxLXvDjPa7dvmlXFKw64xTtCJN\nH1cO18R8MCxqinPio2NKsuP5uxtL8fiCPP6GUnc0G3bVoBgyGLUGXL75i/SE5TAH2o5h1ZlZOpwi\nKFh82GL0OD0hWof7Zs00vQ3AaNASdisCfa7qelyeAGgUl0PZ3INP5QRZInmGzXYFgrNBiB6BQCAQ\n4PYOi55p1PQAVPbU0R7zBpJGqel5t2n/hGP3V3RS0zJwVvPzBLzUDjWRak2esXjZkL6a29fdOO3o\n0OlEeu5sWJaC2aCIQklSaptOZefaDG66cCSaNBt21REsOjOuwPxFehoHWhjwDrIubRXqKVzyBAtH\nSoIZr1/mvieOA5M3Jp0Ik16D36Xs1zZHDm79g56o6FHF9KPSD2FUWdGoRbtIwfwhRI9AIBAIopGe\n6bi3gdLnJiD7oWktkt/CgdZj0YaHp/LSngZ+8MAH3PPYsbOa3/7WowTlENuzN857fUmknic1TQoB\nZgAAIABJREFUwRSN7mQusWI2aseMvfniYi7cmEVOasysdpe36EzzamRQ1auYMixPnp5LnmBh+OZN\na9m+3IrZoEGjVpGVYp3xMYx6DV6HAYm5c3DrsjuRVEoKrKQJIOn8JBpFlEcwvwiJLRAIBB8z2p1d\n6NRaEk0j6VmRmh6Dbnq3hRZHB8nmBEpyN/BGswM5o5b9rUfZlbslOubNQy3c/6TyBLq120koLKNW\nnZlgifTZ2ZY1s9S22SAiepYkmFmWE8/hym5KsuPHHStJEt+4sXTW52DRmfEFfQRDwQmfjnsDXhrs\nLSxNmp6z3WTU9DcCUJiQc9bHEswdMWYd56+O5c6bt+NyB0iInVlNDwz36gmpSTDZ5qxXT+egEunV\nSjrlYQmQl5g6J+cSCCZiWpGePXv28Oc//xmA3t5eGhoa5nRSAoFAIJgbavsa+fYr/8kP3voFYXmk\noabHN/1Ij8s/xKDXQXpMCuevzyLUlwaMTnHbW9bOzx85gsmgpTjLhj8YpmfgzCIVsixT1VdPnDaG\nFGvyGR3jbOgadmNbEm9iy8pUYi06tq1Om9c5mHXDvXomSXG7d/9D/Ovun9Hu7Drr89X0NWDWmRbk\n/RbMHJNBe8aRRZNBiVimmJcw6HXMSe1Yl2MQgIKYkfTPTJuwqxbML1OKnl//+tfcc889PPTQQwAE\nAgG+973vzfnEBAKBQDBzQuEQzfY2Ol09OH0uQuFQdFv3UB8/efc+AqEAHc5uTnRXR7fNJL2t3aEs\nqtOtKZTk2Ei1JiG74ijvquLRsue4/50n+Z+Xn0CX3MYnrzWTUeAGjZ/WbtcZXVOXq4chv5tU/cI0\nMuzqdxNr0WHUa8hKieHP/34ppcXzKwamsq2u72/ig9YjAHQ4u8/qXA6fiy5Xzyi7b8FHF9NwnVqi\nQfn7motoT9+QInoyYlPJjssAIMUiGpMK5pcp727PP/88TzzxBDfccAMAqampuFxnduMSCAQCwdzy\nRMVL/O3EC6Ne02v0mLQG/KEAQ343u3K38FbDXl6vey/auyYS6THopy5ajyyK0mJSkCSJ8zZk8tcD\nGegsdp6oeBEA9bDXwGM1SnqbrjCO1u61rF+6ZMbXVNPXqJzPMP+LpHBYpnvAQ156zLyf+1QskUiP\nb/xIz6Plz0d/7nP3n9W5avuUbI6ChOn1QhJ8uIk86LBplb+vRnsLJUn5s3oOu9sJGkiyxGKLKaXV\n0UGOTdhVC+aXKUWPwWBAp9PNx1wEAoFAcBbIssz7TQfQq3VsyVqH2+/BHfAwFHDjDngJyzKfXH4Z\n1y+/grq+Rva3HWXQ6yDWEDMieqZR09PuVERPRoySnnLuukz+8nI6MfolOLxDBMJ+rj0vl/QUE/6Q\nnxcq36RT7qaxuw+Y+WKqdri+ZCEiPf0OL8FQmCXxs+fEdiZERM/QOOltVb11HOkoJ0ZvweFz0es+\nO6e8iMgsEqLnY0GkyWmsSnkgUd1bzyWFu2b1HA6fCzSwJMbGpszVXJC/jTjDwj5IEHz8mPLulpqa\nysGDBwEIhUL8+te/pqhIuLkIBALBYqPV0UGHq5tNGaXcsfGzk449P38bfzjyOG837uOqkovw+pU0\nuOmkt7WdEukBxSZ3VUESx2p6UUlxfPsz69m2eqTTut3j5MmTL1JvrwM2UtvXyDuNH0QtpB0+F/6Q\nn8uLzhu3CL+2vxG1pCJZP/9uT1ETg1l0YjsToult49RbPFr2HAC3rrmeX37we/rOWvQMR3ric87q\nOIIPB/ExBuUHrxmrzkxVb92sn2MoqGQI2UxWVCqVEDyCBWHKZN3vf//73HvvvdTU1LB69Wr279/P\nXXfdNR9zEwgEAsEM2N96FIBNGWumHLsjZxNatZY36t8HwDuD9LY2RydWvYUYvSX62lXb89FpVHz9\nhtJRggdgdaqSQtcdbAHgt4ce5uXat3ixejcvVu/mvab97G89yr+9+b88Xv484fCIwUIwFKRxoIWs\nuHS0qvk3HI00Jl00oue0mp7yrkrKu6soTV3Olsy1SEhnJXrCcpja/kZSrclY9Asb3RLMD/Gxiujp\nd/ooSsyjx91Pv9s+q+fwhBQ7e+sp3xkCwXwz5R0kOTmZ3//+97jdbsLhMBaL+MAKBALBYmR/61HU\nKjVrU1dOOdaiM7MiuZgjHeU4fa5pu7cFQgG6hnopTsgb9frG5Sk89qMrxrWkLozPRZI1BA09VHTU\n0zDQwuqUZdy86hpkOYxVb6FnqI97Pvgjj594gfLuar6++TYSTfE0DbYRCAdReWw8/HYvpaUyqjO0\nvZ4JDe2DnKjv40hVD7AYRM/Y9DZZlnlkOMpz44or0ag1xBqsMxY9gVCANxv2cqyzAovOjDvgYX36\nqtmbvGBRE4n09A96Kc7O51B7GVV9dWwxrZv2MZo6HPz4oQN87orlbFw+2pXNHwgRwocaIXoEC8uU\nkZ6nn34au92OyWTCYrFgt9t59tlnpzywz+fj+uuv5+qrr+ayyy7jpz/96ajtDz74ICUlJdjts/s0\nQSAQCD6OdA/10WBvYUVyMSbd9Hp1ZMYqtsstgx0jomeKmp5OVw+yLEdT205loh48GrWGeHUaKpOL\nx8tfAuDigh3k2jLJi88myZzAsuQi/vvi77Epo5STPTV855X/4kDbMWqH60s6mrVUt3mpbxuc1rWd\nKaFQmEdfq+Kb//s2v36qjP0VnUgSZCTPvOnjbBI7nA7UOjjirHWk4wTVffVsTF9DXnw2AAlGG30e\n+yg78okIhAK8Wvs233jxX/ndob9yoO0YbzbsAWBpYsEcXIVgMRIVPQ4vJYlKzV1Vz8xS3P7ySiWt\n3S7+5y+HaO12jto24PSBxg8yWLQL+/BA8PFmykjPAw88wDXXXBP9PS4ujgceeICrrrpq0v30ej0P\nPfQQRqORYDDIzTffzMGDB1m/fj0dHR28//77pKXNb58DgUAg+KhyYDi1bWP61KltETJjlOaArY52\nvH41kgQ67eTpbZF6noxxRM9k5MXk0Wdv5kR/ObGGGNakrhgzxqIz8w9bv8jrde/xh6OPc/d7v4ou\n9ge6FCF3qLKLgsy4GZ17unT0DvGzhw9R2TRAYqyBmy8uwWTQkhBnIMk286aPs0madQnp1hQOth/H\n6XMhyzKPlT2LhMQNK66Ijksw2agbaMLhc01YN+EPBdhd/z7PnHyVPs8AOrWWy4vO5+KCHTj9Qwx6\nnaxJXT5flyZYYEwGLUa9mn6Hl7z4bNQqNVW99dPev6XLyd6yDuKseuxOHz/64wF++o0dGIajxgMO\nL5LWj1YyROv4BIKFYErRI0ljn9ydmm89GUajcpMIBAKEQiHi4pQb1Y9+9CO+/e1vc8cdd8xkrgKB\nQCCYgIPtijX0hhmkJWXGKqJHifSkYNCpp0wdi5oYWGcmelanlnDA/hYAO3M2oVGNL64kSeLCgu2U\nJOXz8z2/o8XRgV6tx+NR6ksOVXZz44XF4+57psiyzBsHmvnN02V4fCG2r0nnjutWYTEtHudSSZI4\nN28rfz72JO81HWBgOLJ3TtZ6suJGaqgSTDYA+t0D44qefS2H+cORx+n32NGptVxRfAFXlVwYHSva\nRX48iY8x0O/wolNrybNlUdffhDfow6DRT7nv33bXAHDHdas4XtPL8+83cM/jx/jWp9ciSRIDTi+S\nJoBRLWrEBAvLlJI7MTGRV155Jfr7yy+/TELC9Bx0wuEwV199NVu3bmXTpk0UFBTw+uuvk5KSQklJ\nyZnPWiAQCARR3AEPlT215NuyiTPGTnu/9JhUJCRaBtvx+oIT2lXLsky7o5NOZzetjg5g5pGe9TlF\nyEGl8/u5uVunHJ8Zm8aPLvwun1x+GZts5wGKGKtq6sfp9tPV7+Y3T5dxuLKbcFie0VxOZdClPJn+\nxaNHkSSJb928lm/fsm5RCZ4IO3M2oZZU7K5/n/f6D6OSVFx/SpQHRkTPeLbV4XCYez74Ay7/EFcW\nX8A9V/yQz665TjhpCYiPMTLo8hMIhilOzFcMLYZTSyeju9/N24dbyVxiYdPyVG6/agUl2TbePtLK\nC+8rLoB9g17Q+DFrhegRLCxTRnr+6Z/+iTvuuIO7774bALVazX333Tetg6tUKp555hmcTief//zn\nefvtt/nNb37Dgw8+GB0jy9O7WR06dGha4z6qfByv/+N4zeMh3gfxHpzKeO9FtauRkBxmCfEzfq9i\nNRYa+lrwuwrRaVXR/YPhIM2eTurczdQONeMIjjSl1khqmiobaJGapn0eWZahvQityU9nTRudtE1r\nv3zSqK23Ay4KUg3Udnj520sfsL/KRWufn+fercdmUbO+wMKaPBNmw9TucxEGXEEefK0bpydMdrKO\nT2yJx0o3hw93T/sY802+KZPqQeV9X2ktoqO6lQ5ao9sdTkXsHK06jrorNGpfZ3AIfyhAiSWXZaEc\n6k7UzN/E55iP+3fEWV9/UHEFfGfPAbTDy7I3j7+LL37yZvTvVzgJhWVKc7QcOXIYgEtL9TR3qvjt\nM2UEXZ2c7BhEMoEqKM3Lv5P4LHy8r38yphQ9+fn5vPDCCzQ0KIo9NzcXjWZmtqFWq5WdO3dy4sQJ\nWltbo/VAXV1dXHfddTz++ONTRo/WrZu+i8hHjUOHDn3srv/jeM3jId4H8R6cykTvxcEDlQBctvYC\nihLzxmyfjHz3BxxqLwO1n9gYG4M2H4faj3O8qxJf0AeASWtkS+Y61Co1LYPtLEsqZMPaDTOef+5e\nD1WNAyz/wupovj9AMBTG6w9hMWrH3e+Zg3sAF+css1Db4eWN4y4GXX7WL12Czarn7SNtvHZ0kDfL\nnGxbncalW3NYmhM/bnp2hFAozHfvfQ+nJ8zNFxVzw4XFExoxLCakdh0/fvc+VKj48s7Pkmwefe+0\n9MbxbNebmBItrFs9+rNS3VsPjVCQns+6NR+dv6mP+3fEbFz/sfYTlDXVkp5dyLolS3nqmddx6b1T\nHvdoWzkwyM7NKynKskVfT0jp4V9+vYen9zvJyFQeRGQkpc75v5P4LHy8rx8mF30Tqhe/349Op8Pj\nUbzVMzIyAKU+JxAIROt1JqK/vx+NRkNMTAxer5c9e/Zw5513jqrjOe+883jyySejtT4CgUAgmBmy\nLHOkoxyLzkyGJWPG+2fGpnGovQy/ehCvrZNfHSgHINWazLq0VaxLW0lxYv6ENTgzoTjbxsnGfmpa\n7KwsSORodTf/99hReu0eZBmu3J7H569aMUZ8NHU6SLIZyU7WE2fRY3f5iDHr+OZNpcRa9Nx+5XJ2\nH2zhxT2NvHW4lbcOt5KTGsOlW3PYtTYDk2GsmHrs9WoqmwbYsSadmy4qnlQgLSZWpyxjbdpKLF79\nGMEDk6e39XmU1xJNtjHbBB9vTrWtLslOI8WSRHVvPWE5jEqauBLC6fYDYD0tHXR1YRK3XLqUh148\nyUBoAP0ySDCLNErBwjKh6Lnhhht4+umnKS0tHbNNkiROnjw56YF7enr47ne/Szgcjtb2bNmyZcxx\nBAKBQHDmtAy20++xExPI4eZ/fpnS4mR2rc1g88pU9FM4sQFkxigumpLJgdPQiEVn5ocXfJs065JZ\nn+vSnHiefruOyqZ+VhYk8tLeRnoGPCzNicfu9PHcu/V09bn5x1vWRfsFOYb89Dt8rF+6BJUksWHZ\nEl7b38yXP7GSWItSZG0x6bhqRz5Xbs+jrK6XF/c0sq+sg/ufOM7r+5v56d/tGHW/qW2x88hrVSTZ\njHz1k6s/VPcitUrNd7ffMeHTTJshFkkav0Fp5LVEU/yczlHw4SPhFNtqgOLEfN5u3EfrYMcoo4zT\ncQ4FALCax9bAffK8QqqaBjjQ1gVAvBA9ggVmQtHz9NNPA1BZWXlGBy4uLuapp56adMwbb7xxRscW\nCASCjyuyLI9apB/uUCIzvc1WTAYtB092cfBkF2ajlnPXZnDR5mxy0yY2N4g4uGlSGgmpfJyXt2NO\nBA9ASY6y2D7Z2E8oFOZYdQ/J8SZ+cuc2hrxBfvLHA+yv6OSu+97jn2/fREKskaYOBwDZKVbAy21X\nLGfXugxW5ieOOb4kSawqSGJVQRL9Di8/eegAFQ39dPW7SUkYKaJ+6u1awjLc+ck1E6bUfVhRq9TE\nG+LGFT29Q/3ASDRIIIgQHzu+6KnqrZ9c9Lj9qCQwjdPUWJIk/v5Ta/n678twATGiMalggZm0OCcY\nDHL99ddPKV4EAoFAMHscbi/n6ZMv4wn68Af9+ELKf96Aj1Dt7yhJzOfiwp14Az6eLt8NQIYpj7u/\ndQG9dg+7D7bwxoFmnn+/geffb6AgM46LNmaxozQD82mL/LSYFCQk0Cn1Oxfl75iz64qPMZBsM1LZ\nOEB1s50hb5DtpRlIkoTFqOVfv7iZ+584zqsfNPGPv3iHf/nCZpo6FdGTkxoDeIkx61hVkDStc52z\nKo2Khn5O1PdFRc+A08ue4+1kpVgpLZ76OB9GEkw2avsbCYfDo/qi9Ir0NsEERNLb+gYjokepDazq\nrePCgu0T7ud0+7GYdBNa3ZuNWi7fkcGjJw4J0SNYcCYVPRqNBpPJhNfrxWAwzNecBAKB4ENPXaud\nquYBLt2SM6P0qbAc5o9HH6fD2Y1Ra0Cv1qFX6zDrTASlACazicreOip7RzqmawZy+ffP7cSo15C5\nxMqtly/jlktKOHiyi1c/aOZgZRf3PXGc3z17gs9dsYwrto2YHejUWhIMCfR6e0lUZZNsGRtBmU1K\ncuJ550hb1M62tGhEeGjUKu68fjVpiWb+8EIF/++ed8lItgKQnRpDf8fMXNWW5yk1L+V1fZy/IQuA\nV/c1EQzJXLY190OV1jYTEkw2qvvqsXsdxJtGamb73ANoVRpi9NYFnJ1gMWKLUVJFI5Ge9JgUzFoj\nVad8z4yHyx3Aapo8WuoedoazCtEjWGCmtGHLycnhlltu4eKLL8ZkMkVf//SnPz2nExMIBIIPM4+9\nUc2e4x3EWvScsypt2vsd7zxJh7ObnTmb+dqmW0dtizjztDk6+eFTT9DZ4yNNU8y/3nouCbGjzWXU\nahWbVqSyaUUqfYNK9OfZd+r57dNlZCRbWFOUHB2bZEym19tLrn76jU3PlJJsRfS8c7QVlUpiVeHo\naIskSVx3XiEpCWZ+9vAhalrsqFQSGckW+jtmdq6ctFjMBg0n6vsAxbHt5b2NGPVqzl03c9OHDwuR\n9LU3G/awxJLI+rRVGLQGet0DJJhsH1mxJzhzDDoNZqM2KnpUkoqixHyOdJRj9wyO2/9LlmWcbj8p\nCaYx207F6ROiR7A4mLQ56cDAAL29vSxZsoT6+nrKy8uj/wkEAoFgYtyeIAB/fL6CQDA0xWiFE/V9\n/PngSwBcWrhrwnFDdj2txzMoMW3kp1+9mGTb5IuOhFgj159fxPdv34hKJXH3nw/RM+CJbt+StBN/\nUwnZpvxpzfNsWDpc1yPLUJxlm7Cm5pzVafznHecQa9FRlBmHVjNz9zi1SmJpbgIdfUP0DXrYd6KT\n3kEv567LHNfR7aNCikURko+WP8f/7fs9z1fvJhAKMOh1iHoewYQkxBroH05vg1NS3Prqxx3v8QUJ\nheUpG/k6fE4AYnRC9AgWlgkjPS+++CJ33XUXZrMZn8/HPffcM8Z9TSAQzD0tXU5+//wJvn79Gmwx\nIs30w4LXr4iejr4hXni/gWt2Fkw6XpZlfvbEOziz6si0ZJEXnz3h2HePKo09r9mRP6rfzVQUZ8fz\nhatX8qsnj3Pv347yb19UvtMtqgRCXTkY9XMvBHLSYtBp1fgDIUqLkycdW5Idz2+/dyFnE5hYmZ/A\nwZNdHK7s5vHdNagkRqX3fRTZmbMZjUqDP+TnwcOPUtlTy/Zspa+SED2CiYiPMdDc6cQXCKHXqilJ\nVB6CVPXUsSljrJOvY0ixq44Zx7ntVJw+F2qVGqNW3L8EC8uEkZ7777+fRx55hD179nDvvfdy3333\nzee8BALBMK/tb+ZARRf7K7oWeiqCGeD1h9Bp1ZiNWh55rTq6QJiIli4nAzrFLXOoOYNwWB53XDgs\n897RNswGDWtLJhcN43HZ1hzy0mI5VtOLP6BEoLw+RaAZZyCgzhSNWkVRllJnMh0jAaNeg0F35vOK\n1PX87tlyOnqHuGpHPplLPto1LXqNjvPytnJJ4S7SrEuo6WugZ0hJ8RN21YKJiJgZDAynuOXH56CW\nVBPW9bjcil21ZZKanmAoSNdQLzF6i0irFCw4E4oelUrF0qVLAdi8eTNOp3PeJiUQCEaoalJsZjt6\nXQs8E8FM8PqDWIxabrqwiCFPgEdfq5p0/L7yDlS2bgjqaKuz8NbhlnHHVTb10zvoZfPK1DNK+ZIk\niRX5CQRDYaqbFTcvj08RP/MhegBuvriEGy8ooihz7qMO+RlxGHRq3N4gyTYjN19cMufnXEwUJeTh\nCXo52lkBCOc2wcQkxI52cNNrdOTasqi3t+APjn1o4xhuTBozSXrbO037cfhcbMlYOwczFghmxoSi\nx+/3U1tbS21tLTU1Nfh8vujvtbW18zlHgeBjSzAkU9tiB6Czz73AsxHMBK8/hFGv5vJzcklJMPHC\n+w209UwsXPdU1aLSe1mxpAidRsvvnjnBb54u440DzTR2OAiFwsBIatuONWdeiL9sOPpR0dA/PFcl\n0mPQz1xEnQkr8xO55dKlE9rcziYatSp6vV+9bvW8CbvFQtFwXcbeZqWZqUhvE0xEJNLTYx+p9ytK\nzCMUDlHb3zRmvGtY9ExU0xMOh3nm5CuoVWquLLlwDmYsEMyMCb/9fT4fX/rSl0a9durvu3fvnrtZ\nCQQCALrsAfxBZbHb0Te0wLMRzASfP0h8jAGtRs1tly/nxw8d4A/Pn+CfPrdpzNgBp5cmZyPaRNiY\nvZy1V2Tx22fKee7dkQJinUZFUqwauxusJh2rCs/cWnpZrpLidKJBSXnyDKe3nU0a2WLmq9euoqXL\nyfqlc9N0dTFTlJALQI9bEbgivU0wEYWZStrp0epudq1VHqqUJObzYvVuqnrrWJZcOGq8c2jySM++\n1sN0uLo5L+8cIbYFi4IJ73BC1AgEC09r70hKQWffELIsi7zoDwGyLOP1hzDolMjJ1lWpLM2JZ195\nJ2V1vazMHy1YDlZ0IVmVRemypEKyCtO5YGMWjR0O6loHqWu1U9c2SGPHIOEwXLU9D416UvPNSbFZ\nDaQlmqls7CcUlqOi56MaBUlJMEebk37cyIhNxag14AkoKUti8SmYiMJMG/ExBvaf6CIUCqNWqyiO\nmBmM4+Dm9Exc0yPLMk9VvIwkSVxTctHcTlwgmCZnftcUCARzTmufInoyki24vcEpi+EFiwNfIIQs\nE3VWkySJL1y9AoAHni0fY1Kw70QHKms/Zq2ZjNhUQIm6lGTHc/k5uXzjxlJ+8Q+7+N716dz3nfO4\n7YplZz3H5XkJuL1BGtsHozn885XeJpg/VJKKwngl2mPUGjBpjVPsIfi4olJJbF6RgtPtj0aBbcZY\nks0JVPfWE5bDo8ZHIj3WcdzbDrWX0TTYxjmZ60mxztxwRSCYC4ToEQgWMa29PixGLetKlLQckeL2\n4cDnV4wBIpEegKIsGztK06lrHeStw63R193eAEcbm6P1PCpp4q9ljVoic4n1jAwMTmdZrlLn8pdX\nKtlb1kFWipUl8R/PaMhHnUhdj0htE0zF5hXKQ5e9ZSOdgIsT83H5h2h3jnYQdQ7X9FhPS29TojxK\nv7Frll48l9MVCGaEED0CwSJl0OVjwBWiKNtGaqKyGO3sFaJnLujqdxMMhaceOE28UdEzOl3s1suW\nodWo+NOLFVHzgP0VXYSMPQAsTy6atTlMRcTK+UBFFxq1in/89DrU82AsIJh/ihIiokektgkmZ2VB\nImajln3lnciyEpEuPqVfz6k4hy2rraelt53orqKmv5H16avJikufh1kLBNNDiB6BYJFSNWwnXJI1\nIno6hIPbrNPe4+JLP3qdR16d3FJ6JkT63uh1oyMyyfEmrt6RT++gl2fersPhdfLa8TLUcYroWZZU\nOOZYc0VKgon4GD0At12xjNy02Hk7t2B+KUnMIzcuk3VpKxd6KoJFjkatYsOyJfTaPdS2Ks6h0Sal\nvaPrepxuP2qVNKYW8KmTLwNw7dJL5mHGAsH0EaJHIFikVDcpoqc4J57U4SJs0atn9jnZ2K80/DzW\nPmvHjERxjOO4oV1/fiGxFh1/O7CHrzz7PWqMz6KO78Kqt0TreeYDSZL49CVLuWZnPlduy5u38wrm\nH4PWwE8u/h4XFexc6KkIPgRsOS3FLSMmFavOzN7Ww9SdYl3tHPJjNetGmevU9DVQ1lXFyiUlFCTk\nzOu8BYKpEKJHIFikRPryZCZbSbIZUakk0atnDmhodwDQ1uOiY5bSB73j1PREMBm0nL/TBDkHCYbC\nBLsyydOv5Csbbpm0nmcuuGhTNp+/asW89MsRCAQfDtYWJ6PTqNhXrogelUrFlzZ8Gn/Iz3+9c0+0\ntsfp9o9JbXtyuJbn2mWXzu+kBYJpIESPQLBI6XcojlpxVj0atYpkm1EYGcwBDe2D0Z8PVXZNMnI0\nPQOeMS5sESJGBvpxIj3VvfXs7n8SSSXjqykl0LScv9t2KxvSV89w5gKBQDD7GPQaSouTaely0drt\nBGBTRilfXPcpnD4Xd7/7K0KhMC5PYJSJQZO9lUPtZRQn5M1rqq5AMF2E6BEIFin9Di8mvQqtRvkz\nTU0wY3f6oj1VPqrIssz7x9ujom+uz9XQPhh9Wnnw5PREz9Hqbm7/4au8tLdx3O3RZp+nWUDX9Tfx\nn+/8kkA4yDU5NxAeTKIgMy5asyUQCASLgS0rx7q4XZC/nTUpy2hzdtLtHESWRzu3PXXyFQA+sewS\n0U9OsCgRokcgWKQMOL1YjSOL5pSIg9tHPNrz6gdN/PiPB3j4lco5P1ev3YvTHWBVQRI5qTGU1fZG\n63Em46m3FBej9yeoAxrPva3J3soP3/4/vEEfX998G5/atJO//1Qp37hhzSxciUAgEMzXoag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k2YbL18ct4txBmHtuRODIkFoL6necTrHWsu4ZvbfshPd/+W107+gyZzKwCReu991LUOBD2X6Ocn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\nQgghVE2SHiGEEEIIIYSq/QkjQsd9G7l+WwAAAABJRU5ErkJggg==\n",
    700       "text/plain": [
    701        "<matplotlib.figure.Figure at 0x7f525d563fd0>"
    702       ]
    703      },
    704      "metadata": {},
    705      "output_type": "display_data"
    706     }
    707    ],
    708    "source": [
    709     "# Load pricing data for asset and two market indices\n",
    710     "start = '2014-01-01'\n",
    711     "end = '2015-01-01'\n",
    712     "b1 = get_pricing('SPY', fields='price', start_date=start, end_date=end)\n",
    713     "b2 = get_pricing('MDY', fields='price', start_date=start, end_date=end)\n",
    714     "a = get_pricing('HPQ', fields='price', start_date=start, end_date=end)\n",
    715     "\n",
    716     "# Run multiple linear regression\n",
    717     "mlr = regression.linear_model.OLS(a, sm.add_constant(np.column_stack((b1,b2)))).fit()\n",
    718     "\n",
    719     "# Construct fit curve using dependent variables and estimated coefficients\n",
    720     "mlr_prediction = mlr.params[0] + mlr.params[1]*b1 + mlr.params[2]*b2\n",
    721     "\n",
    722     "# Print regression statistics \n",
    723     "print 'R-squared:', mlr.rsquared_adj\n",
    724     "print 't-statistics of coefficients:\\n', mlr.tvalues\n",
    725     "\n",
    726     "# Plot asset and model\n",
    727     "a.plot()\n",
    728     "mlr_prediction.plot()\n",
    729     "plt.legend(['Asset', 'Model']);\n",
    730     "plt.ylabel('Price')"
    731    ]
    732   },
    733   {
    734    "cell_type": "code",
    735    "execution_count": 11,
    736    "metadata": {
    737     "collapsed": false
    738    },
    739    "outputs": [
    740     {
    741      "name": "stdout",
    742      "output_type": "stream",
    743      "text": [
    744       "R-squared: 0.872829465873\n",
    745       "t-statistics of coefficients:\n",
    746       "const                -21.616393\n",
    747       "Equity(8554 [SPY])    41.517799\n",
    748       "dtype: float64\n"
    749      ]
    750     },
    751     {
    752      "data": {
    753       "image/png": 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tnkuhR0RERESkDztSVNPy894jVXxt2uCQXq8uCC2rvyjcxfu5n5AeM5BbpyxjYuoYjIaT\n7QiyEzPZXbqfw9XHmJQ6tt3zqZGBiIiIiEgfdqS4tuXnvfkVIb9e3Tmu6alqtPHc1lcwm8zce+Ed\nTE4bd1rgARieNBSgw1PcFHpERERERPqwo0W1GE1+xmYlcLy0npp6Z0ivV2d3YzBApKXz09t8fh9P\nb3mROlcD3550HYPj0ls9LjsxE4A8hR4RERERkf7pRG0xbq8bn8/P0ZJqoiZsoXrgp4CffUeqQnrt\nOruLaKsZk9HQ6c8uz/2EL0tzmZY+gYXD5531uERrPAnWOA5XHu3QeRV6RERERET6kMLaEu796DEe\nW/sHTlTYcKfsxxNuw+Ytw5RUzN78ypBev67BRXQX1vMcrjrGP3e/S4Iljv8789sYDG2HpuzEoVQ7\naqiy29o9txoZiIiIiIj0IdsKd+P3+zlQcZgnP/8TYalFRBljcfjrMWccZs+R0SG7tt/vp87u6nBb\nbLurkee+eJUjtuNU2avx+n38YNYtxEZEt/vZ4YmZbCvcRV7VUWZGTm7zWFV6RERERER6meO2Um57\n/SGeXvsWfr+/U5/dWbIXAwbGDRhJqaMIgGuHLePiYXMwWBo45jhAo9MTimHjcHnxeP1Ed6Bdtd/v\n55kvXmbzie00uhtJjxnIbVO/wcTUMR261vDEoQDkVR1t91iFHhERERGRXualbe9S769kXenH/OCl\nv3C8tK79DwF2dyMHyvPIShzCAxf9gETPSNxHx3HhiHF8feyVGDBiSstj75HykIy7rqHjnds+OLia\nrSd2MiZlBH++5jc8ecVDXDHiax2+1rCEQOvtAlthu8cq9IiIiIiI9CJlDZV8WbkTnyMSXFYqrDu5\n++9/4fn39tDQ6G7zs3tKc/H6fYxOHEXu0Rqc+eOIbMgmMdZCclQikxKnYrTYWZW7MSRj7+gePbkV\nh3l111vEWWL50QW3YzKaOn2t6PAoLGERVNqr2z1WoUdEREREpIdV2W2syd9EvbOBd/evxI8fT+Fw\nvpF1K3HmeMIy8lie9xE/+8umNqe77SzeC8C7K+r46bObqLA1MmJwfEtTgJumLcbvM7KnYTMeb/Cn\nuHUk9NQ66vj9pr/iw8+PLridBGtcl65lMBhIikygslGNDEREREREerXDVcd4/LNnsDlq+ev21/D5\nfUSb4imvTCU1OplfT/4xj6z5PWUZh8k/YSTnwGimjxl4xnn8fj85RXvAa8ZXF8d1Fw8nLTnqtGOH\nJA4gqiELe0wen+Zv4vIRZ28L3RV19kAlKuYsa3p8Ph9Pbf4bVY02vjVhCeMGjDyn6yVZEyisLcHp\ncbV5nCo9IiIiIiI9ZOuJnfzn6t9S46jjkqy5JFri8Pq8jLbMAoxYLWEkRyXy8wX3EB8RT1h6Hn//\ndHur1Z5j1YVUO2x4bEnctng8t149jstnDyUpznracVMT5uD3GXljzwe4vW1Pl+us9io9b+77gN2l\n+5maNp4lYxae8/WSIhMAqGxse4qbQo+IiIiISDfz+/0sz/2E3278CwYM/Hju9/jejBv5w6Kf89RV\nj5LsHwFAlCUwMSspMoEbJy3BYPRzzLeDLw9XnHHOj77cAUBWbDaLL8o667WnDh+Ct2wwNa4a1hzZ\nFNT7aiv07CrZxxt7PyAlMpG7Zt2K0XDuUaQl9LSzrkehR0RERESkG3l9Xp7PeY2Xd75JvDWWny+4\nl+kZkwAwGo2kRqdgdwQqMJGWk9PE5mbOIMmShCnlBK9+uuOM8x4qPw7AwokT2tzYc9ywJNxFWRj8\nJt7a9xGuIFZ76hoC54qODDutGlVpr+apzX/DZDRxz4V3EB0RFZTrJVnjW87fFoUeEREREZFuYnc3\n8vhnz7Dq8Hoy4wfxq0vvJytxyJnHOQJNBiItJ5fgm4wmvjnxagxGP3nObew/UnXaZ8odJfj9MDN7\neJtjSIi1kBafiL88k6pGG58e3hCEOwtorvT8K+8fPLLm9zg8Tjw+L7/f9FfqnPXcOuV6shMzg3a9\npMhEQKFHRERERKRX8Pv9/HLdH9lZso8paeN5dMG9LdOzvqq50hNlOb0hwNzMGSRGNFV7Vm9ved3r\n8+EwVhPmiSE+qv0qyrhhSTSeGEq4MZx39q9stxFARzWHniM1R9lffog/fP48r+x8k4OV+Vw4ZDqX\nZQe3cUJSpCo9IiIiIiK9RllDBYcqjzBh4Gjum3snVrPlrMfaHR6MRgMR4afvX2MymvjWpEC1Z3/D\nVg6fCLRrLrDVgMlDfFhKh8YyLisJPOGMiJxCtaOGhz55gmO2E12/uSb1djdGowGnxwlATtGXfHho\nDRmxqXxv+o1tTrvripONDNpuW63QIyIiIiLSDQ5VHgVgStr4djfjbHC4iYwIazUkzM2cQUJ4YtPa\nnkC1J89WDsDg2IwOjWVcVhIA5spRXJo1l2M1hTzw8W/YX36oo7fTqtoGF9GRJtw+D9mJmQyJy8Aa\nZuHeOXdgaSPkdVWk2YrVbFGlR0RERESkN8irPALA8MSh7R5rd3hOW89zKpPRxLcmB6o9u2o2c6yk\nlkJ7JQDj0to/N0BqUiSJsRHsz6/h/0y/gTtn3IzX52VH0+amXVXf6CI6OhAxEq3x/Pqy+/nj1Y8x\nKC7tnM7bliRrglpWi4iIiIj0BoeqjmIyGMlKGNzusXaH+7TObV91UeZM4sMTMKWc4O+f7qDaE/jS\nP21Y200MmhkMBsZlJWOrc1Jc0cCo5ECL63pnQ4c+3xq/30+d3U1UZKA6ZQmLwGwyExsR3eVzdkRS\nZAINLnubxyj0iIiIiIiEmMfr4Wj1cYbEZxAe1vrGnc18Pj+NzrNXeqB5bc9iDEY/OVUbcZpqMPjM\nZMR1bE0PwLhhgc5ne/MriQ6PBKC+nfDQFrvDg8/nx9K0F6olLKLL5+qM5rbVbVHoEREREREJsWM1\nhbh9HkYkDmv3WIfLg99Pm5UegHlDZxJnTsCYfAIsDcQYkzvVKGBs07qevUcqiQoPdHyrd3W90lPf\nGOg4Z7WerPR0h7N1wDuVQo+IiIiISIgdal7PkzS03WOb9+j5arvqrwqs7QlUewwGSI/u3LqZzNRY\noqxm9uZXEmY0YQ2zUHcOoae5XXV4RGBTUoUeEREREZF+JK+pc1tHQk9D0x49bU1vazZ/aGBtD8CU\nwdmdGpPRaGDssERKKu1U1jQSHRF1WqUn50ApBwvabhBw2rjtgXGbw30AbbbkDiaFHhERERGRXiCv\n6iiRZivpMQPbPdbeGKj0dCT0mIwm7pj5TRLNcVyUPbnT4xrfNMVt16EKosMjW9b0+P1+fvPSF/z3\na9vb+vhpmqe3mcyB0KNKj4iIiIhIH9XgsrM6fxNubyAE1DrqKKorJTsxE6Oh/a/fdmdzpaft6W3N\npmdM5P9kLiM5KrHTY50xNhWADbsKiQ6Pwulx4va6aXR6cLi8nCirx+H0dOhc9Y2B6W3dHnqsCj0i\nIiIiIt3qo0Nree6LV/jXnuUAvLnvQwCmpU/o0OebKz1RHaj0nKvBA2PISo9jR24ZFlOg7VqDy05d\n01Q1vx+OFtd26FzNnzGavED3hR6r2UJ0UyOGs1HoEREREREJoryqowC8n/sxa498zsq8daRFD2Bh\n9rwOfb650mPtYKXnXM2dnI7H66e+LvDreped2gZny/v5RTUdOk99UyMDQzeHHoC7Zt3a5vsKPSIi\nIiIiQZRfXUC4yYzf7+eZrS/j8/u4Zcr1hJk6Vrlp6MZKD8BFkzMAKCsPhK16VwN1De6W9/MLOxh6\nmtb0+I2B8VvCuqeRAcDU9PFtvq/QIyIiIiISJLbGGqoba5gwcDQLsi4EYEraOKZ2cGobgL25e5u1\neyo9qUlRjBwST2l5IKzUuRpOr/R0MvT4CPyvxdx9lZ72dE98FBERERHpB/KrCwDIShjC1aMuJcka\nzyVZczt1DntT44DIiO77qn7R5EEc3rQHgHpnA3X26Jb3jhXX4vX6MJnarpc0t6z2GppCTzdOb2uP\nKj0iIiLSa2zdW0JRRX1PD0Oky1pCT2ImVrOFZeOvJjEyvlPnaGiqmER1U6UHYFxWIn5POBBY09M8\nvS01KRKXx8eJsvb/XtY1uogIN+HyBtb29IvQ43Q6WbZsGUuWLGHRokX89re/BWD37t1cf/31LF26\nlOuuu47du3eHaggiIiJyHimpbOCxF7bwixe24PX5e3o4Il2SX3Wy0tNVjU2VHms3VnoSYy3gCYSs\n+lOmt00akQJ0rJlBvd1NtNWMwxP4rMXUD0JPREQEL7/8Mu+++y7vvfceW7ZsYdu2bTz55JPcfffd\nvPPOO/z7v/87Tz75ZKiGICIiIueRnQfLATheWs+abQWd/nx1rQOn2xvsYYl0Sn51AQmWOBKscV0+\nR3Olp6P79ARDfHQEeE+Gnub205NHNoWeDqzrqW88GXrCjGEdbtzQHUI6Eqs10Ovb7Xbj9XqJi4sj\nJSWFurpAP7y6ujoGDmx/V1oRERHp+3YeCoQek9HA31fmMm/KIMLNpjOO8/v91Da4KLc1sv94I8dq\nD7FpdzG5BdXMnZTO/d+e0d1DFwHA5qilqtHWqaYFrbE7PYSHGTGHdd9KFJPJSExEFC5Ob1k9cXgK\nBkP7ocfn82N3uIlOi8XhdmDtRVPbIMShx+fzce2111JQUMC3vvUtRowYwb333ssNN9zAE088gc/n\n41//+lcohyAiIiLnAa/Pz+5D5aQkWJk7KYO31+bx9Bu7GJYeR6PDTbmtkfLqRsptdsptDlynVXQq\nMRogzGRk16Fy/H4/BoOhx+5F+q9gTG0DsDe6u61z26kSo2Io4WTLamtEGLFR4aQlRXHouI2aeidx\n0a2HGbvDjd8P0VYzxR5nr1rPA2Dw+/0hnzRbV1fH7bffzr333suzzz7LjTfeyGWXXcaHH37I66+/\nzt/+9rc2P5+TkxPqIYqIiEgPKqpy8ZePypiSFcllU+J56v1iHK4zv6JERhiJizQRF2UiLjIs8L9R\nJoakRPBRjo29BY3cfU0qCdG9Z1qN9G0ev5cKZzVlrkr21R3mWGMR16VdxvCozC6f88m3irCYjfxw\ncWoQR9q+v6+t4Hja+wywxmPbPhujAX60JI1N++tYtaOGyVmRLJ2d2Opnq+o8PPV+CZOzIikYsIKo\nsEhuH3Jdt44fYNq0aa2+3i3/RYiJiWH+/Pns2bOH3bt38+KLLwJwxRVX8NBDD3XoHGe7gf4gJyen\n391/f7zn1ug56Bmcqr8/i/5+/6fqi8/iyOpDQBmXXDCGi6YOIntEPQWlgenwEWYTKQlWkuOtWMJP\n/+py6rOocuext2AvlvhBTJuU0d230CP64p+FruquZ1Flt7G1cCeHKo9w1HaCotoSvH5fy/tR4ZEs\nmrWQmIjoNs7SNvfrRaSlRHfqfoJx/xvzdlDgNOMx+nC4YUhqDNOmTWPyZB+HStexM7+Wf7tiChOy\nk8/47KHj1UAJmYPSyHd5SYiO6/Y/m20VSkIWeqqqqggLCyM2NhaHw8GmTZv4wQ9+QGZmJlu3bmXm\nzJls3ryZoUOHhmoIIiIicp7YebAMONkpKj0lmvSUzn1pHDE40BY477iNuf0k9Ejo5BR9yWdHt/Bv\nExaTHjOQkvpy/mfb39lTehA/gSpkRFgE2YlDGRo/iKEJg8iMH8SQuAwiwsK7fF23x4fL4yPK0v3V\nysQ4CxSZaXA14HJ7cSXksv6ohXlDZ3HXssn8v6fW88wbu3jq3q9hDjt9vV29vXlDVSNuh6dXbUwK\nIQw95eXlPPDAA/h8Pnw+H0uWLGHOnDk8+uijPProo7hcLiwWC4899liohiAiIiLnAafby74jVQxL\njyU+putflLIHBbplHTpuC9bQpB/y+/2sOLiaV3a+iR8/u0r2sXTMFbxzYCUNLjujk7O5cMgMJqaO\nYWB0MkZDcJsN2B3d37mtWWKsBX+BGZevDsxOyi07ePdAKfOGzmLkkASumjOM5RuP8OaaPL552ajT\nPlvf1HHOagn8OiLM0t3Db1PIQs+oUaN4++23z3h9woQJ/O///m+oLisiIiLnmcMnbLg9PiYMP3PK\nTGdEWsxkpERz+IQNn8+P0ahmBtI5Xp+Xv+14nVV560mwxHH5iPm8ufcD/r77bcKMYdw542YWZM0J\n6RjsjsCIBXANAAAgAElEQVQePZE9UemJtbS0rTbFBbop1rsaWt6/6coxbPqymNc/OchFkzPIOKUa\n2xx6mvsX9Lbubd3XB09ERESkFSWVdgAGDYg553ONGBxPg8NDSWVD+weLnMLubuSJDc+yKm89Q+Iy\n+OVl9/H1sVfyyIJ7uGDwNB65+D9CHnigF1R6mjYoNSUEppzWu+wt70dZzdxx7QTcHh/PvLGLU/uh\n1dtdAISHB9Y39bbubQo9IiIi0qPKqgNfqgYmRJ7zuYY3revRFDfpjAp7Ff/56W/ZUbyXyaljefSS\ne0mODHQpG5E0jP+Y811GJmd1y1h6stKTEHMy9BhjKwBwe924PK6WY+ZMSGPG2IHszqtgTc6Jlteb\n1/SEKfSIiIiInKm0qdIzINF6zucaPqipmcEJhR7pmPyqY/z04yc4VlPIwux53H/R94k0n/ufxa5q\naKr0RPVApSchNgI8gSYMBtPJjnSnVnsMBgN3XjuRiHATz7+3h9qGQCBqnt5mDAvsoaXQIyIiInKK\n5krPgCBUerIy4jAaYP+RKrphK0I5z20r3MV/rv4dNkct3558PbdP+yYmo6n9D4ZQ8zSxnqj0hJmM\nWMLODHynrusBGJAYyY2Xj6a2wcWLy/cGjmkMjNsU1lzp6V2NDBR6REREpEeVVtlJjI0g3HzuXzat\nEWGMHppIbkE1T76ag8PlCcIIpa/x+/2syP2UJzf8GYD/N/d7XD3qEgyGnm1+4fP5Wb7xCADZTVXL\n7hYTHtXyc4o10EL+q6EH4JqLshiWHsvHWwvYf6SqZXqb3xj4O6dKj4iIiEgTr9dHha0xKFWeZj+5\nZSZjhyXy2c5CfvL0Bhqapt2IQGCNyp+/eJWXdr5BnCWGny+4hxkZk3p6WACs3nacwydqmD9lUMtU\nze4WZz3ZkW3SwPHA6dPbmplMRr67JPD+yi1Hqbe7sUaYcPsCFR9rL9unR6FHREREekxlrQOvz8+A\nxOCFnviYCH5x54UsmD6YvBM1PPHKNrxeX/sflD7P4XHy6Jr/ZvWRTQxLGMyvLrufrMTMnh4WAI1O\nDy9/sI9ws4lbrhrbY+NIiAx0UfQ5rGQnDQJar/QAjM9KJjnOwuYvi7HVO4iyhuPwOAFVekRERERa\nlFU1dW4LYugBMIcZ+fd/m8z0MQPZnlvGn9/5Umt8hE0FOeRW5jNz0GQeXfD/Wjq0BVtJZQP/XHmg\nw9MrvV4fT//vLqrrnHz9a8NJSei5RgqpsUn4vSYMdQOJbwpAZws9RqOBuZMzaHB4qKp1Em01K/SI\niIiIfFUwmxh8lclk5Mc3TWNoWiwfbjrKu+vzg34NOb/sKN4DwA0TlxIRFh6Sa5RXN/Lgsxv5x6pc\n1m0/0e7xLreXX7/0Bet2nGDUkASuu3h4SMbVUQNjY3Hsmkd0zUSiwwN/L+ucZ9/36qLJGS0/x0Se\nWulRIwMRERER4GS76mBXeppFWsz87PbZJMZG8ML7e9iypzgk15Hez+PzsrtkPwOjkkmLHhCSa1TX\nOXj4zxspr24EYHtuWZvHNzo9/Pyvm9myt4RJI5J57M45WCK6v2vbqRLjLOCJIC7S2tLUoLU1Pc1G\nDI4nNSnw9zc60kyj2wGo0iMiIiLSorQ6tKEHICXBysO3zSbcbOLJv+doD59+KrfiMI0eB1PSxoes\nS9ufXt9FYXkD1108nIGJkew6WH7W9WR1dhcPP7eJ3XkVzBqXys9un421hwMPQEJsoEITExlOdEvo\nOXulx2AwtFR7TpvepkYGIiIiIgFlVYF/EQ/1Gobhg+O594ZpuNxeHnt+CxW2xpBeT3qfHcWB/WSm\npI8Lyfm/PFzB1n0ljMtK4parxjJ11AAaHB5yC6rPOLaq1sFPnt5AbkE1F08bxE9umRGUlu3BMCAh\nEqMBUuKtRDVNb2sr9ABcPG0w5jAjQ1JjtKZHRERE5KtKq+0kxlowh4X+C98FE9L4ztXjqKp18Njz\nW2h0ag+f/mRH8R7MJjPjUkYG/dx+v79lk87bFo/DYDAwdXRgCt32A6dPcSutsvPAnzZwrKSOqy8c\nxo++ORWTqfd8JU+MtfDYnXO46coxmIwmrGZLm9PbAAYPjOGl/7ycxRdlnww9JoUeERERkZY9ekI5\nte2rls7P5ooLhpJfVMP7n6mxQX9RYa/ieE0R4weMJDwEDQw27i7iYIGNuZPSGTkkAYCJw5MxGQ2n\nrevx+fw8/Nwmiisb+MalI7nj2gkYjT27IWprJg5PIbFpmlt0eFS7lR4ITIczGQ04PE7CjGGEmXp+\nqt6pFHpERESkR1TWOPD5/CHp3HY2BoOBb14W+Jd+re3pP3YV7wNgcmrwp7a5PT5eXrEfk9HAzYvG\ntLweaTEzdlgSeSds1NQHqh/HSmoprmxg3uQMbrpyTMjWFgVTdHhku5WeUzk8zl43tQ0UekRERKSH\nNDcxGJDYvXuSJMZaiLaaKSip7dbrSs/Jry4AYFRydtDPvXLzUYorG7hyzlDSk6NPe2/KqBT8ftjR\nVO358nAFQMvUt/NBdHgUTo8Tt9fdoeMdbodCj4iIiEizzV8G2kenJUV163UNBgOZabEUVzTgdHu7\n9drSM47ZCjEajAyKSwvqee0ON/9clYs1IoxvXjbqjPdnjE0FYPPeEgD25lcCMC4rKajjCKXmDm4N\nHaz2ODxOrAo9IiIiIrBu+wne+yyfjJRoLpyU3u3Xz0yNweeH4yV13X5t6V4+v49jNYVkxKYSbjIH\n9dxvrcmjtsHFdQuGExd95hf9zNQY0pKjyNlfisPlYW9+Jcnx1m5dx3auols6uHU89KjSIyIiIv1e\nfmENT72+E2tEGD/9zkwiLcH9ItoRQ9NigcAaC+nbSusrcHqcZMYPCup5K2saeXvdYRJjI1hyUevT\n5gwGA3MmpOFweXn/s3xq6l2Mz0o6L9byNGuu9NS56ts91uPz4vZ5et0ePaDQIyIiIiFiq3Nid5y+\nDqC2wcUvX9yKy+3l3humMnhgTI+MbUhqIPQcLQ6Enn99nMvKzcfO6Zxrc3fzwsYPz3ls0jV+vx9b\nYw0HK/LZcOwL9pTmAnDMdgKAoUEOPf9YmYvL7eWGy8dgaWNT0TkTA5XM//30EHB+TW0DTtmgtP1K\nj8PtAMASZgnpmLqid/WSExERkT7B7/dz9+/WkBxv5ckfzsNoNOD1+njilS8oq7LzrYWjmDU+uOsr\nOiOzudJTXEtheT2vfnQAa0QYC6YP6vKeQf/zxWu4zdVcUDiJMRndP2Wvv/H5fLy+dzlHqo9T1lBB\naV05nsMn12gZDUaeufqXHA1B6CkoqeWTrccYPDCGS2cMbvPYEYPjSY6zUFETCATjs8+30NM0vc3Z\nfttquzuw6W+kuXubk3SEKj0iIiISdB6vj6paJwcLbGzYVQjAiyv2setQBbPGpba66Ls7RVvNJMdb\nOVZSx+ptxwFodHrYkVvepfPZGhpwhQVaYL+3bVvQxilnl19dwFv7PmRH8R5sjlqSwuOZOWgyV4+6\nlHlDZ+Hz+9hQsLUl9GTGZwTt2i+t2I/PD7deNbbdjUUNBgMXNFV74mMiyEiJbvP43iY6ouOVnt4c\nelTpERERkaBrdJ78F/dXPzyA2+PjnXWHyUiJ5p4bpvaKDRkzU2PIOVDGqs3HMBoN+Hx+Nu4uYua4\n1E6fa+2BvRgMfgB2FR7C6/W1+2VYzk2FvQqAmyZ9nWtGX0ZOTg7Tpk0DoM5Zz8aCbaw/upUGt50E\nSxxxltgOnXfr3hJ2HCzj9mvGE9bK76GtzsnWfSWMykxgxtiBHTrnnAlpvP9Z/nm3ngcgpmV6myo9\nIiIiIqdxuDwtPxdXNvDfr+3o0cYFrWluZmCrd7Jg2mCS461s2VOM2+Pr9Lm2H89t+dkZXsH2pn1Z\neou31uSxZU9xTw8jqKoaA5W1lKjEM96LiYhmatp4CmoKqbRXd7jK43B6+OPrO1m+4Qhvrclr9ZjC\n8sCC/s4EmHFZSfzHt6Zwy1VjO3R8bxKt0CMiIiLSOoczEHoumJCGJTywRqYnGxe0pnldD8AlMwYz\nZ2IaDQ4Puw51fopbQW2gCUKsORZjVC0fbckP2jjPVUOjm78t38sbqw/19FCCqqqxBoBEa3yr788f\nOrvl56EJba+7afbh50ex1TsB+Oeq3Fa7+zWHns5MUzMYDCyYPoTUbt6TKhg607La3tTIINLc+xoZ\nKPSIiIhI0DlcgeltAxMjeeT/XMB/fnd2tzcu2FWyj7/vehu7q7HV9zObOrilJkUydlgSFzatu9i0\nu6hT13G4PDQYyzF5IrkgcwoGo4/txw61fDnuac3jsDs97Rx5fmmu9Jwt9ExJG0dU0xf2jlR6HE4P\nb645RKQljP/41hQ8Xh9P/WsHXp//tOMKywLPM/08W5vTVVEtoacTlZ5wVXpERESkH2ie3maNCGNc\nVhLTx3Rs7UMwvbrzLd49sIr7P/41R6qPn/F+ZmoMl8wYzK1Xj8NoNDA6M5HEWAuff1mM0+1t5Yyt\n23IoH4PZRXJ4OiOTsgDwR9p47Pkt1De62/l06J1o+pLe2MdCT3VT6EmwxLX6vtlk5uKhF2AymhjR\n9PvSlg82HaGm3sU1F2WzYPoQ5k3O4GCBjZz9pacd1xwiBw3oH6HHbDITERah6W0iIiIiX+VoamRg\nCe+Znkm1jjqO1RQSExFNaX05D33yBB/nfYbff/Jf7U0mIz/65tSWCo/RaOCSGYOpb3SzfvuJDl9r\nS/5+AEanZDEqOfDlekiWm8Lyep58ZRteb+fXCAVT85f0RkffCj1VdhtxETGEmc7+Z+yGSdfyx6se\nZUBU222iA1WePKIsYSyZF/g9vKbpf5u7DzYrqqgnymomNir8HO/g/BEdHnned29T6BEREZGga64q\nWCK6tufNudpbfhCAq0Yu4CfzfkBEWAT/k/MP/rj5by0bKLbmyguGYTQaWL7hyGkBqS2HqgLrdy7I\nHktKVBJxllic5gqmjRnA9twyXli+99xv6Bw0T8eyOz0dvqfezu/3U9VoO+vUtmZhRhPJkWc2Oviq\nFRuPUNvg4pp52URHBsLMyCEJJMdb2bq3BLcnEOK9Xh/FFQ1kpESdd13YzkVcRAy2xhrqnG1P2Wxw\nKfSIiIhIP9K8pudcKz1rj3zOExue4/mc13jvwCo2FWzjYEU+VXYbPv/ZKyh7SwOhZ/yAUUxJG88T\nlz/IyKQsNhR8wU8+fpwCW2Grn0tJsDJ7fCr5RTXsO1LV7vgaXA5sFILfyIT0LAwGAyOThlHtqOHW\nazMZPDCG99bns2rLsa49gCA4UVYHgM/nx9WFznS9kd3diNPrIiGy7dDTEY1OD2+tDVR5rpmX3fK6\nwWA4pblFBQBl1Y14vP7zbq+dczU3cyZun4fluZ+2eVxvrvRonx4REREJupNrerpe6Wl0O/jb9tdp\n9LRemTEZTUQbI8moWcfYASOYM2Q6g2IDzRL2lOViCYsgKzETgOTIRB5ZcA//2P0Oy3M/4cFPHueh\n+XczOiX7jPMunpvFpt3FvL8hn3FZZ58W1eh28OjqpzBYGhjgH4XZFGjFPSNjEl8U7mLDiS08fNtC\n7v3DOp59cxcZKdFtni8UvD4/RRUn12I0OjxEmHum+hZM7TUx6IzmKs8NC0cRbT29nfrciRm8tz6f\njbuKmD5mYJc6t/UFC7Mv4r0Dq/jw0BquGnUJsRGt339vDj2q9IiIiEjQNYeeiHOo9Hx2bAuNHgdL\nx1zOEwt/yn1z/y+3Tf0G14y+jDmDp5GVMASv38v+8jze2PsB93z4KH/a8iJVdhtFdaWMSRlBmPHk\nF/wwo4lvT76Ou2bdisvrZv3Rza1ed1xWEkPTYvn8y2IOHG292uP3+3lyw3McqTmCpzKVhRlXtbw3\nZ8h04iJi+PTwZyTEmXjglhn4/fDrl7ZSWtX+uohgKq+2n7bvUF9pZhCs0GN3uHlrTR5RVjOL550Z\ngEdlJpAYa2HznmI8Xl9L6OkvnduahYeFs3TM5Tg8TpbnfnLW4+zuRkwGI+Gm3rEX16kUekRERCTo\nmhsZWDsQerw+L9sKd5NfdaxlzYnf72floXWYjCYWjbiYoQmDmJ4xkStGfI2bJn2dH835Lr+89D5+\nMOwGXvz67/j32d9hWPxg1h/dwu83/Q8A4waMbPV6Fwyeislg5Jit9WYFBoOB268ZB34/v3xxK+XV\nZ7a8rmq0sacsl3hDGu7DExk55GQFJ9xk5rLh82hwN7L26GYmDk/he9dOoKbexS9e2NKtweOrbbP7\nTOixByf0rNh4hDq7iyXzss+o8kCgucWciWnUN7rZkVvW7zq3nerSrLkkWOL48NBaah11rR5jdzcS\nabb2yvVOCj0iIiISdI4ONjIoa6jkP1f/jic2PMsDH/+GO9//Ca/veZ8dxXs5XlvMrEFTiLe23pK4\nmdVsYW7mTB6cfxdJkQnkVgYaC4wfMKrV480mMxmxaRTUFOHznayCuL1u/rrtnzyz9WUmjxzA7deM\nx1bn5JcvbmmpXDUrqgu0MfbXJWIymhiWfvoYFw6fR5gxjA8PrsHn93HlnGEsmjOUo8W1/HNVbpv3\nE0zN7aozUgKbYtodPd9COxiCUemxO9y8vTZQ5bnmorO3tL5kxhAAXv3oACdKA88z7TzcZPRchYeF\ns2TMQpweJ++dpdrTHHp6I4UeERERCbqONDLIqzzK/St/ycHKfGYOmsy8zFm4vG7e2PsBv/nsaQAu\nHz6vw9eMs8Ty4wu/h9lkJiY8iqHxg856bGZ8Bk6vi5KGcgDqnPX8Yt1TrDq8nrVHPqfOWc/ii7K4\nbOYQDp+o4b9f23Fa57PC2hIAqsvDyEyNPWOdTLwllrlDZlBcX8aO4kD3tu9cPQ6AI4U1Hb6nc9Xc\nuW34oASgD1V6WkJP24G4Lcs3HKHO7uba+dlEtVLlaTZ8UDwXTxtEfmENXx6uIDnOgiWify6LvzT7\nIhKscaw8tJYaR+0Z79vdDoUeERER6T8aXW1XehweJ09tfgG728H3pt/IvXPu4K7Zt/Ls1b/k+nGL\nCDeZGZE4lNHJwzt13azETH5+8T38ZN5dGI1n/5qT2RSIjtlO4Pf7+cW6p9hfnkdM0wLt/OoCDAYD\n//e6SYzLSmLjriJe+/hgy+eLagOVHldDJMMHt15tWDRyAQArmjpeWSLCiI+OoLS6+9b1FJbXYzBA\n9qBAOOhzoaeL3dsanR7eWZdHtNXM4jaqPM2+vWgs4U3BNqMfTm1rFm4yc+2YK3B6Xbz/lWqP1+fF\n6XESGa7QIyIiIv1Ey/S2s1R6Xt35FiX15Vw16hIuyZ7bsgbAYrbwb+MX8z9LnuDhi3/UpbUBw5OG\nMjxpaJvHDD0l9ByzneBI9XGmpk/ge9NvBOBwVaDFtDnMyE9umcGABCv/WHmAjbuLACisC1R6/I6o\ns4aeoQmDGD9gFHvKclvWD6UkWCmvbsTn6579ck6U1ZESbyUuOgLoW6En3GQmyhzZpc9v2l1End3N\nVRcOI9LS/qL75Hgr118cCOD9rYnBVy3IupBEazwrD607rdrT2LT/lVWVHhEREekvmqe3tdYeeUfx\nHlYdXs/guHS+OeGaVj9vNVuwhEWEbHyZ8RkAHLUV8kXhLgDmZc5ieOJQAPKrClqOjYuO4KHbZmEJ\nN/H7f24nv7CGotpSIogGXxgjBp292tBS7Tm4GoABiZF4vD6q686+QWqw2B1uqmqdZKREE2kJhM++\nE3pqSLTGd3nB/OptxwG4dOaQDn/m6wtG8I1LR7J4bvuVob4s3GRm6ZjLcXpdvHvg45bXm9tVRyn0\niIiISH/hcHmwhJswGk//UlrnrOfZra9gMpr44azv9Fhr2zhLLPGWWI7ZTvBF4S5MRhOT08aSYI0j\n3hLL4erTNxMdlh7HPTdMw+ny8ujfNlLZWI3fEUWYyUhmWsxZrzM1fTxp0QPYcOwLbI5aBiYEKhNl\nVWd2hAu2lj1lBkRjbVqD0ug4/0OPx+el1lHX5SYGZVV2dudVMC4ridRONCSIMJu46coxDB549t/v\n/uKSrAtJsiawKm8dtsbAGrXevEcPKPSIiIhICDic3jOmtvn9fv5n2z+xOWr5xvjFDE04e6OB7pAZ\nP4hKezVHbSeYMGBUS6vdrMRMKu3V2L6yUPuCCWncfOUYqpwVANhrIhiaHos57Owd6owGI1eOvBiP\nz8PHeesZkBD4QljWtK7H5qil0l4dkvtrbmIwaEBMS+ix94FKj62xBj/+LoeeNTmBKs+C6YODOax+\nxWwyc+3Yy3F53S3VHoUeERER6XccLg/GpEL2lB5oee2zY1vZfGI7o5KzuWbUZT04uoDMU7q7zciY\n3PJzdkJgytOpU9yaLbtkBEsXDgRg5IDB3HzlmHav87Whs4kyW1mVt57E+HDgZOj53ca/8Mjq33X9\nJtrQ3K56UMoplZ4+EHoqGwMhsStNDPx+P6u3HSfcbGLupPRgD61fuXjYHJIiE1h1eD3VjTX9N/Q4\nnU6WLVvGkiVLWLRoEb/97W9b3nvllVe48sorufrqq3nyySdDNQQRERHpIY3+GhoHbuPxz56luK6M\nCnsVL2z/F5awCO6adUubndW6y9CmdT0A0zImtPycnZgJQP5XprhBYOPSqHgXADdePJ2powa0ex2L\n2cIl2XOpcdZR6Ans0VNaZcfn95FfXUBpQ8Vp+wUFy4lTpre1rOnpA9PbKruwMWneCRs//K81fOOn\nKyiqaOCC8WkdamAgZ2c2mblm1GW4vW42H9+OvamRQaTZ0sMja13ImoxHRETw8ssvY7Va8Xg83HDD\nDWzbtg2Px8Pq1at57733MJvNVFVVhWoIIiIi57WSygb+/PaX3LZ43Hm1jsDv9+OJO4oJcHpdPLX5\nBaxhFuzuRr43/UYGRqf09BABGBofmN40InHoaV+gs5oqPc0d3L6quXNbRkxqh691xfCvsTz3Uz4v\n3gRMoKzKTlWjDZc3sFlog9ve0i47WArL6rGEm0iKs7RUePrC9LYTtYEOeumdeP4fbDzC0eJahqTG\nkJ4cxTcuGxmq4fUro5KzgcBmvRmxgd+P3tqyOqQ7K1mtgZt2u914vV7i4uJ4+umnueOOOzCbA+k6\nMTExlEMQERE5b738wX627S8le1AcN13R/jSq3sLhdmFMLsTki2BW5ng2Hc8BYFr6BBZkXdjDozsp\nIzaVb064hnEDTv8CHG+NI8maQH5VAS6v+4xmC0W1pVjCIkjoxMaYyVGJzBo0hc+P5xCVkklZdQzF\ndWUt79e5GoIaenw+P0Xl9QxOjcFgMLSsr+oL09sKbIHQk3lKpa4tXq+PLXtLSIyN4I/3XnxGcw3p\nuvSYQKWzqK605e9Db53eFtLQ4/P5uPbaaykoKOBb3/oWI0aM4OjRo2zbto3f//73REREcN999zFh\nwoT2TyYiItKPHCupZcOuwsDPxWfufN6bbTq2A4PZRaJ7HHdMv5HD1QU4PU6+N+OmLrcYDgWDwcDX\nx17Z6nvZiZlsLdzJLW/+iEFx6WQlDCErYQjDEgZTXF/G4Ni0Tt/LVSMX8PnxHCIGFlF+IKFlg1OA\nemcDBLGYV25rxOXxkdG0p4zRaMAaYeoT09uO1RQSExFNvCW2Q8fvO1pFbYOLKy8YqsATZBazhQRr\nHMV1ZQxLCFRO+2XoMRqNvPvuu9TV1XH77bezZcsWvF4vNTU1vP766+zevZsf/ehHfPrpp6EchoiI\nyHnnn6ty8fvBYIBjJXU9PZxOWXNkIwBpxrFEhlt58vKf4vV5iQrv2kaSPeGGiUtItMaTX13AUdtx\njtlOsObIppb302M7PrWq2fCkoUSarXgtNlweH0erilreq3fZgzLuZoWnNDFoZo0IO+8rPQ63g9L6\ncsYNGNnh0Pn5l8UAzJ6QFsqh9VvpMQPZW3YQW2PgH2f6ZehpFhMTw/z589mzZw8DBw5k4cKFAEyc\nOBGj0Uh1dTUJCQltniMnJ6c7htpr9cf774/33Bo9Bz2DU/X3Z9Ff7r/U5mbjrlLSE82YwwwcK2vg\n8y1fEB52cvF/b30WFa5qDlbn4a1NxOvxdcs4Q3WNSQxnUsJwfPE+Kl02SpwVlDgrqHLVMMid3KXr\npoQlcMxdBEYP+08cbnn9y9w9+IudXRpna+PYnBsIys76cnJyGgAw+L3UNrh77Z+djihyBKYEWpzm\nVu/jq6/5/X7W55QQYTbgrikgp6lddV/VE7+3Zkfgv0t7iwJNOvL2H6IkrLDbx9GekIWeqqoqwsLC\niI2NxeFwsGnTJu666y6ioqLYvHkzM2fO5MiRI7jd7nYDD8C0adNCNdReLycnp9/df3+859boOegZ\nnKq/P4v+dP/Pv7cHKOU7S6aw62A5x8qOkJw+nBGDA/9/2ZufxZ+/+DsAntIhDJqYyrRp40N6vd78\nLFqzP6yAYweKMEbVUO05WcFLSE1m2pjO38fZ7n/r0V1ADfNmTyQrI7DWIuGzdRSU1DFt2jS27i3h\ny8MV3LZ4XK+actie6sMb4ATMGDmVaVmn33drzyLvuI0aeyFfmzqIWTPPnz8nXdFTfxeKc23s3HmA\nKndgk9LZ02YRERbe7eOAtkNfyEJPeXk5DzzwAD6fD5/Px5IlS7jggguYPn06Dz74IIsXL8ZsNvP4\n44+HaggiIiI97pjtBH/+4u+4vW5MRhO3TLmeMSkj2vzMrkPlhIcZmTpqALa6wL/+HyuubQk9vVWN\no5b1RzeTEJFIUfXAlr1h5KThTe2wjdE27P468BswGP2U1dYE9TrNe/SkJ0e1vBYZEYbL7cXr9fHu\n+sPszqvguotHEB8TEdRrh1JBTaCCMCQuHb/fz0efH6XR6SU2KpyykkaikquIjQonNiqCQwXVvPrR\nfkBT20IpPSawb5UfPyaD8YzGH71FyP5rNGrUKN5+++0zXjebzdqbR0RE+o1Xdr5FXtVRIs1W7O5G\nPj68oc3QU1Pv5EhRLZNGJBNuNpGZGlisfT6s61mVtx63z8OUxFkU4W/pGCYnZTWFHlNSCQaDH589\nFtjj2c4AACAASURBVENULRX1wW1WUVheT3K8FcspwbNlg1KXt2VzVLvTfX6FHlshBgwMjkvnYEE1\nz7y5+7T3/7nuszM+M2tcKjPHDuyuIfY7zR3cILCep7dWDvVfIxERkRDZX36I3aX7mThwDD+d/0Pu\nePd+9pUdxO/3n/WLwZ7DlQBMHB7YyyYzLdDS62gv7+Dm8rhYmbeOqPBIRkSNB77EEmHq6WH1OimR\niUSHR1FPIMQOiRnCCd8ebPbghVq7w01ljYPJI07fD6k59DQ0uqmwNTYd2/sbG7i8bmqddSRZEzhW\nU0hqdAoRYeEUNP1DwNVzh5GdEce+3CPEJqRQ2+CitsFFlNXM4rlZDB/c8U1MpfNSopIwGU14fd5e\n28QAFHpERERC5vU9ywH4t/FXYzAYGDNgBJuPb6e0oYLUs2zQuetQOQATRyQD/H/23jMwrupa//6d\n6V2992JJ7h0XmimmgwMEEgL3BlJvCGlvkn9IQsq9yb0kIT1AAgklhAQSElro2IAN7r3ItmRZsppV\nZ0YjTa/vhzMzsqxRtZrN/n3BzOxzzj6jKfvZa61nYdCpyUzRz3jb6r3t1fT6nKyruoKgRxY7ItIz\nGEmSKE8tYl/7YQCWFVXR0nCIPp9rwq5xsks+V37mwL4/MdFzsstJMBQBOCssrJ/e9zxvHt/I7Qtu\nxOV3My+zEoDmaArfBQvzmFuaRoqym6VL507nVD+UKBVKso0ZtPa1z2jRoxh5iEAgEAgEMwu7x8FT\ne/9Ja2/7dE9lSKo7a6nurGVR9hwq0ksBmBNNazvcWTvkcQfqutBrVczK79+dLsy2YO/z4XCOz91r\nKqjpkp3IFufMw+eXF9I6jYj0JCKW4gYwO7uYSEiBOzhxltUtXbIYyBtC9JyaKnk2WFg3954kEonw\n9P7ngf6mpC2d8n2cLu4EU0+ORU4fNGiE6BEIBAKBYMJ4tfYdXqndwLfe+j/eqttEJBKZ7ikN4t16\nuafLTXOuiT/WL3qOJTymu8dDa5eLeWVpKJX9P9HFOXJdT9MMruupsdajlBSUpRbhiYkeYWSQkJiZ\ngYREVXYehNT4wt4JO3+sR09exkAxYNDJf4+m9v6oodsbmLDrThZ2jwOtShvv81SYFBM9TixGDUmm\ns6cm6VwlVtejF5EegUAgEAgmjiNdx1BICtRKNX/a/Qw/++D3OLyTl/7l9Lt4rfYdQuHQqMZHIhEO\ndh7FojVRkV4Sfzw/KQez1kR1V21CoXagLpraVj4w9a0oW67raWyfmSlu/lCAensTxSkFaFUavD75\nddKL9LaExCI96YYU9BodyoiWIHIUzx8KcKTrGOFweNznbx0h0nOqeHafBZEem6eHbFMGP7zka9xQ\ntZZFOXPxB0J0WF0UZJmne3oC+h3cDGrdNM9kaIToEQgEAsFZhTfoo97WSFlKIT+/8j7mZVay++RB\nvvHm/7K37dCkXPNf1a/z5N7n4nUYI3GyrwO7x8G8zEoUUv9PrUJSMDujHKvbTqere8AxtU12nn1L\nTntbGK3niVGcK/dZaTg5taInEAxz70Mf8Py7iSNTMeptTYTCISrT5DQ+bzzSI9LbEpGqT2ZVwVIu\nLlkFgEbSgzKA1x/glZr1/OCdX/Lt9T+hznpiXOdv6exDq1GSnjRw170/ve3USM/MFj2egBdv0Eeq\nPomi5HzuWHgTGqWatm4X4YhIbZsp5JqzATBrZu7fQ2zBCAQCgeCs4pi1gVAkzOzMWaQZUrhvzZd5\nteYdnjn4Evdveoirytdwx8Ib0UxQc7xIJMKO1n0AdLts8cftHgdGjSFhT4qDHUcBmJdVNei5uRkV\n7GjZx7sNW8i35NLlsrGjtoFj7W2Q7SW/wkJuxlUDjsnPNKFWKahr6ZmQexotRxttVNdb8XiD3HTJ\n0DbbtVa5nqcivQwgHukRRgZD87XVn4n/26DW4wWau+2c6GkBoMHezHfX/4y15Rdy2/x18dSukQiH\nI7R2ucjPMKFQDHQI1EfT27z+/ojlTE9vs3vk93yKLmnA483xeh4R6ZkJVKaX8qklH2NJ7vzpnsqQ\niG8jgUAgEJxVxOphYr1uFJKC66suZ35WFb/d9jhv1L3Hoc4avrzyLopTCsZ9nZitdGNPC10u2Uba\nFl2A2T0O7nn1eyRrzXxy8S0sz1s4wIL6UEcNAPOzKgedd25mBQDPH35jwOOKFAAJa6iXw93HWJwz\nL/6cSqmgJNdCfauDQHB0KXYTwd6aTkCOHITCEZSKxDbbNd31gLzwAU6p6RGRntFg1hixBaDZaqW9\nrxONUs23L7qHP+1+hrfqNrG9ZR//ufBmLihaPmIPlG6HB38gNCi1DUjYLHamu7fFPnMe58C5x5qv\nikjPzECSJK6atWa6pzEsIr1NIBAIBGcVR7qOyQXg0ahCjOKUfH6y9l6umrWGlt42vr3+p2w4/sGY\nzx+JRPjN1se496378QS88SgPyGIHoKW3jUAoQJfbxs83P8JP3n+I9j5ZIITDYao7a8gwppGVwJa6\nICmX2xfcyMKkldAyF1/tEmb71/HbK/+P76/5CgD72gan0ZXlJxMMRWhsmzozg5jo8QfDdFgTWypH\nIhFqu+tJ1ibxvQf3cqCuC59fRHrGQrJejlactNlpd3aRbcpkbmYFD1zxXW6bvw5PwMPvtj/Bj977\nDZ3ObtbvaOT9va0JzzWUiQGAQdsflYyZGsz0mh5b9DO3cUc3b21vjD/e0iHfp6jpEYwW8W0kEAgE\ngrOGQCjAMWsDRcl5CdN9NCoNn1ryMRbnzOW3257gyb3PcUnJahSK0e/xvVm3kc1NuwD464EXqOk6\njkqhIhgOxnedY2lu66quoN7exN62ag52/IgbqtayMHs2roCHFfmLh7xG3Z40tu3xYNCl89WbFrBm\nST6SJJEeMqNVadmfoHaoPGphXdfSQ8bEZO4Ni8Pp43irI/7/je195CZYSHe4unH4+jD5imjr6OPd\nXS1xG2StWkR6RkOayQy90Og4iTfoi/dwUilV3DjnKs4vXMbje/7OnrZD/HrrY9RsmEOSScuFi/MG\nnWu4CEgsvQ2gKNvCkRO2GZ/e1tDVAUAkoOMPzx+gNDeJ8oJkmjv70KiVZCTPXLcwwcxCRHoEAoFA\ncNZw3NZIIByMp7YNxeKceSzLXYAv5KfN2Tnq87f0tvGX/c9j1hjJNWfxVt0mGh2tLMiqwqjWx+sL\nut2y6JmfVcV9F3+Zr63+DElaM88ffp3/ee83QOJ6HpDFw3t7WijNS+J3X7+ES5YWxFOWVEoVczMr\nONnXEU+pi3Gq6JkK9tV2EYnA7OJUAJo6EpsoHO2qA8DWLi8+qxus+PxBtBrloJoSQWIyk+S/bZtb\njt6k69MGPm9K51sX3s2y3AXU2U4Q1Fqx9/oSOgAO5dwGA9PbiqI26DPdyOBgo/yarKwsJhgKc/9T\nO+mye2jtciasWxIIhkKIHoFAIBCcFUQikXgEZnZG+Yjji5LzAWiMFoaPRDAU5HfbniAQCvD55Xdw\n93n/iYS8oFqet5BUfXJ/pMdtByDdmIokSawqWMqvrv4+66quAOQO5fMS1PMA1DTKx169qpjM1MHR\nqkXZcwAGRXsKssyolAqODyF6PL5gfME7EeyJprZ95GI5jXCoHkGxfkT0ZVCUbaat20W71S3sqsdA\ndlT09ITkZrsvr+9gX+1AsS5JEtdXXQ6AKvsEwVAYVwLBMlx626miJyfNgEatnNHpbb5AiCabbOP+\nmWuWcdsVVXTa3Hzll+/i84dEPY9gTAjRIxAIBIIZjyfg5eWOd3izbiMpuiTmDxFFOZXiaNf2mBtW\nbXc9v9z8R9x+T8Lxz1W/SoO9mTUlqzgvfxEV6aXcOOdKUnRJLM9fRIo+GVfAgy/oj0d60vUp8eN1\nah23L7yRX139A3582TdJ1lkSXqe2SRY9FYUpCZ+PiZ7T7bHVKgXFuRZOtPURDPXv8IfCEd7cdoLP\n/d967v7pBk60nbmtdSQSYV9tJ0kmDSvm5aDVKBOKnnpbM0e66wg50rhm6XwuXiILTacnIEwMxkCy\nXl68+5SyoA159Dz43H68pwmSqvRyUpRZKFI6kLQu7L2DG5q2dPaRlqRLaFpw6mMZyQYMOhWeGZze\ntnl/KyGFBwmJNGMSH19bwWfXzcPlkeecL+p5BGNAiB6BQCAQzHj+uPsZjjobqEov4/4r7h2VfW9/\npEdOj/l3zXq2texhW8ueQWOPdh3nxaNvkmlM467Ft8Yf//j8dfzhhvuxaE2k6uXdeLunh263DYvW\nlNAWO9uUQVm0+WQiapvsaDXKeMPRQcebM8kypnOw4yhbmnbzeu27uAOyUCvPTyYYCtPpkBd9+2u7\n+Oov3+PB5/bT6/IRjsDm/SdHfG1GoqbJjq3Xx6JZmSgVEgWZJlq7nIRC/Q0zA8EwD7zxTwAygnP4\nxJVVzCnpT8sSJgajx6QxAhAzZrtgdgUdNjd/ffPogHGSJJHim40kgSq7kZ4+34Dnvb4g3Q7vkBEQ\ntUqBWiUv/TJS9Ri0qhmb3hYIhnnhveMoNF6StBYUkgJJkrjhojJ+8NlVzC1NY+W87OmepuAsQoge\ngUAgEMx4jnQew6Q08P1LvhYXHyNhjgqVxp4WwuEwh6K9c/acHNjA1B3w8OD2JwC4Z8Vd6E/rKB6r\nt0nRy31CbJ4eut120g2pY74Pjy9IU3sv5fnJKJVD/wQvzJ6DJ+Dl11v/xBN7/8EHjTsBKM+X51Dd\n5OFHj23nvke20Njey2XLC3jo/12KSqlge3XbmOd1Ok+/fgSAK1YWAlCYbSEQDNNucwNy89EfPrmR\nbqkOVcjEA3fejEmvZlZBMqrofek0ItIzWkxaY/zfaoWaL924kpw0Iy9vOs6xZvuAsX0n04gE1CiS\nurD3DYz0xOt5EqS2xYhFezJT5EjPTE1ve+ato5xoc6DQ+skwDoyKLqnM5CdfvICS3KQhjhYIBiO2\nYQQCgUAQx+sPzrgdeqffhdVjp8SQj0oxtoV0UXI+e9sOsa/9MK5otORAxxECoQDqaFPRJ/c+R6fL\nyo2zr6Iqo2zIc8XE1omeFgKhwLhET11LD+EIzCoYXrjdULUWlUKJLxRgQ/0H9PrkxWxZnnzc5sN9\nQB/zytL49A3z4iYHC2als+doJ+1WF9lpxoTnjkQiuDwBuno8dNk9dNnddPV4CIUjfOTiMpra+9h/\nrJsllZksKJddxAqjaURN7b0km7T8z2PbqPXuQ20Oc+v8KzAbtABo1EoqCpM53GBDlyC9SpCYWKQH\nIMeciU6j4p5bF/Ld32/hd//Yxy+/ejEqpYJgKMzJLjfKND2SzkVPnw/jKX/m4UwMYuij0Z1kkxaD\nTo3PHyIUCg8rwqeaww1W/vXOMTLSVTgJkzLKjQ6BYDjEN5JAIBAIAHhvTwu/fmYPX7p1EZctL5zu\n6cRpcciRiwxN4hqY4ShKzmNv2yH+XfM2AFnGdDpc3RzpqmNB9my2t+zlvYatlKQUcMvca4c9VyzS\nc8zaAECaYfj5tHY5+WBfKzddUo5aJYu12qiJQWXR8MdmmtK5c8mt1FlPsKH+g3h6W1GOhcwUPYGA\nny98dAkr5+UMaFa5cl4Oe452sqO6nRsuGizgHvjLLnYeacfjS9zgdP2OJswGOWXvP6+ZHX+8MJqK\nd/C4lWffrqW+1Y5leSsKpYYryi8YcI65pWmy6BGRnlGjUarRKjX4Qn6yzbLQXFCewdrzCnl7RxMv\nvFfHLZdVcLLLSTAUwSDpCSh76ep1kneK6DnZLfdSGi7Ss3ZFIW5PEH/Ih1Inp8d5fEFMhinwQR8F\nbm+AXz2zhwhw+/XFPFLNqKO7AsFwzBxZLxAIBIJppbmjj1A4wm//vndC6kImiiaHPJcMzdgjK8XR\nup7qzlokJG5b8BEA9rQdostl5dGdf0WtVPOllXehUg6/DxhbeMVEz0iRnpc2HefpN47y+tYT8cdq\nm4c3MTgdg0a2gY6JHrVKwSPfvpwvX5/Nqvm5AwQPwIq5co3DtkPtg87VZfewaV8rWrWK8+Zkc+35\nJdx57Ry+cftSfnrPBfzXjfPxB8O0WV1ctCiPsvz+hWZhtmzK8O/366lvdbBkRYSA5GJNyar4HGPE\n6npEpGdsxKI92abM+GOfun4uyWYtz7xVw8kuJ41RM4k0oyzAu5wDU986bE4knZP0ZO2Q1/nY5ZXc\ndf1cntr3L47pXwJFaEaluD3+72rarW5uWlNOSvQjFttwEAjOBPGNJBAIBAKAAU5RP//rLrSaFSyb\nnTXsMW/Xvc/2lr18ZdWnMGsnxz62OSp60scV6cmP/7s0tZDleQvQqrTsbNnH3rZD9PldfGbpbeRb\nckY8V0z0dEb756Qbh59PW3TX/Z8bjnHlymK0aiW1jXaSzdpRN1Q0qAeKHgCVUjFI7MTnaNFRWZhC\ndYOVpvZeCrLM8bHV9d0A3HxpOR+5eLDl95ySNBZWZLB+RxPrTosSZSTr0WuVeHwhblpTToPhDeiG\nq2atGXSeeWVpLK3KZNW8kV9TQT8mjQGrx05OtDEpgMmg4b9uXMBPntrJ757bx9yooMxLTaPdCjZ3\nL9BviFHnPIxuwRb+b/tB1pSs4pLS1fFGp6fT2tdBSPIjqfx4ZoiZwY7D7by5rZGSXAu3X1XFxsat\ngBA9golBiB6BQCAQAHKKC8A9tyziD88f4P4nd/DDz65ifnl6wvFvHtvIY3ueBeCtuk3cPPeaSZlX\nk+OkbFmrGXuKS44pE41SjT8UYGH2bNRKNQuyqtjZuh+Aj8y+kivKLxrVuZJ0soCINYQcKdLTbpVF\nj73Px5tbT7C4MpNuh5cVc7OHFC2nExM9nkBim+1ErJqfQ02TnS8+8C7pSTru/eRyKotSOVQvi7W5\npWlDHpufaebO6+YOelyhkPj8jQsIhiLMqpB4/e06FmbPIc8y2D1Lp1Hxw8+uGvV8BTIxM4Mcc+aA\nx1cvyGHF3Gy2V7dz4qRsR16UnsFuKzi8A23E7UG5t4/T7+KFI2/wwpE3mJtZwSUlq1mRvxjtKW6D\nLr9sSoEyOK0Obr0+J7/Y/CgZ+nS2blSjUhr5+ieWolYp482ARXqbYCIQ6W0CgUAgAPpFz7I5WXzn\nrvMIRyL86PFt1DTaBo39oHEnj+15liStGb1Kx1t1mwiGE9eJnAmRSIRmx0myTRmoFWPfp1MoFBQk\n5QKwIEuuUVmRvxiAS0pWc9v8daM+l1KhJFnb33tnONETDIXptHsoyDKh1yr521s1fPVXGwFYWpU5\n5HGno1GqUSlUuIboLZSIay8o4fM3zmf1ghy6HV7+9mYNAIeOW9FrVZSO0/HqsuWFXLmyiDfq3gPg\n6lmXjOs8gsSk6VNQSApyzQOjq5Ik8YWbF2DQqXB6ApgNanKS5Cij098vekLhCJ6wbGTwi6u+xz0r\n7mRuZgXVnbU8uP1JPvfyt1h//IP4eKdfFuWSMojbN329eg60H+FI1zE2NW0lULKJ9PN2cqh3J70+\nJ3aPAxCiRzAxCNEjEAgEAgC8flm06DUqllZl8Y07luHzh/jhH7fRcNIxYOzrte+glBR8b81XuKRk\nFXavg23Ng/vfnCk93l6cfhcFybnjPsdlpRewJHc+FWmlAFxQtJz/u/xbfH757aOOuMSILb6UCiVJ\nuqEbI3b3eAiHI5TlJ3PdBaW4PAGMOhVf/fhirlxZPKZrGtS6AeltI6HTqLjuglK+/cnzqCxMYV9t\nJ8dbemjtcjK7JPWMXLp6vX1sbtxJtimDRTlzxn0ewWA+seAjfH/NV0lOkMqVlqTnzmvl17sw20JS\ntPGtJ+wmHJYjjzaHF9ReiEhkGtO5qHgFP7jka/z22v/hpjlX4Qv62ZBA9KAMTGukp6VXNioJtJZh\n9BXiDNv5875/8vmX72VrtKeWED2CiUCktwkEAoEAkCM9kiTbDgOcvyCXr3x8Cb96Zg/ff2QrFy3J\nY29NF6V5Flp07eSYsyhMzuOqWWt4/dh7vF77DhcULZ/QOcXqeQqTcsE3wuAhuLzsAi4v63cYU0gK\nytOKx3WuFEMy2BtJ0yejkIYWD7F6npw0I7dcVkF5fjKLKjIw6NRjvqZRbRiT6DmVS5cXUNNk5/f/\nOgDAvGFS20bD+voPCISDXDVrzbD3Lxg7qYZkUg1DL+6vXFlMj9PPnJJUknTR/jxKH26/3DC2w+ZC\n0njRKYwoFP1/m2xTBh+fv46NDdvp9cuRIH8ogD8kR3ck1fSktzmcPv6xvpZtzmpQg7qnhJ/eeTU6\nQ4hNjTt4t34zzb1tWLSmQb2zBILxIESPQCAQCABZ9Og0ShSK/ujHpcsK8PqD/P5fB3h5Uz0AzbYu\n9Iu98eL/bHMmi3PnsefkQb7+xo9I1pmxaM0kac0k6Swk6czMy6oi0zj2BXeToxVATlHrnICbPENS\ndfIu/GjrebLTjKhVClYvGH+kyqDWY/XYRx6YgAsX5fHHFw9R0yQfP680cX3WaAiGQ7xd9z46lZY1\nJaJmZ6pRKCRuu6ISkBvkAqD24/TIEdoOmwtJ7cOsTvzeNGuNdDhlM4t4PQ+AMohnGtLb1u9o4uX3\n69HOt6JQqPjyTSvJTDUAcF3lZVxbcSkN9iY0Ss2YI7ICQSKE6BEIBAIBILu3JWpMes3qErnRZQTs\nfV5++5rc8yY/qb+I/Za519Lp7MbqtsejM6cyK7WY/137rYTX9QS8vFm3EaPaQKYpjUxjOhmGVFRK\nVdyuuiApl47O6bfRju3EpxtS2X6ojYrCFFIsg3eh263yojI7zXDG1zRodPhDAYLh0Jibs5oNGlbM\nzWbzgZNo1ErKR2iKOhw7W/dh9di5qnxN3GBBMD1YtHJqpaT24/LKkZ4mqxVJERkyFcysNcUb68ZT\n2wBpmtLbjrX0gBRGZfBQnlrEBYvyBjwvSRKlqUVTPi/BuYsQPQKBQCAAwOsPoh+it8qSSrn43h8I\n8ej7biJArrlf9JSlFvHLq78PQCAUoNfnxOHto9fXx5/3/ZP6nmYCoQBq5eD0rj/vfY53GrYMeExC\nIlWfjDvgQaVQkW3KpIPpEz27jnTw87/u5qMflfufqMJGfvzEDvIyjPz8yxcNauzYZu1PbztT9KfY\nVlvGYQt+6fICNh84SVVRCmrV2FLSgqEg9214gDZnJ6GoUcVVsy4e8xwEE4tKoUSr0OFR+XF65b9L\na083SJBlSRxRNUf7APX5XYMiPdMheupbHJiS/YQi4VFZxgsEZ4oQPQKBQHCOE4lEONnXwf72w3S5\nbPT6+liUPZcLi88bMM7jC5FsHj53XqNWkp0foS0CTrsWEmzEqpVq0gwppBlkh6mdrftp7W2n2dFG\naWoh7oCHLpeVwqQ8DnXW8E7DFoqS87mu4jK63FY6nVY6Xd10uqx4Qz4W58wbc4Rjotlb24nLE8DZ\nmUGOKROtNwew0trl4idP7eSHn12F6hSDgHarC61GSbJ56CaRoyXeq8fvHpfoWVqZyc2XlI/YcykR\nNdZ66u1NJOks6LRaluTMIzeBTbVg6jGqTXjVDpweOdLT5bSBGfKTE6cwxvpo9fmcp0V6gri9U5ve\n5vQEaLO6KJsb5iSQJ0SPYAoQokcgEAjOQbxBH4c6atjXVs3e9mq6og01Y+xqPcCK/EVoon07IpHI\nsJGeU9GYPER6Yf8hN1ctGnkupSmFADTYmyhNLeTx3X9nU+N2ZmeU0+22o5AUfGH5f1CaWjjo2GA4\nhHIGFMx3RNPVGptC/OYz/80v/rYbgFkFyew/1s2jLxzkCzcviPfxabe6yU41TEgtQqIGpWNBqVQk\n7L0zGva1VQNw93n/weKceeM6h2BysGjN2Hzd9PXKgsXu7QEzZJqGquk5VfScEulRBXH7Jj/S85fX\nj7DtUBu/+urFHG+Ra5JMKT7wD0yVFQgmCyF6BAKB4ByisaeFv+x7nsNdxwiG5YWMQa1nZcESFmfP\npTA5j/catvJm3Ub2tB1iZcESAHz+EJEI6DTDR1QikQhWXxfKoIkdB7tkK2b98I5kJXHR00w4HGZ3\n20GUCiVHuuoAWFd1RULBA0x7hCdGh01eJB49YSMcjlDTaMeoV/Pj/1rNvQ99wOtbT5CfZeKGC8vo\ndfnx+IJyHdQEcKai50zY134YtULFnIyKKb+2YHhS9RZO9ILD7yEUCuMK9qEEUvUpCcfHooS9PtcA\n0SMpg3imIL1tf20XTe197D7aEXc3ROuURY+I9AimACF6BAKB4Bzi5aNvc6DjCEXJ+SzJmcfinLnM\nSitBeYp4UCmUvFm3kQ8ad8ZFj8cvL3p0I0R6en19OP0uco1lHA+G+WB/64h9ZwqSclAqlDTYm6i3\nN+Hyu7m09HwuLVlNTXc9V87wGpFIJBIXPU5PgMMNVtq6XSypzMSgU3Pfp1bw9d9s4rGXDpGbbsJk\nkEVgTvrEiB5jXPR4J+R8o8Xm6aGxp4WF2bPRqjQjHyCYUtJNSdABfX4PVoeXiFp+f6QNYXtt1kZr\nehKlt7knP73N1ifP7/19/bV5zogNrUobT4UVCCaT6c8ZEAgEAsGEEIlEqO6sxaI18bMrvsNtC9ZR\nlVE+QPAAFCXnU5CUy562Q/HFj9cnF0MbRhA9rb3tAMzLK0KSYMPO5hHnpVaqKbTkcsLRyt62QwAs\nyJpNRXop11ddjiaBucFMos8diPcwAnhx43EAqorkhVpmioHv3nUeSqWCn/1lFzuq5dfobI/0HGg/\nAsDC7PGlxgkml1gTU1fIQ4fdjaSRRUWKbnBzUwCzJpre5h8oehTqyU9vi0Qi2HvlRls7Drdz5IQN\no15Fl7uLfHO26PkkmBLEu0wgEAjOETqcXdg8PczJrBixluSCwuUEw0F2tOwDZOc2GDnSE+ueXpFZ\nyKJZGRw5YaO1yzni3EpSCgiEAqw//gESEvOzKkdzSzOCDpu8QJxfJheIb4+Kmsri/tqJqqJUvvKx\nxXh8QZ7bcAyYGLtqAINmekRPrJ5nUc6cKb2uYHQk62Tbak/YQ0tHH5LGi15pRKVM/Bm2xGt6OLTl\nSgAAIABJREFU+t3bVApV1MhgckWP0xMgGJINF3z+EN09HgoLlQTCQfKEMYZgihCiRyAQCM4Rqjtr\nAZg7ivqL84uWA/B+4w6A+KJnpJqeFoe84M+3ZHPZcrkOZ8POpmGP2XG4HSOyYLB7HZSmFMaLqs8G\nYj13ls/JxqiTF5SSBJWFA1NyLl6Sz8fX9ou5ibCrhumJ9ITDYfZ3HCHdkEqeWSxKZyKxXj1BycfD\n/9qPpPGSpEkc5YHERgYZxlS5Oekku7fZe+Uo1OxTNgrSMuXvnPwkUc8jmBqE6BEIBIJzhOouOcIw\nN3Nk0ZNpTKMstYjDXcfwhwLxSM9I7m2xSE+uJZuV83Mw6FS8u6uZUDiScPzrWxr40WPb2bK9P51m\nQfbsUd3PTCFWz5OTZohHdwqyzAkNHD5xZSVrzyukOMcS7y5/psREj8s/daLnRE8LLr+bBdmzJ8SB\nTjDxJOssABRkg8EYQVKEyTIndm6DU/v0yOltaoWKZF0SEUUAjy9AJJL4MzwRxFLbFlVkUJgtizW9\nRX4sx5w5adcVCE5FiB6BQCA4B5DreWpI0ppHnS5SklxAJBKhra8jXtOj0wwtetx+D3W2E2SbMtCp\ntGjVSi5clEe3w8vBuq5B49/d3czvnz8AQGerCgl58Xy2ip6sNCNzoqKnqijx4lKSJL78scX87huX\nDOjbcyZMR6SnydEKQFlKgkZMghmBJZrelp4W5r+/uBiAHEviHj0AGpUGrUpLr8+Jy+/GpDFiUMt9\nucKKID5/aNLmao+aGKRYdHzkojIyUvToTfL10oZwmxMIJppRfSNv2bKFp59+GoDu7m4aGhomdVIC\ngUAgGBvtzi7sHseo6nlixNJKWnrb8PhGjvRsqN+MN+jjkpLV8ccuWxZLcRtoaLD14El+/exeDDo1\nlYUp+AMS+eY8DGo9FWklY7q36abDKkepslINrJqfQ5JJwwULc6fs+sZpED3NDtlhqyBp6u5TMDaS\no+lt7pAHd6gPgNQhnNtimDVG+qKW1UaNIS6oJeXkmhnYopGeFLOWtSuKePy+K3BF55yiHzolTyCY\nSEYUPY888ggPPvggTz31FACBQIDvfOc7kz4xgUAgEIyeeD1P5qxRHxPrjdHsaBsxvS0YDvHasXfQ\nKjWsLbsw/nhVcQq56Ua2HGyLd3Xfc7STn/1lFxqVgh9+diXL52QBcHXezfzosm+gnuFubafTYXOT\nZNKg16oozLbw9H9fzeLKqUvJmY5IT7/oEfUWMxWtSotGqcYd8mJ1y80+R4qamLVGHL6+aKSnX/Sg\nDMY/v5NBLNKTatH1P+bpQZKkeJqeQDDZjCh6XnnlFZ588kkMBjk3OScnB6dzZKcegUAgEEwdh6P1\nPHNGUc8TI1GkR6dNbGSwrXkPVredS0pWY9L2F+hLksSlywvwB0J8sP8kh453879P7kAhSXzv0yuo\nKkolP1PekXb2qM+6yEE4HKHT7iFrgupzxoNKqUKtVE+t6OltI1WfjFEzffctGB5JkkjSWegLujjc\nJW96DNWjJ4ZFayIQChAhEk1vi0V6Arg8kyh6opGeZLM2/pjN4yBZaxlkqS8QTBYjNifV6XRoNKIp\nmUAgEMxkGuxN6NW6MTltpeiSMKr1tDraySTm3tb/sxCOhDnZ28HR7uP8u+ZtJCSuqbx00HkuWVrA\nX984yvPv1mHr9RIKhfnuXeexoDwDgLxM2TVqNNbWMw1br5dgKExW6sQ4sY0Xg1o/ZaLH7fdgddtZ\nmC2sqmc6yVozXS4rm5t2ISGRPYIpQKxXDzAgvQ1VkJ4+36TNM17TY5YjPZFIBJunhwKLiCQKpo4R\nRU9OTg67du0CIBQK8cgjj1BRMfqdRIFAIBBMLv6gn5N9HVSmlY7JaUuSJPItORyznaBS7QcidHhb\nqDm8g5ruemqt9fF+HgCXlV5Atilj0HkyUwwsKE9n/7FuFBJ88z+WsXxOv/jKTTciSdDS2XdG9zkd\nxE0MpjHSA2BQ63BPkXtbc280tU0sSGc8H5lzFa/v38Cy8kXMz6oiVT9CTc8pVvEDIz1BbFFb6cnA\n3ufFbNCgVskJRq6Am0AoMOJ8BYKJZETRc9999/Gtb32LY8eOsXDhQpYtW8bPf/7zqZibQCAQCEZB\nc28bkUiEouT8MR+bl5RDjbUeu9+KMquJPxx8M/5cljGdpTnzqUgvpSq9bNh+GjdcWMaRBhtfuHkh\nFyzMG/CcRq0kK9VAS+fZF+mJNSadftGjp9tlm5JrNTtkW/KzLRXxw8jyvIUo2oMsrVg6qvEDRY8B\ngyZaY6MMYp1E0WPr9ZGSAo09LRQl52OL1iAJ0SOYSkYUPZmZmTzxxBO43W7C4TAm09nTUE4gEAg+\nDDT2yPbCRcl5I4wcTGw3vyfQjSqrEbVCzZdW3klVehnJY3BVOm9uNv+4/zqUisSRpvxMM7uOdOB0\n+zEZxp4y/c93jrF1XzeLF0dQDHGNiaThpIPqeit7a2Qr7pkgegLhIIFQYNKNIIRz27mL5ZR6vIHu\nbQFsjvGLnsa2Xn7y1E7uum4u580dmGLrD4RweQIYK4/w3fVv8Oi6n2LzOADh3CaYWkY0MnjxxRfp\n6enBYDBgMpno6enh5ZdfHvHEPp+PW265hXXr1nHNNdfwi1/8YsDzjz/+OFVVVfT09Ix/9gKBQCCg\nsacFYFyRnlj0pkM6ikLn5ry8RawsWDImwRNjKMEDkJchb5i1jLOu5+3tjdS2eqlvdYzr+NESCoX5\n+9s1fPVXG3nkhYPsONyOJBE3Y5gujGpZdA1X17O//TC/3PxH/KEzK0hviaa35Y+y35Pg7OH09LbY\n+4ozTG/765tHael08vO/7h6UxmqP1gpF1B78oQDNjpPYPSLSI5h6RhQ9jz32GMnJ/W/K5ORkHnvs\nsRFPrNVqeeqpp3jppZd4+eWX2b59e7w2qK2tjc2bN5ObK3aRBAKB4Exp7GlBQhrXznyBRT7GrWoH\n4NLS1cMNHzf5MTODcaS4ef1B2qK9cnYf7ZjQeZ1KW7eLex/6gKffOEqqWcuXb13Evf+5nJ996UIy\nUvSTdt3REGsi6Q4kXpgGQ0Ee3flXtrXsod7WOKZzh8NhnjnwEl965Xsc7TpOk6ONTGMaOrVu5IMF\nZxWnGhmcWtOj1oTGLXqaO/rYerCNZLMWjy/I/X/eifeUnj/26HkjClmMN/WcxBYVPSlC9AimkBFF\nT6Ki2HA4PKqT6/XyhykQCBAKheLi6f777+eb3/zmWOYpEAgEggREIhEaHa1kmzLQqbQjH3AaKfok\n9LHFrU/P3KzJMaqJiZ7x1PW0dDiJROR/7z7aOZHTAuTXcP2ORr7yy3c52mjnwkV5/O4bl7B2RRHn\nL8ylqih1wq85Vkbq1fPeia10ueWan06XddTn7fU5+d9Nv+OFI2/Q4erm/k0P4vD2ki9S285JLKfX\n9ETfVxpdeNyi55/vyHb5d9+8gOvOL6GpvY8Hn9tPJPqhjTm3hSU/IKdP2uKRHpHeJpg6RhQ96enp\nvPlmf2HrG2+8QVpa2qhOHg6HWbduHatXr2bFihWUl5ezfv16srOzqaqqGv+sBQKBQACA1WPH5XeP\nK7UN+h3cAFS9RSikEX8WxkUsPWw8Dm4n2nrj/65ptNHn9tNhc/PoiwfZc7STcDgy7nk5nD7u//NO\nfvP3fUiSxNc/sYRv3rF0XHVHk4lBIy9OT3XTixEMBXn+8Bvx/+92j87w4LitkXvfup+DHUdZmjuf\nzy79BN6gnIpUKETPOckgI4PohodKE8bh9BMIjm5TO0anzc3GPS0UZJlYMTeHT90wj6qiFDbubeHV\nzQ2AbGIAEIjI/21ytGKP1vSkjtBXSCCYSEY0Mvjud7/L3XffzQMPPACAUqnk4YcfHtXJFQoFL730\nEn19fXz6059m48aNPProozz++OPxMbGdgJHYvXv3qMadq3wY7//DeM+JEK+DeA1O5fTX4rirCQCV\nWxr365QaMkNIibInb9Je60gkgk4tUdfUPeZr7Ngv7wqX5+ioa/Pyz9e3s6PGSYvVz7/fryfFpGRZ\nuYlFpQaMutE3OrQ7gzz+did9njBFmRpuXJWKmU727Jn4aNKZYu3pBuBQTTWBVln4xF7HfY4jdLtt\nlBjyaXC3cLixhiLP8P1aDvTW8FbXFkKREBemLmWVfhGSQ2Jtxmo2dG1F4xj/+2k6OJvmOhmM9v5D\nkVD833VHjqFTaJGQCCNHYzZt2UmyccSlYZzNh/sIhSMsLlazd+8eAK5erKWpXcEfXzpI0NnOsTYv\nSGGCETnlrcHaRJLajEpScvTAkTHZ7I8G8V74cN//cIz4zi4rK+PVV1+loUFW7CUlJahUo/9AAJjN\nZi6++GKqq6tpaWnhhhtuAKCjo4Obb76Z5557bsTo0dKlo7NjPBfZvXv3h+7+P4z3nAjxOojX4FQS\nvRaNhzuhDVbPWc7SvIXjOu+i8CJu+8HLpKakTOprXbL1fWqa7MydtxCdtv93JBgK4/WHMOkTu5K9\ntGsL4OT8OSbq2rxsOODE4fSzbHYWKWYtG/e28vY+B+8e7OOChblcvbqY2cWpwy6mQqEw9z70AX2e\nMJ+4opJb11YOa8Qw3fQ1+NnQvY3sglyWli6NvxcCoQB/eu1fqJVq/r9LPseXXv0+6BVD/h0DoQBP\n7PkH6zs/wKgx8JWVn2JRztz480tZyp2hj6NSju13fjr5sH9HjPX+9Y3P4Al6Wb1sFQqFAkPzM8Q+\nKnlFs8aUzrmv9RDg4OKV86koTIk/npbdxfcf2cKLO/ooz08GZXf8OU/YRzAYJs2YyrJly0Z9rdEg\n3gsf7vuH4UXfkN9qfr8fjUaDxyPnD+fny6kTgUCAQCAQr9cZCpvNhkqlwmKx4PV62bJlC/fccw93\n3313fMyll17K888/P8AoQSAQCASjJ2ZXnW/Jw+sLDhATo0VCgdejQJ89uQvdyqIUjpywcay5h/nl\n6eyr7eS3/9hHd4+HSASuv7CUT98wb5D4aGzvJSNFT1GmlmSTlh6nD4tRw1c/vpgkk5ZPXT+Xd3Y1\n89qWE7y3p4X39rRQnGPh6tXFrFmSj0E3WEz9Y30tRxvtXLQoj49fUTnhu80TzVA1Pe82bMHqtnNt\nxWVkmTKwaE10DVPT8/PNj7C3rZri5Hy+fv7nyErQbPZsEjyCsWPRmlAoFCgUciqrQa3HFZTrbcZq\nW93nlo8zn5YOunBWBndcPZunXjuC1dGOpAsOeF40JhVMB0N+s9166628+OKLLF68eNBzkiRx5MiR\nYU/c1dXFvffeSzgcjtf2rFq1atB5BAKBQDA+3AEPh7uOYVDrefjZWg7UdrO4MpM1S/JZOT8HrXp0\nqV7+QIhIBHSa0aeGjYfZxam8uPE4RxttzC9P5/WtJ+iye5hdnEpPn49/v19Ph9XNN+5Yij4q3npd\nfmy9PpbNzkIhSSyfk8XbO5r4/I3zSTLJxg0mg4YbLirj+gtLOXi8m9e2nGDbwTZ+/68DrN/RxC++\nctGA35u65h6efbuGjBQ9X/jowrPityiR6AmEArxw+E00SjXrZl8BQIYxjaaeVsKR8KD6rEAowN62\naoqS8vjRZd9Eq5pZdUuCqeGORTfhi4ockN9bPR651m6sZgZ9LtmRzWwc/F766KWzqGm0s726HbVG\nTqvLMKTGDTdEjx7BVDOk6HnxxRcBOHr06LhOXFlZyQsvvDDsmA0bNozr3AKBQCCAvx14EYe3l0KW\nsPdoF2aDhl1HOth1pAOjXs0lS/K5YmURJbnDLy48fnkXdjxRorFQVSynzRw5YSMUCrO/tovMVAM/\nvecCXN4gP/3zTnYcbufbD3/A9z61grQkPY1RE4OibDPg5c7r5rJmaT7zy9IHnV+SJBaUZ7CgPANb\nr5efPrWTww02OmxustP6mzK+sLGOcATu+eiiIVPqZhpGjdxPpcfT36doQ/1mrB4711VeTrLOAkCG\nIY3jtkYc3r5Bi8pY8XhRcr4QPB9iVuQP3MyWG9/6gcjYRY/bj0ICQ4LvDkmS+NptS/jm7zahsHjp\nBKoyyulq3AGIHj2CqWdYm55gMMiNN944VXMRCAQCwRC4/R4O9Nby882P8LcDL/L+iR28VbcJizKV\nmp3plOYl8dh9a3n4/13KRy+dhUal4JXNDXz5F+/xtV9v5PUtDbg8iZtWeqI9NRItXCaSVIuOzBQ9\nR0/YqW3qweUNsqQyE0mSMOnV/OCzK7liRRHHWxx84zebaDjpoLFdFj3FOfKi3mLUsKA8Y8ToTKpF\nx/kLZAey6vr+dC97n5ctB05SmG1mceXg1K6ZSr4lmyStma0te/AH/QTDQV448gZapYZ1VWvj4zKM\nsrBMlOLW3xtF7LAL+ok5uKEMYh1HepvJoEExRD2cUa/m119bw8euKgWgLLUIlUL+nhGiRzDVDPsL\np1KpMBgMeL1edDrRpEwgEAhGy/GWHmqa7Fy9qnjc6VPBUJB97dVsatzB7pMHCYQGi5bOAxWkWQx8\n/9Mr0GtVFGSZ+eS1c7jjqip2Hengre1N7DrawcP/OsCfXq7mruvmcN0FpQPO4fXJqSeTHekBOdqz\naW9r3M52cUW/8FApFdxzy0Jy0408+ephvvXg+3Gr66IcC7a2sbmqzS2VDXIOHbdy2fJCAN7a1kgw\nFOGa1SVnRVpbDLVSzaWl5/PCkTfY3LSLY7112D0ObqhaS1I0ygNyehtAl9tKBQP/zv29UcRiU9BP\nLHVSUgbHHOlxugOYDcNHSzVqJb6QfF6L1kSeJZvGnhbRo0cw5Yz4C1dcXMwdd9zBlVdeicFgiD9+\n++23T+rEBAKB4GzmHxtq2XKgjSSTNh5xGC1dLisvHnmTrc17cPpdAOSZsylV53HjimuptzXxxAdv\n09NmoiSpiO9+6jzSkgaayyiVClbMy2HFvBysDg/v7Grm5U31/PHFg+RnmlhU0W9pHIv0THZND0BV\nkSx6Nu1rQaGQWDBrYLRFkiRuvnQW2WlGfvm33Rxr7kGhkMjPNGFrG9u1inOTMOpU8UhPKBTmja0n\n0GuVXLJ0fH2NppO1ZRfy4tE3ef3Yu3T32dCqtNxQuXbAmHRDLNIzuFePTfRGESQgJnr0xrHV9EQi\nEfrcfrLTDCOOdfk90WsZKEzKjYoe8T4UTC3Dih673U53dzdZWVnU19dP1ZwEAoHgrMftkYXEn185\nzHlzslCrRhYU1fVWTnR18lrXX+lyWUnWWbi24jIuLFpOSUohe/bsId+Sg7tHR/feduaVpfGDT68c\nMUKTlqTnlssqWFCezr0PfcADT+/m119bQ0aKvNjxRmt69FMQ6ZkdreuJRKCqKGXImprzF+aSlqzj\nx49vJyfNOKrX73SUConZJWnsOtKB1eHhaKOdboeXa1YXJ3R0m+mkG1NZmruAXa37AVhXdQUWnXnA\nmMxopKc7oegRkR7BYMxaud7NYolg6xy96PH4goTCkVE18nUF5N5SRo2eq2ddglalpTytZHwTFgjG\nyZC/cK+99hrf/va3MRqN+Hw+HnzwwUHuawKBYPJp7ujjiVeq+dIti0ixiDTTs4WYkGizunh1cwMf\nubh82PGRSIRf/30n9sz3UJgc3DTnKm6Zex1KxeDF/vv7ZJvqj1xUNqaUtMqiVD6zbj5/eP4AD/1z\nHz/8rPyd3h/pmXzRU5xrQaNW4g+EWFw5fAPNqqJU/vidtZxJFtr8Mln07DnayXPvHEMhMSi972zi\nyvKL2NW6H42k5vqqtYOeT4/V9LhFTY9gdKTq5f46elOQ9sYAvkBoVM6PvS7ZAc6SwLntdNzRSI9R\nbSA/KYfytOLxT1ggGCdDGhn8/ve/59lnn2XLli089NBDPPzww1M5L4FAEOXtHU3sPNzBjsMd0z0V\nwRjw+kNo1EqMejXPvl0bXyAMRXNHH1bTbhQmB3p3MbfMuT6h4AmHI3ywrxWjTsWSquFFQyKuWV1M\naW4S+4914w/ItTxe39RFelRKBRWFcqRhNEYCeq3qjMRYrK7nTy8foq3bxQ0XlVGQZR7hqJnL/Kwq\nrii/iMszVmHRmgY9b1DrMWoMCdPb7J4eJCSSdUL0CPqJRf7Uevk7yj7KFDenW64xNI1Q0wP9kR6D\nZvgejwLBZDKk6FEoFMyePRuAlStX0tfXN2WTEggE/dQ0youXtm7nNM9EMBa8/iAmvZqPr63A5Qnw\n97drhh2/7VAbypQOCOiwVVewcW9LwnFHG210O7ysnJ8zrpQvSZKYV5ZGMBSmtskOgCdqZDAVogfg\nE1dW8bHLK6goSBl58BlSlp+MTqPE7Q2SmaLnE1dWTfo1JxOFpOAzS29jvqViyDEZhlS6XFYikciA\nx23uHpJ0ZlQJxLTgw0tatMZLofUBjNrBrTfamNQyivS2WH8po3rk+h+BYLIYUvT4/X7q6uqoq6vj\n2LFj+Hy++P/X1dVN5RwFgg8twVCEumY5JaXd6p7m2QjGgtcfQq9Vcu35JWSnGXh1cwOtXUML1y01\ndUjqAAtzK9Go1PzppWoeffEgG3Y2caKtl1AoDPSntl20aPyF+HOi0Y/DDbboXGN9eqZmMTy/LJ07\nrp49pM3tRKJSKuL3+4WbF06ZsJtOMoxp+EJ++qImGCCnT9q8DlHPIxhEWjS9LaSUhUlXj2e44XGc\nUdEzmpoep9+NUqFEozz7aukE5w5Dfvv7fD4+97nPDXjs1P9/5513Jm9WAoEAgI6eAP6gvNhts7pG\nGC2YSfj8QVItOtQqJXdeO5efPLWTJ1+p5rt3rRg01t7n5URvI5p0WJJfycLrivjjS4f49/v9BjIa\nlYKMJCU9bjAbNCyYNbg552iZUyLXfVQ3yHUfU1nTMx184aYFNHf0sWx21nRPZUrIiDq4PbT9z3S6\nuvn0ko9RnFxAIBQQ9TyCQRg1BtRKNWGlvLG2r7aTNUtG3lTpc40h0uP3YFTrzyqbeMG5x5C/cELU\nCATTT0t3fx1Iu9VFJBIRPxpnAZFIBK8/FLeAXr0gh9nFqWw71M7B493MLxsoWHYd7kBhkiN6leml\nlFYUcfl5hZxo6+V4i4PjLT0cb3Vwos1BOAw3XFiKSjlsb+lhSTHryE03cvSEjVA4Ehc952oUJDvN\nSHaacbqnMWVkm+Var71thwDYeGI7lkq5jklEegSnI0kSafpkXAEnqRYdO6o7CIXCKEf4junzjK2m\nR6S2Caabc/MXTiA4R2ixyqInP9NES6eTXpefJJN2mmclGAlfIEQk0t/sU5IkPrNuHl//zSYee/kQ\nv/zKxQNSu7ZXt6Mw2dEo1BQmyzusOo2KqqJUqopS+8ft2EVuUeWo+mKMxNzSNN7e0cSJk454Dv9U\npbcJJpc1xStRKZQUJxfw442/pdZaL+yqBcOSZkihurOWi+dm8MbWZqobrCwoH95oJBbpMY/Cvc0V\n8JBmmPwaPoFgOMa/VSgQCCadlm4fJr2apVVyWo5IcTs78PllY4BTm31WFKZw0eI8jrc4eG9Pv0mB\n2xtgb91JFHons9JLhi0yVyklCrLM4zIwOJ05JXKdy1/fPMrWg20UZpvJSv3wREPOZXRqHZeXXUh5\nWjGz0opp6+uksUeuBROiR5CIlOj7Yk6F/B2w9eDInYD7ojU95hHS2/yhAIFQQER6BNOOED0CwQzF\n4fRhd4aoKEohJ13+IWrvFqJnMuiwuQlGjQImAm9c9AwMpn/ymjmoVQr+8tphvP4gDm8vWw+1EtTa\nQIKKtKnrHxOzct55uAOVUsE3bl+KcgqMBQRTS+w9tb1lLwCpBiF6BINJi4qezCwFRr2abYfaB7n/\nnU5f1LLaPEJ6W8y5TdhVC6YbIXoEghlKTdROuKqwX/S0CQe3Cedkl5PP3b+eZ98a3lJ6LMT63mg1\nAyMymakG1l1URrfDyxMbNvPFV+7jyWO/R5l+EpDreaaK7DQDqRY5VfLO6+ZQkisK3M9FKqLvqTrb\nCQBSRI8eQQJiqWcOn4Plc7Lo7vFQ19Iz7DF9bj9KhTRiLaDbL/9uiUiPYLoRokcgmKHUNsqip7I4\nlZxoEbbo1TPxHDlhkxt+7j85YeeMWUDrE7ih3XLZLCxJYd7pfhF/KIBP0YsqKnpmpZVM2BxGQpIk\nbr9qNh+5uIzrL5g6sSWYWmalliDRH8ETkR5BImJpjzZPD6vm5QAjp7j1ufyYjZoRzXVcsR49ItIj\nmGaE6BEIZiixvjwFmWYyUvQoFJLo1TMJNJzsBaC1y0nbBKUPehPU9MTQaBSkLjiMpPGi6Z6D//gC\nFCgpSs7HrDVNyPVHyxUrivj0DfOmpF+OYHowaPTkJ8mLWI1SLXbbBQmJiR6ru4cllZloVAq2HRpB\n9Lj9I6a2Abj80fQ2tRA9gulFiB6BYIZi65UdtZLNWlRKBZkpemFkMAk0nHTE/737aMeoj+uyewiH\nE+e8x4wMtAkiPX/Z9y86fC1oXPk46gsIWXO5b/X/49sXfXGMMxcIRkesridVnyws7wUJiaW3WT12\ndFoViyszae5w0tLZl3B8OBzB6QmMaGIA4A6I9DbBzECIHoFghmLr9WLQKlCr5I9pTpqRnj5fvKfK\nuUokEmHzgZNx0TfZ12o46YjvVu46MjrRs6+2k0/9+C1e33oi4fPxZp+nWUBvbNjG68fepcCSw93n\n/QcgUV6QzLyCQuGqJZg0KqJpkyniPSYYgiStGYWkwO6W63hWzR8+xc3lDRCJjOzcBv2RHpHeJphu\nhOgRCGYo9j4vZn3/ojk75uB2jkd73treyE/+vJO/vXl00q/V3eOlzx1gQXkGxTkWDtZ1x+txhuOF\n944DsHmIOqBE7m31tkYe3f03DGo937jgv1g1t4Cv3baYL9+6aALuRCAYmtkZ5QBkmdJHGCn4sKJQ\nKEjRJ2GN9nM6b242CoU0ZIrbaO2qQW5MCmAQkR7BNCNEj0AwA/H6gri9QUz6/o9ov5nBuSt6uuwe\nHnu5GoBjTcM7B00EsdS2klwLS6sy8QfDHKzrHvaYls4+9tR0AnC4wYrbGxg0xhcVTrEuzIfZAAAg\nAElEQVSanl5vHw9sfoRgKMiXV95FjjkTSZK4dFmhcE0TTDrZ5ky+v+Yr3DZ/3XRPRTCDSdOnYPf0\nEI6EMRs0zCtNo7apB6vDM2jsWBqTuoWRgWCGIESPQDADsfXJqV2nRnpittWtXeemg1skEuHhf+3H\n4wuiUStp6uglEAxN6jXjoicvieVzsoGRU9xe3dwAQHGOhVA4wv5jXYPGnBrpCYVD/Grrn7C67dw6\n7zqW5M6fyFsQCEbFvKwqUvRCYAuGJlWfTCgSptcr1/HEUty2JUhxG22PHgCXsKwWzBCE6BEIZiD2\nXh8wUPTMKpDz8Q832CblmuFwJJ6yMB0cPN7NriMdLKrI4NJlBQRDERrbExfRThT1MdGTk0RVUQoq\npWLY3hRub4ANO5tIS9Lx+Rtl8bL7aOegcbEUOa1GydP7X6C6s5bz8hZx45yrJuEuBAKB4MyJ2ZnH\nUtxWxqyrE6S4jS29TTQnFcwMhOgRCGYgNocc6THp+kVPWpKe3HQj1fVWQqHwhF/zD88f4M7/eQv7\nFBgIJKIpKnCuOK+I8nx5R/p4i2O4Q86YhpO9mA1q0pN1KJUKctKNtHQ6h+xEvmFnMx5fiKtXFzO7\nJA2TXs3uIx2DxsciPUcdB3m1dgN5lmy+uOKTKCTxlSsQCGYmafqog5tb7hGXnqxnVkEyB49bB22I\njUX0iOakgpmC+AUWCGYg/eltAz+i88vT8fiCHG+dWDFQ3+rgjW0n8AdCE37u0dLdI+8GpifrKctL\njs5r8up63N4Abd0uSnKT4ja++Zkm3N4gPX2+QePD4Qivbq5HpVRw5YpilAqJxZWZdDu8ccEWw+sL\nIhl6eb7uefRqHd88//Po1bpJuxeBQCA4U7LNGQA0O/oNWlbNzyEcjrDzcPuAsX2uaHqbcRTpbQEP\nSoUSjXLksQLBZCJEj0AwA4lFW0z6gZbH88tk96VDx4cvtk+ELxBKGMGIRCI8/u9DxJ46fQE/VXSd\nInqKcswoFdKkCrATbXJT0lONBPIz5eagLQnqpvbWdtLa5eKixXkkm7UALK3KBAb39/H5Q6jzawmE\nA3xpxV3kWrIn5R4EAoFgopgVtTavtTbEH4unuJ1W1+McQ6TH6XNhUOtFjyjBtCNEj0AwA4n1qDGf\nJnrmlaUBcGAEh7FTiUQiPP9uHbd+51Ve29ww6PndRzvZf6ybgix5wd/cMU2ix+5BIUGqRYtapaQw\n20zDyd4hG4CeKW9uawRgdklq/LG8jKjo6Rwsel75QH7trr+gNP7YkrjoGVjX4/R7UFisFCblsyxv\nwcROXCAQCCaBZJ2FTGMax6wN8Q2ygiwz+Zkm9tR0DbDzt8aaZ5u0w56zpbeNNmcnpSkFkzdxgWCU\nCNEjEMxAbENEetKS9ORlGDncMLq6nkAwzC+f2cMTr1QTDkd4/7S+MqFQmMf/fQiFBF//xFJUSmna\nRE+3w0OqRa6tASjLS8YfCNHdN/HNWOtaenhnVzMluZb4Tib0R3paTxM9J7uc7DrSQVVRCuUF/Q0e\nU8w6yvKTBllX2yMtSIoIy4RTm0AgOIuoSCvF6XfR1tcfvV41Pwd/IMTemv7NnZZOJ3qtKh71Hop3\n6rcAcEnJ+ZMzYYFgDAjRIxDMQGy9Pkx6NWrl4HSA+eUZeHxy7U0kEqHT5mbH4Xae21DLA0/v4sHn\n9sUF0fodjby3u4WKwmQKskzUNNoG7Na9taOJ5g4na1cU8f+zd9+Bbd3Xoce/F5MAQRLce4uk9qKG\nNWzJlrxkW46duKmdxEnsNslr3TRp0lc3r+81bV7SdKRN8tqmzo6dNkkTbyvxkGztTW1KpLj3AhdI\ngMS87w8QICluipBI6Xz+sU3ce/G7kEzg4JzfOfkZVtISLdS39U24kT9cfH6Vzt5BEqzD3X3y0gNl\nZy1dc9tRTlVVfjw0C+iZR5bh8bt5t/IA3QO9pCdFAYFZPCMF21Q/PCLLE1S8OBmvT+V8xXD2za6r\nB2B9xqo5XbsQQoRTYULgd9xkJW4+v0qLzUF6kmXSkjWPz8OB2uNEGS2sl4y3mAd0Ux8ihLjRuu2D\nxEaPv/F9RX48bx+r5e9fPIVjwINjcGwmZPOKNNYuTuLwUGbnLz+5gTcOVfPq/krKa7tZVZiIc9DD\nf71dRoRBy8fuXwwEShnqW/vGBCDh1tM3iN+vjnrO/Ixg0DN2+Of1OHW5jYtVNtYtScaa6OL5d/+O\n5r42Kjpr+eONn8RqMY6ahTTg8rL3VD1x0UY2r0wbc711i5P5771XKSlrG9r062fA0AweI7lS0iGE\nWEAKg/t6bNVsz90EBMYlxEYZQ2XV7V1OvD4/GUPlwBM51XSBPlc/DxftRC9NDMQ8IJkeIeYZl8dH\n/4CHuOjxywZWFSRiMuqw9Q4SFxPB1lVpfPyBxfyvT2/g+afXA/BBSQM9fS4uVdlYnB1LgtXEiuB+\noKEmCC9/UElPv4sP31MQCrCykgOZjvobXOI2solBUG5aDFqNQnnTwJwNKfX6/Pz4zVI0CuzYFs1X\n9v4DzX1taDVaLrWVo6oq6UkW2rqcuD2B53z/dAPOQS8PbMpFrxv7K7MwOzbQurqsHVVVudpZg6p1\no3OmSotqIcSCkmXNwKDVj8r0KIrCokwrnb2D9PS5Ql8KpSdNHvS8X30EgHvyNodvwULMgGR6hAgz\nr8+PTjv9D7/Bzm1xE2R6YixGfvbX96PVKBj0o/f8qKpKanwkxy61kJ8Rg1+FLasC2YllefFoFLhY\naaOje4DX9lcSFx3Bh+7KD52fGQx6WvtYW5Q0o/u8HsF21Ykjgh6TUcdDW3J541A1r3xQyUfvLbru\n53nneB1NHf08sCmHEtsxvH4vf7rpGU40nuN4wxla+tvJSLJQWt1Ji81BVkoUbx2uRqdVeOCO7HGv\nGWxdfehcE/VtfZS0XQis3zU2KySEEPOZTqMlPy6Hso5KnJ4BzPrA7+S89BhOXW6juqk31OglfZJM\nT3u/jQttV1ickE9GdOqExwlxI8nXkEKE0S/eKeNTf/sO3X3TH/jZbQ/MiJko6IFAQHBtwAOBb+S2\nF2fgcvv4+dtlQKDUDcAcoSc/w0pFQzc/fOMibq+fTzy4hAjj8HcfwUzPjW5mYBsn0wPwsQcWYzFp\n+O+9V2ntdFzXczgGPPzXO2WYjFp2353BicZzpEensDlzHSuSAuV9l9rKhzu4dfRz7moHje39bF2d\nPmG5IQy3rj51uZXjDWdQ/RosPgl6hBALT2F8LioqlZ21oZ8FZ6dVNfWEMj0Zk2R63q8JZHl25G0N\n30KFmCHJ9AgRRmV13fT2u3n7WB1P3je9TEWwc1vgQ/b0g6Wg7cUZ/OLdclxuH4VZVpLihqdgr8hP\noKKhh6MXWshNi+budaP3nKQlWtBoAh3cGtr6eOHVC3zqoWWjOpaFQ0f3UKYndnTQY47Qc/8aKy8f\n7eIv/vUQCVYTRr0Oo0GLUa/FaNASHWng9+8tItI0ec34b96vwO5w8/EHF3Pedg6v38uOvK0oisLy\n5MCfzaX2cu5MKgSgqrGH8xUdwOg21eMJtq4+VHuStkgbvo5MzIbJuxoJIcR8NLKZwcqUJcDwHsuq\npl7s/W4UJfB+MR6f38cHNccw603ckbn2xixaiGmQTI8QYRTM8Lx9rAaPd+oW0zAc9MRFTZxZmExa\ngoUlOYHZM1uu2Xi/YlFC6N+ffWQ5Ws3ozjt6nYa0hEjqWu18/ScnOV9h4/D5plmtYybG29MTtDzb\nxP13ZOP2+KlptnOxysbpK20cudDM+6cbeO1AFfvPNE56/fZuJ68frCIhJoLdd+axr+owOo2ObTkb\nAUixJBJviqW0rZzUxECQ+PL7FVyt72HbmgwKs2InvX5sVASx0Uba9OfRKhq8LXlEGOQ7JSHEwhNs\nZlDRWR36WaLVRJRZT3VTL00dfSRaTRjHqTYAONtSSvdAL1uz12PUTT28VIgbRd6VhQijnr5AqVqX\n3cWxi83ctSZjynOCgVJcTASD3bN73id2FPCf75SxvXh0JmdpbhxRZj3L8xNYVZg47rmZyVE0tvfj\nHAyUMDTbrq+sbDpsPQPotBpiIsdmRxRF4bknVvPcE6uBQLtUt8eHy+2jqaOf5//tMJerO3loS+6E\n13/pt1fweP18YtcSau21NPW1sjVrPVFGS+g5licXcaD2OG5NDzqtgtensmFpCl94cs207iEypYNB\nQz+b0zey74SJCMP4HwiEEGI+i4mIJjkygaudNfhVPxpFg6Io5KdbOTeU/V4zwfsHwL7qwwDslNI2\nMc9IpkeIMPH5VXr7XSRYTSgKvHmoeuqTGFneNvvyqPVLU/j2F7eP2RdkjtDzg6/cy//8xLoJzw3u\n61mWF485QjeqfXO42HoGSLBGoNFMPPMhSKtRQkPxlubGYbUYKa3pnHC2UEVDN/vPNJKXHsP2tZns\nqwrUmu/MH/2GvDwpUOJ22VbB3cWZbFmZxl88vW7aTSic0VdQVYXi2ECnIsn0CCEWqoKEPBxuJy19\nwwNJgyVuMHHnti5nD2daLpEXm0WOtOwX84wEPUKEid3hwq9CYZaV4sXJlNV1U9PcO+k5bo+Pq/WB\n9M5sy9umEmnST/pBfueGLB7ekstfPL2O9EQLLTYHPn/4hpV6vH56hoLDmVIUhaV5cXT2DtI+tC9o\nZPDj8fp54ZWLADy7exlOj5NjDSWkRiWxJLFg1LWC+3oud1Tw+Y+u4flPrh+3WcR4HG4nA5pu/PY4\nHL2Bcg7J9AghFqqR83qCggOjgQln9OyvPYaqqtLAQMxLEvQIESbB0rbYqIjQ3prLNV0THq+qKt97\n+QINbf3cuyEr1FWtw9HJj0t+RZezJ/yLBlLiI/ns4yuJjYogPdGCx+uno9sZtufr7B1AVcffzzMd\nS3MD84dKqzvp6XPxB19/j6//5ATOQQ8/fvMS5fXdbF+bwcpFiRysO4FnRAODkeLNsUQazLTY22a8\nhuC3oeqAhYb2QOe7kV3xhBBiISmMH25mEJSfMdzQZrxMj1/18371EYxaA1uyJ64mEOJmkaBHiDDp\nDgU9RgqyAm8WlQ0TBy5vH69j76l6FmXE8NnHV4Z+/uqVd3i7cj9fO/Ad7K7wl5qNFOzOE84St/Fm\n9MzEsqGg53JNJ28cqqK9e4Djl1r54394n7cO15CZHMUffWQVqqqyr+owWo2W7Tl3jHutFEsibQ4b\nfv/kTSf8fj/nWy/j8rqB4aDHP2imsS3wWkmmRwixUGVb0zFqDVwd0cwgNT4SkzHwey09MWrMOZfa\nyml3dLIpqzg030eI+USCHiHCpGeoIYE1ykhGUhRGg5bKxvGDnrK6Lr7/6gWizAb+8pMbQl1xvH4v\nx+pPoygKTfZWvnHg/+H0DNywe8i4AUHPZJ3bpiM3LRqTUcvZqx3sOVKD1WJk95152HoHMRl1fOVT\n6zEZdVztrKbB3sLG9NVER4x9w4ZA0OP1e+kamDg49fq8fOf4j/n6gf/H2xX7AWjpH8r0DEaGMj1G\n2dMjhFigtBot+XHZNPa24HQHfkdrNAorFyWSGGsiPmZs+fW+6qH9klLaJuYpeVcWIkyCQ0ZjoyLQ\nahTy02Moq+1i0O0dtcm9u2+Qb/7sFH6/yv/8RPGouTqVznocngF2L74Xu6uf/TXH2Fd1hEcW77wh\n95CWGAlAc0f4OrjVtdgBSIo1T3Hk+LRaDUXZcZy7Gugq9JFdBTyxo5B1S5KJsQQCTmDCBgYjpVgC\n83Za+9tJiIwb87jb6+ZbR3/A2ZZLAFR0BUo/WvoCJXHqoJmOoQ8IkukRQixkhQl5XO6ooLKrNjSv\n58sfK8brV8c0nbG7+jnZdI7M6FQK4ifupCnEzRTWTI/L5eKJJ57g0UcfZdeuXXzrW98C4O///u95\n8MEH2b17N8899xx9fTd2+rsQN0KwvM0aFejCtijTil+FmiZ76Bivz88/vHSazt5BPrFrKasLk0Zd\n45K9AoDtOZt4qPAeANocHTdi+cCI8rb28GR6PF4f+041YDHpWZ4fH/q50zOAz++b8vzKzlp+U7qH\notxoAMwROnZtDrzhrilKCm28dbidHG04TbIlkaVDw0fHk2IJtGFt7R/7Gjs9A3zj4L9ytuUSq1KW\nEmW0UNvdEDi+rwO9RodeHa5zlz09QoiFLNTMYESJW4RRh2WcQdCX2srx+X3cmbNxzH5JIeaLsL4r\nG41GXnzxRUwmE16vl6eeeorTp0+zdetW/vzP/xyNRsM//dM/8cILL/DlL385nEsR4oYb2cgAoGBo\nE2hFYzdLcgNZhJ++dZlLVZ1sXpnKh+9eNPr8QTvVzkbyY7PJiEmlb2g/T9fA5B3g5pLJqCM+JoIm\nW3iCniMXWujpd/Ghbfmh7FdbfwdfevtrGLQGVqcuI8+XOua8xt4WfnnxDU42nQPgsfwPA/DoXflE\njvOGfKjuJG6fhx15W9AoE3/XkxI1ftDT5+rnGwf/laquOjZmrOHzd3yafzj8Pc63XqHf7aC5v40U\nSyIOqzlUCiiZHiHEQlYwTge3iQRLgtOiksO6JiGuR9i/ijSZAnX6Ho8Hn8+H1Wpl0aLhD3erVq3i\nnXfeCfcyxC1IVVUqOmto7e+ga6AHvUaHUWfAqDVi1BmI0AX+mRmTdlM2VXaH9vQEWhgvyhzdzODg\n2UZeP1hFRpKFP/3omjHfjh2pO4WKyrbcwKZ7iyESvUZH9w3q4haUnmjhQqVtTFneXPjtkRoUhVB2\nBuBg7QncPg86jY7DdSc5oegotBVSmJBHh6OTX1/aw4G646iqSnJkAm0OG6qhnx985d5xS+RCDQwU\nDdtzN026nlCmp2846Oke6OX/HvguDb3NbM/ZxGfXfwytRktubBbnW69wofUKA55BUpKSsMeaJOgR\nQtwSYiKiSbYkUjFiSOlEuoeCnlhTzITHCHGzhT3o8fv9PPbYY9TX1/Pkk0+OCngAXn75ZR566KFw\nL0Pcgn5x8XVeuzJ1wFyUkM/Xdtz4TGJ3n4sosx69LvDhNy3Bgsmoo7Kxh6rGHr773+eGNtpvwBwx\nNjtR2hEobduQsRoIzKSJNcXQNXhjg560oaCnxeYgN23mb2gnLrWQmRJFWsLoFqdVjT1cqe1i3ZJk\nUhMCe4dUVeVw/SkMWj3//sjXOddSyneO/Zi/O/RvbMosZn/NMbx+L5kxaTy5Yjd5cdl87o2/pKWv\nnZT4yHGfv6qrjrreJu7IWIs1InrStUYbozDpIkKZnnZHJ1/b/x3a+jt4oGA7n1rzROiNP8caGLx3\ntL4EgNSoZIwjmjHIcFIhxEJXGJ/LobqTNPe1kRE9Nuse1D1UgSBBj5jPwv6urNFoeP311+nr6+PZ\nZ5/lxIkTbNy4EYDvfe976PV6HnnkkXAvQ9xiOp3d7CnfR7w5lseWPEC8ORaf38eg14XL68blczHo\ndXOo9gRXbdU43QOYDTc229PTNxjazwOBzjeLMqxcqrbxtz86jtvj4yuf2kBm8vidxOq6G4jUmogz\nDc9GiDNZKe+sxuf3odXcmExC+tC+nuaOmQc9DW19/N+fnGTdkmT++g9Gt4necyTQBOChLcNZnuru\nelr62tmcGWh5ujlrHVerKvht+0H2Vh0iKTKe31v+CFuz1qPRaFBVFaPOSOuIqeHXerfyIAA78rdM\nuV5FUUixJNLU1xqYm3TyRdr6O3h86YN8dPkjo7JxuUPTxoNNDVItiWhHZJpkT48QYqErjM/jUN1J\nrtpqJg96BgNBjzVCgh4xf92wd+WoqCi2bdvGpUuX2LhxI6+88goHDhzgZz/72bTOLykpCfMK57fb\n8f4nu+d32g/j8XvZYFlOfG8k9LrRApHoiEQHBD58NujTaKGdt46/Q35k5pyuz6+qnK9xUpAWgSVi\ndADi9an0OT3ER2lG3UeUYRBVhS67i3vXxKB3NVNS0jzm2gO+QTqcXeSaM0a/DoN+VFXl0KkjROnG\nz2zMtYHeQDey37x3kZPnyyc8zmzUsCbPTI/XTpw+BkVROHgp0LThcnUHp0+fDgUNTpefD0qaibVo\nUR0NlJQ0ArCv4zgAKd640H2viC7EoNEz6HezPGoR2k4tZzvPhp43RhNJs72N06dPA3C8+zxpEUlk\nm9Ooczazv/kYcfoYPI1OSpqm/v/I4NXh9nnYc/QdStuvkhGRTIE7nTNnzow6TlVVDIoet98DQF9L\nD46e4fk+FVev0Nk8979ib8ffBSPd7vc/krwWw2731yJc9+9zBcq0j5afJKbbOOFxLd1tmLURnD97\nLizrmAn5u3B73/9kwhr0dHV1odPpiI6OZnBwkKNHj/Lcc89x8OBBfvSjH/HSSy9hNE78P9FIxcXF\n4VzqvFZSUnLb3f9k99zW38HFqqukRiXx9LaPTprx0LaYOHbwHF4rFK+cm9fQr/qp7KylryOS148f\nJzctmm/+8dZRJWqBgZtNZKUljLoPn6mVo1dOcP8d2fzxR1ZN2OXmUls51ECyIX7U+ZfO1lB2tYaM\nRVksis+Zk/uZSlbeAL88+C6VLYNUtgxOeqw/wcEHtjd5Zu1HeaBgOy8eeg9D4WlcXSlk5e8I7bl5\ndX8lXl8zj929mPXrAiWvfr+f77/5ayINZj6yZTc6beDXU0lJCU9t+8iEz3lg8AzHG8+Qt3QRfe5+\nDr7zIzSKhk+teYL3mo6hUTR8edvnpv16lV9ooPxKDeXUA3Df0u0UF4z/dyfffoArHZUAbCu+k/ok\nN6+fOArAurWrQk0s5srt+LtgpNv9/keS12LY7f5ahPP+fX4fv2j5Hd3YKS4uZsAziNvnJuaaUuHv\n1L5EclTiTf9zkL8Lt/f9w+RBX1iDno6ODp5//nn8fj9+v59HH32UTZs2cd999+HxeHjmmWcAWL16\nNV/96lfDuRRxC9hfc4y9VYep723Cp/r5veUPT1niVZiQi6IolA19MJ2NC61XqO6u59HF96EoCgdq\njvO9Uy+xybIbgJpmO//48xL+6pmNaIdmFwSbGFz7oXf9kmS++6XtZKdET9rWs7Yn0Ao5yRg/6ufB\nUrfJhmfOtcRYE9/90t102icOeNweH//40mkO1pyGKPjVxTcoiF5Kg+Y0OqsNND4qG3pIijXj96v8\n9mgNBp2GnRuyQte43FFB92AvO/O2hgKe6RjuuNZO89C8HL/q58dnfgXAR5c/MqMAMTir52TjORRF\n4Y6MNRMem2PN5EpHJRE6I9aIaAZih+cZmWRPjxBigdNqtCyKy+ZyewX2wT6+tv872F39fG/3N0L7\nGwc8gwx6XcTJfh4xz4X1XbmoqIhXX311zM/ffffdcD6tuEX9pnQPHY4uMqJTWJO2nE2ZU3+bYdab\nyInJoLKrDrfPg0E7tmHAVH516U0qOmu4I3MtKZZEStuvAlDTXQ+kUJQdy+krbfzojUt85kMrgOEZ\nPbFRozOZiqJMa19MbXeg3Cv5mqAnuEm0+wa2rQbITo0mO3XyJgAPbc3md33voEHB4RngX47+AF1y\n4D40JgeVjT1sXpnGmfJ2Wjud3LshiyizIXT+maG9MRsmCTLGkzoUpLT0tVPRWQvA5+94hl9depMU\nSwKPLXlgRtcLdnBTUVmWWIh1kjfy4L6e1KgkFEUhfkQjA4NeurcJIRa+gvhcStuv8p3jP6KutwkA\nm7ObpMjA+1NwP0+s7OcR81xYh5MKMZd6Xf3kWDP41oP/h4+venzS9pkjLU5chNfvpbqrbsbPqaoq\nDb2BPTflHVUAVHQFNuDbBm1YLUb+5g83kZUSxZuHqnnrcGCeQbd99GDSmarpacCoMxKrHx1o3IxM\nz3StWKVF0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3KJlr52UqOSgOGgJcEcR4QuUJLndE8/6Al2bkuQJgZCCCGEuAVIpkfcFP0u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\n",
    754       "text/plain": [
    755        "<matplotlib.figure.Figure at 0x7f525d4ee4d0>"
    756       ]
    757      },
    758      "metadata": {},
    759      "output_type": "display_data"
    760     }
    761    ],
    762    "source": [
    763     "# Perform linear regression\n",
    764     "slr = regression.linear_model.OLS(a, sm.add_constant(b1)).fit()\n",
    765     "slr_prediction = slr.params[0] + slr.params[1]*b1\n",
    766     "\n",
    767     "# Print fit statistics\n",
    768     "print 'R-squared:', slr.rsquared_adj\n",
    769     "print 't-statistics of coefficients:\\n', slr.tvalues\n",
    770     "\n",
    771     "# Plot asset and model\n",
    772     "a.plot()\n",
    773     "slr_prediction.plot()\n",
    774     "plt.ylabel('Price')\n",
    775     "plt.legend(['Asset', 'Model']);"
    776    ]
    777   },
    778   {
    779    "cell_type": "markdown",
    780    "metadata": {},
    781    "source": [
    782     "# Example: Anscombe's quartet\n",
    783     "\n",
    784     "Anscombe constructed 4 datasets which not only have the same mean and variance in each variable, but also the same correlation coefficient, regression line, and R-squared regression value. Below, we test this result as well as plotting the datasets. A quick glance at the graphs shows that only the first dataset satisfies the regression model assumptions. Consequently, the high R-squared values of the other three are not meaningful, which agrees with our intuition that the other three are not modeled well by the lines of best fit."
    785    ]
    786   },
    787   {
    788    "cell_type": "code",
    789    "execution_count": 12,
    790    "metadata": {
    791     "collapsed": false,
    792     "scrolled": false
    793    },
    794    "outputs": [
    795     {
    796      "name": "stdout",
    797      "output_type": "stream",
    798      "text": [
    799       "Cofficients: [ 3.00009091  0.50009091] [ 3.00090909  0.5       ] [ 3.00245455  0.49972727] [ 3.00172727  0.49990909]\n",
    800       "Pearson r: 0.816420516345 0.816236506 0.81628673949 0.816521436889\n",
    801       "R-squared: 0.666542459509 0.666242033727 0.666324041067 0.666707256898\n"
    802      ]
    803     },
    804     {
    805      "data": {
    806       "image/png": 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EM2cW+yJIklRwdh1Ak/rTAJrJBfPFP/kkHN59663hYd1jj4XWOIsgFREWQkp6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\n",
    807       "text/plain": [
    808        "<matplotlib.figure.Figure at 0x7f525c2c7510>"
    809       ]
    810      },
    811      "metadata": {},
    812      "output_type": "display_data"
    813     }
    814    ],
    815    "source": [
    816     "from scipy.stats import pearsonr\n",
    817     "\n",
    818     "# Construct Anscombe's arrays\n",
    819     "x1 = [10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5]\n",
    820     "y1 = [8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26, 10.84, 4.82, 5.68]\n",
    821     "x2 = [10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5]\n",
    822     "y2 = [9.14, 8.14, 8.74, 8.77, 9.26, 8.10, 6.13, 3.10, 9.13, 7.26, 4.74]\n",
    823     "x3 = [10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5]\n",
    824     "y3 = [7.46, 6.77, 12.74, 7.11, 7.81, 8.84, 6.08, 5.39, 8.15, 6.42, 5.73]\n",
    825     "x4 = [8, 8, 8, 8, 8, 8, 8, 19, 8, 8, 8]\n",
    826     "y4 = [6.58, 5.76, 7.71, 8.84, 8.47, 7.04, 5.25, 12.50, 5.56, 7.91, 6.89]\n",
    827     "\n",
    828     "# Perform linear regressions on the datasets\n",
    829     "slr1 = regression.linear_model.OLS(y1, sm.add_constant(x1)).fit()\n",
    830     "slr2 = regression.linear_model.OLS(y2, sm.add_constant(x2)).fit()\n",
    831     "slr3 = regression.linear_model.OLS(y3, sm.add_constant(x3)).fit()\n",
    832     "slr4 = regression.linear_model.OLS(y4, sm.add_constant(x4)).fit()\n",
    833     "\n",
    834     "# Print regression coefficients, Pearson r, and R-squared for the 4 datasets\n",
    835     "print 'Cofficients:', slr1.params, slr2.params, slr3.params, slr4.params\n",
    836     "print 'Pearson r:', pearsonr(x1, y1)[0], pearsonr(x2, y2)[0], pearsonr(x3, y3)[0], pearsonr(x4, y4)[0]\n",
    837     "print 'R-squared:', slr1.rsquared, slr2.rsquared, slr3.rsquared, slr4.rsquared\n",
    838     "\n",
    839     "# Plot the 4 datasets with their regression lines\n",
    840     "f, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2,2)\n",
    841     "xs = np.arange(20)\n",
    842     "ax1.plot(slr1.params[0] + slr1.params[1]*xs, 'r')\n",
    843     "ax1.scatter(x1, y1)\n",
    844     "ax1.set_xlabel('x1')\n",
    845     "ax1.set_ylabel('y1')\n",
    846     "ax2.plot(slr2.params[0] + slr2.params[1]*xs, 'r')\n",
    847     "ax2.scatter(x2, y2)\n",
    848     "ax2.set_xlabel('x2')\n",
    849     "ax2.set_ylabel('y2')\n",
    850     "ax3.plot(slr3.params[0] + slr3.params[1]*xs, 'r')\n",
    851     "ax3.scatter(x3, y3)\n",
    852     "ax3.set_xlabel('x3')\n",
    853     "ax3.set_ylabel('y3')\n",
    854     "ax4.plot(slr4.params[0] + slr4.params[1]*xs, 'r')\n",
    855     "ax4.scatter(x4,y4)\n",
    856     "ax4.set_xlabel('x4')\n",
    857     "ax4.set_ylabel('y4');"
    858    ]
    859   },
    860   {
    861    "cell_type": "markdown",
    862    "metadata": {},
    863    "source": [
    864     "## References\n",
    865     "* \"Quantitative Investment Analysis\", by DeFusco, McLeavey, Pinto, and Runkle"
    866    ]
    867   },
    868   {
    869    "cell_type": "markdown",
    870    "metadata": {},
    871    "source": [
    872     "*This presentation is for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation for any security; nor does it constitute an offer to provide investment advisory or other services by Quantopian, Inc. (\"Quantopian\"). Nothing contained herein constitutes investment advice or offers any opinion with respect to the suitability of any security, and any views expressed herein should not be taken as advice to buy, sell, or hold any security or as an endorsement of any security or company.  In preparing the information contained herein, Quantopian, Inc. has not taken into account the investment needs, objectives, and financial circumstances of any particular investor. Any views expressed and data illustrated herein were prepared based upon information, believed to be reliable, available to Quantopian, Inc. at the time of publication. Quantopian makes no guarantees as to their accuracy or completeness. All information is subject to change and may quickly become unreliable for various reasons, including changes in market conditions or economic circumstances.*"
    873    ]
    874   }
    875  ],
    876  "metadata": {
    877   "kernelspec": {
    878    "display_name": "Python 2",
    879    "language": "python",
    880    "name": "python2"
    881   },
    882   "language_info": {
    883    "codemirror_mode": {
    884     "name": "ipython",
    885     "version": 2
    886    },
    887    "file_extension": ".py",
    888    "mimetype": "text/x-python",
    889    "name": "python",
    890    "nbconvert_exporter": "python",
    891    "pygments_lexer": "ipython2",
    892    "version": "2.7.12"
    893   }
    894  },
    895  "nbformat": 4,
    896  "nbformat_minor": 0
    897 }