examples/DBCM Latent Factor Example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Latent Factor DBCM Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This example highlights several advanced modeling strategies. \n",
    "\n",
    "\n",
    "**Dynamic Binary Cascade Model**\n",
    "\n",
    "The first is a Dynamic Binary Cascade Model (DBCM), which is the combination a Dynamic Count Mixture Model (DCMM) and a binary cascade (Berry et. al. 2020). When modeling sales in a retail setting, the DCMM (Berry and West, 2019) is used to model the number of transactions involving an item, and the binary cascade models the quantity purchased by each customer. The DCMM models the transactions as a mixture of a Bernoulli and Poisson DGLM:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{equation} \\label{eqn-dcmm}\n",
    "z_t \\sim Ber(\\pi_t) \\text{ and } y_t \\mid z_t =\n",
    "\\begin{cases}\n",
    "0, & \\text{if } z_t = 0,\\\\\n",
    "1 + x_t, \\quad x_t \\sim Po(\\mu_t), & \\text{if }z_t = 1\n",
    "\\end{cases}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where $\\pi_t$ and $\\mu_t$ vary according to the dynamics of independent Bernoulli and Poisson DGLMs respectively:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{equation*}\n",
    "\\text{logit}(\\pi_t) = \\mathbf{F}_{ber, t}^{'}\\boldsymbol{\\theta}_{ber, t} \\qquad \\text{and} \\qquad \\text{log}(\\mu_t) = \\mathbf{F}_{Po, t}^{'} \\boldsymbol{\\theta}_{Po, t}\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A DCMM is useful to capture a higher prevalence of $0$ outcomes than in a standard Poisson DGLM."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Transactions are related to sales by modeling the number of units bought in each transaction. Recognizing that sales outliers often occur due to shoppers buying many units of an item, the probability of each quantity is modeled with a binary cascade. Let $n_{r,t}$ be the number of transactions with more than $r$ units. Then $n_{r,t} | n_{r-1, t} \\sim Bin(n_{r-1,t}, \\pi_{r,t})$ is defined by a binomial DGLM. This cascade of binomial DGLMs represents the sequence of conditional probabilities for purchasing $n$ units or greater, given that the shopper has bought $n-1$. This implies the following expression for sales $y_t$:\n",
    "\n",
    "\\begin{equation}\\label{eqn-dbcm}\n",
    "y_t =\n",
    "\\begin{cases}\n",
    "0, & \\text{if } z_t = 0,\\\\\n",
    "\\sum_{r=1:d} r(n_{r-1, t} - n_{r,t}) + e_t, & \\text{if }z_t = 1,\n",
    "\\end{cases}\n",
    "\\end{equation}\n",
    "where $d$ is the predefined length of the cascade and $e_t$ represents excess units greater than $d$. The cascade enables modeling of very small probabilities, in the rare cases when shoppers purchase large quantities of an item on a single grocery store trip."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Latent Factors**\n",
    "\n",
    "The second strategy in this example is the use of *latent factors* for multiscale modeling. This example features simulated data from a retail sales setting. There is data for an item, and also for total sales at the store. The total sales are smoother and more predictable than the item level sales. A model is fit to the total sales which includes a day-of-week seasonal effect. This seasonal effect is extracted from the model on total sales, and used as a predictor in the item level model.\n",
    "\n",
    "Modeling effects at different levels of a hierarchy - aka multiscale modeling - can improve forecast accuracy, because the sales of an individual can be very noisy, making it difficult to learn accurate patterns."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Copula Forecasting**\n",
    "\n",
    "In this example we are focusing on forecasting retail sales *1* through *14* days into the future. To do this, we will simulate from the joint forecast distribution *1:14* days into the future. This is accomplished in an efficient manner through the use of a Copula, which accounts for dependence in the forecasts across days into the future."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pybats_nbdev.analysis import analysis, analysis_dbcm\n",
    "from pybats_nbdev.latent_factor import seas_weekly_lf\n",
    "from pybats_nbdev.shared import load_dbcm_latent_factor_example\n",
    "from pybats_nbdev.plot import plot_data_forecast\n",
    "from pybats_nbdev.point_forecast import median\n",
    "from pybats_nbdev.loss_functions import MAD"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start by loading the simulated retail sales data.\n",
    "\n",
    "The dataframe 'totaldata' has the total daily sales in a store, along with a predictor, which represents a measure of average price.\n",
    "\n",
    "The dataframe 'data' is the sales of a single item, and has two predictors. 'X_transaction' is a measure of price, and will be used in as a predictor in the DCMM. 'X_cascade' is a binary indicator of whether the item is being promoted within the store, and is used as a predictor in the binary cascade within the DBCM."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = load_dbcm_latent_factor_example()\n",
    "totaldata, data = data.values()\n",
    "totaldata['Y'] = np.log(totaldata['Y'] + 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2014-06-01</th>\n",
       "      <td>5.746203</td>\n",
       "      <td>0.793644</td>\n",
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       "    <tr>\n",
       "      <th>2014-06-02</th>\n",
       "      <td>5.375278</td>\n",
       "      <td>-0.762627</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-06-03</th>\n",
       "      <td>5.375278</td>\n",
       "      <td>-0.752116</td>\n",
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       "    <tr>\n",
       "      <th>2014-06-04</th>\n",
       "      <td>5.613128</td>\n",
       "      <td>-0.791505</td>\n",
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       "    <tr>\n",
       "      <th>2014-06-05</th>\n",
       "      <td>5.429346</td>\n",
       "      <td>-0.496851</td>\n",
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      "text/plain": [
       "                   Y         X\n",
       "2014-06-01  5.746203  0.793644\n",
       "2014-06-02  5.375278 -0.762627\n",
       "2014-06-03  5.375278 -0.752116\n",
       "2014-06-04  5.613128 -0.791505\n",
       "2014-06-05  5.429346 -0.496851"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "totaldata.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Sales</th>\n",
       "      <th>Y_transaction</th>\n",
       "      <th>X_transaction</th>\n",
       "      <th>mt1</th>\n",
       "      <th>mt2</th>\n",
       "      <th>mt3</th>\n",
       "      <th>mt4</th>\n",
       "      <th>X_cascade</th>\n",
       "      <th>excess</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2014-06-01</th>\n",
       "      <td>7.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>0.376729</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <th>2014-06-02</th>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.797680</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "      <td>[]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-06-03</th>\n",
       "      <td>9.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>-1.687661</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>[]</td>\n",
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       "    <tr>\n",
       "      <th>2014-06-04</th>\n",
       "      <td>11.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>-0.188624</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>[]</td>\n",
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       "    <tr>\n",
       "      <th>2014-06-05</th>\n",
       "      <td>5.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.684483</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "      <td>[]</td>\n",
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      "text/plain": [
       "            Sales  Y_transaction  X_transaction  mt1  mt2  mt3  mt4  \\\n",
       "2014-06-01    7.0            6.0       0.376729  1.0  0.0  0.0  0.0   \n",
       "2014-06-02    3.0            3.0       1.797680  0.0  0.0  0.0  0.0   \n",
       "2014-06-03    9.0            7.0      -1.687661  2.0  0.0  0.0  0.0   \n",
       "2014-06-04   11.0           10.0      -0.188624  1.0  0.0  0.0  0.0   \n",
       "2014-06-05    5.0            4.0       0.684483  1.0  0.0  0.0  0.0   \n",
       "\n",
       "            X_cascade excess  \n",
       "2014-06-01          0     []  \n",
       "2014-06-02          1     []  \n",
       "2014-06-03          1     []  \n",
       "2014-06-04          0     []  \n",
       "2014-06-05          1     []  "
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we define hyper parameters for the analysis:\n",
    "-  *rho* is a discount factor which calibrates the forecast distribution. A value of *rho* less than $1$ increases the forecast variance. \n",
    "\n",
    "- *k* is the number of days ahead to forecast.\n",
    "\n",
    "- *nsamps* is the number of forecast samples to draw.\n",
    "\n",
    "- *prior_length* is the number of days of data to use when defining the priors for model coefficients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Define hyper parameters\n",
    "rho = .2  # rho must be greater than 0, and is typically < 1. A smaller rho widens the forecast distribution.\n",
    "k = 14 # Number of days ahead that we will forecast\n",
    "nsamps = 200\n",
    "prior_length = 21"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we define the window of time that we want to forecast over. For each day within this time period, the model will sample from the path (joint) forecast distribution *1:k* days into the future."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the forecast range\n",
    "T = len(totaldata)\n",
    "forecast_end_date = totaldata.index[-k]\n",
    "forecast_start_date = forecast_end_date - pd.DateOffset(days=365)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first analysis is run on the 'totaldata', which is used to learn a latent factor. In this case, we fit a normal DLM to the log of total sales in order to learn the weekly season effect, which is stored in the latent factor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "beginning forecasting\n"
     ]
    }
   ],
   "source": [
    "# Get multiscale signal (a latent factor) from higher level log-normal model\n",
    "latent_factor = analysis(totaldata['Y'].values, totaldata['X'].values, k,\n",
    "                         forecast_start_date, forecast_end_date, dates=totaldata.index,\n",
    "                         seasPeriods=[7], seasHarmComponents=[[1,2,3]],\n",
    "                         family=\"normal\", ret=['new_latent_factors'], new_latent_factors= [seas_weekly_lf.copy()],\n",
    "                         prior_length=prior_length)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The second analysis is performed on 'data', which is the simulated sales of a single item. The latent factor is used to inform on the sales of this item. On each day, a copula is used to draw joint forecast samples from *1:k* days ahead."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "beginning forecasting\n"
     ]
    }
   ],
   "source": [
    "# Update and forecast the model\n",
    "mod, forecast_samples = analysis_dbcm(data['Y_transaction'].values.reshape(-1), data['X_transaction'].values.reshape(-1,1), \n",
    "                                 data[['mt1', 'mt2', 'mt3', 'mt4']].values, data['X_cascade'].values.reshape(-1,1),\n",
    "                                 data['excess'].values,\n",
    "                                 forecast_start=forecast_start_date, forecast_end=forecast_end_date,\n",
    "                                 prior_length=prior_length, k=k, \n",
    "                                 nsamps=nsamps, rho=rho,\n",
    "                                 latent_factor=latent_factor, dates = data.index,\n",
    "                                 delregn_pois=.98)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can examine the results, first by plotting both the *1-* and *14-* step ahead forecasts:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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euvznP0BpqXzH69ULaO984pTz58/j6aefxr59+xAeHo7k5GS88847F1upeMrs2bNx55134je/+Q0effRRPPPMM7jyyisRHR2NegcK3f7x7rBgwQJER0fjueeec/qYnJwcFBcX4/bbb/fqPbhLfn4+7rzzTuTl5fl8LCGiBAKBQMPU1LgOKAfIEtXY2HXwuUAZSktdi1xPsWtd5xDOOaZNm4ZZs2bhyy+/BEACpLS0tIOIslgsF6uKe8K///1vj58jBzk5OcjKyvJIRLW1tanaR08TgeUCgUAgcExVVdePYYwElKgVFRps3boVBoOhQ5Xv1NRU3HjjjcjMzMSECRPwwAMPICUlBRaLBc8//zyuueYaXH311fjggw8AkBCbN28errzyStxxxx0oK7Mlv6elpXXoy/fss89i1KhRuPnmm1FeXn7JeLKzszF+/HiMHj0akydPRklJicvxp6Wl4YUXXsDYsWMxZMgQ7NixA62trXjllVewfPlypKamYvny5WhoaMAjjzyCa665BiNHjsTatZRb9sknn+Cee+7BXXfdhVtvvRX33nsv1q9ff/H4s2fPxqpVq5Cfn48bb7wRo0aNwqhRo1xWYvcWYYkSCAQCDVNcDHTqGuIQxkhERUQoPyaBuuTl5WH06NFO79+7dy/y8vIwcOBALFmyBHFxcdi3bx9aWlpwww034NZbb8WBAwdw/Phx5ObmorS0FFdeeSUeeeSRS47V0NCAUaNG4W9/+xtee+01LFy4EIsXL754v9lsxhNPPIG1a9ciMTERy5cvx/z58/HRRx+5fA9tbW3Yu3cv1q9fj4ULF2Lz5s147bXXkJWVdfH4L7/8MiZOnIiPPvoINTU1GDt2LG655RYAwO7du3Ho0CEkJCRg9erVWL58OW6//Xa0trZiy5YteP/998E5x6ZNmxAREYGTJ0/i/vvvv6Rps68IESUQCAQaxl0RBVDBzbg4Zccj0D5jx47FwIEDAQAbN27EoUOHsHLlSgBAbW0tTp48ie3bt+P++++HXq9H7969MXHiRIfH0ul0F/vkPfjgg5jeKVjr+PHjyMvLw6RJkwCQCzEpKanLMUrHGT16NPLz8x0+ZuPGjVi3bh3eeustAEBzczPOnj0LAJg0aRISEhIAALfddhuefPJJtLS0YMOGDbjpppsQGRmJ2tpazJs3Dzk5OdDr9Thx4kSX4/IUIaIEAoFAozQ1UdZdfHzXjxXuvNBh+PDhF0WRI6LsUjk553j33XcxefLkDo9Zv349mBcBdJ2fwznH8OHDsXv3bo+OEx4eDgDQ6/Voa2tz+BjOOVatWoWhQzu2zN2zZ0+H9xgREYG0tDR8//33WL58Oe6//34AwNtvv41evXrh4MGDsFqtiFDATCtiogQCgUCjuBNULsG5qFoeKkycOBEtLS348MMPL962b98+bNu27ZLHTp48Ge+//z7MZjMA4MSJE2hoaMBNN92EL7/8EhaLBSUlJdi6davD17JarRcF2xdffIFf/vKXHe4fOnQoysvLL4oos9mMw4cPe/W+YmJiUGeXZjp58mS8++674JwDAA4cOOD0uffddx8+/vhj7Nix46JgrK2tRVJSEnQ6HdLT02GxWLwalyuEJUogEAg0SmWl+yIqLAxoaFB2PALH9OrVdUadp8dzBWMMq1evxtNPP40333wTERERF0scnDt3rsNjH330UeTn52PUqFHgnCMxMRFr1qzBtGnT8MMPPyAlJQVDhgzB+PHjHb5WVFQUDh8+jNGjRyMuLg7Lly/vcL/RaMTKlSvx5JNPora2Fm1tbXj66acxfPhwj9/3hAkT8OabbyI1NRUvvfQS/vznP+Ppp5/G1VdfDc45kpOT8c033zh87q233oqHHnoIU6dOhdFoBAD84Q9/wN13340VK1ZgwoQJHaxXcsEkhRcsjBkzhssdOCYQCARq8P33QFmZe+68qiqgf39gwgTlxxXqHD16FMOGDVN7GAIFcPLdOt3KCHeeQCAQaJSSEteVyu0RVcsFAv8jRJRAIBBokIYGyrYzGNx7vKhaLhD4HyGiBAKBQIPU1Hj2eGGJ8i/BFgoj8O47FSJKIBAINEhFhWctXHQ6wGoFWluVG5OAiIiIQGVlpRBSQQTnHJWVlR6XQRDZeQKBQKBBioqA6GjPn9fSQq49gXL07dsXRUVFDlugCAKXiIgI9PWwCaIQUQKBQKAxOAfOnwfaCzK7DWMURxUTo8y4BITBYLhYEVwQ2gh3nkAgEGiM+nrAbKbaT54gqpYLBP5FiCiBQCDQGJ4GldvT3CzfOAQCgWuEiBK4TXW12iMQCEKD8nJAr/f8eXq9yNATCPyJEFECt6ioAL79llwMAoFAWYqK3C+yaY/BIGpFCQT+RIgogVvk5FCga22t2iMRCIIbqxUoLQVMJs+fazAAFy7IPyaBQOAYTYgoxlg/xthWxthRxthhxthT7bcvYIydY4zltP/crvZYQ5GaGuDECdoZiwVaIFCWujrAYvHOnWcwiCbEAoE/0UqJgzYAz3LO9zPGYgBkM8Y2td/3Nuf8LRXHFvIcOkR1Z3Q6aoZ6+eVqj0ggCF58CSo3GoHKSvnGIhAIXKMJEcU5LwFQ0v53HWPsKIA+6o5KANCu+PBhICkJaGoCiovVHpFAENyUlnpe2kBCr6e4xbY2748hEAjcRxPuPHsYY8kARgLY037TPMbYIcbYR4yxbk6eM5cxlsUYyxIVZOXl8GFamPV6IDKSdrlWq9qjEgiCF2+Dyu0RtaIEzjCbaY4J5EFTIooxFg1gFYCnOecXALwPYBCAVJCl6m+Onsc5X8I5H8M5H5OYmOi38QY7jY3AwYOA9JHq9RSrIVKoBQJlsFiovIE3QeUSUtVygcARpaXAf/4DHDum9kiCA82IKMaYASSgMjjn/wEAznkp59zCObcC+BDAWDXHGGocO0YVkDu7BUSGnkCgDLW1ZOnV+bgyCxElcEZpKW2It2wBzpxRezSBjyZEFGOMAVgK4Cjn/O92tyfZPWwagDx/jy1UaWkB9u8HevbseDtjQFWVOmMSCIIdX4LKJUTrF4ErCgqoJ2PPnsB33wnXnq9oQkQBuAHATAATO5Uz+F/GWC5j7BCACQD+W9VRhhAnTpDv3GDoeHtUFNWLEggE8lNSAoSH+3YMxkSZA4FjzGZyF0dFARERQPfuVES5rEztkQUumsjf4JzvBMAc3LXe32MR0ImWlWWLhbLHZKKFXiAQyM+5c74HlYuq5QJnVFWRpZK1X21NJnIfr1sHTJ9OFiqBZ2jFEiXQED//TDEVjnbEBgOVOmhq8v+4BIJgxmymi1xkpG/HMRqFiBI4pqLCJqAkoqPJKrVunSim7A1CRAk6YLEA+/a53pHodOJkEwjkRoqH6nyR8xSDQWTQChxTUODY0hkXR/Pu66+FK9hThIgSdKCggASSqxRrzuUJgBUIBDZqaujc8hXhzhM4wmold3F0tOP7ExIoIWH9epHd6QlCRAkuYrUCe/cC3RyWNLURESGCywUCuSku9t2VB5CIam4WRXEFHamp6bonY2IildnYsAFobfXf2AIZIaIEFzl3jmIynO1UJEwmqjUiEAjkQ46gcnuENUFgj7ulaXr1ok3y5s3UPkjgGiGiBADIjbBvHxAb2/VjIyLohBQnmEAgDy0tZAGIiJD3mAKBRGGh+/OrTx8K7cjMFBbNrghZEVVWBpw8qfYotMP58/QTF9f1Y6XAVxFcLhDIQ02N7wHl9ojWL4LOnD0LxMS4//g+fYDjx6nossA5ISmizGYyVR44oPZItMP+/V278ezhXIgogUAu5O4CYLUKS5TARn09laUxGt1/DmPk2jtyRJ6Eh2AlJEVUXh7t/KqqxEIDUAXbggIgPt795xgMosqtQCAXxcW+NR3uDGPUQFwgALwX6eHhVPJAZHs6J+REVE0N8NNPwGWX0f/V1eqORwvk5JCv3BN3gskkMvQE8pGRkYHk5GTodDokJycjIyND7SH5FbmDyo1GUStKYKO4+NIWXp4gNszOCSkRxTmwcycJBoOBikaG+uSorqbYsO7dPXueyUSfnTDzCnwlIyMDc+fORUFBATjnKCgowNy5c0NGSDU20m7fE1dLV4SFCXe7wMbZs56Fa9gTFQWcOSPveIKJkBJRp08D+flAjx70f1QUTa5QJjfXJig9Qa+n7DxR3VbgK/Pnz0djJ99TY2Mj5s+fr9KI/IvcQeUACTIhogQAhaz40k4oJobCPUSWnmNCRkQ1NwM7dgA9e9pui4qiZroWi3rjUpPmZuDoUceNht2ltla+8QhCk7NOdjLObg82KivlF1EGg9jgCIjOTYc9JSyMNsxyJz8ECyEjorKyKCvPXo3r9SSgQrWFydmztLtwVcHWFTqdiCkT+E7//v09uj3YOHdO3qBywCaihLtdUFrq/Rrf+TiCSwkJEVVaChw8SOmajqis9O94tEJennt1oZwREUGWPIHAFxYtWgRTJxVhMpmwaNEilUbkPzinoF85g8oBm9VBZB8LCgu9j4eSiIkBfv5ZnvEEG0EvoiwWYNs2EguO4n4iI2mShRq1tSQuPSm+1hmRoSeQgxkzZmDJkiUYMGAAGGMYMGAAlixZghkzZqg9NMVpaKAeZb5kTrlCiKjQxmKhja6vls7oaBL7ZrM84womwtQegNIcOQJUVAD9+jm+PyaGRJQvPuNA5MwZz4PJOxMeTjWmWlrob4HAW2bMmBESoqkzSoYSSFXLfbE2CwKb6mrfQjYkdDo6TkUFkJQkz9iChaAWUXV1wK5dtppQjpA6ntfX+2aVCSSsVsrKS0jw/Vg6HWUB+RKcHkjU1dGFT6ejhUmno4uV9Lf9j14vxCVAlhZ3Y3O8yRQNZMrLlXu/nIeGJYpzmmPuwJi8pSS0TkWFfMcKCyNrlBBRHQlaEcU5CSiDwT1TeVVV6Iio8nISjZ5UKHeG1UqiIhRE1IULwJo1VNenK6ulJBruvBPo21f5sWmV8+eBtWvdE1GcA0OHAhMnKj8urVBUJH88lATn1Ooj2NmxAzh82D1PAufAXXeFzjlZWChf0kJsLJUJGj1anuMFC0Eros6eBU6dcu7Gs8dopAyZAQOUH5cWOHlSvt1YRAQV3Rw8WJ7jaZWmJuDbb0k09unj3nOqq8niFyoLtiP27aO4w27dun6s1QqcOAFcd533NW0CCauVRKZSGxCDIfjbdRQX284xdyx6lZU0x0LhnOScRJQcm2WAzslz52gTKXc2aSATlIbzlhYgM5OKarqzO4mODp3gcrMZOHZMHlceQCdTsGfotbYCGzbQ4uFJZfe4OCruGqr1esrLPVvEdTpa+EOkPBTq6qj+jhzp544IdhFlNtM6362b+y7R+HiyprS1KTo0TXDhgrxJC9K1VE4XYTCgCRHFGOvHGNvKGDvKGDvMGHuq/fYExtgmxtjJ9t9u7GeBAwcozsldtRwZSe685mbv30OgUFJCJ1aYTDbIiAja3QVrwVKLBdi8mQSBfaFWd5DipfLzFRma5jl0yPOejPHx9LxQQOn6dEZjcIuo3FzKMvYkDEPqtBAK7b6kIptyEh4eOpscd9GEiALQBuBZzvkwAOMA/Bdj7EoALwLYwjkfDGBL+/+uD9QG7N/vvCaUM3S60KjIeviw7zVD7JGsB8G4WFutFG9RUOB9MGW3brTYh1rRw9pa4Phxz3syRkeTYA2Fc7GsTL7NjCMMhuBtQlxdDezZ4zppyBlGY2j0gjt3Tv7ElthYqhcVauuZKzQhojjnJZzz/e1/1wE4CqAPgF8B+LT9YZ8C+HVXx6qro4XYGxO5vyuyms3+nYwNDWQVUSLlOdj6dHEO7N1LotPdGChHmEwkCEKtoGteHl2svMk8Cwsjl0uwU1Qk74amM8EqoqTNTWSkdyI0Pp7iooK9F1xBgfzJUuHhFNYQjJtmVzCGCGf3aUJE2cMYSwYwEsAeAL045yUACS0ADh0qjLG5jLEsxlhWTU25W0GsnYmJ8b+ZcscOOpn9RWEhuVbkTqnW64PPT37oELUK6tPH9/phRiMlOYQKDQ0koqRG357SvTs9P1hdxAC9t/JyZQN0pdo+7qb/BwqnT9Na5qmVU8JopNCNYN7YNDXRxjbC6aXfezgPDXeoRHtM653O7toU9/YAACAASURBVNeUiGKMRQNYBeBpzrnbtg3O+RLO+RjO+ZjoaO9SXaKiKFPGXwGHZjMJKH/Gf+TmKmOFCrbg8pMnSeD26SNP0G9CAhV9DYVgVoASFwDvPzujkS4CwVwNv7aWBI7SNbGkgpvBQmMjsH275/GJndHrgzuZqKpKueLRUVGh4Q6V+OknAIDTgA7NiCjGmAEkoDI45/9pv7mUMZbUfn8SAMX0rxTb46+GumVl9HoVFf6J/6iqop2vEu4Dk4lcocHgJz97Fti4kWKg5IpXkQq6BpPQdEZLCyV2+Jq2bzIBR4/KMyYtUlPjv/MlmApu7t1LVjxfLSzx8TaxH4ycP69c1mdMDLkKg90dClBcWfs65LThjSZEFGOMAVgK4Cjn/O92d60DMKv971kA1io9Fn+5pc6cIf+yXu8fVf/zz8oFsYaFkcugsVGZ4/uL0lJg/XoSAHJXNY6KCm5RIHHqFFlZfU2rjo+nYwWTFcWe8+f9U82e8+D5DIuLKUbR06QhR0RGkpBVOkNSLQoKlIu3Cwsjq3qwJ39IJTTa3cZOtzyaEFEAbgAwE8BExlhO+8/tAN4EMIkxdhLApPb/FcNk8o+JVyoqGB9PX9ChQ8rGf1itFGMiV20oZwRycHl1NfD11+TuVKLQY3w8CdlgriDd1kbFNeUoHqnXkwAoKPD9WFrk3DnlKpXbEyytX7ypCdUVOh19D8GG2ax8vB3g/0Qsf3PoEF3TuhKjmhBRnPOdnHPGOb+ac57a/rOec17JOb+Zcz64/bei2jcmhjJmlDazV1TQwmYw2OI/lJyQpaVkJVJy58uY/1yhclNfTwIqPFy53ZvkLg5WUQCQRVXOeRYfT3F8wYbZTEHN/qjKHhYWHJlU3tSE6orYWCrDIQenT9P3qgWqq2mtUTLeLiaGNoXBSnU1bQjdKaGhCRGlFSS3lNIWlcLCjq41k0lZ//yxY8pkadgTERG4O5PDh0nIytUewRnBKgoAsnbu2yevtTM6mmIHA1WcO6O2ln4rFfhrTzCUOaiuplgob2pCuSI6mtYsXzsK1NZSHKVWYh7Ly5WfW9HR5F7VinCUE84psSgiwr0QGCGiOsG5sr5ezknU2F+w4+MpI0yJ2IXWVjq20q68QM3Qk74Pb9OlPSGYC0kWFVF8idwuqrCw4Nvx+lMUGgyB7WaXakK5e0HzBElo+Lpu5eXRZ6yV2mZnzyrvKpbKZwRbaRuAYjE9KaERkiIqMzMTc+bMwdSpUzFnzhxkZmZevC8iQlk/eU3NpfU79HqakErEYxUVUbyVUpkaEuHh9L4CbWdSVaW8q9OeYCwkyTlZoZQon5GQoHzMoL8pKVHeMixhNAZ270ZPL2ieEhVFm0xvkWqiDRpE57Xa89RqVb6Iq0RYGFmjgommJhLtnpTQCDkRlZmZicWLF6O8vAwAR3l5GRYvXnxRSEnpm0pRXOzYVx0bq4yr5/Bh+avWOkLa1UmuikChsFB5gWlPMBaSLC2lbLPYWPmPHR4efDWj/BVUDgR2E2K5akK5Ii6OLDfeBt9LMVXh4baAbjWprVW2qbU9sbHBtyHct48+P082OSEnotLT09Ha2vGMaW1tQXp6OgCbRUWpdP3jxx1fbGJi6EIhZ8ptXR3tSpS4uDmC88BzHRw/rowFxRnBWEhy/35ld74mk3wBwGrT0kIXOn9ZPvV6cukHYqHXvXvJsqKk1U5yS3kTz9naSnNfykYNC1M/caSy0j+xdgCdl5WVgV/aRuL8eTJkeNx3V5nhaJdyJ1sF+9sZUyZupaGBAmUd7UIZo5NQzppR+fl0XH+dVOHhnrcDaG1VT1DU1dH3rHQqcGeUTiTwJ5WVNM+8abXkLkrGDPobaZPkr3NSeq1A++zOn5evJlRXREZ6Z1HpXBOtWzcS+2oWHS4s9J+rWCIY4qLa2qiERny851mNISeiEp0UsbG/Xa9XJtOspIROMGcLqBT/IUclWM5JVSt5cetMZKRnQZptbcCmTcC6deos8mr584OpkOTBgySelRQFUsygv3tbKoFaSQWBVivq0CHabCrdFgcgS7Sn8UxSTTT7/pDh4bRRVjNxpLDQP+EbEuHhwXFe5uXR9+aN1ybkRNTMmTNhNHa0pRuN4Zg5c+bF/6OjlTHLnjjh2u0hnYRyCLjKSnIb+NPKEhlJMQHuiECLBdi6lU5Aq1Udd82JE/5zddoTLKLgwgX6DL1tNOwJcXHBUR6iuNg/9aHsCTRLVFMTZWT6awMYFuZ5PNPZs7RWd7b66HQUQqEG9fU0Jrm7LbhCiosK5JZfFy5QfzxvS2iEnIhKS0vDvHnzkJjYEwBDYmJPzJs3D2lpaRcfYzLRCSVnpllLC+0SurpoR0TQhclXTp9Wrs2LM6Qq013VpbFagR9/pPfZpw9dhLOz/ZvZ19xMi50/d232BIMoOHKEvnN/WAtiYmhzEehtOvwZVC4RaFXLz55VvlhkZ8LCyC3tDlYrxWs5EnlxcerF76lhAZMSPwI1eYFzuhYZjd63qvLzZVYbpKWldRBNnbFvRixXZojUoLerhSEhgU7C667zfkdhsVA8gT9qH3WGc7KAOROLnAN79pCA6NuXdsnh4RQb9fPPwNCh/hmnFIflz9gUe6Tq+DU1yhf5VIKmJnLlKZk51RmpZtSoUf57TTlpaiJLgT9d7ADN8UAqc5Cb6/9zQopnuvbarteEkhISLP36XXpfVBSd13V1/t+glZT43rPSGzinWFg1rPq+kp9PBof+/b0/RshZotyFMXnTVX/+2b2AP72eRJAvNaNKSsjSosYJ1VVQfk4OkJVFFih7QdmtG8UY+Cv1/9Qp/weUd0avD9xCklJgvD+tnXLGDKpBTY06ot1oDJys2epquiD7o86RPeHhlGXmjjUnK8u1QGJMnXjLggJ1LOtRUfImRPmLlhZg2zbKrvTlvBQiyglRUfIVv7RY6KLtbip9TAwFunkD5/RctQRCVJTzbLvDh4GdO8kC1bmOiclEC70/GkCbzSRe/FnawBEJCbTrDjRRIKV2+yMWyh7pQheo5SH8mX5uTyC1fvn5Z/+HIUjodF2vP2Vl5JJ1ZSmLjpYnJMMTamspS87f8XaArbZiIK1jUoHg5mbfr5VCRDkhOppOKDkmhhRf5e7iEBtLOxlvdo/Z2STY/O0ykDCZHF/kTp2iQPI+fZx/DvHxNLGVDlIsK/NPFfeukDORwJ+cPk1Cyp8BrBKRkYFbHuLcOXU2N4HS+sVqpU2F0i2qnBEf33U808GDXQuVmBj6rv0VzN/QAHzzDc0tNUR6WBhlKwZSO6uDB8krIkc/RiGinCC51eSowF1Q4NnuijHaFXlqIs3NBXbvJkuPP4My7TEYyFrQ1GS77exZ4PvvacK6cjHGxJDgVLoHX36+/4oddkVERGCJAouFgmrViLcDaHMQiDWjOKeNkb+DygE65wIhJqq01L8tmDpjMpEQcCY4a2poM9iVyJNiav2xOWpqIgHV0qLeOSkRKJvBo0fJI9KnjzwbaSGiuqCy0rfnSw1uPbUMdevmmavn+HHy78o1MXyBMdtCdP488O235Hd2Z3GMjiZrmlJYrWRq10owd0ICiYJAyZ4qKCDXkBpuA0DZPpNK0tBA37EacYoGA4lONVsNZWRkIDk5GTqdDsnJycjIyLjkMceO+b9QZGdcxTMdPkyfpTsbVG8LeHpCSwvw3Xd0Pjopf+g3YmICI77z9Glgyxagd2/53MZCRLkgIsL3mh/eNriNjCQh4k5w+5kzwObNQFKSOou0I2pqyEe/bh0JQncvuvHxdIFUqgdVZaV6QfeOkCyeatWW8QQptVstd4tEIJaH0EJpBrWEekZGBubOnYuCggJwzlFQUIC5c+d2EFItLbSZUHtuxcQ4tgw3NNCcczcOMD6eLthKtdsxm4GNG2mN9WeGrDOio0l8arkBfWEhsGFD1x4RTxEiygUxMb4XRPSlwW14eNcBiufO0cTo2VOdGBVHRESQsFu3jtwXnrgwGKPnHzqkzNj83XDYHWJjvU8k8CdSare/M6c6o0SfSaUpL1evnAagbsHN+fPno7FTg7XGxkbMnz//4v9FRdqIU4yJoXluH44AkLBizP3x6fUkoJTYDLa1kTXl3DnaOGsBqQehVlvAlJaSR6RHD/ndxUJEucBoJCuSL/EEvjS4lWpGOVP3ZWU0MRIS1DeD2xMVRabvsDDvaod0707iUY54tM4cPaodV55ETAyJu5MntZ3h0lVqtz8JC1OmqOGxY/JbBS0W2lSoLT7dsURZrRQzuHMnlRuQg7NOdqL2t+flaaPOkNRr1D4us6UFOHDAc5eZweB+AU93sVopbOPMGQrd0BJSHTetUVlJG/q4OGUSO4SIcgNv46J8bXArtSNwtKhXVdHEiI5Wv95RZyIigIEDvc8Q1OloAZLbOlNTQy5SteJ5nMEYLdCbNgErVtD3rbU2Cu6kdvuTnj0pdk7OjKCaGsog/fpr+er8WK3Ajh10UVZTgHLetSWquBj4z39oY3b0KLBsGYkpX8sj9HdSyVC6/cIFem2tCHSTiTY0Ep0bDbuLVMBTro2R1Onh2DHtCSiA1rCDB7VljaqtpeukyaTcJkaIqC4IC/O+Lk1xse8m/OhosurYc+ECLfQREdpZeDrjq8+5Rw8SUXJmFZ07p65LxRUmE1VAbmsD1q6lE7+sTO1R2ThwQFtiXa8ni+f27fI17N65k86pbt0o48lXVwzn1JPr8GFbdX416eyikqioIOG0ejUJrf79KW6kd28SUxkZZIX01h24aNEimDpNHpPJhEWLFgEgq4pkAdICsbFkQTKb6XzMyvKuJprRSJ+5HEKfc4pHPHRIG3PJEXo9Xa/kOid9pb6erpN6vbJWTk2IKMbYR4yxMsZYnt1tCxhj5xhjOe0/t6sxtpgY702yJ074LnLi4sjVI+0GGxpoYnCufrFIJZFiD+RM/3fkWs3MzMScOXMwdepUzJkzB5mZmfK9oBfExtJFrLaWrFKbNqkf+1NdTUGyagf9diYhgYSxvdXAW06fpszDHj1InEVHk5j15QKYnU1FSdUsOSLhqGr5hQsUW7N8OQnGfv06nh96PYkpyer3+ee0sfE0eHjGjBlYsmQJBgwYAMYYBgwYgCVLlmDGjBngXN3aUI6QMkBLS2ntd9Ro2F3kakh84ADV0Ovc6UFrdOtGVld/FxvtjFT6obVV+ZqJWvk6PgEwxcHtb3POU9t/1vt5TADI9VNVRV+GJ8jV4FaqGZWfT8dcv14bNUH8QWIiLR5yZBVJRS3tg9wzMzOxePFilJeXAeAoLy/D4sWLVRdSAJ34/fqRgP7iC3ncKt6Sm0uWRS3ufnv1IndZp7hlj2hqot2zfZZTTAxdONet8y42LyeHrFBaEFAAWdSl+dPYCOzaRRam/HwaY/fuzr/fsDCySsXH02f9xReex+/NmDED+fn5sFqtyM/Px4wZMwCQeNOiiz08nNx4WVm+XYTdKeDZFbm55Mbr10/9wHt36NWL1itfzklfkEo/NDT4p/SDBk5vgHO+HYAm651KC4unO1I5G9zGx5MZ9/vvySqhdk0Qf2Ew0K5XDkuDo+8jPT0dra0dFVprawvS09N9f0EZkGKl7N0q2dn+zbKqrweOHNHunAsPtzW19pa9e8lt09naEBdH38HXX3smYOUu5icHRiOtHQcO2CxKSUkkHN0VeeHhJLgiIshC+tVXlL3sS/zeyZPaySq2Jz6erCm+ZqN2VcCzK44d0079P3eR45z0FrOZ5qY/Sz9oQkS5YB5j7FC7u8/pfoAxNpcxlsUYy6qvlz+nVK+nnaUnbpWTJ+WLITGZKLj9/Hl5ytQHEomJtBv0td7KyZOXlloodxL04ux2tbB3q2Rl0UUwN9c/NVmOHqWLrJYX8J49Ke7Im2Dw8+dJUPTq5fj+hASyQn/zjXs761On5C/mJwdGI7kr9+whl2VSkvffqRS/Z7WSwNy0ybvz02ym+aVFq7rBQN+7HCET3jYkPnOG5pKW6v+5S8+etPlSuvuEPeXl5KkpLPRv6Qcti6j3AQwCkAqgBMDfnD2Qc76Ecz6Gcz4mOlr+LXOvXnQSSNkqXQU7m810AsgZszRgAC3MoUZ4OLlbfOkS3tpKF5DO30eiE/OKs9vVRnKrdOtG8zAjg1wFShX0a24my4W/Gw17ik5HYicz0zNh2dZG2Xjx8a6tMYmJZIn67jvXVsCCAvfaG6mBwQAMHkwWDbnGFhND8XunT5O1xNNg4uJiOje1JDbtGTBAnoDkmBjPY4S0WP/PE3Q6Oq8yM5VbnyRqaqjY9Fdf0d99+yr7ep3RrIjinJdyzi2ccyuADwGMVWssklslKck9t0pZGS0ocu7etRiP4i+6daOgSm8zPkpL6bmdL5QzZ86E0dix8prRGI6ZM2d6OVL/YDTSQhEVRTvVL7+k+ixyZ8ScOEFmea0JAkfExFDskidlMXJzadF150LZqxdZg7//3nF85LlzJLLcbW+kBkqtIX36kNtp1y7PXHtHjqhfO8sfeNqQuLxcm/X/PCU2ls4vpQoJNzRQrNiyZeRW7tdPnQQFzYooxpi9QW4aANVrOktulR49yK2SkUFuhM673/z8wNw9aJWoKDoZve2X9vPPjhejtLQ0zJs3D4mJPQEwJCb2xLx585CWlubLcP1GRAQtHAYD7Vq/+oqsIXLUmDKbaY5r0dXijMsuo2Bud9zuNTX0WE/c40lJ5P7bvLnj7loqeutJe6NggjES9Tk5tNlxh4YGWieDOcNYQhKv7pTKqakhF2lUlLZKinhLr17kQvY2JswRzc1kxJCuv0lJtHlRy9CgCUMqY2wZgDQAPRhjRQBeBZDGGEsFwAHkA3hMtQF2wmAgt0pLC2X1ZGcD118PXH453a+lBrfBQlwcXdT79/fsZLFYKB7KmRhIS0sLGNHkDJOJfurqKHbnssuA666jxcXbheXnn2l+a9Wq4oiwMBKWO3cCd9zh/L3b14Ty1JXUuzcJ1cxMYMIEWzE/LRa99Sc6HQmpPXtoA5ma6vrx+fm2zONQwGSieLnkZOePkeoaedvpQYsYDPTz44/AlCm+CZ22Ngpf+Okn+jsxURtWck2IKM75/Q5uXur3gXiIlK3S2EjNIBMSgKuuIqWs9TiSQCM2lixRpaWeWQ/Ky+mE02rchZzExNjcWqtXk+C89lrPs1SsVrIoaKl2j7v06EEi5/Rp4Be/cPwYqSaUk0LaXdKnDy3mjJEbQctFb/2JXk/roSRQr7jC8eOk2lBK1+/REnFxFNfprPJ5UxNZM9vagu/a0aOH7ZxzJSKdYbXSpm7XLlvZAi1t7kJkH6As9tkq27dr6wsOJqKjSax6Ev9z9qy2M8uUIC6OBEJVFRXs3LzZs1pHZ8+S+T1QLSuJiVTPyFEMiqOaUJ4iua9OnKC5FQouKXcJCyML6JYtzvuoVVX51g4rEJEaEjvqQtDaSrF2dXXBJ6AAW0zxtm2e1fzjnDbOK1bQui8ZLbR2fRUiSkZiYkhMaTS5K+Dp1o1OoA0bgFWrKFjTVfwP5xTwGko7XnsSEmg+FhRQgcTdu523/pDgnNymgeyOjoy0xXR1xllNKE+R3FehOrdcYTRSLMyGDY6rdZ86pQ03jL8xGi/tftHWRpuc0lLnZTaCAZPJlu3rDmVl5CZft45CMvr1067oFiJKEFBIVr/WVmDNGtc9zqqryfyrtZ2LP2GMrC5JSeRC+fxzKtzqrBRASQktYIHunurVi5qhlpbabispcV0TSiAf4eEUh/jttx2tLxYLBQMHUsKCXEgFPCUruuS5KCgIjfI1vXpRG6TKSuePqa4mq9OKFWQ9799f+2tR0Imos2cLNNEDTaAsUo85e5dV56ysoqLQCVztCr2ehFRCAgV5fvEFWQQ6u0Wzs4Mj7VynIzfbtm104W5ro2DwrmpCCeTDZKLzdN06W8eHkhKySISqJaqlhUSE1Jz66FGKsQsFXDUNr6+nWLply2jd7tcvcKy8QRluK/VAAxDwmVcC1yQk0IWxoICy8K6+mjKDoqLIlSfiVToi1ZhqbKQ4jJ49gRtuoJ1wRQXFIPi7WJ1SSM27jxwhEaVGIT4lkSqoa9XNAZAgt1iomfP06SQatDxepdHpaE4WFtKGxdNs40AnIYHe+4kTlHjQ3EwW8v376bPp3TvwYlgZl6OojIZgLJED4wAAiYk9sXSp5pP8BDJhsdhcByNG0IkZTBdNJbhwgcTF5Zfb2lMEU0yf2UzuXquVsjqDJUuzqAh4+WWy6Pzf/2nfslNVRRfH+nqyiIaqNbCxkUIMGhtpbQo0wSAHLS205lxzDWUBWyy0mdPyuTl1Kh7nHB84uk/Dw/YdrfVAEyiL5LIymymAURQ87ZrYWIo5OH+eFvd+/dQekbwYDDbLh5YXaU8oLwdeecXmvs7LA0aOVHdMXZGQQG6ssLDQFVAAzcXq6sC0uMhFeDjNgV27AretjT1Bsqw4Rqs90ATKYjCETpyBHDBGqdXBmF4NBHamYWdqakhAVVTQxae1lQpcal1EAaEZTO4IsTYFl7U7aPcEgdADTSAQCNyloQFYsIBKewwcCMyfT7fv3StPqx+BQOA5QWmJSkzsiZkzZ8oSVJ6ZmYn09HSUl5cjMTFRtuMKghcxZwRy09ICvPEGFbBMSiIxFRdHbrKKCtcV2gUCgXIEnSWqf/8BWLp0qWwCavHixSgvLwPAL2b9ifIJAmeIOSOQm7Y24H//l+orJSQAr71G6d86HbX1AcilJxDIiVSsuKFB7ZFom6ATUXKSnp6O1taOdepbW1uQnp6u0ogEWkfMGYGcWK3AP/5BWUwxMSSg7IuFSiLqp5/UGZ8geMnIAP74R+Ddd9UeibYRIsoFzrL7RNafwBlizgjkgnNgyRIqGBoZSS68zk2TU1Io46uggDIsBQI5WL0a+Oor+nvPnksLGQtsCBHlAmfZfaGW9dfYSH3IzpxReyTq0tREabnFxc4DecWcEcjFF18A69dTtun8+cDgwZc+xmAARo+mv4VLTyAHmzYBH39Mf/fsSXWctm1Td0xaRogoF8ycORNGY8fGa6GQ9WexUGXhZcuAF14AZswgN8If/+i671Gws3Qp8OabwOOPA7/7HbB4MbUquHDB9phQnTMCeVm7Fli+nOKenn+eKvE7Y+xY+i1ElMBXdu0C3nuP/n70UeDhh+nvH35Qb0xaJyiz8+RCCk4P9kwrzilt+uBBICeHyvBLLSUAgDEOxurQ0hKL3/9+K/7wBxZ0n0FX1NVR7zWAYlPKyqhR5saNVGdp0CCqkp6amobHH2dYtuyzgJkzIptQW2zZQoIdAJ54Ahg3zvXjx4yhIpZHjpCgj41VfoyC4CMnB3jrLYrDu+8+YOpUKlwcHU1eiDNnqLSGoCMhKaIaGigQc/TorgvxpaWlBe0F5eRJ4Lvv6OSpqOh4X58+JArCwvLw3Xf/C7M5CsBiNDffhHfffQpAaPUl3LKFChuOHEnFDs+coc8tJ4cuXqdO0c+qVYDROB7Dh4/HPfcAkydruzeWlE0oBcPL2XeScxKeUvPZrtDpgF/+MrgK8XnKTz/ZAnkffRS4+eaunxMVBVx1Fc3Fffvce06wUFcHbN1KF3t3iIoCbrkleKrXy8Xx48Bf/kKZoHfdBdx/P91uMAA33URu5R9+AObMUXecWiSkplJrK02GFSvo5Bs8mFKHQ7H8flkZ9d5qaU8ki40l0TRiBAkF6UI2Z87bMJurAVQD2ALgVpjNv0V6+qchI6KsVhKbAHDbbTRffvEL+vnNb+gzPHzYZsk7c4bazhw4QM+9/XZ1x+8KV9mEvn6/mzaRy9MTMjOBv/89NM/Jykrg7bc7WgLc5dprae7t2RNaIkoKvPeEqirggQeUGU8gUlAALFxIzYAnTCChZL/xmziRrpuZmcCsWUKAdiYkPg6LhSbAF19Q3ymAFumTJ4ENG4A77lB1eH5HyvppaQFGjQJmziQzraOeVh2zyr4EkAbgJpSX/8c/g9UABw8CJSXUFuWaay69PzycPsdRo+j/6moSEJ9/TlkukydrVxQolU1YUwN88gn9ffPN7rmYduwgAfrNN8CvfuXTywckH35IyQvXXmuzBLjL2LHABx+QcG9poTkZ7JSW0pzR6UhwdmXxbW0Fvv0WWLmSrCuiOTlldL76KjWGHjuW3MedrwODB9NnVVRE88vRGhjKBLWI4pyyyj77jNQ2AAwYQGq6tZWChNPTKeYglPo6/fQTtYowmeikcfXeExMT2wtHAkA5gG8BTIPBEDp23fXr6feUKe6JoW7dgLvvJhdgSQnw44+0aGuRjt9vx9t94eOPaWEeORJ48kn3XJpXXQW8/jrVp7n++tBy6+3bR0G9ERHA3Lmeu4ATE8kyeuoUiX4p2DyYWbOGrHZpacAjj7j3nJYWYPNm4P/+j+aall3tSlNVRaEJVVVUKuOPf3RsZWKMrFGffUZrmhBRHdFEdh5j7CPGWBljLM/utgTG2CbG2Mn23908OeaxY8BLL9GJUlBAi8zTTwPvvEOBmNddR5OhsdEWxBkKNDaSFQoAdLoMPPzwVMyZM8dpRe1Ls81WAmiA2ZyCQ4eUHq36lJfTBS4sDJg0yf3n6fXAtGn096pV2u1tpkQ24cGDFKdiMACPPeb+heqaa+i8bG4mq4yvZGZmYs6cOZg61fUcV5vmZrIiAeRm8lY8hlKWXm0tWXsBYPp09583ezYlhhw6ZEsU8ReezEel5259PVmgzp8n8T1/PjW0dsaECWSh2ruXQmEENjQhogB8AmBKp9teBLCFcz4YFIzzojsHMpspQO6Pf6SA35gY8vG+/z6pacmSwBgt8OHhlKaenS3fm9Eyy5ZR7AVjp1Bf/xW6ak2SlpaGefPmITGxJwCGxMQIXH89WS4++0y74kAuvv+edrvXXUcWJk+YOJESF6QgdC1y6ffbE/PmzfM6Hspspl0+APz2t0Dv3p49/3e/o8KSv8W0TQAAIABJREFUkrXUWwKp/c7y5RSjOHAgBfV6i5TFt3cvhTAEM99+S96EMWOA5GT3nxcba7NaffSR/wSBJ/NR6bnb3EwlawoKyE336qvklXBF9+4UL9vWRi5UgQ1NiCjO+XYAnXN4fgXg0/a/PwXwa3eOVVJCC7DRSIv4kiUUX+FIZffsaYs9+OADW5B1sHL6NPD11wBgBeeLAVgv3ueqNUlaWhqWLl2KdevWYenSpXjqqYGIiwNOnAjuXa/ZTCUMAAoo9xSj0XZRXLVKvnHJTefv15eA8lWrqFxG376eWQgkevSgumQAnZPNzd6NI1Da7xQUkFuKMeC//su32LkBA6glTG0tZVsFK83NJKIAcpt7ysSJ5DqurQU+/bTrx8uBJ/NRybnb1gb8v/9HnprERAooj4tz77kTJ9LvUKsZJSUVOUMTIsoJvTjnJQDQ/runswcyxuYyxrIYY1kAxa4sWQI8+CCltLpi6lRafM6ft5W5D0YsFuBf/yKrCvANgNOXPMbdYOLISODee+nv9PTg3fX+9BMFSPfvDwwf7t0xbruNPq9DhyiRIZgpLqbMVwD4wx/InecNd9wBXH45uVKXLfPuGIHQfsdqpcKGFgvNkyFDfDseY6HRkHjjRrIgXXEFcOWVnj+fMeD3vycX/caN5LFQGk/mo5JzNz2dgsPj4sga5YnreNw4WstOnKAg81Bg+3abZd0ZWhZRbsM5X8I5H8M5H9O7Ny3gCQnuPTcsjB4PUCbV2bPKjVNNvv+eLuLduwPdu3/v8DGeBBNPnkyWvMJC/8cW+AspoPz2270PQI2OJlEPaNsa5Suck8vcbLbt9L1FryerDGNUudubdkOB0H5n82ayCHTrRhs+OZBcenv2BKerva2N5gRAlk5vz8t+/WyW0vffp+MqiSfzUam5m5VF1zidjuKF+/Tx7Pnh4cCNN9LfW7b4NJSAICuLSo50dR5pWUSVMsaSAKD996UpRA7wpobFsGEkCtra6IQKtsWnqorilwCKOZk16x6fg4kNBpvb5YsvKD4hmCgooNpPkZGU/eMLU6fSvNy9m6w1wcj27RRQHhPjfqaUKwYPJvFqtdpbUN1H6+137EtAzJlDYlsOhg2j76C4ODitBTt2kIWyXz/fMxDvuQe47DI61yVhphSezEcl5m5FBQkCgAS7NxY8wObSy8wMXg8EQNbJN9+k9yglCDlDyyJqHYBZ7X/PAqDoNJ81i0ychw97p7K1nAm0dCll5UnZT3IFE990E7lCy8u79hsHGtL7GT++66DLrujenYQY57QT9Af+nI/19cC//01/z54tX9uRBx8ki/Lx47bYNMC99yZ3wLzc2JeAkHb3cnxner0tBT3YXHqcA/9pL083bZrjunaeEB5OfTABchuXlvp2PFd4Mh/lnrsWC7Vzqauj+eZurKKj+ThsGAnPykoEbXb2zz9TVn9rK3DrrbSmuYJxDZhdGGPLQFUcewAoBfAqgDUAvgLQH8BZAPdwzrtsIDFgwBi+eHGWV+PYupXUekwMWaTcvRh0bp0B0M5BC4v2/v3AggUU5PzeexR4Kif79tGEi42lODRfBYcWaGykxptNTcA//iFPv6iiInJRhYWR4PA0088T/D0f//UvKlp75ZWUGevrxc2enTupq0BUFL3OwYPaPdfc5eBB4M9/Jmvu4sVAUpK839nu3RQ8PGQIXTyDBWmt6d6d1hpvY+4689e/koVrzBj6XoKtdtTnn1O8b0IClfjpqtUZ4Ho+nj+fhi++oA3ms88qOHAVKC4GXniBkg5uuAF47jnamEydisc5xweOnqMJSxTn/H7OeRLn3MA578s5X8o5r+Sc38w5H9z+280OXN6TlkZpnHV1tFN0F61mArW02ILi7r9ffgEF0MIzbBg1Pl2zRv7jq8G2bSSgrrxSvoabfftS0K/ZDKxbJ88xneHP+XjsGAkovZ5iC+UUUAAtZKNGUb/Ljz7S7rnmLp1LQCQl0d9yvq+RI2nTdOKE+30LAwEppnDqVPkEFEDuVJOJYmB275bvuFrgwAFK9tDpSPC4I6AA1/NxwgT6f/fujo3qA52KCio+WltL59Azz7iXLasJEaUVGCPzblgYufTy8rp+DqDdTKAVKyjrcMAA5dpoMEauUIDiCmpqlHkdf8G5LaDcm7IGrpDSsTdsUHbx8dd8bGsj6yZA7pX+/WU9PADbOWk0krgtL09y+Di1zzV3cVYCQs7vLCICSE2lv32ptaUljh2jOJWoKIpflZOEBOChh+jvDz8MHmFQVUV9KDmnXowpKe4/19V87NWLjtXaSpbiYODCBaqXVVZGWZ8vveS+UBciqhN9+lDAIWDLNuoKLWYCFRba4gf+8Adlm0ZeeSVZpJqabCnugcrRoxRoGhdHrUfkZOhQylpraCAhpRT+mo9ff02fVa9etpIXSnDZZWS1AQC9fh6AS1c3LWXdOcNVCQi5v7Ngq14uWaFuv12ZkIHJk8n9WVlJbYcCHYuFBFRtLXD11bZrmrt0NR+DqWZUYyOFvBQWksHhlVdoI+IuQkQ54O67qdJyYaF7gcBaywTinOJH2tooMG7YMOVfc+ZMshp8952yAZpKIwWU33qrvC4DCckatW6dewLdG/wxH8vKKCsTIEuR0g1vp02jjCyL5TLodPd1uE9LWXfO6KoEhNzf2TXX0Pl48GDgW1YKC0kMGgzAnXcq8xp6PdWO0umokOfpS8voBRQrVlDgd1yc+24pe7qaj9ddR+f8kSNU4DpQaW0FFi2inpOXXUbFRz3NlBUiygFGI51QAAXkdTVJtJYJ9MMPlGUYF2dztSnNwIGUrdfWBsyb96OqWYreZjnV1FCzYMYudRnIle02ahS1qaiqokQGJbLolJ6PnFNgb0sLxSyNHu34cXK+N4PBdk4y9ht065YCLZxr7tJVCQi5v7Nu3cgt0dZGcTGBROd5869/0QJ8883KJmQMGkQdBuyLoAYieXnAl1/SOvbMM+7XTLSnq/loMtks9Vu3yjZ0v2KxUFJBbi59Rq+9dulnJc1F4PH3nR1HQSdPYDNiBAWaZ2ZSIOiCBa6zNtLS0jSxkF+4QAG4AC3WMTH+e+1Bg37Ctm1j0NJyHYB+KC8/i8WLFwOA3z6bzlklUt8pd8awaRNddMaOpUKichyzM4xRLMzf/w5kZDSivv49mM3NPh+3M0rOR6mvnckEPPqo48fI+ZlJXHUVXUi3bNGhX7+/4JNPAiOTyt0SEHJ/Z9deS+7pn34isRsIXDpvLCgv7wHGOKZNU/7LfuAB2kidOkVWaaUsX0pRW0sZmVYrucBHjvT+WF3Nx4kTSUD98APFXMmdVKIkVivwz3+ShTM6mixQl13W8TEd52Jvp5MvgN62/3nkEQpkPHAgMHy/koWgro784P7WdF9//SGADaBp9RiAcL9nTnmb5WSx2OKUOgeUy50RduONJNKqq00wm1NlO64/qK+n4FuA6jh17+74cUpl0T38MG0MDh3qWDtKq3BOAqq2lmIHb77Zf68ttYDJylK+IrdcXDpvfgXAAKNx38VMRiWJjATmzpXGEliuKquVNmdVVTTXpL6wSpGSQm1jysrI8xEocE61E7dupdinV16hWKjOOFrDHCFElAvi42nRBqieS5Z35af8AudUAXn7dnJHPv64/3fplNGxHEAdgKsB/BVAL79mTnmb5ZSdTUVDL7vs0t2b3Nluej3w64vttC/toKrVTDPO6TyoqKCK4q6yF5XKEIyNpZR0gGKMtJ59lpFBGzCDQZkSEK7o04fiyBoaAuci13F+RAEgv3pLyxd+G8O111L7nKYmusBWVvrtpX1i9Wra8MfE2OobKYlOh4vlDgLByCCxfDklxYSFURbeFVc4fpy7a5UQUV0waRIFtVosVAbeH80qvWHVKjqJ9HqaGH37+n8MlLlRA+CPAIoADATwd8TF3eTnMbh/u4R9WYPOFzolst1uuQVgrA7AFQA6RhlrNdPsu++AXbtot/7ss64XaSUzBCdOpGwjqxX4n/+hmAYtsno1xVTqdMAf/6hMCYiuCLQsvY7z4w4AJgAHkJhY57cxMAY8/TRtFEpLKfW9zn8v7xVHj5LlDAD++7+BHj3887qSiNq1C2hu9s9r+sI331BCjE5HQtOVu9PdtUqIqC5gjOIYJk2iSP7XX6ey8FpiwwbqjccYnUDOAn2VxpbRUQTgWQD7AMTiwoVnsXatf3oSepPlVFJCOziDwbG7RYlst4gIYNy4ivb/bNYorWaa/fyzLa7niScoe9UVSmcIPvggNXY2m4E33qAYFi2xaZOtYO9TT9lca/5Get1AaUhsmzdGAHcBAMLC1vn9nDCZSDz160dN6RcuJMuUFjl7lgKkrVba8I8Z47/X7tOHLDlNTdovVLp1K4W7ANQ9oqsSNo7WMEfoFyxY4PvoNMQ77yxZcPvtc2U9JmM0MQsL6WKyezeZe/0ZtO2MHTsoQA6g7KVbblFvLMnJyejZsydOnTqNxsZa9OhxDCkpI1BUFI8DB2hXN2qUsjWrOo6hEYmJPfG73/3OZYDkypW0kxs/3nEcmTfHdIcRI7ph3ToLrNa+AH5CYqJRluPKTWOjrZLvlCm2Mg2uUOozk2CM5lJxMaWj795NVhe5+vb5wq5d1F6Dc2r4LXdxSICCXl9//XUsXboUmzdvRlxcHJKTky95XEIC8P335JK69lrvMrX8iTRvcnN7o7X1WoSF5eOJJ+IxYUKa38cSHk7r/O7dJFROnqR4RqXdZJ7w00+UVXbhAsVB/fd/u3YZuztvPMFioZY8jY22+lFaY+9eCrjnnEJ07rij6+d0XMP0fMGCOxc6epwmeufJiS+987rCbCZLVE4OBQa/+ab/zKaOyM6mXbjFQnWaPC2o5i9+/JF60DU3A7/4BbkbteKxammhBIK6OtrNDR3q39f/8EPyz48fTwugOzDmv3g3zoG//Y1i7ZKT6TNSuiaUJ5jN1K8vO5vOxTff7JhZ6Smc+/bZ5uTQRa2tjQJ7lQju9bTP3nvvkZC67z7KPtM6FgttCM+fJzfoL3+p7niKi4EXX6QSKNddR2NSW0hZrVTG4Msv6f+bbiILsatzU6memvX1VEqnrY2s1VpZ2yVycym73myma6Q3Rk3N984LFAwGEgBDh1JGwquv0g5ADY4coSajFguZcH/zG3XG4Q433EBNZHv1IrfLM89oI9CVc1qE6uqoRsyQIf4fw69+RTvHbdso2Nydn4cfpoKAShXrtGfTJhJQERF08dCSgALonHzxRdqFS72vvGk9VFREAuz++6lEiDfn9fHjJOja2qje0H33df0cb/A083HcOPq9cSNZDOTYNzc10bnz4IMU4G+1+n5Mie+/JwF12WUkWtSmd29y50VFkVXqvffUdY02NtI8+/JLWjtmz6YYxa7OTaUyZqOjaY5JiSfFxT4dTlZOnSJDg9lM8a4PPij/awgR5SGRkSSeBgwg996CBf6vCPzzz2QRa22lWK3Zs7VfLyc5mSwaI0aQW+hPf6JgbrUWo6YmCkpetYo+u3vuUecz7NnTJqQkC5OrH4BSmD/4gPz6O3bIewGzp6DAFkPw+9+rk6zgDuHhNJ8GDqQF/NVXKSPNHaqqqLr/vHnkhmtspEbajz1GVZ9bus5wBkCf1cKFZG2dMIEyCJWaT55mPl59NX02VVW0brz0EvWi84a2NjpvH3uMAnQvXKCEg6VL5TmXd++2zbkHHlDf4iMxcCAJdKMR2LyZ4t3UWLvOnQOef57cU1FRNKbp092ba0r21Pz1r+mzOXCA1qX33weqq30+rE8UFdH1uamJLHWPPabMOSnceV5SVUU74PPnqV7Gq6/SJFKa4mLghRdIiFx/PZ1QWllo3MFiAT79lC5UALVXeewxZVqsOOP8eSr1X1BAAaTPPkttMgIBzulCk55OCypAVrRZs2xNZ+WguZk+l8JCCrZ/6in5jq0U1dUkEIqLyTK1cKHz3XlDA/WWXLuWNiM6HcUT3nADZdXl5NDjEhLIOnXLLc7Ps/PnaS2oqqK4rJdeUvacnDNnDsrLyy65PTGxJ5YuXerwOa2tJHa++sqWaTZuHDXedUccW63klv/8c1vtpCFDKEbo009JXD3wgG/Wt4MH6TtT0hXqK/v3k2WjrY2sGlJPR3+QlUUb0YYGyvR8+eWuEzzs8WbeeEJ5ObBsGZU7sFrp3Pv1r8lTokS/Q1eUldE5WVFB8cwvv+xbLK4rd54ILPeSyEi68P74I12M8/NpAVayDkxFBTB/Pi3Wqak0SZQM0lYCnY7SSi+7jBakEydocT99mhaHmBjaYSlFTg7t3srLKbPkjTf801tQLhijjKHbbqMYoNOnSTRs3UrB8f37yxM8/N579Fn16+f7AuQvIiNJxPz4IwUCnzlz6TnZ2koxaP/zP7RrtljIZfTSSySUkpLIkjRsGAnIc+fIBbZzJ32ufft23M1WVdE5WV5Om6n585XfEMTFxSE7ez8sdn1JjMZw/O53v3MaJKzXUxbVlCn098mTtG599x2tK4MGOb/QHTxIsXDffEPxL336kLXhkUfomP36kRXv0CE6f71xix8/TgKqtZVcoQ89pE3relISvX/p/cbFUSkEJeGcLObvvkufz7hxwJ//7Pl57s288YSoKEpeuP56SmQoKKCwjY0baf24/HL/bPhraug8LC2lzdSf/uS7gWPZMnyzYAGyHd0nLFE+UlBAC3B9PS2+Tz0lr5DKzMxEeno6ysubodf/FRZLbwwdSsGrkZHyvY4anDpFOyvJoiLRuzeJxNRUujDJIao4J6vDJ5/QLmnMGLK0KCnY5MY2F8qRmJiImTNn4rrr0rBuHVlVJBfWjTfSLtnbCs8//EDZZUYjVUBWo76RLxQW0gajro7M+M88Q9//tm1U/FLyXgwfThY8Z8X2JOtLejpZmwASCLNnUwua+no69wsKKGHijTf8t+N2NBecBQc7euzVV6fhyy/pAme10nd9112UeSk1YD19mqxM7ljlNm2iizxACRJS/SB3KCggoV5Xp8waqgQbNpAbWOpPN368Mq/T3EzZ1zt30v8zZlDogbefjyfzxleOHKH5c/Qo/d+zJ41//Hj3xu/NWBsaaC6dOUMu2EWLLm0o7M1xXVmihIiSgWPHyLrR3Ey9luTqt7Rnzx58/nk6zGYLgGcADAZjBXj88ULcdpvKKSsywTlZUnJy6Cc3t2OMmU5HOz1JVA0d6rlVpKWFLCtS/9vf/pZcD1pfqO3pKrPmwgUq1fDNN+Rq0Osptf63v/Vsx1pURBeF5maKE7r1VgXejB84eZJ2oE1NZI0qKqKLNUDxjLNmUT01d6wdZjOJhGXLyI0OkAivqyMLSt++FJSuhfIKnelq3pw7Ry66H3+k+6Kjyf1SUEAJBQBtNKZPB6ZOdR28vHo1xQrpdHQhkwp9uqKzKzSQrOurVpFI0OvpnBk0SN7jNzSQMM3PtxW4decz1RKckyX3s8/IOgyQuPn/7Z17lFzVdae/3a3WWyCpaSEkIQnJYCSBAEnBmIckDDYvIWAGCCAEcdpR7DGOJ/aM7WUmxDEREJPMxDF2VuTBsYeIsVnEZIgHZ5gJyLxiDJiIJDwMtpAaPbvVerRodUuq3vPHvuUutfpRp7qq7r1197dWra66davr1O/cc+4+Z++zz6pVg7uRe+99h359rKFhJLfeupoPDZB0rafHAttff90G4vfee+yG1aWuUHQjqgoULm2uHNuBL9LU1FAWH3YSyeXsBpg3qt566+jd1MeMsVmAs8+2IPWTTx78RtjaaitZfvlLW2H22c+mZzPWQoqNZ2httYDfp57qXa4/d26vXvPnD+xu6u62LL6bN9to8XOfS6ZLpVhee81cRPlVjPmR8NKlpbkVDh602czHHutNvNjUZK7BOFOdDEax180vfmEGQWH294YGy6dz/fXFG4gPPWQB+Q0NFtR75pkDnxtXXGk5+e53bRa4kkyfbu6ppC7sKIZczgax69eb+7iSNDZam+wv1UmpcWFuRFWJl16yUV250t9v3164VrQV+AawExAef/zx8nxJwunsNL963qhqaTn6/cZGMw7yRkLhyONf/9Ua0759FoP15S/bKsE0snLlSqC/ttr/tbB5s3VYfTefHTnS3Fj5mb3Zs3sNpXw+oenTzc1a7WDQSvDyy7ZX1oUXwpVXlidead8+MxQ2bbL98KZPH/7/rBQh142qxYk9+qi1l5tvDs/5o2ors/7hH2zAs3atuTr7EqcrtJyo2qDl2Wcrs1rv9NMtYWtfl1RaOXTI0rM89ZQ9H4ij731Hc9JJA0fTT55sbfLkk/t/P7Qf7f2cG1GppNKrKdLI7t29BtXGjcfmBJo1y4yDcePs5pnLmXH1hS8kI8N8qZR6LXR19RqhGzeaa6CQiRNNn8ZGG1E3NFgQ8Zw5Zf4BTizE0YfkchZL9+yzNoN1331Hz6J0dVn4w5tv2vF777UAbcfJU6nrthIzUSmKCskeld5/LI00NtqS+89/3twPX/+6rRJatMhmWTZvNpfLww9bZ37tteZWSLMBBaVfC6NHW+xPc7MFqH7ve+am+8hHbNS2d68FXOddEs3NbkDVEnH0IfX1toHv4sWWR+quu2zJOZhr9d57zYBqajJ3qxtQTl8qdd1W4v8mfiZKRN4FOoAccERVB91esZZmoqC6qynSzuHDthJk48beuJ6LLoq7VOWj3NeCqgVc5wP6Z8ywLREGi4Oq1euxUr8rCXrFVYbubjOg3njDAn3vuce2OXr+eTOc7ruveq7Q4a5mrIVrPG0kqU2m2p0XGVFLVLWocLRaM6IcJylUau+tuKnU76pVvUI4cMCCojdtshipgwct9mnt2vKvZhuIkHrwOnP6w915juMMm0rtvRU3lfpdtapXCOPHmzt92jQzoEaOtNmpahlQEFYPXmdOKGnIyKHAkyKiwF+p6rq+J4jIGmANwOTJKcsM6DgpoZJ7b4Ft29LRUf3knpX6XZXWKy1MmmR79v3gB+Zinz+/ut8fUg9eZ04oaZiJukBVFwFXAJ8WkaV9T1DVdaq6RFWXjB8fuCbXcZyiaBpgvftAx0M5cMBWB+bzOlWLSv2uSuuVJpqaLHnrYHmjKvfdxdeD15kTSuKNKFXdFv3dBTwGpCxnq+PUBpVc6dXdbWkpzjzT0lhUkzStBHLCCakHrzMnlES780RkHFCnqh3R848BX425WE4M+IqZ+MnrXYl6aG+3rVRmzbKEj9WkUr+rknpVilpsZyH1EFpntaiXE0aiV+eJyBxs9gnM4HtYVdcO9hlfnVd7+IqZ2iafauGWW2zp+yOP2LE0bQ5dC3g7C8P1yg6pXZ2nqr9S1bOix4KhDKgQenqqH3vhlEZaV8y8/36l91KsDTo6bJuRiRMtR9VZZx2bid6pPGltZyHs2zf4diMhZEEvZ2gSbURVkh07YOvWuEvhFEMaV8z09NhGmzt3xl2S5LN/Pyxc2Ps6vzqvpyee8mSVNLazYjlwALZsgVGjYPv28gyga1kvp3gyaUTlZwdmzPARbxpI44qZ3bvhtNNsCwyf8RyYXA7q6o7eMHTsWNt6xttmdUljOxuK7m7btLynB1asgOuvtzQLW7fatTccalEvJ5xMGlGtreYyOPdccyXUChs2bKC5uZmVK1fS3NzMhg0b4i5SWUjbihlV22R10SLbDNkHpgPT3m7G5qijq5f586GzM54yZZXQdpbk/ubIEdi2zdx3F18Mv/mbtmhBxFaAnneexeENZ7YzKf1SEuoh7jLE+f2JXp1XCXI5eyxYYNl0TzjBDKm0b1DbN8ixtXUXDzzwAEDqgxzTtspp717rsE84wba6eOUVu+bq6+MuWfLo6oLTTz/2+EknmWF16JBluXYqT0g7S2p/09Njg5YjR2y15xln2CbcfVmyxK69116zWdDB9osciCT0S0moh7jLEPf3J3p1XikMtTpv5074wAcgr+2mTfDjHx/tTkgjzc3NtLbuOuZ4U9MUHnzwwRhKlF1aWuC668wQAHjuOdu1/sQT4y1X0ujutuD71avNpdeXn/3MNpOeOrX6ZXMGJ4n9ze7ddj0tWACLFw89MO7pgaeegrffttCONJKEeoi7DNX4/tSuzis3qjay7RvEetxx6XcdeJBjMti/H6ZMOfrGf8YZdt15oPTRtLdbW+zPgAIb7PjqxmSSpP6ms9OCxk84wdx2y5cX51moq7NzZ860YPM0Uul6OHLEgvLjLMNQxP39mTKi2tstYHXy5N5j9fXwG79h76UZD3JMBvv22fVU6B6YOBFOPTX911g5UTUX55w5A58zeTI0Ng7diTvVJyn9TS5nq2BXrICrrjJDKoQRI+DSS+06S+NK2krXw7ZttqflYGkh4r4W4v7+TBlRnZ1wzjnHHp8zx+IvuruPfS8tJCXIMct0dlqyyP5cw2efbbvYO0ZHh7k7jz9+8PMWLvRVekkkKf3Njh3Wp+eDxkth1Ci44gpL7lrtLYeGSyXrYe9em1W/4ILBDcy4r4W4vz8zgeV798K0af3HpTQ0WKDhCy/A9OnVL1s5SEKQY9bZvdtGtf25p5qa7Nras8d2tc86HR22Qmoo8jfHnp6B3X7Vxrf6SEZ/09lpQeOLFw//f40da7NZjz1m94qJE4f/P6tBpeohl7PQhMsvtxnht98eWJe4t8qJ+1rMTGB5Swtcc83ARlJXFzz0kE3rNjRUuJBOzdHdbZ3O6tUDXz9bt8Lf/V1vMsmsksvBrl1w++3HpjbojyefNLdCY2PlyzYUvtVHMlC1OKgVK2D27PL93/Z2+OEPzahK+4rt4bBtm6WCOP98e93aatsxTZ8+vFXGaW0/mQ8sP3DAOuBp0wY+Z/Roz+njlE5bm8VCDWaAT5tmMRtZj/Fpb4cPfrA4AwqSlTPKt/pIBm1tFmc4a1Z5/+/kybBypc2UJuWaqzadndY2C2f4mpos791w48Zqsf1kwojas+fYYN/+mD+dZAycAAAVDElEQVS/N+A1C+RyNpor115SWeXwYRudnXrq4OeJWILXPXuqU66k0t1tRlSxnHSSDXKScJ3GvRKokCNHrP1mLSP+oUP2288/v/Q4qMGYMsWC1NvaaisZczGo2kTC8uXHDnIWLbJ2OBzjMkntp1zUvBF18KBNyxYzYhk3zpajt7VVvlxx09NjGXtPPdWmbrPWEZeT1labxewvqV9fZs606zGrQebd3dbOpkwp/jP19eZaSELQb9wrgfLkcr3ttxxbmKSJHTvMgKqku23GDLj2WovDa2nJzqxUa+vAM3yjRplx1dZmxlYpJKX9lJOaN6J277bRf7F+3Czk9FG1Dviss+CjH7WGkbWOuFzkcqbn/PnFnV9fb9djEgyCONi92wyi0CDxuXOTkTMq7pVA0DsAOu88a78f/vDwtzBJC/kVY/PmVf67pk+HG2+Eyy6zQWZLi8XO1iqHDll/NtgM38yZlr+t1ImjJLSfclPTRlR3t1nPg+Wi6cvEieZqqOWb3NatttXGBRf07iWVpY64nLS1meE9blzxn8mn1EiCe6qa5F3lc+eGf3byZIvLiDuebPny5dxxxx00NU0BhKamKVUNis0PgM4+21YUi1jsyjnn2PEaWyd0FPkVY8uXV28Lpbo6u15vugkuucQyor/3XrrT4QzEzp1Dz/CJ2Dm5XGn9V9ztpxLUdIqDtjYzDkJX2511Frz1lnVIlfC5x8m2bbaaZdmyo2cDFi+2RvHqq6XvJZU1enpMszPOCPtcQ4PFF7z44uCLHWqNjg4b3R93XGmfX7jQtukYP7685Qpl+fLlsXX6W7faLEzhbIGI9XOHDsEbb5grqhbb786dZizG4fkZMcIG13Pm2BZOL75oM6NTptTGau6QGb4JE+z6e+aZ0rZLi7P9VIKanYk6fNiMhJAA1jwnnGAXR60l+duxw7YjueQS6xQKETH3wIIF1lHX8oi2XLS3W/xAKTll8tdlElxU1WL//nCDs5CZM3tzRmWRbdvglFNg6dJj3aF1dXZ8zhw7r9bob8VYHDQ02Mz9rbeaW76tzfROczvOz/AtW1b8DN+8eZZzMeuLZKCGjai2Nhu1FBPs2x9LltTWyozWVrvZX3YZjBzZ/zl1dXDRRTZ9XYsdcX90d9v0/Nat4VP0Bw+aW6UUxozJVkqNXM466OFs9DpmjMVjZLHj3r594AFQnvp6e3/69PTuBdcfg60Yi4vRo202+dZbzXOxc6cNUtNo4O/cab8lZIavvt6M9o4Oj6WtSSMql7PHcIIPp041S3v//vKVKy5277ZGf+WVQxuV9fVw8cXWEe/YUZ3yxcHhw2Yo7ttnncHSpVbXxa5U3LPHNBqOa2H+/N5rtdYJzQ01EPPmZWelVJ7WVosJu+yyoV1HDQ0WbJ7WveD6o1I5ocrB2LE2g79qlV3fW7dafaVlJj+f9X3RovDPlit3VNqpSSMqH+w7nNgJEcsttW9f+coVB3v32gzTihXFBz83NMDHPmYdd601kFzORultbTbbuGqVuTDnz7fn+Sn67dsHN246Ouzzw2HCBDMKspBSo6urNNd6X6ZOtRmprATl5wdAV1xR/Kx6/vw07gXXl0rnhCoXEybYQOymm2xw1dKS/BnTcszwlSN3VNpJvBElIpeLyFsi8o6IfKmYzxw6ZH7r4XLyybZBarkvkA0bNtDc3MzKlStpbm5mw4YN5f2CiI4O02LFivBg3mpsylktHcA6jF27zDhasMAMpsWLj74xjRplLuBVq8wI377dPtN3iv7AAYubK0dQ+MKF5kZMy8i1FLq67CYTkhtqIOrrrW7SbhwUQykDoDz5veDq6pJ/Mx+MwXJCrV+/ntmzZ1NXV8fs2bNZv3599QvYh/yM4fXXW5+7ZUtyw0LyOaGGsw1VOXJHpZ1EG1EiUg98E7gCmA/cLCKDZuTJ5UoP9u1LXZ3NTLS3D/9/5cnvHdTaugtQWlt38cADD5TdgOjstJv9ypXWsEsh3xHX15e/I66WDmD119Ji7oCbb7bUDoPdlMaNs477lltsJePWrXbTzncSe/bYdVGOkfHkyRYMXM5rLGm0t5eWG2og5s6tfRdofgB09dWlr2acMME+f+RIOsMS9u61kIr+wjLWr1/PmjVr2Lx5M6rK5s2bWbNmTSIMKbByX3ON6V9XZ8ZUkhLsFpMTqliGmzsq7STaiALOBd5R1V+p6iHg+8A1g32gvr70YN/+OOUUcx+UK8laNfYO6uqyG9dVVw1/OXClOuJq6LB/v3VekyZZ0rxLLw0zro8/3gJ1b7jBZp5aWqyjmDChvJsIL1pUu9PhqjaTF5KrbSiSkjOqUhQOgCZNGt7/mjTJ2u/779sjLQy1YuzOO++ks0+j6ezs5M4776xSCYdGxPqJG2+08IiDB20RSxJc0cXkhCqW4eaOSjtJzxM1HWgpeP0e8KG+J4nIGmANwIknzixrHpERIyxw8OmnyzPz0NragP2svsdtxqMc1NVZEPn0Y7+mJCZOtA79Rz8qXxmroUNjo23dMG3a8OquqckM0u3b4Z/+yWZVypnsb8oUm/HasqV8/zNJzJlT+mzKQJxzDjz5ZPpjFvujocFmgMvVjzU1mSH1xBPpStuyZMnAGmwZoLEMdDxO6urMOzJ7tuWYeuml+I2NadPKm/V9wgS48EL4yU+SHbs2DAacRxRNsCNTRG4ALlPVT0SvVwPnqupnBvrMkiVL9OWXXy57Wcq1dPWUU05hy5bNxxyfOXMWmzZtKs+XUD7XSSHlXL5bDR1E0tOgVWs3pqBS9ZDG5eTFkvT2Ww0G02D27Nls3nxs/zFr1izefffdyhWqDCShrXubDKO+nnpV+v11SZ+Jeg8ozIk6A4glg1G5OrV77vlj1qxZc9RU9NixY7nnnj+uSMdZTspZvjTrUAnSZPAlhSxeJ8OhlvRau3Ztv/3H2rVrYyxVcdRyW6+la6yQgQwoSH5M1EvAqSJyioiMBG4CHo+5TMNi1apVrFu3jlmzZiEizJo1i3Xr1rFq1aq4i1ZVXAfHcUrF+w8nKSTanQcgIlcCfw7UA99R1UGHGpVy5zmO4ziOk0kGnDtMujsPVX0CeCLucjiO4ziO4xSSdHee4ziO4zhOInEjynEcx3EcpwTciHIcx3EcxykBN6Icx3Ecx3FKIPGr80IRkVbg2Cxs/XMC0FbB4tQarlcYrlc4rlky8HoIw/UKJ02atanq5f29UXNGVAgi8rKqLom7HGnB9QrD9QrHNUsGXg9huF7h1Ipm7s5zHMdxHMcpATeiHMdxHMdxSiDrRtS6uAuQMlyvMFyvcFyzZOD1EIbrFU5NaJbpmCjHcRzHcZxSyfpMlOM4juM4Tkm4EeU4juM4jlMCbkQ5ThkQkQF3+XYcx8kqtd431rQRJSL10d+arsRyIMZVIjIl7rKkhUiz3xeRGerBhUUhInNFZEzc5cg63jcWj/eN4WSpb6xJI0pEfktEXgU+G3dZ0oCIXAu8AdwBPCgiC2IuUuIRkduAp4FzgP1+MxocEVklIv8G3A/8rYiMiLtMWcT7xjC8bwwna31jzRlRInI68B+AHwFLRWSOqqqI1NxvLQci0gj8NvBxVb0CaADmR+/V9MVfKiJyAfBd4D+p6m2quj8/2nLNjkVErgF+F2hW1X8HjAV+J3rP22WV8L4xDO8bw8li31gTjUdEJuSfq+qbwG3AfwNex0YQqGpPPKVLHoV6AYeA8cDU6HUPcJKInFT1giWYvPsDQFWfB14E5kXvfUlErhaR8bU+dV0sIjK+4OVG4HZV/Wn0+i+Aa8HbZaXxvjEM7xvDyXrfmHojSkS+BLwqIn8iIr8VHX5LVduBx4C5IrI0Ojf1v3e4FOj1NRG5VVU7gL8BbhGRXcAWYCFwN3BpjEVNDCLyVeAuEWkqOPxJ4Hsi8s/AROAzwP3RaD/TiMgXgA0icr+I3Kyq73L0puBzgBdiKVyG8L4xDO8bw/G+EVIdlyAiHwGuBD4KzAYeFpGfq+pr0SlvYL7Z3wWeUdUeEalX1VwsBY6ZAfTaqKrfEZE9wHuq+vvRaOwuYC7wf2MrcMyIyCjgc8DtwM8xH/+TAKq6UUTuAF5U1VeiTuTbwCzgzZiKHCuR++PPMHfdJ4APAP9ZRJ5R1a0i0qCqh7GR/cYYi1rzeN8YhveNYXjf2EvaRx8NwKuquklVnwa+Dtxb8P77wKPAARG5W0S+hjWQrNKfXl+L3msHciIyKRqBCXYzzDKHsfiR+cBPgYtF5JT8m6r6LVV9JXreimk4OY6CJoT3gSdV9UZV/WfgH4F/AWYARAYUwJnAsyJymoh8JTK+nPLifWMY3jeG4X1jRNqNqLFAo4iMBlDV+zCf9Q3RawW6sE77U0Crqv4yrsImgP70mioiVwM7gBOxadc/w0ZkP4utpAkgihX5haq+D/wAMwbOjUZhvw6UFJHJkWYLgZfiKm/cqGoX8PcFh44AZwPb8wdEZCbWmf4R8H2gTVV3V7OcGcH7xjC8bwzA+8ZeUmFEici8/o6r6mPYtOqKgsNfw6YZ89wL/BswU1Xvr1ghE0SgXvcDX1DVt4CvAFuBA8D5qvpchYuaGAbRrDv6+y7wHLAMOD06ptHo6wfYSHaZqr5TlQLHzCB6dRS8bAR2qeqWgmOjsGtwF3CBqj5QuVLWPiKyvE88CuB940AE6uV9I4Nq5n0jgKom+gF8A9gEzC44VgeMip7fBDyTfx+YCXwTmBC9Hh33b0iBXt8CxkWvJe7fkCDN6qLn9dHf46JzbwFWA1dHxxvj/g0J1etCYH30/DJgKdahnhT3b0j7A7g8asffBo4rOC7eN5ZVr8z2jUNo5n1j9EjcTFQ/uSQmA3uAS/NTharao6rdIjIHs3Q3AP9FRD4NrMMqtiM6t6tqhY+BMulVpzYti0ZXfi0ToFlPpNmE6Nh+4G3sRvSHQC46XtPuqFL1woymkSLyl1gwrqrqYVXdjhOMGHUicjPwCPANVf2d6LpEREQN7xspm16Z6xuL1Mz7xohEGVH5Coqe53NP/BT4S2AVcGrBuV/E/NIXYiuC/ho4F/hHVf1kNcsdF65XOCVo9gLw4ahzOR34j8D9qvoBVX2iuqWvPiXqdUF0aAHwIeBNVb1AVZ+tWsFrjMKbF7AN+B/AO9F7N4jIDGyWDxG5E8vVk9m27nqFU4Jmz5PhvjGPJMW4FlsSeQnwE+ARVd0mIiOxfCa3Y5l2R2KGwGbgfOD7qrqn4H9kZomu6xXOcDWLgk7r8yPTWqcMeq0AnlPVvXGUv1YoqIdnsRvbHqAZ+DgwCVsBOQLYqaqfjM5fn9W27nqFM1zNstY3HkU1fYcDPYDrsMj9i7FRwAPAoui9P4r+3gzsx/KbNBZ8tp7s+apdr+pqNiLu8qdMr4a4y18rj37q4ZvAacA04D7gnOi8RmA3cFbBZzPX1l2vqmuWub6x7yMRM1Eich+2XPI7IjILuB6Yp6qfEJGXgYOY7/VfsGXTn1LVrkJXQ5ZwvcJxzcJwvZJBP/VwI/DBqB5Ga0Fck4h8G5sd2JDVenC9wnHNhkesMVEivw5Y/RUW1Y+qbgb+NzBRRD6MJT17QVXPVtXVWLbjedG5mapA1ysc1ywM1ysZDFIPfw9MEJGVfW5uf4DFoL0RnZupenC9wnHNykNVjSgROb7geaEV+yjQKbbbO1hyvqew1T3rVfWLBf/mOlV9tSoFjhnXKxzXLAzXKxkE1sMGLFM0InKRiDyNuV/+varurF6p48P1Csc1qwxVMaJE5EMi8r+Ab4vIb4vIKFVV6V3tswcLVv1UVLn7gHFYHpMeEamXaINMrfFlueB6lYJrFobrlQxKrIfxwJjo/XeBT6vqas1A6gjXKxzXrLJU3IgSkYVYoNqj0eMj2MakaO/qhzHA/8Es4HUiMg3b0PBI/jy1ZZc1j+sVjmsWhuuVDIZZD4ei81pU9fUqFz0WXK9wXLPKU42ZqMXAO6r6ELbr9WhgS94fKyJ3Y1bwicDngZ3Aw8BebGVA1nC9wnHNwnC9koHXQxiuVziuWYUp++o8EVkGdKnqi9HrKUAL8KdYbpn3gNejxwPAd4C7tGBfHREZq6qdZS1YQnG9wnHNwnC9koHXQxiuVziuWQxo+XJNTAB+CLRjFTOp4L3TgT8BboteLwOeIMo7Ex2rK1dZ0vBwvVwz1ysbD68H18s1q91HOd15h7DVO7diKeNvyL+hqm9GFfledOiV6Jz8lGKdZi++wvUKxzULw/VKBl4PYbhe4bhmMTEsI0pEbhORZSIyUVW7gf8O/D/gF8ASETmt4PQngT+MfLE3AWcAbWCblw6nHGnB9QrHNQvD9UoGXg9huF7huGbJIDgmKqqEqVjwWQ/wS2zp82dVtS0651TM/9qtqndHx8Zgu2JPwdLr/55mIOLf9QrHNQvD9UoGXg9huF7huGYJJMT3h20wCJZ062+i5yOAbwB/2+fc64BvYbu8jy04d2rcPsxqPVwv18z1ysbD68H1cs2y+RhBEYjICOCrQL2IPAEcB+QAVPWIiPwesE1ElqnqT6Ljj4nIPODHwHgRuVhV3wB2FPOdacb1Csc1C8P1SgZeD2G4XuG4ZslmyJioaMnkK8Ak4B3gbuAwcLGInAu/3kPnq8BXCj53A3An8DSwMKrAmsf1Csc1C8P1SgZeD2G4XuG4ZslnyJgoEbkImK2WrAsR+Ra2c/tB4DOqulhs+4cpwF8AX1TVTdHnUNVnK/kDkobrFY5rFobrlQy8HsJwvcJxzZJPMavzXgEekd59dp4HZqrqd7Hpxc+oRffPAHKqugms8jJaga5XOK5ZGK5XMvB6CMP1Csc1SzhDGlGq2qmq3dq7z85Hgdbo+ceBeSLyI+B/Aj+vTDHTg+sVjmsWhuuVDLwewnC9wnHNkk9RgeUAkSWs2B47j0eHO4AvYzknNqnq1rKXMKW4XuG4ZmG4XsnA6yEM1ysc1yy5hCTb7AEasARdCyPr9w+AHlV9zivwGFyvcFyzMFyvZOD1EIbrFY5rllCCkm2KyHnAC9Hjr1X1wUoVrBZwvcJxzcJwvZKB10MYrlc4rlkyCTWiZgCrgf+qlmbeGQTXKxzXLAzXKxl4PYTheoXjmiWT4G1fHMdxHMdxnGFuQOw4juM4jpNV3IhyHMdxHMcpATeiHMdxHMdxSsCNKMdxHMdxnBJwI8pxHMdxHKcE3IhyHMdxHMcpATeiHMdxHMdxSuD/A2NNyavQMAcOAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "forecast = median(forecast_samples)\n",
    "\n",
    "horizon = 1\n",
    "plot_length = 50\n",
    "fig, ax = plt.subplots(figsize=(8,4))\n",
    "start_date = forecast_end_date + pd.DateOffset(horizon - plot_length)\n",
    "end_date = forecast_end_date + pd.DateOffset(horizon - 1)\n",
    "ax = plot_data_forecast(fig, ax, data.loc[start_date:end_date].Sales,\n",
    "                        forecast[-plot_length:,horizon - 1],\n",
    "                        forecast_samples[:,-plot_length:,horizon - 1],\n",
    "                        data.loc[start_date:end_date].index,\n",
    "                        linewidth = 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "horizon = 14\n",
    "plot_length = 50\n",
    "fig, ax = plt.subplots(figsize=(8,4))\n",
    "start_date = forecast_end_date + pd.DateOffset(horizon - plot_length)\n",
    "end_date = forecast_end_date + pd.DateOffset(horizon - 1)\n",
    "ax = plot_data_forecast(fig, ax, data.loc[start_date:end_date].Sales,\n",
    "                        forecast[-plot_length:,horizon - 1],\n",
    "                        forecast_samples[:,-plot_length:,horizon - 1],\n",
    "                        data.loc[start_date:end_date].index,\n",
    "                        linewidth = 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As well as looking at the mean absolute deviation (MAD) between the forecast median and the observations over the forecast horizons. Interestingly, there is only a small increase in the MAD for longer forecast horizons."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3.122950819672131,\n",
       " 3.0724043715846996,\n",
       " 3.098360655737705,\n",
       " 3.0778688524590163,\n",
       " 3.0614754098360657,\n",
       " 3.133879781420765,\n",
       " 3.0655737704918034,\n",
       " 3.121584699453552,\n",
       " 3.1147540983606556,\n",
       " 3.0969945355191255,\n",
       " 3.127049180327869,\n",
       " 3.1243169398907105,\n",
       " 3.1174863387978142,\n",
       " 3.1256830601092895]"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Mean absolute deviation at increasing forecast horizons\n",
    "horizons = list(range(1, k+1))\n",
    "list(map(lambda k: MAD(data.loc[forecast_start_date + pd.DateOffset(k-1):forecast_end_date + pd.DateOffset(k-1)].Sales,\n",
    "                      forecast[:,k-1]),\n",
    "         horizons))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}