DFT.ipynb

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        "<a href=\"https://colab.research.google.com/github/eafpres/DFT_analysis/blob/master/DFT.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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        "# Using the Discrete Fourier Transform to Imporve Time Series Forecasts\n",
        "\n",
        "Suppose we have a time series we would like to forecast, such as the data shown here:\n",
        "\n",
        "![](https://drive.google.com/uc?id=1TuCTHEoFTP53GVnR3tACzpNUV1SV7mUJ)\n",
        "\n",
        "It's clear there are periodic behaviors occuring in these data.  We could try to model this in any number of ways; I like to try multiple least squares as well as use artificial neural netwroks (ANNs) to tackle such problems.  To do so with MLS or a fully conencted ANN generally requires having some additional predictor variables other than, say, just a time lagged version of the target data.  A simple example would be to add time variables so that any trend with time could be automatically modeled.  In addition, these data have repeating zeros (the original data were sales data, and no sales occurred on weekends).  I typically add binary variables like \"weekend\" which would be 1 on weekends and 0 otherwise, to help the model understand that behavior.  Similarly, we might add the month number, week number etc. (or possible a cosine transform of them, so that 1 is \"close\" to 12, 52 is close to 1, etc.).\n",
        "\n",
        "Another method I use is to analyze the data using a Discrete Fourier Transform (DFT) to find the \"frequencies\" or periods that might be hidden in the data and could be used to improve the model.  You don't really need to completely understand the DFT to use this approach, but there are many references available on the internet if you want to learn (Google things like 'Discrete Fourier Transform' or \"Signal Analysis' to find more).  First, you can consider that the DFT is based on the concept that any arbitrary waveform can be decomposed into an infinite series of sine and cosine functions.  The continuous Fourier Transform is actually an integral from minus infinity to infinity; the DFT uses uniformly spaced \"samples\" of the data and some finite set of functions to approximate the data.  However, we aren't typically trying to use enough functions to perfectly fit the data; that would overfit and lead to very poor extrapolation to future predictions.  More on this in a moment.\n",
        "\n",
        "Next, if we know a data set contains a period, say, 30 days, how do we use that?  To do so, we use the mathematical fact that any given sinusoid at some unknown time offset (\"phase\" in signal analysis) can be represented by a linear combination of a sine and cosine function at the given period.  The coefficients on the sine and cosine functions determine the time offset and the scale (\"amplitude\" in signal analysis).  We will find those coefficients by regression or using an ANN.\n",
        "\n",
        "More or less, that's all you need to know.  Here, I provide a function which uses the DFT built into numpy and the peak find built into scipy.  When you use this function, you can set a threshold to determine how many peaks (each peak is a period found by the DFT) are returned, and it shows a plot labeled with the returned periods.  The function allows you to designate the time unit for one step in the data, so that if you were getting data, say, every hour, and your units were in days, the time unit would be 0.04167 days.  This ensures the results returned are in your units.  Note that a requirement of the DFT is the data are uniformly spaced.\n",
        "\n",
        "If this is confusing, let's simplify with a basic walk-through:  \n",
        "1) Start with data in uniform time steps, either time, value or just value  \n",
        "2) If no time varaible, determine the time step as noted earlier  \n",
        "3) Call the get_dft function which returns a list of the time periods  \n",
        "4) For each period you want to use in the model, calculate:  \n",
        "&nbsp;&nbsp;&nbsp;&nbsp; 4.1) sin(2 * pi * time / period)  \n",
        "&nbsp;&nbsp;&nbsp;&nbsp; 4.2) cos(2 * pi * time / period)  \n",
        "where time is the value of time for a given row of data, and period is the value returned from the get_dft function  \n",
        "5) Add the two series as columns in the \"X\" data for your model  \n",
        "6) Fit the model using whatever regression or modeling method you want\n",
        "\n",
        "Here we'll run a couple of exmaples to demonstrate.  First, we create a complex time series by combining three sine series at different periods, then try to discover those periods with the DFT and finally fit the data with a multiple linear regression model.  Second, for illustration, we create a triangle wave then try to fit that using the DFT results.\n",
        "\n"
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      "source": [
        "## Load modules"
      ]
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      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "from scipy.signal import sawtooth\n",
        "import statsmodels.api as sm\n",
        "import math\n",
        "from datetime import datetime\n",
        "import calendar\n",
        "import matplotlib.pyplot as plt"
      ],
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      "outputs": []
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      "source": [
        "## Define DFT function"
      ]
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      "source": [
        "def get_dft(data, dt = None, \n",
        "            x_limits = None, peak_height_ratio_threshold = None):\n",
        "#\n",
        "    \"\"\"\n",
        "    function to take the discrete fourier transform of a series\n",
        "    the series is assumed to be data = pd.DataFrame(x = [x1, x2, ..., xn],\n",
        "                                                    y = [y1, y2, ..., yn])\n",
        "    where x is time and y are the series values\n",
        "    if x is provided and dt is not provided, then the time step\n",
        "    is calculated as the average delta x over the given data\n",
        "    otherwise dt is used as the time step; if dt is not given\n",
        "    and x is not given an exception is raised\n",
        "    \n",
        "    if no y data are provided an exception is raised\n",
        "    \n",
        "    a basic visualization is given in the time\n",
        "    space to show the peaks found vs period\n",
        "    \n",
        "    if no limits are given for the plot, an exception is raised\n",
        "    \n",
        "    if peak_height_ratio_threshold is given the it is used to find\n",
        "    peaks by setting the lowest height to the produce of \n",
        "    peak_height_ratio_threshold times the max y value in the dft\n",
        "    otherwise a default peak find is used\n",
        "    \n",
        "    ---\n",
        "    \n",
        "    data:                           pd.DataFrame or pd.Series\n",
        "    dt:                             int or float (will coerce to float)\n",
        "    x_limits:                       list of x_min, x_max\n",
        "    peak_height_ratio_threshold:    float\n",
        "    \n",
        "    ---\n",
        "    \n",
        "    return value:                   list of periods of peaks\n",
        "    \"\"\"\n",
        "#\n",
        "    from scipy.signal import find_peaks\n",
        "    import warnings\n",
        "#\n",
        "    class get_dft_error(Exception):\n",
        "        pass\n",
        "#    \n",
        "    x = None\n",
        "    y = None\n",
        "    try:\n",
        "        x = data.iloc[:, 0]\n",
        "        y = data.iloc[:, 1]\n",
        "    except:\n",
        "        try:\n",
        "            y = data.iloc[:, 0]\n",
        "        except:\n",
        "            y = data\n",
        "    if x is None:\n",
        "        if dt is None:\n",
        "            raise get_dft_error('no x (time) data or delta t given')\n",
        "    elif dt is None:\n",
        "        dt = np.mean([x[i+1] - x[i] for i in list(range(0, x.shape[0] - 1))])\n",
        "    if y is None:\n",
        "        raise get_dft_error('no y data provided')\n",
        "    if x_limits is None:\n",
        "        raise get_dft_error('missing limits for peaks vs. period plot')\n",
        "#\n",
        "    real_fft = np.abs(np.fft.rfft(y))\n",
        "    frequencies = np.fft.fftfreq(y.shape[0])[0:real_fft.shape[0]]\n",
        "#\n",
        "# ignore the divide by zero error due to the 0 frequency (DC term)\n",
        "#\n",
        "    with warnings.catch_warnings():\n",
        "        warnings.simplefilter(\"ignore\")\n",
        "        periods = dt / (frequencies)\n",
        "#\n",
        "    if peak_height_ratio_threshold is None:\n",
        "        raw_peaks = find_peaks(real_fft, height = 0)\n",
        "    else:\n",
        "        raw_peaks = \\\n",
        "            find_peaks(real_fft,\n",
        "                       height = peak_height_ratio_threshold * max(real_fft))\n",
        "    peak_values = pd.Series(raw_peaks[1]['peak_heights'])\n",
        "    peak_locs = pd.Series(periods[raw_peaks[0]])\n",
        "    peak_locs = pd.Series([peak_locs[i] + dt for i in peak_locs.index])\n",
        "    peak_labels = [str(round(peak_locs[i], 1)) for i in peak_locs.index]\n",
        "#\n",
        "    plt.style.use('dark_background')\n",
        "    plot = plt.figure(figsize = (12, 8))\n",
        "    ax = plot.add_subplot(111)\n",
        "    ax.plot(periods,\n",
        "            real_fft,\n",
        "            color = \"blue\")\n",
        "    ax.set_xlim(x_limits)\n",
        "    for i in peak_values.index:\n",
        "        if peak_locs[i] < x_limits[1]:\n",
        "            ax.text(peak_locs[i], peak_values[i], peak_labels[i])\n",
        "    plt.show()\n",
        "    plt.close()\n",
        "    return peak_locs"
      ],
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      "outputs": []
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      "source": [
        "class get_dft_error(Exception):\n",
        "    pass "
      ],
      "execution_count": 0,
      "outputs": []
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    {
      "cell_type": "markdown",
      "metadata": {
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      "source": [
        "## Demonstrate with a multi-frequency synthetic series"
      ]
    },
    {
      "cell_type": "code",
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      "source": [
        "#\n",
        "# demo with multi-frequency synthetic series\n",
        "#\n",
        "my_period = 35\n",
        "#\n",
        "# we generate data at my_period and my_period * 1.5, 3.7\n",
        "# so the periods are 35, 52.5, and 129.5\n",
        "#\n",
        "test_data_1 = (pd.Series(np.array(list(range(0, 1000))) * \n",
        "                         2 * math.pi / my_period)).apply(math.sin)\n",
        "test_data_2 = (pd.Series(np.array(list(range(0, 1000))) * \n",
        "                         2 * math.pi / (my_period * 1.5))).apply(math.sin)\n",
        "test_data_3 = (pd.Series(np.array(list(range(0, 1000))) * \n",
        "                         2 * math.pi / (my_period * 3.7))).apply(math.sin)\n",
        "test_data = np.add(np.add(test_data_1, test_data_2), test_data_3)\n",
        "print(test_data.head)\n",
        "plt.style.use('dark_background')\n",
        "plot = plt.figure(figsize = (12, 8))\n",
        "ax = plot.add_subplot(111)\n",
        "ax.plot(test_data)\n",
        "plt.show()\n",
        "plt.close()"
      ],
      "execution_count": 0,
      "outputs": [
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            "<bound method NDFrame.head of 0      0.000000\n",
            "1      0.346451\n",
            "2      0.685341\n",
            "3      1.009317\n",
            "4      1.311440\n",
            "         ...   \n",
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            "999   -1.062408\n",
            "Length: 1000, dtype: float64>\n"
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W7ZISHDK6HcI8IpLsEClDT4eYFsFsfjbdBIg4UN3ZxtHNPQBAY+82yqSEBIaX9Yu8mSfO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\nQmCC\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "X6iN8LYMTEj_",
        "colab_type": "text"
      },
      "source": [
        "Here is where we put in the \"time\" mentioned in the introduction.  We could also just send the series to the function and specify the dt value of 1."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "k48kXgD0yIcK",
        "colab_type": "code",
        "outputId": "40a6c5fb-0245-4f2a-fcfb-cc6103322fb6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 419
        }
      },
      "source": [
        "#\n",
        "# add the time variable which is just integer values in this case\n",
        "#\n",
        "data = pd.concat((pd.Series(test_data.index).rename('x'), \n",
        "                  test_data.rename('y')), axis = 1)\n",
        "data"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>x</th>\n",
              "      <th>y</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0</td>\n",
              "      <td>0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>0.346451</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2</td>\n",
              "      <td>0.685341</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>3</td>\n",
              "      <td>1.009317</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>4</td>\n",
              "      <td>1.311440</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>995</th>\n",
              "      <td>995</td>\n",
              "      <td>-0.774581</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>996</th>\n",
              "      <td>996</td>\n",
              "      <td>-0.844863</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>997</th>\n",
              "      <td>997</td>\n",
              "      <td>-0.918947</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>998</th>\n",
              "      <td>998</td>\n",
              "      <td>-0.992824</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>999</th>\n",
              "      <td>999</td>\n",
              "      <td>-1.062408</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>1000 rows × 2 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "       x         y\n",
              "0      0  0.000000\n",
              "1      1  0.346451\n",
              "2      2  0.685341\n",
              "3      3  1.009317\n",
              "4      4  1.311440\n",
              "..   ...       ...\n",
              "995  995 -0.774581\n",
              "996  996 -0.844863\n",
              "997  997 -0.918947\n",
              "998  998 -0.992824\n",
              "999  999 -1.062408\n",
              "\n",
              "[1000 rows x 2 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 61
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2MixQKQt65bW",
        "colab_type": "code",
        "outputId": "536a5602-ead1-4b94-f63f-72e86a7c60ae",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 551
        }
      },
      "source": [
        "#\n",
        "# now get the discrete transform\n",
        "# x_limits is required by our get_dft function\n",
        "#\n",
        "x_limits = [0, my_period * 5]\n",
        "try:\n",
        "    my_peaks = get_dft(data = data, x_limits = x_limits,\n",
        "                       peak_height_ratio_threshold = 0.001)\n",
        "except get_dft_error as err_msg:\n",
        "    print(err_msg.message)\n",
        "#\n",
        "print(my_peaks)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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FypZeQ/G1117LmDFjOOGEE7j00ku57777+PCHP8zixYu5+OKLAZg+fTrz588HYMGCBUyf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\nDgKpx2G7Sq4UA+zCUCxB2MbpTuCbwN3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Fu3bt4pxt0tTUhKWlJXg8HnktVqYaGhoQCATg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\nPd4UM8YYY4wx1fsP4KJRou6VuwwAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "0    126.000000\n",
            "1     53.631579\n",
            "2     35.482759\n",
            "dtype: float64\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dRqKJBY00NNt",
        "colab_type": "text"
      },
      "source": [
        "We see that we found periods of 35.5, 53.6, and 126 vs. the known values of 35, 52.5, and 129.5\n",
        "\n",
        "This is due to fact that we are sampling at intervals of one but have fractional periods.  Ideally we would \"sample\" more often, however in business data we generally have to take what we get.  \n",
        "\n",
        "Also note that in this case, even if we did not set a peak height threshold, we would always return only 3 peaks becuase the series is constructed from 3 pure frequencies."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6ADA93vm0BZD",
        "colab_type": "code",
        "outputId": "c6c217aa-aed6-4b4f-b344-837585856c3b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 119
        }
      },
      "source": [
        "#\n",
        "# we add sin and cos series to our data using the found periods\n",
        "#\n",
        "model_periods = pd.Series(my_peaks)\n",
        "period_names = ['cos_' + str(round(model_periods[i], 3)) \n",
        "                for i in model_periods.index]\n",
        "period_names = (period_names +\n",
        "                ['sin_' + str(round(model_periods[i], 3)) \n",
        "                for i in model_periods.index])\n",
        "period_names"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "['cos_126.0',\n",
              " 'cos_53.632',\n",
              " 'cos_35.483',\n",
              " 'sin_126.0',\n",
              " 'sin_53.632',\n",
              " 'sin_35.483']"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 63
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Fa6R_oPZe5Yb",
        "colab_type": "code",
        "outputId": "6983f963-08a7-408c-ce0e-9e61b5d352d4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 419
        }
      },
      "source": [
        "for j in range(len(model_periods)):\n",
        "    data = pd.concat((data, \n",
        "                     pd.Series([math.sin(2 * math.pi * i / model_periods[j]) \n",
        "                      for i in data.iloc[:, 0]]).rename(period_names[j])),\n",
        "                     axis = 1)\n",
        "    data = \\\n",
        "      pd.concat((data,\n",
        "        pd.Series([math.cos(2 * math.pi * i / model_periods[j]) \n",
        "        for i in data.iloc[:, 0]]).rename(period_names[j + len(model_periods)])),\n",
        "        axis = 1)\n",
        "data "
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>x</th>\n",
              "      <th>y</th>\n",
              "      <th>cos_126.0</th>\n",
              "      <th>sin_126.0</th>\n",
              "      <th>cos_53.632</th>\n",
              "      <th>sin_53.632</th>\n",
              "      <th>cos_35.483</th>\n",
              "      <th>sin_35.483</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>0.346451</td>\n",
              "      <td>0.049846</td>\n",
              "      <td>0.998757</td>\n",
              "      <td>0.116887</td>\n",
              "      <td>0.993145</td>\n",
              "      <td>0.176153</td>\n",
              "      <td>0.984363</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2</td>\n",
              "      <td>0.685341</td>\n",
              "      <td>0.099568</td>\n",
              "      <td>0.995031</td>\n",
              "      <td>0.232171</td>\n",
              "      <td>0.972675</td>\n",
              "      <td>0.346797</td>\n",
              "      <td>0.937940</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>3</td>\n",
              "      <td>1.009317</td>\n",
              "      <td>0.149042</td>\n",
              "      <td>0.988831</td>\n",
              "      <td>0.344272</td>\n",
              "      <td>0.938870</td>\n",
              "      <td>0.506595</td>\n",
              "      <td>0.862184</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>4</td>\n",
              "      <td>1.311440</td>\n",
              "      <td>0.198146</td>\n",
              "      <td>0.980172</td>\n",
              "      <td>0.451654</td>\n",
              "      <td>0.892193</td>\n",
              "      <td>0.650550</td>\n",
              "      <td>0.759463</td>\n",
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              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>995</th>\n",
              "      <td>995</td>\n",
              "      <td>-0.774581</td>\n",
              "      <td>-0.603804</td>\n",
              "      <td>0.797133</td>\n",
              "      <td>-0.323932</td>\n",
              "      <td>-0.946080</td>\n",
              "      <td>0.259556</td>\n",
              "      <td>0.965728</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>996</th>\n",
              "      <td>996</td>\n",
              "      <td>-0.844863</td>\n",
              "      <td>-0.563320</td>\n",
              "      <td>0.826239</td>\n",
              "      <td>-0.432296</td>\n",
              "      <td>-0.901732</td>\n",
              "      <td>0.425614</td>\n",
              "      <td>0.904905</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>997</th>\n",
              "      <td>997</td>\n",
              "      <td>-0.918947</td>\n",
              "      <td>-0.521435</td>\n",
              "      <td>0.853291</td>\n",
              "      <td>-0.534733</td>\n",
              "      <td>-0.845021</td>\n",
              "      <td>0.578360</td>\n",
              "      <td>0.815782</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>998</th>\n",
              "      <td>998</td>\n",
              "      <td>-0.992824</td>\n",
              "      <td>-0.478254</td>\n",
              "      <td>0.878222</td>\n",
              "      <td>-0.629839</td>\n",
              "      <td>-0.776725</td>\n",
              "      <td>0.713019</td>\n",
              "      <td>0.701145</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>999</th>\n",
              "      <td>999</td>\n",
              "      <td>-1.062408</td>\n",
              "      <td>-0.433884</td>\n",
              "      <td>0.900969</td>\n",
              "      <td>-0.716311</td>\n",
              "      <td>-0.697781</td>\n",
              "      <td>0.825378</td>\n",
              "      <td>0.564581</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>1000 rows × 8 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "       x         y  cos_126.0  ...  sin_53.632  cos_35.483  sin_35.483\n",
              "0      0  0.000000   0.000000  ...    1.000000    0.000000    1.000000\n",
              "1      1  0.346451   0.049846  ...    0.993145    0.176153    0.984363\n",
              "2      2  0.685341   0.099568  ...    0.972675    0.346797    0.937940\n",
              "3      3  1.009317   0.149042  ...    0.938870    0.506595    0.862184\n",
              "4      4  1.311440   0.198146  ...    0.892193    0.650550    0.759463\n",
              "..   ...       ...        ...  ...         ...         ...         ...\n",
              "995  995 -0.774581  -0.603804  ...   -0.946080    0.259556    0.965728\n",
              "996  996 -0.844863  -0.563320  ...   -0.901732    0.425614    0.904905\n",
              "997  997 -0.918947  -0.521435  ...   -0.845021    0.578360    0.815782\n",
              "998  998 -0.992824  -0.478254  ...   -0.776725    0.713019    0.701145\n",
              "999  999 -1.062408  -0.433884  ...   -0.697781    0.825378    0.564581\n",
              "\n",
              "[1000 rows x 8 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 64
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RT8BQgpfTX8f",
        "colab_type": "text"
      },
      "source": [
        "Note that for convenience, we format the column names to no more than 3 decimal places."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wUJh5wrQUbZG",
        "colab_type": "text"
      },
      "source": [
        "## Perform linear regression"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yW19GDUC0EVv",
        "colab_type": "code",
        "outputId": "7f9a74d7-352c-4305-d2e4-b29ba2a1fe86",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 517
        }
      },
      "source": [
        "#\n",
        "# divide data in to X and Y for linear regression\n",
        "#    \n",
        "X = data.drop(('y'), axis = 1)\n",
        "Y = pd.DataFrame(data.y)\n",
        "#\n",
        "# fit a multiple least squares model model\n",
        "#\n",
        "X = sm.add_constant(X)\n",
        "model = sm.OLS(Y, X).fit()\n",
        "model.summary()\n",
        "y_pred = model.predict(X)\n",
        "plt.style.use('dark_background')\n",
        "plot = plt.figure(figsize = (12, 8))\n",
        "ax = plot.add_subplot(111)\n",
        "ax.plot(data.x, y_pred,\n",
        "        color = \"yellow\",\n",
        "        lw = 1, \n",
        "        linestyle = 'dashed')\n",
        "ax.plot(data.x, data.y,\n",
        "        color = \"blue\",\n",
        "        lw = 0.75)\n",
        "plot.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/numpy/core/fromnumeric.py:2495: FutureWarning: Method .ptp is deprecated and will be removed in a future version. Use numpy.ptp instead.\n",
            "  return ptp(axis=axis, out=out, **kwargs)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
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XvyzE6WxGI8GKE6hDvDHjUeeSQjBz5uBHDSIMolEoKwOfzyvpENIpbunSxH3/+AdUV2vD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\nR8HUqemXA8NhKC9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kxaZ8zqkieOtWKC52WiQ4OXIxSL7+vfX1MGdOdjeBcBjKytx5I/D5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\nAACcQwgGAACAc/4HV43PayDq8MsAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dW1cGf5O1xIR",
        "colab_type": "text"
      },
      "source": [
        "The least squares fit to our 3 found periods does a pretty good job reconstructing the original series."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZM4AWUEWUpVh",
        "colab_type": "text"
      },
      "source": [
        "## Demonstrate with a Triangle wave form data set"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7wqXCbFEUndN",
        "colab_type": "code",
        "outputId": "deec35d4-9b02-4fb5-f7ed-d25511ca63e9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 419
        }
      },
      "source": [
        "#\n",
        "# construct a triangle wave\n",
        "#\n",
        "x = pd.Series(np.arange(0, 110, 0.1))\n",
        "A = 1\n",
        "P = 22 \n",
        "y = pd.Series(sawtooth(x, 0.5))\n",
        "x = pd.Series(x.multiply(P / (2 * math.pi)))\n",
        "data = pd.concat((x.rename('x'), y.rename('y')), axis = 1)\n",
        "data"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>x</th>\n",
              "      <th>y</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.000000</td>\n",
              "      <td>-1.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.350141</td>\n",
              "      <td>-0.936338</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.700282</td>\n",
              "      <td>-0.872676</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1.050423</td>\n",
              "      <td>-0.809014</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1.400563</td>\n",
              "      <td>-0.745352</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1095</th>\n",
              "      <td>383.404258</td>\n",
              "      <td>0.709865</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1096</th>\n",
              "      <td>383.754399</td>\n",
              "      <td>0.773527</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1097</th>\n",
              "      <td>384.104540</td>\n",
              "      <td>0.837189</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1098</th>\n",
              "      <td>384.454681</td>\n",
              "      <td>0.900851</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1099</th>\n",
              "      <td>384.804821</td>\n",
              "      <td>0.964513</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>1100 rows × 2 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "               x         y\n",
              "0       0.000000 -1.000000\n",
              "1       0.350141 -0.936338\n",
              "2       0.700282 -0.872676\n",
              "3       1.050423 -0.809014\n",
              "4       1.400563 -0.745352\n",
              "...          ...       ...\n",
              "1095  383.404258  0.709865\n",
              "1096  383.754399  0.773527\n",
              "1097  384.104540  0.837189\n",
              "1098  384.454681  0.900851\n",
              "1099  384.804821  0.964513\n",
              "\n",
              "[1100 rows x 2 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 66
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nHo4SteYfgOY",
        "colab_type": "code",
        "outputId": "b773cbfe-b408-4645-faf2-29318ca991b8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 483
        }
      },
      "source": [
        "plt.style.use('dark_background')\n",
        "plot = plt.figure(figsize = (12, 8))\n",
        "ax = plot.add_subplot(111)\n",
        "ax.plot(x, y,\n",
        "        color = \"yellow\",\n",
        "        lw = 1, \n",
        "        linestyle = 'solid')\n",
        "plot.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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RJM6YpM2FFCskw0bpL2wkbos4AWcpnylGtsi5nJW4pWicxNGWNHuozVAbqkCZ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\nB1ioAQAAAAdYqAEAAAAH/gexbqRDIOytCAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qEHCpAyafaTY",
        "colab_type": "code",
        "outputId": "4a62b1e1-f718-4083-b151-eb7b09f4db58",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 724
        }
      },
      "source": [
        "try:\n",
        "    my_peaks = get_dft(data, x_limits = [0, 50], \n",
        "                       peak_height_ratio_threshold = 0.001)\n",
        "except get_dft_error as err_msg:\n",
        "    print(err_msg.msg)\n",
        "print(my_peaks)\n",
        "#\n",
        "model_periods = pd.Series(my_peaks)\n",
        "period_names = ['cos_' + str(round(model_periods[i], 3)) \n",
        "                for i in model_periods.index]\n",
        "period_names = (period_names +\n",
        "                ['sin_' + str(round(model_periods[i], 3)) \n",
        "                for i in model_periods.index])\n",
        "print(period_names)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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qA7OkFBoLbAZq4y6kizTiDLMkJZeBWVIKjQV+D2yPu5AuYkuGJCWZgVlSylQC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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "0     21.747639\n",
            "1      7.617216\n",
            "2      4.726902\n",
            "3      3.481482\n",
            "4      3.043532\n",
            "        ...    \n",
            "75     1.075480\n",
            "76     1.071405\n",
            "77     1.067375\n",
            "78     1.059450\n",
            "79     1.051698\n",
            "Length: 80, dtype: float64\n",
            "['cos_21.748', 'cos_7.617', 'cos_4.727', 'cos_3.481', 'cos_3.044', 'cos_2.788', 'cos_2.514', 'cos_2.346', 'cos_2.211', 'cos_2.158', 'cos_2.085', 'cos_2.039', 'cos_1.942', 'cos_1.903', 'cos_1.849', 'cos_1.815', 'cos_1.741', 'cos_1.711', 'cos_1.697', 'cos_1.683', 'cos_1.669', 'cos_1.643', 'cos_1.617', 'cos_1.585', 'cos_1.577', 'cos_1.561', 'cos_1.55', 'cos_1.539', 'cos_1.528', 'cos_1.507', 'cos_1.486', 'cos_1.46', 'cos_1.451', 'cos_1.441', 'cos_1.432', 'cos_1.423', 'cos_1.414', 'cos_1.397', 'cos_1.38', 'cos_1.358', 'cos_1.351', 'cos_1.343', 'cos_1.335', 'cos_1.328', 'cos_1.32', 'cos_1.306', 'cos_1.292', 'cos_1.274', 'cos_1.267', 'cos_1.261', 'cos_1.254', 'cos_1.248', 'cos_1.242', 'cos_1.229', 'cos_1.218', 'cos_1.202', 'cos_1.197', 'cos_1.191', 'cos_1.186', 'cos_1.18', 'cos_1.175', 'cos_1.164', 'cos_1.154', 'cos_1.151', 'cos_1.141', 'cos_1.136', 'cos_1.131', 'cos_1.127', 'cos_1.122', 'cos_1.117', 'cos_1.108', 'cos_1.099', 'cos_1.097', 'cos_1.088', 'cos_1.08', 'cos_1.075', 'cos_1.071', 'cos_1.067', 'cos_1.059', 'cos_1.052', 'sin_21.748', 'sin_7.617', 'sin_4.727', 'sin_3.481', 'sin_3.044', 'sin_2.788', 'sin_2.514', 'sin_2.346', 'sin_2.211', 'sin_2.158', 'sin_2.085', 'sin_2.039', 'sin_1.942', 'sin_1.903', 'sin_1.849', 'sin_1.815', 'sin_1.741', 'sin_1.711', 'sin_1.697', 'sin_1.683', 'sin_1.669', 'sin_1.643', 'sin_1.617', 'sin_1.585', 'sin_1.577', 'sin_1.561', 'sin_1.55', 'sin_1.539', 'sin_1.528', 'sin_1.507', 'sin_1.486', 'sin_1.46', 'sin_1.451', 'sin_1.441', 'sin_1.432', 'sin_1.423', 'sin_1.414', 'sin_1.397', 'sin_1.38', 'sin_1.358', 'sin_1.351', 'sin_1.343', 'sin_1.335', 'sin_1.328', 'sin_1.32', 'sin_1.306', 'sin_1.292', 'sin_1.274', 'sin_1.267', 'sin_1.261', 'sin_1.254', 'sin_1.248', 'sin_1.242', 'sin_1.229', 'sin_1.218', 'sin_1.202', 'sin_1.197', 'sin_1.191', 'sin_1.186', 'sin_1.18', 'sin_1.175', 'sin_1.164', 'sin_1.154', 'sin_1.151', 'sin_1.141', 'sin_1.136', 'sin_1.131', 'sin_1.127', 'sin_1.122', 'sin_1.117', 'sin_1.108', 'sin_1.099', 'sin_1.097', 'sin_1.088', 'sin_1.08', 'sin_1.075', 'sin_1.071', 'sin_1.067', 'sin_1.059', 'sin_1.052']\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hHvFoOXJfmA4",
        "colab_type": "code",
        "outputId": "64b53092-ebf2-41ab-a463-7df578ddd0b5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 507
        }
      },
      "source": [
        "#\n",
        "# add the sin / cos series to the data\n",
        "#\n",
        "for j in range(len(model_periods)):\n",
        "    data = pd.concat((data, \n",
        "                     pd.Series([math.sin(2 * math.pi * i / model_periods[j]) \n",
        "                      for i in data.iloc[:, 0]]).rename(period_names[j])),\n",
        "                     axis = 1)\n",
        "    data = pd.concat((data,\n",
        "                     pd.Series([math.cos(2 * math.pi * i / model_periods[j]) \n",
        "                      for i in data.iloc[:, 0]]).rename(period_names[j + len(model_periods)])),\n",
        "                     axis = 1)\n",
        "data"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>x</th>\n",
              "      <th>y</th>\n",
              "      <th>cos_21.748</th>\n",
              "      <th>sin_21.748</th>\n",
              "      <th>cos_7.617</th>\n",
              "      <th>sin_7.617</th>\n",
              "      <th>cos_4.727</th>\n",
              "      <th>sin_4.727</th>\n",
              "      <th>cos_3.481</th>\n",
              "      <th>sin_3.481</th>\n",
              "      <th>cos_3.044</th>\n",
              "      <th>sin_3.044</th>\n",
              "      <th>cos_2.788</th>\n",
              "      <th>sin_2.788</th>\n",
              "      <th>cos_2.514</th>\n",
              "      <th>sin_2.514</th>\n",
              "      <th>cos_2.346</th>\n",
              "      <th>sin_2.346</th>\n",
              "      <th>cos_2.211</th>\n",
              "      <th>sin_2.211</th>\n",
              "      <th>cos_2.158</th>\n",
              "      <th>sin_2.158</th>\n",
              "      <th>cos_2.085</th>\n",
              "      <th>sin_2.085</th>\n",
              "      <th>cos_2.039</th>\n",
              "      <th>sin_2.039</th>\n",
              "      <th>cos_1.942</th>\n",
              "      <th>sin_1.942</th>\n",
              "      <th>cos_1.903</th>\n",
              "      <th>sin_1.903</th>\n",
              "      <th>cos_1.849</th>\n",
              "      <th>sin_1.849</th>\n",
              "      <th>cos_1.815</th>\n",
              "      <th>sin_1.815</th>\n",
              "      <th>cos_1.741</th>\n",
              "      <th>sin_1.741</th>\n",
              "      <th>cos_1.711</th>\n",
              "      <th>sin_1.711</th>\n",
              "      <th>cos_1.697</th>\n",
              "      <th>sin_1.697</th>\n",
              "      <th>...</th>\n",
              "      <th>cos_1.175</th>\n",
              "      <th>sin_1.175</th>\n",
              "      <th>cos_1.164</th>\n",
              "      <th>sin_1.164</th>\n",
              "      <th>cos_1.154</th>\n",
              "      <th>sin_1.154</th>\n",
              "      <th>cos_1.151</th>\n",
              "      <th>sin_1.151</th>\n",
              "      <th>cos_1.141</th>\n",
              "      <th>sin_1.141</th>\n",
              "      <th>cos_1.136</th>\n",
              "      <th>sin_1.136</th>\n",
              "      <th>cos_1.131</th>\n",
              "      <th>sin_1.131</th>\n",
              "      <th>cos_1.127</th>\n",
              "      <th>sin_1.127</th>\n",
              "      <th>cos_1.122</th>\n",
              "      <th>sin_1.122</th>\n",
              "      <th>cos_1.117</th>\n",
              "      <th>sin_1.117</th>\n",
              "      <th>cos_1.108</th>\n",
              "      <th>sin_1.108</th>\n",
              "      <th>cos_1.099</th>\n",
              "      <th>sin_1.099</th>\n",
              "      <th>cos_1.097</th>\n",
              "      <th>sin_1.097</th>\n",
              "      <th>cos_1.088</th>\n",
              "      <th>sin_1.088</th>\n",
              "      <th>cos_1.08</th>\n",
              "      <th>sin_1.08</th>\n",
              "      <th>cos_1.075</th>\n",
              "      <th>sin_1.075</th>\n",
              "      <th>cos_1.071</th>\n",
              "      <th>sin_1.071</th>\n",
              "      <th>cos_1.067</th>\n",
              "      <th>sin_1.067</th>\n",
              "      <th>cos_1.059</th>\n",
              "      <th>sin_1.059</th>\n",
              "      <th>cos_1.052</th>\n",
              "      <th>sin_1.052</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.000000</td>\n",
              "      <td>-1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000e+00</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>...</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.350141</td>\n",
              "      <td>-0.936338</td>\n",
              "      <td>0.100988</td>\n",
              "      <td>0.994888</td>\n",
              "      <td>0.284821</td>\n",
              "      <td>0.958581</td>\n",
              "      <td>0.448799</td>\n",
              "      <td>0.893633</td>\n",
              "      <td>0.590691</td>\n",
              "      <td>0.806898</td>\n",
              "      <td>0.661520</td>\n",
              "      <td>0.749927</td>\n",
              "      <td>0.709751</td>\n",
              "      <td>0.704453</td>\n",
              "      <td>0.767622</td>\n",
              "      <td>0.640903</td>\n",
              "      <td>0.806295</td>\n",
              "      <td>0.591514</td>\n",
              "      <td>0.838823</td>\n",
              "      <td>0.544404</td>\n",
              "      <td>0.851733</td>\n",
              "      <td>0.523977</td>\n",
              "      <td>0.869959</td>\n",
              "      <td>0.493124</td>\n",
              "      <td>0.881363</td>\n",
              "      <td>0.472440</td>\n",
              "      <td>9.057023e-01</td>\n",
              "      <td>0.423914</td>\n",
              "      <td>0.915181</td>\n",
              "      <td>0.403043</td>\n",
              "      <td>0.928355</td>\n",
              "      <td>0.371695</td>\n",
              "      <td>0.936455</td>\n",
              "      <td>0.350789</td>\n",
              "      <td>0.953287</td>\n",
              "      <td>0.302065</td>\n",
              "      <td>0.959638</td>\n",
              "      <td>0.281237</td>\n",
              "      <td>0.962624</td>\n",
              "      <td>0.270840</td>\n",
              "      <td>...</td>\n",
              "      <td>0.954824</td>\n",
              "      <td>-0.297172</td>\n",
              "      <td>0.949690</td>\n",
              "      <td>-0.313193</td>\n",
              "      <td>0.944328</td>\n",
              "      <td>-0.329004</td>\n",
              "      <td>0.942492</td>\n",
              "      <td>-0.334228</td>\n",
              "      <td>0.936840</td>\n",
              "      <td>-0.349759</td>\n",
              "      <td>0.933934</td>\n",
              "      <td>-0.357445</td>\n",
              "      <td>0.930977</td>\n",
              "      <td>-0.365079</td>\n",
              "      <td>0.927968</td>\n",
              "      <td>-0.372659</td>\n",
              "      <td>0.924910</td>\n",
              "      <td>-0.380186</td>\n",
              "      <td>0.921802</td>\n",
              "      <td>-0.387660</td>\n",
              "      <td>0.915443</td>\n",
              "      <td>-0.402449</td>\n",
              "      <td>0.908895</td>\n",
              "      <td>-0.417024</td>\n",
              "      <td>0.906673</td>\n",
              "      <td>-0.421835</td>\n",
              "      <td>0.899886</td>\n",
              "      <td>-0.436126</td>\n",
              "      <td>0.892926</td>\n",
              "      <td>-0.450204</td>\n",
              "      <td>0.889383</td>\n",
              "      <td>-0.457163</td>\n",
              "      <td>0.885799</td>\n",
              "      <td>-0.464068</td>\n",
              "      <td>0.882176</td>\n",
              "      <td>-0.470921</td>\n",
              "      <td>0.874810</td>\n",
              "      <td>-0.484466</td>\n",
              "      <td>0.867293</td>\n",
              "      <td>-0.497799</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.700282</td>\n",
              "      <td>-0.872676</td>\n",
              "      <td>0.200943</td>\n",
              "      <td>0.979603</td>\n",
              "      <td>0.546047</td>\n",
              "      <td>0.837754</td>\n",
              "      <td>0.802123</td>\n",
              "      <td>0.597159</td>\n",
              "      <td>0.953255</td>\n",
              "      <td>0.302169</td>\n",
              "      <td>0.992184</td>\n",
              "      <td>0.124782</td>\n",
              "      <td>0.999972</td>\n",
              "      <td>-0.007492</td>\n",
              "      <td>0.983942</td>\n",
              "      <td>-0.178488</td>\n",
              "      <td>0.953869</td>\n",
              "      <td>-0.300223</td>\n",
              "      <td>0.913317</td>\n",
              "      <td>-0.407249</td>\n",
              "      <td>0.892576</td>\n",
              "      <td>-0.450897</td>\n",
              "      <td>0.857996</td>\n",
              "      <td>-0.513657</td>\n",
              "      <td>0.832782</td>\n",
              "      <td>-0.553602</td>\n",
              "      <td>7.678804e-01</td>\n",
              "      <td>-0.640593</td>\n",
              "      <td>0.737715</td>\n",
              "      <td>-0.675113</td>\n",
              "      <td>0.690130</td>\n",
              "      <td>-0.723686</td>\n",
              "      <td>0.656996</td>\n",
              "      <td>-0.753894</td>\n",
              "      <td>0.575910</td>\n",
              "      <td>-0.817513</td>\n",
              "      <td>0.539772</td>\n",
              "      <td>-0.841811</td>\n",
              "      <td>0.521435</td>\n",
              "      <td>-0.853291</td>\n",
              "      <td>...</td>\n",
              "      <td>-0.567493</td>\n",
              "      <td>-0.823378</td>\n",
              "      <td>-0.594872</td>\n",
              "      <td>-0.803821</td>\n",
              "      <td>-0.621376</td>\n",
              "      <td>-0.783512</td>\n",
              "      <td>-0.630015</td>\n",
              "      <td>-0.776583</td>\n",
              "      <td>-0.655337</td>\n",
              "      <td>-0.755337</td>\n",
              "      <td>-0.667661</td>\n",
              "      <td>-0.744465</td>\n",
              "      <td>-0.679760</td>\n",
              "      <td>-0.733435</td>\n",
              "      <td>-0.691632</td>\n",
              "      <td>-0.722251</td>\n",
              "      <td>-0.703276</td>\n",
              "      <td>-0.710917</td>\n",
              "      <td>-0.714692</td>\n",
              "      <td>-0.699439</td>\n",
              "      <td>-0.736837</td>\n",
              "      <td>-0.676070</td>\n",
              "      <td>-0.758062</td>\n",
              "      <td>-0.652182</td>\n",
              "      <td>-0.764933</td>\n",
              "      <td>-0.644110</td>\n",
              "      <td>-0.784927</td>\n",
              "      <td>-0.619588</td>\n",
              "      <td>-0.803997</td>\n",
              "      <td>-0.594633</td>\n",
              "      <td>-0.813185</td>\n",
              "      <td>-0.582005</td>\n",
              "      <td>-0.822143</td>\n",
              "      <td>-0.569281</td>\n",
              "      <td>-0.830869</td>\n",
              "      <td>-0.556467</td>\n",
              "      <td>-0.847631</td>\n",
              "      <td>-0.530586</td>\n",
              "      <td>-0.863474</td>\n",
              "      <td>-0.504393</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1.050423</td>\n",
              "      <td>-0.809014</td>\n",
              "      <td>0.298844</td>\n",
              "      <td>0.954302</td>\n",
              "      <td>0.762040</td>\n",
              "      <td>0.647529</td>\n",
              "      <td>0.984808</td>\n",
              "      <td>0.173648</td>\n",
              "      <td>0.947667</td>\n",
              "      <td>-0.319260</td>\n",
              "      <td>0.826611</td>\n",
              "      <td>-0.562773</td>\n",
              "      <td>0.699116</td>\n",
              "      <td>-0.715008</td>\n",
              "      <td>0.493600</td>\n",
              "      <td>-0.869689</td>\n",
              "      <td>0.322158</td>\n",
              "      <td>-0.946686</td>\n",
              "      <td>0.155603</td>\n",
              "      <td>-0.987820</td>\n",
              "      <td>0.083646</td>\n",
              "      <td>-0.996496</td>\n",
              "      <td>-0.023762</td>\n",
              "      <td>-0.999718</td>\n",
              "      <td>-0.094485</td>\n",
              "      <td>-0.995526</td>\n",
              "      <td>-2.546711e-01</td>\n",
              "      <td>-0.967028</td>\n",
              "      <td>-0.320520</td>\n",
              "      <td>-0.947242</td>\n",
              "      <td>-0.415319</td>\n",
              "      <td>-0.909676</td>\n",
              "      <td>-0.475521</td>\n",
              "      <td>-0.879705</td>\n",
              "      <td>-0.605362</td>\n",
              "      <td>-0.795950</td>\n",
              "      <td>-0.656030</td>\n",
              "      <td>-0.754734</td>\n",
              "      <td>-0.680173</td>\n",
              "      <td>-0.733052</td>\n",
              "      <td>...</td>\n",
              "      <td>-0.617538</td>\n",
              "      <td>0.786541</td>\n",
              "      <td>-0.577070</td>\n",
              "      <td>0.816694</td>\n",
              "      <td>-0.535457</td>\n",
              "      <td>0.844562</td>\n",
              "      <td>-0.521354</td>\n",
              "      <td>0.853340</td>\n",
              "      <td>-0.478420</td>\n",
              "      <td>0.878131</td>\n",
              "      <td>-0.456629</td>\n",
              "      <td>0.889657</td>\n",
              "      <td>-0.434645</td>\n",
              "      <td>0.900602</td>\n",
              "      <td>-0.412483</td>\n",
              "      <td>0.910965</td>\n",
              "      <td>-0.390158</td>\n",
              "      <td>0.920748</td>\n",
              "      <td>-0.367687</td>\n",
              "      <td>0.929950</td>\n",
              "      <td>-0.322364</td>\n",
              "      <td>0.946616</td>\n",
              "      <td>-0.276635</td>\n",
              "      <td>0.960975</td>\n",
              "      <td>-0.261322</td>\n",
              "      <td>0.965252</td>\n",
              "      <td>-0.215231</td>\n",
              "      <td>0.976563</td>\n",
              "      <td>-0.169001</td>\n",
              "      <td>0.985616</td>\n",
              "      <td>-0.145867</td>\n",
              "      <td>0.989304</td>\n",
              "      <td>-0.122739</td>\n",
              "      <td>0.992439</td>\n",
              "      <td>-0.099628</td>\n",
              "      <td>0.995025</td>\n",
              "      <td>-0.053513</td>\n",
              "      <td>0.998567</td>\n",
              "      <td>-0.007621</td>\n",
              "      <td>0.999971</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1.400563</td>\n",
              "      <td>-0.745352</td>\n",
              "      <td>0.393689</td>\n",
              "      <td>0.919244</td>\n",
              "      <td>0.914907</td>\n",
              "      <td>0.403664</td>\n",
              "      <td>0.957990</td>\n",
              "      <td>-0.286803</td>\n",
              "      <td>0.576087</td>\n",
              "      <td>-0.817388</td>\n",
              "      <td>0.247613</td>\n",
              "      <td>-0.968859</td>\n",
              "      <td>-0.014983</td>\n",
              "      <td>-0.999888</td>\n",
              "      <td>-0.351243</td>\n",
              "      <td>-0.936284</td>\n",
              "      <td>-0.572747</td>\n",
              "      <td>-0.819732</td>\n",
              "      <td>-0.743895</td>\n",
              "      <td>-0.668297</td>\n",
              "      <td>-0.804919</td>\n",
              "      <td>-0.593385</td>\n",
              "      <td>-0.881431</td>\n",
              "      <td>-0.472313</td>\n",
              "      <td>-0.922059</td>\n",
              "      <td>-0.387050</td>\n",
              "      <td>-9.837980e-01</td>\n",
              "      <td>-0.179281</td>\n",
              "      <td>-0.996081</td>\n",
              "      <td>-0.088445</td>\n",
              "      <td>-0.998874</td>\n",
              "      <td>0.047442</td>\n",
              "      <td>-0.990611</td>\n",
              "      <td>0.136713</td>\n",
              "      <td>-0.941628</td>\n",
              "      <td>0.336655</td>\n",
              "      <td>-0.908772</td>\n",
              "      <td>0.417293</td>\n",
              "      <td>-0.889872</td>\n",
              "      <td>0.456211</td>\n",
              "      <td>...</td>\n",
              "      <td>0.934523</td>\n",
              "      <td>0.355902</td>\n",
              "      <td>0.956340</td>\n",
              "      <td>0.292255</td>\n",
              "      <td>0.973712</td>\n",
              "      <td>0.227783</td>\n",
              "      <td>0.978518</td>\n",
              "      <td>0.206162</td>\n",
              "      <td>0.990000</td>\n",
              "      <td>0.141068</td>\n",
              "      <td>0.994101</td>\n",
              "      <td>0.108458</td>\n",
              "      <td>0.997119</td>\n",
              "      <td>0.075854</td>\n",
              "      <td>0.999062</td>\n",
              "      <td>0.043292</td>\n",
              "      <td>0.999942</td>\n",
              "      <td>0.010806</td>\n",
              "      <td>0.999767</td>\n",
              "      <td>-0.021570</td>\n",
              "      <td>0.996307</td>\n",
              "      <td>-0.085858</td>\n",
              "      <td>0.988789</td>\n",
              "      <td>-0.149317</td>\n",
              "      <td>0.985402</td>\n",
              "      <td>-0.170244</td>\n",
              "      <td>0.972663</td>\n",
              "      <td>-0.232221</td>\n",
              "      <td>0.956167</td>\n",
              "      <td>-0.292823</td>\n",
              "      <td>0.946555</td>\n",
              "      <td>-0.322541</td>\n",
              "      <td>0.936061</td>\n",
              "      <td>-0.351838</td>\n",
              "      <td>0.924704</td>\n",
              "      <td>-0.380688</td>\n",
              "      <td>0.899482</td>\n",
              "      <td>-0.436958</td>\n",
              "      <td>0.871061</td>\n",
              "      <td>-0.491175</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1095</th>\n",
              "      <td>383.404258</td>\n",
              "      <td>0.709865</td>\n",
              "      <td>-0.727659</td>\n",
              "      <td>-0.685939</td>\n",
              "      <td>0.864203</td>\n",
              "      <td>-0.503143</td>\n",
              "      <td>0.642788</td>\n",
              "      <td>0.766044</td>\n",
              "      <td>0.714784</td>\n",
              "      <td>0.699345</td>\n",
              "      <td>-0.166038</td>\n",
              "      <td>0.986119</td>\n",
              "      <td>-0.173921</td>\n",
              "      <td>-0.984760</td>\n",
              "      <td>-0.073679</td>\n",
              "      <td>-0.997282</td>\n",
              "      <td>0.335925</td>\n",
              "      <td>-0.941889</td>\n",
              "      <td>0.460297</td>\n",
              "      <td>-0.887765</td>\n",
              "      <td>-0.750886</td>\n",
              "      <td>-0.660432</td>\n",
              "      <td>-0.682327</td>\n",
              "      <td>0.731047</td>\n",
              "      <td>-0.018924</td>\n",
              "      <td>0.999821</td>\n",
              "      <td>2.546711e-01</td>\n",
              "      <td>-0.967028</td>\n",
              "      <td>0.284984</td>\n",
              "      <td>-0.958532</td>\n",
              "      <td>0.683399</td>\n",
              "      <td>-0.730045</td>\n",
              "      <td>0.972222</td>\n",
              "      <td>-0.234062</td>\n",
              "      <td>0.990173</td>\n",
              "      <td>-0.139851</td>\n",
              "      <td>0.410054</td>\n",
              "      <td>0.912061</td>\n",
              "      <td>-0.294755</td>\n",
              "      <td>0.955573</td>\n",
              "      <td>...</td>\n",
              "      <td>0.864686</td>\n",
              "      <td>-0.502313</td>\n",
              "      <td>0.995117</td>\n",
              "      <td>-0.098700</td>\n",
              "      <td>0.892223</td>\n",
              "      <td>0.451596</td>\n",
              "      <td>0.772183</td>\n",
              "      <td>0.635401</td>\n",
              "      <td>0.130281</td>\n",
              "      <td>0.991477</td>\n",
              "      <td>0.292057</td>\n",
              "      <td>-0.956401</td>\n",
              "      <td>-0.686959</td>\n",
              "      <td>0.726697</td>\n",
              "      <td>0.949586</td>\n",
              "      <td>-0.313507</td>\n",
              "      <td>-0.978188</td>\n",
              "      <td>-0.207720</td>\n",
              "      <td>0.717430</td>\n",
              "      <td>0.696631</td>\n",
              "      <td>-0.409590</td>\n",
              "      <td>0.912270</td>\n",
              "      <td>-0.979187</td>\n",
              "      <td>-0.202959</td>\n",
              "      <td>-0.774857</td>\n",
              "      <td>-0.632136</td>\n",
              "      <td>0.596525</td>\n",
              "      <td>-0.802594</td>\n",
              "      <td>0.750672</td>\n",
              "      <td>0.660675</td>\n",
              "      <td>0.025038</td>\n",
              "      <td>-0.999687</td>\n",
              "      <td>-0.801953</td>\n",
              "      <td>0.597387</td>\n",
              "      <td>0.956364</td>\n",
              "      <td>0.292178</td>\n",
              "      <td>-0.638219</td>\n",
              "      <td>0.769855</td>\n",
              "      <td>-0.352343</td>\n",
              "      <td>-0.935871</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1096</th>\n",
              "      <td>383.754399</td>\n",
              "      <td>0.773527</td>\n",
              "      <td>-0.793211</td>\n",
              "      <td>-0.608947</td>\n",
              "      <td>0.685103</td>\n",
              "      <td>-0.728446</td>\n",
              "      <td>0.918216</td>\n",
              "      <td>0.396080</td>\n",
              "      <td>0.989855</td>\n",
              "      <td>0.142084</td>\n",
              "      <td>0.527822</td>\n",
              "      <td>0.849355</td>\n",
              "      <td>-0.821453</td>\n",
              "      <td>-0.570276</td>\n",
              "      <td>-0.812757</td>\n",
              "      <td>-0.582603</td>\n",
              "      <td>-0.560736</td>\n",
              "      <td>-0.827994</td>\n",
              "      <td>-0.494090</td>\n",
              "      <td>-0.869410</td>\n",
              "      <td>-0.955958</td>\n",
              "      <td>0.293503</td>\n",
              "      <td>0.299509</td>\n",
              "      <td>0.954093</td>\n",
              "      <td>0.872265</td>\n",
              "      <td>0.489034</td>\n",
              "      <td>-7.678804e-01</td>\n",
              "      <td>-0.640593</td>\n",
              "      <td>-0.762370</td>\n",
              "      <td>-0.647141</td>\n",
              "      <td>-0.423725</td>\n",
              "      <td>-0.905791</td>\n",
              "      <td>0.121857</td>\n",
              "      <td>-0.992548</td>\n",
              "      <td>0.165779</td>\n",
              "      <td>-0.986163</td>\n",
              "      <td>0.990571</td>\n",
              "      <td>-0.136998</td>\n",
              "      <td>0.840026</td>\n",
              "      <td>0.542546</td>\n",
              "      <td>...</td>\n",
              "      <td>-0.736581</td>\n",
              "      <td>-0.676349</td>\n",
              "      <td>-0.405398</td>\n",
              "      <td>-0.914140</td>\n",
              "      <td>0.132909</td>\n",
              "      <td>-0.991128</td>\n",
              "      <td>0.340775</td>\n",
              "      <td>-0.940145</td>\n",
              "      <td>0.883288</td>\n",
              "      <td>-0.468831</td>\n",
              "      <td>-0.997610</td>\n",
              "      <td>0.069099</td>\n",
              "      <td>0.927332</td>\n",
              "      <td>0.374241</td>\n",
              "      <td>-0.644796</td>\n",
              "      <td>-0.764355</td>\n",
              "      <td>0.179772</td>\n",
              "      <td>0.983708</td>\n",
              "      <td>0.364037</td>\n",
              "      <td>-0.931385</td>\n",
              "      <td>0.999969</td>\n",
              "      <td>0.007815</td>\n",
              "      <td>0.223876</td>\n",
              "      <td>0.974618</td>\n",
              "      <td>-0.246279</td>\n",
              "      <td>0.969199</td>\n",
              "      <td>-0.982403</td>\n",
              "      <td>-0.186772</td>\n",
              "      <td>0.251978</td>\n",
              "      <td>-0.967733</td>\n",
              "      <td>-0.900551</td>\n",
              "      <td>0.434751</td>\n",
              "      <td>0.901326</td>\n",
              "      <td>0.433141</td>\n",
              "      <td>-0.192619</td>\n",
              "      <td>-0.981274</td>\n",
              "      <td>0.982672</td>\n",
              "      <td>0.185352</td>\n",
              "      <td>-0.636278</td>\n",
              "      <td>0.771460</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1097</th>\n",
              "      <td>384.104540</td>\n",
              "      <td>0.837189</td>\n",
              "      <td>-0.850652</td>\n",
              "      <td>-0.525729</td>\n",
              "      <td>0.449250</td>\n",
              "      <td>-0.893406</td>\n",
              "      <td>0.998308</td>\n",
              "      <td>-0.058145</td>\n",
              "      <td>0.882639</td>\n",
              "      <td>-0.470051</td>\n",
              "      <td>0.957694</td>\n",
              "      <td>0.287790</td>\n",
              "      <td>-0.983429</td>\n",
              "      <td>0.181294</td>\n",
              "      <td>-0.968117</td>\n",
              "      <td>0.250499</td>\n",
              "      <td>-0.999291</td>\n",
              "      <td>-0.037651</td>\n",
              "      <td>-0.998266</td>\n",
              "      <td>-0.058856</td>\n",
              "      <td>-0.250914</td>\n",
              "      <td>0.968009</td>\n",
              "      <td>0.977717</td>\n",
              "      <td>0.209926</td>\n",
              "      <td>0.843109</td>\n",
              "      <td>-0.537743</td>\n",
              "      <td>-9.057023e-01</td>\n",
              "      <td>0.423914</td>\n",
              "      <td>-0.899519</td>\n",
              "      <td>0.436881</td>\n",
              "      <td>-0.998392</td>\n",
              "      <td>0.056690</td>\n",
              "      <td>-0.886730</td>\n",
              "      <td>-0.462288</td>\n",
              "      <td>-0.890020</td>\n",
              "      <td>-0.455921</td>\n",
              "      <td>0.147117</td>\n",
              "      <td>-0.989119</td>\n",
              "      <td>0.749781</td>\n",
              "      <td>-0.661686</td>\n",
              "      <td>...</td>\n",
              "      <td>-0.426904</td>\n",
              "      <td>0.904297</td>\n",
              "      <td>-0.741182</td>\n",
              "      <td>0.671305</td>\n",
              "      <td>-0.979678</td>\n",
              "      <td>0.200575</td>\n",
              "      <td>-0.999976</td>\n",
              "      <td>-0.006955</td>\n",
              "      <td>-0.748157</td>\n",
              "      <td>-0.663521</td>\n",
              "      <td>0.421125</td>\n",
              "      <td>0.907002</td>\n",
              "      <td>0.009860</td>\n",
              "      <td>-0.999951</td>\n",
              "      <td>-0.469008</td>\n",
              "      <td>0.883194</td>\n",
              "      <td>0.841495</td>\n",
              "      <td>-0.540265</td>\n",
              "      <td>-0.999675</td>\n",
              "      <td>0.025491</td>\n",
              "      <td>-0.395282</td>\n",
              "      <td>-0.918560</td>\n",
              "      <td>0.792464</td>\n",
              "      <td>-0.609919</td>\n",
              "      <td>0.982635</td>\n",
              "      <td>-0.185548</td>\n",
              "      <td>0.260378</td>\n",
              "      <td>0.965507</td>\n",
              "      <td>-0.977555</td>\n",
              "      <td>0.210679</td>\n",
              "      <td>0.798359</td>\n",
              "      <td>0.602182</td>\n",
              "      <td>-0.034601</td>\n",
              "      <td>-0.999401</td>\n",
              "      <td>-0.774947</td>\n",
              "      <td>0.632026</td>\n",
              "      <td>-0.313923</td>\n",
              "      <td>-0.949448</td>\n",
              "      <td>0.985820</td>\n",
              "      <td>0.167808</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1098</th>\n",
              "      <td>384.454681</td>\n",
              "      <td>0.900851</td>\n",
              "      <td>-0.899395</td>\n",
              "      <td>-0.437136</td>\n",
              "      <td>0.176182</td>\n",
              "      <td>-0.984358</td>\n",
              "      <td>0.866025</td>\n",
              "      <td>-0.500000</td>\n",
              "      <td>0.434545</td>\n",
              "      <td>-0.900650</td>\n",
              "      <td>0.908579</td>\n",
              "      <td>-0.417713</td>\n",
              "      <td>-0.564106</td>\n",
              "      <td>0.825702</td>\n",
              "      <td>-0.428180</td>\n",
              "      <td>0.903693</td>\n",
              "      <td>-0.621452</td>\n",
              "      <td>0.783452</td>\n",
              "      <td>-0.592830</td>\n",
              "      <td>0.805328</td>\n",
              "      <td>0.693012</td>\n",
              "      <td>0.720926</td>\n",
              "      <td>0.664763</td>\n",
              "      <td>-0.747054</td>\n",
              "      <td>-0.075629</td>\n",
              "      <td>-0.997136</td>\n",
              "      <td>5.097997e-14</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.037280</td>\n",
              "      <td>0.999305</td>\n",
              "      <td>-0.318469</td>\n",
              "      <td>0.947933</td>\n",
              "      <td>-0.743967</td>\n",
              "      <td>0.668217</td>\n",
              "      <td>-0.703468</td>\n",
              "      <td>0.710727</td>\n",
              "      <td>-0.907822</td>\n",
              "      <td>-0.419356</td>\n",
              "      <td>-0.433884</td>\n",
              "      <td>-0.900969</td>\n",
              "      <td>...</td>\n",
              "      <td>0.990308</td>\n",
              "      <td>0.138886</td>\n",
              "      <td>0.869664</td>\n",
              "      <td>0.493645</td>\n",
              "      <td>0.511728</td>\n",
              "      <td>0.859148</td>\n",
              "      <td>0.327665</td>\n",
              "      <td>0.944794</td>\n",
              "      <td>-0.359938</td>\n",
              "      <td>0.932976</td>\n",
              "      <td>0.696551</td>\n",
              "      <td>-0.717507</td>\n",
              "      <td>-0.934531</td>\n",
              "      <td>0.355881</td>\n",
              "      <td>0.994356</td>\n",
              "      <td>0.106094</td>\n",
              "      <td>-0.819621</td>\n",
              "      <td>-0.572906</td>\n",
              "      <td>0.411032</td>\n",
              "      <td>0.911621</td>\n",
              "      <td>-0.681808</td>\n",
              "      <td>0.731531</td>\n",
              "      <td>-0.884829</td>\n",
              "      <td>-0.465916</td>\n",
              "      <td>-0.582741</td>\n",
              "      <td>-0.812658</td>\n",
              "      <td>0.755288</td>\n",
              "      <td>-0.655393</td>\n",
              "      <td>0.628220</td>\n",
              "      <td>0.778036</td>\n",
              "      <td>0.170591</td>\n",
              "      <td>-0.985342</td>\n",
              "      <td>-0.869212</td>\n",
              "      <td>0.494440</td>\n",
              "      <td>0.922497</td>\n",
              "      <td>0.386005</td>\n",
              "      <td>-0.678502</td>\n",
              "      <td>0.734598</td>\n",
              "      <td>-0.345201</td>\n",
              "      <td>-0.938529</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1099</th>\n",
              "      <td>384.804821</td>\n",
              "      <td>0.964513</td>\n",
              "      <td>-0.938943</td>\n",
              "      <td>-0.344073</td>\n",
              "      <td>-0.111481</td>\n",
              "      <td>-0.993767</td>\n",
              "      <td>0.549509</td>\n",
              "      <td>-0.835488</td>\n",
              "      <td>-0.181372</td>\n",
              "      <td>-0.983414</td>\n",
              "      <td>0.405043</td>\n",
              "      <td>-0.914298</td>\n",
              "      <td>0.188657</td>\n",
              "      <td>0.982043</td>\n",
              "      <td>0.419274</td>\n",
              "      <td>0.907860</td>\n",
              "      <td>0.264096</td>\n",
              "      <td>0.964496</td>\n",
              "      <td>0.352789</td>\n",
              "      <td>0.935703</td>\n",
              "      <td>0.977158</td>\n",
              "      <td>-0.212512</td>\n",
              "      <td>-0.322096</td>\n",
              "      <td>-0.946707</td>\n",
              "      <td>-0.914569</td>\n",
              "      <td>-0.404430</td>\n",
              "      <td>9.057023e-01</td>\n",
              "      <td>0.423914</td>\n",
              "      <td>0.929570</td>\n",
              "      <td>0.368645</td>\n",
              "      <td>0.761645</td>\n",
              "      <td>0.647995</td>\n",
              "      <td>0.364779</td>\n",
              "      <td>0.931094</td>\n",
              "      <td>0.465034</td>\n",
              "      <td>0.885293</td>\n",
              "      <td>-0.657743</td>\n",
              "      <td>0.753242</td>\n",
              "      <td>-0.984808</td>\n",
              "      <td>0.173648</td>\n",
              "      <td>...</td>\n",
              "      <td>-0.161680</td>\n",
              "      <td>-0.986843</td>\n",
              "      <td>0.196437</td>\n",
              "      <td>-0.980516</td>\n",
              "      <td>0.642957</td>\n",
              "      <td>-0.765902</td>\n",
              "      <td>0.780946</td>\n",
              "      <td>-0.624599</td>\n",
              "      <td>0.999941</td>\n",
              "      <td>0.010887</td>\n",
              "      <td>-0.919083</td>\n",
              "      <td>-0.394063</td>\n",
              "      <td>0.672495</td>\n",
              "      <td>0.740102</td>\n",
              "      <td>-0.272103</td>\n",
              "      <td>-0.962268</td>\n",
              "      <td>-0.218277</td>\n",
              "      <td>0.975887</td>\n",
              "      <td>0.680994</td>\n",
              "      <td>-0.732289</td>\n",
              "      <td>0.944068</td>\n",
              "      <td>0.329752</td>\n",
              "      <td>-0.054474</td>\n",
              "      <td>0.998515</td>\n",
              "      <td>-0.490994</td>\n",
              "      <td>0.871163</td>\n",
              "      <td>-0.919179</td>\n",
              "      <td>-0.393839</td>\n",
              "      <td>0.411901</td>\n",
              "      <td>-0.911228</td>\n",
              "      <td>-0.954334</td>\n",
              "      <td>0.298741</td>\n",
              "      <td>0.841348</td>\n",
              "      <td>0.540494</td>\n",
              "      <td>-0.093898</td>\n",
              "      <td>-0.995582</td>\n",
              "      <td>0.971345</td>\n",
              "      <td>0.237673</td>\n",
              "      <td>-0.642139</td>\n",
              "      <td>0.766588</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>1100 rows × 162 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "               x         y  cos_21.748  ...  sin_1.059  cos_1.052  sin_1.052\n",
              "0       0.000000 -1.000000    0.000000  ...   1.000000   0.000000   1.000000\n",
              "1       0.350141 -0.936338    0.100988  ...  -0.484466   0.867293  -0.497799\n",
              "2       0.700282 -0.872676    0.200943  ...  -0.530586  -0.863474  -0.504393\n",
              "3       1.050423 -0.809014    0.298844  ...   0.998567  -0.007621   0.999971\n",
              "4       1.400563 -0.745352    0.393689  ...  -0.436958   0.871061  -0.491175\n",
              "...          ...       ...         ...  ...        ...        ...        ...\n",
              "1095  383.404258  0.709865   -0.727659  ...   0.769855  -0.352343  -0.935871\n",
              "1096  383.754399  0.773527   -0.793211  ...   0.185352  -0.636278   0.771460\n",
              "1097  384.104540  0.837189   -0.850652  ...  -0.949448   0.985820   0.167808\n",
              "1098  384.454681  0.900851   -0.899395  ...   0.734598  -0.345201  -0.938529\n",
              "1099  384.804821  0.964513   -0.938943  ...   0.237673  -0.642139   0.766588\n",
              "\n",
              "[1100 rows x 162 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 69
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8o2dl8nrU7Wz",
        "colab_type": "text"
      },
      "source": [
        "For illustration, first we use just the largest peak from the DFT.  Note below that we are using only three cycles of the data for the fit."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "swtxZk-CVADh",
        "colab_type": "code",
        "outputId": "cfdf5c1e-8e5d-475b-9720-9ea0dac35909",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 517
        }
      },
      "source": [
        "# \n",
        "# first we'll fit using only the primary frequency\n",
        "#\n",
        "dt = data.x[1] - data.x[0]\n",
        "X = data[['x', 'sin_21.748', 'cos_21.748']].iloc[0:int(3 * max(model_periods) / dt), :]\n",
        "Y = data.y[0:int(3 * max(model_periods) / dt)]\n",
        "#\n",
        "# fit a MLS model\n",
        "#\n",
        "X = sm.add_constant(X)\n",
        "model = sm.OLS(Y, X).fit()\n",
        "model.summary()\n",
        "y_pred = model.predict(X)\n",
        "plot = plt.figure(figsize = (12, 8))\n",
        "ax = plot.add_subplot(111)\n",
        "ax.plot(X.x, y_pred,\n",
        "        color = \"blue\",\n",
        "        lw = 1)\n",
        "ax.plot(X.x, Y,\n",
        "        color = \"red\",\n",
        "        lw = 1)\n",
        "plot.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/numpy/core/fromnumeric.py:2495: FutureWarning: Method .ptp is deprecated and will be removed in a future version. Use numpy.ptp instead.\n",
            "  return ptp(axis=axis, out=out, **kwargs)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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DpqYm3n33XV577TX27t2bb0jiY8PhdiLwJPB20Z8vcZjkv2PeWEX8phSoxXxIu6MbGMZG\nzJK4iJ+Mvv3/VwAYh6mC7o71NPI5tN4eLNbLh2R7U4m74N4ehSgsjcIfuvJ8SyE6Pn7/81GYZf3v\nQDfdsrutiY5jVbTO5ec15bpeicIkD/wd6KbbUG//IZr8Pv8wRMtcff6vq9Sdz25FLXEnUiiVgGnD\n82+AH7nynM42xt8H/p0rzytSOA+whO00u/ys54Hx/DfQ3mjxjRLMqs2h+JUyKHCnwsFsAupdfUYp\nHiXR4hmLgV1UY5alu115zj7Mm6hxDbOwN82V5xbJ33KggTLM77KbzAD0PDABfZSIP3ycYp+1Gdw7\nnOMBdS8MCL3ziWeYRODfYWaEbfl7tDda/OOTwE+sPHNiAPoLUN1o8YVHgF/H703BtEJx2y66Wcwk\nC88shaYkWjxk1O3/v+Tqsx4nee65C3PURC8N8bppwCmm0GMlEUj4NfCw1QhEBjcXcBYumJ9yxR1R\nfkgpj1t4Zik0ZQriCVOBE/we8EPXn3sfMM9x5ZeYEnsiXrYW+CHzML/DNnQCpj/tMUzzFRGv+iSm\nJ0BCiZ1AMNsGR6Im4P6nJFo8YS6wj2VAardK9/0GzayJ900CzlhMBGA/MAcwJSI/YzESkYGUAncQ\nK2vnBcfYTo22QfmekmjxiJnYWVjL5CRqJCHetRLYDticTSPp+WPboMoGfKyIHY8A7zqu3AUcsBHK\nbW3sYTaTLUYghaAkWjyhhIewdUAKoB24x3Hlh2hmTbzrXwH/i7uADtuhxP0vTFwiXvMEsNlxpRbT\n+NumErpABwx9TUm0WHcPZXQwGVNizo6jwHTHlTOY0l225/lE+huOqY3RzQzgQ8vRtAGzAXgfuM9q\nLCKp7gCu434RyKH4DfAJ20FIHpREi3XTWclR3rcdRpp0+VeYGQwRL3kW2Gg7iDjnkcILmLZJIl7x\n+8D/cFwpwbSbs20/Z5jDSNthSB6URIt1URaCB5LoKP0T6XeAR63EIpKZabDizTWSf8EkLSJesRDY\nk3Jlt5VYnEx1m/3ALNuhSI6URItVJVQBF22HAUALsMhxJYpZBtRMgXiFKQYJ3kkEIHkA2kasXoeI\nfdWYVNXJ1LXxhhJt6fA1JdFi1SKeYDe/sR0GAGeBqpSrPwN+z/VYRNL7FPAjwPyunrUaS0ILsDh+\n7zQ6LCXe8K/pXxvaa/q4TCnjbYchOVISLVZVMYqznLIdRlzqEnkDsMz9QETSmowpv+gt54A74/d+\ngmbWxBsmYQZ1CeVAj5VY0tsF3MtvgHtthyI5UBItFlUT5ZztIBx6SNdD6gow2vVYRJwSS9PlQK/V\nWAZyFJhhOwgJvfRbOZYCja7Hktl54E62AGssRyK5UBIt1pTzLD381nYYDg2YN1mnnwLPuB6LiNNz\nmIN75ne0yWosqZwD0NSikSLuWgO8mXJ1LHDZ9VgGcxOdvfEnJdFiTR3Q5LGZ6PRzzs4dnyJ2VAPH\nARiD9xKBBsxr2tCWDrGtBlOA0fu6gQoagCW2Q5EsKYkWS6YymhNcsR1GGulLh13AtDUWsWESJJ0d\n8EKN2/6uYtpaGKdBLY3FmgmQZoJmJKbektc0Asv4BfC07VAkS0qixZLfJ+qxrRwx14BRKVf/J2Y5\nXcSG54gtTY8EbliNZaiOkNyGRcQ96RsS1WFWTLzGDECvYTabiJ8oiRYrRjKJ654p0OXkXJaO2Q/M\ncz0WEaMWOAyY300vHYxK5hyA6iyB2DIbaE+5Ohyz+9iLzOrSh+hQrr8oiRYLJrOMPZ5NBG4Bw9J+\n5SJmN6qIm+4keWnay4mAWZaO6UQz0eK+zCcGvNnl07gG3MGbaODpL0qixYLfZxi/5pbtMLL2S2C1\n7SAkdJxL017cDx2TOgC9jAae4q7fwzTJchqHV3rjpmc6EpwEptkORbKgJFosmEH/AvhecwHS9JBq\nIl0BPJHiSixNez0RgP5J/i/RYSlx12JMCxMnL5aFTGYqdID59Km0GosMnZJocdkYKjlNl+0wBtFM\npqJ2fUCZq7FImI3ALPQaSzC/m17WRfIAVANPcVM5ZFjjLMXLDYoMMwD9OfBxu4HIkCmJFpc9xWJ+\nlmaewFv6yPTi2Arc72osEmaPAFvi98owv5tetov+1W57McmNSLF9BHg/7Ve8vB86xnQv3AMstB2K\nDJGSaHFZHWW0ez4RyOwd4DHbQUho3Adsi9/z8n7omNQB6HvAA1ZikbB5GPh1ytUpwEnXY8leoq1X\n5uPt4i1KosVFfpgLSDhBuiMeNzH1EUTcUE5sEdoviQD0T/Z/jZlRFym2EaSrXTMfaHU9luwlBqC/\nBh6yGosMjZJocdFypvLb242LvW8fMDftVzqAe1yNRcJoLua30JjvuOdtx0kegN5CA08pvmr80uZ7\nIGYA+ju0euMPSqLFRU8wjy3stx1G3n6GKaMkUkwfw1S38J/U1kR7MMMAkWLJ/Hrx0xpoJ1CdVKtD\nvE1JtLhoNH5pWDyw08Ak20FI4FWBR7t6Zu8t4EnbQUigzQIOpVy9Czjoeiy5ayO2AmrSafE2JdHi\nksn4Z0dnwgEybdzoQrU8pXicXdfuwvwu+olzX/QZNPCU4qnAVFpOVQscdjGSwtkEPGU7CBmEkmhx\nyce5m4102A4jSx9iWsOk+hXwuKuxSJg8gfkdM2Zifhf9pB3TJibhBubgl0ihPQD81nYQBWMGoAeB\nu+0GIoNSEi0uuYcZfMhR22EUTDNqIiHFswzTCNi/jgHTHVfeAx60EosE3UPAb1KuluD9uurptAFz\nAFOZR829vExJtLgg81KbH/SR7mBKNO1VkcIoITYflfgvv3sfVRyQ4hhGuk6FC/FHabv+OoEaACJA\nvdVYZGBKosUFqyjhfd8mAruBRWm/0kb/BWuR/C3CtF0wFmJ+B/3IOQBVxQEphmmYtDPVJMwxcP96\nF3jUdhAyACXR4oKHWMRvfJsInAUmpv3K2+jghxTeY5jOmMZE/FujowW413ElfQsjkdw9Dmy2HUTB\nmQHoVUxVK/EqJdHiglFM4IZvE4HMTgBTbQchgTMRU83C/85hCvUlqNSdFNoczKqgUxnQ43oshbOL\nWAvw88CdVmORzJRES5GNBS76fvdwN6YBc/qvaIlaCqWc5I9+570gSK3ZIVIMdUCj7SDycB6YAJgV\nzyesxiKZKYmWInuEct7xfSLQiHlTTrUVuM/VWCTIVgHb4veWAE3WYimM1GFmFH30SGHMhQw9cMeS\nXGndz1I3RYl36J1Mimw5S2nw9YwAwBVM+4tU72HKK4kUwkOY3ynD2XLFnxroPwDdmXJFJDfB3A8d\ncwuoUCUoTytIEr169Wr27dtHe3s7L7/8csrXX3jhBU6fPk1jYyONjY28+OKL8a89//zztLW10dbW\nxvPPP1+IcMRTyhhNlCu2wyia68BI20FIYIwCrsXvBeGj8ypwh+PKO5jDkyL5moo5m+I0AvPO7HeJ\nFdCj9K+6Lt6QfptnFkpLS/nOd77Dk08+ybFjx4hEImzcuJG9e/c6HvejH/2IP/7jP3ZcGz9+PF/+\n8pdZsWIF0WiUnTt3snHjRi5cuJBvWOIJNcCxQCQCYFKbkaR7c44d/DjvckQSLKMhabgZlEQA+g8G\nLmEW20XyUUqmVirLMOsdfpeozfEOptTdD2yGI2nkPRO9cuVKOjo6OHToEN3d3WzYsIE1a9YM6XtX\nr17N22+/TVdXFxcuXODtt9/m6aefzjck8YwnGMmmwCQCDZg351S/Qgc/JH8PAb+O3/P7wahk1zBz\n7AndmAYZIrnK3NVzBHDT1ViKrZ1YD0PxlryT6Orqao4eTTRzPnbsGNXV1SmP+8QnPkFzczM//vGP\nqampyep7xa/uoY5DPm9enHALGJ72Kzr4IYWwEtOhzBhOcBKB1H3R2zF/XpFcPQJssRxD8V2l/wBU\nvMSVg4U//elPqa2tZcmSJbz99tu8/vrrWf+MdevWEYlEiEQiVFVVDf4NYplpVpy+GWvQ6OCHFEI5\n0Bu/F6TfqFv0n3f+LfCglVgkKMYBF9NeDdKG0MQKaAdwt9VYJFXeSXRnZyfTpyc2vNfU1NDZ6WzB\nef78eW7dMqnU3/3d37F8+fIhf2/M+vXrqa+vp76+nrNng9e2I3hM6+IgJQIAXUBl2q8cR41XJHeT\ngVPxe+nTA39zvhekHjcUGbrM6zRLgWZXYymuRIlIHcj1oryT6EgkwuzZs6mtraWiooK1a9eyceNG\nx2OmTJkS/+9nn302fuhw06ZNPPXUU1RWVlJZWclTTz3Fpk2b8g1JPOFRKtkcqBkBMG/OS9J+5V3M\nwQ+RXDxKcqvvINSH7q8LGO+4cpNMG6REBnY/pkZ/qjKS13OCwQxAPwRm2g1EUuRdnaO3t5eXXnqJ\nTZs2UVZWxt///d/T2trKq6++yo4dO/jpT3/Kn/zJn/Dss8/S09PD+fPn+exnPwtAV1cXX/3qV4lE\nzD7Ar3zlK3R1deUbknjCRJZwLqnibTD0Yd6kU+0F/sDVWCRIFgAb4vcy1x3wr2bM0ckt8StbMcnQ\nlrSPF8nsfuDbtoNwjeo/eVvUb7dIJGI9Bt0GupVE4SvRR63HUZzbYxm/9jXrsenm19tXHfeD+tpx\n/rlGRuE/Wo9JNz/evpr2+mSILrAeW+FvpRB9GKLw6SgssB5P2G4D5ZzqWChFYPZDB9UJMu1+Poap\njS2SjUkk74eeApy0FktxOfdFq1GR5CLzcfUFQKursbijj9je23fRtkFvURItRfAwU3k3TR+pYNgL\nzEv7lXcxZZdEsvEQ8Jv4vXmY37EgOg5Mc1yJtTASGap6kktBJgvaQfZk5s92Eh1g9xYl0VIEk5nH\nWfbZDqOI0r9Z7ydTei2S2b0EeeUm2T76v0J+BzxgJRbxqwcwvzepgpxEdwKmi0bUbiDioCRaCszU\nhxaRoSol+TUT5EQA+r87bAPusxOI+NQY4HLK1VnAAddjcc9+YC4w0FqouE9JtBTYAmCP7SCKLnPZ\n+yPADFdjET+bAJyL37sLOGgtFnc4BwmZ+4CKpMpcwK4WOOxiJDaYAeh7mC1g4gVKoqXAHuZu3gn0\njACYip3pU+Ut6OCHDN1HIakQ5EzMMCzI2oHZjivXgRFWYhG/WYbp4Zcq6Cs4EPszHgWmD/xAcY2S\naCmwaczgDB/aDsOa1BRBJLOlJLdVCcNGqNQUYDuwykos4jfOQWdMWDYRtgFzbAchDkqipcDC8FaW\nkH72I1x/B5KPUmLL02FJBED7oiVX4zG9L53CsYkwuYhq5rVQcZeSaCmgeZTQGrhOa5m0YCpip0ot\n5CWSahxwMX5vIcGscZtOlOQB6FXgDmuxiF84D+AmmwScdjUWexL7oj9qNxABlERLQT3CQjaHYkYA\n4CxQlfYrvwUedDUW8aMHMb8rxkTgjLVY3NWCKeyX0Is5NCaSySJgV9qvhGE/dIwZgO4jVqtD7FIS\nLQVUzUROc9Z2GNbtJtMctUjCcmCn7SCsOEf/AWgTZn+4SCYPkW4/dOZ6HcHUAiwGwjV08C4l0SJ5\n6AHKU646F6tF0ivH/AaZRKDHaizucy7M/w6t3sjAJgOnUq7WAY2ux2LPOUxhzIHWQsU9SqKlQKZT\nzmG6bYfhsibMm3iqS8BYV2MRPxkB3IjfqyO5Rkc49AAV8XtKCCQ3YzHvtmGS2BetgadtSqKlQB5k\nKZtDlwhcxvTPSvU+8BFXYxE/WQFE4vfS92ALtkYyDUBF+qsFDqX9Slgq2iTrBipoApbYDiX0lERL\ngcxnDIe5YjsMC9K/iUcwiZJIOvdjSruF1xVgtONKorGxiNMDmIkJJ+d6TniYAWgfOoxrn5JoKZDw\n7gG+DoxMuap2xjKQxNzzCMzvkKhsl2QyFzPIclpGuPZDx1wlNgC9gspD2qUkWgpgHCM5F9pEoBHz\nZp7qFjDM1VjED5xtVcKaCIBJBkbF7x3BND4X6S99K6KwzkQnfACstB1EqCmJlgK4jzo202A7DEtu\nkmnOeQemjJlIsnnAvvi94ZjfoTDKPAAVicl8dDCM+6FjzAB0O0qi7VISLQWwguHs45btMCxK/2b+\nPmYvn0gyZ5OVMEtdq1G3T+nvPmBrytVxhK8qR7IGYBnXSV7LEfcpiZYCGAGhK27ndAGoTLl6EfNW\nL5JsOnAUML8dF6zG4jXvYw5disSswKzqOS0lfGUhk3UTG4CqL4FNSqIlT+VUcin0iUAzmYoN9aE3\nOHFK/D4sIVMj4/A4D4yP3zXoVK0AACAASURBVFO3T+kv/c7nsHUqzGwvMN92EKGlJFryVMdifkuz\n7TAsy1xsaB9mD6wI9O+6pkTADCIWx+/1kq4HqIRV5ldImPdDx5gB6HuoJ4E9SqIlTw9Qxh76bIfh\nAZn3ResNTmIeQPuhnVIHoJmP6krYpF+rmQycdj0W79kFLOE4MMN2KKGlJFryNIFwH+9IOAFMTbl6\nBNNtSwTgXqAFMInASauxeJWq2kjMA8DvUq4uBPa4Hov39KEkzjb9/UtepnCZE7aD8Ih9aGeaDKac\n2PL0fMxuRulfk2MbpiKDyCQ05zwU5zATWuI2JdGSh1nMY1dSxVtJr4vko1MSVs7ehDpumrCP5Ibf\nF9DrRQai/dAJncA0tqCqNnYoiZY83E+JFtWGYCuaWRPTVmRn/J6SaCf9fYhTNXAs5eos4JDrsXjX\nfmAeu4E626GEkpJoycMcSm7XuxWjA7g75WoD2uMpZiC1HTCJwAGrsXjdQXSWIOzuw2ztcZoFHHY7\nFM/rBSpsBxFKSqIlZ3fTRYftIDzmQ2BmylVVGxAw7XhMRfWZmCOnktAO3BO/p6o2sghTN1yGphuV\nh3SfkmjJ0UhmcJoPbYfhG71kqiQtYVGS5r8k5iiml6PRhuqrh136GtHaD52qDZjNb9GWDvcpiZYc\nrcC8dKW/9E1YW1AntjCrgdtDzhKUCGSSeN2olXG4VWBmVp1U2i69Y0ANDejsjfuUREtOSlhJVAW6\n0kqfLm9Fp6fD7H5i+zsXoEQgE2fqfAW4w1osYtMSSNMHV01WMivhIjDRdhihoyRacrKIG+zmmu0w\nPOks6d7KjmNOm0s4JebQJgJnrMbiXS2YdjTGB8Aqa7GITekPFUpmZgCq3sFuUxItOaniKmdtByHi\nG6Vw+wNOmxQyO0tyy4gIZtuYhE9qk5UyoMdKLP6wC1hMG2q64i4l0ZKDWtSweGA9pDsnfRott4XR\nMOAWkOmolCRzbucYbS8Q8ZSlQJPtIDzsHHAnTUC97VBCRUm0ZK2cVfRoP/SAGjFv+k7aFx1OdZjf\nCPM70Wg1Fu/rIbnirebtwyd9q+9xwCXXY/GXEtoxTZ3ELUqiJWtLGUeTqtwO6DIwJuVqM+bAjIRL\nYn/nGMzvhmTWQPIA9EOSC99JGKxC+6Fz0003FaoV7Sol0ZK1MdxSIjAEqXNo3airVBhNwCy2al51\nKJybOLYDK63FIjYspX9ljhHADSux+EsDUMcJ22GEipJoydIIorf3d8rArgMjU66q/m1YKRHIxR5U\nXz1sUmtE12ESRBnYVeAODpPc+1OKS0m0ZGUkS7nBAdth+EID6Xan7Qfmuh6L2DIVbs8MLUOJwFBd\nB0YB6vQZNumP3o5EA9ChKmEvKg3pHiXRkpU6ZtDIftth+MJNTF0GJy1Ph8tKTL1jGI75nZDBOQeg\nSqTDQz0J83WNY4xilu0wQqMgSfTq1avZt28f7e3tvPzyyylf/9M//VP27NlDc3Mzv/rVr5gxY0b8\naz09PTQ2NtLY2Mibb75ZiHCkiIYziptcsB2Gb6Ru3DiAltrCZDGmgqtafWfjFskD0D2Y5EqCr57Y\noDNmLHDRSiz+ZAag2hftlryPcZaWlvKd73yHJ598kmPHjhGJRNi4cSN79yZKoDU2NrJixQquX7/O\nH/3RH/HXf/3XrF27FoDr169TV1eXbxginnQBqLz9/xJGZn+nynNlLzHo2A48TWwwIkE2A1ORJWEp\n8DsrsfjTLaCCGyTXp5fiyXsmeuXKlXR0dHDo0CG6u7vZsGEDa9ascTxmy5YtXL9+HYBt27ZRU1OT\n79OKBeOYyAW1+s5KE+mK2t3AHDOT4DOp4BL61xuQwVwAxgNwFJW5C4vUtTs1KMrFAdJ1KpDCyzuJ\nrq6u5ujRo/H7x44do7q6OuPjX3zxRX7xi1/E748YMYJIJMLWrVtTku9k69atIxKJEIlEqKqqyjds\nycES7qFZhwqz0ke6F1n6ViwSNHfD7deLEoHsqap62KSvX6NaRtnrYh/j9epxhatVuT/zmc+wYsUK\nHn744fi1mTNncvz4cWbNmsU777xDS0sLBw8eTPne9evXs379egAikYhrMUtCGXfRx49th+E7qR8C\nEeAPUEOBoKvH/FtrP3QunAPQWPXoK7bCkaJLbew9GThlJRZ/28UFHqKbLbYDCYG8Z6I7OzuZPj2x\n1FZTU0NnZ2fK4x5//HG+9KUv8eyzz3LrVmKfzvHjxwE4dOgQW7Zs0f5oT6tAe6yydwJT6CzhLKDV\nlOCbB+xnMumaGMtQJAYfO4Dl9gIRFyQGnTELUK2OXPQBJZrDd0XeSXQkEmH27NnU1tZSUVHB2rVr\n2bhxo+MxS5cu5bvf/S7PPvssZ86ciV+vrKxk2DBzBnvChAk88MADtLa25huSFMEU4CR32A7Dl/Zi\n0ikJm1KgjwWA3tVycwKYBpgkut5qLFJsE4Ezgz5KhuoSpluqFFPeSXRvby8vvfQSmzZtYu/evbzx\nxhu0trby6quv8swzzwDwjW98g9GjR/PjH//YUcpu/vz57Nixg6amJt59911ee+01R1UP8Y75TGcv\n522HESDn0Gx0kGkXdCHsIzYAvYQpdiZhornU3B3nANO413YYgVeQPdG/+MUvHIcFAb785S/H//vJ\nJ59M+31bt25l8eLFhQhBim4e/et3ytClfhh8gJlZ+0XKVyQIEvPP2g8tMpix9C8COQs4ZCWWYNjP\nXh7jf+O47UACTh0LZYimgSpz5OwAplZDQiPpmoJLUJj9nUoE8pcYhHQS29whQbMc2Om4otdOvtL3\nzJXCUhItg7oLOKC9VXk5Asx0XFGt6GCrBQ5Ti/m3l9wlenx+AKyyGosUS2oSrRWc/EW1IabolETL\noGZSwYdK+PKW+qGgjwmRwXyI6WMHLaA9ngGVup1D8tfBJWbffvVIcSiJliGYDTTYDsL3ovTfG526\nyUOCYDixphEaJhVSDy63NhBLFqKKNoVwlFamM9t2GIGmJFoGVAJEdaiwIPYAixxXtqPl6SAyTb6V\nCBROYgCavgeo+FlqaTs1WSmU/UCN7SACTe9GMqCFwG7uAZW3y9sZzMdFwn5grpVYpJjMocJJqMlK\nobQQG4C2AvOtxiKFltpkRSs4hRKlj1LtjC4iJdEyoInAWUbbDiOgouglGETqUVhoZ4kNQLV6EzzO\ndt+qsF5YLYznXm2DKhp9gssg7gAu2A4iMLrpv6vzFqadugRJGWYHrxTaEUzlEwmOxBkCMCl1s7VY\nguccbVTp7E3RKImWjMqBHuZiWu5KITQBdY4rzZg9tBIMY4DL/ebWpBBSB6ASROOAi7aDCJTtaAtU\n8SiJloxMIvAgqsxROJcxaVbCB8BKK7FIMZh6t2Mx/9ZSOI3EBqBXgVFWY5FCmYEpYpig/dCFdoZu\nJmi9s0iUREtGZk5tAnDFdigBdhKYajsIKZjUphFSGFeIDUB3Yv6exf+chwpHkLyxQwqlgan9VkCl\nUJREyyB0rrfQrgEjbQchRTKOEVxUIlBUEUzyJf63EFP801iGWXGQwrrKVUarQEBRKImWtEYC1xmP\nqnUWXiPmwyLhAlBpJRYptCh1aANUsZgB6EXMzlnxP2ctDs1EF8sOYI7tIAJJSbSkVQc0sor+9Tsl\nfzcx59ETIsAKK7FIIVUBZxmB+TeWwmsgNgDVCpn/mVZe4oYGrrFAJwmKQEm0pDUcuMkyVGzIDTtR\nEh0EqU0jpLBuERuAngImWY1F8jUHaIvfG4uqchTPVRq4W/uii0BJtAxAc2rFcoHkBemrmHrc4m9L\nGUujEgFXaF+0/zkHnSoLWVy3KO+3AiqFoCRaUqhOZ/E1oerQwTOSJdzU2k2RdQGVNGHSLvGv2UBH\n/F456lRYXJ3ABNtBBI6SaEmxBGhiOqY7mBRDH/0bRxwFaqzEIoWjRKD4THuixMYO8SvtiXZXhC4W\nMd52GAGjJFpSlAJ9rET7O92k5Wl/S20aIcXRh6npIH5WAfTE701CdaCKbxfNPMhi22EEjJJoSWHO\nvTvrd0rhnQCmxO+1APdai0XyVc9k3lci4KpDQK3tICQnizDveYY+bdzQTR/DNQAtMCXR4jAF00NP\nC9PFtxeYH7/XQ/8NHuInC5nPPlpthxESJ4BpvI9Wb/zKeahQBQvFr5REi8N8THKnvWrucH54RFOu\niF+UYzYaiBv2AnNpBxbYDkVyUgMcsx1ECB3gODOYZjuMAFESLWk463dK8ThT5g7gHjuBSB5KgD4N\nf1yn3dFBUIvZmCNu+IB9fIS5tsMIECXRkoaaRrilA7grfm8HWp72oznMokGJgMvMoKUXfYz5zUjg\nevzeXSiJds9+YJ4G/AWkdx+Juws4CJiZ6HarsYTFEWBm/N5+0ByBD9VTy04O2w4jZMy6TQSYZzsU\nyUod0Gg7iJDqQ2lfYelvU+JmEqsMrfqdbkrMCvShPdF+NJsonbaDCJ0PgRk0otUbv9FKp129tFOq\njYMFoiRa+ikjuX6nFJ/zOGEv2ucpMjRRTpC8IUr8YAJwDlBpOztaOcpCptsOIyCURAuQPPestzW3\n7cb8rRutqOKAn1SwkBMqbWdRiVbNfEtNVmxQY69CUhItQHLqXI854CZuOQNMjN/TG5y/LGISuzlt\nO4yQMi2KOoFhtkORIRkHXIjf0+Y1Gw4Ds1RQtUCURAtgkrgzQPLOaHFP4s3sMOrC5if1RNlnO4jQ\nOgtU0QJqZuwTK4hN0pShdl427UY9cgtBSbSIBzj7FWp+wC/KmEovZ22HEWpR9qPVG79YBjQAsBRo\nshpLmN3gLMOpsh1GACiJlqSjhMOBG1ZjCatGzIeKcRPzbyFet5STNNsOIuR66KKcSbbDkCEZDVwB\nYCxw0WosYdYELNVpggJQEi3UEZsRWAJKCay4DIyJ32tGy9N+MJKxXOSS7TBCrgmo44TtMCRLWm+z\nyZy96QEqbIfic0qihTGYJE6HCr1Chwv9oQ7T8kNsMgPQi5hZTvGuycRqcYxAa552nQYm0Yh5F5Pc\nKYmWJIk3OXHfDUxDXDgJTLEaiwxuBHXcoM12GAJAG2a/rXhXoslKHbGd0WJPCVfQ0DNfSqJDbgRw\n3XYQApgPFaUB/lHHTRq1mcMTrtHGSJbYDkMGlNguqJloL7gEjNW+6DwpiQ65ZZhDbckHPsQO53FC\nzRF43Qh6lAh4RCNXWcY122HIgIYBtwDth/aGHcByrgOjbIfiY0qiQ244JnlLLj0k9iRmBTQv7W2V\naNDpHWYA2mM7DBmCsaD1G0/YCSzXJ02elETLbYki+GLPRUxPL/NvscJqLJLZWJZykQO2wxCHS6DK\ntx5Vi2kkZUp5NlqMRGLMdo5bqN9nPpREh9g4kut0VpLcjlXsaCZWL/oC5t9EvGgpU2jWoUJP6aKD\nSu2L9qjEoUJ1KvQe7YvOXUGS6NWrV7Nv3z7a29t5+eWXU74+bNgwNmzYQHt7O9u2bWPmzJnxr73y\nyiu0t7ezb98+nnrqqUKEI0OkqtDe04v5kBFvK2MEvVy1HYYkaaadJWq64lELgL22g5AUZ4CJdAHj\nbYfiU3kn0aWlpXznO9/hYx/7GAsWLODTn/408+fPdzzmxRdfpKuri9mzZ/Otb32Lr3/96wDMnz+f\ntWvXsnDhQp5++mn+9m//ltJSTY67JTEjcCdw3moskpCYFTiP+bcR79Hcjdf0cYMyLUx7lPm0mYSp\nUCxeYXoS7ELtvXKVd8a6cuVKOjo6OHToEN3d3WzYsIE1a9Y4HrNmzRpef/11AH7yk5/w+OOPx69v\n2LCBW7ducfjwYTo6Oli5cmW+IUnWtB/aS04RqxKtfdFeNImJnFJdDpEhKgX6AFgItFqNRZxMv88+\ntAKaq7yT6Orqao4ePRq/f+zYMaqrqzM+pre3l4sXLzJhwoQhfa8Ux2RMSw9DlTm8pBWz+KkKHd60\ngHtoVadCTzrOVaYyzXYY4jAP2AeY0nZaw/GSG8QKq+rfJTe+2Tuxbt06IpEIkUiEqiqdwM7XfJJ3\nqI0C1Vj1oGuogqf3lHAX0GI7DEljH23M5y7bYYhD4lChEjXvOgEafuYg7yS6s7OT6dOnx+/X1NTQ\n2dmZ8TFlZWWMGzeOc+fODel7Y9avX099fT319fWcPXs237BDT8XuRXJVQaxphHhNK6acmnjH3cCB\npCJ34i1HgJnsw6wZSHbyTqIjkQizZ8+mtraWiooK1q5dy8aNGx2P2bhxIy+88AIAn/zkJ3nnnXfi\n19euXcuwYcOora1l9uzZfPDBB/mGJEOQSKKnYsag4iUH4PZ82nHMv5F4QS1wSOfYPawH7e70pruA\nQ7aDkDTM4ULJTd5JdG9vLy+99BKbNm1i7969vPHGG7S2tvLqq6/yzDPPAPC9732PCRMm0N7ezp/9\n2Z/xyiuvANDa2hp//C9/+Us+//nP09fXl29IMohZkNQmIrHUJt5xhNh8mt7gvGQWUzlMl+0wZAAd\n3MndtoOQ2yqAbttByID2YI58Sq6ifrtFIhHrMfj59qjj/l9EYZj1mHRLvT0Gt/9t/sJ6LLqZ26M8\nEoWF1uPQbaDbZ6KPUeOBOHSD5VFYE4X+nzu6eev2lSgQnQ7Re6zH4r3bQDmnbw4WSrEMR/s7vSkK\nlKgpq8fMQE0jvO4DYK7tIAQwq2gfsACVtvO2PqCUo5h3OBk6JdEhk1piKJr+gWLdbrTI5iULgD1M\nIVbzVryqgyjVOjztCebMzRRM/Xvxqv1o4JkbJdEhsxCzA8qYhY56eNcZuN3E+CCobJd1kynhNCNt\nhyGDitLCVBbZDkPENxJnb8wKqAyVkuiQmYhJzgwdKvQHHS70Bm3l8IuzDKdKVTosM/0HyjA1U8TL\nOoB7AFMBXwPQoVMSHWrOliviPT1AOa2YfyuxpQzoZT4adPpFCyXMsh1EyJlOuEuBZtuhyJCdxUy2\nydAoiQ4RkwgMfEW8pRFYShS9VO1aCjRRh7Y/+cUH9DCPctthhNoKYAfjgIu2Q5Eh6MaUJJRs6JM5\nROowSZlRig5Ied9lYCxgBjt6udoyBrik/dA+0kkj91JnO4xQGw+qqe4ju4B7AZNOawA6NPpUDpEx\nmKTMmIs5kSv+oKasNpVQjkpB+stlRjLadhAhNxy4YTsIGaIIsBIwk20agA6NkujQ0qFCv7gOjOAD\ndLjQjhHADe5BOzv95holDLcdREiZWWizK1r84TgwDYAroAHoECmJDgmTCCS7h+Tm3+JdDcAyDoGa\nGVthtkE9hAadftPIdeZoE44VZj/0SDQT7Vcqczc0SqJDIv2MgBqt+MFNzCBI7DBL0jXASduhSFYi\nNPAQy2yHEUqag/ana5jShMn/JQNREh0SwzHJmFGBKnf6kU5P26AZGb86z00maUOHFaMYyzUu2Q5D\nsmTWPWP/pX3Rg1MSHUqLMCXVxS8uAuPYSez0tLhjLLGqHJcHe6h4koZAdpSwhORqUOIPEcxWHHOM\nepjVWPxBSXQIpNbpNPvVxD+agCVsR4cL3WXqQ69AS9N+1cUFxlBpO4xQmQYcpwJ1IfCfLuDO+D0N\nQQenJDoEltC/rsB04KiVWCQ3vUAZ54idnhZ3mHZE9WjQ6Vc7aGIVS2yHESqq/BQUXZg6K5KZkugQ\nUF/CYChJ+l9xUyXqueZXDfSxnDLbYYTKYibRzGnbYUiOzhObjW4GFluNxfuURIeOig751UlgCqfR\nmWl3TAIlAr53Fb1e3FbBAnrYYzsMydEOYvui+1CSOBj9/QTcZOCU44rZ5Sn+0wrMZxs6M+2OhcAe\nJgDnbIcieSnhBDDVdhghUooKqPpXokIHaO1zMEqiA24BJvlKWIH2q/lZG7FZAnGD9nf633H2MpX5\ntsMIhbtREy+/c1aIPoFO4gxESXToTALO2A5CclTCJZJPT0uxmX6F4mcRYKXtIEKinlp+x2HbYUjB\n7AXm2g7Cw5REi/jIQeAuumyHEXi1cDsRGAlctxiJ5G8Xqq/ulnnM4gAHbYcheepE889DoyQ6wGZB\nvzezSlAC5muHgVqOYap/S7HMAg7ZDkIKxHT67MBsNpBi0m7oYHCu3mhfdGZKogOsFjjiuKL9nUEQ\nZT/aF+2GmaCF6cD4EPMvKsVSjhmwiP+1kLx60wHcYy0Wb1MSHSrLUee1IGinRBU6isrMpa0CttsN\nRArkAJqHLrZFLOB99toOQwrArN7EfAjMsBaLtymJDrDURbVRmLqp4md7uMFC7dMtmkRFmwWglCAg\nzPJ0H1qaLp5VTKaJk7bDkKLQJp30lEQH1EL6l7YDfXwEw2lgEldshxFYk4k1WSnFtBsQ/9sPzGUP\nsMh2KIFVjWqqB0k7yZs4oiiDSEdJdECldlubQf8d0uJfUS5g0j0pjnKgx3YQUjBmDvoMMNF2KAFV\nRq+GnIESwZyjMnajAWg6SqJDYyXa3xkcveynLKmrlBRGGdALmI+L3VZjkULrxfwLS+GNYSkH1Qs3\nUMzqTcxZNABNR0l0ACUSgWTpN3iIPzVxkDrNRBfcEridCGjQGTytwAJ6MOsMUkgrGMcuLtoOQwoo\nilLEwelvKICWkq7HWjnpUmvxp0vcYqyOehTcOOASADWYhgMSHOZwYSOotk3BrbhdelOCxbl6040G\noP0piQ6gscBlx5X0c9MiIuFxBJjJZWCM7VACZjgjuMkN22FIwe3BrGIbGoCmUhIdCgvQ/s7guc4Z\nRqh6Z8EMh9tpwGj6D0MlKLR6UwzLOJFm9VP8z3m48AoagPanJDpgRkCa+YCVwAeuxyLF1cAhlqmP\nVMEsI7YNagWww2osUiw3geFcB0baDiUwahjJcVWuDySzeiOZKYkOmDrS9SSciek5JEFyk/2MoMZ2\nGIGRGIAqiQ6uJmApDaDaNgWziij7bAchReNcvbmGBqDJlEQHzAjMXIuEgfqvFUfqqQIJCnO40MxH\nSyGM4R4uc9h2GFI0NzGZhaEBqJOS6MAbhRk7ShBdoIJxqn2bt7HEqnJIsKndSqHVcZomtVkJMLN6\nE3MLDUCTKYkOkHGQpk7ncmCn67GIO5o5zVLush2G7yXqQ09Dpe3C4QJQaTsI3yujnB719gw05+FC\ncVISHSBLgOaUq/WYF4EEUS8RypK6SkluElXUdQg3+C4CY2kCFtsOxfcWEOWI7SCkqFJXb7rQADRG\nSXSApK8GXYmZc5FgOgFMsB1EgNwLtNgOQopqJ7CcPtQ4Il8TWcwZNVkJnWbMpJ0oiRbxvZOMUQPw\nPEwCTsfvVYAWpwNuJ6YCi+RrERXs4ZTtMKTozOpNTB/oJM5tSqIDYjKkeStzpgcSTK0MYwF32A7D\ntxZg+nKZt0MdkAq+RM/CE8BUq7H4WwlRta8JBQ08M8kriR4/fjxvvfUWbW1tvPXWW1RWpu6SWbJk\nCe+//z67d++mubmZT33qU/Gvff/73+fgwYM0NjbS2NjIkiVaIMjVAqA15epKYLvrsYjbdlDCHNtB\n+FaiSOA8YK+9QMR1ezH/6pKLO0jX2kuCaAf9k+jjaAAKeSbRr7zyCps3b2bOnDls3ryZV155JeUx\n165d4/nnn2fRokU8/fTTfPvb32bcuHHxr3/xi1+krq6Ouro6mptTj8VJPpaS7qihBM1OJdEFsQod\nKgyLU5iVOlVaz9VMFnJYTbxC4gow2nFlHxqAQp5J9Jo1a3j99dcBeP3113nuuedSHtPe3k5HRwcA\nJ06c4PTp00ycqDqd7hiGqeoowXaVA0xjlu0wfKgWktpEzAIOWYpE3GWaroCS6FzdzQwOstt2GGKR\nXjt5JtGTJ0/m5MmTAJw8eZLJkwc+3lRfX8+wYcM4cOBA/Npf/dVf0dzczDe/+U2GDRuW8XvXrVtH\nJBIhEolQVVWVT9iBk/6jv4T+7ToluA4zXkl0DpQ2h1WigUQHcLfVWPzqDtTZM0wOgj5lUgyaRL/9\n9tu0tLSk3J599tmUx0ajmZO2KVOm8A//8A987nOfiz/uz//8z5k3bx719fXceeedvPzyyxm/f/36\n9dTX11NfX8/Zs2eH8mcLjVpI03T1HqDd5UjEniPElqclFyOB67aDENfcwqzUmVfOTKux+FNU85Ah\nsw24z3FFA9AhlMl88sknM37t1KlTTJkyhZMnTzJlyhROn05fCWLMmDH87Gc/40tf+hLbtycOusVm\nsW/dusX3v/99vvCFL2Qbv2SkphHhsp0o8ynhtNYfcrIMaLAdhLiqD1Vkyc18qtibpiuBBNl+YK3j\nyofAo8CBdA8Piby2c2zcuJEXXngBgBdeeIE333wz5TEVFRX8y7/8Cz/4wQ/453/+Z8fXpkyZEv/v\n5557jt27tb+qcOagmegwaWUP9SywHYaPOCvaaNAZPnuAhYDZ+KZ51aGbylxO3i4MKWERJV3KGPbX\nTV5J9GuvvcaTTz5JW1sbTzzxBK+99hoAy5cvZ/369QB86lOf4qGHHuKzn/1sSim7H/7wh+zatYuW\nlhaqqqr42te+lucfJ3wWQoa3Mu2JDpc+TjNWGzqy4KytPh7TzFbCYyux5endwCKrsfjNLGCX7SDE\ndTeAEY4rYR+A5tX19Pz58zzxxBMp13fu3Mm6desAkyj/8Ic/TPv9jz/+eD5PL5hdsKlJtKpyhNNN\nSqgAum0HIuIDx4DpAJzBNHyXwZUBversGVI7MVvf3o9facEMQFssRWSbOhYG0hJUHzqMGuhlttqx\nDoFJBGImYtIoERnMEkpo0ppXSG3H1NNPOAuEuV6akmgfKyPTXMB9mJO0Ei7baeRh6myH4QPOYeYq\n1NkzrC5gtvKY99K8lmZDYhwzuJimHpSEQeL1kizM2zmURPtY5n6EmlkLp/NcYipjbIfhA+OAi/F7\ndUCjtVjEpm3Emq40ggagQ1DCAsx+chEjzANQJdE+Nha4ZDsI8ZwwzwoMlfPIrfaRh1cDsBwwbUM0\nAB3YcOAm00DtvkPsKFDtuBLmAaiS6MCZBhy3HYRYc4wbTOx3flqSmUQgphwdkAqz1GoDklkd0MBU\n22GIValNVy4Do63EmbGTCwAAIABJREFUYp+SaJ8agXn7T3U/WmoLs6008CDLbIfhYctI3ryxGJXq\nCrtEka7rmN6Vkt5IxnJdrb5Dbg8qCJmgJNqnMu/iXISpeirhtIcbLGa47TA8zDkA/QgadIbdXmAe\nYDZ3aACaWQnz0aH1sIt1+nQK6wBUSbRPZZ6JdhbvkrDpA8q0L3rInC1XJIy2YVbwzDYfDUDTGwNc\nZgE6hCvmleLcBtVIOAegSqIDRU1WBOAWFylnnO0wPGgMOowr/R3GdOCTgZjVzxnoM0ZgB7DCceUm\nJgMJGyXRPpS5Koc59iFh10ATy1hqOwwPWgo0xe9NBU5Yi0W86QJoAJpGGaX09KtrI2GVergwrJRE\n+5AzEUh2P9qvJrCNXu5X58I0ykne7HQ/ye1rJczOAXcCpva+BqCpSrgLdcIV4xJmOs/pIlDpeix2\nKYn2ocy7nu8Ezrsai3jReWCC5owGdS/QYjsI8YT3MYdMzXurBqBOpn3XcnQIVxISVW1imjDdYMNE\nSbRIQJ3GHJsTYyLm7yTBOS8tYRbWY1FDY2o+zaf/K0jCbD8w13HFHGsPFyXRPjOJTG9jNZhOQiIA\nh9hDLQtth+EhC4HW+L1hJLdckbDrxnSuNE4CU6zF4k1RpQvi8DvggZSrYVsB1avCZxZiSp2nUpMV\nSfZb4EHbQXhKCclv8JkrrUtYJeoLtAILrMbiLSVMQJ1wxekIUJty9SSEqqelkujAcM6zSdi1A3NC\nNyswdDqEK/3tBJbbDsJzZgJHWIEO4cpQ7AXm2w7CRUqiA6MUsyNJJKaEQ6gCLphE4LDjygRMRQaR\nmK3Emq5A/yNT4XU3cIBVqBOupDoDVNkOwiol0T5SCxxK+5XRwFU3QxFfOM9hxiuJBu4i02tHJOYC\nMD5+rwPzexN2ZjWrHE3SSKpEVZuwUhLtI7PoP5sWcx/aDy2p9AaX3hzMyXKR/hIboNLv+AyjEWiS\nRtJrIl1V9Q7MCkYYKIkOhJXAB7aDEM9pAJZpX3SKBzEHL0X6a8MMsgTM3ta91KNJGkmvh+SqNjEf\nYrbQhYGS6EAYAdywHYR4TjcwjD0Q6lJ3C+h/5Dbzmo6EnbNsV2o7iXCZCpzko2iSRjK7gclBwklJ\ntE9kLm1XjhkNiqRzk9MMC3XTlcnAKdtBiE84j+LuJtwDULOKpUkaGch2YFXK1T7CMQBVEu0TmZus\nLEX1biUzle1ymgKcsB2EeFrio/8M5r03jMqAPsowK1oimWwl3dmb3ZhOl0GnJNr3HkD1OyUz8wbX\nQ/jasYL5Mzsbe38UeM9KLOIXpwhv6pywBGiiDjMQF8nkKjAq5epZYKLrsbhPSbQPpCYCyVTvVgZy\nAajMcIY6+JYAzY4ri8i0MUrE+A3wUPxeD2bTXNhUAhd5GLNPXGQg3aQ7YBgGSqJ9YCmmkEx6Ydh1\nJPmJcokSxtkOw4JxwEXHFTUlksG0APfG7zUSzgGokfoKEkm1g3TbBsMwAFUS7QNjgUtpvzIbU5JJ\nZCBhr88Rk/mVJJIQJfmj8TLmNydMhhM7SqgCmTIUv8OUDnUKwwBUSbSvPYj2d8rgfg08HLpCRMOB\nm44r96PzAzI05zBb5cJpGdDIArT1SYbmImYDkFMYBqBKoj1u4OJCqncrQ3ESmEoDUGc7FBfVYdrN\nJNRjlh1FBvMeyTNr14GR1mJx30jgOg+jSRoZul7CmFKG70/sM3UMVMBO+6FlqKLcIHyJgHMAmjo3\nLZKe8yhu2AagxjRUDlKGLv3x9aAPQJVEe1zmmehq4JirsYif7cU08Q0rNYyQbPSSfCTqJuHZCjUG\nnRyQXLyHKSHqFPQBqJJo33oE2GI5BvGPXwOPcJHg71EDkwhcdly5H1MzW2SoLkIIa9rUAU06tC5Z\nOwtUpVwN+gBUSbSHDVxLYB6w37VYxO86gWmhqRed2sdTSbRk67ck74sOS0pdDvTwGPCu7VDEd6KE\nbZupkmgPG7g+tEj2nIvUwVVO/wZF5qiUyNA5a9+GZQBq1KDtgpK99OVUTcuvYFIS7WGZOxXqDU5y\nsR+YazsIC5RASy56SO7C1ot5Tw6yicAZ20GIj70LPJpytQlY7Hos7lAS7UuPoKU2yZ6pF30KmGQ7\nlCJKTQQ+gloXS26uAKNtB+GahcBu1YeWnJ0m3adLH8EdgCqJ9qhJmF/H9OaiQx+SvaPA9MD3L1xI\n/xTgfmCblVjE75z7ok8CU6zFUnylQJRH0aF1yV36NZug7pRWEu1RqYmASOEE9Q0NzJ/N2axY9aEl\nVx8Aq+L3WoEF1mJxyxTMcEEkFzuAFSlXTxDMAaiSaN+ZjplRFMlFBzDbdhAuugO4ajsI8a1ukvdF\nB9lM4AhgFt9FcmW2DfYX1E4FSqJ95xG01Ca5ewd4jEOYpvFBk0gEYh5A+6ElP2dIV/82aO4CDrAE\n2GU7FPG1y5hK/eGQVxI9fvx43nrrLdra2njrrbeorExfxKSnp4fGxkYaGxt5880349dra2vZtm0b\n7e3tbNiwgYqKcIz4B1MLHM741TloP7TkzuyLDmoSfRdw0HFlFbDdSiwSFJuBx+L3DmJ+z4LGbPF6\nBE3SSP5ukK7FShC3EeaVRL/yyits3ryZOXPmsHnzZl555ZW0j7t+/Tp1dXXU1dWxZs2a+PWvf/3r\nfOtb32L27Nl0dXXx4osv5hNOYMwCDtkOQgKsl/AsQg0HbtkOQnxtN3Bv/N5hzERHMFUB52wHIb73\nO8wqoNMB4G7XYymuvD5J16xZw+uvvw7A66+/znPPPZfV9z/22P/f3t1HV1Xf+R5/hzwA8hQgkoMJ\nJlFxiCgQqKBFq1AeSp0K4+UqdpybTr14u5azemtXWxhc3vGuWZ2Fd7qqXb1dzloMFaZXRYtSsB2d\nRAjX9lbwYB5IgECAiDyYBOXBJxAJv/vHjzwccvJwcvY5v71PPq+1fsucffY5+8tvuff57r1/+/ub\ny8aNG/v9+YGnAHjfdRASeJXAdNdBJETkA4VdJ/8W6Z9UvIbWoRjYxyBsbWyReL2NLS0a6Qg2i0kl\ncSXRubm5NDXZp3ibmprIzc2Nut6QIUMIh8O8/fbb7Veix44dy5kzZ2httdOJHDt2jLy8vHjCGQDm\nA+Wug5DA2w7MSblSd8VAfcSSu1E9dfHGIToPgEq1yY1DwAfMBN51HYqkhC+wdwG7MlGXBlevMwCX\nl5cTCnUtTPL44493WWZM9O4pKCjgxIkTFBUVsW3bNmprazl79mxMgS5fvpxHHnkEgJyc1H3I4yZs\nGaXoCulptLRI35wFRtFMapVSDGGfAO9wK/Cki1Ak5WwFFgJrgI7JjescRuSljvHQv3Qah6SStsm+\nz3R5p2sZ0uDqNYmeP39+t+81NzcTCoVoamoiFArR0hJ9epATJ04A0NjYyPbt2ykpKeGVV14hOzub\n9PR0Wltbyc/P5/jx491ua82aNaxZYw9g4XC4t7ADK5fukuhBqPSQeOccMBST0tNha58Rr7xP5xvR\nLcDNzmLxVjpte4nKQYqXtmNPzH4XsbQOu+/UJj2exIhrOMeWLVsoLS0FoLS0NKLyRpvs7GyysrIA\nO4Rj9uzZ7N1r08SKigqWLl3a4+elzXTsWFYRL/wRuKObuaWCJx37uGSHQnTXRrx1idQaxGFNAaoZ\nSbQrhiL9F/3Zm5PA1UmPJXHiSqJXr17N/PnzOXDgAPPmzWP16tUAzJgxo/2qcXFxMbt27aK6upqK\nigpWr17Nvn32puuKFSv44Q9/SENDA2PHjmXt2rVx/nOCrWsi0NkcNL5TvLMDuJ0aYJrrUDwwFaiJ\nWLIAKHMSi6Sqauz/aVYrfbiVGwD2hvt87JAVEa9cortLNKkylAPiPAacOnWKefPmdVn+7rvvsnz5\ncgDefvttpkyZEvXzjY2NzJo1K+p7A9FU7GE6ulHYsawiXrgAZF0eHR18XfeOa1ElG/FWBfC3tB2l\nq7AnoLscRuSdqcCrroOQlFMP/AWwP2Jp2wloKtSCGSjFYgNhFPBx1Hc0Vk0S4UMgJ6WuClg939MR\n6Z/TwJj2Vx8DI53F4o2OKuqp9KiX+Md/AN/osrQKKEl6LImhJDoQ7sLORy/iJTsT2xdEm1sqOAZj\nCyp1uBV4x0kskupSa0rjEqCSG7myOKSIN1qAcV2WptJepCTaJ4ZgJ8qMbhZKCsR7tcCUwE+9YhOB\nzu5GUxdLYpQDHUMYzxHsE9ChwDkWoucHJHE+w95Nj5Qq9z2URPtECfYWR3SpMnpI/Og8aYFPBCJP\nQIej4U+SGFV0PuUM+gmoNQ5bM0EkEbYBc7sstUVWg09JtE90fyU6D+i+frZIfN4FZrgOwkOjUKku\nSZzIuQqDPBRqBPApmVw5GErEW+9gh9hFijwdDS4l0b6nUl2SSOXA/MA+JDUCO76uw1xUClISq60u\nR7DZu593AH9yHYqktOil7rqfGDxYlET7wEi6q8oBMBE4mLRYZKD5FBge2LRgGlcOg5qBJiWSxCrH\nXtywglom0g4S/BpKoiXx9gLFXZamwrhoJdE+MI3u6kNnoVttknjNtJIbyIkjMuhczG4Q9rCcCodm\n8a/I+zbVBPME1O4lmeh5G0m8/wAWdlka1BPQzpRE+0D3VW3vQlUGJPFeBxa5DsIDM4GdroOQAeEU\nbTWjW+luXjb/uhr4kBuAOtehyIDwIdFK3aXCjLlKon3tDuD/uQ5CUl4DMJFmoh3m/OtqrqwpMA9N\nXSzJ8QbRrqwFxc1AHUuwJ9AiyXAaGB2xJIgnoFdSEu3YOGw58uhU2k6S5Uv2kMFk12HEYDKwJ2KJ\nrXorknh7odPe0gSEnMUSOzs/4WjsDXWRZNgCfMt1EJ5TEu1Y10Sg93dEvPcn4M5Oxbv8L3Ki4iLg\nsLNYZCBqhctPEuwFbnIaS2wMY4APXIchA8p+YFKXpR8QrBPQKymJ9q1F6FabJM9bwNdcBxGHvwT+\n4DoIGVAqgDmug4jZtcD7zAdecx2KDDhdZy/cR7S6HcGhJNq3RmPHEIkkwwVgMI1AoeNI+qIAOBKx\nJIS9qS6SLH8E7mx/FZS7ODcAh7iFK/cgkcR7HfhGl6VB2XeiURLtUCHwXtR3xmKfZhVJpt00cgvX\nuQ6jD66j8+CNUWhspyRfK/bn3/6MHoJA7Dt2jsXPXQchA1IlqTFPYQcl0Q4VAY1R3/km8O9JjUXE\nDof4S9dB9MM30NAnceNP2CpK9oJIocNI+srwFWzdXhEXLmDnwOgQnBPQrpRE+1IxdhC+SDJ9AowI\n4FQlU4Fa10HIgLQNO9V8MEwC6rkDzeop7mzlyn3mCME4AY1GSbTvDMMOvhdxYS97mejrSgPF2IdR\nLJW1E5e+xFbosKM6Df4e33kNmXzAYDSrp7jzZ9ru3qQCJdGO3IQti9TVPcDvkxqLSIfXaOY+X5cc\ninyE8JuoKoe49Q52tkxblNTftdZnoaGC4taly/+NTD/9fgLaHSXRjuQCzVHfmYadDFPEhbPASNdB\nxOAr6Na0uFUGLADsxFl+nfVzENBKMRB2HYoMeF2HQdXh9xPQ6JRE+8pw4FPXQciAd4BW8n05HWs6\nHdcx7P7yibNYRKzz2GFF/jaVq6hhuOswRIDtXJlEnwSudhFKnJREO5COLY7U1b3YqTFFXNpCNX/F\nNNdhRDEVqG5/dS+w2VksIh12AbcC9tjuxxPQ0XyVM6rKIb5wCVtmMXLiFQ3nkD6ZSncDNm7G3tQQ\ncek0ZxnPKNdhRBFZEfpm7ChUEdd+T1t5yCqgxGks3SmguydxRJLvVeC+iCUXsY/pBomSaAeiTw0x\nEvg46bGIRNcA5LsOogfZwBnXQYhcduHyf7P4GP89VZDFWL7QUEHxlb1wRR2oKvDlHdCeKIn2jcXo\n1rT4x285z1yGuA6jk8HAF+2v/grY5CwWka46rkb7zXTuoJK3XYchcoXjdL5YY2cqCBYl0UkWmQh0\nFln9VsStT6nkOkp8NEqtBHulwpqIvVou4hdh2krdnQdfnYBeRQ7neN91GCJXeAm4P2KJf35x+kZJ\ndJJNJ1pBrhzgVNJjEenJeSoYwldch9GuY1qVa+hcKVrEP2yRu0rssd4frkP7i/hT15oc5whCrZsO\nSqKTbAj2KkWkbwMvJD0WkZ69RRpTXAcRxV+j/UX86SXgAV9diR7Of+ITKlyHIdKNSmBGxCt/Ppgb\nnZLoJIt+q+Ia4ERyAxHpleFjvmQk2a4DYQRtFaEHAWOAD12GI9KN40Ce6yA6yaKEU1TxuetARLqx\nBfuMi/UFdthrUCiJTqLo9Tdux84lL+I/VWxnGne5DoNptNWHno+dIU7Er2qAqZwFH5SJvI8MtnPR\ndRgi3foCO8ncmPYlQRoXrSQ6iabS+cGoNvcA/570WET6opX3SffBPFIZcDkRmIOd7UrErzYBS6nG\nD+W6SkjjkOsgRHqxHihtf+WPE9C+URKdRBlcOVPhCOwwel0nEP9KoxG4xXUYQAhoBozrQER6cB74\njFbGOp65cBI5VGngkwTAB8A42ub69McJaN8oiXbqAeyDKCL+1cIfGcc3nW3/atpGQP818H+cxSHS\nd+uA7ziO4QFu5lVqHUch0jebaBsb3UpwktOgxBl447DFjyLdABxMeiwisdjDBSZzhCtLESXLZKAO\nLm//pJMYRGLTBIylmQxynWx/KJBGGhd030YC4h3a6qwHiZLoJLkJO8llh6mgawQSAAZI43Xgu062\nnwYYFqEHCiVYXmIPDzDZybYfAl4M1ANaInSqsN6MHcDnd0qik8QmAp0tA152EotI7M4Cw3FX/XYe\nsM3RtkX6owY3Izszgeu5lv2ao1ACZiPwnwF70bHYaSx9oyTaiSJsXegvXQci0ifvAYX8GvibpG73\nWuAItwJvJXW7It54i+Q/lPtfgH/jejRYUILmInAIuNl1IH2mJDoJCrFJSIe/BX7tIBKR/jkMXEcj\nMJFkVvG8HjjMA9iC/CJB83sO8y2Kkra9DOBGrhw8KBIc62h7KDcIw5GURCdBEdDY/moc8NnlJhI0\nrwHfSuL2/gLYhcraSTAZ3qOeIqYmaXsP0VbBJggJiEhXF4GdwGwOAdc5jqY3SqKT7r8C/+o6CJGY\n2TT2j9gJT5L1E303enZAgu1VYDaJ32cysI+w11IM7Evw1kQSx46NPoK9k+9nSqKTaiT2oY+PXAci\nErN92J9o2AB8O+Hbm8RE9nEGuJTwbYkkkqGCNB5I8Fa+DbwAwHjs9BUiwWSwdz3vdR1Ir+JKokeP\nHk1ZWRkHDhygrKyM7OzsLuvcfffdVFVVtbdz586xePFiAJ577jkOHz7c/t7Uqcm65ZU8kaXtlgNr\nncUiEo8m2koO7QSmAFcldHvjmUcTryZ0GyLJsId9TGY8MDhBWxiNrWVQDWjwk6SCrcAcLpHu66FJ\ncSXRK1euZOvWrdx4441s3bqVlStXdlln+/btlJSUUFJSwty5c/n8888pK+uo9/rjH/+4/f2ampp4\nwvGlXGy9Q3ttYAhwzGU4Ih7538CjCfz+Jdji+6pgI8HXAoxjA/DfErSFHwH/DNgfdd27kdTwS/by\nqKNa630TVxK9ePFi1q9fD8D69etZsmRJj+svXbqU119/nXPnzsWz2YD6AfCM6yBE4nIRSAfg6OW/\nrknAVoaTziwu8W4CvlvElQ+AEcAEj793DrAbOAXYabx2e7wFETcO08JHjEvag7mxiyuJzs3Npamp\nCYCmpiZyc3ue4HTZsmW8+OKLEct++tOfUlNTw89//nOysrK6/ezy5csJh8OEw2FycnLiCTtp0rFz\nwNuHo3ahihwSdJHTR/wS+LsEbOUxpvCzyzemRVJDK5DOPwM/wT4E6IUh2HGjL7UvGQ2c9ujbRdx7\nHpgFjHEdSLdMT628vNzU1tZ2affee685ffp0xLqnTp3q9ntCoZBpaWkxGRkZEcsAk5WVZdatW2ee\neOKJHmNpa+FwuE/ruW4zwIwi3cAzzmNRU/OqzY14fZ+Bb3n4/VMNPGLm+ODfqabmZRsJ5itgYKKB\nv/foe//ewISIZdp31FKtfY3hJp3/5Wz7PeWcvZ4Oz58/v9v3mpubCYVCNDU1EQqFaGlp6Xbd+++/\nn02bNnHx4sX2ZW1XsS9cuMBzzz3Hj370o97CCZRRwFm+B/yL61BEEuRV4B+APdgpWeIxGFsC8r/H\nG5SI73yMrc8EDdjptxYAZd1/oFf3Y2d3O9q+JAu4EMc3ivhRFZ9SwvPs4lrw2WT2cQ3n2LJlC6Wl\npQCUlpayefPmbtd98MEHuwzlCIVC7X8vWbKEurq6eMLxHcP12MSg3nUoIp45z5U1Bv4J+CH21nJ/\npQE/BVYzmEt8Ecc3ifjfi9ixzPn9/PwC7MCNyBrq04HKuOIS8Z9PgJHU4LcEuk2/L3GPGTPGvPnm\nm+bAgQOmvLzcjB492gBmxowZZs2aNe3rFRQUmGPHjpm0tLSIz2/dutXs3r3b1NbWmt/85jdm2LBh\ncV9a90sbTK75Kn9nIM1pHGpqXrchYG7vsjzPwD/F8b2rDEwxgLkNzFAf/DvV1LxuX8XuP/b1YAM/\nM23/3/e9zTSwIup7c/sRk5paEJrL/7d7yTndd47H/yAftCHmdn5ohjDUB7GoqXnfoh/Q7jJ2jGas\nJ44PG1jQ/lpjOtVStQ3BJtIdy9KMPYFc0MfvWGjgf3b7vvYdtVRtt9P5BDS5raecUzMWJsQ/MoR/\n4zwDsZSfDFz/F/g98DS2lFdvMoDHgM+Jb2yoSDCc58pBTwY7HCof+DHQXeWpfOBn2IFU/xB1jeHA\np96EKeI7O8GXw/y8qrMjgD0APg6sAz50G4pIArU9JPVxl3dqgX/Ejm/+FzrP1xlpCvYhwl8B+9uX\njsCOfxMZWH6NTZS/g/0dqcQmzPnYmUE/A56AHi7MlABvJzhKEVf8OoGQkmjPLADmAv+DEXyiREBS\nWhUwG3gr6rsfYR80/A7wELZq7VZgHDAZW+/zBHYCoshD4zSUCEhqO0tb5aYrHcNebQZ7kvkpcJy+\nXn/LxE6GJCLJoyS6z9KAJy//Hcb+1N8I3IZNDqoBO+35NODPSY9PJHla6e3gcRH418t/j8ZOOPQB\nsIZo16/bZKBEQFJbNXAHdvBT9zTnoEgQKInuM4Mdi5YO3Ar8DfY29DqunB8qg7aZCkXE7h+bXAch\n4gt25kJv5QAnPf5OEemdkuiYtQI7LjeRgasFew+m+ymWYnM1epJApD9uprcr2yKSCKrO4bGr0RUB\nGRj2ADd5+H2TgdSabkkkumYg18PvG4S9VyoiyaUk2mOTscmFSKozeHsASUOJgAwMe7C/FSISbEqi\nPaYrAiIikiwT8OtkyCKpT0m0iPTbe0ChB99zLUoERPrjBuCg6yBEBigl0R4qwCYVIgPFYaDIg++5\nHjjkwfeIBEUj3uw7aR58h4j0j5JoD12HTSpEBhL9iIvEzqskWkTcURItIiISQJOAfa6DEBnAlESL\nSFz2El+pu0lAvUexiAwk47HzgIqIG0qiPVKMrgjIwNQEhOL4vBIBGajiLXWnoVQibimJ9kgIm0yI\niIj0RTyTrgwCLnkYi4jETkm0iMStFUjvx+cGXf6siMRmClDjOgiRAU5JtAfS0RUBGdiqgWn9+NxU\nYLfHsYgESX9PQEcDpz2ORURioyTaA1OxSYTIQHUWGNWPz2UDZzyORSRI+nsCqvHQIu4pifbAKGwS\nISIiEov+nIBmARcSEIuIxEZJtIh44gtgcAzrZ13+jIjEZjpQ6ToIEVESHa/BKBEQAfujPj2G9acD\nVQmKRSRIzgNDYlh/KPB5gmIRkb5TEh0nJQIi1jnsj3tfDb38GZGBLtYTUI2HFvEHJdFxGoISAZE2\nxnUAIgEUy5Xo4cCnCYxFRPpOSbSIeOYTYEQf1lMiINI/Jejup4hfKImOwwhs0iAiVjX2R743SgRE\nIn0MjOzDehnAlwmORUT6Rkl0HEpQfWiRzi5if+R7k3F5XRGxquhfvWgRcUdJdBzSUSIgIiLxa6X3\nE9Ac4KMkxCIifaMkWkQ81QJc3cP7OcCHSYpFJJXcDNS6DkJE2imJ7qergZOugxDxoT3YH/vu3AzU\nJSkWkSBpBsb18H4aqoAj4idKovtpMjZZEJFIhp7r2CoREIluD/a3RUSCQUl0PykREBERr3V3AjoB\nOJrMQESkV0qiRcRz7wEFUZZfC7yf3FBEUsJE4KDrIEQkgpLofigAjrgOQsTHDgM3RFl+PXAoybGI\nBEkjUBRlue58iviPkuh+uB6bJIiIiHipuyRaRPxHSbSIJEQ9MMl1ECIBlHXF60nAfheBiEiPlET3\ng26rifTuOJDf6fUkbGItIj3bCczp9Poa4ISjWESke0qiY1QM7HMdhEhAnAcGX/57PPCBw1hEguI0\n9iS0p3rrIuKekugYjQeaXAchEhA7gNtdByESQAeAkdjfnFbHsYhIdEqiRSRhLgIZ2APNJcexiATN\nn4EFwG7XgYhIVHEl0UuXLqWuro7W1lZmzJjR7XoLFy6kvr6ehoYGVqxY0b68sLCQHTt20NDQwIYN\nG8jMzIwnnIRLR1cERGJ1GLgPqHEdiEgArccO7xAR/4kria6rq+O+++7jrbfe6n4Dgwbxq1/9ikWL\nFnHTTTfx4IMPUlxcDMBTTz3F008/zcSJEzl9+jQPP/xwPOEk3FSg2nUQIgFzGDvJyhnXgYiIiHgo\nriS6vr6eAwcO9LjOzJkzOXjwII2NjXz55Zds2LCBxYsXAzB37lw2btwIwPr161myZEk84SRcNnDW\ndRAiAfRz1wGIiIh4LOFjovPy8jh69Gj762PHjpGXl8fYsWM5c+YMra2tEctFRERERPwuo7cVysvL\nCYVCXZY//vjjbNmyJSFBRbN8+XIeeeQRAHJycpK23c52ONmqiIiIiPhNr0n0/Pnz49rA8ePHmTBh\nQvvr/Px8jh8/zkcffUR2djbp6em0tra2L+/OmjVrWLNmDQDhcDiumPrrcydbFRERERG/SfhwjnA4\nzMSJEyksLCSJfRFVAAAG10lEQVQzM5Nly5a1X8GuqKhg6dKlAJSWlrJ58+ZEhyMiIiIi4gnT37Zk\nyRJz9OhRc/78edPU1GTeeOMNA5jx48ebP/zhD+3rLVq0yOzfv98cPHjQrFq1qn15UVGR2blzp2lo\naDAvv/yyycrK6tN2w+Fwv2NWU1NTU1NTU1NT60vrKedMu/xHoITDYW699VbXYYiIiIhICusp59SM\nhSIiIiIiMVISLSIiIiISIyXRIiIiIiIxUhItIiIiIhIjJdEiIiIiIjFSEi0iIiIiEiMl0SIiIiIi\nMVISLSIiIiISIyXRIiIiIiIxUhItIiIiIhIjJdEiIiIiIjFSEi0iIiIiEiMl0SIiIiIiMVISLSIi\nIiISIyXRIiIiIiIxSgOM6yBi1dLSwpEjR5K+3ZycHD788MOkb3egU7+7oX53Q/3uhvrdDfW7G+r3\nvisoKGDcuHHdvm/U+tbC4bDzGAZiU7+r3wdSU7+r3wdSU7+r34PcNJxDRERERCRGSqJFRERERGKU\nDjzpOoggqaysdB3CgKR+d0P97ob63Q31uxvqdzfU7/EL5IOFIiIiIiIuaTiHiIiIiEiMlET30cKF\nC6mvr6ehoYEVK1a4DidlrV27lubmZmpra9uXjR49mrKyMg4cOEBZWRnZ2dkOI0xN+fn5bNu2jT17\n9lBXV8f3v/99QH2faIMHD2bnzp1UV1dTV1fHk08+CUBhYSE7duygoaGBDRs2kJmZ6TbQFDRo0CAq\nKyt57bXXAPV5sjQ2NrJ7926qqqoIh8OAjjPJMGrUKH7729+yb98+9u7dy2233aZ+94jzEiF+b4MG\nDTIHDx40RUVFJjMz01RXV5vi4mLncaViu/POO01JSYmpra1tX/bUU0+ZFStWGMCsWLHCrF692nmc\nqdZCoZApKSkxgBk+fLjZv3+/KS4uVt8noQ0bNswAJiMjw+zYscPMmjXLvPTSS+aBBx4wgHn22WfN\n9773Pedxplp77LHHzPPPP29ee+01A6jPk9QaGxvN2LFjI5bpOJP4tm7dOvPwww8bwGRmZppRo0ap\n371pzgPwfbvtttvMG2+80f565cqVZuXKlc7jStVWUFAQkUTX19ebUChkwCZ79fX1zmNM9fa73/3O\nzJs3T32fxDZ06FDz7rvvmpkzZ5qTJ0+a9PR0A12PP2rxt7y8PPPmm2+aOXPmtCfR6vPktGhJtI4z\niW0jR440hw8f7rJc/R5/03COPsjLy+Po0aPtr48dO0ZeXp7DiAaW3NxcmpqaAGhqaiI3N9dxRKmt\noKCAkpISdu7cqb5PgkGDBlFVVUVLSwvl5eUcOnSIM2fO0NraCuh4kwjPPPMMP/nJT7h06RIAY8eO\nVZ8niTGGsrIydu3axfLlywEd4xOtqKiIkydP8txzz1FZWcmaNWu46qqr1O8eUBItgWOMcR1Cyho2\nbBivvPIKP/jBD/jkk0+6vK++996lS5coKSkhPz+fmTNnMmnSJNchpbR77rmHlpYWlfdy5I477mDG\njBksWrSIRx99lDvvvLPLOjrOeCsjI4Pp06fz7LPPMn36dD777DNWrlzZZT31e+yURPfB8ePHmTBh\nQvvr/Px8jh8/7jCigaW5uZlQKARAKBSipaXFcUSpKSMjg1deeYXnn3+eTZs2Aer7ZDp79iwVFRXc\nfvvtZGdnk56eDuh447XZs2dz77330tjYyIYNG5g7dy6/+MUv1OdJcuLECQBOnjzJpk2bmDlzpo4z\nCXbs2DGOHTvGO++8A8DGjRuZPn26+t0DSqL7IBwOM3HiRAoLC8nMzGTZsmVs2bLFdVgDxpYtWygt\nLQWgtLSUzZs3O44oNa1du5Z9+/bx9NNPty9T3ydWTk4Oo0aNAmDIkCHMnz+fffv2UVFRwdKlSwH1\nu9dWrVrFhAkTKCoqYtmyZWzbto2HHnpIfZ4EV111FcOHD2//e8GCBdTV1ek4k2DNzc0cPXqUG2+8\nEYCvf/3r7N27V/3uEecDs4PQFi1aZPbv328OHjxoVq1a5TyeVG0vvPCCOXHihLlw4YI5evSo+e53\nv2vGjBlj3nzzTXPgwAFTXl5uRo8e7TzOVGuzZ882xhhTU1NjqqqqTFVVlVm0aJH6PsHtlltuMZWV\nlaampsbU1taaJ554wgCmqKjI7Ny50zQ0NJiXX37ZZGVlOY81Fdtdd93V/mCh+jzxraioyFRXV5vq\n6mpTV1fX/luq40zi29SpU004HDY1NTVm06ZNJjs7W/3uQdOMhSIiIiIiMdJwDhERERGRGCmJFhER\nERGJkZJoEREREZEYKYkWEREREYmRkmgRERERkRgpiRYRERERiZGSaBERERGRGCmJFhERERGJ0f8H\nGeyDsP41VSMAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RfQ5ACfwVB2B",
        "colab_type": "text"
      },
      "source": [
        "Note that we are getting most of the form, but as a sine wave.  Now we repeat the fit using all the frequencies we found to see the improvement in the fit."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kCV03twYU3sm",
        "colab_type": "code",
        "outputId": "4bb1e3fa-df78-4875-cee2-f2ddb29cf854",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 517
        }
      },
      "source": [
        "#\n",
        "# repeat with all the frequencies\n",
        "#\n",
        "X = data.drop(('y'), axis = 1).iloc[0:int(2 * max(model_periods) / dt), :]\n",
        "Y = data.y[0:int(2 * max(model_periods) / dt)]\n",
        "#\n",
        "# fit a MLS model\n",
        "#\n",
        "X = sm.add_constant(X)\n",
        "model = sm.OLS(Y, X).fit()\n",
        "model.summary()\n",
        "y_pred = model.predict(X)\n",
        "plot = plt.figure(figsize = (12, 8))\n",
        "ax = plot.add_subplot(111)\n",
        "ax.plot(X.x, y_pred,\n",
        "        color = \"blue\",\n",
        "        lw = 1)\n",
        "ax.plot(X.x, Y,\n",
        "        color = \"red\",\n",
        "        lw = 1)\n",
        "plot.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/numpy/core/fromnumeric.py:2495: FutureWarning: Method .ptp is deprecated and will be removed in a future version. Use numpy.ptp instead.\n",
            "  return ptp(axis=axis, out=out, **kwargs)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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AIpysItGhEi3Sa/mAs0OMu99aOvoQmE0d0PUGlCIi7QbSulh6MHDSNEtPHAOG8xjwl9ZR\nJIaoRIv02gLgTQYBp6yj9EoJOygi1zqGiLhaOnC07dY8YLVZlp7aDMzgFM7+/SLRoRIt0mv9gLMd\nrkd7xSvA3QRxJqSIiHRlBk4pdeR1uuV+p3A2HRWJPJVokV5pX6Ueh7OywDuagf2sJ5MC6ygi4hHe\neaVzrkavAm60jiIxQiVapFf+BPgDkwFv7mj+NJ/wIIOsY4iIK83EWUHhmIFXlk5D67zobaDLBBIl\nKtEivTIEaGAUcMA6Sp80APUc4xqGW0cREdfpvFj6T/DCfOiOPqGJgR65ci7epxIt0mNjgb2kAuet\no4Tk55Txt+Tpf38R6aDzYum/BGrwws4cHW0ACqgCfd4mUaB3UZEeWwSsoBAoudJdXa0F+H84/zwi\nIo4CYANxwGPADuC3toH6wFk4vQXNi5ZoUIkW6bEM4CCJOEv0vG0Hm7mKGWRbBxERl4gjlSBPAM8B\na43T9F0FlUzSa5tEgUq0SI+MAI4wDucDTj84ypOkcyd6GRCRXNLZwf8C/g9QYR0nJHU0kclZ6xgS\nA/TuKdIjzlSOa4Dd1lHCppnTvMFA/sI6iIgYy+Qu6vgBcNg6Slhc4BzJmhctEaYSLdIj15DAbh9M\n4+islN0UUA/kWEcRESMppHCeFvDR1dsSdlPMZOsY4nMq0SJXNAj4hCKg1DpKmAWBeF4C/tw6iogY\nKWYWJRcPkfKLJj4kkYnWMcTnVKJFruhO4DVSgXPWUSKgghYmsQ9Ito4iIgYSuZYmNlrHCLMm9pCu\n5YUSUSrRIlc0nVGUe/RwlSurBbJYB9xiHUVEomwcSdQw0DpGROwigfEMsI4hPqYSLXJZKcB5puDV\nY7575gLbSabIOoaIRNkEZrLLd1ehW62jhetUdCRi9HdL5LLmEsdq3x8iW0Izxey3jiEiUZQANDMF\n/632aLWJUm7T5QGJGJVokcu6ntmUELCOEWGNQBI1QK51FBGJkmISKGEU+PYyQRNn6U8/6xjiWyrR\nIt1KAGAwQU4aJ4mGvWxiLNdbxxCRKEllJmd5zzpGhNVziEGMtI4hvqQSLdKtG0jjHU5Yx4iSKhrI\nocU6hohEQQZwkELgj9ZRIuw9tjKXqdYxxJdUokW6dRuzeJdN1jGiqIVTxDPUOoaIRNhU4tnKVeD7\nX5w3AreCdumQCFCJFulWEnE0WYeIqlK2UsRs6xgiEnEzgDXWIaIgCPwjm/i2Xtkk7FSiRbo0m2ms\npdw6RpSdoYL+ZFnHEJEIygcCLATfz4duVc8J/pM07rEOIj6jEi3SpSVcxdscsY5h4DCpjLy4qFJE\n/CeNeBroh/+ncnRUTgOnGMJc6yDiIyrRIpe4nv6UcCam3mDafUQV07TVnYgvpQEnmAmsNU4SfQHe\nZDaZwDXWUcQnVKJFLnEvhbzk2+MHruw9gky3DiEiETAbCPCnwLvWUUzE8VvgG6DdoyUMVKJFOrkD\neI14YuuDzs4usJFxWoQj4kNx5ABbIcYWTbfaSjNT+R7wkHUU8QGVaJE2ccDt5PAmVdZRjJ2gjqFc\nbR1DRMLoOuAjvgj81jqKmYNABodAx69IGKhEi7S5D1jOGOBj6yjmXuMENzHEOoaIhM1IruMQ5cTy\n52wAZ4F+nAD6W0cRj1OJFgEgCcgjiQ00WkdxhUMEyGU2o6yDiEgY9AfOMAf4vXESe6VAEa/iHMIi\n0ncq0SIAPAg8SRHE8ILCT/s+cXwWGGQdRERCVEQhpeywjuEKzUAiFUCBdRTxOJVoEQYAo4EKUoAL\nxmnco4mtPMdUvoYzX1xEvCmOePJo4S3rIK5RTQsTOGEdQzxOJVqEBcCLZAH7rKO4zEHqGcXzwP+w\njiIifZTDHVSx3jqGq9QA49gC5FhHEQ9TiRa5uGb9WmCndRQXOsteUtkG/Kl1FBHptUTGksVeyqyD\nuE4Tm0hknnUM8TCVaBESiKeZoHUMlyoBivkDMAbIM04jIr2RxJdp1DSOLn1APcWawCchUImWGJcE\nNFIA+rCzG81AAgA/Af7MNIuI9MZQiomjhN3WQVzpPJDCWSDVOop4lEq0xLg8oIwBwGnrKC62CxhP\nEDgCpBunEZGe+TrJvKBrrZdRRwWZFFrHEI9SiZYYV0Q6H3DUOobLOYtwAJ4H7jXNIiI9MZMstlLL\nKesgrraDj8hljHUM8SiVaIlx6UznOOXWMTygCUhkH852gCLiXnHAUibxAhXWUVyviSAJ2sRT+iQs\nJXrBggVUVFRQVVXFI488csn3ly5dyuHDhykrK6OsrIwHH3yw7Xv3338/lZWVVFZWcv/994cjjkgv\naDlhTzkLDAGqgQmmWUTkcu4nnmcJ6vWtR9bTTAFXW8cQjwqGMuLj44PV1dXBcePGBZOSkoKbN28O\n5ubmdrrP0qVLg//yL/9yyc8OHTo0uGvXruDQoUODaWlpwV27dgXT0tKu+JyBQCCkzBoazhgVzOOe\n4FDzHN4Z8yAIQ4LwqHkWDQ2NrkZaEL4fLILgAPMsXhmZwXn8iQtyaLhxXK5zhnwluqCggOrqampq\namhsbGT58uUsXry4Rz+7YMECVq9eTX19PSdOnGD16tUsXLgw1EgiPVTMMMqot47hIfuBq2kAhlhH\nEZEufR14goFosXTP1XGc0Qy3jiGeE3KJzszMZN++9nPeamtryczMvOR+99xzD+Xl5bzwwgtkZWX1\n6mdFImEQOXzCHusYnrIdmAw4GwJqRbuIu0wDahnOMY5ZR/GYDxlOHknWMcRjorKwcOXKlWRnZzN9\n+nRWr17N008/3evHeOihhwgEAgQCAdLTtcWWhC6fg2ygxTqG5wSBOF4FPmMdRUQ6uQf49cWNO6V3\n1uH8EiLScyGX6Lq6OkaPbl+tn5WVRV1dXaf7HD9+nAsXnJ0qf/WrXzFr1qwe/2yrZcuWkZ+fT35+\nPkePakMyCVUScTQStI7hQRuAAhpxXj4SjdOISLtEnH10pPfWsZmFzLCOIZ4ScokOBALk5OSQnZ1N\nUlISS5YsYcWKFZ3uk5GR0fbnRYsWsWPHDgBWrVrF/PnzSUtLIy0tjfnz57Nq1apQI4lcUS6T2MEh\n6xiedAoYBMAbwALTLCLSagawWVeh+6yFozSRzkDrIOIhIV9Gam5u5uGHH2bVqlUkJCTw1FNPsX37\ndh577DE2btzIypUr+Zu/+RsWLVpEU1MTx48f54EHHgCgvr6e733vewQCAQC++93vUl+vZV4SeVcz\nnh28bx3Ds44Dw3if4/wQeNU6johwB/CvDEcluu+e4zS3M5Df84l1FPEM8+1Deju0xZ1GKCMFgjfy\n5+Y5vD6c7e6+HYRB5lk0NDR+EBwEwSLzHN4ecfwweJsLcmi4Z0R0izsRrykCSnXqXpi8CHzOOoRI\njBsL7KUAZ98c6bsgm4gnxzqGeIRKtMScRIbTpPnQIdsMzGAnkGsdRSTG3QWsJA7n8piEYgUVLGKS\ndQzxBJVoiSnZwB5m4xxiLaE4CjibTR4ARplmEYlto8jlADusY/jCBWoZQBYp1kHEA1SiJaaMB3ZR\nBGy1juILp4EBLAf+1DqKSIwaCtSTCXS9Qaz03otc4BaSrWOI66lES8xIAJo/9ScJjXNu4SHgauso\nIjHqTlJYyXnrGL6ynRJuptg6hrieSrTEDGdBYRJwwTqKb7TQ+iJSAZpFKGJgMsXs1AS1MGtkN0lk\nWscQl1OJlpiRCpzj88Bq6yi+shO4lhfQLh0i0ZYCnNc5hRHxPHtZxFjrGOJqKtESEzKAg6QBk9Em\nUOG1DxjNaVrPMRSRaLmNbF5jj3UMX/qEKjLJUU2Sy9DfDokJU4FtfAv4sXUUX7oAJPM+cL11FJEY\nUswENlFtHcO3/osWblFRkm7p74bEiHzgj8BJ6yC+VAIU8Qaw0DqKSIyII4EWmrUzdARtpJR5FJFg\nHURcSiVafC+ffgS4C1hhHcW3GoEkmoE4INE4jUgsKKKI1ZRax/C5MzxHf263jiEupRItvjeEz9PA\nv1rH8L2PgTG8AiywjiLic/HAffSjhLPWUXxvK4eZyFWkWgcRF1KJFl9Lo5B6jgKHraP4XhUwkY3A\njdZRRHzur8jgFxyixTpITPiIFUzTVDXpgkq0+FgSs5jJJl63DhIznH2jTwIDraOI+NREIIWpVLDF\nOkrM2AMMvjhE2qlEi4/dSBwfWIeIKaVAIb8D/sw6iogPxQMPAz+1DhJzNvIGs/msdQxxGZVo8a3r\nGM8WKqxjxJQzQH/2AjnAEOM0In7zV8Ay8mkmYB0lxpzgMGmcB0ZaRxEXUYkW3xpJI4c4bx0j5hwB\nRvBj4BvWUUR8xJnGAVsYAjQYp4lFDfyBITxgHUNcRCVafKk//Tmjg3BNfARM4xiwF5htnEbED1qn\ncfyMNOCEcZpYFeATZlMFZFlHEZdQiRZfKiKXUh2Ga+wp4H7QQQUiIfpT4BmgidnARuM0sSyO99E2\nntJKJVp8KZ5JtGjWoJlNwCwA/h34qmkWEe+bTmt1jrMNEvO2cpip2jNaLlKJFt/JAaoYCVywjhKz\nTgBpAGwFhgFXW8YR8bD2GdDX4UyXEjsHgQxOWccQl1CJFt8ZS3/2agqBuZO07qr6BPB3pllEvOtu\n4L8AZ1+IQ6ZZBOAc9aSSaR1DXEAlWnwlCWhkGrDOOkrM20jrssIzwB+BWy3jiHjUtcBO+oGO+HaJ\nEiop5lrrGOICKtHiK8VACXPR0ht7QTrO31yBSrRIbw0HjgFQhHOYkdhrZicJ2qFDUIkWn0kGLpAC\n2t7OFbYDkwGnUuvlRqR3Pge8DDh73DSbZpGOdjGM8dYhxJze1cQ3soBaBqNdVN3jADCq7dYeINso\niYgXjQNqmABUW0eRTmpoYZxOZY15KtHiG5OACm4D3rWOIh2cg4sbQq0GbjfNIuIdI3H2gnB+9dxj\nmES6so4mriPROoaYUokWX4jDmTAAeUCZaRbprBRnPqdzguFY0ywi3nEP8PLFxdLiPuWUcAvF1jHE\nlEq0+EIhrYtu4oEW0yzSWTMdzyxsQS87Ij3hTFBzFkuL+7RwnlRSrGOIKb2biS8MAk6TDhy1jiJd\n2A1cA8CHOJ8WiEj3nAINkIKOjXKvk+xngI6SimEq0eJ57dV5DrDWMIl0pwZniRS8g7a6E7mSe4CX\nOlRpcac/sp2bLu5AJLFIJVo8bwats6B1KK6bOdM6GkAr2kWuwDmbcBKwwzqKXIZzpFTnPfEllqhE\ni4/E07q8UNynhNYFhmeBfqZZRNzL2daufbG0uNcFIIUNQIF1FDGhEi2e1r4XRzawzzKKXMF5Wre6\new+42TSLiHt9FniZQmC9dRTpgXOcIpVB1jHEhEq0eFr7obj3Af9pmkWuzDl8pf2atIh8WjpwjIHA\nJ9ZRpAdKgQKOA8Oso0jUqUSLZw2i9U0mARgINFjGkR5wjgFvBpKso4i40ASgqsPFAXG/UuB6PgRm\nWkeRqFOJFs8qoPXjzoXAG6ZZpOecRTgHcRZPiUi7zwL/pSOjPOU0MMA6hBhRiRbPal9GeBOwzjSL\n9FwAyOcPwDzrKCIuMxSo104PntMEJLIZZ7coiR0q0eJJk2nd+ikDOGiaRXrnFDCYPUCucRIRN5kE\nVJCHcySReMkrwOMcZTQjrKNIVKlEiydl0noIwReB35lmkd47DgzljHUMERdZDLxycVmheMtm4H8D\n9/EJX2DAxX2IxP9UosVzUnC2S3O2t08HDlvGkT5wFuGUoqvRIq2GMJAGTlnHkD46A/wT61lHIV8G\n7rUOJFEQlhK9YMECKioqqKqq4pFHHrnk+1//+tfZtm0b5eXlvPXWW4wZM6bte01NTZSVlVFWVsYr\nr7wSjjjic8XAB4CO+fa2ONYDn7eOIeICU4Bt2hvaB1rYRzzLgDRgmnUciYJgKCM+Pj5YXV0dHDdu\nXDApKSm4efPmYG5ubqf7zJkzJ9ivX78gEPza174WXL58edv3Tp061evnDAQCIWXW8PaY1/bn/xOE\nePM8Gn0bIyA4nQeCkGGeRUPDdnwrCIM6vLZpeHmMhuC1jArCX5hn0Qh9XK5zhnwluqCggOrqampq\namhsbGT58uUsXry4033Wrl3L2bNnASgtLSUrKyvUp5UYlQ3sAZxt7RuAFrswEpIjQDovAF+zjiJi\nbBC5nLq4WFq8bh8wmgPAWOsoEmEhl+jMzEz27Ws/brm2tpbMzMxu7//ggw/y+uuvt91OTU0lEAhQ\nUlJySfkW+bQJQDUAX0ALCsztPhQAACAASURBVL3vDKcZQD3OUlGRWDQNKCcTqLOOImFzAUimyTqG\nRFhiNJ/si1/8IrNnz+aWW25p+9rYsWPZv38/48aNY82aNWzZsoXdu3df8rMPPfQQX/3qVwFIT0+P\nWmZxjwQ6XncejfP7vnjZemAO/84a/ifwD9ZxRAzcRTJPXFwsLX5RAtxAJWvpD9qJyLdCvhJdV1fH\n6NGj225nZWVRV3fp79Nz587l29/+NosWLeLChQttX9+/fz8ANTU1rF27lry8vC6fZ9myZeTn55Of\nn8/Ro0dDjS0eVIzzwgRz0YJCf2gB4jkL1ANjrnBvET8aQDFnKLWOIWHVCCSxE+i604g/hFyiA4EA\nOTk5ZGdnk5SUxJIlS1ixYkWn+8yYMYNf/vKXLFq0iCNHjrR9PS0tjeTkZACGDx/ODTfcwPbt20ON\nJD7VD3Bm1t8BvH7Z+4p37AQm8m/AV62jiETZLUApSTilS/xlL9WM5VrrGBJBIZfo5uZmHn74YVat\nWsWOHTt4/vnn2b59O4899hh33XUXAD/+8Y8ZOHAgL7zwQqet7HJzc9m4cSObN2/mnXfe4fHHH2fH\nDi2tkEu1n0tYgHNwtPjFPmAMZ3H2+x5nnEYkWhKAz5LNiouLpcVvKjlJjuZF+5759iG9HdriLvZG\n+9ZP/xTUtnb+GzdDMInUoLNtoX0eDY3Ij/8WhOu0rZ3Px208EIx3QQ6Nvo+IbnEnEj2TgQq0rZ3/\nlADFnMPZn2C8cRqRSBsBZBDPFpqto0hEldKfIoZYx5AIUYkW18undQLHl4DfmGaRyHAW4QD8B872\nhSJ+9nfATykCLSj0uTOU0Z8c6xgSISrR4npDgAaygQM4u2+KHzkHFJwGUmit1CL+kw9UAg0dFkuL\nf5VxmOlcZR1DIkIlWlwtDedcQvgK8JRpFomsSmAiAK8Ai0yziERGHM4nas8wEjhknEai4RwfMYbp\n1jEkIlSixdVmAwGuAk5fHOJnQSCeAM4uLCJ+8wDwDBBkKrDVNoxETZx1AIkQlWhxNecv6F8Ay2yD\nSFSUAoUA7EWHr4i/DMJZNLvJOohEXQ0bGc1s6xgSdirR4lrTgHISgVScE+3E784AAwB4DrjPNItI\neM0DXgacT9hUpWPJBuopZqh1DAk7lWhxLWfOYAHwgXUUiaIjwAjqcZaU6iVK/CIPKAOcv9knTLNI\ndO0AJtMADLaOImGldyhxpX44VyXhRuB90ywSXeU4n0LAm8B80ywi4RMPBC/uNiSxpYXW1R751lEk\nrFSixZXa908dCHximkWsrAXmGGcQCYdrgF2AM5Vjo2kWsdFMkAQtMfQZlWhxpQSgmWS0L3Rs+hCY\nCcBh0A6r4nm3A6utQ4ipbcBktgFTrKNI2KhEi+vkANUAOs8rZtXDxUU4v0MnGIr3jQZqta1dTNsA\nFHAAGGUdRcJGJVpcZyywB4Ab0KLC2HUSGMxBIMM6ikgInM/VAB2wEtM+xnl3g3M4e06J96lEi6sk\nAY1tt/rTurxQYs9GWhfh/BEoNs0i0nf5wHod8S1tStArml+oRIurFOO8wDi/p58zzSK2grSe87Ua\nmGuaRaTv5gDvUgisN04i1o4D99HMABKto0hYqESLq7QvJbweTeUQZynOOZxND0W8aCBwusOkDold\nP8WZFf937OK/cw1zcd71xKtUosU1MoHatlvt16QldrUvwvkYHQMu3jMYOMl4Wje4E9kC/IDd/DPX\nUAf8O63ntIr3qESLa+QCFW23NJ1DHM4inD8An7GOItJLtwJryKZ1sbRIuyYqSOTX6AgW71KJFleI\nw5kD6xgAnDbLIu5SChRSB2RZRxHppZkksokm6xjiSiVAEeuBAuso0kcq0eIKnRfdXI+zI4OIM4/U\nWYRzBmfHFhGvSKCIoHa7ly6dB/pxDmfevHiRSrS4QufDvbWOXTqrAa7hVeA26ygiPZQN1JCCU5ZE\nulIHXM1J6xjSRyrRYm44cKzTV3Tct3S2GxhHOc4vWCJecDuZvE6ddQxxte3AZMpwzuoVr1GJFnN5\nQFnbrc7XpEVaNRMkgRbrGCI9NIZJ7O+wWFqka0F2EEeRdQzpA5VocZmbgHXWIcSFSoEi1gLTjZOI\nXEkCcTR1WCwt0r0N7CdfB4F7kkq0mOp8FRqcrX4CJlnE3Zyt7jYAC6yjiFzBl8hnORusY4gnnAIG\na+a8J6lEi6nO86ETcE6m04ZQ0rUDnGbUxcPARdwpFZjMIHZqYpr0WD1BhmmXDs9RiRYznWc/zwH+\nGXjGKI14gbMIpwpIt44i0o2vMYyfc9w6hnjKJvYykwnWMaSXVKLFjLOR3Vjgx8Aw4O+AHaaZxP2C\nbCCOhdYxRLowDBhCHh9/apqayJVsJI5rrUNILyVaB5DYFcfdBLkG+Ad0xLf0VIBaZjNQM+fFhR4G\n/sU6hHjSGTaTzXSg3DqK9JiuRIuJXJLZQRbwE1SgpTecRThn0DUAcZexwCfM4DibraOIJx2hPyOs\nQ0ivqESLiUwmUEe1dQzxqHrWM5QvWMcQ6eAvgX/r4vAokZ7ayWnGMMA6hvSYSrREnXMM7mTQBlDS\nRx+yk1mcAXKto4jgbNa5k4Gc5bR1FPGwEtZzq85l9RCVaIm6YqCEKaD16xKSl3Gu/iVbB5GY92Xg\nGQqA9dZRxMNqaGGCipmH6L+VRF0i0ESCdQzxuHJamMYPgUeso0hMm4nzqVozcaBTCiVkO4GJ1iGk\nR1SiJaqygT1cBew3TiJedwQYwQGgCphnnEZi1+eAl7kWp/yIhKaBfQxhjHUM6RGVaImqCUA1NwCl\n1lHEB84A/VkO3I5z/qVINA0ALgAXyAJqjdOIH5QChVxAE9W8QCVaoiYBaAZgGrDFNIv4w3q4uAjn\nB8C3TbNILFoCLCcZp0qLhG4jMIsSnPVD4m4q0RI1RbRef06ktU6LhKIFLs6uPwm8D1rXLlE1Eajs\n8NomEqpzQH8agSTrKHJFKtESNf2AsxeXFYqESyWti3BWAbeZZpFYMgMuHquSBDSaZhF/+QTI4WPQ\n3GiXU4mWqBgJHAJgKvCRaRbxl/Y3mtPAQNMsEkucBYVjgb3WUcRn/i/wAJXka5cOl1OJlqi4jtZZ\n0PrgU8Kv/aPPw8BVplkkFvTHmZJ2/uJiaZFwasZZ43EbLcxSUXOxsPy3WbBgARUVFVRVVfHII5fu\n2ZqcnMzy5cupqqqitLSUsWPHtn3v0UcfpaqqioqKCubPnx+OOOJC7XunXg0csAsivtS+COd1YIFp\nFokFfwb8J/E48/JFIuNHlDKNQm3h6Vohl+j4+Hh+/vOfc8cddzB58mTuu+8+cnM7H8X74IMPUl9f\nT05ODk888QQ/+tGPAMjNzWXJkiVMmTKFhQsX8otf/IL4eP3O5TezcdYbi0RK+3ZQlcAk0ywSCyYB\nFfpcTSLuDL9mAOeBr1lHkS6E3FgLCgqorq6mpqaGxsZGli9fzuLFizvdZ/HixTz99NMAvPjii8yd\nO7ft68uXL+fChQvs2bOH6upqCgoKQo0kLpMGNAAwDKg3zSL+tQ8YDTgfhepETImUabSu63AWS4tE\n1hHWMYJkYLB1FPmUkEt0ZmYm+/bta7tdW1tLZmZmt/dpbm6moaGB4cOH9+hnxduG0FqgAQpwdvYV\nCb+dwLWAM7mjyDSL+Nk9wEtchTMDXyTSyoHpvAHMMU4in+aZuRMPPfQQgUCAQCBAenq6dRzpoXwg\n0HZrFvChWRbxvxYgnnfQm41ERusZcuc6LJYWiYYqnPdQcZOQS3RdXR2jR49uu52VlUVdXV2390lI\nSGDIkCEcO3asRz/batmyZeTn55Ofn8/Ro0dDjS0mUnE2kheJDOcEQ+ewApHwuw14yzqExKBNBJnF\nQesY8ikhl+hAIEBOTg7Z2dkkJSWxZMkSVqxY0ek+K1asYOnSpQB8/vOfZ82aNW1fX7JkCcnJyWRn\nZ5OTk8OGDRtCjSQu0flKTRxaxy6RdhoYADg7wIwyzSJ+dD3wAbOATdZRJKbUA0PZi45fcZfEUB+g\nubmZhx9+mFWrVpGQkMBTTz3F9u3beeyxx9i4cSMrV67kySef5Nlnn6Wqqorjx4+zZMkSALZv387z\nzz/P9u3baWpq4q//+q9paVHR8ouRdCzRE3FmrYpE1hFgBCs5wkLg19ZxxDficK47NZMGnDBOI7Hn\nJGUMZh4nedY6inQQ9NoIBALmGTQuP/pB8IZOX1sahPHmuTRiY8yDIPzAPIeGn0ZhEO4KDoHgbPMs\nGrE44iA4lwfMc8TauFzn9MzCQvGWS/dPnQDsMskisaqRMHzYJnLR7cBq7XsvZoJA3MXl0+IO+i8h\nEZEANDMSuBv4DtpNVaLpQ2AmrwM3WEcR3+iHFkaLtW0cYooOlHINXaaRsJvAA1QzFOccuQ+APwBN\ntqEkphwHZvIh8CjwrnEa8b5rgZ1MAbZZR5GYdoBSpjCfbWy3jiKoREvYJZBNE2/xhHUQiXGnaGQQ\ncMo6iPjAXcBTZKASLdYaOMcQbRjrEprOIWGVyDSaqLGOIcIGoIANtJ5jKNJ3w0jluEqLuEIJ6RSR\nYh1DUImWMCsmmxIqrWOIXFyE8w7wReso4mmjgANdLJYWsdHMOhK5zjqGoBItYZbCIM5zxDqGCADb\nucBkaoE06yjiWYuAFRcXS4u4wXp2cz3XWMcQlWgJn0ygliHWMUTa7Aeu5iXgAeMk4l1jGc9ebdAp\nLtLEbq5ivHUMUYmW8MllBBWcsY4h0sl5jpHKcJyNF0V6YzBwkmxgj20QkU/ZTyPDtDuEMZVoCYs4\nIMhU4I/WUUQ6KQGK+Q3wOeso4jkLSeRVTeMQF3qLUhZSZB0jxqlES1gUAuspAnZaRxHppAlIZCdQ\nYB1FPGc6xWyhxDqGyCUqOcdkUq1jxDiVaAmLgcAnpOLsiSDiLruBcaxBRVp6LhM4SQpw3jqKSJfO\ncoAhjLKOEcNUoiVkw4FjDEDHWohb7QLGswr4rHUU8Yy/52p+Rp11DJFu/Svb+CZTrGPEMJVoCVke\nUMb1aBdVcbNmWkjgAM4VRpHL+RLwErmcY4d1FJFuNQCVBJlEnHWUGKUSLWGSD2y0DiHSLWeB4VPA\nUuso4mpXA+OJ431NThMPeJYNfIV81WgTKtESEucqNEAq6FBccbFzQCqf4Pxd7W+cRtzrm8CPKQAC\n1lFErijIKZ5jMAusg8QklWgJSTpwTGd5iUccBEbxJDp8Rbr2JeBl4AyD0CoP8YrN1DOaYQyzDhJz\nVKKlz5wdOQCmA+WmWUR6Yiswlb3AWNAxBdLJKGACsI5hwHHjNCK9sYn/ZBZ3WceIOSrR0meFtC4l\nvB4dsiJeEQTieA74M+so4irfAP4JgJnAh6ZZRHrrJFCHtvGMLpVo6bN4WneFHgEcMc0i0lMBIJ/N\nODP6RcCZmFYHnLEOItJnm3mL6dxoHSOmqERLn0yCDls/aVWweEcDMBiA14A7TbOIWywE3gCcyWmb\nTbOI9M0R4CoqcKarSTSoREufZAG1AIwB9ppmEemtE0Aaa4C51lHEFSYBFYDzudpR0ywifXeaEgZw\nh3WMmKESLb2WDFxou3UDmg8tXrMRmA3AB0CxaRax1r670ADgtGkWkdCUUk9hh3doiSyVaOm1YpyD\nKxyTgJ1mWUT6ypmE9DI6CjzWtb+iFQLrTbOIhKYFiOcYkGEdJSaoREuvJQGNAPwVsAt0rpd4UDkw\njSDOL4G5xmnEzhxgLeC8IbYYJhEJh0oCXMst1jFigkq09Eo2sJdUnK2gPgSeMc0j0leHgZEA/Abn\nkA2JTc5pq9eiz9TEHz5mP2N0KmtUqERLr+Qwiir+CfhnWneJFvGqM0B/zuMcGzTIOI1EX+cl0vtM\ns4iEzwVOk6QTDCNOJVp6LIG5NDMX51CCQ9ZxREJWQuuywrdxPtaX2HIn8NqnFkuLeF8Jmyim0DqG\n76lES48VMZ5SfgM0WUcRCQtnEQ44+3Xkm2YRC2OAj7keZ58WEb+4wC6Stbgw4lSipYcy6M9Bnecl\nvlMJ5HSo0xIrUoDzQMfF0iL+8TEJjGGgdQxf07uG9MhIbuAg5dYxRMJuL63ne+3BWTorseEW4F0d\nFyW+VUkJEy/uiC+RoRItPXIdg9iitxrxqUYgiTeB262jSNQ4kzgm4nwaIeI/22jmGhW9CNK/W+kh\n7QUt/uUsMPwYZ46sxIYk4mnSvtDiaxsYTgEp1jF8SyVarmg2OWyk3jqGSMRcwDnOHs2NjhETgZ0U\noY06xd9Os4aBmtIRMXq3kCtKYxonWGcdQySi9gGjeQ/0hhMD7gDeoD9osbT43CaOkMcI6xg+pRIt\nlzUEaGAE6Eq0+NxOYBJ/BG61jiIRdxVXcZgj1jFEoqCcFKYz1DqGL6lEy2Xlk0JA//NJjGjhHPEM\nsI4hEZUFHGA6aL8hiRG/BhZah/AllWi5gmnAe9YhRKKiFCigEh0B7mdfAH6rpdISQ46zidHkkWod\nxHdUoqVbU4Gt3Ayst44iEhWngYFsQFM6/CoeGMos6tlkHUUkiup5gWHMt47hOyrR0q0M4CBD0THf\nEkuOUkU6udYxJCLmAasZilZ5SKyp4RRZDFLtCyv925Qu9QPOMgJnzwKR2LGZIDM4ZB1DIuJWBrOG\nk9YxRAwEWE8+N1vH8JWQSvTQoUN58803qays5M033yQtLe2S+0yfPp0PPviArVu3Ul5ezr333tv2\nvV//+tfs3r2bsrIyysrKmD59eihxJIyc/VM/A7xpHUXEwEF0BLjfjACOkg8ErKOIGAiyiTgmWsfw\nlZBK9KOPPsrbb7/NxIkTefvtt3n00Ucvuc+ZM2e4//77mTp1KgsXLuSnP/0pQ4YMafv+N7/5TfLy\n8sjLy6O8XGul3SIBaGYCUGMdRSTqPmQLM8mzjiFh9QXgd8Sh81cldm1nF5PJt47hGyGV6MWLF/P0\n008D8PTTT3P33Xdfcp+qqiqqq6sBOHDgAIcPH2bECG377WYTgGriQAfiSow6Th3DGHLlO4qHjGIK\nB9hmHUPE0AHWMIoZ1jF8I6QSPXLkSA4ePAjAwYMHGTly5GXvn5+fT3JyMrt27Wr72g9+8APKy8v5\nyU9+QnJycihxJEyygT3MBjYaJxGxcwoYxKVT1MSLbgTeZxRwwDqKiKkg56klRYunw+KKJXr16tVs\n2bLlkrFo0aJL7hsMdv8hWUZGBs8++yxf+cpX2u73rW99i0mTJpGfn8+wYcN45JFHuv35hx56iEAg\nQCAQID09vSf/bNIHibTuxXEb8I5pFhFLG3iVAu6wjiFhcQepvMY56xgiLlDK2xRRbB3DN4J9HRUV\nFcGMjIwgEMzIyAhWVFR0eb9BgwYFN23aFLznnnu6faxbbrkluHLlyh49byAQ6HNmjcuPmyCYwtAg\nfN88i4aG9ZjHkiCMNM+hEcoYEoRvBedAMME8i4aGO8ZcvhiEAeY5vDAu1zlDms6xYsUKli5dCsDS\npUt55ZVXLrlPUlISv//973nmmWd46aWXOn0vIyOj7c933303W7duDSWOhEEKcJ5vAv/XOoqIuR28\nRi73WMeQkNwHLCcRaLaOIuISNWxgHPOsY3heSCX68ccf5/bbb6eyspJ58+bx+OOPAzBr1iyWLVsG\nwL333svNN9/MAw88cMlWdr/97W/56KOP2LJlC+np6Xz/+98P8R9HQpEJ1FEAbAZOGKcRsVfHSTI5\nBIyxjiJ9dg3XUMNu6xgiLrKbKq5BU2PDwfxSeW+HpnNEZswjKQhPmOfQ0HDTuInUYAr/aJ5Doy/j\nliDcGZxnnkNDw31jDp8NJjDKPIfbR8Smc4h/OHun3gM8YR1FxFVKOEcxZaBDCjzoThJ57eJiaRHp\nqJT3KeIm6xiephItABQwjvUMAj62jiLiKk1AIq8CD1pHkV65BqihCCixjiLiQuc4QiqDrGN4mkq0\nAHEM4g4+4SnrICKuVEMT49gATLeOIj32ZeBZUoHz1lFEXOogtWQwxTqGZ6lEC8O4j+O8jdaui3Rt\nFzCe3wNfso4iPTIIaOFqTrPfOoqIi23jXaYw0zqGZ6lECzNJ4UN2WscQcbVmWkhgHzDCOopc0VLg\nGSYD262jiLjaOSAB1cG+0b+1mDcWOGQdQsT1SoEiXgTuso4ilxUPjCGOvQSto4h4QICd5FNoHcOT\nVKJj3AxuYDMbrGOIuN5ZoB/7gfHWUeSyFgGvkA96ZRPpgZOUMphc6xiepBId49JJ4ShHrWOIeMJB\nIIODwEDrKNKtG4E/Mhg4ZR1FxBOCnKCFNO3U0Wsq0TFsIKM4TYN1DBHP2ApM5TVgoXUU6VIeUMYw\noN46ioiHbOJ9ZnG9dQzPUYmOYQXkU6odVEV6aRcwwzqEdOke4HlmApuso4h4SjVxZFmH8ByV6BgW\nRzpBDljHEPGUAJDPHiDJOIlcKgg0EmcdQ8SDymlgGhOsY3iKSnSMupbh2tROpA8agCGsB261jiKd\n5AI7mA5sto4i4kFHWMkIbrCO4Skq0TEqiyJqecs6hognnWAbacyyjiGd3Aq8wwjgiHUUEU86zxni\n6M8A6yCeoRIdg5KBRkYBH1tHEfGkjbQwmwOgiQMuMooBHOC0dQwRD1vPexQyxzqGZ6hEx6AiBlOi\n3zRFQhLHDqDAOoYAzi8zQQqB9dZRRDyshd3Ec7V1DM9QiY5BSRTTyB+sY4h42kds5jqmW8cQAKYA\n24gHWqyjiHhcFXvJ0Q5EPaISHWPGAB8zBWebLhHpq0OcZySN1jEEgDlM5C0tlhYJg495mzHMtI7h\nCSrRMSaHAVSRYB1DxBfOUEt/JlnHEEYyhmPss44h4gvNNHKGJIZZB3E9legY4nzUWQystI4i4gul\nbKCIadYxYlwcyTRywTqGiI+U8i5F3GYdw/VUomOIs+jmVqDCOoqIL7TQQLwW6Rq7jmLW6uxVkTC6\nwAGSGYJ2ILo8legY0p+pnNHadZGwquICOYy0jhHD5pBEuWani4TZPrYzmhutY7iaSnSMuAo4zO1o\nKodIeO3lHcZSaB0jZo0hiY9psI4h4juVlDKRidYxXE0lOkZcx1i2UA8EraOI+Mx+GhlBknWMmBTP\nRI5QaR1DxJeCBGkgnnTrIK6lEh0z5gK/sw4h4kslDKKYQdYxYk4802jRdp0iEbOe9yngVusYrqUS\nHQNmMYJNpIDWr4tExAVeJ1mnF0ZdIRNZzw7rGCK+dZqDDGCwdQzXUomOAWks4ISuQotE0E5qmUqW\ndYwYM4B+nOa4dQwRXzvKbtLJs47hSirRPjeYIZwkGbTwRiSiKhjEJJKtY8SMEcRzhFTrGCK+V846\npms//C6pRPvcbG4nwOvWMURiwJsEmaUX1SiZznjK2W8dQyQGNAHNQD/rIK6j13tfSyGOQcAB6yAi\nMSBAKfM0MzpqpgHrrEOIxIQPCZCnBYaXUIn2sSncwTa9yYhESZDTJDFQL6sRNwvYxHXACesoIjGh\nnp0MY5R1DNfRq72PZTCcg1RbxxCJIes4ygztqhphQ8mjXqevikTVKY4yiGusY7iKSrRPpTKOcxy2\njiESY9aymbu0jj2CBgMnuRm01kMkqgKsIV+ns3aiEu1TRRRRynvWMURiTCOQrHNBI6iA6QT0CZtI\n1AU5RRypQIJ1FNdQifapBPrTrG3tRAyUUcZ1uhodMYUEedU6hEhM2sF2cim2juEaKtE+dA0z2c1u\n6xgiMeoNjvEnDLeO4UNTmMU29ljHkP/f3r3HRnnfex5/+4qJA/gGHmI7tpOYAAkQx7GxAyFAoDk0\nPcDmoJRIPbKaLN12pe22e9pCE1XqH60EWqm00mkrHW+UZVdpCRuUQk5PEptrbrYzgDE2YGwHkhiT\nsYFiCGAwHv/2DyemCfgynsvveWY+L+mr4vHMPJ+kj/An49/zeyRmnaGeu7jfdgzHUImOQoXM5ZR2\n5RCx5DIwhcskMMl2lCgznRI+o8Z2DJGYdp1LTGCa7RiOoBIdZRJJph/D4OboImLHy9SzTntGh1AK\nFVyjBbTiXMSqOvZTziLbMRxBJTrKlFNBHUdsxxCJcScw5BDHHbaDRI1y5lGri6VFrOunm0Sm2I7h\nCCrRUSaF+7hOg+0YIsLvOc53mW07RlSoIImj+G3HEBEATtFGoX7XphIdTe4igzNaxiHiED46SSWH\nDNtBXO9eHuUjXech4hgneY97ecB2DOtUoqPIbBZyjN22Y4jIkD9wnf/EBNsxXG0C99Cl/YZEHGWA\nfnpJIM12EKuCKtHp6elUV1fT2tpKdXU1aWm3/5fZ399PQ0MDDQ0N7NixY+jxgoIC6urqaGtrY+vW\nrSQlJQUTJ6bFAQNMBU7bjiIiQy7zAXFUUGA7iGslsIh+Gm3HEJGvqeM9ylliO4ZVQZXoDRs2sHv3\nbmbMmMHu3bvZsGHDbZ/X29tLcXExxcXFrFq1aujxTZs2sXnzZoqKirhw4QLPP/98MHFiWikFeLli\nO4aIfE0//5tEvmE7hmtVkEctR23HEJGvucZpUmJ8R/ygSvSqVavYsmULAFu2bGH16tUBvX7p0qW8\n9tpr43693DSJhXzOG7ZjiMgt+vmYjynQRTjjkoLhGgO2Y4jIbfg4hYeHbMewJqgSnZ2djc/nA8Dn\n85GdnX3b56WkpOD1eqmtrR36JDozM5Oenh78/sHrrU+fPk1OTs6wx1q3bh1erxev10tWVlYwsaNO\nBilcIBX0SbSII7VTTRFzbcdwnek8yGd02I4hIsM4yjs8EMMlOnG0J9TU1ODxeG55/MUXX7zlMWNu\nvwl+fn4+Z86cobCwkD179tDU1MTFixcDClpVVUVVVRUAXq83oNdGu2IWsVv7p4o4Wj9XSOAO/Fy1\nHcU1HuBBdvHvtmOIyLBuAH0Qox/kjVqily9fPuz3urq68Hg8+Hw+PB4P3d3dt33emTNnADh16hT7\n9u2juLiY7du3k5aWRkJCAn6/n9zcXDo7O8f5jxHb4rgbqLYdQ0RGUEc7FczjPWptR3GFOMAwkcHb\nqIuIU3mpo5Qn8LLTsbT6vgAAGAFJREFUdpSIC2o5x86dO6msrASgsrLyKztvfCktLY3k5GRgcAnH\nggULOHbsGAB79+5lzZo1I75eRjaP2TTSZTuGiIyil0NMpMh2DNcoYxr6naOI813iJFOYajuGNWa8\nk5GRYXbt2mVaW1tNTU2NSU9PN4ApKSkxVVVVBjAVFRXmyJEj5vDhw+bIkSPmueeeG3p9YWGhqa+v\nN21tbWbbtm0mOTl5TMf1er3jzhxts4zvGkiynkOj0Yw+c/hvxuOAHG6Y5XzLQI71HBqNZvR5hBUm\njZnWc4RjRumc9gOG+B8oZiaVdFPBd6zn0Gg0Y53nzDKmOyCHsycdTAk/sJ5Do9GMdVLME/yzA3KE\nfkbqnLpjoYuVsZh69tiOISJj9jZQYjuE45UwkYNMth1DRMbsGnHEAbF10zyVaNeKI54MBjhjO4iI\njFknXh6i1HYMh4ujhMH/4BARtzjCYeaw2HaMiFKJdqkZLKCV47ZjiEiALpLAFBJsx3CsecBhFgKH\nbUcRkQB0c4Rp3G07RkSpRLtUHjPp4APbMUQkYO/TwzzSbMdwqKnEc5aJtmOIyDhc5W/cQa7tGBGj\nEu1CydxNH+dtxxCRcXmXA3yTR2zHcKBU4CpzgfdsRxGRcahnL/NZaDtGxKhEu9B8FlKnCwpFXOo6\n6JPW25oP1PGPwH7bUURkHAboIZ5UYqVexsY/ZVSJJ5kUbhDYbdNFxEl8NDGVObZjOEw8MEAKg7cR\nFhE3aucY91FuO0ZEqES7TB6P0sEx2zFEJChv08UKsm3HcJAZQCszgGbbUUQkCJ9QRz6zbMeICJVo\nl5nB/bRSbzuGiASlFZhBL1rY8aW7gU9ZDfyH7SgiEhTDDa6QRIbtIGGnEu0i8aQxwBUGb5QjIu5m\nqCMuRn7pObIk4AYAU0BL1URcr453KY+BPaNVol1kPkuo533bMUQkJA7ip0Q7RgMVQC3TQTePEokK\nfXSSrE+ixUnuIIOrdNiOISIhsQd4gnagyHYUy5KBPlYCO21HEZEQOc0pcim2HSOsVKJdYiqzOUun\n7RgiEjKXgEw+Jp5821EsGlwL/eWf9CGBSLQ4wX5mMs92jLBSiXaJuZRwhL22Y4hISL0GPMMNBtcF\nx6LBXTkmA5/bjiIiIdWPoY947rQdJGxUol0hicH/q67bDiIiIfUhUEotxOQFhoP7QgP8A/Cm1Swi\nEnp11FHGEtsxwkYl2gUeZhEHOWw7hoiExev08TQTbMewYD58sWHnPKDRahYRCb0rnCSVabZjhI1K\ntAukU0CPfsCIRKn3gIWcBnJsR4mwVOAKiUC/7SgiEibn6SST2bZjhIVKtMNNYjqfc8l2DBEJq3+n\nhW/FyD2+Bk0FzgLwOLDPZhQRCaPD7KGYEtsxwkIl2uFKeQwve2zHEJGw2gMsxQBxtqNEyM0FHIuA\nd61mEZFw6vvif6Nv0ZpKtKPFEcckDOdtBxGRsKumnqXMtx0j4rScQyTaNXCAYpbajhFyKtEONpsK\njnHCdgwRiYi3uMy3ongzqJseBg4CUAw0WM0iIuF3nuNkcpftGCGnEu1g05nFZ7rNt0gM2cd5Ssi0\nHSPMMoALAKwC3rKaRUQi4zLdTOIe2zFCSiXaoVLI4hqXAWM7iohEzE4aWBvVN8qdDF9cKn0/g1X6\nss04IhIh9eyhLMp2xFeJdqhyFlGnK9ZFYtBBBu/jF51KAS8A/xX4g9UsIhI5hivEkczgdRDRQSXa\noRJIx0+X7RgiEnH/jwaejdpPo+MAw1oGb3l+w3IaEYmk4xxhFo/ZjhEyKtEOdA+lnKLddgwRscLP\neU6TSZ7tICE3GzjGJGAu2tZOJPZ0coicKFoXrRLtQIXM4aR+wIjEsP/LZZ6Kup067gLO8C/Ab2xH\nERFLrtPDBKbbjhESKtEOk0Aafq4CA7ajiIg1fdSTxHym2Q4SMinAdYqAT4FzltOIiC217KeChbZj\nhIRKtMOUs4RabWsnEvMMLxPHP9iOETLlxFHLD4CXbUcREYv6OUcik4iG+7OqRDtMChlcp8N2DBGx\n7jLHSWUWGbaDhEQiT9DP/0HbdorIx7RSQJntGEFTiXaQ6TzEZ3xiO4aIOEQnr5LDk7ZjBO0e4CRz\ngMO2o4iIA7TzAfcx23aMoKlEO8hsHuIY+23HEBHH+BvXSWYCk20HCco9JHGSVNsxRMQxBvDTSwJT\nbAcJikq0Q8SRiuEG2jdVRP5eLdVUsNx2jHFLAPzMAd6xHUVEHKSO9ylnie0YQVGJdohHeAIvtbZj\niIjD9PMZiS7+JLoCqOVJ0N9vIvJ3eulgIpm2YwRFJdohJjOVzzlpO4aIONDHXKGAHNsxxiUFuMYd\n6LdsIvJ1PjrwMNd2jHFTiXaAdGZygTO2Y4iIQ7Wzn/sotR0jYNOBz8gG7TgkIrfRzD4e5CHbMcZN\nJdoBHqaUQ+y1HUNEHKsLPxkk2I4RoAeAo6wE3rYdRUQcqY/Bm8tNtB1kXFSirUsmjjjgmu0gIuJg\ndUyknDTbMcYsji93hM4Hbd0pIsPw8iGlLr3AUCXasrksppGDtmOIiMP18iYTKbcdY8xKAS8JQL/t\nKCLiYBdpZQrTbccYF5Voy6aSx1mO2o4hIo53Eh9FZNuOMUaTgUs8CnxgO4qIOFwPXaQxw3aMgKlE\nW5RKPlc5ZzuGiLhEM6k86IK1g+nABQAeR/tDi8hoDrCbR1x48XRQJTo9PZ3q6mpaW1uprq4mLe3W\n9XqLFy+moaFhaHp7e1m1ahUAL7/8MidPnhz63rx584KJ4zplPEq9LigUkTF7E1zwg6YEvlikNrjB\nnYjIyHqJIxFIsh0kIEGV6A0bNrB7925mzJjB7t272bBhwy3P2bdvH8XFxRQXF7N06VKuXr1KdXX1\n0Pd/+tOfDn2/sbExmDguk0A8KQxwyXYQEXGNRg6wiEdsxxhFHADZQJfdICLiGkc4xByXXWAYVIle\ntWoVW7ZsAWDLli2sXr16xOevWbOGN998k97e3mAOGxVmsJBWmm3HEBGXuUgCaSTajjGsucBhAL6B\ntrYTkbHqools8mzHCEhQJTo7OxufzweAz+cjO3vkS17Wrl3Ln//856889utf/5rGxkZ+85vfkJyc\nPOxr161bh9frxev1kpWVFUxsR8jjPjrw2o4hIq6zhx5KmWI7xjCmAWcBmAG0Ws0iIu7Syzkmcrft\nGGM2aomuqamhqanpllm5cuUtzzXGDPs+Ho+HOXPm8PbbNz+Z+PnPf87MmTMpLS0lIyOD9evXD/v6\nqqoqSktLKS0t5dw5d1+Ml8Q0bmgZh4iMy/scYIUjl3TcAVwFBn+0DFjNIiLuU8deyllgO8aYjfo7\nweXLlw/7va6uLjweDz6fD4/HQ3d397DPfeaZZ3j99dfp77+5Z+iXn2L39fXx8ssv85Of/CSQ7K5V\nwePUst92DBFxpQEGVx3fvJ2JU5QD+4DBSwsP2IwiIi7k5xIJpAAJgN92nFEFtZxj586dVFZWAlBZ\nWcmOHTuGfe6zzz57y1IOj8cz9OfVq1fT3Bwba4STmMwNhv8PDhGRkdXSTAkP2o7xNTc/f14J7LGa\nRUTcqY0minjMdowxCapEb9y4keXLl9Pa2sqyZcvYuHEjACUlJVRVVQ09Lz8/n7y8PPbv/+qnr6+8\n8gpHjhyhqamJrKwsfvWrXwUTxxXuppQO2m3HEBFX200Xzzrqxis3V0DPBDqBKzbjiIhLfcIB8rnX\ndowxM24br9drPcN4ZxnfNZBgPYdGo3H7LDaP8qSZaD3H4Cwb+vP/NJBkPY9Go3HvPM4/mSSyreeA\nkTun7lgYQfFMYoBruGGdj4g43T7qmcN8B2wJlQTcAOAxoG7oKxGR8ajlHSpYZDvGqFSiI2g+S6in\n1nYMEYkSfjaTwEoG7wxoTwV88Tfb08B2q1lExP36OEsyk23HGJVKdASlMpUrfGw7hohEDT8fsZ17\n+S9WUyQDfTwDvGY1h4hEj9O0kUuZ7RgjUomOkKnMppsztmOISJT5GB8F1DH4KXDk5QEdJAFlwPtW\nMohI9GnhfWbygO0YI1KJjpB5lHBEWz6JSBj0U08is4H8iB/7fuAE64B/i/ixRSSa+TH0EufgZR0q\n0RGRzOCNEa7bDiIiUagOKGcj8J8jetzBfaFTAQ+6xbeIhFo9tcxnie0Yw1KJjoCHWcIhDtmOISJR\n6jowgX4Gd11Kithx5wP1/AD414gdU0Rix2U+4U6ybMcYlkp0BGSQy9+IjbsxiogdnUAObwDfiNgx\nU8ngComgO7CKSJicp4NMx92fdZBKdJhNpoBLnLMdQ0SiXAswEy+wICLHmwqc5dvAHyJyPBGJTQ3s\no5iHbce4LZXoMCvlUbzsth1DRGKAAeLoBSaG/VjzmE4jCcClsB9LRGJZH4N/u02wHeQWKtFhlUg8\nyRgu2w4iIjHgQ6CMV4F/DPux4lgB/K+wH0dE5ADvkUKm7Ri3UIkOo9ks5ChNtmOISIy4DEyiFSgO\n63FKKOIgvcC1sB5HRASgh1Ncc+C9NlSiw+gu7uUMB23HEJEYch7IwAdMCdsxMljM39gWtvcXEXED\nlegwSeEurtNjO4aIxJgGoJjXCNcdDCdRwSXaAH9Y3l9ExC1UosOknMeoZZ/tGCISkzqBorC8cxnz\n+FB/t4mIqESHRxyJpNLPedtBRCQGHQYe4iiQHeJ3XkYcXkyI31VExI1UosPgHso5SYvtGCISo84D\nmVQD/xTS953NTI7p7qsiIoBKdFjcwyxOUms7hojEsCuc5U6mhfQ97+IyZ/Q5tIgIoBIdcglk4OcK\n6AeNiFhUD5RxAMgPyfulMJvrfBqS9xIRiQYq0SH2KIup5V3bMUQkxhkgnneANSF5v3IepFZLOURE\nhqhEh1gKaY7cEFxEYk8Ll5jJQEjea/BiaW3bKSLyJZXoEJrOw5zhlO0YIiIAnAZyaAJmB/U+hUzh\nFHEhySQiEi1UokPoAeZyVEs5RMRB+nifZL4V1HvcSzEfUR+iRCIi0UElOkTiuBNDH9BvO4qIyJA6\neinnwrhfnwD4KQSOhiyTiEg0UIkOkVKW4tW2diLiMDeAJI4BpeN6fTlx1JIb0kwiItFAJTpEJjOV\nS1oPLSIO9Akfks+j43ptCrO4xsEQJxIRcT+V6BBIZxYX6LQdQ0Tkttq5QRGXCPSvfA/gYyGwNxyx\nRERcTSU6BEp4hIP6ISMiDjbAEeJZFNBrHgSOkg/0hiWTiIibqUQHLfmLjZ+uW84hIjK8Ohoo576A\nXmOYCnSEJ5CIiMupRAdpLkto1HpBEXG4qwwwkT4geUzPfwQ4wFPAf4QzloiIa6lEB2kauXRzzHYM\nEZFRddPINBaP6blTgIsUAZ+GM5KIiGupRAfhDgq4ylnbMURExqSJRuaMYbu6NKCHZLQWWkRkeCrR\nQSingjpdUCgirnINmDjiM0qAg/x34K+RCCQi4koq0eOWQDwpDPC57SAiImN2kIOU8c9A0jDPiCeO\nSuADoCFywUREXEYlepxm8BitNNmOISISkB5OkMYbJLKJwcsH/14qc/gJR3gXeN9COhER91CJHqe7\nuZdPOWA7hohIwPbyGYv5H8A84EUGl3dkA5uYxr/RzUmr+URE3CDRdgA3SiKbG1y0HUNEZFxuAD3A\nVF7iLDnArwC4g5/Sq4sJRUTGRCV6HCpYRC37bccQERm3A8AK4E06gX8BoBzYZy+SiIiraDnHOCQz\nmT66bccQEQnKUeCBv/s6HhiwlEVExG1UogOURxkdtNqOISIStE+Bu4E44D6gzW4cERFXCapEr1mz\nhubmZvx+PyUlJcM+78knn6SlpYW2tjbWr18/9HhBQQF1dXW0tbWxdetWkpKG23LJOe7nAU7oqnUR\niRL7gMeBfOATu1FERFwlqBLd3NzM008/zTvvvDP8AeLj+f3vf8+KFSuYPXs2zz77LLNmzQJg06ZN\nbN68maKiIi5cuMDzzz8fTJywi2cyA1xDv/AUkWjRC/R/MSIiMnZBleiWlhZaW0de2lBWVkZ7ezun\nTp3ixo0bbN26lVWrVgGwdOlSXnvtNQC2bNnC6tWrg4kTdvNZSr0+hRaRKPMe6FJpEZEAhX1NdE5O\nDh0dHUNfnz59mpycHDIzM+np6cHv93/lcSdLJZMrfGo7hoiIiIhYNuoWdzU1NXg8nlsef/HFF9m5\nc2dYQt3OunXr+N73vgdAVlZWxI57UxwfsNvCcUVERETEaUYt0cuXLw/qAJ2dneTl5Q19nZubS2dn\nJ+fPnyctLY2EhAT8fv/Q48OpqqqiqqoKAK/XG1Sm8TFc5WMLxxURERERpwn7cg6v10tRUREFBQUk\nJSWxdu3aoU+w9+7dy5o1awCorKxkx44d4Y4jIiIiIhISZryzevVq09HRYa5du2Z8Pp956623DGCm\nT59u/vrXvw49b8WKFebEiROmvb3dvPDCC0OPFxYWmvr6etPW1ma2bdtmkpOTx3Rcr9c77swajUaj\n0Wg0Gs1YZqTOGffFH1zF6/VSWlpqO4aIiIiIRLGROqfuWCgiIiIiEiCVaBERERGRAKlEi4iIiIgE\nSCVaRERERCRAKtEiIiIiIgFSiRYRERERCZBKtIiIiIhIgFSiRUREREQCpBItIiIiIhIglWgRERER\nkQCpRIuIiIiIBEglWkREREQkQCrRIiIiIiIBUokWEREREQmQSrSIiIiISIDiAGM7RKC6u7v55JNP\nIn7crKwszp07F/HjirvpvJFA6ZyRQOmckfHQeTO6/Px8pk2bNuz3jWZs4/V6rWfQuG903mgCHZ0z\nmkBH54xmPKPzJrjRcg4RERERkQCpRIuIiIiIBCgB+KXtEG5y6NAh2xHEhXTeSKB0zkigdM7IeOi8\nGT9XXlgoIiIiImKTlnOIiIiIiARIJXqMnnzySVpaWmhra2P9+vW244gDvfTSS3R1ddHU1DT0WHp6\nOtXV1bS2tlJdXU1aWprFhOI0ubm57Nmzh6NHj9Lc3MwPf/hDQOeNjGzChAnU19dz+PBhmpub+eUv\nfwlAQUEBdXV1tLW1sXXrVpKSkuwGFceJj4/n0KFDvPHGG4DOmVCwvkWI0yc+Pt60t7ebwsJCk5SU\nZA4fPmxmzZplPZfGWfPYY4+Z4uJi09TUNPTYpk2bzPr16w1g1q9fbzZu3Gg9p8Y54/F4THFxsQHM\nnXfeaU6cOGFmzZql80Yz6qSmphrAJCYmmrq6OjN//nzz6quvmm9/+9sGMH/84x/N97//fes5Nc6a\nH//4x+aVV14xb7zxhgF0zgQ/1gM4fsrLy81bb7019PWGDRvMhg0brOfSOG/y8/O/UqJbWlqMx+Mx\nMFiYWlparGfUOHf+8pe/mGXLlum80Yx5Jk6caA4ePGjKysrM2bNnTUJCgoFbf25pNDk5OWbXrl1m\nyZIlQyVa50xwo+UcY5CTk0NHR8fQ16dPnyYnJ8diInGL7OxsfD4fAD6fj+zsbMuJxKny8/MpLi6m\nvr5e542MKj4+noaGBrq7u6mpqeGjjz6ip6cHv98P6OeU3Oq3v/0tP/vZzxgYGAAgMzNT50yQVKJF\nIsgYYzuCOFBqairbt2/nRz/6EZ9//vkt39d5I183MDBAcXExubm5lJWVMXPmTNuRxMGeeuopuru7\ntZ1diCXaDuAGnZ2d5OXlDX2dm5tLZ2enxUTiFl1dXXg8Hnw+Hx6Ph+7ubtuRxGESExPZvn07r7zy\nCq+//jqg80bG7uLFi+zdu5eKigrS0tJISEjA7/fr55R8xYIFC1i5ciXf/OY3SUlJYfLkyfzud7/T\nORMkfRI9Bl6vl6KiIgoKCkhKSmLt2rXs3LnTdixxgZ07d1JZWQlAZWUlO3bssJxInOall17i+PHj\nbN68eegxnTcykqysLKZMmQJASkoKy5cv5/jx4+zdu5c1a9YAOm/kq1544QXy8vIoLCxk7dq17Nmz\nh+985zs6Z0LA+sJsN8yKFSvMiRMnTHt7u3nhhRes59E4b/70pz+ZM2fOmL6+PtPR0WGee+45k5GR\nYXbt2mVaW1tNTU2NSU9Pt55T45xZsGCBMcaYxsZG09DQYBoaGsyKFSt03mhGnDlz5phDhw6ZxsZG\n09TUZH7xi18YwBQWFpr6+nrT1tZmtm3bZpKTk61n1ThvHn/88aELC3XOBDe6Y6GIiIiISIC0nENE\nREREJEAq0SIiIiIiAVKJFhEREREJkEq0iIiIiEiAVKJFRERERAKkEi0iIiIiEiCVaBERERGRAKlE\ni4iIiIgE6P8DQuPMhugC2tAAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B1CaRAMCgYhw",
        "colab_type": "text"
      },
      "source": [
        "Now we are reproducing almost a perfect triangle wave.  \n",
        "\n",
        "##Important  \n",
        "\n",
        "In a time series modeling case, you would NOT want to use so many functions (added columns) because it would severly overfit to the range of the data and simply repeat outside of it, and therefore would lack any power to generalize.  You should only use terms which make sense and consdier testing the best choices using cross validation.  \n",
        "\n",
        "##Conclusion  \n",
        "\n",
        "We've seen that using the Discrete Fourier Transform we can discover repeating periods in time series, and can use these in sine / cosine series pairs as additional predictors (x values) in a model.  Used in analysis of business data for forecasting this can provide significant improvement. The main drawback is the potential for over-fitting."
      ]
    }
  ]
}