IA_InterpolationTutorial.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "IA_InterpolationTutorial.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "toc_visible": true,
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/MedicalImageAnalysisTutorials/ImageRegistrationTutorial/blob/master/IA_InterpolationTutorial.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tqAM8E_eNeUb"
      },
      "source": [
        "# Setup\n",
        "\n",
        "download and install important libs and sample images\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "b3ffty-PpyWq",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "54ed0ba8-932d-430b-81cd-0a9616c41fa9"
      },
      "source": [
        "!pip install SimpleITK\n",
        "!wget https://github.com/yeatmanlab/AFQ/raw/master/templates/mni_icbm152_nlin_asym_09a_nifti/mni_icbm152_t1_tal_nlin_asym_09a.nii\n",
        "!wget https://github.com/yeatmanlab/AFQ/raw/master/templates/mni_icbm152_nlin_asym_09a_nifti/mni_icbm152_t2_tal_nlin_asym_09a.nii\n",
        "!wget https://www.spiedigitallibrary.org/ContentImages/Journals/OPEGAR/54/7/074104/WebImages/OE_54_7_074104_f001.png\n",
        "import os,sys, math, time \n",
        "import cv2, scipy, scipy.special\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import SimpleITK as sitk\n",
        "import nibabel as nib\n",
        "\n",
        "from PIL import Image\n",
        "from functools import partial\n",
        "from scipy.interpolate import splev, splrep\n",
        "from scipy.interpolate import BSpline\n",
        "\n",
        "sys.setrecursionlimit(15000)\n",
        "\n",
        "# from google.colab import drive\n",
        "# drive.mount('/content/drive')\n",
        "\n",
        "\n",
        "import SimpleITK as sitk \n",
        "\n",
        "# plotting lib\n",
        "import matplotlib.pyplot as plt  # the Python plotting package\n",
        "# - set gray colormap and nearest neighbor interpolation by default\n",
        "plt.rcParams['image.cmap'] = 'gray'\n",
        "plt.rcParams['image.interpolation'] = 'nearest'\n",
        "\n",
        "t1_img = nib.load('mni_icbm152_t1_tal_nlin_asym_09a.nii')\n",
        "t1_data = t1_img.get_fdata()\n",
        " # Show the images by stacking them left-right with hstack\n",
        "t1_slice = t1_data[:, :, 94]\n",
        "plt.imshow(t1_slice)\n",
        "\n",
        "# using SimpleITK\n",
        "fixedPath  = \"mni_icbm152_t1_tal_nlin_asym_09a.nii\"\n",
        "f3d = sitk.GetArrayFromImage(sitk.ReadImage(fixedPath))\n",
        "img1 = np.rot90(f3d[94, :, :])\n",
        "\n",
        "img2 = cv2.imread(\"OE_54_7_074104_f001.png\", cv2.IMREAD_GRAYSCALE)\n",
        "plt.figure()\n",
        "plt.imshow(img2)\n",
        "\n",
        "print(\" all done ! ...............\")"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Collecting SimpleITK\n",
            "  Downloading SimpleITK-2.1.0-cp37-cp37m-manylinux_2_12_x86_64.manylinux2010_x86_64.whl (48.4 MB)\n",
            "\u001b[K     |████████████████████████████████| 48.4 MB 33 kB/s \n",
            "\u001b[?25hInstalling collected packages: SimpleITK\n",
            "Successfully installed SimpleITK-2.1.0\n",
            "--2021-09-01 18:39:48--  https://github.com/yeatmanlab/AFQ/raw/master/templates/mni_icbm152_nlin_asym_09a_nifti/mni_icbm152_t1_tal_nlin_asym_09a.nii\n",
            "Resolving github.com (github.com)... 140.82.112.3\n",
            "Connecting to github.com (github.com)|140.82.112.3|:443... connected.\n",
            "HTTP request sent, awaiting response... 302 Found\n",
            "Location: https://raw.githubusercontent.com/yeatmanlab/AFQ/master/templates/mni_icbm152_nlin_asym_09a_nifti/mni_icbm152_t1_tal_nlin_asym_09a.nii [following]\n",
            "--2021-09-01 18:39:48--  https://raw.githubusercontent.com/yeatmanlab/AFQ/master/templates/mni_icbm152_nlin_asym_09a_nifti/mni_icbm152_t1_tal_nlin_asym_09a.nii\n",
            "Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 185.199.108.133, 185.199.109.133, 185.199.110.133, ...\n",
            "Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|185.199.108.133|:443... connected.\n",
            "HTTP request sent, awaiting response... 200 OK\n",
            "Length: 17350930 (17M) [application/octet-stream]\n",
            "Saving to: ‘mni_icbm152_t1_tal_nlin_asym_09a.nii’\n",
            "\n",
            "mni_icbm152_t1_tal_ 100%[===================>]  16.55M  --.-KB/s    in 0.1s    \n",
            "\n",
            "2021-09-01 18:39:48 (115 MB/s) - ‘mni_icbm152_t1_tal_nlin_asym_09a.nii’ saved [17350930/17350930]\n",
            "\n",
            "--2021-09-01 18:39:49--  https://github.com/yeatmanlab/AFQ/raw/master/templates/mni_icbm152_nlin_asym_09a_nifti/mni_icbm152_t2_tal_nlin_asym_09a.nii\n",
            "Resolving github.com (github.com)... 140.82.112.4\n",
            "Connecting to github.com (github.com)|140.82.112.4|:443... connected.\n",
            "HTTP request sent, awaiting response... 302 Found\n",
            "Location: https://raw.githubusercontent.com/yeatmanlab/AFQ/master/templates/mni_icbm152_nlin_asym_09a_nifti/mni_icbm152_t2_tal_nlin_asym_09a.nii [following]\n",
            "--2021-09-01 18:39:49--  https://raw.githubusercontent.com/yeatmanlab/AFQ/master/templates/mni_icbm152_nlin_asym_09a_nifti/mni_icbm152_t2_tal_nlin_asym_09a.nii\n",
            "Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 185.199.108.133, 185.199.109.133, 185.199.110.133, ...\n",
            "Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|185.199.108.133|:443... connected.\n",
            "HTTP request sent, awaiting response... 200 OK\n",
            "Length: 17350930 (17M) [application/octet-stream]\n",
            "Saving to: ‘mni_icbm152_t2_tal_nlin_asym_09a.nii’\n",
            "\n",
            "mni_icbm152_t2_tal_ 100%[===================>]  16.55M  --.-KB/s    in 0.1s    \n",
            "\n",
            "2021-09-01 18:39:49 (127 MB/s) - ‘mni_icbm152_t2_tal_nlin_asym_09a.nii’ saved [17350930/17350930]\n",
            "\n",
            "--2021-09-01 18:39:49--  https://www.spiedigitallibrary.org/ContentImages/Journals/OPEGAR/54/7/074104/WebImages/OE_54_7_074104_f001.png\n",
            "Resolving www.spiedigitallibrary.org (www.spiedigitallibrary.org)... 107.154.251.12\n",
            "Connecting to www.spiedigitallibrary.org (www.spiedigitallibrary.org)|107.154.251.12|:443... connected.\n",
            "HTTP request sent, awaiting response... 200 OK\n",
            "Length: 340851 (333K) [image/png]\n",
            "Saving to: ‘OE_54_7_074104_f001.png’\n",
            "\n",
            "OE_54_7_074104_f001 100%[===================>] 332.86K  --.-KB/s    in 0.06s   \n",
            "\n",
            "2021-09-01 18:39:50 (5.27 MB/s) - ‘OE_54_7_074104_f001.png’ saved [340851/340851]\n",
            "\n",
            " all done ! ...............\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uc5jhJF2ggd-"
      },
      "source": [
        "# Introduction\n",
        "\n",
        "\n",
        "\n",
        "[Interpolation](https://en.wikipedia.org/wiki/Interpolation) is a problem of estimating data points based on available discrete data points. \n",
        "\n",
        "**An Example:**\n",
        "Assuming we have this table of product price:\n",
        "\n",
        "```\n",
        "Date  =  1920, 1930, 1940, 1950, 1960, 1970, 1980, 1990, 2000\n",
        "value =   106,  123,  132,  152,  180,  205,  227,  249,  281   \n",
        "```\n",
        "What is the product value in 1988?\n",
        "\n",
        "\n",
        "**Interpolation function**\n",
        "\n",
        "The interpolation can be computed using: \n",
        "\n",
        "$$\n",
        "f(x) = \\sum_{k \\in Z^q} c_k \\phi(x-k), \\quad x= \\in R^q\n",
        "$$\n",
        "\n",
        "$f(x)$ is the interpolated value of a data point $x$, $\\phi$ is the interpolation function, $c_k$ is an interpolation coefficient. So first we compute the interpolation cofficient $c_k$ from the known data points then we compute $f(x)$ at any point. \n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 530
        },
        "id": "tOVppG7Chrhu",
        "outputId": "6356621f-42d4-4c2a-f8e9-af6e8fd6405b"
      },
      "source": [
        "## interpolation function\n",
        "def phi(x):    \n",
        "    # we compute phi here, see e.g. linear interpolation section \n",
        "    phi_value = 0\n",
        "    return phi_value\n",
        "\n",
        "# interpolation using the above phi function\n",
        "def doInterpolation(x, c , k):\n",
        "    # x is a data point we need to predict its value f(x),\n",
        "    # c is interpolation coefficient computed from the available data points\n",
        "    # k is the integer points contains f(x)  \n",
        "    fx = 0\n",
        "    for i in range(len(k)):\n",
        "        fx += c[i]*phi (x-k[i])\n",
        "    return fx\n",
        "\n",
        "\n",
        "# An example: .......................\n",
        "X = np.linspace(0,10,101) # create data points from 0 to 10, 101 points\n",
        "Y = np.cos(-X**2/9.0)     # create data values based on a function\n",
        "plt.plot(X,Y)\n",
        "\n",
        "print(\"X: \", X[:10])\n",
        "K = np.linspace(0,10,11) # create data points from 0 to 10, 11 points\n",
        "C = np.cos(-K**2/9.0)    # create data values using the same function\n",
        "plt.figure()\n",
        "plt.plot(K,C) \n",
        "# C is now our coeffcient c_k\n",
        "\n",
        "# assuming we want to find the value of f(x)=f(3.9)\n",
        "px = 3.9\n",
        "# this is how the call should look like\n",
        "#print(\"interpolation: f(\", px,\") = \", doInterpolation(px, Y,k))\n",
        "\n"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "X:  [0.  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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pIlBRtdUqGr91TIvG8aKrf5ij3vOsjcGJZMFEhBU6w3hWNBGoqPrIpQvIy0zhMS0ax41drV1AbE4km8hdrL0JZkMTgYqqQNH45f3tuhxAnGho6cTpEFaXxW6hOMBdor0JZkMTgYq6zTXljIzpTON40dDSibs4h4xUp92hXFRghvH+U7ok9UxoIlBRt3R+NjWL5vKEFo1j3uiYj90nuuLishAE9SbQgvGMaCJQtthSU8G7Z/vZrkXjmNbU3svAyFhMzygONt6bQAvGM6KJQNnixpULyM3QonGsa2yN/YlkE7lLdKmJmdJEoGwRPNNYi8axq6Glk6KcNErzMuwOZdrcxTl4eod0BvsMaCJQttlS6y8a/0yLxjGrsTX2J5JNpL0JZk4TgbLN0vnZ1Cz0zzQ2RovGscbTM8iJcwMx2ZHsQsZ7E2gimDZNBMpWm2vLeVdnGsek8fpAnBSKA8Z7E2idYNo0EShb3bSy2F803qFF41jT2NpFqssxvphbPFlRrEtNzERYEoGI3CgizSJyRETuneT5vxaRAyKyV0ReE5HKoOfGRGS3dXth4rEqsQUXjc9q0TimNLR0sqo0lzRX7E8km8hdksMxbx8Dw9qbYDpCTgQi4gTuB24C3MBmEXFP2G0XUG2MuQx4BvjHoOcGjDFrrNvNqKQTmGmsy1PHjqHRMd5p646biWQTjfcmOKO9CaYjHGcENcARY8wxY8ww8ASwMXgHY0ydMSaw+Md2oCwM76sSRFVRNlcszOfxnSe0aBwj9p/qYXjMF3eF4oDx3gRaJ5iWcCSCUuBE0OM2a9tUPg/8KuhxuojUi8h2EbllqoNE5C5rv3qv1xtaxCrmbK6p4HjHeS0ax4jGQEeyyviZSBasLD+D7HQXB07rmkPTEdVisYjcDlQD/xS0udIYUw1sAb4nIksmO9YYs80YU22MqS4sLIxCtCqaPrrKXzR+fOeJi++sIq6hpZPyuRnMz063O5RZERHc2sx+2sKRCE4C5UGPy6xt7yEiG4CvAzcbY8argsaYk9bXY8AbwNowxKTiTHqKkz+9vJSX9mnR2G7GGP9Esji9LBTgLsmhqb2XMV3Y8KLCkQjeBqpEZJGIpAKbgPeM/hGRtcAP8ScBT9D2fBFJs+4XAFcDB8IQk4pDm2sqGB7z8Wzj+/6OUFF0smuAMz1DcVsoDnAXW70Jzp63O5SYF3IiMMaMAvcALwEHgaeMMftF5FsiEhgF9E9AFvD0hGGiK4B6EdkD1AH3GWM0ESSpZUXZVFfm60xjmzVY9YFYb015MW5tZj9trnC8iDHmReDFCdu+EXR/wxTHvQmsCkcMKjFsqa3gr5/aw/Zj57hyyTy7w0lKu1q7yEx1snxBtt2hhKRqfjYpTn9vgo9fVmJ3ODFNZxarmPLRVcXkpLt4XJentk1DSydryvNwOeP74yHV5WDp/Gw9I5iG+P6fVgnHXzQu49f72jl3ftjucJJO//AoB073xO38gYl05ND0aCJQMWdLrb9orMtTR9/etm7GfCbuC8UB7hLtTTAdmghUzNGisX3+WCiOz4lkEwWWpNbeBBemiUDFpM01FRzrOM+O4+fsDiWpNLZ0sqRwDnmZqXaHEhbam2B6NBGomPSxy/xFY12eOnrGJ5IlyGUhgNzMFO1NMA2aCFRM0qJx9B3vOE9n/0hCJQKwmtknwBlB//Aop7oGIvLamghUzPrjTGMtGkdDoD6QKCOGAtzFidGb4PUmD1fd9zrvtIV/IT1NBCpmXbIgm3WV+TymReOoaGztJCfdxZLCLLtDCSt3ib83QVN7fJ8V1DV5yctMGZ8xHU6aCFRM21xTwTGvFo2jobGli8sr83E4xO5QwioRCsY+n+E3hzxcU1WIMwL/P5oIVEz72KpisnWmccR1D4xwyNObcJeFIKg3QRwXjN852U1H3zDXLY/MEvyaCFRMy0j19zT+1TvtdGrROGJ2n+jCGBKuUAxBvQni+IygrtmDCHxw2fyIvL4mAhXzNtWU+2caa9E4YhpbOnEIrC5PjIlkE7lLcmg6Hb+9Ceqavawpz2PunMjM79BEoGLe8gU5XF6Rp0XjCGps7eSSBTlkpYVlQeKY4y7OYWBkjHfjsDdBR98Qe9u6uO6SyJwNgCYCFScCReOdWjQOuzGfYVdrF+vitD/xdLjjuJn9b5q9GAPXL9dEoJLcxy8r0aJxhBz29NI3NJqQ9YGA8d4EcVgnqGv2UJidNj76KRLCkghE5EYRaRaRIyJy7yTPp4nIk9bzO0RkYdBzX7O2N4vIR8IRj0o8GalO/nRtKS/u06JxuCXqRLJg470J4uyMYHTMx28Pebl2WWFEh/WGnAhExAncD9wEuIHNIuKesNvngU5jzFLgu8B3rGPd+HscXwrcCPyb9XpKvc/m2gqGR7VoHG4NLZ0UZKVSMTfT7lAiKh5HDjW2dtEzOBrRy0IQnjOCGuCIMeaYMWYYeALYOGGfjcBD1v1ngBtERKztTxhjhowxx4Ej1usp9T7LF+SwtiJPl6cOs12tXVxekY//VzJxuUty8PYO4ekdtDuUaatr9uByCFdXFUT0fcKRCEqBE0GP26xtk+5jNbvvBuZN81gAROQuEakXkXqv1xuGsFU82lxTwVHved5+t9PuUBLC2b4hjnec5/IErg8E/LE3Qa/NkUxfXZOH6oX55KSnRPR94qZYbIzZZoypNsZUFxZGZnadin2f0KJxWDW2dgGJOZFsovGlJuKkTnCqa4Cm9t6IDhsNCEciOAmUBz0us7ZNuo+IuIBc4Ow0j1VqXEaqk0+uLeWX75zWonEYNLZ2kuIUVpXm2h1KxI33JoiTOsEbzf4rH5GuD0B4EsHbQJWILBKRVPzF3xcm7PMCcKd1/9PA68Z/kfcFYJM1qmgRUAXsDENMKoFtusJfNH52l/7NEKqGlk7cJbmkpyTHGI1LS3I4cCr8yzhHQl2zh9K8DJbOj/xqsCEnAuua/z3AS8BB4CljzH4R+ZaI3Gzt9mNgnogcAf4auNc6dj/wFHAA+DXwJWNMfC8ariLOXZLDmnItGodqZMzH3rYu1iXwsNGJ3CU5HOs4T//wqN2hXNDQ6Bh/ONLBdcsLo1LED8t8cmPMi8CLE7Z9I+j+IHDrFMd+G/h2OOJQyWNLbQV/88xe6ls6uWLhXLvDiUsHT/cwOOJLivpAgLs4B2Ogub2XtTGcAHceP0f/8FhULgtBHBWLlQr28cuKyU7TnsahGJ9IlsBLS0w0vtREjNcJ6pq8pLocXLk4ssNGAzQRqLiUmeriFqto3NWvRePZaGjppCQ3neLcDLtDiZrSvAxy4qA3wRvNHq5cPI+M1OjUbjQRqLi1ucYqGjdq0Xg2drV2JcX8gWAiEvPN7N/tOM+xjvNcd0n0hslrIlBxS4vGs3e6e4CTXQMJvb7QVNzFuTHdm6Cu2QPA9cuLovaemghUXNtSU8FhTx/1LTrTeCYaW5JnItlE7pLY7k1Q1+xlceEcKuZFb+0nTQQqrn18dTFZaS4e16LxjDS0dJKe4hgvniaTWJ5h3D88yvZjZ6MymziYJgIV1/xF4xJ+oUXjGWls7eSy0jxSnMn3EbB0flbM9iZ488hZhkd9URs2GpB8PwUq4WypqWR41MdzOtN4WgZHxth/qjvpCsUBqS4HVTHam6Cu2cOcVCfVC6P7f6OJQMU9d0kOq8vzeGyHFo2n452T3YyMmaSsDwS4S3LYH2OJwBjDG81erl5aQJorukt+aCJQCWFLTTmHPX3jk6TU1Bqtf6O1FckzkWwid3EOHX2x1Zvg0Jk+TnYNcF2ULwuBJgKVID5+WQlZaS4e0+WpL6qhpZOF8zIpyEqzOxTbxGIz+8Cw0WgXikETgUoQc9L8ReNf7j1Nd/+I3eHELGMMja2dSVsfCFhRHHtLTdQ1eVhRnMOC3PSov7cmApUwNtdUMDTq49ld2tN4KifODdDRN5yUE8mC5WakUJafETNnBN0DI9S3dEZ1NnEwTQQqYVxaksvqslydaXwBDa3ngOScSDZRLDWz//3hDsZ8JurDRgM0EaiEsrmmgkNn+mhs1aLxZBpaOslKc7GsKNvuUGznLsnheIz0Jqhr9pCbkcKacnsK+JoIVEL5xGp/0fjR7Vo0nkxjSxdryvNwOiLf7CTWBXoTNLXb28ze5/MPG71mWSEumyb4aSJQCWVOmotPri3lF9rT+H36hkZpau9J+kJxQKyMHNp3qpuOviHb6gMQYiIQkbki8oqIHLa+vu8nTETWiMhbIrJfRPaKyGeCnvuJiBwXkd3WbU0o8SgFsHW9f3nqZxq0aBxsz4kufEbrAwHjvQlsrhPUNXkRgQ8ui9NEgL/38GvGmCrgNevxRP3AHcaYS4Ebge+JSPCFsK8aY9ZYt90hxqMUyxfkUF2Zz2M7W/HF6FLDdghMJLPrOnSsGe9NYPMZQV2zh9VlecyzcV5HqIlgI/CQdf8h4JaJOxhjDhljDlv3TwEewL7Up5LC1vUVHO84z5tHz9odSsxoaO1kWVEWuRkpdocSM9zFuTS199jWm+Bs3xB72rpsmUQWLNREUGSMOW3dbwcu2ElBRGqAVOBo0OZvW5eMvisiU6ZEEblLROpFpN7r9YYYtkp0N60sJj8zhUd3tNgdSkzw+QyNLZ16WWgCd0kOgyM+jnfY05vgN4e8GINtw0YDLpoIRORVEdk3yW1j8H7GP3B7yrQqIsXAw8CfGWN81uavAcuBK4C5wN9OdbwxZpsxptoYU11YqCcU6sLSU5zcVl3OywfOcKYndtaTscuxjj56BkdZm+QTySZy2zzDuK7ZS0FWGpfa3BfioonAGLPBGLNyktvzwBnrAz7wQe+Z7DVEJAf4JfB1Y8z2oNc+bfyGgH8HasLxTSkF/jkFYz7Dk2+fsDsU2wUW49Mzgvca701gQ51gdMzHbw95ufaSQhw2D+cN9dLQC8Cd1v07gecn7iAiqcBzwE+NMc9MeC6QRAR/fWFfiPEoNW5hwRw+UFXA4ztbGR3zXfyABNbQ0kleZgqLC+bYHUpMGe9NYMMZwa4TXXQPjNheH4DQE8F9wIdE5DCwwXqMiFSLyAPWPrcB1wCfm2SY6KMi8g7wDlAA/I8Q41HqPbbWVnK6e5DXmyY9WU0aja1dXF6Rj/9vLhXMrpFDdU0enA7hA8sKov7eE7lCOdgYcxa4YZLt9cAXrPuPAI9Mcfz1oby/UhezYcV8FuSk8+iOVj586QK7w7FFV/8wRzx9fHJtqd2hxKRLS3J4pqENT+8g87Ojt/JnXbOX6sp8ctLtH8WlM4tVQnM5HWyqKee3h720nu23Oxxb7GrtAkj6FUenYkcz+9PdAxw83WNLE5rJaCJQCW/TFRU4RJK2aU1jaydOh7C6PNfuUGLSipLojxx6o9k/BN7uYaMBmghUwluQm86GFfN5qv4EQ6NjdocTdQ0tnawoziYzNaQrwQkrJz2F8rnR7U1Q1+ShNC+DqvlZUXvPC9FEoJLC1tpKzp0f5tf72u0OJapGx3zsPtHFOr0sdEHR7E0wNDrGH450cO0lhTFTvNdEoJLCnywtoHJeZtItT93U3kv/8JiuOHoR7uLcqPUmePt4J+eHx2Ji2GiAJgKVFBwOYUtNBTvfPUezzevPR9Muq0GPFoovzF0Svd4Edc0eUl0Orlo6L+LvNV2aCFTSuLW6nFSXg8eSaP2hhpZO5menUZafYXcoMS2avQnqmj2sXzwvpmo2mghU0pg7J5WPrSrm2caTnB+yvz1hNDS0+heai5Vr0bGqJDed3IyUiNcJWs6e55j3vK1NaCajiUAlla21FfQOjfLCnlN2hxJxnt5BTpwb0MtC0yAiuItz2B/hM4I6a4Z7LNUHQBOBSjLrKvNZviCbR7a34F8wN3E1tlgTybRQPC3ukhyaTvdEdF2qumYviwvmsDDG1nzSRKCSioiwtbaC/ad62NPWbXc4EdXY2kmq08HKUnuXOI4X7uIchkZ9vHs2Mr0JBobHeOvYWa6NsbMB0ESgktAta0vJTHXy6PbELho3tnSysjSHNJfT7lDiQqBgHKnLQ28e7WB41Bczs4mDaSJQSSc7PYVb1pby872n6O4fsTuciBgaHWPvyW7tPzADSwqzSHU6IlYwrmv2kJnq5IpFsfd/ohAQ6twAABHDSURBVIlAJaWttRUMjvj4WWOb3aFExP5TPQyP+jQRzECqy0FVUVZEhpAaY6hr8nL10oKYPEPTRKCS0qUluaytyOPRHYlZNG5s0Ylks+Eu9vcmCPfPxBFPHye7BmJutFCAJgKVtLbWVnLUe563jp21O5Swa2ztpCw/g/k50VtfPxG4S3I4e34Yb+9QWF830BjpuuWxNX8gIKREICJzReQVETlsfZ30zw8RGQvqTvZC0PZFIrJDRI6IyJNWW0ulouLjlxWTm5HCozsSa/0hYwwNLZ16WWgWAr0J9oe5TlDX7GH5gmyKc2NzhneoZwT3Aq8ZY6qA16zHkxkwxqyxbjcHbf8O8F1jzFKgE/h8iPEoNW3pKU5uXVfGS/va8fQO2h1O2JzqHuRMz5BeFpqFFRFYaqJncIT6dztjpgnNZEJNBBuBh6z7D+FvQD8tVsP664FAQ/sZHa9UOGyprWDUZ3i6PnGKxg1WfUDPCGZuvDdBGM8Ifn+4g1GficlhowGhJoIiY8xp6347UDTFfukiUi8i20Uk8GE/D+gyxgQWfWkDtKmqiqrFhVlcvXQej+1oZcyXGEXjxpZOMlKcLF+QbXcoccldnMPBMJ4R1DV5yEl3sbY8L2yvGW4XTQQi8qqI7JvktjF4P+Mvs0/1m1RpjKkGtgDfE5ElMw1URO6ykkm91+ud6eFKTWlrbSUnuwZ4o9ljdyhh0djayeryXFxOHQsyG+7iXI6fPR+WhQl9PsMbh7xcs6wwpv8/LhqZMWaDMWblJLfngTMiUgxgfZ30N8kYc9L6egx4A1gLnAXyRCSwFmsZcPICcWwzxlQbY6oLC2Oz8q7i04fcRczPTkuIonH/8Cj7T/XoZaEQhLM3wYHTPXh7h2J22GhAqCnqBeBO6/6dwPMTdxCRfBFJs+4XAFcDB6wziDrg0xc6XqlIS3E62HRFOXXNHk6c67c7nJDsbetmzGc0EYTAHcZm9q83eRCBD8bYstMThZoI7gM+JCKHgQ3WY0SkWkQesPZZAdSLyB78H/z3GWMOWM/9LfDXInIEf83gxyHGo9SsbKqpQIAn3o7vs4JGqyPZ2nJNBLM13psgDHWCumYPl5XlUZCVFobIIiekFjnGmLPADZNsrwe+YN1/E1g1xfHHgJpQYlAqHEryMrh+eRFPvn2Cr9ywjFRX7F7PvZDGlk4WF84hf45OyZmtQG+CUM8Izp0fZveJLr5yQ1WYIouc+PxpVyoCtq6voKNvmJcPtNsdyqyMTyTT+QMhC0dvgt8c8mAMMT1sNEATgVKWD1YVUj43g0fidHnq4x3n6ewf0UY0YXBpSei9CeqavBRkpbKyJDeMkUWGJgKlLA6HsKWmku3HznHEE/qIkWhrbPV3JNNCcehC7U0w5jP85pCXDy6bj8MR+/2iNREoFeTW6jJSnBKXQ0kbWjrJTnextDDL7lDiXqi9CXaf6KR7YCRmF5mbSBOBUkEKstK4aWUxP2toY2B4zO5wZqSxpZO1Fflx8RdorEtxOli2YPa9CV5v8uB0CB+o0kSgVFzaWltBz+AoP997yu5Qpq1ncIRDnl4tFIdRKL0J6pq8rKvMJzcjJQKRhZ8mAqUmqFk0l2VFWXHV03h3axfGaH0gnNzFs+tN0N49yIHTPTE/mziYJgKlJhARttZWsqetm3fauu0OZ1oaWjoRgdXlsT9CJV64rdE+M+1NEFizKh6GjQZoIlBqEp+8vJSMFCeP7oiPs4LG1k4uKcomOz0+LkXEg+XF/tVbZ1onqGv2UJKbzrKi+CnaayJQahI56SlsXFPC87tP0TM4Ync4FzQ86mN3a5deFgqznPQUKuZmzigRDI/6+P3hDq5dPh9/y5X4oIlAqSlsra1kYGSM5xqnXBTXdoMjY9z9cD29Q6NsWDFVOxA1WzNdaqL+3XOcHx6Lq/oAaCJQakqrynJZXZbLI9tbZjVyJNJ6B0e488GdvHHIy//85KqYboUYr9wlObx79jx90+xN8HqTh1Sng6uXzotwZOGliUCpC9i6vpLDnj7efrfT7lDeo/P8MLc/sIOGlk6+95k1bKmtsDukhOQu9vcmaG6f3llBXbOH2sVzyUwNaT3PqNNEoNQFfOKyEnLSXTG1/pCnZ5DPbHuLg+29/OD2dWxcox1eI8U9g2b2rWf7Oeo9H3eXhUATgVIXlJHq5FPryvjVvtN09M1sPHkknDjXz60/fIu2zgF+8mdXsMGtdYFIKs5NJy8zZVp1gro4HDYaoIlAqYvYWlvByJjh6fo2W+M44unj1h+8RVf/CI9+oZarlhTYGk8yGO9NMI0zgrpmD4sK5rCwYE4UIgsvTQRKXcTS+dmsXzyXx3a24PPZUzTed7Kbz/zwLUZ9hifuWs9aXUoiatzFOTS1916wN8HA8BhvHT3LtTHeknIqISUCEZkrIq+IyGHr6/t+OkXkOhHZHXQbFJFbrOd+IiLHg55bE0o8SkXK7esrOXFugN8e9kb9vevfPcfmH20nPcXJ039xJSuKc6IeQzJzW70JjndM3Ztg+7GzDI364rI+AKGfEdwLvGaMqQJesx6/hzGmzhizxhizBrge6AdeDtrlq4HnjTG7Q4xHqYj4sHsBBVlpPLI9ustT/+6wl8/+eCcFWWk89RdXsigOLzvEu+k0s3+9yUNGipPaxXOjFVZYhZoINgIPWfcfAm65yP6fBn5ljOkP8X2ViqpUl4PPXFHG601nONk1EJX3fGl/O5//ST2V8zJ56u4rKc3LiMr7qvca700wRZ3AGENds4erlxaQ5nJGObrwCDURFBljTlv324GLDWHYBDw+Ydu3RWSviHxXRNKmOlBE7hKRehGp93qjf3qu1KYrKjDAkzsjf1bw3K42vvhoI5eW5vDkXVdSmD3lr4aKsPHeBFOcERz19tHWORA3TWgmc9FEICKvisi+SW4bg/cz/qmXU1bSRKQYWAW8FLT5a8By4ApgLvC3Ux1vjNlmjKk2xlQXFsbvP7iKX+VzM7nukvk88fYJRkJoan4xD7/1Ln/15B5qF83lkc/XkpupC8nZ7UK9CV5v8g8bjdf6AEwjERhjNhhjVk5yex44Y33ABz7oPRd4qduA54wx4yt4GWNOG78h4N+BmtC+HaUi6/b1FXh6h3j1wJmIvP6/vXGEv39+PxtWzOfBz13BnLT4mqGaqAK9CTyT9Caoa/KyfEE2JXF86S7US0MvAHda9+8Enr/AvpuZcFkoKIkI/vrCvhDjUSqiPrhsPqV5GTwS5uWpjTF859dN/OOvm9m4poTv376O9JT4vN6ciAK9CSbWCXoHR3j73XNcG8dnAxB6IrgP+JCIHAY2WI8RkWoReSCwk4gsBMqB30w4/lEReQd4BygA/keI8SgVUU6HsKW2gj8cOcsxb19YXtPnM3zj+f18/42jbKmt4F9uW0OKU6f4xJLx3gQT6gR/ONLBqM9wXZzOHwgI6afNGHPWGHODMabKuoR0ztpeb4z5QtB+7xpjSo0xvgnHX2+MWWVdarrdGBOe3yylIujW6jJcDuGxHaEXjUfHfPyXp/fw8PYW7r5mMd++ZSVObT4fc6bqTfB6k4fsdFfc94LQPzuUmqH52el8ZOUCnm5oY3BkbNavMzQ6xpcea+TZXSf5Lx9exr03LY+rZibJZmJvAv+wUS/XLCvEFedncPEdvVI2ub22ku6BEX659/TFd55E//AoX3ionpf2n+EfPuHmnuurNAnEuIm9Cfaf6sHbOxTXo4UCNBEoNQvrF89lSeGcWRWNuwdG+OyPd/KHIx3806cv43NXL4pAhCrcJvYmqLOGjcbr+kLBNBEoNQsiwtbaSna1drH/VPe0j+voG2Lztu3sbevi/i2Xc2t1eQSjVOF0ael7exPUNXtYXZZLQVb8T/bTRKDULH3q8jLSUxw8Os2i8enuAW774Vsc6+jjR3dUc9Oq4ghHqMJpQU46+VZvgnPnh9l1oivuh40GaCJQapZyM1P4xGUl/L9dJ+kdHLngvu92nOfT338Lb88QP/0PtQnzAZJMRAR3iX+G8e8OezEmPpvQTEYTgVIh2Lq+kv7hMf7f7lNT7tPc3sutP3yL/uFRHvvz9dQsis8VKtUfexO8cuAM8+aksqo01+6QwkITgVIhWF2Wy8rSHB7d3jLpOjR7TnTxmW1v4RB46u4rWVWWGB8cySrQm+DX+9r54CWFOBJkzocmAqVCICLcXltJU3svja2d73lu+7GzbH1gB9npLp6++yqqirJtilKFi7vYn8j9s4kT47IQaCJQKmQ3rykhO831nqY1dU0e7nxwJwty03n67quomJdpY4QqXBYXziHV5cDpEK6piv9howGaCJQKUWaqiz+9vJRf7j3NufPD/GLvKf78p/VUFWXx1N1XsiA33e4QVZikOB2sKs2ldtHchFoeXNe4VSoMtq6v5KG3Wvjy47t482gH6yrz+fHnriAnPXE+LJTfD25fl3DrQWkiUCoMlhVlU7NwLr8/0sE1ywr54e3ryEjVZaQTUSJ2i9NEoFSYfOMTbl4+cIYvXbckbnvXquSkiUCpMFlZmsvKBBlXrpKLFouVUirJhZQIRORWEdkvIj4Rqb7AfjeKSLOIHBGRe4O2LxKRHdb2J0UkNZR4lFJKzVyoZwT7gD8FfjvVDiLiBO4HbgLcwGYRcVtPfwf4rjFmKdAJfD7EeJRSSs1QqK0qDxpjmi+yWw1wxBhzzBgzDDwBbLQa1l8PPGPt9xD+BvZKKaWiKBo1glLgRNDjNmvbPKDLGDM6YbtSSqkouuioIRF5FVgwyVNfN8Y8H/6QpozjLuAugIqKimi9rVJKJbyLJgJjzIYQ3+MkENyGqczadhbIExGXdVYQ2D5VHNuAbQDV1dXvX+ZRKaXUrETj0tDbQJU1QigV2AS8YPxr9tYBn7b2uxOI2hmGUkopP5lsDfVpHyzySeD/AIVAF7DbGPMRESkBHjDGfNTa76PA9wAn8KAx5tvW9sX4i8dzgV3A7caYoWm8rxeYeddwvwKgY5bHxiv9npODfs+JL9Tvt9IY875lU0NKBPFIROqNMVPOeUhE+j0nB/2eE1+kvl+dWayUUklOE4FSSiW5ZEwE2+wOwAb6PScH/Z4TX0S+36SrESillHqvZDwjUEopFUQTgVJKJbmkSgRTLYediESkXETqROSAtVT4V+yOKVpExCkiu0TkF3bHEg0ikiciz4hIk4gcFJEr7Y4p0kTkr6yf630i8riIpNsdU7iJyIMi4hGRfUHb5orIKyJy2PqaH473SppEcJHlsBPRKPCfjTFuYD3wpQT/foN9BThodxBR9L+BXxtjlgOrSfDvXURKgS8D1caYlfgnqm6yN6qI+Alw44Rt9wKvGWOqgNesxyFLmkTAFMth2xxTxBhjThtjGq37vfg/HBJ+dVcRKQM+BjxgdyzRICK5wDXAjwGMMcPGmC57o4oKF5AhIi4gEzhlczxhZ4z5LXBuwuaN+JfshzAu3Z9MiWCq5bATnogsBNYCO+yNJCq+B/wN4LM7kChZBHiBf7cuhz0gInPsDiqSjDEngX8GWoHTQLcx5mV7o4qaImPMaet+O1AUjhdNpkSQlEQkC/gZ8JfGmB6744kkEfk44DHGNNgdSxS5gMuB7xtj1gLnCdPlglhlXRffiD8JlgBzROR2e6OKPmvhzrCM/0+mRDDVctgJS0RS8CeBR40xz9odTxRcDdwsIu/iv/R3vYg8Ym9IEdcGtBljAmd7z+BPDIlsA3DcGOM1xowAzwJX2RxTtJwRkWIA66snHC+aTIlg0uWwbY4pYqxWoD8GDhpj/sXueKLBGPM1Y0yZMWYh/v/f140xCf2XojGmHTghIpdYm24ADtgYUjS0AutFJNP6Ob+BBC+QB3kB/5L9EMal+y/amCZRGGNGReQe4CX+uBz2fpvDiqSrgc8C74jIbmvb3xljXrQxJhUZ/wl41PoD5xjwZzbHE1HGmB0i8gzQiH903C4ScKkJEXkcuBYoEJE24JvAfcBTIvJ5/Evx3xaW99IlJpRSKrkl06UhpZRSk9BEoJRSSU4TgVJKJTlNBEopleQ0ESilVJLTRKCUUklOE4FSSiW5/x89K9FL9xTdVAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RsBr3bklhH3p"
      },
      "source": [
        "## Interpolation vs Regression\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hsdomVBVhRmP"
      },
      "source": [
        "# Linear Interpolation\n",
        "\n",
        "\n",
        "\n",
        "\\begin{equation}\n",
        "    \\phi(x) = \\begin{cases} 1-|x|, & |x| < 1 \\\\\n",
        "                     0    , & 1\\le |x| \\\\\n",
        "      \\end{cases}\n",
        "\\end{equation}"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 860
        },
        "id": "O1k-hT_djTtt",
        "outputId": "049f476c-b66b-4797-8273-706e10341708"
      },
      "source": [
        "## linear interpolation\n",
        "def phi(x):\n",
        "    if abs(x) < 1:\n",
        "        phi_value = 1- abs(x)\n",
        "    else:\n",
        "        phi_value = 0\n",
        "    return phi_value\n",
        "\n",
        "# interpolation using the above phi function\n",
        "def doInterpolation(x, c , k):\n",
        "    # x is a data point we need to predict its value f(x),\n",
        "    # c is interpolation coefficient computed from the available data points\n",
        "    # k is the integer points contains f(x)  \n",
        "    fx = 0\n",
        "    for i in range(len(k)):\n",
        "        fx += c[i]*phi (x-k[i])\n",
        "    return fx\n",
        "\n",
        "\n",
        "# An example: .......................\n",
        "#X = np.linspace(0,10,101) # create data points from 0 to 10, 101 points\n",
        "X = np.array ([0,1,2,3,4,5,6,7,8,9,10 ])\n",
        "\n",
        "Y = np.cos(-X**2/9.0)     # create data values based on a function\n",
        "plt.title(\"X,Y\")\n",
        "plt.plot(X,Y)\n",
        "\n",
        "print(\"X: \", X[:10])\n",
        "#K = np.linspace(0,10,11) # create data points from 0 to 10, 11 points\n",
        "K = np.array([0,3,5,7,10])\n",
        "C = np.cos(-K**2/9.0)    # create data values using the same function\n",
        "plt.figure()\n",
        "plt.title(\"K,C\")\n",
        "plt.plot(K,C) \n",
        "# C is now our coeffcient c_k\n",
        "\n",
        "# assuming we want to find the value of f(x)=f(3.9)\n",
        "px = 3.9\n",
        "# this is how the call should look like\n",
        "#print(\"interpolation: f(\", px,\") = \", doInterpolation(px, Y,k))\n",
        "\n",
        "# X  0 0.1 0.1  1    3       7     10\n",
        "\n",
        "# K  0               3       7     10 \n",
        "# c  2               5       9     12  \n",
        "# c= f(K) = K+2\n",
        "\n",
        "# f(0)  =  2 * p(0-0) + 3 * p(0-3) + 7* p(00-7)  + 10 * p(0-10) \n",
        "#                1              0          0            0\n",
        "# f(1)  =  2 * p(1-0) + 3 * p(1-3) + 7* p(1-7)  + 10 * p(1-10) \n",
        "#                0              0          0            0\n",
        "\n",
        "# p(x) = 1-abs(x) if abs(x)<1 else 0\n",
        "\n",
        "    \n",
        "px = 3.9\n",
        "print(\"Linear interpolation: f(\", px,\") = \", doInterpolation(px, Y,K))\n",
        "\n",
        "#plotting \n",
        "f=   [ doInterpolation(x,C,K) for x in X ]  \n",
        "plt.figure()\n",
        "plt.title(\"X,Y and X,f\")\n",
        "plt.plot(X,Y)\n",
        "plt.plot(X,f)"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "X:  [0 1 2 3 4 5 6 7 8 9]\n",
            "Linear interpolation: f( 3.9 ) =  0.09938335085388929\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7ffb9f19fc50>]"
            ]
          },
          "metadata": {},
          "execution_count": 3
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QThtJw852gR1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "e5f148fc-2836-4e71-cebc-8ad0a0918c61"
      },
      "source": [
        "# 2d linear interpolation\n",
        "# apply on an image \n",
        "# we apply 1d for each row then for each column (or colmns then rows)\n",
        "# an example is to scale an image \n",
        "# the code is slow because it is not optimised \n",
        "\n",
        "def phi(x):\n",
        "    return  1.0- abs(x)  if abs(x) < 1 else 0.0 \n",
        "\n",
        "\n",
        "#interpolation using the above phi function\n",
        "def doInterpolation(x, c , k):\n",
        "    # x is a data point we need to predict its value f(x),\n",
        "    # c is interpolation coefficient computed from the available data points\n",
        "    # k is the integer points contains f(x)  \n",
        "    fx = sum([c[i]*phi(x-k[i])  for i in range(len(k))])\n",
        "    return fx\n",
        "\n",
        "\n",
        "def doInterpolation2D(img,nsz):\n",
        "    # img is a 2d image \n",
        "    # newSize is a larger size to scale the image\n",
        "    sz = img.shape\n",
        "    #nsz = [700,700]\n",
        "    img_interp = np.zeros(nsz) \n",
        "    img_interpR = np.zeros(nsz) \n",
        "    img_interpC = np.zeros(nsz) \n",
        "\n",
        "    #print(img.dtype)\n",
        "    #print (  np.finfo(img) )\n",
        "    mnD = np.finfo(img.dtype).min ;     mxD = np.finfo(img.dtype).max\n",
        "    mn = np.min(img) ; mx =np.max(img) \n",
        "    # print(\"data type : \",mnD,mxD)\n",
        "    # print(\"img       : \",mn,mx)\n",
        "    # print (ok)\n",
        "\n",
        "    for i in range(sz[0]): # for each row \n",
        "        # apply 1d interpolation  \n",
        "        C = img[i,:]                    # C  233 columns\n",
        "        mn = np.min(C) ; mx =np.max(C) \n",
        "        X = np.linspace(mn,mx,nsz[0])     # X = 512\n",
        "        K = np.linspace(mn,mx, len(C) )   # K = 197 rows\n",
        "        # print(\"K : \",len(K))\n",
        "        # print(\"C : \",len(C))\n",
        "        # print(\"X : \",len(X))\n",
        "        # print(ok)\n",
        "        new_r = [ doInterpolation(x , C , K) for x in X]     # f  512 columns\n",
        "        # print(i, len(old_row), len(oX))\n",
        "        # plt.plot(C)\n",
        "        # plt.figure()\n",
        "        # plt.plot(new_r)\n",
        "        # print(ok)\n",
        "        img_interpR[i,:] = new_r\n",
        "\n",
        "    for i in range(nsz[1]):  # for each col in the interpolated image\n",
        "        # apply 1d interpolation on the interpolated image\n",
        "        \n",
        "        # get a column \n",
        "        C = img_interpR[:sz[0],i]        # C  197 rows\n",
        "        mn = np.min(C) ; mx =np.max(C) \n",
        "        X = np.linspace(mn,mx,nsz[1])   # X = 512\n",
        "        K = np.linspace(mn,mx, len(C))  # K = 197 rows\n",
        "        # print(\"K : \",len(K))\n",
        "        # print(\"C : \",len(C))\n",
        "        # print(\"X : \",len(X))\n",
        "        new_c = [ doInterpolation(x , C , K) for x in X]     # f  512 columns\n",
        "        # plt.plot(C)\n",
        "        # plt.figure()\n",
        "        # plt.plot(new_c)\n",
        "        # print(ok)\n",
        "        img_interpC[:,i] = new_c\n",
        "        \n",
        "    \n",
        "    #img_interp = img_interpR + img_interpC\n",
        "\n",
        "    return img_interpC\n",
        "\n",
        "\n",
        "\n",
        "old_size = img1.shape\n",
        "new_size = [512,512]\n",
        "print(old_size,new_size)\n",
        "\n",
        "st = time.time()\n",
        "\n",
        "img_interp =  doInterpolation2D(img1,new_size)\n",
        "\n",
        "et = time.time()\n",
        "print(\"time : \", et -st)\n",
        "\n",
        "f = plt.figure()\n",
        "dpi = 80\n",
        "height, width = img1.shape\n",
        "figsize = width / float(dpi), height / float(dpi)\n",
        "fig = plt.figure(figsize=figsize)\n",
        "plt.imshow(img1, cmap='gray')\n",
        "\n",
        "height, width = img_interp.shape\n",
        "figsize = width / float(dpi), height / float(dpi)\n",
        "fig = plt.figure(figsize=figsize)\n",
        "plt.imshow(img_interp, cmap='gray')\n",
        "\n",
        "\n",
        "# plt.show()\n",
        "\n",
        "# comapre with opencv\n",
        "\n",
        "st = time.time()\n",
        "\n",
        "img_interp_cv = cv2.resize(img1, (512, 512), 0, 0, interpolation = cv2.INTER_LINEAR)\n",
        "\n",
        "et = time.time()\n",
        "print(\"time cv: \", et -st)\n",
        "\n",
        "dpi = 80\n",
        "\n",
        "plt.figure(figsize=[ img1.shape[0] / float(dpi), img1.shape[1] / float(dpi)])\n",
        "plt.imshow(img1)\n",
        "plt.show()\n",
        "\n",
        "plt.figure(figsize=[ img_interp_cv.shape[0] / float(dpi), img_interp_cv.shape[1] / float(dpi)])\n",
        "plt.imshow(img_interp_cv)\n",
        "plt.show()"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(197, 233) [512, 512]\n",
            "time :  142.6619713306427\n",
            "time cv:  0.011023998260498047\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 0 Axes>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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xuGgKOt4AUKlUUCwW8dd//dfY3d3F5uYm+v2+MCLzkVwuFy5evIhMJoNkMolQKIQ33ngDoVBIUCQGBBnHoN/gdrvFQa5UKhgMBkLEq6urU86y1m58lmz2sOFFs9kU34Ixh/n5eViWheXlZdFOo9EIW1tbqNfr2NraEv+I5hYZ27IsBAIBWYdwOCzaKpFIYHl5GdFoFIuLi3C5XCgWi+h0OshkMqjVatjc3ESlUkG9Xke325X8LZpZXBuumRn/cNL4+j/vyxSKTlplVuqJHqeGMY6DV53GLJTqOHtVTw6dXJoLc3NzSCQSIpVJcD6fTyTrnTt38PjxY9y4cQP1eh3tdlsInXh+JpPBmTNn8KUvfQmBQECcYJ/PBwASA6FzrTNlAUhU3LZtQXgajcZUMqJlHaaI0B8iIY1GI9E80WgUbrcb9XpdYiX9fh9nzpxBLpeDZVlidi0tLSGbzWJpaQnNZhPhcBgHBwc4ODhAt9sVAq7VanKPnU4Hbrcb7XYbwWAQtVoNiUQCw+EQiUQCmUxGgo2BQADD4RDhcBjRaBRbW1uSHU2N6ESosyD042jI1BgmvWg6OG6cGsYwh5O9aGqO45jBRB5MzJ7S9syZM0gmk1hfX0cikcD8/LwgOOPxGHt7e3jvvfewvb2NmzdvSh6Rx+OBx+MRH2JtbQ3f+MY3BLrl9ZLJpBAU4whut1sc20gkIiYMzQ/btnFwcCABwG63i/X1dcmxarfbU5m6JPLhcIjhcCj+Ur1ex+PHj9Hv97GxsYHJZIJz586JxCes3Gq1BOKNx+OYm5vDvXv3cOvWLViWhV6vh263i2aziU6nIz7KaDRCs9mEx+PB1tYWPB4Pbt26hXg8jvPnzyOTyWBxcRHj8RixWAzNZhONRgPZbBbVahVPnjxBv98XDUJQwUSRnNAo06Q2zSVzPI/5pMepYwynhzcRBXM42Zumj0Gm8Hq98Pv9iEQi4lAnk0nMzc2JY0tptru7i93dXdy4cQPFYlFsZZoU/X4ffr8fr776Kl5++WWsrKyIFGYulG3bku/EIBwJmf5NOBwWn8Lv9+Pg4AC9Xk/s81gsJqgQNQ0JmTCt+ZxEofb29lCv11EqlZDNZmUO+Vs+L9Ejaoh4PC4CJBKJSHCy1Wqh1Wphf39fmJbBPEbLm80mxuOxaJB0Oo1wOCwar9frwefzSUxkPB6Lb+TUHWSWkHQyv2fRkSkoP3GolJM6dFKxwOxcG/M8JBaXy4VgMChOYzqdRiaTQSqVkkixZVkYDAao1Wq4desWnjx5gkePHqHX64m2oc2ey+WQy+Xw6quv4syZMwAgxEvN0G63BXZlViwZQvs6jF4DENOl2+2iXq9jbW1tiqm9Xu8UTApAIGYyELNxO50OCoWCMCgA8WXoO8RiMXluwrnj8RhnzpzB2bNnBQW7e/eu+FHxeBz1el2kvl6jfr8vKNpkMsHc3BzOnz8v6Sj5fB5+vx/dbhfBYHCqXoR/Tn6kWZ/vRDfH+Zb6c5OpzHHqGEMPbTJxOAVseKyugeZvdAo30ZRYLIbLly8jnU5jfX1dosAAcP/+fezs7ODhw4e4fv06ut2uEG+r1cJkMsEXv/hFvPTSS8jn82g2m8jlcojFYsJ8OvWiVqshGAyiUCjA4/FgMBhIcZJlWUKc9BOYQgIA5XIZzWYTfr8fk8lECCuRSKDb7cLn84mUjUQiCIfDU/lTPp8PqVQK5XIZtm0jHA7Dtm3RTPRXvF4v+v2+QKvVahV7e3t4/fXXhRH9fj+uXr0qqS2XL18GAGxubmJvbw/37t1Ds9lEr9eT9JLBYICbN2/i3r17ePDgATKZDPL5PFZXV5HL5ZBOp1Gv1xGJRNBsNvHkyROpE6EgMenBqZZmllmlaUb/p4b6RDjfTsO0JZ0QBicJYfoilMaRSEQcw2w2i3Q6Ldg9ANRqNdy+fRuPHz+WmARw5Dx6PB6cPXsWv/zLv4xYLAbbtoVIaRrRrKGW4n3QVtfBPjKSNhXpiNKcY6BP52wxc5ZxAfo72lQDDoVBNBpFPp9Ht9uF3+8X55zEa9s2hsOh5Gy53W7s7u4KouXxeJBIJITgE4kEAIggOHPmDCKRCIbDIer1Oh4+fIherydMzOcoFApoNBool8vwer3IZrNIJBLwer1oNBrweDxoNpsCVlBQaFjXSUCag5rluOEkcM1xqhkDeJbITU3hpC41YdK8WFxcRCqVEkl/8eJFRCIReDwedLtdvPvuu7h//z7+6q/+ShiCGaidTgfz8/P47d/+bSSTSfmOyBYDWMlkcqqAh1AvnU/WQeiKPhI1n3E0GompRCcZgJhIlmU9U67KTFqehyYHKwW9Xi+63S5CoRDi8bhE7ClsNjY20Gg00Ol0sLW1JXEX4NAXyWQyGAwGaDabsG1bfCu3241sNotoNIpGoyG5WJ1OB/fv30elUpFofCAQEAi4UqkgkUjg2rVrSCQSuHLlChqNBiKRCGq1Gh4+fCj+h05K1H6Cthq0wDwuwq7fn4RyfeJ2VDqOKfQEURozpSEej4tPkU6nhdCYNXr79m08fPhQgnQ6iHbu3Dm89dZbiMfjYpIQyqXEZ/qDvkcSBM0a2vG9Xk/seRNJ089p1mOT8IkQ9ft9IRwyh35+1o37/X7JkYrH46I5bNsWgp9MJtje3kalUpGIP+eOPtBwOBQESd8rNVsgEIDL5ZJ40Pz8PBqNhiBY9L1arRaKxSLu3r2LQqEAl8uFRCKBubk5pFIp0eQEMDiXuvXQSU63nkeTAY6D9Dk+ksawLGsTQBPAGMDItu03LMtKAfgWgDMANgH8Xdu2qx/hGlPvTWTKCa6l6eF2uyXIduHCBWSzWVy+fBmxWEwI4gc/+AHu3r2Ln/3sZxgMBgiFQrBtG+12G/l8HleuXMFbb70lpkcwGJT0cpaLRqNR1Ot1IUjtB8XjccHq+cfGBTQz+Fza56CNTYeZ2mU0GqFer6Pf78Oyjuov6NNoSerxeCTaTWedxUuWZaHf72N7exuj0UhSyn/hF35BakiSySRSqZQwULlcluo+ggrValXAiFAoJKW7gUAA4/EYDx48wObmJm7duiV+UjQaBQDcuHEDDx8+RLlcxtLSEs6fP4+VlRXJ3L1z5w6q1epUBjJwVIc+y4F2ogmtXZ4nX+rnYUr9B7Ztl9T73wPw/9m2/U+swy3Gfg/Af/1BTzrL4dbv9XHaTqdZwRJTSiFKIrfbLWjN3bt3sbOzg9FoJIQ3GAzgcrnw1ltv4eLFiyK5CJXyOmQWOqdM3dCLQEcXgKRvsyCIGkFLNf2aNjr/aMYQiiVTsLuI09zQR+H59DXa7bY4zJVKRYKcRKz43LojCRmbPhcLrmjCJBIJhEIhRKNRAS0YyykWi+j3+1MatNvt4smTJxiPx8jlcpJE6Xa7sbCwAI/HI064dsZ1HbpJJ3qYWly//vftY3wdwJefvv6/AHwPz8EYJvc7Eb/J8eYgpu/z+aSKbn19HXNzc3jppZfEcSyXy/j+97+PjY2NKU1BQr18+TI+/elPY319HYFAQBzdbrcLl+uwGo/Btn6/j3a7DZ/Ph8FgID4NA26RSATJZFI0CqPldFA5nNIYaGLoVjokQsZFCCqQgPk7XQ+uHVKCBBQM3W4XGxsbAICFhQVBoXw+nwQha7WaJB2WSiWJrZAZGVUnuMG8Ktat53I55PN5FItFbGxs4Ic//CFs25Y8q0KhgL29PXQ6HaytreHll1+WQGs6nYbH45lKZ9eCx0lYkmacNMJxzKDHR2UMG8B3LMuyAfzv9uFmMHnbtgtPv98DkHf6oTW9o9Kx3K5+A/N4rTJpjjBvKJFIIJVKIZVKiW1dr9ext7eHR48eYW9vD6PRaCpZ77XXXsPrr78uRUgkSF2VRmmvUztomlB6axucDjbNIUpeOs5aAGhHkzY5NRLvg0M3ReA8aMTLsixhJFPrsnsI7yWXy4lG0flYRMpY58E2PGQevTWBRsXC4bCUvlqWhVQqhVAohFgshkKhgK2tLbRaLQlu2rYtZl0ul0Mmk8H8/DzcbjdqtZrQgtZQuq7DiSlMv9Okm+PGR2WML9i2vWNZVg7Av7Ms647+0rZt+ynTPDNsY0clJ5vQZAT9vZlcSELw+XyYm5tDPp9HNpvF+fPnkcvl4Pf70W638d5772FjYwO3bt1Cp9NBIBCQif7Upz6Fr33ta4Lx0wFtNpsAjoqLeH9MoWCcoNPpSLoGtQzvKRqNCiO0221JgaCG0fDkeDxGu92W2EQymUQsFhMkSjvbzHalQ0/tlc/nBfaliTgLuJibmxO0zbbtqQ6JNN/IQGzsEI/HRfOMRqOpDijhcBjBYFAYCoDEV/L5PH7lV34Fm5ubePvtt1Gr1QTEaLfbePToEdxuN5aXl/GpT30KmUwGk8kEiURCAoZEARkX0s9jQruzGOI4/wL4iIxh2/bO0/9Fy7L+DQ43pdy3LGvetu2CZVnzAIof5RpOiINpL9LWp73N7Nh0Oi3QJHsqbW9vi9omPNrr9XD16lV8/vOfF3yedr2+DolGaygzdsAGA2Q23nc4HEan0xG0iwSjkSTgSDO12225F/oJRI9oz9MPYGYvW+JQ4+j71y1NAUxFySORiEhX/o5zoCFQagqdo6Xbi7JhHDMIiF6RQRmoZD7W6uoqAoEA9vb2pnpoMb9reXkZuVxONAcApNNpABDNxbnTGsKp5MDJGvlYfAzLssIAXLZtN5++/gqA/wHAnwL4TwH8k6f//+8PeN5nVKBpL5pahX+xWAzJZBJra2syofF4HABw+/ZtQZ9qtZo4mK1WC2tra/it3/qtZzr/hcNh8Qs0wVDCEaWi1mH9M7VJq9WS9G4W/9C3oIPqhJCQAJnHFA6Hpb0NNQbjC7FYDJPJBPv7+2i1WrBtW5xzbYtzvvg6GAxieXlZosT0iWi2MbeJwoBMQKHDZ6ZJlUwmEY1GkU6nkUwmxVTjPCcSCXmuer2OdDqN+fl5SbHf3d0VgWFZFra2tvCDH/wAa2treO2110TQjcdjJJNJSbDk82r/StMI59Y0V2f5IBwfRWPkAfybpxf0APiXtm3/hWVZPwHwry3L+gcAHgP4ux/0xCY3Hxfl5KJRanHhksmkxB0GgwE2Nzel3JOO62AwQCaTwZe+9CWZUEKeXHCmYDCYpr8jA7HJGRnHTGnQjMYoNIlIMyKlHZ9FS9lWqyXmEk2dSCQC4DC3ikiRZU1voaUJQEtTANJFpNFoPJMloGvOdbdEPr8mQGpqCgpqRWpxno8ZAlxLmqxLS0vweDy4c+eOIHmWZaFQKMCyLKyuriKZTCKZTCKTyWA0GkkVZb/fn4K9zWfW7zVzfGymlG3bGwBec/i8DOA//DDnNFWfyRzmsRqGZLHR3Nwc5ufnsbi4iEQigXq9jo2NDbz//vs4ODiQ2ADV/O/8zu9geXlZUsAp2bU5sbS0JEgQzQ3tdC8sLCAUCmFnZ0dsa0olM/DGcxHRMWsx6NsQ5oxEItja2ppyfJkAads29vf3UavVpD0nI9JO5pSeTxLr3NycmGAAxKdhZJzHhkKhqSxg9rxiXlgkEhE/g4zBDOZQKCQtQelDjcdjzM3Nwe/34/z58+JTPXjwQHpZDYdDbG5uIhwO49y5c1hcXMTKygpCoRC63S7C4TAePXokfbm0AJhlZTgF/JzGqUoJOc7uMz/nezqXNE2i0ehUdLdQKEjHjlarNeULJJNJLCwswLIO8fdIJCJmki760Snf2k7n/dKUYH8oQqJ0UDW8zHPw9+YiMijZbDZFE5EhaK4xPZ71DZTEmgl1aoTWEpoJ6cQTEmUyou45xWMsyxJfhBJap7Swl5VOYmRdOJ10bdrRSScsHIlEcPbsWYxGI1y/fh2dTgfRaFTS/6ld5ubmMJlMkE6nJW5EP1Obj7Poi7TzsTrfP+8xy3kykQWNQgFAPB5HNptFPp9HOp1GPp+H1+tFpVLBO++8I00LgEPCHI1GmJ+fx9WrVyVRLhgMwrbtqVpoIh6M1i4vL8vxmtBo8pw/f16eRS8CiVD/8f61RAcOCTaTySASiWB7e1viB6PRCNFoFJFIRPrPsnyUkpuak2kgeu5Mv0zHg+gXkLlmaTPOq8vlkui7bdsIBALiSJPBGGWn/8JoN30CDRrbOS0AACAASURBVJgEg0GMRiN85jOfwfr6OprNJnZ2dqR+vF6v4+bNm6hWq/jKV74iDRcikQiq1SpqtRqGwyFcLpdkBMyCaTWtHTdOFWM4wbWzIEaduUqJw/8sNT04OEC1WkW1WsVkctSHaTweY2lpSZiBUWDawYwGE+cntEqpyP6zps2uM2X1jkaaoWn/z0qT12gXCZNVgkSEJpOJlNKSwAgtEwzQPafMudQajPehy2T1IPNSc7LOhD4aEymZLGhG2fmMnGv6KTTF6J8wh4zxC3Zm1Kkw1WoVpVJJ6vRjsRgSiYQ0vdZOtelbaRo7KeUcOGWMoRfQyWHSpgH/04zSmaNsOHZwcIBarSb9jqhu/X4/zpw5A6/Xi2KxiEwmI/g/NQWJj80KgsEgKpWKSG4d0+BEa/iQBKfNBxKJhk71b7QvQknKajd+FgqFxKZmhJ9dEvmM+jya8bQJp+dUz7XTZ9o84mszBcVE1wgCaOZnCgt9EAorAhbMLMhms6jX65KXxRR/JnzSZOZadDodyTbQAsfJZJrFMOY4VYzBYap/Ds3tNB9CoRDS6bSYUrFYDNVqVaDZvb09ABCmyGQyeOutt/DVr34VbrcbGxsbuHv3LlZWViTFIhAISMEQi4eIpjBam0qlBMHSOD8XxGmzSJqAZAhNNHxeahXLsrCysoJMJoPNzU2Mx2PpGMhnJ76vCVOnhnDOKKH1ewBTfon+XDvtRJoIXWtfiEMjVNS0RIyq1apEwBmTYSM7ggT1el00CP26dDqNcrksPhTRuZs3b6LT6eCtt95CKpXC2tqamM1kJD6bE03pOTjOnDqVjDELWqOpolM/mJ6s7episYidnR2USqWp34zHY1y+fBmf+tSnxFZmZLVarSKZTIpzPBwOJb3DtLnpmJtazSR2fk6zhlJXawo66vrZ+Z9m4vz8vORdaahUS2mej2aXZlK32y2fU6Lq32mAQD+PyTAcJCozv4smJMty2aOXfgbNQ5p7FDrssMjzURCx22G32xUnnuW+nU5HUkyYn8XjnKBbLcD0PM8ap44xZi2E+Z9Ew4o8Ni/udDq4ceMG7t+/j1KpJKZArVbD0tISfvVXf1VgRACS6Hbnzh0Ui0XJGfJ6vVOdB/Wx2WxW7HESnG6cxmtqgjclGaU1GVcvGKFgBq4YHGOeld6TwpwvnUHLudL3pdEm4CjSbs65ZiyeRxdhmffM33BHps3NTbTbbZTLZSnUokNO/4iagl1S9vf30Ww2UalUAEBahd65c0dKeQHg8ePH2NrawvLyssxNLpeTdBHei2YQs1/uJ4YxnHwJ87VGUqjiWaVG4qX6JpLDjh6hUAivvvqqBKKYAs7Fp8OaTCbFPGHKONW+DliRoLSTbUbOdWo5TRkSpq475rl1UI3fA0dEqpmCmsA0GfT3PDdwpIG02aPBAs08RM1M/0EnPfJ+9NBMx8i3Nsv4HOZuT7u7u7K702QyEU3R6/Wk8TTTYdj8rlqtShMLgi66qMqkLZOJPzGolJOm0LCmaUJxz4dEIoFcLodUKiVd9Ji5SULodDr4pV/6JXz2s5+VZmS0h6nyXS6X9JXi+fUWYnrR9VZgtOmZcwUcTjqvwcgsHWhTOrtcLmFQRta186wdeRIij+Ei6yo+zhvnSec7UbvxvDyOqRsaAtcono55aCbRzMbvOVdEr+Lx+JQk54aZk8kExWIR9XodsVhMGmfzXNVqFTdu3ECr1cLy8rJkLRBBe/DgASzLwptvvolQKITl5WV0u13s7+9jMpmII09mNOnrE6cxZn1uPohuTc+8nmazKd29ua8Do9Wrq6siUQjLUirprtw8N7URg3vAkamg74UtNJnERwlJIEBDoxrt4TOZgIJp+mip7bS4eoMZ7VRqgaJ9ED6HqU309ybCxGszvZ3faUbUcZlQKISlpSUxkZj1yzmiwKhWqwiFQsjn86LJef5EIiHVj/F4XBq9UXj0ej1hFAowBicpELQg4H/TxJw1Tg1jODmz/JyDC00okx0wKKW2trakzxGDbu12G8vLy3jllVeQTCaRy+Xg8Xik4GZzcxO2bWN+fh7BYFAkJXN+AExJHQDCTNyrjuiV9jdKpRJCoRBef/31KUIjJk8pzx1V9/f38f7770uDslwuhzfeeEOiv3RqtYPPNjuM1OssX96HNrs003FohqMG0RrFhH71b8kQJhG6XC5JfWFnEKbj64YQFy9elNoZbjVAlMrtdksmraaFR48eSQHW3t4eyuWydH3p9/t4+PChJDfqKj8nRvjEoVLHDW1KMe+fi8t+sjwOOMTOtbYg7KclH/svMSagW2xqE4YbynO7MHbt05KL5gdNKyYMmnELSvtyuYzt7W3cuXMHP/rRj6RNTSAQwP379/HKK6/gzTffnDKJdHIiz0Ozjsygo+0mw5hazDSjNCo1KxDJ702G0cdZliXanM2cdc034yLZbFYc6263K+dhJSDTbNgxhddj/hjrWpgOz9gIBQZ/o5n/E2NKcZhag4tMSUQsnDsAEcJsNpsoFApS+MIkuPX1dXzuc58TXwE4ctwnkwnW1takoQE7iZAgmHvDPeZ2dnbQ7XYl/btcLmMymUjKNTv6AZBsV9Ya6M6D2gdgcwNuScbvO50OvvOd7+DP//zPce7cObz++uu4du0aJpOJdPzQ52JKiD43TRYNQlDC6w4n2lHXjjg3nNG+BnDkf2gm573Ql6KjTo3w2muvCYOxqo8mD+e72+3C4/GIFqbUJ6LHXCz6Yz6fDwcHB9JRXgd42XpHp6Sb1scnwpTSQ0slk1E0WkQGoAPJLhxc/H6/j3w+j2QyOSVdGf8AIKqb5oqWzBz1el3SEdgUjPg7d0Pinnf8LReV/V2Jmmln2rIO6zTm5+cxPz+PW7duAThaQBLM48eP0Wq1sLq6ilQqhVqtJkl6Gh4GDlE5zYREfqgp6ZQyHkImoclE+JQOOTUR59/MYtWxDs1kGpbWz0ITV2sWzgVROaZ5MLgXDAYlG5jd51lzQj+G3SR1gzoOHbvR9PSJM6VMP0M7k1xI+hhs9lUoFGTXU+5DMZlMsLS0NGVjA4cTxUbD7J3EnZD0PQCQDeF7vR5SqRTy+cMS9tFohM3NTXQ6HSnccbrfXq+Her0uG9BT61HiEllj8tzPfvYzkaiaAMvlMv7wD/8Q2WwWX/va15DNZqWsFIAQN7t3HBwcTDnZ1G5OvoTe4hiA9MIi8MDjNSqlpbD2oUyETKNcZCKdCcC51MAGTWNC7hrNi0QiEshjB8VSqSRte3TPL92ATq/pcQzBceoYw3SUTJsVgEgObU4w7UDHFQCItKNEpFbQiXHj8VhKMwFMERAjthod4jW4OxGv4SSl9MYo+nl0aohlHVYf/uIv/iJ8Ph+++93vCvNo238wGKBQKOA73/kOlpeXcfXq1aldYrWW0PEeHQ3XGD+vTb+Gm1JSm2qzisCBiZKZoIlpnjihQCaBcv2IDvb7fXkG+lMkcloL2twjFExrgnEmmmomaKDvYdY4dYxhDu1rUK3TdGE6SKVSkco8Oua01/v9Pg4ODjA3NyfF+Rrh4URyH2ydqkGTK5/PT0W2uVEkr0cm4CIwEMfkQ+ZUUeJq3J/Xsm0bly5dwuXLl7G8vIy//Mu/xMbGhtjiNH9s28bW1ha2trbw3nvvSY37Sy+9JGiWTvAztYPOj6IW7Xa7kt4eiURw4cIFaTytzQ6dpAccSXwy5WQykfJa3WfXrGXhXPC5mfTJjTz5O64v18fv90t0nNus0Z8YDAYS7G00GlJ6q807TUsnjVPHGCYyYppVLpdLpAalH7UFiY1qmRPCTFvCurprBieO6c0agSEj0KQgwZPBWGbKY3lOMoVt2+KD6HNqVEw/Kxnti1/8IjKZDL75zW+iUqlMaRl9X/Sp2u22BMrOnTsnfoueIxIh7W9qkm63iwcPHuDg4ADtdhvz8/N46aWXRBvrYaJQfBb6Lq1WCzs7OwAgSZbU7iza0kyhkUNqZd2Ll4KAgAtTRDTjszs6nXXOkc5Pm2U6fSKcbyeH2zRNgOmaZP7XmoCSitKb0pbfccKooknsbJrAY83UCkrMbrcrRNRut6XAh+YMGYs1A+vr69KuX0OfXFz9vDRVvF4vXn/9dVy8eBEPHjzAn/zJn8imNWRs3jf/arUaqtWq7OsNHJqc3Phlfn5erjkej6d2R2o2m3C73XjjjTfw6quvYmlpSfpI6Qi7TgGhicf0cLb4JAqmu7DQVIxEIojFYrKfOO+HZuni4qLAutQYtm2j0WhgOBwim80KnK5Tcqjt6F/QLNYVmyagYtKcOU4NYwDHtzjRDi2JnYvGmgktkUjI/K3OR+JrXRdN4mQ2Z7/flxwpnoPBuGazKcVPJBrayQBkbz9dYstjeG9sFqARKj0P3LPu0qVL2N3dxc2bN6VjIB1tMoUOAGop2O/3sbOzI8gWo/50qPk7ptG/+uqrOHfu3FSXEd43NYQJ8bK8Vic29vv9KaIHIH1+iZDxfvk8AKR0VgMUwJH014KO7znv1J40pXVsxskKOWmcKsZwQqP0axI44wJcXG06md93Oh0JDJmpDjxWB7Lq9bpIUxbCEBJm9/NqtYpyuSx4vUZVqMVSqZQE9qidaBqMx+OpPbt1HICLTwLzer148803EY/HBS7ms1A4AJCSTh3t5RiPx7K1AZ+bBOjz+bCwsICLFy/i4sWLCIVC0vFEI1hOa+XkTGvY10S0CBVnMhm43W7s7e1JOj19Gpa50rw1BZcO3tEcY4tQJi1y/U3GMCHi48apYoxZQ5szuvie9iYlp8bKyRjsWFcul8Vh1wuutcdwOJTdSqkZmFhIM4x2LOMFxNJ5T6FQSBLi2u027t27h06nI90BV1dX0ev1sLm5CQC4du2a1KFrCQ1AGCSRSIjfcf36dbz99tvodrtyL5Zlyd7hzBPTEt9El3jOXC6H1dVVfOMb38DCwgIAiAmkAYJGoyGlv4wpUFuz4yJz0ojwHRwcTMVKmMdECLbT6eDu3bsCLwcCAel0ruNBmpidUse5ztTy9KPoXzlF9E0B7DRONWOYphQHzQEuhBlw0mWslBwHBweC4OjILVUvzSjgqJsgzSo2HKATSBvWsixpHQNgKuO30+nItlzsDliv18X0sazDRm6NRgOpVMpxoci4hFvPnj0Lj8eDhw8folgsTrXG17/hn6lR9fwtLi7i7NmzuHjxIhYWFuDz+cQm52/pI2xubgp4kc/nRRtyvpmyr+vZAYi5SMmvwREG6ViW6nK5UKlUMBwOEY1Gp1JrdC4anXPtv/A7pobwGXUavxOUfNw41YxhMoWudwCOFqDb7YoEpfNNacM0c6/XKxJqcXFxyk9hwFDXV3Bhut0uKpUK/H4/8vm8pH5wlyFul8VKO2ofNmJgVmkkEpFIOCPjfr8fN2/elE57pnOrNQcX9dy5c/jN3/xNbGxs4O233xZnlf6NU4yA1yOyk81m8dWvfhXLy8ti1lBTUOC43Yeb6mxvb0s/Wa/Xi3a7Lc0LSLDUCLqp2tzcnMDaGoGybVv21CCh09lmxjMFGgENCqZer4dSqTQV2+CckTGYL6X9uQ/iW3CcWsbQElQ/kJk3pZlHSyzNPJZlCQHfvn0b5XIZly5dmoJntROrA2LE+RmJ1czE35AhiadTyulCKGqkQuGwETxNHTZrIALDewYwZV5xsHsiyzz39/dRKpWwt7cnsLU+D5sXsO3mmTNnsLi4iMXFRYE/WUrK+eCc1Wo1lEqlKU1MwqZJBECyB+izcE7N7GQSKfPIOJdkpslkMrUpjQ6OMmNZm1M6fsSUIL3uTmbU844TGcOyrH8G4FcAFG3bvvz0M8ddk6zDq/9vAH4ZQAfAb9m2/dfPcyM6EGUyAjBtVuluFTpKTVtVB5FIXJQmy8vLePLkCa5fvy6NFNgWB4A43oRcSVDcC8Pj8YiD3mq1pCseq89MqUTEJpPJiNNNW79Wq+HOnTvw+/147bXXpLiJz6sBBs4Fny2ZTOLq1auC4bdaLfT7fen3RPBA2/ixWAyrq6vSB9a2bTlOxzto+jx8+BD3799HLBaTFH5mL3MwxbterwuxkmD7/T729vZgWZaYmZZloVwuCyG3Wi0UCgWp1mNgTtddcCddpqNrGF87+zp+5GSGay368/Ax/jmAPwTwL9Rns3ZN+o8AnH/69yaAf/r0/4cas+xuwnTAs8VDlG56oZm2wZwhNuui2UVYk3Yvz82iGpoRuiqPJkC1WpX8KTqgvO/hcIjd3V1Bx+gb0USo1+uo1Wq4e/cuYrEYLl269AzUDDy7vRoHbWg+K0s8NWJEQmUXcvafIiEBmIJAtY/Cmm0SPaU4z0tJH4vFJJUcOGQW1rtwo5d+v490Oi3xItaGc7NKpptHIhHZGq3VaqFWq2F7exu2bUuCoBkHIhqlBYhpcWiB9Tza40TGsG37+5ZlnTE+nrVr0tcB/Av78C7+0rKshPV0S4CTrmMiBprL+acXj2qdhGbmxtBPoC28ubmJfr+PK1eu4LOf/ayck8Q6Go2kqwW3ywIwFayq1+vY39+fSnOmZKSKp5RvNpuSfauLnmge0Mb2er0SlNJJb3xWpzwrvtZOp0ajtAlGNE2nnZs+GueU5zTzuNjEjqYkc8q4iX2hUMCNGzfED6NGn5ubkz28G40GKpUKms2mrAsrHgnR7u7uyvwxLjGZTKRvrk5j8fl8IsS0Cag1ip47E6Ez59McH9bHmLVr0iKALXXc9tPPnmEMy9hR6elnz3CzfhD9oGZCnI4sm74CHdNcLoe5uTlhHjIFr8mOINQmmvE0cdHMoj3NXChdu5DNZsXnYLanDpJNJhOpH7l06RJWVlamtCCvY86N1kisV+cuqIxisxEBn9Hv90vjAG7jzPY1RPV4TT3/kUhEUCgSJ48h8cViMeRyOYzHY/j9fqysrMgcAIepIaw3iUajSCQSEnlnlix9PIIk9M+ICBKBI4LITGjdB1ingJhzN2sujxsf2fm27dm7Jp3wu6kdldTnz5gOJrJAqUfpSAYYDAYIh8NTLfhZ5be2tga32416vS5llJTw4/EYvV5PYh6EILnzKBlwd3dXru92u8V0YYYu08WBw95WuryS56N0azQayGQyOHv2LNbW1qaYziRSM/muVCpha2sL77zzDkqlElqtlpiBTgE+4JCAw+Ewtre3sbi4iGvXrk3tisSESjILAMzPz0tOmMfjkQRFAhL0EWzbxtra2lTSIAvBCDJoqT8ajRCJRKbQP84R15XxEB7/+PFj3Lx5E8ViUfwpbToRGaSAMufC1LYnxTI+LGPM2jVpB8CyOm7p6WcfejipPds+agxMDWHu6EmJwn0o2MKS3cMZEKPapuSlJKWZxWATSyjpgDOYxgWhScTzFYuHU8JFdrsPO2ZEo1FxYi3LQjqdlpiI9iucBgOB7Jv16NEjSZ40TS4zRYRw5+bmJgaDAVZWVuByHe7JzZiPdkpdLpdoz729PXk++ijck4PXovBi0JXbIQCHGpsN8XRcgwRKwUPtrVP5J5OJ5JwxAEvBqIWUqQV4ftPRfp7gHvDhGWPWrkl/CuB3Lcv6Jg6d7vrz+BeAc97+LMiWkp6oC6FQLj41ycrKCtbX15HL5aSuuNlsim3PKkD6KP1+XzacpG8AQFAoRsUTiYQ0KWYhUigUko7fRLJI6Hq3VyIt3HZseXl5Co83C/hpO3u9Xty7d08i3zqGQDNNI3QkLgITTLTjPnetVgsXLlzA2bNn8corr8Dv90+V1k4mh03MotEocrmcIHjU5qzdYLsaDY8y6mzbR3ls7JjCGAO1FNeY0WrdLYT3opsn/PSnP5X0F80c1IhkLNKAph0NnZ80ngeu/Vc4dLQzlmVtA/jvcMgQTrsm/RkOodoHOIRr/7MT7+DoOs/1uZY0AKYiw/yMREEJzQmnA8zvqfatp3EOpnywhSQnkXlLVOG8DzrcJNJWqyXxklQqJZpsMpkI9Es1T0IzU90ZIASOmMTnO9yi7Mc//jEePHgghMFGEACmNId23okkEawYDodotVp4+PCh5BitrKzItslm84BIJCLFUOZ6kHB5ryRoChoyqy435Xl0rhN9uFAoJPPEuWOGL3OvCCbovDL+npnW1JZmYFHf90nM8Tyo1N+f8dUzuyY9RaP+0UnnnDVmOd/mg1AKkch0ajQXNxwOS1krP/d4PAiHw1O2qcfjkZJIBoi4wJRo/J5d0XUzApoSw+EQ29vb6PV6yGazmJubQzqdljQLNhOjrb60tAS/3z+VAUyi5rMQkvze976H69ev486dw01xab9roEEH9ng+DtOWt21birsePHiAWq2GV199FZ/73OcEMdPmCudBV/DpddBIIhG4ZrMJ27bFoabWY5zJ5XLJ3LCZxPz8vJhpjUYD1WpVzF0KKOCoIyIH082DwSC63a50bdG+hl5Pzs/HgUp9LENPsMkgfBCNUHGCuXiU4jqfBjiKZfD3JGQAspBmfbAmUDqToVBINm2npKM0plap1+vw+XziqDJwyPsE8EyxjZPpSALZ2trCD3/4Q+zv7wM46tpOicjn4/PrUk4+AyUtmZ7f2/ZhsdO9e/cwHA5x9uxZiapr0MHpPvn8PJZzTRCBn+mcJd4DGYVgBIuqyDTNZlMClXrd9XNSW/A8uqSVc2M63XoNzPk2x6liDA7TQeLD6MIc/YDEsvma3+nmyNyQkmqevYroONIx1OfodrtCAEz70Cnsmom1yVWtVpHNZqfS2fXQv9WOK49jLtLbb7+NW7duYWtra8ocohTUrf21TwJAnom9XRmXYcyFnUBY5LSxsYGf/vSnuHz5Mubn5yVYada48Nw0fbiHB00aXSDGZ+FrMgTr9bWZyznsdruSfMm0EW01aC2gy5zpGzI+1Ov1nkGlTA3xiWEME6fXn+mH0gEtOoG0Q5mAxmPMc9DJ4/eVSgWDwQALCwvyO+DQZt/d3RUJp6V9o9GQWm5GkWnf0t9g02Fg2p4mkWh7HIDApb1eD3/8x3+MGzduoFAoSCyCqJWuEqQvQQ0Vi8WwtraGRCKBubk5+Z1Gfnge5liVy2U8fvwY7XYbf/EXf4G7d+/i13/915FMJiXCr8+jCZWNsum36PuLx+MIBoOIx+PPxIt0sZgm+Hv37qFWq0nFnqlZ2SqHSYc8FzfUBCAtd8ggphA16WrWOFWMoYcTrEZioNZg5FMTGJ1HxiWIhLAljK5647m0RCeSA0C2v6KWYJKervwznUjeI51uagxKXR2918Pr9aLRaOC9997D97//fbRaLZGw2jTSg1WCmUxGAnfcIpk2Nk0ancrh9XqxvLyMfD6PZrMJv9+PUqkk2a21Wk36ZDnNv753vdkO5wvAVC8o87lNa4CFVKVSSczR8XgsiZo61sQtnTn/7DFME9NMAtXaQjPDR3a+/30Pra6BaahNp1PoFvOM5Gq0iYX5VPEABFliVmq/35cUdG0nu1wucegoyQix6pJXml9kMr3oOgvUsizJyzJtfMYmdnZ28Ad/8AfY29ubkpTapqaUvnLlCpaWlmR/bEpyMp9TFNh0OmlqBYNBrK6uSoMJzp/J7DolXfsYfE2IOxqNPsMEZnzEhE9brRb29/elfnx/f18EGJM82QmSuyYxJYQRfXN92QdAm5bPA9NynDrGMIdeXO04kzFoTtFOZXaoZVkieajiieczJkEYUtdv8JoejweJREIcVKp3Sq5msylIEwcdfLO2+rhn6/f7KBQKePfdd3FwcDBFfCQoEun6+jrW19dx5coVcXo1QKAZggxDraX9DwDPHMvf644dJCxdsQdMb5KjtYrJxBx6jjQTa4HCe2BEnNdmvlmlUpE9EHkeZiiQoWnK0o8yA5zaFDxpnErGcHK8SbzMamXAiu3iU6kUXK7DBl2JRALD4RA7OzvY3d1FNpuV5gJM7qtUKkgmk6KWGZ3N5XJyrUwmI1v9tlotLC0tYTQaSTYoy2VZ5EQQwOPxiEmjJTmJgc/U7/fxN3/zN/jxj3+MW7duTdncwBFCdvnyZbz22mtYX18XE4PMHwqFRHqSqAeDgST+sUacAUnt4FO76HLdXq+HSqUiWtNMR9exgVlrpE0XJxOKMK8GD9LpNBYXF9Fut6faEjWbTdy8eVO6oNBvBA6DjJlMRtan0WhMFW45CaVPrCkFOKNSesK11mDqB4NdDPAQ8SmXy1KLwMxQwoCEBWmGaTNHmwupVEqiqgyksWmAxvbpjBO7B6adbG1CcWEYjdY7LmnMPpPJ4Atf+AJyuRyAQ8w+Ho/LMbolEHDUXoimISFMakZCzbqpMwCJQTCny4Q5meqiTSi9Vtpk0YJAm5YUbPRnyAA0HZkew63GGBh1u92iCSj1gaNWonxevcsutbdmDidwZ9Y4lYxhPoBeJNu2ZQ/odruNfr8vDmgymZRMTEZPr1+/jkgkgpWVFUGvuPD1eh1bW1uIRCI4e/YsLMsShElHaZkztbq6CgCSb6X7wQKQDux01vksLtd0fbJ2xC9fviyR8ocPH2I8PiwLXVpawpe+9KWpDTM18EATSZs1vH9NpMARKqZrU3SQTGs1bQoxWEqG0tfSJgk/13ESmqyNRgMez2HHc6JXxWJxKvBG4ZJMJqVmhOn+NEepoSeTo7LgVCqFVCqFeDyOJ0+eoFKpoNVqCRSv70uvx/OMU8kYgHPVlUaliIC0Wi0hRrMFvWVZ2Nvbk7rj0WgkaRlsbWN2ByfqRElsEgwAiQuwQwZw1CGRTKUZgM9hoiK2bUs/p9XVVdTrdViWhWw2i2g0KhFunRo+K0ClJTMHmQmAo+/C81G78Tqmo619LxNs0IzEv/F4jGKxiFqtJg0R+BvdBKFWq4lG9nq9qFarUubL8zDmRFOJjEcTlkKIMC61hb5HDlPAHjdOHWM4qTqNbnB7MPZ3ikQiWF5eRi6XQz6fR7vdRqVSEUlUKBTwzjvv4I033gBw1D2CfgEZp9lsSkM1Ik5sUMB8sqsPEQAAIABJREFUH5ZmkqgZNNNEZN6v6UAD05tN2vZhNRp3nuVgsFATnIY9aVJqQua1eU/mdU3o0iQcTezaBNEZwpoBeT+8/mQykc4nrJPXxErNYNu2zHWr1cLGxgbC4TCWl5en+lq5XC7UajU8evQIOzs70lvX7XYjk8lgaWkJiURCAAym4HOPP5MRtCVykuY4dYwBPFvFpz8HjiQh7U6aTkyTJnrB329vb0t3C51TRA1BB5WwL/dnYHSZ5hVNApoVWosB0yYJ75cmD3O6nFLLddo1f6NRID20BKf01Ncz543nNqW+033o8+g555+Z3Mjza8ZlnIGRcTIITSo6+ZPJRKBWmkA7OztIJBLIZrMADh3v7e1t1Go1qTWndmN9B31FMhmDktqPc5rDk8apYwy9sCaCwIdl1Hp/fx+BQACtVgvZbBZnz55Fu91GoVAQRy0QCKDT6eC73/0uPve5z0kF387ODlqtFqLRKBYXF6Vmud1uY2vrsAiRDRcYwPJ4PFLRpu/TjE0wKEVJSsdc2+TaLNExD54PmK5Y1L/TZb1aA2j7X8PWfAY9v/qPzEupb0pWah6z7aYJyVJYWJYljdO8Xq90GykWi6INQqEQFhYW4Pf7cf78eYzHY0l/YZFXsViUDih62wfGXubn59FoNLC3t4dqtSodV8ygLedEa8STxqlhjFlc7PQ5o5usG2bgjZtPsjySnUE8Hg/u3bsnyWrj8WErFgCYm5uTrctIQD6fD7VaTSBQYuVkFGB6fzrgKACpkTO+1jlEPFZrG/7XdRl68XTaiNaaTv6Lk5bVTKjnVWsozRDAdOzBRJhMraivyViITukfj8dSxkqprptR8Brnzp3DeDzGvXv3AEDMZTr/vI9YLCZ193t7ewKfEzF0gmT1Z/o5Z41TwxjHwWgmAkJorl6vi0SKRCLI5XIYDocieQjdejyH3fv4m0AggFdffVUqzbxer9RjVCoVeDweiW7TOeQOTlwgPdFcXJ2NSgeQ6IuJ9pB59HueizZ9sViEbduYm5uTJDkd6+DxJtqliZvEaQYwNSNpc4h/ZtasCSZoJtNRf8ZVeB1uMxyNRsW5Zlq73iaAOVmvvfYa7t+/j263i52dHWl2Ry2Zz+extLQkaN2TJ09QLpfF2de5ZLwHrpOmtZPGqWEMPUwmMZ1GSmciU4xHsIQ1k8lIxw/a6wAE7kskErKRJCUaUaV0Oi2ESaSLgS4nG1y/t+2jvbC1uUTCpAPrhCxpFc98oVKpBJfLJfdKRtf9XbVTrk0hE7HSRG4ygTnvmrn4W20mmkiV/q3Wbvzc5XIhmUxKagcbTDvtoUitTaiXqBmfL5lMSicS+hYM6jEWpEEFc65Ns3PWOJWMwcGb12peB8BY8ri7uystWBKJBF555RVZoL29PTGJer0eCoUCzp07J6iSDsC53e4pTWGmMmibXJtU/J6Sl69JvJphgGk/inCvfk8EhrsGEWXrdDqSmuLz+QShIfO6XC6pluN9am2g00N4TQIDfK/BBGoNp5wjOrnUuPrZCVoMBgMBQlgQRs3HDAZGsknU7Pm7sbEhsCyZIpFI4NKlS0gkEmi1Wtje3sbOzo6gUdrx1uum79v8bNY4tYyhTRRTqpEwR6PDVphsDEY7ltBnrVYTxiCqtLW1hWq1ipWVFXESgSMYV9uypkNNZIm+hukzmBi/KXnN2IBpt2sUjHAto/mM8LvdbmkSzRR5mn5+v1/qsmfdg55HAFMEbx5DTcE6eaaRkOCZfsNtpfl7wrHc8pmMR7PK5/NhOByiXq8L0VOjlctl7OzsoNlsyvU0XM6uiFtbW9jb25Om2ZwzJ/+C75/Ht+A4lYwxS8Vr9UfThPu3EdILBAJIJpNYXFxEs9nEvXv3ptrD7+/v4+HDh3jllVckOKgdRq2CKfVouzJhMZPJTDni2gRiAhtwaCqwJ+3z2LzaEacmIqN0Oh3p79RsNuX5eW3WoTAFW2sN7WOYppxJMKYUHY/HqFarGA6HEnhj5gEFE2sndJES548tQPmeWr3X60lNDTV3o9HAxsYGSqXSVI+uUCiETCYjcY7RaISDgwPUajWJW5hazZxjk74+Mc43h9MCaWmmpTjVLyOoLOxZXV3F2bNn4ff78fjxY2xvb0vPqNFohO9+97v4whe+gHg8jmKxOOVDUML2+33s7u5KLhMXio4i2/1Tm9RqNWlNAxxBq4uLi5ibm5MoNp9F+x6sOOM9xGIxNJtNxGIxSYgjaJBIJOByuSSRkozIPTj4XhcXaV9EEwWRPTIiETseZ9ZJEEUajUbCGESD2FqTjje1L6vqiAKyrQ4ZgX12J5MJvve97+H999+HbdtSgx+NRnHp0iWsr68jnU6j3W6jVCrh/v37qNVq2NnZmUpINJl8FjJl0pg5Th1jOEGPpvnB/5qomGIQi8Vg27Z00Zufnxd7ndKs1+vhzp07uHLliuDeejNGpiyw412j0QAAMRdoVpFBG40GisWi2LjUZB7P4YY1gUBAglHANOza7/dRq9VQr9elBiQWiwE4srtZ/MN6cm5hRuTLtm1JyOOfZkDOIQeZWadZaFve1Jo0iyzrqEGd3nKYrTrNMlbWeEwmE1QqFdEeusae5lOj0cDPfvYz1Ot12TKBpbkrKytSDck4Fe9dFyY5mU8aoZsFmjiNU8cYHMdxs5Z4AKRSb3NzE6PRCMlkUgjs6tWriMfjqFarEn0NBAL49re/jTt37uDrX/+6RLOJ/HAHIRJsv9+XTe6Z0cn7Gw6HePz4sdQos7Uko/HUJkRSdCXdaHTYr5U4PLcSWF9fRygUkkBmq9WSuuqDgwP53u12C1HRj6IppR1tjRDxb3NzE9VqdYq4l5aWZMsvABJ/6HQ6qFargnpRMND3ASB1E5wX3gu1cT6fx8HBgbQP5e+r1SreeecdbG9vo9PpSA6b3+/HG2+8gTNnzkgLUFY47u/vY2trC81mUzTkLN/CFK7m61nDuY323/J4HgdJ2+WU8FSzlLButxvZbBarq6tinzPBcDQa4datW+Ic0h5mTQIzQTudjiSsEV70eDyy6SRxeW1DA0dbFRBq1IvH+59MjqoRyVjUOswCpgYgVEu73rZt0US8Du9NI09mzhBwSPCshNPSv9lsTgXJdM4U087NOmpdHEQtSnufiBn3z2BuGRn+4OAAm5ub2NjYEISRPbf0ugGQCLfOhzqpptuJZj7RzjcwO5lQf88FYHVesVjEeDyWAFGr1cLy8jKCwSA+//nP49atW7hx4wbG48PW9b1eD9/61rfwla98BdeuXZMCH0pC1ltks1lpUckoOWu0C4WCSE2NxXNLMsZHdJRZm4EcJEhqjXQ6LT4Gi5+Y07Wzs4NUKoVsNotUKgWfz4dqtSoazYRd9fxNJhOUy2UpCKIwoAbqdrvSeZ2ERNSoUqkILEyCpJ/BvQhDoZAwGgUIfR4GYxl3ePfddwWSZp/gUCiET3/601hZWcHi4iJcLhdu376N/f19HBwcYGtrC41GQwSKObQfepyTfRKDnEqNcRJD6M+4OFT7LFstlUriNEejUSwtLWF9fV3abjIFY29vD2+//bZIQ6ads/Mdg2l0vIEju50+CP0i2vxut1s0Bctu+Tvt2DLgp5sJAJA+uSQmno+gAOMZPD8jy4xrmAE8TSyM/2hTSKNHOrWCTMyYDFO7uUkOgCkNpsuNaYJRAwOQZgbFYhF3795FvV6fyiQIh8PI5XJYWVlBOp0WM5RMUSqVhCnMeIWmDxOVckIFTzKlPuyOSv89gP8CwMHTw/5b27b/7Ol3/w2AfwBgDOC/tG373550DfOhdAzDfEDTMQcg6ejE27e2tmQRotEokskkLly4gFQqhVarhfv372NjYwOTyQTRaBSPHj3CH/3RH+HNN9/E2bNnxW7N5XLSdVBLf2aIsvWOlq4kDEKm7KnK+yQuT39EmxrFYlE66rXbbSmt7XQ64thqqLTb7UptCDF/+gHan9AQMAmZMDdfMyMgEolgf39f2u8QXYrH49jb20O73Za8MRI0uxHSJO33+xKIJAE/evQI9+7dw8OHD/Ho0SNY1mEHQmYuh8NhXLt2DcvLy+JncFu4u3fvSlsdMjV9NSfo2Xxt0gq//6jO9z/HszsqAcD/atv2/6Q/sCzrZQB/D8AlAAsA/l/Lsi7Ytn18G+8Z4ySu5tBYvsvlkpYwBwcHaDQakpKeTqextraGwWCA3d1daWIcCoWkEwgJzOVyYWlpaar0kkgKNQsXXUeW+d4sJSVhahSJvglNDsKwDN7RJItGo2Iu6kZi/K+vZ86fmVRHn4XPwmvZ9mHVHbcUY4NrnR2sS2Z1/YeOeNPnYCd0j+dwC+P3338ft2/fRrFYFH+N9SaJREJyoFjp1+12USwWUS6XBdHSqN8HpR29Ts9DWx92R6VZ4+sAvmnbdh/AI8uyHgC4BuCd5/mxCclq3N8prqE5XmelMkBEjbG0tCQoyRtvvIGlpSW0221sbm5ib28PLpcLkUgEu7u7+Pa3v421tTVcuHDBnAcxg1i2qXcPpb3O9AymbDi1wZlMJlKaSwiUm9Y0Gg3k83nU63Vp85nP59Hr9fDkyRPRRrodpY5R8Dr8jvdI34NJkaVSCZlMRswUBgjJOKVSCfF4XLTRZDLB4uKiMBcw3WeLmpOxJLay+dGPfoQ7d+7g8ePHwuT0UehkX7lyRcCRbreLJ0+eoFAo4OHDh7IVGbWPiUA5WRCzTCf9mVmkZY6P4nz/rmVZvwngPQD/lW3bVRzunvSX6hjuqPTMsIwdlTTebBz3zG9nOeYa6WGiWqVSgc/nkwbPmUwG+XxeUpy1ORQKhVCr1XDv3j3Yto2rV6+KxCMcqpu26bgH/Qv6I7T/gWfTLvQiA0cp7H6/X+6bkChNN6JHDARqKa3f8z8FA7cgoJbQmcN+vx/xeBw7Oztyfmosrc1CoZDEFagFgUPkjVskEK7lvW5vb8uWy3TK6WsRIl5cXMT8/DwWFhZgWZbsyVcoFFAulyWbgaaeE8Km0cnj6EV/d5JjDnx4xvinAP5HAPbT//8zgP/8g5zANnZUMgN7Wu09PX7K/3CSFiQUqlza5rVaDYFAAHNzc0IYb731lkTHNzc3sb29DZfLJekK169fR6vVwltvvYVr165JrTKhUV3bze2weG6v1yvt82mWMfZBtIy5PdrcIeH0ej3JROXvSBjE+u2ngUXuIsUMXBJIpVJBvV6XwNxoNJI+WMFgELlcDuVyWfyvvb09iYksLi5Kxw2XyyUBRTItfQyeu9Pp4N133xU4fG9vT/axYEWeDsTl83ksLy/j5ZdfRjgcFobc3NxEqVTC48eP0Wg0UKvVpmq4OU6S9ibhm0jV85hTH4oxbNve52vLsv4PAP/P07cfekclU2OcBNfOejiN3xObt6zDpggApA1NMpmEy+XChQsXpA6DfgOl9P3799HpdHD27FnpXdTr9WTnUeBQW7DGmftd0DfQ6dJ0UtvttlzHsixBv0jUZGy/3y8OOuFTmkv0hZrNppzPhFiZSkLi7vV6gn5NJhOBq+nkW5aFSqUi0pmxHt1uR/eVorYj+sRWRffu3UO1WoVlHW59QJOP54pEIrh8+TLy+bzsJMXUcdbfNxoNietoc1GvsV5nJ3NJ04JmlOcJ7gEfkjGs6Z1Y/2MAN56+/lMA/9KyrP8Fh873eQDvPuc5n/nMRBZMLaEfnJ9pB9i2bRwcHEgf2EajAcuyMDc3hwsXLkh84/z584hGo9jc3MT9+/dFEsbjcZTLZfz+7/8+zp07h9/4jd+QPf5oZzNSzpgCU7/Zo4kO6/7+PtrttqRZ6/vVEXzWGNDeZmyFfkg0GpW6EhI9c8UWFhakuXS9XpfaB9awcxtnFmYx/lEqlbC0tIRWqyVp4oFAANVqFQDElGROExEx+gHVahUbGxuSM8XdbPkXDAZx4cIFzM3NIZ/PC0rHnVwfPHggLTgZqCVyZ1YWmv6l/u4kondyyGeND7uj0pcty7qCQ1NqE8BvP73QTcuy/jWAWwBGAP7RB0GknByp44bThOiJorRhdz0AIh2ZZpBKpeDxeHDhwgX4/X4JQGm/otfr4fbt2/izP/szXLlyBS+//PKUacMsWkKb1BYMjPV6PdRqNcH/GZfQ5yAEzM0cTciVUtvn802ZUjTrGo0G4vG47Io6HA6Fgbg3ID+nE85cJJpkhIZZelqr1QAcpd4w3Z1dHqkhdD9ZfbxlHbYCymQyuHTpkuzfR01WKBTEuW42m5JFoHPATNqYJfVn0cxx/uhHMqVs5x2V/s9jjv/HAP7xSeedNTSBm37G0/M/kxB2nApldJypBAAkeJTL5bC2toZ4PI4333wTFy9eRDabxfb2NgqFAu7cuSOxApfLhXfeeQc/+tGPsL6+Lk2Ve72e7GHHgCDNmn6/L3UiXHiaE6Z5QMDALPohREvNoZ9ve3tbIt7xeByVSkW6FNLvITGzuIcFXRpuTaVSkijZaDRw48YNrK6uYmVlBYPBAFtbW6jVatjd3UWz2US1WsWTJ0/EQSeyRvCBu1nNzc3h3LlzkjRI/2p7exuVSgWPHj1Cs9lEuVwWiFanoei1daKF56WnWTGN48apSglxQqaOeyjThnQ6H/+I0lQqFUwmE6TTaUwmE+n4wVSPc+fOIZFIIJlMijSr1WoiecfjMR49eiR9jFKplOQc8RrA0XYCLKJhwJG9ZZmlyj8GFdmBnMRGlIc5XmwBxDgHo+WMZFtPoVufz4e5uTkUi0XU63UJpPF+6EPQF9ON0dhBhQS7u7uLVquFvb09Mc90t3mXyyU5W3Nzc0ilUnj55ZcRi8WmtBvnc2dnR/oH69w0XVMxC1xxGicRu2mGm/TmNE4VY3DMgtOoLegccsyaGP05g3FMP9/b28N4PMbBwQH6/b74BdlsFsFgEJFIBI1GA1tbW7h//74QLrVCv9/H/fv3EYvFsLS0JCWehBe5yETIuPB6mzBqNEpL4AjxIYFrxgCOKg1ZRzEcDqei0LzHeDwusREyRzqdFqYymzS4XC6pMwcOU9w5N2ymbHYbt6yjfrfz8/MiWFKpFBYXFwWxGgwG0sK/1Wpha2tL6lxoPur4hBOidNL4IL95Hg10KhkDmA6oaZgWcLYRj9Ma/M14PJYMUsKKrIyjybS4uCjwZyqVQq1Ww09/+lNsb2/j4cOHsvEhE/aGwyG+9a1vIRAI4Nd+7ddw4cIFcZABCOFTk/A+qMlI/NQIzOQlfGvbtuQ0scaDxDwcHm4TzPQNbs7o8Xhw/vx5DIdDFAoFZLNZvP322wiHw3jllVfkesyLYmnwu+++K/2ZOEfa7NJ73aXTaUQiEczPzyMej2N9fV1SzKkB6VCXy2VpnMbGaHweCgm9ViZRH+c/OB3vxBSzQJtZ41QxxnH+xPPYhvrhtSSkJNXnoO1dLBbR7Xb///auJkaOowp/L/baK8+Mh9k/2zIWONhrK0oksCKUQ5QjEF8Mt5zIAYkLkeDAwSiXXEGCAxJCAhEpIEQugIgPSPwIiROBBMVxQuRNYqyYnSXrHY/x+I/Fu8Vh+qt98/yqp+3szvTK/aTR9HT3VL2uqvf/6jVarVZ0L/JNRdxH/eijj2JmZiZmprbb7YHSPPV6HdevX8eZM2dw7NgxPPbYYzh27FjcoGNT0QlUeWi0k3h0oqEumU+1h1m8AGKUnWkW9BzR5RxCiPvEL1++jFqtFh0KfFHLpUuXoorDXCpgo4oH31nRarWiyrl///4BwmAGMSUSUzm4f7vdbke8GUS02bF5qpNlgjxnYxp50sKq3rkerCJiaqtBRAJz9SkVtLTQx/phtBE+jEtYYHyh0WjErM6pqSnMz8/HDf6zs7NRT+Y+4+XlZZw7dw6XL1/GBx98EAu+EQemXO/duxczMzM4cuRIfNsrFzD70/VeV1ZW0G63MTMzg+PHjw/UqKLhSiO20+mg2+2i1+th3759qNfrMW2cOjoDg3fu3MHS0hLOnDmDbreLbrcb9XortZgsOT09jVqtFtVKEgQ3MWkvHGMbjOUsLy/j2rVruHjxInq9HhYXF7G6uhqlhFabdCxCz5c3h/cyt0VUKqp5N27ceD2E8Li9XlqJYQ1xyxX0PTznGWy2PT0ZIhvvu+BLJuv1egxara+vx5QK2h/knsvLy9i9eze63W70v1OC7Ny5M26m6Xa7aDabOHToEOr1OmZnZ2PBMb65iFtzqcdfvXr1ruAY3ayrq6tYWVmJBRHo6aL7l44Gtnf27FksLCzg/PnzAyniDNzpKD2lAGMNtVotlrwhMdAhQAlBdazT6UTJwL3Y2o6glPCMX884zvM0enPurSXbptYghgmEUkkMLRG0lLCZnDy24HmwvPQBO+j06fO93Hv27EGz2cThw4exd+9eHDhwIOryLPy8vr4eI7YLCwu4cuUKLly4EIN0TGTUO+CAjVd8MWhnd9xxseo9HWyH+riWCsxd4h5wVvtjDhifj22yaMH+/fvRaDTQaDQwNzc3sAGLKfb0jpE5cR4oIei5un79OpaWlgYkBCurkPHojFjLpOz8FZEQKZVLq0nDiGzbSIx7sSW8/3rHw9oLIUTdnWoN9WBWxKO7kXsWpqenIxE1Gg3s2bMHnU4nlrahr56RZP02U9objCqTi+kdfrSJAAwY5tp+0t+0I3QUncRG24NvhTp48CCazSbm5uZi3heNZhIEvVxalWVyJoNz3AXYbrdjOU3ul2CUPZUNm2JUeXPlzW+KgLz/ply2KSgVYRTxR6c4RiqmYaWIFaM8R25MLwzVhF27dqHdbseNOrVaLer1zPdptVqYnZ3F/Px89EBxsz4rfHc6nfjNsqK60ojGh2oRgUEvLnp9jfaBThlhkmCj0cDs7CxqtVpUARmIpDTQuwP5m30xNtLpdKIUYCkflhaizUKCsJmw2o7x5kc/TxGXqz5HgtVjp5mFVp3sehhGHKUiDA2pB+B5Hc+wC0sPkGe3WNBxEb1ngj74EMLAOzTW1tZQr9cRQoi5U7pgwsTEBI4ePYrbt2+j1Wrh5s2bMfLNWkp0iTL1hARF6aBVD24OotpF+0AXQeAL5/m6Lhag5ptpuQGLhEGJQGlDIqU9wARM5l3dunUr2jY6Ws3aViQIj3j1b4+B6YWcZ0tarm9VMqtGpTxZ205iEKytQdCcx2ZVenpkSpfV99CNy/s5gVqX5x6Iq1evxuIINKSZzk5PE1UTulHn5+cHJBKr5rFgMVMx9MLwJIm1uZg2QjWM7lm+WIXGMRkHs3k5FiR4zQC4HZV5XSsrK7GWLHflcesqbQfialM5vLHmfd6CLcLJvY1r3jyn1GqLS15fpSQMDSmuoEUzcHeFa4/L6DbteUoN3Q4nmlswNWFyU36j0cDa2lqMhrP4Ad9AyrL43CjUbDYhIlHiNJvNqIszq5epFnYLpyUObZ/ot8QSbM6VTUFhjERLMe4pp4eMm520Z0kThLaLNKTUIutit/Og1SMt+b014KllefaEJ41SUErC8B6OIt/eR7Aqlf6dGgR73SMuLVW4FZUSpNPpxADf5ORkNHB1LIABNQYLqdtrw5fuYmtDaa8WFzlT3rnFlcYtPT87duyIKSbM3WKCIhc37QTGXJhdS9WJ77DTaeaa2WjJmpo3Oz/enHn/SaWZ8zivD0tw/I8lkJQTQENpCMNDMjUo+nfRtlNbH3W7VqrYnYI8r92nNFaZMs1UkV6vh1qthqmpKUxOTsbqGjpS/dBDD0WXqlaDbJBT7zFh8TXmYYnIQHU/Sh6qPdybzngCJV2v14vRZx6ziBmfz9oLWoJZbp5SkYqAJ1nsfGs1LCUFUn3aORwmLYASEYZnH3iLmGBTPDxOpL+tUWalkSUeL7CoJQgniTq3iMRSoQBiFUHGBvjKZRJGs9nExMRE3M7KAgeUJszH0pyZXjPtNSKhMkOV2bP0EtHNzBq9NPCZEWwTGq1k8MYRGCxDo+es6Fxb9cpuMPPm1WNeRRZ9nuqWglIRxjBkPe6dsh2Au8Vono6a0lfz8NAcjJybRMVzjIaz9qwOoumXv4jIQJE2/mYf5Na6eqF+sywNZxII7QGqVLrEJ4nJ2ggp5lLkXGoehqXtpMY+7z7bjvYq5vVBKELEpSEMDR4B2EHWi94ucHsvz2sjMdW2XfQp3HSQzeIDbFQqJ7GwciAJR3uRNGEwvQPYeKORxZnntIuU6hWv6f3S+jl1O8TbXvOYhoYUs7Hfenw84rHH3hx7xOoxNCs9PMlgA6J5xFEqwvDEYR7y1lgm6IHyBo73ewtcX/MkUIqz2nvs/zy7AdgwqoENdYpBO50OwucFNvaWUKUjAWhCsKpOajyt1LMMI8UcvPvt8xexO1KqU4pQvf68tuz8azUsj/ERSkUYGviANo4B3D0AHtfSg2D/r397KkDehHs46t8p9UEvWN2WLphGqWaloSYMLfV0rMXaB94zaBw9XT31XHZ88hZ4kXvyII9IPNw8hshje58N+m4LiWEfXi8OPpCO1gKDYtyTBvrY40D23hQe9n95toi2B7xnJKGTIHSgjmoRPV16XwYNb7uIbeqFxT3FeW0ahpWaeeqUt8C9diyD8tr32ijaTx4R6vuta3kYcQIlJYwU8AFTm5es2pRqOxWvyCMo3U5KdbLt6b6s5NDGot5QpCfSpoXo1/VqnIZJN0+1tP/P09m9NlOc25tHj2BTcRDbV2ruUvPmtZXCc1tIDM+I5UNp/Vzfa8EboGHgLSLdVpE2U2pDqj/LsRm95m+d3q0lUAhh4JjfdpJTXLTo+NzLsxdpZzPb9NrOO5eCFHESSkMYhBR3sYtp2H9tG0UkkoUiuvKwe6yxbaWd5eYABlRHtuHFGOwzp54xpRKlrlupO0w650FK4npg1aO8TUX3Ymemfm8riQH4OS32XEpUeuBJhNR93mCmOJE9r++10o3XmMxH0ITDLNoU7lbFGkYoXjt5BOLZaCnYDOk87LqXHpLCO4/7p2BbEEbuHhyJAAADrUlEQVQRzuNNakoN0mANw5SxbfvR11P3ebjkLYDUJNqq5dqNy7a9OIzFcZiOX/RcEfWwiLpmxyQ1j96YFVEP83AZBttClbofiv8okOKOedKB/7tffZn2RVHcbO2svNjEMIkxLsjj8qPqKwXbgTBWANzIvkcCOdxxJoSQxKOo6jKszyEwgxGORQ58ZDyGqXajwiMHPuGdLEUxBAAQkdeCsyn9QcSjDDg86HiU8q2tFVQwbqgIo4IKHCgTYfxo3AhkUAY8yoAD8ADjURobo4IKygRlkhgVVFAaqAijggocGDthiMgXROS8iLwnIqdH3PdFETknIm+IyGvZuSkR+b2IvJt9t7ag3xdFZFlE3lLn3H6lD9/PxudNETmxxXi8ICKL2Zi8ISIn1bVvZXicF5HPbyIeh0TkTyLyDxF5W0S+np0f+ZhE0Also/4A2AHgfQAPA9gF4CyAR0bY/0X0A3r63HcAnM6OTwP49hb0+xSAEwDeGtYvgJMAfgtAADwB4NUtxuMFAN907n0km5/dAA5n87Zjk/A4AOBEdtwAsJD1N/Ix4WfcEuOzAN4LIVwIIawCeBnAqTHjdArAS9nxSwC+uNkdhBD+DOBKwX5PAfhp6MNfAHxMRA5sIR4pOAXg5RDCf0MI/wTwHvrztxl4LIUQ/p4d9wC8A+AgxjAmhHETxkEAl9Tvf2XnRgUBwO9E5HUR+Wp2bl/YeIf5vwHsGxEuqX7HMUbPZSrKi0qVHAkeIvJJAJ8B8CrGOCbjJoxxw5MhhBMAngbwNRF5Sl8Mfbk9cn/2uPrN4IcAPgXg0wCWAHx3VB2LSB3ALwF8I4RwTV8b9ZiMmzAWARxSvz+enRsJhBAWs+9lAL9GXzX4kGI5+14eETqpfkc6RiGED0MIayGEdQA/xoa6tKV4iMgE+kTx8xDCr7LTYxuTcRPG3wAcFZHDIrILwDMAXhlFxyJSE5EGjwF8DsBbWf/PZrc9C+A3o8Anp99XAHw588Q8AeA/Sr3YdDC6+pfQHxPi8YyI7BaRwwCOAvjrJvUpAH4C4J0QwvfUpfGNyWZb8/fhkTiJvhfifQDPj7Dfh9H3spwF8Db7BjAN4I8A3gXwBwBTW9D3L9BXU/6Hvn78lVS/6HtefpCNzzkAj28xHj/L+nkzW4AH1P3PZ3icB/D0JuLxJPpq0psA3sg+J8cxJvxUKSEVVODAuFWpCiooJVSEUUEFDlSEUUEFDlSEUUEFDlSEUUEFDlSEUUEFDlSEUUEFDvwfy4O1lfzk2zkAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 209.7x177.3 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ovtZ9tc8sH4ZooLbeVto8y/824FZXV2N7ezvG4/GgUsjXKHaN5fvz95qiyfNh1yOKImJ+QyPG26LybJQC2ShmbDN/xGPYxLNMYPav1dxGLlgZBI1yloaFkvswGo1K+hvpbtbsCEksF8bCfVaCtpItRL34Vm5Z0VkRtsbpecxuIc9jbV0slJ9aTMw1JmiVlhuLT+rJyt9za1egvxsF1dyDnqeszGqutKH5dMwoGy88bxTl2Aq/0/9s/dmatUHl8XqevB6mqcwrmV49jrw2tXHX1i3PS21Nh+5dpg2vv8eeeaVWt8dpfrKhBK/i+kRmgDQ8v7l/LUXBHFNq8qqmUCIen+jA833fl7hHxCzpxpsgF5VnoRQoTID9ynYfYZnZzWHGRZgDF/Okux2E98nJSayszI6dsFCv+V1vbm5ifX09rq6uouu6smvZwoZnWBiIDU2N5QFUzQTsYK4FOb5hMyoCgOsOKlIf59XYCmeuuU67zKutXwjLVr4VG5Ddgo05wMWXhZeD1C33UQ6qmcFzkNpCwUKO+fd8wDjZ+mZdvCYUz0+mN69Vy2ef59/3uf6a8mBNs/Xr852YQ8ZGm57TTNv02ePNSsFInfsd8zIPeq0Qop5D+sf6Z2Xk+4w2s4LNJSuwHEtEbnhu7bqNmG1K9Z+NMq7hduq6Lk5PTx8lBri0BLuVWO6/x1Grz/RnQ9p9dlJDLei8qDwLpdB1XQk8ZgvPhGTI5IVmEh1oNnHUrBPqOD09jZWVz9lE3G8BksvV1VVsbm7Gp0+fSr+dknp1dVUCfMfHxyWukAPN+OCdhUFeuTec9P1n3/D9/X1RCrZyIR7Gbh9w388yrLLV3/ruMVs48zv1W2iTxcH/CNc8FlulEDTKzHCXZ30eVSv7yDEF5qDvZ5k3+MD5RDnbpWMLOsNt6ASF/vDwMLdvBh+3D4qjXdYOHzZtIuDItHE/PX7aZt0tJBm7la2D8hYAo9FoLibi4LWfRblY+DqbzfPNOtQKc2/aYj0XFebTpeu66vVlnh1qlyQIr6PpM2IWrxmNRrG1tRVbW1txdHQUq6ur8erVq3j9+vVcnZYbHn+WJxmN5fHWFIqNGhsg0Abrb6+H945YCQ6VZ6EUzDxAM65jiduagXlsadi37YBtDvJyPSJKzvnKykpxI1FqliLPrK2tlUDcZDKZC/w60Ly2thabm5vlGQSLx+E4A9d9sigL65TUrBRsWYxGo0d+71qg2ZYEQTbmlIIgcWZYTkm1gMpIwcI5u3d89pHXkTlBEFjQ1ZSCrWvm0ejGlp/9xVYKpsOcBdV13aOzp2w8ePOTLVEYFYVeCzS7796nYFeNN5o5aIuBYcRhRWlUAE3AD4zFKMGWs+ckp5Xe3NwURQ/voGiZl+vr67LGHgv7ODY3Nwsy51nmEZcripD+EcQnG9GBZgLIDjSbzlHim5ubc3SfA83IFTLoWF/iiNAja3pyclJkzVNLRn3+zEjXvEeWX6ZtbwaFhuB92rMBNFSehVKIeOyaMLHWIKuhYrZIsp+Ua7mwsCCFnApa09aXl5exubkZx8fH0XVdbG1txeXlZWEO3Eu0iYbOSAHis1LgMysFMliyUvC4eNY59FYK1Jlz5tfW1uZyw5+qFBDshrJWCrbkvW5cz0rBFroNBFusNaXAd9YMy4/rjMVKwetKH63Q6RvzPxqN5nY0R8wyWzhSPVtvd3d3j47yZs68ycvuCwf2EVw2eqCNjBQ8VzXBzp8VDX3ISIG18kGKrI+PoqgpBVvbros129zcLAIuKwWepc9ZDmD1O1HD/GZlxNwyhppSYM2cTu1ArZEC/R6Px9F1XRweHsabN2/m1sT0lJEC16HLHEv095qXwgX6tayEDywToQWM638pB+L9lDKdfj77PZ+fD0PCXLaw8+R5QWBsW0YUo4X7+/ti8V9eXj4KSNYWiIn1zkvvpMSK4N78R730EbcDVmFtbvys3UcRM6XgPsDEVgpct0BEcN3c3MzFFqjHLjrmIVvWCDj6mpUCz/GbmSUjBYjYmVRWUrZY+d9utvy/obYLffB4sjvO/1thuq9Z0WX3m9tx8fq477bwPEa7u/LYvU7UTWHdEfh2HzF2o07ugebcX4p3SfMsdMl9pBKz7uYNhJZ3GTNe98c0s7KyUp5FwHsntnmA9uwqQYk7ZmiZ4nusAOFtlDWogLmZTCbx/v37aJXML5kGWm4j0xPXWUeQAuPJxq6VDmOkz5m2WuXZKIXz8/OqK8MCJGL+2N0cg3B9EfV0OiuFu7u7ckoqwjkLM39GPHYfOfDE73mfAn8ghohZXrQtLFupFm5GCjB19kfmo7NrSIFrdh9lpFBTCt6H0UIKWFisG8Rn1GPB6YB7Rgp22zimACN5M5bnj7ocp6Fd1rXFRHx6XrMSyIZCFsRZyLNWCGGuWbnbsKD/Zly/qCkrCx+dbWua62yipA8W+PY1W5Ez1uvr60LPFmw+4qO1o5n+QPPMK6iK/njdvG8iI9LV1dWyT4F5zvMYMXM9OdmDfnpdQFe4rBmXXUfmSZQY7ma3nRFnjbZaCML7Cxgnn1Ya/O7+m/ZZAyMF0xrju7+/L/HOofJslMLl5eUcHM5C35kMhpr271IXpQbPKJ502rIS8u/ZUoLAYfSsFBCiNzc3BTnAIAg872jOSqHlPuL52uY1mAnm5w+hYqEA0SHMzRCeKwgwuwAMWx3vsDXtIG226Oy/zkrB2Uesi9fBgjlbW14DYhZmomwF+rna9ZpFX7PwLegyCrPwt4LAQKCP2XKmH9CZhV+m93yIHP2yvzu7j+CTrFDoD/RkA4v+GBGwHlkp8GyOKdTQhN2bCHaehTZubm7mkKDnkTqJZfCsBWJGjigFxkZMIbvXMq/ZPVOz1F1qSCHTa0b8NVRZQ8TMjWUlCp05YMx4Yu7v78sJzkPlWSiF29vb+Oabb2J9fb2cMQIxsPC2LnOWkScyo4GaleRJxlLKu6Mj6soEKxRLan19/dFrFWHw6+vr0j7t5qwGC0uY3lZStvYZk5+F4SwYeJb7Heh0TGEo0AxhOZvEyMxBZT/PNY/FSMHuGDMZRM690ALogDY3NjZKzIDgH35oZ3TZoLCiiainAfq60YHXwlY7grfvP+/iZb0R1Ah+3HN5Z7SF55ArxgjRdMZa5xN7WWvTqHkgGyK2Mhk3vuecyeQsK6diWxj5pU01i31jY2MOzbk/+ewj1szPQpt8ZtTDs4wln31kF5bH4sCtDSfoz2cfrax83q+Q3Ufm50UlG3b+bhcS6MV/rE0NKdgNaUPy4eEhPn36tLBfz0IpgBRgHAZJ0ChiPgBphrUgt7LgGZSJC0Tu4CPHLtgKtHbOlqX93maO29vbAtsnk8mccOj7WeDV7iPGAfFa2NJPBxwhYLtDrBQgfJ61oMjuIyuFGlKImJ20WFMKRjsIdVvodoWZ2G3JZ4sHAWMDASWwuvr5bXdWfE6FjZht1KkhPdaPz6wMqJc58v3UZas7B5RZZ45N5/WsdkEgbHBBWpDi/qgpBSMFhCFWoK191ho6zErB2VD52G2Kz1PK7iPoAXq1co+YoQ+fV2X3Ee81N8rPz9qFYvcRdOA4llGGBTrrVlMozHMt+8jGEQYYBuva2uczkLiWDbgcl8z0Z1qy4ZtRg/tgoQ968dqZh+Bvy8u+7+Py8jLu7u7i/Pw8FpVnoRRub2/jL/7iL2J9fb1Ye56kiJmVasHke7J1nGEWxYRvv6uFVL7PBSIxQ2RmtS8ehMBf9lUiUIHREfM7cGnT4zDSgaD8rF0h2TI0s6AsnPLruUKJ5MwQz30mSvpDH2pMkhnP/1uxb25uFiTAu7Q5YgTFaAPBAp26WFtfd/+sIKxMrRSMNDISYp7sLkKJc5x23uiIoXB1dVWY3DQE09sAyG5B+46hRcbAdVJAa6ekMj6Up+nJ1nVWCrbwM1KwEM6CneusR27XAs/tGil4LVmPzFOL2rVhZL6Ar6E9o2lb6xiqGJLOOFu2ZISc/8yLNsa4Rvvr6+tzblvmzAqNNSa++atCCldXV3OHTTHI7MPOzJiVhS0/u5bMMF7s7D6ouYzcHs/ZqnfAkJgCY0IAZKVgFxD99dhqyq5l+fpa655a3RGzd7bmcef/TaD+vUXgtJ/deyZ4/mBCW/xsuDLj2ljwKahGeDX4bSMiK1yPF4YyBOe3FsTPBeFrt2VEFAWBUsCthFD3XhorBcdk7KPPbgILdJAs9XFfpiX6WXN3PFXQ5VKjUYrdrU+9J18f4tdcatl9rZL5D2Wwvr4eW1tbc/Imz5952v/7WnYdtejLdGzeQnHbpcjzuJXsESFj8lcTU7i/v49vv/22IAVPctZ+mdjsCslCwcLJxRYXftec8ePn/B0m8lutWkghowTDS5jdwj4rKrdv4VcjMogjuzq43wSaYwq2kvLzEfMBeyuDfL+VMiVnkWB12V0FEXtXNPVneqgpJsbpeI6DoGZEuyc9FitV319bE9Nb/u51sULMfmrTM/02yvB3+m20YBpoCTvmwnQNLWZkVHuWfmf6r6EDfzfyzM9SZ0avzEd+1nVGzOjJY3jqs17HHJTNtOHrGKo2XHz20VNLFvZZKdTcRzZs4BP4h75YljHvGN3Hx8cL+/UslAJ+USworMeIeaK0pRMx78Kg5ImtCXgzspWC685tUoDPKIWMFDLjZiauWQ/LFFuQtWLfLWURw+fv+XnfYwEa8fhIjJqSyELYsRAjJwtOu2IY9zLF6+Z599zTPyvJrJh9n9FpHtsyFmqrztafx+JxWGnYyDAioA0jULuKarQY8fg4bl+zO8f3W2DmObSCrhk31GHUnQ2j1vW8znyapxh/DVl7v4751dcoNaRg5UB9ttRbJdftNrKBYwVAyW1npYAr2qnjji/Ya4G8GyrPRilcXV098rH79xZDtqBbxMwKs2LIv0Moy8JQFpjnWv7l2vdMwJnwzWS5zdp9+R6erSnBIeuu5UqjnmzRUOyft1WTkV7NjcP/Dw8PjzJcqMf3tvpg4V/7y2jCY7bvucac/s1MuYxgd8kMj3XK/6ZRfN0RURWsVhTQYRb+lEyjNaVghJkVa40WMur0s1mAZwTWup6ftUFXq9P9cR9z/fl6jqsx36aLGg9Y2bJ+XdcV6/unlCEDo4Zk+czZRznWETHjOdMKmXG/mn0Kfd/HZDKZy4TJjB/x2BoeYsT8bM0KckaHBdwyVnxWBP6eLSJfW1awt65nYdd61uNepBTys/n3GoFyn5+x0DSMtzsoKxWsGvy1ZIFtbGzE5uZmbG1tFT8uAefNzc0Yj8exsvL5jXns8iTw9/DwUFIII+aPkvY6u+/8WdAxVltdPkIh+/lpwwKbObD7wdk/KCeyeqwY2ENCccaNLVT3wzGIHGuwUjCt16zvGoKgrSEa9vWfQynUns1tP1WhuJ/ZSFvGMDJdtGJUtTqeihZqvBIxf/qtkzSyUvD84om5uLho9pfybJRC9mFmC89EPKQUFgnNiLpAr1latQLx/KlK4edCCkPWWc1izqWmFPJ1E25NmLrd3JaZyJYWFg7EjEBHKWxubpa/9fX1cu4MSoFsJH6nDnY7k87a97Ozb9yXPI7avHiMCHTmOrs1uceH5iH8XQcuUpSG5957TLBMLci4Bq/UXCotus+0WDMaWnQzZGC4nRpt1/oyZKgMxdXc76F2W3NQezavYX4+o4oWbecyNH5+p92IeXSTESK/5fVGZqEc3FejcmJTJPIsKs9GKZCxQ7EGz4LaC2HLj5IFvCez5ZusCYYhaz4zRL4nt7UsUhjqxzJIoeaLz8ztUrOah/plhZxdKTmQ7ADyyspscxmCHOt/e3s71tfXYzweFwt/e3s7Njc3y2+7u7tzaapWCs5eQijn99TW1qulzG1BM7a8F4L7EORra2sl/55sDzLR2I8AU5KCOplMYjqdzu18J74G5EdxcA8ZS+Ttk1XiTXQR8+duUcwPGT3keVlGgdToyfUMGT3L0HrtelaAyxpVretZAdaQglGkFUFGbLm0eD0rlkXfM/o2YsD4cOJGRjDT6SzDbRl317NQChSYsaYtLdQMbS0E86Ib9ru0/K61/uTv7p/7YALIyqBmybWIekjg1xg4z01L2bQYuDXOFuPma1YKCE9nFxkVsPnHSgEFwDiTTDoAACAASURBVCcW/s7OToxGo9je3o6NjY3yvgsjh67rygmuMILTk+26ybRTG2trzjJqqO0F4bWsjouxOYr0WW9k9FlWCHy/e8Fn7tgiXFubHcEOcrAPGQRSG0tN4NVooEUjNQXRunfoM6PKmmDne+YNI73cfo49tsbmdhehLfczywgL3xoNDSmFGg/l5yi1+Br1OpOtVoczrpyUMFSehVLo+1lmTYZoVhQ1Jq35GBdZM74+FGhuPdv6LddvyO5+5e+tskjYL1Oe8lytP0YInndvNuM7rh8CYFjxdv0g8NfW1mJ3d7cIfCuHjY2NuVgCSgD3DMLXG3roX0aHEfMBW9bEQUej0ZbSzmO3kDKq8LxBnzAmbWJhbm5uPkpBBSGQKYK1D3owUuBedk3zuxWNEQXjZIevs5laBkeLpjJvDRkW+Xqt/nxvS1lky7zGU4sQREsZtdByRug2MLLvvjVfriu30VISmf5slETEI/p3e9Az8g3kuky21LNQCpTaIvrPpWXJRcwHaoaUAkybLZAhSypbnBZE/J7/rymGWv9r/az1Y5EyGaqrhr6WgbmZOB0kdhAVRIByQMCvrX0+h340Gj1CAbiNxuNxOVsGReKz9y38cx9rY3H8x2tdowmYxbteM0LIJVuxoARSeJmTjY2Ncs6RkYQPI1xZWSku1NXV1XLGEEjBAWpbh9TjoH7EZwvRx2gwRmcrtegrjy3Pcy0I7e81Qy3TU77eos/aXLfqrPEw97SMytqzWWlkeQQNYhDVSubzVn9qtNVSCvyW46605ywrKxDoYhmUEPGMlEItk8O/1QiQzyyE86TmkpGCEcrPoRTyn8syiKTVfosxhkq+t1bPEEMyjw4KI+jIEoI5MiIYj8cFGfC5ubkZe3t7sbGxUa6jNFAmRhsgA7b2O9MiK6WMFmpojYK1jhCm+EgR/5atMeYnP+vdpD76Ih9UCELget/3sb29HX0/2/TovQmgBiy+6+vrmE4/nxnGYXy+Trrk1dVVPDw8xOXlZUEJPpeJfng+QCxGXaaVmnId4sf8fYjPai6gmnCtWfutzKgh48vP1u7JfTYq9FizrFlkbLUUIf9neeQ/+uDEDSsOowHayGs6VJ6NUoho+9Rr9+XvQ1bAImGaNXHLSsjPPEU4P6X8XPX+lHryPBgRZGFtF5GVgC1/kEFWCiAFxxp86qNPhLRSMCrJDJHXvuYWwfAg7bOG5Mz8Q/PasiI9lz7jx0oh+4UjZgrGbh3gv+MPZFdFfD758+rqqhyWyHlKXDeCIJZBBhPohHH4JTW1MWeBn+fDc/9UwyVbvfn/ZVHHTyk/ld9aVn4NAWTk6U8/m6/nelrPutTQzlPKs1AKNWs24vEE1AglCzG+17KS/FwLGrb6ZaExBP/MOD77ptaXmsU01IenlhYxtOBqxHzaqDOHENDZreOMIWIEu7u7RfijDHAjOaMIhMArSjnSwpkUIJKc+eM5sxB3RojPE+LPJ6jmUz4jHqdE58B1DbHSpumBenwku+kTC90CL+/2ttIiJuBjPCKixBQuLy8LImCT0s3NTUwmk3Kd7BN2t3JIGigD91VGEPSTtjMCqyHj2v+19fM8LqLZ2n2tOofo/Sm/Z+FqQySjx1q9yyi02liGkIKv51gC9dSCz8uWZ6EUIh4La65FPD6uYciSodRSM3M7EYuzjxZZi4vaGEIUNYb5pdBHq2RCzGmlKAOnk+IisgtoNBrF/v5+jEajggRQBsQKnE7quAEIwXEDoxPPTXZlZIva/nIgc1YKztLBas8K3kqBzxqjZkXkuXQxonE2FPcaPbgfpg27s+iPs66m09mJqKPRKCaTSXFP8d4P3jlAnMJHuON6AlVkdIMyi5hHM7V+Mo6sQJfliUyjLdngtfo5eGeRELUs+qkpqfxWQw98H1IKOX6U42zmB18bkmcuz0YpRAxDpSFCqt0/FCPw5HBPvt/3umRFZcZx3QilZcvQ2IYYaAhlLCqebyMDxwpIEUWAY+Uj8Pf39wtiODw8LMrBbiTSNQk8O62U61YAXkfHmrL/22cCWSlYcPm8G/vNEXAtYQzj5WPDM01aMZg2HGuwknUchPvM7Li1QGf0D/eQUSiKDUs/YnZ89PX1dUwmk3Iq5vn5eclSOj8/j77/fMb+1dVVcUkZbVxfXz/KdCJtlnnMLw1i7DVerQnx2m/5ek0h+Dc/30Ib+Xq2/nN9rZIFtHcO10pLKSxCCm7D99SQQkR9zr23wZ/LlGejFFpIAYZzqWlX7vdzEfOIIaME/z5UX6u/Q/f9VVj8y0Dn2v3Z6rDQQoBnN9HW1tZcxhBoAAWwtbU1hxByABnhn91GRideMwt2BDnHTg8pBa77e1YI/r02LxGPlYID2lhp2aK3P97CAh++z723MeL0WKMIKytn1FmB2Orvupnbz+iHcnt7W4L5oIfNzc3iRnJmFDEJFBTKgewn3++UXx+zQRmylIf+r30fuvaUsoyhNfQsqDMrqp/Sv5qSsPD32kMvXG8J+4zg7I5cVJ6NUmhNYp6gIQuk9uwit5D3KWTCzN+Z3BZqWQbN/JSyqF7/PmSdZIFiAeKNZSgBKwOQwcHBQWxubsbu7m5sbW3FwcFBeY6sovF4PJeNRMzAiod2I2auCAt8/Nt5wxf+bpRBfrOdM3by0eXeC2CkkGG659H+47w5zpuXGEstIyTHZzijhnpz/MSWaLbyPG+uk7bJdLq5uYnRaFRSYXd3d+diCn3/+c1s/N3f38fFxUXZaX11dRWTyST6/vO5ZPf39yWjibgD74dAWfd9P7fngrU1krLhVqPbTLNDNO16fqmySDn90kih5j5qGcW1MtS/Vnk2SmFIcw+5coYmJqOMmsCvQdNWn1r9WKYs4/r6KfW2iLZGeEYFTi9FUOczhvD/O2Nof38/tra2SjB5d3e3CH6yj1AoWSkgAI0MUACkW/qclqwUai+m4ZNNWhwlkQWUlYRdHl57zxnWGILZh4/5fwvuiFlcxtlSxE38alErDCMH1qYmKExLbtN10beI2eYq+sQOax/NgUsPy59P7rObanV1tcw/z5Ii62C9XbGZf2vp4y26/lME/qJnhwy71v21MpSNtaj91v/ZmG0phUVtuC/LpKJSno1SiFjsG8z3PoVgWgphqNQIZ8gPWas3o5s/ldCH+pr/55qVARapg8fOInLMgM/xeFyUwsHBQYxGo5JptLOzU4QIriW/OtOuDAgTgc/O3clkUjJoEPT5/B/O+Knl63vHr5VC7R0E9svnnPM8ZxGPs4+yUmhdd5zEKGx1dfZqUe7Bvcb+DhQD7rWMBrxXo+u6ciSG78l7PDgo8P7+vhwRwnyyHsQULi4uYjKZlLOZzs7O4v7+Pi4vL+Py8rKgDO+PwNVkBJHRX21n+U91vf6piPyXdO8uy9+Wc/l7psshuZEVyJ9anpVSaEFIM+sQIdXgV01o+3tt81q+Z+hay+IYIrohdNK6f5l7WjDUuf8IG4QU3/OeAoT+3t5eQQbEFEajUVEiBItHo1E55dTHXVghIKRxAbHx6uLiohzry+8IKL8cBFdHPgqCT4QQ6Zq1QKi/t4pTDXEPWeD3fT+nEGzZOVBPPcyTg/Xc44A7Pn/qQIj67XPetEdB8FK834Hx+H4QBHTigDZjA9kQU2CjnU+BRSnBQ27Pr4psWan5+jLG4M9dFnkfhoQyvNUqy7qP8vWWm8i0tizK4dqvckdzxGNhmV08lKHB157LENb/t1JXc121MuTyqWn/Vt8XtdOqP3+HkOzXzhYplmo+lTTvNvau462trXI0BcrCG9S6rivCDWGJpQ4iuL29LcL/8vIy7u7u4vz8vGTDWDmQXw+K4Bks27wbFwsY5ZORgOcXgVibS8+pg3vLlJxNZDeZM7l8ICBKmU18KF6fHstzKAbq8rsn7PpxeqtjJ/Sx7/u5FGCERdd1sbm5GRER4/G4KOCIKOtCNtN0Oo2Li4u4vr5+pNC9w5q196Y7n7uUFTbrVON1I7mWgB76P5dcT8tVnK9lOfNTUlLz9RbKz3ydjdf8XO2aY6CtjYm5PBulMOQvMxMPae5atkZrsY0U3L7rH0IAOSXVC90Kqv3UsoiA3X9nJMD0tT0GWPtY+Hm3MRvPiB34tNIcPwCFILhgFvz9bKQ6OzubUw7n5+dxfX0dZ2dncXNzE6enp8UVdH5+Xp5FGSBsWLe8mYqS1yOXzByZzljTWsnt2cjI2Uc5IMz8tPZ6XF9fz23uI2MJlAF68JvquIayQzHhsrGvn/7Z3VV71wSKndNd19Y+n9rKeoMayEZirwN7IKA3EJvjEmRi0ZZ5xTyY183WcebrmlIfMiJr9y/Ln9noeipSWGTQug3/3/J+1ALJ9M1IBnT3q1IKZq48mUMZPy41wVAjMF9bxn3E92VdRS2F4lKzFpZFC5mYsyCyu8hHUmCpevMYVut4PC6IwEhga2ur/GHFOiBNJg2WKZkpFuinp6dF6IMIUBJ8YnXikwZNkBmTd9nmjVN5rWquv9Zc1hjFCsJ1WIhlAyAzP38gGR+HzQYxhOrGxkbc3d3NxXUuLy/LPg8yurwbHAQxnU6LALcwQPhmo4px+H8LOxQLMSi/WzsiygviUTh+hwV1IYScKRYRc4f61XjUxlZez0XGVba8vXatZ5/Cd9Tjuatt1HPd7letb0OIPyuv7D7yulo51RDMr3Lz2rJIgeuZAGxp+K8lxGuWSO0+fzcqaG1ei4hHsD333XU/xULJ487EYgvPaaY5iIybAnSwvr4eBwcHsbW1Ffv7+8V6rSkFdifjT2a8uH3u7+8LAjg5OYnLy8v49OlT+f/29rb8fnp6Gnd3d0Up4CrykQuL3HtDa1b7rYbgaszooGitDpgsf7pu/+927GJyFhjuJOaYdaqtmZU3LkG/vY6dzSiHPE5voMvptKAHI83pdBo7OzvFpcTGNxT/9vZ2PDw8zKE/FIU3xJH55J3U0DX9zG6/LBOGBHyr1KzxmkFWUyi1uozEF7XZUhZD/9eCx1bclCy3aMsKxJ//v0AKhuUtYsiMGDGbyExg2YJ0Boqfy3W32myNo3VPHsMi6yeXrCgNFTMysJDhfQWrq6slPkC8wDEFW6IgAgQTlmPOKkGQY92fnp7G1dVVfPr0qXyiBEAG+KFvbm7Kc/ih/cawIcZcdM1BYteVfdi5DKFC6vP880wNrdiazL8hBPne932Zy7W12VHZo9Eorq+vY319PS4uLopSIPC/srJSkB7KezQaFSue7Cb6a4GGW8j7LbIFbLcSNLC5uVnuw/L3DnHGBK14PZwq61hQVgRWGK1S8yzk/xddf2pBHi16P0Gr79mQrRV7LizY8QQMIYVsTFnR/qqQQkSb0Yc2YAwNEoGZmZVPK6GaFq0RnCeZNlqCpfZpuNyyJFpjqVmbOasIVxAIwa+23N3dLaiAoDFBzd3d3RiPx3O7kQlO48/GsiRwiGAnPfHk5CRubm7i+Pj4EUKwe4jNUN78VEMFNQhNDr53GpthcGGQPcN3r4PdXP7fgi3i8QtdImLOus5ozZ9uy0dQeAMdApFXJHJiqd1/CGIremd/eY3H4/Hca0wR3qBB5sjGA4oD5Act0Wcri2x0gHLYMNf3fWxubhbFRd2kwV5dXZX72UTns5jIWjJPZcXa4hnz1CIl0no+G56L6mJ+Wu3+nEgh839NVhr10adsvCxTnpVSWOTqGdKsNQs8ov76xZoVN1Rvq62famkM1Z1LbgfCgMGdx47rwK+5xG0EMsAtgZJA4PMdhbK1tVVcCRC+89AJFp+enpZAMu4hlAJKAoTAPgQ2mrWUgb/bsnVuPhvAvOfCsQ4EqJ9hvWvvUUY5eW9DphFD9yy8a5vZGBvxELKwcm6/4yQR8+jWygpXEEF3v7zn6uoqtra24vLysgjgiCgIgrkg6A2t2MWThTP3m4dYD7sp6aMLioXxex2Ye+grYnaibUZe9hQsy1NPEYCL6qrV6e953JlX87X8fP4/o4hstGYarCkzF+YOml6mPCulEPE0v2BLESxrgTPRT3URLdPXp5aalZL76awRCyEfY21/s5UBZxOtr6+Xg+u4vrKyUu5FeOBHRngj0ElLPD4+LqhgMpkURIAScAYRwWKEn5nN7juErAVtPnbDY3W8xGM3womIMpaImNvwBnLJ6a64O1rIpe/7ueA96AzfPgqMucMthruMOTw/P59zo7Enw6/OxMXkY77tKnRGEwZBditZ2RttbG1tRUSUZ0EMtv4JVmfU7ZRWCnRDP0AO0M1kMimvIEV5kcGEqyzHGqwUrTRr/OO1GrLea7/VZMtPKU+VCTWFUOP9n6v86t1HtckYWsj87JBrJ6MGw65aW1kjQ7RDfsNlEUUmhtqn0YGFgncmb25uzvmVc+wAZeHr7G51oNJZKLg2OGXz7OwsLi4u4vj4OK6vr+P4+LgI19PT0xJIxk3U931BBlYIEY+Z24oOlIPLy7ulHfPwpjvG5jx+6mWdrRS8T4JMJyuFGtqk2FWHK45+si6gKxAJwj+n4uJe45MdxATbbTVnhWpBCeJhV3dEzCEIUB+KAuWDy4kxcewFyhQlh/B2Kia0At2YPukvLiGUPgoH9GD05rRaozSXlkvWPOPfh/jtpyB+G2850LwMUsh9aPWrhhR8PRvFteC040G/un0KEU8P6rq0FEgtbdHf+b3mP675HflcFo0s6nMm7Lz4DjJ5l7B3I3tPAYjAJ5kaKaytrZUMI5RHxLwPHsFJcPj+/j4+fPgwpwRACggyLF2nj+YzhrLFDSpBSB0cHBR3x+HhYdlJDVIwgsi7sr2bOiLmYiAwBPRA/xCMm5ubc4HuiMfM5JRKB3D9QiH66XxwEFJEzL3Mhg15HCtxfX0dnz59islkEu/fv4+rq6s4Pj4u7jqetcvNB8+R7np5eTmXHQaSoV8ZKWAQgKxIVcbK515oDiGPywlFY/QKPUGvxBQuLy9jNBoVV9p4PI7r6+sYjUZxf38fo9GoxB18nhKuKDa+RcTcetZ4cRnlsOi3Ib6lLNodX2tjkfGbhX8rg6jl0rJyWDad3+XZKIUWTPJkLBpYzrCoCd2IeeHuzWsuFmLuS1YmWNQmzOwiWbbULAJbXjA1QtEuA9xFRgSkMTqdESvcfmWEHL5kw30E0/v374tSmEwm8enTp7ndyLZsvalsqDCO/f392NnZid/85jexs7MTu7u78cUXXxQ3iH31/NFfxxS8mzpvdjJ9YaWiEBGorC/1MO+MyTupUUBOEaUfpgX6HjF7pSaKknniqA4U7mg0iouLi1hdXY2rq6s59FBzcfnP+wIQ4AhZxkU8go2ANaUQ8Tke4aM3ans0GKctZ1xEoAIEp5EC6+U1gA77vp87DTfvCzC/tQTjsh6FZUpuAzlTS0l9akyhNY5WSiq/ec5bCAF0lj0bi8qzUQomNk+mr2WIOCTIhyx53+fNa617KFkxtdxDuR8Z5tW0em0xQQdYXM4oQhhxnDWf4/G4IIG9vb2SieJ3Io/H47lANcFf/NvX19fxww8/xMXFRVEGP/zwwxwyID8d2J8Dxp4Tj8l9f/PmTezu7sa7d+9if38/3r59O7cvAuHtOhEIPsKDeWI8mYY837Y47RphHJ5rBPp0Oi2KDxcTCgCEgPICbUXMrFn7x2HMPF8PDw/x5s2buL6+jtevX8dkMonvvvuu7Ac4OTmZOyIE5eBDBHOmE8qMneCMifGhwGrHcEREQQokI3CkCTQFykNBgtiMIMbjcfR9X5QQ83N9fV12R4PUcHMRQMddhXvSb4aD5hgv89ni/xa6z/zbki2+5uBty91c60O+3mozGzH+hL6RWa19CjmB5ledkpqFZ2amliCuWdktdLEMEWRiyu1mpODn8t/QePO4bQ3ktEQsex99QHoi/u3t7e1HWUc+vI6skWzNcgopZ+mz8ezs7Cwmk0kJIuMHRzgugwrs+sJNtLOzE+/evYu9vb343e9+F/v7+/H69euSYw8ywMrMisfHNNgislLI8Du7HhD4Tl3FenVGEYLI5/Ywj6xHDrxmoWHUZ3+5aRx31sPDQ2xtbc25ljg2Ahfd1dVVTKfTErT2qbJ9388FqyNmbi/79EEPjAfERLAXheLjLEajUVE4zj5ySi4ogHWioIyur6/LHNA+Rgn9WFlZKdlauARRAuY3+8otMGsGZL6W+bD1f42ejd6HZFKNL7LBUmu/hRScfURfhvrpdfnVIYWI+gagoesuGVK2lEJ262Bp5PzyVlu003IfZddRi0iHCBR0gODBV+03n/GyG7/oZm9vL3Z2dkqMgUwcrELGi3V5cXERfd/H+fl5cQe9f/8+JpNJfP/99yV2QFDWLiKEdXYjeEy4HXBXHR4exvb2dvzmN7+J/f39+Oqrr2I8Hsfr169LLn3XdUWwEax03AeBZkuRtYZJ7Z6gP079RAFidRNMhwac/smc2c3o9UWA0Tf3gzos/KjHaab8T70oUSsdKzDTKqfH4sYjLfjs7Ky4noijMF+kiCLQnbQAvTDPKEiUOsoLNEGQmgyn3d3dmE6nhRZ5fn19vbiEcGdxQCMuroiIyWQSe3t7JZvr5uYm1tfXYzKZFP7y/KHAQEo1t23NA2F+q/1fE9zct2jz47Kl5T3IMsWfKGCMHSvkjGTgU39fJi312SiFGszj/2UnflnXjj+Hshvyd+63BcvCtNpY1P9sLfAdoZKzjBCeWNQ5jRRBjNVr94sFKa6I+/v7ODs7K7uQiRmAFDh6AkvUO1Cp1wqSfhCYZD8Eimx7ezsODg7i4OCgBMIR4NSVd8bmXGu7ZVgDz7ezW1yn4wL5zWEWkl43++tNA/k3X7NyNPKDgemvGToHLI0WvY52q62vr5ezpMbjcQme39/fx3g8LpliDw+zI8hRCrTvGJB3Uvt3Zx9FzFxwCBuULErXVrsP9fOGOOie8WEEQPPQUUTMuZO4j5IFZA0ZtPj5KfKiVlpHoXgNa3XUDMOWIvL92dJ3EDnLTGI65oFF46E8G6WQSw1a1RbME1JzH+Vn86etyWWIItedoV62bGv11AjJ1q4tNJ+Dg+vFn5ubm7G/v18+fW4RlhhWJtYy+wo+fvxYXqjyhz/8oSAE+7BxQ+SxZCFIjj5944U8uLPW19fLW9tev34dBwcHcXh4OKecsZx9vEGeb/cDIYdA4GgHW+AwiJVgVnR2MSGgLBhRJMRfYLiu64pwxJVF2/yxyc7KzmtOWxsbGwW5IYxBC45xED9ib4bPmur7Pj59+hQREZ8+fYqTk5P49OlT3N/fx8ePH4ubiTOncEGBlrLr0i4Hu+dQEHYVYazgsvRpuzYMQBLEJ/q+n4st7O/vl42R29vbJfZwdHRU0qA5UdbuLwfUbRXbss68l7/XlIj/535npmV3zlPKUF9qv9VkT0tJOAPuqeXZKIVsZUUMB0cWWQRZG9c+bW0uqxTy9dYzQygh99O+QoQ41j6WP7EBp2AaMVAvvniY3cxDmilHU6AATk9PSyCZw+nIiLFFmNeq67oSn0AJjMfjePPmTXl1J/1bWVkpri8sPYSr58JQGMI2oWcr1vMJQvDa26eOhYuyw6USMdvLYIGc19frmZGE3UcoM/u7OcWUPuLSIciNT92pvAhfu5H8Eh4bNljVOzs7c8aSrXDiRbSJf99HXDO2fMwF/3Mtp54irBnT5eVljMfjkoZ6cXFRaGB7ezsioqQZ44JDYd/c3Mz1ByUQESVtFRoy0hpyHxlFGBXwWVMavheaMz1kYymXmmzwb0Pfh5BCTlE1yuXT52rR1yxfW+XZKAWXIavai56RQE2Ttp7NRJCVQks50E4tpjCkCFxMkCyoj6rwwXT7+/vVeMHh4WGxFnd3dyMiyvk3PtYB18F0Oi1HUoAQvv3227i8vIyLi4v4+PFjQRE+6sH99R99BrEQMD44OIi3b9+WvkGkCEzcSriYsnVKSqIzeczUMKENhlY8yeiIs3awkFEKETMhl63kTIOZfmjbAskbtbgfReUMKcZAkJU/+gviYD+Bjx9BIFOvkQTK4/DwMI6OjooSYA/ExcVFfPfdd2U3OrGH6XQ6F3/wxrnsUrPydl+c0USaNJv7vEcG2gb1oFiIU9hd5kwmt8kudOaxxsM2GvzbUy3omqyImMV+WvVluqn9Vvv/pyAFy6XMV773V6UUMtFxLeKx37+1CC0rocbMFBNUfrbVRp7cZSY6992Llt0NWIR+fwEC3y+3IcYwGo2i72dv1GJc5LVfXFzE/f19HB8fx/n5eXz48CEuLi7KhjTeveu88DyXOW6AoHr9+nXs7OzE/v5+fPnll7G/vx+Hh4dzAsJBwOyKyIIYqM98ZD+/LXrGmjO1PM/2myO8+WNM7o/XwsIkZzXVDI6sLGq0YUVCNpNjHO4r43CfPEe14rmwEgGhEIcgi6nrZnsxmGvacaDdsROEj/mVfjuQ7p3RDt47PkCyBMeXRMzQx9bWVol3WPHiMsx7GXJsyXLD9JDnbpE8aV1/Sl2LSk1J1JQB9ECpua+YL69hdl0OlWejFDKjWTm0MoNadbSQgp/n09kruf6W68cWa01BZAslf/cngsjBQweQa0rBp2NidSMwbYXe3t6WQOTt7W18+vQpTk9Pi1I4Pj4uvvarq6tCTLUxWyiTf763txdffPFF7O/vl30GKAgHEAlCOqBrhYAQsjC239pM7uMjnG7noCzPOyCN8PChd97QkxGLacKMl++vzVELbVIc7K8Fah389ty4by1kzB9KGRQREeUIC3YROx6CUDU/GC3Qb4/VCJA5d9B6Y2Mjbm9v54LXKD/WdjwezwWnjXxQZBGzlGTatVIgYYD7WHPPE/1a1vgbKtCd+S2XZZVDDRHwvYUWsvVfqxNDh/lbxoNBeTZKoYUUfM2D8oJnJLCoHX861TDXtczzQ/e4vix4WDgHDXET4Z930BbYzdHW3kHLhiGYEWVwcnJS3AWXl5fx3XffzZ1bdHp6+sgydb89GSDh8wAAIABJREFU91iexA3evXsXBwcH8fXXXxc/MQft4d+mnmxRZcasCVSuc6/dMQgFFARzCsrCosVXzzEcCF/86FivGSXYR5vXtWYA2Lds6zti5mJgDlAGKGv2HBDHmU6n5YRTrOesrBg7FjVjZT5ABvYze01ISKA9BC4K2Md+RMyO5yAeY5qpbR7jzymj19fXsbKyUtJn19bWyqF4u7u7sbu7G3t7e9F1XXE5se4crmfBuL6+XpQaMTNiDawBiiHHSjKCaFn7LXeL41QtpbCotJQB/1seZUOEPpkeXFpIYVm08GyUQguW58yBGhznN9fja7lYGLXubbVTc6fk/mV46cU1czvl1Mc1kFWEsM2b1SwQsFZsRSH4Li4uimvo/Pw8zs/P4+LiohzMZreOCa1WUGAcQ0EG0atXr+b6RmwkIz1buJ4b+ozQrxkFVqYI/awgbB1REFqgFKOFPO7MeLSXFUOLVtyfbNWaLowEELJ+/zQxBgtyt5vnAmsaZYCgqgk6lBUC1bEIt8cGNtdDvaAKil1KmQ9stTtNmNRZssAcl3Acyntr2DF+c3MzpzBwkZKWjVHkQLmNEyPpPD8tgZkFuOnNrhxoIT9Xu1ZTBHmtas8sI9+GkMIyCGahUui67h9FxL8XEe/7vv9Xf7x2FBH/XUT8tYj4fyPib/d9/6n73OJ/ERH/bkRcRsR/1Pf9/76wFzFvLdau8z31rXw3YXrismWXvy+bfZQVSS3QXGsjMzLCFaZGoJJGenh4GJubm/Hq1asYj8clGLe3t1eOfyBYSx2MH6Hy8ePHOD8/jz/+8Y9xcXER33zzTTm3CKs0Z8tYaHsMuLGOjo5KMJmjKba3t2N/f38uYwolx9x43pwmiHCMmL0EZ0iJWxBGRBGIEfXD6/q+L0IX14zdNBZS3mxmtOC15poD5jVF1Oo/n0Yw+bWlZN10XVd2pNstZlejzyjy7mSMBgK0ZPa4j3YtgVI9v4yZ0215GQ6fbIBkA+DDw8PcW/NYX4Q7dMB6rK2tFeNkbW0tPn36FOPxOD5+/Birq6txeHhYEiigeWgFpQHvgCy8wQ0FRj996i3IwTElGxktYW35wJiy8G7Jp5bnwPdlxbGsUqgpiJrMXMaLQlkGKfzXEfFfRsQ/1rW/FxH/c9/3/7Drur/34///WUT8OxHxN378+5sR8V/9+PnksoyQyPf4uq/lZ4faXKaOVr1DBBURcwxu5iaGAKP71YpsVsLNREaOhbiDynd3d3F+fh5nZ2dxfn5e0hCdcVM7miKPh/pRCmQ+cXgdJ68STLYwzemc2Udvt0tOlauhxdwv98/Mml1MZn7HFWrtDaEE/u/7xxunch9qzFyjHQebcW1dX1/PIchWHfSHP1wFKCh2HtP/lZVZ2qfHTDukDENjWOQ15OA0W+YoC1nmOBsFXhfui4jywh0MJtxnfhucBTH9ZqxkqqHkUI4RMRdEhxazAVpbu6FiOl5W0HJ/rY2sELLiyOg593eIzp4i/ygLlULf9/9r13V/LV3+WxHxb/z4/b+JiP8lPiuFvxUR/7j/3PL/1nXdQdd1v+n7/ttF7QwJ1NqkqH9NDZphdA1x5GyVNPbmtdw/f8/aGeGBNY01hzuGQ+yIIbDrl+tsXuN5EzZppJxkenFxEX/84x/j5OQkvvvuu+pGNPrnDBtbd2tra+X4gjdv3sR4PC5HU7x9+3buqGiUVGZMZ6k4Z9ow3pYlli3zWLPAa+vLd7dXc9GAGFCKtoztQkHgGC3Q58xkWZF4J7kPncPStZ+fv3yeVPahI/gzDebAPEqRM7AYI/SN4HXfQaB5oxljYJMj/WN3tI/y5l0UvgcDxW40rxn04sD/1dVVOQzv6uoqNjY2YjKZxPb2dhwdHc2lXmM0TafT2NnZidvb27JjmjO6Njc3S9/hEW9Y9NvuvAku833NWDJKHIopZKSQrw/9XzM0slyroZX8fDYEllF8PzWm8KUE/XcR8eWP399FxF/qvm9+vPZIKXRd92cR8Wf837JcDddqk9vS2l03fyBZ69Puo1wWoYrKmKrXWByY2PED0AFnGxklwKDOc/e4sHzZa/Dp06fyGszz8/OygxVob+sxz7VdWyAD75nw+wpwu5gpzCz87znwb7hg8GsvErj5/6zwrXBqKCRbs8u4CqwQnNVkv3Tum5EFxfsWIuZ92d6k5mBvtgBbTJ/pCzeS19mfjnPYWPEmSSxt0mVZ877vy8YxrPCbm5uSHcdxFrgxceEgfOkD7SKIHQx1LICd4CAc6BlXETKB+XU9dgc688kpzq2183zX5FGOZw0J2T9FKWT+yWsdMc9zvh/Z4PJXGmju+77vuu7J+V193/95RPx5RATP1yZxSMMtsiStSFran3tqGn8IKeRAc1ZQ7g9CFDcRmUZs69/d3Y1Xr17FaDQqsQSQQ365TN/PMozw875//z7Oz8/LURXffvttXFxcFCuOTT65mKhRBkdHRyWTyEdT4OfFneUNRQg9/7nUrF2EQsRsZ7Pdd3a15Tr47vvtksj7EYwWEFIo2Kxo8j6F2tpnusquG6ON3EYem7Of8l9GQx67n2cdnfHkDCwQCe5DFBBGAOuK8jdiol4CvLh28nxyNAUZbycnJ3F/f1+Qg7N+asqOvkLfa2trcXV1Vd43zflH29vbBaXawPIf80Hq6+XlZVmrrusKasKNCg3SHxtOQ8boz4UU8nUL+YwU7DZ2PdlDYZoy3fySSOH77ke3UNd1v4mI9z9e/0NEfK37vvrx2lLFTE5xdgOlNbCsALAAsjsn/x7RPtyqpVlbfr+aYoJ5sfr9Niz/sVnN2Tz262IZgQ54r8HJyUmcnp7Gp0+fCgx32mVtjhFm9AmI/sUXX5SYgfdBcF+OGeSSFXJNKOa1JTV0CAk6zTIrBe7Nir/myst1ZyFc66tTSv3pusx8VpZ5zDUFZIFmZZDryMisNa9YihgOEfPK0gI6K6csgDBIcFXyXC1jCXRALAAL3cet2IXWWmtowq+CzXWCaki4gL82NzdjOp2WrD3caDmFNrtNPXeegxqqtCKpZad5TMt6FLLcy0iB9UCZ25BtyUO7bnPsbqj8VKXwP0bEfxgR//DHz/9B1/9u13X/JD4HmE/7JeIJlGWETO33rNFrfrhcagpkmZIFS62fmfE5mI6zi3hdJtlFe3t7cXR0VN5C5renefPOw8NDObn0w4cPMZlMCkI4Pz+P7777rhyb7LRL991WBMJ/c3Mzfv/738fe3l58+eWXJYAcEYUIcXdly7W1VrZ0sgVMsRsJFwpCozaXEY9zs2sum6wQMjPUYgdZGLs96reSs//ZAjtnMtXmxkYChoDnif0JeR4s/BzY95zaR89f3/fFjegzn+gLSt+Kn7GjfI3YGL83unHm0s7OTkwmkxLXAF1wtDdII28my595w+HKykqJWYAg2L9Diuvq6mr5jJidrQQtk4UEArLRZOHpdfX6eR35PoQUTDeZDlr31u55Snu5PPX+iOVSUv/b+BxUft113TcR8Z/HZ2Xw33dd959ExF9ExN/+8fZ/Gp/TUf95fE5J/Y+f0pkhd80iDdd6dpGl/9S4wVDJi2qYnzONvGMZZOCD7iywsJxg9vPz8zg5OYnJZBJnZ2clhmCo3lIIETGHDvb392Nvby9++9vfxs7OTrx69aoIf6A8xUKuNre1ay1lWfP5O7bQqmtozlu/5X5ka75ldVuIM75FDJst/FbfUCBYvI4pZNSQ26opZtBLTsdFEOage8QMfVpB+qgQJwRERIkB5bk0mnDMADcnMQDvRqdPttiz4qc+W/g8y65s+slc+Bwl3uYWEaUfflES/aROK4RavKC2Fi23dOse/l/WCM33/9RnnyLLlsk++juNn/7Nyr19RPynS7e+ZBmaiGXg2TIKo4UAWiUzvIUBAsev0OTY4PF4XHb+8n13d7e8KAe3DYIZhuANXN9//32cnJzEH/7whxI3+OGHHwqCsGAwY3XdbFfy0dFR7OzsxNdffx2vXr0q70cmHRZBYKXgYyVaQpv5sKBFSNhy9v4IGDRbhYa7JuoaEvH81/5sUfs4kew2sRDONECfsmWe2/b6txQVbg3OBuKFMn6LnE9D9R4Qv+nNc8A61d7IFhHlKBM2LTIH0JrP0aJNB75tHFiYMm7upT7QRN/3JavKO445c4u+WwijQJgv729BuTEXxNWIQ5Ag4QQNK6Oum8V9cGl1XVf2iDgOkxMTWmWR4ZmvtYS0f6spoKG2FvXvKYrk2exojmhbe2bCRZOSrbxFCsEZILX7cnHqo/tWs56MEIgl+L23oASQA0zqt2sRKIWpQQYgBWcZ5f0H2Z1GHOP169exu7sbv/3tb0sKLMdmOPA55C8dmqOa9Zznhrn0ethfn1FDbqtmxWVlkK1/p+BmN1FNGbjd7HeujbmGOnLd7ovRo++z0kKJZeWWlQ7Wbj4/ycjBG/fs6nKsCOWE4HcgG0XmwnOOC02n0+I+wlJHEdE3f6fvfNJm9qvneAB19n3/iHeYP/qL0XF7ezuHBJyIYeVj9JIVg9czo+dME8sYrS3kWbvWMjZ8r+nIhtiy5VkpBVuDZsgW/FqkUS1ochv2N/t/1zNkAWSmN9P6xSOj0ahYL2z8AimwI5ijI+wTxYLiqArOLfrLv/zL+PTpU3z//fflVYzsKoWY8/wheDi87q//9b8eu7u78fbt2xKQcxaHLTaYLgvnzLR5/hA6EVFSFnkJDX21ErOLDOvQDIm1R/3ZfZKzlFqKwZa80YN99MxfdnHZLdNyk+V2W/Mync6OcSBLBnTInJHu6fRkvx7TSBJl4GOwb25u4vLysiCHm5ubIuhBBnZhGTVgebP+ETMXlGmAcWUk6NfIRsz8+awz7d3d3RW3pzdWese53Ur0g08se+5/eHgosTJv9tzd3S3GH+PmKPWu60qsAzSRFVVNHtgV1uKD2nP+rXXN9GPa7ft+zrgZKjmIvmx5VkohM3qNsVqCusb8tfuzUshHJVBXq63sA7VfGiKGISA+71Z2ZlH+nzogSjIwQAik+pH2R4aRfbNZIRghHB4exuvXr+PNmzclfoAiQgDnNMrpdDqXPx4xf27RIqSA8HKaJ4KGvtYEsP8smDKd1KzwTEd5LYeeqTGaXXLZpZARZq1ulKHRJRb5dDota29l4mw1/+XAOMWK1m4Wgsp+9Sh06c2QXqeVlZVi6YMAuL61tVVSOo1wvLaMh7em9X1fznNaXf28O9rvZ+77viBdBLvpwnyRBR2ZeKurq7G9vV3elzEejyMiymY+0nK7bvbCo9FoVI7BAO1wrDdrazrPNMectORTS44MIQVKja6ycmjRLevRdTPXWR7DUHlWSqFWWu6DiHbmkX/PmrKlFFoCoSX0TLQ5ywRIjsD3yaccLU32ERlJ1IGAJ0bw7bffxtnZWXzzzTflxFMOt6v5PG3BoZzevn0bBwcH8fvf/74cYudUwru7u7kMFJQSaMXEbUuqBrEtLE2YPsI5Bw1zFhLuAPqHOyHTQ4sm/Ft2S9XqqDEcisD7HOg7/WdsNQXlPnBSqBUvn/bBM18RUaxsPqERCyK7ha6uruLh4aF88kKd8/Pzso4I7O3t7VKnY1/+xPpmje3GjIiy34E+4ecHlXjDJHMCqgHhOOWaTWkc5BgRxc8P3aDIvO4oPY51ubq6iu3t7bi6uord3d04PDws4wZp9X0fu7u7RZmQ1Ucw2jSaXU4WsDZwavT4cymFmqHB/7UYVw3B/JVuXvulS0uzLbJQ+cxIY+jZRUrB9UIQdkFg/QD1a8ggn2dkPz6L6V3KPt307OysHJzmM3yyEKKP9IkU152dnbJBydAcSJoDr1YIrju75Zw7nefUSMp/2UfvwF7OSKqt4dA61X7LTJ1Lbf3t87ZbA2GZBQL1LCq05VhBRqy25I0Q3E8rLh/rcX9/P3f4H8UIxQK25m5DcOf5y+uWBaJpZEjxQp8RUY6ooO8oF9OX68zKm3Xquq4gElxvt7e3c8eGM25cZCAHDKOImDOYLPjNW563luH6FKWQ665Z/3waabcQMWvpTDIbHUPl2SiFFrPawuP/RYrCgqRGqDVCri1CazGzoMSa4nsOImZ3kc8+QjhD3Ah8lADuorOzs2KB+eUnNaEN4+/t7ZW3o4FSeBOXXQVmFlti9q/X5sRzVxMGGWbXBIPXGCHn+fBu57yGGUbX6CErsJYQaz2HwM3uo6zYhhg0Yhaf8f12q3knbl4Pr5fnzH3EsrdywJqHJn0uk/ec+LPWhuvFgraCtVVKXzBanAnn8ZqXUIp2veLrt6HgQHSeZ6eqRkScnZ1FRBR0kAU553OxWxvU5SC3ES3jMC1l67tlmAwZlq2SEYGVtVFKK/CcPSRei0Xl2SiFFmPzW8TyARvKELTLBF2Da612uBeCduCO1FOOsNja2iovzDk8PIydnZ04ODgohGlLkY1nV1dX8e2338bx8XH8i3/xL+L8/LwElieTSXVxrRDG43FJM2UPwt7eXnmvs90VOQ6SfZAea034WzG1rEOjECsb/hCGDjR7M5E3tWXFPrRWvtdCzC6NljDH+sTa9vuA+372lrsaClrE+BbSEVF88J4b4kA2HtxPGxH8sY+FA+D4bsOEevkeMdsdjNIwEiGQ6xN2+Q06RJCiENgo1/f9XHaR42wkHtjq5aTY7e3tuL+/j48fP5bU1drpvjnRAfcZygsXFkeM393dxc7OTkESRrf0BTcY642SYWxWTqxXzS2Z+SLT6iKLfRn3Ua3k3/5/k33Uur6MlsvP1ZRCDT0gmLjWQgp5YS0UDE1htBpSQBn4GGwTsl1HFxcXCxECfaZtjrj+4osvyomr7FL2jlVbbdl9kP945qlrwPgQhDlAn+seEuJDMHwILbT60/pzDMJ/7qPbtLW9iHE9VhjW60lduI4cR8jjqlnxTkXFZWB0YAXtjC0HsCNibtw1az0LR5Q2StTZRhEzV4xRNP1hzChh9h9EfN5fwe8W0KyT9zOgYOCjiCg7qTF28lEzXdeVoDSGmXdQR9R3O9eMoxryrMmfZVCCvR2Znp7Cg7/67KOnlJqAzt+Z1EWTOFSXf8/MD7TP70EwQuB/XjuIXx8GAWpPJpOYTCbx/v37ODs7iz/+8Y9xfHwcHz58KMcV5KAyBaam/q+++ioODw/j3bt3sbW1FXt7e3Mug5ySSR38FjHvT+X/iGG/8dC8OtCMcnMAmfqMDOyqyYbBorV3MaLJ7pJs4dtFlIVsHhfCtranIPfDQh3r0vc7M4m6/TKmPN/0kVevYhX7jXoRUWJK29vbpT4nFXCP41usiVM+azukHVvhu+MZoD/oiPpx54CEmLu+/xyU39vbi4eHh9je3o7JZBJbW1txfn4eHz9+nHOx2sVj33nXdXPnNIGy6DvxBqN1I4XV1dWSqeRjOUBePnY701grmSHTY620PCI191PNMPy5yrNSCovcR4vu8+81i60lzCz8eL6FEhxcgtAdaAYd+EgLb1CDCWztQHAcWwFKILc8v0A9EwZWHwjh1atXcXh4WLKcaBfmyAFLjzG7MWp/uSyjHLIAzvW7nowUPNZa3cuUDMFr7Xs8GSXY3+/5sZ88++NbdFtDZl7LiKj+nvuXlae/046D1dnlZQPAfTJSyvUjhDFmrBSMeLO7z4YUAtivls0KijkfjUYl+GwXlsdp4QwfO8awtvb5TW+4jSKi7CLvus+uOowBhD5KKyLmgvbZ/Wh5QJ895iFjJtOF/28Zuf5tiPazMYdxtQy/PCulsKz7aNHAfH8OMua6arCvxthZiNhKJMWPwO7R0VGJIYAUeNkKh3TBPOw3eP/+fZycnMQf//jHODs7i++++664kTKj26fqgPLvf//72N/fj3fv3pU3pdmCzQoSxrUgsNDMLoaaNZSD+r5Ofz1fCAYEqxEI/YmIOWGU3UdmOq9ZTbh7XRlnRkruR0Q8UgZ5j4GfqQncrORagsAozfPBMzWXEXMBGsgxBaeKkvYMfTJG9zkLas89bTimkPc9eLzMbz6uhN+gV5CVj6Ng/rDUqZdNaGdnZ7G6+vloCo51oV/mD7tHI2KuLygKjnJB+ZAOu7OzU4w13FeksPLmOV5BCoKyAm0ZM14/1p7/hwwHGwtZ9mTFk1EG82F337Ll2SiFlhY0cwzBrtrkYYnn4noMb10f92WEYIvQ71fmZfYoha2trbn3Jtina6uCkyPJNgIp8C5lIHxrvtbW1soZ8z7gzq/K5MA1u0j6vi8ZLzCpidZ+7Zpf09k0Fla1TJ8sTGnXiMlzYstrEVLwei0qRggtJJTppMbceUwZfTy1f2Z2u5JyX/w9I4Xs5oI2HEDGDWWlmOeC+r0mdqdFzHY25/XlPmjGGx6hQwQyyBnlRfsgg7u7u9jd3S1CmTetkZYdEXNvd2NclJx+SRCadFPvtyDwTp9RqgSor6+vi8JirlCWETGnmGzIIH9qtON5ztdrtOjrNXmXi/cImX5+VUghM38mTAuzPJE15s3WWq2tiNkmlRpks5ugZnVSHAw0I/JKS5QDRMsRwHd3d/HDDz+UGMLJyUn88MMPRUnYEnHpuq4I/b29vfjqq6/Ksdfb29vlAD4Iw9aChW7f92VXrS2nnIHSIiQHG7PbwYxBfYyf7JO8L8J1woDZysv99xobvrsPpgn64b8WiqqNJf9hKAyhA1vLRnq5eExGWrY+7b7BUuZICxSDBW1+F4bnoWaEZTcKCoe2OFIFpOC4CIYFljT95DdcTrhlTBugSGgeuuQ4+cvLy3j9+nV5wc7JyUl5wRRxFaz5fDwG6wdCRSHw+lva5/wvjpN/eHiYi9VEzLKRvAfEiLKGbrNRV1MKWfYMKQvLJq9ppl9oLmIWg2rRnsuzUQpDVmBLYLfqeApSqLXv9hz4g+AgOohnf38/Dg4OSrbP4eHhXKaRU/2Anbznlp2n3ofgF5JktxbEwOY43l3LHoR8Fn8ed7bqW4GxGrHmYmFV+/Nc1xBXjaAzcjAxt6z2Wtu5b3lMNUs500drLC5DKCPPZa3Py17P99jHb6TAs3mehyzPrKw8d14DI5Ms/DJP1pCd0WL+33zGs+6Xz4LivcwRUY6s8K5jW+lWDCizruuKAiGrz7SIAYfyYuc3Cpd2QbwRMzdVLW11kesmz1MNEXgOFyGFGvrzvC4qz0YpPKVk4vP3jDJaz9YYfRHjwGQQDe8v9h/HVnA0Nql3ETNf7dnZWXlL2vfffx+np6fx8ePHslU/uwHcTwLHX375Zezu7sbR0VG8e/euvMKTzTqOB5iBzcQR877HbFXnvQW1eTcD1oR3RlcwHRDdriujAWeXwHzZx57XNVv2uT8WPLU/C8+sEFq0kBkwC4Fch10ctfqzH741PlvwPv2UeuwycptuJ7vQ3E5WAFj5eSc9hhLz1/ezfQtuj9/5dLqtA81ZcYMWIqJY+qPRKA4PD8sZR7xg6vLyMi4vL0sf6Zvn0AHytbW1gnw4o2lrayt2d3djbW2tZA1GzFxIRjS4Px1bAc2xrjZysnGS6TcjiBp9tAR7y6iptbOoPBulsAykztA8T5DrsLAaqtMMmK1aWxt2ozi2YKaAwHHtkF3BYmKpkGJKGipn3zuzgmLlBlFubGwUJQRawV2Uj0RYNN8tBVtzMXB9UT21/2Fyw94smPLz2WLNfWiNL1u8XMtCPfdh0ZjyeKgrt52ZOdPwItRrxdAqtuKzwPHRKZ7b2mee+xrqsjJyv+lrXsMs2DMtGSlkBdXaZOX74K2+78vrNznAD8RQW0MbFrjhcD2trq6W02rhdZQQQXricnziUjL6qRmdi2Jj2fDL65zXiPqGeNweAD6XUQgRz0gpDBGwoV1tYDUibzFtxPzkW1DViBkBi9AFDayvr8eXX34Ze3t78ebNm3j16lX87ne/i52dnTg6OionY7KRBmVwc3NTYgcXFxdlX8LJyUm5r6YI8RMfHBzE4eFhfPXVV+VwPd6JANzNm4L6vi/BsIiZ9YLVQx77yspKCYoz9tFoFOfn53OWouMHEfPpbs4yiohiBZpIHx5mxxwTw8jMa4XgrCQY0JuWvPaesyzMbNnm46J53seOZAGf6Sq7QxwkpR8+ZwelDr1xve/7crw4z2UUYtrlzyjAfeGgReaNe7wmuEExKGiLvo/H4+LeZE2hK2iUNGxoyWtFTj91k3m3v78fXdeVPq6trZXNYxFRrHe/sY22Ij7H47a3t+Po6KjsaTg5OSl0+u2335YNoA5AwwfMAYHyyWRS+j6ZTKLv+5Kuyh4P4iHj8Thub29jf3+/HNzHjnH6fHFxMZe+6uM+suyh1AS7lUxNLllZZNnpNc98M2QoljVYeMdfUTGxW/jXrK6sOGpWQRYQtbYiHr/jNyuTDIudukfmEIHh09PTEiTzcwTtIFb2INSyjGr97bqupLR6AxxxCwK3MCHMSV2kEWZrz68onE6nJUUQocX4/GxGVF433AzUy9hrlpE3P+W1od6sePJ99MXt+/4cM8mWa+5TxCyAW6OnbNVmRcQRC7hcLLxRDg544hePiKIoW/NREwTOnMupww6MZ9ebf+MEV5Q0v19cXJT3HDAn3incdbPNYDyLu89BWJSh60dh9X1f5gQFQOC867o5S/z8/LzMHbwE8s4b/TY2NkqAGEMmK1h+Y92m0+ncKzyZU4wW+AVBTzowMUAQB5sHudfxF8s3r20uNXTuP7t0bZSYZrL72fJlUXk2SqGlwey6aU1irsd/WaH4O8KJdjLjR8Rc/GB9fb1Y5RsbG/H69etynMTR0VG8ffu2pKjCtBDL1dVVeZfy+/fv4+PHjzGZTEpsoZV+CnHu7e3FwcFBfP3117G/vx9ffvllsWRACHYdUWpuiJb7wGO37zciymcOoNka5zyblj+fdURhgKayD9p1+vkslGvFz2aG5FkfEY0C59mWMeK2fVgdfaFNv7eAOpiTnCboNfYYbai0kC9rxDiw2BFuKB6vd20s/t9w9fi7AAAgAElEQVRrW3PBmC6ok/iVlblTjSNizpjyIX+OK2S0WFPI9NNuUowjgsDsqLbQrglD+nZ7e1s2iaJMnIXnN+PxbgaO4djZ2Yn7+8/vp8DAW1tbKy+/IqnERsIit2CmCfe1hhQWPV+j7UXl2SiFVoczgUY8zhTy8zVtnInb9zgTh0m3dUA9WHIsbG1xvBmMdqwYCIRxWBkQu6bFqTefZ8QfLiwgfcTjF7ovIoIWUWUomo9vqD1nC72G3Nw/5s9xGf7PPuWa66am9DNCqCmWLFwsZKljCK15DNlCY62dheJ2Wy6pXH9W0jX3gD89f+5bnptanTXE01pXxs4zoJrsmskKDiVRi78h3K1kjHKMcHJ/aZPnSewgrZQzk1DUDo57XFj+fT9zH11cXJSUcpQ67j4QUtd1c8jQCNHGiN1HQ7zha5m+85hrLu9cnEDC569OKSyDAJ4q5Fr/ux4Hms3s2arEQsB9Mx6P4/DwsGwaOzg4mDt4js0y19fXZUPahw8f4vT0NI6Pj0ue9WQymUs/NWGsra2V3crv3r2L169fx1dffVXSULnHm8HMpHmMtfmrCQhfR+FgzWffrK3aGlNkoQJSiPhsZZJdArOZ4FvCbhGtWCG4f7YwfeAcJfffjET7RgmeaxQBiM/vMfD82L3TWoshpYDizCecghRAXjWjyKU2r61Ss9BBO8SPjBQwnnjO524Znfl7VrC1vkbMXrgDbTEP29vbMZ1Oy9ve/H6ElZXZYXp53hn3/f19iZ3hjmVjKGebsSF1NBqV+nFNcU5T38/2QXizH22ZF1tIzmvv3xfRfR5Tnr9fnVIYKnmQtckcUghZGVjB5PtaFiGCwK4HByrz0QERs5eF4z66vLwsCAE/ZGvHMm2Savrq1avyTgQfe2yGyq6VlgCtCZ2huatZlbU1qVnoOWPFc4pwsVKjrprvflFf3ZfcHvOTrdNsoWZ04Xaya82CLO8s9m5exlebk1qxkK39hvLPiCtiPl7gufB8OIjdmkM/4/Hbwo+Y0R+xA6+bDQqfEWa0AL+01jXTn9OsQSHMMXt3VlZmZxyhDOAzC2jmK2J2UjEJIRsbGwVtkJVE+xgxPoocN5HPaoqYbd6zMTWkDPL4l73eKqbRZZ9/VkphGUt/SNvVBEiNAWuuqAzDIQIQAi4bXlizubkZb9++jaOjo/jiiy/i8PAw3rx5E2tra8Vd9PHjx7kUVNxHvD3NAeDcJ4iPN6bt7u6W4yt84qiFUxZUT5nzzJi4O8yQLYsS1wmfWbi2BJOtToKIrFkWvouU0hATWaDU6mMM7nfL9ZTz7f1sVgoWPC1l4zlsuUjz3LE+2S9PW4uETU3JL5rDjFYyzbk+I9aIGW/hCrX7KBsxGTXQ14zMoE/3gw1lfd8XtE7qKgiuNtdeIxQDSSErKytFKUREOWtsOp3G0dFR6QtH1JCw0ff93NHbNzc3c0ppUdDXtFWTa75eK1nxM1/LlGelFFrFGrbGOFYWeaJr6MB1tooJ1PCR/QFYJQTaum6WUcO+g8lkEqenp8Vt9MMPP5Sso4uLiyJIsu93dfXzMdgElg8ODuK3v/1tSYfNioAgndNBDd+xkuxK4VlbwCY6t4EVj2sgIkpgz/23tUy7XM8EioCIiJInbr8srgZOzfRRDV637KP3umbBYzRX22VOgBJl7QwO+utD3LDWcRuBCJ1ZxbPcWzMALNyGlAPXmRt86T6oLm+W4hpjtdB23KymdC14bdVno8TGV5577nfarzfWOXMJNxxtOiANTeGGshCnPea667qSQfTw8PBo13M+PgZap+2Li4vCT6SsYpDR/5WVlZK6enBwUOiM90tfX1+X9F34JSMFr2mWPUOxh3y9JccyXyxbnrVSaAn4p9xfmxRfy98zU9plkANktgTv7u5K9oHTT1ECPsLCDFxrb3V1tcQN9vb2Ym9vr2Q/5QC4oak3LdlNYeFnoZmFQbaeswVn10S2UiyAsj+/Juhgeqy6iM8xBp63MMmuObdb6yuf9NsKMrvYQDe14xtsjeX199q3nqfNFm3V6HcZX7PXJMc3jFBqz7bWt7WuGSF4LmuG1SLa8vz7s9XX2nN5bvJ9WO9OA3YMhjVyYc1QOPBw13VxeXkZa2trcXV1NXdWGON3nMlxkox68hq36IH+871WsrGb1yHLvWXoj/JslEImUF/PDFabiEzQeVL9TA09OMNmdXWWgsorNHml5ddff12Oxv76669LsNmHaH377bclJe7k5KQEltmghuuotkicJPn27dv48ssvy2F3r1+/fiT4mZPV1dkxxE59dO749fV1CX5iASOMeTlQ13UlsAZx9/3nrIyu60oONozjnPXsZoHJYBT7k7nGHNFH+kOwjxRAkBP1IQyd9sgbu+g3rgO7U7AeQX0IOWeQWNhT2OTFWVNmdh8zUROcnNXDd9JFcQ86Xz+/h4A5M+riet/3xU2B9UufUK74xDc3N4uQIquG75ubm3No5e7urox1ZWWlJEKwn4W2TR/Zdba3t1esbtbEL6CC5mg7Yvbeg729vdIm8+lYgd+pcH9/H+PxuLwQh4w86uL1m33fx+HhYVxcXJSNZufn53OolLmGP1AIzMf9/X05kO+LL76I8Xgcr169io2NjTg6OiobUMfjcRwfH8f6+npxP2EYZkSXDacsy7heU941txIlexL4XORaLPS+8I6/otJyA9jq4veatZMFbM65zrDN7XZdNxcoczDr6uoquq6L8/Pz6Pu+5CZvb28XAjs7OyvMPp1O4/379/Hp06f4/vvv4+TkpLwzgc0ttfQwxuQz8FE0zoZAiGE1Q8wIfCwi5g23iC1ixo2QhUGwcBwow2L2+fk8z3xRJ30g15v5Q4DYagJO2+0AzM/pjqAU2nVw3nTj1F5oxsiK+WJeUMx+DzPuI+rEHZcZj3Z4zu81cPAS90Ft5zDCLCLKJiyErsdqf7DHhhsEVIWSJM0Z2sZ9ZEUGLSG4iIUxNxzSiD/cghiFzFvJ6D91o8CgS5Q9O/rH43E5twh6w/gg3uYAMm9egzbgJQtvHxuDwYLg9YmuznbK2UF24yETSCVfWVmJDx8+RMTsbXanp6cREXFyclLkwIcPH8p+JCeVYJQNKYUs2PN1Iyb4z9dMm+YzPhfFMSjPRilE1LNlWpB2qA4/15oEW7QRM6SAFcfLPY6OjmJvby/evn0bu7u78fbt2zg8PIz19fV48+ZNHBwcFDfH/f3nl+aADj58+BAfPnyI4+PjuX0JKAWPCwv64OAgXr9+He/evSv1+61tEAIve6dtBDzCHKFG4Cti9gpF/w7z+e1shukQG0Ida9FHT2TLpQZVvY4mYCx3u5G4n/WwBU6pMZFTTVFytgTxR8NUfokMVpyFLsIWpMAceS5her8Gs4VmPe81Gq7ReQ0BWxCATvNxCtC2Uz8J8uZXb3od3U52m9J3ns3GDetEnbRH+8ynkSMKz0IOOkQp05bdrYsyxMg+QpGBqlhL/P/395/felgzmFA8p6encXt7G9vb2xERJYZAGjr7js7OzgpScPbSxcVFcT/lTW21ZAyvRY3OM7/VCtedgLCMQoh4ZkqhxjBP8YVxf/7M1yjZHWX/Lxaaj7ne2NiIm5ubmEwmsbOzU96LQLDP1mJOPc3pp5n58X9yhAVnGeW3U3mzjoWgmTXPm5FPVgo5HpGtDhOXlZGtKytf15EFWksQ0ods1fNbpodaXb4/Kwh+y/EWu43yMSOuL/uHoQ/2I1BPfr41ZuoYUhzLGj52y6EEWAdoxZleeX1qpeaft1Lw2npN3KecpeUMJLtqraRRIBExt+udftd2XNeUEgoRxWTk64PwImIuKynisfCETnDB8nd5eRnHx8cxmUwKf/Ma3cvLy7mUc/4cd6odh+K5zDxoI5a1GFpDGze1cQ2VZ6UUaozUIj5KzXpsuZhyW0YKEB5WFO8m2N3dLYfOEfjd3d0tPlKsTza/TCaTeP/+ffzwww8FJVxcXBRLspYWRgxjPB7HF198Ea9fv47Xr1/H0dFR8f9ipdKeDyKzdVYT6Nn14O9moOxuoYBIKLb6cG15Hm2ZWhjVUB/PZKWQx1Bba38ijBAmEbMMKegBtwdCwO+tcBqpBZv3ojgGgTvg6upq7uhqM3jNuHEAe0j4W7nUjCLWGjTEm8nogwU7SNObxnKwPPfDblTWvqZcjUw8b3bV0D5GBW4073WIiLnjJVjHWvwoz5OLFR+fdkGTSdh1n2MtHLUdMXN/+n7cTxGf3UQREfv7+3F/fx+vXr0qCSF935cxjsfj6Pu+0AYxHtAPc2YjI8sF8zHzW7teK7X6GNevzn0U8bTNGWaqZbXgULue+Jxt4qwjEx6E4+MsQAn4UGtHWWRrkvRLTo/EB+3AKgKK/nnsNRiaLboskJ02aReC58R1RczcSEYI2QWAUshWYa6z1iff00KIreu2nDc2NuaYnDE4Q8j+Xa7ZiraAo//c61Nj8+5nj6Gm1Kw0FqGCmiJsjZksGwQP46mtRU241Cxvz0NGnhlNeByZX7J71rxGX/J9TprIxmHNhYTCoj7ayvMdEXNJEghxB/PtVgMtwN85RkAfnX2EghuNRiU9lftqKPo5lWelFFqC/SkQO9exSIBkIYhA4aA5bxzb3d2N3d3dcggXAhIF8MMPP8Tp6Wl8++23JePo7Ozs0WF3Jm6sIhDJ0dFRyXhiSz1Iwu4h6kIYUX9mzAzhMxpAqWUhlpWWFWVElGyUra2tubFZCPkF6Zkh8vrldmsCKn/3fdSd4wZGMnw6oIrwtCVqJYyFzW9+BSbuIyNAM3tm+hpt1ui6RrfZ8ssIyfGYiCiuTr7bPWiDxtZqLtAK47cxRN9t7FjQIyCZQ/z43o1PvIixMQaUgekyC9Js6Ji2UASOTWShHREFnfPmNbsBnaKKsiBG8OHDh7i7u4tXr17FdDqNV69elbgYmUq7u7tlf8PDw0PJgsqnqFpR1WSVvR7mmyGEOfT/MuXZKIXWQL3Yy8CfFlPWPm3xQixY6biIDg8P4+joqKSjHR0dxf7+fvR9XzKQyFLo+77EH/ze3No5QBQYyCeeGurb2rJANTJAOAFLKTzjozks2IfmKc8pn960RN8QuLTp4GxEzFnaQ+1QhhQ5v7ee//+oe3cfSbN1zev5IvIa94y8VFd1dXXvvQ/bx8LAQcICZ7zxEIOQxgEDCYMRf8FYSGMhHQmDkZBmkEACAwchYWCAwQgJY5x99t7d1dVVlbe45z3jw8j+rXi+t9YXGTXniMm9pFRkRn6XdXnXe3ney4IpuNbsm84tg3U5Cbn5QgOvw4TrmNWmCk1uHja5zveIw3w0j7iJmqpUjbpx6CEyeU9CdCEVhQJ04oLBS1vDqHmn07ULLk/EywkF/y5aHHz6uzzPxUNeO52OHh8fNZ/PVRSrkuA+N6y9R2M1Gg11u10dHR2p0+kkhYOENwQAVVWbzWbaq/AK+JqXa/e5ifMa+VYdfcS58MCQ59qLEQp1zD6GpG7ynBys5MTF307MEFXcEDAR1wivr6+1u7ubSlecnZ1pPB7rp59+0ng8ThnMOJw8WSZqvMRgU84CB7NnjbpGHLVe11Y9g5j7nMFh3RCj76Z2Tnv3FjefMyAYiTsxPWLlOWYeGXdu7epa/F9OcHr4K/PlDkTW3f1KDoHBFGAILuzje30zMheeYOZz7mPMzckmAoE58EAAmI8HIMTr47NdOPqYyrKs+GkIby3L1TkhMBzfM/gRsBLA8T3qyWkOmqEPMDNatFhg8DB3F2Y5ocB9NI7cBN4h1JXDcxiv0zsQMeUsfvrppxQGOxgM0lp7ZntOYWCOXEnxv/l/pIOcZVdHJ/E58fd17cUIhRyhRk2rbgNFScrvbua61sOnS1wwfJy7r1+/Vrvd1rt379KpaoPBQK9fv04YZCTGVquVTEwXOs7colCIUIVbBd5fNDXpidjRNiBUCB6LxZm43+saHIedMB4/9KUsy6TdEY/uDm3f2MxDLlIEBuKZyi4w0JDqLEFfzxzD4v2e9BV9A7Q6v4u/K5eRSt+i/yGuq59pAGS2u7uboAP8RvTNq2zijMzRdt0cRMc5f3M0JWOmTES8ryzLymlxrFuj0VCv11Oz2azkDHifmWOwdYSs7yVJKRmSwAyYsCfruXZOfzw8+PHxUb1eL0X4AOn4aWgPDw/q9/tpfdziYM49/+T6+lrdblfT6VRXV1fa3t5OloJHJPn8s3ewfDqdjk5OTvTdd9/p+PhYu7u7arfburu70+XlZUrkOz091c7Oji4vL9VsNpOPgUxpxhthq6jgunUUaS/yQNYshqhvomi8GKEg1eNhrlXU4bB+rZQ/gUqqxu26phIlK9YB1sBkMknvoSoiZuSf/vQnnZ+f6w9/+IMmk4k+f/6cEnFiXX0+YQzUU0KLpw9osTB8Ng+b2R2d0ZntWgZEtLW1pel0mvwXCAW+9zLDzAeJQTRn5m7mutD2TSmpgp06bu/JVa6l+jNdW3OmljOxmbfnojg8ph9m5kyP9fGxuqPRfTfuu+B3tGoibBCeHpNPX6+vr9O9j4+PaQ18PnMaIy3SFv3i++jQZd7IvoY5uhVA30i45G/GR3E4+oygQKj4euJsJReAJLDoL4AulsulRqNRZU4YGxFebrWxhjzn6uoqjdsZq8+HR5pxr2ddsy4emebjur+/12Qy0c3Njf7whz+kyMKTkxPt7+/r6Ogo9UVS5Yhdb85nIpQZ90OdUPC/fS+wD6UqfBQVorr2ooRCrkVJ+Fzzje2T5n9zHZMLYSPp2+12OscAn4KfmbCzs5O0Z4jF8UbPbF0nEFzr8EgJNpLnFdDi/2P8MxuGayPjcq0MzY7//102t6Ryz46Qkf/4d7ln1MGJufcwvhx8FxtzFf0fuf45HcH0Ha6AwUefUBR46+Zv05bTHP33aJ0+9+yc7wEBF7F5V6i4BwEXLa5N4Yvc+Hz/eiQPfZG+LKedg6RcoDMmDztmL6LBS1WfC83plHcRXIF1gtVRlmWCpKbTqba2ttLZC1jnCFgXhJtYCuvWkHv4+y/SUoitbgBxUuImkOoz/6I2yHdEHBFt1O/30wHhw+FQh4eHyfncaDQSrszh5rPZTPP5PFkHrrXG/iEM9vb2NBgM1O/3U3QRDiw0Dce6XQtzYeACAmdXDq5xs5w6SR43HvHuOL8RC3eoJkfAfi1jcYbO7zkNP97r6+33rmseKYVGeHt7m5zjMHBMbKAjd8z6WHlmUawqZXqylePlPDsysAhp1QnM3Hc+F3HsOcXJGWm07mjOrPmeMcU95A581s3pwPvKHNGPqKzVNX9uRAiYS/wmkpKvAsveYURXiHgm1j3WA5b/crlUv9+v7D2s2bgm9An/w2g0SrDX4eFhChjZ3t7WcDhMlldRFJpOp6k8jqRU6iS+K+4R3pubr0gff9v2YoTCus0RtUdvcYPlJtYJ0SW7b/TotAU64Wi+3d3ddI4r0MqnT580m8306dMnff78Wefn55WzEnIN5kQ4HCe5dbvdytGaHgPtDnE38aMGCxHlwiwdAsBCwMmKhsLGi1rFOiYVNei4dm4teR9z30erIAoCmgvb3PrHzePapYf1uk8pWpbOvP1/Hs3iQiH6IKJFmhMEdZ/xuzorKs77pprguuvcknW/W7SgokXinw65xHfVjZFPVxD8Mzpj/TkOkbjwoo8xoa9OeEIfHnkWS1+40jUej5NSQfG9ZrNZyTUiLB1ICv4Sw6Gjz6pOKPDj8+rj8n3HnPD3poLjxQiFXHvOTMotrpQnvHhtTrhEc9mZlE8oi4gQiQXDHPLJWTWEa7ZaLfV6vZQt7WUZ0Oqd8bipHhmr99XhLPrrmzpqs5IqZnPdHLlVkJubHEOvswhyZjLXR8J25l33rmhue99dA/aoLmfcfDrE44IhJwTch4DggQlhjUTLIM5tjtHzDNd0c3PktBAVn+eESHyGt2hFu2KV+/F5dqWrDjKK/XDoJMKgvBtGDM3GPjkt5/iCM9HY96g0uFCIgsrHsFwuU8E8zlGgorBbjbwzp5w4vdXxKKfpTYT+37a9KKFQJwBymlTddXUb0B12kiqmsBMC+QJES+BjIDLo8fGxUvtkNBrp7OxMFxcXmk6nCVbKbQZC4DhaczAY6Pvvv9dgMFCv10vMgB8iEsA764gnN1aHahAe+BJck0KI+TxI9WZ+ZM45hh83PNe4BhSjk7g+JxT8vVJVoOQshagVsRH39/crcBv9gAF6KKozeZ7hwhkoyLVJFy4eyZNbI18nhzhyf0dhx3xHJcjvje/ynxyDi0yS73LPc8uJlhMQ8Rru93G5huwOYEkVGBbN2v0ZCGVnrNF/4eHIzFGcV1c+gKfILyiKonKCmq/z/f29rq6uNBqNtFwuKzXR3OJCCfRDsghWwXdRZ0muEwzP8QK/72vaixEKdQOMUn0T8yen9UfT151mW1tbybk8GAx0cHCQ6ppw1OZgMND+/n4qpU21Q0kVJhNNX28wFs5dpqZSv99Xp9NJGhHp9GhL9DtCH3Ez5zSo6HBiA9JvruF3h6podXOOv8MZcbw/Mnn/O7du69Y3Mif/PWcpRJjJk6kcBmAuXUOERpyW3EcTrQl3RnKd02DE3Ncx69wa+JijNZTTkDfZJ+uuyVkD0SKJ73ShwnV1fXVr2i0DYFPpKXLHIRsUpBxE5xaEPxeLnn3k1nyEMH0cKBK5daOR80MeBtZ/p9PR4eGhDg4OJClVXJ5Op7q7u0tntSNwPAEUdMD7783pbZMW8z02aS9GKKxjPHWWQp0k5T7fyNGZVparYltc71UvgYWIYV4ul6kc7ng8rpSzoIa6F9fKmdKUy/j22291fHyswWCQDuwg+xeNnU1C8ht/w7h8flxLL4pVrD1M2+cnxt67ZYKGFTX23BxznScPuWbpjMT/F6/x9aBFQeOtTkuKjJU582sQCK1WKz3Dx42vJ0JEkUFESKiO4Uet3/sdLTr+R58dB8/9P1pROZgp16ecJeZzGvvoz/Dfo8BY19YJvrJcHY8JDIsw8Ag+NH6KHELLPANBzztgqDiV0fY9CAPBFKP4EDJYCi5I+FtSpf7Rzc1NCtqYTCZ6eHgqkEnRPU5edF9C3Y/3K6dkxT22rrnw3VSQvBihUEdkrulGTdDvjc9wPNaZj0ekYNbt7u4mJv3u3TsdHR3pd7/7nfb29vT27VsdHByk6KCzs7NUq50TvDypJTI5FhWz1I/Z5BAdP+cZonCM1HHW+Hw2AdoGv8O4gL3YFGykong6x7Ysy5RFLa2KiHmoHpESzuhd6Hm/o4ZYtzb+tz8nmse5dc61HNPzeYK5Yq3xt+d/AB/yHhcK0fGce69DSTSvj+U0QV+83IIzgMg8fa1dQ84JcXe8+hx44/keeunzTOmHm5ubigXUbrcTPLK3t1ehOTT8drud7oXeHh8f05kG8/k8PQdav76+VqPRUKfTkfQU5+/KAafmoUmz10i8bDabCYK9u7tLtbl4L3SMUvXw8KC9vT1dX18naNH3DZYl8+zWA6GrBIdQkWB3dzdVOP7+++/TGSwIBeAlxsb5DF5eg6xqSZXKu6wjfYn7K64fc+fJaw6HrmsvRihIX0ah8F3EsePmjJvCr2UT+TOYTI86gvHiL8A/QDkL3vXhwweNRiOdnp7qj3/8Y/qdgzYkfSHxKTFBWexvvvkmZU57YT20/OVymQqIYSnAmB0C8XE6Q3AnlsfNO8btkAeQlcNIzAlaG/c4HELyD05C12qdkTLXbqmg+XkZCX8HLQdj1LWIyUfLBlpxnBfmTGKUb6L4Pn++Py+eue2wRU7b4z7XPoERolCIVgb94Br/P9d47Lvvo6itS6ty0XEvzefzL6wutHcULk8cc8HjOTyu2Mxms4rGj++Nw6eurq4qloIn5zFm4D2ECNnR9/f3ms1mieZgqASA0FcP48ZCoSTNZDJJsC3M32kDf+F8Pk/7CUsA4dJoNDQajfTw8KDJZKKjo6NknRC+HpNNfZ3dcvSkNqdB52fR+o7r61ZHDo7KtRclFOqkXo5R5LSfnKXgf0uryoxowcQTt9ttdbtdDQYDDYdDHR8fa2dnR8fHx0nzKcsynY8gfVlfJGLK9Altgne4hQBTdG0Ey8OfEzMSc0zSGa87S104er/QfFwj9uYMxT/9/854Y98YF3MTYYfcGubaOo1o02fE++KcMz++uXyMzKFvXv7vf0v151dEBceFhb8nKkXeohUUn19nKcXvc8+u+z53XU5o1rXYH/+BWXmoJszShRrCO1qpUQGTVrBgjGZyge3CAcHhTDPyDIQ8/cBaqStLjiLY7XZT39xfyFGns9lMRVFosVh8EWAQYcPYr3WKkisuXOuf69qLEgqbtBwcIX1JpOtgDMcMEQxEGXU6nVQmm4S27e3tRDiz2UzT6VTT6TQdqhMrlLok39raSg7sN2/e6Pj4OFkJfhANDMo1KTT8oljVY4GogJzclPZDTbAWHCqJ8+b3Ax/xDBdIzK8zLddQECbRQvHIooiDOpP0zR9jtKWqX8L7HYWLCzfvq1tIOQe9jyHHkCOTX8e0/zYt0mhMJnS68p8IWUVhGdcxd120wJ8bV52Q9s9Id97KclWqhcNoOH8ES4FES9Yzl1Tnz/N5QDvnHcCnWCO88/HxsXIIlke2cWa4a+cOtcG42ZdF8ZTX1Gw2NZvNNJvNdHh4mJ5VFEVyOvf7fd3e3qaDe7ByYsFGF4BfI4hzzWlpXXtRQqFOI4kb8DmtMacdOYNwDYXJR0uBYGazWcoZoD7Q3d2dPnz4kE5VG4/HyRwEQnCcFwaN0KEKKv4JZ6KO9Uem60zCrQn6hlBxfwACIcIz0XrKJXTVrUnU9HPWgGvgvi45jdu1Il+n+P8cA/B1pzFO1/h9zFxfpzXl6CrSZO6eOmaaoz/aOjM+rjvX+zxzHZqr9y3Xx01ggzrr+28r+CLN5N4bLbGcZbOu39FKcmsAiwBIyo9Q9SjSvnYAACAASURBVHBin1dpFc7KXkIoAX0tFosU0oywAFY6OzvT1tZWUrba7bbK8gmWw3cQc5s8fDb++Phy8FFscb1dyXquvRihEIkm97drf35f7hk5ZiWtNGFihgk1ff36tY6Pj/Wb3/xGx8fH+u1vf5uuazQaqchdu91OlRqdqdLA13GgUUlxOBzq5OREg8FA7Xb7iyQZ37h1Vg0NPDwmwiAovFwDzm2yo13bAotttVoqiiI5EP09WClxjumX+y3ohzMzJ0ZPRuJ35su1cT49dNbn1yGEHMNBcObMZxd+OUFRx8h9TNKXpY3rtDD6wtw6c/fn5vpTR8NRsDt8yXcuUGnrIKS4z6ja6mcLFMWTcxmtODqaWSfyQbiO98Iw5/N5OpRGUrLE/Zm3t7cpMRDlij553g7Xl+WqUGUM60QZpMgf46JvWMowafrrhyexF/ANSKrUSvKDe/jZ399Xv9/Xzs6ODg4O1Gw2NRwO9fDwoN3d3XSM52QySYJiOp2mfkMrCLSc0pijYVcymYeoOKxrL0YoRHjCv8tpi9KX1kG8N06ka1Zct739dMbtaDRSURSJsJh0QkU/f/6s6+tr/fTTT/r8+bMuLi5StUTMXd5BX2DmpL374Tm+qHHj5jQEjybguS4UYD5uITBONkBkSmxEnHb+v+jDYL7rNO2cpsZnxL3XtU2INtKGVA0Bjv3a9Fnx75zC4fTkz3fM25/hGuC6vuQsoVy//DPOFX2La7HuXbmGguBChed5VBAOZUnJAS0plYiJgpmQTEkJBoUZokiBu0cGR6QSgoX3eUKb5w7hFKbsjNcSk1anvCGceI4HCEjVc75h0DBsqii7Ykh5b0kJWt7d3dXBwUGKAlwul4mHXF5eJjiaIJfr6+s0RiwJt3p9r0bhwFq5g5lPh2nXtRcjFKTNHM2bDMphDBYTBgnD7PV6arfbGgwG2tvb08nJiY6Pj1MOwZs3b9Imu7+/18XFhaQVYYNNRqye37EScFwPh8N0xKZXj/QMzOgAcw2B8aCdUI3Rs5D9edEBRr+4Js5lZLKOrcbx0WAarvXHa90JiNbGWrhW68+sex//h+hzGr6/N6cVP8eYcyZ2rq85JSUy7cjc/V6HheoUA5hefIcLqNy766ydujFHIb/JHovX+dzlhJpbar4nEabQso/PIZJIOzyf7yVVNHv2qfsOCD0tiiLlqiAcfM9x72w2q1QBQDnjWmkVcoylQK4C+84LX1J4D2Wz3W5ruVyF+ZITVZYrnyJWD/yhDi6qW7M6S3dde1FC4TnNZlMt0xlctEC4hlhmCOH6+lqLxSKdLcACsjDn5+eaz+eaz+eazWaJ0PzgDvrgGjtE4uWxYdwu6b3Psd+Rmfgm8npJ0Ufg7/L74+aPFlY0T6P2ST/ZkNGJnHNU+xpF52lc1/idO6ylfPz9OoYUrcWcxZOzfuJ8xfE8Z9XE++KzGWvdc54TYDkmHscdx1dnAdV9lxtDnZKWG583v9ehTBgzDJg5iXBqXFtnlmj4MFMvN1MURdqDKGSeLFoURUUoNJvNJBhcMLtgKMuyUjjT4Sh4S1EU6na7KcfCkyYnk4kmk4nm83kKZ+cI3+hr8LBmxv2csHd6oP3F+RTWtZxmtO7a+LszX+oPAelQ5paEMiwIMFI/ZGc6naaqhziYcxopwoD6RoPBICW3oMGzMSRVmKwTZ8Q4GZNbAp5w5WGoLnR4R5yfyEA8SsevoW+u9XskBkTK+Pgk58L77UIh/h77GB1/uTWOYXtuKdD/+D9/ThQY7sTzPvr3dXT4XAjgOuGSW5do/bAWLohzSk9c87q5i++OTm1XELwfrsjEuV0nSHw+y7JMARcPDw/JRwAzh9H6fMTIPBpKCHAUQoF+secJA280Gtrd3dVyuUwCyS11rpWUzkNAmGCNgBawb9zCZhzwDoSOpBQZSHALIamcyuawEeNnzd0q2rTlhPdz7S9CKNC+RjDkCBGnKJi8a/GtViuFpeKEhim7487DxaS89HXnMO+IRdaiBu5E6Z/8xLE7A3DIKFog7oisgzWi85MGwbsZy6bzOWCewXy5NzLYurV6rkXmGO+PNOHCjr/raGcdA8v1r04rz7Wc9p2z1DZpEZ6JVtvX9tHp4rk+577btK1T0lCOyCZGCyf5DmvBhZQrT9JKgGG1w0hhoIRucxSon/PsDln6hVUhKZXOwKJhL3gFXHf++9h8vZ0fkKxKmGyr1UrBHmVZpvOipdWxqa481tHOc2vyNWv2YoRC3QbJmcPPXe/3uXYVtV4WmEXwJJqrqyvd3NxoNBppOp3q/Pw85SYQxZArDwABttttHRwc6ODgIFkf+/v7CUainxA4Wg6x2tRR8vIUvkmiOQlsFCEpn5foOHS82rF6SWljIhj9MBCu92iisiwreR97e3vq9XqSVtpR3Zrm1syZXWRg/rs7xNmojlW75px7R462+DsKbdcInUF7QMM6LT8KYJ9vVxIifPZcP32evG9uxcbPKGAcrvFnx8+4n/x5br3E98fnoMFDFzBLP7UQx65HE7lFgJKGUHDL1cPBgYu8nEyEgny/kFOwu7srSZX3w6j5pC/0jfpkrPvZ2ZkWi0VSMvv9fjqbxSEu5so/PZPc5/U5Bu/jiQrhJu3FCIWcCR3N+uc0M57juDsLD85ONvHBwYH6/b4ODg7UbreTg/nbb7/VwcGBWq2W5vN5uq/dbqdSt5iSXkyPfjqkgxkafQoR/oh5EvwAI/n1jjHmiMV/ojBcJ1wjA2RjIvw82oNnO0NzXJdn+DxF5ljHrHLCwplufEbMfmXtabkY/nXzEJm3X8MY+d2/i9pshFXqxsaaRjgod31co3WtTiHKXUOL81v3e51Q9TmJ+zU3LhgtSWJS9Qx1D2Cgb75fYMpAK9CcB2QgCGLUX4TEoqXoPARYx2FSFA+sHGjAQ96pvNxut1NNJKov39/fazAYaHd3N0UxksCGcrpcLlMklpfq8PXK0Zf/36HPvzhHcx3Dd+KOzC93rfRl1UrukVZM1cv0koGIpnt9fa3t7W3NZjN9/vxZl5eXev/+vabTqS4vL1PFw2gpoPn0ej31+30dHh5qOByq1+tVjugjrM61gmgpgGVKSlqPh5s6FBEho9z8RS2V/3kf0MqWy6Wurq5SvyDSyCRdM+N+EnnQnjDX2Ty+FrFFAndm6CGC4LUcou6WFevQaDRSoiDHnVJyoC5hMDK7SEfRUoj3uJDO3R+x/ihM6hSeHBP2OXPfyzotMgclbtI2hW1zfYhC1b+PSh8aOtei0PE30KUrJj7+5XKZrFKgInwVrsz5PvHEM54HXRAJhM/OhQ/3UwobxYTns5fIKSIBlmKARfGU/Yx/EicziiBCAV7lkFkce918Qy9ucWzSXoxQqMOLo4bnGlNsTJBLeEkVgiAsFIb96tUrdTod/f73v9fR0ZFev36tfr+voijS2au7u7v65ZdfJEmtVquymb2Ri8AhOkBH7lfwukbOJFg814IYt/sLcjBRURTJIsGy8I3WbDaTUwyzl2uurq7SOREeOgqD9xjxSFgRQqG/Ed/1qA6a/+7rmxNqvKssyyQwKVhI/ggZ576JqUT78PCQygvwbtegcv1YZ0XkvmNuowUF3ZHw5AyMpC3uzTH9dczY6ccZLA7+HI3GMddFinmlU5+Tvb299B3nEjvUUxRFuhctnntRbK6uripJZ15hlecTnkl1WXwCi8UiXff4+Kj9/f30XvdNuBJFMtnDw0MKgEDgkN28vb2dGLMXevTEUKx83g0M5IoQtEUFAyyDN2/e6NWrV3r79q36/b62t7c1mUw0HA41nU51f3+v6XSa/A3kPqEweO6GC8a4br73gVCllTW6SXsxQiGnCeVM4HUtam+OkyPFF4uFyvIpi1BSIob379+neiWU7x2Px3r//r3Oz8/1888/p+gjklIc2nFtxM1jN135QXDVLSz3cp0fI4km5NAMxB2dmB7JAJPARwGhkenpBckItYMJYwW4yR21FWfeXOvafUyGgzFF4UCL2g8a2u3trRaLhSaTiRaLhc7OztIZF/SVZ6IATCaTVLJ4e3s7RYO5Qy9G2+T6s87CYT5csJVlmeYTS4H+4bTnfrBof158Z7QO4/u9H9CQv5c++fw69OnPWywW6X9uAQFxSKpUMfVxIzScBsqyTAy90WikMtZR6WNvSSt/FoLEq686TTNvNzc3aZ/4nF9dXaUgCCCZRmNVhhvhF7VxBCaOZq92ChO/vr5O5yd4TgORR4+PT5VUUTInk4m63W4ScBcXF1osFvr06ZPm83k6wfHu7i5ZEH62c1SOXTFkntkv0sqaj2jLuvasUCiK4jtJ/1TSK0mlpL8uy/KfFEUxlPTPJf0g6c+S/n5ZlqPiqXf/RNK/L+lK0j8oy/JfPNuT+vd/MWg+6zapM1RpdbgKCWWdTkfD4VBHR0c6Pj7W/v6+vv32Ww2Hw+RPgMFEJ6m0MjmjqUkV1KOjIx0cHFSgIzBOT9KJ43MhwjiwMiigR39woPnxkQ6D0FxAwhjYUNfX14lhsyn4Gw3W8zGcqfncRkJDMBBJQVloNmWuPaedwyA44Ojnn3/WZDLRjz/+qMViocvLyyQAaaz7YDBQq9XSd999p06no3fv3unw8FCHh4dp3VxbXgfB1F2D5UF/c5i1w3wuHH3t6n5cGLulwzP8+e5H4fnO2HPWkAcnxLnwd+eUAtYp/p6bx2ghR2GEpeP+BvYu15KQBvNjvAgQFDSgG0nJ0nAlhD3s+8NpHOipLMsUNotywx5ttVoJ0qRPWBOgDPgWCT5BKbm+vlan00mCcDqdpnBVaNmT/XwOc0mNOTqNwQfraJu2iaXwIOk/L8vyXxRF0ZX0fxdF8b9K+geS/reyLP9xURT/SNI/kvRfSPr3JP0bv/78W5L+618/17Y6CZYz2eP/40CjhuPaLKcwUfSOgy4uLy+TZt1qtXRzc6PLy8t0/jIVUT06QqomUhVF1dHsDDtufJpvdASG46kQt/84DIWWG5+bgyHQtl3jQQh4kTCIsizLZMai/UNkHlrrTC72gXtzSTi+vvEnrj8bAT8Qa8h6ALnFzbJcLpMjD2hjuVwm64iDhli7aJ1K+QS7upZj6Ln/x7napDH3Llz8ufH7yJydMbhFkWu5PVf3u7/L/45rnIPqco3+OW37cxAc+BlYn5jUSSQg8Cs5CpEG4/7kebzfYRxXBCmj4UlnwDTQ4tbWlm5ubnR+fi5J6fTGbrebeND19bVGo1FKjkXoOW2zhyJfq1OO45x/jS/pWaFQluVHSR9//X1WFMW/lPStpL8n6d/59bL/VtL/rieh8Pck/dPy6e3/Z1EUg6IoXv/6nNq26QapEwxRK+MT4nLNgZOSwPvBHcEki6JI2DULxeI7YfsmJRSz1+slCwEfQ3RueV/dOijLMpmaXmzOszE9qoJ7XcvzH4gIpxfaB8IAZy2by7MowXLdv+H5Fm6NeYy5VA1vRdDSdzQwn0eHljz+3DevCwUEws3NTfr0OvzMrScBSkqa2NnZmQ4ODnR2dqZut6t3795pd3e3crA62llOWOessedoO1qGfk90NkdNPgpc+hWtELc2/dk5ZcGtC7ciXWuOAtqDEmKLDAjmlWNGOaGfQwKgM/aCY/oenePafBQKOK89/DVq2r7GniDGOuAvcd8BNY1AE+qUV09G9ZpKQMFYHYPBIMFes9kswaTsTfqcEwLxO4dQv1bxkL7Sp1AUxQ+S/k1J/5ekV8boP+kJXpKeBMZ7u+3nX7+rCIWiKP6hpH+4wTu/pouV++Imck0bJoXW7aGjruFLX0bw8HxffLQXjxDKRQbktGE2J31zvD2nxTgD8H7khALYNX4ChAFajm8uFww4Rj3FH+YVIQoYS85i4xm5s2md+bkwcJM+MtM6WCK37rExvvF4nDB88F3KmjhG7cqEa9Y5yyEnGDZh9s5IndnG63IKj3/GsefgghwziYzb593n3r+Pz6yz9pw2cwLVhYf3KX4HjcHg0cSxQnkmUJLvm5yFHv+GnuPe9qQxLAdXFugTRTXdd+b7NQpvVwRd4XL+w/vc0Y2f5DnrINe+ho9uLBSKouhI+h8k/WdlWU4DsyuLotg8xu3pnr+W9Ne/PrusG9C6gW7Q5y8YumucQCI4ap0RLhaLZCWQrIbzlf4gNNDm2+22+v2+ut2u2u12wkJ9HI4hIwgkVa6lP9wXCQsNPSd0fEOzYeg7kMlisUhCgRBUhILHf/vG4nhQL8strUqR0yfvs6T0bMp0I4QcW2YuIyPwH8dwb25u0ifPZVOvg0TYsMBJd3d3qSput9vVzc1NwnsZK4La8yDot8MwOYEYmUwU3q79OT250HRIzBlmdBDXQVzRj+RwnlsEPpbYckqHj8vf49fH79cxMn9Ojt6hL88/8usZY4TVvB/Rl8cnmrVbCmVZVjKrvQ+cPY3FErV0Fww41Dmfpd/vJ2HiZzuQm+T5Sihovk6xPcfsnXY2bRsJhaIotvUkEP67siz/x1+//lz8CgsVRfFa0umv33+Q9J3d/vbX7557R3aAOY04aunxWjcHJSVNkHpEvV4vnZ9wcHCg/f19fffdd+r1epVIn8fHR338+FFXV1fJVIQg3MwEzvGsZXf+0nzz0V93VEcm4Yw9jtPnLKe5cT/mZyxVjMWA78DPsvW8BNeUo8WVY5J1a+mEHbFtN9Pd2efaFgKHuQbu29nZSRDCug1CH5nf+/v7JCQvLi50f3+fIpJwMPI818w8gsz77i0y0fgMXxsX4n6NCw2nCZ/LnC/JGWK0GvmJVptrsLF5f+I4vE912mt0dPoz4xy51RT74nvf/+dCwucjWmZRgCII4u8IFl8X5oo5Agbt9/vpHIbFYlGJfCK3iDpqHPVLcMubN28q60uu1O7ubtqjJMtitUTBsE4BYqzwwAitrmubRB8Vkv4bSf+yLMv/yv71P0v6DyX9418//yf7/j8tiuKf6cnBPCmf8SdI65PXfDB1xJe73iEJ3xQcDr5YLFJs/+npqRaLRWLUHz9+1OfPn/Xp06dU4sKTyrwPxL+7Ju2Yb5jPCizlCTUQHibjcrmsxHozjpxGnZsHCMHPhvX7HSIjjhvNBauJTecWAv1zoeDWAeOh+fx7dJAzVvfPMHfMMxuxLEsNBgM1Go2k5ZN06MXJYosOWeYSIXl6eqrZbKblcpnCASlV0mq1Kg5oV1LoKwqCb0A+oafIoNxpLq2SKnkuz3ALyB2qUSBgaXrZZhcoCH3HqLmffkemynyto7W4Z+O6OeQWmX28N1qLfn1OKYxKSITMovCKfeOdWIL+vWvYPgZfS6xvwmXJr4ghtezp+/t7bW9vp4AVn09CrDn/wRPZ4t6JFl6cf/rtfc/5duraJpbCvy3pP5D0/xZF8f/8+t1/qSdh8N8XRfEfS/pR0t//9X//i57CUf+gp5DU/2iDd2S1Xr6v09r8GqlaaAtJXRRFqoi6t7en4XCofr+vb7/9Vq9evUohqb///e9TYlqj0UgO6IuLCz08PKjb7SYIA+YDgZDOzpkMx8fHyckcidnxQWcY0uq0JRcAaMGe8BZDW4uiSKddYcm4gw6CwtrhHZi/JOMAqXgSDv0nNNbxVBfWrm3CvDDZXQjSvAaUMyLmg3d76CtOvVarpX6/r+VyqW63m8bmGdl1NOafzAXx5JPJRFtbWxoMBklgM2ZfG8eqsShZlwjHgBPDBGD4jJWGcGGNuYbnx5wYmBnM0OPwO51OEgQwOxQCj18HFkTAQ2PNZjM94+bmJq01849ihCLBOueS12hcT84Bp6gxXoRjq9WqwJc0oojIVXDcPXeva9YciYniADxLrSVyCcgtYN5cAHMN6/z4+Kh2u53mh+zk3d3d1B8KbTYaDR0fH+vo6EjfffedXr16pR9++EFFsYJFf/75Zy0WC/V6PS2XyxSBxPrj5HZeEvdf3ENR+Dntr2ubRB/9H5LqnvTvZq4vJf0nz765/n1Zk5XPqCHE/0c8lk82jkfiUBL7+vpaZ2dnKUOxLEv9+c9/1sePHyuWAhaGtNJiYL6cuNRutzUej3Vzc6Nut5uYnzsr6VdcyIjL+iZ2WAVikVZYMgTvmDG5B0QzQFSeBwHTwwLAWuC57mh2QVOnNTI+rvFoC4/CWC6X6Z3OSLnX19Sd3BQpK8sy+RX6/X4KIfYSARGOiBAIf3sNe0qjc1TrmzdvUnw5AtFhPRiIpMSwYLiOcTMO97uwvjA7GJ3TrjM3+swzPZkJyIEsYGcaPlYYhmfoeh9593g8/kIBg1nxHXvFrfyiKFKCm793uVymhFGHbHz/SkrHUXogQ7PZ1Hw+T0LA+YB/Nx6Pv4CX+J7AAmesMNvHx6eTFz1s2unU/WzsJ3xyy+UyafhEw5GvECP3lstl5WhcD5mdTqe6urrSYrH4ovaZO7DjpysKDnf53Lp1/HdlKfxra05U/t2665zZ5kx9D/EElwajjuUBosnv2LZrxWiURDA506wTYN53H5M709gQ3JPDfOsWOcJxvlkitBW1DTQYF1I538G6NYn9c3PWGUlkKrHFZ7MGaG0HBwcqikLD4VCPj4/JnPdTuKQvBYM3rkMDRrNfLpfJmsI680qb9C868zyj28dM3DoMm+9g3sAD/A4duYXi8+hz45aEX+tWjTMQt8L8f+vWZBOG8q+jPdevOhpkDtnz/hPnIM4LVuDj42MlIAElx63kHE9yXkT0I/QWn+vPwWKIUFsdn6z7XNdelFCog48i0dJyTM9/mEx3TlKTpNfrpQNwdnd3k5NZUmXzxuc7hIT2TO4DMFKv1/vC2RyJ0AWNf2IuwpSBCGgxu9PnwYne++xVKOMco7E5ploURYKaYC5oljnB9FzzTegby/+OePM64m00GqnAYFk++RkeHx/V7XZTnPdsNtNkMqnMRR3mTB/xp5CBfX5+rsvLS7Xbbb1+/VrtdjvVsuE4VIS2MxPftA6duSkfrRiPevG+1glRX/s4f6yX9LyFl7PGI9P0a3MWSBQo0I4LPEkpt+b29jYxvjgfwKBengElBevIhR5MmHvR8n3PAVWhxUtKECnaf7PZTNAj/fF15e+traeCl0C7Dw8P6US1slzVKMIycYgQmkOg7OzsqNPppBpYwFnwIior4PfEIkLZiLTi++Nv016UUPCB8rdUjV2XvnQ0+b0Qo7Ry+AEXFcVTTZetrS1NJpNU98grKXIu6/v37/Xx40edn5+nbEOHJKSVxs1zZrNZKrm9u7urbrdb0fQhvjoJD8E4k0YI8f+ckzHe7xYBGwgmwXW827VHh2nqLK7cjz8z1+qsOxeIfp33KTKm+H/KGAyHQz08POjy8jIJTU/Yiy1qWpGWEA6LxUKPj0/Fz4ALEP5bW1uVjOgIh+To2YV2jiHnrq8TCv7p+8Pbc9aY7ymfC55Ztxf53Z/D9xxmH9cNHwM+BObL9zcQnAvVoijSvdCxw6o85+rqqgKF0byCLkIDGJb3+JkIPg+RRsuyrMCyd3d3CYImfB2a84Q5+kwBP8pgcPwvkPPFxUUKmeaYTgJc6LeHFOf2ln/v6+Z/r2svRihERhMZFt/lNF7/hAF6aGGr1VKn09H+/n6qSfT69Wu9evUqWQpv375Vo9FIizMajXR9fZ2cSTAfMhs9UYZT28hPoN4JAiqGsEaNlfHxe7PZ/EK79/E5vMT3kTGhITFnVF+M2jF9cU3VLQSeF5OCvkZAuGDxn1x4p29A35DO+CB6HKLgsmSFnp+fp7IC0+k0YdmxuTBy3wlzRnRSs9lMFSypj394eJjoiTO9gZicyUVmHDX6+L1r6nyfEwpOM1FQwDj8udAt8+bzypjr9pTPfVTG4hpLSlZAfB7C2jHv2Fzz9wbt5ZiavzfOvT/TcwHctxDfh1XFHHsGPpbCcrmKXms0nhzN8AjgSxcKjlD0er0U4HJ0dJTKu9/c3CQnPUKm0WikEi2es+CtTpD53NQpWNk1ePaK/5/aOk0mZymsewYECRPEqewOJY8vxsFcFEWqz//+/Xt9+vQpnbxG2QcazweeoY7J7u5usja63W4WPmCjOwOJ4+Na1zQi1MS1OSbs/o9YmoLmZijvqsuLWGeZrGtRA81ZHbn/OUTg88E8+LOxGB4eHjQcDtOzJpNJwmDdAZ3rV8TXI0QDEyHxT1KKKQcGAKIsitWpXQ655SwGZ7I817XkOmd5bNARdIxCAjP2UGKKKvo6RNqITCWuR6TX3Di4j/75eCPdM0fAL67cSKuQXYdvvRVFkRzvHtUmqRL662hC9P24hc06xPUoiqJiKczn84QkAFsCU7mFTgjyzs6Obm5uEq1cXl5qd3c3WRjj8VgfPnzQ7e1tshqwGIC36P9zWj906/P4F2kp+N/+fTSH4nW5Z0H4xJzv7e2lsw7evHmjo6OjVH308PAwEStx+WwinELSqi45k+ybCQ0NhyUav8f1O5OIGh/NGXgUAIw/4u9R05NUgZ4cVqN5AhP9Wafl1wmBHJzhnz6HrEmMfnFtNK63vzNai8xDq9VKc02C0M7Ojk5PT7W9vZ3Ka6Ml+vhyc8mc8QlTceVha2srZa5Tprvf76dkJZgxWLon/EWhUJYrP0CdheH9c+YKw1kuV5VvSX5iH2BR+aFD+KuiwuDvjhqm02xUkuLcOcNlbwDTRFqELni+WzVRO87RaGxOR3H/IBCYH/aB96EoijQ/3M/eBQXY3t7WwcFBCuve2tpKobQxUMRL65BMS7VmkAzPsCcHAiEE7aHgOAzt44z8MRfh9Vx7MUKhrkWNLff/Om0VYnYMDhPy6uoqTfr29rZGo5GWy6UuLy/TglDP3MMO3RLxPvlmRQMhNM0hGe6JzCFqWzkNDibwXIvPio4n37h12mvc8Ll5j7BFfH4cR52ge24s8bp4jwtozw05Pj6WpIT1crJd1Jr8eayJwyrxXWilMDzyTqCXra2tFB5KVitFF71ESFzrOL+xXzkFCeZGccP5fK6HEP5U2gAAIABJREFUh4cU2lgUTzksvg680zXiOoGfU9ai5eNz6evhzmb2HQwOIQtdkMTJvAM18RkZoQvTdc33gNNhfEaO5qPCFuE3GDaYPwoHRRsjLFwUT+G6zWZTo9Eo5VNgBVA+2yuveoXUOh9OHV/MfW7SXoxQcILPaYx1kpCGdEYjI0R0a2tL/X4/1dR/8+aNDg8P9Vd/9Vf65ptvUi7B0dGRyrLUx48fU1hjUTwdjOGWQTR/wRgHg4GOj49TRJPjiWVZpmQZ+uc1Uxzq4XqICPyVMEmYClgmTBw80515y+Uy+VWAv8CXmUuYF0IQgef9e3h4+KJCKrCMv8v9HI7BkgjoZ1YDYXheggtHnxPmHAiHDcvcwBzpH8wXXBeIkFwOsNmc1eUhhYwjCk7PL2AObm9vE5wE0ycaBu3PK+ZijXocu1fRhN6ZUxdgMEfP/aCi5nQ61XK5TDTMHMcqu9Bhq9VKY3LfF8mBCBbmAKhVUup/TK4CmnWmdn19rVarlbByzinmmcxBq9VKdI+mjmbNqWxeZsUhT8I6494goYwAkLu7O81mM0lKDlx8ePjiWKO9vb207kCEHqV4d3envb09XVxc6OLiQo1GI8FKTjdErH3zzTc6OjrS7373O3W7XX377bfqdDopV2Y0Gmlvby9lNrPvmV8UTWiBPkc+yt7xpFf+/1x7MUKBltM4/bNOg41RER7WxmRubW2lowDH43FyIG5tbSUN8uPHj1osFvr48aNOT081mUyST8Gbp68Dj1BDB2Hh+RBoQ1I1MceFXR2E4hmtEH20BmazWWKmru1zzCYb3+cRc/T+/j5lcoJtckqWtMomdhPb3+HPd0HnYZE4YREAvBsG4GsMc3Li9/c5Xu7wBD9F8eQcPD4+To7/+Xyubrer8/Nzffz4MR3hGeGoGKlUZ2VBZ/QLLX06narRaOjs7Cxpv0BbVGQlcqnVaqWS6/zt0INbLbwLxsv8wfz9tC7opSxLdbvdxKg7nU6qxcM70dwZO3SFEhFhCvw00GW0OpfLpU5PTxONzufzZJlTBkJS+j/jBWqDgUE79BVmzZyxNvhIGo1VMh/Civlz/8H19XUlooe+zOfzStg1FqfX1WIMTveNxtPJbpS64IdxQh9YSuS9cNjX4+OjOp1OWtvpdJr4Df308jNuNfDs6HN1aM4F0yYog/QChUK0FOJ3/B0tBmewLCIaBQTnZxHs7++r1Wppf3+/cvoWJyn5iU8xtMyhEMcJ0YK9uTbqfYv9XwfF5ObDP/2eOhgn19y89xor7oCuc25GAR3hKjRhHPFoqm5617XcWPndaSD3HP6GWRTFU2IbAQCSUo0rYtRdELhVGJvTl1uOvgnpO1qkR6phLWBN4Hgk5JX3u/KAJcSawJSAF6jgO51OK1m2zDOWGrk0WFGOn28KLeSui7TsQgxhiaPX/TkI9ehsd0tcqkZrAcn6uvsYcpCS04cLIN/TnoHvezR+OvwEXSN4ETJ7e3vJondhzrv5ccsZK5+9h7VE2Gr0xUUf0Lp9kNtHz7UXJRQiXJT7/3P3x8mPAoGkJw9TRUtDGLAQ8TkRH3TB4xnSrs14ITkXNDlYIifN181HxES5Lsew/XcEARuWAlxgvpj99L+OaeSEgjvX2+22ms1m0tZhSDmsvo7h+Lo6dMT3vibRN8MG8mq4QIbj8Vh/+tOfEkMlssMhmzjvQE8+zzFKyK1T2nQ6reDRCEtoAp8DSY/UCHJHMAyD5C0yrtFewehxgMJsTk5ONBgM9Pr16xR+7edT+9r5uPg+0pJH4fg6cR3MH8uVQ+m9zEoMekAw8Fx3UpNgJinBR4QgkwksVYs7xn4hBIGSXFgCU9E3Xxd3NPt+73Q6iWlLUq/XS3uHGkqeaMZ9cc74HiSBeaDOmofDk08FrQMn5ZTlOA9f216UUJDWR5s8p9W4WVcURWJsSHHwvq2tLV1cXEhaHaQyn8/1+PioDx8+aDab6ezsTJeXl+kYTq/54o3NiwnfaDRSYS4cfHUO1lxkh3/WCYS4WR1Oyc1VnSaHlhx/3KlVZyVEhzREznygCaGxO4Pz59T1j9/jmHJWFi1q+VwHQ26323p4eEilMSaTSXJAYzl4y2lgHkcf++FCKWqrDme4NYHDGsYEsyqKImH/Pi+ewATmz7rRPyCrvb09dbtd9fv9Sv5MVEbi2vr/cgpGHU0wB1hgrik7vUVGlsvh8Xe5EMGPw15yXx3zF2mEvriDH8sNqIn3uiLoForP2Ww2U1E8+Rsl6fz8XBcXFxqPx4lfLBaLrAKGZfjp06dUbhvoSnrKccAJ7TWVYo4FQqyOV/h6+OcmVuGLEQpRIvtgc5IvDs6tBBg9mqknlnFgO+cpoJVRIgETfzAYpOQ1Jxj655r03t5esjy83LKbmu6gxTmWi/pwphF/pJVWBVNwfNHnIDIz35xeHhsNDseW1w1Ca4qWDM92s5v34iwEO3fLgXVax2jqBM5zjrJ1MAZMgPIB+Ja2traST2k6nabCaZ6rkaM9d0Szjv6Z6wv3MW8wDN7h6+bO6BzclhN+0Hyr1VK329WrV6+0v7+vt2/f6uDgQEdHR0kgMCYfR5z/6GyP44/QE7SIYAUHJ3IPSEtahfW6ds57HdLJWcDkG/nhSkBq0GosS43PgbVxSw2BhHPc4c4cMoBlF/0O8BqK8rkwYFzOJ3q9nvr9vg4PDzUcDiuJb0QkIXywujxwgOYCza3kulyLTWCkFyMU1mkgUQtedz9alKQECYAh393dJScjkp4Es729Pd3d3emXX37RfD7Xx48fdXZ2pvF4nGqls3l5n6QU6UCtHUkVYSR9KfDcaoiMj7+dEJ3AmQ+IzbV9TGoEUkwA4n7ui8KhLtszOrRio+8OpXm0EozNn1O3hrwjRhq5JhR/z2lLDjf590SUNBoNDYfDZOWhOXL+c6S1GO/t8+DMM0YvrWsucOIauQadEwo5WAOBTDRcp9OpnALo9ODBDnzWKSP+bs9Gzgk+SclS8IYiBeMFBqM/0AcM3aNmynJVcZQcAa8VhDN8sVgkOkQAFMWTs5t193F6KQqsBt6dSzrknvF4nObi5uZGP/74oy4vL3VxcaHLy0tNJpNUd4t9inJUlmWChDqdju7v79NZ8UVRpGq/d3d3+vDhg8bjscbjcaV8hoepuhLpLe61qGitay9GKKzTAHOQQ7zPidetBd8orVZLx8fHGg6HKTQVRk/yCAKEEDjOGkCj4fkQKdghBABjlb6U4jk4wsfomzVq+4zb49IRBhAL2g9wTe4EMYSmx1N7yV+yNT1yAy1LWm1g16LcSsCngg/BhScb1efRGYxbPn4WgDPyGOPP7y5M3WqK2iY+DgQ2JasJJ5zP5+kMjZjk5uONGizvZR3Wadr+vLhxWeNccyYF09rf309j6nQ6evv2barXv7+/r5OTk1S8z9/hfY5zyN9RUYnzznP8M44x/nhklY/bLWGnN76Llhlz4clcCJqiKCrRgsvlMoV2YjXkHPtuDcRClLkx7+zsqNfraT6fp/ecn58nRcsj5OBFQHheQJMEtkajkYoxkvcCTT4+PlYOAfOQ8LqGgJNW0V5/cZZC3fcR54wDyzEIfogCISQVHG8ymagoikrlRmoekewEnucMDS2EhgTGEehaO7Hzrm1HWMOZgo8vjtPHA0Pnh1jrHPOGebimHp/nDNlhKUlfMHI3T6Nm7nishy3y3Ovr60rkhGd7cy3vR9vMPVuq4rw+R+s0I//bzf+Dg4OEFUMjxIMzD75e3qIQcigkMtQcba/7X1x/xuaQAD4IrILBYJDOCfd6THFOnOaes8Lr+p3bm5sobfFZ3pccjUK7jAGaRXP3PQH9k7fBGlJ1FMiJZ7vCGftYJ+h49+3tbYIdp9Np8icAxQKnOV1TtG86nerx8TH5uRAK9/f3Ccb08+FRNlGachZrrn2NL4H2YoTC32XLaSf8AG0gtR2zdc0yEngOxqC5pQCTRjuQVsd1wrg99jsyLSc6/1/MDCWDFbjD4SMPcST6yoWl99+ZvTsEif5woeD3eMgjOD0hdEQYYTlx/CAJPTBPj0pymGC5XKbxYT2VZZksn5wvJtfq4EjG4EyToAA2K4EDZAh7UhnNGYpHVDkDQzhEayFeG/8X6Y/nuEDd29tLMNHbt281GAz0ww8/6Pj4WCcnJ8npj+bpeSo55sc7ncF636EJ5iFnCbnlSJ/5PQdJwbSjkGI+o0BzRQGhgIWApbtcLpN2zRqQi4S/z4U876oTWnXf1QnCuvv4Hosy+m6YV1eCvPy+t000fq77GoEgvSCh8NwgN50Ebx6SCvMhs7DT6ajf7ydtYX9/X7e3txqNRirLMjE4Mk19U7pG7v2CoTrk4uatS/loNbiGGRl4vDZaJWwMNioRGJ7kEx2mbkX4RvYx5bQ8Z+qReNH6uZakQZJwMOmj1u/3RauFuSPkEodcZC65TcNPTtg68yETtt/vq9F4OriH9fIEp2hpsG7+TnfiuqKREwxf09w6QLnZ29tTr9dTt9vVcDhMFTjJvI3M97nmQgHlA5pCAWAM/nvsp0fvOMONgtz75lZrZGSshV8b94Rbzyho7Df2C+sBT4CGwfod1orKGv317xuNRrLKgHQ5DZBwV/rnuQnwIg+Np8w+/SZfAf8D/Ij5iAK7rtXtj3XtxQiFTcxs38ybNJxi4O7NZjMd93d5eSlJ6YAMmBZmIM5lQv7c6SetHI/Sl1AGC4tgAHLyOGM3XXPmLM5iH4v/RIHgWc4wUN+4EXpxZk7fwF4dKvPyCISagsMSbkrSHp9o/GR6TqfTFGLnmhCMwH1Arj15NIukJKRzBxita1FDjcIEBnpycpIOUJlOpxW/A8lh0blX9+7od/AWrYTIgHIbnfXipEAKO759+1a9Xk/v3r1Tv9/Xq1evkuPSw4uj1ZvrD3QE/YOVo01jTcHQGCfXuMLgGcncz57gPubIoc0YveUC1a+LChKCgeASP5PafXX0xR3JLnD4nzvK4zo6dDWbzTQajVI4qoeQxoCQsixT+RzOZ6FUtgc7QGtUU3Do6Gu0fuYz0thz7cUIhZwmwfeOiT93PwTpcAbOnG63q3fv3mk4HOq3v/2tjo6O0r27u7sp6mQymej8/FyPj48JZ4a5o9G6FsuGoVImMAcEDmMDz/SzEqLAc6eba93OjLhundbk1kxOW4PpewQGY3EtOmaFO2yEUOGHjQZT99hqfqQVo3DB5pCBVIULmLuiKL7AhDehq+doDJohu30wGCSoBN8TdZOiUNgUcqi7JgcT8X3sO1otBzh1u93KCYIkY7qTdNN5ctiIcEii6cpydcIZexGlpW6/skb87tCXr4VDgU7DXBOFWp2lDX9wpcmFgrQ6CwWlRVKyqhkT74jRU7RGo5Ec9x7qSsIr51NDKySComBhyR0dHanb7ert27c6PDxM1XURCvhBCIlvNBrJ4o6Z+HUWG6gBY9/UUn0xQkHKWwI5xle3Ed0MhYFIStE1jUYjhZMRbUToI4W+Pnz4oOl0qrOzM11cXGg2m6U4aBgj72MTAZ1QXA6mCKFT/wWt3C0EqVo22AnUNasoDHwzRebEHAB5ODTkgsbhNbcY+L8zfBcCCEGylik8yDvQktCaPEva++mWD0yY8UU4CT8NEBR+iAiLuUntkBF/x3l2OAjT/uTkJAl4SamyJVaPCzinO6nK1OsYMmPyAITYXOsG4trb29NwOEw+hMPDQ7179y4xGSLmPCLOtdzoFKe/zDv1eyaTSXKa0pwGYHDuj2PPRWc4Asq1ef7P/Q7fcK2vY5zLKBA8KML9CC4cHP5FKBRFkSAy+uR07O9iDv0eFJoff/xRo9FIo9FIFxcXyRdFkAvWMBb8w8OD9vf3dX19rd3d3VSVGcFL/Soc2H6egicr1lmVvvY5v89z7cUIhXWYY9Qk6u530xVYA60K7PXk5ETD4VDfffddshQkpXh14pDPz89VlmViaggFNAuHbEh9Z8N2Oh1JSpFLRLJQTheG5s3NajaGVHU+1zGPyOB8w7ij081oICC0nO3t7RRDzmaFAbgActgJjNTnBYHkUSGuteWc+TmHW1x33/gO40Ra8Q0c/5/78WsYN2UUlstlshqm02nF6nNLxjdfZF7rNqNrvXEcrBFrAD1DX1T+7ff7SRiguUaY5bnma0Z1U9ey2Vdor/wPBYK9AcNvtVrpOShRbo3e3NwkJglNYAFCh2j1NKBD929Eq5ujLskpYi6BG1GQ0J5dgSOHwRUVnx8UFUqh85yyLFNZi0ajkSwF5p+55HpPou31eqlq6sHBQZrb2WyW/CLNZjMJCZ5NiZM6oRmVIGjJUYh17cUIBd9IOdM3N3AffLwmYo0eGcT5pyTCSEpZriSezOfzSp1zGgscq3wiVNA4XTsnkuPi4iJpn2joECxaQtRS3FKQVkzRN70zOdcA0SYWi0VF88a3gZbG5mVTOezk/aSQ4Pb2dqqfAwONAiGm40vVyBS3WHKaoK+vrycWH4KBzeiWmf/t1kGu5eAMopLQhqmsO5lMtLe3p8VikQ7sIdrlOfPc14YGlOHaNYIX5QHBS6mKN2/eqNfrpUzlw8PDyrrk4Jw4B1FRoJIuvgR+mF+HDl3zxEcEjUctHH8ea8Jeajaf6hn5Xqfv7g/znAQUK/w/PPfq6io5YDnPAnphfChm5BzFiskIe6zfOFf0E8wfXwvr9/nzZ11eXqYkMyoOu8ObZxG4QHFGjnlFIEpKFZvhVe7XdMsuJ/gZO4Ivtk2UhBcjFL6m1VkT61rUSN3EpEXNNpr3EIebZr656AdaM4wPhobZuVgsks8jN7acpudEuqkWWGct5DRyZ9g+FmcqMbKEzcP1zBkCoc7BGRk+wtXX0IUJ74AZ4LyL8IgzmagZRatgXXNtG62w3+8nZga053AA43cLLzbvQw76c+sM+sCBj4VAhBE+BZLXfD3iO+N+ccXBGSc/HgWUs6xYM3+XBzrAzN3Cy81FTiBHWDR3n7doda67lhb9Ek6/0io3x5/vf7OnoS+w/si8/R3QU4yIgp6BmBwSi35E3r9JyynZm7YXIxTqmJwzhOcWnb+RlEy4+xQoWnd+fp5wft4zn89TETwiZ/xYQ3fc0HwxfcPH0Ew2CPH69M99BNzr8FHUJt28rcOjfd54P8/iMwqeuDGdmPjeP9n8/j4+0ZJyRO1r5pZFhFqiRRQFj48/J2zqaCS2HIzka4hmiiMQq2q5XCa4jdIMCAof+7r3umPdLQSgOSKN9vf3K45lP1rTnf/M6XMCyRu+J/9xZSmuOZaAr4WkNBesHZovCgn3OpzhTHndGtY1v98/665zWvd7uQ86jP4i+uv9Wi6X6WCq8/Pz5EcAYcBiYT4lVaz1mLwGjCsp3UskpKMW9DGnbK2bo02FifSChAItJxE32djeIj6fg0Fw3DmxkmHrDNo1l9y7IjFzT4zFJ6qDjMWyLFNxLYqYgZF6/SInYMxrNq9H77h24/3yjRJhlchwmato+bAeTuTOwKM2BUOsI2LucbPaNVi3rvjxirdEaURtNbdOUVPNab65e7H4WJNms5nw+/l8rn6/n/JaCFmloCDCn/65JZGbM95LMiUWAmcpe7TK69ev1W63dXR0lJzhzlTXWWbxGuYVhkMmLv2O93gMPQmTrLUHUKAoAQkh7LwMRW49YnSSM/oc/biV6f3LWROuSPieilaPh0o7b2Afu+9lPB6ng4MIpKhTXFG24hj5DrhSWllwwMoe2RfpO7fnHab8WitBeoFCITYWMEf0/L/uPpw7ucN1MMUdwySahkqpfvYB10RN/rm+u2MLRuZRBLGEBgSJhuVWSFEUFSHAJnA/gL/bN7VHc/A+x4e5Jt7Du3mPb2CaCxpfp02tmajt87+oyYHdr3tuZPQ+9thHnyf/3fvjgQtg5Kwnh+hQ655jHh8eHipM0xOqfGy8h3XGQkBh6fV62t/fV7vdVr/fTxASZbERVq5I5SyyyGh97qMPKGeBuUPT/8/1klLYJfQFLUurA+/d+n3OkvKxrBMKbom45eL/R1C4UOAaWrzOIUQXIliD7h/xCD6cxTi2XShiBeb4EfXCnF6hAz+HhT6687+urVNm17UXIxR8geP3X2v++PNYRJLXiL3mCDwIuSzLyrF6SH5n0G565ibcCdEbwgTGEoXD5eVlin3mgB53QDsj5l40Oo/0QbBgZaCpQawQcdSm/HmEfjpBu/WA8PH7nbk5Y42Mp84x5hsvWjjEZeP4ZPwcdEL0Ux0W7bCXr2McQ7Qg+I77URJwAJMc1uv1UmKelx73mlk4VZ2JOuNFKBBOCjQ0GAxS4bTBYKD9/X0dHBykwoOuWUYLOyfs4pihQWjeS3rEvUj/3fLL+X3oj2vwMFlXflzB4Bncx3zd3NwkxsxceZQb98AcPWmU31kH1/oR8tzv8JvPF/e4L/Dh4SE5tJkvEsw8XJR3uqMdh3lRFF/A2V6OBoViNBqlozlzpwTGvvr65gT6pu3FCIW4mWmRMGPLwQe+8GhclAF49+6djo6O9Nvf/lYHBwcVJkfUwN7enk5PTxNhgpc68/FS2mxox3ldU+L5Hg4qPZminOXKJzgyDMIPp0FTdYegM120zZxQIJzPhQz9ipYLQsFD69atW5x7/nYm4Th7dBDn1tQtA2raIFgajUYqJcD6xWNQ40bx8WzSonaNMMFyJJIFgUF4Lwcs0V/3M0QHedSkEXDQQL/fT9okWcrQV4QWcwpVbjw+x86EPRSVZ+aimXJKWt3e9ffAILke5u1C2q0WFAJ/DsKEfeQWZKQxt6DjqXqu3DiNxCS7KPzYJ4TSuhbPPJIEy/5nzXkuCsXBwYF6vZ5ev36tw8NDffPNN8l/RfTRzs6OLi8vEzSHICEk1ek5ZxlKK16Tu66uvRihUOdMrtOCvKFF+ESxGRuNp4O1CQG7vLxUWT7VNiKpjHZ9fZ1qmF9cXGg0Gmk2m6VwO7A9aYXHQqzEEzcajZSF6E5sCJHwOJiwM040HojYidPNdMdyo8bk2CME4QlH4JdxjumLO8aKoqhEwGBxxDVwjdchJ8aILwXi9lDLKEj4ZCOiJZFDwqYDriHhTFJWi3RIwempThj5evlnhJPcwoEu6J9bb+60dcjI+8SaARFgJXJMJ2N0HxVr5sy2TivMMXLWGp+Ch9nyHGoo+bzClKFJnske4dnAKNCkz7czcUmVo0WxWJbLZVK8yCa/urrSYrFIYdA8F4e2h4mj1XvFUsZJwADXsR9YR36AiLBSXVsvyzL5m9g71PlCkeQ7X2uCW3g+h/s8Pj6m/QBfIcwVJ7Y/O+evqxPgkbafay9GKESN0yGaiOvFwbuWirbs5zF7SWGSRX744QcNh8MKVIIA6HQ6Go1GCWrJCQUvGFYUhVqtVgX3hVCdOTh26zi+R2p4yKdUdWxJSoTvzMq12Rx0Ar4Zi9Y5pOK+CvehMFZwYs94rtMYuZ85cq3ZIR8YXYR+eIZrscBaPIMYcyAGz3B2oeCbwWmIFv/vLXddhJZgkDBOaVWnyP0YHgjgffR1Yl686ixzHstKRF9LdC66IIhCwS0Vn2fKx5dlmZhdnDugGfrtodusDf2FcbolxP3AmfTdlQZpFbGH5YoyQuIbjNyZMnsIpur0wjuYP6oPIHB4juckASEjYHCgA/UeHByo0+mkOaCUNgIWwebPRMiDXMCPXr9+nWiYNWBMZJZTZdhzY2KAidNmpFf/XNdejFBYJ9H8u8iE/BomMsYAOy49n8+1s7OTzld1rXyxWCTp7GczQ6x8snCesCNJk8mkkpnJ/yAuElfcie1VEz1iw4UCMNPDw1MBLk+oQ3N1E94jdlyTxApxEzsKFGcuaFpuutYxHG8uBD18lufjIKXf/m4P26PvPCNq8s6QXHOvoyNvuU3iPodIc1Gg1G0u9z15kICPNTLwaCnASN0/5HQe1yCOK+6d3Fr538yjwyOEW8aDmh4fVwmDDgd6ngLXeBYzTlJplZhGP4CJXAPmXXwSyr2zs5P8gsybR/hhnXhWNsKHhDWEAJ8IcLe0GZ9j+C6cGU+dVQZ9epQgY3l8fEyMfjKZpPBjhALzQTgqvs54OiLC0JUP3h3p/C/SUpC+zhmyieSr+986DHRdf567zzUmaRVFwCJKSv4HNEMiDPjOw/jYYGjpjrV61qin8KOVOpaKlcGzEHBRW3VG7cSU00T8dydCZzaukTrTd9y2Tjvn/pxz2i1Dty7q1m2Tlrsnx3T9fxHTdmYQGXEd7TCOdZs2pyB97TjrxpKb17i33BLJCUZfh+g/QLt2izwyLpr76OL72EuR1nxOPTIqwquMw691SwQrnX3lY6Fv7A+PFPNSGQieaLFu0uK8fy0N5/bpv2p7UUKhjihz3+Xu9YXjBzyc0C8SgCgR4HDJ7u6uBoOByrKs1DKHKbvjDUyQRuggoWWYecA9klLS0eHhYaWyKFaFVI2WkVamPv3wkshFUVRgBgjRNSQXTBAuVgdWkEMTOE1dS3XT3vHxqJnznWO4nubPeB3qKYp8eC9jAHpiriM0SH+jBu5+kXWbZdPN5+NzHwyaG/305C+HQxhjNO1ZQ4R+hNX8HpgjzZmHM7A4rtwYnaGzZ7BW3ZfBNTQvx8Lvzog9UgfYD4a1vf10+hn0jALiBfG2trbSnKL8EI3kcJD3nfnGz3R/f5+e6XPmgim3Ds7coUuncSBkikACFzN+aIDfud8FD45pjk/t9XqpjhWlyZmzTqeTeBB07paaR3H5OkelLX73XHtRQiFK9qg9rdO6oskmrWqIUF/k/v5enz59SoXpLi8vKzVYFouF/vznP2s8Huv09DTVSUfbYfNCONRjKYoi4aT+XYQOEBw4yhAyztBhlO7QZhNKq7LTEDV9kqoRTj4n3E+fPAqK8URNiP74vfQ1apf+e1mWydlKRI4LBZiPC8EIDWHt8AwS1hDWnLFMmfJYKjrSBf2qg742EQwOtXiUFji8C6/oaI6OTuHfAAAgAElEQVQM2+cMOiDqqNlspjpGy+UyzaUL/vgM76P0ZaXWuD7+bmjAixvSnLZorAnKhq8hCg4BHvTdLQ3GxPOhd89xKMsy0Q734IxGsXBmj6KEQNrd3f0CzoIu3V/Ge3zu+N1p0Gnn9vZW4/E48ZPd3d00zzc3N6kaAnzDo+Z4L/R6c3OTDve6v79PaAGIwKdPn1L11clkksKeUTSjbzHSgdNCzuKuay9KKLil4AON2lHdvU7knrkME+n3+zo8PNRwONTr1681HA4rWZb4Efb29nR2dlaBfiK+6xqQpEq4IP2BAcO8OKC72+0mZovQ4Hd3AjN21w5w1rEpIDJJXzBvGL77DohywIpA+wLH9rh/WhRYfOcCw98PI/RcD/oE84k4tVTVdNDGvfz2crlMJ11xIE6n06lYHQ5NRGVinUBYp03zTHd8E5RAzHpMWvPM4JgF7uN0ocBRkZ1OJ5XJJlGNkFTO8o3WQw6OifvKlQnX9tFQYbxcG0OrGQtKjmvt0BDXsK8I3eX+VquVlCJXDlBUPOyYuSTqBtol2AF6w2rHMnX/H890ASApWRJeYC8Ka/wbYPwICMaP1euCH5pHABGVxhy6o7ndbuv4+FjHx8f65ptvKsX5yrJM/o/xeKzb29tUKw2LgTnLwU6Rd7Lmm1gML0Yo+CaNUi9H8HWakpvuEDkJInd3d2q325pMJnp4eEjHLkpPCz6bzfThwwdNJpNKOBhEitON61k8mBLOWDQhtBqHZBx/9U2dEwoO0fjC+0KjnfG3O8kgkgjTsAFyP85w/LsY4cL7mPfcevg4+LvuumgBusDz5yPgPZksbo4cjfj8bWJeu1WBQCA80ctaUFl0NptVzsvGYnAnefQ1uRKztfV0hjCaNowTmnXNFkEShXXOivC1Za38f9APDNetm7h+rsDEZ0WFAc2f/BiujwmZ0Xpx5c6tW2llZbhQkFYOZ2m155xpuoOb5o5m3xv+fodhgcbcSoQ/eDg3568sFou05g6PAn8SFkuZcbLii2KVpwAvorYSeVQxTynXmLPnwpVz7cUIhUi8ue/rzJ/cxnaCJwGo0+no8PBQBwcHSdP0RBAgHsLVIGDH3SUlTSSn8VGmwLF+SvI6LOPCzjefa/sRBsiZ/rxXWoVCQiyRGXnYqW+COJceBRXHHbVv37QuNFxYep+9785copbj2pdrs5wwFk8Zi3MjVctvRLqp+97nhLnDIri+vtbFxYXm87nOz89T7SOYgMe0u3WQ85l4X5ljLE2gscVikbDnu7u7lMWN5ehQilsMUQBGoQC9IYzQQNHqPfwyhgyzF6AnaNQj8XhHFB7g/tGyhe79WsJOfW9KquSl+J5xCDYKC+BkwlgRBg5leeiq07/vUxjyfD5PuTM7OztJceTauK99Leh/q9VKvs3hcKjj4+PUF2hosVhouVwmGnOr/DmN3613n9dN2osRClIeD8595u6Lk+RS2qNx/DwFzE4WcrFYaLFYJMjC4Q9pxTBzkTvO6BAOhLs5rOKbjn4TRidVwyK5Hk3V782N35mwM70oiCKTiJqabw7XxiPTj+sStRaPC/fG8zwZKwp9NJxosbhwrbMWvS91VkwORoraNNbg3d1d0tQ4jY8qu9PpNFXh9Ygvj4RZB+3wHt6NFeeMqyzLdCYy50aTOe3zl7MG6vYM13v4KwImzncMw3ShwF5w+nV65Jm802nU1zb6wtz68ag4F4TReua5niPh1qwzyAjTRodyrp+eQY/PgzUnI9xPGszNB+MlidXD5bk2d56Cl+WOFkId/4ufmwqGFyUUpPWbOHfdcxsgMmJfDPIGHB6IDkJ30LjTBi0JgvaIgn6/nywUJ0yYc870843oTAliAFMFW/fsS9/I/p1rqvTZ58R/eLdrOvQZ7c7LNEez3gVXXBN3SDJWfC0wHZ5HX8kDccgFJ2wsGR0JPudT2ITGaIzj5uZGo9FIV1dX+vjxo2azmT5//qz5fJ5yUtzBXJbVg9LrBELsF8KTHBfqEZGXwuHuJC+RHOl7wNcFBSQyhCj8mXs0dzRphxeBQ4mlJ4KG/rIPwL9xMrui4+viIdQeNRZzDXwvoDixz5zmndl7AqjDc259MDdxT7pvw5UgnyfmB4SBqgisFWN06xAa8LnwsTl/4jsPJQcqioml/ux1NP2cQpJrL0oo5OAj//5rpB2L6dBRp9PRYDDQcDjUycmJBoNBYrLSU1jp5eWllstlgpF2dnaSdoSGBHwkrSAbhAAObnwJEUKJJqlDJRGecYIBjnBHXA42iQw7wlA5gRCFRyRq13RiHoX05UHndVqLMyrmzstdeN8829UhAtdcI9Pxd/nfdQKgjpZ4Pw5kztlAGGBNIrQ3tQiioIhMmjliLjzhizItCAZKfeCcrPOr5MYYLQHwdWeETj++TpISY3Z8nXnj/R4OzXM8iq8sy4rVByPnJ0KtvuZx3WM0Uo6PuMCMFjXN90+uuZApiiJVSSDwgIgk75/vbVdqOB/j8PBQh4eHOjo6SpYhhfbwfbZaLd3e3iah9JyVHOem7n917UUJBVpuAM8Nqo45OhH47242Q7gQok/6OgzPIRYXPDgGYXb0D+0pB+HkNnOOgUcr5jlrI2oWbkHUWUPuaIzCgnF7aCxEz3Mi0fJs75fDAgiaaMJH5uV+HsdXN6GPXIP5+Tosl8skEDiedTabpU8cyvii3DJY13ICIVpRaIv0C0tWUmL+CIfFYpG0d+aRMa1jbD72CM841Bn3jjv9EQq8o9lsfhH14/vN5zpCRjmoJjL92J9oKcT9/tzYeWachxy/iNcwDx5y3Wq1Uj6FCzpvPM9p3n88WjBa/3W8qG6cPKNuzM+1FyMUvMNRU4lQ0TprwjUPJj/WLm+32+p2u+r3+5VU8UbjqZgdFTg9PJNFi6Y44WUnJyd6+/ater2ejo6OEuFgTjvjBauGEQKF8B60Ku5xGAlm5NBJJDaYrz/DncwwNUxT37xsajR1PyM2RlW5me1jdH8BmDPCJUJUPMPX1/surbLAEb6e/PY1dBW/80+fo7OzMy0WC11cXOinn35KsJHDOtEqiHAEY2Ytc80FhI/XEwWvr68Tlj2bzVSWpbrdbtJKPZolx2DXWS/QNHTO0aP0ByuCMFJ37DcaT45xQm8bjUYlbJR6QYyvKIoE+8FQ3U8AfVDwkNBX5o6S8sBOMD3miXkhcdIZqls2TrccsiUphZYyL67QcT1CeDAYpPW7v79P50Rvb2+nWlxuPUH3BEy02+10rCqO5sFgUKnjRFgrfXch64LCAw2cFusExyaC4cUIhchsXQtlc0VtLKeNYvpLT178sixTzZTHx0ednZ0l7HYymSSnDlrYzz//rNFopPPz8xRy5mavtDIJifTpdrvJeU1WJcweRkrfpBUhMz53pLmm6Js8al9RM6rTlByjdN+Kh9rlLBc2CIec837mNqexu/XFRshpTbScGex0QL9cKEeNdlNI0RWLaJmxNghAjkFk/QkF9LpRNPffOE3maHVTa4ZnEesvPdGypCQYJpOJtra20jnNnhDp/cjNa+wXigRWB+8mMsnLdT88PCSfAgK/KIpKUAGBGlwPbXHC287OTnLEupVRlmXKhPbnNxqrWkZESvFcGD3vdYEKjVxfXyfh4MoJfgF/Dpa/+7mgY+ZlPB5LUnIEX1xcpBD28Xicqrm6sC+KIu2L+/t7tdtt3d3dpZBUqrc+Pj5qOp3q/v5enz9/Tolr8/k8ObC9wnKEZKEfV3SkVY7FJjT4YoSCtN4C2MQcpsGY0PaBdjhXgfrlJK/BrKfTqcbjsba2tvTx48ek0UNoDjWRgchRia9fv9b333+vXq+nwWCgRqORSjO4wJL0hXBA25P0hXAA70VDY6M4xh7N8BzDwxmKlQBxQVQ8hw3jAtkjuOgLDMihONaBTe01l3zMfo9jx/4u19rQsNx6c+brxB79J+7kc2vNNweOfPwGP/74Y8pVOTs7S1Fr0cKBLh0acy2V+XDI0H+PAiWuGfAUjkYUGMJz5/O5pCfHJ6HT3W63AiX5HEVfBv32EM+Hh4eEkzcaqyAD1sqjjyLkEuHIOF91EJpfm+un0wyf7m+KUJU/m+b/c0TBYRvG6WGzOcWk3+9XHOYPDw8pjJhKqc6UoQmOWG2323r16pX6/b7evn2rw8ND9Xq9JCB3dnZ0f3+vy8tL3d/fV8Lk2atudUcI1CFA9ym4z2ddezFCISfFfKP7oHNCwgnMzdnlcqnJZKJG46kue6vV0ng81vX1dUpeY/PlktfIVM1pvEh/mC2Wghero28RL4/4fAyR84iKsiyT85pn+clszlxz1pMzd3dc5yKF/Po4x8BN/I7g4L0wC3ckOhNhXN7fnLXA3PJ/6sU4bOX0QYvMJtJR7vflcpmqgrLeXiXX69b7mkbLyiGiaPFGv48LhkgPXBPvd5qWniyGra0tTSYTlWWpXq8nSZV5irTgz4twLRaDW2SsqSscObqI1lEcf25NcmteZ8nU+Shc8EZLLMcfXNnyZMAYDeXH8CJ4/Hnz+TxZzUSmcf4KZ7BMp9OKUHAhcn9/r/Pz83QYz2QySdDd3d2dRqOR7u7u9NNPP2k0Guni4iJZrCh3KGlxfFL+bJq/SEthnQTLLbr0vHOPTeyO4LroIwgPs84dQE6YTP5yuUxWCJEEfn5uHJPDFq69xsimKNnRYCAwTGD6hvbsmlROI4wav/sb1m1QFxRluSr65diwtNLoEVwIHebPrQz8Ap6V7BAWa1aWZfIHUaTNBYz3Mzdm/8mNEQ2czfz+/XtNJhN9+PAhZS57bazIlHxuY1/cKsnRZWSw7hiMgoS157mc0rdYLPT4+Jgs036/n57XbrcrWnSur3xyDRYDc4NgjwLLhRnWrlsJOYssx7B9Xzu05wzcoRu3FPyeHMQaf9wvgHVUFIXa7XbFGnclzYsben/5ga9cXl6mvYXTGb4CPeOfwZ85GAzU6/V0fHysg4ODVL4En4QLB5Qit5Ai/Uf+6FYWn3W+rdhejFDYRIKtu9cnxc1Q8hJubm60tbWVojaoyQ5BPz4+VuqXx9PR4oQ7sbm27hpaJHq+i0wwhrv6O8BvHTZZLpfpnbmyATR/p7/bP2Nfc/f7xsYE9dpJblkwH/QZhsZGRpD52QHeB65D2MRrc9Zajh5y37m/pizLZOFNJpMkGPxMXDQxX+s4R66B5ZhiZKi+tv6907C/y5tbfGS4AiGNRiOVZZnOdcZxmlvXdS1nDfjeyilozwniuA/i97G5QHAhkGP6UYDE/cV3HojRbK7CxaEvqRp9CJQW1ytq3/P5PJ094XW6/Fxuh9E8R2p7eztlRbOvbm5u0pnP8CJPpHXId5PGe9cFHMT2YoSCtF4w5KyEqInHTybPNeSYSSitBIMn4/j9EJhPrDNkl+TOdOoYmBNwhH1ywoPnopnzXcTzGYv3PWpc9DtqHFHbinPtjGK5XKZIE8dj3dcAU2eO3HfR6XTSvNEXqQo7+f0eXeNr4nBaZMJRU2dd8BMtl0udnp5qPp/r/fv3uri40C+//JLqGLmgcwsh9x73g/j819Fu/C4yUP+MDVqlrAY+hrIs1e/3JSnlUJDHEN/nTMVpNdJ8VLai1eiCMGeFRkXNxxvn08fG9VEwRKHs+wOm73PptEzQB6Vn2u22iqKoVKR1v4dDrKypO/Hxr3iYuCtIOSvRlaaYCMq4CW2N50G7X67OGovCOu7xTduLEQo5U7JOW/FWJ0hYOJgg2pNnHQ+Hw2QNcG2v10vQUAz1w3zzvuScnr5g7gzzPvuPm6f83zeARz55pUfXfKUvMXXf/G5Cu9aEhhIdcXGOo2AAXri7u6tARk7obDbvH8IgaokuwBibCz/vB042mjMy+hj9JTwP0x7zfDqd6uzsLPkRUAx83nxu/Z3SyonuUR5+TR3d+rh9/LExzrjBib6hTg7HP45GI21vb6vb7VZKYUeGn3u/X5djbPFeGGEujyZnNbjCFIWKz2VOSHofcnPFPuFZ0CGfnljqNEgAB4yZ9xMGHuEjh2cRNN1uN1VpxSkMFIfg5t2tVivxn263q6OjIx0cHCSBRkju7e2t9vf3kyWRK++REzyRdv7i4aNIoOu+r7vOGQeMCwcwMejgdldXV8kZulwuNZvNkqOIOkhEfMQwSBbIa9V4qCeb2H0ETlAwnlxUDlqem83+nDgHbslEzctNbQSk5xu4xRKZNAJNWiXEuEaDEMBS4LnEbHvdfLd0EEY0+s0ceOiv+3L4jvWKeSMewugbmf8TGXJ6eqrFYqE//elPldIVlGpgjNE6jALO++NQg0eGrGu+Vr7GUdONmqALqqurq+S4xAGKpUOJdj/Zz5mxN39mhMScacb9GPdcTjFhLP6eqMzkmG+0XCMU5pa2+7Z4v0O7hNUSdgu0Ca04kuAQna8V/SrLMgWYzOfzpFSgZAAlFcXKl8Y8UCcLWru8vEw8ZLl8qujMmS/n5+eVZ8azmXNCO1oKHvq+aXsxQqEO+3RNu04y+oKxuRyeaLfbybHz5s0bDQYD/fDDDzo+Pk4EwWa6ublJh+zwP54PE6K/JKEMBgMdHh7q+Pg4JdkQQphjTr6JHLd2Ez6Gj0G8EdP150lfWguOq7qlgICQqucw5DQwt1x4NuMinh1idTjIN7SHADrD9PV0qMY3fhRW0dSPmqfPTxQKi8WiYiEsFovkR8BP4u/z57n14e9zy8JN/Do6jfdHhukwiCsDOQuaNeB8D/IXOOSl1+sljdhhRp/72Kf445Za9IfR3IoBIydSzb/3A5hyVi4JZZ5ngKbfbDbTfnHLmf6Q5OeZ4V51Fvr08G/2YLPZrJwUyLpG2tva2lKv10uQMYKEPJHFYpHucYiJ0x9PTk50eHio77//Xp1OR+/evdNwOEwCZDwea3d3N8HbOJ8lpaKLMb8oWlesqSMMzGkdLOntxQgFJ8K4Kdk8TqTxOpfGxMkTKTOfzxMxXlxcJI8+MAJEOp/P9enTp0pZA/BZqRoZtL29nSqtcvg2NU329vYSg3ENHCJBq3UT1QUPQsGJt85MdEbo5rukpLHyTvpDNJOfEve12CPvJZ690WikqBieR/9d4EQG5H4CWtQGuT6+O8fA/B42/GQy0d3dnX755Redn5/rp59+0tXVlU5PTysZ28+N15l/1HIjJBMZuFsEzDUCEuWFiBgsRK53LdphKv8eRnF5eZmYSLfbVVEU6vV6+uabb1IJd2fy3l8XoLnxuzJA8wACxkF+itM+exZmzydzyLr5vonRRviwHFrFgqXvQDS54A8y4RkfmjfFF2G60Jb3hTmHpyCg7u/vKwmvhI9itTE+3kn2M5FFZIUjhMbjsX755Rfd3t7q9PRUl5eXKXnt6upKy2X18CpfP1+rCEn/xYak1mmqOSZR9ww3GYnq8TOaORP16OhIx8fHabNvbW1pOp3q4uJCu7u7KYHHS2vDsHnP/v5+et7BwYGOjo5SYlGj0UhZqGzsnHbruKxbCu7LyGn/3uKzotZaN585Zs01zxGPMwl31EdnfWTUuWfw+3NazNdeS5/m83k6C4GNdn19nQqPMW/R7+Nmdx1TlDaL7HBL1vHsZnN1/CbQRg56AgoF3oifjBdodDweqyzLFC8/GAwSc0NY5+ZsE6bhY4qWKPvPLV/flygk0R9Gc2cuz3OYyAWYv9sFCHASAoFIIzRlVyBhxigQKErOF3ydG41GqlJL9QIivzgQCYbtASL4MofDYUp2bbVaCbmg/Eyz2Uzl2FutVsWnAP/h05U/X0Pmhf66pfsXZSnQ6rSs3O/xPsfW/QfzemdnJ51uxQEmLP7u7m62VG2M6XcNjkgmYtqJGweqcAshQgRx4/N8z4B03BzsPqeper0UtzwgTK7BnI8bLrc53XrwMfsYeAcaNKUNPAHK4Zc6zb5OcNQJjfi99515uLq6SlrWjz/+qNlspvfv31dO04PR8lzvKxvKhUKEj2KfXTNGqINnNxqNdD53p9NJMesoF9R2QvNlXre2tirHkSLIOK8XiNJDIK+vrzUajXR9fa1ms6l+v6+dnR0NBoN0LG3OavPf1zEPh7wYNwINGAQI1RmW7wO/P/oMPIrNo+uiIPBnIoj8Hqc7x+2ZLzRuqpFSSsMZKVaQ0xaJg9SfQpMH94ePuGLh1q3TN4II5zKJb0Cd8ZnQRfTf+B6OQs+to03aixMK3uIEbqLJ+OS7ExCoxoUD9UkQHl4kLjqeXChAnGxWnkVZ4zpNjObEHRcs9tslft38uMbgERxuMuacgOvm2y2zaKXloB3v83PJcZv8ve6a3O+M0Y9gpX4Voafj8TgxU583V0LihopCwNefe92qQ9NFEFCiA2wb65LvgTU8Xh7tEgGxv7+f6njBbLe3txPmjLB3/wYQKhg3jAzhFEOZ/1Wb06f7qbwIXd28+TPinvBkSIdPY16L+xBdS84pO06n7HHf62715qAf9g08AYF8dXWlq6urdJY0z6SPbo2wR/DFIdihS54DSuH8KAYAxLHVCfIIbT7XXpxQyEEabopGqej3OYE4fER8MuFgVCc8OTlJ5iwHZkynU7VarYTrEd0hVc94bTablZror1690nfffZc2PLkQDumwaRqNRjIVHReWVv4QZ/hFUSTGgOYJbusHhYN5OtbIBgOP5Z2eqENGJ/WcYB4494iU8BBWnp+DnpzZkLHMRnUNmuvdOevBAlI1p8PH5f3HMgNTn8/nOj091d/8zd/o4uIiRXOAGXN/tNqi1eB9ivQZhQDOTMqmHxwcJGtgMBhouVym/zvWDW3t7+9XSiKgse7t7VWiTbAYSHBC0I1GIz0+PqZkNmiB+jmfP39ODKbX66nRaKT9wPObzWaiPyKXiNDjmUAaRVEk5y19pm+tVqtyTjHaME7k2WyWnMLQIhVfvQIsQlOSOp2Oms2nZD33i7lw7HQ6kpQSVVHmQATwLTE3KIeSUj4H1i50DmxTlmWCgFhjBALVlq+vr9VutxPtYLUsl0v1+/3k2/nmm2/0m9/8Rnt7ezo5OVG73U6HOT0+PhXtpFgfFiSh38y1+52i1coedDp3lOC59mKEQp0lEKVilIh+T/TCw0Qnk0nS7NvtdjIXLy8vK5rNYrHQH//4R81ms4Q9czB3ZCRuPh4cHCSnVK/XS7iiO5ohDtfq3J/AOzx6gh8Ijnnw39mUZGO7HwTi53cEDGYoGgmbnOYVMR2Oo8X5//+4e5cQ2bY0v++/IyNPZrwyIh/ncR9VXbeobjxqbAQC44lo8MQW1kSiGxmhgaCnAmFsNLIG8kAj2SAj0dCDliaF3WAkDJ5Jwhg0cSPwwB50uar73nvuOSef8c5nxPYgz2/FP75ce0ecutWQ5QVBvPZeez2+92u5Yw7iC/O6vb1NiAVRd+nWcxkg/M4soy/H9xmnJsRwNBrp3bt3SUtAQ0CicxiLNvtol42mPRgDzIh493a7rZ2dnVTeBILR6/XWiBfMC7MCkiRr7I5XngmzYzzeX7fbTYwQGEYDwozIWrsGRxglTAjtljVgnS4vL5+YkrieNpvN1sbLmD35z02b7AO+D4cll6ghpo5DPMvNQs7Ui6JIeO5MfLlc6uLiIj0XaZ5zMTA1upbghR4pXV4UjwUIqZKKFjYcDvWzn/0sZcWfnp5qPp8nuHcn+d3dXTJTE710dnam/f19jUYj3dzcpECIu7s7nZ6epsqrWCTcd+c4EU2BwLO/b2NpkZ4RU8iZDOJ/dRPK/QeAQMDJ8PSqqQBQp9PR3t6ezs7OJClV5Ywx8/68nJlBelrVkbHE8UZbY1QHc/OJn6NWBcFxhJS0xhQgEk7s49z8Oa6SOzJWzckJRF3LaYS5V27uDhOLxeMh56PRKCESMd7YZH2/mI+b0+Iccs1hqd1u68WLFzo4OEgSLpI3Jho0Cc+YdT8NjM/Xl+YIz2f6Yxw4rJGoYQpIuy7IRLOJ778zo2hKy8HEpv2U1qOSHHccJv168CVGHUUTa86MytqxTj52FxgxEfsLRukMESGOfnKCKs/tdrva399PmgfwsVwu1wrrITD4GQovXrzQ4eHhWj7Pzc1NCm/1Y3A9XDqGylbtwS/bNjKFoij2Jf3vkvY+Xv/HZVn+t0VRfCXpp5KOJf2JpL9VluVdURR7kv65pL8k6ULS75Zl+WebnlPHxbYBSO/DpRQka0wfFxcX6Wi75XKpbrebpGeSSohXdmezIzXSq2fHwrldtYsA7TZ/CDPSntu5cTA6gfL1ifZY/w0iyXycIHAdzwcpMOswRjfX+bOrtDWQxxmCm81y9zqzyf2e29sc8+N4zJ///Od6//69fvaznyWtgQq3OXurr2vUhPx5mNxwpFL0sN/va39/P5U8Rojw4mrSSrJF+4uSbnyOaxWRIUKs0Bgwi2KeuL+/1+vXr5Pjkr3E2UwEnjPTyIDjXlXhGXAVTWvefH9zNvrICKNvwT/nGImPJY47/g4+c6IeNnw0Bcdzki8xd2HyjALcdDpNVUxHo1E6S4GwVcdfcA5tmsRYNKOLiwvN5/Ok4d7e3qazFHys9FXlr8vtVe5zXdtGU7iV9DtlWU6LotiV9H8URfG/Sfp7kv5xWZY/LYrin0n6O5L+6cf3q7Isf1IUxe9J+keSfnfTQ6oIQpRS+S03Wa7Fn4A9Gwmu1+ulOuZfffWV3rx5k1TDXq+XEAmJE4Ahjt0TQSSlmGhCXU9OTjQYDNRqtRLD8AYiujrvL66JiLOpAbAuMcFwpKfSGcSaeTnRcfPNtupmbFXMrKqvuLc5SS82CPl8PtdkMtH5+bnOzs4ScsHYq8YXCYmvjzcIMM7iwWCgXq+XJDwvWe2HzzSbzSe5DzlGyL65MOHzj1Fq3hfSZFEUKZGq2+0+EQjKslS73U4VdT0/IJqI4ppvQ3hii5VV+Q3JH/u4zwUfColvUQDyrHhvjh8IfpE5sLYIcO7EpTgdGoNr79yHBsJeIdnv7DxW8724uEj/40BeLBZrMHexe5IAACAASURBVEE11B/84Ad68+aNfvKTn6zVAcPUib8Q5gWeuiYY1yeHI+5TiHu6cf82XVA+9oYhcffjq5T0O5L+5sff/0jSP9AjU/hrHz9L0h9L+idFURTlFqOqAtC4yXX3uyMUZ+58Pk+2WBxv7XY7OV8bjceyw6SWExZGmFlkCtJK3V0ul7q8vNSLFy90fHysh4cHHR0dJWLrgIykgM334eFh7QB4lyTrpGZpPbTVHcOoqpISk3MkkJTe3dEHM9jf318jUPFVNY5o6olhhv4552vx+cT5R8FguVymUgI///nPdXl5qT/90z9NNe2dycb1437fF5dmQXSk/8FgoHa7rZcvX2p3d1f9fj8dTwnDoB/gw8frviE3/0TNL0bQRGLoCO4aKNdCfKIQwXcnyt6Pa165tfbfnYH6PjEHZ2g5c6Oktfh9v4b5xD3hGRBrJ3J+L/CcEyo8dDdGAPl3JPCYfIfGgKDF6XcXFxeaTqd69+5dohmEk3I99Ih8A7TYs7MzNRqNdNYLpVdOT0/1/v173d/fPylxAdPywIOoTbJnMA7X0KrMorFt5VMoimJHjyain0j6HyX9v5KGZVkiCn0r6YuPn7+Q9M3HAT4URTHSo4npPPT5+5J+P/z2ZFNzxDFyRwc+1xRw9Lgvodfr6eDgIJ2+BnJztgLHMRKt4Q6pmMjiZwaTmHJ0dJQiOshABDAcGJFMINZEf1RpS3XNEd8PSkHKdHuy+xpcI/EIIP+vStKvY1ZVan98j0Ql9pv7D0cbJoCLi4vEDEj6YazeV5S4qxgc0iqRQ4eHh+p0Ojo+Ptbe3p663W4yL/j4I4K69uYEzolpJK7OGB2eXaOITMP7dYYWYclh1+ef28eqPckx/qjRQESBM++TJLLr6+tkvpVWmf7Soy8PWPVnUbvJj/HEtAN+Ieh5gIS0On/ZM/hhMPzmnxEcoin04eEh4TwmO0yKjmMwLs5bkaTj42OdnJzo888/1+vXr/XVV19JUmLmktIxnBcXF8m3gKmbgALHxZzJ0/fGzXvbWBxoWzGFsiwXkv7DoigGkv4XSf/B1k+o7vMPJP2BJBVFUYb/4rVPtIeKPhOXJEYaYMD5Rvo5oaeosvgI4hkKbDZc2p+Fij4cDtVut3V2dpaudYRwDs9YYECz2Sw9y6uy+nMcOD+u19q8i6JI5rKyLNdC5lgLYqGJwPA54cQCYZ0Z0I9LlRADNz1Fx7Iz99yLPiPjYbyu9bl/AocypQV+8YtfaDgc6vLyMjHhKFQ4AuWkJdYcgeHVq1dJgDg+Pk5OQpDMCayP3c1C0aTna1Ll5K6C502aWh2DhUB55Bzr7ASStfHAgxwe+lpGqZ71Iava7/NIOL67H4u+vXYQc/LoPGeo3MtvRNG5ZoEQRngs48HERW5IWZaJ2MeAAPBc0prEjpmSsGBs/+C+hxbHfaQPgiAuLi40mUxSwqXnLPh5CsyZvcox9Ry8bxP4Qfuk6KOyLIdFUfwbSf+xpEFRFM2P2sKXkt5+vOytpB9I+rYoiqakvh4dzt+7bTOpyOmlldkGAPGDLkBSHL4suPS07pITFHfiYdeeTCaJgDhT8PBDnu1aAoCTI1hRYokquRME15AAeGybriLHSIso8TrQOcGIGoPvR878wPjq2jYqLUyBMFoS0UajUTLzEUGCOSw6QeNYpZUZBsm/3++nkiVEqJF9jM2e+3ztnTj6XsS1cFMfQgL/I93Tb5TA/bloBa5NYB5CO47mHfDCmaSbF6r2KmruVfvzKZKo74OPL/5ep83k+orfc0KKm/JyvhW0BtfkwAUES3KBMC3HYBP2NcfIWXt3bNMXTAD64KGnTn+ikLCNwLzpP2/bRB+9lHT/kSG0JP2nenQe/xtJf12PEUh/W9K//HjLv/r4/d99/P9fl1uOpk4dd3U1B6S+4dF+CrLwwtzT7/c1GAy0u7ur169fp4Wfz+c6OztLMcnYdV3aAniIOCESBcKC/dEBhWxHpABsna4lOMF1pxqaDERfWh203mg0EiOaTqdrzKDRaOjw8DCZwYqiSOU40FRIAMKvwfMxpZAM1GisTlpzpGFPWNtWq5XMGKxdREh31rlGEM0i0iPSEkJ4dnams7MzvX37VpeXl6mOEZJkJE45xGEs7N3r16/V6XT0xRdf6OXLlxoMBpKUTETu/2Av/DckXg5uIaKEPWg2mykJDFMGY8OZ2G631zQoCAZnfi+XyzU4dBMhY+WFxMueumQK3KIdttvttMYe+si5IpwjLD0KNa1WK0ndmGu4F/g5ODhIuTWu9XHkJFo6Qsru7m4S0Hq9XtIq/F5Cfb3EBBI/CWiYbSHeCIKtVisl+u3t7SW8llZHmpIkiOWAz/SPUAKcA7dluUrqBF/Bu1arpX6/r2azqc8++0yvX7/WD3/4Q71580ZffPHFmsXg/Pxci8UihcGDC87gXShwpu80MWqjfs+vUlP4TNIfFY9+hYak/6ksy/+1KIr/W9JPi6L4h5L+vaQ//Hj9H0r6F0VR/EzSpaTf22okeupodo6Yk1Qjh4zXsDgg9/39fTpPgfpHxJlfXDwqM+/fv9f19bU+fPiQHEmohk4Y6JuDNSTp8PAwcXq3F3sUTNQ4XKuJuQRuLgLwi6JI4/f/IS4u+QMYPN9NMhBhzENu8nBnG4DufeckMGfo0kqajSGvNH6PjsO4r8zR60z50Ydu7vPm0nxEBmzvJJxxRi5aQXQSe+y8tCrh4MgZYc61CA9+cNMF9mdgHKIOU/DfIlPw5wPjCD80J+aYUqKwQTAGDJ/1opCewwCCju+JN2DIkyFZE6Rh5uqmHsdzktQcFuiTfXUC6NozRQBde3t4eDyDm6TBKIljRYChwTTdfg8cY/6CkZAwSqQi/WIaw/rQbD6e9AYD5NwW4Pn+/l5/9md/lvo6PT1NTGw+n6ekOQ9b9xBzX6uoUXiQS05zybVtoo/+L0n/Ueb3n0v6y5nfbyT9jY1P3rK5JBqek/0cNQbeMQFQ7oKwwn6/r729Pf3gBz9QURTp5KPhcJgACukvp8kgdWEOgmhJWjMVOAI7IXEnFn05IYdAeBQKc3KzhCMKhIbmGg0SZFmWqcS3R0W5zRcAc8RljX2tIT6sL7V8Yj0axhJNH06McvuM6j6fz1M8OCelxbOU/d1hgndqDhGeTE17ahKROARxQCtg7ejDy3VAcDxsMpYEwVfi64I5E03RD4pBY/AwS/rn+VEAcEbhjk/3c/HZYdnhMkc0/DrWJTYXGnJ7kTNT5a7P9ZPz1UjrPhCPHnImE2mD4xHaE4yO3wlTB67d3+amXDLa8U2CCzDzdrudyp3gYP7Rj36kk5MTHR8faz6fp+CIy8tLSUpl/qVVmQyECF/3Kv9i3Leq/ahrzyajuaqxAQ4MVRMDCFxKkB5DM1Enz8/Pk6R9d3eX6h8BFFdXV7q9vU1EB0cP6m0EcqR47Nz7+/saDAZPGEBO8nQJzR3R1E5yiZ5nYS9nvL4WEXlBAIAMhIFwsZ5e0I3fIWJVtuJIjIpiVScmF/1S9znnT4mI7b4Q16y2kX6YM2Pr9XrpONZOp5Pq7fj4WT9eFKLzfnyP3fSV25O4V/6br6Xvn5vfIDTsl4e/buqD53rosfuUchqPr13cj6r5bGueiPOPv+Xe3WLgWjXaj1cIdpzxfh2WvVKB9wvjcSElBlvAbMfjcRJUYoVir820u7ur4XConZ2dxECwPlDe4ttvv13Lt6H6qie5ucbvfqaoKfh+VPkh6tqzZQqRaOQA1lsEXj5H4sUmkcjDNYSmUlyOYneEhblpJY6DjOnJZKJWq5VS2AE8ZwKRIHu9GhgMwIt5AQCDKbjJoU4iwxQhrQgJUinSrEcgIVXy3Qke82A9IYpoBvg1SJLi2ZGZR+K1SdLJ7XPcY0dqlypZD4g9WuGbN290dHSkN2/eJPMRyO/JXay9+1MgGm5iclU+jp9XlID5n36cAeeYAvvJtdEc5327psizPUM+Jkt6i5K2X5Pbx7r9ikSqam285Z4JkecFgcTn4f6TnLnT18x9QQ6LnoEcTYOsRdSkvcicC3vsFRrp3t6eBoOBjo6ONBgM1O/31el0JClpKS5MuWbgGqGvUU6rzu0BMOUC4ab2bJmCpLUNqQOwXHOgdkTw5DHsimgRXOtShm+IM4WoysWIAufkDixID+6g8zkijWLTjweyVK1TlZQKAkRzkkdPuf/D/RqRwDoiuZqMjd0PGI9E3/evShr0ebgULumJ1O7PcILhsMI1lKDgEKTXr1/r6OhorZIp1xNLz3zdLMP+5+ZW1aquqdMgaK71+m/+nlvX3BiikMX+OVx4tE0UwiJB2TTuKgZR10cuyoZrvNSM5/YQCQRTiPfyHGcK7ntxf0wULHJmX59jWZZrOB9DdOM8ucb9GERBxohEzH25nKJNdHAbwl/XnjVT8BYXokqK9MamuuqFw3g8HiduTuKKtAobpE4MZYApWxAZBoBxe3ubqk96XDP9xRBFfkfK8QgHHL0OzNwTgdPXIqrIbq7iOwwG6dFzOdzujAbj6+pmJqRWnLU7Ozspsctt3q6S+xiqiIrPjzUryzJVIz0+PlZZlqkkAGN3RztEvNPppPLE3W5Xn3/+ufb29nR8fJwkOJgZTJJcDycqvmdVsLcNgay6L65HRP5oEsnZk50RQpwiIfHvrsE48fW4ehcK4ljiWjgj8fHlGFZcD8bl9ca8Tzd3NRqNtTMLckdU5p7reOjMH43W4SanbboZjjESjup5Ta6tNRqrREjOp2Zt8T8Sys5BPRwBjGM5FjD8FIL/qYI07dkwhSoi4YQ0SjabkAwV201Gfizn4eFhMhG9evUqlXomsoA69NSCBxAceSIhjrkOPgeXej2XgPscGWhRUtk0ZykfBRO/S6sa/i7xez0kCBHjcZMQfgoyul3iqiL8VRpNVfO1RWPq9Xq6u7tLx0vi70H78lh96hS9efMm1bKn3gzho+yHJxy5z2aTMFKHdHWSXYTjOqbCeyTMNNf0IG7c4wzFzUJVpqE4R8e7CFd16xL3OseMfPwumBA67c52xk8kkOcdRYndTZ6uoaB5RRh1ocnnEscZP+/srM42QQtwgeTg4EBHR0dJO3358qXevHmTzs6Gpuzu7ur8/FyNRiOV0QCO0SriXm7LHHLMeFN7NkwhEnz/Paqz0U5ddT2ITumD+/v7FHHDhiyXS7VarfSiT1Q6d2ZiIoqObySz0WikZrOZsqZzmgUAyBgBJCQl+suFHQKk7mCLpg5fB1+fOukJBkoKP5qCP68sy7UDc2BmfmKYH0gSmUI0S9TBQXSO8bxms6mXL1+mBMHb21v9xm/8RlK3Cf9jnJSzxpfQ7XYToYnJaNtIVVW23Cq4zSGy/+7zzUn1vv5SdcSJm7Ucj2Iipo/LCeW2LTKvOoIZNY1cY3yEZZK7g5bKGKnphcTudYs8usrre0Uzr9vp0YbBUQ/1lVYCiIdz8ky0ehzMnHPAnN0P5ZUUZrNZ0kxns1mqbfT27VtNJhN999136QjZ4XCo+/v7lJSJicyj2Xy/63Cqao/q2rNhClGNdsLC/1VI6de4DR9zhydU4UA+OTnRq1ev0gHav/mbv6ler5cIRKfTUafTScldhD864vlY0US8zhJAEJHQCb07oQEqronzkp6aFLiHuXooKxJ9q9VaOz3Nnci3t7dqt9taLlcp92X5GK6K3dXvBXmQ3tDCouq8yWySM01EwcC/M17ODoD5kCgFgcH0V5Zl0mJwfDebzYRgLmS4FL1pTL4HPjffO88FQWvxQ2WcYHm4aXxmbhz+bBhtxAn2wwMaqubhWpIzDpLpSCKTlJK8mAun/cGMgT1i8mO5C8J9IZBeYpp39g6hBOLcbrdT7D/4gkZLdE673U55CM7wOPsCBuAh1BB+aiu5mca1Dj6ToLlcLtMZLOAFghPVdI+OjvTVV1+p3W7rt37rt3RycqKjo6N0et35+bl2dnZSpCOHE3H4FeuMFsJ8XVCoshw4PXGY3UZbeDZMgZYjCjnHl/Q0XM0RIS4CkjjhY24Oouplv99PxOPi4iLFEOMEQiqIDiWI0fn5ue7vH09im81m2tl5rGPPMYFskDMvjwiSlAixM0SigVwFdsKOTwPg9HF5VAX3Sutmrslkkq7PmcRAVDcPQdCw00YHnUfN+D7QGEeV8zzuK/uJD4Dn9vv9J85FzxGoMu25BhfHFwWUaL50Zhf/jzAHw/LfITROgO7u7tYSz3ICksNOnZSPuSFqHC5QMA7PYnezC3WynIktl8u1k9o8GY3kSknJp+baNL/zHfPsYrFIEjFl6uMZ2i9evFgzqUAk8SUg0JAjBENyAQzhAP+XB3DgD+Q38hSgJTiDOaODBFeyogkjZ715PmMqisdT4VizFy9epNMBv/nmG43HY7179y4dqwqNopaSl3BxmuDw7fDgsO1759poXXt2TCGnBeS0h6rJsVBuw3fzixM1P6iE8xbQKLBRHh0d6e7uLqXZIzlFac+lqZubm2Sm8tpGkWg4grszy6UBfyHJeD9OIPgMgfbwPCcOkajFMfka+lo703EGFwnotjZPJ1w5Kdal3Nz+erkDJ2jsiSNETtJ2LcS1B59PXJtN71Ua0jbrkVufXHMGvM31OYYQP9f1tQ3exXvj3KuEvcioXQqO/hAIdW6usU83ETm85sy3jJHnAgsuQHE+ClqJCz7ePxo2uTDHx8dqt9s6OTlRv99PmsRisUgMIub3uL+D8X+KpO/NaeA2eyc9I6bgSBs1gE9xrLg0zHdphUg7OzsprwB1lwznq6urpBJypCMJKl5SwSs2erE7NpZzXWPBu5z0Kq1H5MQ58JszM18nZwRcz4ssaa6HkFYlPvkYqlrumqp7qswhvq/RD1JnOsl9jvey19F04uOsQ47opPTfvZ8ckv4yhL+q1c3Xn+/r6BpBDp+qmICbSZxJg3exXx+ja2mMrW4dXGPNMYS4Bmhb8dk+Rr83wrHnYyBAEGFWFMVaZWLuiXkpfjAPFgPql7kDXHpkIGg2HMBDKRx8jY1GQxcXFzo7O9PXX3+t6XSqDx8+pAxnNAWikFzb933OrXXcn1wk2qb2bJhCnGCcdE5KqZtkBCK0BI9XZuMpKucF3QCGwWCgh4eH5G/A7udEh4YN9fLyUovFQkdHRylCAcBxaTpHyEECSlEwLk+j9zILDtixfEFVbR1UaJciImOpIr65feMdgI/SaCTW0qoWiyN1/B7vdQ0qhwzxer8n+mQiUY1z9HX0eeU0gW0l6E9pPq7cPkTBJ2cmiv/79ziPHJF1puD3xb5jf/Tp7zlJHoLn6+r44fc4I/FnR3OgO5alVdl6wljv7++TQEhoKnk2LjgWRZEEOmocXV1dpc/el+c94L8gY/7Vq1fa29vT0dGR9vf3n+Sd+L7mcMlhL+7Fpwpw2wotz4YpSPWhe/4e1XS/NictOTHy8tnYL3F+EbVSluVahck6ruy/Aex+MDjahSeMSU9jyPkM4APMqKn0gaoJINNfjknhd+BZzWYzhY/Sh7eqOcZx5ghoruX2zvfE1yFn++Q9p/rWaSzRDBTH+Ksm4Nu0qmfmzCxR2ssR4m20nm00v9hHxJ14XZ1g5niSMzc504nCgLSe6In5hv/BLYi944v3ERMNKVHhpw26P8sd/R4oICnhrpe6odaWCzf0Ja3DM7hMkl1RFMkHMp1OU7FNLBFegjtqUd5v1K434d+ntmfDFDZNbltpLCKMAxTSf1EUqZQxpYOn02kqc4BdEF8DPoWyfCyW5RmMcYNubm7SkZCHh4dqNBrpXo9SYKNjmQlnWFwDcOQ0hZ2dnScltXmGn161XC5T/R5pFXbHyzUKrnfHsb9LKzNLVdhhlVkqErMcA4825ciUo8+ojuBWMbmcFB5/z/VbxWSqXvGa2HJwHxmFr0GuzyoG4fdGDS4n3cf15xqHg08lNFFIc2LpzlNg2/GjLFdFA8ERkkwdTn1s9OH5P8vlMoWXE30Wy2vjKHYhCsf35eWlZrNZOkyHaqnRZykp5ft4BCJ4SbLdw8ODRqNROlAHBoGjHMbDywW+nDWlrm0rQHh7NkyhSqoBYLZhGBGZkBjcZATxJFSTTEOS2ahPUhSryISiKNYOaPdcBZdieUcyIJ6ZyCD3LTgCevkNz20A0JCepFVEkT9fWlXWZO7Sqp6SI6QjDMlonjmc014cAXOamPfv0RC+Dz5W9jrao+Nn38uq96rrtxEiqp7rc2KcOcduVZ+5Ncx9r2tVzHTbe3le3Rjr1qgODvicG1OO0Xg/VVoCgokzoBhxA954EIEzLZiCaxz0jzDXaDRSNJHjmjt7aeQTXF9fpzBRl96pnwYNkaSDgwO1220dHx/r9evXKWESUzKhu8PhUL1eL5mUyMUgkklalTz39XP/4yZN8NfefFQnSYGU2wCwSxrSeuQJgII90UtfvH37Njl23DGEZO1MRVpJylH6Wi6XqZ/z83MVRaHBYJAcUK6muq1zPp+vATtx2UhQMQbeEYQiep7jwNyjnd9LepBHsVwu1xBIykvEOadwTr3lf2cCHjHkjMjXgjH7PDyyw8e2rcnK4cLHnZtHhJfcvFnDCItV3x0m47P8Ohd8gHXWzW3uPpcqhpHDk8iAo6ZQR8irCP028899d0bgwhsNRgxDiJ8hzk4oPdETX4EXkyO3gPwI8o7QGvyQKRzS+A44yMnDaNkLfH+MG8kekxXnRvDb+fm57u7u9PbtW52enurs7Eyz2UyXl5e6vb1N1VPLskzmqwiPzszrmLMLgv7bpvZsmEJOMorqb5RwfDOk9SgeJ5JeRK3Vaml3d1fdblcHBweJs79+/VqvXr3Sl19+qZcvX6rX62k6ners7ExXV1epNPZ4PFaj8XjWs5RfaIgIEgkHlXtVRSQhNxsB6I3GqmYKzmHPxJSU4rDRHBqNVaVHj1BwJzTPZg2J+ab+U5T08VtwwElsVUyhSnqPGkPODOREwv/fJNlyf9We1LVtrt8ksVchJowwInd8XoR7/5yT9qI5yJ8Z57SJYOcakjVwQ6O2F589aRDTbK/XU1mWqWYY48Q0OxqNUj9eALLReCwPQV2gRqORCCPBEZPJJAkTEGcECepwlWWZYLrRWJ0uN5/P0+FK4AY5Eoyfvrjeo41cq4CGYB7a399Xs9nU69evdXBwoB//+Mf68ssv9aMf/SgxIxLsvL/5fK6dnZ0UmeSmbvbZmbMHhdQJR04H6XeTZkF7NkwhSiVRsojEJie9RJu39+kLCqEEoClxy5mro9FIg8FANzc3yd7nlRnh+tgW43NpIAQlGfBZcGALfWA+cq2g0+kkooyZB4Chb4+fRmvwuToAxTMAJCVEBFl8TWESLrmDLNGcFyVgxsIckZR8D9005vvqzvgIF/6dzzk42tRcAmcsmxjPtowjEnCYtv+WG2uE521V/ZyW4Ouc8xFU9eFMyM8m8GeQgFYURcq4ldZNHcPhMMGIh2zjKwNuucf3nAOquB/JHb8CRN/x0M+74DtzJnqI+SEsUmBRWglv4BH7RvmN6XSarkFw8nfHSegEpuOzs7Nkprq5udE333yjm5sbff311zo/P9eHDx9SZBMJfIzDBUX2z3Hacdz3P77cXP3/C00hfo735L47h4wSp5svcArFE9n6/b5OTk50e3urbrebnEztdlunp6eSVk5lr+oYgeTm5kaz2UzT6VS7u7vJyeTI4Kow40aKdzuna0E05ucMzvtwtZrr/RWJUJRCoyN3G7MFwIf/xNX+bSX4OsK8zb3bthwRzknnVeOoWocIu/G3qmd/SttmfJ/CxD5lPLk12lYz83sjvMWSDAgmwDcmRy97TT8u8Dj8+3y4TlKy4RPVJ63nt7iZymtr8VxOVkP76XQ62t3d1cnJiQaDgT7//HN9/vnnevnyZdIMZrOZ2u12Ekz9ZDXPQ2LcMbLKmUJunxwu6+jppvZsmEJVqwK2TQSKe93EgYQhrZt2pEdVkfAw6qcsFou1wzKkR0cSUgURC7naMdj6Jens7Cw5rIlKoMGo0CAAmv39/aQp8PLQOpcWIlA7YsTDdWB+ONu5xpmIM1X6dSBzpPP3uGfOCNy85L4TpD2XbFyiiRokc88BeRQKXPLPjYNrXbL0MgrOHCMRi+PxNQd5udZ/c7MmhNDXMBL0yEijUOASq69N7noPFIjX8p4zNVUJZLGv+J//Hk2EaJ6+J7FPzG6EUsMc/DySGFzhpVh83+J+YV5qNpupFAWRSUjolK4mVBSNxqP8EC7BVyojdDqdVOsJLWE6nWo0Gun6+jpFHTm98XBU9ivuf24/claT79OeDVPIIb8jhv+WIwa+EDlHHhtKXRjslgDecDhMZZUh1CARqi8qLM+kXzcP+FwwC/EcnMlOgJES3IcgrSKOovTgxM0JHvOOJiI/nMef4ZEW30dSzTGLqv4Yd860l7OPb3p+3PcqzcWRDKbqWd25+TAXJ9oQsZykG/uI2lZOwnNNqk64caIWpcXYf06Cr3te7llVv20DJ3X9+toxnojzXOtSPcTRM41jn/H5jgO+LjnLgZeYcAEPc1SsdiwpafkwBffrYQYaj8fJfIU/Eqf1eDzWeDxOx226GdnHEJPd2MNoFYhr77jl37dpz4Yp+MbFzc5NPE6QBaKx6W57i5IwtkjMSJRX7vf7ev36taTHWia8Y+/rdrvp7AXffGdADiD8j5ZAljPv+/v76vV6iWgj1Xv0kVd5bDQaybYbcxQAVF5+sDhhuPy3t7eXTGRl+VjUzCN9SHTDqZ5jxr6uUYWXViYAb87QXFOokmLr4CT+50iANOk2WpKIkDhZXycWjIW18IQqJFxfD5CUqqFoH41GY61cclEU6QhYXxuuy6n/cd0jE/a15TeiZ2CA8V5fIw9l9us6nU5K3PKEMSqRAh/sn0e19Xq95C/ziq04fCkBgTbeaDSSJt3pdNKewQCAXYrSUbUXIY0CemjgDw8PKUS00Vg54xYwKgAAIABJREFUmjm6059HFBLH7nJdPP3s4eEhCVTkHxweHqrT6ejw8FDHx8dqtVr6yU9+osPDQ33xxRd69eqVGo2GLi8v0xqAx44j3qJpN6fl+L5HgYTfcjAUNfqq9myYQuRs/ltO7c3dGx1sRVE84agAsKTElVH/CEEl2ggg3dnZ0cXFhW5ubjQejxMgebJZPOCDFwDFtSSNIWEQ6+xqbySiOQkRm2hcl1hYy+2xbupyojkajZJ5yrUjkN/NYjmprE46rTJVREbwfVXeCAe+9oQNwhQ874N5M/eYNOhCRE4r8f8iokqrU7p8jFwPQWS9c2dRVGkkOXzg97i2VYIU4/M+aNPp9InJFVjherRu/qN52WsvYw1RLssyEXY37Upac/b6mlGx2J/NftH/bDZLAgpBFI1GQ+PxOPXJPrtUTlKZZxKjIcQ5ugmXPAbminBHItr5+bkWi4WGw6FOT081HA71i1/8Qjc3N3r79q2Gw6Gurq6S79Ed8NAu8NFhLWqhOfzj3XH319bRnPutzqQUJUy/11VriIA7mpGAJK0ltsEkdnd30zm+rVYrmZwwvwyHQ+3u7iZgjQjGRvA/9zYajTX7PowhOpT95RI8pq1oc4wmI5gEyMB3rnWGWbUnVXvk0irvPNNNRC55+/W5Patq8Zk5TQHgZ11Q4SlBDCEgCoz9wXzgDkaXfl0L8wz2nPTmc445I9EUyN65ppVbq/gbe+eml7g2zqQcFuuYAy2a9fz6HI7Fe3OSaBynN1/PnAkR2Pf5k2PEfgLf7E80oUpPT6urgiVMjLmSFsADMNHr9dKJfi9fvlS73daPf/xjdTod9ft99Xo9jcfjJGjGeTh9Ys9yJsqcFrBJ6o/PiPOva8+GKVRJizng9P/i787VXRJxjslCsdmknZdlmULeSB67v79PqqXbGJHCfdOqGBTSVkxZjwShigh4c+LCPL0vacX4IHo+d64FsHJaSfzuyBUJuxPGeH8kVP5bbp51n6ueEZs7sF31dwe3S4NOUFgfr2zr5hU3HcU1jMQ0ahU5Zh/XaBPzq1qbbZirC1B165jrO/c9J5n6920JUGzRMuDEWloFZkirM7z532PxXfCoG4/TENcioi8hEmP23c9NkJQqnHKs5mg00vn5ud69e5cqL2NxwBRGLoTDJsJVXG9gMBcAEfcEuhMFiE3t2TCFuratZBm1CO51gslCsuCYFjgDAW3g5uYm2XmLokjSPNnJRVHo4uJCRfF4gAbAlBsT6uD19XWywzqBjmFpbqNHUvLfudYlJye8birDLuths1EzcEIdpVH6d6mWayOD4j+v4IpJxM01zow8AoU99nkwvhxM5NYaxAYx/XhHd9x5BVmQnxdOP8aAcCCtl0NgfnHfWfcoxcf1c39XZAD+e9Q6ImN1whcJNt+jqdElSP8eBawqvOOZLnxVCUgRf2Of3pfjkY+N/iNO8L8nfTHf2Dd9unkQmEHrgMhHGAAO3JrAWe8nJyd6+fKlWq2Wjo6O1oRFGMZ0OtVkMkmRRvQf83dy+xv309sm5rutH8HbrwVToH2KVOTv8XdaTsJxQIzmg6IokkM6RvK4rS/Xp0utDgz0GwltlIhiqKgT48gU6NPNONjOI5C4ShsZaQTGnGRSRYSc+OUIVuyvqi/eI5Hxa1wYcCRnjSNBiMQ0SvqRwTvBw0Ht2pgnX1VJZXFucf0io8hJ5DlJPfeb950jxH6dM5poYoqEit99XXyNfQzxiNa6FtcdOz7vEH3wL/YZ95d9om/XIqIm58/EP+hhoXG9+A7+EcjR6XRS0IgzMWdAvlautVZZQuqYga9d3Rp/KkOQnhFTyBGFut+r+uAdghMlXJfw/EUEEpt8cHCgVquVTkzy6w4ODtJBPLu7u+lYPiROojAcMJFIY2lcWiT08bMTWWcePqdNTDAyDcYW124TMFbtRY7A5/qt+j/2/SkSUpQ2/RXNOi7d5gQDJxhxfRypQX53+sUxRK3M+4rMMjLKbaW8SPDrvm9qVSawSLic2Dpj9CitOMdNmgfr7dqeE1f3C1Yxxtwe554R4SEKbu6sZy94FlGEL1++1Js3b/Tll1/q9evX2tvb06tXryQpRU+Rj+B+Q69y7JFvOVyJaxUFqSr4qsK/beDp2TCFX3XLST11ZiWcwKPRSM3m4xnN7XZb3W5XRVGkc5ZRG2EcZVmm8toU0HIzBc8nRK/ZbGo6naZkHMLtpMcNJyQVwAEZPMHMTU3cx5yiqiytEsRcoo0E188Hzq1lfI+Iz/OqgDAnxTqD89hzJ7B10pNf45EhEblj3DeSpBM15uTICSN35sL5Gz523yO0u1ar9YQA5r5vQtIcEY3r4hpn7DunHeTu9fXx0s2R8LofDiHHnbxI8mT4RliNjMalaBK4ONEMOzvPk5Qi9VybZg8Yt6SsBM51CG44k4fDoS4vL1OJbGoyxXXje6PRSLWPBoNBOocdfL27u9PV1ZWWy6Xev3+vDx8+6OLiIp3xTCi7n+bogQ5xr3PfIy7Ga34ZDYH27JmCI4AjbxVCcY07AHPI6CYCj8fmgHCO0Wu320lqIVcBP4QnnrkdPTcmnvPw8LBWldEdoY7A0fmckxCqCCQvl7gAvMgUpfUzjWO/VVId7854pHVTi+co5IgT3yMjqCJmfk/VmKrGnFsnl+ilfDSIawg+b89FKctV1Aj/R8JV1+o0r03/59ZpG02B39zkybycqcbrWQdgihBeHJqSUhKY763jcR3BikweuAJ26dfXW3p6WFMUyuIc6JuDtmJtM9dMuBczLlYF98t42fvr62tdXFzo4eFB5+fnurq60mg0SslqMKSc1cBhMQqy/J8zM8a99bWMa7upPSumUCdV1qmgOSYBcYuELiaveYiqE2BCRnu9no6OjvT69euU5HV7e6vLy0t1Oh0Nh0MtFoukSXBcJ44rd/CR3TydThNQzWazlPTkhBngAxj39vbWjhCMCE3FSmLBAVTssdRdcsnWywnTP+GsZfl4oFCj0UhVUnGqsq5I5iCrJ82RVBcJLGtPlJf7ORiX75WbYFwi9gQyJ+YRXvg/Oh5zJhLWlubRJ9HcEAlSURRpD2AKrCXJg5QzoU8/J9wTwSLjjsSBeWK3x1zJvrG25AK4o7woivSdPrCnA6N3d3fpdzQjYJgzRsgDgIkURZH6JJwbuCT5ksRJTjl0KZmqqN1uVzs7OwlH0EQoGcEz0JxbrVaCEa9A6n4IEkX9gB5CWSk5MZlM0gE6rrW6P29/f18HBwf64osvdHR0pN/+7d/WF198oc8++0wHBwcJH4gqur29Xbuf5rATNSjX+v33qIHnYD3+D0w4/G6jQTwbppDjas7ZfZFyHDJqFG5C8UXzxYJwsYioqyTBdDqddC7C2dmZut1uKoF9e3ubJAAyIN3UEKV/xoUZyV8kwgHIjBsiCYFnPQA2JyB+djRqNGo46rCrxM4UKdQFowCIPTEoEkXG5GYY1tcZmaQnzvhGo5GOOo1Ez/eV/6NUG4WDnDbiyOF9uOTPerD2SLjSqgxGjISJz3LYI4NXUhII3HTBmkK8PVEL02Ik/N7idzeR8J2+fIxO5MpyFQ3HGNykgvQ8mUzW9p/ma4aD1n0smH/I+ie7eG9vT6PRKO2H+9vIbKYO0GQy0WKx0HQ6TfA1Ho+fwNLOzmNZd9b86uoqMT9POqPcvZt3hsOhptNpCg0dDodJes813w/mTabybDbT/v5+EvpGo5G+++473d7e6uuvv9ZwOEzVUM/Pz/Xw8JBMzeBBhKuoObN/UchyE7jDYqQ9uSinqvZsmEKU9P13R+p4fZU5IveS1uONY3ibS7oQTDQGzl8gugDA7ff7Go1G2t3d1Ww2SzWOpNVG0CCkk8kkbSTOaj+y030IUSp2gukEG2R2gCNp6/r6ek1FpU8c57mEPjd5OPHFXOLhnjEckL4ouOcJejw7SjY+p9w+VpmHcmY3pGMkaYiBI0t0LnrSEOZATCJ+nfsgchoH43VHdI5ZRZjN/e/SYI5pshbOVF1KjM+N+MN3X4sYyosGR4Oh5HJAXCOLuQReayquAUQumkmBa9dkFovFWtY+c4fRAOMQW38G+Hd9fa3Ly8uUR3B5eanpdJoYZKxMjImYpLSXL1/q8PBQP/zhD/XmzZskUNEvQhtrx/p4NQHHk5wEX8UU4l7WSf4OC1E4rmvPhilIegK0/OaaQu6eHJK4ROgtSpAkJyFdQUguLy91c3OTarFgRun3+5JWzlskP/ry09VyCI2K7sd1cvqax7zH+iiuVnpfzNGdfjG0Ljq/ParJgdaJWE6i4DmslzOFGEnlwO7aGQjmexyJXY74xT33ueeYgjP4aF7ye1lrvqOd4Uzkd+bhZTD8+bk1q2JwPke/rupe5ly1DrlImcgEcs37Bs/YS3c0Ow65o57rHH6iNB3Dr90XkJOAHXYc/pmnaztRcPLsY4cL9zNQUgKG4LkDOVohKQkYlMkmJP329lbn5+dpHPP5XBcXF7q6utJ3332XSl14ohpmXE+GdRrn+5jDC9cUqnwK3jY5rnPtWTGFqpaTdKSn0vI2yBURlU1xyYcEtqIokm2z3+9rd3dXnU4nAUm329Xu7m4qfDWZTNRsNpOqi1nIG2oyhOXi4kLNZlP9fl/L5VIvXrx4Eu7oCWC5kD8QkCqsfrbscrl8YsrgPjdB5SRbb8wDoOaAcRhOBD6YJFKlq+X4KnJz8T3yPWSPndjwXVpndF6WwqU1ad1sxN4zh6gxFsXqdDpgw53LrvZXIbVrpv5bdBQ6QXVNwWE1EnFJa8zfCYbnpVQxLcadYwgIFpF5ucPXzUeeOVsUKzMZ764lRs3XQ015oV24tuCRT+y5O4VhUI7XrgWVZZmqk75//16TyWTtEC33XzG2ZrOpVqulTqej4+NjnZyc6OTkJJ3YSOShZzFTHw1TGCX5Ef6iBcEFpzptj1ZH2Ks0DvfHbWrPiilUEfXc75s45KbmSOJIA1J4GGdOGgRg3FGLqclD8dx+68+GUHIIDzZlJ1jYut1ZHoHD1X6Xynz8TsSilpGTRCOR5rObqOLzIlNwIPTrHXH5P86rar9dgoXRQSg82gciwf74fjrxdWLImruzP2pqEBtJa/OokuajZpBjDFVCS2zxd2ASYsTc3DTndvtcf/F39tFfMFXG7LAR4Qzp1TUJ78tt33GN3CTkDJl5EL7Nd5euXeNnr5xpo5njmyASiCJ7wHQcH+tJwmq73Var1UpJq6yzm4c4XY5XZJwudG0jtVe1OkH4+7ZnxRRcyuJzTnKtAvJcf5EY+nUuWQFwSCcc0t3pdNRoNNIhO51OR2VZrtniB4OBpEdn7/7+vobDoXZ2dpIjkXea26UplTEYDHR3d5fK8rrEG+O8nbDjOHNTDp8BSj+f2aOvcmaNKkKBuou047Hs0c7Os5xQSUpRIX6mQRWRjPsIkfFTrDxah0NOWDtJKdpF0hpCwrAYB/95QhFjAvk9DBGG5NqDExRnKMw/pwn49XXMMe43+4Ezlr2AEeLcBU6rBKuoeThxg5hFE4VrOFzvmgL9eh9+KA7E3+GM+zxBtCzLtN6uLYA/ruVxv2srvk63t7epJtHp6WnyIwDLwIPvV7PZTL6wo6Mj9Xo9nZyc6OjoKCW2SkpHac7n8+Rgvrq60unpqW5ubnR1daXZbJY0a3wdDo9VpkHec4LFtu2XYTzPhilUAW7Osx6lnNz3KNlUmY/4TAihv7Ahoj52u92UtLZYLJLEANE9PDzUYrFIBAoiE5vbR6+vrxPQ7O7uptA8CCpSPogAkXNpCeRz3wFI5PkJ7ufIMQRfH19vJxY5jcSR0PcIpu7al18X96/q3bU495d4xivI4kc1Sit7sKREnNwh6kwiSrdIvm4CclOTS8YRrpwZ5LQ8H2O8t0oCZKwQQ9YDptBoNNZO6/NxVjF93+eoBfgaRek7Ny7pacKkw6ObJ6PmENetLMvknPajaSWtMSAfUxyHawmYiNy0Q02snPmG8OFWq5U0BPCaF/SgLMtkFcDnAKzBYHh301GV1pAzH/nYIozk4CXC1qe0Z8MUYotSDJ/9/6oJc11Oy/AFjYwCAowddD6fq9FopAqIV1dX6VAaIpIwUTSbj6e2LRaL5GMYj8dJkncnGHN6eHjQZDJRWT5WZSVnodfrJelXWpXsjZICCIcEgqP5+vo6aQ+u1mNiiRFW0Y7uaw/xQaryDNbIEHx+OSdYztzgTDtKRdEEQNKPFyxz7QJC4hqWj4c9wFbuES0wV0KVXYuUtJY5WxRFitOPPhU3gbiG4GaobVoUgFg71n82m6VIM2LrGXuO8bL3OTyJzN/NjlFDhZi7WciJssMN+RCcTMb68Rx3iDtDcB8Dz4QQS+uhuL73TmyB1+FwqNlslo7EPT8/X3MsO6Flj8FtDtE5OTlJh29hKbi9vdW7d+90e3urDx8+JMf1d999p/F4nJ4HzcAXB8xVaQnMJ647/zks+W+xufn2UxnDs2EKVVJrlFyr7uNz/C0SJv/shAugQyKglEW/39dgMEhhaJ9//rkODw/VbDZ1eHiobrebiPDh4aEuLi40mUy0u7ur8/PzVL8fRGBsECII3XQ6TYwIZHrx4kWS9kAIpMFoyycmHAe5IxnqOKYpJBlOpGq324kBtVqtJJVhihiPx8nhyhpCEF0jixFXjUYj+VrcNLOzs6NWq5WSvWieqxE1IidEjMEJQ0RwN1u5OeLh4WHtHGZ/FoTB69EwL6RUENlDd92vgaTOmqJZQhR5Ns/Ch4Rk6WGwbspykwNM0p2ITnQhrF5QLu4Jz+l0OpIeTXskpu3s7KTyLp7D4TCBiQoJGRhvNBppb+mHNeh0Our1erq7u0sJdqwlc6eqwHw+T8lr19fXOjg4ULfb1XQ6TdezN7x7Ip439jcKZ+yhM6NGo5GkfcbNmcuDwUAHBwc6PDxcC4mVlPadw4nIdSI8nfV2Jh8ZfxRYqywguesiHfSQYOA20r+q9myYQs6GllNrI+fMXcd/EItci0zDJUbMQcT5cyLbYDDQdDrV8fGxms2mXr58mbSD5fLxVCocxhTXA5AZS5TgkOwpq9FqtXR4eJiyjQE8oqAkJc2F5yI5Y2enRjuaj0trRbFeImB3d1eTyUQPDw8JsD0iicS38XicEA5i6mMA0F2b8Thy1hvkZw4OtOwB10EIcSy7tkDCIM8kUY7xY49mHJj5PH6cubAujjBEy/DuyXeYFty/wNjd7Pfw8LCWDe65D2VZrp0k5qHNDh+eF4BWiEmEvfYxMAdMIzSSEiWtwRWwQ9+YpDBpMh7mzb1oLTzbT1ubTCbp4Hr+K8tSo9Eo2elhBuAehN5LnZO8RmTdbDaTpOQchrFDAFmbsiw1HA51fX2t09NTTSaTVHbCS2KzLzQO1+r1ehoMBjo+Pk5mY5LTcFAzL0n65ptvUuG7d+/eaTqd6vLyMiUBejBA1JAjM6DVOeWdwedMTeCNN8fTTe3ZMIWqluOim67nPapaOW4cJUy/NmenlFYOKaKN+A1mcHBwoLu7Ox0cHOjm5iZJ/JwPHCVc/pOUSgD42QsuJbtk7b+5Ou+b71JzdHzyGcLptm83wcX+c+YCX1Pv281Svi91++x75f1HU5UT4Zw/wOcfpcEIF9IKcerW0/txYuYSa/RD5DTgyCyr4DjCozuC4zh5njNtd/a6Vhfnnmtx3f177r7YbyR+uevjfkdtD+Ln6+hEMO6TM0/ORYFZuD3f/UrR0U0pbBgYPg1pHUZYY8/ujntTZSKK8B73u8q6UaUdxBbNlXHf69qzYQpVixOvqZpYvD+3YJsYikurSGgciEEVVb7HGjZEvuzv7ydzy/v375Nzi5jtmEbPnHAWnp6e6v7+Xv1+X0WxOsjcgVJaAbVLqE4YnUAB2Kj7HlGDrTkeHgOQI1nFao6RSPua89wYZuhFA3MMKEc4fV+cMKK1ePQPpgyeDdK5qccjnlwwoG/mGMslkMnumgImGuaD7Rt48Ag1h0efyyYfA2vAHrj/CG3HAwyiNOlrD4GVVhpabD5G9pp+pfVkPbft58wgDh/87lqqC1su/TI2z2MBv5gr80bQAl7RaD98+JAyjKvwzuH0xYsXGgwG6nQ6evXqlQaDgY6OjpLg505ino9fhxBX8h7IScgxiJzQkxN8qxhH/H0TTftl2rNhCo74UWKPQJRbiJxEEplI/FwUq2QcEGi5XK5FPWA739nZSer0ZDJRt9vVcrnU5eWler1eMifwjJ2dHfV6Pc3nc7XbbS0Wj+GDkpI67XMBgQi3pB6RF/dy5IxSW5RKXELORcLkImPiWJwIO/HnvUoKktbDMnPSTQ6gq7SDqmc5wXF7u0tyOSEhJ707oYtmIElrzIb1k9bPy8a0Eue+TdsksUdJOEqs+BQgkB6K66GzaDfbSo2uhfC8Koc1zfNifG1hbG4a9T30fYzPcEYd10NSMjvh33OzWOzT9wWNH9MRr5iPUJaryrCUv766utJisdD79+8TM6CGEqbcaDZiLZlHldac0xQiU4jmowgv7B/vv3aawl9Uq1NzI+BGQgiCIYVESc1t7DATkA6nNQ5rHJxlWaboFynPFHZ3dzWdTlPVRyRgN8O4+ltlNtoksXukR5Tao4kmMp2caSBHdHOv+P8mYI2M3ptLmXXj5bnRTOb9QTiiaUBSWn+XYqWVE5v194iuHPOJjWe6dJ2bf9wPZwquwQGzng3sTMEJcbRFV609uBCd/dGc6MTJf8/dw745s/H7IsGM+8S88Gnc3NykXAHqi7nPI/bjJiOvb9bpdJI/hAAJ1sGT02BCaCv+3WlCFN7ieucYQ04w/hSN4PtqD78WTCECbZUaVnVfbkNyUoxHc4AAlKQgcoWImdvb2+R8cgLRbDZTotvJyYmkx6Q2/ASUokBbiEyJ0LUPHz7o4eEhFeEiOgXHp2slLj26mk5xPY/zzoVMSitAcvXYszKjthBNA/ThhN8ls1yYZt2euWksmqii6Yn984QrpDppPcokjs/NcMwJk1Gz2UwObZz8MGYIv5uVXFOIjKEOnh0O/T8nrL4ffIYYekZuNEkwXsbnxd5gEHUEy6XxyABihm4UqhwuYao5cwr9SEoElWujwIPGAGEmCIRqxcPhUPf392sVVunbmRYaQKfTSYEdOJb90BxJKQyY2kWj0ShpCtQ3IszVHctRg63b+9xv0UwUcXWbtq124O1ZMYUqVSrnFIzSaezDpZDYfKGQUBxRHJEiEYXgIumA/Kif9LW7u5tC89rttu7v71PYKM+KYwOIimJVc4myvwcHB2uOYV+TGNWQG7sTwSjBRm0FQlCVcBalH2fMUTJ2FdcZxbaMPBLKnPnJTT9Roo7rXKfBOGMALrBFE3dPtAtwgETO+uTMcz633LzrpPaoJcTEQf/PYdLNXjBL5ogm4Vpabo39+XEv0KiqNEgn5q4ZMF/fE9a6LFd1qIDBnMbKOkB8vVwM1YuJDMr5UDy8ltBTNAScyzAEtHeP9IIRw7xiYAG457iR2/c64dbhoQpWN8EVe4kAuS2DeFZMIQJWVKmrzAhxgXyRHPjidfwPEPumOkEBwAgvpF78ixcvkrOJ9HUckEQhLZfLdEarx15Lq7jpON/7+8eDOogFpzT37e2tDg8Pk9TPHFBZ6QNfCGGZIADIEJlEXDuPpIgIXLVn7ElEDEfAWPBsk8QTCVFkdm52YZwQDAg4CMF9nofg4+A5rAdMFiKFRuCF3fjuoaT0l3Mw+zrVSYdx/pEwsj9oELyc4dKPmwqBd0KPXduMe+cEKJp30Ihc+o34GvfEte8oZDijc2JLRN5isVjTWglPvb6+1ng8Tg5l/Ai0OBeHR/yABwcHOjk5UavVUq/XS05laRXiivOaZ6EpoJUMh8M1sxKMODLUuMdVRDoKPf7OnOqYTYQpZ97btGfFFOIiSE/LXPjn3KLF+xzoHXBpIH/k9E5Y3flE7gFAdHR0pKOjIx0fH+uzzz5L4adIF8vlUt1uN5mCHh4eU+HjqWzeynLldxiNRomxkDWNHVtaISnq8GKxSEyDtHyOFCUKCaJAvLifaoX92E9g4zwGH1cOGGFARErRD325P4OxeI6AE44IEx5Z5OYZl4R8vyPhYXwuxXmGN0gMM3GpVNITswdj876YN/0AR81mMwkWxPizBjwX82CuRS0mZ5Pnu//uiVrueOc6hBj2tdlspnyJg4ODFGHjUrOf+sd54mVZpoRK5gKMUSKGV6/XSzDqGeWMtdvtPjl0yqPxOKjHI5MQYBy/PZLOhR/wgoQ0P2e51+slLR/hCEYFsXfhEaGLHBmHYWDy+zKFSPyBed/n3P05DWnb9qyYQk4rcCk+agG5+2g5gptjCqjZvhGuKSClQMyJPiA8rt/vazgc6vDwUJeXl6lOymKxSE7ifr+vnZ3HQzj29vZ0c3OjRqOREsMiUEur2u/n5+eJIRwdHenm5kbdbjdlnPr1ALRL0EhWIIj7HSAEjNO1BMpvU8yPdYo2eH+5U5NxuLnBGbWXKvb9gyFgPnDi7MRYWtn3GU90qLpZjetxLCLNs04+VmdOThgIKy6KIhFE+swJGx4xwxq4GcelWnxTEdGjpBc1h1zZEbRX11hYN/xW7XY7Zc77mvNsonjAEfctQXCZU8Q3yrWQ1QyR9hpfjt+sgzuOCfcFVubzuc7Pz3Vzc6Nvv/12zZ7vyWEOH66JwLQR6I6OjtLxmuAS6wcuUkX18vJyTVPAiY2/Eb+Ga3BuEsvRp1xz4dZhwH/3dYZWxfm6UMXnT9EWnhVTkPJJG9uoSbl7c2o7776ofn1U3bw5guYIFojCd6RmmAmhqd1uNxFbL4ERGRiMYbl8LPlbFEU6C9qlXgiaExUHmKp5VZkqXMp2gK7SaqLWFp+f82Pk1jb37ua9KPV7fz7+HCH1sTmh4l4Qjv3L9Rsjm7zPnI8oNvcd5ByPcW2rYNA/+/r4M2AKOa3HTTpVLe4h97G20eYd9y2/HPTbAAAgAElEQVQ37nidr620Ilw+FzcJejY7piIXqGjsr8MHDNILXXqpe4/sY82IKOJZHBfqOQi5dfP1c6G2ai/9Hr8317cLfJ/S3OS0qT07prBNyy3KNgzBATMyiNhc+kWqlh4lKCRyVGvq3Mzn8yRFAmR+MA/aBpVQkUQop+FRGIwLR9q3336bYqB7vZ5evXqVgLvdbq8RO8YX/QhucoGBRWaQC7XNtZz04ypu7lVHxH0M0qochiepuTaFaQaTDf+5Ix+tgT1kDXAkOmOPTJ4x5JhlJMTObLhvGyZRJUFGYpFbU/53wunrQB9uIpO0ZiJCY8o5SVkr+nAfixPQKHDkmJZrMc6s+J9IHTQrYBg7/XA41NXVlf78z/9cs9lM3333XZLOvTaTj4uxAfu9Xk/tdjtFGL18+TLV/8IkxtoRcUYxPYraeZhr9OvkBIY6YapKOIu/RVrl/dUxD4cZ6ekJbHXt2TEFX4ScVLHpXn/PAWn8LZqPaL6YAIur0xR684xKbLGYcjyTFmflYrFQr9dLmoKbmqokcwD2+vo6JcCR++AaibccsjvSR2CKkltc7zoNyv93B7BrMi5xVu1b1Viif4DnIBVjKor357QM7oVhwzQcPlxK3tRywoXPfxtkrCIQcU3jHpblyjHua+W+A0pcxIilnCkhanVObCnkB8F2B76PtW6Pc8w1agYwBwSim5ublCns5xJAhH3sEV7xPTF+Lwbpfi7G5yY5jzJybcHNRh4w4msfcWcbqT7ue53A5dp5Dq9c841ru81Ynh1TyCGISyE5Is9/vkCRsURNIapS3o8DtxO2aEeV1s+cxbbsv3v438HBwZMKlUQkYfv3jfR5ev0WEnSo4thoNJLzjGf7i4qUHoXEdTj9sE1Hh6pHmdQRSydeHuUTcyRyZqQc83abvEdCcT1MECcfhNDvdR8HGhwahj8H04S0KkDn+5/77OuwSWJzGPE1dLNCXFs+A484ZpHuo1+E/YqlvFl3P7DG8weq9o2yEmi3wJLjjj8XWCrLMhFe1ow5UYkYbSM6wsuyTPk819fXurq60mg00jfffKPJZKK3b98mEw7amOeDOMHkP3wIJycn2tvb08nJSQoWITgD4YKQU3wHFxcXurm50Wg00t3dXaqA6uaqHBxswxQ2aQ8Rx3IamcNdxCfud8d0pHlV7dkwBZcOnaC7ms5vVYQ/9lGlYfhv3neOIbGoSP8gFdmOqL5Uiez3+1osFinqx4kwGkOr1Uq+Aaqs4neAOMVxMWYclZiccGBL684kXthGebYTPfrCRhodlhAXX5cq6Z1xupTp73XAmNs/NztEKdef55J/ro+chORjq4I33v3aHMzFz7l5xagiGELVHucYZpXWFx34cb98/Vya5TcnPjnzlOdiSOsOce5Hi/bPMAc/VwFHModJ0adL3JSRv7+/1/v379PZBGgLrGVOQvZkRcyEnplMWXjuu7u7S8yWMw+oyOrndiCQIWCgGcAcopmRvcgxiG2IMvPz5rjkWmIOt3wc7kf6tdMU6qQtR8RtFtWlrtwi+OK4+Sj24X05UcZe7acrLZdLtdvtZK+FyGP3R1rzcxE4i2F/fz9FAgF4mJOi2kgUiPQoJd/e3qZ4a+q8t9vtNSnKozJcZeY3J7515gXWLjIFN2kgZfp71BByElJkBu5PQIuJTJ75uJaQYyhoZhBMxouU7dJq1JR4Vs4ElmOKVWvmMMwz3EcSpbtIrCP8xKKGEAqXCMtyFSrreQye2+CF8oALL+jn2i6am6+bM2oXIiCaMBGitlxYoaHdIKGfnp4m38F4PE4SO4KXJw/yTvMSM51OJxW14+wT/G+Mn/Mabm5uNB6Pkw/DM5fxX8RaStE6IT3VCnOEeBMNy9HCqCnk7qnq61Pbs2EKVVzMf/fF9haR0a/PmWK835xaFT9HpgRgAvBe5x9HXqPRSIjgJ4Fh6oFwE7eNxsBJWq6O+zicOUmPSMB5DfP5fO2UqyhZw1gYR25d4ryjxBPt9M48q6TYiDg5hpuTdmKLBNiJqdvvczCTk9aqNE23Dcexxha1qLrmBNHDVZmD+wIirDvTXS6XazAF443Mx/cq7lsO/p0pIG0vl8snyYZ8d99GTgvBCeuJhN54NpL4cDjUeDzW+/fvUzg25SPQcHMmSB8/jJO8CMxEOJQZL+uPpozJyn0J+BPckRyFppwAtS1TqNIg6phCToOo+76NRhvbs2EKm9qmhfyUfuqYS2xuAuAzUhAaAwSJbGUSZDAVIZWCvNj49/f3dXNzk8pgtFqtlCMAskRpEkB0dbbZbGo+n6vT6STNodPpZJHWk3qcGLnpIvdygubStNdT8ignf0VnsxPyuLdR0o8moChZuyrtQgB9+B7xPTra6ddLe1QxvggXOYZWpTEwJqT03BnBEHyCFCQlYleW5drhPmiFwBl5JcBnhBOYjhM4nwv74+eUO6yzj+6gd+LojI4oIn8uTAYiy/vl5aXm87nevXun0WiUmMJ4PF7bC88JiesNk0QbQDNw7Rn/k6//crlMdZPQDIgywoyFhuD+miohNNeqaM4m60S8bxsNI9fvp7ZnxRSqJLEqKbPqnm36dAIfNyFKIN5PZAw4zNzUQblrfwdBnHgWRZEO/qYkxtXVlSSlwnk5gu026YeHh1Sml3tBhFartTb2RqOxpv47IcpJ4bQo4boGEol89CVs2qPcuuZ8ATnpv2qsLrW6ZBjNTHF+/vwqzTXes0m7za2fw4rPwfclwiJEGZOOR7Z5aC5SuYemuj8mSri+HjzLgxQc3nyP0Sr8Hu8j2tk9TNjt+Pf398lc9OHDBw2HQ11eXibTDnOKGmfETQQQz5ym2qkLAjBINILF4vF0wdlslnwK5D/EIIccbLhgk4OFnCYcYT5H06ponsNGHWx+HwbxrJjCNggmVU80x73dpBD788WNv0XiEaVZNg7EQmKHEaApYMN01dVt/h6RhE9iMpkkzWM4HK7FREcgWy4fz4Ml05Ozno+Pj1UURSrPge04StluA82ts0vRIKpH9CA1OrHwVyR09OvrCaK5VOvSrRO0OLa4/+4/YYxIr/wHgYjwwjhcOkW7cEkYogyTieYx11ji/LyIm/uNWD+X3mMEj2djA0+EObufwrOoff08R4D5+DUQOPbNS71zXc4ZzT0OR6wTGg05PDAHKpne3t7q9PRU8/lcV1dXa/WLfN40F2T4j8zk3d1dnZycqNPp6ODgIJ237nPlzAWimB4eHpIPgQqnZPPzP47zqFkxjjoCHa/3NctpD/EaPjtzdh+KP6NKO/1UBrE1UyiKYkfS/ynpbVmWf7Uoiq8k/VTSsaQ/kfS3yrK8K4piT9I/l/SXJF1I+t2yLP9si/6z6lT8rW4DqhYy1+jHiUjsJ0qkvHvUShwfyIc00mg0EvKDIFRTLYpVaCEnrPX7fUlSp9NJIYiOZPG5bvYYDocqy1K9Xk+NRkODwUBlWSbnpCMwDI0+cgDjSO4OYAhQzr6Z0xp8vLmoEZdco1QbTUdV4+M9p3F4n8w7Bxf+HH9FEwkMR3p6zkJubjlNAeLtTMGDGNwx7sSDoAaYPNoDtYfcvARz8PX1Ofl6AAuRMUCEIlP2Pfe9p7FWROpgqqE/ykXc3t7q/Pw8Rf+47wANgbm6pgd84UMggZQzEdrtdkoilZ5mKXsZe/wJ8ZRBXjnN0eE8wmNcm01MI8JNHS3kVUV/fGzSqmx81Abr2qdoCn9X0v8j6eDj938k6R+XZfnToij+maS/I+mffny/KsvyJ0VR/N7H6353U+ebkD6n5ub68Our1Cz/zZlClMKrNtmf71IlmgJOaIAZE5FHGEnrZz1TAoNcA+yphJtW2TOjND+bzdL5DaPRSGVZppR+l0aZr/sG6vYlEmue7RqCv+cczVFbcMZc5UfY1CJDcJ9Cjqg7EkeCFqX9yBjcDu+Zt06065hNjklFrc/nD+ON/WMqkZRMMV4EcWdnZ62AWxxDDs/8N+bg+xYZfJUQ4fN082cM4+SEQYg0Y3XBwtczjo8Xpa/b7XZKUCMay/1Mvm9k7cMAnAlEH0yVOTEnqGzLFDZpCjni77+7UFonZEl/gSevFUXxpaT/XNJ/J+nvFY+j+B1Jf/PjJX8k6R/okSn8tY+fJemPJf2ToiiKcsOIcsDm0mX8jeYMIIfkdZvGtUgeseU0hXhPtMsDaI1GIzmsGo1GMuEsFos1CQZpiIM+yrJMWcudTkeSUo14wuKiSohUSfQEvonlcqmjo6NUf4nCfG72QBuhD9bb54aNFeRxpx/EyMMYCUXFtAQB88gR1telSZDVmUOOgOWQzRkj6+JE1Qkyzc1dztwcdiAmmFAYv4dpEgPv0q3b4REW3LwD4aHhm3KNAWLmfaIRkAnvhJ/mgg7FEN3HErWvqHEVRZH8UXd3d0nTLMsyOZ+L4tGExV55cT1PCuO5zB/bPfkIvg4eqBBxzuEIIWdvby+VrTg+Pk5agvs83O/nZiMvaodDmfIWdY5lZ1Qxiu/7aAq5+cbfNzEL/+wJqnFvN7VtNYX/XtJ/Lan38fuxpGFZlkD1t5K++Pj5C0nffBzIQ1EUo4/Xn3uHRVH8vqTf57sDqC8mCB3V6DhBX3gnmr6hOQbhUq+N7YnW4f/xHaLjNlkIvteCb7fbkpRCVjEjuTQEEW21WirLMpmP0BzItqwiBD4HDh05Pz/X3d2dWq1WMktRBlxaHRxDQlGUrjCBgdi+/h5Z5DWVqiQ9b06k3V/i0qRLd1V7nZPk+R4jY6okPvqO0rCPU9IaweYaiL6bc+J8nem57d+laBcsql4O826uik5hL/lO9rBL25Eh5DQXhA9KuLjEjLbLWjAHpH7OOCD4AUJL1dXJZLJmonHhCthzZh6FO3IQvKR9p9NJvhWYGKYzHMqMZzKZpAN58Bl4klpcixzjdNpRR2Rdi6/6L/7Ge474R5yKnyPceb9VQlaubWQKRVH8VUmnZVn+SVEUf2Vjj1u2siz/QNIffHxG+fE99/wn3DgS6nh95JzcF54vqdp8VLWZXOtqOX0Q3ywpEV7UeQ7vgBBT2qLb7arRWJ3cNhgMkrkJPwOOZ0xJIJibH0CisizXYrtJjDs6OtLd3Z36/b6Ojo6SNMXYXfpnXSDQTswATGo/UVzOY9ujszna2+kbxyvZ2fheIoHPrbsTWY/+wqwjrQg5mlGVCYz1c62BdeV6Pz4VTQH7vyeUeT/OoGKEGlFq0oqwO7NwZ76vO/3u7e0lIu2mF+bF+sWIq9wa8BzpkfD4GcRFUayVzWbeMA8YA8EO4/E4HVv58LA65N4lcyf8CETu/I8Cj2sInU5Hg8EgBVAMBgP1er2kOUErEDTI+6E0DOODiWFydQHIhZKcuZYWfQo5OlFHR2KfOck/d43DZ+6a+Jsz3G3aNprCfyLpvyiK4j+TtK9Hn8L/IGlQFEXzo7bwpaS3H69/K+kHkr4tiqIpqa9Hh/PGlht0TlPYtg9HhKpn+H+RKcTrc4vuxAWTghMA7LvSIzFvNpvJBAQz8FIYOJ673a7KstRgMNDOzo4mk0nKR+C5TjijVFWWqzyHs7OzNQZBCCNRUHGNIEQ5+z4ELMcEcr4Eab2Il489njccHaO5vY0SW/RFsCZOlHN7yTydKcRxu7/AmZATUIgZGoSb5nKw4gTfzUe+b1UvH7PnDFC7ijFLq6xkAhX8WYyFffVoJZgAL+Dabewe1QWMeWkIiC4RRl7mGlzOmesYl2ts+EkajUaqdHpwcLB28JXnTbgPg3ExHr7jVOYaDz117Sm39v55W8l7W2IcCX/8r4pZ1GkrcT7btI1MoSzLvy/p738cwF+R9F+VZflfFkXxP0v663qMQPrbkv7lx1v+1cfv/+7j//+63HI0ddJ/ZlzpvypmQnP1uUpz2PTsOo7vEnuMTsGngJ0dxrG3t5dC3VyFBsnxQxRFoclkorIsU+YyZyu4dBxt5SBGWZY6PT1NElu/39fd3Z06nU4qDubx6K5BRbsq5gkQFcLj43afgmfCukYFAqLxuPTo+xAlLe+D8eUQ2/935HZzkj/DJdblcpls5fTjZhXuhRHCzDAjEcbptlyYAUTUM2eBDYcjNxsxD/aId9YWs4lrrsChS7+YM71PZwbMDbMQYbNFUawdMUkZF/wEEH9KUVxeXmo6nWo8Huvh4SHZ633tGDtmKG++FziN8YUNBoOkKbh26owPwg4zwlyE2Qo8wKzFPPxe10Zz2mqkD3UWhW1ahPlI6Ks0iG3633YM3r5PnsJ/I+mnRVH8Q0n/XtIffvz9DyX9i6IofibpUtLvfY9nZKX3T7k315f/V+VTqGpV5qWouoNMRVEkswg+Bb5jVvLKkSAKhAJnc7/fV6PxeAYDfdG/E5Pc2PFFEC++t7enbre7RgRxDkbJOEbJ5LQBl/rc7hk1F6Q4N6G4bZnx56QfX2sfW9RoIOYRVqK24PsYtQUP2fX19TlEJuZhpJFI+9gg1MzdzXhRM4gMLZoAIKy8nBlBWD2fIre30npkGxI3moFrCpiV0CYgupSouL291Wg00mw2S5Fv19fXTwQWb/wXtQN8B61WSwcHB3rx4kUyrSLIuFmS+YBb8/l8ra4RlVW9jEU0jeb8CJtoTh2t+FSmsIn4O258Ki38lPZJTKEsy38r6d9+/PxzSX85c82NpL/xywymSuLPbc62hNuR0/ujD767RlClTcQxRUTjHURytR0HND4FitlJq6M0kaCQgIhKarVaWi6XOjh4jAYeDodqNBopmoLDeqLd2x13d3d3urq6ShEf7XZbs9lMg8FA3W43HdqDSclzLZhjPGvZ36OW4M5TEA+zGfHgnhzEurpEHPfZpe5cJI+bSKoQu84s4xFVzuDdLOUlGtz0ht0b6dr9GL4HxONDrLxsQ2R0HrrsJgVnuhBQxuf5E0SWQSzdl+Oh0b62jAOiL0mz2SxpdBBdJHGKyJF4NplM1hLQWIdcwhVMCAaGIORnoFPUrtFopN99fyDo4AL+N5gU46HCKszChREXLBxGtml1pulNdCReF3+DvrgZNpqWIkP5VbRnk9FcpTZFohDv4d2JufdVFf1C8xBG/qvbzMgEYpSEawxue5X0RFOAsO/u7urm5iY5m11q3dvbU1EU6VBxTEnz+TwRXz8LINoPnTlAQFHxi6LQ9fW1Op2OdnZ21Ol0EmHGdkwCnpcxcODMaQr87xK1OyXd1OMO1TjeOkCPDlOX8nL3ReSN1/E5agr+n2shTuydcfi7+1J8HdzRvFgskrM+ZzZyKRiYcY2B9WJ/XFOI++ZM1U2CPh/myTiXy2WKfCNiZ7l8DH6gkuj9/b2urq4S42BeLv37PsT9cXNRs9lMjmPMRX5mCPjg2mVZrg7kQSNgHDjAGbfnKLCm0UwU32NjTjEk1dsmOhK11Fz/8Tff7yo497FJf7EhqX/hLarFNAfWTROLEiH3110bmUJVf1X/OYFxJxqbDiFBoiZuGk0B6Q6TUVEU6cAc9y8cHh4mUxL/EWO9t7en6XSqZrOZEBMGEQGvLFemp4eHB11dXaVyGhxXSGSRpDQuzoZwZgvwucYAQWVtl8vl2lm37gdwf0Bk4NFUkpPwndAyT8+C9aiWKuHAYcoTwvjd8zpg8C6R0zwbGaaaU/Mjc0CKl5QYcDwRLjLbHOPlO6Ux/HAjnunRTzBiiC2wuVwu0wln5MegicIUKBZHvD8RPAgS0YTnOOJ7QkQeVYMpVQEzINSUon/sk/tKEJIwW+HLGA6HKbLNw02BezefwSC3bU5bcjSn7h7m4C0n7bumEIVd+nLNMd4PU875xja1Z8MUctxRWicOVRzX748LlGMk3k9c2HjNtiak+GxnChAt7LFILY4YpNy7+QbiVhRFSn6jhAWaRaPxeGIUWoekJ2YkxutjWi6XyXyDyWc2m0lSKhcAwkYCyBxdEszNHSnMw0b5zphcIpZWET+bkC1nGorMqmp8cX8dySBaLnW7hhTvcenex8YzYfSe3+D3Q6ypf+XIC4y4aSMKSTlEhyHEufMsfkPyds2WCB2kamL8eSe5y/MSuM/9Eq55RVMX6wzs9/t97e/vr1U23d3dTWWvnbm5qREzGMIGtIKxuEnR4T4Kco4bvn85mAe26jSFSHPqCHEdQ4hj8f1EEGCNY/OCibkx1bVnwxQigsf/cgvsBDkSwboN8d/gpDnimbvfgYn73EHqzZEDQEKSxGSE9IKpqNFYVVclwxmCtLu7m5xuMIb5fK79/X1Np1Pt7u5qNpvpxYsXa7HiMeQQSRjEAdGbzabOz8+1t7enXq+nvb09HR0dpVwKaWUS451olLIsE+KCiJgqkNQ89NSjPpCyY+YzaxhNKs5k6Itr8XuQXe3aTdzHaAJy7YDxO0F1Yh3DSd0sBFNnLfxcDQ5EYlwgNwTWVX9MSg5jPh+cyG6uiaYp1g1TCuGZL1680MXFhYpiVVwPs0rUFIjYgTngH3LYiqa2qEEC24SSElW0t7enfr+fzETNZjPVLYLIk/TG+nBe8/39vUajUYoqYsxoO16JlUi8nIm1jvZEmAEW+O6+kthHFQ2q0hT8e52mwHfXRmMfLkT4HH/tNIVfVR857kuLRD9+9r42SQxV3NelSCQ9JxBINpKStMTxhIQpkk2KNuAlI8gxgHhifuh2u2vZ1LE6qI83Mj4PGXRfCDHiNzc36XhFJ9RODDzPgHeP7nAiFSOHWC8H9NzLCXOU+tyv4aUhYkRUbq98H2FIMLucbTwKDVGzWS5X1Sx5NiYtzyhnDqxpjJUHfrxvZ1QQfCR0hA63l7tPx81HMDBgzZkCTtrF4vHgJ8ySbvJzmInaMnvBnDFHckQmpUEwD1HETlodp+l4FDVuz3EBp7xMSq5cSu71fdo2xH2b++JvOc02R5u2Gd8vQ1efDVOQ6r3wvjg5RM5dF6/NaRx1atUmLSOOJ5oGAEaILBIfBAIiSjgqEhvSN9JNo9FIh4TAHDA3eCRRu93WfD5Xu93WeDxOh/iMx+O1JDHmisbgJgoiR2azmXZ2djSbzdTtdtN/FO6jTr1rBRCWqLK6RO+OTohWXNuc1uf75ozFTT9I4hAh1tMzjWNtoqj1sS7RVABBiubG2C8MgJekNCa0PA5VOjg4SFFYmHVYLyR4ZxhoA6w3mgJCgBNS4A4C6mGwXO/OZElJc41hnLljKCNR9WQ61r/ZbKrb7erFixfq9XoprBTGwOdOp7Om2fEciDwmKjSV0WiUkuE4GAdfgoeewhzcdFRlV99EPJ2++D5HR36uz9zvmxiDmypzNM6ZcK6vHJzmnPy59myYQhXnzgFh1cRyfWyS6KL5KHdv/G0bTh2fw7MgnPwPIgDMqMjUQPI4dJAOQuEOu4eHh2SDxbfAsZ7UWoJQxPX0SKo4XjSX0Wikoig0GAx0f3+/JtXRYhaxq7nxtWn93NYb19G1Br8uagrRQRuZS67POPZc41nMOWokXOPNQ10RDGD+0ckZo4Nce3LnqDMrXxOYQUyUcwm7LFfnO6CxeMgw18U9c2Lk6w5sYvbxjGN8VPze6XQS4/CAhrIsk28NDYa54ERGm/aaSghHnjWd00xz+50j3HV7zxoz/zoHdR2diJJ//BzX2H9jreo04Gg+8v3b1J4NU8hxPZeuo7mD/2Mf8b2KScR7ImfOMRH/P+dT4P8ogbpZxhGJSBGkbY4LpOZRu93Ww8NDIiYQY6RI7MtIw8Sk7+/vJ02B8hgkFsXCX4zbQxkhPovFQqPRKIX3XVxcaLFYpHyJfr+volglUNGPS9Wsgzsj3bQR97GOsXvLma9YBy/D4czTkSdqHI40mxCdZzkhjIcN+by8DAhhx+57gGFEs1/s181IHlXiEXTcOxqNNB6P9eHDh3TesYdpQvzxJzlTICrKGVCcu5fTaDRWBfg6nY6KokgVSzn9bDAYqNFoqN/vJxgm6sm1Hp4vKZmtptNpykEgGgqmgIbgDASG51qpm7mq3rc1tXgwg5dCycHKNkwhfs/RQX8HR3NaQqRn0Tf3a60puClm02Si2SYnpedUXimf0Rz7iL/nTEZ197pEjqmGfrDRe9azRxJhJsKk4YQHgodjFeDv9XoqiseMagrvEfEE0QSB4ho4ALoUTuTUxcWFbm9v1w4BQirEfBH3LeYT5ExGvpdVCFIVTRRV6bhGufv82a4ZVcFM1FRdI/FEvqo55BzpnkSGyUNa+RrY06IokkTtY4foYZpjn5bLx9Lpw+Ew7RfnEJM85+YZf26UoqNWhPYKPCKc7O3tpUz5RmNVp4iwUgQIDsOBEUCs0GL9RDqYGM7x6XSq5XK5FkQBA/M8GNciozYZ931bRhDXPmrZm66PLWoB/ru/8zlqCfye83cxLjRJ7tlGS5CeEVOIElZEdCm/mVWLGH/jvsg43HwUCXyVhBo1hRwTyrWcyQP7sScKSUr17Pf393V/f/9EEnXzCASJaCWiOB4eHlKNJWrkzGYzlWW5dhIW82IfeHdCCcIhcVKVstvtJoJEYhGIzvpEp3KU2nzfNu1jnUbpDCF+jvf5GHwcvjc5lTtqCrEgoEdORdiINX8gaDhv2TOPzloul2v5H5GpcT0RTmTuXl5ephe2d7REghr8cJncmkSi4zkgZOiTYYxgQJJlv99PWcmYjKRVuKwnt/FsiDzjc81mOp1qOp2qLMvkW/A1ytW+yjH0bQljXXMhJZep7ddV0YNNdKuOWcTPOcYGDCKIbKslSM+IKdBygB85alyY2OqIdASSKp9CHfBEINt0bfzuEinEx52VHhUi6UnBNKRTj0jyMEzME51OJzmgKYY3nU51eXmp6+trXV1dJY2BZ8W1cqQty3KtDv35+blms5kODg50eHioL7/8Uu12O0mFkpKJJEpyTuRc0sak5o5ixuQA7kQLG73fgz27KFYHxsQzI7xf+oOouETmCOYF7yCKOEsbjUaq9c/eIM27FgFzoPAemoKfiQyzKIoimWFgRmiU0qOJhXDMxQ8TMk8AACAASURBVGKR9vTy8lLj8VhXV1eJkPo+AHcuDHj8fYQz1pRxE/2GI5k6Rd1uV5KSpuCl1dGACIAAxjA3koxJWClOZBiCZ/OzRm4u8sS5Kgk+SuibJPWccJrD5br2fZlC/D2aJ/13/z/XtmEMz4Yp5KQ5/51WtcCb7vN7c0zBfQp1zU0iPCeaQ7xvd6pGhuR2fVR3nI+ECXoNGZcovU8Q1gkqSWlIarPZTI1GI70jdZEEx3iw+0dpN+YIjEajdKAJTIJyBJivpJV07NFCEBwntl5DSdKaX4DxQLQhJDF7FmJcFMVaApfH9nvGNeuKBgccMEZ/rjOwxWKRomtgRGSB40SFKUS4dqLU6XTSPGC4HlLpvgLugWBjXsR3QITZxcWFlsvH2j/4g6RVZFEuEdGZAXP0RDNMgxx5yTwxF3l0Ee+sA/kJLlwsl0t1Op0UISQpwT0MA5MWe83aeRhsxL+4vj6/nHCWI7xV3/nNtQNPdNzU3OSTe84m2lWlKfhvLojlktfKMn/CZGzPhinQcpya73HxHemqJPacOShnE8wBTa7l/AJV9+Zshv4/SMpmoVJjb8XfQFy7V111xyOmHLQEALXX6+n+/vH0toeHBx0dHWk+n+vVq1eaTCb68OFDstdeXV2l2HSX6h3hHAkWi8f6Mt9++612d3f17t07XV5e6uDgQJ9//nkqW4CZITqEYSjOEDwskfBbj07BtwIDZe9dU4A5EvaIZMtzc81NP84gMOcw3+VyuWZDh/gRZuqEFcIeNQXmgk3fTYp+L6fnQRAdXlj75XKZErmwsbt50MNNaRB6NDPWB9hxGELr8bwCmAW+AxLNqPaLvwDHszvEiWoChvk+HA61WCw0HA7Xym4Ph8OUH0HBO+YGc/CQUw9RzuG9f4/Mo0p7iITX4SOnJURTY9X/Ofrm98XvVbTEGcI2BH+b9iyYQuR0Tmg3cfA6NbBOVfJNcQ5aRehj8wiAKsZTtZnxegiHtKpuiVrspSvQIEAMTBg4LNFK3DEIQYagYM/d2dnR9fV1KsPAMYsQJNbIpVVpVfWSPv2Ut0ajkSJEer1ecnSTABft0TBB+oyalEs+7liHMbspKMJClS+B/iOM+edNWqOPJVdfiT11ZuLE3RmBR0D5eQscawljgcCjLRJtM5/PUwQRNnl/LuN1J7fnEhRFkfwCTuAlqd1uJ7PQzs5OCkNutVrJRwDjQGNCS3VTG3Dj6x8T6jz72JPS+N0zkXP5LttI63XEdduWg7GqvnMMZ5ux5LTK+Nzc744v8X0TPfT2LJgCLXI7l5CcaOQWy6/n8yYp3t9zhCAHbA4IPMedODlJok6DicgrrUJXIeAvXrzQ7e2t2u22bm5ukvMZpPW4buzPqOKYc6SV03owGGg+n+vw8DBpCu/fv9d8Pk+HpQyHwycJTIwRqZa5Qowoyvfu3Tvt7e2lIn7UsuHErE6nkyRSwjRd+nYnOeYHmIcTPy+yxz5w4Ar9RhhhzDC8KCE6zLgTF/ML0ihjwgTivhJv7gdyM43PBfv/d999p/F4rK+//lrz+TyVoyZ/xZPNYDIeOurEBPMc2heEHa3GTTyu7XBto9FI64+fBo0LTUxamf5gPNznEVUIDzAxNASc32gEfiYDvoTlclXEDj+C509EZlOFZxHnc0SyTpDzFgMZWPs6puBtGwZRxRR4tv+e689hre7ZufasmIITff8eJchN98ff4mf/zSVhJwi5a3P9bGI8sZ/cM/jsPgaQH/8BRJkCZiCMmzQ8bNVtii5Vg7TL5TJVPpUecw5i7f2YR+E+B4iSM2x+R3qVHh2ht7e32tvbSwwNuzPPhxkgPbqPA9MQhNRLNMTaR6wTRNuLr0lPjwWNsAUM5EIk2Q9n+O7TyAkzrjFwD+3+/j7VFOJkvPfv32s8Huv8/Dxl7vp83dwY/ViuibGmRVGsJZHxH/4AnNeEibrpDbjCLATcuD8F4cDnDhFn39whjAACk4NBuLaD5ullNNyXxV7lNIQcjsXfI55+qtbga58TArx9ClOI33PMJWonzpxiH9G0ta02JT0jphC5nr/XxQLnJL2o0uXuyZkctmEKfHcbeUTQON4IoM7pnWDADFzqXC5XGaZEFXl0UavVSvb529tbtVqtdEYDTkAQG0kOaZ0w1el0qsPDw5TkdH19vRaphH0XxPUCez4/ABHknkwmajQaOj09TSUPiFmn6J6PBYkVKdalVogQxMHDFdG2MH/t7+8nR6UzRTelSVrL03DGALEnv8PDOH3OaGiMLUpmbkKSVgfCQBzPzs40nU71zTffJKaATR0GSB/RmermK0lrYaEeBeRJZAgOZBmTNU+1VDQJNDUYhIffosF51Bf+Ht8fzJ7MZTab6fr6OgkJ19fXa5rCw8NDOsWN5DovVcF+uNktWg5y+MaabUsQY4v9OxH2JL7YonZa9X8Vg6hiClXmo9iipuAC56b2bJhCFdePnFmqXtAcN8xF/3hfjmy5MdX9VgWQdVpGnFu8j3EgFcV6RY6wIKHbh9l4tAYkTRiD9P+1d3axliXXXV91+/bHjGe6e2YSWzaOMBGWkB+IQRY4Ig9OEMhYiLxEUSIkPmTJL0EKEhLEQkKCp/BCCBJCsQQCJCABgUVkIYJxwiP5dhIHY+IgI2yFWB6756PvTPd0n83DOb99f+d/q/Y5t6dn+s70WdLROWfvXbWrVq1a31VV87P8px0ES9lqA02e+AW7VRLDsOYOg3BbqZv7nOBll5iFBRqss1sIemIxIQAQlD5RDAbpU+gcsKcOaML+d18H9/ZtEyB133gO/KM5V22fcY314rMIEAonJyezcOAUMwuDqtMYBooC7iGni5Iay3GVZIBxWhkppF5oRlAY2nC8gRgRVgIMxoLAPn3SqH3QTlXNu5Wy8ypBZFYoY0EQJ8lN7Rxct8Wa3oNU9NLjsDSnR5AeAcD8aJSSuo9QyHqXfttdlbGCDDC7XbxjlFDTgwsjFKqWfWs96Elxl6vq7zXuwXZeuu8t/bbb5EG1kCRaDxoMwNqYXSYwOjRDArpsWHdycjL/J4BIcNBBaGf/cOrajRs36u7du/Xss8/WSy+9VM8///yc6uiVsWxZzI6a1mydsQNznaZpZhS3bt06k/IIQ4NppaWASwmw+waGwHMwNxgh39TB82Y61kAzqOlMM5iyM3aybvvBsWbwod+5c6du3bpVr7zyymx9sd+PXVHp8nPKLgsVEaSttfnoStYHPP300zVN0ywQnCJLfICYFRYBygTM3a5GyjqeZAFK6usrr7wyZ0NN0/rwm/v3788ntZFphNWAkMx4kYPrDiwz30aK1cg9u+/c7il6S3N3n8Vr+Y4l91GPb43cR6N3uo6l9o3gQgmFXa6eHvMflU9LYF8rZKm+UfzAzD1/LwkuILUKtwuGZOFFiiMTxfv8MIFhuN6EDYZgxgkzdQYNWiKZJWQmERs4OTmpy5cvz5q+99BxQJD225dvS4j+wAA40wGmhSvJQsFEb20aZuU9eWBwLLrinhmaXRHg2gug/A409Gma5vrBJQyTT27mhpsOrZnN3CxEwUe6J5zvz4IwrxM4Pj49whJLASGPReCgOxaGhQL36YuFoIOp/Ib2vJkewgFXEdYh8RNWJmMVsH+RF6DxSQvO83TEsNNtnJbCPgrcLtezn4G+R8/3LJVd9fXKpFvc47EExtt54EIJhTcTllw7S9rGEiTzz4HtaQsjQWZ3BgzHbhoWp5ECSP4+WwCwqIyc8mvXrs2xBsricqiq2X3w5JNP1jRNc9zixo0btVqt6rnnnpsthZOTk/rmN785Z4zgFmGNAxqgtzG2VgmhEptgoZ7xYjdJ1ekinEyvy2yMxC919XBu09/Mpqco5IRMUx6w6wlrxlsx9ASN96/Cgsp1Ad4+gl1HHTtAGDi7CNci1hZ4skWF5emUVbtmUEIYP/rgwPC9e/fqxRdfnBMgHFB2vADrAKsSa8ob8TmgbOGcSsV5GG1e7zHvfVw8uxS6XS6jfSDpeBd4LmS5npdkH7hQQmGE9PMgKevq+dt63+kKWhIKyfydgbP07HkBBtra6Qpq/ONOCfXeO2jmjh+g0VWdrsLEB54+UTRGNHS7m+7evTtvzY2FwDeCCKuCe95SobXTdQ9V/XiPrQA/n4FNwMyOconDHAMLph7OR1aeXYymSdpmZmqrYxQTYxxt0SCsL1++PGdp+cxup/USLK6q2QWX6wWwuqzhIxTspnTwkjbaouKbsScWYKEwTdNsEbDw7qWXXto6Oc3rbBCcPhUtV6knfRhez9zap+w+gidTUvP+vvXk/x6z38d9lMDzvZXsI7hQQmHkwskJnEgb1eNJ6v9+Zldm0+h6z43U+16qe6n93Lcf1W6gaTrdfweNkIAyp6RhKZClRKyB3U2JNbTW5uM3OSOafH/7zlerVT3zzDPzymc2WmMvGgKlbG2MxeCskp6bybGB0ThxzbEcIM3pnsY/qntpnHoCK2lqNP4GxwXArS2DdAHhGuIge04nw5Lz1hq4B33AEN95rCs4maZpFv70CzqCORO/Ojo62tp87uTkpFprs5XAmH7rW9+q1Wo1jz1CgW+nnfasDgSo6WCX62PX2O3LPFNh6CkRqSTwPQo0V+0vFHrlkr4RCMx7178Eb2n3UY/R25VQtb/EtYth1+TNFbuj53zdmjtaou+ndr8P+H0mJgsEt8U+bNxJVdsnoLXWZqaBcCGTCAvCaWr8tqvGaxtaW69+fe211+ajOa9cuTJnm5BRhDXhIDhWBgf/YLl4AZm1mZ7QHwmCkSvJCoXx27vWGwt+WwjsUiJ6Wp6tMxYV4tYhNffKlStbO4viMmKrD7R9r0nht9NHLXSgDeIgtM+BY39s5eDrPzo62soOOjk5ma8RUEYRcECZtFKC6D4r2fEIBAS47SkEvfHfB0ZK5uhejuMI9k1JfT2urn0shZFiTNs8lz3mu+DCCAVPPiOzN4l3+fGcFtmb8CaM0eI1l10irmTWqUXuq4n2+tMrb0HjIC6TnUAdLhwY9BNPPDG7dFjXgAuC7TN4hqwfslxWq9UZ7ZbrN2/enH3DMA+0RVsOrFD1nj5k5VDOgdfcrmHkV+4JhdE45bVeTKHH9Efv9Xg59uFgvjcrJLsKZo/WT7zg+vXrW2m4ueK76jT2g0XguAAuQwQ4bcNVCD6heZQCxwimaZo1fRZM+pSz27dvV1VtxQ58njML0oijYGU4iOx35/x2HK03jucRDD13cK/OXrneWANL/CXrGb1vxMx7bTB9w9z533MpMc5OGslY1hJcGKEwshR6TH8EmcY18huacduvyr0lYkomAzPOutO0PK8J2Wuzwe9kdbHXCXjrB+88SnDaqYWkr1adroNA0yQugOYBzjI1s6rmk+KuXbtWJycnszVx9erVeWGdUzBhPLggWKXtPfUJUsPMkjkbjIP0offGiHq4x7Mj67Bn0vNO3mcXjoUCQeHj4+O6cePGLHjJILp06dIspO1mok7qt7Ax88d6YAwZb9qaNGN3DXQKrlkv4P23ENoEg19++eV57JxUgGuwFy9wAkVmFOV4PoiVMFIWR2V3Mea8zge8ogAYLLxGvGtXX0Z80PTWs0r9fC9BY593V10goTByn4yeqzrbQUvw3vP877kS7KtfMmGtldOGkVB42OA6exlK0zRtuQ3INSeW8PLLL9fly5fr9u3bc1ojWin+7JdffrmuXr1at2/fnrVZPqySRriQyohGyyZpN2/enBmFt3MgJdNMJlM0CTbCXBx/8NYH+Z1ppMZT77fxmZaG/zOZWBnNN8y5Z0HhGsJiIHCMwPCCPMri+/deQt4G3AF/2mVhbzcRNECfYc5eTNdam6003DisLbBraJpOt/TuHXTjsUSI4yaapumMULCyMhIGpufkBUtMzc+YaeZ1w5L113sfc44+uEz2oycUltqQkMqplR7X27MUUrntZdSN4MIIhSXIDp7n2ZGmb+adlkLvu1c+r71RsERQVf0zHszMmJisQiaegKXgHS29eynMijqxIDJIyX2YEwwPq4OgJxkxLHZjC4knnnhidj/BuHAleedMMxuvcsX9UXXqlmDSZrA5J5TNbzNea4P0zambuU6BVeJYTrYUEJyOy/A+49OLCW0peA0KOE6N0bQA87WLBhcfQqGq5g0F7TZarVbzOgO253aqsTfoo6zTbX3YjS2CdF/ssuAvOvSUv1HbH4aXYMk6Xnpn0sc+cKGEwhKhnAexPcY/qs/pb/u0J68/6ID3tKER9IRBWg1ZRwo5nrEWOk3TrL2uVqutE8pwOzlLBMbHoifWOFDGmra1Z+4jJAg2clSoM6JgLE888cTsSkJQuC0wPBiQc+mtJafl0BsvCzQz68SX9xrythCp1fs6GjwBYwSH34vgwfpyOXDH82YOFnQIQfuSsa6IGXGNfYm8AR3CwEKB/1gKxAsIHHv3WAsHZ5N5bYrjQvvOoQdharsUu13vSiY8mqfTNO21n9A+jHzkLupds8sqLYT8/5bOPurBLhMyJ8lSPb3yvcF6s7T+bNsu6A2+zcSqbS3RaxZgDHyTCYRb6fj4uE5OTuYT2hwMJZ2VNEnKsHkdW2d462WYnzVeM25rr6Q5EqSEsfgweZgMv81kYDQOnhJjWbIajFdnk1Rtnz/gvuDumaZpZt4WJlhavbUUCEX7e6tOrZJpmraEKM9RZwY3HStxFg8nmBHQdwaRz2tYrVazto8bL2M9/MdF5BPRcvfWtODAtZWudHUmPb9Z8KDvG5VLevLvJS0/y/T4Wta51JaHhcMLJRR2SdB9yprxjzRsayp89xa59QjXsYcHhYcxeCOXUjK+TPOjn2a0uCFwwaCZYhGgncNgcGtkgNvMC62ZNmaaMMwORohbizgBLg6vZcBSMINJt5CZf/qwjR9wZLdRBo/BgQWcc8VtUdAvnvHERsjwrPdJcp0Ijd5YJ9323ERo8JcuXdpyDbXWtoQCwvfk5GRrARqrjXET2QogLgHzt+Vm2sm1Bj1t/UEVoyXLvceMH7S+fcp5bHmnIZW4EaRA4LdpKoVFr8yozrfF4rVeh0dE5O8ek0yGuGS6mpmacWX7eu3pgQd0H1fRw7BSsi+ONTg9jf9or1gRXq3sLRNYUcuZCA5Ek07p83q9sR0att0yZo6r1WpeXOW1CxBx+qotFGwpWCPNBX8eT1tS4CnXPNBWLIKq02AuYOZv/OfE5Zr7jbsu6cF7KFGW/uQmg2bS3s4cIUBMgAAwwXzvxYQ7yCmnWAZkH6EUWDDz/rT+aHMvdtCbT4bR/Ogxy32FSs69fL43Tr068lk/54STUdmRVTTid733pbLSe6737re0+6jXuURMj5kvmVwjM9XXIPL0wY9+J+O19cD9kZm8j0a0y9QcwchMTS2TNuGyMIPEXQHT8qZ7VadbbMCAHAhlsZytDeryc1Xb6wmcRcP9ZH4IBTOojCFk9pGFggWA71sopNVA+xxoTovAwsNj0BsLu5QQMEk3fvfIAvLeSq212R2EsGTbc1aUZwYRWWAZLPYeRKSk5m6l3oICnGc7U/HaRccjhc5jsFRmqV4/2+Mto3ftmqfQQS8lNZ+pWhaII0thxPx7wqLqrKfD9EsberHHHlwYoWDwgKXJzP2EJMKett/7vbSieYnwksmep+w+sI9Acz/yt//3tGa0PpgdVgRxBywG1hsQQyBlFauA3Hv25SEO4QVw5Nl7da4DrCNCZ+JVrXP1ewzHAeeq7eyjnqUAY7NQQED2tEEm/Ugo0I4MpNKWqu31D621WdB5HYsnrHdvpY0+wQxXXlWdyQLC7ebD7rEKCDx7TYEtgjwH2tteuI/uc29MzkP7S/T7emDJ6ui9Z2QpJLgOu8lcR9LSyFLIOnuWQe869JrWqgWDeaZpbh+4MEJhxBzy/4g5pnnV0/wBX1ta1NEbzPRN+xrPMVlGFoPbvESM+2hE+4AFmAnIVgNCoWp7dS4Co6pm7RS/srOU2CuJoDK7tnohF9k1vMub7jF2fOfH+724HzCq3D/HY2EBAbM7r1BwO2HybkNv5XXV6apzj0W6vlLTznMEpmk64993Wi8uJGv7PjEOoeCU1FwD4tiRM7zczrQGRr+X6J3nRhbCiHGPGOnomn8nLxhp5yPw844jOUlgxJN6fRn1eV+hkKnI6cb0fPFc3lfwXRihUNWPEQAj4us9w8T1xO9p3lWncYc0v7K+nuSl3gw+9+ITIwGwizD3mQzuzxK4ffatYx04m8ZZK8fHx/PCNx/6TkwBoeDjNTO2QJomu4ASh/AOryZkr3dwLn+miqbQsD+7x6BxP3mBV8YKLORTYIFHCwQ0e+pxmiKxHK7bYvGW2hkr8I6h0zRtnT2Als91NP68TrAZYUKdvHdkEVgY0N+0CHw96W8050b0uo+1kAzU15P59p45L4zm2UjbPo9QsOU6Eg52S1pAUF+vr8mDoGXT91tKKKQ0HN1PRC2ZaA9CDEvCxv975dzWJU1pXzhPH/atO7WzJeFpzbjq1B0Ck0P7YOuMqpo1WTKXvAEci7pWq9XW7q4wfrQayjnWQXs8Pk4H7eEh/f1Vp5PavmBiJ7ZSXJ8/SVvW9G0FmLma6dI/NPXcCoL/LNbD8rHLJ/cpgtGb4adriOv8nqbtk+dob/bBfdxHILxR8LCs5n3es8R/elZG1ZuDgyXoWRNVD3amwoURCtb6Uqv2hExCHJlZIKOnDVraU69NTGuBwIi59CyQZAqvR0AsWU89WNJWeu80k0PjxRIiU6m1trXG4ejoqG7fvl2XLl3aOgjmqaeeqqtXr9aLL764ZU1gXXBeABaEj7K0NeCT5Ox6wkKoqi1h0lMYPKa9iWyhYGGDS6wHPe2ZVdakgsLMYbattXm19t27d6uqtlZnswjs6Oho1vZ9LjSCwmsFYPrTNM3lc70Aa0Bwq3mDwVwvki7Rnta/S7N1udRykx4fRGlbcsX4vfwfvXd0bdc8of6etTrqF3jIOndZ/+Zf/LflmRZAplJ75b13SZ2maYvuR3AhhEIirGcqpcmUEtH3PXl7E9zPepO1kYuJ3yNCzmtu70jzcH27BMRogp3nmSWzG0GQ5ieAcKiqOR7g1FYHd2Fs3krj3r178xYXxB7YTsPuJZu8tI+JZYuA63bhJc24DznBHJ9wfZTJ8bQbyowUoUC6LNo6loA3hbPPnv+4hBxDwMdvAYBQcUzBAsRWRX6PtpzIOdWzAnr3HBAfMfUl9xHjmvXssq73cUkttc303muDf+d7cu7wLNl4PUhFs9en/J9Wbk+5wVWagtAKk9vuZId9hfCFEApVpzsOWvOjc5lXbmCCJwNOSyEBBJFCOUpJ9X8TUi+mwPt6gWa3Md/jvvbauY9VsSQUehpe73fWlT55x19w/TiDia25WRWNFUGmErEGr2dgXyCEg/cSwiXlRXHWghAqVhAYG9qUFmeuScjrjB/jynsQeunrt0CAwWdcAK3eq4Bh9P6PpYZw4bpjAl47sBQX8PYf9IGx7MUKRrTYo6ceE+vR9hKjz2f47r3X92yF9N47shBc1gpQr6xpw8/zsaXg1elL/ezhL9/p+9Ckkxp4JhMjUNJsHTB3UiFaai9wYYRCdhBIjZVn+e5JalsJvYngOnumcxKo25jak7+ToE2EI8ab9Se4/iXiXxIe+wiFJM7eBMl+2iLDIqg6XXAGUcPQrF35/2q1momYeIMn4DRNW8y/Z0GkMpBM39eWLIHsn/uJoLDQd0psWgcIDG9A5z2JcAn1hIIFi6/ZEoD5e7HfeTTDJWWjhz/GvwcPQyiM6l8SCtmGUb9MO70+7mLQVdtuGtrklPaRRbDrek+Qjd5rayBX1Vso9OJpI36ZcCGEAjnsaIsjhgdhjDS8Xr15PYUEgzqqJ5my0x1pQ8+6sKXQExiZseR3LL3/PAQ2KpsTYSQUelqSy6Y7wu9Au/dOqd78jlPYHHNgi2mevXbtWt27d29eCGd/qd/H5EgB7cwhAJrwxPZYuS8pFChrYQCDZ18gH0aPW8c7vloosLIYhu9AM4wfoWDLYMkiyDhYjmFPIPboZckt0mN2vt5zR/r5TBhYEiiu02WX2jOaQ73rvThET1hARzDjqtN9q0a4og/2//eeyXalYsy1VJQ8H7zux0LB9M7ZJrvgQgiFqu3AIQih856cicSemyCFSG+ipFDIiWMfpr/trgLMMEZt8DW/bzTJfK1nZYwEZ0IK0h6Y8P3+nlBI/2bV2TzpaZq20j7tL2+tzQFXmJ/dQ3YJgW8zfoBnjHOP3S4teR/IMTKO6JcZOesFnCWEUJim6YxQIGaQloKFgjOYLIT3sQhy3MyUe+OcQtX3PbZLzNz1LzHnJXrtlTWT83PnEQopAHp9GQlQCwULh6XAbdKMr2ffenyG371AMte9jUxuyWK+5P3MdsGFEApHR+sDWkhfzHSqzPvuSXRDmvp2cwAQfs/3xn1/u25fT8ZkptTz47r+njaUfXL5FJJutzWp0btGv3cJjSRK+m2tCQ3FGouDZbTbKZguTwqrt9hGOyZlFLcTmUjOxGASuf8jZpbfVaeWDbhMPNJ+2uV1AVgGeegMz6VQQFg4gwhtH6vAcQPalOOeAirHHPpLBcP9G9HDeTXzVJJ6jNUWXNLckkXAHOsJhSzbU7ZcZ/bT8yeFgp+FVvM7kxYeBHpCIq1bzy8zeAsF8zJbtbbY99kY78IIBeeygwA619O6q7bjEIaU9kmYZhrsLc97ezEGf6e2C7IBZ6ew+yflTagOnvcYu2GJyfsafc92p/naYwLG26jOnv/eAhz/pvcLss8z62Yigj8vQKOcd+G0pmY8pyY8gh7eduGR9jjTyn58mLy/HYzm+arachHZXWV8GJa0e49HurcABB2ZXtlH2mT66wmLEQ5Hv9PK9rto18hqyGd6190H+ue+LNXptmKlZtlev03raOrXrl2ra9euzfdzDEYu6aW4l2k8rfJc5JkLTi2gjGN4ZDQMvAAAHRtJREFUkQ9YWoILIRRaa7NQYOuDniYKeACYOKnd9DQVwM9Sr08T45neNymZCAUYl60amECa/D0CdpvTIqrqnx/siZyE3yNEC4XeRE4LpcdceFfPUkDj8kpkytkl2BMYOS6MjV1O4BImZ60aXFC2Z1n1IJUFX8+20A4sFaehjgSBPz0Fo/fuVBIAcG2LADxO0zQrKlmP42Vug+nHNGewoE4rYMTs/AzvzX7Q9pFWb4bYs+6cd5/a/nnKWvvmGVubqbxB36bhq1evzkJhyVLoWTX52+/kfSNBkVuv5AFQ9CNd5Cjfu+BCCIXj4+N69tln5xWvDJBTvlJTsvTnnpHVI7iqsxo0u0pyaMpoAhvBx8fHs4XhHUK5j3sEF4K12pFQ8Dt72quFQo/IelrYPrBEzD0CTqFAmxiH1Fi8wAyhgdmLuetjKHub5MHgYAAwZ1sZtI0sKBahWcjwTGrptgIYL94xTdPW4jTcRE4rxY1EsDlTUnmff4Of3ni5fWizdkVCE1YSqM/XvQaHMj2L1XgBRq6h1wMj6+A8Zd8MMO3xXtw2bPRYVfXUU0/Vk08+uVjP6Dr9N6/ynPJ1fnuOVZ2N5dHe5GX375/uffWWEQq2FFjlasltxPQQVlVnNCEmBdDzbeK/5RqD1dPkbCn4fi8bCaZ47dq12VfOBMcfyAphm60wOgtAMwgHblML6gkFM8Q0nSmD+yu1E+PUQa9cCWwXhS0C3uNjOnkGN6GzJfg4WJZ1mgZyXGyNmaFCD7a4TCN8nE1kt9ZqtdoSCqwg7h0P6vcnrZkucrUpuGQ8TVMpFDw24BmlBGHAN663jJdY2zfNma6YFy5Lec85WzFc9/bprpP56PUt9NPt4Rm7BukL9OH+gEfwkK4n11lVWzjlGu1hHmQfnQhjTRwa6Vl5PYGaipYZPOB2mPdRP14NWy+2kGxRg1s8MG8ZoXD58uV65zvfOVsKNteMAAuDqrN5tz0hsstSePnll2dTMDWqfB6tkQVaVWst986dO3NZMlCqapbOdiOZgFMosN2BGa81TCZKz33EhCBdk7IwuzSdueeYiLN+eNYT0YwNfDMZ0k3Ee7wVgONEPnrSk83X2BaDBASu2/pIAWG3jRmyhWm69KxREUC2UCBgfHR0tJV26mCwjwq1Fgg+wI0Xk6ULiOfNhLFM3U76Cp6TGYIT6DCtJvvSU6DQHtyjue0H6cS0rScUwJUZO2VXq/XZ3O6v28NGjBYoR0dHW+d628pbrU4zayjrxATaU1Vn1sJgUdK2pGHGifagyLzjHe+o1lpdv369rl+/XiPoWQo9l1FaDCmYUjgkWOmArmwROxtuybIBLoRQaK3NTAJLwdKPSUpnnd0Cc0jmnRqg/dT2R6alAHiCGJIpMwl5lj7Qr/QtWzMxA8BdwW/f80ROn3BqduT025IZxRS4Dn5NiNzfVyh4MllTs1DgGVsGVbU1GX04D5aWNZxLl9a7qzLB8afaVUW/ksEaetag6TG1OPpG8gD303KEIdEOn26X1gRZVL0xAjzuqbGnpWCmwLiBS1vHCBroxmWp04kUbg/M05bteSwF2gX903/ag1JoGkIogDO7zNxGtGHGKNtDWdN9Wu49oYDFi4LCuE3TNAzcLrnG0spPRdc0Z2t7ad5QB/wIngFPyXm0BBdCKFy6dGkrppCDkwzLARUzZMCBpB5YYLz00kuzpZCTJ5nKNK3TB69cuVK3b9+eJ5MDfU77Il3RWScQ1J07d7bM6Nbalraf7WTi9CwF6jNT5ZNWRtW2X92BcruJqk5dUnnWMnVQxtoJY2ezO4UC/lkmvssyBhAwliIaIpPSp7n16MH4sxvNTNixHujG7hXTVAoGu1yS9uy6ee2112ZmYm3fGr4Ffc9SgLkmLYKrZODgdclS4FnG3u4P6NxzjT6OLAVr+3fv3p2ZWVoKMG+YcAoFytI+8MzOrtCBXWzQfM9SQAhSFjzwXgSFhYLjlIwLNIfV2tra5f3MM89sjUm6h4w7X+O3+VtaCktCA2Du2NozXSKw4UX7wIUQCiDdzCL9ZGYsRmRaClXb8QX/5tsaExPTbgWeHQkVtIf80JeU9kxU37fWzDUzbcD9Sn++idBZFOCj915bNmZEI/PUuE9LweUYC19LfGTdPUss++xro48ZLd8WALbYdgkFhCjCkvG228caP/SSbXE/sj89ujH+PbZpveW4eDx7c4VvcG3apM/JlFynY1SpbPXKuC9ut/vbozfTC9+JA/fZjL2nqLh9jJHp3q42vv3JGFy2nQ8C2eOc9D4SClaeXHcqN/lOhGDywt785l6uZViCCyEUkLrHx6c7ZhopDKKRVnXWUshBsabt//YhJ0JHUtl1ejDMjAHq94Ti20SXxJvfyWySOfhZ98XaWY9As19J7NlnXxtNVvfNbRgxuST07JfHK8fODD0DsEdHR1spwn4+A7jWnqEHB46dsICwyBiRBUwKi/y4P2lhmNH1hGLiZyRoenX43qi+FBo9ukmB76ynHu30hJ4VnxSOpqPRfOwJkV6be/Vn+byegoG6Mtmh571YGqcRfVf1F9xZSPkZ84xev2ztAdSJq+ktJRSwFDLyjrlOR3PyJOOoqq1Bo/4EGMMLL7xQR0dH846ertOEyverr746B8paa7NJmhOF9yZBZ5t6THEJ3La8VnV2//tkqqPfPaHj53xtdK8HPcHSu780uXqWwS6LwYye713uI1x8ybjtsutZBqM29NpHG9JNlR/6nYIFmnT9vDPnhPvRE0y99/baYJr2+0bzMOsGMiaSc9r170O3Flg9etlnXo0EWQqPFD4osnYfjepOAQ2Y8ZsvmE/02ug+ppvbfYd3OobijLcRXAihUHWWyXgCp0bvlLCepWDix5/fI3qyTY6O1ofG9AYiCYtIPr5P6mcwMy89FzT5OQf36E++0y4Na6LWIow/rJPRx4zFE7CnSZop0S5PbPpiovMYgJ+ehWPmmJPN4+PJSTtzsnGPughK0g7alq6kFAq2FNwfxpE1KTyzWp1uUOeDbmg7H8babWRc6YvpIOkNpmxcefyoJwWR9/XyvVyBj7usF9S2dUUbkoH3hFEKINOUy/uaGdqS8Mr+p6BYEnBJVymoct73XJJ8v/rqq/XNb37zTB9N5+6nry8JLSvFPN/a6eFTdh85Bmcc0GYn0ozamXAhhILNGzMQTDV3Gkhmhd9sZAL2BmC1Ws2B5rQUKJeIJND8wgsvzNrCK6+8Mr+Lw9Kr6owrwhPfDMrMlXYBPQ3KHxMD3yMhYAHiCZB1GOweyrZZc7YZ3NNqwadda6P7qaGDJwjeWjsBQo9ZrjC3UOBaCgWYRQoFxtEpqPsKhRToOR7ZTlsO9MUMf+RqcCYP76ZOcL1kXfmdHo/RmFsY967jokjG583Y/NsuEcqaIU7TtPW86b73XrfNdfLf2TuUzYB64gP8HR+vzwe5dOlS3bx5s5577rkHFgo91xe/c94lWBimKxJeWHXqwmZR5ltmQzwmFRMxEWXiQkJyPzVm/97luiD7CPdRxgB6QuHu3bvzts9YLZmFgXRmwrm9/EYIVp01UR3M9WR2BlEydPAGA6APVacLc3rpmr6W6xRgZG5n9gWGRRZQxhnIHqo6FQRoOBb49INneqa86SWtQeMAJkzfSVE0Q04A/+k3Ny24bbawjBtr2AiF1MApb9w4bmah4EyhtBS82p/x9XgBzkiz8DHtmQ6Mn6V1Chm74bfXKRhHzj4arVPwWh3TKtlHXmsAHrPs0nvdVjPJzD6y2+XoaJ0IQ1onWU63bt3aog/jrUezvm7BlgKBcXHdeZ855xiHvQQoKE6Bv3///pxVtgQXQijk5IcI0+dmyQhRWNqCHO+i6fr5DbgOhELV2QH0Nc4EePHFF6u1dUyBxWuttfmAdLdzyZTtaSYjDWGkxRkHed84yn6N8OKywK6A2lL5ESOmT6P/Pa22alvzNaOknbYi0aR7VtO+JnVPSGVQD/cL9ZtRwKjN/GBojimkQOW5FBT0i+sWVn7G9G/tPhnSLuWpx5TyPam9G0eJx6X3jrTnfAf49Ty3hyCtG3/zO63ldNv0XJZVNe/kfPPmzXPHFAD3Zd+ySVPmM+aNVtCgt1Qml+BCCAUkG1o3Gk2m0hkZKUGBnrY3IvrVar2i+ejoaF40R3tG9eM+wu3EimbeeefOnTk/nL31HcDMZfXuZ65ToC3UceXKlVn7tPZetbx4zczI/YIpWWszoYLn1PYBCA9ttmcpOEnA7yD12NaUNVYELu+jX621eVU5DBENybnuHCZiVxP9dGwmJxcphnYfgX/WlaB54r7CPEc7Y3wRSL2YAnWCK1sKnsC7LIVpmuYtONJSgA6hm56lgJWblgIaJXjnnb11CklXWBBs8XJeS6G10zUOS5YC3x53LIW0XMCD6b5nKXiBLH3EUmCBLc8yr0ewSygsKVNLZbnucUkF2tvF0OfVajW7tpdgL6HQWvtKVb1UVfer6t40TR9qrT1bVT9TVe+rqq9U1Q9O0/Sttu7NT1bVx6rqpKr+yjRNv7ZUvxn95n1b2p5NRU+MRJ4RxT3/T6lr9xFCwfX0NFxOCzs5Oamq9aRJ3zCEwpYJ9idDZBCWidcuD4N90rTb6YCUAUf0jzqNS09AGM6ubS4AmJR/0wfaZKFgbbhq231E/XZhgW/qzQ3dAARwMknG3O6jZNKZNtrTuKx1GYcZi6A+12tBkmOVGp1XtdMOFIUcg1SE3O58N8+ajtw3r2jmGcozB5LhA2byoxXNo+B4Bu4Zd+MlY2wod8ZnjpnrN/0bP9lXlKEUWKZbykDPHh+Uk5wjhp6nIRUyIH8nzSfPoz5na3qeoWD6SABobhecx1L43mmavqH/P1ZVn5um6cdbaz+2+f+3qurPVdX7N58/WVX/ZPO9CEYsBJrEkdpObuTW+64am79+jw/3yQH0NfZAqTpddPfqq69uaTpoNfjwHKj0iua0FBgwa+Mm7jcSjo6OthbimAjR3nw9TXWyIrylQ1XNqz/RYLEKrKnaL0x/e5PGWrbdRKYNl68aB+2zj8l0e/X1rFV/m8ED6ZKsOmWO+XwyPK6lkkR9tMfaNTRWVXMQPJkp/90uLE2+wUFPE/bhP4Z81nUBpnM/799YJL2yvetcs7DKcnmd9pvmvRtBunYQIMfHx7Or+fr16/X000+faU9CCo30RKTyaca/y1IAV1aKiH/04I12H31/VX1k8/tfVNV/q7VQ+P6q+pfTujf/vbV2s7X27mmafm9UkYnA2gZaRWodPcbuCW+GkPf4pm67bJbcTSnhvYsk7UOjcdYKg5VrJ3JTNxNGZkJQJ+4CM0WYjrV9a6PWcKgztWueS980Ze0+wpqg3XZZ5CfxihDxe3L/Fr7927hwu9LCtLWUloIDzbYU/Ixpwz5sj0sKBsrg4nDwF8UFHPJO3Dm5zUWmJtPu3oZ4COJpmra2m+dTdeoucVAf3FA2d0nlOzdYtPDA9eeDj3rBYgL84KPnPgJ/6T6yYnTp0qWtvY/AC7jCxZXuI+PQZe0+SneuFReu444BN2y3f+/evXljzKSjhB4PMiSv8X/zJVxc4MWWApaXN2fMxA0LwRHsKxSmqvovrbWpqn5qmqZPVdW7xOj/X1W9a/P7D1TV/1XZr26ubQmF1tonquoTVVU3btw4o6Vbc8vgnInUkzSve4LovVvvODk5qaOjo9l/nRI7gewjiNL7AlFnBrYgIDNE7ifzq9q2FGxC281ipuX2ZgYVTMCxBsqkOZxtg8gRCjCJxC8MysEtxs4aC0zVvlvaYKHjPvYENH2zhm5NyQzKjL9nVSRd5GQ0XtxO45I2mLbSVWLGbmYG5C6prscuHfffWTa0z/RnYeY+Gz+2tG19WHlJy6e311SvztyYzhv1ZX/Txei4gOnam9oZD25P4sHxNmjBMQVw6/KmR/qCNYy1/+STT9YzzzzTZfQ9JdXX7fbqQSpDSZ8jC8LzBU8GZXe9E9hXKHzPNE1fa629s6o+21r7n745TdO0ERh7w0awfKqq6j3vec9kX7U1QEu9HkCQmzrPWAq2FswIrEFaozVSU2LzDvbT590erNRS0fI90c1wU/tLTdH9GkHPovFvMw5PeAsXax0eh6rTHRaZnNZMmIB5PoKFggWYGYYZggUpeICgq2pL+0PzRaAkY3Z91Jk4SeZp/GQ7KGfmSjkgd0t1XbQ5aTOfo93p/rDg9fuy39Rhocw7RrTQo5deOYPHylZdXs/5ZIuU/ligGS8pFJhT4MCWgq8htDx2Vm5sOVvJAc/QZs9SYNcFkhhswYDb/D36WKj5d46FcZ6WoJVlg/udlle6xXqwl1CYpulrm++vt9Y+XVV/oqp+v23cQq21d1fV1zePf62qvkPF37u5NgQ3OicWA1F1NniXkzOZQo+gfW21Ws3rDZzp4mdzomA+Y2EQaOb9ZKFU1XwKlwUTkzF9vBB+byLa3dHzLfeI0fd3aQcWBGkpGJ9MGO7bTWSh4knJNbsITNx+B/fon4WUtbd8rxlTPmuayPEHVz3GaEGW45LPLwnsJVjSMHvP5PNmMLYUALtu7G7LQLaVg2Skdp9lGQtWtytjYoDnuJ8xPs2kjW9b5FZsPNZe+ObxygVxPYFgus6x9v/j4/V5CkdHR3X9+vW6efPmUBCAK+a7nwGH+TzPmK787TJ+3v+tdI2OGV6CnUKhtfaOqjqapumlze8/W1V/r6p+tqr+clX9+Ob7P26K/GxV/bXW2k/XOsD8wrQQT6ChMNmq7VhAL3tjhHi+08zuvY9yJycnZ4SChZLwMJdBm/NEhHDwI1ed3VGTNlLeE9FunHy3LR7+e6A9QfdhNK7bfckJkJofZa0FpkDpCRi3w0Rtd0qOiy0L7mVg0pML7a/qNJbj8fK7TCvZrt47/HxvQo7wmtZL0pUZGmX4pJWBcOKdPW3XjBLGa8ug187R+Pia//fwmHjAt8/zic9MGbWQ6KWVHh2dnqcw2jq7qn9AT9UpPbgsWXeZkppj7Qwl4761VicnJ3X79u1FoTCiHdxqPSXAllyCxzJjCn6ntwt3mYeVffSuqvr0ptLjqvrX0zT959baL1fVv22tfbyq/k9V/eDm+f9U63TUL9c6JfWv7nqBGYQn4dKz6baBiaQGsOu9TCwO6DCktdFam/3DBJvYG56J7/OaydIYCTFrqj3LB+i5LPaR+PtCj0nYxeVndlkdPYa5JMTNtI0LPwf4v105FjSMkekiBZD/Z3/TCkuaTCa5BGmtcC2FKu1OIUjZZLApVHweBmU8N8wwbAEtzbGcW6NnaI/nbArenkDyO1zWfU0+gPCnfM+q4b+vWWEDXE8ycGiI5xDIjAUu0aeffrpu3rx5pq4Rrftez0Xs3z3cL123MoqSaSWDcr1ssoSd3HOapv9dVd/Vuf58Vf3pzvWpqn5k55sF9+/fr+eff35rcve0/RGTGQmRZPI9zRUm7rUGPDvS2o+Pj+vVV1+dtWy7F+7fv781OFkX7bJ1kcIn/5tYsy9ZR7bZ2ir49eShLb0MoHxXz1VgBuu4kBmE35u4SKbhbC7KILyZWGh51pZdP+tD6CNlexqu+4gWaQsQhuBJnhvZcb0npEbv6lllPavCrjKDD2fykbW21rzAL3Fttx5tWhr/njKSv60Fux++bsvOtML7WMTKdejTabzgO8s6G4rr9+/f30pZNYM2j7FghWb8TI4l7xitjUgBkQqHvQI9nI4shbzn+e9EDrtq/Z6HvU7hDYP799eLyKq2s0Wqtt0GqamZASZzAUZaDt/EFHqWQo8xYnJSzgFQa5tmJv4wGW0+WjvsTUqIyumB6aaByDzoEK4ZQ9W2bxcXl91IvN+MkPdk9hF9zs0IwYnTOO2OyufcH/rrVFgzGDM0t5U6vDjLWnEy7B64PVkWRuEJbdr0YjtriGZMvp++/cQJ9adbwzSxWq22LFUzNC/Iomy6M3MBmoWj6c/04r67bAqFZP6ZZu42Zzv5zfj2GDtt4r0w9rRAMz25NwbMAdrE+HMfmjo6OtrasSADzX4H7+wpCCN+1YOc6+Z3I+WVvmDVmJ52wYUQCq+99lp99atfrara8sfnwJuwq7bNREMy9xFYe3TAsleXpS0MtKq6/lETUk6w1IIYXDRkuwvScvF3r22p0S9ZKqP7o2/K9d4FTuibJ3quueBdPJtEisDkmbwODvnvrBUnJKSgtRDYdzImUM7aaQqXkbB5kOu020KBdoBbmH/VWcuAhAdbX/u8e3TPzHf0nP87tgOsVqthrnzPGhldH/3u8YPes/vUZcZ+6dLpqZDEIa5evVq3bt3aqjPrTyGx6/38X7IUloB5451gU8HcWceDvPhhQ2vtpar60qNuxwWCb6uqb+x86vGBAz624YCPbTjgYxt24eMPTtP07aObF8JSqKovTdP0oUfdiIsCrbVfOeDjFA742IYDPrbhgI9teL342M/PcoADHOAAB3gs4CAUDnCAAxzgADNcFKHwqUfdgAsGB3xswwEf23DAxzYc8LENrwsfFyLQfIADHOAAB7gYcFEshQMc4AAHOMAFgINQOMABDnCAA8zwyIVCa+2jrbUvtda+3NYnuL3tobX2z1prX2+tfUHXnm2tfba19jub72c211tr7R9t8PObrbU//uha/sZAa+07Wmu/0Fr7H621326t/ejm+mOJk9batdbaL7XWfmODj7+7uf6HWmu/uOn3z7TWrmyuX938//Lm/vseZfvfCGitXWqt/Xpr7TOb/48tLqqqWmtfaa39Vmvt8621X9lceyjz5ZEKhdbapar6x7U+wvMDVfXDrbUPPMo2vUnwz6vqo3GN403fX1Wf2/yv2j7e9BO1Pt707Qb3qupvTNP0gar6cFX9yIYOHlec3Kmq75um6buq6oNV9dHW2oer6u9X1U9M0/SHq+pbVfXxzfMfr6pvba7/xOa5txv8aFV9Uf8fZ1wA3ztN0we1JuHhzBfvy/Fmf6rqu6vq5/T/k1X1yUfZpjex7++rqi/o/5eq6t2b3++u9YK+qqqfqqof7j33dv3Uehv2P3PAyVRV9WRV/Vqtt6H/RlUdb67Pc6eqfq6qvnvz+3jzXHvUbX+IOHjvhsl9X1V9pqra44oL4eQrVfVtce2hzJdH7T4aHd35OMJ5jzd9W8LG3P9jVfWL9RjjZOMu+XytD6/6bFX9blXdmqaJHQ/d5xkfm/svVNVzb26L31D4h1X1N6uKjY2eq8cXF8BU6yOSf7Wtjzauekjz5aJsc3EAwTSd/3jTtwO01p6qqn9fVX99mqYXYyOvxwon0zTdr6oPttZuVtWnq+qPPOImPRJorf35qvr6NE2/2lr7yKNuzwWCh35EMvCoLYVzH935Nobfb+tjTau9zuNN34rQWrtca4Hwr6Zp+g+by481Tqqqpmm6VVW/UGsXyc3WGoqc+zzjY3P/RlU9/yY39Y2CP1VVf6G19pWq+ulau5B+sh5PXMww6YjkWisN8xHJVa9vvjxqofDLVfX+TSbBlar6oVof5/k4AsebVp093vQvbTIIPlx7HG/6VoO2Ngn+aVV9cZqmf6BbjyVOWmvfvrEQqrX2RK3jK1+stXD4gc1jiQ/w9ANV9fPTxnn8Vodpmj45TdN7p2l6X635w89P0/QX6zHEBdBae0dr7Wl+1/qI5C/Uw5ovFyBg8rGq+l+19pn+7Ufdnjepz/+mqn6vql6rtX/v47X2e36uqn6nqv5rVT27ebbVOkPrd6vqt6rqQ4+6/W8APr6n1j7S36yqz28+H3tccVJVf7Sqfn2Djy9U1d/ZXP/OqvqlWh91+++q6urm+rXN/y9v7n/no+7DG4SXj1TVZx53XGz6/hubz2/DNx/WfDlsc3GAAxzgAAeY4VG7jw5wgAMc4AAXCA5C4QAHOMABDjDDQSgc4AAHOMABZjgIhQMc4AAHOMAMB6FwgAMc4AAHmOEgFA5wgAMc4AAzHITCAQ5wgAMcYIb/D2rMEud7+zLLAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 460.8x460.8 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 177.3x209.7 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 460.8x460.8 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gSYKEM4FPMQN",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 374
        },
        "outputId": "4aa43d01-3099-4784-a116-f8b3a8b6c7a7"
      },
      "source": [
        "# what happens if we convert nd  to 1d, interpolate, then convert back\n",
        "\n",
        "# 2d linear interpolation\n",
        "# apply on an image \n",
        "# we apply 1d for each row then for each column (or colmns then rows)\n",
        "# an example is to scale an image \n",
        "# the code is slow because it is not optimised \n",
        "\n",
        "def phi(x):\n",
        "    return  1.0- abs(x)  if abs(x) < 1 else 0.0 \n",
        "\n",
        "\n",
        "#interpolation using the above phi function\n",
        "def doInterpolation(x, c , k):\n",
        "    # x is a data point we need to predict its value f(x),\n",
        "    # c is interpolation coefficient computed from the available data points\n",
        "    # k is the integer points contains f(x)  \n",
        "    fx = sum([c[i]*phi(x-k[i])  for i in range(len(k))])\n",
        "    return fx\n",
        "\n",
        "\n",
        "dims =2 \n",
        "sz=img1.shape\n",
        "img1d = img1.ravel()\n",
        "mn = np.min(img1d)\n",
        "mx = np.max(img1d)\n",
        "nsz = pow(512,dims)\n",
        "K = np.linspace(mn,mx,len(img1d))\n",
        "X = np.linspace(mn,mx,nsz)\n",
        "\n",
        "\n",
        "out1d = [  doInterpolation(x,img1d,K) for x in X]\n",
        "img_interp = out1d.reshape([512,512])\n",
        "#img_interp = img1d.reshape([sz[0],sz[1]])\n",
        "\n",
        "# \n",
        "\n",
        "# old_size = img1.shape\n",
        "# new_size = [512,512]\n",
        "# print(old_size,new_size)\n",
        "\n",
        "# st = time.time()\n",
        "\n",
        "# img_interp =  doInterpolation2D(img1,new_size)\n",
        "\n",
        "# et = time.time()\n",
        "# print(\"time : \", et -st)\n",
        "\n",
        "# f = plt.figure()\n",
        "# dpi = 80\n",
        "# height, width = img1.shape\n",
        "# figsize = width / float(dpi), height / float(dpi)\n",
        "# fig = plt.figure(figsize=figsize)\n",
        "# plt.imshow(img1, cmap='gray')\n",
        "\n",
        "dpi = 80\n",
        "\n",
        "plt.figure(figsize=[ img1.shape[0] / float(dpi), img1.shape[1] / float(dpi)])\n",
        "plt.title(\"oriignal image\")\n",
        "plt.imshow(img1)\n",
        "plt.show()\n",
        "\n",
        "\n",
        "height, width = img_interp.shape\n",
        "figsize = width / float(dpi), height / float(dpi)\n",
        "fig = plt.figure(figsize=figsize)\n",
        "plt.title(\"linear interpolation\")\n",
        "plt.imshow(img_interp, cmap='gray')\n",
        "\n",
        "\n",
        "plt.show()\n",
        "\n",
        "# comapre with opencv\n",
        "\n",
        "st = time.time()\n",
        "\n",
        "img_interp_cv = cv2.resize(img1, (512, 512), 0, 0, interpolation = cv2.INTER_LINEAR)\n",
        "\n",
        "et = time.time()\n",
        "print(\"time cv: \", et -st)\n",
        "\n",
        "\n",
        "plt.figure(figsize=[ img_interp_cv.shape[0] / float(dpi), img_interp_cv.shape[1] / float(dpi)])\n",
        "plt.title(\"linear interpolation openCV\")\n",
        "plt.imshow(img_interp_cv)\n",
        "plt.show()"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "error",
          "ename": "KeyboardInterrupt",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-5-6431c3d8cedb>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     30\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     31\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 32\u001b[0;31m \u001b[0mout1d\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m  \u001b[0mdoInterpolation\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mimg1d\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mK\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     33\u001b[0m \u001b[0mimg_interp\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mout1d\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m512\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m512\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     34\u001b[0m \u001b[0;31m#img_interp = img1d.reshape([sz[0],sz[1]])\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m<ipython-input-5-6431c3d8cedb>\u001b[0m in \u001b[0;36m<listcomp>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m     30\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     31\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 32\u001b[0;31m \u001b[0mout1d\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m  \u001b[0mdoInterpolation\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mimg1d\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mK\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     33\u001b[0m \u001b[0mimg_interp\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mout1d\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m512\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m512\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     34\u001b[0m \u001b[0;31m#img_interp = img1d.reshape([sz[0],sz[1]])\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m<ipython-input-5-6431c3d8cedb>\u001b[0m in \u001b[0;36mdoInterpolation\u001b[0;34m(x, c, k)\u001b[0m\n\u001b[1;32m     16\u001b[0m     \u001b[0;31m# c is interpolation coefficient computed from the available data points\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     17\u001b[0m     \u001b[0;31m# k is the integer points contains f(x)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 18\u001b[0;31m     \u001b[0mfx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mc\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mphi\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m  \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     19\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mfx\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     20\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m<ipython-input-5-6431c3d8cedb>\u001b[0m in \u001b[0;36m<listcomp>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m     16\u001b[0m     \u001b[0;31m# c is interpolation coefficient computed from the available data points\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     17\u001b[0m     \u001b[0;31m# k is the integer points contains f(x)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 18\u001b[0;31m     \u001b[0mfx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mc\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mphi\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m  \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     19\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mfx\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     20\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m<ipython-input-5-6431c3d8cedb>\u001b[0m in \u001b[0;36mphi\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mphi\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m     \u001b[0;32mreturn\u001b[0m  \u001b[0;36m1.0\u001b[0m\u001b[0;34m-\u001b[0m \u001b[0mabs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m  \u001b[0;32mif\u001b[0m \u001b[0mabs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m1\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0;36m0.0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     11\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     12\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "r68OzNm5hWHX"
      },
      "source": [
        "# Nearest Neighbor Interpolation\n",
        "\n",
        "\\begin{equation}\n",
        "      \\phi(x) = \\begin{cases} 0, & x < \\frac{-1}{2} \\\\\n",
        "                      1, & \\frac{-1}{2} \\le x < \\frac{1}{2} \\\\\n",
        "                      0, &  \\frac{1}{2} \\le x \\\\\n",
        "         \\end{cases}\n",
        "\\end{equation}\n",
        "\n",
        "\n",
        "This is an important interpolation that does not introduce new values (useful when working with segmentations or binary images)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jdMHINocjKYd"
      },
      "source": [
        "## nearest neighbour interpolation\n",
        "def phi(x):\n",
        "    if (x) < -1/2:\n",
        "        phi = 0\n",
        "    elif (-1/2 <= x  < 1/2) :\n",
        "        phi = 1\n",
        "    elif  1/2<=x:\n",
        "        phi = 0\n",
        "    return phi\n",
        "\n",
        "\n",
        "px = 3.9\n",
        "print(\"NN interpolation: f(\", px,\") = \", doInterpolation(px, Y,K))\n",
        "\n",
        "#plotting \n",
        "f=   [ doInterpolation(x,C,K) for x in X ]  \n",
        "#plt.figure()\n",
        "plt.plot(X,Y)\n",
        "plt.plot(X,f)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rwYw9QhXV1wV"
      },
      "source": [
        "def phi(x):\n",
        "    if (x) < -1/2:\n",
        "        phi = 0\n",
        "    elif (-1/2 <= x  < 1/2) :\n",
        "        phi = 1\n",
        "    elif  1/2<=x:\n",
        "        phi = 0\n",
        "    return phi\n",
        "\n",
        "#interpolation using the above phi function\n",
        "def doInterpolation(x, c , k):\n",
        "    # x is a data point we need to predict its value f(x),\n",
        "    # c is interpolation coefficient computed from the available data points\n",
        "    # k is the integer points contains f(x)  \n",
        "    fx = sum([c[i]*phi(x-k[i])  for i in range(len(k))])\n",
        "    return fx\n",
        "\n",
        "\n",
        "def doInterpolation2D(img,nsz):\n",
        "    # img is a 2d image \n",
        "    # nsz is a new larger size to scale the image\n",
        "    sz = img.shape\n",
        "    \n",
        "    img_interp = np.zeros(nsz) # result\n",
        "    tmp = np.zeros(nsz)        # temporary result\n",
        "\n",
        "    for i in range(sz[0]): # for each row \n",
        "        # apply 1d interpolation  \n",
        "        C = img[i,:]                    # C  233 columns\n",
        "        mn = np.min(C) ; mx =np.max(C) \n",
        "        X = np.linspace(mn,mx,nsz[0])     # X = 512\n",
        "        K = np.linspace(mn,mx, len(C) )   # K = 197 rows\n",
        "        new_r = [ doInterpolation(x , C , K) for x in X]     # f  512 columns\n",
        "        tmp[i,:] = new_r\n",
        "\n",
        "    for i in range(nsz[1]):  # for each col in the interpolated image\n",
        "        # apply 1d interpolation on the interpolated image        \n",
        "        # get a column \n",
        "        C = tmp[:sz[0],i]        # C  197 rows\n",
        "        mn = np.min(C) ; mx =np.max(C) \n",
        "        X = np.linspace(mn,mx,nsz[1])   # X = 512\n",
        "        K = np.linspace(mn,mx, len(C))  # K = 197 rows\n",
        "        new_c = [ doInterpolation(x , C , K) for x in X]     # f  512 columns\n",
        "        img_interp[:,i] = new_c\n",
        "            \n",
        "    return img_interp\n",
        "\n",
        "t1_img = nib.load('mni_icbm152_t1_tal_nlin_asym_09a.nii')\n",
        "t1_data = t1_img.get_fdata()\n",
        " # Show the images by stacking them left-right with hstack\n",
        "img1 = t1_data[:, :, 94]\n",
        "\n",
        "print(np.min(img1))\n",
        "print(np.max(img1))\n",
        "\n",
        "# create binary image\n",
        "th = 70\n",
        "img1[img1>=th]= 90.0\n",
        "img1[img1<th] = 0.0\n",
        "\n",
        "print(\"img1 : \",np.unique(img1))\n",
        "\n",
        "plt.figure(figsize=[ img1.shape[0] / float(dpi), img1.shape[1] / float(dpi)])\n",
        "plt.imshow(img1)\n",
        "plt.show()\n",
        "\n",
        "\n",
        "old_size = img1.shape\n",
        "new_size = [512,512]\n",
        "print(old_size,new_size)\n",
        "\n",
        "st = time.time()\n",
        "\n",
        "img_interp =  doInterpolation2D(img1,new_size)\n",
        "\n",
        "et = time.time()\n",
        "print(\"time : \", et -st)\n",
        "\n",
        "# TODO: we we have new values???\n",
        "print(\"img_interp : \",np.unique(img_interp))\n",
        "\n",
        "f = plt.figure()\n",
        "dpi = 80\n",
        "height, width = img1.shape\n",
        "figsize = width / float(dpi), height / float(dpi)\n",
        "fig = plt.figure(figsize=figsize)\n",
        "plt.imshow(img1, cmap='gray')\n",
        "\n",
        "height, width = img_interp.shape\n",
        "figsize = width / float(dpi), height / float(dpi)\n",
        "fig = plt.figure(figsize=figsize)\n",
        "plt.imshow(img_interp, cmap='gray')\n",
        "\n",
        "\n",
        "plt.show()\n",
        "\n",
        "\n",
        "# compare with opencv \n",
        "\n",
        "st = time.time()\n",
        "\n",
        "img_interp_cv = cv2.resize(img1, (512, 512), 0, 0, interpolation = cv2.INTER_NEAREST)\n",
        "\n",
        "print(\"img_interp_cv : \",np.unique(img_interp_cv))\n",
        "et = time.time()\n",
        "print(\"time cv: \", et -st)\n",
        "\n",
        "dpi = 80\n",
        "\n",
        "plt.figure(figsize=[ img1.shape[0] / float(dpi), img1.shape[1] / float(dpi)])\n",
        "plt.imshow(img1)\n",
        "plt.show()\n",
        "\n",
        "plt.figure(figsize=[ img_interp_cv.shape[0] / float(dpi), img_interp_cv.shape[1] / float(dpi)])\n",
        "plt.imshow(img_interp_cv)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7uOF7ycG2l6a"
      },
      "source": [
        "#2d nn interpolation\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Azmj8Ydkha6e"
      },
      "source": [
        "# Polynomial Interpolation\n",
        "\n",
        "source [wws-en-03.pdf](https://tu-dresden.de/bu/umwelt/hydro/iak/ressourcen/dateien/systemanalyse/studium/folder-2009-01-29-lehre/systemanalyse/LBE/wws-en-03.pdf?lang=en)\n",
        "\n",
        "[Linear methods for image interpolation](http://www.ipol.im/pub/art/2011/g_lmii/article.pdf)\n",
        "\n",
        "The interpolated point can be computed  using a polynomial of degree n. \n",
        "$$\n",
        "f(x) = a_0+a_1 x +a_2x^2+...+a_{n}x^{n}=\\sum_{i=0}^n a_ix^i\n",
        "$$\n",
        "\n",
        "\n",
        "We still can use a kernel e.g. using Cubic e.g. n =3 we get:\n",
        "\n",
        "\\begin{equation}\n",
        "      \\phi(x) = \\begin{cases} \n",
        "           (a+2) |x^3|-(a+3) |x^2|+1 , & |x| \\le 1 \\\\\n",
        "           a|x|^3-5a |x|^2 + 8a |x|-4a , & 1 <|x| < 2 \\\\\n",
        "           0, &  otherwise\\\\\n",
        "         \\end{cases}\n",
        "\\end{equation}\n",
        "\n",
        "where a is a free parameter e.g. $a = -0.5$. \n",
        "\n",
        "\n",
        "Lagrange interpolation polynomial is a polynomial of degree $d<=n-1$ that passes through $n$ points.\n",
        "\n",
        "$$\n",
        "f(x) = \\sum_{i=1}^n L_i(x) f(x_i) \\\\\n",
        "L_i(x) = \\prod_{j=1, j\\ne i}^n (\\frac{x-x_j}{x_i-x_j}))\n",
        "$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mtppGB7tr6rA"
      },
      "source": [
        "# An example: .......................\n",
        "X = np.linspace(0,10,101) # create data points from 0 to 10, 101 points\n",
        "Y = np.cos(-X**2/9.0)     # create data values based on a function\n",
        "plt.plot(X,Y)\n",
        "\n",
        "\n",
        "Xo = np.linspace(0,10,11) # create data points from 0 to 10, 11 points\n",
        "Yo = np.cos(-K**2/9.0)    # create data values using the same function\n",
        "plt.figure()\n",
        "plt.plot(Xo,Yo) \n",
        "# Yo is now our coeffcient c_k\n",
        "\n",
        "def fx(x,a,n):\n",
        "    a = np.zeros(n+1)\n",
        "    f= 0.0\n",
        "    for i in range (n+1):\n",
        "        f += a[i]*pow(x,i)\n",
        "    return f\n",
        "\n",
        "np.set_printoptions(suppress=True)\n",
        "np.set_printoptions(precision=2)\n",
        "\n",
        "def getA(x,y):    \n",
        "    c = np.zeros((len(x),len(x)))\n",
        "    for i in range(len(x)):        \n",
        "        for j in range(len(x)):        \n",
        "            c[i,j] = round(pow(x[j],j),2)\n",
        "            print(i,j,x[j],c[i,j]) \n",
        "        # print(x)\n",
        "        # print(np.array2string(c[i]))\n",
        "        # print(ok)\n",
        "    # print(np.array2string(c))\n",
        "    # print(c.shape)\n",
        "    # print(y.shape)\n",
        "    # solve the linear system for a \n",
        "    #a = np.linalg.inv(c).dot(y)   \n",
        "    a = np.linalg.pinv(c).dot(y)         \n",
        "    return a\n",
        "\n",
        "# we n+1 data points \n",
        "\n",
        "n = 3 # we need 4 data points \n",
        "\n",
        "a = getA(Xo,Yo)\n",
        "\n",
        "Yn = [ fx(x,a,n) for x in X]\n",
        "\n",
        "plt.figure()\n",
        "plt.plot(X,Yn) "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7QNLldYY0M6J"
      },
      "source": [
        "## lagrange polynomial interpolation\n",
        "# https://tu-dresden.de/bu/umwelt/hydro/iak/ressourcen/dateien/systemanalyse/studium/folder-2009-01-29-lehre/systemanalyse/LBE/wws-en-03.pdf?lang=en\n",
        "def Li(i,px,X):\n",
        "   phi_value =1\n",
        "   for j in range(len(X)):\n",
        "        if i != j:\n",
        "           phi_value = phi_value * ( (px - X[j]) / (X[i] - X[j]) )  \n",
        "   return phi_value\n",
        "\n",
        "def doInterpolation(n,px,fX,X):\n",
        "    # find px \n",
        "    i = 0; idx = 0\n",
        "    for x in X:        \n",
        "        if px >x:\n",
        "           idx = i \n",
        "           break\n",
        "        i = i+1   \n",
        "    # get n points when current point is the center\n",
        "    tmpX=[]\n",
        "    a = int((idx-n)/2) if int((idx-n)/2) > 0 else 0\n",
        "    b = int((idx+n)/2) if int((idx+n)/2) < len(X) else len(X)-1\n",
        "    for i in range( a, b ):\n",
        "        tmpX.append(X[i])\n",
        "    # print(len(tmpX))      \n",
        "    # print(ok)\n",
        "    fx = 0.0\n",
        "    for i in range(1, len(tmpX)):\n",
        "        fx += fX[i] * Li(i,px,tmpX)\n",
        "    return fx\n",
        "\n",
        "n= 2 # degree\n",
        "px = 3.9\n",
        "print(\"Polynomial interpolation of degree \",n,\" : f(\", px,\") = \", doInterpolation(n,px,C,K))\n",
        "\n",
        "# #plotting \n",
        "f=   [ doInterpolation(n,x,C,K) for x in X ]  \n",
        "plt.plot(X,Y)\n",
        "plt.plot(X,f)\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 860
        },
        "id": "9G_I98QEqSpS",
        "outputId": "df6e92f2-2139-4572-aaed-22a63e069900"
      },
      "source": [
        "## Bicubic interpolation\n",
        "def phi(x):\n",
        "    a = -0.5\n",
        "    if abs(x) <= 1:\n",
        "        phi_value  = (a+2) * pow(abs(x),3)-(a+3)* pow(abs(x),2)+1\n",
        "    elif 1<abs(x) and abs(x)<2:\n",
        "        phi_value = a * pow(abs(x),3) - (5*a) * pow(abs(x),2)+ 8*a*abs(x) - 4 * a\n",
        "    else:\n",
        "        phi_value = 0\n",
        "    return phi_value\n",
        "\n",
        "# interpolation using the above phi function\n",
        "def doInterpolation(x, c , k):\n",
        "    # x is a data point we need to predict its value f(x),\n",
        "    # c is interpolation coefficient computed from the available data points\n",
        "    # k is the integer points contains f(x)  \n",
        "    fx = 0\n",
        "    for i in range(len(k)):\n",
        "        fx += c[i]*phi (x-k[i])\n",
        "    return fx\n",
        "\n",
        "\n",
        "# An example: .......................\n",
        "X= np.linspace(0,10,101) # create data points from 0 to 10, 101 points\n",
        "#X = np.array ([0,1,2,3,4,5,6,7,8,9,10 ])\n",
        "\n",
        "Y = np.cos(-X**2/9.0)     # create data values based on a function\n",
        "plt.title(\"X,Y\")\n",
        "plt.plot(X,Y)\n",
        "\n",
        "print(\"X: \", X[:10])\n",
        "K = np.linspace(0,10,11) # create data points from 0 to 10, 11 points\n",
        "#K = np.array([0,3,5,7,10])\n",
        "C = np.cos(-K**2/9.0)    # create data values using the same function\n",
        "plt.figure()\n",
        "plt.title(\"K,C\")\n",
        "plt.plot(K,C) \n",
        "# C is now our coeffcient c_k\n",
        "\n",
        "# assuming we want to find the value of f(x)=f(3.9)\n",
        "px = 3.9\n",
        "# this is how the call should look like\n",
        "#print(\"interpolation: f(\", px,\") = \", doInterpolation(px, Y,k))\n",
        "\n",
        "# X  0 0.1 0.1  1    3       7     10\n",
        "\n",
        "# K  0               3       7     10 \n",
        "# c  2               5       9     12  \n",
        "# c= f(K) = K+2\n",
        "\n",
        "# f(0)  =  2 * p(0-0) + 3 * p(0-3) + 7* p(00-7)  + 10 * p(0-10) \n",
        "#                1              0          0            0\n",
        "# f(1)  =  2 * p(1-0) + 3 * p(1-3) + 7* p(1-7)  + 10 * p(1-10) \n",
        "#                0              0          0            0\n",
        "\n",
        "# p(x) = 1-abs(x) if abs(x)<1 else 0\n",
        "\n",
        "    \n",
        "px = 3.9\n",
        "print(\"Linear interpolation: f(\", px,\") = \", doInterpolation(px, Y,K))\n",
        "\n",
        "#plotting \n",
        "f=   [ doInterpolation(x,C,K) for x in X ]  \n",
        "plt.figure()\n",
        "plt.title(\"X,Y and X,f\")\n",
        "plt.plot(X,Y)\n",
        "plt.plot(X,f)"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "X:  [0.  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9]\n",
            "Linear interpolation: f( 3.9 ) =  0.9998579364212534\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7ffb9d5d8590>]"
            ]
          },
          "metadata": {},
          "execution_count": 9
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1wu8SLUFhdyo"
      },
      "source": [
        ""
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hdIX-OG5TwI2"
      },
      "source": [
        "# Convolution\n",
        "Convolution [1,2] is an importnat mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions.\n",
        "$$\\tag{101}\n",
        "(f∗g)(t)≜\\int_{-\\infty}^{\\infty} f(\\tau) g(t−\\tau)d\\tau \n",
        "$$\n",
        "the symbol  ≜  means \"equal by definition\", $\\tau$ is dummy variable, after the integration is done, we end-up with a function of $t$. \n",
        "\n",
        "For programmers this is the discrete form:\n",
        "\n",
        "$$\\tag{102}\n",
        "(f∗g)[t]= \\sum_{\\tau=0}^m f[\\tau].g[t−\\tau] \n",
        "$$\n",
        "m  is the range where the two signals are available at the same time.  m  should not t be larger than  g  length. The Greek letter \"tau\" $\\tau$  is the current location of function $f$ . Usually  $f$  is a large signal or an image while  $g$  as asmall signal or a filter. When  $g$  is an even function e.g.  $g(t)=g(−t)$ convolution is equivalent to correlation.\n",
        "\n",
        "Note: When you give an impulse function as input, the output will be an impulse response. By the linear and invariant property. If the input signal is a linear combination of impulses, the output will be a linear combination of impulse response. Therefore, if the input is $f[t]=\\sum f[\\tau].\\delta[t−\\tau]$, output will be $y[t]=\\sum f[\\tau].g[t−\\tau]$, where $\\delta$ is an impulse function, $g$ is the impulse response, so $y[t]$ is the definition of discrete convolution as above.\n",
        "\n",
        "Remark: Why convolution is defined with flipping one signal, multiply and sum?\\\n",
        "It is because in a Linear time invariant(LTI) system, the output signal = input signal * impulse response. As the example below, $f$ is the input signal and $g$ is the impulse response. The input signal $f$ starts with $1$ and the impulse response start the response with $3$. So we need to 'flip' the $g$ such that $1$ matches $3$ in the starting time. As time goes on, $g$ slides over $f$ so to response to the signals at all time instances.\n",
        "\n",
        "\n",
        "An example:\n",
        "\n",
        "f=[1,4,2,5],g=[3,4,1] \n",
        "\n",
        "c=f∗g=[3,16,23,27,22,5] \n",
        "\n",
        "Note:  length(c)=length(f)+length(g)−1 \n",
        "\n",
        "source: https://toto-share.com/2011/11/cc-convolution-source-code/\n",
        "\n",
        "</br>\n",
        "\n",
        " <center>\n",
        "<img src=\"https://drive.google.com/uc?export=view&id=10qhfmI9XZQc8Iz79e_ZIrxXSB4HrI0w6\" width=\"500\"/>\n",
        "</center>\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xe5fjoRKUEQA"
      },
      "source": [
        "# 1d convolution \n",
        "def mpConv(f,g,isSame=0):\n",
        "    #print(\"1D convolution\") \n",
        "    fLength = f.shape[0];    gLength = g.shape[0];    \n",
        "    l = fLength + gLength - 1\n",
        "    #print(\"al = \",fLength);    print(\"bl = \",gLength);    print(\"l = \",l)\n",
        "    c = np.zeros(l)\n",
        "    # we visit all elements of x\n",
        "    for t in range (l):\n",
        "        tau = t\n",
        "        for m in range (gLength):      \n",
        "            #print(\"tau : \",tau,\"   m: \",m)      \n",
        "            if ( (tau>=0) and (tau<fLength) ):\n",
        "                c[t] = c[t] + f[tau] * g[t-tau]  \n",
        "            tau =tau -1      \n",
        "    # # support \"same\" method\n",
        "    # # this part is still not working\n",
        "    # if isSame:\n",
        "    #    nL = (gLength + 1) / 2  if ( not ( ( (gLength - 1) % 2)==0 ) ) else   ((gLength - 1) / 2)\n",
        "    #    y = np.zeros(fLength) \n",
        "    #    for i in range(fLength):\n",
        "    #        #print(i,nL,y[i])\n",
        "    #        y[i] = c[nL + i];           \n",
        "    #    c = y    \n",
        "    return c"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cKqDo5fNrzwU"
      },
      "source": [
        "# 1D convolution example\n",
        "f1 = np.array([1,4,2,5])\n",
        "g1 = np.array([3,4,1])\n",
        "conv1 = mpConv(g1,f1,isSame=0)\n",
        "print(\"output signal by mpConv:\", conv1)\n",
        "# using scipy library\n",
        "from scipy import signal\n",
        "y=signal.convolve(f1,g1)\n",
        "print(\"output signal by scipy:\",y)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "N2scHGZl679U"
      },
      "source": [
        "# # Convolution example using B-spline # TODO need normalization\n",
        "# # Bernstein function (B-spline basis function)\n",
        "# def getBernstein(i,n,t):\n",
        "#     if (n==0 and i == 0):\n",
        "#         B = 1\n",
        "#         if ( t<-0.5 or t>0.5) :\n",
        "#             B = 0\n",
        "#     elif n==i :  \n",
        "#         B =  t * getBernstein(i-1,n-1,t)       \n",
        "#     elif i==0: \n",
        "#         B =  (1-t) * getBernstein(i,n-1,t) \n",
        "#     else:\n",
        "#         B = (1-t) * getBernstein(i,n-1,t)  + t * getBernstein(i,n-1,t) \n",
        "#     return B\n",
        "\n",
        "# #define a range \n",
        "# t = np.linspace(-5,5, 500)\n",
        "\n",
        "# # beta 0 is a square pulse function centered at 0 \n",
        "# B0 = [getBernstein(0,0,x) for x in t]\n",
        "# plt.plot(t,  B0  ,label='B0') \n",
        "\n",
        "\n",
        "# # beta n is a onvolution of beta 0 n+1 times \n",
        "# n = 3 ; \n",
        "\n",
        "# # initislisation \n",
        "# Bs = [getBernstein(0,0,x) for x in t]\n",
        "# for i in range(n): # we stop at n as we already initialised once \n",
        "#     Bs = mpConv (np.array(B0),np.array(Bs))\n",
        "\n",
        "# r1 =  int( (n)   * len(Bs)/ (2*(n+1)) )   \n",
        "# r2 =  int( (n+2) * len(Bs)/(2*(n+1)))+1 if n%2==0 else    int( (n+2) * len(Bs)/(2*(n+1))) \n",
        "# Bs = Bs[r1:r2] \n",
        "# # for plotting as the range is changing   \n",
        "# # output of convolution is a signal larger than each input signal\n",
        "# print(\"B-spline basis function, n = \", n)\n",
        "# # plt.plot(t, Bs   ) \n",
        "# plt.legend()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zDUx3DA7sksK"
      },
      "source": [
        "# 2D convolution # TODO still some variations on different sizes of output after convolution\n",
        "# Ref: http://www.songho.ca/dsp/convolution/convolution.html#convolution_2d\n",
        "# g is the filter/kernel, after convolution will get an array same size as f\n",
        "# for filter/kernel with odd numbers only\n",
        "def mpConv2D(f,g,isSame=0):\n",
        "    #print(\"2D convolution\") \n",
        "    fLength = f.shape[0];    gLength = g.shape[0];\n",
        "    fWidth  = f.shape[1];    gWidth  = g.shape[1];  \n",
        "    # l = fLength + gLength - 1\n",
        "    # w = fWidth + gWidth - 1\n",
        "    kCenterX = int((fWidth - 1) / 2)\n",
        "    kCenterY = int((fLength - 1) / 2)\n",
        "    # print(\"al = \",fLength);    print(\"bl = \",gLength);    print(\"l = \",l)\n",
        "    # print(\"aw = \",fWidth);    print(\"bw = \",gWidth);    print(\"w = \",w)\n",
        "    c = np.zeros((fLength,fWidth))\n",
        "    # we visit all elements of x and y\n",
        "    for t in range(fLength): # rows\n",
        "        for k in range(fWidth): # columns\n",
        "            for m in range(gLength): # kernel rows\n",
        "                mm = gLength-1-m # row index of flipped kernel\n",
        "                for n in range(gWidth): # kernel columns\n",
        "                    nn = gWidth-1-n # column index of flipped kernel\n",
        "\n",
        "                    # index of input signal, used for checking boundary\n",
        "                    tau = t + (kCenterY - mm)\n",
        "                    kappa = k + (kCenterX - nn)\n",
        "\n",
        "                    # ignore input samples which are out of bound\n",
        "                    if( tau >= 0 and tau < fLength and kappa >= 0 and kappa < fWidth ):\n",
        "                        \n",
        "                        # print(tau,kappa)\n",
        "                        c[t][k] = c[t][k] +  f[tau][kappa] * g[mm][nn]\n",
        "                        # c[t][k] = c[t][k] +  f[tau][kappa] * g[t-(tau-kCenterY)][k-(kappa-kCenterX)]\n",
        "    return c"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XBZYG_HRdLm3"
      },
      "source": [
        "# Ref: https://github.com/ashushekar/image-convolution-from-scratch\n",
        "# for filter/kernel with odd numbers only\n",
        "def convolve2d(image, kernel):\n",
        "    \"\"\"\n",
        "    This function which takes an image and a kernel and returns the convolution of them.\n",
        "\n",
        "    :param image: a numpy array of size [image_height, image_width].\n",
        "    :param kernel: a numpy array of size [kernel_height, kernel_width].\n",
        "    :return: a numpy array of size [image_height, image_width] (convolution output).\n",
        "    \"\"\"\n",
        "    # Flip the kernel\n",
        "    kernel = np.flipud(np.fliplr(kernel))\n",
        "    # convolution output\n",
        "    output = np.zeros_like(image)\n",
        "    # padding size\n",
        "    kCenterX = int((kernel.shape[1] - 1) / 2)\n",
        "    kCenterY = int((kernel.shape[0] - 1) / 2)\n",
        "\n",
        "    # Add zero padding to the input image\n",
        "    image_padded = np.zeros((image.shape[0] + kernel.shape[0] - 1,\n",
        "                             image.shape[1] + kernel.shape[1] - 1))\n",
        "    image_padded[kCenterX:-kCenterX, kCenterY:-kCenterY] = image\n",
        "\n",
        "\n",
        "    # Loop over every pixel of the image\n",
        "    for x in range(image.shape[1]):\n",
        "        for y in range(image.shape[0]):\n",
        "            # element-wise multiplication of the kernel and the image\n",
        "            output[y, x]=(kernel * image_padded[y: y+kernel.shape[1],\n",
        "                                                x: x+kernel.shape[0]]).sum()\n",
        "\n",
        "    return output"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ET5estCfvqpL"
      },
      "source": [
        "# 2D convolution example\n",
        "# f2 = np.array([[1,2,3],[4,5,6],[7,8,9]])\n",
        "g2 = np.array([[1,2,1],[0,0,0],[-1,-2,-1]])\n",
        "f2 = np.array([[25,100,75,49,130],[50,80,0,70,100],[5,10,20,30,0],\n",
        "               [60,50,12,24,32],[37,53,55,21,90],[140,17,0,23,222]])\n",
        "# g2 = np.array([[1,0,1],[0,1,0],[0,0,1]])\n",
        "# f2 = np.array([[0,1,2],[3,4,5],[6,7,8]])\n",
        "# g2 = np.array([[0,1],[2,3]])\n",
        "# f2 = np.array([[2,2,3,3,3],[0,1,3,0,3],[2,3,0,1,3],\n",
        "#                [3,3,2,1,2],[3,3,0,2,3]])\n",
        "# g2 = np.array([[2,0,1],[1,0,0],[0,1,1]])\n",
        "# g2 = np.array([[2,2,3,3,3],[0,1,3,0,3],[2,3,0,1,3],\n",
        "#                [3,3,2,1,2],[3,3,0,2,3]])\n",
        "conv2 = mpConv2D(f2,g2,isSame=0)\n",
        "print(conv2)\n",
        "y2 = convolve2d(f2, g2)\n",
        "print(y2)\n",
        "y=signal.convolve(f2,g2,mode='full')\n",
        "print(y)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p5A36jl9l2L-"
      },
      "source": [
        "# Z-transform\n",
        "\n",
        "\n",
        "$\\color{red}{\\text{Todo: add examples and implementation}}$\n",
        "\n",
        "ref with example: https://www.tutorialspoint.com/digital_signal_processing/dsp_z_transform_inverse.htm\n",
        "\n",
        "\n",
        "The [$\\color{blue}{\\text{Z-transform}}$](https://en.wikipedia.org/wiki/Z-transform#:~:text=In%20mathematics%20and%20signal%20processing,equivalent%20of%20the%20Laplace%20transform.) of a signal $x[n]$ is defined as:\n",
        "$$\\tag{1}\n",
        "X(z) = \\sum_{n=-\\infty}^\\infty x[n]z^{-n},\n",
        "$$ \n",
        "where $z$ is a complex variable. \n",
        "\n",
        "\n",
        "$$\n",
        "z = A. e^{j\\phi}= A.(cos(\\phi)+j. sin(\\phi))\n",
        "$$\n",
        "\n",
        "where $A$ is the magnitude of $z$, $\\phi$ is the angle from x-axis to the complex number axis and $j$ is the imagenry unit. \n",
        "\n",
        "<img src='https://upload.wikimedia.org/wikipedia/commons/7/7a/Complex_number_illustration_modarg.svg' />\n",
        "\n",
        "The $z$-transform is a discrete analog of the [$\\color{blue}{\\text{Laplace transform}}$](https://en.wikipedia.org/wiki/Laplace_transform#:~:text=In%20mathematics%2C%20the%20Laplace%20transform,(complex%20frequency).) of continuous functions.\n",
        "\n",
        "$\\color{red}{\\text{Laplace transform equation}}$\n",
        "It exists at all points in the complex plane where the series on the right hand side is absolutely convergent. That is, all points $z \\in \\mathbb{C}$ where\n",
        "$$\\tag{2}\n",
        "\\sum_{n=-\\infty}^\\infty \\Big|x[n]z^{-n}\\Big|\n",
        "$$ exits. The region of the complex plane where $X(z)$ exists is called the region of convergence $ROC$ of the $z$-transform.\n",
        "\n",
        "The $\\color{blue}{\\text{convolution}}$ of signals $x[n]$ and $y[n]$ is defined as \n",
        "$$\\tag{3}\n",
        "u[n] = (x \\star y)[n] = \\sum_{m=-\\infty}^\\infty x[m]y[n-m].\n",
        "$$\n",
        "\n",
        "\n",
        "It can be shown that the $z$-transform of a convolution of two signals is a product of the $z$-transforms of the signals. This is analogous to the property of discrete Fourier transform (which is a special case of $z$-transform), the continuous Fourier transform and the continuous Laplace transform. \n",
        "\n",
        "\n",
        "In mathematical terms:\n",
        "\n",
        " $U(z) = X(z)Y(z)$\n",
        "\n",
        " We can unravel the original signal $x[n]$ in a convolution by taking the inverse $z$-transform of $U(z)/Y(z)$ at all points where $Y$ does not vanish, that is become $0$.\n",
        "\n",
        "\n",
        "The adjoint of a signal is defined as $x^\\ast[n] = \\overline{x[-n]}$. This is analogous to the definition of the hermitian adjoint of a matrix. It is just the complex conjugate of the transpose. The $z$-transform of the adjoint signal is \n",
        "$$\\tag{4}\n",
        "X^\\ast(z) = \\sum_{k=-\\infty}^\\infty x^\\ast[k]z^{-k} = \\sum_{k=-\\infty}^\\infty \\overline{x[-k]\\bar{z}^{-k}} = \\sum_{k=-\\infty}^\\infty \\overline{x[k]\\bar{z}^{k}} = \\sum_{k=-\\infty}^\\infty \\overline{x[k]\\left(\\frac{1}{\\bar{z}}\\right)^{-k}} = \\overline{X\\left(\\frac{1}{\\bar{z}}\\right)}.\n",
        "$$\n",
        "In the case of a real-valued signal $x^\\ast[n] = x[-n]$ and\n",
        "$$\\tag{5}\n",
        "X^\\ast(z) = \\sum_{k=-\\infty}^\\infty x^\\ast[k]z^{-k} = \\sum_{k=-\\infty}^\\infty x[-k]z^{-k} = \\sum_{k=-\\infty}^\\infty x[k]z^{k} = \\sum_{k=-\\infty}^\\infty x[k]\\left(\\frac{1}{z}\\right)^{-k} = X\\left(\\frac{1}{z}\\right).\n",
        "$$\n",
        "\n",
        "Up-sampling a signal means increasing the number of sample points by a certain factor. We can up-sample a signal by a factor $m$ by inserting $m - 1$ zeros between successive values of the signal. Mathematically, an upsampled signal is defined as\n",
        "$$\\tag{6}\n",
        "x_{\\uparrow m}[n] = \\begin{cases}\n",
        "x[l] & \\text{ if } n = ml \\\\\n",
        "0    & \\text{ otherwise.}\n",
        "\\end{cases}\n",
        "$$\n",
        "We can easily get an expression for the $z$-transform of an up-sampled signal.\n",
        "$$\\tag{7}\n",
        "X_{\\uparrow m}(z) = \\sum_{k=-\\infty}^\\infty x_{\\uparrow m}[n]z^{-n} = \\sum_{k=-\\infty}^\\infty x[n]z^{-mn} = X(z^m).\n",
        "$$\n",
        "\n",
        "We can down-sample a signal by a factor of $m$ by selecting every $m$th of its sample. Mathematically a down-samples signal is defined as\n",
        "$$\\tag{8}\n",
        "x_{\\downarrow m}[n] = x[nm].\n",
        "$$\n",
        "Let us now get an expression for $z$-transform of the downsampled signal.\n",
        "$$\\tag{9}\n",
        "X_{\\downarrow m}(z) = \\sum_{k=-\\infty}^\\infty x_{\\downarrow m}[k]z^{-k} = \\sum_{mk=-\\infty}^\\infty x[mk]z^{-k} = \\sum_{k \\in m\\mathbb{Z}} x[k]z^{-mk}.\n",
        "$$\n",
        "The set $m\\mathbb{Z}$ is the set of all multiples of $m$, that is $\\{\\ldots, -2m -m, 0, m, 2m, \\ldots\\}$. Evaluating this sum involves a bit of care for the sum is not over $\\mathbb{Z}$ but $m\\mathbb{Z}$. To proceed, we use the fact\n",
        "$$\\tag{10}\n",
        "\\sum_{j=0}^{m-1}\\exp\\left(\\frac{2\\pi ijn}{m}\\right) = \\begin{cases}\n",
        "m & \\text{ for } n \\in m\\mathbb{Z} \\\\\n",
        "0 & \\text{ otherwise.}\n",
        "\\end{cases}\n",
        "$$\n",
        "It allows us to define the pulse sequence\n",
        "$$\\tag{11}\n",
        "p_m[n] = \\frac{1}{m}\\sum_{j=0}^{m-1}\\exp\\left(\\frac{2\\pi ijn}{m}\\right) = \\begin{cases}\n",
        "1 & \\text{ if } n \\in \\mathbb{Z} \\\\\n",
        "0 & \\text{ otherwise.}\n",
        "\\end{cases}\n",
        "$$\n",
        "We can then write\n",
        "$$\\tag{12}\n",
        "X_{\\downarrow m}(z) = \\sum_{k \\in \\mathbb{Z}} p_m[k]x[k]z^{-k},\n",
        "$$ where the summation extends over all integers. After substituting the expression for $p_m[k]$ we readily get\n",
        "$$\\tag{13}\n",
        "X_{\\downarrow m}(z) = \\frac{1}{m}\\sum_{j=0}^{m-1}X\\left(e^{-2\\pi ij/m}z^{1/m}\\right).\n",
        "$$\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0hykp4dGNQkx"
      },
      "source": [
        "# Interpolation using Z-transform\n",
        "\n",
        "source: http://www.ipol.im/pub/art/2011/g_lmii/\n",
        "\n",
        "Given input image $v_{m,n}$ the interpolation finds a function $u(x,y)$ that approximate the image:\n",
        "\n",
        "$$\n",
        "v_{m,n} = u(m,n) for all m,n \\in Z\n",
        "$$\n",
        "\n",
        "One can use Fourier transform and bilateral Z-transform:\n",
        "\n",
        "$$\n",
        "\\hat{f}(\\zeta) = \\int_{-\\inf}^{\\inf} f(x) e^{-2 \\pi i \\zeta} dx \\\\\n",
        "c(z) := \\sum_{-\\inf}^{\\inf} c_n z^{-n}\n",
        "$$\n",
        "\n",
        "where:\n",
        "\n",
        "* $\\hat{f}(\\zeta)$ is the Fourier transform of $f(x)$ \n",
        "*  $c_n$ is a sequence and $c(z)$ is its $Z$ transform.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sBxkFmaEbsRs"
      },
      "source": [
        "## Interpolation Kernels\n",
        "\n",
        "Linear interpolation can be described as a linear operator $Z$ mapping samples $v$ to a function $u = Z(u)$. If $Z$ is a linear, shift-invarient local operator then there exist a unique function $K$ called the **interpolation kernel** such that: \n",
        "\n",
        "$$\n",
        "Z(v)(x,y) = \\sum_{m,n \\in Z} K(x-m,y-n) \n",
        "$$\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1ZhfVMnvdEX0"
      },
      "source": [
        "## Two-step interpolation\n",
        "\n",
        "\n",
        "Interpolation can be expressed as a basis function $\\phi(t)$ and a linear combination of compact support functions.\n",
        "\n",
        "$$\n",
        "u(t) = \\sum_{n \\in Z} C_n \\phi(t-n) \\\\\n",
        "f_m = \\sum_{n \\in Z} c_n \\phi(m-n)\n",
        "$$\n",
        "\n",
        "This way the interpolation can be computed in 2 steps: \n",
        "1. solve for the coefficient $c_n$\n",
        "2. compute $\\sum c_n \\phi(t-n)$\n",
        "\n",
        "\n",
        "$u(t) = \\sum_{n \\in Z} C_n \\phi(t-n)$ is equivalent to convolution $f_n=(c*p)_m$, where $p_m = \\phi_m$. Which means we can use $Z$ transform to solve for $c_n$ \n",
        "\n",
        "$$\n",
        "f(z) = c(z)p(Z) \\\\\n",
        "c(z) = \\frac{1}{p(z)}f(z)\n",
        "$$\n",
        "\n",
        "\n",
        "Assuming $(p)^{−1}$ the convolution inverse of $p$,then we have \n",
        "$$\n",
        "p (p)^{−1} = \\delta\n",
        "$$ \n",
        "\n",
        "where $\\delta$ is the unit impulse ($\\delta_0 := 1$, and 0 otherwise). \n",
        "\n",
        "Using  $(p)^{−1}$ we obtain $c_n$ by “prefiltering” as:\n",
        "$$\n",
        "c = (p)^{−1} ∗ f.\n",
        "$$\n",
        "$(p)^{−1}$ can be factored into pairs of recursive (infinite impulse response) filters, allowing for an  efficient in-place calculation.\n",
        "\n",
        "$$\n",
        "u(t) = \\sum_{m \\in Z}((p)^{-1}*f)_n\\phi(t-n)\\\\\n",
        "u(t) = \\sum_{m \\in Z}f_m \\sum_{n \\in Z}((p)^{-1})_{n-m}\\phi(t-n)\\\\\n",
        "u(t) = \\sum_{m \\in Z}f_m K_1(t-m),\\\\\n",
        "K_1(t)=\\sum_{n \\in Z}((p)^{-1})_{n}\\phi(t-n)\\\\\n",
        "$$\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wm6WApvJjjHS"
      },
      "source": [
        "## Nearest Neighbor\n",
        "\n",
        "The interpolation kernel for Nearest Neighbor is:\n",
        "\n",
        "$$\n",
        "K(x,y) = K_1(x)K_1(y),\\\\\n",
        "K_1(t) = \\begin{cases} 1 , & \\frac{-1}{2} \\le t < \\frac{1}{2} \\\\\n",
        "                     0    , & otherwise \\\\\n",
        "       \\end{cases}\n",
        "$$\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LXntlkI5kwmH"
      },
      "source": [
        "## Bilinear\n",
        "\n",
        "\n",
        "The biliner interpolation kernel is:\n",
        "\n",
        "$$\n",
        "K(x,y) = K_1(x)K_1(y),\\\\\n",
        "K_1(t) = \\begin{cases} 1-|t| &, |t| < 1 \\\\\n",
        "                     0    &, otherwise  \\\\\n",
        "         \\end{cases}\n",
        "$$\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JEMFyXgNNG2D"
      },
      "source": [
        "## Bicubic\n",
        "\n",
        "The bicubic interpolation kernel is:\n",
        "\n",
        "$$\n",
        "K(x,y) = K_1(x)K_1(y),\\\\\n",
        "K_1(t) = \\begin{cases} (\\alpha+2)|t|^3-(\\alpha+3)|t|^2+1,   & |t| \\le 1 \\\\\n",
        "                       \\alpha|t|^3 - 5 \\alpha|t|^2+8 \\alpha |t|^-4 \\alpha   &, 1 < |t| < 2  \\\\\n",
        "                       0    &, otherwise  \\\\\n",
        "         \\end{cases}\n",
        "$$\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KdXXq6ujmkBq"
      },
      "source": [
        "## Splines\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rLjUrti8I-9j"
      },
      "source": [
        "## From Interpolation to Convolution"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GypQcK58NFAZ"
      },
      "source": [
        ""
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mdYMrBbtJEzb"
      },
      "source": [
        "\n",
        "\n",
        "\\begin{equation}\n",
        " f(x) =  \\sum_{k \\in Z^q}^{} f_k \\psi_{int}(x-k) \\forall x = (x_1,x_2,...,x_q) \\in R^q,\n",
        "\\end{equation}\n",
        "where an interpolated value $f(x)$ at some (perhaps non-integer) coordinate $x$ in a space of dimension **q**. Here, $f(x)$ is the linear combinations of $f_k$, which is the sample value evaluated at integer coordinates $k=(k_1,k_2,...,k_q)\\in Z^q$, and the weight $\\psi_{int}(x-k)$.\n",
        "\n",
        "The summation is performed all over the integer coordinates $k\\in Z^q$. But in fact there are not actually exist a sample $f_k$. Since the number of known samples is finite, thus in order to satisfy the above equation, we need to extend this finite number to infinity by setting suitable boundary conditions over the interpolated function, for example using mirror symmetries.\n",
        "\n",
        "Now the value of any $f_k$ is defined.\n",
        "\n",
        "Consider the above equation with $x=k_0$ which are integers:\n",
        "\\begin{equation}\n",
        " f_{k_0} =  \\sum_{k \\in Z^q}^{} f_k \\psi_{int}(k_0-k) \\forall k_0 \\in Z^q,\n",
        "\\end{equation}\n",
        "This equation is the $\\textbf{interpolation constraint}$.<br>\n",
        "We introduce $p_k=\\psi_{int}(k)$.\n",
        "\\begin{align*} \n",
        " f_{k_0}\n",
        "&= \\sum_{k \\in Z^q}^{} f_k p(k_0-k)\\\\\n",
        "&= \\sum_{k = -\\infty}^{\\infty} f(k) p(k_0-k),\n",
        "\\end{align*}<br>\n",
        "where $f,p$ are defined on the set $Z$ of integers.\n",
        " This equation is equivalence to a $\\textbf{discrete convolution}$(We will prove it in a later section) . Thus the equation can be rewritten as\n",
        "\\begin{equation}\n",
        " f_{k_0} =  (f*p)_{k_0} \\forall k_0 \\in Z^q,\n",
        "\\end{equation}\n",
        "\n",
        "The first equation is not a convolution since $\\psi_{int}$ may be evaluated at noninteger values.\n",
        "\n",
        "Convolution will be discussed in later section.\n",
        "\n",
        "\n",
        "Generalized interpolation:\n",
        "Now we consider\n",
        "\\begin{equation}\n",
        " f(x) =  \\sum_{k \\in Z^q}^{} c_k \\psi_(x-k), \\forall x \\in R^q,\n",
        "\\end{equation}\n",
        "We have to determine the coefficient $c_k$ from samples $f_k$ and $f(x)$ from $c_k$. Now the function is not necessarily finite support nor satisfy the interpolation property.\n",
        "\n",
        "Consider again integer arguments $x=k_0$,\n",
        "\\begin{equation}\n",
        " f_{k_0} =  \\sum_{k \\in Z^q}^{} c_k p_{k_0-k} \\forall k_0 \\in Z^q,\n",
        "\\end{equation}\n",
        "where $p_k=\\psi(k)$.\n",
        "The equation is a system of linear equations $f=Pc$ with unknown coefficients $c_k$. The dimension of the system is infinite since the number of integers $k_0$ in the set $Z^q$ is infinite, and the system is infinite with respect to the number of unknowns(since all indexes $k \\in Z^q$ are considered in the sum). We can reduce the system to finite dimension(finite number of equations) with number of known samples $k_0$, and at the same time constrain $\\psi$ to be finite-support(limits the number of unknowns). Then we solve for $c=P^{-1}f$.\n",
        "\n",
        "Another method is to treat the above equation as a $\\textbf{discrete convolution equation}$ which can be written as\n",
        "\\begin{equation}\n",
        " f_{k_0} =  (c*p)_{k_0} \\forall k_0 \\in Z^q.\n",
        "\\end{equation}\n",
        "Convolving both sides by $(p)^{-1}_k$, we have\n",
        "\\begin{equation}\n",
        " c_{k} =  ((p)^{-1}*f)_{k_0} \\forall k_0 \\in Z^q.\n",
        "\\end{equation}\n",
        "\n",
        "The problem becomes a $\\textbf{digital filtering problem}$.\n",
        "\n",
        "$\\textbf{Note: Discrete convolution is a digital filtering operation.}$\n",
        "\n",
        "\n",
        "**New part:...**\n",
        "\n",
        "\n",
        "Ref: https://zipcpu.com/dsp/2018/01/16/interpolation-is-convolution.html\n",
        "\n",
        "Here we show Interpolation is just a special type of convolution.\n",
        "\n",
        "Let $f(t)=\\sum_{n=-\\infty}^{\\infty}f[n]\\delta(t-n)$ be the discrete input signal, $g(t)$ is the impulse response and $y(t)$ is the output signal.\n",
        "\n",
        "By definition of convolution,\n",
        "\n",
        "\\begin{equation}\n",
        "\\begin{split}\n",
        "y(t)\n",
        "&=\\int_{-\\infty}^{\\infty} g(t-\\tau) f(\\tau)d\\tau\\\\\n",
        "&=\\int_{-\\infty}^{\\infty} g(t-\\tau) \\sum_{n=-\\infty}^{\\infty}f[n]\\delta(\\tau-n)d\\tau\\\\\n",
        "&=\\sum_{n=-\\infty}^{\\infty}f[n]\\int_{-\\infty}^{\\infty} g(t-\\tau) \\delta(\\tau-n)d\\tau\\\\\n",
        "&=\\sum_{n=-\\infty}^{\\infty}f[n]\\int_{-\\infty}^{\\infty} g(t-\\tau) \\delta(n-\\tau)d(t-\\tau)\\\\\n",
        "&=\\sum_{n=-\\infty}^{\\infty}f[n]\\int_{-\\infty}^{\\infty} g(t-\\tau) \\delta(t-\\tau-(t-n))d(t-\\tau)\\\\\n",
        "&=\\sum_{n=-\\infty}^{\\infty}f[n]g[t-n], \\textrm{(by translational property)},\n",
        "\\end{split}\n",
        "\\end{equation} \n",
        "\n",
        "which is same as the interpolation. We will see $f[n]$ is our coefficients $c(k)$ and $g[t-\\tau]$ is our b-spline basis function $\\beta(x-k)$ in later section.\n",
        "\n",
        "$$y(t)=\\sum_{n=-\\infty}^{\\infty}f[n]g[t-n]<=>f(x) =   \\sum_{k=0}^{N-1} c(k)\\beta^n(x-k)$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EoSTD6G4PLYc"
      },
      "source": [
        "## B-spline by Convolution"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iegtJU5N2otn"
      },
      "source": [
        "Ref: 1999 IEEE Unser Splines_ a perfect fit for signal and image processing\n",
        "\n",
        "Mathematically, $\\beta^n(x)$ is the B-spline basis function of degree $n$ is defined through $n+1$ convolution with rectanglar pulse function $\\beta^0(x)$. \n",
        "$$\\tag{1}\n",
        "$$\n",
        "\\begin{equation}\n",
        "  \\beta^0(x) =\n",
        "    \\begin{cases}\n",
        "      1 & -\\frac{1}{2} <x< \\frac{1}{2}\\\\\n",
        "      \\frac{1}{2} & |x|=\\frac{1}{2}\\\\\n",
        "      0 & \\text{otherwise}\\\\\n",
        "    \\end{cases} \n",
        "\\end{equation}\n",
        " <br>\n",
        "\\begin{equation}\n",
        "\\beta^n(x) =    \\underbrace{\\beta^0*\\beta^0*...*\\beta^0(x)}_\\text{$n+1$ times}\n",
        "\\end{equation}\n",
        "\n",
        "The convolution is defined as follows: <br>\n",
        "$$\\tag{2}\n",
        "$$\n",
        "\\begin{equation}\n",
        "\\beta^n(x) =  \\int_{-\\infty}^{\\infty} \\beta^{n-1}(x-t)\\beta^0(t) \\,dt  \n",
        "\\end{equation}\n",
        "\n",
        "Using the convolution theorem of Fourier transform, $(f*g)(x)=\\hat{f}(\\omega)\\hat{h}(\\omega)$.\n",
        "\n",
        "$$\\tag{3}\n",
        "\\hat{\\beta}^n(\\omega) =  (\\int_{-\\infty}^{\\infty} \\beta^{0}(x)e^{-j\\omega x} \\,dx)^{n+1}= (\\int_{-\\frac{1}{2}}^{\\frac{1}{2}} 1\\cdot e^{-j\\omega x} \\,dx)^{n+1}\n",
        "= \\left(\\frac{\\sin(\\frac{\\omega}{2})}{\\frac{\\omega}{2}}\\right)^{n+1}\n",
        "$$\n",
        "\n",
        "Consider the one-sided power function\n",
        "$$\\tag{4}\n",
        "$$\n",
        "\\begin{equation}\n",
        "  (x)^n_+ =\n",
        "    \\begin{cases}\n",
        "      x^n & x \\geq 0\\\\\n",
        "      0 & x< 0\\\\\n",
        "    \\end{cases} \n",
        "\\end{equation} <br>\n",
        "\n",
        "The $(n+1)$th order derivative of $(x)^n_+$ is $D^{n+1}(x)^n_+=n!\\delta(x)$ and in Fourier domain, it gives $(j\\omega)^{n+1}X^n_+(\\omega)=n!$. Thus,\n",
        "$$\\tag{5}\n",
        "$$\n",
        "\\begin{align*}\n",
        "\\hat{\\beta}^n(\\omega)\n",
        "&=(\\frac{\\sin{\\omega/2}}{\\omega/2})^{n+1}\\\\\n",
        "&=(\\frac{e^{j\\omega/2}-e^{-j\\omega/2}}{j\\omega})^{n+1}\n",
        "\\frac{(j\\omega)^{n+1}X^n_+(\\omega)}{n!} \\\\\n",
        "&=\\frac{1}{n!}(e^{j\\omega/2}-e^{-j\\omega/2})^{n+1}X^n_+(\\omega)\\\\\n",
        "&=\\frac{1}{n!}\\sum_{k=0}^{n+1}{n+1 \\choose k}(-1)^{k}e^{-j\\omega(k-(n+1)/2)}X^n_+(\\omega)\n",
        "\\end{align*}\n",
        "\n",
        "Thus, by inverse Fourier transform,\n",
        "$$\\tag{6}\n",
        "\\beta^n(x)=\\frac{1}{n!}\\sum_{k=0}^{n+1}{n+1 \\choose k}(-1)^{k}(x-k+\\frac{n+1}{2})^n_+,\n",
        "$$\n",
        "since the shift in x domain is the exponential phase factor in fourier domain.\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6strxNqAFm2i"
      },
      "source": [
        "# Using the equation 6 above which is the explicit mathematical expression after convolution:\n",
        "# TODO: create a separate document for the previous part \n",
        "#       and re-number the equations\n",
        "def Bn(n,x):\n",
        "    Bn = 0\n",
        "    # print(\"n ------------------------\")\n",
        "    for k in range(n+2):\n",
        "        t1 = scipy.special.binom(n+1, k)\n",
        "        t2 = math.pow(-1,k)\n",
        "        if x-k+((n+1)/2.0)>=0:\n",
        "           t3 = float(math.pow( x-k+((n+1)/2.0),n))\n",
        "        else:\n",
        "           t3 = 0\n",
        "        # print(\"t1,t2,t3 : \",t1,t2,t3)   \n",
        "        Bn = Bn + t1 * t2 * t3  \n",
        "    Bn = float(Bn   / math.factorial(n) )  \n",
        "    # print(\"Bn : \", Bn)\n",
        "    # print(\"--------------------------------\")\n",
        "    return Bn\n",
        "\n",
        "# As a comparison, this is the result from B-spline by interpolation \n",
        "def  B(n, i, x, t):\n",
        "    # \\beta^n_0: the recursion stopping condition\n",
        "    if n == 0:\n",
        "        return 1.0 if t[i] <= x < t[i+1] else 0.0\n",
        "        # return 1.0 if t[i] <= x =< t[i+1] else 0.0\n",
        "\n",
        "    else:    \n",
        "        #\\beta^n_i recursion with two branches\n",
        "        # handling division by zero situations\n",
        "        C1 =0.0  if t[i+n]   == t[i]   else ( (x-t[i])/(t[i+n]-t[i]))          * B( n-1 ,i  , x,t)\n",
        "        C2 =0.0  if t[i+n+1] == t[i+1] else ( (t[i+n+1]-x)/ (t[i+n+1]-t[i+1])) * B( n-1 ,i+1, x,t)    \n",
        "    return  C1 + C2  \n",
        " \n",
        "# Using the equation 6 above which is the explicit mathematical expression after convolution:\n",
        "plt.title(\"B-spline basis function\")\n",
        "y = np.linspace(-5,5, 1000) # smaller the division, higher the accuracy\n",
        "y0 = [ Bn(0,k)    for k in y]\n",
        "y1 = [ Bn(1,k)    for k in y]\n",
        "y2 = [ Bn(2,k)    for k in y]\n",
        "y3 = [ Bn(3,k)    for k in y]\n",
        "plt.plot(y,y0,label='n=0')\n",
        "plt.plot(y,y1,label='n=1')\n",
        "plt.plot(y,y2,label='n=2')\n",
        "plt.plot(y,y3,label='n=3')\n",
        "# this has same result as convolution but with shifting\n",
        "b0= [B(0,0,k,y)  for k in y]\n",
        "b1= [B(1,1,k,y)  for k in y]\n",
        "b2= [B(2,2,k,y)  for k in y]\n",
        "b3= [B(3,3,k,y)  for k in y]\n",
        "# plt.plot(y,b0,label='b0')\n",
        "# plt.plot(y,b1,label='b1')\n",
        "# plt.plot(y,b2,label='b2')\n",
        "# plt.plot(y,b3,label='b3')\n",
        "plt.legend()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "R-kfNuOYpsdV"
      },
      "source": [
        "### Example: Cubic B-spline Basis Function"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JfCkmVHFFCLp"
      },
      "source": [
        "By eq 6 and take cubic b-spline as an example:\n",
        "\\begin{equation} \n",
        "\\begin{split}\n",
        "\\beta^3(x)\n",
        "&=\\frac{1}{3!}\\sum_{k=0}^{3+1}{3+1 \\choose k}(-1)^{k}(x-k+\\frac{3+1}{2})^3_+\\\\\n",
        "&=\\frac{1}{6}\\sum_{k=0}^{4}{4 \\choose k}(-1)^{k}(x-k+\\frac{4}{2})^3_+\\\\\n",
        "&=\\frac{1}{6}(x+2)^3_+ -\\frac{2}{3}(x+1)^3_+ + x^3_+ - \\frac{2}{3}(x-1)^3_+ + \\frac{1}{6}(x-2)^3_+\\\\\n",
        "& =\n",
        "    \\begin{cases}\n",
        "      \\frac{1}{6}(x+2)^3 & x \\geq -2\\\\\n",
        "      \\frac{1}{6}(x+2)^3 -\\frac{2}{3}(x+1)^3 & x \\geq -1\\\\\n",
        "      \\frac{1}{6}(x+2)^3 -\\frac{2}{3}(x+1)^3 + x^3 & x \\geq 0\\\\\n",
        "      \\frac{1}{6}(x+2)^3 -\\frac{2}{3}(x+1)^3 + x^3 - \\frac{2}{3}(x-1)^3 & x \\geq 1\\\\\n",
        "      \\frac{1}{6}(x+2)^3 -\\frac{2}{3}(x+1)^3 + x^3 - \\frac{2}{3}(x-1)^3 + \\frac{1}{6}(x-2)^3 & x \\geq 2\\\\\n",
        "    \\end{cases} \\\\\n",
        "& =\n",
        "    \\begin{cases}\n",
        "      0 & x < -2\\\\\n",
        "      \\frac{1}{6}(2+x)^3 & -2 \\leq x < -1\\\\\n",
        "      \\frac{1}{6}(4-6x^2-3x^3) & -1 \\leq x < 0\\\\\n",
        "      \\frac{1}{6}(4-6x^2+3x^3) & 0 \\leq x < 1\\\\\n",
        "      -\\frac{1}{6}(-2+x)^3 & 1 \\leq x < 2\\\\\n",
        "      0 & x \\geq 2\\\\\n",
        "    \\end{cases} \\\\\n",
        "& =\n",
        "    \\begin{cases}\n",
        "      0 & x < -2\\\\\n",
        "      \\frac{1}{6}(2+x)^3 & -2 \\leq x < -1\\\\\n",
        "      \\frac{1}{6}(4-6x^2-3x^3) & -1 \\leq x < 0\\\\\n",
        "      \\frac{1}{6}(4-6x^2+3x^3) & 0 \\leq x < 1\\\\\n",
        "      -\\frac{1}{6}(-2+x)^3 & 1 \\leq x < 2\\\\\n",
        "      0 & x \\geq 2\\\\\n",
        "    \\end{cases} \\\\\n",
        "& =\n",
        "    \\begin{cases}\n",
        "      \\frac{2}{3} - |x|^2 + \\frac{|x|^3}{2} & 0 \\leq |x| < 1\\\\\n",
        "      \\frac{(2-|x|)^3 }{6}& 1 \\leq |x| < 2\\\\\n",
        "      0 & \\textrm{otherwise}\\\\\n",
        "    \\end{cases} \\\\\n",
        "\\end{split}\n",
        "\\end{equation} \n",
        "\n",
        "We showed here the cubic b-spline basis function by convolution is the same as the cubic b-spline basis function by interpolation before."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VJmEqQdUFKAb"
      },
      "source": [
        "### B-spline Basis Function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6eCRMdNzoskx"
      },
      "source": [
        "# Ref http://shulgadim.blogspot.com/2014/01/introduction-to-splines-b-spline.html\n",
        "\n",
        "# this function compute the basis B-spline function from degree 0 to 3 of a point x\n",
        "# maunually computed, no recursion is used\n",
        "# how these functions are computed ??? is it the same as de boor ?\n",
        "# I showed in the above cell for cubic b-spline\n",
        "\n",
        "def iaBnx(n, x):\n",
        "    #print(\"BSplines::bspline, degree, shape \",degree, x.shape)\n",
        "    betta = 0\n",
        "    if n == 0:\n",
        "        t= 0.5 \n",
        "        if x > -0.5 and x < 0.5:\n",
        "            betta = 1.0\n",
        "        elif abs(x) == 0.5:\n",
        "            betta = 0.5\n",
        "        elif abs(x) > 0.5:\n",
        "            betta = 0.0\n",
        "    elif n == 1:\n",
        "        t = 1\n",
        "        #if x <= -1 or x >= 1:\n",
        "        if x <= (0-t) or x >=  (n+1)-t:\n",
        "            betta = 0.0\n",
        "        elif x > -1 and x < 0:\n",
        "            betta = x + 1\n",
        "        elif x > 0 and x < 1:\n",
        "            betta = -x+1\n",
        "        elif x == 0:\n",
        "            betta = 1.0\n",
        "    elif n == 2:\n",
        "        t = 1.5\n",
        "        if x <= (0-t) or x >= (3-t):\n",
        "            betta = 0.0\n",
        "        elif x >= (0-t) and x < (1-t):\n",
        "            betta = ((x+t)*(x+t))/2.0\n",
        "        elif x >= (1-t) and x< (2-t):\n",
        "            betta = ((x+t)*(x+t)-3.0*(x-1+t)*(x-1+t))/2.0\n",
        "        elif x >= (2-t) and x< (3-t):\n",
        "            betta = ((x+t)*(x+t) - 3.0*(x-1+t)*(x-1+t) + \n",
        "                    3.0*(x-2+t)*(x-2+t))/2.0\n",
        "    elif n == 3:\n",
        "        ax = abs(x)\n",
        "        if ax >= 0 and ax < 1:\n",
        "            betta = 2.0/3.0 - ax * ax + (ax*ax*ax)/2.0\n",
        "        elif abs(x) >= 1 and abs(x) < 2:\n",
        "            betta = ((2-ax)*(2-ax)*(2-ax))/6.0\n",
        "        elif abs(x) >= 2:\n",
        "            betta = 0.0\n",
        "\n",
        "    return betta\n",
        "\n",
        "# As a comparison, this is the result from B-spline by interpolation \n",
        "def  B(n, i, x, t):\n",
        "    # \\beta^n_0: the recursion stopping condition\n",
        "    if n == 0:\n",
        "        return 1.0 if t[i] <= x < t[i+1] else 0.0\n",
        "        # return 1.0 if t[i] <= x =< t[i+1] else 0.0\n",
        "\n",
        "    else:    \n",
        "        #\\beta^n_i recursion with two branches\n",
        "        # handling division by zero situations\n",
        "        C1 =0.0  if t[i+n]   == t[i]   else ( (x-t[i])/(t[i+n]-t[i]))          * B( n-1 ,i  , x,t)\n",
        "        C2 =0.0  if t[i+n+1] == t[i+1] else ( (t[i+n+1]-x)/ (t[i+n+1]-t[i+1])) * B( n-1 ,i+1, x,t)    \n",
        "    return  C1 + C2  \n",
        "       \n",
        "x = np.linspace(-5, 5, 500)\n",
        "x2 = np.linspace(0, 10, 500)\n",
        "t = [0,1,2,3,4,5,6,7] # define the knot vector\n",
        "\n",
        "# this has same result as mathematical expression from convolution\n",
        "b0= [iaBnx(0,k)  for k in x]\n",
        "b1= [iaBnx(1,k)  for k in x]\n",
        "b2= [iaBnx(2,k)  for k in x]\n",
        "b3= [iaBnx(3,k)  for k in x]\n",
        "\n",
        "# this has same result as convolution but with shifting\n",
        "B0= [B(0,0,k,t)  for k in x2]\n",
        "B1= [B(1,1,k,t)  for k in x2]\n",
        "B2= [B(2,2,k,t)  for k in x2]\n",
        "B3= [B(3,3,k,t)  for k in x2]\n",
        "\n",
        "plt.title(\"B-spline basis function by convolution and interpolation\")\n",
        "plt.plot(x,b0, label='n=0 by con.') # basis function degree 0, step \n",
        "plt.plot(x,b1, label='n=1 by con.') # basis function degree 1, linear\n",
        "plt.plot(x,b2, label='n=2 by con.') # basis function degree 2, quadratic\n",
        "plt.plot(x,b3, label='n=3 by con.') # basis function degree 3, cubic\n",
        "#this is same as B-spline by convolution but with shifting\n",
        "plt.plot(x2,B0, label='n=0 by int.') # basis function degree 0, step \n",
        "plt.plot(x2,B1, label='n=1 by int.') # basis function degree 1, linear\n",
        "plt.plot(x2,B2, label='n=2 by int.') # basis function degree 2, quadratic\n",
        "plt.plot(x2,B3, label='n=3 by int.') # basis function degree 3, cubic\n",
        "plt.legend()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FHi3IIxmf1nh"
      },
      "source": [
        "Ref: 1999 IEEE Unser Splines_ a perfect fit for signal and image processing\n",
        "\n",
        "Simon Haykin, Barry Van Veen - Signals and Systems-Wiley (1998)\n",
        "\n",
        "In order to interpolate the function that fit the discrete signal $f(k)$, where $k\\in\\mathbb{Z}$ the corresponding coefficients $c(l)$ are determined for the B-spline curve.\n",
        "\\begin{equation} \\tag{1}\n",
        "    f(k) =   \\sum_{l=-\\infty}^{\\infty} c(l)\\beta^n(x-l)|_{x=k},\n",
        "\\end{equation}\n",
        "\n",
        "which can be written as the form in discrete convolution.\n",
        "\n",
        "\n",
        "\\begin{equation}\\tag{2}\n",
        "    f(k) =   b^n_1(k) * c(k),\n",
        "\\end{equation}\n",
        "\n",
        "where we define the discrete B-spline of order n with a expanded factor $m$: $b^n_m(k)=\\beta^n(x/m)|_{x=k}$. Here we take $m=1$.\n",
        "\n",
        "The Z-transform of a function $f(k)$ is defined as :\n",
        "\n",
        "$$\n",
        "   F(z) = \\mathcal{Z}(f(k))= \\sum_{k=0}^{\\infty} f(k)z^{-k}\n",
        "$$\n",
        "\n",
        "Apply the Z-transform on (\\ref{2}) and property of convolution,\n",
        "\n",
        "\\begin{equation}\n",
        "   \\mathcal{Z} (f(k)) = \\mathcal{Z}  (b^n_1(k) * c(k))\n",
        "\\end{equation}\n",
        "\n",
        "\n",
        "\\begin{equation}\n",
        "    F(z) =   B^n_1(z)C(z),\n",
        "\\end{equation}\n",
        "\n",
        "Thus,\n",
        "\\begin{equation}\n",
        "    C(z) =   \\left(B^n_1(z)\\right)^{-1}F(z),\n",
        "\\end{equation}\n",
        "\n",
        "By inverse Z-transform and define the inverse convolution operator $(b^n_1)^{-1}(k)$. The coefficient $c(k)$ could be obtained by inverse filtering\n",
        "\n",
        "\\begin{equation}\n",
        "    c(k) =   (b^n_1)^{-1}(k) * f(k),\n",
        "\\end{equation}\n",
        "\n",
        "\n",
        "\n",
        "where $(b^n_1)^{-1}(k)$ is the inverse z-transform of $B^n_1(z)^{-1}$. We define the transfer function\n",
        "\\begin{equation}\n",
        "    S^n(z) =   B^n_1(z)^{-1} = \\frac{1}{\\sum_{k=0}^{n+1}b_1^n(k)z^{-k}},\n",
        "\\end{equation}\n",
        "\n",
        "$S^n(z)$ is also the response of a recursive infinite impulse response(IIR) filter. \n",
        "\n",
        "A transfer function $H(z)$ could also be obtained from difference equation of a system. An $N$th order difference equation relates the input $f[n]$ to the output $c[n]$ as\n",
        "\n",
        "\\begin{equation}\n",
        "     \\sum_{k=0}^{N}a_k c[n-k] =   \\sum_{k=0}^{M}b_k f[n-k] ,\n",
        "\\end{equation}\n",
        "\n",
        "If the input $f[n]=z^n$, the output is $c[n]=z^nH(z)$. Thus,\n",
        "\n",
        "\\begin{equation}\n",
        "     z^n \\sum_{k=0}^{N}a_k z^{-k}H(z) =   z^n \\sum_{k=0}^{M}b_k z^{-k} ,\n",
        "\\end{equation}\n",
        "\n",
        "\\begin{equation}\n",
        "     H(z) =   \\frac{\\sum_{k=0}^{M}b_k z^{-k}}{\\sum_{k=0}^{N}a_k z^{-k}} ,\n",
        "\\end{equation}\n",
        "\n",
        "The transfer function $H(z)$ is also the z-transform of the response.\n",
        "\n",
        "Ref: 1991 IEEE Unser Fast B-spline transforms for continuous image representation and interpolation\n",
        "\n",
        "From equation (6), the b-spline could also be represented by\n",
        "\\begin{equation}\n",
        "\\beta^n(x)=\\sum_{j=0}^{n+1}{n+1 \\choose j}\\frac{(-1)^{j}}{n!}(x-j+\\frac{n+1}{2})^n \\mu(x-j+\\frac{n+1}{2})\n",
        "\\end{equation} <br>\n",
        "\n",
        "where \n",
        "\\begin{equation}\n",
        "  \\mu(x) =\n",
        "    \\begin{cases}\n",
        "      1 & x \\geq 0\\\\\n",
        "      0 & x < 0\\\\\n",
        "    \\end{cases} \n",
        "\\end{equation} <br>\n",
        "\n",
        "Note that this is similar to equation (6) but without shifting to the origin.\\\n",
        "For discrete B-spline, we take $x=k$, where $k$ is an integer.\n",
        "\n",
        "\\begin{align*}\n",
        "b^n_m(k)\n",
        "&=\\beta^n(k/m)\\\\\n",
        "&=\\sum_{j=0}^{n+1}{n+1 \\choose j}\\frac{(-1)^{j}}{n!}(\\frac{k}{m}-j+\\frac{n+1}{2})^n \\mu(\\frac{k}{m}-j+\\frac{n+1}{2}),\\\\\n",
        "&=\\frac{1}{m^n}\\sum_{j=0}^{n+1}{n+1 \\choose j}\\frac{(-1)^{j}}{n!}(k-jm+m\\frac{n+1}{2})^n \\mu(k-jm+m\\frac{n+1}{2}),\\\\\n",
        "\\end{align*}\n",
        "\n",
        "\n",
        "\n",
        "To find the coefficient $c(k)$. We use cubic B-spline as an example.\n",
        "By sampling the cubic B-spline at integers, we take $m=1$ and with Fourier transform,\n",
        "\\begin{equation}\n",
        "\\begin{split}\n",
        "B^n_1(z)\n",
        "&=\\sum_{j=0}^{n+1}{n+1 \\choose j}\\frac{(-1)^{j}}{n!}\\sum_{k=-\\infty}^{\\infty}(k-j+\\frac{n+1}{2})^n \\mu(k-j+\\frac{n+1}{2})z^{-k}\\\\\n",
        "&=\\sum_{j=0}^{n+1}{n+1 \\choose j}\\frac{(-1)^{j}}{n!}\\sum_{k=-\\infty}^{\\infty}(k-j+\\frac{n+1}{2})^n \\mu(k-j+\\frac{n+1}{2})z^{-(k-j+\\frac{n+1}{2})}z^{-j+\\frac{n+1}{2}}\\\\\n",
        "&=\\sum_{j=0}^{n+1}{n+1 \\choose j}\\frac{(-1)^{j}}{n!}P^n(z)z^{-j+\\frac{n+1}{2}}\\\\\n",
        "&=\\sum_{j=0}^{n+1}{n+1 \\choose j}\\frac{(-z^{-1})^{j}}{n!}z^{\\frac{n+1}{2}}P^n(z),\\\\\n",
        "&=\\frac{1}{n!}(1-z^{-1})^{n+1}z^{\\frac{n+1}{2}}P^n(z), \\textrm{(by binomial theorem)}\\\\\n",
        "&=\\frac{(1-z^{-1})^{n+1}}{n!}z^{\\frac{n+1}{2}}\\frac{A^n(z)}{(1-z^{-1})^{n+1}}\\\\\n",
        "&=\\frac{A^n(z)z^{\\frac{n+1}{2}}}{n!}\n",
        "\\end{split}\n",
        "\\end{equation} \n",
        "Thus,\n",
        "\\begin{equation}\n",
        "\\begin{split}\n",
        "B^3_1(z) \n",
        "&=\\frac{A^3(z)z^{\\frac{3+1}{2}}}{n!}\\\\\n",
        "&=\\frac{P^3(z)((1-z^{-1})^{3+1})z^{\\frac{4}{2}}}{3!}\\\\\n",
        "&=\\frac{z^{-1} + 4z^{-2} + z^{-3}}{(1-z^{-1})^4}\\frac{(1-z^{-1})^{4}}{6}z^2\\\\\n",
        "&=   \\frac{z+4+z^{-1}}{6}\\\\\n",
        "\\end{split}\n",
        "\\end{equation}\n",
        "\n",
        "\n",
        "\\begin{equation}\n",
        "    B^3_1(z)^{-1} =   \\frac{6}{z+4+z^{-1}} = 6(\\frac{1}{1-\\alpha z^{-1}})(\\frac{-\\alpha}{1-\\alpha z}),\n",
        "\\end{equation}\n",
        "\n",
        "where $\\alpha=\\sqrt{3}-2$. We have two filters for the system. The first one $\\frac{1}{1-\\alpha z^{-1}}$ is a causal filter which runs from left to right. The second one $\\frac{-\\alpha}{1-\\alpha z}$ is an anti-causal filter which runs from right to left.\n",
        "From the first filter, we have\n",
        "\n",
        "\\begin{equation}\n",
        "    \\frac{1}{1-\\alpha z^{-1}} \\Longleftrightarrow c^+(k)- \\alpha c^+(k-1) = s(k) \n",
        "\\end{equation}\n",
        "\n",
        "From the second filter, we have\n",
        "\n",
        "\\begin{equation}\n",
        "     \\frac{-\\alpha}{1-\\alpha z} \\Longleftrightarrow c^-(k) -  \\alpha(c^-(k+1) = -\\alpha c^+(k))\n",
        "\\end{equation}\n",
        "\n",
        "Thus, we have the following recursive algorithm\n",
        "\n",
        "\\begin{equation}\n",
        "    c^+(k)=   s(k) + \\alpha c^+(k-1),    (k=1,...,N-1)\n",
        "\\end{equation}\n",
        "\\begin{equation}\n",
        "    c^-(k)=   \\alpha(c^-(k+1) - c^+(k)),        (k=N-2,...,0)\n",
        "\\end{equation}\n",
        "\n",
        "We specify the initial conditions for the recursion, $c^+(0)$ and $c^-(N-1)$ as follows:\n",
        "$$c^+(0)=\\sum_{j=0}^{n+1}s(k)z^k$$\n",
        "$$c^-(N-1)=\\frac{\\alpha}{1-\\alpha^2}(c^+(N-1)+\\alpha c^+(N-2))$$\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_iX4V8FmNaNa"
      },
      "source": [
        "### Cubic B-spline Interpolation1D"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "y1sCjBqwZcF4"
      },
      "source": [
        "# Ref: http://shulgadim.blogspot.com/2014/01/1-d-b-spline-interpolation-via-digital.html\n",
        "# for general degree, we have to loop over number of poles\n",
        "# the mirror boundary data points also different for different degrees\n",
        "\n",
        "# this function is used only for higher dimensions e.g. 2D\n",
        "def doReset(N,cplus,cminus):    \n",
        "    cplus  = np.zeros(N)\n",
        "    cminus = np.zeros(N)\n",
        "    return   cplus, cminus\n",
        "\n",
        "\n",
        "# this function apply Z filter on a signal \n",
        "# TODO: write the equations \n",
        "# which equations?\n",
        "# Note: we can reduce the number of control-points by using less data \n",
        "#       but this may results less accurate interpolation\n",
        "def getCoeffs( s ):\n",
        "    # compute c plus using z filter of cubic B-spline \n",
        "    # compute c minus from c plus \n",
        "    # add mirrored boundaries \n",
        "    # print(\"Direc Z filter s:  \",len(s))\n",
        "    z     = -2.0 + math.sqrt(3)\n",
        "    N = len(s)\n",
        "\n",
        "    #TODO: is this convolution ???\n",
        "    # this is the recursive filter obtained from the system\n",
        "    # if yes we can use convolution function\n",
        "    # -------------------- c plus\n",
        "    cplus  = np.zeros(N)\n",
        "    for k in range(N):\n",
        "        cplus[0] = cplus[0] + 6.0 * s[k] * pow(z, k)\n",
        "\n",
        "    for k in range(1,N):\n",
        "        cplus[k] =            6.0 * s[k] + z * cplus[k-1]\n",
        "    # print(\"c plus  ------------------------------\")\n",
        "    # print(cplus)\n",
        "    # print(\"--------------------------------------------\")\n",
        "\n",
        "    # -------------------- c minus    \n",
        "    cminus = np.zeros(N)\n",
        "\n",
        "    # compute the last element\n",
        "    cminus[N-1] = (z/(z*z-1.0))*(cplus[N-1] + z*cplus[N-2])\n",
        "    # compute from the opposite side to the first element except the last one \n",
        "    for k in range(N-2, -1, -1):\n",
        "        cminus[k] = z *(cminus[k+1]-cplus[k])\n",
        "    # print(\"c minus  ------------------------------\")\n",
        "    # print(cminus)\n",
        "    # print(\"--------------------------------------------\")\n",
        "    \n",
        "    # We should do mirror in a separate function, otherwise it is wrong in higher dimension\n",
        "    #--------------------- mirrored signal \n",
        "    # the starting values should be specified,\n",
        "    # To get these values the mirror-symmetric boundary condition is used e.g.\n",
        "    # s[-1] = s[1], s[N]=s[N-2]\n",
        "\n",
        "    # since we have cubic number_control_points = number_of_knots + n\n",
        "    # the curve points are considered knots in this case\n",
        "    # the first  n control points are the same \n",
        "    # the last n control points are the same\n",
        "    # ???? it should + 6 so we have 3 at first, 3 at last\n",
        "    control_points  = np.zeros(len(cminus) + 3) # to add -1,N-1,N index\n",
        "    # mirror boundary\n",
        "    control_points[0] = cminus[1]\n",
        "    for k in range(len(cminus)):\n",
        "        control_points[k+1] = cminus[k]\n",
        "    control_points[len(control_points) - 2] = cminus[len(cminus) - 2] # modify the second last value which uses the mirror boundary, the last one is zero value which is a dummy.\n",
        "    return control_points # return control points \n",
        " \n",
        "\n",
        "# cubic B-spline interpolation of a point x using signal control points Pc\n",
        "# TODO: I thought we supposed to use the inverse z filter???\n",
        "# the two filters used in recursion is for finding coefficients in B-spline\n",
        "def doInterp(Pc, n, x):\n",
        "    #print(\"CubicInterpolation1d interp............\")\n",
        "    k = int(math.floor(x))\n",
        "    #k = math.floor(x)\n",
        "\n",
        "    # compute the curve at this point \n",
        "    # TODO: how we get J ?\n",
        "    # we use J to get x-k+1,x-k,x-k-1,x-k-2 \n",
        "    # can we use recursion to combute funcitons ?\n",
        "    Cx = 0 ; J= [1,0,-1,-2]\n",
        "    #t = np.linspace(-10, 10, 10)\n",
        "    for i in range (n+1):\n",
        "        Cx= Cx + Pc[k+i] * iaBnx(n, x-k + J[i] )\n",
        "        # s(x) = \\sum c(l)b(x-l)\n",
        "        # Cx = \\sum Pc[k+i]*iaBnx(n, (x-k) + J[i] ) , where J= [1,0,-1,-2]\n",
        "       # Cx= Cx + Pc[k+i] * B(n,n, x-k + J[i], t )\n",
        "    #y1 = Pc[k+0] * iaBnx(3, x-k+1)+  \n",
        "        #   Pc[k+1] * iaBnx(3, x-k+0)+\n",
        "        #   Pc[k+2] * iaBnx(3, x-k-1)+\n",
        "        #   Pc[k+3] * iaBnx(3, x-k-2)\n",
        "     \n",
        "    return Cx  # return a curve point\n",
        "\n",
        "# cubic B-spline interpolation of a signal s \n",
        "def cInterpolate(s, rate, Cp):\n",
        "    # do interpolation using the control points \n",
        "    # create a new larger range \n",
        "    s_interp = np.zeros(rate*len(s)-(rate-1))\n",
        "    degree = 3 # cubic B-spline \n",
        "    for k in range(len(s_interp)):\n",
        "        s_interp[k] = doInterp(Cp, degree ,  k*(1.0/rate))\n",
        "\n",
        "    return s_interp # return interpolated signal \n",
        "\n",
        "# main function for 1D Bspline  \n",
        "print(\"=================================================\")\n",
        "print(\"BsplineMain example ...........................\")\n",
        "print(\"=================================================\")\n",
        "#create y function\n",
        "\n",
        "# x = np.linspace(-5, 5, 10) # 10 data points, they are considered knot points  \n",
        "# The knot points has to be integer in this implementation\n",
        "x = np.linspace(0, 10, 11) # 11 data points, they are considered knot points  \n",
        "y = np.array([math.sin(k) for k in x])         \n",
        "\n",
        "Cp = getCoeffs(y)\n",
        "print(Cp.shape)\n",
        "print(\"control points ------------------------------\")\n",
        "print(Cp)\n",
        "print(\"--------------------------------------------\")\n",
        "\n",
        "# for k in range(len(y)):\n",
        "#     x[k] = k\n",
        "\n",
        "# create a new signal larger 6 times \n",
        "rate = 6\n",
        "\n",
        "print(\"calling interpolation using the data and the new range\")\n",
        "y_interp = cInterpolate(y, rate, Cp)\n",
        "\n",
        "x_interp = np.zeros(len(y_interp))\n",
        "\n",
        "for k in range(len(x_interp)):\n",
        "    x_interp[k] = k/rate\n",
        "\n",
        "print(\"data_s:\\n\", y)\n",
        "print(\"interpolated value:\\n\", y_interp)\n",
        "#TODO print the control points \n",
        "plt.plot(Cp,'bx',label=\"control points\")             # control points \n",
        "plt.plot(x,y,'ro',label=\"original signal\")            # original signal\n",
        "plt.plot(x_interp, y_interp,label=\"interpolated signal\")  # interpolated signal \n",
        "plt.legend()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kxXc4k4diBR1"
      },
      "source": [
        "### Cubic B-spline Interpolation2D\n",
        "\n",
        "http://shulgadim.blogspot.com/2014/02/2d-cubic-b-spline-interpolation-via.html \n",
        "\n",
        " Notes: when trying to understand a code, first translate it as it is  e.g. from Java. After it works, one should simplify it as much as he can for more readibility. Finally, one should add comments to explain everything. \n",
        "\n",
        " From the above source, one can extend the 1d B-spline to highr dimensions by using tensor-product basis functions e.g. for 2D:\n",
        "\n",
        "[//]: <> (TODO: where did this equation comes from)\n",
        "\n",
        " $$ \\tag{301}\n",
        "   B^n_{k,l}(x,y) =\\beta^n(x-k)\\beta^n(y-l)\n",
        " $$\n",
        "\n",
        " where $x,y \\in \\mathbb{R}$ and $k,l \\in \\mathbb{Z}$. In this case, we have a grid of control points e.g. $c$ is a matrix of size $MxN$. To get the interpolated value at location x,y:\n",
        "\n",
        "\n",
        "[//]: <> (TODO: where did this equation comes from)\n",
        "\n",
        " $$ \\tag{302}\n",
        "   s(x,y) = \\sum^{M-1}_{k=0} \\sum^{N-1}_{l=0} c(k,l)\\beta^n(x-k)\\beta^n(y-l)\n",
        " $$\n",
        "\n",
        "Because of the cubic b-spline function compact support for certain $k,l$ there is only 16 neighbour b-splines should be multiplied with coefficients  to get the output sample. In the case for  are integers and placed on uniform dense grid we have:\n",
        "\n",
        "\n",
        "<img src='http://3.bp.blogspot.com/-FQUQVPzVkk8/UwpvNWPhNoI/AAAAAAAAE1Y/ZX1PuDFWnDk/s1600/fig1.png' />\n",
        "\n",
        "and the equation now looks like: \n",
        "\n",
        "$$ \\tag{303}\n",
        "   s(m,n) = \\sum^{2}_{a=-1} \\sum^{2}_{b=-1} c(k+a,l+b)\\beta^3(\\frac{m_1}{r}-k-a)\\beta^3(\\frac{n_1}{r}-l-b)\n",
        " $$\n",
        " where $M$x$N$ is the original size image, $m$x$n$ is the interpolated image size with $m=k*r$ and $n=l*r$ $m_1,n_1,a,b \\in \\mathbb{Z}$ and  $m_1=m+i, n_1=n+j$, $r$ is the rate as in the figure. If $r=2$,this means double size image e.g. if the origianl size is $256$x$256$ with $r=2$, the interpolated image size is $512$x$512$.\n",
        "\n",
        "[//]: <> (TODO: the figure is still not clear)\n",
        "\n",
        "[//]: <> (TODO: what is the size of the grid? e.g. number of control points?)\n",
        "\n",
        "\n",
        "First, B-spline coefficients must be computed e.g. by direct B-spline filtering. Due to the separable kernel (2D B-spline function is tensor-product), 2D  filtering can be replaced 1D filtering along rows then along columns (or vice versa). For correct boundary processing the mirror-W boundary condition is used working on the same principle as for 1D case. The second column and the second row are added to the matrix, the corner location is added from location $(1,1)$ see figure bellow:\n",
        "\n",
        "<img src='http://2.bp.blogspot.com/-SBxH6fRAAzg/UwpvqLjVK9I/AAAAAAAAE1g/ElJx0nsXbNI/s1600/fig2.png' />\n",
        "\n",
        "\n",
        "[//]: <> (TODO: the mirror is also not clear, the filtering is not clear but it seems we do columns then rows or rows then columns. We should check the c code as well.)\n",
        "\n",
        "Notes from the code:\n",
        "* original image size = rows, cols\n",
        "* r = 2  ; rate, double size\n",
        "* M =    r * rows - (r-1); it seems we use r-1 for boundaries???\n",
        "* N =    r * cols - (r-1);\n",
        "* k,l = M,N\n",
        "* s[k][l] =    cubicInterp2d(coeffs, k/r ), l/r)); ??? why we divide by rate (since for our last s[m][n], m=k*r , but the index in python is integer and cannot be decimals, so our final image will be larger by the rate. In a function f(k/r), the scale will be increased by rate r for r >=1)\n",
        " \n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Nft7DgT34qv7"
      },
      "source": [
        "In order to interpolate the function that fit the discrete signal $s(k,l)$, where $k,l\\in\\mathbb{Z}$ the corresponding coefficients $c(k,l)$ are determined for the B-spline curve.\n",
        "\n",
        "\n",
        " $$\n",
        "   f(m,n) = \\sum_{l=-\\infty}^{\\infty}\\sum_{k=-\\infty}^{\\infty} c(k,l)\\beta^p(x-k)|_{x=m}\\beta^p(y-l)|_{y=n}\n",
        " $$\n",
        "\n",
        "which can be written as the form in discrete convolution.\n",
        "\n",
        "\\begin{equation}\n",
        "    f(m,n) =   b^p_{1}(m) * b^p_{1}(n) * c(m,n),\n",
        "\\end{equation}\n",
        "\n",
        "where we define the discrete B-spline of order p with a expanded factor $r_1,r_2$: $b^p_{r_1}(k)b^p_{r_2}(l)=\\beta^p(x/r_1)|_{x=m}\\beta^p(y/r_2)|_{y=n}$. Here we take $r_1=r_2=1$.\n",
        "\n",
        "\n",
        "Apply the z-transform,\n",
        "\n",
        "\\begin{equation}\n",
        "    F(z_x,z_y) =   B^p_1(z_x)B^p_1(z_y)C(z_x,z_y),\n",
        "\\end{equation}\n",
        "\n",
        "Thus,\n",
        "\\begin{equation}\n",
        "    C(z_x,z_y) =   \\left(B^p_1(z_x)\\right)^{-1}\\left(B^p_1(z_y)\\right)^{-1}F(z_x,z_y),\n",
        "\\end{equation}\n",
        "\n",
        "Define the inverse convolution operator $(b^p_1)^{-1}(k)$ and $(b^p_1)^{-1}(l)$. The coefficient $c(k,l)$ could be obtained by inverse filtering\n",
        "\n",
        "\\begin{equation}\n",
        "    c(k,l) =   (b^p_1)^{-1}(k) * (b^p_1)^{-1}(l) * f(k,l),\n",
        "\\end{equation}\n",
        "\n",
        "\n",
        "\n",
        "where $(b^p_1)^{-1}(k)$ is the inverse z-transform of $B^p_1(z_x)^{-1}$, $(b^p_1)^{-1}(l)$ is the inverse z-transform of $B^p_1(z_y)^{-1}$.\n",
        "\n",
        "\n",
        "Similar to 1D case, we get\n",
        "\\begin{equation}\n",
        "    B^3_1(z_x)^{-1}B^3_1(z_y)^{-1} =   \\frac{6}{z_x+4+z_x^{-1}} \\frac{6}{z_y+4+z_y^{-1}}= 6(\\frac{1}{1-\\alpha z_x^{-1}})(\\frac{-\\alpha}{1-\\alpha z_x}) 6(\\frac{1}{1-\\alpha z_y^{-1}})(\\frac{-\\alpha}{1-\\alpha z_y}),\n",
        "\\end{equation}\n",
        "\n",
        "where $\\alpha=\\sqrt{3}-2$. We have two filters along x direction and two filters along y direction for the system. \n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OZ_JS_oFiQLS"
      },
      "source": [
        "# get coefficient \n",
        "def getControlPoints2D( s, n):\n",
        "    print(\"find 2d control points rows, cols: \",len(s),len(s[0]))\n",
        "    #coeffs = filter2d(s)\n",
        "    print(\"compute the 2d control points .......................\")\n",
        "    M = s.shape[0] # number of rows \n",
        "    N = s.shape[1] # number of columns \n",
        "\n",
        "    print(\"image size = \", M,N)\n",
        "\n",
        "    # temporary variables  \n",
        "    CProws = [] ;\n",
        "    # first we get control points of each rows\n",
        "    for i in range(M):\n",
        "        CProws.append( np.array(getCoeffs(s[i,:])) )   \n",
        "    #CProws = [x[:M] for x in CProws]\n",
        "\n",
        "    # is the filtering in two directions correct?\n",
        "    #then we get control points of each column of the output control points    \n",
        "    CPcols = []\n",
        "    for i in range(N):\n",
        "        CPcols.append( getCoeffs(CProws[i]) )   # since in 2D, we do twice the filter as in 1D, so we need to process 2 filters again for the coefficients from 1D.\n",
        "\n",
        "    print(\"CProws size = \", len(CProws), len(CProws[0]) )\n",
        "    print(\"CPcols size = \", len(CPcols), len(CPcols[0]) )\n",
        "    # then we do mirroring \n",
        "\n",
        "    # # create a grid of control points with the same size of the image \n",
        "\n",
        "    # print(\"mirrorW2d ........................\")\n",
        "    rows = M + n # 259\n",
        "    cols = N + n\n",
        "    coeffs   = np.zeros( (rows,cols)  ) # 259x259\n",
        "\n",
        "    for i in range(M-1):\n",
        "        for j in range(N-1):\n",
        "            #coeffs[i+1][j+1] = s[i][j] # index 1 to 255 are filled with original signal???\n",
        "            coeffs[i+1][j+1] = CPcols[i][j] # index 1 to 255 are filled with coefficient\n",
        "        \n",
        "    for j in range(N-1):\n",
        "        coeffs[0  ][j+1] = CPcols[1  ][j]\n",
        "        coeffs[M-2][j+1] = CPcols[N-2][j]\n",
        "\n",
        "    for i in range(M-1):\n",
        "        coeffs[i+1][0] = CPcols[i][1]  # index 0 filled\n",
        "        coeffs[i+1][len(coeffs[0])-2] = CPcols[i][N-2] # index\n",
        "\n",
        "    coeffs[0]     [0]      = CPcols[1]  [1] # filled the 0,0 index\n",
        "    coeffs[0]     [cols-2] = CPcols[1]  [N-2] # filled 0,257 index\n",
        "    coeffs[rows-2][0]      = CPcols[M-2][1] # filled 257,0 index\n",
        "    coeffs[rows-2][cols-2] = CPcols[M-2][N-2] # filled 257,257 index\n",
        "    # index 258 is value 0\n",
        "    return coeffs\n",
        "\n",
        "# get interpolation\n",
        "def cubicInterp2d(n,Cp, row, col):\n",
        "    k = int(math.floor(row)) \n",
        "    l = int(math.floor(col)) \n",
        "    J = [1,0,-1,-2]\n",
        "    Cx = 0\n",
        "    #TODO repeat first and last rows ???\n",
        "    for r in range(n+1):\n",
        "       for c in range(n+1):\n",
        "           Cx  =  Cx +  Cp[k+c][l+r] * iaBnx(n,row-k + J[c]) * iaBnx(n,col-l+J[r])\n",
        "           #Cx  =  Cx +  Cp[k+c][l+r] * Bn(n,row-k + J[c]) * Bn(n,col-l+J[r])\n",
        "\n",
        "    return Cx\n",
        "\n",
        "def doInterpolate2d( s, rate, control_points):        \n",
        "    print (\"the party starts here ............................\")\n",
        "    print(\"image size: \", s.shape)\n",
        "\n",
        "    # resize the image \n",
        "    M = rate * len(s) - (rate-1)\n",
        "    N = rate * len(s[0]) - (rate-1)\n",
        "    s_interp = np.zeros((M,N))\n",
        "    n = 3 # cubic Bspline \n",
        "    for k in range(len(s_interp)):\n",
        "        for l in range(len(s_interp[0])):\n",
        "            s_interp[k][l] = cubicInterp2d(n,control_points, k/rate, l/rate)\n",
        "    return s_interp\n",
        "\n",
        "def imageToArray( file_path):\n",
        "    itkImage = sitk.ReadImage(file_path)\n",
        "    imageArrayrgb = sitk.GetArrayFromImage(itkImage)\n",
        "    return imageArrayrgb[:, :, 0]\n",
        "\n",
        "\n",
        "# imageLink = \"https://upload.wikimedia.org/wikipedia/en/7/7d/Lenna_%28test_image%29.png\"\n",
        "# !wget  $imageLink -o lena.png\n",
        "# !ls  \n",
        "# file_path = './lena.png'\n",
        "# import cv2\n",
        "# image = cv2.imread(file_path)\n",
        "# gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)\n",
        "# print(ok)\n",
        "\n",
        "# resize to be larger 2 times \n",
        "rate = 2\n",
        "\n",
        "# file_path = '/content/drive/MyDrive/BSpline/lenaG256.png'\n",
        "file_path = '/content/drive/MyDrive/BSpline/lena.png'\n",
        "\n",
        "n = 3 # cubic\n",
        "img = imageToArray(file_path)\n",
        "print(\"original image size:\", img.shape)\n",
        "\n",
        "tm = time.time()\n",
        "control_points = getControlPoints2D(img,n)\n",
        "print(\"control_points size:\",control_points.shape)\n",
        "print(\"computing control points time: \", time.time()-tm)\n",
        "\n",
        "tm = time.time()\n",
        "img_interp = doInterpolate2d(img, rate, control_points)\n",
        "print(\"computing interpolated image time: \", time.time()-tm)\n",
        "\n",
        "print(\"interpolated image size:\", img_interp.shape)\n",
        "\n",
        "# ax = fig.add_axes([0, 0, 1, 1])\n",
        "# # Hide spines, ticks, etc.\n",
        "# ax.axis('off')\n",
        "dpi = 80\n",
        "\n",
        "f = plt.figure()\n",
        "height, width = img.shape\n",
        "figsize = width / float(dpi), height / float(dpi)\n",
        "fig = plt.figure(figsize=figsize)\n",
        "plt.imshow(img, cmap='gray')\n",
        "\n",
        "height, width = img_interp.shape\n",
        "figsize = width / float(dpi), height / float(dpi)\n",
        "fig = plt.figure(figsize=figsize)\n",
        "plt.imshow(img_interp, cmap='gray')\n",
        "\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HugoFwPcC4P5"
      },
      "source": [
        "from google.colab.patches import cv2_imshow\n",
        "\n",
        "imgResize_linear = cv2.resize(img, (511, 511), interpolation=cv2.INTER_LINEAR) # width, height\n",
        "imgResize_cubic = cv2.resize(img, (511, 511), interpolation=cv2.INTER_CUBIC) # width, height\n",
        "imgResize_blur = cv2.GaussianBlur(imgResize_cubic, (7, 7), 0) # width, height\n",
        "\n",
        "vis = np.concatenate((img_interp, imgResize_linear,imgResize_cubic,imgResize_blur), axis=1)\n",
        "cv2_imshow(vis)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d76bY6vbZoqo"
      },
      "source": [
        "### modify"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "S4tjfp_6Zq7t"
      },
      "source": [
        "# Ref: http://shulgadim.blogspot.com/2014/01/1-d-b-spline-interpolation-via-digital.html\n",
        "# for general degree, we have to loop over number of poles\n",
        "# the mirror boundary data points also different for different degrees\n",
        "\n",
        "# this function is used only for higher dimensions e.g. 2D\n",
        "def doReset(N,cplus,cminus):    \n",
        "    cplus  = np.zeros(N)\n",
        "    cminus = np.zeros(N)\n",
        "    return   cplus, cminus\n",
        "\n",
        "\n",
        "# this function apply Z filter on a signal \n",
        "# TODO: write the equations \n",
        "# which equations?\n",
        "# Note: we can reduce the number of control-points by using less data \n",
        "#       but this may results less accurate interpolation\n",
        "def getCoeffs( s ):\n",
        "    # compute c plus using z filter of cubic B-spline \n",
        "    # compute c minus from c plus \n",
        "    # add mirrored boundaries \n",
        "    # print(\"Direc Z filter s:  \",len(s))\n",
        "    z     = -2.0 + math.sqrt(3)\n",
        "    N = len(s)\n",
        "\n",
        "    #TODO: is this convolution ???\n",
        "    # this is the recursive filter obtained from the system\n",
        "    # if yes we can use convolution function\n",
        "    # -------------------- c plus\n",
        "    cplus  = np.zeros(N)\n",
        "    for k in range(N):\n",
        "        cplus[0] = cplus[0] + 6.0 * s[k] * pow(z, k)\n",
        "\n",
        "    for k in range(1,N):\n",
        "        cplus[k] =            6.0 * s[k] + z * cplus[k-1]\n",
        "    # print(\"c plus  ------------------------------\")\n",
        "    # print(cplus)\n",
        "    # print(\"--------------------------------------------\")\n",
        "\n",
        "    # -------------------- c minus    \n",
        "    cminus = np.zeros(N)\n",
        "\n",
        "    # compute the last element\n",
        "    cminus[N-1] = (z/(z*z-1.0))*(cplus[N-1] + z*cplus[N-2])\n",
        "    # compute from the opposite side to the first element except the last one \n",
        "    for k in range(N-2, -1, -1):\n",
        "        cminus[k] = z *(cminus[k+1]-cplus[k])\n",
        "\n",
        "    return cminus\n",
        "    # print(\"c minus  ------------------------------\")\n",
        "    # print(cminus)\n",
        "    # print(\"--------------------------------------------\")\n",
        "    \n",
        "def mirrorW1d(coeffs):\n",
        "    #--------------------- mirrored signal \n",
        "    # the starting values should be specified,\n",
        "    # To get these values the mirror-symmetric boundary condition is used e.g.\n",
        "    # s[-1] = s[1], s[N]=s[N-2]\n",
        "\n",
        "    # since we have cubic number_control_points = number_of_knots + n\n",
        "    # the curve points are considered knots in this case\n",
        "    # the first  n control points are the same \n",
        "    # the last n control points are the same\n",
        "    # ???? it should + 6 so we have 3 at first, 3 at last\n",
        "    coeffs_mirror  = np.zeros(len(coeffs) + 3) # to add -1,N-1,N index\n",
        "    # mirror boundary\n",
        "    coeffs_mirror[0] = coeffs[1]\n",
        "    for k in range(len(coeffs)):\n",
        "        coeffs_mirror[k+1] = coeffs[k]\n",
        "    coeffs_mirror[len(coeffs_mirror) - 2] = coeffs[len(coeffs) - 2] # modify the second last value which uses the mirror boundary, the last one is zero value which is a dummy.\n",
        "    return coeffs_mirror # return control points with mirror conditions\n",
        " \n",
        "\n",
        "# cubic B-spline interpolation of a point x using signal control points Pc\n",
        "# TODO: I thought we supposed to use the inverse z filter???\n",
        "# the two filters used in recursion is for finding coefficients in B-spline\n",
        "def doInterp(Pc, n, x):\n",
        "    #print(\"CubicInterpolation1d interp............\")\n",
        "    k = int(math.floor(x))\n",
        "    #k = math.floor(x)\n",
        "\n",
        "    # compute the curve at this point \n",
        "    # TODO: how we get J ?\n",
        "    # we use J to get x-k+1,x-k,x-k-1,x-k-2 \n",
        "    # can we use recursion to combute funcitons ?\n",
        "    Cx = 0 ; J= [1,0,-1,-2]\n",
        "    #t = np.linspace(-10, 10, 10)\n",
        "    for i in range (n+1):\n",
        "        Cx= Cx + Pc[k+i] * iaBnx(n, x-k + J[i] )\n",
        "        # s(x) = \\sum c(l)b(x-l)\n",
        "        # Cx = \\sum Pc[k+i]*iaBnx(n, (x-k) + J[i] ) , where J= [1,0,-1,-2]\n",
        "       # Cx= Cx + Pc[k+i] * B(n,n, x-k + J[i], t )\n",
        "    #y1 = Pc[k+0] * iaBnx(3, x-k+1)+  \n",
        "        #   Pc[k+1] * iaBnx(3, x-k+0)+\n",
        "        #   Pc[k+2] * iaBnx(3, x-k-1)+\n",
        "        #   Pc[k+3] * iaBnx(3, x-k-2)\n",
        "     \n",
        "    return Cx  # return a curve point\n",
        "\n",
        "# cubic B-spline interpolation of a signal s \n",
        "def cInterpolate(s, rate, Cp):\n",
        "    # do interpolation using the control points \n",
        "    # create a new larger range \n",
        "    s_interp = np.zeros(rate*len(s)-(rate-1))\n",
        "    degree = 3 # cubic B-spline \n",
        "    for k in range(len(s_interp)):\n",
        "        s_interp[k] = doInterp(Cp, degree ,  k*(1.0/rate))\n",
        "\n",
        "    return s_interp # return interpolated signal \n",
        "\n",
        "# main function for 1D Bspline  \n",
        "print(\"=================================================\")\n",
        "print(\"BsplineMain example ...........................\")\n",
        "print(\"=================================================\")\n",
        "#create y function\n",
        "\n",
        "# x = np.linspace(-5, 5, 10) # 10 data points, they are considered knot points  \n",
        "# The knot points has to be integer in this implementation\n",
        "x = np.linspace(0, 10, 11) # 11 data points, they are considered knot points  \n",
        "y = np.array([math.sin(k) for k in x])         \n",
        "\n",
        "Cp = getCoeffs(y)\n",
        "print(Cp.shape)\n",
        "print(\"control points ------------------------------\")\n",
        "print(Cp)\n",
        "print(\"--------------------------------------------\")\n",
        "Cp_mirror = mirrorW1d(Cp)\n",
        "# for k in range(len(y)):\n",
        "#     x[k] = k\n",
        "\n",
        "# create a new signal larger 6 times \n",
        "rate = 6\n",
        "\n",
        "print(\"calling interpolation using the data and the new range\")\n",
        "y_interp = cInterpolate(y, rate, Cp_mirror)\n",
        "\n",
        "x_interp = np.zeros(len(y_interp))\n",
        "\n",
        "for k in range(len(x_interp)):\n",
        "    x_interp[k] = k/rate\n",
        "\n",
        "print(\"data_s:\\n\", y)\n",
        "print(\"interpolated value:\\n\", y_interp)\n",
        "#TODO print the control points \n",
        "plt.plot(Cp,'bx',label=\"control points\")             # control points \n",
        "plt.plot(x,y,'ro',label=\"original signal\")            # original signal\n",
        "plt.plot(x_interp, y_interp,label=\"interpolated signal\")  # interpolated signal \n",
        "plt.legend()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PsIidr7sJSDD"
      },
      "source": [
        "# modify 2D cubic B-spline\n",
        "# get coefficient \n",
        "def getControlPoints2D( s, n):\n",
        "    print(\"find 2d control points rows, cols: \",len(s),len(s[0]))\n",
        "    #coeffs = filter2d(s)\n",
        "    print(\"compute the 2d control points .......................\")\n",
        "    M = len(s) # number of rows \n",
        "    N = len(s[0]) # number of columns \n",
        "\n",
        "    print(\"image size = \", M,N)\n",
        "\n",
        "    row = np.zeros(len(s[0]))\n",
        "    col = np.zeros(len(s))\n",
        "    filt_row = np.zeros(len(s[0])) \n",
        "    filt_col = np.zeros(len(s))\n",
        "    coeffs   = np.zeros((len(s), len(s[0]))) \n",
        "\n",
        "    #################### filtrations along y ##################\n",
        "    for i in range(len(s)):\n",
        "        for j in range(len(s[0])):\n",
        "            row[j] = s[i][j]\n",
        "    \n",
        "        filt_row = getCoeffs(row)\n",
        "        for j in range(len(s[0])):\n",
        "            coeffs[i][j] = filt_row[j]\n",
        "    #################### filtrations along y ##################\n",
        "\n",
        "\n",
        "    #################### filtrations along x ##################\n",
        "    for j in range(len(s[0])):\n",
        "        for i in range(len(s)):\n",
        "            col[i] = coeffs[i][j]\n",
        "        filt_col = getCoeffs(col)\n",
        "        for i in range(len(s)):\n",
        "            coeffs[i][j] = filt_col[i]\n",
        "\n",
        "    return coeffs\n",
        "\n",
        "def mirrorW2d(coeffs):\n",
        "    # then we do mirroring \n",
        "\n",
        "    # # create a grid of control points with the same size of the image \n",
        "\n",
        "    # print(\"mirrorW2d ........................\")\n",
        "    rows = len(coeffs)+3\n",
        "    cols = len(coeffs[0])+3\n",
        "    coeffs_mirror   = np.zeros( (rows,cols)  ) # 259x259\n",
        "\n",
        "    for i in range(len(coeffs)):\n",
        "        for j in range(len(coeffs[0])):\n",
        "            coeffs_mirror[i+1][j+1] = coeffs[i][j] # index 1 to 255 are filled with coefficient\n",
        "        \n",
        "    for j in range(len(coeffs[0])):\n",
        "        coeffs_mirror[0  ][j+1] = coeffs[1  ][j] # first element is filled\n",
        "        coeffs_mirror[len(coeffs_mirror)-2][j+1] = coeffs[len(coeffs)-2][j] # second last element is filled\n",
        "\n",
        "    for i in range(len(coeffs)):\n",
        "        coeffs_mirror[i+1][0] = coeffs[i][1] \n",
        "        coeffs_mirror[i+1][len(coeffs_mirror[0])-2] = coeffs[i][len(coeffs[0])-2]\n",
        "\n",
        "    # fill the values for four corner points\n",
        "    coeffs_mirror[0]     [0]      = coeffs[1]  [1] # filled the 0,0 index\n",
        "    coeffs_mirror[0]     [len(coeffs_mirror[0])-2] = coeffs[1]  [len(coeffs[0])-2] # filled 0,257 index\n",
        "    coeffs_mirror[len(coeffs_mirror)-2][0]      = coeffs[len(coeffs)-2][1] # filled 257,0 index\n",
        "    coeffs_mirror[len(coeffs_mirror)-2][len(coeffs_mirror[0])-2] = coeffs[len(coeffs)-2][len(coeffs[0])-2] # filled 257,257 index\n",
        "    # index 258 is value 0\n",
        "    return coeffs_mirror\n",
        "\n",
        "# get interpolation\n",
        "def cubicInterp2d(n,Cp, row, col):\n",
        "    k = int(math.floor(row)) \n",
        "    l = int(math.floor(col)) \n",
        "    J = [1,0,-1,-2]\n",
        "    Cx = 0\n",
        "    #TODO repeat first and last rows ???\n",
        "    for r in range(n+1):\n",
        "       for c in range(n+1):\n",
        "           Cx  =  Cx +  Cp[k+c][l+r] * iaBnx(n,row-k + J[c]) * iaBnx(n,col-l+J[r])\n",
        "           #Cx  =  Cx +  Cp[k+c][l+r] * Bn(n,row-k + J[c]) * Bn(n,col-l+J[r])\n",
        "\n",
        "    return Cx\n",
        "\n",
        "def doInterpolate2d(s, rate, Cp_mirror):        \n",
        "    print (\"the party starts here ............................\")\n",
        "    print(\"image size: \", s.shape)\n",
        "\n",
        "    # resize the image \n",
        "    M = rate * len(s) - (rate-1)\n",
        "    N = rate * len(s[0]) - (rate-1)\n",
        "    s_interp = np.zeros((M,N))\n",
        "    n = 3 # cubic Bspline \n",
        "    for k in range(len(s_interp)):\n",
        "        for l in range(len(s_interp[0])):\n",
        "            s_interp[k][l] = cubicInterp2d(n,Cp_mirror, k/rate, l/rate)\n",
        "    return s_interp\n",
        "\n",
        "def imageToArray( file_path):\n",
        "    itkImage = sitk.ReadImage(file_path)\n",
        "    imageArrayrgb = sitk.GetArrayFromImage(itkImage)\n",
        "    return imageArrayrgb[:, :, 0]\n",
        "\n",
        "\n",
        "# imageLink = \"https://upload.wikimedia.org/wikipedia/en/7/7d/Lenna_%28test_image%29.png\"\n",
        "# !wget  $imageLink -o lena.png\n",
        "# !ls  \n",
        "# file_path = './lena.png'\n",
        "# import cv2\n",
        "# image = cv2.imread(file_path)\n",
        "# gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)\n",
        "# print(ok)\n",
        "\n",
        "# resize to be larger 2 times \n",
        "rate = 2\n",
        "\n",
        "# file_path = '/content/drive/MyDrive/BSpline/lenaG256.png'\n",
        "file_path = '/content/drive/MyDrive/BSpline/lena.png'\n",
        "\n",
        "n = 3 # cubic\n",
        "img = imageToArray(file_path)\n",
        "print(\"original image size:\", img.shape)\n",
        "\n",
        "tm = time.time()\n",
        "Cp = getControlPoints2D(img,n)\n",
        "print(\"coeffs shape: \",Cp.shape)\n",
        "Cp_mirror = mirrorW2d(Cp)\n",
        "print(\"control_points_mirror size:\",Cp_mirror.shape)\n",
        "print(\"computing control points time: \", time.time()-tm)\n",
        "\n",
        "tm = time.time()\n",
        "img_interp = doInterpolate2d(img, rate, Cp_mirror)\n",
        "print(\"computing interpolated image time: \", time.time()-tm)\n",
        "\n",
        "print(\"interpolated image size:\", img_interp.shape)\n",
        "\n",
        "# ax = fig.add_axes([0, 0, 1, 1])\n",
        "# # Hide spines, ticks, etc.\n",
        "# ax.axis('off')\n",
        "dpi = 80\n",
        "\n",
        "f = plt.figure()\n",
        "height, width = img.shape\n",
        "figsize = width / float(dpi), height / float(dpi)\n",
        "fig = plt.figure(figsize=figsize)\n",
        "plt.imshow(img, cmap='gray')\n",
        "\n",
        "height, width = img_interp.shape\n",
        "figsize = width / float(dpi), height / float(dpi)\n",
        "fig = plt.figure(figsize=figsize)\n",
        "plt.imshow(img_interp, cmap='gray')\n",
        "\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EY426BAWoeS9"
      },
      "source": [
        "from google.colab.patches import cv2_imshow\n",
        "\n",
        "imgResize_linear = cv2.resize(img, (1023, 1023), interpolation=cv2.INTER_LINEAR) # width, height   polynomial n = 1\n",
        "imgResize_cubic  = cv2.resize(img, (1023, 1023), interpolation=cv2.INTER_CUBIC)  # width, height   polynomial n = 3 \n",
        "imgResize_blur   = cv2.GaussianBlur(imgResize_cubic, (7, 7), 0) # width, height\n",
        "\n",
        "vis = np.concatenate((img_interp, imgResize_linear,imgResize_cubic,imgResize_blur), axis=1)\n",
        "cv2_imshow(vis)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "75Si7u1mBx8a"
      },
      "source": [
        "### Cubic B-spline interpolation3D TODO"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aWdaiI8uo2n9"
      },
      "source": [
        "# file_path = '/content/drive/MyDrive/BSpline/lenaG256.png'\n",
        "file_path = 'drive/MyDrive/YOLOv5_detection/verse005_64x64x64.nrrd'\n",
        "!ls\n",
        "# get coefficient \n",
        "def getControlPoints3D(s, n):\n",
        "    print(\"find 3d control points rows, cols, slices: \",len(s[0]),len(s[1]),len(s[2]))\n",
        "    print(\"compute the 3d control points .......................\")\n",
        "    M = s.shape[0] # number of rows \n",
        "    N = s.shape[1] # number of columns\n",
        "    L = s.shape[2] # number of slices\n",
        "\n",
        "    print(\"image size = \", M,N,L)\n",
        "\n",
        "    row = np.zeros(len(s[0]))\n",
        "    col = np.zeros(len(s))\n",
        "    sli = np.zeros(len(s[0][0]))\n",
        "    filt_row = np.zeros(len(s[0])) \n",
        "    filt_col = np.zeros(len(s))\n",
        "    filt_sli = np.zeros(len(s[0][0]))\n",
        "    coeffs   = np.zeros((len(s), len(s[0]), len(s[0][0]))) \n",
        "\n",
        "    #################### filtrations along y ##################\n",
        "    for k in range(len(s[0][0])):\n",
        "        for i in range(len(s)):\n",
        "            for j in range(len(s[0])):\n",
        "                row[j] = s[i][j][k]\n",
        "        \n",
        "            filt_row = getCoeffs(row)\n",
        "            for j in range(len(s[0])):\n",
        "                coeffs[i][j][k] = filt_row[j]\n",
        "\n",
        "\n",
        "    #################### filtrations along x ##################\n",
        "    for j in range(len(s[0])):\n",
        "        for k in range(len(s[0][0])):\n",
        "            for i in range(len(s)):\n",
        "                col[i] = coeffs[i][j][k]\n",
        "\n",
        "            filt_col = getCoeffs(col)\n",
        "            for i in range(len(s)):\n",
        "                coeffs[i][j][k] = filt_col[i]\n",
        "\n",
        "\n",
        "    #################### filtrations along z ##################\n",
        "    for i in range(len(s)):\n",
        "        for j in range(len(s[0])):\n",
        "            for k in range(len(s[0][0])):\n",
        "                sli[k] = coeffs[i][j][k]\n",
        "\n",
        "            filt_sli = getCoeffs(sli)\n",
        "            for k in range(len(s[0][0])):\n",
        "                coeffs[i][j][k] = filt_sli[k]\n",
        "\n",
        "\n",
        "    return coeffs\n",
        "\n",
        "def mirrorW3d(coeffs):\n",
        "    # then we do mirroring \n",
        "\n",
        "    # # create a grid of control points with the same size of the image \n",
        "\n",
        "    # print(\"mirrorW3d ........................\")\n",
        "    rows = len(coeffs)+3 # n=3\n",
        "    cols = len(coeffs[0])+3\n",
        "    slis = len(coeffs[0][0])+3\n",
        "    coeffs_mirror   = np.zeros( (rows,cols,slis)  ) # 259x259x259\n",
        "    print(coeffs_mirror.shape)\n",
        "\n",
        "    for i in range(len(coeffs)):\n",
        "        for j in range(len(coeffs[0])):\n",
        "            for k in range(len(coeffs[0][0])):\n",
        "                coeffs_mirror[i+1][j+1][k+1] = coeffs[i][j][k] # index 1 to 255 are filled with coefficient\n",
        "    \n",
        "    # in 2D, we have a square boundary\n",
        "    # in 3D, we have a cube boundary\n",
        "\n",
        "    for j in range(len(coeffs[0])):\n",
        "        for k in range(len(coeffs[0][0])):\n",
        "            coeffs_mirror[0  ][j+1][k+1] = coeffs[1  ][j][k]  # first element is filled\n",
        "            coeffs_mirror[len(coeffs_mirror)-2][j+1][k+1] = coeffs[len(coeffs)-2][j][k] # second last element is filled\n",
        "\n",
        "    for k in range(len(coeffs[0][0])):\n",
        "        for i in range(len(coeffs)):\n",
        "            coeffs_mirror[i+1][0][k+1] = coeffs[i][1][k] # first element is filled\n",
        "            coeffs_mirror[i+1][len(coeffs_mirror[0])-2][k+1] = coeffs[i][len(coeffs[0])-2][k] # second last element is filled\n",
        "\n",
        "    for i in range(len(coeffs)):\n",
        "        for j in range(len(coeffs[0])):\n",
        "            coeffs_mirror[i+1][j+1][0] = coeffs[i][j][1]  # first element is filled\n",
        "            coeffs_mirror[i+1][j+1][len(coeffs_mirror)-2] = coeffs[i][j][len(coeffs)-2] # second last element is filled\n",
        "\n",
        "    # fill the values for eight corner points\n",
        "    coeffs_mirror[0]     [0]      [0]= coeffs[1]  [1]  [1]# filled the 0,0,0 index\n",
        "    coeffs_mirror[0]     [len(coeffs_mirror[0])-2] [0]= coeffs[1]  [len(coeffs[0])-2]  [0] # filled 0,257,0 index\n",
        "    coeffs_mirror[0]     [0] [len(coeffs_mirror[0][0])-2]= coeffs[1]   [0] [len(coeffs[0][0])-2]# filled 0,0,257 index\n",
        "    coeffs_mirror[0]     [len(coeffs_mirror[0])-2] [len(coeffs_mirror[0][0])-2]= coeffs[1]   [len(coeffs[0])-2] [len(coeffs[0][0])-2]# filled 0,257,257 index\n",
        "\n",
        "    coeffs_mirror[len(coeffs_mirror)-2][0][0]      = coeffs[len(coeffs)-2][1][1] # filled 257,0,0 index\n",
        "    coeffs_mirror[len(coeffs_mirror)-2][len(coeffs_mirror[0])-2][0] = coeffs[len(coeffs)-2][len(coeffs[0])-2][0] # filled 257,257,0 index\n",
        "    coeffs_mirror[len(coeffs_mirror)-2][0][len(coeffs_mirror[0][0])-2] = coeffs[len(coeffs)-2][0][len(coeffs[0][0])-2] # filled 257,0,257 index\n",
        "    coeffs_mirror[len(coeffs_mirror)-2][len(coeffs_mirror[0])-2][len(coeffs_mirror[0][0])-2] = coeffs[len(coeffs)-2][len(coeffs[0])-2][len(coeffs[0][0])-2] # filled 257,257,257 index\n",
        "    # index 258 is value 0\n",
        "    return coeffs_mirror\n",
        "\n",
        "# get interpolation\n",
        "def cubicInterp3d(n,Cp, row, col, sli):\n",
        "    k = int(math.floor(row)) \n",
        "    l = int(math.floor(col))\n",
        "    m = int(math.floor(sli))\n",
        "    J = [1,0,-1,-2]\n",
        "    Cx = 0\n",
        "    #TODO repeat first and last rows ???\n",
        "    for r in range(n+1):\n",
        "       for c in range(n+1):\n",
        "           for d in range(n+1):\n",
        "            Cx  =  Cx +  Cp[k+c][l+r][m+d] * iaBnx(n,row-k + J[c]) * iaBnx(n,col-l+J[r]) * iaBnx(n,sli-m+J[d])\n",
        "\n",
        "    return Cx\n",
        "\n",
        "def doInterpolate3d(s, rate, Cp_mirror):        \n",
        "    print (\"the party starts here ............................\")\n",
        "    print(\"image size: \", s.shape)\n",
        "\n",
        "    # resize the image \n",
        "    M = rate * len(s) - (rate-1)\n",
        "    N = rate * len(s[0]) - (rate-1)\n",
        "    L = rate * len(s[0][0]) - (rate-1)\n",
        "    s_interp = np.zeros((M,N,L))\n",
        "    n = 3 # cubic Bspline \n",
        "    for k in range(len(s_interp)):\n",
        "        for l in range(len(s_interp[0])):\n",
        "            for m in range(len(s_interp[0][0])):\n",
        "                s_interp[k][l][m] = cubicInterp3d(n, Cp_mirror, k/rate, l/rate, m/rate)\n",
        "    return s_interp\n",
        "\n",
        "def imageToArray( file_path):\n",
        "    itkImage = sitk.ReadImage(file_path)\n",
        "    imageArray = sitk.GetArrayFromImage(itkImage)\n",
        "    return imageArray\n",
        "\n",
        "\n",
        "# imageLink = \"https://upload.wikimedia.org/wikipedia/en/7/7d/Lenna_%28test_image%29.png\"\n",
        "# !wget  $imageLink -o lena.png\n",
        "# !ls  \n",
        "# file_path = './lena.png'\n",
        "# import cv2\n",
        "# image = cv2.imread(file_path)\n",
        "# gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)\n",
        "# print(ok)\n",
        "\n",
        "# resize to be larger 2 times \n",
        "rate = 2\n",
        "\n",
        "\n",
        "\n",
        "n = 3 # cubic\n",
        "img = imageToArray(file_path)\n",
        "print(\"original image size:\", img.shape)\n",
        "\n",
        "print(len(img[0][0]))\n",
        "tm = time.time()\n",
        "Cp = getControlPoints3D(img,n)\n",
        "print(\"coeffs shape: \",Cp.shape)\n",
        "Cp_mirror = mirrorW3d(Cp)\n",
        "print(\"control_points size:\",Cp_mirror.shape)\n",
        "print(\"computing control points time: \", time.time()-tm)\n",
        "\n",
        "tm = time.time()\n",
        "img_interp = doInterpolate3d(img, rate, Cp_mirror)\n",
        "print(\"computing interpolated image time: \", time.time()-tm)\n",
        "\n",
        "print(\"interpolated image size:\", img_interp.shape)\n",
        "print (\"done! ..............\")"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JdR3I4MqAJ2P"
      },
      "source": [
        "from PIL import Image\n",
        "\n",
        "# def ArrayToImage(image_array):\n",
        "#     data = Image.fromarray(image_array)\n",
        "#     data = data.convert(\"L\")\n",
        "#     data.save('/content/drive/MyDrive/BSpline/verse005_64_interp.nrrd')\n",
        "#     return data\n",
        "\n",
        "print(\"interpolated image size:\", img_interp.shape)\n",
        "# ArrayToImage(img_interp)\n",
        "writer = sitk.ImageFileWriter()\n",
        "writer.SetFileName('/content/drive/MyDrive/BSpline/verse005_64_interp.nrrd')\n",
        "writer.Execute(img_interp)\n",
        "print(\"saved interpolated image\")"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rgPr8DGKmZFA"
      },
      "source": [
        "### Recursive Filtering \n",
        "\n",
        "C code from Quantifcation chapter, HandBook Medical Image Processing and Analysis 2000 by Isaac Bankman:\n",
        "\n",
        "\n",
        "To find the control-points $c_n$ of 1D signal $f_k$ that satisfy: \n",
        "\n",
        "$$\n",
        "f_k = \\sum_{n \\in Z} \\left( c_n. \\phi(k-n) \\right), k \\in Z\n",
        "$$\n",
        "where the function $\\phi$ is represented by its poles e.g. $z_1$ and $ z_2$. The values of these poles for B-splines of  degree 2 and 3 are: \n",
        "\n",
        "$$\n",
        "\\quad \\quad z_1 \\quad \\quad \\quad \\quad \\quad  z_2  \\\\\n",
        "\\beta^2 \\quad \\sqrt{8}-3 \\quad \\quad \\quad NA \\\\\n",
        "\\beta^3 \\quad \\sqrt{3}-2 \\quad \\quad \\quad NA \\\\\n",
        "$$\n",
        "\n",
        "Cubic B-spline:\n",
        "\n",
        "$$\n",
        "\\beta^3(x) =\n",
        "    \\begin{cases}\n",
        "      \\frac{2}{3}-\\frac{1}{2}|x|^2 (2-|x|)& 0 \\le |x| < 1\\\\\n",
        "      \\frac{1}{6}(2-|x|)^3 & 1 \\le |x|< 2\\\\\n",
        "      0 & \\textrm{otherwise}\\\\\n",
        "    \\end{cases} \n",
        "$$\n",
        "\n",
        "\n",
        "**Mirror (or symmetric) boundaries:**\n",
        "\n",
        "A signal  $X=[0,N-1]$ can be extended to infinity by these conventions: \n",
        "\n",
        "$$\n",
        "    \\begin{cases}\n",
        "      f(x) & = f(-x) & x \\in R\\\\\n",
        "      f(N-1+x) &= f(-x+N-1) & x \\in R\\\\\n",
        "    \\end{cases} \n",
        "$$\n",
        "\n",
        "The extended signal is symmetric with respect to the origin and mirrored around $x=N-1$. \n",
        "\n",
        "The z-transform:\n",
        "\n",
        "$$\n",
        "B^{-1}(z) = \\prod_{i=1}^{[n/2]}\\frac{z(1-z_i)(1-z_i^{-1}))}{(z-z_i)(z-z_i^{-1}))}\n",
        "$$\n",
        "where $z$ is ? , $_i$ is ? and n is ?\n",
        "\n",
        "**Casual and aanti-casual recursions:**\n",
        "The poles of this filter are power-conjugate which means every second pole is outside of the unit circle. To gain stability, the filter is realazed as a cascade of casual filters that are impleneted as a forward recursion, and anti-casual filters that are implemnted as a backward recursion.  \n",
        "\n",
        "**B-spline derivatives:**\n",
        "\n",
        "The derivative of the basis B-spline function:\n",
        "\n",
        "$$\n",
        "   \\frac{\\partial \\beta^n(x)}{\\partial x} = \\beta^{n-1}(x+\\frac{1}{2})-\\beta^{n-1}(x-\\frac{1}{2}), n>0\n",
        "$$\n",
        "\n",
        "The derivative of a signal can be computed using its B-spline representation:\n",
        "\n",
        "$$\n",
        "   \\frac{\\partial f(x)}{\\partial x} = \\sum_{k \\in Z}(c_k \\frac{\\partial \\beta^{n}(x-k)}{\\partial x}=\\sum_{k \\in Z}(c_k-c_{k-1})  \\beta^{n-1}(x-k+\\frac{1}{2})\n",
        "$$\n",
        "\n",
        "where $c_k$ is a control-point\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NbBVGrjzknG8"
      },
      "source": [
        "# Reading and sources:\n",
        "\n",
        "* [Handbook of Medical Image Processing and Analysis by  Isaac Bankman](https://www.amazon.com/Handbook-Processing-Analysis-Biomedical-Engineering/dp/0123739047) Ch25 Image Interpolation and Resampling by Philippe TheÂvenaz, Thierry Blu, and Michael Unser\n"
      ]
    }
  ]
}