GM(1,1)_Model_(Grey_Forecast).ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "GM(1,1) Model (Grey Forecast)",
      "provenance": [],
      "toc_visible": true,
      "authorship_tag": "ABX9TyPEpz8zb0z5xWwNe6FuGMcj",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/charindukavishan/GM-1-1-Model-Grey-Forecast-/blob/master/GM(1%2C1)_Model_(Grey_Forecast).ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fJMcwJxLTtTS",
        "colab_type": "text"
      },
      "source": [
        "# **Gray GM (1,1) Model**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SDFUm8qCPRRP",
        "colab_type": "text"
      },
      "source": [
        "Importing the libraries"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "C_RPWXjR7U3l",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import math"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JAlfTJ9HPa8g",
        "colab_type": "text"
      },
      "source": [
        "Import the dataset"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oIgOwdhW7gs8",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "x0 = np.array([520.3,482.4,635.7,1078.5,376.9,1095.8,724.3,593.1,416.7,531.5,617.7,999.1,757.9,483.7,591.5,288.9,486,475,899.2,775.1,766.4,762.4,615.4,885.8,885.9,718.1,675.4,644.3,533.2,482,836.5,690.1,856.2,510.4,1365.9,509.7,693.4,351.1,557.2,798.2,473.6,753.3,857,627.1])\n",
        "# x0 = np.arange(1,101)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4esXlKSXQJOp",
        "colab_type": "text"
      },
      "source": [
        "According  to  the  gray  system  theory  on  the  original  sequence  of  first-order accumulation (1-AGO) generated\n",
        "![image.png](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAskAAAH/CAYAAACl/kDAAAAgAElEQVR4Aeyda8wV1b3/eX0S3vjiJLz4h6SJMbYhxJjWhsaoLQEjxtYGWjw9cNRqUeqleOkpWmvrvVYoikGhtkq9gFoscDyolFaxVOvtUFoKCBGwKgJeihQRCrL++U77213PetbMntnP7L1n7/ms5Hlm9po1a/3WZ62Z+c5v1qwZ5ggQgAAEIAABCEAAAhCAwAACwwb84gcEIAABCEAAAhCAAAQg4BDJdAIIQAACEIAABCAAAQgEBBDJARB+QgACEIAABCAAAQhAAJFMH4AABCAAAQhAAAIQgEBAAJEcAOEnBCAAAQhAAAIQgAAEEMn0AQhAAAIQgAAEIAABCAQEEMkBEH5CAAIQgAAEIAABCEAAkUwfgAAEIAABCEAAAhCAQEAAkRwA4ScEIAABCEAAAhCAAAQQyfQBCECgJwmsXLnSvfvuu4nta9ascdOmTXP79+9Pfq9du7ax3pOVw2gIQAACEOg6AURy15sAAyAAgaIEJIofeOCBZLdNmza50aNHDxDJips9e3bRbEkPAQhAAAIQaBBAJDdQsAIBCPQCAXmPFyxYMMBUieIrr7xygPdYQlp/BAhAAAIQgEArBBDJrVBjHwhAoGsEYuI3JpJjYrprRlMwBCAAAQj0HAFEcs81GQZDoN4Eli5d6iSK/RATyRqfPH/+/AHeZX8f1iEAAQhAAAJZBBDJWXTYBgEIVI6AxhrnFcnXXXdd4+W+ylUEgyAAAQhAoNIEEMmVbh6Mg0D/Eti1a5ebO3eumzBhwiDRm1XrIiJZ45RDQZ2VN9sgAAEIQAACRgCRbCRYQgACHSNw5MgRt3fv3kQka2aKIkK2iEjGk9yxJqUgCEAAAn1HAJHcd01KhSDQOwQ013FRkayp3/xZKySwlcewYcMGTAPHmOTe6QdYCgEIQKCKBBDJVWwVbIJATQhI7BYVybHZLWK4mN0iRoU4CEAAAhDISwCRnJcU6SAAgSET2Lx5s5s6daobPny4O/HEE92NN944SCSbZ9i8xfbbxLQ8xJrholnIK6ab5cN2CEAAAhCoJwFEcj3bnVpDoOMENmzY4E4++WT3+OOPu8OHD7t169a5E044YYBI1lAKDZvQn8YTSyCHHwmR4a+++mrTWStMZHe8ohQIAQhAAAJ9QQCR3BfNSCUgUG0C8v5OmzbNzZo1y+mlPQt33333AJFs8RLI4Rhj26alhlIoPy1jIRy3HEtDHAQgAAEIQCCLACI5iw7bIACBUgisX7/eHXvssW716tUD8pO314ZR+BtsiEXdvMFr165tzPQhBpMnT27cCOTxnvsMWYcABCAAgaERQCQPjR97QwACOQhI7MozHIreNJFsnmd5hOsSJIo1vZ2CPOTjx49P/sxbrqU87GJDgAAEIACB9hNAJLefMSVAoPYETCQvW7ZsAIs0kSyP6rhx4wZM6TZgxz77IeEbfkJbojgcUiIhneelxT7DQ3UgAAEIdIUAIrkr2CkUAvUisH37djdmzBh3ySWXuAMHDjQqHxPJEocLFixIvM7yppontbFTH67ExG9MJMfEdB/ioEoQgAAEKkEAkVyJZsAICPQ3Ab2sN2fOnGTqNy0l9j744AN3/fXXuxEjRrgnnnjCXXXVVU7DKySQJRAlHDVeWUK631/EUx3154eYSNZ24+OnZR0CEIBApwnoPK5zeJFhcXov5eKLL3bvvfdep81tqTxEckvY2AkCEChK4NChQ27RokVu1KhRbuTIkcn426eeesqdfvrpbsWKFe6aa64ZMG5ZJ2ANN9BY5iIn4aJ2VSF97CYgTSTHPstdhTpgAwQgUB8CeiKodySmT5/u9u3bl7viug7ccsstbsqUKW737t259+tWQkRyt8hTLgQgAIF/EigiknVhCr3OZYJU3roxqcPNSZncyAsCdSIgh8dJJ53ktm3bllptzY2vufDD89X777/vJk2alIhlieYqB0RylVsH2yAAgVoQKCKSO+FJlhdb089pyAsBAhCAgE/gzTffdKeccsqgee/9NBpOp6+rxmY1UrolS5YkTxRfeuklf7fKrSOSK9ckGAQBCNSNgDwt/pASiVS9tKgLTPjyYifGJMuWsNy6tQn1hQAE4gQkcI8++ujkq6mxFPYOit43SRPJb731VvIFVo1p9j8wFcuvm3GI5G7Sp2wIQAACziUe2zxTu3VqdgsN6dAfAQIQgIBP4ODBg27GjBluwoQJTsMmYkE3/RpzfPvtt6eK5I8++igZzzxx4kS3Z8+eWDaViEMkV6IZMAICEKgKAZ3giwpE3/OrfeWJ9b8k6M/UoXrabz+NRLJEcFbQfnnEdFYezbZZXVQH/ckTlOYNapYX2yEAgf4iYOcHvbAnoRsGvYx31llnOQ2jsPNHOCbZ9rnpppsGnCctvkpLRHKVWgNbIACBrhMoKpJN8OqCoBB+CMUuFBKaEtBKf+WVVw4SxG+88YbTX1ZQ3s2EdNb+ebbJPn3IRX9WJ9nN8Is89EgDgf4msGXLFnf88cdHHQmHDx92t956azLdp4ZQ2LkvTSRr+/Dhw93zzz9fWWiI5Mo2DYZBAALdIFBEJJtXxcSk7DXRHHqj9VtCWdPaxYSu4iSetX8syC6/nFgaxVk55gGOLbMEb+zCprJ9r3da2cRDAAL9TSDt/KZa6zwhL7JN7RY7l/h0mm3303ZrHZHcLfKUC4EaELj33nvdf/zHf1Tqrxn2IiJZgjQUvXYRUT5+SIv301RhXXXSnx8QyT4N1iFQXwJpnmQJY40v1tz3FpqJYG3Hk2y0WEIAArUjsHz5cle1P78R5L21D5bEPK4WF/O8poneNEFpZenCUNVgnvFQ4MvmGIOq1gO7IACB9hCwc0ToHFi8eHHj/QU7b/rL2JMo3YzH4ttjeWu54klujRt7QQACfUpAAjH0pMaqGhOOJoTDC4j2D8cqx/IsI062+xen2Hqa4JXw11hkLS1Ynaos7s1WlhCAQHsJ5JndwizQOUPnn/CmW9uZ3cIosYQABCDQQwTyimSJ0VAM20UhFNnyvmh+Y+WdJlCrgEj2x+pUZZurwA0bIFAnAponWXMgv/zyy5nVtvNhTCRv377djRkzJvODJJmZd2gjnuQOgaYYCECgNwjkFcm6APiPCvVbX8OToFy5cqWbP3++u+aaa5KX7ewDIP4QDaWPXTy6SUni3hf4YR27aRtlQwAC1SCwY8cON3bs2FSBu3nzZnf11Ve7UaNGJZ7kE088MZkz+W9/+1ujAhLaxx57bOoHSRoJu7yCSO5yA1A8BCBQLQJ5RbKNzbPhDBKUJoJNPEtw+o8bbeiC4pS+aiGsU+hVrpq92AMBCHSHwKJFi9xnP/tZJ0FcNOgjJJMmTUqmi9O0cVUOiOQqtw62QQACEIAABCAAgYoROHTokLvllluSr+bt27cvt3Wt7pe7gJITIpJLBkp2EIAABCAAAQhAoN8JHDhwwN1xxx2FnoqtXr3aXXXVVW7v3r09gQeR3BPNhJEQqB8BfbFp27Zt7vrrr3df/vKXnYYCECAAAQhAAAKdIoBI7hRpyoEABAoR+Pjjj53Grl1xxRWpM0LYC3GFMiYxBCAAAQhAIAcBRHIOSCSBAAS6R+Duu++OimSbVq17llEyBCAAAQj0MwFEcj+3LnWDQB8Q0CwQsXl6NXNEFWeI6APkVAECEIAABJxziGS6AQQgUBkCGof8/PPPu9NPPz2ZOu3MM890//3f/z1AJEsY27RrWtp0a5WpBIZAAAIQgEBfEEAk90UzUgkI9AeBZ555xp188snuxRdfdJo/81e/+pUbOXLkAJGsmmou45h3uT8oUAsIQAACEKgCAURyFVoBGyAAAbdr1y53xhlnOH2JyYKE8syZMwcJYnmT+dCFUWIJAQhAAALtIIBIbgdV8oQABAoTWLVqlTvuuOPcxo0bB+wbjkm2r9YxHnkAJn5AAAIQgEDJBBDJJQMlOwhAoDUCEr2x8cWhSLZPJ2vIBQECEIAABCDQLgKI5HaRJV8IQKAQAYnhESNGuJdffnnAfqFIZjzyADz8gAAEIACBNhFAJLcJLNlCAALFCEgcSyTPmjXLaZYLC6FI1m/GIxsdlhCAAAQg0C4CiOR2kSVfCECgEIEDBw64yy+/PJnN4uGHH3aHDh1yO3bscNOnT0+GYbzwwgvunXfeSQSy5kiWR1mCmQABCEAAAhBoBwFEcjuokicEINASAb2UN2fOnEQojxo1yj300EPu3nvvdVOnTk1E8d69exORrPmRJZQJEIAABCAAgXYRQCS3iyz5QgACEIAABCAAAQj0LAFEcs82HYZDAAIQgAAEIAABCLSLACK5XWTJFwIQgAAEIAABCECgZwkgknu26TAcAhCAAAQgAAEIQKBdBBDJ7SJLvhCAAAQgAAEIQAACPUsAkdyzTYfhEIAABCAAAQhAAALtIoBIbhdZ8oUABCAAAQhAAAIQ6FkCiOSebToMhwAEIAABCEAAAhBoFwFEcrvIki8EIAABCEAAAhCAQM8SQCT3bNNhOAQgAAEIQAACEIBAuwggkttFlnwhAAEIQAACEIAABHqWACK5Z5sOwyEAAQhAAAIQgAAE2kUAkdwusuQLAQhAAAIQgAAEINCzBBDJPdt0GA6B4gQeeOABN2zYsEF/06ZNc/v37y+eIXtAAAIQgAAE+pQAIrlPG5ZqQSBGYPbs2W7Tpk2JIL7yyisb6/Pnz0ckx4ARBwEIQAACtSWASK5t01PxOhOQ19hEcp05UHcIQAACEIBAGgFEchoZ4iFQIoGzzz67xNyGnhUieegMyQECEIAABPqbACK5v9uX2lWEwL/92791zZKdO3c6/fkBkezTYB0CEIAABCAwmAAieTATYiBQOoFuiuRjjz3W/eUvfxlQJ0TyABz8gAAEIAABCAwigEgehIQICJRPAJFcPlNyhAAEIAABCLSTACK5nXTJGwL/JIBIpitAAAIQgAAEeosAIrm32gtrSyawefNmd8IJJyR/Wm9XaKdIvu666xrzHq9Zs2ZQFcLhFu+++64bP3585j6DMikp4sCBA27VqlXu2muvdRMmTEimoCsp645ns2/fPvf000+7qVOnuueee67j5acV+PHHH7vf/OY37ktf+pL7xCc+4b7//e872UqoFwEda88++6zT+aGXjrXt27e7xx57zGnu9htuuKH0Rmt3/nkMPnLkiHv77bfdz3/+c6eXunVOzhtk/4MPPuimTJnSFj557VA62XLPPfdUwpYidhdJi0guQou0uQjs3bvXLV++PJli7Mtf/nKhE0CuAkpKdOjQIXf99de7lStXujvuuMNdffXVTnHtCO0UybJX4ljCN3ayDUVyO+qXN08JuNdeey05qY4ePbpnRfLf/vY3d/vtt7tPf/rTyc1G7OYkL5My0+niqwuo+rWE8aOPPuouvPBCt3v37jKLIa8eINCrx9oHH3zg7rzzTjd8+PBE4JeNut3557FXDpnLLrvMHXXUUann7bR8dFw/8sgjbsSIEW3hk1ZuLL5KtsTsKyOuViL5/fffTy7OVbmgldGAVcxDQnPt2rXJwZ8m3Kpg9x/+8Ae3bt26xBSJi2eeeca99NJLbTGt3SJZ3iL9xUI3RbL6wlNPPZV4TXzbZGtVRfKWLVvc5z73Ofetb32r6QdW7AuG7Tyn/PGPf3Qvvviijy+5KfrUpz7lZs2a5Q4fPtzYtn79ejdq1Cj3/PPPN+KK1KexU84VvQC6bNkyp5sGC4oTOzFU2YTuEqjysZZGRh880vkh7ZyWtl/e+FbzTzuf5S3XT6fjRN7yVq6Rrdrvl9/Kul4Al1PJD92yxbehneu1Esl6zKu7U3lZJIp6NeiCHLtAdqs+sQNnKCeAWD1iF+NYuqrGtVMk2/CJNKHWTZG8aNEid/zxxw/yGFf5wl1EVLZbJNtwIJXjh7RzwMKFCwfdfBSpj19Gs3WJ81tvvXXQRR6R3IxcZ7dX+VhLI9Fu4dVq/mnns7R6ZMUP5RrZqv1Z9jTbpqdRZ5555qAbl27Y0szWMrfXRiTrhD5z5szk0ejYsWPdjh07yuTY0bzSLpAdNeKfhaUdOEM5AYT1SLsYh+mq/LudIln9Icsr202RnHaBTouvchvGbGu3SFbbDhs2zIUiOWaL4jrJtcxjPK0+xA+dQCf7xNCt/UcO7RZereZfJsuhHD+t2j+U9kkrMy1+KGVVad/aiOStW7cmL7LoZRZ5k+VVJgydQNoBMpQTQGhVmXmFeeukJxGiv6VLlyZeMcWVHbJEsjGUDXr8Nn/+/EzRG9ome20/q4vElYVuiGQNbbr44ovdMccckxxvJ554ohs3bpz71a9+lZhlF5snnnjCnXPOOUkaDRP45S9/Oegpj27E9PLZFVdc4b7whS8k6xr3rqdBeopx3333ua985SvJEJ85c+a4kSNHJn9333134THmetnpd7/7XTI+Xfar71lQeRs2bEhutr/3ve8ltsR4K/22bduSIQczZsxwp5xyipMtyluPa1955ZXkaZaGJKjtrf5iZMMkdGOoF2I++9nPJn3zuOOOS/jdeOON7q9//WsyhOWb3/xm48WdNN7/8z//k1of2Sm2N998c9JOqos8RfYCq+qrIUl6MVHnTH+bXtg566yzEs4aV6k6nnHGGU5DQ+S5njdvXnK+Vf38oN8aI61Pout9BY3LFCsL4q2+K2633HJL0qYqN7TN0ldx2SpT1WXXrl3JS2u6Tq1evdrJc6njQoz1smsrL2DqWDv66KPd7Nmz3emnn56w1FLDy8Inqmn9tihn/+VR9R0dk/7xqGPhF7/4hVOfj9XNzonhuTgtX+X3+OOPJy/BnXzyyclxpWNIceprOo78G820/FX/Sy+9NLHJPx7Tji87n8kurV9wwQXuvPPOc6eddlpy3Pl8ZaPOd5dccon7zne+0zjmhjLcQucOMbJzns4P7733XtJcevnR3pnQeVh96eDBg8n7N2KuP+3rD5VKa+f//d//deKqtlReOperHjoPG0s5IR966KGkvyrd+eefH30Xoqw+lmZr2fG1Ecm64KgRV6xYkZwkrrnmmgFj+QysOphOzhIdOvF/9atfbXyIQSfwu+66K2n8L37xi8lFUmNa1fn1mFMXasXr8bfi7r//fjd9+nSnC5yJlqyLpF2EdCLUCc06vn9y0TaN8fQvkDoQi4gF2bBkyRI3efLkRMjoYvfqq6+6N9980910003JG6vGI2uZdeCYsJXXXvbahc4/8VjeYpV2wky7GP/pT3+y3Vta2hAFOwnLXq3LI2tt5Wds9TFRlLZUv1HaMKSJZJ24fS+wxnLrBJSWT5iv1UP2KC+z0z/xdkMkm53GVCdSPyheNqvvaZvEp97A10wjuqG1oC8Fqu+oDykonXhdddVVyTGmC7146aQ8adKkRFhIpJ177rlJXNGbYZ30da7Qsee3gS6CeiFOwk7HiYKOIw3dUj38PiMbZZONd//1r3+dvGSzYMECp5eGLH+VoXOS7FUa1T18yqV8rW2TQp1z77zzTiKOVWfrv7Yt5J1WH6XXjBy6mGu8swTF73//++RCqJkxdJ757ne/m5zTdE4UZ9kr8aoLrUKsrykfaxO/Xyu94jVMTHVV0HGv+uuiK0Go4NdN8RpzrXOAXkBU+ZoJoBWhmGQe/LOLu/jqxlTt7bd5kDzXz6Ey1U2JjgnZpBtCiTzVXy8VK059p2hQn5BIVl4S8HqpWm0jnmoTC1n91hd7lj5tqfbR8WmiXn1eNnzjG99I2k43YRLpusapL+l6q7ppbLsFaxu/fzfLV/1JN9J+v5PdqrfyzxLJOpZ1YychqONRLHQ8Tpw40e3Zs8fMalwj/POZytC5QX1TdbXzgs67dg7Qcaibbl1fZaeCZrfQOc8/VzcKarJifCTK33jjjcRmHZuqpzSHHSMqX3ZoJgzZoKClfut8VKRdrUy/TZSfxas/SfPonK28dX7S8euXUVYfa4Kn1M21EMnqMLpo6oL51ltvJQdCeDESVR2w3/72t5M/dXTdPdqFV9vnzp3rvva1ryUHjTr65ZdfnohjbVNandz8Dq8Lq/ZRx7WLqH/R0gXDLpI6QaiT6c5PZeiiEbvY+xcR66z+hamZWFCH1YlW3gkdQPqtji0bdbetKWn8Tt2st9kBYrZYeruAKl+duHSil4dOJx6JHvFSyHPCtLx8tlZOK0sTlqHNOomWVUZoV0wkhwJZ+5ht/gk9zMv/bSLK+pe2hfWoqkhWH9y4cWOjOrpxU3+xi6X6oU6y/oXK+sKYMWOSPqWd1Y5hXi+//HIiTHVRKhqsDXzBpONRb5PLRj+ItX9867wgD4svJi0/q4f9lsfpww8/bGQn0aDj17zJ2mDtG/aHtONOLHyRoDysPL8+8ljK8xvWx4x5/fXX3UknndQQZbJT9vrHh7WFH2f7h3ZYef7FWmn1oqH6p5wREhgKVjeJLDsX6dwsphrfrvPiUINxteNGLyOJW8i5SDlWx6EwVXnWp+zGQXE6f6rPSwB99NFHRcyKCju7cbNzcZ5+m7dQ2W/5xvaRaNXxqrZX0DlAv/3zsfUBP65Zvsor7HeKs7b22zbMX31PfdCcZ+p36n/hsRTLXzf1uq7ZecsvU8e0rs86DymN7wDIOn6UR1YI7Vda6Rx5b3U+sj5o7apjzHhrqfYpOuQ0VqbKtXj/eNX1XWXYOU/pzJasc2NWnbu1rRYi+YUXXkju2NQp1GElTNWRwrc07WJy0UUXNbyBumDp7sc6tB6DKZ2CDm47ydr28IJhJzxLp/2sHP8iaReBPBd765T+CUT56nez/SWyTz311AF3lnYCbuWFxjRbjIduRuS9UDDRI7EhEaOQ54RpeYVskwxa+CdOsbwUHzJtIfvoLqFINm7+iVs7Kl5eSC3zBO3vix/tozi/flUVyeEFKLyY6UQrT4tuHtWP9JRGN7uKk1fK+pXaLMzL+LbSnnZ8Gte0Y9NY+yJZAk5Czh5JyvOsR6I65uRdU18O87d2jp0rQiaWNq1+MRax8nRBD88Vlne41HGrJ03qU36/yjouQztUj5jnW146XUjl6TSvW5G6hbbm+W35++dk4+zH5cnLT1MGU+UX6wexNvTLzloP20JpQ+55+m1WGbbN8vUFk22LLeWM0jC3cDozayM7fvPmG6urta24Wgjzt3hbSivIMxyeV2L5L168ONETcjLp3K3hSXpKq3U9IbXrq3+9VzlZx4/ZkbZMs199UOcjaRxpHQWL0xNpBTnJQg9vsqHJv7QyY/GxupXVx5qYWfrmvhfJOsFL/Nkdoghap/E7kuJ1pyPvsDqZOroe6csbrKB8NN5R2/SoSJO06wC3EOsU2lbkhBc7AGMdMBansvLsb/uaANB+QzkBW34q2w9FeNh+aSfMtLxsvyJLsze8GBqDML5I3llpQ5EsXn4b2L7qL7F42+4vjYt/8tf2MO9eFcnWVmHf8hlYfcOLWd59w7z02/qCtYP9DstQ2vD4jl2QwzIsP8vftod5KT4tv7T6iVVoZ6y8WDqzw5bqXxqepqdpP/jBD5Ixxq2KZKtb2JbWh/0bjSJ1M1uLLGVDaIc4+3Urkp+lLYOp8jJW/rko1oZWbrNlzC7jbk8u0vpZs7zD7WltF6aT111PWXXj+6Mf/Si5SfLbJMwn/B3mZ79jdY3VLZafrj9Kq5taaQMtw2Mpln8szuzR0soPj3drg1b6Xcx+vyz/iYMEv5wMeoqjdXmb5TgsGtLKjMXH6mYc1L97KfS9SLYOopNw+Bc+/lDDyTslb5Wl1bp5rPQ4Q+P0dGLRdolle8kl1imUX5ETXuxgi3XAWJzKyrO/eZI19kpDTxTscVE7PMnhCSDGo9kJM41tYnzBfyo/tElZKD48IfpZmw3WL9KW4YnQ8vBFsl3wVKYfLF7tmCeoH4ReZ8tDJyQLvSqSzQMTPqK3etkyT7+3tHmWxtDa0sbw6bj3uSqvsD/bMI/wBtwvN8zftoV5KT7twlLkHBArT49/1YfDp2lmi855elwqEaMx2Nb//WMnFmf7h21ijgn/4q20lofv1S5SNysv7zJ2zGhf2WvtnTevMF0ZTJVnrB/E2jAsP+132BZKZ8NnbNhSnn6blr8fb97CrGNWfVpPh8RLjqlYe4dxefKVHbG6xo6hMH/1Qz1Bliaw911iecXiNKQi61jSExI9KdHTJF1/LVjf948p29ZsGdpv6TVER7bIJgvyKMtJKG+9xt7rxVkbs2xp8izTyozFx+pWVh/LY2uZafpeJGtsTjg+yjqNOpON3fGhymusN9AlgpUmFI96O1OeZm2zE2usUyjPIie82AEY64CxOJWVZ3/VTS8Z6IKvA0YCQCcrTfyvfIuGNFvy8shzwkzLq6itxsjazPa3k2gYb9vLWPoi2ZipXAtWR/UpP962x5bqW6HN6gNh3FBEso4VPZrTCVYvtvhPT2I2hXGyxxdAtj3WV60dVC8Fncj1yFNl28teilcf1phZe5wYy8sYa1vREAoSladzgNpGQyZ8BuHxbTfluuHSMC0L2kc2K4T5W5owL8UbE70Y7Ie0+sVYxMqzOePlVfIvmHqsrfOblWuPza1/+hd0i/OHVJmNoR3KU+cYvbirF40sSIxrf/+FvCJ1s3zyLsXYr4P2Mz7W7/LmFaYrg6nyjPUDszE8tkMbYr/DtlAac4zo3K/jKE+/jeUdxmUds3Ioqc/IHh1LNuY61t5hXJ58ZYvy1vnChvMpzvqy375h/vbbHxIR46a48HyW1e566dUcU7rm2gvIssuOn7A/hkxjv81e2WNB5ymdq2POHrNR3GOax/LIWlqZdk6wtBbv2xKrW1l9zMrt1LKvRbINFI+9EazHDTqY/JOzDia9dKP9FHQy10ldJ6Y//OEPyeMXe+FMFxO9YGcd3DqF3ZlbAxY54cUOylgHjMWpvLz764SjaXE0/ZLeLNa4YHtpxuzOuzRbwgPHeBgfyy/kIZubnTAtr9jF2PLNu1T5/klEv9W+sqlOMbMAACAASURBVFM3DRof147gi2S74NlJRb81hk1tIjvk3RNXBfVJveApT4A4WDAmst+C8gt5a9tQRLJOvHpjXx5r5WMvf1iZzZYaB6f2/fGPf5yIRs2koDzVX/x2UD7mBfEFoc2qoOmKNFWZ2Mjjo7racar1MK/Yy0DNbLXtJtz8C6Yu8PIyqS568UTtowuP3UhrWIKC6mY3oRqXrPrr+PrP//zPZKo6CRJr/1DwqN7KX21uwbxQ6h8qU/VXva1+/nFnXMOLeKw+OgfIq6vy1Gc0e4TGVuplPd2Q6NPhqq/+NLTMnxFBb67LiaC6yGOui//DDz+cfK1SnGJ2+Fx0ztFNg+J0wVb/9uts5xQ7PoxrrM8Yp7xL5RlyV1zIPW9+froymCq/8BypOGvD0Ha//LR1q5+mStTwQZ079ERU3l7lq+C3T1q/Tcs/jPePWQ3TUZ/Vy9vqb3LKqM3FWzdoupFUf1Af0rsGGsOrWR9i/btZvrLDnljoCbD6kY5LPTVVebrBVX3FIMzfXjSTh1t56Fykc57s0nCQp59+Oqlm7Hzmt7vOB9pfrPVirGYrUtD0a8pL+f/0pz9NblKkS8Q6vHFMdmjyz44RMbObTp1bdSMqvmpPP5hQ958g+9vzrNukB7JXekjnP+kGY+kfr/akwr9ml9nH8thbVpq+Fsk62eviaS+E+NDsEaqEso3PUcfT4HvzWtndtk5admHTTBBqbDuo7E5cedtjF03Xo32VVuXrANXBpX20r53w/Iuw4nURCC9w1gH9i2EsTuWrkzYTC3p0qgNLgkdzGurg158uUnYD4HNqtp524NhBEoo2EwLmRchzwky7GDezLbbd2lFtoj+/bUN2sf1bjfNFsvKwC6FsMEYW559sNB2XnUjDfmwnSquLv59v51BEsuWj9tJJ3p95wbZlLSW2dOGQyNVFSo9Nb7jhhuRiIbs13lXCShcWcVCcZnjRRUYvzOm40MXRxKhEm/qthKLm9wzzkn36U77KS+x++MMf5poLVPWQLTouVVfZLEGsi7aCplnUb13oND3XI4884n7yk58kZeiY0rpslgBUv9bFRDYoreZQ1cVZ+WsWHMtfTORhVn1tTlNxEA8FCRrdICm9nojps+maJcbqJ1vEQNMu+SyUh84/f/7zn1PrIy+X5lVVHspfT8dkn4K4a85qnY/0J+YSO1qXV11eIQXZI7uVh85/ihdvcVfd1W6y1/LUxfXrX/96Yr+mxNKNobzMFpTW2traTvz9PFX3ov3Q8tcxZseb3WjquFGczoEmaix90eVQmKofqA+JsdhZPwj7pPqM9ck89kk8qU+Lp0SUXpSUGLWbTMsjq99amjzL8JhVfSQMrTyJSl3PdHypT2vqQbWvjm0dUzrnWR9Qv5KgV32b5Svb1Ka6mdZ+uuHTcSXvrfLWdVlTuPo3t37+6lM6Zq0vyxut37op13lM5YfnMzsO/HZXvXQD4Pdrs10v/ktzaLzzb3/726RdpDl0E2zHSR7G0i933nlncm75xCc+kQzl0I2IX6afj8oXc//dLH97nnVdh6VjVD9x0flAN9DWVupfcjSpH6uPKp3OK+p7dl4pq4/lsbesNH0pknXxVCOps9tFShNrW9ABp4udGlHblU4XGInX2267LTmgdCcq748udmpYdRAdcLoT00lanVwHnA5KCzpQ9IEAHQQafyQPkk4OukjqRKwLjTqVf5FUvOzxL3B2EdBBoxOlbLQLhk4gzS6Qtn9MLOjgEgvlp3z9P3VoecF0QOUNsQNHd7bGV3nqYpgmBJqdMI1veDFu1fOdt15lpwtFctH85eULRXLePIYqktX/5e1Rv2rlRiqvnaSDQLsJ+DfJdlNsN6eteGnbbS/5D53A3//+9wFDpIaeY+/loOtsqy/s9V5ty7W4L0VyuYiGlpvunm2GjKHlVN7eemSuqakkuiSIZZ8Ete62/XkNyyuRnIYikuUlvOOOOxqemKI0hyKSdYHR1+5006mbQAIEIAABCPQWAT0JDN8/6K0adM9aRHL32HelZD32kBiWh9wP9jgGkexTKW+9VZGsz/xqPJt51FuxaCgiuZXy2AcCEIAABKpBQE4WzVITezerGhZW2wpEcrXbp3Tr7NGixhP5QR5vvbSouaCLDLfw82A9nUCrIjk9x/xbEMn5WZESAhCAQL8Q0BBSjfu2oUX9Uq9O1gOR3EnaFShLQy0kmvTmrl7o0HhTjTPVG7waT62xS4TyCSCSy2dKjhCAAAQgkE5AIlmf2/Zn8UpPzZYYAURyjEqfx+kNbr08qBcX9acXsp588snav9zQzmZHJLeTLnlDAAIQgAAEyieASC6fKTlCYBABRPIgJERAAAIQgAAEKk0AkVzp5sG4fiHQTZGs6QU1xy8BAhCAAAQgAIH8BBDJ+VmREgItE+imSG7ZaHaEAAQgAAEI1JgAIrnGjU/VO0dAH7ghQAACEIAABCDQOwQQyb3TVlgKAQhAAAIQgAAEINAhAojkDoGmGAhAAAIQgAAEIACB3iGASO6dtsJSCEAAAhCAAAQgAIEOEUAkdwg0xUAAAhCAAAQgAAEI9A4BRHLvtBWWQgACEIAABCAAAQh0iEAlRfLHH3/sfvOb37gvfelL7hOf+IT7/ve/3/Rzydu3b3ePPfaYmzZtmtO8sAqxuA5x7VoxR44ccX/4wx/cOeec4/7f//t/7oILLnD6NGUvhL1797pf//rX7rrrrks+pfnuu+/2gtnYCAEIQAACEIBAHxKonEiWyHvwwQfd9ddfnwjjRx991F144YVNhd4HH3zg7rzzTjd8+PBEZKmtYnF92IYDqvTMM8+46dOnuz179rhnn33WTZkyxW3ZsmVAmqr+OHTokHv66afdCSec4MaPH+8QyVVtKeyCAAQgAAEI9D+Byonk9evXu1GjRrnnn3++MP1Nmza50aNHN0SyMojFFc64wA6HDx92s2bNcp/61KfcmjVrCuw59KQ7duxwY8eOdYsXLx56Zl3KYf/+/cnTAERylxqAYiEAAQhAAAIQSAhUTiQvXLgwEboSt0VDTBDH4ormWyR9N0Xy6tWr3bBhwzouzovwaZYWkdyMENshAAEIQAACEOgEgcqJZI1HlTe4V0VyJxotrYwHHngAkZwGh3gIQAACEIAABCBQgEBlRPL777/vLr74YnfMMcck44pPPPFEN27cOPfkk08m1Xnrrbfc1Vdf7S655JJknO3Xv/715AU1jWG2EPMax+KUXh7L++67L3nB7Vvf+pY7/fTT3S9+8Qt34MABd/DgQTd//vzEFnlmZYteClRQfl/5ylechjb46TQW+tvf/rZ79dVX3c9//vMkPxtuobK0PmPGDHfLLbe4tWvXujPPPDMRtFpu3rzZqpAs33vvPXfzzTe7s88+O6mrXlzUGOMXX3zR3XrrrUm5/g6yWWO4jzvuuCTPz372swm7n/zkJ0myrLoqgRj+5S9/SXiobr/73e+SthgxYoR75JFH3K5du5L660VKeasXLVqUDIkZOXKku/vuu93f//5398orr6TWacOGDW7mzJlOdknIKyjuxhtvTDhpDLVsVNBSL1+Gwy1UR7WP2uKoo45y1157bdOXOZMM+QcBCEAAAhCAAARaIFAZkWy2xzzJElR6mev+++9PBJ1mv5A4k1iSYDOhHBPEsbh9+/YlL7edf/75DaElkXfssce6Sy+9tBFnnlmVZeGee+5JhOjKlSuTKJUtwXbTTTc5DbXQzBJnnXXWAI/uO++8k8y4ISGtmwCNWdbMG3opUUJTYlg2KehlQ90ATJ06NVlXvOxUXSXk//SnP5kpg5Zmr4lzJchTV9mtF/50UyJhLNbnnntuMq5afP06nXHGGW758uXutddeS+xSnU499VR32223pdZJjB5//PGEiYlk2SYGEr0SxVkiWTcRqvvs2bOTGwTdaOjmZdmyZYMYEAEBCEAAAhCAAATKIFB5kWyexZNPPtnJm2zBXlI76aST3Ouvv55ExwRxLM7EpAld7SyheM011yRebAk6BdvXRJwEpwStBJq8wvIky8MrUfzCCy8k++if5e+LVctLgtpEvfZXPscff3xjBgrtI+HpC3OJQcX5+TUK81Zi5Vpcs7oqG92gqG4LFixo2GjZWz7yJFt4+eWXE1HdrE5KL9uVt/KxoNkr5DE2voq39vY9yWoPvcyplzoVNm7cmPyWvQQIQAACEIAABCDQDgKVF8kmLn0hJRAmMCW8TABaWl88hXEmwmLjniVGlZ+GBkg0W1p5Vrdu3erWrVuXzN38uc99LvG2Wpy8vhLLFkxQ+qI2tMPShp5z29cXkzGBafv7S9vXyjX789RV+cgWiVGJ0DCEeWt73jopbawOeUWyb4umiVu6dGkizv129tOwDgEIQAACEIAABIZKoPIi2cRVKJJVcYkk3zsZE21hnAmzmHCMlWXiUMJMwyT024ZcaF1/GgbgB9vHxKq2hXZY+lAkax95jU2oK92SJUta8iQXrWtoi9mo5VDqpP2NrfKxYPb5bWvC3vckK73GRc+dO9d98YtfdD/60Y/c0UcfPWCqP8uTJQQgAAEIQAACECiDQOVFsj3SnzBhgtPLfX4wkWxDAGJCNIyTx3fixImJ6AznYjYh5w8f0CN+jVX+r//6r2SohbzH+pN3Wfnoy3ay0Q9DEZQ2hlgi/ve//7174403EmHoj5X2y/LXw3KL1rWqIlntorHbGvetF/jCNvUZsA4BCEAAAhCAAATKIFB5kSxhPGnSpMRz+H//93+NOn/44YfuvPPOSz6eofHJCjHxFMZpPPCcOXMSD/S8efMGjL3VHM3y4q5atapRjj6VrK/W+cMwJNQ0y4biJJT9oRbaMRSrabYpPiZMNUOG8tU2eak1q4WGGTQLYblF6xqzxcoM81Z8yNbSxvKxGxDf657Xk6z8xDrrZsjKZgkBCEAAAhCAAATKIFApkSxRJy9uOC5WMy/Ik6ipwuRpVZCXVTNFaIoyC/ZCl+8JjsXt3Lkz8c7KG6yZMxQ07ZqEqaaD0yN/P0jYheJZQlpxvuizfSS2fVGn+JigtPr6Qz80vlp1lS1a12ea9adp4zQOOyvEys1bV7MlZG/lxfKOsU3LRzNZjBkzJvHA//rXv07Gd+tz4+KkoRV//vOfk/r5Nz+7d+9OitdwE6XTLB9qL81uIfZ6uqBp4d5++20zkyUEIAABCEAAAhAohUBlRPLf/va3ZJo0CUQTTpryzYThtm3b3GWXXeZOO+00d/nllzsJLE1NJlGmoLl9NU2Y9lUe3/3ud5OpysI4E1QS2/IkS6DJK6xhEzZPckhWwykkyMxjre1aV5w/q4Vs1dzLn/70pxM7bH5l3zYJ+x/+8IeJsNNSv2WzvOUa/iG7ZLtEoOL9P1/U+zaqXM2JLIGr9Cr/9ttvd2Kq0KyuSufbImbGXts0BtjyFi/VJ61O8vpqujq/TrJB7aQ5r1UH1fmqq65yejKgMcZqSwlf5anZPrS/6q9ZQ4yJbnwUr3mldYMke5WXbpLCmxqfDesQgAAEIAABCECgFQKVEcmtGN+P+2gO6AcffNBddNFFjTHYEoGali3Nc92rHFRXDV0hQAACEIAABCAAgaoRQCRXrEX08Q4NS9DLgX7Q0IOxY8dGh3f46ViHAAQgAAEIQAACEBg6AUTy0BmWloNNfxZ+OEUFSDSfcsop7qWXXiqtPDKCAAQgAAEIQAACEIgTQCTHuXQt1uZgvuKKK9ybb76ZfNREn2XWDBv+J7i7ZiAFQwACEIAABCAAgRoQQCRXrJE11ZvEsD63rZff9JKbXljU7BgECEAAAhCAAAQgAIHOEEAkd4YzpUAAAhCAAAQgAAEI9BABRHIPNRamQgACEIAABCAAAQh0hgAiuTOcKQUCEIAABCAAAQhAoIcIIJJ7qLEwFQIQgAAEIAABCECgMwQQyZ3hTCkQgAAEIAABCEAAAj1EAJHcQ42FqRCAAAQgAAEIQAACnSGASO4MZ0qBAAQgAAEIQAACEOghAojkHmosTIUABCAAAQhAAAIQ6AwBRHJnOFMKBCAAAQhAAAIQgEAPEUAk91BjYSoEIAABCEAAAhCAQGcIIJI7w5lSIAABCEAAAhCAAAR6iAAiuYcaC1MhAAEIQAACEIAABDpDAJHcGc6UAgEIQAACEIAABCDQQwQQyT3UWJgKAQhAoFsErrvuOvfAAw90q3jKhQAEINBxAojkjiOnQAhAoF0ENm3a5EaPHu2GDRs24E9x2kZojYDEsZgiklvjx14QgEBvEkAk92a7YTUEIBAhsGbNmoaQk6AzUbd06VJEcoRXkSifZ5H9SAsBCECgVwkgknu15bAbAhDIJICoy8RTeCM8CyNjBwhAoMcJIJJ7vAExHwIQiBPolqjbsGGDe/bZZ+NGdTn2iSeecLt3727Jim7xbMlYdoIABCBQAgFEcgkQyQICdSdwySWXuHvvvbdSGLoh6iSQ582b5w4dOlQpFmbM+++/72bPnu327dtnUcny3XffdePHjx8wjltjkP2x3N3gOcBIfkAAAhDoMAFEcoeBUxwE+pFAN0Xyo48+6vQXhk6Luv3797tbb73V7dq1KzSl8G/NJBG+fKjfih9qeOmllxIhf+TIkUJZtYNnO+tZqHIkhgAEIBAhgEiOQCEKAhAoRqCbIvn88893ixYtGmRwO0TdoEK8iKeeesr97Gc/82JaW5XYlniUd1d/06ZNa6wvWLCgtUy9vQ4cOOCuvvrqwi8yls2z3fX0qswqBCAAgZYIIJJbwsZOEICAT6DuIlnDF775zW+69evX+1iGvO6L5CFn5mWwbNkyd9NNN7nDhw97semrEsjm2dZ62aFd9SzbTvKDAATqRQCRXK/2prYQaAuBqolk/zF+GUMUmkF7+eWX3VlnneX27NnTLGmh7e0Sj1u2bHETJ050b731ViF72pW4XfVsl73kCwEI1IMAIrke7Uwta0xAQxGGDx/uLrroIqdH3O0IVRPJ7ahjVp56Ge7aa691Rcf5ZuWpbe0SjxLzEskrV65sZkJHtrernh0xnkIgUFMCekH5vvvuK/RUSu9snHvuue6VV17pCWqI5J5oJoyEQGsE3nzzTXfppZe6tWvXuqlTpzqNm21HaJdI1sdBmj3mTxuT3I56xvLcu3evmzJlilu4cGFs85Di2iUeDx486GbMmOFmzpyZe8jFkCrSZOd21bNJsWyGAARaJKChWhLIZ555ptu5c2ehXJ555hk3ZswY99xzzxXarxuJEcndoE6ZEOgAAZ3EVqxY4d57772kNHmR5VVudZ7cLJPbJZJVpgTU5MmTU18067ZI1tCF448/vqlX1h/Xa8Lflno5L+blzyMe/aEllp8ts4aaaEyyvMllDxFJ+zS4bPKnlPP7U1o9xURsrD5aGiv/Biorb78c1iEAgXII6PjT8azZcvyg9x3849XWlyxZ0kimJ25z5sxxX/ziFwsL7EYmHVpBJHcINMVAoJ8JtFMkS1xqDl8JqVjotkg2saZls2AC0n/5zeJidUwTj2E5MRsszkRluI9skLiXyC87mLj1y7Y4XTRDVs3qaTcYsf3EzedZdl3IDwIQGEjggw8+SJ5M6ryv2XL8cPfddzudk59++unG329/+1unJ25+2Lp1qzvhhBMSsVz2MDW/nKGuI5KHSpD9IQAB106RLG9olke02yJZAm3UqFFu48aNTXuCRF7Mm2reYF8EmnjO4yWVDaHINlEaK0+GLl68OBmr/vzzzze1u2gCid6YeFX9VB+/PfPUM5af1c9nVtRO0kMAAsUJvPDCC27EiBGDnp5J7OrdjDw3rXrSqeFep556qnvnnXeKG9GhPRDJHQJNMRDoBgFfgOjEJXESiqky7MoSyUOxwRdHst8e3fnCqNsiWZ6TNCEaslUdfO+qtpvYG0q7qF194al8jV1YntlkgnX16tUWVdpSbT5u3LhBQ2SsDf32y1uoX0djpvwIEIBAZwnoReXYUyg7LvMe37pRl9jW7EBVDYjkqrYMdkFgiARMBNkJa+nSpYlwCcXUEItJdk8TyUO1wcSWBJcJItnvC8pui2TZk0ck2wXE6iFwFpdn/7R2MjFs7ax0FudzCve3tvHtCdO0+lt5huJccbrJabU8P09fMLdqI/tBAALFCdg5a8KECU6fufeDzjtnnHGGO+ecc9wxxxyTPKmaNGlS8oJebEiFnmJp5qVWzwl+2e1aRyS3iyz5QqCLBMx76wunZqJIwsM8tWnLNNEVE8mt2BAiM2EV1sMXlWWIZGOTVm+L9+0wW/OKZONheWnp18PyK7qM2Z7WTn7etl/ZFyi7iPr11PpQyxE/vcApL1YowP16sQ4BCLSPgISxBHLsGNT0bppB6Y033kj+7rnnnkQsjxw50mlGizDYOVEvEVc1IJKr2jLYBYEWCZhIkXjzg0RRGaLMz9PWQ5Fclg0xj2FYjzJEstWjlWVekSy7Q/GqfYcqICU+/QuWsVe+KjMtaNtQy47lbV5sv2wry7cztm9WnOUbMszah20QgEC5BOw4zHssSzTLWxxLbyI5vFaVa/HQckMkD40fe0OgcgQkSGJiWGKqXQIjFMll2GAnY19sCXZYj14RyboQhBcKE7Sx9srTsWz/8CJj7LLa24TrUD28oZ1ZbT8UUd4ue0P7+Q0BCKQTyPIkx/bSVz1PPvnk6LXHRDKe5Bg54iAAgbYQiIkxE02hmPIN0DaJmKy/NNEViuRWbfDt0Qk0fPnLRKEv7MoQySbAsuqubUoXhjwv7hl/327LR6xaFcl2kQntMk5p7aWyrc5lv7gXa3u/vBgDY5G1VL5Z9cnal20QgEA5BPKcW/ySNC//2LFjk48X6SNGfrBzUKvnBD+vdq3jSW4XWfKFQBcI2AlMgsIP+i2R166TkS+Sy7JBtoaeV8WFQqkMkeyzKrqe5w1tXQxiQthEblinvDbEeGhfu/iE/Px89UlqPQYtcwq4tJsB6xNpNxq+XbF1yzfs17G0xEEAAu0lkDa7hT5T/fe//31A4Zou7lOf+lTUwZDn3Dkgsy78QCR3ATpFQqCdBEKPm37Pnz8/8cpKPC1YsKD04n2RrMzz2iAvw1e/+lV3+umnu9dee22AXcpDfxYkCGNCs9si2d7QFttYMIEYCmETskMVjqEQFiflGWPl26d0sWmc/DRF161sn4UJXNnkt2eRvLVfq5yKlENaCECgOQGbJ1lf17Pw8ccfu+9///vu05/+dDJ/ssTy5s2bk/P7Y4895sLZLeRVnjFjRvJZ63CWDMuzCktEchVaARsgUCIB805KVJiwMEEWCrWyig1Fcl4bdu7c6U477bRErIXi3RdXqkcoBs32bovk7du3uzFjxiQf5zCbbGmi0doiXKbVyfZPW5poDPOz33nEqLxBZX2WOmxvs8OWzQR7Wj1j/FplllYG8RCAQDEC+/btc2effXbyESn/i3tr1651mvJNT6iOO+44d/3117vXX389mrl9cU/n/VBAR3foUiQiuUvgKRYC/UQgFMlF66av1d1///1Fd0vSd1sk63OrU6ZMcRqb3CvBvnalL15pnQABCECgCAE5XnTz6z81yru/RPGcOXMSL7KeJlY5IJKr3DrYBoEeITAUkaxxbBoOsm3btpZq222RLKPlle0lwWnCXuOSCRCAAASKEpDQffDBBxOhqyeCRYLmTNaMFxs2bCiyW1fSIpK7gp1CIdBfBFoVyXv27Ek8yJp8vtVQBZGsz6qeeeaZg75A1Wqd2r2fhojowxyanokAAQhAoBUCGof8yCOPuB/+8Ie5n0jpgyMXXnih09PDXgiI5F5oJWyEQMUJtCqSy6hWFUSyxujpxL9u3boyqtT2PORBvuaaa3Jf2NpuEAVAAAIQqCABRHIFGwWTINBrBOouktVeq1atSoZdVPklFNmpMciavH/9+vW91s2wFwIQgEBHCSCSO4qbwiDQnwQQyc7pLW+Jz1bHVneqZ8jbPXfuXLzInQJOORCAQM8SQCT3bNNhOASqQwCR/I+20AssmuVCLyNWMWhYiF4yrPK8pFXkhk0QgEA9CSCS69nu1BoCpRLopkgutSIlZLZly5ZSv2JXgkmNLJYvX+6Kvone2JkVCEAAAjUjgEiuWYNTXQi0g8Af/vAHpz8CBCAAAQhAoF8IIJL7pSWpBwQgAAEIQAACEIBAaQQQyaWhJCMIQAACEIAABCAAgX4hgEjul5akHhCAAAQgAAEIQAACpRFAJJeGkowgAAEIQAACEIAABPqFACK5X1qSekAAAhCAAAQgAAEIlEYAkVwaSjKCAAQgAAEIQAACEOgXAojkfmlJ6gEBCEAAAhCAAAQgUBoBRHJpKMkIAhCAAAQgAAEIQKBfCCCS+6UlqQcEIAABCEAAAhCAQGkEEMmloSQjCEAAAhCAAAQgAIF+IYBI7peWpB4QgAAEIAABCEAAAqURQCSXhpKMIAABCEAAAhCAAAT6hQAiuV9aknpAAAIQgAAEIAABCJRGAJFcGkoyggAEIAABCEAAAhDoFwKI5H5pSeoBAQhAAAIQgAAEIFAaAURyaSjJCAIQgAAEIAABCECgXwggkvulJakHBCAAAQhAAAIQgEBpBBDJpaHszYweeOABN2zYsEF/48ePd++++25vViqn1WvWrBlUb2OhbQQIQAACEIAABOpLAJFc37ZPai6RrD/Cvwhcd911DpH8Lx6sQQACEIAABOpIAJFcx1b36twOkbxy5cqGF1reaHmlR48e7TZt2pSUvH//frd27VrPimqtIpKr1R5YAwEIQAACEOgGAURyN6hXqMyyRbI8sL5n2gSnBPKVV17pJJAVlKaq3lqzuULNhCkQgAAEIAABCHSYACK5w8CrVlyZIlle4wULFjSqqN8SnBLG+pNINm+yEiltFcc9I5IbTcgKBCAAAQhAoLYEEMm1bfp/VLxMkSzPsO8dDr3HofgM02c1xdtvv+0ee+wxd/Dgwaxkg7Y98cQTbsuWq2vq2AAAIABJREFULYPisyJCO7PSsg0CEIAABCAAgf4kgEjuz3bNXasyRfLSpUsHeIolkmfPnt2wJRSf2q59moXNmze7e++91x06dKhZ0kHbtc+8efPchg0bBm1LiwjtTEtHPAQgAAEIQAAC/UsAkdy/bZurZmWKZAlifzhFHpHsi+iYwR988IG79tpr3a5du2Kbc8W9//77bubMmW7nzp250iOSc2EiEQQgAAEIQKCvCSCS+7p5m1eunSK52ZhkiWj/Zb6YtbLvnnvuiW1yf/zjH93UqVPd8OHD3ciRI93VV1/t3nvvvWjaJUuWuFtvvdUdPnw4ut2PRCT7NFiHAAQgAAEI1JMAIrme7d6odTtFsgox73JMEIee5oZR/1zZsWOH+9KXvuTWrVsXbnIagjFx4kR33333OU05d9FFFyViedKkSU6e4zBs377dnXnmmW7r1q3hpkG/EcmDkBABAQhAAAIQqB0BRHLtmnxghcsUycrLf3FPJcmbHM6TbBZIJGeNSV62bFkihPfs2WO7NJaPP/64++tf/9r4feTIkWS2DH0xb/Xq1Y14W/nwww/deeedl+qVtnRaIpJ9GqxDAAIQgAAE6kkAkVzPdm/UuohIlqjVR0FMCNtv+1BIkdkqZEBWes1iMWPGjOQv74wWGzdudKNGjUo8y40KeisSv1OmTHF79+71YgevIpIHMyEGAhCAAAQgUDcCiOS6tXhQ37wiWenkpdWfRKQEcjieWHMhZ3mGg6Iz50nWkIkJEyYkZYX7pf2WSD7ttNNSh1SoDscff3zTKeEQyWmEiYcABCAAAQjUhwAiuT5tHa1pXpFsO0tASihPmzat8fU826blq6++musDIRqGobRpwbzUsi9v0Mt5c+bMcRp6EQsaviHbzRMeS6M4RHIaGeIhAAEIQAAC9SGASK5PW0drWlQkm3hNE5oSvxLQWqYFeZwlRLPSKH8J2rwiWR8bUZ6aMi4tWJ6LFy9OS5LEI5Iz8bARAhCAAAQgUAsCiORaNHN6JYuKZAlcieC84jW95OwtJmjzlHPgwAF31113NZ0HOW+eiOTstmErBCAAAQhAoA4EEMl1aOWMOhYVyWvXrnXjxo1LHW6RUVShTXkFrb6opzq8+eabTfPPmyciuSlKEkAAAhCAAAT6ngAiue+bOLuCRUSyhkcsWLAgGdOrad2yhktkl9p8ax5BK4G8aNEi99ZbbzXP8J+zaWgIB8MtcuEiEQQgAAEIQKDWBBDJtW5+l3hhmw1pkGdVaSSQJYz9ccmKl6AtO1gZCxcujGatYR/6gp7Kf/rppxt/mj/5lltucbt37x60n+ZP5sW9QViIgAAEIAABCEAgQgCRHIFSpyiJTP1lBYlkX1zauOQiL9Zl5R/bljUFnD4i8s1vfjOxSTaEf2mfsVY9mQIuRps4CEAAAhCAAARCAojkkEjNfucRyd1AcvjwYTdz5kw3ffp099FHH5Viwk033cTHREohSSYQgAAEIACB/ieASO7/Ns6sYVVFsoxeuXKlO/XUU90777yTWYc8GyW0JbjTvMx+Hry459NgHQIQgAAEIFBPAojkerZ7o9ZVFsm7du1ykydPduvWrWvY2+qKXu77yle+kvo1Pj9fRLJPg3UIQAACEIBAPQkgkuvZ7o1aV1kky0jZN2vWrNSv6DUq0mRl1apVyQt9GsbRLCCSmxFiOwQgAAEIQKD/CSCS+7+NM2tYdZG8b98+973vfc9t27Ytsx5ZG5XHzTff3PRjI5YHItlIsIQABCAAAQjUlwAiub5tn9S86iJZRu7cuTOZ7k1it2g4cuSIW758eTJtXd59Ecl5SZEOAhCAAAQg0L8EEMn927a5atYLIlkVefvtt91jjz3mDh48mKteluiJJ54oJJC1HyLZ6LGEAAQgAAEI1JcAIrm+bZ/UvFdEciebCZHcSdqUBQEIQAACEKgmAURyNdulY1YhkgejRiQPZkIMBCAAAQhAoG4EEMl1a/GgvojkAAjDLQYDIQYCEIAABCBQQwKI5Bo2ul9lRLJP4x/reJIHMyEGAhCAAAQgUDcCiOS6tXhQX0RyAARP8mAgxEAAAhCAAARqSACRXMNG96vcDpH87rvvJp+UtnJUxrBhw5JZIyxOaV599VX7WaklnuRKNQfGQAACEIAABLpCAJHcFezVKbRskbx///5EDEsEK2zatMldeeWVzuLXrFnTqPzs2bMLT8/W2LmNK4jkNsIlawhAAAIQgECPEEAk90hDtcvMskXy0qVLBwhf5W/CWEsJUAsSzvPnz08EtMVVYYlIrkIrYAMEIAABCECguwQQyd3l3/XSyxTJMdHrC07fq2wVD0W1xXdz6dvcTTsoGwIQgAAEIACB7hFAJHePfSVKLlMka4jFggULBtTLH1IRE8nyLpunecCOwY+PP/7YrVixwm3ZsiXYkv5TX+mTCD906FB6osgWRHIEClEQgAAEIACBmhFAJNeswcPqXnjhhU5/ZQSJYIliP+QRyRLqWUEid+HChQOGcWSl97dt2LDBzZs3r5BQ/vznP+/uuusuPxvWIQABCEAAAhCoGQFEcs0aPKxumZ7kmEhW/uYpDscky5ZYXGjjU0895R566KEwOvfvZcuWJfsfOXIk1z54knNhIhEEIAABCECgrwkgkvu6eZtXrt0i2RfOMfEpkZzlSd61a5ebPn2627Fjx6DKaDjFBRdc4I466ig3cuRIN2fOnOhLgO+//747//zz3ebNmwflEYuI2RlLRxwEIAABCEAAAv1LAJHcv22bq2ZlimSNSZbA1At8flAZ4TzJtl0iWX9p4Z577nEzZ850hw8fHpBEwvcHP/iBW7dundu5c2cyPEJiee7cuQPS2Q8N+5g1a5bL401GJBs1lhCAAAQgAIH6EkAk17ftk5qXKZJjs1s0w5s1u8WePXvcxIkTnYZLhEEe6vfee68RfeDAAXfJJZckXuePPvqoEW8rq1evdmPHjo16pC2NLRHJRoIlBCAAAQhAoL4EEMn1bfuk5kVFsgTktGnTGt5i/fa9xGvXrs39gl0zUf3yyy+7Y445xmnZLEhQT5kyJZnNIpZWonr06NEDvgQYS6c4RHIaGeIhAAEIQAAC9SGASK5PW0drmlckayjF+PHjE0EssSnRGROTEr4SynnCG2+84fSXFhYvXpwIW5WVFjQ13GuvveYuv/xyp6EZadO9mf033XRTWlaN+Fi9GhtZgQAEIAABCECgFgQQybVo5vRK5hXJloN5ZOU9ThtLnCfPtPHLVo6WEqsS5kqbFpRGtujv9NNPTxXoNnTD94Jn5ZlWt7R9iIcABCAAAQhAoL8IIJL7qz0L1yaPoA0zlTDNIzbD/Yr8lkdaZTQTycpz3759bvny5YnX+ZRTTnFvvvnmoKIsvwkTJji99JcV8CRn0WEbBCAAAQhAoB4EEMn1aOfUWrYikuVlzSNeUwvNscFEbZFy9HLeiBEjnJZhKJIfIjmkx28IQAACEIBA/Qj0tEjWjAarVq1y1157rZOHMGvsav2aNl+Ni4pkiU2JSI1LbueQhCKi1mpq444RyUaEJQQgAAEIQKA9BLZv3+7OPvvsQtpLmuP6669vvPzfHsvKy7WnRbK9tKVZDexlsvLQ1COnoiJZU7bpxTwNhdC+7QqtiGS9BDh58mS3bdu2QWZZfgy3GISGCAhAAAIQgEAhArre6j2gBx98MNf3ByxzDY/UB8KuuuqqZKikxVd12dMi2aCaZxNPshHJv8wjksVV4lOeY4lkBTGXUNaBonWJ0LKD8tXcxrt37x6U9U9+8hN33nnnuVdeecXpZklf5Lv44ovdokWLogfshx9+mKTPM5Za5bbTSz6oMkRAAAIQgAAEeoSArvcXXXRRMquUnujHgmaa0nVUHwM788wz3eOPP95IJkfWSSedVFhgNzLo4AoiuYOwY0WZh9NmaNDShJw6mB/fDm95XpGsss0u1cNsKzJmOFb/rLisKeCeffZZN2rUqISP5lK+7LLL3IYNG6ICWWXYUAymgMsizjYIQAACEIBANoGnnnrKjRw50r3wwguDEuqrtr/+9a/dCSec4K644orkyW74pVv91hdwP/e5z0Wf/A7KtIsRiOQuwveLlliVIA49mCbu2jW0IY9I9u3s5Lo+OX3ssce6559/fsjFbtmyxR1//PF8TGTIJMkAAhCAAATqSsC+bqthrnv37h2AQeJXwy/+/d//3d1///3JU94BCbwfur4fffTRbR226RXX8mplRPLvfve7xscqdIdyww03uL/97W/JY/wLLrggeUFPtfTTyYupoQB6PC5P5xNPPOHOOeccN3z48MTL+Mtf/nKQZ1EN/NBDDyWP5s866yynv40bNyYA5dWVSJ0xY4aTx/HJJ59M8vnqV7/aeOSvR//f//73kzukL3zhC8l62FFaaY2YGDYvcyicW8k/bZ8qi2Rx1YFYxg2ChPa4ceP4LHVaRyAeAhCAAAQg0ISAXtYbM2ZMopHCpC+99FLiYdaLeWkf9rJ9NBWr3hGS3jp48KBFV25ZGZEsMhK8Erv+Hcr69esTb6LGtRw+fDgBqNkLzjjjDLdr167kt0SyvLASvMpDj90FX+7+rVu3NqCr0W655ZZkwLjWNYD8/PPPdza37jvvvJOIc4ls2fHFL34xGUuj8TQSxzt37kx+61GDgspROg1Ab9YhGkZkrKge+lMwgVyGQMwoMhGg7S4jq/xm22Sb3/bN0qdtv/vuu5PHO+Fjn1h6tUE7b0xiZRIHAQhAAAIQqDoBXRultzQc0g/mYf7EJz7hbrvttuSlPqWTM1HDL8Jr70cffZS8wNfOIZu+fa2uV0okmzCU8JTYVdCnhgVady66g1GYPXv2AMEjUaPxqeYRVpolS5Yk+y1btizZR/80fkbjV19++eVGnESY8rd0JtRNOFtCG0MzceJEp6+3KZi9vm2WvpWlbLFxv75gbiWvvPuoTP1VNehGSE8H/JudorbqZuiSSy5p9Klm+yOSmxFiOwQgAAEI1JGAxLE0U+hIMg+z9Jv011tvvZUspbk0OiBML3a61moYpIZDVjVUSiQLkolWQdbjdolGeXLVKBZ37rnnDhC6Au0La+Vjdzu+ANQQCnmJTzzxRHfqqacm4uvLX/5y4nV+7rnnkjYykay5l/07H3s0oMbWjAvyMssOeay/8Y1vNIZjDKWhVbZmkdBNgInlZvmZUBefrL+0/C688EKnvyqHZ555xs2bN29AexSx9+mnn3YPP/xw7v0///nPu7vuuqtIEaSFAAQgAAEI9D0B02ih6NWQRumrUGuYwzI2rCKm3aoGsHIi2USqgGoGA00z8uKLLyZDLgRfc/R+/etfb3hzBTQGOhTJJiabufatfOXph7R4P81Q121ccjMbh1qOv786vH8j4W+ryrpuVh555JHol/Sa2aghMqpfkeEwavvwBNCsHLZDAAIQgAAE+p1AmifZNFcoks3DHNM1utbiSS7YY/RoXF9wkbdXHk7dhdhYF810oPGp8rT6IY9I1sBwCW+9Tam3KtNCmhi2hvbHS6fl0Wq8dbJOitZeEMniqbmQV6xYUeixzNtvv+0ee+yxpP8UaRNEchFapIUABCAAgboQSNMpNoOUPyRVTMz5F8bndVx2m2vlPMkCopesNHTg5JNPTsa1KM5c9iNGjBgw1ELb8ohkpbPxzeGbl3phz2aoSBPJJt5VvgahW5CX8/XXX2+8VGjxrSxVj9jdVlZe1tGyhlpoW3h3Z3n2ikg2ezuxRCR3gjJlQAACEIBArxEwh2H4zQHTSKEj0tJrXuTYENbYMIwqMamkSNaLdRKj11xzTUN86otqGgsc3o0IusYPh2OSNQOGxOHChQsbvPXoXWOJFT916tRkzlx5pTXFm74cp6CX//QSYDgmWds0NlZjko866ih38803J/trOIhElbzdQwl2t6W8OhkQyYNpI5IHMyEGAhCAAAQgYE/2Qy0mMvIySyPps9MSzdJnmi9Zukv6yw+m8+QArXKopEjW7BGTJk1qzI0sgJr+TaLZvxvRPMqaT1mNIuGrfTZv3pzMVCGPrOI+/elPu/vuu68xD99f/vIXd+mllyZCV/tdffXVjZfuNPBceWg/bdPXYpSfBTW4hLK+V640mmJOcy4PVSArfwkz5alO1smASB5MG5E8mAkxEIAABCAAARFYtWpVopFiX9z74x//mLw3JmGsL+H+8Ic/bGgsoyctJS0XziJm26u0rKRIrhKgdtsikSpx7P+lDY1ohy2I5MFUEcmDmRADAQhAAAIQEAEN89RTdP1pvWjYtm2bO+mkk9yiRYuK7trx9IjkjiOvVoFVEcmavULDWL7zne+U4pkfCmVE8lDosS8EIAABCPQ7Afu4mj5DLc9w3qBhGBqOoQ+7FZl1Km/+ZadDJJdNtMfyq4pInjt3buJN18wmOoi6GRDJ3aRP2RCAAAQg0AsENIOUBK8mPMgbpDnuuOOOrjvD8tqLSM5Lqk/TVUUka4o3fbClCt9wRyT3aWenWhCAAAQgAIECBBDJBWD1Y9KqiOQqsUUkV6k1sAUCEIAABCDQHQKI5O5wr0ypiOTBTYFIHsyEGAhAAAIQgEDdCCCS69biQX0RyQGQf07H1+mp+AZbQQwEIAABCEAAAt0kgEjuJv0KlF0VkcyY5Ap0BkyAAAQgAAEIQKBBAJHcQFHPlaqIZGa3qGf/o9YQgAAEIACBqhJAJFe1ZTpkV1VEMvMkd6jBKQYCEIAABCAAgVwEEMm5MPVvoqqI5CoR5sW9KrUGtkAAAhCAAAS6QwCR3B3ulSkVkTy4KRDJg5kQAwEIQAACEKgbAURy3Vo8qC8iOQDC7BaDgRADAQhAAAIQqCEBRHING92vclVEsr79vnfv3kp8yx1Pst9DWIcABCAAAQjUkwAiuZ7t3qh1VUQys1s0moQVCEAAAhCAAAQqQACRXIFG6KYJVRHJzG7RzV5A2RCAAAQgAAEIhAQQySGRmv2uikiuEnaGW1SpNbAFAhCAAAQg0B0CiOTucK9MqYjkwU2BSB7MhBgIQAACEIBA3QggkuvW4kF9EckBEGa3GAyEGAhAAAIQgEANCSCSa9jofpURyT6Nf6zjSR7MhBgIQAACEIBA3QggkuvW4kF9EckBEDzJg4EQAwEIQAACEKghAURyDRvdrzIi2afxj3U8yYOZEAMBCEAAAhCoGwFEct1aPKgvIjkAgid5MBBiIAABCEAAAjUkgEiuYaP7VUYk+zT+sY4neTATYiAAAQhAAAJ1I4BIrluLB/VFJAdA8CQPBkIMBCAAAQhAoIYEEMk1bHS/yohkn8Y/1vEkD2ZCDAQgAAEIQKBuBBDJdWvxoL5li+T9+/e7pUuXNkpZs2aNGzZsmJs2bZrTNgUt165d20hTtRVEctVaBHsgAAEIQAACnSeASO4880qVWLZInj17ttu0aVNSx3fffTcRx1qG5ei3BHQVAyK5iq2CTRCAAAQgAIHOEkAkd5Z35UoLxetQDJTo9YWv1pW/goTzlVde2fAmK27BggVOArpqAZFctRbBHghAAAIQgEDnCSCSO8+8UiWWKZJD0evn7XuVDUAoqi0+XB45csS9+OKL7vnnnw83Nf29ZcsW9+STTzrlkTcgkvOSIh0EIAABCECgfwkgkvu3bXPVzBeyuXZISaRxxvPnzx/gKVbe5lmOiWR5l/3xy7GsJW6XL1/eyCeWplnc6tWr3SOPPJJbKCOSmxFlOwQgAAEIQKD/CSCS+7+NM2t44YUXOv0NNUgES1zay3nKL49I1hjmrLBu3Tr34x//2B0+fDgrWeY2Ce158+a5Z555JjOdbfz85z/v7rrrLvvJEgIQgAAEIACBGhJAJNew0f0ql+VJjonkZmOSY+OUfdskuGfMmOHWr1/vR7e0vnXrVnf++ee73bt3N90fT3JTRCSAAAQgAAEI9D0BRHLfN3F2Bdspkn3hHCtHIjnLk7xq1So3depUt3fv3uxK5Nh68ODBRHAvWbKkaWpEclNEJIAABCAAAQj0PQFEct83cXYFyxpuIa+vxKWEsR/kTQ7nSbbtWWOSTdRmiWjLJ+9y4cKF7uyzz3b79u3L3IXhFpl42AgBCEAAAhCoBQFEci2aOb2SZYlklRDObpFe6j+2ZM1usX37djdmzBi3bNmyZtnk3q7yjj76aKdxzlkBkZxFh20QgAAEIACBehBAJNejnVNrWUQka8jE+PHjG95i/fa9xPIMF/mSXpao1nRvw4cPT53VQl5rlZ1lT1hp2Td69Gi3ePHicNOA34jkATj4AQEIQAACEKglAURyLZv9X5XOI5I1lEKflZYo1Z+9kCeRHAZtyxM0LOPVV19NTaq8JWglbNOCyrLPXUs0ax/F+cLZ39e800qbFRDJWXTYBgEIQAACEKgHAURyPdo5tZZ5RLLtLGErASqhHBPISieR2kyEpo1ftnK0VB7NRLLS6M/EsfbTeppINvunT5/uPvroI7+4AeuI5AE4+AEBCEAAAhCoJQFEci2b/V+VLiKStVeWCP1XrkNfayaSTfCaSFaJ5vFWXCzYPuZ9jqVRHCI5jQzxEIAABCAAgfoQQCTXp62jNS0qkjX8Ydy4cZnDIKIFFYxsJpJtfLEveE0Ep3m5bbu/T8wsRHKMCnEQgAAEIACBehFAJNervQfVtqhI1qenNQwiTYgOKqDFiGYiWeWHwzE01COM84s3kcxwC58K6xCAAAQgAAEIxAggkmNUahRXRCRLhNqY47QhDWWhkwgeNWqU27hxYzRLlR96hLVPGOfvrK/tjR07tumYaTzJPjXWIQABCEAAAvUkgEiuZ7s3at1MJMv7Onny5EQca8o2BYlRvRz3xhtvJIJTacoOWVPAmUdYdljwxyOnTS1nQzSYAs6osYQABCAAAQhAII0AIjmNTE3i84hkCWJ/xggTm1lDG4aK76233nInn3xydE7j2LhoE842RV2sfAnvY489lo+JxOAQBwEIQAACEIDAAAKI5AE46vejmUjuFpHDhw+7mTNnuuuvv94dOXKkFDPkQeaz1KWgJBMIQAACEIBA3xNAJPd9E2dXsKoiWVavXr3anXvuuW7v3r3Zlcix1UT3kiVLmqZmTHJTRCSAAAQgAAEI9D0BRHLfN3F2BasskjXO+KKLLnIvvPBCdiVybN2xY4fTrBa7du1qmhqR3BQRCSAAAQhAAAJ9TwCR3PdNnF3BKotkWb5hw4bk5cADBw5kVyRjq4ZraKjFM888k5HqX5sQyf9iwRoEIAABCECgrgQQyXVt+X/Wu+oiWWZq2MUjjzzS8thkvei3fPny3Psjkmt+UFB9CEAAAhCAgHMOkVzzbqBp1Pyp1KqIQ57gF1980Wl2iqJhy5YtbsWKFe7jjz/OvavmYNZ80AQIQAACEIAABOpLAJFc37ZPat4LIrnTTYRI7jRxyoMABCAAAQhUjwAiuXpt0lGLJJI1t3D458+L3FGDOliYvMVhve03nuQONgRFQQACEIAABCpIAJFcwUbBJAhAAAIQgAAEIACB7hJAJHeXP6VDAAIQgAAEIAABCFSQACK5go2CSRCAAAQgAAEIQAAC3SWASO4uf0qHAAQgAAEIQAACEKggAURyBRsFkyAAAQhAAAIQgAAEuksAkdxd/pQOAQhAAAIQgAAEIFBBAojkCjYKJkEAAhCAAAQgAAEIdJcAIrm7/CkdAhCAAAQgAAEIQKCCBBDJFWwUTIIABCAAAQhAAAIQ6C4BRHJ3+VM6BCAAAQhAAAIQgEAFCSCSK9gomAQBCEAAAhCAAAQg0F0CiOTu8qd0CEAAAhCAAAQgAIEKEkAkV7BRMAkCEIAABCAAAQhAoLsEEMnd5U/pEIAABCAAAQhAAAIVJIBIrmCjYBIEIAABCEAAAhCAQHcJIJK7y5/SIQABCEAAAhCAAAQqSACRXMFGwSQIQAACEIAABCAAge4SQCR3lz+lQwACEIAABCAAAQhUkAAiuYKNgkkQyEPg3XffdePHj3fDhg0b9PfAAw/kyYI0EIDAEAls2rTJjR49etAxqOOS43CIcNkdAl0mgEjucgNQPARaJSCRPG3aNKclAQIQqBYBCWREcrXaBGsgUJQAIrkoMdJDoCIEEMkVaQjMgECEACI5AoUoCPQYAURyjzUY5kLACFRdJO/fv9+tWLHCTZ482emRNAECdSKASK5Ta1PXfiWASO7XlqVefU+gyiJ5z549bs2aNe6KK65Ixmsikvu+O1LBgAAiOQDCTwj0IAFEcg82GiZDQASqLJKthSQU9FITItmIsKwLAURyXVqaevYzAURyP7cudetrAojkvm5eKtfjBBDJPd6AmA8B5xwimW4AgR4l0E8iOWsaLQ3bIPQ3gaz2l9jsxYBI7sVWw2YIDCSASB7Ig18Q6BkC/SaSr7zySqeX/QgQMAK9LDR72XbjzxICdSeASK57D6D+PUsAkZzddOKzcuXKJJHEt+aUNq+0tr366qvZGfTJVtV96dKljdpcd911jfl7tW3t2rWNbVVb6WWh2cu2V60fYA8EukUAkdwt8pQLgSESQCSnA5T4kxgUIwWt6wtoJpIVN3v27Fq8UOjXU8It/BKc4nwu6VQ7v6WXhWYv2975lqZECFSTACK5mu2CVRBoSgCRnI5IntNwRg0JZV8MSkjPnz+/r4d4qL5+nUUsJt4WLFjQuKFIp9r5LTFbO29FayX2su2t1Zi9INB/BBDJ/dem1KgmBBDJ8YZOE7+hSNbeMTEdy/XIkSPuxRdfdM8//3xs84C4t99+O8n30KFDA+K78SMmfmPiLSam0+xV/R577DF38ODBtCTR+Fa4xGyNZl7ByF62vYI4MQkCXSGASO4KdgqFwNAJVF0kf/zxx27u3Lnu6KOPdi+99FJmheX1LevFPXGROAxDTCTnEYcSyMuXLx/kkQ3z939v2LDBzZs3z3VTKKfdLMTEm/j745b9uvjrmzdvdvfee2/L9SrKJWarb0+V13vZ9ipB6iX2AAAgAElEQVRzxTYIdJIAIrmTtCkLAiUSqLJIlm3jx49Pxr9qDKz+JFLTQpkiWXlpHG4Y0kSyxExWWLdunfvxj3/sDh8+nJVs0LZly5a5hx56yElkdyOoDVRniWU/xMRbGjN/vw8++MBde+21bteuXX504fUiXGK2Fi6wSzv0su1dQkaxEKgcAURy5ZoEgyCQj0CVRXK+GvwrVTdFcpZ4l8CcMWOGW79+/b+M/eeaROODDz7ovva1r0XH877//vvu/PPPd/K+diMUFcnNPPkSfffcc0+0Ku+995678cYb3ciRI93w4cPdpEmTUmfNKMKlHUJTTzj+9Kc/uYsuuii5iYlWqITIdthegllkAQEIFCCASC4Ai6QQqBIBRHK8NdK8oq14kletWuWmTp3q9u7dO6Cw3bt3O22bMmVK4jFXW8SCPNqzZs3qije5qEiOed+tTjt27HBf+tKXnLzqYdCNxGWXXZZ4rcVE+RxzzDGJYE4bZpOXS9lC8+9//3si3n/2s5+5ESNGNKbCC+tUxu+ybS/DJvKAAASKEUAkF+NFaghUhgAiOd4UMXEogWzDPvzZHrLGJOvFNHmRs8Sj8tWwkjSRvHr1ajd27FgnkdnpIPEq+3zbJNyMg9Yt6MYia0yyhkhMnDjR7dmzx3ZpLOWVDcWzfh977LHJ8IzYcJO8XNolNFXf0aNHI5IbrcgKBCAQI4BIjlEhDgI9QECP8T/5yU927XF+mYiKDLeQ6JMwNZFnvyX+JHolDvNO7ZY1u8X27dvdmDFjnARiWmgmkk2M2UdN0vJRfBEGlo/K10dSVGcF/fbHf8dmt7B9/WWemwXdMOSd0eLDDz905513nps5c2Z0LHdeLr0ski+88EKnPwIEINC7BBDJvdt2WF5zAhKHEki+p7BXkeQViBJz5glV3d94440oA31FTnlmhWZiWtO9aXytykwLzUSyCfibbropLYtGfF4G2sHyFQt5RLWvbAltVXyeL+pliWmNIZ4wYUKSf8PYJismkpcsWRJNafY349LLIrldtkeBEgkBCLSFACK5LVjJFALtJyCh0S8i+YknnnCf+cxnnF4AyxMkQCQQ04Y6SAA3E4cS2PpLCyrDBGhammYiWcMTNEzB9/am5VVEJFse2kc2ikUokC1NWrxtVz/K+kS3lSEeecPWrVvdBRdc4CSwYyEvl3Z5Y1upU6weWXGI5Cw6bINAbxBAJPdGO2ElBAYRqLNINk9klnDLEinaXwLXhikMgvvPoQtDFcnKXwJZntg0wWhltyKSta/qkSXCJZKVJhZkn7aJR1rQ/hLhWaz9fTU3tKbMC8cp+2nyckEk+9RYhwAEOk0Akdxp4pQHgZIItFMkSzhJGGX9hV5cvahV5O/rX/96g0RRT7J2lI1p4q+R8RBWlHdZIjlkZfZn8dW2ZuUrH4nYWP5DqPqAXYuIZL2k96tf/crpxbysYCK5md2I5CyKbIMABNpNAJHcbsLkD4E2EWinSG7FZL3oVvTPyikqkuV1lfe0mciy/FtZtlskhza14kk2T7DEtMRsO0IRkay0zz77bNMp7xDJ7Wgp8oQABMomgEgumyj5QaBDBKomkodS7SIiWQJLs1dozPG4ceOavqDXql1liuR2DbfQ7BzioBuGvMMhivLIK5Kfe+65RKjHpnwLyzSR3IwLnuSQHL8hAIFOEkAkd5I2ZUGgRAJ1E8kSgRKuNm2b6i9PsuIl5MoWicpv1KhRbuPGjdFWO3DggLviiivciSeemHjQY4lsloesMcO2X15PstJNnjw5qbPNbSwuKkMvImpdIrSsoPLkqV64cGE0S4niFStWuFtuucU9/fTTjT99WOS2225zv//97wftl5dLu0SyPnJy9NFHu7lz5zp9ga8dQf2n7D7ZDjvJEwIQSCeASE5nwxYIVJpAP4nkPAJRgkPjdH3hIUGoOC3LDllTwJlw9McU+3aZLSbkm011pvR5GFg6iVZfeJu3tx3DT7KmgDt8+LD7+c9/7o466qjo+PWzzz7b7du3z3A0lnm5iGmMayOjFlasz1jbtYOZzGqH7S1Ul10gAIEhEEAkDwEeu0KgmwTqJpI7zfqtt95yJ598slu8eHHLRW/ZssUdf/zxLs/HRFoupM07SgjroyDTp093H330USml5eXSy0Kzl20vpZHJBAJ9QACR3AeNSBXqSQCR3N52N3F4/fXXN30RLc0SeaM1brobn6VOs6mVeIn8U0891b3zzjut7D5on7xcello9rLtgxqMCAjUlAAiuaYNT7V7nwAiuf1tqKnMzj33XLd3796WCrv77rvdrFmzWhbZLRXahp127dqVjIPOmvu4SLF5ufSy0Oxl24u0JWkh0M8EEMn93LrUra8JIJLb37x6Ae6iiy5yL7zwQuHCNBb3kksuadvsG4UNGuIOEn1lCP4iXHpZaPay7UPsKuwOgb4hgEjum6akInUjUGWRrM9L33jjjW7kyJFu+PDhbtKkSZmfic770lo32njDhg3Ji4GazaJI0EwPDz/8cM97ka3OErff+9733LZt2yyqpWURLr0sNHvZ9pYalp0g0IcEEMl92KhUqR4EqiqS5X297LLLEmGpacBmz57tjjnmmEQwa+qtWKiySJa9GnbxyCOP5Ba8O3fuTGY30Cea+ymoXrfeemt0xoo89SzKpZeFZi/bnqctSQOBOhBAJNehlaljXxKoqkj+05/+5MKxq/qtT1Zfe+21UaFZdZGsuYBffPFFpxfOmoW3337bPfbYY66o57lZvlXZbvU7ePBgIZNsvyJcello9rLthRqWxBDoYwKI5D5uXKrW3wSqKpJj1O3jEZpKTLNGhKHqIjm0l9+dIdDLQrOXbe9M61IKBKpPAJFc/TbCQghECfSiSF6yZEm0LojkKJbaR/ay0Oxl22vf8QAAgX8SQCTTFSDQowQ2b97sPvnJTzotqx62bt3qLrjgAqevt8UCIjlGhbheFprt+qQ2vQICEOgcAURy51hTEgRKJdArnmS9vPbjH/940DhlHwYi2afBuhHoZZHcy7Ybf5YQqDsBRHLdewD171kCvSCS9cLbr371q2R2iCzQEsmjR492w4YNG/S3Zs2arF3Z1gcEstpfYrMXAyK5F1sNmyEwkAAieSAPfkGgZwj0gkiWwH322WejM1r0DGgMhUALBBDJLUBjFwhUjAAiuWINgjkQyEug6iL5ueeecxLJ8iYTIFA3AojkurU49e1HAojkfmxV6lQLAlUVyRLFK1ascLfccovT19XsTx8Wue2229zvf//7WrQPlaw3AURyvduf2vcHAURyf7QjtaghgSqKZM2B/POf/9wdddRRg8YWa7zx2Wef3fLX2mrYxFS5hwkgknu48TAdAv8kgEimK0CgRwlUUST3KErMhkDpBBDJpSMlQwh0nAAiuePIKRAC5RBAJJfDkVwg0A4CiOR2UCVPCHSWACK5s7wpDQKlEUAkl4aSjCBQOgFEculIyRACHSeASO44cgqEQDkEEMnlcCQXCLSDACK5HVTJEwKdJYBI7ixvSoNAaQQQyaWhJCMIlE4AkVw6UjKEQMcJIJI7jpwCIVAOAURyORzJBQLtIIBIbgdV8oRAZwkgkjvLm9IgUBoBRHJpKMkIAqUTQCSXjpQMIdBxAojkjiOnQAiUQwCRXA5HcoFAOwggkttBlTwh0FkCiOTO8qY0CJRGoMoi+YMPPnAPPvig+9rXvuZkJwECdSOASK5bi1PffiSASO7HVqVOtSBQVZG8e/dup09QT5kyxY0fPx6RXIveSCVDAojkkAi/IdB7BBDJvddmWAyBhEBVRbI1z3XXXYdINhgsa0cAkVy7JqfCfUgAkdyHjUqV6kEAkVyPdqaWvUkAkdyb7YbVEPAJIJJ9GqxDoIcI9ItIlpgYNmzYoD+GavRQZyzB1P3797tp06YN6gfqG4rX9l4KiOReai1shUCcACI5zoVYCFSeQD+JZAmKMsPatWvdpk2bkiy1nDx5cmNs9KuvvtpYL7PMXshr5cqVjbr3ChfZeeWVVyKSe6GDYSME+owAIrnPGpTq1IcAIjne1hJVs2fPTjaKkTzSvldacRov3WueyXht88euWbPG2c1IL3FBJOdvY1JCAALlEkAkl8uT3CDQMQKI5MGoJXznz58/QADHOEl4LV26dHAGfRojBgsWLBhQu17hgkge0Gz8gAAEOkgAkdxB2BQFgTIJxEROmfkPNa+8s1uUOXYzJn5jnGJiOq2+H3/8sVuxYoXbsmVLWpLU+CeeeKKl/VIzbHGDvMj688NQuezdu9ctWrTI7du3z882c/3tt99Obk4OHTqUmc7fiEj2abAOAQh0kgAiuZO0KQsCJRKIiZwSsx9yVt0QyXnFoConz6oYZgWJuYULFzbGN2eljW3T/vPmzXMbNmyIbe5YnLzmEpt+SOs/ebhoLuw777yzkEC2ssVCTPIKZUSykWMJAQh0mgAiudPEKQ8CJRFIEzklZT+kbA4cOOCuuOIKd+KJJ7rt27dn5lWmJ1l55fGYyiCNWw6FY2joU0895R566KEwutDv999/382cOdPt3Lmz0H5lJo7VNa3/xNL6tkjc3nzzzU3Z+fuE68uWLUu4HjlyJNw06DcieRASIiAAgQ4RQCR3CDTFQKBsAmkip+xyiuYnUTN69OgBU3nZC2OxvLolkuXpDgW1b9+uXbvc9OnT3Y4dO/zoltaXLFnibr31Vnf48OGW9h/qTjHhm9Z/mnFZvXp18uLjUOqiG4fzzz/fbd68uWnVEMlNEZEAAhBoEwFEcpvAki0E2k0gTeS0u9yy8++WSI4JR79u99xzT+IBjolBeUCfeeYZd/rppyc3A8ccc4y7/fbbB7ww6Oclb/qZZ57ptm7d6kd3bD1W17T+E0trhmr88dlnn+00lVwsaMzxBRdc4I466ig3cuRIN2fOnFQmKmfWrFmumTe5HSJZZW7bts394Ac/cDfccEOsKkOOK7NfD9kYMoAABFoigEhuCRs7QaD7BNJETvctK2ZBmWJCnmHlZ0GMNP2bPkjhTwOn7Vljb/fs2eMmTpzoNCwgFlTOpEmT3KOPPuoef/xxd9ZZZyVlXH755U5DTcLw4YcfuvPOO89JeHcjiInvNW+Vy8svv+xOOeWU6BAaeYclOtetW5cMLbnrrrsSsTx37txoleWRHjt2bFNPfTtE8vr1690vfvGL5ImHPOftCGX263bYR54QgEBzAojk5oxIAYFKEkAkD24WCao8U7s1m91CYlDeYS3DcPDgwaQMXwxrnO5VV13lRo0a5TZu3BjukvyWGJsyZYrTrBCdDhLIvkhOK78ZF3l/dfOgm4gwiP17773XiBafSy65JBmy8tFHHzXibUXpNSwnzSvtp2vHx0TsRgGRbKRZQgACIQFEckiE3xDoEQJ1FMkmrEzw2W+JLa0rSCRL7GUFpc0S04sXL04EnOWZlZdtk2f06KOPTjypFucv5Vk8/vjjc00J12xcsJ+v1o1DGhfxyKqv5ZfFRUJXY7TzfiJaQlo3BWnlmki96aabrPjoUjYhkqNoiIQABNpMAJHcZsBkD4F2EaibSJbI1LAJ/UlEpomnN954w+kvK+iz1VlCWvmHwzOy8tM2iWSNO9awg1jQ0A3ZbkI2lsbiiojkvFzyfI47i4uJWtmWFTSv9GuvveY09ETDS9KmerMhLc1Ed1o7Z9mQZ1ve+uTJK5aG4RYxKsRBoLcIIJJ7q72wFgINAv0iki+88EKnv7xBIk1iM01cSfzK8yhxFQsSqRIwaUH7K+8iIlkvgmkoQprXVGWpXNktL3WzUEQkW17NuDTrL824iKc89s1EstmhuurFRgnvWDDOEyZMSL2x0H76IMtnPvOZAUM5YvkVjUMkFyVGegjUjwAiuX5tTo37hEAz0dOpamocql7SKvpn9hUVySbW8nhkrYwiSxNvRUSyPpChKd7SvKYq30RylkA3O1sRye3mYvk3E8mqg2bBWL58eSKq9aLfm2++aVVrLPNyRiQ3kLECAQh0mAAiucPAKQ4CZRFoh0g24SIvYNaf78WVSL7ssssK/UlQWygqks3GPGLTyiiytPzziuS//vWvTjM4NPs8c5pINvGZxVvbmolTs7tdXMzOZnb4rDUEZcSIEclQFD9e62ZvM86I5JAcvyEAgU4RQCR3ijTlQKBkAu0QySWbmCu7oiJZj+/HjRuXOtwiV6EZifKKN2UhYfzTn/4014wVJpLbNdyi3VxaEck2pEFiOQzGmeEWIRl+QwACVSGASK5KS2AHBAoSqKNIVp01v7EEZzMPZEGcA5LLW6o5fHfv3j0g3v8hgbxw4cJcAln7SSjKIyzbmwWVnyed5dMJLiZ4r7322qYfADG79ALl5MmTkw93WJwtbe5o/6mEbfOXeJJ9GqxDoDoENLzsvvvuc5qhJvbRpZil+pLpueee61555ZXY5srFIZIr1yQYBIF8BPRJ309+8pO5Pu2bL8fupMrjSZZo1DAC+wCIeTUlJBVfRFDmqWWzKeA0xOTqq69OPjby/9s7u1eriv+P9w+cG++88ipEIbyICIRISyq6CcE0kETLKOv0INiF3QRFqZEGCdoTUhf2IBh6KM0w1IjEB5AyNBXMSE9qICpqaeZ8ee/fbw7rrL0e916z1sxer4HD2mc9zHzmNfuc/VqzZ83s2rXL2J8vv/zSvP3224kzZyjOqqeAq5NL3hRwH374YWfBFH34aYYLLef9/PPPm88++yxRqq10500B50qStQriPffcY5YtW5a4AEyR90nWOUXe11nXcwwCPhOQFEuQNaPP2bNnS4Wq1UqnT59ufvzxx1LXNXEyktwEdcocKAKSn7TxpHm9ZP2AkGQof21DTuKnn6wkGYz2wtqv6rUv79qsfNOOadW4KVOmmL1793adot5RfTAktfnQ0JDZuXNn1zXaIRksuphI0Z7kurm89957Jm14xPfff99ZTEVctBCLxqnrgca0ZadPnDjRuWloYjGR+N9sdJ7txMbrYWeR93UP2XIJBLwgoI4J/d0cOHBgLJ7431X0f6T+N6ozQUn/E7Rk/SOPPFJasMcKq+kFklwTaIoZbAK2ZzMqbHafq2EBbZLkut89WhVPQhttz35isL2wTS1L3U/s0Wt183DvvfemTq8XPTfvtW5ANLZcPc5ZSX9HLhYTySqzimNIchUUycNHApcuXTILFizorKgZXXlUN+2PPvqo+eqrr8a+XZMYv/vuu2bhwoXjHm4+efKkufvuuzuynHYj7UPdkWQfWoEYgidg76r1gR5N8Z6+6LF+XyPJ/RLMvl6Ss3z58sJj7bJyO3PmjJk7d67RB0PIyfbg5/X+FqmjeqVXr16d2tNs80CSLQm2EPCDwL59+zqz1kT/D9y4ccOsWrWqa6yxJFpDmnbs2DEueA3X0P/Xhx56yPz111/jjvn0C5LsU2sQS7AEJFTxoRVWKOhJzm5WX3vc9IDJokWLKhFbDcFYuXJlJcKdTdP9UT2AqNX0oj1IZUvVQ48vvPBCoR5pJLksXc6HgFsCWjip6PMVGo6hb+WSViLVsx+aIvLgwYNuA+4jdyS5D3hcCgERsDIs2bPJ7nMx1tGW4WtP8s8//9z5Kk5j0CZNmtR5wE0PuqUlXyVZ8eoBk3Xr1uX2dqbVTfslhCtWrPB+7F1WHaLH9ES7PiSjYxGjx4u81lewX3zxRSGuSHIRopwDgXoI2M+2tGcTolHoRlo31Js3b47uHnutIVf6nIh+do4d9OQFkuxJQxBGuAT0IS4Zjj6kUFSO7XCM6LXx12k90T5KsmbcmDNnTuepZ30VNzw83PknqHFqST0JanWfJVlj5TZt2pS4GEaRd6yu18pzeo8MUpL4a4XBsk+1i4GuUZtnrU4YZYUkR2nwGgLNEtD/cQly/JvTpKg0LGPevHmp//vtZ2feDDdJede1D0muizTlDCwBjUeOi6yVX5d3yD5Ksh7Y0Ap0NkkSNW2bxD9pQQmd57MkKz5NZ7Zt2zaj2RjKJk1fNmiCbBno4UZN7yZhLpr+/PNPo2nyygzVQJKL0uU8CLgnoM8dfd7lSbLtcc76DLSSrM9LXxOS7GvLEFcwBPQHHv+HYf9BFO1R7qWyPkpyUj2OHj3amRos+pBH9DzfJTkaK6/rJ4Ak18+cEiGQRqBoT7Ie1MubvcZKMj3JabTZD4HACdi76qS7ZclzniTbHuf4EIvo7/FeaossJEl++OGHUx+AQ5Jti7JNIoAkJ1FhHwSaIWA7gNI+lxSVRFpD7PKmvNS3sPqsS/r8bKZ23aXSk9zNhD0QKEwgbeo3e4ec9Y+kcCEpJ4YiyXpoQxPHp82FiSSnNDC7OwSQZN4IEPCLQN7sFvqfPnPmTHP69OnMwJndIhMPByEQNoG0O2p7d6w7ZL12lUKQZI1BVW+5Jp9PS0hyGhn2iwCSzPsAAn4RsPMkb926tSswibEEOatjRBddv37dLF26tLN6adpD3V2ZN7CDnuQGoFNk+AQkdtEhEfHX8THKLmrsuyTr4az169fnzoCAJLt4dwxOnkjy4LQlNRkMAnpYVyvoaa7z6EO4mrHmjTfe6IjvqVOnMitrV9zTg91p3zJmZlDTQSS5JtAUA4GqCfgsyfpnKfnN+7pNTNJuOFwOVam6LcivfwL2m5n4Dad+r+Oms/8ajM+Bm7/xPPhtsAjYoYa9fFsqKVZP8+zZs8358+e9BoMke908BAeBdAK+SrIEWVODaSlmEgTaSgBJbmvLt6PeEt2NGzd2RLfsfOlapGnGjBnmyJEj3sNCkr1vIgKEQDIBHyVZvYFaZEKCoFXV7I/mT9ayzL73GiSTZi8EyhNAkssz44qwCGgOeS22tGrVKnPz5s1CwZ87d84sWbLEaGrQEBKSHEIrESMEEgj4JslaROS5555LHaudNx1QQhXZBYFgCSDJwTYdgUNgjACSPIaCFxAIi4BvkhwWPaKFgFsCSLJbvuQOgToIIMl1UKYMCDgggCQ7gEqWEKiIAJJcEUiygUCDBJDkBuFTNAT6IYAk90OPayHglgCS7JYvuUOgDgJIch2UKQMCDgggyQ6gkiUEKiKAJFcEkmwg0CABJLlB+BQNgX4IIMn90ONaCLglgCS75UvuEKiDAJJcB2XKgIADAkiyA6gVZ6mJ9idPnmzmz59vqlp6VdPsvfTSS2bChAlmZGSk4ojJrioCSHJVJMkHAs0RQJKbY0/JEOiLAJLcF75aLtb80ENDQ2bWrFlmdHS0kjIvXbpk5s2b15lqj2n1KkHqJBMk2QlWMoVArQSQ5FpxUxgEqiOAJFfH0lVOWpXq4sWLRr2/Vabr1693eqY1mT/JTwJIsp/tQlQQKEMASS5Di3Mh4BEBJNmjxiAUCMQIIMkxIPwKgQAJIMkBNhohQ0AEkGTeBxDwlwCS7G/bEBkEihJAkouS4jwIeEYASfasQQgHAhECSHIEBi8hECgBJDnQhiNsCCDJ/r8HGJPsfxu5ihBJdkWWfCFQHwEkuT7WlASBSgkgyZXidJIZs1s4wRpEpkhyEM1EkBDIJIAkZ+LhIAT8JYAk+9s2NjLmSbYk2rdFktvX5tR48AggyYPXptSoJQSQ5JY0NNUMkgCSHGSzETQExhFAksfh4BcIhEMASQ6nrYi0fQSQ5Pa1OTUePAJI8uC1KTVqCQEkuSUNTTWDJIAkB9lsBA2BcQSQ5HE4+AUC4RBAkv1vK2a38L+NXEWIJLsiS74QqI8Aklwfa0qCQKUEkORKcTrJjNktnGANIlMkOYhmIkgIZBJAkjPxcBAC/hJAkv1tGxuZZreYNGmSmT9/vrlw4YLd3df22rVrZnh42EyYMMGMjIz0lRcXuyOAJLtjS84QqIsAklwXacqBQMUEjh8/bqZOnWq0JUEAAn4RWLJkidEPCQIQCJcAkhxu2xF5ywnQk9zyNwDV95oAPcleNw/BQaAQASS5ECZOgoB/BJBk/9qEiCBgCSDJlgRbCIRLAEkOt+2IvOUEkOSWvwGovtcEkGSvm4fgIFCIAJJcCBMnQcA/Akiyf21CRBCwBJBkS4ItBMIlgCSH23ZE3nICSHLL3wBU32sCSLLXzUNwEChEAEkuhImTIOAfASTZvzYhIghYAkiyJcEWAuESQJLDbTsibzkBJLnlbwCq7zUBJNnr5iE4CBQigCQXwsRJEPCPAJLsX5sQEQQsASTZkmALgXAJIMnhth2Rt5wAktzyNwDV95oAkux18xAcBAoRQJILYeIkCPhHAEn2r02ICAKWAJJsSbCFQLgEkORw247IW04ASW75G4Dqe00ASfa6eQgOAoUIIMmFMHESBPwjUJck//fff+bw4cNmeHjYfPrpp/6BICIIeEgASfawUQgJAiUJIMklgXE6BHwhUIck37hxwxw6dMhs2LDBTJw40eiDnwQBCOQTQJLzGXEGBHwngCT73kLEB4EUAnVIsi36119/NdOmTUOSLRC2EMghgCTnAOIwBAIggCQH0EiECIEkAkhyEhX2QcAPAkiyH+1AFBDohwCS3A89roVAgwR8lGTF9OCDD5rbbrut64ehGg2+WQa06B9++KHrfWbfezrWZEKSm6RP2RCohgCSXA1HcoFA7QR8leSnn37aKDYSBJoi8NprrxkkuSn6lAuBwSGAJA9OW1KTlhFoiyRfu3bNbNmyZax1JUC2V1rH9GAhqXoC4qqx6EraPvbYY2M3P8eOHRt7XX3J/eeIJPfPkBwgAAFjkGTeBRAIlEBbJHnNmjVjsiY51tfpVpLVdHrddK9hoG+h1LAlxeKupPeZhtDox35DoK1EVDcpPiYk2cdWISYIhEcASQ6vzYgYAh0CbZBkyW9cgCXFUUkWjA8++GBM4Hh79EdA4vv++++PE+Ck95pEOtrD31+p1V6NJFfLk9wg0FYCSHJbW556B08gSVxcVUpCVGQKuKpjSpLfJElOkukkFrdu3TL79+83e/fuTTrc6L7t27ebEydONBqDCk+S3+4tW0kAAA0cSURBVKR2TZLptOC1IM22bdt6qp+YfPPNN0ZtVzQhyUVJcR4EIJBFAEnOosMxCHhMIElcXIV74MABc/vtt5u1a9caCU9aqjKmNAlLkuQksYvHKMkaGRnp6pmOn9fU7//++69Zt26dOXLkSFMhdMpNuuFIa9ekm5h48KrXJ598MjZkJn68yO979uwxmzZtKizKSHIRqpwDAQjkEUCS8whxHAKeEkgTl6rDlXDYabW0jY5NjZdVZUzKS2XHx72mSbIdQxuPyf7+008/mXfeecfcvHnT7vJue+HCBbN8+XJz9uzZxmIT3/gQl7R2jY4XTwt4x44dfS9nrhsc3UDs3r07rZhx+5HkcTj4BQIQ6JEAktwjOC6DQNME0sSlybiqjKmsJL/88stdQm1ZSLSXLl1qfvnlF7vL2+3mzZvNW2+91ZjMl5HkPBk9d+6cefbZZ83o6GjfvE+ePGmeeuopc/78+dy88uLKzaCCE5Ju5irIliwgAIEaCSDJNcKmKAhUSaBKIa0qripjKivJWT3JO3fuNAsWLDCXL1+uqqo95aOhKocPHzbDw8OpvaunTp0ys2fPNpLCJlIZSc7rSf7oo486PeNV9N5fv369c6Ojm4i85EKSdaOlcdWaCk/De/ISkpxHiOMQ8J8Akux/GxEhBBIJVCmkiQX0sLPKmCQlkh3laZPEww790GubssYkW7nKkmibj8vtjRs3OnM6b9iwwUycOLFrhg5b9tWrV83ixYuNBLOJpKEWUbbib1dRjA+1yRqTfPHiRTNnzhyzdevWyqqhsc0LFy40V65cycyzaklWXcRl2bJlnQdYkeRM/ByEwMAQQJIHpimpSNsIVCmkVbGrOqYsCYvGnPSwmT2untnp06dXKms27162Eqy8mUIkeY8//ngjPd9ZNxzR+uomJj5VXPT4wYMHzeTJk422VSW1sx4g1fjyrFS1JNuydPOgtkOSLRG2EBhsAkjyYLcvtRtgAlULaRWoysYkmdEy1hIuJf2unmJtlSQjRVbUy5JpTfc2NDTU9TBap4D/L0Pio3JtD6rqYXtPJWZVpiKSrDjuvPPOQlOmlRVCW76tl/09Kn+a/9i2SVrddV3WPMmff/55plDato72TqveaofoeyJavo1VeWelskyy8ooeQ5KjNHgNgcEngCQPfhtTwwElUFZI68Bw/PhxM3XqVKNtVopKqJWzNLGxMpeWn/LSMslpqYjYSAglZipLIqZxp3/88Udnn66vMlnRy8pXQxQki3l1V1xp3JJiVpnKVz+6TrEkPfCouusnK+nmJUuklX9UgJPyUv2sEOt8xad9adfZbwV0bla67777zPr167NO6emY4rPv17wMdK5+SBCAQLgEkORw247IW04gZEm2TWeFMUsIJU1pUiRJ0zGxSEs6nic2iuOBBx7oCJrOV75W5KsWHVvnrHxVZzHJ6zFVnRWvzi+TdI3yt4Iav1b1lzwr1qSk8rLi1/XKO012bZ6KQz/Ky9ZBr9Ous22iGTP+/vtvm03XFknuQsIOCECgBwJIcg/QuAQCPhBwJclPPvlk54ErPXRV9MfyKNqTbM/XVpKUJmvR83p9rfzzJFlipt5jiaEVbklb3nW9xFRGkrNE1Jat+lnBtPvytjaGstfl5WuPF5FkK7xWknWtvU77kpK9Ju/9giQn0WMfBCBQlgCSXJYY50PAEwJFJFkSpB7DvJ+oLH399dem7I9F0oskq+y0nkObbz/bIpKsc8QoyiGtR9OKXB7TNJGzgpolwLbd4ufYa/PKTpNMy9HWIZ6/Pd7v1uaf1a62LlFOVoLT4rLHo9ckxYokJ1FhHwQgUJYAklyWGOdDwBMCRSS57lDLSrJkykpsVFCrjNvmLylLSla8omJpJS+6L+naXvZZOUwTQeVpJdnVcAuNJ9bwkjzZ7KV+usbyy5Jk1T/eU696x/dFY7BtxXCLKBVeQwACrgggya7Iki8EHBMYBEnW7AgSNslaljT2g1L53nHHHebo0aOJ2VhpjUq6lbHovsSLe9hpy8uq7549e7p6ttOKksiXiVN102wguiZLYtPKK7pfcc2aNSt1hTwdj0u6mMT3RcvTanvKM+/mhZ7kKDVeQwACvRJAknslx3UQaJhA2V7bOsItIu6SRI3/laTZKcSsMGlGBb1WT2RVKW8KOIlZXBYVm3o0FZ+Nsap4Dhw40Jnrd+3atUYr8CUlxVT1FHDiqnztdHlW1lVX7de2ypQ1BZy9CVG5NtneZ8VpY7TH7NbGnNfDrjyqro/aSm2meZrVhnlpyZIlRj8kCEAgXAJIcrhtR+QtJxCyJEtAoz2GEhqNs43LahVNfObMGTNjxozUmSIkVPqJJsmb4onGGD3e62uVEx1PnFbfN998s/BiIkWF0JZt5dFKqeKJymqvdYtfpwU/pkyZYnSTEk+SXQ330NYmK86Kx8Zoj9mt8lKedS8mEo3Ntl/8PWNjtFsk2ZJgC4FwCSDJ4bYdkbecQKiSXHez3bx50yxfvty8/vrr5tatW3UXX7o8TW2mMbdNLUtdOuCUCy5fvtwR/SoFXD3ITSxLnVLFzN1IciYeDkIgCAJIchDNRJAQ6CZQZGhD91Vu9/gYk2qsMb5PPPFEI8s8lyWunu+5c+eakydPlr3Uu/MlyLpB0Y1Kv8ne7GzevDk3q6K967kZ9XGC6l7lDUIfoXApBCDQIwEkuUdwXAaBpgn4KKQ+xqR20tCC4eFhs2/fvqabLbf8nTt3mpUrV1YilrmFOT7h3LlzZtGiRZUI/+joaKeHXXnmJSQ5jxDHIQCBIgSQ5CKUOAcCHhKoQ0gll1reV7NDaCzm/fffb7777rvUYQt1xNRrUxw5cqQz9viff/7pNQvn1125csWsWLHCnD171nlZdRWwe/dus27dutT3TJE4NExGQy2UV5GEJBehxDkQgEAeASQ5jxDHIeApAddCqq+316xZY1588UXz7bffmo8//tjcddddZmhoKHXGB9cx9dsUGnaxadOmvoSt3xjSrpcIjoyMjHuYLe3ckParXmIu9r0mPeAnNkXHlCPJvZLmOghAIEoASY7S4DUEAiLgWkh///33ziwDUTE5ffq0mTlzplm8eLG5evVqFy3XMXUVWHKH6rJ///7EGRdKZlX56du3bx84QbaQNH3atm3bzIkTJ+yuwltdo2vTpstLyghJTqLCPghAoCwBJLksMc6HgCcEmhBSSearr76aOj1ZEzF50hyE4REBJNmjxiAUCARMAEkOuPEIvd0EmhBSK8mrV69O/Oq7iZja/S6g9kkEkOQkKuyDAATKEkCSyxLjfAh4QqAJIb1w4YJ55plnzG+//ZZIoYmYEgNhZ6sJIMmtbn4qD4HKCCDJlaEkIwjUS6BuIVUv8saNGzsP8aXVtO6Y0uJgf7sJIMntbn9qD4GqCCDJVZEkHwjUTKBuIT106JDRQg6S5bSkmLTUsl26N7plYYU0auzvlYBdzjz6PrOv05a27rWsstexmEhZYpwPAf8IIMn+tQkRQaAQgTolWVNwbdmypdQMA4UqwUkQGFACSPKANizVahUBJLlVzU1lB4lAXZJ87Nixzhy1ZabgGiTO1AUCvRBAknuhxjUQ8IsAkuxXexANBAoTqEOSDx48aF555ZXOKnu7du0y9kcrqG3durVwrJwIgbYRQJLb1uLUdxAJIMmD2KrUqRUEXEvyjh07zOTJkxPHF8+aNcuMjo62gjOVhEAvBJDkXqhxDQT8IoAk+9UeRAOBwgRcS3LhQDgRAhDoIoAkdyFhBwSCI4AkB9dkBAyB/yMgSWYmCd4NEGiWgB5qnTZtWuI3LhJlEgQgEC4BJDnctiNyCEAAAhCAAAQgAAFHBJBkR2DJFgIQgAAEIAABCEAgXAJIcrhtR+QQgAAEIAABCEAAAo4IIMmOwJItBCAAAQhAAAIQgEC4BJDkcNuOyCEAAQhAAAIQgAAEHBFAkh2BJVsIQAACEIAABCAAgXAJIMnhth2RQwACEIAABCAAAQg4IoAkOwJLthCAAAQgAAEIQAAC4RJAksNtOyKHAAQgAAEIQAACEHBEAEl2BJZsIQABCEAAAhCAAATCJYAkh9t2RA4BCEAAAhCAAAQg4IgAkuwILNlCAAIQgAAEIAABCIRLAEkOt+2IHAIQgAAEIAABCEDAEQEk2RFYsoUABCAAAQhAAAIQCJcAkhxu2xE5BCAAAQhAAAIQgIAjAkiyI7BkCwEIQAACEIAABCAQLgEkOdy2I3IIQAACEIAABCAAAUcEkGRHYMkWAhCAAAQgAAEIQCBcAkhyuG1H5BCAAAQgAAEIQAACjgggyY7Aki0EIAABCEAAAhCAQLgEkORw247IIQABCEAAAhCAAAQcEUCSHYElWwhAAAIQgAAEIACBcAkgyeG2HZFDAAIQgAAEIAABCDgigCQ7Aku2EIAABCAAAQhAAALhEkCSw207IocABCAAAQhAAAIQcEQASXYElmwhAAEIQAACEIAABMIl8D9m5NTCP7PJPgAAAABJRU5ErkJggg==)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TiTi4pd07mQ6",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def accumu(lis):\n",
        "    total = 0\n",
        "    for x in lis:\n",
        "        total += x\n",
        "        yield total\n",
        "\n",
        "\n",
        "x1 = list(accumu(x0))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eo77ePR68FV8",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def avg(lis):\n",
        "  pre = lis[0]\n",
        "  for x in lis:\n",
        "      avgVal = (pre + x)/2\n",
        "      pre = x\n",
        "      yield avgVal\n",
        "\n",
        "z1 = [x * -1 for x in list(avg(x1))]\n",
        "\n",
        "z1 = np.delete(z1 ,0)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Moe1-IGj8YMM",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "B = pd.DataFrame({'0':z1})\n",
        "B['1']  = 1\n",
        "\n",
        "B_ = B.to_numpy()\n",
        "B_t = B.transpose().to_numpy()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TjIg47kh8pA-",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "E1_pre = B_t.dot(B_)\n",
        "\n",
        "E1 = np.linalg.inv(E1_pre)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XVQggQkw9PKE",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "Xn = np.delete(x0 ,0)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XvrZGZ3v9DL0",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "E2 = B_t.dot(Xn)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bBbezwQF9tgH",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "parameter = E1.dot(E2)\n",
        "\n",
        "a = parameter.item(0)\n",
        "b = parameter.item(1)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "diRoeVewRP-E",
        "colab_type": "text"
      },
      "source": [
        "The time response sequence "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xlzaOf7W97ht",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def dif_eq(k):\n",
        "  return (x0[1] - (b/a)) * math.exp(-1*a*(k-1)) + (b/a)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G3mUotkqRVvw",
        "colab_type": "text"
      },
      "source": [
        "Compare the real value with the forcaste value"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Dzg-4dU-BZu2",
        "colab_type": "code",
        "outputId": "bbb850e7-9a6f-498e-909f-397c3b1f94e3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 50
        }
      },
      "source": [
        "K = 30\n",
        "X_forecast = dif_eq(K) - dif_eq(K-1)\n",
        "\n",
        "print(x0[K])\n",
        "print(X_forecast)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "836.5\n",
            "683.6988373522181\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3LsRG8N5va9_",
        "colab_type": "code",
        "outputId": "92b3628c-e4e9-4c2e-ac7c-8799813e541e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "x_range = np.arange(1,x0.size+1)\n",
        "\n",
        "def x_forecast(lis):\n",
        "  for x in lis:\n",
        "    x_fcst =  dif_eq(x) - dif_eq(x-1)\n",
        "    yield x_fcst\n",
        "\n",
        "fig = plt.figure()\n",
        "ax = fig.add_subplot(1, 1, 1)\n",
        "\n",
        "ax.plot(x_range, list(x_forecast(x_range)), color='tab:blue')\n",
        "ax.scatter(x_range, x0, color='tab:red')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f61256cf160>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 65
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Fr/4VIz/8PpWZKSozM9V/Y4blV67g2l/4+RSY9UGawnNkhGWVamBWa7iatV0lveYVlYVr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\nAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Jl6g63e8Ti2G",
        "colab_type": "text"
      },
      "source": [
        "# **Accuracy Test**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DW8BJml3SAmT",
        "colab_type": "text"
      },
      "source": [
        "![image.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6Hyw_5tgDvIM",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "x0_mean = np.mean(x0)\n",
        "\n",
        "S1_sq = np.var(x0)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DOL6DR5qSPfl",
        "colab_type": "text"
      },
      "source": [
        "![image.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XVpE6Ou0GiIM",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def residual():\n",
        "  for K in range(len(x0)):\n",
        "   res_val = x0[K] -(dif_eq(K) - dif_eq(K-1))\n",
        "   yield res_val"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uBZWwnvfSTo7",
        "colab_type": "text"
      },
      "source": [
        "![image.png](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOwAAABKCAYAAAC4lrjnAAAMgElEQVR4Ae2d2ctPXRTH/QNuXChXriS5cCERCRHKBYqQJEUKkcxKpAiFUEIiZQ6hEJEhGUISyUyZh0wh8377nFre/Rxn2Gd0zvOsXY/fGfZ0vmt911577X2OZkaTIqAI1AaBZrXpqXZUEVAEjBJWlUARqBECStgaCUu7qggoYVUHFIEaIaCErZGwtKuKgBJWdUARqBECStgaCUu7qggoYVUHFIEaIaCErZGwtKuKgBJWdUARqBECStgaCUu7qggoYVUHFIEaIaCErZGwtKuKgBJWdUARqBECStgaCUu7qggoYVPowK9fv8z169fNpEmTzPbt21PU8H+RrVu3mmbNmpmzZ88a+/j/HHpUFwREfiLPIvqthE2I6vfv383Vq1fNpk2bTKtWrTySJayiQfZbt26ZhQsXmv3793t1cYzgNdULAeSIDEkY3w4dOhiu5Z2UsCkRRRgIJSu5qGfYsGFmxYoV5suXL2bGjBmFCDrlY2qxFAggx/Hjx3vETVE8sogSNhKe8Jt5ERbCI1yETJ0QlmNN9UYAT4mRNu+khE2JaB6E9Y+o6g6nFEbFiiHX9evXF2J4lbAphZ0HYe0RFSEz0maZ+1y8eNELhqV8JC0Wg8DDhw/NmTNnzO/fvyNzEuNAtkUkJWxKVPMgbMqmA4vdvHnTC4TFKVNgYWO80UCCJuSR57MNCEYFZWyqCWx37txpLl26FAoBuBGPKCrVmrBlhNHDgBeFzhp0Cqs/yXWItHTpUvP27dskxRrkRcl4JhL1SfDrzZs3XhSbaySet4i5mVd5Df4B43nz5gViDX52DAIDKLjl9Wi1JSzgyIhQZBg9DOgqEfb48ePe6BrW17jr4GeTkGPm05L8AZQNGzYYiNxU0969e/9aHQAz1l/tvyKMeW0JaysLVqyoMLrdjn1cFcJ++vTJTJ48+c/oaPfR9dhPQBTNVjb/uZ/gYe2wweTw4cPm7t27YVlCrz9//twzyD9+/AjN869uPH361EycODFwlC26T42CsIDkHwWKBo55TJs2bcyaNWsMivmv0o0bNzxj9fHjx1RdwNj5I5p+gvrPbe8mrFGItmXLlkyGhHn52rVrTdVI++3bNzNt2jSDZ1N2ahSEDVK6IoHEONiuT79+/SJdxB07dpjmzZs3KGOXdzm2XVb72datW2fmz58fG7m0y9jH/jkq9/wE9Z9D2LjAytGjRzNv26QvBw4c8OpJG0yzn9V/vHLlSuP6xw43O4E7c9mfP3/alws/bhSELTKMnocEGCEYiYW0EyZMMLiycYly58+fN926dTOnT5/+K7tMBSBU2hRE2Lg5LIS1gyv+tl++fGl4xmfPnvlveef0V4xUmCGSggR5xo0bZ+7cuSOXcvudO3eucf3zExZ59O/f37x+/Tq3/rhUVEnCiiKKUGUEC3LFXKy9CxBF50lLWvqFcuzateuvLj569Mh07dq1QcDor0wxF4IIC/4SJQ4iZxzmGzduNHPmzIkcfSCtyDWmi95ovnz58tReRFz9ae5fu3bNdO7c2fBbZqocYYWsdpQSpUK49pogIPmVqYgwep7CgLTLli37M9JOmTLFaaR99eqVwcX0J0bfdu3aZVIa8AZrMLYT2IK3H3PycE8i9HYZjt+/f2+GDBniubL+e/Y5bcqWTPt60DEGq0+fPqEjdlCZoq8RSOvYsaO3Llt0W3b9lSMsLlKQkqBQCFgUi3wyAstvFtfQBqXIY0i7ZMmSP33HJXNxj4P6xPMGYRWUN+qaP0oclZd7YB/myl6+fNm0bdvW8BuWxAC7ykuMx7Fjx8KqLP26PMPixYtLbbtyhBXh+BWCkSDMqpeKWA6N5UValIWRhxE4KmEQiLb26NHDMxQtWrQwY8aMMbjUJDBPsoMpiuDsBIozIraM/QG8IBIXTY6vX7+aPXv2eHNS4gz8DRo0yFy5ciUUVunT1KlTDVHjslLlCCsuMaNmkPDKAqbodlASCCfewYIFCxLtiiFqSnQ4bh744sULM3ToUDN9+nTPpaTctm3bTPv27RuQ1G8gw54fRb19+3bYbc+9jusTcrXzcB7lHoubHZUntEMxNzBmTE1GjBhh7t+/782TT5065XkJhw4dCi0telpEn0IbNaaa/z+sgIEy23PZqAeJuydWXQgS9lumkeA5Iar0BQJDZJckGNmKH1SOEa9nz56Gxf6oBGHjsKZN8kDaoOTaJ+oQRQfvOMyl3gEDBuS+WSFtHED6FId/EE5ZrlVuhLUfBsGizCJc+16Zx6tXrzZJ/969e+fURSw881ieE1fsyJEjTuVcFYZRolevXn/cX6fKU2Zy6ZO4kpAU+caRla641Juyy56X0aVLl8gN/UF1F9mnoPbkWmUICwBBc1QEijIj3H+VZs+ebZL+uRKWZ4K0rFsSjGJ+65JcFQZ30g5ysdziX1N0ac8lj0uf/J6Oi1yj6sUzEA8l6jfM5afuzZs3m5YtW3r1jBw50rjsGovqkwtWafNUhrBYXoIZ/iQW2R5lbSG5WGjq9CtKmHBd6/P3M8s580yIlORtmziFYa7KaN2pUydz8OBBZ0OQ5Tni+kTd4CtuJHKU46h2pd68XWKCSt27d/f0jjaSJOmTS/+T1BuXtzKEhVDDhw//a34khBVLbBNbSBhmPeMevgr3xSVm32ySFKcwDx488Bb27W2LEmCZOXNmYZFN5BQVuea+GF/k17dvX8+YRj3758+fzdixY/+Ui8rreg/jOHjwYK9e6ifJOjkBqA8fPkRWFYd/ZOEMNytDWHF9RZjyTAg4apmA+/9iVJT+ZflFQdiTS1QyaYqLEvNSAJsqUHRcPBRs0aJFhiWd3bt3J23OOX/Uso4YX5GXfY7Rlev+xiRfnmuebJvEsDBqP3782CMrLyvgGrOrKm6PsBDWr6/+vud9XhnCytqejJrissa5HAg5TNB5g5VnfRCObxrzx3GahAKzNVHWU+06MAa8dMD2ObBs3bq1Yc2QkTxte3b9Ycds1cNQEH31J5Gt7RFhcOkfv2FJdhXluXECDE6cOGF69+7ttS9r0+fOnXN6+0qWmpr8OmyY0MKuC9HD7lf1OsThTRHXIFPQc2CooryPoDJFX2M0HzVqVK5GFPLjOoe9TFD0MwXVX8SoH9SO/1plRlh/x1zOsdhJdui41FlGHoJMbGTg1zVBbH90F0Vm5IzaBuhaf575MCRxm/+TtMerbFXb/C8vXjAFKDPVlrBYONwo5hJ1SmmDTLiRFy5caPCoojRBr941yFjyCa/XsfWRwFfWBF5Zv6iRtQ9B5RksWL8t21jWkrCQlck+vyTmNnIcBG5VrqUNMrH7iR1RKImdJPBBsKRqiUAa+5ezzpdPnjzpvVqYtZ688cGA6vuwDqhK4EKCUnEBC4cqS8uS9OsJEPzevXue+4xyBBkl3MU83c+8wIBgRKOzjP5MGXCvs8zz83oefz0YSf3ihB+VRnROkEkitraxcT1meUbWC21YWL4ZPXq09x6qfb0Kx1k/wrZv3z7nvdVlPi9LPmwn1W86lYl6irYY4Vhmskd1cUu5Fra8xEgxcOBAr5wrQf35wkZR3OVZs2Zleok9BRRNugifhWE5J8nOtLwAq+UcNq+HT1uPbNaAwOzOwk3nWthaYtHvS+J2rlq1KvN8MS0eTa1c1u9AZ8FLCZsQPRllCXRBUM5llA0jbMImEmdnlOXL/0+ePElcVgskQwBZg3XcRwOS1eqeWwnrjpWXk+ggbrF8pIyLEgizd/AEVStkT7LZASMQ5mrbbfBVQb7MWMUAjd3POh/nEUjL+vxK2IQIQh7/fBWiupAQwrJvFRJiqeNSUFtRZdhIUfZX/KL609ju8b/X8TG8f7nEpIRNoFXi+vo3fENA/7WwaiG3y4gp5cmbJL+U09/GiYASNoFcxaW1CSQktq9FVcnbObjTjNIuo7ISNgrNpndPCZtA5kGur8xf+VpG0Av4dvUQntGYX/n/bKjTv4TDuYzYSlgbQT1WwibQAcgjRJJiQri41wDJT15GWFkKkjqifpWwUeg0vXtK2BJlLu6wTW4hvH+UFcOghC1RQDVoSglbkpBsd5g5LC60y6uBStiSBFSTZpSwJQmKkZT5K8k1qgxZZeTlWJMioIRVHVAEaoSAErZGwtKuKgJKWNUBRaBGCChhayQs7aoioIRVHVAEaoSAErZGwtKuKgJKWNUBRaBGCChhayQs7aoioIRVHVAEaoSAErZGwtKuKgJKWNUBRaBGCChhayQs7aoioIRVHVAEaoSAErZGwtKuKgJKWNUBRaBGCPwHiAHuF/y6uVAAAAAASUVORK5CYII=)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gHe3dY-CIHz5",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "S2_sq = np.var(list(residual()))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Szz29WboSbz9",
        "colab_type": "text"
      },
      "source": [
        "![image.png](data:image/png;base64,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)  C is the mean square deviation"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6Zjgjbv9MMHB",
        "colab_type": "code",
        "outputId": "26eeb25d-f816-4384-a049-ee33d55966cf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "print(math.sqrt(S2_sq)/math.sqrt(S1_sq))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.9976030367520015\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s-m2x2AWUN3S",
        "colab_type": "text"
      },
      "source": [
        "# **References**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MrwRuBtMUbEh",
        "colab_type": "text"
      },
      "source": [
        "https://www.researchgate.net/publication/319605877_Application_of_Renewal_Gray_GM_11_Model_to_Prediction_of_Landslide_Deformation\n",
        "\n",
        "http://iieta.org/sites/default/files/Journals/MMEP/02.1_05.pdf\n",
        "\n",
        "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6112867/"
      ]
    }
  ]
}