PyTorch_SimpleRNN_Sine.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "PyTorch SimpleRNN Sine.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "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/delhub/public-temp/blob/master/PyTorch_SimpleRNN_Sine.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1qUhA9xGJoar",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import torch\n",
        "import torch.nn as nn\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qCALJCSw6LbJ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "8abc484c-6243-44c9-afe3-ea6d7baebe75"
      },
      "source": [
        "# make the original data\n",
        "N = 1000\n",
        "series = np.sin(0.1*np.arange(N)) #+ np.random.randn(N)*0.1\n",
        "\n",
        "# plot it\n",
        "plt.plot(series)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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8svettesA4rJ4syGL8FiaxRvnsVEMKkJdo8kU/dE03wTGIcUgso32/L0UI4LBPDWhdUnR3cwuTLE+BZ2g1xZhF/1ZTQvQSYfULoo1FbM+6T4aTbIW2YWgnmJfxnLxe8Mx1lIhgt44R2OxdpFKDmwg2O3PilIpqCFjcFqffC7BGMRaq0DBRHPBRechW1d3OKM59P+b6A4nomMO9gbLAQqIpXPm0V2c85hdr5h17Q5mziO2WL/dH6Fe0y2yQBydY+jHjXYB3QnRhfk+G4VseTiWtdzu9uftIjaomxZZoGAXEZTtzPbj12W+o7GLihq6TlJ03mutOohiCowzXhmI5OIHulhZq1GmS+48uoNldCH9jnuZ8yg6IkB2zfIsMttQK5nOrqALaVasTOO8i3ax3mqASB5U9L1cTBDk13+1VQeRtov1dkNMJ5jrbK57GmpIf09jHz0BnbNIM80cLv/6mxbZZDWCrLlkfl3C679gF7pYXxWLr4vo/vpZVF5t1sVc5O4CIojL1mZZJBDnPLpZVrZWMGBp8c04j1WDVNrxgSB3Hk0TCPjXPy9WduaDSk/Y2lpEBLUaYb0lv/67g1mLLBB5L4fj3MkCOsPdFaM7Yxfz6EJiF7sL1JBxcF0BIjAB1zhaY2siuxhNoApF7NiW273BJL9e9axYL7+Xk7l7GZOgpZKDGwgKER4AVloNUUYK6CLnaiHCrzbluordCUAcF98dTECE/AlNG1nxTTIRWeY8AFm3g/k+piBuApVkw890xTsP/T6NyIystOqi7NasLdm9HE6Wski5Xej3dRozRDCaKAzGfLuwojvB2hapodVWRIKQff5qO14XoNGdsVcgrli/GAhi0F0qSfWEsruJ6FEiOktEby35+7uI6LPZf18hoiuFv00Kf7s/xXp8Ms2c4ZzzbskRQW8hW1tty53H3gIiiHFE3eEEq80inaDXuCMwYNPRU6QTAFn/s3nPYhYvCZ57C/TXSgS6UEqhN5rfpKutuii71WubzN3L1VYj6l6uFNa1FkHnGEc0ox/lVMfOQiA290GK7oCZ016NsItcV2YPJuhJkKJSCrvDcb5/zNpiko3VhQQh5pDKFNLwv8QtRFQH8G4APwTgHICHiOh+pdQj5jVKqf+p8Pr/HsArCip6SqmXx66DI73RvMGZf8tv7LLzeOqy3HmstxcC1GgCpVTu0EOlN5o3uJUs8PWH/MzPbCCTla5F8KQ5usiu2VoMBWACVFPrqGdny/QEzrs/mkKp2XUC9L+lNJNGBAV00ayLkeIiNRRjF4sI1tjb3mCMExttlq7eAmVo7oNk6nwWCBJQQwtBpVaj7PrLdCmF5AlaCl2pJAUieBWAs0qpx5VSQwAfAHCP4/VvAPAnCT5XLN2F7BbQBiO9Gb2FbG2l2ZD3Pi8ggtVWA5OpwlAwGm8KjLN1ZRnWSJJ5G4c7n61JukMWr7/5vyQrKg/qsgxrL3dqaRKEvQVqKGbD9xac90qrDqUgonMWEWwMiuoOJ2jUCK2MfjSIQPI9F+/lapSu+YK40StBd/lsT2c+QZMkG0B54ii1sVSSIhDcDODJws/nst8tCRHdBuAOAH9d+HWHiM4Q0YNE9FrbhxDRm7PXndna2opacG8479SAzHkIYWO3jE6Q1htKssjimjnSXaxdRPCkvdEEK80ZnRCla1geVKTfsajD6BU5D0uCIPmOZhBqrQTdSWSvxHkU1xyjKy+wC9bWG02Wrpf5DLauhW6m2CYCvZ7C9RdStot1KL1GebLXG07mkPpqqyEOKqnkWheLXw/gg0qp4re+TSl1GsA/BfCbRPTCsjcqpe5TSp1WSp0+ceJE1CJMRryYYUmMZDiZYjJVyeoN3SUjidmk49IN35c4j0G6LHKW+env2azrc+xlzmPZea+15RSAXleCoGI6thZsLMp5FHXl6E7yPRdppkb+GZJ1LSZU+vdyasjoa+R2EUMzFdYmbOJYXJfWJbOL0WSK4WQ6Rw11hLpSSopA8BSAWws/35L9rkxejwVaSCn1VPb/xwF8HPP1g32RMiNZE27SMnSx0qpjMJ6Khq36o8mSruKaObJIDUV1YQwnOVQvriuGGuo0Z+anszUJNVQW1BtiB6l1LdIJgnWZ77jgiIZCu1h03isRiGARqeSoU3gvU9pYcT2APEErSxCkgXgxccl1Cewi9z0Lyd5wMo16NnmspAgEDwG4k4juIKIWtLNf6v4hohcDOALgk4XfHSGidvbv4wC+H8Aji+9NLf1SI5FBvdLMQ5jFl3WtxFBDvUUKIDaLbJZkpEIKYKXQzQToDEuCCGzZmqR9cRbUF4vFksJzGf0Y0R215HDlWXx3sXYUsS5NDc3THFqXzOF2mrWcfgTkCZptX8YFlZm7lAYoW7IByPZlKokOBEqpMYC3APgwgC8B+DOl1MNE9HYiek3hpa8H8AE1P7XyEgBniOhzAD4G4J3FbqP9EpuRRMHGhaCi/8bTZ2imTgnUlg3VjJeyGEAO24uIwMB2Ka9cvPaAzpBSZX4pqSExUiwJBNIsfjyZYjieb3eeBWLBvbTYhQTdaWpo5kZajRoaNRLupfl1mbVFOdzmfOYtoh9HBsEuJBuJbMzolVC2qSS6fRQAlFIPAHhg4Xe/vPDzr5a8728AvCzFGjjStWRrPUE7Xi+/scWBMtmGN22d5dSQYGMtUUMRWeRw2Xl3mjWxrpXFQBAZiFcXArGI5rC0FUvsIiVSLFvXSkQWuWQXUUXZcudtusx4uuZpUUDexFFODclagW3oLpm/iKDTUsmBnCxe7E4A9I1RCuypWyfUY97YPItM1B1i5W+FLXSLG35VOI29WGA0a5NSQ806oVkv1BuadVkraoldrAjtIq8RlFJDTLvIeeVlXaLCv6XeIEM+06Wgviak0xapTLM26RETzfqsrRWQZ/G2oCKxC2OXqeoqqeRABoLS1jJh5t0tcd7SjVVGJ0iNZDpVS/xtu1EDkbzHe4nOadXRExxXUa5LzsUvBhU5nZDOLvqldiGj+VzogqtrUjJVb+xCRg2NLUFdhu6Wg4qc109tF2X7Mg26a4h0pZQDGQjKhpDEzruMV27LKJjFUyHn1sU0kln74kwXEYnbIXUH0jwi0G1vaTa83HksI5W19mzqlrsusxYjKYO6tPBvssiVsmK91C7a83YRw3kv13vkLbdl1FCqekNxGpu7LsCW7PHWVkYNxTSEpJKDGQiG84exAfJjDmZnmsQX8sq4yJmRMJFKiVMzP0u7htbKdCXK1qQdHeVBRTaNXWYX0XROaRbPdB4lzlta+J8lGyVFWWHhv7N4L5tyXj8ZNVQWoFp1kV30RxPUCGjVl+1CGtRT2EVKOZCBYPEwNiBik2av77RKjISbrZlicUmBlx+gHBteSDOVbVJ519ByvUHG65dQACYQMwuWKe3CBNtOSeGfTSeUBhWDOpk1rcEyUjRrS8XrSxGBNYuXJhtL31GG1I2NlduFDJGlmuxOJQc2ECwbiezGlvPKMuddRifUs3NcpM5jacMLDj7rj/WhW8UhGKNLzN+W1hvSZX6AhDYZLwfOpsx5lM2qSJ1HfqRyYW3GLrhDTTakKLmXw/EU46kqR53J7EJWO3LaBff6j5bX1WnKdM0e8FRRQ9ddesNxqSMC5IGgrOWTm+GWcZFmbfx6Q7ku3VrJ7YyyOA+x8y4vMI4mCkPmIWqLZ90As4AlodNSOY+893yuayVdsRiQOW87UuRPY5f11+t1CoczLQ0Jw8kUIyad011olDC6AP717w9L6K+8wMtnEIgWpuqrrqHrI5oCWKYm9N/4zrvdqKFeW4aNfAhqioKLnCs/wzLfY20hi18VFHjLWiGBiMzP0jVU/CzO2pZ0CbO1tOhigla9hkZ9fhpVr1nK68cnCKbdcTmo1MR2UUbnpOoaktdoxnPn+QDyzNvWMSdZVxn9WFFD10lKs0jxjR0vGUmzXkOzTnznUYIuABl/a9Mlcd7mqONiEVXr5sN281AgG9Tmt+OV88oA2ENN5byyzHmX6TJTt+zaUQllaNbGtTHTkLB4LyUnYJbN0Jh1cltRJ1ONBsu+IyDpwFt23rMn4fGTPWsdShBUluyiXkNN2NadSg5mICjrTjBj3gIuftERGX38zGO5WAzIWuiM8y5CUEAfgsbPIssRwUqrlk9XhorNqZl1Dsbxztsc9Ma/l8tBXVzvKSliA7IumMHI3Mt4RDAL6vHdOTZqqN2oZQ/5CbcLW1CRN1446oACXWXX3vyNI/3RdOnaE5GYTkslBzIQlB+XYJwHv+Vw0eAAWZGrN1puXwRkm3SW+S3TJtxNZUMEkjbNsq4JQH79y44lMI8lZAeV0XSuV7+4zhSZn9Encd712vz0NCAr/JtrspggrDTr7CnlshZZAGg3zfVn2EVe05q//sZ+ZQlaGuddziDIhsAG4wnazWW3q+ttVfvoNZWy3mfj5LgGVzbZCuiN1mc6IqNr8eySlaTOW0INlQeV2WFZ8RveOCbO9S87rXVeFy+oDEo2vLl+3CeBldkYICuk9rM61KJICv/mmiwlCAKayVbE7kgCgUkQrEgxXJdSCv1x2R6XBZUydNdp6mlsCc26eO0BE9QrRHBNpezG1mqEVp3vvPWNXb6M7QafJy3rpgFknGseCJboHD5SmVETy0EFAKuFsazLCpBt0sFYP2N4ccN3hDRfmcMlIrQbNQwEuhYdJGBokzQ2Jin8z4L6MiKQZMpA2fXPnDfje1p1CexiNFEWu5AH9cUEIcYuFvcRIB+oTCUHMhAMSrIFAGg3a7nTC9c1LdXVadb4Bjcs19UW6LIVBTvNWn7cdajYEIGENpm1yC6vCwD6jO9p486l6M4e1PnOu4yyAvRaOd9Rr6vcXiXtu33LNZM8TKnsMDag6Lwl93L++rcFQb1vCXaSoGJeb72XiWysI0D9KeVABoL+aFoalTvNOptXtsH2tsBI+hZeuSNAFzZqaAbbeZk3gCVuM+/0YQSCgSXzkyECW7DjUxPm9eVBvS4I6pZkQ5RF2gMUP3HRn90qQQQAj/Oe1RssiExgY7YsXhJUbHaRog4FmH2ZMHEUHOCYSg5cIFBK6YJNCU/XadZEN7as+KOzBT4ELaUTROuaZKdKztcbZtlyuD5b15AkqPQtXSsS5+0LdtxrZgvqkszPGtSFiKDcXmUJQrNOc3MvRhfAo3Ny571wzSSIzIZg24LCvw3Bzuo9/DpU2b3USJ1Ls1oSxwY/CU0pSQIBEd1NRI8S0VkiemvJ33+aiLaI6LPZfz9T+Nu9RPRY9t+9KdbjkvFUYaqWISgg4/UH40kOOed18emc7nDsyEj5vL7NqQFCRGDZ8JxMZuCgrAAZIli8ZrrDhlgZ6Xiij0tIlSD0RpOlwicgQwQ6i7QgAgFlaLNX81kcXcByHUoSiG1trbN6g0DXwjXL64BMXWX1BkCOCFLZWEqJfkIZEdUBvBvADwE4B+AhIrq/5JGTf6qUesvCe48C+BUApwEoAJ/O3ns5dl02sbVVAjJevz+yIwLuhu+Npji00lzWVejLDn0akm5TK/+OZt2hYuPi4ygAC53DyiLLAxTAp9NMC2zZvWw36uwmAvP83aV1CWgmjVTKMtJ65qg4dmG3V/NZoWKnYGKCugXdcVCnY49rdM3XlaozcGCxi28FRPAqAGeVUo8rpYYAPgDgnsD3/giAjyilLmXO/yMA7k6wJqvYsgVAyMVbNmlH0h0ymn/+qxFJX/bAUgeRQG07bI/I1iywnZetlWek+ne8DCsvopaiKD5/27e0j3aYjghwOW9+Fj8oGWgS6xpPUSOgYaOZWOjCTRlyu8kAe1Dn2X55EpTr4trFcxQRpAgENwN4svDzuex3i/KPiejzRPRBIrqV+V4Q0ZuJ6AwRndna2hIvdsZr7m8XQLtZE3DB5UYigu2OOgjAh+2uDS/K1myZnyAjLXPe3A3vCiqa1+fxytp5lzsPfoJgs4t6/vdQ6VsGmqTF+k7J3EsMIlhcmyhBGLn2OC+o2xoSzFoliMBah7rBEUGI/F8AbldKfRd01v9+rgKl1H1KqdNKqdMnTpwQL8TmiAB+VHZt+E6DTw25jMT8PVyXfb4BSLPhUyKCZl0f3McKKk7nzdzwDprJHJkQKsOJ5pXL7x01l7cAACAASURBVKWAfrQ471nLLdcuyhEUwG0iSGhjluuf24WkfdTWxJGgm0mvNV3XkKQDLKWkCARPAbi18PMt2e9yUUpdVEoNsh9/D8D3hr43tbg3vMxI7BE+TQeSjDaxt6mZv4eKbcPLYLs9w+owHa7rXnLRnXPDM4v1Xrtgns/kC+rcDDcVZejqZgKYMyGO699hFsXddpHSxnhdQ7OGBHuA4j5GM5WkCAQPAbiTiO4gohaA1wO4v/gCIjpV+PE1AL6U/fvDAH6YiI4Q0REAP5z9bt/ElUVyB8rcG76GyVSxzlEfjKdWykr/nUfBpEQEqSgrn/NO5XDbDR5st9VBAIPuBN/RkvlNlZ5+DdbnCep8ROBAF0z7L01cBJPF5vq36imCenk3GSCoEXjQRYpuJr2uGhTTLlJKdNeQUmpMRG+BduB1AO9VSj1MRG8HcEYpdT+A/4GIXgNgDOASgJ/O3nuJiH4NOpgAwNuVUpdi1+SStI7IbXD6NdOlw8Jc+twdHTyj2+gs314pIrC1L3LX1bfMN+i18aC26/rzdZVTVloXr8DrRD2FoL441GXVZ6MMhUH98Gpr6fciRDCyJC7C40Ja9RpqtQR2sS+IoDyop0KdxXpbqF2klOhAAABKqQcAPLDwu18u/PttAN5mee97Abw3xTpCxOk8mJyfz+AAvRnW2/7LrNFDeR+7ZBDGeoxGQkTQqOvz9bnOo+x66bVxW/vcQX27Pwpfl6V9UetPSzMBeu0bnXB9Ll4/RVCX9OvbahfNOqFG3A6k8mAH8NGdbaAM0Hv8SpdvF/bEUTB3YUGw5jWbneUW8v2WAzdZ7HIe3B5jd/siz+GGZJFJCnnCNsGyDW/WxqcTlq+XXpsMEdiKxZL20RTzJb7CMxAe1KfZMd+2mQQgFc0nQwRl35GIRDUal10ko2DYe9zRbi7VZZkJAXiBOKUcuEDgyxbGU4VxIK/v6j3n0iah6CJUfIU8Ln9bRgEAZrqVi1RsQYWpK+FAma19Ua+LaRcJg7rTeQi7ttLVCMptTOvjBXVbTcusTTL3YqOtuEjFpqvN9Bcu1CmpA6aUgxcILKccFn8Xaii+3vPia/y63G1qnHWZ15Z+RyF/mwwRWNoXzdq46yp7YAvAHygLyeJDu2BcvHKnwQvqQUiR6STdNsa7/tagLuDPrTYmsAsiTVEtCht1jtyIwHxeiLhQp6TellIOXiBwIQIunePhqLUublBJgwj6o/IjJpp1AnH5W4fzliACV+aXKouUdoe4CnmhKMp1L7lT4u62SlkTQdk1M7w+//o7EAF3Et5mY9ygnn3H8oYE3llP7iNpuP4irIngesgBDAT+CB+c+bnaR3PYHnZj3Rw1L/PLB91s/C0zw7IVBQEJr+8qFvPbR+1BRdjy6aJNuM7bgQjC7cI92ao/j5vFL69LP2gl3fVvsRGB3cbYiMCCegBjY2laxLnt07aHRc3pqhDBtREXf8jtqLEdzwxIMj9/R0Gokdie0DRbG7/4mYq/1Wcg2bJIbuZn3/DcB/C420e5hX9XssEL6r6zsfS6Qu1CX49UiMxPGabpJuMW622NEkaXzC7ii/XOWRUBzZdSDlwgcPGH3BY630AZIHAeCRCBq1gJyDhXe4bFG8LrO6khJlJxbnhujSastS9sXQFZPLOJoDRxYSICV1ABBIjMSQ0xkw1v4Tm+UcLoMq8J1dWoERpldShmILadvFv8XVUjuEZipnfL+MM2O1tzFIsbTF2OInbKDiTzGbyCmcd5JzjrJteVaMNzr1l/ZB9okvL6ts40QBDUk9iFHcHq3zNrNB5EwH3Ijb2bTJK42GcSAN5eslKZ0kCcqH03pRy4QKCLqPZM2bwmRGxPaAJmRsIuFpcYCRGhxSjKugKU+Qw+F5wGEbi4YO6JrT5qwnxe8LocCAoQFAUTTIm7OpByuwhFKg4Ea9YWer2UUhg67II7nOkqPOuBsnRFbCDcLnR9zP4d9eeFJhshDSEVIrgm4uMizWtCxPaEJmBmJOxisaMdL3xd6RDBxDHQpHXxD+qzdYd0GnUMx1NMQ/lbR6cJd2O5BpqklKHzSWDMDiRXm2YwUnF0wJi18ecbHDaWqPDcbmq7CD2Qzd1EkA4RcM96CkIEzBOLU8mBCwR9R4GRWywOah9NUCw2+vi95/GIYOgwXv17Zo3Agci4U8+ubiZuFu9rRdXrCt/w9joUzy5c3WRGX/h3tNOPgOkAi5974a7L6HNRVsXPjNIlQP1eu2CifmeNgHlicSo5cIEgCBEwDM460MQeHPI4XEbxzVWUMrr4lFU6ROCjYIIdbgB/y9rwjolnrSs887b1sfPtwn39eXbhRwQputzM75NNFqcM6oKhUX+A4gXishNWJWeApZSDFwicNzadwXEflD0r5MV3+riGYPRnSLLIVDUCd7G4+Jl+XQ4umDmN7Sti63VxsshyXcYuUgyUATy78NM5DF1e+lFy1pC73sOj+dLVAV2UFU+XPUHQCSWxOq1SyoELBCEthymMBDDZWhpEwKOGfG2CtZzy8esKQwQh/O046992nTUEpMniJZvU32kSX3jWawsftnK1ohpd4Ucc+JoIBHbhOigukNcf5/MNvg4wzvW3r4ujy1l45g6UOWZotD7+Y0xTyYELBO4eYx5P59Kl9YV3TuSw0QG1OQYHlBcrZ+tKwwVzHqjRDwh2+nXhaMV7L5MUBfnowrXhOY849AX164UIXAcual3hTtJHZcquf6L20SCkki5BuKERARHdTUSPEtFZInpryd9/nogeyR5e/1Eiuq3wtwkRfTb77/7F96YWd48xN1uw6wJ455oMxhM064R6SR+71iUoFjs2AzuL9KGoAOftaqvUuvgttykHytJRVm6kyJnGdrWPmrWlDOopjksAil1zfn1+KpM/0JdsoMzz/Az9eYxkw+EvuM+9SCnRgYCI6gDeDeBHAdwF4A1EdNfCy/4OwOns4fUfBPC/Ff7WU0q9PPvvNbHr8YnLSLg8nQ8RcM41cfHKAK/lMyV/G0IzFT8zSJenC4OzNpdT4+sqX5exi3CkYu9mAsywVXhnlCtBSB3UUxygZnQBgQlCAFIB0lC2/FZg+xwB98FMrtZpAOxH5aaUFIjgVQDOKqUeV0oNAXwAwD3FFyilPqaU6mY/Pgj9kPrrIt5sjQm13Rs+nAt2cdQAr+XT9RS2fF1cmsnBBQNhm9TfchjuvKdTM9CUhk5wJQhAdv1ZiMCli2EXDvoLSB/U+dPT8XWV0GQjxGbzAxd9LeIM5+1Gdxz615MgMAc9U0qKQHAzgCcLP5/LfmeTNwH4y8LPHSI6Q0QPEtFrbW8iojdnrzuztbUlXmx/ZDcSwPRSM7hI1yZthLdW+jY8p+XTN1DWbtQxCXygRig1FOJAvIVPRqfPcOLhzhMX/jkDUj4umPOIQ3+CwB8oc3XNhT5oxZ9shN9L18Nf5nRxgkqyoVF/UOcgglSoP7Vc02IxEf0kgNMA/lXh17cppU4D+KcAfpOIXlj2XqXUfUqp00qp0ydOnBCvwVuwYY3suyM8y3n7OpAEiCBFUdw73yDJ/DzrCnIePu5cUBT0F3jjKSuAhxS9joiTuARm8ZwCbwqH652qF9nrtSnwchBBStSfWlIEgqcA3Fr4+Zbsd3NCRK8G8EsAXqOUGpjfK6Weyv7/OICPA3hFgjVZJWST8nrP00C9wWhi7RjK18XY8DXLZCvAG2efHbUdX5T18cqcdfmOXmjUa6gz+FvXTAjA4299dsGrHfkcEaMhYTQBUflAk9YV7iT9raiCJgLHJHzxdU5dHqTSzOyCRQ15k700Qf1GRwQPAbiTiO4gohaA1wOY6/4holcA+B3oIHC+8PsjRNTO/n0cwPcDeCTBmkrFxysD/MzbRTPxsgU3ZcWZ4DV8d9ngitaVHhGwisWO5ySErst39AIA1vlM3noPZ6AvwHnz6lBpGhIM6rTZRUpEwDluO2QSHgi0Vw8tav4Wsi/NwXrOAm/CoH49EUEjVoFSakxEbwHwYQB1AO9VSj1MRG8HcEYpdT80FbQO4N9mRviNrEPoJQB+h4im0EHpnUqpfQsEPl4Z4CEC13AawOUP/ZTVaKIwmSprB8lMl79NDQilc9J1hwTXCBKsC8hok4B1+QaatK5abj/etfkyP0btyIdUig9a8dqFpyDOQQTezjTGcSG+9lGRXXiSqpDBOV8RW+viBXU/ZXh9EEF0IAAApdQDAB5Y+N0vF/79asv7/gbAy1KsIURcTyczwuWCfc6Dk5FudJrWvxcpmNWW+7Z5i9gC/tbXppki85MMIfnrPQHf0bMuIKP5WC2HiWimAAQL6MMBV1r2ex6ii3f93RQM5xj24HoDCyn6EAEn2LmDOq8zzVdvuHFrBDeMhER47iFeybjgAHRhXucTfxGb0+OtX2OrX8j6xcs3luGuU3DB5m9hhWd3RgpkXDCnXzwRnROSRQLhvL5vXeG6dB2q4ZhvAAJrR9fYLkI7rcJQJ2do1L/Hq0BwDSQ4wnPaR52tqOHUkI9X5rRWpgwqg/HUO9AEhGZ+7sli/QD1sE2aNPNLiC6MvmRnUPmK2By7CFgXEH4v3XUoQftoArsIqxGEcfHBdpHqrKFmPZh+TC0HKhD0PQYHhGd+0+yBLT6D64/CDt7yDw5xMqywzC+Uv3XTTJwOpIBAHJrFB3DB4Zmfm/7SusKch+8B8UZXsF14mwh4mXcqu/DXoThIJaVd+J13aB0wDF2ErUspFZDs1YLtIrUcqEAQgghCM7+QwrO56SFRPrzAG5Ytp+OCwzZ8MqjN5G/dQT2Mc/UVsc3n8ByR28aAQLsYTawHuxU/J8wu/I4ICEedvlpbsC4PUjRr4zQ3pJgJCUGdoe27o4mCUp7EJfvb9UAFBysQBCCC0DZN3wmfRpf+3LDN4N5YPETgOy4BCO8OCXFqyWB7oMPNH+runfpM0x0Smvn5DtYDmNPYwYE4PovnrctTh+LQj44HtuT6Qu0ioY2Foc56YBt2WBKkX1sFgn2VEAga3mkSlsUA4Vx8qk3qOkBtbl0JNjzn4C3DUdt4ZSB8CC+cCw533r5AnLLeAIQG4rCWz5TJRniCYP+O+YOZAu2i1aih5mh/DZ3jCKYMGQEqxUkEs+lpPyK4HgXjAxUIwqKydkQ+ni6UZgL8NzZo0I3V8ulBBMyjHFy6gBm3GbYut8mFHssRzAWHbNKE3WRh9QZeguCraQHhXLzvO5rP9K/LbWMAI6kKtAvW9ffMlyQrFnPRRaImjtRyoAKBryde/62GacCDVkJopnZgtpbXG1Jla95+cd6Ajus7AryN5cqIAE5HR7pCXkj7aCfwoL6QekOoXYwnU4x9g26soBKILgJtzG8XYd1RvnkcINwufEdfaF3pisWdRthBfawEoaKG9ldCEUHxtTYJpZlCdIXSHFpXKM2Ujtf3ZWuhRzn45i6A8DOVwrng8MwvJPP2XbOQYnEn1C6CaCZeW3EyytCDOs3aQltRfUEldOo2dC+lQp2hdhHWkBDetZVaDlggCEMExdfadXFubJiusHWFZUWudbXqNRCFIwLvhm+GFszc7YuAKb6FrateIzQcBcZO4Ib3HXFQ/JsPkfkO1gOKXHB8Fsm3C7sunl34E4TgQByQbHB6//WDhHy9/6nQRege59SOKkSwrxIE20M3fMKiICfzC81kXFwwd3DLSwEEFszCNnx4IS+ZI2Lcy+ANn6DTh2ev8QNlrMEtj42ZtT0X6w0pZxK4qD/VHEdqOVCBIPSIieJrbTI7njmegpllHvEGF3JiotYX3oURggjCN3xAIEiELjqNen5Qn0+X/uz4AjtnjuBaBhXfk7tm+sLtwmdjoQeyhQSV4LbuEKTSqGE49g9uhdBMs7qKZ48HMQhVjeCaSFinT9iNDe09Z+lK6YhCsvgExxIYXSlmEoDwg7dCO02AEC4+oPc/MFsLnVUBQuzC39YaTj/6nZr5eyhSTGZjnuG0XFeCgjjA2UvhyZ4vSPF8T4UI9lV8DwIHCu14oc4jwbEQrCK2z3kEGBwQ3vbmO6hMf1Z4F0YQzZQwQAEB2Vpg4bn4Wr+u+CYC35O7gNlhgKH0oxdFMQ7qC+v0iZ9VYa0rpJuJkaC5DtYDCkElNKgnat9NLQcqEIT2xJvX+nQBadpHQ/hDXQDzP1kpxOAAzoBOQNcQY5OG0Uzx5ymZdZnP9elqeQbdQrO10OckaF0+u/AnG8Yu/DbmX5f5ezq7SFs7CkeKgXs8oEbjOlhP6+Lt8aBuvqpYvL/SD2pTC20fDTviAAhxHqGw3X8yakhGCoQjgrBOn/AuDG/mlyECH3/rO0/JrMt8rks0NRGILkI3fIq24oC2VvNZ4fRjSIHdrYtTb0haLA7h9QPrDea18brSof4bvn2UiO4mokeJ6CwRvbXk720i+tPs758iotsLf3tb9vtHiehHUqzHJhxEENral6LTJKRYbPSlMDj9d3/mHXKSZq4rQdcKoDMmpfwHb4U5j3BE4HNqbC4+wXEhIcmG1hduFyEF9hTzDebv6YbTwg5kC603AGEJQojta13pBspuyPZRIqoDeDeAHwVwF4A3ENFdCy97E4DLSqkXAXgXgN/I3nsX9DOOvxPA3QD+daZvX8T35CggvIUr7IgDbiEvnr8N54L9xbfQwnOIIzL6QtBF8bNdupJlaynRBeMogRRtxfrv/nmJkDoIgKAjPkLXFUoZcugc7/cM2uPhxeJwe03XCnyjIoJXATirlHpcKTUE8AEA9yy85h4A78/+/UEAP0iaeLsHwAeUUgOl1NcAnM307Yv0g7pWwrP4hmegqVEj1AIGdMKzeD9PGmJw+u/+drz8MLYQCiCo9z+k0ye8KB6KCEIcW8h3NK91SX809dYbcrtIFNRZSDHBER/hutLVG9qBtEnYfEl4shcS7Mzn+nT5Cs/Nephd7IekCAQ3A3iy8PO57Helr1FKjQFcBXAs8L0AACJ6MxGdIaIzW1tbooWe3Gzj206sOV8TXhT0G4ke0PFP3YZu+FZARw0PtvuyK0YWGVIjCCkWB2bLQZlfICJI3YoaahcpjiXQawtAivmx6SEF3jS6Utah8mM5ArpzvDRfcDcZp/Aclmy4EoTcX1yH9tEkD6+/FqKUug/AfQBw+vRp0SN83vGPXuZ9DafH2GdwRp83qATD9hBqKDSLDwgqoRx1YXDL1po7Dq43hBdl/WcghWdraXX57SKkoyaUMgxCigxEENw6HVBvMAey2ZBzcB0quIkjHBH4vyenRhCfbOi1hT/6MqWkQARPAbi18PMt2e9KX0NEDQCHAFwMfO81lQ6DAvBlRECYww3N/DoBxbeQ3nMgbHBrdlprWLY8dHxPTh+7fn3IJg0bHApxbMmGkAKO5ADCeP2QQTetKySoJ0SKjHoD4L5mnAHI4me79CVrEQ+oQ3HsIiRBCB2cSy0pAsFDAO4kojuIqAVd/L1/4TX3A7g3+/frAPy10n1g9wN4fdZVdAeAOwH8bYI1iaVZJxCFFfJCEEFogdd3gBqAoMPdQgbd9N9DaKZwXYD7mqXf8GHDaUAIBeB33ubpWSHF4vDMLzCoJ0CK/ZRIkVHELr6+VFdwZxSjAywV6gxsazWv9ekKSRA6gXM0qSWaGlJKjYnoLQA+DKAO4L1KqYeJ6O0Aziil7gfwHgB/SERnAVyCDhbIXvdnAB4BMAbwc0qpa38VChJ68FZI4RMIg+3BziMAEYQMugHGeaTrWim+vkw4RWytK6QomNJ5uHWZJ26FIMXgzC/BoBugkeL5RPRjCFIMbkUNqKuEz0qEz+QkQ50BCQIRodXwd1px7OJ6tI8mqREopR4A8MDC73658O8+gB+3vPcdAN6RYh2ppNOshxWLQ2oEAUXBEOPVumpO+gVg9J4XBnRsjibkGF6At+FTdG1NpwrDScqWTz8FYPQFFYuDM7+QnvgQdJGurbgdYBfhNJO/ayvUXkOy+JAn/YXqMn8PD+pp7CL0uO3UkmSg7FtNQqJycPEnxEgCClwAb44gxeAWFxG4rhln0A1wZ35mzalaPkOGkIBwh5sUKQYmCP7aUXgHEuCzC67zDkkQAts0HbryJ/0FDqclK/CGJnuhTQQ3aLH4W07CeqkZzjtkCCaZ8wgvChZf79KVYqgm5DwlILDAyCh8+tYFhLWiGn0h1z8M3YUhgjAbS9tWXHy9U1foUQ7OBCFd7WjW1pqwWBx6/UMSx+AmggoRPCckdGOF0jnpOgrCes99g25AoR0vCLaHZmsJdbnWFdhNY3h9b+E50OGGtPaF1o7CjoUIDyoh6IJjF87Cf2hQD2kiMEOLAYcRAu6gHmoXzXoN9VrAQX0MRJaiFdXoqhDBc0SCNhajLziMAkjTacIxOCBRp0/AUbzszC8AXaTgb/UBav6jBMznpZojCDtAkEM/hhQrw+0iKBAnaB/th6ILBiJIZxehLeKBdhE6d1QFgueGhLbQpcrigyFowBO3wp1aCAUT3nIIBAaVBLA99KhtIGu5degaTRSmyu/UzOf56z0Mmi9ZUJ8Nbtl1hWW3IeiOWyxO0T4agghYduGpA44mCkr5GyX02kJagQORYlUsfu5IaAtdWHdIQgogoDsnPPML2VjcQl688w5ZV+hR2/o17usfWvjMdSUYQgIy5xE0KxFWYAQ8BV7GACTgC+qhvf/hCUKKmRCeXbgdbijqAYzzTpQ4Bhz6tx9SBYISCYXaQZ0mQUYSnkUCfgomLPMLQwREs2Eq77oSOG9z8FaKDiTAD7VDKSv9eWFNBKnsgkvnONs0g9udw4rFNdL3yq2LUzvy2YXm9Z2UYUq7CEQ9ua4AKjl04rx6VOVzRIKKggk7TcKHTcKgNgcR+LK1dsBAU8r20dmBbPFIBciyNcd37AcWK83nJbOL0NpRYFureb1VV3AROwSR+Z/cBaRtHzWvCapDBdtFfItsvi7vZHc4IqhqBM8R8T3GcTJVGE38B2UBMyNxPVkpFBGEDG4FZ34hhbyA0xdD18Uq5Hmz+LDaRZiucETgm+OY2UU4InDbRdi5Rfn1T4kIvKgzrD4D+BIELs3nRxehduFGF1ykaF+XUmGDbkVdviexpZYqEJSIz3mY6d4wg9ODW6OJY8OPQidbAzYWoyhlPtuqi2G85vUuXUCgw/UE4tCD9fTaPFkkhwLwDG6xqImGn9cPDcS5XSRABEG1I24HUgidExiIU3S5mbWF2UX8SbKh8zhmXcX3XCupAkGJ+Hi60J744mt88Dg0IwrRla7wzOtAcjvvlLx+OGzvNN3HKoceqWzW5Tr0jxNUwgrs4UdfFD/fqouFOt3Xn+XUggq88W2yPDonXbHY98wRbrIBVIHgOSHeDc+BswHwOHTqMHRwK2nhOUBXyIFsg7H/yV3FtYVka6FtgukckSdB4FBWQcNW4QNlgN8uQhGsb12hRWxzgKMvEIfahe9kTl4gDiwWB9tYOtRTfM+1kioQlEi7UcfQwdOlRARmcCWUOwfczpvDRbrWpf8W5oi0Pl8hLyxAAQEbnhGI/bo46CKt8yi+Z1GUUsFHj4TUaMLtIgwRhFwvo88X1EPaWo2ukAPsUkxjs4J6YB0qtCEBcO/x/ZAqEJSIDx6n5PxC+6iLunw8Kaf3PAW6AMxmSBdUQjZ8K3RwKwARhLb2uQa3cufB6vQp15UPNLE6wNzOKMwu0tWOAHgP6tOIINQufHQOEymmovl8djEKRwShT2JLLVUgKJG2p5A6yzwYUM+ii5ctpKSGAttHA76j0eelv4IzP8+Gzw8Xi+/957YJ6vdY7iUDEXQ8SJHbGeXSBfApwxTJBuAfqAx9ohsQkHlfx840/R73Hg9CnQEzIfshVSAoER+dw215A+wdHQNGthB67n/IusyT2LxFwdBsLQARhFND/k0acoBakC5mvUF/vidBSFA74tQuwjvA/Otq1PRAny/ZCEFjgKmruNpaw2oXRpd7aG6CZp2sz81eXleaeoMvQeMeiVJ8z7WSqEBAREeJ6CNE9Fj2/yMlr3k5EX2SiB4mos8T0T8p/O33iehrRPTZ7L+Xx6wnlfiKshxE4EMXEkTgG9wKWRcReUfj+6Mpb8N7Bt14G96NCLi6rPUeVubn3qTc9kW3LgZSabqTDSC8IYGIvHWVfuCULGAomPhWVCAg2QgczJzpcgcVIMwufAka90gU4MarEbwVwEeVUncC+Gj286J0AfyUUuo7AdwN4DeJ6HDh7/9SKfXy7L/PRq4nifjgMa9ryGckDP7Q4zw4A03mM30tnzxeP77TxOjyFyvDdU0VMLYc1MftNCm+Z1FCj0sofp6XTkhQeB5PphhPVTi689RVQo/RAPxDeBxE4JsG7gcmQcAscbElCCJEYE32JM0lN1YguAfA+7N/vx/AaxdfoJT6ilLqsezf3wRwHsCJyM/dVwmmAAKHo1y6WIjAy0WGBxUgpNMnnL8NoXOCg4rPeTAQQTi6ix/c4hT+fbUjXlAJtDGWk/QE9YQJAq9GkAgRBO/xePqXMwDZySnDG4gaAnBSKfV09u9nAJx0vZiIXgWgBeCrhV+/I6OM3kVEbcd730xEZ4jozNbWVuSy3eLr5eWOsmtdCToKvEXs8CKq0Rdypky4rjTO2+s8As/zAQq0iQPd1Uhz4yHrAlIjArfz4NUu4u0VCCnKcqmha9OKyrELX4LAsotApMhqH32uIQIi+isi+mLJf/cUX6c0xrKeo0BEpwD8IYA3KqXMt3wbgBcDeCWAowB+0fZ+pdR9SqnTSqnTJ07sL6DwnebIPShL6/JteL+R1GuEZt1+AiN3w4cUUnlzBPFdK0BYd0jKzK/T9B+gpnWFZd6sNkGbjTGCiu9JbH2GvQL+Iz5CC8+A/1GtHETgo5kGI0ZzQ0DwDLWLYNSfoA61X9LwvUAp9Wrb34joWSI6pZR6OnP05y2v2wTwFwB+SSn1YEG3QRMDInofgF9grX6fxHczZll8Ctgezh8afd6MlNXyaa83vqAJuQAAIABJREFUDCecTh9fvziDzikM9JVtxNCCuFkXAGuQ4nYzmc8vEwmd4Cs8pyjKhj5gKNflCMTGLjjr8k0Wc5z3cDLFZKpKO4N47c7uLJ43K+FL9jhU8nMUEXjkfgD3Zv++F8CHFl9ARC0A/x7AHyilPrjwt1PZ/wm6vvDFyPUkEV9RkIUIcl3xiMB8ppdO4EBti8FxDtbLdXkLz7yN5criOcVi/R43IgjT5e7a4thFytoF4K6rcGgmwE3BcPrrtS4/IuAkLsDMNpd1cdqd/cke1y781z/NER/7IbGB4J0AfoiIHgPw6uxnENFpIvq97DU/AeDvAfjpkjbRPyaiLwD4AoDjAH49cj1JxFsUZBwx4YeNPETgyry5m9Sli5PFAPCez8StNwDuQMzfpPGIwNcBFvogH70uTxbJdrj2usrsoe7hdmG3fSbN5CnwcuzCh8gkiMAV1LnJhpdBSHQG2H6IlxpyiVLqIoAfLPn9GQA/k/37jwD8keX9PxDz+fslobAxhD/MB7cSIgJfvYGzGS53h+W6uEHFN6DD2KTzG765vDZW5hdWIwjSldAufINb7CzeQedwHJF53cVdW72Bj1R8rahcROBEd4zahfl8qy5uZ5q1RhN+sJ55EtuNRg19S0pKIzEnMKZCBC2HLv4mdTkPXubn0mUO1gunrPwUDN952LLl8FbI1HYRgshYXVu+oUUOnZOgm0nr0oigrF9/OtUPbElV4JXVCBIgRe/pAeEH6xl9Nxo19C0pIQNloUai9YXwt/FccF4UTHCIl4QLth28xXdEAR0dibqGQh/YErIuvl3Y6ypch+uiYNh24QjqnIlnva66daDPPJSHm3mnQAQh3WThsxL+gbLQ72jWViGC54CEthyGinOTZr8P4ZUB3VXgcx4cCsY7k8Cmc0oCARddeK8/r+VQv8eOCFIVi7l24To7Jw/ECXrs+Vm8fV0SRKDft3z9JZQVkAoR7EftyGWvPLu4oc4a+laVRr2GRo2c8Dh0IwD+jdVq1FALGFwBMs41UbHY1T7KGYIxuvQaltfGrjd4nLd+QPy1RwSt1IjAkSD0R1O06gy7cNI5vGKxuzONH6AAi12w0XC6BM13DLuoduTsQAq3C998z35IFQgs4jpvhTMNaXS5EEFyOiHBmT78mQT7ZmB3IDmch1JKB+JE2RqnA8kM9CVDik7KMHxKFnA7j9kxJik607gNCfYEQdIxB5QnCHy7cCcbQ4ZdEBFaDn/B6YwC3AnafkkVCCzSdpzAyEYEHgqGyx+6+qgBfr2hrJDHOViv+Jllm4Gry9XjPXNE3I4OO3/OCcSug88kiMCFevg0U6IjJjIbm5bw+uwitmPYStIxB5Rz8abekAopcmZVjD4XUmT7iwoRPDek4xmq4UR4V+bHRQTuTpN0XLzEeWhd8YigkzsPV1BJVG8QbFLXER+pioKc01pDdJnXBOnKrsewpPDPtwt7IZVzTv+cLgfNxLYL56xKqoYQAVK8wY6h/pYVFxcvQgSu1jKm83ANDoU+sMXoAtwFXvY0cIkB8zM/ByJgOqJWveaZ4wjvNDFrS4YIPAkCyy5crcBMu3A96IZd+HcMgXHO6QeKCUIZUuQPzdnWZT6Dlex5UD+LGnIkG/slVSCwiIuL59cI3N0h6VpRuc7DvhnyadTQTero1xd3hyRABGaOw15gD+80MZ/rdB6Jusm4yYZroI+dbDgedMOeXnd0WqVEBHniEmgXvoE+PiJwIEXG2VhGV4UIniPiQwTpnAd/k6biIjsuhytFBKVFQVm/eArKCjBZ/PI1G2UHmLEQgaeQyg3qKXri9brswY7viOyIQDLxDLgRAb/TJx4R6AShvK5iHuTDTfbsJ8kyEUHVPvrcER8iSMUFs2sEjTpGE4WJpZDHg6AORCDlgp3OO0XvOc95GH2uAMUN6q4jPvjrSlVvqGNiGeiT0ByA2y5SHAPOR4p2dMHtmAPsdBr35NeZrjTto1Wx+DkkTufNLOS5zmSXIALAxp/z4axZw9K6xpOsXZI7ULa/zoPbcqjXVp75ydBFuqDu6ybjfUd3vYcX7NwdYDXSZ2iFrctOGaacOOciAqOvHPXw7BXwNYTwB8pc5zPth1SBwCI25wEYqM0s8CacIwBssJ078ezuwuDSHOZ9i8LNvF0DffuCCFjO23XEh2SC1EXn8HQB9kIqryDuDuqhD2yZ1xWPCMwDeJzDaewOPFeA4gb1RIjAgRT3S6pAYBFbv/7sAfFM55FsjsA9wSsLKhbnwXS25n1L6xJm3q4CY4qWW8m6bEd8TJkP8gE8cwSCOhRgD+q8ydaUNuYaKOP1/mt95dcspY1JEIEt2TD1Bk4g9j3kaT+kCgQWsWVr3K4Jrct+AiN/jsBHDUmct8V5SDZ8gk4fwGTe6RBBim4ms66yBIFLc+jPdQ308dtHi+soimS+wbxvaV1MG5s95Cl+vgTw8/pcCsxtYwmSDZFd2Af69kuiAgERHSWijxDRY9n/j1heNyk8lOb+wu/vIKJPEdFZIvrT7GlmzwnpWLI1bh+11mU/gVGKCGy8vgxd2CmAYF2ulkPGA1uM2Ab69sd5xAcVCVIxry0f3Ao/nhnwtO8KaheADRGkQ7ASu7B153DPQNK6bHYhRASuZINpr0C5XeyXxCKCtwL4qFLqTgAfzX4uk55S6uXZf68p/P43ALxLKfUiAJcBvClyPcnEhgi4B6hpXe5BGBGdY8lkuIdbaV3ljqglopkszqMRzisD9vZd7nEVgCnkOTLSBM5DglR8bbIS52ErFqdMEDj26nowk2m35dlFeb1NggjslKEMXbjslTu0CNinnvdDYgPBPQDen/37/dDPHQ6S7DnFPwDAPMeY9f79FtuwjwQ22igYc1AWbwjJ7Ty4PfHmfYvCpSbMwVt2aoJnar4Mi30sRIIitv5cN2UoCeqL11/CK8+cRzkikNA5tmvGsVcisnbUcFEnkB4RuNHd9UEEvkdy7ofEBoKTSqmns38/A+Ck5XUdIjpDRA8SkXH2xwBcUUqNs5/PAbjZ9kFE9OZMx5mtra3IZfulbenXlxlJufPOD8qSwHZLL3WqAiO3FRXQdI6NTuNcL8DencOdeDavdR5XkeAkWWntQq9j/ntKulZ86E42UGahDBn2CtiL4twBPMCeoIlqBBbKMGmNQDgAWVzHtRDvM4uJ6K8APK/kT79U/EEppYjIVt24TSn1FBF9G4C/zh5Yf5WzUKXUfQDuA4DTp0/vexWl2K+/2ppdJhEisBTMYpxHucPlDg45JkjHExxd45VsXM5bggjS1WjK6w3SAqNJEOqFZwWIEIEF3cU5Dxudk6aJYDCa4PAq0y6cSJGLCNL1/lsTBCEiME/oK57pFJUgXENE4A0ESqlX2/5GRM8S0Sml1NNEdArAeYuOp7L/P05EHwfwCgD/DsBhImpkqOAWAE8JvsO+SPH4haLdD4QGByxHeBmd4G7HSxVUuFyw0Zei8Gx07fTHS783DwIPfWCL1pVwoMybIPBaUY2uuXVJ+tidQ3gypGilhthZvJ2L59tYHVe6w1JdzTrNBWf/uiwJQkyyN54PBDN/kaZ9d78klhq6H8C92b/vBfChxRcQ0REiamf/Pg7g+wE8onTP3McAvM71/uslOX+eYpNaOL+BxHlYdE2yPnbOulwHb3GDil5bOX+b0nlwp7oBV3eIgJqz0jlyRLDocGMQweL35D4gHvAN9MmCeoo6FGC6+cprNJzvqNdVniCkpH9TN5fsl8QGgncC+CEiegzAq7OfQUSniej3ste8BMAZIvoctON/p1Lqkexvvwjg54noLHTN4D2R60km1g0vHDYBXBs+foJXMt9gDt6ybnj2xrIjAk6BMdeVyHnYHsAjGiizJAi9oXzDLyECURZZ7jwk9Jf57BT1Bq3LjggkzttWo5HYWFmnTy+7hiut+ARNhC4c6G6/xEsNuUQpdRHAD5b8/gyAn8n+/TcAXmZ5/+MAXhWzhv0SGzyTIIIVi/PoZs5jlWFwdufBH7EHTPEt1Ya369pcaTJ1OZyHYF3AMsrhPswEsHfUSJyHbcPP2hfjM9I8QWA6XNsRK9wj2LUuW4F3grU2zwVZ0Z2EysyGA6dTNUc19oZa/4rg+i8le4Lr7zoMcr+kmiy2iA2e9Yaat+ZkfsY5mKwx1xWTkVrQBT8rsvPnXF0pqSHbaY4SR2RzuL3RBM16+MF6ALDS1I6rO5yvX/QEQT2/l8PFLF7iPDwJggSRJUQEthND+UGl3F57ownr2gOze7WUoI3GaDVqrHqDzV/I5kvsNZr9kioQWMSWYc02fHgms5o5j6VAINBlDK634IgkNBNQ3mOvlNLZs4CLt00Ws7lgi/PoDiesTA0odkctX3+uLhPUlxIEgwgY+owj6i3SORF0Qgr6ESjvAFNKsWcSzNpslCEHQc10ldsFNxCYe9Vd2Jf9CLtYvJeiY0wcHWD7JVUgsIiN8+uO+JmfMZJuAudRqxFWmvUl45VMMJrPXnJEgqMXADu66Al7z8ucR28ocx7AclDvDsdsXea+L15/8zNHn9URCZAiEZUeiyKZu9CvX67R6DoLH13YkGJ3OMEqu95THgh6Q36AsiF1SVAxydyiLgkiWLGg/icvdfHnnzmHq70Ra20hUgUCi9g4v95Qn4/CifB5FmlxHhJIa8s8JJth0XglvfpGly2L537HdqNWOtAnoQBsnGtvNGWhMWC2SZc3/AQ15rk5Nkc0c96867/aaixRVpK5F/36ZRsz6+RmyzakKAnEnewBPKPJMs0npYaWvudIgAgsQV3STZYnjgv38jPfuIyf/7PP4cLugLW2EKkCgUVsnKuhEzjno9iMRFIjAMqdt6TwCejNsGhw3ZH+mVvIW2ktIxXAZPE8XbYHmkiCSsdCm/SG42QUgF5Xg2UXeRaZgFcGUIoUzb2VIJ8lXQI0DJTTj0DmcAW6gHJ0lyqox6CLskDMnXtZdSCV4t9TShUILGJ76HZXkHnUa/ocHuNgjRieX8Jt2ugE7sZaaTasNAc7w2rWl2oX48kUw8lUnK0tBU/BJrWdqdQV0Ey2TdoT1EFyu7DWjuITBPPzGtNJlgWCnjioNJbWNZpMMZooPjVk4c+5p/gCRee9fC/FheeS5hKurma9hmadlqjk2b6MavYslSoQWGQG25e7Q7gGB2hDWaSGTJsaV99qq75kJHt5UOFv+FQUgFlXsV9fmkXaONeuYGO5KIBUBcaeAKkYfYs2ljSLFweVRsm6ZI7IoM6iXUjabYuvT2EXOSIYLX/PlLUjbrAza1sO6rLEMUSqQGARV0Yq3fDLUHuMNrNNDci4+IT1hsV17Q1kQWWl1YBS8ygqDyrSjVWySaUUwN4gXddQWfDk6gLszruRPZaRtbZS5yG8/qU0kxypTNU8nSPpmANmyKZsbRKkotey3Gkl7UxLsS6ztkWaaW/Ib3cOlSoQWCR3HiU8KZfvBjLYvghnY4xk0UEOhDRTCZ3QFWZrs+A5W1uM8wDmnfd0qttauZvU1DpSZH6teg01KslIBXw3UG4XZl2cegNgENmi85AG9bRBBZh3kjGJi37/7HtK7aJMl1mbpDOt1C6GY3atDSivt0mTjRCpAoFFTJvmMjU0xgqzAwPIKJiEsNFWyOManaGG5mB7pPOe3/AZzdGUZX7Fa9YT00wWRCCghogoy9bie8/N2socrgR1lq1L6nDX2iU0n9R5t5eH8My/JbRocS2A3C46OTWUzi5Kg3oiakhSEA+VKhA4ZK1dX0IE2kgEEb6sHW80QUeaRZY4D25bK6CdhzmwzojZZJICIzC/saRBJSW6sBZ4hxN2gAIsWfyIz1ED5UF9bzhmX/t8XftqFxm6YF6zsusvt4tlakgyw2Fbl/lZUgcsy+IlXW5mbal0hUgVCBxSSpsI6ZyVkmxNnvktO6K9gUYXXDqhrIVO3h2SjgIo4+IlB7vpz9bOY68QVJRSWR87fwuUI0VpUG8sDxqKKUOL80hkF9LOtByRpaCG2ssJQr6uBLy+UkqECMznlxX+V6XUUCK7CJEqEDhkrdXIC6dGpDzdSrNW2nIo0lXGH45kBlfmvPekzrvkHB5ptmYy4iKdY/hvLiKr1wjtxvz1H06mmCpZK56t00pC8602ywv/IkdUhggS2oUckS3bhbRryL0umV0UWz6HkykmU5Ws8C+2i9ZyUNkTdEaFShUIHFJGAUizBRt/KIKg2amJxanbGOdh3l/UZT6HI2vtEnQhdN5lAzpSOsG8Z69El2TDd0roHMlwlFnXcmeUjAtebTYwnEwxXqD54uyiJKgLef1yaohLM5kEYbneIEF3i867b04eTdQQspew3tMTdMyFShUIHLLaqi8hAjk1VD4EJnVqei2zte0N5EUpYJka6jR505Dz60rXHVLmPOTtePG8sllbiuE0AOjYmggi7KLojKR2UcbF66E5uV2UUUNJgkpODclqd3N2MRrnv+eKtfAvpIZS2UWIVIHAIYvOY5I97UnqcEudh4gaWj6aoDeStamVwXZJr/7cuhI472a9hla9loRXNu/pDpadR4oCr7R9EbD360uTDWAZkcUlG/MdYHF2UZbFx9tFDFJcWQjqUboW7uXITNVfZ7sIkahAQERHiegjRPRY9v8jJa/5r4jos4X/+kT02uxvv09EXyv87eUx60kti7AxxnnYpislEHS1JIuPpgAWNoPoO+azFyWdPsJayJzzEBYFAd3CuPgdpboWs7VYu1hs3+0Ku4ZsiEzmvMttTHK91spaPiOddy9BHcq8p6x2Iesamqd/Y1FnbzTBdDrvL56riOCtAD6qlLoTwEezn+dEKfUxpdTLlVIvB/ADALoA/p/CS/6l+btS6rOR60kqy3SCyWL4G6vTLJ+ulDoivZ7C2sQUwD4ElQVdrXpt7oHenLXNOw9ZFglkGdYgjfNYLBZLjhM3Yqaxi3YRSw0tOlzpdyzTlcouJA8FMrLWmm/rjrn+q81GaWeaNBEqq2nJBsr0e4qntu4NnrtzBPcAeH/27/cDeK3n9a8D8JdKqW7k514TWV3MFiKyyMVDqaLa1MocrpgaKusaGouCXdl0ZU9w1HBxbd2SDEuyGdba6dDdIgUwo78kHLXegkbfxNBMknpDydk53eEkz8g5smrpAJNcr1ZdH6OyqEs6JbuEyKLRRUlQSaBrNtUdH4gnEfRjiMQGgpNKqaezfz8D4KTn9a8H8CcLv3sHEX2eiN5FRG3bG4nozUR0hojObG1tRSw5XNYW4Fms8wBmNzZvU4ugYIrcZncQyyvPBzwJlVM2dRtT4FptNeay+Kjr31rM/GQTz6W6YjLShRqN+b+MGioftpJ2wADLcxwSG9N2sRw85QlCo5R+FNn/YrE4MtkrQxcxqN/oiLH9EPEGAiL6KyL6Ysl/9xRfpzTJqSxqQESnoB9i/+HCr98G4MUAXgngKIBftL1fKXWfUuq0Uur0iRMnfMtOIvkhahk8i+Uiizri0EX5hhdlfhZdUoPTLXTzvL50wy92WkmnZIGMTkhEDZn2XdOmuSc856n4+Saox3VG2Qq8Al6/XaJrJKcmFjtqusIJfaOrDN1xn86Xr6vMeQvtYjSZPTQnn9CPQOpmbflUt0BXiHi1KqVebfsbET1LRKeUUk9njv68Q9VPAPj3Sqn8OWsFNDEgovcB+IXAdV8TKW6G4pnqEue9vnDeym7mPNY7kmzN0Alax3SqxIXnsmOVpT3xQBmvLw8qa606Lu4N858NncCdkgWWYXtMB1JuF6MJNuu1fOhNci8XnXfMuhazyBj60TjVZXQRk8UvUIZCmmO1VcdW4SldRhe3rRXQk8rFBGEn+/eGaF/OrtmhlVqOWlIE9Zz+eo5SQ/cDuDf7970APuR47RuwQAtlwQOkd/ZrAXwxcj1JJXeS2Ubf6cuNxASC3f58INgQRPi19nwWHwMby6YrpV0rQBnUHrPPpjGyujDZHYNU1jI6wXTn5IFYcP3N/Z/dy5FYl8mKzXpi6iCLzqM/0s8Yljii/NnYg3jKEFg+fiGKMmzP04+7g7EoCAPAers5N71u7ulGu8nWtbaQ7MW1oi5ShteZGvLIOwH8EBE9BuDV2c8gotNE9HvmRUR0O4BbAfy/C+//YyL6AoAvADgO4Ncj15NU8hs7WnTefCMxhmoyDmNwEgM2Dmenrx3Q7JA4oZNsN/LvZvRJM7+1dmOpkBdDDRV17fRH2Ojwr73RVeza2u2PUSPZxlrP7r+5ZiZBSBFUuhEFRmOve4MFXRGZd7FYvzeQNSTotc0nCDv9sSihAkwH2EzXdn8sSqgAff2Hk2n+SNrdwQj1GrGf8Wx0AcV7afalrLkBmB2xIp27CJUowkkpdRHAD5b8/gyAnyn8/HUAN5e87gdiPn+/ZZHXN45X4rxN8DBGshORka61GiCa6YrpWgG0ARtnpg9jiynw1rHdL0Dt/hi3Hl0V6VpbcES7gwjnUbiXnWZdZ5Ft3jOGjeRBfRHdSexiQdeMV5b0688nG3kWKXbeM0SmlIq6/iutBq72clYYu4Mxbj++Jl5XsQNpNyKoFJF6e72O3X6EXWS6theCusR5m4TH+BwTEKSB2CfVZLFD8qchZTdhNyLzM85jdwERSAy4ViOstxq5wRmdUkSgA4E2uN5ogslUYXNFlnlvrjRzXUCWrQmz+LV2A7v9GZ2zk21Ska6FM2q2I9BF7jwW7qVkky7qkj6/AdA033p7di+3s/9vCp1kMUHYG04wVTJ7BYD1RS6+P4oIKvWE1ND89d8ZyG3M2JPRlTtvQYK2mCDE0NIhUgUCh8yMZJT9Xz9asiXpWskyvNx55IhA5ow2Oo0CNTHKfifU1W7murZ7cQa3WXAeZm1SR7S50sR4qvJHX0Zlfp35o6h3I4LKbJPO24VkOGp9QZe5/psr8c7b/H9TaheFBCHWxjY78wlCDDW03m5kdjFL0OLvpXHe8nUt2sVOf4RmPZJmSrTHfVIFAoeYzWg2506EkbQbdbQatRmdEFEjMO+bZX4pnYfJIqXOY7bhh+MpBuNp9MbaLmwsaeA038fcyxiaY7Hwn8QuCkgFgBiRFZ33di8yQeg0k2WkG51Gfu1zuxA6b3NtzPfTNJ8Q3S0i9ShEMG8X2/0RNjtNEc3UbtTRqtcKtm+CeoUIrrnkBle4GTEReaPdyNHFzmAMInkhb6PTXMoWpM57vRAItvPMQ7gZ2g30R1MMx9MkWSQw2/AxDncW1AvOIxJdFKkhqfMA5lHUdl/bxbq43rPsvKUJwuacLnlnlNHVG00S2cVygiC3V8PFF+5lZIKQ38veWBzQgfkEbbs/ApGMZgqRKhA4ZD0ryubOoz+K2vBFh7vb1y2akt5nABkXbAwuLovc7DTzTTVDF/KMFNCbM0UWadY0nepipZhm6iwHdem9NE66WCyWOg9A38vdwr3caMvtogzdyRFBY8kuxM57ZVb8jGndBYBDma6rvXF0EXsW1GfJRkwdighz6C6G01+k+dYj7MInVSBwSK1G2GjPF2WjAkFhw+8O4oLKRqfgPBI43N2BdrZ5UIng9QFtuDuJnMd2f5Q9SF1OpR1aoBNiOOpaVpRNQScA83RaTBF7WVd8vcfYRSw1UeTiYxOEObvIitjioL443xNrF615ak6K0oFlu4jR5ZMqEHhkc6WZxHkA81n8TgQEBbSRbBeyyNVWXVSs1Lr0URrd0SRBgbEYCOJopiI1lCK7BXQWCcQH4mJQ19mafJMWg0pKOmGnP8JKM8YumlAK2B2Oo69/EZHlcxcJ7CJmQh8oBKjCTEgM/bK+kKBJaTmztiLNtF8dQ0AVCLxSpE1infehlWbeS325O8SR1dgNX8wi44IKsEjnxFNDKTJSrWsc1boLAI16DWutOrb7IwzHU/RH06jMe3OlgSs9ffzFlST3slhgjHQeBacW64iMnmRZfG8WVKTJRrHeE1sQN12AV3sj9EcT9EYTHFlriXTpdcxTtnGIYL5rq0IE11E2V2bdDhf3BjgWYSRH11q41NXO4/LeCEdW5boOrzYxGE/RG+osPtbgAL1JtyNa3uZ09UcJNvwsi7ySbfhDEdmyQXeXsvOLjkbey8t7IyilcGlvGKXr8GoTlzO72O6NohDBZqeZBbpJNM1U5PV3+iPxJDYwbxex93KGLsb5WVTSfUlEOLrawqXdYX4Pou7lSivXowNx3L3MOxYjg7pPqkDgEYMIusMx+qMpjq5ZT8r2inYeQ+08unHOwxj+xb2BziIjDO5oUVdPOw9Jyxsw29xXuqN8QxwWZsvthn4s4dXeCBezQ8aOrcuvmbmXF/cyXZGB4OLeAL3RBIPxNCqLPLrWxqXMLmKDurmXl/aGmmaKRLCAvpeX9kY4utYS20Wx5dMEYum97DTraDdqyYL6kTXtvI2umATt2HoLF/eGGI6n6I0m4hZZYJY4KqVwNRJd+KQKBB7ZXGniSneEi7txmQegb+x4qrDdG+Py3jDaeQB6w1/eG0VlyifWta4Lu0Nc2B3geISzPZ7purg3xIXdIdqNmpjOISKdLWe6ivolYqi5y3s6I41FBJf2Zs7jaITzOL7ewmiisN0f43J3GHUv8+uf3ctjEdfLOOoLu4PMLuS6DHV2qTvExd0BVpr1qKdt5fsyQSA4tqadd0q7uBKZBAH6Xg7HU+wMxri4N8DxDfn190kVCDxyYqONC7uD3ODinLd+7xOX9jCeqijnYTbpxd0hzu8McFOEkRzLnccAWzsDnIjQ1WnWsdFpYGtngAs72nlIs0gAuGmzja2dQR6IY7K14xstrWsvHl0cXW3hSm+UB6gUdvHkpS66wwlu2kzjvGPvZZ4g7MQHgtVWA+vtBs5v63sZc+0B7SQv7A5wOUEWnwf1nBqSO+9j621c7g7x9NU+AODERidCV+YvLnTRH02jEjSfVIHAIyc32hhPFb56fhdAPAQFgK9u7c79LBGDTIxjiwkEh1eaqNcoyyKHuQOa+8DBAAALaklEQVSQyon1NrZ2B9jajc9iTqy3cX5ngEt7AxxaaYqO9zBy00YH57cHBTohjuZTCvjaBWMX8XTOl57eztYpX9fx7Ds9u93HpW7cvTyy2kK9RriwO0zivG/a0HZxYW8YhawB4OSmsYshNjqNKLswgSBFUDmW2cVXnt0BgMigrt/7pWe0XcQEdZ9UgcAjJzd1RDebNMaAzXvPnk/nPB59dgdKASc25ZlHrUY4utbKs8iYzA/IsrUsiz8eueFv2uhodJHEeXSwMxjjqcs91Ciu8Hw0u0bmXkYhlUzXl5/JnEeCLPIrz+5CKUQF4lqNcGxNo6hYRADotWxt66AeQ1kBwMmNDp7d7uNiArs4utbCTn+MZ7f7oEi7MNf/S0+bexkR1DNdX850nViX24VPqkDgkZtMIMii8tEYOsE472zDH4vISNfbOgv68jPxWaReSwtPXOyiN5pEZx4nTOaXwHkYam5re5AkIwX0vTycZbtSOZbfy93s5zh0ARQQQUQWudZuYKVZz3XForvj6218I6OsYu+lQQQXd9MgAp249KNQOjC7/l95dheHV5poCOcuirrMvoy5ZrMEIdO1UVFD101OZpvys9+4grVWPaoL4ORmBzUC/vZrlwAANx9ZEesiIpzcbONzT14FEB8ITmy08fA3r+b/jpHj662cgok13ps225gq7SRj12XQ3d994wpOHYrLrsz7//ZrF7HebkS19uk6CvD5c2nu5fGNVrJ7eWKjnSdBsYH4xEYbT1/t4cJuXO0C0AnaVOlrduqQfB8BwPMP63v50Ncv4fmH43QZG/vCuas4tNJEJ+LRkrpLC3j4m2mCukuiAgER/TgRPUxEUyI67Xjd3UT0KBGdJaK3Fn5/BxF9Kvv9nxLR/oU8oRiD3RtOcOvR1ajCZ7New6lDK9ju62OLY7OiFxxdzScrnxfp2F5wdDUfAIvdWDcfWcHuYIzxVOEFwofSGDEba2cwxm3HZA8ymenS97I7nESvyziM7f4YNx9eibKLVqOG5x9ayY+zjqEmgPl7aZycVJ5/eAVXuqNcb4ycOtRBfzTFaKJw27E0dtEdTnDL0Th7vfWIXsvV3gg3RwaCW46s5OcNPS+CrgW0v3j+oRVc7Y3Qadai6EefxCKCLwL4rwH8B9sLiKgO4N0AfhTAXQDeQER3ZX/+DQDvUkq9CMBlAG+KXE9yaTfqudG+8MR6tL5vO6Gd2Z0n16OcBwB823G9nrVWPdro7ig8LerOk3Hf80U3zd7/bZHX7NtPbuT/viMyELyg4HzMfZBKp1nPHeOLIq9XcT0p7WI1gV3M38u4a3bnTbN7eXvkvSyu64XH465/8Ql6RXuTSLtRxy0Z0o/dR8Dsmr/wxPq+HTgHRAYCpdSXlFKPel72KgBnlVKPK6WGAD4A4J7sgfU/AOCD2eveD/0A++ec3HVqEwDwvbcdidb1PS/QOl5286FoXa+84ygA4M6TG9HO4/vuOAZAP2Q8Fqm84tbZdXrp8+O+ZzELNd9XKu1GPad0Tt8WpwsAvuN52mmYexojxraK104q5jrddWoz2i5eebteT43iitgA8F23zGzhu289HKXrtoJdfO/tcdes06znfPz33Ba3LgB4yfPS+QtjpylszCX7N7M8k5sBPFn4+RyA7wNwDMAVpdS48Pul5xobIaI3A3gzALzgBS/Yn5Va5H/5sZfgjuNreP2rbo3W9c/+8zswnEzxxv/s9mhdd3/n8/AvXn0nfvSlp6J1vfTmTfz6a1+KO46vRTuPI2st/O8//t3oNOvRD9uu1wjvufc0tnYGc6hFKr/7U6fxsS+fx9/79hPRun7lH96FO29ax+tfGW8Xb/z+OzAcT3FvArv4sZc+D+fu/g78/QTf8WU3H8L/+g9egruevxmt69h6G//qdd8VzZ0DuqPp99/4Spy73EuC1N//z16Jv3rkPP7Lb78pWtcv/8O78O0nN/ATp+Pt4k3/xR2YKJXExlxC5nmw1hcQ/RWA55X86ZeUUh/KXvNxAL+QPbR+8f2vA3C3Uupnsp//G+hA8KsAHsxoIRDRrQD+Uin1Ut+iT58+rc6cWfqoSiqppJJKHEJEn1ZKLdVzvYhAKfXqyM9+CkAxnN2S/e4igMNE1MhQgfl9JZVUUkkl11CuRfvoQwDuzDqEWgBeD+B+paHIxwC8LnvdvQA+dA3WU0kllVRSSUFi20f/ERGdA/CfAvgLIvpw9vvnE9EDAJBl+28B8GEAXwLwZ0qphzMVvwjg54noLHTN4D0x66mkkkoqqYQv3hrBc1GqGkEllVRSCV9sNYJqsriSSiqp5IBLFQgqqaSSSg64VIGgkkoqqeSASxUIKqmkkkoOuNyQxWIi2gLwhPDtxwFcSLicG0Gq73wwpPrOB0NivvNtSqmlkfMbMhDECBGdKauafytL9Z0PhlTf+WDIfnznihqqpJJKKjngUgWCSiqppJIDLgcxENx3vRdwHaT6zgdDqu98MCT5dz5wNYJKKqmkkkrm5SAigkoqqaSSSgpSBYJKKqmkkgMuByoQENHdRPQoEZ0lorde7/WkECK6lYg+RkSPENHDRPQ/Zr8/SkQfIaLHsv8fyX5PRPRb2TX4PBF9z//f3tmEaFVGcfz3ZyZHNNCZFjJqMApDMZsyIkZyEZZWErVxMwQONdAm6INAHFpIyyAyFyFCVBBikUnJLBKaWo8fKDak5ohRI9pImEIro9PiOXfmOgX5vjO9l/e55wcX7nOeszjn/i+c9/l471NtBs0jqUPSKUlj3l4nacJz+8w/e46kLm9PeX9flXE3i6SVkg5JOifprKSNuess6XV/ryclHZS0NDedJX0oaUbSZMnWsK6Sht3/gqThRmKoTSGQ1AG8DzwNDABDkgaqjWpR+BN4w8wGgEHgZc9rFzBuZv3AuLch5d/v10vAvtaHvGi8Svq0ecHbwB4/9e46MOL2EeC62/e4XzuyF/jazO4HHiDlnq3OktYArwAP+8mFHaTzTHLT+WPgqXm2hnSV1APsJp3++Aiwuyged4SZ1eIinZlwtNQeBUarjut/yPMrYAtwHuh1Wy9w3u/3A0Ml/1m/drpIJ9qNA5uBMUCkf1t2ztebdBbGRr/vdD9VnUOD+a4ALs2PO2edmTvvvMd1GwOezFFnoA+YbFZXYAjYX7Lf5vdfV21GBMy9VAXTbssGHwpvACaAVWZ2xbuuAqv8Ppfn8B6wE/jL2/cAv1s6CAluz2s2Z++/4f7txDrgGvCRT4d9IGk5GetsZpeBd4CfgSsk3U6St84Fjeq6IL3rVAiyRtLdwBfAa2Z2s9xn6SdCNvuEJT0DzJjZyapjaSGdwEPAPjPbAPzB3HQBkKXO3cBzpCK4GljOP6dQsqcVutapEFwG7i2117qt7ZF0F6kIHDCzw27+VVKv9/cCM27P4Tk8Cjwr6SfgU9L00F5gpaRO9ynnNZuz968AfmtlwIvANDBtZhPePkQqDDnr/ARwycyumdkt4DBJ+5x1LmhU1wXpXadCcBzo9x0HS0iLTkcqjmnBSBLprOezZvZuqesIUOwcGCatHRT2Hb77YBC4URqCtgVmNmpma82sj6Tjt2b2PPAdsN3d5udcPIvt7t9Wv5zN7Crwi6T73PQ48AMZ60yaEhqUtMzf8yLnbHUu0aiuR4Gtkrp9JLXVbXdG1YskLV6Q2Qb8CFwE3qw6nkXKaRNp2HgGOO3XNtLc6DhwAfgG6HF/kXZPXQS+J+3IqDyPBeT/GDDm9+uBY8AU8DnQ5fal3p7y/vVVx91krg8CJ1zrL4Hu3HUG3gLOAZPAJ0BXbjoDB0lrILdII7+RZnQFXvTcp4AXGokhPjERBEFQc+o0NRQEQRD8C1EIgiAIak4UgiAIgpoThSAIgqDmRCEIgiCoOVEIgiAIak4UgiAIgprzNysWWh1UCf8qAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "btELP9jx6PlI",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "86d17036-cedf-4f8c-cc6a-908eca5addaa"
      },
      "source": [
        "### build the dataset\n",
        "# let's see if we can use T past values to predict the next value\n",
        "T = 10\n",
        "X = []\n",
        "Y = []\n",
        "for t in range(len(series) - T):\n",
        "  x = series[t:t+T]\n",
        "  X.append(x)\n",
        "  y = series[t+T]\n",
        "  Y.append(y)\n",
        "\n",
        "X = np.array(X).reshape(-1, T, 1)\n",
        "Y = np.array(Y).reshape(-1, 1)\n",
        "N = len(X)\n",
        "print(\"X.shape\", X.shape, \"Y.shape\", Y.shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "X.shape (990, 10, 1) Y.shape (990, 1)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "v_ieVtveiazD",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "1a2de462-2423-4d70-8d04-823ab3289dee"
      },
      "source": [
        "# Set device\n",
        "device = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")\n",
        "print(device)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "cuda:0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VY_czyLe6W3c",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "### Define simple RNN\n",
        "class SimpleRNN(nn.Module):\n",
        "  def __init__(self, n_inputs, n_hidden, n_rnnlayers, n_outputs):\n",
        "    super(SimpleRNN, self).__init__()\n",
        "    self.D = n_inputs\n",
        "    self.M = n_hidden\n",
        "    self.K = n_outputs\n",
        "    self.L = n_rnnlayers\n",
        "\n",
        "    # note: batch_first=True\n",
        "    # applies the convention that our data will be of shape:\n",
        "    # (num_samples, sequence_length, num_features)\n",
        "    # rather than:\n",
        "    # (sequence_length, num_samples, num_features)\n",
        "    self.rnn = nn.RNN(\n",
        "        input_size=self.D,\n",
        "        hidden_size=self.M,\n",
        "        num_layers=self.L,\n",
        "        nonlinearity='relu',\n",
        "        batch_first=True)\n",
        "    self.fc = nn.Linear(self.M, self.K)\n",
        "  \n",
        "  def forward(self, X):\n",
        "    # initial hidden states\n",
        "    h0 = torch.zeros(self.L, X.size(0), self.M).to(device)\n",
        "\n",
        "    # get RNN unit output\n",
        "    # out is of size (N, T, M)\n",
        "    # 2nd return value is hidden states at each hidden layer\n",
        "    # we don't need those now\n",
        "    out, _ = self.rnn(X, h0)\n",
        "\n",
        "    # we only want h(T) at the final time step\n",
        "    # N x M -> N x K\n",
        "    out = self.fc(out[:, -1, :])\n",
        "    return out"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BF4a_yEojXNZ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        },
        "outputId": "721f1d61-ac33-4038-8bbd-cf59a941781a"
      },
      "source": [
        "# Instantiate the model\n",
        "model = SimpleRNN(n_inputs=1, n_hidden=15, n_rnnlayers=1, n_outputs=1)\n",
        "model.to(device)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "SimpleRNN(\n",
              "  (rnn): RNN(1, 15, batch_first=True)\n",
              "  (fc): Linear(in_features=15, out_features=1, bias=True)\n",
              ")"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 56
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9ul064ps6eYa",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Loss and optimizer\n",
        "criterion = nn.MSELoss()\n",
        "optimizer = torch.optim.Adam(model.parameters(), lr=0.001)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6mmUZhAy6rt8",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Make inputs and targets\n",
        "X_train = torch.from_numpy(X[:-N//2].astype(np.float32))\n",
        "y_train = torch.from_numpy(Y[:-N//2].astype(np.float32))\n",
        "X_test = torch.from_numpy(X[-N//2:].astype(np.float32))\n",
        "y_test = torch.from_numpy(Y[-N//2:].astype(np.float32))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HF9Cna0Cm0wW",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# move data to GPU\n",
        "X_train, y_train = X_train.to(device), y_train.to(device)\n",
        "X_test, y_test = X_test.to(device), y_test.to(device)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9_kc7ihu6gB5",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Training\n",
        "def full_gd(model,\n",
        "            criterion,\n",
        "            optimizer,\n",
        "            X_train,\n",
        "            y_train,\n",
        "            X_test,\n",
        "            y_test,\n",
        "            epochs=1000):\n",
        "\n",
        "  # Stuff to store\n",
        "  train_losses = np.zeros(epochs)\n",
        "  test_losses = np.zeros(epochs)\n",
        "\n",
        "  for it in range(epochs):\n",
        "    # zero the parameter gradients\n",
        "    optimizer.zero_grad()\n",
        "\n",
        "    # Forward pass\n",
        "    outputs = model(X_train)\n",
        "    loss = criterion(outputs, y_train)\n",
        "      \n",
        "    # Backward and optimize\n",
        "    loss.backward()\n",
        "    optimizer.step()\n",
        "\n",
        "    # Save losses\n",
        "    train_losses[it] = loss.item()\n",
        "\n",
        "    # Test loss\n",
        "    test_outputs = model(X_test)\n",
        "    test_loss = criterion(test_outputs, y_test)\n",
        "    test_losses[it] = test_loss.item()\n",
        "      \n",
        "    if (it + 1) % 5 == 0:\n",
        "      print(f'Epoch {it+1}/{epochs}, Train Loss: {loss.item():.4f}, Test Loss: {test_loss.item():.4f}')\n",
        "  \n",
        "  return train_losses, test_losses"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sT1vrTj77slE",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "21413936-9c44-4505-aeac-b5e45152e276"
      },
      "source": [
        "train_losses, test_losses = full_gd(model,\n",
        "                                    criterion,\n",
        "                                    optimizer,\n",
        "                                    X_train,\n",
        "                                    y_train,\n",
        "                                    X_test,\n",
        "                                    y_test)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch 5/1000, Train Loss: 0.3693, Test Loss: 0.3684\n",
            "Epoch 10/1000, Train Loss: 0.3410, Test Loss: 0.3394\n",
            "Epoch 15/1000, Train Loss: 0.3114, Test Loss: 0.3091\n",
            "Epoch 20/1000, Train Loss: 0.2806, Test Loss: 0.2775\n",
            "Epoch 25/1000, Train Loss: 0.2478, Test Loss: 0.2439\n",
            "Epoch 30/1000, Train Loss: 0.2148, Test Loss: 0.2111\n",
            "Epoch 35/1000, Train Loss: 0.1828, Test Loss: 0.1785\n",
            "Epoch 40/1000, Train Loss: 0.1496, Test Loss: 0.1450\n",
            "Epoch 45/1000, Train Loss: 0.1173, Test Loss: 0.1127\n",
            "Epoch 50/1000, Train Loss: 0.0882, Test Loss: 0.0843\n",
            "Epoch 55/1000, Train Loss: 0.0659, Test Loss: 0.0632\n",
            "Epoch 60/1000, Train Loss: 0.0529, Test Loss: 0.0517\n",
            "Epoch 65/1000, Train Loss: 0.0476, Test Loss: 0.0469\n",
            "Epoch 70/1000, Train Loss: 0.0436, Test Loss: 0.0427\n",
            "Epoch 75/1000, Train Loss: 0.0390, Test Loss: 0.0385\n",
            "Epoch 80/1000, Train Loss: 0.0362, Test Loss: 0.0362\n",
            "Epoch 85/1000, Train Loss: 0.0343, Test Loss: 0.0343\n",
            "Epoch 90/1000, Train Loss: 0.0322, Test Loss: 0.0322\n",
            "Epoch 95/1000, Train Loss: 0.0303, Test Loss: 0.0303\n",
            "Epoch 100/1000, Train Loss: 0.0288, Test Loss: 0.0287\n",
            "Epoch 105/1000, Train Loss: 0.0273, Test Loss: 0.0273\n",
            "Epoch 110/1000, Train Loss: 0.0260, Test Loss: 0.0259\n",
            "Epoch 115/1000, Train Loss: 0.0235, Test Loss: 0.0230\n",
            "Epoch 120/1000, Train Loss: 0.0192, Test Loss: 0.0185\n",
            "Epoch 125/1000, Train Loss: 0.0158, Test Loss: 0.0155\n",
            "Epoch 130/1000, Train Loss: 0.0130, Test Loss: 0.0124\n",
            "Epoch 135/1000, Train Loss: 0.0099, Test Loss: 0.0095\n",
            "Epoch 140/1000, Train Loss: 0.0070, Test Loss: 0.0065\n",
            "Epoch 145/1000, Train Loss: 0.0045, Test Loss: 0.0040\n",
            "Epoch 150/1000, Train Loss: 0.0024, Test Loss: 0.0022\n",
            "Epoch 155/1000, Train Loss: 0.0012, Test Loss: 0.0011\n",
            "Epoch 160/1000, Train Loss: 0.0007, Test Loss: 0.0006\n",
            "Epoch 165/1000, Train Loss: 0.0005, Test Loss: 0.0005\n",
            "Epoch 170/1000, Train Loss: 0.0004, Test Loss: 0.0004\n",
            "Epoch 175/1000, Train Loss: 0.0003, Test Loss: 0.0003\n",
            "Epoch 180/1000, Train Loss: 0.0002, Test Loss: 0.0001\n",
            "Epoch 185/1000, Train Loss: 0.0001, Test Loss: 0.0001\n",
            "Epoch 190/1000, Train Loss: 0.0001, Test Loss: 0.0001\n",
            "Epoch 195/1000, Train Loss: 0.0001, Test Loss: 0.0001\n",
            "Epoch 200/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 205/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 210/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 215/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 220/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 225/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 230/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 235/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 240/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 245/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 250/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 255/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 260/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 265/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 270/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 275/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 280/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 285/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 290/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 295/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 300/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 305/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 310/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 315/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 320/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 325/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 330/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 335/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 340/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 345/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 350/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 355/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 360/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 365/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 370/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 375/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 380/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 385/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 390/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 395/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 400/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 405/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 410/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 415/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 420/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 425/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 430/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 435/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 440/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 445/1000, Train Loss: 0.0001, Test Loss: 0.0000\n",
            "Epoch 450/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 455/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 460/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 465/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 470/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 475/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 480/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 485/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 490/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 495/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 500/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 505/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 510/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 515/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 520/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 525/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 530/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 535/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 540/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 545/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 550/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 555/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 560/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 565/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 570/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 575/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 580/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 585/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 590/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 595/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 600/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 605/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 610/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 615/1000, Train Loss: 0.0001, Test Loss: 0.0001\n",
            "Epoch 620/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 625/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 630/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 635/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 640/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 645/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 650/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 655/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 660/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 665/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 670/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 675/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 680/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 685/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 690/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 695/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 700/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 705/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 710/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 715/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 720/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 725/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 730/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 735/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 740/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 745/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 750/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 755/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 760/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 765/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 770/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 775/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 780/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 785/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 790/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 795/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 800/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 805/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 810/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 815/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 820/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 825/1000, Train Loss: 0.0000, Test Loss: 0.0001\n",
            "Epoch 830/1000, Train Loss: 0.0001, Test Loss: 0.0000\n",
            "Epoch 835/1000, Train Loss: 0.0001, Test Loss: 0.0000\n",
            "Epoch 840/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 845/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 850/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 855/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 860/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 865/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 870/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 875/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 880/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 885/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 890/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 895/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 900/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 905/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 910/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 915/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 920/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 925/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 930/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 935/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 940/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 945/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 950/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 955/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 960/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 965/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 970/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 975/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 980/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 985/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 990/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 995/1000, Train Loss: 0.0000, Test Loss: 0.0000\n",
            "Epoch 1000/1000, Train Loss: 0.0000, Test Loss: 0.0000\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CI3tQel68Abo",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "3fc9971f-baad-4ea5-81e7-b20b1be64857"
      },
      "source": [
        "# Plot the train loss and test loss per iteration\n",
        "plt.plot(train_losses, label='train loss')\n",
        "plt.plot(test_losses, label='test loss')\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0orQOQQv8GNV",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# \"Wrong\" forecast using true targets\n",
        "\n",
        "validation_target = Y[-N//2:]\n",
        "validation_predictions = []\n",
        "\n",
        "# index of first validation input\n",
        "i = 0\n",
        "\n",
        "while len(validation_predictions) < len(validation_target):\n",
        "  input_ = X_test[i].reshape(1, T, 1)\n",
        "  p = model(input_)[0,0].item() # 1x1 array -> scalar\n",
        "  i += 1\n",
        "  \n",
        "  # update the predictions list\n",
        "  validation_predictions.append(p)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "neQZ0GhI8nct",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "0e4837a2-5d0d-4f7d-daf2-4f8a55e45da4"
      },
      "source": [
        "plt.plot(validation_target, label='forecast target')\n",
        "plt.plot(validation_predictions, label='forecast prediction')\n",
        "plt.legend()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f72c9d60438>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 64
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ELa4guNy8rbw",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Forecast future values (use only self-predictions for making future predictions)\n",
        "\n",
        "validation_target = Y[-N//2:]\n",
        "validation_predictions = []\n",
        "\n",
        "# last train input\n",
        "# last_x = torch.from_numpy(X[-N//2]) # 1-D array of length T\n",
        "# last_x = torch.from_numpy(X[-N//2].astype(np.float32))\n",
        "last_x = X_test[0].view(T)\n",
        "\n",
        "while len(validation_predictions) < len(validation_target):\n",
        "  input_ = last_x.reshape(1, T, 1)\n",
        "  p = model(input_)\n",
        "  # [0,0] # 1x1 array -> scalar\n",
        "  \n",
        "  # update the predictions list\n",
        "  validation_predictions.append(p[0,0].item())\n",
        "  \n",
        "  # make the new input\n",
        "  last_x = torch.cat((last_x[1:], p[0]))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "REBo8rNK9zle",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "6dce5a87-e79b-4f6a-8d5d-e3070c1ba045"
      },
      "source": [
        "plt.plot(validation_target, label='forecast target')\n",
        "plt.plot(validation_predictions, label='forecast prediction')\n",
        "plt.legend()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f72c9d267f0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 66
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}