QML_Finance.ipynb

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        "<a href=\"https://colab.research.google.com/github/AndrewSpiro/CVQC/blob/main/QML_Finance.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Saving AAPL max.csv to AAPL max (1).csv\n"
          ]
        }
      ],
      "source": [
        "from google.colab import files\n",
        "uploaded = files.upload()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 99,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WBWEFUf8OtBd",
        "outputId": "e28c94b2-4eb3-4d04-b8cf-69dc5fd6fb15"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Requirement already satisfied: scikit-learn in /usr/local/lib/python3.10/dist-packages (1.2.2)\n",
            "Requirement already satisfied: numpy>=1.17.3 in /usr/local/lib/python3.10/dist-packages (from scikit-learn) (1.22.4)\n",
            "Requirement already satisfied: scipy>=1.3.2 in /usr/local/lib/python3.10/dist-packages (from scikit-learn) (1.10.1)\n",
            "Requirement already satisfied: joblib>=1.1.1 in /usr/local/lib/python3.10/dist-packages (from scikit-learn) (1.2.0)\n",
            "Requirement already satisfied: threadpoolctl>=2.0.0 in /usr/local/lib/python3.10/dist-packages (from scikit-learn) (3.1.0)\n"
          ]
        }
      ],
      "source": [
        "!pip install scikit-learn"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 100,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6twnHJ_oLxXg",
        "outputId": "83c65cca-0aee-41dd-8738-8a091c51442e"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Requirement already satisfied: tqdm in /usr/local/lib/python3.10/dist-packages (4.65.0)\n"
          ]
        }
      ],
      "source": [
        "!pip install tqdm"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 101,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "W3hWOpY3wrdT",
        "outputId": "5542c887-df7c-40ac-9dad-068352f8ab3b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Requirement already satisfied: pennylane in /usr/local/lib/python3.10/dist-packages (0.30.0)\n",
            "Requirement already satisfied: numpy<1.24 in /usr/local/lib/python3.10/dist-packages (from pennylane) (1.22.4)\n",
            "Requirement already satisfied: scipy in /usr/local/lib/python3.10/dist-packages (from pennylane) (1.10.1)\n",
            "Requirement already satisfied: networkx in /usr/local/lib/python3.10/dist-packages (from pennylane) (3.1)\n",
            "Requirement already satisfied: rustworkx in /usr/local/lib/python3.10/dist-packages (from pennylane) (0.13.0)\n",
            "Requirement already satisfied: autograd in /usr/local/lib/python3.10/dist-packages (from pennylane) (1.5)\n",
            "Requirement already satisfied: toml in /usr/local/lib/python3.10/dist-packages (from pennylane) (0.10.2)\n",
            "Requirement already satisfied: appdirs in /usr/local/lib/python3.10/dist-packages (from pennylane) (1.4.4)\n",
            "Requirement already satisfied: semantic-version>=2.7 in /usr/local/lib/python3.10/dist-packages (from pennylane) (2.10.0)\n",
            "Requirement already satisfied: autoray>=0.3.1 in /usr/local/lib/python3.10/dist-packages (from pennylane) (0.6.3)\n",
            "Requirement already satisfied: cachetools in /usr/local/lib/python3.10/dist-packages (from pennylane) (5.3.0)\n",
            "Requirement already satisfied: pennylane-lightning>=0.30 in /usr/local/lib/python3.10/dist-packages (from pennylane) (0.30.0)\n",
            "Requirement already satisfied: requests in /usr/local/lib/python3.10/dist-packages (from pennylane) (2.27.1)\n",
            "Requirement already satisfied: future>=0.15.2 in /usr/local/lib/python3.10/dist-packages (from autograd->pennylane) (0.18.3)\n",
            "Requirement already satisfied: urllib3<1.27,>=1.21.1 in /usr/local/lib/python3.10/dist-packages (from requests->pennylane) (1.26.15)\n",
            "Requirement already satisfied: certifi>=2017.4.17 in /usr/local/lib/python3.10/dist-packages (from requests->pennylane) (2022.12.7)\n",
            "Requirement already satisfied: charset-normalizer~=2.0.0 in /usr/local/lib/python3.10/dist-packages (from requests->pennylane) (2.0.12)\n",
            "Requirement already satisfied: idna<4,>=2.5 in /usr/local/lib/python3.10/dist-packages (from requests->pennylane) (3.4)\n"
          ]
        }
      ],
      "source": [
        "!pip install pennylane"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 102,
      "metadata": {
        "id": "90lDBjOHnSfq"
      },
      "outputs": [],
      "source": [
        "import pandas as pd\n",
        "from matplotlib import pyplot as plt\n",
        "from scipy import signal\n",
        "from sklearn import metrics\n",
        "import pennylane as qml\n",
        "from pennylane import numpy as np\n",
        "from tqdm import tqdm\n",
        "from sklearn.preprocessing import MinMaxScaler\n",
        "import numpy"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 258,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 424
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        "outputId": "292779c4-f15e-4242-bc33-3909dd4372a2"
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              "             Date       Close\n",
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              "10716  2023-06-15  186.009995\n",
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          },
          "metadata": {},
          "execution_count": 258
        }
      ],
      "source": [
        "apple = pd.read_csv(\"AAPL max.csv\", usecols=[\"Close\", \"Date\"])\n",
        "apple"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 259,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 569
        },
        "id": "SXrgNWRfnUa9",
        "outputId": "0541d57e-1cb2-42bc-fb14-7de96358b752"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[1.28348000e-01]\n",
            " [1.21652000e-01]\n",
            " [1.12723000e-01]\n",
            " ...\n",
            " [1.83309998e+02]\n",
            " [1.83949997e+02]\n",
            " [1.86009995e+02]]\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fb819804400>]"
            ]
          },
          "metadata": {},
          "execution_count": 259
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "apl = pd.read_csv(\"AAPL max.csv\", usecols = [\"Close\"])\n",
        "apl = pd.DataFrame.to_numpy(apl)\n",
        "np.concatenate(apl)\n",
        "#aapl = apl[:10080]  # Limiting dataset to what was used in the paper.\n",
        "sample_size = 201\n",
        "aapl = apl[:sample_size]  # A small sample to play around with\n",
        "print(apl)\n",
        "plt.plot(aapl)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 260,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 452
        },
        "id": "fYAAs_fuZI9Y",
        "outputId": "3bed4a47-3aaa-4f37-8a3f-3018adb23aff"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<function matplotlib.pyplot.show(close=None, block=None)>"
            ]
          },
          "metadata": {},
          "execution_count": 260
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "N = sample_size -1\n",
        "pc = np.zeros((N,1))\n",
        "for i in range(N-1):\n",
        "  pc[i] = (aapl[i+1]-aapl[i])/aapl[i]\n",
        "\n",
        "plt.scatter(np.linspace(0,N,N),pc)\n",
        "plt.ylim(-0.6,0.6)\n",
        "plt.show"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 261,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7NzFL6KlbXhW",
        "outputId": "472bafb8-f60f-4373-de32-d40e28c61f9a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "200\n"
          ]
        }
      ],
      "source": [
        "print(len(pc))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 262,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TIgaUz-daSOe",
        "outputId": "7f0b9fc3-46a6-4297-e445-dc286d2a931b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 100/100 [00:01<00:00, 76.63it/s]\n"
          ]
        }
      ],
      "source": [
        "P = np.zeros((N//2,1))\n",
        "nu = np.zeros((N//2,1))\n",
        "for k in tqdm(range(N//2)):\n",
        "    sum = 0\n",
        "    for i in range(N):\n",
        "        sum += (pc[i] * np.exp(2 * np.pi * i * k * 1j * 1/N))\n",
        "    P[k] = np.abs(sum)**2\n",
        "    nu[k] = k/N"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 263,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 503
        },
        "id": "95bdHxUGcFPq",
        "outputId": "4d988823-0d72-4da3-84ee-a2d44a9f4cc6"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[1.25518002]\n",
            " [1.09236469]\n",
            " [1.17578809]]\n",
            "[tensor([0.07], requires_grad=True), tensor([0.085], requires_grad=True), tensor([0.155], requires_grad=True)]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "threshold = 1\n",
        "plt.loglog(nu, P)\n",
        "\n",
        "amp2 = []\n",
        "DC = []\n",
        "for i in range(N//2):\n",
        "    if P[i] > threshold:\n",
        "      amp2.append(P[i])\n",
        "      DC.append(nu[i])\n",
        "amp = np.sqrt(amp2)\n",
        "print(amp)\n",
        "print(DC)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 264,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "E_NH2mE0pfHP",
        "outputId": "b7825407-aa15-461e-f4a8-951638c873e1"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[[1],\n",
              "         [2],\n",
              "         [3],\n",
              "         [4]],\n",
              "\n",
              "        [[5],\n",
              "         [6],\n",
              "         [7],\n",
              "         [8]]], requires_grad=True)"
            ]
          },
          "metadata": {},
          "execution_count": 264
        }
      ],
      "source": [
        "a = np.array([[1,2,3,4],[5,6,7,8]])\n",
        "a.reshape((2,4,1))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 265,
      "metadata": {
        "id": "Iwu731pYo2hY"
      },
      "outputs": [],
      "source": [
        "c_n = [0, 0.2, 0.5, 0.8, 1]\n",
        "noise = np.random.uniform(0,1,N) * (c_n[0])\n",
        "noise = noise.reshape((N,1))\n",
        "trend = np.array([np.zeros(N), 5e-2 * np.linspace(0,N,N), 2* 5e-5 * np.square(np.linspace(0,N,N))])\n",
        "trend = trend.reshape(3,N,1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 266,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LwoMgxUWhmI_",
        "outputId": "fc1423e7-a5d7-4fcc-fea1-27c62b792155"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[0.],\n",
              "        [0.],\n",
              "        [0.],\n",
              "        [0.],\n",
              "        [0.]], requires_grad=True)"
            ]
          },
          "metadata": {},
          "execution_count": 266
        }
      ],
      "source": [
        "a = np.zeros((5,2))\n",
        "a = np.sum(a, axis = -1)\n",
        "a =a.reshape(5,1)\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 267,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "Cd5AY6yYeiTB",
        "outputId": "26f59a7d-3644-4c93-ff0a-22826314d887"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fb819490f70>]"
            ]
          },
          "metadata": {},
          "execution_count": 267
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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0HSxaBsLBIjdN5pGESDMWDb0jGPcGZB4NaYG0rLYiwcECANaEm28dbR5K+GMRkXLpOlg0h88IUcqMRb4tBbkZVgRF4GwXZy1o7s6Ed4QsL0p8sIjUWXDGgkjXdB4swjMWOcqYsQCAKmk5hHUWNEeDo150OENnzyxLwozF2vCMRU3LEAJBNsoi0ivdBosRjx/94SKzcgUFC3bgpHiRCjfLs9NgS8Kup8UFmciwmjDqDeB893DCH4+IlEm3wUJaBslOtyTlTXem2IGT4iWZ9RUAYDQIqC4L/fwe5bZTIt3SbbBoCS+DlGcrZ7YCmOiOeL5rBF5/UObRkJqdTmJ9hWQtCziJdE+3weKCAusrAKA0KxW2FBO8gSDqejidTLN3riv087MsicFiTbkDAAs4ifRMt8GiZSC8IyRHGTtCJIIgYEWxdIQ66yxodvyBYOQcnCWFieu4eTHpWPamvlEMu3nmDZEe6TZYTDTHUtaMBRBdwMk6C5qdloExeANBpJgNKHGkJu1xczOsKHGkQhSBk9zZRKRLMQWLb37zmxAEYdLX0qVLEzW2hFLiVlOJVGdxijtDaJbqekLn4CzMz4DBICT1sVeVhn5+T7YxWBDpkSnWO6xYsQI7d+6cuIAp5kvIzuMPoMM5DkB5SyHAxIzF2U4XAkERxiT/YSD1qwtv91ycwIPHprKy1I6XT3XhBIMFkS7FnApMJhMKCwsTMZakaRschygCaRYjcjMscg/nXebnZSDFbMCYN4CmvlEszM+Qe0ikMpEZi4Lk/+xUh+ssjrcNJf2xiUh+MddY1NXVobi4GPPnz8fWrVvR0tKSiHElVPRWU0FQ3myA0SBEKvlZZ0GzUdcdChaJPCp9KtJSXtvgOAZ40imR7sQULDZt2oQnn3wSr7zyCh577DE0NTXhmmuuwfDw1NsiPR4PXC7XpC+5XZDOCFFgfYVEWg45wzoLilEgKKKhVwoWyZ+xsKeaURk+6fQEZy2IdCemYHHbbbfh3nvvxapVq3DLLbfgpZdewtDQEH7/+99PeZ8dO3bAbrdHvsrKyuY86LmaKNxUXn2FZHlR6FOf1JaZaKbaBsfg8QdhNRlQJtOuJ6mAk3UWRPozp+2mDocDixcvRn19/ZS32b59O5xOZ+SrtbV1Lg8ZF22DocJNud50ZyL6zBBR5IFONHPSMsiCvAzZCn9XljBYEOnVnILFyMgIGhoaUFRUNOVtrFYrbDbbpC+5tQ2GZixKs5K3vz9WSwozYTQIGBj1osvllns4pCLnwx1bF8lQuCmpLnMA4FIIkR7FFCy+/OUvY/fu3bhw4QL27t2Lu+66C0ajEffff3+ixhd3oihOzFhkKXfGIsVsxMK80B8GduCkWNSHZywWFyS/cFOyotgGgwD0DHvQzWBMpCsxbTdta2vD/fffj/7+fuTl5eHqq6/G/v37kZeXl6jxxZ1z3IcRjx+AsmcsAGB5sQ213cM40+nCluUFcg+HVCK6OZZc0iwmzM/LQH3PCE53OFFgS5FtLKQ/vkAQfzjchv95uxEGQcBNy/Lx/uriyHEJlFgxBYtnnnkmUeNIGmm2IjfDihSzUebRXN6KYhuePdbOLac0Y8GgiPoe+XaERKsqtoWCRbsLNy5lMKbkqO8Zwad+dRiNfaOTvveLPY34r63rcGuVuvswqYHuzgppHQjVV5RlK3u2AgjNWAChAk6imeh0uTHuC8BsFFAuc3Gy9OnwFIMxJYnbF8Bnnz6Cxr5RZKdb8LU7luMn96/BtYvzEBSBR545hiPNA3IPU/N0FyykGYtSBddXSFYUTTQaco7xpEia3oXwp7Ty7DSYjPL+eq8oYTCm5Pr2i2dwvnsEuRlWvPr5a/GJqyvxvupi/PLB9diyLB8efxCfeOpw5PeEEkOHwUL5O0Ik9jRz5GRK9rOgmZCmfytz5W8DHx2Mh8bYgZMS65VTXXj6QKgT9A/vq0ZepjXybyajAT+5fy1WlzkwNObDjpfPyjVMXdBdsGhVwY6QaDxCnWLR1BsKFvPz5G/+Zk8zR5Yc2UGWEikQFCNh4dPXzsc1i969oSDVYsS/3bsKBgF49XQ3jrcOJXmU+qG7YKGmGQtgYp2ab8w0E019ocJNqaW23KRZC9ZZUCL97XQXmvvHYE8145Eti6a83cL8TNy9thQA8G9/q03W8HRHV8EiuoeFWoKFVMDJpRCaiabIUogygkUV6ywowURRxM/2NAIA/s8VFUizXH6z4yM3LYLZKOCtuj7sbehLxhB1R1fBYmDUizFvAABQ7FBHsJCWQup6RuD2BWQeDSmZ1x+MLPXNV0iwiOwMaeeMBSXG4eZB1LQOwWIy4MEr5017+7LsNHxkYzkA4KdvTn0cBc2eroKFNFtRYFN+DwtJkT0FWWlmBIIizndPfYosUevgGAJBEekW46TCNTlJO0Ma+0Yx5vXLPBrSop+HZyvuWVsy45/7v79mPgBgb0N/ZHmc4keXwUINW00lgiBEPvVxOpkuRyrcnJebDkGQ5/Cxi+VnpiAv0wpRBM5yOY/irGfYjdfPdgMAPnH1/Bnfryw7DVcuyIEoAn860p6o4emWroJFq8oKNyWROgsGC7oMpdVXSKrY6I0S5NVTXQiKoUPvYm1hf+/6UBHnH460IhjkCdLxpKtgIU15qWWrqYRbTmkmpB4WSqmvkLDOghLlxROdAIA7Vk59wvZUbl1RhEyrCW2D49jf1B/voemazoKFunaESKRgcbZzGAEma5pCZKupAnpYROPOEEqEnmE3Dl4Itee+bWXs53+kWoy4o7oYAPDHw21xHZve6TRYqGvGojI3AylmA8Z9gch0N9HFmhTUdTOaNGNxvnsYXn9Q5tGQVrxyqguiCKwpd8z6PV1aDnn5VBd33cWRboKFKIroGAoFi2KHuo5wNhoELC1kPwua2qjHj26XBwBQmaOsGYvSrFTYUkzwBbizieJHWga5fRbLIJI1ZQ6UOFIx7gvgnXr2tIgX3QQL57hPdT0sorHOgi5Hmq3ISbfAnmaWeTSTTd7ZxJ9fmrselxuHIssgsw8WgiDgpmX5AICd4d0lNHe6CRYdQ24AoTdetfSwiMbW3nQ5F/ontpoqEessKJ52ne+FKALVpfbIQY2ztWVZAQBg59ke7g6JEx0Fi9AySJHKlkEk0ozFqXYnRJE//DRZc39ox1NFtjLrh7gzhOLp7brQssW1i9992FisNs3PRobVhN5hD07w5zMu9BMsnOH6Crv6lkEAYElhJkwGAYNjPnQ43XIPhxSmJRwsynOUGSykGQvubKK5CgbFSD3E1Qtz53w9q8mI68IBZecZLofEg36CRXgpRI31FQCQYjZiUUEmAOBkG1M1TdY8EFoKqVBosKjMzUCq2Rje2TQi93BIxc52udA/6kWaxYg15VlxueaW5ayziCcdBQt17giJtrJkYjmEKFpkxiJbmTUWRoOAZUWhYMw6C5oLaRnkivk5sJji8yfshiX5MBoEnOsaRusAzw6ZK90Ei05pKUSlMxYAUFUSXqdmZT1F8fgD6HSFZuSUOmMBRP38MhjTHLwdx2UQiSPNgrXljknXp9nTTbCQlkKKVFpjAUx+Y2YBJ0naBschikC6xYicdIvcw5nSCp4ZQnPk9gVwsCm0zfTqRfELFgBw5YLQ9fY2sL33XOkiWASCIrrCn+jmujVJTsuLbDAaBPSNeCPPh0haBinLTlPMqaaXEn1KL4MxzcbhC4Pw+IMosFmxKMZDx6Zz5YIcAMC+hj7+fM6RLoJFz7AbgaAIk0FAXqZV7uHMWorZGPllOtXOT30U0tyv7MJNyaKCDJiNApzjvkh7faJY7G0ILVNctTA37iF6dbkDKWYD+ka8ON/NAuO50EWwkAo3C2wpMBqU+4luJqRPfSe5Tk1hzeFiswqFtfK+mNVkxKJ8FnDS7B1uHgQAbKrMjvu1rSYjNswLXVcKMDQ7OgkW0lZT9e4IkXBnCF1sYkeIsmcsgIk6izMsQKYY+QJBHG8dAgCsq4jPNtOLsc4iPnQSLNS/I0SyspSV9TTZxIyF8oPFxM4mzlhQbM50uODxB2FPNWN+gk7wleos9jf2wx/gSbyzpYtg0elUd3OsaMuKbDAIQM+wB90s4NS9YFBEixQsFNrDIhoP06PZkpZB1lVkwZCgJe2qEjsyU0wYdvu5XDcHuggW7dKMhV39SyFpFlNknVqaFiT96hn2wOsPwmQQVLHUt6zIBkEAul0e9A575B4OqcjRqGCRKEaDgCvmh2YtuBwye7oIFlpojhVtVXg55ARbe+uetCOkJCsVJqPyf53TrSZUhk9g5awFzZQoijjcHOpfkchgAUwUhh4OH8tOsVP+O1EcaKE5VrTqMgcA4HjbkKzjIPlJ9RVqKNyURPezIJqJ9qFxdLs8MBoEVJc6EvpY68M7Q460DPIY9VnSfLAY9wYwMOoFoO7mWNGkX6wTbezAqXfSjhA1FG5KJnaGMFjQzBwJL4OsKLYh1WJM6GOtKLYhxWzA0JgPjTwwb1Y0HyykZZB0ixG2VJPMo4mPJYWZsBgNcI770NzPA3P0rHUw3HUzSz3BoioyY8GlEJqZI0mor5CYjYbIh7fDFwYT/nhapPlgEVkGcaQqut1xLCwmA5aHP/VxOUTfpJMYy1S1FBL62b3QPwaX2yfzaEgNjrUMAQDWxumY9Omsnxd6HGknCsVG+8FCY4WbkmoWcBKA1nBrbDXNWGSlWyI7tM5yOYSm4fEHcK4r9HOyOlxflmjrK8J1FgwWs6L9YKGhrabRVoWn6rjlVL/cvkBky2ZZtrqC84oSFnDSzJzvGoEvIMKeakZpVnJ+zqWZkaa+UfSNcFt0rDQfLDqHtNMcK5q0M+RUh5Md4nSqLVxfkWk1wZ5qlnk0sZGWQ06xzoKmcaJ9CEBom32ylrPtaWYsKQj1C+KsRew0Hyy0uhQyPzcdmVYT3L4g6npYuaxH0jJIqcKPS78Uacspd4bQdKTjC6R28MmyLlxnwWARO80HCy113YxmMAiRc0NquByiS23hws1kTQ/HU1X4ML26nhG4fQGZR0NKJtWRrUpysFgf3oHCRlmx03SwEEVRs0shALCm3AFgotUt6YsaCzclhbYUZKdbEAiKqO0alns4pFBuXwDnu0M/H8mesVgTrrM41eGCj8vNMdF0sBga82E8/GmoUGMzFsBEgdHRFgYLPZrYaqq+0CwIQtSBZFwOoUur7RqGLyAiKy15hZuSeTlpsKea4fUHca6T4TcWmg4WUn1FboYFKebEdmuTg5SoG3pHMTTmlXk0lGxqbI4VbQUbZdE0TobrK1aWOpJeRyQIQqRIvob9gmKi7WChsTNCLpadbsH88IFOUgMZ0o/WgfBSiIqaY0Wb2BnCGQu6tJPh+oqV4ZqcZFst1bHx/TUmmg4WE6eaam8ZRLKGyyG65HL74BwPda1UY/EmMBEsznW6uGWaLikyY1HikOXxV4fr2NjhODaaDhaRHSEaLNyUrK1wAGCw0Ju28GxFdroF6VZ1noEzLycdGVYTPP4g6nu5ZZomiy7clHbAJZt0ZkhD7wjbz8dA08FCWgop1uhSCDBxKE9NyxACPOJXNybqK9T7s20wTBRwnmRrerpIfc8I/EERjjSzbO0CcjKsKMtOhSjyZzQWmg4WnTqYsViUn4kMqwmj3gC37emItCOkVKX1FZJV4U+i0pQ3keRMZ6j2ZlmhTdYGcNKsBfsFzZymg4V0TkiRhmssjAYhcjAPl0P0o03quqniGQsgVO0P8DA9erezUrAokqdwUyK9vzJYzJxmg4U/EER3+ICmEg3PWADA2gq2ntWbNpVvNZVI3RTPdLIJEU0mBYulRZmyjiM6WIgil5tnQrPBomfYg0BQhNkoIC/DKvdwEmpDuKf9wSa2ntULtW81lVTkpCEzxQSvP4i6bhZwUogoijgbbkq1XOYZi6oSO4wGAb3DHnS53LKORS00GyykraYFthQYDOo6oClW6yqyYDIIaB8aj6y9k3aJohjZ8aT22ThBELCyRKqzGJJ3MKQYnU43nOM+GA0CFuZnyDqWFLMRi8JjYAHnzGg2WLTrYEeIJM1iimzH4qyF9rncfox4/ADUHyyAia2ErLMgibQMsiAvXRFdk6VzSk6xyHhGNBssupzaL9yMtqkyBwBwoKlf5pFQorWHCzdz0i1Itcj/pjtXq8LNj7gzhCRKKdyUTMyq8Wd0JjQbLDqdoRkLLR4+dimbKrMBAAc4Y6F5Wmv8Jm05PdvpgsfPI9QJkfoKpQSLqkiwcLGAcwY0Gyy6wsGiyKaPYLF+XhYMAtDcPxZ57qRNHRqpr5CUZqXCkWaGLyDifBcLOEl5MxbLi2wwCEDfiAfdLo/cw1E87QYLlzRjoY033+lkppgjp0VyOUTbtDZjEV3AyTMZaMzrR1P/KABgmcxbTSWpFiMW5YfGwuWQ6Wk3WEgzFjpZCgG4HKIXkR0hKm+OFY1NiEhS2zUMUQRyMyzIz1TO+3cV6yxmbE7B4tFHH4UgCPj85z8fp+HEhz8QRE+4OZZeaiwAYGM4WOxv5IyFlknFm1pZCgGANeFTJI+xe6zuSQePLSlUxmyFRDq6nTtDpjfrYHHo0CH87Gc/w6pVq+I5nrjoG/EiEBRhNAjI1XhzrGib5ufAIACNvaORdXjSHq30sIg2cYrkaOQ4eNKn2nCdzZICZdRXSFbyXJsZm1WwGBkZwdatW/GLX/wCWVlZ8R7TnEWaY2VaYdR4c6xo9lRzZEr5rbpeeQdDCeHxB9ArtarX0FJIToYV5eEuoidYZ6FrEzMW8jbGutjyIjsMAtA77EE3O3Be1qyCxbZt23D77bdjy5Yt097W4/HA5XJN+kq0bpe+tppGu2ZRHgBgz/k+mUdCidAZbvyWajYiK80s82jia2I5ZEjWcZC8asPBYnGBspZCUi3GSBdQduC8vJiDxTPPPIOjR49ix44dM7r9jh07YLfbI19lZWUxDzJWnZHCTe18opupaxeHgsXb9X0IBLnfWmsmdoSkyHqUdCKwgJMGR72RGblFCgsWAAs4ZyqmYNHa2opHHnkETz/9NFJSZjYbsH37djidzshXa2vrrAYaC2lHSIFOelhEqy61w5ZignPcxyllDZrYEaLuw8cuhadIkrQMUpqVigyrSebRvNtKtvaekZiCxZEjR9DT04O1a9fCZDLBZDJh9+7d+PGPfwyTyYRA4N1d86xWK2w226SvROvU4VZTiclowFULcwFwOUSLJnaEaO9ne3mxDRajAQOjXrTwMD1ditRXKHC2AmBr75mKKVjcdNNNOHnyJGpqaiJf69evx9atW1FTUwOjURnnFnTprJ33xaTlEBZwao/Wum5Gs5qMWF4c+uDB5RB9kuorlLgMAoTCr0EAeoY96GEB55RiChaZmZmoqqqa9JWeno6cnBxUVVUlaowxk7pu6nHGAgCuWRSasTjWOsStexqjxeZY0aTlEBZw6pPU0l1pO0IkaRYTFuSFCzg5azElzXXeFEVR9zMWpVlpWJifgUBQxK7aHrmHQ3EUKd7UaGHyuorQ9vXDzeweqzeiKCp2R0g0LodMb87BYteuXfjRj34Uh6HEx8CoF95AEAAU1Q422W5eXgAA+NvpbplHQvESDIqR7aZanbHYMC/UPfZMhwvDbs626UnvsAfOcR8MAiKzAkpUxQLOaWluxkIq3MzNsMJi0tzTm7FbVhQCAN6s7YHbx6OotaBvxANvIAiDABRqdMdToT0FZdmpCIpcDtEbabZiXm46UszKqNe7FHbgnJ7m/vLq8fCxS1lVakeRPQVj3gDeruPuEC1oCy+DFNpSYDJq7lc3YkNFaNbi0AUuh+hJbZeyd4RIlhfZIAhAt8uDnmEWcF6K5t6dunTcdTOaIAiR5ZBXT3fJPBqKhw6NF25KNlQyWOhRXXeocFOpO0Ik6daJAk4uh1ya9oIFZywipOWQnWe74Q/XnZB6ST0sijW41TTahnmhAs5jLUPw+vlzqxf1veFgka/c+gpJpICzLfFHVKiR5oJFp467bl5sY2U2HGlmDI75cJCf/lRPyz0soi3Iy0BWmhkefxCnOtTzibDb5cav9zfj316txXPH2nG+e5gdRGdIFEXUhWssFqogWLC19+Upr2fqHHW5Qm++nLEIdeF8z7IC/OFIG/5S04ErF+TKPSSaA633sJAIgoD187Lx2pluHGoawNpy5Z2gHK11YAz/988n8E59/7v+7baqQnznrpXITrfIMDL16B3xwOX2wyAAlbnpcg9nWtKMxWkVBd9k0tyMhd57WFzs7rWlAIAXT3Ri3MvdIWrWppOlEADYOE+qsxiUeSSX98qpTrz3x29FQsWacgc+vKEMG+ZlwWQQ8PKpLtz8wz3Y28AC6sup7wktg5Rlpyl6R4hkeXGogLPT6UbfiEfu4SiOpmYsRFHU9cmml7KpMhtl2aloHRjHq6e78IE1JXIPiWZJWgop1UGwiC7gDARFGA3KO8n1V/su4OvPnwYArC134Ef3rUF5zsThcCfbnPjC72tQ3zOCT/3qCJ797JWKL0yUS0OPeuorACDDakJlbjoae0dxst2JG5bkyz0kRdHUjMWwx4+x8Kdyre7zj5XBIOCe8KzFH44k/mRZSoxhtw8utx+APmYsqoptyLSGTulV4nTzK6c68Y2/hELFx6+qxO8+vXlSqABC/Q5e/IersakyGyMeP/7+V4cxNOaVY7iKVxcOFgtUEiyAqOUQ1lm8i6aChbQMYk81I9Wi/Om0ZJGCxd6GfrQN8tRINZLqKxxpZqQr8DjpeDMZDbhiQQ4AXLJ2QU6HLwzgc8/UQBSBrZvK8bU7lsE8RV+RFLMR/7V1LUocqWjuHwvfjwWdF5OWQhYquOPmxdjae2qaChZ6Pi79csqy03DF/GyIIvDno+1yD4dmQS87QqJdvTBUbPxOvXLqE5xjPjz8m2Pw+oPYsqwA37qzCoJw+WWanAwrfvHAeqSYDdhzvhcvnWRfmYtFgoWKZixWFEutvbnl9GKaChbdLNyc0ofWlwEAnj7QDI+fRZxqo5ceFtGuCgeLgxcGFNGWXhRFfPW5k+hyuVGZm44f3796xrUfy4tt+PS1CwAAO14+q4jnoxQutw89w6ECSDUthawosQEIzSYOjHKJK5qmggVnLKZ2+6oiFNis6HZ58HxNh9zDoRi1S4eP6ShYLMhLR4HNCq8/iCPN8u8Oea6mHX890QmjQcAP71uNNEtsS1Kfvm4+CmxWtA2O44l3LiRmkCokzVYU2lJgSzHLPJqZs6WYI1tj2YFzMk0FC6mHRaFNP2++M2U1GfHxqyoBAD/f04hgkOu8aiLVWJRqvIdFNEEQIrMWb8u8HDI46sU3wjtAHrlpEVaXOWK+RprFhH+6ZSkA4Kdv1qOf2xQBAPXd6lsGkawoDs1asM5iMk0Fi87IUohV5pEo00c2lSPTakJ9zwjeONcj93AoBu3hols9LYUAyqmz+OHO83C5/VhamInPXr9g1te5a00JqkpsGPH48b/7m+M4QvWSWnmrMVis5BHql6SpYDHRHEtfb74zlZlixtYrKgAA/7WrntXpKtKhw6UQYKLO4mS7E4MyrWOf7x7G0wdaAABff9/yOZ0sazAIkVqLX+9nvRMwsRSipvoKSSRYKHBLtJy0FSxcrLGYzsevmgeryYCjLUP468lOuYdDM+D1B9EdPp5Z6+28L1ZgS8GSgkyIIrDrfPJn2URRxLdfPINAUMQtKwri0hb/1qpCFNpS0DfixYvH+TtYr7LmWNFWhINF68A4e5RE0UywGPcGMDTmA8BdIZeTb0vBZ69fCAD4zl/PYtTjl3lENJ1ulxuiCFhNBuTo8MyJLctDXQ13nkl+sHiztgdv1fXBbBTw1fcui8s1zUYDHrgyNHP4y3eadD1z6PYF0Bpe5lPjUog91Yzy7FBjNG47naCZYCHNVqRbjMjUQQOhufj0dfNRlp2KTqcbP32zXu7h0DSkM0JKHKnT9kzQovcsLwQA7KrtSerSgS8QxP978SyAUHfNipz4HY51/4ZypJgNON3hwsEm/Z483NA7AlEMNX5Ta2hmo6x300yw6HSG3nwL7Cm6fPONRYrZiK/fsQIA8Iu3Gll4pHDSjhC9FW5KVpXYkZ9pxag3gH0NyevC+b/7mtHYN4rcDAsevnFhXK+dlW7BXWtCHXF/c7AlrtdWk+iOm2p9365incW7aCZYdLGHRUy2LMvHlmUF8AVEfPp/j/CEPgXTY9fNaAaDgC3LCwAAr53pTspjDo568aOd5wEAX7p5CTIT0F/hQ+tDweJvp7t1uyQZOXysQH3LIJKqcKMsfkCboJ1gEV4KYQ+LmREEAf/+oWpU5qajfWgcn336KHyBoNzDokuQum7qrXAz2nvCwWLn2e6k9GCRtpcuK7JFutbG2+oyBypy0jDuCyQtMCmNtNV0gYrOCLlYVbi1d3P/GJzjPplHowzaCRacsYiZPdWMXzywDhlWEw42DeATTx3mL4YC6X0pBACuXJCDdIsR3S5Pwqeco7eXfu2OZQk7sl0QBHxgdQkA4Nlj+jzDp07FzbEkWemWSOM6JZ7EKwfNBItOnhMyKwvzM/GfH1kTOSDprp++gzMdM69uDgZFtA6M4a26Xrx0shN/PNKGt+v60Dowxu6ecaL3pRAg1Dn2+iWh3SEvnkjcFs1EbC+9nA+sCQWLt+p60Tusr+VIfyCIC/2jANQdLICJWQsuh4RoZvtEpDmWjcEiVtcvyccfP3MlPvWrw2jsG8V7f/wWtiwrwEc2laGq2I68TCsEQYDbF0Bt1zDOdLpwpsOFM50unOt0YdR76Ur90qxUfGRTOe5bX4acDHZDnQ1RFHXZzvtS3r+6GH892Ylnj7Xjn25ZMqdGVVORtpdajIa4bS+9nMrcdFSXOXC8dQgvnujAx8Jt9/WgeWAMvoCIVLMRxSpvariy1I5XTnfhJLecAtBQsOCMxdxUldjx/MNX4xt/OYWXT3Vh59lu7DwbWvdNMRsQCIrwBS49A2ExGlCRkwZHmhkpZiM6nW609I+hbXAc33ulFj99ox7fvXsl7gxP+9LM9Y964fEHIQihZlF6dsOSfGSnW9A77MFb9X24ITyDES/R20s/dvW8uG4vvZy7VhfjeOsQnq/RV7CIPirdkKDlpmSpYmvvSTQRLERRxEevrED7kFv3n+rmIi/Tiv/aug4NvSN4/O0mHGjsR1PfKNy+iaLOnHQLlhfbQl9Foa95uekwX/Tp0e0L4MUTnXjinSac7nDhkWdqsL+xH998/wpYTcZkPzXVkgo3CzJTYDFpZuVyViwmA95fXYwn917AH4+0xT1YTNpeekN8t5dezntXFuGbL5xBTesQul1u3QTI6GChdlXhw8ia+kbhcvtUdUprImgiWAiCgIdvXCT3MDRjQV4GvnvXSgChjqY9w25YTAakmo2wp5pntN88xWzEB9eV4gOri/Hj1+vwkzfr8duDrXC5/fjJh9eo/hNKskwUburjj810PriuFE/uvYDXznTDOeaDPS0+b+ADSdheOpV8WwpWlzlQ0zqEnWe7sXVTRdIeW05aChY5GVaUOFLRPjSOU+3OhNfmKJ2+PwLRtFItRlTkpKPIngpHmiXmJjYmowFfvHkJHn9wPcxGAX890Yl/feVcgkarPZHCzaw0mUeiDCuKbVhamAmvP4gXT3bE7bo/SsL20st5T5L7dChB5PAxFW81jVZdFloOOd7K5RAGC0qKG5cW4F/vWQUA+NmeRvzmgH67DcYiup03hWYnP7gu1Fjqf/c1x+WcjVPtTvw6fIR5IreXXs7N4WCxt75fF82ygkERDb3qb44VrbrUAQA40TYk6ziUgMGCkubutaX48s2LAQD/769n0BY+fIim1h7ZasqlEMm968qQYTXhXNcw3jg3t4PJAkER//zsSQRF4I5VRbJNYS/Mz0BFThq8gSD2nO+VZQzJ1OlyY8wbgNkooCJbG7Nxq8LB4njrkKzjUAIGC0qqz16/EBvnZWPMG8DXnjul65MdZ2JiKYQzFhJ7mhl/d0WoDuE/36yf08/Q0weacbzNiUyrCV+/Y3m8hhgzQRDwnmX6WQ6p6x4GAMzLSU/ItmE5rCy1QxCADqcbPcNuuYcjK228oqQaBoOA7969EhajAW/W9uKFBDY70oKJGQttfKqLl09cXQmryYBjLUPY3zi700E7neP4/iu1AIB/unUJ8mXejSHVWbxR2wO/xtvra6lwU5JhNWFR+Pmc0HmdBYMFJd3C/AxsC2/n+9YLZzA+RYMtvRv1+DE0Fmqxzl0hk+VlWnHfhlCR5U/eqIt51iIQFPH5Z2ow7PFjdZkDH1HATox1FVlwpJkxNObDcY2v00fqKzQULICo5RCNv37TYbAgWTx0/QKUZqWib8SD3+r42OjLkZZBbCmmpG5/VItPXTsfZqOAvQ39eL4mth0i//lGPQ40DSDdYsQP71stS8HmxUxGA65aGKrx2HO+T+bRJFZkR4jGgkV1mQMAcLyNMxZESWcxGSKzFv+9uwFuH2ctLtbGw8cuqzQrDY/cFOpf842/nEaPa2br2nsb+vAfr4d6Vnz7A1WozE1Oh82ZuHZRKFi8VafdAk5RFFGnwaUQAFgdVcCp5/oxBguSzT1rS1FsT0HPsAe/P9wq93AUp4NnhEzr09ctQFWJDc5xH7767PTFwDWtQ/jkU4cRFIG715Tg7rWlSRrpzFy9KA9AaJzOMW2eNNw/6sXQmA+CoJ0eFpIlhZmwGA1wjvvQ3K/fXW8MFiQbi8mAh8KzFo/taoDHz1mLaO3sYTEts9GAf7u3GmajgJ1nu/HPz51CYIpTdU+1O/HA4wcw6g1g8/wcfPfulUke7fRKHKlYkJeOoBiaWdEiaRmkNCsVKWZttfe3mAxYHm7vrec6CwYLktWH1peiwGZFp9ONV051yT0cRWnnUsiMLC204f99oAqCAPzmQAse/s1RDI56I//u9Qfx49frcPd/7YXL7cfacgf+58H1iv2jdu3i0KzFnjptB4tF+ZkyjyQx1pQ7AABHmwflHYiMNHFWCKmX1WTE/RvL8aOddfjtwRaegBqFPSxm7r4N5chMMePzz9Tg5VNdeO1MN65elAtRBE53uNA34gEA3LAkDz/68BqkW5X71nftojw88c4F7DnfC1EUY26jr3Ra3GoabV1FFp545wKOtgzJPRTZcMaCZHffhjIYBGB/40BkGxpxKSRW711ZhKc+vhHLi2zwB0Xsqu3F7vO96BvxIDvdgv/48Gr88qMbYE9V9g6bTfOzYTEa0D40jqa+UbmHE3eRYKGx+grJ2vIsAMCZThfGvNpvz34pyo3tpBtF9lTcuDQfO8/24JmDLfjn2+XrgKgU/kAQXeFdDgwWM7d5QQ5eeuQa1PcM4/WzPchIMWFpYSaWF9mRalHm0sfF0iwmrKvIwr7GfrxT34f5GvsDrNWtppJiRyqK7CnodLpxvNWJzQty5B5S0nHGghTh/o3lAIA/Hmnj1lMAXS43giJgMRqQm2GVeziqszA/E5++bgG2bqrAuops1YQKyZXhP0b7GvtlHkl8Dbt9kcCs1aUQYGLW4miLPussGCxIEa5bnIciewoGx3x49TSLOKVlkCJHCgwKaN5EyXVFOFjsbxzQVD+Eht7Q0k5+plXxS1JzsbYiHCx0WsDJYEGKYDIaIsdhv3Cc54d0OFlfoWfVpQ6kmA0YGPXifLd26o60XrgpWVcxMWOhpWA4UwwWpBjvqy4GAOw53wuXW5vNgWaKhZv6ZjEZsL4iGwCwX0PLIdKpplo7I+Riy4tssJoMGBzzabIAdzoMFqQYiwsysSg/A95AEDt1cHT05bCHBUlFf/saNBQspB4WBdrsYSGxmAxYVWoHABzR4XIIgwUpyu2rigAAf9X5certQ+EdIexhoVtXzA8FiwNN/QhO0U1Ubep69DFjAUzUWTBYEMns9pWhYLGnrlezZyXMRPtg6JwBLoXo16pSO9IsRgyO+VAbXkJQszGvH23hJT6tz1gAwIbwUtbBpgGZR5J8DBakKIsKMrGkIBO+gIi/ndHn7hBRFNExxB4Wemc2GrB+nnbqLBp7RyGKQE66BdnpFrmHk3AbKrMhCEBj3yi6Z3jybjwcbBpA77AnaY93KQwWpDjScshLJ/W5HDI45sN4uJdHkSNF5tGQnK6YHwoWBxrV/6n3fHjWRes7QiT2VDNWhA8kS1YwDAZFfPp/D2PDd3biZJszKY95KQwWpDi3rCgEAOxt6Me4V3/NsqQdIXmZVlhN6mrsRPG1MTxjcbhZ/dsWpcLNxTpYBpFcUTnRjyQZTnU4MTjmQ6bVhKVF8v3/zGBBirO4IAPF9hR4/EHsa9TmCY+XI+0I4TIIrSy1w2IyoG/Eg+b+MbmHMyd13dKOEH3MWABRBbhJmrF4K3wi7uYFOTAb5fvzzmBBiiMIAm5Ymg8AeONcj8yjSb52nmpKYVaTEdXhbYuHLqh7OaS+R19LIcDkOoueJNRZ7DnfCwC4ZnFewh/rchgsSJFuDAeLN8/1qn4KOFZsjkXR1oV3Fxy+oN5ti25fAC0DoRmXRfn6WQqZVGeR4N0hIx5/ZGvrtYtyE/pY02GwIEW6ckEurKbQ0dHS2qxedHAphKJsmBfqh3CoWb0zFg29IwiKgCPNjNwM7e8IibYpUmeR2OWQ/Q398AdFlGenoSInPaGPNR0GC1KkVIsx0nlQb8sh7LpJ0aRzJxp7R9E/Iu82wtmSzghZnJ8JQdDXoXpSncX+BHdQfasutAxy7WJ5ZyuAGIPFY489hlWrVsFms8Fms2Hz5s14+eWXEzU20rkbluizzoLFmxTNkWbB4nDBo1q7OEqFmwt1VLgp2TQ/G0aDgMa+UbQOJK4AVyrcvGaRvPUVQIzBorS0FI8++iiOHDmCw4cP48Ybb8Sdd96J06dPJ2p8pGNSncWR5kEM6+RQsjGvHwOjXgAs3qQJ66O2naqRnlp5X8yWYo7MOu2qTcyHpNaBMTT2jcJoECIzvXKKKVi8733vw3vf+14sWrQIixcvxne+8x1kZGRg//79iRof6VhZdhoqctIQCIq6aYsrFW7aUkywp5plHg0pRaTOQqU7QyKHj+mocDPa9UtCswi7ansTcn1pVndtuQO2FPnfN2ZdYxEIBPDMM89gdHQUmzdvnvJ2Ho8HLpdr0hfRTF25ILRe+E69+lsaz4R0lkJJVprMIyElkY5QP9XuVF3TOI8/EOnBoaceFtGuXxyafX2noQ9uX/xfP+n4g5uXF8b92rMRc7A4efIkMjIyYLVa8ZnPfAbPPvssli9fPuXtd+zYAbvdHvkqKyub04BJX65aGJrW29ugj0ZZbeH6ilIug1CU0qxUFNis8AVEHG8bkns4MWnqG0UgKMKWYkJ+plXu4chiWVEmCmxWuH3BuM++Osd8kc6eN68oiOu1ZyvmYLFkyRLU1NTgwIEDeOihh/Dggw/izJkzU95++/btcDqdka/W1tY5DZj0ZXO4ovpc1zD6VFoRH4u28KmmDBYUTRCEiToLlS2HTHTc1N+OEIkgCJFZizfjXGfxRm03AkERSwszZd9mKok5WFgsFixcuBDr1q3Djh07UF1djf/4j/+Y8vZWqzWyi0T6IpqpnAwrlhaG1mW1cMLjdNrYHIumsCFcAKi2As6J+gp9LoNIpDqL3XGus/jb6W4AwM3LlTFbAcShj0UwGITHo/1PkiQfPdVZSMWbpayxoItIMxZHmgcRCKqnG60eW3lfylWLcmEKbztt6huNyzXdvgB2h9t437xCGfUVQIzBYvv27dizZw8uXLiAkydPYvv27di1axe2bt2aqPER6arOom2QNRZ0aUsLM5FhNWHY7Y8cQa4G56OWQvTMlmKObAV98XhHXK75Tn0fxrwBFNtTIq3DlSCmYNHT04MHHngAS5YswU033YRDhw7h1VdfxXve855EjY8IGytDDWaa+8ciNQha5PYFInUkZZyxoIuYjAasKXcAUE+dhdcfxIXwp/PFOt0REu191cUAgL8c74jLGUgvhAPKzSsKFVW/ElOwePzxx3HhwgV4PB709PRg586dDBWUcJkpZqwsCZ3weKBRHW+osyHNVmRYTbClmmQeDSnRhvByyCGVHEjW3D8Kf1BEhtWEQluK3MOR3S0rCmExGlDXM4LaOc46udw+vHI6tM30rjUl8Rhe3PCsEFKFjZXSG6p2g0V71FZTJX36IOVYLxVwquT3QCrcXJifwZ9phE47vS5cxPmXmrkth7x0ohNuXxCL8jOwqtQej+HFDYMFqcLEJzV1vKHOBrea0nRWlztgMgjocLojQVTJIltNdV64Ge394eWQF07MbTnkj0faAAAfXFequNDGYEGqIH1Sa1DxCY/T4VZTmk6axYTl4SI9NRxIdj68I2Sxzgs3o920LB+pZiNaB8ZR0zo0q2s09o7gcPMgDILylkEABgtSiaz0iRMe1bK+HCtuNaWZkA60OqKC2bt6HZ9qOpU0iynSIfPpAy2zusafjoZmK65bnId8BdauMFiQaqi18+BMcSmEZiISLFqUHbC9/iAa+7gUcikPbJ4HAHi+ph09LndM9x3z+vHMwVAH6w+uU+YRGQwWpBobNV5nMXEAGYMFTU0KFmc7hzHq8cs8mqk19o3AFxCRmWLi8t5F1lVkYW25A76AiF/ta47pvr850IL+US/KslNxi0LOBrkYgwWpxobwzpBTHS5Fv6HOhtsXQM9wqHaESyF0OUX2VJQ4UhEIijg+yzX6ZKjtCtVXLC3U7xkhl/PJa+YDAH59oBlj3pm9n7l9Afx8TyMA4LPXL4TJqMw/4cocFdEllDgm3lCPtQzJPZy46nSGpkPTLEZkpZllHg0p3ToVnBtytjMULJYUsnDzUm5eUYjy7DQMjfnwp/AOj+n84XAreoY9KLan4J61pQke4ewxWJCqrJ8XekM9qLHlkOj6Cn66o+lE6iwUHCxqu1wAgKWFymk1rSRGg4BPXF0JAPjRzjoMjHove/tRjx+P7WoAAHzm+gWwmJT751u5IyO6BGnb6TGFF67FiltNKRZSsDjaMoigQg8kOxe1FEKXdv/GciwpyET/qBf/8sLpy972m385jQ6nG8X2FHxovTKLNiUMFqQqa8pDb6g1rUOKfUOdDW41pVgsLcxEmsWIYbc/0t1SSZxjvsjy3mIGiylZTAZ8/95VMAjA8zUdeO1M9yVv98LxDvzhSBsEAfjhfauRYjYmeaSxYbAgVVlamIlUc+gNtaFXeW+os8WtphSLSQeSNStvWfBceBmkxJEKWwprhi5nVakDn7w2VMj55T8cx1t1vZP+/dCFAXz12ZMAgIdvWIhN83OSPsZYMViQqpiMhkhf/KMaWg7hVlOK1bpy5dZZcBkkNl/Yshhryh1wjvvw4C8P4l9fOYfna9rx7RfP4EM/24dhtx9ryx343E2L5B7qjDBYkOqsldaXm4fkHUgctXEphGK0LtzXRdHBoojBYiZSzEb89pNX4N51pQiKwGO7GvDIMzV4/O0miCJw77pSPPXxjTArdHvpxXg2M6nOmjIHAOBYq/LeUGfD6w+iezi0Hs2lEJqpNeUOCALQ3D+G3mEP8jKtcg8pQloKWcIdITOWYjbiex9chSvm5+DV010Y8fghCMDHrqzEluXKbIQ1FQYLUh2pgLOuZwQut0/1a7idznGIIpBiNiAn3SL3cEglbClmLCnIxLmuYRxpHsStVYVyDwkAEAyKOB+esVjGpZCYCIKAe9aV4p51yu1RMRPqmFchipKXaUVZdipEEajRQKOs6K2m7GFBsVgbte1UKdoGxzHqDcBiNGBebrrcwyEZMFiQKq0tl/pZDMk7kDjgVlOaLamvi5IO5jvd4QQALC7MUE1NAMUXX3VSJSlYKOmT2mxxqynNltQo61S7C25fQObRhJzuCNVXrCiyyzwSkguDBanS6nAB5/G2IYiiuhtlcaspzVZ5dhpyM6zwBoI41e6UezgAJmYsVpSwcFOvGCxIlZYWZcJsFDA05kPrwLjcw5kTbjWl2RIEAesqHACUs+30lDRjUcxgoVcMFqRKVpMRy4pCb1zH24bkHcwctQ9JwYIzFhS79RWhfhaHLsgfLHqG3egd9kAQEPn9JP1hsCDVkjpwnlBxsPAFguh0hoMFDyCjWZBO/D3cPCD7+TlSfcX83HSkWdjNQK8YLEi1VpU6AADH25SxtjwbXU43gmLoMKLcDOU0OCL1qCqxI9VsxNCYD/Uyn59zOlznsaKYhZt6xmBBqiUVcJ5qdyKg0pNOI/UVjlQYDOxhQbEzRx1IdrBJ3m2n0oxFFQs3dY3BglRrQV4G0ixGjHkDqFfg0dEzIW015Y4QmosN86Q6C2UEC85Y6BuDBamW0SCgqiT0BqbWAs7WQRZu0txtrAwHCxlnLJzjPrQMhIIyd4ToG4MFqVq1ygs4W/pHAQDl2Wx9TLO3ptwBk0FAh9MdmQVLtjPh2YoSRyocaTzzRs8YLEjVpALOEyot4JQ+4VXksIcFzV6axYQV4dk7ueosIo2xOFuhewwWpGrV4WBxttMFj18ZLY1j0RJu7lWezWBBc7MxvO1UrjqLY61DAIDqcFE16ReDBalaWXYqstLM8AVEnOsclns4MRn1+NE34gEAlDFY0BxtrMwBIN+MhXTS8BoGC91jsCBVEwQBKyPLIUOyjiVWreG1cHuqGfZUs8yjIbXbMC8LggA09I6iZ9id1MfuHfagfWgcggCsLOWOEL1jsCDVkwo41dYoq6U/FCy4DELx4EizYFlhqL5hf2NyZy1qwssgC/MykJnCkKx3DBakeqtUOmMhFW6Ws3CT4mTzgtByyL6G/qQ+bk1r6JyS1VwGITBYkAZIMxb1PSMY9fhlHs3MRYIFZywoTjbPDwWL/Y3JDhZDAIDV4Q6gpG8MFqR6+bYUFNlTEBRD7b3VgsGC4m3j/GwYBKCpbzRyuF2iBYMiTrSGfu84Y0EAgwVpxMRJpwwWpF+2FDNWhvtZJGs5pLFvBMMeP1LNRiwpyEzKY5KyMViQJkycdDok6zhmKhgU0cYeFpQAVyS5zuJYeJvpyhI7TEb+SSEGC9KIapV14OxyueENBGEyCCiyp8g9HNIQqc5iX5LqLFhfQRdjsCBNkPbOtwyMYXDUK/Nopictg5RkpfJTHsXVhnnZMBkEtA2Oo3Ug8eeGHL4Q2hGylsGCwviORppgTzWjMjd0kNcJFRRwsr6CEiXdasKa8B/5PXW9CX2sgVEvartDHW+lzp9EDBakGVIB50kV1FlInyTZypsS4brFeQCA3bWJDRYHm0LLLYsLMpCdzhNNKYTBgjRDqoZXQ51Fc7jrZgWDBSXAdYvzAQB7G/rhCwQT9jhSh88r5nO2giYwWJBmSDtDTqpgKaS5fxQAj0unxFhRbENOugUjHj+ONg8m7HGkRlybuAxCURgsSDNWFNtgEIBOpzvphzDFQhRFNPWFgsW8cF0IUTwZDAKuWZQLANh9PjHLIUNj0fUV2Ql5DFInBgvSjHSrCQvzMwAouwPn4JgPLneo9XhFNoMFJcZ1S8J1FgkKFgebBiCKwIK8dORlWhPyGKRODBakKStLHACA463KDRbSbEWRPQWpFqPMoyGtumZRKFic7nAlZAaP9RU0FQYL0pTIzhAFz1hckJZBcjhbQYmTm2GNFDTvOd8X9+sfCO8I2cRgQRdhsCBNWRl1ZogoijKP5tIu9LO+gpLjhvByyN9Od8X1ur3DHpzpdAEArmB9BV2EwYI0ZXmRDUaDgL4RD7pcyizglJZCKnO5I4QS65aqQgChOotRjz9u191V2wNRBKpKbMi3sSU9TcZgQZqSYjZicfiERaX2s4jMWHAphBJseZEN5dlp8PiDcS3ifONcDwDgpqUFcbsmaQeDBWnOqhKpA6fygoUoirjQF2qOVcmlEEowQRBwW3jW4uVT8VkO8fqD2BMOKTcty4/LNUlbGCxIcyJ1Fgos4Owb8WLE44cgsJ03Jcet4WDxxtluuH2BOV/vYNMARr0B5GVaUVVsn/P1SHsYLEhzos8MUVoBp7QMUmxPRYqZW00p8apLHSiyp2DUG8A79XPfHfL6uW4AwI1L8mEwCHO+HmkPgwVpzpLCTJiNAgbHfGgbHJd7OJNMFG5yGYSSw2AQcMuK0KzFSyfnthwiiiJePxuqr7iRyyA0BQYL0hyryYilhTYAyutnEelhwR0hlER3rCoCALx8qhMjc9gdUtczgpaBMViMBly9MDdewyONiSlY7NixAxs2bEBmZiby8/PxgQ98ALW1tYkaG9GsRfezUBLuCCE5rKvIwvy8dIx5A3jheMesr/OnI20AgGsX5yHdaorX8EhjYgoWu3fvxrZt27B//3689tpr8Pl8uPnmmzE6Opqo8RHNSmRnSPuQvAO5SBN3hJAMBEHAhzeUAQCeOdQ6q2v4AkH86Wg7AODe9aVxGxtpT0yR85VXXpn0308++STy8/Nx5MgRXHvttXEdGNFcSEeon2hzIhgUFVFkJopi5Lh0dt2kZLt7bSm+/2otjrcO4WynC8uKbDHdf3dtL/pGPMjNsODGpayvoKnNqcbC6QxNM2dns6UrKcuiggxYTQYMu/1oHhiTezgAgA6nG2PeAEwGAeXcakpJlpthxXuWhxpa/W4WsxZ/OBK6z11rSmA2sjyPpjbrn45gMIjPf/7zuOqqq1BVVTXl7TweD1wu16QvokQzGw1YXhz6RHaibUjewYTV94wACM1W8I2Z5PDhDeUAgD8dbYPL7Zvx/fpGPJHdIPeuL0vI2Eg7Zv3utm3bNpw6dQrPPPPMZW+3Y8cO2O32yFdZGX8oKTmU1oGzIRwsFuZlyDwS0qurF+ZiQV46ht1+/M9bTTO+3+8OtcIfFFFd5oi0zCeayqyCxcMPP4wXX3wRb775JkpLL1/Es337djidzshXa+vsCoeIYrUyqs5CCep7w8Ein8GC5GEwCPjie5YAAB5/qxEDo95p7zM05sXPdjcAAB7cXJHQ8ZE2xBQsRFHEww8/jGeffRZvvPEGKisrp72P1WqFzWab9EWUDFIHzlMdTgSC8nfglJZCFuSzcJPkc1tVIZYX2TDqDeC/w4Hhch7b1QCX24+lhZm4c3VJEkZIahdTsNi2bRt+/etf4ze/+Q0yMzPR1dWFrq4ujI8rq7shEQAsyMtAusWIMW8AdT3Dcg8naimEU8kkH4NBwJdvWQwAeGrvBbRepri5Y2gcT+y9AAD4yq1LYVTA7ipSvpiCxWOPPQan04nrr78eRUVFka/f/e53iRof0awZDUJk2+nx1iFZxzI46kV/eNqZMxYktxuW5GPjvGx4/EF8+n+PYMz77m6cwaCIf3nhNLz+IDZWZuP6JXkyjJTUKOalkEt9ffSjH03Q8IjmprrMAQCoaZW3zkKqryhxpCLNwo6FJC9BEPCjD69GboYFZzpd+Kc/nph0YJ8oivja86fw6ulumAwCvvreZRAEzlbQzPAdjjRtdVmozkLuGYuJ+goWbpIyFDtS8djfrcNHfrEfL57ohHPch8/dtAgGQcDvDrXg94fbIAjAD+5bjdXhgE40EwwWpGnSjEVt9zDGvQGkWuQ5qryeW01JgTbMy8Z37lqJ7X8+ibfq+vBW3eRj1b/zgZV4f3WxTKMjtWKXHtK0InsqCmxWBIIiTnXItxwSCRacsSCF+dD6Mrz5pevx4Q1lMBkE2FPNuH1lEf7ngfX4yKZyuYdHKsQZC9K86lIH/namG8dbh7Bhnjzt5xksSMnKc9Lw6D2r8K07q2A0CNz9QXPCGQvSvIkCziFZHn/M60f7UGhLNoMFKZnFZGCooDljsCDNWy1zsGjsDZ1ompVmRna6RZYxEBElC4MFad7KUjsEAWgbHEffiCfpj3+uK9Sci2csEJEeMFiQ5tlSzJHdGMdahpL++Oc6Qyf6LitiO3si0j4GC9KFdRVZAIAjzYNJf2xpxmJZEWcsiEj7GCxIF9aWh4LF0ZbkBgtRFHE2PGOxtJAzFkSkfQwWpAtrwzMWJ9qG4AsEk/a4vSMe9I96YRBYY0FE+sBgQbowPzcd9lQz3L5gZAYhGc51hpZB5uWmy9b1k4gomRgsSBcMBgFryx0AkltncZaFm0SkMwwWpBsTdRZDSXvMSOFmIZdBiEgfGCxIN6SdIUdlmLFg4SYR6QWDBelGdZkDBgFoHxpHl9Od8Mfz+oNo6A2dEbKsmMGCiPSBwYJ0I91qiswcJKPOoqF3BL6AiMwUE4rtKQl/PCIiJWCwIF1ZPy+0HHLowkDCH+tcV7hws9AGQeDBTkSkDwwWpCubKnMAAPsb+xP+WKfapR0hLNwkIv1gsCBd2ViZDQCo7R7G0Jg3oY91PHyaqnRsOxGRHjBYkK7kZVqxIC8doggcupC4OgtfIIiT7U4AE8e2ExHpAYMF6c6m+aHlkAMJXA6p7RqGxx+ELcWEeTnpCXscIiKlYbAg3dkUXg450JS4As6aqGUQg4GFm0SkHwwWpDtXhGcsTnc44XL7EvIYUn0Fl0GISG8YLEh3CmwpmJeThqAIHElQnUVkxqLUkZDrExEpFYMF6VJk22lT/Ossht0+1Ic7bnJHCBHpDYMF6dLmBaFg8U59X9yvfbLNCVEEShypyMu0xv36RERKxmBBunT1olwAoSZWfSOeuF67pm0IALA6fEw7EZGeMFiQLuVmWFFVEjo35K263rheuyZ8LPtq1lcQkQ4xWJBuXbsoDwCwuzZ+wSIYFHEwfA7J2vAx7UREesJgQbp13eJQsHirrg/BoBiXa57pdGFozIcMqwnVpfa4XJOISE0YLEi31lZkIcNqQv+oF6c7XHG5plQMuqkyGyYjf72ISH/4zke6ZTYacGV4d8ju8z1xueY7DaHtq1cuzI3L9YiI1IbBgnTt2vByyO7zc6+z8PqDOBRuEy4FFiIivWGwIF2T6iyONA/OedtpTesQxn0B5KRbsKQgMx7DIyJSHQYL0rWy7DSsLLEjKAKvnu6a07Wk+orNC3J48BgR6RaDBenee1cWAQBeOtk5p+vsbQgFi6tYX0FEOsZgQbp3ezhY7Gvon/VyiHPch2PhxlhXLWCwICL9YrAg3SvPmftyyKunu+APilhSkInynLQ4j5CISD0YLIgA3L4qNGvx1xOzWw554XgHAOB91UVxGxMRkRoxWBBhYjlkf2M/eobdMd23f8SDveH+FXesKo772IiI1ITBggih3SFryh0IisAzB1tjuu/Lp7oQCIpYWWLHvNz0BI2QiEgdGCyIwh7cPA8A8Ov9zfD6gzO+H5dBiIgmMFgQhb13ZRHyM63oGfbg5VMzq7Xodrkjp5nezmUQIiIGCyKJxWTA311RAQB44p0LM7rP4283QRSBjfOyUeJITeDoiIjUgcGCKMr9G8thMRpQ0zqEoy2Dl71t77AHv9p3AQDw0PULkjA6IiLlY7AgipKXacWdq0NLGv/ywhkEguKUt/35nga4fUGsLnPg+iV5yRoiEZGiMVgQXeRLNy9BptWE461DeHLvhUvepmfYjf/d3wwA+PyWRRAEng1CRAQwWBC9S6E9Bf/3vUsBAP/2ai1aB8Ym/bsvEMT2P52E2xfEmnJH5IRUIiJisCC6pPs3lGNjZTbGfQE8+MRBnO10AQACQRFf+v1xvH6uB1aTAV+7YzlnK4iIogiiKE69iJwALpcLdrsdTqcTNpstmQ9NFJMLfaO47+f70O3ywGIy4IYleWjsHUVdzwhMBgE/f2AdblxaIPcwiYiSYqZ/vzljQTSFebnpeOlz1+DGpfnw+oN49XR3JFT86MOrGSqIiC7BJPcAiJQsJ8OKxx9cj5dOdqFjaBzzctNRVWJDkZ09K4iILoXBgmgagiBETj8lIqLL41IIERERxQ2DBREREcUNgwURERHFTczBYs+ePXjf+96H4uJiCIKA5557LgHDIiIiIjWKOViMjo6iuroaP/3pTxMxHiIiIlKxmHeF3HbbbbjtttsSMRYiIiJSuYRvN/V4PPB4PJH/drlciX5IIiIikknCizd37NgBu90e+SorK0v0QxIREZFMEh4stm/fDqfTGflqbW1N9EMSERGRTBK+FGK1WmG1WhP9MERERKQA7GNBREREcRPzjMXIyAjq6+sj/93U1ISamhpkZ2ejvLw8roMjIiIidYk5WBw+fBg33HBD5L+/+MUvAgAefPBBPPnkk3EbGBEREalPzMHi+uuvhyiKs35A6b7cdkpERKQe0t/t6TJA0o9NHx4eBgBuOyUiIlKh4eFh2O32Kf9dEOcy/TALwWAQHR0dyMzMhCAIcbuuy+VCWVkZWltbYbPZ4nZdJdH6c9T68wP4HLVA688P4HPUgkQ8P1EUMTw8jOLiYhgMU+/9SPqMhcFgQGlpacKub7PZNPlDEk3rz1Hrzw/gc9QCrT8/gM9RC+L9/C43UyHhdlMiIiKKGwYLIiIiihvNBAur1YpvfOMbmu7yqfXnqPXnB/A5aoHWnx/A56gFcj6/pBdvEhERkXZpZsaCiIiI5MdgQURERHHDYEFERERxw2BBREREcaOZYPHTn/4U8+bNQ0pKCjZt2oSDBw/KPaRZ2bFjBzZs2IDMzEzk5+fjAx/4AGprayfd5vrrr4cgCJO+PvOZz8g04th985vffNf4ly5dGvl3t9uNbdu2IScnBxkZGbjnnnvQ3d0t44hjM2/evHc9P0EQsG3bNgDqfP327NmD973vfSguLoYgCHjuuecm/bsoivj617+OoqIipKamYsuWLairq5t0m4GBAWzduhU2mw0OhwOf+MQnMDIyksRncXmXe44+nw9f+cpXsHLlSqSnp6O4uBgPPPAAOjo6Jl3jUq/9o48+muRncmnTvYYf/ehH3zX2W2+9ddJt1PwaArjk76UgCPj+978fuY2SX8OZ/H2YyftnS0sLbr/9dqSlpSE/Px//+I//CL/fH7dxaiJY/O53v8MXv/hFfOMb38DRo0dRXV2NW265BT09PXIPLWa7d+/Gtm3bsH//frz22mvw+Xy4+eabMTo6Oul2n/zkJ9HZ2Rn5+t73vifTiGdnxYoVk8b/9ttvR/7tC1/4Al544QX84Q9/wO7du9HR0YG7775bxtHG5tChQ5Oe22uvvQYAuPfeeyO3UdvrNzo6iurqavz0pz+95L9/73vfw49//GP893//Nw4cOID09HTccsstcLvdkdts3boVp0+fxmuvvYYXX3wRe/bswac+9alkPYVpXe45jo2N4ejRo/ja176Go0eP4s9//jNqa2vx/ve//123/da3vjXptf2Hf/iHZAx/WtO9hgBw6623Thr7b3/720n/rubXEMCk59bZ2Ylf/vKXEAQB99xzz6TbKfU1nMnfh+nePwOBAG6//XZ4vV7s3bsXTz31FJ588kl8/etfj99ARQ3YuHGjuG3btsh/BwIBsbi4WNyxY4eMo4qPnp4eEYC4e/fuyPeuu+468ZFHHpFvUHP0jW98Q6yurr7kvw0NDYlms1n8wx/+EPne2bNnRQDivn37kjTC+HrkkUfEBQsWiMFgUBRF9b9+AMRnn3028t/BYFAsLCwUv//970e+NzQ0JFqtVvG3v/2tKIqieObMGRGAeOjQochtXn75ZVEQBLG9vT1pY5+pi5/jpRw8eFAEIDY3N0e+V1FRIf7whz9M7ODi4FLP78EHHxTvvPPOKe+jxdfwzjvvFG+88cZJ31PLayiK7/77MJP3z5deekk0GAxiV1dX5DaPPfaYaLPZRI/HE5dxqX7Gwuv14siRI9iyZUvkewaDAVu2bMG+fftkHFl8OJ1OAEB2dvak7z/99NPIzc1FVVUVtm/fjrGxMTmGN2t1dXUoLi7G/PnzsXXrVrS0tAAAjhw5Ap/PN+n1XLp0KcrLy1X5enq9Xvz617/Gxz/+8UmH7qn99YvW1NSErq6uSa+Z3W7Hpk2bIq/Zvn374HA4sH79+shttmzZAoPBgAMHDiR9zPHgdDohCAIcDsek7z/66KPIycnBmjVr8P3vfz+uU8yJtmvXLuTn52PJkiV46KGH0N/fH/k3rb2G3d3d+Otf/4pPfOIT7/o3tbyGF/99mMn75759+7By5UoUFBREbnPLLbfA5XLh9OnTcRlX0g8hi7e+vj4EAoFJ/ycBQEFBAc6dOyfTqOIjGAzi85//PK666ipUVVVFvv+Rj3wEFRUVKC4uxokTJ/CVr3wFtbW1+POf/yzjaGdu06ZNePLJJ7FkyRJ0dnbiX/7lX3DNNdfg1KlT6OrqgsViedebdUFBAbq6uuQZ8Bw899xzGBoawkc/+tHI99T++l1Mel0u9Tso/VtXVxfy8/Mn/bvJZEJ2drYqX1e3242vfOUruP/++ycd8PS5z30Oa9euRXZ2Nvbu3Yvt27ejs7MTP/jBD2Qc7czceuutuPvuu1FZWYmGhgZ89atfxW233YZ9+/bBaDRq7jV86qmnkJmZ+a5lVrW8hpf6+zCT98+urq5L/q5K/xYPqg8WWrZt2zacOnVqUv0BgElrmitXrkRRURFuuukmNDQ0YMGCBckeZsxuu+22yP9etWoVNm3ahIqKCvz+979HamqqjCOLv8cffxy33XYbiouLI99T++undz6fDx/60IcgiiIee+yxSf/2xS9+MfK/V61aBYvFgk9/+tPYsWOH4ltHf/jDH47875UrV2LVqlVYsGABdu3ahZtuuknGkSXGL3/5S2zduhUpKSmTvq+W13Cqvw9KoPqlkNzcXBiNxndVvXZ3d6OwsFCmUc3dww8/jBdffBFvvvnmtMfMb9q0CQBQX1+fjKHFncPhwOLFi1FfX4/CwkJ4vV4MDQ1Nuo0aX8/m5mbs3LkTf//3f3/Z26n99ZNel8v9DhYWFr6rmNrv92NgYEBVr6sUKpqbm/Haa69Nexz1pk2b4Pf7ceHCheQMMI7mz5+P3NzcyM+lVl5DAHjrrbdQW1s77e8moMzXcKq/DzN5/ywsLLzk76r0b/Gg+mBhsViwbt06vP7665HvBYNBvP7669i8ebOMI5sdURTx8MMP49lnn8Ubb7yBysrKae9TU1MDACgqKkrw6BJjZGQEDQ0NKCoqwrp162A2mye9nrW1tWhpaVHd6/nEE08gPz8ft99++2Vvp/bXr7KyEoWFhZNeM5fLhQMHDkRes82bN2NoaAhHjhyJ3OaNN95AMBiMBCulk0JFXV0ddu7ciZycnGnvU1NTA4PB8K4lBDVoa2tDf39/5OdSC6+h5PHHH8e6detQXV097W2V9BpO9/dhJu+fmzdvxsmTJyeFRCkkL1++PG4DVb1nnnlGtFqt4pNPPimeOXNG/NSnPiU6HI5JVa9q8dBDD4l2u13ctWuX2NnZGfkaGxsTRVEU6+vrxW9961vi4cOHxaamJvH5558X58+fL1577bUyj3zmvvSlL4m7du0Sm5qaxHfeeUfcsmWLmJubK/b09IiiKIqf+cxnxPLycvGNN94QDx8+LG7evFncvHmzzKOOTSAQEMvLy8WvfOUrk76v1tdveHhYPHbsmHjs2DERgPiDH/xAPHbsWGRHxKOPPio6HA7x+eefF0+cOCHeeeedYmVlpTg+Ph65xq233iquWbNGPHDggPj222+LixYtEu+//365ntK7XO45er1e8f3vf79YWloq1tTUTPrdlCrp9+7dK/7whz8Ua2pqxIaGBvHXv/61mJeXJz7wwAMyP7OQyz2/4eFh8ctf/rK4b98+sampSdy5c6e4du1acdGiRaLb7Y5cQ82vocTpdIppaWniY4899q77K/01nO7vgyhO//7p9/vFqqoq8eabbxZramrEV155RczLyxO3b98et3FqIliIoij+5Cc/EcvLy0WLxSJu3LhR3L9/v9xDmhUAl/x64oknRFEUxZaWFvHaa68Vs7OzRavVKi5cuFD8x3/8R9HpdMo78Bjcd999YlFRkWixWMSSkhLxvvvuE+vr6yP/Pj4+Ln72s58Vs7KyxLS0NPGuu+4SOzs7ZRxx7F599VURgFhbWzvp+2p9/d58881L/lw++OCDoiiGtpx+7WtfEwsKCkSr1SredNNN73ru/f394v333y9mZGSINptN/NjHPiYODw/L8Gwu7XLPsampacrfzTfffFMURVE8cuSIuGnTJtFut4spKSnismXLxO9+97uT/jDL6XLPb2xsTLz55pvFvLw80Ww2ixUVFeInP/nJd304U/NrKPnZz34mpqamikNDQ++6v9Jfw+n+PojizN4/L1y4IN52221iamqqmJubK37pS18SfT5f3MbJY9OJiIgoblRfY0FERETKwWBBREREccNgQURERHHDYEFERERxw2BBREREccNgQURERHHDYEFERERxw2BBREREccNgQURERHHDYEFERERxw2BBREREccNgQURERHHz/wGUDLRfkGdoDwAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "num_components = len(DC)\n",
        "DC_sample = DC[0:num_components]\n",
        "amp_sample = amp[0:num_components]\n",
        "interval = (np.linspace(0,N,N)).reshape((N,1))\n",
        "components = np.zeros((N,num_components))\n",
        "for i in range(N):\n",
        "    for j in range(num_components):\n",
        "        components[i][j] = amp_sample[j] + np.sin(DC_sample[j] * interval[i])\n",
        "DC_signal = np.sum(components, axis = -1)\n",
        "DC_signal = DC_signal.reshape(N,1)\n",
        "full_signal = DC_signal + noise + trend[0]\n",
        "plt.plot(range(N),full_signal)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 278,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PO0crIQR7zgh",
        "outputId": "cadb3199-a804-4345-fff6-7515a0bf3d59"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "4\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(0.26816914, requires_grad=True)"
            ]
          },
          "metadata": {},
          "execution_count": 278
        }
      ],
      "source": [
        "r = num_components\n",
        "#r = 16  # Following the paper\n",
        "N_QUBITS = (r + 1)\n",
        "print(N_QUBITS)\n",
        "n_layers = 2\n",
        "\n",
        "dev = qml.device('default.qubit', wires= N_QUBITS)\n",
        "\n",
        "def block(weights):\n",
        "    for i in range(1,N_QUBITS):\n",
        "        qml.IsingXX(weights[0][i-1], wires=[0, i])  # Are the qubits in the right place?\n",
        "    for i in range(1,N_QUBITS):\n",
        "        qml.IsingZZ(weights[1][i-1], wires=[0, i])\n",
        "    for i in range(1,N_QUBITS):\n",
        "        qml.IsingYY(weights[2][i-1], wires=[0, i])\n",
        "\n",
        "@qml.qnode(dev, interface=\"autograd\")\n",
        "def PQC(weights,x):\n",
        "    qml.AngleEmbedding(x,wires=range(N_QUBITS)[1:])   # Features x are embedded in rotation angles\n",
        "    for j in range(n_layers):\n",
        "      block(weights[j])\n",
        "    return qml.expval(qml.PauliZ(wires=0))\n",
        "\n",
        "weights = 2 * np.pi * np.random.random(size=(n_layers, 3, r), requires_grad=True)\n",
        "x = 2 * np.pi *np.random.random(size = (r))\n",
        "\n",
        "PQC(weights, x)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 289,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5-2m13qRxbFx",
        "outputId": "14c6c2cc-9475-489b-e0f7-96ccff0d7d94"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.48744154 0.52499089 0.56196903 0.5978165 ]\n",
            " [0.63199706 0.66400866 0.69339359 0.71974757]\n",
            " [0.74272773 0.76205904 0.77753927 0.78904229]\n",
            " [0.79651957 0.8        0.79958789 0.79545935]\n",
            " [0.787857   0.77708327 0.76349241 0.74748135]\n",
            " [0.72947973 0.70993933 0.68932302 0.66809374]\n",
            " [0.64670352 0.62558304 0.60513176 0.585709  ]\n",
            " [0.56762621 0.55114038 0.53644907 0.52368692]\n",
            " [0.5129238  0.50416467 0.49735106 0.49236427]\n",
            " [0.48902999 0.4871244  0.48638149 0.4865015 ]\n",
            " [0.48716011 0.48801831 0.48873262 0.48896537]\n",
            " [0.48839486 0.48672506 0.48369467 0.47908525]\n",
            " [0.47272827 0.46451085 0.45438004 0.44234563]\n",
            " [0.42848119 0.41292358 0.39587073 0.37757783]\n",
            " [0.35835196 0.33854539 0.31854758 0.29877613]\n",
            " [0.27966694 0.26166376 0.24520733 0.23072459]\n",
            " [0.2186179  0.20925487 0.20295878 0.2       ]\n",
            " [0.20058854 0.20486791 0.21291058 0.2247149 ]\n",
            " [0.24020385 0.25922547 0.28155499 0.30689878]\n",
            " [0.33489975 0.36514437 0.39717093 0.43047903]\n",
            " [0.46453992 0.49880757 0.53273015 0.56576167]\n",
            " [0.59737356 0.62706577 0.65437735 0.67889608]\n",
            " [0.70026698 0.71819958 0.73247365 0.74294336]\n",
            " [0.74953977 0.75227149 0.75122365 0.7465551 ]\n",
            " [0.73849397 0.72733165 0.71341538 0.69713964]\n",
            " [0.67893647 0.65926504 0.63860071 0.61742377]\n",
            " [0.59620823 0.57541082 0.5554606  0.53674926]\n",
            " [0.51962248 0.50437247 0.49123189 0.48036934]\n",
            " [0.47188636 0.46581623 0.46212439 0.46071062]\n",
            " [0.46141275 0.46401197 0.46823952 0.47378451]\n",
            " [0.48030287 0.48742703 0.4947761  0.50196647]\n",
            " [0.50862227 0.51438574 0.51892702 0.52195321]\n",
            " [0.52321651 0.52252116 0.51972899 0.5147636 ]]\n",
            "[0. 0. 0. 0. 0.]\n",
            "[[0.49832988 0.48703202 0.47389868 0.45916712]\n",
            " [0.44312697 0.4261133  0.40849854 0.39068336]\n",
            " [0.37308679 0.3561358  0.34025466 0.32585416]\n",
            " [0.31332119 0.30300882 0.29522703 0.29023457]\n",
            " [0.28823191 0.28935557 0.293674   0.301185  ]\n",
            " [0.31181494 0.32541957 0.34178661 0.36063997]\n",
            " [0.38164549 0.40441812 0.42853038 0.45352179]\n",
            " [0.47890924 0.50419783 0.52889212 0.55250741]\n",
            " [0.57458083 0.59468189 0.61242242 0.62746545]\n",
            " [0.63953293 0.64841216 0.6539606  0.65610913]\n",
            " [0.65486354 0.65030437 0.64258486 0.63192735]\n",
            " [0.61861797 0.60299989 0.58546524 0.56644589]\n",
            " [0.54640335 0.5258179  0.50517748 0.48496621]\n",
            " [0.46565327 0.44768193 0.43145945 0.41734768]\n",
            " [0.40565491 0.39662891 0.39045152 0.38723477]\n",
            " [0.38701871 0.38977095 0.39538792 0.40369788]]\n"
          ]
        }
      ],
      "source": [
        "train = full_signal[:int(N*2/3)]\n",
        "test = full_signal[int(N*2/3):]\n",
        "\n",
        "train_size = (len(train)//N_QUBITS) * N_QUBITS\n",
        "test_size = (len(test)//N_QUBITS) * N_QUBITS\n",
        "\n",
        "train = train[:train_size]\n",
        "test = test[:test_size]\n",
        "\n",
        "scaler = MinMaxScaler((0.2,0.8))\n",
        "scaler.fit(train)\n",
        "scaled_train = scaler.transform(train)\n",
        "scaled_test = scaler.transform(test)\n",
        "\n",
        "grouped_train = scaled_train.reshape(train_size//N_QUBITS, N_QUBITS)\n",
        "grouped_test = scaled_test.reshape(test_size//N_QUBITS, N_QUBITS)\n",
        "print(grouped_train)\n",
        "print(np.zeros(5))\n",
        "print(grouped_test)\n",
        "\n",
        "final_train = grouped_train\n",
        "final_test = grouped_test"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(grouped_train.shape)\n",
        "print(final_train.shape)\n",
        "print(grouped_test.shape)\n",
        "print(final_test.shape)\n",
        "print(train_size//N_QUBITS)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dRuj6JVTAKPm",
        "outputId": "3daaa52d-0e47-4214-83d5-85ba86ab135f"
      },
      "execution_count": 280,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(33, 4)\n",
            "(33, 4)\n",
            "(16, 4)\n",
            "(16, 4)\n",
            "33\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 271,
      "metadata": {
        "id": "wunO2LiVqmHZ"
      },
      "outputs": [],
      "source": [
        "#train = full_signal[:int(N*2/3)]\n",
        "#test = full_signal[int(N*2/3):]\n",
        "#\n",
        "#train_size = (len(train)//N_QUBITS) * N_QUBITS\n",
        "#test_size = (len(test)//N_QUBITS) * N_QUBITS\n",
        "#\n",
        "#train = train[:train_size]\n",
        "#test = test[:test_size]\n",
        "#\n",
        "#grouped_train = train.reshape(train_size//N_QUBITS, N_QUBITS)\n",
        "#grouped_test = test.reshape(test_size//N_QUBITS, N_QUBITS)\n",
        "#\n",
        "#scaler = MinMaxScaler((0.2,0.8))\n",
        "#scaler.fit(train)\n",
        "#scaled_train = scaler.transform(train)\n",
        "#scaled_test = scaler.transform(test)\n",
        "#\n",
        "#final_train = scaled_train\n",
        "#final_test_ = scaled_test"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 290,
      "metadata": {
        "id": "kltfe7ZszUf7"
      },
      "outputs": [],
      "source": [
        "def square_loss(targets, predictions):\n",
        "    loss = 0\n",
        "    for t, p in zip(targets, predictions):\n",
        "        loss += (t - p) ** 2\n",
        "    loss = loss / len(targets)\n",
        "\n",
        "    return 0.5*loss\n",
        "\n",
        "def cost(weights, x, y):\n",
        "    predictions = [PQC(weights, x_) for x_ in x]\n",
        "    return square_loss(y, predictions)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 291,
      "metadata": {
        "id": "Qwz98CdirzKM"
      },
      "outputs": [],
      "source": [
        "x = np.zeros((train_size//N_QUBITS, r))\n",
        "target_y = np.zeros((train_size//N_QUBITS,1))\n",
        "for i in range(train_size//N_QUBITS):\n",
        "  x[i] = final_train[i][:-1]\n",
        "  target_y[i] = final_train[i][-1]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 293,
      "metadata": {
        "id": "Oj2_3OnNG_pC"
      },
      "outputs": [],
      "source": [
        "max_steps = 10\n",
        "opt = qml.AdamOptimizer(.1)\n",
        "batch_size = train_size//max_steps\n",
        "cst = [cost(weights, x, target_y)]  # initial cost"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 294,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ofHc1WGqKw4r",
        "outputId": "ff13342b-741c-4f86-e963-43f3cab014d4"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 10/10 [01:42<00:00, 10.29s/it]\n"
          ]
        }
      ],
      "source": [
        "epochs = 10\n",
        "\n",
        "for i in tqdm(range(epochs)):\n",
        "  for step in range(max_steps):\n",
        "      # Select batch of data\n",
        "      batch_index = numpy.random.randint(0, max_steps, batch_size)\n",
        "      x_batch = x[batch_index]\n",
        "      y_batch = target_y[batch_index]\n",
        "      # Update the weights by one optimizer step\n",
        "      weights,_,_ = opt.step(cost, weights, x_batch, y_batch)  # Calculating weights using the batches.\n",
        "      c = cost(weights, x, target_y)  # Calculating the cost using the whole train data\n",
        "      cst.append(c)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 295,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        },
        "id": "1mzZ8cEBMlyf",
        "outputId": "d595f374-b4f9-446d-ecd7-402849da5e59"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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TnJxcrz0AbNu2zdXeZrPBZrNBqaz/tVQqFRwO71tno1QqoBULorIcBhERkWRkHXJIS0vDtGnTkJiYiBEjRmD58uWoqKjA9OnTAQBTp05FVFQU0tPTAQBz5szBmDFjsHTpUowbNw7r16/Hvn37sGbNGgBAcHAwxowZg3nz5sHPzw/du3fHjh078K9//QvLli2T7Xtej06thLXGAQunwIiIiCQjawCaNGkSCgsLsWjRIhiNRiQkJGDr1q2uhc65ubn1RnNGjhyJdevW4YUXXsCCBQvQu3dvbNq0CQMHDnS1Wb9+PebPn48pU6bg0qVL6N69O1599VU8+eSTkn+/ptCplSiDcyE0ERERSUMhCAK3H13FbDbDYDCgtLQUwcHBHv2skekZuFBajc2zRmFw1w4e/SwiIqL2rDm/3+1uF1hbI5bDsHANEBERkWQYgGSmVTn/FVgZgIiIiCTDACQzcReYpYaLoImIiKTCACQznZojQERERFJjAJJZ3QgQAxAREZFUGIBkpmMAIiIikhwDkMy0nAIjIiKSHAOQzLS19cAYgIiIiKTDACQzToERERFJjwFIZpwCIyIikh4DkMzEgxB5DhAREZF0GIBkptNwBIiIiEhqDEAy04mlMFgNnoiISDIMQDJzHYRoYwAiIiKSCgOQzHTiNniOABEREUmGAUhm3AVGREQkPQYgmelYDZ6IiEhyDEAyYzFUIiIi6TEAyYxTYERERNJjAJKZuAiaI0BERETSYQCSGUeAiIiIpMcAJDOWwiAiIpIeA5DMXKUweA4QERGRZBiAZCaOAHEKjIiISDoMQDLTa7gNnoiISGoMQDLTqmpLYTAAERERSYYBSGbcBUZERCS9FgWgl156CZWVldc8X1VVhZdeeqnVnfIlYimMGocAu0OQuTdERES+oUUB6MUXX0R5efk1z1dWVuLFF19sdad8iTgCBHAUiIiISCotCkCCIEChUFzz/MGDB9GxY8dWd8qXXBmAeBYQERGRNNTNaRwSEgKFQgGFQoE+ffrUC0F2ux3l5eV48skn3d7J9kytVECpABwCR4CIiIik0qwAtHz5cgiCgEcffRQvvvgiDAaD6zWtVouYmBgkJye7vZPtmUKhgFatRLXNwa3wREREEmlWAJo2bRoAIDY2FqNGjYJa3ay3UyN0ahUDEBERkYRatAYoKCgIx44dc/35888/x/jx47FgwQJYrVa3dc5XcCs8ERGRtFoUgJ544gmcOHECAHD69GlMmjQJ/v7+2LhxI5599lm3dtAXuMphsB4YERGRJFoUgE6cOIGEhAQAwMaNGzFmzBisW7cOa9euxSeffOLO/vkEsSCqxcZdYERERFJo8TZ4h8M5WvHtt9/irrvuAgBER0ejqKjIfb3zERwBIiIiklaLAlBiYiJeeeUVfPDBB9ixYwfGjRsHADhz5gzCw8Pd2kFfIJ4GbbExABEREUmhRQFo+fLlyM7OxqxZs/CXv/wFvXr1AgD85z//wciRI93aQV+gU9cWROUIEBERkSRatI998ODB+OWXX655/o033oCqtro5NR13gREREUmrVQf5ZGVlubbDx8XFYejQoW7plK8RAxBLYRAREUmjRQGooKAAkyZNwo4dO9ChQwcAQElJCW677TasX78enTt3dmcf2z0dR4CIiIgk1aI1QLNnz0Z5eTmOHDmCS5cu4dKlSzh8+DDMZjOefvppd/ex3asbAWIAIiIikkKLRoC2bt2Kb7/9Fv3793c9FxcXh5UrV+LOO+90W+d8hY4BiIiISFItGgFyOBzQaDTXPK/RaFznAzXVypUrERMTA71ej6SkJOzZs+e67Tdu3Ih+/fpBr9dj0KBB+Oqrr65pc+zYMdxzzz0wGAwICAjA8OHDkZub26x+SYmLoImIiKTVogD0m9/8BnPmzMGFCxdcz+Xn5+OZZ57B7bff3uTrbNiwAWlpaVi8eDGys7MRHx+P1NRUFBQUNNh+586dmDx5Mh577DHs378f48ePx/jx43H48GFXm1OnTmH06NHo168ftm/fjkOHDmHhwoXQ6/Ut+aqS0NbunOMIEBERkTQUgiAIzX1TXl4e7rnnHhw5cgTR0dGu5wYOHIjNmzeja9euTbpOUlIShg8fjhUrVgBwjixFR0dj9uzZeP75569pP2nSJFRUVGDLli2u52666SYkJCRg9erVAICHHnoIGo0GH3zwQZO/j8VigcVicf3ZbDYjOjoapaWlCA4ObvJ1WmrJ1uNYtf0UHh0Vi0W/i/P45xEREbVHZrMZBoOhSb/fLRoBio6ORnZ2Nr788kvMnTsXc+fOxVdffYXs7Owmhx+r1YqsrCykpKTUdUapREpKCjIzMxt8T2ZmZr32AJCamupq73A48OWXX6JPnz5ITU1FWFgYkpKSsGnTpuv2JT09HQaDwfUQQ51U6kphcBs8ERGRFJoVgL777jvExcXBbDZDoVDgjjvuwOzZszF79mwMHz4cAwYMwI8//tikaxUVFcFut19TOiM8PBxGo7HB9xiNxuu2LygoQHl5OV577TWMHTsW33zzDe677z7cf//92LFjR6N9mT9/PkpLS12PvLy8Jn0Hd9GyFAYREZGkmrULbPny5ZgxY0aDw0oGgwFPPPEEli1bhptvvtltHWwOcQH2vffei2eeeQYAkJCQgJ07d2L16tUYM2ZMg+/T6XTQ6XSS9fOaz1ezGCoREZGUmjUCdPDgQYwdO7bR1++8805kZWU16VqhoaFQqVQwmUz1njeZTIiIiGjwPREREddtHxoaCrVajbi4+uto+vfv79W7wHgQIhERkbSaFYBMJlOD299FarUahYWFTbqWVqvFsGHDkJGR4XrO4XAgIyMDycnJDb4nOTm5XnsA2LZtm6u9VqvF8OHDkZOTU6/NiRMn0L179yb1Sw5iMVTuAiMiIpJGs6bAoqKicPjwYVf196sdOnQIXbp0afL10tLSMG3aNCQmJmLEiBFYvnw5KioqMH36dADA1KlTERUVhfT0dADAnDlzMGbMGCxduhTjxo3D+vXrsW/fPqxZs8Z1zXnz5mHSpEm45ZZbcNttt2Hr1q344osvsH379uZ8VUnxHCAiIiJpNSsA3XXXXVi4cCHGjh17zbk6VVVVWLx4Me6+++4mX2/SpEkoLCzEokWLYDQakZCQgK1bt7oWOufm5kKprBukGjlyJNatW4cXXngBCxYsQO/evbFp0yYMHDjQ1ea+++7D6tWrkZ6ejqeffhp9+/bFJ598gtGjRzfnq0qKAYiIiEhazToHyGQyYejQoVCpVJg1axb69u0LADh+/DhWrlwJu92O7Ozsa3ZqtTXNOUfAHTKOmfDY+/sQ39WAz2d5b1AjIiLyZs35/W7WCFB4eDh27tyJp556CvPnz4eYnRQKBVJTU7Fy5co2H37kwGKoRERE0mp2MdTu3bvjq6++wuXLl/Hrr79CEAT07t0bISEhnuifT3AdhMgAREREJIkWVYMHgJCQEAwfPtydffFZOg13gREREUmpRaUwyL3qSmEwABEREUmBAcgL1JXCYC0wIiIiKTAAeQGWwiAiIpIWA5AXuLIURjNOJSAiIqIWYgDyAmIpDIcA1DgYgIiIiDyNAcgLiGuAAG6FJyIikgIDkBe4MgBxKzwREZHnMQB5AZVSAbVSAYAjQERERFJgAPISLIhKREQkHQYgL1FXD4xnAREREXkaA5CX0LEgKhERkWQYgLyEVobDEE+ayvDg3zOx9fBFyT6TiIjIG7S4GCq5l3gWkMUmTQCy2R2Ys/4Ajl40QxAEjB3YRZLPJSIi8gYcAfISUhdEXb39FI5eNAMAjhvLeAI1ERH5FAYgLyFlQdQcYxne/u6k689l1TW4WFrt8c8lIiLyFgxAXkKqgqg1dgf+vPEgbHYBKf3D0Sc8EIAzFBEREfkKBiAvIdU5QGt+PI1f8ksRrFfjf+8biL4RwQCc02BERES+ggHIS0ixDf7XgjIs3+ac+lr0uwEIC9ajX0QQACDHaPbY5xIREXkbBiAvIe4C8+QI0OLNR2C1O3Bb386YMDQKANA33BmAOAJERES+hAHIS3h6CkwQBOw9exkAsOCu/lAonLXH+taOAJ0qLIdNwjOIiIiI5MQA5CV0Hi6FUVJpc4Wrbp38Xc93DfFDoE4Nm13A6cIKj3w2ERGRt2EA8hKeHgEymp3b3DsFaF3TbQCgUChco0DHuQ6IiIh8BAOQlxAPQrR4aBrKWHvOT3iw/prX+roWQnMdEBER+QYGIC+h04gHIXp2BCjCcG0A6scAREREPoYByEtoVbW7wDw8AtRQAOJOMCIi8jUMQF6irhSGhwNQA1Ng/WoPQ8wvqYK52uaRzyciIvImDEBewtOlMFxTYA0EIIO/xvX8CY4CERGRD2AA8hJ1u8A8sw3edJ01QACu2AnGAERERO0fA5CX0Hq4FMbF66wBArgQmoiIfAsDkJfQefAcoGqbHaVVzrU9DW2DB7gVnoiIfAsDkJfwZAASF0D7aVQI1qsbbNPPVRXeDEEQ3N4HIiIib8IA5CXE05k9MQUmLoDuYtC7aoBdrWdYAFRKBczVNa72RERE7RUDkJfwZCmM650CLdKpVegRGgCAC6GJiKj9YwDyEloPFkO93inQV+I6ICIi8hUMQF5CijVANwpA3AlGRES+ggHIS2g9eBDi9U6BvlLf2oXQxy6yKjwREbVvDEBewlUN3gOlMMQpsOutAQLqRoBOFZbD5qETqYmIiLwBA5CX0Glqd4F5IHjc6BRoUVQHPwRoVbDZBZwtqnB7P4iIiLwFA5CXEEeArDUOt57DY3cIKCizAHBug78epVKBriH+AOpOjiYiImqPGIC8hE5T96/CneuAisotsDsEqJQKhAbqbtg+LNjZRgxNRERE7ZFXBKCVK1ciJiYGer0eSUlJ2LNnz3Xbb9y4Ef369YNer8egQYPw1VdfNdr2ySefhEKhwPLly93ca/cSR4AA9+4EExdAdw7UQaVs+BDEK4UFOUeJCso4AkRERO2X7AFow4YNSEtLw+LFi5GdnY34+HikpqaioKCgwfY7d+7E5MmT8dhjj2H//v0YP348xo8fj8OHD1/T9rPPPsOuXbsQGRnp6a/RalcGIHeeBt3UM4BErhEgM0eAiIio/ZI9AC1btgwzZszA9OnTERcXh9WrV8Pf3x/vvvtug+3feustjB07FvPmzUP//v3x8ssvY+jQoVixYkW9dvn5+Zg9ezY++ugjaDQaKb5KqyiVinrrgNylqVvgRWFB4hQYR4CIiKj9kjUAWa1WZGVlISUlxfWcUqlESkoKMjMzG3xPZmZmvfYAkJqaWq+9w+HAww8/jHnz5mHAgAE37IfFYoHZbK73kIMnymE0ewRInALjCBAREbVjsgagoqIi2O12hIeH13s+PDwcRqOxwfcYjcYbtl+yZAnUajWefvrpJvUjPT0dBoPB9YiOjm7mN3GPunIY7gtApibUAbsSF0ETEZEvkH0KzN2ysrLw1ltvYe3atY1WPr/a/PnzUVpa6nrk5eV5uJcN80Q5DHE7+422wIuunAJz53Z8IiIibyJrAAoNDYVKpYLJZKr3vMlkQkRERIPviYiIuG77H3/8EQUFBejWrRvUajXUajXOnTuHP/3pT4iJiWnwmjqdDsHBwfUecqgrh+G+gqimJp4CLRKnwKptDpRZatzWDyIiIm8iawDSarUYNmwYMjIyXM85HA5kZGQgOTm5wfckJyfXaw8A27Ztc7V/+OGHcejQIRw4cMD1iIyMxLx58/D111977su4gbvLYQiC0Ow1QH5aFYL0agBcB0RERO2XWu4OpKWlYdq0aUhMTMSIESOwfPlyVFRUYPr06QCAqVOnIioqCunp6QCAOXPmYMyYMVi6dCnGjRuH9evXY9++fVizZg0AoFOnTujUqVO9z9BoNIiIiEDfvn2l/XLNJB6G6K5yGGWWGlRanaNJTd0FBjinwcqqa1BgrkavsEC39IWIiMibyB6AJk2ahMLCQixatAhGoxEJCQnYunWra6Fzbm4ulMq6gaqRI0di3bp1eOGFF7BgwQL07t0bmzZtwsCBA+X6Cm7j7m3w4hZ4g58GflpVk98XFqTHqcIKLoQmIqJ2S/YABACzZs3CrFmzGnxt+/bt1zw3ceJETJw4scnXP3v2bAt7Ji2durYgqpsDUHNGf4Ard4LxLCAiImqf2t0usLbM3ecAiet/wpu4/kfk2gnGNUBERNROMQB5kbpzgNyzC0wcAerS3BEgVz0wBiAiImqfGIC8iLvPAWrxCBCnwIiIqJ1jAPIi7p4CM7V0DRBHgIiIqJ1jAPIiOjeXwmjuKdAiVoQnIqL2jgHIi4i7wNw2AtTMU6BF4iLocksNKq08DZqIiNofBiAvUlcKo/UByFJjR3GFFUDTT4EWBerU8NM4wxhHgYiIqD1iAPIirikwW+t3gYnBRatWIsRf06z3KhQKVoUnIqJ2jQHIi7hOgnbDCJCrBliwHgqFotnvv7IqPBERUXvDAORFXOcAuaEYaktPgRaF1b6PU2BERNQeMQB5EdcUmBtGgMSpK3Eqq7nqRoAYgIiIqP1hAPIiWjfuArtU4QwunQK0LXp/3VlAnAIjIqL2hwHIi2jdeA7QpdodYB0DWjkCxCkwIiJqhxiAvEhdKYzW7wIrLq8NQIEtHAFiOQwiImrHGIC8iDtLYYgjQK2fAuMIEBERtT8MQF7EnaUw6qbAWhqAnCNAJZU2t1WnJyIi8hYMQF7ErSNAla0bAergr3GdS1TIUSAiImpnGIC8iLtGgGrsDpRU2gAAIS0MQAqFAp25FZ6IiNopBiAv4q5iqJdrw49CAYT4tywAAawKT0RE7RcDkBdxVzFUcf1PBz8NVMrml8EQsRwGERG1VwxAXkRcc9PaYqjFtYcgtnQBtMi1E8zLR4D2nLmEtzNOotoNRWSJiMg3qOXuANXRadw7AtSphYcgitrCCFCFpQZPfpiFSxVWnL9cidcfiJe7S0RE1AZwBMiLiCNANrsAh0No8XUut3ILvCg82PvPAlq786wr8H287zzW78mVuUdERNQWMAB5EXENENC6UaDi2kDQ0h1gos5evgjaXG3Dmh9OAwBu6tERALBo8xH8cr5Uzm4REVEbwADkRcRdYEDrtsK39hRokbdXhH/3pzMorbKhV1ggPnwsCSn9w2CtceCpj7JQUnsOEhERUUMYgLyIRlW3Y6s1W+GL3TQFJi6CLq6woKaV65LcraTSin/+eAYAMDelN9QqJZY+mIDunfxx/nIV5m440KppRCIiat8YgLyIQqG44jDElu9oulRbCLVTCwuhijoFaKFSKiAIdaHKW/zjx9Mos9SgX0QQ7hrYBQBg8NNg1ZRh0KmV2J5TiFU7TsncSyIi8lYMQF7GHeUwWlsHTKRUKhBaG6JMZu/ZCVZcbsF7P58FADxzRx8orzjrKC4yGC/eMwAA8EHmOQgCR4GIiOhaDEBexh3lMMQ6YK0NQIB3ngX09x9Oo9Jqx6AoA+6MC7/m9XsToqBVKWE0VyP3UqUMPSQiIm/HAORlWlsOQxAE1zb41p4DBADhwd61ELqwzIJ/ZZ4FAKTd0QcKxbUnXftpVYiPNgAAdp0ulrJ7RETURjAAeZmGymFYaxxNXoRsrqpBTe3i35AATav701kcAfKSwxC35xSg2ubAgMhg3Nq3c6PtburRCQCw6/QlqbpGRERtCAOQl6krh+EMPIIg4H/+sQsjX/sO5ZaaG75fLIMRqFPX21bfUt62Ff7IBTMAILlHpwZHf0R1AaiY64CIiOgaDEBepq4chnMXWHbuZew7dxkFZRbkGMtu+H53LYAW1VWE944RoMP5zkMOB0YZrttuaLcQaFQKXCytRt6lKim6RkREbQgDkJcRR4DENUCfZue7Xjt/+cYLet11BpAoorYchskLFkHbHQKOXnSOAA2IDL5uWz+tCvFdOwDgOiAiIroWA5CXEUeALDUOWGrs2HLoouu185dvPJJx2U2nQIsiDM4AdLFU/hGgs8UVqLTaodco0aNz4A3bXzkNRkREdCUGIC/jWgNU48D3xwtRWmVzvdaUAOSpEaCickurziZyB3H6K65LMFTKxtf/iLgOiIiIGsMA5GW0V5wD9Nn+8wDqQkhTpsDcvQaoY4DWFcrk3gkmLoC+0fof0dDuHaBRKXChtLpJ4ZGIiHwHA5CXEXduFZZZ8N3xAgDAE2N6AADym/Aj7u4ApFAoEG5wLoQ2yjwN5loAHdm0AOSvVWNw7TqgTE6DERHRFRiAvIw4ArRpfz5sdgH9uwQjpb/ztOPzJVU3LPDp7ikwAOgS7AdA3nVAgiDUTYHdYAH0lW7q0REA1wEREVF9DEBeRgxAYgmH+4dEIcKgh1Lh3BlWVH793ViXas8Bam0h1CuJC6HlrAd2/nIVzNU10KgU6BMe1OT3ieuAdvNARCIiugIDkJcRa4EBgFIB3JMQCY1KiS4G5yhM3g2mwS5XOBdNd3RDGQyRN+wEO3LBOfrTNyLIFRKbYlj3EKiVCuSXVCGPdcGIiKgWA5CXufLHfVSvUITXLoCOCnEGoBsthBZPgnbXNnigbhG2UcYRoMP5tQugm7j+R+RcB8S6YEREVB8DkJfRqer+ldw3JMr1n7u6AlDjI0CV1hpU15bQCHFnAKodAZJzEfTh2hGgAU3cAXYl1gUjIqKrMQB5GZ3GuQvMT6NC6oAI1/NdQ/wBXD8AFZc7F0Br1UoEaFtfB0wkdwC6cgH0jU6AbggPRCQioqt5RQBauXIlYmJioNfrkZSUhD179ly3/caNG9GvXz/o9XoMGjQIX331les1m82G5557DoMGDUJAQAAiIyMxdepUXLhwwdNfwy2iOzqDzr0JkQjQqV3Pd23CFNilK06Bvl6h0ObqcsUi6BvtQvOEgjILisqtUCqA/hHND0DDuodAxXVARER0BdkD0IYNG5CWlobFixcjOzsb8fHxSE1NRUFBQYPtd+7cicmTJ+Oxxx7D/v37MX78eIwfPx6HDx8GAFRWViI7OxsLFy5EdnY2Pv30U+Tk5OCee+6R8mu12LhBXbBuRhJevHdAvefFAHS9s4DcfQaQqHOgDkoFUOMQUFQhfU0wcQF0r7BA+LVgZCtAp8ag2qmzfec4DUZERF4QgJYtW4YZM2Zg+vTpiIuLw+rVq+Hv74933323wfZvvfUWxo4di3nz5qF///54+eWXMXToUKxYsQIAYDAYsG3bNjz44IPo27cvbrrpJqxYsQJZWVnIzc1t8JoWiwVms7neQy4qpQIje4a6DkQURYtTYNc5C8hTAUitUqJzkHNXmalU+gDU0gXQV0qI7gAAOJhX6o4uERFRGydrALJarcjKykJKSorrOaVSiZSUFGRmZjb4nszMzHrtASA1NbXR9gBQWloKhUKBDh06NPh6eno6DAaD6xEdHd38L+NhTTkL6JKbC6HW+/xgcSu89CUlXOt/WrAAWhQf7XzvofMl7ugSERG1cbIGoKKiItjtdoSHh9d7Pjw8HEajscH3GI3GZrWvrq7Gc889h8mTJyM4uOH1I/Pnz0dpaanrkZeX14Jv41lNOQtIPAXanTvARK6F0DJshRdrgLVkAbRILIlx5IIZNru8RV2JiEh+sk+BeZLNZsODDz4IQRCwatWqRtvpdDoEBwfXe3ijG50FdMkDZwCJxPAl9U6wyxVW5Jc4A19zSmBcLbZTAIL0alhqHDhhKnNX94iIqI2SNQCFhoZCpVLBZDLVe95kMiEiIqLB90RERDSpvRh+zp07h23btnltqGkO10LokoZHgOrWALnvFGiReCCj1AFIHP2J6eSPYL2mxddRKhWuAxEPnec6ICIiXydrANJqtRg2bBgyMjJczzkcDmRkZCA5ObnB9yQnJ9drDwDbtm2r114MPydPnsS3336LTp06eeYLSOxGZwF5ohCqqItM5TBacwDi1cRpsIN5Ja2+FhERtW3qGzfxrLS0NEybNg2JiYkYMWIEli9fjoqKCkyfPh0AMHXqVERFRSE9PR0AMGfOHIwZMwZLly7FuHHjsH79euzbtw9r1qwB4Aw/DzzwALKzs7FlyxbY7XbX+qCOHTtCq3V/OJDKjU6DviwugnZjIVSROAIkdUFUcQF0a3aAieJrR4AOcgSIiMjnyR6AJk2ahMLCQixatAhGoxEJCQnYunWra6Fzbm4ulMq6gaqRI0di3bp1eOGFF7BgwQL07t0bmzZtwsCBAwEA+fn52Lx5MwAgISGh3md9//33uPXWWyX5Xp5wo8MQpRoBEgTBrQctXs9RNyyAFokjQCdMZaiy2lt0phAREbUPsgcgAJg1axZmzZrV4Gvbt2+/5rmJEydi4sSJDbaPiYmBIEh/WrEUxLOA8i9XXRNCrDUOlFXXAPDQNvjaAFRls8NcXQODX8vX4zRVpbUGZ4orAAD9u7Q+AHUx6BEaqENRuQVHL5ZiWPeOrb4mERG1Te16F1h7I54FZKlxoPCqs4AuVzpHf1RKRasWCzdGr1Ghg7/zulIthD5uLIMgAJ2DdK6DGFtDoVAgofY8oAM8EJGIyKcxALUhV54FdPU6ILEQaoi/BkqlZ6anpD4M8dhF5/SXO0Z/ROI0GA9EJCLybQxAbUxUIwuhPVUG40oRBmkXQtcFoCC3XZNb4YmICGAAanMaWwh9qdLzAUjqrfDHLjoPLIzzwAjQmaIKlFbZ3HZdIiJqWxiA2pjGzgK6VC6eAu3+QxBFUm6FdzgEHPfAFFjHAC2iOzpD5C8cBSIi8lkMQG1MY2cBSTEFJuUIUN7lSlRY7dCqlegRGuDWa7sOROQ6ICIin8UA1MY0NgXmyUKooggJ64GJ63/6hAdCrXLvf01dByLyRGgiIp/FANTGXH0WkEgcAfLEGUAicReYFBXhj9au/+kf4f4abvGunWCcAiMi8lUMQG1MY2cBefIU6Cs/GwBKKm2osto99jmAZ7bAiwZGGaBUOINcgcSlPYiIyDswALUxjZ0FdFmCEaBgvRp+Gmf5CE+PAoklMOLcUALjagE6NXqFBQJgXTAiIl/FANQGXXkW0AlTGZ76MAsnC8oBAKFuODG5MQqFwrUQ+kbrgFZtP4Vp7+5BSe32/OYorbIhv8QZ7jwxBQawMjwRka9jAGqDxIXQS7/JQeryH/Dfw0YoFMCDiV3Rq3OgRz9bnAYzmhs/Dbq43IJl23Kw40Qh3so42ezPELe/R3Xwg8HfMzXH6irDl3jk+kRE5N28ohgqNY94FtC5YudOsN8OjMAzd/RBn3D3nZjcGNdC6FJLo20+258Pm925QPuDzHOYmhyD2GZsZffECdBXG9ItBACQde4ybHYHNG7eaUZERN6Nf+u3QWP6hCJQp8Zv+oVhy+zRWPX7YZKEH+CKEaBG6oEJgoD1e/MAAAY/DWocAl7777FmfYZ4ArQnFkCL4roEI8Rfg0qrHQc4DUZE5HM4AtQGDeveEb/89U4oFJ4peno9ETc4DDE79zJ+LSiHn0aF96YPxwOrduLrIybsOXMJI2I7Nukzjhk9twNMpFQqMLJXKL48dBE/nizC8Jim9U1Knx/Ix7s/n0WIvwbhQXqEB+sQFqzHmD6dEd3RX+7uERG1aQxAbZQc4QeomwJrrBzG+j3O0Z+7B3fB0G4heGhEN6zbnYtXvzyKz/446oaV6mvsDuQYPT8CBAA31wagn38tQtodfTz6Wc2VeaoYf/r4IGocwjWvBWhV+PvDiRjdO1SGnhERtQ+cAqNmEbfgNzQCVFZtw5ZDFwEAD42IBgA8k9IHAVoVDp4vxReHLtzw+meLK2CpccBfq0J3D49yjOrlDBAH8kpQVu09hVHzLlXijx9locYhYOyACCyZMAhpd/TBlKRuGBAZjAqrHdPX7sEXB298P4mIqGEcAaJmCTc4t9kXlluuWTz8xcGLqLLZ0SssEENrFxl3DtLhqVt74s1vTuD1rTlIHRABfe1ZQg0RT4DuGxF0w9Gi1oru6I/unfxxrrgSu09fQkpcuEc/rynKLTX4w/v7cLnShkFRBix/KKHe/bLU2JH28UF8eeginl6/H8XlFjwyKlbGHhMRtU0cAaJmCQ3QQa1UQBCunQbbsDcXAPDQ8Oh6U3SPje6BLgY98kuq8N7PZ697fXEHWJyHp79Eo2tHgX76tUiSz7seh0PAMxsOIMdUhs5BOvxjauI1YVGnVuHth4ZganJ3CALw1y+O4s2vc+qVRSEiohtjAKJmUSoV6N7JOTU1419ZOGlyjtgcvWDGwfOl0KgUuG9IVL33+GlV+NOdfQEA//fjaVTbGi+jIZ4A7en1PyJvCkBLt+Vg21ETtGol1jw8zLXg/GoqpQIv3jMAf6pdt7Ti+1+xascpKbtKRNTmMQBRs708fiA6Bmhx7KIZd7/zEz7Ydc41+nNnXAQ6BV57GvX4hEhEGvQorrBi83XWrniyBlhDknt2gkIB/FpQLkmV+8bsOFGIld87Q8ySCYNc5xQ1RqFQYPbtvbH4d3EAgKXfnMCeM5c83k8iovaCAYiabWTPUGydczNu7h0KS40DCzcdxvuZ5wAAk4ZHN/getUqJqSNjAADv/nSmwSmb4nILCsosUCiAfhHSnGvUwV+LwVHOU6F/lmkUqKzahvmfHAIATE3ujvuGdG3yex8ZGYP7hkTB7hAw+9/ZKC5v/IBKIiKqwwBELRIWrMf700dg4d1x0NYuhI7q4OeaUmrI5OHd4KdR4bixDJmni695fe9Z5whG947+CNBJtz5f3A0mVwBasvU4LpRWI7qjH57/bb9mvVehUOCV8QPRs3MATGYLnvn4IBwNbJ0nIqL6GICoxZRKBR4bHYvPZ43C/UOi8PoDg6+7c8vgr8EDw5yjG+/+dLbea+ZqG17e4jwxOqW/tLuxrlwHJPVi4p2nivDhLuf04ZL7B8Nf2/zgF6BT429ThkGvUeKHE4X42/Zf3d1NIqJ2hwGIWq1/l2Asm5TgGkm5nkdGxQAAMo6bcLaowvX8y18cRX5JFbp19MczEh9KOLR7CPQaJQrKLDhZUC7Z51Zaa/D8J78AAP4nqRtGNuH+NaZvRBBeuncgAGDZthPY1cAIGxER1WEAIkn17ByI2/p2hiAAa3eeBQB8e9SEjVnnoVAAb06Ml3T6CwD0GpWrFMZPJ6WbBnvz6xPIvVSJLgY95jdz6qshDyZGY8LQrnAIwNz1B2D2osMdiYi8DQMQSe7R0c6D+z7el4dzxRV4/lPnKMiMm3s0uV6Yu42WeB1Q1rlLeG/nGQBA+v2DEKTXuOW6L48fgJhO/jCaq/Haf4+75ZruJAgCTOZqnDCVca0SEcmKJ0GT5Eb3CkWf8ECcMJVjwqqdKCq3ondYoKz1uEb3DgX+C+w6XXzNCdfuVmW1488bD0EQgAeGdcWtfcPcdm1/rRrp9w/G5H/swrrdubgnPhI39ejktus3lyAI+OLQRez8tQgnC8px0lQGc3UNAODm3qH4f5MSENrAsQlERJ7GESCSnEKhwKO15RuKyq1QKRVY9mDCdUtkeFr/iGB0DNCiwmrH98cLPPpZr399HGeKKhAerMPCcXFuv35yz06YXFuLbf6nv1z34ElPulRhxYx/ZeHpf+/H+r15yDp3GebqGigVgEalwI8ni/Dbt37EzlPyH0JJRL6HAYhkMX5IFDoGaAEAs27rhUFdDbL2R6lU4N6ESADAs58cQm5xpUc+Z+epIlc5kCUTBsPg756pr6s9/9v+CAvS4UxRBd7OOOmRz7ien38twtjlP+DbYyZoVUrMuDkWb08egq1zb8axl8fiy6dvRu+wQBSWWfD7/9uN5d+egJ1TYkQkIYXAIkLXMJvNMBgMKC0tRXCwNCcS+6I9Zy7hYF4JHhkV49Epp6aqttkx6e+ZOHi+FH3Dg/DpH0e6dUF2uaUGY5f/gPOXqzB5RDTS7x/stms35OsjRjzxQRZUSgU2zxqFAZGeD5nWGgeWbsvBmh9OQxCAnp0D8M7koYiLvPZ/R5XWGiz+/Ag2Zp0HAIzs2QlvTx7CKTEiarHm/H7L/6tDPmtEbEfMuKWHV4QfwLkb7O8PJ6JzkA45pjKkfXzArQt1X/3yGM5frkLXED/8xQNTX1dLHRCBuwZFwO4Q8Nwnh1Bjd3j08y5XWPH7f+7G33c4w8//JHXDltk3Nxh+AOd6pTcmxmPZg/Hw16qw81Qxxr39I/adZUkPIvI8jgA1gCNAvi3r3GVMXrMLVrsDz6T0wZyU3hAEARdLq3HofAlyL1VCo1JCp1ZBp1ZCp1EiIboDuob4N3rN7TkFeOS9vQCAf8+4Cck9pVmYXFBWjZSlO2CursFdgyLw5sT4Fh22eCOnC8vx6Nq9OFtciUCdGm9OHIyxA7s0+f2/FpThyQ+z8WtBOdRKBebf1R+PjoqBQtH4wZpy23f2krN2nUIBpQJQKhTw06jwm/5hCHbTrr72RBAEHDeWIaZTAPy08q33o/atOb/fDEANYACij/fm4dna+lw39w7FcWMZCssar7OlUirwu8Fd8MSYnvUKuRaVW7Dl4AWs+P4UisoteGRkDP56zwCP9/9KWw9fxOx/74fNLiCuSzD+MS0RUR383Hb9zFPFePLDLJRW2RDVwQ/vPjIcfVtQy63CUoPnP/0FX9QWyx03qAtem+C+IwLc5bjRjNf+exzbcwobfL1HaADWTh+Bbp0aD8S+5GJpFT7JOo+NWedxrrgSvcIC8a9HRyDSjf8dJBIxALUSAxABwF83H3Ed1gg4Q06f8CD0DguEQxBgqXHAUuNAaaUVB8+Xutrd1rczUuLC8e1RE344WeRa3NsrLBBfzBoty//73Xf2Ep78MAtF5VZ0CtBi9cPDXIc/tpQgCFi/Nw+LPj8Mm11AQnQH/GOqcwqxNdd8f+dZvPrVMdjsAqI6+OGNiYMxsmfLT8l2l4ulVVj2zQn8J/s8BAFQKxUY06czNColHIIAAcCh8yUwmS0IDdTi3UeGY3DXDnJ3WxaCICDjWAE+2HUOP54sxNUzyZEGPf71WBJ6hQXK00FqtxiAWokBiADAZnfg/doAlBDdAQMiDY2Gl8P5pVi94xS++uXiNX/Zx3c14L4hUbhvaFcY/OQbzcgvqcLj/9qHIxfM0KgUmJvSBxMTuyIsSN+s6wiCgB9PFuGNr3PwS74z+I0b3AVLJ8a77SiD7NzLmLN+P/IuVQFwVr1/bmw/WcJjuaUGq7efwv/9dBrVNuc6qnGDumBeal/EhAbUa2syV+OR9/bi2EUz/DQqrJwyBL/p55naduZqG7QqpazHR1zN4RCw9YgR73z3q3N6sFZSbEc8mBiN+GgDHv8gC6cLKxDir8Ha6SMQH91Bvg5Tu8MA1EoMQNRSZ4sqsObH0zh20Yybe4Xi3iFR6NnZe/5fbpXVjj//5yC+PHQRAKBUAKN6heKe+EikDoy44dqV/bmX8frWHGTW1hoL0Kow8ze98OQtPa9bCLclKiw1ePWrY1i321kstkfnALzxQDyGdQ9x6+c0psbuwPq9eVj+7QkUlVsBAMNjQjD/rv4Y2q3xPpRV2/DHj7Lx48kiKBXAS/cOxJSkbm5bz1RUbkH6V8fxSbZz91xooA5dQ/wQFeKHwVEGTBsZI3kosjsEbDl0ASu++9VVTy9Aq8KUm7rjf0Z0qxcUi8stmL52Lw6dL4W/VoU1Dyc6DyIlcgMGoFZiAKL2TBAEbNibh/V783Agr8T1vEqpQGigFp2DdAgL0iMsSAer3QGTuRrG0mqYzBaUW5ynOGtVSky5qRtm3tbL49vWt+cU4LlPDsFkdq7BuqVPZ8y6rZfHyqbYHQK+PWbCG1/n4NfaH/PY0AA8/9t+uDMuvElBxmZ3YP6nv+A/tVv8UweE45Xxg1o1PWh3CPho9zm88XUOympP026IMygOxrDuni8rI051vfF1DnJMZQCAIL0a00fFYvrIGITUnvV1tXJLDZ74YB9+/rUYGpUCr4wfiEnDu3m8v81hLK3GtmMm/HyyCBEGPR5MjG50RyN5DwagVmIAIl9xrrgCXxy8gE0HLrh+7K9HpVTg/iFRmJPS+7q73tytpNKKV788hk/357vWVA2PCcEfb+2F0b1D3XKUQlm1DRv3ncf7mWdxrvYgzBB/Deam9MH/JHVr9mcIgoBVO07h/207AZtdQIi/Bi/eOxC/G9ylWaNBDoeAzNPF+N+vjuHIBee00oDIYLw8fiBiOwUgv6QK5y9X4lxxJf750xkUlFmgUACPjorFn+/s67Fpw92ni/H61znIOncZABCsV+PxW3pg6siYJu2Cs9TYkfZx3WjktOTueOHuONmOxaixO3D4ghk/nCjEtqMm1/TulQZFGTBpeDTuSYiUfadfldWOS5VWXK6wosJSg85BOnQx+Pn8DjsGoFZiACJfIwgCCsosKDBbUFBWjcIyCwrKLFCrFIgI1iMiWI9wgx5dDHqPbKNvqtziSqz+4RT+s+88rLXnGuk1SgyO6oAh3ZyP2NBA+GtV0GmU8NOo4KdRQd3Aj2pZtQ1niypxprgC2ecu4z9Z510jXMF6NX5/U3c8MaZnq9dtHbtoxp8+PoijtWtixg6IwONjemBAZDB06sZ/rM5frsQnWfn4JPs8ci9Vuvo1L7Uv/iepO1QNTDmWVtrw0pajrumxmE7+mH9Xf6T0D2+wfUvkl1Thr5uPYNtREwDn/X90VCyeuKVns082dzgErPj+VyzbdgIAcFOPjvjblGGuU+I9SdyWv/NUMTJPFWH36Usos9SNrCkUwNBuIbi1T2ccN5bhm6NG2OzOn0s/jQpPjOmBJ27pKVngqLbZ8dn+fHy46xxOFZa71qNdrYO/BhHBenTv5O/ctBEehL7hQYgNDYBW7R1nrnkSA1ArMQAReTeTuRr/9+NpfLzvPEqrbDdsr1E5z+jx0zoDUbmlxrWu50o9Owdg+qhY3D80yq1Bz2Z3YOX3v2LFd7+ipnYES6tWIr6rAUO7hyA6xB+lVTZcrrCipMqG3EuV2Hv2EsS/nQN1aowfEom5KX2aNOX4/fECzP/0FxjN1QCA7p388cjIGExMjEZgC083r7E7sHbnWSzbdgKVVjvUSgUeGhGNp3/TG2HBzVtIf7VvjhjxzIYDqLDa0TXED6/dPxgje3Zy+7oyc7UNP58swvc5BdhxotA1rSoK0qtxU49OSOkfht/0C683ZVlcbsFn+/OxYW+ea51TF4Mez/+2H+6Jj/TYmVUFZdX4IPMcPtqdi0sV9f87q1Ep0DFACz+NCgVlFlRaG6/7p1IqEB3ih9jQAMSGBiK2cwB6hAagR+cARATrvfrMreZgAGolBiCitsHhEHC6qAL7cy9jf14JDuSWwGiuRpXVjuoaO270t1tooBYxnQIQGxqAcYO74Jbend3+o3ulw/mleOe7k9h79vI1P2YNGdmzEyYmdsXYAV2aPdJgrrZh1fZTWLc71xUSg/Rq3D24C6I7+iM8SI/wYD06B+mgUgLWGgE2uwM2uwMOwfnjqlUroVMrUVhmxctbjrpGsUbEdMSr9w1E7/Dmn/fUmBOmMsz41z7X9GNEsB73JETi3oRIxHUJbtEPtM3uwMG8Evz0axF+/rUI+3NLXAEUcI5ejYjthFE9O2Fkz1DERQbfcKRMEAR8+ctFpH91HPklzl2KQ7t1wOO39ERiTIhb1sRV25xFmTcfvICMYwWu0c6uIX54ZGQM7ogLR6dAHQK0Ktd9EQQBZZYaGEurcaGkCqcLK3DCVIYTpjKcNJXXG926mp9GhdjQAPQKC8Tg2lB+oxFKb8UA1EoMQERtn1B7VpMYhiqtdlRZ7aiy2aFXqxAT6i/bIYuCIOBMUQX2nbuMrLOXUVxhRYi/BiEBWnTw16CjvxajeoUiumPr11lVWmvwSXY+3vvpDE4XVbTqWgY/Df5yV388MKyrR4JiSaUVr3+dgy8OXqi30Duqgx8Mfhr4a52jeHqNClqVEiqlAmqlAiqlAgqFsxadpcYBa40DFdYa/HK+FBVXjYr0CA3ArX3DcGvfzhgR27HFO+aqbXb834+n8bftp+qNvHTv5I+h3ZwBQq9RQVXbP5VCAQGA3eFAjUOA3SHA4RCgUimhUSqgVimhALDzVDG+PmJ0TccCwLDuIfjD6FjcERfe4HTujQiCAKO5GmeKKpyPQuc/TxdVIPdSZYOFiLVqJQZGBiO6oz+UCuf9VSqc38NPq0KgTg1/Xe0/teraEVbnsQzivx+1SgG1UgmtSgm7IKDSWoNqmx1VVgcqrTWIDQ1wa4gG2mAAWrlyJd544w0YjUbEx8fjnXfewYgRIxptv3HjRixcuBBnz55F7969sWTJEtx1112u1wVBwOLFi/GPf/wDJSUlGDVqFFatWoXevXs3qT8MQETU3jgcAnacLMTeM5dgql3rZTJXu04416iU0KiUrnUi1hoHrHZnmHA4BNw5IALz7+onSbHaapsd23MK8fmBfGQcL4C1puV17EL8NRjZKxSje4ViVM9Qt5/QbTJXY9X2U9h5qggnTDfeSNBUkQY9fpcQiXviIz1ayNha40De5UqcLqxAjtGM/bkl2J9X0qQRytaadVsv/Dm1r1uv2aYC0IYNGzB16lSsXr0aSUlJWL58OTZu3IicnByEhYVd037nzp245ZZbkJ6ejrvvvhvr1q3DkiVLkJ2djYEDBwIAlixZgvT0dLz//vuIjY3FwoUL8csvv+Do0aPQ6288V80ARETkHczVNhy/WOYaPai0Oh81dgfsQt2IiiDAWZtPraydulOhV1gg4roEe3Ra80qlVTYcyCtB9rnL+LWw3NlHB+AQBNQ4BCgVzhPElQoF1CoFFFCgxuFAjV2AzSGgxu5Az86BuCchEsO6hUjW76sJgoBzxZXYn3cZxeVWCILzOzhq73el1Y4KSw0qav9ZZXOOrlbbnCOsVTY7bDUCahzOAG2zC1ArFdDXrsHzrx3FmzA0Cg8nx7i1720qACUlJWH48OFYsWIFAMDhcCA6OhqzZ8/G888/f037SZMmoaKiAlu2bHE9d9NNNyEhIQGrV6+GIAiIjIzEn/70J/z5z38GAJSWliI8PBxr167FQw89dMM+MQARERG1Pc35/ZZ1T5zVakVWVhZSUlJczymVSqSkpCAzM7PB92RmZtZrDwCpqamu9mfOnIHRaKzXxmAwICkpqdFrWiwWmM3meg8iIiJqv2QNQEVFRbDb7QgPr18rJzw8HEajscH3GI3G67YX/9mca6anp8NgMLge0dHRLfo+RERE1Da0/1ORmmD+/PkoLS11PfLy8uTuEhEREXmQrAEoNDQUKpUKJpOp3vMmkwkRERENviciIuK67cV/NueaOp0OwcHB9R5ERETUfskagLRaLYYNG4aMjAzXcw6HAxkZGUhOTm7wPcnJyfXaA8C2bdtc7WNjYxEREVGvjdlsxu7duxu9JhEREfkW+Yr61EpLS8O0adOQmJiIESNGYPny5aioqMD06dMBAFOnTkVUVBTS09MBAHPmzMGYMWOwdOlSjBs3DuvXr8e+ffuwZs0aAIBCocDcuXPxyiuvoHfv3q5t8JGRkRg/frxcX5OIiIi8iOwBaNKkSSgsLMSiRYtgNBqRkJCArVu3uhYx5+bmQqmsG6gaOXIk1q1bhxdeeAELFixA7969sWnTJtcZQADw7LPPoqKiAo8//jhKSkowevRobN26tUlnABEREVH7J/s5QN6I5wARERG1PW3mHCAiIiIiOTAAERERkc9hACIiIiKfwwBEREREPocBiIiIiHwOAxARERH5HNnPAfJG4skArApPRETUdoi/20054YcBqAFlZWUAwKrwREREbVBZWRkMBsN12/AgxAY4HA5cuHABQUFBUCgUbr222WxGdHQ08vLyeMiiB/E+S4P3WRq8z9LgfZaGJ++zIAgoKytDZGRkvSoSDeEIUAOUSiW6du3q0c9g1Xlp8D5Lg/dZGrzP0uB9loan7vONRn5EXARNREREPocBiIiIiHwOA5DEdDodFi9eDJ1OJ3dX2jXeZ2nwPkuD91kavM/S8Jb7zEXQRERE5HM4AkREREQ+hwGIiIiIfA4DEBEREfkcBiAiIiLyOQxAElq5ciViYmKg1+uRlJSEPXv2yN2lNi09PR3Dhw9HUFAQwsLCMH78eOTk5NRrU11djZkzZ6JTp04IDAzEhAkTYDKZZOpx+/Daa69BoVBg7ty5rud4n90jPz8fv//979GpUyf4+flh0KBB2Ldvn+t1QRCwaNEidOnSBX5+fkhJScHJkydl7HHbY7fbsXDhQsTGxsLPzw89e/bEyy+/XK92FO9zy/zwww/43e9+h8jISCgUCmzatKne6025r5cuXcKUKVMQHByMDh064LHHHkN5eblH+ssAJJENGzYgLS0NixcvRnZ2NuLj45GamoqCggK5u9Zm7dixAzNnzsSuXbuwbds22Gw23HnnnaioqHC1eeaZZ/DFF19g48aN2LFjBy5cuID7779fxl63bXv37sXf//53DB48uN7zvM+td/nyZYwaNQoajQb//e9/cfToUSxduhQhISGuNq+//jrefvttrF69Grt370ZAQABSU1NRXV0tY8/bliVLlmDVqlVYsWIFjh07hiVLluD111/HO++842rD+9wyFRUViI+Px8qVKxt8vSn3dcqUKThy5Ai2bduGLVu24IcffsDjjz/umQ4LJIkRI0YIM2fOdP3ZbrcLkZGRQnp6uoy9al8KCgoEAMKOHTsEQRCEkpISQaPRCBs3bnS1OXbsmABAyMzMlKubbVZZWZnQu3dvYdu2bcKYMWOEOXPmCILA++wuzz33nDB69OhGX3c4HEJERITwxhtvuJ4rKSkRdDqd8O9//1uKLrYL48aNEx599NF6z91///3ClClTBEHgfXYXAMJnn33m+nNT7uvRo0cFAMLevXtdbf773/8KCoVCyM/Pd3sfOQIkAavViqysLKSkpLieUyqVSElJQWZmpow9a19KS0sBAB07dgQAZGVlwWaz1bvv/fr1Q7du3XjfW2DmzJkYN25cvfsJ8D67y+bNm5GYmIiJEyciLCwMQ4YMwT/+8Q/X62fOnIHRaKx3nw0GA5KSknifm2HkyJHIyMjAiRMnAAAHDx7ETz/9hN/+9rcAeJ89pSn3NTMzEx06dEBiYqKrTUpKCpRKJXbv3u32PrEYqgSKiopgt9sRHh5e7/nw8HAcP35cpl61Lw6HA3PnzsWoUaMwcOBAAIDRaIRWq0WHDh3qtQ0PD4fRaJShl23X+vXrkZ2djb17917zGu+ze5w+fRqrVq1CWloaFixYgL179+Lpp5+GVqvFtGnTXPeyob9HeJ+b7vnnn4fZbEa/fv2gUqlgt9vx6quvYsqUKQDA++whTbmvRqMRYWFh9V5Xq9Xo2LGjR+49AxC1CzNnzsThw4fx008/yd2VdicvLw9z5szBtm3boNfr5e5Ou+VwOJCYmIj//d//BQAMGTIEhw8fxurVqzFt2jSZe9d+fPzxx/joo4+wbt06DBgwAAcOHMDcuXMRGRnJ++xjOAUmgdDQUKhUqmt2xZhMJkRERMjUq/Zj1qxZ2LJlC77//nt07drV9XxERASsVitKSkrqted9b56srCwUFBRg6NChUKvVUKvV2LFjB95++22o1WqEh4fzPrtBly5dEBcXV++5/v37Izc3FwBc95J/j7TOvHnz8Pzzz+Ohhx7CoEGD8PDDD+OZZ55Beno6AN5nT2nKfY2IiLhmY1BNTQ0uXbrkkXvPACQBrVaLYcOGISMjw/Wcw+FARkYGkpOTZexZ2yYIAmbNmoXPPvsM3333HWJjY+u9PmzYMGg0mnr3PScnB7m5ubzvzXD77bfjl19+wYEDB1yPxMRETJkyxfWfeZ9bb9SoUdcc43DixAl0794dABAbG4uIiIh699lsNmP37t28z81QWVkJpbL+T59KpYLD4QDA++wpTbmvycnJKCkpQVZWlqvNd999B4fDgaSkJPd3yu3LqqlB69evF3Q6nbB27Vrh6NGjwuOPPy506NBBMBqNcnetzXrqqacEg8EgbN++Xbh48aLrUVlZ6Wrz5JNPCt26dRO+++47Yd++fUJycrKQnJwsY6/bhyt3gQkC77M77NmzR1Cr1cKrr74qnDx5Uvjoo48Ef39/4cMPP3S1ee2114QOHToIn3/+uXDo0CHh3nvvFWJjY4WqqioZe962TJs2TYiKihK2bNkinDlzRvj000+F0NBQ4dlnn3W14X1umbKyMmH//v3C/v37BQDCsmXLhP379wvnzp0TBKFp93Xs2LHCkCFDhN27dws//fST0Lt3b2Hy5Mke6S8DkITeeecdoVu3boJWqxVGjBgh7Nq1S+4utWkAGny89957rjZVVVXCH//4RyEkJETw9/cX7rvvPuHixYvydbqduDoA8T67xxdffCEMHDhQ0Ol0Qr9+/YQ1a9bUe93hcAgLFy4UwsPDBZ1OJ9x+++1CTk6OTL1tm8xmszBnzhyhW7dugl6vF3r06CH85S9/ESwWi6sN73PLfP/99w3+nTxt2jRBEJp2X4uLi4XJkycLgYGBQnBwsDB9+nShrKzMI/1VCMIVx18SERER+QCuASIiIiKfwwBEREREPocBiIiIiHwOAxARERH5HAYgIiIi8jkMQERERORzGICIiIjI5zAAERERkc9hACIiIiKfwwBERG1WYWEhnnrqKXTr1g06nQ4RERFITU3Fzz//DABQKBTYtGmTvJ0kIq+klrsDREQtNWHCBFitVrz//vvo0aMHTCYTMjIyUFxcLHfXiMjLsRYYEbVJJSUlCAkJwfbt2zFmzJhrXo+JicG5c+dcf+7evTvOnj0LAPj888/x4osv4ujRo4iMjMS0adPwl7/8BWq18/8TKhQK/O1vf8PmzZuxfft2dOnSBa+//joeeOABSb4bEXkep8CIqE0KDAxEYGAgNm3aBIvFcs3re/fuBQC89957uHjxouvPP/74I6ZOnYo5c+bg6NGj+Pvf/461a9fi1Vdfrff+hQsXYsKECTh48CCmTJmChx56CMeOHfP8FyMiSXAEiIjarE8++QQzZsxAVVUVhg4dijFjxuChhx7C4MGDAThHcj777DOMHz/e9Z6UlBTcfvvtmD9/vuu5Dz/8EM8++ywuXLjget+TTz6JVatWudrcdNNNGDp0KP72t79J8+WIyKM4AkREbdaECRNw4cIFbN68GWPHjsX27dsxdOhQrF27ttH3HDx4EC+99JJrBCkwMBAzZszAxYsXUVlZ6WqXnJxc733JyckcASJqR7gImojaNL1ejzvuuAN33HEHFi5ciD/84Q9YvHgxHnnkkQbbl5eX48UXX8T999/f4LWIyDdwBIiI2pW4uDhUVFQAADQaDex2e73Xhw4dipycHPTq1euah1JZ91firl276r1v165d6N+/v+e/ABFJgiNARNQmFRcXY+LEiXj00UcxePBgBAUFYd++fXj99ddx7733AnDuBMvIyMCoUaOg0+kQEhKCRYsW4e6770a3bt3wwAMPQKlU4uDBgzh8+DBeeeUV1/U3btyIxMREjB49Gh999BH27NmDf/7zn3J9XSJyMy6CJqI2yWKx4K9//Su++eYbnDp1CjabDdHR0Zg4cSIWLFgAPz8/fPHFF0hLS8PZs2cRFRXl2gb/9ddf46WXXsL+/fuh0WjQr18//OEPf8CMGTMAOBdBr1y5Eps2bcIPP/yALl26YMmSJXjwwQdl/MZE5E4MQEREV2lo9xgRtS9cA0REREQ+hwGIiIiIfA4XQRMRXYUrA4jaP44AERERkc9hACIiIiKfwwBEREREPocBiIiIiHwOAxARERH5HAYgIiIi8jkMQERERORzGICIiIjI5/x/G9RUqMfHlyoAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "plt.plot(range(len(cst)), cst)\n",
        "plt.ylabel(\"Cost\")\n",
        "plt.xlabel(\"Step\")\n",
        "plt.show();"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 296,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NdDf7mhSAyUk",
        "outputId": "96925546-a50f-4796-fb26-01c4313b2e9c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0.12431051] [0.00115156]\n"
          ]
        }
      ],
      "source": [
        "print(cst[0], (cst[-1]))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 305,
      "metadata": {
        "id": "hr1IydXhPgvk"
      },
      "outputs": [],
      "source": [
        "from pennylane.pauli.conversion import Y\n",
        "x_t = np.zeros((test_size//N_QUBITS, r))  # Already grouped and scaled\n",
        "target_y_t = np.zeros((test_size//N_QUBITS,1))\n",
        "for i in range(test_size//N_QUBITS):\n",
        "  x_t[i] = final_test[i][:-1]\n",
        "  target_y_t[i] = final_test[i][-1]\n",
        "\n",
        "y_index = []\n",
        "for i in range(int(N*2/3)+N_QUBITS,N,N_QUBITS):\n",
        "    y_index.append(i)\n",
        "y_index = np.array(y_index)\n",
        "y_index.reshape(16,1)\n",
        "\n",
        "t_predictions = np.zeros((test_size//N_QUBITS,1))\n",
        "for i in range(test_size//N_QUBITS):\n",
        "  t_predictions[i] = (PQC(weights, x_t[i]))\n",
        "t_predictions = t_predictions.reshape((test_size//N_QUBITS, 1))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 302,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IyqsPyetPWPY",
        "outputId": "9cd3e8e9-9c71-482e-8640-2b9696d5681e"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.0018253858973802115"
            ]
          },
          "metadata": {},
          "execution_count": 302
        }
      ],
      "source": [
        "metrics.mean_squared_error(t_predictions,target_y_t)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "real_predictions = scaler.inverse_transform(t_predictions)\n",
        "print(real_predictions)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lT90FuX2CnS2",
        "outputId": "5f473e26-c3af-48eb-c1b9-2876a9050deb"
      },
      "execution_count": 306,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[3.60073647]\n",
            " [3.19676248]\n",
            " [2.77408829]\n",
            " [2.49047696]\n",
            " [2.42481382]\n",
            " [2.6102453 ]\n",
            " [3.06786471]\n",
            " [3.72589906]\n",
            " [4.36754381]\n",
            " [4.75431338]\n",
            " [4.76648095]\n",
            " [4.42399521]\n",
            " [3.87321167]\n",
            " [3.34272531]\n",
            " [3.02077543]\n",
            " [2.98033927]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(full_signal)\n",
        "print(len(x_t))\n",
        "print(len(t_predictions))\n",
        "plt.scatter(y_index,real_predictions)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 482
        },
        "id": "bxxmwCmP_MXR",
        "outputId": "4a82f7fa-13d5-4695-89d0-9b20919d1a33"
      },
      "execution_count": 307,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "16\n",
            "16\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7fb819ac9120>"
            ]
          },
          "metadata": {},
          "execution_count": 307
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyOogZPL9of8P19FR8GAMJNf",
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}