Test_AutoEncoder.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "82de83db-a578-430f-bb31-ba756b443dea",
   "metadata": {},
   "source": [
    "### Test the trained AutoEncoder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "fc8c5d87",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "Installing collected packages: tensorboard-data-server, google-auth-oauthlib, tensorboard\n",
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     ]
    }
   ],
   "source": [
    "!pip install  tensorboard==2.10.0\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0f85abd8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Collecting setuptools==59.5.0\n",
      "  Downloading setuptools-59.5.0-py3-none-any.whl.metadata (5.0 kB)\n",
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    }
   ],
   "source": [
    "!pip install setuptools==59.5.0\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f6f8107a-2188-4a2a-bd51-999071a008fa",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.optim as optim\n",
    "import torchvision.transforms as transforms\n",
    "from torch.utils.data import Dataset, DataLoader, random_split\n",
    "#from torch.utils.tensorboard import SummaryWriter\n",
    "import torch.nn.functional as F\n",
    "\n",
    "from pathlib import Path\n",
    "import random\n",
    "from datetime import datetime\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "from model import VPTREnc, VPTRDec, VPTRDisc, init_weights\n",
    "from model import GDL, MSELoss, L1Loss, GANLoss\n",
    "from utils import KTHDataset, BAIRDataset, MovingMNISTDataset\n",
    "from utils import VidCenterCrop, VidPad, VidResize, VidNormalize, VidReNormalize, VidCrop, VidRandomHorizontalFlip, VidRandomVerticalFlip, VidToTensor\n",
    "from utils import visualize_batch_clips, save_ckpt, load_ckpt, set_seed, AverageMeters, init_loss_dict, write_summary, resume_training\n",
    "from utils import set_seed, get_dataloader\n",
    "\n",
    "set_seed(2021)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "85dcbb92",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\sc23gd\\AppData\\Local\\anaconda3\\envs\\vptr\\lib\\site-packages\\tqdm\\auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n",
      "  from .autonotebook import tqdm as notebook_tqdm\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import torch\n",
    "from MovingMNIST import MovingMNIST\n",
    "from pathlib import Path\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "61d57ab8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset generation and saving complete.\n",
      "Train data shape: (8000, 20, 64, 64, 1)\n",
      "Validation data shape: (1000, 20, 64, 64, 1)\n",
      "Test data shape: (1000, 20, 64, 64, 1)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import torch\n",
    "\n",
    "# Download and load the Moving MNIST dataset\n",
    "url = \"http://www.cs.toronto.edu/~nitish/unsupervised_video/mnist_test_seq.npy\"\n",
    "fpath = \"D:\\\\video_dataset\\\\VPTR\\\\mnist_test_seq.npy\"\n",
    "dataset = np.load(fpath)\n",
    "\n",
    "# Swapping the axes representing the number of frames and number of data samples\n",
    "dataset = np.swapaxes(dataset, 0, 1)\n",
    "\n",
    "# Adding a channel dimension since the images are grayscale\n",
    "dataset = np.expand_dims(dataset, axis=-1)\n",
    "\n",
    "# Ensure dataset has 20 frames (for 10 past frames and 10 future frames)\n",
    "dataset = dataset[:, :20, :, :, :]\n",
    "\n",
    "# Splitting into train, validation, and test sets using indexing to optimize memory\n",
    "indexes = np.arange(dataset.shape[0])\n",
    "np.random.shuffle(indexes)\n",
    "train_index = indexes[:8000]\n",
    "val_index = indexes[8000:9000]\n",
    "test_index = indexes[9000:]\n",
    "\n",
    "train_dataset = dataset[train_index]\n",
    "val_dataset = dataset[val_index]\n",
    "test_dataset = dataset[test_index]\n",
    "\n",
    "# Save the datasets as .npz files with the key 'clips'\n",
    "np.savez('MovingMNIST/moving-mnist-train.npz', clips=train_dataset)\n",
    "np.savez('MovingMNIST/moving-mnist-val.npz', clips=val_dataset)\n",
    "np.savez('MovingMNIST/moving-mnist-test.npz', clips=test_dataset)\n",
    "\n",
    "print(\"Dataset generation and saving complete.\")\n",
    "print(f\"Train data shape: {train_dataset.shape}\")\n",
    "print(f\"Validation data shape: {val_dataset.shape}\")\n",
    "print(f\"Test data shape: {test_dataset.shape}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "88818a86",
   "metadata": {},
   "outputs": [
    {
     "ename": "IndexError",
     "evalue": "index 0 is out of bounds for dimension 0 with size 0",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[3], line 2\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[38;5;66;03m# Generate datasets\u001b[39;00m\n\u001b[1;32m----> 2\u001b[0m train_data \u001b[38;5;241m=\u001b[39m \u001b[43mgenerate_moving_mnist_dataset\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mMovingMNIST\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnum_samples\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m60000\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[0;32m      3\u001b[0m val_data \u001b[38;5;241m=\u001b[39m generate_moving_mnist_dataset(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mMovingMNIST\u001b[39m\u001b[38;5;124m'\u001b[39m, num_samples\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m5000\u001b[39m)\n\u001b[0;32m      4\u001b[0m test_data \u001b[38;5;241m=\u001b[39m generate_moving_mnist_dataset(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mMovingMNIST\u001b[39m\u001b[38;5;124m'\u001b[39m, num_samples\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m10000\u001b[39m)\n",
      "Cell \u001b[1;32mIn[2], line 13\u001b[0m, in \u001b[0;36mgenerate_moving_mnist_dataset\u001b[1;34m(root, num_samples, seq_length, image_size)\u001b[0m\n\u001b[0;32m     11\u001b[0m all_sequences \u001b[38;5;241m=\u001b[39m []\n\u001b[0;32m     12\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(num_samples):\n\u001b[1;32m---> 13\u001b[0m     seq, _ \u001b[38;5;241m=\u001b[39m \u001b[43mdataset\u001b[49m\u001b[43m[\u001b[49m\u001b[43mi\u001b[49m\u001b[43m]\u001b[49m\n\u001b[0;32m     14\u001b[0m     all_sequences\u001b[38;5;241m.\u001b[39mappend(seq\u001b[38;5;241m.\u001b[39mnumpy())\n\u001b[0;32m     16\u001b[0m all_sequences \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mstack(all_sequences)\n",
      "File \u001b[1;32md:\\video_dataset\\VPTR\\MovingMNIST.py:78\u001b[0m, in \u001b[0;36mMovingMNIST.__getitem__\u001b[1;34m(self, index)\u001b[0m\n\u001b[0;32m     75\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m new_data\n\u001b[0;32m     77\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mtrain:\n\u001b[1;32m---> 78\u001b[0m     seq, target \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mtrain_data\u001b[49m\u001b[43m[\u001b[49m\u001b[43mindex\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m:\u001b[49m\u001b[38;5;241;43m10\u001b[39;49m\u001b[43m]\u001b[49m, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mtrain_data[index, \u001b[38;5;241m10\u001b[39m:]\n\u001b[0;32m     79\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m     80\u001b[0m     seq, target \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mtest_data[index, :\u001b[38;5;241m10\u001b[39m], \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mtest_data[index, \u001b[38;5;241m10\u001b[39m:]\n",
      "\u001b[1;31mIndexError\u001b[0m: index 0 is out of bounds for dimension 0 with size 0"
     ]
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "672b8acb",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "2f335546",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset generation complete.\n"
     ]
    },
    {
     "ename": "AttributeError",
     "evalue": "'NoneType' object has no attribute 'shape'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[13], line 2\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mDataset generation complete.\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m----> 2\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mTrain data shape: \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mtrain_data\u001b[38;5;241m.\u001b[39mshape\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m      3\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mValidation data shape: \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mval_data\u001b[38;5;241m.\u001b[39mshape\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m      4\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mTest data shape: \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mtest_data\u001b[38;5;241m.\u001b[39mshape\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m)\n",
      "\u001b[1;31mAttributeError\u001b[0m: 'NoneType' object has no attribute 'shape'"
     ]
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2a32337f-fc33-404a-8cd0-e9e2819d5a51",
   "metadata": {},
   "outputs": [],
   "source": [
    "resume_ckpt = Path('/home/ryukijano/work/VPTR/checkpoints/epoch_2.tar') #specify your trained autoencoder checkpoint file\n",
    "num_past_frames = 10\n",
    "num_future_frames = 10\n",
    "encH, encW, encC = 8, 8, 528\n",
    "img_channels = 1 #Set to be 3 for BAIR dataset\n",
    "N = 4\n",
    "device = torch.device('cuda:0')\n",
    "loss_name_list = ['AE_L1', 'Dtotal', 'Dfake', 'Dreal', 'AEgan']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "272cb7e0-54ad-4756-a7f8-9801e8c28739",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "initialize network with normal\n",
      "initialize network with normal\n"
     ]
    }
   ],
   "source": [
    "VPTR_Enc = VPTREnc(img_channels, feat_dim = encC, n_downsampling = 3, padding_type = 'reflect').to(device) #Set the padding_type to be \"zero\" for BAIR dataset\n",
    "\n",
    "#Set the padding_type to be \"zero\" for BAIR dataset, set the out_layer to be 'Sigmoid' for MovingMNIST\n",
    "VPTR_Dec = VPTRDec(img_channels, feat_dim = encC, n_downsampling = 3, out_layer = 'Sigmoid', padding_type = 'reflect').to(device) \n",
    "\n",
    "init_weights(VPTR_Enc)\n",
    "init_weights(VPTR_Dec)\n",
    "\n",
    "loss_dict, start_epoch = resume_training({'VPTR_Enc': VPTR_Enc, 'VPTR_Dec': VPTR_Dec}, \n",
    "                                         {}, resume_ckpt, loss_name_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "453740c6-f295-4c1c-8d7b-449b3038e277",
   "metadata": {},
   "outputs": [],
   "source": [
    "_, _, test_loader, renorm_transform = get_dataloader('MNIST', N, '/home/ryukijano/work/VPTR/moving-mnist-example', test_past_frames = 10, test_future_frames = 10, ngpus = 1, num_workers = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c90f3928-97a8-4296-9c53-def87cf9a51c",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = nn.Sequential(VPTR_Enc, VPTR_Dec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "be60c62e-9c6f-451d-b1d0-bad71c08e3d3",
   "metadata": {},
   "outputs": [],
   "source": [
    "sample = next(iter(test_loader))\n",
    "past_frames, future_frames = sample\n",
    "past_frames = past_frames.to(device)\n",
    "future_frames = future_frames.to(device)\n",
    "x = torch.cat([past_frames, future_frames], dim = 1 )\n",
    "pred = model(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "914283bb-3513-4afd-82d0-8765e45b3345",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_model_result(pred, fig_name, num_frames, n = 2):\n",
    "    fig, ax = plt.subplots(1, num_frames, figsize = (num_frames, 1))\n",
    "    fig.subplots_adjust(wspace=0., hspace = 0.)\n",
    "\n",
    "    for j in range(num_frames):\n",
    "        ax[j].set_axis_off()\n",
    "        \n",
    "        img = pred[:, j, :, :, :].clone()\n",
    "        img = renorm_transform(img)\n",
    "        img = torch.clamp(img, min = 0., max = 1.)\n",
    "        img = img[n, ...]\n",
    "\n",
    "        img = transforms.ToPILImage()(img)\n",
    "        ax[j].imshow(img, cmap = 'gray')\n",
    "    fig.savefig(f'{fig_name}.pdf', bbox_inches = 'tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5fa095ce-6158-4009-8a5e-c9c8e559aca5",
   "metadata": {},
   "outputs": [
    {
     "data": {
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3e/x3mdlsJj09nRdeeMH53VRWVoaXlxdz5syhpKSEnJwcsrKyGDt2LNHR0ZSXl7Njx44+K/01KJIQgYGBPPfcc4wdOxaHw0F3dzenTp1i3rx5lJWVUVxcTHNzM2PGjGH8+PEYDAZOnz7NyZMnsVqtPPjgg0RERKDX69Hr9fj6+rr6I7nE/fffz9y5c7l06RJPPvmks1QV/L8abP/8z/+MxWLh1Vdf5cyZM1dkFcPDw/H19SU5OZnhw4czefJk3njjDY+tXQeX993ChQsxGo2EhoYSHByMwWBAURQOHDjAmTNnOHHiBDt37rxq8kfAY489RlZWFtXV1bz00kuuDkcIIYQQQgghBgWLxYKPjw9nz5716FnDPTQaDdnZ2Xh5eXH06FGqq6uv2Gbs2LEsWLCA0aNHc+HCBT7++GOPrAARERHB3Llzee6551AUhb1791JWVnZFqaWxY8cSGBjI+fPn2bJli4uidb22tjbefvttVq1a5azO8reJK0VR+Oijj3jzzTdZsGABDoeDL7/8kpdeeomWlhYXRu7+tFotS5cuRavVsmfPHo4dO+bqkFzKYDAwffp0Hn30UUaMGOF8/p577uGuu+7CbrfT2dlJc3MzJpMJX19fNBrNNSvj3CoDOgnRUx7omWeeITs7m8DAQOBytufxxx+no6ODtrY2mpub6erqwtfXF5PJhKIodHd309nZidVq5cknn8RgMABw4cIFjhw54sqP5RJBQUHEx8cTGRkJQHx8fK8kRM/siISEBABKS0uv+iM7Z84cUlJS8Pb2RqvVMmTIkP75AG7O398frVbL4cOHOXXqFHC5h4mfnx8zZ85k5MiR2O12SUJcQ2hoKAkJCRiNRmejHCGEEEIIIYTosWTJEoYOHUpjYyO///3vXR3OgJCcnMyIESOIiori7Nmzrg7HLej1ep566inS0tL49a9/zdatW6mrq3O+bjQaWbBgATNmzKCrq4uVK1fS0NDgcasgvLy8mDx5Mvfddx86nQ5VVblw4QKJiYlotVqqqqooKSlh5MiRjBw5El9fX86cOePxfUcaGxtpaWlx9rH9ps7OTmdFl82bN7Nt2zaampr6O8wBxWw2M3z4cHQ6HSUlJdTV1Xlkz5G/pdPpiI2NZdiwYVRVVbF+/XoKCwudx5a3tzfZ2dlMmjQJRVHQaDRUVVWxf/9+9u/f33dx9dk79wNFUTAYDMyaNQuz2cyZM2coKSmhvr7euU1cXBzR0dEEBwej0WhQFIWioiJnh/S5c+cSHh4OXD7Zc3Nz2bt3r0s+jytlZ2cTExODwWCgpaXFWSOsR2hoKOnp6ZjNZgBOnDhBY2PjFe+zePFiYmJi0Gq1tLe3D/pO9GFhYXh7e9PV1XXVRkFms5mMjAwyMzNpbW3lwIED5OXlYbVamTBhAn5+flitVry8vCRhcw3PPPMMWVlZGAwG2traepVYE0IIIYQQQgi4fO8/evRoqqurnbWuxbdLTU0lKSkJq9VKQEAAOp2O7u5uV4flMlqtloCAAEaNGkVsbCzx8fEcPXq0VxIiKCiItLQ0oqKiqKur48yZMx53rOn1erKzs5k9ezaZmZmoqoqqqowbN46kpCSampqoq6ujpqaGmJgYwsLC0Ov1dHR00NDQ4OrwXcrhcHxrwkqj0TBixAgMBoNzEqunJbhulL+/P4sWLQIuT5hubGz0uHPym7q6usjJyeHNN9+kq6uL/fv3U19f7xxPM5lMHD16FF9fXzIyMrDZbBw5coT333//qqu/bpUBnYRQVRWHw0FlZSUVFRWcOHGC3NzcXjts2LBhzJgxgylTphAYGIjNZmPTpk0cOnQIVVWZOHGic9vW1lby8vI8aiWEoij4+flx++23ExkZSUdHB6WlpVy4cKHXdmFhYaSnpwNQWVnJ+fPne62EUBSFlJQUxo0bR0BAgLN7/datW/v18/S3ESNGkJKSQmNjI5988kmvGnWKohAYGMj8+fNJSkri6NGjnDhxgoqKCiIiIli8eLGzYVNbW5ssfb0Kk8nEgw8+yJAhQ2hoaECj0UgS4m+MHz8em81GS0sLDQ0NXLx40dUhCSGEEEII4RL+/v7OxreKorg6nAEhIiKC0NBQVFWltbXVWVPdU5nNZlJTUwkLC3OWJvmmhIQEwsLCsFgsVFZWUlBQ4IJIXUuv1zN58mRGjx6NXq/n3LlzNDc3o9PpCA4OJiYmBh8fH7y8vNDpdJhMJpqbm6murqa2ttbV4butniRYSkoKbW1tFBYWUllZ6eqw3J6Xlxfjx4+nu7ub48ePU1tb6/GJm56kwpkzZ7Db7VedRH727FnuvPNOUlJSKC8vZ/fu3Wzbtq1PE9EDPgnR1NTEP/7jP2K322lubr5iIHfPnj2Ulpbi5eXF7NmzuXjxIv/3//5fzp07x9ChQ3ttW1dXx4ULF646o32w0uv1jB8/nmXLluHl5cXp06fJz89HVVXn7BGdTkd4eDgpKSnY7Xa2bNlyRTkcnU7HU089hdVqBS5n3SorK/nyyy8HbT8IjUbDnDlzmD9/PjU1NRw4cIDc3Fzn63q9nsjISB544AGMRiObNm1yHluRkZHcfffdzhkDOTk55OXlueiTuCdFUYiJicFisRAaGkpISAiXLl1ydVhuQ6PR8Oqrr9LS0kJ+fj779u3j/fffd75uNpvR6XQ4HI7vbOA0WPn7+zuXufaU4BNCCCGEEIOPXq/H398fjUZDdXW1R8/mh8v3UjqdDkVRrlnK1mAwOFfmNzQ0sHbtWo++XtZoNAQHB3PHHXfg4+NDbW0tubm5lJaW9tpu/PjxBAUFYbfbqa+v58CBAy6K2HU0Gg3h4eFoNBqOHDnC2rVreyVjEhMTmTp1KnPmzMFgMKCqKidPnmT37t2cPn3ahZG7N6vVypgxY1AUheLiYhoaGjx+Rv/1sNvttLS0UFhYyOeff055ebmrQ3ILHR0d3znZ2WKxoNFo2Lp1Kzt37uzz34ABnYTo8V2zfxVFQVEU7HY7v/3tb6moqLjqibx+/XqOHz/eV2G6Hb1eT3h4OC+++CImkwlVVampqaGpqYn58+dTWFjIqVOnSE1NZfz48aSnp2Oz2di+fft3HpgdHR1UVFRw8ODBfvo0/a+nT0FoaCjd3d0kJib2SkL4+vqSmJjo7KNRUlJCe3s7EydO5Mknn3Ru19zczIYNG/q07tpApNfrue+++4iOjsZoNALg5+eH0Wj06ItjuPydFhUVhcViYejQoYwdO5bY2NheSYiHH36YMWPGUFVVxc9+9jMXRus6mzZtoqamhtOnT7N3716++OILV4ckhBBCCCH6QHZ2NiNGjCA4ONjVobgFLy8vsrKy8Pb2ZtOmTVe9f5o5cyZz5swhPDyco0ePevy1cnh4OLNnz+aHP/whDoeDgwcPUlFRcUUSJysri4CAAAoLC9m2bZuLonWtlpYWXnjhBQwGA52dnb3KVfVYtWoV//Ef/8HSpUtpamri1VdfZc2aNR5/L/9tgoOD+eEPfwhc7ld76dIlj0+oXo/z5887yzGJ66fValm8eDGKorB//35OnjzZ539zUCQhvktycjIzZsygu7ublStX0traitVqJS4ujjFjxji3Ky4u9pilYTqdjpSUFH784x+TlZWFVqsFYOLEiYwfPx673U5HRwctLS3odDp8fHzQarV0dXVdV9mg3NzcQX8Rc99995GamoqiKJSVlfH111/3ej0hIaFXua8tW7ZQXV1NWlpar+3q6uo4ceLEFSWwPJ1er+cnP/kJer0ejUZDQUEB27Ztk4sWLu+b5cuX90rQ+Pr69tomJCSEuLg49Hq9xyVuFEUhMjISi8XC5MmTGTduHPHx8YP+O0kIIYQQg8MjjzxCVlYW9fX1vPjii64OZ0CYOXMmYWFhWK1WoqKiPO7695vCw8P52c9+xogRI1i0aBEnT57stTrabDbz7LPPkpmZSW5uLh9//LFHN7/18fFhzpw5PPnkk85KDvn5+QwdOhRfX19nyers7GzGjx+Pv78/x48f98hVED0uXbqEoijfWvmiZ0Lwa6+9xvHjxz36nLweWq0Wo9FIQ0MDf/7zn2WMSPQZq9XK2LFjURSFc+fOUVtb2y8Jr0GfhEhISCAyMhK73U5RUREtLS04HA5n/4L4+Hg0Gg1/+tOf2Lp16xUNmQcrrVbLkCFDmDhxInV1dWzcuJHi4mLa29uBy0mKqVOnMm7cOAwGAxqNhtbWVo4cOcK+fft6zQbQarX4+/szYsQI9Ho9AA0NDZSUlLjks/U1rVbL0KFDefzxx4mMjKS8vJzTp0/T3Nzca7uwsDDS0tJwOBxs27aNtra2q/5Ar1+/nrKyskFbtupaQkNDiYiIQK/XX7EKJDQ0lIceegiDwQBcnmlx/PhxNm3a5IpQ3Y7BYOCpp55yNoovKSm5opeNn58fiqJQXV19zSXYg5Ver2fRokWEhoZiMpkwGo34+/u7Oiy38pe//MVZgvDkyZPs3LnT1SEJIYQQ4n+EhoaSlJREVVUVBoPB467lboafnx8Gg4GSkhJ27drl0fvMYrEQHh5OcnIyfn5+xMXFceHCBWcSomdVdXJyMt7e3jQ3N1NRUeHiqF3HaDSyZMkSlixZQnJysrNk8r333svixYtpb2+npaWFxsZGAgICGDJkCBqNBpvN5vF9Hb9tDMPX15cZM2YAsHXrVulfeB2Ki4v5u7/7O8xms7PPhhB9ISgoiEceeQSAoqIi6uvrJQlxK2RnZ5Oenk5nZyfFxcV0dHQQERHBbbfdxvTp07FYLKiqyqZNmygtLfWYzKzNZqO0tJQVK1bQ3d3NwYMHqampcR50Wq2WU6dOYTabycjIwGQyUVJSwptvvklVVVWvJi9ms5nMzExSUlLQ6/Xk5OSwe/duzp4966qP12c0Gg1+fn7cc889xMTEYDAYuHTpEjU1NaSlpVFXV0dVVRVDhgwhOTmZhIQE7HY7+/bto7u7G6PRSFBQEOHh4c73zMvL88hZJykpKSxYsICAgADOnz9PbW2t8yLGaDQSExPj3LanKdOpU6dcFa7b8Pf3Z9asWURERADQ2dlJfn4+e/bscW4TGxtLTEwM3t7edHV1eVyCy2AwsGzZMqxWK4qiUFtbO2iTojdKURR8fX3JysrCYDBQVVVFcHCwJCG+4ZlnnqG5uZmqqiqKioqkZ48QQoh+5evri8lkoq2tDbvd7upwXMrX15fAwEB0Ot1V7y8VRSE9PZ2hQ4eiKAp5eXns3bvX465//1Z4eDhZWVkEBgbS2dnJxYsXnZMN4fI97ahRo/D29kaj0VBTU8OZM2dcGLFr6XQ6srKySEpKoqGhgX379lFVVeV8PSgoiJiYGIYNG4ZWq8VgMFBZWcnZs2cpLCx0YeTuy8fHh+joaAICAqiqqqKiosLjEzbXo6OjQ3pmiH7RM+bW1tbGjh07uHjxYr/8bg76JERmZiYxMTE0NTVx5MgRuru7iY2NZeLEiQwfPhy73c7Fixc5fvy4RzVvtdvtFBcX88c//tHZKf2bB1xubi5z5swhOjqa1tZWDh8+zKpVq3rNKjEajURGRrJgwQJCQkLQaDTs2bOHHTt2DLpmMIqi4OPjw8iRI1myZIlz1YfBYCAmJoa7776biooKCgoKiI2NZfz48YSEhNDd3c25c+ew2WwEBweTmJhIfHw8AOfOnePs2bO0tLS48qP1O71eT0pKCvPmzSMkJITXX3+d+vr6azZdqqio4MKFC70uBj2Vr68v06dPd/67vb2d/Px8Dh8+7HwuKyuLmJgY5w2sRqPplTgczMxmM6mpqc5SaDabjXPnznHo0KHrfg9/f39CQkLQarWD7iJQq9WSmpqKt7c3YWFhREVF0dDQ4Oqw3IrJZOLJJ5+ktbWVCxcusHPnTklC/I3x48c7yzU2NDR4TBlLIYToL/7+/gQHB2MwGGhqavL4JERUVBQTJ07E29ubP/7xj1esLjcYDMyfP5/09HSqqqo4ceLEoJwMd72sVisjRoxg5syZmEwmCgsLOXfuXK+xDo1G46x40FPBwJMn7KiqSmNjI7m5udTW1vL1119TXFzsfD0qKooJEyawdOlSgoODsdlsHDhw4IrtxP8TGRnJqFGjcDgczoobnnI/KsRA0NbWxrFjx6itrWXz5s39dk836JMQnZ2dXLp0iaKiIj777DMsFguxsbH4+fmh0+loaWnh008/pbq62uMavnR3d3Pp0qVv3cZoNKLT6cjJyWHVqlW9ZlAADBkyhMmTJ/PEE0+gqirt7e0cP36cgoKCvgzdJXQ6HbGxsTzxxBMkJSXR0dGB3W4nNjaW2NhY53Y2mw2dTofRaERRFLq6umhtbUWr1TJy5EjGjBlDZGQkNpuNN954g71793pUAgwuHzdRUVFERESg1WoJDw/nxIkTztcVRXEmeQD2798vqyCuob6+nsLCQs6fP+98buzYsQQEBKDT6fD19UWv13vMKq+IiAgee+wx57/b2trIyclhx44d1/0eo0aNYtmyZZjNZh566KFBNZPOYDBw5513EhwcjE6nQ1EUZ9kzcTlJExMTg8ViISkpiaFDh2IwGHjjjTdcHZpb0Gq1/OlPf6KyspIzZ86wa9cuPvvsM1eHJYRwYxaLBY1GQ3d3t8dci3xfWVlZpKWlERQUhEajcXU4LqUoCpmZmTzxxBNER0ezYcMG8vLynBOXNBoN3t7ePPLII/j5+bFmzRqOHDlyxT2rp1AUhbS0NObNm8fcuXPp6uri8OHDdHR0OI8lh8OB0Whk1KhRGAwGDh8+7PGTLdra2njllVec90xXm6Czb98+goODWbp0KTU1Nbz//vusX7/eo8t+fZuUlBTmzp2Lw+EgLy+P1tZWSUII4UbKysr48Y9/3O9/d9AnIX7+85/z85//HLg8iPxf//VfzgEYuNy74J/+6Z9cGaJbmz9/PkFBQZw9e/aqg3heXl6EhoY6a9N/9tlnnDx5clDWrtNoNAQHBzNlyhQuXrzIihUryM/Pd65i0Ov1LF26lAULFmAwGJwzKnbu3MnWrVvJzMzk2WefJTs7G1VV6e7u5quvvvLIZYm33XYbEydOxGKxUFlZyfbt251JQLPZTGRkJGPHjnVuX15eTk1NjavCdWubN2++oh+Er68vBoOBvLw8NmzY4NE3/U1NTRQUFNzQigYfHx/i4uKc/SQG0zlqNpudv3mqqpKfn8/evXtdHJX7MJlM3H///YSHh6PX69Hr9Xh7e7s6LLeg1WqJjIzEbDYzZcoUxo8fT3BwsCQhhBDf6l/+5V+Ijo5m+/btvPPOO64OZ0CYMWMGISEhWK1WIiMjPbrBcmBgIPHx8cTFxWEwGEhJSaGgoMCZhDAajSQkJJCSkgJAdXW1R6/QCwgI4Ac/+AEzZ87E4XBgt9s5c+YMM2fOpLS0lKKiIhobG8nOzmbs2LHo9XpOnDhBfn6+q0N3ubq6uu/cpqfJ8htvvMHJkyclAfEt9Ho9Op2O2tpa/vjHP3rcpEshxNUN+iTE39LpdDz11FMYDAYUReH48eMyu/EatFotY8aMQa/XU1paSkVFxRUXvw8//DB33nkn48ePdz730ksvUVRUNCiXDXd2drJ7926mTZuGzWajoqLiivJBX331Fb///e+ZO3cufn5+HD9+nKeeeorm5mYiIiKcs9IvXbrEqlWruHjxosfNCBg9ejRPPvkko0ePprGxkd27d/dKWsXHxzNr1iwyMjLQaDSsXr2aDRs2DMrVNTcqKiqKSZMmMW7cOOdzZWVlzgSNVqtlwYIFzJkzB4fDwYEDB9i8ebOrwnULGzZs4OjRozf031itVry9vSkoKBhUN/2JiYk888wzzn+3trayZ88e1q5d68Ko3IvFYuGf//mfnatDzpw5I0ma/2E2m1m+fLkkaK7T888/z4IFCygoKODgwYO888471yw5KMRgFhMTQ1xcHKdPn5YGy9epZzLJ2bNnWbt27aC6FrlRs2bNYtKkSVitVqqrq9m2bVuvY8jX15e5c+c6/33o0CFyc3NdEarLmc1mfvKTnzB37lxn7ziDwcBPf/pT7HY7nZ2dtLe3093djclkcq467+7ult+n6xAQEMDixYsBWLNmjUc38r4eX3zxBevWrUOj0dDa2joox4eEEDfOI5IQPeVeli9fjtFoBOD8+fPs2LGDjRs3ujg696TX63nssccwmUzk5+dTXV19xQXw9OnTmTx5Ml5eXtjtdv6//+//o7a2dlD/wLS3t1NYWOhcyfBN3d3dzudPnjzJqlWraGpq4oc//CF33323sxdEZWUl//mf/0l7e/ugKvXybXoa4j711FPExcWh1Wppa2ujqKiIadOmUVlZiV6v5/bbb+e+++5Do9GgqioHDx6ktrbW45I1VzNixAjuuecekpOT0Wg0vPPOO2zevJmSkhIURcHLy4snnniCoKAgNm3axIEDBzyq6bnRaCQkJIShQ4c6nysrK7uhGXGJiYlkZmYSERFBfn7+oDo/NRoNJpPJ+e+mpibOnz9/S2a/9dQeNhgMvPzyy9/7/VwhJiaG+++/33md0NbWxpEjR/j6669dHJl7MJvNPP74484Ezfnz5zl58qSLo3JPgYGBzh5QycnJDB8+nBUrVsggz0267777mDFjBsXFxZw+fZrVq1fLvhxAAgMDaWtro6GhweNK335TcHAwkZGR6PV6Dhw4cMXrGo2GyZMnk52dDcDx48fZuXNnf4fpNtLT01m2bBnjxo2jvb2dY8eO0dTU1OvazGq1MmrUKBRFYffu3VRVVXnsPYNOp2PixIkYDAYOHTrE8ePHe/VoHDZsGMOGDSMuLs753PHjxzl48KD0NfgOQUFBJCcno9PpKCoqoqmpyeO/z77L346LCCFEj0GfhNBqtSQlJTF9+nTuvvtuAKqqqtiwYQOrV6+WDPY1aDQa4uPjnXUkz54967zg0+v1zJgxg/T0dPz8/Ghvb+f8+fN89tlng77+pqqq3zmDKy0tDS8vL86fP8/u3btRFIUHHniAtLQ0LBYLRUVFbNu2jXPnzvVT1K6nKApms5l58+YxefJkfH19AfD29mbChAkkJydz6dIl7HY7w4cPd/bYUFWVS5cuyaw5cA6uDx8+HIvFgqqqbNq0icLCQtrb2zEYDISEhDBmzBhMJhMlJSWUl5d71I1Yzz5KSkpCo9Gwfft2Dh8+fEMNzdPS0khKSsLb29vZV2OwDnadPn36ikaFNyssLIxx48ZhNpsH7D4zm829+vu0trZSUFDAmTNnXBeUmwgODmbmzJlER0cDl1cGnjp16oYavnuSnkEePz8/TCYT3t7eHl/X/WZ5eXmRmprK9OnTaWlpYdiwYaxfv35Afse4i+zsbIYNG0ZNTQ2lpaUcOXKkTyYQKYpCfHw80dHRVFVV0dXVNagS+zcjKSmJhQsXEhgYyIULF6itrXXuE0VRMJlMLF26lOjoaE6dOkVOTg4XL150cdSuYbFYWLx4MZmZmfj5+XHx4kXOnz9Pamoq9fX1XLp0CaPRSHx8PBkZGQAcOXLkukrqDFZdXV18+eWXGAwGSktLKSgo6LU/Dh8+zKxZs7j99ttJSEigvb2d999/n6NHj3rUpKWbkZCQwJQpU1BVlaKiItra2jzqHksIIW6VQZ+E8PPzY9y4cdxzzz0MHz4cuDxDff369ezfv18GN6/B4XBw6tQpGhsb2bx5M2fPngUuz7BISUnhkUceISoqis7OTioqKli9ejXHjh3z+Gy3r68vaWlp6HQ6ysvLKSsrIyUlhXHjxuFwOGhububQoUOsWbPG1aH2q55Z+suWLSMsLIxLly7R2tpKV1cXwcHBBAcH4+vri8ViwWKxoNVqUVWV+vp6qqur5TwFZ73b4OBgHA4HFy9e5OTJk86bBpPJRHJyMkFBQcDlPhqeVBPXarUybNgwpkyZwpAhQwD4/PPPycnJob6+/rrfJyYmhrCwMFRVpbOzc9AMHPasguhJAAKcOHGCkpKSW/L+VquVoKAg7Hb7oNlnpaWlXLhwgerqaleH4nLBwcFMnz7d+e/W1lZOnTrFsWPHXBiV+5o2bRrp6emYzWYcDgctLS0eP/h6s2JjYwkNDSUwMJCYmBiioqLQ6Vxz+xIbG4vJZKKhoWHADgwbDAYmT57M8uXLuXjxIjk5OZw4caJPkhAajYaxY8cSFhZGW1ubsxzuYDoXIiMjCQ0Npa2tjcbGRioqKq75+fR6PcnJySxYsIDw8HD+9Kc/UV9f36vBsr+/P/Pnz8fLy4szZ86Qn5/vkdfAer2ezMxMFi9eTHBwMKqqOhtQL126lIqKCkpKSrBYLIwbN46oqChUVeXChQvOXn2eqLOzk7feegu4vHr/m5MD8/LyUBSFjIwM4uPjycvL4/PPP6e8vHxQVzK4FSIjIxk1ahRdXV0cPXqUtra2QfVdJoQQ/WVQJyE0Gg0ZGRnMnDnTmbluaGhg7dq15OfnD/pZ+99HR0cHzz77bK/ntFot/v7+/OhHP2LhwoVYLBYqKirYuXMnv/nNbzy+2ZBWq3U2+KqsrKSuro7IyEief/55HA4HNpuNnJwctmzZwr59+1wdbr9SFAW9Xk9aWhplZWVs2rSJU6dO9RrcW758OVOnTsVkMjnLXe3YsYP9+/ff0CDyYGQ2mxk+fDjx8fEYDAY6OztZuXIllZWVzsSfj48PkydPBi4vfz19+jRFRUUujLp/JSUlsXjxYpYsWYKqqnR0dLBr1y7nsaMoClqtFkVRrpks1ev1zmRYfX09a9asGTQ3/1arlaioKIYNG4aiKLS2tlJaWnpLZgxqtVq8vb3x9vYmNzd3wO4zrVbba3Bz586dzgS86K2uro7z58971HfM9TKbzSxatIjU1FTnd9GmTZtkgOcmTZ8+neHDhzv7j5jNZpfF8uSTTxIVFcW2bdv4y1/+4rI4vo+QkBACAwMJDQ0lNTWV4cOH88tf/pKOjo5b/rd6SgsZjUa8vb3x8fFBr9cP2N+Ib1IUhaVLl/LII49w7tw59u/fz2uvvXbNfRkUFER0dLSzHFNERAQnT57s1WA5Li6OmJgY4HKDZU+c1a/RaPDx8eGZZ54hIyMDnU5HW1sbZrOZe+65B7i8Utpms6EoCgaDAa1Wi81mk7rzfHdzZa1Wi16vx26389Zbbw36Usq3it1up7W1leLiYj788EMZRxJCiJs0qJMQaWlp/OxnP2PixInA5dkBPbOIxY3z8vJi0qRJPPLII87nTp8+zapVqzx+kBgu3zw8//zzmM1m5wqI0aNHc8cddwBw6tQpfv3rX/P111/T1tbm4mj7l91up6KighkzZmCz2aivr7/iJvTtt98mMDAQVVVxOBxUV1fz6KOPygxS4Oc//zkPPvggkZGROBwOOjo6+PGPf9xrGy8vL8aNG4eiKKxbt47KykoXResawcHBBAYGYjQa6erqYsWKFZSVlTmPM29vb0aNGoW3tzcbN2686iDIbbfdxty5cwkNDeXgwYN8/vnn/f0x+kxycjLTp08nLS0NRVH4zW9+wxdffEFZWdn3fu/MzEzGjRtHXFzcgG0GabVaiY6OZsyYMc7nSktLuXTpkgujcl9r1qzh1KlTrg7DLf3iF78gLCwMuJwQrqqq4q233pLyQTdp+fLljB492rk6zZX9IKKiooiPjx/QDZZvu+02xo8fj7+/P3C50aqiKH3ytxRFwd/fH61Wy65duwbdCvTg4GACAgIIDw8nIyODSZMm8dZbb10zCTFr1iwmTpyI1Wrl4sWLV22wPGfOHOe/jxw5MmB/U7+PnrJUs2bNoqGhgQ0bNlxRlmrJkiXMmDGD0NBQ533D9u3b2bZtGzU1NS6M3v0lJiYyffp02tra+Pzzz/skATkYrVq1ilWrVrk6DCGEGPAGdRLi3nvvJTk52TlrSpIPNy8wMJApU6bw29/+1nmz8sADD7B27Vq5ePkbJpOJpqYmNm/eTFxcHAsWLHC+9vHHH5Obm+txCYgeqqo6e7D0JBV6Zju99NJLzj4HABUVFbzyyisen4BQFIWAgAB+8IMfMGTIEFRVpby8nHfeeYdFixZRUlLCuXPn8PX1ZeLEiWRlZQGwe/dujxo8ffHFF1m8eDEJCQnA5SXoP/rRj3o1fo+MjOSnP/0pw4cP5/bbb7/iXDSbzfzwhz8kPT2d06dP8/nnn9Pc3OySz3OrDR06lEcffZT77rvPuT/Wrl17y46RMWPGkJaWhtFodJYrGWi/Cz0159PS0tBoNLz88susWrXqlpWr+jYRERE8++yzBAQE8Pzzz9PQ0NDnf/NGWCwWYmJieiVoiouLPXKG7o3q6uri4sWL7N+/X65Bb8JLL71EZGQkADabjerqat566y2Xlf4MDg6msbHR2d9gILr//vsZN24ccPn43LBhw03tz/T0dEJCQmhvb2f//v1XvO7r68usWbOYPXs2tbW1bNmyhZycnO8bvluZPXs2EyZMwN/fH0VRCAwMvGZCZ/To0Tz++ONMmDCBpqYm9uzZc8U1rtVqZfz48c7JJH/bUNhTPPbYYzz44IOcO3eO//7v/2bDhg2Ul5dfUX9/w4YN/PjHP+auu+4iPT2d6upqHnvsMaqqqmRW/7dITU0lNjaWjo4Ozp49KyWFhBBC9LtBnYRYsmQJISEhOBwOLl26xLp16+SH9iYlJSUxa9Ys5+w+gObm5kEzSHcr9MxOT09PZ968eYwbNw6DwUBbWxuLFi2ioKDA42fn/O35p9VqiYqK4t577+Wuu+7CYDA4X6uvr2fDhg0efb4qioK3tzdPPvkkPj4+aDQaVFUlMDCQ++67j8WLF9PU1ERDQwNarZbQ0FBnKau2tjaPuglbtmwZ0dHRmEwmKioq+OCDD3olGCwWC2FhYaSkpBAYGEhCQoKzqRxc3tcREREkJyfj5eVFY2Mj5eXlg+b4GzJkCCEhIXh7e9PV1cWWLVsoLy+/ZYNoXl5eWK1Wmpub2bp164AbnEtMTOTOO+/kjjvucJ5nmzdvpra2tl8Gjk0mE0lJSQQGBmI2m2lsbHSrYy8+Pp4xY8aQmJiIRqPhL3/5Czt27BiwNfH708WLF9m0aZNbrYLQ6XQ8/fTT+Pj4sHLlSvLz810d0jWZzWZnj5nu7m5qa2s5dOhQv/++KYpCVlYWSUlJFBcXu9X5eSOeeOIJYmJi0Ol0zlWpn3766U0lIebMmcO0adNoamqivLyc0tJS52tarZaIiAgeffRRfHx8+Pzzz50DnoPJggULGDVqFIqiYLPZ2Lt371XPdV9fXx577DESExPRarW0t7dTWFjI5MmTqaqqorS0FIvFwogRIxg2bBhwuYGwp60y9/f3Jzg4mPj4eJKSkhg6dCjvvvsuDQ0NV5xz3d3ddHR04HA4qKur44MPPqC6utqjrn2/zfPPP09UVBSlpaXk5eU5exHOnDmTsWPH0tnZSWFhIR0dHQP2+0wIIcSVzGYzr7/+OkVFRRQUFHD06FG3W1U5qJMQzc3N2O12ampq2LNnDytWrJAf2puUmJjIlClT0Ol02O12jhw54lEzra+Hw+Hg6NGjJCcnk5iYSEREhPP57du3uzg69+Pn50dmZiZ33XUXYWFhztljbW1tVFdXO1dNeCKNRsOQIUOYOnUqd911F3q9ntraWs6fP9/rRj8xMZGUlBTMZrOzln1hYSFnz54d9I35FEXBbDYzffp0oqOjsVgs1NXVkZOTw+rVq3ttGx4ezsiRIwkMDKSzs5Pq6mo6Ozudr2u1WkaNGoWvry9arZaamppB0wtg5syZLFiwgOTkZBRFoaOjgzfffJOGhobvHGA3Go2Ehoai1+spLCy86s19YmIi6enp+Pn5UV5eztatWwfcjO/Q0FCSk5OJjo529lO5cOFCv63m0Ol0BAUF0d7e7nb7LjQ0lOnTpzNz5kznarX169dTUlIy4Fa79LWe76To6GhnUr2pqcntylb1NAsOCgri66+/pqCgwO2Ou6tpaGjg0KFDNDY29vvf1mq1jB8/Hj8/PxobG/Hy8kKr1Q64Ac+EhATn6nCbzUZdXd01B86/jZeXF+np6YwaNYra2lrnYGcPs9lMREQEWVlZaDQazpw5Q319/YA4zq7X9OnTnb99drudlpYW1q1b1yuh01NWaO7cuUydOtVZAstqtTJmzBji4uKora2lqqoKg8FAamoq/v7+qKpKbW1tr+sUT5CWlkZiYiL+/v6YzWa8vb1xOBzXvHePjo4mODiYhoYG1q9f71bJXlfy8fFh+PDhjB07loaGBs6cOeNMQoSHh+Pn50dtbS3bt28fcN9hrjJv3jxCQkKora2loqKCo0ePujokIYS4Qk8P3ylTpjBq1CiKioqw2+2ShOhPq1evpqamhoqKCjZu3CgDwd+Dn58f4eHhqKpKSUkJH3/8sUcPEn+bOXPmEBUVhV6vp6OjwyOXU38Xo9FIamoqM2bMYNSoUcDlwRqLxeKcVedpN19/y2KxkJKSwoMPPsiIESNQFIX8/HzWrVvXq6n5lClTWLRoEcnJyej1etrb21m7di2nT58e1EkIRVHw8vIiJSWFJ5980rni6OTJk2zatKlXyQeLxcLIkSOZPn06ZrOZ4uJizp49S2trq3MbjUbDuHHj0Ov1NDU1UVpaOmga7j788MNMnTqV4OBg2tvbKSgo4Kuvvrqu/9bHx8f537799ttXJC40Gg0zZswgKysLnU7H6dOnB1y5jdjYWIYPH05oaCharZbW1lY+/vhjLl261C8350aj0Tn789ixY3R1dbnVZInY2FgmTZrE6NGjsdvt1NbWcuzYsV7nj7isZ3VfRkYGZrOZuro6CgsLKSwsdHVovSiKQlhYGAaDAb1e32f9AL4vvV7vTAzD5Warf/v7158URSEzM9PZzNVut6PRaAb0AF57ezvnz5+nuLj4hv/bhIQEoqOj8fX1pa6urtdKVrg8oz0+Pp6goCAAioqKBt13xm233UZAQABwue9ZfX09mzdvviIJYbVauffee4mIiKChoYHW1la6urqIiIggIiICb29vzGYzer0erVaLRqOhoaGBmpoaj7sOnjhxIsOHD8dsNqOqaq+Smt/k5eVFYmIiwcHBlJSUcOLEiX6O1n31nHthYWHExsb2qmJQWlrKkSNHaGtrY8uWLS6McuAwGAwsXbqUkSNHUlZWxvHjxyUJIYSLaTQaRowYQVtbG62trTQ0NEiFFi5PAklOTsZisRAZGUl0dDSHDx92dVhXGNRJiJdfftnVIQwa58+fZ9euXUyYMIF33nmHN998c9DdUNwqs2bNYsiQIXR3d1NSUsI777zj6pDcTkxMDHfeeWevJuc5OTlkZGRw6dIlioqKPO7mq4eiKERHRzN16lTmz58PXF7VtW3bNtauXdvrRmvHjh10dHSwbNky0tPTqays5N/+7d9obW11q4HMW81gMJCcnMyzzz7LggULUBSFvLw8Pv30U1asWNGrzFJaWhoLFixg/vz5dHV1cejQIdra2lAUBUVRUFUVg8FAVlYWBoOBgwcPkpeX5+JP+P31zMC84447sFqt2O12CgoKeO211677PcLCwnjiiScYMWIE+/bt4/jx472SWxaLheXLl5OQkMCRI0fYuHHjgPtd+NGPfsTChQsJDw93lnX4z//8z377+2FhYc6m3sePH3erAWGj0UhERAQBAQHo9Xra2tr49NNPqa6udpsZpyaTCUVR6OzsdOks657BxlmzZpGUlITRaGTDhg2sWLHC7RJzOp2OkJAQ8vPznSuG3Y1GoyEoKIiRI0diNpux2Ww0Njb2SUJHo9E4z7tr7QuDwUBAQAAajYYDBw5w/Phxl/WluFmKojhXTAJUV1ezdu3aG34frVbr7MGkKAqVlZUcOnSo1zZRUVGMHj0auLzi4sCBA4N69XR3dzcXL17k+PHjvZ5XFAW9Xk9mZiYVFRVs2bKFEydOUFVV5dxm4cKFzJ49m4iICGdia+fOnezbt8+j+u4YjUbmzZvHyJEjUVUVm83Gxo0br3mejRgxAj8/PxoaGigtLZWVeX/j9ttvJykpybl60WKxOF97/fXXef31110Y3cATHh6Oj48PcXFxZGRkMHz4cF588cVBfZ/Vl0wmk3Mlod1uH3C/pf3Jy8sLu92Ow+HAZrO55fWaq1gsFj766CPy8/PJyclhy5YtfP31164Oy+UCAwNZtGgRgYGBwOXz7ZsTRdzBoE5CiFtn/fr1rF+/3tVhDAgbNmxg/vz5XLhwgRUrVvDGG2+4OiS3M3fuXLKzs/H29nZexJlMJtra2tizZw+ffPKJiyN0nfj4eB577DF+8IMf9HruWjejPYPplZWV/Pd///egXgHRIyYmhttuu4377rvP+dy6devYu3dvr1kQAQEBPPnkk8yYMcN5AZebm8ttt91GWVkZhYWFNDc3M3HiRMaNG4dOp+P48eMUFBS44mPdMj0DeP/+7/+OXq9HVVUKCgpYs2YNX3zxxXW9h7e3N1FRUSQnJztnVZw7d855fGk0GhISEkhJScFqtdLY2DggV8c99thjWK1WVFUlNzeX3/72t/369+Pi4pg0aRIajYa4uDgsFst1lcrqD7/61a9YsmSJs7RgY2Mjzz77rIuj+n/0ej3/9V//RWBgIL/97W9dOtMnMDCQyZMn8/LLL6PT6XA4HJw4cYIDBw64LKar6VndlJ6ezoULF1wdzjUZjUbmz5/PsGHDMJlMrFmzhnfffZfdu3ff8r+Vnp5OWFgY7e3tV31/Pz8/5s2bx5w5c6ipqWHz5s0DbhZsT9PkCRMm4OPjA0Brayvnzp27offRarVMmDCB5557Dh8fH/Lz8zly5MgVyefw8HCGDx+Ow+Hgs88+o729/ZZ9FndUWVnJBx98cMXzdrudixcvMnXqVGcPjm/2TPrqq694/vnnuffee8nMzKS6uppHHnmE5uZmjxrkfPHFF0lISABwrrr705/+dM1j5x/+4R9ISEigrq6OCxcuDPpj7EY888wzBAUFoaoq9fX1rFu3ztUhDWhLly4lMzMTb29vAOcKKHFz/vu//5sRI0aQn5/PwYMHJSl2DSaTiSNHjpCbm0tOTg5bt27tk2uggchgMBAZGYnZbGbOnDlMnDgRh8MhSQggMjKSZ5991nn9sG/fPrcrCwuShBDilvvxj3/MT37yE+x2u8fO5v8uc+bMcc52amtr46233uI3v/kNnZ2ddHV1efTNxG233cbYsWOdF7vAt96IZmdnk5GRwcmTJ6/ohTAYxcbG8uijj/Lggw86Z68mJSVx8eLFXueb2WzmhRdeYPbs2c6l6EajkX/+53/GbrfT0dFBe3s73d3dzlIIAF1dXQN6Vo5eryctLY0nnniC+++/H71ez9mzZ3nzzTf561//et1JqmHDhrFw4UL8/f1pbGxk165dvRJhWq2WefPmYTQagcvlNvbu3dsnn+lW60nS/Mu//AsGgwFVVTl79izr16+/7lJVt4rJZHLWvf7oo4/cJgGhKAqPPfYY3t7eaDQacnNz3e5GUVEUYmNjCQwMxM/Pz9ls1xXMZjORkZHOGafr1q3j0KFDNDQ0uCSea/H19eW2224DLs9Wd/V+uxp/f3/Gjx/Pr371K/R6PQ6Hg9zc3D5L6Nx9993Mnz+fhoYGnn766V4D8zqdjtjYWJ577jnMZjMff/wxZ86cGXCzro1GI3PnziUzMxOr1cr27dt5//33b2hAQ6fTERoayksvvYTJZHL2LWhoaGDhwoUUFRWRl5dHYmIi48ePJyMjA7vdzvbt2wfVtbCiKPj7+zNu3DhnQqetrY3z589fdXtVVamsrERV1W+9llMUhaqqKn73u995XALim7q6uqiurubAgQPX/G4ymUx0dHRw4MABVq5c2c8Ruiej0ci//du/OX+Hurq6KCws5N1333VxZAPb3/3d3xEdHQ1cnoyxefNmjz4/v4+wsDB8fHxITk5m6NChTJgwgTfeeEP25zfo9XrnIPusWbMYN24cgCQh/kdQUBDLli0jJCQEjUaDt7d3rxVfnmratGm9qow0Nzezdu3aK1arugNJQghxi3nCTPTvKz8/n9TUVKxWK2vWrOGPf/wjVVVVbjH45mrTpk0jIyMDuHxj+9VXX10xc65HamoqAQEBtLW1UVZWRlNTU3+G6hKTJ08mKyvLWWsa4NKlS84STD10Oh2TJk1Cr9dz+PBhTp06RWVlpfP1oUOHMnToUGJiYpzJjJMnT3L48OFeDTYHmrCwMCZMmMCSJUucCYJdu3Zx5MgRamtrr+tCPzY2ljlz5rBw4UIAjh07Rl1dXa/BAK1WS1ZWFnq9nlOnTnH27NkBkbzR6XQkJCRw5513ctddd6HVaikpKWHlypV8+umnt2zQWKPRkJ6ejtVqJS8v76rNdNPT08nOziY1NZWKigrWrl3r8sFNjUaDv78/Dz30EFarFY1GQ0lJCbt27WLDhg0uje2bFEUhODiY6upqWlpaXLZMfdKkSSxYsIDZs2c7n3v77bfZt2/fNb+7XUWr1RIYGIhGo2H37t1UVla63fL+noROz1LyvXv3kpOT0yelaQICAoiPjycmJgaTyURsbGyvJISXlxfR0dGkpKSgKMqA7G3g5eXF8OHDefbZZzGZTACcPXuWgwcPXvd3tlarJTIykocffphRo0Y5yzqlpaURFBREW1sbTU1N1NbW4u3tTXx8PAaDge7ublpaWgbVAJNOp2PixImkpqZisVjIyclh5cqVHDly5Jr/zXdd22ZmZpKQkEBpaSkbN24cVPvrZvTM3v+24/MXv/gFXl5e1NXV3VRfk8FIURTnxAGAjo4OLl68yLFjx1wc2cCk1+t57LHHCAwMRKvV0tXVRXl5+XWvKBZXmjFjBklJSfj4+KDRaAgNDXV1SG7J19eXOXPmEBgYiNFoxGAwOJPeAoYMGcJDDz3k/K7Lzc1169W9/cVgMGA2m53/bmxs5NSpU27Zn1aSEEKIfrd27VpKSkowmUwcOHDghksCDGadnZ10d3fT1NTE4cOHeffdd685kDV79myGDBniLIUzmGYbXsvEiRNJSUlBq9XS2dnJkSNHrjqI1t3dzaZNmzAYDBQVFXH27NleNamPHDnCrFmzmD9/PjExMXR2dvLXv/6V48ePX3XAeCDw9/dn4sSJzJ8/n/DwcABeffVVNm7cyNmzZ69rsNFsNjN16lSys7OJiIigs7OT/Px8oqOjMZvNNDY20tXVRXR0tLNRa15e3oBp5B0QEMDIkSO58847CQ8PR1EUjh49yt69e8nPz79lA7I6nY7bb7+d6Oho3n33XU6cONErUdYzkJWdnY3JZGLbtm0UFRW5dEa6RqMhLCyMKVOmsGzZMrRaLbW1tWzfvp21a9e6VXLOYDAQFxdHZGQk5eXl2Gw2lw3cjRs3joULFzpr5G/fvp0TJ070ew38iIgIjEYjjY2NV/3b/v7+pKSkkJycTGNjI19//TVVVVVuNeCZnJxMdnY2s2bNct5crl69mmPHjvVJgi4rK4vY2FjMZjPt7e3U1tb2ej0oKMg52Axw5syZAff7YLFYiI2NZejQoWg0Gs6dO8eZM2duqHyeVqslODjY+f/LoUOHqK2tdQ4S95TnGzlyJHq9Hp1OR3d3N0VFRZw7d86tVtp8H0ajkdjYWO69914CAgLQarXk5+ezc+fOm06ShYWFERYWhlarpbq6mrKyslsctfvrSTz2JMlaW1u/s3yEu/XacUeVlZWcOHHC7VbkDRSKopCSkuJMunZ1dVFVVcX+/ftdHNnAtXDhQmJjY533cAPl3qG/+fn5ceeddzonk1VVVV1xfeKpoqOjmTRpErGxsaiq6uz3OBj6Od5qR48epaKiwi0rjEgSQgjR77Zu3crWrVtdHYZb2rlzJ1qtFrPZzFdffcWmTZuuue3UqVPx8/NzDrIPhJno31dUVBT+/v60t7dTVFTEihUrrpqk6ejo4LXXXkNVVdrb26/4AT516hR2u52kpCSio6MpKCjgo48+oqKiwu1mBl+vpKQk5s6dy/Tp053Pvfjii9e9Okuj0ZCcnMz8+fMZOnSoc3BSq9WyYMECqqqqKCsro6WlhREjRhAbG4tGo6G0tJTq6uo++Uy3kslkIiMjg2nTpjFq1CgADh8+zIYNG8jPz79lSTxFUbBYLCxatIj09HROnDhBaWlprySEl5cXEydOZNiwYbS0tPD111+7fBWE1WolMzOT5cuXM3r0aBRF4cyZM6xfv57t27e71ax+q9XK2LFjCQ0NxWKxoNPpnI3m+4tGoyE8PJwRI0Y4S8/U19fzzjvvuKQJ7/jx4wkNDSU3N5e9e/f2Op4VRSEuLo6ZM2eSkpLCqVOnOHz4MPX19f0e57eZMGECDz/8MFlZWSiKQnFxMevWreuTm0tvb28WLlxITEwM3d3dlJeXk5+f32ub8PBwMjMzAairqyMvL69X3yF35+/vT2JiojNhDLBlyxaOHj16Qys6VFXF4XDQ0dHB3r17Wb16NSUlJc7vNK1Wy4wZM3jggQcIDg5Go9FQXV3N+vXryc3NHTRJCKvVSnp6OkuWLEGn01FfX09BQQFnz5696fccN24cAQEBNDc3U15e7hGTSf6WRqMhIiKCjIwMLBYLTU1NFBcXX7O8lbi6nsbz3t7eztW9JSUl37pCR9yYxsZGCgsLZeXNTVAUhejoaKZOncqQIUNwOBw0NjbKWMBVeHt7k5qayrRp01BVFbvdzrFjx77X78xgkpCQwKRJk5z/bmlp4eDBg1dcv3manrGjvy1LtWfPHpfcj1wPSUIIIYQbeeutt3jrrbeua1uHw0FdXR379+/3mMbx+/btY8iQIRiNRt57771vbfz+XT+8Go3GOWPz9ddfp7a2dsAmIABmzpzJ8OHDsVgsztkhN8JkMvF3f/d3ZGdn4+/vT1dXFzabjQceeAC4PBBls9lwOBzO2a49/TUGwsBJbGws999/P3fffbfzuenTp19Ryuv76mmYFh8fj9lsJiQkBD8/v17LYaOjo4mNjcXf398tykkoikJ8fDzTpk1j7ty5qKpKa2srGzZsuGIVhzvw9vZ23oQEBQVhtVrRarX9Otjp4+PD3//935OVlYXD4aCtrY1t27axfv36fi+NpygKDz30EKNHj+bLL7+ksLCw1wxDo9FIVlYWd911Fzqdjk8++cTtvu8MBgOjR49m2rRpOBwObDYbv/vd76iqqrrlf0un0zFu3DgefvhhfHx8yMvL49SpU3R1daHRaHA4HM6VQWlpaTgcDjZs2DAgvuf+1rRp03jooYeYNm0aiqLQ2dnJu+++e8P9Nbq7uzlx4gQPPfQQdrudmpqaKxJ+W7ZswdfXl9tvvx0/Pz9yc3N58cUX3e6742ZptVp8fHyIiYlxzk7dvn07hw4d+l6rY+69916ioqKorq6msLBwwB1j35fRaGT27NmkpKTg5eXFli1beOeddzh8+LCrQxtQdDodwcHBZGVlOa9ra2trPXJlza2iKApardb574KCAhk0v0k6nY4f/ehHeHl5AThLW61cudKtVmO6g6ysLO6//37nv1taWtixY4ckFK+htraWvLy8G1rdORj5+PgQHx9PamoqcPkcu3Dhgtteg0kSQgghBqh77rnH1SH0u1/96lf86le/uiXvlZKSwvTp02lpaWHlypUun4n+fS1evNi5gqGxsZE//vGPN5SI0Ov1zlUUGzduZNeuXb1qbE6bNo2pU6eSkZHhvGnYs2cPW7ZsoaCg4NZ+mD6wZMkSRo8ejZeXV5/e9ISEhLB8+XICAwNpbGzk0KFDV5ScmzlzJiEhIQA0NDS4vN9CUlISzzzzTK8ETUhIiFsu4YXLN7T+/v5oNBo+++wzzp8/328JiJ6VLv/7f/9v7r33XgIDA6mvr2ffvn08/fTT/T7rSFEUIiIiSElJISAggNDQUOLi4nolIUJDQ0lKSiImJsbZrNSdEhBms5kXXnjBmYDo6Ohg27ZtfPTRR7d8f+p0OiIiIvjlL3+J2WxGVVVqampobGxk0aJFFBYWcurUKVJTU8nOzmbo0KHYbDa2bNky4H4jJk6cyJIlS5w9CX7+85/fdMKzq6urV1+lq1EUBUVROHToEG+//faA65/xbebOnctDDz3Uq/fLK6+88r0bhZpMJtrb29m/fz8ff/zx9w1zQPH19SU7O5tf//rXmM1mHA4HZ86cYefOna4ObcDx9/dn3rx5ZGZmotFoePvtt3n//fclmXOTepI6kyZNwmAwALjFhJHBoqOjg/LyciltdR3q6uo4ceKElK66hg8//JCSkhJXh+Fy48ePZ/LkySQkJNDV1cUvfvELNmzY4L73ca4OQAghhOhvqampREdH09HRQUFBgdv+SN+I3bt3O+tU//Wvf+XXv/71DSUhmpqauOuuu4DLA+MNDQ29BnY3bdrEwoULeeKJJ5gyZQqNjY0899xzt7SUUV9asGABaWlpqKpKU1MT77333i0fuI6IiGD27Nn8wz/8A4qicODAASorK6/YP2PGjMHf358LFy7w9ddf39IYbsaCBQsYOXIkVqsVwKUz00aPHo23tzelpaVX7RcUGxvL/PnzmTZtGiUlJaxevfo7B0dvJaPRyIQJE1i+fDne3t4AFBcX8+mnn/ZJ8+TvotfrWb58OaGhoXR1dXH27FmOHj3aa5usrCzn7Ci73c6GDRvcYkBdURRMJhM/+9nPWL58OeHh4TQ1NXHkyBGeffZZLl269J1NfW+ETqcjMTGRZ599lhEjRjhrfY8dO5bhw4djs9loa2ujubkZg8GAv78/Op2Orq6uAfEd18NkMvH0008zZcoUHA4HXV1d7Nq1i5UrV/Zpkmzu3LmEhISwbt06tm/f3md/xxXGjBnDokWL0Ov1KIrCr371q1syIPnII4+g1+vp7Ox02xmLfcVkMhEZGeksH7F161b27dvnku/RgaznuuNf//Vfgcu/3/v37yc3N9fFkQ1cvr6+zJo1i4yMDAwGAx9//DErVqyQ2ei3SG5uLqtXr3Z1GAPCypUr3aonmyt5e3uTlJTE0KFDnc+582z//jJ69GieffZZxo8f76yEsHr1arcqo/tNkoQQQgjhcaZPn86oUaOcjdE6OjoG/JLgN998kzVr1gBQWlp63b0geqiq6hz0tdlsV8yU7uzspLm5me7ubmw2Gx988AHFxcVuMZh5PfLz852NzNavX8/rr79+S/uoWK1WJkyYwJIlS7Baraiqyvnz54mJicHhcFBTU0NlZSXp6elkZmbi4+PDmTNnOH78+C2L4WbNnj2bxMRE4HIyav369S6bKX/vvfeSnp7O9u3beffdd3v1G9HpdIwcOZI77rgDq9XKRx99RGVlZb9daFutVlJTU3nhhRfw9vZGo9Hw+uuv8+GHH3L+/Pl+/w6xWCykp6fz6KOPYrFYOH36NIWFhVec+0lJSURFRdHa2sq+ffvc5pzV6/UMGzaMu+++m9DQUHQ6HZWVlaxfv57S0tJbmoCAyyX4AgMDmTRpEs3NzXz99deUlpY694dGo2HChAmMHDkSg8GARqOhvb2dEydOcPjwYbe+oethNBp55JFHWLZsGcnJybS1tZGXl8fLL7/MxYsX+6R3lEajIS0tDS8vL+rq6rh48eIN//64K4PBwOLFi5kwYQJGo5Hu7m5ycnL46quvbklCx1ObBmdlZTF//nzmzZvnfO7jjz92u/5DA4G3tzdhYWEEBQWhqio7duzg7Nmz/V4WcLAICgpiwoQJPP300+h0OlRV5ciRI5w6dcojeu/dahqNBl9fX4YOHersTdTQ0CAz+6/CbDYTERFBQkKC87nz588Pmt/T7ystLY2RI0cSGxuL3W5nxYoV7Nu3z2N/R3uEh4cTEhKC1Wqlvr6enTt3UlFRccuvoW8lSUIIIYTwODExMQQEBFBbW8uuXbvcqjTJzcrPz//ejbm+a7ZvYGAg0dHRdHd3s3r1alpbWwdM8uaLL77g3LlzqKp6y5uY6XQ6srKymDlzJllZWaiqiqqqpKamEhAQQF1dnXNwLjExkcjISAwGAy0tLdTW1t6yOG5Wd3e3s7HyoUOH+mSVyPXw8vJizJgxZGRkUF1dTVhYWK8khI+Pj7PRrqIo5OTk0N7e3m/HYFBQEBMnTmT8+PFoNBrgcpP771uS5WbodDrCwsJYtGgRSUlJOBwOysrK6OrqIiYmhqamJmprawkLCyMlJYWwsDBaWlrcpvxBT++U+++/n7i4OHQ6HTt27GDNmjVs3769TwZ7HA4HtbW1bNy4EZvNxu7du7l48aJz0FOj0XDmzBmeeeYZkpOTMZlMVFRU8N5771FWVub2vxNarZaYmBjuvvtuZ1KgrKyMnTt3cuDAgT5bzaHVapk3bx4Gg4GSkhJqamoGxUCyTqdjypQpLF26lPT0dDo7OykvL+f9998fNCsoXWXYsGHceeedJCcnoygKu3fv5siRI1y8eNHVoQ0ow4cPZ+rUqWRnZzt/k/76179y7ty5QXEOuoKvr6/zOkNVVfLy8sjPz3eLa7WByGw2k5qaSkpKCnq9ntzcXA4fPizN568iKiqK1NRU54SpPXv2cPLkSUkoAmFhYdx2222MGTMGi8VCZ2cnq1evpry83GO/63Q6HZMmTWLevHkEBQWhKArV1dW8//77bn9/LkkIIYQQHqeyspKTJ0/S3NzMxo0bXR3OgGAymYiKiiIxMZG6ujqOHDkyoGaFrV27lrVr1/bJexsMBmbPnk12djbe3t5UVFTQ3t5OTEwMMTExGAwGjEYjRqMRnU6H2Wymvb2dhoaG79XU9FbZtm0bdrsdm83G6tWrXdKjQqPROBM0ZrPZuc/+Vnh4ONHR0QQEBNDZ2dmvvSDg/5W9sFgsOBwOLl265JK694qiEBQURFZWFnfccUev2U7Jycn4+vpSUVFBfn4+w4cPJzMzk4CAAEpKSsjLy+v3eK/G19eX0aNHs3z5cmdZpFWrVvH73/++z/6mzWbjwoUL/PrXv3Ym3b55k5aTk8PYsWMJDQ2ls7OTnJwc3n//fbcvx9Qz23TmzJnOWftlZWXs2bOHjRs39mm5Aq1Wy2233YZWq+XChQuUlZW5JIl5KymKQkBAAA8//DDTp08nMDCQ2tpaDh48yPvvvy+DQjdJURRCQkIYPnw4I0aMwG6309jYyHvvvdevZfUGi9tvv53FixeTmpqKqqqUlZXxxRdfSEmrmzRkyBCSkpJITk52ztr/6quvOHv2rNusIBxI9Ho9oaGhzJkzh4iICDQaDbt27WLz5s2yEuIbrFYr48aNY/To0QwZMoTu7m4++OADTp486fHlhuDyte2cOXMYOnQo3d3dVFVVcfjw4QF1H3qrGQwGnnrqKWbNmoWvry9NTU2cPn2aL774wtWhfSdJQgghhPA4r776Kq+++qqrwxhQUlJSiIqKoqOjgwsXLgyKEla3ilarJTk5GS8vL3Jycli7dm2vwd6UlBSmTZvGzJkzr5hBf+LECVeF7eQO54PRaGTZsmUEBwc7EwwnT57stc3w4cNJSkoCLjfK/frrr/v1GIyIiGDOnDkAtLe38+mnn7qk7rbBYGDixIk88sgjpKam0t3djcPhYObMmcycORNVVbHZbHR2dqLX67FYLCiKgs1mc5vZ2xEREdx+++34+vo64+2PpePd3d3U1NR86zY9SZHjx4/zySefDIgBAG9vb0aNGsUvfvELZ/LulVde4Xe/+12/xVBbW8v69esHRTPcnt4vS5YswWKx0N3dTUlJCV988YVbJI4HKm9vbx5//HGmTp2Kw+Ggs7OTbdu2sXbtWplpfoP0en2v1Zetra38+te/HhDfV+7qnnvu4a677iIrKwu4/HvxyiuvUFVV5eLIBqaQkBCmT5/Oj370I1RVpbu7m2PHjt3SlciDRWZmJo888gjZ2dk4HA46OjrYsmWL20+A6A96vZ7IyEh8fHzQ6XRUV1fz+eefU1NT49Ylh/qSoih4eXlx7733oqoqdrudPXv2sGLFCleHdn3U6wTIQx7ycNOHnKPy6K+HHGue+/jlL3+p5uXlqTU1Neo777zT539voB1rQUFBanh4uBoQEHDV1xMTE9WPP/5Ytdls6qVLl9TFixerRqPR5XG7w8PHx0edO3euqqqq6nA41J07d6oPPPDAFdv98pe/VM+ePavW1taqf/nLX27Z37/eYy07O1tdvXq12t3drb788stqaGioS/aX1WpVf/rTn6oVFRXq+fPn1ZdeekldtmyZunTpUnXp0qXqU089pa5atUq12+2q3W5XbTabeuHCBfUPf/iD6uXl5fL/vwH1jjvuUG02m2qz2dT29nb1T3/6kzp+/HiXxwWo5eXlqt1uV//whz+ofn5+t/S9++p7bejQoerbb7/t3Kc2m0398Y9/3K/7TVEUl/9/dyse3t7e6pQpU9SqqirVZrOpdrtd/Zd/+ReXx3WjD3f7DbVYLOpvfvMbtbS0VLXb7WpDQ4O6detWNTAwcNAcO/25L1955RXnvqypqVE/+eQT1cfHxyX70t2OtZt9rF+/XnU4HKrdblfb2trUZ555RrVYLC6Pa6A+UlNT1Z///OfO36QPPvhAHTt2rKrX610em7s9li5dqh45ckS12WxqVVWV+oc//EE1m8235L0H8vlpMpnUV155RS0vL1c7OjpUm82m7t271+VxufKh1+vVYcOGqe+8847zOn/v3r3qY489plqtVpfGdr1kJYQQQgghvpPJZMLhcHDhwgXefvttV4fjdnrKH3zbzHxFUVAUhTfeeIPTp0/LDCcu1wtOT0/n+eefd/bSKC4uxtvbm1mzZlFRUUFubi5ZWVmMGzeOyMhILl68yM6dO/s91sOHD/PII49gNBppaWlxWbPAtrY23nnnHdavX093dzelpaXYbDbnsafRaPjqq69wOBzMmTMHu93O6tWr+Y//+A+XlI+6mqqqKrZt28aMGTN46623eO211ygsLHRpTBqNhtGjR2MwGCgvL6eysnLAlOCIiori7rvvBi7P3v3iiy/Iycnp1xgGy8q48PBw7r77bvz9/Z3PDZbP5ip6vZ5x48bxwAMPEBgYCMDFixf58MMPr1oWTVxdT9m1F154gQceeAA/Pz+qqqrYsWMH//Zv/0Zzc7Psy5tgNpv5yU9+QnJyMqqq0tjYyJ49e1i5cuWA+Q1wNw888ABLlixh/Pjxzud++ctfcv78eY8uofNNBoOBf/3Xf2Xp0qVER0cDUFZWxs9+9jM59rj82/HYY49hMpnQaDTs3r2bv/zlL64Oy2UMBgMzZszg/vvv54477gAur6z/z//8T3bt2jVgVsJJEkIIIYQQ3+mdd95hw4YNdHZ2XlEmR/CdS4K9vLyYMGECAFu3bu3VcNlT6fV6Ro0axdKlSxk5cqRz8GTy5MlkZGTQ2tpKc3Mz1dXVBAcHk5mZicFgwG6309zc3O/xdnV1cenSpX7/u9+kqiq1tbU0NDTgcDiu2pTPbrc7Sy99/fXX7Nq1i+rqarcZoDpz5gwvvvgif/jDHygoKKCoqMjlzQX1ej3Lly/HZDJRVFREdXW1y2O6Xs3Nzc5k3Zo1a/jzn//M8ePHXR3WgBQaGsrChQvRaDTY7XZ27tzpNr1UBiKTyURCQgIvvPACAQEBaLVaPvroI95++23y8/M9tpzGzbBarQwbNoy7774bX19fNBoNBQUFbNu2jdLSUrf5fh8oFEXBarXy4IMPctdddxEaGkp9fT1Hjhzht7/9LbW1tXJ83qRp06YxZcoU/Pz8sNvtvPPOO1y8eFESEN+g0+l44IEHCA8Px2AwcPr0aVauXOnxZf+0Wi0RERHcddddWK1WVFXl3Llz7NixwyWTkNxFfHw806dPZ/r06VgsFgA2btzIqVOnaGhoGDC/AZKEEEIIIcR3On36NKdPn3Z1GAOSl5cXERERhIeHc+nSJYqLiwfMbJW+pNPpSE5OJjs7G41Gw6FDh6irq8NutwOXB6/i4uKYNGkSWq0WvV5Pc3MzJSUlHt/U0GazfWvzX41GQ3JyMlqtloMHD3Ly5EnnfnUH9fX17N+/39Vh9KLRaEhPT8fhcHDixAkKCgoGzABUcXExb731Fvv27WPbtm0cPnzY4wcxblZPfWWAY8eOsXLlSkm8fw9+fn5kZ2czceJEtFotAHl5eWzdutXFkQ0sFouFpKQkli5dSlxcHACrVq1iw4YN7N27VwZ3b4LRaCQ2NpZ7772XpKQk9Ho9BQUF7Nq1iwMHDnzrb6y4Op1Ox/jx48nIyGDIkCF0dnZSXFzMp59+6jY9qdyBoijO78b4+HhUVaW6upr9+/d7/HejVqslLi6OqVOnsmzZMlRVpaamhvXr17Nt2zbKyspcHaJLBAQEMGfOHCZPnkx4eDidnZ28+eabfPXVV1RXV7vVNf53kSSEEEIIIUQfCg8PZ9iwYTgcDoqKimhraxswg5t9TafT0dHRwYEDB1i1ahWFhYXOC2k/Pz8mT57M8uXLMZvNqKpKYWEh27Ztc0lD6IFCo9E4GxV3dnaSl5dHaWmpq8Nyew6Hg5KSEjQaDZs3b+bMmTOuDum6lZaW8uabb7o6jEGhqqqKNWvWMGXKFD766CO+/PJLLl686OqwBqygoCDmzZuHxWJBVVXq6+tdVspuIAsODiY7O5sHHnjA+dxrr73G9u3bXRjVwKXT6QgODmbGjBlMmjQJgMLCQnbt2sWOHTtkoshN0Gq1xMTE8PjjjxMTE0N3dzdVVVVs2LCB/fv3D5iVhX2tJwExYsQInnjiCVRVpa2tjYMHD7J9+3aPT3r3rBy/7777GDNmDAAnT57k888/5+DBgx57HKWnp7N06VKGDx8OQHt7O88++6yLo7pJ0phaHvIY+A85R+XRXw851uTRX4/BdKzdc8896v79+9XOzk71/fffV319fV0ek7s8vLy81LCwMHXIkCFXfd1oNKoffPCB2tzcrNbV1an/5//8n1veKHIwHWtwudH3vHnzVLvdrp4+fVqdPXu2NIJ0k8dgO9bk4b4PdznWZs6cqXZ1dak2m01tbm5W33zzTXXq1Kkuj2ugPW6//Xb1yy+/dDb57ezsVKdNm+byuMB9jrUbeYSGhqrLly9Xa2pqnM1d58yZ4/K4BupDo9GoAQEB6htvvKE2NzerdrtdLS0tVd99913V39/f5fG508NkMqm33367+sUXXziPvYMHD6pz5szpk0boA+n8VBRFHT9+vPr++++rdrtdtdlsaltbm/r000+r4eHhLo/PlY/f/va3amlpqWqz2dTu7m61qqrK5TF98yGNqYUQQggh3IBWq0Wr1VJdXc3vf/97mWH3N663wbNGo+GTTz5h3bp1sv++Q3h4OM899xwABQUFXLp0SUp1CCFcoqqqinXr1rFw4ULeeOMNXnvtNY8vp3czRo0axYIFC4DL/Yn++Mc/UlJS4uKoBq4RI0awZMkS/P39B0wddXfm7e3NlClTePTRR1EUBcDZ36C+vt7F0bmXjIwMFi1axO233+587q9//Su5ubkef32blpbGSy+9xMSJE4HL/a4CAwNl9Tjw0EMPOXusFBcX895777k6pJsmSQghhBBCiD705Zdfsm3bNrRaLbW1tTIgfAN0Oh2LFi3CaDSyf/9+Tp065eqQ3J5Go8FkMtHY2Mj7779PcXGxq0MSQnio/Px8Hn/8ccxmM83NzTQ3N7s6pAHp7NmzHDhwgBEjRvDWW2/xX//1X9TW1ro6rAErMzOTOXPmANDd3S2/ld9DQEAAkyZN4j/+4z/QaDQAPPbYY6xdu1ZKr31DYmIi//RP/8SMGTNQFIW2tjYyMjKor6/3+AQEwN13301SUhImkwkAVVUlAfE/tmzZwsyZMykoKOCTTz7h7bffdnVIN02SEEIIIYQQfaitrU1uLm6CyWQiNTUVi8VCRUUFtbW10tjwOpSVlfHiiy/i7e3NgQMHaGpqcnVIQggP1d3dLYPlt8CuXbuoqKggICCAs2fPUlNTM6AakbqbmpoaCgsLSU5OZvXq1fzpT3/y2Ia331d8fDzTp08nOjra+VxNTQ01NTUujMo9zZ49m4yMDPz9/YH/14tKXLZw4UKCg4MBqK6uZvPmzS6OyH385je/4YMPPqCpqYni4uIBfW0vSQghhBBCCOF2/Pz8mDlzJnB5YL2hoQGbzebiqNxfU1OTNCsVQohBpKysTAbJb6GcnBzefvttEhIS2Lx5MydOnPDYhrffV2JiIpMnT8ZgMGC328nNzaWxsdHVYbml2267jfDwcDQaDc3NzZw4ccLVIbmlixcvcuDAAT788ENXh+I2Dh8+7OoQbhlJQgghhBBCCLfj5+fH3LlzsdvtnDlzhoaGBpn5KYQQQojvJScnh5ycHFeHMSgEBweTlJSEqqpUVVXx0UcfScLsGoYOHYqPjw9tbW3k5+fz17/+1dUhuZX169fT2tpKcXExq1evZv369a4OSfQBSUIIIYQQQgi3pCgKtbW1fPjhh5SWlro6HCGEEEII8T8uXLjAnj17yM7O5s9//jOvvfaa9IK4hi1btjB37lyKior44IMPeOutt1wdklt58cUXXR2C6AeKqqrqdW34P13uhRDuR1VVOUdFv5BjTfQXOdYE4Gxy2JeN6eRYE/1FjjXRX+RYE/1FjjXRc62mqirXObzokRRFcZ4r/bWv5PwU/eV6j2dZCSGEEEIIIdxSXyYfhBBCCCHE9yPXatdHkjRCgMbVAQghhBBCCCGEEEIIIYQQYnCSJIQQQgghhBBCCCGEEEIIIfqEJCGEEEIIIYQQQgghhBBCCNEnJAkhhBBCCCGEEEIIIYQQQog+oajSGUUIIYQQQgghhBBCCCGEEH1AVkIIIYQQQgghhBBCCCGEEKJPSBJCCCGEEEIIIYQQQgghhBB9QpIQQgghhBBCCCGEEEIIIYToE5KEEEIIIYQQQgghhBBCCCFEn5AkhBBCCCGEEEIIIYQQQggh+oQkIYQQQgghhBBCCCGEEEII0SckCSGEEEIIIYQQQgghhBBCiD4hSQghhBBCCCGEEEIIIYQQQvQJSUIIIYQQQgghhBBCCCGEEKJP/P9j5iVI6+Ni0AAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 2000x100 with 20 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_model_result(x, 'AE_gt', 20, n = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "0dcf2524-dc39-4be5-963a-d56e7eff141d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2000x100 with 20 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_model_result(pred, 'AE_rec', 20, n = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5a468b0d-54bb-40f0-8e44-b8ceef60364f",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}