notebook_inference.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Copyright (c) 2022 Graphcore Ltd. All rights reserved."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Inference using GPS++ on IPUs\n",
    "==========\n",
    "\n",
    "This notebook demonstrates doing inference on a single sample and the entire test-challenge dataset split using the model we used for our OGB-LSC PCQM4Mv2 submission.\n",
    "\n",
    "We will use IPUs for this, which allows us to do inference on the entire validation dataset split in less than a minute.\n",
    "\n",
    "In the process of doing this we will see some of the additional features we generate from the original dataset and feed into the model.\n",
    "\n",
    "**Requirements:**\n",
    "\n",
    "* A Poplar SDK environment enabled (see the Getting Started guide for your IPU system or take a look at this projects README).\n",
    "* Python packages installed with `pip install -r requirements.txt`\n",
    "\n",
    "**Troubleshooting:**\n",
    "\n",
    "* If you see an `Unexpected error` when starting the machine, refresh the page and try again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "%pip install -q -r requirements.txt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This example requires building a few things:\n",
    "* An optimised method to get the path lengths of a graph\n",
    "* IPU optimised grouped gather scatter operaions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "! make -C data_utils/feature_generation\n",
    "! make -C static_ops"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import os\n",
    "import yaml\n",
    "from pathlib import Path\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import random\n",
    "import pandas as pd\n",
    "from rdkit import Chem\n",
    "from rdkit.Chem import AllChem, Draw\n",
    "\n",
    "import tensorflow as tf\n",
    "from argparser import parse_dict\n",
    "from data_utils.load_dataset import CustomGraphData, load_raw_dataset\n",
    "from data_utils.pcq_dataset_28features import smiles2graph_large, CustomPCQM4Mv2Dataset\n",
    "from data_utils.preprocess_dataset import preprocess_dataset\n",
    "from notebook_utils import predict\n",
    "\n",
    "# Set the tensorflow log level \n",
    "tf.get_logger().setLevel(\"ERROR\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If running on Paperspace we will run some additional configuration steps below. If you aren't running on Paperspace, ensure you have the following environment variables set: `DATASET_DIR` - location of the dataset, `CHECKPOINT_DIR` - location of any checkpoints, `POPLAR_EXECUTABLE_CACHE_DIR` - location of any Poplar executable caches or update the paths manually in the below two cells."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "if os.getenv(\"PAPERSPACE_METRIC_WORKLOAD_ID\"):\n",
    "    !mkdir -p /tmp/exe_cache\n",
    "    !rm -rf /tmp/ogb_lsc_pcqm4mv2\n",
    "    !cd /graphcore/ogb_lsc_pcqm4mv2/ && find -type d -exec mkdir -p \"/tmp/ogb_lsc_pcqm4mv2/{}\" \\;\n",
    "    !cd /graphcore/ogb_lsc_pcqm4mv2/ && find -type f -exec cp -sP \"${PWD}/{}\" \"/tmp/ogb_lsc_pcqm4mv2/{}\" \\;\n",
    "    os.environ[\"DATASET_DIR\"] = \"/tmp/ogb_lsc_pcqm4mv2/datasets/\"\n",
    "    os.environ[\"CHECKPOINT_DIR\"] = \"/tmp/ogb_lsc_pcqm4mv2/checkpoints\"\n",
    "    os.environ[\"POPLAR_EXECUTABLE_CACHE_DIR\"] = \"/tmp/ogb_lsc_pcqm4mv2/executables\"\n",
    "\n",
    "checkpoint_directory = os.environ.get(\"CHECKPOINT_DIR\", \".\")\n",
    "dataset_directory = os.environ.get(\"DATASET_DIR\", \".\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets also set a few things to enable us to use the executable caches, saving us from compiling the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "executable_cache_dir = os.environ.get(\"POPLAR_EXECUTABLE_CACHE_DIR\", \".\")\n",
    "os.environ[\"TF_POPLAR_FLAGS\"] = f\"--executable_cache_path='{executable_cache_dir}'\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Loading a configuration\n",
    "\n",
    "There are 3 configurations available with the model sizes of 11M (GPS_4layer), 22M (GPS_8layer) and 44M (GPS_16layer).\n",
    "By choosing the model name, the corresponding config path and checkpoint path will be used.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Choose model\n",
    "model_name = \"GPS_4layer\" # choose from [\"GPS_4layer\", \"GPS_8layer\", \"GPS_16layer\"]\n",
    "\n",
    "# Set configs\n",
    "model_dict = {\"GPS_4layer\": \"GPS_PCQ_4gps_11M.yaml\", \n",
    "              \"GPS_8layer\": \"GPS_PCQ_8gps_22M.yaml\",\n",
    "              \"GPS_16layer\": \"GPS_PCQ_16gps_44M.yaml\"}\n",
    "cfg_path = Path(\"configs\").joinpath(model_dict[model_name])\n",
    "cfg_yaml = yaml.safe_load(cfg_path.read_text())\n",
    "cfg = parse_dict(cfg_yaml)\n",
    "\n",
    "# Set the checkpoint path for the corresponding config\n",
    "sub_directory = model_dict[model_name].split(\".\")[0]\n",
    "checkpoint_path = Path(checkpoint_directory).joinpath(f\"{sub_directory}/model-FINAL\")\n",
    "\n",
    "# Turn off dataset caching for this notebook\n",
    "cfg.dataset.save_to_cache = False\n",
    "cfg.dataset.load_from_cache = False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Predicting the HOMO-LUMO gap of a single molecule\n",
    "\n",
    "The competition requires predicting the HOMO-LUMO energy gap of a number of molecules. To demonstrate inference of our model on the IPU we will start by predicting the HOMO-LUMO gap of a single molecule.\n",
    "\n",
    "Lets create a smile string:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "smile_string = \"CC(NCC[C@H]([C@@H]1CCC(=CC1)C)C)C\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get an idea of how this molecule looks lets visualise this smile string using [rdkit](https://www.rdkit.org/docs/GettingStartedInPython.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<PIL.PngImagePlugin.PngImageFile image mode=RGB size=300x300 at 0x7F80DF38C240>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mol = Chem.MolFromSmiles(smile_string)\n",
    "AllChem.Compute2DCoords(mol)\n",
    "Draw.MolToImage(mol)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now convert the smile string into some features our model can understand. The competition provides a method to do this (`smiles2graph`). We have written a custom version of this that uses [rdkit](https://www.rdkit.org/docs/GettingStartedInPython.html) to generate more features from the smile string."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "graph_obj = smiles2graph_large(smile_string)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can take a look at the features that have been created that represent this molecule."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['edge_index', 'edge_feat', 'node_feat', 'num_nodes'])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graph_obj.keys()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see the features that have been created:\n",
    "* `edge_index` - The sending and receiving node indices, representing the edges in the graph.\n",
    "* `edge_feat` - The features of each of the edges in the graph.\n",
    "* `node_feat` - The features of each of the nodes in the graph.\n",
    "* `num_nodes` - Number of nodes in the graph."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One thing to note is the size of the node features. They have a size of 28 compared to 9 that the OGB-LSC provided `smiles2graph` function creates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "28"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(graph_obj[\"node_feat\"][0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we will wrap this single graph in our dataset wrapper, which contains some metadata and the dataset object itself."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Getting stats for train split: 100%|██████████| 1/1 [00:00<00:00, 3554.49it/s]\n",
      "Getting stats for valid split: 100%|██████████| 1/1 [00:00<00:00, 2970.47it/s]\n",
      "Getting stats for test-dev split: 100%|██████████| 1/1 [00:00<00:00, 6657.63it/s]\n",
      "Getting stats for test-challenge split: 100%|██████████| 1/1 [00:00<00:00, 4424.37it/s]\n"
     ]
    }
   ],
   "source": [
    "graphs = [graph_obj]\n",
    "graph_raw = CustomGraphData(graphs,\n",
    "                            use_extended_features=True,\n",
    "                            use_conformers=True,\n",
    "                            trim_chemical_features=cfg.dataset.trim_chemical_features,\n",
    "                            use_periods_and_groups=cfg.dataset.use_periods_and_groups,\n",
    "                            do_not_use_atomic_number=cfg.dataset.do_not_use_atomic_number,\n",
    "                            chemical_node_features=cfg.dataset.chemical_node_features,\n",
    "                            chemical_edge_features=cfg.dataset.chemical_edge_features)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now lets feed this through our dataset preprocessing pipeline."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Checking size of graphs against given options...: 100%|██████████| 1/1 [00:00<00:00, 1132.37it/s]\n",
      "Generating senders_receivers features...: 100%|██████████| 1/1 [00:00<00:00, 2924.90it/s]\n",
      "Generating bond_lengths features...: 100%|██████████| 1/1 [00:00<00:00, 2220.38it/s]\n",
      "Generating laplacian_eig features...: 100%|██████████| 1/1 [00:00<00:00, 13.21it/s]\n",
      "Generating random_walk features...: 100%|██████████| 1/1 [00:00<00:00, 248.15it/s]\n",
      "Generating chemical_features features...: 100%|██████████| 1/1 [00:00<00:00, 582.87it/s]\n",
      "Generating graph_idxs features...: 100%|██████████| 1/1 [00:00<00:00, 3412.78it/s]\n",
      "Generating shortest_path_distances features...: 100%|██████████| 1/1 [00:00<00:00, 506.80it/s]\n",
      "Generating centrality_encoding features...: 100%|██████████| 1/1 [00:00<00:00, 4760.84it/s]\n",
      "Generating atom_distance features...: 100%|██████████| 1/1 [00:00<00:00, 422.39it/s]\n"
     ]
    }
   ],
   "source": [
    "graph_preprocessed = preprocess_dataset(dataset=graph_raw, options=cfg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets take a look at the additional features created."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['edge_index', 'edge_feat', 'node_feat', 'num_nodes', 'ogb_conformer', 'senders', 'receivers', 'ogb_bond_lengths', 'nan_in_conformer', 'lap_eig_vals', 'lap_eig_vecs', 'random_walk_landing_probs', 'node_graph_idx', 'edge_graph_idx', 'shortest_path_distances', 'centrality_encoding', 'atom_distances', 'direction_vector'])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preprocessed_single_graph = graph_preprocessed.dataset[0][0]\n",
    "preprocessed_single_graph.keys()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can see we now have many more features. Ones of note are:\n",
    "\n",
    "* `lap_eig_vals` - The laplacian eigenvalues used as positional encodings in the model.\n",
    "* `lap_eig_vecs` - The laplacian eigenvectors used as positional encodings in the model.\n",
    "* `random_walk_landing_probs` - The random walk feature used as structural encodings in the model.\n",
    "* `shortest_path_distances` - The shortest path distances (2D graph structure information) used as attention bias.\n",
    "* `centrality_encoding` - Degrees of the atoms.\n",
    "* `ogb_conformer`, `ogb_bond_lengths` and `atom_distances` require the 3D position information which is only provided for training data. You will see these values are NaNs or zeros for our inference case."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Checking the size of the node features you will see that is smaller than before. From the 28 features we had before we have selected 11, based on how beneficial the features were for training. For example, we found the features related to the atomic number group, period and family to be very beneficial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(preprocessed_single_graph[\"node_feat\"][0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we are ready to run on the IPU. We have wrapped this functionality in a single function for simplicity. We encourage you to check the contents of this function.\n",
    "\n",
    "The first time running the model in inference on IPUs will require the model to be compiled. This can take a few minutes. We have cached the executable so any subsequent runs we want to do will not require this compile phase."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now lets predict the HOMO-LUMO gap of the molecule."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Creating input specification...\n",
      "Configuring the IPUs...\n",
      "Creating TensorFlow dataset from preprocessed dataset...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1/1 [00:00<00:00, 3765.08it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Constructing the model...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading the checkpoint from /localdata/adams/checkpoints_tarballs/GPS_PCQ_4gps_11M/model-FINAL...\n",
      "Running `model.predict` to generate predictions...\n"
     ]
    }
   ],
   "source": [
    "prediction, _ = predict(graph_preprocessed, checkpoint_path, \"test-challenge\", cfg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.76"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prediction[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Predictions on the validation dataset split"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Doing a single prediction at a time is very inefficient. In this next section we will generate predictions for the entire `valid` dataset split, which on IPU is very fast."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "cases = (\"valid\", )\n",
    "split_mode = \"original\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now lets load and preprocess the dataset. These steps are the same as those we took when preprocessing the single molecule, but does the preprocessing only on the molecules in the `valid` dataset split. This will be done from scratch so can take a few minutes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 73545/73545 [00:22<00:00, 3229.34it/s]\n",
      "Getting stats for valid split: 100%|██████████| 73545/73545 [00:00<00:00, 382705.36it/s]\n",
      "Checking size of graphs against given options...: 100%|██████████| 3746620/3746620 [00:01<00:00, 1959736.58it/s]\n",
      "Generating senders_receivers features...: 100%|██████████| 3746620/3746620 [00:09<00:00, 408979.96it/s]\n",
      "Generating bond_lengths features...: 100%|██████████| 3746620/3746620 [00:08<00:00, 438366.68it/s]\n",
      "Generating laplacian_eig features...: 100%|██████████| 3746620/3746620 [00:43<00:00, 86439.51it/s] \n",
      "Generating random_walk features...: 100%|██████████| 3746620/3746620 [00:43<00:00, 86487.97it/s] \n",
      "Generating chemical_features features...: 100%|██████████| 3746620/3746620 [00:21<00:00, 172752.68it/s]\n",
      "Generating graph_idxs features...: 100%|██████████| 3746620/3746620 [00:08<00:00, 419893.12it/s]\n",
      "Generating shortest_path_distances features...: 100%|██████████| 3746620/3746620 [00:25<00:00, 145223.80it/s]\n",
      "Generating centrality_encoding features...: 100%|██████████| 3746620/3746620 [00:08<00:00, 465480.78it/s]\n",
      "Generating atom_distance features...: 100%|██████████| 3746620/3746620 [00:22<00:00, 168390.45it/s]\n"
     ]
    }
   ],
   "source": [
    "graph_data = load_raw_dataset(cfg.dataset.dataset_name,\n",
    "                              dataset_directory,\n",
    "                              cfg,\n",
    "                              split=cases,\n",
    "                              load_ensemble_cache=True,\n",
    "                              split_mode=split_mode,\n",
    "                              ensemble=True)\n",
    "graph_data = preprocess_dataset(dataset=graph_data,\n",
    "                                options=cfg,\n",
    "                                load_ensemble_cache=False,\n",
    "                                folds=cases,\n",
    "                                split_mode=split_mode,\n",
    "                                ensemble=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now lets get predictions on the entire `valid` dataset split."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Creating input specification...\n",
      "Configuring the IPUs...\n",
      "Creating TensorFlow dataset from preprocessed dataset...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 73545/73545 [00:04<00:00, 17060.98it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Constructing the model...\n",
      "Loading the checkpoint from /localdata/adams/checkpoints_tarballs/GPS_PCQ_4gps_11M/model-FINAL...\n",
      "Running `model.predict` to generate predictions...\n"
     ]
    }
   ],
   "source": [
    "predictions, ground_truth = predict(graph_data, checkpoint_path, cases[0], cfg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets take a look at the mean, variance and histogram of the predictions and histogram of the ground truth labels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean = predictions.astype(float).mean()\n",
    "std = predictions.astype(float).var()\n",
    "\n",
    "plt.hist(predictions, 30, alpha = 0.7, label = 'Predictions')\n",
    "plt.hist(ground_truth, 30, alpha = 0.5, label = 'Ground truth')\n",
    "plt.xlabel(\"HOMO-LUMO Gap (eV)\")\n",
    "plt.ylabel(\"Counts\")\n",
    "plt.title(\"Histogram of HOMO-LUMO gap predictions\")\n",
    "plt.legend()\n",
    "plt.text(5, 15000, f'mean: {mean:.2f}, std: {std:.2f} \\n')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We could compare the predicted values with the true labels and calculate the MAE (Mean Absolute Error) as below. The model we test here is a small one (11M parameters). To achieve a better MAE we could select one of the larger models (22M or 44M) and re-run the predictions. For the challenge submission we ran the largest model (44M) with 16 GPS layers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.08999300505693687"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_MAE = np.mean(np.abs(np.array(predictions) - np.array(ground_truth)))\n",
    "mean_MAE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets have a look at some molecules with their corresponding label and prediction. First, we have to load the raw data..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load raw SMILES strings with corresponding label and select only validation molecules\n",
    "smiles_only = CustomPCQM4Mv2Dataset(root=dataset_directory, only_smiles=True)\n",
    "valid_idx=smiles_only.get_idx_split()['valid']\n",
    "valid_smiles=[]\n",
    "for i in valid_idx:\n",
    "    valid_smiles.append(smiles_only[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can plot random molecules in the `valid` dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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RERYWFhwc7Ofn5+7ubmNjIx5numjRooSEBKYrbaQmTpwIAHw+v+EusWbNGgDw9PRsuEvUn7U16dqViLsdfHzI5s2MFtQoRUZGintS/Pz87t69K/WAkpKS0NBQbW1t+payyqDzSYWFhaGhoXSPRhlv0leuXBF3u3To0CEu7p/aXvSTMjOFo0aNpp0DlpaWUrOuFixYQK/eq1cvyeM1T02vv/v374uH3bRp0yY2Nla+51cAFkcZQsj27cTBgWzaRPr3J9nZ5MEDUteRi9KKiopo/g2kLT+IkBcvXty8eTM2NnbHjh2LFy+eOnWqr69vt27dzM3Naa9tDehIanNzc1mmJCC5c3R0BIB///234S5RVFRE270vyT4wUuGsrYmJyYdZAhhlFOzGjRviPpSOHTuePn1a6gEikSgiIkK8YH+VQadWpG7SMTExVT5McgitlZVVZGRkg46VlOwF69Kly8WLF+nxjRs30oPjx4+nR168eCHj1PT6i4uLa9euHS3Ax8cnPT29gS7UENgdZYRC4uxM3N1lHfZbA4FAIPUrcvPmTdqicODAgfqenVUSExMjIiKWLl0aFBQ0ZMgQNzc3S0vLyhvQS2natGl1PXcCgUAoFNKXsH79+uF4agUrKChQUVFRU1Nr6GXE5s2bBwAjRoxo0KvUh7U1CQ8nJiaEJmqMMgqTnZ0t7i0yMTGJiIioPCb34sWLLi4u9PXE0dHxn3/k1igSFxdnb28vvklLDlWp/xDauqGhzdTUFAC4XK6/v39OTk50dDQt8tdff6VT0+nqlDweT8ap6fVUVlbG5/N1dHQAQFNTMyQkhC39EuyOMoSQW7eIqqpMUaa4mDx8SC5eTD906NDq1at//PHHgICAvn37tm/fnk61jxDPiXrv999/BwB9ff3Gs1beunXrxIs0SOLxeFVO4k1JSZGx7ffp06d0xYgG7eZAlSUmJtI3fw19oczMTLq2ZAPNk6o/a2ty5QoJDCT0TS9GGQWgvUVaWloAoKGhERoaWvnu+PjxYz8/P9rtUl3QqSd6k9bV1QUANTW14ODg3NxcqSG0mZmZ8r3oJ0n2gunr68+dO5e+3gYHB7dp04Z+PGDAgLS0NEVWlZmZKbVAsCKvXjesjDIbN360kMwvv5D58z96wJMn5I8/yOzZZNQo0rMnadeO6Om9G/bbvfvaKhsVVFRUKt9iRSLRgAEDAMDT07MxTM2gy01qamqOGDFi1qxZf/zxx759+86ePXvv3j26BnY9HT58GADU1dVv3LhR/7MhGa1YsQIAvv/+ewVca9SoUQAwZ84cBVyrDmiUefWKGBmRf/99F2VcXIi9PfH3J3w+OXcOBwLLWVxcHL0p9uvXLzU1VeqrBQUFISEhTZo0EQedGhZjrL+MjIyhQ4fS13w66BgAXFxcGrTv9ZMkp0ZLsra2PnToEFNVJSYm0o5pYMMCwayMMlOmkBUrSA3tXpcuVTF3SU2NWFiQESPODBo0aMqUKYsWLdqyZctff/117dq1rKys6pJKTk4ObQP85ZdfGur5KA0FLNs6btw4AGjXrp1cshGShZ+fHwDs3LlTAddKTk7mcDi6urpyXKNMjmiUIYRs2UK6dCH9+5ONG98tRS/+T0+PeHuT+fPJsWNE4e/SP0N0bYvjx49LHZecK0TnGT355Bq6cpKUlNSmTRtzc3MzM7Mql7FhRFRUlLW1NYfD4XK5hoaG4eHh5eXlzJZUVla2cuVK2pRlY2OjzO/n2RdlUlIIh0O0tUleXrWPefmSBAWRJUvIzp3kxAly8ybJyan7FU+ePMnhcHg83mewjlANHj58qKKioqGh8fz581p9o1AozMrKotsQbtq0KTQ0lO6Z7OjoWLllsrCwkI6nnjRpkvxqRzWhgygV1kZNB0WtWrVKMZerFXGUEQqJiwtp0oRs3kyKisi5c+SPP8jw4e8Wm5f8z8KCDBlC1q17Fh8fX3n2LPok2nsiNXvo+vXrPXr0oO/427dvf+rUKQVXtWzZMgCYMWOGgq9bs4KCAtoTV8/BzvKVnZ3t5uampaX1ww8/MF1LtXhV9rYos1WrgBAYNw7etw5WoVkzWLNGblfs27dvcHDw6tWrR40adePGDToZ5/Ozbt06oVDo7+9vYmIi9aXy8vKnT5+mp6dnZWVlZ2dL/b+0tLS6c969e1fqiJaW1t69e11dXcPDw7/88stvvvlG/s8ESXjxokAgMNTVzRd3vTe0mTNnJiQk8Pn8adOm8XjK8gqTkwOSv9dcLmzdCp07AwA0aQIeHuDh8e5LhYXw339w7dq7/27fhmfP4PXrG4mJAwHAzMzMycnJycnJw8PD1dWV3nhQDQghACC1NmlCQsKZM2datmy5YsWKYcOG1bxyacNRU1Nj5LrV0dbWpqsV064AJWFqajp8+PB///23hpd6xinLC42MsrNhzx7g8WDmTIVed9myZYmJif/999/EiRMjIyMVem2FyM/P37p1K4fDmT17ttSXunbtevPmzbKyshq+3cjIyNTU1MLCwsTEpEWLFvT/pqamNjY2lR/8xRdfLFmy5Icffpg8ebKLi4t44iVqCElJOjk51wcNKqOTRxTAx8enXbt2aWlpR48epX1bjEtLAw8PGDECjh0D8dLwDg7w339QeTtwbe2Pks2jR3D5Mty791Yo9Lh+/Xp2dnZ0dDSdaaKhodGpUydnZ+euXbs6Ozu3bt2aqVuyMhOJRAAg9es3derUkpKSadOmMfXOsMqqlIFyFqacVUliWZTZsAEEAvDzAysrhV5XXV193759Xbp0OXTo0O7du8U7y382tm7dWlBQ0KdPn/bt21f+qkgksrGxMTMza968eeX/0+mCtTJ79uwzZ87ExMSMGjUqISFBvPsVkrvLlwEA2rdX3LtPDocTHBw8ZcqUVatWKUOUycmBgQMhNxcyMsDeHiTbid7Pz62JtTVYWwPAyJ9/HllRUZGampr03u3bty9dunTp0iX6SFtb2//++48u7IbEqrwLqquri5eDU4CMjIxTp05ZWVn16dOnhqqUgXIWppxVfYTpHq5aKCwkTZsSAJKUxEwBmzZtAgBtbW2l6sisv7KyMjr47u+//6781ezs7IYYoiseT71kyRK5nxyJ9e5NAMixYwq9aHFxMd2mmNmJIYSQ3Fzi4EAAiKfnJ/YlTk8na9eSS5dqMYOpvLw8JSUlIiIiODi4c+fOTZs2bdq0qUAgqH/ZnxNluNHQPcK+/vpr8ZFffvkFAH766ScGq6oSXcysoZeAqq2VK1cCwOzZs5kupFpKHLIq2bULcnPB3R26dmWmgEmTJn3zzTeFhYXfffddzR0u7HLo0KHMzExHR0fxWxZJpqamdKqkfBkbG+/YsYPD4YSGhl68eFHu50cAIBJBUhIAQLduCr2upqbm5MmTAeCPP/5Q6IU/VloKX38NqanQsSP89Re830KjaidOQFAQuLiAhgbY2sLo0bB6NZw/DzUMD+DxeA4ODqNHj169evX169etrKxyc3Pj4uLk/kTYS0nezVcuQ0kKq0w5C1POqiQpb2VSRCJYtQoAoNJYDoXatGmTpaXl1atXFy5cyGQd8kMIWb58OQDMmDFDwZfu169fUFBQRUXFqFGj3r59q+CrNwb378ObN9CiBSh+EGFQUJCGhsbRo0cfPnyo6GsDAIBQCMOHQ2IiWFpCbCx8ckhG+/YwcSJ07AgqKpCeDrt3w4wZ4OkJRkYwblzU3Llz//zzz8zMzBrOMGzYMACgm9EiSklugdVFGSUc26QkPzEpylmVJOWtTEpUFNy/D61bg68vk2UYGBjs2bNHRUVl2bJl//zzD5OlyMmZM2eSk5ObN28+cuRIxV99+fLljo6O6enpU6dOVfzVP3u0ScbZmYFLGxsbjxgxQigUrl1b9aKUDS0oCI4fBwMDiI0Fc/NPP757d9i8GZKTobQUUlIgPBz8/cHeHoqK4MKFPStWrBg6dKiFhYWenp6Hh8e8efP++uuvV69eSZ6BRpmoqKiKiooGelKsoyS3wMplEEJACQqrTEl+YlKUsypJyluZlN9/BwCYMQMY/2F6enqGhISIRKKAgACp1zI2opszTJs2jZF5iXQ8dZMmTfbs2bNnzx7FF/B5u3IFgKEoAwCzZs3icDjbt2/Pz89X8KWXL4eNG0FDA44dAweH2n0vjwcODhAYCLt2QWoqPH4MS5d+N3fu3B49eujq6r59+/bChQvLli0bNGhQy5Yty8vLxd/YunXrDh06vH79OiEhQc7Ph7WU5BbIug4mZWsuUtofl5jyVibp2jU4fx4MDGD0aKZLAQCARYsWubq6ZmZmBgQEkPfj2tjo9u3bsbGx2tradGQDI+zt7emYsilTpty7d4+pMj5LDLbKAED79u29vb0LCgq2bNmiyOvu3Anz5oGKChw8CN271/dsLVrA0KG+y5YtS0hIyMvLS01N3blz59SpU52dnZ2cnKT2hKeL4mMfk5iS3AKra5VRtsQgrkrZClOSf8caKG9lktasmejuHj5nTq6SzHPk8Xh79uzR1dWNjY2l05pYim47NWbMmDpMqJajKVOmDB48mI6nlnybi+pDIID//gMVFejShbEaZs2aBQCrV69W2D9rYuK/P/+cTQiEhcGgQXI+OZfLtbe3DwgIWLdu3eXLl8+ePSv1ABpljh07JhQK5XxtdlKSWyBbWmWUsypQ4sLElLcysYcPH+7du+PatRkTJihRD7SNjc369esBYNasWTdv3mS6nLp4/vz5rl27VFRU6P2GWdu3b6fjqRctWsR0LZ+J5GQQCKBdO2DwDUC/fv06duyYmZlJdxJtaMnJyb6+/QHcf/ope84cBVxQWvv27e3s7HJycs6fP8/A5ZWPktwCMcrUk3I2YklSuh9ZZWvXrhUKhSNHjjSuvDAno0aNGjVq1KjS0tKRI0eWlJQwXU6tbdq0SSAQ+Pr6WltbM10LGBgY7N69W0VF5bfffouPj2e6nNpJT0+nr0FKhdneJbHg4GAACAsLEwgEDXqhu3fvent7v3nzpnfvnosXM7bu+5AhQwD7mN5Tkntz5TuxkhQmRTmrAowy9Zefn799+3YOh6MMLQeVbdy4sU2bNqmpqfPmzWO6ltopKSnZsGEDAFTeqYAp3bt3nzt3rkgkGj169OvXr5kuR1ZZWVkuLi5ubm7p6elM1/IRLhesrZnsXaLat2+vpqb24sULDQ0NW1tba2vrH3744fz58/JNNtnZ2V999dWrV68GDx68efNmBl9zaR/Tn3/+yepRdPKiJLdAbJWpJ6UtTEx5K6M2b95cUFDQt29fh9rOQ1AIbW3tbdu2qaiorFu3btGiRSxaN2/Xrl0vX750dXV1c3NjupYPFi9e7OLikpmZOXHiRKZrkVVmZiaPx7t8+bKLi0tMTAzT5cC2bXDqFADA999Dejo0bw7XrjFWzOXLl318fMrKygghqqqq6enpGRkZK1eu9PT0NDEx6dOnz08//RQVFfX8+fP6XCU/P79v376PHj1yd3fft28fs/tgfPHFFzY2NpmZmZfpnhGNm5LcAjHK1JPSFiamvJUBQFlZ2Zo1a0CZWg4q8/DwGDt2rKGh4cKFCy0sLObNm5eVlcV0UZ8gEonoMqzK9oPl8Xh79+7V1dU9evRoeHg40+XIpGvXrmlpacOHD3/58qWPj8/o0aOLiooYrOePP8DPD8Rrue3dC//+y0wlhw8f9vLyevXqlY+PT3p6enFxsXiZfycnp4KCgri4uCVLlvj6+pqZmenr6/fu3XvhwoWV12upmUAg+Prrr2/dutWuXbvjx49ramo23DOSEfYxiSnJLRCjTD0pbWEfMLJdgox27doFAJ07d2a6kE/Yu3cvAIinZero6MyYMePRo0dM11WtqKgoALC1ta2oqGC6lipEREQAgIaGxs2bN5mupRYiIiK0tLQAwM7O7saNG0yVYW9P+vUjQ4e++9TPj6xZw0AZmzZtoq0jgYGBVf6aFRQUnDt3js/n+/v7V95B3czMzM/Pj8/nnzt3rob9aO7NwLYAACAASURBVCoqKgYPHgwALVq0ePr0aUM+oVqgG3FYWVmJRCKma2EYbW8zMTFhtoyNGzcCwOTJk8VHgoKCAGANI38b1aMrMOnp6TFdiLS5c+cCwLJly5gupFrKG2VEIlGHDh0AYNeuXUzX8gk0ygBAbGysv78/j8cDAC6X6+3tHRUVxXR1VfDy8lLCP2NJdOHULl26KGfYqk5aWlqnTp1oDuPz+YzcyeztSVwcsbYmR44QwlCUCQkJoX8RoaGhMv4QMjMzo6KiQkNDfXx8mjZtKhlreDyevb29v79/eHh4SkqKUCgUf9eUKVMAwMDAICUlpcGeTa2JRKIWLVoAwLVr15iuhWG0idrMzIzZMuhs0++//158hC4vvm7dOgarqiw3N5f+PjNdiLQ5c+YAwIoVK5gupFrKG2VOnz5N32zRjnZltm/fPvqae/ToUUJIenp6cHAwfYNOW5UiIiLKy8uZLvMd2oVvaGjYEPtdy0tBQYGhoeHkyZNLZd+nWDmUlJQEBwfTcY6DBg169eqVgguwtyfnzpFDh0jLlqSwUNFRRigU0psEj8fbtm1b3U5SVlaWlJS0bt260aNH29nZSQ0aNTMz8/X1XbJkyfjx42lqTExMlO+zqD86b2v+/PlMF8KwZ8+eAYC5uTmzZdDdM6ZNmyY+QkPwhg0bGKyqMtq1amhoyHQh0ui0m99//53pQqqlvF1fdEH9qVOnSq2nqcyuXbsGANbW1qtXr87KyuLz+RYWFjdu3AgICGjduvWyZcsUv4J7ZXw+HwAmTpzYEPtd183jx4+ljiQlJb1+/To6Olqpe2eroqGhsXr16mPHjhkaGkZFRTk4OPz999+KufTp05CX9+7jYcOgY0dYulQxV36ntLR02LBh69ev19TUPHz48Lhx4+p2HlVV1a5du06dOjUiIiItLU0gEFy9epV2Rdnb2z9//vz48eMLFiw4duwY3Rihe/3X9JU3Oo/p0KFDTBfCMCUZY8GusTKMT/iqTDl/XJKUorK3b9+mpaXFx8fv3r17+fLlM2bMGDhw4MmTJ7W0tCZMmMB0dbVw9epV8ce6urrTp09/+PBhREREhw4dMjIy5s2b17Jly+nTpz99+pSpCh8/fnzo0CE1NTXaVawMnj171rp16169ekkukMrGICtp0KBBqampffv2zcnJ+eqrr6ZPn95wy90WFcHq1dCqFfTuDZJbN/7+O2zaBM+eAQBMnw5Ll0JpaQOVAADw5s2br7766ujRo4aGhvHx8b7y2/dVVVXVyclp+vTpu3btSk1NzcjIOHToUFBQUF5enqqqav/+/eV1ITny8PAwMzO7f/9+SkoK07UwSUlugeyKMspWFShxYWI8BVxDKBTm5ORkZ2dnZWVlZ2enp6fTD+j/88RvJD82YMCA4cOHGxoaKqDCehKHaMkoQ6mpqY0ePXr06NHnz59ftmxZTEzMmjVrNm7cOHjw4Dlz5jgrfP2yNWvWVFRUBAQENG/eXMGXrs6qVavKy8tbtGghnkN7+/btEydOaGtrT5o0idna6sPExOTEiRNr1qz54Ycf1qxZc+nSpX379tna2srxEq9ewaZNsH490LnMLVt+tAV069YwYwb8/DP07g3r1oFIBFu3wsqVMGSIHEv4UMnIkeVPnjw3NTWNiYn54osv5H+N9ywtLS0tLYcNG3b37t1Tp04dP3589Md7sxUWFmozvcUJl8sdNGhQeHj4kSNH2rdvz2wxDFKSWyBbogzB/brrTF49VcXFxQ8ePDh37tyBAwdWrVo1Z86cUaNG9ejRo127djo6OjXXoKmp2apVK09Pz2+//XbGjBkrVqzYvXv39evX5VVbQ9u/f7/4udQ8cSk5OTkwMFBDQ4M+2N3dPSoqSmGDQ/Pz83V0dDgczq1btxRzxU/Ky8urXBJtigsKCmKwMDm6fPkyTTC6urp79+6V0zmJnx9RUyMABID4+JC4OEKHww4bRsTTp4qLSa9e5MABkpRE3NzePbhrV3LhglyqeCc9nbRtSwCIm9vjhw8fyvPUNaLT9QcNGiRRSbqjo2PHjh0VVkMNTp06BQAdOnRguhAmPXjwAABsbW2ZLWPFihUAMHv2bPGRsWPHAsD27dsZrKqyzMxMAGjevDnThUj7/vvvAWD9+vVMF1Kt+kaZvLy8jRs36uvr1xxW1NXVrays3N3dhw0bFhwcHBYWFhERERcXl5qampeXJ5dnwiDJKHPo0KFPPj47Ozs0NFQ8TaNNmzZ8Pr+4uFjuheXn56empp4+fXrXrl1hYWF04pKXl1flR0rOClEk+hLTp08f8ZHs7Gx1dXUVFZX09HRGSmoIb968GTlyJP3n9vf3LygoqNt5KipIZCRxd38XSjQ0SGAgkXHet0hEIiNJixYEgHA4xM+PPHlStyo+cuECadqUABBPT5KbK4cTyi4nJ0dFRUVdXf3Nmzf0SEVFhZGREQDcvn1boaVUpby8vFmzZgCQlpbGdC2MoXvdt27dmtkyli9fDgA//PCD+EhAQAAA7Ny5k8GqKqNjDywsLJguRNrkyZMBYOPGjUwXUq36RpnvvvuOvnYYGBg4OTn5+PgEBgaGhoaGh4dHRUVdvXo1MzOzhmUhPg+SUWbevHkyfldBQUF4eHibNm3oN5qYmISGhtZqwktFRcXDhw/PnTsXGRnJ5/NDQkL8/f29vb3t7e2r2+nayMhowIABUicJDQ11dnYWCAS1eM7yUFZWZm5uDgB///23+OD//vc/ABg2bJiCi1GAiIgI2vHRtm3b2jY6CgSCAwcuODq+CzE6OmT6dFKHFpDCQhIaSjQ0CADR0iKhoaQ+f53R0URLiwCQYcMII1PNaDo/cOCA+Aid1vTrr78yUE0l9K3/0qVLmS6EMXfu3KG/8FLH8/LyFLlQRUlJSW5uruTbRX9/f1C+lT7oBAhLS0umC5EWGBgIAOHh4UwXUq16RZmHDx+qqKhoaGgoT4cFIw4cOCDOCpINDLIQCoVRUVGurq7027W0tAIDA+/cuSN+QHFx8f3798+ePbt///5Vq1bNnj37u+++8/LysrOz++SAgCZNmrRu3drT03PEiBEzZsyYM2cO7dvas2eP+Py5ubk0TyxYsEBuPxHZ7NmzBwAcHR3FRwoLC2ljVVJSkoKLUYw7d+507tyZtlOGhYXJ0hj29OnT4OBgPT09NTU1E5PMdu1IRES98gch5MkT4u//LhW1aEEiIupyks2biYoKASCTJxOmVv+hq4H7+fmJj8TGxoLSrKsZHR0NAE5OTkwXwpjbt28DQLt27aSO0w4LLy+v5ORkRgr77rvvpF4JlcGjR48AwMrKiulCpNGdZDZv3sx0IdWqV5SZMWMGAIwdO1Ze1bCUZJQxMDCow9gXkUh08uTJ3r1705Ooqqq6u7vb29vr6enVHFY0NDSsra3d3d39/PymT5++bNmyXbt2nT59OjU1NT8/v/KF1q1bBwB6enqS3Tfnzp1TUVHhcrlxcXH1+kHU8il37NgRAHbs2CE+SBfldHNzU1gZildaWhoSEkIH0PXu3Ts7O7u6R965c2fy5MniOfNdunQ5ejRZjusTxceTjh3fBZqePUmt7imhoYTDIQAkLExu9dTBs2fPuFxukyZNCgsL6ZGysjLaJPngwQMmK/u4GEUOIVIqqampAGBvby91fO3atXRYgpqa2pw5c8RdhAozYsQIANi3b5+Cr1uzhw8fAoCNjQ3ThUijjZ1bt25lupBq1T3KVDlgs3GSjDIAcP/+/Tqf6sGDB8HBwdra2uJdHs3MzKrruavb8nF0lmzXrl0l1x4MDQ0FABMTk+fPn9e5+FqJj48HAAsLC3EZQqGwdevWAHCErlP7WTt16pSpqSkAGBsbnzhxQvJLFRUVkZGR7u7u9BeAx+P5+/s30LqxQiGJiCBGRgSAcLnE35+8ePHpb5k2jQAQHo9IpFDG0BZNuhM1RfsOli9fzmBVYvTd/8qVK5kuhBm3bt0CgGbNmj1+/FjqS3l5ecHBwXRt9KZNm/L5fEUu7U3n8Nd5FccGcv/+fQBo1aoV04VIU85R0pLqHmXoQKq+ffvKsRqWOnjwoGSU2b9/fz1P+Pr16+Tk5Js3b+bk5MilQkkvX76kM7H/97//iQ8KhcIePXoAwFdffaWYGVUDBgyAj4cRHD9+nP4ZMzUGWcHokjMAwOFwgoODBQJBUVERn89v1aoV/UXS19cPCQlRwGZeubkkOJjweASAGBgQPp9U1/ZTUkK+/poAkCZNyPHjDV2XTFauXAkA3333nfjIsWPHAKBbt24MViX2559/AoCrqyvThTCjoqKC/gM1adJk8eLFlcdNpqWl9e3bl/7Cd+rU6ezZsw1d0qNHj/z8/DgcjoWFhY6OTlhYmOKHCVYpJydnxIgRWlpaBgYGf/31F9PlfFBeXk7fMCjbKGlJdYwyAoGADrA4deqUfAtiI6koM2fOHKYr+oQzZ87QHqX4+HjxwadPn9JxKgrYlyQ1NZXD4Whra+dKTHqha7auXbu2oa+uPOiYa7qgTtu2bWk7DQAYGRktXLjwxSdbSOTqzh3Sv/+7/qa2bUlMDJk7l9jYfJiXtH07+eYb4uJC9PSIxC8Owx49esThcHR0dMS3ydLSUl1dXQ6HU7klQPGKi4u1tbU5HM4TuUwYY6Hs7OzAwEDao9q8efOIiIjKb5aioqKsrKzoL7+Pj08D/cOVlJT89ttvurq6tGNLvImpk5PTBfmuT1BL5eXlGzZsoBNoxKuU9e/f/+7duwxWRQgRiUQRERGWlpYAEBAQoPhtWGRXxyhDB2x26tRJvtWwlFSU6dGjR23PkJ+f361bt1wFTmalO51aWFhI/nYePnyYjr9p6LF4lVeOuXTpEij9zlByd/78eU9PzylTprRq1crFxQUAOnfuvGbNGsUPHaBEIrJ//7sJ26qqZOxYoqNDJk1699WNG4mvL3n1iijbhuVOTk4AEB0dLT7y7bffAgCfz1dwJXfv3q38C+zn5wfKvXurAly5coX+hgNA9+7d//vvP6kHFBcXh4aG0nkJTZo0CQ0NlePU14qKivDwcNoazeFw/P396T7qUVFR4kDj4+PDyAIQkZGR4oZYT0/PK1euREVFtWzZknYuBwYGvnz5UvFVEUJSU1P79etHC2vTpo3k35cSqkuUEQ/YVObmJkWKjIyUjDI6Ojp16CKJj49X5EbKZWVl3bp1A4AhQ4ZIHqf75jg4ODTEOjdUlSvHDB8+HAB+/PHHBrqoctq6dSt9u/P69eusrKzo6Oj58+cDwKJFixisqqiIhIaSuXNJUBCZOZOYmZFLlwh5H2WU0NKlS+Hj+Qf0T9LT01ORZTx69MjMzMzV1VXqPcnixYs1NTUb85Rsir7FNzY2BgAul+vv71+53fHp06d0qBPta46MjKz/dRMTE2nYBQB3d3ep2ZECgYDP59N1XDU1NUNCQuq87FNt3bhxo2fPnrQwGxsbydnpRUVF4mCn+IFEWVlZ/v7+tH3IxMQkIiJC+Tv96xJl/vnnH/h4wGYjJxVlQLZFsRj/5Xjw4AH9A96yZYv4YGFhoZ2dHTTkYrs///wzAAwdOlR8JCMjg8fjqampZWZmNtBFldOiRYvg4/2Tx4wZA0ozUyAoiISGku3bSadOpLxceaMMXYfN0NBQ/IpUVFSkpaXF5XIV9huVnZ1tbW0NAIMHD5a869y9e9fIyIjD4SjV6AcGyTLa959//hHv9uDt7Z2amlq3az18+NDHx4eex8rKKjIysrq3i5mZmeKbt4WFRUTd1ieQWXZ2tr+/P+1009PT4/P5VY7XefDgAW3So+21ChhIRNvGtLS0aPN8aGiowoJdPdUlytCx3/gmQ6xylNm9e3fN35KZmdm+fXtF9ihVaceOHbQ5VzJ7Xbt2TV1dncPhHG+AgZ3ilWP+/fdf8cGZM2cCwJgxY+R+OSVHF56SXA6cTsiXmtPEFBplRCLi6kr4fOWNMoSQDh06wMdD977++msA2LBhgwKunpeXRwtwc3OTbM7MyMigYwqHDRvG+FsXpSI52rdz587nzp2TekB5eTmfz6erUaiqqgYHB9eq1zU/Pz84OFhNTY02k4eFhcnSzJyYmOjo6Eir6tGjR0P0s5eUlIizAo/HCw4OlhqAMm7cOMnpeISQ06dP29vbi3vBGmggEW0zs7CwEPfBsWt0V62jTJUDNhu5Q4cOSUWZGTNmfPK7pk2bpgxL8tAF9Tt37iw5tZtuTG1kZJSVlSXfy1VeOaYxz+qnbxmPHj0qPkJfs5haN0wKjTKEkBs3iKEh+eUX5Y0yCxcuBIBJ4nE978fz9erVq6EvXVpaSrsJ7OzsJG9Lr1+/pv+a3t7eSjJHRtmIR/tyOBw/P7/KN+mnT58OHz6cNpa0bNlSloWvKioq+Hw+3YdYRUUlMDCwVi1zQqEwIiKCjsCV71AVmhVatGhB7xEDBgyosvH+zp07la9YVlbG5/PpgGW5DyQihJw/f75r1660MFdX10u0R5lVah1lPrOt/uSicpTx8PCo/DCpZWBKSkro0DNm5efn04bxWbNmiQ+KRCI6Wbp3795yfDdZ5coxlbdhajzoyr+Snfd03TAlmSkgjjL0Y2Nj5Y0ydP0SExMTcW/F27dvNTQ0VFRUGnQimFAopMO8zMzMJMd+FRYW0rFonTp1YmoQNytIDgrR0tIKDQ2tvFzW1atX3dzcuFzu1atXaz5bbGxsu3bt6Itw9+7d67waU25urnzXvLlw4YKzszMtrEOHDnVbjFRyCIutra1cBhKJp6YDgKWlZQ19cEqudlHms9zqr/4qR5kmTZqUf7w0x507d+zs7JSz3/Hy5cuqqqocDkdyjHpOTg6dGyzH1b0qrxxT5TZMjQcdAil+11hYWAgAGhoaSvJqIhll3r4l5ubKG2UIIXSM15kzZ8RHaBxv0IFHs2fPBgB9ff2bEtO6ysvLaXublZVVYxv+VTeSg0Jat25debJMRUVFzS8RKSkp3t7e9Ay2trZy2eApLS2tT58+NfSCySIjI0OcFYyNjcPDw8vrt2J3UlISTcm00TElJaVu53n79m1ISIimpiYAaGtrh4WFsXr2aO2iTOUBm4hUFWUAoHJ3ybRp0yQ3i1EqtH3e2NhYch39kydPcjgcVVXVy5cvy+UqlVeO2bt3L3y8DVPjIRAIOBwOj8cTv+Gjw1eVZ9ny69cJfZ1MSEgQCoU3bpDz55muqXp08pdkg/H27dsB4KuvvmqgK9LF39TV1RMSEiSP0w1rjI2N67PwdyN0+vRpBwcH+vrp4+Mj49YTL1++DAwMVFVVhfdDaOU7H6XOa97QrEA3HlFXVw8JCcnLy5NLSZK9YHUYSFR5avqzZ8/kUhiDahFliouL6c9OcsAmIu+XY5GyY8cOqV+voqIiBweHukX7hiYUCml/f9++fSWbBOg2W61atXr79m09L1FeXj59+vQWLVpInuqLL76Aj7dhajwyMjIAwNzcXHwkISEBFD6F+JNEIlHv3r1fv37NdCGfcO3aNfrzFP8C5+XlqampqaqqNsTAvp07d3I4HC6XK7kvN3m/B4iWlpa83gA0KpKDQuhNuoZXHoFAEBYWRqcRqKioVB5CKy+SvWCyDFURCoXh4eG0vRkA/Pz8ZAy1u3fvNjAwkHFnbNoLRhfYNDU1DQ8Pl2UwQGJiIn3VBQAPD4/PZuPeWkQZOmCz0a7AXYMqo8ywYcPs7Oykmuyq3OJRSYhX+5VcWKy0tJSO55gwYYJcriLZ5Uzv3GZmZo1zUOSFCxcAoGvXruIjdKTqt99+y2BVrGZrayv1XovOCNu1a5d8L3Ty5EnaDCA5+4wQsnbtWgDg8XhKvp6YksvKyvrkAsGRkZFt27alL7b9+/e/fft2Q1f15MkTWda8OXv2rHgZGxcXl4sXL8p+idLS0tzc3Fo13vz333+enp70cl26dKmhoeHBgwfiqenW1tbsHRZTJVmjjHjA5uHDhxu0IDaqMsq4uLiMGzcuICCA6epqgT4RdXX1GzduiA/eunVLQ0NDX19f7rOZ6N/VkiVL5HtatqBz+AcPHiw+smzZMvh4/DWqlTlz5gDA7NmzxUc2bdoEAL5yHeNz7do1uiDT3LlzJY8fPnxYRUWFw+F8ci0GJIukpCTxAsFeXl7iaX3JycniYTEODg51G0JbZ5Jr3kgNVZFcxkbBQ2jFCwTTDiOpXYHp1HQavnV1dWWcms4uskaZxrbVX60cOXKkcpTR0NDIy8tr27bt3r17mS6wFuhm7u3atZNsTzp27JjcFzPAWf2rVq0CgKlTp4qPTJ8+HQB+//13BqtitYsXLwKAlZWV+BaSnZ09ZMgQqT6g+qBL3gHAmDFjJG9UZ8+epR0Qv/zyi7yuheigEPECwX5+fqNHj6YTi4yMjMLDwxlZprXymjfPnj0TL2PD1BBayV4wbW3t0NBQgUBQeWq63N+RKglZo0wj3OpPdlVGGQC4cePGxYsXO3bsyKL8J17tV3KJjoZAh0ZOmzatQa+izPIXLnzu7HxX4m9qwfjxxlpa9d9ZvdESiUR067tPztqtm+fPn9M+rH79+kneRP/77z96Y5s+fXpDXLeRy8nJGT9+PJfLpfOAVFRUJkyYIDlBgRFPnz4dMWIELYkO7gGAoUOHPnz4sM7nzH2vzsvGpKSk9OrVixZjZ2cnHkbt7OzM7JaZDU2mKNM4t/qTXXVRZvv27aTScjLK79q1a/TtxcGDBxvoEjirnxBCRo4kAERyIzM3NwJAEhOZq4n1goODoWE28yooKOjSpQsAuLq6Sr4Sipf09fPzY9GbFtZJSkpatmzZwoULK29FyYh9+/Y5OTnNnDnTzc1t9uzZ3bt3nzVrlre3d0xMTN1OKBQKDd5bvnx5fWqLi4uzt7fX0tLS0tKS19R0JSdTlGmcW/3JLiEhQbwzu5ihoSF7Z7jRWaYGBgb17FcSCARPnjz5999///zzzzVr1ixYsCAgIKBv374WFhYcDmfQoEHyKpiVvLwIAJHs6be0JACkHu/qUGJiIgC0bt1avqcVCARffvklALRt21ZyMVZc0rfR+uOPPwBg5syZQqFQJBIJhUK6fqzklnYMKioqOnPmTEJCQiNpgOBV2Zwg6fHjx4cPH1ZTU5s2bdonH9w49ejRY+/evZcuXTIxMREIBGvWrNm9e3e3bt1onzobzZo1KyEhISYmZtSoUQkJCXS+X5XevHnz7Nmz7OzsrKysyv8vLS2t7hsXL148dOjQhimfJTIzAQDez9gEkQiys4HDgebNGSyK7Tw8PMzMzO7fv3/r1i26L5Jc/Pjjj/Hx8c2aNTt+/HizZs3owaKiIjp3plOnTkeOHKFtmaiREIlEAMDlculMKw6HIz7CcGUAANCkSRMvLy+mq1CcT0eZ1atXV1RUjBkzpjm+wlZvxIgRI0aMoB9zudwnT56Ih7KzEYfD2b59u6Oj47lz58LCwsaNG0ejiZg4r+Tk5NA/4CpxuVwTE5PmzZubmZk1f8/MzMzc3NzGxoYOL2i8srIAJKLMy5dQXg6GhqChwWBRbMflcn19fTdt2vTrr7+uXLlSvOVNPU2bNu38+fNbtmwRTwCuqKgYPnz45cuXraysYmJixKMlUCNRObgoVZRpbD4RZfLz87du3crhcOj63EgWdI0stjM2Nt6wYcOQIUPCwsJ++umn6h7G4XBMTExMTU0tLCxMTU3Nzc3p/2leMTExqaFFp1HLz4fiYtDRAfEtUKqRBtXV8OHDnz59GhkZGRkZqaOj07FjRycnJycnJ09PT7rdWB1YW1tfvHhR8i71/fffR0dHGxsbx8XF4du8RkjuUSYjI+P169fiTzt37oypSHafiDJbt24tKCjo06ePeCY9ajy+/vrriIiIEydOnD59WhxWLCwsTExMJD+myxWg2qHBRfIWKNVIg+rKy8urSZMmXC43KSkpJyfnwoULdDVCDofTunXrrl27Ojs7d+3atXPnzhq1aQCTvK8sXLhwy5YtWlpaf/31V6tWreT/HJDSk3uU2bFjR0xMjPjT8+fP1+r3s5GrKcrQ2fMAgE0yjdbo0aNHjx7NdBWfo8ptMNgqIz9du3aNiooCgPz8/KtXr54/f/7atWuXLl26d+/evXv36M5fAGBjY+Pu7k7bbLp06SLjnWPt2rWLFi3i8XgHDx4Ub3eMGhu5R5lFixYtWrRILrU1QjVFmdzcXEdHR319fbr4N0JIbmgbjGSrDEaZBqCvr+/t7S1eHDYrK+vChQs02Vy7di09PT09PX337t0AwOPx2rRp4+Tk5OHh4e7u3q5duyrvSUeOHJk5cyaHw9mxYwfdeRs1TjhWRqnUFGVMTExiYmJKSkoqzzRGCNULtsowoXnz5n5+fn5+fgBQUVFx9+5dcbK5c+fO7du3b9++TZNNlYNszp07N2rUKKFQ+Ouvv44aNYrhJ4MYhVFGqXx6BpOmpqYC6kCocak8MgajjGLxeDwHBwcHB4fAwEAAyM7OTkpKSkpKunz58pUrV96+fSseZAMArVu3trOzO3v2bGlp6fjx4+fPn89o7Yh5hBAAkHyfX58o8/LlyzNnzkgesbW1FW9hjT7p01EGISR/2CqjZMzMzHx9fX19femnWVlZtBPqwoUL//777/379+/fv+/m5mZubr5582ZsqEbybZV59OjR/v376fZS9FQeHh4YZWSHUQYhJixYAMOGwfuNfwEAuFxQUwMzM+ZqQh/QNZAGDhwIAKWlpdevX09KSho2bJihoSH2ICCQd5TZtm1bu3btlixZQj+Nj4+fOHHijBkz5FFpo4BRBiEmdO0KZmawZQtkZYGuLgwfDsnJTNeEqqahoeHm5ubm5sZ0IUiJDNfVdXR1bS+xzudkC4uvPD074wxqJuDbC4SYcPUqdO4MeXnQowfo60OvXrBjB9M1IYRk1T431+/ixXZFReIjfTMyAs+da1lRwWBVjRa2yiDEhKlTYcYMWLDg3adffAF+uvXrqwAAIABJREFUfjBkCDTyzRwQYgu6YYtkd1LlI7Vx8uTJvLw8+nEmHTmHZIZRBiGFKy2Fq1fh4MEPR776CvT14fp16NmTubIQQjKrHFwIAQCo65BwS0tLT09P+nFqampKSkr96mtcMMogpHCZmSASSe+AbW4OT54wVBBCqJYqB5f6tcrY29uL9ySOj4/fv39//eprXHCsDEIKZ2oKHA68evXRwZcvcfoSQqwh7w4mVB/4Q0dI4bS0wNYW/v77w5HbtyEzEzp0YK4mhFBtYJRRJtjBhBATFi2C6dNBVRW+/BLu3IHgYJg0CVtlEGINuUaZhQsXitfHAwAXF5e/Jd/qoE/BKIMQE0aOBH192LQJFi8GCwuYOhUmTWK6JoSQzOQaZcw+fhvTpEmTVq1a1aO4RgejDEIM6d8f+vdnugiEUJ1gB5MywR86QgghVEsYZZQJ/tARQgihWsIoo0ywgwkhhBCqpSFDoFUrcHb+cGTUKOjeHTe3ZwSH0HV+EEIIISQ7kQi2b4eoKCgpARsbmDMHWrdmuqZGCltlEEIIodqbOBEuXYKlS8HYGGJjwdkZ4uOhc2emy2qMsFUGIYQQqqUbN8DNDe7fBwuLd0dmzoS7dyE2ltGyGikcoIQQQgjV0pUr4OLyIccAgJ8fJCUxV1CjhlEGIYQQqqXnz8HI6KMjxsbw+jWUlTFUUKOGUQYhhBCqJQsLyM7+6Eh2NpiagpoaQwU1ahhlEEIIoVrq1g2SkuDp0w9HIiPB1ZW5gho1nMGEEEII1ZKDA0yeDN7eMH8+GBnBqVNw4ACcP890WY0UzmBCCCGEao8QOHgQTpyAkhKwtYVJk8DKiumaGimMMgghhBBiMRwrgxBCCCEWwyiDEEIIIRbDKIMQQgghFsMogxBCCCEWwyiDEEIIIRbDKIMQQgghFsMogxBCCCEWwyiDEEIIIRbDKIMQQgghFsMogxBCCCEWwyiDEEIIIRbDKIMQQgghFsMogxBCCCEWwyiDEEIIIRbDKIMQQgghFsMogxBCCCEWwyiDEEIIIRbDKIMQQgghFsMogxBCCCEWwyiDEEIIIRbDKIMQQgghFsMogxBCCCEWwyiDEEIIIRbDKIMQQgghFsMogxBCCCEWwyiDEEIIIRbDKIMQQgghFsMogxBCCCEWwyiDEEIIIRbDKIMQQgghFsMogxBCCCEWwyiDEEIIIRbDKIMQQgghFsMogxBCCCEWwyiDEEIIIRbDKIMQQgghFsMogxBCCCEWwyiDEEIIIRbDKIMQQgghFsMogxBCCCEWwyiDEEIIIRbDKIMQQgghFsMogxBCCCEWwyiDEEIIIRbDKIMQQgghFsMogxBCCCEWwyiDEEIIIRbDKIMQQgghFsMogxBCCCEWwyiDEEIIIRbDKIMQQgghFsMogxBCCCEWwyiDEEIIIRbDKIMQQgghFsMogxBCCCEWwyiDEEIIIRbDKIMQQgghFsMogxBCCCEWwyiDEEIIIRbDKIMQQgghFsMogxBCCCEWwyiDEEIIIRbDKIMQQgghFsMogxBCCCEWwyiDEEIIIRbDKIMQQgghFsMogxBCCCEWwyiDEEIIIRbDKIMQQgghFsMogxBCCCEWwyiDEEIIIRbDKNMo7N+//8yZM0xXgVCD2Lp1a1JSEtNVIKQId+7c2bx5c2FhIdOFKBcOIYTZCjZu3Jienl75uKur65AhQxr00pcvXz527FhGRkbTpk179+7t4+PD4/HEX83Pz9+9e/fVq1c1NTU9PT1HjBjB5XLFX9q2bduNGzc0NDR69+79zTffcDgcqZOvWrXqzp07ZmZmCxcurFVVP/zww9u3bwFAW1u7bdu2Xl5ebdu2rdfzBLC2tvby8tq5c2d1DxCJREeOHDlz5szr16+tra2HDRvm5OQk9YCDBw+ePn1aIBA4OTmNHz9eV1f3n3/+iYyMrHy2lStX6ujo1LPmz8bjx4/5fH6VX/rf//7XtGnThi4gNjb2+PHjALBixQpdXV3JL92+fXv37t2PHj0yMTEZOnRo9+7d6fHc3NydO3fS33A3Nzd/f3/6p1FeXh4ZGXn69Ony8nJ7e/sJEyYYGxvLXgkhZPLkyfRjHR0dS0vLL7/8sn379vV8gurq6rNnz166dGnNDzt79uzevXsBIDQ0tHnz5pJfevDgwbZt2x49emRsbNy7d++BAwdKfjUuLu7kyZPPnj0zMzPz8fH58ssv6UsBISQ2Nvb06dOZmZktWrTw9fX19PSs/FLQeCQlJe3fv7/ycVVV1eXLlyuggG3btiUlJWlpaf3xxx/VPWbJkiVPnjyxtbWdO3eu+GB0dHR0dPTbt2/bt28/btw4U1NTejwvL2/nzp3Xr1/X0NBwdXX19/dXVVWVvZ6EhIQDBw4AAIfDMTMzs7W19fX1redr49atWydOnPjkyZMWLVrU/MjFixdnZma2adNm9uzZksdFIlF0dPSJEyfevn3bqlWrwMBAc3Nzqe/dsGFDcnJy06ZNf/vtN6kvxcTEREVFgbK9zhOmzZw5s1evXr169bK2tgaAFi1a0E/5fH6DXnfBggUcDsfS0nLQoEGDBg3q2LFjSUmJ+Ks3btwwMzMzNTUdNmxYz549AeDLL7+sqKgghGRnZ1tZWTVp0sTX19fLywsAvvnmG5FIJHny+Ph4DofTrFkze3v72hZmYmJiZmbm7e3t6upqYGDA5XJXrVpVzydrZWUVEBBQ3VffvHnTs2dPLpfr6Og4dOjQHj16BAYGSj5AJBJ9/fXXANCzZ89BgwZpamq2atXqxYsXR44c8f5Yy5YteTzemzdv6lnw5yQtLa3ve82aNdPR0RF/+vz584a++suXL5s1a2ZmZgYAUpdbv369qqqql5fX+PHjaXINCwsjhFy9etXY2NjOzm7MmDEDBw5UUVH58ssvy8vLBQKBt7e3mppa//79R40aZWhoqK+vn5ycLHsxQqEQAOzs7Pz8/Pr27WtsbMzlcjdu3FjP56impvbjjz/W/JjCwkIrKyv6c0hJSZH8UmxsrKampo2NzZgxYzw8PABgzJgx9EsVFRXDhw8HAGdn57Fjxw4YMMDLy4v+sQsEAh8fHw6H4+bmNm7cuL59+w4YMKCeT4Tt/v77b/HvtoaGhqmpKf144MCBCrh6cnKyqqqqmZlZ06ZNq3vMn3/+yeVyTU1N3d3dxQeDgoLoi9u4ceOaNm1qZGR07949QsiNGzdMTU3btm0bEBAwaNAgHo/n5eVVVlYme0lr164FgAEDBgwbNszFxUVFRcXa2vrp06f1eZpbtmwBgCdPntT8sMjISC6Xa2Ji4uXlJXlcIBB89dVXenp6Q4YMCQgIMDEx0dbWvnnzpuRjLl26pKKiYmZmZmlpKXXaFy9eiF9PXrx4UZ8nIl/MRxmx+Ph4AIiNjVXAtQ4fPgwAoaGhUhFEbOLEiS4uLgUFBfTTX3/9FQCio6MJIePHj1dVVU1MTKRfou8Fo6KixN9bUFDQsmXLr7/+2s/Pr25RRhw7SkpKaFtRPe95NUeZcePGqaqqnjt3rroHHDp0iP646KdJSUk8Hu/777+XephQKGzbtu3IkSPrU+rnrW/fvh07dlTkFb/99ltbW9uVK1dKRRmBQODo6Lht2zbxkQEDBmhoaJSVlc2ePfubb76hwZ0Qsn79egD4+++/4+Pj9fT0Ll68SI8/efJES0vrm2++kb0YGmXEsaOwsLBbt25aWloCgaA+z1GWKDNt2jRjY+NNmzZVjjL9+vUbMmSI+BYVHBwMAKmpqYSQVatWAYDkT0mMtrYeOnSoPpV/xiwtLb/99luFXa6srMzR0bFXr17Tpk2rLsrQWD916lRvb29xlDl37hwATJkyhX766NEjAwODvn37EkLmzp07dOhQ8R9CeHg4AMTExMheFY0y4tiRkJDA5XKnT59et+dIyRJlcnJyDA0Np0+f3qNHD6koc+HCBSsrq4yMDPrp8+fPtbW1R4wYIX5ASUlJ27ZtBw0aNHbs2MpRxs/Pr23btr///jtGmWpVjjJlZWVhYWHZ2dnR0dEhISHHjx8vLCwMCwu7fv26+DEnTpxYt24d/fjBgwfLly8PCQn5/fffs7Oza7iWh4eHhYVFzS+gRUVF4o8zMjIAYMmSJWVlZTo6OpJvvwoKCqRe0GfNmqWnp5eVlVX/KEMIoT04cXFxd+/eXb16dWlp6caNG3/88Uf6clxeXn7kyJEff/xx/vz5Uinw0qVLixYtmjdvHp/PNzQ0rC7KvHr1SlVVtYagQwihjaLFxcXiI3379jUwMBD/kVO01fHatWu1fcqNR+Uoc/bs2QMHDmRmZi5evHjmzJkvX778559/JNvhSkpKwsLCrly5QgipqKg4dOjQlClTJk+efOzYseqCuNixY8cA4OTJkzSOSAViqX++efPmiV+eJL909uxZANi5cychRPJ3gBBCez9lf/pSUYYQsnr1apotrl+/vnXr1tevX4eFhQUHBz969IgQUlpaumPHjsDAwGnTpiUkJIi/SyQSxcXFLViwYOrUqStXruTxeDVHmXPnznG53F27dh08eLBylBGJRJItsnRU2b59+4RCoYWFhaura+UTCgSCpk2b9unTR/bn3thUjjJHjx49derU7du3582bFxISIhQKDx48uGvXLvEDnj17FhYWlp6eTggpLi7esmVLYGBgUFBQDe+yxJYtW6ahoXHv3r2goKDqoszYsWObN2/+5s0bySgzZcoUlf+zd+dxMad/AMA/c3SaEkV3SyW6iCJUyMaGLJbc49YSm+NnFUthHbnWyFnryhHGHRa1lpQjOujCakroTqeuqZnn98fD1+wUwlzpeb/2tS/z9J3v88z9+T7P53keBkP0ozFv3jw6nZ6fn4/++0G4c+cOAOzbt6/pT4JYKIMQwjkDCKF9+/YlJCTcvn170aJFW7duxX999uzZihUrvLy81qxZI9qk169fh4SE/PLLL0uXLp04ceInQxk2m21oaFheXt4wlEENPvhmZmYDBgygbq5cuZLFYmVlZTUMZc6dO4evavDjUqhQRqHTfvl8vp+f3+jRo2fMmBEREZGenl5RUeHn53fv3j3qmLNnz+J+kStXrlhZWYWEhPB4vF27dnXt2vXVq1cAsHz58p07d4qetrq6+t69e4MHD1ZWVk5PT4+KiiopKWlYu7q6umhLAEBJSenVq1cVFRUDBw6k/sRisXr16vX48WN88+7duxwOZ/Xq1bgL7usVFBQAgI6OTmpq6sKFC11dXbds2XLp0qXKysq6ujp3d/fx48c/fPgwKSnJw8MD/xoBwPz583v37n3+/Pn09PTTp09XVFQAQFxc3Jw5cwICAkTPf/v27bq6uuHDh9fV1cXHx9+7d6+urk6sDU+ePOnTp4+amhpV4urqWlJSkp+fL3rY1q1bBwwY0KNHD4k88BYiMjLy119/7dOnD5fLvXbtmqqq6qVLl0Rfo6qqKj8/v9u3b9fW1g4aNIjNZpeUlBQVFY0ePXrRokUAcP/+/VmzZj19+lTszKWlpd7e3ngop9GqGQwG9e+8vLyTJ0+6uLi0a9dO9E98Pn/Pnj0aGhqDBw8GANH3AABUV1crKyt/zcPPzs4GAB0dnbt37y5evLh///6hoaHXr19HCBUXFzs4OCxatKi6uprH47m6uuKUo7q6uhEjRvzwww8JCQlVVVWXLl3CEVJaWtqsWbPi4+PFqqipqZk1a5arqyubzW60DTQaTVVVlbpZVVUFAEpKShkZGa9evRoyZEhtbW1iYmJ0dDROYgOAlJSU4uLioUOHVldXx8fHx8TEVFZWfs3z0BIcO3ZsyZIlffv2vXbt2r179+h0+sGDB3GQjT1//tzPz+/Zs2cFBQXdu3f39fWtqal5+vSpi4sL7k67cOHCrFmzqFeBkp6evmrVqqVLl3bq1OlDtUdGRh48eHDr1q1i6WLPnj3r3Lmzrq4uVeLi4iIUCnk8Hoh8EOrq6vbs2dOqVasPfZqaora2tqioSEdHBwC2bdvm7e3t7u5+69atpKQkADh16pSVldWVK1fq6+sPHjxI/YTFxcVZWFisWrWquLj4+fPn1M/frl27Fi9e3LCWa9euHTlyhMPhfCiRRfSDf/HixYyMjNGjR+ObDx8+3LBhg7+/v4mJidi98PfJuHHj8FeBwpF3LPVew14ZnKTt6upKXTPl5uYCwO7du6ljZs+ebWBgUFNTo6ur+/333+Ne4sLCQg0Njf/9738IIWNjY3d3d9GK8Jf+mDFjunbtip8EVVXV9evXf6RtmzdvptFo+OsMAI4ePSr61/Hjx7dp0wYhxOfzbW1te/fuLRAIEEJf3Cvj4eERFxf34MGD/fv36+jomJub8/n8s2fPgsgoD0KIw+HQaLS///4b31y+fLmqqmp+fj6+9Ny8eTN1JB5gSk5OBoCgoCDR6vDPw8KFC6n8U0NDQ/xbQmnVqtWUKVNESw4ePAgA9+7do0rwB0x0oI1oqGGvzMqVKwHg/PnzVMmiRYs0NTWpm69fvwYADoeDX6lbt27h8tWrVzOZzKysrLCwMBqNdvPmTbG65s2bp6WlhbsnG+2VwXx9fZ2dnVu1auXu7l5YWEiVnzlzxtXVVV9fv2PHjrGxsQ3v+Pz5cwaDsXz58qY/fBxzTJs2LS4uLjY2dseOHerq6rjbA7dwy5Yt1MELFixQU1PDWQsIoenTp7dt2/bNmzc4gfTEiRPUkXiAKTIykkajnT59WqzSgIAAfL2OEGq0V0bM7NmzWSxWUVHR33//DQDjxo2jfudUVFRCQkIQQvjDOGnSJG1tbfwndXX1Y8eONf2p+OY17JUZM2aMurr6w4cPqRJ3d3dHR0fqZkxMDABcu3bt559/ZrFYuGcOITR+/Pj27dvX1NT4+/vTaDTcX0IRCoUDBgzo3LlzTU0NQqjRXhmcKTV06FB8U7RXxtLSUrRPAr37JeJyufjm+fPnXV1dDQwMvvvuO2p0tYlw78Xly5fj4uJu3ryJMw5xR5S1tbWxsXFOTg7VQi0trREjRuCu1oKCAhaLtXDhwvr6ejMzMwsLC+qzSQ0wjRo1SldXV6xGnN7g4eGBbzbaK4MPc3Nzs7OzYzAYGzZswJXW19f36tXLzs6urq4OISTWKzN37lzq+0QBe2XeT9hRWO7u7qLXTI1KSUnJz8+fOXNmVFQULjE1Nb19+zYAZGVliR1cW1sLANHR0Rs2bBg+fLiSktL8+fOXL1/u6Ogo2t1CSU9PX7t27aRJk+zs7G7cuAEAohOdAIDBYNTX1wPA5s2bHz9+HB8fT811+jI4nR4AVFVVhw4dunXrViptfuTIkdRh169fNzQ0RAjh71xtbe2ampr4+Phjx44ZGxs3DNhtbGwEAoHYDIuamhoAuHPnDpfLdXJywp+QsWPHPn/+nMVi4WMEAoFoIE89A/hRY9u2bbO0tPTw8PiaB94y0en0ESNGfPKwW7dutW/fPi8vD6cuMZnM+vr6Bw8eTJgwYcKECWIHx8TE7NmzZ9u2bdRcjA/p16+fhoZG+/btr169evjwYept06lTp+HDh3fu3DksLGzz5s2HDx8W7ZIRCoXe3t46Ojq+vr6f92gBDh06hCfTqaurjx07NjAwkPrT5MmTqX9HR0ebmpo+fPjw4cOHANC6devi4uKnT59yuVwHB4dx48aJndbNzU0oFIoVpqambtiwwc/P7yPX66JiYmIOHTq0Zs0a/GkCgISEhMOHDzs5OVVWVrLZbG9vb2dnZ/ynR48enT592tHRsbi4eMKECTNmzHB2dm54OUtQOnbs2K1bt08eFh0d3alTpwcPHjx48AAA2rZtW1BQwOPxVq9evXr1arGDDx48ePPmzYiICBUVlQ+dcNWqVXl5eZGRkQ3/VF9fL/blhm9SX27m5uY//vjjv//+GxYWtmnTpqNHj4p22DfFsGHD8D86duy4b98+qnfQ0dGR6rxPTk4uLS01MzPDeZwAYGxsfO/evfj4eB6Ph69pxU6L42kxK1euLCoqEhuIaEhZWXnUqFG5ubkCgWDv3r2DBg2yt7ffuXNnXFzc3bt3xX7gACA6Ojo4OHj79u2f/D6Rl2YQyjQFzmU5f/78tWvXcAmTycQXTA3nRuJrrAULFkyfPh2X7Ny589ixY2fPnm0YyuTk5AwZMsTExARfE+NJa2IDKwUFBUZGRjweb926dSNGjGCxWHh6+Zs3b/h8fkZGhqGh4Uc+Zg2NHz9+9+7dANCmTZuPP+o3b95Qg0oAYG9vz+fznz9/3rlz50bDqYaF+NkIDg62s7MDAAsLi5UrV06YMOHWrVtDhw7FxxgYGOBxLtGHDABGRkb4Jo/HO3369K5du1ryTFRpe/HiRW1t7caNG6kSe3t70WiSUldX5+3tbWJi4u7ujt+KRUVFAJCVlaWqqtq6dWvRg4cOHYpf6OXLl//666/Dhg3Dk/9tbW1tbW0BYNKkSS4uLs7OzgsWLMB3QQjNmzfvxo0bf/31l1h3fVMsXLjQ39+fTqeLtURMVlYWnU4Xe7yVlZXPnz8fMmRIUyoSCoVz585t3bq1p6cnfh7w+xZPq244DT4lJWXUqFE//PADnryKPxr+/v64Rx1P8bWxsblw4UKvXr0AYN26dQMGDAAAQ0PDwMBAJyeny5cvz5079zOeC6IxWVlZLBZL7KVvdCWVwsJCX1/f/v37m5mZ4Ze4rKxMKBRmZGTo6enhmOPRo0fbt2+fMmUKnU7Hx1RXV9fU1GRkZJiYmBgaGjb65UZNdba2tra2tgaAKVOm9OnTZ8+ePWJzmz8pOTnZ0NBQTU3tI9fk+JL76tWr1NW4urq6trY2/mnDDfikhISEnTt3zpgxQyAQUI8UIYQfqWiAoqys7O3tDQArV67s3r377Nmzw8PD/f393d3ddXR08H0rKirq6+szMjJ0dHS8vb2/++67wYMH4z/hruKsrCxlZeWPf4pl5hsJZfDiFtu3b3dzc/vkwe3atVNRUcFDoRiLxVJSUsJXWqISExPHjBnDYrEiIyNxYGRoaMhkMhMSEqhjBALBo0eP7O3tDx06VFVVdebMmTNnzoiexMzMLD4+/rMySFRUVD4exGDt27fX0NDAnU+itm3bVl1d3cS6cDiSnp6OQxl4Fz+JnsHExCQxMVEoFFKRUHx8vIqKCnVJsWPHjrZt206ZMqWJlRJfoH379gihuLi4Tx5569YtPJgotiKRo6Pjli1bPvRF7OrqumHDhkePHondy8nJSVlZOTExEd+srKycPXv2uXPnTp8+jX/IP5eamlpT3t66urqWlpbURSpFW1u7iW/v5ORkPCKMYzKKu7v7smXLxNahiYyMnDhxop2dHZfLxZ2g1EeDOgZ/a/P5/IZ/0tLSgnc9vsRX0tXV7dOnz9GjRz955MmTJ4uKiqKioszMzETLzczMLl++jGP0P//8s66ubv/+/fv37xc7JiMjo2PHjvfu3SsvL6eCcpxuZWpqKlZX79691dTUqA9C07Vu3fqTb3gcN+/YsUPschr3uOP8rU8KCQmpr68PCQkJCQkRLTczM/vQOjTKysp9+/Y9cODA4cOHy8vL//rrr7/++kvsvlu3bk1JSYEG3yc9e/b8448/cMae3Cl02m9DrVu3ptPphYWF+CaONwHA0tJSSUnp4sWLDe9SVFRUWloqWkKj0VxdXc+dO1dWVoZLzpw5w+fzHR0dRQ/buHFjr169nJ2dY2NjqXXAcErBhQsXcNYOAFy4cKGgoGDMmDGLFi3i/deQIUPMzc15PF4TY+rP1a1bt8TERJwaJsrS0jIxMRFfiANAeno6Tq6sra3Nz8/HATWld+/erVq1wsO3uOTEiRN0Or1nz57UMWPGjMnJycETlAAgPz//4sWLI0aMwCmfr1+/3rdv39y5c8VyQokvgzNCqF9rKubu1q1bSkpKZmam2PHFxcXZ2dk4sxvr27ev2FsRd8vHxsbOmjWLOmznzp2ibx7cmW9kZPT333+LdsU/evSI+vFOSkrq3r37vXv3YmNjqW5zKenWrdutW7eoDymlS5cu0dHR1IVHTEwMzsovLy/Pzs4WTeHv0qWL2POAx/ivXr26ZMkS6jCBQODn5+fu7j5z5syrV69Sb2M9PT0rK6sTJ07g8wMATrVxdHQ0Nzc3MTE5duwY1SuGV0LDvTVEE7Vt25b6moL/vtX/+eefhpnU2dnZ2dnZoj2RbDZb7CWeMmWKlpYWj8ej4uxVq1aJHePk5GRvb8/j8YyNjUeNGlVTU3PgwAF8cGVl5fHjx3v37m1gYHDjxo2rV69SdaWkpFRXV1Nd0ZJlZWXFZDIb/oR16dKFRqOJfh5xKg8AFBcX5+XliR78+++/iz1SR0fHXr168Xg86rKztLR08+bN1HMoFAoTEhL09fW9vb3F7jtmzBgDAwMejzd9+nSxP+GVCB48eDBjxgxpPBtfQp6JOv/1obTfjRs3ih7Wr18/AwOD48ePc7ncYcOGaWtrGxgYIIT8/PzodPrixYtPnDgREhIyduzYc+fOocbSfhFC9+7dU1FR6dKlS2BgoK+vb6tWrXr06FFVVRUVFdW1a9eoqCjcS9y+ffulS5f6voOn4SUlJbFYLEtLyx07dvz+++8aGhoODg6NrpskkcnYFDwympiYSJW8fPmyXbt2Xbp0OXDgQFhY2KpVq3DWWFpamrq6eu/evY8cOXLgwAELCwtVVdUPpf0ihNatWwcAQ4YM2b59O14QDGdMr127tmvXrgKBoLq6umvXriwWa926dUFBQZaWlq1bt37y5Am++/r163G68ec+0hao0bRfOp0uWnLnzh0ajTZ9+nQul7t+/fqOHTsymUwOh5OTk2NgYNChQ4egoKCwsLA1a9YMGzZMIBDgFWxF5yo3JJr2u2PHDisrq4yMDAsLCz09vbVr1+7du3f+/PnKysoDBgwQCoXTpk1jMpnz588PDg5eu3atgYGBjo7OixcvIiIiNDQ0aDTa1KlTfUWUl5c38eGoCHVtAAAgAElEQVQ3nIzdaAux5ORkDQ2Nbt26BQcHHz16dPny5fhzER0djRcrO3To0MaNG3V1dXHab0REBHxqoRfRtN+jR49aWVk9ffoUx2Tm5uaiD+rMmTMIoQsXLjAYDAcHh1WrVs2aNYvBYAwZMgQn9R87doxGo/Xp02fNmjVTpkyh0Wienp5NfB5agkbTfq2trUVLcDfJihUruFzukiVL8PD9tWvXEhIS1NXV7e3tQ0JCjhw54uvrO3v2bITQihUr4APZ6xTRtN+FCxc2OpdeNO1XKBQOGjSITqcvWbJk165ddnZ2ysrKMTExCCH8int7ewcHB69bt87Q0FBbW5tKRm6KhpOxKdbW1mPGjBEtWbp0KZ1O//nnn8PCwkJCQjw9PS9cuIAQwksM+/r6Hjt2bPLkyTjUfvHixYgRI9q1a/fxBoim/Q4bNmzq1KkRERHKysouLi5BQUE7duwYNGgQAOzatavhfRtdV0b0cZG038Y9e/YMz2qmBsIZDIabm1uHDh1EDwsNDf3ll19Wrlyprq4+YcKEOXPm4H7I9evX6+vrHzt27Pz58ywWa8CAAXiC0oIFCxqure7o6PjPP/9s2LAhJCSExWJ5e3uvWLFCTU2NTqerqqrS6fTXr1/jsSrRsSSEEADY2treuXPH399/27ZtDAbDy8tr5cqVja5mbWtr+wWZBP369bOysmpY3r59ezc3N9H5dUZGRjExMatXr96wYQONRjMyMpoxY4ZQKLS0tLx169bGjRtxkLFixYrMzExVVVWE0IoVKxqmRi5btqx9+/b79u3bvn27gYFBSEgIvnZXUlLCg7uqqqo3btxYs2bNoUOHBAJB9+7dz5w5Q3U2/vvvv76+vp+1gH2LZW1tLZY3Z2pq+v3334uW9OnT58CBA8HBwVFRUfb29levXl27dq2JiYm+vn5sbOzKlSt37NjBZDItLCzYbLZQKKTRaKtWrfp4lpKxsTFeqBcAVFVVtbS0tLS07t+/v2nTpuPHj1dXV7dq1WrlypWLFy+m0WgHDhxwcXHZv3//X3/9RafThwwZ8ttvvxkbG1+7dg33XOKLY+rkDWfvfwiNRnNzcxMbC2jYQszGxubevXv+/v6bNm1SU1OzsbHB+ZLOzs4REREcDmfDhg2tW7fet2/f33//bWZm1pTnQVdX183NDeezq6ioUKNC+MMuOpEbv0w//vhjRETE+vXrDx8+3KZNGzzjFw+zTpw4sXXr1ps3bz506JCOjk5gYGCjM2NbLAcHB7HxCFtbW7G8iqlTp+bm5p49e/bEiRPff/99bGzs9OnTtbW1u3fvfvfu3YCAgI0bN6qrq9va2uLBazqd/smXGC/cgv/dqlWrRjM5evToQQ0F0mi08+fPb9my5eLFixcvXrSxsdmzZ0/v3r0BICQkxMnJad++fVevXqXT6T/88MNvv/0m9nv0cfhd3WiKTO/evcUyxAMDA01NTQ8cOBAZGamvr0/9hO3bt8/c3DwiIuLUqVN9+vS5fv26v7+/qqrqhAkT8OLUH2Fvb4/edbdramqyWKxBgwY9ePBgw4YNOPuzQ4cO586dE51NQrGysvrQgGnDT6vcyX8PJoIgCIIgiC/WzHJlCIIgCIIgRJFQhiAIgiCIZoyEMgRBEARBNGMklCEIgiAIohkjoQxBEARBEM0YCWUIgiAIgmjGSChDEARBEEQzRkIZgiAIgiCaMRLKEARBEATRjJFQhiAIgiCIZoyEMgRBEARBNGMklCEIgiAIohkjoQxBEARBEM0YCWUIgiAIgmjGSChDEARBEEQzRkIZgiAIgiCaMRLKEARBEATRjJFQhiAIgiCIZoyEMgRBEARBNGMklCEIgiAIohkjoQxBEARBEM0YCWUIgiAIgmjGSChDEARBEEQzRkIZgiAIgiCaMRLKEARBEATRjJFQhiAIgiCIZoyEMgRBEARBNGMklCEIgiAIohkjoQxBEARBEM0YCWUIgiAIgmjGSChDEARBEEQzRkIZgiAIgiCaMRLKEARBEATRjJFQhiAIgiCIZoyEMgRBEARBNGMklCEIgiAIohkjoQxBEARBEM0YCWUIgiAIgmjGSChDEARBEEQzRkIZgiAIgiCaMRLKEARBEATRjJFQhiAIgiCIZoyEMgRBEARBNGMklCEIgiAIohkjoQxBEARBEM0YCWUIgiAIgmjGSChDEARBEEQzRkIZgiAIgiCaMRLKEARBEATRjJFQhiAIgiCIZoyEMgRBEARBNGMklCEIgiAIohkjoQxBEARBEM0YCWUIgiAIgmjGSChDEARBEEQzRkIZgiAIgiCaMRLKEARBEATRjJFQhiAIgiCIZoyEMgRBEARBNGMklCEIgiAIohkjoQxBEARBEM0YCWUIgiAIgmjGSChDEARBEEQzRkIZgiC+Vk0NZGSAQPD2pkAAGRmAkFzbRBBEi0FCGYIgvlZsLJiZwR9/vL1ZUgJmZlBfL9c2EQTRYpBQhiAICdDVhS1b4NUrebeDIIiWh4QyBEFIQLt2MGsW/PKLvNtBEETLw5R3AySprq7u33//TUlJKSoqYrPZmpqa8m4RQbQgy5aBpSVcuABOTvJuCkEQLUkzDmVqa2tTUlJSU1PT0tJSU1Pj4+Nzc3Pxn5SVlZcvX75z5042my3fRhJEy8FiwR9/wIIFEBPztqS6GtTU5NomgiBagOYUyhQVFSUlJaWkpKSkpCQnJ6emplZUVIgeoKys3LlzZxsbmzdv3ly8ePHnn3+2tLR0cHCQV4MJoqXx9IR9+4DDAQBIS4PevcHTE379FWxt5d0ygiC+XTSkqDMm8/PzcbwSHx+flpb27Nmz8vJy0QNUVVWtra2trKzs7e3xPwwMDKi/LliwICgoSFdX9/79+yYmJjJvPkG0CFeuwJ9/wvz5sGABJCcDAPz7Lzg4QEUFcDiweDEIhUCnw9ChsHAhfP+9vJv79V68gOBgePYMVFVh8GCYMAEYDHm3iSBaOkUJZSorKxMTE6mhorS0tJKSEtED6HR6ly5dcMiC/29hYaGkpPShEwoEgpEjR166dKlbt24xMTEsFkv6D4IgWhA+H5Ytg23bACHw84NLl96GMgCwejWsWgV8PmRnw969EBIC+NNsZga//AIzZ0Jz/TimpYGLC0yYAO7uUFICgYHQtSscPy7vZhFESyf/UGbOnDl379598uQJn88XLdfQ0LCysuratauNjY2NjY2trW27du0+68wVFRV9+/ZNSUkZOnRoeHg4g1w8EYSEJCfD+PGQlgbq6rBnD4wdC0VFYGT09q98Prx6BR07Ao0GAFBRAQcOAIcDz58DAGhqwrRpsHgxfPedvJr/pTw9QVsb9u59e7OgAExNISIC+vaVa7MIoqWTZygjFAr79euXlZX16tUrFovVrVs3aqjI2tq6TZs2n3vC2tpaFRUV0ZLMzExHR8fCwkI/P78NGzZIru0E0XJt3w5+flBTA7a2cOIEWFk16V58Ppw4Adu2wcOHAAAqKjBuHCxaVGNnpyrV1kpSx44QEgKDBr0vGToUfvgBFiyQX5sIgpBrKBMREfHDDz906NDh4sWLnTt3/shoUaNyc3Pj4uKoMan09PQ5c+Zs375d7LDo6Gg3Nzc+n//nn3/OmjVLcs0niBanpARmzYKzZwEAfHxg40ZQ/fw4JD4etm+H48ehvh7s7BYxGNE+Pj4TJ05kMhV+FoKKCjx4AF27vi+ZNg10dWHjRvm1iSAIACQ/kydPBoB169Y15WA+n5+UlBQWFrZs2TIPD48OHTo0fCxDhw5t9L4HDhwAAGVl5Zs3b0r0ERCETAkE1S9eLExNtU5ONn32bGh9fbksa4+JQSYmCAC1aYPOnGnqvR49arz8yRO0ZMmbVq3eZs1YWFjs3r37zZs3kmqtVHTogCIi/lPyww8oKEhOrSEI4i259cpUVFTo6enV1tZmZWUZGhqK/VUgEDx58gTn/4qtGUPR0NDo2rVrE8ekFi5cuH37dh0dndjYWFNTU8k/nm/Lq1evkpOTV65c2alTJ3Nz806dOuF/fG66EiFZeXnrS0svdOx4gsFoXVUVr6k56NP3kQShENasgXXroL4enJwgLAyaOCnw0SOwswMLC/D2Bi+vRtaYqaioOHDgAIfDef78OQBoaGhMmDBh8eLFnTt3lvBjkAixXJm8PDA1hZgY6NFDrs0iiC+EEFq4cGF+fn5YWBid3pxX/5dXDHXw4EEAGDhwoFj5gQMHnJycWrduLdZOBoNhYWExevRof39/Lpf7+PHjurq6pldXX1/v4eEBAFZWVmVlZRJ9KN+g0aNHqzY2cqCsrGxqaurm5ubl5cXhcCIjI3k8nkAgkHd7W4qMjPEvXvjIuNKCgoJZs5YxmXU0GlqwANXUfMZ9T51CrVsjAASAjIxQYCAqLm7kMIFAEB4e7vRukWA6ne7h4REZGSmphyAxqalIWxv5+qKYGHTxIurWDU2dKu82EcQXqqurw0kXTCbzwYMH8m7OV5FbKDNw4EAAOHjwoFj55s2bceBiZWXFZrMDAwPDw8N5PN5nBS6NKi8vt7GxAYAhQ4bU19d/5dm+YQ8fPqTRaCwWKyoq6vTp04GBgTNnzuzXr5+enl6j0bCWlpaDg8OECRNWrlx5+PDhu3fvFhYWyvtBfJtevz4aH6/y8uXi6upUXCIU1kq1xsjISH19fQAYOnTNxYtfcoaaGhQaimxs3gY0ysqIzUZJSY0ffP36dQ8PD+rqcMCAARe/rFbpycxE3t7IzQ15eKC9exGJ44nmqbCwsG/fvgCgo6Nz+/ZteTfna8knlMnKyqLT6SwWq+HQ+IsXL27fvl1aWiqNejMyMvAQia+vrzTO/20YM2YMAPzvf/9r+Cc+n8/j8SIjI4ODg318fNzc3ExNTRvtliT9N1JSXv43jzc6IYGVkTFBKOQ/eeL06JH+s2ce2dkBpaXhdXWvJVVRZWWll5cXjUYDgGHDhhUUFHzN2QQCdPYs6tfvbUCjro7Gjp35zz//NHpwZmamr68vHi92dXV98uTJ11QtSUVFKDYWvXjxvuR//0PW1igmRn5tIojP9vTpU3NzcwCwsLB49uyZvJsjAfIJZdatWwcAkydPln3V0dHRysrKAPDnn3/KvnbFl5SURKPR1NXV8/LymniX4uLi2NjYo0eP+vv7T5gwwcHBoeH4INamTZtVq1ZJtf0tBJ+f8/ChdnHxqcRErbg4oP6Lj1dKS7PPyppbVHSwujoVoS+MHZOSkqytrXFIyuFwhEKhpFoeF4cmTUL9+qXit4S5uTmHw6msrGx4ZFFR0ejRo+X1RdG4lSsRAPL3f18yaRICQIcOya9NBPF5oqOjtbW1AcDZ2bmoqEjezZEM+YQyFhYWAHDt2jW51I4nNCkpKUl7QtM//6D799/fjI9HKSno6VP08OH7wooK9NdfUm3F5xk/fjwA+Ph8bUJGTU1NSkoKl8sNDAz08vLC/TcAYGho+Ouvv0qkqS1cWppdUdFhgaD6zZu7+flBmZnslBTLuDi6aGSTmKj59OlAHs//3Llzr169auKZORyOmpoajjPi4uKk0fhXr175+fm1bdsWBzT6+vpr165tOC4ZERGBO2ak0YYvsXcvAkAzZ74v8fVFAKhp0zAJQu7CwsLw6mvjx4+v+azEN8Umh1AmNjYWAIyMjOQ43LBw4UI8Rpieni69WlxckIYGevny7c05c1BAAPL3RzNmvD8mNRWpq0uvCZ/n8ePHDAZDTU0tJydHGuc/fvw4ALi4uEjj5C1BZubUrKx5ubmBmZlTkpKM6+rEf/uFQn5VVUpRUejz514pKVY4sgkN7Y4jBk1NTScnJ19f3/Dw8Pz8/Ibnf/369ahRo/DBkydPLi+X7mTvN2/e7N69G1/YAICampqXl5doD01aWhruA5dqMz7DpUsIALm7vy8JCkIAyNtbfm0iiKYKCAjAQ8YBAQES7GpVBHIIZebPnw8AS5culX3VFIFAQE1oklJeDkLIxQX16oUmTHh7U/FDGTabDQDeIt/LT548GTt2bFpamkTOn5eXh4eZJHK2FkUorBMIKvj8nKKi0NzcwMLCP+vrP/2+rasrKC39KyJi+7Bhw8Qm0tPpdGtr6+nTp+/evTs+Pp7P50dFRRkbGwMAi8UKDQ2VwYOiREdHe3p6MhgMBwcH0fKysjIAUFecT0hiIgJANjbvS86cQQDoxx/l1yaC+DQ+nz9z5kw8HPFNJlfIOpSpqanBvcqpqakyrlqMDCY0ubig48dRx44IT8JQ8FDm6dOnDAZDWVn5hUhW45QpUwBg2rRpkqoF/6C+pLqqiKYpKNj56JFBScm5rzlJRkbGiRMnFi9e7OzsrK6uLhrZqKqq4m5nKyurpA/NL5KyxMTEqKgosUINDQ0AKCkpkUuTxBUUvF0ikBIbiwCQvb382kQQn1BWVjZo0CDcLxshtsbjt0LWocy5c+cAoEePHjKut1GZmZn4l1WCXUR8PkpKQmFhKCkJubigc+cQl4ssLFBNzftQRkcH9ez59j9bW0UJZWbMmAEAs2fPpkqePHnCYDCYTCaPx5NULa6urgBw5coVSZ2wJairK0xMbBMXB6WlkpyZnJ2dzeVyfXx8nJycmExm27ZtBw0a1GgGrhzhtfKSk5Pl3RCEEEJCIVJVRQCIepZevUIASFdXrs0iFF2vXqhnT0RdMk+fjtavl1HVWVlZtra2AGBiYiKvqxQZkPXqfkeOHAEAPJAhdx06dDh79qyKisqmTZv+/PPPLziDQACpqXD4MPj5wfDhYGAAysrQtStMnAinTr09xtMTvvsOtmx5f68BA+DYsbf/bdokiUfy1TIzM48cOaKsrPzbb79RhRs2bBAIBJMnT/7i9ZGfPn26adOm06dPUyX4Q5WSkvKVDW5RcnICBIISTU331q09JHhaAwMDT0/P7du3x8TEzJs3r7i4eODAgWK9NXJnZGQEANnZ2fJuCAAA0Gigrw8AQLVHTw+YTCgsBD5fju0iFF9WFuzaJetKExIS+vTpk5yc3KNHj7t37+Kv32+STEOZoqKiS5cuKSkpTZw4UZb1foSzs/PevXsBYN68eVFRUZ88vrS09M6d+OBgmDcP+vUDHR2wsYGpU2HjRrh0CXJzgUaDjh3BwwPe5TICAOzcCX/88f7bT1MTOnV6+18TF4CXtsDAwLq6uokTJ3733Xe45NmzZ0ePHmUymStWrPji06ampvr6+oaGhlIleIovCWWarro6uagomEZTMjb+Q3q1dOzYERQnYhCBdzVRoIYZGQGIhDIMBujpgVAIDXZWIQhRfn6wejXI8o186dKl/v375+TkeHh4REVFGRgYyK5umZPpVrRcLpfP5w8bNqx9+/ayrPfjpk2blpSUtG3bttGjR8fGxpqZmVF/KigoSEpKSk1NxVtBpaamlpaW0mh0Fqu+ooIGAHQ6WFmBtfX7/1tYALXDd0jI239YWMDcubB+vYJu1ZKVlXXw4EGxqGXjxo0CgWDSpEmiT8jnwtlIycnJVAnplflcL18uREjQvv1cVVVL6dWCI4ZXr16JFpaXl/P5fB0dHenV+0mNNkye8IZxou0xNIRXr+DVK3h3GUBI14sXcOoUFBZC27YwZgw0kz31LC1hyhTw8YEzZ2RR3a5duxYsWCAQCObNm7d9+3YGgyGLWuVHpqGMQo0uidqyZUt6evrFixeHDBmybNkyHo+XmpqanJycmZkpFApFj2zTpo2NjU3fvqUmJm2srcHGBrS1P3haDQ1QVn777+XL4fx5UFUFgQBUVN4fQ6dDq1bSeEyfYfPmzXV1dZMnT6ailszMzMOHD9PpdNHxpi9gZmampqb24sWL8vJyTU1NALCxsaHRaGlpaQKB4Jv/dH290tLwiop/mExtA4M1Uq2o4TjOsWPHJk+ePH78eDyFXl4UrlcGhzKi7TEygthYmV5ut2S3b8PQoTBxItjaQloa2NrC+fMwSEb7qn6l1avB0hIuX357c8YMyM8HFxdwcQEHh//8LnwNoVC4aNGioKAgOp3O4XAWLFggmfMqNtmFMk+ePLl3756WltaIESNkVmkT0en00NBQOzu7oqIinP2K6enp2djYWFlZ4f23zc3NP7SObaOotywAqKsD7okICYHXr9+Xd+kCBQVf/QC+QnZ29r59+8Silk2bNtXV1Y0bN87S8qt6AhgMhqWlZUJCQmpqap8+fQBAQ0PDxMQkKyuLx+NZiA7CEQ0gVPvq1WIA0NcPYDA+uOu7RDTs/MDBjdy7Q5pBKNOwn4aQEoRgxgz4/Xfw8XlbYmkJs2YBjwdMmV6WfxlNTdi2DRYtgl69AAAuX4aCAvjrLwAABgM6dwZnZ3BzA1dX+OKe0KqqKjabffbsWXV19SNHjvz0008Sa71ik93Lf+zYMQDw9PRsdMtluWvTpk2nTp2uX7/es2fPUaNGWVtb29jYdOzYES8oJCnPn8OCBVBTAxYWMGeOBE/85bZs2VJbWztu3LguXbrgkqysrP3799PpdH9//68/v42NTUJCQkpKCg5lcElWVlZKSgoJZT6uoGBHbS1PTc2mXbu50q5LX1+fwWDk5+fX19czmUxQmJEdAwMDDQ1NoVDeXZfv1JqYoE6dSgQC/Xclp83MdhobDywslMCnhfi47Gx49gxErjZh9mxYtAjS0+Hd15eCGzsWDhyA8HCwtoaoKLh9G2Ji4PZtePYM0tIgLQ1CQoDJBDs7cHaGfv3A2Rn+uyDUx+Tn548YMSI2NrZ9+/bh4eGOjo7SfCiKRUahjFAoVKjRpWfPngmFQjzPE8vLy4uKilJSUrp8+XK7pr93PlOHDnDsGHh6wvz5YGQEHpKcj/IlcnJy9u7dKxa1bNmypa6u7qeffrKysvr6KnC6jGhyjK2t7eXLl5OTk1vOFcMXqKvLy81dAwDGxhwaTeqfUyaT2b59+9zc3NzcXLxQHg5l8LrPkg3oP4uhYa+KirK4OHnVLy5eX9/p2bNebdrEviup1daOevlSLzNTns36BlRXQ1ERFBRAYSEUFkJRERQVQX7+238UFcGbN3DyJGhpAYv1/l7KyqCvD8+fN5dQBgBCQgB/s3bpAl26wMyZAAAVFRAb+zasuX377cYjHA707//w33+HOjs7Ozk5OTs7d+/evdHtewHg8ePHw4YNy8zMtLS0vHz5Mk7kbzlkFMrcunUrKyvLzMzM2dlZNjV+3O+//37kyJHg4GAvLy9cEhYWVl9fP3z4cOnFMdhPP0FAAAQEwMSJcPcuWFtLtbZP2LZtW01NzejRo6moBY830Wi0lStXSqSKhqEMLklNTZXI+b9VubnrBIIKTc3BGhrfy6ZGIyOj3Nzc7OxsHMqoqam1bdu2uLi4sLBQjnn6+vrAZEJREdTUgCL05zYc8FKs6eIKSSgUFhUVFRYWFhQU5OXlFRYWFhYW5uXlFRQUFBYW5ufnzzMyWnzr1qdP1KoVlJdDff1/hpNevwZdXek1/uvdugV79oC5+dubJiaQkACamv85RkMD3NzAzQ0AoLLyfVhTW3sjNzf31KlTp06dAgBdXV0c0zg5OfXo0YP57nm4efPmTz/9VFJSMmDAgLNnz+Jd5VsW2SxfgxNQAgICZFPdx5WWlqqpqTEYDNEN9uzs7ADg1KlTMmiAUIgmTkQAqGNH1GAHPdnJz89v1aoVjUZ7KLK/5aJFiwBg+PDhkqrl5cuXANC+fXuq5OHDhwDQpUsXSVXx7UlOTu7Z0/jmTeeqqhSZVTpy5EgAOH36NFXStWtXAIiPj5dZGxplbIwAkOSWafwqfD6fTqczGIy6ujpc8uzZMwDo0KGDfBumsJYsWfKhjgTKbBsbpKKCjIyQvT0aOhRNnYqWLEFbt6LDh9GVKygxEWVno9paVFuLNDXR33+/P/vdu0hNDVVUyO/xfcLLl4jFQoaG6Mu2oK6vr09ISAgKCho3bhwOoymtWrVydXX19/dfunSpsrIyALDZ7NraWkk/guZBFqFMZWWlpqYmjUaT6t6NTbd//34AGDhwIFXy6NEjANDW1pbZ+6C6GvXqhQCQiwuS13tv2bJlAPCjyPYxOTk5qqqqNBpNsr9eWlpaAEDtX1hTU8NkMplMZnV1tQRr+WYIhUInJycAWLRokSzrnTdvHgBwOByqZMiQIQAQHh4uy2Y01Ls3AkANtjSQG11dXRDZfKOqqgoAlJWVv7H9+SQlICAAANq2bWtpaeni4jJmzJh58+atWrVq165dZ8+ejY6OfvLkyWdshBcYiMzN0fXrqKAARUUhS0ukGFfIHzJiBAJAU6Z88IC8PBQXh94Fxp+Ql5cXHh7u6+vr5OSk/G5+LF4u4ddff5XjDs1yJ4tQBif8Ojk5yaCuphgwYAAAHDx4kCpZsmQJAMyZM0eWzcjJQUZGCOA/WzLJTGFhIYvFEotafv31VwAYMmSIZOvCo4p/i1xL4YlRiYmJkq3o24B7kvX09MrKymRZ7/r16/EXIlUya9YsANizZ48sm9HQmDEIAIWFybcV79nb2wPAvXv3qBK8r1yjm40T1dXVfD5fkmfcswc5OiJTU9SzJ9q+HSlwBBkejgCQlhbKy/vgMdu3IwDEZCJ7e+Tjg7jcpnbVFxcXX7x4cdq0aQDQqVMnSbW5mZLFar8KlfCbmZkZFRXFYrE8PT1xiUAgwMGWjFuorw8XLoC6Ohw4ADt3yrJmAICgoKA3b964u7v3eLdsX2Fh4e7duwFAIhOXRDWa+QtkobzGVFVVLV68GABWrVqlKTacLmUNcz4UZCJ0w+nP8tVwbpeCPFGKSVVVVYlaNlQi5syBe/eAx4P798HHB0pKYMoUePxYklVIQmUlzJ8PALBmzceSeVRVwdISBAKIj4egIBg7FvT1wd4eFiyACxdScnJyPnTHNm3aeHh4rFmzBgCqq6sl/wCaFamHMtnZ2REREWpqauPHj5d2XU1x7NgxhNDIkSNbvVuZLjIyMjc3t3Pnzn379pVxY3r0gP0HLroAACAASURBVD17AAAWL4bo6FqZ1VtSUhIUFAT/jVo4HE5lZaWbm1vv3r0lW13DUIZsX/Ahf/zxx8uXL7t164Z7RGRJgZeWAVC8UIZk/iqK9evhyBFgs6GuTt5N+Y+NG+HFC+jeHby9P3aYlxekpUFFBURHQ2AgeHgAiwUJCRAUBIsX+xkaGurp6Q0fPnzjxo0xMTG1teI/Ezglv6CgACEkvcei+KQeyhw/flwoFHp4eIgtLocQqqiokHbtYhBCeD8g0Q4Y3Gk0adIkGTcGmzIF/P3B0fHATz8Zy2xSz44dO/C271TUUlxcvHPnTgBYvXq1xKv7UK+M6IYGBAC8ePFiw4YNNBpt586dsl8KWWF7ZfCuR/IOqN5r+LQoyBo8LdSaNdC5M8THw1fsFidxT5/Cxo1Ap0NwMDTlo9yqFTg7g68vXLwIubkQHQ2bNgmtrRlt27bNz8+/dOmSn5+fi4uLvr6+h4fHH3+8345NRUVFU1OTz+eXlZVJ8fEoPKmHMmpqapqammIrlJSXlw8fPrx///6VlZXSboCoe/fupaenGxkZueFJbwBlZWXnzp2j0+lTpkyRZUtE+fujtm0vFBUVenp6yuDtWFFRsX37dgBYtWoVVRgUFFReXj5gwABpdE1Rw0nUdUPD4IYAgBUrVlRVVf30009yWbOA+oWmXiYF+YVWtF6Zhp1VChLztVDq6hAWBkpKsGUL3Lwp79a89csvwOfDtGnQs+dn31dVFZyd4ddf6eHhF16/fp2dnc3lcn18fOzt7cvKyi5fvnzx4kXR43HHTGFhoaQa3yxJOxnn0KFDAKClpfX48WOqsLCw0NTUFAAmTpwoy7T/uXPnwn8TG/Fspv79+8usDY2qqqrq2bMnALi4uEh7FhXO7hwwYIBooZeXF41Gu3btmpQqxZuyZmZm4psCgUBdXZ1Go5WUlEipxmYnOjqaRqOpqqpmZGTIqw14rlnRu2mjr1+/BgBNTU15tQdLT0cAyNhYvq14LzIyUuxLIyQkBACmT58uv0a1eKtWIQDUoQOSbbJ8o7hcBIB0dL5wAvZH5OTkcLncS5cuiRbihdRjYmIkXFmzIvVQRiAQ4E2XOnToIJrhz+Px8BSyFStWSLsNWE1NDV44CHcPYHg20759+2TTho/Izs7G13bS+EIsKyu7c+dOcHDwvHnzNDQ0AKBh1JKWlibxeimDBw+G/07rdXBwAIDbt29Lr9JmRCAQ4Hkxv/32mxybgXOYRNcZUlNTA4Dy8nI5tqq6GtFoiMlE9fVybMV7aWlpAGBmZlZXV5eZmXnr1i18lTx48GB5N60Fq6tDjo4IAE2bJt+GlJYifX0EgGQ28w//wp49e1ZG9SkkWUzGrqio6NatGwA4OTnV1NRQ5VFRUcrKyjQa7ejRozJoxunTpwGge/fuVElGRgaNRlNXV5fxrNcPiYuLU1dXB4Bt27Z9zXkqKiqio6M5HI6Xl5eTk5PYyo/a2toA4O/vL6lmNwWelbN+/XqqBM8h3Lt3ryyboVD4fP7Lly/v3Llz+vRpPL7ZcAL2/fv316xZI7Mm4Yjz8uXLVIm5uTkASDXMbQptbdSunTzXkxRVVlZmbW09dOjQHj166Orq0mi0du3aeXt78xRkFb8WKz0dsVgIAHG5cmzF5s03lJVr7exkF3nPnj0bAIKDg2VUn0KS0Wq/WVlZeF2pqVOnipbv27cPAFRVVe/evSvtNvz4448A8Mcff1Alv//+Ox7kknbVTcflcmk0Gp1Ob/q6ZAKBID09/dy5c2vXrh03bpy1tXXDqY9MJtPKymrs2LG///770qVL8QFz5syR2ejegQMHxJ7qLVu2AMAvv/wimwbIRX19PY/Hi46O5nK5HA7H19fX09PTycnJ1NS04aaq2traffr0EX1FysrK8IIlmzdvlk2D8arcISEhVEn//v0BIDIyUjYNaCgtDYWHo6qqtzezs/+z1qu8nDp1Cg/G6enpUbuiamho+Pj4KMhCoC3Url1vh3ZycuRS/+PHj5WVlc3Nre/erZRZpcuXLweA33//XWY1KiAZhTIIoTt37uCvb7Hv5fnz5+NvhKysLOnVnpeXx2QylZSUqEEuoVDYqVMnALhy5Yr06v0Cv/32G/5aTEpKavhXgUCQkpLC5XIDAgI8PDxMTU2ZDXa3V1FRsbe3Z7PZgYGB4eHhOJFT1MWLF1VUVADAy8tLNgtE3r9/HwC6du1KlVy9erVhyk5zVF9fn52dfe/evXPnzgUFBS1btozNZg8cONDS0pKa8N8oGo2mp6fXo0eP4cOHjxkzBr8iq1atEj15eHg4k8mk0Wh//vmnDB4L3nhLdIORiRMnAsChQ4dkUHuj1q1DAOjEibc3z59HvXrJqy0IIVRSUkItScVms/HQW1xcHJvNpj6JTk5O4eHhZPFfORAK0bBhCAANHiz7pfOEQiFO2P/5559lWe+2bdsAwMfHR5aVKhrZhTIIocOHDwMAnU6/cOECVVhfXz9s2DAAsLOze/PmjZSqxnN2hg0bRpXcvXsXAAwNDRVtsWc+nz927Fh4l12Uk5MTHh4eGBjIZrPt7e1xpovYL6KpqamHh0dAQACXy01JSWnK2pqXL1/GkeXMmTNl8AxUVFQMGDBAdCV+PAFER0dH2lVL3N69e3/55ZeRI0c6OjoaGBh8fNa0mpqaubl5v379Jk2atGTJEg6Hc+rUqdu3b7948ULsZbp+/TqOZkQ7DtG7lFIGg3HmzBkZPDT8lqBKli5dCgBr166VdtUfsm4dcnBAJiZvt9mRbyhz9+7dDh06AACLxQoNDRX7a2Zmpq+vLzWe26lTJ7xWk1ya2nK9fIm0tOqYzIfHj8u4ZryuR7t27V6/fi3LevESr+PHj5dlpYpGpqEMQsjPzw9/ETx69IgqxGPPADBq1Cgp/aziJNMT1MUdQt7e3gCwZMkSaVT3NWxsbNzd3Tt37gwAja73qq6u7uDgMGPGjK1bt0ZEROR8aVfqlStXcFLnhAkT6pq4BYhE4ayd3Nxc2Vf9Nfr16yf6cigpKZmamrq5ubHZbF9fXw6Hw+Vy4+LisrOzRTPDmiIsLIxOp9NoNLGfSbzYj5qa2q1btyT6UMRdunQJANzd3akSfA0wd+5cqdb7EevWoZ9/RtOnI3zNKa9QRiAQBAQE4H6X3r17U3PxGiovLw8ODsafX/zD5uvrK7pzLSFt5SdP9rax0dDQkGX2UklJCU6ikE0Hqqjr1yMNDPS8vCbIuF6FIutQRiAQ4A14v/vuO9EJTRkZGXhC0/LlyyVeKV6KTUtLi9q/sKamBmchiM5mUgS3b98GAGNj42fPnk2dOlVfX79Vq1ZOTk5eXl4cDic6Orq4uFiC1d28eZPFYgHA2LFjJbxPShPgmCAiIkLG9X6lI0eObNu27cSJE9HR0ZmZmZ8br3wcXqhQSUnp6tWrouU+Pj4A0Lp1a9HpRRKXmJgIALa2tlQJTpYX3XNUxnAok52N2rZFjx7JJ5TJzc3FK1HR6fSAgICmfFIEAkF4eDi1fpWysjKbzRa9fiOkaurUqQBgb28vs681/Ant06eP7Lv5q6oexsVBaqrtpw/9dsk6lEEiE5r69u0r+jNw69YtvNXn4cOHJVujr68vAMyaNYsqOXv2LPx3NpOC+PnnnwFg2bJl+CaPx9u3b5+pqan0khVu3bqFB63GjBkjy2jm+fPnXbp0UVNTc3BwiIuLk1m9ig9v6qmhoSH6tAgEApyiYWBg8Pz5cylVXVBQAABt2rShSvLz8yMjI6Wax/ZxOJRBCP3xB3J2fhvKlJUhqT0H4q5cuYKXINPT0/uC9Of4+Hg2m01l4js5OXG53HoFmVb+7aqoqMCT72QzVTMxMZHBYDAYjISEBBlUJ4bPz4mLg0ePdGVfteKQQyiDRNZQmfLfvc/xgnWqqqp37tyRVF319fV4fbaoqCiqcNSoUQ2TEuSuqqoKb+8gOvcVTyGRat7lP//8gxNUOQsWIOlHM/n5+QsWLMB5IXgaCAAMGzZMdKvhlkwoFE6fPh0nEj158oQqr62tHTRoEE7CkNImzEKhEGdQKUiGR03N+1Cmrg7Z2qLx41GvXuj33xGdjtzcUHi4FJM7+Xy+j48PjUbDg25f85zn5uYGBATgnmAAMDc353A40ksNJBBCMTExDAaDyWRK8NekUUKhEC+SPm/ePKlW9OEG8OPiaPHxDIQUK+9TluQTyiCEHjx4gBM1Nm3aJFqOu+l0dXUldSGYmpqqpqZmYmJC9fsVFhYqKyuLzmZSECdPngSAnj17UiU8Ho9Go7FYLGl/6926dWtcv361yspoxAgk0RETUXl5eV5eXrjvTVVV1dfXNyMjIzAwkMqUxFM/pFR7M8Ln84cOHQoAHTt2FM2FKisr6969OwD06tVLSm+Jjh07AsC///4rjZM3XVERGjECubujtWsRNR0kOhrR6ahXL7R8OVJVRQAIAPXpg7hcya/hkZ6ejhfgVlJS4nA4EpmOVFFRERwcbGlpid/trVu39vHxefHixdefmWgUTs00NTWV6hqPeKUJfX19Oa5P9vBh27g4qKtTjJWX5EFuoQxC6OTJk3gNlfPnz1OF9fX1Hh4eAGBlZSWpd0ZJSUlsbCx1E6cjiM5mUhD4gQcFBVEleAN3Npsti+oTEpCODgJA/fohSX/yS0tLfX19cV4Ok8n08vIS/QYvLy8PDAykrln79OlD5rJWVVU5OTnhzBXR7R3y8/PxIgLDhg2TRrK2i4sLANy4cUPiZ2662FhkaooAkKYmWrYMicx7Q7Nno++/RwihsjLE4SATk7cBja4uCgiQ2DrxYWFhOOPezMzs/v37kjnpOwKBIDIy0sPDA/f3KCkpeXp6ymBhrRaIz+fjeHT27NlSqqKoqAhPX5DjggUIoZSUznFxUF2dKsc2yJc8QxmE0LJly6DBhKby8nK83eCQIUOkMajs6OgIACdPnpT4mb9Gbm4uXvkGb9eOEBIKhXi4V3aJsWlpb9fcdnKS1FYmVVVVgYGB+NNOo9E8PT1Fd+MSVVFRweFw9PT0cEDTrVs3LpfbkgOaoqIifAU/YMAAKmMdIZSeno7nSkyaNEmyz8/r169xHtv06dOrqGXpZKi+HgUEIAbjbUT98uUnjhcIUHg46tPnbUCjooLYbJT6Fd/nb968YbPZ+B04YcIEqV5nJyYmenl5UYslkjQaaUhLS8Pd/6dOnfqyMwiFwoKCgtTU1Js3b3K53B07dgQEBHh7e//00094q2oajWZnZyeW7bt9+3ZXV1fJzgn4iCdPXOLioLz8pmyqU0ByDmWEQiFeQ+W7777Ly8ujyjMyMtq1awcAfn5+kq3x8ePHYrOZFATet110qgiezWRkZCTTlPgnT5ChIQJA9vZfe5ErENw+dcrMzAx/Uzs7O0dHR3/yTm/evOFwODi9CfdJhIaGKtraPzLz8uVLExMTABgxYoToj9yDBw9wF5ekPiBJSUlsNhuP/eFoEq9d+5FZxxL38iXq3x8BIAYDBQR8xpiRUIiuXUPu7ohGQwCIyUSenig29lNxUAMPHz7s0qULALRq1arhsjFSkpmZuXjxYmrZhSFDhsim3pYjKCgIZ541XPeBz+fj9bjDw8NDQ0MDAwN9fHzYbLaHh4e9vb2+vn7DVbkbUlVVNTExKRL5tiwrK8PJoKJLNEkVjzc6Lg6Ki+W5Y4N8yTmUQQhVVVXhRV/EJjRdu3aNyWS2bduW6qWQCLyWrpeXlwTPKRE4B0L00gHPZlq6dKmsm5KZiTp2RADIzg592ZMvEKDgYNShQ62pqSqT2a9fv8/dtbWmpiY4OBh/HQCAjY1NaGhoy7xgTUlJwUNvc+bMES2nltTbunXr15w/Kipq5MiRdDodAOh0+vDhw9evX0+tnYNnEctgXgaXi1q3RgDIyAjd/NJrSx4P+foiLS3Uvr1ARUWzW7duwcHBTeleEgqFHA4H/25169btQx2H0lNTUxMaGmptbS06vkxIhEAgcHV1xa/sokWL2Gy2u7u7nZ2doaEh/gR9kpaWVufOnZ2dnUeOHDlnzpyVK1cGBQUdP378xo0b8fHxeAzLwcFBNH0tNTUVz2mQzRSqrKw5cXFQULBTBnUpJvmHMujDE5qOHj0q2fRDgUCAr3Gb0j0gS48ePQIAbW3t2tpaXELNZkr9mu7yL5aVhczNEQCytEQN9j34hBs33vf4d+oUf/bsFw+C1NbWBgcHGxkZ4S8UKyur0NBQuazmJ193797FU8zEtpY8fvx4o0vqNUVVVRWHw6H2D9LS0vL19RXtg/n33399fHzw/qYAYG9vHxoaKo3p+pWViM1++3758UcJ5LsUFKDt2x/hMTjcrxkYGPiRBViLiorw3sI0Gs3Hx0eO/bX19fXUNwAhQdnZ2d26daN6iClMJlNfX9/e3t7Dw4PNZvv4+AQGBoaGhoaHh+NVLpsSB+fk5Hz33XcA4OHhIXq5dePGDdzNefDgQSk+NoQQQtnZ/nFxkJ0dIO2KFJZChDJIZFPojRs3SvbM9fX1T548OXXqVEBAwMCBAwGgQ4cOipaBsWTJEvjvzh1cLhcAevToIbc25eYia2sEgDp3/nTOAiYaxJiaIi4XSWJgqLa2NjQ0FKcNAUDHjh2Dg4NbWkCDN2MCgB07doiWf2hJvY/Izs729fXFa6UAgImJCYfD+dAUj4KCgsDAQCqa1NfXDwgIkOC67MnJb99l6upIskM6eJG6Pn36UN1Lnp6eDSf8R0VFGRsbA0Dbtm3PnTsnyRYQikQgEAQHB2/atOngwYOXLl2KjY3NysqSVEIY1Qfzv//9T7QcT25SUlKSdr5jfv6OuDjIyvKWai2KTFFCGSSyKbTohKbPVV9fn5KSEhoa6uvr2+huiyNHjpTv7IxGCARlLi5h/frdFVmWHs9m2rZtmxzbhV6+RJ07IwD0396yRsTHIze395NJgoORpC8u+Xx+aGgo1YvQoUMHDocjs6w6RUBtxnT69GnRcrx+gdie841KSUlhs9lUp3rv3r3Dw8ObkodUW1vL5XJ79eqF78hisby8vL5+FOb48eMDBmyj0ZCpKRKZYihhDfd6xNm19fX1AQEBeAutfv36kUnRxNeg+mDELjbwttWamppSXeu5uPhkXBzweGOkV4WCU6BQBr171cUmNH1ccXFxVFTU7t2758yZ4+LiQi25JkpPT8/NzW3RokX79+9PTk6W6kP4EleuvO38eIeazST/lW9yc9HEiQhPBi4pQVu3Ii8vtHgxevDg7QFPnyJPz7f5lpqaKDAQSXMJHIFAwOVyqQ1ucI+ComVwSw+enK+qqiq6GZNAINi/f/9HEomEQiFeRB/P/mUwGJ6enl82xhodHe3p6Yl//ul0uoeHxxcsgIsQevPmzYwZM/CL+L//PSwt/YJzfJ7U1NTZs2dTWZydO3e2s7PDg0q//vqr7HftIL49eIlXBoMhejUuFAonT54MAIaGhi+b2L39+crL/4mLg2fPhkrp/IpPsUIZoVA4btw4aDChiVJQUBAZGcnhcLy8vJycnBoNXPT19T08PHx9fUNDQ1NSUprB2PPEiQgArV5NFdTs3p3q4rKxCdfZsvP0KdLTQ9OmoaNH0ZYtSEcHbdyIioqQuvrbSSOzZyNZ7ZmHAxpqqTFjY2MOhyOXycOyt2DBAgBo3bp1YmLiJw+uqqoKDg7u2rUrfqLU1dV9fHzS09O/sg3p6ek+Pj44fQcAunfvHhwc3PSA8vbt2zi3QEtLS6yHSdrKyso4HA5OmLO2tjYyMrr5xTnGBNEAtbyIaKZ8bW0tzjvu0aNHBd7hXdKEwrrq6n/Ly69XVz+VxvkVn2KFMgihqqoqnBDet2/f4uLi6Ojo4OBgHx8fNzc3fX39hoELi8VycnLy8fEJDg6W+G6LslBejtTVEY32n01levRAAEihVr7x8EAiqTwoLg4pKaGsLDR3LvLyQvLYo6euru7QoUN4vTg85LR3795vfpaTQCDA6xcYGBh8ZKZ0YWFhQEAAlfpqaGgYGBhYWCjJxUBLS0s5HA5ONMF9nwEBAUUfzdoV3V+6b9++0ttM6uNqamoOHTqUkZHR6PUSQXwxqg9GX19fdMH6oqIiPDg+dOhQaeT5ZWXNefRILz19VGqqbX6+XNMS5EThQhkksqgMtQcbhU6nm5mZjRw58rfffjt58mRKSkqz7xk+cODtcmCUpCQEgLS0kEKNm2hpiaczdO+OTpyQ/IrxnwmPnuD5/KJ7PnzDqM2YzM3NGw5BpqamiibE4Hns0uub5PP5XC63d+/euDoVFRU2m93otLucnJzvv/8e3u0v3dISt4kWguqDsba2Fl2nm8fj4Vx7iS8FUlWVkpCgXl//9jJeKPzGL+capYihDELI399fTU2NRqNZWVl5enoGBASEh4fzeLxv8OvP1RUBoH373pcsXYoAkEKtfFNejgDE5zF5eKD/7p8lRwKB4MSJE1+Wt9EclZWV9ejRA0dvuMuaSojBK8TQaDQPDw9ZLjogml1Lo9Hc3NxEd5/466+/8Pe4vr7+33//LbNWEYTsUX0wP/zwg+hvVnR0NM7WkuxOxpWVD+Li6NXVaZ8+9NuloKHM4MGDQe7zd2QgMxPRaEhd/f0uAfX1yMAAAaDPXFNO6lgsJLZOmqMjOnJETq0hUEFBAf66HDhw4K5du3ASK04K9vLykup0iY/g8Xi+vr5UElu3bt127drl7e2NM46HDBki/0x2gpA+qg9GbMFfLpdLp9PpdPqZM2ckV5swM5OdkKDK440rL78uudM2J4oYyrx8+ZJOp6upqclxo1EZWbcOAaAJE96XREQgAGRhIb82fUDfvmjDhvc3c3KQqipKSZFfgwiUlpamra2NowQA0NDQWLhwoSy3GviQgoKCNWvWUNtp0Wg0BoMxffr0gwcPKtqSTgQhJVQfTGBgoGj52rVrAUBNTe3OnTtfWUVFxa2SkrchUU3Nvzk5qxITNQoLg7/ytM2RIoYyGzduBIBx48bJuyHSZ2GBANCVK+9L8LqnIrOZFMXVq0hLCx09ivLy0MOHyMkJjR0r7zYR6O7du7t27erSpcumTZtKZTCnucnWr18/7P/t3XtATOn/B/Bnmm5UUxKVRKQoXb6ua4ndFCpFy1oVyjUsy8Yitx9frEu0lVttSu1KKqplZYWECpn4tiKRSEm6iNJ1pun8/nh2z85OtFiZRu/XX3OeeWbOc2bOnPmc5/mc54wfv2XLFmdn582bN1+4cIHefgGZttB+0D4YDocTEREhXr5gwQJCiJaWVm5u7ju8rVD4rLh4e1ZWn4wMkpnZRST6K6uypGRPdvaAf9tuGdQWQxlTU1NCyMmTJ6XdkFaWns4Qwujp/TUlblUVo6IieTVT23HxIuPgwPTuzVhaMj4+730SPPiY0FsBiF9rbW5uTgi5fv26FFsF8IFt3bqVDvumpaWxhQKBgGbu9+vX763mzq6vv1dQ8O3//qeRkUEyMsjNmwbFxTsEghKh8I8rBwsKlubmtsc7kv5tJty24MaNG9nZ2To6OuPGjZN2W1rZoUOEEOLqSuTk/iiJiyM1NWTUKNKzpxTb9VqjRpE/7zII0DJ6r4PHjx+Ll2RlZRUVFdGEZYD2YPXq1YWFhYGBgRMmTLh8+TLNb1NQUIiKiho+fPjdu3cTExNdXV1bfhOGEVZUHCkt3V1be50QwuHId+o0pWvXJaqqVoSQ6urUBw9cFBS6NDU1MEyjoWHcB9iutqbNhTKHDh0ihLi6ukrccOAj1KcPMTIibm5/ldDgxt1dWi0CeF/oDWKLiookSsSDG4D2ICAgIC8v78yZMw4ODleuXKFTjWhqaiYkJKSnp7ccxwgEhWVl+549+0kofEoIkZfv0qXL1126eCoodGPrqKpamZvnNzaWMAyjoKDL4XBbe4vaoLYVLgiFwsjISELIjBkzpN2W1rd0KVm69K/FwkKSnEw6diRTpkivTQDvx+tCGfESgPZAQUHh2LFjI0eO/P333ydNmnTu3Dk67ZOhoWHzm3WzMjIyLl2KtLYObGqqJ4R06GDepcuizp2ny8mpNK/M4cgrKOi13ia0fW0rlDlz5kxpaamFhcWAAQOk3ZZWJhKREycIn084HDJ0KHFyIjU1xMmJqKkRHk/ajQP4t5r3wdAhJ4Qy0A6pqaklJCQMGzYsNTXV3d09KiqKvfBQQk1NTUhISFBQUE5ODiGEzx/UpcugLl08O3Yc9GGbLGPaVihDR5foxM8fM5GIODmR4uI/RpfWryehoeSXX8gvv0i7ZQDvR/PABb0y0J7p6ekdP378s88+i4mJMTY23rx5s0SFgoKCH3/8MSQkpLS0lBCira3t6enZvfsCHZ1ur3o/+BsOwzDSbsMfXrx4oaurKxQKCwoKunX7qL+84GCyaxfJyiJ0dvm6OmJsTDZvJjNnSrlhAO9JdXW1mpqasrJybW0tPQHNysqysLAwMTHJzs6WdusApOO3336bMGFCY2NjYGAgvSS7sbExPj4+ODg4KSmJYRgOh2NjY7NkyZLx48fLsVeEwD9pQ70yKXV1dlu3diku/sjjGELIhQvEzY38eZcc0qEDcXMjFy4glIGPhqqqqrq6emVl5bNnz7S0tAh6ZQAIsbe337dv3/z585csWaKlpXXr1q2QkBD6o1BRUZkzZ87XX3/dt29faTdT9rShUOZEVVXhqFGevXpJuyGtr6CAWFv/raRHD8LnS6k1AK1CT0+vsrKyqKiIhjKampodO3asqqp6+fKlmpqatFsHIB2enp6ZmZmBgYHTpk0TCASEED09vQULFsybN4+9lT28rbYSyjxuaMisru7I5Vr/efeWj1nXruTZs7+VPHtGsBPDx0VPTy87O/vx48eWlpZsSW5ublFRUb9+/aTbNgAp2r17t6Kiokgkys/PX7p06ejRozGW9C+1lVDmVEUFQ4ithoZye/hGzc1JcjLx9v6r5Px58tFPCQjtTPPM3yn/MlFg1AAAIABJREFU+Y+ihga3tJQglIF2TF5e3t/fXyQScbntcQ6Y1tAm4gaGkFPPnhFCHDp3lnZbPoiFC8nNm2TDBpKfT/LzyZo15P594ukp7WYBvE9L+vfPGzFiUmUlW/K9ouIGPt/o4UMptgqgjUAc8x61iVDmZnX144aGbkpKg9rJCLqODrl4keTmkjFjyNixpLCQXLpE2kkYB+3Gf1RUeqelad29+1dR9+6EEILMXwB4r9rEAFNCRQUhxE5T89VzBn2UjI1JZKS0GwHQmmjgIn6nAj09QhDKAMB7Jv1emYampjMVFRxCHNEtAfAxaR64IJQBgFYg/VAmpbKyWiTqr6LSg51nBQA+As2Hk2gogztKAsB7Jf1Qpn0l/AK0H1paREmJPH9Oamr+KEGuDAC0AimHMhVCYVpVlSKHY9epk3RbAgDvGYdD6MzdT578UaKjQ7hcUlpKBAIptgsAPjJSDmVqm5o+U1cfpaHBk28TCcgA8D5JZP5yuURHhzQ1kadPpdgoAPjISCeAiCsvz6mtpY81FBTcMdEtwEfplZm/RUXk8WPSo4e0GgUAHxnphDJXKys7cLmf8nh0UQUzBQF8lHA9NgC0PqkN6/Tr2NFOU1NaaweAD6F54ILMXwB436QWyrxobCxsaCCEKHI42oqK0moGALSi5qFMv35kwADSTub1BoAPgsMwzIdf68q8vKyaGg15eUJIT2Xl7b17f/g2AECre/SInDhBzMyItTUpKiINDaR7d4JTFwB4r6QWygxQU3Pt2vXDrxoAPjQ+n3h4kJcvCY9HiovJd9+RNWuk3SYA+HhIf4o8APiYvXhBHB3JokWksJDcvk2uXCH79+MGZADwHiGUAYDWdPw40dYmixb9sdi3L1m2jAQHS7VNAPBRkU4oY6GqijsuAbQLOTlk4MC/lQweTO7ckVJrAOAjJJ0rmKZjTjyAdqKpicj9/ZSJwyHSSNEDgI8VBpgAoDUZGkr2wdy5Q/r0kVJrAOAjhFAGAFqTkxO5dYucPPnHYnk58fMjbm5SbRMAfFSkczE2ALQjv/5KZs0i/fsTHo+kp5MvviCBgZKjTgAA7wqhDAC0vtpacv06aWgg/fr9ce8CAID3BKEMAAAAyDD08QIAAIAMQygDAAAAMgyhDAAAAMgwhDIAAAAgwxDKAAAAgAxDKAMAAAAyDKEMAAAAyDCEMgAAACDDEMoAAACADEMoAwAAADIMoQwAAADIMIQyAAAAIMMQygAAAIAMQygDAAAAMgyhDAAAAMgwhDIAAAAgwxDKAAAAgAxDKAMAAAAyDKEMAAAAyDCEMgAAACDDEMoAAACADEMoAwAAADIMoQwAAADIMIQyAAAAIMMQygAAAIAMQygDAAAAMgyhDAAAAMgwhDIAAAAgwxDKAAAAgAxDKAMAAAAyDKEMAAAAyDCEMgAAACDDEMoAAACADEMoAwAAADIMoQwAAADIMIQyAAAAIMMQygAAAIAMQygDAAAAMgyhDAAAAMgwhDIAAAAgwxDKAAAAgAxDKAMAAAAyDKEMAAAAyDCEMgAAACDDEMoAAACADEMoAwAAADIMoQwAAADIMIQyAAAAIMMQygAAAIAMQygDAAAAMgyhDAAAAMgwhDIAAAAgwxDKAAAAgAxDKAMAAAAyDKEMAAAAyDCEMgAAACDDEMoAAACADEMoAwAAADIMoQwAAADIMIQyAAAAIMMQygAAAIAMQygDAAAAMgyhDAAAAMgwhDIAAAAgwxDKAAAAgAxDKAMAAAAyDKEMAAAAyDCEMgAAACDDEMoAAACADEMoAwAAADIMoQwAAADIMIQyAAAAIMMQygAAAIAMQygDAAAAMgyhDAAAAMgwhDIfrUePHgUHB5eXl0u7IQAfVHh4+JUrV6TdCoAPITo6OikpSdqtkD4OwzBSWbGfn9+TJ0+al1tbWzs4OLT22isrK1evXi0SiZycnBwdHWnhw4cPt2/f3rzy119/bWlpyS6eP38+OjqaELJ58+auXbvSwry8vPDw8NzcXG1t7SlTplhZWb1Ve65fvx4cHEwf6+vrm5qa2tnZdezY8R02jXXixImJEydmZGQMGjSo5Zr+/v537tzR1dXduHEjW7h27drmYdDQoUPnzJlDCKmrqwsPD3/48OG6det4PB59dsuWLYWFhWxlDoezf/9+OTmEy3/ZunVrWVlZ83J7e/uxY8e29tqfPXu2du1ahmG+/PLLMWPGSDwrEoni4+MvXLhQXl7es2fPyZMnDx06lD7122+/JSQklJeXd+/efebMmWZmZrS8sbHx8OHDycnJtbW1AwcOXLx4saqq6ls1adGiRY2NjYQQVVXVnj17fvbZZ+K/tXejrq4+Z86cH374oeVqV65cCQ8PJ4SsXbu2R48eEs9WVlZGRkby+XyBQNC/f/9p06axdZ49exYZGXn9+nWRSGRpaenm5tatW7d/2eaP2N69ex89etS83MrKauLEia200sTExLi4OPGSOXPmsPvz119/LRKJJF4ybty4SZMm0cenTp06e/ZsUVGRvr7+xIkTR44cyeFwaHlsbGxDQ8PgwYNnzZqlrq7+Vq3y9vZ+/vw5IURFRaVv376jRo0yMTF5tw1k9e3bd9CgQZGRka98du/evVlZWeIl27dv79SpEyHkwYMHO3bsaP6SxYsXm5ubNzY2RkREnD9/Xk5Oztra2s3NTUFB4V82tVXJS2vFOTk5eXl5hJDs7Ozi4mIjIyN6pOjbt+8HWLu3t/exY8fKy8u7devGhjINDQ0PHjwQr1ZaWnrz5s2vvvqKLamqqvLw8Kivry8vL//uu+9oKJOamjp27Fh1dXUrK6vz58/v2bPnhx9++Pbbb9+8PXl5ecHBwUOHDuXxeKmpqTk5OT169Dh//nyvXr3ex+a25MKFC8uWLevcuXOXLl3EQ5mCgoKnT5+yiwzDJCcnNzU1ffHFF/v27du7d29paSkhZNGiRWwoExQUpKioaGhoSBd5PB7iGAl5eXlFRUWEkBs3bpSVlZmbm9N/wcGDB3+AtS9btuzs2bP05yYRylRXV9vZ2V29etXKyqpPnz58Pr+kpIQe+leuXLlr1y4nJydjY+OUlBQ/P7/Y2FhnZ2eRSDRhwoTTp09bW1srKChs2rQpIiIiNTVVQ0PjzZsUEhJiYGBgaWlZUFAQGRnp5eXl5+e3ZMmS97zlzdTV1Xl4eFRXVxcXF3t6ekqEMtnZ2TY2NnV1dVZWVl27do2KitLW1p49ezYh5MaNG2PGjGEYZuTIkZqammFhYQYGBl9++WVrN1h23bt3Lzs7mxCSm5tbUFBgYGBADxEGBgatt9Jz584dOnRoxIgRbAmXy2UfP3z4kAbQlEAguHTpUrdu3SZNmiQQCGbMmBETE2NiYtKvX79bt27du3dv1KhRhJDZs2eHhYWNGDFCXV19w4YN/v7+aWlpenp6b96qyMhIoVBoZmZWW1sbHh5eWVm5ffv2FStWvI8tfrWIiIjCwkJTU1O2hD1Drq+vl/i/KykpycrKcnFxqa+vt7GxSU9PHzNmTGNj49y5c4ODg5OSkpSVlVuvqf8WI23x8fGEkMuXL3+wNZ49e5bD4Rw+fJgQsnHjxhZqenh49OnTRyQSsSXz5s3r2rVrQEAAIeTevXsMwzQ1NZmamnbv3v3x48cMwzQ2Nk6cOFFZWZkuviHazZORkUEXr1+/rqysPG3atHfZvD8dP35c/D1f6eXLlwYGBs7Ozl999ZWJiUkLNU+dOkUI4fP5Z8+edXR0DAkJoRF9fn4+rdDY2CgvL79r165/0+b2g+5+mZmZH2yNx48f53A4v/76KyFk586dEs8uXLiQy+UmJydLlFdWVsrJyXl6etLFxsZGCwsLc3NzhmFCQkIIIUFBQfSpS5cucTicFStWvFWrFBUVvby86OPa2tqRI0cqKyvX1NS85cb9DY/HY9/zdZYvX66lpXXw4MHmvxH6Z9OjR4+ioiKJV9XV1RkaGvbt27e0tPTftLB9On36NCEkKSnpA6zLzc1t8ODBb1g5ODhYQUGhsLCQYZgNGzYQQmJiYiTqnDx5khCyZs0aupiVlaWkpOTu7v5WrdLX13d1daWP6+vrv/jiCy6XS9f7zoyNjdn3fOUaly1b9oZv5e7u3q9fv6ampu+//54QEh0dTcuPHTtGCPH19f037WxtUuuVacHLly/3798/b968CxcuXLt2bfTo0YMHDz5w4ICTkxMbXR4/frysrGzu3LmEkJycnPj4+MrKSl1d3enTp3fu3LmFN6+pqfH09Bw/fryLi8u0adNaqFlYWBgZGenn58d2LSQlJYWEhISHh4t3Nvzvf//Lzs7+/vvvaXjO5XJXrFhx/PjxY8eOLV269N0+gYEDBw4ZMuTGjRuEkCNHjujr62tpaUVGRqqoqKxatYq27ejRo6WlpZqami4uLuw5ZV1d3dGjR7Ozs5WVlUtKSv5xRRs3bnz27Nnu3bu/++67lmv6+vpaWVnRzgNbW1tCCP0bYJWVlTU2NqKn/Z09f/48ODh44cKF8fHxfD7f2dnZ3Nw8PDx80qRJRkZGtM6xY8dqamo8PDwIIbdu3YqIiHj+/LmhoaGnp2fLfSEvX7785ptvXF1dP/vss+bPVlRUHDx40M3N7fPPP5d46smTJ01NTWzvIJfLNTIyunjxIiEkMTGRx+PR3yAhZOTIkZ9//nlcXJyPj8+7fQIdOnSYPn16SkpKTk6OvLz81atXp06deuDAgYKCgqVLlxoaGgoEgqioqMuXL8vLyzs7O9P9kPzZZZicnFxRUdGrVy+BQNDyijIyMvz9/QMDA195rDh9+vStW7fCwsKa78xxcXF5eXmxsbFdunR5t20EcfX19QEBAbNnz75y5crly5dHjhw5cuTIwMBAe3t7CwsLWichIaGwsHDBggWEkNzc3Li4uOfPn+vo6Li5ubHj+809efLkDY9FTU1Nvr6+kydP7t69u1Ao3Ldvn42NzZQpUySqJSYmcjgcb29vumhmZvbFF1/88ssvDMPQsae3paSk5OHhER8ff/PmzYaGhhMnTixatCg8PDw/P9/FxcXCwkIkEv366698Pp9hmBEjRjg4OLAr4vP5p0+frqmp0dHRqaysbGHTnj59qqur+ybtKSwsPHLkSEBAAIfDSUxMNDQ0ZIcjJk+ebGJiEh8fv2zZsnfY0g+jLfb/V1VVeXt7Ozk5LV68ODEx8dGjR2VlZd7e3pmZmWydyMhIOhYeExNjZmb2888/P3jwwNfX19LSkmZ4eHl5hYaGNn/zzZs3l5aW7t279x+bsW/fPh6PN2vWLLpYV1e3cOFCGxsbd3d38Wo5OTmEEBsbG7Zk+PDhysrKd+7ceZeNJ4QQwjBMaWmplpYWIeTAgQNeXl5Dhw5NSEi4fPkyISQtLc3ExGT37t33798PDw83Nzen68rNzTU3N1+8eHFmZuaNGzfYXDAHBwd6IJBAD+ibNm3S19dvuT303ZYvX95CneLiYkIIj8dLTk6+dOlSRUXFO216+1VeXu7t7W1vb7927dq0tLSnT58+efLE29v79u3bbJ3w8HC66wYGBlpaWqampjY2NgYEBAwYMIAe0ebPn//TTz81f/M1a9a8fPnydekj6enpDQ0NDg4O1dXV165du3LlSn19PX3K0NCwR48eu3btoqfUjx8/PnfuHP0JCIVCLpcr3m9vZmZWUFDQ1NT0zh8CHX3T0tLi8/nffvuttbV1SEjI+fPnGxsbKysrP/nkk2+++aampubRo0djxoyh/YIikeirr76ytbXl8/n19fWnTp0SCoWEkNzc3Llz5169elViFUKhcM6cOcOGDWODMAk0UHNwcCgtLb106dLNmzeZPxMKL168yOFw7Ozsnj59evHiRfGvBt5BbW2tt7e3s7Ozp6fnmTNnHjx48OLFC29vbz6fz9Y5evQo/aJPnDjRv3//gwcP5uXlBQQEWFhY0GPOypUrAwMDJd756dOnOjo6169fP3fu3P3791toQ0JCwt27d+m5XFZWVnl5uZOTk0gkysrKSk1NZX8IQqGQw+HIy/918m9qalpVVfXs2bN33nw6Rq+lpZWTk7Ns2TJra+sdO3acPHmyqqqqsbHR0dFxypQp169fv3Xr1oQJE9jDr5eX1yeffBIbG5uXlxcXF0d/+FlZWQsWLGAjLaq8vFwoFGpqaqakpFy4cEE8YaC5vXv3qqur09MkoVAokRnTv3//hw8fvvOWfghS7RNimFcNMD1+/JgQMmHCBIFAQEtouHD48GG2Dh0Qqays5PF4zs7OjY2NDMMUFBQoKSlt2rSJYRg1NbWpU6dKrCsjI0NeXn7btm0Mw9C0r9cNML148YLH47HdiQzDrF69WllZmQ4qHTp0iPw5wER/Zg8fPhR/eY8ePcaPH//mHwIdYDp06FBGRkZKSgqNn+hgjbW1dadOnXJzc2lNkUjUp0+fQYMG1dXVMQxTXV2to6Pj4eHBMMyIESN0dXXZlrADTPPmzWv+RQsEAgsLi0GDBtGPruUBpmnTphkZGYkPtDEMQyNFdoCJ/tVxuVx1dXU5OTl5efn/+7//e/NPoL1pPsB07949QsjUqVPpN8IwDO2Wi4+PZ+uMHz9+8ODBxcXFioqKc+fOpYW5ublcLpfu1QoKCmw5KyUlRU5Obv/+/QzDVFVVkWYDTPSfYNasWWzSroaGxqlTp+izfD6fRtX9+vXT19efPXu2UChkGIYOswYHB9NqWVlZNB346dOnb/45KCoqurm5ZWRkpKen79+/X01NbcCAAU1NTXT0KiAggK25atUqRUXF27dv08UFCxbweLwXL17s3r2bEBIeHs7WpANMdMArIiJCYo1bt25VUFC4desW85pB2ClTpigrK8+bN4/tfDU1NX3w4AHDMOPGjevUqdOMGTPY8+MBAwY0H4eCV2o+wETjgHHjxtXX19MSmiAcEhLC1vHw8DAwMKipqdHU1LS3t6f7XnFxcceOHVevXs0wTNeuXSdMmCCxrk6dOnG53A4dOtD0jpEjR5aVlb2yVZ999tmoUaPoYzqSMn/+fDYDRlNTkw42RUREiP9w8vPzaRfmW40R6+vrjxs3LiMjg8/nh4WFde3a1cDAoL6+no5e0c2h9u/fTwj57bff6OLGjRsVFRWfPHlCc5m///57tiYdYLp79y77l8GiCb9cLldNTU1eXp6OFEscxin6f0evCWAYZsWKFbRvhi7y+XxjY2Mul8semtqgtjjARI0fP/4fU6b5fH5VVdWQIUOSk5Npib6+flpaGiGkebcbPRszMzP7x8EUQsjBgwcFAgGbfnjjxo2dO3euX7+e7epn0fQx8WidLtJTw7cyY8YM+qBbt25+fn7s+JS5uXmfPn3o44KCgvv37y9atCg1NZWWGBkZpaWl5efnp6Wlbdu2rXkyXVBQUFBQkEThrl27bt++nZ6eLn5W/UoFBQXR0dEBAQEt5/COHTuWz+f37t1bU1Pz5cuXS5Ys2bRp04ABA5ydnf95y+FPjo6O//iNpKenCwQCfX39o0eP0hJtbW3a/dB8bKW+vn7u3LmffPLJ/PnzX/eG9NTzzp07Z86cGTRoUEFBweTJk93c3PLz83k8XmhoqFAo/OGHH65evZqQkHDs2DFbW1tXV9cFCxbEx8d7enr+8MMPAoGgvLycjkO9ba53ZGQkvf6iQ4cOkyZN2rlzJxsoiO88KSkpBgYGt2/fpn0hampqVVVVt2/fpv2y9GxS3MiRI5v3D925c+e///2vl5dX//79X9eehoaG+vp6kUiUk5PTq1evlJSUiRMnzp07NykpqaGhgR70c3Nze/bseebMmcmTJy9atIiej8G7sbe3V1JSarlOZmZmRUXFkCFDLly4QEsMDAzoof6VnQ03btxoaGigF5EcOXLEw8Nj8eLFUVFREtXS09MvXrxII1ry5w/h0qVLgYGB1tbWlZWVLi4u7u7uw4YNc3FxiY2NXbFixY8//sjhcIqKimi2w9vu7YmJiYmJiYQQJSUlOzs7X19fdtvF9/akpCRtbW15eflz584RQjp16iQQCK5du3b48GEdHZ2VK1dKvK2xsbFIJJIY6jIzM8vMzNTW1tbR0WloaFi/fv3OnTtpz73Ey0NDQ8X/79asWXP27Fl7e3sTE5Oqqqq6ujp6MtOWL+Nou6HMm8jPzyeEREVFsdfdqaur0wvkmo9f7tu37/fffw8LCysoKCCE0MPc8+fPCwsLJUZY6IHbxcVFW1ub1ly0aJGWltaXX35JU77p9bSFhYVaWlp0RLakpKR79+7sO5SUlFhbW7/t5iQnJ1taWiorK3fo0KHlTT579qx4z7m2tjYtF89UZzXf/x48eLBlyxZnZ+dOnTrRLaqurhYIBA8ePNDT05M4rOzevVtDQ2PmzJktN57D4bCX4aipqQUHB0dFRUVFRSGUee/omWtcXBwbQOvq6rLXkUnw9fW9e/dudHQ03UNqamoIIRUVFY8fP2b3WLqf+/v7f/LJJ4SQPn36bNy4cdKkSUlJSfX19UFBQb/88gu9braiosLV1dXd3X3w4MFGRkZnz549d+7c7du3dXR0Ro8evXz58nv37mlqar7V5ixcuPD777/ncDgtp/s8evSooaFB/PJR2jeZn58/fPjwN1kRwzBLlizp2LGjm5sb3e1pPllRUZGBgQGbN6Otra2iosIOT1tbW8+cOXPPnj3Pnz+n/wrs8LSDg8PUqVMjIiKad8jD+0X33tjY2ISEBFrSoUMHelHxK1NVxM/oXF1dExISoqOjm39Nfn5+JiYmTk5OdJH+EHx8fOhlraqqqtu3b7eysjp16tT8+fPp2une/vnnn/v7+2dkZLxtduDkyZMPHDhACKGNb2F76+vrxQeMBg0aJBQK8/PzjY2NJc6cqVfGGezUBkpKSjt27IiJiYmKipIIZYRCoZ+fn6urK5t7pKGhceXKldjY2MePH/fq1cvW1nbKlCnV1dXvlhX0Ych2KEM/+tDQ0CFDhvxjZdplx+a+UAEBAadOnaJ9+6xjx44VFRWxY5PXr1+ncYPEmZyNjc2GDRtoHuWNGzfY6Vvu3r1bU1PzDpcaqqmptbx/kz83+b///a+Li4t4+c2bNwkhtbW1b7Ki8PDw2tra2NjY2NhY8XJDQ0OJeWhevHgRHBxM/wDecCsoBQUFdXX1urq6t3oVvAl6wD18+HALXQssuttPnTpVvHDbtm2nTp1ik89oTHP//n0ayhBCaFTR0NBA9/xx48bRck1NzVWrVp05cyYjI8PIyEheXt7Ozs7Ozo4Q0tjYePXq1cGDB/9jr5IEZWXlf9ztCSFdu3bV09OjV2CJ09TUfMPd/t69e/Qc9z//+Y94+cSJE728vNhEIj09vZqamuLiYjZfkv009PT0nj59Wl1dLT4SJxKJEMq0Nnrc279/P70u+m117ty5sbFRIBCIf015eXnHjh3bs2cP+w/N/hDYOnTPpL01HA7H0dGRnbzj8uXLffr0afkqk+YUFRXfcG/ncDjiOUNUcHDwixcv3mqNLA6Ho6mp2fyYfPTo0aKiIomUXnoJLX1cW1ubmZn5DifnH1Lb7S8SR797dsY2kUhEg3QLCws5ObnmRzdCSFlZmcQYU1JSUp6Y3NxcQsjSpUubT5Xo6+tra2vLzgNmYWGR93f0qJeUlLR06dIRI0bo6OjQTnha/8CBA3JycpMnT35/H8Bfevfuraqq2nyTe/furaSkRI/U1KVLl+iDoqIiiauZvv32W4ktcnBwMDQ0zMvLY7ea3RahUPjNN9/8Y8MePHgg3lGUkpJSUlLyJiEmvA49SrK7vUAgoB2K9OKOV+72T548kTjSXb58WfyLpiHv6tWr6fA8NXjwYB6P9/PPPzN/5rdGRUVxOJwhQ4bQMSOatUPRd2g+nUZwcPDDhw9fmWD+XlhaWqalpTVPJ+/Xr9/ly5dpbxP5c9CZEPLy5cuioiLxrMzevXtL7PZ0Xsrjx4+vXbuWrUZT+NnsaYFAEBsba2BgoK2tbWNjwzDMzz//TJ+qra09fvy4ubn5v5zNElgSh/qmpibaf2ZmZsblcl+5z5eXl0sc6kUiEU1woYu1tbW//fabqampioqKeLU9e/Z06tRJfGjS2Ni4e/fuhw8fZmedoWNSbIjPSkhIuHbtGp0vtDVYWlpmZWXRvzlxJiYmWVlZ7PE8Pz+f9tEKBIKSkhKJSU3LysrOnj3LLt65cyc7O1vimMwwjI+Pz9ixYyWO/OL8/f0rKipab2PfD6lm6jDM69N+f/zxR/FqlpaWvXv3Pnr06JEjR2xsbDp37kzTVBcuXCgvL7969ero6OigoCBnZ+dz584xr0n7FSee9ltSUmJhYUFnyDh//jwh5PTp0y28Vjztl10cO3ZsUFDQ4sWLORzO119//VYfgsS8MuKsra3ZrDRq586dhJAFCxYcOXIkNDR0xowZYWFhDMMsX75cTk7O29s7JiZm9erV9Hf7urRfCeJpvzNnznR2dmYYhp6Gzpw5U6Kyj4/PqlWr7O3tCSELFy5ctWpVZmbm9OnT5eXl3d3df/zxx+XLl6uoqBgbG1dUVLzV59B+vC7t99ChQ2yJSCTq27dv3759IyMjw8LChgwZ0qVLFzpbhoeHh4KCwrJly44cObJ//35HR8e0tDSGYbhc7uzZs1tYr3ja76NHj0xNTenO4+fnRwixtbXdsmULjcIXL17MMExRUZGOjo6uru6OHTuio6PXrl2roqIyevTopqYmgUDg5ua2Y8cO2jvN5XKdnZ2bmpre6nMQn1dGHE37ffToEVuSk5Ojrq7ev3//wMDAiIiIdevWubm5MQyTnp6uoKAwfPjwsLCwXbt26erqKikpeXl50QuRxD/P5sTTfmNiYkxNTWlasZOTk5yc3MyZM7dt2zZw4EA5ObmjR48yDNPU1GRtbS0vL+/p6bl169b+/fvLy8u3fKwA1uvSfv39/cWrDRs2rEePHtHR0dHR0XZ2dp3J7MIyAAAEh0lEQVQ7dzYwMGAYxsvLi051ER0dHRwcPHny5JMnTzKvSvv99ddfORzO0KFD/f39fXx8TExM2K/J3t5+/vz5DMOUl5erqKisW7dOopE0hLWysvLz86Op3/R/pKmpac6cOVu2bNm9e/esWbMUFRVHjRrFZiu/IfF5ZcTR84r09HS25MmTJzo6OkZGRqGhoZGRkZs2bXJ0dBSJRPfu3VNVVR0yZMihQ4fCwsL69evXoUOH16X9ent7czicSZMmBQYGrlu3TlNTU0dH59GjR/T/jv7D0jN5NsOXevny5Zdffunr67tr1y5nZ2cOh8POLNVmSX+AKSsra+jQofn5+Z9++iktUVJSsrW1lTjti46OXrJkibe3N4/Hc3d39/T0pMlTe/bsMTAwiImJiY6OVlNTGzNmjLGxMSFk1apV9MHrcDgcW1vb3r1708fKysp0AJLP50+dOrXlWeR1dXVtbW3ZU7Hp06erq6v7+Pj4+Pioqqr6+/svWrTorT4EbW1tW1vbV6Y7DBw4UCJ78bvvvtPU1AwNDT1z5oyKisqwYcPorKw+Pj66uronT56MiYmxtLRMSUlZuXIlj8cTiUTr1q1ruQHm5uZsn7mioiJNl/n9999NTEy8vLwkKt+6dYvedMLW1pZ2btnZ2YWFhX3++efh4eGpqamKiooLFixYu3btm3Sltk+ZmZnDhw8vLi5mB7M7duxoa2srPgmEnJxcXFzcmjVrNmzYoKmpuWzZMqFQSLu+QkNDzczMIiMjjx8/rqenN2bMGLonb9iwQWL0RIK8vLytrW3Pnj3p+2toaNDv+ttvv9XR0dm9e/fBgwd1dXX3799P+1e6deuWmZm5Y8eOuLi4srIyNTW1devWLV26lMPhVFdX074coVBoaGgYHBzs4eHxtqPpo0ePfuXvVE9Pz9bWVnx20b59+167dm39+vU0U7J///7Tp09nGGbo0KHnz5/39fXdvn07j8fbu3fvlStXDA0NORzOxo0bW25Ply5d2N+doqKihoYGHR07evSoj49PTExMamqqsbFxYmIincOGw+EkJCRs2bLll19+SU5ONjExCQoKetu7lLRbOTk5Q4cOzc3NHT16NC1RUFCwtbWVmGo5IiLim2++WbNmjaqq6vTp0+fPn08vLNq1a5e+vv6RI0diY2NVVVVHjx5NB1iXLVsmkezo6Oh45coVf39/enWbpaXlTz/9RHsjlJSUFBUVCSHp6emffvrpwoULJRrp7u6uoqKye/fuPXv2aGlpbd++nR4A6+rqNDQ0oqOja2pqtLS0du7cOX/+/H/MVpZgZWX1ys4PLS0tW1tb8dsg6OrqpqSkbNq0id5Lp3v37rNmzWpqajIyMrp06dL27du3bdumqKi4cuVKekU6IWTdunUS/xRbt24dMGBAcHDwzp07uVzuV199tX79+m7dupWVlbH/dxkZGS4uLhJzf1dWVnbs2DE0NLS+vt7AwODIkSPiU963TVK7BxMAAADAvycbuTIAAAAAr4RQBgAAAGQYQhkAAACQYQhlAAAAQIYhlAEAAAAZ9v9fWh/tXW2iDQAAAUp6VFh0cmRraXRQS0wgcmRraXQgMjAyMS4wOS40AAB4nHu/b+09BiDgZUAAfiAWAOIGRjaGBCDNyAyhmZhgNDuDBpBmBoqDaRY2BROQOCMLXCFYgBEo4ABV4ZAB1sFIDIODAcxgZORmYGRgZGJgYmZhYWbRYmJmYuJjYWVhZmVjYWRnY2Fi52Dg4Mxg4uRK4OLOYOLmSeDhzWBi4VNhYWdl4OVIEGECqmRn4+Ti5uHlEN8HchDci+uW7j6we9mt/SDO/S/LD9gYrwMpYNiXVnDg0FpHMFuR1fOA8ZNp9iC2A8vl/V7Wq8Ds702u+4Pbn9uC2CevyO3v7t0ANufhBgn73qkMYLbFelaHfec2g82ZfcHWoXXbCbD4uZV9DnnxW8HsuVGLHNw2eOwFsV97tjkE104Fm39NQNfBRq0JzGZ1bNk/e5WOA4gtBgBYHE4dm7LXRgAAAal6VFh0TU9MIHJka2l0IDIwMjEuMDkuNAAAeJx9k01u4zAMhfc+BS8Qgb+SuOiiSTpFUdQB2rR36H7ujyEdpHIBYeRQsIRPIvP4vECO9/Pr91/4GXxeFgD8z8/d4UsQcXmDfIHj0/PLCqfr4/G+c7p8rtcPIAOqcSae3+zj9fJ23yE4wcFKr+LN4EClYWcSwILbGGf5RrL2qgwHLKLIYhNSkpTSrHKjJKk7iU9IhTVJUnTpQIVa71PQ8koqVbvVFqCwu+gErAliaY0sVpGaBI0mYLuBlVHjorhbmgvjhOxBYjGvqp5HDJk7T0APkAv23uOeFMiIepuAhBvp1bq1zG21Y5vlpuyPFrUeOZNUqtmoCZn9sYJNrG6io3b3OiNlu5MiPUuKXkP1aZm6ldlQQ8wAMUif/fFw2iWLQxEOMblEjT410dN6/mW/myGPl/U8DJkPD9fFAmRYiyJ0+IcjbLiEIurwAkVEo/88P9DoO0VHb5syWpybPhqpEbTvl+ZEtOuL5kS8019zItnprDmR7gTNAsl2wmXin4rje9WkfK/XXp1c3z/1eF/+AUuiy8KJUYRaAAAA3npUWHRTTUlMRVMgcmRraXQgMjAyMS4wOS40AAB4nCXOOWpDQQwG4KuktGGerH3hETBMkyo5QEjla/jwkexpNHxo+ffet+/Pfbn9XH/3/f71R7trlwc95tHH83IYpEvFOggCk2mdTazpug4EUWSxNoEw5xijLJJ6GSmWLgKKTG0hcE2LFuEqeQmKsCwGr6jZjhBBJqsXkaC9yRlVdEJIlPA6EaxcteagIXO2MWBmfyaXEWUMlVv6DJontiioZR9sUeqb6zTAEPMZQ80q5+miHuSJ7pE1iwKVrAFbal2f/2I3QeVaow/TAAABTXpUWHRyZGtpdFBLTDEgcmRraXQgMjAyMS4wOS40AAB4nHu/b+09BiDgZUAAfiAWAOIGRjaGBCDNyMymYAKiGVkgAkxM7AwaQJqZmV1hAYjPyAammRnZHMDiLGwOGWB5RjwMdohaZjaIWSwcEJoJZik3IwMLEyMTAxMzUJKBhZWBlY2BjT2DiZ0jgYMzg4mTK4GLO4OJmUeBh1eDiYePgZWRgZstQYSJlZGJmYWVjZ2Dk4ubTXwfyCy4z26LJtpF5Jg7gDg509n3r20/YQ9ia8UxHtiTuAXMfuwpeiCCJ28viH3YqWX/ir1++0Hs6a+X2u7w8rQDsW8YHLPf8fAVWE35GQYHbaejYDVtW+Mc5km+BbPdSvsdGHfZgNkOsxsc5PMMwOYX+io7NPE1gNn8P3MOLDXVBqu5973swHV3rgMg9taQuQdO1ESC7RIDAMspSSzvOFo6AAABtXpUWHRNT0wxIHJka2l0IDIwMjEuMDkuNAAAeJx9k8FuIzEIhu/zFLzAWoAxxocekkwbrXY7kbpp32Hv+/4quJp6IlnrBGtCPrD5YRaI9bb++vsPvhevywKA//m21uAjI+LyCvEA5+frzw0u99N591xu79v9D1ABUo/xzyN7ut9edw/BBTAxNSMETqalmbkH+xqR7NwPTIWbFgFKRVWFJmAOkBMy5coOCjbOeQIKbAHmzJpL5MZiRHVCliApoaNWgzSszh5IeDutTwwfp99PvEdprwy9rlAhkV+8yjwm7zHVY7w2sawaBxGJTuUwB71IYqkt7laE0HgCNgdzcsq4g1Y4i0xAl/8Ckvxo1C5Hdf1oJhxRJ5GslThSrZHhDGQXjlMppBit8D9Fphl703KqyBUpDle1arNekMAtUCtmUTonTx4NnKAlskpq5EOFfco4t9lFn7f1YSi/xvR829YxpuQj6IW/XEe3uDvzmDxykzFf5FbGEJGbjukgtzoaL2422itubTRR3OjYK4mN6NATiY34IH735YPIHBvJQUvqnnKQLK41kmik4HHPUOqoS/zeX31/Xj4BeLXPnZScxXgAAADuelRYdFNNSUxFUzEgcmRraXQgMjAyMS4wOS40AAB4nB2PO27EMAxEr5LSBmSBpPjTGgECqEm1OYDhNNvnBHv4jKRKeJzhDMfYPn/2J49rfH3f29ivcW8veeH9yX49b/54b4fWzm69UBWW1st5tBokUQ6q7hkZC6VlZjmkspM3IKmtCX6QkSVzyIIk3KJwVeoyZVRNupsCmbtrOWdQTy5SE7l9AkomtkQHhjYgglqzrRLM6og+sZtF0WHOmEBa1ejZJkmTBptWuGjZogWqTESc3bDbs/PaY8aOPkSk8MBNOKVPU1LglrKXX37gCn3/Axk7Q0Gjmk6kAAABZHpUWHRyZGtpdFBLTDIgcmRraXQgMjAyMS4wOS40AAB4nHu/b+09BiDgZUAAQSAWBuIGRg4GDSDNzMQGoVnYFFSANBMLG0MCiGbCSYPVMbKwM2SA9TOyOUANgNNgCWZGPAxGsKUMcJqbgVGDiZGJgYkZaAADCysDKxsDGzsDOwcDB6cCJ1cGExd3AjdPBhMPbwIvH5DHqMDOxMDHmcDEz8LELsDCKMLMxsjFycHOxMbMwsoGpLh5ePk4ucSvgQyH+z3A2Whf1wKTAyBOyia1fZVOK/eD2Pkak+zT2EXB7LZb0g4dh1eD2U8i8x1aOKXA7M9CBQ6bP6fag9hLfGQd1lleAbN7Zk22v/g1C8zunsC/b++ua2D22Q879r//ng9mv0ratd+DVQBszuUNBgeyDi4DsyfubjygxcwNZnPGNx7g/VUCVr/VTv/AGeubYHbgtgn26o6sYDev4plqf2iPlAOILQYAxqpTHmo8QRAAAAHOelRYdE1PTDIgcmRraXQgMjAyMS4wOS40AAB4nH2UQY7bMAxF9z6FLhCDnyJFadHFxJmZFsU4QJvpHbrv/VHSTkYeVKgSCo7yKImfH55SjB+X77//pI/Bl2lKif7zba2lX5mIprcUD+n8/PptTcvt6fxYWa7v6+1ngiU0z/HPZ/bpdn17rCBd04lmmFDVdOK5MrMfQTNto+dyWjaysDVKJ8yZOQsGZHYSMwRVW6RoZYgMQHGQZ8nKyNuOgkY6ANXBPFtutSB2LASjOgDLDiqgxf+urbLSgLP9ZLVK2e9atBJGXN1L0QyNAhqs+lX/5VpaN3GE2Jd9QzO1Ucl+yhKlikiVkLlly2YjEndSS6gXOhbWOhIcW294tkLWeFOS2GwkEKI5J5lJBVK2XSW7miNU7qhw1Ti2aWkyUgl6Pz9XJo7ymyEP9yzpawiaSYtECrk3PGVA2k4WV6pFr2Bmo+Kf18snR+8eP1/XS/c4R3Qjx0LuboWHdE/CQ7vz4FG6v+Bh3UbwqN0t8GjdFIg49l5iAg49lpjAh1ZKTMiHjklMkENjJCbooQGIffigc1wlH9SUjeqXqVvdDi4vr1862LZE52MZR5GPksbvxyvHn6e/oLbkSClcPH4AAADrelRYdFNNSUxFUzIgcmRraXQgMjAyMS4wOS40AAB4nC2PS4rEMAxErzLLBNxGpY8lExoasunVzAFCVrlGH34Uu7UST6Wi6nifx/56neA9Z67L8T7XfXn+rReu5crB+ss/nwUVTdUKV4W7ly2BCaxQ7fCAlC1P5lFQmwWhbFLdgJaK6ME2gPRo5UG1EZxi/IgxygNVFH3YKqbGgqE6kJAl4kqJypY3NPY+vphFJ3KlsFsVyRIh8zTosGpsgclUY6QWl7tH6l2C79jdcVtpJeWpsda/xDS73k4qGX2+NfpmIM7eI4PScHI3L+vnH9JMSUxB2v1WAAABT3pUWHRyZGtpdFBLTDMgcmRraXQgMjAyMS4wOS40AAB4nHu/b+09BiDgZUAAASAWBOIGRk4GBSDNyOagAaSYWdgcMkA0MyM2BpoSdgYwg4mRjQEiwwGhmfAZBlXpAFXJkACynZmbgZGBkSmDiYk5gZklg4mFNYGVLYOJlV2BnUOBg1ODiYNLgYs7g4mbJ4GHN4OJly+Bl5+BjTGBjytBhImNkY2VhZmJlZuLj5dH/BTIPLg3XyR1HFCOFz8A4txdlX9gNlfpfhB76eRpBw4WutuB2DpsbQcM1c/ag9i/SnQPLH3zFsyW/nh/v8MnEzC7XljwwOZ6Y7DeSs7ufeq1ZWDxrzkG9n3LHfeB2NtZDOxe554Bq5m9ictBkaPTFsQu4DJ1+PdgC1h9PkeXw+upM8HsM5aTHDyS+8B6l/X6O2gXV4H1vvbd6/B9QgGYLQYA3u1RLkU7mCoAAAG1elRYdE1PTDMgcmRraXQgMjAyMS4wOS40AAB4nH2UW47bMAxF/70KbiCCSPGlz0kyLYpibKBNu4f57/5R0kYqD6pWCgU9jmTp8iILZPl2//r+C/4Uui8LQP3Pr/cOP1utdXmD7MD19fOXFW6Pl+tz5rb9WB/fARXQYk/Uj+zLY3t7ziB8ggsXUqrW4EKlqaAT1FL3MvYS3ODSijF7ZbjU0sWwtwnZkuRiVYRyHTub1QnIB4juJA2waCWTPgElQSqGlVQCdHFznoCaIMYlu7DEulV1wglox4mk6ij5GquIahPSYc11MhTJ9a7kPAN7HFmLekdtuQOjFzn4G8QKW8piQbS8rvR42ew5iHEmlbgYyv4K1Y4zJZF20MlNKQRibP/4diaHS8Mm1APE3t19BvIOinYROQRwrDMpQ78NWiFuNaROY5g3mt4y0yOlo5geZIuXz8z2ut4/2PQw7nVb78O4WWm4kyPasCBnDKNllWGnGIAO03CEDWtgDH3kHyP6yDJF4DmZmBN4yhlng3RKDmeD7ZQFzgb5JDdng3KSFfcZPcnHcbtxruUeOX07ZTuLlOPnP0P0l98wudP0z0bMIgAAAOF6VFh0U01JTEVTMyByZGtpdCAyMDIxLjA5LjQAAHicHY/LjQNBCERT2eOM1EYUND+NfLK0x3UQE4ATcPBL9w09VT3gdeO+7+N1PN/n3y09/p4N5Pzg53sYFSx8PJhKKyDjmmRetpFEgrGQQk0HCFVZ4xJKya6BJnSVhOABG0zsXl1h8iy4Lg16gi+G6LkZyHrZuPYOmEUXyyVnNAPFLFuuYE9ZMSFxTyxZcLtWTDs2c19ugbZej9kx4RidVzfkRsFm0jLUjNgEmWJ9u7P0D8seYFnfpGV0S0mmsmx3pMo4v/+Od0Nn5jJ6mAAAAUF6VFh0cmRraXRQS0w0IHJka2l0IDIwMjEuMDkuNAAAeJx7v2/tPQYg4GVAAH4gFgDiBkY2hgQgzcjMxqABpJlZOCA0E0SciYndAcxnZnPIANOMCAGIBnQabgBMA0xCwAHZZEZmbgZGBkYmDiZGZqAkAwtrAitbBhMbewI7RwYTB2cCJ5cGEwd3AjdPBhMPbwIPHwMnSwIve4IIExsLJwc7GysrNwc7L4/4PpBZcG+l8S9z6BXl3Q/i/IkocYiwSLcFsXcpZTk8VDpmD2LnnVRzWHo1GKzGjn2eva9RIsgQht2zOu2vHloEVtN7ePq+uPYPYPZ//oP7Jx6tA7NrFq/ZHyH5D6x+E8cum/tevWBz9Jda2f2XVDsAYhd+0j0w6SNE/F5A3gHl+AZrEDu1wu7AmS/LwOZsf7TsgHyiPNgcMQD+f00BXUrybAAAAZx6VFh0TU9MNCByZGtpdCAyMDIxLjA5LjQAAHicfZPdTsMwDIXv+xR+gUX+TeJLtiGEEJ0Eg3fgnvcXdqeRIkUkTdQ6n8/aY2+BHG/nl69v+B18XhYA/Odyd/gURFxeIW/g+Pj0vMLp+nC8R06Xj/X6DmRANXJi/mUfrpfXe4TgBFaouzSHAxYzIoqMgtsYqRyglE7NhfLYqtqME7gEV61LC/ViGgk+4TT0uFSsqJo/3LkFOgEN1tBhUfOaIJM79QlYQ5EKNkOxzGhkjSZcC8HU8aqkAfbmJDOwh+AhPgG7YJ67GyNPQL+Bor3J5qJ65d4mZFh7yjBzQ88cQuk6JSmMxKhMoAQHLuYmMiWzNAG0qA3zTTTqaTNUEpXSWGqvGyBzM8OZ9xT1VtF7uCSoonVGWmpa1MWoWX49WTSHTtDH9fyn+W7teLys59GOOXk0XU4ZvRVnoKOFKJaNRokHqKMdNFYbVddYfdRWY/mooMaifZ04N6JdPTaEd7ZrbiQ7dzU30p2LtEVs55am8AjkewbX9ybtLcnn+7877pcf9sPI8olOK7UAAADdelRYdFNNSUxFUzQgcmRraXQgMjAyMS4wOS40AAB4nDWPu40DMQxEW3G4C8gChx+RhOBoC3ARyp1c6uKPWsDpo97M6LqO1/u8PlifxetY67jOPz4XXu/H97COSIn2pG4GoE3pAU9p1MmGGvFGw0K8oZt6apvcBw3SbQV7sTbRWXRswshEbEJuJGWxw7zNfcuh0ELhCSlUkRS7LNN4dxURDb+zNQfHFrl7beJWR1DtLSTdWUbumSQJt9rwtCo33L+B1Xq93fSBqhRSsTZLYHb6pUncDFEQrV5bmmg7v/9lCEAUnC+ILQAAAN16VFh0cmRraXRQS0w1IHJka2l0IDIwMjEuMDkuNAAAeJx7v2/tPQYg4GVAAE4obmBkY0gA0ozMHAwKQJoJwmViYnPQANLMLGwOGSCamVEAIgCXYIfQzDD93AyMDIxMDEzMQLkMJhbWBFa2BDb2DCY2DgZ25gQRRlZmFlY2dvEykGK4K14ENh2wjf1pB+K0/VY5MElC1h7EXup6Z3+CgNx+ELt9Rfq+Gz6/94HYlWaO9snCF8DiAcc4HB51tYLZl1czOJwQew42R/oIj/2hL15gc155ezr8D90OZosBAKWLLiiihKChAAABK3pUWHRNT0w1IHJka2l0IDIwMjEuMDkuNAAAeJx9UttqwzAMfc9X6AdqZF0s+7FtyhijCazZ/mHv/X8mbWRuwUyKQFKOD9KxJwh7n9++7vBnNE8TAP7ztdbgkxFxukIkcLq8vC5w3o6nvXNeP5btBs0dw5+Rx2297p0MZzhIQiNpFTBJNWQ/lfDH+lGCFQ6U1Kwq+f+SuWgZADkYczLCagqHQJqwDZASSExEhahFJg0r5QFSHYnJVMyJnLyQaqMBsMANKGW2jBJAFGYcMZozUkKH1RhNNLOMtqmweFddnBI4a2RttEtzPk5ZlLRCTsLEeTTgZZmf9P+9kdO6zP1Gwqnr7gVwVzd7SJcwXLtOXkDpaoiH9Z3Fo/bVspetbyDeksdBH8eKen9ink/f0t6DvSjbaYoAAACbelRYdFNNSUxFUzUgcmRraXQgMjAyMS4wOS40AAB4nB3NOw7DQAgE0KuktKU14j+LXPoAOYT7NGl9+LApeQzD9b5uub/3du0feT3b4cTQGEw+wVbjPJQCmItSLCObhKA85ziWwQ1tTKqpWgu9eKqMkwnh6HVfpEZ0nZIYZAG72ZpZ2Gs9DDHvdiPx0BxCbmr/lvCaic6gFIWxPz8XkyX2wbCwiQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Choose 6 random indices from validation dataset\n",
    "r_idx = random.sample(range(len(valid_smiles)), 6)\n",
    "# Extract SMILES, RDKit molecular objects, ground_truth labels, and predictions for these molecules\n",
    "Smiles = [valid_smiles[r][0] for r in r_idx]\n",
    "GT = [valid_smiles[r][1] for r in r_idx]\n",
    "Mols = [Chem.MolFromSmiles(r) for r in Smiles]\n",
    "Pred = [predictions[r] for r in r_idx]\n",
    "\n",
    "# Create labels\n",
    "labelList = [\"True: \" + str('%.3f' %gt) +  \"\\v Pred: \" + str(prediction) for gt, prediction in zip(GT,Pred)]\n",
    "# Display molecules with labels\n",
    "Draw.MolsToGridImage(Mols,molsPerRow=3,legends=[label for label in labelList],\n",
    "                    subImgSize=(250,250), useSVG=False)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets now look at the mean absolute error compared to a global molecular property such as number of nodes.\n",
    "\n",
    "First, we have to extract the number of nodes from our graph data..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_nodes_list = []\n",
    "for i in valid_idx:\n",
    "    num_nodes_list.append(graph_data.dataset[i][0]['num_nodes'])\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For simplicity we create a dataframe with columns ground truth, prediction, and number of nodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ground_truth</th>\n",
       "      <th>prediction</th>\n",
       "      <th>num_nodes</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4.587840</td>\n",
       "      <td>5.558594</td>\n",
       "      <td>17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.971520</td>\n",
       "      <td>5.558594</td>\n",
       "      <td>17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5.496700</td>\n",
       "      <td>5.519531</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5.485815</td>\n",
       "      <td>5.519531</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.748387</td>\n",
       "      <td>4.761719</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   ground_truth  prediction  num_nodes\n",
       "0      4.587840    5.558594         17\n",
       "1      4.971520    5.558594         17\n",
       "2      5.496700    5.519531         15\n",
       "3      5.485815    5.519531         15\n",
       "4      4.748387    4.761719         14"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(list(zip(ground_truth, predictions,num_nodes_list)), columns=['ground_truth','prediction','num_nodes'])\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, lets plot the mean HOMO-LUMO gap and mean prediction per molecule size... "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting a line graph\n",
    "plt.plot(df.groupby(\"num_nodes\")['ground_truth'].mean(),color='red', label = 'Mean ground truth')\n",
    "plt.plot(df.groupby(\"num_nodes\")['prediction'].mean(),color='green', label = 'Mean prediction')\n",
    "plt.legend()\n",
    "plt.ylabel(\"HOMO-LUMO Gap (eV)\")\n",
    "plt.xlabel(\"Number of Atoms\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, lets add the mean absolute error to our dataframe and compare it to the molecule size..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Add MAE to dataframe\n",
    "df['mae']= np.abs(df[\"ground_truth\"]-df[\"prediction\"])\n",
    "# plot\n",
    "plt.plot(df.groupby(\"num_nodes\")['mae'].mean(),color='orange', label = 'Mean MAE')\n",
    "plt.legend()\n",
    "plt.ylabel(\"Mean Absolute Error (eV)\")\n",
    "plt.xlabel(\"Number of Atoms\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It seems that our model struggles to predict the HOMO-LUMO gap for larger molecules. However, there are only very few molecules (31 in total) that consist of 40 or more atoms. Therefore, lets see how much molecules of a particular size contribute to the overall error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Add MAE to dataframe\n",
    "df['mae']= np.abs(df[\"ground_truth\"]-df[\"prediction\"])\n",
    "# plot\n",
    "plt.plot(df.groupby(\"num_nodes\")['mae'].size()/len(valid_idx)*100,color='green')\n",
    "plt.ylabel(\"Contribution in % to final MAE\")\n",
    "plt.xlabel(\"Number of Atoms\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Follow up tasks\n",
    "\n",
    "* Try changing the smile string and seeing what HOMO-LUMO gap is predicted.\n",
    "* Try a larger model (`GPS_PCQ_8gps_22M.yaml` or `GPS_PCQ_16gps_44M.yaml`) and the corresponding checkpoint.\n",
    "* Take a look at the `predict` function to get an understanding of what is required to run on IPUs.\n",
    "* Use the 'test-challenge' split of the dataset to predict HOMO-LUMO gaps for the molecules in the challenge."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or head to `notebook_training.ipynb` to try out training the model from scratch using IPUs!"
   ]
  }
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