examples/pytorch_minimal_demo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pytorch example\n",
    "\n",
    "This file shows a minimal pytorch example running on adult data, and demonstrating head-merging.\n",
    "\n",
    "In general, we strongly recommend that you *do not* use neural networks on tabular data. Boosting is typically higher performing and much faster to run.\n",
    "\n",
    "However, this is a toy example, and unlike computer vision examples, it will train and run in a matter of minutes. The techniques shown directly apply to computer vision and NLP without modification.\n",
    "\n",
    "In brief, the steps are:\n",
    "1. Train a two-headed network.   \n",
    "    The first head should predict the target attribute using binary cross entropy.  \n",
    "    The second head should predict binarized protected attributes (use a 1-hot or 0,1 encoding) using mean squared error.\n",
    "2. Create a FairPredictor using `DeepFairPredictor` with the output of the network on validation data.\n",
    "3. Call fit to enforce fairness. Use `evaluate_groups` and `plot_frontier` to explore trade-offs. \n",
    "4. Finalize the network. Use `merge_heads_pytorch` to generate a fair network with a single head.  \n",
    "    If you are not using pytorch you can still do this by hand.  \n",
    "    Call the methods `extract_coefficients` or `extract_coefficients_1_hot` and look at the code in `merge_heads_pytorch` or read the paper for instructions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2024-06-17T19:19:04.140766Z"
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   },
   "outputs": [],
   "source": [
    "# Load libraries\n",
    "\n",
    "import oxonfair\n",
    "from oxonfair import group_metrics as gm\n",
    "\n",
    "import numpy as np\n",
    "import torch\n",
    "import torch.nn.functional as F\n",
    "from torch import nn, optim\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-17T19:19:04.142997Z",
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     "shell.execute_reply": "2024-06-17T19:19:12.274964Z"
    }
   },
   "outputs": [],
   "source": [
    "#Load adult dataset, using sex as the default groups and discard sex from the raw data\n",
    "train, val, test = oxonfair.dataset_loader.adult(discard_groups=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-17T19:19:12.278230Z",
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     "shell.execute_reply": "2024-06-17T19:19:12.282509Z"
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   },
   "outputs": [],
   "source": [
    "#Normalise data\n",
    "std = train['data'].std()\n",
    "train['data'] = train['data'] / std\n",
    "val['data'] = val['data'] / std\n",
    "test['data'] = test['data'] / std"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-17T19:19:12.285243Z",
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     "shell.execute_reply": "2024-06-17T19:19:12.289119Z"
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   "outputs": [],
   "source": [
    "#define a basic nn with 2 hidden-layers. 1 of width 100, and the second width 50.\n",
    "network = nn.Sequential(nn.Linear(train['data'].shape[1],100),\n",
    "                        nn.SELU(),\n",
    "                        nn.Linear(100,50),\n",
    "                        nn.SELU(),\n",
    "                        nn.Linear(50,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-17T19:19:12.291648Z",
     "iopub.status.busy": "2024-06-17T19:19:12.291459Z",
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     "shell.execute_reply": "2024-06-17T19:19:12.294038Z"
    }
   },
   "outputs": [],
   "source": [
    "# Define a custom loss that trains the two-heads as required.\n",
    "def loss(x, y, g):\n",
    "    output = network(x)\n",
    "    loss0 = F.binary_cross_entropy_with_logits(output[:,0], y)\n",
    "    loss1 = F.mse_loss(output[:,1], g)\n",
    "    return loss0+loss1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-17T19:19:12.297813Z",
     "iopub.status.busy": "2024-06-17T19:19:12.296845Z",
     "iopub.status.idle": "2024-06-17T19:19:13.143869Z",
     "shell.execute_reply": "2024-06-17T19:19:13.083352Z"
    }
   },
   "outputs": [],
   "source": [
    "# Copy variables to tensors\n",
    "target = torch.tensor(train['target']).float()\n",
    "data = torch.tensor(np.asarray(train['data'])).float()\n",
    "groups = torch.tensor(train['groups']==' Male').float()\n",
    "\n",
    "optimizer = optim.Adam(network.parameters(), lr=1e-4)\n",
    "from numpy import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-17T19:19:13.146915Z",
     "iopub.status.busy": "2024-06-17T19:19:13.146763Z",
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     "shell.execute_reply": "2024-06-17T19:19:27.845472Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch is 0\n",
      "epoch is 10\n",
      "epoch is 20\n",
      "epoch is 30\n",
      "epoch is 40\n",
      "epoch is 50\n",
      "epoch is 60\n",
      "epoch is 70\n",
      "epoch is 80\n",
      "epoch is 90\n"
     ]
    }
   ],
   "source": [
    "# Train the network\n",
    "batch_size = 50\n",
    "\n",
    "for epoch in range(100):\n",
    "    #shuffle data\n",
    "    perm = random.permutation(target.shape[0])\n",
    "    target = target[perm]\n",
    "    data = data[perm]\n",
    "    groups = groups[perm]\n",
    "    if epoch%10==0:\n",
    "        print ('epoch is %d'%epoch)\n",
    "    for step in range(target.shape[0]//batch_size): # This discards the final incomplete batch\n",
    "        optimizer.zero_grad()\n",
    "        l = loss(data[step*batch_size:(1+step)*batch_size],\n",
    "                 target[step*batch_size:(1+step)*batch_size],\n",
    "                 groups[step*batch_size:(1+step)*batch_size])\n",
    "        l.backward()\n",
    "        optimizer.step()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-17T19:19:27.861148Z",
     "iopub.status.busy": "2024-06-17T19:19:27.860200Z",
     "iopub.status.idle": "2024-06-17T19:19:27.979998Z",
     "shell.execute_reply": "2024-06-17T19:19:27.978176Z"
    }
   },
   "outputs": [],
   "source": [
    "#convert test['data'] to tensor via numpy and then move the output back to numpy\n",
    "test_output=np.asarray(network(torch.tensor(np.asarray(test['data'])).float()).detach())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To see if training works we visualize the outputs of the second head (corresponding to gender)\n",
    "\n",
    "Ideally, this should be a two peaked distribution centered on 0 and 1, with more values at 1 -- corresponding to the male label.\n",
    "\n",
    "Instead, we find we have 1 peak centered on 1, a broader central peak corresponding to 'don't know' centered around 0.5 and a third smaller peak around 0.2 and 0.\n",
    "\n",
    "This is fine. The broad central peak reflects the ambiguity of the task, and otherwise we do have something of a split into male and female."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-17T19:19:27.986127Z",
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     "shell.execute_reply": "2024-06-17T19:19:29.231943Z"
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   },
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot the outputs of the second head\n",
    "from matplotlib import pyplot as plt\n",
    "_=plt.hist(test_output[:,1],bins=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-17T19:19:29.247695Z",
     "iopub.status.busy": "2024-06-17T19:19:29.247389Z",
     "iopub.status.idle": "2024-06-17T19:19:29.289863Z",
     "shell.execute_reply": "2024-06-17T19:19:29.287757Z"
    }
   },
   "outputs": [],
   "source": [
    "#Let's train a fair classifier using the two heads \n",
    "#convert val['data'] to tensor via numpy and then move the output back to numpy\n",
    "val_output = np.asarray(network(torch.tensor(np.asarray(val['data'])).float()).detach())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-17T19:19:29.294341Z",
     "iopub.status.busy": "2024-06-17T19:19:29.293700Z",
     "iopub.status.idle": "2024-06-17T19:19:58.363387Z",
     "shell.execute_reply": "2024-06-17T19:19:58.345518Z"
    }
   },
   "outputs": [],
   "source": [
    "fpred = oxonfair.DeepFairPredictor(val['target'],\n",
    "                                   val_output,\n",
    "                                   groups=val['groups'])\n",
    "# Enforce fairness on validation data -- i.e. demographic/statistical parity should be within 2 %\n",
    "fpred.fit(gm.accuracy, gm.demographic_parity, 0.02,grid_width=75)\n",
    "# Varying the grid with can improve accuracy at the cost of a longer search time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-17T19:19:58.436634Z",
     "iopub.status.busy": "2024-06-17T19:19:58.434899Z",
     "iopub.status.idle": "2024-06-17T19:19:58.756768Z",
     "shell.execute_reply": "2024-06-17T19:19:58.756355Z"
    }
   },
   "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>original</th>\n",
       "      <th>updated</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Accuracy</th>\n",
       "      <td>0.847011</td>\n",
       "      <td>0.831859</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Balanced Accuracy</th>\n",
       "      <td>0.737473</td>\n",
       "      <td>0.704057</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>F1 score</th>\n",
       "      <td>0.622626</td>\n",
       "      <td>0.566420</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MCC</th>\n",
       "      <td>0.544495</td>\n",
       "      <td>0.489700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Precision</th>\n",
       "      <td>0.759862</td>\n",
       "      <td>0.739658</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Recall</th>\n",
       "      <td>0.527379</td>\n",
       "      <td>0.458932</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ROC AUC</th>\n",
       "      <td>0.902655</td>\n",
       "      <td>0.888533</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   original   updated\n",
       "Accuracy           0.847011  0.831859\n",
       "Balanced Accuracy  0.737473  0.704057\n",
       "F1 score           0.622626  0.566420\n",
       "MCC                0.544495  0.489700\n",
       "Precision          0.759862  0.739658\n",
       "Recall             0.527379  0.458932\n",
       "ROC AUC            0.902655  0.888533"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Check performance drop\n",
    "fpred.evaluate()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-17T19:19:58.803222Z",
     "iopub.status.busy": "2024-06-17T19:19:58.802592Z",
     "iopub.status.idle": "2024-06-17T19:19:58.886894Z",
     "shell.execute_reply": "2024-06-17T19:19:58.886449Z"
    }
   },
   "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>original</th>\n",
       "      <th>updated</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Statistical Parity</th>\n",
       "      <td>0.153123</td>\n",
       "      <td>0.019611</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Predictive Parity</th>\n",
       "      <td>0.000197</td>\n",
       "      <td>0.270249</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Equal Opportunity</th>\n",
       "      <td>0.100120</td>\n",
       "      <td>0.262595</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Average Group Difference in False Negative Rate</th>\n",
       "      <td>0.100120</td>\n",
       "      <td>0.262595</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Equalized Odds</th>\n",
       "      <td>0.078853</td>\n",
       "      <td>0.145533</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Conditional Use Accuracy</th>\n",
       "      <td>0.056217</td>\n",
       "      <td>0.219375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Average Group Difference in Accuracy</th>\n",
       "      <td>0.114673</td>\n",
       "      <td>0.108514</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Treatment Equality</th>\n",
       "      <td>0.123767</td>\n",
       "      <td>1.587736</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                 original   updated\n",
       "Statistical Parity                               0.153123  0.019611\n",
       "Predictive Parity                                0.000197  0.270249\n",
       "Equal Opportunity                                0.100120  0.262595\n",
       "Average Group Difference in False Negative Rate  0.100120  0.262595\n",
       "Equalized Odds                                   0.078853  0.145533\n",
       "Conditional Use Accuracy                         0.056217  0.219375\n",
       "Average Group Difference in Accuracy             0.114673  0.108514\n",
       "Treatment Equality                               0.123767  1.587736"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# and fairness\n",
    "fpred.evaluate_fairness()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-17T19:19:58.891498Z",
     "iopub.status.busy": "2024-06-17T19:19:58.891329Z",
     "iopub.status.idle": "2024-06-17T19:19:59.377465Z",
     "shell.execute_reply": "2024-06-17T19:19:59.376942Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Visualise the possible trade-offs\n",
    "fpred.plot_frontier()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-17T19:19:59.382198Z",
     "iopub.status.busy": "2024-06-17T19:19:59.381925Z",
     "iopub.status.idle": "2024-06-17T19:19:59.789703Z",
     "shell.execute_reply": "2024-06-17T19:19:59.789389Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#To quickly select another point from the frontier, you can call it with recompute=False\n",
    "fpred.fit(gm.accuracy, gm.demographic_parity, 0.05, recompute=False)\n",
    "fpred.plot_frontier()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-17T19:19:59.792911Z",
     "iopub.status.busy": "2024-06-17T19:19:59.792623Z",
     "iopub.status.idle": "2024-06-17T19:19:59.795145Z",
     "shell.execute_reply": "2024-06-17T19:19:59.794795Z"
    }
   },
   "outputs": [],
   "source": [
    "# to evaluate how it's working on the test set, we'll create a new dataset holder\n",
    "test_network = oxonfair.DeepDataDict(test['target'], test_output, test['groups'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-17T19:19:59.797298Z",
     "iopub.status.busy": "2024-06-17T19:19:59.797154Z",
     "iopub.status.idle": "2024-06-17T19:19:59.854729Z",
     "shell.execute_reply": "2024-06-17T19:19:59.854107Z"
    }
   },
   "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>original</th>\n",
       "      <th>updated</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Accuracy</th>\n",
       "      <td>0.850545</td>\n",
       "      <td>0.840799</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Balanced Accuracy</th>\n",
       "      <td>0.742136</td>\n",
       "      <td>0.737372</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>F1 score</th>\n",
       "      <td>0.631090</td>\n",
       "      <td>0.618375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MCC</th>\n",
       "      <td>0.555519</td>\n",
       "      <td>0.529675</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Precision</th>\n",
       "      <td>0.770864</td>\n",
       "      <td>0.725138</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Recall</th>\n",
       "      <td>0.534223</td>\n",
       "      <td>0.539014</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ROC AUC</th>\n",
       "      <td>0.902339</td>\n",
       "      <td>0.888278</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   original   updated\n",
       "Accuracy           0.850545  0.840799\n",
       "Balanced Accuracy  0.742136  0.737372\n",
       "F1 score           0.631090  0.618375\n",
       "MCC                0.555519  0.529675\n",
       "Precision          0.770864  0.725138\n",
       "Recall             0.534223  0.539014\n",
       "ROC AUC            0.902339  0.888278"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#And evaluate\n",
    "fpred.evaluate(test_network)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-17T19:19:59.857148Z",
     "iopub.status.busy": "2024-06-17T19:19:59.856991Z",
     "iopub.status.idle": "2024-06-17T19:19:59.937419Z",
     "shell.execute_reply": "2024-06-17T19:19:59.937029Z"
    }
   },
   "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>original</th>\n",
       "      <th>updated</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Statistical Parity</th>\n",
       "      <td>0.154577</td>\n",
       "      <td>0.046572</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Predictive Parity</th>\n",
       "      <td>0.008904</td>\n",
       "      <td>0.245004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Equal Opportunity</th>\n",
       "      <td>0.104299</td>\n",
       "      <td>0.231262</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Average Group Difference in False Negative Rate</th>\n",
       "      <td>0.104299</td>\n",
       "      <td>0.231262</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Equalized Odds</th>\n",
       "      <td>0.080281</td>\n",
       "      <td>0.124072</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Conditional Use Accuracy</th>\n",
       "      <td>0.059483</td>\n",
       "      <td>0.198959</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Average Group Difference in Accuracy</th>\n",
       "      <td>0.112338</td>\n",
       "      <td>0.095505</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Treatment Equality</th>\n",
       "      <td>0.137020</td>\n",
       "      <td>2.032479</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                 original   updated\n",
       "Statistical Parity                               0.154577  0.046572\n",
       "Predictive Parity                                0.008904  0.245004\n",
       "Equal Opportunity                                0.104299  0.231262\n",
       "Average Group Difference in False Negative Rate  0.104299  0.231262\n",
       "Equalized Odds                                   0.080281  0.124072\n",
       "Conditional Use Accuracy                         0.059483  0.198959\n",
       "Average Group Difference in Accuracy             0.112338  0.095505\n",
       "Treatment Equality                               0.137020  2.032479"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fpred.evaluate_fairness(test_network)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-17T19:19:59.940294Z",
     "iopub.status.busy": "2024-06-17T19:19:59.939973Z",
     "iopub.status.idle": "2024-06-17T19:19:59.942597Z",
     "shell.execute_reply": "2024-06-17T19:19:59.942335Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-2.107, 1.824)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Now let's merge the heads\n",
    "# We examine the coefficients first.\n",
    "fpred.extract_coefficients()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The block below shows the merging step for two groups. \n",
    "\n",
    "When only two groups exist, we are using a binary encoding of groups and trying to predict either 0 or 1.\n",
    "The parameters we learn correspond to a scalar `a`, and bias `b`, and the predictions made by the merging:\n",
    "\n",
    "    classification_head + a * group_head +b\n",
    "\n",
    "should be fair and performant.\n",
    "\n",
    "When more than two groups exist, you should have trained the second head to output a one-hot encoding of the groups and the merging:\n",
    "\n",
    "    classification_head + a.dot(group_head)\n",
    "\n",
    "should be fair and performant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-17T19:19:59.944167Z",
     "iopub.status.busy": "2024-06-17T19:19:59.944036Z",
     "iopub.status.idle": "2024-06-17T19:19:59.959314Z",
     "shell.execute_reply": "2024-06-17T19:19:59.958777Z"
    }
   },
   "outputs": [],
   "source": [
    "# We copy the network and create a fair version\n",
    "import copy\n",
    "fair_network = copy.deepcopy(network)\n",
    "# We replace the final linear layer with a 1 dimensional head.\n",
    "fair_network[-1] = fpred.merge_heads_pytorch(network[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-17T19:19:59.962110Z",
     "iopub.status.busy": "2024-06-17T19:19:59.961919Z",
     "iopub.status.idle": "2024-06-17T19:19:59.983719Z",
     "shell.execute_reply": "2024-06-17T19:19:59.983212Z"
    }
   },
   "outputs": [],
   "source": [
    "# Now let's check the fair classifier on the test set.\n",
    "test_fair_output=np.asarray(fair_network(torch.tensor(np.asarray(test['data'])).float()).detach())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-17T19:19:59.986126Z",
     "iopub.status.busy": "2024-06-17T19:19:59.985985Z",
     "iopub.status.idle": "2024-06-17T19:19:59.994638Z",
     "shell.execute_reply": "2024-06-17T19:19:59.994199Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Accuracy             0.840799\n",
       "Balanced Accuracy    0.737372\n",
       "F1 score             0.618375\n",
       "MCC                  0.529675\n",
       "Precision            0.725138\n",
       "Recall               0.539014\n",
       "ROC AUC              0.888278\n",
       "Name: 0, dtype: float64"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# As expected the accuracy is identical to what was reported before.\n",
    "oxonfair.performance.evaluate(test['target'],test_fair_output.reshape(-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-17T19:19:59.996913Z",
     "iopub.status.busy": "2024-06-17T19:19:59.996781Z",
     "iopub.status.idle": "2024-06-17T19:20:00.038725Z",
     "shell.execute_reply": "2024-06-17T19:20:00.037915Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Statistical Parity                                 0.046572\n",
       "Predictive Parity                                  0.245004\n",
       "Equal Opportunity                                  0.231262\n",
       "Average Group Difference in False Negative Rate    0.231262\n",
       "Equalized Odds                                     0.124072\n",
       "Conditional Use Accuracy                           0.198959\n",
       "Average Group Difference in Accuracy               0.095505\n",
       "Treatment Equality                                 2.032479\n",
       "Name: 0, dtype: float64"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# And so is the fairness\n",
    "oxonfair.performance.evaluate_fairness(test['target'],test_fair_output.reshape(-1),test['groups'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-17T19:20:00.041072Z",
     "iopub.status.busy": "2024-06-17T19:20:00.040869Z",
     "iopub.status.idle": "2024-06-17T19:20:00.044125Z",
     "shell.execute_reply": "2024-06-17T19:20:00.043628Z"
    }
   },
   "outputs": [],
   "source": [
    "# Finally, let's compare to a range of other oxonfair based classifiers.\n",
    "# These don't support head merging\n",
    "# 1. The base method that just picks the most likely group label instead of keeping track of the value returned \n",
    "fpred_standard = oxonfair.DeepFairPredictor(val['target'],\n",
    "                                              val_output,\n",
    "                                              groups=val['groups'], use_fast=True)\n",
    "# 2. A classifier that enforces fairness by using the actual group labels instead of inferred.\n",
    "fpred_true_groups = oxonfair.DeepFairPredictor(val['target'],\n",
    "                                              val_output,\n",
    "                                              groups=val['groups'], use_fast=True,use_actual_groups=True)\n",
    "\n",
    "\n",
    "# 3. Single threshold. This adjusts the global bias only, without considering group membership.\n",
    "# It works surprisingly well for criteria like recall.min, but is less useful for fairness\n",
    "fpred_thresh  = oxonfair.DeepFairPredictor(val['target'],\n",
    "                                              val_output,\n",
    "                                              groups=val['groups'], use_actual_groups='single_threshold')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-17T19:20:00.046278Z",
     "iopub.status.busy": "2024-06-17T19:20:00.046145Z",
     "iopub.status.idle": "2024-06-17T19:20:00.065088Z",
     "shell.execute_reply": "2024-06-17T19:20:00.064691Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Fewer groups used (1) in infered groups than in the true groups (2)\n"
     ]
    }
   ],
   "source": [
    "fpred_standard.fit(gm.accuracy,gm.demographic_parity,0.05)\n",
    "fpred_true_groups.fit(gm.accuracy,gm.demographic_parity,0.05)\n",
    "fpred_thresh.fit(gm.accuracy,gm.demographic_parity,0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-17T19:20:00.067975Z",
     "iopub.status.busy": "2024-06-17T19:20:00.067792Z",
     "iopub.status.idle": "2024-06-17T19:20:01.051254Z",
     "shell.execute_reply": "2024-06-17T19:20:01.050803Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.75, 0.8792014742014742)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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zQZ962XN1vs9hDwwAgGamXmtWZGMtriKD8zq/IlfiQh9+pSa8Tjj+5vhz9BxJ6pJABA3R1t5d627kfjk1J+zMI3XliDl05X+KVN+z8z5oVhK0L23urDUTmJV9KuNyuSYmJnS6TP7bVH3AEZRJacmuZCCEaDREEIipe7amxBohOoEQTaFEyl0fyz7KIoaMCITE8rOpIgYNgRANoeVnUz2s9Wr7XlJTU2NiYoqLi/FlD0LxDt04U6gh0g+/qOJuRr6zuWYTygwKDAAAWWnanXlsG115/uLkveKPHw3xqR7pa1akQaPAe8zUPUtXLMLlIgt91FdqJ9TJnGGerJn8Xvm9eIcEIrLLsnffuXzs7Ed3hZdt1LRMLZ9VPLXIfeeAXmbcNU3P1CvX/6Rvl2l3MPUgvkVFRcXLy8va2rqu2X2lD8oYHCmNy5kC/IFGQzTFIgYnQ1BmjhAS1vCk3KXN0ZYuQ724m5FPrhxSka57UlNTjx07Ri3hoGp3xfTr1UhEhyGEckok9N8YQIEBACATsu+OyOIE8dVWkxZSVlWt/OAtKOlIlOSs++NdUb+OP7p1ETF0SINGgfeYZXgIEUirXIslYFUwKnKInKDYILzQJ/5KZQvY3XO6J+gkSNRhCKELNx64KVbSENLWeoMQ0tJ68/GDGdKx6PmC8VhQZF5lT21cXFx87NixkSNHStdhIvrgPUu/hKHMFXwS0fl4D+yDxldrbqThJSgzE1arknr63waIpsvRtdexR02HdO0isVYoFMbExIjKRkMEgbopZmVVqhNfW746PFbj5aQCCgwAgLoR3x3JLqqYduiB+O6IjI4Sop51CkVt1a7ZVZcrI4QQSvvn1eakuAEUQ4di0AiZumcNPhl0zrfjCD6bNWWMshTNlLV31/Y27C3hlYpoBCLs8uzec96LryUalAtHaN2i6dIQDalrvEcIaWi8NzNPRAQiTAhBlkXVl52wrx5ITIylpaWUtUSRNz5Bo9/Q7DEg5yKB/u0LP4G71vnE190T/xpe9MoP3uw2h/AUyOkghBZ0W9C0HhzStYvE2jdv3pArh1RoNMRFVbr0kmzh570rvAfWzUzUJmskEIkDAP7TCITE7fS8v5Pe3U7PEwgluHQJhIKE93eXXDlI56QjJKQhQo9ebEbP06UX0xCx/GyqQEgIhIJ72feiX0XvTt4dFBtE9ZrLKcsJig268uYKtcM1d9dQtRdCyLDMwPljdw6lsKS4+NixY6mpqfiSNGgYnIw2VcrOH7uzBWyyMVvAdspxon+kX02+KvmVimgcAUerQku83KbKwND4eRujNEPDNPRZAMLQMK2NUZqh8XMljkBceyGEiouL37x5U8tDRUjSGz9due0FHc9ShjJZUsYSXLf/mKlXTpYQBBJWqwrKzL6Ih7Tpjht7b9Lh6JBtdDm68vCh72amoa/KEp8qDSH9WnRPaWmplA7ZqJrsASEU6m3d5KfBwAIDgP8u0lcFhULhybsnjz8+/qHmQ6VaLkcd6Re3s8uzI1/AnwjFOyXGu++dPpW5Q9zVG0N1lMAWw4OcB6KNCWSXZ4ekGjqkQUNnFIs3Jm2snPwcKfNlCb5SKrgHPc6Ahw8yrazj2OxiOp1ACNHpBEGgsjKVtNTeZWVqtfUm/fWN9UF2UQVVUacrt83gmNow8sIHmL6ozgjN3Ey1vbAXYuUHb2xakO/9/qb6fY37yDsSB4NOC/W2nnboAQ39+3eEdN3D5XKldFiOFPEHvYaeA6sTUGAA8L1Rm6uFSPnl1Gwpq4Kpqamnz52uKquyRJaWyLKMUZalnGVRbPHFMQ0hvF2vlH4m8fYHZcnaC4MdJR7kPMA+3+K+c1oVWuRioAjY0DEzMyMNGu0aNoeoEW+Jbayat4VSJKlgfLWsp8vRXdBtASO5JO5tcXKSV3fnr3bOkpO8amqYUnqT/vquTR8QNPr0nzw72uh3RG7cN0bU5VZ1Je2KDz+Ulnw+B0Z97zPojKb1mJeIl43+rp/tqX/TSNc9JiYmKioqEk1eFRWVTd79Pn6qkmskDlBgAPBdIWJU6akqjXUTmOkKMz7QD8YysouqPperMCtqRFYMhXROBl2hZOnFLAPU4+Tx49h4wnVsAdui2AKJ2D00JGVvSQRSb4n7zokYRiJgQ4c0aJiVWkipVufyopSnNI4aoaCIaCLbSkSZQnkeKw8hNMNuhrGKMWnKvClJ/ufOPRWND9j7gPxXReVD/gddOo0uVFAUH0hFRcXExET6lOvUB/1M+rkbuVNNK/FIHNKHaHK8bPQ9rPVklIFOp3t5eYm4zHzux8vLun1TOklKBBQYALQCJBpV4s5+Iq4WCrzHJdpndz8vQs8RQkioraog9MaHZLO/PmpK9UqvINAfp9+wEFNkjU6iYOTeUi47V/oUSL1lr2Ovy9HNKcsht8FEDCMRsKFDGjTq5XlIqdbGVYUFzJLiCkPzz1oIQxAIoTdKqbrKugu6LRDZPTKytlH9tEdLKxMhVFysnfHKwaxtoqrqRy2trLKUKscfht1MShEfyMvLS5bTYHXqA3HTqmlPSjUABp0muwzW1tYjR46kngOT8ZhBkwAKDADkTiOPT1GMKiGDk6GuUjHByba9Pn3dvXVUZ7//dV2w/Cydqr1Yhoeo/dAUiliGh8hAD6iWlloVWiypS2fiSDehRHy+GXTGwm4Lg2KDSM86TuEnVFOJGEqiZtPXho6Xjf5aB/Tm+LUyjq0EGwshNpPJKCuhIYTepVfqGhOKnxUdraaK+SFr3NBhXgPGi+8e0emMQaN/vhG3NKPE9i2/E0L0lOT+bfQf0YuKnd369PYZZmBh2ZgXdL30QWvE2tra0tISR+Ko10HvxgMKDADki4zHp2o7O0U9/ISNpEqEdj9H2KgiySnLmRcXVC78GSGsnIRM3bMIffWSFwn08KVYtKV0bSQRKSaURJ/vfib9Nrltwts/xtls94faNbwsUbMJIfS1oSMUCgqu/UVHiPkhU4KNRaO52He+m3QLIaRYUqhQUijg8AgFRVpNNdZqtqaOtfk+tHdyQWjl1ai97IoX+JbKd2yPifMsnHugZn1BtxbodLqZmdm3HxcUGADIERmPT9V2doo8/CRuTiHqeaIvJ4pI5cTgZIiffkVigR4QQuItpS/oiUAgopxRnsuqdf0QO0qI+3zj7Z/E7Pu3wzbVoE+KJYUiZhNdUDN81CiqofMu7QlORCLemFZT1adXL1eP/qmnj+I2NIQUyv7dKuNpahladZQykfZOLuZdnWrL1NVcL2hAOqDAAKAhyLIqKCm43L+OEn0sJykpKCBJp3rx2alNbpuUa7rglUNxc0rinhT9i3KSHkOPWiveMpeVW8YoYwvYIvteIgdpyc8pmik02lfHbAlEzLCbYcRto8QvN0BaKqWaQqFAPHMjg87QL2DXFH3Cl+JmkwoaSW1fWvhvKHfxxloDveh0Rh+/KRJTlriPn1Jn6kg6nWHU0VZ6G6BFAQoMAOpAXFfJuCp4NyOfX1TG4GTQFEqIGh6N8Ympe/6zowRC/f46tsxlkbuRu/ipXvLs1PR2+5AkI0kKdIUSwVehHCSAa2kIqXIUFZU0RQ0uGkrWTO6e053qhYglfKf5rm1526qyz66MeDeoh3IPEfNxQbcFJtmca3v2lubnYv+H2jI3UnUSEjObRGq5aupSGuPa9k4ug4MWUZNG8jS13MfXnTQSaI2AAgMAaYjrqsF2+nv/yZC+Kog3tCKfnlFuf5mu8NnCEMlcVFD1MSg2aLrddIlHgPHZqSLhc1RXSHKR23SqWUx6XlmFVkmVKk2xSMyZHBE1qoIyM1y8ZlinPpZ9+v11rKDqq7NZ75Xf39G50yW/C/OLNweTw7TpYbOs+zIaoonsBlkjaxFf8Ff37oiYQaX5uWc2rR4ctEhEkYjoJBFEag2tOnI1tEjNRIW6Qih9MRD4ngAFBnznNCxVR21HfflFFXv+yfhyJSStK2GZGZlygrqhRf/6N0zMbw4dSjskWkRBS61SX5X1sVqaOUVi+MmwS34XJlGCj0l9etcvWfs2X5lyQosS6IF6IGmZy6Kg2CD09SLhe+X38wbMa4faiXsumJmZ1dRUJV+MfnX9opqunp3nQAUFJdIXXCgUXIvaK1HC6wf2mnd1oqoTGXUSRvYVQlgM/I8ACgz4fmjwWh/m68ZCba13laiQzuEIyszEo4aKpPMQVqt+/OB9N6PzJ4WHIhtaJOLai0BEUZW0tUEdtvYcJ8aeK6rCEtNc5de02n3fDD8ZOuU4UXenlBFy+eicxkpLVfgcTlBXWW+o8fQ2nbuJ6HKqT+DnlrV4XmDiDu1PPHeaIISfLw/ud/jBp/fPE/El6WohTkle7ru0J1TVUt9dK1ghBKhARmbgO0GWtT4aQggJ5w9RNNMV1uatjiQpp8oP3tSzU6RP4NcnZdEok0Wxuftqiwr4pSnSqvicBCSXlYtoSFVJtbiqWETn0RDNqsaqW1G3kuLP64dljLIkjWQ+V1JCEAL98PYHpqTDWyoqKj1G9citJesjleqaqtjbf+d+fK+lbeDmPERRQfJp4bhD+++fPSle7ug9DOuwtFtx0b+ur22UgYHBVq69RQpf3Imvl04SCgWwQvhfoM73OSgwoPUh0dISWeuTSG1ZEAVCosfaa1j51aacKOd/hcrt1tIUJGwv8RTVSmsKKUWiusrgk4Fd3ldJQJI1k4e6Dt2ZtBN9vYJn8Mmge053EfkJRJBJrfQ4esFdg9VZ6h/LPtIL6AlnE2qb9fjx4+t0ARdRIbX5XNTUVP368wjS9qJCo9MDDx5XUFDKepJybMWi2gYauWy1xMU90EmAOHW+z2EJEWjRyLIquHSQ1crzaV+017/7UiJLf+JHqcS81ZEs53+/8gn8WkVRtZe4rvoSDPdfcKLFHgo92rm1+2oFj63b60OvKlQl8jRoiOb+yb1T/046XB2qOfXo0SMpz1B60HSE0Is78TL6XCRfjJaovRBChFCYfDHaYZBPvba1SGDXCmgAoMCAFoFEVwsZPQCn//EQ6y0GN1VRNYn0+vt66U+CZhLxVke1O6xTz/+SPoESzSlsHonbT5KD4SIaQujSxUtz5syhOvJplGmQCexFqPhUYc2wNtP7yqKSHhZdem29fC4KP2RL6QrXNvIwFgDIjtwDouzcudPMzIzFYjk4ONy4cUNim8OHD9vZ2XE4HH19/QkTJuTl5Yk0OHLkCI1G8/Hxkbe0QLMQ85jvuuba6IiE2UeSRkckuK65FvOYj1cFScOIwUn/SCT8dv8Kgb6yAHCUCuV2azkmEUzNW6T2Ql9C/ynwHqMvmkmiGwXprY7qclinKZTQEEI1PPRFRYnkVOye092iyoJG0CQmrMI/4t3ijCE4qOvAtgO76nUt+1QmRQxxiwpntZDYuM6g6XX6XFBL1HT1pHRF1mJXC67Gv9kjeZpa4vYcADQS+VpgR48enTNnzs6dO11dXffs2TNgwIDU1FRjY2Nqm5s3b44bN27z5s3e3t7v3r0LCAiYNGnSqVOnyAZv3ryZP39+z5495Soq0JTkpaPKEgFBPHlXnF9WpcFR6miowqDREJOHNM3FXdUDDj2g3p1dXBFw6IEaR1HUpYJAWhVazCqNkiKH959sCURDEmMsfYG69CddM2Fv9eyiijrP/+qpspb+MGxT2hm7TMk5FR0KHAp4BbVlt6oNEZ1UX4tKelYL6YH7RA4LS6+18xwYd3B/bXtgdp4DyUs4jAV8A+SrwDZt2uTv7z9p0iSE0JYtWy5evLhr167w8HBqm4SEBFNT08DAQISQmZnZ1KlT161bR9YKBIIxY8YsX778xo0bhYWFcpUWaBry0tE2e4QQAyHxPY1/PGMWxJaRq4K6Koql6IWCSqH4llVhWTWi6Kev1+uqPrHu36kyzxSqSYixRIFc+pOumXSVdUK920w79EBYZiasVhV30EAIqSpq7/5pVPe22gw6rexTwOPUxxKGQ7Sqsqqf2v309sNbKcOJI6KTpOcJlGhRNTirRb2OEisoKDn84CPRC9FhkI/C146LsK0FyBs5KrCqqqrExMSFCxeSJf3794+Pjxdp5uLisnjx4ujo6AEDBuTk5Bw/fnzQoEFk7YoVK7S1tf39/WtbfkQIVVZWVlZ+Tm4k8XcekDdfGVWsYil/aa87k8gnPu/fKPAel+qcpSsW4WU4cW91cuPKsEx0S4mDCHfF9Dg6N0+GGEs0hZKaYlthtSpdoUhkDY/M9MHQY+Dcgx8/eLMMD1EDnWMzK8x1kauJDi7poNzhMZKgwDBt1dq+RfVQYOI6qWEWVW1B06U7+NXX5wL7ylPPgdHodIdB/54DA4BvhhwVWG5urkAg0NXVJUt0dXWzs0U3gV1cXA4fPuzr61tRUVFTUzN48OBt27bhqlu3bu3bty8pKUn6QOHh4cuXL29S2YFakegWGHYmNbv4s1HVi/vu99pvr1e2qs8uFQSSuKVE0FBXojTm66DsElni6aTOsHpbOW/P01AkFpSWzPTxJfdg5+tZpjH8PWR0JfFTvdKX+KTYTxKRqJMaZlGJB02v0z++AT4XvX+e6Drq5+SL0YUfsslIHDJMFACaGLl7IdIoazEEQdDElmZSU1MDAwOXLVvm6enJ5/ODg4MDAgL27dtXUlLy888/R0REaGlpIamEhIQEBQXhz8XFxUZGRk07hf8msrsFUkIrIYRQ3qcqRDlQK0DoAYv5kcHQFgjsK8gswDJlq8IbV1oVWhK3lGgIKSMkPRcwNrDGdnFn0BkIDe2gx5MebwLnHnQ2910gHCExOxdG+hKfmZlZbfaTi4vL48ePZdRJjU9DJaN/fAPCWygoKDkM8qmXMADQ5MhRgWlpaTEYDKrJlZOTQzXIMOHh4a6ursHBwQghW1tbZWXlnj17rlq16sOHD69fv/b29sbNhEIhQkhBQeHZs2fm5ubUHphMJpNZvwSyABUZIzAhhKQGBpTAFQ57jab6B4XP/810a2oE2a9QiZmM2arwxpX0/Irsak1UiwITT6WIc1BJ0Uwk4oneqdS5xCfFfurXr5/sOqkxaajq5R8PPhdAa0SOCkxJScnBweHy5ctDhw7FJZcvXx4yZIhIs7KyMgWFf8VgMBgIIYIgLC0tqcczlyxZUlJSsnXrVjCwGoMsukriWSuqWyBGTUBTIhBCBIP1jqZQRtRwBBWGCNE49M+rSVc47CAdLeotOQwGYXhZ4Z0uotVIERIbXmocxVVDhi1K/KuCLi2/4gTHUSufr0CUhUESiQH9pGsm2alzia82++mbpUasV0xCBD4XQCtEvkuIQUFBY8eOdXR0dHZ23rt3b2ZmZkBAAEIoJCTk3bt3v//+O0LI29t78uTJu3btwkuIc+bM6datm4GBAULIxubf/Xw1NTWREqC+yKKrJBpVuAF2C8SoCWiTS74YRqXtvm7erlBJn6fAX6OpTqCvVgkJGg0RiKl7tuL9j1LkxIbXmmGdvGz0lVSXzYsNkphfESGkoqIy3GmYuoEadWFQnan+Q9sf3I3dpYf+azx1LvE1bxrfevnHA0BrRL4KzNfXNy8vb8WKFXw+38bGJjo6Gntb8fn8zMxM3MbPz6+kpGT79u3z5s1TU1Pr06fP2rVr5SrVfxPxaIF1LgBKCcukJCnsYB6XXqVIIxBxmefEZ1aU0pWqlQoQQjSiQqHmS3xbGqIrFiFESPRWx9mqtBQsl//cCceM72/qsdl9c8SVCMssS2p+RQxer5N9YbDJacmZ5uvlHw8ArREI5tvqkTG3PRmsVjaESprXFDVu0RXKP19/7eOuU0OMrqoS0qvoQiXFKlUaouVx6TsHqdXWnfr7+f/qMITK341ChALL8BANifoQBliuCOjqIzILgVBwPuH845uPRXIB13nI6btExri3QqEgYoZ/bf7xk7bvg10uoIUDwXy/c+qT214m7UVDhIFyCk/1bqVSUS6j/N9yio+7MT3fRTmjiPv5GBBdoMQtblelKOqeQ4WgfeWI8cWv3eJU5g5y6U+Po1dbDioGnTHYZfAP3X9ojEve94GMYeMRxCQE/gOABdZqkCWHCDZbqLntMX8nvZt9JIlSIHlt0Jie76SUrvylETU6LUIIEUhYo6r1aoqb4quvzmQRCCFURnT+3d20NuHV+EsUq9+gL37tMcNj8CqfQCholqW/Voq4WzxGSpjB+qbaAoCWA1hg3wl15RD5DD7US+a2J8u1uIoMTjrWWDTGJ6buefFsjcb0fHfF9C99IPQlOi2ZgArREF2hqDvzNRJ+vexHQ4hAZcpZCJnWJr9apfon+htxv/am8gn8L1Avt3gS8I8HvmNAgbUCxC2tLzlEJEAgxC+quJuR72yuiUuuvLmy5uEajsnnlTqCQIhAWuWfs1h9ZOayDA9Vvh3jVC1ANAnRae3y7N5z3uNirQotNiGUEPmChgiGNM94plDpE72ORPWAdOrrFk8C/vHA9woosOakNv8LarmDifrys6nillYtfF4bTODTupl50hDt5N2T+xP3CxgCxPpsWRl8Muic/3UWK43kSrVbyrkO4t3REI0j4JDRLqSfKZbCDx1+cGsXAIuEjQHc4gFABFBg3wgZo1142eiLlGsoK+Z/qq6943/5N+0IQvvTjyQ8O2CXZ1dVVtUNdUNfNrQQQt0/iiZa7P6x+wuVF1J6JvUWR5mDPtZv4hiPTh6dVaXFD/wvI6NXIbjFA4AIoMCangZHu5h26MGUXmYi5bJrL2psXINPBpY5lpWokvb1hlYVvQpJymJlXGqMaqeCUYFbBvQOeJT/SGIMQCUladG8/pseg7Igu1dhfcPGA8B3DyiwJqaR0S4ibmTI7hVKQ4QuvYSDqssQvUT3FCKjXtQWvh0RTKEENUNDNJaQpcRSqqqoEpOKKGeU57Jy1Zhqoc6h/Uz6GXoZSowBOMCt9595tepaLgNWDiUgY7BdDLjFA4AI4EbfcGTxa5cfJvR8Z6UsFvqscqgu71rlWr2ze9e3w25O3e7euUstwdEFUwxSPLt5TradTG5fpaamSowB+KqsslQgEAqF2fzssvIyDpujp69Hp9O5DEZbDkRbFqVhB43BLR747wBu9PJCRr92+SA0Yz/rRZRSnQGpLu8Nc7WwsrQyNTGlaiYmh2nTw2ZZ92Uinhe1xQD8V0upikRHBCTQMK9CcIsHABJQYKLIEpmpXn7tjeCr48bqykrFxDMGN1VRJakrvxcSsFEtLu94y6o2xCMKoi9Jgel0uowJqFpyDMDWQoO9CsEtHgAwoMC+QpbITAIhUR+/9vpBpyGCQMTXLoUIISTgKLMVa6qKEEJa5bUlePzi8s7KlRi+nUBEFb1KSSgheS6ZFBg0UxMi3b0QvAoBoJGAAvsXiXbVtEMPRCIzyR5XsE5oFM2HVc3knmYR/7wyUE5RUb1RUa2Yq/ClglFW9MXBQvoKIUvAQjSUrJncPae7iLFFQzTnfs5tVdteunipXonqgQZQp3sheBUCQCMBBfaZ2uwq8chMOSUN0V7iumpKL7MzyXxSF+qpskK9rdvQ8qpVU4SVVSjXCYlHI0QIfXFqrw1c+175/WPDxw4FDhLDt1tbWUNUXLkii3sheBUCQCMBBfaZ2uwq8chMOrw6XCRk1FVeNvr/87Ki7rf9dePo7etpiOL+LhqNECGEkJQVQuzyjhBSZ6r/OeZPBbqCREUF64RyRfaghe2dXAYHLQKvQgBoGKDAPiPdrqLWdjPT0FdlZRdViJhrNIT0VFlLB1mvPJ9ap67C9hyDTutmpobDse9NeZPxTwYbsaVHI8Sl4iuE2OU9WTOZRqMhhJY5L1NSUEIIgaL69tTLvRC8CgGgwYAC+4x0u4pay6DTQr2tpx16IG5pYV3laaMnyY9RqKD8SpH2UYGjjZCaQIge5Dy4nnn93KtzBZUFCB/eEkg4vCUSjRDzXvl9gk6CXd6/IQ3LGeV4sVFKVi3g21Bf90LwKgSAhgEK7DPS7apuZhrUQi8b/V0/21P9FfUo/ooMOo1cbxQIBfeyv1JUCCFVJVVEQ0WVRdQ+63bN+Jr3yu/fc95rV2izBKwJ9hNMTEzcKtwgq1ZLANwLAeDbAArsM9LtKvHTYF42+h7WEi2tf7ny5sqau2vIjMMkRVVFSAxZXDNEoSGGJiOoWxDYWy0KcC8EgG8DKLB/kW5XiUO1tEjIFMNvit/8lfAXs4ZpLjCvZFRWKFTksnIlZNL6gnTXjBqVGlW6Kmm0qTPVf2j7g7uxO9hbLRBwLwSAbwPEQhRFlkgcpJYSWbIjTS6DTwbUDSqMRJ94KgafDLrndEcUL0TsmtHFo4u3szdCSOKgQMsEghYCQCOp830OCqzeiCwM6nJ0F3Zb2M+k35U3V4JigwhEiOshDNZGIj7xIohovjJGmX0v+1G9R8lpLkCDkSWJl4yJvgAAkAgosCbm0utL8+LmUUuwltrQe8O6e+s+lH1ABBqQNUB8JRCD1wMvGF2QspaICKRVocUSsDjKnIDeAR5mHk08B6DRyJ7ECwCABgMKrCm59PpS8D/BQkIoUk5DNDWm2r/e8HWlMonTi6P6xIugrKC8pPsSXWVdWCdsmYhH2cBITOIFAECDgXQqjYK611VQUSBie5EQBMEoZLQRtKlgVLBq6k5lIt1jflWPVeBV2GKRPcoGAADyBhRYrYjsddFpkgMGiuxaVdFEkxqLo8BSUGWqipwDQwjpsnUXOi0E7dWSaVgSLwAA5AEoMAkIhIKIRxE7knZQC8VXDhHFb5BEkVCU3jlLmXVy/Ek6nY5tO022JkEQ+RX54FvYKmhwEi8AAJocUGCiXHlzJfxOeE55Tt1NCWSXZ4e+9jaU6LtBZfCgwYoKigihrnpdGyUo0BxAlA0AaDmAAvsK0hVelsaWhZYSE0vWBo1GGzFiBGTeatVAlA0AaDmAAvsXgVCw5u4aGbWXwScD68L6qaLhw4d37AgvuBaN+MktoVBYVfXVvmZvv6nXo/aI39tr/NSqqmqEqr+VsADw/aCkpNSAxISgwP7lQc4D8biFkvmyeCgFDodTVlaGP0PW41aB+OkuN78pSE1TKPx6+1NFzXXqnIrSEuJLOY1OZ3F5BJOZkZHxjWUGgO8DnKRQSUmpXneBAvuXj2Uf62xDp9GFhLDOxUMVFZXAwMCsrCzIetxakJRDOe9lWqq5k6vEr48giOrKCqFASGfQFZksnIYNAIAGIBQK379/z+fzjY2N6/WrBArsX7Q52tIb0BBtfa/1Fe8rHlx6IL2ll5eXgoICJJNsLUg83aXI4WiYtOUo0NlstsRfKjab/U2kA4DvH21t7ffv39fU1Cgq1uHITQXMgn8pqJDmA63L0d3ktqmfcb+XCS+l9+Pm5garha0Liae7FJgsOoNBI4jqivJmkQoA/jvgxUOBQFCvu8AC+4xAKFh3b11ttdPspk21ncqgMzIyMoqLi6X0w+PxevXqJQcBATki8fwWaXXV95cKAID60rBFeFBgn5HswfElrm5bQVt8wKu0tFR6PwMGDIDtrlaH9PNbDAacLgeAlggosM+Ie3BQY0QlnE1IjUv18vLicrlSOoHFw5aGjAlNpJzuYjAUFFmw1/Xfws/Pr7Cw8PTp080tCFAHMtkKpqamK1asyMzMlLc0zYiIBweOEcUW/PvmKi4uPnbs2KdPn2qLiwyLhy2NF3fiI2b4H1uxKPrX9cdWLIqY4f/iTrzEljiHssQqZTX15vUwpNWCn59fk4+VnZ09e/bsdu3asVgsXV3dHj167N69mzwN0uy4ubmJPISamprGd/v69WsajZaUlESWbN26NSoqqvE9A/JGJgU2b968v//+u23bth4eHkeOHKmsrJS3WN8eex17Vabq5wtJMaIwly5d8vT0lNgDLB62KLBbPNWoKs3PPbNpdW06rL2Ty+CgRVwNLbKEo6bOVlFlKivXa1yBkLidnvd30rvb6XkCYRPkKuJ/YcuWLSoqKuTl1q1byTbV1U1wevrVq1ddunS5dOnS6tWrHz58eOXKlblz5549e/bKlSvijZtkxAYwefJkPgUFha/WkESOnDcYVVVVNTU12dsTBNEkqhSoLzK9cGfNmpWYmJiYmGhtbR0YGKivrz9z5swHD+pwJW99fHnbaFVocQQciVENi4uLORzOyJEjqXaYiorKyJEjYfGw5SA96YlQKNkpo72Ty+Qd+0YuWz0wMHjkstU/Ll2lyGTWa9yYx/wea6+NjkiYfSRpdERCj7XXYh7z6y391+h9QVVVlUaj4c8VFRVqamrHjh1zc3NjsViHDh0KCwvr3LkzedeWLVtMTU3Jy8jISCsrKxaLZWlpuXPnTokDTZ8+XUFB4f79+yNHjrSysurUqdPw4cPPnz/v7e2NG9BotN27dw8ZMkRZWXnVqlUIoV27dpmbmyspKXXo0OHgwYO4mYhBU1hYSKPRYmNjEUKxsbE0Gu38+fN2dnYsFsvJyenRo0e42Zs3b7y9vdXV1ZWVlTt27BgdHS1RSA6Ho0cBIWRqarpq1So/Pz9VVdXJkycjhE6cONGxY0cmk2lqarpx40byXlNT09WrV0+cOJHH4xkbG+/d+/l/CD7u0qVLFxqN5ubmhhDy8/Pz8fHBtQRBrFu3rm3btmw2287O7vjx47gcz+XixYuOjo5MJvPGjRt1fJGAHKiHxWBnZ7d169Z3796Fhob+9ttvXbt2tbOz279///eREvNBzoOiqs/5TaTn6yotLbW2tp4zZ8748eOHDx8+fvz4OXPmgPZqUdSZ9KS2G+l0hlFHWyvX3kYdbeub2SvmMX/aoQf8ogqyJLuoYtqhB43XYbWxYMGCwMDAtLS02lYFMBEREYsXL/7ll1/S0tJWr169dOnSAwcOiLTJy8u7dOnSjBkzlMUsTuoKamho6JAhQx49ejRx4sRTp07Nnj173rx5jx8/njp16oQJE65fvy6L2MHBwRs2bLh3756Ojs7gwYOxMTdjxozKysp//vnn0aNHa9eulb7ZLML69ettbGwSExOXLl2amJg4cuTIUaNGPXr0KCwsbOnSpdTFwI0bNzo6Oj58+HD69OnTpk17+vQpQuju3bsIoStXrvD5/JMnT4p0vmTJksjIyF27dj158mTu3Lk///xzXFwcWfu///0vPDw8LS3N1hbS6DQD9XDiqK6uPnXqVGRk5OXLl7t37+7v7//+/fvFixdfuXLljz/+kJ+I3waqE0cFo0JKS/yrhQOfyF0soEF8+6QnAiGx/GyqyJ9yBEI0hJafTfWw1mPQm34jbc6cOcOGDauz2cqVKzdu3IhbmpmZpaam7tmzZ/z48dQ2L1++JAiiQ4cOZImWllZFRQVCaMaMGWvXrsWFP/3008SJE8nPfn5+06dPRwgFBQUlJCRs2LDB3d29TnlCQ0M9PDwQQgcOHGjTps2pU6dGjhyZmZk5fPjwTp06IYTatm1b2707d+787bff8OepU6diA6tPnz7z58/HhWPGjOnbt+/SpUsRQhYWFqmpqevXryf3CwcOHIgFXrBgwebNm2NjYy0tLbW1tRFCmpqa2KSj8unTp02bNl27ds3Z2RkLdvPmzT179vTu/Tnr+ooVK/BcgGZBJgX24MGDyMjIP//8k8FgjB07dvPmzZaWlriqf//+34fnAtWJI5eVW02rViAUxFcR2Wy2iYnJtxUNqDffPunJ3Yx8qu1FQiDEL6q4m5HvbK7Z5IM6OjrW2ebjx49ZWVn+/v54eQ0hVFNTo6qqKrEx1di6e/euUCgcM2YMdc+bOmJaWtqUKf96vri6ulK35aSAlQFCSENDo0OHDmlpaQihwMDAadOmXbp0qV+/fsOHD6/NoBkzZszixYvxZ3KbSkSqIUOGUKXasmWLQCDAZyHIbvFibE5OHVmTUlNTKyoqqCqqqqqqS5cu5KUsXwEgP2RSYF27dvXw8Ni1a5ePj49InA9ra+tRo0bJR7Zvir2OvS5HN6csh0CEwScDBQIOGLRivn3Sk5wSaVa79NoGQ13uo9Pp1MV80skCRyKOiIhwcnIia8VPtrVr145Go+ElNQw2g0TCZYksMFIVHkEQ+BK7MpHC1Onuge+aNGmSp6fn+fPnL126FB4evnHjxlmzZok3VlVVbdeunUghVSpSDPKS2pL6+qLRaKJhmsXADc6fP29oaEgWMik7o+IrrsC3RKY9sFevXsXExPz444/iUaqUlZUjIyPlINi3hkFnLOy2ECFEI2hd8rrQEE2iE0d5efmbN2++uXSAKEKhIOtJStqtuKwnKeJOGVLc4t3HT6nv5pYs6PCk7ZtKr20StLW1s7Ozyfc16UOhq6traGj46tWrdhTEV781NTU9PDy2b9/+6dMnGUe0srK6efMmeRkfH29lZYUlQQjx+XwRSUgSEhLwh4KCgufPn5PLOUZGRgEBASdPnpw3b15ERISMYohgbW0tIpWFhYX0o+hSghhZW1szmczMzEzq0zMyMmqYbECTI5OdkZOTk52dTf0L7s6dOwwG4zszn/uZ9NvktmnX9V0sYR1OHN9MJEAi4nlP+vhNae/kQm2D3eKpzXiaWu7jRZs1Fd3MNPRVWdlFFSLbYDSE9FRZ3cw05DEoFTc3t48fP65bt27EiBExMTEXLlwgHWXDwsICAwNVVFQGDBhQWVl5//79goKCoKAgkR527tzp6urq6OgYFhZma2tLp9Pv3bv39OlTBwcHiSMGBwePHDnS3t6+b9++Z8+ePXnyJHa4Z7PZ3bt3X7NmjampaW5u7pIlS0RuXLFihaampq6u7uLFi7W0tLC/35w5cwYMGGBhYVFQUHDt2jWsCxvAvHnzunbtunLlSl9f39u3b2/fvr02r0sSHR0dNpsdExPTpk0bFotFXV/l8Xjz58+fO3euUCjs0aNHcXFxfHw8l8sV2UEEmguZLLAZM2ZkZWVRS969ezdjxgxZ7t25c6eZmRmLxXJwcKjN0/Tw4cN2dnYcDkdfX3/ChAl5eXm4PCIiomfPnurq6urq6v369cPOQnKln0m/ZfbLpLepl38U0OTIfsBLxC1+0vZ9ctJeCCEGnRbqbY3QV2Y7/hzqbS0PDw4RrKysdu7cuWPHDjs7u7t375JODQihSZMm/fbbb1FRUZ06derdu3dUVJRE/yNzc/OHDx/269cvJCTEzs7O0dFx27Zt8+fPX7lypcQRfXx8tm7dun79+o4dO+7ZsycyMhL7oCOE9u/fX11d7ejoOHv2bOxwT2XNmjWzZ892cHDg8/lnzpwhDaAZM2ZYWVl5eXl16NChTq1TG/b29seOHTty5IiNjc2yZctWrFhR54lvBQWFX3/9dc+ePQYGBtT9M8zKlSuXLVsWHh5uZWXl6el59uxZ8N5qOdBkcYLncrkpKSlU16CMjAxbW9uSkhLpNx49enTs2LH4L7s9e/b89ttvqampxsbG1DY3b97s3bv35s2bvb293717FxAQ0L59+1OnTiGExowZ4+rq6uLiwmKx1q1bd/LkySdPnlAXo8UpLi5WVVUtKiqqLV5GnWRkZIg7GZNwOJz58+fDgeXmQigURMzwr21za9L2fU24PFhRUZGRkYH//JLxlpjH/OVnU0lvDn1VVqi3tZeNflOJ1NqJjY11d3cvKCio1zFh4L+AxF+3Ot/nMi0hMpnMDx8+UBWY+Bl4iWzatMnf33/SpEkIoS1btly8eHHXrl3h4eHUNgkJCaampoGBgQghMzOzqVOnrlv3OSr84cOHyWYRERHHjx+/evXquHHjZJG5wRgZGdFoter1gQMHgvZqRuo84GXUsTmP43jZ6HtY693NyM8pqdDhsbqZaXwD2wsA/rPI9C728PAICQkpKvp8zrewsHDRokV1nn6oqqpKTEzs378/WdK/f//4eNF1HhcXl7dv30ZHRxME8eHDh+PHjw8aNEi8t7Kysurqag0NCXsJlZWVxRRkmZEU3mRmSbFKwemoefn2B7zqC4NOczbXHNLZ0NlcE7QXAMgVmRTYxo0bs7KyTExM3N3d3d3dzczMsrOzqTFaJJKbmysQCHR1dckSXV3d7OxskWYuLi6HDx/29fVVUlLS09NTU1Pbtm2beG8LFy40NDTs16+feFV4eLjqFxrpIBTzmD//jwQpDcCDQ95Idy/89ge8gCbEzc2NIAhYPwSaCpmWEA0NDVNSUg4fPpycnMxmsydMmDB69GgZEz9LPClCJTU1NTAwcNmyZZ6ennw+Pzg4OCAgYN++fdQ269at+/PPP2NjYyXuRoSEhJAuVcXFxQ3WYTgUkC6dsFOqtQ14cMiVOt0Lv/0BLwAAWiyyHtdVVlamnrqXBS0tLQaDQTW5cnJyqAYZJjw83NXVNTg4GCFka2urrKzcs2fPVatW6et/3vresGHD6tWrr1y5UtvhfCaTyaxn0FVxcCggI3q+k2Ktx7xUVFQgDIf8wO6F1BLsXjg4aBGpw/ABL5FmGDkd8AIAoMVSj3gTqampmZmZ1IQFgwcPltJeSUnJwcHh8uXLQ4cOxSWXL18W91ItKyuj+oPgI4fkLtT69etXrVqFQz7LLmoDuJuRr1jy3l0xXUobLy8v8OCQE9Ljx5t3dSKV0zc+4AUAQItFJgX26tWroUOHPnr0iHTPwyuBEs+uUwkKCho7dqyjo6Ozs/PevXszMzMDAgIQQiEhIe/evfv9998RQt7e3pMnT961axdeQpwzZ063bt0MDAwQQuvWrVu6dOkff/xhamqKLTkulyunRbwPxWVOipkIIYnJCxXZykO9B0HIeflRL/fC9k4u5l2dZEm1DADAd4xMCmz27NlmZmZXrlxp27bt3bt38/Ly5s2bt2HDhjpv9PX1zcvLW7FiBZ/Pt7GxiY6OxktwfD6fzO/s5+dXUlKyffv2efPmqamp9enThwx9vXPnzqqqqhEjRpAdhoaGhoWF1XeSsqBYlq9MqzVom52rB2gvuVJf90Kc90SeEgEA0NKRSYHdvn372rVr2tradDqdTqf36NEjPDw8MDDw4cOHdd47ffp0nL+Aiki67lmzZkkM3Pn69WtZxGsS2vBo92qvNVKBlUP5Au6FAADUF5neywKBAC/caWlpvX//HiFkYmLy7Nkz+Yr2bVHh8RpcCzQe7F4osQrcC4Gmxc3Nbc6cOXLqHGdqLiwslFP/VKjJr7/luC0HmRSYjY1NSkoKQsjJyWndunW3bt1asWKFlKRzrRETE5PaopWA8+E34NvHj28t0GqhzhB/DSA7O3v27Nnt2rVjsVi6uro9evTYvXt3WVlZkw/UMExNTbds2UIt2bJli6mpqTzGanX6wMXFhc/n15bpDSNXzd0syLSEuGTJEpxkYdWqVT/88EPPnj01NTWPHj0qZ9m+KXQ63cvL69ixY+JV4Hz4bWj17oV56ahSUnRQJg9pmje4VzIvydGjR5ctW0aufFAzdVVXV8t4LlMKr169cnV1VVNTW716dadOnWpqap4/f75//34DAwNxf+MmGRGQSMOeLQ4EIQ95qqqqcMDllghRf/Ly8oRCYQNu/AbgeFdFRUUNu/3JkycbN24M/cLGjRufPHnStBIC0hEIajIfJ6fejM18nCwQ1DSjJOXl5ampqeXl5TK1zn1JhKrU+pP7svHyREZGqqqq4s8ZGRkIoaNHj/bu3ZvJZO7fvz80NNTOzo5svHnzZhMTE/Jy//79lpaWTCazQ4cOO3bskNi/p6dnmzZtSktLRcrJX3aE0K5duwYPHszhcJYtW0YQxM6dO9u2bauoqGhhYfH7779TZXv48CG+LCgoQAhdv36dIIjr168jhM6dO2dra8tkMrt165aSkoKbvX79+ocfflBTU+NwONbW1ufPnxeX0MTEZPPmzdQS6jTHjx8/ZMiQsLAwbW1tHo83ZcqUyspKXFVaWjp27FhlZWU9Pb0NGzb07t179uzZuOrgwYMODg5cLldXV3f06NEfPnwgp0Ayfvx4/BzWrl2Lo83a2tr+9ddfpBjnz59v3749i8Vyc3PD+RELCgrE5UcI7dy508vLi8VimZqaHjt2jPrEqN+mlK/szp07nTt3ZjKZDg4OJ0+eJB81frbkuDdv3uzVqxebzVZTU+vfv39+fr5ICpiMjAyCIGJjY7t27YqV34IFC6qrq/HtvXv3njFjxty5czU1NXv16iU+lyZH4q9bne/zuhVYdXU1g8F49OhRE8gofxqpwAiCEAgEr169SklJefXqlUAgaELZgNZF/RTYu4fSFNi7h42XR1yBmZqanjhx4tWrV+/evZOiwPbu3auvr49bnjhxQkNDIyoqSqTz3NxcGo0WHh4uRQCEkI6Ozr59+9LT01+/fn3y5ElFRcUdO3Y8e/Zs48aNDAbj2rVrhAwKzMrK6tKlSykpKT/88IOpqWlVVRVBEIMGDfLw8EhJSUlPTz979mxcXJy4AHUqMC6X6+vr+/jx43Pnzmlray9atAhXTZs2rU2bNuSgXC6XVGD79u2Ljo5OT0+/fft29+7dBwwYQBBETU3NiRMnEELPnj3j8/mFhYUEQSxatMjS0jImJiY9PT0yMpLJZMbGxhIEkZmZyWQyZ8+e/fTp00OHDuFYDbUpME1NzYiIiGfPni1ZsoTBYKSmpkr8Nmv7ykpLS7W1tfEcz549i/dxxBXYw4cPmUzmtGnTkpKSHj9+vG3bto8fPxYWFjo7O0+ePJnP5/P5/Jqamrdv33I4nOnTp6elpZ06dUpLSys0NBSL2rt3by6XGxwc/PTp07S0NCn/K5oKeSkwgiDatm2blJTUWAG/CY1XYID8aDnWlSy0fAW2ZcsWslaKAjMyMvrjjz/IqpUrVzo7O4t0jrMknzx5kizR1NRUVlZWVlb+3//+h0sQQnPmzCEbuLi4TJ48mbz88ccfBw4cSMigwI4cOYKr8vLy2Gz20aNHCYLo1KlTWFiY9CdQpwLT0ND49OkTvty1axeXyxUIBCUlJUpKSiKDkgqMCs44WFJSQogZNKWlpSwWKz4+nmzs7+8/evRogiBCQkKsrKxIO3XBggVSFFhAQAB56eTkNG3aNELSt1nbV7Znzx6ROUpUYKNHj3Z1dRUXgGp6EgSxaNGiDh06kJLv2LEDPzHcsnPnzuI9yI+GKTBZ98BCQkIOHTokMRg8AMiCLGmUgXohS3iajx8/ZmVl+fv7T548GZfU1NTUttVPDVV69+5doVA4ZsyYyspKiSOmpaVRw8u5urpu3bpVFrGdnZ3xBw0NjQ4dOqSlpSGEAgMDp02bdunSpX79+g0fPry2uHHSwXlxyVFKS0uzsrIKCwurqqpEBiVvefjwYVhYWFJSUn5+vlAoRAhlZmaKH/pMTU2tqKigpuCoqqrq0qULQigtLa179+7koyMHkj53/Bk7EGLIZyvlK0tLSxOZo8RRkpKSfvzxRyliYNLS0pydnUnJXV1dS0tL3759i1M2yjv4UZMgkwL79ddfX758aWBgYGJiQs0n8uDBA7kJBnxXyBLnEKgv1F9GOp1OUNIAVVd/PpWPX8oRERFOTk5kLQ7YRqVdu3Y0Gu3p06dkCV6eorqKILF0QhJDdWOPJ1IYUpLawHdNmjTJ09Pz/Pnzly5dCg8P37hxo/jZUBUVFTKpE6awsFC6352U3H4IoU+fPvXv379///6HDh3S1tbOzMz09PSkRssjwY/x/Pnz1IS6OASrlP7rhPoAyWcr5SuTcSyRb602iK+jqxOUKEuolaSOkkmB+fj4yFkM4HtG9jiHQIPR1tbOzs4mX0nkn/a6urqGhoavXr0aM2aMlNs1NTU9PDy2b98+a9YsGd9cVlZWN2/eJBPMxsfHW1lZYUkQQnw+HxsoVCMDk5CQgP/GLygoeP78uaWlJS43MjIKCAgICAgICQmJiIgQV2CWlpb37n0Vb+DevXtUcyo5Obm8vBy/vhMSErhcbps2bTQ0NBQVFUUG7d27N0Lo6dOnubm5a9aswSks7t+/T3aF/e7IaHnW1tZMJjMzMxPfSMXa2vr06dPU2Ul5aAkJCeQTS0hIwI9IBClfmbW19cGDB6lzlDiKra3t1atXly9fLlKupKREjf9nbW194sQJ8v9MfHw8j8eTnvK+pSGTAgsNDZW3HMB3TAtPo/x94Obm9vHjx3Xr1o0YMSImJubChQvkucawsLDAwEAVFZUBAwZUVlbev3+/oKCAzEBEsnPnTldXV0dHx7CwMFtbWzqdfu/evadPnzo4OEgcMTg4eOTIkfb29n379j179uzJkyevXLmCEGKz2d27d1+zZo2pqWlubu6SJUtEblyxYoWmpqauru7ixYu1tLTw38dz5swZMGCAhYVFQUHBtWvXsC4UISgoyNXVdcWKFTi83IkTJ2JiYqg5cquqqvz9/ZcsWfLmzZvQ0NCZM2fS6XQul+vv7x8cHEwOSp6KMTY2VlJS2rZtW0BAwOPHj1euXEl2ZWJiQqPRzp07N3DgQDabzePx5s+fP3fuXKFQ2KNHj+Li4vj4eC6XO378+ICAgI0bNwYFBU2dOjUxMVEkzJAIf/31l6OjY48ePQ4fPnz37l2RvFEktX1lP/300+LFi/EcX79+XVs8v5CQkE6dOk2fPj0gIEBJSen69es//vijlpaWqanpnTt3Xr9+zeVyNTQ0pk+fvmXLllmzZs2cOfPZs2ehoaFBQUGt7MiQvLbkmglw4miBpN6M3TByUG0/qTdjm1tAybR8Jw7SUQKza9cuIyMjZWXlcePG/fLLL1Q3+sOHD3fu3FlJSUldXb1Xr15UZw0q79+/nzlzppmZmaKiIpfL7dat2/r160mXAYTQqVOnqO0lutETBJGamtq9e3c2m925c+dLly6hr504zp4927FjRyUlpa5du5LeYTNnzjQ3N2cymdra2mPHjs3NzZUo4eXLl3v27Kmurq6urt6jR4/Lly+TVdiNftmyZZqamlwud9KkSRUVFbiqpKTk559/5nA4urq669ato/oy4FjhTCbT2dn5zJkz1Ke6YsUKPT09Go1GutFv3bq1Q4cOioqK2tranp6epKvk2bNn27Vrx2Qye/bsuX//flS7E8eOHTs8PDyYTKaJicmff/6JyyV+m7V9Zbdv37azs1NSUurcuTN2lZToRh8bG+vi4sJkMtXU1Dw9PXH5s2fP8PeCZHCjl+jnIj8a5sQhbYGYhE6niyeiRDJEo//2FBcXq6qqFhUV1RZWA/j2ZD1JObZiUW21I5etbpkWWEVFRUZGBj73U3frvHS0zb7W2lkPGnOW+bshNjbW3d29oKBAHkmZ/fz8CgsLqat5LQ0ajXbq1CnYkZGIxF+3Ot/nMi0hnjp1ivxcXV398OHDAwcOiC+wAoBE/hNplDXN0awH8ojEAQBAbcikwESyUI4YMaJjx45Hjx719/eXj1TAd8V/JY0yaCkA+LbItIQoTnp6uq2tLQ6Q2KKAJcQWi8g5sJYf57B+S4gAADQCOS4hilBeXr5t27Y2bdo0UFLg+6I6t5yoFAiFgo8Zr8pKijk8FW2ztnQ6g8ZkKGr9ex4F0igDANC0yKTA1NXVSScOgiBKSko4HM6hQ4fkKRjQOqjOLf+w4fPpGRpCyoiOUGkuSsEluvMdqToM0igDANCEyKTANm/eTCowOp2ura3t5OSkrg5JcgFEVErzRJVeCwAA0BhkUmDySJ3XYhEIibsZ+TklFTo8VjczDQZdwvkBgEQolKaipNcCAAA0BpkUWGRkJJfLpUaH/Ouvv8rKykQSzHwHxDzmLz+byi+qwJf6qqxQb2svG/3mlaol8zHjlRQN/zHjlZGRhGA5AAAAjUemqCFr1qzR0tKilujo6KxeLcErulUT85g/7dADUnshhLKLKqYdehDzmN+MUrVwykqKG1wLAADQGGRSYG/evDEzM6OWmJiYZGZmykek5kEgJJafTRU5UoAvl59NFQgbHnD6+4bDk3ZcQXot8J+CRqM1MkyGm5vbnDlzmkaaBhEbG0uj0QoLC5tRBoCKTApMR0cnJSWFWpKcnKypqSkfkZqHuxn5VNuLhECIX1RxNyP/24vUKtA2a9vgWkBG/Pz8aF/Q1NT08vIS+X1sgYSFhXXu3PnbjBUVFUX7mt9++61JehZRmS4uLnw+X3oCF+BbItMe2KhRowIDA3k8Xq9evRBCcXFxs2fPHjVqlJxl+6bklEjQXjLW/peRfpbrP3jSSyAUPMh58LHsozZH217HntFET8DLyysyMhIhlJ2dvWTJkh9++OE7WwJpJCoqKs+ePSMvRXRMdXW1oqJi40fBQW/rdUtVVRXOzALIA5kssFWrVjk5OfXt25fNZrPZ7P79+/fp0+c72wPT4UmLtiC99r8MjSntBS299vvjypsrnic8J16cuODGgokXJ3qe8Lzy5kqT9MxkMvX09PT09Dp37rxgwYKsrKyPHz/iqgULFlhYWHA4nLZt2y5dupRMIJmcnOzu7s7j8VRUVBwcHMhkV/Hx8b169WKz2UZGRoGBgRLj6WD7af/+/cbGxlwud9q0aQKBYN26dXp6ejo6Or/88gvZsqioaMqUKTo6OioqKn369ElOTkYIRUVFLV++PDk5GdtDZIaR3NzcoUOHcjic9u3b49DvmLi4uG7dujGZTH19/YULF9bU1ODyT58+jRs3jsvl6uvrb9y4UcrzodFoehTYbDY5hbZt2zKZTIIgMjMzhwwZwuVyVVRURo4c+eHDB+pkDx48aGpqqqqqOmrUqJKSEoSQn59fXFzc1q1b8Sxev34tsoRY25M0NTVdtWqVn5+fqqoqmVUZkAcyKTAlJaWjR48+e/bs8OHDJ0+eTE9P379//3f2Z0U3Mw19VZa4Qx0NIX1VVjczjWaQqTWgqMXWne+oM6uL1gxbYiD3U08hMZCrNcNWZ1YXkVPM3z1X3lwJig36UPaBLMkpywmKDWoqHYYpLS09fPhwu3btyDV8Ho8XFRWVmpq6devWiIiIzZs34/IxY8a0adPm3r17iYmJCxcuxCbIo0ePPD09hw0blpKScvTo0Zs3b86cOVPiQOnp6RcuXIiJifnzzz/3798/aNCgt2/fxsXFrV27dsmSJTiVIkEQgwYNys7Ojo6OTkxMxLnB8vPzfX19582b17FjRz6fz+fzfX19cZ/Lly8fOXJkSkrKwIEDx4wZk5+fjxB69+7dwIEDu3btmpycvGvXrn379q1atQq3Dw4Ovn79+qlTpy5duhQbG5uYmFivZ/Xy5ctjx46dOHECJ9X08fHJz8+Pi4u7fPlyeno6KRWe7OnTp8+dO3fu3Lm4uLg1a9YghLZu3ers7Dx58mQ8C5z0kkT6k1y/fr2NjU1iYuLSpUvrJTNQP+Sa4uXb05h8YBcevTddcM50wTmTLz/48sKj900uJ9DyqVc+sBpBTd9jfW2ibER+OkV16nesX42gpjGSjB8/nsFgKCsr41zJ+vr6iYmJEluuW7fOwcEBf8aKTaTB2LFjp0yZQl7euHGDTqeLzzE0NJTD4RQXF+NLT09PU1NTgUCALzt06BAeHk4QxNWrV1VUVMi0WwRBmJub79mzB/dgZ2dH7RMhtGTJEvy5tLSURqNduHCBIIhFixZ16NBBKBTiqh07dnC5XIFAUFJSoqSkdOTIEVyel5fHZrMlJqnCi6vKX9DV1cUCKCoq5uTk4DaXLl1iMBiZmZn48smTJwihu3fvik82ODjYyckJfxZJi0XNuSXlSZqYmPj4+IjLCUihYfnAZNoDGzFihKOj48KFC8mS9evX371796+//mp6jdp8eNno7/rZnnoOTA/OgQGy8SDnAdX2IiEQkV2W/SDnQVe9ro3p393dfdeuXQih/Pz8nTt3Dhgw4O7duyYmJgih48ePb9my5eXLl6WlpTU1NWTY06CgoEmTJh08eLBfv34//vijubk5QigxMfHly5eHDx/+LB5BCIXCjIwM8QzIpqamPB4Pf9bV1WUwGGSuXl1d3ZycHNxbaWkp1Z+rvLw8PT29tlnY2n4OJKasrMzj8XAnaWlpzs7OZKwfV1fX0tLSt2/fFhQUVFVVOTs743INDY0OHTrU1jOPx3vw4AH+TMppYmKira2NP6elpRkZGZFWlLW1tZqaWlpaWteuXUUmq6+vjwWTjvQn6ejoWGcPQOORSYHFxcWFhoZSS7y8vGrLZt2q8bLR97DWg0gcQH35WPaxwbWyoKys3K5dO/zZwcFBVVU1IiJi1apVCQkJo0aNWr58uaenp6qq6pEjR8i9orCwsJ9++un8+fMXLlwIDQ09cuTI0KFDhULh1KlTAwMDqZ0bGxuLj0j1eqDRaCKXQqEQISQUCvX19WNjY6k3SklWKbETgiCo+XIJgsC1RH0SZdDpdPL5kGCDlexWJCsvtUSiYNKR/iSpQwPyQyYFVlpaKrLjpaioWFz8fZ5RZdBpzubf1QkB4BugzdFucG19odFoeLUKIXTr1i0TE5PFixfjqjdv3lBbWlhYWFhYzJ07d/To0ZGRkUOHDrW3t3/y5In4u75h2NvbZ2dnKygomJqailQpKSnJmLHd2tr6xIkTpDqJj4/n8XiGhobq6uqKiooJCQlYKxQUFDx//rx3794NE9Xa2jozMzMrKwsbYampqUVFReJ2p+yzaNonCTQMmZw4bGxsjh49Si05cuSItbW1fEQCgNaHvY69LkeXhkTtdRqi6XH07HXsG9l/ZWVldnZ2dnZ2WlrarFmzSktLvb29EULt2rXLzMw8cuRIenr6r7/+SiZPLy8vnzlzZmxs7Js3b27dunXv3j38sl6wYMHt27dnzJiRlJT04sWLM2fOzJo1q8FS9evXz9nZ2cfH5+LFi69fv46Pj1+yZAl2dzQ1Nc3IyEhKSsrNza2srJTSyfTp07OysmbNmvX06dO///47NDQ0KCiITqdzuVx/f//g4OCrV68+fvzYz8+PXBtsmKi2trZjxox58ODB3bt3x40b17t37zoX+kxNTe/cufP69evc3FwRs6xpnyTQMGSywJYuXTp8+PD09PQ+ffoghK5evfrHH38cP35czrIBLQKhUABJvOqEQWcs7LYwKDaIhmjE5xAuCOuzBd0WNP40WExMjL6+PkKIx+NZWlr+9ddfbm5uCKEhQ4bMnTt35syZlZWVgwYNWrp0aVhYGEKIwWDk5eWNGzfuw4cPWlpaw4YNW758OULI1tY2Li5u8eLFPXv2JAjC3Nyc6oxXX2g0WnR09OLFiydOnPjx40c9Pb1evXrp6uoihIYPH37y5El3d/fCwsLIyEgpAcENDQ2jo6ODg4Pt7Ow0NDT8/f2XLFmCq9avX19aWjp48GAejzdv3jy8pd9gUU+fPj1r1qxevXrR6XQvL69t27bVedf8+fPHjx9vbW1dXl6ekZFBrWraJwk0DFkXms+fP7969eqkpCQ2m21nZxcaGqqiovLNTtrLDmRkblpE0ihzNbT6+LXoNMpNSAMyMl95c2XN3TWkN4ceR29BtwX9TPrJTUYA+E5oWEbm+u2UIoQKCwsPHz68b9++5ORkGde4vyWgwJqQF3fiz2yScFx9cNCi/4IOa4ACQ3KLxAEA3zcNU2AyLSFirl27tn///pMnT5qYmAwfPnzfvn2NFRlowQiFgmtReyVWXT+w17yrE6wlSoRBZzTSYx4AABmpW4G9ffs2Kipq//79nz59GjlyZHV19YkTJ8CD47vnXdoTcuVQhJK83HdpT4w62n5jkQAAAKjU4dUzcOBAa2vr1NTUbdu2vX//XpZtT+D7oLSwoMG1AAAA34A6LLBLly4FBgZOmzatffv230YgoIXAVVNvcC0AAMA3oA4L7MaNGyUlJY6Ojk5OTtu3bycDYAPfPYZWHbkaWhKreJpahlYdv7E8AAAAItShwJydnSMiIvh8/tSpU48cOWJoaCgUCi9fvozTDQDfMXQ6o4/fFIlV7uOngAcHAADNjkwn2zkczsSJE2/evPno0aN58+atWbNGR0dn8ODB8hYOaF7aO7kMDlpEtcN4mlr/ER96AABaPvU+B4YQEggEZ8+e3b9/PzUlXQsBzoE1Of/ZSBwNOwcGAEADaNg5sIbEFmMwGD4+Pi1QewHygE5nGHW0tXLtbdTR9r+jvVo1r1+/ptFoOIujFKKioqREjm+qUZoKHAvq248LtGQaHhwTAIBvRlZWlr+/v4GBgZKSkomJyezZs/Py8mprbGRkxOfzbWxspPfp6+v7/PnzppZU7sgyOz8/Px8fn28lEdBsgAIDgCZGWFGRu3uPsKKiqTp89eqVo6Pj8+fP//zzz5cvX+7evfvq1avOzs75+fnijauqqhgMhp6enoJCHYdk2Gy2jo5OUwnZAKqrqxtwl4yzawBVVVVN3icgV0CB/RcRCgVZT1LSbsVlPUkRCltcQMvWTsmlSx+3bCm5fLmpOpwxY4aSktKlS5d69+5tbGw8YMCAK1euvHv3jkwDZmpqumrVKj8/P1VV1cmTJ4sssp05c6Z9+/ZsNtvd3f3AgQM0Gq2wsBB9vYQYFhbWuXPngwcPmpqaqqqqjho1ivQ0jomJ6dGjh5qamqam5g8//CAl4TKJqanpypUrf/rpJy6Xa2BgQA2AQKPRdu/ePWTIEGVl5VWrViGEzp496+DgwGKx2rZtu3z58pqaGtzyxYsXvXr1YrFY1tbWlykPU2R2T548GTRokIqKCo/H69mzZ3p6elhY2IEDB/7++28ajUaj0XC+zUePHvXp04fNZmtqak6ZMqW0tBTfjm218PBwAwMDCwuLen83QLMidwW2c+dOvC/n4OBw48YNiW0OHz5sZ2fH4XD09fUnTJhAXRvBYauYTKa1tTWZ6whoDC/uxEfM8D+2YlH0r+uPrVgUMcP/xZ345hbqu6L4Qgz5b+PJz8+/ePHi9OnT2Ww2WainpzdmzJijR4+STljr16+3sbFJTExcunQp9fbXr1+PGDHCx8cnKSlp6tSppM4TJz09/fTp0+fOnTt37lxcXNyaNWtw+adPn4KCgu7du3f16lU6nY7TOtcp9vr1621tbR88eBASEjJ37lyqBgoNDR0yZMijR48mTpx48eLFn3/+OTAwMDU1dc+ePVFRUb/88gtCSCgUDhs2jMFgJCQk7N69e8GCBRJHeffuHVZy165dS0xMnDhxYk1Nzfz580eOHOnl5cXn8/l8vouLS1lZmZeXl7q6+r179/76668rV67MnDmT7OTq1atpaWmXL18+d+5cnfMCWhaEPDly5IiiomJERERqaurs2bOVlZXfvHkj0ubGjRt0On3r1q2vXr26ceNGx44dfXx8cFV8fDyDwVi9enVaWtrq1asVFBQSEhKkj4gzBhUVFcllPq2f5wm3NowcJP7zPOFWc4vW4igvL09NTS0vL5elcfXHjx82bMgOX5MdvibNplNqB8s0m0748sOGDdW5uQ0WIyEhASF06tQpkfJNmzYhhD58+EAQhImJCflbQxAEzlz18OFDgiAWLFhgY2NDVmEFVlBQQBBEZGSkqqoqLg8NDeVwOMXFxfgyODjYyclJXJicnByE0KNHj0RGEcHExMTLy4u89PX1HTBgAP6MEJozZw5Z1bNnz9WrV5OXBw8e1NfXJwji4sWLDAYjKysLl1+4cIF8CNRxQ0JCzMzMqqqqRAQYP378kCFDyMu9e/eqq6uXlpbiy/Pnz9Pp9OzsbNxSV1e3srJSfBbAt0Tir1ud73P5WmCbNm3y9/efNGmSlZXVli1bjIyMdu3aJdImISHB1NQ0MDDQzMysR48eU6dOxRldEUJbtmzx8PAICQmxtLQMCQnp27fvli1b5Crw9430APOwltgYaj5+zD/we35UVP7vBwihECFECIX5vx/Ij4rKP/B7TU5Ok49IEARCiEb7nAO6tuTCz54969r13+j43bp1q61DU1NTHo+HP+vr6+d8kTk9Pf2nn35q27atioqKmZkZQigzM7NO8Zydnamf09LSyEuqqImJiStWrOB+YfLkyXw+v6ysLC0tzdjYuE2bNuK9UUlKSurZs6eioqJ0YdLS0uzs7JSVlfGlq6urUCh89uwZvuzUqZOSklKdMwJaIHJUYFVVVYmJif379ydL+vfvHx8vulrl4uLy9u3b6OhogiA+fPhw/PjxQYMG4arbt29Tb/f09BS/HZCdOgPMf2N5vidYVlZmJ44rtW2LEA3hPHkCAUI0pbZtzU4cZ1lZNbjndu3a0Wi01NRUkfKnT5+qq6traX0+Zk6+nUUgCIJUcuiL2pMIVQ3QaDRyndDb2zsvLy8iIuLOnTt37txBDXJ2oMpAFVUoFC5fvjzpC48ePXrx4gWLxRKRk3o7FeqyqhREHoJIn7U9OqDlI0cFlpubKxAIcH5xjK6ubnZ2tkgzFxeXw4cP+/r6Kikp6enpqampkVu+2dnZdd6OEKqsrCymIIepfCdAgHm5wmzf3vTPPxD1zUsQpn/+wWxcIGxNTU0PD4+dO3eWl5eThdnZ2fi3prY3O4mlpeW9e/fIS3J5Q0by8vLS0tKWLFnSt29fKyurggJZ/5PglU/ys6WlpcRm9vb2z549a/c1dDrd2to6MzPz/fv3uNnt27cl3m5ra3vjxg1xb0YlJSVqul1ra+ukpKRPnz7hy1u3btHpdHDZ+A6QuxOHyF9/4r9vqampgYGBy5YtS0xMjImJycjICAgIkP12hFB4eLjqF4yMjJp6Bt8PEGBe3pTdvy+iwMoSExvf7fbt2ysrKz09Pf/555+srKyYmBgPDw9DQ0Ps7yCdqVOnPn36dMGCBc+fPz927FhUVBSq3aARR11dXVNTc+/evS9fvrx27VpQUJCMN966dWvdunXPnz/fsWPHX3/9NXv2bInNli1b9vvvv4eFhT158iQtLe3o0aNLlixBCPXr169Dhw7jxo1LTk6+ceNGbb4nM2fOLC4uHjVq1P3791+8eHHw4EG8MGhqapqSkvLs2bPc3Nzq6uoxY8awWKzx48c/fvz4+vXrs2bNGjt2LPWPY6CVIkcFpqWlxWAwqDZTTk6O+H+a8PBwV1fX4OBgW1tbT0/PnTt37t+/n8/nI4T09PTqvB0hFBISUvSFrKws+czmewACzMub4kuXEUJsB3vTI3+y7e3JkkbSvn37+/fvm5ub+/r6mpubT5kyxd3d/fbt2xoaGnXea2Zmdvz48ZMnT9ra2u7atQtrAiaTKePQdDr9yJEjiYmJNjY2c+fOXb9+vYw3zps3LzExsUuXLitXrty4caOnp6fEZp6enufOnbt8+XLXrl27d+++adMmExMTPO6pU6cqKyu7des2adKk2lS1pqbmtWvXSktLe/fu7eDgEBERgRdCJ0+e3KFDB0dHR21t7Vu3bnE4nIsXL+bn53ft2nXEiBF9+/bdvn27jBMBWjINiYUoO05OTg4ODjt37sSX1tbWQ4YMCQ8Pp7YZPny4goLC0aNH8eXt27ddXFzevXtnYGDg6+tbUlISHR2NqwYMGKCmpvbnn39KGRFiIUrnxZ34M5tWi5dDiF5xGhALMf/3g0RVpcaECTQGgxAI8iMjaUpMjXFj5Spnvfjll192794t77/zTE1N58yZM2fOHLmOAnxPNCwWYtOfZqcSFBQ0duxYR0dHZ2fnvXv3ZmZm4uXBkJCQd+/e/f777wghb2/vyZMn79q1y9PTk8/nz5kzp1u3bgYGBgih2bNn9+rVa+3atUOGDPn777+vXLly8+ZNuQr83YMDzF+L2kt6c/A0tdzHTwHt1SRQdRWNwdCcNKkZhSHZuXNn165dNTU1b926tX79euoRKABo1chXgfn6+ubl5a1YsQLHLouOjsbrA3w+n/TE9fPzKykp2b59+7x589TU1Pr06bN27Vpc5eLicuTIkSVLlixdutTc3Pzo0aNOTk5yFfi/QHsnF/OuTv/NAPP/TV68eLFq1ar8/HxjY+N58+aFhIQ0t0QA0DTIdwnx2wNLiEBTAelUAOCb8e3SqQAAAABAswMKDAAAAGiVgAIDAAAAWiWgwAAAAIBWCSgwAAAAoFUCCgwAAABolYAC+z6BnMtAS4NGo50+fboxPbi5uck1ugc1RbU8MDU1/WYJoajP6luO+40BBfYdAjmXvzP8/PxoX9DU1PTy8kpJSWluoeogLCysc+fOzTVWYWEhjUaLjY2Vx3CtTh/cu3dvypQpUhrIW3PLD1Bg3xs42iE171dpfu6ZTatBh8mbwg9lHzNLxH8KP5Q1vnMvLy8+n8/n869evaqgoPDDDz80vk+gddGANGwYbW1tDofTtMIghAQCAZk0rrkABfZdATmXm4vCD2WHQxOOrb4n/nM4NKHxOozJZOrp6enp6XXu3HnBggVZWVkfP37EVQsWLLCwsOBwOG3btl26dCmZHCs5Odnd3Z3H46moqDg4OJCZwOLj43v16sVms42MjAIDA8ksWVSwTbN//35jY2Mulztt2jSBQLBu3To9PT0dHR1qbPiioqIpU6bo6OioqKj06dMnOTkZIRQVFbV8+fLk5GRsNeIcLgih3NzcoUOHcjic9u3bnzlzhuwkLi6uW7duTCZTX19/4cKFNTU1uPzTp0/jxo3jcrn6+vobN25s2KOLjY2l0Wjnz5+3s7NjsVhOTk6PHj0ia6OiooyNjTkcztChQ/Py8sjy9PT0IUOG6Orqcrncrl27XrlyBZe7ubm9efNm7ty5eGrSH2lOTo63tzebzTYzMzt8+HBtEvr5+fn4+Cxfvhw/xqlTp5K6ys3NbebMmUFBQVpaWh4eHgih1NTUgQMHcrlcXV3dsWPH5ubm1vmsqCZjYWHhlClTdHV1WSyWjY3NuXPnYmNjJ0yYUFRUhGcUFhaGECooKBg3bpy6ujqHwxkwYMCLFy/Ix6Wmpnbu3Dlra2smk/nmzZuGfCVNByiw7wrIudxcVFdK++NAem29KC0tPXz4cLt27TQ1NXEJj8eLiopKTU3dunVrRETE5s2bcfmYMWPatGlz7969xMTEhQsX4jwjjx498vT0HDZsWEpKytGjR2/evFlbbN/09PQLFy7ExMT8+eef+/fvHzRo0Nu3b+Pi4tauXbtkyRKcr5IgiEGDBmVnZ0dHRycmJtrb2/ft2zc/P9/X13fevHkdO3bEVqOvry/uc/ny5SNHjkxJSRk4cOCYMWPy8/MRQu/evRs4cGDXrl2Tk5N37dq1b9++VatW4fbBwcHXr18/derUpUuXYmNjExuRXC04OHjDhg337t3T0dEZPHgwVvN37tyZOHHi9OnTk5KS3N3dyXHxcx44cOCVK1cePnzo6enp7e2Nw7eePHmyTZs2OL4rzvok5ZH6+fm9fv362rVrx48f37lzZ05OTm3iXb16NS0t7fr163/++eepU6eWL19OVh04cEBBQeHWrVt79uzh8/m9e/fu3Lnz/fv3Y2JiPnz4MHLkSNmflVAoHDBgQHx8/KFDh1JTU9esWcNgMFxcXLZs2aKiooJnNH/+fCz5/fv3z5w5c/v2bYIgBg4cSP5hVFZWFh4e/ttvvz158kRHR6fB30jTQHxfFBUVIYSKioqaW5DmIfVm7IaRg2r7Sb0Z29wCtibKy8tTU1PLy8tlaZzzpnj71Ku1/eS8KW6MJOPHj2cwGMrKysrKygghfX39xMREiS3XrVvn4OCAP2PFJtJg7NixU6ZMIS9v3LhBp9PF5xgaGsrhcIqLP4vt6elpamoqEAjwZYcOHcLDwwmCuHr1qoqKSkVFBXmjubn5nj17cA92dnbUPhFCS5YswZ9LS0tpNNqFCxcIgli0aFGHDh2EQiGu2rFjB5fLFQgEJSUlSkpKR44cweV5eXlsNnv27NnisxYfC2eOvn79OkEQ169fRwiJ9HP06FGCIEaPHu3l5UXe5evrq6qqKt4/QRDW1tbbtm3Dn01MTDZv3kxW1fZIcWrNhIQEXJ6WloYQot5IMn78eA0NjU+fPuHLXbt24SdAEARWV2TLpUuX9u/fn7zEaXGePXsm/VmRAl+8eJFOpz979kxEgMjISOrEnz9/jhC6desWvszNzWWz2ceOHcMtEUJJSUkSn1JjkPjrVuf7XL7R6IFvDORc/l5xd3fftWsXQig/P3/nzp0DBgy4e/cuzu1w/PjxLVu2vHz5srS0tKamhgx7GhQUNGnSpIMHD/br1+/HH380NzdHCCUmJr58+ZJcziIIQigUZmRkWFlZiYxoamrK4/HwZ11dXQaDQafTyUtsTCQmJpaWlpK2IEKovLw8PT29tlnY2triD8rKyjweD3eSlpbm7OxMLse5urqWlpa+ffu2oKCgqqrK2dkZl2toaHTo0KGBjw8hkX6wOklLSxs6dCi1TUxMDP786dOn5cuXnzt37v379zU1NeXl5WQCDRFqe6TPnz9XUFBwdHTE5ZaWllIcJezs7MhtKmdn59LS0qysLPz9kj3gsa5fv87lcqn3pqenl5eXy/KskpKS2rRpY2FhUZsYmLS0NAUFBTL1h6amJvnEEEJKSkrk99jsgAL7rsA5lyWuIkLO5VaNsrJyu3bt8GcHBwdVVdWIiIhVq1YlJCSMGjVq+fLlnp6eqqqqR44cIfc/wsLCfvrpp/Pnz1+4cCE0NPTIkSNDhw4VCoVTp04NDAykdm5sbCw+Il5yxNBoNJFLvHsvFAr19fVFnP2kvKYldkIQBKm98CWuJWROlKGiooL/VCcpLCxECKmqqtZ2Cx5RyhDBwcEXL17csGFDu3bt2Gz2iBEjavOhqO2RYguMOrV6Qd6IzW5yLG9vbzLhFEZfX5/co5IOm82WpZn4Y6F+R2w2u8GTanJAgX1X0OmMPn5TJOZcdh8/BfJ+fR/QaDS8SIUQunXrlomJyeLFi3GVyKa6hYWFhYXF3LlzR48eHRkZOXToUHt7+ydPnpC6sJHY29tnZ2crKCiYmpqKVCkpKQkEMu38WVtbnzhxgnxFxsfH83g8Q0NDdXV1RUXFhIQErF8LCgqeP3/eu3dv8R4sLS3fvn2bnZ2tp6eHS+7du0en06nTFOnH0tISD40388g25OcbN274+flh+6y0tPT169e1Ta22R2plZVVTU3P//v1u3bohhJ49e4bVqkSSk5PLy8uxgklISOByuW3atBFvZm9vf+LECVNTUwWFr17d7dq1k+VZ2dravn379vnz5yJGmMiMrK2ta2pq7ty54+LighDKy8t7/vy5uI3eEgAnju8NnHOZq6FFlvA0tQYHLYKcy62aysrK7Ozs7OzstLS0WbNmlZaWent7I4TatWuXmZl55MiR9PT0X3/99dSpU7h9eXn5zJkzY2Nj37x5c+vWrXv37uEX0IIFC27fvj1jxoykpKQXL16cOXNm1qxZDZaqX79+zs7OPj4+Fy9efP36dXx8/JIlS7C7o6mpaUZGRlJSUm5ubmVlpZROpk+fnpWVNWvWrKdPn/7999+hoaFBQUF0Op3L5fr7+wcHB1+9evXx48d+fn7kGqYI/fv3t7KyGjVq1K1btzIyMv7+++/58+cHBASQS6AIoRUrVpD9aGlp+fj4IIQCAwNjYmLWrVv3/Pnz7du3k+uH+MGePHkyKSkpOTn5p59+ovqLm5qa/vPPP+/evcMegLU90g4dOnh5eU2ePPnOnTuJiYmTJk2SYgBVVVX5+/unpqZic3nmzJkSJztjxoz8/PzRo0ffvXv31atXly5dmjhxokAgkPFZ9e7du1evXsOHD798+XJGRgZ20sEzKi0tvXr1am5ubllZWfv27YcMGTJ58uSbN28mJyf//PPPhoaGQ4YMkfIlNhtNvhfXvPzHnThIBIKazMfJqTdjMx8nCwQ1zS1Oq6RFOXGQv7A8Hq9r167Hjx8na4ODgzU1Nblcrq+v7+bNm/FufGVl5ahRo4yMjJSUlAwMDGbOnElO5O7dux4eHlwuV1lZ2dbW9pdffhEfUcQtYvz48UOGDCEve/fuTToIFBcXz5o1y8DAQFFR0cjIaMyYMZmZmQRBVFRUDB8+HC8nRkZGEgSBEDp16hTZiaqqKi4nCCI2NrZr165KSkp6enoLFiyorq7G5SUlJT///DOHw9HV1V23bh11XBH4fP6ECRNMTEzYbLalpeWKFStI1xLsxHH27NmOHTsqKSl17dqV6oOwb9++Nm3asNlsb2/vDRs2kL4MGRkZ7u7u2DN++/bt1KFv375ta2vLZDLJ92dtj5TP5w8aNIjJZBobG//+++8i3h8ij3fZsmX4e5w0aRIpvPiUnz9/PnToUDU1NTzTOXPmYP8XKc+KOm5eXt6ECRM0NTVJN3pcHhAQgPcyQ0NDCYLIz88fO3asqqoqm8329PR8/vw5bibi7tGENMyJAzIyA4Bk6pWRGZ8Dq612zPLuarpNf5IUkIXY2Fh3d/eCgoIWG2zCz8+vsLCwkXG2WjsNy8gMe2AA0ASo6XLGLO8u8byXIpMB2gsA5AEoMABoGkBLAcA3BhQYAADfM25ubi18o4QMtQXUF/BCBAAAAFoloMAAAACAVgkoMAAAAKBVAgoMAAAAaJWAE0erRCgUvEt7UlpYwFVTN7TqCDGiAAD4DwIKrPXx4k78tai9ZMReroZWH78pECkKAID/GrCE2Mp4cSf+zKbV1Hjzpfm5ZzatfnEnvhmlApoLGo3WmAgOOPNyYwTA+Y6lhKltMDj5b71uef36NY1GS0pKEq+Sn5yy4+bmNmfOnGYU4PsDFFhrQigUXIvaK7Hq+oG9QmGTpf0FWhQ5OTlTp041NjZmMpl6enqenp63b9/GVXw+f8CAAd9SmO/vLWxqakqjIDEMfAMQV5knT55cuXJlk3QOYGAJsTXxLu2JxFxfCKGSvNx3aU+MOraURHP/WeSxPTl8+PDq6uoDBw60bdv2w4cPV69ezc/Px1VkApEWTnV1NTUZWEtjxYoVkydPxp8ZDNGvrKmE19DQqFd7gUCAU+c0fujvFXg0rYnSwoIG1wLfgBd34iNm+B9bsSj61/XHViyKmOHf+KXdwsLCmzdvrl271t3d3cTEpFu3biEhIYMGDcK15BIiXj07efKku7s7h8Oxs7MjrTSEUEREhJGREYfDGTp06KZNm2pbmouMjLSysmKxWJaWljt37hRv4OfnFxcXt3XrVmyskFmyEhMTHR0dORyOi4sLTuSIvqxP7t+/v23btkwmEwcXnzJlio6OjoqKSp8+fZKTk3HL5ORkd3d3Ho+noqLi4OCAE7JgLl68aGVlxeVyvby8+Hw+LhQKhStWrGjTpg2TyezcuTM1DQqV6OhoCwsLNpvt7u5OTeglDo/H0/uCtrY2frC7d+8eMmSIsrLyqlWrEEK7du0yNzdXUlLq0KHDwYMHyXtpNNpvv/02dOhQDofTvn37M2fO4K/D3d0dIaSurk6j0fz8/NDXxmtVVdX//vc/Q0NDZWVlJycnMikoXjg9d+6ctbU1k8kUSfAGiAAKrDXBVVNvcC0gb+S0Pcnlcrlc7unTp6Vn1cIsXrx4/vz5SUlJFhYWo0ePrqmpQQjdunUrICBg9uzZSUlJHh4ev/zyi8R7IyIiFi9e/Msvv6Slpa1evXrp0qUHDhwQabN161ZnZ+fJkyfz+Xw+n29kZESOu3Hjxvv37ysoKEycOJFs//Lly2PHjp04cQLvSw0aNCg7Ozs6OjoxMdHe3r5v377YlBwzZkybNm3u3buXmJi4cOFC0twpKyvbsGHDwYMH//nnn8zMzPnz55NibNy4ccOGDSkpKZ6enoMHDxZPSZyVlTVs2LCBAwcmJSVNmjRp4cKFdT49EUJDQ4cMGfLo0aOJEyeeOnVq9uzZ8+bNe/z48dSpUydMmICztGCWL18+cuTIlJSUgQMHjhkzJj8/38jI6MSJEwihZ8+e8fn8rVu3inQ+YcKEW7duHTlyJCUl5ccff/Ty8iKnUFZWFh4e/ttvvz158kRHR6e+Yv+3kEdml2bk+84HJhDU7A4Yv2HkIPGfPdPGQ96vpqVe+cDk+tUcP35cXV2dxWK5uLiEhIQkJyeTVehLkq2MjAyE0G+//YbLnzx5ghBKS0sjCMLX13fQoEHkLWPGjCFTOlHzfhkZGf3xxx9ks5UrVzo7O4sLI5KhCr/Hr1y5gi/Pnz+PEMIPLTQ0VFFRMScnB1ddvXpVRUWFzHRFEIS5ufmePXsIguDxeFFRUSIDRUZGIoRevnyJL3fs2KGrq4s/GxgYUNOYde3adfr06eRDePjwIUEQISEhVlZWOFcWQRALFixACBUUFIjPyMTERElJSfkLW7duxQ92zpw5ZBsXF5fJkyeTlz/++OPAgQPxZ4TQkiVL8OfS0lIajXbhwgXyyVBHJB/dy5cvaTTau3fvyKq+ffuGhISQs6ZmLPuP0LB8YGCBtSbodEYfvykSq9zHT4HTYM1InduTjel8+PDh79+/P3PmjKenZ2xsrL29fW3hX21tP2+C6uvrI4RycnIQQs+ePcNZ7THUzyQfP37Mysry9/fnfmHVqlXp6ekySihxXISQiYkJXpFDCCUmJpaWluKcjZiMjAw8RFBQ0KRJk/r167dmzRrqoBwOx9zcnOwZd1tcXPz+/XtXV1eymaura1pamohIaWlp3bt3p9Fo+NLZ2VmK/MHBwUlfGDduHC50dHSk9iZlRHL6ysrKPB6PnH5tPHjwgCAICwsL8lHExcWRE1dSUiI7BKQDThytjPZOLoODFlHPgfE0tdzHwzmwZkbe25MsFsvDw8PDw2PZsmWTJk0KDQ3F2yoikItv+MUtFAoRQgRBkO9xfCl+I24ZERHh5OREFoq7M9SGxHERQsrKytQh9PX1yc0eDN6NCwsL++mnn86fP3/hwoXQ0NAjR44MHTqU2i3umSq5yIyol1KmWRtaWlrt2rUTKaQKL31EETnJ6deGUChkMBiJiYnUJ8zlcvEHNpstPh1AIqDAWh/tnVzMuzpBJI4WxbfcnrS2tq7X2S9LS8u7d++Sl1QXCRJdXV1DQ8NXr16NGTNGem9KSkoCQUMObNjb22dnZysoKJiamorXWlhYWFhYzJ07d/To0ZGRkViBSURFRcXAwODmzZu9evXCJfHx8eJmpchTSkioNV+2LFhZWd28eZM0zuLj462srKTfoqSkhBCS+Ky6dOkiEAhycnJ69uzZGKkAUGCtEjqdAR7zLQpDq45cDS2Jq4g8TS1Dq44N7jkvL+/HH3+cOHGira0tj8e7f//+unXrhgwZInsPs2bN6tWr16ZNm7y9va9du3bhwgWJf+CHhYUFBgaqqKgMGDCgsrLy/v37BQUFQUFBIs1MTU3v3Lnz+vVrLpdbL7/wfv36OTs7+/j4rF27tkOHDu/fv4+Ojvbx8enYsWNwcPCIESPMzMzevn1779694cOHS+8qODg4NDTU3Ny8c+fOkZGRSUlJhw8fFmkTEBCwcePGoKCgqVOnJiYmNjLnVnBw8MiRI7HjydmzZ0+ePHnlyhXpt5iYmNBotHPnzg0cOJDNZpMGFkLIwsJizJgx48aN27hxY5cuXXJzc69du9apU6eBAwc2Rsj/ILAHBgBNgPy2J7lcrpOT0+bNm3v16mVjY7N06dLJkydv375d9h5cXV137969adMmOzu7mJiYuXPnslgs8WaTJk367bffoqKiOnXq1Lt376ioKDMzM/Fm8+fPZzAY1tbW2tramZmZsotBo9Gio6N79eo1ceJECwuLUaNGvX79WldXl8Fg5OXljRs3zsLCYuTIkQMGDFi+fLn0rgIDA+fNmzdv3rxOnTrFxMScOXOmffv2Im2MjY1PnDhx9uxZOzu73bt3r169WnZRxfHx8dm6dev69es7duy4Z8+eyMhINzc36bcYGhouX7584cKFurq6M2fOFKmNjIwcN27cvHnzOnToMHjw4Dt37pAunYDs0Oq1UtzyKS4uVlVVLSoqUlFRaW5ZgNZNRUVFRkaGmZmZxNe9RETCVLbM7cnJkyc/ffr0xo0bzS0IAPyLxF+3Ot/nsIQIAE1Gi92e3LBhg4eHh7Ky8oULFw4cOCDxkDIAtDpAgQFAU9Iytyfv3r27bt26kpKStm3b/vrrr5MmTWpuiQCgCQAFBgDfP8eOHWtuEQCg6QEnDgAAAKBVAgoMAAAAaJXAEmKLQB45OAAAAL5vQIE1PyK+11wNrT5+Lc73GgAAoKUBS4jNjJxycAAAAHz3yF2B7dy5E59Nc3BwkHh20s/Pj/Y1HTv+G3dny5YtHTp0YLPZRkZGc+fOraiokLfA3xKhUHAtaq/EqusH9gqFDYk4BwAA8B9Bvgrs6NGjc+bMWbx48cOHD3v27DlgwADx2DNbt27lfyErK0tDQ+PHH3/EVYcPH164cGFoaGhaWtq+ffuOHj0aEhIiV4G/MXLNwQH8FyAzMjcMnDS5MQLExsbSaLTCwsLGdCIRnJu4XrfgtNQ4eaYI8pOTxNTUdMuWLXLqvAFPo8FQn9W3HLcByFeBbdq0yd/ff9KkSVZWVlu2bDEyMtq1a5dIG1VVVTKZN44fOmHCBFx1+/ZtV1fXn376ydTUtH///qNHj5YYSLv1Iu8cHMD3QU5OztSpU42NjZlMpp6enqen5+3bt3EVn88fMGDAtxTGzc1tzpw533JEeSP+R8CcOXPqDHXYMFq4PhDH19f3+fPn0tvIVXNLR45OHFVVVThBOFnSv3//+HhpWzv79u3r16+fiYkJvuzRo8ehQ4fu3r3brVu3V69eRUdHjx8/XvyuyspKMtt6cXFx081A7nzLHByAvKnOLScqJaz60pgMRS12Y3oePnx4dXX1gQMH2rZt++HDh6tXr+bn5+MqPT29xvT8zaiurqYmzQK+MQRBCAQCBYV6v/DZbDab3aj/vbVRVVWFM840BjlaYLm5uQKBQFdXlyzR1dXNzs6urT2fz79w4QI1yM2oUaNWrlzZo0cPRUVFc3Nzd3d3qjokCQ8PV/1C64rojHNwSKxqZA4O4BtTnVv+YcP9nG0PxX8+bLhfnVve4J4LCwtv3ry5du1ad3d3ExOTbt26hYSEDBo0CNeS1gNePTt58qS7uzuHw7GzsyOtNIRQRESEkZERh8MZOnTopk2bajMCIiMjraysWCyWpaWlxHiJfn5+cXFxW7duxdvVr1+/xuWJiYmOjo4cDsfFxeXZs2e4EK9P7t+/v23btkwmE2eInzJlio6OjoqKSp8+fZKTk3HL5ORkd3d3Ho+noqLi4OBAXWi5ePGilZUVl8v18vLi8/m4UCgUrlixok2bNkwms3PnzjExMRKnEx0dbWFhwWaz3d3dSVHri5ub28yZM2fOnKmmpqapqblkyRIyAHpOTo63tzebzTYzMxPJ57Jp06ZOnTopKysbGRlNnz69tLQUIRQbGzthwoSioiL89MLCwhBCVVVV//vf/wwNDZWVlZ2cnKgJP6OiooyNjfG3lpeXJ1E8/L0fOXLExcWFxWJ17NiR7AGvBF68eNHR0ZHJZN64cYMgiHXr1rVt25bNZtvZ2R0/frzOZyViMp45c8bR0ZHFYmlpaQ0bNgw/nzdv3sydOxdPCjc7ceJEx44dmUymqanpxo0bydtNTU1XrVrl5+enqqo6efLk+n0TkpC7E0ediVNJ8JPy8fEhS2JjY3/55ZedO3c+ePDg5MmT586dW7lypfiNISEhRV/IyspqUvHli/xycADfGIm2l4y10sEp50+fPk0uM0hh8eLF8+fPT0pKsrCwGD16dE1NDULo1q1bAQEBs2fPTkpK8vDw+OWXXyTeGxERsXjx4l9++SUtLW316tVLly49cOCASJutW7c6OztPnjwZb1qTfy8uXrx448aN9+/fV1BQmDhxItn+5cuXx44dO3HiBN6XGjRoUHZ2dnR0dGJiIs6thU3JMWPGtGnT5t69e3jNhrTVysrKNmzYcPDgwX/++SczM3P+/PmkGBs3btywYUNKSoqnp+fgwYNfvHghImpWVtawYcMGDhyYlJQ0adIkiX/7ysiBAwcUFBTu3Lnz66+/bt68+bfffsPlfn5+r1+/vnbt2vHjx3fu3JmTk0PeQqfTf/3118ePHx84cODatWv/+9//EEIuLi5btmxRUVHBTw9PZ8KECbdu3Tpy5EhKSsqPP/7o5eWF53Lnzp2JEydOnz49KSnJ3d191apVUiQMDg6eN2/ew4cPXVxcBg8eTNV2//vf/8LDw9PS0mxtbZcsWRIZGblr164nT57MnTv3559/jouLk/1ZnT9/ftiwYYMGDXr48OHVq1cdHR0RQidPnmzTps2KFSvwpBBCiYmJI0eOHDVq1KNHj8LCwpYuXUpNxrZ+/XobG5vExMSlS5c27Ov4CkJuVFZWMhiMkydPkiWBgYG9evWS2FgoFLZr127OnDnUwh49esyfP5+8PHjwIJvNFggEUgYtKipCCBUVFTVO9m/K84RbuwPGbxg5CP/smTb+ecKt5hYKIMrLy1NTU8vLy2VpXPm2JGvBP7X9VL4taYwkx48fV1dXZ7FYLi4uISEhycnJZBVC6NSpUwRBZGRkIIR+++03XP7kyROEUFpaGkEQvr6+gwYNIm8ZM2aMqqoq/hwaGmpnZ4c/GxkZ/fHHH2SzlStXOjs7iwvTu3fv2bNnk5fXr19HCF25cgVfnj9/HiGEH1poaKiiomJOTg6uunr1qoqKSkVFBXmvubn5nj17CILg8XhRUVEiA0VGRiKEXr58iS937Nihq6uLPxsYGPzyyy9ky65du06fPp18CA8fPiQIIiQkxMrKSigU4jYLFixACBUUFIjPiHyGJLNnz+7duzc5X5F+rKysCILAhmZCQgIuT0tLQwht3rxZvP9jx45pamqSkyIfPkEQL1++pNFo7969I0v69u0bEhJCEMTo0aO9vLzIcl9fX+qNJHjKa9aswZfV1dVt2rRZu3Yt8eWrOX36NK4qLS1lsVjx8fHkvf7+/qNHj5b+rKgCOzs7jxkzRlwGExMT6sR/+uknDw8P8jI4ONja2pps6ePjI94DUcuvW53vczlaYEpKSg4ODpcvXyZLLl++7OIi+XxuXFzcy5cv/f39qYVlZWV0+r8SMhgMLLScBG4u2ju5TN6xb+Sy1QMDg0cuWz1p+z44xQxQGT58+Pv378+cOePp6RkbG2tvb19bfmFb28+B8PX19RFC2CZ49uxZt27dyDbUzyQfP37Mysry9/fnfmHVqlXp6ekySihxXISQiYmJtrY2/pyYmFhaWqqpqUkOkZGRgYcICgqaNGlSv3791qxZQx2Uw+GYm5uTPeNui4uL379/7+rqSjZzdXXF+oNKWlpa9+7dySUfZ2dnGecijkg/L168EAgEaWlpCgoK2ApBCFlaWlKX2q5fv+7h4WFoaMjj8caNG5eXl/fp0yfxnh88eEAQhIWFBflM4uLi8BNIS0ujyixdfrIWi0R9GqSEqampFRUVHh4e5Fi///47OZYszyopKalv375SxMCkpaWJfDv4iYnI0yTINxJHUFDQ2LFjHR0dnZ2d9+7dm5mZGRAQgBAKCQl59+7d77//Trbct2+fk5OTjY0N9XZvb+9NmzZ16dLFycnp5cuXS5cuHTx4MIPxHS6stcwcHEDLgcVieXh4eHh4LFu2bNKkSaGhoX5+fuLNyMU3/DISCoVIbOle4p+AuGVERISTkxNZKPvvmsRxEULKysrUIfT19al7PAgh/NIPCwv76aefzp8/f+HChdDQ0CNHjgwdOpTaLe6ZKnmdexOy/6XL4/HwX/okhYWFqqqq0u/C/UvcE3nz5s3AgQMDAgJWrlypoaFx8+ZNf3//6upq8ZZCoZDBYCQmJlIfNZfLrZf84lClIr8C/KWcP3/e0NCQrGUymbKPJaM3h/T/b9T/Eo1HvgrM19c3Ly8PL4/a2NhER0djD0M+n089EFZUVHTixImtW7eK3L5kyRIajbZkyZJ3795pa2t7e3vXtnwPAP8drK2t63X2y9LS8u7du+SlxLMourq6hoaGr169GjNmjPTelJSUyL+m64W9vX12draCgoKpqal4rYWFhYWFxdy5c0ePHh0ZGYkVmERUVFQMDAxu3rzZq1cvXBIfHy9uVoo8pYSEhNo6tLS0vHfvHunhTBBEYmIi9XAC9d6EhIT27dszGAwrK6uampr79+/joZ89e0YeMrt//35NTc3GjRvxAhI1l43I0+vSpYtAIMjJyenZs6e4/CLj1iY/rsVPo6amJjExcebMmeJtrK2tmUxmZmZm7969xatkeVa2trZXr14ljznVNilra+ubN2+Sl/Hx8RYWFnIyPOQeC3H69OnTp08XKRRZAFFVVS0rKxO/V0FBITQ0NDQ0VH7iAUALJy8v78cff5w4caKtrS2Px7t///66deuGDBkiew+zZs3q1avXpk2bvL29r127duHCBYl2Q1hYWGBgoIqKyoABAyorK/GhzKCgIJFmpqamd+7cef36NZfL1dDQkF2Mfv36OTs7+/j4rF27tkOHDu/fv4+Ojvbx8enYsWNwcPCIESPMzMzevn1779694cOHS+8qODg4NDTU3Ny8c+fOkZGRSUlJIk6ACKGAgICNGzcGBQVNnTo1MTGxtkVXhND8+fPHjx9vaWnZv3//8vLyvXv3pqenz5gxg2yQlZWF+3nw4MG2bduwW12HDh28vLwmT568d+9eBQWFOXPmkAaKubl5TU3Ntm3bvL29b926tXv3burTKy0tvXr1qp2dHYfDsbCwGDNmzLhx4zZu3NilS5fc3Nxr16516tRp4MCBgYGBLi4u69at8/HxuXTpUm2elpgdO3a0b9/eyspq8+bNBQUFVD8aEh6PN3/+/Llz5wqFwh49ehQXF8fHx3O53PHjx8v4rEJDQ/v27Wtubj5q1KiampoLFy5g5xRTU9N//vln1KhRTCZTS0tr3rx5Xbt2Xblypa+v7+3bt7dv3y7HDOC1bY61UlqjEwfQMmkhThwVFRULFy60t7dXVVXlcDgdOnRYsmRJWVkZrkVfO3Fg/wWCIAoKChBC169fx5d79+41NDRks9k+Pj6rVq3S09PD5VQnDoIgDh8+3LlzZyUlJXV19V69elE9sEiePXvWvXt3/LLOyMjAngKkc8TDhw9xuXjnBEEUFxfPmjXLwMBAUVHRyMhozJgxmZmZlZWVo0aNMjIyUlJSMjAwmDlzJn7mIv4Op06dIt9XAoFg+fLlhoaGioqKdnZ2Fy5cwOUiD+Hs2bPt2rVjMpk9e/bcv38/qsWJgyCII0eOODo6qqio6OjoeHp63r9/n6zq3bv39OnTAwICVFRU1NXVFy5cSDo78Pn8QYMGMZlMY2Pj33//nerLsGnTJn19fTab7enpifdKyKEDAgI0NTWxPiAIoqqqatmyZaampoqKinp6ekOHDk1JScEt9+3b16ZNGzab7e3tvWHDBilOHH/88YeTk5OSkpKVldXVq1dxlchXQxCEUCjcunVrhw4dFBUVtbW1PT094+LipD8rkW/hxIkT+H8IdqPHhbdv37a1tSVXIwmCOH78uLW1taKiorGx8fr168nbRdw9qDTMieOrZeXvgOLiYlVV1aKiIhUVleaWBWjdVFRUZGRk4EiedTbG58Bqq9Wd79jIs8xNyOTJk58+fSoxMCkgjpubW+fOnZsr0kSdvH792szM7OHDh40MCdbsSPx1q/N9DulUAKAJUNRi6853lFMkjsazYcMGDw8PZWXlCxcuHDhwQI5LOgDwDQEFBgBNQ7NrKSncvXt33bp1JSUlbdu2/fXXX6nxbgCg9QIKDAC+f6iOcEC9EPH7b2mYmpp+Z9tA9QIUWHMiFArepT0pLSzgqqkbWnWE2FEAAACyAwqs2XhxJ/5a1F4yHxhXQ6uP3xSIwQEAACAjcg/mC0jkxZ34M5tWU7NZlubnntm0+sUdaelmAAAAABJQYM2AUCi4FrVXYtX1A3uFwoZHLgcAAPjvAAqsGXiX9oRqe1Epyct9l/bkG8sDAADQGgEF1gyUFhY0uBYAAADAgAJrBrhq6g2uBYAmBOfzxdkmmxycEZgMcdty8PPzoybOBVovoMCaAUOrjlwNLYlVPE0tQ6uO31geoCVDqwWJ6VRaNW5ubiJzxBmlG4m4kt66dauU2L5AKwLc6JsBOp3Rx2/KmU2rxavcx0+B02CtGqFQ+ObNm9LSUi6Xa2JiQs3I2jBwmnaE0NGjR5ctW4YTASOZkzO1LiZPnrxixQryUkHhqxdUVVWVkpJS40epM9eXCARBCAQCEWGAlgBYYM1DeyeXwUGLqHYYT1NrcNAiOAfWqklNTd2yZcuBAwdOnDhx4MCBLVu2pKamNrJPvS+oqqrSaDQ9PT1dXd1OnTpduXIFN+jcubOOjg7+fPv2bUVFxdLSUoRQZmbmkCFDuFyuiorKyJEjP3z4UNsQr169cnd353A4dnZ2t2/fJsvj4+N79erFZrONjIwCAwPJnMKHDh1ydHTk8Xh6eno//fQTmX8ZIRQdHW1hYcFms93d3V+/fk2Wv3nzxtvbW11dXVlZuWPHjtHR0RIl4XA4ehQQQqampqtWrfLz81NVVZ08eTJC6MSJEx07dmQymaampjizCcbU1HT16tUTJ07k8XjGxsZ793529DUzM0MIdenShUajubm5oa+XEAmCWLduXdu2bdlstp2d3fHjx3E5Xv+8ePGio6Mjk8mE2MctE1BgzUZ7J5fJO/aNXLZ6YGDwyGWrJ23fB9qrVZOamnrs2LHi4mKypLi4+NixY43XYSLQaLRevXrhEEcFBQWpqanV1dV4lNjYWAcHBy6XSxCEj49Pfn5+XFzc5cuX09PTfX19a+tw8eLF8+fPT0pKsrCwGD16NF64e/Tokaen57Bhw1JSUo4ePXrz5k0yTWJVVdXKlSuTk5NPnz6dkZFBLmZmZWUNGzZs4MCBSUlJkyZNWrhwITnEjBkzKisr//nnn0ePHq1duxYnHZaR9evX29jYJCYmLl26NDExceTIkaNGjXr06FFYWNjSpUupi4EbN250dHR8+PDh9OnTp02b9vTpU4QQTuZ55coVPp9/8uRJkc6XLFkSGRm5a9euJ0+ezJ079+eff46LiyNr//e//4WHh6elpdnaQsL0FklteVZaKZAPDGgq6pUPTCAQbNy4MVQSGzduFAgEjZeHmpnp119/tbGxIQji9OnTjo6Ow4YN27FjB0EQ/fv3X7BgAUEQly5dYjAYmZmZuP2TJ08QQnfv3hXpE2eT+u2336jN0tLSCIIYO3bslClTyJY3btyg0+niTwOrh5KSEoIgQkJCrKysyHRZCxYsQF/SSnXq1CksLEz6BHv37q2oqKj8haCgIIIgTExMfHx8yDY//fSTh4cHeRkcHGxtbY0/m5iY/Pzzz/izUCjU0dHZtWsXIZYkjCCI8ePHDxkyhCCI0tJSFosVHx9PVvn7+48ePZr4kkzr9OnT0mUGmoqG5QMDCwwAmoA3b95QbS8qxcXFb968adrh3Nzcnjx5kpubGxcX5+bm5ubmFhcXV1NTEx8fjxPGp6WlGRkZGRkZ4fbW1tZqamppaWkSeyPNC319fYQQXhLEmXm5X/D09BQKhaQyGDJkiImJCY/Hw4tymZmZeNDu3buT6Z6dnZ3JIQIDA1etWuXq6hoaGpqSklLbvMaMGZP0hZCQEFzo6OhINkhLS3N1dSUvXV1dX7x4QeazJyeC11qpa5sSSU1Nraio8PDwIKf5+++/p6enkw2oQwMtENiWBIAmAG87Nay2AdjY2GhqasbFxcXFxa1YscLIyOiXX365d+9eeXl5jx49EEIEQZCKBCNeQqKoqIg/4AZCoRD/O3Xq1MDAQGpLY2PjT58+9e/fv3///ocOHdLW1s7MzPT09KyqqsJD1CbwpEmTPD09z58/f+nSpfDw8I0bN86aNUu8maqqart27UQKlZWVa5uFyIjkRPBc8ESkgBucP3/e0NCQLMSZhcWHBlogoMAAoAmQvqlTry0fWcDbYH///ffjx4979uzJ4/Gqq6t3795tb2/P4/EQQtbW1pmZmVlZWdgIS01NLSoqsrKykn0Ie3v7J0+eiKuTR48e5ebmrlmzBvd8//6/eaitra1Pnz5NXiYkJFBvNDIyCggICAgICAkJiYiIkKjA6sTa2vrmzZvkZXx8vIWFBYMhzXEXOy6SVppIb0wmMzMzE5utQKsDlhABoAkwMTGpLeu5ioqKiYlJk4/o5ub2xx9/2NraqqioYH12+PBhvKCHEOrXr5+tre2YMWMePHhw9+7dcePG9e7du14LYgsWLLh9+/aMGTOSkpJevHhx5swZrHKMjY2VlJS2bdv26tWrM2fOrFy5krwlICAgPT09KCjo2bNnf/zxB9W9Ys6cORcvXszIyHjw4MG1a9fqpUqpzJs37+rVqytXrnz+/PmBAwe2b98+f/586bfo6Oiw2eyYmJgPHz7gPRUSHo83f/78uXPnHjhwID09/eHDhzt27Dhw4EDDZAO+PaDAAKAJoNPpXl5eEqu8vLwafxpMHHd3d4FAQGqs3r17CwQC0pKg0WinT59WV1fv1atXv3792rZte/To0Xr1b2trGxcX9+LFi549e3bp0mXp0qV4h0xbWzsqKuqvv/6ytrZes2bNhg0byFuMjY1PnDhx9uxZOzu73bt3r17970lHgUAwY8YMKysrLy+vDh067Ny5s2Gztre3P3bs2JEjR2xsbJYtW7ZixYo6D3QrKCj8+uuve/bsMTAwGDJkiEjtypUrly1bFh4ebmVl5enpefbsWex2D7QKaFKWrVsjxcXFqqqqRUVFtf05DAAyUlFRkZGRYWZmxmKxZLwlNTU1JiaG9OZQUVHx8vKytraWm4wA8J0g8detzvc57IEBQJNhbW1taWnZtJE4AACoDVBgTYlQKHiX9qS0sICrpm5o1RGCQv0HodPpsAYFAN8GUGBNxos78dei9pKJvrgaWn38pkBwDQAAADkB6xtNw4s78Wc2raamqSzNzz2zafWLO/HNKBUAAMB3DCiwJkAoFFyL2iux6vqBvUKhhAMoAAAAQCMBBdYEvEt7QrW9qJTk5b5Le/KN5QEAAPgvAAqsCSgtLGhwLQAAANAwQIE1AVw19QbXAgAAAA0DFFgTYGjVkZqakgpPU8vQquM3lgf4j/P69WsajZaUlCS9WVRUlJqamrxHaSpwbJFvPy7QkgEF1gTQ6Yw+flMkVrmPnwKnwYDGk5WV5e/vb2BgoKSkZGJiMnv27Ly8vNoaGxkZ8fl8Gxsb6X36+vo+f/68qSWVO7LMjppzGfiOAQXWNLR3chkctIhqh/E0tQYHLYJzYEDjefXqlaOj4/Pnz//888+XL1/u3r376tWrzs7O+fn54o2rqqoYDIaenp6CQh2nPNlsto6OjnxElonq6uoG3CXj7BoATgoDtCbkmWOzGWjejMwCQU3m4+TUm7GZj5MFgppmkQFoKuqVkZlKTU15RsaOmpp631gbXl5ebdq0KSsrI0v4fD6HwwkICMCXJiYmK1euHD9+vIqKyrhx40RyEP/999/t2rVjsVhubm44QjzOkkxN8RwaGmpnZ/f777/jsPq+vr7FxcW46sKFC66urqqqqhoaGoMGDXr58iUuF890TGJiYrJixYrRo0crKyvr6+v/+uuvZBVCaNeuXYMHD+ZwOMuWLSMI4syZM/b29kwm08zMLCwsrLq6Grd8/vx5z549mUymlZXVpUuXEEKnTp0SH/fx48cDBw7k8XhcLrdHjx4vX74MDQ2lvuKuX79OEERKSoq7uzuLxdLQ0Jg8eTJOIU18yc68evVqfX19ExOThn5FQGNpWEZmUGAAIJkGK7D3/FNXrrbl85smG31eXh6NRlu9erVI+eTJk9XV1YVCIUEQWOusX7/+xYsXL168oL7iMzIyFBUV58+f//Tp0z///BNnbpSowLhc7rBhwx49evTPP//o6ektWrQIVx0/fvzEiRPPnz9/+PCht7d3p06dBAIBUZcC4/F44eHhz549+/XXXxkMxqVLl3AVQkhHR2ffvn3p6emvX7+OiYlRUVGJiopKT0+/dOmSqalpWFgYQRACgcDGxsbNze3hw4dxcXFdunSRqMDevn2roaExbNiwe/fuPXv2bP/+/U+fPi0pKRk5cqSXlxefz+fz+ZWVlZ8+fTIwMMCzu3r1qpmZ2fjx47E848eP53K5Y8eOffz48aNHj5rkKwMaACgwggAFBjQdDVZgSUmTr1xtm5Q8pUnEwGkh8bubyqZNmxBCHz58IAjCxMTEx8eHrKK+4hcsWGBjY0NWLV68uDYFxuFwSKsrODjYyclJXJicnByEEH7RS1dgXl5e5KWvr++AAQPwZ4TQnDlzyKqePXtSdfPBgwf19fUJgrh48SKDwcjKysLlFy5ckKjAQkJCzMzMqqqqRATAdhV5uXfvXnV19dLSUnx5/vx5Op2enZ2NW+rq6lZWVorPAviWNEyBQSxEAGgCKqtyszL3E0QNQigv/x+EUF5e3IsXqxFCNJqCsfFEJSXJfqoNhiAIhBCNRsOXtSWrfPbsWdeuXcnLbt261dahqakpzuaMENLX18e6CiGUnp6+dOnShISE3NxcoVCIEMrMzKzTQ8TZ2Zn6ecuWLeQlVdTExMR79+798ssv+FIgEFRUVJSVlaWlpRkbG7dp00a8NypJSUk9e/ZUVFSULkxaWpqdnZ2ysjK+dHV1FQqFz54909XVRQh16tQJZ20GWh2gwACgCaiqzMnMiiSIKoToX5SKMDMrEiEhjaakq/tDgxVYu3btaDRaamqqiFvd06dP1dXVtbQ+d0u+nUUgCIJUcuiL2pMIVQ3QaDSsqxBC3t7eRkZGERERBgYGQqHQxsamAc4OVBmoogqFwuXLlw8bNozamMViichJvZ0Km82WZXSRhyDSZ22PDmj5gBciADQBPJ51t65/czjmCCGCEJD/cjjm3br+zeM1PKelpqamh4fHzp07y8vLycLs7OzDhw/7+vrW9mYnsbS0vHfvHnl5//79eo2el5eXlpa2ZMmSvn37WllZFRTIGlYGr3ySny0tLSU2s7e3f/bsWbuvodPp1tbWmZmZ79+/x81u3779//buPKyJa20A+AmBJEAA2UFlc2GrLEIQoiKgLPXTW7y9LSgWoRWr1gXqUsFaoYqIVutWxMpl0VpwAQWryFIV6sNSFBEUIiiLwV6oouzKPt8fp07TACGihATf38MfmTlnzrwzHPIyM2dmBlzc3Nz8xo0b/Ucz0mi03t6/n0Fqamp6586d9vZ2PJmTkyMlJWVoaCjktgCxBQkMgLeDyTRkWZ9DiPfQgWBZn2My3/SL8ocffujs7HRzc/vtt99qa2vT0tJcXFwmTJhAnnkTYOXKlffv39+yZUtFRcXZs2fxKMQh0x5JWVlZVVX1+PHjDx8+vHbt2oYNG4RcMCcnZ+/evRUVFREREefOnfP39x+w2vbt20+ePBkSElJaWsrhcM6cObNt2zaEkLOzs5GR0bJly4qLi2/cuIEv3fW3du3alpaWxYsX37p168GDBz/99FN5eTlCSF9fv6SkpLy8vKGhobu7e+nSpQwGw8fH5969e9evX1+3bp23tzc+fwgkGiQwAN6apqYCvgTW1HRz0NpCmzp16q1btyZPnuzp6Tl58uTPP//cyckpLy9PRUVlyGUNDAwSExPPnz9vbm4eGRmJMwGdThdy1VJSUqdPny4sLJw2bdqXX3753XffCbngxo0bCwsLp0+fvnPnzv3797u5uQ1Yzc3N7dKlS5mZmTY2NnZ2dt9//72enh5e74ULFzo7O2fMmOHn5zdYqlZVVb127VpbW5uDg4O1tXVUVBQ+EbpixQojIyMWi6Wurp6TkyMnJ5eenv78+XMbG5uPPvpo3rx5P/zwg5AbAsQZRcA5cUnU0tKipKTU3NysqKg4vBZ6enpu3rzZ2NiorKxsY2MzEvdLAonQ0dFRXV1tYGDAYDCEXKS0bFN9/QUlJdbUKYEPHu5ubi7U0vrwPVNhv/RFYNeuXceOHautrR3Rtejr6wcEBAQEBIzoWsBYMuCf25Df5/Dt/A8ZGRl5eXlkUs/IyGCz2a6urqMbFZAUigrTmPJTdXX9KBSqtVUCl/tfKSlhj3VGztGjR21sbFRVVXNycr777ru1a9eOdkQAvB2QwP6WkZGRm5uLCAK9ukJA9PXl5uYihCCHAWHo6PiSnykUqp7eytGL5W8PHjwIDQ19/vy5rq7uxo0bg4KCRjsiAN4OSGB/6enp4cteCCFEoSCCyM3NnTt3LpxLBBLqwIEDBw4cEOUaa2pqRLk68M4a8UEcR48exac1ra2tb9y40b+Cr68v5Z/ee+/v9480NTWtWbNGW1ubwWCYmJikpqaOUJx5+bkIIdR/dBaF8ncpAAAAsTGyCezMmTMBAQFff/11UVGRvb39/PnzuVwuX51Dhw7VvVJbW6uiovLxxx/joq6uLhcXl5qamsTExPLy8qioKPwkt5FQdEfQaDHBpQAAAERvZE+Lff/998uXL/fz80MIHTx4MD09PTIycvfu3bx1lJSUlJSU8Ofk5OTGxsZPP/0UT8bExDx//jw3NxcPjcXja0dId3fHsEsBAACI3ggegXV1dRUWFvIOf3B1dcVjIgYTHR3t7OxMJqqLFy+y2ew1a9ZoampOmzYtLCyM9+56UmdnZwuP4UWrY6A97FIAAACiN4IJrKGhobe3l/d2d01Nzfr6+sHq19XVXblyBR+uYVVVVYmJib29vampqdu2bdu/f/+A9zPu3r1b6RUdHZ3hRev+f16otwf1vyuOIFBvj/v/eQ2vWQAAACNkxAdx8D1IVMAzbOLi4saNG8f7xNK+vj4NDY3jx49bW1svXrz466+/joyM7L9gUFBQ8yvDvkOTTmPoGKrhKP+eSxAIIR1DNTpN2FtZAQAAiMYIJjA1NTUqlcp7yPXkyZPBnj9GEERMTIy3tzfvew20tbUNDQ2pVCqeNDExqa+v7/8kbDqdrshj2AEv9w7QmaKMenna7+3SmaK83Dtg2G0CIM5qamooFMqdO3dGovGsrCwKhdLU1DQSjQvg6Og4cg8BEeVG8f52RmtnirkRTGA0Gs3a2jozM5Ock5mZOXPmzAErZ2dnP3z4cPny5bwzZ82a9fDhQ/K1DhUVFdra2iP65p7l3gFB24OnWelr68hPs9IP2h4M2QuMLsogfH19Rzu0t0xfX5/3tWEIoYMHD+rr64/EuiQuH8ycObOuro4c7zagEc3c4mlkRyFu2LDB29ubxWKx2ezjx49zudxVq1YhhIKCgv7444+TJ0+SNaOjo21tbfnekrd69eojR474+/uvW7fuwYMHYWFh69evH9GAEUJ0GuOjD3xHei0ACKmurg5/OHPmzPbt2/HT1pHQr8IC4qa7u3vIN3D2R6PRtLS0RiKerq4uyX2f58heA/P09Dx48OCOHTssLS1/++231NRUPMKwrq6O94aw5ubmpKQkvsMvhJCOjk5GRsbNmzfNzc3Xr1/v7+8fGBg4ogEDMGxVLzpLWl/0/6l60fkmzWq9oqSkRKFQtLS0NDU1zczMfv31V1zB0tJSQ0MDf87Ly5ORkWlra0MIcblcd3d3JpOpqKjo4eHx559/Dhp5VZWTk5OcnJyFhQXvm7dyc3PnzJkjKyuro6Ozfv168n1ap06dYrFYCgoKWlpaXl5e5LubEUKpqamGhoaysrJOTk68z+N49OjRv/71L2VlZXl5+ffee28YTyTw9fVdtGjRt99+q6GhoaiouHLlSvJqQnt7+7Jly5hMpra29v79+3mXGjDUmpoaJycnhJCysjJ5LEsQxN69eydNmiQrK2thYZGYmDjkRvGhUCiRkZHz58+XlZU1MDA4d+4cno/PBJ49e9bR0ZHBYJw6dQohFBsba2JiwmAwjI2Njx49SjZSUFAwffp0BoPBYrGKiorI+XyHjDk5OQ4ODnJycsrKym5ubo2Njb6+vtnZ2YcOHcIH6DjO7OzsGTNm0Ol0bW3twMDAnp4evLijo+PatWs3bNigpqbm4uLyur8LMUKMLc3NzQih5ubm0Q4ESLyXL1+WlZW9fPlSmMqV7R2a14oG+6ls73jzeGJjY5WUlPDnDz/8cO3atQRBPH/+XEZGZty4caWlpQRBhIWF2draEgTR19c3ffr02bNn37p1Kz8/38rKysHBoX+b1dXVCCFjY+NLly6Vl5d/9NFHenp63d3dBEGUlJQwmcwDBw5UVFTk5ORMnz7d19cXLxUdHZ2amlpZWZmXl2dnZzd//nw8n8vl0ul0f3//+/fvnzp1Cl/wbmxsJAhiwYIFLi4uJSUllZWVv/zyS3Z2dv9g9PT0Dhw4wDvnwIEDenp6+LOPjw+TyfT09Lx3796lS5fU1dW3bt2Ki1avXj1x4sSMjIySkpKFCxcymUx/f38Bofb09CQlJSGEysvL6+rqmpqaCILYunWrsbFxWlpaZWVlbGwsnU7PysoSvFF8EEKqqqpRUVHl5eXbtm2jUqllZWXkTtbX109KSqqqqvrjjz+OHz+ura2NJ5OSklRUVOLi4giCaGtrU1dXx9v4yy+/TJo0CSFUVFREEMT169fJ9RYVFdHp9NWrV9+5c+fevXtHjhx5+vRpU1MTm81esWIFfihET0/P48eP5eTkvvjiCw6Hc+HCBTU1teDgYByqg4MDk8ncvHnz/fv3ORzOwB1OtAb8cxvy+xwSGAADe60EVtzSLiCBFbe0v3k8vAns8OHD06ZNIwgiOTmZxWJ9+OGHERERBEG4urpu2bKFIIiMjAwqlcrlcnH90tJShFBBQQFfm/i79b///S9vNfyN5u3t/fnnn5M1b9y4ISUl1X9vFBQUIIRaW1sJgggKCjIxMenr68NFW7ZsIb9zzczMQkJCBG/gkAlMRUWlvf2vPRkZGclkMnt7e1tbW2k02unTp/H8Z8+eycrKkglssFB58wFBEG1tbQwGIzc3l6y8fPnyJUuWCN4oPgihVatWkZO2trarV68mXu3kgwcPkkU6Ojrx8fHk5M6dO9lsNkEQP/74I982DpjAlixZMmvWrP4BODg48G741q1bjYyMyMgjIiLwHsM1LS0t+7cwioaXwOCFlgBIHkdHx9LS0oaGhuzsbEdHR0dHx+zsbPxAagcHB4QQh8PR0dEhb4s0NTUdN24ch8MZsDVzc3P8QVtbGyGEz7MVFhbGxcUxX3Fzc+vr68PfxUVFRe7u7np6egoKCo6OjgghfEWAw+HY2dmRt8qw2WxyFevXrw8NDZ01a1ZwcHBJScnwttrCwkJOTo5svK2trba2trKysquri1yXioqKkZERuchgofIpKyvr6OhwcXEht/fkyZOVlZWCN6o/3lI2m827w1ksFv7w9OnT2tra5cuXk+sKDQ0l18W3jQOu5c6dO/PmzRMQBsbhcNhsNhn5rFmz2traHj9+zBePRIMnrAMgeaZNm6aqqpqdnZ2dnb1jxw4dHZ1du3bdvHnz5cuXs2fPRgPdc9l/DokcU4Ar4HG/fX19K1eu5Bs2paur297e7urq6urqeurUKXV1dS6X6+bmhi9HEYO/HdfPz8/Nze3y5csZGRm7d+/ev3//unXr+OooKiri/7hJTU1NgsfdUSiCXskrIFQ+eJMvX77M+7RV/N5qAe0PiXeHy8vL864rKirK1taWLMU3Cwm5LiHH7/D9xnHj5BwyHokGR2AASB4KhTJnzpyUlJR79+7Z29ubmZl1d3cfO3bMyspKQUEBIWRqasrlcsn7+svKypqbm01MTIRfhZWVVWlp6ZR/otFo9+/fb2hoCA8Pt7e3NzY25h3BYWpqmp+fT07yfkYI6ejorFq16vz58xs3boyKiuq/RmNj45s3//HU7Js3b/IeThUXF798+ZJsnMlkTpw4ccqUKTIyMuS6GhsbKyoq8GcBoeJxd+Sj6UxNTel0OpfL5d1YfPwqeKP48NU0NjbuX0dTU3PChAlVVVW86zIwMMDr4tvGAddibm5+9erV/vNpNBrvw/ZMTU3xSVE8mZubq6CgMHLPQx8dI3ZKc3TANTDwtojzNTCCIA4fPkylUlksFp5ctGgRlUrdvHkznsSDOOzt7QsLC3///Xdra2sBgzjwVRaCIBobGxFC169fJwiiuLhYVlb2iy++KCoqqqioSElJwcNGnjx5QqPRNm/eXFlZmZKSYmhoSLbw6NEjGo325Zdf3r9//+eff8bDvvFlG39//7S0tKqqqsLCwhkzZnh4ePQPJi8vT0pK6ttvvy0tLS0tLd2xY4eUlFR+fj4uxYM4lixZUlpampqaqqmpGRgYiItWrVqlq6v766+/3r1794MPPiAHcQgI9fHjxxQKJS4u7smTJ/iq2Ndff62qqhoXF/fw4cPbt2//8MMPeGCFgI3igxBSU1OLjo4uLy/fvn27lJQUHlnDt5MJgoiKipKVlT148GB5eXlJSUlMTMz+/fsJgmhtbVVTU8PbePny5SlTpqCBroGVl5fTaLTVq1cXFxdzOJyjR48+ffqUIIgVK1bY2NhUV1c/ffq0t7cXD+JYs2YNh8NJTk7mG8Qx4GXCUQSDOAgCEhh4e8Q8gd29exchtGnTJjyJX1l56dIlssKjR48++OADeXl5BQWFjz/+uL6+vn+bAhIYQRAFBQX4spC8vLy5ufmuXbvw/Pj4eH19fTqdzmazL168yNvCL7/8MmXKFDqdbm9vHxMTQ37nrl27dvLkyXQ6XV1d3dvbu6GhYcBtzMzMtLe3V1ZWVlZWnj17dmZmJlnk4+Pj7u6+fft2VVVVJpPp5+fX0fHX2M7W1tZPPvlETk5OU1Nz7969vN/OAkLdsWOHlpYWhULx8fEhCKKvr+/QoUNGRkYyMjLq6upubm7kUMnBNooPQigiIsLFxYVOp+vp6SUkJAy4k7Gff/7Z0tKSRqMpKyvPmTPn/PnzeH5eXp6FhQWNRrO0tMRDJfsnMIIgsrKyZs6cSafTx40bh4fREwRRXl5uZ2eHTzBWV1fjajY2Nvgesi1btuDxpcQYSmCCziBLopaWFiUlpebm5jd5phQACKGOjo7q6mr8OtYhK5e0vnC9VTFYaQbL0FxB7q1G987x9fVtampKTk4e7UAGRaFQLly4wPs0VyC8Af/chvw+h2tgALwFzFdP7BxGKQBgeGAUIgBvwSQ5eq6tSdtA76tjUqmT5OiiDwmAMQ8SGABvB2SpERUXFzfaIQxhjF2OkQhwChEAAIBEggQGAABAIkECA0AQOC8EgAgM7w8NEhgAA8NP9xnwyUMAgLcL/6FRX3O8LgziAGBg0tLScnJyT58+lZGRkZKCf/UAGCl9fX1Pnz6Vk5OTln69lAQJDICBUSgUbW3t6urqR48ejXYsAIxxUlJSurq6gz1vejCQwAAYFI1Gmzp1KpxFBGCk0Wi0YZzngAQGgCBSUlLCPEoKACB6cGYfAACARIIEBgAAQCJBAgMAACCRxto1MHw3XEtLy2gHAgAA4I3gb3IB9ziPtQTW2tqKEMLvAgcAACDpWltblZSUBiwaay+07Ovr+9///qegoPC69xPwamlp0dHRqa2tFee3YkpEkEhC4pSIIJGExCkRQSIJiVMigkQjFidBEK2trePHjx9shP1YOwKTkpKaOHHiW2lKUVFRzDsNkpAgkYTEKRFBIgmJUyKCRBISp0QEiUYmzsGOvTAYxAEAAEAiQQIDAAAgkSCBDYBOpwcHB9PpYv2CXYkIEklInBIRJJKQOCUiSCQhcUpEkGj04hxrgzgAAAC8I+AIDAAAgESCBAYAAEAiQQIDAAAgkSCBAQAAkEjvRAI7evSogYEBg8Gwtra+cePGgHWys7Otra0ZDMakSZOOHTvGW5SUlGRqakqn001NTS9cuPC6LYsgyKioKHt7e2VlZWVlZWdn54KCArIoJCSEwkNLS+tNgnzDOOPi4ij/1NHR8VotiyBIR0dHviAXLFiAi0S/M+vq6ry8vIyMjKSkpAICAvhKxaRnCghSrHqmgDjFp2cKCFKseub58+ddXFzU1dUVFRXZbHZ6ejpvqWh6JkIIEWPd6dOnZWRkoqKiysrK/P395eXlHz16xFenqqpKTk7O39+/rKwsKipKRkYmMTERF+Xm5lKp1LCwMA6HExYWJi0tnZ+fL3zLognSy8srIiKiqKiIw+F8+umnSkpKjx8/xkXBwcHvvfde3StPnjwZXoRvJc7Y2FhFRcU6Hq/VsmiCfPbsGRnevXv3qFRqbGwsLhL9zqyurl6/fv2JEycsLS39/f15i8SnZwoIUqx6poA4xadnCghSrHqmv7//nj17CgoKKioqgoKCZGRkbt++jYtE0zOxsZ/AZsyYsWrVKnLS2Ng4MDCQr85XX31lbGxMTq5cudLOzg5/9vDweP/998kiNze3xYsXC9+yaILk1dPTo6CgcOLECTwZHBxsYWExvKjeepyxsbFKSkrDblk0QfI6cOCAgoJCW1sbnhT9ziQ5ODjwfZ2JT88UECSvUe+ZAuIUn54pIEhe4tMzMVNT02+//RZ/Fk3PxMb4KcSurq7CwkJXV1dyjqura25uLl+1vLw83jpubm63bt3q7u4esAgvLmTLogmS14sXL7q7u1VUVMg5Dx48GD9+vIGBweLFi6uqqoYR4VuMs62tTU9Pb+LEiQsXLiwqKnqtlkUWJCk6Onrx4sXy8vLkHBHvTAHEp2cKadR7pmBi0jOFJFY9s6+vr7W1lfzNiqBnksZ4AmtoaOjt7dXU1CTnaGpq1tfX81Wrr6/nq9PT09PQ0DBgEV5cyJZFEySvwMDACRMmODs740lbW9uTJ0+mp6dHRUXV19fPnDnz2bNnwwjyrcRpbGwcFxd38eLFhIQEBoMxa9asBw8eCN+yaIIkFRQU3Lt3z8/Pj5wj+p0pgPj0TCGNes8UQHx6pjDErWfu37+/vb3dw8MDT4qgZ5LG2tPoB8T7ahWCIAZ80wpfHd45AhYXpmXRBInt3bs3ISEhKyuLwWDgOfPnz8cfzMzM2Gz25MmTT5w4sWHDhlGJ087Ozs7ODs+fNWuWlZXVkSNHDh8+LHzLIgiSFB0dPW3atBkzZpBzRmVnDm9xEe/MIYlJzxyMWPXMIYlVz0xISAgJCUlJSdHQ0BBm8be4M9GYPwJTU1OjUqm8Sf7Jkye8/wJgWlpafHWkpaVVVVUHLMKLC9myaILE9u3bFxYWlpGRYW5uPuCK5OXlzczM8L+WoxgnJiUlZWNjg4MRw5354sWL06dP8/6Ty0c0O1MA8emZQxKTnimk0e2ZQxKrnnnmzJnly5efPXuWPLBGIumZpDGewGg0mrW1dWZmJjknMzNz5syZfNXYbDZvnYyMDBaLJSMjM2ARXlzIlkUTJELou+++27lzZ1paGovFGmxFnZ2dHA5HW1t7GEG+rThJBEHcuXMHByNuOxMhdPbs2c7Ozk8++WSwFYlmZwogPj1TMPHpmUIa3Z45JPHpmQkJCb6+vvHx8eRofkwEPfNvbzICRCLggZvR0dFlZWUBAQHy8vI1NTUEQQQGBnp7e+M6eFD1l19+WVZWFh0dzTuoOicnh0qlhoeHczic8PDw/kNC+7cs+iD37NlDo9ESExPJcbStra24aOPGjVlZWVVVVfn5+QsXLlRQUBh2kG8eZ0hISFpaWmVlZVFR0aeffiotLf37778Lbln0QWKzZ8/29PTka1n0O5MgiKKioqKiImtray8vr6KiotLSUjxffHqmgCDFqmcKiFN8eqaAIDEx6Znx8fHS0tIRERHkb7apqQkXiaZnYmM/gREEERERoaenR6PRrKyssrOz8UwfHx8HBweyTlZW1vTp02k0mr6+fmRkJO/i586dMzIykpGRMTY2TkpKGrJl0Qepp6fH939JcHAwLvL09NTW1paRkRk/fvyHH37I98cg4jgDAgJ0dXVpNJq6ujoegDRky6IPkiCI8vJy/J8jX7OjsjP5frN6enpkkfj0zMGCFLeeOVicYtUzBfzGxadnOjg48MXp4+NDLi6ankkQBLxOBQAAgEQa49fAAAAAjFWQwAAAAEgkSGAAAAAkEiQwAAAAEgkSGAAAAIkECQwAAIBEggQGAABAIkECA2AsiIuLGzdu3IBFvr6+ixYtEmUwISEhlpaWolwjeDdBAgPvEF9fX/zOdRkZGU1NTRcXl5iYmL6+vtGOa2QdOnQoLi5O+Pq8e2nSpEmbNm1qb29/rTVu2rTp6tWrZGsiTp/g3QEJDLxb3n///bq6upqamitXrjg5Ofn7+y9cuLCnp2e04/pLV1fXW29TSUlpsIOzweC9VFVVFRoaevTo0U2bNgm5IEEQPT09TCaz//sHAHjrIIGBdwudTtfS0powYYKVldXWrVtTUlKuXLlCHqA0Nzd//vnnGhoaioqKc+fOLS4uxvPxObGYmBhdXV0mk7l69ere3t69e/dqaWlpaGjs2rWLbJ/L5bq7uzOZTEVFRQ8Pjz///JMsCg0N1dDQUFBQ8PPzCwwMJE+y4WOU3bt3jx8/3tDQECF06tQpFouloKCgpaXl5eX15MkTXDMrK4tCoVy+fNnCwoLBYNja2t69e5d369LT001MTJhMJs5AvO3jz319fXv27JkyZQqdTtfV1eWNvP9e0tHR8fLyWrp0aXJy8pBRpaens1gsOp1+48YN8hRiSEjIiRMnUlJS8CFdVlbW3Llz165dS67o2bNndDr92rVrr/M7BOAvkMDAO23u3LkWFhbnz59HCBEEsWDBgvr6+tTU1MLCQisrq3nz5j1//hzXrKysvHLlSlpaWkJCQkxMzIIFCx4/fpydnb1nz55t27bl5+fjFhYtWvT8+fPs7OzMzMzKykpPT0+8+M8//7xr1649e/YUFhbq6upGRkbyhnH16lUOh5OZmXnp0iWEUFdX186dO4uLi5OTk6urq319fXkrb968ed++fTdv3tTQ0Pjggw+6u7vx/BcvXuzbt++nn3767bffuFzugIdNQUFBe/bs+eabb8rKyuLj44V5G5OsrCxeheCovvrqq927d3M4HN6Xfm3atMnDwwNn07q6upkzZ/r5+cXHx3d2dpK7Zfz48U5OTkOGAcAA3vBhwABIEB8fH3d3d76Znp6eJiYmBEFcvXpVUVGxo6ODLJo8efKPP/5IEERwcLCcnFxLSwue7+bmpq+v39vbiyeNjIx2795NEERGRgaVSuVyuXh+aWkpQqigoIAgCFtb2zVr1pAtz5o1y8LCgoxKU1Ozs7NzwJgLCgoQQvgtJNevX0cInT59Ghc9e/ZMVlb2zJkzBEHExsYihB4+fIiLIiIiNDU1+ba6paWFTqdHRUUJv5d+//13VVVVDw+PIaNKTk4mS4ODg3m3jnefd3R0qKio4JgJgrC0tAwJCREcDwCDgSMw8K4jXr3XvLCwsK2tTVVVlflKdXV1ZWUlrqavr6+goIA/a2pqmpqaSklJkZP4fBqHw9HR0dHR0cHzTU1Nx40bx+FwEELl5eW874Dn/YwQMjMzo9Fo5GRRUZG7u7uenp6CgoKjoyNCiMvlkqVsNht/UFFRMTIywu0jhOTk5CZPnow/a2trk6f4SBwOp7Ozc968eUPuk0uXLjGZTAaDwWaz58yZc+TIkSGjEvC+Sl50Ov2TTz6JiYlBCN25c6e4uJjvSA4A4UmPdgAAjDIOh2NgYIAQ6uvr09bWzsrK4i0lhz/wvq8Zj9DjncRDGclcSOKdw1tE/PM1RvLy8uTn9vZ2V1dXV1fXU6dOqaurc7lcNzc3AYM7yGb5QiL6vSlJVlZ2sEb4ODk5RUZG4vdL4WaHjIp3EwTz8/OztLR8/PhxTEzMvHnz+r8zDAAhwREYeKddu3bt7t27//nPfxBCVlZW9fX10tLSU3ioqakJ35qpqSmXy62trcWTZWVlzc3NJiYmCCEjIyN82g27devWYI3cv3+/oaEhPDzc3t7e2Ni4/4EUvt6GEGpsbKyoqDA2NhYyvKlTp8rKypID3AWQl5efMmWKnp4emRSHjGowNBqtt7eXd46ZmRmLxYqKioqPj//ss8+EbAeA/iCBgXdLZ2dnfX39H3/8cfv27bCwMHd394ULFy5btgwh5OzszGazFy1alJ6eXlNTk5ubu23bNgGZpj9nZ2dzc/OlS5fevn27oKBg2bJlDg4O+NzaunXroqOjT5w48eDBg9DQ0JKSEr5jNRJ+NfCRI0eqqqouXry4c+dOvgo7duy4evXqvXv3fH191dTUhL/LisFgbNmy5auvvjp58mRlZWV+fn50dLSQyw4Z1WD09fVLSkrKy8sbGhrI8SZ+fn7h4eG9vb3//ve/hWwHgP4ggYF3S1pamra2tr6+/vvvv3/9+vXDhw+npKRQqVSEEIVCSU1NnTNnzmeffWZoaLh48eKamhphxumRKBRKcnKysrLynDlznJ2dJ02adObMGVy0dOnSoKCgTZs2WVlZ4SF8DAZjwEbU1dXj4uLOnTtnamoaHh6+b98+vgrh4eH+/v7W1tZ1dXUXL17kvXg2pG+++Wbjxo3bt283MTHx9PQU/kBqyKgGs2LFCiMjIxaLpa6unpOTg2cuWbJEWlray8trsJ0AgDAGOFEOABhpLi4uWlpaP/3002stlZWV5eTk1NjY+Lo3Joub2tpafX39mzdvWllZjXYsQILBIA4AROHFixfHjh1zc3OjUqkJCQm//vprZmbmaAc1Crq7u+vq6gIDA+3s7CB7gTcECQwAUcDnJ0NDQzs7O42MjJKSkpydnUc7qFGQk5Pj5ORkaGiYmJg42rEAiQenEAEAAEgkGMQBAABAIkECAwAAIJEggQEAAJBIkMAAAABIJEhgAAAAJBIkMAAAABIJEhgAAACJBAkMAACARIIEBgAAQCL9P8sULNzEcwOLAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot of curves on validation data\n",
    "# This shows that the first three approaches are basically interchangable\n",
    "fpred_true_groups.plot_frontier(prefix='True Groups ', new_plot=False, show_original=False)\n",
    "fpred_standard.plot_frontier(prefix='Base method ', new_plot=False)\n",
    "fpred_thresh.plot_frontier(prefix='Single threshold ', new_plot=False, show_original=False)\n",
    "fpred.plot_frontier(prefix='Two heads ', new_plot=False)\n",
    "plt.ylim(bottom=0.75)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "py3.8",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.18"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}