Pythia_Tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
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   "source": [
    "# Pythia in Python + Train Binary Classifier in PyTorch\n",
    "This tutorial uses Pythia8 in python3 to generate a ttbar signal dataset and a QCD background dataset. A neural network is then trained to distinguish between signal and background."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba8ce6b7",
   "metadata": {},
   "source": [
    "### Import Pythia and Other Dependencies\n",
    "The Makefile.inc in the pythia8312 directory includes some paths that must be added to your system paths in order to import pythia into python. If you are able to run this block, then your setup was successful!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "cad5dea5",
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   "outputs": [],
   "source": [
    "# Add the necessary pythia build paths to the python paths\n",
    "import sys\n",
    "with open(\"Software/Software_Path.txt\") as f:\n",
    "    path = f.readline().strip()\n",
    "cfg = open(path+\"/pythia8312/Makefile.inc\")  # Read necessary paths from this file\n",
    "lib = \"../lib\"\n",
    "for line in cfg:\n",
    "    if line.startswith(\"PREFIX_LIB=\"): lib = line[11:-1]; break  # Find build paths\n",
    "sys.path.insert(0, lib)   # Add build paths to system path\n",
    "\n",
    "# Import Pythia8\n",
    "import pythia8\n",
    "\n",
    "# Import ML Libs\n",
    "import numpy as np\n",
    "import torch\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "import torch.optim as optim\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83956717",
   "metadata": {},
   "source": [
    "### Initialize Pythia with Signal and Background Processes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "bd83d7bf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " *------------------------------------------------------------------------------------* \n",
      " |                                                                                    | \n",
      " |  *------------------------------------------------------------------------------*  | \n",
      " |  |                                                                              |  | \n",
      " |  |                                                                              |  | \n",
      " |  |   PPP   Y   Y  TTTTT  H   H  III    A      Welcome to the Lund Monte Carlo!  |  | \n",
      " |  |   P  P   Y Y     T    H   H   I    A A     This is PYTHIA version 8.312      |  | \n",
      " |  |   PPP     Y      T    HHHHH   I   AAAAA    Last date of change: 23 May 2024  |  | \n",
      " |  |   P       Y      T    H   H   I   A   A                                      |  | \n",
      " |  |   P       Y      T    H   H  III  A   A    Now is 11 Jul 2024 at 20:30:36    |  | \n",
      " |  |                                                                              |  | \n",
      " |  |   Program documentation and an archive of historic versions is found on:     |  | \n",
      " |  |                                                                              |  | \n",
      " |  |                               https://pythia.org/                            |  | \n",
      " |  |                                                                              |  | \n",
      " |  |   PYTHIA is authored by a collaboration consisting of:                       |  | \n",
      " |  |                                                                              |  | \n",
      " |  |   Javira Altmann, Christian Bierlich, Naomi Cooke, Nishita Desai,            |  | \n",
      " |  |   Leif Gellersen, Ilkka Helenius, Philip Ilten, Leif Lonnblad,               |  | \n",
      " |  |   Stephen Mrenna, Christian Preuss, Torbjorn Sjostrand, Peter Skands,        |  | \n",
      " |  |   Marius Utheim, and Rob Verheyen.                                           |  | \n",
      " |  |                                                                              |  | \n",
      " |  |   The complete list of authors, including contact information and            |  | \n",
      " |  |   affiliations, can be found on https://pythia.org/.                         |  | \n",
      " |  |   Problems or bugs should be reported on email at authors@pythia.org.        |  | \n",
      " |  |                                                                              |  | \n",
      " |  |   The main program reference is C. Bierlich et al,                           |  | \n",
      " |  |   'A comprehensive guide to the physics and usage of Pythia 8.3',            |  | \n",
      " |  |   SciPost Phys. Codebases 8-r8.3 (2022) [arXiv:2203.11601 [hep-ph]]          |  | \n",
      " |  |                                                                              |  | \n",
      " |  |   PYTHIA is released under the GNU General Public Licence version 2 or later.|  | \n",
      " |  |   Please respect the MCnet Guidelines for Event Generator Authors and Users. |  | \n",
      " |  |                                                                              |  | \n",
      " |  |   Disclaimer: this program comes without any guarantees.                     |  | \n",
      " |  |   Beware of errors and use common sense when interpreting results.           |  | \n",
      " |  |                                                                              |  | \n",
      " |  |   Copyright (C) 2024 Torbjorn Sjostrand                                      |  | \n",
      " |  |                                                                              |  | \n",
      " |  |                                                                              |  | \n",
      " |  *------------------------------------------------------------------------------*  | \n",
      " |                                                                                    | \n",
      " *------------------------------------------------------------------------------------* \n",
      "\n",
      "\n",
      " *-------  PYTHIA Process Initialization  --------------------------*\n",
      " |                                                                  |\n",
      " | We collide p+ with p+ at a CM energy of 1.400e+04 GeV            |\n",
      " |                                                                  |\n",
      " |------------------------------------------------------------------|\n",
      " |                                                    |             |\n",
      " | Subprocess                                    Code |   Estimated |\n",
      " |                                                    |    max (mb) |\n",
      " |                                                    |             |\n",
      " |------------------------------------------------------------------|\n",
      " |                                                    |             |\n",
      " | g g -> t tbar                                  601 |   9.089e-06 |\n",
      " | q qbar -> t tbar                               602 |   1.084e-06 |\n",
      " | q q -> t q (t-channel W+-)                     603 |   7.347e-06 |\n",
      " | f fbar -> t tbar (s-channel gamma*/Z0)         604 |   8.592e-09 |\n",
      " | f fbar -> t qbar (s-channel W+-)               605 |   1.527e-07 |\n",
      " | gamma gamma -> t tbar                          606 |   6.575e-11 |\n",
      " | g gamma -> t tbar                              607 |   7.382e-08 |\n",
      " |                                                                  |\n",
      " *-------  End PYTHIA Process Initialization -----------------------*\n",
      "\n",
      " *-------  PYTHIA Multiparton Interactions Initialization  ---------* \n",
      " |                                                                  | \n",
      " |                   sigmaNonDiffractive =    57.17 mb              | \n",
      " |                                                                  | \n",
      " |    pT0 =  2.65 gives sigmaInteraction =   328.48 mb: accepted    | \n",
      " |                                                                  | \n",
      " *-------  End PYTHIA Multiparton Interactions Initialization  -----* \n",
      "\n",
      " *-------  PYTHIA Flag + Mode + Parm + Word + FVec + MVec + PVec + WVec Settings (changes only)  ------------------* \n",
      " |                                                                                                                 | \n",
      " | Name                                          |                      Now |      Default         Min         Max | \n",
      " |                                               |                          |                                      | \n",
      " | Top:all                                       |                       on |          off                         | \n",
      " |                                                                                                                 | \n",
      " *-------  End PYTHIA Flag + Mode + Parm + Word + FVec + MVec + PVec + WVec Settings  -----------------------------* \n",
      "\n",
      " --------  PYTHIA Particle Data Table (changed only)  ------------------------------------------------------------------------------\n",
      " \n",
      "      id   name            antiName         spn chg col      m0        mWidth      mMin       mMax       tau0    res dec ext vis wid\n",
      "             no onMode   bRatio   meMode     products \n",
      "\n",
      " no particle data has been changed from its default value \n",
      "\n",
      " --------  End PYTHIA Particle Data Table  -----------------------------------------------------------------------------------------\n",
      "\n",
      "\n",
      " *------------------------------------------------------------------------------------* \n",
      " |                                                                                    | \n",
      " |  *------------------------------------------------------------------------------*  | \n",
      " |  |                                                                              |  | \n",
      " |  |                                                                              |  | \n",
      " |  |   PPP   Y   Y  TTTTT  H   H  III    A      Welcome to the Lund Monte Carlo!  |  | \n",
      " |  |   P  P   Y Y     T    H   H   I    A A     This is PYTHIA version 8.312      |  | \n",
      " |  |   PPP     Y      T    HHHHH   I   AAAAA    Last date of change: 23 May 2024  |  | \n",
      " |  |   P       Y      T    H   H   I   A   A                                      |  | \n",
      " |  |   P       Y      T    H   H  III  A   A    Now is 11 Jul 2024 at 20:30:36    |  | \n",
      " |  |                                                                              |  | \n",
      " |  |   Program documentation and an archive of historic versions is found on:     |  | \n",
      " |  |                                                                              |  | \n",
      " |  |                               https://pythia.org/                            |  | \n",
      " |  |                                                                              |  | \n",
      " |  |   PYTHIA is authored by a collaboration consisting of:                       |  | \n",
      " |  |                                                                              |  | \n",
      " |  |   Javira Altmann, Christian Bierlich, Naomi Cooke, Nishita Desai,            |  | \n",
      " |  |   Leif Gellersen, Ilkka Helenius, Philip Ilten, Leif Lonnblad,               |  | \n",
      " |  |   Stephen Mrenna, Christian Preuss, Torbjorn Sjostrand, Peter Skands,        |  | \n",
      " |  |   Marius Utheim, and Rob Verheyen.                                           |  | \n",
      " |  |                                                                              |  | \n",
      " |  |   The complete list of authors, including contact information and            |  | \n",
      " |  |   affiliations, can be found on https://pythia.org/.                         |  | \n",
      " |  |   Problems or bugs should be reported on email at authors@pythia.org.        |  | \n",
      " |  |                                                                              |  | \n",
      " |  |   The main program reference is C. Bierlich et al,                           |  | \n",
      " |  |   'A comprehensive guide to the physics and usage of Pythia 8.3',            |  | \n",
      " |  |   SciPost Phys. Codebases 8-r8.3 (2022) [arXiv:2203.11601 [hep-ph]]          |  | \n",
      " |  |                                                                              |  | \n",
      " |  |   PYTHIA is released under the GNU General Public Licence version 2 or later.|  | \n",
      " |  |   Please respect the MCnet Guidelines for Event Generator Authors and Users. |  | \n",
      " |  |                                                                              |  | \n",
      " |  |   Disclaimer: this program comes without any guarantees.                     |  | \n",
      " |  |   Beware of errors and use common sense when interpreting results.           |  | \n",
      " |  |                                                                              |  | \n",
      " |  |   Copyright (C) 2024 Torbjorn Sjostrand                                      |  | \n",
      " |  |                                                                              |  | \n",
      " |  |                                                                              |  | \n",
      " |  *------------------------------------------------------------------------------*  | \n",
      " |                                                                                    | \n",
      " *------------------------------------------------------------------------------------* \n",
      "\n",
      " PYTHIA Warning in PhaseSpace::trialKin123: maximum for cross section violated\n",
      "\n",
      " *-------  PYTHIA Process Initialization  --------------------------*\n",
      " |                                                                  |\n",
      " | We collide p+ with p+ at a CM energy of 1.400e+04 GeV            |\n",
      " |                                                                  |\n",
      " |------------------------------------------------------------------|\n",
      " |                                                    |             |\n",
      " | Subprocess                                    Code |   Estimated |\n",
      " |                                                    |    max (mb) |\n",
      " |                                                    |             |\n",
      " |------------------------------------------------------------------|\n",
      " |                                                    |             |\n",
      " | g g -> g g                                     111 |   1.397e+04 |\n",
      " | g g -> q qbar (uds)                            112 |   1.022e+02 |\n",
      " | q g -> q g                                     113 |   7.922e+03 |\n",
      " | q q(bar)' -> q q(bar)'                         114 |   1.072e+03 |\n",
      " | q qbar -> g g                                  115 |   5.178e+00 |\n",
      " | q qbar -> q' qbar' (uds)                       116 |   1.351e+00 |\n",
      " | g g -> c cbar                                  121 |   5.348e+01 |\n",
      " | q qbar -> c cbar                               122 |   5.495e-01 |\n",
      " | g g -> b bbar                                  123 |   3.842e+00 |\n",
      " | q qbar -> b bbar                               124 |   2.248e-02 |\n",
      " |                                                                  |\n",
      " *-------  End PYTHIA Process Initialization -----------------------*\n",
      "\n",
      " *-------  PYTHIA Multiparton Interactions Initialization  ---------* \n",
      " |                                                                  | \n",
      " |                   sigmaNonDiffractive =    57.17 mb              | \n",
      " |                                                                  | \n",
      " |    pT0 =  2.65 gives sigmaInteraction =   328.54 mb: accepted    | \n",
      " |                                                                  | \n",
      " *-------  End PYTHIA Multiparton Interactions Initialization  -----* \n",
      "\n",
      " *-------  PYTHIA Flag + Mode + Parm + Word + FVec + MVec + PVec + WVec Settings (changes only)  ------------------* \n",
      " |                                                                                                                 | \n",
      " | Name                                          |                      Now |      Default         Min         Max | \n",
      " |                                               |                          |                                      | \n",
      " | HardQCD:all                                   |                       on |          off                         | \n",
      " |                                                                                                                 | \n",
      " *-------  End PYTHIA Flag + Mode + Parm + Word + FVec + MVec + PVec + WVec Settings  -----------------------------* \n",
      "\n",
      " --------  PYTHIA Particle Data Table (changed only)  ------------------------------------------------------------------------------\n",
      " \n",
      "      id   name            antiName         spn chg col      m0        mWidth      mMin       mMax       tau0    res dec ext vis wid\n",
      "             no onMode   bRatio   meMode     products \n",
      "\n",
      " no particle data has been changed from its default value \n",
      "\n",
      " --------  End PYTHIA Particle Data Table  -----------------------------------------------------------------------------------------\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pythia_sig = pythia8.Pythia()                  # Define a pythia8.Pythia() object\n",
    "pythia_sig.readString(\"Beams:eCM = 14000.\")    # Beam energy is 14TeV\n",
    "pythia_sig.readString(\"Beams:idA = 2212\")      # Incoming particle 1 is proton\n",
    "pythia_sig.readString(\"Beams:idB = 2212\")      # Incoming particle 2 is proton\n",
    "pythia_sig.readString(\"Top:all = on\")          # Turn on all top processes\n",
    "pythia_sig.init()                              # Initialize object with user defined settings\n",
    "\n",
    "pythia_bkg = pythia8.Pythia()                  # Define a pythia8.Pythia() object\n",
    "pythia_bkg.readString(\"Beams:eCM = 14000.\")    # Beam enegery is 14TeV\n",
    "pythia_bkg.readString(\"Beams:idA = 2212\")      # Incoming particle 1 is proton\n",
    "pythia_bkg.readString(\"Beams:idB = 2212\")      # Incoming particle 2 is proton\n",
    "pythia_bkg.readString(\"HardQCD:all = on\")      # Turn on all HardQCD processes\n",
    "pythia_bkg.init()                              # Initialize object with user defined settings"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85e0b0de",
   "metadata": {},
   "source": [
    "### Generate Dataset\n",
    "Generate events and append stable particles to a list. Then histogram pT, eta, and phi for signal vs background."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1bf86af5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_events = 1000\n",
    "\n",
    "# Begin event loop. Generate event. Skip if error.\n",
    "stbl_sig = []\n",
    "for iEvent in range(num_events):           # Loop through events\n",
    "    if not pythia_sig.next(): continue     # Standard pythia syntax to trigger next event generation\n",
    "    for prt in pythia_sig.event:           # Loop through particles in each event\n",
    "        if prt.isFinal():                  # Check if particle is final state particle and store pT, eta, phi\n",
    "            stbl_sig.append([prt.pT(),prt.eta(),prt.phi()])\n",
    "            \n",
    "# Begin event loop. Generate event. Skip if error.\n",
    "stbl_bkg = []\n",
    "for iEvent in range(num_events):          # Loop through events\n",
    "    if not pythia_bkg.next(): continue    # Standard pythia syntax to trigger enxt event generation\n",
    "    for prt in pythia_bkg.event:          # Loop through particles in each event\n",
    "        if prt.isFinal():                 # Chekc if particle is final stat particle and store pT, eta, phi\n",
    "            stbl_bkg.append([prt.pT(),prt.eta(),prt.phi()])\n",
    "\n",
    "num_particles = min([len(stbl_sig),len(stbl_bkg)])   # Determine which list is shorter\n",
    "stbl_sig = np.array(stbl_sig[0:num_particles])       # Balance the dataset\n",
    "stbl_bkg = np.array(stbl_bkg[0:num_particles])       # Balance the dataset\n",
    "\n",
    "# Plot pT for signal and background\n",
    "plt.title(\"Particle p   $\\mathregular{_{\\tT}}$\")\n",
    "plt.hist(stbl_sig[:,0],bins=40,range=(0,10),histtype='step',label='signal',color='r',density=True)\n",
    "plt.hist(stbl_bkg[:,0],bins=40,range=(0,10),histtype='step',label='background',color='b',density=True)\n",
    "plt.yscale('log')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "# Plot eta for signal and background\n",
    "plt.title(\"Particle \\u03B7\")\n",
    "plt.hist(stbl_sig[:,1],bins=30,range=(-10,10),histtype='step',label='signal',color='r',density=True)\n",
    "plt.hist(stbl_bkg[:,1],bins=30,range=(-10,10),histtype='step',label='background',color='b',density=True)\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "# Plot phi for signal and background\n",
    "plt.title(\"Particle \\u03D5\")\n",
    "plt.hist(stbl_sig[:,2],bins=16,range=(-4,4),histtype='step',label='signal',color='r',density=True)\n",
    "plt.hist(stbl_bkg[:,2],bins=16,range=(-4,4),histtype='step',label='background',color='b',density=True)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "345bf45e",
   "metadata": {},
   "source": [
    "### Split Dataset Into Training and Testing Samples\n",
    "It's best practice to use a training and testing dataset to verify that your model is not overfitting. Its also best practice to shuffle the dataset before training."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "475d1e0e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X_train shape:\t torch.Size([159019, 3])\n",
      "Y_train shape:\t torch.Size([159019, 1])\n",
      "X_test shape:\t torch.Size([68151, 3])\n",
      "X_test shape:\t torch.Size([68151, 1])\n"
     ]
    }
   ],
   "source": [
    "# Convert python lists to numpy arrays\n",
    "X_sig = np.array(stbl_sig)\n",
    "X_bkg = np.array(stbl_bkg)\n",
    "\n",
    "# Generate labels sig=1 bkg=0\n",
    "Y_sig = np.ones(num_particles)\n",
    "Y_bkg = np.zeros(num_particles)\n",
    "\n",
    "# Combine sig and bkg arrays\n",
    "X = np.concatenate((X_sig, X_bkg),axis=0)\n",
    "Y = np.concatenate((Y_sig, Y_bkg),axis=0)\n",
    "\n",
    "# Generate random permuation of the indices\n",
    "p = np.random.permutation(len(X))\n",
    "\n",
    "# Shuffle X and Y according to randomized indices\n",
    "X = X[p]\n",
    "Y = Y[p]\n",
    "\n",
    "# Split dataset into training and testing samples\n",
    "# 70% train, 30% test\n",
    "num_particles = len(Y)\n",
    "X_train = X[0:int(0.7*num_particles)]\n",
    "Y_train = Y[0:int(0.7*num_particles)].reshape((-1,1))\n",
    "X_test = X[int(0.7*num_particles):]\n",
    "Y_test = Y[int(0.7*num_particles):].reshape((-1,1))\n",
    "\n",
    "# Convert numpy arrays to float32 torch tensors\n",
    "X_train = torch.from_numpy(np.float32(X_train))\n",
    "Y_train = torch.from_numpy(np.float32(Y_train))\n",
    "X_test = torch.from_numpy(np.float32(X_test))\n",
    "Y_test = torch.from_numpy(np.float32(Y_test))\n",
    "\n",
    "# Print shapes of samples\n",
    "print(\"X_train shape:\\t\", X_train.shape)\n",
    "print(\"Y_train shape:\\t\", Y_train.shape)\n",
    "print(\"X_test shape:\\t\", X_test.shape)\n",
    "print(\"X_test shape:\\t\", Y_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93298a2a",
   "metadata": {},
   "source": [
    "### Define the Model and the Training Loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b5a628a8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the Model\n",
    "# Define a class that inherits from torch.nn.Module\n",
    "class NeuralNet(nn.Module):\n",
    "    def __init__(self, in_dim, hidden_dim, out_dim):    # Called when object is initialized\n",
    "        super(NeuralNet, self).__init__()               # Call init function from parent class\n",
    "        self.lin1 = nn.Linear(in_dim,hidden_dim)        # Define linear transformation 1\n",
    "        self.lin2 = nn.Linear(hidden_dim,out_dim)       # Define linear transformation 2\n",
    "    def forward(self, data):                         # Define a forward pass\n",
    "        hidden_layer = F.relu(self.lin1(data))       # Transform using lin1 and use relu activation \n",
    "        output = F.sigmoid(self.lin2(hidden_layer))  # Transform using lin2 and use sigmoid activation\n",
    "        return output                                # Return the models prediction\n",
    "\n",
    "# Define the training loop\n",
    "def train(model, data, epochs=20):\n",
    "    X_train, y_train, X_test, y_test = data        # Unpack data\n",
    "\n",
    "    history = {'train_loss':[],'test_loss':[]}     # Define history dictionary\n",
    "\n",
    "    # Loop through epoches\n",
    "    for e in range(epochs):\n",
    "        # Train Model\n",
    "        model.train()                        # Switch model to training mode\n",
    "        optimizer.zero_grad()                # Reset the optimizers gradients\n",
    "        outputs = model(X_train)             # Get the model prediction\n",
    "        loss = loss_fn(outputs, y_train)     # Evaluate loss function\n",
    "        loss.backward()                      # Backward propogation\n",
    "        optimizer.step()                     # Gradient Descent\n",
    "\n",
    "        # Validate Model\n",
    "        model.eval()\n",
    "        y_pred = model(X_test.to(device))    # Get model output on test data\n",
    "        test_loss = loss_fn(y_pred,y_test)   # Evaluate loss on test preditions\n",
    "        \n",
    "        history['train_loss'].append(loss.detach().cpu().numpy())        # Append train loss to history (detach and convert to numpy array)\n",
    "        history['test_loss'].append(test_loss.detach().cpu().numpy())    # Append test loss to history (detach and convert to numpy array)\n",
    "        if e%100==0:\n",
    "            print('Epoch:',e,'\\tTrain Loss:',round(float(loss),4),'\\tTest Loss:',round(float(test_loss),4))\n",
    "\n",
    "    return history"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0e9b68a7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GPU Available on linux system: True\n",
      "Integrated GPU Available on Mac: False\n",
      "cuda:0\n"
     ]
    }
   ],
   "source": [
    "# Check if GPU is available, if not use cpu\n",
    "gpu_available = torch.cuda.is_available()\n",
    "mps_available = hasattr(torch, 'backends.mps.is_built') and torch.backends.mps.is_built()\n",
    "\n",
    "print(\"GPU Available on linux system:\", gpu_available)\n",
    "print(\"Integrated GPU Available on Mac:\", mps_available)\n",
    "\n",
    "if gpu_available:\n",
    "    device = torch.device(\"cuda:0\")\n",
    "elif mps_available:\n",
    "    device = torch.device(\"mps\")\n",
    "else:\n",
    "    device = torch.device(\"cpu\")\n",
    "\n",
    "print(device)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00823d7d",
   "metadata": {},
   "source": [
    "### Train Model and Plot Training History"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d04323f2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NeuralNet(\n",
      "  (lin1): Linear(in_features=3, out_features=64, bias=True)\n",
      "  (lin2): Linear(in_features=64, out_features=1, bias=True)\n",
      ")\n",
      "Trainable Parameters:  321 \n",
      "\n",
      "Epoch: 0 \tTrain Loss: 0.702 \tTest Loss: 0.7017\n",
      "Epoch: 100 \tTrain Loss: 0.6703 \tTest Loss: 0.6711\n",
      "Epoch: 200 \tTrain Loss: 0.6539 \tTest Loss: 0.655\n",
      "Epoch: 300 \tTrain Loss: 0.6422 \tTest Loss: 0.6435\n",
      "Epoch: 400 \tTrain Loss: 0.6335 \tTest Loss: 0.635\n",
      "Epoch: 500 \tTrain Loss: 0.627 \tTest Loss: 0.6285\n",
      "Epoch: 600 \tTrain Loss: 0.622 \tTest Loss: 0.6237\n",
      "Epoch: 700 \tTrain Loss: 0.6183 \tTest Loss: 0.62\n",
      "Epoch: 800 \tTrain Loss: 0.6154 \tTest Loss: 0.6172\n",
      "Epoch: 900 \tTrain Loss: 0.6131 \tTest Loss: 0.615\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Initialize model\n",
    "model = NeuralNet(in_dim=3,hidden_dim=64,out_dim=1)    # Declare model using NeuralNet Class\n",
    "model.to(device)                                       # Put model on device (cpu or gpu)\n",
    "print(model)                                           # Print layers in model\n",
    "\n",
    "# Calculate and print trainable parameters\n",
    "pytorch_total_params = sum(p.numel() for p in model.parameters() if p.requires_grad)\n",
    "print(\"Trainable Parameters: \", pytorch_total_params,\"\\n\")\n",
    "\n",
    "# Declare optimizer and loss function\n",
    "optimizer = optim.Adam(model.parameters(), lr=0.0001)  # Adam = Adaptive Moment Estimation, lr = learning rate\n",
    "loss_fn = nn.BCELoss()                                 # BCE = Binary Cross Entropy, used for binary classification\n",
    "\n",
    "#Train Model\n",
    "data = X_train.to(device), Y_train.to(device), X_test.to(device), Y_test.to(device)   # Send data to device (cpu or gpu)\n",
    "history = train(model, data, epochs=1000)                                             # Train the model!\n",
    "\n",
    "# Plot Training History\n",
    "plt.plot(history['train_loss'],label='train')\n",
    "plt.plot(history['test_loss'],label='test')\n",
    "plt.title(\"Loss\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "622a1f46",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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x8eLFAkOgi7q/vOHSCxYsEJ9//rnw9vYWSqVStGrVSvzxxx8F8tu4caOoWrWqsLGxEQ0bNhR79+4tMOxeCCF+++03ERgYKGxsbEocgp/3OTp69KgICwsTFSpUEA4ODqJfv37i3r17hb7nxx9/FABEWFhYyT/UQhQ17D48PLzQ9Pr8OT+rpJ+PEPmf66Jex48fF0II8e2334oaNWoIpVIpateuLdauXStmzJhR4POcd68bN26U0r/00ksFfm+EECIpKUmEh4cLb29vYW1tLTw9PUX79u3FqlWrpDQcdk9CCKEQQg+94YiIjODGjRvw8/PDggULMG7cOGMXR2s///wzevTogWPHjklD14nIuNiHiIhIZqtXr0bVqlXRsmVLYxeFiP7DPkRERDLZvHkzLly4gF27dmHp0qVGHdVFRJoYEBERyeTtt9+Gg4MDhg4divfee8/YxSGip7APEREREZk99iEiIiIis8eAiIiIiMwe+xBpITc3F7du3YKjoyM7QRIREZkIIQQePXqEypUrF1iP8lkMiLRw69YteHt7G7sYREREVAr//PMPXnzxxWLTMCDSgqOjIwD1D9TJycnIpSEifUhLAypXVm/fugX8t4yXYfPMTEPlz9WZ3vrwFuxtZMiU8hmj0smoUlJS4O3tLX2PF4cBkRbyHpM5OTkxICIqJywt87ednOT5brTMtARs8/J0YkAkN2NUOpUJ2nR3YadqIiIiMnsMiIiIiMjs8ZEZEZklKysgNDR/W5Y8LawQ2iBU2iaZGaPSyWRwpmotpKSkwNnZGcnJycX2IcrJyUFWVpaMJaOywNraGpZP900gIqIyQdvvb4AtRHohhEBiYiIePnxo7KKQkbi4uMDT05PzVBERmSgGRHqQFwy5u7tDpVLxS9GMCCGQnp6O27dvAwC8vLyMXCLSlhBAerp6W6UC5Pi1FUIgPUudqcqafytkZ4xKJ5PBgOg55eTkSMFQpUqVjF0cMgI7OzsAwO3bt+Hu7s7HZyYiPR1wcFBvp6bKMwI7PSsdDnPVmaZOTuWwe7kZo9LJZHCU2XPK6zOkUqmMXBIyprz6Zx8yIiLTxIBIT9j0bd5Y/0REpo0BEREREZk99iEypPh44O5d+fJzdQV8fPR+2bZt26Jhw4ZYsmSJ3q9NRERUFjAgMpT4eMDfP39EgxxUKiAmRuug6NlA58iRI2jXrh0ePHgAFxcXw5WTiIiojGFAZCh376qDoY0b1YGRocXEAP37q/M1QCuRvgkhkJOTAyvOFktERGUAv40Mzd8faNTI2KUoYNCgQTh69CiOHj2KpUuXapyrUKECACA0NBTr1q0DAGRnZ2PkyJH47rvvYG1tjREjRmD27NlSZ+LvvvsOS5cuRWxsLOzt7fHKK69gyZIlcHd3B5Df+rR792589NFH+PPPP7Fv3z60bdtWtnsmepqlJfDGG/nbsuRpYYk3At6Qtklmxqh0MhkMiMzU0qVL8ffff6Nu3bqYPXs2cnJycOrUKbzxxhuIjY2Fk5OTNL8OAKxfvx5Dhw7F77//jrNnzyIsLAw+Pj4YNmwYAPVw848//hi1atXC7du3MXbsWAwaNAi7d+/WyHfSpElYuHAhqlatKgVeRMZgawts2fLfjrb9/Z6zn56tlS229N5SckIyDI1KJ9LEgMhMOTs7w8bGBiqVCp6engAgTSzp7u5eoA+Rt7c3Fi9eDIVCgVq1auHPP//E4sWLpYBoyJAhUtqqVaviiy++QJMmTZCamgqHvInQAMyePRsdOnQw8N0R6UCX/n469tMjItPBgIi00rx5c425doKCgvD5558jJycHlpaWiIqKwsyZM/HHH3/gwYMHyM3NBQDEx8cjICBAel/jxo1lLztRsbTt72di/fSISDcMiOi5paWlISQkBCEhIYiIiICbmxvi4+MREhKCzMxMjbT2nCqfyoi0tLxVHBohFSrYy9DfLy0zjUt3GFN+pXPpDiqAAZEZs7GxQU5OjsY+AI1jeU6fPq2xf+rUKdSoUQOWlpb466+/cO/ePcybNw/e3t4AgLNnzxqw5ERERPrFmarNWJUqVXD69GncuHEDd+/eha+vLxQKBXbu3Ik7d+4gNTVVShsfH4+xY8ciNjYW33//PZYtW4bRo0cDAHx8fGBjY4Nly5bh+vXr+OWXX/Dxxx8b67aIiIh0xhYiQ4uJKbP5jBs3DqGhoQgICMDjx48RFxeHWbNmYdKkSRg8eDAGDhwoDbsfOHAgHj9+jKZNm8LS0hKjR49GWFgYAMDNzQ3r1q3DlClT8MUXX6BRo0ZYuHAhXnvtNX3eIRERkcEohBDC2IUo61JSUuDs7Izk5GQ4OTlpnHvy5Ani4uLg5+cHW1vb/BMmMFM16U+RnwMqszS6k8Ae9lHHi+9DdO4cEBgIREWVuq8R+xAZGfsQmZ3ivr+fxRYiQ/HxUQcn5WAtMyIiovKOAZEh+fgwQCEiIjIBDIiIyCxZWgJdugBIToblyYIjKw2Sp4UlutToIm2TzKRKB5fuoAIYEBGRWbK1BXbtAnDuGhCYIU+eVrbY1XeXLHlRIaRKJyqIw+6JiIjI7DEgIiIiIrPHgIiIzFJamnrUtX2LBkiDSp48M9Ng/6k97D+1R1pmmix50lOkSrdXbxM9hX2IiMhsqacJk7dzbXqWjHOTUUFyzg1HJsWoLURz585FkyZN4OjoCHd3d/To0QOxsbEaaZ48eYLw8HBUqlQJDg4O6NWrF5KSkjTSxMfHo2vXrlCpVHB3d8f48eORnZ2tkebIkSNo1KgRlEolqlevLs3ATETlWHy8ekLFwl7R0cYuHRGVIUZtITp69CjCw8PRpEkTZGdnY8qUKejYsSMuX74srYo+ZswY7Nq1C1u2bIGzszNGjhyJnj174uTJkwDUC5F27doVnp6e+O2335CQkICBAwfC2toan376KQAgLi4OXbt2xbvvvouIiAgcPHgQ77zzDry8vBASEmKw+4uP57yMREZT4mzxKgD/PTaxU6l/gYjIfIky5Pbt2wKAOHr0qBBCiIcPHwpra2uxZcsWKU1MTIwAICIjI4UQQuzevVtYWFiIxMREKc3KlSuFk5OTyMjIEEIIMWHCBFGnTh2NvN58800REhKiVbmSk5MFAJGcnFzg3OPHj8Xly5fF48ePNY7fvCmESiUEIN9LpVLnq6v4+HgxePBg4eXlJaytrYWPj494//33xd27dzXSXblyRQwaNEi88MILwsbGRlSpUkW89dZb4syZM1IaANJLpVKJ6tWri9DQUHH27FndC2ZCivockBFFRal/MTZuVG8/80o9cV763UmNidf+elFRpS5SakaqwEwIzIRIzUgt9XWolFJT8/9gpvLnbw6K+/5+VpnqQ5ScnAwAqFixIgAgKioKWVlZCA4OltLUrl0bPj4+iIyMRPPmzREZGYl69erBw8NDShMSEoIRI0bg0qVLeOmllxAZGalxjbw0H3zwQaHlyMjIQEZG/rwkKSkpOt/L3bvq/5hu3Kj+T6qhxcQA/fur89Wllej69esICgpCzZo18f3338PPzw+XLl3C+PHj8euvv+LUqVOoWLEizp49i/bt26Nu3br4+uuvUbt2bTx69Ag///wzPvzwQxw9elS65tq1a9GpUyc8efIEf//9N1atWoVmzZphzZo1GDhwoAHunqgY/v6Frz32dJ9ab2/ZikNEZVOZCYhyc3PxwQcfoEWLFqhbty4AIDExETY2NnBxcdFI6+HhgcTERCnN08FQ3vm8c8WlSUlJwePHj2FnZ6dxbu7cuZg1a5Ze7quov8VlRXh4OGxsbLBv3z7p5+Dj44OXXnoJ1apVw9SpU7FixQoMGjQINWrUwPHjx2Fhkd/1rGHDhhg9erTGNV1cXODp6QkAqFKlCjp27IjQ0FCMHDkS3bp1Q4UKFeS7QSIiIi2UmYAoPDwcFy9exIkTJ4xdFEyePBljx46V9lNSUuBdDv8Hef/+fezduxdz5swpEBR6enqiX79++OGHHxAWFoZLly5h06ZNGsFQnmcD1sKMGTMGGzZswP79+9GnTx993QJRqVlYAG3a5G9rLSam5DRFdOizUFigjW8baZtkVupKJ3NQJgKikSNHYufOnTh27BhefPFF6binpycyMzPx8OFDjS/dpKQkqQXC09MTv//+u8b18kahPZ3m2ZFpSUlJcHJyKhAIAIBSqYRSqdTLvZVlV65cgRAC/kU80/P398eDBw9w5coVAOrHlaWV994bN26U+hpE+mRnBxw5osMbXF0BlUr9bLokKpU6cHomKLKztsORQbpkSnqlc6WTOTFqQCSEwKhRo7Bt2zYcOXIEfn5+GucDAwNhbW2NgwcPolevXgCA2NhYxMfHIygoCAAQFBSEOXPm4Pbt23B3dwcA7N+/H05OTggICJDS7N69W+Pa+/fvl65h7oQQz3VelzwUCsVzX4vIKHx81EFOSUNHS9uhj4iMyqgBUXh4ODZt2oSff/4Zjo6OUp8fZ2dn2NnZwdnZGUOHDsXYsWNRsWJFODk5YdSoUQgKCkLz5s0BAB07dkRAQAAGDBiA+fPnIzExER999BHCw8OlVp53330XX375JSZMmIAhQ4bg0KFD+PHHH7HLzBf5q169OhQKBWJiYvD6668XOB8TEwM3NzfUrFkTAPDXX3/hpZdeKlVeMf89Zng26CUyKT4+DHKIyimjPkRduXIlkpOT0bZtW3h5eUmvH374QUqzePFivPrqq+jVqxdat24NT09PbN26VTpvaWmJnTt3wtLSEkFBQejfvz8GDhyI2bNnS2n8/Pywa9cu7N+/Hw0aNMDnn3+Ob775xqBzEJmCSpUqoUOHDlixYgUeP36scS4xMREREREYNGgQGjZsiICAAHz++efIzc0tcJ2HDx+WmNeSJUvg5ORUYLQfkbGkpQFubuqXXKs4pGWmwW2BG9wWuHHpDmMwRqWTyTD6I7OS2NraYvny5Vi+fHmRaXx9fQs8EntW27Ztcf78eZ3LWN59+eWXePnllxESEoJPPvlEY9h9zZo1MX36dCgUCqxduxbBwcFo1aoVpk6ditq1ayM1NRU7duzAvn37NIbdP3z4EImJicjIyMDff/+Nr7/+Gtu3b8eGDRu06oBNJBc5J06V8kw3QqaUzxiVTiahTHSqLs+0GZBizHxq1KiBM2fOYObMmejTpw9u374NIQR69uyJ7777DiqVetHLpk2b4uzZs5gzZw6GDRuGu3fvwsvLCy+//DKWLFmicc3BgwcDUAezL7zwAlq2bInff/8djcry/ANERGTWGBAZiC4DUvRFVcrVB6pUqaKxttuMGTOwaNEiXLhwQeqrBQA1a9bE+vXri72WPjpgExERyY0BkYFoOyBFn/S1ltmsWbNQpUoVnDp1Ck2bNi107iEiIqLyhAGRAZnygJS8x15ERETmgP/1JyIiIrPHFiIiMksWFkDjxvnbsuSpsEDjyo2lbZKZMSqdTAYDIiIyS3Z2wJkzMudpbYczw2TOlPIZo9LJZDBEJiIiIrPHgIiIiIjMHgMiIjJL6elAlSrqV3q6THlmpaPKkiqosqQK0rNkypTyGaPSyWSwDxERmSUhgJs387flyVPgZvJNaZtkZoxKJ5PBFiIyGVWqVCmwTIghJCYmokOHDrC3t5fWXivsGBERlR8MiMzYsWPH0K1bN1SuXBkKhQLbt28vkEYIgenTp8PLywt2dnYIDg7GlStXpPMZGRkYMGAAnJycULNmTRw4cEDj/QsWLMCoUaNKLEt6ejomT56MatWqwdbWFm5ubmjTpg1+/vlnKc2ZM2cQFhZW+hsGMGjQICgUigKvTp06SWkWL16MhIQEREdH4++//y7yGFGxYmKAc+c0X9HR+eejo4H4eGOVjoiewUdmZiwtLQ0NGjTAkCFD0LNnz0LTzJ8/H1988QXWr18PPz8/TJs2DSEhIbh8+TJsbW2xatUqREVFITIyEr/++iv69u2LpKQkKBQKxMXFYfXq1Th79myJZXn33Xdx+vRpLFu2DAEBAbh37x5+++033Lt3T0rj5uaml/vu1KkT1q5dq3FMqVRK29euXUNgYCBq1KhR7DGiQhW3kKE1gKn/bbdsCVir1IGTqU5pT1SeCCpRcnKyACCSk5MLnHv8+LG4fPmyePz4sRFKpj8AxLZt2zSO5ebmCk9PT7FgwQLp2MOHD4VSqRTff/+9EEKIESNGiIkTJwohhEhPTxcAxO3bt4UQQoSEhIitW7dqlb+zs7NYt25dsWl8fX3F4sWLpf2YmBjRokULoVQqhb+/v9i/f3+h9/G00NBQ0b1792LzACC9QkNDCz32rPLyOShXoqKEANT/FiI1VX0aUG/r1c2b6nyfeaWePiEwEwIzIVI3fFNs+cgADFrpVBYV9/39LLYQGVJaWtHnLC0BW1vt0lpYqCcUKymtvb1u5StBXFwcEhMTERwcLB1zdnZGs2bNEBkZibfeegsNGjTAd999h8ePH2Pv3r3w8vKCq6srIiIiYGtri9dff12rvDw9PbF792707NkTjo6OJabPyclBjx494OPjg9OnT+PRo0f48MMPS32vec6cOYOBAwfCyckJS5cuhZ2dHTIzMwscIypWUQsZZqYBv/63Xau2rEUiouIxIDIkB4eiz3XpAuzalb/v7l70MNA2bYAjR/L3q1QB7t4tmE7PoyYSExMBAB4eHhrHPTw8pHNDhgzBhQsXEBAQAFdXV/z444948OABpk+fjiNHjuCjjz7C5s2bUa1aNaxZswYvvPBCoXmtWrUK/fr1Q6VKldCgQQO0bNkSb7zxBlq0aFFo+v379+PatWs4cuQIPD09AQBz5sxBhw4dSryvnTt3wuGZupkyZQqmTJkCNzc3KJVK2NnZSdcFUOgxMm0KBRAQkL8tT54KBLipM5UpS3qaMSqdTAYDInou1tbWWL58ucaxwYMH4/3338f58+exfft2/PHHH5g/fz7ef/99/PTTT4Vep3Xr1rh+/TpOnTqF3377DQcPHsTSpUsxa9YsTJs2rUD62NhYeHt7awQoTZs21arM7dq1w8qVKzWOVaxYUav3UvmhUgGXLsmcp7UKl977L9Nz5+TNnIxT6WQyGBAZUmpq0ecsLTX3b98uOu2zixDeuFHqIukiL9hISkqCl5eXdDwpKQkNGzYs9D2HDx/GpUuX8M0332D8+PHo0qUL7O3t0adPH3z55ZfF5mdtbY1WrVqhVatWmDhxIj755BPMnj0bEydOhI2Njd7uy97eHtWrV9fb9YiIyPQxIDIkXfr0GCrtc/Dz84OnpycOHjwoBUApKSk4ffo0RowYUSD9kydPEB4ejoiICFhaWiInJ0eafC4rKws5OTk65R8QEIDs7Gw8efKkQEBUq1Yt/PPPP0hKSpIe6Z3hoo3mJT6+8EfHeWJi5CsLEZk8BkRmLDU1FVevXpX24+LiEB0djYoVK8LHxwcKhQIffPABPvnkE9SoUUMadl+5cmX06NGjwPU+/vhjdOnSBS+99BIAoEWLFhg/fjwGDx6ML7/8ssj+QADQtm1bvP3222jcuDEqVaqEy5cvY8qUKWjXrh2cnJwKpO/QoQOqVauG0NBQzJ8/H48ePcJHH30EQN1PozgZGRlSH6g8VlZWcHV1LfZ9VIbExwP+/iUvv6BSqYfBFyI9HWjSRL195ow6qaGlZ6WjyWp1pmcar4IMWdLTjFHpZDIYEJmxs2fPol27dtL+2LFjAQChoaFYt24dAGDChAlIS0tDWFgYHj58iJYtW2LPnj2wfXqEHICLFy/ixx9/RPRTE8+98cYbOHLkCFq1aoVatWph06ZNRZYlJCQE69evx5QpU5Ceno7KlSvj1VdfxfTp0wtNb2lpie3bt+Odd95BkyZNULVqVSxYsADdunUrULZn7dmzR+MRIKBucfrrr7+KfR+VIXfvqr/cNm5UB0ZFcXUtco4fIYDLl/O35SCEwOU76ky5cIQRGKPSyWQohOCnoiQpKSlwdnZGcnJygdaKJ0+eIC4uDn5+fiV+EZNhnTx5Ei1btsTVq1dRrVo1WfPm50Bm584BgYFAVBTQqFGpLpGWlj8Q9MQJzZktClNMbKV9nplpcJirzjS18wnYN2v5XPdAOnq60lNTZet+QMZT3Pf3s9hCRCZr27ZtcHBwQI0aNXD16lWMHj0aLVq0kD0YItPXsmXJaVScVJqoXGNARCbr0aNHmDhxIuLj4+Hq6org4GB8/vnnxi4WmaBvvgH+6/pWqJgY9Uocd+8yICIqrxgQkckaOHAgBg4caOxiUDlQuzafWhGZO652T0RERGaPLUREZJYUCsDLC0hIkDNPBXydfdXb8mVLeRQKwNc3f5voKQyIiMgsqVTAzp3qwWpyrderslbhxgc31DtcukN+KpVsM/2T6WFARETlFiezJiJtMSAionJJD5NZE5EZMWqn6mPHjqFbt26oXLkyFAoFtm/frnFeoVAU+lqwYIGUpkqVKgXOz5s3T+M6Fy5cQKtWrWBrawtvb2/Mnz9fjtsjIiN6ejLrqKiCr5MngYAAoHp1wM1NnjI9znqMJquboMnqJnic80SeTCnf48fqpTuaNFFvEz3FqAFRWloaGjRogOXLlxd6PiEhQeO1Zs0aKBQK9OrVSyPd7NmzNdKNGjVKOpeSkoKOHTvC19cXUVFRWLBgAWbOnIlVq1YZ9N5I/woLmg3hr7/+QvPmzWFraystalvYMTIN/v7qIfXPvho0UK/icOECkJsrT1lyRS7O3jqLs7fOIpeLBMgvNxc4e1b9kqvSyWQYNSDq3LkzPvnkE7z++uuFnvf09NR4/fzzz2jXrh2qVq2qkc7R0VEjnf1T07FHREQgMzMTa9asQZ06dfDWW2/h/fffx6JFiwx6b6Zg5cqVqF+/PpycnODk5ISgoCD8+uuvGmnyVrCvVKkSHBwc0KtXLyQlJUnn79+/j27dusHBwQEvvfQSzp8/r/H+8PBwrSZLvHPnDkaMGAEfHx8olUp4enoiJCQEJ0+elNIkJCSgc+fOz3XPbdu2LbTV8d1335XSzJgxA/b29oiNjcXBgweLPEZEROWHycxDlJSUhF27dmHo0KEFzs2bNw+VKlXCSy+9hAULFiA7O1s6FxkZidatW8PGxkY6FhISgtjYWDx48KDQvDIyMpCSkqLxKo9efPFFzJs3D1FRUTh79ixeeeUVdO/eHZcuXZLSjBkzBjt27MCWLVtw9OhR3Lp1Cz179pTOz5kzB48ePcK5c+fQtm1bDBs2TDp36tQpnD59Gh988EGJZenVqxfOnz+P9evX4++//8Yvv/yCtm3b4t69e1IaT09PKJXK577vYcOGFWh9fPox6rVr19CyZUv4+vqiUqVKRR4jIqJyRJQRAMS2bduKPP/ZZ5+JChUqiMePH2sc//zzz8Xhw4fFH3/8IVauXClcXFzEmDFjpPMdOnQQYWFhGu+5dOmSACAuX75caF4zZswQUC9GrfFKTk4ukPbx48fi8uXLBcplqipUqCC++eYbIYQQDx8+FNbW1mLLli3S+ZiYGAFAREZGCiGE6Ny5s1i5cqUQQojLly8LlUolhBAiMzNTNGjQQJw5c6bEPB88eCAAiCNHjhSb7tnPyMmTJ0WDBg2EUqkUgYGBYtu2bQKAOH/+fJHXaNOmjRg9enSxeTz9KuyzMGPGjALvK2+fgzIvKkoIQP1vKZOkpqrPA+rt58xOK6kZqQIzITATIvX0Cf1clLSnS6VTuZCcnFzk9/ezTGaU2Zo1a9CvX78CK4mPHTtW2q5fvz5sbGwwfPhwzJ07t9StCZMnT9a4bkpKCry9vXW+TlpmWpHnLC0sYWtlq1VaC4UF7KztSkxrb1P6lZtzcnKwZcsWpKWlISgoCAAQFRWFrKwsBAcHS+lq164NHx8fREZGonnz5mjQoAEOHTqEd955B3v37kX9+vUBAPPnz0fbtm3RuHHjEvN2cHCAg4MDtm/fjubNm2tVbykpKejWrRu6dOmCTZs24ebNm1q1RJUkISEBwcHB6NSpE8aNGwcHBwe8++67BY4REVH5YhIB0fHjxxEbG4sffvihxLTNmjVDdnY2bty4gVq1asHT01OjzwsAad/T07PQayiVSr08mnGYW/QXZ5caXbCr7y5p332hO9KzCh8f3Ma3DY4MOiLtV1laBXfTC06uImbo3knzzz//RFBQEJ48eQIHBwds27YNAQEBAIDExETY2NjAxcVF4z0eHh5ITEwEAEyaNAkjRoxAtWrVUKVKFXz77be4cuUK1q9fj8jISLz77rvYt28fGjdujNWrV8PZ2blAGaysrLBu3ToMGzYMX331FRo1aoQ2bdrgrbfekgKsZ23atAkKhQKrV6+Gra0tAgIC8H//938aj+yKsmLFCnzzzTcax77++mv069cPnp6esLKygoODg/T5cHBwKHCMiIjKF5PoQ/Ttt98iMDAQDRo0KDFtdHQ0LCws4O7uDgAICgrCsWPHkJWVJaXZv38/atWqhQoVKhiszKaiVq1aiI6OxunTpzFixAiEhobi8uXLWr/f2dlZaqE5evQoAgICMHz4cCxYsAARERG4fv06YmNjoVKpMHv27CKv06tXL9y6dQu//PILOnXqhCNHjqBRo0ZYt25doeljY2NRv359jRbDpk2balXmfv36ITo6WuP12muvaX3PVH64uso/B5GryhWuKk58ZDTGqHQyCUZtIUpNTcXVq1el/bi4OERHR6NixYrw8fEBoH40smXLlkJHKkVGRuL06dNo164dHB0dERkZiTFjxqB///5SsNO3b1/MmjULQ4cOxcSJE3Hx4kUsXboUixcvNvz9TU4t8pylhaXG/u1xt4tMa6HQjFtvjL7xXOV6mo2NDapXrw4ACAwMxJkzZ7B06VJ8/fXX8PT0RGZmJh4+fKjRSpSUlFRkS8natWvh4uKC7t27o2fPnujRowesra3Ru3dvTJ8+vdiy2NraokOHDujQoQOmTZuGd955BzNmzMCgQYP0dbsA1EFc3j2T+bK3B+7ckTlPG3vcGf9fply6Q37GqHQyGUYNiM6ePYt27dpJ+3n9dkJDQ6WWgc2bN0MIgbfffrvA+5VKJTZv3oyZM2ciIyMDfn5+GDNmjEb/H2dnZ+zbtw/h4eEIDAyEq6srpk+fjrCwMMPeHHTr02OotLrKzc1FRkYGAHWAZG1tjYMHD0pzP8XGxiI+Pl7qZ/S0O3fuYPbs2Thx4gQAdb+kvJa5rKws5OTk6FSWgICAIucdqlWrFjZu3IiMjAzp8eaZM2d0uj4REVEeowZEbdu2hShhcrKwsLAig5dGjRrh1KlTJeZTv359HD9+vFRlLM8mT56Mzp07w8fHB48ePcKmTZtw5MgR7N27F4A6mBw6dCjGjh2LihUrwsnJCaNGjUJQUBCaN29e4HoffPABPvzwQ7zwwgsAgBYtWuC7775Dx44dsWrVKrRo0aLQcty7dw+9e/fGkCFDUL9+fTg6OuLs2bOYP38+unfvXuh7+vbti6lTpyIsLAyTJk1CfHw8Fi5cCEA9gWNx0tPTpT5QeZRKJR+hEhGZMZPoVE2Gcfv2bQwcOBAJCQlwdnZG/fr1sXfvXnTo0EFKs3jxYlhYWKBXr17IyMhASEgIVqxYUeBae/fuxdWrV/Hdd99Jx0aOHImzZ8+iWbNmaNq0KWbMmFFoORwcHNCsWTMsXrwY165dQ1ZWFry9vTFs2DBMmTKl0Pc4OTlhx44dGDFiBBo2bIh69eph+vTp6Nu3b4GRiM9avXo1Vq9erXEsJCQEe/bsKfZ9VL48fgzkzfP566/yrHj/OOsxOkeoM/21zqeQIUt6mjEqnUyGQpTURENISUmBs7MzkpOT4eTkpHHuyZMniIuLg5+fX4lfxGRYERERGDx4MJKTk2En8x86fg5kdu4cEBioXpSsUaNSJUlLA/JmUEhNVXcveY7stJKWmSaNPk3tfAL2zVo+/0VJe7pUOpULxX1/P4stRGSyNmzYgKpVq+KFF17AH3/8gYkTJ6JPnz6yB0NERGT6GBCRyUpMTMT06dORmJgILy8v9O7dG3PmzDF2sYiIyAQxICKTNWHCBEyYMMHYxSAionLAJCZmJCIiIjIkBkRERERk9vjIjIjMlkplhDytjZAp5TNGpZNJYEBERGbJ3l49ClvWPG3skTblv0y5dIf8jFHpZDL4yIyIiIjMHluIiIiMKSam+POursB/i10TkeEwICKToVAosG3bNvTo0cOg+fz1118YNGgQoqOjUbt2bURHRxd6jEzbkyfAf2sW46efAG0mGC8pdgGKj1+eZD9Brx/Vmf7UfDFsVSqgf//iL6hSqTNmUPT8SlPpZDb4yMyMzZw5EwqFQuNVu3ZtjTRPnjxBeHg4KlWqBAcHB/Tq1QtJSUnS+fv376Nbt25wcHDASy+9hPPnz2u8Pzw8HJ9//nmJZblz5w5GjBgBHx8fKJVKeHp6IiQkBCdPnpTSJCQkoHPeOkSl1LZt2wL3rFAo8O6770ppZsyYAXt7e8TGxuLgwYNFHiPTlpMD7N6tfuXkFJ/W1VUdl/Tvr17Co7iXvz8QH19Enrk52H1lN3Zf2Y2cF19QBzpRUUW/Nm4E0tOBu3f1/wMwR7pUOpkdthCZuTp16uDAgQPSvpWV5kdizJgx2LVrF7Zs2QJnZ2eMHDkSPXv2lAKVOXPm4NGjRzh37hxWrlyJYcOG4ezZswCAU6dO4fTp0/jiiy9KLEevXr2QmZmJ9evXo2rVqkhKSsLBgwdx7949KY2np6c+bhnDhg3D7NmzNY6pnhp5cu3aNXTt2hW+vr7FHiPz4eOjjl1KiktiYtRB0927Wjbo+Piw5YeorBBUouTkZAFAJCcnFzj3+PFjcfnyZfH48WMjlOz5zJgxQzRo0KDI8w8fPhTW1tZiy5Yt0rGYmBgBQERGRgohhOjcubNYuXKlEEKIy5cvC5VKJYQQIjMzUzRo0ECcOXOmxHI8ePBAABBHjhwpNh0AsW3bNmn/5MmTokGDBkKpVIrAwECxbds2AUCcP3++yGu0adNGjB49utg8nn7NmDGj0GPPMuXPgUmKihICUP9byiSpqerzgHpbjmKlZqQKzITATIjUDC0y1eI+SQeGqHQq04r7/n4WH5kZUFpa0a8nT7RP+/ixdmlL48qVK6hcuTKqVq2Kfv36If6ptv6oqChkZWUhODhYOla7dm34+PggMjISANCgQQMcOnQI2dnZ2Lt3L+rXrw8AmD9/Ptq2bYvGjRuXWAYHBwc4ODhg+/btyMjI0KrcKSkp6NatG+rVq4dz587h448/xsSJE3W59UIlJCSgTp06+PDDD5GQkIBx48YVeoyIiMoXBkQG5OBQ9CuvX18ed/ei0z7bbaZKlcLT6apZs2ZYt24d9uzZg5UrVyIuLg6tWrXCo0ePAKgXT7WxsYGLi4vG+zw8PJCYmAgAmDRpEqysrFCtWjVs27YN3377La5cuYL169dj2rRpePfdd1G1alX06dMHycnJhZbDysoK69atw/r16+Hi4oIWLVpgypQpuHDhQpFl37RpExQKBVavXo2AgAB07twZ48eP1+q+V6xYIQVhea+IiAgA6sdyVlZWcHBwgKenp/Tvs8eIiKh8YUBkxjp37ozevXujfv36CAkJwe7du/Hw4UP8+OOPWl/D2dkZmzZtws2bN3H06FEEBARg+PDhWLBgASIiInD9+nXExsZCpVIV6LfztF69euHWrVv45Zdf0KlTJxw5cgSNGjXCunXrCk0fGxuL+vXrw/apUSJNmzbVqsz9+vVDdHS0xuu1117T+p6JiKj8YadqA0pNLfqcpaXm/u3bRae1eCZsvXGj1EUqlouLC2rWrImrV68CULeWZGZm4uHDhxqtRElJSUV2cF67di1cXFzQvXt39OzZEz169IC1tTV69+6N6dOnF5u/ra0tOnTogA4dOmDatGl45513MGPGDAwaNEhftwhAHcRVr15dr9ckIiLTxoDIgOztjZ9WF6mpqbh27RoGDBgAAAgMDIS1tTUOHjyIXv8944uNjUV8fDyCgoIKvP/OnTuYPXs2Tpw4AQDIyclBVlYWACArKws5Og5zDQgIwPbt2ws9V6tWLWzcuBEZGRlQKpUAgDNnzuh0fTJd8QnWuIuXgBi7ItOUNGeQvb26d62c7G3sIWbInCnlM0alk8lgQGTGxo0bh27dusHX1xe3bt3CjBkzYGlpibfffhuAuiVl6NChGDt2LCpWrAgnJyeMGjUKQUFBaN68eYHrffDBB/jwww/xwgsvAABatGiB7777Dh07dsSqVavQokWLQstx79499O7dG0OGDEH9+vXh6OiIs2fPYv78+ejevXuh7+nbty+mTp2KsLAwTJo0CfHx8Vi4cCEA9QSOxUlPT5f6QOVRKpWoUKFC8T8wKhPi4wH/NwKQjnOAFnMaurrKUy4iMm0MiMzYv//+i7fffhv37t2Dm5sbWrZsiVOnTsHNzU1Ks3jxYlhYWKBXr17IyMhASEgIVqxYUeBae/fuxdWrV/Hdd99Jx0aOHImzZ8+iWbNmaNq0KWbMmFFoORwcHNCsWTMsXrwY165dQ1ZWFry9vTFs2DBMmTKl0Pc4OTlhx44dGDFiBBo2bIh69eph+vTp6Nu3r0a/osKsXr0aq1ev1jgWEhKCPXv2FPs+kkl8fLET/tyNsUP6E39sRD/4b/xIPRNiEbjqBRFpSyEE2w9LkpKSAmdnZyQnJ8PJyUnj3JMnTxAXFwc/P78Sv4jJsCIiIjB48GAkJyfDzq7oRymGwM+BnsTHqwOc9PQik5zDSwjEOUTZtkCj2O9LHfE8eQL893QY332nn1Uczp1Tz1YdFQU0alRIntlPMGCbOtPvXv8OtlYlZFrSBUk3hqh0KtOK+/5+FluIyGRt2LABVatWxQsvvIA//vgDEydORJ8+fWQPhkiP7t5VB0MbNxbd8hNjp35U9r//AT5epc4qJ0d9CQAoYjCj3uXk5uB/l9WZrusuU6aUzxiVTiaDARGZrMTEREyfPh2JiYnw8vJC7969MWfOHGMXi/TB37/kFhGv0gdDRETPYkBEJmvChAmYMGGCsYvxXEroLgOA/WCIiOTAgIjISLToLgNAPVIqJqbkoEib4ApggEVEVBgGRHrCvunmrTT1r1V3GS1XT9c2uAK0D7CIiMwJA6LnZG1tDUA9tw0785qv9P8ikbzPgy606S5TEm2CK0D7AIuIyNwwIHpOlpaWcHFxwe3/1t5QqVQlTgxI5YcQAunp6bh9+zZcXFxg+eyaLHpS0qzLeef1EVwREZkjowZEx44dw4IFCxAVFYWEhARs27YNPXr0kM4PGjQI69ev13jPsxPo3b9/H6NGjcKOHTukCQSXLl2qsSL5hQsXEB4ejjNnzsDNzQ2jRo3Sa2fcvHW9bhe3IBmVay4uLkWu7/Y8XF3Vj7j6lzAjM8BZmXWlUuWvN6hSyZSntQqpk1OlbZKZMSqdTIZRA6K0tDQ0aNAAQ4YMQc+ePQtN06lTJ6xdu1baz1u3Kk+/fv2QkJCA/fv3IysrC4MHD0ZYWBg2bdoEQD0pU8eOHREcHIyvvvoKf/75J4YMGQIXFxeEhYXp5T4UCgW8vLzg7u4urd1F5sPa2tpgLUM+PurWH3aW1j+FwnDrAhadpwL2NjJnSvmMUelkMnQOiNavXw9XV1d07doVgHro86pVqxAQEIDvv/8evr6+Wl+rc+fO6Ny5c7FplEplkf/zjomJwZ49e3DmzBk0btwYALBs2TJ06dIFCxcuROXKlREREYHMzEysWbMGNjY2qFOnDqKjo7Fo0SK9BUR5LC0tDfbFSObLx4eBDhGRoekcEH366adYuXIlACAyMhLLly/H4sWLsXPnTowZMwZbt27VawGPHDkCd3d3VKhQAa+88go++eQTVKpUScrfxcVFCoYAIDg4GBYWFjh9+jRef/11REZGonXr1rCxsZHShISE4LPPPsODBw8KXdAzIyMDGRkZ0n5KSope74nI2ErqkwTot8VJ6ykBEqwhV+yXkQEMH67e/vpr4JnGZ8PkmZ2B4TvVmX796tdQWsmQKeUzRqWTydA5IPrnn39QvXp1AMD27dvRq1cvhIWFoUWLFmjbtq1eC9epUyf07NkTfn5+uHbtGqZMmYLOnTsjMjISlpaWSExMhLu7u8Z7rKysULFiRWk188TERPj5+Wmk8fDwkM4VFhDNnTsXs2bN0uu9UPlg6nP96NonaetW4Km1fgu9njbzI2k9JYBtAGLgLUtQlJ0N5HVRXL5cnu/G7NxsrP9DnenyLsuhBL+QZWWMSieToXNA5ODggHv37sHHxwf79u3D2LFjAQC2trZ4/PixXgv31ltvSdv16tVD/fr1Ua1aNRw5cgTt27fXa15Pmzx5snRfgLqFyNvb22D5kWkoD3P9aNsn6c4doGdPoFOn4tNpc5+6TQlgibtwla2ViIgoj84BUYcOHfDOO+/gpZdewt9//40uXboAAC5duoQqVarou3waqlatCldXV1y9ehXt27eHp6dngZFd2dnZuH//vtTvyNPTE0lJSRpp8vaL6pukVCoLdN4mKi9z/WjbJ6mkwEnX++SUAERUlukcEC1fvhwfffQR/vnnH/z0009Sf56oqCi8/fbbei/g0/7991/cu3cPXv8t6hgUFISHDx8iKioKgYGBAIBDhw4hNzcXzZo1k9JMnToVWVlZ0qR5+/fvR61atQp9XEZUEm2/2LWdO6is0iVwep7zRERlgc4BkYuLC7788ssCx0vT5yY1NRVXr16V9uPi4hAdHY2KFSuiYsWKmDVrFnr16gVPT09cu3YNEyZMQPXq1RESEgIA8Pf3R6dOnTBs2DB89dVXyMrKwsiRI/HWW2+hcuXKAIC+ffti1qxZGDp0KCZOnIiLFy9i6dKlWLx4sc7lJdKGucwdZC73SUTmoVTzEB0/fhxff/01rl+/ji1btuCFF17Ad999Bz8/P7Rs2VLr65w9exbt2rWT9vP67YSGhmLlypW4cOEC1q9fj4cPH6Jy5cro2LEjPv74Y43HWRERERg5ciTat28vTcz4xRdfSOednZ2xb98+hIeHIzAwEK6urpg+fbreh9wT5TGXuYPM5T6JyDzoHBD99NNPGDBgAPr164dz585Jw9OTk5Px6aefYvfu3Vpfq23btsUuirl3794Sr1GxYkVpEsai1K9fH8ePH9e6XETPy1zmDjKX+ySi8s9C1zd88skn+Oqrr7B69WqNhSxbtGiBc+fO6bVwRESGolIBt2+rX3Iu3XF73G3cHnebS3cYgzEqnUyGzi1EsbGxaN26dYHjzs7OePjwoT7KRERmLAb+QIxd0ef11ElboSh+jiVDUCgUcLOXOVPKZ4xKJ5Ohc0Dk6emJq1evFhhif+LECVStWlVf5SIiM+PqCqhsc9D/SQRQQkdtdtImIn3TOSAaNmwYRo8ejTVr1kChUODWrVuIjIzEuHHjMG3aNEOUkYjMgI8PEPO/y7j7aiiwMaLYyZ700Uk7IwPIm3910SL5lu4Yu1ed6aKQRVy6Q27GqHQyGToHRJMmTUJubi7at2+P9PR0tG7dGkqlEuPGjcOoUaMMUUYiMhM+XlnwwXnA/zFg4Ekcs7OBFSvU2/Pny7d0x4qz6kznd5jPpTvkZoxKJ5Ohc0CkUCgwdepUjB8/HlevXkVqaioCAgLg4OBgiPIRERERGVyp5iECABsbGwQEBOizLERERERGoVVA1LNnT60vuHXr1lIXhoiIiMgYtAqInJ2dDV0OIiIiIqPRKiBau3atoctBREREZDQ6z1QdFxeHK1euFDh+5coV3LhxQx9lIiIiIpKVzgHRoEGD8NtvvxU4fvr0aQwaNEgfZSIiMjg7OyAuTv2yK3pibP3maW2HuNFxiBsdBztrmTKlfMaodDIZOo8yO3/+PFq0aFHgePPmzTFy5Ei9FIqIyqH4eODu3eLT6GtdDi1YWADPTLhv+DwVFqjiInOmlM8YlU4mo1TzED169KjA8eTkZOTk5OilUERUzsTHq2eeTk8vOS3X5SAiI9A5IGrdujXmzp2L77//HpaWlgCAnJwczJ07Fy1bttR7AYmoHLh7Vx0MbdxY7JIcAPSzLocWMjOBqVPV23PmADY2Bs8SmTmZmHpQnemc9nNgYylDppTPGJVOJkPngOizzz5D69atUatWLbRq1QoAcPz4caSkpODQoUN6LyARlSP+/kAjA6/JoaWsLGDhQvX2zJnyfDdm5WRhYaQ605ltZzIgkpsxKp1Mhs4BUUBAAC5cuIAvv/wSf/zxB+zs7DBw4ECMHDkSFStWNEQZiQyujHVvISIimZVq6Y7KlSvj008/1XdZiIyC3VueE6PJAoq63cfZ+dv//APUriZPeYioZFoFRBcuXEDdunVhYWGBCxcuFJu2fv36eikYkVzKYPcW08FoUoOrq/o2+/cvIoE1gP+6sDQKBP66wM8TUVmhVUDUsGFDJCYmwt3dHQ0bNoRCoYAQokA6hULBkWZksspQ9xbTwWhSg4+PunWoqAazx9lAy1//205XpyvnPxIik6FVQBQXFwc3Nzdpm4hIA6NJiY9P0UFOWiaAX2UtDhFpSauAyNfXV9q+efMmXn75ZVhZab41Ozsbv/32m0ZaIiIiIlOgc6fqdu3aISEhAe7u7hrHk5OT0a5dOz4yozKnpD6/Ztbfl/5jZwdcvJi/LUue1na4OOIiLscAfWZx6QjZGaPSyWToHBAJIaBQKAocv3fvHuzt7fVSKCJ90bbPrxn096VnWFgAderInKfCAnXc6yDjXwAFu2GSoRmj0slkaB0Q9ezZE4C64/SgQYOgVCqlczk5Obhw4QJefvll/ZeQ6Dlo2+fXDPr7EhFRMbQOiJydnQGoW4gcHR1h91Rzo42NDZo3b45hw4bpv4REesA+v/SszEwgbzq1KVPkW7rj0+OfIiEBgOUUAJwpWVbGqHQyGVoHRGvXrpWG2i9btgwODg4GKxQRkaFlZQGzZqm3x4+Xb+mOWUf/y9RiPBgQycwYlU4mQ6c+REIIREREYMqUKahRo4ahykREZQFnoCYiM6JTQGRhYYEaNWrg3r17DIiIyjPOQE1EZkbnUWbz5s3D+PHjsXLlStStW9cQZSIiY+MM1ERkZnQOiAYOHIj09HQ0aNAANjY2Gp2rAeD+/ft6KxwRGRl7oxORmdA5IFqyZIneMj927BgWLFiAqKgoJCQkYNu2bejRowcAICsrCx999BF2796N69evw9nZGcHBwZg3bx4qV64sXaNKlSq4efOmxnXnzp2LSZMmSfsXLlxAeHg4zpw5Azc3N4waNQoTJkzQ230QERGRadM5IAoNDdVb5mlpaWjQoAGGDBkizXOUJz09HefOncO0adPQoEEDPHjwAKNHj8Zrr72Gs2fPaqSdPXu2xpB/R0dHaTslJQUdO3ZEcHAwvvrqK/z5558YMmQIXFxcEBYWprd7ISIiItOlc0D0tCdPniAzM1PjmJOTk9bv79y5Mzp37lzoOWdnZ+zfv1/j2JdffommTZsiPj4ePk/1WXB0dISnp2eh14mIiEBmZibWrFkDGxsb1KlTB9HR0Vi0aBEDIiIzZmsL/P57/rYseVrZ4vd3fsdfscDAbJkypXzGqHQyGRa6viEtLQ0jR46Eu7s77O3tUaFCBY2XISUnJ0OhUMDFxUXj+Lx581CpUiW89NJLWLBgAbKzs6VzkZGRaN26NWyemm8iJCQEsbGxePDgQaH5ZGRkICUlReNFROWLpSXQpIn6ZWkpU54WlmjyQhPUcWkCCJkypXzGqHQyGToHRBMmTMChQ4ewcuVKKJVKfPPNN5g1axYqV66MDRs2GKKMANStURMnTsTbb7+t0Qr1/vvvY/PmzTh8+DCGDx+OTz/9VKN/UGJiIjw8PDSulbefmJhYaF5z586Fs7Oz9PL29jbAHREREVFZofMjsx07dmDDhg1o27YtBg8ejFatWqF69erw9fVFREQE+vXrp/dCZmVloU+fPhBCYOXKlRrnxo4dK23Xr18fNjY2GD58OObOnaux3pouJk+erHHdlJQUBkVE5UxmJrB0qXp79Gj5lu5Yemop/u//AFiOBmeqlpkxKp1Mhs4B0f3791G1alUA6v5CecPsW7ZsiREjRui3dMgPhm7evIlDhw6V2EepWbNmyM7Oxo0bN1CrVi14enoiKSlJI03eflH9jpRKZamDKSIyDVlZQF5j8nvvybd0x4QD/2Vq8R60Doi0mRGc80GVzBiVTiZD54CoatWqiIuLg4+PD2rXro0ff/wRTZs2xY4dOwr07XleecHQlStXcPjwYVSqVKnE90RHR8PCwgLu7u4AgKCgIEydOhVZWVmwtrYGAOzfvx+1atUyeJ8nIqLn4uqqngm8f/+S06pU6sCJQRFRqegcEA0ePBh//PEH2rRpg0mTJqFbt2748ssvkZWVhUWLFul0rdTUVFy9elXaj4uLQ3R0NCpWrAgvLy+88cYbOHfuHHbu3ImcnBypz0/FihVhY2ODyMhInD59Gu3atYOjoyMiIyMxZswY9O/fXwp2+vbti1mzZmHo0KGYOHEiLl68iKVLl2Lx4sW63joRkbx8fNRBjjZryvXvr07HgIioVHQOiMaMGSNtBwcH46+//kJUVBSqV6+O+vXr63Sts2fPol27dtJ+Xr+d0NBQzJw5E7/88gsAoGHDhhrvO3z4MNq2bQulUonNmzdj5syZyMjIgJ+fH8aMGaPR/8fZ2Rn79u1DeHg4AgMD4erqiunTp3PIPRGZBh8fBjlEMtA6IMrNzcWCBQvwyy+/IDMzE+3bt8eMGTPg6+sLX1/fUmXetm1bCCGKPF/cOQBo1KgRTp06VWI+9evXx/Hjx3UuHxEREZkHrYfdz5kzB1OmTIGDgwNeeOEFLF26FOHh4YYsGxEREZEstA6INmzYgBUrVmDv3r3Yvn07duzYgYiICOTm5hqyfEREREQGp/Ujs/j4eHTp0kXaDw4OhkKhwK1bt/Diiy8apHBEZCDx8cV31NVmmLeJs7UFDh/O35YlTytbHA49jL//BoZz6Q75GaPSyWRoHRBlZ2fD9pkPkLW1NbKysvReKCIyoPh4wN8fSE8vPp1KpR72XU5ZWgJt28qcp4Ul2lZpC6f7AIrvIkmGYIxKJ5OhdUAkhMCgQYM0Jix88uQJ3n33Xdjb20vHtm7dqt8SEpF+3b2rDoY2blQHRkXhRH9EZEa0DohCQ0MLHOuvzWRhRFQ2+fsDjRoZuxRGk5UFrFql3g4LA/6bt9WweeZkYVXUKvzzDwCLMAAyZEr5jFHpZDK0DojWrl1ryHIQEckqMxMYOVK9PWiQPN+NmTmZGPnrf5laDgIDIpkZo9LJZOi82j0RERFRecOAiIiIiMyezkt3EBGRfpQ0uwH7tRPJhwERmaySptIBzGI6HTJRdlosYs8F7Inko1VA1KhRIxw8eBAVKlTA7NmzMW7cOKhUKkOXjahI2k6lA5T76XTIRJ2LAtKTiz7PBeyJ5KVVQBQTE4O0tDRUqFABs2bNwrvvvsuAiIxK26l0AD52oLLJ2xuwr2bsUhBRHq0CooYNG2Lw4MFo2bIlhBBYuHAhHBwcCk07ffp0vRaQqDhmPpVOQXyOqDWlEti5M39bljytlNj59k5pm2RmjEonk6FVQLRu3TrMmDEDO3fuhEKhwK+//gorq4JvVSgUDIiIjIXPEXViZQV07SpznhZW6FpT5kwpnzEqnUyGVgFRrVq1sHnzZgCAhYUFDh48CHd3d4MWjMwXGzlKic8RiYhKTedRZrm5uYYoBxEANnLoBZ8jaiUrC4iIUG/36yff0h0Rf6oz7VevH6wtOVOyrIxR6WQySjXs/tq1a1iyZAli/vtvekBAAEaPHo1q1dhDkJ4PGzlILpmZwODB6u3eveVbumPwz+pMewf0ZkAkN2NUOpkMnQOivXv34rXXXkPDhg3RokULAMDJkydRp04d7NixAx06dNB7Icn8sJGDiIjkpHNANGnSJIwZMwbz5s0rcHzixIkMiIiIiMjk6LyWWUxMDIYOHVrg+JAhQ3D58mW9FIqIiIhITjoHRG5uboiOji5wPDo6miPPiIiIyCTp/Mhs2LBhCAsLw/Xr1/Hyyy8DUPch+uyzzzB27Fi9F5CIiIjI0HQOiKZNmwZHR0d8/vnnmDx5MgCgcuXKmDlzJt5//329F5CIiIjI0HQOiBQKBcaMGYMxY8bg0aNHAABHR0e9F4yIyJCUSuDHH/O3ZcnTSokf3/hR2iaZGaPSyWSUah6iPAyEiMhUWVmpp6KRNU8LK/SuI3OmlM8YlU4mQ+dO1URERETlzXO1EBGRTLjAm95lZwPbtqm3X39d3Xhg8Dxzs7EtRp3p6/6vw8qCf4JlZYxKJ5PBTwNRWccF3gwiIwPo00e9nZoqz3djRnYG+vxPnWnq5FRY2eg5U22CYnNe88YYlU4mQ6dPQ1ZWFjp16oSvvvoKNWrUMFSZiOhpXOCNSuLqqg6G+/cvOa1KpQ6c+DkhuWjTwg0Y/e+XTgGRtbU1Lly4oLfMjx07hgULFiAqKgoJCQnYtm0bevToIZ0XQmDGjBlYvXo1Hj58iBYtWmDlypUawdj9+/cxatQo7NixAxYWFujVqxeWLl0KBwcHKc2FCxcQHh6OM2fOwM3NDaNGjcKECRP0dh9EsuACb1QUHx91kKPNY9X+/dXpGBCRHHRt4TZisK5ze2H//v3x7bffFljLrDTS0tLQoEEDDBkyBD179ixwfv78+fjiiy+wfv16+Pn5Ydq0aQgJCcHly5dha2sLAOjXrx8SEhKwf/9+ZGVlYfDgwQgLC8OmTZsAACkpKejYsSOCg4Px1Vdf4c8//8SQIUPg4uKCsLCw574HIqIywceHQQ6VPdq2cJeBYF3ngCg7Oxtr1qzBgQMHEBgYCHt7e43zixYt0vpanTt3RufOnQs9J4TAkiVL8NFHH6F79+4AgA0bNsDDwwPbt2/HW2+9hZiYGOzZswdnzpxB48aNAQDLli1Dly5dsHDhQlSuXBkRERHIzMzEmjVrYGNjgzp16iA6OhqLFi1iQERERCQHE2jh1nnY/cWLF9GoUSM4Ojri77//xvnz56VXYWuclVZcXBwSExMRHBwsHXN2dkazZs0QGRkJAIiMjISLi4sUDAFAcHAwLCwscPr0aSlN69atYWNjI6UJCQlBbGwsHjx4oLfyEhERkenSuYXo8OHDhihHAYmJiQAADw8PjeMeHh7SucTExAILylpZWaFixYoaafz8/ApcI+9chQoVCuSdkZGBjIwMaT8lJeU574aIiIjKslKPObx69SquXbuG1q1bw87ODkIIKBQKfZbNaObOnYtZs2YZuxhEZEA2NsDatfnbsuRpaYO13ddK2yQzY1Q6mQydA6J79+6hT58+OHz4MBQKBa5cuYKqVati6NChqFChAj7//HO9FMzT0xMAkJSUBC8vL+l4UlISGjZsKKW5ffu2xvuys7Nx//596f2enp5ISkrSSJO3n5fmWZMnT8bYsWOl/ZSUFHh7ez/fDRFRmWJtDQwaJHOeltYY1FDmTCmfMSqdTIbOfYjGjBkDa2trxMfHQ6VSScfffPNN7NmzR28F8/Pzg6enJw4ePCgdS0lJwenTpxEUFAQACAoKwsOHDxEVFSWlOXToEHJzc9GsWTMpzbFjx5CVlSWl2b9/P2rVqlXo4zIAUCqVcHJy0ngRERFR+aVzQLRv3z589tlnePHFFzWO16hRAzdv3tTpWqmpqYiOjpY6Y8fFxSE6Ohrx8fFQKBT44IMP8Mknn+CXX37Bn3/+iYEDB6Jy5crSXEX+/v7o1KkThg0bht9//x0nT57EyJEj8dZbb6Fy5coAgL59+8LGxgZDhw7FpUuX8MMPP2Dp0qUaLUBEZH6ys4Fdu9Sv7GyZ8szNxq6/d2HX37uQnStTppTPGJVOJkPnR2ZpaWkaLUN57t+/D6VSqdO1zp49i3bt2kn7eUFKaGgo1q1bhwkTJiAtLQ1hYWF4+PAhWrZsiT179khzEAFAREQERo4cifbt20sTM37xxRfSeWdnZ+zbtw/h4eEIDAyEq6srpk+fziH3RGYuIwN49VX1tpxLd7z6vTpTgyzdQcUzRqWTydD509CqVSts2LABH3/8MQBAoVAgNzcX8+fP1whutNG2bVsIIYo8r1AoMHv2bMyePbvINBUrVpQmYSxK/fr1cfz4cZ3KRkREROZD54Bo/vz5aN++Pc6ePYvMzExMmDABly5dwv3793Hy5ElDlJGIiIjIoHTuQ1S3bl38/fffaNmyJbp37460tDT07NkT58+fR7Vq1QxRRiIiIiKDKtUDVGdnZ0ydOlXfZSEiIiIyilIFRA8ePMC3336LmJgYAEBAQAAGDx6MihUr6rVwRERERHLQ+ZHZsWPHUKVKFXzxxRd48OABHjx4gC+++AJ+fn44duyYIcpIREREZFA6txCFh4fjzTffxMqVK2FpaQkAyMnJwXvvvYfw8HD8+eefei8kEZG+2dgAX36Zvy1LnpY2+LLzl9I2ycwYlU4mQ+eA6OrVq/jf//4nBUMAYGlpibFjx2LDhg16LRwRkaFYWwPh4TLnaWmN8KYyZ0r5jFHpZDJ0fmTWqFEjqe/Q02JiYtCgQQO9FIqIiIhITlq1EF24cEHafv/99zF69GhcvXoVzZs3BwCcOnUKy5cvx7x58wxTSiIiPcvJAfLma23VCniq0dtweebm4Hi8OtNWPq1gaSFDppTPGJVOJkOrgKhhw4ZQKBQas0pPmDChQLq+ffvizTff1F/piIgM5MkTIG9y/dRUwN5ehjyzn6DdenWmqZNTYW8jQ6aUzxiVTiZDq4AoLi7O0OUgMk/x8cDdu8WnKeQRNRER6ZdWAZGvr6+hy0FkfuLjAX9/ID295LQqFeDqavgyERGZqVJNzHjr1i2cOHECt2/fRm5ursa5999/Xy8FIyr37t5VB0MbN6oDo+K4ugI+PvKUi4jIDOkcEK1btw7Dhw+HjY0NKlWqBIVCIZ1TKBQMiIh05e8PNGpk7FIQEZk1nQOiadOmYfr06Zg8eTIsLHQetU9ERERU5ugcEKWnp+Ott95iMEQ6Y/9hIiIqq3QOiIYOHYotW7Zg0qRJhigPlVPsP0xljbU1MH9+/rYseVpaY37wfGmbZGaMSieToXNANHfuXLz66qvYs2cP6tWrB+tnPlSLFi3SW+Go/GD/YSprbGyA8eNlztPSBuNbyJwp5TNGpZPJKFVAtHfvXtSqVQsACnSqJioO+w8TEVFZpHNA9Pnnn2PNmjUYNGiQAYpDRCSPnBzg3Dn1dqNG8i3dcS5BnWkjr0ZcukNuxqh0Mhk6B0RKpRItWrQwRFmIiGTz5AnQtKl6W86lO5p+o86US3cYgTEqnUyGzkPFRo8ejWXLlhmiLERERERGoXML0e+//45Dhw5h586dqFOnToFO1Vu3btVb4YiIyAC0md+CoxvIzOgcELm4uKBnz56GKAsRERmSq6t6Xov+/UtOq1KpAycGRWQmdA6I1q5da4hyEBGRofn4qIMcbWZI7d9fnY4BEZmJUi3uSkREJsrHh0EOUSF0Doj8/PyKnW/o+vXrz1UgIiLKx+4+RPLQOSD64IMPNPazsrJw/vx57NmzB+M5AygRmQhra2DGjPxtWfK0tMaMNjOk7eKwu48BGKPSyWToHBCNHj260OPLly/H2bNnn7tAROUCV7It82xsgJkzZc7T0gYz22qXKbv7GIAxKp1Mht76EHXu3BmTJ09mp2sirmRLesLuPkTy0VtA9L///Q8VK1bU1+WITBdXsjUJubn5jXT+/oCFztPUliJPkYuYO+pM/d38YaGQIVPKZ4xKJ5Ohc0D00ksvaXSqFkIgMTERd+7cwYoVK/RaOACoUqUKbt68WeD4e++9h+XLl6Nt27Y4evSoxrnhw4fjq6++kvbj4+MxYsQIHD58GA4ODggNDcXcuXNhZcVBdmRAXMm2THv8GKhbV70t1yoOj7Meo+5KdaZcusMIjFHpZDJ0jgh69OihsW9hYQE3Nze0bdsWtWvX1le5JGfOnEFOTo60f/HiRXTo0AG9e/eWjg0bNgyzZ8+W9lUqlbSdk5ODrl27wtPTE7/99hsSEhIwcOBAWFtb49NPP9V7eYmIiMj06BwQzcjroS8TNzc3jf158+ahWrVqaNOmjXRMpVLB09Oz0Pfv27cPly9fxoEDB+Dh4YGGDRvi448/xsSJEzFz5kzY2NgYtPxERERU9pnUA9TMzExs3LgRQ4YM0XhsFxERAVdXV9StWxeTJ09G+lOdWSMjI1GvXj14eHhIx0JCQpCSkoJLly4Vmk9GRgZSUlI0XkRERFR+ad1CZGFhUeyEjACgUCiQnZ393IUqyvbt2/Hw4UMMGjRIOta3b1/4+vqicuXKuHDhAiZOnIjY2FhpkdnExESNYAiAtJ+YmFhoPnPnzsWsWbMMcxNERERU5mgdEG3btq3Ic5GRkfjiiy+Qm5url0IV5dtvv0Xnzp1RuXJl6VhYWJi0Xa9ePXh5eaF9+/a4du0aqlWrVqp8Jk+ejLFjx0r7KSkp8Pb2Ln3BiYiIqEzTOiDq3r17gWOxsbGYNGkSduzYgX79+ml0bNa3mzdv4sCBA1LLT1GaNWsGALh69SqqVasGT09P/P777xppkpKSAKDIfkdKpRJKpVIPpSYiIiJTUKpx57du3cKMGTOwfv16hISEIDo6GnXzhjIayNq1a+Hu7o6uXbsWmy46OhoA4OXlBQAICgrCnDlzcPv2bbi7uwMA9u/fDycnJwQEBBi0zERUdllbA+PG5W/LkqelNcYFjZO2SWbGqHQyGToFRMnJyfj000+xbNkyNGzYEAcPHkSrVq0MVTZJbm4u1q5di9DQUI25g65du4ZNmzahS5cuqFSpEi5cuIAxY8agdevWqF+/PgCgY8eOCAgIwIABAzB//nwkJibio48+Qnh4OFuBiMyYjQ2wYIHMeVraYEFHmTOlfMaodDIZWgdE8+fPx2effQZPT098//33hT5CM5QDBw4gPj4eQ4YM0ThuY2ODAwcOYMmSJUhLS4O3tzd69eqFjz76SEpjaWmJnTt3YsSIEQgKCoK9vT1CQ0MN+niPiIiITIvWAdGkSZNgZ2eH6tWrY/369Vi/fn2h6Urq41MaHTt2hBCiwHFvb+8Cs1QXxtfXF7t379Z7uYjIdOXmqpedA9Srp8i1dEd8sjpTH2cfLt0hN2NUOpkMrQOigQMHljjsnojIVDx+DPj5qbflXLrDb6k6Uy7dYQTGqHQyGVoHROvWrTNgMcjUxcer1zQtSt56ikRkQrT5xeUCxVROcHVTem7x8ep1TJ+aILxQKpX6bycRlXGurupf2P79S06rUqkDJwZFZOIYENFzu3tXHQxt3KgOjIpSLv4jWVJTGMDmMDJ9Pj7qz7E2n/X+/dXpTP6Xm8wdAyLSG39/oFEjY5fCgLRtCgPYHEamz8eHQQ6ZFQZERNrStikMKCfNYURE5oMBEZGuyn1TGBGR+WFARERmycoKeO+9/G1Z8rSwwnuN35O2SWbGqHQyGfxEEJFZUiqB5ctlztNKieVdZc6U8hmj0slkcJpOIiIiMntsISIisyRE/qhyV1dAjon4hRC4m67O1FXlytn/5WaMSieTwYCIiMxSejrg7q7elmsVh/SsdLgvVGfKpTuMwBiVTiaDj8yIiIjI7DEgIiIiIrPHgIiIiIjMHgMiIiIiMnsMiIiIiMjsMSAiIiIis8dh90RklqysgNDQ/G1Z8rSwQmiDUGmbZGaMSieTwU8EEZklpRJYt07mPK2UWNdD5kzlEBNT/HlXV8DHR56yFMcYlU4mgwERERGVjqsroFIB/fsXn06lUgdNZSEoIioCAyIiMktCqCcuBtTf13It3ZGepc5UZa0y/aU7fHzUgU7echiFiYlRB0x37xo/IDJGpZPJYEBERGYpPR1wcFBvy7l0h8NcdablZukOHx/jBzraMkalk8ngKDMiIiIye2whIsoTH19y0z8REZVLDIiIAHUw5O+f37+gKCqVuiMpERGVKwyIiAB1y1B6OrBxozowKkpZGT5MZGq0aWHl7xcZEQMioqf5+wONGhm7FETlh7ZD8wEOzyejYkBERESGo83QfKBsDc8ns8SAiIjMkqUl8MYb+duy5GlhiTcC3pC2zUZZGZpvjEonk1Gmh93PnDkTCoVC41W7dm3p/JMnTxAeHo5KlSrBwcEBvXr1QlJSksY14uPj0bVrV6hUKri7u2P8+PHIzs6W+1aIqIyxtQW2bFG/bG1lytPKFlt6b8GW3ltga6XfTGNigHPnin/Fx+s1S9NjjEonk1HmW4jq1KmDAwcOSPtWTy3IN2bMGOzatQtbtmyBs7MzRo4ciZ49e+LkyZMAgJycHHTt2hWenp747bffkJCQgIEDB8La2hqffvqp7PdCRKRv7KJDpB9lPiCysrKCp6dngePJycn49ttvsWnTJrzyyisAgLVr18Lf3x+nTp1C8+bNsW/fPly+fBkHDhyAh4cHGjZsiI8//hgTJ07EzJkzYWNjI/ftEBHpFbvoEOlHmX5kBgBXrlxB5cqVUbVqVfTr1w/x/7X5RkVFISsrC8HBwVLa2rVrw8fHB5GRkQCAyMhI1KtXDx4eHlKakJAQpKSk4NKlS/LeCBGVKWlp6qWsFAr1tix5ZqZBMUsBxSwF0jL1l6mPj3pwZHGv4maTMBvGqHQyGWW6hahZs2ZYt24datWqhYSEBMyaNQutWrXCxYsXkZiYCBsbG7i4uGi8x8PDA4mJiQCAxMREjWAo73zeuaJkZGQgIyND2k9JSdHTHREREVFZVKYDos6dO0vb9evXR7NmzeDr64sff/wRdnZ2Bst37ty5mDVrlsGuT0RERGVLmX9k9jQXFxfUrFkTV69ehaenJzIzM/Hw4UONNElJSVKfI09PzwKjzvL2C+uXlGfy5MlITk6WXv/8849+b4SIiIjKFJMKiFJTU3Ht2jV4eXkhMDAQ1tbWOHjwoHQ+NjYW8fHxCAoKAgAEBQXhzz//xO3bt6U0+/fvh5OTEwICAorMR6lUwsnJSeNFRERE5VeZfmQ2btw4dOvWDb6+vrh16xZmzJgBS0tLvP3223B2dsbQoUMxduxYVKxYEU5OThg1ahSCgoLQvHlzAEDHjh0REBCAAQMGYP78+UhMTMRHH32E8PBwKJVKI9+daShpAXiAi8ATEZHpK9MB0b///ou3334b9+7dg5ubG1q2bIlTp07Bzc0NALB48WJYWFigV69eyMjIQEhICFasWCG939LSEjt37sSIESMQFBQEe3t7hIaGYvbs2ca6JZOi7QLwABeBJyIi01amA6LNmzcXe97W1hbLly/H8uXLi0zj6+uL3bt367toZkHbBeABLlJNpsfSEujSJX9bljwtLNGlRhdpm2RmjEonk1GmAyIqG7gAPJVHtrbArl0y52lli119Zc6U8hmj0slkmFSnaiIiIiJDYAsRERGVHdqM0uAzejIABkRU/nGoHBUiLQ1wd1dv374N2NvLkGdmGtwXqjO9Pe427G1kyNRUyLFKrTEqnUwGAyIq3zhUjoqhzcdC73lmGSFTUyDXKrXGqHQyCQyIqHzjUDki0+Hjw99BMhoGRGQeOFSOiIiKwYCIiIhMDztfk54xICIiItMhR+drMksMiIiIyHTI1fmazA4DIiIySxYWQJs2+duy5KmwQBvfNtI2lVJpO18bo9LJZDAgIiKzZGcHHDkic57WdjgySOZMKZ8xKp1MBkNkIiIiMnsMiIiIiMjsMSAiIrOUlga4ualfaWky5ZmZBrcFbnBb4Ia0TJkypXzGqHQyGexDRERmq6SBSgbJM90ImVI+Y1Q6mQS2EBEREZHZY0BEREREZo8BEREREZk99iEi0xUfr91stURERCVgQESmKT5evYJ9enrJaVUq9fpHRERERWBARKbp7l11MLRxozowKg5XvKZCWFgAjRvnb8uSp8ICjSs3lrZJZkVVujatzQD/lpRzDIjItPn7A40aGbsUZILs7IAzZ2TO09oOZ4bJnKm5e/ax+ddfax6/cwfo2VP71uaYGAZF5RQDIiIiKn9cXdUBTP/+JadVqYA9e9QTNhYlJkZ9rbt3GRCVUwyIiIjMiDbjDMrFkyEfH/XN8lEYaYkBERGZpfR0ICBAvX35srqRwOB5ZqUjYLk608vhl6GyliHT/+jaYFIungz5+GjehDEqnUwGAyIiMktCADdv5m/Lk6fAzeSb0ractG0wKddPhoxR6eVZOZv6hAEREZGZeLbBhEqhpC94c3n8Vg6nPmFAREREVBJtnzmWm+eNJSiHU58wICIiIiqJNs8cy/XzxiKUo6lPGBARERFpg88cy7UyPVXq3Llz0aRJEzg6OsLd3R09evRAbGysRpq2bdtCoVBovN59912NNPHx8ejatStUKhXc3d0xfvx4ZGdny3krRERE+eLjgXPnSn7Fxxu7pGajTLcQHT16FOHh4WjSpAmys7MxZcoUdOzYEZcvX4a9vb2UbtiwYZg9e7a0r3pqKGVOTg66du0KT09P/Pbbb0hISMDAgQNhbW2NTz/9VNb7IaKyQ6HIH4GtUMiVpwIBbgHSNsnMGJVeGF07JJtDn6QyoEwHRHv27NHYX7duHdzd3REVFYXWrVtLx1UqFTw9PQu9xr59+3D58mUcOHAAHh4eaNiwIT7++GNMnDgRM2fOhI2NjUHvoawqZ6MliXSmUgGXLsmcp7UKl96TOVPKZ4xKL4y2HZLNsU+SEZXpgOhZycnJAICKFStqHI+IiMDGjRvh6emJbt26Ydq0aVIrUWRkJOrVqwcPDw8pfUhICEaMGIFLly7hpZdeKpBPRkYGMjIypP2UlBRD3I7RlMPRkkREpqccdUguD0wmIMrNzcUHH3yAFi1aoG7dutLxvn37wtfXF5UrV8aFCxcwceJExMbGYuvWrQCAxMREjWAIgLSfmJhYaF5z587FrFmzDHQnxlfmR0uy+YqIiGRmMgFReHg4Ll68iBMnTmgcDwsLk7br1asHLy8vtG/fHteuXUO1atVKldfkyZMxduxYaT8lJQXe3t6lK3gZVib/c8LmK5JJejrQpIl6+8wZ+ZbuaLJanemZYWdkXbqDYJxKJ5NhEgHRyJEjsXPnThw7dgwvvvhisWmbNWsGALh69SqqVasGT09P/P777xppkpKSAKDIfkdKpRJKpVIPJSedlfnmKyovhFAvZ5W3LU+eApfvXJa2SWZyVXpJLdiGaOHWpmUd4N/NYpTpgEgIgVGjRmHbtm04cuQI/Pz8SnxPdHQ0AMDLywsAEBQUhDlz5uD27dtwd3cHAOzfvx9OTk4IyBttQGVPmWy+IiIqhq4r6OqrhZuj1vSiTAdE4eHh2LRpE37++Wc4OjpKfX6cnZ1hZ2eHa9euYdOmTejSpQsqVaqECxcuYMyYMWjdujXq168PAOjYsSMCAgIwYMAAzJ8/H4mJifjoo48QHh7OViAiItIfbVfQBfTbUqPrqLXjx4tPZ6atSGU6IFq5ciUA9eSLT1u7di0GDRoEGxsbHDhwAEuWLEFaWhq8vb3Rq1cvfPTRR1JaS0tL7Ny5EyNGjEBQUBDs7e0RGhqqMW8RERGRXhhzNuuSWtZ1WY9t61bAza3oNOVwYEuZDohKesbu7e2No0ePlngdX19f7N69W1/FIiIiMj3atGDduQP07Al06lTy9crZwJYyHRARERGRHmnTgmWMx35lAAMiIjJLCgXg65u/LU+eCvg6+0rbJDNjVLo+yD1qzUwXsWVARERmSaUCbtyQOU9rFW58IHOmpVTSd6xJNg4Yo9Kfh7FGrZkpBkRERCTRpd8tR28bmLFGrZkpBkRERCTR5juYa47KyEwfXxkDAyIiMkuPHwOtW6u3jx0D7OxkyDPrMVqvU2d6bNAx2FnLkGkplNvvYGNUOpkMBkREZJZyc4GzZ/O3ZclT5OLsrbPSNsnMGJVOJsPC2AUgIiIiMja2EJF8tFl8sBzOfkpERGUfAyKSh66LD3L4KBERyYgBEclD28UHAQ4fJSIi2TEgInmVtPggERGRETAgIiKzZYwns64qPg42Kj6OpyIwICpn2G+ZSDv29uqFvWXN08Yed8bLnKkBafO3pEw9ATdGpZPJYEBUjrDfMhHJQdcltrjEB5kCBkTlCPstE5EctF1ii0t8kClhQFQOsd8yUckePwY6d1Zv//qrfEt3dI5QZ/prv1/L7NId2jDJ5T2MUelkMhgQkX6U1HmJHZeojMnNBY4ezd+WJU+Ri6M3j0rbJDNjVDqZDAZE9Py07bzEjktERFRGMSCi56dt5yV2XCIiojKKARHpDzsvERGRiWJAREREBmVy8xWRWWJARMXjTI9EVEqcr4hMCQMiKhpneqRyTqUyQp7WRsjUSMrkfEXGqHQyCQyIqGic6ZHKMXt7IC1N5jxt7JE2ReZMjUyX+YoM/mjNGJVOJoMBkQkx2lQ/7CxNRAbER2tUFjAgMhGc6oeIyqsy+WiNzA4DIhPBqX6I9OvJE6BXL/X2Tz8BtrYy5Jn9BL1+VGf6U5+fYGslQ6YmQpalQIxR6WQyGBCZGL09veLoMTJzOTnA7t3527LkmZuD3Vd2S9skM2NUOpkMBkTmiKPHiMiElfR/NbaUU2mYVUC0fPlyLFiwAImJiWjQoAGWLVuGpk2bGrtY8uPoMSIyQdp2vlapgK1bATc3zeMWj4GG/21HRwO5Wi52zz+D5sFsAqIffvgBY8eOxVdffYVmzZphyZIlCAkJQWxsLNzd3Y1aNqM9veLoMSIyIdp0vr5zB+jZE+jUqeA5FYC8QfctWgJatJGr31dEgPUsBk6mzWwCokWLFmHYsGEYPHgwAOCrr77Crl27sGbNGkyaNMlo5dL70yv2DSKickybztdFBU0WjwG0VG+fPKFdC1FxAdaztJkSQJs/0bpgEKY/ZhEQZWZmIioqCpMnT5aOWVhYIDg4GJGRkUYsmQ5PrxIS4Iq78LmbBRT1y5T3m8u+QURkxooMmp6ak7FhQwD22l1PlykBjh8v+m+5Ln+itaVt65U+ldcgzCwCort37yInJwceHh4axz08PPDXX38VSJ+RkYGMjAxpPzk5GQCQkpKi97Klpqr/9fYGqlcvItE//wC9mwCPH6PEEtjZqYeTlhTsVKoEuLgABrgnIlPw9ITFKSnyDDpKy0wDnuTlmYIcG450klUpK93FRf0qjlKp/vNbUv8mbf9Ea+PuXXV+2rRe6ZOdnfo/8SXdg6en+qWVvC/D1FS9fi/lfW8LIUpMaxYBka7mzp2LWbNmFTju7e1tsDzbtNHThR4/zp9ng4i0UrmyEfKcZ4RMKZ8xKh3l40+0Qe9Bb1+Gmh49egRnZ+di05hFQOTq6gpLS0skJSVpHE9KSoJnIeHr5MmTMXbsWGk/NzcX9+/fR6VKlaBQKAxe3vIiJSUF3t7e+Oeff+Dk5GTs4pg11kXZwbooO1gXZYeh6kIIgUePHqGyFgGwWQRENjY2CAwMxMGDB9GjRw8A6iDn4MGDGDlyZIH0SqUSSqVS45hLSe2lVCQnJyf+sSkjWBdlB+ui7GBdlB2GqIuSWobymEVABABjx45FaGgoGjdujKZNm2LJkiVIS0uTRp0RERGR+TKbgOjNN9/EnTt3MH36dCQmJqJhw4bYs2dPgY7WREREZH7MJiACgJEjRxb6iIwMQ6lUYsaMGQUeP5L8WBdlB+ui7GBdlB1loS4UQpuxaERERETlmIWxC0BERERkbAyIiIiIyOwxICIiIiKzx4CIiIiIzB4DInouy5cvR5UqVWBra4tmzZrh999/LzLt6tWr0apVK1SoUAEVKlRAcHBwselJN7rUxdM2b94MhUIhTVpKz0/Xunj48CHCw8Ph5eUFpVKJmjVrYvfu3TKVtnzTtS6WLFmCWrVqwc7ODt7e3hgzZgyePHkiU2nLp2PHjqFbt26oXLkyFAoFtm/fXuJ7jhw5gkaNGkGpVKJ69epYt26dwcsJQVRKmzdvFjY2NmLNmjXi0qVLYtiwYcLFxUUkJSUVmr5v375i+fLl4vz58yImJkYMGjRIODs7i3///Vfmkpc/utZFnri4OPHCCy+IVq1aie7du8tT2HJO17rIyMgQjRs3Fl26dBEnTpwQcXFx4siRIyI6Olrmkpc/utZFRESEUCqVIiIiQsTFxYm9e/cKLy8vMWbMGJlLXr7s3r1bTJ06VWzdulUAENu2bSs2/fXr14VKpRJjx44Vly9fFsuWLROWlpZiz549Bi0nAyIqtaZNm4rw8HBpPycnR1SuXFnMnTtXq/dnZ2cLR0dHsX79ekMV0WyUpi6ys7PFyy+/LL755hsRGhrKgEhPdK2LlStXiqpVq4rMzEy5img2dK2L8PBw8corr2gcGzt2rGjRooVBy2lOtAmIJkyYIOrUqaNx7M033xQhISEGLJkQfGRGpZKZmYmoqCgEBwdLxywsLBAcHIzIyEitrpGeno6srCxUrFjRUMU0C6Wti9mzZ8Pd3R1Dhw6Vo5hmoTR18csvvyAoKAjh4eHw8PBA3bp18emnnyInJ0euYpdLpamLl19+GVFRUdJjtevXr2P37t3o0qWLLGUmtcjISI16A4CQkBCtv1tKy6xmqib9uXv3LnJycgosfeLh4YG//vpLq2tMnDgRlStXLvDBJ92Upi5OnDiBb7/9FtHR0TKU0HyUpi6uX7+OQ4cOoV+/fti9ezeuXr2K9957D1lZWZgxY4YcxS6XSlMXffv2xd27d9GyZUsIIZCdnY13330XU6ZMkaPI9J/ExMRC6y0lJQWPHz+GnZ2dQfJlCxEZxbx587B582Zs27YNtra2xi6OWXn06BEGDBiA1atXw9XV1djFMXu5ublwd3fHqlWrEBgYiDfffBNTp07FV199ZeyimZ0jR47g008/xYoVK3Du3Dls3boVu3btwscff2zsopEM2EJEpeLq6gpLS0skJSVpHE9KSoKnp2ex7124cCHmzZuHAwcOoH79+oYsplnQtS6uXbuGGzduoFu3btKx3NxcAICVlRViY2NRrVo1wxa6nCrN74WXlxesra1haWkpHfP390diYiIyMzNhY2Nj0DKXV6Wpi2nTpmHAgAF45513AAD16tVDWloawsLCMHXqVFhYsA1BDp6enoXWm5OTk8FahwC2EFEp2djYIDAwEAcPHpSO5ebm4uDBgwgKCiryffPnz8fHH3+MPXv2oHHjxnIUtdzTtS5q166NP//8E9HR0dLrtddeQ7t27RAdHQ1vb285i1+ulOb3okWLFrh69aoUlALA33//DS8vLwZDz6E0dZGenl4g6MkLVAWX/ZRNUFCQRr0BwP79+4v9btELg3bZpnJt8+bNQqlUinXr1onLly+LsLAw4eLiIhITE4UQQgwYMEBMmjRJSj9v3jxhY2Mj/ve//4mEhATp9ejRI2PdQrmha108i6PM9EfXuoiPjxeOjo5i5MiRIjY2VuzcuVO4u7uLTz75xFi3UG7oWhczZswQjo6O4vvvvxfXr18X+/btE9WqVRN9+vQx1i2UC48ePRLnz58X58+fFwDEokWLxPnz58XNmzeFEEJMmjRJDBgwQEqfN+x+/PjxIiYmRixfvpzD7qnsW7ZsmfDx8RE2NjaiadOm4tSpU9K5Nm3aiNDQUGnf19dXACjwmjFjhvwFL4d0qYtnMSDSL13r4rfffhPNmjUTSqVSVK1aVcyZM0dkZ2fLXOrySZe6yMrKEjNnzhTVqlUTtra2wtvbW7z33nviwYMH8he8HDl8+HChf/vzfvahoaGiTZs2Bd7TsGFDYWNjI6pWrSrWrl1r8HIqhGA7IBEREZk39iEiIiIis8eAiIiIiMweAyIiIiIyewyIiIiIyOwxICIiIiKzx4CIiIiIzB4DIiIiIjJ7DIiIiIjI7DEgIiK9UigUxb5mzpxp7CLqJCcnB/PmzUPt2rVhZ2eHihUrolmzZvjmm2+MXTQi0iOudk9EepWQkCBt//DDD5g+fTpiY2OlYw4ODsYoVomKWll+1qxZ+Prrr/Hll1+icePGSElJwdmzZ/HgwQPZy0JEhsMWIiLSK09PT+nl7OwMhUIh7aelpaFfv37w8PCAg4MDmjRpggMHDmi8PyEhAV27doWdnR38/PywadMmVKlSBUuWLJHS/PXXX2jZsiVsbW0REBCAAwcOQKFQYPv27VKaf/75B3369IGLiwsqVqyI7t2748aNG9L5QYMGoUePHpgzZw4qV66MWrVqFXo/v/zyC9577z307t0bfn5+aNCgAYYOHYpx48ZJaXJzczF//nxUr14dSqUSPj4+mDNnjnT+zz//xCuvvAI7OztUqlQJYWFhSE1NLbEsJd0DEekPAyIikk1qaiq6dOmCgwcP4vz58+jUqRO6deuG+Ph4Kc3AgQNx69YtHDlyBD/99BNWrVqF27dvS+dzcnLQo0cPqFQqnD59GqtWrcLUqVM18snKykJISAgcHR1x/PhxnDx5Eg4ODujUqRMyMzOldAcPHkRsbCz279+PnTt3FlpmT09PHDp0CHfu3CnyviZPnox58+Zh2rRpuHz5MjZt2gQPDw8AQFpaGkJCQlChQgWcOXMGW7ZswYEDBzBy5EiNazxbFm3vgYj0xODLxxKR2Vq7dq1wdnYuNk2dOnXEsmXLhBBCxMTECADizJkz0vkrV64IAGLx4sVCCCF+/fVXYWVlJRISEqQ0+/fvFwDEtm3bhBBCfPfdd6JWrVoiNzdXSpORkSHs7OzE3r17hRDqFbY9PDxERkZGseW7dOmS8Pf3FxYWFqJevXpi+PDhYvfu3dL5lJQUoVQqxerVqwt9/6pVq0SFChVEamqqdGzXrl3CwsJCJCYmFlkWbe6BiPSHLUREJJvU1FSMGzcO/v7+cHFxgYODA2JiYqQWotjYWFhZWaFRo0bSe6pXr44KFSpI+7GxsfD29oanp6d0rGnTphr5/PHHH7h69SocHR3h4OAABwcHVKxYEU+ePMG1a9ekdPXq1Suxr05AQAAuXryIU6dOYciQIbh9+za6deuGd955BwAQExODjIwMtG/fvtD3x8TEoEGDBrC3t5eOtWjRArm5uRp9q54ti7b3QET6wU7VRCSbcePGYf/+/Vi4cCGqV68OOzs7vPHGG3p/BJSamorAwEBEREQUOOfm5iZtPx2kFMfCwgJNmjRBkyZN8MEHH2Djxo0YMGAApk6dCjs7O72U+dmyaHsPRKQfDIiISDYnT57EoEGD8PrrrwNQf+k/3Um4Vq1ayM7Oxvnz5xEYGAgAuHr1qsaIrlq1auGff/5BUlKS1E/nzJkzGvk0atQIP/zwA9zd3eHk5KT3+wgICACg7h9Uo0YN2NnZ4eDBg1Kr0dP8/f2xbt06pKWlSUHPyZMnYWFhUWRHbjnugYg08ZEZEcmmRo0a2Lp1K6Kjo/HHH3+gb9++yM3Nlc7Xrl0bwcHBCAsLw++//47z588jLCwMdnZ2UCgUAIAOHTqgWrVqCA0NxYULF3Dy5El89NFHACCl6devH1xdXdG9e3ccP34ccXFxOHLkCN5//338+++/OpX5jTfewOLFi3H69GncvHkTR44cQXh4OGrWrInatWvD1tYWEydOxIQJE7BhwwZcu3YNp06dwrfffiuVxdbWFqGhobh48SIOHz6MUaNGYcCAAVJAVxh93gMRlYwBERHJZtGiRahQoQJefvlldOvWDSEhIRr9hQBgw4YN8PDwQOvWrfH6669j2LBhcHR0hK2tLQDA0tIS27dvR2pqKpo0aYJ33nlHGmWWl0alUuHYsWPw8fFBz5494e/vj6FDh+LJkyc6t7aEhIRgx44d6NatG2rWrInQ0FDUrl0b+/btg5WVupF92rRp+PDDDzF9+nT4+/vjzTfflEbGqVQq7N27F/fv30eTJk3wxhtvoH379vjyyy+LzVef90BEJVMIIYSxC0FEVJR///0X3t7eOHDgQJEdl0+ePImWLVvi6tWrqFatmswlJKLygAEREZUphw4dQmpqKurVq4eEhARMmDAB//d//4e///4b1tbWAIBt27bBwcEBNWrUwNWrVzF69GhUqFABJ06cMHLpichUsVM1EZUpWVlZmDJlCq5fvw5HR0e8/PLLiIiIkIIhAHj06BEmTpyI+Ph4uLq6Ijg4GJ9//rkRS01Epo4tRERERGT22KmaiIiIzB4DIiIiIjJ7DIiIiIjI7DEgIiIiIrPHgIiIiIjMHgMiIiIiMnsMiIiIiMjsMSAiIiIis8eAiIiIiMze/wNf6gnuOBe4sQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define traditional ROC curve\n",
    "def roc(y_pred,y_true):    \n",
    "    sig_eff = []\n",
    "    bkg_eff = []\n",
    "    \n",
    "    # Iterate over thresholds and calculate sig and bkg efficiency\n",
    "    for threshold in np.linspace(0,1,50):\n",
    "        sig_eff.append(((y_pred[sig] > threshold).sum() / y_true[sig].shape[0]))   # Sum over sig predictions > threshold and divide by total number of true sig instances \n",
    "        bkg_eff.append(((y_pred[bkg] < threshold).sum()  / y_true[bkg].shape[0]))  # Sum over bkg predictions < threshold and divide by total number of true bkg instances \n",
    "        \n",
    "    return sig_eff, bkg_eff\n",
    "\n",
    "# Define ATLAS Style ROC curve\n",
    "def ATLAS_roc(y_pred,y_true):\n",
    "    sig_eff = []\n",
    "    bkg_eff = []\n",
    "    thresholds = []\n",
    "    \n",
    "    for threshold in np.linspace(0,0.95,50):\n",
    "        sig_eff.append(((y_pred[sig] > threshold).sum() / y_true[sig].shape[0]))\n",
    "        bkg_eff.append(1-((y_pred[bkg] < threshold).sum()  / y_true[bkg].shape[0]))\n",
    "        thresholds.append(threshold)\n",
    "        \n",
    "    bkg_rej = [1/x for x in bkg_eff]  # ATLAS inverts bkg eff and uses bkg rejection instead\n",
    "    return np.array(sig_eff), np.array(bkg_rej), np.array(thresholds)\n",
    "\n",
    "# Get Models predictions\n",
    "y_pred = model(X_test.to(device)).detach().cpu().numpy()\n",
    "\n",
    "# Find indices of sig and bkg labels\n",
    "sig = np.where(Y_test==1)[0]\n",
    "bkg = np.where(Y_test==0)[0]\n",
    "\n",
    "# Plot Tradiation ROC Curve\n",
    "eff_sig, eff_bkg = roc(y_pred,Y_test.detach().cpu().numpy())\n",
    "plt.title(\"Classic ROC Curve\")\n",
    "plt.plot(eff_sig,eff_bkg,color='b',label=\"Trained Model\")\n",
    "plt.plot([1,0],'--',color='k',label=\"Random Model\")\n",
    "plt.xlabel(\"Signal Efficiency\")\n",
    "plt.ylabel(\"Background Efficiency\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "eff_sig, eff_bkg, cut = ATLAS_roc(y_pred,Y_test.detach().cpu().numpy())\n",
    "# 10% WP\n",
    "idx = max(np.where(eff_sig>0.1)[0])\n",
    "cut1 = cut[idx]\n",
    "# 30% WP\n",
    "idx = max(np.where(eff_sig>0.3)[0])\n",
    "cut2 = cut[idx]\n",
    "# 50% WP\n",
    "idx = max(np.where(eff_sig>0.50)[0])\n",
    "cut3 = cut[idx]\n",
    "\n",
    "# Plot Model Predictions split by sig and bkg\n",
    "plt.title(\"Predicted Output by Truth Label\")\n",
    "plt.hist(y_pred[sig],histtype='step',label='ttbar',color='r',bins=45)\n",
    "plt.hist(y_pred[bkg],histtype='step',label='QCD',color='b',bins=45)\n",
    "plt.axvline(x = cut1, color=\"r\", linestyle=\"--\", label=\"10% Sig Eff\")\n",
    "plt.axvline(x = cut2, color=\"g\", linestyle=\"--\", label=\"30% Sig Eff\")\n",
    "plt.axvline(x = cut3, color=\"b\", linestyle=\"--\", label=\"50% Sig Eff\")\n",
    "plt.legend()\n",
    "plt.xlabel(\"Tagger Score\")\n",
    "plt.ylabel(\"Number of Particles\")\n",
    "plt.show()\n",
    "\n",
    "# Plot ATLAS Style ROC Curve\n",
    "plt.title(\"ATLAS ROC Curve\")\n",
    "plt.plot(eff_sig,eff_bkg,color='b',label=\"Trained Model\")\n",
    "plt.xlabel(\"Signal Efficiency\")\n",
    "plt.ylabel(\"Background Rejection\")\n",
    "plt.yscale('log')\n",
    "plt.grid(True,which='both')\n",
    "plt.xlim([0, 1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d22969d8",
   "metadata": {},
   "source": [
    "Notice the steep increase in background rejection, however, we must cut over 90% of our signal samples to achieve such high background rejection."
   ]
  }
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