deep_hedging.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Deep Hedging\n",
    "\n",
    "Deep Hedging was proposed in [[1802.03042]](https://arxiv.org/abs/1802.03042)  by Hans Bühler, Lukas Gonon, Josef Teichmann and Ben Wood.\n",
    "\n",
    "The idea is to use a neural network architecture to hedge a portfolio of derivatives without computing the \"greeks\".\n",
    "\n",
    "This notebook is based on lectures given by Josef Teichmann."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import tensorflow as tf\n",
    "import scipy.stats as scipy\n",
    "import keras.backend as K\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from keras.layers import Input, Dense, Subtract, Multiply, Lambda, Add\n",
    "from keras.backend import constant\n",
    "\n",
    "from keras.models import Model\n",
    "from keras.layers import Input\n",
    "from keras import initializers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Paths generated using the Black-Scholes model\n",
    "# The trajectories are not needed afterwards\n",
    "\n",
    "N = 20 # Time steps\n",
    "S0 = 1 # Initial stock price\n",
    "strike = 1 # Strike for the call option \n",
    "T = 1.0 # Maturity\n",
    "sigma = 0.2 # Volatility\n",
    "R = 10 # Number of paths\n",
    "\n",
    "logS = np.zeros((N,R))\n",
    "logS[0,] = np.log(S0)*np.ones((1,R))\n",
    "\n",
    "for i in range(R):\n",
    "    for j in range(N-1):\n",
    "        increment = np.random.normal(-(sigma)**2*T/(2*N),sigma*np.sqrt(T)/np.sqrt(N))\n",
    "        logS[j+1,i] = logS[j,i]+increment\n",
    "S = np.exp(logS)\n",
    "\n",
    "# We plot the different paths\n",
    "fig = plt.figure(figsize=(6,4)) \n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "for i in range(R):\n",
    "   plt.plot(S[:,i])\n",
    "ax.set_xlabel('time')\n",
    "ax.set_ylabel('stock price')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Price of a Call option in the Black-Scholes model with initial price 1 strike 1 maturity 1.0 and volatility 0.2 is equal to 0.07965567455405798\n"
     ]
    }
   ],
   "source": [
    "# Black-Scholes Call option price\n",
    "def BS(S0, strike, T, sigma):\n",
    "    return S0*scipy.norm.cdf((np.log(S0/strike)+0.5*T*sigma**2)/(np.sqrt(T)*sigma))-strike*scipy.norm.cdf((np.log(S0/strike)-0.5*T*sigma**2)/(np.sqrt(T)*sigma))\n",
    "\n",
    "# Initial price for the call option:\n",
    "priceBS = BS(S0,strike,T,sigma)\n",
    "print('Price of a Call option in the Black-Scholes model with initial price', S0, 'strike', strike, 'maturity', T , 'and volatility' , sigma, 'is equal to', BS(S0,strike,T,sigma))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Definition of neural networks for hedging strategies\n",
    "\n",
    "m = 1 # Dimension of price\n",
    "d = 2 # Number of layers in strategy (depth)\n",
    "n = 32 # Nodes in the first but last layers\n",
    "\n",
    "# Architecture is the same for all networks\n",
    "layers = []\n",
    "for j in range(N):\n",
    "    for i in range(d):\n",
    "        if i < d-1:\n",
    "            nodes = n\n",
    "            layer = Dense(nodes, activation='tanh', trainable=True,\n",
    "                      kernel_initializer=initializers.RandomNormal(0,1), \n",
    "                      bias_initializer='random_normal',\n",
    "                      name=str(i)+str(j))\n",
    "        else:\n",
    "            nodes = m\n",
    "            layer = Dense(nodes, activation='linear', trainable=True,\n",
    "                          kernel_initializer=initializers.RandomNormal(0,1),\n",
    "                          bias_initializer='random_normal',\n",
    "                          name=str(i)+str(j))\n",
    "        layers = layers + [layer]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Constructing the model and implementing the loss function\n",
    "# Inputs contain: 1) The initial stock price S0\n",
    "# 2) The initial hedging being 0 \n",
    "# 3) The increments of the log price\n",
    "\n",
    "price = Input(shape=(m,))\n",
    "hedge = Input(shape=(m,))\n",
    "inputs = [price]+[hedge]\n",
    "\n",
    "# Strategy at j is the hedging strategy at j, i.e. the Neural Network g_j\n",
    "for j in range(N):\n",
    "    strategy = price\n",
    "    for k in range(d):\n",
    "        strategy = layers[k+(j)*d](strategy) \n",
    "\n",
    "    # Update the log price of the stock  \n",
    "    incr = Input(shape=(m,))\n",
    "    logprice = Lambda(lambda x : K.log(x))(price)\n",
    "    logprice = Add()([logprice, incr])\n",
    "\n",
    "    # Update the price at time j+1\n",
    "    pricenew = Lambda(lambda x : K.exp(x))(logprice)\n",
    "\n",
    "    #Calculate the price increment \n",
    "    priceincr = Subtract()([pricenew, price])\n",
    "\n",
    "    # Update the value of the hedge\n",
    "    hedgenew = Multiply()([strategy, priceincr])\n",
    "\n",
    "    # This is only used for m > 1:\n",
    "    #mult = Lambda(lambda x : K.sum(x,axis=1))(mult)\n",
    "\n",
    "    hedge = Add()([hedge, hedgenew]) # building up the discretized stochastic integral\n",
    "    inputs = inputs + [incr]\n",
    "    price = pricenew\n",
    "\n",
    "# Payoff of the call option\n",
    "payoff = Lambda(lambda x : 0.5*(K.abs(x-strike) + (x-strike)) - priceBS)(price) \n",
    "\n",
    "# The output will be payoff-priceBS-hedge\n",
    "# Loss function L = (payoff-priceBS-hedge)^2\n",
    "outputs = Subtract()([payoff,hedge]) \n",
    "\n",
    "inputs = inputs\n",
    "outputs = outputs\n",
    "\n",
    "model_hedge = Model(inputs=inputs, outputs=outputs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Print summary of the model\n",
    "#model_hedge.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Number of trainable paths. This number can be 1e6\n",
    "Ktrain = 10**5 #2*10**4 #10**5  gives very good results\n",
    "\n",
    "# Initial stock price\n",
    "initialprice = S0\n",
    "\n",
    "# xtrain consists of: 1) The stock price S0\n",
    "# 2) Initial value of the Hedging is 0 \n",
    "# 3) The increments of the log price process\n",
    "xtrain = ([initialprice*np.ones((Ktrain,m))] +\n",
    "          [np.zeros((Ktrain,m))] +\n",
    "          [np.random.normal(-(sigma)**2*T/(2*N),sigma*np.sqrt(T)/np.sqrt(N),(Ktrain,m)) for i in range(N)])\n",
    "\n",
    "ytrain = np.zeros((Ktrain,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3125/3125 [==============================] - 32s 7ms/step - loss: 0.0066\n",
      "3125/3125 [==============================] - 12s 4ms/step\n",
      "Average value of the prediction = 8.563238e-07\n",
      "3125/3125 [==============================] - 19s 6ms/step - loss: 6.8504e-04\n",
      "3125/3125 [==============================] - 12s 4ms/step\n",
      "Average value of the prediction = 2.4127594e-05\n",
      "3125/3125 [==============================] - 19s 6ms/step - loss: 6.5595e-04\n",
      "3125/3125 [==============================] - 12s 4ms/step\n",
      "Average value of the prediction = 1.4106679e-05\n",
      "3125/3125 [==============================] - 20s 6ms/step - loss: 6.3805e-04\n",
      "3125/3125 [==============================] - 12s 4ms/step\n",
      "Average value of the prediction = -2.8179173e-05\n",
      "3125/3125 [==============================] - 20s 6ms/step - loss: 6.2641e-04\n",
      "3125/3125 [==============================] - 14s 4ms/step\n",
      "Average value of the prediction = -1.4905783e-05\n",
      "3125/3125 [==============================] - 19s 6ms/step - loss: 6.0737e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = 3.2747984e-08\n",
      "3125/3125 [==============================] - 19s 6ms/step - loss: 5.9796e-04\n",
      "3125/3125 [==============================] - 11s 3ms/step\n",
      "Average value of the prediction = -2.658665e-07\n",
      "3125/3125 [==============================] - 18s 6ms/step - loss: 5.8715e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = -7.8217774e-05\n",
      "3125/3125 [==============================] - 19s 6ms/step - loss: 5.8009e-04\n",
      "3125/3125 [==============================] - 11s 4ms/step\n",
      "Average value of the prediction = 1.7128186e-05\n",
      "3125/3125 [==============================] - 19s 6ms/step - loss: 5.7252e-04\n",
      "3125/3125 [==============================] - 11s 3ms/step\n",
      "Average value of the prediction = 3.614019e-05\n",
      "3125/3125 [==============================] - 19s 6ms/step - loss: 5.6148e-04\n",
      "3125/3125 [==============================] - 11s 3ms/step\n",
      "Average value of the prediction = 2.9933864e-05\n",
      "3125/3125 [==============================] - 19s 6ms/step - loss: 5.5389e-04\n",
      "3125/3125 [==============================] - 11s 3ms/step\n",
      "Average value of the prediction = -2.7411577e-05\n",
      "3125/3125 [==============================] - 19s 6ms/step - loss: 5.4209e-04\n",
      "3125/3125 [==============================] - 12s 4ms/step\n",
      "Average value of the prediction = -2.2714858e-05\n",
      "3125/3125 [==============================] - 18s 6ms/step - loss: 5.3419e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = -2.612176e-05\n",
      "3125/3125 [==============================] - 18s 6ms/step - loss: 5.3276e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = -3.4249937e-05\n",
      "3125/3125 [==============================] - 18s 6ms/step - loss: 5.2230e-04\n",
      "3125/3125 [==============================] - 11s 4ms/step\n",
      "Average value of the prediction = -2.4464829e-05\n",
      "3125/3125 [==============================] - 19s 6ms/step - loss: 5.1515e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = -3.889603e-05\n",
      "3125/3125 [==============================] - 18s 6ms/step - loss: 5.0620e-04\n",
      "3125/3125 [==============================] - 11s 3ms/step\n",
      "Average value of the prediction = 1.610038e-05\n",
      "3125/3125 [==============================] - 18s 6ms/step - loss: 5.0268e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = -7.6336946e-05\n",
      "3125/3125 [==============================] - 19s 6ms/step - loss: 4.9277e-04\n",
      "3125/3125 [==============================] - 11s 3ms/step\n",
      "Average value of the prediction = -5.3330023e-05\n",
      "3125/3125 [==============================] - 18s 6ms/step - loss: 4.8796e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = -3.9144445e-05\n",
      "3125/3125 [==============================] - 19s 6ms/step - loss: 4.8026e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = -4.8591188e-05\n",
      "3125/3125 [==============================] - 18s 6ms/step - loss: 4.7433e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = -2.3302717e-05\n",
      "3125/3125 [==============================] - 19s 6ms/step - loss: 4.7135e-04\n",
      "3125/3125 [==============================] - 11s 3ms/step\n",
      "Average value of the prediction = -3.6169342e-05\n",
      "3125/3125 [==============================] - 18s 6ms/step - loss: 4.6635e-04\n",
      "3125/3125 [==============================] - 11s 4ms/step\n",
      "Average value of the prediction = -5.3342425e-05\n",
      "3125/3125 [==============================] - 18s 6ms/step - loss: 4.5943e-04\n",
      "3125/3125 [==============================] - 11s 3ms/step\n",
      "Average value of the prediction = -6.104452e-05\n",
      "3125/3125 [==============================] - 18s 6ms/step - loss: 4.5431e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = -4.9412494e-05\n",
      "3125/3125 [==============================] - 17s 5ms/step - loss: 4.5102e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = -3.4918838e-05\n",
      "3125/3125 [==============================] - 13s 4ms/step - loss: 4.4744e-04\n",
      "3125/3125 [==============================] - 5s 2ms/step\n",
      "Average value of the prediction = -4.8960857e-05\n",
      "3125/3125 [==============================] - 17s 5ms/step - loss: 4.4465e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = -5.5555716e-05\n",
      "3125/3125 [==============================] - 18s 6ms/step - loss: 4.4242e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = 2.0448922e-05\n",
      "3125/3125 [==============================] - 18s 6ms/step - loss: 4.3735e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = -5.661238e-05\n",
      "3125/3125 [==============================] - 17s 5ms/step - loss: 4.3567e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = -7.599065e-05\n",
      "3125/3125 [==============================] - 17s 5ms/step - loss: 4.3114e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = -6.130482e-05\n",
      "3125/3125 [==============================] - 17s 5ms/step - loss: 4.2514e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = -8.7638065e-05\n",
      "3125/3125 [==============================] - 17s 5ms/step - loss: 4.2563e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = -4.0494386e-05\n",
      "3125/3125 [==============================] - 17s 5ms/step - loss: 4.2208e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = -4.7023674e-05\n",
      "3125/3125 [==============================] - 17s 6ms/step - loss: 4.1983e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = -7.86298e-05\n",
      "3125/3125 [==============================] - 18s 6ms/step - loss: 4.1622e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = -3.900008e-05\n",
      "3125/3125 [==============================] - 22s 7ms/step - loss: 4.1482e-04\n",
      "3125/3125 [==============================] - 11s 4ms/step\n",
      "Average value of the prediction = -0.00010418232\n",
      "3125/3125 [==============================] - 18s 6ms/step - loss: 4.1285e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = -8.6222666e-05\n",
      "3125/3125 [==============================] - 18s 6ms/step - loss: 4.0876e-04\n",
      "3125/3125 [==============================] - 11s 3ms/step\n",
      "Average value of the prediction = -0.0001214366\n",
      "3125/3125 [==============================] - 19s 6ms/step - loss: 4.0804e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = -7.3777745e-05\n",
      "3125/3125 [==============================] - 18s 6ms/step - loss: 4.0554e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = -7.5522235e-05\n",
      "3125/3125 [==============================] - 18s 6ms/step - loss: 4.0509e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = -9.476755e-05\n",
      "3125/3125 [==============================] - 19s 6ms/step - loss: 4.0086e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = -4.1595413e-05\n",
      "3125/3125 [==============================] - 18s 6ms/step - loss: 3.9859e-04\n",
      "3125/3125 [==============================] - 11s 3ms/step\n",
      "Average value of the prediction = -5.732535e-05\n",
      "3125/3125 [==============================] - 18s 6ms/step - loss: 3.9635e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = -6.4316264e-05\n",
      "3125/3125 [==============================] - 19s 6ms/step - loss: 3.9572e-04\n",
      "3125/3125 [==============================] - 10s 3ms/step\n",
      "Average value of the prediction = -7.689171e-05\n",
      "3125/3125 [==============================] - 19s 6ms/step - loss: 3.9354e-04\n",
      "3125/3125 [==============================] - 11s 3ms/step\n",
      "Average value of the prediction = -5.5863886e-05\n"
     ]
    }
   ],
   "source": [
    "# ======= Train the model =======\n",
    "\n",
    "# Optimizer: sgd\n",
    "#sgd=optimizers.SGD(lr=0.0001)\n",
    "#model_hedge.compile(optimizer=sgd,loss='mean_squared_error')\n",
    "\n",
    "# Optimizer: adam\n",
    "model_hedge.compile(optimizer='adam',loss='mean_squared_error')\n",
    "\n",
    "for i in range(50):\n",
    "    model_hedge.fit(x=xtrain,y=ytrain, epochs=1, verbose=True)\n",
    "    print('Average value of the prediction =', np.mean(model_hedge.predict(xtrain)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Histogram of the predictions**\n",
    "\n",
    " - The results concentrate around zero\n",
    "- Loss has a mean of 1e-5 which is already good"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3125/3125 [==============================] - 10s 3ms/step\n"
     ]
    }
   ],
   "source": [
    "# ========= Generate predictions =========\n",
    "\n",
    "# We generate a new set of paths to test the model        \n",
    "xtest=([initialprice*np.ones((Ktrain,m))] +\n",
    "          [np.zeros((Ktrain,m))] +\n",
    "          [np.random.normal(-(sigma)**2*T/(2*N),(sigma)*np.sqrt(T)/np.sqrt(N),(Ktrain,m)) for i in range(N)])\n",
    "\n",
    "ypred = model_hedge.predict(xtest)          \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Standard deviation of prediction =  0.0203435\n",
      "Average value of the prediction = -7.9399346e-05\n"
     ]
    }
   ],
   "source": [
    "# Histogram of the output of the model  \n",
    "fig = plt.figure(figsize=(5,4)) \n",
    "ax = fig.gca()\n",
    "plt.hist(ypred)\n",
    "plt.title('Deep hedging predictions', fontsize=13, color='black')\n",
    "ax.set_xlabel('model output')\n",
    "plt.show()\n",
    "print('Standard deviation of prediction = ', np.std(ypred))\n",
    "print('Average value of the prediction =', np.mean(ypred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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+/fqJ5ORkqaZx48YGt3o8fiwfv0XiwoUL4m9/+5uwt7cXZmZmwt3dXYSFhYmCggKDuopuORFCiOLiYrFkyRLRoUMHYWlpKSwtLUWzZs3EkCFDRFxcnFQXGRkpunbtKuzt7YVSqRQNGzYUAwYMMBj7k6xatUr4+flJ83ZychJvvvmm2Lt3b7nahIQE4efnJ6ytrYVKpRKenp4Gt87oVXTLiRBCxMTEiHbt2gmlUimcnZ3FzJkzRUZGRrlbSPS17du3FyqVSgCQjntFt5zoj9X8+fNFy5YthVKpFPXq1RP9+vUTp06dMqh70vZCCBERESEAGNyKQi8eEyH4rjMREZEcfE+TiIhIJoYmERGRTAxNIiIimRiaREREMjE0iYiIZGJoEhERyfSX/nCDsrIyXLt2DdbW1kZ/dBYREb0chBC4d+8eXFxcnvqxkX/p0Lx27RpcXV1rehhERPQCuHz5Mho2bFhpzV86NK2trQH8caDUanUNj4aIiGpCXl4eXF1dpUyozF86NPUvyarVaoYmEdFfnJy36XghEBERkUwMTSIiIpkYmkRERDIxNImIiGRiaBIREcnE0CQiIpLJqND8+OOPYWJiYrC0bNlSWv/w4UOEhITAzs4OVlZWCAoKQnZ2tkEfWVlZCAgIgKWlJRwcHDBjxgyUlJQY1CQkJMDLywsqlQrNmjVDVFRUubEsW7YMbm5uMDc3h6+vL44cOWLMVIiIiIxm9Jlm69atcf36dWk5cOCAtG7atGnYsWMHNm/ejMTERFy7dg3vvvuutL60tBQBAQEoKirCoUOHsG7dOkRFRSE8PFyqyczMREBAAHr06IGUlBRMnToVY8aMQVxcnFQTHR2N0NBQRERE4Pjx42jXrh38/f1x48aNZz0ORERETyeMEBERIdq1a1fhupycHGFmZiY2b94staWnpwsAIikpSQghxK5du4RCoRA6nU6qWbFihVCr1aKwsFAIIcTMmTNF69atDfoeOHCg8Pf3lx77+PiIkJAQ6XFpaalwcXERkZGRxkxH5ObmCgAiNzfXqO2IiOjlYUwWGH2mee7cObi4uKBJkyYYOnQosrKyAADJyckoLi6Gn5+fVNuyZUs0atQISUlJAICkpCS0adMGjo6OUo2/vz/y8vJw+vRpqebRPvQ1+j6KioqQnJxsUKNQKODn5yfVPElhYSHy8vIMFiIiIrmMCk1fX19ERUUhNjYWK1asQGZmJrp27Yp79+5Bp9NBqVTCxsbGYBtHR0fodDoAgE6nMwhM/Xr9uspq8vLy8ODBA9y6dQulpaUV1uj7eJLIyEhoNBpp4Ye1ExGRMYz67Nk333xT+nfbtm3h6+uLxo0bY9OmTbCwsKjywVW1sLAwhIaGSo/1H9JLRC8Ot9kxNT0EycX5ATU9BHrB/KlbTmxsbPDKK6/g999/h5OTE4qKipCTk2NQk52dDScnJwCAk5NTuatp9Y+fVqNWq2FhYYH69evD1NS0whp9H0+iUqmkD2fnh7QTEZGx/lRo5ufn4/z583B2doa3tzfMzMywZ88eaf3Zs2eRlZUFrVYLANBqtUhNTTW4yjU+Ph5qtRoeHh5SzaN96Gv0fSiVSnh7exvUlJWVYc+ePVINERFRdTAqND/44AMkJibi4sWLOHToEPr37w9TU1MMHjwYGo0Go0ePRmhoKPbt24fk5GSMHDkSWq0WnTp1AgD07t0bHh4eGDZsGE6ePIm4uDjMnTsXISEhUKlUAIDx48fjwoULmDlzJjIyMrB8+XJs2rQJ06ZNk8YRGhqK1atXY926dUhPT8eECRNQUFCAkSNHVuGhISIiMmTUe5pXrlzB4MGDcfv2bdjb26NLly747bffYG9vDwBYtGgRFAoFgoKCUFhYCH9/fyxfvlza3tTUFDt37sSECROg1WpRt25dBAcHY968eVKNu7s7YmJiMG3aNCxZsgQNGzbEmjVr4O/vL9UMHDgQN2/eRHh4OHQ6HTw9PREbG1vu4iAiIqKqZCKEEDU9iJqSl5cHjUaD3Nxcvr9J9ILghUD0vBmTBfzsWSIiIpkYmkRERDIxNImIiGRiaBIREcnE0CQiIpKJoUlERCQTQ5OIiEgmhiYREZFMDE0iIiKZGJpEREQyMTSJiIhkYmgSERHJxNAkIiKSiaFJREQkE0OTiIhIJoYmERGRTAxNIiIimRiaREREMjE0iYiIZGJoEhERycTQJCIikomhSUREJBNDk4iISCaGJhERkUwMTSIiIpkYmkRERDIxNImIiGRiaBIREcnE0CQiIpKJoUlERCQTQ5OIiEgmhiYREZFMDE0iIiKZGJpEREQyMTSJiIhkYmgSERHJxNAkIiKSiaFJREQkE0OTiIhIJoYmERGRTAxNIiIimRiaREREMjE0iYiIZGJoEhERycTQJCIikomhSUREJBNDk4iISCaGJhERkUx/KjTnz58PExMTTJ06VWp7+PAhQkJCYGdnBysrKwQFBSE7O9tgu6ysLAQEBMDS0hIODg6YMWMGSkpKDGoSEhLg5eUFlUqFZs2aISoqqtz+ly1bBjc3N5ibm8PX1xdHjhz5M9MhIiKq1DOH5tGjR/HPf/4Tbdu2NWifNm0aduzYgc2bNyMxMRHXrl3Du+++K60vLS1FQEAAioqKcOjQIaxbtw5RUVEIDw+XajIzMxEQEIAePXogJSUFU6dOxZgxYxAXFyfVREdHIzQ0FBERETh+/DjatWsHf39/3Lhx41mnREREVCkTIYQwdqP8/Hx4eXlh+fLl+OSTT+Dp6YnFixcjNzcX9vb22LBhAwYMGAAAyMjIQKtWrZCUlIROnTph9+7d6Nu3L65duwZHR0cAwMqVKzFr1izcvHkTSqUSs2bNQkxMDNLS0qR9Dho0CDk5OYiNjQUA+Pr6omPHjli6dCkAoKysDK6urpg8eTJmz54tax55eXnQaDTIzc2FWq029jAQUTVwmx1T00OQXJwfUNNDoOfAmCx4pjPNkJAQBAQEwM/Pz6A9OTkZxcXFBu0tW7ZEo0aNkJSUBABISkpCmzZtpMAEAH9/f+Tl5eH06dNSzeN9+/v7S30UFRUhOTnZoEahUMDPz0+qqUhhYSHy8vIMFiIiIrnqGLvBxo0bcfz4cRw9erTcOp1OB6VSCRsbG4N2R0dH6HQ6qebRwNSv16+rrCYvLw8PHjzA3bt3UVpaWmFNRkbGE8ceGRmJf/zjH/ImSkRE9BijzjQvX76MKVOm4F//+hfMzc2ra0zVJiwsDLm5udJy+fLlmh4SERHVIkaFZnJyMm7cuAEvLy/UqVMHderUQWJiIr7++mvUqVMHjo6OKCoqQk5OjsF22dnZcHJyAgA4OTmVu5pW//hpNWq1GhYWFqhfvz5MTU0rrNH3URGVSgW1Wm2wEBERyWVUaPbq1QupqalISUmRlg4dOmDo0KHSv83MzLBnzx5pm7NnzyIrKwtarRYAoNVqkZqaanCVa3x8PNRqNTw8PKSaR/vQ1+j7UCqV8Pb2NqgpKyvDnj17pBoiIqKqZtR7mtbW1nj11VcN2urWrQs7OzupffTo0QgNDYWtrS3UajUmT54MrVaLTp06AQB69+4NDw8PDBs2DAsWLIBOp8PcuXMREhIClUoFABg/fjyWLl2KmTNnYtSoUdi7dy82bdqEmJj/XVUXGhqK4OBgdOjQAT4+Pli8eDEKCgowcuTIP3VAiIiInsToC4GeZtGiRVAoFAgKCkJhYSH8/f2xfPlyab2pqSl27tyJCRMmQKvVom7duggODsa8efOkGnd3d8TExGDatGlYsmQJGjZsiDVr1sDf31+qGThwIG7evInw8HDodDp4enoiNja23MVBREREVeWZ7tN8WfA+TaIXD+/TpOet2u/TJCIi+itiaBIREcnE0CQiIpKJoUlERCQTQ5OIiEgmhiYREZFMDE0iIiKZGJpEREQyMTSJiIhkYmgSERHJxNAkIiKSiaFJREQkE0OTiIhIJoYmERGRTAxNIiIimRiaREREMjE0iYiIZGJoEhERycTQJCIikomhSUREJBNDk4iISCaGJhERkUwMTSIiIpkYmkRERDIxNImIiGRiaBIREcnE0CQiIpKJoUlERCQTQ5OIiEgmhiYREZFMDE0iIiKZGJpEREQyMTSJiIhkYmgSERHJxNAkIiKSiaFJREQkE0OTiIhIJoYmERGRTAxNIiIimRiaREREMjE0iYiIZGJoEhERycTQJCIikomhSUREJBNDk4iISCaGJhERkUwMTSIiIpkYmkRERDIZFZorVqxA27ZtoVaroVarodVqsXv3bmn9w4cPERISAjs7O1hZWSEoKAjZ2dkGfWRlZSEgIACWlpZwcHDAjBkzUFJSYlCTkJAALy8vqFQqNGvWDFFRUeXGsmzZMri5ucHc3By+vr44cuSIMVMhIiIymlGh2bBhQ8yfPx/Jyck4duwYevbsiX79+uH06dMAgGnTpmHHjh3YvHkzEhMTce3aNbz77rvS9qWlpQgICEBRUREOHTqEdevWISoqCuHh4VJNZmYmAgIC0KNHD6SkpGDq1KkYM2YM4uLipJro6GiEhoYiIiICx48fR7t27eDv748bN2782eNBRET0RCZCCPFnOrC1tcXChQsxYMAA2NvbY8OGDRgwYAAAICMjA61atUJSUhI6deqE3bt3o2/fvrh27RocHR0BACtXrsSsWbNw8+ZNKJVKzJo1CzExMUhLS5P2MWjQIOTk5CA2NhYA4Ovri44dO2Lp0qUAgLKyMri6umLy5MmYPXu27LHn5eVBo9EgNzcXarX6zxwGIqoibrNjanoIkovzA2p6CPQcGJMFz/yeZmlpKTZu3IiCggJotVokJyejuLgYfn5+Uk3Lli3RqFEjJCUlAQCSkpLQpk0bKTABwN/fH3l5edLZalJSkkEf+hp9H0VFRUhOTjaoUSgU8PPzk2qepLCwEHl5eQYLERGRXEaHZmpqKqysrKBSqTB+/Hhs2bIFHh4e0Ol0UCqVsLGxMah3dHSETqcDAOh0OoPA1K/Xr6usJi8vDw8ePMCtW7dQWlpaYY2+jyeJjIyERqORFldXV2OnT0REf2FGh2aLFi2QkpKCw4cPY8KECQgODsaZM2eqY2xVLiwsDLm5udJy+fLlmh4SERHVInWM3UCpVKJZs2YAAG9vbxw9ehRLlizBwIEDUVRUhJycHIOzzezsbDg5OQEAnJycyl3lqr+69tGax6+4zc7OhlqthoWFBUxNTWFqalphjb6PJ1GpVFCpVMZOmYiICEAV3KdZVlaGwsJCeHt7w8zMDHv27JHWnT17FllZWdBqtQAArVaL1NRUg6tc4+PjoVar4eHhIdU82oe+Rt+HUqmEt7e3QU1ZWRn27Nkj1RAREVUHo840w8LC8Oabb6JRo0a4d+8eNmzYgISEBMTFxUGj0WD06NEIDQ2Fra0t1Go1Jk+eDK1Wi06dOgEAevfuDQ8PDwwbNgwLFiyATqfD3LlzERISIp0Bjh8/HkuXLsXMmTMxatQo7N27F5s2bUJMzP+uqAsNDUVwcDA6dOgAHx8fLF68GAUFBRg5cmQVHhoiIiJDRoXmjRs3MHz4cFy/fh0ajQZt27ZFXFwc3njjDQDAokWLoFAoEBQUhMLCQvj7+2P58uXS9qampti5cycmTJgArVaLunXrIjg4GPPmzZNq3N3dERMTg2nTpmHJkiVo2LAh1qxZA39/f6lm4MCBuHnzJsLDw6HT6eDp6YnY2NhyFwcRERFVpT99n2Ztxvs0iV48vE+Tnrfncp8mERHRXw1Dk4iISCaGJhERkUwMTSIiIpkYmkRERDIxNImIiGRiaBIREcnE0CQiIpKJoUlERCQTQ5OIiEgmhiYREZFMDE0iIiKZGJpEREQyMTSJiIhkYmgSERHJxNAkIiKSiaFJREQkE0OTiIhIJoYmERGRTAxNIiIimRiaREREMjE0iYiIZGJoEhERycTQJCIikomhSUREJBNDk4iISCaGJhERkUwMTSIiIpkYmkRERDIxNImIiGRiaBIREcnE0CQiIpKJoUlERCQTQ5OIiEgmhiYREZFMDE0iIiKZGJpEREQyMTSJiIhkYmgSERHJxNAkIiKSqU5ND4CI6EXlNjumpocguTg/oKaHQOCZJhERkWwMTSIiIpkYmkRERDIxNImIiGRiaBIREcnE0CQiIpKJoUlERCSTUaEZGRmJjh07wtraGg4ODggMDMTZs2cNah4+fIiQkBDY2dnBysoKQUFByM7ONqjJyspCQEAALC0t4eDggBkzZqCkpMSgJiEhAV5eXlCpVGjWrBmioqLKjWfZsmVwc3ODubk5fH19ceTIEWOmQ0REZBSjQjMxMREhISH47bffEB8fj+LiYvTu3RsFBQVSzbRp07Bjxw5s3rwZiYmJuHbtGt59911pfWlpKQICAlBUVIRDhw5h3bp1iIqKQnh4uFSTmZmJgIAA9OjRAykpKZg6dSrGjBmDuLg4qSY6OhqhoaGIiIjA8ePH0a5dO/j7++PGjRt/5ngQERE9kYkQQjzrxjdv3oSDgwMSExPx+uuvIzc3F/b29tiwYQMGDBgAAMjIyECrVq2QlJSETp06Yffu3ejbty+uXbsGR0dHAMDKlSsxa9Ys3Lx5E0qlErNmzUJMTAzS0tKkfQ0aNAg5OTmIjY0FAPj6+qJjx45YunQpAKCsrAyurq6YPHkyZs+eLWv8eXl50Gg0yM3NhVqtftbDQERV6EX6FJ4XCT8RqPoYkwV/6j3N3NxcAICtrS0AIDk5GcXFxfDz85NqWrZsiUaNGiEpKQkAkJSUhDZt2kiBCQD+/v7Iy8vD6dOnpZpH+9DX6PsoKipCcnKyQY1CoYCfn59UU5HCwkLk5eUZLERERHI9c2iWlZVh6tSpeO211/Dqq68CAHQ6HZRKJWxsbAxqHR0dodPppJpHA1O/Xr+uspq8vDw8ePAAt27dQmlpaYU1+j4qEhkZCY1GIy2urq7GT5yIiP6ynjk0Q0JCkJaWho0bN1bleKpVWFgYcnNzpeXy5cs1PSQiIqpFnulbTiZNmoSdO3di//79aNiwodTu5OSEoqIi5OTkGJxtZmdnw8nJSap5/CpX/dW1j9Y8fsVtdnY21Go1LCwsYGpqClNT0wpr9H1URKVSQaVSGT9hopcY30Mkks+oM00hBCZNmoQtW7Zg7969cHd3N1jv7e0NMzMz7NmzR2o7e/YssrKyoNVqAQBarRapqakGV7nGx8dDrVbDw8NDqnm0D32Nvg+lUglvb2+DmrKyMuzZs0eqISIiqmpGnWmGhIRgw4YN2LZtG6ytraX3DzUaDSwsLKDRaDB69GiEhobC1tYWarUakydPhlarRadOnQAAvXv3hoeHB4YNG4YFCxZAp9Nh7ty5CAkJkc4Cx48fj6VLl2LmzJkYNWoU9u7di02bNiEm5n9/EYeGhiI4OBgdOnSAj48PFi9ejIKCAowcObKqjg0REZEBo0JzxYoVAIDu3bsbtK9duxYjRowAACxatAgKhQJBQUEoLCyEv78/li9fLtWamppi586dmDBhArRaLerWrYvg4GDMmzdPqnF3d0dMTAymTZuGJUuWoGHDhlizZg38/f2lmoEDB+LmzZsIDw+HTqeDp6cnYmNjy10cREREVFX+1H2atR3v0yTie5q1Be/TrD7P7T5NIiKivxKGJhERkUwMTSIiIpkYmkRERDIxNImIiGRiaBIREcnE0CQiIpKJoUlERCQTQ5OIiEgmhiYREZFMDE0iIiKZGJpEREQyMTSJiIhkYmgSERHJxNAkIiKSiaFJREQkE0OTiIhIJoYmERGRTAxNIiIimRiaREREMjE0iYiIZGJoEhERycTQJCIikomhSUREJBNDk4iISCaGJhERkUwMTSIiIpkYmkRERDIxNImIiGRiaBIREcnE0CQiIpKJoUlERCQTQ5OIiEgmhiYREZFMDE0iIiKZGJpEREQyMTSJiIhkYmgSERHJxNAkIiKSiaFJREQkE0OTiIhIJoYmERGRTAxNIiIimRiaREREMjE0iYiIZGJoEhERycTQJCIikomhSUREJJPRobl//368/fbbcHFxgYmJCbZu3WqwXgiB8PBwODs7w8LCAn5+fjh37pxBzZ07dzB06FCo1WrY2Nhg9OjRyM/PN6g5deoUunbtCnNzc7i6umLBggXlxrJ582a0bNkS5ubmaNOmDXbt2mXsdIiIiGQzOjQLCgrQrl07LFu2rML1CxYswNdff42VK1fi8OHDqFu3Lvz9/fHw4UOpZujQoTh9+jTi4+Oxc+dO7N+/H+PGjZPW5+XloXfv3mjcuDGSk5OxcOFCfPzxx1i1apVUc+jQIQwePBijR4/GiRMnEBgYiMDAQKSlpRk7JSIiIllMhBDimTc2McGWLVsQGBgI4I+zTBcXF0yfPh0ffPABACA3NxeOjo6IiorCoEGDkJ6eDg8PDxw9ehQdOnQAAMTGxuKtt97ClStX4OLighUrVuDDDz+ETqeDUqkEAMyePRtbt25FRkYGAGDgwIEoKCjAzp07pfF06tQJnp6eWLlypazx5+XlQaPRIDc3F2q1+lkPA1Gt5jY7pqaHQDJcnB9Q00N4aRmTBVX6nmZmZiZ0Oh38/PykNo1GA19fXyQlJQEAkpKSYGNjIwUmAPj5+UGhUODw4cNSzeuvvy4FJgD4+/vj7NmzuHv3rlTz6H70Nfr9VKSwsBB5eXkGCxERkVxVGpo6nQ4A4OjoaNDu6OgordPpdHBwcDBYX6dOHdja2hrUVNTHo/t4Uo1+fUUiIyOh0WikxdXV1dgpEhHRX9hf6urZsLAw5ObmSsvly5drekhERFSLVGloOjk5AQCys7MN2rOzs6V1Tk5OuHHjhsH6kpIS3Llzx6Cmoj4e3ceTavTrK6JSqaBWqw0WIiIiuao0NN3d3eHk5IQ9e/ZIbXl5eTh8+DC0Wi0AQKvVIicnB8nJyVLN3r17UVZWBl9fX6lm//79KC4ulmri4+PRokUL1KtXT6p5dD/6Gv1+iIiIqprRoZmfn4+UlBSkpKQA+OPin5SUFGRlZcHExARTp07FJ598gu3btyM1NRXDhw+Hi4uLdIVtq1at0KdPH4wdOxZHjhzBwYMHMWnSJAwaNAguLi4AgCFDhkCpVGL06NE4ffo0oqOjsWTJEoSGhkrjmDJlCmJjY/Hll18iIyMDH3/8MY4dO4ZJkyb9+aNCRERUgTrGbnDs2DH06NFDeqwPsuDgYERFRWHmzJkoKCjAuHHjkJOTgy5duiA2Nhbm5ubSNv/6178wadIk9OrVCwqFAkFBQfj666+l9RqNBr/88gtCQkLg7e2N+vXrIzw83OBezs6dO2PDhg2YO3cu5syZg+bNm2Pr1q149dVXn+lAEBERPc2fuk+ztuN9mkS8T7O24H2a1afG7tMkIiJ6mTE0iYiIZGJoEhERycTQJCIikomhSUREJBNDk4iISCaGJhERkUwMTSIiIpkYmkRERDIxNImIiGRiaBIREcnE0CQiIpKJoUlERCQTQ5OIiEgmhiYREZFMDE0iIiKZGJpEREQyMTSJiIhkYmgSERHJxNAkIiKSiaFJREQkE0OTiIhIJoYmERGRTHVqegBERPR0brNjanoIkovzA2p6CDWGZ5pEREQyMTSJiIhkYmgSERHJxNAkIiKSiaFJREQkE0OTiIhIJoYmERGRTAxNIiIimRiaREREMjE0iYiIZOLH6BHVgBfpI9GISD6eaRIREcnE0CQiIpKJoUlERCQTQ5OIiEgmhiYREZFMDE0iIiKZGJpEREQyMTSJiIhkYmgSERHJxNAkIiKSiaFJREQkE0OTiIhIJoYmERGRTLU+NJctWwY3NzeYm5vD19cXR44cqekhERHRS6pWfzVYdHQ0QkNDsXLlSvj6+mLx4sXw9/fH2bNn4eDgUNPDoxcMv46LqGq8SD9LF+cHPNf91eozza+++gpjx47FyJEj4eHhgZUrV8LS0hLfffddTQ+NiIheQrX2TLOoqAjJyckICwuT2hQKBfz8/JCUlFThNoWFhSgsLJQe5+bmAgDy8vKqd7B/Ya9GxNX0EIjoJVYVv7/1fQghnlpba0Pz1q1bKC0thaOjo0G7o6MjMjIyKtwmMjIS//jHP8q1u7q6VssYiYioemkWV11f9+7dg0ajqbSm1obmswgLC0NoaKj0uKysDJcuXYKnpycuX74MtVpdg6N7dnl5eXB1da21c6jt4wc4hxdBbR8/UPvnUFvHL4TAvXv34OLi8tTaWhua9evXh6mpKbKzsw3as7Oz4eTkVOE2KpUKKpXKoE2h+ONtXbVaXaue5IrU9jnU9vEDnMOLoLaPH6j9c6iN43/aGaZerb0QSKlUwtvbG3v27JHaysrKsGfPHmi12hocGRERvaxq7ZkmAISGhiI4OBgdOnSAj48PFi9ejIKCAowcObKmh0ZERC+hWh2aAwcOxM2bNxEeHg6dTgdPT0/ExsaWuzioMiqVChEREeVetq1Navscavv4Ac7hRVDbxw/U/jnU9vHLYSLkXGNLREREtfc9TSIioueNoUlERCQTQ5OIiEgmhiYREZFML11o3rlzB0OHDoVarYaNjQ1Gjx6N/Pz8SrdZtWoVunfvDrVaDRMTE+Tk5Bisv3jxIkaPHg13d3dYWFigadOmiIiIQFFRkUGNiYlJueW33357IeYgt99Tp06ha9euMDc3h6urKxYsWPBcxv/w4UOEhITAzs4OVlZWCAoKMvjgiqioqAqPr4mJCW7cuAEASEhIqHC9Tqd7IeYAoMLxbdy40aAmISEBXl5eUKlUaNasGaKioowef3XN4eTJkxg8eDBcXV1hYWGBVq1aYcmSJeXG/yzPg7Ff87d582a0bNkS5ubmaNOmDXbt2mWwXgiB8PBwODs7w8LCAn5+fjh37tyfPkbPaw7FxcWYNWsW2rRpg7p168LFxQXDhw/HtWvXDPpwc3Mrd6znz5//QswBAEaMGFFufH369DGoqernoVqJl0yfPn1Eu3btxG+//Sb+85//iGbNmonBgwdXus2iRYtEZGSkiIyMFADE3bt3Ddbv3r1bjBgxQsTFxYnz58+Lbdu2CQcHBzF9+nSpJjMzUwAQv/76q7h+/bq0FBUVvRBzkNNvbm6ucHR0FEOHDhVpaWni3//+t7CwsBD//Oc/q33848ePF66urmLPnj3i2LFjolOnTqJz587S+vv37xsc1+vXrwt/f3/RrVs3qWbfvn0CgDh79qxBXWlpqVHjr645CCEEALF27VqD8T148EBaf+HCBWFpaSlCQ0PFmTNnxDfffCNMTU1FbGzsCzGHb7/9Vvz9738XCQkJ4vz58+L7778XFhYW4ptvvpFqnuV52Lhxo1AqleK7774Tp0+fFmPHjhU2NjYiOzu7wvqDBw8KU1NTsWDBAnHmzBkxd+5cYWZmJlJTU6Wa+fPnC41GI7Zu3SpOnjwp3nnnHeHu7m5wvJ/lGD2vOeTk5Ag/Pz8RHR0tMjIyRFJSkvDx8RHe3t4G/TRu3FjMmzfP4Fjn5+e/EHMQQojg4GDRp08fg/HduXPHoJ+qfB6q20sVmmfOnBEAxNGjR6W23bt3CxMTE3H16tWnbq//Ya8ocB63YMEC4e7uLj3Wh+aJEyeeZeiS6pqDnH6XL18u6tWrJwoLC6WaWbNmiRYtWlTr+HNycoSZmZnYvHmz1Jaeni4AiKSkpAq3uXHjhjAzMxPr169/6tyNVZ1zACC2bNnyxH3PnDlTtG7d2qBt4MCBwt/f/4WZw+MmTpwoevToIT1+lufBx8dHhISESI9LS0uFi4uLiIyMrLD+/fffFwEBAQZtvr6+4v/+7/+EEEKUlZUJJycnsXDhQoP5qVQq8e9//1sI8ed/1qp7DhU5cuSIACAuXboktTVu3FgsWrTI6PFWpDrmEBwcLPr16/fEfVb181DdXqqXZ5OSkmBjY4MOHTpIbX5+flAoFDh8+HCV7is3Nxe2trbl2t955x04ODigS5cu2L59u9H9Vtcc5PSblJSE119/HUqlUqrRf6n33bt3q238ycnJKC4uhp+fn9TWsmVLNGrU6Ilf87Z+/XpYWlpiwIAB5dZ5enrC2dkZb7zxBg4ePChr3M9zDiEhIahfvz58fHzw3XffGXwdUVJSkkEfwB/PwZOOQ03N4VFP+lmQ+zzov+bv0f0+7Wv+nnacMjMzodPpDGo0Gg18fX2lmqr8WauOOVQkNzcXJiYmsLGxMWifP38+7Ozs0L59eyxcuBAlJSVGjb+655CQkAAHBwe0aNECEyZMwO3btw36eF6/t6tCrf5EoMfpdDo4ODgYtNWpUwe2trbP9L7Wk/z+++/45ptv8MUXX0htVlZW+PLLL/Haa69BoVDgp59+QmBgILZu3Yp33nmnxucgp1+dTgd3d3eDGv2nK+l0OtSrV69axq/T6aBUKsv9InB0dHziNt9++y2GDBkCCwsLqc3Z2RkrV65Ehw4dUFhYiDVr1qB79+44fPgwvLy8njr25zGHefPmoWfPnrC0tMQvv/yCiRMnIj8/H3//+9+lfir6uru8vDw8ePDAYL41NYdHHTp0CNHR0YiJiZHajH0enuVr/p50nB79v6xvq6ymqn7WqmMOj3v48CFmzZqFwYMHG3wY+t///nd4eXnB1tYWhw4dQlhYGK5fv46vvvrqhZhDnz598O6778Ld3R3nz5/HnDlz8OabbyIpKQmmpqbP7fd2VakVoTl79mx8/vnnldakp6c/l7FcvXoVffr0wXvvvYexY8dK7fXr1zf42rGOHTvi2rVrWLhwId55550Xag7P4quvvsKaNWsqrXle409KSkJ6ejq+//57g/YWLVqgRYsW0uPOnTvj/PnzWLRoEb7//vsX4jn46KOPpH+3b98eBQUFWLhwoRSaT/MizEEvLS0N/fr1Q0REBHr37i21P+15IOMVFxfj/fffhxACK1asMFj36O+dtm3bQqlU4v/+7/8QGRn5Qnyc3aBBg6R/t2nTBm3btkXTpk2RkJCAXr161eDInk2tCM3p06djxIgRldY0adIETk5O0pWUeiUlJbhz584Tvy7MGNeuXUOPHj3QuXNnrFq16qn1vr6+iI+PB1Dzc5DTr5OTU4VftQYAM2fOxPTp06tl/E5OTigqKkJOTo7BWc6TvuZtzZo18PT0hLe3d6XjAQAfHx8cOHAAQPU+B8bOQc/X1xf/7//9PxQWFkKlUj3xOVCr1bCwsHhh5nDmzBn06tUL48aNw9y5cysdD2D4PDzuWb7m70nH6dH/y/o2Z2dngxpPT0+ppqp+1qpjDnr6wLx06RL27t371K/c8vX1RUlJCS5evGjwx0tNzuFRTZo0Qf369fH777+jV69e1f57u8rV9JuqVUn/hvKxY8ektri4uCq5EOjKlSuiefPmYtCgQaKkpETWeMaMGSPat28ve/xCVN8c5PSrvxDo0St+w8LCnulCIGPGr78A5ccff5TaMjIyKrwA5d69e8LKysrgas3K+Pn5if79+8se//OYw6M++eQTUa9ePenxzJkzxauvvmpQM3jw4Ge+EKg65pCWliYcHBzEjBkzZI/nac+Dj4+PmDRpkvS4tLRUNGjQoNILUPr27WvQptVqy10I9MUXX0jrc3NzK7wQ6Fl/1qp7DkIIUVRUJAIDA0Xr1q3FjRs3ZI3jhx9+EAqFotwVqjU1h8ddvnxZmJiYiG3btgkhqv55qG4vVWgK8cely+3btxeHDx8WBw4cEM2bNze4dPnKlSuiRYsW4vDhw1Lb9evXxYkTJ8Tq1asFALF//35x4sQJcfv2bWmbZs2aiV69eokrV64YXDqtFxUVJTZs2CDS09NFenq6+PTTT4VCoRDffffdCzEHOf3m5OQIR0dHMWzYMJGWliY2btwoLC0tn+mWE2PHP378eNGoUSOxd+9ecezYMaHVaoVWqy3X95o1a4S5uXmFf9gsWrRIbN26VZw7d06kpqaKKVOmCIVCIX799Vejxl9dc9i+fbtYvXq1SE1NFefOnRPLly8XlpaWIjw8XKrR33IyY8YMkZ6eLpYtW/anbjmp6jmkpqYKe3t78be//c3g5+DRX+jP8jxs3LhRqFQqERUVJc6cOSPGjRsnbGxshE6nE0IIMWzYMDF79myp/uDBg6JOnTriiy++EOnp6SIiIqLCW05sbGzEtm3bxKlTp0S/fv0qvOWksmNkjKqeQ1FRkXjnnXdEw4YNRUpKisHx1l/hfujQIbFo0SKRkpIizp8/L3744Qdhb28vhg8f/kLM4d69e+KDDz4QSUlJIjMzU/z666/Cy8tLNG/eXDx8+FDqpyqfh+r20oXm7du3xeDBg4WVlZVQq9Vi5MiR4t69e9J6/a0h+/btk9oiIiIEgHLL2rVrhRBCrF27tsL1j56oR0VFiVatWglLS0uhVquFj4+PwaX7NT0HOf0KIcTJkydFly5dhEqlEg0aNBDz589/LuN/8OCBmDhxoqhXr56wtLQU/fv3N/ijRE+r1YohQ4ZUuN/PP/9cNG3aVJibmwtbW1vRvXt3sXfvXqPHX11z2L17t/D09BRWVlaibt26ol27dmLlypXl7l/ct2+f8PT0FEqlUjRp0sTgOazpOTzp/1njxo2lmmd9Hr755hvRqFEjoVQqhY+Pj/jtt9+kdd26dRPBwcEG9Zs2bRKvvPKKUCqVonXr1iImJsZgfVlZmfjoo4+Eo6OjUKlUolevXuLs2bNGHSNjVeUc9M9PRYv+OUtOTha+vr5Co9EIc3Nz0apVK/HZZ58ZBFJNzuH+/fuid+/ewt7eXpiZmYnGjRuLsWPHSiGsV9XPQ3XiV4MRERHJ9FLdp0lERFSdGJpEREQyMTSJiIhkYmgSERHJxNAkIiKSiaFJREQkE0OTiIhIJoYmERGRTAxNolqqe/fumDp1quz6qKiocl/7RUTGYWgSUZVyc3PD4sWLq6VvY/9QIKpqDE0iIiKZGJpEVah79+6YPHkypk6dinr16sHR0RGrV69GQUEBRo4cCWtrazRr1gy7d+822C4xMRE+Pj5QqVRwdnbG7NmzUVJSIq0vKCjA8OHDYWVlBWdnZ3z55Zfl9l1YWIgPPvgADRo0QN26deHr64uEhASjxp+amoqePXvCwsICdnZ2GDduHPLz8w3m9/iZXmBgoPQdn927d8elS5cwbdo0mJiYwMTEBMD/XhreunUrmjdvDnNzc/j7++Py5ctSPyNGjEBgYKBB31OnTkX37t2l9YmJiViyZInU98WLF42aH9GfxdAkqmLr1q1D/fr1ceTIEUyePBkTJkzAe++9h86dO+P48ePo3bs3hg0bhvv37wMArl69irfeegsdO3bEyZMnsWLFCnz77bf45JNPpD5nzJiBxMREbNu2Db/88gsSEhJw/Phxg/1OmjQJSUlJ2LhxI06dOoX33nsPffr0wblz52SNu6CgAP7+/qhXrx6OHj2KzZs349dff8WkSZNkz/3nn39Gw4YNMW/ePFy/fh3Xr1+X1t2/fx+ffvop1q9fj4MHDyInJweDBg2S3feSJUug1WoxduxYqW9XV1fZ2xNViZr+mhWil0m3bt1Ely5dpMclJSWibt26YtiwYVLb9evXDb7Yec6cOaJFixairKxMqlm2bJmwsrISpaWl4t69e0KpVIpNmzZJ62/fvi0sLCzElClThBBCXLp0SZiampb70t5evXqJsLAwIcQfX3Gn0WieOPZVq1aJevXqifz8fKktJiZGKBQK6aucunXrJu1Tr1+/fgZfF9W4cWOxaNEigxr91+s9+jVT6enpAoD0fZ7BwcGiX79+BttNmTJFdOvWTXpc0f6Jnqc6NZzZRC+dtm3bSv82NTWFnZ0d2rRpI7U5OjoCAG7cuAEASE9Ph1arlV7KBIDXXnsN+fn5uHLlCu7evYuioiL4+vpK621tbdGiRQvpcWpqKkpLS/HKK68YjKWwsBB2dnayxp2eno527dqhbt26BuMoKyvD2bNnpXE/qzp16qBjx47S45YtW8LGxgbp6enw8fH5U30TPS8MTaIqZmZmZvDYxMTEoE0fjmVlZVW2z/z8fJiamiI5ORmmpqYG66ysrKpsPwqFAuKxr+AtLi5+4fsmqip8T5OohrVq1QpJSUkGgXHw4EFYW1ujYcOGaNq0KczMzHD48GFp/d27d/Hf//5Xety+fXuUlpbixo0baNasmcHi5OQkexwnT55EQUGBwTgUCoV0Vmtvb2/wPmVpaSnS0tIM+lEqlSgtLS3Xf0lJCY4dOyY9Pnv2LHJyctCqVasK+waAlJQUWX0TPS8MTaIaNnHiRFy+fBmTJ09GRkYGtm3bhoiICISGhkKhUMDKygqjR4/GjBkzsHfvXqSlpWHEiBFQKP734/vKK69g6NChGD58OH7++WdkZmbiyJEjiIyMRExMjKxxDB06FObm5ggODkZaWhr27duHyZMnY9iwYdJLsz179kRMTAxiYmKQkZGBCRMmICcnx6AfNzc37N+/H1evXsWtW7ekdjMzM0yePBmHDx9GcnIyRowYgU6dOkkvzfbs2RPHjh3D+vXrce7cOURERJQLZDc3Nxw+fBgXL17ErVu3qvRsnUgOhiZRDWvQoAF27dqFI0eOoF27dhg/fjxGjx6NuXPnSjULFy5E165d8fbbb8PPzw9dunSBt7e3QT9r167F8OHDMX36dLRo0QKBgYE4evQoGjVqJGsclpaWiIuLw507d9CxY0cMGDAAvXr1wtKlS6WaUaNGITg4GMOHD0e3bt3QpEkT9OjRw6CfefPm4eLFi2jatCns7e0N+p81axaGDBmC1157DVZWVoiOjpbW+/v746OPPsLMmTPRsWNH3Lt3D8OHDzfo+4MPPoCpqSk8PDxgb2+PrKwsWXMjqiom4vE3EYiIqlhUVBSmTp1a7qyUqLbhmSYREZFMDE0iIiKZ+PIsERGRTDzTJCIikomhSUREJBNDk4iISCaGJhERkUwMTSIiIpkYmkRERDIxNImIiGRiaBIREcn0/wGV7e3qjuDXBQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 500x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Standard deviation =  0.015461428641899205\n",
      "Average value = 0.0020508674370250646\n"
     ]
    }
   ],
   "source": [
    "# Calculate the analytic hedge using Blach-Scholes solution for all the 'Ktrain' paths\n",
    "logincrements = xtest[3:3+N]\n",
    "hedge = np.zeros(Ktrain)\n",
    "price = S0*np.ones((Ktrain,N))\n",
    "\n",
    "# Loop that iterates over all time steps\n",
    "for k in range(N-1):\n",
    "    helper = logincrements[k][:,]\n",
    "    helper = helper.transpose()\n",
    "    price[:,k+1] = price[:,k]*np.exp(helper[:])\n",
    "\n",
    "    # Call Option price as a function of time:\n",
    "    hedge[:] = hedge[:] + scipy.norm.cdf((np.log(price[:,k]/strike)+0.5*(T-k*T/N)*sigma**2)/(np.sqrt(T-k*T/N)*sigma))*(price[:,k+1]-price[:,k])\n",
    "\n",
    "# We add the initial (priceBS) and final condition (payoff)\n",
    "hedge[:] = hedge[:]-0.5*(np.abs(price[:,N-1]-strike)+(price[:,N-1]-strike))+priceBS\n",
    "fig = plt.figure(figsize=(5,4)) \n",
    "ax = fig.gca()\n",
    "plt.hist(hedge)\n",
    "plt.title('Black-Scholes solution', fontsize=13, color='black')\n",
    "ax.set_xlabel('model output')\n",
    "plt.show()\n",
    "\n",
    "print('Standard deviation = ', np.std(hedge))\n",
    "print('Average value =', np.mean(hedge))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get the weights of the model\n",
    "weights = model_hedge.get_weights()\n",
    "#print(weights)\n",
    "\n",
    "# Use the weights to construct Delta(S)\n",
    "# This works when the number of layers equals d=2\n",
    "def deltastrategy(s,j):\n",
    "    length = s.shape[0]\n",
    "    g = np.zeros(length)\n",
    "    for p in range(length):\n",
    "        ghelper = np.tanh(s[p]*(weights[j*2*d])+weights[j*2*d+1])\n",
    "        g[p] = np.sum(np.squeeze(weights[2*(d-1)+j*2*d])*np.squeeze(ghelper))\n",
    "        g[p] = g[p]+weights[2*d-1+j*2*d]   \n",
    "    return g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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xy/NFGo2GihUr8v7773P8+HHs7e1ZuXLlSw/0zerf77TamjVrVpKeqxdvo0aNMtZfuXIl58+fZ9q0aRQuXJg5c+ZQqVKldAcGA3z66adcu3aNefPm4evry7Jly6hVqxZjx47NsveT1iJlplrvKCd+jvmZ9IyIdHXu3JkDBw6wbNkypk+fnm79xL8QLly4QLNmzZK8dvHixSR1stqlS5do3759mvvcs2cPDx484LvvvqNfv35J6n700UdZEodWq6V169bGLvBt27bRpk0b5s6dy9dff53kGP1Xdh2j1P4DT+x5SimWy5cvo9frXzmW+Ph4gHR72L7//nsaNmyYbAbU9evXk9UtXbo0ly9fJjY2Fq1Wm24M48aNw9fXlzFjxpCQkMDKlSuTfIGsXr2a6Oho43MrK6t023R2dsbX15dTp04RHByMm5sbpUuXZsuWLQQFBWW4dyQ9L/6++Pr6JnktI78vpUqVAgynJ//bc5WaChUqUKFCBT788ENCQkLw8/Nj3LhxDB06NN0VS0uUKMHw4cMZPnw4MTExBAQEMHPmTEaNGoWrqyslSpRg+/bthISEJOtxvHjxInZ2djg7O6fafuLspadPnyZ7LaU/mjKzwmpOfB5EctIzItI1YMAAypQpw+zZs1OcmguGMRALFy4EoHnz5hQqVIj58+cn+fIJDw9n/vz52NjY0Lx582yJ9ZtvviE0NNT4PDQ0lEWLFuHg4ECjRo2Af/+C+e9fLDt37sySqXiJs0leVK1aNeDf/zyrVatGsWLFWL58OYGBgcZ68fHxzJo1C5VKlSypelU2NjZJYkiUOPXy119/5e+//zaWK4rCjBkzAOjYseNL71dRFOPvTfXq1dOsq9Fokv1cIiMjk8yCSNSjRw+ePXvGp59+muI+U/Lhhx/yxRdfsHr1arp3757kr+h69erh7+9vvCXOZImKikpxyjcYTslcvHgRZ2dn4ymdHj16ABjH/mQkrvS0a9cOlUrFrFmzjIkdwMOHD1m+fDne3t5UrVo11e0DAgJwdXXls88+S/ELPDo62vhZffr0abK4HRwcKF68OFFRUcTExKS6n9DQ0CTxgWEcUeLp08TTbB06dECv1/PZZ58lqfv7779z+vRp2rVrl+L4mkTFixfHzMws2dizQ4cOceTIkWT1bWxsePbsWYaOf3Z/HkTKpGdEpMva2prffvuNNm3a0KFDB1q0aEHz5s0pXLgwjx8/Zt++fezYsYMxY8YAhv+4Zs6cydChQ/Hz8zNOqV2xYgXXr19n8eLFSQaZZqXE5ccTezyWL1/OnTt3WLZsmfFUS/369Y3TaW/dukXRokU5c+YM33//PRUrVuT8+fOvFEOLFi1wcHCgQYMGeHl5ERISYlwHpVevXoDhS3fBggV07NiRmjVrMmjQIGxtbVm3bh1HjhxhwoQJxr9ms0rt2rVZsGABQ4YMoU2bNpibm+Pn50fx4sX58ssvadSoEQ0aNDBOZfztt9/YsWMH3bt3T9bDlZqEhAR++OEH4/NHjx6xceNGDh48SIsWLdJtp0uXLixevJiuXbvi7+9PUFAQ3333nfH8+4vee+89fv31Vz799FOOHz9OixYtsLS05MKFC1y5ciXZF1Wi999/HwsLC4YNG0ZCQgI//vhjmoteRUVF0bhxYypUqEDLli0pVaoUiqJw+fJlVq1aRUxMDF9//bXxy/ONN96ga9eurFq1imvXrtGuXTscHR25evUqO3bsSPIFl1FlypThww8/ZObMmTRs2JCuXbsap/ZGRESwevXqNE/jFSpUiFWrVtGhQwfKlClD//79KVmyJCEhIVy+fJmNGzeyadMmGjduzKpVq/jiiy/o2LEjJUuWxNzcnD/++IMdO3bw5ptvptljtG/fPgYNGkTnzp0pU6YMNjY2nDx5kmXLluHn52ecFt23b19WrlzJ559/zq1bt2jYsCHXr19n4cKFuLm5pdsDa2NjQ9++fVm2bBndunWjcePGXLt2jeXLl1OpUiXOnj2bpH7t2rX57bffGDZsGHXr1kWj0dC0adNUx6Rk1edBZELOTt4ReVlkZKQyd+5cpV69eoqDg4NiZmamuLq6Kq1bt1ZWrVqVZGqhoijKxo0blTp16ijW1taKtbW1UqdOHWXTpk3J2v3vNMREKU39VJSUp/olTpPctWuXMmnSJMXLy0uxsLBQKlSooKxevTpZ22fPnlUCAgIUBwcHxcbGRmnUqJFy4MCBTE8LTCmWJUuWKP7+/oqbm5tibm6uuLu7K61atVL27t2bbPv9+/cr/v7+iq2traLVapUqVaooy5YtS1YvtRhS2n9qdDqdMmrUKMXT01NRq9XJpkaeOXNGad++veLo6KhYWFgoZcuWVT7//PNkP9fUpDS119LSUqlQoYIybdo0JSYmJkn9lH6+kZGRyujRo5VixYopWq1WKVmypDJjxgxl9+7dKU7ljI6OVj799FOlfPnyilarVezt7ZUaNWooX3/9dZr7URTDzylx6viL02X/Kz4+Xvnuu++Ut956SyldurRia2urmJubK0WKFFE6duyY4s9Vp9MpCxYsUKpWrapYWVkpNjY2SsWKFZUpU6YY6yT+ziZOqf3vsUzp571kyRKlSpUqilarVWxtbRV/f3/lwIEDyeql9pk6f/680qNHD6VIkSKKubm54urqqtSpU0f55JNPlCdPniiKoiinT59Wevfurfj6+irW1taKra2tUqlSJWX27NnJfob/dePGDeWdd95RypYtq9ja2irW1tZK2bJllY8//jjJlHtFMUyvHzdunFK8eHHF3NxccXFxUXr27KncunUrSb3UfsfDw8OVt99+W3FyclKsrKyU+vXrKwcPHkzxMxwZGan0799fcXV1Nf7uJx731Ka8Z/TzkNaUeUDp06dPmsdMGKgURUbXiLxvxYoV9OvXj3379uWbq5UKIURBIWNGhBBCCGFSkowIIYQQwqQkGRFCCCGEScmYESGEEEKYlPSMCCGEEMKkJBkRQgghhEnJomfp0Ov1PHjwAFtb20wtKSyEEEIUdIqiEB4eTpEiRdJcVVeSkXQ8ePAALy8vU4chhBBC5Fl3796laNGiqb4uyUg6Ei/5fvfuXezs7EwcjRBCCJF3hIWF4eXlZfwuTY0kI+lIPDVjZ2cnyYgQQgjxEtIb5iADWIUQQghhUpKMCCGEEMKkJBkRQgghhEnJmJEsotPpiI+PN3UYogAyNzdHo9GYOgwhhHhpkoy8IkVRCAwMJCQkxNShiALMwcEBd3d3WQtHCJEnSTLyihITEVdXV6ytreXLQOQoRVGIiori0aNHAHh4eJg4IiGEyDxJRl6BTqczJiKFCxc2dTiigLKysgLg0aNHuLq6yikbIUSeIwNYX0HiGBFra2sTRyIKusTfQRm3JITIiyQZyQJyakaYmvwOCiHyMjlNI4QQQuRziqIQp9MTE68nNl5HdLyOmHg9McbHhucuthZU93bK8fgkGRFCCCHymOg4HY/CY3gUHktQWAyPw2MJiYonNDrpLSQqjtDoBEKj44jXKem22/I1d6r3kmREmMiUKVOYOnUqYOjyt7W1pVixYjRq1IihQ4dSrlw5E0eY3P79+2nSpAnHjx+nRo0a2bKP999/n82bN3Pr1q1Mbde3b19OnDjB33//nS1xCSHyL51e4WFoNHeeRHHnqeEWGBpDUHgMj8IMyUdYTMJLt69WgaW5BitzDZbmGrTmaizNNFhZaCjhUigL30nGSTIijKysrNi7dy8A4eHhnD9/niVLlrB06VK+/fZbevbsaeII846PP/6YyMhIU4chhMilFEXhfkg0V4PCufE4ktsvJB73nkVlqBfD0lyNm50lbraWuNhqcbA2x97K3HhvuFkY7q3NsdGaYWWuwVyjynXjzCQZEUZqtZratWsbnzdv3pwhQ4bQpk0b3n77berWrUuJEiVMGGHe4evra+oQhBC5gKIoPAqP5WpQOFcCw7kWFMGVoHCuBYUTGadLdTtzjQovR2u8nKwp5mRNEQcr3Oy0huTDTournSW2WrNcl1S8LJlNI9JkaWnJ/PnziYuLY9myZUleW7FiBZUqVcLS0hJPT08mTpyITpf0w3Xv3j169uyJs7MzVlZWNGzYkJMnTyap4+Pjw7Bhw5g1axaenp5YW1vTvn17Hj58mKEYnz17Rvfu3bG1tcXb25uZM2cmq3P48GGaNm1KoUKFsLe3p3v37saFwhI9ePCAdu3aYW1tjaenZ4rtAPz1119UrVoVS0tLKlWqxK5du6hSpQp9+/Y11unbty8VKlRIcqxUKhWnT5+mVatWFCpUiFKlSrFq1aokbSuKwieffIK7uzs2Nja88cYb7N69G5VKxf79+zN0PIQQpqEohtMr2/8OZOb2y/RcdpSq/9uF3/Q99Pr2GJ9uvcS6E3c5czeEyDgd5hoVZd1taVPJgyGNffm8c0XWDPTj4LimXP5fK/aObszK/rX4X4cKvNvYl07VilKvpDMlXW2xszTPN4kISM9ItlAUhej41DPenGBlrsmyX9Ty5cvj6enJ4cOHjWVz585lzJgxfPDBB8yZM4dLly4Zk5HPPvsMMCQJ9evXx8bGhvnz52Nvb8/8+fNp2rQp165dw9XV1djepk2b8Pb25ptvvuHZs2eMHTuWTp06JdlnagYPHkyvXr3YtGkTmzdvZuzYsVSqVImWLVsChkSkcePGtG7dmnXr1hEZGclHH31E+/btk7Tfvn177t27xzfffIODgwOfffYZd+/exczs34/Jw4cPadmyJdWqVeOnn34iNDSUd999l9DQUKpUqZJurD169GDgwIGMHDmSpUuX0rdvX2rWrGkckzN//nymTJnCmDFjaNq0KXv37mXAgAHptiuEyHkhUXGcvRfKubshnL0Xytl7ITwOj01WT60CH+dClHGzpZSbLWXcbCnjboN34UKYa6RPACQZyRbR8TrKT9ph0hgufhKAtUXW/Xi9vLwIDAwEDONJJk+ezJgxY5g+fTpgOKVjYWHByJEj+fDDDylcuDDz5s0jJCSEY8eOGROPZs2aUbp0aWbPnp2k5yE8PJzff/8de3t74/6aNWvGjh07CAgISDO2zp07M2XKFGP7W7duZcOGDcZkZNy4cdSoUYONGzcaE7SKFStSoUIFtm3bRuvWrdm+fTsnTpxgz549NG3aFIDGjRvj5eWFk9O/I8u/+OILzMzM2Lp1K7a2tgAUL16cBg0aZOg4Dhs2jCFDhgBQt25dtm7dys8//8xHH31kTOT69etnTOhatGhBcHAw3377bYbaF0Jkn+CIWI7dfMrRG084evMplwPDk9XRqFWUcrWhclEHKnnZU7moAyVdbbA0l5WR0yLJiMgQRVGMX+SHDh0iIiKCN954g4SEf0d0+/v7Ex0dzd9//02jRo3YuXMnTZo0wcnJyVhPo9HQqFEjjh8/nqT9Jk2aGBMRgKZNm+Lk5MTRo0fTTUZatGhhfKxSqShXrhz37t0DICoqioMHDzJ79uwkp5BKly6Nl5cXx48fp3Xr1hw9ehR7e3tjIgJgb2+Pv78/p06dMpYdP36cJk2aGBMRgPr16ydJWDIaa6FChfD29jbGeu/ePR4+fEi7du2SbNO+fXtJRoQwgUdhMRx5Ifm4/igiWZ3izoWoVNSeSkUdqFzUnteK2GNlIYlHZkkykg2szDVc/CTtL9CciCEr3bt3j9KlSwMQHBwMQLVq1VKse/fuXWO9I0eOYG5unqzOfwd4vnjK5sWyjIwbcXBwSPLcwsLCeBXlZ8+eodPp+OCDD/jggw9SjfXhw4e4uLgke93NzS3J84cPH1KqVKkUY82IlGKNiYkxtg0kiyOjbQshXk1cgp7jt56y/8oj9l95zLUUko+y7rb4FXfCr0RhahV3wtlGa4JI8x9JRrKBSqXK0lMkpnbhwgXu379vHKCZ2AuwceNGvLy8ktUvXry4sV7Lli353//+l6yOVpv0A/zfwaSJZa96FVoHBwdUKhUTJkygQ4cOyV53dnYGDFe7ffz4cbLXg4KCkjxPrV5K8WdW4nv9b/tZ0bYQImX3Q6KNycfB68FEvTDDRaWC8h52+BUvjF8JJ2r5OOFYyMKE0eZf+ecbU2SLmJgYhg8fjlarNQ6krFOnDtbW1ty7d4+OHTumuq2/vz8//PAD5cqVo1ChtBfS2bdvH6GhocZTNXv37uXp06f4+fm9UvyFChWiTp06XLp0iU8//TTVerVq1SI0NJS9e/caT9WEhoaye/fuJKdgatasyeLFiwkPDzeeqvnzzz95+vTpK8UJULRoUdzd3dmyZQvt27c3lm/evPmV2xZCGOj1CqfvPmPHhSD2XX6UrPfD2UZLo9IuNCnrQoOSLthbJ+/ZFVlPkhFhpNfrOXLkCAARERHGRc9u3LjBihUr8PHxAQy9DZ988gljxozh3r17NG7cGI1Gw40bN9iyZQs///wz1tbWjBw5ktWrV9OoUSPee+89ihUrxuPHjzl69ChFihRJctrE1taWVq1aMW7cOEJCQhg7diy1atVKd7xIRsyaNYumTZvStWtX3nrrLRwdHbl37x67du2iX79+NG7c2DhDpkePHnz++ec4ODgwY8YM7OzskrT1wQcfsHDhQtq0acOHH35ISEgIU6dOxdnZGbX61UbFazQaxo8fz/vvv4+bmxtNmjRh37597N69G+CV2xeioNLpFY7dfMr2vx+y/UIgQWH/znhRq6BaMUcal3GhcRlXynvYoVbnnymzeYUkI8IoOjqaOnXqAGBjY4OPjw/NmjVj06ZNlC1bNkndUaNG4enpydy5c5k/fz7m5ub4+vry+uuvY2Fh6MYsXLgwR44c4aOPPmLs2LE8efIEV1dXateunaxHpWPHjhQtWpTBgwfz7NkzmjdvzqJFi7LkfdWtW5e//vqLyZMn069fP+Li4ihatCjNmjWjZMmSgOHU2pYtWxg8eDDvvPMOjo6ODB8+nKCgoCQ9Ex4eHvz++++MGDGCLl264Ovry5dffsmwYcOSDMB9WcOHD+fZs2csXLiQr776Cn9/f2bNmkXXrl2zpH0hCop4nZ4jN56w7Xwguy4GEhwRZ3zNVmtGs3Ku+Jd3k96PXEKlKEr6a84WYGFhYdjb2xMaGprsr+SYmBhu3rxJ8eLFsbS0NFGEeZ+Pjw+vv/46CxYsMHUoL+XatWuULVuW7777jj59+mR5+x9//DFz5szhyZMnWFlZpVhHfheFMJyCOX7rKZtO32f7hUBCouKNr9lbmdOivButK3pQt2RhtGYy4yUnpPUd+iLpGREik8aPH0+lSpUoUqQIN27cYPr06Xh4eNC5c+dXbvvSpUv88MMP1K1bFwsLC/bv38/s2bN59913U01EhCjobgVHsvH0fTadvsfdp9HG8sKFLGjxmjutK7pTu0RhWWAsF5NkRIhMiouLY+zYsQQFBWFlZUXjxo2ZNWsWNjY2r9y2tbU1hw8f5ptvviE8PBxPT08+/PBD46JuQgiD0Oh4tp57yMZT9zhx+5mx3EZrRuuK7nSo6olf8cJoZPxHniCnadIhp2lEXiC/i6Ig0OsVDv4TzI/H77LrYhBxCXrAMAi1fikXOlfzpEV5d1l0LBeR0zRCCCHyhZCoODacvMcPR25z60mUsby0mw2dqxWlQ1VP3OwkCc/L8tQJtAMHDtC2bVuKFCmCSqXK0PoL+/fvp1q1ami1WkqWLMmKFSuyPU4hhBCvRlEUztwNYdRPZ/GbvodPt17i1pMobLRm9K7jzW/D67Pj/Ya808hXEpF8IE/1jERGRlK5cmX69+9Pp06d0q1/8+ZN2rRpw+DBg1m9ejV79uxhwIABeHh4ZMn6FUIIIbJWVFwCv5x5wA9Hb/P3/TBjeXkPO3rW9qZ9lSIU0uapry6RAXnqJ9qqVStatWqV4fqLFi2iePHizJkzB4By5crx119/8cUXX0gyIoQQuUhQWAwrDt1i9ZHbhMUYLqxpoVHzeiUPetT2ploxB+PFOkX+k6eSkcw6fPgw/v7+ScoCAgJ4//33U90mNjaW2Nh/V+cLCwtLta4QQohXcy0onCUHbrD5zH3idYb5FF5OVvT08+aNGl445fdrwSgK6OKe3+IN9wmx/z5OLNfHP79P+Pf23+f6BNDrQNEb7vUJoOiel+lArze8pjyvk1gv8bGiB7fXoFrvHD8M+ToZCQwMTHbVVTc3N8LCwoiOjk5x3YYZM2YwderUnApRCCEKHEVROHrzKUsO3GDv5X8vBFnd25FBDUvQvJxb7lqSXa+D2PDntzCICfv3cVwExEVCXBTE//c+yvBaQiwkxLxwi016n5uUfV2Skdxg/PjxjBw50vg8LCwsxSvTCiGEyJwEnZ4dF4JYcuAfzt4LBQxXxm1R3o1BDUtQ3dspnRaygC4eIh5BRCBEPoHopxD1FKISHz95/vwpRD8zJB1x4dkfVyKVBjQWz2/mYKYFtZnhsdocNGaG52rz5+WJz5/fVGpQawztqM1eeKx+fq8x1FEl3qteKFODS7mce68vyNfJiLu7e7JLwAcFBWFnZ5fqapZarTbZ5e0LiilTpiTpFdJqtRQvXpx+/foxevRo1Go1t27donjx4qxfv54uXbpk6f5VKhWzZs1i9OjRmd529erVfPnll1y5cgVFUfD09KRevXpMnz4dV1fXDLWxYsUK+vXrx+PHj3F2ds50DNnVlhB5XYJOz5YzD5i/95pxaq7WTE2X6kV5u35xSri8+oKBAMRGQMgdCLkNofcgIgjCH0J4EIQHPk9AgoGXXF5LowVLO9Dagjbx3hbMrcHCGswLPb+3BotC/96bWRpu5s/vzbT/lplZgpmFoW2NuSExKIDydTJSp04dtm3blqRs165dxovBieSsrKzYu3cvYLhw3r59+xg3bhx6vZ5x48aZOLqUzZw5k3HjxvHBBx/wySefoCgKf//9N6tXr+bBgwcZTkaEEFkrQafnl7MPmL/3OjeDIwFwtDanVx0fetfxxtkmk3/4KQqE3Yfgq/DstiHpePE+Kjhj7ag0YOMGhZzB2gmsC4PV83vjc0fDzdLekHhY2hmSCJEt8lQyEhERwfXr143Pb968yZkzZ3BycqJYsWKMHz+e+/fvs2rVKgAGDx7MggULGDNmDP3792fv3r389NNPbN261VRvIddTq9XUrl3b+LxJkyacP3+ejRs35tpk5KuvvqJv377GWVNgmHn14YcfotfrTRiZEAWTTq/wy9n7zN9znRvPkxCnQhYMaliCXrW905+aq9dD2D14dBkeX4bHV+DxJXh8Nf1TJpYO4OgNdkXB1h1sPcDWzXBv8/zeurDhtIXINfLUT+PEiRNUrVqVqlWrAjBy5EiqVq3KpEmTAHj48CF37twx1i9evDhbt25l165dVK5cmTlz5rBs2TKZ1ptJtra2xMfHp/r6qlWrqF+/Pk5OTjg6OtK4cWOOHTuWrN6lS5fo1KkTTk5OWFtbU7lyZdauXZtquzdv3sTX15dWrVoRHR2dar1nz57h4eGR4mvq//yHs2rVKqpWrYqlpSXOzs60bt2a27dvJ6lz9+5dWrVqRaFChShVqpQxuX3R4sWLKVOmDFqtFh8fHz799NN0E5/Y2FgmTJiAt7c3Wq2WcuXKsWbNmiR1Lly4QOvWrSlcuDDW1taUKVOGmTNnptmuELmFTq+w+fR9ms/9gw/WneVGcCSO1uaMbVmWP8c0YXAj3+SJiF5vSDLOrIWto2FpU5hRFOZVhDVvwK6P4cwPcP+kIRFRm4FzGSgVALUGQYtp0PUHeOdPGHcHxt2Gdw5AtzXw+lxo9KFhQGap5uBRCWxcJBHJhfJUz0jjxo1J61I6Ka2u2rhxY06fPp2NUaVAUQyjqE3J3NowMOklJCQY5vgnnqb5+eefmTBhQqr1b926Re/evfH19SUuLo61a9fSsGFDzp07R+nSpQG4du0aderUwcvLi6+++gp3d3f+/vvvJMnji65cuUKzZs3w8/Nj7dq1WFikPr2vevXqxjVlXn/9ddzd3VOsN2vWLMaMGcPbb7/NtGnTiI+PZ+/evTx+/Bhvb29jvR49ejBw4EBGjhzJ0qVL6du3LzVr1qRcOcPArvnz5zNixAiGDx/O66+/zqFDh5gyZQohISHMnj071TjffPNN/vrrLyZPnky5cuXYtm0bPXv2xNHR0bh+Ttu2bXFzc+Pbb7/F3t6e69evc+/evVTbFCI3UBSF3/8OZPbOK9x4bOgJcbA2Z1DDEvSu44PNiwlI2ENDYpF4e3DaMCvlv9Tm4FwKXMoYBlW6lAHXcuBUwjC2QuQreSoZyTPio2B6EdPGMOGBYeBUJkVGRmJunvSD3rVr1zRP0ST2TAHo9XqaN2/OsWPHWLFiBdOnTwcMg2MtLCw4ePCg8WJJ/10DJtHZs2dp0aIFAQEBLF++HI0m7QFdCxcupGPHjgwcOBAw9Ii1bduWDz74AB8fHwBCQ0OZMmUKgwYNYvHixcZt27dvn6y9YcOGMWTIEADq1q3L1q1b+fnnn/noo4/Q6XR88sknvPXWW3z11VcAtGjRgri4OObMmcP48eMpXLhwsjb37dvHL7/8wo4dO2jRogUAzZs35+HDh0yePJlWrVoRHBzMzZs3+fLLL2nbti1gOE0mRG52/NZTpm29xJm7IYAhCRnYoAR96j5PQiIew9U/4MZ+uPmHYYDpf5lZQZEq4FkdilQF90rgVFySjgJEkhGRhJWVFQcOHAAMpxVOnjzJpEmTGDhwIN99912K21y6dIkJEyZw6NAhHj36d82Aq1evGh/v2bOHLl26pHnVRoDjx48zbdo03nrrLRYuXJhkxUWdTpekZ0yj0aBSqahQoQIXLlxg9+7d7Ny5kz/++IOvvvqK5cuXc+DAAapUqcLhw4eJiori7bffTvcYJCYLAIUKFcLb29vYO3H58mWCg4N54403kmzTtWtXZsyYwbFjx1JcJXjnzp04OTnRtGlTY88TGBKSwYMHo9PpKFy4MN7e3owfP56nT5/SrFkzihYtmm68QpjC9UcRfL79MrsuGmYsWltoGNCgBAP9XLANOgH7lxsSkKC/k26oUoNrefCsZkg+PKsbej408nVUkMlPPzuYWxt6Jkwdw0tQq9XUqFHD+LxevXokJCQwatQoRo4ciY1N0il44eHhtGjRAhcXF+bOnYu3tzeWlpYMGDCAmJh/F/N58uQJRYqk31u0e/duIiMjefvtt5Mt/dysWTP++OMP4/N9+/bRuHFjACwsLGjdujWtW7cGYMeOHbRp04ZPPvmEjRs38uTJE4AMxeDg4JDkuYWFhfG9PHv2DCDFxfQAnj59mmKbwcHBPH36NFmvU6KHDx9StGhRdu7cycSJExk6dCiRkZFUr16duXPn0rBhw3TjFiInPAqP4cvd1/jx+F10egWNWsU7lc151/UCtre+gsPHDKuFvsitIpRoBCUaQ7E6oM2iqbwi35BkJDuoVC91iiS3ShwrceHCBfz8/JK8dvjwYe7du8dvv/1G5cqVjeWhoaFJ/qovXLgwDx6kn6CNGTOG48ePExAQwP79+6lYsaLxtcWLFxMe/u9I+jJlyqTaTkBAAJUrV+bSpUvG/QM8ePDglXobnJwMizK92AMEGNezSXw9pe1cXFySTTVPlDj9uHTp0qxfv574+HgOHTrEhAkTaNu2Lffv30+WCAqRkyJjE1j65w2WHLhBVJwOL1UQIzwu0db8KJaXzsKlFyrbFwPfxlC8keFm42KqsEUeIcmISNfffxu6WVNavCtxlsuLA0wPHTrErVu3eO2114xl/v7+bNiwgc8//xxbW9tU96XRaFi7di2dOnXC39+fAwcOGJOO1JKPoKCgZD0V0dHR3L171xhDnTp1sLa2Zvny5dSqVSsjbztFZcqUwcXFhfXr19OxY0dj+U8//YSFhUWqbfv7+zNz5kwsLCyoVKlSuvsxNzenUaNGjBs3jnbt2vHgwQPjYGAhcpKiKGw+c5/p2y5jHXGbPupjdLY5QcmE6/AssZYKvOtB+XaGWSuOxV96AL0omCQZEUno9XqOHDkCQFxcHCdPnuTTTz+lfPnyNGzYkPv37yepX7t2bWxsbBg6dCjjxo3j/v37TJ48GU9PzyT1Jk+ezG+//Ub9+vUZM2YMHh4eXLx4kaioKMaMGZOkrrm5ORs2bKBt27Y0a9aMAwcOUKJEiVRjrlixIm3btiUgIAAPDw/u37/PggULCA4O5r333gPA3t6eyZMnM3bsWPR6Pe3bt0ev17Nv3z66deuW5NRUWjQaDR9//DEjRozA1dWV1q1bc+TIET7//HPef//9FAevgmFsSNu2bWnZsiVjxoyhUqVKREZGcuHCBa5fv86yZcs4d+4co0aNomvXrvj6+hIaGsqMGTPw8fHB19c3Q/EJkZUuPAjls83HKXZ/K99p9lJRe8vwQgKGsR8+9aF8B8P1TGzd0mhJiLRJMiKSiI6ONq5Qa2ZmhpeXFz179mTy5Mkpjndwc3Nj/fr1jB49mvbt21O6dGkWL17M559/nqReqVKlOHToEOPHj2fIkCEkJCRQunTpVGfpaLVaNm/eTKtWrYwJSWrXCJoyZQq//vorI0eONC6/XqlSJfbs2ZNkNsqYMWNwcXHhiy++YMWKFdja2lKnTp1Mr9A6fPhwzM3NmTt3LgsXLsTDw4MpU6akOf0ZYMOGDXz22WcsXLiQ27dvY29vT4UKFejXrx9guHyBu7s7M2bM4P79+9jb29OgQQN++OGHdGcUCZGVQqPiWb3lVxwufs836kPYmBvGTCkqDariDeG1DoYEpJBc6kBkDZWS1sIdgrCwMOzt7QkNDU02EyQmJoabN29SvHhxLC0tTRShEPK7KLKGPiaCE9u+xercKiry72rX8Y4lMa/VHyq9BYVS7v0TIiVpfYe+SHpGhBCioAu+zuO987G6tJ5aimHRsnjMCPFuiUvjwZj71JcxICJbSTIihBAF1aNLxO+fiebiJlyeX8n2ruLGw1JvUbXdUFzsZByIyBmSjAghREET+DccmIly8RfMnychu3TV+MenO5269KCW/cutUyTEy5JkRAghCooHZ+DALLj8GwAqYJuuFhttuvF2l/YM9pXxIMI0JBnJAjIGWJia/A6KNN07CQdmwtXtAOhRsVXnx0J9J5o0aMSCZqWwNJcZW8J0JBl5BYlTXaOiorCysjJxNKIgi4oyXCU6teXmRQEVeg92fgQXNgGgR80WXR0WJHTAukh55nSuRPkiaV8vSoicIMnIK9BoNDg4OBiXBre2tk52PRUhspOiKERFRfHo0SMcHBxkPRJhEB8Dh+fDn3MhPgo9ajbr6/NVfHsCzTwZ3boMfev6YKZRmzpSIQBJRl6Zu7s7kPxaJULkJAcHB+PvoijAFAWu/A47xsOzWwBcMH+NDyN6cFHxoX5JZ1Z1rEixwjJAVeQukoy8IpVKhYeHB66ursTHx6e/gRBZzNzcXHpEBARfg+3j4PpuAKK0Lnwc/RY/h9fG1tKcWa+Xp0v1otJ7K3IlSUayiEajkS8EIUTOiw2HP2bCkW9AH4+iseA3646MfRxAFJbUK1mYWV0qU8RBxrWJ3EuSESGEyKv+2Qubh0L4AwAC3RoxIKgTfz92QWumZkqrsvSu44NaLb0hIneTZEQIIfKauCjYPQWOLQZA5+DDYutBzLzhA0DlovbMebMKJV1tTBejEJkgyYgQQuQlD07DxkEQfBWA+6V68tbN1twNBI1axYimpRjSxBdzmSkj8hBJRoQQIi/QJcBfX8Afn4E+AcXGnbUeY5hw3jCLytelEF90rUKlog6mjVOIlyDJiBBC5HZP/oFN78C94wBElnydQU97cPC8YeXdvnV9GNeqrKyiKvIsSUaEECK3UhQ4uRx2TIT4KNDacarCRHqf8CEiVoe9lTmz36hM8/JydV2Rt0kyIoQQuVFsOGx+Fy79CoDOuwGzrN5j0cE4QEdNH0e+fKuqTNkV+YIkI0IIkds8vQFru8PjS6A251Ht8fT6uxpXrkShUsGwJiV5r1kpWc5d5BuSjAghRG7yz15Y3w9iQlBs3NhVcTYj/jQnJj4KF1stX3atQt2SzqaOUogsJcmIEELkBooChxfArkmg6NEVqcZUq/Gs2hcP6GlY2oW5b1bG2UZr6kiFyHKSjAghhKnFR8Ov78G5dQCEl32T7g+7cv5GLBq1ijEBZRjYoISspCryrTx3wvHrr7/Gx8cHS0tL/Pz8OHbsWJr1582bR5kyZbCyssLLy4sPPviAmJiYHIpWCCHSEXoPvmtpSERUGq5U+Yi6lztzPigWZxstawfW5p1GvpKIiHwtT/WMrFu3jpEjR7Jo0SL8/PyYN28eAQEBXLlyBVdX12T116xZw7hx4/juu++oW7cuV69epW/fvqhUKubOnWuCdyCEEC+4fQh+6g2Rj1GsnFhf4n+MOeII6Kjh7cjXParhZmdp6iiFyHYqRVEUUweRUX5+ftSsWZMFCxYAoNfr8fLyYvjw4YwbNy5Z/WHDhnHp0iX27NljLBs1ahRHjx7lr7/+ytA+w8LCsLe3JzQ0FDs7u6x5I0IIcX6DYSEzfQIJLq8xxnwsG28Y/j7sW9eHCa3LYWGW5zqvhUgio9+heeY3PS4ujpMnT+Lv728sU6vV+Pv7c/jw4RS3qVu3LidPnjSeyrlx4wbbtm2jdevWqe4nNjaWsLCwJDchhMhSx5bCzwNAn0Bo8da0DP+IjTfMsDRX80XXykxp95okIqJAyTOnaYKDg9HpdLi5JV1p0M3NjcuXL6e4Tffu3QkODqZ+/fooikJCQgKDBw9mwoQJqe5nxowZTJ06NUtjF0IIwDBj5sAs2DcNgGve3Xj9WltiExS8C1uzqGd1ynlID6woePJ16r1//36mT5/OwoULOXXqFBs3bmTr1q3873//S3Wb8ePHExoaarzdvXs3ByMWQuRbej1sH29MRPa796f5ldeJTYBmZV35ZVh9SUREgZVnekacnZ3RaDQEBQUlKQ8KCsLd3T3FbT7++GN69erFgAEDAKhYsSKRkZEMGjSIiRMnolYnz8W0Wi1arczjF0JkIV08/DIczq4F4HuHd/n4VgMA3vcvxYimpWS2jCjQ8kzPiIWFBdWrV08yGFWv17Nnzx7q1KmT4jZRUVHJEg6NxnBVyzw0blcIkZfFR8O6XnB2LYpKwwzL9/k4sAFW5hoW9azG+/6lJRERBV6e6RkBGDlyJH369KFGjRrUqlWLefPmERkZSb9+/QDo3bs3np6ezJgxA4C2bdsyd+5cqlatip+fH9evX+fjjz+mbdu2xqRECCGyTUwYrO0Gt/9Cr7bgPf37/BpShSL2liztU4PXitibOkIhcoU8lYx07dqVx48fM2nSJAIDA6lSpQrbt283Dmq9c+dOkp6Qjz76CJVKxUcffcT9+/dxcXGhbdu2TJs2zVRvQQhRUEQ8htWd4eFZ4sxs6BP9AYd15ahazIHFvarjaivrhwiRKE+tM2IKss6IECLTIh7DitYQfJUIMwe6Ro7hguJDp6qeTO9UEUtz6ZkVBUNGv0PzVM+IEELkelFP4fsOEHyVJxpnukSO5xYejG1ZlsGNSqBSyfgQIf5LkhEhhMgqMWHwQ2cI+psnKkc6R43nkXlRlrxVlebl3dLfXogCSpIRIYTICnGRsOZNeHCKZ9jyVsx44u1L8HOfGrJ+iBDpkGRECCFeVXwM/Ngd7hwmTLGmZ9x4tEXKs7pvTRmoKkQGSDIihBCvIiEO1veBG/uJUCzpEzcW19I1WdC9GoW08l+sEBkhnxQhhHhZugSUjQNRXd1OjGLO23EfUrZmM/7X/jXMNHlmTUkhTE6SESGEeBl6PbrNQ9Bc3EysYsag+JE0CujAu418ZcaMEJkkyYgQQmSWohC75X2059eRoKh5T/cend/sQ/sqnqaOTIg8SZIRIYTIpNDfPsL+7Er0iooJquH06TeUOr6FTR2WEHmWJCNCCJEJD/d8g8fJBQB8Zj6EgQM/pJSbrYmjEiJvk2RECCEy6Mpfm/D9cwIAqyy7M2DIJFztZOquEK9KhnsLIUQGHDu8n6K7BmOGnv2W/rQf8aUkIkJkEUlGhBAiHb8fPIHX9n4UUsVwybIKfu/9gL21hanDEiLfkGRECCHSsGr/33jv6I+H6imBFj6UHL4ZKysrU4clRL4iyYgQQqRAURTm7rhAsT1DKK++TYSZE66Dt2BeyNHUoQmR70gyIoQQ/6HTK0zcdB73Pz+iseYs8WothfpuQO3kY+rQhMiXJBkRQogXxCXoGbH2NLYnF9LdbC8KKszfXI6qaHVThyZEviXJiBBCPBcTr+Od70/AhU2MN18LgKrlDCjbxsSRCZG/yTojQggBRMUlMHDVCcL/OcYii28MhX6Dofa7pg1MiAJAkhEhRIEXHhNP/xXHuXnrFr9pv0CriofSLSFguqlDE6JAkGRECFGghUTF0ee7Y1y494QfLb/CnadQuBR0WgJqjanDE6JAkGRECFFgBUfE0nPZUS4HhjPdci01uAQWtvDWGrC0N3V4QhQYkowIIQqkoLAYeiw7yvVHEfSxPkx3/e+GFzotBpfSpg1OiAJGkhEhRIFz71kUPZYd5faTKBrb3meyfqnhhUZjZeaMECYgyYgQokC5/SSS7kuPcj8kmoqOcSwzm4c6PMYwYLXROFOHJ0SBJOuMCCEKjJvBkXRdfIT7IdGULGzJhsJLMAu/D06+0HExqOW/RCFMQT55QogC4VZwJN2WHCEwLIZSrjb8UnYH2nuHwMLGMGDVysHUIQpRYEkyIoTI924FR/LWC4nIz/XvYX1yseHFDt+Aa1nTBihEASfJiBAiX/tvIvJTu0LY7RxleLHBaCjfzrQBCiHyXjLy9ddf4+Pjg6WlJX5+fhw7dizN+iEhIQwdOhQPDw+0Wi2lS5dm27ZtORStEMKUbgVH0m2pIREp6WrD2l7lcPytPyREQ8nm0GSCqUMUQpDHZtOsW7eOkSNHsmjRIvz8/Jg3bx4BAQFcuXIFV1fXZPXj4uJo3rw5rq6ubNiwAU9PT27fvo2Dg0POBy+EyFG3nxgSkYehzxORAX44/z4AQm6Dgzd0XiorrAqRS6gURVFMHURG+fn5UbNmTRYsWACAXq/Hy8uL4cOHM25c8il5ixYtYtasWVy+fBlzc/OX2mdYWBj29vaEhoZiZ2f3SvELIXLG7SeGUzOJiciagX64XlwJv48BtTm8vRM8q5k6TCHyvYx+h+aZ0zRxcXGcPHkSf39/Y5larcbf35/Dhw+nuM0vv/xCnTp1GDp0KG5ublSoUIHp06ej0+lS3U9sbCxhYWFJbkKIvOP2E8OsmYehMfi6FDIkImEXYcdEQ4UWn0oiIkQuk2eSkeDgYHQ6HW5ubknK3dzcCAwMTHGbGzdusGHDBnQ6Hdu2bePjjz9mzpw5fPrpp6nuZ8aMGdjb2xtvXl5eWfo+hBDZ586TKLotOcKD54nI2kG1cTWLgfV9QR8PZV8Hv3dMHaYQ4j/yTDLyMvR6Pa6urixZsoTq1avTtWtXJk6cyKJFi1LdZvz48YSGhhpvd+/ezcGIhRAv60FINN2X/ScRsdHCL8OejxMpBu2/BpXK1KEKIf4jzwxgdXZ2RqPREBQUlKQ8KCgId3f3FLfx8PDA3NwcjebfQWrlypUjMDCQuLg4LCwskm2j1WrRarVZG7wQIls9Couh+9Ij3HsWjU9ha9YOrI2rrSUcXQKXfjWME3ljhSxsJkQulWd6RiwsLKhevTp79uwxlun1evbs2UOdOnVS3KZevXpcv34dvV5vLLt69SoeHh4pJiJCiLznSUQsPZYd5daTKDwdrFgzsDaudpZw/xTsTBwn8j/wrG7aQIUQqcozyQjAyJEjWbp0KStXruTSpUu8++67REZG0q9fPwB69+7N+PHjjfXfffddnj59ynvvvcfVq1fZunUr06dPZ+jQoaZ6C0KILBQaFU+vb49x7VEE7naWrB1YmyIOVhAdYhgnoot7Pk5ksKlDFUKkIc+cpgHo2rUrjx8/ZtKkSQQGBlKlShW2b99uHNR6584d1C9c6MrLy4sdO3bwwQcfUKlSJTw9PXnvvfcYO3asqd6CECKLhMfE03v5MS4+DMPZxoLVA/0oVtgaFAV+Gf7COJEFMk5EiFwuT60zYgqyzogQuU9UXAJ9vzvOsVtPcbA258dBtSnr/vzzeXQJ/P6hYZxI/x1QVE7PCGEq+W6dESGEAIiJ1zFo1UmO3XqKraUZP7zt928i8uBM0nEikogIkSdIMiKEyDPiEvQMWX2Kv64HY22hYUW/WlTwtDe8GBsBG/obxomUaSPjRITIQyQZEULkCQk6Pe/9eJq9lx+hNVPzXd+aVPd2/LfC9nHw9B+wLSLjRITIYyQZEULkenq9wriN5/n970AsNGqW9q5B7RKF/61wYROc/h5QQaclYO1ksliFEJknyYgQIldTFIVp2y6x4eQ9NGoV87tXpWFpl38rhNyFX98zPG4wEoo3ME2gQoiXJsmIECJXm7/3Ot/+dROAzztXIuC1F1Zc1utg4yCICTUsatZ4fCqtCCFyM0lGhBC51spDt5i76yoAk14vT5fqRZNW+HMu3DkEFjbQeRlozE0QpRDiVUkyIoTIlTadvsfkXy4A8F6zUvSvXzxphbvHYP8Mw+M2c8CpRA5HKITIKpKMCCFynV0Xgxi9/hwAfev68L5/qaQVYkLh57dB0UHFN6BSVxNEKYTIKpKMCCFylcP/PGHomlPo9Aqdqnky6fXyqP47TXfraAi5Y1juvc0cmcYrRB4nyYgQItc4dy+EASuPE5egx7+cGzM7V0Kt/k+icXYdnP8JVBro/C1Y2psmWCFElpFkRAiRK1x/FE6f744RGaejTonCLOheFTPNf/6LenoDto4yPG48Drxq5XygQogsJ8mIEMLkHoRE0+vbYzyLiqdyUXuW9qmBpbkmaSVdPPw8EOLCoVhdaDDKNMEKIbKcJCNCCJMKiYqj93fHeBgag69LIZb3q4WN1ix5xQOz4P4J0NobVllVa5LXEULkSZKMCCFMJjpOR/8Vx7n+KAJ3O0tWve2HUyGL5BXvHjMkIwCvzwUHr5wNVAiRrSQZEUKYRLxOz9A1pzh1JwR7K3NWvV0LTwer5BVjw2HjQFD0him8FbvkfLBCiGwlyYgQIscpisK4n8+z9/IjLM3VfNe3BqXdbFOu/Ps4eHYL7ItB61k5GqcQImdIMiKEyHGfbb/Mz6cMF75b0K0a1b1TucruxS1w5gcMV+NdLNN4hcinUhgllj6dTscXX3zBTz/9xJ07d4iLi0vy+tOnT7MkOCFE/rPszxss/uMGADM6VcS/vFvKFcMe/Hs13vofgHfdHIpQCJHTXqpnZOrUqcydO5euXbsSGhrKyJEj6dSpE2q1milTpmRxiEKI/GLz6ft8uvUSAGNbluXNGqkMRNXrYfO7EP0MPKrI1XiFyOdeKhlZvXo1S5cuZdSoUZiZmdGtWzeWLVvGpEmTOHLkSFbHKITIB/ZfecTo9WcB6F+vOIMbpXFhu6OL4MZ+MLOCTkvBLIUZNkKIfOOlkpHAwEAqVqwIgI2NDaGhoQC8/vrrbN26NeuiE0LkC2fvhvDuD6dI0Cu0r1KEj9qUS369mURBF2D3FMPjgGngUjrH4hRCmMZLJSNFixbl4cOHAPj6+rJz504Ajh8/jlarzbrohBB53q3gSPqvOE50vI4GpZyZ1aVy8uvNJIqPMayyqouF0i2hRv+cDVYIYRIvlYx07NiRPXv2ADB8+HA+/vhjSpUqRe/evenfX/7zEEIYPImIpe/yYzyJjKOCpx3f9KyOhVka/+3s+QQeXYBCLtBugVyNV4gCQqUoivKqjRw5coRDhw5RqlQp2rZtmxVx5RphYWHY29sTGhqKnZ2dqcMRIs+Iikug29KjnL0bQlFHKzYOqYurrWXqG/yzD77vYHjcbR2UaZkjcQohsk9Gv0NfamrvgQMHqFu3LmZmhs1r165N7dq1SUhI4MCBAzRs2PDlohZC5AsJOj3D1pzm7N0QHK3NWdm/VtqJSNRTw+wZgBpvSyIiRAHzUqdpmjRpkuJaIqGhoTRp0uSVgxJC5F2KovDxlr/Ze/kRWjM1y/rUxNfFJq0N4NcREP4QCpeCFp/mXLBCiFzhpZIRRVFSHAn/5MkTChUq9MpBCSHyrvl7r7P22F3UKviqW1WqezumvcHpH+DSr6A2h87LwMI6ZwIVQuQamTpN06lTJwBUKhV9+/ZNMnNGp9Nx7tw56tbN3lUSv/76a2bNmkVgYCCVK1dm/vz51KpVK93tfvzxR7p160b79u3ZvHlztsYoREH104m7zN11FYCp7SsQ8Jp72hs8+Qd+H2t43PQjKFIlewMUQuRKmUpG7O0N14VQFAVbW1usrP69wqaFhQW1a9dm4MCBWRvhC9atW8fIkSNZtGgRfn5+zJs3j4CAAK5cuYKrq2uq2926dYvRo0fToEGDbItNiIJu35VHjN94HoAhjX3pVds77Q108Yar8cZHgk8DqDs8B6IUQuRGLzWbZurUqYwePTrHT8n4+flRs2ZNFixYAIBer8fLy4vhw4czbty4FLfR6XQ0bNiQ/v378+effxISEpKpnhGZTSNE+s7dC+GtJUeIitPRqaonc96snPqiZon2fgoHZhkufvfuIbAvmjPBCiFyTEa/Q19qzMjkyZNzPBGJi4vj5MmT+Pv7G8vUajX+/v4cPnw41e0++eQTXF1defvttzO0n9jYWMLCwpLchBCpu/s0iv4rThAVZ1jU7LPOldJPRG4fhj/nGB6/Pk8SESEKuAyfpqlatWr6/8E8d+rUqZcOKDXBwcHodDrc3JJe4dPNzY3Lly+nuM1ff/3Ft99+y5kzZzK8nxkzZjB16tRXCVWIAiM0Kp6+y48RHBFLOQ87FvaolvaiZgAxobBxECh6qNwdKnTKmWCFELlWhpORDh06ZGMYWS88PJxevXqxdOlSnJ2dM7zd+PHjGTlypPF5WFgYXl6pXFlUiAIsNkHHwO9P8M/jSDzsLVnRrya2lubpb7jtQwi9Aw7e0Orz7A9UCJHrZTgZmTx5cnbGkS5nZ2c0Gg1BQUFJyoOCgnB3Tz5i/59//uHWrVtJVoTV6/UAmJmZceXKFXx9fZNtp9Vq5fo6QqRDr1f4cP05jt18iq3WjOX9auJml8aiZonOb4Bz60ClNlyN11LGYQkhXnLMCEBISAjLli1j/PjxxgXQTp06xf3797MsuBdZWFhQvXp14zVxwJBc7Nmzhzp16iSrX7ZsWc6fP8+ZM2eMt3bt2tGkSRPOnDkjvR1CvILZO6/wy9kHmKlVLOpVnbLuGUgqQu7Ab897HRuOgWJ+2RukECLPeKnl4M+dO4e/vz/29vbcunWLgQMH4uTkxMaNG7lz5w6rVq3K6jgBGDlyJH369KFGjRrUqlWLefPmERkZSb9+/QDo3bs3np6ezJgxA0tLSypUqJBkewcHB4Bk5UKIjFtz9A4L9/8DwGedK1GvZAZOg+p1sGkwxIZC0ZrQ8MNsjlIIkZe8VDIycuRI+vbty8yZM7G1tTWWt27dmu7du2dZcP/VtWtXHj9+zKRJkwgMDKRKlSps377dOKj1zp07qNUv3dkjhEjHvsuP+HjL3wC871+KLtUzOAvmz7lw+yBY2ECnJaB5qf96hBD51EutM2Jvb8+pU6fw9fXF1taWs2fPUqJECW7fvk2ZMmWIiYnJjlhNQtYZEcLg7/uhvLn4MFFxOrpUL8qsLhmYwgtw5wgsbw2KDjp8A1Wy7w8WIUTukq3rjGi12hTX37h69SouLi4v06QQIhe7HxJNvxXHiYrTUb+kMzM6VcxYIhL9DH4eYEhEKnWFyt2yP1ghRJ7zUslIu3bt+OSTT4iPjwcM16q5c+cOY8eOpXPnzlkaoBDCtEKj4+m3/BiPw2Mp627Lwp7VMNdk4L8ORYFfhkPoXXAqAW3mQAbXKhJCFCwvlYzMmTOHiIgIXFxciI6OplGjRpQsWRJbW1umTZuW1TEKIUwkLkHPuz+c5GpQBG52Wr7rWxO7jKwlAnDiu3+vxtvlO9Dapr+NEKJAeqlRZPb29uzatYuDBw9y9uxZIiIiqFatWpKl2oUQeZuiKEzYdJ5D/zyhkIWG7/rWpIiDVfobAgRdhB0TDI/9p0CRqtkWpxAi78t0MqLX61mxYgUbN27k1q1bqFQqihcvjru7O4qiZHjJeCFE7rZg73U2nLyHWgULelTjtSL2GdswLgo29IOEGCjZHGoPyd5AhRB5XqZO0yiKQrt27RgwYAD379+nYsWKvPbaa9y+fZu+ffvSsWPH7IpTCJGDtpy5z5xdVwGY2r4CTcq4ZnzjHePh8WWwcTPMnpHp9kKIdGSqZ2TFihUcOHCAPXv20KRJkySv7d27lw4dOrBq1Sp69+6dpUEKIXLOsZtP+XD9OQAGNihOr9reGd/4wiY4uQJQGdYTsZHZdUKI9GXqT5a1a9cyYcKEZIkIQNOmTRk3bhyrV6/OsuCEEDnrxuMIBn1/gjidnpavuTO+VbmMb/zsNvzynuFx/Q+gRONsiVEIkf9kKhk5d+4cLVu2TPX1Vq1acfbs2VcOSgiR855GxtF/xXFCouKp7OXAF12roFZncAyYLt6wnkjicu9NJmRvsEKIfCVTycjTp0+NS6+nxM3NjWfPnr1yUEKInBUTr2PgqhPcehJFUUcrlvWugZWFJuMN7J8B946B1h46fwuaDE7/FUIIMpmM6HQ6zMxSH2ai0WhISEh45aCEEDlHr1cYvf4sJ28/w87SjBX9auJiq814A1d3wp9zDI/bfQmOmRhjIoQQZHIAq6Io9O3bF6025f+oYmNjsyQoIUTOmb3zCr+de4i5RsWiXtUp6ZqJxcme3YaNAw2Pa7wNr8mMOiFE5mUqGenTp0+6dWQmjRB5x7rjd1i4/x8AZnSqRF1f54xvHB8DP/WGmBDwrA4tZ2RPkEKIfC9Tycjy5cuzKw4hRA47eD2YiZv+BmBE05J0qV40cw1sHwsPz4CVE7yxEswycWpHCCFeIKsRCVEAXQsKZ/APJ0nQK7SvUoQPmpfOXAOnV/+7nkjnZeDglR1hCiEKCElGhChgHofH0m/FccJjEqjp48jnnStl7jIOD8/B1pGGx00mQMlm2ROoEKLAkGREiAIkcQrvvWfR+BS2ZnGvGliaZ2IKb3QI/NTr3+vONBidbbEKIQoOSUaEKCD0eoWRP53hzN0QHKzN+a5vTZwKWWSmAdg0GJ7dAvtihuXe5bozQogsIP+TCFFAzNxxhW3nAzHXqFjcszolXGwy18DBeXD1d9BYQNdVYO2ULXEKIQoeSUaEKADWHrvDoj8MU3hndqmEX4nCmWvgxh+w93+Gx61nQZGqWRyhEKIgk2REiHzuz2uP+WizYQrve81K0bFqJqfwhj2ADf1B0UOVHlAt/fWGhBAiMyQZESIfuxoUzpAfTqHTK3Ss6sn7/qUy10BcFPzYHaKCwa0itJ4NmZl5I4QQGSDJiBD51KPwGPotP054bAK1fJz4rHPFzE3h1eth82B4cNqwsFnXVWBhnX0BCyEKLElGhMiHouN0DFx5gvsh0RR3LsTiXtXRmmViCi/AvmlwcQuozeGt1eBUInuCFUIUeJKMCJHP6PUK7687zdl7oTham7O8b00cMzOFF+Dsj/DnbMPjdl+Bd92sD1QIIZ6TZESIfOaz7ZfZcSEIC42aJb1r4ONcKHMN3D4Mvww3PK4/Eqp0z/oghRDiBZKMCJGP/HDkNksO3ABg1huVqOmTybVAnt6EdT1AFwfl2kLTj7MhSiGESEqSESHyif1XHjH5lwsAjGxemvZVPDPXQEworOkKUU/AozJ0XCwrrAohcoT8TyNEPnA5MIxha06j0yt0qubJ8KYlM9eALgHW94XgK2DrAd1+BItMnt4RQoiXlOeSka+//hofHx8sLS3x8/Pj2LFjqdZdunQpDRo0wNHREUdHR/z9/dOsL0Re9Cgshv7LjxMRm0DtEk581imTV+EF2D4O/tkL5taGRMSuSPYEK4QQKchTyci6desYOXIkkydP5tSpU1SuXJmAgAAePXqUYv39+/fTrVs39u3bx+HDh/Hy8qJFixbcv38/hyMXIntExSXw9soTPAiNoYRLIRb1rI6FWSY/1keXwPGlhsedlkCRKlkepxBCpEWlKIpi6iAyys/Pj5o1a7JgwQIA9Ho9Xl5eDB8+nHHjxqW7vU6nw9HRkQULFtC7d+8M7TMsLAx7e3tCQ0Oxs7N7pfiFyEo6vcLgH06y62IQToUs2DSkLt6FM3lq5eIvsL6PYal3/ylQ/4NsiVUIUTBl9Ds0z/SMxMXFcfLkSfz9/Y1larUaf39/Dh8+nKE2oqKiiI+Px8kp9RkGsbGxhIWFJbkJkRtN23qJXReDsDBTs7R39cwnItd2/3vNmaq9oN772RKnEEKkJ88kI8HBweh0Otzc3JKUu7m5ERgYmKE2xo4dS5EiRZIkNP81Y8YM7O3tjTcvL69XiluI7LD84E2+O3gTgDlvVKa6dyan8N46aJjCq4+H8h2g7ZdyzRkhhMnkmWTkVX322Wf8+OOPbNq0CUtLy1TrjR8/ntDQUOPt7t27ORilEOnbdTGIT367CMDYlmVpWzmTg03vnzRM4U2IgVIB0GkpqDO5VLwQQmQhM1MHkFHOzs5oNBqCgoKSlAcFBeHu7p7mtrNnz+azzz5j9+7dVKpUKc26Wq0WrVb7yvEKkR3O3QthxNrTKAp0q1WMwY0yeb2YoAvwfSeICwefBvDmSjDL5FLxQgiRxfJMz4iFhQXVq1dnz549xjK9Xs+ePXuoU6dOqtvNnDmT//3vf2zfvp0aNWrkRKhCZIt7z6Lov+IE0fE6GpV24X/tX8vcFN4n/8CqDhATAp41oNtaMLfKrnCFECLD8kzPCMDIkSPp06cPNWrUoFatWsybN4/IyEj69esHQO/evfH09GTGjBkAfP7550yaNIk1a9bg4+NjHFtiY2ODjY2Nyd6HEJkVGh1Pv+XHCY6Ipay7LQu6V8VMk4m/JULuwsp2EPkI3CpCzw2gtc2+gIUQIhPyVDLStWtXHj9+zKRJkwgMDKRKlSps377dOKj1zp07qF9Yvvqbb74hLi6OLl26JGln8uTJTJkyJSdDF+KlxSXoefeHk1x7FIGbnZbl/Wpia2me8QbCg2BVOwi7B4VLQa9NYOWYfQELIUQm5al1RkxB1hkRpqQoCh9uOMeGk/coZKHhp8F1eK2IfcYbiHoKK9rAo4vgUAz6bQf7TF6zRgghXlK+W2dEiIJo/t7rbDh5D41axYIe1TKXiEQ8glXtDYmIjTv03iKJiBAiV8pTp2mEKEg2nb7H3F1XAfik/Ws0KeOa8Y2f3jDMmnl2Ewq5GBIRp0zOvBFCiBwiyYgQudChf4IZs+EcAO80KkEPP++Mb/zwLPzQGSIfg6MP9NwIhX2zJ1AhhMgCkowIkctcCQznnVUnidcptKnowdiAshnf+MYf8GMPwzoi7hWhx89g65b+dkIIYUKSjAiRiwSGxtB3+THCYxOo5ePEnDcro1ZncC2RvzfCpndAF2dY0OytNWApg66FELmfJCNC5BLhMfH0XX6Mh6Ex+LoUYknv6liaZ3CZ9mNLYduHgALl2xuWeDeTlYSFEHmDJCNC5AKGtUROcTkwHBdbLSv61cLBOgPLtCsK7JsGB2YZntccAK1myrVmhBB5iiQjQpiYoiiM23iOv64HY22hYXnfmng5Wae/oS4Bto6EUysNz5tMhIYfytV3hRB5jiQjQpjYF7uusvHUfTRqFV/3qEYFzwysJRIeCBvehtt/gUoNr38B1ftme6xCCJEdJBkRwoR+PHaHr/ZeB2BahwoZW0vkn32wcaBh6q6FDXRcDOVez+ZIhRAi+0gyIoSJ7LvyiImb/wZgRNOSvFWrWNob6HXwx+fwx0xAAbcK8MZKcC6Z/cEKIUQ2kmRECBP4+34oQ1efQqdX6FytKB80L532BuFBsHEA3DxgeF6tD7T6HMytsj9YIYTIZpKMCJHDbj+JpO/yY0TF6ahf0pkZnSqiSmvQ6Y0/4OcBEPkIzAtB23lQ6c0ci1cIIbKbJCNC5KDgiFh6f3eM4Ig4ynnY8U3PaliYpXK9Sr3OMGV3/2eAAq7lDadlXNLpRRFCiDxGkhEhckhEbAL9lh/n9pMoijpasbJfTWwtzVOu/OQf+PU9uPWn4XnVntBqFlhkYMqvEELkMZKMCJEDDIuaneT8/VCcClmwqn8tXO0sU6gYBX/OgUNfGZZ1N7eGNnOhSrecD1oIIXKIJCNCZDO9XuHDDWf589q/i5qVcLFJWklR4PJW2D4eQu8YynybQetZcsVdIUS+J8mIENls+rZLbDnzADO1im96Vqeyl0PSCk9vwO9j4dpOw3N7L2g5A8q+LqupCiEKBElGhMhGSw/cYNlfNwGY9UYlGpV2+ffF+Gj46wv4ax7oYkFtDvVGQINRYFHINAELIYQJSDIiRDbZdPoe07ZdAmBC67J0rFrU8IIuAS5uhj2fQMhtQ1mJJoZTMs6lTBOsEEKYkCQjQmSDP64+5sP15wB4u35xBjYoAXGRcHo1HJ4PIc/Hhdh5Gk7JlGsnp2SEEAWWJCNCZLGzd0N494eTJOgV2lcpwsTGrqj2fwbHlkD0U0Ml68LgNxhqDwGtTdoNCiFEPifJiBBZ6GpQOH2er67aqXg8s2xWo573AyREGyo4+kDd4VC5u6wZIoQQz0kyIkQWufs0in7L/qJKzEnetj9K/cC/UD3UG170qAL13oPy7UGtMWmcQgiR20gyIsSr0iXw7OIezm5ewtaEwzhYRELs89d8mxmSkOINZUyIEEKkQpIRIV6GXge3D8GFjegv/oJjVDCvA6hAZ+2C5rUOUK03eFQycaBCCJH7STIiREaF3IHbh+HOIbjyO0QEAaAGnii2/KGpQ732g3Cr2FROxQghRCZIMiJESvR6eHzZkHjcPgx3jkDYvSRVFEt7Dmhqs+xZVS5aVGbNoAa4uduaKGAhhMi7JBkRIi4Sgq9C8DV4fAWCLsDdIxD9LGk9tRl4VIZiddB5N+C94w78duEJ1hYaVvf3o4wkIkII8VLyXDLy9ddfM2vWLAIDA6lcuTLz58+nVq1aqdZfv349H3/8Mbdu3aJUqVJ8/vnntG7dOgcjFianKBAbbjitEvYAnv4Dj69C8BVDAhJ6N+XtzK2haA0oVhe860DRmmBRCEVRGP/zOX67cA8LjZqlvWtQtZhjzr4nIYTIR/JUMrJu3TpGjhzJokWL8PPzY968eQQEBHDlyhVcXV2T1T906BDdunVjxowZvP7666xZs4YOHTpw6tQpKlSoYIJ3ILJEQhzEhkFM6PP7sH+fRz2F8ECICDTcJ97iI9Nu09oZnEuDS2lwLgNetQy9IBrzJNUURWHa1kv8dOIeahV81a0q9Uo6Z+ObFUKI/E+lKIpi6iAyys/Pj5o1a7JgwQIA9Ho9Xl5eDB8+nHHjxiWr37VrVyIjI/ntt9+MZbVr16ZKlSosWrQoQ/sMCwvD3t6e0NBQ7OzsXv1NxEbAtR2v3g4Y/uLP0jaU1MsVBRT9v49TvNcbHut1zx+/eNMZyvUJoIs33CfeEp/r4iAhBuJjDPeJtxefx4T9u4BYZmntwMYNnIobEg/n0uBSxnBv7ZSBQ6Uwe+cVvt73DwCzulTijRpeLxeLEEIUABn9Ds0zPSNxcXGcPHmS8ePHG8vUajX+/v4cPnw4xW0OHz7MyJEjk5QFBASwefPmVPcTGxtLbGys8XlYWNirBf5fUcGwoX/WtllQWdiApb0hybC0M9xbOYKt+ws3D0MCYuv+ylfC/WrPdWMiMrXda5KICCFEFskzyUhwcDA6nQ43N7ck5W5ubly+fDnFbQIDA1OsHxgYmOp+ZsyYwdSpU1894NSYWYJPg+xr/79SXGhLlUYdVerlKlXq9yr183vN88cv3NQaw2tqc8MgULUZaMz+faw2N9Qx0xqOj5klmFs9f/78PvH5i4lHDk6fXbj/Ol/svgrAR23K0aeuT47tWwgh8rs8k4zklPHjxyfpTQkLC8PLKwv/ArZ1h76/pV9P5BrL/rzBzO1XABjTsgwDGpQwcURCCJG/5JlkxNnZGY1GQ1BQUJLyoKAg3N3dU9zG3d09U/UBtFotWq321QMW+cKqw7f4dOslAN73L8WQxiVNHJEQQuQ/alMHkFEWFhZUr16dPXv2GMv0ej179uyhTp06KW5Tp06dJPUBdu3alWp9IV605ugdJm25AMDQJr6816yUiSMSQoj8Kc/0jACMHDmSPn36UKNGDWrVqsW8efOIjIykX79+APTu3RtPT09mzJgBwHvvvUejRo2YM2cObdq04ccff+TEiRMsWbLElG9D5AHrT9xlwqbzAAxqWILRLcqgkgvdCSFEtshTyUjXrl15/PgxkyZNIjAwkCpVqrB9+3bjINU7d+6gVv/b2VO3bl3WrFnDRx99xIQJEyhVqhSbN2+WNUZEmjafvs+Yn88B0LeuD+NblZVERAghslGeWmfEFLJ8nRGRq/169gHv/XgavQI9/IrxaYcKkogIIcRLyuh3aJ4ZMyJEdtt46p4xEXmzRlH+114SESGEyAl56jSNENll3fE7jNt4HkWBt2p6Ma1jRdRqSUSEECInSDIiCrzvD9/i4+ezZnrX8WZK29ckERFCiBwkyYgo0Jb9ecO4jsiA+sWZ2KacnJoRQogcJsmIKLC+3nedWTsMK6sObeIr03eFEMJEJBkRBY6iKHyx+xpf7bkGwMjmpRkhC5oJIYTJSDIiChRFUfh8+xUW/WG4+u64VmUZ3MjXxFEJIUTBJsmIKDAUReGT3y6y/OAtACa3LU+/esVNG5QQQghJRkTBEK/TM/bnc2w8dR+AaR0r0MPP28RRCSGEAElGRAEQFZfAkNWn2H/lMRq1ipmdK9G5elFThyWEEOI5SUZEvvY0Mo7+K45z5m4IluZqFvaoRtOybqYOSwghxAskGRH51r1nUfT+7hg3HkfiYG3Od31rUq2Yo6nDEkII8R+SjIh86XJgGH2+O0ZQWCxF7C1Z9XYtSrramjosIYQQKZBkROQ7x24+5e2VxwmPSaC0mw0r+9fCw97K1GEJIYRIhSQjIl/ZcSGQ4WtPE5egp6aPI8t618Te2tzUYQkhhEiDJCMi31h99DYfb/4bvQLNy7sxv1tVLM01pg5LCCFEOiQZEXlegk7Pp1svseLQLQC61fLif+0rYKZRmzYwIYQQGSLJiMjTQqPjGb72NAeuPgZgVPPSDGtaUi54J4QQeYgkIyLPuhkcydsrj3PjcSRW5hrmvlmZVhU9TB2WEEKITJJkRORJB68HM2T1KUKj4/Gwt2Rp7xpU8LQ3dVhCCCFegiQjIs/5/vAtpvx6EZ1eoYqXA0t6V8fV1tLUYQkhhHhJkoyIPCNep+eTXy/y/ZHbAHSs6smMThVlxowQQuRxkoyIPCEkKo6ha05x8PoTVCr4MKAM7zbylYGqQgiRD0gyInK9k7efMXzNKR6ExmBtoWFe1yq0eM3d1GEJIYTIIpKMiFxLr1dY9tcNZm6/QoJeobhzIRb2qEY5DztThyaEECILSTIicqVnkXGMXn+WPZcfAfB6JQ9mdKqIraUs7S6EEPmNJCMi13nxtIyFmZrJbcvTvVYxGR8ihBD5lCQjItdI6bTMgu5Vea2IrB8ihBD5WZ65eMfTp0/p0aMHdnZ2ODg48PbbbxMREZFm/eHDh1OmTBmsrKwoVqwYI0aMIDQ0NAejFhn1LDKOgatOMH3bZRL0Cm0rF+GXYfUkERFCiAIgz/SM9OjRg4cPH7Jr1y7i4+Pp168fgwYNYs2aNSnWf/DgAQ8ePGD27NmUL1+e27dvM3jwYB48eMCGDRtyOHqRlj+uPmbcz+d4+Py0zJS2r9GtlpeclhFCiAJCpSiKYuog0nPp0iXKly/P8ePHqVGjBgDbt2+ndevW3Lt3jyJFimSonfXr19OzZ08iIyMxM8tYHhYWFoa9vT2hoaHY2cksjqwUGh3Pp79dZP3JewByWkYIIfKZjH6H5omekcOHD+Pg4GBMRAD8/f1Rq9UcPXqUjh07ZqidxIORViISGxtLbGys8XlYWNjLBy5StfdyEOM3nicoLBaVCvrVLc7ogNJYW+SJX0khhBBZKE/8zx8YGIirq2uSMjMzM5ycnAgMDMxQG8HBwfzvf/9j0KBBadabMWMGU6dOfelYRdpCouL45NeLbDx9H4ASzoWY2aUSNXycTByZEEIIUzHpANZx48ahUqnSvF2+fPmV9xMWFkabNm0oX748U6ZMSbPu+PHjCQ0NNd7u3r37yvsXBjsvBNL8iwNsPH0ftQoGNSzBtvcaSCIihBAFnEl7RkaNGkXfvn3TrFOiRAnc3d159OhRkvKEhASePn2Ku3vay4KHh4fTsmVLbG1t2bRpE+bmaS+apdVq0Wq1GYpfZMzTyDim/HKBX84+AKCkqw2zulSiajFHE0cmhBAiNzBpMuLi4oKLi0u69erUqUNISAgnT56kevXqAOzduxe9Xo+fn1+q24WFhREQEIBWq+WXX37B0lIuM5+T4hL0rDp8i6/2XCMsJgG1Ct5p5Mt7zUrJlXaFEEIY5YnZNACtWrUiKCiIRYsWGaf21qhRwzi19/79+zRr1oxVq1ZRq1YtwsLCaNGiBVFRUWzatIlChQoZ23JxcUGjydiXocymyTxFUdh96RHTt13iZnAkAOU97JjRqSKVvRxMG5wQQogck69m0wCsXr2aYcOG0axZM9RqNZ07d+arr74yvh4fH8+VK1eIiooC4NSpUxw9ehSAkiVLJmnr5s2b+Pj45FjsBcmlh2F8uvUiB68/AcDZRsuHAaXpUt0LjVrWDRFCCJFcnukZMRXpGcmYx+GxzN11hXXH76JXwMJMzYD6xRnSpCQ22jyT8wohhMhC+a5nROROUXEJrDx0m6/3XSciNgGANpU8GNeyLF5O1iaOTgghRF4gyYh4KaFR8aw8fIvlB2/yLCoegEpF7fn49fLUlKm6QgghMkGSEZEpQWExfPvXTVYfuU1knA6AYk7WjGhWik5VPVHLuBAhhBCZJMmIyJBbwZEsPvAPP5+8T5xOD0BZd1vebexLm4oemGnyzAWghRBC5DKSjIhUKYrC+fuhLDlwg23nH6J/PtS5hrcjQ5r40qSMq1xZVwghxCuTZEQk8zg8li1n7rPh5D0uB4YbyxuXcWFI45LUKi5jQoQQQmQdSUYEALEJOvZeesTPp+6x78pjdM+7QSzM1LSq4M6ghiV4rYi9iaMUQgiRH0kyUoApisLf98PYcPIuW84+IOT5rBiAKl4OdKlelLaVimBvnfb1fIQQQohXIclIARMaFc/Bf4I5cPUxB64+5kFojPE1NzstnaoVpXO1opR0tTFhlEIIIQoSSUbyOZ1e4czdEEPyce0xZ++GGAeiAmjN1LR4zZ0u1YtSv6SzLNkuhBAix0kyko8oisK9Z9FcehjG5cBwLjwI5fA/TwiLSUhSr6SrDQ1LudCwtDN+xQtjZSFX0BVCCGE6kozkQXq9wtOoOO48jeLyw/DnyUcYlx+GEx6bkKy+naUZ9Us507CUCw1Ku+DpYGWCqIUQQoiUSTKSw6LiEvjjymMUQFFAQXl+b+jZ4Hl5gl7hWWQcwRGxPA6P5XFELMERhudPImKTnGp5kYVGTUlXG8p62FLO3Y5q3o5ULmovi5IJIYTItSQZyWHB4XG8u/pUlrTlaqulrIcd5dxtKedhR1kPW3xdbDCXxEMIIUQeIslIDrM0V1PD2xGVClSoeP4PlQrUKpWxXK1W4WhtjrONFhdbLc42WpxtLIzPnQpZSNIhhBAiX5BkJIe52lmy4d26pg5DCCGEyDXkT2shhBBCmJQkI0IIIYQwKUlGhBBCCGFSkowIIYQQwqQkGRFCCCGESUkyIoQQQgiTkmRECCGEECYlyYgQQgghTEqSESGEEEKYlCQjQgghhDApSUaEEEIIYVJybZp0KIoCQFhYmIkjEUIIIfKWxO/OxO/S1Egyko7w8HAAvLy8TByJEEIIkTeFh4djb2+f6usqJb10pYDT6/U8ePAAW1tbVCqVqcPJUWFhYXh5eXH37l3s7OxMHU6+IMc0a8nxzHpyTLNWQT+eiqIQHh5OkSJFUKtTHxkiPSPpUKvVFC1a1NRhmJSdnV2B/BBlJzmmWUuOZ9aTY5q1CvLxTKtHJJEMYBVCCCGESUkyIoQQQgiTkmREpEqr1TJ58mS0Wq2pQ8k35JhmLTmeWU+OadaS45kxMoBVCCGEECYlPSNCCCGEMClJRoQQQghhUpKMCCGEEMKkJBkRQgghhElJMlLAff311/j4+GBpaYmfnx/Hjh1Ls35ISAhDhw7Fw8MDrVZL6dKl2bZtWw5Fmzdk9pjOmzePMmXKYGVlhZeXFx988AExMTE5FG3uduDAAdq2bUuRIkVQqVRs3rw53W32799PtWrV0Gq1lCxZkhUrVmR7nHlFZo/nxo0bad68OS4uLtjZ2VGnTh127NiRM8HmES/zO5ro4MGDmJmZUaVKlWyLL6+QZKQAW7duHSNHjmTy5MmcOnWKypUrExAQwKNHj1KsHxcXR/Pmzbl16xYbNmzgypUrLF26FE9PzxyOPPfK7DFds2YN48aNY/LkyVy6dIlvv/2WdevWMWHChByOPHeKjIykcuXKfP311xmqf/PmTdq0aUOTJk04c+YM77//PgMGDJAv0OcyezwPHDhA8+bN2bZtGydPnqRJkya0bduW06dPZ3OkeUdmj2mikJAQevfuTbNmzbIpsjxGEQVWrVq1lKFDhxqf63Q6pUiRIsqMGTNSrP/NN98oJUqUUOLi4nIqxDwns8d06NChStOmTZOUjRw5UqlXr162xpkXAcqmTZvSrDNmzBjltddeS1LWtWtXJSAgIBsjy5sycjxTUr58eWXq1KlZH1A+kJlj2rVrV+Wjjz5SJk+erFSuXDlb48oLpGekgIqLi+PkyZP4+/sby9RqNf7+/hw+fDjFbX755Rfq1KnD0KFDcXNzo0KFCkyfPh2dTpdTYedqL3NM69aty8mTJ42ncm7cuMG2bdto3bp1jsSc3xw+fDjJ8QcICAhI9fiLzNHr9YSHh+Pk5GTqUPK05cuXc+PGDSZPnmzqUHINuVBeARUcHIxOp8PNzS1JuZubG5cvX05xmxs3brB371569OjBtm3buH79OkOGDCE+Pl4+VLzcMe3evTvBwcHUr18fRVFISEhg8ODBcprmJQUGBqZ4/MPCwoiOjsbKyspEkeUPs2fPJiIigjfffNPUoeRZ165dY9y4cfz555+YmclXcCLpGREZptfrcXV1ZcmSJVSvXp2uXbsyceJEFi1aZOrQ8qz9+/czffp0Fi5cyKlTp9i4cSNbt27lf//7n6lDEyKJNWvWMHXqVH766SdcXV1NHU6epNPp6N69O1OnTqV06dKmDidXkbSsgHJ2dkaj0RAUFJSkPCgoCHd39xS38fDwwNzcHI1GYywrV64cgYGBxMXFYWFhka0x53Yvc0w//vhjevXqxYABAwCoWLEikZGRDBo0iIkTJ6JWy98LmeHu7p7i8bezs5NekVfw448/MmDAANavX5/sNJjIuPDwcE6cOMHp06cZNmwYYPgjT1EUzMzM2LlzJ02bNjVxlKYh/9MVUBYWFlSvXp09e/YYy/R6PXv27KFOnTopblOvXj2uX7+OXq83ll29ehUPD48Cn4jAyx3TqKioZAlHYrKnyGWjMq1OnTpJjj/Arl27Uj3+In1r166lX79+rF27ljZt2pg6nDzNzs6O8+fPc+bMGeNt8ODBlClThjNnzuDn52fqEE3HxANohQn9+OOPilarVVasWKFcvHhRGTRokOLg4KAEBgYqiqIovXr1UsaNG2esf+fOHcXW1lYZNmyYcuXKFeW3335TXF1dlU8//dRUbyHXyewxnTx5smJra6usXbtWuXHjhrJz507F19dXefPNN031FnKV8PBw5fTp08rp06cVQJk7d65y+vRp5fbt24qiKMq4ceOUXr16GevfuHFDsba2Vj788EPl0qVLytdff61oNBpl+/btpnoLuUpmj+fq1asVMzMz5euvv1YePnxovIWEhJjqLeQ6mT2m/yWzaQwkGSng5s+frxQrVkyxsLBQatWqpRw5csT4WqNGjZQ+ffokqX/o0CHFz89P0Wq1SokSJZRp06YpCQkJORx17paZYxofH69MmTJF8fX1VSwtLRUvLy9lyJAhyrNnz3I+8Fxo3759CpDslngM+/TpozRq1CjZNlWqVFEsLCyUEiVKKMuXL8/xuHOrzB7PRo0apVlfvNzv6IskGTFQKYr0BQshhBDCdGTMiBBCCCFMSpIRIYQQQpiUJCNCCCGEMClJRoQQQghhUpKMCCGEEMKkJBkRQgghhElJMiKEEEIIk5JkRAghhBAmJcmIECJXU6lUbN68OUf25ePjw7x583JkX0KIf8lVe4UQWaJv376EhITkWOKQHY4fP06hQoVMHYYQBY4kI0KIAi8uLg4LCwtcXFxMHYoQBZKcphFCZNiGDRuoWLEiVlZWFC5cGH9/fyIjI5kyZQorV65ky5YtqFQqVCoV+/fvB+D8+fM0bdrUuM2gQYOIiIhI0u53333Ha6+9hlarxcPDg2HDhqUaw+TJk/Hw8ODcuXMpvj5lyhSqVKnC4sWL8fLywtramjfffJPQ0FBjnb59+9KhQwemTZtGkSJFKFOmDJD8NE1ISAjvvPMObm5uWFpaUqFCBX777Tfj63/99RcNGjTAysoKLy8vRowYQWRkZGYPqxAFniQjQogMefjwId26daN///5cunSJ/fv306lTJxRFYfTo0bz55pu0bNmShw8f8vDhQ+rWrUtkZCQBAQE4Ojpy/Phx1q9fz+7du5MkG9988w1Dhw5l0KBBnD9/nl9++YWSJUsm27+iKAwfPpxVq1bx559/UqlSpVRjvX79Oj/99BO//vor27dv5/Tp0wwZMiRJnT179nDlyhV27dqVJMFIpNfradWqFQcPHuSHH37g4sWLfPbZZ2g0GgD++ecfWrZsSefOnTl37hzr1q3jr7/+SjOREkKkwrQXDRZC5BUnT55UAOXWrVspvt6nTx+lffv2ScqWLFmiODo6KhEREcayrVu3Kmq1WgkMDFQURVGKFCmiTJw4MdX9Asr69euV7t27K+XKlVPu3buXZpyTJ09WNBpNknq///67olarlYcPHxpjdXNzU2JjY5Ns6+3trXzxxReKoijKjh07FLVarVy5ciXF/bz99tvKoEGDkpT9+eefilqtVqKjo9OMUQiRlIwZEUJkSOXKlWnWrBkVK1YkICCAFi1a0KVLFxwdHVPd5tKlS1SuXDnJoNB69eqh1+u5cuUKKpWKBw8e0KxZszT3/cEHH6DVajly5AjOzs7pxlqsWDE8PT2Nz+vUqWPcp7u7OwAVK1bEwsIi1TbOnDlD0aJFKV26dIqvnz17lnPnzrF69WpjmaIo6PV6bt68Sbly5dKNUwhhIKdphBAZotFo2LVrF7///jvly5dn/vz5lClThps3b750m1ZWVhmq17x5c+7fv8+OHTteel//ld6smfRii4iI4J133uHMmTPG29mzZ7l27Rq+vr5ZFqcQBYEkI0KIDFOpVNSrV4+pU6dy+vRpLCws2LRpEwAWFhbodLok9cuVK8fZs2eTDOo8ePAgarWaMmXKYGtri4+PD3v27Elzv+3atWPNmjUMGDCAH3/8Md0479y5w4MHD4zPjxw5YtxnRlWqVIl79+5x9erVFF+vVq0aFy9epGTJksluafW4CCGSk2RECJEhR48eZfr06Zw4cYI7d+6wceNGHj9+bDwd4ePjw7lz57hy5QrBwcHEx8fTo0cPLC0t6dOnD3///Tf79u1j+PDh9OrVCzc3N8Aw+2XOnDl89dVXXLt2jVOnTjF//vxk++/YsSPff/89/fr1Y8OGDWnGmrjPs2fP8ueffzJixAjefPNN4ymajGjUqBENGzakc+fO7Nq1i5s3b/L777+zfft2AMaOHcuhQ4cYNmwYZ86c4dq1a2zZskUGsArxEmTMiBAiQ+zs7Dhw4ADz5s0jLCwMb29v5syZQ6tWrQAYOHAg+/fvp0aNGkRERLBv3z4aN27Mjh07eO+996hZsybW1tZ07tyZuXPnGtvt06cPMTExfPHFF4wePRpnZ2e6dOmSYgxdunRBr9fTq1cv1Go1nTp1SrFeyZIl6dSpE61bt+bp06e8/vrrLFy4MNPv+eeff2b06NF069aNyMhISpYsyWeffQYYek7++OMPJk6cSIMGDVAUBV9fX7p27Zrp/QhR0KkURVFMHYQQQmSVKVOmsHnzZs6cOWPqUIQQGSSnaYQQQghhUpKMCCGEEMKk5DSNEEIIIUxKekaEEEIIYVKSjAghhBDCpCQZEUIIIYRJSTIihBBCCJOSZEQIIYQQJiXJiBBCCCFMSpIRIYQQQpiUJCNCCCGEMKn/A4xHCgHT/TlbAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compare with the analytic Black-Scholes solution \n",
    "\n",
    "# Stock price vector\n",
    "s = np.linspace(0.5, 1.5, 50)\n",
    "\n",
    "# Select a random point in time [0,N-1]\n",
    "k = 11\n",
    "\n",
    "# Delta strategy obtained from the model weights\n",
    "y = deltastrategy(s,k)\n",
    "\n",
    "# Analytic Black-Scholes Delta(S)\n",
    "z = scipy.norm.cdf((np.log(s/strike)+0.5*(T-k*T/N)*sigma**2)/(np.sqrt(T-k*T/N)*sigma))\n",
    "\n",
    "fig = plt.figure(figsize=(6,4)) \n",
    "ax = fig.gca()        \n",
    "plt.plot(s, y, label='Deep hedging')\n",
    "plt.plot(s, z, label='Black-Scholes')\n",
    "plt.title('Comparison to Black-Scholes solution', fontsize=13, color='black')\n",
    "ax.set_xlabel('stock price')\n",
    "ax.set_ylabel('Delta')\n",
    "plt.legend(prop={'size':11})\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.12"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}