MLAS2024_GPS_Session_3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "9dJqhrz38o8T"
   },
   "source": [
    "# **GPyTorch Deep Gaussian Processes Tutorial**\n",
    "\n",
    "This notebook illustrates the use of deep Gaussian processes for regression and classification using GPyTorch. We will consider the implementation described by Salimbeni, using doubly stochastic variational inference (https://arxiv.org/abs/1705.08933).\n",
    "\n",
    "Deep GPs are only partially implemented in GPytorch and we will have to do many high level things on our own, such as creating the model, propagating samples across layers, etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "s0FYBD9Z81xT",
    "outputId": "9aaff460-dfd2-43ab-ec62-4c885cbbce6d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Defaulting to user installation because normal site-packages is not writeable\n",
      "Requirement already satisfied: gpytorch in /usr/local/lib/python3.10/dist-packages (1.11)\n",
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      "Requirement already satisfied: linear-operator>=0.5.0 in /usr/local/lib/python3.10/dist-packages (from gpytorch) (0.5.1)\n",
      "Requirement already satisfied: torch>=1.11 in /usr/local/lib/python3.10/dist-packages (from linear-operator>=0.5.0->gpytorch) (2.2.1)\n",
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      "Requirement already satisfied: filelock in /usr/local/lib/python3.10/dist-packages (from torch>=1.11->linear-operator>=0.5.0->gpytorch) (3.13.1)\n",
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      "Requirement already satisfied: nvidia-cuda-nvrtc-cu12==12.1.105 in /usr/local/lib/python3.10/dist-packages (from torch>=1.11->linear-operator>=0.5.0->gpytorch) (12.1.105)\n",
      "Requirement already satisfied: nvidia-cuda-runtime-cu12==12.1.105 in /usr/local/lib/python3.10/dist-packages (from torch>=1.11->linear-operator>=0.5.0->gpytorch) (12.1.105)\n",
      "Requirement already satisfied: nvidia-cuda-cupti-cu12==12.1.105 in /usr/local/lib/python3.10/dist-packages (from torch>=1.11->linear-operator>=0.5.0->gpytorch) (12.1.105)\n",
      "Requirement already satisfied: nvidia-cudnn-cu12==8.9.2.26 in /usr/local/lib/python3.10/dist-packages (from torch>=1.11->linear-operator>=0.5.0->gpytorch) (8.9.2.26)\n",
      "Requirement already satisfied: nvidia-cublas-cu12==12.1.3.1 in /usr/local/lib/python3.10/dist-packages (from torch>=1.11->linear-operator>=0.5.0->gpytorch) (12.1.3.1)\n",
      "Requirement already satisfied: nvidia-cufft-cu12==11.0.2.54 in /usr/local/lib/python3.10/dist-packages (from torch>=1.11->linear-operator>=0.5.0->gpytorch) (11.0.2.54)\n",
      "Requirement already satisfied: nvidia-curand-cu12==10.3.2.106 in /usr/local/lib/python3.10/dist-packages (from torch>=1.11->linear-operator>=0.5.0->gpytorch) (10.3.2.106)\n",
      "Requirement already satisfied: nvidia-cusolver-cu12==11.4.5.107 in /usr/local/lib/python3.10/dist-packages (from torch>=1.11->linear-operator>=0.5.0->gpytorch) (11.4.5.107)\n",
      "Requirement already satisfied: nvidia-cusparse-cu12==12.1.0.106 in /usr/local/lib/python3.10/dist-packages (from torch>=1.11->linear-operator>=0.5.0->gpytorch) (12.1.0.106)\n",
      "Requirement already satisfied: nvidia-nccl-cu12==2.19.3 in /usr/local/lib/python3.10/dist-packages (from torch>=1.11->linear-operator>=0.5.0->gpytorch) (2.19.3)\n",
      "Requirement already satisfied: nvidia-nvtx-cu12==12.1.105 in /usr/local/lib/python3.10/dist-packages (from torch>=1.11->linear-operator>=0.5.0->gpytorch) (12.1.105)\n",
      "Requirement already satisfied: triton==2.2.0 in /usr/local/lib/python3.10/dist-packages (from torch>=1.11->linear-operator>=0.5.0->gpytorch) (2.2.0)\n",
      "Requirement already satisfied: nvidia-nvjitlink-cu12 in /usr/local/lib/python3.10/dist-packages (from nvidia-cusolver-cu12==11.4.5.107->torch>=1.11->linear-operator>=0.5.0->gpytorch) (12.3.101)\n",
      "Requirement already satisfied: MarkupSafe>=2.0 in /usr/lib/python3/dist-packages (from jinja2->torch>=1.11->linear-operator>=0.5.0->gpytorch) (2.0.1)\n",
      "Requirement already satisfied: mpmath>=0.19 in /usr/local/lib/python3.10/dist-packages (from sympy->torch>=1.11->linear-operator>=0.5.0->gpytorch) (1.3.0)\n"
     ]
    }
   ],
   "source": [
    "!pip install gpytorch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "NOzwp1aS9fnx"
   },
   "source": [
    "For simplicity, we avoid using GPU acceleration and do the necessary imports.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "iuzD6h8R9lmt",
    "outputId": "3092190c-1e64-4e60-d2bd-5544dcbb85f7"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "env: CUDA_VISIBLE_DEVICES=0\n"
     ]
    }
   ],
   "source": [
    "%set_env CUDA_VISIBLE_DEVICES=0\n",
    "\n",
    "import torch\n",
    "import tqdm\n",
    "import gpytorch\n",
    "from gpytorch.means import ConstantMean, LinearMean\n",
    "from gpytorch.kernels import RBFKernel, ScaleKernel\n",
    "from gpytorch.variational import UnwhitenedVariationalStrategy, VariationalStrategy, CholeskyVariationalDistribution\n",
    "from gpytorch.distributions import MultivariateNormal\n",
    "from gpytorch.models import ApproximateGP, GP\n",
    "from gpytorch.mlls import VariationalELBO, AddedLossTerm\n",
    "from gpytorch.likelihoods import GaussianLikelihood\n",
    "\n",
    "from gpytorch.models.deep_gps import DeepGPLayer, DeepGP\n",
    "from gpytorch.mlls import DeepApproximateMLL\n",
    "\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ZR1uOAu-9y9G"
   },
   "source": [
    "## **Generating the Training Data**\n",
    "\n",
    "For simplicity we will consider a simple dataset given by the step function considered in the lectures. This dataset is highly non-smooth, which means that standard GPs may have problems here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "POA-K0e3-j0O"
   },
   "outputs": [],
   "source": [
    "N = 20\n",
    "\n",
    "# Training data are N points regularly spaced in the interval [-2,2].\n",
    "\n",
    "train_x = torch.linspace(-2, 2, N).reshape((N,1))\n",
    "\n",
    "# True function is 0 or 1 depending on the input location\n",
    "\n",
    "train_y = torch.remainder(torch.round(torch.remainder(train_x, 2.0)), 2.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "SPoGFMss-2GR"
   },
   "source": [
    "We plot the data for visualization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 545
    },
    "id": "r9U2kQGP-4xJ",
    "outputId": "904016c6-cd14-46e4-bba4-1d61fecedc2d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f508272d030>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Initialize plot\n",
    "\n",
    "f, ax = plt.subplots(1, 1, figsize=(8, 6))\n",
    "\n",
    "# Plot training data as black stars\n",
    "\n",
    "ax.plot(train_x.numpy(), train_y.numpy(), 'k*')\n",
    "ax.set_ylim([-3, 3])\n",
    "ax.legend(['Observed Data'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ZwCrDcU6_xMM"
   },
   "source": [
    "## **Defining GP layers**\n",
    "\n",
    "In GPyTorch, defining a GP involves extending one of our abstract GP models and defining a forward method that returns the prior. For deep GPs, things are similar, but there are two abstract GP models that must be overwritten: one for hidden layers and one for the deep GP model itself.\n",
    "\n",
    "In the next cell, we define an example deep GP hidden layer. This looks very similar to every other variational GP you might define. However, there are a few key differences:\n",
    "\n",
    "*   Instead of extending ApproximateGP, we extend DeepGPLayer.\n",
    "\n",
    "\n",
    "DeepGPLayers need a number of input dimensions, a number of output dimensions, and a number of samples. This is kind of like a linear layer in a standard neural network (input_dims defines how many inputs this hidden layer will expect), and output_dims defines how many hidden GPs to create outputs for.\n",
    "\n",
    "To facilitate training, each layer will model variations across the identity function. For this, we consdier a mean function for the GP of each layer equal to the identy function, except for the last layer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "TkkmSEjyAN99"
   },
   "outputs": [],
   "source": [
    "from gpytorch.means import ZeroMean, LinearMean\n",
    "\n",
    "# We create our layer object. Each layer will have a constant mean equal to the\n",
    "# identity function, except the last layer.\n",
    "\n",
    "class DeepGPHiddenLayer(DeepGPLayer):\n",
    "    def __init__(self, input_dims, output_dims, num_inducing, inducing_points = None, initial_inducing_values = None):\n",
    "\n",
    "        # The last layer should have output_dims equal to None.\n",
    "\n",
    "        if output_dims is None:\n",
    "            batch_shape = torch.Size([])\n",
    "        else:\n",
    "            batch_shape = torch.Size([output_dims])\n",
    "\n",
    "        # We use a clever initialization of the layers to be similar to the\n",
    "        # identity function. This facilitates training.\n",
    "\n",
    "        if inducing_points is None and initial_inducing_values is None:\n",
    "            if output_dims is None:\n",
    "                inducing_points = torch.randn(num_inducing, input_dims) * 2.0\n",
    "                initial_inducing_values = inducing_points[:,0]\n",
    "            else:\n",
    "                inducing_points = torch.randn(output_dims, num_inducing, input_dims) * 2.0\n",
    "                initial_inducing_values = inducing_points[0,:,0]\n",
    "        else:\n",
    "            inducing_points = inducing_points[None,:,:]\n",
    "\n",
    "        variational_distribution = CholeskyVariationalDistribution(num_inducing_points=num_inducing, batch_shape=batch_shape)\n",
    "        variational_distribution.initialize_variational_distribution(MultivariateNormal(initial_inducing_values, torch.eye(num_inducing) * 1e-5))\n",
    "        variational_strategy = UnwhitenedVariationalStrategy(self, inducing_points, variational_distribution, learn_inducing_locations=True)\n",
    "        variational_strategy.variational_params_initialized = torch.tensor(1)\n",
    "\n",
    "        super(DeepGPHiddenLayer, self).__init__(variational_strategy, input_dims, output_dims)\n",
    "\n",
    "        # The mean function is zero.\n",
    "\n",
    "        self.mean_module = ZeroMean(batch_shape=batch_shape)\n",
    "        self.covar_module = ScaleKernel(RBFKernel(batch_shape=batch_shape, ard_num_dims=input_dims), \\\n",
    "            batch_shape=batch_shape, ard_num_dims=None)\n",
    "\n",
    "    def forward(self, x):\n",
    "\n",
    "        mean_x = self.mean_module(x)\n",
    "        covar_x = self.covar_module(x)\n",
    "\n",
    "        return MultivariateNormal(mean_x, covar_x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "xraMONPIITAI"
   },
   "source": [
    "## **Building the deep GP**\n",
    "\n",
    "Now that we’ve defined a class for our hidden layers and a class for our output layer, we can build our deep GP. To do this, we create a Module whose forward is simply responsible for forwarding through the various layers. This also allows to evaluate individually each layer. For example calling, output_layer_2 = self.second_hidden_layer(inputs).\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "2n6MrGWqI6ZB"
   },
   "outputs": [],
   "source": [
    "# We create the deep GP\n",
    "\n",
    "class DSVIDeepGP(DeepGP):\n",
    "    def __init__(self, train_x, train_y, train_x_shape, num_hidden_dims, num_inducing):\n",
    "\n",
    "        to_sel = torch.randperm(train_x.shape[ 0 ])[ 0 : num_inducing]\n",
    "        inducing_points = train_x[ to_sel, : ]\n",
    "        inducing_values = train_y[ to_sel, 0 ]\n",
    "\n",
    "        # We create the layers. Recall that the outputdims of the last layer should be none.\n",
    "\n",
    "        hidden_layer = DeepGPHiddenLayer(input_dims=train_x_shape[-1], \\\n",
    "                output_dims=num_hidden_dims, num_inducing = num_inducing, inducing_points = inducing_points,\n",
    "                initial_inducing_values = inducing_values)\n",
    "\n",
    "        last_layer = DeepGPHiddenLayer(input_dims=hidden_layer.output_dims, \\\n",
    "                output_dims=None, num_inducing = num_inducing)\n",
    "\n",
    "        super().__init__()\n",
    "\n",
    "        self.hidden_layer = hidden_layer\n",
    "        self.last_layer = last_layer\n",
    "        self.likelihood = GaussianLikelihood()\n",
    "        self.likelihood.noise = 0.01\n",
    "\n",
    "    def forward(self, inputs):\n",
    "\n",
    "        # The forward method simply let the data go through each layer by\n",
    "        # sampling from the predictive distribution of each layer.\n",
    "\n",
    "        hidden_rep = self.hidden_layer(inputs)\n",
    "        output = self.last_layer(hidden_rep.rsample())\n",
    "\n",
    "        return output\n",
    "\n",
    "    def predict(self, test_data, num_samples = 100):\n",
    "\n",
    "        # We compute predictions for the test data for the whole model\n",
    "\n",
    "        with torch.no_grad():\n",
    "            means = torch.zeros(test_data.shape[ 0 ], num_samples)\n",
    "            variances = torch.zeros(test_data.shape[ 0 ], num_samples)\n",
    "            for i in range(num_samples):\n",
    "                with gpytorch.settings.num_likelihood_samples(1):\n",
    "                  preds = self.likelihood(self(test_data))\n",
    "                  means[ :, i ] = preds.mean\n",
    "                  variances[ :, i ] = preds.variance\n",
    "\n",
    "        return means, variances"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_FY4kMaaLSLM"
   },
   "source": [
    "After this, we are ready to create our DGP using the training data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "_t48B4qeLWMN"
   },
   "outputs": [],
   "source": [
    "num_inducing_points = 10\n",
    "model = DSVIDeepGP(train_x, train_y, train_x.shape, 1, num_inducing_points)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "RmAY7XnPN1fN"
   },
   "source": [
    "Now, we are ready to train the model. We will use ADAM for that. The loss is the specific loss for DGPs that will consider the DSVI objective. This loss is already implemented in gpytorch."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "id": "u3cWoeBVRWHh"
   },
   "outputs": [],
   "source": [
    "from torch.utils.data import TensorDataset, DataLoader\n",
    "\n",
    "def train_dgp_dsvi(model, train_x, train_y, mini_batch_size, num_epochs, num_samples = 1):\n",
    "\n",
    "  optimizer = torch.optim.Adam(model.parameters(), lr=0.01)\n",
    "  mll = DeepApproximateMLL(VariationalELBO(model.likelihood, model, train_x.shape[-2]))\n",
    "\n",
    "  for training_iter in range(num_epochs):\n",
    "\n",
    "    # Within each iteration, we will go over each minibatch of data\n",
    "\n",
    "    train_loader = DataLoader(TensorDataset(train_x, train_y), batch_size=mini_batch_size, shuffle=True)\n",
    "\n",
    "    for (x_batch, y_batch) in train_loader:\n",
    "\n",
    "        # We iterate over the batches\n",
    "\n",
    "        with gpytorch.settings.num_likelihood_samples(num_samples):\n",
    "            optimizer.zero_grad()\n",
    "            output = model(x_batch)\n",
    "            loss = -mll(output, y_batch.T)\n",
    "            loss.backward()\n",
    "            optimizer.step()\n",
    "\n",
    "    if (training_iter + 1) % 100 == 0:\n",
    "      print('Epoch %d/%d - Loss: %f' % (training_iter + 1, num_epochs, loss.item() * train_x.shape[ 0 ]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "i66cL9VSSxZr"
   },
   "source": [
    "Now, we train the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "TcnAX8ZyTAFk",
    "outputId": "f3016326-646e-4a66-e4ff-6067c52feb35"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.10/dist-packages/torch/autograd/__init__.py:266: UserWarning: CUDA initialization: CUDA unknown error - this may be due to an incorrectly set up environment, e.g. changing env variable CUDA_VISIBLE_DEVICES after program start. Setting the available devices to be zero. (Triggered internally at ../c10/cuda/CUDAFunctions.cpp:108.)\n",
      "  Variable._execution_engine.run_backward(  # Calls into the C++ engine to run the backward pass\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 100/10000 - Loss: 36.086957\n",
      "Epoch 200/10000 - Loss: 30.476875\n",
      "Epoch 300/10000 - Loss: 24.692116\n",
      "Epoch 400/10000 - Loss: 17.246428\n",
      "Epoch 500/10000 - Loss: 15.996978\n",
      "Epoch 600/10000 - Loss: 14.459707\n",
      "Epoch 700/10000 - Loss: 21.126127\n",
      "Epoch 800/10000 - Loss: 17.541778\n",
      "Epoch 900/10000 - Loss: 14.176818\n",
      "Epoch 1000/10000 - Loss: 13.523682\n",
      "Epoch 1100/10000 - Loss: 17.196932\n",
      "Epoch 1200/10000 - Loss: 15.408027\n",
      "Epoch 1300/10000 - Loss: 11.191123\n",
      "Epoch 1400/10000 - Loss: 19.881700\n",
      "Epoch 1500/10000 - Loss: 13.697321\n",
      "Epoch 1600/10000 - Loss: 11.702187\n",
      "Epoch 1700/10000 - Loss: 11.745254\n",
      "Epoch 1800/10000 - Loss: 11.137624\n",
      "Epoch 1900/10000 - Loss: 13.513527\n",
      "Epoch 2000/10000 - Loss: 9.894646\n",
      "Epoch 2100/10000 - Loss: 10.440809\n",
      "Epoch 2200/10000 - Loss: 15.520961\n",
      "Epoch 2300/10000 - Loss: 12.446579\n",
      "Epoch 2400/10000 - Loss: 9.520720\n",
      "Epoch 2500/10000 - Loss: 10.584604\n",
      "Epoch 2600/10000 - Loss: 27.250192\n",
      "Epoch 2700/10000 - Loss: 10.239211\n",
      "Epoch 2800/10000 - Loss: 7.047403\n",
      "Epoch 2900/10000 - Loss: 5.482697\n",
      "Epoch 3000/10000 - Loss: 14.025781\n",
      "Epoch 3100/10000 - Loss: 8.821604\n",
      "Epoch 3200/10000 - Loss: 11.378106\n",
      "Epoch 3300/10000 - Loss: 7.132576\n",
      "Epoch 3400/10000 - Loss: 5.938027\n",
      "Epoch 3500/10000 - Loss: 55.061646\n",
      "Epoch 3600/10000 - Loss: 28.275476\n",
      "Epoch 3700/10000 - Loss: 9.031737\n",
      "Epoch 3800/10000 - Loss: 10.532374\n",
      "Epoch 3900/10000 - Loss: 22.593722\n",
      "Epoch 4000/10000 - Loss: 21.554010\n",
      "Epoch 4100/10000 - Loss: 4.469256\n",
      "Epoch 4200/10000 - Loss: 19.785621\n",
      "Epoch 4300/10000 - Loss: 7.981446\n",
      "Epoch 4400/10000 - Loss: 8.808908\n",
      "Epoch 4500/10000 - Loss: 12.890372\n",
      "Epoch 4600/10000 - Loss: 12.683098\n",
      "Epoch 4700/10000 - Loss: 10.789242\n",
      "Epoch 4800/10000 - Loss: 10.182517\n",
      "Epoch 4900/10000 - Loss: 7.726729\n",
      "Epoch 5000/10000 - Loss: 7.307224\n",
      "Epoch 5100/10000 - Loss: 8.645833\n",
      "Epoch 5200/10000 - Loss: 8.991742\n",
      "Epoch 5300/10000 - Loss: 2.569420\n",
      "Epoch 5400/10000 - Loss: 6.870360\n",
      "Epoch 5500/10000 - Loss: 20.137928\n",
      "Epoch 5600/10000 - Loss: 8.402452\n",
      "Epoch 5700/10000 - Loss: 6.943705\n",
      "Epoch 5800/10000 - Loss: 8.813102\n",
      "Epoch 5900/10000 - Loss: 5.556488\n",
      "Epoch 6000/10000 - Loss: 3.823528\n",
      "Epoch 6100/10000 - Loss: 5.820744\n",
      "Epoch 6200/10000 - Loss: 10.767441\n",
      "Epoch 6300/10000 - Loss: 4.422731\n",
      "Epoch 6400/10000 - Loss: 4.463081\n",
      "Epoch 6500/10000 - Loss: 4.932961\n",
      "Epoch 6600/10000 - Loss: 2.842083\n",
      "Epoch 6700/10000 - Loss: 13.111250\n",
      "Epoch 6800/10000 - Loss: 12.256546\n",
      "Epoch 6900/10000 - Loss: 6.097167\n",
      "Epoch 7000/10000 - Loss: 8.484421\n",
      "Epoch 7100/10000 - Loss: 3.190391\n",
      "Epoch 7200/10000 - Loss: 1.790857\n",
      "Epoch 7300/10000 - Loss: 10.791297\n",
      "Epoch 7400/10000 - Loss: 4.052458\n",
      "Epoch 7500/10000 - Loss: 8.211346\n",
      "Epoch 7600/10000 - Loss: 5.128310\n",
      "Epoch 7700/10000 - Loss: 4.255517\n",
      "Epoch 7800/10000 - Loss: 6.629710\n",
      "Epoch 7900/10000 - Loss: 7.112598\n",
      "Epoch 8000/10000 - Loss: 4.102519\n",
      "Epoch 8100/10000 - Loss: 4.706364\n",
      "Epoch 8200/10000 - Loss: 5.105040\n",
      "Epoch 8300/10000 - Loss: 5.480194\n",
      "Epoch 8400/10000 - Loss: 3.270671\n",
      "Epoch 8500/10000 - Loss: 8.584597\n",
      "Epoch 8600/10000 - Loss: 7.782876\n",
      "Epoch 8700/10000 - Loss: 6.165166\n",
      "Epoch 8800/10000 - Loss: -0.296531\n",
      "Epoch 8900/10000 - Loss: 2.163761\n",
      "Epoch 9000/10000 - Loss: 2.829869\n",
      "Epoch 9100/10000 - Loss: 2.688262\n",
      "Epoch 9200/10000 - Loss: 2.525721\n",
      "Epoch 9300/10000 - Loss: 2.985630\n",
      "Epoch 9400/10000 - Loss: 8.648858\n",
      "Epoch 9500/10000 - Loss: 12.536523\n",
      "Epoch 9600/10000 - Loss: 0.357845\n",
      "Epoch 9700/10000 - Loss: 2.425158\n",
      "Epoch 9800/10000 - Loss: 2.410927\n",
      "Epoch 9900/10000 - Loss: 0.758083\n",
      "Epoch 10000/10000 - Loss: 5.932007\n"
     ]
    }
   ],
   "source": [
    "train_dgp_dsvi(model, train_x, train_y, train_x.shape[ 0 ], 10000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "bZdbFNCjUThP"
   },
   "source": [
    "We now compute predictions and plot the predictive distribution.\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 545
    },
    "id": "vJnvMyxtWbor",
    "outputId": "9069a88d-c72c-4e8c-82bf-9c1fba10b6e9"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_325420/3428919590.py:20: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
      "  f.show()\n"
     ]
    },
    {
     "data": {
      "image/png": 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FsWzZMgYOHGgbI9IqICCA3r17M3fuXETENn3cuHHUrVuXbdu28b///Y+hQ4eyYsUKAH766Sc+/fRTpkyZwsGDB1m0aBG1a9e2zTt48GD+/vtv5syZw44dO+jWrRsdO3bk4MGDtjJJSUl8+OGHTJ06ld27d9O7d298fHz46aefbGUyMzOZO3cuvXv3BuDw4cN07NiRhx9+mB07djB37lw2bNjA4MGDbfP07duXEydOsHr1aubPn8+XX35pSwxzq3r16nTq1IkFCxbYpqWnp/Puu+/y77//smjRIiIiImzJZXBwsC3+/fv3ExkZyYQJEwBITExk2LBhbNmyhVWrVuHg4MCDDz6Y/zW9UojFxsYKILGxsfYORSmllCqUkpOTZc+ePZKcnHxT8wO2h8lkyvLX+shrGzduFEAWLlyY4+uffPKJAHL27FkREQkJCZGOHTtmKdOjRw/p1KmTiIh8/PHHUrVqVUlLS8u2rGPHjonZbJZTp05lmX733XfLiBEjRERk+vTpAsj27duzlBk6dKjcddddtufLli0TFxcXiY6OFhGRfv36yTPPPJNlnvXr14uDg4MkJyfL/v37BZB//vnH9vrevXsFkE8//fQqe0fk7bfflrp16+b42quvvipubm5XnXfz5s0CSHx8vIiIrF69WgBbzFdz/vx5AWTnzp05vn6t91lu8jWt8VRKKaVuY7NmzcLR0biRoVyqYbT+dXR0ZNasWfm2brmiRvN6wsLCsj3fu3cvAN26dSM5OZmKFSvy9NNPs3DhQjIyMgDYuXMnmZmZVK1aFQ8PD9tj7dq1WS4tOzs7U6dOnSzr6N27N2vWrOH06dMAfP/993Tu3BkfHx8A/v33X2bMmJFluR06dMBisXD06FH27t2Lo6MjDRs2tC2zevXqtvlvhohkGVMzPDycLl26UL58eTw9PWnTpg0Ax48fv+ZyDh48yKOPPkrFihXx8vKiQoUKNzTfrdJbZiqllFK3sd69e1OjRo0syZHVpk2baNCgQZ6vs3LlyphMJvbu3cuDDz6Y7fW9e/dSsmRJ/Pz8bmh5wcHB7N+/n5UrV7JixQoGDhzIuHHjWLt2LQkJCZjNZsLDw7Pd6tHDw8P2v5ubW7ZB0hs3bkylSpWYM2cOzz33HAsXLmTGjBm21xMSEhgwYECW9qRW5cuX58CBAzcUf27s3buX0NBQwLhc3qFDBzp06MD333+Pn58fx48fp0OHDqSlpV1zOV26dCEkJISvv/6aoKAgLBYLtWrVuu58t0oTT6WUUkoB4ODggMVisf3NL6VKlaJ9+/Z8+eWXvPjii1naeZ45c4bvv/+eJ554IksiuHHjxizL2LhxIzVq1LA9d3Nzo0uXLnTp0oVBgwZRvXp1du7cSf369cnMzOTcuXO0atUq17H27t2b77//nnLlyuHg4EDnzp1trzVo0IA9e/ZQuXLlHOetXr06GRkZhIeH07hxY8Boa3mzQxvt27eP33//nREjRtieX7x4kQ8++IDg4GCAbCMSWG+lar21KsDFixfZv38/X3/9tW2fbNiw4aZiyi291K6UUkrd5vz9/QkICKBhw4ZMnjyZhg0bEhAQgL+/f76t84svviA1NZUOHTqwbt06Tpw4we+//0779u0pW7Ys7733Xpbyf/75J2PHjuXAgQNMnDiRefPmMXToUMDolf7NN9+wa9cujhw5wqxZs3BzcyMkJISqVavSu3dvnnjiCRYsWMDRo0f5559/GDNmDL/++ut14+zduzdbt27lvffe45FHHsHFxcX22quvvspff/3F4MGD2b59OwcPHuTnn3+2dS6qVq0aHTt2ZMCAAWzatInw8HD69++frUNVTjIyMjhz5gynT59m586dfP7557Rp04Z69erxyiuvAEatqrOzM59//jlHjhxh8eLFvPvuu1mWExISgslkYsmSJZw/f56EhARKlixJqVKl+Oqrrzh06BB//PEHw4YNu25MeeK6rUDtSDsXKaWUUtd2q52LrFJSUsRisYiIiMVikZSUlLwI75oiIiKkT58+UqZMGXFycpLg4GB5/vnn5cKFC1nKhYSEyDvvvCPdunUTd3d3CQgIkAkTJtheX7hwoTRt2lS8vLykRIkS0qxZM1m5cqXt9bS0NHnrrbekQoUK4uTkJIGBgfLggw/Kjh07RMToXOTt7X3VOJs0aSKA/PHHH9le++eff6R9+/bi4eEhJUqUkDp16sh7771nez0yMlI6d+4sLi4uUr58eZk5c6aEhIRct3MRlzp2mc1m8fX1lZYtW8qnn36a7bjMnj1bKlSoIC4uLhIWFiaLFy8WQLZt22YrM2rUKAkICBCTySR9+vQREZEVK1ZIjRo1xMXFRerUqSNr1qy5ZoevvOpcZBLJRcveAhYXF4e3tzexsbF4eXnZOxyllFKq0ElJSeHo0aOEhobi6upq73BUMXWt91lu8jW91K6UUkoppQqEJp5KKaWUUqpAaOKplFJKKaUKhCaeSimllFKqQGjiqZRSSimlCoQmnkoppZRSqkBo4qmUUkoppQqEJp5KKaWUUqpAaOKplFJKKaUKhCaeSimllFKqQGjiqZRSSqkC17dvX0wmE88++2y21wYNGoTJZKJv374FH5jKV5p4KqWUUsougoODmTNnDsnJybZpKSkpzJ49m/Lly9sxMpVfNPFUSimllF00aNCA4OBgFixYYJu2YMECypcvT/369W3TLBYLY8aMITQ0FDc3N+rWrcv8+fNtr2dmZtKvXz/b69WqVWPChAlZ1tW3b1+6du3KRx99RGBgIKVKlWLQoEGkp6fn/4YqG0d7B6CUUkqpvCMCSUn2Wbe7O5hMuZvnqaeeYvr06fTu3RuAadOm8eSTT7JmzRpbmTFjxjBr1iwmT55MlSpVWLduHY899hh+fn60adMGi8VCuXLlmDdvHqVKleKvv/7imWeeITAwkO7du9uWs3r1agIDA1m9ejWHDh2iR48e1KtXj6effjovNl/dAE08lVJKqWIkKQk8POyz7oQEKFEid/M89thjjBgxgmPHjgHw559/MmfOHFvimZqayvvvv8/KlSsJCwsDoGLFimzYsIEpU6bQpk0bnJyceOedd2zLDA0N5e+//+bHH3/MkniWLFmSL774ArPZTPXq1encuTOrVq3SxLMAaeKplFJKKbvx8/Ojc+fOzJgxAxGhc+fOlC5d2vb6oUOHSEpKon379lnmS0tLy3I5fuLEiUybNo3jx4+TnJxMWloa9erVyzLPHXfcgdlstj0PDAxk586d+bNhKkeaeCqllFLFiLu7UfNor3XfjKeeeorBgwcDRgJ5pYRLG/Prr79StmzZLK+5uLgAMGfOHF5++WU+/vhjwsLC8PT0ZNy4cWzatClLeScnpyzPTSYTFovl5oJWN0UTT6WUUqoYMZlyf7nb3jp27EhaWhomk4kOHTpkea1mzZq4uLhw/Phx2rRpk+P8f/75J82bN2fgwIG2aYcPH87XmNXN0cRTKaWUUnZlNpvZu3ev7f8reXp68vLLL/Piiy9isVho2bIlsbGx/Pnnn3h5edGnTx+qVKnCzJkzWbZsGaGhoXz33Xds3ryZ0NBQe2yOugZNPJVSSilld15eXld97d1338XPz48xY8Zw5MgRfHx8aNCgAa+99hoAAwYMYNu2bfTo0QOTycSjjz7KwIED+e233woqfHWDTCIi9g7iauLi4vD29iY2Nvaab0illFLqdpWSksLRo0cJDQ3F1dXV3uGoYupa77Pc5Gs6gLxSSimllCoQmngqpZRSSqkCoYmnUkoppZQqEJp4KqWUUkqpAqGJp1JKKaWUKhCaeCqllFJKqQKhiadSSimllCoQmngqpZRSSqkCoYmnUkoppZQqEJp4KqWUUqpYExGeeeYZfH19MZlMbN++nTvvvJMXXnjhmvNVqFCB8ePHF0iMtwtNPJVSSillN2fOnOH555+nYsWKuLi4EBwcTJcuXVi1alWereP3339nxowZLFmyhMjISGrVqsWCBQt4991382wd6sY42jsApZRSSt2eIiIiaNGiBT4+PowbN47atWuTnp7OsmXLGDRoEPv27cuT9Rw+fJjAwECaN29um+br65sny1a5ozWeSimllLKLgQMHYjKZ+Oeff3j44YepWrUqd9xxB8OGDWPjxo0AHD9+nAceeAAPDw+8vLzo3r07Z8+etS1j5MiR1KtXj++++44KFSrg7e1Nz549iY+PB6Bv3748//zzHD9+HJPJRIUKFQCyXWo/d+4cXbp0wc3NjdDQUL7//vts8cbExNC/f3/8/Pzw8vLirrvu4t9//73hWAAsFgtjx46lcuXKuLi4UL58ed577z3b6ydOnKB79+74+Pjg6+vLAw88QERERF7s7kJBazyVUkqpYkRESEpKssu63d3dMZlMN1Q2KiqK33//nffee48SJUpke93HxweLxWJLOteuXUtGRgaDBg2iR48erFmzxlb28OHDLFq0iCVLlhAdHU337t354IMPeO+995gwYQKVKlXiq6++YvPmzZjN5hzj6du3L6dPn2b16tU4OTkxZMgQzp07l6VMt27dcHNz47fffsPb25spU6Zw9913c+DAAVsN6rViARgxYgRff/01n376KS1btiQyMtJWs5uenk6HDh0ICwtj/fr1ODo6Mnr0aDp27MiOHTtwdna+oX1bqEkhFhsbK4DExsbaOxSllFKqUEpOTpY9e/ZIcnKyiIgkJCQIYJdHQkLCDce9adMmAWTBggVXLbN8+XIxm81y/Phx27Tdu3cLIP/884+IiLz99tvi7u4ucXFxtjKvvPKKNG3a1Pb8008/lZCQkCzLbtOmjQwdOlRERPbv359lmSIie/fuFUA+/fRTERFZv369eHl5SUpKSpblVKpUSaZMmXJDscTFxYmLi4t8/fXXOW7vd999J9WqVROLxWKblpqaKm5ubrJs2bKr7qeC8N/32ZVyk69pjadSSimlCpyIXLfM3r17CQ4OJjg42DatZs2a+Pj4sHfvXho3bgwYvc89PT1tZQIDA7PVVl5vPY6OjjRs2NA2rXr16vj4+Nie//vvvyQkJFCqVKks8yYnJ3P48GHb82vFsnfvXlJTU7n77rtzjOPff//l0KFDWeYHSElJybKOokwTT6WUUqoYcXd3JyEhwW7rvlFVqlTBZDLlSQciJyenLM9NJhMWi+WWl3ulhIQEAgMDs1zit7oyQb1WLG5ubtddR8OGDXNsX+rn55f7oAshTTyVUkqpYsRkMuXYZrKw8fX1pUOHDkycOJEhQ4ZkizkmJoYaNWpw4sQJTpw4Yav13LNnDzExMdSsWTPPYqlevToZGRmEh4fbalH3799PTEyMrUyDBg04c+YMjo6Otg5KuVWlShXc3NxYtWoV/fv3z/Z6gwYNmDt3Lv7+/nh5ed3UOgo77dWulFJKKbuYOHEimZmZNGnShJ9++omDBw+yd+9ePvvsM8LCwmjXrh21a9emd+/ebN26lX/++YcnnniCNm3a0KhRozyLo1q1anTs2JEBAwawadMmwsPD6d+/f5Yaynbt2hEWFkbXrl1Zvnw5ERER/PXXX7z++uts2bLlhtbj6urKq6++yvDhw5k5cyaHDx9m48aNfPPNNwD07t2b0qVL88ADD7B+/XqOHj3KmjVrGDJkCCdPnsyz7bUnTTyVUkopZRcVK1Zk69attG3blpdeeolatWrRvn17Vq1axaRJkzCZTPz888+ULFmS1q1b065dOypWrMjcuXPzPJbp06cTFBREmzZteOihh3jmmWfw9/e3vW4ymVi6dCmtW7fmySefpGrVqvTs2ZNjx45RpkyZG17Pm2++yUsvvcRbb71FjRo16NGjh60NqLu7O+vWraN8+fI89NBD1KhRg379+pGSklJsakBNciOte+0kLi4Ob29vYmNji80OV0oppfJSSkoKR48eJTQ0FFdXV3uHo4qpa73PcpOvaY2nUkoppZQqEJp4KqWUUkqpAqGJp1JKKaWUKhCaeCqllFJKqQKhiadSSilVDBTivsKqGMir95cmnkoppVQRZjabAUhLS7NzJKo4S0pKArLfmSm38vXORWPGjGHBggXs27cPNzc3mjdvzocffki1atXyc7VKKaXUbcPR0RF3d3fOnz+Pk5MTDg5ap6TyjoiQlJTEuXPn8PHxsf3QuVn5mniuXbuWQYMG0bhxYzIyMnjttde455572LNnT5G4nZdSSilV2JlMJgIDAzl69CjHjh2zdziqmPLx8SEgIOCWl1OgA8ifP38ef39/1q5dS+vWra9bXgeQV0oppW6MxWLRy+0qXzg5OV2zpjM3+Vq+1nj+V2xsLAC+vr45vp6amkpqaqrteVxcXIHEpZRSShV1Dg4OeuciVegVWEMQi8XCCy+8QIsWLahVq1aOZcaMGYO3t7ftERwcXFDhKaWUUkqpfFZgl9qfe+45fvvtNzZs2EC5cuVyLJNTjWdwcLBealdKKaWUKqQK3aX2wYMHs2TJEtatW3fVpBPAxcUFFxeXgghJKaWUUkoVsHxNPEWE559/noULF7JmzRpCQ0Pzc3VKKaWUUqoQy9fEc9CgQcyePZuff/4ZT09Pzpw5A4C3tzdubm75uWqllFJKKVXI5GsbT5PJlOP06dOn07dv3+vOr8MpKaWUUkoVboWmjafeN1YppZRSSlnpfbWUUkoppVSB0MRTKaWUUkoVCE08lVJKKaVUgdDEUymllFJKFQhNPJVSSimlVIHQxFMppZRSShUITTyVUkoppVSB0MRTKaWUUkoVCE08lVJKKaVUgdDEUymllFJKFQhNPJVSSimlVIHQxFMppZRSShUITTyVUkoppVSB0MRTKaWUUkoVCE08lVJKKaVUgdDEUymllFJKFQhNPJVSSimlVIHQxFMppZRSShUITTyVUkoppVSB0MRTKaWUUkoVCE08lVJKKaVUgdDEUymllFJKFQhNPJVSSimlVIHQxFMppZRSShUITTyVUkoppVSB0MRTKaWUUkoVCE08lVJKKaVUgdDEUymllFJKFQhNPJVSSimlVIHQxFMppZRSShUITTyVUkoppVSB0MRTKaWUUkoVCE08lVJKKaVUgdDEUymllFJKFQhNPFW+Sk1NZfPmzVgsFnuHopRSKg8kJSURERFh7zBUEaWJZx5LTU3l3Llz1ywTGxtLampqAUVkPykpKbRt25YmTZrw5JNPkpmZeVPLOX78OF999RUJCQl5HKFSSqnc+OOPP6hWrRqhoaF89tlnVy0nIjlOT05Ovqn1ZmRk3NR8eU0rUW6dJp63KD4+nnXr1jF27Fg6dOhAyZIlKVOmDL169SI6Ojpb+R9++IHAwEBq1KjBiRMnCiTGVatWMXHiRNLT069b9sKFC4waNYqffvqJuLi4a5bNzMxk9OjRvPbaayxZsoSLFy/aXhMR+vXrx99//w3AzJkzeeyxx7LEICLExMRw9OhREhMTc1zH0aNHCQsLY8CAAbRr1862T+Pj43n99dd544039ItAKaVu0Y4dO/juu++YPn06U6dO5ccff2Tt2rXs2rWLf//9l7///puXX36Zu+++m5MnTwIwdOhQPv74Y0SEJUuW0KZNGwIDA/H09MTFxYXHHnuMpKQkwKiUeeyxxyhRogTPPvss8fHxNxzb119/jY+PDyNGjMiS0MbHx7Nv37482X6LxcKvv/7K0qVLc3w9JiaG559/nhIlSnDfffexYcMGRIRVq1bxyCOP0KpVK2bOnJktQT537hzDhw+nZMmSDB069JZijIqKIjIyksTExKsm9mCcW48ePcrixYtvaX35Rgqx2NhYASQ2NrZA1jd8+HCpUqWKtGvXTvr16yejRo2Sb7/9VtasWSM7d+6UXbt2yY4dO2T27NkyYMAAqVmzpphMJgFyfJQtW1Z+/vlnuXjxomRkZMirr76a5fWqVavKmTNnssWxfv16eeaZZ2TYsGEyduxYmTlzpixfvlx27NghBw4ckPDwcFm9erVMmTJFnn32Wbnzzjtl+PDhcvbs2SzLOXfunPTq1cu2vkcffVQyMjJERMRiscivv/4q27dvt5VPS0uTli1b2so7OjpKu3bt5O+//85xf7344ovZtjksLEwmTZokr7/+um0Zr732mjg5OQkgzZo1k9atW0vZsmXFbDbb5nN1dZX7779fZsyYIefOnRMRkdOnT0vFihWzLL9OnToyf/58qVChgm3a+PHjs8WWkJAgK1eulIkTJ0p0dPTNviWUUqrYmz59+jXPZf99DBgwQP73v//ZnleuXPmqZRs3biz79u2Ttm3bZpkeEhIiK1euvG5sP//8szg4ONjme++990REZNOmTVK2bFkBZODAgZKcnCwiInFxcTJp0iRZtmxZjstLTEyUwYMHS7ly5aRz584yceJEmTx5slStWtW2jrFjx9rKZ2ZmyvTp08XPzy/btpUuXTrbtKpVq8pbb70lw4cPl759+4q7u3uW12fOnGlb9p49e2TUqFGyZMkSiYmJkczMTNmzZ4988803MmvWLImPjxcRIxd6/vnnsxwjR0dHqVatmnTt2lVeeuklefXVV+XVV1+Vxx57TIKDgwUQs9kscXFxN/2+yI3c5GuaeF6ha9euN/zBu/IRHBwsDz74oIwfP1527dolGzdulCpVqmQp4+LiYvt/yJAhUr58eQGkdu3acv78eRExksFx48ZlSchy83B3d5cXXnhB3njjDXn88celVKlSAoiDg4M4OjoKIE8//bQcO3ZM7rnnHgHEyclJ5syZIyIiL730kgDi6emZ5UNoMpnkxRdflISEBNu++vrrr22vP/zww1KtWrUcY5oyZYqIiPzyyy/i7OycY5mcpjdo0MC2DytWrCjLly+XMmXKZCnj4+NjS1r37NkjIiLbtm2TVq1a2bYXkMcff7xA3j9KKVXUfPvtt7aEpkmTJnLvvfdKly5dpHXr1lKtWjUpXbq0BAQESGhoqDRp0kR+/vln27yjRo2yfc+WKFFChg8fLuHh4XLo0CFZsWKF7RxkfXh4eMgnn3ySpeLg1VdflbS0tBxj27hxo7i5uQkgDRs2tM3Tp0+fbOeNunXryhtvvCElS5a0nbdmz56dZXn//PNPlnPbfx8lSpTIknxu3bpVwsLCbNNq1Kghc+fOlWeeeca2fk9PTxk0aJCMHj062/ZaH40aNZK+ffva1rF//3755ZdfxMPDw1bGwcFBvL29s8zn6ekpffr0kaCgoCzlbiQfcHR0lLCwMDlw4EC+vn+sNPG8SSdOnJDVq1fLjBkzZNSoUdKvXz9p166dVKlSRfz8/MTPz09Kly4t9evXlxdeeEEWLlyYY42liFHjNmTIkCzJkqurq+2DcPDgQQkICLC9QVq1aiXt27e3lX3kkUfk5Zdflscee0zatWsntWrVklKlSomHh4cEBQVJtWrVpH379jJ8+HCZNGmSNGrUKMc3X506dWTz5s0yd+5c2xvWWvt4ZWLZp08f2/MFCxaIiMiBAwfk8ccft00PCgqSvn37yvvvv29L7N555x3bNp86dUo++ugjqVOnjgAyfPjwLPtk69at8sEHH8isWbPk77//lpMnT0pycrJYLBb5999/ZeTIkVKvXr0ssQUGBsqRI0ds8VgT9meeeUZiY2OlQ4cOti+lyZMnZ0nwrb+GnZycJDIyMj/eMkopVWRs375d7rnnHvH09JSGDRtKt27dbEnnwIEDxWKx5HqZM2fOlPfee89WgXKlgwcP2hK9gIAA2bp1q4iIxMfHy7PPPmv7rm7RooWsWbNGvvnmGxkyZIg8+OCD0rJlS/Hy8hJAOnXqJOnp6fLGG29kOT907dpV5s+fn6020tfXV8Co8VuwYIFERETIgAEDbOetoKAgmT17tnzwwQfSqlUrqVOnjnzyyScSFxcnI0eOzHJutCaLY8eOldTUVNu2nT59WpYtW5alRjEuLk4++ugj6d+/v7z44ovy1ltvyW+//SYWi0UyMjLkzjvvFEDKlStnW3bdunWzVFS5urpKq1atstUiV65cWVasWCEWi0USEhLk+PHjsmLFCvnss8/kpZdekmHDhsmwYcNk5MiRsmLFiiwVRQVBE89CJikpSfbt25ftku/OnTulZs2aWd5cTk5OMmnSpFx/AVgsFvnll1/k0UcflQEDBsiYMWPkp59+yvJL8ptvvrGtJywsTHbv3i2DBg3Ksv6XXnop27KXLl1qq7q/8tGjR4+rxhkVFZWr+K8UGRkpM2fOlBdffFH279+f5bX4+Pgsv+BOnTpl+4VrfXTu3NmWrDZv3lwAGTly5E3Ho5RSRZXFYpFdu3ZJv379rno5/bnnnruppPNGREVFyZdffiknTpzI9tr8+fNtyeXVHo0aNbJdcrZYLDJs2DBxc3OTd999VzIzM0XEOA/cd9990qRJE5kzZ46kpaXZKk2cnJyyVLZ069ZNLl68eM2Yr0w+e/TokWPsN+PUqVNZLs8//fTTtnP0yZMnZdu2bbbkNjMzU/744w957rnn5IMPPpCkpKQ8iSG/5CZfM4lco4WqncXFxeHt7U1sbCxeXl72DiffHDlyhJUrV3LgwAF69OhB48aN821dS5YsISoqit69e2M2mxER3nvvPd58803atm3LsmXLcHJyyjZfUlISa9asYcOGDfz111/4+fnx7bff4u7unm+x3qi5c+fSs2dPHBwceO+99xg+fDgODg5ZXitTpgzHjx/H2dnZztEqpVT+S0hI4IMPPmDevHkcOHDANr1Hjx68+OKLnDp1ih07dlCqVCkGDRpk+84saIcPH6Z///7s3r2b2rVrU69ePSpVqoSfnx/+/v40b9482zkpIyMDR0fHay43IyODXr16MW/ePADuvvtu3n77bVq1anVDcS1dupSSJUsSFhZ2cxt2FatXr+all17iySefZPDgwZhMpjxdvr3kJl/TxFMBcPr0acqUKYPZbLZ3KDdlxYoV+Pv7U7du3SzT09PTqVChAqdPn2bWrFn07t3bThEqpVTBEBF69OhhS7qcnZ255557GDFiBM2bN7dzdAUnPT2d7777jmrVqtGiRQt7h1OsaeKp1BXee+893njjDZo0acLy5cs5cuQIaWlp1K1bF1dXV3uHp5RSeWrmzJn06dMHR0dHpk6dyoMPPqjnUJWvcpOv6Tieqth75plncHFx4Z9//sHHx4cGDRrQrFkzvLy8CAsLY/z48dccE00ppQojEWHevHlUqVKFhg0bsnTpUo4ePcrgwYMBeOedd+jTp48mnapQ0RpPdVsYPHgwEydOBMDPzw+A8+fP215///33GTFihF1iU0qp3NqzZw8DBw5k7dq1WaZ7eXkRFxdHixYtWLt2bZFtPqWKFr3UrtR/ZGRkEBERQZkyZfD09LTd2WHmzJm88847APz4449069bNzpEqpdS1JScnExoaytmzZ3F1dWX48OEkJSXx+eefk5qaiqenJ//++y+hoaH2DlXdJnKTr127W5hSxYSjoyOVK1e2PTeZTFSsWJGRI0cSExPDhAkTeOKJJ/D29qZdu3Z26+GplFLX8+OPP3L27FmCg4NZv349ISEhAAwZMoSpU6fSrl07TTpVoaU1nuq2l5mZSdeuXVmyZAkAPj4+tGrVikGDBtGhQwc7R6eUUlk1a9aMTZs28d577/Haa6/ZOxyltHORUrlhNpv54Ycf6NWrFx4eHsTExPDLL7/QsWNHBg4cSGJior1DVEopALZt28amTZtwcnKiX79+9g5HqVzTxFMpwMPDg++//57o6Gg2b95s6xU6adIk6tevz969e+0coVJKGd9JAA899BBlypSxczRK5Z5ealfqKlatWkXfvn05efIkderUYcuWLTne1UkppQpCbGwsQUFBtjvJtWnTxt4hKQXopXal8sTdd9/Nli1bKFWqFDt27GDcuHH2DkkpdRv77rvvSEpKombNmrRu3dre4Sh1UzTxVOoaypQpw/jx4wEYNWoU+/fvt29ASqnb1rRp0wB47rnnis09vtXtRxNPpa6jd+/edOrUidTUVPr374/FYrF3SIXa5s2b2bx5s73DyKIQtyiyq6SkJJYuXUpsbKy9Q7FJSEjgl19+KVQxFQZHjx5l27ZtODg40LNnT3uHo9RN08RTqeswmUxMnjwZDw8PNmzYwPz58+0dUqF0/PhxunfvTpMmTWjSpAndunUjIiLC3mGxc+dOqlevjqurK0FBQdSpU4cff/zR3mHZ1fHjxxk+fDjlypWjc+fONGvWjFOnTtk7LM6cOUPLli25//77KVu2LAMHDmTPnj32DqtQ+PnnnwFo1aoVpUuXtnM0St0CKcRiY2MFkNjYWHuHopS8+uqrAkivXr3sHUqhM3XqVHFzcxNAHBwcxMHBQQBxcXGRTz75xG5xHTlyRAIDAwXI8vDw8JDjx4/bLS572rVrl5QoUcK2L6zHqmLFinL06FG7xXXkyBGpVKmSAGI2m23xOTk5ybp16+wWV2HRunVrAWT8+PH2DkWpbHKTr2mNp1I3qHPnzgAsW7aMzMxMO0dTeERGRjJw4ECSk5Np2bIlW7duZfv27dx1112kpqYybNgwpkyZUuBxnT17lvbt2xMZGUnt2rXZs2cP4eHhhIWFkZCQwODBg2/LS/AjR44kMTGRunXr8vPPP3Pw4EEqVqzIkSNHaNWqFYcOHSrwmPbt20eLFi04fPgwoaGh7Nu3jz/++IPWrVuTnp7O8OHDb8tjZXX+/Hk2bNgAQNeuXe0bjFK3Kt/T4FugNZ6qMElLSxMvLy8BZNOmTfYOp9Cw1gSHhYWJxWKxTbdYLPLWW2/ZatUWLVpUYDGdP39e6tWrJ4BUqFBBTp06ZXtt165d4uTkJIDMnz+/wGIqDHbu3GmrSdyxY4dt+smTJ6V69eoCSGhoqERGRhZYTMePH5fg4GABpHbt2nL69Gnba5GRkbaa9MWLFxdYTIXN1KlTBZAGDRrYOxSlcpSbfE0TT6Vy4eGHHxZARo4cae9QCoWYmBhbMp5TYmCxWKR///4CiKurq6xYsSLfYzp58qTUqFFDAPH395cDBw5kK/PGG28IIAEBARIdHZ3vMRUW3bt3F0AefvjhbK+dOXPGdqm7bt26EhMTk+/xXLx4UWrWrCmAVKtWTc6fP5+tjPWHTZ06dSQzMzPfYyqMOnfuLIC8++679g5FqRzlJl/TAeSVyoWpU6fy9NNP06xZM/7++297h2N3H3zwASNGjOCOO+5gx44dODhkb72TkZHBgw8+yJIlSwDo378/H374Ib6+vlnKpaamcvz4cY4ePcrRo0eJiooiJSWF1NRU3Nzc8PX1xdfXl+DgYCpWrEhQUFCW9YkIO3fupGvXrhw9epRy5cqxYsUKqlevni2mlJQU6taty4EDB3j33Xd544038njPFD579uyhVq1aiAj//vsvderUyVbm8OHDtGjRgrNnz9KmTRs+//xzatWqlWXontTUVI4dO2Y7TkePHuXEiROkp6fj4OCAo6MjZcqUISgoiODgYKpXr07VqlVxc3OzLUNE+PPPP3n55ZfZtGkTZcuW5a+//qJ8+fLZYoqKiiI0NJS4uDh++OGH265Hd3x8PH5+fqSmprJz505q1apl75CUyiZX+Vr+5sC3Rms8VWFz4sQJAcRkMsmFCxfsHY5dJSUlSZkyZQSQmTNnXrNsYmKiPP3007bLvL6+vtKsWTNp06aNtGzZUsqVKycmkylbJ6BrPZydnaVatWrSsWNHefDBB7N0IqpcubJERERcM6aJEycKIPfcc09e7pZCq2fPngLIgw8+eM1yW7duFU9PT9u+rFGjhvTu3VtatWp1U8fJ+nkJCQmRli1bSs+ePW01q4D4+PjIzp07rxnTu+++azuu6enpeblbCr0ff/zRtu1XNmVRqjDRGk+l8lGdOnXYuXMns2fP5tFHH7V3OHYzefJknnvuOcqXL8+hQ4du6HaiGzZsYMCAAVcdIsfd3Z3Q0FBCQ0Px9/fH1dUVZ2dnkpOTiYqK4sKFCxw7dozjx4+TkZGRbX4nJyfuuusuZsyYQUBAwDVj2bZtGw0aNMDb25uoqKgca2uLi4sXL+Ln54eIsG3bNurVq3fN8lu2bGH06NH89ttvpKWlZXu9RIkStuMUGhpKSEgILi4uiAipqamcPXuWU6dOERERwd69e4mOjs62DA8PD7p168bLL79MzZo1rxlPfHw8wcHBxMbGsmnTJpo0aZKr7S/KHnroIRYuXMgrr7zC2LFj7R2OUjnKTb7mWEAxKVVsdOzYkZ07d/L777/f1onn3LlzAXjhhRdu+B72LVu2ZNu2bWzYsIG4uDhbUhMSEkJoaCh+fn43dEeWjIwMTp48yZEjRzhy5AhxcXE0atSIxo0bZ7mkey21a9fGzc2N2NhY9u/fT40aNW5ovqJo27ZtiAiVKlW6btIJ0KhRIxYtWkRsbCy//PILp06dsh2j3BwnMC6rnzt3jsOHD3PixAlOnDhBUFAQDzzwACVKlLihZXh6etK0aVOWL1/Otm3bbpvE8+TJkyxevBiAPn362DkapfKGJp5K5VKnTp0YN24cv//+OxaLpVjXlF2NXGonCHDnnXfapqelwbffgpMT9OkDOeUmzs7O3HXXXbe0fkdHRypUqECFChVueFkpKbByJWzYAL17Q+3ajjRq1Ij169ezadOmYp14Wo9V3bp1bdNE4OxZOH0a6tQBxxzOBt7e3jz22GO3tG6TyUSZMmUoU6bMDZXPyIDwcChRAoKDwdvbmF6/fn1b4nm7mDJlCpmZmdx5553ccccd9g5HqTxx+50xlbpFLVq0wMPDg3PnzhEeHm7vcOzi9OnTREdHYzabqVGjBiKwaBHccQc88ww8+SQ88ABERdk7UoiJgb59wc8PunSBDz+Exx4zEq9mzZoBsHHjRrvGmN+siWe9evVITISuXY39ERgIDRtC8+Zw8aJ9YwSIjYW774ZmzaB2bfDxMZLPo0ehQYMGALdN4pmWlsbXX38NwKBBg+wcjVJ5J18Tz3Xr1tGlSxeCgoIwmUwsWrQoP1enVIFwdnbm3nvvBbhtb724Y8cOAMqXL8+9995L9+7nePBBOHTISGhcXOCXX6BePbiy8/+WLVu466672LJlyw2t51bLR0ZCmzZGLWxCApQrB25usGMH/PEHtlsP/vHHHze+8UWQNfGcN28eH310lJ9/NhJNBwfjWG3eDHfeaewvq/w8VjmVPXPGOFbr1hnHqGRJY/rJkzB69Gk++eQTwHjv5dS+t7j56aefOHv2rK1ZglLFRb4mnta7Y0ycODE/V6NUgbMO6TJnzhwsFoudoyl41sTT0dGR1avDWbCgFAD/+x8cPmwkm5Urw4kT0Lo1jBsHFgvMnDmT1atX8913393Qem6l/KFD0KKFkWSWKQNr1sDx49C/v1H2k0+MO+YAHDp0iISEhNzthCIiNTXV1plr586dfP+90dFnyBAjGQ8PN2o+d+2CVq1g925jvvw8Vv8t+++/0LKl8bdMGfjrL6O23LqoBQvMbNq0CScnJ1JSUmzHrTiznjefeeaZG25DrVSRkJ/d668EyMKFC3M1jw6npAqr5ORk28Dp69evt3c4BSoiIkI6duwowKV7fncVEAkJSZYtW7bYhjGKjRXp2VPEuKgt0rJljPj6NrYN7B4eHp6l/JXL37Jli4SHh4u/v/9NlPcWd/exUqJExqW40uTw4cvl1649KSaTRUDE17eFbVifr776KsflF2URERHy/fff24Y0ArOYTDECItOm7bVt6+HDIqGhxnFydMyU/v1Pi59fcJ4eq5zK+vmVl759I8VsNo5HaKjIoUOXy69Zs1WcnTMvvYdq2e449c477xSr4/Rf27dvF0AcHR2z3MlJqcKqUA6nZDKZWLhw4TXvM5uamkpqaqrteVxcnG0IDR1OSRU2ffv25dtvv2XQoEF88cUX9g6nwGTvzTwZGABMAF4AsN1XWwQcHJ4BPgNcL5XfB6wEYgET4MjAgcNJTITERJg//zegBOBE1uEgLZceSfTocS9eXuDlBR9//DaQDpQGAoB7AZ9L69oE3I/I2f/EvwB4EPjqUuxZFdDXYr7LfqxaA2uB8xj7ymLb1shICApaDNx/qWwE8A9wBIjG2Kc+9OjxHDExRtvZTZtyuqx+5b7LoEOHMHx8YO7cyUDMpYcvUBVoBJS7VHYeZ850w9oH6XLsi4AHgFHA21nXVEyO0389//zzfPHFF3Tr1u22bc6jipZCOYA8N1Dj+fbbb+c4+LDWeKrC6LfffrPV8NxOg1rPmDHjP5/RY5dqpDqKo6OjzJo1K0v5WbNmidlcX2ClQLqtBjR/HzsFHhGz2ekq8bS5VC5JwN22LTnFX5TNmjXrPwO+f3Bpu2fmuK3ffTdLHBy6C5wuoOMkAifFweGhHI+To6OjwGOXyu3O8r4rTsfpSqmpqVKqVCkB5LfffrN3OErdEK3xVKoApKenExgYyMWLF1m+fDnt27e3d0gFYseOHVcMy1Md2AukAL6Eh2+w9T6+0tatW2nYsCHgDbQDmgNmHn30UQID/SlRwhg+x8PD+Hv27BH+979hGDWilx9jxozD3z+U+HiIizMe8fEQGXmBxYu/Ac5h1Kj+Bgjh4eE5xhMevpVGjTKBxkBPwBiTdMuWLZfiLD6aNGnC5s2bLz3bCdQCehIePvwax+pOoC1QEagEePLoo52oWtUfHx+j44+3Nzg7G+1jhw4dcmnuyzWs48dPICSkMrGx2GpIDxw4y+zZS4EEYP+lx1+Eh6+/RixtMY6ry6VYjlCiRAni4uKK5VBmixcv5oEHHiAgIIATJ07gmNM4V0oVMkV2AHkXFxdcXFzsHYZSN8TJyYlHHnmEKVOmMGfOnNsq8bQyme7F+Om6Dki+7rwODvFYLD/h4LAQi8XCyy+3okED/2zltm6N4X//+xkHBwfbWKkWi4V77nmNBg1Ccyh/nMWL//ef8lf/TW1cxZ2HkXh2xJp4njlz5rrbUJSICAcOHLj0LBAj6cwElgPDrzFnPA4OS7Ls+5dfDr/KsYoDfst2rFq1epf/5pJbt55i9uynspW9tjhgBXAf0AsYTWJiIkePHqVSpUo3sBeKlpkzZwLQu3dvTTpVsVT8fi4qVYCsdy766aefSElJsXM0BWPnzp2AcXtLT89uAAQH7yYgIAB//+yJCYC/vz8BAQE0bNiQyZMn07BhQ7uUT0tL4/fff8fNzQ0fH2PsoLJlu+Du7g4Yd4opTk6dOkVsbCwA5csPBMDDYycBAS52OVY3u+zQUGO8XDe3vrZkrDiO5xkVFcUvv/wCwBNPPGHnaJTKJ/l5zT8+Pl62bdsm27ZtE0A++eQT2bZtmxw7duyG5tde7aqwy8jIkHLlygkgP/zwg73DKRDWHu0ff/y5ODsbvZF377ZISkqKHDt2TAYNGiSvvPKKpKWlZZkvJSVFLBaLiIhYLEb5a8nr8vv375eGDRsKIA899JDs2ZMiIOLiItKzZy8BZOzYsbnaF4XdkiVLBJCaNWvKvfcax+r99y0yf/58mTZtmvz666+yfft2236zys9jdb2yFotF/v77b/nss8+kT58+0rNnTzl2LFacnIw2oY888qQA8tprr+V6fxR2kyZNEkDq1q1r71CUypXc5Gv5Wo+/ZcsW2rZta3s+bNgwwLjn7IwZM/Jz1UoVCLPZzFNPPcWoUaOYOnWqbXzP4sx6qV2kIWlpJsqXh4CAGN54430+//xzWzvt3bt3M2/ePFtt4pXNaEwm03Wb1eRVeRFhxowZPP/88yQmJgJGO7rJkxNxc3MhORl8fEIAOHbs2A3tg6LCOnB87dr1+Plno/1lcPAmHnnkkSzlOnTowPz58/Hw8ADy91hdq2xycjK9evXKdrORNm3aUL36s+zcCf7+jYHpbN269ZoxFUXWy+xa26mKs3y91H7nnXciItkemnSq4uTJJ5/EZDKxatUqjhw5Yu9w8tWFCxc4ffo0AAcP1gKgY0fo0aM7H330EampqTRv3hw3NzeWLl1Kx44dbZd67SEmJoaePXvy1FNPkZiYSNu2balevToZGRksXryQatWMciaTkXgeP37cbrHmh+3btwNQtmxdUlKMDkGnTq0DIDAwkPr16+Pi4sKyZcto164dF+1438yYmBg6dOjAokWLcHFx4b777qNNmzYArF+/nurVjXKOjvWB4nep/dChQ/z99984ODjQq1cve4ejVL7RlstK3aIKFSrQvn17li9fzrRp0xg9erS9Q8o31vadoaGh/PuvJwDNmiXw9derAPj555/p0qULf/75J/fddx/r16+ncuXK9OzZk169ehEQEEBSUhKJiYkkJiaSlJREamoqZrMZJycnXFxc8PHxoWTJkri7u+Pk5ISTkxMZGRmkpqaSkpJCSkqK7X/rX4vFgqenJ97e3jg6OhIdHc2JEyd49dVXOXbsGI6Ojrz77ru88sorjB07ltdee405c+ZQs2Y/tm+H5OTyQPGr8bTWTnt6GqMQVKoEW7YYPdyHDh3Kq6++yqZNm7j33nvZtGkTrVq14vnnn6dGjRoEBwcTFxdHVFQUiYmJZGZmkpmZiZOTE+7u7lkeJUqUsP3v7OxMfHw8MTExtkdsbCwpKSk4OTnh6OhIiRIl8PX1xdvbmxMnTrBjxw6++uordu7ciZeXF7/88gutW7dm1apVrF27lnXr1tGnjwAm4uLuAODs2bPExcUVmxFPrLdtbd26NQEBAXaORql8lK8X/W+RtvFURcWPP/4ogAQFBRXrMT0nTJgggDzwwANSqpTR5u6bb9YJIGXLls1Sdtu2bRIcHJzj2LwF+ahYsaJs2rTJFtfhw4cFEAcHB/nf/84IiHTpYowR6e3tXcB7NP9kZGTY7vTz5pvGWKvduomEhIQIIKtWrbKV3b17t5QtW9bux6pMmTKyfft2W1wJCQmXxvJEPvnkqIBImzZiG+dyx44ddtiz+aNfv34CyIgRI+wdilK5VmjaeCp1u7j//vspXbo0p0+fZtmyZXTu3NneIeUL6z2yQ0Nr8vPPxrTz540ex40aNcpStl69ehw+fJiVK1fy/fffs3jxYjIzM7PVkLm4uGCxWMjIyCApKYnY2Fiio6NJSkrKsjwHBwdcXV1tDxcXF9tfBwcH4uLiiI2NJSMjg5IlS1KyZEmaN2/O6NGjs9SKVaxYkcaNG7N582YuXvwJGMiJE0aNZ2xsLLGxsXh7e+fTHiw4Z86cIT09HbPZzIULQQAEBp631epeOV5pzZo12bhxIxMnTmTnzp3s2bOHyMhISpYsia+vLx4eHpjNZsxms+04WWusrY+0tLQs67fWXvv4+ODt7Y2rqysZGRmkp6eTmJhIVFQU0dHRBAQEUKdOHerWrcszzzxDcHCwbRklSpSgUaNGbNy4kdjYdUAF9u83rjJcvHiRiIgIateunf87swBYx1pt0qSJnSNRKn9p4qlUHnBxceGJJ57gk08+4euvvy62iac1aXF1NcbSLFsWdu0yEs+cBl53cnKiU6dOdOrU6abWl5mZSXp6Oo6Ojnk6pmHPnj3ZvHkz27bNAQZy4IAHvr6+REVFcfz48WKRzFjbq5YtW5ajR637zkhuqlWrli25LleuHGPGjLnp9WVkZJCcnExKSgqenp64urpef6Yb0Lp1azZu3MiRI+uAJzhzBpo0qUB4eDgRERF5sg57S0xMZNeuXYAmnqr403E8lcojffr0AWD58uWkp6fbOZr8YU08MzKMzjhVqxqjV0DOieetMpvNuLq65vlA2t27dwdgy5b1ODqeJCkJAgOLV89263aEhIRw+LAxLTbWSDwbN26c5+tzdHTE09MTPz+/PEs6wUg8ATZuXIe16aOnZwWAYpN4bt26FYvFQtmyZQkKCrJ3OErlK008lcojtWrVomTJkiQnJ2e5u09xISK2ZCYhwUjSKlSIZ//+/UD+JJ75pVy5crRs2RKA0qV/AsDT07jcXlx6tlu3Izi4PNb87MSJ/Es880uLFi0wmUwcPHiQChWMQf/N5gpA8Uk8//nnH0BrO9XtQRNPpfKIg4MDTZs2BWDjxo12jibvRUdHk5CQAMC5c0aS5ua2DRGhXLlylClTxp7h5Vq7du0AcHMzeuo7OhbPGk8fnxDS08HJSdi1q+glnj4+PtSta/TKL1FiPQApKcax0sRTqaJHE0+l8lCzZs2A4pl4WhMZf39/jhxxAyA19ertOwu7ihUrAiBijL2alla8Ek9rjaezs/EjITj4BOfOncPR0ZF69erZMbLcs15uT0kxEs/o6AqAJp5KFUWaeCqVh8LCwoDinXiGhIRw4IAx7dy5nHu0FwXWxDMx8SgA0dHF61K79XhlZhoJtbe3UdtZq1Yt3Nzc7BbXzWjVqhVwefD7U6eMbYqKiiIuLs5uceWF8+fP2xLoovgDTqnc0sRTqTxkrbE4dOgQFy5csHM0eetyjWcISUlgNsP+/fnXsSi/hYYaPfMvXjwOpHP6dPGs8UxMNBJqk6noXWa3siaex47tBKI5csQLX1/fS9OK9vGyDqNUvXr1YjGMl1LXo4mnUnnIx8eHGjVqAMWv1tN6gnd3NxK0kJA4Dh40qj6LYuIZEBCAq6srFosFk+kEiYnGdkVGRmYbk7KosY5HCnDxopF4xscX3cSzTJkyBAcHIyKYzftISYGgoApA0b/crpfZ1e1GE0+l8lhxbedpTTwdHIwEzc/P6FgUHByMv7+/PUO7KQ4ODlSoUAGAsmWPAn44O7siIpw8edKusd0qa22nr68vx455ABZOnTJqp4tqgmOtoS5TJgIAb+8KgCaeShU1mngqlceKa+JpPcFbexS7uBTdjkVW1naeJUseAUz4+BSPe7ZbE8/LY3ieIikpDkdHR+644w67xnazrImnj08EAE5OFYCifaxERBNPddvRxFOpPGbtYPTPP/+QmZlp52jyjvUEHx1tJJ7JyUW3Y5GVNZlxcjI6GFmbERT1DkbWY1WmTHni4wGMGtyyZcvm+WD8BcVaO209VhkZxvOiXON57NgxLl68iJOTE3Xq1LF3OEoVCE08lcpjNWvWxMPDg/j4ePbs2WPvcPJEYmIiFy9eBLB1womNNdp3FtUaNLhc45mRYQypZDYXrxpPLy/jWPn6GonnlfdBL2qsiWdGRgQAcXHG86KceFpvk1m9enVcXFzsHI1SBUMTT6XymNlstl02Ky6X262JmJeXFxERPgBcuBABXK41LIqssVuHVLLeCrSoJ57W+B0djUTax+cEYNyxqaiyHqu4uAgAzp6tABTtxHP37t2AMcSVUrcLTTyVygfWdp5///23nSPJG9ZEJjAwhIwMcHFJICrKGC7KWhNVFFlrPC9eNGo8rUMPFfVL7db4rYm0m5tR41mUE0/r++zs2WOAhbNnjW27ePEi8UZ7giLHWuNZlK8aKJVbmngqlQ+aN28OwIYNG+wcSd6wJp7e3sbJvnz5CABKlixZpMcetNaixcRcAOJt7VeLS41nQoJ1DM+in3iWLVsWs9lMWloarq6RgBc+PkV7LE+t8VS3I008lcoHLVq0wGQycfDgQSIjI+0dzi2zntidnY3ErHRp49J0Ua7tBKPpQKlSpQAwmY7a7vJz/PhxLBaLPUO7aenp6Zw+fRqA8+eNxDM1tegnno6OjpQvb2yPdUil0qWL7j3bMzMz2bt3L6A1nur2oomnUvnAx8fHdj/stWvX2jeYPGBNPC0W40RfokQEULTbd1pZt6FUqaNAWUwmE6mpqZw/f96+gd2kkydPIiK4uLhw4oQxvmpcXNFPPOHyDx1v7wgAPD2N50Ux8Txy5AgpKSm4ubkVi8+RUjdKE0+l8kmbNm2A4pV4WsfwFCkeNZ5wuZ2nh8cRwJmSJYOAonv51tq+s1y5YM6edQAyuXDh9KVpxSPxdHEx3n/Ozsbzoph4Wtt31qhRA7PZbOdolCo4mngqlU/uvPNOoHglnjEx1jE8I4DiVeNpHR/S09MYcujEiRN2i+lWXB7DMwQRcHE5S2ZmJmazmYCAADtHd2usx0okAoDMzApA0Uw8tX2nul1p4qlUPmnVqhUmk4m9e/dy7tw5e4dz09LS0mxtBq09iWNiIoDiVeOZmWn0bHd2LtqJp7XG09vbaA/p52dcZg8MDCzyNWvW95v1h09SkvG8KCae2qNd3a408VQqn/j6+lK7dm0A1q1bZ+dobt6VbQYTE402g6dPG7WDxanGMynJ2CaRop14Wms8XV2NHwk+PsWjfSdcTjyjo41jFRVlPC+KiafWeKrblSaeSuWj4tDO88rbL4ID/v4xxMTEAMa9wIs6a41nVNRRQEhJKdqJp7XG08HBqPF0dy/6dy2ysiae584dBzI5d+7yWJ4JCQn2CyyX0tPT2b9/P6A1nur2o4mnUvnImniuWbPGvoHcAmvi6eNjnOQvD2VTGg8PD3uFlWfKly+Pg4MDaWnJwFni4opH4pmWZhwvB4eif9ciq6CgIJycnMjIyMDR8TQWizfe3iWBotUZ7ODBg6Snp+Ph4WEbIkqp24Umnkrlo9atWwNGe64LFy7YOZqbc/SocVnT3d24JO3lFQEUj8vsAE5OTlfUBh4p0omniNgSsPh4I6HJzCw+l9rNZrMtUfP3P3rpbwWgaF1uv7J9p8lksnM0ShUsTTyVykd+fn7UrFkTgPXr19s5mptz5IjR6cZkMhJN61A2xaFjkZU1iXZ2PgoYiWdkZCQZGRl2jCr3Ll68SHJyMgAXLhjbkZRUfBJPyD6Wp5eX8bwoJZ7avlPdzjTxVCqfWS+3F9UORtYaz7Q0oy2kdSib4lLjCdhq0by9TwBlcHR0wmKx2HrzFxXW2s6AgABOnXIBICameCWe1vedq2sEAC4uFYCilXhqj3Z1O9PEU6l81qJFCwA2btxo50hujjXxjI3N2vu7ONV4WpMyV9eTgAM+PmWBone5/fLg8SFERwNYOHfu1KVpxSPxtL7vrD+ALBbjeVFKPK01npp4qtuRJp5K5bNmzZoBsHXrVlJTU+0cTe6kpKTYav3OnDESz+joCKB41Xha23iaTEaiWaJE0Wznaa3xLFXKqMH19DxPeno6JpOJwMBAe4aWZ6yJZ0qK8QMoKalo3a89ISGBgwcPAtiGW1PqdqKJp1L5rGLFipQuXZq0tDS2b99u73ByxXoy9/DwICGhNCBERhrTilONpzXxTE83Ek1Hx6KZeFprPD09jWTM39+4zB4QEICTk5Pd4spL1h881psYxMRUAIpO4hkeHo7FYqFcuXLF5seAUrmhiacdxMZCEav4ummHD8Onn0JUlL0jsR+TyURYWBhQ9C63Wy+zBwSEAiZKl44iPj4eKB5jeFpZE8/4eCPRzMwsmomntcbT0dGo8SxOg8dbWX/wnD9/AsjgzBnjfXjhwoUiMZbnP//8A0DTpk3tHEnuZWTAr79C9+7QsiXs3Zv19fPnYf9+SEvLef6YGFiy5OqvF1WZmca2Xc3FizBmDGzbVmAhFWqaeF5FejqkpFy7THKy8WZLSTE+kOfPw+7dsHMniOQ8z8KFEBQEVavCvn1XX3Zm5k2Hno3I1eO5VVFRxnYkJmZ/7fBh48tp2DCoXx9uNufasAHefRdOnbq1WO3Jern977//tnMkuWNNPEuWNGqZrGN4BgQE4ObmZq+w8pw1MUtIuACkkJxcNBNPa42niJGMGW1Wi8fg8VbW2tvMzExMptOkpfng7e0DFI2xPDdt2gRAkyZN7BzJZZmZ8MUXMHAgPP88vPACPPssPP44PPggtG8PzZtD2bJw330wbx78+Se0aQP//gsWC3z8sfF69erg7g6VK8MHHxivAZw9ayyjSxfo2vX659crnT4No0dnP2fOnw8vvmgs+1aJGNuyY8fVy8TEwPbtWWP/+2+44w7w9zf24X/Ptb/+CrVqwWuvQbt2t3YeO3AAzpy5sbJHj8JPP938uvKVFGKxsbECSGxsbIGs78wZkenTRR55RMTLS8RsFnnuOWP6lY4fN6Y7O1tTuuyPFi1E/vnn8jwWi8gnn4iYTJfLlColsnlz1mXHxYk89piIo6NI584i8+eLJCaKnDhhLG/VKpE1a0TWrxf56y+RTZtEwsONMldas0ZkwACRli1FfH1FypUT+fXX6++D6dNFypc31j1pkrGtV7NoUdZ9ULq0SL9+IkeOiJw+LVKxojHdus2OjiKjRomsXSty7JjI4cMiS5aIfPSRyNdfi+zaJZKZaSw7M9PYrk6dLi/fw0Nk3DiRc+dEpk4Vad9epGtXkaio62+Xva1atUoACQkJsXcoufLSSy8JIK1bvyAgEhY2TwAJCwuzd2h5ymKxiLu7uwACB8XF5WcBpGHDhvYOLVf8/PwEkPvv3yYg0qrVqwLIkCFD7B1anqpYsaIA4ue3TkCkatV6AsiSJUvsHdp1BQcHCyCrV6+2dygiYpxzOne++rnsvw8/P5GhQ0UaNDCe+/iI3HXX5dddXLKWf/BBkaNHRWrVyjq9UyeR5OTrx/fvv8b5y3oOWLzYOD+MGHF5WWXKiCxfbpTfu1dk7FjjXJaSkvMyLRbj3LZzp8jff4tMmCBSt66xLAcH47nV7t0i3boZ50Xr+ry8RPr2FRkyxCh/5Xb17SsSGSmyYIHIo49enm4td/fdl89zV5OamjX2kyeNc511WdWrG+f3sWNFZs40zu0LFojMmiXy2muX97Wjo0hMzPX3cV7ITb6miecVWrfO+YPm4WG8mfr2NQ6+k9PVP5S+vlk/eJ06iTz8cNZlP/20SKNGl5f9ySdGArppk0jlyjf+BXDlw9NT5KmnRL77TqRNm5zLODiIfPyxSFqayMKFxodi0KDLCd/w4TnPV7euyBtviGzcePkDs2CB8aYGETe3rOUdHUXKljX+r1RJZP9+44N7o9tRsmTWD7Ojo/FBu9o8deoYH3SLxUhk27YVqV1b5I47ROrVE1mxokDePtcUFxcnJpNJADl9+rS9w7lhDz30kADSps0EAZE77xwngDz66KP2Di3PVatW7VLi+YfAVgHE39/f3mHdsKSkpEvxI61bRwmING/eWwAZO3asvcPLU23bthVAqlT5TkCkceOuAsgXX3xh79Cu6fTp0wKIg4ODxMfHF9h609KMH/xvvWVURlSqJPLEEyLTpl1OuFxdRV5+WeT110X+9z+RkSONSoHJk43zysKFxjLS0oxlRkeLhIVd/h52dTXKWiwip04ZFRfWigmz2fgbGGis091dLn2fiEyZYlSUXLiQPe7ly41zwpUJrckk0qTJ5fVak1KTSaRataznhsBAYxsuXry8zPBwYx/kdC6xxgkigwcb++C/53trPFc+nnhC5P33syeh1riGDRPZvv3ydo8daySEM2aIPPus8frIkSIvvSTSvLmxrY6ORp7w1FOX12k2Z628utbDbDZygf378//9JaKJ50378EORhg1F3nzTSLL++ONygvjfR9u2xoclJUUkNtb40Fg/kCdPGm/EnOYbN874YMbFZf2VeOUjOFjkp5+MD39Q0OU3UblyIjVrGh+uypWNGsWQEKPm9L/LcHY2Etzvvzc+aP37X/uDU6nS5f+HDxcZM8aotf3vB8nPz0girUlnr14i6enGh2jNGpEOHS6XDQgwajVFjG3++mvj117lysaH2cXFSBq7dze+gKwfyisT5Z49RQ4eNBLeadOMWlUwksq33jLWAcYy77475/1ZpkzWLx57qV27tgCycOFCe4dyw+rXry+ANG36i4BI69YDBZARI0bYO7Q8d/fddwsgnp7fCpy3JXEpV6s2KWT27dsngHh4eEiVKhYBkbp12wggs2fPtnd4eapv374CSJ06owVEWrZ8QQB5+eWX7R3aNS1atEgAqVWrVr6vy2IR+e03I3Hx9b12kuLvb5zzcis+3rhC2KqVUXv4X3//bSR/1u/hffuM6atXZ/++B+P8NmCAcf68shKmTRuRs2dFBg68PM3JSeTbb0WSkozkzTrd0dE4D1kTUmvy16iRyEMPXU7czGbjfBYaapzrvvjCOE+MHZs9rvvuM85v0dHGuWjdOuOq5z33iPz88+XtXbHi8vm4WjUjef3778uvT516Ocb/1gxf79G0qciOHUaMCxca5+nHHhNp187IW1q0MP7v3duo+Szoc54mnjfJYsk+LTPTqN0bOdJITMePF/nzzxtbXni4UZs5caLIN9+IbNmS9fXkZCMRvffey18MXbtmfcNkZBhJ7bWq5jMzjV+i/fsbNYODBhmX5v+7bRMmXE4ky5Qxfl099NDlac7ORrX9lc6fN37t9ugh4u2d9YPw2GNGfP/155/GL7i9e68ec0ZG9nnT040vr927jUv1OZ3vExONy/TWY3XwoEiFClkT7ldeMb4AVq4UqVHjcqz29vTTTwsgr776qr1DuWHe3t4CSLVquwREGjW6VwD56quv7B1anrMmM+XKjRawiLOzqwBy6NAhe4d2Q5YvXy6A1KxZ03YVonz5SgLIunXr7B1ennr77bcFkHr1nhYQadFivADSrVs3e4d2Ta+99poA0q9fv3xdT2Ji9qtMpUsbP+S/+kpk6VKRV181krFWrYxL4fnl1CmR994T+e/HaNs2kRdeMK4KhoZePeF68sms54KpUy9X/Fxp2TKjBtF6/kxNNc67depkX2avXtnPkVf66ScjMfb3F5kzJ+fc4Gqio41tzonFYiTq1jhq1DASyOHDjYR74EBjGw4cMI7JDz8YtdDTpuV8ri1MNPEsgiwWo+Y0v23ZYvwKttbOihhv8DFjsrZJzUlamlEL/PLLRlvNwvJBOHlSpGNHI7k8ciTra3//fTmxXrzYPvFZffPNN2JcBm1t30BuUFRUlK3Wz8srQUCkYsUaAshya4OqYuTNN98UQCpVevbSibqKFKa2eNczdepUAeTuuztdOrFZxMXFRQA58t8PRhE3bdq0S0l2BwGRhg2NmsTGjRvbO7RrstaqT5kyJU+Wt3ev8X0cFCRSpYrIBx8YbSIbN75cKzhwoPG9nZ6eJ6vMN+fPGzV5L79sNO1aujTv2u+fOmVUqgwfLrJhw43NExV1Y21Qcysx0Ugkt2/PXUJb2OUmX3PMg/5JKg+YTODllf/radgw+7QKFeB//7v+vE5O0Lat8ShMypaF337L+bVmzeCll2DcOHj6abjnHmM4q5iYy39r1oRJkyC/RweyDqm0efNmMjIycHQs3B8/a492f/8ynDtXAq4Yw7M4DR5vdbnnt9GT3cUlGDhYZHq2W3t0+/gYQyn5+V3k/Hlj3LagoCC7xZUfrLc4jY83tjk6ugJQuMfytFgsbN68Gbj1Hu0i8MQTMGtW1un/+9/l7/JSpWDBAmjd+pZWVWBKlzZ6u3ftmvfLDgoyeujnRsmSeR8HGD3+n3wyf5ZdVOhwSqrYe+cdY/iqs2fhu+9g8WJYt84YOuPYMSNpbdAAfv89f+OoVq0a3t7eJCcns3PnzvxdWR44cuQIYB3DE0qVOkdycjImk6lYDc9jZR1SKTXVmmgWrSGVrEMpubsbv6Csg8f7+/vj4uJit7jyg3UM2fPnjwHCyZPW5+dJzGlst0Jg//79xMXF4ebmRq1atW5pWVOnGkmng4MxPNGiRTBtGljz2erVYdOmopN0qttL4a5yUSoPuLkZY6nNnm382vT2Nh4+PkYt7vDhsGUL3Huv8QgIMGoL6tY1anfz6uYiDg4ONG3alOXLl/PXX39Rv379vFlwPrHWeHp7G4mnv38EFy9C2bJli10iA5drPGNjjUQzJaVoJZ7WGk+TyagN9PIqfoPHW1mPVUpKMo6OF0hL88PLy4e4uBiOHTtGzZo17RxhdtaB4xs2bHhLVztOnoSXXzb+/+gjYxxLqyefhCNHjKtAxfAjqooJTTzVbaFyZXjrrZxf27DBGDB58mQjQf2vmjVh4kS4885bj6NFixYsX76c9evXM2jQoFtfYD6yJp7OzhUB8PaOAIrXrTKvdPnuRdFAIrGxRSvxtNZ4ZmQYtX/WweOLY+Lp4uJCYGAgkZGRlC17jGPH/ChdOoS4uBgiIiIKdeJ5K5fZReC55yAuzqjdHDIke5mKFW968UoVCL3Urm57Li5GG8/16+HLL407ZAwebNxtyWSCPXvg/vuvfUeLG9WqVSsA1q9fj4jc+gLzkfVSe1qaUePp7m4kosWxfSeAt7c3np6eADg4nCQjo+gknhaLxRZnQoJR4+ngYDwvjs0i4PLl9tKljZpeD48KQOFs5ykirFy5Eri1W2XOnWvcctLJybi0bjbnVYRKFRxNPJW6pGVLozbh9dfh889h61a4cMGo6YyPh86djVu33YqmTZvi5OTE6dOnbTWKhZU1vuhoI9E0mSKA4lvjCZdrB/38TlCU2nieOXOG9PR0zGYz584ZHYkyMopvjSdcTjw9PY2aXgeHCkDhTDzXrVvHgQMH8PDwoFOnTje1jDNnjB/EAG+8YdymUamiSBNPpa7B19foGVq9utG26r77ICHh5pfn7u5Ow0tDC6xfvz6Posx7FovFdgI/dcq4dpeYWLxrPOFy7WDJkicAI7GJjo4mOjrajlFdn7V9Z9myZTlwwGhBlZxcvBNPa892Bwdj21NTjfflwYMH7RbT1UyZMgWAXr162WrVc0MEnnkGLl6EevVubBQSpQorTTyVuo6SJY22n35+sG0bDBx4a8u78nJ7YXX69GnS0tIwm81ERxuJy8WLEUDxrvG0Jp7u7icBT7y9jeRzR160s8hH1vadQUEhREUZ06Kji3fiaa3xTE01Es+4uHoAbN261V4h5ejChQv89NNPAAwYMOCmljFjBvzyCzg7w8yZxl+liipNPJW6ARUrwk8/GcOXfPed8bhZRSHx3LdvHwABARUAR4KDLRw7FgHcHjWe1vaRXl51Afj333/tFtONsNZ4enkZtYDBwcKpU7dH4hkba2x7ZGQ9wEjCL1y4YK+wspkxYwZpaWk0bNiQBg0a5Hr+48dh6FDj/1GjoHbtPA5QqQKmiadSN6hVK3j7beP/556Dm72i16JFCwAOHDjA2bNn8yi6vLVp0yYAypZtDECFCmdsNaDFNZGBy0laerq1XWcdoPDXeB4+fBgAJycjGatUKYakpCTAuPxeHFkTz9Onj+HuDhaLNyEhlQHYtm2bPUOzERG++uor4OZqO+PijAHV4+MhLOzyMEpKFWWaeCqVC6+/Dm3aQGIi9OwJaWm5X4avr69tAOkNGzbkcYR5Y+PGjQCUKGH0wPX3N9p3litXrtDfcelWXB5SyUg8ExOLRo3nli1bAHB0NMaGDQgwajtLlSqFm5ub3eLKT9bEMyoqitBQo+F1+fJG++nw8HC7xXWlNWvWcPDgQTw8POjZs2eu5k1JMZLObdvA398YMF57saviQBNPpXLBbDZOAL6+Rq/3ESNubjmF+XK7iNhqPNPSjMTTwyMCKN6X2eFy4nnhgpG4RUUZieeuXbvIyMiwW1zXkpycbKuRTU42xoj08Snel9kBvLy88Pb2BiAoyLjc7u1tXMouLO08p02bBuS+U1FmJjz2GKxeDZ6ext3VdHxOVVxo4qlULpUrB9OnG/9/8snV7xN/LYU58YyIiOD8+fM4OTlx9qxRg2Y2RwDFu2MRXE7U4uJicXePByrh7l6ClJSUQtlbGozLyhkZGZQpU4bjx43E2cWl+CeecLnW09fX6FxlMhWeGs/U1FQWL14MwBNPPHHD84kYwyb99JPRiWjRIuOWvkoVF5p4KnUT7r8fnn/e+L9PH4iMzN381sRz+/btxMXF5XF0t8Za21mnTl2OHnUFIDm5+A+lBODp6WmrRStb9jjgQPnyRm+Ownq5/fIdcZpy+LAJABEj8Syug8dbWRNPFxejxjM21vihdOTIEbsPgbVy5Uri4uIIDAwkLCzshud75x3jLmomE3z/Pdx1Vz4GqZQdaOKp1E0aO9a4n/v589CrFyQn3/i85cqVo2LFilgsFmbPnp1/Qd4Ea+JZrVpTMjPBwwPOnYsAin+NJ0DlykYHFR8fo4azdGnjcnth7WBkPV6VKzchPR3c3CAuzmijervUeFosRuIZEeFre49u377dTlEZ5s+fD8DDDz+Mg8ONnWonTTISTzBu0/vII/kVnVL2o4mnUjfJ1dW4hV2JErBmDXToALmpZBl6aYyUd999l+TcZK35zJrI+Pk1A4zB8613MSruNZ4A1apVA8DZ2RhSysXF6Nle2Gs8fX2N9p1VqlDsh1KysiaeSUlG4nn8ONSrZ//L7WlpaSxatAiAR24we1y7FgYNMv4fOdIYOUOp4kgTT6VuQbVqsHQpeHsb93pv3dq4w9GNGDBgAMHBwZw+fZpJkyblb6A3KC0tzdYxw2w2OhZVrZppG6D8dqjxrF69OgDp6fsByMgovD3bL1y4wJEjRwAwmYyhr6pVg5Mnb6/E88yZY/j4GNPKl7d/B6PVq1cTExODv78/LVu2vG751FQYMMBo39mnD7z1VgEEqZSdaOKp1C1q3dpIOgMDYdcuaNfuxi67u7i48PalgUHHjBlDfHx8Pkd6fTt27CA1NRVfX1/OnzcuOQcFnSIjIwMnJyeCgoLsHGH+syaesbFGjWd0tFHjeerUKS5evGi3uHJire2sVq0ax4/7XPr/9kk8rc0i9u3bR5UqAoCXl/1rPK2X2R966CHMNzAG0kcfwf79xrBJ48cb7TuVKq408VQqD9SuDX//DUFBxgnkzTdvbL4+ffpQpUoVLly4wPjx4/M1xhthHb+zSZMmHDhgnP28vCIA497YN3ISLeqsiWdk5D5AOHbMk4qXxrIpbO08rYln06ZN2W9U0BIcHGf7EVNcB4+3ql69Og4ODkRFRVGunLWHn9HB6MCBA3bpuJeens7ChQsB6Nat23XLHz4Mo0cb/3/6KbaaW6WKK008lcojISFw6SYlfPIJ/PXX9edxdHRk1KhRALz//vt88cUXWCyWfIzy2qztO5s0acqlu2YCxl1xbof2nWDUoplMJuLiYjCbzxEbC1WqFM7L7Zd7tDexJZ5eXkZtp4+PDx4eHvYKrUC4ublRpUoVADw8dgFw4oS/rabXHsdrwYIFXLx4kdKlS9O6detrlrUOnZSSAnffDY8+WkBBKmVHmngqlYc6dzbaaInAk0/e2CX37t2707lzZ1JSUnj++edp27Ytu3btyv9gc2BNPKtWbUpsrHFv+jNntgPY7rZU3Lm5udnaslapYmRz7u6Fr4ORiNgSz5o1m3DmjDH9dhnD06r2pZuXOzvvBGDdOmjY0LjcvnLlygKLQ0T45JNP6N27N2AMGn+9u3z9+iv8/rsxXueXX+oldnV7KL73vlPKTj79FJYvhwMHjDsbXe8KuoODA4sXL2by5MkMHz6cdevWUbt2bWrXrk23bt2oWrUqrq6uOT7c3NyyPHdycsJ0k2evpUuXcvDgQRwcHLBYjB7SlSvDzp3Gfa8b3EajWFevXp2jR48SHLyPfftaEx9v1HiuW7eOlJQUXF1drzm/xWIhKSmJzMxMMjIycvybmZmJ2WzGyckJR0dH21/rcb3ecTxy5AgXL17E2dkZV1cjvjJlIDr69ko8a9Wqxfz580lO3omjIxw9Cs8/342ff/6Zjz76iKeeesrWCelmiIjtYbFYsjwyM42Od//++y8LFixgwYIFADz++ON88MEH11xuejq88orx/4svQtWqNx2iUkWKJp5K5bGSJeHrr+G++2DCBAgLgx49rj2Pg4MDAwcOpFOnTrz00kssWbKEnTt3snPnzlyt22QyZUtMrTV4NWvWpHbt2nTs2BE/P78s8505c4a+ffsCMHjwYNavLwVAu3YWZs40Es/69evnKpairFq1avz222+4uRntDY4da4ufnx9Hjhxh2LBhfPnll1nKHzlyhG+//ZZVq1Zx8uRJTp8+TXp6+k2v38nJCV9fX8qVK0dYWBgtWrTgrrvuwt/fHzBGH7AmNvXr1+fIEedLcV/uWFTcB4+3stZ47tu3k7Awo6Ofu3svWrf+inXr1jF06FDb0EZXOn36NH/++Sdbtmxh27ZtREVFkZSUlOWRnJycq6YvZrOZTz/9lMGDB1/3h8PXX8O+fVC69M3felepIkkKsdjYWAEkNjbW3qEolWuvvioCIu7uIjt25G7eqKgomTZtmjz88MPStm1bCQsLk/r160uNGjUkNDRUAgICxMfHR1xdXQXI1cPR0VHuu+8+mTNnjly8eFEyMzOlY8eOAkjt2rUlKSlZypY1Yv/66wMCiKurq6Snp+fPjiqEJk+eLIC0a9dJjIYTInPm/G7bhz/++KNkZGTI/PnzpU2bNje0381mszg7O4u7u7t4enqKj4+PeHp6ipubmzg6Ot7QcevRo4csWrRIGjdubJv+zTffyBtvGDE+/bRI//79BZB33nnH3ruxQBw4cPk9+vbbGQIi3bqJ7Nq1y7ZfFy9eLCIiSUlJMnfuXOnQoYOYTKZcf3Zyenh6ekqLFi3kueeek40bN95QzDExIqVLG8ds4sT83DtKFYzc5GsmEZG8SmLzWlxcHN7e3sTGxuLl5WXvcJTKlcxM6NQJVqyASpVg82ajNjSviQipqamkpKRkeSQnJ5OSkkJCQgKHDh1iz549/PXXX1nGNzSZTFSqVIlDhw7h6urKli1bSE+/g/r1wd0dJk+eyxNP9KRJkya29p+3g7Vr13LnnXdSsWJF3N0Ps2uXce/sLVteY8yYMXh5eVG6dOkrxtA00b59ex599FGqVq1KuXLlKFWqFE5OTpjNZhwcHK5bAyYiZGZmkpycTExMDFFRURw4cIA///yTdevWsW3btizlS5YsyYwZM7j//vtp3Bi2bDFutbhwYUeWLVvG1KlT6devX77to8IiMzMTT09PkpOT+eGH/Tz6aFV8fY07io0Y8Spjx47Fz88PPz8/9u/fT2Zmpm3eBg0a0LhxYxo2bEjZsmVxd3fP8nB1dcXR0REHB4ccH9YrDLlt3vK//8GHHxo11Dt3gpNTXu8VpQpWrvK1fE6Cb4nWeKqi7sIFkZAQo2ajZUuR+Hh7RySyZ88eGTFihNSoUSNLzc0XX3whIiKjRxvxduki8uqrrwogAwYMsHPUBevMmTMCiMlkkqefThYQeeEFkfT0dGnRooVtn/n6+sqbb74pJ06cyPeYtm3bJk8//bS4ublJ8+bNJSIiQkREDh40jpfZLHLmjEUCAgIEkA0bNuR7TIVFw4YNBZA5c+aLp6exP8LDRRISEqR8+fJZ3ufBwcHyxhtvyKFDh+wS66+/GscKRC5VxCpV5OUmX9M2nkrlo1Kl4Oef4c47YcMG6NLF6Mnq7m6/mGrUqMH777/P+++/T2RkJKtXrwbg0Utjufz6q1Guc2dYsOD2a98J4O/vb/v1XrnyQaA269YZw1/NmzePt956i3r16tG3b19KlChRIDHVq1ePr776ii+//BKz2WyrZfvxR+P1u++G9PRTnDlzBrPZfFsds9q1axMeHs6+fbu4886H+eUXWLkSGjQowbJly/j999+pVq0aderUISgo6KY74N2q8HDo3t24GvLkk0Y7cKVuNwUynNLEiROpUKECrq6uNG3a1DYEiFK3g7p1Ydky8PQ07unetSskJd3csrZs2cJdd93Fli1b8qR8YGAgvXr1olevXphMJlau3M7ffxudKTp1Ettl+dupRzsYl86tA8l7exsdjLZvF1q3vo9Tp07x9ddfM2jQoGsmnXl9rKwcHR0xmUy28tOnG2+mnj1h8+bNANxxxx242/PXTQGzdjDauXMn7doZ0z74YAtbtmyhevXqvPDCC3Tq1ImyZcvmmHTm17G60pEjxo+5xES45x6YMkWHT1K3p3xPPOfOncuwYcN4++232bp1K3Xr1qVDhw6cO3cuv1etVKHRpAn89huUKGG0+WzZEiIicr+cmTNnsnr1ar777rt8KT927A7AgdKlT+HgcIoLFy5gNpttJ/bbiTXxPH9+PxUrgsViYv36jHzb9zdX/iyHDrnj5AQPPng58WzcuPENLaO4sI4xe2XiGR19B9On/3BD8+fnsYqMhJdeglq14OxZ44fovHnarlPdxvL7un+TJk1k0KBBtueZmZkSFBQkY8aMue682sZTFTfr11/uzVqqlMjSpSIWy7XniYiIkC1btkh4eLj4+/sLIP7+/hIeHi5btmyxtfXLi/IuLgsu9cQfL5988okAUq1atbzeDUXC+++/L4B06tRJ7rvvwqXe7aNvaF9u2RIufn7BAmbx88ufY2WUf0dApHXraNmyZYu0bNlSAJk8eXK+75/C5PTp0wKIg4ODbNjwpzg4RAqI+Pg8ko/7/trlT54UGTJExNVVbCMjNGsmcupUvu8OpQpcoenVnpaWhru7O/Pnz6dr16626X369CEmJoaff/45S/nU1FRSU1Ntz+Pi4ggODtZe7apYOX4cHn7Y6IUMEBgI7dpBvXrg4mLcxcTJ6fLf7t0fBzwBD8Dr0l8PwAVwBVxp164LKSnGrfe2bNl5aXoycAE4D+wCNgD/AElc+bG/fOmxIrAV8AZaAn/ayuTj10ShtXDhQh566KFLz54EpmHsx6bA5bYSIkJmJixeDA89NAOoCVTHOFZW6UAGkIGPjydOTuDoCJGRxy9Nz8Q4ni6ACYjCOHZH+PHHJ+jUCTw8+M9lYhOwD6gK9AIu1+6Fh4ffVs0jRAQHhysv4E0H+gLbgNZAgq2clbEv3THe622AYMAP8MXoh5TOnXe2xMnJ+BwuXboAiANigfgr/sZcmh7P4sXrOX3aaMv57beQlmasKywM3n7buMSul9dVcVRoerWfOnVKAPnrr7+yTH/llVekSZMm2cq//fbbOY6TpjWeqrhJThYZOFDEze1ybUjBPNKkQYPjsmCBSGqqEcusWbPEbK4lcOpSmR0CDrbP32OPPWbfnWUne/bsueJ7qIxA7KX9s0LAVRwdHWXq1B/kyy9FKlfO3+Pm4iLy4IMir766UsxmJ4ESAoMvvZ4oUELMZrMA4uLiImlpafbefQWuevXqVxyvCgJnLu2f38RsdpVZs2aJiEhSksisWSK1ap0WSM3X49aqlcjKlde/qqFUUVdke7WPGDGCYcOG2Z5bazyVKm5cXWHiRPj4Y/jrL6MH7vHjRg3Jfx+urpCZGc0ff/yMUXMTDyQCybz66lCqVi2PqytZHhER++nXbzBQGggEmgAtgGC2bg3moYeMMUWbNYN69Xrj5dWd6GgnYCfQDrh8t5b+/fsX8N4pHCpXrmz7BQ9ngU7A7xj75xceeKAuL77oR3y8Ub5kSejXD/z9jzB8+H3AaYxm9I6AI0uWLKN69dpkZJDlsWvXPvr27QekASkYNZm+fPjhNC5cqMjChXDoECxcCHA3ZcvGc+pUGkYtOMCPQCLvvDOaN954g3r16uF0GzYgbNeuHfv27bv0LAK4D1gDdKR160j+/deHn36CP/6A2FgwPhcAx4A/gD0YtcwX+fTTTylfvhLp6dgeycmwb98pPv98BkZttvelv17UqNGUjIwSeHlBUBCUK2f0Xr/zzgLaeKWKkvzMgFNTU8VsNsvChQuzTH/iiSfk/vvvv+782sZTKUN4eLitDduVf8PDw3NVft683TJ8uEhAQE41NJvFZCotQJa7usTExBTw1hYeTz31lG0/GPuwhUB8lv1WqZLIhAmXx2jNq2NlLW+xiPz7r8jzz4t4eV15vA4I/E9MphICSK9evQSQwYMHF9TuKVS+/fZb27Gyvn9Npi4CGdne6xUqiLzzjsjChbvy9FgpdbvKTb6Wr73anZ2dadiwIatWrbJNs1gsrFq1irCwsPxctVLFir+/PwEBATRs2JDJkyfTsGFDAgICbPfuvtHyzZp58eGHcOIEbNpk1Lo++ST07JmIv38vGjUKZfLkyZQvXx64XOt3u7KObWoymahfvz6TJz9O9erDcHTcQ9euSaxeDQcOwJAhRhtMyLtjZS1vMkGdOvDZZ3DqFEyefBFf3640atSbyZMr0KhRTQICAjh48CBw+/Vot3rooYfwuHQQqlSpwuTJk2nU6Aze3gO5555knn8eJkyAtWvh8GF46y1o1Mg7T4+VUuoG5HcWPGfOHHFxcZEZM2bInj175JlnnhEfHx85c+bMdefVGk+lLktJSRHLpcZiFotFUlJS8qV8RkaGVK5cWQCZMGFC3gRfRGVkZEiZMmUEkF9++UVE8nff32z5hIQEcXNzE0D27NlzQ9tWHA0aNEgAefDBB0WkcBwrpW4HhabGE6BHjx589NFHtjt9bN++nd9//50yZcrk96qVKlZcXFxsvZpNJhMuLi75Un7RokUcOnQIX1/f2+Je39diNpvp3r07AHPmzAHyd9/fbPnDhw+TnJyMp6cn1apVu/6GFVPPPvssAIsXL+bUqVOF4lgppbIqkDsXDR48mGPHjpGamsqmTZto2rRpQaxWKZVLIsKHH34IcN0789wurJfbFy1aRNIN3nJKRMjMzMzPsLKwDhzfqFGj/wwrdHupVasWLVu2JDMzk6lTp9o7HKVUDgpVr3al1I3JzMzk/PnzREZG2h5nzpzh7NmzXLhwgQsXLuDm5kZQUBBBQUE0a9aM1q1bX7d2Zt26dWzevBlXV1cGDx5cQFtTuDVr1owKFSoQERHBkiVLbDWg/3Xw4EHmzp3Lxo0b2bRpExcuXMDDwwMfHx/KlClD+fLlKV++PCVLlsTd3R0XFxcSEhKIiorK8khJSaF06dL4+/tTrVo1Hn/8ccqVK3fV+KKiovjkk08A9Ec98Nxzz7Fhwwa+/vprXn/9dRwdr32ai4+PZ+XKlRw6dIhTp4x73ZtMJpydnXF1dcXf35/AwEACAwMJCAggMDCQoKAgnJ2dC2iLlCpm8v3C/y3QNp7qdpaWliZr166VL7/8UoYOHSqdO3eW+vXrS0BAgK03bW4eJUqUkK5du8q8efMk1TqI5xUSExPl7rvvFkCee+45O2xx4TVixAgBpHnz5hIVFZXltZMnT8ozzzxjG0czrx8ODg5y//33y9KlSyUjIyPLupOSkmx3KwoKCpKTJ08W5G4plFJSUsTPz08AefvttyU9PT1bmfj4ePn222/lvvvuExcXl5s6JhUrVpROnTrJ66+/LmvWrMnxM6XU7aLQ3LnoVuVqJHyligERYdmyZcyZM4fFixcTHR191bImkylLbUxgYCBlypTBz8+PUqVKkZSURGRkJEePHmXFihWcOXPGNq+fnx+9evWifv36VK1ala1btzJ69GjOnDmDg4MD+/fvp3LlygWxyUXC/v37qVOnDmlpaQQFBfHll1+SmZnJvHnzWLRoESkpKQB07NiRTp060bRpU0JDQ4mLiyM6OpozZ85w/Phxjh8/TlxcHMnJybY2mb6+vpQsWRJfX198fX1xcXHhwoULnD17lmXLlrF27VpbHCEhITz99NPUq1eP9PR0pk+fzuLFi/H29mb9+vXUrl3bXruoUHnvvfd44403AGjYsCEfffQRDg4OREZGsmLFCubOnUtCQoKtfJUqVWjSpAlly5YlMDAQBwcH0tLSSEpK4uzZs1muLERGRpJmvSXRFUqUKEHv3r0ZPXo0fn5+BbatShUGucnXNPFUqpDYuXMnQ4cOZfXq1bZpfn5+NG3alKpVq1KlShXKlStnSzL9/f2vexnRymKxsG3bNubPn8+MGTOyJKFXqlChAp9++mmWW9wqw6ZNm+jTpw/79+/P9lrLli354IMPaNGiRZ6vd+/evXz11Vd8++23Of4QcXZ2ZtmyZdypo5XbWCwWvvnmG1555ZVLNwDIrnLlyjz++OM8/PDD1KxZ8z+3I706EeHMmTMcOHCAffv2sX79elasWMG5c+cA8PHxYdSoUTz33HM3/PlUqqjTxFOpIkREGDFiBOPGjcNiseDq6kr//v3p1q0bLVq0wGw25+n6MjIyWLp0Kb///jsHDhzgwIEDODs7M2zYMPr3769t164hOTmZN998k88++4ygoCC6devGI488QpMmTW44cbmVdc+bN4/vvvuO6OhonJ2d8fDw4KWXXqJDhw75uu6iKjIykpdeeolly5ZRqlQpAgICqF69Ok888QQtWrTIs2NmsVhYt24dL774Itu3bwfghRde4NNPP82T5StV2GniqVQR8tVXXzFgwAAAHn74YT766CMqVKhg36DUNWVmZuLg4JDvyaYqWjIzM/n888958cUXcXZ2JiIigsDAwOvPqFQRl5t87fYdd0OpQmD37t0MHToUgA8++ID58+dr0lkEmM1mTTpVNmazmaFDh9K8eXPS0tJsow0opS7TxFMpO0lOTubRRx8lJSWFe+65h1deecXeISmlbpHJZOK1114DYNKkSURFRdk5IqUKF008lbKTESNGsHPnTvz9/fn2229v64G/lSpO7r33XurUqUNiYiJffPGFvcNRqlDRM51SdhAVFcXkyZMBmD59OgEBAXaOSCmVV66s9ZwwYUKWoZuUut1p4qmUHfzwww+kpqZSr1497r33XnuHo5TKY4888giVK1cmKiqKcePG2TscpQoNTTyVsoNp06YB8NRTT9k5EqVUfjCbzYwePRqA999/n/DwcDtHpFThoImnUgVs+/btbN26FWdnZ3r16mXvcJRS+aR79+488sgjZGRk0KdPH9sdrpS6nWniqVQBmz59OgAPPPAApUqVsnM0Sqn8YjKZmDRpEv7+/uzevZu3337b3iEpZXeaeCpVgFJTU5k1axagl9mVuh2ULl2ar7/+GoBx48axbds2O0eklH1p4qlUAVq8eDFRUVGULVuW9u3b2zscpVQBuP/+++nWrRsiwueff27vcJSyK008lSpA33zzDQB9+/bN83uwK6UKL+sdyn744Qeio6PtHI1S9qOJp1IF5OjRoyxfvhzQy+xK3W6aN29OnTp1SElJYcaMGfYORym70cRTqQIydepURIT27dtTsWJFe4ejlCpAJpOJ5557DoDJkycjInaOSCn70MRTqQKQnp5uG7vzmWeesXM0Sil76N27Nx4eHhw4cIA//vjD3uEoZReaeCpVAJYsWcKZM2coU6YMDzzwgL3DUUrZgaenJ48//jgAkyZNsnM0StmHJp5KFYApU6YA8OSTT+Lk5GTnaJRS9mK93L5o0SJOnjxp52iUKniaeCqVz67sVNS/f387R6OUsqfatWvTqlUrMjMztdZT3ZY08VQqn40dO9bWqahSpUr2DkcpZWfWoZWmTJlCcnKynaNRqmBp4qlUPlq/fj2TJ08GYMSIEXaORilVGDzwwAOUL1+eixcvMnv2bHuHo1SB0sRTqXySnJxMv379AOMSe9u2be0ckVKqMHB0dGTw4MEATJgwQYdWUrcVTTyVyifvvPMOBw8eJCgoiHHjxtk7HKVUIdK/f3/c3d3ZuXMna9assXc4ShUYTTyVygfh4eF89NFHgDFsio+Pj30DUkoVKiVLlqRPnz4AjB8/3r7BKFWANPFUKo+lp6fz1FNPkZmZSc+ePbn//vvtHZJSqhAaMmQIJpOJxYsX20a+UMVTYmKiNqm4RBNPO4iJiSE1NdXeYah88uGHH7Jjxw5KlSrFhAkT7B2OUqqQql69uq2t59NPP018fLydI8oqOjqaP//8k19//ZW5c+cybdo0PvvsM95//32++eYb0tPTbWUtFgtffPEFn332GadOncpxeZs2bWLw4MGcOHEiT+ITkSwx2EtERATLli27amL5xRdf4OvrS8+ePTX5BJBCLDY2VgCJjY0t0PVmZmbK5MmT5dlnn5Xz58/nWMZisciuXbvk0KFDYrFYbnjZv/76q5QoUUKCgoLkr7/+yrHM8ePHZfr06be03RcuXJC5c+fKqVOnbnoZeWHx4sXy0EMPya+//pqr/VRU7d69W5ydnQWQWbNm2TscpVQhl5CQIKGhoQLIs88+a5cYjh49Kg8//LDUr19fWrRoIXfffbeEhIQIcM1Hly5dJDk5WTIyMqRPnz5ZXmvZsqX88ssvtnXs2LFDvLy8BJAGDRpISkpKrmJMTU3N8jwmJkbuuece8fDwkEmTJuXJ+eX8+fMSHx+fbXpGRoZkZmbmOM+6dets2/X6669nm2/o0KFZ9sukSZNuKraMjAxZsmSJHD58+IbKHzp0SH744YebWtfNyE2+ponnf5w4cULatWtne5PUqlVLzpw5k6VMfHy8PPbYY7YyISEh0rdvX3nvvfdk2rRp8scff0h6enq2Zc+aNUscHR1t8zk5OcnkyZOzfGBmzZplexOXL19efv/9dxERSUpKkt9++02mTZsmP/74o/z2229y8ODBHD9se/bsyfKl0bRpU/n4448lMTHxutufkJAgf/zxR7Ztvtq+euSRR6RevXrSsGFDCQsLk7Fjx0paWpqIiPzwww9iNpttcbRp0+aqyfaV0tPTZdGiRfLUU0/JY489Jn369JGBAwfKrFmz7J5IX0tSUpI0a9ZMAOncufNtkWgrpW7dH3/8YfueXLFiRa7nz8jIyPH7JioqSqZNmyadOnUSb29vKV26tISEhEiTJk3kgw8+kGPHjsmMGTPE09PzqsllSEiINGrUSNq0aSOdO3eWHj16SJ8+fcTV1VUAadu2rfTo0UMAMZvN0qRJkyzzv/zyyxIRESHlypXLMn3QoEG2OKOjo+XcuXM5btu5c+ekX79+4uDgIPfee6/s3r1bIiMjpW7dulmW17VrV9m6dat8//33MmzYMHnooYekRYsWUqtWLRk3btxVv48PHjwo77//vjRr1kxMJpO4urrKF198IRaLRdLT02X06NHi7u4uJUuWlM6dO8v7778va9askcTERFmyZIltP1gf48ePFxGRvXv3SqdOnWzT77nnHgHEzc1N9u3bl6vj+++//0rjxo0FEJPJJA899JCsX79eLly4IPHx8ZKYmCgnTpyQ7du3y5dffinNmze35RgXL17M1bpuliaeN2n27Nni4+Nje3P4+/sLIFWrVpWIiAg5f/68/PXXX1K9enUBxMHBQZycnHL8sJYvX17GjRsnBw4ckCVLlshLL71ke61Xr17y8MMP257XrFlTevToIffff79tmouLi+3/Jk2aZHtzWx9lypSRhx9+WD755BP5559/ZMWKFbZtsP698gtkwYIFYrFYxGKxyIULF+Tw4cOya9cuWbNmjQwYMMD2BWQymSQsLEzeeustef/992XUqFEyYcIEOXjwoIgYX5R+fn45xlS3bl157733xMHBQQBp3rx5lu2pX7++fP755/Lrr7/Kyy+/LE2bNpWmTZtKz549ZfDgwdm+oP778PPzEy8vL3F0dJTQ0FAZM2aMnDt3Tk6cOCFjx46VNm3ayCOPPCIfffSR/PXXX1f9pZqX9u/fL3Xq1BFAPD095fjx4/m+TqVU8fHss88KII6OjvLyyy9f97y3bNkyee6556RJkybi4uIipUqVkh49esiUKVPkzTfflObNm2ep6Ljeo0WLFrJ48WL56aef5LvvvpO1a//f3v3HRHnfARz/HKfyQ+TqD1BZDyuy1c3ZXRXFumlxuGm0mZqq69IZYFTdQrXOrg67KrUbo87L6obWsq1Boy5qcNOqmYnpqm5Zq2RWVxaxokEQ1J1S75DVQ+4++8PsIuVHOep9D8r7lTx/cPfA88Hn5N73PM/BMf3oo4/a3f7Ro0dbBGvfvn117969qnr3oMTy5ctbPZ89/PDDunPnzsDtv/71r3XJkiUaFRWlkZGR6nQ6tbm5WVXvvpB//fXXdeDAgS3mtFqtOnToUBURTUhI0Ly8vHafh+9dXn755cDsjY2NWlJSolOnTm13/VmzZmlqamq79/fp0ydwYGX27Nm6du3awH3Tp09Xi8US+N737NmjPp9PMzIyVEQ0NTW11RHc5uZmPXv2rJaUlOjSpUv1ySef1MzMTF20aFFgP0ZHR3d6f0ZEROi3vvUtPXfuXBcfkcEhPLvA7/cHXpFMmDBBKyoq9Pz585qUlNTmTk1MTNTjx4/rrVu39PDhw/rSSy9pVlaWzpgxQ4cMGdLug2H58uXq8/nU7/fr+vXrWxwR/P9/qldeeUVv3rypy5cvDzx4RUTtdrvOnDlTp0yZomPHjg2c0m1rmTx5srpcLq2rq9PNmzer3W5vMfu9IdhW2HX0gB49enQgKh0Ohx44cEAPHTqkmzZt0kGDBrVY95lnnlGfz6fV1dWanZ3d4cz3LkOGDNGVK1eq0+nU9evX6/PPP6+pqakt/j3uXfr27dvufdOmTdNLly61ud9v3rzZ4Q/Xjh4v1dXV+vbbb6vT6dTY2NjAD8J33nnnsz0YAfQ6DQ0N+sQTTwR+bg0bNkyzs7O1oKBAS0tL9fLly6qqevXqVV24cGGnA2Ts2LH6yiuv6KlTp/SDDz7QEydO6O9+9ztNT09Xi8Wiffr00YKCgkDwBaOsrEwHDx6skZGRevDgwVb3l5aWBuI0ISFBL168qKqqeXl5HT53LVmyJHDmT+TuwYzS0lKdO3du4Lbk5OTAgZBTp06pw+HQ6Ohofeyxx3TZsmVaVFSke/bs0ZdffjnwOfn5+bpu3boWz9ERERE6Y8YMLS4u1suXL+tvfvObFs+PDzzwgG7btk1Pnjypr732ms6fP1+HDx8euP/pp5/WpqYm9fv9rU6rz5kzR8+cORP496ipqQkcEIqKitIxY8ZoRkaGfulLX/rU58Z58+ZpbW2tlpeX6w9+8AONiYlp1Q4JCQk6ceJEdTqdxs8OEp5ddPnyZS0oKAicKlZVraqq0q985SuBnRsbG6vz5s3Ta9eutft1Pv74Y33zzTd17NixarVadcyYMfr9739fd+zY0epw/5UrV/TQoUP6q1/9Sn/84x/riRMnWtxfVlamb7zxhn7wwQetPvfjjz/Wv/3tb1pYWKizZ88OPKAXLlyo//3vf1use+vWLX3xxRdbPbj79++vQ4YM0aSkJP3e976nf/3rX9Xv92tNTY1u2bJFs7OzNScnR5csWaLTp09v8Qo6MzOz1XauXbumTz31lIrcPZXyyaONLpdLN27cqOPGjdOUlBTNycnR7du36969e9XpdOqKFSt0x44d7V7/U19fr++//76eO3dOq6urddu2bS1elU6dOlU3b96sr776qs6ZMyfwnzMuLk6Li4v16NGj+vbbb+vmzZv1m9/8plqtVrVarTp79mzdvXu3njx5Uvft26ebNm3SpUuXalpamo4YMUJ/+ctfBr6Xuro6nTJlSqsfDI8//ni3vhQAQPd38OBBTUlJaTM+Ro4cGTgCGBERoUuWLNFdu3bphx9+qH//+991zZo1mp6erk899ZT+/ve/D4Ree2pra9t9Ud5Zbre7w0uzPvzwQ33hhRe0vLw8cNudO3c0IyNDLRaLzpkzR48dO6Z/+MMfWp3yHzFihP72t79tcena0aNH9aWXXtIrV6602lZ7p9MLCwtb/Vs+9NBDWlBQoDU1Na3W/9e//qVTp07VhQsXtvkz3e/368WLF/X48eMtnuN8Pp/+7Gc/0+zs7BbBea+33nqrRVTfu0RHR+uUKVP0hRde0E2bNun69et1zZo1eujQoTa/VnNzszY2NqrH4wn7pV3B9JpFtfu+xcrj8YjNZhO32y1xcXFhm0NVpb6+Xmw2m/Tp0yeoz/X7/RIRYeaXB/j9frly5YokJiaKxWJpc526ujqpqqqSxMREGT58uERGRga1jY8++kgOHz4s0dHRMmfOnHa3c+vWLYmNjQ36e+iqiooK6d+/v9jt9ha3V1ZWyqJFi+S99977zNuYNWuW5ObmyjPPPCNXrlwRq9UqycnJkpKSIhkZGfLcc88F/fgAgE/yer1y4MABOXv2rJw/f17Ky8vlzJkz4vf7RUTE4XDIm2++KePGjQvzpF3X3NwsDQ0NMnDgwMBt1dXVkpeXJ/369ZPMzEx5/PHH79vz589//nNZu3atPProo7Jq1SqZP39+2H5eNzc3y6VLl+T8+fNy7do1sdvtkpycLHa7XaxWa1hm+qyC6TXCE597zc3NsmHDBtm5c6f4fD6xWq0yZMgQeeKJJ2TevHly584d2b59u+zevVtu374tX/jCF2T48OHy5S9/WRwOh1y/fl1+8pOfyO3btwNfc8yYMbJv3z5JSUkJ43cGoLfweDzy7rvvyu3bt2XWrFnSt2/fcI/U49y8eVNsNlu7B0zQdYQncJ+dPn1a5s+fLxcuXJAnn3xSSkpKZMCAAeEeCwCAsAum1zgvCHSCw+GQM2fOyNmzZ2X8+PG8YgYAoAsIT6CT+vfvL6mpqeEeAwCAHos/mQkAAAAjCE8AAAAYQXgCAADACMITAAAARhCeAAAAMILwBAAAgBGEJwAAAIwgPAEAAGAE4QkAAAAjCE8AAAAYQXgCAADACMITAAAARhCeAAAAMILwBAAAgBGEJwAAAIwgPAEAAGAE4QkAAAAjCE8AAAAYQXgCAADACMITAAAARhCeAAAAMILwBAAAgBGEJwAAAIwgPAEAAGAE4QkAAAAjCE8AAAAYEbLwLCgokMmTJ0tMTIw88MADodoMAAAAeoiQhWdTU5MsWLBAfvSjH4VqEwAAAOhB+oTqC69bt05ERLZu3RqqTQAAAKAHCVl4doXX6xWv1xv42OPxhHEaAAAA3E/d6s1FhYWFYrPZAovdbg/3SAAAALhPggrPvLw8sVgsHS4VFRVdHmb16tXidrsDS01NTZe/FgAAALqXoE61P//885KVldXhOsnJyV0eJjIyUiIjI7v8+QAAAOi+ggrP+Ph4iY+PD9UsAAAA+BwL2ZuLqqurpb6+Xqqrq8Xn88np06dFRCQlJUViY2NDtVkAAAB0UyELz7Vr18q2bdsCHz/66KMiIvLOO+9Ienp6qDYLAACAbsqiqhruIdrj8XjEZrOJ2+2WuLi4cI8DAACATwim17rVr1MCAADA5xfhCQAAACMITwAAABhBeAIAAMAIwhMAAABGEJ4AAAAwgvAEAACAEYQnAAAAjCA8AQAAYAThCQAAACMITwAAABhBeAIAAMAIwhMAAABGEJ4AAAAwgvAEAACAEYQnAAAAjCA8AQAAYAThCQAAACMITwAAABhBeAIAAMAIwhMAAABGEJ4AAAAwgvAEAACAEYQnAAAAjCA8AQAAYAThCQAAACMITwAAABhBeAIAAMAIwhMAAABGEJ4AAAAwgvAEAACAEYQnAAAAjCA8AQAAYAThCQAAACMITwAAABhBeAIAAMAIwhMAAABGEJ4AAAAwgvAEAACAEYQnAAAAjCA8AQAAYAThCQAAACMITwAAABhBeAIAAMAIwhMAAABGEJ4AAAAwgvAEAACAEYQnAAAAjCA8AQAAYAThCQAAACMITwAAABhBeAIAAMAIwhMAAABGEJ4AAAAwgvAEAACAEYQnAAAAjCA8AQAAYAThCQAAACMITwAAABhBeAIAAMAIwhMAAABGEJ4AAAAwgvAEAACAEYQnAAAAjCA8AQAAYAThCQAAACNCFp5VVVWSk5MjI0eOlOjoaBk1apTk5+dLU1NTqDYJAACAbqxPqL5wRUWF+P1+KS4ulpSUFCkvL5fFixdLY2OjOJ3OUG0WAAAA3ZRFVdXUxjZs2CBbtmyRixcvdmp9j8cjNptN3G63xMXFhXg6AAAABCuYXgvZEc+2uN1uGTRoULv3e71e8Xq9gY89Ho+JsQAAAGCAsTcXVVZWSlFRkSxdurTddQoLC8VmswUWu91uajwAAACEWNDhmZeXJxaLpcOloqKixefU1tbKzJkzZcGCBbJ48eJ2v/bq1avF7XYHlpqamuC/IwAAAHRLQV/j6XK55MaNGx2uk5ycLP369RMRkbq6OklPT5dJkybJ1q1bJSKi863LNZ4AAADdW0iv8YyPj5f4+PhOrVtbWyvTpk2T8ePHS0lJSVDRCQAAgM+XkL25qLa2VtLT02XEiBHidDrF5XIF7hs2bFioNgsAAIBuKmTheeTIEamsrJTKykp58MEHW9xn8Dc4AQAAoJsI2bnvrKwsUdU2FwAAAPQ+XHQJAAAAIwhPAAAAGEF4AgAAwAjCEwAAAEYQngAAADCC8AQAAIARhCcAAACMIDwBAABgBOEJAAAAIwhPAAAAGEF4AgAAwAjCEwAAAEYQngAAADCC8AQAAIARhCcAAACMIDwBAABgBOEJAAAAIwhPAAAAGEF4AgAAwAjCEwAAAEYQngAAADCC8AQAAIARhCcAAACMIDwBAABgBOEJAAAAIwhPAAAAGEF4AgAAwAjCEwAAAEYQngAAADCC8AQAAIARhCcAAACMIDwBAABgBOEJAAAAIwhPAAAAGEF4AgAAwAjCEwAAAEYQngAAADCC8AQAAIARhCcAAACMIDwBAABgBOEJAAAAIwhPAAAAGEF4AgAAwAjCEwAAAEYQngAAADCC8AQAAIARhCcAAACMIDwBAABgBOEJAAAAIwhPAAAAGEF4AgAAwAjCEwAAAEYQngAAADCC8AQAAIARhCcAAACMIDwBAABgBOEJAAAAIwhPAAAAGEF4AgAAwAjCEwAAAEYQngAAADCC8AQAAIARhCcAAACMIDwBAABgBOEJAAAAIwhPAAAAGBHS8PzOd74jSUlJEhUVJcOHD5dFixZJXV1dKDcJAACAbiqk4Tlt2jTZs2ePnDt3Tvbu3SsXLlyQ+fPnh3KTAAAA6KYsqqqmNvbWW2/J3Llzxev1St++fT91fY/HIzabTdxut8TFxRmYEAAAAMEIptf6GJpJ6uvrZefOnTJ58uR2o9Pr9YrX6w187Ha7ReTuNwQAAIDu5/+d1qljmRpiq1at0piYGBURnTRpkl6/fr3ddfPz81VEWFhYWFhYWFhYethSU1PzqV0Y9Kn2vLw8Wb9+fYfrnD17VkaPHi0iItevX5f6+nq5dOmSrFu3Tmw2mxw8eFAsFkurz/vkEU+/3y/19fUyePDgNtdH8Dwej9jtdqmpqeHyhR6I/dfzsQ97PvZhz8c+vL9UVRoaGiQxMVEiIjp++1DQ4elyueTGjRsdrpOcnCz9+vVrdfvly5fFbrfLP/7xD3nssceC2SzuE66b7dnYfz0f+7DnYx/2fOzD8An6Gs/4+HiJj4/v0sb8fr+ISIujmgAAAOgdQvbmohMnTkhZWZl84xvfkIEDB8qFCxdkzZo1MmrUKI52AgAA9EIh+z2eMTEx8qc//UkyMjLk4YcflpycHHnkkUfk2LFjEhkZGarN4lNERkZKfn4++6CHYv/1fOzDno992POxD8PH6O/xBAAAQO/F32oHAACAEYQnAAAAjCA8AQAAYAThCQAAACMIT4jX6xWHwyEWi0VOnz4d7nHQSVVVVZKTkyMjR46U6OhoGTVqlOTn50tTU1O4R0MHNm/eLA899JBERUVJWlqanDx5MtwjoZMKCwtlwoQJMmDAAElISJC5c+fKuXPnwj0WuujVV18Vi8UiK1asCPcovQrhCVm1apUkJiaGewwEqaKiQvx+vxQXF8u///1vee211+SNN96QF198MdyjoR27d++WlStXSn5+vpw6dUq+9rWvyYwZM+Q///lPuEdDJxw7dkxyc3PlvffekyNHjsidO3fk29/+tjQ2NoZ7NASprKxMiouL5ZFHHgn3KL0Ov06pl/vLX/4iK1eulL1798qYMWPk/fffF4fDEe6x0EUbNmyQLVu2yMWLF8M9CtqQlpYmEyZMkE2bNonI3b/mZrfbZdmyZZKXlxfm6RAsl8slCQkJcuzYMZk6dWq4x0En3bp1S8aNGyevv/66/OIXvxCHwyEbN24M91i9Bkc8e7Fr167J4sWLZfv27RITExPucXAfuN1uGTRoULjHQBuamprkn//8p0yfPj1wW0REhEyfPl3efffdME6GrnK73SIi/J/rYXJzc2X27Nkt/i/CnJD9yUx0b6oqWVlZ8sMf/lBSU1Olqqoq3CPhM6qsrJSioiJxOp3hHgVtuH79uvh8Phk6dGiL24cOHSoVFRVhmgpd5ff7ZcWKFfL1r39dvvrVr4Z7HHTSrl275NSpU1JWVhbuUXotjnh+zuTl5YnFYulwqaiokKKiImloaJDVq1eHe2R8Qmf34b1qa2tl5syZsmDBAlm8eHGYJgd6j9zcXCkvL5ddu3aFexR0Uk1NjTz33HOyc+dOiYqKCvc4vRbXeH7OuFwuuXHjRofrJCcny8KFC+XAgQNisVgCt/t8PrFarfL000/Ltm3bQj0q2tHZfdivXz8REamrq5P09HSZNGmSbN26VSIieD3ZHTU1NUlMTIyUlpbK3LlzA7dnZmbKzZs3Zf/+/eEbDkF59tlnZf/+/XL8+HEZOXJkuMdBJ+3bt0/mzZsnVqs1cJvP5xOLxSIRERHi9Xpb3IfQIDx7qerqavF4PIGP6+rqZMaMGVJaWippaWny4IMPhnE6dFZtba1MmzZNxo8fLzt27OCHZjeXlpYmEydOlKKiIhG5e7o2KSlJnn32Wd5c1AOoqixbtkz+/Oc/y9GjR+WLX/xiuEdCEBoaGuTSpUstbsvOzpbRo0fLT3/6Uy6ZMIRrPHuppKSkFh/HxsaKiMioUaOIzh6itrZW0tPTZcSIEeJ0OsXlcgXuGzZsWBgnQ3tWrlwpmZmZkpqaKhMnTpSNGzdKY2OjZGdnh3s0dEJubq788Y9/lP3798uAAQPk6tWrIiJis9kkOjo6zNPh0wwYMKBVXPbv318GDx5MdBpEeAI91JEjR6SyslIqKytbvVjgREb39N3vfldcLpesXbtWrl69Kg6HQw4fPtzqDUfonrZs2SIiIunp6S1uLykpkaysLPMDAT0Qp9oBAABgBO9CAAAAgBGEJwAAAIwgPAEAAGAE4QkAAAAjCE8AAAAYQXgCAADACMITAAAARhCeAAAAMILwBAAAgBGEJwAAAIwgPAEAAGAE4QkAAAAj/geDbeFynnDwMQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "x_test = torch.linspace(-5,5,200).reshape((200, 1))\n",
    "means, variances = model.predict(x_test, num_samples = 1000)\n",
    "\n",
    "mean = torch.mean(means, -1)\n",
    "var  = torch.mean(means**2 + variances, -1) - mean**2\n",
    "\n",
    "def plot_predictive_dgp(mean, var, title):\n",
    "  f, ax = plt.subplots(1, 1, figsize=(8, 6))\n",
    "  lower = mean + 2.0 * np.sqrt(var)\n",
    "  upper = mean - 2.0 * np.sqrt(var)\n",
    "  ax.plot(train_x, train_y, 'k*')\n",
    "  ax.plot(x_test, mean, 'b')\n",
    "  ax.plot(x_test, upper, 'black')\n",
    "  ax.plot(x_test, lower, 'black')\n",
    "  ax.set_ylim([-3, 3])\n",
    "  ax.legend(['Observed Data', 'Mean', 'Confidence'])\n",
    "  ax.set_title(title)\n",
    "  f.show()\n",
    "\n",
    "plot_predictive_dgp(mean, var, \"Pred. Dist. DGP\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "jq9GVGpWatGu"
   },
   "source": [
    "Now we do the same for each layer.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 545
    },
    "id": "BLMO4HTqV80I",
    "outputId": "b27e52ed-b516-47ca-871d-f1d38acd0591"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_325420/3428919590.py:20: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
      "  f.show()\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# First layer\n",
    "\n",
    "x_test = torch.linspace(-2,2,200).reshape((200, 1))\n",
    "with torch.no_grad():\n",
    "  with gpytorch.settings.num_likelihood_samples(1):\n",
    "    pred = model.hidden_layer(x_test)\n",
    "\n",
    "mean = pred.mean.mean(-1).T\n",
    "var  = pred.variance.mean(-1).T\n",
    "plot_predictive_dgp(mean, var, \"Pred. Dist. First Layer\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 545
    },
    "id": "apgOK9lZcMkP",
    "outputId": "e4771d04-4e31-4042-e877-45515dd7cdb4"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_325420/3428919590.py:20: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
      "  f.show()\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Last layer\n",
    "\n",
    "x_test = torch.linspace(-2,2,200).reshape((200, 1))\n",
    "with torch.no_grad():\n",
    "  with gpytorch.settings.num_likelihood_samples(1):\n",
    "    pred = model.likelihood(model.last_layer(x_test))\n",
    "\n",
    "mean = pred.mean.T\n",
    "var  = pred.variance.T\n",
    "plot_predictive_dgp(mean, var, \"Pred. Dist. Last Layer\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "n_Hxtp2nKikU"
   },
   "source": [
    "## **Comparison with a standard Sparse GP**\n",
    "For a reference, we show also the results of a standard sparse GP with the same number of inducing points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "id": "Ize71TrTKn22"
   },
   "outputs": [],
   "source": [
    "from gpytorch.models import ApproximateGP\n",
    "from gpytorch.variational import CholeskyVariationalDistribution\n",
    "from gpytorch.variational import UnwhitenedVariationalStrategy\n",
    "\n",
    "# We define our approximate GP method based on the VFE approach\n",
    "\n",
    "class VFESparseGP(ApproximateGP):\n",
    "    def __init__(self, inducing_points):\n",
    "\n",
    "        # We use a zero mean and an RBF kernel\n",
    "\n",
    "        mean_module = gpytorch.means.ZeroMean()\n",
    "        covar_module = gpytorch.kernels.ScaleKernel(gpytorch.kernels.RBFKernel())\n",
    "\n",
    "        # We use a cholesky factorization to represent the parameters of the\n",
    "        # variational approximate distribution q\n",
    "\n",
    "        variational_distribution = CholeskyVariationalDistribution(inducing_points.size(0), mean_init_std=0.0)\n",
    "\n",
    "        # We initialize the variational distribution\n",
    "\n",
    "        init_dist = gpytorch.distributions.MultivariateNormal(torch.zeros(inducing_points.size(0)), \\\n",
    "            covar_module(inducing_points) * 1e-5)\n",
    "\n",
    "        variational_distribution.initialize_variational_distribution(init_dist)\n",
    "\n",
    "        # We use an unwhitened variational strategy. Whitening is also possible and\n",
    "        # described later on.\n",
    "\n",
    "        variational_strategy = UnwhitenedVariationalStrategy(self, inducing_points, variational_distribution, learn_inducing_locations=True)\n",
    "        variational_strategy.variational_params_initialized = torch.tensor(1) # XXX DHL This avoids random initialization\n",
    "\n",
    "        super(VFESparseGP, self).__init__(variational_strategy)\n",
    "\n",
    "        self.mean_module = mean_module\n",
    "        self.covar_module = covar_module\n",
    "\n",
    "    def forward(self, x):\n",
    "        mean_x = self.mean_module(x)\n",
    "        covar_x = self.covar_module(x)\n",
    "        return gpytorch.distributions.MultivariateNormal(mean_x, covar_x)\n",
    "\n",
    "\n",
    "def train_model(model, mll, train_x, train_y, training_iter = 10, likelihood = None):\n",
    "\n",
    "  model.train()\n",
    "  losses = torch.zeros(training_iter)\n",
    "\n",
    "  # We check if we have to optimize the likelihood too or it is already in the\n",
    "  # model\n",
    "\n",
    "  if likelihood is None:\n",
    "    params = model.parameters()\n",
    "  else:\n",
    "    params = list(model.parameters()) + list(likelihood.parameters())\n",
    "\n",
    "  # We instantiate the LBFGS optimizer, which will optimize the hyper-parameters.\n",
    "\n",
    "  optimizer = torch.optim.LBFGS(params, \\\n",
    "      history_size=10, max_iter=4, line_search_fn=\"strong_wolfe\")\n",
    "\n",
    "  def closure():\n",
    "      optimizer.zero_grad()\n",
    "      output = model(train_x)\n",
    "      loss = -mll(output, train_y)\n",
    "      loss.backward()\n",
    "      return loss\n",
    "\n",
    "  for i in range(training_iter):\n",
    "\n",
    "    loss = -mll(model(train_x), train_y) * train_x.shape[ 0 ]\n",
    "    print('Iter %d/%d - Loss: %f' % (i + 1, training_iter, loss.item()))\n",
    "    losses[ i ] = torch.from_numpy(np.array([loss.item()]))\n",
    "\n",
    "    optimizer.step(closure)\n",
    "\n",
    "  return losses"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "aN-JGNRELCUc"
   },
   "source": [
    "We fit the model and we print the predictive distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "7xvfm6a-KrZv",
    "outputId": "42be28bc-e8f1-4fbb-faf4-d148ede6940a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iter 1/500 - Loss: 83.524208\n",
      "Iter 2/500 - Loss: 46.822212\n",
      "Iter 3/500 - Loss: 40.542583\n",
      "Iter 4/500 - Loss: 36.714863\n",
      "Iter 5/500 - Loss: 34.119858\n",
      "Iter 6/500 - Loss: 33.901077\n",
      "Iter 7/500 - Loss: 33.801804\n",
      "Iter 8/500 - Loss: 33.768261\n",
      "Iter 9/500 - Loss: 33.752182\n",
      "Iter 10/500 - Loss: 33.744076\n",
      "Iter 11/500 - Loss: 33.744076\n",
      "Iter 12/500 - Loss: 33.744076\n",
      "Iter 13/500 - Loss: 33.744076\n",
      "Iter 14/500 - Loss: 33.744076\n",
      "Iter 15/500 - Loss: 33.744076\n",
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      "Iter 445/500 - Loss: 33.744076\n",
      "Iter 446/500 - Loss: 33.744076\n",
      "Iter 447/500 - Loss: 33.744076\n",
      "Iter 448/500 - Loss: 33.744076\n",
      "Iter 449/500 - Loss: 33.744076\n",
      "Iter 450/500 - Loss: 33.744076\n",
      "Iter 451/500 - Loss: 33.744076\n",
      "Iter 452/500 - Loss: 33.744076\n",
      "Iter 453/500 - Loss: 33.744076\n",
      "Iter 454/500 - Loss: 33.744076\n",
      "Iter 455/500 - Loss: 33.744076\n",
      "Iter 456/500 - Loss: 33.744076\n",
      "Iter 457/500 - Loss: 33.744076\n",
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      "Iter 459/500 - Loss: 33.744076\n",
      "Iter 460/500 - Loss: 33.744076\n",
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      "Iter 462/500 - Loss: 33.744076\n",
      "Iter 463/500 - Loss: 33.744076\n",
      "Iter 464/500 - Loss: 33.744076\n",
      "Iter 465/500 - Loss: 33.744076\n",
      "Iter 466/500 - Loss: 33.744076\n",
      "Iter 467/500 - Loss: 33.744076\n",
      "Iter 468/500 - Loss: 33.744076\n",
      "Iter 469/500 - Loss: 33.744076\n",
      "Iter 470/500 - Loss: 33.744076\n",
      "Iter 471/500 - Loss: 33.744076\n",
      "Iter 472/500 - Loss: 33.744076\n",
      "Iter 473/500 - Loss: 33.744076\n",
      "Iter 474/500 - Loss: 33.744076\n",
      "Iter 475/500 - Loss: 33.744076\n",
      "Iter 476/500 - Loss: 33.744076\n",
      "Iter 477/500 - Loss: 33.744076\n",
      "Iter 478/500 - Loss: 33.744076\n",
      "Iter 479/500 - Loss: 33.744076\n",
      "Iter 480/500 - Loss: 33.744076\n",
      "Iter 481/500 - Loss: 33.744076\n",
      "Iter 482/500 - Loss: 33.744076\n",
      "Iter 483/500 - Loss: 33.744076\n",
      "Iter 484/500 - Loss: 33.744076\n",
      "Iter 485/500 - Loss: 33.744076\n",
      "Iter 486/500 - Loss: 33.744076\n",
      "Iter 487/500 - Loss: 33.744076\n",
      "Iter 488/500 - Loss: 33.744076\n",
      "Iter 489/500 - Loss: 33.744076\n",
      "Iter 490/500 - Loss: 33.744076\n",
      "Iter 491/500 - Loss: 33.744076\n",
      "Iter 492/500 - Loss: 33.744076\n",
      "Iter 493/500 - Loss: 33.744076\n",
      "Iter 494/500 - Loss: 33.744076\n",
      "Iter 495/500 - Loss: 33.744076\n",
      "Iter 496/500 - Loss: 33.744076\n",
      "Iter 497/500 - Loss: 33.744076\n",
      "Iter 498/500 - Loss: 33.744076\n",
      "Iter 499/500 - Loss: 33.744076\n",
      "Iter 500/500 - Loss: 33.744076\n",
      "Total training time: 10.390832901000977\n"
     ]
    }
   ],
   "source": [
    "from gpytorch.mlls import VariationalELBO\n",
    "import time\n",
    "\n",
    "likelihood = gpytorch.likelihoods.GaussianLikelihood()\n",
    "likelihood.noise = 0.1\n",
    "\n",
    "M = 10\n",
    "inducing_points = train_x[ torch.randperm(train_x.shape[ 0 ])[ 0 : M ], 0 ]\n",
    "model_vfe = VFESparseGP(inducing_points)\n",
    "mll = gpytorch.mlls.VariationalELBO(likelihood, model, num_data=train_x.size(0))\n",
    "\n",
    "start = time.time()\n",
    "result_unwhitened = train_model(model_vfe, mll, train_x[:,0], train_y[:,0], 500, likelihood)\n",
    "end = time.time()\n",
    "\n",
    "print(\"Total training time:\", end - start)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "SJLdRTYuLpc-"
   },
   "source": [
    "Now we plot the predictive distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 528
    },
    "id": "Nz2uRqgKLseG",
    "outputId": "87394b71-d6f6-4cdb-de32-0a9cb7593542"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_pred_dist_model(model, likelihood):\n",
    "\n",
    "  model.eval()\n",
    "  likelihood.eval()\n",
    "\n",
    "  # Test points are regularly spaced along [-2, 8].\n",
    "  # Make predictions for y by feeding model through likelihood.\n",
    "\n",
    "  with torch.no_grad():\n",
    "      test_x = torch.linspace(-3, 3, 200)\n",
    "      predictions = likelihood(model(test_x))\n",
    "\n",
    "  # We plot the predictive distribution (mean +- standard deviation).\n",
    "\n",
    "  f, ax = plt.subplots(1, 1, figsize=(8, 6))\n",
    "  lower, upper = predictions.confidence_region()\n",
    "  ax.plot(train_x.numpy(), train_y.numpy(), 'k*')\n",
    "  ax.plot(test_x.numpy(), predictions.mean.numpy(), 'b')\n",
    "  ax.fill_between(test_x.numpy(), lower.numpy(), upper.numpy(), alpha=0.5)\n",
    "  ax.set_ylim([-3, 3])\n",
    "  ax.legend(['Observed Data', 'Mean', 'Confidence'])\n",
    "  return ax\n",
    "\n",
    "ax = plot_pred_dist_model(model_vfe, likelihood)\n",
    "\n",
    "with torch.no_grad():\n",
    "  ax.plot(model_vfe.variational_strategy.inducing_points, torch.ones(M).numpy() * -2, \"ro\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "W7rBWwqkMhtc"
   },
   "source": [
    "## **Task 1**\n",
    "\n",
    "Try to add another hiden layer in the previous DGP model to see what impact it has in the predictive distribution. Ideall, it should improve it a bit. Use the same settings, e.g., number of inducing points, training epochs, etc. Plot the latent function learned at each layer: first, second and last."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "O4hN9y9mODXd"
   },
   "source": [
    "## **Training DGPs by Minimizing Alpha-Divergences**\n",
    "\n",
    "In this part of the notebook we will focuse on training DGPs by minimizing alpha-divergences. Training by minimizing alpha-divergences is not implemented in gpytorch. However, gpytorch is very easy to extend to incorporate this funcitonality. We only need to create a custom loss function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ZhohiaSQVv8t"
   },
   "source": [
    "The implementation is veary easy. It simply duplicates the data fed into the model times the number of samples used in the Monte Carlo approximation of the $\\log Z_i$ terms. The loss function ueses these repeated predictions to estimate $\\log Z_i$ acordingly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "id": "wZVQe-ruVuIw"
   },
   "outputs": [],
   "source": [
    "# This class implements the approximate alpha-divergence objective\n",
    "# It only changes the computation of the data-dependent term w.r.t. DSVI.\n",
    "# The regularizer, the KL-divergence, is the same.\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "class VariationalELBOAlphaDivergence(VariationalELBO):\n",
    "    def __init__(self, likelihood, model, train_size, alpha_value, n_samples_train):\n",
    "        super().__init__(likelihood, model, train_size)\n",
    "        self.alpha_value = alpha_value\n",
    "        self.n_samples_train = n_samples_train\n",
    "\n",
    "    def _log_likelihood_term(self, variational_dist_f, target, **kwargs):\n",
    "\n",
    "        mean = variational_dist_f.mean\n",
    "        variance = variational_dist_f.variance\n",
    "\n",
    "        mean = mean.reshape((mean.shape[ 0 ], self.n_samples_train, int(mean.shape[ -1 ] / self.n_samples_train)))\n",
    "        variance = variance.reshape((variance.shape[ 0 ], self.n_samples_train, int(variance.shape[ -1 ] / self.n_samples_train)))\n",
    "        noise = self.likelihood.noise[ 0 ]\n",
    "        target_new = target.reshape((target.shape[ 0 ], self.n_samples_train, int(target.shape[ -1 ] / self.n_samples_train)))\n",
    "\n",
    "        # This is the log value of the expectation of a gaussian factor to the power of alpha\n",
    "\n",
    "        log_probs = self.alpha_value * (-0.5 * np.log(2 * np.pi) - 0.5 * torch.log(noise)) \\\n",
    "            + (0.5 * np.log(2 * np.pi) + 0.5 * torch.log(noise / self.alpha_value)) \\\n",
    "            + (-0.5 * np.log(2 * np.pi) - 0.5 * torch.log(noise / self.alpha_value + variance)) \\\n",
    "            + - 0.5 * (mean - target_new)**2 / (variance + noise / self.alpha_value)\n",
    "        expected_log_probs = torch.logsumexp(log_probs, 1) - np.log(self.n_samples_train)\n",
    "\n",
    "        return (1 / self.alpha_value * expected_log_probs.sum(-1)) * self.n_samples_train # We multiply by the sample size to account for the size of the actual batch inserted\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "4WEqb8mEWoB9"
   },
   "source": [
    "Now we slightly change the optimizar to take into account the new loss."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "id": "H-aXcAS8Wol8"
   },
   "outputs": [],
   "source": [
    "from torch.utils.data import TensorDataset, DataLoader\n",
    "\n",
    "def train_dgp_alpha(model, train_x, train_y, mini_batch_size, num_epochs, n_samples_train = 25, alpha = 1e-3):\n",
    "\n",
    "  optimizer = torch.optim.Adam(model.parameters(), lr=0.01)\n",
    "  mll = DeepApproximateMLL(VariationalELBOAlphaDivergence(model.likelihood, model, train_x.shape[-2], alpha, n_samples_train))\n",
    "\n",
    "  for training_iter in range(num_epochs):\n",
    "\n",
    "    # Within each iteration, we will go over each minibatch of data\n",
    "\n",
    "    train_loader = DataLoader(TensorDataset(train_x, train_y), batch_size=mini_batch_size, shuffle=True)\n",
    "\n",
    "    for (x_batch, y_batch) in train_loader:\n",
    "\n",
    "        # We iterate over the batches\n",
    "\n",
    "        with gpytorch.settings.num_likelihood_samples(1):\n",
    "            optimizer.zero_grad()\n",
    "            x_tiled = torch.tile(x_batch, ((n_samples_train, 1)))\n",
    "            y_tiled = torch.tile(y_batch, ((n_samples_train, 1)))\n",
    "            output = model(x_tiled)\n",
    "            loss = -mll(output, y_tiled.T)\n",
    "            loss.backward()\n",
    "            optimizer.step()\n",
    "\n",
    "    if (training_iter + 1) % 100 == 0:\n",
    "      print('Epoch %d/%d - Loss: %f' % (training_iter + 1, num_epochs, loss.item() * train_x.shape[ 0 ]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "s2KcXC3AXKEC"
   },
   "source": [
    "Now we are ready to train the method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "NYQhyPtiX1m5",
    "outputId": "79e88fa4-c67d-4d0a-f5a4-d1545b1c2a2c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 100/10000 - Loss: 19.546047\n",
      "Epoch 200/10000 - Loss: 16.166290\n",
      "Epoch 300/10000 - Loss: 13.073494\n",
      "Epoch 400/10000 - Loss: 11.357417\n",
      "Epoch 500/10000 - Loss: 9.174577\n",
      "Epoch 600/10000 - Loss: 8.815639\n",
      "Epoch 700/10000 - Loss: 6.427895\n",
      "Epoch 800/10000 - Loss: 4.128145\n",
      "Epoch 900/10000 - Loss: -0.462499\n",
      "Epoch 1000/10000 - Loss: 2.499678\n",
      "Epoch 1100/10000 - Loss: -5.132198\n",
      "Epoch 1200/10000 - Loss: -1.681070\n",
      "Epoch 1300/10000 - Loss: -11.277971\n",
      "Epoch 1400/10000 - Loss: -15.225170\n",
      "Epoch 1500/10000 - Loss: -13.732581\n",
      "Epoch 1600/10000 - Loss: -12.403026\n",
      "Epoch 1700/10000 - Loss: -14.503086\n",
      "Epoch 1800/10000 - Loss: -12.106879\n",
      "Epoch 1900/10000 - Loss: -14.277060\n",
      "Epoch 2000/10000 - Loss: -13.194141\n",
      "Epoch 2100/10000 - Loss: -17.876639\n",
      "Epoch 2200/10000 - Loss: -18.651726\n",
      "Epoch 2300/10000 - Loss: -16.265521\n",
      "Epoch 2400/10000 - Loss: -16.951611\n",
      "Epoch 2500/10000 - Loss: -16.907041\n",
      "Epoch 2600/10000 - Loss: -17.494082\n",
      "Epoch 2700/10000 - Loss: -17.615409\n",
      "Epoch 2800/10000 - Loss: -16.722527\n",
      "Epoch 2900/10000 - Loss: -18.474071\n",
      "Epoch 3000/10000 - Loss: -19.401193\n",
      "Epoch 3100/10000 - Loss: -3.876846\n",
      "Epoch 3200/10000 - Loss: -17.108603\n",
      "Epoch 3300/10000 - Loss: -19.460406\n",
      "Epoch 3400/10000 - Loss: -20.215237\n",
      "Epoch 3500/10000 - Loss: -20.656426\n",
      "Epoch 3600/10000 - Loss: -20.187194\n",
      "Epoch 3700/10000 - Loss: -22.135277\n",
      "Epoch 3800/10000 - Loss: -17.768176\n",
      "Epoch 3900/10000 - Loss: -16.365271\n",
      "Epoch 4000/10000 - Loss: -21.282649\n",
      "Epoch 4100/10000 - Loss: -21.218348\n",
      "Epoch 4200/10000 - Loss: -20.439537\n",
      "Epoch 4300/10000 - Loss: -19.746468\n",
      "Epoch 4400/10000 - Loss: -22.994642\n",
      "Epoch 4500/10000 - Loss: -19.128160\n",
      "Epoch 4600/10000 - Loss: -21.288905\n",
      "Epoch 4700/10000 - Loss: -20.109174\n",
      "Epoch 4800/10000 - Loss: -18.396168\n",
      "Epoch 4900/10000 - Loss: -16.533148\n",
      "Epoch 5000/10000 - Loss: -19.766726\n",
      "Epoch 5100/10000 - Loss: -18.787398\n",
      "Epoch 5200/10000 - Loss: -17.752175\n",
      "Epoch 5300/10000 - Loss: -23.025556\n",
      "Epoch 5400/10000 - Loss: -17.245851\n",
      "Epoch 5500/10000 - Loss: -21.063039\n",
      "Epoch 5600/10000 - Loss: -22.340465\n",
      "Epoch 5700/10000 - Loss: -16.733248\n",
      "Epoch 5800/10000 - Loss: -19.925256\n",
      "Epoch 5900/10000 - Loss: -21.749387\n",
      "Epoch 6000/10000 - Loss: -20.361848\n",
      "Epoch 6100/10000 - Loss: -18.181467\n",
      "Epoch 6200/10000 - Loss: -20.882738\n",
      "Epoch 6300/10000 - Loss: -21.386867\n",
      "Epoch 6400/10000 - Loss: -15.544508\n",
      "Epoch 6500/10000 - Loss: -17.992389\n",
      "Epoch 6600/10000 - Loss: -21.837466\n",
      "Epoch 6700/10000 - Loss: -20.415723\n",
      "Epoch 6800/10000 - Loss: -18.109603\n",
      "Epoch 6900/10000 - Loss: -20.102167\n",
      "Epoch 7000/10000 - Loss: -20.931487\n",
      "Epoch 7100/10000 - Loss: -19.604883\n",
      "Epoch 7200/10000 - Loss: -19.379964\n",
      "Epoch 7300/10000 - Loss: -20.507538\n",
      "Epoch 7400/10000 - Loss: -20.294228\n",
      "Epoch 7500/10000 - Loss: -20.878079\n",
      "Epoch 7600/10000 - Loss: -14.308980\n",
      "Epoch 7700/10000 - Loss: -22.948172\n",
      "Epoch 7800/10000 - Loss: -14.250171\n",
      "Epoch 7900/10000 - Loss: -21.046090\n",
      "Epoch 8000/10000 - Loss: -23.665018\n",
      "Epoch 8100/10000 - Loss: -15.983953\n",
      "Epoch 8200/10000 - Loss: -19.173253\n",
      "Epoch 8300/10000 - Loss: -23.236120\n",
      "Epoch 8400/10000 - Loss: -20.903487\n",
      "Epoch 8500/10000 - Loss: -16.807606\n",
      "Epoch 8600/10000 - Loss: -23.933046\n",
      "Epoch 8700/10000 - Loss: -20.491936\n",
      "Epoch 8800/10000 - Loss: -19.711092\n",
      "Epoch 8900/10000 - Loss: -16.576481\n",
      "Epoch 9000/10000 - Loss: -19.579754\n",
      "Epoch 9100/10000 - Loss: -14.126954\n",
      "Epoch 9200/10000 - Loss: -10.385070\n",
      "Epoch 9300/10000 - Loss: -20.056968\n",
      "Epoch 9400/10000 - Loss: -19.476748\n",
      "Epoch 9500/10000 - Loss: -19.894829\n",
      "Epoch 9600/10000 - Loss: -14.442990\n",
      "Epoch 9700/10000 - Loss: -21.294529\n",
      "Epoch 9800/10000 - Loss: -22.630606\n",
      "Epoch 9900/10000 - Loss: -19.732637\n",
      "Epoch 10000/10000 - Loss: -21.197073\n"
     ]
    }
   ],
   "source": [
    "# We instantiate the model\n",
    "\n",
    "num_inducing_points = 10\n",
    "model = DSVIDeepGP(train_x, train_y, train_x.shape, 1, num_inducing_points)\n",
    "\n",
    "# We do the actual training\n",
    "\n",
    "train_dgp_alpha(model, train_x, train_y, train_x.shape[ 0 ], 10000, alpha = 1.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TKsEDH15biTt"
   },
   "source": [
    "We now compute predictions and plot the predictive distribution.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 545
    },
    "id": "FQn5QqSXbhne",
    "outputId": "85298086-5138-43ee-83fc-d8ad08ab26c1"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_325420/3428919590.py:20: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
      "  f.show()\n"
     ]
    },
    {
     "data": {
      "image/png": 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79i0OHDiAwYMHS2tEitzd3dGtWzds3LgRRCTdP336dFSuXBnXrl3D//73P4wYMQKHDh0CAGzduhWzZs3C4sWL8fDhQ+zYsQMVK1aUzh06dCjOnTuHDRs24ObNm+jUqRNatGiBhw8fSmkSExPx559/YunSpbhz5w66desGJycnbN26VUqjUCiwceNGdOvWDQAQEhKCFi1aoGPHjrh58yY2btyI06dPY+jQodI5vXv3Rnh4OI4dO4YtW7ZgwYIFUmCoqTJlyqBly5bYtm2bdF9aWhp+//133LhxAzt27EBoaKgUXHp5eUn1v3//Pl6+fIk5c+YAABISEvD999/j8uXLOHLkCExMTNC+fXv9t/RSPhYTE0MAKCYmxthVYYwxxvKlpKQkunv3LiUlJWl1PgDpJpPJVH6KN107f/48AaDt27dnefyvv/4iAPT69WsiIvLx8aEWLVqopOnSpQu1bNmSiIhmzpxJpUqVotTU1Ex5PX36lExNTen58+cq9zdu3JjGjBlDRET//vsvAaDr16+rpBkxYgQ1atRI+vvAgQNkaWlJ7969IyKivn370rfffqtyzqlTp8jExISSkpLo/v37BIAuXrwoHQ8ODiYANGvWrGyuDtFvv/1GlStXzvLYTz/9RNbW1tmee+nSJQJAcXFxRER07NgxAiDVOTuRkZEEgG7dupXl8ZxeZ5rEa9ziyRhjjH3C1qxZAzMzYSNDet/CKP40MzPDmjVr9FY2ZWjRzE1gYGCmv4ODgwEAnTp1QlJSEooXL47+/ftj+/btkMvlAIBbt25BoVCgVKlSsLOzk24nTpxQ6Vq2sLBApUqVVMro1q0bjh8/jhcvXgAA1q5di9atW8PJyQkAcOPGDaxYsUIl3+bNm0OpVOLJkycIDg6GmZkZAgICpDzLlCkjna8NIlJZU/PKlSto27YtvL29YW9vjwYNGgAAwsLCcszn4cOH+Prrr1G8eHE4ODjA19dXrfPyirfMZIwxxj5h3bp1Q9myZVWCI9GFCxdQrVo1nZdZsmRJyGQyBAcHo3379pmOBwcHw9nZGa6urmrl5+Xlhfv37+Pw4cM4dOgQBg8ejOnTp+PEiROIj4+Hqakprly5kmmrRzs7O+l3a2vrTIuk16hRAyVKlMCGDRswaNAgbN++HStWrJCOx8fHY8CAASrjSUXe3t548OCBWvXXRHBwMPz8/AAI3eXNmzdH8+bNsXbtWri6uiIsLAzNmzdHampqjvm0bdsWPj4+WLJkCYoWLQqlUokKFSrkel5eceDJGGOMMQCAiYkJlEql9FNfChcujKZNm2LBggX47rvvVMZ5vnr1CmvXrkXPnj1VAsHz58+r5HH+/HmULVtW+tva2hpt27ZF27ZtMWTIEJQpUwa3bt1C1apVoVAoEBERgc8++0zjunbr1g1r165FsWLFYGJigtatW0vHqlWrhrt376JkyZJZnlumTBnI5XJcuXIFNWrUACCMtdR2aaN79+5h//79GDNmjPT3mzdvMHXqVHh5eQFAphUJxK1Uxa1VAeDNmze4f/8+lixZIl2T06dPa1UnTXFXO2OMMfaJc3Nzg7u7OwICArBo0SIEBATA3d0dbm5ueitz3rx5SElJQfPmzXHy5EmEh4dj//79aNq0KTw9PTF58mSV9GfOnMG0adPw4MEDzJ8/H5s3b8aIESMACLPSly1bhtu3b+Px48dYs2YNrK2t4ePjg1KlSqFbt27o2bMntm3bhidPnuDixYuYMmUK9uzZk2s9u3XrhqtXr2Ly5Mn46quvYGlpKR376aefcPbsWQwdOhTXr1/Hw4cPsXPnTmlyUenSpdGiRQsMGDAAFy5cwJUrV9CvX79ME6qyIpfL8erVK7x48QK3bt3C33//jQYNGqBKlSr44YcfAAitqhYWFvj777/x+PFj7Nq1C7///rtKPj4+PpDJZNi9ezciIyMRHx8PZ2dnFC5cGP/88w8ePXqEo0eP4vvvv8+1TjqR6yhQI+LJRYwxxljO8jq5SJScnExKpZKIiJRKJSUnJ+uiejkKDQ2lXr16UZEiRcjc3Jy8vLxo2LBhFBUVpZLOx8eHJkyYQJ06dSIbGxtyd3enOXPmSMe3b99OtWrVIgcHB7K1taXatWvT4cOHpeOpqak0btw48vX1JXNzc/Lw8KD27dvTzZs3iUiYXOTo6JhtPWvWrEkA6OjRo5mOXbx4kZo2bUp2dnZka2tLlSpVosmTJ0vHX758Sa1btyZLS0vy9vamVatWkY+PT66Ti/B+YpepqSkVKlSI6tWrR7Nmzcr0vKxbt458fX3J0tKSAgMDadeuXQSArl27JqWZOHEiubu7k0wmo169ehER0aFDh6hs2bJkaWlJlSpVouPHj+c44UtXk4tkRBqM7DWw2NhYODo6IiYmBg4ODsauDmOMMZbvJCcn48mTJ/Dz84OVlZWxq8M+Ujm9zjSJ17irnTHGGGOMGQQHnowxxhhjzCA48GSMMcYYYwbBgSdjjDHGGDMIDjwZY4wxxphBcODJGGOMMcYMggNPxhhjjDFmEBx4MsYYY4wxg+DAkzHGGGOMGQQHnowxxhhjzCA48GSMMcaYwfXu3RsymQwDBw7MdGzIkCGQyWTo3bu34SvG9IoDT8YYY4wZhZeXFzZs2ICkpCTpvuTkZKxbtw7e3t5GrBnTFw48GWOMMWYU1apVg5eXF7Zt2ybdt23bNnh7e6Nq1arSfUqlElOmTIGfnx+sra1RuXJlbNmyRTquUCjQt29f6Xjp0qUxZ84clbJ69+6Ndu3aYcaMGfDw8EDhwoUxZMgQpKWl6f+BMomZsSvAGGOMMd0hAhITjVO2jQ0gk2l2Tp8+ffDvv/+iW7duAIDly5fjm2++wfHjx6U0U6ZMwZo1a7Bo0SL4+/vj5MmT6N69O1xdXdGgQQMolUoUK1YMmzdvRuHChXH27Fl8++238PDwQOfOnaV8jh07Bg8PDxw7dgyPHj1Cly5dUKVKFfTv318XD5+pgQNPxhhj7COSmAjY2Rmn7Ph4wNZWs3O6d++OMWPG4OnTpwCAM2fOYMOGDVLgmZKSgj/++AOHDx9GYGAgAKB48eI4ffo0Fi9ejAYNGsDc3BwTJkyQ8vTz88O5c+ewadMmlcDT2dkZ8+bNg6mpKcqUKYPWrVvjyJEjHHgaEAeejDHGGDMaV1dXtG7dGitWrAARoXXr1nBxcZGOP3r0CImJiWjatKnKeampqSrd8fPnz8fy5csRFhaGpKQkpKamokqVKirnlC9fHqamptLfHh4euHXrln4eGMsSB56MMcbYR8TGRmh5NFbZ2ujTpw+GDh0KQAggM4p//2D27NkDT09PlWOWlpYAgA0bNmD06NGYOXMmAgMDYW9vj+nTp+PChQsq6c3NzVX+lslkUCqV2lWaaYUDT8YYY+wjIpNp3t1tbC1atEBqaipkMhmaN2+ucqxcuXKwtLREWFgYGjRokOX5Z86cQZ06dTB48GDpvpCQEL3WmWmHA0/GGGOMGZWpqSmCg4Ol3zOyt7fH6NGj8d1330GpVKJevXqIiYnBmTNn4ODggF69esHf3x+rVq3CgQMH4Ofnh9WrV+PSpUvw8/MzxsNhOeDAkzHGGGNG5+DgkO2x33//Ha6urpgyZQoeP34MJycnVKtWDWPHjgUADBgwANeuXUOXLl0gk8nw9ddfY/Dgwdi3b5+hqs/UJCMiMnYlshMbGwtHR0fExMTk+IJkjDHGPlXJycl48uQJ/Pz8YGVlZezqsI9UTq8zTeI1XkCeMcYYY4wZBAeejDHGGGPMIDjwZIwxxhhjBsGBJ2OMMcYYMwgOPBljjDHGmEFw4MkYY4wxxgyCA0/GGGOMMWYQHHgyxhhjjDGD4MCTMcYYY4wZBAeejDHGGPuoERG+/fZbFCpUCDKZDNevX0fDhg0xcuTIHM/z9fXF7NmzDVLHTwUHnowxxhgzmlevXmHYsGEoXrw4LC0t4eXlhbZt2+LIkSM6K2P//v1YsWIFdu/ejZcvX6JChQrYtm0bfv/9d52VwdRjZuwKMMYYY+zTFBoairp168LJyQnTp09HxYoVkZaWhgMHDmDIkCG4d++eTsoJCQmBh4cH6tSpI91XqFAhneTNNMMtnowxxhgzisGDB0Mmk+HixYvo2LEjSpUqhfLly+P777/H+fPnAQBhYWH48ssvYWdnBwcHB3Tu3BmvX7+W8hg/fjyqVKmC1atXw9fXF46OjujatSvi4uIAAL1798awYcMQFhYGmUwGX19fAMjU1R4REYG2bdvC2toafn5+WLt2bab6RkdHo1+/fnB1dYWDgwMaNWqEGzduqF0XAFAqlZg2bRpKliwJS0tLeHt7Y/LkydLx8PBwdO7cGU5OTihUqBC+/PJLhIaG6uJy5wvc4skYY4x9RIgIiYmJRinbxsYGMplMrbRv377F/v37MXnyZNja2mY67uTkBKVSKQWdJ06cgFwux5AhQ9ClSxccP35cShsSEoIdO3Zg9+7dePfuHTp37oypU6di8uTJmDNnDkqUKIF//vkHly5dgqmpaZb16d27N168eIFjx47B3Nwcw4cPR0REhEqaTp06wdraGvv27YOjoyMWL16Mxo0b48GDB1ILak51AYAxY8ZgyZIlmDVrFurVq4eXL19KLbtpaWlo3rw5AgMDcerUKZiZmWHSpElo0aIFbt68CQsLC7Wubb5G+VhMTAwBoJiYGGNXhTHGGMuXkpKS6O7du5SUlERERPHx8QTAKLf4+Hi1633hwgUCQNu2bcs2zcGDB8nU1JTCwsKk++7cuUMA6OLFi0RE9Ntvv5GNjQ3FxsZKaX744QeqVauW9PesWbPIx8dHJe8GDRrQiBEjiIjo/v37KnkSEQUHBxMAmjVrFhERnTp1ihwcHCg5OVklnxIlStDixYvVqktsbCxZWlrSkiVLsny8q1evptKlS5NSqZTuS0lJIWtrazpw4EC218kQPnydZaRJvMYtnowxxhgzOCLKNU1wcDC8vLzg5eUl3VeuXDk4OTkhODgYNWrUACDMPre3t5fSeHh4ZGqtzK0cMzMzBAQESPeVKVMGTk5O0t83btxAfHw8ChcurHJuUlISQkJCpL9zqktwcDBSUlLQuHHjLOtx48YNPHr0SOV8AEhOTlYpoyDjwJMxxhj7iNjY2CA+Pt5oZavL398fMplMJxOIzM3NVf6WyWRQKpV5zjej+Ph4eHh4qHTxizIGqDnVxdraOtcyAgICshxf6urqqnml8yEOPBljjLGPiEwmy3LMZH5TqFAhNG/eHPPnz8fw4cMz1Tk6Ohply5ZFeHg4wsPDpVbPu3fvIjo6GuXKldNZXcqUKQO5XI4rV65Iraj3799HdHS0lKZatWp49eoVzMzMpAlKmvL394e1tTWOHDmCfv36ZTperVo1bNy4EW5ubnBwcNCqjPyOZ7UzxhhjzCjmz58PhUKBmjVrYuvWrXj48CGCg4Mxd+5cBAYGokmTJqhYsSK6deuGq1ev4uLFi+jZsycaNGiA6tWr66wepUuXRosWLTBgwABcuHABV65cQb9+/VRaKJs0aYLAwEC0a9cOBw8eRGhoKM6ePYuff/4Zly9fVqscKysr/PTTT/jxxx+xatUqhISE4Pz581i2bBkAoFu3bnBxccGXX36JU6dO4cmTJzh+/DiGDx+OZ8+e6ezxGhMHnowxxhgziuLFi+Pq1av4/PPPMWrUKFSoUAFNmzbFkSNHsHDhQshkMuzcuRPOzs6oX78+mjRpguLFi2Pjxo06r8u///6LokWLokGDBujQoQO+/fZbuLm5ScdlMhn27t2L+vXr45tvvkGpUqXQtWtXPH36FEWKFFG7nF9//RWjRo3CuHHjULZsWXTp0kUaA2pjY4OTJ0/C29sbHTp0QNmyZdG3b18kJyd/NC2gMlJndK+RxMbGwtHRETExMR/NBWeMMcZ0KTk5GU+ePIGfnx+srKyMXR32kcrpdaZJvMYtnowxxhhjzCA48GSMMcYYYwbBgSdjjDHGGDMIDjwZY4wxxphBcODJGGOMfQTy8Vxh9hHQ1euLA0/GGGOsADM1NQUApKamGrkm7GOWmJgIIPPOTJrS685FU6ZMwbZt23Dv3j1YW1ujTp06+PPPP1G6dGl9FssYY4x9MszMzGBjY4PIyEiYm5vDxITblJjuEBESExMREREBJycn6YuOtvQaeJ44cQJDhgxBjRo1IJfLMXbsWDRr1gx3794tENt5McYYY/mdTCaDh4cHnjx5gqdPnxq7Ouwj5eTkBHd39zznY9AF5CMjI+Hm5oYTJ06gfv36uabnBeQZY4wx9SiVSu5uZ3phbm6eY0unJvGaXls8PxQTEwMAKFSoUJbHU1JSkJKSIv0dGxtrkHoxxhhjBZ2JiQnvXMTyPYMNBFEqlRg5ciTq1q2LChUqZJlmypQpcHR0lG5eXl6Gqh5jjDHGGNMzg3W1Dxo0CPv27cPp06dRrFixLNNk1eLp5eXFXe2MMcYYY/lUvutqHzp0KHbv3o2TJ09mG3QCgKWlJSwtLQ1RJcYYY4wxZmB6DTyJCMOGDcP27dtx/Phx+Pn56bM4xhhjjDGWj+k18BwyZAjWrVuHnTt3wt7eHq9evQIAODo6wtraWp9FM8YYY4yxfEavYzxlMlmW9//777/o3bt3rufzckqMMcYYY/lbvhnjyfvGMsYYY4wxEe+rxRhjjDHGDIIDT8YYY4wxZhAceDLGGGOMMYPgwJMxxhhjjBkEB56MMcYYY8wgOPBkjDHGGGMGwYEnY4wxxhgzCA48GWOMMcaYQXDgyRhjjDHGDIIDT8YYY4wxZhAceDLGGGOMMYPgwJMxxhhjjBkEB56MMcYYY8wgOPBkjDHGGGMGwYEnY4wxxhgzCA48GWOMMcaYQXDgyRhjjDHGDIIDT8YYY4wxZhAceDLGGGOMMYPgwJMxxhhjjBkEB56MMcYYY8wgOPBkjDHGGGMGwYEnY4wxxhgzCA48GWOMMcaYQXDgyRhjjDHGDIIDT8YYY4wxZhAceDLGGGOMMYPgwJMxxhhjjBkEB56MMcYYY8wgOPBkjDHGGGMGwYEnY4wxxhgzCA48GWOMMcaYQXDgyRhjjDHGDIIDT8YYY4wxZhAceDLGGGOMMYPgwJMxxhhjjBkEB56MMfaRunfvHg4fPmzsajDGmIQDT8bYJ+natWto27YtGjZsiMDAQDRv3hxhYWHGrpbOXLx4EdWqVUPTpk0xbdo0Y1eHMcYAAGbGrgBjrGC5f/8+jh8/jlOnTiEyMhILFy5E8eLFjV0tjcTFxeGrr77C48ePVe7v1q0bjh07BjOzgv3WGBISgjZt2iApKQkA8NNPP8HBwQEDBw40cs0YY586bvFkjKnt77//RpkyZTBw4ECsXbsWBw8eRKdOnZCSkmLsqmnku+++w+PHj+Hj44MNGzZg/fr1sLe3x+nTpzF16lRjVy9PoqKi0LJlS0RGRqJq1aoYNWoUAGDw4MFYs2aNkWvHGPvUyYiIjF2J7MTGxsLR0RExMTFwcHAwdnUY+6Q9efIE5cuXR1JSEj777DM0aNAACxcuxJs3bzB8+HDMmTPH2FVUy86dO9GuXTvIZDIcO3YMDRo0AACsXr0aPXv2hKmpKU6fPo3atWsbuaba6dKlCzZt2gQfHx+cO3cO7u7uGD58OObNmwdzc3NcuXIFFStWNHY1GWMfEY3iNcrHYmJiCADFxMQYuyp6FxERQfPnz6cXL14YuyqSe/fu0bZt2+jt27d6LScqKooSExP1WgbLG6VSSa1btyYA9Pnnn5NSqSQiot27dxMAAkDbt283biXVEBERQa6urgSAfvjhB5VjSqWSvv76awJAxYsXp+joaCPVUnsxMTFkYWFBAOjixYvS/QqFgtq2bUsAqEqVKpSSkmLEWjJWcCgUCtq3bx89e/bM2FXJ1zSJ1zjw1NDDhw/p9evXaqeXy+W5pjlx4gQVLVqUAFDJkiXp1atXeakiERHdvn2bxowZQytXrqQ7d+5QbGws3blzh/bt20c3btxQSatUKmnfvn20ePFiWrx4MU2ZMoUCAgKkgMLKyop69epF58+fz1Od0tLSMn2Y3759m+zt7alw4cK0ePFiksvlpFQq6cyZMzRlyhR6+vRpnspkurFt2zYCQObm5hQcHKxybPTo0QSAnJycKCIiwkg1VM+ff/5JAKhChQqUnJyc6fi7d+/Ix8eHAFD79u2lALugWLt2LQGgMmXKZKr7y5cvqXDhwgSAfv31VyPVkDHdS0tLozFjxlDfvn3V/syQy+V09+5dWrNmDa1YsSLLz2qlUkkjR44kAOTs7EyHDx9Wu07R0dE0ePBgmj17ttrnEBHdvXuXmjVrRuXKlaNRo0bRmTNnSKFQZJv+6dOntHfvXoqPj1e5PyUlha5evapR2XnBgaeWzp8/T9u3b6ebN29mehKTk5Ppxx9/JJlMRo6OjiovwHPnzlHPnj1p6dKlUsvdiRMnqGbNmmRra0ujR4+WgtX79+/TjBkz6JdffqFp06bR6NGjycTERAryAFDlypXp3bt3dOPGDfryyy+pePHiFBQURP/++y+9fPky18dx+vRpcnR0VMkz483U1JSOHj0qpf/555+zTefn56dyX/fu3TUKvImEf/AVK1aQl5cXWVtb07Fjx4hI+CZZt27dTI+9ePHi0t+urq506tQptcu6e/cuVa9enWrXrk3du3enCRMm0PHjx7Nt4Xn9+nWmVub4+Hj666+/6OTJkxo9zo9VXFwceXl5EQAaO3ZspuMpKSlUoUIFAkB///23EWqoviZNmhAAmjNnTrZpLl68KLUaTps2zYC1y7t27doRAPrll1+yPL5p0ybpfztjiyhj2cnpy5dCoaBdu3bRtm3b8lRGamqqWo00WUlKSqL27dtLnxk2NjY0ZcoU2rx5M3Xs2JFsbGyoTJkyNHbsWDp69CjNnj2bWrRoQba2tiqfPX379s0U4E2bNi3TZ+LcuXPp2LFjNGvWLBo0aBD17t2bgoKCaOjQofTw4UMiInr16hVVqVJFOm/z5s1SnikpKbRnzx7asWMHHTt2jK5evUohISEUFRVFM2fOJEtLy0yfxdWrV6fnz5+r1O3ChQvUpUsXMjU1JQDk4uJCU6dOpQsXLtCIESOocOHC5ODgQAkJCVpdV01x4Kmlb775RuXJLlasGLVv357++OMPqlSpksoxMzMzmjdvHo0YMYJkMpl0f6FChejzzz/P9MKxsbGhsmXLZhsM9ujRg65fv05FihQhAOTt7a2Sr3iztLSkMWPGUGxsLBEJQd39+/cpNDSUkpOT6cCBA2RjYyN1qdWrV0/6B3N0dCRPT0+pno8ePZI+iABQy5YtqV27dtSxY0eaP38+RUREkFKppLNnz1KPHj2k+jg7O9OMGTPo2rVrlJaWluk6KhQKOn36NC1fvpx+/fXXTNeucOHC9OTJE1qyZAkBIFtbW5o0aZJKsGxraysFoObm5vTvv//m+vy9ffuWSpYsmeX1tbOzow4dOtDly5el9GvWrCEbGxuysrKiLVu2EBFRbGwsffbZZ9J57dq1owcPHujmBVZALViwgACQr69vtm9iM2fOJABUr149A9dOfYmJidKb+t27d3NMu3DhQgJAJiYm0hel/C42NlZ6fNevX882XdeuXQkA1alTx4C1Y7okl8tp27ZtNH78eJo0aRJNmTKFpk+fTrNmzaL58+fTkydPVNJfvHiRBgwYQJs2bcpyWNODBw9o0qRJNG3aNLp//z4RCb1RPXv2JEtLS7K3t6cSJUpQvXr1aOTIkbRp0yb6999/qUyZMtJ75ZgxYzIFqQqFgnbs2EHdu3enLVu2qBy/cOEC/fDDD1S3bl2ytLQkBwcH+vXXX6WhXcnJyXTjxg06cOAArV27lubNm0dz5syhOXPm0Lx582jLli105swZaty4sfTZWLNmzWw/Y7O62draUu3ataXGn4EDB5JSqSS5XC59PgGgKVOmUPfu3XPNz8zMjPr37y99DpmZmUm9QWFhYfTu3Ttq0KBBrvk0b96c1q5dS0FBQWRnZyfFIzdu3KBr165RixYtMn2mZpVP0aJF6dq1a7p98WWDA08tTZgwgapXr07Ozs5ZPokuLi60adMm6tatW6ZjX3zxhdRFJ34zGjRoEG3evJmqV6+u8sJs1qwZDRkyhHr06EEdO3akNWvWSP+Q169fVwnAOnfuTLt27aKxY8dS1apVpfuLFClCjRs3Jnt7e5V6iMFhy5YtpSBBLpdLgWpiYiLVqFGDAJC/v78UpI4aNSrX63Px4kWVb3HiP25QUBA9fvyYiIhCQ0OpYcOGma6Po6OjShd+hQoVpOs8a9YsIhJaH2fOnEnr1q2j+Ph4io+Pp6+++krK46uvvsq2G0Uul1Pz5s2loH39+vU0ZcoUCgoKksb0idend+/eNGjQoEzXbfLkyVS7dm3pcYlvRqamplS2bFlq3bo1/fzzz5lej3FxcRQXF6fVa64gEN/kpk6dmm2a8PBw6VqGhYUZsHbqO3DgAAEgT0/PXLvQlUol9ezZkwCQh4dHlt3y+c2GDRsIEIbr5PT4nj17Jr3m37x5Y8AaMk3Fx8fT6NGjqWTJktShQwdatmwZrVq1KsdGDADk4OBAhw4dIiKiQ4cOSe/z4rFOnTrRt99+S8OHD6c6depkOt/X11ft4C3jZ9Dw4cNJoVDQw4cPafHixZnqWb9+fVq3bh01bdo0x7pXqlRJCtrUudnZ2dHRo0dJqVTS6tWrqXjx4uTr60s//vgjXbhwgdatW0cdO3aUPjenT59ON27ckFpZ16xZI312Vq1alRwcHKS8xc9GpVJJU6dOJScnJ/Lz86P27dvTzz//TFOmTKG//vqLWrVqpVInPz8/unv3rvR5W6dOHalnyM7OjmrWrEmlS5cmDw8P6flxcnKixYsXq/z/Pn78WArwraysVGKJnj17Sg1AK1eupNKlS5OFhQV99dVXtHfv3iwbhvSFA08dePPmDZ04cYKmTZtGHTt2pAEDBkhjL5VKJU2cOFH6Bz1w4AARqX4LzdiiolQq6dChQ7Rhwwa1JupcvnyZRowYQVeuXFG5X6lU0o4dOzK16llbW0tdgwCoa9euOU4eeP78uTSmFAA1a9ZM7RdoWloazZs3j5o2baryz2lhYUG9evWS7rO1taXmzZvTgAEDaObMmRQVFUVERGFhYeTm5iadV61atRzLVigU9Ntvv0lBoLW1Nf32228qwU1cXBwNHz5cOv7hNzyFQkGXLl3K8hvrL7/8QoMHD1a5z9nZmS5fvkx37tzJ9GYCgFq0aCG9YQUHB1ORIkXIwcGBdu3apdY1LEji4uKk19adO3dyTCu2FM+YMcNAtdOMOBa1d+/eaqVPSEggDw8PApDnrkRD6NixIwFCy1NuxIBg69atBqgZ08bhw4czDXXKeHNycqJvvvmG+vfvT9988w316NGDgoKCqHLlylJgMnLkSKkVvHr16uTt7Z1lXiYmJtSiRQtq1qyZFPDJZDLq2LEjnT17lh48eECnT5+m1atX05AhQ6hq1ark7+9Pf/75J8XExEi9IuJ7/4eNDkFBQSpBk/iFPigoiFasWEH379+nLVu2UMWKFTM9xkqVKlGjRo2oY8eO1LVrV+ratSt16NCBAgMDydvbmypVqqSTYSPLly/PFACPGjUqU/d7Tl/qTp48SY0bN6aGDRtKQ7gePnwotVqKX2Sz6pFITU3N9rPw7du3Kg06Xbt2lbr1P5TTeFB94sDTQMLCwozSEpKSkkKrVq2ixYsXS9/alEolRUVFqd3adPHiRXJ0dKRy5cpp3eohl8vp3Llz0rg58RYYGEiPHj3K9rxTp06Rubk5mZiY0KVLl9Qq68aNG1S/fn2VcurVq0ctW7ZUCbo3btyYYz7nz5+nevXqkYeHB+3evZuIhDeSmTNnkkwmI1dX10xvCk+ePKGDBw/S3LlzydramgBhRnR4eLg09lG8TZgwwWj/+Pqwfft2AoRZ3rm1Es6fP58AUI0aNQxUO82IH8hr165V+xwxWG3fvr0ea5Z38fHx0mvzwy+sWRk6dCgBoMGDBxugdkwT8fHxKj0yXl5etHLlSvrtt9+oevXq5OvrS5MmTcp21YWkpCRpOIV4a9++PSUnJ5NCoZAaVCZOnEhjx46lWbNmqYxzf/fuHf33338aDzFasWKF1EBgaWlJtWvXpmnTpkmf30+fPqWvv/6a7O3taeDAgVIvWUYKhYIOHTpEO3fupKdPnxp8ct/evXtp7ty5dPXqVa3HnGZl9erVJJPJqEyZMhQaGqpVHikpKbR8+XKDThjSBAeeTC2xsbE6aYoXZ8U3b96c/vzzT7XyvHTpEp05c0bjctavX68yBlO8lShRghYtWqRRXh968OBBri3SYnem+M0VAJUuXZoGDBgg3d+6dWuNJ2DlV3369CFA6ELLzevXr6UPnpy+eBjDq1evpOdHk+fmxo0bUot+fu6W3rx5s9S9p86HtfiFonTp0gaoHVPXhQsXyN/fX3qtDhkyRBompQmFQkFjx44lExMT6t27t8G6XG/fvk2XLl3KscetoK0UoSshISEFYsiOtjjwZB+98PBwmjNnDk2bNo3u3Llj0DezsWPHSh8Mnp6e0jfY5cuXS62vbm5uUotqQaVQKKTJbuJ4sdyIY7cmT56s59ppRlxmqHLlyhqfK06O0+SLjaGJLVwfrk2anbdv30pfEnh9QuNLS0uj8ePHSzOUPT091f6fy4mhZjQzxoEnY3qkUCioX79+VK5cObp9+7bKsevXr1P58uWlwHTgwIGZluYqKC5cuCCNdVJ3wfGlS5cSAKpYsaKea6eZ3r17EwAaPXq0xudOnz6dAFDdunX1ULO8S05OliZ4nDt3Tu3zxEmPq1at0mPtWFaePXtGe/fupZMnT9KJEyeoVq1a0ntGly5d8nXrOmNZ4cCTMSNKSkqi7777TvogKVWqlNpjWfOTX375hQBQp06d1D7n7du3UquvOmMNDUGpVErLiIkTATXx7NkzacZrSEiIHmqYN3v37pWGfmgyvvinn34iANSrVy/9VY5lkpKSQsWKFcs0XMjR0VGj8ceM5SeaxGsmYIzplJWVFf766y8cOnQIRYsWxYMHDxAYGIjt27cbu2oa+e+//wAAbdq0UfscZ2dndOjQAQCwZMkSvdRLU8HBwXj+/DksLS3x2WefaXy+p6cnGjduDABYu3atrquXZzt27AAAfPnllzAxUf8tXXxMR44cARHpo2osC//99x+ePXsGGxsblCpVCh4eHmjbti1u3ryJoKAgY1ePMb3jwJMxPWnSpAlu3bqF9u3bQy6XY+TIkUhJSTF2tdQSHh6OGzduwMTEBK1atdLo3G+//RaAEKTFx8drVX5UVBSio6O1OvdDmzdvBgA0atQI1tbWWuXRo0cPAMC6det0UiddUSgU2LlzJwCgffv2Gp1bt25dWFhY4NmzZ3j48KE+qseysGzZMgDA8OHDcf/+fbx48QK7du2Ct7e3kWvGmGFw4MmYHhUqVAhr165F0aJFERYWhsWLFxu7SmrZunUrACE4cXFx0ejchg0bwt/fH3FxcdiwYYPa57169QpTpkxB7dq14erqCldXV3Tq1AmHDh2CUqnUqA4iIpLq0LVrV63yAIB27drB3Nwc9+7dw4MHD7TOR9fOnz+P169fw9HREQ0bNtToXBsbGwQGBgIQWj2Z/oWHh+PAgQMAgD59+hi5NowZBweejOmZtbU1xo0bBwCYNGmS1q2AhrRp0yYAQOfOnTU+VyaTSa2e6gba0dHRqFWrFsaOHYsLFy4AAORyObZs2YJmzZqhYcOGiImJ0bgut27dwr1792BhYYEvv/xS4/NFDg4OUmAnDkHID8Ru9tatW8PCwkLj88Xu9j179uiyWiwbK1asgFKpRIMGDeDv72/s6jBmFBx4MmYAffr0QYkSJRAZGYk5c+YYuzo5CgsLw7lz5yCTydCxY0et8ujVqxcsLCxw+fJlXL16Ndf033//PcLCwuDj44NFixbh+fPnuHHjBoYOHQo7OzucOnUKTZo0wdu3bzWqh9ja2apVKzg6Omr1WERt27YFAOzatStP+egKEUnjhjXtZhd16tQJALB//368fPlSZ3XTt1u3bhW44QFKpRLLly8HAPTt29fItWHMiPQ90ykveFY7+5iIa0k6ODhIW4jmRzNmzCAA1KBBgzzlI64tOWDAgBzT7dmzR9qi79SpU5mOX7t2jQoXLiytwxkREaFW+UqlkooXL04AaMOGDVo9hoyePHkibfWXH56/mzdvSrvExMXFaZ2PuFf31KlTdVg7/bl79y6Zm5uTm5ubQfeizqvDhw9L//+8vib72PCsdsbyoa5du6JSpUqIjY3FoEGD8u1M4rx0s2c0YMAAAMJkikuXLmWZ5t27d+jfvz8AYOTIkahXr16mNFWqVMHx48dRpEgR3LhxAx06dIBCoci1/MuXL+Px48ewsbHRaGZ+dnx9fVGpUiUoFArs27cvz/nl1cGDBwEIk9js7Oy0zkdsfVu+fHm+fU1m9PPPPyMtLQ0RERG4efOmsaujNnGVh6CgINjY2Bi5NowZDweejBmIiYkJ/vnnH5iZmWHz5s2YP3++sauUSWhoKC5evAgTExNpWSRtNWjQAJ06dYJcLkdQUBDi4uJUjiclJaF79+548eIFSpUqhUmTJmWbV4UKFXD8+HHY29vj9OnTmDZtWq7li93sbdu2ha2tbZ4ei+iLL74AkD+6269cuQIA0gQhbXXu3Bm2trZ48OABTp8+rYuq6c2FCxdUliU7e/asEWujvvv370urK4jjnxn7VHHgyZgB1apVC9OnTwcgjGvMriXQWMQPxwYNGsDd3T1PeclkMixevBheXl549OgRhg8fLh2LiYlBixYtsHfvXlhZWWHlypW5tgKVKVMGc+fOBQCMGzcux7GjcrlcarnNy2z2D4mB5/79+42+NJb4+AMCAvKUj52dHbp06QIgfamf/IiI8L///Q8ApC8S586dM2aV1Pb7779DqVSibdu2qFq1qrGrw5hx6bvfPy94jCf7GCmVSmrfvj0BIF9fX4qNjTV2lSTiNooLFy7UWZ4nT56U9gXv0KEDDR8+XNr/3MHBgU6cOKF2Xkqlkjp27EgAqEyZMtmOlZs1axYBoMKFC1NSUpKuHgopFAry8PDQehckXYmNjZV2U3r16lWe8ztz5gwBIBsbm3z7frt//34CQBYWFrRs2TLp/ye/Cw4Oll7/+WU3L8Z0jbfMZCyfe/fuHfn4+BAA+vvvv41dHSIiioqKkrbve/36tU7z/vXXXzNtEejm5kbXrl3Tqp5i8NepUyeSy+Uqx1+8eCHtXf7PP//o6BGk69+/PwGgoUOH6jxvdZ08eZIAkKenp07yUyqVVKZMGQJAv/32m07yzKmsly9f0smTJ2nlypV07NgxSklJyfGcpKQkqlixIgGg7777jmJiYqTA+8WLF3qtb14FBQURAPryyy+NXRXG9IYDT8YKgHnz5hEAKl26NCmVSmNXR5p1W6JECZ3nrVQqaffu3TRjxgwaM2YM/e9//6PHjx9rnd/Ro0fJ3NycAFC/fv1Url+3bt0IANWsWVOjvcvVtXnzZgJAAQEBOs9bXbNnzyYA9MUXX+gsT7EVEQDNnz8/1/TPnj2jS5cu0cmTJ2nfvn20ePFi+umnn6hPnz40ffp0On78OEVFRVFKSgoplUq6efMm/fDDD+Tp6ZnpS4itrS21bt2aDh8+nGVZAwYMkFqwIyMjiYikVvOtW7fq7Bro2t27d6UA+erVq8auDmN6w4EnYwVAbGys1DJ38OBBY1eHZs6cKXWHFwSbN2+WujCHDRtGZ86ckZaskslkdOnSJb2U++jRI2kZo9TUVL2UkZsePXoQABo/frxO8/3555+lYPDff//NdDwhIYFWrVpF9evXzxQ85nQTnyfxJpPJyNfXlxo2bEhubm4qx7755ht6+/atVOaqVaukczIObxCD0dGjR+v0GujS4MGDCQC1a9fO2FVhTK848GSsgBg2bJjOW660JQYzEydONHZV1JaxlS7jbeDAgXorU6FQkIODAwGgW7du6a2cnJQvX54A0H///afTfJVKJY0YMUK6jj4+PtSlSxf69ttvqVq1alIrsxgIFitWjPz9/aly5crUunVrGjp0KP3222/UoUMH8vLyUnlOzM3NqV27drRt2zZKTEyUylQoFHT9+nUaPHiw1Dro6upKnTt3pjFjxpC1tXWWQfbKlSsJANWpU0en10CXqlSpQgBoy5Ytxq4KY3qVbwLPEydOUJs2baTxWNu3b9fofA482ccuODhY+hB/8uSJUesidl3u3LlT7XMuXbpEn3/+udqti/pIv3z5cqpcuTKVKFGC3NzcyMHBIdsu27zWR/TZZ58RAFq1apVG5+lCfHy81IL4/Plztc9T97EqlUoaOXKkFAR+ePP19aWJEydSWFhYrvknJSXR27dv6fnz5yqT6LKry5kzZ6SxphlvtWvXpoYNG6qkf/DggTTZKDk5We3rYCgJCQlkampKACg8PNzY1WFMr/LNAvIJCQmoXLlyvlyvkLH8oEyZMmjatCmICAsWLDBaPVJSUnD37l0AwoLt6lq1ahWOHTuG1atXGy39N998g+vXr+PRo0fo0qULYmNj1V5nU9P6iMRrdP36dY3O04WbN29CqVTC3d0dRYsWVfs8dR+rTCbDrFmzpPUmAwMDMWbMGGzevBlPnjzB48eP8euvv8LLyyvX/K2srODs7IyiRYvC3t4+17rUqVMH169fx549ezBjxgz069cPvXr1ktZxzZi+ZMmScHFxQWpqKq5du6b2dTCUa9euQaFQwMPDA56ensauDmP5hpk+M2/ZsiVatmypzyIYK/CGDh2KQ4cOYenSpfj9999haWlp8DoEBwdDLpfDyckpU0DxoadPnyIqKgoymQwbN24EICzW3qtXLxARXFxc4OPj89Gkz4oxA09x/c5q1arlmjYv10ZcqD0kJATz5s0DEUEmk0Emk2mVv7ppLS0t0apVK5QvX15KL36OfJi+Tp062LVrF86ePYvatWvn9dLq1MWLFwEANWrUULlmjH3q9Bp4aiolJUVlUebY2Fgj1oYxw2jdujU8PDzw8uVLHDt2DC1atDB4HcQAqkqVKrl+SPr6+kq/i2kjIyNVFjKnDFsv6iv9q1dAcDDQqNEUAEUByAH0AfAMERHbdFafrIiLgF+/fl0KyAxF3LFIncBTu2tvA6A+hGtpi4gIOwQEnAaQCCARM2ZMhI0NYGMD9O49+v39SQDKAyiPiAhzBARMBGALwBZ//fUPEhKAX39dCUDx/tYXgAIREUoEBGwCYAHAEqNH/4yUFCAlBfjnn6MALAHEAHAGEJGp7lOmTMGuXbvy5ULy4uYQNWvWNHJNGMtndN7Rnw2oMcbzt99+y3JMEY/xZB+7b7/9Vu+TYnIycuRIAkAjRozINe2aNWvIzMwsy/9VMzMzWrNmjUr65cvXk4nJEAIuEPCEgNcEvCHgFMlks2jo0JMUEaFO/g5kYtKGmjULplKliICcbpEETCJTU89M9dG0/llJTk6W8nj69Kla11hXKleurPaYeU0e69mzROXLvyAgOZdra4xbKgFzCSisUvdDhw4RIGwmkN+UKFGCgPyxYgVj+qbJGE8ZUS5f7XVE7Lpp165dtmmyavH08vJCTEwMHBwcDFBLxoxj7969aN26NYoWLYrw8HCYmBh2N9vPP/8cx48fx/Lly/HNN9/kmv7q1atZbtV45coVqSVOqQSmTQNmzgSionKvQ7VqQIMGQOnSANEDDBo0BEBZAOUA1AZQCRl3+TUxAfz8hPQ2NpHYsmUrhJazhgCKAwCcnNJw6ZI5SpbUvP65qVy5Mm7evImdO3dKW2nqW3JyMuzt7SGXy/H06VN4e3vneo46j3XlSuDbb4HUVPHoUwCnAbwFEA9AgW7d+sPOrggSE6Fyi4pKwJ07TwDIACjf3xJRq1Z5uLs7wNYWsLUFLCyAV68isXXrdgjPo+n7mxwdO7aFp6crLC2FdOLPyMhwzJx5DYB4fZ8BqIArV46iWrVquHv3LsqXL49ChQrhzZs32l5WnXvz5g1cXFwAAG/fvoWzs7ORa8SYfsXGxsLR0VG9eE3vYfB74FntjGUrKSmJbG1tCQBdvHjRoGUrlUpydnYmQP1Frq9cuUJA+vqMWW0J+Ouv6S1WRYsmEzCMZLLaBJQnmawyAd2pS5fXVLmy+i1fnp7J9O23RFu3EkVHZ1cfE5LJOhJwmwCiMmVU06pb/9z06tWLANCECRPUPievLl++TADIxcVF7U0HcnqsCgXRjz+mX98OHYi2br2t0bXR5Fpqet3F9DJZYwKeva9nkJQ+MjJSasE11pqqWdm3bx8BIH9/f2NXhTGDyDez2hlj6rGyspLGdu7cudOgZYeHh+Pdu3cwMzNDuXLl1DrHzc0N7u7uCAgIwKJFixAQEAB3d3e4ubkBALZtA37/XUg7axZw5kwk3N03o3p1BRYtGobq1S3g7n4YM2ak4vp14NUrYM0aYMQIoFUrwM8vDaamj+DkdAItWlxDiRJj4OpaGefPR2LxYqBDB8DRMbv6LED16mFwdQ2Cu7sc9+4BXboAcrn69VeHOMHIkDOqHz58CAAoW7as2uNKc3qsM2cKrdIA8MsvwObNQM2ajnB3d0e1atXwww8/wM3NDdbW1rh8+TJiYmI0yl+btLdv38aAAQPQqFEjtGvXDqampqhQIQLNm0cAAKysOkrpCxUqBFNTUwDC2NX8gsd3MpYDfUbAcXFxdO3aNbp27RoBoL/++ouuXbum9pgobvFknxJxh5YKFSoYtNxdu3YRAKpYsaJG5yUnJ0utbkqlUlpL8dYtIltboQVt5Mjc02ua/4c2bdpE9erVozp16lDDhg3p22+/pZSUFEpOTqarV4lsbIS6fLjBjab1+dCxY8cIENa1NJQ//viDAFCPHj00Oi+rx/r0afq1+ftv1fQrVqzItKMQ3o+t/OKLL+jGjRu55p+RXC4nuVyeY1qlUknLli0jKyurTOUOHjyYTp4U6lqokJLeZ0VERO7u7hq11htCmzZtCADNmTPH2FVhzCDyzQLy4hvzh7devXqpdT4HnuxT8ubNG2nB6ZCQEIOVO3HiRAJA3bt3z3NeqalE/v5CgNCoEVFamg4qmIObN2+SpaVlpveYdevWSWk2bxbqY2FBFBWlu7Lfvn0rlffu3TvdZZwDcRLauHHj8pxX+/bCdfnsM6KMvfYPHz6UrqmjoyN9/fXXNHz4cCpVqpT0eGUyGfXs2ZN27NhBBw8epNOnT9Pjx48pNTWVUlNT6dChQzRkyBAKCAggDw8PMjExIQcHBxo0aBBdv349U11CQkKoZ8+eUv4tWrSg1atX04IFCwgA2dvb07t3ceTsLNT59On0c8XJVvv378/zNdEFpVIpBe3nzp0zdnUYM4h8E3jmFQee7FPTsGFDqXfAUDp27EgAaMaMGXnOa8MGITBwcyOKjNRB5XKQkJBA5cqVIwDUrFkz2rJlizTuslGjRippq1YV6jVrlm7r4OvrSwDo+PHjus04G02bNiUAtHz58jzls3u3cD3MzIQWapFSqaQmTZoQAGrSpAmlpKSonHfnzh3q3Llzlg0KeD9mU9ziMqdbiRIlqE2bNjR8+HCqUaOGyvlTpkwhhUIh1UcMeBctWkRduwr1HjMm8zUxxi5SWQkNDZVah5OSkoxdHcYMggNPxgqoWbNmEQBq0KCBwcoUl305dOhQnvOqW1cIDH77Le/1ys2AAQMIALm7u1PE+/WYnj59Km31+OjRIyntggVCvcqXV23dy6t27doZ9IuCv78/AaBjx45pnUdiIpGvr3A9fvhB9djq1asJAFlZWalcvw9dvHiRvvrqK6pVqxZVqlSJihcvrtLy7OrqSv369aMtW7bQlStX6MWLF3T48GHq3Lmzyn7vGQPOxo0b08mTJzOVJf5PVKpUiVauVBJAVLly+vHu3bsTAJo+fbrW10SXNm/eTACoWrVqxq4KYwbDgSdjBdT9+/cJAFlaWmZqbdKHd+/eSR/+UXnsh756Nb0V7cWLzMcVCgWFhobS/v37aeXKlRQfH691WTt27JC6fD/cl71ly5YEgP73v/9J90VHE1lbC/U7e1brYjMRx1y2a9dOd5lmQ6FQkIWFBQGg0NBQrfOZOVO4DsWKEcXFpd8fFRVFLi4uBID++OMPrer38uVLunv3rjSeMytRUVF05MgRWrBgAX3//fc0f/58evXqVbbp3759K7Wi/vffaZLJhPqL259///33BIB++DCKNpJRo0YRYLw1eRkzBg48GSuglEolOTk5GWyyxNGjRwkA+fj45Dmvb74RAoKvv8587Pr161S4cGGVVq42bdqovSRQRnK5nEqXLp1tsLF161apJTTjEju9egn169NH4yKzdfHiRWksZJqeB7SGh4cTADI1NdW6rPh4YRgEQLR0qeqx//3vfyRObstPSxMREfXt25cAUFBQENWuLdR/8WLh2NSpUwkA9ezZ07iVfC8wMDBfdf0zZgi8nBJjBZRMJkP16tUBAJcvX9Z7eeK+31ktMK6JqChg3Trh92HDMh//448/8ObNG5ibm6NcuXKwtLTE7t27MWvWLI3L2rBhA+7fv49ChQrhl19+yXS8bdu2cHNzw6tXr7Bnzx7p/n79xPMBXe3GW61aNTg7OyMmJkbvz1doaCgAwNvbG2Zm2u12vHAhEBEBFC8O9OypeuzIkSMAgJ9++gnm5uZ5qarODRo0CACwZcsWNGz4FgCwd69wrEiRIgCAiIgIo9Qto5SUFGlL0zp16hi5NozlTxx4MpbPGCPwVHe3nuwsWybsr12tGlC7tuqx8PBwbN26FYDwmO7cuSMFnD/99BMuXLigdjlyuRwTJ04EAIwePTrLHTLMzc3Ru3dvAMCSJUuk++vWBcqUEXbb2bBBk0eXPVNTUzRq1AgAcOjQId1kmo0nT54AAPz8/LQ6Pz4e+PNP4fdffgEyxpYJCQnSa6F+/fp5qqc+BAQEwNvbG6mpqShV6h4A4PBhYXcscU3P169fG7OKAIT/p9TUVLi6uqJ48eLGrg5j+RIHnozlM4YMPMXWmby0eCqVwKJFwu/DhgEfrmu+YMECKBQKNGzYEJUqVQIADBw4EJ06dYJcLkeXLl0QHR2tVlnr16/HgwcPULhwYQwdOjTbdP3eN2/u378fcXFxAIR6ia2e8+YButosuGnTpgAMF3j6+vpqdf78+ULLdIkSQI8eqscuXLgAhUIBLy8vtbbhNAaxXhYW4ZDJgIQEIDIyf7V4nj17FoDQ2qnuAv+MfWo48GQsnxEDz1u3biE5OVlv5cTFxeHBgwcA8tbieeoUEBoKODgIOwRllJiYiH/++QcAMGLECOl+mUyGJUuWoHjx4nj69Cmmidvn5ODD1k57e/ts0/r7+8PT0xNKpRI3b96U7u/TR9g3/NYtocVMF5o0aQIAOHfuHOLj43WTaRbErnZtWjyTkoDp04Xfx40DPuypP336NACgXr16eamiXomB58uX4fDwEO4LC0tv8YyIiADp6tuEljIGnoyxrHHgyVg+4+3tDRcXF6SlpeHWrVt6K+f69esgIhQrVkyjrSI/tHq18LNTJ8DaWvXY2rVr8fbtW/j5+aFt27YqxxwdHfHXX38BAP7++2+8ffs2x3IWLVqER48ewcXFJcfWTpG4peX169el+5yd01s9Z8zINQu1lChRAn5+fpDL5Thx4oRuMs1CXrra9+wB3rwBvLyAoKDMxwtC4Onl5QUACAsLg9gomzHwTEtLU7vlXB+ISAo8AwMDjVYPxvI7DjwZy2cMNcFIFxOLkpKATZuE3z+crEJEmDt3LgBg6NCh0p7aGX3xxReoXLky4uPjMWfOnGzLuXfvHn788UcAwPjx42FnZ5dr3bIKPAFg5EjAxAQ4eBDI0BiaJ4bobhdbPLXpal+/Xvj59deZWzvlcjnOnTsHoGAEnuHh4Xj/K8LDAUtLSzg6OgIw7jjPp0+f4tWrVzAzM5P+fxljmXHgyVg+ZIjAUxzfmZdu9p07gbg4wNcX+DBmuXr1Km7fvg1bW1v06dMny/NlMhl+/fVXAMCcOXOybLFKS0tDjx49kJSUhKZNm0oznHNTtWpVAJkDT19foXUWAGbOVCurXInd7Yd11X//AblcjvDwcACat3jGxAgtnoAQeH7o5s2biI+Ph6OjIypUqJDXquqN2NUeHh6u0uIJ5I9xnmJrZ9WqVWH9YdM/Y0zCgSdj+ZAYeF66dElvZeiixXPVKuFnjx5CK2JG4mz1+vXrw8nJKds82rdvj/LlyyMmJgZ///13puOTJk3C5cuX4ezsjH///RcmHxaUDbHF89atW5DL5SrHRo8Wfq5bBzx7plZ2OWrUqBFkMhnu3LmDFy9e5D3DD4SHh0OhUMDS0hLu7u4anbtjh7DiQJkyQOXKmY+fOnUKAFC3bl21r60xZNfVDuSPme1iqzGP72QsZ/n3XYaxT5gYeN65cweJiYk6zz8hIQHBwcEAtG/xfPVK6K4GMs+SBtSfMW9iYiKtxzlr1iycOXMGAKBQKDB58mRMmjQJALBw4UJ4enqqXT8/Pz/Y29sjJSUF9+/fVzlWvTrQoAEglwuzvfOqcOHC0nXUxzhPsZvdx8dH4+AwYzd7VhOtC8L4TiA98IyMjIS7uzDp7sPAMz+0eHLgyVjOOPBkLB8qWrQo3N3doVQqM3UV68LNmzehVCrh4eEBD3GKsIbWrwcUCmHdTn//zMfFYQLqtKh26tQJlSpVwrt371CvXj307t0bjRs3xi+//AKlUolBgwahy4dT5nNhYmKCyu+b+K5du5bp+MiRws+lSwFdLB4gBp5iQK9L2k4sioxMn72fVTc7ERWYwLNQoUJSF7alpdBM/X70gdG72hMSEnDjxg0APLGIsdxw4MlYPqTvCUa6GN+5caPwM6vWzqSkJNy5cwcA1JpoYWpqiiNHjqBv374AgJUrV+LEiROws7PDypUrMV/LZsnsJhgBQJs2wizvqChg82atsldRpkwZAPoJPLWdWLR5s/DlICAg6y8Hjx8/xqtXr2BhYYEaNWrkvaJ6JJPJpHGeCoXQ1PnqlTCMwNhd7ZcvX4ZCoYCnp6fUMssYyxoHnozlU2IgoI9xnnkd3/n6NXDxovB7+/aZj9+8eRMKhQJubm5qd4+7uLhg6dKlOHfuHD777DM0atQI165dQ8+ePbVejDu7CUaAMLt7wADh9wULtMpehRh43rt3L++ZfUDbFs+M3exZEYc1VK9eHVZWVlrXz1DEoC42NhxidZ89M36L5+3btwHkfQcwxj4FHHgylk+Jgef58+d1nrfYKlexYkWtzt+zR9j5p3p1IKue+ozd7JoGjbVr18bJkydx5MgRlCxZUqv6iTK2eGa1uHi/fsLWkefPA+9jca2VLVsWAPDgwQMoFIq8ZfYBbQLPiAjgfVyJzp2zTiMGyZWzmnWUD4mB57Nn4Vmu5WmsFk+xdb9cuXJGKZ+xgoQDT8byqcDAQMhkMjx69AivXr3Sad6PHz8GICx+ro3//hN+frAmvETsyjf2eoblypWDmZkZ3rx5g+fPn2c6XqQI8NVXwu95nWTk7e0NKysrpKamSl3juqJNV/u+fcKXg6pVgex6fx89egRA2OmpIMhqSaXwcOO3eN69excAUL58eaOUz1hBwoEnY/mUk5OT1CIpdonqQnx8vPQBXbx4cY3PT05On82eXeCpycQifbKyspJaIrObpDVkiPBz3Trg3TvtyzI1NUWpUqUA6HacZ0pKirREkyYtnrt3Cz/btMk+jRh45rVl2VBy272IWzwZy/848GQsHxNnGoszj3VBbO0sXLiwtOOLJo4dAxITAU9P4H1PtoqkpCSpBcjYgSeQ3t2e1cx2AKhTR1jfMjkZ2LAhb2WJQa4ux3k+fvwYRAQ7Ozu4uLiodU5qKnDggPB7doEnERXYwDPj7kUZA8+4uDgkJSUZtE6RkZGIioqCTCaTnn/GWPY48GQsH9Nn4KlNayeQ3s3epk3W60LeuHFD44lF+pTTzHZAeAzi/uXbt+etLH1MMBLXIC1durTa42VPnRJ2lCpSRBiHm5XIyEjExcVBJpNptf+7MWS3e5GjoyMsLCwAGL67XfyS5evrCxsbG4OWzVhBxIEnY/mYGHheu3YN8fHxOskzJCQEgHbjO4nSu3Bz62avXr261rPRdSnjDkbZEWfmHzsGvH2rfVn6WFIpY+CpLvE5at06845SIrG108vLq0DMaAcyzmqPReHCMQCEwFMmkxltEXmxm53HdzKmHg48GcvHvLy84O3tDYVCIW1BmVd5afG8cUOYzGFtDTRqlHUadXcsMhTxcYaFhWU5sx0Q1risWFHYyUgM2rQhdrUGBwdnW5amHjx4AADS+NHcEKm2SmenoHWzA4CtrS2cnZ0BAKamwurx4eHCYxYnGBl6nKfY4snjOxlTDweejOVzuu5uz0vguWOH8LNpUyH4zEp+Czw9PT0hk8mQkpKCyMjIbNN16CD83LZN+7L8/f0hk8nw7t07REVFaZ9RBpq2eD54AISEABYWQJMm2acriIEnkN7dLpcLgWd8PBAdbbxtM3liEWOa4cCTsXxO14Gntl3tCgWwYoXwe6dOWadJTk6WPojzS+Bpbm4Od3d3AMLYwOyIgeeBA0Iwow0bGxv4+PgA0F13u9jiqW7gKbbYNmwI2Ntnn66gBp5id/vr12EQ51qFhRm/xZO72hlTDweejOVzYuB5/vx5yOXyPOWlUCikNSE1bfE8dAh4+hRwdgY6dsw6TWhoKJRKJezt7fPFxCJRxtnQ2alYEShRQpjdvn+/9mXpcmb7u3fvpFZaddfaVGcZJaDgB54fTjAyRotnVFSUVJ44vpcxljMOPBnL58qXLw9HR0fEx8fj5s2becrr2bNnSEtLg4WFhcaB4ZIlws+ePbPvZhe78f38/PLFxCKROoGnTJY+ySgvs9t1ObNd7Gb39PSEnZ1drumjo4UZ7YAwsSgnBTXwzG0ReV1vtpCTjDPa1Xl+GGMceDKW75mYmKBOnToAgFNiVKElMTD09fWFqamp2ue9fAns2iX83r9/9unErR21XapJX9QJPIH07vbdu4GUFO3K0mXgqenEov37hSER5coBOT0Fb9++xbv3q+Xnt+cqN9m1eBYtWhQApMX2DYEnFjGmOQ48GSsAxMDz0qVLecpHHN+pabCxYoUw47tOHSCnoWwZWzzzE3UDz1q1hIXxY2OBZcu0KyvjzPa80nRikabd7EWLFoWtra3W9TOG7HYvKlasGAChVd9QeCklxjTHgSdjBUDVqlUBZL/7jrq02aNdqUzvZv/2W/Xyz2+taOoGniYmwJgxwu/jxwsBqKbEFs+nT58iMTFR8wwy0CTwlMuF/dmB7NdYFRXUbnYg/bl89uwZihUTlqwKC4M0dOT58+c6W8oqN9ziyZjmOPBkWSISJpKcOwcYeAc6lgUx8Lx3716etgTUJjA8dgx48gRwdMx+Nrsov3e1h4WF5Zr222+BUqWAyEhg2jTNy3JxcUGhQoVARFLgqC1NutrPnxcWvy9UCKhdO+e0BTnwFMdypqSkwMVFWH4gPDy9qz0lJQVv3rwxSF14KaWP37t3wMiRwNatxq7Jx4MDz3zi6lXg99+FD3ldfFmfPRvw9QVatQImThSWiHk/pCtbr18D8+YJazS6uAjn16kDFC4s5LNkiTB+TNeuXRMCG5Y9Dw8PuLq6QqlU5rgDT260WUpp3Trh59dfAzntCEhE+b6r/cWLF1Dk8iI2NwemThV+/+sv4PlzzcqSyWSoUKECAOD27dsa11WkVCrx8OFDAOq1eIrd7C1bAmZmOactyIGnjY0NrN/PbrO2FtZKffECMDOzlGa2G6K7/c2bN9LSTbxH+8dJoRDe9+bMAb76Cvj+e6FnQR1EwPHjwrq6miACXr0CHj4UvlBFRuomJshPcnl7+rQsWgScPg34+Qm38uWBmjXT96N++VII6FJSgAYNgM8+E97wTp0CgoOFgK1t2/Qt6kJDheM1a6p+ENy7J7yYrKyE1sRZs9IX5gaA+vWBwYOFYOzMGSFttWpCK8bnnwPvP0OzNXcu8N13wu9Pn6Z3vwFCS07LlkI3opOTcN+dO8Do0cDBg0K3qsjcXEgTGSnksW8fsGGDEIi8b3RQW2go8OefQpfYwoWQxmatXy/sk21mJnyrHDcOSEsD1qwB9u4V6uDsLATBI0cKrTm5efUKSEwE3NwAW9us9xMXxcQIby4Z8w0JAWbOBAIChBnc5uaaPVZ9kMlkqFq1Kg4ePIhr166hZs2aWuWjaYtnamr6gupdu+ac9u3bt4iLiwMgTF7KT9zd3WFmZga5XI6XL19K4wGz064dUK+e8H7w66/A8uWalVexYkWcPHkyT18SwsPDkZycDHNzc2lt0JyoO74TKNiBJyC0KoeHh0Mmi4SpqR/kcuGLs6enJyIiIvD8+XNpq1R9Ecfwent7wz6nBVP1JDUViIsTGgZERMDjx0DRoqorTxABUVGAgwNgaZk5L4VCeG9OTgbs7IT3TfEzKy1NyPPePeEz0M8PKFsWKFYMSEgQ6uDmlvN7s1KZ/datuqBQCF8Sw8KE1Rw+/zz9cSoUwk0sPzFRWKc3483BAahcOfNnxbhxQqONhYVwvWfNAq5fF/7HkpKE9JUrC5/xrq7p5wUHA0OHAkePCtfzzBmgUiXhWGoqcPKksMZumTJC3ocOCTHAuXPCZ2Vysmo9qlUDtmwRrj0gXM+LF4GbN4XP71evgNKlhbo4OACXLwMXLgD37wvH9XnttUL5WExMDAGgmJgYg5TXqROR8C+afqtQgWjRIqLJk4lsbTMf//BWsSLRlClE9eun31esGNFvvxHNnk1UtWrW58lkRI0aEVlY5Jy/mRnR6NFEMTFECQlEc+cS1axJ9OWXRCtXCn+Lab//Xvi7WzeikiVV8ylalGjXLqI//1Qts2ZNor/+IrpyhSg5mUipJLp1i+iPP9Ifv4cH0Zo1RPv3Ex05QvTiReZrmZpKdP++UEbfvkK9xTJ8fYkePyY6cSLz43V1JbK0zPqxV65MFBmZ/fOnVBJNnKh6jpUVkbc3UUAAUbt2RGvXEiUlEcXHC2ltbYXyBg0iCgkRHru1tWpdlywRzjG2n376iQDQwIEDtTr/3bt3BIAAUFxcnFrn7N6d/pzL5TmnvXjxIgEgDw8Preqnb97e3gSAzp49q1b68+eFx25iQvTkiWZlLVq0iABQixYtNK/oewcOHCAAVLZs2VzTPn4s1NXUlOjt29zzdnV1JQB09epVretnTNWqVSMAtGfPHipWTHjsFy4QtW3blgDQokWL9F4H8Tlu2bKlXst58YLon3+E55hIeJ9btYqocGHhcVetSvTLL0RDh5J0LcT3dyKiu3eJPv88/T3NxYWofHmi6tWJ6tUTPrOye89V92ZpKXzGJSYKZT5+LHy2dOxI5OcnvC7btCG6dk04rlAQXbxINGsWUZ8+RDVqENWtSzRtmvA+HBFBtG+fkMdvvwm38eOJpk8nWriQaNMmIQ2R8LNxY9X62NsT+fsTOTmp/xjq1iU6eFC4vmlpRBs3ph9bt45o69acYwAPD6JKlYTP/oyfdwCRlxfRy5fCc1m7dubP9A/zMjERHkPGz0cXF+Ezc88eoipV1H9cwcF6fXlKNInXOPDM4PBhoqlTiQYMIGrWLOsXWa1aQpBStqzwt60tUdOmRN9+K7xQPgwmHRwy52FuLvxTeHsTubsTff218OZARBQeLryBlCtH9NVXQiC0fj3RqFFCUCjmUaSI8ELM7sU2erTwD5RRVBTRtm1C2R+mb9WK6MGDnK/P3btCvbL6J2ndWvhHnTWLqEmTrAPopk3Tyy5WjMjZWfi9fXui//4jKl5cNcj86y8h6PvzT+HxAsKb5OvXmeuWkkLUu7dqwJndtXF2Ft4kcvpnrV07vUxAeAMbMIDow5glLY1oxgzhdZOWpu0rTz3r168nAFSrVi2tzr9y5QoBoCJFiqh9To8ewuMfPjz3tBs2bCAAVLduXa3qp29169YlALRx40a1z2nSRHj8P/6oWVmnT58mAOTp6alhLdPNnTuXANCXX36pRlqhng0a5J5vdHQ0iV9ADPXeqmvNmjUjALRy5UoKDBQe+5YtRIMGDSIA9Msvv+i9DsOHDycANGrUKL2Vcfas8Bkhvg81apQ5yMrp1qCB8HmjTloLC+G9Mav3bg8PooYNhc+qWrXSP9dMTVU/9/z8hAAup3I++yw9aM7LTSYTyvL0FP62sRHer3J7bxc/sxwchAC9VCnVwNvRUchb/Pu779Kfj9u3hYaU7t2J+vUTfoqxwIe3tm2JLl8W8geEYLFoUeF3e/v03wEiHx+iESOI9u4levRIaLgRhYcTVauWOX87O6IWLYQGpunThQA+IEBoZOrShWjmTKLTp4UGJEPgwFNH3r0TAqmyZYnKlBFa+RQK1eMZg423b4kmTBCC1j/+IAoLE5709euF++rVI5o3TwgAtbVnj2rg6OdHNGeO8I2wYkXhvhEjMgedGSUkCIGsGBgvX55z+ozi44UgpHp14R9J/KfK6mZjI6Tp3p3ozBnh/BcvVP9Ra9US6kMktCpu2yZ8E/6wPsHB6W8oxYsT/fyz0OJ6/LgQmNaqlf5GuGiRcH5cnPDN+/x5IbD97Tch2BfL9vUVnptjx9IDDHt7osWLhfMTEoTgV2xFEG/t2gnP7evXqi0JTZqo19qkrXv37hEAsra2JnluzY9Z2Lx5MwGgwMBAtdInJaV/qIjPX06mTJlCAKhHjx4a180QunbtSgBoxowZap+zc6fw+AsVSm/NUUfG4O6tli+KoUOHEgD6UY2oV/ywnzkz93wvX75MAMjNzU2reuUHQUFBBIBmzpwp9VTNnk00adIkAkDffPON3uvQuHFjAkDLly/Xed5KpfC+LAaBbm6qwZClpfAZ8+wZ0YoVREFBQiD033/Ce9CPPwrBlZi+TRvhvTAqiujGDaGRZfduIVjfs0doZcz4lpKaKvz/JyVlHbgolcL/g1Ip3DZvVn2flMmE98Pp04Wyrl4VgtaMj8HBQQjOxo0Tzl+4UAisxXqXKiUEUIMGCbcBA4TAsl07oWEi43tymTJEd+4IdVMohB67kyeFxpKICOGz+s0b4fEnJWX+fHn+nGjkSNUGC5mMqGtX9RoUoqOFz639+4VetVOn0o89fCi8f4j5lisn3Eck9Fw+fpz7529CAlHnzsL5VlZCw1JOvX/GwIHnRy4lReh62bw58z9FbKz6+YSE5C0IFt27J7zRlSolBGIzZwqBYsYgPaPXr4Vv4jVqZN16mZ0HDzIHgR9+A9y7N+c85HKhO2XTpsxvqHfupHfffHjOkSNEPXumd4vY2aUHwra2QpAtvlnev6/+Y9KEXC4nGxsbAkB3xSZyDUydOpUAUPfu3dVKv3278Ji8vLJ/LjPq378/AaBx48ZpXDdD+OGHHwgAjRgxQu1z5HLhCwpAtGyZZuWJXfsnT57U7MT3mjZtSgBoWS4Fh4Skt+I8f557vitWrCAAVL9+fa3qlR+IrY1jxoyh778XHv+oUemPrWnTpnqvg4eHBwGg8+fP6yzPx4+FYV3ly6e/r3XoIHyJDg0VGjaGDcu9d4qI6NIlom++IdqxQ/2GhbyIixOC/1mzhIA4KzdvCq3zp06ptuplFB0tBGS5CQsTGnImTNDscy8nb98KdXz1KvehRZo4cUJoue7cWfu6KpVER4+q9z9uDBx4so9WVJTQ/d6zp9DyWayY8MY8bZrQRaFvt24R1amT/qFQurQQsF67JgRo4jf5rVv1U35gYCABoLVr12p87jfffEMAaPz48Wql79o1/QNdHU2aNCEAtGLFCo3rZghi13WHDh00Om/atPSuMk0+wFu3bk0AaP78+RrWVCAGrqcyNp9kYcIEoX7qxlrfffcdAaBhw4ZpVa/8YOLEiQSA+vfvT3/9JTz+Ll2IDh06RACoXLlyei3/7du3Uot2Xj+fXr8m+vtvkoYMiDcLC+G5VedLH8v/DBH8G5Mm8Vp+m+vEWI4KFwb69QNWrhRmn4eHC+ur/fADoMEKQVqrUEFYxWDFCmDsWGFmYblyQJUqwu916wqLjnfsKCy9kZqq2/LF9TyvX7+u8bni0j7iUj85SUwE/vtP+L1LF/Xyz6+Lx4s0Wcszo759hRUorl8XZqeqq2LFigCg1cz2d+/eSfXMaVccImD1auH3Hj3Uy/vGjRsAgMqVK2tcr/zCxcUFABAVFSWt8hEebrjdi8SF4728vODg4KDx+fHxwKpVQIsWwgz0YcOEGc0mJkCTJsKuWa9fC7Oq892MZKaVnFZX+dTwS5oxDZmYAL16AZMnC0tXiNzdhXVYR40S/p41S1h2qmtXYO1a9dd/y4m4RIymOxgplUppsWt1As/ly4WlUkqUAKpXzz1/uVwuBUr5bQ1Pkff7Nbxy273oQ4UKAd26Cb/Pnav+eXkJPMXg0NfXF87Oztmmu3ABePRIWF+1ffvc8yUiKW99LzekTxkDT3FlrGfP0ncvio2NlZb20oe87FiUmChszdqrl7BUj0IhLMcze7bwGA4dAvr0SV/ujrGPDQeejOmQuTkwY4awJpu7OxAdDWzcCHTvLrRIEeUt/4xbZ5IGmYWGhiIxMRGWlpa5Lh6fkiKsuQoIrbbqfFN/9uwZ5HI5LCwspB1k8huxxfP169dISUnR6Nzhw4WfW7cKa+OpI+Mi8po8V0D6F4vcgkOxtbNDB2G9wNy8ePECb968gampaYHeXzyrFs/nzwEbG3upBfK5piv/ayAve7RPnAjcvSus+zhxorBQ+IULwIgRgIeHrmvKWP7DgSdjevDll0Lrxdmzwt7fZmbC4vuLFuUt3woVKsDU1BRv3rzR6INV7GYvW7YszHLZ1mblSqHuHh5Cy4s6xG52X19fmOTTvkEXFxdYWVkB0DwoqVRJ2BxCqQT++EO9c8qUKQMzMzPExMRo3PUrDqUQv2hkJTVVeE0Bmnezly5dWroWBVHGwNPdHTA1FVoOX782THe7ti2eN24IX0wBYOlSYXOCArqGP2Nay5+fEIx9BExNgcBAIVARt2AcOVLYVUJbVlZW0vZ8mnS3qzu+My0NmDJF+P3HH4WxjerIr3u0ZySTyaSgRNPudkAYbwcIwybeb/yTIwsLC2mrS02729Vp8dy3T9ib3cMDaNxYvXw/hvGdAOD6fpuYN2/eQCZTQmxkN9Q4T21aPBUK4NtvhZ8dOgBffKGv2jGWv3HgyZgBfP+90Aqamgp06iRsQ6qtgIAAAMClS5fUPkfdwHPtWmHLNjc34UNSXfl9YpFI7G7XJvCsXh1o1UoIHNRt9dRmnGdycrLUopZTi6fYzR4UJHzJUcfHEngWfr9PpFKpxLt377Ic56mvrvbo6Gi8ePECgGZ7tM+bJ0xAtLfXbKwwYx8bDjwZMwCZTJgJ7+cnBHa1awv7+Wqjdu3aAIDz58+rfY46gWfGbuTRo4UJK+oSWzzz68QiUV4CTyC91XPVKuD9Q86RNoHnnTt3oFAoULhw4Wz3lH/3Ln3VAXW72YGPJ/A0NzeHo6MjAMPPbBe/FBQrVkyqQ262bk2fdDhlCvA+Nmbsk8SBJ2MG4uQE7N0rBJ+PHwvd8AcPap6PGHheuHABSqUy1/RpaWm4d+8egJwDzxMnhIkODg7AoEGa1elTaPEEhNnIzZsLrZ7TpuWeXpvAM2M3uyybmV2bNwut5xUrAurGkImJiXjw4AGAgh94ArnPbNd34Knu+M7du4WVLRQKoHdvzf+3GPvYcODJmAGVKSPMYK1XD4iJEbpud+zQLI8KFSrAxsYGsbGxUkCZk4cPHyItLQ12dnbSkkJZWbVK+Nmli3ozpDMKCQkBkP8DT/HxP1GnuTIbP/0k/Fy3DkhKyjmtGHgGBwcjOTlZrfzVmVik6dqdgNDqrVQq4erqCnd3d/VPzKdyW8tTX13tmgSeJ08Ka/rK5ULwuXQpr8vJGP8LMGZgrq7A4cPC2DyFQgj0jh5V/3wzMzPUqFEDgHrd7Rm72bNrQUtMBLZsEX7v2VP9ugDCYudRUVEAgJL5fIquOCZPDB600aAB4OMjbBSQ25cGHx8feHh4IC0tDWfUXH0+t4lFT54Ap08LwzeCgtSvd8b1O7N7HRQk2bV46rurXd2JRUolMHSo0DLdrp3wxU7dsbiMfcw48GTMCCwthWWL2rcXPpi+/BLQYK6QRuM81RnfuWOHsJuKn5+w+5ImHj58CAAoWrQo7DRtKjUwMVgICwtDbGysVnmYmKQH5ytX5pxWJpOhWbNmAICDaoyrUCqVUoCYXYvnmjXCz8aNNRsr+LGM7xRl1+IpdrVHRkZqvF6rOsT/p9xaPHfuBG7dEiYTLV8urPHLGOPAkzGjMTMTumsbNxaCvlatgFev1DtXk8BTHF+YU+CZsetW08YwMfD09/fX7EQjKFSoEDzer9IttlxpQww8Dx0C3k9wzpYmgeejR4+QkJAAKysrlCpVKtNxbbbIFH3MgafY4vniBeDkVBiWlpbv/87lydHQ48eP8eLFC5ibm6NSpUrZpiMSFocHhM0Hcth8irFPDgeejBmRlRWwfbswQSQqChgwQL3djWrVqgVAaH3JbWvA3Fo8X75Mn+TUvbv6dReJE1ayCpTyI/E65CXwLFlSaBlWKtNbILPTpEkTAMLYzdevX+eYVhzfWalSpSwX+r90SZgAZmMjrAWpLiLCzZs3AXycgafqIvIyvXW3Hz58GIDwxS+n1v3du4Hr1wFbW+C773RaBcYKPA48GTMye3uhFcvcHNi1K32ST048PDzg4+MDIspxPc/ExERp4k92gef69UIAFRgIaNNoKQaeBaHFE1DdyjIvevUSfq5cmfOXBTc3N6nbXAxcsiOO78yum33bNuFnmzaaTQB79uwZYmNjYW5ujjJlyqh/Yj6WMfA0NYW0iLw+1/IUnz/xy0RWMrZ2Dh0KvF9ylDH2HgeejOUDFSsCEyYIv48YIXx45iYwMBBAzt3twcHBICK4uLjAzc0t03GlUhh/Bmg+qUgkdrUXtBbPvAaenTsLLdZ37wJXruScVuxuP3DgQI7pxC8RWU0sIhLWgwSEmdKaEL8cFC9eHOYfyWBDcfcicWJbVjPbnz59qrPylEoljr6fBZhT4Ll3r7A7mY1N+tqdjLF0HHgylk/88IOwTmRMjLBrUG5d7uqM8zx37hyA7Ge0794N3LkjtJ516aJ5nYmowHW1ixOM8hp4OjoKk8MAYPz4nJ+vjOM8KZuE0dHROHHiBADg888/z3T8zh1hq05LS6BlS83qWtCeI3WILZ6R77cByzizXWwxPn78uM7Ku3HjBt68eQN7e3tpVYkPyeXCVrMAMGSIsIIFY0wVB56M5RNmZkK3rYWFsA93Lo1jKoFndsHM8vfNmV9ksTE0EfD778LvQ4ZoNwEiIiICcXFxMDExyfdreIrE2civX7+WWsu09csvwvO1Z48wZCE7devWhbW1NV6/fp3tYvJ79+6FXC5H2bJlpT3eMxK72Zs2FYZnaKKgDYdQR8audkC1xbNVq1YAgGPHjiExMVEn5Ynd7A0bNsy21XjpUqEFvHBhYOxYnRTL2EeHA0/G8pHSpYFhw4TfR48WWlCyU6VKFVhYWCAyMlIKLDK6cuUKrl27BgsLC/TIYgr0gQNCl6C1tbCXvDbEcn18fKSZxPmdvb09fH19AeRtghEAlCsnBJ+AMHs5IiLrdJaWlmjYsCGA7Ge373i/KGh7sRn1A9u3Cz81mVQkKmjDIdQhBp4xMTFIS0uDuDfCw4fCeq0+Pj5ISUnBsWPHdFJebuM7Y2LSt1QdP17YqYwxlhkHnozlMz//DBQqJHStiuMvs2JpaSl1yc6fPz/T8SVLlgAAOnToIH1IizK2dg4cCGQx/FMtBWkppYx0Nc4TAP73P6BSJeDNG2F8bnaaN28OANizZ0+mY8nJydi3bx8AoF27dpmOP34szJI2NQXattW8jh9jV7uTkxNM3m8D9ObNG9SsKdx/9ixAJJNaPffu3ZvnspKTk3Hq1CkA2Qeef/wBREYKu5MNGJDnIhn7aHHgyVg+4+yc3nLy669ATqsljR49GgCwdOlSaawbAMTHx2PdunUAgP79+2c67/hx4QPa0lJoWdVWQQ1oxHGeeW3xBITVCJYvFxaW37BBWNszK23btoWJiQmOHz8ujeUUHTlyBPHx8fD09ET16tUznSu2djZoAHzwHSJXaWlp0hahBe0LQk5MTU1RqFAhAEJ3e7VqQuv9mzfAvXtQCTyzG4qirnPnziEpKQkeHh7S7lcZhYYCs2cLv8+YwYvFM5YTDjwZy4cGDRLWioyIAKZOzT5d48aNUb16dSQlJWHu3LnS/Zs2bUJcXBxKlCghdfFmJObZt2/6MjTaKKhjB3XZ4gkAAQHC0jkAMGlS1mmKFy+OAe+bwr777jsoFArp2Pb3kWW7du2ynAQmju/Upps9NDQUcrkcNjY2KJqXJzsfyjjO08JCmJwHCFuKfv7557C0tERoaCju3buXp3LEbvbGjRtn+fxMmSLsQNa4sbARBGMsexx4MpYPWVgA06cLv0+fDmQXH8lkMowZMwYAMG/ePGkbyKVLlwIA+vXrJ3VHiu7fFxaMl8nyvtxLQR07mDHwzGtrmOjHH4WWrpMngey2ZZ8wYQIcHR1x7do1rHy/36ZCocCuXbsAZD2+88ED4P3iBMiiFz5X4nNUsmTJTK+Fgu7DCUaffSbcf+oUYGtrK33pykt3e3x8PNauXQsg62728HDg33+F38eP13znL8Y+NR/XuxBjH5EvvwS++AJISwP69RN2ZclKu3btULp0aURHR2PgwIEIDAzEuXPnYGpqil7iKucZLFgg/GzTBsjLRHSlUolHjx4BKHgtnmXKlIGJiQnevXuHly9f6iRPT8/0ReWnTMk6jaurK8a9H0cxduxYPHr0COvWrUNkZCScnZ1Rv379TOdMniyMyW3TRrO92UUFdTiEOj4MPOvVE+4/fVr4qYtxnj/++COePn0KHx8fdMxiAdVp04T/0YYN08tnjGWPA0/G8imZTAgSHRyACxeAv//OOp2JiQl++uknAMD69etx/vx5mJubY9KkSdK+5KK4uPTWGbFrWFvPnj1DcnIyzM3N4ePjk7fMDMzKygolS5YEoJtxnqIffxTGeu7ZA7zfGj2ToUOHomTJknj9+jX8/f3R8/3K/W3atMm0TM+jR8D7xjb89pt2dSqowyHU8WHgGRgoXP/QUGE9TzHwPHXqFN68eaNx/kePHsXChQsBCEuTfbhN5suXwPs5fPj1Vy0fBGOfmMybATPG8g1PT6FFZeBAYbb7l18Cfn6Z03Xr1g1LlizB8+fP0a9fP/Tv3x/u7u6Z0q1eLQSfpUsDOWy+ohYxoClRokSW+4rndxUqVMCDBw9w69YtNG3aVCd5+vsDnToBGzcK42izWtvTwsIC8+bNQ+vWrQEARYsWRYkSJfCjuPJ4Bn/8IbR0t2oFZDHnSC0FdTiEOj7cvcjeHqhaVdhJ6vRpoGvXkvD398fDhw/h5+eHnj17ok2bNlAoFEhKSkJSUhKSk5ORnJwMV1dXlCxZEr6+vpDL5Xj79i369OkDABg0aBAaNWqUqfwZM4CUFKBOHSCLNf8ZY1mhfCwmJoYAUExMjLGrwpjRKBRE9esTAUTVqhHFx2uXj1JJVLaskM/cuXmv14IFCwgAtW3bNu+ZGcH48eMJAHXv3l2n+V67JlxjExOiy5ezT5eYmEhpaWnZHg8JITI1FfI6f177+nh7exMAOnPmjPaZ5FMzZ84kABQUFCTdN2KEcM0GDxb+PnnyJPn7+xMArW6+vr4UFxeXqezQUCJra6GsffsM9IAZy6c0idcKXjMFY58YExNgxQqgZk3g6lWgRw9gyxbhfk0cOQIEBwvbY2Yx9FNjBX3soLjtobg/uq5UqSLs475pExAUJDxntraZ01lbW+eYz+TJQmtn8+bps7U1lZSUhPDwcACfRlc7IEwwmjMnfZznZ599hnv37uHo0aNYvHgxgoODYW1tDWtra1hZWcHa2hoWFhZ49eoVQkJC8PLlS8hkMtjb28PHxwdLlizJ1MWuVAJ9+gBJScK4zvdLtDLG1MCBJ2MFgJ8fsGMH0KiRsKbj2LE5L7P0oagoQFzOs1cvYdxoXhX0sYPiepn3799HbGwsHHRxUd5buFCY2f7gATByZPo4QHXt3Jm+eYC4pqs2QkJCQERwcnLKtInAx0B8TBEZtowSJ/jcugVERws7CJmYmKBJkybZLv6eUUpKCszNzXNcAWDhQuDoUWHd0OXLeSY7Y5rgyUWMFRB166YHI3/+KcycVmcloLQ0YdxhaChQogQwcaJu6nP//n0AwgzxgsjNzQ3e7/dZvHLlik7zLlRIGE8rkwn7d2/dqv65Dx4A7+cbYcQIYfygtjJ+Ochq/cmCTpzUJgbYAFCkiDDWlij7Za1yYmlpmWPQGRIiTCIDhC9/BfR7F2NGY5DAc/78+fD19YWVlRVq1aqFixcvGqJYxj46pUtfhp+fEH2OHSsEJtktswQAly9fhp/fDhw/Lky82LVLCIpySt+oUSNcvnw5x3okJydLu+EU1MAT0Ky7Xd1rI7K3vwwvL2FKeo8eQitZTl8ULl++jAYNWqFlyyTExgotd+JartrW52OeWASkr00aFxeHV69eSfeXLy/s4jVwYDKeP889H3Wf27AwYRhFYiLg5HQNtWur91pgjKXTe+C5ceNGfP/99/jtt99w9epVVK5cGc2bN1fpGmGMqWfVqlV48qQvPvtM2Mrm77+Br74CLl9WDWqIgP37gS++cMbz5+0AKLF2LVCuXO75Hzt2DKtXr84x3aNHj6BUKuHo6Ag3bTd6zwc0CTzVvTYZ04eF9YaPz10kJQGDBwuz00NCsk7/xx/ncPLkBDx+bA13d2GMaE5bL6pTn4I+Djc3lpaW8PX1BZDeAg8Azs5zATzGs2dWaNwYeP0653zUuZabNwOVKwtjdi0tExEd3QFr16r3WmCMpZMR6WjbjmzUqlULNWrUwLx58wAIi057eXlh2LBh+N///pfjubGxsXB0dERMTIxOx18xVpA8ffoUUVFRkMlkaNmyJSIiIuDm5oaRI89j3DgfyOXC90d/f2Fiy7NnyQgPB549s3qfQwrs7CbgxImvQERwcXFRWXczu/z37duXZXoA2LJlCzp16oRatWrh/PnzBroSunf06FE0btwYPj4+CA0NzXRc02uTVXpX1yLo2fMS5s3zREqK8FyVKSNMSCGKxrt3ybh/3wYXLwrvcTJZPJYufY7KlePz/FzVr18fp06dwrp16/D111/r6SoaV6tWrbBv3z5MnjwZzZs3z3BtrGFicgpKpRe8vZPRrl0y6tRxQokSgKMjEBMTjpSUSFhZAa1aqV7L1FTA3NwVSqUXDh8G9u0TdkMCgAoVEvDixed4+/ZSrv8njH0qNIrX9De5niglJYVMTU1p+/btKvf37NmTvvjii0zpk5OTKSYmRrqFh4fzckrsk4cMS7vIZDKVn0AtAjZIy7qo3uIJ+IuAohnSCzf188+cnojo999/JwDUq1cvA10F/YiOjpYeY0RERKbjml6bnNOXJeCgtERS5lsKAXMJcNfZc+Xm5kYA6NKlS7q/ePnEyJEjMy2BlH5NShDwLJvrLd5SCYh6f4shICmbdAoCfifATO3/E8Y+FZosp6TXrvaoqCgoFAoUKVJE5f4iRYqojMcRTZkyBY6OjtLNy8tLn9VjrEBYs2aNtEA7ve+gEH+amV3BmjVyvH4tLFY+ezYwePAZmJi0AOAN4HsALzKkN8OaNWs0yD9zegC4d+8egII9vhMAHB0dUbp0aQBZd7drem1yTv8Qa9ZEICpK6EYfOhRo0uQBZLK/APwCoAyA4QBeaZm/avrXr18jIiICMpkM5XIbY1GAic9f5cqVM10bIARAdZiYjELDho8QGAgUKyas6iDEjABgDqDw+5sDACsp70KFhE0bFiwAZs3aBTOzCQDkav+fMMayoJfQ973nz58TADp79qzK/T/88APVrFkzU3pu8WQsa1euXMnUqgOArly5YpT0AQEBBCBTb0ZB1L17dwJAEyZMyPJ4frv26qY/ePAgAaBSpUppcDUKnqNHjxIAKlGihEbXUqEgOnnyGgGe71ujyxJQkgBvOnbsOsnlmcvS9Lli7FORb1o8XVxcYGpqitcfjOx+/fp1ltv5WVpawsHBQeXGGEsnLvOS03Iv+k5PRB9Niyeg/gSj/HDtNUl/4/1m8ZUrV1Yrv4JKbPF88uQJUlNTAah3LU1MAFtbJYDnMDG5DyAYJiaPAYTBwUEBU9Psy9T0uWKMpdPrf42FhQUCAgJw5MgR6T6lUokjR44gMDBQn0Uz9lFxc3ODu7s7AgICsGjRIgQEBMDd3T3bGeX6TP/8+XMkJCTAzMwMJUqU0OnjNIaMgSdlMdcyP117TdKLgWelSpXUvhYFkYeHB+zs7KBUKpGYmJgvrj1jLHt6n9W+ceNG9OrVC4sXL0bNmjUxe/ZsbNq0Cffu3cs09vNDPKudsXQpKSmwsLCATCYDESE1NRWWlpYGT3/48GE0bdoUpUuXllo+C7KkpCQ4ODhALpcjLCwsy7Hl+eXaa5K+cuXKuHnzJnbt2oW2bduqcSUKrho1auDy5cvYtm0bWrVqZfRrz9inRpN4Te/9BF26dMGMGTMwbtw4VKlSBdevX8f+/ftzDToZY6osLS2l3WdkMlmuH3b6Sv8xdbMDwp7pFSpUAJB9d3t+ufbqpk9NTUVwcDCAj7/FE0jvbr9//36W10YulyMiIgLBwcEICQmBUqmUzs3uWqakpCApKSlTWZo+V4wxVQbZq33o0KEYOnSoIYpi7JMVFxeH1NRUFC5cWK/liIGn+GH/MahevTquX7+OS5cuoUOHDsauTp7du3cPaWlpcHR0lLYF/ZhlDDw/9PPPP2Pq1KkqwaaDgwOqVq2KMmXKoEiRInB1dcXz589x8+ZN3L17F5GRkUhISICFhQV+//13/CjukckYyzODBJ6MMf169eoVAgIC8OLFC1SsWBGNGjXCwIED9dIq+bG1eAJCV+3SpUvV2sFIF06dOoX+/fvj7du3sLW1hYuLCxYsWCCNN82rjOM7P8Y92j+UXeC5ZcsW/PHHH9Lfzs7OSExMRGxsLE6cOIETJ07kmG9qaip++uknREdHY/LkyZ/EtWRM3zjwZKyAIyL07dsXL168AADcunULt27dwurVqxEcHKzziQ8fa+AJCHt2E5FeA4yHDx/iyy+/xLt37wAAkZGRCA0NxahRo3Dy5EmdlHHz5k0AH/+MdlFWgWd4eDj69+8PAPjf//6H33//HWZmZkhLS0NwcDCuXLmCp0+fSuudurm5oVKlSqhQoQKKFi2KQoUKYcmSJfjpp58wZcoUxMXFYe7cuRx8MpZXeljOSWc0WReKsU/VggULCABZWlrSiRMnaNOmTVSuXDkCQEFBQTotKzY2Vlq78M2bNzrN25hSU1PJysqKANCDBw/0Vs6bN2/I39+fAFCtWrXo+vXrdPjwYTI3NycAdPr0aZ2U07RpUwJAS5Ys0Ul++V1CQoL0uoyMjCS5XE4NGjQgAFSjRg1KTU3VOu+FCxdKOxRt3LhRh7Vm7OORb9bxZIzp17179zBq1CgAwJ9//on69eujU6dOWLFiBUxMTLBu3Trs379fZ+U9ePAAgLCsTKFChXSWr7GZm5ujSpUqAHJfz1NbcrkcX331FR4+fAhvb2/s3LkTlStXRuPGjdGzZ08AwNSpU3VS1qeylJLIxsZGGst6584dDB8+HCdOnICtrS3WrVsHc3NzrfMeOHAgxowZAwCYM2eOTurL2KeMA0/GCrABAwYgKSkJTZs2xbBhw6T7a9SogeHDhwMABg0ahISEBJ2U9zF2s4vUXUheW+vXr8exY8dgZ2eH3bt3q6zs8eOPP0Imk2H37t24detWnsrJuFWmOFv/UyB2t3fu3BkLFiwAACxcuBAlS5bMc95Dhw6Fubk5zp49i8uXL+c5P8Y+ZRx4MlZA3b9/HydPnoSpqSmWLVuWaReV33//Hd7e3ggNDcXkyZN1Uubt27cBfFwz2kX6DDyJCLNmzQIgjDesWLGiyvFSpUrhq6++AiC0XOeF2Nrp7+8PGxubPOVVkIivyYiICNja2mLr1q3o0aOHTvL28PBA586dAQB///23TvJk7FPFgSdjBdSaNWsAAM2bN89y0XM7OzvMmDEDALB69eosd+XR1MGDBwEAderUyXNe+Y0YeF69ehVyuVyneZ86dQrXrl2DlZUVBgwYkGWa//3vfwCADRs24MmTJ1qX9alNLBKJz5+fnx/OnTun82WxxB6FDRs2ICIiQqd5M/Yp4cCTsQKIiKTAM6dWnTZt2sDa2hrPnj2TAhJtvXz5ElevXgUAtGzZMk955UelSpWCg4MDkpKScPfuXZ3mLbZ29uzZEy4uLlmmqVatGpo0aQKFQoFly5ZpXdanNr5TFBQUhAMHDuDatWuZWpR1oVatWqhZsyZSU1Pxzz//6Dx/xj4VHHgyVgCdOXMGoaGhsLe3xxdffJFtOmtrazRp0gQAsHv37jyVuXfvXgBCy9LHuPOYiYkJAgICAECn4/hCQkKwc+dOAMDIkSNzTNuvXz8AQgt1xgXPNXH27FkAQiD7KTEzM0OzZs3g6OiotzLEcdMLFy5EWlqa3sph7GPGgSdjBdDq1asBAB07dsx1HF+bNm0A5D3wFM8X8/sY6WOc59y5c0FEaNGiBcqWLZtj2i+++AIODg4ICwvTak3PJ0+e4PHjxzAzM8Nnn32mbZVZNjp16gQ3Nze8ePECR48eNXZ1GCuQOPBkrIBJSUnBpk2bAOTczS5q3bo1AODChQtaj01LSUnBoUOHVPL7GFWvXh2A7gLP+Ph4LF++HADw3Xff5Zre2tpamsSyatUqjcs7cuQIAKFb2N7eXuPzWc4sLCyksaNbtmwxcm0YK5g48GSsgNmzZw+io6Ph6emJBg0a5Jre09MTVatWBRFh3759WpV58uRJJCQkwN3dHVWrVtUqj4JAbPG8efMmUlJS8pzff//9h/j4eJQoUQJNmzZV6xxxTc/NmzcjMTFRo/IOHz4MANLwCqZ74uoDO3bs0PkkNMY+BRx4MlbAiJOKunXrBlNTU7XOyWt3+549ewAIrZ0fLtv0MfHx8YGbmxvS0tJ00pW6ceNGAEDXrl3V3mqxXr168PPzQ3x8PHbs2KF2WUqlUqpz48aNNa4rU0+DBg1QuHBhREVF6WyLU8Y+JR/vJwhjH6GYmBhpkk9QUJDa54mB54EDB5CamqpRmUQkBawfczc7AMhkMnz99dcAgHnz5uUpr+joaKmFuWvXrhrVQWz11KS7/datW4iMjIStrS1q1aqlWWWZ2szMzNCuXTsA3N3OmDY48GSsANm5cydSUlJQtmxZjZbLqV69Otzc3BAXF4dTp05pVOaDBw8QEhICc3PzT6ILd+jQoZDJZNi3bx8ePXqkdT47d+5EamoqypUrp/EOQuLY3UOHDuH58+dqnSN2s9evXx8WFhaaVZZpROxu37ZtGxQKhZFrw1jBwoEnYwXIhg0bAGjWdQsISwWJrZXbt2/XqExxIlPDhg0/iQkrJUuWRMuWLUFEmD9/vtb5ZOxm11SJEiVQr149KJVKrFy5Uq1zxIlFn8KXA2Nr1KgRnJyc8Pr1a5w5c8bY1WGsQOHAk7ECIioqSppZrk0wI86W3rBhg9rd7UqlUlrMXOz+/RSIu9QsX74c8fHxGp//5s0b6bnq0qWLVnXo27evVIfc1vRMTU3FiRMnAHDgaQgWFhb48ssvAQBbt241cm0YK1g48PxIpaSk4Pz581p9aCYnJyMiIgJPnz5FaGgodyXlE1u3boVcLke1atVQqlQpjc9v0qQJ3N3d8ebNG7Vntx8+fBhPnz6Fk5MTOnbsqHGZBVWzZs3g7++P2NhYrZY12rZtG+RyOapUqaLVcwUIa0ba29sjJCQk10ks58+fR2JiIlxdXTXu1mfaEf8fNm/erPG4aVZw3Lp1C2XLlkWfPn20+jxlmXHgmUFycrJG+1mnpaXpZP9rXUtJSUGrVq0QGBgIZ2dn1KlTBxMmTEBUVFSO5yUnJ2P06NGwt7dHkSJF4OvrCz8/P9jZ2aFq1aoYMmQIoqOjDfMg3ktISMDgwYNRvHjxT34GacZudm2YmZmhW7duAKB29+3SpUsBAN27d4e1tbVW5RZEJiYmGDp0KADg77//1ngXofXr1wPQ/rkCAFtbW+n83LbQPHDgAABhNvvHvOpAftKsWTO4u7vj5cuX0lqt+UFuDQVElO0yUESEe/fuYcOGDbhz547KsbS0NNy+fRvPnz//ZHZtSkpKQteuXXHv3j38+++/qF27Nu7fv6+Xsg4fPow///wT4eHhKvd/lEt2UT4WExNDACgmJsYg5Q0ZMoSsrKyoVKlS1LRpU/r+++/p1atXmeq0atUqat26NZmZmZGdnR3VqFGD+vTpQ6dOndK4TIVCQVevXqXp06dTu3btqFatWlS8eHFycXGhEiVKUM2aNalt27b0448/0qpVqygkJETl/Hfv3tHkyZNp7969pFQqSaFQULdu3QgAyWQyAiDd7O3tafz48RQdHZ2pHtevX6eKFSuqpLeysiILCwuV+ypVqkTPnz/X6nHu2bOHFi1aRCkpKdL9crmcVq9eTUeOHMl0zoULF8jf318q28PDgyIiIjQuOyfJycn09u1bUiqVREQUFhZGM2bMoJYtW9KPP/5IYWFhOi1PW8+fP5eez9DQUK3zuXnzJgEgc3NzioqKyjFtREQEmZubEwC6fv261mUWVDExMeTg4EAAaOPGjWqfd+PGDQJAJiYm9OTJkzzV4fz589L/4rt377JMk5KSQh4eHgSA1q9fn6fymGbmzp1LAMjT05OSkpIMVm5sbCz16dOHWrRoQRcvXiQi4b105syZZGtrSxUqVKAlS5ZQYmIihYWF0dKlS6l3795Uu3ZtcnZ2JgBkYWFBzs7O5OXlRWXLlqWAgAAqVKiQyvt9mzZtaPfu3fS///2PihQpIt0vk8nIx8eHfvjhB7p9+3am+j148IBGjRpFQ4cOpQkTJtCiRYvo2bNnBrs+ujJs2DACQEWKFCF3d3fpc/Srr76iUaNG0aJFi+jNmzcq5zx//pz++ecf6tChAzk5OVH9+vXp7du30vGUlBQ6ceIEPX78mIiE57J///7StTUxMaH27dvT2LFjqU6dOmRmZkZVq1al4OBgKY+kpCQ6ePAgnT17lsLDwyk+Pp7u379PBw4coJUrV9L8+fPpzz//pHHjxlFycrJBrpUm8RoHnhm0bdtW5Z8OADk7O9OyZcvo0aNHNGzYMLK1tc2UJuOtbdu2dPbsWdq9ezdNmjSJfvrpJzp48CAlJydTZGQkTZ06lUqUKEFWVlZkbW1NlpaWOeb34c3U1JRGjBhB0dHRdOLECfL29paOffbZZ9S3b18CQGZmZnTgwAF68uQJLVu2jKpUqaKSj6urK1WtWpXKlStH9vb20v1ubm60a9cuUigURCS8mT169Ig2bdokvfH4+PjQ7t27acGCBTRw4EAaPXo0bdmyhZ4/fy4FcERESqWSXrx4QUuWLKEyZcpIZVStWpXu3r1LoaGhVL9+fen+9u3b09OnT+nSpUvUo0cPMjU1JQBUrFgxKlmyJAGg1q1bq5TxocjISJo9ezZNnTqV5s2bR4sXL6ZffvmFvv76a2rRogX98MMPtGnTJtq8eTN16dKFbGxsCABZWlpSsWLFsrzenTt3prt372ZbZnJyMiUmJuruhZiFsWPHEgCqU6dOnvMSXwvz58/PMd2MGTMIANWoUSPPZRZUEyZMIABUunRpSktLU+ucoKAgAkCdO3fOc/lKpZIqVKhAAGjBggVZplm/fj0BIHd3d5UvdUz/kpKSpPeNOXPm6KWMP//8kzw8PGjYsGEUGhpKd+/eVXk/lclk1Lt3b6pVq1am9y9ra2uNPl/ELzlVq1bN1HABgGxtbaX35Yy3ihUr0vDhw2n9+vXUu3fvLNOYm5tTnz596OrVq3T79m06ceIEbdy4kaZOnUoDBw6kb7/9lmbNmkX79++n9evX03fffUcNGzakpk2bUvfu3WnUqFH0559/0ooVK+jIkSMkl8ulaySXy2nZsmU0ZMgQGj58OH3//fc0Y8YMOnToEIWHh9OOHTuoT58+VLp0afr8889p+PDh9M//27v36Jjv/I/j70lVSDBuCYu4K9YezQVBe2yokqpT2kW36yCOdam4rS5NrG2qq40Sag/qcrYN3XJQbGx2W5euSy9qZV16aJOsRJHGbSRnJ0TNROb9+8Mv39M0QqKZzyT1fJzz+WPm+535vJPvzHde38/3851Zt053796t6enpeuXKFT137pymp6drZmamOhwOTU1NtWrftWuXXrx4sdTnVUkLCAjQadOm6fvvv69DhgxRPz+/MuuEhYWpw+HQzMxMDQ8Pt+5v06aN9fqx2WwaFhZW7napX7++bt26VdeuXXvHz6ryWlUP1pSH4HmfXC6XZmVl6b59+/Tdd98t90XwyCOPaEJCgp46dUq//vpr/eCDD3TChAl3fLOVtHr16mmdOnXKXTZ06FBdunSppqSk6Oeff64nT57UTz/9VFNSUnTlypX64osvap8+fazHNGnSxNoxtGrVqkyATU5OLvW3FRcX65YtW0rtsH7Ynn32Wb18+XK5/5/s7GwrAJbXAgMDtVOnThoZGalNmjQptaxBgwbWEXXdunWt0aSAgACtVauWFZi//5hf//rXmp+fr19++aX1Ny5btqxM+HQ4HBofH6/16tWr9I72+81ms2m/fv100aJFOmDAAOv+WrVq6dy5c/XatWtWn5cuXdL4+Hi12+0aHByshw4dqtLXY4nNmzdbdWzatOlHP9+yZctURLRXr17lruPxeLRz584qIrp27dof3WdN5XQ6rdfshg0b7rl+dna29cFz7NixKqnhrbfesj687nTQ1bdvXxURffXVV6ukP1TOmjVrVOT2qFhhYWGVPverr75aav9Uq1YtK0y2bNlSn3/++TL72LfffluTkpK0TZs2KnJ7BK1Pnz46f/583bp1q3755ZfqcDj0/Pnzmp6ermlpabp//35NTU3VI0eOWAcvmZmZ+tvf/laDgoI0Ojpad+zYoW63W4uLi/XKlSu6Y8cOHTZsWJl9dkkbMmSIzps3TydNmlTqs6uqWufOnXXTpk16+PBhjYiIqPLnL2kzZsywtkdRUZF++OGHunz5cp01a5Z27979jo+JjIzUBQsW6Pbt2zUoKEhFRDt27GgNXAUGBpb6v7Vt21YPHDigqqqnTp3SmTNn6tixY/Wdd97Ro0eP3jHwBgcHa+vWra3nCQwM1G7duumTTz6pzz33nI4dO1anTp1aarTVmwieVaSoqEiXLFlivdGjo6N1z5495Y64ZWRk6K9+9SvrVMfo0aM1JibGGqIXEQ0PD9fk5GT95ptvrOZ2uytc0+7du/WRRx6xnm/8+PFaUFCgOTk5OmHCBA0MDNRFixaV+3iPx6N5eXl64sQJTU1N1T179mh6erpev369Qv1fvnxZhwwZoi1bttSnnnpK4+LidPLkyfroo4/e8UjPz89Pu3btqkuXLlWn06m5ubk6aNAga3mfPn00KytLT548qY8//riK3D4yHjNmjHUKqcTKlSutx9ntdg0PD9devXpZb+ySFhYWpjExMTpixAgdOnSoTp48WRcvXqxr1qzRKVOmaHh4uHbp0kXnzJmjR44c0Rs3buiZM2f00KFDZaYRnDhxotRIeOPGjbVbt24aGhpa5kDC399ft27dWuFtWRGfffaZFbh/97vfVclzXrp0yTpIKu8UesloZ0BAgM/ef9XFokWLVES0Xbt293yvTp06VUVEBw8eXGX9OxwO67X23nvvlVp29OhR6z1z8eLFKusTFedyubRt27YqIpqYmFjpx1+4cEH37dunqampumXLFk1JSdEDBw5oXFyctW+ZNWuWPvHEE9bt/v37W4MEhw4d0gEDBuioUaM0JyfHet6ioiI9duxYuVM0qsqVK1d0y5YtGhsbq2FhYfrMM8/o4cOHy6x36NAhHTZsmPr7+2vjxo21U6dO+thjj+no0aN1/vz5+oc//EGfe+457dq1q/bq1UunTZumycnJumHDBl28eLH+/ve/1zFjxuigQYOs6QLfb3a7XV966SWdN2+ezpkzR0eMGGENlLRp00anT5+uqampmpycrLNnz9bo6Gjt1q2bNQDi7++vjRo1sm6XfF7f7WyWx+PRvXv36pAhQ7Rr164aHx+vmZmZpdb5+uuvrakwJdvu22+/1WvXrlmnxgsKCu76P3a73Tpr1izrAOfPf/6zNbXj1q1b6nQ673om0ASCZxW7ePGiZmVl3ffjS+ZxHj9+vEpeHC6XS9etW6cffvhhmWW+fPHduHFDT58+rfv379cPPvhA//Of/9zxTVtcXKzJycm6atWqUqcvPR6Pfvrpp2Xm1X5/+eTJk8s9Mg0LC9OUlBSv/A9SU1O1Xbt2dzyy3bZtW6lwmpiYWCU1nDlzRps2baoiosOHDy91aunHGjZsmIqItmjRotTcIVXVjRs3Wn/L0qVLq6zPmur69esaHBysIqJr1qwpd71Lly5ZAbFk9KKqvPHGGyoi2rRpU3U4HNb948ePVxHR3/zmN1XaHyonOTnZOtC+1xSWEh6PR9etW1dmHv0PW1JSkvWYtLQ03bhxY4WnffxUOZ1OXbhwoTZs2FBFRMeMGVPu54bL5brn/rhkalmJoqIidTgcVfZ/Pn36tA4bNkyXLFnyo/bj2dnZVT6qXlUInvhJKyws1JMnT2pKSoru2LFDjx07ZuR0wnfffaeff/65fvzxx/rRRx9pWlqatUO7deuWNRFdRPSFF174UTuImzdvao8ePVRENCIiosIj0hV18eJF7datm3XK5siRI3rmzBndsmWLdUHRzJkzfX4UXV0sX75cRW7Pf3vnnXfKLL9x44Z1UV/v3r2r/P/mdrutuZ7jxo1T1dsHJiWj4d6a5oGKKS4u1kmTJlnv//j4+Lu+Bm7cuGEdNJSMpvfo0UP79eunkZGR2rlzZ+3YseNdD3Rw+8Kc06dP+7oMKMET8JlVq1ZZc27CwsL0T3/6k06ZMkXHjh2rn332WYWfZ8aMGdap/XPnznmlVofDUeais5I2atSoMqMAD7KbN2/q008/XWqKy8mTJ/Xy5cv6ySeflJr+cqczEVXhiy++sOZ1Dxw40JouERERwQFCNeDxePS1116zXgfDhw8vNTpd4sCBA9ZBn5+fnyYmJvJeQ41H8AR86MCBA2XmnZZ8yLz22mv3PNWyfft26zGpqalerTU/P9+6iMrf319DQkJ0/Pjxxr6CoyYpLi7WhQsX3nEus8jtr/vauXOnV2uIjY0t1We/fv30q6++8mqfqJy//OUv1lmD5s2b686dO/X48eO6e/dufeGFF6xt17RpU/344499XS5QJSqT12yq1fAb0P9fQUGB2O12cTqd0qBBA1+XA1TY+fPn5Y033pCioiJp2bKl/Pe//7V+u/uXv/ylzJs3TwYMGCC1atUSVZXs7Gz517/+Jbt27ZJdu3bJzZs3Zc6cObJ48WIj9d64cUPq1q1bqd9/f1Dt27dPXn75Zfnmm28kLy9PbDabxMTEyLJly6Rhw4Ze7bugoEBmzJghjRo1kokTJ8rPf/5zr/aH+3P8+HEZPXq0pKenl1lms9lk0qRJ8vrrr0uTJk18UB1Q9SqT1wiegCHvvfeeTJ06VQoLC0VEpFmzZhIaGipHjx4t86tSTz75pPzzn/+Uhx9+2BelooJu3bolbrdbAgICfF0KqpnvvvtO4uLi5N1335XAwEAJDg6WDh06yPz58yUiIsLX5QFViuAJVFNZWVmybNky2bp1q+Tl5Vn3165dW3r27CnR0dHy1FNPSVhYGD99CACoEQieQDXndrtlz549kpOTI+Hh4RIaGir+/v6+LgsAgEqrTF6rZagmAN9Tu3ZtGTp0qK/LAADAKM7lAQAAwAiCJwAAAIwgeAIAAMAIgicAAACMIHgCAADACIInAAAAjCB4AgAAwAiCJwAAAIwgeAIAAMAIgicAAACMIHgCAADACIInAAAAjCB4AgAAwAiCJwAAAIwgeAIAAMAIgicAAACMIHgCAADACIInAAAAjCB4AgAAwAiCJwAAAIwgeAIAAMAIgicAAACMIHgCAADACIInAAAAjCB4AgAAwAiCJwAAAIwgeAIAAMAIgicAAACMIHgCAADACIInAAAAjCB4AgAAwAiCJwAAAIwgeAIAAMAIgicAAACM8FrwfP3116Vv374SEBAgDRs29FY3AAAAqCG8FjzdbreMHDlSXnzxRW91AQAAgBqklreeeMGCBSIisn79em91AQAAgBrEa8HzfrhcLnG5XNbtgoICH1YDAACAqlStLi5KTEwUu91utZCQEF+XBAAAgCpSqeAZFxcnNpvtri0jI+O+i4mPjxen02m1nJyc+34uAAAAVC+VOtX+0ksvSUxMzF3Xad++/X0X4+/vL/7+/vf9eAAAAFRflQqeQUFBEhQU5K1aAAAA8BPmtYuLzp8/L/n5+XL+/HkpLi6WEydOiIhIx44dpV69et7qFgAAANWU14LnK6+8Ihs2bLBuh4WFiYjI/v37JSoqylvdAgAAoJqyqar6uojyFBQUiN1uF6fTKQ0aNPB1OQAAAPiByuS1avV1SgAAAPjpIngCAADACIInAAAAjCB4AgAAwAiCJwAAAIwgeAIAAMAIgicAAACMIHgCAADACIInAAAAjCB4AgAAwAiCJwAAAIwgeAIAAMAIgicAAACMIHgCAADACIInAAAAjCB4AgAAwAiCJwAAAIwgeAIAAMAIgicAAACMIHgCAADACIInAAAAjCB4AgAAwAiCJwAAAIwgeAIAAMAIgicAAACMIHgCAADACIInAAAAjCB4AgAAwAiCJwAAAIwgeAIAAMAIgicAAACMIHgCAADACIInAAAAjCB4AgAAwAiCJwAAAIwgeAIAAMAIgicAAACMIHgCAADACIInAAAAjCB4AgAAwAiCJwAAAIwgeAIAAMAIgicAAACMIHgCAADACIInAAAAjCB4AgAAwAiCJwAAAIwgeAIAAMAIgicAAACMIHgCAADACIInAAAAjCB4AgAAwAiCJwAAAIwgeAIAAMAIgicAAACMIHgCAADACIInAAAAjCB4AgAAwAiCJwAAAIwgeAIAAMAIgicAAACMIHgCAADACIInAAAAjCB4AgAAwAiCJwAAAIwgeAIAAMAIrwXPs2fPyoQJE6Rdu3ZSt25d6dChgyQkJIjb7fZWlwAAAKjGannriTMyMsTj8cjatWulY8eOcurUKZk4caIUFhZKUlKSt7oFAABANWVTVTXV2ZIlS2T16tVy5syZCq1fUFAgdrtdnE6nNGjQwMvVAQAAoLIqk9e8NuJ5J06nUxo3blzucpfLJS6Xy7pdUFBgoiwAAAAYYOzioqysLFmxYoVMnjy53HUSExPFbrdbLSQkxFR5AAAA8LJKB8+4uDix2Wx3bRkZGaUek5ubK9HR0TJy5EiZOHFiuc8dHx8vTqfTajk5OZX/iwAAAFAtVXqOp8PhkLy8vLuu0759e6ldu7aIiFy4cEGioqKkd+/esn79evHzq3jWZY4nAABA9ebVOZ5BQUESFBRUoXVzc3Olf//+EhERIcnJyZUKnQAAAPhp8drFRbm5uRIVFSVt2rSRpKQkcTgc1rLmzZt7q1sAAABUU14Lnnv37pWsrCzJysqSVq1alVpm8BucAAAAUE147dx3TEyMqOodGwAAAB48TLoEAACAEQRPAAAAGEHwBAAAgBEETwAAABhB8AQAAIARBE8AAAAYQfAEAACAEQRPAAAAGEHwBAAAgBEETwAAABhB8AQAAIARBE8AAAAYQfAEAACAEQRPAAAAGEHwBAAAgBEETwAAABhB8AQAAIARBE8AAAAYQfAEAACAEQRPAAAAGEHwBAAAgBEETwAAABhB8AQAAIARBE8AAAAYQfAEAACAEQRPAAAAGEHwBAAAgBEETwAAABhB8AQAAIARBE8AAAAYQfAEAACAEQRPAAAAGEHwBAAAgBEETwAAABhB8AQAAIARBE8AAAAYQfAEAACAEQRPAAAAGEHwBAAAgBEETwAAABhB8AQAAIARBE8AAAAYQfAEAACAEQRPAAAAGEHwBAAAgBEETwAAABhB8AQAAIARBE8AAAAYQfAEAACAEQRPAAAAGEHwBAAAgBEETwAAABhB8AQAAIARBE8AAAAYQfAEAACAEQRPAAAAGEHwBAAAgBEETwAAABhB8AQAAIARBE8AAAAYQfAEAACAEQRPAAAAGEHwBAAAgBEETwAAABhB8AQAAIARBE8AAAAY4dXg+cwzz0jr1q2lTp068rOf/UzGjBkjFy5c8GaXAAAAqKa8Gjz79+8vW7dulczMTNm+fbtkZ2fLiBEjvNklAAAAqimbqqqpzv7+97/L8OHDxeVyycMPP3zP9QsKCsRut4vT6ZQGDRoYqBAAAACVUZm8VstQTZKfny8bN26Uvn37lhs6XS6XuFwu67bT6RSR238QAAAAqp+SnFahsUz1srlz52pAQICKiPbu3VuvXr1a7roJCQkqIjQajUaj0Wi0GtZycnLumQsrfao9Li5O3nzzzbuuk56eLl26dBERkatXr0p+fr6cO3dOFixYIHa7Xf7xj3+IzWYr87gfjnh6PB7Jz8+XJk2a3HF9VF5BQYGEhIRITk4O0xdqILZfzcc2rPnYhjUf27Bqqapcu3ZNWrRoIX5+d798qNLB0+FwSF5e3l3Xad++vdSuXbvM/d9++62EhITIoUOHpE+fPpXpFlWEebM1G9uv5mMb1nxsw5qPbeg7lZ7jGRQUJEFBQffVmcfjEREpNaoJAACAB4PXLi7697//LWlpafL4449Lo0aNJDs7W/74xz9Khw4dGO0EAAB4AHntezwDAgJkx44d8sQTT0jnzp1lwoQJ0r17dzl48KD4+/t7q1vcg7+/vyQkJLANaii2X83HNqz52IY1H9vQd4x+jycAAAAeXPxWOwAAAIwgeAIAAMAIgicAAACMIHgCAADACIInxOVySWhoqNhsNjlx4oSvy0EFnT17ViZMmCDt2rWTunXrSocOHSQhIUHcbrevS8NdrFq1Stq2bSt16tSRyMhIOXLkiK9LQgUlJiZKz549pX79+hIcHCzDhw+XzMxMX5eF+7Ro0SKx2Wwya9YsX5fyQCF4QubOnSstWrTwdRmopIyMDPF4PLJ27Vr56quv5K233pI1a9bIvHnzfF0ayrFlyxaZPXu2JCQkyLFjx+TRRx+VwYMHy5UrV3xdGirg4MGDEhsbK4cPH5a9e/dKUVGRDBo0SAoLC31dGiopLS1N1q5dK927d/d1KQ8cvk7pAffRRx/J7NmzZfv27dKtWzc5fvy4hIaG+ros3KclS5bI6tWr5cyZM74uBXcQGRkpPXv2lJUrV4rI7V9zCwkJkenTp0tcXJyPq0NlORwOCQ4OloMHD0q/fv18XQ4q6Pr16xIeHi5vv/22LFy4UEJDQ2X58uW+LuuBwYjnA+zy5csyceJE+etf/yoBAQG+LgdVwOl0SuPGjX1dBu7A7XbL0aNHZeDAgdZ9fn5+MnDgQPniiy98WBnul9PpFBHhPVfDxMbGytNPP13qvQhzvPaTmajeVFViYmJkypQp0qNHDzl79qyvS8KPlJWVJStWrJCkpCRfl4I7uHr1qhQXF0uzZs1K3d+sWTPJyMjwUVW4Xx6PR2bNmiWPPfaY/OIXv/B1OaigzZs3y7FjxyQtLc3XpTywGPH8iYmLixObzXbXlpGRIStWrJBr165JfHy8r0vGD1R0G35fbm6uREdHy8iRI2XixIk+qhx4cMTGxsqpU6dk8+bNvi4FFZSTkyMzZ86UjRs3Sp06dXxdzgOLOZ4/MQ6HQ/Ly8u66Tvv27WXUqFGSmpoqNpvNur+4uFgeeughGT16tGzYsMHbpaIcFd2GtWvXFhGRCxcuSFRUlPTu3VvWr18vfn4cT1ZHbrdbAgICZNu2bTJ8+HDr/nHjxsn//vc/2blzp++KQ6VMmzZNdu7cKZ988om0a9fO1+WgglJSUuTZZ5+Vhx56yLqvuLhYbDab+Pn5icvlKrUM3kHwfECdP39eCgoKrNsXLlyQwYMHy7Zt2yQyMlJatWrlw+pQUbm5udK/f3+JiIiQ999/n51mNRcZGSm9evWSFStWiMjt07WtW7eWadOmcXFRDaCqMn36dPnb3/4mBw4ckE6dOvm6JFTCtWvX5Ny5c6XuGz9+vHTp0kVefvllpkwYwhzPB1Tr1q1L3a5Xr56IiHTo0IHQWUPk5uZKVFSUtGnTRpKSksThcFjLmjdv7sPKUJ7Zs2fLuHHjpEePHtKrVy9Zvny5FBYWyvjx431dGiogNjZWNm3aJDt37pT69evLpUuXRETEbrdL3bp1fVwd7qV+/fplwmVgYKA0adKE0GkQwROoofbu3StZWVmSlZVV5mCBExnV0/PPPy8Oh0NeeeUVuXTpkoSGhsquXbvKXHCE6mn16tUiIhIVFVXq/uTkZImJiTFfEFADcaodAAAARnAVAgAAAIwgeAIAAMAIgicAAACMIHgCAADACIInAAAAjCB4AgAAwAiCJwAAAIwgeAIAAMAIgicAAACMIHgCAADACIInAAAAjCB4AgAAwIj/A51vfkKQCPWzAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "x_test = torch.linspace(-5,5,200).reshape((200, 1))\n",
    "means, variances = model.predict(x_test, num_samples = 1000)\n",
    "\n",
    "mean = torch.mean(means, -1)\n",
    "var  = torch.mean(means**2 + variances, -1) - mean**2\n",
    "\n",
    "plot_predictive_dgp(mean, var, \"Pred. Dist. DGP\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "aagVcFV1yJJ9"
   },
   "source": [
    "Now we do the same for each layer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 545
    },
    "id": "ebWxJLK1yNHo",
    "outputId": "24486da3-396c-4732-b4cd-9ab6238f3a3a"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_325420/3428919590.py:20: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
      "  f.show()\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# First layer\n",
    "\n",
    "x_test = torch.linspace(-2,2,200).reshape((200, 1))\n",
    "with torch.no_grad():\n",
    "  with gpytorch.settings.num_likelihood_samples(1):\n",
    "    pred = model.hidden_layer(x_test)\n",
    "\n",
    "mean = pred.mean.mean(-1).T\n",
    "var  = pred.variance.mean(-1).T\n",
    "plot_predictive_dgp(mean, var, \"Pred. Dist. First Layer\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 545
    },
    "id": "U7F1-UM3yR_3",
    "outputId": "db9e29e0-3f35-4daf-b7fb-5601fb187757"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_325420/3428919590.py:20: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
      "  f.show()\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Last layer\n",
    "\n",
    "x_test = torch.linspace(-2,2,200).reshape((200, 1))\n",
    "with torch.no_grad():\n",
    "  with gpytorch.settings.num_likelihood_samples(1):\n",
    "    pred = model.likelihood(model.last_layer(x_test))\n",
    "\n",
    "mean = pred.mean.T\n",
    "var  = pred.variance.T\n",
    "plot_predictive_dgp(mean, var, \"Pred. Dist. Last Layer\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TOmMMldXyYMw"
   },
   "source": [
    "## **Capturing Input Dependent Noise**\n",
    "\n",
    "In this section of the notebook the goal is to DGPs to capture input dependent noise, using high values of alpha. For this, we consider a simple toy dataset similar to the one described in (https://arxiv.org/pdf/1605.07127v1.pdf)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 545
    },
    "id": "lU_k0R5NzMzw",
    "outputId": "9695a129-2c2d-48b5-fcd8-4b5bfe8b4a61"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f507c8a7ee0>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 1000\n",
    "\n",
    "# Training data are N points regularly spaced in the interval [-2,2].\n",
    "\n",
    "train_x_h = torch.rand(N) * 8 - 4\n",
    "train_y_h = 7 * torch.sin(train_x_h) + 3 * torch.abs(torch.cos(train_x_h / 2)) * torch.randn(N)\n",
    "train_x_h /= 4.0\n",
    "train_y_h /= 5.0\n",
    "train_x_h = train_x_h.reshape((N, 1))\n",
    "train_y_h = train_y_h.reshape((N, 1))\n",
    "\n",
    "\n",
    "# We plot the data for visualization\n",
    "\n",
    "# Initialize plot\n",
    "\n",
    "f, ax = plt.subplots(1, 1, figsize=(8, 6))\n",
    "\n",
    "# Plot training data as black stars\n",
    "\n",
    "ax.plot(train_x_h.numpy(), train_y_h.numpy(), 'k*')\n",
    "ax.set_ylim([-3, 3])\n",
    "ax.legend(['Observed Data'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "uhpn4IuT07o4"
   },
   "source": [
    "Now we train the model, first by we will try using DSVI."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "yvC-ejpr1Agh",
    "outputId": "4bba8894-3f58-495e-8238-5495b631a3ae"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 100/5000 - Loss: 3006.707907\n",
      "Epoch 200/5000 - Loss: 1739.332914\n",
      "Epoch 300/5000 - Loss: 1235.853076\n",
      "Epoch 400/5000 - Loss: 897.409916\n",
      "Epoch 500/5000 - Loss: 748.076677\n",
      "Epoch 600/5000 - Loss: 850.495815\n",
      "Epoch 700/5000 - Loss: 602.849662\n",
      "Epoch 800/5000 - Loss: 587.048233\n",
      "Epoch 900/5000 - Loss: 554.021955\n",
      "Epoch 1000/5000 - Loss: 541.680396\n",
      "Epoch 1100/5000 - Loss: 536.218941\n",
      "Epoch 1200/5000 - Loss: 523.750603\n",
      "Epoch 1300/5000 - Loss: 528.423727\n",
      "Epoch 1400/5000 - Loss: 519.804120\n",
      "Epoch 1500/5000 - Loss: 568.347633\n",
      "Epoch 1600/5000 - Loss: 515.129566\n",
      "Epoch 1700/5000 - Loss: 517.536461\n",
      "Epoch 1800/5000 - Loss: 516.944170\n",
      "Epoch 1900/5000 - Loss: 514.585674\n",
      "Epoch 2000/5000 - Loss: 512.180209\n",
      "Epoch 2100/5000 - Loss: 506.964743\n",
      "Epoch 2200/5000 - Loss: 510.726213\n",
      "Epoch 2300/5000 - Loss: 509.536564\n",
      "Epoch 2400/5000 - Loss: 513.230622\n",
      "Epoch 2500/5000 - Loss: 507.331729\n",
      "Epoch 2600/5000 - Loss: 513.834298\n",
      "Epoch 2700/5000 - Loss: 507.775605\n",
      "Epoch 2800/5000 - Loss: 509.540021\n",
      "Epoch 2900/5000 - Loss: 512.785316\n",
      "Epoch 3000/5000 - Loss: 508.763194\n",
      "Epoch 3100/5000 - Loss: 505.815983\n",
      "Epoch 3200/5000 - Loss: 508.442640\n",
      "Epoch 3300/5000 - Loss: 507.342637\n",
      "Epoch 3400/5000 - Loss: 510.713458\n",
      "Epoch 3500/5000 - Loss: 511.773527\n",
      "Epoch 3600/5000 - Loss: 510.171294\n",
      "Epoch 3700/5000 - Loss: 504.897118\n",
      "Epoch 3800/5000 - Loss: 507.609427\n",
      "Epoch 3900/5000 - Loss: 516.950130\n",
      "Epoch 4000/5000 - Loss: 507.958949\n",
      "Epoch 4100/5000 - Loss: 505.957663\n",
      "Epoch 4200/5000 - Loss: 516.973197\n",
      "Epoch 4300/5000 - Loss: 505.169630\n",
      "Epoch 4400/5000 - Loss: 506.919563\n",
      "Epoch 4500/5000 - Loss: 507.569253\n",
      "Epoch 4600/5000 - Loss: 511.019647\n",
      "Epoch 4700/5000 - Loss: 508.866489\n",
      "Epoch 4800/5000 - Loss: 509.059131\n",
      "Epoch 4900/5000 - Loss: 515.368521\n",
      "Epoch 5000/5000 - Loss: 511.456549\n"
     ]
    }
   ],
   "source": [
    "# We instantiate the model\n",
    "\n",
    "num_inducing_points = 10\n",
    "model = DSVIDeepGP(train_x_h, train_y_h, train_x_h.shape, 1, num_inducing_points)\n",
    "\n",
    "# We do the actual training\n",
    "\n",
    "train_dgp_dsvi(model, train_x_h, train_y_h, train_x_h.shape[ 0 ], 5000)\n",
    "#train_dgp_alpha(model, train_x_h, train_y_h, train_x_h.shape[ 0 ], 5000, alpha = 1e-3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "G0xCqPk-Wp8j"
   },
   "source": [
    "We plot the predictive distribution. In particular, we sample from it and plot the corresponding samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 545
    },
    "id": "ZypPAxzF36C2",
    "outputId": "d15c0801-4305-4416-c041-c368cb2511a3"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f507c4007f0>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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LgmVZKC0txWmnnYbly5fj6NGjOb/2z3/+czQ3NxulzbewWF9fb9fLmDFjUF9fjyuuuAKPP/544LxkgbsQIMGTIAiCIIgh4eKLL8aePXvw4osv4otf/CK+/vWv484771SmPXLkSGTXnTx5MiZMmBBZflGzfPly7NmzBzt27EBraysmTpyICy+8ELfffvtQFy1rSPAkCIIgCGJIKCsrQ21tLaZOnYrrr78eF154IdavXw9gUFt3++2346STTsKZZ54JAOjr68MVV1yBiRMnYvLkyfjIRz6Cnp4eO89jx47h5ptvxsSJE1FZWYmvfOUrYJJ2W55qP3z4ML761a9iypQpKCsrw2mnnYb77rsPPT09mDNnDgBg0qRJsCwLCxYsAAAMDAxgxYoVmDZtGsaMGYOzzz4bP/vZzxzX2bRpE8444wyMGTMGc+bMcZTTiwkTJqC2thannHIK3v/+9+O//uu/cMstt+BrX/saduzYYd/ntddea1//zDPPxKpVq+w8vv71r+OBBx7AL37xC1uD+sQTTwAAvvrVr+KMM87A2LFjceqpp+KWW27BO++8Y1S2bCHBkyAIghh+0PrMEcmYMWMcms3f/va32LFjBx577DG0t7fjnXfewUUXXYQJEybg97//PZ5++mmMHz8eF198sX3eXXfdhTVr1uBHP/oRnnrqKfz1r3/Fww8/7HndT3/60/jv//5v3H333di+fTu+//3vY/z48ZgyZQoeeughAMCOHTuwZ88eW7hbsWIFWltb0dLSgj/+8Y/4whe+gKuuugpPPvkkgLSA/LGPfQyXX345nnvuOfzLv/wL/vVf/zV03dx0001gjOEXv/gFgLTgW1dXh5/+9KfYtm0bvva1r2HZsmX4yU9+AgD40pe+hCuuuMLWKu/Zswfnn38+gLRgu2bNGmzbtg2rVq3CD37wA3znO98JXbYglOTlKgRBEAQRJbQ+M3dYVt7rlzGG3/72t3j00UexePFie/+4cePwwx/+EKWlpQCARCKBgYEB/PCHP4SV+fi4//77MXHiRDzxxBOYN28eVq5ciaVLl+JjH/sYAKClpQWPPvqo9tp//vOf8ZOf/ASPPfYYLrzwQgDAqaeeah+fPHkyAKC6uhoTJ04EkNaQfuMb38BvfvMbzJ492z7nqaeewve//31ccMEFuPfee/Gud70Ld911FwDgzDPPxAsvvIBvfvOboepo8uTJqK6utrWmo0aNwm233WYfnzZtGjo6OvCTn/wEV1xxBcaPH48xY8bg8OHDqK2tdeT17//+7/Z2fX09vvSlL2Ht2rX4yle+EqpsQSDBkyAIgiDCMgRCWs7J4/20t7dj/PjxeOeddzAwMIBPfvKT+PrXv24fP+uss2yhEwD+53/+Bzt37nStz+zv78dLL72EAwcOYM+ePTjvvPPsYyUlJYjH467pds5zzz2H4uJiXHDBBcbl3rlzJ/72t7/hgx/8oGP/kSNH8J73vAcAsH37dkc5ANhCalgYY7bADQD33HMPfvSjH2H37t04dOgQjhw5gnPOOcc3n3Xr1uHuu+/GSy+9hLfeegtHjx5FeXl5VmUzhQRPgiAIggjLSBM688ycOXNw7733orS0FCeddBJKSpxiybhx4xz/v/XWW4jFYnjwwQddeVVVVYUqw5gxYwKf89ZbbwEANm7ciJNPPtlxrKysLFQ5/Hjttdewf/9+TJs2DQCwdu1afOlLX8Jdd92F2bNnY8KECbjzzjvR2dnpmU9HRweamppw22234aKLLkJFRQXWrl1ra2ZzDQmeBEEQBEEMCePGjcNpp51mnH7WrFlYt24dqqurtRq6E088EZ2dnXj/+98PADh69ChSqRRmzZqlTH/WWWdhYGAATz75pD3VLsI1rseOHbP3NTQ0oKysDLt379ZqSmfMmGEbSnGeffZZ/5vUsGrVKhQVFdnukZ5++mmcf/75uOGGG+w0L730kqvsYrkB4JlnnsHUqVPxb//2b/a+3t7e0OUKChkXEQRBEAQxLGhqasIJJ5yAj3zkI/j973+PXbt24YknnsCSJUvw8ssvA0gb4fznf/4nHnnkEfzpT3/CDTfc4OmDs76+HldffTU+85nP4JFHHrHz5EY6U6dOhWVZaG9vx/79+/HWW29hwoQJ+NKXvoQvfOELeOCBB/DSSy+hu7sbq1evxgMPPAAA+NznPocXX3wRX/7yl7Fjxw78+Mc/xpo1a4zu8+DBg9i7dy/6+vrwu9/9Dtdddx3+4z/+A7fffrstqJ9++ulIJpN49NFH8ec//xm33HILurq6XPf2/PPPY8eOHXj11Vfxzjvv4PTTT8fu3buxdu1avPTSS7j77rt9ja+ihARPgiAIgiCGBWPHjsXvfvc7nHLKKfjYxz6GGTNm4Nprr0V/f7+tAf3iF7+IT33qU7j66qvtKeiPfvSjnvnee++9+PjHP44bbrgB06dPx2c/+1m8/fbbAICTTz4Zt912G/71X/8VNTU1WLRoEQCgubkZt9xyC1asWIEZM2bg4osvxsaNG+2p8FNOOQUPPfQQHnnkEZx99tloaWnBN77xDaP7/NrXvoYTTzwRp512Gj71qU/hwIED+O1vf4uvfvWrdpqFCxfiYx/7GObPn4/zzjsPr732mkP7CQCf/exnceaZZyIej6OqqgpPP/00PvzhD+MLX/gCFi1ahHPOOQfPPPMMbrnlFrMHEAEW0622LQDefPNNVFRU4MCBA3lb9EoQBEEQw4n+/n7s2rUL06ZNw+jRo4e6OMQIxes9CyKvkcaTIAiCIAiCyAskeBIEQRAEQRB5gQRPgiAIgiAIIi+Q4EkQBEEQBEHkBRI8CYIgCGI4QvHqiWEICZ4EQRAEkW+iEBolpzQF7KSGGAEMDAxEkg9FLiIIgiCOC5LJJL7yla/gjjvuQDweH9rCRCgkjho1CpZlYf/+/aiqqnLE8iaIbGGM4ciRI9i/fz+KiorsSE5hIcGTIAiCOC5obW3F5s2b0dbWNvSCZ4QUFxejrq4OL7/8Mnp6eoa6OMQIZezYsTjllFNQVJTdZDk5kCcIgiBGLL29vXj11VdhWRYuueQS7Nu3D9XV1fjlL38JxhhOOOEETJ06daiLGQnHjh3DO++8M9TFIEYgxcXFKCkp0WrTg8hrpPEkCIIgRiz19fX2Nh809+/fj1gsZu8vYP1LIIqLi1FcXDzUxSAIT8i4iCAIghixJBIJlJSkdSyMMTAMCpolJSVIJBJDWDqCOP6gqXaCIAiisLCsSI1vYFlQTRCmUinMmjUruutI1/S8B/F41PdLEHmGYrUTBEEQw5ccCWHcKCJb4wgjRKHS67i8nQ/I6p0YQkjwJAiCIAqOZDKJuXPnIplMqhMEEJ5e7utDbW0tYrEYWlpaEIvFUFtbi+rq6lD5BSKXQmXYMpN2lRhCyLiIIAiCKDh8XR8FEJ7q6urQ09OD0tJSWJaF6667DkeOHEFZWVmo/CIhiul18XyarieGCSR4EgRBEAWB6Ppo3bp1AIC1a9fi6quvzs71kWWhTJj6thhzCp2GeUQq2EUtJEaRHwmvRB4gwZMgCIIwJ4fCiZ/rIwaor+1XJt16ynwIWvkyIoriOiR0EnmA1ngSBEEQBYHs+kj8LSkpwYM610d+ApO4FlLc1pynXF8aVijLlxHRUBorEUQASPAkCIIgzMmhUNPU1ITOzk7lsc7OTjQ1NYXLOKBQJq4vDU0Qwx+dYDyUFEo5iBEHTbUTBEEQBUdRUREGBgbs38AEnG5WrS9ddffd6A67vjSIgF6I2spCKQcx4iDBkyAIgigYqqurUVtbiylTpuDaa6/Ffffdh76+PqfrIxMCCk5T6+tRn9nm60uLLAtsBIbWJIihhKbaCYIgiNwQYrqWuz7q7OzEwoULcc899+DMM8/E3r17IymSzj/ogz7rSyMPramrG5riJkY4JHjmGupECII4XgmpISwrK7O1jm1tbXjyySfN11v69LmO9ZtC2kjWl6qubRK5yGQ/QYwQaKo911AnQhAEEQgjf5719er+VbFPm18qBZZKudZvhl5f6lce8pNJECR4EgRBEAVCRjBTrbcU/XkCBustBSHPzz8ozy/U+tIgwqQuHQmkxHEECZ5RQp0HQRDHOxH0gw8mEihZsABHjx5Vrrdcs2ZNoPwYgFElJb75GYXWdGUeQZ8/XKIO0RhHRACt8YwSapAEQRzvZNMPZs4NvN5S5QdTclFkmp+4vtQqKvIPrVkoPjjlKf1cX4MgQpJTwXPFihVobGzEhAkTUF1djX/8x3/Ejh07cnlJgiAIYhigsy6X4aJOUZF+uEp2dQ3m5SMc8Xy88hu8uIGgpfDBaXpvSvyERhOhkgREooDJqeD55JNP4sYbb8Szzz6Lxx57DO+88w7mzZuHt99+O5eXJQiCIAocZXQgQaji6y0BoKWlBbFYDLW1tcr1liaRhnh+sVhMnZ8k0IUSHjN5ZBX5yE9oJKGSGOZYLI8ecffv34/q6mo8+eSTeP/73++b/s0330RFRQUOHDiA8vLyPJSQIAiCyBWidfkll1yCffv2obq6Gr/85S+V0YEOHz6MstGjAcbAGHOstwyUV2Zt4uHDh+31m3J+8vrFJUuW4O7Vq3HTkiVYtWqVfn1jZr9ReURLfJP1kjwNra0kCpwg8lpeBc+dO3fi9NNPxwsvvIB3v/vdruOHDx/G4cOH7f/ffPNNTJkypbAFT+oQCIIgXCSTSXzlK1/BHXfcgXg8DmDQopxvM8bsX47pkKTLa4AxWMhM0QewfAfcwuwr+/ahJiM8zorF0NvTow2bKZdngLF05KOg9xZ2TKGxiBhCggieeTMuGhgYwOc//3n8/d//vVLoBNJrQisqKuy/KVOm5Kt44aGGThAE4UI13Txv3jx7O9voQMuXL7e3B4S8rExeD5rkJfXf9fX1iMfjiMVi2L9/PywMul2y4HTLZJMROBNS5CNLdW8m0YqCjClhzyOIISRv7pRuvPFG/OEPf8BTTz2lTbN06VLcfPPN9v9c40kQBEEUPipH7Q8++CDOPfdcAEAqldKe29nZiVmzZhlfa//+/eZ5idpAjynzRCKBBQsW4J2jR2GZunESLPFnzJjh8A3qKo8u+lFY/54kbBLDkLwInosWLUJ7ezt+97vfoa6uTpuurKzM33UFQRAEUZCoHLW/9tpruOqqq4Jl5CEcppJJh2ALAEWZ9HzKfeHChbj33nvtKX5T6/QmADNmzIDlJTx6lY+XJ2jkI11+HmtKCWK4ktOpdsYYFi1ahIcffhiPP/44pk2blsvLFT4Ut50giBGMPN3sR1FRERjgtlbXnGsB9lT4K/v2CckHtZNjx45FMpnUW5QbCm28bNzt0iyFMJoulGVbwO/Zs8e2nGeAr+W8WCalFT1PT1PqxAgip4LnjTfeiEQigR//+MeYMGEC9u7di7179+LQoUO5vGzhQh0GQRAjEC40nXnmmVpH7Sq6urrABgbQ09ODvXv3+rovEgVbUYRjAIqLi9Hc3Iy3//Y3AOlY7N3d3UilUujt7fUvTEa4E90uAYPC48t9fcIFnb47+XrWX//61+jp6UnXQcZpfU9Pz+BMn8eUOs8j3tioTBLIvZNKwCXFB1EosByCdH/g+rv//vuNzj9w4AADwA4cOJDLYhIEQRBZsHjxYgaALVmyhKVSKQaAFRUVOX5V+1KplDIPL3j+4h8Tti3LcvzaaTi6bYH+/n42MDDAGGNsYGCA9ff3u9L09PSwZDLJUqkUq66uZgBYdXU1S6VSLJlMsp6eHnfG0vX88hDTm9aP130RRK4IIq/ldI0nIw0fQRDEiERlSLR27VpcfPHFqKysxMknn4wbbrgB9913H3p6egCk14Bee+21uO+++9DX14cjR44glUq58rj66quVfj1FxHWU1sAAiouLcezYMXvc4W6VXEZBBuOS6NvTYiz9v7S2UrWelVvAD17K+1qqPF7Zt8+xxjSZSiEWj2NdZrpeWz9i+WjsJQqZ3MrA2UEaT4IgiMIEhlpGrjFUaRGN8pCGqb6+PlZbW8saGxtZS0sLa2xsZLW1tWzTpk3KGTauVe3q6mJz5sxhXV1djvyU+1VDo7QvkUiwkpIS5TVLSkpYIpHwq0DfPFT1w6R0nmUmiDwRRF7Lmx9PgiAIYuSgMiTiv8XFxZgxYwaSGQv0srIylI0ebWv1+D45DybkYfu+lLR3dXV19jrKhQsXorOzE3v27kVNTQ2AQWMgWeenC2MZKrylZaGpqcm1npVfs7OzE00q10nSOktVHpzOzk5lHfMcXH5PSctJDBNI8CQIgiAC4yU0ffzjH8f27dudwpxCMDrzzDNxzjnn2P+LYplWeEN6KlwUYsGYKxY7AFRVVWHv3r2ANJW/ceNGJBIJbNy40bHfNkbKLA3wskIX4cJucZHPkKoRDkXr+SIhDz/B1FE/ZDxEDBPy5kCeIAiCGJnw9ZY8VOTkX/8agP96zTvvvNO20jbyfenhCJ5rQstGjwa2bAG77jrsLyrCpZdemk6ecTi/f/9+XHbZZUKW7rWVDPDWIArCLgNwbizmWLvqcA2lK3/mt7q6GidUVmLckSNYtGgRfvOb37jyYEgLtQMDA2BwCuiDiYTyqnx9kv9PokAgjWe20FcmQRDHKaKWUZwmf/311wEMGtvE43HbkKa3txewLHR3d2PDhg12XtOnT8fSpUvx7ne/28z3pQIxAImViURUUlLiKNuAJHypprB9w21mzuFuksRpf4f7JM15InV1dZg/fz4OHjyIt99+25VHdXU1ThQ0uec2Ng7Wj4lGlqchoZMoECzGCvdtDBJ0PifQFyJBEIQnhw8fRmlpKX784x/j6quvxrFjx1xpuGV5U1OTrWH0or+/Hy+88AK+8pWv4PHNm9VaTpMwmAC6u7uVYSwTiQSarrrKFji5JjGVSqWdxTNmdj2/cvhEYdq+fTuu+tSnYCEtZP7yl78c1BDX1wOM2XXMIzMdOXLEO8pfkLGLxjkiAoLIazTV7gU1RoIgCE+4AGQUqzxAntzo56YlS7BKlcgvvrkkUBUppqotYX9xUREgT/HrriE5kPcsh8cUOA/p+anM/y53TJlfhya3qAhlGqF37pw5uOOOOxD3m3bX3UvUkFBLKKCp9myhqXaCII5XxP5P2FYZygDp6DszZsxw7efw6EPd3d3eRj8yKkFQWEPJANdU9RlnnOEwRjo2MDA4he0nLBkaHeno7e3FfzQ3o7i4OH2afTqzozA5LPp1ITOF7SWLFw9a5wcJsZnLMYyETkIBTbWHIexXHH39EQQxgnn55ZfR2NiIKVOmOIxturq6UDdlCpYsXozVq1dj3rx5+HXGAEkHn1bmvxym0fZ59a3iVDUsC4f7+22n8CxjFOWYwg44ZW5iiCTfm4jKYKirq8vWiOoQnfhfcskl2Ldvn3u6XuOAnyCiJIi8RoJnGEJ0NARBEMcFkjD34osv4uDBgw7hiPfrgFPo+vKXv4zvfOc7OHr0qCvbkpISvHP0qLGwmVNCrDUVjz/44INYsGCBfZ9iHfDtJUuWYNUq5SIDR372sgFBUOdRmwCggId4YgRBgmc2mHQiYReWk0BKEMRIwqBPE7V7svaSE4/H0dfXh2QyiX379inXiaZSKec60Sg0kFH05X7l8DguC5sio0aNwo9+9CPMmDFDr7m0LIwqKdEK6tygyxMal4gICCKv0RpPGZMGqFtYrjrXZBE6QRBEoWGy9s+gT1NF3+HwtYxbtmxBb28v6qZMSacT0ujWgypdBhmWSZlWJzz6nadLL601lY93p1IA3PfHU7/zzju46lOfcriiUpVD5WCewdsBv5wHQeQTEjy9MOlcCIIgRiIRCSRe0Xe2bNliu1gqKyuznbKPGzsWADBnzhzEYjGnX09Ovo1idIJuhmQyiblz5tgO8ZXlE/KYlbmvWCyGz1xzzWDW0inFxcVgyPg/ldEYdAWqGRrPiDxDgmcY/ARSasgEQQxHgvZdGqt23T6dtTuQFqxSqRT27duHcePGAQD++Mc/YktXF37+85+n/YMaWHf7ltOj/547d+6g4CinVeQhCputra14XBXzXVdHjNkx5390//3qIgG2X1Sl1pO5Q4VyZ/7a6EmKPHIGjYWEAhI8w5ClKw2CIIiCJGgfZij8ycKRw3VRhvr6esTjccRiMewTwltaAM4///y04OWjdXRgKGyKiO6IksmkWxCVzrvnnnvw+ObNuOuuu7Bu3TpYGHT/BGS0lLo6ymh5eaz55ubmdBJFMUeVlKTdK8lltiw7VKgYPelwf78+elIuoDGRCAAZF4Uhl4uxaaE3QRAjEG30HcHSm0cSkq28R3FDmauuCmdNLiKk9XJHdMcdd2DdunWD1uWZ83p7ezG1vh7dqZTLCEplJMRkYVmzlvTlvj6cc845eO2111yHXYZVPvdltD8f0Hh23EBW7bmAQpARBEFEg0Zo5OEtZcGzmwteUfetPpblgDuMZX19vdL9kYzSqtzHMv7ZZ5/Fe2fPRrEUZckheObAut5oqQKNaYQHZNUeFUEtJWk9C0EQxys+azy1U9eSwY2Iay1okH5Y1x9L+7nFvQ4expJbl9tT3jw7sXjC9jtHj6aFzgDeAerq6nCisCSBR1mS6yUQKut61XGTPGiMIyKABE+ZEOuCXOnpy5AgiJFEWNdKwj4ee91lfCPwcl8famtrcW5jo20oc6LKol3Acy2mQZm5xb1KgGQYnCovyayz9HNR5CUsJ7u6BsuqqK+6ujrs2bvXsV6zRw4TarKu1s/oKyw0thER4P2pR6gxWbNjepwgCGKoyVU/ZVloa23F3XffjZdeeglA2vjm6lQKLJVKO0YXjIbqpkxBT3+/vRb0uuuuG1wLqimnKNA6QkwG6aeRFhgHMhGXeFpRZOvs7HSts+TniMRiMfT19eHlri7USdd2lLWxUVsm7nTfKipCGWP6exG3g0yXR70elMY5IgCk8ZQJYjUp4+O3zTdtNtAUCEEQfgSxBBcJKVRYAD796U8jmUzi9ddfB+CeupbzLisrg5XRGtr+PaVy9Pb2ApaF7u5urFu3DoDCmlyH1Mdzi/tjAwNoaWnBjBkz7Gsz6B3Ycyt9Bti+RgHYWsq6KVMwadIkfPuuu5BKpdxlTaWQSqXse1GWTyhn1mQTzMTv+iR0EgEg46J8Ql+FBEEMJfmYobEs9Pb04He/+x1uvfVW7Nq1S5nM0/jGRzvHhUIrsz3AGIoy1vJ8v9aaXLF9+PBhlI0eDTCGvr4+NDY24pRTTsG1116L++67D319fdizd6/jvH+44ALceeedaGxsHLTSz+QBAGeffTaef/55R7nlMosGSp4GQyYGRUGebS4t4GmcOy4JIq/RVLtMWBcdJlBjJAhiKAnSB4UVThhDvYGGzp66DuExJJFIAFddlblcRoDL5DGqpASJNWsCTUOLWtUpU6agt7c3Pd1fVITrBgZw5MgRYPRoO82SxYvx5OrVSCQSaGxsdGhmE4kELMvC/zz/vO0aqliakhfXja5ZswYQhW+/ughqJKSqX5M8wo5/NM4RPtBUu4xuOsJkqkNlTUlT4ARBDBcYGzTW6erSplFiWXb0oS9+8YvppLrLGJTDa7+XgY9tTS6VzRfhmmWjRw+usxSESj5lfvfq1QDSU+awLKRSKWzYsAEA8KlPfQpXZYRiDhc65VLY8dQtIWpS2DEjirEmiCcXGtuIkJDGU8Zk4bbuS1CVNoovSIIgiLAE1FxyAxgv4xclPppOPs2MzG+faUhHEUWZi4qKcGxgwKVVNMKgf547dy7uuOMONAJAxniJp9qfibAUl/YDznuVKSoqgjUwgJSwzzY60pVPVU4TLaffGBbWQCns2Ebj4HEPaTy9CDqlEQT6WiQIQiIr10A6DPoxrqkUDWBqqqvR3d09aACjQprdSSQSDr+YYi/Ht4uLi8EA75COhpo3buADOA18PM9T7BdjrstpuEAo31s6GbPvSV7XxqTfiooKNApuohiAvXv3oru7GzUZIdzT6EiFrp5Us3UGhmOO9081c2c6Re8FCZ0EK2AOHDjAALADBw4MTQFMqkdMU9jVSRBEgbN48WIGgC1ZsiQ3F9D0UUjLRwwAsyzL8Yu0qGCcXyqVcpwH6W/Tpk3+/aZJvwqw/v5+NjAwwBhjbGBggPX39w+mNylzZlus956eHsYAlkqlWHV1NQPAqqurGQNYIpFw3ZfqHsX9/PfWW29lc+bMYV1dXeky+9S5tt4D3JfReQLa94/GNsKHIPIaaTxldF+QunWbuqmQKK5PEERBEqVmUqVt5K6BPLWNYdBom0RtHsuk4b8lJSV4UIzWY9hHWZbl1HhmzqupqfEvk9cUskBZWZlyLabfecCgyyVe7wzpeq+vrweQ1qC+sm8fgPSUugW41m7K96jT5RUVFWH79u14PKM9tSwLDwp1PqCoczlC0uBFAmoMVdpKoT7y+v4RBFDYnzFDovHMpkoKuzoJgoiIKDWTMNF85ZqMhs9xzcxvKpVypfXcBlhtbS07++yzGQPY2LFjWXl5ub2/r6/PKA9dOX33C3l0dXXZWkb3KYP3aFkWY0K9y9pKvl1SUsIqKioYA1hLSwtrbGzUaj8ZwIqLixkD2Hve8x42adIkW3uaSqUYA1h7e7vyPM861+FXp9rTQmpeg5aPGNGQxjMqglqni4u1g+RNEETBkyvNkJ+2Uav5yhbFzA3DoMP0Yo3jdO1aQoGHHnoIkyZNAgAcPHgQ+/btAxsYSDtWl9d2+uVnMgulyo8xR6QgrqXm54n16qr34mJl1rfccgvOOeccALBDWjqKKm0fO3YMFoCtW7e6HOgDwGWXXeY4v6ioSGmMFBi/ehS2EyaaVz8tay7XbdJYOfLIrQycHQWl8Qz6xZkPCvvxEcSIAjnUTMraRv7n0nwp8NLqGQOwvr4+VltbyxobG21tnq2hFK5jspaQa4RDay5NtHce28lk0rFGkwFs/vz5DABbsGCBI6397ITt5uZmpSby9NNPZ4BT093X18cqKyuV6a+//nqX5pBvl5SUsLvvvpvV1ta6NKi8zn01wCZonpGI8fsXQJNKHF8EkdcK+s0ZcsEzaCOLopMgCKIgSSQSrKSkRDlAl5SUsEQiETpvPvAXFRU5fk0Ez0DT/j59k9JYx/A6PT09LoGPTysnk8nA0+Tyvq6uLnv63PNeFM9H3sfLxKe6i4qKXEJjVVUVYwC78cYb7Slz8Xh7e7t9Xzt37rQFyHvvvVd5TZVgqqpz0/rwrANV/XrUF3//ePlc718UYxqNiyMaEjzzCTUmgjhuyEYz6YWftlHGS8hrbW1ls2fP9teA+vVdgH0dlslfFiZ7enoc6bnwEsgyXlUmRdrFixczZiJgZz4EZCFPJ4RWVVWxhoYG+zwxjUp4VOU3Z84c9vTTT9vlbmtrM8rD+Fmo6sh0v+q4lFb1/jFA+/5lXVZixEGCZ64J0mEEbXjUUAmiYMlGM+mHl7ZRxmTaP5Dhk6rfkYQk2fBGJTzJAp+RRthDwye7NuICsEvwlfLgxjs6YROKsvqlVwmeYh5Lliyxy7F+/Xo2Y8YMZb7Tpk2ztakmz8W1vMGv7nzqVLctuqJyvX80LhE+kHFRVBg43I2cXOZNEERWVFdX207LuSPw2tpaVIeJwiNh7BoI3gZJnECGT6p+hzHMmzcvXR4hf94rutwsMeYytuHYoSE5Ut+qc00lujbiUYK4cU4sHreP6/rNIoWBFE/Z2dkJMGbXpaq3Z5ptzpo1a+zttWvXItHWhoaGBnz4wx/Gtu3blWXatWtX+l7EMmsMf5YsXozNmzcr80kXKp2HlwN83bOVKSsrs/dbloUyITa9Mg8y+iHCkmspOBsKao1n0DRh0pqmIQhiyAiimcwluml/SBpKe5+Mpq9RTeOrNIAqLa+sEWYeaTnKtaOZsiUSCa320UuLyl02NTY2sng8rtRmxuNxezmCTkM6b948T40n4NQ4q/KQ9xUXF7Pm5mbP8YXXPz/Xb62s5/pblcbThCjGIhrPjhtoqj0qgkxj5PLaBEEQErKQp/sLavjkJby6BE+pLxQFvpaWFsYA5VpVUbj1Fa40Ap9DmAUcVvc9PT3smWeeYclkklVWVtrLAJYtW8YaGhrY6NGj7fx4XSqFdYBVVFQ46njcuHFG0/IqwVM+LpZfrn9RqJXz4HXI4I6wxO9FuQxBcT0vAdjlLcFkXMrH+EgUHCR4RoVh4zTaRxAEESGyQUhDQ4NeQAyAynpfJWht2rTJbWDEDDXCGo2hLJT19PTYYSpV5RCFK1HrJ6bVaSL5diqVYhs3btTer5+A6fenujZfGyrWh7itM3ISz5PvUSWo8vw814lq8NJEexJkrCRGDCR4RoVHx+CZPqzAShAEEQDRICSZTDJRAxrI8Enqj0yMc2QNnC4v5X5BuJKFNC5cdXV1eV6b71ctC+BT2V7Cn2rby6pd3lb5+vTTePJtv2fi6T0B6mUI8rat5Rb2+T0XnbcElqln+SODIDhkXJQNuigZ4rYuvQrdebr9BEEQhogGITU1Nf6GT379lWVh7ty52LZtG4BB4xzdWcXFxVi5cqU+b4/reRkiAUBra6vrmKrXjMfjmCUYHwHpCEM65OhCAGxDLR6VyO+8xngc73nPe1BZWYnyCRNwzTXXaMsHDMapl3ZqryXDn8O2bdtsI6KmpiZ0p1LK8gHA9OnT0d3d7djHjc10166vr0c8HncZc1lI17NtzOVV/iBGR0ENlMigaURAgqcXQa3aVfujaJwEQRA+1NXVoaenB52dnXY4R1eISoMP3s2bN2Pz5s04MSPEenHs2DF8/vOfd+4M+FEtW55v374d3amUHZbUC251n76s+ro8f/4rpuLbnZ2dmH/FFUrLemBQcOR5JJNJ/PrXv8b8+fPx5sGDOHTokGc5x40bh6VLlwKA2gtCJv/e3l7AsvDKK6/Y15wwYQKODQygsrIS69evx+OZEKAAMCvzfCzLctwXFxTF51dkWYjFYojH485rC/WmC5/JoAjfGoVSJagChhQ2I4Oc61+zoKCs2oNUVRR5EARB5AGdoU9HRwfr6upiK1eu1E7pFhcXuw2XDPu/jo4O2/BnwoQJrrx1hjX8r7y8nE2aNMlzilt2is6vx5ch8GskEgk2ZswYO4+Ghga2dOlSNmPGDFZUVMSmT5/OWGY/P2fSpEn29SdOnMgmTZrEGMBOOukkNnXqVMYy+3l5uJ9P3ZrX9I96al6uA25EJK5N1T0j+c9lbCY9IzmKEf/zXB5AY9txD63xzIZMA3rggQcYA9K/wn4RV4xknsakERqstyEIglAStp9QnKcS2mTr7k2bNimFmE2bNrnzNunbpHxU1uSq63kJVCphTTZ04qEtuTCqy1vMg49DQcq0a9cu9vTTT7NPfOITDmGeQVgrqagn3bpNeZ9cX6qQnrrypVIp59gllUMVJIELpFmNbdmmJQoaEjyzIdMQZs6cyQCws88+27Ff3DYO4SadRxAEMeRg0EhF5TaJidqxzD4uhCgNl1T9m6Lf5HhZz5sIUV7CFbdkVwp5gC2M+gmyYh2JZfUqx80336y9F1Xeqnryqg9Ze7l8+XKXr1JVnTqeWWbf/PnzXc/FM3xr0DEsV2MejaUFBwmeIXnqqacYA+yOmH9ZJhIJ1tbWxp566inPEG4MUHZyWUONjCCIsGj6D3GKXTVl7RAs4Z62dvnn9Oun4PS1yZjbejsKwVMlgGnrA2ltoSoPrkUU05pqPLXlyPxyYV5XJpWQr7tX7vZIFC55Gr604IwzzmAs8/+mTZtYWVkZA8DKysqUArqsKTZ5tr7wNDSejUhI8AyJSQcm7heFU0enGU1h1Nsm6QmCIPzQ9G86wdMWRoBB/5xBBBLA5RuSf7DLApNJ2UyEvOLiYtbQ0GAvh+JTy6JTdNFPqHiuSjgUBUIxrTgGlJeXO6a+5bTNzc3KuhG3uZDPAPtXvLa4NlV0I8XXpvI8du7caaR5VQroBs9TuU0cl5A7pZBcf/312mMsczyRSGCUECNZjGEMwGn1B4S3XhfydGybpCcIgjCAWzBzxF6koqJi0PqascFY8oypY8mr+jrG0Nvbm3bhA9iW6qvuvhvd3d3Yu3cvANguoPh1dWViAKqqqrBo0SIwpN05AU5XQmL6j3/849i2bRvijY0ABl00catwWBYmT57sOg+AvV+Eu6v6zxUrHHXHxwALwMGDB3Hs2DF3XWT40Ic+5N4p9ffcOwEYs91L1QpeBvj1rrrqKocbqW3btmHFihWwAPz85z/HgQMHlGXQjhaamPG6Z+ubR5jjxMgnx0JwVgzVGk9ovlQ5ns59M3mYXCfQfoIgCBWqPsOwH9H1ZbqY4HLeLgNL+doemkFxv7jmsr+/31Eurz75mWee0aZhgL2EgGswueW5uDyqo6OD1dTUMAawlpYWFo/HWU1NjXtNI5xa30OHDrEf/ehHvlP+8n3byxNMtId8W7p2W1ub1qCIO+BXlUn1p9V4asrhC2lCj0tI45kDHpQ1mUj7dGMY9O02y8fnHfn0JAgiclSap4DaKNnXJdds+hFvbMRmwa+k6tqib0gmaAaBtMb1wURi0MF6RrMq9qWqEvP8pkyZgtraWgBAeXk5xo4d60j3xhtv2NtXXXUVXn/9dQBpp+hcezh79mz09vaCDQxg4cKF2LJlC/a+8orT/2kGW+sLYPTo0bjmmmscTtxFTqistK8Rj8dRU1MDAIP5BpnJEjXOmXvZsmWLsm64hpTXEU8ja45FioqK3LN1EtzHqe3rVKcR1c3WhR3naHwccZDgqcCyLIwePRqjhamkgYEBpFIp9Pb2YlYmIgjvVHiEkJf7+tKJdR2KyfQ5TZkTBBElOqEAQHV1tT7akSRYzJ07F8lkEr09PUilUo6oOGvXrgUsy+4jRZqamtDZ2amcDu/s7ETTVVcpy1pbW4sZM2Yob4kLV9xpPhsYwL59+3Dw4EEAcAm6MuL+RCKRFupEoTsAssKBC++vvvYaurq67PLK9WIUoISnkdL29vZi+/btyinz7du329c0ZeXKlWhqavIsk2uZgomAmWXEJlfeYfMgCotcq1+zYSim2iFMO4guRuTpiCgW2vtuEwRBZItP/yJbMOscnAODTtDlftHlh1M4r6enx2XAw8/TWndnppb5lL88Re/yKSndlxxrXnVtvq3KQ7a+V9UH9wogl6+hoYFVVlayjo4O5XmBtjXHdfcibqv8cerS2v5YM9fh979+/XpH7HYGhRcXgmBk1Z4dgMu3HG+cok873bmOX4IgiKHG5MNW0XeJ7pa45TQXPnQuiPj6QjHfUMJf5lf2KckAtU9Jabutrc0hEIq/DE4rel19eAmmcvnl6zgE8KCKBYP03K+oqn75OMXrjgG2C6yqqip2wgkn2Ofx5ymvO+U+qlWKmEBeXILeOzFsoTWeWcKnKJhif1NTk/5EYT2OEpoeIAgi35gs8VEwtb7ejvf9yr59AGBbUOustrklNkdnbW5KXV0d9uzda8ef79qyBWeeeaZtDa+EMTz++OOwkLaAb2lpwQBjKCoqwsyZMwEMLo8C0msW586day8VEJcQ1FRXo7u727bKF6+hWrvK45uXlJT436/PGknXmkohLV++4ChS5vf+++9H01VXYe/evXjooYfs+/33f/93TJkyBXfccYdwKYZnOzrwyiuv4L777gOQXnqwbt06WEh7DbBj3DPGJU37fL91ob7T5H7T8rmExuOhI8dCcFbkW+PJHejK00L8K7m9vd2RXvQJ5/AP56dV8Nrv95VMX5AEQYQlgIZKFVkIGU2XrPHUhlUUZpBU2rnm5mb//k8qH5COuCOHKxanvrkmr6qqyi7TCy+8oFwexX2LylpM1T65nPKUPt/m+13T9QH6ckdkPCktX76guja33F+yZInTb6pGe6l6LqpIVp71IT0jY2gMGzHQVHtIdJ2joyNKJ2SMOTsGr05CczG/wkRwRznMjyCI3BC2rUbxwSsd5+sEZYFj06ZNrmlcBiinwFV58D9HyE2xHFIefMqf5zFmzBjGAHbllVfaCgOVskA3LSwKqaNGjbLTqJYQAMIyK6mcOgf4YlmNnmcmjSoyHhckW1tbXfeq2+YCaHl5OWMAq6io8ExbXFxs16lX3vK9et2L370SIwsSPEMif0GqOh6xY6isrLQbOO8cKisrWSqVUscIFvHbT42TIIgoCPIhLB2XhUYx3rdoUOkIq+gjeHKhsLKyUimoyn5BdRo3ef/KlSu16x4ZMCg4avJTGZM6BElFffHyi2tQeVhKMQ8+JmifRWZbVU8qIbC5uVnrx1NXT35pZe2nblsZLlX1LineJ6PjXvuJgoUEz2zQNLZEIsFaW1t9Oz/VvrDlUG7r0pjsJwjCE6VD9KHEpC0HGdwD9g0qAxWH0KHKW9on5nHvvffa2tGdO3e60ovT3mIequl61basaVRqVgH2uc99zig/sf/3qtN/+Id/sJdZqQQ60/FAXt4g3wtfmmAiiAcVPP3qgAumSi8uQcYiGrdGJEHkNYsxxlCgvPnmm6ioqMCBAwdQXl6el2uKPtwYnM53g2yXlJRgzZo1aR91vIoNnTK70gY5jyCI0CxZsgSrV6/GkiVLsGrVqqEuTniC9h88jeK8w4cPo2z0aCCtqEj7u/TKW5NHaWkpLMsCYwxHjhwZDLlpWUglk7AsC7NisXQYYgDdqRQYYzjhhBPw2muvIRaLefa9DyYSmDFjBmbFYiguKsKxgQEUFxVhYGAADHCUSWVWospb3qe870x+S5Yswaq778aokhIcPXrUlYc9JnADVd0zEsonXl9VTr/ym+Rhuj150iT89fXXkUomccIJJ2Bqfb36vQo7zhHDmiDyGlm1S0TRBBg0FvC6BuYXBzdswySrPYLwhccS7+7utmOJr1271rZmdjn+LgT8HHPr+g8hDbfmdlhNK/oaMSa7Z0QjIfqQKg/+Ua+K886t50VisRji8XhawFFdTvq/qakJ1dXVODHjEP/7gkN8AI6Y8RyxpJZmGxiMCS++C0on+gDWrFmjLK+nVxSfPl4++rnPfU65P0geMpZGIOfwqE/xeBz1stCpe/dUVutDMS7RWFhQlAx1AQoOxtDx7LOYPXu2Nomug7KQjlphDQxAGURN94Vrqo0ICn1JEoQv9YJgw4UjMaQiABTExJBHn5FMJhHnv/G4Pg/hvNbWVjvcpccZ3uUIUs4QszglJSV4cM0aXJCJsATBjRIDUJTRoHJ4JKPS0lJYRUW4bmAAR44cAcrKUJ95tjphU0TWEnL3UfX19WmtLwBk6pnnt3///vR+MRKTjEHdvNzXh9rGRkyePBnYtk2ZDRcCTbCkX9X2qFGjcM4552BLVxfOOftsPP/8847yiXlwza32GfqNbUGVKlFoRbPVzBKRQhpPBaWlpcZpr7jiCpSUlGDUqFFgAMaNG4fKysp0yDnAvGHJ24XyhVYo5SCIHKHyx8h/S0pK/H0V5gsPTZIrnKGIlFap3U2l8q7dlTWGKriWkAuUQDqUJheu4/G4rdHklI0e7dauWpbjOXOYtP3Rj340fV5mn9z78XeBAe68GLP3V1RU4NzGRrS0tNhltscEjhCGVHy2dVOmoKenx36m4r0AQPPy5bZ/TgB2WFELwGmnnYalS5faxyoqKpSaTnnfRz/6Udsv6NatWx0x7mVsza1ubMulMBdFCE4OCZ1DR64WmkbBUBkXydEyTj/9dMcia/7HF5z/6U9/YocOHbIXxt94442O/JTbAcuUdR4EQWjhltfyn8uaOQeENWjSRRbyCmco3psq2o62rzHZDnieeE1V3cv1z+vp6aefdvvjVF1fcW35OfNrc68k8+fPZ5WVlUoDJflevd4Z2eLfLqOQh8PHpgLRYl5XX7q6U+33yoN7Y3G8N5nj3Eerw1er7tl77Tc9TgxLyKo9GzKNor+/n+3atYslk0nfRmt3kMI+U/cZntsEQeQFXVzrfAiefgKIjdQ3+AmRKr2Cl1N4l6/KoAQUQnWW6lzAkV32OHwl664n7peOq5yu87/x48czhrTgvmbNGsag9gUqXsPL1ZRXfcg+SfnHQjKZZOvXr2cMsD9C+vv7bSF7+fLldt2EEUK9zlP6O808Ay74Ony1BnjOodLSmDjsIMEzGzKNnkecMPlaNO78TRoTNTKCyDvyLIevr8Is8dJW2j6AM4j9kYhOiOT9klKIVAhMRtrdsAKCR1rPcgCsv79f6VBdqdVVXUfaZ9KXuwQwDPqtlO9P9c44BDNNfcjXVvnPXLJkie2e6YEHHgg8Fsl1eumllzIGsI997GNswoQJnmnPO+88u6yi4Ovw1SrgiNpn8k5I9ZEzaCzNKyR4ZgOcIdS8wr3JaeQ/7sw46PUdv7rjJnkQBGGMPcgypp7CjRATbSUfyL00okZLBKT+QKWp48KdUb/jt22Yh4mWWSWg6aIReZYDsAV1L6FL7Lvb2toYY8zTb6V2Sl1Rjq6uLtbQ0KCNjlRcXMzKy8sZ/wiZP38+YwCrr69X3rdOsym/W8zjuGp/WVkZa2trY/F4PK2B9Xm2nppor+fjtT+b8S/K8whjSPAMgRznV9QaqBqr2AnIHTn/VcUtNt6mhkIQIxYvbSXvW6688kpfjWjgJQKAt1N4qS9SaluD9F0ewoSvc3rmjiYnb4vRiMTr6MocRGMY5F6USHlwAe3KK68MVA7+y0N7BhE2VeNS0G1HXWZ+s9JE+9WX6X6ioCgYwfPJJ59kl112GTvxxBMZAPbwww8HOj+fgqfY2FRflvJ2Q0OD3Wm2t7crOwHeaQZqhKr9QTs8giAKHp22UiVMiAKpnY45p3sZNNPCim1Zu6vrV5TaVr/+yKRvE8rBt7Xl0NSNTqvrVebm5mZtXct9v0n5PeF9vyCgAWlDJvHapqEq/d4Vv+2wgif/CBKXf6jeS9060UB15lfXUYx/NIbmhIIRPDdt2sT+7d/+jf385z9nhS54qjQQYsObNm0aW716NYvH44wBbPfu3XanadIxeBKkYeW70VAjJYicIGsrTf9cRkCAe4mAifCnOa6a/RG1rb5CgUl/FkSwyNy3aF3tEg7hNtrhAp+oIeZaXVUfv2zZMrfgDgOtrw5DwW7s2LGRCJh+6eV9Qd87ZOpYZaQlb+s00UbP22R/0GdB5JyCETwdF0JhC56M6V1t/OhHP7I7IPGrnH/N+n1FezZCedtrX5g0BEEEIrJ47T7tU9RWXnPNNcaDv+daTNW1DbdVBpWBXC5Jebnqz0TI0OSn0uqKU/LKj31pn5ifKMiKaVyCO9Iullx5GJbfzwBM3udlte4lVBYXFwcWXidMmGBb85sKtXbdMud4qa1rk+dvejwoND7mlWErePb397MDBw7Yf319fcY3EgW8Qxe/qJHpeBjci/tNvyyVmAwGpscJgogMY/dGESBaDXPXbfIfF/pCu3gy6WuE/mr58uXa6V+XwaRqO5PWVX8QBNKA/Z/S8Es6TzdjJZfZZHmCqPUdM2aMnZ/K64DfvXgJaPJ2Q0MDu/HGGwMLnqKmVye8qvbdcMMNWoFVd21RkSJeT/l+hh3baMwbdgxbwfPWW29VNoB8CZ6iw97bb7+dMaQd61ZWVjLAvXhaN92gFTxNGpNfI4siD4IgHBi7N8ph25Kn3rnA2dDQwFpaWmzNn8sIiGPSH0jb/J75usNJkybZGj6VEKIzmBTXMvK03OjErj/oBVLPezDs83QzVqoyy26CZEHWS/gKrNXD4AeEiZDHn/Npp52mLYesHEmlUr4adFlQFJ+RSZlU45nKBVkk41KQdyIoND7mhGEreA61xpMxZndEYmPzdOOhaaii8ZGYt++26XGCICJDpWH0c8YeNSq/kDU1NWz37t2MMQ8XTyEHZhNhQ64LLsTJmkvVh7dOa+oSSNWFC7bNfCz8DYUh2Yezrn8P1D/DuVRAVe/8j6/f7e/vZ7t372Y1NTVs+vTpjAFsxowZ7IQTTrCVI66PEeY0GpM16Kp7MTVs0gmeJppo13bQsc2gfiPNjwjFsBU8ZYbKj+ecOXPY8uXLHVM3ciNUTTeIv8lk0tsPYBDB02Q/QRCh8VqLFzqij6atOtaQSmk8fYlG0faFPFauXOnyKakTPACnttXWXGby00UEUgk+LoE+iGCh2w93qOMwQQBEH866dZN8v2/5hOP8uW7atMlTsFNpZxctWsSAtH/pp59+mjGAbdmyxZG3qj5kN3/yOl35nsTxi6fhRrVcwJWvoQtuoKybIIInjX/DDhI8s0HqVP2+dlXrhXgnGOSaRvvC7CcIwoicxmsX2mde1pAa9Ad+Gk9R8GYAe+aZZ4ym0uW+UuUwnUEj0PsJJz7bouDuJZSJ26plFgxpo1HVGMCFbN+61vTrNTU1rKGhwZG3rFGWPQvwX25vsGDBAuW9iIKg7CeVAfayMfm+Vq5c6RDaeT1cc801zrqU7sn3XQ4reOabQinHMKZgBM+DBw+yrVu3sq1btzIA7Nvf/jbbunUr6+3tNTo/X4Kn2PHInapuOkLE0yeeyfZQUijlIIghJpfx2r36GM8pZ5EgbdVAGBKDY6gETr5Pt3ZS7hd1EZH4deQ+VBnTPKzgqbpHw7RimVQhM+V62bRpkzovHYrxYvfu3ay2tpbF43G2evVql3bW9LlwIZVfR9TY8mtt2bLFFkY7OjqUz+LKK69kO3bssJ+Ll1N4XbAVpbstv+eiq6co3vVcnUcoKRjBc/Pmza5GA4BdffXVRufnS/A06VTlbeVgoXqRoxBCgzYQvwZOEISLXMZrF/uYnK0hhcaNkZRG5Mtf/rJW0JIFHNVSBL6fawHlSEQsI6ipBFKl4Kkpp3J/wP5U6SYL8HV5NG3aNFtjWFNTY/4+GPTrumUVcnhPlQAq7vcyjBPz6OjoYBMnTmTTpk1jY8eOtfdXVFS43lEGf0FcF8bT87nQuDQiKRjBM1vyJXiKHY+XsKnbthEaViCnw0GE0CBQAyeIQEQar11of5GsIfXrJ+BcJmSSn255ATBoIMnXdcoaTZXmUhW7XCXQMwjLkfyEkyyETZEgMe/5PXZ0dASeuudk43iel0kncOrGIvljxk97G2T/vHnzGGNuoVhMa+puy6/uAj1nGucKgiDyWhEINDU1obOz0zi95ZeAMbS2tmLz5s0AgLlz5yKZTEqZaHJhzH1cl1aXhm/zvLzyIAjCpqysDFamrViWhbKysvCZCe3Pq4/p7OxE01VXqfMQ263YnjP09vYilUqhu7vb3rd27VoAQCqVQm9vr2dfUl1djcrKSjCk71e8wh+3bUNPTw/q6uqURSsqKnL2hYyl6ytTTl5/dXV1eOihhzB+/HjEYjG7HnT5ulDct2ca4R7F+lm3bh2AdP10d3cP1o90TwBQnPktLS213wcA/u+DUA5xDPDF4znzMtmHhe3uVAqJRAIlJSWwALDMuX41pjtuacYJBuC5554DLAsrV67EnXfeqRwHxXecj3n22Kd6juK+oNvqG/A+ThQGuZeDw5NP4yLV+i4Gt780vl1cXOxaZK5a+8KdD1955ZXRfNHpHpnfl+VQUijlIIghxGsNqVG0JEU7Evsm/mtsNZ7Zv3PnTsYwaBgZi8WUFsy+SxE8+p3FixczBkHb6NcnBOkfPdKIdaCbFu7q6nL4cNb6pDTpx+A97a11PK+4F7G+ly1b5iizHDbUS3Mtvx9eUY6WL1+uzUf1Xsnvcjwet99h1zMP8NwCjRm5HF9o7DKGptpDoJsOuvvuu5UNWRcGU9fo+V88Hmfr1693XjxIgyuUBkkQRCA8BTcI0+QBCDyFr+lrZIfq3G2PLQhn0spT6V4fvKJTedlYReuUXyW8BhU8hX2q+pEF9CVLltiurbiborDLLLwEPnu/afkz+3k919bWslgsZgvIotAvR91TuU7ivytXrvQVUsvLy5VT6fyXh9psaGiwg62Ia0b9DJSU9x20boiCggTPkPBOdc6cOWzLli2sv7/f4XdNbIS2ZaPUcHRrX1Tb4nmu7aCNLWzjpEZNENEBbwMfcQ3prl27bBdFWu2YSfvU9C+exju6/Zl9ntoqQGuoI/6qhDylQZWJ8GF6XIFOGzhp0iRbMNK6KTIRgIVtlb0A//Vc/2iAl7P29vZ2WxD0Eyr5dklJCZs6daq9PXHiRDuNHNFIvhfZ+DaZTLKqqirlNVUGSkpCvKc5gQTgUJDgmQ0QNA9ITy/V1NSweDzOWlpaWDwet/fz9IwNft2vXLnSV/DkX5O29hOKGMZRNM4Q904QRHiC+OhUTWN6TpNr2mcgN1AewpOXhtI+nkkru+1x5Jf51YUU9ps18isnY24Lda+lCnL9+P1ptXM6pPLJRlhMytfrvjy3Pa7NPxROPvlkz+AnQHoWjwHs0KFDtjbV7z00UaSoljIon3k2901jVMFCgmdA/Hzscf9mjOmjiZg0TrFxi/uvuOIKBsD+6hbzdW2LhOigCIKIFl2cd95/6AQY3TQ5g9NFkRKp7ctujLRuoDwGepVGSxYm/Nz26PJV3aOuHPwDXJ7mF7dVa0ZdAn8mrbh+85prrtGWSVlOE6TyhfIH6yeAKcoifyjwMnN7ApW2sqOjw5Wf13sIpIVZ+f3g283NzZ6zfNpn7nffYaFxbsggwTMgqsZmrHnIbM+bN0/ZOLUdWuZ33Lhx9vbo0aPNnfCabmcLNWSC8ET+qFT2Hxp008CikYYJKjdGQgHV286b8Ax7KQsWqvtUCUmiECbmoRXCAO00v0ojO2nSJEe5tQI/oIxhrhOYeH1oNake9dje3s5KS0tZQ0ODO566Sb+u2q84bjLW8Ofj8p0qXUPnKgvC89AJ0yaGTbZAbHKvXtt+5GocJHwhwTMgRpoHkcwLreoI/Tozv23Pr0OCIAqHTBvNxkenKtoPP9fYGtjveJBtH0HMyH+jlG9lZaUjRCTXporrWGWtMYN7ml8WqFT9plbgF7ZNpt65gBYmvCk/Z/HixYwx6UPAROhS7Vfcixh5ymtMMfGdqorrzrf5WtiKigo2c+ZMV36yYZP4LovlqKiosNeizp49O9CHlW89EUMOCZ4hUH218QbpAoPT66qGKufh5dTXczsI1CAJYsgIG+edW7rPnDmTLV26lDU0NNj9RShDIxUhBE/ZnRy/D9mpORPvUyMkmfRzcn8p9ps8rdeaUV+FgVAm0buAnAe/30QiESi8qV8YSd/1oibPSHNcV7/FxcWsra1tUNvrcQ1eJ0ZjFHMK0+JSBhOlivbDKmwdBCWKdkS4IMEzBL7rchQvnV9HWFpayhjAZsyYYR+Px+PejVroeG38GqEJ1GgIImdkE+e9v79fOeB7TtcH6RN0x1V5AA6hTPZnyTVWctl4X6hyl6OLCseFw66uLjZjxgxWXFys7BNFIdJrWtelMPDoQ7mFODceFd0UidcXn4UsfDlv061o8F1uYfIMheeiSivWh1y/rnfPZ0zhyzW81nsyQP0hhLRw62dQJv5q/ZuakMsxkcbKUJDgGQL+xcdgMDUhoun4Ojo62F/+8he7oZ5wwgmMIT1t4Sd4TpgwwfPr2pewAxFBEKHINs670XR92MFWSusXylH26SmuH/XTNPJfMV8+JSz3c4lEgvX09NhT06JRjJyWI68ZlYU87VpGqUzi2k35fu+//35tv15SUsKWL19u52Hy/Pi9RoZ0L5WVlcrnElTw5Nte6z11z0XeNhE8XcK8iSBIY1vBQoJnSIycIyu2xQ5PbPRiJ6BqZCaN01PTYbLfr/wEQURCtnHeVQO+UoCQCdj2PV0heZzHWAAXSfZp/tOufD9fSygKkXI5ZQH/7LPPZkVFRezss89mLS0trKGhgZWWlqY1sx51pKwDKb1Ok6ozftLFew/c96rSe5Rz586drKamhjGA3Xvvvbb21ldposnPz1hI9yHEhfm2tjZ7zPN63n75KbeJgoUEz2wI0THU1tY6Fs/zRs+/jHUNbtWqVa4IEYE0HdRQCWL4oWifPT09Ss0gMKgZDCRgSvtVaxBNXCGptr2md1Xn8Sl0P8FT3tZpjWUB/8CBA/b/ixYtYlAIhbyOg4SzVGnnEomE9lx5uQU/1/HhEFYI9Xi2vE74tvajR3FtlesqcfZPJUQrl5/B+UFTWlrKTj/9dFZeXs7Gjh3LysvL2emnn6589r6BDohhAQmeUeHT2BlLd2bPPPMMu+KKK1yN88ILL/QUPPk0j65D1jVw3+0g90IQxJBjohnURkTyE06E/Bn0jr5defgInjoDJLkc8+fPV15PJ5AWFxezRCLhmubnecvBNlT+LFWGWeI1POuAuZdeqc6VNXpyvHcGmC+3MOi/VUskHO6e/MYrxfNU+UNljDnGJfE5y4Ki6oNmzJgxDEj7pd6xYwc7duyYIz8xX6/3xrNuaDwrOEjwjAqfTljVoXl9zcsd3pIlS1x5iNu+mo4ggidBEEOHgVDgZYTD/QTLAgJj/ms2GbxjlmsFT135oTZAEgUsUbsor2vn2sPly5cry+G3NtHWaGb264RCR75MvQ6Tp1GFsxQ1q7fddpunxlaMwsTP4XlEhW6JhFwfqjoT8RLUuTDJz/N7ziZjnij8e9pR6IhibKPxMeeQ4BkVPp2wqtP00ljIf7xDVjVaudNUlimI4Bm04QUZiAhiJJCvd1pzHZ1LNz69yzwEBJVAIm/r1iB6CR66/PzWs+qEW/H673//+x3/OzRq0vW8IkOtXLnSOAKUpzso1TPCoGbQV2g3fM46VB8QquUB/J1IJBK2YZHL3ZPq2sK4pdPe2u9SJr1oeLVlyxbG4JyW9/LtqtoOZUfhV7dBztPlQWQNCZ7ZYPJCY/ALWnRCLHesXl+CftsM6SmnlStXZlfWsPdOEER2BGxPXtbEOt+WoiDFhTZX5DON0OX1wZvtvXgJJEVFRezWW29lo0ePtu9t2bJl9jp5V4QfD0EJQj2o7ksWKIO4vVIJfbpnkTVQG32phETd+yE/T79no3sPRO2tiDgtz6f2169f7+tW0MunaujtKMY7E2hMNIYEz6gwaAg6LUUQwdNrAHANAiYNTtU4g94vQRA5R9RyiRbbS5cutQWzUH2Goi1zgW7atGkuLxxiHkrBw2Rb2ucl6Hp+oCvyUy1DEIUaUz/M8jpML7dXstCnuhfXuX59qHRcp9HkHxA6ba7uzzNSlvTcdO+SV/kY0trV+fPnG41zqmcQ+L0KUqch3lPjvAlPSPDMhqAvv8/AoDvut80wuMjetBy+aQiCGBo07VMOycinIvn+K664Qjm4Nzc3e/r91F2PT53qppwjEQrgFDxlK28vIVopeDL/yFAqP6oM6vWD4jIBBv06TD/NYFtbm9kaTo/6EvNTaTTte/SoLzEPr0h74rV1BmK68gFqrSoy45TXeOYpeAatsyB5RA2Nq54EkdeKQDhhTL2t4TPXXOP4f+rUqSgqGqxWy+CSRZY7lQVgw4YNaGpqMsgBRmUdzNygVCZpCOJ4QNcWQraR3p4epFIpdHd3Y926dQCAtWvXYuPGjfjpT38KAPb+xx57LHOp9LV43/KhD30InZ2dANIjvEhnZ6e2HysbPdrOS8yP051KqQtt0i9K9VFdXY0Ta2sRi8XQ0tKCcxsbUVFRgeLiYke/yHMrLi523YsML69c7rq6OvT09KCzsxMLFy6066aurs6VR1lZ2WAdMIaysjLltZqamux8ZLpTKVx11VXuc1XvhEfdJRIJlJSUZA6lj/EcSkpKHPXB71m1r6ioyDnWiOXg1xSuXV1djdrMswGAWCyG2tpavNzXpywfE8onc+zYMeU4N23aNADAnj17XMeSySTmzp1rl5P/n0wm3RkFHJNzxlBee6SRczE4Cwp5ql2eHqmoqGDxeJw98MAD9nSE6NsTHl/8X/rSlxxflPw3Ho+r3aeoyhTkXoKkL+xXhCCiI4p3XZeHsB9wa5FEbRLz2C+GsJTXhPJfT4fzUE85M8ARGtN1L0G3M6iMkHRrAr2i+2QbGUqLT/mNNINh3xt4L0ng+1X3XlVVxaqqqow0vMq+HFBHqPIpn6qcurHt3HPPZYDCEwPc61l1bp08tz3q1ChtUGgs9ISm2nOB9EKrGpy4r7+/n+3evdtI8OR/otuKsWPHDjZauH3XeZZPU2aCIIYeP9dGqv18+lwUEGRfk1x4dAkfHoO4LBQG8gspbxum3bRpk/JeN23a5HmekZP0qBAE9CACr6P+DNEtSZAdz8vPShbqfYW1kB8SYvl076nuj8HpMWHDhg32Pn48kUiw8vJyBqQ9vXh6V/DD5N30GyuJUJDgmQ0GL6s4cKiESQanWwuVo2R5+8wzz2S/+MUv7HP5cb6gGwBbsGBBsC/BIGkJglATZAAzzEMXHpNHL1JqvxT5ORysQ1ivGLTtC3mIH7yB8BNwMnBta1VVFUPmt6amxm3N7lf+KJ6LH/B3HSXiWLNreC+ycKv9gAhYbpNra9NK5WNIK0SWLVumHcN0wqdqbaiXhb4jrWlZDe/FKA8TaAx1QYJnNhi+ULqBw2QKwiSN7jw5GkfQcgdOSxAjhDDaqMjQCJ6yFTYXPJXW2T6Cg1Zb6bMtOhTnfY2RX0ife1Tt04Xu7OjocIet9LtGLvuxAHkHCsWpuYbW4MmgTn3LH0RY06QVp+VramrsePCNjY2stLTUeGwT3Q96jYkOV4JRC4oqgTab/AjGGAmeuUF6cb187jE4HRf7aTy5I3ld3HavRq0rn2f5o64PghgGyBbkOUfXRuBet8eQ1nJxJ93KqV2DNu6rrVTsF/sYbeSfAPl5ldPkgzwUAcvhuz/gtWXtnkvLFzA/43Lmq1+XhORdu3bZHybjx483FjxNfMk6xtKg95uveiJckOCZDSYvqDBwNDQ0KBuQ6EKCr2nSNTi/Rij/ydE4XOXm29TYiOOc0NqoXJJplzotVxDtl3h/vM/w1FYqtnVug1iQvkZxf1zzKmqYE4mE1i2P1gdlRMJhrvByu+TpVzMI+RIwdWmkMcXr40G3nUqltG685O2ioiLv4Cl+5fTaDpPW5NrHOSR45gLFi8nXV/GGIv6KgqesHeUdr5d/O6/G6fKLptseis5qKPMjCAlRCIhEG+XM3HtfkMEMBgaEytPcfYZnFBuPbc++xqPcun2ipbIcu13Vv8nGNL7bhQJ8IieFFfIMr501ujw8yiQL26rnWVJSwuLxOAPAysrKGAPYqlWrXJ4aPBUwPuUIdS9+FOI7NgwgP57ZIPo/U/lCE7bLysrwcl8fKisrMW7cOCxduhSxWAwMaT9pHO4zDQBaWloQj8dRW1uL++67T1mE8ePHAwA+8YlPOPbLvut8EcschV9OMT+CGAao/CTy35KSEiQSifCZ8/bg00+4tjVs3rwZbW1tyrTJZBKwLJefw0QigVGZ+xu8FAOD5v58ylGs8ZPpQHe/loXe3l4AcPkora+vRyweRywWw+uvv+7w+xioZzLp04L0dRH3i6JfTaY4rr227l3Jhz9lk+sJ73pvby+mT5+Od44eHTxNccrRo0fRlXlfDx8+DAC46aabMCBcT+XPFUj7dLXfXVXdmIzTJvv90hK5IddScDYM+VS74Vf3DTfcwJD5sndZPcKpHWUsbRm5Y8cO7y+9zC9fyB3Id53fl6LJF6SfNsfv2kHPI4gcYRrHOzQh32/RqEdcBsDgnib3XJ8ahbYScLhmcvmFBIyMs8RyyBpmL+1WRUWF3qo9KFH2XYbkxc+o33G/fj0bbaCQRh6jTMYxcVu1T7VtfC9RP1sar0JBU+25BvBcO8aP87TieeK2V0NlSBsl/ehHP2IMYLNnz2Zr1qyxBwBXfppyBtpvcN8EMdzwjeMdJQEGQZ2QphIgxTjZrvWpcC/3cQiehsLJ008/bQuWLr+QzMw4S3YOL/5xI0tZyEgmk+Y+OXMsQBqjqEdPv5pRXi8X6U3zA3z90Ppt+419noJnFEIokRNI8MwGk5dYaiC6L3u/6wT9Kjz77LMZQ4DoDiaNl4RQYoSTM22UCkPBaM6cOWz58uVKf8BiXyL+L/Y1Yh8jO5I3imKjKKtLsIT3B7bOOEunYfZ0FRUGgz42a4L2lfnuF6MWugyFPPkZBxE8/bSj/F03dhsYxRjmMdYTZpDgGRUeL6PXV5+pdWZzc3MgwZNvT5o0ibW3tzs1q6rrRN2YosiPGjgxBARxAm5KIL+gwvstOxnXtfd58+Z59gNiH+MZ1cfjo1MWLJkkWKqEYa1xliSUyAImA3L3ARBFH1Qo18tH+cL2w8IzZnAbyI4fP95XIA0qpCrfX493OtQ90viTNSR45hqp8cmNxdQ6088XqMl0hN3xmzQ4v+NBGrhJfmGhToAYBiinnjXvrk5zKLdzUahTHed/yj4m6ADMmKMv0WlVebhO1Qe26jpeGmbf+OD5Jt99TZYCX9ZpIspbjGYkPuOdO3cG0nj6pV2+fHkwjWdYgTRo3eXqvRnGY18Qec1pDknosax0cwAGf5G2yisqKsLAwEDaInRgwHmekJbT29uLV5NJ7HvlFViWBUuRxpEF9Jafxla5Yvl1+8Xjqn3aAhqkCULU+RFERPT29uLVV1+FZVkOq+2rr74ajDGc0NODqYrzptbXoz6zbWUsaPfv3+9Kx4R3f9++fc5jAIosC4wx7Nmzx7ugqracvvjg/5aFRCKBBQsWwDp6FGAs3c9kjo8qKUFizRrMmDEDiMUGs8j8dnZ2ArNmua5TN2UKevr7UVpaCsuycN111+HIkSMoKytzpLUA5z6xfLr+KmoCXCOZTOIrX/kK7rjjDsTj8Wivp3tGpsdN0wS5tiqPzL66ujoA6XfAsiws/NzncLi/3/E8rUxaPj4C6bHy2MCA/Q75eTfYtm0besU2pSqbSZ361UXQdy1X7+bxMvblWgrOhiHXePp8Jemij/h9aUGjxYDwpWfy1WikWfXa57U/CIX9GhFEZKjaqt/UM2NOv4ey5odrDnXHtX2Fu3DqbV2aDOLMjap/0U2reobxNLx2JGnl9Hw76n4pc985j3yVg3KHukbY54XBJRUMaa1oVVUVYwCbMGGCUqvut+1a7+kzxmZVfpP9hAvy4xkVuq+PjMairq4Oe/buRWdnJxYuXAg2MICenh79l1ZmO5FIQMw57DfOrFgMyWQSc+fO9U8sf9Wq9oflePlKI457RL+gvBWxzPvv8psptIumpqa0hlCCAfZ+/qvzbci3S0pKnH0Gb88+/ZXXfj5zA7h9eHKfxLFYDC0tLQCA2tpah69iLQa+FHkf5vBRmo0GSjezE4Le3l6kUil0d3ejJnO/a9euRXd3N1KplO231JOg1w5y7zp/ln5pdeNBRL4ve3p6HO91X18fbrzhBhw8eBBVJ5wAxhhOO+007/IKxONx1NfXa68Xinz4SCXU5FwMzoIh13jq8PvCMvjq0ll+8j+vr7/TTz/dXjNlHH866JdgrrQGBDHM0Vn0cg2gzuDIz62TLsKZ/OeyAg+iBVKcp1uTKecR1jjL1wgrCk1iCK2eqV9SSM/DMzJUFITNLwqtXRCttcn1MtpK7hZQfr9145xcv2Lo1jlz5oQfz8RtGtsihTSe2aD7+jP5OuJfYQE0DzzCBV/3xc/0utrll1+Ob3zjG6ibMsXWQKy6+277K9y+TlDNJkVvIAhjuGawWNAQLlm8eDACkQSPYMY1h7FYzKE55MfPbWxES0sLZsyYoewbAACW5a0lDNAHOWZuPvc5dHZ2umduhHJYljW4ls+gX2xtbXXVSWhNol9kHb99PuWSCRz5aigjxPmdF2QMMznXcBYtHo/jM5/5jGtdJ/Mor3zknHPOwZlnngkgHeFLS5AxO2g9+2l9CXNyLQVnQ8FqPIPgoYUQ18GcffbZLqtS/uf1Jci3feNPR/E1TBAjGZhF55E1hDNnzmSVlZVs06ZNvr4utU7GM7+iW6Tdu3fba+TENeSumQ6/9m6omfI8L2Aefv4/VX2XSwOWA6L0S6r0P5orbWUu+++o85C25bXLOi0nA9iMGTO049y8efPYqFGj7H3iu5Sze6Rx0xhyp5RPgqj8peOya5Ft27bZAw0DWH19vW9DlbcdLk5MBpGAZTY+L2h+BFEAzJ8/nwFg8+fPH9ypeGdFAVEcJL0iECkR2qos9HZ1dTEGsC1btthpnnnmGYcxkBhiM5BwqNsOIGzy8qmEdPG+dVPUsh9kcb94bUe9ZNl/6J6V10d7ziJfDae+MIgALG37LSsrLy+335WNGzeyyspK+/0uKytTjnMmBn2BxjnDewmV33ECTbUPFSrVvcfC/rKyMtvlhGVZabclGDQy+Mtf/hK4CEczblGMy6mbLjE9HpSw00gEkSPEad/169cDANavXz847dvT4zqnrKzMfpd107EWDKZjhfbwrW99C5s3b0a8sRHJZBKtra12/pzzzz8fMcG10f79+2EBbvc+HlOfngaJAfqG1tZWWIByqjqRSKC4uDiTDXP88jpRGVsBmf5PuLZjSlzXfxj2TfKzYopyyfgtkdASZKo3SN8ath82mYYOspQh5NQ9k7bffPNNAGlXYZdeeilee+01+/jhw4eVLpcGMvkWFxc7p+V174dfXQe9l7D1QaTJqQicJcNO46naF2Bb9WXf3NwcSOM5bdq0YFrMqL8K/dISRD4xePcAvTbGbl9CfqqpeFUwCBhoxfjULwPYmDFj7PPmzZvHJk2axBgGp4IZ1C6X+H6jNgnY0/Rh2rDXVDWDM5La/PnzlX2UbEylijEfZkrclEBT5xk8I1+F7d9MzstV3xk0X79xTrcfcIR05TMB4pS56dgmbjv2eVw7VPnzxVBfP2LIgXxUBHW6nqXTY/HLPo60ZmLTpk34VkUFcOBA+hI+eezatQtAWosztb5+sDwmTodF/Bw5B7lP0nISQ4Vf+wyopViyeDE2r16dbqNcy2hZQCrlSMcdZXerMhHKwR3LMwCHDh1KFxmA9etfp5MCwL59iMViYMjMaCjo7Ox0OHmX4Y7vY4Dt+B4Auru7wRiDfabOgXjmt76+Pl0+OB3h21rY+nokk0lYloVfZ+7BrhOp/rkmccqUKbj22mtx33334cS+PnRVV2PKlClCdSmuA9iaSldZDeGOzUUH5zpkx+iyM/xQmJyXq77TpO48HMgHKVtdXV3aWG30aLzxxhs4Nm4cDh49ihdeeAFobBzMOuAtAMD1118PWFbayfzUqc6DfmNbhGM3EZCci8FZMCI0nj5wp7iqUHp8vRn/uuMaAQT4Kly/fr13+YJoPULeI0FESsTvXiKRYMXFxUotWHFxMVu5cqU23CXXVopaHe6SiO/nZeYzGnKbk9uv7o8BrLm52dUnwEdbJ/cNOufdnvWc2RYd4Xv1QYB7nSv/4+EWGdNrEuXriNewXesEQbgXr5CexyW69hRkbDMZR/j+zK9u7axXe1Dtt9uQaTmCEMVYeZxAxkW5IKxQ5tMIxYYjLpiWO/TKykrW0NDAPvShD/k2SHkwMylHVvfidy41UsKLAng/EomEsl3J+3VtlTGnwZFqOlY3xa0T0FTtWiXg2kKTxyCpE+QAQ4NEEU1ZU6mU7WtRVf6SkhJ2//33Gz+TXFqTe06dByXs2KDbP5TtIYpxzjAP/s7OnDmTLV26lDU0NBhHNJLfwZUrV+a3/FE88xEGGRdlQ9QGNLI6X9ovLmZnLL3YXabIsvDaa69h27Zt2Lhpk+/l5Tvo7u5GKplU+8bzm17IZvoh4JQMcZySy/fDsD1PnjxZu98vWhFHNR1rGy6lUo4p7kQigcbGRmxYvx5tbW3aaEXAoL/QRFsbPv3pT+Ohhx4CACxcuBCdnZ3Ys3evHTtbB4+cpKpphzGPwbPoziwrUEU6ampqwsb2dvt/8b7WrFmDs846y90P+TwjXUSlbLANOy3LPXVuUCYHQd5fn/HALz9llCcVYccx3bX9fEObjHlSmerq6nC4vx/PP/88VqxYgT9u22a3K7/Sy8c///nPo1147zyvHda/ZxA/1+QT25tcS8HZUFAaTx0Rfe3CR9MBQDsdqEuv3CeXI8hXXxRfgoXyZU8QAn19faympobF43HW0tLC4vE4q6mpsadfPY2HPN5jsf2p3PcwgG3atEmr4Vm2bJmt1bzmmmsYoIjwo2rXCuSpTSbeg5yXT115TlWb9FEGeGp3j1OMI9WJRNnPeoxhxmmktFwbr2oDJSUl7NZbb/XVeIrHjcsUxVhEY5gNTbUPFYYDgJxGHBDEAcpLqAwjeNrrorLoJEJBwiYxDPCafg3ry1E1qIp/5eXltuBZXFzMpk6dam9XVVUxhvTa0I6ODjsPcX0pXyPOGPMddGWBkQHegpxH3yD7IBbr6u6771beKxckgqzPjHRKfJiSSwt/FyaCZdj8PIQ/0Tet66PIYGzLWvAksiaIvGYxVrh64DfffBMVFRU4cOAAysvL83NRnVVnWMs/k/MsCydmrDu3dHXh7xoasG3bNliWBfnxMPhPQ/A0YloGGJXDtR20PsJCVoVEAfPyyy+jsbHRYYHd19eHrq4u1E2Z4tlGuru7MSsWc7RFO3xgpo3zfQMDA7CKitB/6FB6Cnj0aFday7IwwJi7bZu0VcsCGxiwp5kP9/enp5ml9pdMJtP+RLu63D5CRTTXefbZZzF79mxX8lQqhVmzZvlVt/4axyHcqp9v83dAHBsCD+MhxijPZxB2fMwgtxFOKpXCrFgM1VVV2L9/v71fHtssAOPHj8fBt95C+4YNOOuss/y9uhi2l1D3fRwSRF6jNZ4yupco6P4g5zGGnp4ee63Vr371KzCknUK3tLQo12UBcOxXpREbcbfo7sXESbCq3LrjQdbP6KDGSw6ICxjuEqazs9O9ttLw3bUUz5c7wh6VcV7O04wePdped8jXkfK0XMjQOTzPJNJu2+VgzL22MYOXc3jf61gWSktLAYRYn+kXxCKXhGx/xusuQ+IVL54B+nfAC7++3jRNkDw0jtvb29vx1FNPOU8DUFFRgd/+9rcAgG9+85v2fh1vvfUWAODyyy9HvSh0mpTD5B1TjXO5fDdH8niQK7VrFIyIqXY/db9mvzzFtGbNGte0gvjnNx3hmE4zeexhX42oX6nCfkWJ4w2/91HR3rn1bmNjI1u2bJmy3WrXWQLK9aVMPEfV7wSAu3lav369nW+oKV3h+pGuzyzEPkXII9S6y4DoLPyjvpcw77fReWIa6TyvMUw3znmltSzL9q7gWb6w5Q97PNv0BQ5NteeaKNTvQVT0loVfbtqED33oQ8opBh0MaYv4M888E9v/9CeHRiLQNEuYMpsQdT0Rxy/5ek9CLkc5fPgwSktLsXXrVsyKxVCUmSrlzssZoM2jO5VCLBZzOTy3p62DLIvJbItT6a2trbh79WrH8hw+nc/LyWHydTzg98ynhY8cOaLVsIZiCPsG7pDfsixccskl2LdvH6qrq/HLX/4SjDGccMIJbofmMgHK393d7f0O5Its+mzNmFKscOAvjm3isgK+XzcOMgD/fOWV+O///u/w70cul5SNYGiqPRuimDY2yTvIVDVjOOuss1BTUwMAaGlpwbRp07QuWMTtE088EX/6059c+QUqn1+ZdXn4EbYcBCET9D3xe0+jcL8i7Ofue3h8b76M5tjAAGpra/FyX582Dx7h59jAgB0rnAHescI9ptoB4Lvf/S4A4K677rLdPJWXl6NEiK9uZX4BaVrfsK5tl0WAvV41Uoawb6ivr0c8HkcsFrPXHvLISvF4PD3VyzFZ2uRD6HjxUaGaWg46Pmrut6urK31Yc9pAwOf86KOPul0I+rVnk2eUK9lgJE+p68iZ3jUCht1UexRopiMYc0+/+01NyMfb29vdU2ZBpiP8yhz2OEEUEHzqWY7HrsVk+lHa5u2YAeyCCy5wXktqL11dXeyCCy5gW7ZsYYwNtn3Pcij2i1HSVH2FlyN7P+v94w0/h/yBIysZkLWFv8/7kRMMxhfdUhIg7d3Bb5xTvceOfSb36FdOXZqhrtMCghzIDxVBvqR0X08eX3eyBkGHKgcLwGWXXYZ4PJ629lNdL4iWczh9pQ2nshL5RfFutLa2YvPmzf6GNZwQmjex/T755JP6a1kWWltb8eSTT6Lx3HNd5/I0qvPk8tXX18MCHPHO7eQY1G7yazBE67Q9UDuMwNAnl0Y/3CG/is7OTjQ1NUV+TZcGOaplC9loMYPkraG6uhpVVVUoHTUKU6dOtZcoVFVVYcOGDcrlZLoZvvQlFVp6EX6PJvfqpwk1mO0YijotdEjwDEMEUye+eZtMQwOora3FySefbORiCXBGWnHlF3YKwq+sQafoqaESJkTxnmTejd7eXsCykEgkbE8Sa9euTU/ZpVKuaDsqoSaZTGLunDlGgk4qlUJ3d7f9v3gtXh6+LUY8EtPI9+BHIpEw8oRRWVlpu1DiU7qzFMKq++SQSxKyTSsgfjQE/oDwQ7i/ZDKJhQsXAshNZCXTcgQiyvHJa7/fmCEdr6urQ19fH4688w527dqFXbt2AQD6+vrs5WWqum1oaEBlZSXKMh4UAKfNwztHj2b/AWAyztkXD/lchqtCJxtyrn/NghE31R5UnW+QX39/P0smk75T7fyvvb3dbDrQ73iQPHT5EUQuCPGOqdqLHDdazNthyazaJ5dD2pbbqG46kSnKwbddeRv2L3KfwP+4U/yOjg63c/iA/RLHsWwhR21fdLBeWVnJALBJkyaxSZMmMQCssrIycmfr/FmPHTtWH8FpuBBkLDJ5hn75BRgHVUEPampqfMc5vt8VZMHkHqJ4T8PW0zAeHyly0UjApDMQGifvcHWDmdwgvfLzvH625xFEgdHT08Oam5s9hb9EIuFYI8mjB1VWVrJEIsESiYTdBrkLIgaoBR3AXh8ot1Ee5cgvjKByDaFhu+ZCppi3GJpTKTiFbdeZ/AO7GgpwPZ0grfsLiyqCUFVVFUsmkyyZTLJdu3ZFE1kpX4JPlAQYr4KOF6q1rTrB02jM8yqb6b34kcv6L9AxlgTPXBP1Cxjky0fTQHbu3MkqKiqMGiQD2FNPPeWZn7KTMCFIHgXagIiRidJoKICwImtDVecyeGtK+bZsUMF/xdjvcrhAiGlEAg6qXIPEABaLxVhNTY1Tu+mVrwGigMbLH1mIR0WZvAx9ZKHe5d8x0KXd2nD5PRix5EoYDjo+ZrYTiQQrLi72FTaLiorYZz/7WbVBbVDBM+y9hK27YfY+keCZDUPxsMN+jUnb/f39bOPGjUaCp25ANCqbyXk6hlljIkYO4lS4KIT6CS7Nzc2MMWYLLV7aFfm4rZn0ETwdQqUkePIpcIdwKmLaljPkOv65TkCLQuuoQ+dgXXwW2VrmD4Ul+5AStbCpek+DnCfl0dzc7PvMc6bxDNjm8soQlYOs2rOBMfX+KCwyTSzZg4TzEvezdPi72tpaaFI7qKqqMrP29CubV/mGMvwdMfIxaJPcSKe7u9s20lm7di2+9a1vYfPmzbjnnntsC2XVm1lZWYkFCxYAgMtQwe/q3amU1rjhyJEjqKysBABMmDABDGkDildeecX2P1hdXY0TBd+Nf9fQgNLSUuzZs0fdf0j9wWBBnSX1tI4Oaumr2PYK8egZ5jMCVEYoRUVFvs/KhKGwZM8LURi3hDVCzcKY5pZbbklnGzYDk7EorMFcNhbz2TIcxtici8FZUFBT7UG+bKL4kgqZHw/P5+X/jG+LhhHavKO+l6AEyaOwX2diKFBo3+S/VCrFEokEg6BdFA1t5HdaTifukzWU4nmqMjEMTtfq/A9y7eSiRYu82630/nOt7lC0SZ0GMlf+QEUjlBUrVrCSkhI2atQotmLFikiNfvh9ye/JsPNzGlTrGCSt39hgMnb45Z0Z43Rjm7hdVlaWDgfrdx2/ewl73nECTbUXEkFfxrCCp7T94osvKqcCxQbJB8oNGza4Lf+C3Mtx2MiI4YFuepTBPVABcFjP2sKK9K6LVraNjY2sqqqKVVVVuaybvdqIbDwkD5h82pavl2xra7PTcMOmeDxux1d3XQPwjyHu19dkga+AFqSvMURcQnDo0CF26NAhxli0ywlkK+tha8keNUHGtiACpse2l+N5Vdt2WbhHJAD7ltmPETKWUqz2qMhlbPIgeQeIwezYtixtPFulU16xPJq4ur7lp/i4hAm5fMZS3jzOtQhvA/y3pKQEP/jBD3D11Venp6EtC4f7+9PT0NK7ebi/3xGD3Coqcu07cuRIOkSkR/vs7u7GrFhMGXtaTCu3Wx5H3d4vpO3t6cGrr76KWDyOmupqVwzxWDzu339EwMsvv4zGxkZMmTIF1157Le677z709fWhq6sLdXV1kV1nKMh5DPpCwe+diGIMMEmrGdu6Uyk7fKzOybxu/DMe2wzG2NDtJso8CoAg8lqJ59HjnVw+UD8hz6QcBvt55+iFZVlYvny5v7CpzyBcByQeF9MVSEMicgB/5tk845DtpaioCAMDA+kspGOdnZ2YNWuWIw+lKCHutyxYmWvZgkdmn6kgYmXKhYEBu60m2tpwFdLrU6cCKC4uxrFjx4QiDN5feXk5YFlIJZM4oafHjhHOADuG+Cv79sESBG82mJFRGb1vQP0s6urq0NPTYwto11133YgR0MR7iDSC0HBA12eLRDG26dII2zx+Pfbuxfjx4/HWW285BEyxjStXU+rKFrRMfvnphFe/ejRhmI6VZFyULUGi/QTJz2TBt4GBEjcg8ioRY8xeqK04GGx/0DTE8UUU74Suc9fAB6hYLIZly5Y5jhUHjTYT1mBOMXiK5QLSBn8A8PjjjwOALUSKQqfMwYMHAQDxeBz19fVIJBIoLi7OXCZ9HV5iT8OegHXqeV6GrI2Yhgsj6V5EwgplunEpyHkG4x//uAGAV199FU8//bTjeOieJkj5dQoTXR40JgLIk+B5zz33oL6+HqNHj8Z5552HLVu25OOy+UH1smWhoQytAfSxcvXLwWUNKn6hmV7PpGxRYFIm4vjC4x3kA1RnZyeuv/56TJ48GePHj8fSpUtxbGAAtbW1qK6udp4UZOAwaQuKgbSurg579u7F9773PXSnUraguHHjRnR3d6O5uVl7T4OXY/ZSAYa05fXHP/5x5Yfm/fffr7e8zrcHipE0AI+kewmCiZeWIAQ5T5ppKCsrwymnnIKxY8Z4njZ+/Hj19UwESBVBFUQEgDwInuvWrcPNN9+MW2+9Fd3d3Tj77LNx0UUXYd++fbm+dP6JaurKa18QodayUF1djcrKSq3Gk5/FpyDtr8YgjSVXaXWYfFkSI58AHX1ZWRmsoiLU1dXhyiuvxFtvvYW3334bbGAAPT096XWHYV2gZKnpaGxsxKxYDK+++iqA9NR4LBbTz0IouPPOO5FKJtHd3Y1f//rXyjQbN27U36Pfh2bUmAzYxPAhX32vakYwQ11dHf526BA+9alPaU9/66233Hl5EUIYDnzecUjOBc9vf/vb+OxnP4trrrkGDQ0NaGlpwdixY/GjH/0o15cePkStPRTS1NXV4X//93/xxhtv4F/+5V98T33f+96H3t7eaL5aVRrgKL4sddcjji8CPPve3l4AaUOjn/3sZwDS/jy3bt2KP/zhD+bvfJApaUPhSvZ5Ke9Pn245fmW+8IUvIBaPIxaL4Y033nAWOfP72GOPoTuVQiqVSt/vUAp/NEgPf7IxiMlV3gBOP/309GXE7ITtIsvC5z73OQCD/YKWXCpKolymN8w+3nIqeB45cgSpVAoXXnjh4AWLinDhhReio6PDlf7w4cN48803HX8FT9QvZpjjPueVlZWhYuJE/OAHP8Df//3f+zpTrq+vz919mUzP5HvajxieBPgYqa+vhwUgFovZRjf79+9HLBaz10caXSfIu2m4X+eU/JxzzsHG9nbU1tYiHo8DAGbOnGkLn8uWLbOn2MePH48SaW2nXeTM71//+lfn/fot8XFkErw/SCaTmDt3rlmgCmJ4MBQa8SAwhosvvtj1gSb+N8AYvv/97wMYXEdtNC75KVWCCtSqWYag+anOEylQgTSnguerr76KY8eOoaamxrG/pqYGe/fudaVfsWIFKioq7L8pU6bksnjREPVXX9ipdsMX7Prrr3d8/Xmddf755xvlGaixmJQ/bOMjji8CvCeJRMJ+77lgxn+VRjfSe6oUoBhL77MstXAllclLELPgXmedTCZx6WWX2etTAWDr1q32us5vfOMbOHr0KADg7bff9jRC4vfLdPfrR4h+rrW1FZs3b0ZbW1vgc4kCJeh7kKtlWB4CYWNjI9544w0sXLhQfRlh+yMf+Yi31jPITJxJfxR2qU5YClRhU1BW7UuXLsWBAwfsv76+vqEuUvaYaGXyoV3McMYZZzhP02RnAW6tdDYGT2EJYuREHF8E6KSbmprQnUopj/FwhzrBcMnixWoByrLQ2toKAIPHPMrBBbF4Y6Oj3Ny6/d3vfjeWLl2ayXrw3v74xz+iu7vb3i+GpBzMZvC6lmWl3cpo2oZneMcs25MuRGl3d/fgFD9RuOSjPw1iZKtL7zMLUV5ejpaMVhNwjnPi9i9+8Qvv2Q4/ggqNUc/sDdfxL1LX9RKHDx9mxcXF7OGHH3bs//SnP80+/OEP+54/IiIXBSXIIxHTqs7THYd/pAe+XV1dzVKp1GDUB9Nrh70n4vggm3eCn2uSh5BGjKbD4I6mI0b64RGDUqmUoy0wpCN9bdiwgTFhH28nDGCzZ89mXV1djAGOfKqrq+22xduUeC8mbVK+F0jHKysrWWNjI2MAa2hoYMBgKM58hHcUy8OvqwwFSuSfqOs+yBiQTX6qbZO0jLEPfOADrnYkt63m5ma7rQYuk0kdHCfjY0GFzDz33HPZokWL7P+PHTvGTj75ZLZixQrfc49LwdOPIC+6R6Phg6yqQYr7dQOfUZmiaJx+QkbUHR5R+Ph9ZGlQhTtkANu4caNDMOTCpEqAktuLLs46j6cuth2eRs6Dl18Ooymm5fs5OiG6o6PDDhu5e/duVlNTwxjguN9chnfUhSjl98JDgRLDjELpI4MIngDbsmWL8diGIHmbljPqtAVMQQmea9euZWVlZWzNmjVs27Zt7LrrrmMTJ05ke/fu9T33uBY8TV7GIA1E2tfX18fGjBljpGlRDXyBypRLoZEY/uTrPQAc8bwHBga0AqZqoOLbRUVFtqDnNVPAkNam6IRJLrSKdSBqWMW0spbSNGa4fL/amOURPgOVNjbXmlZihOH3PpqMKZntH/zgB2ohU3o/V65caZ63aTk1ZRqJBJHXcr7Gc/78+fjWt76Fr33tazjnnHPw3HPP4Ve/+pXL4Oi4JshajyhcUVgW6urqsHbtWn0SnlXmlxsxcLSGEn7X1qUN604pCMN1PcxIJ8g7kyVyNJ0HhfWSA5lyMJY2wuERgGS6urrQ1dWlPMbfsP3798MCcMstt+Do0aPqWNKM4aYlS5R5cEMjXWQl0Sn+woUL0dnZOeiPVL7foiLMnTsXqVQqHT9eRQ6eAb8HV3AKglARdh2/z/Gzzz7b99IMwOc//3ncdttt+ryDjFcmHMfjUV56hEWLFqG3txeHDx9GZ2cnzjvvvHxcdvgQttMPK+RlcMSmlpP7ZBdvbPS3WFWVLws3Gb6EtagnhidBHb4rnn9TU5PSnZEF4IEHHgAwKPwVFRW5fAPqhCouvJaUlOC9732vtj3ZhjfJJHp7e1FdXQ2GtNunlpYWz8hKthBtWfCLGW631Ty0ATEUaEtLC2KxmPoeiKFjJAk9Pu90Y2Mj3jxwAF/72tcc+y3F9te//vVoyhSFdfpIekYS9ClaqAT1d+kn5GkiPby0cyfKy8tdVrL2adL/3GK1JjOIrF27FrAstcVqFH7IghD1FykRirz5bzR5Zwy0/5xiSUM3efJk1NbW4tjAgC1AMaQFKy5E8TjrDQ0N6ctJ2a9ZswYvvvii9vI8SlEs41uTayy5JtMRWcnvvoR7Ea3LxbbqZV3u+dwCtCdTbSwxhAynj/AAbVh3XnlFBT7ykY84D2u2AeDmm292xX6PxBVSEGXMcHpGQcn1vH82HDdrPKN4DFmsrYTHWjV5HYx8XDa48C1HkPUzQY4HpbBf/WGNaB2eFVG3Cw1e6yX7+/vtPOQ1kvb6SYAlk0ltG1K1EdX2vHnz3GUOsi3t8y2HVE+LFy9mLPPcurq62Jw5c9LW+SHqlCByQpBxQtru6+tjo0aN8m2H8Ggjru2gY1u+x7k8UlBrPAkDgnzZhF3j6aE1vf766/WXk/6XpxZZJq9QTqmdGTnK5HncUcARpNkcynspFP+NUfhrNZzm4s7f9+7di56eHmzp6rI1dHv27kVdXV16+jqThzydXTZ6dHqqmzHU1NSgtrYW5zY2oqWlBaeeeurgOmmpDLo7ee6552x/nUqNZFeXtyZZug6fxRDLYcHZVu3nlkph3bp1sJB+bt/61rewefNm3HPPPb7XGbwx9Z1RBCNCi25WLmxoSfHdlN7Turo6vPPOO7Z206hHsSxs2LDBJKWZ9tNvrA+7pGwow9+GIddScDYMC41n2CqM+ssnbH6Z/YlEwlfj6bVtW6z6fd2ZaHCCUNiv8HEDhPch5/4b/d4r3X4pjajh80xrqKWXtaMdHR1GbYf/yu6WVOUAPDTJUloT63JVmVTpXX58TQGi04AThUW++uwg7V2XJrN9/fXXBx7bdG3RuEx+/UqIvqsQIY1nPgmirYzivCCRkEy0R8J5ft9JquOywYUvuq8/v/owWfNKDBliNB2WeSb811cbHvQLXfXMNe+BQ0vImK3hg2U5NHxemkbTd0zUhlqWhdLSUgCDbYTPFpxQWYlp06ZpZw8AOOqLa5I5Lk2yKm60gJd1OX9uXk/AKJ69hKxJVZabGN74zVLJBLFOD9vH+1zje9/73mBSwyzLy8sdBoDa6wWtjyDaz5E2zuVaCs6GgtV45rvagn75mH6hCWzZsoUxgJWVlbk0MVBsNzQ0sDPOOIM1NDTY62eMymFyX2G/cHUU9ms+YhA1bOK7Esh/Y5BnpXhneMQge22iqCVUaPO0msYA19S9u+LaUQbYa0d37tzJBgYGtPWl0nKKaTzXagrw6zPA09enTjMqXqOkpCSQ83cxH4pgRAQmTDv02hZIJBKe77rfNmPMXgMduBxBxvKg4/4QQxrPXBO1tjLs9fzWdQQ4r7GxEX944QUcPnxYWwx+1oknnoh4PI4///nP+MAHPgAA2VusRvhV60oz0r4Wc02Wa4RkDd+sjOW30fVM3llN2rlz5+Jb3/oWLAB33XWX26I7lUJzc7MrhjlTaRp9tC98vaLXusW6KVNs624AtnX3u971LliWhT179oAhrR1VeY/g2hVVXHbHWk3VDEfGV29PTw/YwIDaulxIz+DWiIpl8ozvroBrUjMjtV1ufj9ZrQcnRj5B+oGA551xxhkoKiqy3Z25knpkv3z5cgCD7gSNyqErk2p/1OszC3W9Z46F4KwoWI1nPjDREgbJw3Ab8ted5uuP/1VWVjIGqNeA+Wkuo3j9gtRTYb/uwx7TaDpR09PTw+bPn88AuKJxBflzaGZ93lPH+lCTd1CxLV5bV2YG9VpNBs266hCIz23ZsmWO62QT331YRzCiviI8Yesux2ObuH3gwAHGkI5ktmnTJrZixQo2YcIEX43n5Zdf7oguVl1dba+BDnzfPH02Y30BjXMFFTIzG45rwdMEvxc2RIPkcZZVgqduoJS3PcsXVvCMQhAnco5xiMZsEN5vLzdGpu+vr0CUuV5PT48t8Mlx3e0PrwCDhWzQJ/7ZU9uC4MmFQB6f3VPwDNgu+HPjQmgsFsv640FV7mEjeBL5IQphLcs8wvQZfFtcPhL52DbMoKn24wU/Fb6Jil/aVkVxsQ97FCXn02diOQt1+uB4RHoWckhKr2g6XnBXR8qp7My7YAGIx+P2dhDk9BUVFc7IOop3jBvXxGIx7N+/Hwzp0JjIlIMfV7oOyuQnTtHrpq4ZhKltxpSRgE4UIwFFsJSEPzc+Pd8luJYK6/ydIhgRvgTt1/3GNhFDF0Ne7gTFq6hyYMLykQfDjn/ZtN/hOhbmXg4Oz7DVeEZRrSG0lVHkIU+PmX79tbe3668fVFsZ5L5M9hO5I6y2wQcTFzyJRMLW0OveTa6R4No2VdpkMulwheR1PZXWgwGsuLiYJRIJZ7kV77F4nGtIVeVKJBIODaqRJjkbLVCOyIsGnCgshvLdy2JMUbVDrzFPPObS4ocdp00o0DGRNJ5DhY9bk9B56LZFVPuDpM3AtRQMcBthaM8CLrvssvSGZIhhYoThOi/M8cz1AqUfKoabs18vgr7rHum5ayBTJ/RinHU5V/7uDjDmCHcJwDYs4MY0lmXhhRdeACC8p4pnJGsoLeH3Ax/4AGbMmIG7V6+2yw2kjYR46D1+XyxzvL6+ftC5u1hFAK666qq0BjVTX16aZNtBe1cXlAzhOxaVBpwoQAol1GNQl0aK8onaSrkt2tmpstKVIywmY0OQcS7fz8IQEjyjJMqHnI2gFcTCXRJq+VQbADz//PN46ve/x+c//3l38QzL1NraCgBoa2tzly3IUoACbUChMPmQGKl4vNfyVDYA7JNimTvy0ORlAZgxYwZqamoAwJ4yfmnnTnvq9/sZYRRIf2y1trbCgvCe+t6GZQ86DMCvf/1rOz/AOQX/vve9z3Vf/Ff19JUW6/L9CtvcwtZR9uP5HSPyQ9TvVb4/kBSW7q4kHqe3tLQAgHr5SFgFkUm7DeKxpVAVG3nQwIZm2E61Z4PfIwmiUg867SBtQzGlAMV+Ps3Iz+vp6WHJZNI2wmAYtP7jx4OUI3DaoOT7vKjzyBdZ1NMcXdxvAd3UOaDxIwk4LLJXr17N4vE4YwDbvXu3clpXnPrdtWsXYwCLx+Ns0qRJDLr3VLqmV1uQt0tKShzRUnTn+k7dSchtjOehjDI0nN4x4vjC5N0MO1Xtt1/K94UXXmALFy70bM9A2nPG7t277fP6+/ttv56i/2Djexwh7ZOs2o8Xoha6pG0vQUAePBkbdN4tHuPOrn3DAZqUL0j5o2aEdA6RY1AvynWPmvPa29uV71gikdAKVHKoStMPE9V7bBK28v7772fFxcVGQqhoeW4qeDrO06DKQ+ugnd5dYrgR5J01ae+qbWmfn4KF/02YMIExgH3729+283CF3zW5lyBCdBTn5Rha43k8Ik1xO369tj1oamrCO0ePqi+n2Men1efNm6cNnzhKZ/3uV76hnjIIMq1kEqp0pKCpFztkorxeM5VKr9fMLOcA4KgXe60wnO/YVVddpQ3bKIeq9JquSiaTOP/889HW1obm5mbXe8yE9Kr3NNnVhdbWVqxZs0a5PpMjh5LtTqXs/QxOZ+21tbUAgDlz5gAAxo0dOzh1p3ln5s2b59o3kCm7y8METbUTw4Gw4SfDvt/SeWLYX/vSYvLM78GDBwEAN998MyxAuSYdljW4Jt3vXkzGi5EWECXXUnA2kMYzAH4ajiBfXdJxYNB3IDJ/S5cuZbFYjE2cOJExgLW1tTmm1VVhyWCgyTEtUyiCaoEK9MuSMRa8HPkut/DMxZCJDs2ez3niH4NP2EbD58m1rzpNo7itzDtz/Morr2RMaBf8HhsaGmz/lwxCKFlA6Vy/o6ODPfPMM3a74dfWTZnz6XVdPRm3MYIYKZhoOQ3P82pbqr5C3uc1Y+IK5+tXJpN7LCBoqn2kEVRolF54421NHmK86VgsxmpqahgD2MDAgKNhaqfVMejOJpIGFLaj0eWRi/THGfIaJ7/1ml712dHRoezUjV2WSKjWQ6oGE3k/vy8GsNbWVsegxCN2NTQ0MIZ0HHbeLhhTTPkzjWshqf34CcByWiPBM8t317V+jSCGmojGNnkfb+PieOUlhKqEUb4tfyTz6fj58+fr25NJWy3QsYgEz+FALoWksHmo0gCDA2ZG2NyxY4ctCIwaNcqz8Z166qkODU+gjiGq+4ryvKgplHJkicrvJvcJK3fefhq5UBFvPAYflUZC9742NDQ43lM+WMjp5YglSh+Vhu86F8Tla8gaXi9hvqioiJ166qnhQ5R6vIcmPlUJIlKi7tc1Y5u83dfXZ39IXnPNNZ5jm+7DT/xglKOdMaSNk/isidKAMcy9FABB5DWLMcZQoLz55puoqKjAgQMHUF5ePtTFGT7I69zkfUG2Ffu4KxlxjZtq+4orrsDatWvT6RnDkSNHUDZ6dLhy+N2fVx143Euo/MISRR65ukaI83p7e/Hqq6/Csixccskl2LdvH6qrq/HLX/4SjDHs3bsXl112GYqKijAwMGD/plIpzJo1S5vvyy+/jMbGRkyZMgXXXnst7rvvPvT19aGrq0sfQUdXfsvCg4kEFixYgHeOHtW6R+FlSyaTmDBhAg4ePGjf1yv79mnPKykpSa+D1lzb5H3r7u52uGLibSiVSmFWLKZMK7e57lQK73nPe9JtLAJfmX7P9oQTTsDUqVOzvg4xRAyX/iyqcgQYDw4fPozS0lJYloVNmzbh0ksvBaAe57zGQT5Wiujy6O3pSbcnj36sIOrag0DyWm5l4OwY0RrPKIjii8hDU6Q/xXuKQdxua2tjDGDr168PV2a+37BsoRhmX5ZDhlQfEJ61uI5T3C+va2SAkUZOtlT3jdTjg7x2i2+r1mSKx13rUqVtnq+yTCbvFdyx2Pk1XHkztxY5sDbYEJNnSxChiOLdCZqHql16tE++PMdknBP3lZSU2Mtwenp6PGcpmPyrK6fJvRQAZNU+nAli+WzylRckXzE/8UtQIpFIoFjhbFfFpz71KQDAhz/8YaP0/Jo8Gksg/KwDs6kPwlUfohUoyxzjv9yyuqenB1uEuN+H+/vTWkuf+i8rK7OvZ1lWWlPuhYFlqAW4nET/cds2xGIxR9lEi3DGmFLbqXI2nTnBv3xSO6uurgYD7Jjm5zY2DjqllvKrrq5GZWUlAGDp0qVm8c9DvMcmz5YgQmHyPoa1ZI8o3nt9fT3i8bij7ftGLgJw9OhRvPbaa3YesmcYMT3PT+vpRUfU4/5QkFsZODuGncaz0Kozmy8mvy8wxRccPL4Ey8vL3Za60DgWh9P62LOcQe83yvNGEiHvlWvg5Gfv0MCFrUdDTaLK+IXv42nFtVtLly5lDGCjR49mDHrfe6r7YoBbexvB+xMkpvnHP/5xBqSNFHIZ/1x8ttA9W4LIhqi1n0HGPI+0XFPpp/H0GgeXL19u5+eXh+daT829OKzkDfvKXEIaz6GiUDRkqnjvQePqqvZr0qq+4mQOHjyIWCzm8sVoh/rL+D1LZfwdcr9oQHpdG4BBv2hhNZdRxxYu1K/JMAStA+neuQZQqQlU5R2FNj5Da2srHhdDRmZCtW7evBk3LVkCAKirq8Ph/n785Cc/wV/+8pdMsvR1lb73hPuSNaVce8vzjYKy0aM9Y5qLflE3btwIAFi/fj22bt2KP/zhD65yR4nnsxUZSe2ByA8mY5SIXzjoIGOeR5/X1NSEzs5Oz5CZrmyl/7dt22bcLlX+if36SEeYX4/+sSDJgyAcmmGn8RxK/L5ycvBVOHnyZO1XnLgt73vve9/rcG3Drf3ENCqXTFCVKcjXXdRf14VCLstk8F6p/FNq13EGKatHWpWLpMrKyrQVeGabv1upVIpt2LDB6N0U3zHRjZjSK4NpHQWtA8VxuazQlTtbhHzEcKRGzzZA3sRxTDbvQRT9h2Eb9nKtpGuLunHwzjvvdK315Gkc3it8+hJdOGoGuP3+Bq2vLCF3Ssc7UQpgiobAXUSsWbPGqBH6NU4vAw5xn9J5uEnn4iewDhOGxJ+iQZ3p/FNGem3XIe+OHsK75ZdG+Y4B/vcVVggN8B7yZ+51v/a+HBBkCQBBDAlh25nueGabf3jNnDmTLVq0yPjDVbetc05vtCwps18eN+U+bih1iTTVPtyIYooqCqMkw+lPPi2wYMECd9aKbdU+QHArkSlPSUkJmpubldf85yuvRFNTk7ZM7oIo7tHkvv0IOx0UFM3UymZxSjkf5TCYtikrK/OcJg6Eh5HQ3LlzkUwmAaSNX1TvkrzN3y3dNLGYR3cqNfiOMTZ4X5blfV8ehkOB0ijS8mc+b9487f0yqMN7RkGkz5YgosIkvKZfO/M5XldXhz179+L555/Hd7/7XeW0u66HFffLxkO8L1L2rD73kkgkMEph9McgGP0NA+MiEjwLAYPBPVQeOXrpxJffBNNSdHZ24kMf+hAsDK6/4zz66KPo7u5OrwENGrc2RKfjIop1s175avLQxjzP1IXnGqIo3itdfn6eAkzqSThuC5Wa57Jk8WLHeuDp06fjQQNhi+fQ1dXlcfl0+WYJvjSNnq1fmzN5TzXX4c/87tWrAQDPPfcc/kPzUfZgImH+UVagAxFBOAj7npr0OwG9nHAPD6oWbNLDvnP0KKZPn44jR47gxNpa23sFANTW1jr7HUfm7nvxspLv7OxM9wNR9/s5gBzIHy+YOEwP4lTdsnwdyPNtv+OcRCKBd73rXXjv7NnaNHyfcTkLHZ86FwVw7oif/3ICN2E/h/r5QLq2BWDJkiVYdffdjv2pZBKWZWFWLAYLaXdC+/btA+D9LnGH8Hx/KpXCHXfc4TBa4+edOm0aDh06hD1796rrw6+9BK07VXphn8kzF9m0aRMuueQS/2sQRCETxHl6WKfxJscV27qgKV59kAoGgA0M2DMph/v7nbMIhmXiBo/HBgZQbBiYI9cEkddI43k8omuwJg05Q3fG+tzX0tW0SACuuuoqzJ49G2vuvx/FxcWu4wBs34KDBzRfuPnQ7EQx7e6jQcupP8WwWt+wxwV6e3psrV5Nxgfl2rVr0Z1KOTS58XjcEdVn//799ruguxoDHFqFkpIS/P73v8fajNDJtRcTJ04EAFxwwQXo6ekxK3iQOshsc5+0fJmA/M4mk0nMnTMHra2tmDt3LpYvX6595kB6qUtLSwvi8Thqampw1llnuctBQicxHDCZFYhi2ZSfJtSnvTQ3N/sKlZ/O+Kx2ZQ1nXy1+WJaVlQWfwUNaUxqLxfD9lhY7kpnty3c4zGrkYpFpVJBxUYSIj1q3HeA82eJ12rRpDNAvsFb9ycdF6z5PH4JSmZVGN6py6+41l80ggrwj96cY5f0avkvyMxLvQ1wkL74TuqgfDGDFxcXKd62jo8NhEMMU1xHTMwxavjPA4WPW9x5V96vYd8UVVzAg7XdTlYbHgz/77LPtMuni3Hd0dJCxD0GImPRBIdqtuJ/761X1H+K+jo4OZX9l99V+1za8F9noL9CYniPIuIhwE1S75UPdlCno6elBZ2cnFn7uc/jud7/rSiNOQUCxDWm/vUZF+GLj6b00q9wAI97YqMnc536j0A5F7SNUgbE/RT/ClimIDz0J2TCKawHSpzH718KgdoD70uPpRR544AEAg3XBI2mVlpaibPRodHd3o7u7GxXClA9TlM9CWovKtapKf3q6+7UzcWssent7ActCd3c3NmzYAIa0303uk/bpp5+21ysnEglYAJ5//nkAwORJk/D73/8+fX+ZvIuE+9Ma+wwHTQdBDAWqfspvDahAXV0dnu3oyBwWlsIAmDRpEgDg2s98BqWlpQAG2ytPu23btvDlVJRJNnzU5lGgfQIJnscLQV9Ag+kI0eJ15syZqKmpAQBcf/316eTGl3Jfq7q6GrW1tQCAlsx0ghgaUGV0U1NdPWh0o5o6DTqdHGTqPoeNndcFnz42CpMoE0WZAq5j9DSMSibxyCOPKE9VfYAUC0K3BWDy5MkABqfUjw0MOOqET9EfePPNweKLxRP2cYE0cOg6zX0DaQHWypTv0KFDAIBDhw4hllmr+r73vc8Oyff66687yvH666/j85//fLp8jNnPnAGRh8YkiGFPNv16AN47ezZqa2sRj8ex/LbbMGPGDDAMCpltbW34/e9/j8rKShwbGEBLSwuqqqoApAOlBC6/5fTk4ckwEDYd5FT3miU01Z4jophGVGxzP4d9fX3shBNOUE61y1MTq1evdoYfVOTH99nTilIesrN5+1iYOgiaJldI1wvlTzEfZfa4hvgsdAEBgEEHzUVFRc5pKebjxBxwTKmL7wefole9g7pyhJny0h33eu/5n2oZgXy8ra2NMUbT6sRxQL762CBjg7Tf7od9xh/ej02aNIkxgE2aNIm1tbWxeDzO1q9fb1QOHjbaFdJX1TcVgChHDuQJc4IMqgEENC40fvKTn2RAOsrRl770JVdDTaVSylizcqxt+bhXLF1HJIigBBU+TI+HTZsNJs8rivw0aVXPSBREV61aZUcDUkbGUXyAONYzedyfbo3ksmXLWENDg/0eMkHw1TpyDtFGEokEKy4u1gq9iURCG+ee/+U1JnoBDFwEMWSE+OjURSIy2XbkLV2PRybiaV2RiaIciyKEBE/CG5MXM4jgKZ2nCuulaoSysYcI/9pTXjOzr62tTTmwqwyQQt2L7tywhO0w/Mo9FIKsYf3KhlFM+E2lUuyZZ55hu3btYowptHqqDxDxOh73za+r0qbu3r2b1dTUeIfDDPssBBKJhFbw7OrqsssoRx7h/3sKniQoEkRuMGzjQYVNvj1+/HinMaN0Pfk8VWQ/V/lM+qscQ8ZFhDeMDW77rX0R04p4rCOpr69HPB7HrFgM+/fv16YbEPJuXr7cXhMIy3L4W9Q5S29vb9cbLqnKLe4LUgdiesVx7i6Hu8MJbWikO64rt2m+QLB1P1GUX9gWzxJzjsViOP/88zFt2rTMZS2UjR7tyJIbJQUtM18XO336dJxxxhmYPn26vX/KlCnY+8oracMlxtDZ2el2p2RSpz7l4OtQAXcdtLW1obq6Ggzp9dEMwNixY1FeXo6ZM2f6r+ENWz6CGA5EsU4xIgfyujx0UfYAb3+eb731lr3WWzZmvGjePFd6lmnrtksmv/FgOJB7OTg8pPHMA0G0cIZaID7NKH6lqf50X4WAft0m/0JMpVKssrLSnvLgU6hVVVX2+r+s68CwbmR3OK41ORLamOthm6PJeVE3dcP8+vr6WEVFhfY586l4EVljzs9LpVKD001e5YFzih4AW7x4sUubqjvP8/5U+zVp+/r6WE1NDZs5cyZbunQpa2hosLUX3IUT1/j29/ezzs5OdsEFF7AtW7aEW89Z2N05QQwPAvRtujHOb+wT0zC4p9dV46OnSyZd+QtU41nQPRUJngWAobApb+san1fDam5u1vpn5Os2xX18EHcZrniVL4r7ZYPCUXt7u72AnJejvLyctbe3a4Uk7aLxIOXLpkMJUkdBBDOPtMlkUtn5qqaTxWfvaTjmcz15nZRDcPWrxyD14ZG2v79f2QZUxlZZvRcEQZgR9qNTAffbyZf0mChVvParfA3LgqdDcRGkH84xJHgS4Qg4qHrtb25uDtTwdA1O3MdYet2crlEzYNCoKIiQFKI+TDsXLiSptHiuReNRk8tOx+/9kJCNffivaj2uznG8TkPqLpr7vZLXUQZ6v4O8S4pt+X7k96a5udnWgspCcj4HDoLIC0P9Tkfc9quqqmyDRZU3Db9tk7Rjx461jS6VH6hDJGyKkOB5PBLFy+aXh0mDzGyL0xCqgdbPIpB/QYp5cHTWwPF4fHD6OqzgadiAvQRg/ldcXMxWrlyZycqd1iUM5QHtNL8JQd4PCdktEgOcFuxSHjqjJIeg6vEO6gYA2+NB2MEnZFpd9CkjITlbhnqgJ4hCImx7ULVznzGA7x81alRgwRMAmzBhgr0/kUiwRCLBKisrmbHiIo9tnwRPInv8hDXDbUBtWSyvZxH/ysrKXAIKw6CFM7dm5/mJQqpymjKs4KDpaOT78/tjzC2oKoWhqMuswPG1bNIp+eVtcu3Mftktkuh3U07L3w/5A8TUY4HKnRLfb3QvJvs111Zti1b24n2pPsL4n6zdzeqjgSAKnVwKSUHasEkaYTzwchvH+51bb73VSPCUp+x1+fEPVEd+Qe4lB5BVOxEOlWVflqEga2tr7SgOsVgMJ0rWumL4v8GsGe69917E43EAsC2OuYXz5s2bUVtbi3e/+91YtnQppk+fbp/PI+PwyDlGZRWP67YD3jcAFBcXg6duampCdyqlTGdH6glynQBl1kYQSqWU3gKMrmN6XNhfVlZmb1tFRY5wj3KEDv6O8MhEAAYtvQ3qRg5Rpw0zGiBsnjaNQR3MykSb4qE5efSpBQsWoLOzE6qzeLhQjhx2lCBGFAH61sjz1h1XhMOVt8XQvjpuu+02d9bS/xMnTsSxgQFcfvnl6Ut45pgeJ8UQw8OKnIvBWUAazyzJ5vFqNHyB8ga0Wi4+9QrFV5+8rbJw5ou65a8/T0OjoPfilwZpbezpp5+u/DLdtGmTVusl/hpbK5qgKLNcT+KvWM+++TGm9qsZokzyPkAdoUMZrUmVh3TeNddcY98Xd07PAPfUvl85fa7DUWojpfPEqCfi/cj+PEU/nuLaYF5PLkMpgiDcZNtHmaRB2tOKn+2B1zYfR+TxwyQPx/gR5r4jhKbaCXMMBQ7XPkPB0+s80eLXpHGqhCav81yGRkHLr7kXUcjo7+93WWxrHYBnOhgx/KOvMBQUxT16GbfI0/x+07muhe1B3gNxG+4PClWEDqX1pkbw9HLDZJRHWMET8A544FMf/CNMrAe+/lX1Xg3F2mCCKCiCjFsmeYTNTxICTQRF1djW398fWHhVhRgeSkjwJHJDxIKnSePkwpEu7Xvf+15t4zQuR5B7h9vtDTekUsYTl9Cuc8wGg05TZ9wid1oqi0ku0DHA26+mVL+evkoVz1MVoUMuCxcgVfmK5+k+UlTlCFKP8n6jevG4jli3VVVVDJnfjo4Olkwm2cqVKz3XgIYODUsQhJqAwqvKC4ep4Mn7PI6un542bRqbOHGinX7ChAm2JX1HR4e+/EHHuSwgwZPInigGZtVxaTuRSNhfbrovung87tuo5bjbvkKGCRoBQeX2ZseOHepp4SgI23koOjR58bo8nau6N5XWzfXVLpczs3/+/PlaAVRleQ6kvQE0NzcrNaFXX331oDCqeJd0HykuN0wRCZ5egi4M8jbRaJp+NBDEcUMWfXkkaaX+Q+eFw0/wrKiosPs2Pssjjn1eAqur/x1iSPAksiessGaar7B99913KxvZ3XffbWvgTBo1Q8C42x5lUqUx1qblgxAdb2VlJWtoaLBddFiWxTZt2uQSflQdm+6Lngt8jDHlesQxY8YwBrArr7zSpQHUWZ77ddiyMCo6hNdF/3BZw6vqL0Sd6qxZXdpIj/fKT6PpuzaYIIjo8Girrm2ffsevH1OlFZdjjRkzxreP9PSIksdxiazaj0eCWKSbwFj2+RmmZ9K1xP+4FTYDUFNTo82jqKgIq1au9I67nUX5H0wkUFJS4igvjzVfUlKCB4NYFQaxmDZN75cdgNdeew3btm3DW2+9BSBd/g996EMABuuc35v4TBKJBB555BEo3gg8mEhg+vTp6O3txdT6esTjcdtyGwAOHToEC2kr+vr6ek8rem55Xlxc7DrGpO39+/cDAOLxuB3vOJlMYuHChY68nJkw9bYfHs+is7PTYZ3KhP1NV13lfz3GtBax3NsBjzvPLfy5RbxnLHeCGIlEPc4FuZ6q/8j8VldXY2JFxeBpmuxUvYCFdJ/HLdN//OMfY/Hixejv78ehQ4c88+tOpdIeUXJZB7kgx0JwVpDGcwgJ8mqE1ShmtrkFclVVFWtpaXFp4MRfrz/fL1XA3/rYY9tTm2ZC2OYWVjsnlV+e2ua/Xj7o+L2p6lq1T6W906WVnco3NjayqqoqtmrVKt+vfPF6/ItfNPBRrrdVPdvMr+u9CPhOBNJGSs/ORKNpW8SzHCzlIIjjkaB9qEFavjRJ15/q+sJ58+bZ3kK80mrHPKlfGgp/v6TxJLIniEYoBL29vUglk+ju7sbGjRsBpH15NjY2gmFQ68Uk7aKrmJlfl5ZM86XKfSHGGxvVBdNpxTLbFgTNnKhVC6KhDKrxDItUZ1yzxnO2pP1A+t4Y3BrDVatWOYsnbIt+5HheurdHTFtXV4eenh5s6erCwoUL0dnZiX379+Omm24yuj0LwCOPPILp06c7fJQCsP3AbunqQk9PD+rq6jzzam1txeMZH5ncn6jtV9TjnaiursaJgjby2MCAWhup05wARhrNsrIyh89b0QcqQRBZElGfbAXot8VegPunBoBLLrnEMy3frqiowMt9fcq8bX+/haoJzb0cHB7SeOaZKDRrhvlBocWS1xWK2/xXXg/Kt2WfmeK2sVW2XGap/LL1OgPU2rQgBK1fw+uoNLu6eOltbW1s9uzZrLKy0qUp5F/xXmuYRD+ksk9K+U/5hS7dq2m8Y1kjoHt/dHXH14Zyoyr+fsyfP58BYAsWLPB+Fhm4NrKrq4v9wz/8A3v66aeNnpEqD8ZIo0kQOSXsOOeXFwZncRoaGgKPbaq+UredTCbZ008/7XA3p/L3y/fnw98vGRcRuUc3oBs2YF0ISd6wmpublY1zxowZjqlNvt/Tia5BB2BaflFAYIA67KNHOTyBj99KZhA2MZNW5RZJFy+dL3W44YYb3MKPQaco1j2/hly/Yr371ZfKituvw1Ztqwx8xPoV0+qs9T1dRkmo6tyXsAMeQRBu8tWePK7D+83a2loWj8dtZUVVVZVj7PITMFV/3PgzlUqxxYsXM5bpb1Qf4NqQmjmCBE8iOkwEKr9zJSGKf5lNmjRJ2/hUQtLYsWPt475aR2nbyxeo13me9+J33yZ5CNu6OOqisKkUbjJpZQ0e/+oVhSfeKfK0HR0d2rSMuZ3PqwTC9vZ2Rzl0Ha/D24CiHrlA2NbWZiQU8ufa3NysfLYqS3axfr0cNivvVfHsTOrcExI8CaKw0PXfQdICrkhluo9pr3FJ/ng/7bTTWGVlJdu0aZNjlkbXd/E+Mh/+fknwJHKDiRDq12gNGxljLD1lCbDW1laWTCZtB9sMaeE1mUyyXbt2+Wsdmb+7Cy4oBL2XUNvCPpOQiNx35ZVXXqlMw5A2mlIJa7oQoqqvaJ0PSp0fySuuuML+4lahCxGpg3/BX3PNNbaQKkZ4UnWqqVTKZeAjCp66+uXvUHt7u9H7qOu4dZoGV50TBJFfggiQYc8LMCZ6fdR69UHFxcWMZeQgVb/t1XfZH+B5gARPIk0Ug16AhmVyTT8NGneoy9igICIP7HIj85ue5gKK7ppGTr8FoS3MfWvxEFxMOyjAGbJRlcbx1Qu3tk/OWxS05LWhvHyTJk2yv7i5YKeLYqSrR906y46ODjs/LrwCg46VxXBxuiUEcshJVd3I+Xp9CKnwCkcq16PvMgmCIHJPlOOiyXiQ2TaZYVEd57NGXnl49V0keAaEBM8cYdLwshCkPPdB7TgcSGs2zzvvPJcgomtY4vS5K5KNBJ+K9xLmXNFtVPfgd9xkW9gnCi5+nZLqT47yIy5f8P3q1VzPkRbQrtv0FNwN61EWaBn0WlouXDLAFedea5wDvbFSSUkJW7VqlSNf1QeJXB9e9ehV56HWgBIEURj49OXatNJ+U4WCvC26evM7r6ioiE2bNk0bujkXkOBJ5BcPgU+FLHhybRO3JjZpWIBTa6eLZCNq1PhUvS4Kj2tNYNT1oemsdIJ4cXGxtj7k8qu0wbxudcKTUUScTFou2C1fvtwpFErlUE5Je3TYXloAR36At+W36hos/fwTiYQ2b77ulWtVa2pqbCOA6upqdxQszXNV1SMDfMORRvK+EQSRHUEFSNVx3baU3ku5IB8X+/V58+bZ2k9x3FTlkUql7D4tX5DgSeQGk5dYlUZqkKIG7fbbb2cNDQ2MIR3S0UTQUmmlXBZ8GNSomXxNKgVPD4HJuA4M8lAJ4lyw9uuguHCqE0iVIUQziFPU2rTStmpKX65zz/pQ7BOXQcjPxXNa2qTT93nmPK1sbMXgnvLXoatHearfN547QRC5IWw70/UrQa4h5VFTU2MLkCUlJdo+3KvvqqqqcszSiGMHQ/6m10VI8CTMCdIgo2i8GVSueqLwdSZb8HmtZeR/lZWVRpbxxvcYUPAUBXHRmIbHUZfdbyxbtowxpKee5Vjr/I9r0zyNeqDRIkrl0/lBVU2NB6oPxhyujcT1mzw/e1rarx49tnXvlbi0Qn4PxfMcAqLmOjptrNea5nxZmxIEEQCTcc6vD9LlB6e1+6FDh9gTTzzBKisrbVeBpoqSrq4u1tHRwWpqahxjh2N6PeyYHQISPIncYNKw/PZL+/jA7NfI5H2f/exnlYO56MxcvKaX8AqkNV1GVu1BhFEdivNEgY8LLrJAGovFWE1NjS0g9/f3u6bL+T22tbX5XtP0uYn17lp/mfn1XEvkUY/cgGzs2LFs5syZjAGsoaHBvo6n4ZKh4Kl6r+x3JZM2iJGQcT1mkD0quN5VgiDyTxRCWQjB07UtffQG0X4CsL2/dHV1uafXC1TwpJCZhDmMhTtPFy7QstDU1ITOzk5HCEbVthz4680333T8z0M9itfp7e1FKpXCDddf71k8BmD27NmIx+PO6/jdr3Qvym2/8zKUlZXZ+y3LQtno0XZISQBYuHAhurq6sPeVV9LhHxlDWVmZK9xiTSbM4ubNm6MJl2ZZSCQSKCkpgQWASWUfVVKCtrY2d1hKj2v39vYCgB3m0gIwbtw4PP/88wCAbdu2AUg/l/379yMWi8ECUF9fn86Al8Hj+aRSKXR3d2tuyRp8VzJ58PfQTiOk706l0NTU5LqvZDKJuXPnItnVpS2HmB8PQyqHI/U+sUBD3hHEcIW3qbDjmYiYRxb5lZSUANCHhtadwwCsXbsWANDW1hYoZOeQkns5ODyk8SxgDLVNJufp/DCKf6K2LZFIONaDLlu2jDU0NLCqqirHFIN4rpyv6hqBrdqz+dr1Oy5tc1c8unJ0dXWZh0sLcS86rZ3RfUv7xfN1luyqbdHQyMs1kVw+3bZqaQWgnvJX3Ze43tUL2d2TazqMIIjCx09cCjsGMLWBqd82X0Ymrkn3dGuXY2iqnRg6QghaqhjoXkIjF1hU+8W8vdbXqYQoI+Mik3sNcp4OKQ+XKx6FwCTel87Yyqj8ijS6KX2tqyGPbb9pbd3zEhHDxcnX8HJRVVJSwtra2tTrXgFfATGslbqXuyeCIHJMkHYWoF+M6no6zyYmQqinG7o8QoInkV/CNmppvxgDvaamhjU2NrLVq1fbFoArV650WQDyRqbTVoqaOq/G6yt4qvaZdEphhVBAa9Sj+qpVCdh8P/8yDlWODKqPA5fWTrqGrKUVtZQ8LKb8LLglv0rrKNcH/3XVB1NHW7LrTiwr4NCc+kVbCvTxQxBEYRC2Xfr15REJqdwDhp/gecEFFzAGsNLSUjOjxTz2RyR4EoVFCGFNFgD4cVmg8BMaxWl8+aswFot5x3tXlc+nI+JW2sZugDzSyF+1orDjEHKg/mJWClq66xs+F5UFvDJyFHNPRTu0lFI5RQFTpXWU0+s6Zrk+ZI8AKsETUAQg8Ng2tlI3ee9NjxMEMbQE6TdD5HHhhRcq+xXev33uc5+zP7irqqrsj3S/2aF8URCC53/8x3+w2bNnszFjxqTDIIaABM8hxK+RmWybHhf2u9buSQKfvB7U4fRckbdufZ0oRDGkvyT9wm563lcGrylgr/tWbRu74lEInkpn8Abl9yuTa1sS3FRa2kmTJrFEImGHQ+WhNoHBOMR8jS6D+6ODC7gqDwhiZysKfaJHgDlz5thp+vr6XGE65elyL5+djOlj1/O6Vq4/JcGSIEY2AcY5Tk9PD2ttbWXxeFwbdU7s13Wu3uS0Jv1Y1BSE4Pm1r32Nffvb32Y333wzCZ4jHQPhxDQPv7CC8pSv1lBDKgcXZObMmZN2PyGlVV7TUIiW1/1xoUs1BRwUnZAjly1nBiyKOhDvl9edGN5U1tLK+3X7/KapxShEqvro6emxPx7Wr1/PnnnmGYcArBLQ5Q5dWQ7pmfsJ+YFCY5JAShDDD792a/jxrpvB8ewjg/SneexfCkLw5Nx///0keA4Xon5JDRunkeAm5OUZOtHjOg6BIPNV6GkJbihEe32R2h2DLg9dHUGt4RU7GhmVL1CvvH33Gd6v+Kvq/Ez2mzhTN+lsucZZdT0vLQFPq1wTK9He3s5KS0tZQ0ODvVSjqqqKbdy4MbQWlSCICMiloGU4Hpjs5+NLc3Oztr8y+VN5gnH0Y3lk2Aqe/f397MCBA/YfX3BLgucwxbATMJlKMGrgim1T7ZxSeFJdR3GNIPHGjesos1/WZDLAO6ylSd34HffJT7xfVYfX3NzsK2zK+5RrUaVrJxIJe2pezqOoqIg1NzfbQl95ebkjrSzkymV0lcMD/gGzePFiu2xiHhQakyCGMWHbqkkfah8201bqtrnA+cEPflB53Lc/zQHDVvC89dZblYMBCZ4FQlBhxy9tBqOoMSYNSFE+XQP3EoKUX4segiff1uUtpnEZHxnWqbgeVRXW0qsOjAj6bDXPKpVKubS0KkGMn8c/NOxISx71y5i/lwKVGyl5u7293ZWHX4xjLw8DyWSSrVy5MpzREUEQhUXQsUa1z6cP1a3fNxU8Gxoa2MSJE7V9YSKRcM/a5ZicCZ5f/epXlR2r+Ld9+3bHOaTxHKGEFWo0iGsZ5UbkyiPAtpdPR507HE9LcB/BUzZ6ktO4jI909WSy7bUvQB7GwrCH4Cmuc5TX4Z5++ukMADv99NNtreioUaPYihUrbCHuM5/5jNG1RWt1Bv1Uk+6jgv9t2rTJFlInTJjAGhoaWGVlJevo6HDUC3cH5aXR5Mf9jI4IghhhBBA2VftVgufkyZO1Aqk8u2YipOaLnIXM/OIXv4jt27d7/p166qlBsnRQVlaG8vJyxx9RoDCm3h8kZJcirTasoHg93bYifVNTE945elSZZPz48a5ra3IbvI50bR42cWN7uyN0ZSwWQ21tLQDYoTsBYN26dQDSYc66u7sBy7JDSHoRJDyjMZn6b21thYV0yDX5vhwI9/5yXx9qa2txbmOjfb8MQHV1Nerq6nC4vx+dnZ1YuHAh/vziiwCAiy++GADwhz/8AUfeeQfz5s2z82tvb7dDXHrVR3V1NRiAWCwGZH55Pdu3pTlXfLYf+tCH7LRvvfUWtm3bhtdeew2zZ8+207S2tqZDjwJ22NB0b84y1ZH+HVVSgkQiYZ/H313tuxSW4RIOjyCOF0zGIhGPMW8wm0z/ojj9r3/9K4DBEJs8jRxmukTqkwqOXEvBZFxEmGrQdG6PXGlNriPgF46M/zU2NjIGOMJu+iH6qtS5ARKvabz+T9rnGZ7RpH6l9F4uhRjArr76agZImlkpb9nISz7utbaW/+q0hzwPpY9QqP2JAu7pfbn+b731Vs9oVitXrtRGJpIt6nneXKNJoTEJ4jgjqJZTQHT5phoj/MYrR38p7T9u13j29vayrVu3sttuu42NHz+ebd26lW3dupUdPHjQOA8SPEc4UqPwtFY3FF512+PHj/ecjkgkEsbX9FvvJ1swJxIJe2pY7ji01oeAMjwjv44tPHrVKaCOZ24o/HGhq62tjcXjcbZ+/Xr1dTTXlutaXH+p60hl/6S28Kt6FtI+LvQxwJ7el/8SiYTWJZM8Va5bm6r0IZshsMcFgiCGL1kIngyDH++qNZ9e49X1119vJnjmkYIQPLnGRP7bvHmzcR4keB5H+DVgw4as2/6nf/onz0ZtnJ90nknMeMYYO+2005TX9op17icEiZpBVR6y+ygxjZclvkk9+TpJB5Rra7lwqbt2e3u7UlOaSqVYa2srmz17tjYqlKhx9uu8RcFRFCD9nPZXVFSQRpMgiDS6McckvbRPt0bcTwhVpZ05c6ZTUZAHCkLwjAISPEc4HoKicVqPNKJmcsyYMa7GyYU4rfCnydtPOOFpn3rqKVvIk79ORYFVd22vr2BbeFSU09Q/qZdBl2q7vLzc1ury/V5T8Z5hPAXhj8HfSEiuA9X1GBs0lFq+fLm27vgz0i3r8DISEjWaDMi9RtNkMCMIIjhhBUXTc/3Oy2zzccrPLZ9XH+nbV+YBEjyJ3GAo8AU+bnKdoOdpGqG87ekTU7Wd+W1vb1fmzR0Cz54926iT8LueKKSJ5+qEZVWZdD5RTSzEdfUnC5KuJQZwx0uXw5uKU+Oi8GfiZsR1zcw9iV4DPK3MoVgnmkEut7LOJZQaYIIghjdBxjaTPBT7VX2U/Cd+IG/atMnoHN6v5yuABQmeRPYE+VIKKlhGfD2vdYxeAhMA9rOf/YwxgMXjcWUe+iL4C7VnnXWWp+B53XXX+QqebW1tDg2pMga7dJ5uitulZVUIf5WVlY7rmQieskDLhbD29nZbmOQdJwNsd0s6Yywu1Ps9Q/4nG0oxpLW8XNPsWXcKwhgJeRp/BYSEWII4Dsj0FV4u/4qLi+0xgPeR/MNY9lns11fmGhI8iaFD9YL7CFfG24p9fusYvTSN8rbWiEXczvyuWrXKVzPIhThVGmU0I8X2NddcYwtSRpGLoJ7iBsAmTZpk7+davx07djiEv507dzIGsGnTprEPf/jDxgJ8cXExmzFjBuvq6nJoHeUwnr7vB2PK66m2uSGSuE8XslQrQGo6ZJMpdZXxVxRhMgPFeicIorDRCX3Cfl2frfpI5h/GKi8hqv65qKiIffGLX8y51pMEz+OdPHzdRIKfgOlxnu+An8mPW/+phBfLstjo0aMdglkikWAbNmxwN1JF+fw0nl4dglcYTT9XRzt27PDszPzcR3nGkQ94X/z3sssuYwxgV155pbLMnvUpba9atcr42ox5r7llGIyKpLQyD9pWNPXka2TmQ66EWIIgIiLqcVUheIrLknhfztPOmTOHrV+/niWTSdbR0cGqqqrsccx0/MklJHgS+cVDCMo6D01auWGpGh9jjG3atMlY46nadpUvI0Rt2LDBSMDkf6WlpeyTn/wkGzt2LGMA27Jli/a+dUKyuF87DQs4poqvueYaT8FNZ6AUVPBUCXx+Aq6rboXtjo4OX42yfJ4ura6essXPyExZt5prq4RYivVOEHkiivYVNg+hz2ZQLEvKpNGNeaplUfJfUVGRvj+KCBI8icJCJcCZptfkoVsTYw/4mfR8PaFOeFFt+zVSL2FItf3kk0+yY8eOMQbYv+K9yE7S/awbtUKxsC1OcSeTSX/BTapreQqbb3/72992OD3WlVO+nkvD61N+Od47/1u2bBljcC838DKUUl5Hc9++SGmyCZMpruUMLcQSBFEYmPQ1HmObKiCH7KGkvLxcOx4UFxdr++R8+PXMWchMgggFY+ptk/Q8xBhzhnHs7OxUntrZ2Ymmpib7/7q6OgDA5MmTIV5ZDjEm0tXVlc5DDG/Gty3LDkXmdydFRUWwkA7NWVRUBDBm/4ps3rzZDle5fPly3H777do8R5eV2dvd3d12KE6ZMiGdlSm7KwypiGE4xurqavT09IANDBiHZOtOpRzPxJNM3VRXV+NEIQQpA1BbW4vrr78ebGAAPT09jtNmZUJnxmIxfF8KWeqJeN+q905TPpkwYTJ5SM62tjY0NTUZv9MEQRQgJuOcRx9TVlYGK9OP8D47Ho/b4YEB4ODBg8qQwBaABx54wN4ueHIuBmcBaTyPUzRfhaLlsLyOUbUmRjyXT93KGjT5z5GHR9mam5uVWkT+d8UVV2hDcIrr+fh54kJxOT/dF664T1l3GNT6ilbaKo2hXOdbtmyx61S5REA4T1cHnlpHA+2A1sDHIL1x1KAQWk6RoBbwXms5uZbZKzJSoHITBJFbsmmHfn0h9B5KgMGpdt5Pb9q0yV73OXXqVDZ16lRWUlLCqqqq8hLkgqbaifwS9SAo5KcLG7lp0yZWWVnJZs6c6T/gA+z8889nDHAIX5Zl2c7ElY3UQ2DiLi50wiFj6rCffErdVMD02gacDuu1Zc5se1ppK847cOBAemkAY8olAoy5p7jFcsqO2f2uZ7wdJUHzVaQPIvCKz1C3lpMiIxHEMCGKfsmjn9Mt5amsrHT0EwxpBUd/fz87dOgQGxgYsKfr8xW2lwRPorAwESA0+0VBRhc7mzGFqx5hW9SUigLCgQMH7OhCW7ZsYYcOHWIMbr+gXFjkv3PmzGGXX365r+CpunfuakhlBR1km/9yralvXft1kEGfkSCIi75AY7EYq6mpYX19fQ7fnKGuF4SweQR8H7PFby3n/fffT7HeCSKX5OojNurrQR2EgyE9gyevB1VeL4/3Sms8iaFDtTaOMfW2QR6JRAIlJSWZU5njl+9Pn+K+biqVQnd3N+5evRoAUFNdja1btyKVSmH37t0oLy/HunXrYGWuM3r0aADCmstMnq2trQCAe+65xz7+m9/8xr5OQ0MDAODd7343ampq8HJfn6McGzZsQGNjIwBg3bp1AICJEyemyy3etn/N+KcxqWthvar/BTVrIIV9PT096fWJjKGrqwu9vb2oq6uDZVmOtaYAHOt0va6XTCYBy0r/mpQ14Hvli0l+IfBby7lgwQL7XVbVH0EQWZKjth36eh79UnV1tb12vSWzdv3E2lq7f4VlIZVKoTEeRzweT/eXbNAeItnVFfHNRETOxeAsII0nwb/6VFo/P20fT6/TLoqRbiZMmMBmzJjBysvL7amMRCLBEokEmzhxonKNjapMLg2flEbnc00V1hJIu2GSr8uPK6dhg2g/A2g2HVpfk+tp0qgi/Kgi9YhO6LV5R6it1N5fyPy88AwlShDE8MSknwgx8yQH4ZCXb/G+EhgMghJlJDVTaKqdGB4YCj5hYmczuGN+q4THIM53vY4zOF0GiWtTuTCry++aa65hDQ0Nyin49vZ2xgDW0NDAvvKVrzim2js6OlgymQw+zaISPH22AwuCwrbKmIo/V15+AGzBggWuDwKlE/UgQqhhmnxGCwoTkpMgiGFEEIEvaN8Fpy/pSZMm2X3ohAkTGMOga6V8BqEgwZMoLAJqxWQ8B2qPvHULs5ubm5VCoE44FPd7HRfLIWs5dXnw83bv3s0Y4LI8l/2QeuURpE5N0vpFUBIjRPE8uPbSqz78BHjxg0DphD7M/SnudyijBYWywCcIorDIpg8KkoeUJsi45Pg/h5DgSRQWOuEwSIMD1AO1Rx6eU5o+go/uTz4uCkYPPPCAyyG4TugSz+N4uQ+SnQPzX77Y3J4ilupDNY2trDPpuUycOFF5nyohWjxPOcUDb7cgJnXNEMAJvQ+8TozujyAIwoSg/YVfP+xxXiKRcHkS8RrPiouLCypyERkXEbmHMf9tEY2Bkm10UVSkNrqQzuMLs48NDOD/t3fv4VHVd/7A32cyJCFqwiUJAYMJFw1UbpIJGNYtBXksSKt9urutGmywPILd1th6q3RXrdDWS1n7Ex53cfsAkYRttC2o5dJat+BuXRwzExQFtELJNKgkBDThIoFkvr8/Zr4n55w5Z2bOZGYyk7xfz5OHcOY753zPmZkzn3wvn+/69evR4/ejqKgIhYWF0VU7ijKTJ09GTk4OAODpp5/G7t274aqoUCeRWA0bd7lcIQnOs7KzdZOktOfY09Njuh+/3w8AagJ6HUVRk5S7gpObjI+rDK/FZ599hiuuuEK9BkIIGYmpZWQCeZ/Ppyayl5OngN4E9z45+ciCsPjdKGwSdav3kgl5TW644QbdxDXt+Q1xOqNOkE9EZOcepCsfwyIWVVVVaNRMHIp05J6enpRahMIZuQhRjBQl9MNoti3WfUUoXywCM65FZiZWKApw113YunUr2traMGPkSODkSWRkZAAmQZ3D4QCCQR0Q+GA7MzIwRFFwb00N/vjHP+Ljjz/GAw88gHvvvRfKuXNQ9u9Xy+/YsQOfffYZBIAMh0MNEIHASj7ua67BhQsXgOBM+kgyMjIsg08AaGhoQHV1NYTHg/NvvIHs7GyUIzQQFEKg3GwHioL6ujooigJ5e2oxzM433garqqqAJUtQWlraW+bECfV3ueKGAHDSsMKSw3BNjBwOBxS/P3w5G+8Hn8+H9vZ2KIqiXpO3334btbW1WLJkSaDumvJutxszZ86Mev9ERKYifXdZPRbF/S3aPB333XdflCWTQxEiliggOTo7O5GXl4eOjg7k5ub2d3WoP8QaqJrsQ9uaKND7obXzu9XjWsbtFRUVWLZsGVbcdRdGFxXhk+PH9X/tmv1uqP/0adOwf/9+y3o4FEVttdOlaApul//K8hBCd7xor40MotV9ANiyZQuWLl2K7u7ukH04nU5c7O7GsZYWVFRU4JPjx/Hc+vXYsGED/vrXv+LkyZNqcOlwONDj9yN/5EiMGjUK3d3dcDqdOHXqFBobG9XlT229J0xee0VR4BdCvWZasi5er5eBJ9FgF8fvn7gdI1j+2LFjmDlzJj799FNc7O6O/B2W4FDPTrzGrnZKP1ZdEGZrq2toc4Ja7jrCdtkFa+yGNftIO51ObNq0CW63GytWrACAkDXG9Tux7mbZH2xNzbBYb13bRfyd73wHTqdT13Us/7U6/0i3pIKCAgAIXQNdUdRhBdp9yNrL/J7FxcXqua9YsQJvNTbC7XbrhkLIFlK324358+fjL3/5C66//no0Nzf3Bp12Bc87XD5YABg3bpxah6KiIswsN20XJqLBJNZgLZruc/l7pMct6lRcXIyWlhacPn0aQLCXDqHfYRkZGak3bCj+Q0zjh5OLBoi+vM3sDMCOYrKJcY13+fOLX/wiqkHaxmMYn6P9scwzGkX9zVIQycHkK1euDDs5SnueYetkqIdcK9x4DWpra9XVMczyyJkdzziRy+pctROqjh49KgQizKK3uF6W2zW/W10T4yognGFORGlBc3/buXOn6Xfbzp07k1IVO/Eax3hS4sW7iT+O+5Pdu8oPfhDzPmTXbaQu+Ig056UdNynUhwO/Pf744/iZSR2EENixfTsWa7Y7NF3j0dbJWNbpdIaupmPoHiosLEROTg7OnTuHefPm4U+7d2O02UQuw/O0E6jGjRsHgUCrqjzeiRMn1JZQlJZG111kMYFNtmJqu/b9fj8yMzO5WhDRQBOPbvJk6Es9Nc8bNWqUYbeB76Umw/ZUwK52io2d5QejeV6EbgXLsjafJ2e6A9B17z722GOBp5nsSnZhGGehy23Tpk0DAOTk5KhjW9TZ8xY3FHXpSIv6C4R2i4cLuuRji7/yFQChS63p6mRGUXDVVVep53rbbbeps/Wvuuoqy+MCgaVJ29racPbcOQDAgQMHAABbt24NTIgyq7fJNm13kDwf9V/D47E41tKiXhMZ4OquSazvaSJKPekQdIZj9T1ncZ+S9/xZFRVYv349XC6Xuj3VcHIRJVeYCTRxne1uNmkn+G9XV5fayiWEgOJwAELgzTffxLWVlSEtg16vFzPLy9F1/jyysrN1++06fz6wL4cD/p4eXLx4EZmZmbhw4UJoy6CmHjV3341169bpJukYyzZ5vWqQpK1TRkYGunt6QlpY5XbtPoTfr67p23X+vGlrpfbYnZ2dyM3LA4QItApmZFjWT56LsR7aiUxyu9VrYdTU1NTbwml8DeRkn1gH62tfr2Ad1dcpmv0SEfW3MBNSu7q61O8o7XdbMnByESVGPFqE7KaOkMeMppUzTF5K7basrCxd16rcnpmZCaC3hdNhmMhj1gWr3ZcjmF/UMs8oEJLvclRhoZrvMhKHwwEB4PnnnzftNn/rrbf0G7SzuYUIrZPJdczNzVWvh/H8rVi1zDrNcmHK1yXMRCrtsU3roL3pmgnzHjO+9rprEuMNWrZeezyemJ5PRBQihl7ArKws9XElHt/XCcLAk6IXjxl+dstH2U0bst3smBG6LmSXhOye1iWcj8MYHAVQuz9OBPNdtra1oby8XN2uZew6kS2BI0aMCKRQijIwDBzcxmsQLCsDKbOAytPYGBgqAKjJ4bVHEMHtVVVVkV8XjZnB7m/5GoR0h2tF+mMlSWRCetMk/kREsYhmtnukoWgpipOLKDZ2uiX70tQvjxNtsBkuUI1QD5myx+12B7pily9Hs7HL3GLiSsT6IzBGcenSpUB3d8h4TafTCWjyYMr6NDc3B7pO3noLy5cvBxwODB8+HPkjR2LSqFGBJO+nT8PhcKC1tRVejwf5Ph9KSkpif42Cv2/evBkuBFZFcrlcujKuigrsBnBPTQ2q5dMQCD6Nyfctj2OhublZ7Q5fvnx5oDvcMMQhpLte+3sSupbMEtKrSfyFQH5+fuA1ICKKVqTvsGjLR3peP2OLJ8UmHm/oaLoS7BzH6nlm3fVhAtmwM5wVJeLEICtVS5ZYLh3pdrvVVkRtC6NZ10llZSXaT57EwYMHcebMmWC1BW688UaUu1y9M+LtXLvgvn0+X2B8aVOTLqBqamoCFAXbt29HU1MTRgVbIBsaGtDa2oqRI0cC0E/YMm2ljOKahe0OT4BYuspLS0vhcrlQXl6utl7LGfgu7WtARCRFGjIWTe+Q2fdcivT+RIuBJ/WfeHfdR/qQ2ejyDVdGdq3eU1MT+TgWzLrJXRUV5l22hnqEm/2tW2PczvUIkgGTWUClAPjqV7+qe6y1rQ033ngjTp48CSCQHF4G11ZJ38MGetG0bMf5r/hYusrDJaQ3HdtKRJTA+1jC9xtHDDwptdn5qzAO4zDDBWsVFRWor6tTWwKfWbvWfGJQmDoVFhZitGYM4/Rp0zBy5Ei0traqZRoaGtDk9cLr9QZaIA2qqqpCtkkXu7vDPq49F9l6q62nMahV0BtQORwONWD2mwwV2BJ8rhKh+ydsoBfNJLLeCoZ/PAyfzwev12vasmt13bXkak1m1LGtRESxsttQEkvZfsJ0SpTa7IxT7ENKpvnz5uGpp56Cq6LCdB+y61eb2sh0/XNjPSxSF2nTHJmlIzImpLdKYyQT4JutoW5ZD80xa2pq8Mwzz1g+riUAyxRPdXV1WLJkicmzArRjIhctWoS2tjYUFhZi165dmFleDl9zc3LHRGrO0Ww9ewCIdGuUqZ+MCem5zjsRRa0vadwipKdLJqZTooEjUuocs7JGZmM8DdQWOMNfmbJVTG7V7kG2+oWsfx7FeJtwqS5Cumwt9idnfwMma6gHyW7t373yCrZv344tW7ZgxPDh6uN1dXXYsmULtv/ud6atfNHOnt+xY4fu/HTd6YqijomcadKFD2hWagrT4hl2bK3N4Rdb4tBVbkzSH3YGPhFRJLG2VqZu+6G5OCzRmTBcq32QivVtGel52seBkLXQCwsL1e3Nzc3qdgTns2v/1f5s3749ZN+NjY1i3rx54vnnnxfz5s0TjY2NvWU0x5Zrkpvt2+v1hj0H7Trn6hrjhnrcfffdIfs2Owf1seDzcnJy1LIVFRWiqKhICATWNR82bJhaRu4rLy9P1NfXi9/97ne6a1dTUyOECKwD73Q6TesgAFFfXx/x9ZTnIvcZ7rWNRtj17KNk+hoQEUVi53vOzndbrMfoIzvxGrvaKf1E061g0cVtnCEOhO/iHuJ0otuQ5siMrosbgS7sdevWYfr06XjnnXdQU1OD22+/HQ8++CD+tHt3VOu6q122UXTdax/3NTeHdGvn5ubi9OnTEEKYHlMAeOb//T9cd911UBQFCxcuxIkTJyAAeD0eXLhwAWPGjFFbJuU+tPvS/l5YWKh2p7e2tcHr8eD48eP4SnBJT23ZcF3T4broRV/SFim9K0Oxq5yIBox+6na3Fa8lOAjuE7Z4ppj+fLvYPXakFjBAbYEztr45nU61BU62ipm1eMrf77//fiEA8corrwiPxyMEIIYPH64rM3z4cN0+rI4NQDgcDiEAsWPHjkDrodl5Gc5P26qq3Z+iKBFbOc0el8+T/8oy9fX1av3C7SPc7/L5DocjtIXR8FpFqlNfbmEtLS2iqKhIVFRUiPXr16stuy0tLTHvk4hIJ4bemKjLplAIZyde4xhPil4i/4qKdQZzrLlAhYg8K1mzb4fFcfbu3Yuuri4AwE033aSuQPTpp5/qyn366ae6Vsba2lrzegPqbPLFixdHnQ9SO0tcpvrRzkjX7d9iH/J5QvM8+a+ctV5VVYXGxkb9xCeNjIwMAKEtqk6nE88884w6o/85zZjImSZrswd2oiQ0bZFM0O92u9U0UM3NzZZpoIiIbIv0XaRllREl1lntKTrDnYEnpQY7H0g7z4tiHxlW64ILoU4gkROJjHs4cuQIXnjhBSgIrHOekZFh2XWuramcAW46ezzYHa4GVhY3IznxSWpoaAAATJo0CS+99JLueHIPw4YNAwCUlJQEhhIMGYKCggIca2kxTREk92FMESS3a+uvAPi3f/u3kPNREAi0/+7v/g6vv/56INC76y410DOcvO73qOsU4QZrlTs02cnqiYgsWX2fWQWhkb7/UnQkJQNPSg/x/gApihpU9vj9livuyFYxIDCLXABYt26d+viSJUvUsZCnT59GT0+PZYuiVYqib3/726blX3rppdB8kJqbjlw5R5KzxV0ulzqW0mEIqnft2oXzn3+Oo0ePQvj96OzsREtLC4rHjtUdxnQmu2FNe6fTiZKSEpSUlGDIkCEQAL7//e+r56W1ZMkSuFwuXFVWFhroRfnayjplmNUtwj42b96MP8W6nnqKthoQ0QBg9/6SosGkHQw8adDSBpWyq7Xr/PmQrlbZCibLfu9739MFMLJrXNutrQZXmv1Y3S42btxoul0Gj1aMaZxkPWS3NoCQVD/FxcXIHjoUiqJAURRkZ2frWvlkUCmfN6uiojdFUPD8iouL0XX+PE6fPo1mnw9Hjx5FZ2cnAOD+++8Pqac8b22SeTtiTVvU1yTxvSeQ/jd6IkpR8bi/BL9vPB4P5s+bZ2v53/7AWe2U3iLN+A63Pdb9BckE4gBCZnfPmD4dR48eRUdnJy695BKcPXs24kxw7e8AsHbtWtx9992WM9nlrGwtgUCS95kzZ6KrqwuZmZlqYvQLFy4EgswISYcjPk97bSwSzxvPRa1flNc2hCHpftf58xG7xRVF0WUsEMJ+kngiItv6sJhJXwLRmpoarF23DvfIhUGSiAnkKXXFu9vSzsDteOzPpP7G7mwA2LdvH9ra2uDv6cE777yjJndfuXJlcDeB/WiTueuqAQSCTqvja4Mn9SF93XTjFx2O8IGa5rlRPc/iWstWWLOW3tWrV5vWP5o6IRg0yt+jGYtZX1+PIVxPnYiSze5k2EjPCyNczw4UJfqenSRi4EnJFcduhZDf7RwzmpVuzMpo9qXtAtbO0g48NTB+0ZGRgQkTJqC5uRkKgMcff1y3O+PsdxlcNWnXf7eovzz+qGCXc0FBAUZru6DtTMiKZlC74fjycXXiTmOjOhHI+KyRI0di6dKl9l5/Ozdvk1WTysrKuJ46EaWPaL7PDGXkqnDlwVXhFPSuCqcAUWdGSSYGnjTwmS2ZGc0swQhBklU6HjNZWVmmqYGMCgoKQscvmtyMfM3NaG1txbZt29Da1qbuc9u2bWhtbbX/V67NJSe13eubN2/WpXMCetNPyVbg7du3W6cpiscfEhqm9bHKXEBElCzxmIVu+O4Kl3JOACnZs8O7MKU3Ox9Uu3nRoiij7Zb2er1YtGgRAJim7jFLDSQNGzZMnaAUKXicP38+SoJ/5VZWVqrb29vbcW1lJVwuV+Cv3DAthvPnz7c+qShaSmX3DgC1e+eZtWvR2tqKkSNHwi+EOhFodHBSk91j2Kmfr7nZtLtJ1mfKlClcT52IBpxw3ytNXm9q9uzEL299/HHlIkoGua56Y2Oj/oFIHw/D43It8enTpwvAfE1xuTa8XLVH+yMQutKQkTzGDTfcYLr6EaBZecmi/tr12yPSltH8rj1euBWF/H6/+XEs9mv5u4FcpUm+Znbqw/XUiSglWd3zItyr5Qp78ntF/hvVPT5OuHIRUaTWSs3jZl2zAKLqFpEtfzt27FC7NPbv3w8AqKurw44dO3pT9wTHZQKBdEV33HGHyS4DxxyimfyiHTy+NphD9A+vvmq6+pEAsGnTpsBfuYYWXmOL4KjCQvPUQlEMPRBAyCpHMsm+duKOYjVL02pIQ5RjQDdv3gwAIas1QVMfYVEfJoknopQUzRAwk6FJ2vkGAtDNN0hFTKdEA59J8OPz+dDe3g5FUbBo0SK0tbWhsLAQu3btghAC+fn5KCkpibjfiOmDNNvlR+0vf/kLOjs74XA4MDM4ANxY1htMiWR1HGNaIO3xbr3lFvzqV7/Snbd2xrt8rrHOtm4FwXROZvXX1T3KfUWzcpWvuRnt7e0od7kwqrAw5DU7fvy4ae5T2/UhIrKrj6mQot63nTR42dmJq5OBnXjNGfZRooHA5IOnnekngzI5E1B9mva5hg+7x+OBC8CqVauwatUqoLtb9zwZjMmE7trWyavKykyD1HBttE6nE92aY/iDyeIB4PLLL0d1dTWeeuopoLsbf/zjH9HU1ATh8SDf5+tdHjO4D+1z5b4vavZteZPT/i4EEFyu0+FwwO/3G05Gwfx58/DUU0/BVVER8aYZkRAo1QbPwVWajK+Ztj6m9SIiSoREBnhR9Appe3LsrgqXbOxqp9QTj1yfEfYhu4qB3i5is65Zq/3Krt729na43e6QNcu1x1FT9wSfu0XbLWxyiLy8PMzUBlNCWA4eB4BjH32En/3sZ+jp6QEAnDp1CuXl5SiXk4yCwqUWiqW727jKEQDdxB11+EKkdFZRpk2S3ena7n3ta7Z27dqYVjgiIkprabasLwNPSj3xTgQvGYIdGYgZP7KmOR6D4zkBqOMkFQBbtmzBzp07ba3Prp2FaHx88+bNmDFjBjyNjab1Nq5Tvnr1assk6YCNVBrRzDI3jDOSM9VlOqnmo0exdetWtLW1qblFQ5ao1LSYqvk/rZZ3M7yG8rqZ1fRidzfuvvtu0/RWlmmcwkmzGzkRpZBk3T/sLMiRQhh4Unqz8wG3+HDKrQ6HQx9AGgKt0tJSKICaqBcATp48iYcfftiym1ygt2XQ7PjGY+/YsQOvv/56yEQnOXi8x+/XraG+dOlSXUumth7GVBpyHwBCWyjtpppST6B3RaFx48Zhzpw5KC8vV3OLyq5wNcVTNJO6omDMyykT7utWXerLRKI0u5ETUQpJ1v3DzuIoKYSBJ6W3PnzAjYGYHCtotfJPNAnggd5gMiMjAwB6W9w0iezlsWdVVOCnP/0pJk2aBAB47bXXAARyYqothcFWu+bmZgi/P6Q1T3bLG4Mxud3j8WD+vHk4fvy4bh/C7+9tEbR7szI5f+316S0WOnzBanm3kNn1JrSzN9mdTkSDjo3V9VIVZ7XTwBHNpBhDWdOZgGatZHIfmhnmVixndxvqIY+tXU1H1kM7a10AvRN1XC7T8xtdVISxY8di2bJl2LBhA1paWtDY2Iji4mLU1NRg7bp1uKemBs8880zY62F53uHKaDQ1NakpPbTXSV4L2RopEFjdKJbZ9f09e5OIiPTsxGts8aSBI9IEGZMJLWG7Zk3+mpRdurJrXBs0yt914zDDTKLJysqC4nBEnDQDaCbqWIzpUcc23nUX3G43Xn/9dbS2tpq3LHo8al7RiGxMOvJ4PIH12NG7ZCYQCDIPHTqEuro6TJw4ERkZGeoqTVphJ3VpmL5m8Q4606C7iogGsAF8D2I6JRo4IrXIhZs9HSnJeZDs6h07dizQ2Ijy8nJ1ffbS0lJdi+Mnn3wCIJh6SbZUmhyjCsDkyZMBQyonBQikYVqyBEAgcHwGgdZDXZ5RIaBto1UUBWVlZbr/A73jLeW+LcezRkPTAiyf66qowLvq7nr3pwDqOQCBa9gWHAOqPo7AJKWUybfJ1lMiSqR45v2MpscqhTDwpIHD6gMWqavYxgdTjrXMzMwEFAXuYFcvALX7d/ny5bhw4QIeeOABfAVATV2ddeCpTfKO3hyUMhhbsmQJbg+WkROa5L5EmPOqr69H1ZIlupZF3apItbVAX9bw1RzP6/VCURREGzLKoFN2lUeVbzNFb6BERCGiuV/19XGrssZ8yymIXe1E0dB8gI1dve+++y4WLVqkTo5pamrCgQMHrCfPmHShFBYWqkudrV+/Xtcaqc0zKhPSW95OgmWrqqrUYQFGxryiwROJ5iqEUBAIhMvLy0O61yORgfCUKVPMJwhFk+szVgO4G4uI+ll/3q9izVCSRGzxpPQQjxavvjw/zPG1aYHWrl2reYrFikgm+ykuLkbX+fNwB1tNcddd2Lt3LyorK0MS0lfMmAFoc19a/bUb5HA4oERaySfGrvb6+nosXbo0ZEUkO7e7/fv34/z584Gxmsn6az1FWwKIiELYHSaW4tjiSemhvz9chuP7fD5dWiCBQMvm6tWr1dY+OWNbOzu9vr7esiVP25IKIQLd+dCnSVIQGDN6T01NxCpbpR6aWV6upliyTN4uRUgsX7VkiWkyfAHgC1/4AtavX4/LL7/ccvdyQlFM+TZT9K95IqKkiGd3fRIxnRJRNH81GsooiqJO0lEUBX4h1PRAVkLSK0U4xrFjx1BRUYFPjh/Hj1auxMsvv4wDBw9CQSCo3LVrF4QQ+olGBmrqIYcDwu9X00XV1NRg3bp1qJEplqK5HhZpmJq83kBXu6FF1ePxBFp6w6Sg8nq9gXyj0abBCrediIj6hZ14jV3tNHj0ZXKRIRiqr6/HkKVLge5udewlNC2bcqJQj9+PjGgmzxjroSgoFiIwYz47G48//nhgc/Dh1rY2KMHue2F1DoqCLE239d98PrS3t6Pc5cILwTGloxoaUF1dHTGADUc70//SSy/F7t27IQAcGzUKAHCspQUjZ8zAyZMnQ3J2hpx3NOmbGHQSEaUtBp40eMQjYNFM3pk8ebI6dtMYUMlA7Llly1AeTK+kWxHJIlD0NDbiwQcfxJ+Cm2QXtNPpRHd3d8hxnE4nttTWwnR+uuEYpaWlvYcKzpA3HX8aYcyoUU9PD7Zu3YrMzEzceOONAIDCggL8vq0Nb7/9NgBg48aN+NrXvgYIgcsuuwzFxcVoa2tTMwKYYssmEQ1WA/j+x8CTBo5IH1S7H+QoV/hRFAWK6F1tqMnrRfPVV6td3Ms1XdyRjiEnKt1TUwO1A1wIuIMrAhkn70Sd+1JR1IlAF7u7oRhSLAkAW8ySt0dqgRQCpZqxlnKMatuJE2qLrK4aAJQzZ3Do0CEAQGVlpfXwhAF60yUiimgA3/84uYgGjkhpJOx+kCN0y8su5oKCAgBAQUGBOnkn7IpIhmBOnajk9aopmOrq6lBRUYG6ujrd+uXG9dhDhEmRVFVVpU4EMmryegMpluwKBrTGNezVANnkdTBbv52IiAYHBp40MCX4r0Wfz4fW1lZs27ZNl6B927Zt6uOW9TAEY6WlpWouTJkk/tNPP4XH48G3vvUtlJSWqkFuj9+vm6EekvsyitZDOf5U/hupfmEJETag/cY3vmH5VDWfKBERDRoMPImshGk9lMFiZWUl2tvbAQDt7e1q3k3teMoQJqsMGddq1/rJ6tVobW3F66+/DuH3Y8WKFXirsRHNzc0oLi6OmPJIW39tiiWZsF620po9z+PxYP78+ZHTLgXJQFa2dL766quaKii6f411IyKigY+BJw188QhsLILFwEOh4yWj7kJWFLXF0KqWDz/8MFwuF8rKyqDIFkohervvY1jy0+12w9PYiEsuuQS//e1vLcu7KirU5PjhaAPaQJUCdfrss8/UMtq8prrW2gE8lomIqN+k6B/1CQs8m5ubsWzZMowbNw5Dhw7FhAkT8Oijj4afxUqUCLEGNmHGjFZVVeFid7fp0yKOl7RIIG9VSwHNeMho8o1a1FmS4083b96MPXv2qONKtc+TyfGlkGU/DcfQBrRmQbk0xOlEXV1db2stERElRor+UZ+wWe3vv/8+/H4/nnvuOUycOBHvvfce7rzzTpw9exZr1qxJ1GGJEiPMB1gmTjddktJsZrzJvgoLCzG6qAhfGDECBw8eDHk86tnrEfh8PpSUluomMjU0NOAZBJK55+fnoxQAXK5AVYPPs1z207DyEhA+1VS8zoOIiNJTwlo8Fy5ciE2bNuGGG27A+PHjcdNNN+H+++/H1q1bE3VIGixSpPvgWEuL5ZKUpjT1No6dlC2GmzdvDhYNlJWTgMLtSydC+qPS0lIogG4i04kTJ6AAcLlcKC0t1bVYKuqu7M1El9cg7CQmIiJKnBT5rjRK6rdBR0cHRowYYfl4V1cXOjs7dT9EIfqz+0DzQdZ2L69YsQJutzuw0lCklXiC3dzGsZNZWVkYNWoUioqK4BcittnrFnWV5bVBpd8wNlUGldr1143szEQ3m8QUch5ERJQYKdrVnrS12g8fPozy8nKsWbMGd955p2mZH//4x3jsscdCtnOtdkpbmq52X3DJSkVRsGjRIrS1tUEgMCZUu2Slur56MCG9Lvl8lEnttTweDx588EE89dRTcLlcaAomozeugqRdS16W0Q4j6PH70RRpvXkN0/PIzk7ZmyEREcXGzlrttls8H3roocBKLWF+3n//fd1zPvroIyxcuBD/9E//ZBl0AsDKlSvR0dGh/rS0tNitHlH/s5g8VGKSr9OhKCgvL1e7uQFEn3zebJtJ14pZ6yoAZBhSH2nHlmpnqcuW19F2WiyD9Q45D4ug027aJiIiSk+2A8/77rsPhw4dCvszfvx4tfzHH3+MefPmYc6cOfjP//zPsPvOyspCbm6u7oco7VgEV1tM8nX6bY6djPbY6mpITU144YUXINA7M/348eMoKChQg0q58tLu3bvV3VgNIwiZiW4IdNUAsrHRVrWtguP+wCCYiChxbM9qLygoUL+oIvnoo48wb948lJeXY9OmTZxgQINa1ZIlmOz1mq5hHrfZ3sFud20Ce0VRAmukG2am79y5U/eZ3LZtG/bv349Gjwe+5maUlJTo9mG61rwhyNYGkK7gzHgr2qEH2hn21dXVuqEHyWbnHIiIyJ6EjfH86KOP8KUvfQklJSV4/vnnkZGRoT5WVFQU1T7sjBkg6lcRxllKxrGTcpyl1+sNzASP08dxy5YtWLp0KbpNco0ax3bKMZgh5aKsi9nY1cLCQuzatStsAKldwUjWwViXJA1Bj/kciIjIXryWsMCztrYWd9xxh+lj0R6SgSf1qyiDSTuOHTuGiooKjB07FsuWLcOGDRvQ0tKCxsbG2BOqW9Uz2NIJ6INNr9eLQ4cOWQamALB69WosWrQocsClOUbgv9EHkOGCY6fTidra2qSt5Z5KQTARUbpJicAzHhh4UsqIRxAa3EfYWetxZDYz3e/3q7PX5eORRLpFRAogL3Z3W147qzp4bcyej4dUCoKJiNJNQme1Ew1K8fj7LLiPsLPWY2GRJNhsZrqdXJpRTXjSrDVvxu12R3Xt5FjT/hoHHukcGHQSEcVHwpbMJKI+sNPCalFOzkyXravLly/Xta7KwHREX5bpNBzbOHY1ElkH49CD/kw0H3YJVCIi6hMGnkSJFEPC93jStqYaW1dlYPree+/B5XKpXf+xBFzGAHLWhg0oiiKAjBQcJ1MqBsFERAMNx3gSxUMig8lE7Tu433hNeErW2NVEGgjnQESDWBIbNrQ4uYgoFcVxglIi9iv8/r4FXP10wyMiov7FyUVEyaad4GMx2SeeE5QSsd8+T3hi0ElERBEw8CSKB23QFWsAZhWw9rUsERFRimDgSZQq7ASs2rIMQomIKE0w8CRKd/EIQq2GCljtj8EuERHFgIEn0UASaze/1VABq/3FY5IUERENOgw8iVJRMgKz/gz+OBGJiGhQYuBJlIqtb8mYoBSn4M/j8WD+/PnweDxx2R8REQ1cDDyJkt36lshAtx9aEjdv3ozdu3ejrq4u6ccmIqL0wsCTKNkSGRxaBLXxbpX0+Xzwer1oamrCCy+8AABoaGhAU1MTvF4vfD5fXI5DREQDC9dqJxoEtK2SLperz/srLS1Vf5eJ50+cOIHy8nJ1ewovikZERP2EgSfRQKIJ9nw+H9rb26Eoiq5Vsrq6GkII5Ofno6SkJLbDABjidKK7u1sNMOW/TqcTtbW1fToNIiIamBh4EqUTG+uhJ7RVUgi4m5p0+5LcbjdmzpwZ236JiGhA4xhPonRiI1Csr6+H0+kMPi20VbK+vj4uVXI4HLp/iYiIrPCbgshKpNnn8VglKIGqqqrgdrtNH3O73aiqqurT/gsLC1FUVITy8nKsX78e5eXlKCoqQmFhYZ/2S0REAxe72omsRGpdjMcqQUnicDjg9/vVf+OhuLgYzc3NyMzMhKIoWL58OS5cuICsrKy47J+IiAYetngSDWBxbZU0aanNyspSx48qisKgk4iIwlJECuc86ezsRF5eHjo6OpCbm9vf1SFKS11dXWqrpBCCrZJERBRXduI1drUTDXDaIJOtkkRE1J/Y1U5EREREScHAk4iIiIiSgoEnERER0UCQpHR9fcHAk4iIiGggSN354ioGnkSUPGnw1zgRESUOA09Kbwxk0ksa/DVORESJw8CT0hsDGSIiorTBwJOIiIiIkoKBJxERERElBQNPIiIiIkoKBp5ERERElBQMPIlSUbJn6zM7ABERJQEDT6JUZGe2fjyCRmYHICKiJGDgSZTuGDQSEVGaYOBJREREREnBwJOIiIiIkoKBJxERERElBQNPIiIiIkoKBp5E6Yjpj4iIKA0x8CRKR3ZnsicxUPV4PJg/fz48Hk/SjklEROmBgSfRYJDElEubN2/G7t27UVdXl7RjEhFRenD2dwWIKEhR0jYnp8/nQ3t7OxRFwQsvvAAAaGhoQHV1NYQQyM/PR0lJST/XkoiI+hsDT6JUkaZBJwCUlpaqvyvBbv0TJ06gvLxc3S7S+PyIiCg+2NVORH1WX18PpzPwd6wMMOW/TqcT9fX1/VY3IiJKHWzxJKI+q6qqwuTJk3UtnJLb7cbMmTP7oVZERJRq2OJJRHHlcDh0/xIREUn8ZiCiuCgsLERRURHKy8uxfv16lJeXo6ioCIWFhf1dNSIiShGKSOER/52dncjLy0NHRwdyc3P7uzpEFEFXVxcyMzOhKAqEELhw4QKysrL6u1pERJRAduI1jvEkorjRBpmKojDoJCIiHXa1ExEREVFSMPAkIiIioqRg4ElEREREScHAk4iIiIiSgoEnERERESUFA08iIiIiSgoGnkRERESUFAw8iYiIiCgpGHgSERERUVIw8CQiIiKipGDgSURERERJwcCTiIiIiJKCgScRERERJQUDTyIiIiJKioQGnjfddBOuuOIKZGdnY/To0bj99tvx8ccfJ/KQRERERJSiEhp4zps3Dy+++CI++OAD/Pa3v8WRI0fwj//4j4k8JBERERGlKEUIIZJ1sFdeeQVf+9rX0NXVhSFDhkQs39nZiby8PHR0dCA3NzcJNSQiIiIiO+zEa84k1QmnTp3Cli1bMGfOHMugs6urC11dXer/Ozo6AAROiIiIiIhSj4zTomrLFAn24IMPipycHAFAXHvttaK9vd2y7KOPPioA8Ic//OEPf/jDH/7wJ81+WlpaIsaFtrvaH3roITz55JNhyxw6dAiTJk0CALS3t+PUqVPw+Xx47LHHkJeXh+3bt0NRlJDnGVs8/X4/Tp06hZEjR5qWj7fOzk6MHTsWLS0t7No34LUxx+tijdfGHK+LNV4bc7wu1nhtzCX7ugghcPr0aYwZMwYOR/jpQ7YDzxMnTuDkyZNhy4wfPx6ZmZkh248dO4axY8fi//7v/1BZWWnnsEnBMaXWeG3M8bpY47Uxx+tijdfGHK+LNV4bc6l8XWyP8SwoKEBBQUFMB/P7/QCga9UkIiIiosEhYZOL3G43Ghsbcd1112H48OE4cuQIHn74YUyYMCElWzuJiIiIKLESlsczJycHW7duxfXXX4+ysjIsW7YM06ZNw+uvv46srKxEHbZPsrKy8Oijj6Zs/foTr405XhdrvDbmeF2s8dqY43WxxmtjLpWvS1LzeBIRERHR4MW12omIiIgoKRh4EhEREVFSMPAkIiIioqRg4ElERERESTHoAs+f/vSnmDNnDnJycjBs2LConiOEwCOPPILRo0dj6NChWLBgAT788ENdmVOnTqGqqgq5ubkYNmwYli1bhjNnziTgDBLDbv2bm5uhKIrpz69//Wu1nNnjDQ0NyTiluInltf3Sl74Uct533XWXrszf/vY3LF68GDk5OSgsLMQDDzyA7u7uRJ5KXNm9LqdOncLdd9+NsrIyDB06FFdccQVqamrQ0dGhK5eO75lnn30WpaWlyM7OxuzZs/HWW2+FLf/rX/8akyZNQnZ2NqZOnYqdO3fqHo/mnpMO7FyXX/7yl/j7v/97DB8+HMOHD8eCBQtCyi9dujTkvbFw4cJEn0ZC2Lk2tbW1IeednZ2tKzMY3zNm91lFUbB48WK1zEB4z/zP//wPvvrVr2LMmDFQFAUvvfRSxOfs2bMHM2fORFZWFiZOnIja2tqQMnbvW3HT99XY08sjjzwinn76aXHvvfeKvLy8qJ7zxBNPiLy8PPHSSy+Jd955R9x0001i3Lhx4vPPP1fLLFy4UEyfPl28+eab4n//93/FxIkTxa233pqgs4g/u/Xv7u4Wn3zyie7nscceE5deeqk4ffq0Wg6A2LRpk66c9rqlg1he27lz54o777xTd94dHR3q493d3WLKlCliwYIFYt++fWLnzp0iPz9frFy5MtGnEzd2r8u7774rvv71r4tXXnlFHD58WPz3f/+3uPLKK8U//MM/6Mql23umoaFBZGZmio0bN4oDBw6IO++8UwwbNky0traaln/jjTdERkaGeOqpp8TBgwfFv/7rv4ohQ4aId999Vy0TzT0n1dm9Lrfddpt49tlnxb59+8ShQ4fE0qVLRV5enjh27Jhaprq6WixcuFD33jh16lSyTilu7F6bTZs2idzcXN15Hz9+XFdmML5nTp48qbsm7733nsjIyBCbNm1SywyE98zOnTvFv/zLv4itW7cKAGLbtm1hy//1r38VOTk54t577xUHDx4U69atExkZGeL3v/+9WsbutY6nQRd4Sps2bYoq8PT7/aKoqEj8/Oc/V7d99tlnIisrS/zqV78SQghx8OBBAUA0NjaqZXbt2iUURREfffRR3Oseb/Gq/4wZM8S3v/1t3bZoPiSpLNZrM3fuXHHPPfdYPr5z507hcDh0Xx7/8R//IXJzc0VXV1dc6p5I8XrPvPjiiyIzM1NcvHhR3ZZu75lZs2aJ7373u+r/e3p6xJgxY8Tjjz9uWv4b3/iGWLx4sW7b7NmzxYoVK4QQ0d1z0oHd62LU3d0tLrvsMvH888+r26qrq8XNN98c76omnd1rE+n7iu+ZgF/84hfisssuE2fOnFG3DZT3jBTN/fHBBx8UV199tW7bN7/5TfHlL39Z/X9fr3VfDLqudruOHj2K48ePY8GCBeq2vLw8zJ49G3v37gUA7N27F8OGDYPL5VLLLFiwAA6HA263O+l1tise9fd6vXj77bexbNmykMe++93vIj8/H7NmzcLGjRsh0ih1bF+uzZYtW5Cfn48pU6Zg5cqVOHfunG6/U6dOxahRo9RtX/7yl9HZ2YkDBw7E/0TiLF7vebmOsNOpX0QtXd4zFy5cgNfr1d0fHA4HFixYoN4fjPbu3asrDwRee1k+mntOqovluhidO3cOFy9exIgRI3Tb9+zZg8LCQpSVleE73/kOTp48Gde6J1qs1+bMmTMoKSnB2LFjcfPNN+vuE3zPBGzYsAG33HILLrnkEt32dH/P2BXpHhOPa90XCVsyc6A4fvw4AOgCBPl/+djx48dRWFioe9zpdGLEiBFqmVQWj/pv2LABkydPxpw5c3TbV61ahfnz5yMnJwevvvoq/vmf/xlnzpxBTU1N3OqfSLFem9tuuw0lJSUYM2YM9u/fjx/+8If44IMPsHXrVnW/Zu8p+Viqi8d7pr29HatXr8by5ct129PpPdPe3o6enh7T1/L99983fY7Va6+9n8htVmVSXSzXxeiHP/whxowZo/tyXLhwIb7+9a9j3LhxOHLkCH70ox9h0aJF2Lt3LzIyMuJ6DokSy7UpKyvDxo0bMW3aNHR0dGDNmjWYM2cODhw4gOLiYr5nALz11lt47733sGHDBt32gfCescvqHtPZ2YnPP/8cn376aZ8/n30xIALPhx56CE8++WTYMocOHcKkSZOSVKPUEO116avPP/8c//Vf/4WHH3445DHttmuuuQZnz57Fz3/+834PIhJ9bbTB1NSpUzF69Ghcf/31OHLkCCZMmBDzfhMtWe+Zzs5OLF68GF/4whfw4x//WPdYqr5nKHmeeOIJNDQ0YM+ePbpJNLfccov6+9SpUzFt2jRMmDABe/bswfXXX98fVU2KyspKVFZWqv+fM2cOJk+ejOeeew6rV6/ux5qljg0bNmDq1KmYNWuWbvtgfc+ksgEReN53331YunRp2DLjx4+Pad9FRUUAgNbWVowePVrd3traihkzZqhl2tradM/r7u7GqVOn1Of3h2ivS1/r/5vf/Abnzp3Dt771rYhlZ8+ejdWrV6Orq6tf15BN1rWRZs+eDQA4fPgwJkyYgKKiopAZhK2trQAw4N8zp0+fxsKFC3HZZZdh27ZtGDJkSNjyqfKeMZOfn4+MjAz1tZNaW1str0NRUVHY8tHcc1JdLNdFWrNmDZ544gm89tprmDZtWtiy48ePR35+Pg4fPpw2QURfro00ZMgQXHPNNTh8+DAAvmfOnj2LhoYGrFq1KuJx0vE9Y5fVPSY3NxdDhw5FRkZGn9+DfZLwUaQpyu7kojVr1qjbOjo6TCcXeTwetcwf/vCHtJtcFGv9586dGzIz2cpPfvITMXz48Jjrmmzxem3//Oc/CwDinXfeEUL0Ti7SziB87rnnRG5urjh//nz8TiBBYr0uHR0d4tprrxVz584VZ8+ejepYqf6emTVrlvje976n/r+np0dcfvnlYScXfeUrX9Ftq6ysDJlcFO6ekw7sXhchhHjyySdFbm6u2Lt3b1THaGlpEYqiiJdffrnP9U2mWK6NVnd3tygrKxM/+MEPhBCD+z0jROD7PCsrS7S3t0c8Rrq+ZyREObloypQpum233npryOSivrwH+2LQBZ4+n0/s27dPTf2zb98+sW/fPl0KoLKyMrF161b1/0888YQYNmyYePnll8X+/fvFzTffbJpO6ZprrhFut1v8+c9/FldeeWXapVMKV/9jx46JsrIy4Xa7dc/78MMPhaIoYteuXSH7fOWVV8Qvf/lL8e6774oPP/xQ/Pu//7vIyckRjzzySMLPJ57sXpvDhw+LVatWCY/HI44ePSpefvllMX78ePHFL35RfY5Mp3TDDTeIt99+W/z+978XBQUFaZdOyc516ejoELNnzxZTp04Vhw8f1qU36e7uFkKk53umoaFBZGVlidraWnHw4EGxfPlyMWzYMDVjwe233y4eeughtfwbb7whnE6nWLNmjTh06JB49NFHTdMpRbrnpDq71+WJJ54QmZmZ4je/+Y3uvSHvzadPnxb333+/2Lt3rzh69Kh47bXXxMyZM8WVV16ZFn+sadm9No899pj4wx/+II4cOSK8Xq+45ZZbRHZ2tjhw4IBaZjC+Z6TrrrtOfPOb3wzZPlDeM6dPn1ZjFQDi6aefFvv27RM+n08IIcRDDz0kbr/9drW8TKf0wAMPiEOHDolnn33WNJ1SuGudSIMu8KyurhYAQn52796tlkEwj6Dk9/vFww8/LEaNGiWysrLE9ddfLz744APdfk+ePCluvfVWcemll4rc3Fxxxx136ILZVBep/kePHg25TkIIsXLlSjF27FjR09MTss9du3aJGTNmiEsvvVRccsklYvr06WL9+vWmZVOZ3Wvzt7/9TXzxi18UI0aMEFlZWWLixInigQce0OXxFEKI5uZmsWjRIjF06FCRn58v7rvvPl1aoVRn97rs3r3b9LMHQBw9elQIkb7vmXXr1okrrrhCZGZmilmzZok333xTfWzu3LmiurpaV/7FF18UV111lcjMzBRXX3212LFjh+7xaO456cDOdSkpKTF9bzz66KNCCCHOnTsnbrjhBlFQUCCGDBkiSkpKxJ133pmUL8pEsHNtvv/976tlR40aJW688UbR1NSk299gfM8IIcT7778vAIhXX301ZF8D5T1jde+U16K6ulrMnTs35DkzZswQmZmZYvz48bqYRgp3rRNJESJF85QQERER0YDCPJ5ERERElBQMPImIiIgoKRh4EhEREVFSMPAkIiIioqRg4ElEREREScHAk4iIiIiSgoEnERERESUFA08iIiIiSgoGnkRERESUFAw8iYiIiCgpGHgSERERUVIw8CQiIiKipPj/li3aIxHF/cQAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "x_test = torch.linspace(-1,1,200).reshape((200, 1))\n",
    "means, variances = model.predict(x_test, num_samples = 100)\n",
    "\n",
    "# We generate samples from the predictive distribution\n",
    "\n",
    "samples = torch.randn(*means.shape) * torch.sqrt(variances) + means\n",
    "\n",
    "f, ax = plt.subplots(1, 1, figsize=(8, 6))\n",
    "ax.plot(train_x_h.numpy(), train_y_h.numpy(), 'k*')\n",
    "for i in range(100):\n",
    "  ax.plot(x_test.numpy(), samples[:,i].numpy(), ',', color = \"red\")\n",
    "ax.set_ylim([-3, 3])\n",
    "ax.legend(['Observed Data', 'Predicted Data'])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "qO511VfCXbZv"
   },
   "source": [
    "As we can se DVSVI results in a predictive distribution that cannot capture the input dependent noise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "JrjmDYJnW5pP"
   },
   "source": [
    "## **Task 2**\n",
    "Try to improve the modeling of the predictive distribution by:\n",
    "\n",
    "\n",
    "*   Optimizing alpha-diverngences. In particular, try to use alpha != 0.0, for training the model.\n",
    "*   Adding more units to the hidden layer. For this, simply specify a higher number of units in the hidden layer when instantiating the DGP objecto.\n",
    "\n",
    "Take a look at the resulting predictive distribution and see what values of alpha/architectures work better.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}