example_quantum_boltzmann_machine_QBM.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "56f0b47e",
   "metadata": {},
   "source": [
    "# Example: Quantum-Boltzmann-Machine Implementation on Dynex"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5fc41b9b",
   "metadata": {},
   "source": [
    "Quantum computing algorithms for machine learning harness the power of quantum mechanics to enhance various aspects of machine learning tasks. Here is a summary of some prominent quantum computing algorithms for machine learning:\n",
    " \n",
    "1. **Quantum Support Vector Machine (QSVM):** QSVM is a quantum-inspired algorithm that aims to classify data using a quantum kernel function. It leverages the concept of quantum superposition and quantum feature mapping to potentially provide computational advantages over classical SVM algorithms in certain scenarios.\n",
    " \n",
    " \n",
    "2. **Quantum Principal Component Analysis (QPCA):** QPCA is a quantum version of the classical Principal Component Analysis (PCA) algorithm. It utilizes quantum linear algebra techniques to extract the principal components from high-dimensional data, potentially enabling more efficient dimensionality reduction in quantum machine learning.\n",
    " \n",
    " \n",
    "3. **Quantum Neural Networks (QNN):** QNNs are quantum counterparts of classical neural networks. They leverage quantum principles, such as quantum superposition and entanglement, to process and manipulate data. QNNs hold the potential to learn complex patterns and perform tasks like classification and regression, benefiting from quantum parallelism.\n",
    " \n",
    " \n",
    "4. **Quantum K-Means Clustering:** Quantum K-means is a quantum-inspired variant of the classical K-means clustering algorithm. It uses quantum algorithms to accelerate the clustering process by exploring multiple solutions simultaneously. Quantum K-means has the potential to speed up clustering tasks for large-scale datasets.\n",
    " \n",
    " \n",
    "5. **Quantum Boltzmann Machines (QBMs):** QBMs are quantum analogues of classical Boltzmann Machines, which are generative models used for unsupervised learning. QBMs employ quantum annealing to sample from a probability distribution and learn patterns and structures in the data.\n",
    " \n",
    " \n",
    "6. **Quantum Support Vector Regression (QSVR):** QSVR extends the concept of QSVM to regression tasks. It uses quantum computing techniques to perform regression analysis, potentially offering advantages in terms of efficiency and accuracy over classical regression algorithms.\n",
    " \n",
    "As both, Quantum computing and Neuromorphic computing are sharing similar efficiency, all the algorithms above can be computed efficiently on the Dynex platform, but without the limitations of number of available qubits, error correction or availability."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ca56c81",
   "metadata": {},
   "source": [
    "A new approach using simulated quantum annealing (SQA) to numerically simulate quantum sampling in a deep Boltzmann machine (DBM) was presented in [1]. The authors proposed a framework for training the network as a quantum Boltzmann machine (QBM) in the presence of a significant transverse field for reinforcement learning. However, they demonstrated that the process of embedding Boltzmann machines in larger quantum annealer architectures is problematic when huge weights and biases are needed to emulate the Boltzmann machine’s logical nodes using chains and clusters of physical qubits. On the other hand, quantum annealing has the potential to speed up the sampling process exponentially.\n",
    "\n",
    "The Dynex Neuromorphic Platform does not have these physical limitations and can therefore overcome such scaling problems and expand to large, real-world datasets and problems.  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "baf0ec06",
   "metadata": {},
   "source": [
    "We demonstrate a Quantum-Boltzmann-Machine (QBM) implementation using the Dynex platform to perform the computations and compare it with a traditional Restricted-Boltzmann-Machine (RBM). RBM is a well-known probabilistic unsupervised learning model which is learned by an algorithm called Contrastive Divergence. An important step of this algorithm is called Gibbs sampling – a method that returns random samples from a given probability distribution. We decided to conduct our experiments on the popular MNIST dataset considered a standard benchmark in many of the machine learning and image recognition subfields. The implementation follows a highly optimised QUBO formulation available at [2]."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46f62c6c",
   "metadata": {},
   "source": [
    "## Problem Description "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a037e77",
   "metadata": {},
   "source": [
    "Restricted Boltzmann Machine is a variant of a Boltzman Machine – a stochastic, generative machine learning model inspired by statistical physics. It can model the underlying probability distribution of a training dataset. An RBM is a bipartite graph with two groups of nodes called visible and hidden. Learning an RBM corresponds to fitting its parameters such that the distribution represented by the RBM models the distribution underlying the training dataset. There is a weighted connection between each pair of vertices from different layers. A bias value is also associated with each vertex from both layers:"
   ]
  },
  {
   "attachments": {
    "rbmfig1.png": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "67fbb42e",
   "metadata": {},
   "source": [
    "![rbmfig1.png](attachment:rbmfig1.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5d1ddd2",
   "metadata": {},
   "source": [
    "An RBM is an energy-based, probabilistic model, which means that there is a scalar value assigned to each possible state. The probability of observing a given state depends on the energy function. We refer to the equations in the references."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0532b570",
   "metadata": {},
   "source": [
    "## Quantum Extensions to RBM "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "876337f5",
   "metadata": {},
   "source": [
    "The Dynex Platofrm and the D-wave Quantum Annealing algorithm provide an efficient way to solve such a function.\n",
    "In order to do that, a QUBO (Quadratic Unconstrained Binary Optimization) Eq. (11) needs to be constructed:"
   ]
  },
  {
   "attachments": {
    "rbmeq1.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "5f96f1bd",
   "metadata": {},
   "source": [
    "![rbmeq1.png](attachment:rbmeq1.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c26c3be",
   "metadata": {},
   "source": [
    "In the next step, the QUBO representation is transformed into a Binary Quadratic Model which can be used by\n",
    "the Dynex Neuromorphic campler (as well as the D-wave quantum sampler) in order to obtain samples from\n",
    "the model’s actual probability distribution. With an energy-based sampler it is possible to obtain accurate samples from the original distribution, which is computationally expensive for a classical computer. Instead of classical sampling as described in [2], we get the samples as a result of a quantum annealing process. The only\n",
    "input we need to encode for the quantum annealer are model parameters. In this example will the quantum annealing process be replaced with the Dynex Neuromorphic sampler."
   ]
  },
  {
   "attachments": {
    "rbmfig2.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "b79ef0cd",
   "metadata": {},
   "source": [
    "![rbmfig2.png](attachment:rbmfig2.png)\n",
    "Schematic representation of the Contrastive Divergence algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae661420",
   "metadata": {},
   "source": [
    "## Implementation "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0acd380",
   "metadata": {},
   "source": [
    "We create a classical RBM model as well as a QBM where the classical sampling steps are being replaced by the output of the Dynex sampler. We test the models on the well known MNIST dataset of handwritten digital images with 60,000 training samples and 10,000 testing samples. To monitor the quality of the training process we apply a popular Mean Squared Error (MSE) measure between the input image which activates the sampling process and the generated image. We start by importing the libraries:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4c52a895",
   "metadata": {},
   "outputs": [],
   "source": [
    "import dynex\n",
    "import dimod"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0f9a8b92",
   "metadata": {},
   "outputs": [],
   "source": [
    "from itertools import product\n",
    "import json\n",
    "import random \n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import networkx as nx\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4c3a8b7a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import timeit\n",
    "from tqdm import tqdm_notebook as tqdm\n",
    "from skimage import data, color\n",
    "from skimage.transform import rescale, resize, downscale_local_mean\n",
    "from skimage import img_as_bool\n",
    "import cv2 as cv\n",
    "import random\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "db7b186e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import QRBM.MSQRBM\n",
    "import QRBM.classicalRBM"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a43b3d6",
   "metadata": {},
   "source": [
    "We then define the settings. The MNIST dataset consists of images of size 28 x 28 pixels each. We also set the number of epochs for training the traditional RBM. The input size of the network is 784 (based on the image size) and a hidden layer of size 60."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "12cec9f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "image_height = 28\n",
    "image_width = 28\n",
    "\n",
    "# images will be flattened\n",
    "len_x = image_height * image_width\n",
    "len_y = 0\n",
    "\n",
    "digits = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n",
    "THRESHOLD = 100\n",
    "n_hidden = 60\n",
    "qpu = False\n",
    "epochs = 500 \n",
    "lr = 0.1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6dc18a0",
   "metadata": {},
   "source": [
    "The MNIST dataset can be downloaded from https://www.kaggle.com/datasets/oddrationale/mnist-in-csv and will be loaded in a DataFrame object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d806deb8",
   "metadata": {},
   "outputs": [],
   "source": [
    "mnist_dataset = pd.read_csv('datasets/mnist_train.csv')\n",
    "mnist_test = pd.read_csv('datasets/mnist_test.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90aae634",
   "metadata": {},
   "source": [
    "We then preapre the train and test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "fca35c1d",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = mnist_dataset.values[:,1:]\n",
    "X_train2 = mnist_dataset.values[:,:]\n",
    "\n",
    "X_test = mnist_test.values[:,1:]\n",
    "X_test2 = mnist_test.values[:,:]\n",
    "\n",
    "X_train3 = []\n",
    "X_test3 = []\n",
    "\n",
    "for digit in digits:\n",
    "    X_train3.append(mnist_dataset.values[np.where(mnist_dataset.values[:,0] == digit), 1:][0])\n",
    "    X_test3.append(mnist_test.values[np.where(mnist_test.values[:,0] == digit), 1:][0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "79a8622b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "imgs = []\n",
    "imgs_test = []\n",
    "for digit_index in range(len(digits)):\n",
    "    imgs.append(np.resize(X_train3[digit_index], (len(X_train3[digit_index]), 28, 28)) / 255)\n",
    "    imgs_test.append(np.resize(X_test3[digit_index], (len(X_test3[digit_index]), 28, 28)) / 255)\n",
    "    \n",
    "plt.imshow(imgs[0][0])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7523d5c6",
   "metadata": {},
   "source": [
    "Before feeding the data to the model, we have to perform some pre-processing steps due to the fact that an RBM\n",
    "can only process binary data. We transformed the original MNIST images to binary representation using a threshold of 100 pixel brightness out of 0÷255 greyscale, and also flatten the images so they can fit into the 1-dimensional RBM visible layer of length 28 x 28 = 784:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d7a5af2d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# resizing images\n",
    "images_resized = []\n",
    "images_resized_test = []\n",
    "for digit_index in range(len(digits)):\n",
    "    images_resized.append([resize(img, (image_width, image_height), anti_aliasing=True) for img in imgs[digit_index]])\n",
    "    images_resized_test.append([resize(img, (image_width, image_height), anti_aliasing=True) for img in imgs_test[digit_index]])\n",
    "\n",
    "plt.imshow(images_resized[0][0])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "01c49fe4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# normalizing images\n",
    "images_normalized = []\n",
    "images_normalized_test = []\n",
    "\n",
    "for digit_index in range(len(digits)):\n",
    "    images_normalized.append([cv.normalize(image_resized, image_resized, 0, 255, cv.NORM_MINMAX) for image_resized in images_resized[digit_index]])\n",
    "    images_normalized_test.append([cv.normalize(image_resized, image_resized, 0, 255, cv.NORM_MINMAX) for image_resized in images_resized_test[digit_index]])\n",
    "\n",
    "plt.imshow(images_normalized[0][0])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "1ebba8e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# converting to binary\n",
    "data = []\n",
    "data_test = []\n",
    "for digit_index in range(len(digits)):\n",
    "    data.append([np.where(image_resized > THRESHOLD, 1, 0) for image_resized in images_resized[digit_index]])\n",
    "    data_test.append([np.where(image_resized > THRESHOLD, 1, 0) for image_resized in images_resized_test[digit_index]])\n",
    "\n",
    "plt.imshow(data[0][0])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "4d79f1b0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# flattening the image\n",
    "input_data = []\n",
    "input_data_test = []\n",
    "for digit_index in range(len(digits)):\n",
    "    input_data.append([x.flatten().tolist() for x in data[digit_index]])\n",
    "    input_data_test.append([x.flatten().tolist() for x in data_test[digit_index]])\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "83c40598-0210-4299-bd61-38ab592af683",
   "metadata": {},
   "outputs": [],
   "source": [
    "# save layer features to file:\n",
    "import pickle\n",
    "pickle.dump(input_data, open('datasets/MNIST.pickle', 'wb'))\n",
    "pickle.dump(input_data_test, open('datasets/MNIST_test.pickle', 'wb'))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ee9833f",
   "metadata": {},
   "source": [
    "Now after preprocssing, we can prepare and shuffle the training and test data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a4852000",
   "metadata": {},
   "outputs": [],
   "source": [
    "result_picture_tab = []\n",
    "for digit_index in range(len(digits)):\n",
    "    result_picture_tab.append(np.mean(input_data_test[digit_index], axis = 0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "334a9eab",
   "metadata": {},
   "outputs": [],
   "source": [
    "# shuffling the training data\n",
    "for digit in digits:\n",
    "    flat_input_data = [item for sublist in input_data for item in sublist]\n",
    "    flat_input_data_test = [item for sublist in input_data_test for item in sublist]\n",
    "\n",
    "random.shuffle(flat_input_data)\n",
    "random.shuffle(flat_input_data_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "553cbc18",
   "metadata": {},
   "source": [
    "## Traditional RBM"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35071deb",
   "metadata": {},
   "source": [
    "For benchmarking and testing the correctness of the RBM implementation, we train a traditional RBM by maximizing the product of probabilities assigned to some training set V and optimizing the weight vector using Constrastive Divergence (CD)[3]:\n",
    "\n",
    "1. Take a training sample v,\n",
    "   compute the probabilities of the hidden units and\n",
    "   sample a hidden activation vector h from this probability distribution.\n",
    "\n",
    "2. Compute the outer product of v and h and call this the positive gradient.\n",
    "\n",
    "3. From h, sample a reconstruction v' of the visible units,\n",
    "   then resample the hidden activations h' from this. (Gibbs sampling step)\n",
    "\n",
    "4. Compute the outer product of v' and h' and call this the negative gradient.\n",
    "\n",
    "5. Let the update to the weight matrix W be the positive gradient minus the negative gradient,\n",
    "   times some learning rate\n",
    "   \n",
    "6. Update the biases a and b analogously: a=epsilon (v-v'), b=epsilon (h-h')\n",
    "\n",
    "            "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "769bf602",
   "metadata": {},
   "source": [
    "We als added learning rate decay, which is a mechanism that decreases the learning rate α every couple of iterations. It is used to further optimize the learning process after getting stuck close to the optimum. We also added Momentum, which is a popular improvement of gradient based algorithms, such as SGD or Adam. The main idea behind the method is to calculate the gradient, not only based on the current data sample, but also the previous gradient direction. Another improvement that was added is a different variant of the learning algorithm called persistent CD. The main difference is that in most iterations, instead of taking the input data as vector v, we use the v' vector from the previous iteration to calculate the negative phase of the gradient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "7bae9408",
   "metadata": {},
   "outputs": [],
   "source": [
    "bm = QRBM.classicalRBM.classicalRBM(n_visible=len_x, n_hidden=n_hidden, use_tqdm=True);\n",
    "bm.image_height = image_height\n",
    "bm.tqdm = tqdm\n",
    "bm.result_picture_tab = result_picture_tab"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "392aa57b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "74b3b092e29a48959d16ba6b0d80347d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/500 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Better model found at epoch 0 mse= 0.30739795918367346\n",
      "Better model found at epoch 1 mse= 0.2997448979591837\n",
      "Better model found at epoch 2 mse= 0.20535714285714285\n",
      "Better model found at epoch 7 mse= 0.17857142857142858\n",
      "Better model found at epoch 8 mse= 0.1568877551020408\n",
      "Better model found at epoch 9 mse= 0.1556122448979592\n",
      "Better model found at epoch 14 mse= 0.1096938775510204\n",
      "Better model found at epoch 18 mse= 0.10586734693877552\n",
      "Better model found at epoch 24 mse= 0.09438775510204081\n",
      "Better model found at epoch 26 mse= 0.07908163265306123\n",
      "Better model found at epoch 47 mse= 0.058673469387755105\n",
      "Better model found at epoch 68 mse= 0.04974489795918367\n",
      "lr= 0.09000000000000001\n",
      "Better model found at epoch 106 mse= 0.042091836734693876\n",
      "Better model found at epoch 198 mse= 0.036989795918367346\n",
      "lr= 0.08100000000000002\n",
      "Better model found at epoch 200 mse= 0.03188775510204082\n",
      "Better model found at epoch 214 mse= 0.030612244897959183\n",
      "Better model found at epoch 236 mse= 0.029336734693877552\n",
      "Better model found at epoch 243 mse= 0.02423469387755102\n",
      "lr= 0.07290000000000002\n",
      "lr= 0.06561000000000002\n",
      "Better model found at epoch 492 mse= 0.021683673469387755\n",
      "lr= 0.05904900000000002\n"
     ]
    },
    {
     "data": {
      "image/png": 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rAtDcuXMxdepUTJ8+HUuWLMHw4cMxYcIEbNu2Tbl/ly5dcPvtt2PBggVYtmwZJk+ejMmTJ+PNN9+09nnwwQfxyCOPYPbs2Vi4cCHKysowYcIENDY2Zuq0lHQsLkDXskIAwP+277dtT2dGaD/CFJnAEixctwsA8LdFG7LcE4IgCKI1yboANHPmTFx33XWYPHkyhgwZgtmzZ6O0tBRz5sxR7n/qqafi29/+No488kgceuihuPHGGzFs2DB8+OGHAOLan1mzZuFXv/oVzj//fAwbNgzPPPMMtmzZgpdffjmDZ6aGaYHWbLMLQOkURFx9gPg8QFQY2kaM1GIEQRDtmqwKQOFwGIsXL0Z1dbX1XSAQQHV1NRYsWOD6e9M0UVNTg1WrVuHkk08GAKxbtw61tbVCmxUVFRg7dqy2zaamJtTX1wv/WgvmCL12e4NtW2tbwHQV4EkDZIfkH6K9Qj5ABBEnqwLQjh07EI1GUVlZKXxfWVmJ2tpa7e/27t2LDh06oLCwEOeccw5+97vf4YwzzgAA63d+2pwxYwYqKiqsf3369EnltBzpVBo3ge0+ELZtS68GyP4dX/6CosCcaY0CtQRBEETukHUTWDJ07NgRS5cuxSeffIL77rsPU6dOxfz585Nu77bbbsPevXutfxs3bkxfZyUCLauvpma73SmdWgdVZBdv6iInaGcoMo4gCKJ9k9VEiN26dUMwGERdXZ3wfV1dHaqqqrS/CwQCGDRoEABgxIgR+PLLLzFjxgyceuqp1u/q6urQs2dPoc0RI0Yo2ysqKkJRUVGKZ+ONYIsEFFaEwafT78RHJQzSACkgoZAgCKJ9k1UNUGFhIUaNGoWamhrru1gshpqaGowbN85zO7FYDE1NTQCAAQMGoKqqSmizvr4eCxcu9NVmaxFgAlDELgClUw5RCTU6rQZpO+xQHiCCIIj2TdZLYUydOhVXXnklRo8ejTFjxmDWrFloaGjA5MmTAQBXXHEFevfujRkzZgCI++uMHj0ahx56KJqamvD666/j2WefxWOPPQYAMAwDN910E+69914MHjwYAwYMwB133IFevXrhggsuyNZpWgQNvQDU+j5A3HYqheEIacWI9opB5VAJAkAOCECTJk3C9u3bMW3aNNTW1mLEiBGYN2+e5cS8YcMGBAIJRVVDQwNuuOEGbNq0CSUlJTjiiCPw3HPPYdKkSdY+t9xyCxoaGnD99ddjz549OPHEEzFv3jwUFxdn/PxkmAaoKRK1bUvnpKvS6gjZn/njkgRkg64JQRBE+ybrAhAATJkyBVOmTFFuk52b7733Xtx7772O7RmGgbvvvht33313urqYNpw1QOk7jkqWEqLABB+g9B23vUBRYARBEO2bNhkF1pYJtlzxplY3gTlrgPjt5ANkh4RCgiCI9g0JQBmGmcBU1eBbXQDSfKbJ3g6ZwIhcIhyJ4YXFm7B178GU26JEiAQRJydMYPlE0GH0SWdJCrdM0KBM0I7QNSFyiT99sBYPvfU1OhaFsPyuCdnuDkG0C0gDlGFYHiAV6XWCVn7LHat1jtteIAUQkUvMX7UdALCvKZLlnhBE+4EEoAwTcNAAtX4eIO6zxiGaIIjcg15Rgkg/aROATNPEtm3b0tVcu8VBAdTqGiBd+QvSABEEQRD5hmcBqLS0FNu3b7f+Puecc7B161br723btgmlJwg1mTKBuTpBpxgG39hsz2NEEETrkM5ITfKBJog4ngWgxsZG4SX84IMPcPCgGJFA4dTuBBwFoPQdR5kHSGMC8yt43fbiMhxxxzysrtuXbPcIgvABjawEkX7S6gNkUHylK05RYOkUINWZoNV+P36P+7dFGwEAf/zgf8l1jiAIX9DakiDSDzlBZ5hMaYDcaoGZGn8ggiAIgsgHPAtAhmEIGh75b8IbThqgdFYgV5q1BK2Py74EQeQMaX1DadwmCAA+EiGaponDDjvMEnr279+PkSNHWoVKyf/HG05O0Gk1gbl8F0vRCZogiAxC4ytBpB3PAtCTTz7Zmv3IGzLnBO3iAyTkAUruwLSOJIjMQOIPQaQfzwLQlVde2Zr9yBscS2GkNQze/p0+DJ6GV4LIZegVJYj0k1ItsMbGRsydOxcNDQ0444wzMHjw4HT1q90SdPC6ymQ1eMEJOo01yAiCyG1Ic0sQcTwLQFOnTkVzczN+97vfAQDC4TDGjRuHlStXorS0FLfccgvefvttjBs3rtU62x7IVCkMtQ80bwJLQBoggiAIIt/wHAX21ltv4YwzzrD+/stf/oJvvvkGq1evxu7du/Hd734X9957b6t0sj3hJABlUgMklsUgAYggchmTvIAIIu14FoA2bNiAIUOGWH+/9dZb+M53voN+/frBMAzceOON+Oyzz1qlk+0J51IY6TuOayboNESBUTQtQWQGWqMQRPrxLAAFAgHBb+Tjjz/GcccdZ/3dqVMn7N69O729a4c4R4G1ciboNJvAaFAmCIIg2iqeBaAjjzwS//73vwEAK1euxIYNG3DaaadZ27/55htUVlamv4ftjEyVwlBGgemcoEmQIYicJp2LDdLcEkQcz07Qt9xyCy655BK89tprWLlyJc4++2wMGDDA2v76669jzJgxrdLJ9kTAQeSMpjEay081+KTzANFAShAZgdYoBJF+PGuAvv3tb+P111/HsGHD8NOf/hRz584VtpeWluKGG25IewfbG5nKA6TMBK0phhojFRBB5DSUaZ8g0o+vPEDjx4/H+PHjldumT5+elg61d5ydoFvbB0h9LJJ/EgQDRlprshEEQRC5iWcBaMOGDZ7269u3b9KdyQecnKDTuchz9QES9k22FEb7s4EFDCCa7U4QRCvS/t5agkgOzwIQ7+/DtAt8NXjTNGEYBqJRmj6cyFwpDOe2dCHx+U78maYLAgBzPlyHfy7ehGevGYOuHYqy3Z28ht5Rgkg/ngUgwzBwyCGH4KqrrsK5556LUCilKhp5SzbzAMW/jwuqYhQYja4MXkCNxUxHjV175+5XvwAAPFKzGnedPzTLvclvKBEiQaQfz1LMpk2b8PTTT+PJJ5/E7Nmz8f3vfx/XXHMNjjzyyNbsX7sjE5mgnRwmTTMevSWawNJy2HYBL+9ETRMBMhigsZmKxWUbWqMQRPrxHAVWVVWFX/ziF/jqq6/wz3/+E7t378bYsWNx3HHH4fHHH0eMKmp6wkkDlK5IDyeBhm0iDZAaXuNDztBxSPvQvjAofwVBAPAhAPGceOKJ+POf/4zVq1ejtLQUP/jBD7Bnz540d6194mRRSdd86yRIMWEnJvgAOR94f1MED8z7Cis27xW+b4/jKK+hi5AAROQI6XwS2+FrSxBJkZQA9N///hfXXnstDjvsMOzfvx+PPvooOnXqlOautU8yUQrDUQPUss2PCezBeV/hsflr8a3ffahsqz0hmMCi7fAECYIgCAA+fIC2bt2KZ555Bk8++SR2796Nyy67DB999BGGDiXnSD84R4Gl5xhOghQzZ/ipBr9yS316OtYGEDVAZNYF2qeg29agRIgEkX48a4D69u2Lxx57DJMmTcLrr7+Oq666CrFYDMuWLRP+JcOjjz6K/v37o7i4GGPHjsWiRYu0+z7++OM46aST0LlzZ3Tu3BnV1dW2/a+66ioYhiH8mzhxYlJ9SzeOUWAZMLlY46iPavC6HrdHExgP+QARuQI9iQSRfjxrgKLRKDZs2IB77rkH9957LwD7qiSZPEBz587F1KlTMXv2bIwdOxazZs3ChAkTsGrVKvTo0cO2//z583HppZfi+OOPR3FxMR544AGceeaZWLlyJXr37m3tN3HiRDz55JPW30VFuZHHJDMmMPd2hMrwtLq04K8E+QDFoavQvmjvCxeC8IpnAWjdunWt0oGZM2fiuuuuw+TJkwEAs2fPxmuvvYY5c+bg1ltvte3/l7/8Rfj7iSeewAsvvICamhpcccUV1vdFRUWoqqpqlT6nQmZMYPptTNbhrTtuAlM+DZj8tSANEJEz0KNIEGnHswDUr1+/tB88HA5j8eLFuO2226zvAoEAqqursWDBAk9tHDhwAM3NzejSpYvw/fz589GjRw907twZp59+Ou6991507dpV2UZTUxOampqsv+vrW8/nxakavKyJicVM7GhoQo+Oxb6O4ZgHqGUk5TVA7iaw/JGAeDMkaYDikIIw+9AtIIj0k1QUWLrYsWMHotEoKisrhe8rKytRW1vrqY1f/OIX6NWrF6qrq63vJk6ciGeeeQY1NTV44IEH8P777+Oss87SmudmzJiBiooK61+fPn2SPykX/JTCuOEvSzDmvhp8uHqHr2N4igITfIBoeGXwVyJKTtAAKA9QLkBmaoJIP226nsX999+P559/HvPnz0dxcUJLcskll1ifjz76aAwbNgyHHnoo5s+fr6xmf9ttt2Hq1KnW3/X19a0mBPkphTFvZVwI/NN//ocTB3fzfAxnDZD9WMmOre3RNMZfi2YKg2+35HOZk3zS6BKEE1nVAHXr1g3BYBB1dXXC93V1da7+Ow899BDuv/9+vPXWWxg2bJjjvgMHDkS3bt2wZs0a5faioiKUl5cL/1qLZJyggz7HK2cNkD0MzDX6LI/GS5N8gNo9byzfimF3vYX3vtqW7a54hp5Egkg/WRWACgsLMWrUKNTU1FjfxWIx1NTUYNy4cdrfPfjgg7jnnnswb948jB492vU4mzZtws6dO9GzZ8+09DsVnExgOk2Mk9ZI3Y67BojfJermBO3r6G0bXuYhH6AW2tll+OFflmB/UwSTn/ok213xDFnACCL9ZFUAAoCpU6fi8ccfx9NPP40vv/wSP/zhD9HQ0GBFhV1xxRWCk/QDDzyAO+64A3PmzEH//v1RW1uL2tpa7N+/HwCwf/9+3Hzzzfj444+xfv161NTU4Pzzz8egQYMwYcKErJwjj2MxVM2E6/QbZTteosC4EZUG1wRiFBj5ABG5AflhEUT68eQDNHLkSM8F9JYsWeKrA5MmTcL27dsxbdo01NbWYsSIEZg3b57lGL1hwwYEuNCpxx57DOFwGN/5zneEdqZPn44777wTwWAQy5Ytw9NPP409e/agV69eOPPMM3HPPffkRC4gpygwneCSVg2QyaLA+ON6D4Nv786YQh4g8gEicoR2/toRRFbwJABdcMEF1ufGxkb84Q9/wJAhQywz1ccff4yVK1fihhtuSKoTU6ZMwZQpU5Tb5s+fL/y9fv16x7ZKSkrw5ptvJtWPTOBkAtOZovw6azqNlQkNUOI7VwGIM4K194GYfIDs0FVoZ+STTZsgHPAkAE2fPt36fO211+InP/kJ7rnnHts+GzduTG/v2iFO2hyddsVJaFLhXAvMfiw/87zYdtscSeetqMXnm/bg5jMPtwmX5ANkp71r/doCdAsIIv34DoP/xz/+gU8//dT2/fe//32MHj0ac+bMSUvH2ivx2mTqAU0bBeZTA+QtCsz5u2Tabiv84LnFAIARfTphwlFitCFpgOzQVWj7/GvpZoQjMXx3dOvlOCOItoZvAaikpAQfffQRBg8eLHz/0UcfCbl4CD1Bw0BEIXTo5lu/TtDe8gDxYfDO7fGHb09JE7fta7J9Rxogor3RFInixueXAgDGH1npvDNB5BG+BaCbbroJP/zhD7FkyRKMGTMGALBw4ULMmTMHd9xxR9o72B4JBAyltKPXAPlr30lGSTUTdDuSf2zIgiNFgRHtAd6Z/0A40kYN1wSRfnwLQLfeeisGDhyI3/72t3juuecAAEceeSSefPJJXHzxxWnvYHtE59OTrjxAzj5Apu1YrnkQ+SiwdmwQkS8bZYKO056F3rZCuvyw5Ghe0zQ9R/gSRHsjqVIYF198MQk7KaATaJzyANXubURzNIY+XUpd23ccK5V5gLxHgfFdbG/jpiw4tidzH9G2SeVJdFwQme3vPSYIrySVCHHPnj144okn8Mtf/hK7du0CEM//s3nz5rR2rr2iU+g45QG64NGPcNKD72Hr3oOu7XuKAvO4v5+22xrybZDPrD2dK9G2SeVRdLLk0hNO5DO+BaBly5bhsMMOwwMPPIBf//rX2LNnDwDgxRdfFDI2E3qYBihkC8FWD0dNzTHU1jcCAJ77+BvsORB2rN/lJRM0kjWBtSO3GHnla9MAtaNzTQWaJLNPKqZnPr+YgfxKbEoQTvgWgKZOnYqrrroKq1evFqK+zj77bHzwwQdp7Vx7hUV1FYbEy68LwW6MRK3Pj763FiPufhvXPK2vY+QcBRbfJkSB5akGSEY+NbcaafkCTZJtG8HcLW2jO5s7hCMxetcyjG8B6JNPPsH//d//2b7v3bs3amtr09Kp9g5LvicLQPyE2xxNqB8OhqOQeW/Vdm37Tq8Qk6v4ffy8c5l6PVPNV5TcMTN7PILwSmomMFP5GWjfC5q2xJ4DYQy/6y1c+7Q9xx7RevgWgIqKilBfX2/7/uuvv0b37t3T0qn2DosCK5Ti23U5aA422wUgJ5ydHtOnAWqtsXPNtn049r538OcP11nf3fnKSpz4wHvYe6C5dQ4K+3WIkgkMAGkJcoFU7kHU4Z0l+Sc3eG35VhxsjqLmq23Z7kpe4VsAOu+883D33XejuTk+ERmGgQ0bNuAXv/gFLrroorR3sD0S1GiAeI1DhJt9m5r9zcSOTo9J5AHiw2TFfVtn9Jz2r5XYsT+Me179wvruqf+ux+Y9B/G3Tza0yjGB3HCC/tFfl+Dapz8h7VMe8vYXdTj9oflYtmmPbVtKGiDut7JZ9/SH5mPpRvvxiMxiUHamrOBbAHr44Yexf/9+9OjRAwcPHsQpp5yCQYMGoWPHjrjvvvtao4/tDlYRXhaAeMGFz0HTEI74at+Lw6QYBea8L/9qCoJTK2lInDIweylPMe1fKzB17lLfQkS2w+APhqN4bdlWvPPlNmze4x7tlzFIFssI1z3zKf63owFXP6X370sGwQRmmsJku2VvY9qPR/iHUhFkB995gCoqKvD222/jo48+wueff479+/fjmGOOQXV1dWv0r12iN4FxGiBOutjX6FMA8pQJ2nseIJ5kTWfpIuKSnDASjeGZBd8AAO741hB0Liv03LZ8Ok6Rdq0NKYC8U9/YjJ///XOcP6I3zhnWM9vdSZldDWHFtylEgcWc3/X9Tf7GFyL9kPyTHZJKhAgAJ5xwAk444QQAsELhCW8wJ+giWQPE+wBxE73fAapVM0Fz+7baHO3QsFtkFq898hvFZSuFkUUhhAQg7zz63hq89UUd3vqiDucMOydt7a7YvBdzPlqHmyccjp4VJWlr1w3V+5iaCYyPLk2+HYJob/g2gT3wwAOYO3eu9ffFF1+Mrl27onfv3vj888/T2rn2CtMAFQT1PkB8FNi+Rn+Ov540QEhOk5NtDZCbViYa894/2e4uN51pPxwxXDl3JKBc6ouKnftVGpPUee7jb/Diks14bdnWVmk/U2T7nSXcIRNYdvAtAM2ePRt9+vQBALz99tt4++238cYbb+Css87CzTffnPYOtkd0TtCiCYwXhlLzZeFhW3j/HT+WHsHvp5XGUqcJ102r4xTxEv/OPULOaivDJrBcnZxytFsWrTV3hCPxh70pkn21SUpRYMK7btJkm4OQE3R28G0Cq62ttQSgV199FRdffDHOPPNM9O/fH2PHjk17B9sjukSI/Hzb7EFXrStk6JwJusUEpvhOB3+EZk4CykkNECcsqgQYp5/L2/ya0GIxE/9cvAkj+3bC4MqOvn4rHz/bQkdbikJrrQmdPd/Z9AVLB4IGKPuynJJwJIYXlmzCCYd2Q9+u7vUO2x0k/2QF3xqgzp07Y+PGjQCAefPmWc7PpmkiGvWXryZfsTRADk7QXrQ+un2cM0Hb9/ETBi+amFy7qORgOIpXl21Bvca059QdN61MxMUE5sU/yks/VPzr88245YVlOOM3yWVEFxzTk2ohfZg5JIxlC/Z65UJG8FQEUj9m4WzxwdfbcduLyzHjjS+z3ZWk2dfYjFeXbcEBn1G7gBxpm5v3qD3iWwN04YUX4nvf+x4GDx6MnTt34qyzzgIAfPbZZxg0aFDaO9geYSXAHE1gHjRAzdGYrQ3AefJU5QHyY+rhnbOTfU1/9fIKvLBkE04a3A3PXmPXGjq16xQiD8gRL/btbpWxdW15YemGPb72lxE1QNkdBHN1olTRWuaDTGuADEMvbKbSAzcfoFxQPrDF0N6DrZfotLW56fmlqPlqG84b3guPXDrS12/FXGtAMBduSh7gWwP0m9/8BlOmTMGQIUPw9ttvo0OHDgCArVu34oYbbkh7B9sjulIYujxAOnRmMucBm5nAvGty+HcxkgYT2AtLNgEA/rN6h+/fbtlzELV7G7Xboy6DvZMJINU8QCpzpB/SoV1LF9k+vh9aywTGhNBMaYDkqFCxL8m3y9/LXBVsWR/ZAqexOYpVtfuyvhDwA8vi/MrnW1JqJ9O+h/mMbw1QQUEBfv7zn9u+/+lPf5qWDuUDLArMHgbPO0G7a4DCGudML34ufrQN/ATDC2atNTg5tcvCnb++9yyl9svdB8i7BijTvh9+zJKtDS8g53oUWKv5ALW8XpkKHS8KBdHoM+u7F2TBOhedoNnzzvr6ndn/xYrN9Xj8itE4Y0hlNruWEfhbku13P5/wJAC98sorOOuss1BQUIBXXnnFcd/zzjsvLR1rzwS0PkCJz24J/wAgrBmZnSYsVSLEGPddQziKDkX6x0I2MTVFojBgKIWRdKESiHYfCKOyvNj2vaihsrfFDy7yRGDXAPnrZ6oTSy6t1HPBB+hgOIrCUMDymdPTyiawnNAAJd8H0QnazEmfLnZ+TAO0YnO83uQLizflhwDEPcJuZn4ifXgSgC644ALU1taiR48euOCCC7T7GYZBjtAeCGqiwHR5gHTonaD1v7ESIXLfsQHyzldW4ukF3+AfPxiHY/t3QTRmQp57eN+kcCSGUfe8g6JQAJ/cXm0Jdqkid1+lydnX2KwUgNyy3vJNyb21+QD5NYGlOBGLCetyxwcoGz3Ze7AZw+96C0f2LMcbN56UVBvRmOlBeNIjayVam6ICBwGI/6yJ/tTB9z9q2gWgXJhuWRejkuY7F7VVrQF/ntl+9/MJT8v2WCyGHj16WJ91/0j48QYblEOOpTA8aIC0JjAvGiB+//j/T7eUkJj51teIRGOonvk+Lv7jAuH3fL+27m3E/qYIdjaEfVesd0Luvupa7NFUhXfLBO2cB0j8278PkLfj6MilcOVsawkWrI37h325td51X9Ukefe/v8CwO99MqaZawlycKQ1QUL8xBY2cIMyauWnSZH2UNd95IwBxiycSgDJH69ktCC1MU1IgrU795gHS7eP0AqlMYPJkHQgAq+r2Yd2OBnyyfrdYTVrTdjonCbklVds6AUjwd1BcHmf/KMkE5nMg4u9mMsnzhMi8PI8CS9UMMOejdWgIRzF7/tqk28h0FBhvApPfSVPz2QsxKRFitoVbFQkNkCQA5USMWuvDC6UkAGUOTyawRx55xHODP/nJT5LuTL7AQhwdNUCp+AC1/LQgaNjMZE4mMEbAMISBR8xK7U/ouu+1L7BySz2euXqM7Xy9omp7jyZc1i3niZNpxy54ee4iAHG12tQcQ3GBw4peQS6ZwESTS+aP7+X5ZzhNkaloEKxJOQs+QM1RE4UhdedjpomgD8EgKj1XuTi9WhF3eTr588Nqvl6DbOBJAPrNb37jqTHDMEgA8gAzgcn+Cfw4m0oUGHuBikJBNEfFpFzsGE7mFsMwRKc87u3UJRrUrdgf/886APGQ99OO6KE5EwlpwlEKQAfU9Z/4fijzADkISPLffgci/thNkSiAAl+/zykn6Cyb4PxogJyEnFT0B+xZyWQUGONgc1TwERQ1tv7alU1guSgBWddaPrn8UACJi59cVNG1UzwJQOvWrWvtfuQVrBRGQVA2gfGaFveXQKuNaWmnMBQAmtS/NR0m24AhRSVE1YIOf3y3FbsXk57VN+lvlSCiS5gmO3zKiEKGdFzb3/4GIl4gdQtn3rznIO577Qtcc+IAjOrXpaU/vFCa3yawdJ1/KrmZMm0C4xdETc1RoCQhQIsmMH/9kYX+XNQBWXmAZB+gLPQlGwj3yOV5290Qxq/+tQLfGXUITjvc46KSUEI+QFkgoQESLz8/eXvNBK2CTdxymH18m/i//BmIC2gBbuLgTW18lAYvpLkJOG4T0V8WfoNH31uj3KYSZDz5ALmZwGQ/C1kDlIIAFNcA6fnZ35fi9eW1uOixhJO5mUOrQL0HSmZo9uEF3tqZoDN1L3jBRA4qSCUtgbAoyNEweF3EXarJRdsK/DPmpv188M2v8NqyrZj85Cet3a20YZomHpz3Ff61dHO2uyLgOxEiAGzatAmvvPIKNmzYgHBYNEXMnDkzLR1rz/ToWAQAqCwvwie3V+Pvn27Er99cJZnAPPgAaU1g8f9VYbWWD5BD0r24AJT4mxdueKEnIghGzv11G8Zuf2kFAODso3t6KknhxQdIHQavX2nJh/G78G/yoQHauMsenSRop7JsgrKZTTJMuvwg0uEDlCkNEH+d0xlV6aT1zBXYuedrDhwvgSaMLXv0mfBzlY/W7MQfWgISzh/RO8u9SeBbA1RTU4PDDz8cjz32GB5++GG89957ePLJJzFnzhwsXbo0qU48+uij6N+/P4qLizF27FgsWrRIu+/jjz+Ok046CZ07d0bnzp1RXV1t2980TUybNg09e/ZESUkJqqursXr16qT61hr8bMLhePrqMZh4VBW6dyzCod3LAPg3gYU1+8S8aIAU+zPiwg/nBC0IPVwfeY1VCjM2/8KrTFv+fIB4ocy+XRX+3xSJ4on//A9rtu0X9vU78fFan0YXDZAqP00u+QG41Y9qbbw8/wynVD+paIcyXQqDv84Hw/rnx+/9kLWeuShisF7Z8gBlozNZICZp6Zxoi0qxHfs1vhhZxrcAdNttt+HnP/85li9fjuLiYrzwwgvYuHEjTjnlFHz3u9/13YG5c+di6tSpmD59OpYsWYLhw4djwoQJ2LZtm3L/+fPn49JLL8V7772HBQsWoE+fPjjzzDOxeXNCtfbggw/ikUcewezZs7Fw4UKUlZVhwoQJaGzMDcm5vLgApxzW3YqKYmpe38VQXfIAqTRAquy2KhOYUP4ipjOBqZ2j/dIsaZLkIVolW3nxAXIzgbHPf3r/f7j3tS/xo78u0e7rBcEE5qIBUgpAfLhytlfCWdYayBOhE05mklQmC/YsZer8+ePIGkShNEkqJjDTzMn6WnItMEamJvtNuw/ghcWbPI27rYGfCNA2KP/kpN8ZkIQA9OWXX+KKK64AAIRCIRw8eBAdOnTA3XffjQceeMB3B2bOnInrrrsOkydPxpAhQzB79myUlpZizpw5yv3/8pe/4IYbbsCIESNwxBFH4IknnkAsFkNNTQ2A+Apn1qxZ+NWvfoXzzz8fw4YNwzPPPIMtW7bg5Zdf9t2/TBCwBKD43wfDUby2fKttP9lpWhcGz14gpQaI/S9McJIGKCBFpAm+PmptkJsTtNNAxp+HSuhQaZe8JEJUC0CJz59v2osvttTjs417lG35HQtFE5izBkiltcilMPhsR6SlyxSSUhRYxk1giePIz4/gA+SzXVHoz8kgsIxn3ZY55dfz8bN/fG4lg800sp8WkRl8C0BlZWWW30/Pnj2xdm0i0diOHf6qe4fDYSxevBjV1dWJDgUCqK6uxoIFCxx+meDAgQNobm5Gly7xSJp169ahtrZWaLOiogJjx47VttnU1IT6+nrhXyZhkyEbAB988yt8VbvPtl9IcprWVoNveX9UmWXVJjBx8DUMQ1uWg385w1G1NkiFkwDEa7IiUbuTpjoRotoExk9Wqnmb7/+/P9+Csx/5j9aE4nfibxKcoJ2vR0BxQZyE0kyTisYhHUR9mMCcSEWDkOncNF59gPxqcGwmMPnnOTDf6nyAMqXtYPeYZSDPNPw9cTO5tkXH8BxUOgJIQgA67rjj8OGHHwIAzj77bPzsZz/Dfffdh6uvvhrHHXecr7Z27NiBaDSKykqx2F1lZSVqa2s9tfGLX/wCvXr1sgQe9js/bc6YMQMVFRXWvz59+vg6j1SRNUB/WbhBuV9I1gDpTGBMA6QsrhjfJjtB88JMwDCEMbFZEwbv5gTtdaDm21+3owH7GsXcRSrZSqf9irispFR9UgkjQGomMDcNkJsPULYEoLXb96M5GsspDVAqJpvUwuDj/+eCD5C8YPGDnGQvF+eiRM4l2QSW2ck+ldpxMnsPNmPrXm+lWMRklS6LyZR6lT7qG5uxxWOpmXYjAM2cORNjx44FANx1110YP3485s6di/79++PPf/5z2jvoxP3334/nn38eL730EoqL7YUxvXLbbbdh79691r+NGzemsZfusHecDYB9Opco9yuQTFo6IYC1I5vMAH0YPD95Bww5ySGvoVFXW1c5rXodqHnt0S9fWo4Nuw4I21UmMJ3Jzd0HyP4bWbBUteUFP07QKqFLNIH5OnRa+NfSzRj/8Pv4v2cXOyaMzARRF00eT6slQsxwHiDHSCBT89lLu8K9RE7ORnwpDEEbneF+pFMAGn7XWxg3413s9OAALJrA0taFVmXk3W/j+PvfRe1ed9/a3Hvi4vgOgx84cKD1uaysDLNnz0764N26dUMwGERdXZ3wfV1dHaqqqhx/+9BDD+H+++/HO++8g2HDhlnfs9/V1dWhZ8+eQpsjRoxQtlVUVISioqIkzyJ1ZA1Qny6lWLu9wbZfSHo5myMaIaBlAFGaWaT/48c1BQHIgOiQy5uomjWTgUpYiAkDmX5gcTOfqRZEkZaBUl4humaCVnwp52Ny+r0TTak6QftQg7cGT7Rk7X73q22467yjrO+z4ZLAO97HTBOBZKfCNDhBZywPkEMUoGCS9JsIUdIs5uJkJPspWbjcP9M00RTxX3ZGh24sSIVVtftw/CDn+UW4923EB4j187MNu3HW0T0d981Fx3sgxUSI+/fvT8l3prCwEKNGjbIcmAFYDs3jxo3T/u7BBx/EPffcg3nz5mH06NHCtgEDBqCqqkpos76+HgsXLnRsM5swQcW0NDfq22ITgFx8gFSTLHsO5UFRSHZoSiH5wupEfUxV4jpB2HDyAXLx99BNQCpH2WjM2SynFIA0ffM7EAkmMFcNkP07wSyZdSfo7PaF9wFyO7qTcJ1aGHxLX7KgAYpJ0VqyxtYPUele5uJcxJ8rr/F1u38/+/vnOOKOefhmp33BmAy6scAv/Pl4qYHopxZYG3QBykmhG0hCAFq3bh3OOecclJWVoaKiwsrH06lTJ3Tu3Nl3B6ZOnYrHH38cTz/9NL788kv88Ic/RENDAyZPngwAuOKKK3DbbbdZ+z/wwAO44447MGfOHPTv3x+1tbWora3F/v3xHC6GYeCmm27Cvffei1deeQXLly/HFVdcgV69euGCCy7w3b9MwCZD9uDr/EcKQh5NYDEHDZDJfIC4/SUTWCQaE7Z7CXdXmaS8DrRuGiCd0KU6Jt+USthR9SmgUXun5ATtogFSHdNPMrTWgNcN5JIPkNvxHU1g0jY/wpwqZURrwl//219agZN//R4OhCOK/fwhm8ByUQeU7LP/4mfx9CdPfrQ+Lf1IlwaIHwu8mNX85QDLLQnIk0CWe48cgCRMYN///vdhmibmzJmDysrKlJ3UJk2ahO3bt2PatGmora3FiBEjMG/ePMuJecOGDQhwD+Vjjz2GcDiM73znO0I706dPx5133gkAuOWWW9DQ0IDrr78ee/bswYknnoh58+al5CfUmrDJkL0EuiRosgbIrRiqapK1TGBSZAjfVnPU1EYB6X1v7H3xOpDpBLlEO+rvm2MxlCAo7av2UUp8Z/9Svq5O+zrR1OwjEaKLD1A2hA5Ry6AxSWQIPz5ATshX2c91TfgAJX98P8jH2bjrIN5YXouLRh3imLjUtV2bZin5PrYWuiSwXqeXdJlYdGOBX/gxTeWLKSP6/yUfUZsd3DuUi0I3kIQA9Pnnn2Px4sU4/PDD09aJKVOmYMqUKcpt8+fPF/5ev369a3uGYeDuu+/G3XffnYbetT4JE1j8bxYCe8GIXnh56RYA8YdeXknoTWBMA2TfpnKCjpniiiUSi2knPZ1Qo3aC5n2A9OgSOrodUyWMuUUPqZrSrdBSKYWRnAYodwQg/tyzYb938+XicXq25MnC5luj8COTj5uNKDCrD4ptvk1gkjYtNwWgxGd+XPM616dLSNdpg/3Cv/+6KFOetuYELaZN8bJ/K3YmBXzr+4499tiMR0m1d9g7J2uAOhSHuH0M24ukDYNvaUelZbBqgXHfRWOiD1AkamonYG0FeqW/TeKzk6bQ1QdIKwA5a51UE5eqLZ0A5EcVH42ZwqTtVgxVeW8EM4DnQ7cK2dYAidGG3k1gsrAm+5DITTndY/b8ZKMWmPi9KLSk5ASdo2Hw/H3jFxJetR3pWjCkSwPEv/9e+iaaAHM/DF4Y2z3sn4vPHJCEBuiJJ57AD37wA2zevBlDhw5FQUGBsJ2PyCK8YUhRYEwDVFaYuD1Bw7AJEW5O0Eqhw2T7iKtC0QQW0676dSYwVV885wFyeeF1K3BVRJq42rX/xo82w8+gKgujbsVQVa4G2a4FZmo+Zz0M3mVf/jmPmaIjq00DJD0UUdPUDoLZrAZvfafS2Pjsji0TdA4ux/k+6hZ2Xn+fCukKg+eFOC8LKT8pMHLBBCZo6Tx0KAcfOQBJCEDbt2/H2rVrLSdlIJE52DAMRKPpq2KcL9g0QC0CUCknAAUCdpOWTnPCXjhV8AF7F+WoEsEJOmZqV/1aJ2gXYcQJNxOYbgWu0gAlYwLTCXV+BlVZ4+NeCsPZCTobkVdycszE5/j/kWgMv35zFY4f1A2nHNa9Vfviywma+xwzTQS5b+SrLAszTrI325aNPEAM07SffyqJENVmtuzPTny3xJQc3mb7dPlppUsA4s/BkwbIRXOda/BjuzcNUG6ek28B6Oqrr8bIkSPxt7/9LS1O0ITCB6jFBFZWFBT2kV9OXbkFNpEpw+AtE5heAyRHgfFoI7JcTGBOuJnAdEKX6nduNXVUg5Hu+H4GVXnV6raKda0Gn+UweMEfqKUvLyzZhD9+8D/88YP/Yf3957Tq8QUNkI/7YLu/0vgkt+U0OWWzGrzQD9vfiW/e/qIO2/c14Xtj+3pqty34AIUzbALjn7X0mcB4DZCHPvhwgs4F+DG5LfsA+RaAvvnmG7zyyisYNGhQa/QnL0kkQjQRjZnWy1NW5GwC07307IVTCafsJ3JkiFjXy8EHyKM2Zt2OBry0ZJNrX+PHS9IJWpUh2sUEphaANH5NvjRAYhuq49R8WYdQMIBTDuuu8QHyrvVobVQO2Vs9ZHxNF/y9dV09Cj5AkoOmtKt8T53ucSI7sfPh04WqKybs7yL/583//Bx7DjRj/JE9UFmujnJtG2HwiT65+c+pf5/ccXc3hDH304RPa7JO0LK2mY8I9WQC8+EEnUpuq3Thd4EmmNcdAg8yjW8n6NNPPx2ff/55a/Qlb+FLYfCmk9JCTgMUMGwmMJ1mhA3qaido+YM9D1A0pheAVGYn9hue0x6aj0feXZM4rsNE4xYGz/pSGArgz1eORmV5UUtfVBogZ9WzqhsqQcqtzzLyoC13be/BZlzz9Ke4cs4iNDZH1VFgLqaKTCJGhMX/SFe2XS/w99bPWBszRfOtLQ+QzQSmbzzTTtC651X+mv9zf0vdvL0Hm7XtRiVhNhdX4/y7xo9FXvua7Pvyk+c/w/1vfGX9nawGSB7/wj6c+OP78G3lfhi8sEDxeelz6fnzrQE699xz8dOf/hTLly/H0UcfbXOCPu+889LWuXyBL4VxUBCA+Cgwu9+IbmBmg4lTtmExz4/kBB1zMoF5N0eJfdVvc9MAMUHvmL6dMP7ISoT+tVL7O/4rtQ+QdxOYn1WO7PQsH3t/UyKhXTgac80DlI0oMNkvTP5cxCXibO1VHK9pdBNE+RVxzBSv4/odDVixeS+G9q6Ib5edoB3uMTtuxhIhKjVA9uMnkpkmIg91ucMASQOUo1Fg/G0QzEcer32y9+g/q8Xq715C1lXIi1E+DN7LOBL18e7zXYzFTOw52IwvttTj+EO7pi2M3w23aFsbkhCedGmbNONbAPrBD34AAMocO+QEnRwsIigWM62BrKQgKDgxB5UaoOQTIYomMKDJcxi8P82QfFz1b50nITaAh1ouFEss5l4Kw96eajDSarV8jKn1jeIKXL5+/K0wY6IPEBMmsp19mUdlAuM1QI3NMZQUtp5GSFd0l7FzfxP2HmzGwO4dxAmhxYzMeHnpFry8dAsW/6oaXTsU2Z2gHS6zZQLLog9Q3Ana/h0gPssHHZzu5Xc916PAeAHIq/YtXUq6ZJuRxxW/QpxYC8z76idqmjj7t/9BbX0jfnvJCJw/orfn36aCoKH1cPFNzeds49sEFovFtP9I+EkO3geIDWQlhUFhha3KA6RbWbCvlauZlm2yv4l3J2iNAOTyEiTrA2SadoGO1dZR/c4tekhtAnPWpHmh/qBYskC+TqKWwhQmbXb8VAoibtx1IGVTjewYn/gc95XgtQz7mvQml3TAD7Cq+zDq3ndw+sPvY8ueg8L3Zkx9jzfuju8nXyKn5zLT1eD9+gDxz62TBshmAkutm62CqAHi/GdaWQMkk6xwKDsFh7m50Mvz4xa8wcOPJdGYidr6uG/eu19t89zfVOH76Db2A2qTei7gSwBqbm5GKBTCihUrWqs/eYlgAuM0QIGkBaD4985RYNx3JrB9X5P1d7OTD5A2CsxFA5SkD1DMNDmfpvh3zE6v9gESJ876xmZX52KnkiKNzVHXkHYAqD8oa4D0+0ZipnBv2HmIfgDeB4lnP/4GJz34Hu74V2rvpWD24r4/EI5g5D1v4+5Xv7C+a2hq3cUO/0w4XYkVm/fawuBVkyYTlv2YwNi+2dYAyZFr7B0WBCAnDZBkAstFCUjnA+T1NUhGcNl7sNnm85Ns9KVNA+TXBMYXQ3XbXbF4AoAORb4NOknjttCUfdJ0hX2zjS8BqKCgAH379iVNT5qx8gDFRA0Q/24GA4YteZ5WAGr5XqkAMsX/GbPfX2t9dtIA6cxV7hog/bbmiNMqnM9rFD+hghYNkEro4q/J2u0NGHXP27jtxeWO/XAq8Hrsve9g+F1vufopsRe+uCDeN3lAlkPceR8gdh5iuQPvo8RDb64CAPxl4QbPv1EhCsWJv3bsD9v2Zc63rUWzRydS26LAVAvvbFKVtzkKQC2bMhWV7N0HKP5/lHsXHTVAtiiw3ENIhBhNwgTm8x4t2bAbw+96y/buJ6vsk52Cm3zmAUraBMY9A5kUgJw0Vr9/dzWG3/UWXm4pVAvYF9y5gm8T2O23345f/vKX2LVrV2v0Jy8pavGtaIrEEgKQrAEK2Af7pKLATPfJ1dEHyEFYcMLpkE7CBe/TEbRMYEbL75w1QF9srUdz1MQXW+uF9rwef19jM/Y1RdAUiQkaMhXMB6hzaaGtH/LfkVhM8M9KaIC4QcXHKNEavshuh+edulsD/p449SUQEAfXGOczxsMmVfm+OLVtZYLOYhQYFAId+5vPoO7dB8h0LReSDfg+yhGpXvCrpfvDe2uU3ydtApPGooNCGLz77/04QfPw5sLMaoD09+iht74GANz64jLrO1G7nDsSkO8r9vvf/x5r1qxBr1690K9fP5SVlQnblyxZkrbO5QtlLc6k4WjMMqWUFASFiU2VB8hNA6Q2gbmvcpodi6FqTGAeQ9mVx/P4W0sD1KIKcyuGynJxuPmT6IQ3/lu3gZhpgDqVFmLr3kat4yo7Hn9nEj5A/PEcD9cq+Kn/1foCkF7FLhZiNGwRa6q+N+s0QB58gDJnArN/p3pf2Z+CE7RTFJgkWMuHyYUJSVcKw9FHy0ekoP146u/TZQI7wL0f6Q6D5891Z0NCO9uaQQkyXnyWCrkoHnGR0lq98o9vAeiCCy5ohW7kN3zCQ2ZuiJvARB+goCTPuDlBq8KUVStAmUhUv0/yJjAnAch5EmLHZNcjZEWBOZvADrRMCm71wXT+S3y/mJD2yfpduPWFZbjzvKNw0uBEOQgmuHYuLbD6LfSL+1suNaIygflxFEw2dFdG1qQ40dDKApBTLhj+fgZayvAwYjoTGPMBcmhLJmECy8yIrXrnVBpb9ie/cHDSAIl+camZIEzTxI/+ugQGDDx62THJN2RrN/HZq/lIdO72dzxdu8mbwMQfNnACqe9SGC6LH/5+7lSYpzMBf766BUKhlDZD9Tnb+BaApk+f3hr9yGsKggEUhgIIR2LYsT9uarGbwLw7QbuawFz6E3F0gvYnGHnB2QSWGEBCtigwZw0QmxSaHdS1qnaCAaOlurtYHw0Avvf4x2iOmrj8z4uEchB7D4omMJ3ZgvWBHwRSdYJOmwFD0qQ4sa+VBSCnRGsRQQCyry5VAkuz1gSmP9FM5wFSO0Gr6vK1aKa8OkHzgkLMTEnjs7MhjNeX1wIA7jsQRqeW590rb62sxRP/WYeZk4bjkM6lyj56NYGJCxt/56TbPdl7LWttDoR5E5h7m6JGxS0zfuLzzoaEad5LNFa6EK69Bw0QTy5pgHz7ADEWL16M5557Ds899xw+++yzdPYpL2FmsG318Qe6VHaCVpjA3MK31Tmx9MINj9/kgOkIg//x6YPQtUwcUHkfoIBlAmNRYPaBgn8ZWXJCt4FSFsBUUWZsH911SZjAWjRAcs0pyQeI7we7dsnWAmsdH6DUNEBb9x7E9c98igVrdyZ1fCcTGH+/goZhi3JSm8DUwoyTeYvdg0z5AKmOwi8ArP0sDRAnAPkxgaVwOqlqw65/djEWrd+F218SIxZFDRCvPXHoS6togJI7P3n8OxhOvB++q8G79IHfl9cAubkhpBN+bNSawAQNELehLQtA27Ztw+mnn45jjz0WP/nJT/CTn/wEo0aNwvjx47F9+/bW6GNewMxgtfXxfCXlJQWCwGMYdoEmGjPx6fpduOWfn2Pn/ibhe0CTCNFBBX7W0Crrsy40XKetcQuDd9rMzBMdikK2cgtmLDG4BCUTmMohm+9Ho9IHyH58nQDER6O4FTetb4mKYgLQqrp9uPkfn2PjrgMAZCdHcQ3OBq7k1cTpl4BcfYBcosB+8cJyvPVFHS59/OOkjt/sYAbh76dhGLYIE9UEYpnApNvoyQSWoQFbJVyoTHpsN68+QGk1gSX/U4E9B0TTTTI+QJFYsu9L+jVAsgbctwnMhxO0YALLAQ2Q7rgFgg9Q8tq61sS3APTjH/8Y+/btw8qVK7Fr1y7s2rULK1asQH19PX7yk5+0Rh/zAubBzwpOdiwO2cPgFSaw78xegL9/ugm/56Ia2PMYMAx8e6SYGdTp0RvYPeHQrhV0tJmgU9EAxbcVBAM2x20+qocJPswEplrxqMwCbhogue9BhYbJTQCSTWDRmIl/LN6Ea57+JH5c7ud2HyCmneDOw8cgkS4NkLhIcz6+mxP0phbBL1mc8gA1S1IMf6m0UWAt98+WCVpzW1NJSgnEn52Zb63Cf9fscN/ZOqainZhdY8PujVcfIDkKLBWS1VLKyIsznQ+QlzxNyfRF93wnq0SRj38w7C8KzI8TtF4DlDnBgl9o6p4pQQDidskd8ScJAWjevHn4wx/+gCOPPNL6bsiQIXj00UfxxhtvpLVz+QQrfForCECJQSIYMGzCAS9584mnElFgwIwLj8Zz14zFyL6dALAoGY3KMpjQvuiSE2p9gNwiFxy2sdV+QShgS0zGJ7Zj16PAIRFiRDEoulWIl8+VCVgxzaAMiOpdwC4AMb6u22+dB98vwQSmCoP3MRCnS/+TW1FgvA+QXgMka0h0TtBWIkQH3yzx+8TnZKLAXlyyGY+8uwbfe2Kh59+o+hJVCUAqDZDHRIiy/xlj4f924rmPv3Hto5+MxU7I/omZ9gHyIvj6QR7/PuQEXy/Pj3hdve/LR4HZHLGbInhs/lqs39Hgeny/yP39x6cbsWTDbmEfwQTGfZ9LGiDfTtCxWMxWABWIJ0mMZSpjWDuEmcCY81x5cYEgABmGYVvp8+rPgd0S2hteYCguCOLEwd3w2PtxDVFTJKpV/4aC8WOYplN2ZH+aIYbTwMIGj8KgYVsZxkx7IkTLCdolCkzVZ90kw6NKHyBfj+KWl3v5pr1Ys32ftZ2ZwJyO0RyNiU7QVhRYYn8/vhat4QOUahRYKkNcVNKQ2ZygHfyDYiZgKA6uzQTtwRckGb+Xjbv9a8BUR5GFZYAvhWE396qQo6VUx5n0p7ipcmD3Mhx/aDd9Wx6if7xgf88TbTUJwq++DcEM41P7oXu+kxXqnI7v5fkRFz/O8ygv6Oxq0PsAPTDvKzyz4Bv85p2v8fW9Z7n2wQ98H977ahsWrY/nBeQDQ3gBSEzymtaupIRvDdDpp5+OG2+8EVu2bLG+27x5M376059i/Pjxae1cPiEnsepYXCDlAbKHO/MPEu87w5vAGL07lQAANu0+qJ2cggHDyrEjazwYrZEJOsyZwGQNkGnaEyGyYqiNzTG8tmyr4E+gLHbq4isgn5Pch3gfY8IAw3JunPv7D/HTuZ8DiAsi5SVqAcgeBWbvn2B28WMCS5MOiD+i24TipgFKJdRVNr/Kt1SO6pMzaKuegbAi0g7QT06pTvQhOW27B5TmWYUAxP7m79EBRyfoxGfTxQl6w05nwa3Zg/OrF+waoMTnsMdCovw2t1xiALCqdh8WrYtP1LpWkz0lr5oqHb6coHUCkHQcdq5u5vtk4M+JCT+AaIngo8BSydnUmiSVCPG8885D//790adPHwDAxo0bMXToUDz33HNp72C+UGYTgOwmMHVUVxxVWCKvyejXNa4hWr+zQbv6CRoGQkED4ah+QFFpXQAPTtBOPkDMBBYM2IS8mGkP62eTyyM1qwEAZx9dhT9cNqqlH84Cjuq07CYw+4VuikSxh3u5i0L2pGMqH6bEefAaH3FSU2knsqEBEoQylwnFbcJJZYizC0Bia7IGSPQBAgKKo1s+QLIGSHOdBZ8FMz5oq/Jq6VA9Q26ouqKLagN8JEKUTWAOd8ftvonjjMvODsjyIT8pevUBErWq7k/chFkfAAA+uvV07SScjmKoMl5MPn5Mi7yA1MRp/uQxONn8YNv2NaJ2byOGHdJJu4/ufFfV7rM+ixqgxD65I/4kIQD16dMHS5YswTvvvIOvvvoKAHDkkUeiuro67Z3LJ8qkLJ7lJQXCIGEoiqHyyBWfATFqrH+LAPTNzgPaFWAgYCQioBwKhKpwG4CcxgA24RUEDdvEETNNq96NXAqDwfKS6Prn11dAtXoPR2LYza22VAJAgcJRPXHcxOe12/YLGhTWv2SdVZ2ei027D6CsMITOZe75WviJUVfyhKHTELHjpbLIcytXIdQJi4n9jsZMZf4HFlptr9Gm7oPKtOZHpilIQgBSaicVPjvsT/4eOZrAJB84nU+R/FkFf+3lCbcpEsWGnQcwuLKjcyOwP7OiBihxLk4CiWxW9sqGnQf0QmWSD27qGiDv+/MCbdhBI6dbjLkx5r4aAMCrPz4RQ3tXKPfRmemWbdpjfebfgVT8tVqTpIqHGIaBM844A2eccUa6+5O3qDRA/EMTNOz+MTxRxYsQEDRA8aRj3+xsEAaVgJF4+YJGwr9GHwbvbjJQ4TSQJQQgdRSY5dMkFUNlHFbZwfqs1AAJSfXcXz7VwNEUiQnqZpXTaSgY0Grp+Otz72tfiv1T1gJz7aYrO/Y34cQH3gMg2ua94KoBUlznndzx+nQp8XU84dhS2zYNkGSesgmOiq436aLAPPgAAfH752dCSc4EZv8uqihLwwQ+fhJyzAQtmQidHi236D+niezyJxZh0fpdmP39YzBxaE/HdlTvOaPJqwmM9wHyOf7oxgE3WSUSjWH3gWZ071gkfu8kAHkYc3xlghYcxhP3XR6bneYLL3yyfpdWANItgJZt2mt9DgV1maBT6lZaSUoAqqmpQU1NDbZt22ZzfJ4zZ05aOpZvyAJQeXEB9h5MTLiuJjBFBA+/ymIC0I79YezjcriEAgHLBBTkNEB+VlSAl1pg+m1CGLzCz8kKg2caIOlCDOAcwNW5VOLfBwKGJxu/0gcoEh/4GCqTQ0HQQQPkcGBVLbB0mMC+5tTRXkw4Kr8kHaoV4MotXNHZFMwjbucuOLVL/lRx+cf++yZFUkzV34l2pb99jtr86ter+Uw1KUdj9mNbGiCPPkCyb5nTqbidZsRhoma+IM9/stFdAPLqA+TwHOkix9T7Jj6b0JsV3e7zZU8sxMJ1u2zaEafxz+15bo7G0Bjhw+adz4U/lJNPVhJKSIGQJpOz6liMFZsTAhD/GqosFLmA72XKXXfdhTPPPBM1NTXYsWMHdu/eLfwjkkM2gXUsDikSITpogBQrM36Q6VhcgG4d4maQ9TsTYZGymY1pV3Rh8Dr8rsB43DRArO1ELbCAtI97P9gL6OXl02mAdnPO1k2RmG1gCwXsPkyqPsqwwTPdmaD54ogHwlHXgVj0AXLe1227k0bCDTcNkJglWg7fV4fBJ0xg4vdeosAA/w6//DPqNUGdXgOkvh5ew+DttfD0/XHracTBBMaQNbQq7HmA1Bog5+jRxLbmaKxFGFbvLyzoTAcNkMu9WtjiWPz3Tzdq+yLjNJSaponTH56PFZsTiwc37a9oAks0Li9akzWBMQocfq873+377Al5AdkRP6VupRXfGqDZs2fjqaeewuWXX94a/clbeA1QYTCAYqkWWDBgL4XBo8p/I+/epawQO/aHsYfTZASlYzD/mnDE31PqnghR833MtF7cwpA915FpcgKdVAojsQ9/7nrfpYKgtygPlQaoKRKzhX7zqzYg7puks3w4qcFTToSoiQLjJ6IPvt6Om/+5DFeM64dbJh6h3J+/jm4aQNV2fkLc19hs2+4VWdiQ75ng1G5zgjaV16NJ4wStN4VIApDPUZt/jpujMVehQFt8OKZKhJholxGOxLRmuqh0fRxPxeU8vThB62pA8aQ7D1BjcxRnP/IfdOtQhOeuHWvb1y5Uq9v0qp3wUpfxkmP74PlPNjo+O+FoDBt3HZTactEAaRZKch9SLZKcjAaIrxEo5l9LfM4lAci3BigcDuP4449vjb7kNXwYfHlJ/DP/+AYNZxNYTPGwyYMh80vgBxh+JRY0DGUZCC/oosPkPqm+d8sErcsDxHjny2044f538fnGPQ6JGuPfJ+sDFI7EbGYv+W+VCc86D0cTmF0DlA4TGH8tXl9Ri/1NEfxh/lrMW7HVdX83rYVq+/4mvT+CH9yElGbJBCbXhFINzkwAsmt21H2Qm/CbC4g3gXkJQ3aakHUmMPk8dY7QpvRcOco/Lv3kfb90E7sXB3B7FFjiM18LzEl44Iec+sYIvqrdJyQg5OF9JE2knglafudU70NRKBGtev0znwrnBQCz3vkaJ9z/nqIPLotJzXb5nfMTiVjzZR2On1Ej1O5TLQRf+XwLTrj/XXwmJT1U9lMznqVSjDfd+BaArr32Wvz1r39tjb7kNaWcANSxOJ5LRq4G76TSVEnb8v4FIdG8JZvVAgHOBBbxZ8Jwd4Jm/9tXYqw/oYAqEzRXC0zKA8Szec9BXP/sp9p+MNW9F1OGauXTFInaND6N0sRWENRr6byUAlEJsV7QPRW8uYKPYGNqfBkxsZxLMjaFgONWH8wrbqt1Wxg8ty2e50YhALUIB15NW3Ibfk1g/HvlRQDSaoCi+mrw8j3Q+QHJ5nGnRYDbYxcVcjCpz8tJc8CwR4Hx2kdvCwGdcKQ6v2YhEEKvvfIaBi8vdFTXgl9cvvVFHWa8/pWwfdY7q7GDq+GYaMuU9vsaF/9xQaK2oc7Mn0IY/DVPf4otexvx/T8nMperBKif/O0zbN5zEC8v3WLbZu+PuDBRfc42vk1gjY2N+NOf/oR33nkHw4YNs2WFnjlzZto6l08cytXh2tBSR4l/fgN+fIBa3gN5Mi5seaDZZBCQtErBQMJsokuEqMM1EzSYBkb8Pq4BcjKBJWo7JfIAqa/DgXBUa2pQmZl06JygZdMKX/E5/jtvUWC6baIJzL2fDJ3QxU8kdfWN1mfdveInFDcNkMoElorZi8cu/Il/88KZnFRS9gliJExgbsdqaTdFE5io0UheA6TKBM32le+RSgP014Ub8F9uVR8znbU8bgKAW04tQO8DxLdt1/QmPovFUPV90QlgMdPuAMz3u1nhV5X4rbf7LPswqd4XWUiav2obgKNc27YLQPF8Z2+urMX5I3rrF3myE3QSPkB828lEMuraEgvy5o4E5FsAWrZsGUaMGAEAWLFihbDNT6IwQuSQzqW441tDcM+rX+DClgKmgnkqYC+FwaPKXCu/gLKDswFJA2QYlnaFRc14xT0Roti3xPemNTipTWAJYUBnAmOYGvMHwAsZ7i+fzglabpo3+cT7r9fS+XWC9mUC07XL3ZNaXgDSXSN+knDTAClNYGnSAEXlZ0TczpthZI2GzsdFZwLzUgsM8O+3IPi0eLCr6PoRjsZw2wvLlX2R3zmVI/QvXxJ/K0fNycd2O02Vr6FMocb0wgvk9mjPxDbBBJaEc7HKF4p/npsdBFKvCw95LFb1U+6D14zMfB/468LGb92zYivqnKoPUIpO1DqhJ5c0QL5FvPfee0/779133/XdgUcffRT9+/dHcXExxo4di0WLFmn3XblyJS666CL0798fhmFg1qxZtn3uvPPOlrpZiX9HHKF2+sw1rjlxAP5zy2m479tHAxDzuQVcEiGqyj3Iz2+BlOMnYIgmm4BhWNk7ZXu1G16rwatWs2yC0PsAJcL04/upr0M0ZqbFB0g1wIQjMdsKW3aKDikyWQPAvz/fghlvfGn73qlvvkwuHnyA+NQHOvOW4APkcj/VGqD0CEC2Z0S6Fnz/ZY2GzsTDnmevJjBbzTCfo7ZOo6FD91h+uGYHVtXtk/aN7yzfI6ds0Il+2a+Pn1PTCUD88yAXClbto6r5l9hPFGh16O7JXf9eiQ++3q7dV1Ve5IRBXQEkbwJT+bzJ5xj2KF3xmq167p2qaCmzo9cASSawFAWYFBVAorO2cF1zRwJK8RRTY+7cuZg6dSqmT5+OJUuWYPjw4ZgwYQK2bdum3P/AgQMYOHAg7r//flRVVWnbPeqoo7B161br34cffthap5B2+nQptQYQWTvj1QlalQgRUJi3DEgmMCNpExjbv3ZvIx5+a5VtO3v+ZUVRNGYKYfCyFpF3gmbno1PNRk11HSggod3wMtirlFkqJ2ibAKTR0v34b5/hG4caSxFF3/yYXHSCsd+6bcKE5laQUdF2ugQguX/ykUQzjFwLTH3tmEbTqwZI/tq/AMRpgDyZwLz1A0hcD3nCc8oFlDiOmwnM+feC+ZHbmV8c6DS0EQcNUDImKd09+cvCDbhijriQ5q9Vc9SuzR3co6Njm4AoHLF3Lhoz8bua1fj4fztt+8vn6NWvku8DX+fQVQMkm8C44ydTt82P1lM1N4k+jVB+zjZJJUJMFzNnzsR1112HyZMnA4iH2L/22muYM2cObr31Vtv+xx57LI499lgAUG5nhEIhRwGprWBIwomTRC9mx43/L0+MhSEW4q43gRWFkhOA9jdFEI2ZuPqpT/DF1nrbdjZ42Os6xawXrSBoD2COm7Xin61EiBoNUCxmOmg31BOgCuUEGonaJo4GyQfIqRaYE82pRoFpvtddC515i58k3DRAqgF1f1N6fIBk3w5bHiA+CkwyecVrXdnR+gBpo8C8CUo6+MnSzQR2IBzBE/9Zp9ym8qdJmMDEPjmVw2DETGcJyO08hWAL7jNvftOZXvjrIO+i94HS98XPIoHX0ESidi0YG1uczp/vP3vN536yEQ+//bVyf3m89hoZyb9bfPZ59r0+0EMSgLjjhyMxIS+YF/wIKsUFQZsAritCnUMuQNnTAIXDYSxevFioIRYIBFBdXY0FCxak1Pbq1avRq1cvDBw4EJdddhk2bNjguH9TUxPq6+uFf7kAL5y4JUKUK2IDcadmHlm7Y3eCTmiAvAymMs8uWK8UfuL9s/cTECOpVBqgHfub8M6XdfH+GYa1nwq5LIKwzYcTtEr4CEdVGiBFHqAk7O4q7VQ6sqV60fRYx4uJ1869FIZ9e7p8gORDy5dCiAKTBJ4Y5zTPY5nAZNOWVydon8tW/hzcNED3vfYlfvOOehJVmaK1JjCvAlAK6MpPNIbVmiEeXvBONh+TsM3HPZHNdXKzLELWqUlV+pAvNeMdoNAAeYyxFzVAiUUFu0bJOEH7TWsC+HtWigvswpUusWubzgSdLnbs2IFoNIrKykrh+8rKStTW1mp+5c7YsWPx1FNPYd68eXjsscewbt06nHTSSdi3b5/2NzNmzEBFRYX1j1W5zzaCAARnE5jKNi9PxkxwqG+J1glJyRWDAXA+QP5fmDv//YV2m+UDJDXLVzMuCAZs2oyrnvzE+swGHacK3jpnbFWouQ6V4NDU7MEHKBBIqjI7c+oVSxaI++w5EMZ7q7Ypz11rAnO5FjzypOVWDFXlcJ4+E5jYb3m8FCZSUxb+1QOs1gla+yylpgHyYwJ7bbk6LxOg1taxluXn1JMPUCw1Dww5As86drO747KYvkDql04QVbTV2BzFu1/VCUn33BCcoBU+QCy5qtP4wN9HpqvW3dtQwLAtQKMxvYle3o/Ba4ASi0j17+RFCz8seHXA5vETrVWs8Ptql5mgc52zzjrL+jxs2DCMHTsW/fr1w9///ndcc801yt/cdtttmDp1qvV3fX19TghBvMDjXgrDHjqqE4A+37gHADCosoOQhyLAlcJoSqGUgQrLB0h6+vmVSTyPjr4NpqZ2GujTEQWmdIKOJgSgLmWF2NUQtglAhSEjqciLqAcT2IWP/Rf/296Aad8agqtPHCBs0x1Sp3JXCUbydXPTAMXbjyEYSKz80pUHyK0Ol5jyQTTp8D5jPOFIDKZpeg5vl5vwu4DWlXZQwa/yZVQTl2UCkzp1wMM7G9U4iTN8mcA0PkA68yn/rtsFUe/9uevfK/G3RRt9LTZEB397tTg3/xpA7D97buTcYIzCUEDpsiC/M+rjJPrAl99hfdMtbJzq3CWnAfK+r0oDZHtPrXZzRwLKmgaoW7duCAaDqKurE76vq6tLq/9Op06dcNhhh2HNmjXafYqKilBeXi78ywWEWmBwTjPAHrad+5uspHeyPwoLT127PV4LbPghnWw+QKlogJyw1LfSw8+cU1kSQacxjU0Gsu8Njz4KjAkZ7n3VTaCNLX3tVBqPxpDD4J1qgTmhdILmtEL/274f/2u5Z68uc09AJrfh5Xv5unmpXyXv42dF7tyupAFyOK6cKTlm6u9xsyKpoG7fVGuBCVFgSUw+qnYYiWrw4sZGDxog12rwLqfJCzf8feA1QLoJzskEpnWCVlyAvy3a6KmvPBHJB0g+PnPcdnLT4YVRJnzq0oUUhdRZ4b2Mq7yzNC8AWfUMNU3IZmnB7Odw3GTMjzJFbgJQDgk9PFkTgAoLCzFq1CjU1NRY38ViMdTU1GDcuHFpO87+/fuxdu1a9OzpXJ04F5EXEE7ahWjMRGNzFKPufcfK+SLvLvvODO9TYas3VphEFJhcyFWF1geoZeBkfXMS8pjpriikP57uPeMFCjd0pRTYIF/ekqlb9s9I1gcokaTRPmA89v5anP7w+9z38f8PhCPWteOvGX9+fpygo9LI7+YErWo/XYkQ3SbHZmklzm/WFUMF4oKIzQdIc41SrQbvNwrMX9vx/2UNn+wDpPT1Mp0FBzc5z4sTdCQW15YekBYqcg03Hu17m6aJkxeqw9GY7dqw1BpO44MgALX8XpcupCgUVAZEsGfX0dTGPZO7GhQ+QDpzofQ8eNUANWqEOH8aIIUJTGPSzyVhKKsmsKlTp+LKK6/E6NGjMWbMGMyaNQsNDQ1WVNgVV1yB3r17Y8aMGQDijtNffPGF9Xnz5s1YunQpOnTogEGDBgEAfv7zn+Pcc89Fv379sGXLFkyfPh3BYBCXXnppdk4yBexO0Pp9ozFTyPYLKBIhSnbaYYd0krJNG9ocHk506VCIBqmgn4zWB6hlUGHmLdUpDuxWhkO6lOLCYw4BAFx4TG+8+1UdQoEA5q305i+mEjJ0xNXUhjiARGLWCrtjcUjoO6MgEEgqd0ZCOLN/9+A8MaWAacYF3SHT3kRZYRAr7pogXLOYmciCqzWBRU00RaKCIClrXdwSW8rtR6Ix7UDqhNwPwN1B1u4EbQr7ajUQEfvEd1A7+HvTUOgQNECtpU11SITYFIkqhYp46RD9ubgW4oyptTi89ikSNTHmvnfi9bnumWiZRwQTmFcNUJrmSlkDJL8bXkxg/PvOBBndQrF7xyLlYog9C04a1mauEDVfwoZdep02Uvbbk8cvHbKgyvDnA+RdA5RD8k928wBNmjQJDz30EKZNm4YRI0Zg6dKlmDdvnuUYvWHDBmzdmnAQ3LJlC0aOHImRI0di69ateOihhzBy5Ehce+211j6bNm3CpZdeisMPPxwXX3wxunbtio8//hjdu3fP+Pmlis0J2iUMXn7hdHmAGId0LrFpgLwUMpTpUlroug975uUBhg0gluClOPx3Rh+CZ64egy5l8eMUFwTxxJXH4opx/Tz30U8UWHPUtAmbTZGoQgMkDirJa4AUPkCaUcIEsLGlVEpDOIpozBSE2IhmguL59JvdGDLtTazYvDexr03LIv5dpBCM+WMlYzL9fOMeHD39LTxSs1r43i4Aib9rlvzd+N2dTWD2Egg6rZUXExibIFQThRAG75D/xWsk0zF9O2Fo77hpnv1CnvCYb9xLn23CUdPexEufbVYez2kCci+Bwq3qNRqgpkjMSuDH579yjALTHM9vEVodYqHfmE3AZ2Ojk7UyrOi//NwP7FaGo3qVY9YlIxw1QE4LDP44sg+QY200WQDy6Iemyx/lLwrM2QlaztaeK2TdCXrKlCmYMmWKctv8+fOFv/v37+8qlT7//PPp6lrW4Sc2w7DnBZIlbHnuteUBCooapcJgQAqDBwqD/nJFAEDnMncBKGatWmUBSDSBqQQIXUp2P6VX/GqA4v1I7NvQFLXaYBogeWIr0GSCdoONd7Ivi4r4fU4cozkq3nd+XHVKZhiNmbjn1S8w9//GWX/zyOatwmDANojq/EG88osXliEcjWHm21/jJ+MHJ/pm076Iv5MTIdpMYJq+xMuZiNt0oftuUUpf1dbjsscXYlCPDviqdh9+/72ROGlwd+X+TuaHPQe9mQ1DgUBC+Gj5j5k8ygqDaAhHLQHop3M/BwDc9uJyWzuSz7h9u8t9VJXcAUQzCq9t4E1ESUWBpcsExkeBRU2bidevCYzdC9kEdvbRPfHzCYcDgFCDTW7DKScQfxxeOIkpnPh5ZNO2LlO3jFYA8rGmUYbBx8T3lJE74k+WNUCEM055gGTzViRq2h5YXSkMACgpCMKQymsEDAMFoVbSAJni/4yEE3SLD5Dit7rMz36SDlqRVh4m6oQAlIBf4XYoUpvAQgEjSROY3UFbX6JBvK/NMbFIq1DQ1MWP56BD5I4s0PDmUzZZeKkL5QS/uuVxN4GJ0URynSEnJ1y5m/sbI4jFTFz79Ce49ulPtQk75fnjFy8sx86GMBau24W9B5tx+Z/FzMNeTWDb99mrgasIBBL3nZmwmIDbsUUjKfsAqWRxt0SIboKs7p7zx+YFPl4wapbuG49uXjfN9BTPbJaEAVkgSGiAvAkmOidooX6jygTW8juvxxGvmfPv7IsYbyYwXVBJqnmAxGCFxPdtuhgqkTnE+V0KsZberYXrduF7T3wsfCcLCLwAxB5YWy0wTZJBJ8pbatQ4wQQPWxRYJBEFpkOX+dlP0mUrD5BHE5hOuDIMoIwJQNLgVxBKMgpM4aCtzXUEURCOSBqgqOSX4wSfTkA+3n9W7xD+5u9PcUEQzdGI0L6XsHmZ3Zrwb9/FULltpiYMHojfV/me1TdG8MXWerzzZbz8zoFwFGVFIdsgbXPM9qEpSYcAFAwkVMCyL0iH4hBQbxeAepYXY8te0S8wGnPzAdJve/yD/2H2+2uV+/Jh8DoNkMqExHBMeGjaq7v7hfddikRjNkGPjTGOYfARe//lRRA/RquGUssHyOF9CUfjKRsMwxCO6eTgD9iFV36sdXoGdWlF/MgpKhOYLq1HDsk/pAHKZWQNkIP8AwDYtFt0RLblAeJW8cVWvbHE9mAgOSdolX+IDHvm7T5AchSY/bc6DZAfE5ifPECRaEybY6SkIGgJA7L6uyCQZCZo1jdujNLXhhKnr+ZoTHgWBA2QyyQtRu4478s/F0x4bk7RBMYPypOfXITVLUU/7RFCeg1QNGYXHHW3OByJWavdXhXFAOLlO1ZuSfhCsfOwlcyQGnW7zUIeIIfJbuNufY04nmAgkSSUtcwERWaSbWyOCia9ypZzFPvlPAGFozFMnbsUT360zrbtvtfFgr6CBiisEYA8aoCSqfnlB/5ZDSvC4Nn443ZtrPZafi8nR+WFHtVYwPrhlmiU7Rf2oQFi70U4EsOUvy7BonW7lH2XSYcPkCoyV+cEnS7H9nRAAlAO4+bT44aTD1BxS+i6LQ+QRgPkpBnSaWh4ElFgOg0QM4F59wHyYwJL+ACptwtmJQcNUElB0MoZYneCDvjSStn7ph4weOKJ/sRJhd9TqOflMtI0esjey+C1hyxrrheHa6+8t2o7rnvmU2VbcsuiL4mY2ydm6v1GwtGYla2aCQf7GiNYzjmDs0kkmTxAsrnC+j6i/+3XdfoM9TxBbgFklcKQTGAHwlF8s7PB+o3qnZU1ZjJvrazDi59txl0OWd35thiNOhOYxgfIrlHzdpxk4Y+tKvPDFjVOPjZKE5isAeIWa6oxxIsGCEhcQ0EDFHPOJB0z4/u8vHQzXl0mZhd39gHy5gfnhFsiRF6pm0smMBKAchg5EaKcGdoNRxNYiAlA4v66OltFChUnY/yRldptDPbMyy/V/W981dK3eEdUyp50mMCY0KB7+eS6ObqcS8UFQUsgU0WBGYZzNmtl35SJENX7xleBib/jyf14VTO/zbsJzC3snZ9MmQCYigZor8L5l2kwXfMA8SvLmKIWmIMPEMve3dPSAEWwfBMXDafRFHqZhLfsSWhgRSdofRSYZwGI0y7qNEAHw1Eh6koV+eOWCXr7fm8mOUCfCJGftAXn6CRqgQHJC0CiE27i2CqTjxwGH4uZmPnWKtR8mUjU6yUPkLsGyD0MHkgkLpS1Zm6CeCRmKjOy51YUmOdmWx0SgNoIhmEPa3fD0QmaaYB4p70AtCYwlYTPOKZvZ/xm0nDHvuiiwOx9s5+jThvjRyOWyLbsLgABevNacUHA6qtsVy9okd78lsNQ+QA5mcAikj8DL7uotDJV5XZTCOCtfhODN3MygTQVHyBeWJCPYReAxP2EXDTShG46RIGFIzHLRFRVXgIg7gT9dd1+a59EXTbxt14mA1748OoEzR/biWAgoRtNaIBaBKCihAmMv678pHf3+Ue1/NY5CsdPzqLG5ij+MH8NVm7Zq40CO8hpF/jJ3H599cdJVrvICxm8sK4qGsvM7OzReufLOjzy7hpc8/Sn1j5NiuddFiwEjbpi3GqyNEDO56TUADloNxnRmFp77ZwHSOcDlKIJTDOeOesgMws5QbchRI2Q+yTrlAeISey2KDCdBsjFz2d0vy6O2xMaIPXDzwQvleyg65MfAcgtD5AstOgsfiWFQUsAUGWCTvTL+0uuqgUW92Wxt2GaspbHSQMU//6SMX1wZM9ydCwO4XuPL0zsyzXvtiI9rLIjPm/RlDBBT8ytEv9cXBCwJURkDp08ctJOIJFOX+4Lfx3W72jA68truW3iZBqPAlOfQ3M0IQAxDdDOBjESLaoRlL3Id5s54UPMA6T+8Z4DYV9O0AkTWPz/hAmsRQPUHBUmZPZ89utaiqN6VQBgUXOeDunK4x/8Dw3hKB6ctwoXjOhlfc9rehrCGhOYDw2brJw0DG+OtGLlek4oczCBsX7UKe5Ls0IDJPeDFz5UCyEmBLppZ1Xh8rGYPdLX1n4s5lsAOpgGE1hhKGC7L3xfRW2Q93ZbG9IAtRG8CDwyNh8gLsRdZQILGIZW0NF9zwYOnZDCsFTLmqffKQxeqwHy8fS65QEKBgwr0dzYAV20wlVxKGgJACofIMCbeVLdt8R3sZipVFubECcPObmfGAaf8K+acFQVencq0fbBbZX9reG98Nhlx+BfPzrBEvRUie1KC+1rKmXtMcUKmJnZZA0Of8vOf/QjW9v8itLNBMbMA1UKB2EgEVquKiy5bNMefLJ+l61PDDk8n6FzQF2/05sDNBB/N9kYYDeBJXyA+CLGzAE5FDCs9zwdDsUMQbjRRL29saIWa7bFtVy6RIgfrt6BbQ6CoM0B3WP/xPeE0wB5MIHxwsvBcBT//nwLdjYk+hiJqhcoIUmjLsOuje4+BDnzummatgKyrhogjf+ik8ClE478mMAKg/ZC0LzQKYbBe2621SENUBshieAieykMXgNUaA+Dd/IBCgUCKAgaigzBQeu3TrAXQDf+OoXB67b5MTVZzq0OA8+cq47FPxdvwsWj++D833+k3K8gGEhogOQw+JZr4Mc5G1D7nURNU5mkz5ScoCMxMbfNB19vR98upUKiTHb9Qop7y7QzOpX8od3LcNXx/XHy4G7Ws8IGef43bIAtVgjKqkuuGsiZFtCmAeIEHNl3KGqaUvScfnJp4qLAKjVmQVVZEiB+fue1PBOfTz/T8besHwzdBKNyxtURChjWzJ/QAMU/sLQM4UhMMNPwAQbsmUxXZmUZIecM14fPN+5B9cz3sf7+c5TV4FfX7cP3/5zQSqr4um4fOpcV4rDKjgBaxiwPs2hU43StNIExJ+iWLvKvyp2vrMTcTzcK+0diMeUChde6O/sAqZ+J4lAADeFoS64iuynY7f4lowHSRSmyQ5mmiQVrd2JIr3JtG6GWZ0zO/WOaJr7ZeQBfbKnnvs8dCYgEoDaKl7nfqRiqUgPkEAbPMkc3Sw6dTDPkXkLDxJpt+7XJ79jkrBo0gmkIg3eLAgsGAujRsRg3nBqvKafTLoWCBhcFZs8EDfiP1lOp06Mx03LY5VE6QXMnNf2VlWiKRHH9yYda/izMv0EVTdcQjqJDUUgrNIwZ0BWXj+svfMfOX5UUrzAUUGYpt52H4njsWbI5IDuo/eNpAUzxb60JLHFNy0tCVgZlcR91FNge7rn1EjUjRkipT8BLwVlGgNPisPO1BKCWxUxTJCoI5XyKCfZMJptZ2c0fRKcBEvZRCCRefKAm/Sme34zVFfP6dsm+cgyVBoi9I+w8+THnhSWbbPs3R02l70xQWlDKhC0TmPp6FhfEn8lwJGbTHHpxgo7GTMcEjCp094tdi38t3YKb5i7FkT31AhAvZIt9Bk59aL7YrraVzEMmsDaC/Gh5GQScosBKCu2TddDQ1wILBgxbMVUg4RztpvVYVbsP1TPfx+QnP1FuL3QwHxXoTGC+osDcTGDS3xohpjAYsPojj0VsFek7CkzRt6ZIImSbRx4EVfWt/v5pfMBmgz7rl0oAqm/RqOgmRtU1tjRAipD7UDBgO45q0FYdj0Ua2hMh6ofMaEwKg4/pzQTNXBh8h6JQPIGgor34McXvZV8hFbrEb7s0v2XmNi/JR4OcCYw1ze5vaYsGKGaKwhmfZJQ9k0nkq4z31UVY47WSuglVZQLz866o3gfnPnHvCfdZpXljt8AygfHRXIqXIBozlYIwPw6qfudmAuMLxzZHFAKQmyCqMYElIwCxa/G3RRsAAF9urVfuB8SfMdWYqdJ05ZIGiASgNoIfbQdDfhEKlRog/oXVR4EFA+ocQWzScvMBWrJhj+N2Jnj58QFKJg+Q7t2TX16dFofXAMmwa+DXBKbzT9qjyJRsSiaeSNS0TdbsXCyhhGmAFP3e2pIpWFcF3MkpXa6wHT+W/TlRDdqqCYD9Tu4L21PlxxCNQVhSxp2g1Td5W32TJRR0KApZvjM8zRonaF6I0WludCYwXWg5a4dPMaF7zUNBw5YHiB2PaYAAUUhgE1uIW527VXvn4bU+bmkSBA2Q4j7J/iys6SQs+56FJv654++NSnPDxle2n07rzGiOxtQaII+lMHQ+OSw4RakBinkLg1eNP7K5XuiTVgCK/69KWSFTEAwgqFg8Kx+b3JF/SABqq3gRiGwmMN4J2iqFkdgedEiEWH1kpVI4KvboA+RGIhO0vR19HiDvx2QTn1YDJB1Dd8wQ5wNk2xbgo8C8o6oFBkBwumSY0iowHI3ZBkW28vSiAbrosf+ivrFZO6kri9MqnKDZBKnSFJqKQVB1H5igpssEXa8YiE3J6dmpGOpv3vna+lxWFLJquvEksnLrBSDd5KUL+925v8lqV5U6gE8xoUv6GVDkl2L94B3PVVqSQt4E5sMHSNQ0upteVJ8ZTZGYMgosmWzuXgNCVD5qgNoHyMqx1PITN//CSMzUaJKcTWAsKabufeM1QLJg4uTfZvUrqvYBcsrvpNMOxRzeO5mCYMCz6Y00QETKeDKBOThBlxTa8zYEDLUP0KVj+uJHpw1SbmOrV93A7RUnDZK+FIb39h+pWY0Xl2zSC0BSY7pjFgQMKwrMts3yAfLeLyBhlpD9LHbst5tOZEdIVTQKu5RsVZ5wglZ3bPPug9rrohSAFGHwUUvbZDejqjVA9mMxk5A9DD7+v6pyetRUJUK0t81TFIrncurTpdS2LZEJWvxe0ABpDqCrdxQz47+f+fbXGHH321i7vSUqqmV/PsJSt5AI8YkQW9pmQklhKHHN9zXar1EomPAf8uMDrYoo1OEl67iQ1K9lf3/1/Fp+L/2mVDGWAXZNqRPs/Wfn7CXfjtIJWkorwrA0Oy0+lLrrxZ4Fvz5A7Drq2t282553i8EErW4disTjtbRV78H0GAoanqPPckj+IQGorZBMFJi9FEbidrMXjX8YVU7QN084HDMuPDq+sldM/EwDZBjqF8ArTnmA0mECA4Cpf//cwQlaFhbVbRc4aYCEPEDe+XJrPY6fUYN1OxqE73cqVm0x05Ty79grnLPBnA0+TJ0v3z+WCycaM10nMB6rGjxfG4mZwIIBmzCrGrRVWho2EMvb2J8qk6CcL8nLKplNXMMPqbBt05kjvWiAmHA66Y8L8NR/1wvbtu9rwiM1q7G/KYIH58Wzn6s0QDrhmvcniZkm9hwIY1NLHbGeFSVWNKZKA1QQDFiaFjdTlnA+3K5uz4fbNT/YHBW0SMlogFgf5F+UaJK0qvJU6TAsAZGZF52vU3M0pjQrhTQaoLIWLR27Brr7UMgJQPJzdu9rX+IqnQ8li6BU1DkDxBxVMuy9u2JcP+F71owqGtV2fI0TtErwJA0Q4Zuk8gA5OkHHBw1+/awKg+cn82bFS8unQE9FAGIDh+o8U0mEKK8OncLghf7o0gEEA1rhSKc18sKWvY1Yu10UgFQaDxPiZBOOxGyrVXbfrTB4ZpqTzpGdc8TBt0BtArOXwkj4TtifIVUEkWqFbdVJsglA8b/3HowLIUf3rsBd5yUyG8vRV14z2I7o08n2XcQyR4pt7PToA7RuZwMWckUoGTsUwqzlA8RrgBxSPhicBujDNTsQM4HBPTqgV6cSqw3Vap13UPUh/9jyTTnhpiE6GI5KRWzVwoyXY8iPpEqbzR/DS/+sNAGSdk3Xx0jUtEWBAvbM+nIfE7XA4u2fOKgbvr73LBzSuQTH9u9svTvNChMYoH6OgMSiZ9KfFiiTa27f16TsL5AwU/XpUoJrThxgfR8zTaVGUUUooF4Aq84hd8QfEoDaLF4eInspjMQXbMXIj/NBhQmMb6NR4fTHp0DXRWt5wakafCqlMOTEfF5NPXoNkKE3j3koCusHVRi8KanBIzGFCczSACW0MipClqBkjyRjqC69qhgq+8wn3WO8tnwrLv3Tx6jdm8j+rBK42ECsK4bKNECdSgsEIY/fWxaInGDZkXl0JVNEE5jeZ0IVYg1AOSmxBYUXH6BgkCuFAeD9VdsBAKcc1h1AQgOgmrCSDYP34wPkbgITfdXYQsSPspT1QV4keTKBSf3r26UU3ToUWn8HLAHRtP1WRdwHyP4cBDUmMKYBYs94hFswFIYCmP/zUzH3+nGiCcxHWRKWzuFAOIq7X1UXst26x559HRDzRf3qnCNx2di+AOLvkZPmiKcgpNYAXfr4x7bvqBgq4Rt5oPDyENnMOnw9p4DoTwC0RIE5aIBUzoNFadIAsQH82yN727bpBAvd4fjv+cGxY1HIIRFjwPFv/nudCcwtEs4vqqKGMVOVCVrcJyAJKNpJlUtoqFsgOwmkzaooMG6yZTz38TdY8L+d+M/q7dx52G9EsyZE+I6XV+C9r7ZZAlBFSYHgsyGYwBzC4GVKCoM4qiW5W68Wc6BlApOuhxdhIKpxjAXsTqgz3/7aKgTMa4B0JqEg5wQdM0180HItTzm8u9CGyi8lFAhwYfDeJ5+YDw2Km4/NweaoWMS25aOfuZA9zzYNkMYE5iQAHdmzI3jdToC7tvL+qlsST4To3Qm6rEjWACVSFAAt7w3nghCO2n2AnBg3sKt2G3P21wkzrE+FLaZSNo6Zpol3v9rm6fgFAbUTtOqYOST/kADUVpAfLS/jmJMPkEpYCSpqgfFNqASgYk4DpNM0eIENBEN7V2DBbafj1JaBXddXQK8B4s+BF4DKSwo8F0PVCQ2hoEO27JZzSNf7rcsEzU9M0/610pZnxgqDt4QSZ5NdNGZqfR6cTGCqyB+VKpydh1ukkE4DBACTn/rEMgl2Ki2wzAty4kOnMHjGGUMqrc///MHxWHDb6ejXtQyAe8kUwMEEZprKdwQQNUANTVE8UrPa8tfhNUC6JQRfDX5V7T7U1TehuCCAY/t3AaAuRskoDOlL3DihKyWholFjXrG2N0smMIWg4UZCAySiK9SsS4QI2AsEs0VDzGzRsjoUbo23p3aCFvIAce8O00SHIzF8ubUet764HIDdbM7GaL8aoNmXj8JHt56u3Mac/V0FIMkPsykSw18+3uDp+DonaBV+HPFbGxKA2iheHMnsZh27AMQbEAItjsz8g8yvSFUqX94HKBUDEN/XuFNnol2tD5DmheMFvTIu1LlTaYF29SELPNpcPwF7or9EG+l9nRoUidZipvukwfv2OPVL9AHSNKYygUlO0P9ds8MKMY8X7RR/1NBkj3zRhUrrtgHA3pZszJ1KCoW8LbZaYA7X54whlXjkkpHW3yWFQfSsKLFVuHd6vVS+cOw38jvStSxuZuEd2uXzEzVA6mPy1eDfWxVflY8b2NWa/HX5u4D4+1NeYs955IagAXJxHlKZ/koLg5aj/cFwVCyT4NHUxKPTQnkxgckCXKVUC44ff0wP71gkFvMVBs/62ByNCWV25MUJG+vCilIYThQXBCwtpsygHh0AAB+v3anczhYe7Bli1+JPH/wPm/ccRJeyQhxW2cHx+PK84UQuVYMnAaiNYDOBefiN/ECqVidyFBggChBuz3QRv3pNQQKSX3bezq/XAKnbUmWsBoDOpYWeNUC6fEhOGiAv53/e8F7uO7WgNoE5T/CAPg+QTKL+kd5s5BQGz0wa33tioZVQsSBo9wFiGiA5Xw8AnDu8F+779lAA7llymcakY3GIM4GJ5irTJQx+3MCuSqfZkCQ0OmafdjCByRqgihbBg9fmydda1AC5m8D+1+Isf8KgbtZ2Jw1PKBBAcUFQWKx4wZcGSCEM9O9ahr4t2oeDGg2QH58knVDixQla1nBWlRfbcqAxvJSc0GmAhMz6CgFIDm+XF1OFLj5AZYVBvHTD8fjtJSOE75mTvGoM+u6oQwAAry7bKgjizy/agEXrdlnHKbIEIPH3D313mC1EXiZgeHeBIA0Q4Rt5Ve3FB8jpebR8gBTbeJ8bN0djVfHLZJBXd/wEpA0N1prAOL8lbmVaGAp4N4ElEQbPcLo1I/t2cqzKzrO/SWFWMN0nDda9hAbI2QfonS/r8IkicgnQOEErwuATbdp9gBhiLaj4/0WhAM44Mm6SapYcRGWYwMXXHTJteYCctQrMF0PGqm8WdZ+YI7GYchWrqt/WsUUA4qOznDRAOuJCrXhde3BmnCIH4YYlQO1UUqjdR4WfKCqlQ3DAsISTxuaoUgPoFG4uv5NhKwpM/L6kQF3S0skHSDaBGdzli0qpJlSCji4RYkgzdrJyJbJfj6xpdgqDB+LPwci+ne0mvJZjqfxwjunXGUN6liMcjVm+Y4vW7cKtLy7HxX9cwPkA2asDAMDJg7srk4bKx/esAcohJyASgNooXqRopxwbVUxdqminkPMn8KMBSgX5ZefPTxsarOkcr6HhB6lIzNSGAdt9gPSRXn5NXXzTXlTFTPukjAKDF/V8i39FNCEwqGCC0V8WbsArn29R7qPSSCQyQdv7oYoCY6g0QHzkYcyMT7Q64YNpvuJmtvh39jxAzmHwZZqBnI+IY33RodOGxEy7AGRpgDgBSL5/vAZIJ6CrrmsFZ9Zy8gFiC4hOpf7MYH7yAKkcdgMBw3JQjvsA2U1gTs7TsmBoCadSX1hdQxm+z/L40kMjQAD2cjM6VKUwdBqgMikMniEHeLj5ALE25UUY0/qq3AJCAQOHdI4vupg5ev3ORMoN2QQmzxvBgKEsGyMc35cA5Gm3jEACUBtBfrRYDpOOLpK5zJNXHYt7LhiKob0rAKjtscJLyb0MTHNxdMtvAaBfV3s23WQIOxTA1GkwdPIdb77iTRJO4d7yMZxy/ei2JSbXxDF+Wn0Y7vjWEK7PegGBwVbNKodaLyawhCYlUZ5ChZcBS3WNE5mg1YngdL5ZKg1AQMobFI7GHE1M7Des71/X7ROcO+UoORmtACTlNnISonT+MHENkHjPylsKrtZz4emyNoV/nnRH5YU+uW3AuaAqu74VPv2A/OQBUhE0EhFaB5ujwnVjj4KToGEXgNQmUjnVBcPJ6b5HeZEwpvKak2jMdNV4AeogBdHNIPE9EyBkrZHN9B7i8gCpNKxM08MtwoQFluKF5TP8q+6j7AQdkIZ/wzDQUVE4mKesKORaPoSRSz5A/mZPIntIz9aj3zsGs99fi8vH9cP4h9/33MxpR/Rw3Uf3Ej97zRg8/d/1+L9TDsUXW+rx2cbdOHtoT8/HdsLJBOZUH0kF7xDap0spV/DTdDCBeQ2DVxdD/dU5RypNWzdWD8aLSzYljmPoBQRGWWFQW4DQy+o0kW2WaYDsxzMMtZbrxEHd0L1jEV76bLN1PJmECUyhAQoa2vuimpCCAfF+qRI7MniTHhts5XIhbqUwyjSTZUID1OID5NCIXgNkd1xnzse7uUg9+f7xz5NO8Io7QYvXVdAAOZjAmLbArwbITx4gFcGAgWImzIdjogDsIQqsvKQAu7ns38wEKgug+igwe/9PHNQNE4dWoVzSaPCPrJxtXYdKQ6vLA8QECHlRo40C0yRCZGNzUKNpUi1q+ALFqjZ1TtD8cXQmsOnnxhd33TsWuY5rDD/JOFsbEoDaKFUVxbizJRtuKqgnOH51kXioB3bvgLvOjzus9upUgmounDhV5CgVfvDVajA8hMFP+9YQfGf2f61EbLpxzR4F5uADJO17zrCeuPakgeqGIQ9Q7n5VOqdOwJuDpqUBsiq02ydHncq6d6cSTD9viCUAqSKeVJmgGUEHE5hYLT1hAgu1aDdMU13cVfUbnXk3FnMzgWl8gFhuIw8msEhUbUqNKXyAmJDSwJlL5FU4n0BU13WVBkg0gekFoMIkNUD8YoFfoHTvWKRM7CgTMAwrTcZBjQnM6VnuVFqIb3YeEPoQU7zDnTWCnegDFO//NScNwGmH2xeB/Lvg5kfGUApAGmGECVwHm6MIBoxElnbZBMblc1JpaywBSBOpq3r3+PxCjhogRS1DdhydBujy4/r5Tn+SO/ofMoG1GXQr19aAn+A9CvUt+NrZovrIHriaS8EOiBOBbrLTyRG88NKzotgKe444aYA04aj2tu21rmSBRj4EL4AYhntRE51KH2gRgFyM6GxAS9QCU6nF1Zo12SSlMkex3+kquuudoBOhw7w5i0++Fo7EtM7bKhOYjGry4icZ3UrWiojTZIIWziOmFtKiDj5APLLgyE8gTpnKbSYwjz5ACQ1Q8k7QTPty3MAugknXibgTdPzcbE7QprsAJAs2kaj62e9Spj4vVTFUL9rkWMybBsjNBMZ/tjRA4agQtq/TPDdHTaW2hvWTH+N02iAe3rlah8oHiLWnW5QJx/Mo2VAtMMIz088dgmP7d7YJCOlC9SjyA7KfYoXJ8sSVx9omJi8rMF3f+Am8qCAohHvrnC5tGiCtg7VhW43LyiL5CMKgqAlV5dHlNQFY0kKvPkBslWl/zQ2ohYhgQDx31UQg5xni4auWyzzy7hocf/+7qG9stiYyNngXcQIQ0w7IWjjebKZbdKpMYGJiTJ0JTAztdxqkm6Om0g8oFjNtkXsdikK2+y07z/Ln6aSh5J/30sKgcF5ueYCAJHyAFFFgBUF1xl8VQZsTtJhcUC7rItNZEtiaNYKnTgASS7XotaGAuNBz07IygVr29wLE51I0gbVogCQBSKcBCkeinjVA4med6Z6Z1tx9rlQmMJWZUZXzyxO5I/+QAJTrTD5hAP7xg+NdwxCTRWUu4F/K1hd/1PjJDyLDmwMKudIMukrJgKJsiEMpDEAMzXezfQs+VQH3wrZOAlDMdHdIbY6awuSiMucZhvp72bykmujZ+ahCmINBA05BcrsawvhmxwEhoguAUAKAHVNXVT4YCGgHXjlTNv87QK8Bks/J2QQWUwp/UdPEAckHKBQw0EESug5K+/DPklYDFBCfGtmHxckEVpCkD9C3fvchZr+/FoCoQfEa7RMwDGviPNgctb17URdNiyywRaLq/WVBiW8/8Vux9IQMn0MnZjonfmRClMoEposCY8/dweaoULpDl3+sOWqiyUkA4o4jLMY0j4EnDZDCBMbGNp0AxOPVuZk0QETOoNQACSaw9IpAnUsLPJnV3CKdnOALq/Jh63HnRvUA4D0KzFkF7dZ2MgVcZVR5SXiapQlaaeoyDOVqUf5OJTDyNcRknDRAjHA0auUBCkgCUHMk4V9jE4A4rZHumsdM+wDLXwtdMkDZsdvZBKbWJMZM+6QYMAx0kPwnGhw0QLo5RBZMZeHAMQy+5Tr6zQMEwKpXxnyjQkF10UsVwQAnAIWjNn+yuLlS/yzLfifNmgjBipICnHxYd9v37Nk1TRM7W5zlnYRAqyCqgwYoGDCs90mVqV2nYSpt8T2LmZLJUzbXtuRsao7G0Byx94Fdeq0GyEUrzhZP8l589GZA0baq3po8rniVa3JH/CEBqE1x9tAqBAzgpMHdXPc9bmCXpI/Dv6DprO7QpawQn9xejS/vmei6byqrhMryYhzSuQSj+naGwTn7RhzMR/LEry2F0fJ9SDMAAXatmjxYpWICA4AmRdI5nuZoTDCzqM7F0PgAybvqcv0A/n2AGE2RmODQDCSu66x3vsai9buE4yT6wnya9L4OcR8p8Tv+nmuLjVqh/WzS1Pe/WeOoHTeBiZOiYei1TgwvPkChoKQBKhHbdDKBsWvlVwPEwwS+wmBAq2WQCRiGGAavSHXhpAGSr1skpl7AdCgK4enJx2K8FOHK7tGuhjD2NUVgGMAhnRNpO+RHIcgJQLqot8cuO8YSWFUmMH4Y4e8lfy789422vEB8GHzU1k9VHiD+fdNpo4skDZD8mPHPD3881rZq4ZBs8evbXlyOfy3dnNRv003WBaBHH30U/fv3R3FxMcaOHYtFixZp9125ciUuuugi9O/fH4ZhYNasWSm32Zbo2qEIX9w9Ec9cPcZxv5snHI6/XnucpzadwpyB9GqAQoF4CLnTapWRRNStRXFBAO/+7FTM/b9x8ePyPkCaAdfJB4i/HqwtIVLOZSDwrwFyvj5sYNRuj8Rwz6tfAAAqy4uUqzddFJh8LmoNkCgs8DglQuT7xzs0A4kBuIarPi1rgJjgF+Sqm8uoNEAnDIpXyh7QrUzbJzm7tZMPyKx3VqO2vtH2vSoPUMBDDhU+Ckx32ICUP8quAXL3AdLlQPICEz7jRS+9TRvBQMJ5tqEpYnte3PzZ5OR7EY3gWVYUEhY61v4t+65viSTrVVGiDZkHEhO/rl8zLx6OM4+qsgRWNyfoTtw96lpWyPkOJX4n11CzfNGipqUBKhYS09p9gHRmNx52bHYfZW0cLwCJ7cX/V103mwZIeWQ1/1y8yX2nDJBVAWju3LmYOnUqpk+fjiVLlmD48OGYMGECtm3bptz/wIEDGDhwIO6//35UVVWlpc22RnFB0NXxrKQg6Dkng9oElpwTtNuuOsdiFamkSw+1hH3KDoO66B1+H0ah5EfEsDRAgpDo3J+ATwGoxMUEpio7wNMcNfHasq0AgAcuGqYcFHUaIPk7tRN0/H+lcOSQB4jRxOX6YatuVSI/2UeJVRwPBvSqfpUPULcORfh82pl486aTtX2SHbuT0UBGTdNmFgkEgA4uWXS9aIBkh1M5bYRTHiArcijJFfuUvy7Bqtp9LW04O0Hzi4VgwLBqgS3ZsMcWOh91cTaWTYfNGh8gVf4aIPF8ftOS9dgtaStfH1F1HLYwkZ9VVdg4EL+vK++agC/unoBQMGAJEbyQLOcFKuRMYCw/D699UfkACcfX5UZr6TPzK5K1cbr6j6w91SLKqyCsws2MnymyKgDNnDkT1113HSZPnowhQ4Zg9uzZKC0txZw5c5T7H3vssfj1r3+NSy65BEVF6uJsfttsj7jVqhLIoBO0n3wRfqpEy8gvpqXajukTrzmVwuCFIXZt+O3yoCMfQTaXuQmVZW4mMJfBIxyNWcLCkF7lyn0MqFeL8rno6n0BLYklZR8GBwdlq39cpBd7JFQFbOUJm2mAnNLux6PAxD4FDAMVpQWOZiKrGKrlA+R4Cupjx0zbit6TBshrJmjub7sTtEMYvMJs4odXl23FP1pW7AUuTu7iRGpgaO8KXH5cP+W+MTcNkM0Epl/AAHZzvawBkgUgORiBPVNxHyB9CLpsmuN99uT3p6woZG1nAhSvOZIzQwth8FFWpDRxb617GbALRYBeG11g+djFMPeTDfjD/DXCdp0GKOEE7f5++lm0OjljZ5KsCUDhcBiLFy9GdXV1ojOBAKqrq7FgwYKMttnU1IT6+nrhX1vGj23WTQOUVhOYjwE4BfnH9mJ60QA5JULkBwd2bQQzoZ8oMMNdqHRKhAgA/9bU7WLE62PFP+smxgDnzCl/z6Mzc7FtcrSeUyJEhsoEVqQQjmUTGJssQg5CVtwEJn7n5RG2iqFyjrN+kYtoAi0CkJsPEPe+aTNBG+KDU16s9wGSr3/QEtpTf5dDDrXwAoYoyLLnfmTfTsr93aLAZMFRFwXGkJ+JmE0DpDeBxn/P9Uthg7cEIKlfKg2NCpUWRRaAEiawGJpZlXauffa+BDVuCq4aoEgMv3hhOerqm5TbAXUeINU4kqwPEJBcaZXWIGsC0I4dOxCNRlFZKWYTrqysRG1tbUbbnDFjBioqKqx/ffr0Ser4uYKueroK1Xgb9GHe8YOfATiVKDBdZXenGj/2MPjE38IKjE0mQQcNkNR1QaD04ASdrgKzgN035IiqjgCAs4/uqRTc5HNRCYxswFX5SoSC7mHS4ajCBKbQzugEoICLE7T87HgR4u3FUP0/f8rq3R40QF7yAAWDYikM+Rnh77M80bJzS8VkkWhL7wQdCgRs2s5439TPsyppJY/SBOYwcdq0ly1tb94drxXXp7OzCSyhAXKOfpR9qfjzc1oMqfxojhvYVfibN4Gx/vP3lp2j4FfI3Q/d8dn7pQrd57cDGhOYYlEmL2j9vDF5rwHKJW677Tbs3bvX+rdx48ZsdyklUpHMAdEpM52JEP1UUU8lCsxuzuI0Fh41QLokc2yl5BQF5tQfL0nkVNoQL9xzvr00iiwAPXftWDz4nWG445wh6igwaVBTTep83SybAOQhCkw0gekFILsPUIsTtOFQcT5m2opIenmCE6Uw4v3ykglYRp251z0Dc4EgAOk1QPw5y/eVv37y8azIoTSsZgocfLyCAUP5rOtMj05pKQBVFJg6/xJDPj0mzLK0A7JAJZ8GHwavOg4TLjoU6YVPp2ssCxGXjumDK4/vL3zHxp1I1LTePUE4aWlfp/XR5gFq2bCv0YsApDKBecgD5OOVURV6zQZZE4C6deuGYDCIuro64fu6ujqtg3NrtVlUVITy8nLhX1vGj6lJlbxKzASdli4BUOfW0Y0XqSRClF9My2eFU6HPuPBoDD+kwrYPQ/AB4q4HuzZ+osDkiA13DVByr+X3xoq+FoUhu6moW4ciXDy6D0oKg+o8QB40QEFOoybfJ1bXy4l4wdP4ZzbYqp4NWZPJJ3bUTcKqRJFeNEDBYOIZAYADLY6qbuYrHpVvlmEY2kR9DNEEpumfdF1loYL3CbrhtEPF3yoih5IlXgtP/XzyRWr54+ki1FyjwIpEP6dmh0SmgP0+s3edaQ7doivZ5dEJZrrCoDrhQUY+/ndG9bFpOdm1DUdjQuoBuQ+6yFK3PED7GtVFlt2coIs9+Oj5Ie81QIWFhRg1ahRqamqs72KxGGpqajBu3LicabMt4ssHKI1h8G578v1idvNhh3Ty3C+v2HyAmMmGizo57fAeOH9E78RvbLXAEn8XKlZ4TokQnfIAeVGCeUkToEL2v3EKjQZ0eYDUk4iwT8v5HghHsHTDHtvvBzqEmwPxwV3WAKkyb+sEeTcnaHlw9XLNmdYzYmkN4itlOdrKCZ0GqEuZWxSYBwEtIJnApHs7sk8n/OyMw/DsNWNsZpVQWn2AAtrrGQwaovncQbsHAF9urdeWpgHsGhtdBm6GzgeIOabLpkFmDrb6ywdLqHyAWk5DNoEVO2R25tGZJnlEE5hdA8Ta503pQpSpiwlsnwcTmKHQAKkCWOQFVFs0gWW1GvzUqVNx5ZVXYvTo0RgzZgxmzZqFhoYGTJ48GQBwxRVXoHfv3pgxYwaAuJPzF198YX3evHkzli5dig4dOmDQoEGe2swH/IWbq36vd6hMBf4l+tePTsRT/12Hn4wfrNw3tSgwSQDisvxGuIlXF74q91UwgbV8LvBxjeTVmlspDDfBxYmCYMDSRLgJUuoiqZIA5GACW7u9AVfMEXNshYIGfnjqIOw+0IznFn6jfL6aVHmAlAKQ+jrE7536GpqmKnmjNwEDSAh8zFfCzX+HR1e80k2I0pVdkfvnpAEKBAz8uOVdWrejQfptwGojVQoCeuEz7gNk11bY+mrENXXXPP0pDq8UhRAelTDulDlavozhqIn1Oxqs8iSyGeeB7wzDb95ejcvG9m3pV8IE5uT7JmsFCxU+Oirk46uuo2gCa9EAaXyMQgEDzVHTUxh8QZImMKe5xGnbizccjwv/8F/tdhKAAEyaNAnbt2/HtGnTUFtbixEjRmDevHmWE/OGDRsQ4F6oLVu2YOTIkdbfDz30EB566CGccsopmD9/vqc22yOzv38MHnxzFf63PT7w+XF2VEaBtVIiRF6rcnhVR8y4cJh233QKQOxF5e3OfOp3fh9VXwUTmEID5McE5iUTdCoCUKEgAPnXAMnaCJX5xmkiDQUCKCkM4p4LhmL9zgb8Z/UO2z5hRR4glRakUKMZifuaqI8fjZkKE5i2uxb8xAMkcrX4EYBUJrBAQF+sk+FlwRI3nfLPpF64lSdBVei0Ex2LQlpNQSgY0PZXrhOmM4EVhYJW/ptVdfsc+zL93CG469/xRW8zZxZiqLIWM2a/v9aqZQbYfXB6dCzGjAuPtvVX5wOkcoLuWBySHJK9m8BUYysT+sNc0kfRBCb/3vSUCNEpBQQgaqf4JpzOx3YsbrVzTN/O+L+TB+KPH/xP+VtVnbNskFUBCACmTJmCKVOmKLcxoYbRv39/T+GpTm22RyYO7Yn+3cowcdZ/AKSecLCglXyAMuUErQuDF74LGspwT4bOx4cNUI5RYPKxNPZ6Hcn6AAEtYchN3tqRHZ6BRP+euGI05ny0DndfMNS2j5PJxsu5KvMAqTRAmufFSQMUUThBe/IB0pnAXJIY8jRF7Bm6DcNwLUEhn/uDFw3Dq8u3YkjPcmsCl32rnIRbnXOv6n7LXHTMIaitP4iP1uzU9NXZCVrlmyL3tSBo4KDaFcXG5BMGIBQM4I6XVyiLGVd2LLY+uwVslLpEV/Jh8E4aIN40172jOh+dCpsJTOX3xmVsbo7aFzL84jYUMNAEeBOAXLSMxYIAxLXncEndMkE73Y9wJAbTNNMaZJMMFAXWTtAlxkqurcTv0xsF5r2t1KLAZMdCxUpLMoE5lcLgN7EBqkSRm8PCFgYvtuV2FZxW9zz3nH+UTbuhC99X4eQDVD2kEn+97jj07lRi28dJoPASHReORi0NUMIJ2vtQFI+IUrfNTxyJ/rq3KRdDTcYEptQAeXGClmaZi4/tg2euHoPOnOAkJ0L0UvtLbl++30dUdRT8YH4yfjAevni4cG3PGioGj4QC+jxAoaAh+sa17CaEiRv+I4B4/yxeM3NEVUc8ceVooW0n3PJrJUxgugzoLQIQpwHq3sG7AFTsQQPEBBXTTJiJRAHI3h9dYVQAuKdlAeOmAeIFIL5bTnOJe/Sr42ZtvbVMQgJQO4Ef3JLN+Jr4fWv5AHlvLBUNqTzQK/PdSE6lstAkaMEU35fx2V99msDc1Golhd5ey4BCE8L3280E5iUKTIWTJs9LiRA+EWLCCdq+84Fmdc2zgIMfiqqKthchXq5vxkxgfpygVQJQ0DBchTvd9RS0kIZ3DZD8TKgmSgCYd9PJOGNIwjVAFS0mC4ChYMCqWC4TDBjKnDhCEEEw4FrKRYaNR3wU2LBDKjDvppMxtDcfyel8n93fh/jvTU0maFUUmB8NUGmBeC1V/eXHXlbQWOUEze+rK7Vz+9lHWlm4/ZnAvGmsbXmAJHmGH0tG9+uMSaPF/Hq5EApPAlA7gX8Y/ZialFFgPk02XvFTCiOVWmCywKPWAAUkJ2hxOz/5CIOOwg/ATWiQw5zdrmhJYchb9mKFAFToQwDyEgWmws0HiOFoAjNFAUh+Nvp3LcVQTRkP2X+LR6UB8nQtmQYoBROYLgrMDZXwB4hZlUNSIkSnCU1+/a1EiIoLIUYwwbafXJC00CUMXhWynYpPG8Bp5zgNkBcHfp4SDzUUeROYKgqMbS9LUgCSFzaq949/FpiflCwIy5/FcYzX3qvbdesbf3udNUDO91UWzOTdc8ERmgSgdkKyJrB05gG679tHO273YwJLJQ+QbD5TD5ay7VwanPh6aIb9c2mRWmUMKHyAPCS64ykMBpTZvEsKgsIqSjWoCBogF58HpW9UigKQkzqewTt4qkxgpYVB1PzsVH0ZD0OfCDEcVYTBe9JqpW4CU+FF+6RbGBQGpQlE0ADp761OA6QSGkXTh30/OedNKGho/UmCgYBSW8F/l8zCho1tH63ZKfhEyThdarccQEBCYPNlAvMhAMn3THU/+PeeCUBaDZBCsNX5A7mawBQV5+U2ZOw+QNK4K4TTA/LSjwQgIm2ItncfAlAa8wCdMaQSK+6aoN3uywk6hSgwWQMgHzfuUCqaFGxRYNxvVFeggx8TmHQN3S5pYSigXbHxfgzBgGFrmzdPJKMBcotoY8fVtunh2Yk7QYttFQbFgd0pWk513ozmSEzhBK3tLnfMhAmsKRK1/BP8mMBUeNIAaXbihUL2zDIcfYA0ApCKEkUOG1EDZDeB6UzZBUFDGU7NC0zJRHfyx1v8zW6hrzxOY5Uqk7H9OMzUpq4ZmKoPkGwKVT3DvHlX6QOkEE5EgYVrS4gadDGBFdoFYbkNGbdxz6YBknYnAYhIG24Ttg7VcCSoUX32gx8cBnQrw+zvH2P97aaG5bnhtHhep/OG9/LZA/uLJb946oFD3MltIhdMYD58gLwM/0WhgLI6ugnTthpMzQdIoQHyoS1RwU8cOmGqiQuDZ7vwWhB2DrrD+DeBedHCGFb/WRZoIHUNEOvnxKP0meh1GiCdGRZIzgdIBW/6UPkAdSgSzbElBUGtABQMGEptBX9+yaxrVOOGajHl9Bq6OUADicCGxuaoMhO0Kgqsmw8BSL5uuvsin6+qFAbfns5kxe/rxwlaZ1KTsVeDF7fL46v8Goajah+/TJL1MHgiPfBmllR96wUn6BS8oIMBAz3Ki4W/vfJ/Jw/EyYO7Y3BlB9/HVU2AwYCRKKUQsA8cTrXAVIqrsiK1yhiwq/n5tk3T9BAFFtA6zhZJE4w8qPDbXaPAFBNLqiYwXnOnk3eFRIgKExjrl05wUTl/Mxoj0eSqwbecU3M0hv0t5q+iUMB15ewGu1SPXDoSa7btx60vLsOyTXvFY2s1KuJ76NkJ2uYDpN9XcH5VmMpCwQBKCoKWQ25leZG22HIoYAh17NKReDHersJZ36f20osJjAlJzyz4xlYtnT8mv8jz0i5DFmz0ApDoKK5LtMg+65yW+X3dHPGTcYKW+29zguYOaSgiN1VBA5mGNEDthHSkuWeITtDJtyNP9n5CnQ3DwJBe5b5+w1CFV6p8U5w0QPxgpTIT+tEABQJiW04aCabdUJlFDNidTOVjdypJhFy75gHyOLH42Yf33dJNSCon6ALBBBbvl9YEZuhNYLz2xuqHj8i2aMy0HKDLikIpBwGwe10YCmBIr3JbLhjAXvOMURjir4khPIeOTtA+NECqlT8/T4cCYhRbVXmxNgovGDCEZy5dARQqAVFpvk3RBMbuzYdr7Mk74+3H/+eFz/7dyjyX7bGZwDyYPgGpTpdiHNP53QWk++h0O3gNmagB0v/Gbc6R8wnJe5MJjEgbyQpApxzWHQDQlctWKzpBJz+ImRBfgnQKaU6oVhZimgD7Yy8Psvw+Kn8Apygwp/HQzQTABj+VCQwQhRqVCYxPupdcFJhz/3S/YwgmMAcfILkURoFgArMLqEIfg3bnbwYTXng8+QBZCehMKwS+rCiYshZDPgeVxsCTBsgwBN8mJ+2e3GevApDKWToUNKxSEgDQtcXkozNLCQJ6mmYX1SJIF9igw8vY4yYksXtpGAZe/fGJmHv9cajkNNxuyJosryYwXbV55UJOcDxOfDZc0jEUF6jHfL6PJw3uJvVfbO/klrmkosVvzm4CE88rFwQgMoG1EwQ/Ex+RFj8/83AM7F6G0w7vYX2XrBO0DVN6CVLMT+QVVTFOdw2QPkS1X9dSW3t8HiA/ZsJuHQodTWBWrTFtZJAkAEnHrhAEoNRrgXn9HaMHl5lXp6UJR2O2CBb1wK45vkMfVTlm3Gqv8cePxmJWBFhZYUi4vgVBw3fyNrmvpYX2IVc3OcvPLD9hOGmA5MvjNPmrTB9BadHCn7OlsQsE0Ai56KzaCTpVvJRscTuel+hLN3MWfz/4/ENeT9NmAtP80KYB0uYBsr8nupxAAFAUDGiFDl0maP7z7y4diX8v24q7XlmJSMy03ZebqgejT5cSnNoylwQlAczuA0QCEJEmeOm6wkfkSklhEJeN7Sd8F0rSoVrGhJSLwkcUWDK8dMPx+HT9bqXjtCp81Ek7xQ9Cpx3RAz0rSnD0IYlBT/QBcu/bk1cdi+37mzCwewfHAZMNdrpJq6jAOQpMMIElUwvMwz3SCUAzLjwaQ7jcPU4msEDLilMVKs2uvU5w8auV8bI7O/6BcBR7W+o0lBWFhOtbFAqiOaqukaVDvtcqLYNOyypH/PC+bY6pCHw5QSsEIOFd0fj7KASQaCymnaxTQbUYUF1H/n0ef0QP3HrWETjjNx8AABxqqFqozJM8qZ5P0iYwjVCpcloXnxmpXa5MjoyuFhg/RnQqLcTlx/XD72pWY9u+JtuCtrhAnEsCUr9kgYw0QERamTVpBHa0TLKpkK5iqPFaL+p2W4ORfTtjZN/Oym1uGgYns4FpAlefOEDY3sHBB0i12DztiISGzUkjwTQ8qhW+CdOuAZKaEkxgrj5AilW0BxlV9bvDKjvg0jF9xbY0pxmOxGxmLn6iTThB64/vJ52MFzPuIZ1L0am0AHsONOO/a+M+IGVFIeF6JDP/eTGBaX8rPbOyc7/XYzppzEoUiRCF43owzzEOhKNCGZdkBIYeHYuwbV+TUIJFNW6oriN/3lNOH4TBXKV5VVSXjFyqwql9Hq/PYtJRYEH7PeJ/L5isHMZuJ4d+lSAMqBcxVnSfy/2V8wDJe+eCAEQ+QO2IC0b2xrUnDUy5Hf4FTNEClhUfIBUqDZDhsW8qHyDelCFPsKrkkl4pctEAyREh8rE7lXg3gSmja3w4DAu/8+FQHY7GLF8oZydovWakMBTA7Wcf6dpXwLtZ78RBcR+H15ZtBQB0KAoK1yOZ3JzyZeEn7oqSAtyrKDZr/VZa7Ycj3jogT1pOJlpVIkQheog7AV7oVwlAB8PRlE1gf73uOFx4TG88e82YRL8UCwaVKdFpQePFcummAUp1+JIFEF17jhoghXZOFRkWb1/SamtKmABiIkT+Z8pcRQrNkwrBNGfYzfW5YAIjAYiw4aWcgRdMyQfITymMdKPKlK2zndt+q1iB8pNBk6ZmlRauubnXH4dBPRIaOzbY6a67HAYvD0IVPpyg05kJWnVr2TnIq3WxFlj8OznpX/z36uOze3XdyQMtx0snvD7CLCCgvjHhA8Sfq84x3Qn5PvIr7dvPPhLfP66f/BPut4nPfjRAfuCdX1kWbF1U0aHdE751ytpt4ajt+VTx+++NxJlDKvH94xIaw14VxXjou8MxqEcHzLx4hKDFVp23Slhx8n/xkljVjw8Qj9fnKyRpb3UCvjxOasPgLad1dR/l/iajAXIaI1yjwKT7Ie9NYfBETiKYwFJ8QnT25Eyj8mtw005NOW0QzhhSieMGdLVt4yeORr8CEMfYgV3x1ORjrb/dBCDZx8IxDN7NByiNeYCcVopyOYWwxzxAqmtgK3Tr4ZHy+tgdxplMgLgJjJ+khvQsxznDeuLi0YdgzIAuntqUj11a6N1E5OQEnS54DVA4En+OxUWLgcevGI2RfTth1iUjue81JjDNZM3zrWG98KcrRqNrWSKJ4B8vH43vjDpEuf+QnuW2RJKqxIZ8v+VDe8lA7aoBSnH8EszwDlKTWAJFbb7nP+ucluXuOkeBeTeBsa/caoHJwpos8LWGQO8X8gEibIiV0FPQAEHyAcoRAcht5cT4+YTDte3xL/NBSQByM5XIR+K1U2yVphsfebOWKhEi7wPklv01WQ2Qahe1r0D8/47FIWzbl/C+5GuBJbIFc5oWh2tgM+/oVtEBw6rn5DWVQ5kkqMlh8MGAgUe/d4z192cbduNnf/8cV53QH9P+tVLZpnxsfpJ184mTc7q0xoTBv+vMJMHPk6GAgTOGVApV49n3MgfCEV9O0KoQfBWBgIHZl4/C6Q/Nx/92NADQ+QAlPvtJBaDqjwov5mEnRFOWfj9xMRAQ3gOVdsZLKQyAZa3epzymzglaV64j3k/vz69h2N9n8gEichJdMi2/yEn/smkCU4WP8sKdnzplMgfD/l5keSDgD+1XA+SUB8hNEPObTI7BMmvzOA2UHRQV1ZskbYPKBKYSXGx11TR95K+T13lLLnshR4HJ12tk38549+enYvyRonDAYzeBJY7BP3PPXjMGnUsL8MfLR1nfHVFVjmGHVOD0I3rAMNJjAnMSBNiEpPIzkVEJ115NYAxei+olQIKPgFSawBSakHsvGIouZYWYcaFzoWbAvVxGqlFgIQ/XFRDHyVDA0D6DVioJfrx2MAOq0nkwRL9PtcbJ+s6rD5Ck8ZJ3zwUBiDRAhA2hrlgafYD81AJLNyo1suDsl8LgJmuA/MIPhlYdLMX4aJqiWStg2MPg+YnBrV+qc/YaqSfnmnLKKVSuqKfF+maFwUurXkAt3MjH0T2fhaGAVb7Bqx+bTQNUKEWBaZ4RJ82AkwmMv9YnDe6OJXecYZt8/vWjE6y/wz5zEOn6GtU46bMJSZhwNc+D1knfRxkdrxqgxP6JtlVO0CpNyfeP64fLxvb1NI4pk1QKmkTXJhwRE1vq95MLAwc0Ao5bIkT5mvbvas+PxhALoIL7rNcSu2eCFtuRrQm5IACRBoiwEQqqX4Zk4H/uZjNuTfzmAfICy4wq+y7c9+34avMnpw9S/k4eCNzs+jxCVtig3QQmmObCzgJQslFggD3btWoCO6Iq7lMzjMufxGAJC1UmMNX90R1Hp1QUBUX1PjKlBUHhepYViU7Qumvj9Fg7OUHLz5xqkja4SL90aICc+toUFe+Jqo8MbaJODz5ADEED5OEm8fdUJazoNNdeF3FuuYVSNYHJpi0v+xUEA1rTnls6D1kAddIA8YhClmK7pQHy7gMUr98nbs+FKDDSABE20pUJ2jTNnNYAuUU7uPH05DHY1xgRIq+AuEA0/oge6MyVF+GRL2koYL/eTpoNq88KUxQA9O1Sig27DuDUw50jpNR5gLxqgNzbOn9Eb5w8uDsaI1E8+t5aZTtqJ2hmBnTvMy9MFgYD1qDK+0p5fYYDAQNlhSGrGKocBq/LieOoAZL6Wyr4APlbEKRjxezUV8sE5sFszd+vSaP7YO6nG/GT0wdJPmrOfSkO+dUABZWfGV6LeOqQzWqFQTF5TcomMI8LS8EEFjRcNTxBxfihOkZ/RYZ8FYLmxsFP0F8UGGwDH2mAiJxEyASdqgaI+30qfjapovJr4N/fZJI0BgKGTfhh6IQfwH5Ng4oVl6o3hiFN7AofIAB486aT8dGtp7smxFTWAkvyhusmnM5lhY4ThyoPECsEq3SClr5U+U8B7hFwOsRK3yGbH4MKRwdeaROvAVIVvHUiPRog+zEry+PRWGe0+DJ50QDx78tNZwzGez8/FT894zBfeYD8msDcNEBOTtBe4O/N9ScPxKd3VAvvoW5R8t3RcQ3w0b3tmk4eXmh08s+Tc2LporJUvnJOGsu+XbxpgAyNwGX1wbAfS4UsrMm750IYPGmACBupZoIe1a8zFn+zG98ZdYjSZp0N1D5AudE3dYi+el/BuVezX0lhEL0LS+wbHI7r9J0XHIUch2eIbVOFwasmHCezUVEogP0twWbJJuTjS5zI1eD1eWCcBCBJA+QjDF6mtZyg3556CjbsPGDVt1IFDMjw9ysYMDCgRbugiwIzDPukLxf2dYMXmFQCEH8fkpHjSwsS02G/rqUoLy7w9OxcMKI3BnbrgMGVzgsOXrBxqk1W6KgBSuzHTFCq7NCA/bnURbnZU0s4P/NsTHdbNIpZ1BU+QGQCI3IRIQw+iYHkqcnH4tNvduPEQd2wnQt/zqYJzG1Vm0ntlM0HSLHC8+IDFDPNlHKTJJsHSIUXLY8Kdtn5vrCBXfUruS3+Ouk0QH5OiY9Y6yBFgWmr00sHcHKcFaLAcsQEVl5cIBT39CL06XLa6JygLxx5CF5YsgnH9u9sfcdrM728f7zJTBWxpTMFeaW40K5h8tKMYRgY3qeT6378OTqlJZL94XTBGlbpEs0zqrp3H9x8GlZu2Ysf/mUJAOAv147F4B6i4ObqBO01Ckzql80HiDRARC4SclhFeKFjcYFVXT6XM0HzkUzZ1ACJZpb4/6rrbpriJB+JmSk5ZqZVA+Sk5fEgHBUqImRU10CeJ/mm+WsjhsF7P6cORaKWQTThagQgqf2iUAARTQRaqUuuGSdOObwH/v35FvT36Myqwq/ArCtgrNPs6pyg77ngKJwwqCtO52riFQTVbWj7wpVy8FsKwwtiXTS9EJ4sXjVAshO0zrE5aGmL7UKR/JnRt2sp+nYtxV+uHYuSwiCOUdROdAsOsTRAbiYwSViTX0MSgIichBdUvKSQd4J/R/z6PKQTlVqfP7VMJml0mo8TGiD1dr6fHT2q6HWoVt3JtpesBohNkvwzx26LHGoP2PvM97dI0AAlJ2jwk2CHohAaI4lIOp3wIF/GwlAADRoBiNdcRHyaAO779lCM6NMJ3xrW09fveLwIzHwtOy+O3/x10eUBKi0M4cJjxGhJoQCuh/ePf19VeYBSNYGpkgGm8n7J8P1z8gFyNoHZhZOgQiiSjydzQkvdO3U/E5+VTtDJRIEZ9kzQJAAROQm/UomkKAClM4oiFVSDRCxHNEA8TiHgQHxQe+yyY7D7QDN6dyrB4MoOWLR+V1LHUuYBSvI6OGkW3LL8AmrzqGqSkJviL1M6nKD5B7asKCT43egUmLJQEVJos1T9avaZ16e8uADXnDjA129kvDzn/HXXaoD491ojhLoJD341QLxAzIfQq46XjGaUv2+WmbqVhgUnDZBsDtZptpRh8Jr74gc3Mxq79qp7wGNIQrJNA0Q+QEQuwq/MvNTQcSJXTGAqH6BcFIBUSRplzjo6oQH4xVlHIBQwcN6I3r6P5aTeTkdbDE9O0Nwzx26LapJw8gHitT5FQpVz7eFtyAKVlygweaJ3SgbITwpuE0hr4MXVzYtp2IsJzI0OXIJML+9fjJsvlTmT+P6lqLlhGdXTqQHi8WwCC4iaE/46MWFTdkhnJNt3N0HyR6cNQr+uZTj18B62bTxyXia5P6QBInKSAkVSumRJNddOulBFgfFDUKpJzvzgJWpINXj16mSP7CovLsBd5w9Nqh/p9AFyGmy9aIBEQSF+Z1Syt6x2F3yAuInAqfK1E3JP+edCd99kIcctj9Y95x+FtdsbMKpf56T6mApennMvpmGd4y0vALktnnpWlODHpw9CcUHQsVBnol/O7fFbk538771gKL6u24fjD40XQG6tYcHp0vCpGEJBQ6n1AYCLRh2CzXsO4sJjEosfMWt0cn0TnKAV9390/y4Y3b+LazuCP5JhrypJAhCRkxiGgRtOPRS7DzR7Tp6lQ4woSLFjKaDSAPEr3VQrPfvB6UgqDdA/fjAOv31nNe48b0ha+5HOPEBO85eTwKcSjpw1QOLf2iiwNGlXvD4XwYBhTfiFLhFol4/rn46uJYWX8+Evu9bvSWOW4QXP5pj7BPezM/UFh2X8KKOTnfy/f1w/4e/WGhVU/m2M8pJEJKKcCZp/3g+r7Ijfc8V5AXvunWQQ8wAl1QQAsa+GYc9Z1kQmMCJXuWXiEWlph5f7c8cHqMUElqX3z9EJWqEBOrZ/Fzx37di09yMUDOCSY/vg+U82Wt+1Rhi84+800W6AvdwGYF/ZGxoBKGkNkNQdr6fF19jiTcitZULxinx4bxogd0lDV3aCN3NH01C7zG+/GOm67qnUQnTCSZir4ASgUMDwpUV3KobqlVSj6VS/Dap8gHJAA0SZoIlWxdAk6co0Kg1Q1MeAmikSTtCZOd79Fw3DHd9KaJZawwTm+DuHEUi1SpbNKjoTGK8B8tMz2U/N6/Xgz6MgiUr0rYXNpOdFA+SlXQ+mwZQDKFIgXQJQa72HTsJcOZeLKhgI+BJqvOStckOXeTqldgz7cxKOpFZEOh3khAD06KOPon///iguLsbYsWOxaNEix/3/8Y9/4IgjjkBxcTGOPvpovP7668L2q666yioiyP5NnDixNU+B0JBqfZ50IfoAxR97JzV0a+LFBJbJa8UfKdMyqlIDxHyAFBOoLADxP+d9bzqX6kuROPHzMw9HRUkBbqoeDMD7fRBMcWmqpZcO5EnHS3+8vBdeNEmpBlDI/LT6MHQqLcCPNUWGedKV17S1NEBOl7hCMIEZvjQyOs2cH9JVAFYWpGw+QDlgAsu6ADR37lxMnToV06dPx5IlSzB8+HBMmDAB27ZtU+7/3//+F5deeimuueYafPbZZ7jgggtwwQUXYMWKFcJ+EydOxNatW61/f/vb3zJxOoSEzn6daXjnWVUeoFzBWnFl8FLxtyXZAT/ZS+nkA6SyoMhaBbHYbuIeD0jSd21AtzJ8dscZuKn6MFv/nC5NUNOPrAtA0t9+w+B1ODVzTN9OKAgaOHGwPtdMMvTtWoolvzpD6zck+PSlywSWllb8UV4iZgvXJTpUkY7SQ255gLwiR6TJTZEJDMDMmTNx3XXXYfLkyRgyZAhmz56N0tJSzJkzR7n/b3/7W0ycOBE333wzjjzySNxzzz045phj8Pvf/17Yr6ioCFVVVda/zp07Z+J0CIlc8QEqURReHDMgHsnQvWNRRvvi6BTcsu3yFmfMk9I8iSj7k4Y2klGmGQq1OOCcCNFuAuNMm2kQgAA5M7dXE5i6H9nOrmAvHpseHyCnZ/ifPzgey++cIGgy0oVnp/S0+QClpRlf8NctGotJpTD8JR9MhmSef2Vf5CiwHAyDz6oAFA6HsXjxYlRXV1vfBQIBVFdXY8GCBcrfLFiwQNgfACZMmGDbf/78+ejRowcOP/xw/PCHP8TOnTu1/WhqakJ9fb3wj0gPQlbZLK6GWcVrIGEO69ahCEunnYEPf3FaRvty6Zi+AIARXP2g3i0h7hOHVgEARvbtjE9ur8ZTk8dktG/Jkow50e15UDUZkTzX+Sb2HAhbn/t0LlXv5BM/UWAM3gTWWiYUz9icoN1/4uVOuqU20BXezBTpuux2w03rw4fBNzRFxcguNx8gvgBp0v58fHvJn7+cmTsXNUBZjQLbsWMHotEoKisrhe8rKyvx1VdfKX9TW1ur3L+2ttb6e+LEibjwwgsxYMAArF27Fr/85S9x1llnYcGCBQgG7S/mjBkzcNddd6XhjAgZ3jG1a4fk/DKcuGxsX/xl4QZ8Z9QhjvtVVRRbn/mXulOSviKpcMaQSrwz9RT06ZLI6/P21JNRV98kaC4ypZlKxySdjAZIN0A7hcHLkUX8KnfLnoPWZz8J+bziNBnqTHHZJhkTmN8osFwkXYJnNk6T7/uBcEQKJ3f+bTr8d9LlBG0LyZf64zcTemvQLsPgL7nkEuvz0UcfjWHDhuHQQw/F/PnzMX78eNv+t912G6ZOnWr9XV9fjz59+mSkr+2dUDCA+T8/FVHTRFlR+h+36ecehXOH98LIvp0c96ssTwhAmaz7pWOQVIG5tDCEAd3a7utoJuEFpBugTYdEiM0OUWCb9zRan1vjDjunL0h8zikBSOqzJ7OIJx+g7L9DmSDbGrwD4agoALnsnw4naP6UUxkrXX2AojGYppnVa5zVN7Vbt24IBoOoq6sTvq+rq0NVVZXyN1VVVb72B4CBAweiW7duWLNmjXJ7UVERysvLhX9E+ujfrQyHdu/gvmMSFIYCOG5gV9fil1WcAJTJpIf5QjIaIJ0W4diWLLNKDZCDD9AZQ+Kp+YcfUpFx3w3+XHJJAJIFlXRpgHLxFWoNfUK25bwD4aiQSsQNMRN0GjRAaTIfx6PA7G1lOxIsq29qYWEhRo0ahZqaGuu7WCyGmpoajBs3TvmbcePGCfsDwNtvv63dHwA2bdqEnTt3omfP5KsoE20b3gR2MJz9/BO5RDoG+WQmH3l8fu/np+LX3xmGi0fHta8qvyK5gjq/evzl2UdixoVH48nJY0T/gyT65hcxI3XuSAfJmMAOr3JfAOaPBii7x29oioiaUh8msLTkAUrh/AVfIk1fsu0HlHWd+9SpU3HllVdi9OjRGDNmDGbNmoWGhgZMnjwZAHDFFVegd+/emDFjBgDgxhtvxCmnnIKHH34Y55xzDp5//nl8+umn+NOf/gQA2L9/P+666y5cdNFFqKqqwtq1a3HLLbdg0KBBmDBhQtbOk8guvFPmjv1NWexJ7pGOMd5rlt6AkTBtyZPxgG5lgg+UygTmlAixY3GB5WCeaXJVA5RMHqALR/ZG/cFmjO7fWbtPLmpRW8XsmZVA+AR2E5hzf/ityfsAce2lEgUmCVKqxJh5LwBNmjQJ27dvx7Rp01BbW4sRI0Zg3rx5lqPzhg0bEOBC/44//nj89a9/xa9+9Sv88pe/xODBg/Hyyy9j6NB4QchgMIhly5bh6aefxp49e9CrVy+ceeaZuOeee1BUlNlwZyI32b4v7L5THpEWZ2uPKqDCUACNzfFBz00boRKqnPIAtTZOR8pZAUj624sGKBAwcPWJA5z3yT35p1VMYNk6z5KCIA42R3FYZQcpT5f3NpJNBpku7amcwdo07cJOtk1gWReAAGDKlCmYMmWKctv8+fNt3333u9/Fd7/7XeX+JSUlePPNN9PZPaKd0Rr5SdoyZw6pwjUnDsBwLizfL14nn16dSvC/7Q0A3IUXVTZnJw2QjkzISHy/enLm1myTlBO0B7KZ0iKTZMtB919TTsAT//kffnz6YDEZp8vvhCSGadEAJdUEANhMd/yry4oHZ1sDlDtLFYJoZZ67ZiwmHFWJX0z0XoE6HwgEDNzxrSE4b3ivpNtwywP0yKUjcc6wnvjBKYda33UqdRZELxnTB+cN74WZFw+3vpM1QJmcoJwOtXVvIgS/R3kuCUBip9MVAdmxOCfWzq1OtsS8wyo74sHvDEefLqW2qupeSUddv1ReL8FMaooaXZaYNtsCUH48xQQB4MTB3dKenp+I46YBOm94L5w3vBfmrUjk63IzvRWFgnjk0pEAgKl//1y5TyYX6E6TD5/TpKgVchAlizwHpit/zyVj+uLdVdtx2uHd09JerpILiq5kNTLJ9t2Pz5FzO+Lf/BqppDCI/U0RNJEARBBEW8drXTVeOOjeIXXfo1yLRiopCOL0I3pgzIAuGNa7ItvdsTtBp0kAKi4I4pmr20aW8lTIdh4guQ+uJjC+9FCSfRd+looJTHrWeA1QcUF8HCAfIIIg2jxeS2HwGZrT4XztRaORyUievl1KURAM4O//p0/LkUlsTtDZn8/bFLno7O2VtJjAUji+vDjhhwhWISDbJrDc0dUSBNFmeOTSkcIA69UJOt0CUK7BlzfJBWxO0G15Rndh4tAqVJQU4Iwhle47eyTdwvPs7x+DYMDAby8ZkVx/XLojRoxlOQxeGB9MQQNUGMoNHyASgAiC8M15w3vhq3smJr7wGgYfTK8AlCth8JeOiSdv/OkZh2WmMx6RJ7BrWsLbzz5anzm/rVJeXIBPf1WNP10+Km1tpvvxmji0J766ZyLOH9Hb1+9YZOGRPVu/SkGraYC4z2whlG0BiExgBEEkBZ/vxmstMEED1MF7tNRN1YMx653V+Gm1KGDkikLj/337aNx29pEoL86tFAvy5TmqVwWW3XkmOrZCXb5cIJdyMOlIpo8f3HIamqMxlBY637d0vA7J5h2Skd9NQQPUYovNtg9Q7j8tBEHkPDGP41iyJrAbxw/Gf245DT8ZP0j43osGKBNKIsMwckr4mXBU3Ax03UkDbdvKiwtywrm3LXDl8f0BACcM6prVfhQEA67CT7rgn41UNKzyMyb4AJEGiCCItk5VeTFq6xsxYag3vwt+QPUjABmGgT5dShXfe24iaQwjPnifNLjthHz/7tJj8HXdPgzJgMmkPXPJsX1wdO8KDOrROsWc083ANBedTtfrZZpALMZrgEgAIgiijfPGjSfhy631GHeotxVyOZdAr1MaMnJnwgdo4S/HY932BowdmF0tgB8KQwEMzYEw/LaOYRht6jpWVRTj31NORHlJmqb2NL5eMYUGqInC4AmCaKt0LivE8YO8J5fs2qEIf7vuOJQVBdMSkXR4VceU23CjR8di9OiYO9mdCcKJow9Jn8CWzii4XIwCIwGIIIiM4lVb5IUTBnXDw98djsGVetU/ebsQRHKkM1WFEAVGJjCCIIjUuWjUIdnuAkG0K/585WjU1Tel1ffJFDRAJAARBEEQBJFjjD8yfckkGbwJjJXECUejaT+OHygMniCIdk2HPKlcThC5DO8EfWj3Mowb2BV9OtsjOzMJjQwEQbRL7jx3CBZv2IOJR7W/rMcE0ZYwIeYBunxcf1w+rn+2umNBAhBBEO2Sq04YgKtOyHYvCIIIBgyEciVtOwcJQARBEARBpJ3rTx6Ij9bswHnDe6GxOYo3V9bi/BG9st0tC8PkXbMJAEB9fT0qKiqwd+9elJdTJlWCIAiCaAv4mb/JCZogCIIgiLyDBCCCIAiCIPIOEoAIgiAIgsg7SAAiCIIgCCLvIAGIIAiCIIi8gwQggiAIgiDyDhKACIIgCILIO0gAIgiCIAgi7yABiCAIgiCIvIMEIIIgCIIg8g4SgAiCIAiCyDtIACIIgiAIIu8gAYggCIIgiLyDBCCCIAiCIPKOULY7kIuYpgkAqK+vz3JPCIIgCILwCpu32TzuBAlACvbt2wcA6NOnT5Z7QhAEQRCEX/bt24eKigrHfQzTi5iUZ8RiMWzZsgUdO3aEYRhpbbu+vh59+vTBxo0bUV5enta2iQR0nTMDXefMQdc6M9B1zgytdZ1N08S+ffvQq1cvBALOXj6kAVIQCARwyCGHtOoxysvL6eXKAHSdMwNd58xB1zoz0HXODK1xnd00PwxygiYIgiAIIu8gAYggCIIgiLyDBKAMU1RUhOnTp6OoqCjbXWnX0HXODHSdMwdd68xA1zkz5MJ1JidogiAIgiDyDtIAEQRBEASRd5AARBAEQRBE3kECEEEQBEEQeQcJQARBEARB5B0kAGWQRx99FP3790dxcTHGjh2LRYsWZbtLbYoPPvgA5557Lnr16gXDMPDyyy8L203TxLRp09CzZ0+UlJSguroaq1evFvbZtWsXLrvsMpSXl6NTp0645pprsH///gyeRe4zY8YMHHvssejYsSN69OiBCy64AKtWrRL2aWxsxI9+9CN07doVHTp0wEUXXYS6ujphnw0bNuCcc85BaWkpevTogZtvvhmRSCSTp5LzPPbYYxg2bJiVDG7cuHF44403rO10nVuH+++/H4Zh4KabbrK+o2udOnfeeScMwxD+HXHEEdb2nLvGJpERnn/+ebOwsNCcM2eOuXLlSvO6664zO3XqZNbV1WW7a22G119/3bz99tvNF1980QRgvvTSS8L2+++/36yoqDBffvll8/PPPzfPO+88c8CAAebBgwetfSZOnGgOHz7c/Pjjj83//Oc/5qBBg8xLL700w2eS20yYMMF88sknzRUrVphLly41zz77bLNv377m/v37rX1+8IMfmH369DFramrMTz/91DzuuOPM448/3toeiUTMoUOHmtXV1eZnn31mvv7662a3bt3M2267LRunlLO88sor5muvvWZ+/fXX5qpVq8xf/vKXZkFBgblixQrTNOk6twaLFi0y+/fvbw4bNsy88cYbre/pWqfO9OnTzaOOOsrcunWr9W/79u3W9ly7xiQAZYgxY8aYP/rRj6y/o9Go2atXL3PGjBlZ7FXbRRaAYrGYWVVVZf7617+2vtuzZ49ZVFRk/u1vfzNN0zS/+OILE4D5ySefWPu88cYbpmEY5ubNmzPW97bGtm3bTADm+++/b5pm/LoWFBSY//jHP6x9vvzySxOAuWDBAtM048JqIBAwa2trrX0ee+wxs7y83GxqasrsCbQxOnfubD7xxBN0nVuBffv2mYMHDzbffvtt85RTTrEEILrW6WH69Onm8OHDldty8RqTCSwDhMNhLF68GNXV1dZ3gUAA1dXVWLBgQRZ71n5Yt24damtrhWtcUVGBsWPHWtd4wYIF6NSpE0aPHm3tU11djUAggIULF2a8z22FvXv3AgC6dOkCAFi8eDGam5uFa33EEUegb9++wrU++uijUVlZae0zYcIE1NfXY+XKlRnsfdshGo3i+eefR0NDA8aNG0fXuRX40Y9+hHPOOUe4pgA90+lk9erV6NWrFwYOHIjLLrsMGzZsAJCb15iKoWaAHTt2IBqNCjcVACorK/HVV19lqVfti9raWgBQXmO2rba2Fj169BC2h0IhdOnSxdqHEInFYrjppptwwgknYOjQoQDi17GwsBCdOnUS9pWvtepesG1EguXLl2PcuHFobGxEhw4d8NJLL2HIkCFYunQpXec08vzzz2PJkiX45JNPbNvomU4PY8eOxVNPPYXDDz8cW7duxV133YWTTjoJK1asyMlrTAIQQRBafvSjH2HFihX48MMPs92Vdsvhhx+OpUuXYu/evfjnP/+JK6+8Eu+//362u9Wu2LhxI2688Ua8/fbbKC4uznZ32i1nnXWW9XnYsGEYO3Ys+vXrh7///e8oKSnJYs/UkAksA3Tr1g3BYNDm7V5XV4eqqqos9ap9wa6j0zWuqqrCtm3bhO2RSAS7du2i+6BgypQpePXVV/Hee+/hkEMOsb6vqqpCOBzGnj17hP3la626F2wbkaCwsBCDBg3CqFGjMGPGDAwfPhy//e1v6TqnkcWLF2Pbtm045phjEAqFEAqF8P777+ORRx5BKBRCZWUlXetWoFOnTjjssMOwZs2anHyeSQDKAIWFhRg1ahRqamqs72KxGGpqajBu3Lgs9qz9MGDAAFRVVQnXuL6+HgsXLrSu8bhx47Bnzx4sXrzY2ufdd99FLBbD2LFjM97nXMU0TUyZMgUvvfQS3n33XQwYMEDYPmrUKBQUFAjXetWqVdiwYYNwrZcvXy4InG+//TbKy8sxZMiQzJxIGyUWi6GpqYmucxoZP348li9fjqVLl1r/Ro8ejcsuu8z6TNc6/ezfvx9r165Fz549c/N5TrtbNaHk+eefN4uKisynnnrK/OKLL8zrr7/e7NSpk+DtTjizb98+87PPPjM/++wzE4A5c+ZM87PPPjO/+eYb0zTjYfCdOnUy//Wvf5nLli0zzz//fGUY/MiRI82FCxeaH374oTl48GAKg5f44Q9/aFZUVJjz588XwlkPHDhg7fODH/zA7Nu3r/nuu++an376qTlu3Dhz3Lhx1nYWznrmmWeaS5cuNefNm2d2796dQoYlbr31VvP99983161bZy5btsy89dZbTcMwzLfeess0TbrOrQkfBWaadK3Twc9+9jNz/vz55rp168yPPvrIrK6uNrt162Zu27bNNM3cu8YkAGWQ3/3ud2bfvn3NwsJCc8yYMebHH3+c7S61Kd577z0TgO3flVdeaZpmPBT+jjvuMCsrK82ioiJz/Pjx5qpVq4Q2du7caV566aVmhw4dzPLycnPy5Mnmvn37snA2uYvqGgMwn3zySWufgwcPmjfccIPZuXNns7S01Pz2t79tbt26VWhn/fr15llnnWWWlJSY3bp1M3/2s5+Zzc3NGT6b3Obqq682+/XrZxYWFprdu3c3x48fbwk/pknXuTWRBSC61qkzadIks2fPnmZhYaHZu3dvc9KkSeaaNWus7bl2jQ3TNM3065UIgiAIgiByF/IBIgiCIAgi7yABiCAIgiCIvIMEIIIgCIIg8g4SgAiCIAiCyDtIACIIgiAIIu8gAYggCIIgiLyDBCCCIAiCIPIOEoAIgiAIgsg7SAAiCILwwPz582EYhq2YI0EQbRMSgAiCIAiCyDtIACIIgiAIIu8gAYggiDZBLBbDjBkzMGDAAJSUlGD48OH45z//CSBhnnrttdcwbNgwFBcX47jjjsOKFSuENl544QUcddRRKCoqQv/+/fHwww8L25uamvCLX/wCffr0QVFREQYNGoQ///nPwj6LFy/G6NGjUVpaiuOPPx6rVq1q3RMnCKJVIAGIIIg2wYwZM/DMM89g9uzZWLlyJX7605/i+9//Pt5//31rn5tvvhkPP/wwPvnkE3Tv3h3nnnsumpubAcQFl4svvhiXXHIJli9fjjvvvBN33HEHnnrqKev3V1xxBf72t7/hkUcewZdffok//vGP6NChg9CP22+/HQ8//DA+/fRThEIhXH311Rk5f4Ig0gtVgycIIudpampCly5d8M4772DcuHHW99deey0OHDiA66+/Hqeddhqef/55TJo06f+3b/8gbUQBHMe/kmoMqIQkEoJ/BzEkoJGAU4Qg6uTiFAcHxdFFRHE4wSE3JLOIruLoKnGIDi6Hji4SSFTQMaJBEJ0MHUqPhkJb2tqY3u8DDx7cu3fv3fTj/QHg8fGR7u5u9vb2SKVSzM3NcX9/Tz6ft99fX18nl8txeXlJsVgkHA5zfHzM5OTkd2M4PT1lfHyck5MTJiYmADg6OmJ6eprX11daW1vf+S+IyN+kFSAR+fCurq54eXlhamqKtrY2u+zv73N9fW23+zYc+Xw+wuEwhUIBgEKhQCKRqOk3kUhQKpV4e3vj4uICl8tFMpn84ViGh4fteigUAqBcLv/xHEXk3/pU7wGIiPzM8/MzALlcjq6urppnbre7JgT9Lo/H80vtmpub7XpTUxPw5XySiDQWrQCJyIcXjUZxu93c3d0xMDBQU3p6eux25+fndr1SqVAsFolEIgBEIhEsy6rp17IsBgcHcblcDA0NUa1Wa84Uicj/SytAIvLhtbe3s7a2xsrKCtVqlbGxMZ6enrAsi46ODvr6+gBIp9P4/X6CwSAbGxsEAgFmZmYAWF1dZXR0FNM0mZ2d5ezsjO3tbXZ2dgDo7+9nfn6excVFtra2iMVi3N7eUi6XSaVS9Zq6iLwTBSARaQimadLZ2Ukmk+Hm5gav10s8HscwDHsLKpvNsry8TKlUYmRkhMPDQ1paWgCIx+McHBywubmJaZqEQiHS6TQLCwv2N3Z3dzEMg6WlJR4eHujt7cUwjHpMV0TemW6BiUjD+3pDq1Kp4PV66z0cEWkAOgMkIiIijqMAJCIiIo6jLTARERFxHK0AiYiIiOMoAImIiIjjKACJiIiI4ygAiYiIiOMoAImIiIjjKACJiIiI4ygAiYiIiOMoAImIiIjjfAaM9cJBTyK4TQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bm.train(flat_input_data, len_x, len_y, epochs = epochs, lr = lr, lr_decay = 0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac264c95",
   "metadata": {},
   "source": [
    "Normalised MSE values changing with an increasing number of epochs for a two digit problem"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4061c0e",
   "metadata": {},
   "source": [
    "## QBM on the Dynex Neuromorphic Platform"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09f0e1ae",
   "metadata": {},
   "source": [
    "In our QBM, the classical sampling steps are being replaced by the output of the Dynex Neuromorphic sampler:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "7d828ebc",
   "metadata": {},
   "outputs": [],
   "source": [
    "bm = QRBM.MSQRBM.MSQRBM(n_visible=len_x, n_hidden=n_hidden, qpu=qpu)\n",
    "bm.image_height = image_height\n",
    "bm.tqdm = tqdm\n",
    "bm.result_picture_tab = result_picture_tab"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bdf76901",
   "metadata": {},
   "source": [
    "We expect the QBM to evolve significantly faster to lower MSE values and therefore reduce the training epochs by 96% to just 20 training iterations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "0f391fa0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "16573b07812a475cb279c2cf98f1ff1e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/10 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Better model found at epoch 0 mse= 0.14923469387755103\n",
      "lr =  0.09000000000000001\n",
      "Better model found at epoch 1 mse= 0.09948979591836735\n",
      "Better model found at epoch 2 mse= 0.06505102040816327\n",
      "lr =  0.08100000000000002\n",
      "lr =  0.07290000000000002\n",
      "lr =  0.06561000000000002\n",
      "lr =  0.05904900000000002\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bm.train(flat_input_data, len_x, len_y, epochs = 10, lr = lr, lr_decay = 0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "730baf2e",
   "metadata": {},
   "source": [
    "## Performance Comparison RBM vs QBM "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b33c523",
   "metadata": {},
   "source": [
    "The QBM evolves much faster to an attractive Mean Squared Error (MSE) than the traditional RBM, which means a significant lower amount of training iterations is required. In addition is the achieved MSE much lower, meaning the QBM created models have higher accuracy. This finding is in line with the results from the papers referenced. However, [1] demonstrated that the process of embedding Boltzmann machines in larger quantum annealer architectures is problematic when huge weights and biases are needed to emulate the Boltzmann machine’s logical nodes using chains and clusters of physical qubits because of the limited number of qubits availabe. The Dynex Neuromorphic platform provides a more scalable alternative and can used to train models with millions of variables. Especially when real-world models are to be trained, the number of training iterations and accuracy are important."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ebf10556",
   "metadata": {},
   "source": [
    "References:\n",
    "\n",
    "[1] D. Crawford, A. Levit, N. Ghadermarzy, J.S. Oberoi, P. Ronagh, Reinforcement Learning Using Quantum Boltzmann\n",
    "Machines, arXiv: 1612.05695 (2016).\n",
    "\n",
    "[2] K. Kurowski, M. Slysz, M. Subocz, R. Rozycki, Applying a Quantum Annealing Based Restricted Boltzmann Machine\n",
    "for MNIST Handwritten Digit Classification, CMST, Volume 27 (3) 2021, 99-107\n",
    "\n",
    "[3] https://en.wikipedia.org/wiki/Restricted_Boltzmann_machine\n",
    "\n",
    "[4] K. Kurowski, J. Weglarz, M. Subocz, R. Rozycki, G. Waligóra, Hybrid Quantum Annealing Heuristic Method for\n",
    "Solving Job Shop Scheduling Problem, [In:] Computational Science – ICCS 2020. Lecture Notes in Computer Science 12142, Eds. V.V. Krzhizhanovskaya, G. Závodszky, M.H. Lees, J.J. Dongarra, P.M.A. Sloot, S. Brissos, J. Teixeira, Springer, Cham (2020).\n",
    "\n",
    "[5] J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, S. Lloyd, Quantum machine learning, Nature 549, 195–202 (2017).\n",
    "\n",
    "[6] S. Lloyd, M. Mohseni, P. Rebentrost, Quantum algorithms for supervised and unsupervised machine learning, arXiv: 1307.0411 (2013).\n",
    "\n",
    "[7] M. Benedetti, J. Realpe-Gomez, A. Perdomo-Ortiz, Quantum-assisted helmholtz machines: a quantum-classical deep\n",
    "learning framework for industrial datasets in near-term devices, arXiv: 1708.09784 (2017)."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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}