challenge-3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## IBM Quantum Challenge Fall 2021\n",
    "\n",
    "# Challenge 3: Classify images with quantum machine learning\n",
    "\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "    \n",
    "We recommend that you switch to **light** workspace theme under the Account menu in the upper right corner for optimal experience."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "Machine learning is a technology that has attracted a great deal of attention due to its high performance and versatility. In fact, it has been put to practical use in many industries with the recent development of algorithms and the increase of computational resources. A typical example is computer vision, where machine learning is now able to classify images with the same or better accuracy than humans. For example, the ability to automatically classify clothing images has made online shopping for clothes more convenient.\n",
    "\n",
    "The application of quantum computation to machine learning has recently been shown to have the potential for even greater capabilities. Various algorithms have been proposed for quantum machine learning, such as the quantum support vector machine (QSVM) and quantum generative adversarial networks (QGANs). In this challenge, you will use QSVM to tackle the clothing image classification task.\n",
    "\n",
    "QSVM is a quantum version of the support vector machine (SVM), a classical machine learning algorithm. There are various approaches to QSVM, some aim to accelerate computation assuming fault-tolerant quantum computers, while others aim to achieve higher expressive power assuming noisy, near-term devices. In this challenge, we will focus on the latter, and the details will be explained later.\n",
    "\n",
    "For this implementation of QSVM, you will be able to make choices on how you want to compose your quantum model, in particular focusing on the quantum feature map. This is motivated by the tradeoff that a more complex feature map would have greater representation power but be more susceptible to noise, which could be especially critical when using noisy, near-term devices.\n",
    "\n",
    "Many of the concepts that appear in this challenge are explained in the 2021 Qiskit Global Summer School (QGSS). The materials and lecture videos are available, and it is recommended that you study them as well. Refer to the links in each part for the corresponding lectures.\n",
    "\n",
    "<center><img src=\"./resources/ecommerce.jpg\" width=\"640\" /></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Challenge\n",
    "<div class=\"alert alert-block alert-success\">\n",
    "\n",
    "**Goal**\n",
    "\n",
    "Implement a QSVM model for multiclass classification and predict labels accurately. \n",
    "    \n",
    "**Plan**\n",
    "\n",
    "First, you will learn how to construct QSVM for binary classification of a simple dataset. Then apply what you have learned to a more complex problem, 3-class classification of a different dataset.\n",
    "\n",
    "**1. Tutorial - QSVM for binary classification of MNIST:** familiarize yourself with a typical workflow for QSVM and find the best combination of dimentions/feature maps.\n",
    "\n",
    "**2. Challenge - QSVM for 3-class classification of Fashion-MNIST:** implement a 3-class classifier using binary QSVM classifers. Perform similar investigation as in the first part to find the best combination of dimentions/feature maps. Achieve better accuracy with smaller feature map circuits.\n",
    "\n",
    "</div>\n",
    "\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "\n",
    "Before you begin, we recommend watching the [**Qiskit Machine Learning Demo Session with Anton Dekusar**](https://youtu.be/claoY57eVIc?t=1814) and check out the corresponding [**demo notebook**](https://github.com/qiskit-community/qiskit-application-modules-demo-sessions/tree/main/qiskit-machine-learning) to learn how to do classifications using QSVM.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# General imports\n",
    "import os\n",
    "import gzip\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from pylab import cm\n",
    "import warnings\n",
    "\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "# scikit-learn imports\n",
    "from sklearn import datasets\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler, MinMaxScaler\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.svm import SVC\n",
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "# Qiskit imports\n",
    "from qiskit import Aer, execute\n",
    "from qiskit.circuit import QuantumCircuit, Parameter, ParameterVector\n",
    "from qiskit.circuit.library import PauliFeatureMap, ZFeatureMap, ZZFeatureMap\n",
    "from qiskit.circuit.library import TwoLocal, NLocal, RealAmplitudes, EfficientSU2\n",
    "from qiskit.circuit.library import HGate, RXGate, RYGate, RZGate, CXGate, CRXGate, CRZGate\n",
    "from qiskit_machine_learning.kernels import QuantumKernel"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 1: Tutorial - QSVM for binary classification of MNIST\n",
    "\n",
    "In this part, you will apply QSVM to the binary classification of handwritten numbers 4 and 9. Through this tutorial, you will learn the workflow of applying QSVM to binary classification. Find better combinations and achieve higher accuracy.\n",
    "\n",
    "Related QGSS material:\n",
    "- [**Lab 3**](https://www.youtube.com/watch?v=GVhCOTzAkCM&list=PLOFEBzvs-VvqJwybFxkTiDzhf5E11p8BI&index=17)\n",
    "\n",
    "### 1. Data preparation\n",
    "\n",
    "The data we are going to work with at the beginning is a small subset of the well known handwritten digits dataset, which is available publicly. We will be aiming to differentiate between '4' and '9'. \n",
    "\n",
    "There are a total of 100 data in the dataset. Of these, eighty are labeled training data, and the remaining twenty are unlabeled test data. Each data is a 28x28 image of a digit, collapsed into an array, where each element is an integer between 0 (white) and 255 (black). To use the dataset for quantum classification, we need to scale the range to between -1 and 1, and reduce the dimensionality to the number of qubits we want to use (here N_DIM=5)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Load MNIST dataset\n",
    "DATA_PATH = './resources/ch3_part1.npz'\n",
    "data = np.load(DATA_PATH)\n",
    "\n",
    "sample_train = data['sample_train']\n",
    "labels_train = data['labels_train']\n",
    "sample_test = data['sample_test']\n",
    "\n",
    "# Split train data\n",
    "sample_train, sample_val, labels_train, labels_val = train_test_split(\n",
    "    sample_train, labels_train, test_size=0.2, random_state=42)\n",
    "\n",
    "# Visualize samples\n",
    "fig = plt.figure()\n",
    "\n",
    "LABELS = [4, 9]\n",
    "num_labels = len(LABELS)\n",
    "for i in range(num_labels):\n",
    "    ax = fig.add_subplot(1, num_labels, i+1)\n",
    "    img = sample_train[labels_train==LABELS[i]][0].reshape((28, 28))\n",
    "    ax.imshow(img, cmap=\"Greys\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Standardize\n",
    "ss = StandardScaler()\n",
    "sample_train = ss.fit_transform(sample_train)\n",
    "sample_val = ss.transform(sample_val)\n",
    "sample_test = ss.transform(sample_test)\n",
    "\n",
    "# Reduce dimensions\n",
    "N_DIM = 5\n",
    "pca = PCA(n_components=N_DIM)\n",
    "sample_train = pca.fit_transform(sample_train)\n",
    "sample_val = pca.transform(sample_val)\n",
    "sample_test = pca.transform(sample_test)\n",
    "\n",
    "# Normalize\n",
    "mms = MinMaxScaler((-1, 1))\n",
    "sample_train = mms.fit_transform(sample_train)\n",
    "sample_val = mms.transform(sample_val)\n",
    "sample_test = mms.transform(sample_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Data Encoding\n",
    "\n",
    "We will take the classical data and encode it to the quantum state space using a quantum feature map. The choice of which feature map to use is important and may depend on the given dataset we want to classify. Here we'll look at the feature maps available in Qiskit, before selecting and customising one to encode our data.\n",
    "\n",
    "### 2.1 Quantum Feature Maps\n",
    "As the name suggests, a quantum feature map $\\phi(\\mathbf{x})$ is a map from the classical feature vector $\\mathbf{x}$ to the quantum state $|\\Phi(\\mathbf{x})\\rangle\\langle\\Phi(\\mathbf{x})|$. This is facilitated by applying the unitary operation $\\mathcal{U}_{\\Phi(\\mathbf{x})}$ on the initial state $|0\\rangle^{n}$ where _n_ is the number of qubits being used for encoding.\n",
    "\n",
    "The following feature maps currently available in Qiskit are those introduced in [**_Havlicek et al_.  Nature **567**, 209-212 (2019)**](https://www.nature.com/articles/s41586-019-0980-2), in particular the `ZZFeatureMap` is conjectured to be hard to simulate classically and can be implemented as short-depth circuits on near-term quantum devices.\n",
    "\n",
    "- [**`PauliFeatureMap`**](https://qiskit.org/documentation/stubs/qiskit.circuit.library.PauliFeatureMap.html)\n",
    "- [**`ZZFeatureMap`**](https://qiskit.org/documentation/stubs/qiskit.circuit.library.ZFeatureMap.html)\n",
    "- [**`ZFeatureMap`**](https://qiskit.org/documentation/stubs/qiskit.circuit.library.ZZFeatureMap.html)\n",
    "\n",
    "The `PauliFeatureMap` is defined as:\n",
    "\n",
    "```python\n",
    "PauliFeatureMap(feature_dimension=None, reps=2, \n",
    "                entanglement='full', paulis=None, \n",
    "                data_map_func=None, parameter_prefix='x',\n",
    "                insert_barriers=False)\n",
    "```\n",
    "\n",
    "and describes the unitary operator of depth $d$:\n",
    "\n",
    "$$ \\mathcal{U}_{\\Phi(\\mathbf{x})}=\\prod_d U_{\\Phi(\\mathbf{x})}H^{\\otimes n},\\ U_{\\Phi(\\mathbf{x})}=\\exp\\left(i\\sum_{S\\subseteq[n]}\\phi_S(\\mathbf{x})\\prod_{k\\in S} P_i\\right), $$\n",
    "\n",
    "which contains layers of Hadamard gates interleaved with entangling blocks, $U_{\\Phi(\\mathbf{x})}$, encoding the classical data as shown in circuit diagram below for $d=2$.\n",
    "\n",
    "<center><img src=\"./resources/featuremap.png\" width=\"1000\" /></center>\n",
    "\n",
    "Within the entangling blocks, $U_{\\Phi(\\mathbf{x})}$: $P_i \\in \\{ I, X, Y, Z \\}$ denotes the Pauli matrices, the index $S$ describes connectivities between different qubits or datapoints: $S \\in \\{\\binom{n}{k}\\ combinations,\\ k = 1,... n \\}$, and by default the data mapping function $\\phi_S(\\mathbf{x})$ is \n",
    "$$\\phi_S:\\mathbf{x}\\mapsto \\Bigg\\{\\begin{array}{ll}\n",
    "    x_i & \\mbox{if}\\ S=\\{i\\} \\\\\n",
    "        (\\pi-x_i)(\\pi-x_j) & \\mbox{if}\\ S=\\{i,j\\}\n",
    "    \\end{array}$$\n",
    "\n",
    "when $k = 1, P_0 = Z$, this is the `ZFeatureMap`: \n",
    "$$\\mathcal{U}_{\\Phi(\\mathbf{x})} = \\left( \\exp\\left(i\\sum_j \\phi_{\\{j\\}}(\\mathbf{x}) \\, Z_j\\right) \\, H^{\\otimes n} \\right)^d.$$\n",
    "\n",
    "which is defined as:\n",
    "```python\n",
    "ZFeatureMap(feature_dimension, reps=2, \n",
    "            data_map_func=None, insert_barriers=False)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.8/site-packages/sympy/core/expr.py:2451: SymPyDeprecationWarning: \n",
      "\n",
      "expr_free_symbols method has been deprecated since SymPy 1.9. See\n",
      "https://github.com/sympy/sympy/issues/21494 for more info.\n",
      "\n",
      "  SymPyDeprecationWarning(feature=\"expr_free_symbols method\",\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 327.397x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 3 features, depth 2\n",
    "map_z = ZFeatureMap(feature_dimension=3, reps=2)\n",
    "map_z.decompose().draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note the lack of entanglement in this feature map, this means that this feature map is simple to simulate classically and will not provide quantum advantage.\n",
    "\n",
    "and when $k = 2, P_0 = Z, P_1 = ZZ$, this is the `ZZFeatureMap`: \n",
    "$$\\mathcal{U}_{\\Phi(\\mathbf{x})} = \\left( \\exp\\left(i\\sum_{jk} \\phi_{\\{j,k\\}}(\\mathbf{x}) \\, Z_j \\otimes Z_k\\right) \\, \\exp\\left(i\\sum_j \\phi_{\\{j\\}}(\\mathbf{x}) \\, Z_j\\right) \\, H^{\\otimes n} \\right)^d.$$ \n",
    "\n",
    "which is defined as:\n",
    "```python\n",
    "ZZFeatureMap(feature_dimension, reps=2, \n",
    "             entanglement='full', data_map_func=None, \n",
    "             insert_barriers=False)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 808.997x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 3 features, depth 1, linear entanglement\n",
    "map_zz = ZZFeatureMap(feature_dimension=3, reps=1, entanglement='linear')\n",
    "map_zz.decompose().draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that there is entanglement in the feature map, we can define the entanglement map:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mIyf2kdTugSLt5Z21pPe2tKxmqlMNHrkdTubAhjQ4cBwyTsGZXGN5wzrGfabioowfu8YWiIiIWIa+lq9TJe1YRjeIZ8f+deRePMf5C2eoFlJ0yqJ9h7eQm3eW7JxjpB/bVWR5zdAwsrIzOH76MFU9PD7QqlYxZkob2QMmX3Epzl9+DQ91N2bzs2IxBZCyZRGp6Rt4+7M/MmFOEjv2r+PkmSPM/2oqsQ07EBwcwvh/9sBuD+Lmxp2LPD66QQIZWakA7D+6nab148gvyCM75xgnzmSWOc/Ha16je5shDE2cQNqRrew/st1tuTeZMo6nerx+rryzenpvvc1qBWHV4Y62MLon/PXuy+1PDzQmsWjbSMWUiIiI1Vh0l1Ou1ZU7lgCjBvyNVT99wON3vc59SX9kxsKHycvP5eF+LxZ5rMPpYO6yCfzpgfcpcFxk1pLfM/WRz9zWebjfi0z53/sBih16JZ71aj+MXu2HFWkf3nsiAI8N/keJj7fb7bRt1oM9h37kwd5/KWx/e8LWEh5VvLt7jCv87+ceXgzAwWM7Wbh6OlHhsSTEJBbJdOj4Hv61/M/cHj+UvYc306pJV+we9vTLO6un99bbrCIiIiK+sLnMnj/Y4l7/0hhWZoaYevBEX+/X37gQsjMCl+eRGTfTvc2Qwpn+rvbuikl8s2Uxbz+9nSB7ELUbQqdyGll1aSa0WcPL5/nKItC/F7l25bmtloWVt+viVMTMIqXRdi0iJdEZqlJE1ak4z12jXmByXLLktZJnRhv/X1MYz5Ryy1NR6H2wPv2ORERExFcqqEpxdyezE3ivZS+zE4gn+r2IiIiIXL90IYGIiIiIiIiPVFCJiIiIiIj4SAWViIiIiIiIj1RQiYiIiIiI+EgFlYiIiIiIiI9UUImIiIiIiPhIBZWIiIiIiIiPVFCJiIiIiIj4SAWViIiIiIiIj1RQiYiIiIiI+EgFlYiIiIiIiI9UUImIiIiIiPhIBZWIiIiIiIiPKpkdwOqWbIRDp8x57qg6cHcn79fftQrOHgtcnrKqUQ9a9jI7hYiIwWqfkVKUvjdEpCJSQVWKQ6dgbwX5Aj57DLIzzE4hImJN+owUEZFA0JA/ERERERERH6mgEhERERER8ZEKKhERuWYuF5w6d/nfh05BgcO8PCL+4HTB0TOX/330jNEmInIlXUMlIiI+cblg/3FYkwo7M+Fc3uVlf18OQXZoHAZdmkP7JlBZ3zhSATidsOMwrN1tXEOdV3B52d8+hSqVIKYedI+FVpFg16FpkRuevt5ERKTMTp2DD7+DnzOLX8fhhLTjxs+yn+C+ztC2UblFFCmzgydgwTrIPF38OnkFRsG14zA0qA0PdoVGYeUWUUQsSAWVFJowJ4mdB9YRFBSM3R5Eg7BohveeRI/4e8yOJiIWsvMw/M+3cCHf+8ecvQDvfA3dYuHeTjqqfy30WR0YKT/DJ5vKNqQvMxteXQFDOkKPlgGLJiIWp680cTO8z2Q+nZrDkhdO0LPdMKbMv5+MrFSzY4mIRezKhH+llK2YutLa3bDwO2O4oPhOn9X+lfwz/N8Pvl0f5XTBRxuNgkxEbkwqqMSjoKBK3NltLE6ng7TMrWbHERELOJNrnJlyOItfZ9Zw46ck3++D9Xv9m+1Gpc/qa5eWBZ/8UPI63mzXH/9gXFMoIjceFVTiUX7BRT5ZO5tKQcFERyaYHUdELOCjDXD+on/6+vgHyD7vn75uZPqsvjYFDliwHvxxwtQFfLDOOrNbXiyAs7mQb5E8Iv5wId8YQl7SgT0zWPoaKqfTySuvvMLcuXNJT0+nZcuWvPbaa4wePZrExETeeustsyNedz74aiqLUmYSHFSZyPDmPPfwR0SFNzc7loiY7Mhp2Jzuv/7yCuCbXfDr9v7r80aiz2r/2JwOx86Uvp63jp2BrRnGrJZmOXgCvtoBW9ON4YiV7NChKfRuDfVrmZdL5Fpsy4DVO42ZNwFCK0PXGOjVGqqHmJsNLF5QjRo1iiVLljB58mQ6duzI2rVrGTZsGFlZWTz11FNmx/No8ZQkGrfpQ+e7JnnVbjUP9p7I8D7Wzigi5W/tbv/3uX4vDIiHSkH+7/t6p89q/1gTgMvOvk01r6DalgH//bVxtuzSdYoFTtiwD346CGN6QbObzMkm4qsvt8Fnm8Fmu9yWexFW7YQfD8KT/aB2VfPygYWH/C1YsIB58+axdOlSnn76aXr27MnEiRPp2rUrBQUFdOjQweyIIiI3jNQj/u/zXB4czvZ/vyLeuFhgTOnvb2lZ5gyzO5dnXOPochWd9MWFkemdr60zJFHEG2lZRjEFniczyj5n3OrAbJYtqKZNm0b//v1JTEx0a2/evDnBwcHEx8cD8Nxzz9GiRQvsdjuLFy82I6qIyHUtrwCO+nFY1JUOnghMvyKlOXQqMLNNOl1w+JT/+y3N9/uMoqm4l+RyQc4F2OLHobsigfZtKthKWO4Cdh3x79BdX1hyyF9GRgbbtm1j/PjxRZYdPHiQuLg4qlSpAkD//v357W9/yyOPPFKm57DZSvr1XHbPxNU0bJVUpr79JSUlmT/06+n1+jN/v5qEmKTABSqjlJRkbhnmff5r8eT/Gl8h3v5eRSoCq2zXNW9qxshX97m1lTbjWXHLx813//czE19i/eLnriGd96z2GSlFlef3RvNb7uFXT7ofiPXXdt17wBD2bvzY93A+uHPCpzRJGIDdXvwYWqfTwdMvvsXqeWPLMZmI7343+whVa9Uvdb1eg3/H9uR/+f35XV4edbFsQQUQERHh1p6bm0tKSgoDBgwobOvWrVu5ZvPG959M5YflM93a8i/k0LhNH5MSeeflMclmRxARCwpkQWezWXaghGXps9pPAnqgovwPgthKKKQKuVzerSdiEd5uryUdSCgPliyowsPDAUhNTWXgwIGF7TNmzCAzM5OOHTte83N4W3G+/uXlGUW81XnwRI+TUpRVYmISi6d4Px5h40LIzijz0wRMYmISrjnlc/fOS0cHvf29ilQEVtmucy/Cs4vc264+In/JpSP4xS2/2rS/TiTp3xN9D1cGVvuMlKLK83tj91GYvdK9zV/b9eefLSGmnu/ZfLF8M3yxreR17EGV+OufR/PVO6PLJ5TINZq7Gn7OLH147rJ/v0njum+WTygPLFlQRUdHEx8fz7Rp0wgLCyMqKorFixezfPlyAL8UVCIi4p3QyhBeHY7n+L/vRmH+71PEGw3rBKZfGxAVoL5L0rW5MRtacfudNiC4EnRqWo6hRK7RbbGw83Dxyy/9vTWuW26RPLLkWAu73c6iRYuIi4tjzJgxjBw5kvDwcB577DGCgoIKJ6QQEZHyER2Ao+2Vg6ChCioxSWhliAxA4RNVB0KC/d9vaepUgyGdjP++esDhpX8/2AWqmJBNxFeto6BztOdlNhtUrgTDupZvJk8seYYKoEWLFqxevdqt7aGHHqJ169aEhoaalEpE5MbULdaYRcyfOjaDKpb9FpIbQbfmsHiDf/vsGuvf/sri9pZQMwRWbDVuxn1J47owMAFaNjAvm4gvbDZ4oAtE1ILkn+FM7i/tQOtIGNQOGtQ2MeAvKtRX2caNG+nSpYtb2+TJk3n33XfJyspi69atjBs3jpSUFGJiYkzJeO+k5DK1i4hUBE3qGjcETcvyT392m7HzJ2KmTs2M4iPngn/6qxFi/pC6dk0goTGM/8D4919+DfVqmptJ5FrYbdCrNSTeDBMWGG3PDzH/Zr5XsuSQP09ycnJITU0tckPfl156iYyMDPLy8jhx4gQZGRmmFVNWsvPgdzz5RjfGzb6NOUvdp58/fvowz7zZiyff6Mam1JW4XC7O5Z7mvS9ewOF0cP7CWY99Dp5ci3eWPwvA/K+mcv9Lkby74vLkG++umMRdk2vjcBQE7oWJiClsNnjgVqjkp2+Nvm3MP6pY0uckwJyl4xn/zx7M/uRJAHJys9m8N5nNe5PJyc0GYFHyTPYc+jFgGT/fMI+RM1qyeW+Kx0yHju/h0Vfa8e6KSew9vJkPV8+wRNbjpw8zZlYHBj4bUvidUFxWM4UEw32d/dff/bdaY0jdlRMYqpiS60XQFd8/ViqmoAIVVNWrV8fhcPDEE0+YHaVCqF+7CX9/dBWzHvuW7JxjpGVuLVz24erp/OaOl5j+uy+Y/9UUChz5LFs/l+371zJ/5UvkXMj22GeziLaMGvg3AAZ2/i+eHeY+3dHI/lOIiWwXqJckIiarXwvuLWXnc9z80mdCi60PfeP8l8tXJX1O7s7YRG5eDq+O/YaCgovsSt/AtrRvWfnD+3z5w3ts2fc1TqeT7fvX0DyqfUBzDk18hoSYRI+ZosKbM3bwLABiIhPYeWAdLpfL9Kw1q4YxY/RXtGp8eVRJcVnNFt8IbmtR8jrebNe3t4Q2Df2XS0QqjgpTUEnZhNWMoHJwCABB9mC3+fnTjmwlrmk3QqtUp2qVGlwsuFDkPjNT5w9jz6GfSMvcyl/fH1qk/zo16pt+s1ERKX9dYmDoLb7fZadFBPxXIlSywK1wSvqc3HlwPR1b9AWgQ2wfdhxYV+Tx+zI3ExneHIDNe5MZ8lwdJsxJYvjUJjz37uAy51m/YxlvLXsGp9PJs2/359ipg27LvckUFR7r8SxUeWetHBxCjaolz/hQXFYz3N3JmE3MVz1awF2agFjkhlWhrqGSstt3eAunz2XRpH7rwjan01FYDFULqUVO7il+detoLlw8x/A+k8m7eJ6xd85i2gcPYrcF8cz980xKLyJW1L2FMTvagvVw7Ix3j6lkhwHxkNTKfdiGFXj6nMzJzaZBmDG1VLWQWuw/up02zW4jtEp1AGIi2/FD6hfUr9MUgLbNbqdlo85M/93n/L8FDxeezS+LLq0HkbL537z60Wi6tP419eo0dlvuKdPVIupGk571M51vHmhqVm9cyhrbsEPpKweY3Qb33GLMZvnRBjh30bvHVa9inLVtV/aXLyLXERVU17Ez50/yxsePM2nEv93abbbLezPn8s5QPbQO1UJq8nC/FwCoGlKDqiE1aBAWjd1mJ7xWZHnGFpEKoNlN8MxA+PEAfJsKB094Xq9aFeOsVrdYqFu9fDN6o7jPyWohtTifZ1SLxudkbaqH1iYhJsljP5kn9xUWO1mn0wmvFeW2/OSZI0yd/4BbW1iNCCaOWOjW9qsujzLxnQE8MWR2kefwlKk4ZmetiGw26NDUmAnvu72wdnfx914Lr24cWOgcbWzjInJjU0F1nXI4Cpi+YASjB80krGaE27LoBvHs2L+OZpHxnL9whmohRa9Y3Xd4C7l5Z8kvyCP92C4a1dN0XCLiLjjI2KHsHA3n8iD9JJzMMe5oH1rZuMdUeA3j6L8VlfQ52bpJVz5bP5fEhPv4cfdK+nX6bZHHR4XHsivdmHP7wJHtNImIw+F0uB20uiSsZgQvj0kuMY/T6WT+ypcY0fd5Plw1nYf6PV/mTEdO7COp3QNF2ss7qzeKy2q2alWMGcV6toLs88Z2fTYXsBlTkjeqC7VC3Sd+EJEbm8UGXoi/pGxZRGr6Bt7+7I9MmJPEjv3reONjY0KP+5L+yLsrJvKnuX0Y1usvRR7rcDqYu2wCY+6cxdjB/2DOp+OLXDj8n+/fYe6nE1i1aT6vLXmsXF6TiFhXtSpwcwPjTFT3FsaR/no1rVtMgefPyZNnjjD/q6nENuxAcHAI4//ZA7s9iJsbF52NI7pBAhlZqQDsP7qdpvXjyC/IIzvnGCfOZJY5z8drXqN7myEMTZxA2pGt7D/iPqTPm0wZx1M9Tg5U3lkLHPn8cW4f9mVu5s//uoOdB7/zOqtV2GzGzXLjGxnbdPdYaNvImF1MxZSIXMnmssIUOxb2+pew95g5zx1TD57o6/36GxdCdkbg8jwy42a6txlS7Hj7d1dM4psti3n76e0E2YOo3RA6ldPBx0uzL80aXj7PJ1IetF37VyA+Ixclz6R9bO+AzZ739ZbFLFw9nUcHvUxCTGKR5YeO72H6ghHcHj+UDrF92LBrBQ/0/FOFzVqe3xvXO31+yPXIqtu1CqpSqKDynQoqkWuj7dq/rPYZKUWpoPIffX7I9ciq27WuoSpFVMmzvlrquWvUC0wOX1ktj4jc2PSZZH36HYlIRaSCqhR3dzI7gfda9jI7gYiIdekzUkREAkGTUoiIiIiIiPhIBZWIiIiIiIiPVFCJiIiIiIj4SAWViIiIiIiIj1RQiYiIiIiI+EgFlYiIiIiIiI9UUImIiIiIiPhIBZWIiIiIiIiPVFCJiIiIiIj4SAWViIiIiIiIj1RQiYiIiIiI+EgFlYiIiIiIiI9UUImIiIiIiPioktkBrG7JRjh0ypznjqoDd3fyfv1dq+DsscDlKasa9aBlL7NTiIiIiNVYbZ9F3GkfrmxUUJXi0CnYW0H+4M8eg+wMs1OIiIiIlEz7LHI90ZA/ERERERERH6mgEhERERER8ZGG/ImIiIhcB07nwtZ0OHjicts/voAGtaBxXWjbCKpVMS+fiC+OnIYdhyD95OW22Sshsg40C4e4hhAcZF4+UEElIiIiUqFlnYXPfoIt6eB0uS9LyzJ+1u6BxRuhY1MYmAC1Qs1IKuK9fcfgP1tg99Giy3YfNX5SMA4SdGsOfdtAZZMqGxVUIiIiIhWQywXfpsLSHyHfUfr6BQ74bq9ReA29BTo0DXhEkTIrcBjb9De7wFX66pzLgy+3w48HYHg3aHZTwCMWoYJKCk2Yk8TOA+sICgrGbg+iQVg0w3tPokf8PWZHExERkSu4XMZO5+qdZX9s7kV4bw2cyYWkVv7PdiPRvpN/5TvgnRT4ObPsjz2eA7O/glG3Q6tI/2criSalEDfD+0zm06k5LHnhBD3bDWPK/PvJyEo1O5aIiIhcIeVn34qpK328CTbt90ucG5r2nfznw/W+FVOXFDjgv7+Gw+V8D1kVVOJRUFAl7uw2FqfTQVrmVrPjiIiIyC+OnIZlP5W8zqzhxk9pFm8wzlTJtdO+07XZfBA27i95HW+263wHfLAOHE6/RSuVpQsqp9PJzJkziY2NJSQkhISEBFJSUmjZsiWjR482O951Lb/gIp+snU2loGCiIxPMjlOs3IvGGNtLvt8HFwvMyyPiD9nn4fMrvot3HAJnOX4xiIi1Ld0EBX76TDh/0bjwX65dRdl3siKHE5Zs9F9/Gadg/V7/9VcaS19DNWrUKJYsWcLkyZPp2LEja9euZdiwYWRlZfHUU0+ZHc+jxVOSaNymD53vmuRVu9V88NVUFqXMJDioMpHhzXnu4Y+ICm9udiyPNu2HBevdL8T9YB18/AOMvB1i65sWTcQnLhes2ApfbDP++5K3kuGmGvBoTwivYVo8EbGA42dh52H/9rkxDe5sD6GV/dvvjaIi7TtZ1bYMY9p/f1qTasz+Z7P5t19PLFtQLViwgHnz5pGcnExiYiIAPXv2ZNOmTSxZsoQOHTqYnPD69GDviQzvY+2iD4zxte+v8Tz7S24+zF0NT91h3KNApKJYvdP9zNSVjufAGyvhjwOhqu4jI3LD+vGAdzOflUW+A7ZmQOdoP3d8g6go+05WFohr+Q5nG8NjG9T2f99Xs+yQv2nTptG/f//CYuqS5s2bExwcTHx8PKdOnWLQoEG0aNGChIQE+vXrx549e0xKLOXpP5uLX+ZygcMBX+0ovzwi1+piAXy+rfjlLpcxFPC7feWXSUSs58qbm1aEfkW8ceXNqCtCv1ezZEGVkZHBtm3bGDp0aJFlBw8eJC4ujipVqmCz2Rg3bhypqals3ryZQYMGMXLkSBMSS3nKOgsHTpR8hM4F/HRA11NJxbH9EOTll77ed+U4JlxErCczOzD9HglQvyKlycuHU+cD0/eR04Hp92qWHPKXkZEBQEREhFt7bm4uKSkpDBgwAIDatWvTp0+fwuXdunVjxowZXj2HzcsBlfdMXE3DVklerXvJ959M5YflM93a8i/k0LhNn2Ie4VlKSjJ/6NfT6/Vn/n41CTFJZXqOQEpJSeaWYd7n91aD2G7c9/yaUtdzuCCsXhTnTvl5sLlIACT0fZyk37xe6nppGVnYbPXKIZGIWNEj/zhIjbqN3NpKmvWsuGXj5rv/++tv1/F4327XmM57VttnEXeB2ofzJLRGOKPnZLm1lTaTn7fb9azXZnPX/zzuczaXy7sBtpYsqMLDwwFITU1l4MCBhe0zZswgMzOTjh07enzcrFmzuOuuu8ojYok6D57ocVIKq3t5TLLZEbySm3Pcq/WczgLyzmcHNoyIn3izXbtcTnLPerf9i8j1yZF/ISD9FgSo3+tdRdl3srJAbnuB+nu5miULqujoaOLj45k2bRphYWFERUWxePFili9fDuCxoHrxxRfZs2cPq1at8uo5vK04X/8S9h7zPrs/JSYmsXiK95eeblwI2RkBDFRGiYlJuOb4+9JZ41qSmf8xbtpWXO82oH2TSuRfOOf35xcJhAv58NySkoep2mx2HhrQivee8f/flYhUDP9KMWZEu9LVR+Xh8hF8T8s8GTa4Jx9NLb/PFqvts4i7QO3DFef5Je6z/BW33ZZ1u57x4gS6zJ9wbeG8YMlrqOx2O4sWLSIuLo4xY8YwcuRIwsPDeeyxxwgKCiI+Pt5t/SlTprBs2TJWrFhB1apVTUot5cVmg/5tSy6mbDboHVeeqUSuTUgw9GpV/HKbDaqHQFfNxCtyQ2sUFqB+6wamXxFvBGr7K6/t2pJnqABatGjB6tWr3doeeughWrduTWhoaGHbiy++yPLly/nyyy+pXbt2OacUs7RtBPffCou+B6fr8j0GXC4IDoLf9IDG+nKQCqZfW+Mmm1//crNq2y//43JBrVDjPlTVQ8xMKCJma9fE/zfirWSHNg3926dIWbRvUvTM67WqVxMia/u3z+JYtqDyZOPGjXTp0qXw39u3b+eFF14gJiaGpKSkwvaffvqp/MP94t5JyWVqF991bQ5xUcadsNNPGEVVTD24JRqq6uaEUgHZbXB3J+geC+v2GPeeCg4ydnQSGkGlILMTiojZ6teEFhGQesR/fbZvCtV0fzsxUUIj+L8QyPHjJU/dY8vnpr5QgQqqnJwcUlNTGTt2bGFbXFyc19dCyfWpZij0a2N2ChH/ql8L7vI8946ICHe2h1dWGCM0rlVIMAyML329QNp58DveXDoem81Oy0a3MObOV92Wz1k6ntSMjTSP6sBjg/9BTm42ew//BEBMZDuqh9ZmUfJM2sf2pnlU+4Bk/HzDPBau/hvj7nmLqPBYJr87iANHd/DplByCgipx6Pge/vrevXRpPYjb44eycdfn3N/zj6ZnrRwcUuS9LS6rmSoFweD2MH+df/qLqGUUVOXFktdQeVK9enUcDgdPPPGE2VEqhJ0Hv+PJN7oxbvZtzFk63m3Z8dOHeebNXjz5Rjc2pa7E5XJxLvc0733xAg6ng/MXznrsc/DkWryz/FkAZi1+lCff6M642bex77Ax9uDjNW9w34sRHDqumyuLiIgESsMwuKNtyeuMm+/dhftDOkKdav7J5av6tZvw90dXMeuxb8nOOUZa5tbCZbszNpGbl8OrY7+hoOAiu9I3sC3tW1b+8D5f/vAeW/Z9jdPpZPv+NQErUC4ZmvgMCTGJ1KwaxozRX9Gq8eVRU1HhzRk7eBYAMZEJ7DywDpfLZXpWT+9tcVnN1qkZtC1l6Kk323WQDR7sWr6jOipMQSVlU9KH04erp/ObO15i+u++YP5XUyhw5LNs/Vy271/L/JUvkXMh22OfzSLaMmrg3wC4v9ef+cfja3j6vnd5/8sXAbir++N0atk/4K9NRETkRtevzbVPUtO/Ldwa45881yKsZgSVg40LRIPswdjtl/eEdx5cT8cWfQHoENuHHQeKnsLYl7mZyHDjzdi8N5khz9Vhwpwkhk9twnPvDi5znvU7lvHWsmdwOp08+3Z/jp066La8cnAINarWKbGPqPBY9hz60fSsJb23pWUtbzYbjOgO0Tf53ofdBg/fVv7X0auguk6V9AeUdmQrcU27EVqlOlWr1OBiwYUiNzqeOn8Yew79RFrmVv76/tAi/TcIawZApSDPf5wiIiISODYb3NcZBiYYR+TLonIl47H9TR7qd7V9h7dw+lwWTeq3LmzLyc2mapWaAFQLqUVObjZtmt1Gn44P0bfjw8RH386h47upX6cpAG2b3U7LRp15eUwy8dGJ/OHuf5Y5R5fWgzh19iivfjSaLq1/Tb06jcvcR0TdaNKzfrZMVk/v7dVZraBKJfh9L+gcXfbHXpq8KaHsv65rVmGuoRLfePoDcjodhQWU8eF0il/dOpoLF88xvM9k8i6eZ+yds5j2wYPYbUE8c/+8Yvt/5z/PMuS2PwT6ZYiIiMhVbDbjTFWbKFj6I/ycWfL6dpsxS+6d7aFu9fLJ6K0z50/yxsePM2nEv93aq4XU4nzeGQDO5Z2hemhtqofWJiEmyWM/mSf30SDM2BvPOp1OeK0ot+Unzxxh6vwH3NrCakQwccRCt7ZfdXmUie8M4Ikhs6/lZVkia3HvrVVVrmQM2WvXGJZvgYyTpa9/azQMSDBvUjIVVNex4v6AbLbLJyaND6c6VAupycP9XgCgakgNqobUoEFYNHabnfBakR77X/LNLJrUa02bZrcF7DWIiIhIySLrGEf1s87C5oPGzLdHz0C+w9jZbFDLGALVrgnUtuDtOh2OAqYvGMHoQTMJqxnhtqx1k658tn4uiQn38ePulfTr9Nsij48Kj2VX+gYADhzZTpOIOBxOh9v+ziVhNSN4eUxyiXmcTifzV77EiL7P8+Gq6TzU7/kyv6YjJ/aR1O6BIu3lnbWk97a0rGZrHQWtIuHACdhxCNJPwokccDohtDJE1YEm4caU6yHB5mZVQXWdKukPKLpBPDv2r6NZZDznL5yhWkjNIo/fd3gLuXlnyS/II/3YLhrVa+m2fOOuL9i+fy2TRnwY0NchIiIi3rmpBvSpgDe1T9myiNT0Dbz9mTHT3KgBfyMirBn/2fAOw3tPJDg4hPH/7EFMZDtubty5yOOjGyTw3hcvALD/6HZaN+lKfkEe2TnHOHEmk7o1G5Qpz8drXqN7myEM6voof33vXvYf2e62vMCRz1/+NYB9mZv587/u4JEB02jV+Fa3dTKOpxIT2c70rJ7e29ZNu3qV1QpsNmgabvxYmQqq65SnP6BVP33A43e9zn1Jf2TGwofJy8/l4X4vFnmsw+lg7rIJ/OmB9ylwXGTWkt8z9ZHP3NaZ/ckTVK1Sk6ff7Emjm1oy7t655fK6RERE5PrSq/0werUfVqR9eO+JADw2+B8lPt5ut9O2WQ/2HPqRB3v/pbD97QlbS3hU8e7uMa7wv597eDEAB4/tZOHq6USFx5IQk8iMR1e6PebQ8T38a/mfuT1+KHsPb6ZVk67Y7UXPOpV3Vk/vrbdZxXs2lxXmSbSw17+EvcfMee6YevBEX+/X37gQsv18l+krPTLjZrq3GVI409/VPl7zBp+te5Mpoz6jfp0m1G4Inax3BllERERMFuh9Frk22ocrGxVUpViyEQ6dMue5o+rA3Z28X3/XKjhrUvHnSY160LKX2SlERETEaqy2zyLutA9XNiqoREREREREfKQBkyIiIiIiIj5SQSUiIiIiIuIjFVQiIiIiIiI+UkElIiIiIiLiIxVUIiIiIiIiPlJBJSIiIiIi4iMVVCIiIiIiIj5SQSUiIiIiIuIjFVQiIiIiIiI+UkElIiIiIiLiIxVUIiIiIiIiPlJBJSIiIiIi4iMVVCIiIiIiIj5SQSUiIiIiIuIjFVQiIiIiIiI+UkElIiIiIiLiIxVUIiIiIiIiPlJBJSIiIiIi4qP/D6Ej5SzcQRspAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1110x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 3 features, depth 1, circular entanglement\n",
    "map_zz = ZZFeatureMap(feature_dimension=3, reps=1, entanglement='circular')\n",
    "map_zz.decompose().draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can customise the Pauli gates in the feature map, for example, $P_0 = X, P_1 = Y, P_2 = ZZ$:\n",
    "$$\\mathcal{U}_{\\Phi(\\mathbf{x})} = \\left( \\exp\\left(i\\sum_{jk} \\phi_{\\{j,k\\}}(\\mathbf{x}) \\, Z_j \\otimes Z_k\\right) \\, \\exp\\left(i\\sum_{j} \\phi_{\\{j\\}}(\\mathbf{x}) \\, Y_j\\right) \\, \\exp\\left(i\\sum_j \\phi_{\\{j\\}}(\\mathbf{x}) \\, X_j\\right) \\, H^{\\otimes n} \\right)^d.$$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1411x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 3 features, depth 1\n",
    "map_pauli = PauliFeatureMap(feature_dimension=3, reps=1, paulis = ['X', 'Y', 'ZZ'])\n",
    "map_pauli.decompose().draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The [`NLocal`](https://qiskit.org/documentation/stubs/qiskit.circuit.library.NLocal.html) and [`TwoLocal`](https://qiskit.org/documentation/stubs/qiskit.circuit.library.TwoLocal.html) functions in Qiskit's circuit library can also be used to create parameterised quantum circuits as feature maps. \n",
    "\n",
    "```python\n",
    "TwoLocal(num_qubits=None, reps=3, rotation_blocks=None, \n",
    "         entanglement_blocks=None, entanglement='full',  \n",
    "         skip_unentangled_qubits=False, \n",
    "         skip_final_rotation_layer=False, \n",
    "         parameter_prefix='θ', insert_barriers=False, \n",
    "         initial_state=None)\n",
    "```\n",
    "\n",
    "```python\n",
    "NLocal(num_qubits=None, reps=1, rotation_blocks=None, \n",
    "       entanglement_blocks=None, entanglement=None,   \n",
    "       skip_unentangled_qubits=False, \n",
    "       skip_final_rotation_layer=False, \n",
    "       overwrite_block_parameters=True, \n",
    "       parameter_prefix='θ', insert_barriers=False, \n",
    "       initial_state=None, name='nlocal')\n",
    "```\n",
    "\n",
    "Both functions create parameterised circuits of alternating rotation and entanglement layers. In both layers, parameterised circuit-blocks act on the circuit in a defined way. In the rotation layer, the blocks are applied stacked on top of each other, while in the entanglement layer according to the entanglement strategy. Each layer is repeated a number of times, and by default a final rotation layer is appended.\n",
    "\n",
    "In `NLocal`, the circuit blocks can have arbitrary sizes (smaller equal to the number of qubits in the circuit), while in `TwoLocal`, the rotation layers are single qubit gates applied on all qubits and the entanglement layer uses two-qubit gates.\n",
    "\n",
    "For example, here is a `TwoLocal` circuit, with $R_y$ and $R_Z$ gates in the rotation layer and $CX$ gates in the entangling layer with circular entanglement:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1049.8x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "twolocal = TwoLocal(num_qubits=3, reps=2, rotation_blocks=['ry','rz'], \n",
    "               entanglement_blocks='cx', entanglement='circular', insert_barriers=True)\n",
    "twolocal.decompose().draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and the equivalent `NLocal` circuit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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5ZiYkYWZCUuET612dWzeDiawOndqC1qFPAgBaNnkCRqOp8L3Us7sQ3Tjuj/cex9Ez20VELJVabpPRBKNRKY38gnwE+jcRktFe8+fPFx2hCG+TcpvLto2tblqCyahcDvZ0C+XSMPJcstX1fWo95MiZ7TAYjPjbFz3w0ZIXkX0vS1TMItQyX7h2EkF1lBurBNdtgcNntgnJaC/Z6sNgUA7KdGvu2GL4TmHAyx21uySM9EmmulbrGwaDAdUr1y6yfeWK1VGpQlUAgJfJG0aDCSLYmxsA0i4fxeh5nfDF6r/a/EBErfE//TLKuHMd//55It6aH4fF6z9Exp3rhe9l3b2Jij7KxaiVfKoi8+5NQSlLUssNAClpv2H431tj3/ENqOMXJCilfRISEkRHKMHbpKzLeCVOuVbZFk1qA2N7KLfp5VBCMtY1oN5DbmRcwvWMC5j2lzWIbNgeP26X4+GEapnr1QzDgZPJAIB9xzcgK/umoJT2kbE+jAagR5TyjI8gf9u+p251YMRjyt2uOJSQTHVt7fOSJVdvncfu1HWFw4GrOZJ74bvHMCthEzLv3MD2Iz+4IGVJulljIqvKFf3wcrcP0D7yGew4sgpXbj14yk0ln6q48sdTb+7cvQ1fn2qCUpaklhsAmjZoi3kjd2F58kys3fklnus8WlBS2yUlJYmOYFFkIBBRFzh+CdifBpy9Dpy5prznW175pVzfT7nrVUBVsVlJLrLWtbXe16xRR5iMJrQI6YrlyTMEJn1ALXNIYAs0CmiGsZ92QaOAZqhWytFEGclaH4Byw4yR3YD068Du00DaNeDirQcPbA2qqfS9RxoCjfx5IIYekKmurX1eKs29vBx88t+XMabfv2Ayifmo7Uju+5dvtW/WG8fP7UX7yGecHbMEHpcoo2ZBHXHwpLL4fv+JJJjN+YXvhdZvU3gEbs+xXxDeUJ5HY6vlzs27V/j3Sj5VUM6bt17SgsEANAkA+rYFRnd/8PrUvsDwx4CnH+FQQvqh1kPC6rdB2mXlqc0nzu9DgCRnXdUyA8CLT0zAjNc2okrFGmgX/pSIiG6pnp9yaeobTwAfPnRJ+8gngT+1VgYUDiUkK2t9ozRzEofhmfYj0LB2hLPjWWRv7ux7Wcj/Y5vDp7eibg0xC1x5xqSMggKawcvkjbfmxyGiYQx8ylVCvjkPAFDdtxaaN+6MUXM7ola1BvhTp1Fiwz5ELfeJ8/vw+Y9vw2gwonIFP7zbf5HgtEQkG7UeUs23JqIax2LMvM4o710R7w1cLDitQi2z2WzG2591hdFowiMhjyG8QTvBaYlIBmp9AwCmLIrHodNbcO7qMfw57h1U862FLYdW4NKNM1ixeQ76dByJjs37SJ+7VvWGmLl8CCqU80WAXxBeenKyyzMDHEw0MbTn9MK/bzqQiKUbP0KgfxNEB8fi+S7v4vku7xa+n52TiY+WvICw+m1ERC1CLfeshOQi28qU25KjR4+KjkCkOZnrWq2HPNd5dJFLQGXpIWqZZyYkldj+/S97wa9KHRcmtI/M9UHkKNnqWq1vjH9xWYntV07NKPGaiF5ib+75o/aUeM3VuQ0Fopbd68TvG4CMy2J+duVaQFhXx75XVO6yZFaTkpJidZtly5YhPj5edZumTZuqvu9K92+XOWeg2Bz20mtuGcla1+x79mHfs48ee4geM8tK5rrWYw/Ra7+2hGdMrHDGLxtX0Gvuspg4caLVRkakNyLqWq/9Q6+5y4J9j9yRqLrWYw/RY2Y1XPxORERERETCcTAhIiIiIiLhOJiQ25g3b57oCESaY12TGtYHuSPWtefiYEJuIzIyUnQEIs2xrkkN64PcEevac3EwIbcRGxsrOgKR5ljXpIb1Qe6Ide25OJgQEREREZFwHEzIbbRpI+/DH4kcxbomNawPckesa8/FwYTcxs6dO0VHINIc65rUsD7IHbGuPRcHEyIiIiIiEo6DCRERERERCcfBhNxGYmKi6AhEmmNdkxrWB7kj1rXn4mBCRERERETCcTAht9G3b1/REYg0x7omNawPckesa8/lJTqA7H7fAGRcFvOzK9cCwro69r2icpclMxHJgX3PPux7RO5Bjz1Er/3aEg4mVmRcBm6mi05hP73mJiLx9No/9JqbiOSgxx6ix8xqeCkXuY0RI0aIjkCkOdY1qWF9kDtiXXsuDibkNl5//XXREYg0x7omNawPckesa8/FwYTcRufOnUVHcGv5ZuD8jQdfX8sECgrE5fEUrGtSw/pwLnMBcOn2g68v3VZeI+diXXsurjEht3HlyhXREdxObj6w9wyw4ziQdg3IMz94b8r3QKXyQFgA0DEUCKoJGAzisror1jWpYX1oz2wGjpwHth0DTlwGcvIevDf9B6C8FxBcC+jQBAivCxh5iFdzrGvPxcFEI2/Nj8PRM9thMnnDaDQhoHoQBjw2DrHR/URHs0iPmcl1jpwD/vsrcCvb8jZZOcCeM8qf0ADg+XaAn6/rMpJYeuwhesxMrpN2DViyHbhwy/I2OXnK4HLkPFCnGjAgBqjv57KIJJgee4ieMnPO19DAx8fjhw8zsWLSNXRrMwjTFw/AuavHRcdSpcfMlkRERIiO4BbMBcCKXcDnSepDSXGpF4H/9yNw2I3uDiID2etajz1Ej5ktkb0+9CQ5BZjzk/pQUtyFm8DstcDm350WyyPJXtd67CF6yczBxAlMJi/0aPcK8s15OHF+n+g4NtFj5uK+/fZb0RF0r6AASPwN2OTgL9mcPGDBJuDwOW1zeTK91LUee4geMxenl/qQXVIK8L/djq0fMRcA3+5SBhvShl7qWo89RPbMHEycIDfvHlZtmw8AqOcfKjiNbfSYubgJEyaIjqB7O08B26wcQJkzUPljibkAWLQVuHlH22yeSi91rcceosfMxemlPmR26grw/W71baz1PQD4bjdw+qp2uTyZXupajz1E9sxcY6Khxes/xPLkGcjOyYDJ5I0x/b5A47pRAIBp3wxA10cG4NGIXgCAiQt74+mY4Wgd9qTIyKqZ1/y2AL/sXlS47YXrJ9E8qBPeG/CNqLiqli9fjg8++EB0DN26nQ38b5c2+7qbCyz7FRjWRZv9ldXdXCA3D6hYHjDp7HCM7HXNvieW7PUhu7x8YMkOQIsbbRUAWLwdeKcn4GXSYIdldC8PyMkFfMoB3hLksYfsdc2+5zxS/4o2m82YMWMGmjRpAh8fH0RHRyM5ORlhYWEYNmyY6HglDHhsHL6bchOJk66ibdOe2H98Y+F7Cc/OwcKfxiM7JxObD65AJZ+qwosUUM/co+1QzExIwsyEJIwbuBQ+5SphcPcPBaYlZ9p6DMjO1W5/R84D525Y386Zjp4H5v4C/HUZMH4FMC5RuVzDnrUzpI59j/Rs/1ng8m3r29nq8m3goOB1dmnXgK82P+h77y1TBqZLdqydIXXse84j9WAydOhQTJkyBa+++irWrFmD+Ph49O/fHydPnkSrVq1Ex7OocsXqGNPvC/ya8iO2HfoeAFDdtxb6dByJud+/icXrp+K1Z2YLTllUaZnvM5vNmL5kIIb2mI4Av0ZiApJT5ZuB7ce03+9WJ+zTVskpwGcbgeOXH7x2N1d5fdYa5TkspB32PdKjrana73OLE/Zpq0PpygL+A2cfrJfJMwM7TwIz1yqXrZF22Pe0J+1gsmTJEixcuBArV67E2LFj0aVLF4wbNw4xMTHIy8tDy5YtRUdUVaWiH57rNAZfrv0bzGbl4Q/d2gxC+pVU9O7wJqpUlO/egqVlBoBF6yYjKKA5OjTrLS6cDZKTk0VH0K1Lt4Dbd7Xf77GL2u/TFunXlTMjQOkPgbydDXy9zbWZHKWnumbfcz091Yds7uUBp5ywJuTUFeUZUK6WlQP8e4vS84r3vQIomRZsUi5fk52e6pp9T1vSDibTpk1D9+7dERsbW+T1kJAQeHt7IypKuS5uwoQJCA0NhdFoRGJiooioFvXpNBLXb1/Aut3/KXytbo0QBPqHCEylrnjmPcfWY3fqz3jlqY8FJ7Pu8OHDoiPo1tnrztnvlQwg+55z9q1mSyqg9qzHAigfHkRfamYLvdU1+55r6a0+ZHLuRukHLsrKXACcF9BbfjupDB+W/pEKCoDMu8rZFNnpra7Z97RjKChwxn+WZZOeno769etjwYIFGDJkSJH3+vfvj5SUFOzduxcAsG3bNgQEBGDIkCF4/fXX0bdvX5t+hsHGR1TPeG0jooPj7Mqv5uOlg9Cz3V/QLKij1W33n0jC2E8dWz2sRe7rty9i7GddMG3oGptP6ZUls5rRo0db3Wb27NlWt5s9W55TqiO/Vv7T+/sL4h+X3rb3+4jpO6XIa9buQGPJqGJr5f7zTjhunHftfTQHzT6JqjWDrG6XvGgk9v30DxckKp2sdc2+x77nTLL0vpA2z+GpkUUPaGrV91bN6YMTu75zbGcOeuatH9AwugeMRssr3c3mfBza8Dk2LhzuwmRFyVzXWvY+d+97gH25bR03pLwrV3q6snIsICCgyOvZ2dlITk5Gjx49Cl9r3769S7N5kq9/mYKsu7fwyX8HFb5Wv2YYRvX9TFwochLnfUAwOHHflqj9Yn6YwcbtyHOw73kQGw9QOrhzJ+7bwk+0pZ8VFLDvUQky9T0pz5gcP34cTZo0wezZszFq1KjC1ydPnoxJkyZh7ty5GD686LQfFxdn1xkTW+1aCtwUdIeNavWA1s879r2icpcls5qUFOtH3MPDw3H06FHVbZo2bapVpDK7f4TN0SN0WtqaCizfadu29/MWP0JoydTnAF8fx3I56qtNwIF065dpvP44EFLbNZlKI2tds+/Zh33PPrL0vmOXlLv22cLevvfGE0BwLcdyOWr1fuDnQ9a369cW6NDE+Xkskbmu9dhD9NqvLZHyjEnjxo0RFRWFadOmwc/PD4GBgUhMTMTq1asBQOo7cpE4kydPFh1Bt+o5aW1etYquH0oAoEOochtQSwwGoGZl139wcATrmtSwPhxXr7pz9msAEOikfauJCQHWHbK8xsQAwNsLaN3IhaEcxLr2XFIufjcajVi+fDkiIyORkJCAwYMHw9/fHyNGjIDJZCpc+E70sPj4eNERdKtudcDHW/v9ivrg36Q20NHCA20NBsDLCLzQ3slXcmiEdU1qWB+Oq1BO6X1aC3RSP7WmeiWgT2vl78Vb2/2vBzwKlBeQzV6sa88l5WACAKGhodi4cSOysrKQlpaGKVOm4ODBg4iIiECFChVExyMJhYeHi46gW94moE1j7fcbI+iGJAYD8FxroE8r5azNw5rWAUZ1AxrUEJPNXqxrUsP6KJv2TuhRMQIvk+ocBgzqCNSuWvT1BjWA17oCLRqKyWUv1rXnknYwKc2uXbtKXMY1fvx41KtXD9u3b8err76KevXq4cSJE4ISEulX51DApGFHqO8n9lIpgwGIbQpMePbBaxN7A692EXOZBRHJp3WQtpebVvYRf6lUi4bAu089+PpvTwOjuwNhdcRlIrKVbgaTzMxMpKamlniw4pQpU5Ceno6cnBxcu3YN6enpCA4Odmm2Bavfw5h5nbFg9Xv4aedCDP44DPtPJCMvPxdv/l8Mnh7ni3NXjwMAsnMy8cb/PYqPFr/g0oylsZT7vs0HV2DA1PoA5MpNzlGzCtC9uTb7MhmB/o/KcamU8aEuV72SuBzuxlL/OH5uH96aH4e35sfhxWlBWLF5DgDg/S97YdRc67fNdGXW0no0ACxL+gSj5nbE9MUDkZefy/7nxny8gfi22u3vz+3kuFTq4d5bq4q4HO7Cnh5yK+sqRv6zPcbMj8X4r55BTm62sB5ib+/bnboOb3/aFW/Nj0Nq+m4huXUzmPj6+iI/Px9vvPGG6ChFnLp4CFl3b2PW8E24feca7t7LQr/YtxEdHAuT0QuTB32HTs0f3CmsQnlfjBu4VGBihVru+zYfSETNaspgIktuNXFxcaIj6F7XCOVSJzWjvrF+Z5o+rZxz7bYnkrGu1fpHSGALzExIwsyEJATViUK78F4AgKlDVkmXtbQefSPzMvad2Ig5I7YgqE4Uth76Tur+J2N96E1Ufctr0u6zpe91DgOa1dMulyeTqa7t7SG+Fapj9vAtmJWQjNDAVthxZJWQHmJv7pzcbPy44zN8NGwdZiYkIbReKyG5dTOYyOrQqS1oHfokAKBlkyeKPD/BYDCgemWB9yJVoZYbAH49uhotmzwOg0E/JTJ//nzREXTPZASGdAYi6jr2/QYoQ4m1X/JkOxnr2lr/AIDse1m4kXFR+JOP7e3RqWd3Ibpx3B/bP46jZ7a7LKsjZKwPPfpTa6BjGdaGdAoFevOGoZqRqa7t7SEmownGP07V5xfkI9BfzKIje3MfObMdBoMRf/uiBz5a8iKy72W5NO99+vnUKamMO9fx758n4q35cVi8/kNk3LkuOpJNrOVet/vfeKylvi5bSEhIEB3BLZTzAv4SC/RuCXjZ8Rwu/8rKvftj5Xpkgu7JWNe29L2dKWvQOqy7gHRF2dujs+7eREUf5dqXSj5VkXn3pgtSOk7G+tAjowF4rg3wUgegUjnbv8+3PDCok/K9RgkuXXUXMtW1I5/zUtJ+w/C/t8a+4xtQxy/IBSlLsjf3jYxLuJ5xAdP+sgaRDdvjx+1iHior5XNM9KRyRT+83O0DtI98BjuOrMKVW4KecmMntdx7j29ARMMYeHvZ0Z0lkJSUJDqC2zAagbhwILoBsO0YsP0EkHm39G3r+SlHGls2UoYa0paMdW1L39t66H+Ij3tHQLqi7O3RlXyq4sofTyu7c/c2fH2quSCl42SsD70yGJQ+FlYH+PWE0vuuZpa+rb+v8rykto2BSuVdGtMjyFTXjnzOa9qgLeaN3IXlyTOxdueXeK7zaBckLcqR3tesUUeYjCa0COmK5ckzXJS0KJ4xKaNmQR1x8OQmAMD+E0kwm/MFJ7KNWu7TFw9h++GVeO9f3XHm0mF8tfZ9UTFJsOqVgKdaAB/8CRj3NPByR6BfG2Wx6KtdlKe6j+0BPBrCocSTWOt7efm5SLt8FMF1o0XEK8LeHh1avw0OnFRuArLn2C8Ib/io0zOSXCqVV9bbjXtGuZPfkM5K3+vXFhjaGZjUR3mvSziHEk9gbw/JzbtX+PdKPlVQzlvMIy7szR1Wvw3SLh8FAJw4vw8Bgs708KNEGQUFNIOXyRtvzY9DRMMY+JSrhHxzXuH7UxbF49DpLTh39Rj+HPcO2jd7VmVvrqOWu0/HN9Gn45sAgFFzO2Jw96kio5IEjAblrl01eXcXgvW+t/f4BrQI7iow4QOO9OjmjTtj1NyOqFWtAf7UaZS48CSUwaAcnOHd/DybvT3Er0odfP7j2zAajKhcwQ/v9l+ki9ztmz2LqMaxGDOvM8p7V8R7AxcLyc3BRANDe04v/PumA4lYuvEjBPo3QXRwLMa/uKzIttk5mfhoyQsIq9/G1TFLUMt935wRWwDIlduSo0ePio5ApDlZ61qtf7QJ64Y2Yd2KbP/+l73gV0XMgxTs6dEA8HyXd/F8l3cLv5a5/8laH0RlIVtd29tDZiUkF/laVA+xN/dznUcXuexMRG4OJhrrHNUXnaP6Wny/Qnnfwg/7MtFr7octW7YM8fHxomMQaUoPdW2tfwDibhdcnC1Zi5O5/+mhPojsJXNd67WH6CU3BxMrKgt8cnVZfrao3CL/fU2cOFHaRkbkKBF1zb6nj58LsO+RexJV13rsIXrt15ZwMLEiTI7LpO2m19xEJJ5e+4decxORHPTYQ/SYWQ3vykVERERERMJxMCG3MW/ePNERiDTHuiY1rA9yR6xrz8XBhNxGZGSk6AhEmmNdkxrWB7kj1rXn4mBCbiM2Ntb6RkQ6w7omNawPckesa8/FwYSIiIiIiITjYEJERERERMJxMCG30aaNfE9lJior1jWpYX2QO2Jdey4OJuQ2du7cKToCkeZY16SG9UHuiHXtuTiYEBERERGRcBxMiIiIiIhIOA4m5DYSExNFRyDSHOua1LA+yB2xrj0XBxMiIiIiIhKOgwm5jb59+4qOQKQ51jWpYX2QO2Jdey4v0QFk9/sGIOOymJ9duRYQ1tWx7xWVuyyZiUgO7Hv2Yd8jcg967CF67deWcDCxIuMycDNddAr76TU3EYmn1/6h19xEJAc99hA9ZlbDS7nIbYwYMUJ0BCLNsa5JDeuD3BHr2nNxMCG38frrr4uOQKQ51jWpYX2QO2Jdey4OJuQ2OnfuLDoCSeTybWDjUeA/Wx689s9fgBW7gD2ngXt5wqLZhXVNalgf9LBb2cCWVGDx9gev/f1nYNmvwI7jQFaOuGz2YF17Lq4xIbdx5coV0RFIAqevAmv2A79fLPne8UvKn02/AxXKATEhwJPNAB9v1+e0Feua1LA+CACuZAA/7gMOnAXMBUXfO3VF+bPtOJC4C2jVCOgZDVStICKpbVjXnouDiUbemh+Ho2e2w2TyhtFoQkD1IAx4bBxio/uJjmaRHjMTWZJvBn7cD2w8AhRY3xzZ94ANR4C9Z4CBMUBIbadHdDt67CF6zExkSUGBcoZk5V4gN9/69nn5wK8nlAGmXxugZSOnR3Q7euwhesrMS7k0NPDx8fjhw0ysmHQN3doMwvTFA3Du6nHRsVTpMbMlERERoiOQIPlm4KvNyqBhy1DysBtZwPz1wMGzTolWZrLXtR57iB4zWyJ7fZDzFBQoA8m3u2wbSh6WfQ/4z1Yg6ahzspWV7HWtxx6il8wcTJzAZPJCj3avIN+chxPn94mOYxM9Zi7u22+/FR2BBEncCRwqw+0S8wuAhVuAtGvaZdKKXupajz1Ej5mL00t9kPaSU5R1dGXx3R5lzZ1s9FLXeuwhsmfmYOIEuXn3sGrbfABAPf9QwWlso8fMxU2YMEF0BBLgyDlgu5WDPnMGKn/U5JuVBaP2Hnl0Nr3UtR57iB4zF6eX+iBtXbwFrNqnvo0tfQ9QDuzcztYklmb0Utd67CGyZ5Z6jYnZbMasWbPw2Wef4ezZswgLC8M//vEPDBs2DLGxsfj8889FRyxi8foPsTx5BrJzMmAyeWNMvy/QuG4UAGDaNwPQ9ZEBeDSiFwBg4sLeeDpmOFqHPSkysmrmNb8twC+7FxVue+H6STQP6oT3BnwjKq6q5cuX44MPPhAdw6qCAuDkQ+v6ftgLtAsGalURl0mvzAXKXba0cvEWsDUViAvXbp9lJXtds++JJXt9POz8DWDnqQdfp10DGtQQl0fPVu4B8sza7OvOPWDNAeDP7bTZnxZkr2v2PeeR+ozJ0KFDMWXKFLz66qtYs2YN4uPj0b9/f5w8eRKtWrUSHa+EAY+Nw3dTbiJx0lW0bdoT+49vLHwv4dk5WPjTeGTnZGLzwRWo5FNVeJEC6pl7tB2KmQlJmJmQhHEDl8KnXCUM7v6hwLT6l3lXuXXj/6178Nr6I8C0H4ClO5Sj9mS73y8AVzO13efWYyXvakOWse+RNffygIWbgY9XF730aNZaZX1X9j1x2fToagZw9Ly2+9x1iv8/2IN9z3mkHUyWLFmChQsXYuXKlRg7diy6dOmCcePGISYmBnl5eWjZsqXoiBZVrlgdY/p9gV9TfsS2Q98DAKr71kKfjiMx9/s3sXj9VLz2zGzBKYsqLfN9ZrMZ05cMxNAe0xHg10hMQDeQbwY+3QCcuVr6+ztOAP/T8Oi/J9h9Wvt9XskAzkq41kR27HtkyZIdwL600t/7/SKwIFk5k0y22XvG/pt8WJObDxwswzo9T8W+pz1pB5Np06ahe/fuiI2NLfJ6SEgIvL29ERUVhRs3bqBXr14IDQ1FdHQ0nnzySRw/LscdBqpU9MNzncbgy7V/g9msHAbv1mYQ0q+koneHN1Glop/ghCWVlhkAFq2bjKCA5ujQrLe4cDZITk4WHUHVoXQg/Yb6L5Stx4Cbd1wWSfectVj97HXn7NcRstf1w9j3XE/2+rhwU/kgreb4ZeUP2cZZ/Yl9zzHse9qScjBJT0/HoUOH0K9fyfsrp6WlITIyEuXLl4fBYMCoUaOQmpqK/fv3o1evXhg8eLCAxKXr02kkrt++gHW7/1P4Wt0aIQj0DxGYSl3xzHuOrcfu1J/xylMfC05m3eHDh0VHULXzFGAwqG9TAGD3KfVtSJFvBq7cds6+L9x0zn4dIXtdF8e+51qy18dOG/qZAcDOk06P4jac1Z8uOmm/jpC9rotj39OOoaBAvhOoO3bsQExMDH788Uf07Nmz8PXs7GwEBwejR48eWLBgQYnv27VrF3r37o30dOvnIw3WPiH+YcZrGxEdHGdzdms+XjoIPdv9Bc2COlrddv+JJIz9tItDP0eL3NdvX8TYz7pg2tA1Np/SK0tmNaNHj7a6zezZs61uN3u2uFOqf560AwEh6qsLzeZ87Pvp79j8zVsuSqVfXuUrYsSCrCKv2XIHmtKMKra+78imr7Du8yEOJrOdrHXNvse+p5Unhn2Fph1egNFk+V47ZnM+0g78hO9nPOXCZPo15O9pqFyjfpHXHOl9xfvehWPbsWxy+zIks43Mda1l73P3vgfYl9vWcUPKu3L5+/sDAFJTU4sMJh9//DEuXLhgceH7nDlz0Lt3b1dE9Ahf/zIFWXdv4ZP/Dip8rX7NMIzq+5m4UDqWnXEFZnM+jEaTxW2MRhPuZlhYhEJFmPOUlZoFBQU2H2iwVd69u5ruj/SDfU9b2RlXYTBYuzijANnsezbLz3VOf8pz0n5JfjL1PSnPmJjNZjzyyCO4cOECZsyYgcDAQCQmJmL16tVIS0vDjh070K5d0SPPkydPxpo1a7BhwwZUrFhRsyy7lgI3BS0Iq1YPaP28Y98rKndZMqtJSUmxuk14eDiOHlV/2lTTpk21imS33aeBRVutbzf+WaCGr9PjuIUPVyqL1a25fzSx+BFCS/7UGugc5nguW8la1+x79mHfsyz9OjBjjfXtXusKNK3j/Dzu4Itk2x4oa2/f69gE6NvW8Vy2krmu9dhD9NqvLZFyjYnRaMTy5csRGRmJhIQEDB48GP7+/hgxYgRMJhOioqKKbD916lSsWrUKa9eu1XQoIX2ZPHmy6AiqousDtaso11Nb0iaIQ4k96jtpTaGz9usI2euaxJK9Pur5AZGBlt83AGhYAwgNcFkk3XNa35PomTKy1zU5j5SDCQCEhoZi48aNyMrKQlpaGqZMmYKDBw8iIiICFSpUKNxu8uTJ+OGHH7Bu3TpUq1ZNXGASLj4+XnQEVV4mIOExIKCa8rXBoPxSvj+oRDcA4iV6wJUePNJQ+31Wr6R8UJKF7HVNYumhPl7q8OBsyP2ed//qywY1gFfiAKO2V2O6tRZO6HteRqBZPe336yg91DU5h5RrTCzZtWsXHn300cKvDx8+jEmTJiE4OBhxcXGFr+/bt8/14Ug4W079ilatIvB2D+XhWHvPANm5ymvtgvkEZEdEBALVKwI3NLzFcocmgFGiQzZ6qGsSRw/1Ud4beLULcOqKcpeu29lApfJAq0ZAkwAOJfaqXUU5w5R6Ubt9PtJI+f9EFnqoa3IO3QwmmZmZSE1NxfDhwwtfi4yMtHmVP5EsjEYgsp7yh8rGZAR6twK+2qzN/vx9gU4uWFtC5GkMBqBxLeUPld0zjwCz1gJmDT4C+XgDPaOsb0fkCroZTHx9fZGfny86RqkWrH4Ph09vRWSjDqhXMwxLN07HqOc+R63qDfDx0pdggAH+Vevh3f6LYDKa8P6XvZCZfRNzRmyRMnd0cCyeHV8VIXUfAQBMfHkFqlT0kyY30cOiGyhHXtWeAm/L4k+jAegfA5TXTVcUz1IPaR7UCR8vfQmXb6bBy1QO415YinJePnjn88cRWCMEfx3wtRQ5Ixu1x5h5nXHq4kF8OnofAv1DkJefW+K17JxMYdmJSlPPD+jWHFhzwPI2ti5679NKuYSVLLOnh9y3+eAKzP9+JBa/f1ZYD7En9/Fz+zB/5SgAwOUbZ9Cn00j8qdMol3/2k+iCBX06dfEQsu7exqzhm3D7zjXcvZeFfrFvIzo4Fr4+1TB18CrMGr4JAX5B+C1lNQBg6pBVglOr5waAoIDmmJmQhJkJSYVPLZUht5qHL+cjz/L8o2VbPGsAMCAGCJbwaK6sda3WQ06c3wcvr3KYNXwTurUZjPV7vkGF8r4YN3CpVDlNRi9MHvQdOjXvW7h9aa+Jym4LWeuDnO/JZkBMGZ/f1725cimxbGSqa3t7yH2bDySiZjXleTMieoi9uUMCWxR+7guqE4V24b0AuP6zHweTMjp0agtahz4JAGjZ5Ikiz6ioXLE6KlWoCgDwMnnDaLD8/ApXU8sNAGmXj2L0vE74YvVfdXO53Pz580VHIEG8TcoC2vYO/JKu7KN8b+sgrVNpQ9a6Vush/lUDYTYrZ7gzs2+iSkVxC6jUchoMBlSvXLvI9qW9JjNZ64Ocz2AA4tsCPaMBk53rdMp5Kd/bXdJLuGSqa3t7CAD8enQ1WjZ53IZn+DiPI7kBIPteFm5kXBT21HoOJmWUcec6/v3zRLw1Pw6L13+IjDvXS2xz9dZ57E5dV1ggMrCWe+G7xzArYRMy79zA9iM/CEppn4SEBNERSCBvk3JXs4Sutt1Vy9ukDDJ/7aUsopeVrHWt1kOqVPJHTm42hnwSjlXb56Nj8z9JmdMdyFof5BoGg3Lm5K0etj0HxmhQLn999ymgfRPn53OUTHXtSA9Zt/vfeKzlCy5IZ5mjvW9nyhq0Duvu5HSW8WrqMqpc0Q8vd/sA7SOfwY4jq3DlVtGn3NzLy8En/30ZY/r9CyaTPP+6reW+f/lW+2a9cfzcXrSPfEZETLskJSWJjkASCKuj/Dl7DTh0Tvnfq5lAvhmo4A3UrQ408gdaNAAqSnQXGktkrWu1HrI79WdUrVQTX759FJsOJGJ58gy8+MQE6XK6A1nrg1yrbnXlIZVXMoD9aUrfu3QbyM1Xzo7Uqarc+bFFQ+VOkLKTqa7t7SF7j29ARMMYeHuVc1HC0jna+7Ye+h/i495xcjrLeMakjJoFdcTBk5sAAPtPJBVevnDfnMRheKb9CDSsHSEinkVqubPvZSH/j68Pn96KujUkvACVyIr6NYAeUcCwLsDfngbGPwuM7amsJWnfRB9DiczUekhBQUHhwY2qlfyRdfeWkIyA9R5N5E5qVgYejwQGd1bOBo9/Vjk78lJHIC5cH0OJbOztIacvHsL2wyvx3r+648ylw/hq7fuuiFmCI70vLz8XaZePIrhutLPjWcTBpIyCAprBy+SNt+bHwcvkDZ9yD25tceT0dmw5tAIrNs/BW/PjsOXg/wQmLUot97krx/D6P9pgzLzOuHLzLDpFlVzURUSeTa2HtA59EmmXj+Kt+XH4908T8EzMcJU9icsJAFMWxWP3sZ/x8dKXse3Q9xZfIyLPZG8P6dPxTXzy2gZMf2UtGtaOxODuU3WRG1DO9rQI7ioibiF5ri3SsaE9pxf+fdOBRCzd+BEC/ZsgOjgWK6dmlNj+/S97wa+KDReDOpla7vmj9pTYXpbclvBhTOSOZK5rtR4y4aXEIttm52TioyUvIKx+G1fHVM05/sVlJbYv/prI7NbIXB9EjpKtru3tIffdv8WuqB5ib+42Yd3QJqxbkddc/dnPUKCXWy4J8vsGIOOymJ9duRYQ5uDgKip3WTKrSUlJsbrNsmXLEB8fr7pN06ZNtYpEVGay1jX7nn3Y94hsJ3Nd67GH6LVfW8LBhHTBlkYWHh5u9SgLf0GTTFjXpIb1Qe6IdU1quMaEiIiIiIiE42BCRERERETCcTAhtzFv3jzREYg0x7omNawPckesa8/FwYTcRmRkpOgIRJpjXZMa1ge5I9a15+JgQm4jNjZWdAQizbGuSQ3rg9wR69pzcTAhIiIiIiLh+IBF0gVbbgs4ceJE3j6QdIV1TWpYH+SOWNekhs8xISIiIiIi4XgpFxERERERCcfBhIiIiIiIhONgQkREREREwnEwISIiIiIi4TiYEBERERGRcBxMiIiIiIhIOA4mREREREQkHAcTIiIiIiISjoMJEREREREJx8GEiIiIiIiE+/+9nVNuvN5pUQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1049.8x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "twolocaln = NLocal(num_qubits=3, reps=2,\n",
    "               rotation_blocks=[RYGate(Parameter('a')), RZGate(Parameter('a'))], \n",
    "               entanglement_blocks=CXGate(), \n",
    "               entanglement='circular', insert_barriers=True)\n",
    "twolocaln.decompose().draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's encode the first training sample using the `PauliFeatureMap`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First training data: [-0.47556152 -0.42256069  0.30048785  0.00534385 -0.8948025 ]\n"
     ]
    }
   ],
   "source": [
    "print(f'First training data: {sample_train[0]}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1591.6x686.28 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "encode_map = PauliFeatureMap(feature_dimension=N_DIM, reps=1, paulis = ['X', 'Y', 'ZZ'])\n",
    "encode_circuit = encode_map.bind_parameters(sample_train[0])\n",
    "encode_circuit.decompose().draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "\n",
    "**Challenge 3a**\n",
    "\n",
    "Construct a feature map to encode a 5-dimensionally embedded data, using 'ZZFeatureMap' with 3 repetitions, 'circular' entanglement and the rest as default.\n",
    "    \n",
    "</div>\n",
    "\n",
    "Submission format:\n",
    "```python\n",
    "ex3a_fmap = ZZFeatureMap(...)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "##############################\n",
    "# Provide your code here\n",
    "\n",
    "\n",
    "ex3a_fmap = ZZFeatureMap(feature_dimension=5, reps=3, entanglement='circular')\n",
    "\n",
    "\n",
    "##############################"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submitting your answer for 3a. Please wait...\n",
      "Failed: Gateway Time-out\n"
     ]
    }
   ],
   "source": [
    "# Check your answer and submit using the following code\n",
    "from qc_grader import grade_ex3a\n",
    "grade_ex3a(ex3a_fmap)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 Quantum Kernel Estimation\n",
    "\n",
    "A quantum feature map, $\\phi(\\mathbf{x})$, naturally gives rise to a quantum kernel, $k(\\mathbf{x}_i,\\mathbf{x}_j)= \\phi(\\mathbf{x}_j)^\\dagger\\phi(\\mathbf{x}_i)$, which can be seen as a measure of similarity: $k(\\mathbf{x}_i,\\mathbf{x}_j)$ is large when $\\mathbf{x}_i$ and $\\mathbf{x}_j$ are close. \n",
    "\n",
    "When considering finite data, we can represent the quantum kernel as a matrix: \n",
    "$K_{ij} = \\left| \\langle \\phi^\\dagger(\\mathbf{x}_j)| \\phi(\\mathbf{x}_i) \\rangle \\right|^{2}$. We can calculate each element of this kernel matrix on a quantum computer by calculating the transition amplitude:\n",
    "$$\n",
    "\\left| \\langle \\phi^\\dagger(\\mathbf{x}_j)| \\phi(\\mathbf{x}_i) \\rangle \\right|^{2} = \n",
    "\\left| \\langle 0^{\\otimes n} | \\mathbf{U_\\phi^\\dagger}(\\mathbf{x}_j) \\mathbf{U_\\phi}(\\mathbf{x_i}) | 0^{\\otimes n} \\rangle \\right|^{2}\n",
    "$$\n",
    "assuming the feature map is a parameterized quantum circuit, which can be described as a unitary transformation $\\mathbf{U_\\phi}(\\mathbf{x})$ on $n$ qubits. \n",
    "\n",
    "This provides us with an estimate of the quantum kernel matrix, which we can then use in a kernel machine learning algorithm, such as support vector classification.\n",
    "\n",
    "As discussed in [***Havlicek et al*.  Nature 567, 209-212 (2019)**](https://www.nature.com/articles/s41586-019-0980-2), quantum kernel machine algorithms only have the potential of quantum advantage over classical approaches if the corresponding quantum kernel is hard to estimate classically. \n",
    "\n",
    "As we will see later, the hardness of estimating the kernel with classical resources is of course only a necessary and not always sufficient condition to obtain a quantum advantage. \n",
    "\n",
    "However, it was proven recently in [***Liu et al.* arXiv:2010.02174 (2020)**](https://arxiv.org/abs/2010.02174) that learning problems exist for which learners with access to quantum kernel methods have a quantum advantage over all classical learners.\n",
    "\n",
    "With our training and testing datasets ready, we set up the `QuantumKernel` class with the PauliFeatureMap, and use the `BasicAer` `statevector_simulator` to estimate the training and testing kernel matrices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "pauli_map = PauliFeatureMap(feature_dimension=N_DIM, reps=1, paulis = ['X', 'Y', 'ZZ'])\n",
    "pauli_kernel = QuantumKernel(feature_map=pauli_map, quantum_instance=Aer.get_backend('statevector_simulator'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the transition amplitude between the first and second training data samples, one of the entries in the training kernel matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First training data : [-0.47556152 -0.42256069  0.30048785  0.00534385 -0.8948025 ]\n",
      "Second training data: [ 0.05258832 -0.67204637 -0.28157158  0.02261103 -0.38696331]\n"
     ]
    }
   ],
   "source": [
    "print(f'First training data : {sample_train[0]}')\n",
    "print(f'Second training data: {sample_train[1]}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we create and draw the circuit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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d2eF4nJ83SWkGD3EoDXu24/OVGT5fPFVDplTXtY9X0oc/PqGJN7+v8PpRkqR9R7ZrzPRonc86J0n6Iu5lffTjk+YE6sXoi87nSe3arecAu/feezVv3jxNmTJF0dHRSkhI0LBhw3T48GFNnDjR7PAAwKlycqTFm6Uf1kn2nL/mp8hxXK4fWsMxF0uNQLOjBAC4s+VOvqMn44wjqRbdxLn1VhSfL56qOfHT5GvzU/2QZnryzi/dcl4cd3beLv2W7Nw6kw445rmrW8259RZleP/JGjHgCZ08fVyvzLlX67Yv1aAu90qSQkOaqVfboZq95HkN6HSn4tbO1vRxCeUboBejL7qOJ7Vrt02AzZo1Sx999JHi4uIUExMjSerbt69Wr16tefPmqWPHjiZHCADO9ctW6du1F/996VVf+49Lb/4sPXq1FOBb7qEBADzA8VNS8iHn17tqFwmw0rrwxRCl9+d+6dRZ59e7epd0tUkXAFWtXEMTb35fd73QVAkb56tHm8GSpFtiH9VDb/bQ71t/0Ojrp8vPx9+cAL0QfdH1PKFdu+0tkM8995wGDhyYm/y6oFmzZvL19VVUlOOSuieffFItWrSQ1WrV3LlzzQgVAMrsXJa0cH3Br+fIManxSif/AgoA8B57jrquXm7Fh1lc2a7NFFQ5WEN7T9QHCx9Xdna2JMnH5qu24X2UkXlcbZr0MjdAoBTcvV27ZQIsJSVFGzdu1M0335zvtT179igyMlL+/o6s4cCBA7Vw4UL16dOnvMMEAKfZvL/oCYstcv4tAAAA75Ga7pp6M846boUEzOCqdm32RPiSdEPvh3TsRKoWrfqvJGnXgU3atOtXdWg2QN+vfM/k6IDSced27Za3QKakpEiS6tatm6c8MzNT8fHxGjRoUG5Zjx49SrWN+Ph4SZLFYilllN7poU8dP+9xXIDy1e6KcYq9641Cl8mRtGPvYVkstcsnqAqEsa/8cKzhbdypTfe89QV1uu4fecqKeiJeQa8//Fnef4c1CteJwzvLEJ1zTHtgqdo1jTU7jAohPj5OnYf1NTsM3fCPn9Sw7RV5ypzRrg8dSZPFUqOM0TkUp12+MjouX1lgQJDm/euYJMcD4F6b94DG3zBDYSEt9NCMHuoROVg1qtYptF53eJ/ol87nKe+rp7Vrt7wCLCQkRJKUlJR3Fs+XXnpJqampio6ONiMsAHCZM6eOFblMTna2zmQcL4doAACeyJ7lgomSLtR9nkvASuqV0XHMOeQErmrXWW7Wpr9ZMVPNQ6PVIixalQOq6u6rntFbCx42OyyvQF80j7u1a0tOjvvd0Z+dna0OHTooNTVV06ZNU2hoqObOnavvv/9ee/bs0W+//aauXbvmWSc2Nlbjxo3TTTfdVKxtxMbGSpLi4uKcHL1nu/CrSFG/qgBwrsxz0pPzHE86KsygKOmqtuUTU0XC2Fd+ONbwNu7Uplftkj75tXjLXoj38iu9jAT4Ss/f/NfTiU2WOFtKSzE7ioqhepjU6Tazo5Dmr5aWbinesiVp183qSOMGlD6uS5nZLt3hfaJfOl9Ff1+Ls/+lyem45RVgVqtVc+bMUWRkpEaPHq177rlHISEhGjt2rGw2W+4E+ADgLSr5STEtC37dIqmyn9SDpzUDAArQMNg19TYIdo/kFyqmBi5s1wAqFrecA0ySWrRooaVLl+Ypu+OOO9S6dWtVqlTJpKgAwHWujnI85nvFdkfC69LLcwP9pQf6SVUZ/gAABQipKtWvIe138t3y7Rs6tz6gJFrVl/x8HE/MdibaNVDxuOUVYAVJTEzMN//XlClTFBYWphUrVmjUqFEKCwtTcjKPSQPgeaxW6dau0iODpB7NL5bf1k16cogUxi+VAIBCWCxSr+ZFL1cS/j5SdBPn1gmURCU/qVNj59bZIFhqWNO5dQJwfx6TAMvIyFBSUpI6duyYp/yZZ55RSkqKzp49q6NHjyolJUVNmzY1KUoAKLuwYOnmLhf/3a2p45dPAACK0iVcql/defVd3c4xBxhgpqvaSpWc2A4Hd+S2Xlc7kr5fo6d31NX/DJDdnvfyvRnzH9LEmTEa/3pXbdx5ceLCs+czdcvTdbU66ecCy3Ye2KiHZ/TSQ2/21I796yVJq5IWafwb3fTI232159CfkqRPfnpaD77RXQ++0V2rty2WJM1e8oImzYzVpJmxuu7xQJ04fUyJW3/SwzN6afwb3fTBD5MlSacy0/XEB9dq0sxYzVs2XZJ05txpTf7PNZo0M1ZPfjhY5y55OMOXv7yqh2f0KnS5mQsmaMJbvTVj/kO56y1K/K8efae/Js2M1ZH0fWU/6CiSx3ylqlKliuz2ImaHBgAAACowH5s0vLv06o+SPbvg5YozSXjT2lLvCOfFVl627FmptxdMkMViVUSDzhp9/avaeWCjps8dKavVpvo1m+mRWz6Q5ZIMyIFjuzT+ja5qWLuVfGx+enHkT5IcX1B/WvWxsrPt+ufwzxRSLVQzF0xQUkqimoV21NjBrxkuV6NKHb0w63YdzzioiLDOuv/al3K39eUvr2rZhi81fexy2e1Zhsv98edCzV76giQp5fBWPXjjTDWt3z5fjEb7alRnaY6JO6lWWRraWfo0ofDlitOu+0Q4JsB3F0fS9+mLuJfVt8OwfO+RJwuqHKyXRi7WUx/fkO+1UddOk4/NVweP79br88Zo6r3fSZJ+WPm+mtTL+7Sny8s+XjhFj4+YJavFqtfnjdG/7pmvT3/+l14atVinz5zQzAUP64nb/6cBne7UHVf+nzIy0/Tkh9erY/P+uq3fY7qt32NKP3VE//rvTQqqHKz2zfqqU8SVkqRH3u6rtIzD+inxI/XrMEL9OgzT0x8PVf+Ot2v9jl/UsmFX3XHFk/ps8VQl/rlQPdo4ElzJ+9fmxvfH1oX5lqtVvYEyz2bo1THL9NqXo7V17x+qGVRf63fE6+VRi11w9N3PkfR9+vec+3TqTLqpbdxjrgADAAAAULSwYOmuXpK1DLmM+tWlv/UpWx1mqVO9kV4etUTTxy5XWsYh7UzdoAa1IvTauAS9OmaZJCkpJTHfetHNr9Aro+Nyk19H0vflfkF9ZXScQqqFalvK6twvsllZ57R17x+Gyy3f+JXC67fTtAeW6mxWppL3r5OkfF+WC1quc8uBemV0nF4ZHafa1RuqY/MBhjEa7atRnaU9Ju6kUxPH07DLIqqB4+ovd7IqaZGiW1xh+B55Mj/fAFWtXMPwNR+b43K+zLMZCq/fTpJ0Puuctuz5TZGNe+YuZ1R2MvO4aldvoJBqoco4k5ZbXskvUDWD6mn/Ucd0SPWCHfdu+/r457vcb8WmBere+vo8sdiz7apRta4qBwQp9egOhddzNLZGdVpr694/VL9mU505d0qSdCozTUGBjntoF/7+H13R6a7cuo2W27LnN0W3uEKS1LH5AG3evUKJW3+UPduuR9/prze/Hi97tndf7LMqaZH6d7zd9DZOAgwAAADwMlENpFF9pWqleHhKmzBp3ADHA1g8UXBQXfn5BkiSbFZfWa223C+5kuMLca1qDfKttzZ5qSa81Vtf/uK4KsHoC2pxv8imHrv4Bbpp/fbavMtx6dLlX5YLWi739aM7VL1qHVXyr2IYo9G+GtVZ2mPibq5q65gmwtdWsvUscjxt+65eks3Eb8DrkuN0w5M1NGlmrEZMbaQnPxys9TviFRUeY/geebOnPrpBj713ZW5y96fEj9S/4+15ljEqy8nJvvQfuf97/ORB7Tn0p/Ye3JJn+f/+9JSu7TYqT9mvG79Sz7YXr0z77rd39beXIhRUuab8fPzVoHaE1u+Ilz3brvU7f1FGZppCQ5pry+4Vum9apJJSEtW6UQ9l2c9rXXKcOjTrl1uX0XIZmWmq7B8kSQoMqKaMzDQdzzioLPs5vTxqsfx9Kyth0/xSHEX3Y9TGJWn9jnj1iBxsehsnAQYAAAB4oYh60j+ukXo2L17CIKSqdEcP6d4+UmUPTX5dasf+9Uo/dViN6rSWJCVsWqD7p7VR2smDuVdvXBAcVE8f/iNJ00Yt1eptP2vH/vWGX1CL+0W2Qa0IrU+OlySt275UGWfSDL8sGy13qeUb5qlnmxsKjNFoXwursyTHxF31bO5o123DHImtojQKkcZfId0QbW7yS5LaNumjiAZd9MroOEWFx+jBG9/SmXOnchOcUv73yFs9dfdXemP8Sn3ww+Oy27OUuPVHdWk5KPd1ozJJea7mslgcb+j9V7+kqZ/dptlLXlDrS64WW77hK504fVT9OgzPLTt95qTSTx3JvUJMkq7pNlIf/j1JR9JTtH3fGg3qer8270rQ4+8PUs2g+qpRtY4WJX6sbq2v0/uPbFLXltdo8epP9fOqT/LULclwucCAajp99oQk6dTZE6pSqboCA6opKjxGktS+WT/tOZQ3ceepjNp4Tk5OnnZuZhv3mDnAAAAAAJRMZX/HFTPXtJNW75Z2HZZSjkunzzlubwwOlBrUlFrVl1rU9axbHo+dOKCpn92Wpyy4al1Nvn22Tpw+pje/Hqcnbv8i97UekderR+T1evPr8fpt87fqdckVIH4+/pIcWb9ura7VroMb831BTUpJVJWA6vm+yNqsPvmWu63vY1qzfbEefae/6tZorBpV6hh+We7W+rp8y11qxZZv9NSd8wqMMbx+VL59LajOkh4TdxZSVbo3RjqW4WjXe45K+9Okc+clm02qE+R40mNUQ8d/3UXqsR2qFxwuSTqcvldpGYdzbwGUjN8jb3Qu66z8fPxVyb+KAvwCdTzjoA6l7dE/3xuo/Ue3a+WW7/T03V/nK2seFq2gSsE6nJYii8WqygGOZHTrxt017YGlSjm8TfMT3pTkSLIsSJihZ/+aX+yCP7b+oM6XJNUuxGK1WhXgFyg/30qq5Beox4Z/Knu2Xc9/PlytG3XX3kN/qmplR2MKCgzRqTPpOpyeouT9a/Xtire1++Amfb38DVmttnzLRTbuqe9+e0cx7W7Rmm0/68pOd8vH5qfvV74nSUrevzZPQs4TFDT+3j3w2TxtPKRaqLbvW5vbzs1u4yTAAAAAAC9X2V/q1cLx5y2Cg+rqldFx+covTAI/8tppCg6qK+nil1xJquwfJH/fvPeGnj5zUpUDqkqSNu36VYN7jZevzT/fF9QGtVoW64uszWrTuCFvSJJenTtSnSKu0lfLX8/3ZXlIr/H5lrvg2IkD8rX55V6ZZRSj0b4abbs0x8QTBFeRBkSaHUXx7T6wSY3qRsqebZfFYtXqbYsU3dxxS63Re+TJsuzn9fj7g7QjdZ0ee/8q3T7gSW3ctVwj+k/W1E9vVUZmmrJz7Lp30PMKqRaqGQ/9Iclxy2Kbxr0My6pWrqE7r3xaz356qyRp/A0zJEmfLZ6qNdt+VlDlmnp46DuSpHe/e1THMw7qn+9dpcCAavrXPY5bDJdv/ErD+0/OjfPHPz5U3NrZys6xq114rBrWbqmklFV699tHZJFFt8T+Xf6+ldSvw3A9++mt+nnVJ/Kx+Wry7f9TUOWL2dWHZ/TSkF7jlZGZZricr2+AJrzVW03rt1fLho7Hvfv7VtKkmbGqFhiiob0nuPgdca6Cxt+EjfPztHFJue3cHdo4CTAAAAAAXiN+/Rwl7f1D7333d0nSvYOeV1rGIc1d9m9Jjjl6oltcqWMnDuiHP/6jEf0na8POZfr4xyny9fFXmya91aphV0n5v6D6+vgV64vskfR9ev7zEbJarBoQfadCqoXq/mtezI3xwpdlo+UuSNg0X90jB+f+2yjGJWtm5dvX2jUa5qvTaDmjYwLX2nVwk1o36q7zWWeVlnFIq7f9rJv6TJJk3G5bN+5uZrhl4mPz1Uujfs5T1q6p40rJp+/+usD17rzyqULLwutH6bVxv+Z5fUT/yRpxSVJLkl64/0fD+iePmJXn39d1f0DXdX8gT1mLsGhNe2BpnrIqlaoXWKckTR+7vNDlLjwx9lKjrptWYH2e6vI2fvREqpJSEnVTn0mKW/c/09u4JSfnkpnjKpDY2FhJUlxcnKlxuJsLjw6ePsLcOADQH8sTx7r8cKzhbWjT5StxtpSWYnYUFUP1MKnTbUUvh9K3y/h1Xyim3S1l2rY7vE/0S+fzpve1NO28OPtfmpwOV4ABAAAA8AhVa5sdQcXBsS6+0h6rwWFlS36VZdvO5A4xeBt3OKbOiqE07dxV+08CDAAAAIBHiOhX9DJAeavo7bKi77+38sb31eQHwQIAAAAAAACuRQIMAAAAAAAAXo0EGAAAAAAAALwaCTAAAAAAAAB4NRJgAAAAAAAA8GokwAAAAAAAAODVSIABAAAAAADAq5EAAwAAAAAAgFcjAQYAAAAAAACvRgIMAAAAAAAAXo0EGAAAAAAAALwaCTAAAAAAAAB4NRJgAAAAAAAA8Go+ZgcAVGRbl0gnD5kdRcVQtbYU0c/sKAB4Isbq8sNYXTJmtk0z3yv6pOtVxPe3LPs8L1Had9y58RRXaA3pxk7mbJu+6Hpm9kVvbNckwAATnTwkpaWYHQUAoDCM1XBXFbVtVtT9rig88f3dd1xKroCJIE98r1B83tiuuQUSAAAAAAAAXo0EGAAAAAAAALwaCTAAcDOnzkrbDlz894F0KTvbvHiAssrJkdJOS1v2Xyw7muEoBzxVdo506MTFf29NlU6eMS8eAABQOOYAAwA3kHFG+i1ZWpksHT6Z97UXvpX8fKTW9aWeLaRmtSWLxZw4gZI4fFJK2Cat2iWdyMz72jPzpUB/qUNDR7uuV92MCIGSycmRdh+Vfk2SNqRIZ85ffG3mEsd/gwOlzuFS92ZS9crmxAkAAPIjAQYAJsrOcSQIFqyRzmUVvNy5LGntHsdfRF3ptm5SjcDyixMoiXNZ0g/rpbgtUmEXeZ06Ky3f5vjr3kwa3FEK8C23MIESOXlGmvO7tH5v4csdOyX9uEH6eZM0sK3Ur7VkM/Gei0kzY7Vl9wrZbL6yWm2qW6OJhvefrJh2N5sXFFBGtGsApUECDECxXP5Bo15wuEb0f0K9o4aaHZrHOpclfbxc2rSvZOttPeC4KuxvfaSIeq6JDSittNPSO0uk1PSSrbdiu+MWsgf6SbWDXBNbRcF47Xy7j0jvxUkZZ4u/jj1b+m6d49bf+2Kkyv4uC69IIwZM0YgBT8huz9L8hDf1/OfD1Sy0g0JDmpkXVAVAX3Qt2jWKi76IC5gDDECxjRgwRd9MzdC8p46qb/thevazW5VyOMnssDxSll36zy8lT35dcDZLejdOSjpQ5KJAuTmZKb35c8mTXxccO+VY/8jJopdF4RivnWfvMemtxSVLfl1qx2Hp7aXS2fNFL+tqNpuPBnW9X/bsLCXvX2t2OBUCfdH1aNcoDvoiJBJgAErBZvPR9T3GKDvbrp2pG8wOxyP9tNFxtUthpo9w/BXEni3991fH/GGA2XJypFm/FZ28Kqpdn8iUPkngwQ/OwnhdNmezpI+XOf5bkKLatCTtOSrNX+3c2ErjfNY5fZswU5IUFtLC5GgqFvqi69CuURL0xYqNBBiAEjufdU7zE2bIx+ar8PrtzA7H4+w/7pgbxhkyzkhfr3JOXUBZrNolbd5f5GLFsvuI9MtW59RV0TFel80P66QjGc6pK2G7tO2gc+oqqc8XT9WQKdV17eOV9OGPT2jize8rvH6UJGnfke0aMz1a57POSZK+iHtZH/34pDmBejH6ovPRrlEa9MWKza0TYNnZ2Zo2bZqaN2+ugIAAtWvXTvHx8YqIiNDIkSPNDg+ocC580Bj+bJhWbJqvJ+/8knkWSmHpFsfk986yapd0zElf0IDSyMlxXlL3gqVbHFc5onQYr8vu9Fnp123OrXOxk/tJcQ3vP1lfP5OmuU8dUZeWV2vd9qW5r4WGNFOvtkM1e8nzSj22U3FrZ2t4/8nmBOqF6Iuu48nteu6zsfr962eLXY6yoy+6nie0a7eeBP/ee+/VvHnzNGXKFEVHRyshIUHDhg3T4cOHNXHiRLPDAyqc4f0na8SAJ8wOw6OdPiut2e3cOnMk/ZYsXc2PWDDJzsPSgVLO+1WQ9EzHHHlRDZxbb0XBeF12f+yUztudW+efqdLRDKlmFefWW1xVK9fQxJvf110vNFXCxvnq0WawJOmW2Ef10Js99PvWHzT6+uny8zFxxn4vQ190Pdo1ioO+CMmNrwCbNWuWPvroIy1YsECPPPKI+vbtq8mTJ6t79+7KyspSx44dzQ4RAEps1xEpywVXtZh1Ww0gSdtd1P5o1zCTq9q1q+otrqDKwRrae6I+WPi4sv+abM/H5qu24X2UkXlcbZr0MjdAoBRo1wCKw20TYM8995wGDhyomJiYPOXNmjWTr6+voqKidPz4cV177bVq0aKF2rVrpyuvvFLbt283KWIAKNreY66pd98xJg2HeVzVrlOOuqZeoDhSXNWuXVRvSdzQ+yEdO5GqRav+K0nadWCTNu36VR2aDdD3K98zOTqgdGjXAIrilrdApqSkaOPGjZowYUK+1/bs2aPIyEj5+/srMzNTDz/8sAYMGCBJev3113XPPfdo2bJlRW4jPj5ekmSxWJwbvId76FPHxEQcl/Ix7YGlatc01uwwKoT4+Dh1HtbX7DDU9+4ZihowJk9ZUU8PK+j1hz+7+P/n7FKlqtV17rST70OrIBj7yuaWp1aoXrNuecpK064vbdOStHbzDlkGNi1jdGXHWF1+3GWslqRxH52Vzccv99/OGKsl6YNP5uimLreUMTqH4rTNV0bH5SsLDAjSvH85MnHZ2dl6bd4DGn/DDIWFtNBDM3qoR+Rg1ahap9B6zXyv6JOu5+7vryvadVn2eejkpQprVXjMl/t9/lSt+n5anrLzZzLUsM2AEtUTHx+nB6903/cKZWNmX/TGdu22CTBJqlu3bp7yzMxMxcfHa9CgQZKk6tWr5ya/JKlHjx566aWXyi9QoAIx+qCB0nBdgsXiwrqBwriu7dGmS4Px2llc0/4sFve6AeObFTPVPDRaLcKiJUl3X/WM3lrwsCaPmGVyZJ6PvmgeT2jXXQZPVpcheeekmvtsrDnBeDn6Yvlx93btlgmwkJAQSVJSUpKuvvrq3PKXXnpJqampio6ONlxv+vTpGjJkSLG2ceHWyri4uDLF6m0u/EqZk+PER9ShQImzpbQUs6OoGGJiYpUz0/x2vXC9tHBD3rLLrw644MLVBAW9filfm3T65HFZ3et7lcdg7Cub9+OljZeNZc5o11Gtm7jFe8JYXX7cZayWpKe+ktJOX/y3M9q0JN09Yqi+fc05++iMtjm459g8/+7ZZoh6thlS5Hpmvlf0Sdfz9Pe3NO26LPv8xiIp+VCpVi2zmJhYzX3Wc98rFM7Mvuju7To2NrbE9bplAiw8PFxRUVF67rnnFBwcrNDQUM2dO1fff/+9JBkmwJ5++mlt375dS5YsKe9wAaDYGgS7pt7QGiL5BdOEBedPgDmDq/oLUBxhwXkTYE6rt6bz6wQAAEVzy69LVqtVc+bMUWRkpEaPHq177rlHISEhGjt2rGw2m6KiovIs/+yzz+rbb7/VwoULVblyZZOiBoCiNa4l2Vww8jat7fw6geJq7qL214x2DRO5qv0xXgMAYA63vAJMklq0aKGlS5fmKbvjjjvUunVrVapUKbfs6aef1vfff69FixapevXq5RwlAJRMoL/UvqG0apfz6rRI6t7MefUBJRVeW6odJB064bw6qwZIbcKcVx9QUp3DpW/XSllOfMJui7pSrarOqw+AZ7rpibgSlQOewBPatdsmwIwkJiaqW7eLT5natGmTnnrqKTVt2jTP/Z9r164t/+AAoJhiW0mrd0nOupu/fSMphC9UMJHFIvVvLc36zXl1xraUfGzOqw8oqUB/x48Ly5KcV2f/1s6rC3nNXDBBSSmJahbaUWMHv5Zb/tLsu7X30Bb5+VbSNd1Gql+H4Tp3/oze+GqsDhzbqUZ1IzVuyBuaveQF/b71B509d1rD+j2uXm1v0MLfP9BnPz+jyMY99djwT3PrzMnJ0QOvdtDgnuN0ddf7ir2u0XaPpO/Xi7Nu17msM7rryn+pY4sBhtt4a/7DSt6/VpK0I3WdvvrXcZ0+c1LPfz5cJ04f07XdRumKTnfqxz8+0uylzyu4aj21bNBF91978QFhM+Y/pJOnjubGM3vpi1qdtEj27Cy9PGqJrMylACegL9IX3ZnHJMAyMjKUlJSkMWPG5JZFRka6xeS4gCtt2bNSby+YIIvFqogGnTX6+lclSYsS/6ufVn2s7Gy7/jn8M4VUC81d50j6fk358FrtPrhZ3zybIZvN0dUvPyHZ7Vl6YdbtOp5xUBFhnfMMzF/+8qqWbfhS08cuN4zhwLFdGv9GVzWs3Uo+Nj+9OPInw3ULiqeg/bo8xoKWu3w7Be2zO2oQLPVrLS3eXPa6Av2kG42fCwKUqy7hjsTu1gNlr6tBsCNR7GmMxquixqbCXr90jDtz7rSe+eRmnTl3SoEB1fTEHV9o35Ftmj53pKxWm+rXbKZHbvlAuw5uyld29nxmsda1WCzaeWCjYfnl55ydqRs0e+kLkqSUw1v14I0zcyeYvvwcYFRW2DnMnVzTXtq4Tzp+qux1dQmXIuqVvR5nOZK+T1/Evay+HYYVeJ71FNtSVivzbIZeHbNMr305Wlv3/qGIBp1zX39s+GcKDbl4qfRXy19X3w7D1bF5/9yym2Im6bZ+jynzbIb+/u4A9Wp7g7pHXq+24X30yU9P5dneis3fqHqVWiVe12i7/1v6gu666hk1rd9OT3xwbe6X7su3MWbwdEnS9n1rNDf+FUnS9yvfU2z72xTb/jY9+nZfxba/TZJ0c8yjurrrfXliPn7yoA4c26lA/yBJ0p97fteZsxl6adTPxT7OnuZI+j79e859OnUm3aPbtyehL9IX3Z3HpBarVKkiu92u8ePHmx0KUK7qVG+kl0ct0fSxy5WWcUg7UzfoSPo+rd8Rr5dHLdYro+PyfXEIqhysl0YuVquGF6+YvPSElJV1Tlv3/qHlG79SeP12mvbAUp3NylTy/nWSpHNZZ3N/2SgoBkmKbn6FXhkdlyf5dfm6BcVjVKdRjAVt+/LtGG3DnQ2MKnoemIc/K/ypYlaLdHtPqWqlgpcByovFIg3vLtUILHy5otp1FX/pjp6umSvP1YzGq6LGpoJev3yM+2PrQrVs2FWvjI5TRMMuSvxzoRrUitBr4xL06phlkqSklETDsuKuK8mw3Oic07nlQL0yOk6vjI5T7eoN1bH5AMO4jcqKOoe5kwBf6a5ejiftFqSoNi1J9WtIN7jZjxWrkhYpusUVBZ5nPcmWPb8pusUVkqSOzQdo8+4Vua9ZLBa9NPtOTfngOh08vluStG5HnFZsXqBJM2OVsGmBJMnH5itJOns+U43rtpEkVQsMkc2a/we1pWs+z/2CW5J1jba788AGRTbuoUr+VVTZv6pOnTlhuI0Llm/8Sj3b3pi73x1bXCGb1abw+u2099CfkqSvlk3XxLf6aPW2xbnrzVs2XUN6Xvwe9duWb5V+6ogeebuvPln0r8IOr8dalbRI/Tve7vHt25PQF+mL7s4DP14CFUtwUF35+QZIkmxWX1mtNiVu/VH2bLsefae/3vx6vOzZ9jzr+PkGqGrlGnnKjE5Iqcd2KLye46ESTeu31+ZdCZKkhb//R1d0uqvQGCRpbfJSTXirt7785eKvaZevW1A8RnUaxVjQti/fjtE23JmvTbo/1jEfTGnX/1sfqVV9p4YFlEm1ytK4AaWf46haJWnsAMd8Yp7IaLwqamwq6PXLx7j6NZvqzDnHZUinMtMUFFgz94O+JPn6+KtWtQaGZcVdV5JheWHnnNSjO1S9ah1V8q9iGLdRWVHnMHfTOER6oJ9UybfoZY00rCmN6SdV8nNuXCWxLjlONzxZQ5NmxmrE1EZ68sPBWr8jXlHhMQWeZz1JRmaaKv91NUVgQDVlZKblvjbqulf02rgE3dr3H3rnm0mSpNSjyera8ho9e+93+uznZ2S3Z0mSXp83RqP+HaUOzfoVuK3ErT8pKjxGVkve41ScdY22m51tl8ViyY39VGZagdtwbH+hOkcMzN3vwEv3+0yaerYZoncmrteTd36pd799RPZsu06cPqa0U4cVGtI8t560kwdVpXINTXtgqfYc3KxtKasLjNvdGbVvSVq/I149Igd7fPv2JPTFit0XPQEJMMBD7Ni/XumnDqtRndY6nnFQWfZzennUYvn7VlbCpvlFrm90QmpQK0Lrk+MlSeu2L1XGmTRl2c9rXXKc4Unj0hiCg+rpw38kadqopVq97Wft2L++0HWLs1+FnTQvXa4023FHAb7SA32lwR1LNtdReC3p79cwQTjcU80q0iODpF4tSrZep8aOdl2vuiuiKl+XjlelYTTGhYY015bdK3TftEglpSSqdaMekqSETQt0/7Q2Sjt5UEGBNQ3LSrKuUXlh55zlG+apZ5sbCozbqKw05zCzNa0t/ePakv3oYLVIV7aRHrxCqhLgutiKo22TPopo0EWvjI5TVHiMHrzxLZ05dyo3cSmVvd2aKTCgmk6fdVytcersCVWpVD33taDKwZKkNk166djJA7nLRzWNUSW/QNUPaabjGQclSQ/e+JY+ePRPfb54aoHb+uH393VV53vylRdnXaPtWiwXv46dOntCgZWqF7iNlMPbFBIUqgA/x1PvAytV06m/9vv0mROqElBdVSpVl9VqVfUqtRRWq4WOnzyor5a9psE9xuaPJTxGktSuaV/tObSlwLjdnVH7zsnJydPGPbl9exL6YsXui57AfSfJASqYYycOaOpneS+vDa5aV5Nvn60Tp4/pza/H6Ynbv5CUd6Bs36xf7q0rhTE6IXVrfZ3WbF+sR9/pr7o1GqtGlTr6edUn6tdheL71L4/Bz8dfkr8kqVura7Xr4EYlpSQarlsQo/0yOmlevlxBMXoiq1Xq20rq0EhasV1amSylnc6/nM0qRdR1JBVa1nd8sQLclb+vdFNnqWdz6dckadVuKfOcwXI+UruGjnbdsGb+191VScbr0jAa4xYlfqxura/TLbGPak7cNC1e/amu6HSnekRerx6R1+vNr8frt83fqlfbG/KVHT95oNjrSspXXtg5Z8WWb/TUnfMKjNuorDTnMHdQvbI0MlbafsjRrjfuk7IMLl6rEiB1aSL1aO4+DyhJPbZD9YLDJUmH0/cqLeOwwuu3y33dGe3WTK0bddd3v72jmHa3aM22n3Vlp7tzXzt15oQCA4K099DW3M8VrRv10M7U9WoW2lEHj+1StcBaOpd1Vn4+/vLzrZT7Y5yRlMNJ+r+PhujIiX1STo7aNOmlusFNirWu0XbD60Vp864ValI/Sqf/itVoGw1rt9SvG7/KTThLUuuG3bVm22LFtLtFyfvXqkHtlrn7e/Z8pvYd2abqVWrpwLGd+s/3/9TZLEdZ/Lov1LqxI5bOEVcpef9aDYi+o8zvg6sVNPbePfDZPO07pFqotu9bm9vGPb19exL6YsXoi56MBBjgJoKD6uqV0XH5yi9MVD/y2mkKDnLcL9e6UQ99v/I9SVLy/rWqF9ykyPqNTkg2q03jhrwhSXp17kh1irhKXy1/Xcn71+rbFW9r98FN+nr5G7qu++h8MZw+c1KVAxyf7Dft+lWDe43X8g3z8q07pJfxvH3G+5U/RqPl9h7eWuzteIrqlaVBUY6/9NPSvuOOhIHNKtWsKtWrxhPx4HnqVZdu6iLd2Fk6miGlpknnsxxtuW41x62Snvigo5KM16VhNMZZrTZV/evX86DAEJ06k577JUGSKvsHyd+3kmFZjnKKta4kw/KCzjnHThyQr80v9+oxo7gPp6fkK2vTpHeJz2HuwmKRmtdx/NmzpYPp0qGTkt3uSPyG1nCM5xY3+5Fi94FNalQ3UvZsuywWq1ZvW6To5o4pB5zVbs3UPKyjfH0DNOGt3mpav71qV2+ozxZP1Yj+k/XC5yN0MvO4LBaLHrxxpiTp1r7/0Euz79Lpsyd0ddf75evjp+lfPqC9h/5Ulv2cbo59VJL02+ZvNXvpC0o9mqynPx6q/7vrS70zca0k6cc/PpI9O0sNa7cs9rpG270l9u96afadOns+U3de+bQkGW5DklZu+VZP333xislBXe/T858P1/xf39DVXUfK18dPs5c8rz+2LlROTrZu6/uYfGy++sew/0qSDhzbpY8WPqGYdrfIbs/Sv+fer4kzY9SwVktFNu7h8veprAoaexM2zs/TviXltnFvaN+ehL5YMfqiJ7PkVNDHKMbGxkqS4uLiTI3D3VyYxHX6CHPjqCgSZ0tpKYUvs2TNLL01/0E1qhMpSbp30PNq3bi73vnmESWlJKpaYIj+OfxznTx9TD/88R+N6D9ZWfbzevz9Qdq2b5WahXbU3wY9p1YNu2rG/Ie0fd9qNa3f/q/H/e7T85+PkNVi1YDoO3VV57vzbPvhGb00fexywxhOZh7Xxz9Oka+Pv9o06a37r3nRcF1JhvGkHt1huF+Xx1jQ/l++nYL2+YLqYVKn/PNXApIY+1C44ozVkvF43aJBp3xjU53qjYocry+4MMZlZKbp2U9v1fmss/Kx+Wry7f/Txh3LNHfZvyU5bpGcMPRd/bb5m3xlp8+eKNa6VqtVCRvnG5Zffs7x9fHTtyveUVb2eQ3pOS7fsbj0HGBUZlSfxFhdUsVtm58vfk6tG3VXy4ZdNf6NrqoZVF/P3fuDrFZrkefZgpj5XhV3v1F6nvT+Xt6+X7j/J81c8LAeHz5Lcev+V+z2XZZ9fmORlHyodOuWVdPa0vgrzNk2fdH1zOyL7t6uS5PTIQFGAiwPvgSWL04a5YcvVSgMYx8Kw1hdfhirS6a0bTN+3ReKaXdLmbbtSQkSlJynv7+laeMkwEqOvuh6JMAKVpqcjgfeeAAAAACgtMqa/ALcHW0cgBHmAANMVLW22RFUHBxrAKXF+FF+ONYlY+bxqqjbrigq4vtblu2G1nBeHJ60bfqi65l5jL2xXZMAA0wU0a/oZQAA5mKshruqqG2zou53ReGJ7++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      "text/plain": [
       "<Figure size 1591.6x2070.88 with 1 Axes>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pauli_circuit = pauli_kernel.construct_circuit(sample_train[0], sample_train[1])\n",
    "pauli_circuit.decompose().decompose().draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The parameters in the gates are a little difficult to read, but notice how the circuit is symmetrical, with one half encoding one of the data samples, the other half encoding the other. \n",
    "\n",
    "We then simulate the circuit. We will use the `qasm_simulator` since the circuit contains measurements, but increase the number of shots to reduce the effect of sampling noise. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "backend = Aer.get_backend('qasm_simulator')\n",
    "job = execute(pauli_circuit, backend, shots=8192, \n",
    "              seed_simulator=1024, seed_transpiler=1024)\n",
    "counts = job.result().get_counts(pauli_circuit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The transition amplitude is the proportion of counts in the zero state:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Transition amplitude: 0.028564453125\n"
     ]
    }
   ],
   "source": [
    "print(f\"Transition amplitude: {counts['0'*N_DIM]/sum(counts.values())}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This process is then repeated for each pair of training data samples to fill in the training kernel matrix, and between each training and testing data sample to fill in the testing kernel matrix. Note that each matrix is symmetric, so to reduce computation time, only half the entries are calculated explicitly. \n",
    "\n",
    "Here we compute and plot the training and testing kernel matrices:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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K9u+t52/fpf36eCDjsIzVkiGKsL9n3qh9CY0S2QhzztD+2ke6sG3Ux6RTyQ/wIxJLSQ7kseeoR5ZMw75MqSyMyyxvbaOx4Ai3wbTWFm1s8ur6wikqV3EUHEfRceQbS65hNOd+kt1YHuNrZAnu8RXbvPMnlhfGZZaPOQqOJduPTa+Kyyw5Av4Yc/9XN6gJ6RkjS+LyOTTEG2muAaA3ybFt6yCUwQ3DMDoL9gTKMAzDMAwjS+wGyjAMwzAMI0tyKuHl5yXiKC3OBxbGnXFuO5YyONqOZbtRZ30+Li997D+9uupIrinvpXLHZjINZAmRI6nakyjq96vcwuaRfbprXWxgGHg8YjdJcCyjsAzD8k73wMCQI7uKSarjqDYeYz6fDRMBXyZlk81dJIlxe4nwYgiWtLY0ajucN42j6Ng4E/BlLO4zy4ktrSwzal/CSMXvzVsTl284eWhc7kVGrb1pvjiysl8P3/xyfu3OuHzyEJUmWaLivrNst2Bdo1cXzxEbVrKExnM/c3Cxdz7LnNw+y5GHaYxWblU57nDSl9R47jlidUK5Gpfy+r57iebFu/Hk9NGbAFAaRazy/BiGYXQm7AmUYRiGYRhGltgNlGEYhmEYRpbkNBde2Yjx7qr/ug8AcMNcffwf5grbTNIPR1yx4SVH23HuvHHnftGra9OzP4jLLCc8s6YhLp8yXCWZTZTP7I/Ltnp13XCKykAsDbLBJkeosTyUDCLEOCptJ5kuckRcBcleDy31+1LRSz+bMEjllvuWqEnmlLJ+cZmlybzArHP55t1pP9u2VyXAGYPViLJhL0tVvrTIcihHxbFsyOabLMcBwN2LNsblc4eXxmWWt1hK5fUR5sLjtc3Dz0dx1CJfy0Mr/fG+bLyanT67Vs0kZ1WrvMaSL0uWYb8WbFQ5cO4wXXssuW7ZpeMVmquOLtOoT15jz6/VNT2H6uWzbyFDUAD44mm6pnkmuE3+rvGazA/kOZ6jts9OnTMDCy0XnmEYnRB7AmUYhmEYhpEldgNlGIZhGIaRJXYDZRiGYRiGkSVH3AMlIr8AcBGA7c658dF7RQB+D6AaQA2Ay51zjZnqaGPqtOnumedfAuCHwieCPR5eUtJu6Z0WDtNeI96PFO6nqjzlxri886X/pjbURoD30XSjUHDemwT4ofR1u3S/yshy3ZPC48lDy3ubQrplCD9/kZLhTq/q553Tg8aF2+Qktj3IBiCfrpGtCgB/LwtbB+yk8HV2z2arhlc2+tM+oKfuB+P9MlxvK10jX3sI74/isH5ORszJdENHe3aV78d7s2i8eK8Prwm2JAD8a+Hx4zHeReu2f28dh9odvh0Gu4fzfPEeovBaGN5bxmPB+9d4vx+vw9CBgl3hh5WqvcRhskdgq4Q8qrdpn58k+en1mjx6RGHqO/Gx95yJFa8tsj1QhmF0OjryBOpOAOcF790E4Ann3AgAT0SvDcMwDMMw3hEc8QbKOfcMgJ3B25cCuCsq3wXg3Ue3W4ZhGIZhGG9f3qwTealzri3OexuA0vYObiPpHPZHUhYnw2V5BADqKSFvzxLt4uu1u+IyJwZmh3F29QZ82a5oxmfi8tbnb4/Le0kGcTQkBYH7N/fr1bom7X8/7f9+kurYdiG0W++al/7elSUZPiYUWrkvLGOxDMRu2KvJjXpoqdoIpM7XPnPSYk7A20qSKUubc4f5Ltk19SpX9WVXdjpmf7NKP6GkxPIU9/8hspQ4Y8SAuMzSIMt8ANCNJEB2PGfZrIgkX3ZOD60eWK5i9/D9Gcae1xQ7hwN+MmNOWM02Bsl2pHWWtfvR+WyXwOPICZ5D64GqYrW34Gth2Y4tIB6heXgPWTsAwBlDdV7a5qJbF9tmaRhG5+Qt/3RzqQ04GX/ai8i1IrJARBbsaGjIdJhhGIZhGMYJw5u9gaoTkXIAiP7fnulA59wdzrnpzrnpxf37ZzrMMAzDMAzjhOHNSnh/AXA1gG9H/z/QkZOc0ygzlu3CSECWYlgKYUlnDiWk5cTA7DAO+A7aLNuVz7khLte/+MO4zNFyL23wt35V91Pp68Ix5XGZE+0WBVGAbYRSBkfb/W25yiLnjyqLy3PJIf2rj630zr9i/MC43J+kwiaKHmsm2WpsZZ+4XFOvztIA8Kdl2+Lyp2ZXx2V2Tz9E/R1UnD4iDQB6kJv3T15YH5cvGKEqbxWdHzqR37lQncgvoTG+cJyWeexYMhwzUKMhgTc6eLfBktoumrvVjXvi8jkjy7xz7ntNHd4XblI59Fvnj47LvF7OGaPXuyOI5uT1/tw6jbQ8a5RKYC009izXAsBLG/XvlbmU2PjVTU1x+ZQR+j6P959e2+zV9Z7CirjMciivaZbw3jdxEDLB0bBjKlJzEUqhhmEYnYUjPoESkXsAvABglIhsEpFrkLpxOkdEVgM4O3ptGIZhGIbxjuCIT6Ccc1dm+Oiso9wXwzAMwzCME4KcJhOeMnW6m/fcfAB+EtfSvgWZTkHDHpUF2MCRk/ZyxFGf0ICQLm9vBtPFklmfjcs75mvUHkduAb4c0bBHZRmOyuJzemYwuwR8iYSviyU4lgPfYH5JkiBLRN3JmLIXRdFxJBZHDQLARjJ65LlgKZXLa+tUwgrr2kcSaB9qn40dOdIvLwjDO0TzymarHN3IkWv7KYKwZ4H/9wCbQfLcsQlrt3yVrXiOOPkxAAyk6+QINYblZo7AbA7WEUc99qHEyLyOub9he2zoyjIlG9Ly94MjOwvy/chSjsrjNvn62fizntZ9/0CuDg1xAeCU2SdZMmHDMDolFmNsGIZhGIaRJXYDZRiGYRiGkSVvNgrvTbG3+XAcJTe5ojB+PzT3Y4mDI4NY7eE8Z4P7qxngmm0qLwHAMDKNZJNMjrZj2a54ppptbnr2B15dr5KR52AyIORotftf1yinq6YNTtteeA4rHyzP8DiwWSbgR0ax7Mc52LY06liw4WIoCbHcxBIkS0oM50zjvIWAL4N5cmZCx55nuznoC/eNPysgaXIVmYJy33sEMukBar9Hhhx/Jb1Z9tLzw0vnOeKISh4jNh5lw8npgzQSFPClVZayt1J+xQmVfePy959Z551/5hCtb9ZQNTJlyZIlz4Mk/4YGri9Q5CBLpkOK6XtDY1HSW2W7lmCQ8mhm2zMCNQzD6AzYEyjDMAzDMIwssRsowzAMwzCMLMmphFfQJQ+jB6QM9rw8cQGtyfTmmSzvcCTWRoow+yNJJwDw8Z5V2j7JOGx6OHuIyiAs21WecqNX14ZnbovLnLesmKKRppX1QzryA+mka4/0MhDnYxtAYxTmU+MoKz6Hy2Mr1DyT5ZbQYPK3i9W8sukASaMUfTV3sBozchuVQR5Djm7k6MD1ZHg5sUrlqcUbfbPST/7y5bj80i3nxGWOAuSx4LkPTUz5KlkazRT5xpGCy7erXAv41/UrMvu8dLQafP7bwyvi8s+umBSXG/f5Mud7/m9+XP7BZRPi8phyNQJlCe66mSoFA360HPefo+36dk8fAfmdp9Z6dV0yUs07pw0pjMu+kaa2sfeg9qt3EPW4heTItu+nSXmGYXRW7AmUYRiGYRhGltgNlGEYhmEYRpbYDZRhGIZhGEaW5NSJfPLUae7JZ1P7P3hPStcg0e7KLZrUlR23eU9QI4Xuc1g42x4AvoM3n8N7R3gfD1sVjC73k9MOPvVf4vKyx78Xl3k/1rzV9XH5XWP9hLQMJ0BmZ2wOpe9PIeOhy/M22m9St1fL06p0DxY7Y/M4HgxczXfTfpcn1mv/r51VHZd5TwxbArAjOwC8uEmT414+WRPP8jpje4LQKoH3lr1a1xSXeQ9WL0pYnMktHfCtI7j/f6Z9cheM1KS/vI7C5M+7DuhYcp85Ue/DlJR5eJFaPQwdoJYAAPD8Wh2jSZWFcZn3NrF7+aEg4TJbCfAc89iNLNf2d9JetNX1vs1HeR/t/36yyhhENh1sM8LrMNzXx5YMFf1S++fmzjIncsMwOif2BMowDMMwDCNL7AbKMAzDMAwjS3JqY+AccDiSI9bWqUw3gcLaAWDXQZVbJg7Sz9Zv3xeXN+zScv1+lShOrS7x6mIphCWhC8do+DnLUOwwzpII4Mt2Y8/5Qlze/sIP4zJbIjChVMpyTd8e6RPPFlK4PruNA36C1xFlKte8vL4xLo8nGwO2gGAJCAB6kiR2XdmQtHU9vEalPQ6rD60Dvv/XVXH59CE6F8XkkM7Sz7YmtSEAgEEkp7LDPCcw7pLQujh0f0BgjcFSIYfcXz1NrS04kTInhb7qV694dd327vFxmaXVJRtV8j1jhFoCsAS4udFPTDx9sMqsvCzW0DVy8mKWawF/7lmyLu+n77NEvoK+a5WFOqaAL+9NHqzftcdW1MXlsh5a7wdufyYur7rtEq8udovPYGJvGIbRabAnUIZhGIZhGFliN1CGYRiGYRhZktMovKnTprvnXkw5TR+myKIwemoPJajlyKhdFEnVl5yh2ek5jMLj1/tI7tlFbZT2VYmCk/xKEDvU6iUA1g8HzP5sXN763O3a3qHMrs1eMmEvsknLHC3HkXqAP2bsLM7jyt33XKpp7MLjGHawZjmMo9tCh3ReTywP8XHsTi3BIPN1sgy2m6LguI1u+Tq/YVJqlknDduL2MiQvDuvi81lOHUBrh93heX0cCuautZX7r9fIEXV8XXlBBCbPPa8jdi9nOY3XUVgXzwW7/nOSaI66ZCm4R7fMa7qNk2dbFJ5hGJ0TewJlGIZhGIaRJXYDZRiGYRiGkSU5jcJrPpzE2rpU9BzLQ9UlvtFg2zEAMH5Q+kiy7bub43Kf7ipJtQRyiXN6j8gSB0ePHaTIt/tf3xyXw8TAG3dpxBZH27FsVz73hrjc+PKPqB++vLF1j/af+9KiXfEky8KevuzGSXR/Ml+T2149uSIuV1BE2/ZdGsnF4wD4kX9sPFraV6PafKksQcf7ddVQ0mCOCmOpiIdiQ4PONQDU79VxKeml7a9o0EiywX00kowly/GVulYAoHaHRr/xGN+zuDYunzdCjTRZ2mzxl5E3f33ouPlrNRlyf2qDxzGcuzVkZjlnmK4jlil7khx267x13vlfOXt4XOZoO/5O8fsNZNpaVexH4bGpJ8/RxAqNyGPJliXxcE1zwmrT7AzD6OzYEyjDMAzDMIwssRsowzAMwzCMLMlpFN60adPdc/MXAPClti55b+0+zrUT1ZUp2u1osoOizYpJxul30vVxeevzt3vnFOT70YJtZIoCzBRFFpJpPjt6fqa63sz5b4aOtMnRkGFU2bFu+2icczTh/I6FJC22F+XaEd7M9ybdWMydOR2vWBSeYRidkCP+ZBWRQSLylIgsE5GlInJD9H6RiDwuIquj//sdqS7DMAzDMIzOQEf+NG0B8Hnn3FgAswB8WkTGArgJwBPOuREAnoheG4ZhGIZhdHqOGIXnnNsKYGtU3iMiywFUALgUwOnRYXcBmAfgS+3V1eoc9jenIo3y25HtDochUEeAlZNQbeAIIg4NYpNGloH4+LCP+XQOyxVsksnvs2xXPkej8wCgjvLndckgkfjGiL7kl8wgY7HcwpGKnCeO3wf8XHhsAMnSj0vqnLBfYsMev64yNpakAzlaj9sPo8L4Wngs2YySx4LNJ0OzUb4WNpZsIXmrJ80dS4OtSb8u7hefz+abvKYyRcSF7dRSLj6Wf9nUMpTQWP5m2Y7nZV+zjkvXLhwd6EdNcnQljzfPHf+Q4O9aqBbzdR08nGq/NYdbBAzDMHJJVpsjRKQawBQA8wGURjdXALANQGmm8wzDMAzDMDoTHb6BEpFeAP4I4Ebn3G7+zKX+dE37p6aIXCsiC0RkwY6GhrfUWcMwDMMwjLcDHbqBEpF8pG6e7nbO/Sl6u05EyqPPywFsT3euc+4O59x059z04v79j0afDcMwDMMwjitH3AMlqXjknwNY7pz7L/roLwCuBvDt6P8HjlTX4VaHrU0pR+xCSi5bFDg18/6RTeSi/NCqurh81dRBcZkdnMsLdQ9OSFfai8Jh3pxol/cWde3h319upr7wnhjeh8IO4wP7qRM473kCgFJKQPzao/+p51D/eU/Jaxt3eefz3pKxFerAvZ/2vrD7OO/PWbSp0atrXJm6TpeR+/hfl26JyxeNLY/LWxp1HCroGgHE8wv4zt6ceLaskJP8eqd7r7/5xOq4/H5qf2R5r7jMe6D69/YTG79Wqw9KJ5CjPTu8M5zYtznYh7eJXM15TxKvN94jt367Oqz36ObvX2NXdF4jfC1LN2nfx1T09s7nvvF65f173MezbnsmLj90/Vyvrpp67edWWi8tTtsYOUDb37FHbRPGBs7v/Ai6bSzEPMkNw+ikdCSVy1wA/wTgNRFZHL13M1I3TveKyDUANgC4/Jj00DAMwzAM421GR6Lw/oHMqa3OOrrdMQzDMAzDePuT02TC+XmCskjyYIuA0MF5bZ0mWy2lsPgrJlXG5QaSEjjp7U5yBQeAPt3TX+Lflm+Ny5dN0AS8HDHOEhrgh8n37aFtslzC8gwTWhWwbDfhXV+My5yAmGW3+gO+XcCUysK4zAle80n+PNSa3mqhvJcvuyUyhKYP66tSGUtKvTj0PwhTZ1d2Hi+eRx6JxRt8aXJKdWFcvvakqrg8gM4/SFLVekpGnB84bg8doEmqPXsKOm7GVx6Ly3d8YkZcnlrl+8LublbZr2d++jXFya6HlWrbYSQ/21Os2qrjOn6QSqkTqrQc2np4iYpJJl21Tb83LOvec83MuMwWDABQSQmnQ0uJNupJlh5Rpmvi8eV13nFTB+mYbYrsGQ4GtgmGYRidBcuFZxiGYRiGkSV2A2UYhmEYhpElOU0mPH7SVPfHR/8BACglZ2yOfgJ86SyUHNpgWYEjvFjeAXxJjaPtepLsxTIDu0ZztBngy479KHKQ2+D+djTRLUuAnID4H/d/Ky6PJOkEALZRxFSf7toXlup2HVDZieXAboGrOY/ZFoqiY/dylu1YpqsPXM1ZEuIoPI4O5HE5eNiXp9hlm+eLx7hH1/TO6WFEH0dnspTbRFF4/Xry3Gnba+tUGgR8SY7r5XHZTePdncY4TObLc8dReLwOOVIwdDIvoWhDlr/ZfZxlP14fv164wavryskqk/Ic8TlJ+hnBYxeu7wdJFj9vZBkA4MIz52DJ4lcsFM8wjE6HPYEyDMMwDMPIEruBMgzDMAzDyJKcRuF1yRM1O2wnKSlLN726pe9iEUkvLJEUB1FwT61Ug3Q20pw7XF3R2ehwX7PKKCxhAYF5JrXPEV4svXB04P5AWmSZkuU1lu1OvuzmuBwacXLkHbfJ7/clGWYvyTP5QXQhG5eyGSVLcAz3dxhFuoV18TWyTMmSVGh7eoAWA48/m0fyWLKEF0quHIXHa4xlx94ZpMlRA33zSr4Wlm9ZQuO6uI+hhOfJjvQ+r0++djbYBPxoP5ZAOQKTkxHz3F86ZqBX16qte+LysFKViVkOZTNMliZDg9B3jdB0mN94Yg0AYOuegzAMw+iM2BMowzAMwzCMLLEbKMMwDMMwjCzJaRTe2IlT3N1/fRoA0JvkJc6/BgA19fvjMkdPsaTEUhubCT6yfJtX1ylDVarjK73t2XVx+UunD4/LHLnGEVqAHyWVzCBPsVxTQHJHaMrJue3YJPP0ESVp+8u58wDgtp98IS5fOlZlmV8u2BiXzxys1z6QouNYagKA+5ZsisuXk1kpRxRuJnmMxyWUTF8nw02el940j3z+jsD4lLU2zoN4oEXHfnyFmkz+8Dmdx5vPGulVxdJmT5KbWAKr26Vjz/M4uL9vKsnnvFyzMy7PGVactj2WHMMxYtlvO8mJHF34zLr6uFzV2+8Lnz+wn4qgNz+0Ii7/7+UT4/IXH9T3r5+lUXeAb3DK+fv6k4R4P+VEvHh0WVzuGcjrLO22SbmnzpmBha8ssCi8ToyInA7gN865yuj1UgCfds7NO9Kxb6Kt/wGw2Tn39TfZ3Uz13gJguHPuqqNZ75voxzykxudnx7MfbYjIzQCGOuc+frz78nYkp3ugDMMwjM6Nc27c0ahHRD4C4OPOuZOp7uuORt3vdDp6I+uc+1Z7n7/TMQnPMAzDMI4CItJpHkp0pms5VtgNlGEYxjscEfmSiNwXvHe7iPwwKn9URJaLyB4RWScin2ynrhoROTsqdxeRO0WkUUSWATgpOPYmEVkb1btMRC6L3h8D4H8AzBaRvSLSFL1/p4h8g87/hIisEZGdIvIXERlInzkRuU5EVotIk4j8WMLEq+n7ny8i94jIH0Wkq4gMjMr1IrJeRD5Lx94iIveJyG9EZDeAj4jIPBH5uog8F13XYyLSn86ZJSLPR316NXoadESitv4QtbVHRF4TkZEi8mUR2S4itSJyLh2fds5EpCeAhwEMjMZ2b3SN6a7lFhH5TXTeB6Lr7xO9Pl9EtolISZruviPI7R2m071A29mNudAPZufwc94jw/tF9pAbNLsjVwSJctmlnMPXrxiv+4Y4uSxvVWJnagDYRi7d5dRnPn9jg+7fGlmuofDJYA8UJ+HlxMDsUs2WBLznCQD+5VPf0/Pvi3+e4KKRGkr+0Gq1cLiuojour9yioesAcP4o3dfCVg15GfYE8c+g0J5hNIX/czLhbl3S36uH+7F4T97WfboHalm97s+ZUKl7oK6eMiguh2PcQq853L+BXOz5uthxO3RY30z7sRIU1v/wMt1zdzLtt3tuQ0NcvnS8JqsG/HXF18tO5jsP6rq/e4HuQQKAH75nQlzmJNU3n6l7+XjP1pXjdX7X7/Qd1ivICZ33qfGevaun674pTtYdzh3v++rA7ynj7cXvAHxFRHo75/aISB6AywFcFn2+HcBFANYBOBXAwyLysnNu4RHq/QqAYdG/tl/czFoApwDYBuD9AH4jIsOdc8tF5DoEEh4jImcCuBXAuQCWAvhedB2n0mEXIXXT1gfAKwD+CuCRTJ0Vke4A7gNQD+AqpLai/hXAAwCuBFAJ4O8istI592h02qVR3z8MoFt03gcBnA+gNrrmLwC4SUQqAPwNwD9F/TgLwB9FZLRzTjc+ZubiqL2PAPgFgEcB/AxARfTe/wIYEh2bcc5E5HwEEl70nQ2v5Uttnzvnfi8ilwD4oYh8HsDPkZqfjvS7U2JPoAzDMN7hOOc2AFgIvWE6E8B+59yL0ed/c86tdSmeBvAYUjc+R+JyAN90zu10ztUC8AztnHN/cM5tcc4lnXO/B7AawIwOdvtDAH7hnFvonGsG8GWknlhV0zHfds41Oec2AngKwOR26uuD1E3NWgAfdc61InXzVeKc+5pz7pBzbh2A/wNwBZ33gnPuz9E1tP2l9Uvn3Kro9b3U7lUAHnLOPRQd/ziABQAu6OA1P+uce9Q51wLgDwBKoms8jNTNY7WIFAJves7SXQvzaaTWxjwAf3XOPdjBfndK7AbKMAzDAIDfIvWUBUg9Qflt2weRXPNiJJU1IfULv/8bq3gDA5F6CtOGl4xRRD4sIosjOasJwPgO1ttWd1yfc24vgB1IPY1pg8Oy9wPwk4r6zAIwEakbkrZHsIORkrqaqI83Ayil82rxRjK1OxjA+4P6TgZQ3k6/mDoqHwDQEN3otb1GW1tvcs7SXUuMc64JqRu38QC+38E+d1pyKuF1y8/D8MjteE/grsw07lOZgF2fW1q1u+zmXEzu2V2D8HOWZTjZKodps0zYRG2Hztb7W/T8EZTcl+WOn8xXG4EfvFuDUcLEq2Mr+sTlTK7iXGarAsCX7U5/37/H5aWP/WdcvnqayltLatU2YUy577K9nNyo2VJh1mAN0e9Dcs3GHSpTVhT5kmkzWT2wHQUn423KcI0A8NIWtQi4YJT+THl5s/aRx3Jtw964zOsA8OUtlrTmb9oRl0t66zpgKbYkcKHndcjWB2MLdB5XbdW+jCrS93fs8eXA3766OS5fP3dIXN5KEvG7x+rvgPHFKlkCvlTZnWQ3ls04YTTLlKGz/3KSc3mJsmUIO6SXke1BaM3hWXuYgnci8gcA3xeRSqSeRM0GABHpBuCPSMk6DzjnDovIn+Eb6WdiK4BBSElsABDrwSIyGKmnOWch9eSjVUQWU71H8tjZgtQNSVt9PQEUA9ic8Yz2eQzAEgBPiMjpzrk6pG4o1jvnRrRzXjZeQLUAfu2c+8Sb7GOH6MCcZepzu9ciIpMBfAzAPUg9TTzvaPT3RMWeQBmGYRiI9rLMA/BLpG4alkcfdUVqP0w9gJZo/8y5aSt5I/cC+LKI9ItuzD5Dn/VE6hd2PZDa9IzUk4026gBUioj/l5FyD4CPisjk6IbhWwDmO+dqOti3N+Cc+y5ST96eiDZ+vwRgj6Q22XcXkTwRGS8iJ7VfU0Z+A+BiEXlXVFeBiJwejc3R5EhzVgegWET6pjs5HSJSgFT/bwbwUQAVIvKpo9flEw+7gTIMwzDa+C2As0HynXNuD4DPInUz1IiUvPeXDtb3VaRktvVIPeH5NdW7DCkZ6AWkfqFPAPAcnfskUk+utolIAwKcc38H8B9IPWnZitRG9SvC47IlMun8M4C/A+iL1EbsydE1NCC1abvDNx5B3bVIbdS+Gambm1oAX8RR/l18pDlzzq1A6gZ0XSQlDkxbkc+tAGqdcz+N9pxdBeAbItLe07lOTU6dyEdPmOJ+8acnAfhu1EOChLTfm7cmLt94ytC43EyRVCw9jCpXOe3hlb4T+WlDNMKSz+cIMU7cytFaoYTHst3rm9Vxm6PCVlC/Jg/W98OoJJZ1WC5haZKjyH5EjtuAH23Xi+S1ced+MS6/8MCtcbmI3LB7kmQIAN94Usf7M7PjJ+Jevau3qTw1bUi/uBxGvj1ByZvPGKljzwmX2YWe3d0BYEFNo7YzWNu5Y35NXH7vOP2ucyQYu9YDwEqS1AaR1MhSHUfXcV+KewcSHs3RaySH8rh6yabp+NCxu57mntfeH5eo8rCmQfs1qsSXSSeV6bjwdT2zRoNhTiNH+407tK7QFZ1lOC6/VKtS6mqSbE8aqGuaXdgB//vVJtFfeOYcLFn8igl6hmF0OuwJlGEYhmEYRpbYDZRhGIZhGEaW5FTCGzdxqrvnb6lkwtUlKtt1DUwWOVpuPyUN5vcZlg4SQfgPJypmGY2jxViG4UiqoYG0yNGBLG+x7LabogtLKCqsfo+fNJeNRFkuKsjXsehLUtcSSj4MAPM2aiQZR9txhNjsS78clzc9+wPqix8VxpFVrDTm57HBqK4TXjJs/ggAPWlc8jIYbrLUxvMbnv/AayppdUloX84YrvIU9zFkFcmOwykKkCPyeO1xmRMZA7681UBzyVIdRyRy1OPUwYVeXTzGvHa+//RaPYciJQf08I1m2fCyktrk6EaWNl8mWbR7F1++HV+p0YIbyAS2qlgj99ggk8ehW74/9hz12Lgv1ZdLzp5rEp5hGJ2SIz6BiqIEXoos55eKyFej94eIyHxJ2ej/vp1ICcMwjLclInKeiKyMfo7ddLz7YxjGiUNHJLxmAGc65yYhFYlwnojMAvAdALc554Yjtcv/mmPWS8MwjKNMlK7kx0il3BgL4EoRGXt8e2UYxonCEY00I0fWNi0kP/rnkLJz/2D0/l0AbgHw0/bqKshPxPnh9pHUFRrysUTEBoZd8lQJ2E5SFRtRlgV59Vh6Wk3y3NgM0oVn3Bn0i6O3WAY63KrHsTTHEVYDAmNGzg3HcgtHgu0lyXJgYFjJue1YLqrur1IVy3aVp9wYl7c9f7tXF0tSPF5sMsljv5KMNzkyEfDHooU82Via5Ii8UEBmU9MLxqiR5lOU14+lqvU7NLfbzCFFXl2cr5Aj5Lh9jpBjiZcjIwGgR9f0xpQsTe4hOXPmMO1LcxBpyGu3lOTTkwdpdB2bnbIpJuDnhOSoUTbJZDlycJH2l6NfAV8C5ehINrrlseA8gt2DaE4e4zYjUl43b0NmAFgTpeeAiPwOqRDzZekO7t+/2FVXRT6QrbSdIC/4MbqLIu77kvHzAcpB2aw/J9BTfxYhz193Hk2Ucqy3rhV0yXBOc5CJo0B/hritajgt5VU4IuFWj0NUdxdaUy0k6ZPs7h0DAEn6TuTROmql9/l89uxsDbZy8PVzP5N03J4mLRdS7tuk/93EIZoXbofniH8vHArGuCv9/knQdbUcSv++43yrwXclSZ/xGsv0ldpL2zzCNcFjyXsIuI18+h3F7b1hmw8njKUx4vEO55vJVHc4F20cpi0n4XUd1N/d6EFzdJByftLlunr9PSKV1X5d/H3ppt+VV159rcE5lzZhcoecyKO/1F4BMBypv9jWAmiK8vEAwCb49vmGYRhvdyrgp67YBGBmpoOrq6rw8jMpGxbsVZsH9PbtHJIP/zIu513wsbjc+upTetCG1XFRpp+h5aLMGT2Sf/pfPe6s92q5mCx8eK/i+te882X4FO3Lt66Py13+vd2/e1N1Hfb3Tbqa17XeMnXTdw2b9CD6JSQD1B4FALBfbWDQi24Gd+veTnSnP874pmMPjT0AFFJWFf4lvEfrSj71J63q3del7weAZO1yfbFH9w4mppEH5WG9yUrWLAWTqBypL3oWxkVXrxkqpDf9oddMNwAJ/w8Sd0D/4Be+EfduwHS+ky9QWroS35dTutLNEd/k0Y0Gz6O3plv9fa7eGmsk2yAaLxlAN+WBhQ9fv+Mbbv4Dg9vYqntDpdj/fiRXLIjLienn0vvz9SAar5Y7/jsud/3Oz/y61uuaTgybpOX+g7z0Q0yHovCcc63OuclIZaKeAWB0R84DABG5VkQWiMiC+oZ3bNJmwzBOQPyfX2/wcjQM4x1MVrnwnHNNIvIUUjmSCkWkS/QUqhIZ8g855+4AcAcAjJs01a2tS91Vs3QwqNiXp/aSfMARdvcs1r9uPj6zOi5zxFSYc+7AQf2LZChFYtXU6503RxyxNNclqIvlEo6w4ye6LOkwLLsAwKJNerde3kuvfxxJi/lUcRhttpIMO1nu4agujrZj2a5szg1eXWue1JyQLGk1klTG0ZrclwPB9bIMxlGTBSRDcRTergP+43g2elxU06TttGg7oQyVCZ6LOpJWWXqqIfmWJbjQ3PXh5b5Ba7p+XTBa/zqqp/lmiRbwpdFfvaJ/3EwZUBiX19Tp+uRIOcCX59gQVujvoX1e9CpHQPqP41ky5np5LPj98PvF8Pe2R7SOchfj+6bYjFSetjbe8HOMf35NnzjOuYbUAytXp08UEmNne5Umzr5Sz2/S3K/u5Wf0oJ30FKVUH9673f7TlcTI6frZFv35l+iphqbJ1/9Bx0/T4zes8OpCga5pGa7m0W433Rh2padGdHwoUwo/4aAnLcnf/VBPeT9l+WCpCIDbTg/+SPKUylH6/kF9AsNPV/hJQ+o4/VmYfPI+fX+gPvVKXPbPcbnl8zo/iQ9+1KsqUU1b4AZTea/+vAY9QUlU+CbcPJZCY+nJr8Uk1vATs+5+jlJhSa0bzUUDjV2xzkNi9kVxufV/v+rXdemHtTxoDH2g32fvKRnNaSjhtd717bjc5RO36GF9SeUiydBtUaNmAN6TSU8m5aecfAzJ1cmnH/CqSpyv1+VJkA368zpxxuXa34tq9JgegZk8SckSzEUmOhKFVyIihVG5O4BzACwH8BSA90WHXQ3ggbQVGIZhvD15GcCIKKK4K1JpQDqaosQwjHc4HXkCVQ7grmgfVALAvc65B0VkGYDficg3ACwC8PNj2E/DMIyjinOuRUSuB/AogDwAv3DOLT3CaYZhGAA6FoW3BMCUNO+vQ2o/lGEYxgmJc+4hAA917GiBRFKWjJujbzcG8m7fAVo/bQTOu5Kkc4724k22vfxIUpAEmPcv/6nv79wSFxPjT4nLyeUvarWjVf4DAOmv0pGcrbKGt2GYpSqW8Li/gCc9Cck1eVd/iRokgSPYiCxDdZOu27RSP+CoNIpITJzyHjomEIZpU3di1rv0/R4kw+wgU97v3Z25LoqqSy59XuslmTa58iU9/dlHvNPzPqCb83lePSmWI/d4XIPIteQjv9HzL/2knk9Sl3B0H52f98mveHV5G8954zxJ8l4AA8mn3qZzAHkf+hft4zbN0Zoo07y1vOVD+vsb2r2IxAIKFOAN5XQt0kelQbnkE15VnjzI/exL36PGrXr+6Knad5K+ASBB32nHm/vbIas9UG+V/DyJQ8vbnIqBNybaXVTbFJeHl+gAXzdbowR4782QEt3DtHSTH1XBbuK8F+RPy/SH3nvGlsXlErIb+O1i1YQBYNZA/UHTs5suyO60vycMWU93PACMK1P9lbeVHKTr4hDw+5ZQdAuA80dpn5eTrcD9KzRM8ytnqz7PVgW85wkAhp/5+bj8mzv/LS5fQOPCP2e65evcHTjs723gvT/sAl9LCWnZhb5HEAr/kbsXxeVvXaCxCkW90u974n1p4ToqpblkSwNeO+yyzRYWYb/OGqG/FD/0q1fi8k/er78IbqWkzF87T/dytLT6Y/Qq2U5M6K/rYHiprnW2EdjS5P/yatirYzylqjAu8563/rTPivd8bWzwfzDw94P3nz26Sn/ojO6ne7AGkO1CaGOwlfrZ5tT/tjYxMAzDeAtYLjzDMAzDMIwssRsowzAMwzCMLMmphJdMaqhzeeAYzrBsF1oJtMEu4Wx1EIZZs8zAcs2nZlfHZVbBOay76YAvxz2xXkNRryPTsdYMfWESgbzE8hbLYxxW35+sEi6f5OvIfJ31B1S6+cxsDd31DGepEbYqAHzZ7qqPfDMuL3roO3GZQ9Q5kfHlE3z/1GEkCfF4s6TEY7xrv783gudrB8mO7BzPklhBfua/ATI5x68iyXNgPw2XZZmwIUj+zA73t16o4c3c/5JeKgF6ewCCuf8MyZRPf+n0uMxzyo7sVYHNR0U/7QuvvRV1el1z6Fr4+Jc3+2HypbQON5LMemq1Spbcr37kSs7JtQE/wXZ4zZ2C5gNIrkuZUyYmqPQqxf53oHX5C3E5b8zsI77v7bc4FOy94PD/ZrW2SLKNArWfGDpBj+ewbsDb++J4DxMd4ugYz/Bwy2owbLrY+oAafCYu/jgdRN/N0PyS9v5IkW4VAFsq8D4YMtvcefZcr6p+jz2r/dy2Xj/YofvE3Ct6DEaM0/5OVhNTAEi+/py2WckWBfo9S/D+LTYBBYA+ZHhJ+75aF/5d6y3Tn9GunqwpxoR2GB/Qft31LT3/lAv1/fv/R0/oSXY2J6ulAQC4OrVLkUG6vaD1f74Wl/Nu0J/3bEPg2TEAcGS+ue9Tuiepx4cu09PP/aCe0MO3YUkuekKPq9a5SC5Wm4/EDLWqEBpTF7jQS5X+LOafOY6MR3lOE2QmK4X6Mw6Ab2rarQc6gj2BMgzDMAzDyBK7gTIMwzAMw8iSnEp4h1uT2NyYenTL8krf7n6CQHa65sgolhi60DG7SMbYttePWBqwT+ULdoRO0jkJkihYEhkcyIwXjdUwz5fXa7jvjKH6GLfUk+a0LnZzBoC/LtXHy8P6qmRZRYlqOYkrJ18GfFll1mCNDsynyD0eR3a/bgxkM462Y9luygUakrzi79+Ly1t3qXQTJkles03DXznCi6PaeO53H/D7cj1JqxxdyTIDO7/zOBwMIiAziUhjKvSR8gvrVI6cUa2SxYu1O7xzzuupYzSq3E+g3EYhzRdLzFsa/TX50bNU/uB1cYikSU5YHEbx8TktlLy5sq8+as+jx9mv16osM6fKz9vG/RxJjvYseTI8X70Ch/XCHjrHbUml3+ZO5NnRvScSY2elyhRiH8oKiSEqo7W+rGHuialn6zmc7JQSpLoNQR5jCuuXwslaF+Xq8vYAcDLiMESfJLEE5Y9z+5q0jX70PsmHMoTaAzwbA88NmkLUk68+reeXVXunC7lWu60aCu85nFNYOufY6/e4H37uSTcsDZJU5clIHMbPtg0I5ojz4lHSXNeo1hJSEEg9B6huGj92iPfme1d6yTJ1vraZuPpmPYccwxPvJbd3ttNgJ3EAMlLlKh6vvM+qq3imZL6Oc9TBlwN7/eFRrZfc6t0ucl4PLCwSU8/RF2Tp4JYv0fdPVdsKLw9j0Bcey9ZVGh2dmET5JWlNg93SyQoEgOfC79k4tIM9gTIMwzAMw8gSu4EyDMMwDMPIkpxKeHkJiWUOjkpLBJFza+v18dmsPio5sGzXn6KMmkiSmjHYd/LdSZFCrSSFHGLpo8iPMmhj7uD+3mtu5+E1+ohyUpVG5HQjU03v0XKQTJPlQDb/DGWRNjY3HvBes8TTh85ZQiaN3C825XTBo31+ydF2LNuNPvsLcXnh31TmC+Wlv69TI8/9K/WzG04ZFpcPkzy0fZefZJmvi6WqXSQdLduq4/Xadi1/bEa1VxdHsvE1s+zYdEiPWbpZ65pa7kfX3P+6OhlfNl6jnn6zUB+nf2S6RtccpvVVGsicl40bGJfXU1JrhueBjUeBNyaWbmM+RdixKWcpSdH9A0NSHtcGMuJkyfUXC/QaWeK+agrn4fU/a4v07FSxeIm8OMkqrye30ZfdZJAawGIjOSVPI+mCI+RIxpBydXMG4EtP7NLNUUIsN3DS2RY/SpIlIu/nESdOJTdodhgPf355ztaSfj0mJp2etm0AnjwllLSXI77c3iY9vp9K6GGEp6PrlBJak/m67hM0J54kFMpWHJ04eLyeU6uJmaVypB4fjjE7i/Pccb0spY4gaS+QutCF1gg50nvRYzwP/enaw+viayZpVFhO3E3bFrpS20Fd3hhnmHtPos0gDabaoW0H16hMKSzfskQeJgAmElX0vaPvpzfGhCsaGLxBknW4XjO12aGjDMMwDMMwjBi7gTIMwzAMw8iSnEp4zml0z37KR9Y7kK2mDVb5hPOWNZEcx9IRy4ENe/1HqhwZtZM+G0TmhGvr9BH4MJI+tgSy2Ygyyss3U+Ua7mMmeSUZBMRw3SzbsezUjSSsfj39R4r8GJujE6cN0bFjqWwlmUeGfeTcdmySydF2LNtNvVCj8zY9+wOvrisn6+NdNlrkHH9s6tktMMKsIUmLzVY52m5alV5jn675aY8BgBIyIm0JJyDipAqVfPn8p2vqvePOHUFmf1TVlZP0ejnajqMpw4i2W/66Ki5/+8IxcZnzJbIE2C2I4OQ8eWw8Oq1Mx4XltD0k04WSGkd6cju1O3V9fopyUHK9YQRlAcnXnSr6rg3n4NokLpagyMwPAJK/0simxGXX6vuLntT3R2ly2eTy+VoXRwwBkGGTtfnVi7W8ea3WdYoaGDpKmpu8gyKsANQ+sCAuD3n5ZT2HItFa//s/4nKXL/9I+5Hw16Ajw0vXRN+VLvSzvJmkSZY1Ac9Ys/V7N+lxV1wTlxMVKvu77TV6bmCAmHzsd3F53+8ejMs9r71K66KoruRTf9D3T9OxA4DkRpXqOIGw9CLpiCPHttd65y+/4Mq4PHbeX/U4Ggtw0l6SGRFKk3VqCsqyXfKPP9WDSmi9lKgklZhwqlcXduscJVspgrK0Oi63/vxWff/CK7TtiuFeVf87Usflk1s1EbS3DiihNg4G2xQ4mTJFCyYf1STPiXdfp8eQfJlcpJGdAIAe+js5MVGTarMhbZLmyFuHYZQqRQ46kozbw55AGYZhGIZhZIndQBmGYRiGYWSJhBFZx5JJU6a5x55+EYAv24VReMy+ZnpUTu+3ZpBkmgO5ZMlmjUqbO0wj+tiAkKUbNjM8HNS1r1kffXLeNJbgmsnMkSPyQjmQjS1baQ7W1unjTs4rFxpxsgTKEXZdSZ5jCY37yJIjABzIkEuQo9VYMuV8f5Wn3OjVVfP0bXGZ57ieIry4L3nBY2ueb5ax2FCV555lo2SwljPJYH6OQCrTC5awAF9O5Gg1zqXHEjH3N1yTvK5YWgznOH4/kFwLSLZjeI6WbNR1P6W6MC6vqfMfp7MszRI5j2sos7axNzB3/c48lZVuOTcVqXTqnBlY+MqCThGMN33iePfy3+5NveBch/39PJUc5SUUbcfyGvqpjOPWam7EMGLIi37jiC+OEmJjyBaKturtm6ayGSWbVyYmnqYHcVQVR4VxRByA5EY1mUyMJ+mEz+E+HvajbUGmi14k2T5dt+hOhrUcicWRboBnpuhFJNL1u82ay08qyWAzpInMKLlfLYffeCwA9Ayiwjg6kq+FJdD8DBFuCX8ri6t5PS4L5YzzxpXHoks7Jqqc543WlCPzTSnVbSlexGbNUq8qqdboRG+++Xp5fgNTT29c2ciUpVEaF1erWx7Y6BSAJ7uhQH9fcu5Gt5f6tVYjZvMu+2evKi/ajyLyEn0HvOKcm4402BMowzAMwzCMLLEbKMMwDMMwjCyxGyjDMAzDMIwsyamNgYjusWG7gTAh7U+eU33+kjG6V6CMEvVuaFBNl/drcDJfABjQU1/X1Os5PShkvEc3SoJI2jFbIADAE2vVZfv7FIr+4r+fmbaNUQPV4besr5+YeGuTatdsXcBO3Ly36XVyKweA0VQ377t6do2GF58yXJ3UeT9Q6ORbv1v3J/C+K04MzA7jbFXAe54AoPq0f4nL21/4YVxmGwbe8hYm2i2htbB+u+7XYUWf5+gA7QHgsQP8/Vy8H6yO3M9f3KLh1OeN0JDgPy7d6tV1zUlVcbmC9j1tp7Hjdcx7ucK9TV1pvbHFwSbadzWE5qFulz9GvJbY0mD5NkoaTPv9VtM8FgZ2GC+t0+ufNEj3c/BevNWNaoGxlObkpjNGeHV9dq7aHSSkU2x78nA7t6P1t/8NAMi7+gsZj0uuVIuAxNg5+gE5HycXPaHHDJ8Sl1t/+Q2/spNO1+OGapJiUAJgdhJPLnhM3w9cohPjZsZlV6v71UAh78mn743LeWd8QI8JrAPE21ND+3goZN0doP01oYN0Mx23T9etW/CUnjPnPC33oawQXf2fpV6C2V5qS+LZSbz/ej1mP+2JCVyyk5yQdvQM/aAHubUXUDnp7wNMvq6Jjr09RfR9YJdtL9w/QGhdeHuw9tP1cvLi3nrtrb/0LSzyrvs6na/XL2X6neV9Um6bWii4VbpHDwCkiKwTOCl1PVk69FZLleRv/N8ReR/5V33RizI+tOjPPP7p4TmvN/i2EcllL8XlxLhZ+gF9J4Sd9imptQv29SGPbFi2rkVHsCdQhmEYhmEYWWI3UIZhGIZhGFmSUwkv6YCDkdxUTDYAYULaj8+sjsssw8xbpTLSnKH6SJctAkJ7gwpKFNy3u0pyP3lBH1F+kto7SHLYjsDV/HKSrk4foskSOXy9vF/weDkidMJmB+jDdP38Pl9LKCfyOSwbnjGSkjhSky0kgrG8BPjSKIfcDyUZiRMDsxxWVezLZizbDZj9We0jSX1sNxCG5HNoPI9lL5K9dtMxv1uioeGfPdlPxMrrooxsCIZQXbw+VpBb+xfP8N13f0Sy8rRSlSP6FFAyTjqeXdA3BZYIg2jMtpCUy/IzW02wRA34sh/baZT11mvk5cbXGLqa5+dpqDgntWaH81lVKgeOK9FrZ2sKwJcqO6MTuRQWI/Huj6RecDLhIGQ8MYakBJZ4WHrhsHY+Zrg60wNAYpCG3LstugY5oW1yBTmZj1HZya1/zasruZLkqQs/lrZfMnAI0hFeo+eYvldlYLdTpW8hl2tP3gEglCTePf+w9usDugWApbnkK4/rMZPIdgHwpMo9l50bl3t+RR3OHfVx73Uf12M+eKlXVeL9+jPLcwJnSwgKvWepK/UGJaQlGYtd2UFyZPLBn2nb537Ir4slWLIFSK57Vc+pJBn9sP5cTlwY1MU2Emyt0agu3+yqnhg+WbsxyF+TBz/53rhc8D/k6j6K1h45zed9UMcUgJdAmNd+6/dVFs/73Hf1GBrT5A5/a0VizsV62BZK3N1N22AJj5Mct9L3BgAS/VVil6px6AgdfgIlInkiskhEHoxeDxGR+SKyRkR+LyIdS19sGIaRQ0TkFyKyXURep/eKRORxEVkd/d+vvToMwzBCspHwbgCwnF5/B8BtzrnhABoBXJP2LMMwjOPLnQDOC967CcATzrkRAJ6IXhuGYXSYDjmRi0glgLsAfBPA5wBcDKAeQJlzrkVEZgO4xTn3rvbqmTptuvvHC6kIFZanDhz2IyG6k2TxKjkqTyVHZXYv5yi0UC5h+YKT6HIU35ASlVR4OMLItwmD+sRllkg4YoDlqS7U3p4g8WqPDJFYPB98jaF7OLt88/k8rtzHAnKTZkd1AKilZMT9ySGdZdZ8kmc4MfDeQA7kaDvuM0fn1ZHMdzCY+007dP444TO7l/M1cjlMksyyaSaz+zABcRu7D/jXxYl+OaqNo+Wa9ukcsxwX1sWRc9x+fxrv9r6VPN8sm2W6Rl6Hyzf7a5qdyBkeV47azKfIUI7sBPzkwn0iufy0uTOw6G3gRC4i1QAedM6Nj16vBHC6c26riJQDmOeca8eiGpjQvcD9uTol4w+d/7zW3cV/+M7yRfJJkjjOv1qP2aRJa6Vck+a+PvVkr67xCzWqiyPGkmvIvXzcXH1/sUaxucUvenXJSRptlxhGEV4FJMOT27kU6NpwHLkGILmcop9IUksueYbeP13ff+AO73xXo1FOeTf+px732K/1mKUqVeV97vv6PrlMA4CjSCxs3qD9P1MTCLOc5pp0K4jbQ07YCFzVuQ1KZizsrN3Lf3CZvFuvxS1X1+vEDV/V88mtnCWlN7RJLuGeqzxHYLITOkl+rb/8pldX3rv1+UZbJCkAJC7RhMtumUaPYpBKg4kxGr0JAMknf6+fnf5+ff+RX2ldK9S9XE6iSFQAiZnn6wtyD0/+7gd6zlkqE3Jk5/Z/8p/TlD2ja7x1/t+0jel6K8JrL3EeSZut/u8ez+2e5iXRq99bdiL/AYB/BdD2k7sYQJNzrq3FTQAqOliXYRjG8abUOde2oWIbgNL2DjYMwwg54g2UiFwEYLtz7pUjHZvh/GtFZIGILGhoqD/yCYZhGDnEpR77pn3oxz+/dra0pjvEMIx3KB2JwpsL4BIRuQBAAYA+AG4HUCgiXaKnUJUANqc72Tl3B4A7gJSE1yYNsDzFchTgm0yybMbSxzY6ZjjJEBw5BgD7Sa7a36wSQxXJQxx5xlrDxCrf/I3lJpaLkl5EDtLChosAUFZIxmr0Pks6LL0U9EyfQBYAmvbrdbEE5xtOat/7dPfHu7pEx8y7RpKHOAEuX2+vYO5YRuLjWLYrpei8xQ9TtAV8M8xMyXV5jDgp9LxV/g06y02njCihc/RaWMrlBM99w6hHuv4hNF6cgJjNWblf4RgxfC2Z5MQwspQjMHmMWL6uJOma18GYCv0+hfDcc8JoHsf9zfp+/R4/SpW/ezuiCL3W1vbEyONKnYiUk4S3Pd1B/PNr+pTJbujTf0+9v5EkiqGTM7cyXM0vPdluoEZ5ujqVncbPV4NNwI8gSm6jBMDDtE2OcPPklqETvbqS6zU5bfKx3+o5nFQ1meEmMc//PrhH7tfyQI1+TYz3JciYQX6EbN7ZZNLZSJFV2zThcd7HyHCRkwSziSeA5l/fE5e7natyIkcKcvJkKdHkz1KkRs0AkLz3B3E5cbbKUxxFl6T58oxSAWDsVK27q/488cyLScLzEtgGCZfZ6DHRr0zfp7lw65boMSNVZcr70OeQCelJSXd3ahQehmi0nZfUer8v+yemnkF91t/DiTkXxOXkQDURTYwLxoiiBb1Iw/Haf5Y5W3//07hc+qhGYwKAIyNlKVERrPXfPqrvX6Lz2HyDyujdbrvT7xdJ2aHZdCaO+ATKOfdl51ylc64awBUAnnTOfQjAUwDeFx12NYAHOtSiYRjG8ecvSP3cAuznl2EYb4K3YqT5JQCfE5E1SO2J+vnR6ZJhGMbRQ0TuAfACgFEisklErgHwbQDniMhqAGdHrw3DMDpMh6LwjhZTp013zzyfipjIJFcAvnzAUh9LCSxbsYzRNYjE4idxHL3Eubq4LyznLQ0ilsZXqvzB+ePYGLGmXiMGhpWqtMgSUNivxRs0woWjojhybm9z5ig8jqLjqEOWT3iWm4O+9CDTRL6u3iT1baf8cd2oX2GOP5Yq2SSTr6WRotUmn0+P6QEs/Nt34vIAimRjA0ier2dXa+6/Ab38vvAYcVQc95Ej50aW69izjAz4ee54LlpbM63VzH+bcI6//lQvR+F1aydqktcxy4Y8dwMpXx+vD34f8Ncrm3KyatiX1gGby9YHsvSocpWb1kf1fuji07BsyaLjHoV3NJg+bpR76Z7/BQBI9Xj9IHzcT3nekCDp/QDJUGT050kalM8M8HOrcQ44zp/ntbG7gd73pWNH0VtSrKaBLM8ll2tUE0f3eRJa2GeK3OOcea3/oRFTXb55p98XMqNMLiCTTI7QIgNF7KMoQM5tFrbPEZEk73jRcmxiGkiT2LlFy5S7EHt2pK9rR7BzhUwqPTk0SddCkWegiL7kP/7kVZWYTFJZFzJY/vX39JhLVJLycr5xPwDPlFSKVepyhyhqnfroaB1JT38ri9ulWyWknAyHWYqlCM43yMJ8/Wwuy33x5ovWd4u/bSC5eJ4eNpkMVnleeU3Qd9Az3gQgJFsm7/kvPf0TX3/LUXiGYRiGYRhGhN1AGYZhGIZhZIndQBmGYRiGYWRJTpMJt7S6OPFuSZ8MIZ7wQ8v95LyqhbLjNSe3/cOSTWCumloVlzkc/M6FG+Py1dP1GN5f8slfkjMrgD9cr3sCBtFeIw4rr9+r+0I4rDvc88WXPIUc1pvoWg7w/rRgrxrvXXtpizofD9qt+7FOHqFJK3nvCjuMA8BH7lZXY04ie/3s6rjM9gK8b2Zfge+yzfPKiYHZYZzr4j1PADD1wi9pO5SAOC+Rfq/epMrCuMxu4YBvJcCWEN3I6b6iqEva48M1yZ89tEK1/kvG6j6Jbz6pmvq3zldT69DC4n23zYvLT39FHXPZRoCvNkz+vI7Gf9Ywf89MG7znjvfoPbh0i3fcqGLd18cJq9migPvPe8HC/W+bKXlz2/6/bvmZ7TdOOPbuhnvuEQCADJ0Uvy0J/+9Qx6HZFKae3KQO2t7+om60P4ZclwEgMeokfUEJZb2fB7Q/ydEeD+mr338AEN5Xkq9zx2s9MXRC2vddvj/XyQf+jzqpc+wWLtC3r7kRmaE2T2XXadprdYi+N/01kXvyTz/2akpcTO7UZAWQrKuhLlIyXrI08ML1AaCHfh9cvf6OkP5qfcBz5A7488X7i5LPqtVDYiZlEuK5o/1BiSlneXV5e9bIST3vCrWBST51n54w4+y09QKAq9ffi8J2CXQcX6PwHqpW/+ePDKjWF7Q3jdceKOmvt18QgXM/J5XmfWK0n8qzethFe/wASIW6+LPDPNsggCwgpFdhXE5uXOXXNXisvhg6Eh3BnkAZhmEYhmFkid1AGYZhGIZhZElObQxGT5jifvGnJwEAkwcXxu8n2+nDss0a5pgpLJ3Dx3fu9cMci0jqY7uDLRSmzpIW2yOEUtdfSP64ZJxKN2yvsG57ehuDZOAm/a0n9XH+tSephLifHMNZLuEEtgCwdZ/KJbOr9VE9X+NjKzUZ5QVj1HE3TJLMY7mDpJthpSpBcr27aIzChLI8/iy/dqE5KiBZ51Crb6nAUhknIF72uIbulvTWeWHJtSCQi7bt0jnmsbxzgToJf3iaOuayzLp4Q5NXF/efpeBRAzV0mJMssyv4kMAdn9thofAA2Xf87CXt4xUT/TST7CTP64rtKXjd/99LNXpugT9Gcyp17fx6sYZkf+E0dY7uksEdP4TXRZuUO3fmdLzyNkgmfDSYPnKIm/+jrwAAEtPP0Q+6BCHjLMORGzWHTXtyGssY22q8qmSASlee9MNyCcstLIElAvmUpUWSNViGYYmDcYGM40k3JJVJCfWX5DCQbQEAL0ydkwNzYmXvuqi95Co/q1higrqft37jeq1rjiZPRk/9Wbz4o7fE5amLn/X7RW7UrT/9f3E571Pf0GPYKoKlIsCzAkiuWah9nEgh9pwUmpMvBxKeF7LPYfl0vqtRd3m2hgitNdhxXchqwrE9w36Sf8npPtw+knyCXOzZdoJsNpIr5usxY2YhI111K0zykbv0nHMo6S9L5GTHAPiJnVvpfBk7I21zUqnSHDv4A/64sMSd6F1kNgaGYRiGYRhHC7uBMgzDMAzDyJKcRuHl5wnKClOPxpZv0Udx48jhGwDW1umjRE7o+yrJKhx5x7JCeaEfLcLS00PLdGf/heP0keZOcqNmx+wwme3cwSp3cB/Z3XlFg14XS3ihVPX+sdr+AIpm2n1A+8KSzIEgE/wyisR6mWROlmiGF+nj5adWa4RCWBc7UI+lueCHwLuoXyxBhYly+WFvr276WZe89CqOiD/GHG3Hst3Yc74Ql+tf1MTE7BjOSX4BP+E0S30nlal8wBGUzmkfR5f7bscHeS5IqtvSqG0MI6mOpdjQHf8ARdvxGnt4pa7PVSQFr23w5dtTKbqSHfVbSM7j0R7bX9fhtEEkHcGfv8vHqazTQFIuS5Pb9ur1nj5SEzQDfhRfW8Lmt20q4TdDshWIoq6Sy8ixe9Lp/mG1y/UzlrRI4nCUEFcOk9T/6//26sq7Sde620ByzfOPaRuXaBSaI2dnjggD4Lmfu7r1ehy5nzty1vbOD+TA5OOawBeVQ/Qcln4o2uufB1E0IYAfffniuJz3KZXKak5WqavqPz6h9Y7RaLnESD9y7vAXPhyX8797p35AkXduu0riU5eQu3uB/z13JLvlXXOzfsDyWF+SegJnbLd1rb7YphJR64MqLeb9y616zKLntczO40GfPcdvz+Gcovg42q2v/93kfiZ/qy7bifdSImmSTF0tJb6uGOFVlTib5LUmTUacXKzXcvjOX2q1Z77m96Vco/0SU1W2dEtf1TbP/0hc3v3uM+Nyr+9936+repyWya2d5XL30J+13lka/Zo4g5JFA290b+8A9gTKMAzDMAwjS+wGyjAMwzAMI0tyKuE5p1JKBUVohZGAfUkK4Cij4ZRol5PLcuQWAqVoD5k5njFCH71y9FhRT21v1VaVS9isEwB6kVFjlwQ97qT+D+5DURzU9zBCjBPXskTCiX1ZBhpf4Sd0nFCpr1lSY+mFr4ujC8PrYlpI0uLAwWVbNXJvWpXKQK1BdCGPxW4ae05Iy/1tL6k0R9uxbFcy67Np3w9zunJyW47UrCQT1N0HtI+7SaZjOQrwx4XP50S9meSqUArOJGeO7Kf9fc9lKp9wRB/gR7vxXO4hmTWf2jxtRPA4n+DE3eMH6ZrieWSZlBM8N1I/AN/IVFxbPRmbPvEQiaUsL2IquMhESaV/TluxjCLMOHEqH1MRyG7c/ECVUuTdGj3qdmq0rVRolFH92RSFBqD4+1/TPo6box+wdLOZIgVZwjvsm8Em3vNpfUFyZPIulacSV2oU7U+bSNoKSD79x7g8+O6favskz7jNGqkX9iVvhsqD9w6dHJff95/X6kEDNdL58H33xuX8m0lOg59QFrt024Nnglo1Rt9fpcahAHDwth/E5YKbVALscp4m/XUt+r2RMy7Rk8MIM45IbKFr3q8/ix2VpTtJwc/92asrMesifdGDjiMptvkvD+khv/yrthFEYC4ZMzkuT1wwT9sYr9GQ+VdqfxMnv9s735s/klnlNDUVZhPR3vc/EZdb//2jXlV5X1VD18Q0lfo4EbUbpKbG0q9U3yfjzfAc4SjVdrAnUIZhGIZhGFliN1CGYRiGYRhZklMJr2uXBKqivFxhVBrDhpksy/SkqC6OqmJJJJSE2NiR87zV1Otj52rKzca53DZSTj7AN5xkabBXgcooLA1yXzgvXPh6fYNGXM0cqhExHGH1w+c0fxMAXD1Fo3s4Sotzw+VT9Nf6HX7OJuYgyTgchcj9f227Piru01XlrTCC8sAhlXt+t0Qjej49RyN1WHJ9qUbz+L2x/9o+y0iZ5LyG+X4EUytJKwVddO7rKbcbR+Hx9XJeOsBfe2yWyvPIcibLfPV7fMmBr5+jSWfQ3O+gc8JIR15jvA6fWV8fly8dr/LLw8tV4jl/jP9oei/l2VuySc0KTxqSXqblNcXfQcC/rli27BQWmhHdeyExMRXFw9FaMnyqd1jy0d/F5cSFKt14MgwbXrKp5giKKgqOcw36fUr+73e1/Q98RMvdNRK0+OsauQoAUkayH5kISrFGBLtARooJovC8iMAGNRhO/JPmsuTr3X3pud75vX/2M32xR9fd3n/9Vz3mNyrtuT0aBSel1V5d139Sv/c/eun32pexs/UgMuLsOuV0fb+H//OL8+wlzniPtllAEb4k9SSmkqEqgG4Vv9LPqkbH5dY//kjff9dVWlUtSaaVKjWFffYMO7tT5CDPC5mrJuaQNAh4MvPhx1QS63bbnXG5a73+nHDtGLJOePjXcTm5bon2vxdtM+mrP8uST+r3AQCwQ6WzxHs0ClCK6WdTD60rOU8l17zPfwsZoWjS5N0arefqSOKeqN9Vz6wTAEg2REEvdAR7AmUYhmEYhpEldgNlGIZhGIaRJTmV8ADNe8dRabuCaB6OWhJJL4OxrNA3iJhiOJqK6x0zMH2EVg961FkU5MLjyCTOrcaMDyStNg4HkmV/ijDL965Xj9nSqJE6N5+l0TWAH51YTHVlik6cOUQfb4ZIGL4WwTLWx2ZUx2WWusI8hoNJDv3syZpPjeXIeatUahrYR6UuwI/k4nPYJJO7y7Jd/5mf8era+vztcZnnjtfEdpLzMs0p4EdEsuTLUjTnjOO+hxF9PH4sC3OkH6/pcH44apM5d6Q+AudT2DQ2zMnI+R75+jk6sYKMYtkEtFu+/+ODDUP/vjJlsLfnoP/dNgzD6Czk/AbKMAzjhGTfbiRffBQAkHexumS7ZHBDO2qililRcHLRk3E5MWySHnNQ91omRgU5S7vTH2RddO9I3k3kyEz7eA587DI99bY7vKp4D5W3b4uyAey56StxufBhdsYO7Ep43xMnyiXHa7dLk+72uffP3vmeM/ZGdUXv+W+6B8ptUesD9wdNFOuu8v/o+vF6dRaXPurS72rUATsxROfEsXv4Id8iJHH2B9L2X9jlm5PbHvSzBMhVap2QnP+I1lVPjt0L1EVeKsiqIEhKnVz8lB5H+6lcHTmUl9K+NnIFlxZ/3yXvsyv4vz/rOfSHZd4H1C2dndfZdiFVgf4xm6AEvK0//qq2f8F79fhmvy8yRe0OPCd1sqBwnJC7iJzfe+v3CQCST9+n5zz6YFzO+7buRWN3eG//XJhsm/fDddB/xSQ8wzAMwzCMLLEbKMMwDMMwjCzpkIQnIjUA9gBoBdDinJsuIkUAfg+gGkANgMudc42Z6gBS+4C27Uo9zutHezzCPUyrt+ljUd5T88L6HXF5CoW7f2+ehoJ+/jR6JApgbzPt2aA9QbxfhfdG8R6PcGcQ711pzuBaXbtDHwlXUd8TwT6W12rVFmAoJaHlvSf8frhPjBPH8rWwPQPvE+Mky/uDPTSltPfF249Fx+wgOwh2COeQesAfI97DxQmX2Z6gdxCiz/u2du7TR7+cGJgdxtmqgPc8AUD5nBvi8oZnbkvbR96DtJkSA/O6A4DGffoZWxrwk14e7y279PjQiZz3eXFfeIyZ4mAvXjeymuB1xW7zPCurtmpo+qTBhV5dnIibXdXZhuHpVSpl9KJ9T3sP+9YcU6u07pmDU4/ae3btRLsE8roARSlX92Q7yVbx6nwtj5kZF72kw3vJvqOHrueW/3edV1WX72rIuFCC2IZLLozL/f+qDtLdrvtkXG79uVodAEDiQ+Qe7slYulZ7fyxIsKqt+3VNVtdnTtzKLt3sMr3/w5d653f/FtkwFKvsVnPdv8floY+rG3beDeqijiBJ8vxhE+LySX8mG4Ih+r5jqY6lsiBc3e1Rewe3Va1jWP5MjJ2lJwQ/13fe+OW43P9RleCS3fRaEtPO1no3r9KTAyk4MVrXDstLUkhu2nU1Wt6rtgfCSawDDl6rMm+321Xqav3mjdr2576udQWJiZP/eEBfjKIkz9eobQbLjG7lUr8DZGMgJK0m1yzSuoZP0fIIlZu98QKQmExu+zPP17oe1e+N5/TPEmBPP7sH2Jm8jy8VZiKbJ1BnOOcmO+faRPqbADzhnBsB4InotWEYhmEYRqfnrUh4lwJo29l3F4B3v+XeGIZhGIZhnABImMg37UEi6wE0IqUM/K9z7g4RaXLOFUafC4DGtteZmDx1mnvs6RcB+I7GYSj8fpLdWL5g12SWflj2SQRO5By2zWH5LH2wQzn3heUNwJekuP3e3VXC2+s5lOsxzYGzNUs3B0hS43N4WMIxYvdwdoRmG4NMDu0skQLASJbEaLw4rJ7lIbZ36BqMETtr96RrYZmRx7UlsHfI9Bkn1C3tq3Iky2PhWmapcvCpmti05mmV81gK5fO7B8mf2fGbZT+WXFma46TOZSSfAv4YL9moj91ZZu1HiaDDdcjrheVQlpU5KXV4fqa+uAxrn53b+bvCbQD+WLbNy9yZ0/HKKws6hR+5iNQD2ACgP4CGIxx+rDiebVv7NvfvxPYHO+fSZmTv6AaFk51zm0VkAIDHRWQFf+iccyKS9k5MRK4FcC0AVA6qSneIYRjG2562H6IisoC2MuSU49m2tW9z/05uPx0dkvCcc5uj/7cDuB/ADAB1IlIOANH/2zOce4dzbrpzbnpx//7pDjEMwzAMwzihOOITKBHpCSDhnNsTlc8F8DUAfwFwNYBvR/8/kLmWqC5ILN1xVBlLIoAvUTTScSwDtUXzAUAvkk44Qgrwo7Q4yqlfT44kU+lj5z5tr093v64/L9sal6+elv5p2j2LNYrjE7PSJ9AF/OvnyDeWylg64agoAGigZLPzN2l04mUTKuMyy4Y8pt0D6YU/44itMRUa+ZHJpTs0Ma+jeRnSLf3yYmmOncABoBtJZ/cv1ciXk8rUCM5L1Evnt+f4zbJd9Wkq56196r/SHh/Ca4fXK69JlrBYcg0TE6+rU5M4jrTk9cbJk/cc8KPdWBLkZNncPtfLY7y/2a+rmaRglgBHlGl0EsuJrJKGCcFZFm+b447Z0RmGYZx4dETCKwVwf5ROoguA3zrnHhGRlwHcKyLXILUv4PJj103DMIy3DXcc+ZBO2ba1b3P/Tm7/DRzxBso5tw7ApDTv7wBw1rHolGEYxtsV59xx+0F+PNu29m3u38ntpyOnLneHWpLYHEVTDS/rlfG4Hz1fE5f//Ww1qWOpqYDMBDkKbvNOP7cRyy0cPcYSWt8eappY0ltliNYg8eoFI9XAbCOZDg4v1Ws5b0Qp0tGzIPNQz/iK5kZa+p0L4jJH+rFBJ+AbPZb0JjPInWxeqVIPS5s1Ddp3wJdu2PDyhXUqDTYdUqnopIqitMcDwItb1CCwgqS2AjJg3EDtc8Rl6hw97sPTNM8Ty6wc+Xa4HTmQ556jFlm2G3bG5+LyPXf9W1yeWqGSIfBG2bMNjs5jmZMjBUPYCJNlt3XbVdrrT3PK8wv4ki9Hbb5eqxF9HJnZl6TBUIrlyDtOWsznL9zQpOdTX3YGxp8s++2K5ihMom0YhtFZsFQuhmEYHUBEzhORlSKyRkSOuXGwiPxCRLaLyOv0XpGIPC4iq6P/+7VXx1tsf5CIPCUiy0RkqYjckKs+iEiBiLwkIq9GbX81en+IiMyP5uD3ItL1SHW9xX7kicgiEXkw1+2LSI2IvCYii0VkQfReTuZfRApF5D4RWSEiy0Vkdg7bHhVdc9u/3SJyYy7XfkexGyjDMIwjICJ5AH4M4HwAYwFcKSJjj3GzdwI4L3gvlxkgWgB83jk3FsAsAJ+OrjkXfWgGcKZzbhKAyQDOE5FZAL4D4Dbn3HCkvAmvOQZtMzcAWE6vc93+8coAcjuAR5xzo5HawrM8V20751ZG1zwZwDQA+5GK/n/bZT/JqYSXSKgU0p6B5ymUr4sN/dbWaf64wSUqYa0n6YMjhgBf7mEjzNWNGm3GUV0cLcdGlIAvl3AkFEtgnNePrzGUA1nGueMTM6h9rYsjv95gEEp1s6TDEV9sMsnyzJ4Dfl49HjOWOWdUq1S3dLOOPUerJYPrYglzBUX0zRiqfyywJNWtyL+H5/HndpzT8m4abz4mlKc4t12m/HMs21159Tfj8s6X/tura1NNU1zeQ7kAWdpj2YujE4MhyiglcxRhfgYTVADYdzC9hMnw+iigyMYwIpCNV/dRhB5HF5b20bXOxrZhHkSOHBxS0jO6jk7zN9oMAGuiPaEQkd8hlY1h2bFq0Dn3jIhUB29fCuD0qHwXgHkAvnSM2t8KYGtU3iMiywFU5KIPLvXDs83xNz/65wCcCeCD1PYtAH56NNtuQ0QqAVwI4JsAPhcZRues/Qwc87EXkb4ATgXwEQBwzh0CcEhEcrb2iLMArHXObThO7bdLp/npZhiGcQypAFBLrzdF7+Wa0ujGBgC2IRUlfcyJbuSmAJifqz5E8tlipDwGHwewFkCTc67tTv9Yz8EPAPwrgLa/Uopz3L4D8JiIvBIZUgO5GfshAOoB/DKSL38WWRgdj7V3BYB7ovJxWfvtYTdQhmEYJyDRU5pjbrUlIr0A/BHAjc653fzZseyDc641knEqkXoCOPpYtJMOEbkIwHbn3Cu5ajMNJzvnpiIlG39aRE7lD4/h2HcBMBXAT51zUwDsQyCX5WLtRfvLLgHwh/CzXK39I5FTCW/foZbY9PHcHmXx+yyvAMCEgYVxmQ0jRw/UnG2LNjbF5X49VFZ4aKWaXQLAzIriuMxSyDkjtX3Os8Zyy/LtGtUEAHOHqJP6Vb/S79XdH54Wl0nF8WSz1qQvtbDsN7VK5a21ZLI4iq43hA0kS0i6KiZ5jK+LpcUhZLII+DnNOIfbi7UahTe1XPv4dE19XObxBYA/LtXx/+IZw+OyH/Wofand4UcE8pjV7VJJaDTl62OpK5SkGI5UZNmL4Wg7lu2KZnzGO27Tsz/QNmnuupMUu4UkrCKSRSVwG+XotUHF2keOTnR0DEefAsC4SjU47UHfnQmD+sZllhN5HH+1cJNX1/nDNcUTrws2lK0qVon7pXWNcXn6EH8PJ0dBhvJ3J2AzgEH0ujJ6L9fUiUi5c25rexkgjhYiko/UzdPdzrk/HY8+OOeaROQpALMBFIpIl+gp0LGcg7kALhGRCwAUAOiD1L6gXLXvZQARES8DyDEe+00ANjnn5kev70PqBiqn847UjeNC51xd9DrX7R8RewJlGIZxZF4GMCKKwuqKlLTwl+PQj7YMEEAHM0C8WaI9Pz8HsNw591/00THvg4iUiEhhVO4O4BykNjI/BeB9x7JtAHDOfdk5V+mcq0Zqrp90zn0oV+2LSE8R6d1WRioDyOvIwdg757YBqBWRUdFbZyG11y9nay/iSqh8h+PQ/hHJ6RMowzCMExHnXIuIXA/gUQB5AH7hnFt6LNsUkXuQ2jTbX0Q2AfgKUqmzcpUBYi6AfwLwWrQXCQBuzlEfygHcFUU/JgDc65x7UESWAfidiHwDwCKkbvByyZdy1P7xzgDyGQB3R38srAPwUUTzkIu1F900ngPgk/R2Ltd+h7AbKMMwjA7gnHsIwEM5bO/KDB/lJAOEc+4fADJpsce0D865JUhtWg/fX4eUlJUznHPzkIr4yln7xzsDiHNuMYDpaT7K1drbh9SmfX7vbZf9RNqzEzjaTJk63T31j5Ssupv2pHBoNJB5X8tXH18dl79wiibqnV+r7tdnj/Q35vP2kyba1/HI6m1x+Z/I8ZojxncHSVzZdZrHjV2nee8J2x60BOHmq7bujcu7m7Vf06t1X4m/h8qfp2WbdC/n+EG6J4anczPZNrBVw8PL9doB4KwRA+JyD3Is53m4/3WV+s8dofvHerSTmPi3r+p+m+tmVaftYzJYf2xjsKZOx6iS9grxWLLDelhXI803h+uzPQTbEDTt0/dHlfv7zypPuTEuP/77r8dldsRnawsO3w9tCLjN59Y0xOURA7TNw7SOCoIx5j1U7FbfmxzHe9G4cILqxn2+ezjvE2NbAt7PxE7m7JY+sUr3XL3xnNQesLNOnYnFC1/pdBuiDMMwbA+UYRiGYRhGltgNlGEYhmEYRpbkdA+Ug8OhSH5h6SOUONgFeS/JZjfOrY7L3chd+WSyF3h2rYbYA8DMwSqjssSycJPKQx+YpHIJSz2/WrjRq+uS0eVxuT+5UbP006eH74TeRkvg2szO4j0p0S7LhuwQ/mKNypQAkKCtCXW7mqmsIeus+rFUE/IhsmS49ULNTjGqXJPDXjae/OKo3vo9fgLfCkouPK1UJZ7V23S821yqAWBfEKL/0Aq1QRhXrNIkS4MsR7KkVB1cI8t7vMQ4yTDDDuNsVQD4st05H/gP7e89X43LP3l0VVz+4WXjqG1/ffOY8dpnh/hM6wDwHeY5YfR+GiMus6z87EaVDAFgcP+qtPWu36HjehLJyixXh/YMfp9TYykZt9AYhmGc2NgTKMMwDMMwjCyxGyjDMAzDMIwsyWkU3oTJU92fH3sOALCb5IrRgeM2SwHsUs5yTX9y3GaJokfgat6dpD5OvMryFssoLB9yclQAGESOzEs2qkv5JEp+PH+tSm2cQDeM6MsER2ixpBLO08PLNJKOHdI5yoplw3KSev623HdrP6Va3ajZMZwlvJ+/VBOXr5ykhsxhhBg7pHO027BSle04AfHewCGcpVl2s95CiYFZ/uVIu5HUX8CP9uM1wnPMkZU89vmBkzavvT2UdPeCK78Sl1/+67e1j1TXQJKOAaCFrn8juY/zOuRj2nMiZzhyjyMSeeWEdbVJbSFrKQKSpdDaRu3vuIF+P3ju2jht7gwsemWB6XiGYXQ67AmUYRiGYRhGltgNlGEYhmEYRpbkNAovLyFxRBFHQoUmkSxlbNyhZpAcScZGhSxbsSQCZDY3fGmDSm2TKwrjMhsT/tvDK7y6rpyqUXhnkPkkGzv2J1NQjlLi6D4AyKfXLC+xtMl9CaWXk4eqbMemnDyuHDHFEV4XUDQhANz65Jq4XNJLI744ae9HpqvZKMtp3QMJbwAlNuZZZRNTllkTQQTmN6kvXzptaFweRoluuV5eO12CuvgzloJZHuP+8jxsCeRbXkccbcey3UkXa8Ly+hd/GJebg4i+e5fU6jllRXGZJciael3HFf18CZATMPN3goPiuiR0fbEUHEapzq7WdcTGr1wuo3XEiavD6Fk2d22TGU27Mwyjs2JPoAzDMAzDMLLEbqAMwzAMwzCyJKdReCPHT3Y/uvdxAMC0Ko1Q65bv38exlLLrQPr8c31JXsoj7SLMo1dIUUYc8cUSBfPIMo1QY5kOADaQPDi81I/4amPFlj1xeSxFS4W58Fii4Qi1/c1kgEjnHApkoOc2qCHiqCJtp4oiBZdRX2YOU6mII+UAoIhkRx5jlrp4mbBsF14XS418nBdhRtGB+wNpkqW2pSQJFfVKHy1WTtJaaFi5aafKvyxjJTPkMeRrCSVTlmO5j9vIxLSM5NOSWZ/Vfjz7A6+uVsfSYnqZlsub6ToAYEyFRq2GZpZtNNP3gMehmkxMAaCmXqMLWabs7eVx1P5mGkfAn+O2pXPK7JOw0KLwDMPohHToCZSIFIrIfSKyQkSWi8hsESkSkcdFZHX0f78j12QYhmEYhnHi01EJ73YAjzjnRgOYBGA5gJsAPOGcGwHgiei1YRiGYRhGp+eIEp6I9AWwGMBQRweLyEoApzvntopIOYB5zrlR7dU1cfI09+ATKSPNPt1VgmtPwmOJoolMHjl6asG6xrg8osyX1jiqjU0DOTKqF0kybKwY5q/j/HdsssmRSTvJPHIg5YUL2dKosgpHOYURiW2ESg2Pyw7KrcYGo1yXZ6wYNMF1c70s/ZTSNXIE4eFAwstkRMpjz/JpaKS5rzm9zNo1L31UGeeVKwzyELLJJstTLPNyZCavu1AyZXmqR9c3GkYC/ppis9DKU270jlv++PfiMkuT3AabYh4IZGleCixR83eZjVt5rQ0Z4Et4HFHJsl2f7lpmg0xea8W9/ZyCbMLaNncm4RmG0VnpyBOoIQDqAfxSRBaJyM9EpCeAUudc24ahbQBKj1UnDcMwDMMw3k505AaqC4CpAH7qnJsCYB8CuS56MpX20YmIXCsiC0Rkwc4d9ekOMQzDMAzDOKHoyA3UJgCbnHPzo9f3IXVDVRdJd4j+357uZOfcHc656c656UXFJekOMQzDMAzDOKE4ohO5c26biNSKyCjn3EoAZwFYFv27GsC3o/8fOFJdIkBetOeE9+SEodi8L2MAhYbz5p39tFeG92ss2KgO4wBw2gi9aeOQc94vwq3zvpv3/N98MDedPSIuTx+sQYettFdqTb26gvMeqHBvE+994VB+dlXnsPyyMCEt7T367aub4/KVkyricjG1sZ2uvSTYu/JqrSZG/szdi+LyR88aEpcvGzcwLt/yV3XivvWC0V5dXSksf1CxumSHiZnbWE9JegHgfbfN035996K4zPuAOMkw71MLnbHZboDHf12dtsn773hOeC8b4If/874r3tvFDuOXjdN54D1PADDmnC9oXeRYftjb+6fH9+3u7+3y9+npOf9YsyMunzy8OC7zXqVn1vhPgav66nXxHihee5wUmvdcsbs94NteGIZhdHY6msrlMwDuFpGuANYB+ChST6/uFZFrAGwAcPmx6aJhGIZhGMbbiw7dQDnnFgOYnuajs45qbwzDMAzDME4AcupEPnXadPfciy8D8BPghtYDmeQ9dtBmSwGWwLoGSXs5tJoliufWqdxxxkiV+VhqCt2o2bWaw/VDG4b4GAqRZ8dnwJf3XicJbdLgwrjMglRd4B7O8zYgQ4JXnlqWV371ygavrgn9+2r7g7TMY7me+s9WCaGNQXcKeeeEvCyN8jywNQXgX3Nb4mnAj1DgxMzs/D56YG8wbEWwktbbUArl53FhSSq0oHiR1guPcWkvXRPc3ijqSyjfstLIjuVbnrs9LvN3YF9g9cAu9BeNVWk1kwUEsysY7x4kubJzPFsfFJFsx+MVJsjeTOe0jd9pc2dgkdkYGIbRCbFceIZhGIZhGFliN1CGYRiGYRhZ0tFN5EeFA4da8eqGlFw1abBKRWEU3qs1KmlNGKSJctlVnKPV2E06EURisTs1R/edNUoTBbMMtXWXHjOm3JeEuJ9r6lQSGtxfo83YAbqK3i8OkuGyA/d4ks3YJZvdt0P3ax4Llh3nb9IoxPU79f2TB2nU4JQBhV5dnBiZ5alDgTzXBke37feD1Xz3coqg5KS53EaXYL74+g8c1vYfXqlJnkf203mZMVSTJIeJjTl6jJMOc9TmOooC5LXCiaMBYMQAbZOlPr6WkeU6jpmSKgN+tB3LdgPn3hCX/3H/t+JySW9/7YwhyZUjEgvy0zvqHzycOUkyZwRgeY/luVXbdK2v36XlC8eWe3WVeYmdU/+bdmcYRmfFnkAZhmEYhmFkid1AGYZhGIZhZElOJbxDrUls2puSRsp26eP+0CSyop++3tecXgph6YSjxVZs06gsAKgmGY0jmziaiOuaUKnyyP5A7oBTKYSjtDjZas8MZoIsYQHA0k27tc0qbbOBTBo5uu6Zdb4B4s6DKk+9e6yaNq5pUAntpAqVP1mOXFPnRwSy3MOyF0uTLDkebs0cucnJalkuynRGGMHIx/3wH+vi8iqS2t5zmV4vJ7ftGyQTZjiijyVPjijMJznMBUaaLLuxTMtt1tTvT/t+KFOyYs0ReizbnXzZzXH58d9/3Tt/Iq0XXm4cqTmoSNfnwlpNEtAtz5cTq4r1uB+/sD4u//Osau0vHT+ySNdRmHCZ5fPQ1NQwDKOzYU+gDMMwDMMwssRuoAzDMAzDMLIkpxKeCJCfSN2zcc64kj5+bjaWzlgK6VWgcsPjK7bF5ZmDNe9XKJdkgk05Wd75/jMqG103c7B3Dst+20gGGlepUtmt8/T87108Ji6H0YFjKlQKYXmIzTdZNqvqrXIaANy9YEtcHl+sks6oEh2jAT1UCmWZcTz1F/ANL1nS4ag2zgXHEVrhaNdRFCNHhbH8yrJVcyADsRnkFRNVqlvboOuFI/3YMDKM5uTIRx7XPSTBcV5Alp3CaDXOAcfrhSVmlp5rd2gfB5f4c9fXi3zjHIXaBst253zgP7zz7/u1vj59pEaTltL3iIdi9hD9fuwJTDm5nx+k8eboxFEk/26n7024pnldtK3dZA6Neg3DMHKJPYEyDMMwDMPIEruBMgzDMAzDyBK7gTIMwzAMw8iSnCYTnjx1mnv86RcB+Htywm1LvAeKnZJ57wzvtWFLgaZ9fvg52wfw+U+u1tDus0eVxuWXa9TJe0yZv1eIHax5Tw3DLtW9qe+hSzbv/Wkmp2jeX5MpGS7gWz8k6bp47HhceX9QmHC5dqeG32dKJszLhPfRhNYBvJ+L+8+rjJ3fw+W3kmwoRtPeG05AzI7ZbKnQO0igyxYJ7MbN64D7z0l7Q3sFtn7gcWGrh9odOo7sfB7up+K5eHJNXVxmh3FOePzsGt/C4n3/pPujFj30nbjMlgzsXL+L1iTvvwIC53u6LnbtLw9sRtpgF3TAX3tt83r2qTOxeOEr5mlgGEanw55AGYZhGIZhZIndQBmGYRiGYWRJTiW8adOmu+fmLwAAHKTH/QVBstWd5ALtSSwU4s5yDcs4oQMyyz0sj7GbNNfFo9EauIrvp/Y5LJ+TGbM0x/JIYSB1sUUBy4wcGu5LVb4EyHYN3JcEyUMcys4SVlhXrwwyZyY3aR6VUA7kuSsiG4HQtbqNMMydQ+G5rn49/YS6bbCcGFpY8LjwNdft0lD8CnLsZvk1lCZZ0hpIdgW8RLh5XpPhGLVkkDBZEstgaA/AlwqnXPCluFzz9G1xmRM+Z1prALCNpHC2ffBcxTOsqdA2gl+1jffpc2di0cIFJuEZhtHpsCdQhmEYhmEYWWI3UIZhGIZhGFmSUyfygy1JrK1LRZNx9FIy0CuaSLpilYClNnaALqCIqefXNnh1TawopLq0slc3NcXlU0eWxGWOIgtdm+vIsbucZJz8PO0/yzAs24WSDEdmrdqmEXajB2rkGSe3/eJfV3jn33zm8LjM17Vgo0YRTqJrZ5lOgvvmekrIu6JOo+Aq+6q8NX+z1jutrF9cHlney6tr+TZNklzWW8eI55udxNtLOsufsQs8S23PrNcItXNHlnnn8zrieeG6Xq/dlbbtCRSNCAC9KQKTo806Im+FMvk/1uyIy5MpeTU7t3Ni4NLAqZ+j7Vi2qz7tX+Lyzpf+Oy5z8uTugVzOUa7sMs7zdeuTq+PyNdOr4nK3QJpkV/i2uRMT7wzD6KTYEyjDMAzDMIwssRsowzAMwzCMLMlpFN74SVPdfY88CwAo66vyThiFx9FuLH1xZBFHu/ElhBFPHAlXkMG8kyPPWBrk9kLYSJOjqvh9jjzjCMKwTY6Maj7cmvb90LSQ62ZTUu4Lt8HjwtcYfsZRcSxPsZzG9b4WSGBTqgupLn0/0zoLI7kOZ4jW8xL90hh50mQgF2WSeTPNkRcRGHSXxyiTWSnXy/MYyreZ1pVnUErSWnhd3E1vvqgzRTM+E5frXvhh2uMBf455jbG5K7fPEadhXdz/Nrn91DkzsPAVi8IzDKPzccQnUCIySkQW07/dInKjiBSJyOMisjr6v9+R6jIMwzAMw+gMHPEGyjm30jk32Tk3GcA0APsB3A/gJgBPOOdGAHgiem0YhmEYhtHpyTYK7ywAa51zG0TkUgCnR+/fBWAegC9lOA9ASmJoyw/HklaYd4zlEo5W+/Hz6+PyxygaiPPETaryo6dYZdjQoAaEVcVkoEjSAxtOhrIZ50rjaLWpVfrwrYEizKpLNJ9Z1y6+EeRZtz0Tl++5ZmZc7k9mhntpjL728Brv/CvHa8QZR0yxQeiWXdqXwUV6TCjhcWRWBUUXvl6rEXWllA+No+BYsgOA1RRRyCaVLEeynMdzAgCDirWfP3l+XVwe21+j/U4boVGTDy/fFpcvHFfu1bVqK83REJ0jjjbrS9F1XhQcGUwCvnTFsh9H5/G6bYs2TUcxRdEVkbkrr72FtZqrcfaQYu98lq95hXK0Hct2pbM/G5frX/whmJfXN8blTXt1LqaW63ixEedrDSrZXjF5kFcXm53mcmuAYRjG8SDbTeRXALgnKpc657ZG5W0AStOfYhiGYRiG0bno8A2UiHQFcAmAP4SfudSfm2n/5BSRa0VkgYgs2NHQkO4QwzAMwzCME4oOR+FFkt2nnXPnRq9XAjjdObdVRMoBzHPOjWqvjjETprhf3v8UAGB0hRpGhjnMmDV1++Ly0AEqia3bru/vPqiS0oOr1FgRAL50xrC4zLnVXqhVM8OLxw6My2zq+Z15a7263jVcpZTyPipPlZO8xeaCnE+Mo7JCWihv2n2vb4rLl47RfrEpJACs36nXzxIPyztrSEYaVa7jHeb420gy2spGlb3mVGm9JSQ77aBxDM1GOYccy1Ms7Y2p6BOXwxx5Dy/fGpebmvWaeSzYsDHRjlMjXyVHqNXU69ixzMoRm//9D5WLAeA9Y1UyfXaj/iFw0WiVDRfUqtnoacMHxOWwi8+s0TU6rVKlsl0Z5NcRA3yzUp4LnsvNjXpOGa1J/n6VzFI5DwAaX/5RXGZps6S3ynEs+fL64vkF/DkeUZbq89xZJ1kUnmEYnZJsJLwrofIdAPwFwNVR+WoADxytThmGYRiGYbyd6dANlIj0BHAOgD/R298GcI6IrAZwdvTaMAzDMAyj09OhKDzn3D4AxcF7O5CKyjMMwzAMw3hHkVMn8klTprnHnn4RgL+PJdwgsZb2Nw2iUPiNO3SvTgklWO1BYfjhnhre11FFIfKZts68sE73RnXP8+8vi8higPdTjaH9XIs2NsXlk0f0T98I/H04lXSNvD2Jw/CHlfr7YHhfy/ItlADYsw7QceEw/IPBfixeAmwv0ZLByZwtCcLktC+t031AI6jPnAiaHbv5GgH/+nnf0pASnTt2yWarh+JevlUEt8N7hdbQXp0wGXIbSzft9l5zkmeGndQ53H8L7Udip3jAX6NsQcFzyuuzdofWBQClfdPvR+N54fFeUKNWBbOH+5YI/U66Pi7P/8utcZnXRJVnk6H70sLx5rFoiBJUX3zWXCxZ/IrtgTIMo9NhufAMwzAMwzCyxG6gDMMwDMMwsiRbJ/K3RGvSxeH4LDGEDC/V0PK1ZGPAMhJLUu3kgPWkL05SHEpPbXBY/LQhhd5nLOtMHqyO513aSbCqffTf30pO1ywt7iVLBu77epI1Ad8BO1NiZHb57k3JacOEyyzFsEw6kqwP2iQZwLdqaNqnEhIATBqk48LjNZEc4llCLApkoEKyQfja46vj8uXj1EZgPLWxZJM6Yw8gWRcAaula2GrCc/Km+Wb5cghZZgDA4db0cibDsjTbCLBNBeCvfU6kvYusKn78gtoofHBihXc+t89zx3J1P7IYYIfx7bt9yZJlu5mXfDkus2P5zn3aL07eHDrac8LmtrkI3fwNwzA6C/YEyjAMwzAMI0vsBsowDMMwDCNLchqFN3XadPfM8y8BAJZv1uircZV9vONYLupBkgFHrm3dqxLYhHKVdPp096VBlvpYotlPSYpZ9uLIr1DmY3nvufXqRn3yUI22YyfzPiSbtQTu3/PXa7Tf3GHpo/U4Eqt+jy+VcZ9bWlWSWrJNJa2zRqgbNjuG8zgAwPO1ei2nVus5LA9xGyzplAayGTvEc//ZRZ6T5jYHUZN8XRxF2EDXzxF5fHwoKfFaYKmOE1TzfPN3ga8R8CPn1u/QaxzYR6U6lvBYTgyd33kd1WeQRtnFfl0g37IT+QCKyOPzOVKRHcqHBtLkKkrEPYykc3Ys3/jMbXH5gWVb4vL7JlR6dXE4bWskW5516kwsXmhReIZhdD7sCZRhGIZhGEaW2A2UYRiGYRhGluQ0Cm9vc0tsVDl9cFH8fhi5du/rKhN8eOqguMzRR2eMLInLjSS3cPJhABhGkgUrKVzmCC3nHeP3i6WYsh56Dht5sjzEMkw40CMHaIQbyzgsmwlpIvcv1TEBgKunV8XlriRT/nGpJuM9eYjKOJzkN4wiG91PJdS8DImdf7FgY1z+1OwhcTmMslpNyYhnUTJiltDy6ZyCfH9kOJKsS0I/O0jjurVJ5Vuek4p+aiIKAE+vUmlyXLleI0eoLdzQFJdLSY6rKvbr4gi5k6o1AXATrb2yvno+S34FgRTM5pdFPXW+V5HBJ48qJ4IGfKmOufVJjVr8/KmaRHuvJ9/6MiebZLJsybJd1an/om3c/rm4HMqvLLm2rcn2kj0bhmGcyNgTKMMwDMMwjCyxGyjDMAzDMIwsyamE16tbF8wakpJ1Vm7NHIV3/nCNBGN57LF19XH5HFLX7l6i8tYNJ6u8BAB5JBc9skzlrfdNVGmQI9xKequksvegL3ewRPGB25+Jy69+58K4nMmgM1QydlCbI8rU3LCJpKLulEPt4tFqJAn4ufhYOjppoEYksrzFkY2hTDeAzu9HUh/nPeO6uBxKeEspYmxcifaFo9L2N6v0w9GQ4XEs+22jqEuOPOMoywNBjr9e+elz9rEyO4Ai2lg+fWmd5o8DgHwas1Iar9rG9PkZWSbdQWMPAIUk27Hku34X5egrUtmOZU3Azw/J6+oaknV5XF5r0MjMSjJtBfzoSjbJvH/p5rjMst2Xb/gvbe8FNdsE/Llsi0A1Ac8wjM6KPYEyDMMwDMPIEruBMgzDMAzDyJKcGmlOmTbdPf1cykiTZaRQUmo+nN7okCWdjZTnjSPMQklpP0UdcZ41jpDjM1ppPMIIIu4Ld5n7xePJ7ydDM0Wq4PHldXF5epVGeBV6cppvfsn51DJJaiyptBcNxfJWI+W242ivvRy9RdcYSpY9SQbi6MJ+JFtxjr79gannBMpzx+ajXWi8Gknm5HHtHZiovrhuZ1w+dYSalR4i2WoZ5evjfIGh4WSmeeX+s+krH8+5EgFgD0mjBSTT8hRxFF8i+H7wvPCy4np7Zcg1GX7XMhmReqac1BeW1AfMVrNNANjy3O1xuS3y78Iz52DJYjPSNAyj82FPoAzDMAzDMLLEbqAMwzAMwzCyxG6gDMMwDMMwsiSnNgYC3W/EWzHC/UEcAs57fzisPtzv0kZ+sN/k6fVqXXDGULVHqNul+3PGko1CHu2I2kKO1yEF+doOu0nzvh3a3vKGhLL8auog3ff04HLt77tGlMZlTkwM+PtSkp7FALmfZ9hnxs7UgO/szXtnCnvoBXD/ed/OVx9f5dX12blqI+HPo84d7y86HLhZc+Jbbof3g7GdREur9qtrMPdTqwr1uGT6vW1sIcHjEFoH8J4mXpN8LbyfavwgXVPsYh72Zcdevd4ycsTnfU+h8zjvbWOrC547Th7N+89WkX0IAAwr1evnNc3rk8eb2+Y9TwAwcO4Ncbnm6ZSTuRmRG4bRWbEnUIZhGIZhGFliN1CGYRiGYRhZklMbg6nTprtnnn/pjZ0InvOzxMQWBSwjcSh8KTlAd8v37wmXbFQXZpZbWO7IZENwKJCXOGSfFTnPBoElPJJeOMQ8/GzlFpVVBlJC3G88sSYuf/+SMd753GeWQxvI4Zz7wi7ZoZyYyZKhNYONAJ8drh+Wx/gTrquJrBI4sS7gS0osAbJjNtfF/Z23ertX18zBmsyY1xHXtY2kXF5H7dlhJDJIo5nGqD1aPWlR329Pcs2UmDlTIuhM7wO+VOm7xZNMSOuer70+kDl5vqpPSyUgbl55L5L7t5uQZxhGp8OeQBmGYRiGYWSJ3UAZhmEYhmFkSU4lPBGpB7APQEPOGn0j/a3949b+O/naj3f7x6vtwc65kuPQrmEYxjElpzdQACAiC5xz03PaqLX/tmj/nXztx7v9433thmEYnQ2T8AzDMAzDMLLEbqAMwzAMwzCy5HjcQN1xHNq09t8e7b+Tr/14t3+8r90wDKNTkfM9UIZhGIZhGCc6JuEZhmEYhmFkSU5voETkPBFZKSJrROSmHLT3CxHZLiKv03tFIvK4iKyO/u/XXh1voe1BIvKUiCwTkaUickOO2y8QkZdE5NWo/a9G7w8RkfnRHPxeRLoeqa630Ic8EVkkIg8eh7ZrROQ1EVksIgui93Iy9lFbhSJyn4isEJHlIjI7h3M/Krrutn+7ReTGXF6/YRhGZydnN1AikgfgxwDOBzAWwJUiMvYYN3sngPOC924C8IRzbgSAJ6LXx4IWAJ93zo0FMAvAp6PrzVX7zQDOdM5NAjAZwHkiMgvAdwDc5pwbDqARwDXHqH0AuAHAcnqdy7YB4Azn3GQK38/V2APA7QAecc6NBjAJqXHISfvOuZXRdU8GMA3AfgD356p9wzCMdwK5fAI1A8Aa59w659whAL8DcOmxbNA59wyAncHblwK4KyrfBeDdx6jtrc65hVF5D1K/QCty2L5zzu2NXuZH/xyAMwHcd6zbF5FKABcC+Fn0WnLVdjvkZOxFpC+AUwH8HACcc4ecc025aj/gLABrnXMbjlP7hmEYnZJc3kBVAKil15ui93JNqXNua1TeBqD0WDcoItUApgCYn8v2IwltMYDtAB4HsBZAk3OuLTvtsZyDHwD4VwBtmXuLc9g2kLpZfExEXhGRa6P3cjX2QwDUA/hlJGH+TER65rB95goA90Tl49G+YRhGp+QdvYncpUIQj2kYooj0AvBHADc653bnsn3nXGsk41Qi9QRw9LFqixGRiwBsd869kov2MnCyc24qUpLxp0XkVP7wGI99FwBTAfzUOTcFqfRFnlyWo7XXFcAlAP4QfpaL9g3DMDozubyB2gxgEL2ujN7LNXUiUg4A0f/bj1VDIpKP1M3T3c65P+W6/TYi+egpALMBFIpIl+ijYzUHcwFcIiI1SEm1ZyK1JygXbQMAnHObo/+3I7X/ZwZyN/abAGxyzs2PXt+H1A1Vruf+fAALnXN10eucrz3DMIzOSi5voF4GMCKKxOqKlLTwlxy238ZfAFwdla8G8MCxaCTa8/NzAMudc/91HNovEZHCqNwdwDlI7cN6CsD7jmX7zrkvO+cqnXPVSM3zk865D+WibQAQkZ4i0rutDOBcAK8jR2PvnNsGoFZERkVvnQVgWa7aJ66Eync4Du0bhmF0WnJqpCkiFyC1NyYPwC+cc988xu3dA+B0pDLR1wH4CoA/A7gXQBWADQAud86FG82PRtsnA3gWwGvQfUA3I7UPKhftT0Rqo3AeUjfK9zrnviYiQ5F6KlQEYBGAq5xzzUe7ferH6QC+4Jy7KFdtR+3cH73sAuC3zrlvikgxcjD2UR8mI7WBviuAdQA+imgectR+TwAbAQx1zu2K3svZ9RuGYXR2zIncMAzDMAwjS97Rm8gNwzAMwzDeDHYDZRiGYRiGkSV2A2UYhmEYhpEldgNlGIZhGIaRJXYDZRiGYRiGkSV2A2UYhmEYhpEldgNlGIZhGIaRJXYDZRiGYRiGkSX/H5B5E81M9S75AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "matrix_train = pauli_kernel.evaluate(x_vec=sample_train)\n",
    "matrix_val = pauli_kernel.evaluate(x_vec=sample_val, y_vec=sample_train)\n",
    "\n",
    "fig, axs = plt.subplots(1, 2, figsize=(10, 5))\n",
    "axs[0].imshow(np.asmatrix(matrix_train),\n",
    "              interpolation='nearest', origin='upper', cmap='Blues')\n",
    "axs[0].set_title(\"training kernel matrix\")\n",
    "axs[1].imshow(np.asmatrix(matrix_val),\n",
    "              interpolation='nearest', origin='upper', cmap='Reds')\n",
    "axs[1].set_title(\"validation kernel matrix\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "</div>\n",
    "    \n",
    "<div class=\"alert alert-block alert-success\">\n",
    "\n",
    "**Challenge 3b**\n",
    "\n",
    "Calculate the transition amplitude between $x = (-0.5, -0.4, 0.3, 0, -0.9)$ and $y = (0, -0.7, -0.3, 0, -0.4)$ using the 'ZZFeatureMap' with 3 repetitions, 'circular' entanglement and the rest as default. Use the `qasm_simulator` with `shots=8192`, `seed_simulator=1024` and `seed_transpiler=1024`.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0068359375\n"
     ]
    }
   ],
   "source": [
    "x = [-0.5, -0.4, 0.3, 0, -0.9]\n",
    "y = [0, -0.7, -0.3, 0, -0.4]\n",
    "\n",
    "##############################\n",
    "# Provide your code here\n",
    "\n",
    "zz_map_3b = ZZFeatureMap(feature_dimension=N_DIM, reps=3, entanglement='circular')\n",
    "zz_kernel_3b = QuantumKernel(feature_map=zz_map_3b, quantum_instance=backend)\n",
    "zz_circuit_3b = zz_kernel_3b.construct_circuit(x, y)\n",
    "\n",
    "counts_3b = execute(zz_circuit_3b, backend=backend, shots=8192, \n",
    "              seed_simulator=1024, seed_transpiler=1024).result().get_counts(zz_circuit_3b)\n",
    "ex3b_amp = counts_3b['0'*N_DIM]/sum(counts_3b.values())\n",
    "\n",
    "print(ex3b_amp)\n",
    "##############################"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submitting your answer for 3b. Please wait...\n",
      "Congratulations 🎉! Your answer is correct and has been submitted.\n"
     ]
    }
   ],
   "source": [
    "# Check your answer and submit using the following code\n",
    "from qc_grader import grade_ex3b\n",
    "grade_ex3b(ex3b_amp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Related QGSS materials:\n",
    "- [**Kernel Trick (Lecture 6.1)**](https://www.youtube.com/watch?v=m6EzmYsEOiI&list=PLOFEBzvs-VvqJwybFxkTiDzhf5E11p8BI&index=14)\n",
    "- [**Kernel Trick (Lecture 6.2)**](https://www.youtube.com/watch?v=zw3JYUrS-v8&list=PLOFEBzvs-VvqJwybFxkTiDzhf5E11p8BI&index=15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3 Quantum Support Vector Machine (QSVM)\n",
    "\n",
    "Introduced in [***Havlicek et al*.  Nature 567, 209-212 (2019)**](https://www.nature.com/articles/s41586-019-0980-2), the quantum kernel support vector classification algorithm consists of these steps:\n",
    "\n",
    "\n",
    "<center><img src=\"./resources/qsvc.png\" width=\"1000\"></center> \n",
    "\n",
    "1. Build the train and test quantum kernel matrices.\n",
    "    1. For each pair of datapoints in the training dataset $\\mathbf{x}_{i},\\mathbf{x}_j$, apply the feature map and measure the transition probability: $ K_{ij} = \\left| \\langle 0 | \\mathbf{U}^\\dagger_{\\Phi(\\mathbf{x_j})} \\mathbf{U}_{\\Phi(\\mathbf{x_i})} | 0 \\rangle \\right|^2 $.\n",
    "    2. For each training datapoint $\\mathbf{x_i}$ and testing point $\\mathbf{y_j}$, apply the feature map and measure the transition probability: $ K_{ij} = \\left| \\langle 0 | \\mathbf{U}^\\dagger_{\\Phi(\\mathbf{y_j})} \\mathbf{U}_{\\Phi(\\mathbf{x_i})} | 0 \\rangle \\right|^2 $.\n",
    "2. Use the train and test quantum kernel matrices in a classical support vector machine classification algorithm.\n",
    "\n",
    "The `scikit-learn` `svc` algorithm allows us to [**define a custom kernel**](https://scikit-learn.org/stable/modules/svm.html#custom-kernels) in two ways: by providing the kernel as a callable function or by precomputing the kernel matrix. We can do either of these using the `QuantumKernel` class in Qiskit.\n",
    "\n",
    "The following code takes the training and testing kernel matrices we calculated earlier and  provides them to the `scikit-learn` `svc` algorithm:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Precomputed kernel classification test score: 70.0%\n"
     ]
    }
   ],
   "source": [
    "pauli_svc = SVC(kernel='precomputed')\n",
    "pauli_svc.fit(matrix_train, labels_train)\n",
    "pauli_score = pauli_svc.score(matrix_val, labels_val)\n",
    "\n",
    "print(f'Precomputed kernel classification test score: {pauli_score*100}%')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Related QGSS materials:\n",
    "- [**Classical SVM (Lecture 4.2)**](https://www.youtube.com/watch?v=lpPij21jnZ4&list=PLOFEBzvs-VvqJwybFxkTiDzhf5E11p8BI&index=9)\n",
    "- [**Quantum Classifier (Lecture 5.1)**](https://www.youtube.com/watch?v=-sxlXNz7ZxU&list=PLOFEBzvs-VvqJwybFxkTiDzhf5E11p8BI&index=11)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 2: Challenge - QSVM for 3-class classification of Fashion-MNIST\n",
    "\n",
    "In this part, you will use what your have learned so far to implement 3-class classification of clothing images and work on improving its accuracy. \n",
    "    \n",
    "<div class=\"alert alert-block alert-success\">\n",
    "\n",
    "**Challenge 3c**\n",
    "\n",
    "**Goal**: Implement a 3-class classifier using QSVM and achieve 70% accuracy on clothing image dataset with smaller feature map circuits.\n",
    "\n",
    "**Dataset**: Fashion-MNIST clothing image dataset. There are following three dataset in this challnge.  \n",
    "- Train: Both images and labels are given.\n",
    "- Public test: Images are given and labels are hidden.\n",
    "- Private test: Both images and labels are hidden.\n",
    "    \n",
    "Grading will be performed on both public test and private test data. The purpose of this is to make sure that quantum methods are used, so that cheating is not possible.\n",
    "    \n",
    "</div>\n",
    "\n",
    "### How to implement a multi-class classifier using binary classifiers\n",
    "\n",
    "So far, you have learned how to implement binary classification with QSVM. Now, how can you scale it up to multi-class classification? There are two approaches to do so. One is the One-vs-Rest approach, and the other is the One-vs-One approach.\n",
    "\n",
    "1. One-vs-Rest: In this approach, multi-class classification is achieved by combining classifiers for each class that classifies the class as positive and the others as negative. Since one classifier is required for each class, the total number of classifiers required for N-class classification is N. The advantage is that fewer classifiers are needed, and the disadvantage is that the labels are likely to be imbalanced in each classification.\n",
    "2. One-vs-One: In this approach, multi-class classification is achieved by combining classifiers for each pair of two classes, where one is positive and the other is negative. Since one classifier is required for each label pair, the total number of classifiers required for N-class classification is N(N-1)/2. The advantage is that labels are less likely to be imbalanced in each classification, and the disadvantage is that the number of classifiers required is larger.\n",
    "\n",
    "Both approaches can be used to solve this problem, but here you will be given hints based on the One-vs-Rest approach. Please follow the hints to solve it.\n",
    "\n",
    "<center><img src=\"./resources/onevsrest.png\" width=\"800\"></center>\n",
    "\n",
    "Figure via [cc.gatech.edu](https://www.cc.gatech.edu/classes/AY2016/cs4476_fall/results/proj4/html/jnanda3/index.html)\n",
    "\n",
    "### 1. Data preparation\n",
    "The data we are working with here is a small subset of clothing image dataset called Fashion-MNIST, which is a variant of the MNIST dataset. We aim to classify the following labels.\n",
    "- label 0: T-shirt/top\n",
    "- label 2: pullover\n",
    "- label 3: dress\n",
    "\n",
    "First, let's load the dataset and display one image for each class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Load MNIST dataset\n",
    "DATA_PATH = './resources/ch3_part2.npz'\n",
    "data = np.load(DATA_PATH)\n",
    "\n",
    "sample_train = data['sample_train']\n",
    "labels_train = data['labels_train']\n",
    "sample_test = data['sample_test']\n",
    "\n",
    "# Split train data\n",
    "sample_train, sample_val, labels_train, labels_val = train_test_split(\n",
    "    sample_train, labels_train, test_size=0.2, random_state=42)\n",
    "\n",
    "# Visualize samples\n",
    "fig = plt.figure()\n",
    "\n",
    "LABELS = [0, 2, 3]\n",
    "num_labels = len(LABELS)\n",
    "for i in range(num_labels):\n",
    "    ax = fig.add_subplot(1, num_labels, i+1)\n",
    "    img = sample_train[labels_train==LABELS[i]][0].reshape((28, 28))\n",
    "    ax.imshow(img, cmap=\"Greys\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, preprocess the dataset in the same way as before.\n",
    "- Standardization\n",
    "- PCA\n",
    "- Normalization\n",
    "\n",
    "Note that you can change the number of features here by changing N_DIM."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Standardize\n",
    "standard_scaler = StandardScaler()\n",
    "sample_train = standard_scaler.fit_transform(sample_train)\n",
    "sample_val = standard_scaler.transform(sample_val)\n",
    "sample_test = standard_scaler.transform(sample_test)\n",
    "\n",
    "# Reduce dimensions\n",
    "N_DIM = 5\n",
    "pca = PCA(n_components=N_DIM)\n",
    "sample_train = pca.fit_transform(sample_train)\n",
    "sample_val = pca.transform(sample_val)\n",
    "sample_test = pca.transform(sample_test)\n",
    "\n",
    "# Normalize\n",
    "min_max_scaler = MinMaxScaler((-1, 1))\n",
    "sample_train = min_max_scaler.fit_transform(sample_train)\n",
    "sample_val = min_max_scaler.transform(sample_val)\n",
    "sample_test = min_max_scaler.transform(sample_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Modeling\n",
    "Based on the One-vs-Rest approach, you need to create the following three QSVM binary classifiers\n",
    "- the label 0 and the rest\n",
    "- the label 2 and the rest\n",
    "- the label 3 and the rest\n",
    "\n",
    "Here is the first one as a hint.\n",
    "\n",
    "### 2.1: Label 0 vs Rest\n",
    "Create new labels with label 0 as positive(1) and the rest as negative(0) as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original validation labels:      [3 3 2 0 3 0 3 2 3 2 2 3 2 2 2 3 0 2 3 3]\n",
      "Validation labels for 0 vs Rest: [0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0]\n"
     ]
    }
   ],
   "source": [
    "labels_train_0 = np.where(labels_train==0, 1, 0)\n",
    "labels_val_0 = np.where(labels_val==0, 1, 0)\n",
    "\n",
    "print(f'Original validation labels:      {labels_val}')\n",
    "print(f'Validation labels for 0 vs Rest: {labels_val_0}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See only places where the original label was 0 are set to 1.  \n",
    "\n",
    "Next, construct a binary classifier using QSVM as before.  \n",
    "Note that PauliFeatureMap is used in this hint but you can use a different feature map."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy of discriminating between label 0 and others: 90.0%\n"
     ]
    }
   ],
   "source": [
    "pauli_map_0 = PauliFeatureMap(feature_dimension=N_DIM, reps=1, paulis = ['X', 'Y', 'ZZ'])\n",
    "pauli_kernel_0 = QuantumKernel(feature_map=pauli_map_0, quantum_instance=Aer.get_backend('statevector_simulator'))\n",
    "\n",
    "pauli_svc_0 = SVC(kernel='precomputed', probability=True)\n",
    "\n",
    "matrix_train_0 = pauli_kernel_0.evaluate(x_vec=sample_train)\n",
    "pauli_svc_0.fit(matrix_train_0, labels_train_0)\n",
    "\n",
    "matrix_val_0 = pauli_kernel_0.evaluate(x_vec=sample_val, y_vec=sample_train)\n",
    "pauli_score_0 = pauli_svc_0.score(matrix_val_0, labels_val_0)\n",
    "print(f'Accuracy of discriminating between label 0 and others: {pauli_score_0*100}%')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can see that the QSVM binary classifier is able to distinguish between label 0 and the rest with a reasonable probability.\n",
    "\n",
    "Finally, for each of the test data, calculate the probability that it has label 0. It can be obtained by ```predict_proba``` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of label 0: [0.91 0.95 0.1  0.34 0.19 0.16 0.64 0.28 0.9  0.79 0.18 0.23 0.09 0.58\n",
      " 0.1  0.06 0.3  0.65 0.18 0.32]\n"
     ]
    }
   ],
   "source": [
    "matrix_test_0 = pauli_kernel_0.evaluate(x_vec=sample_test, y_vec=sample_train)\n",
    "pred_0 = pauli_svc_0.predict_proba(matrix_test_0)[:, 1]\n",
    "print(f'Probability of label 0: {np.round(pred_0, 2)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These probabilities are important clues for multiclass classification.  \n",
    "Obtain the probabilities for the remaining two labels in the same way.\n",
    "\n",
    "### 2.2: Label 2 vs Rest\n",
    "Build a binary classifier using QSVM and get the probability of label 2 for test dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original validation labels:      [3 3 2 0 3 0 3 2 3 2 2 3 2 2 2 3 0 2 3 3]\n",
      "Validation labels for 2 vs Rest: [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0]\n",
      "Probability of label 2: [0.01 0.01 0.03 0.17 0.05 0.2  0.   0.23 0.02 0.   0.01 0.23 0.99 0.32\n",
      " 0.07 0.99 0.15 0.02 0.21 0.5 ]\n",
      "Accuracy of discriminating between label 2 and others: 90.0%\n"
     ]
    }
   ],
   "source": [
    "##############################\n",
    "# Provide your code here\n",
    "\n",
    "labels_train_2 = np.where(labels_train==2, 1, 0)\n",
    "labels_val_2 = np.where(labels_val==2, 1, 0)\n",
    "\n",
    "print(f'Original validation labels:      {labels_val}')\n",
    "print(f'Validation labels for 2 vs Rest: {labels_val_2}')\n",
    "\n",
    "pauli_map_2 = PauliFeatureMap(feature_dimension=N_DIM, reps=1, paulis = ['X', 'Y', 'ZZ'])\n",
    "pauli_kernel_2 = QuantumKernel(feature_map=pauli_map_2, quantum_instance=Aer.get_backend('statevector_simulator'))\n",
    "\n",
    "pauli_svc_2 = SVC(kernel='precomputed', probability=True)\n",
    "\n",
    "matrix_train_2 = pauli_kernel_2.evaluate(x_vec=sample_train)\n",
    "pauli_svc_2.fit(matrix_train_2, labels_train_2)\n",
    "\n",
    "matrix_test_2 = pauli_kernel_2.evaluate(x_vec=sample_test, y_vec=sample_train)\n",
    "pred_2 = pauli_svc_2.predict_proba(matrix_test_2)[:, 1]\n",
    "print(f'Probability of label 2: {np.round(pred_2, 2)}')\n",
    "\n",
    "matrix_val_2 = pauli_kernel_2.evaluate(x_vec=sample_val, y_vec=sample_train)\n",
    "pauli_score_2 = pauli_svc_2.score(matrix_val_2, labels_val_2)\n",
    "print(f'Accuracy of discriminating between label 2 and others: {pauli_score_2*100}%')\n",
    "##############################"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3 Label 3 vs Rest\n",
    "Build a binary classifier using QSVM and get the probability of label 3 for test dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original validation labels:      [3 3 2 0 3 0 3 2 3 2 2 3 2 2 2 3 0 2 3 3]\n",
      "Validation labels for 3 vs Rest: [1 1 0 0 1 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1]\n",
      "Probability of label 3: [0.06 0.07 0.79 0.45 0.59 0.96 0.07 0.13 0.05 0.05 0.6  0.09 0.02 0.08\n",
      " 0.76 0.02 0.61 0.19 0.98 0.06]\n"
     ]
    }
   ],
   "source": [
    "##############################\n",
    "# Provide your code here\n",
    "\n",
    "labels_train_3 = np.where(labels_train==3, 1, 0)\n",
    "labels_val_3 = np.where(labels_val==3, 1, 0)\n",
    "\n",
    "print(f'Original validation labels:      {labels_val}')\n",
    "print(f'Validation labels for 3 vs Rest: {labels_val_3}')\n",
    "\n",
    "# pauli_map_3 = PauliFeatureMap(feature_dimension=N_DIM, reps=1, paulis = ['X','Y','ZZ'])\n",
    "pauli_map_3 = ZFeatureMap(feature_dimension=N_DIM, reps=1)\n",
    "pauli_kernel_3 = QuantumKernel(feature_map=pauli_map_3, quantum_instance=Aer.get_backend('statevector_simulator'))\n",
    "\n",
    "pauli_svc_3 = SVC(kernel='precomputed', probability=True)\n",
    "\n",
    "matrix_train_3 = pauli_kernel_3.evaluate(x_vec=sample_train)\n",
    "pauli_svc_3.fit(matrix_train_3, labels_train_3)\n",
    "\n",
    "matrix_test_3 = pauli_kernel_3.evaluate(x_vec=sample_test, y_vec=sample_train)\n",
    "pred_3 = pauli_svc_3.predict_proba(matrix_test_3)[:, 1]\n",
    "print(f'Probability of label 3: {np.round(pred_3, 2)}')\n",
    "\n",
    "\n",
    "##############################"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Prediction\n",
    "Lastly, make a final prediction based on the probability of each label.  \n",
    "The prediction you submit should be in the following format."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample prediction: [0 0 0 0 0 0 2 2 2 2 2 2 3 3 3 3 3 3 3 3]\n"
     ]
    }
   ],
   "source": [
    "sample_pred = np.load('./resources/ch3_part2_sub.npy')\n",
    "print(f'Sample prediction: {sample_pred}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to understand the method to make predictions for multiclass classification, let's begin with the case of making predictions for just two labels, label 2 and label 3.\n",
    "\n",
    "If probabilities are as follows for a certain data, label 2 should be considered the most plausible.\n",
    "- probability of label 2: 0.7\n",
    "- probability of label 3: 0.2\n",
    "\n",
    "You can implement this with ```np.where``` function. (Of course, you can use different methods.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction: [2]\n"
     ]
    }
   ],
   "source": [
    "pred_2_ex = np.array([0.7])\n",
    "pred_3_ex = np.array([0.2])\n",
    "\n",
    "pred_test_ex = np.where((pred_2_ex > pred_3_ex), 2, 3)\n",
    "print(f'Prediction: {pred_test_ex}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can apply this method as is to multiple data.\n",
    "\n",
    "If second data has probabilities for each label as follows, it should be classified as label 3.\n",
    "- probability of label 2: 0.1\n",
    "- probability of label 3: 0.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction: [2 3]\n"
     ]
    }
   ],
   "source": [
    "pred_2_ex = np.array([0.7, 0.1])\n",
    "pred_3_ex = np.array([0.2, 0.6])\n",
    "\n",
    "pred_test_ex = np.where((pred_2_ex > pred_3_ex), 2, 3)\n",
    "print(f'Prediction: {pred_test_ex}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This method can be extended to make predictions for 3-class classification.\n",
    "\n",
    "Implement such an extended method and make the final 3-class predictions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction: [0 0 3 3 3 3 0 0 0 0 3 2 2 0 3 2 3 0 3 2]\n"
     ]
    }
   ],
   "source": [
    "##############################\n",
    "# Provide your code here\n",
    "\n",
    "pred_temp_0 = np.where(np.logical_and((pred_3 > pred_2) , (pred_3 > pred_0)), 3, 0)\n",
    "pred_temp_1 = np.where(np.logical_and((pred_3 <= pred_2) , (pred_2 > pred_0)), 2, 0)\n",
    "pred_test = pred_temp_0+pred_temp_1\n",
    "\n",
    "print(f'Prediction: {pred_test}')\n",
    "\n",
    "##############################"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. Submission\n",
    "    \n",
    "<div class=\"alert alert-block alert-success\">\n",
    "\n",
    "**Challenge 3c**\n",
    "\n",
    "**Submission**: Submit the following 11 items.\n",
    "- **pred_test**: prediction for the public test dataset\n",
    "- **sample_train**: train data used to obtain kernels\n",
    "- **standard_scaler**: the one used to standardize data\n",
    "- **pca**: the one used to reduce dimention\n",
    "- **min_max_scaler**: the one used to normalize data\n",
    "- **kernel_0**: the kernel for the \"label 0 vs rest\" classifier\n",
    "- **kernel_2**: the kernel for the \"label 2 vs rest\" classifier\n",
    "- **kernel_3**: the kernel for the \"label 3 vs rest\" classifier\n",
    "- **svc_0**: the SVC trained to classify \"label 0 vs rest\"\n",
    "- **svc_2**: the SVC trained to classify \"label 2 vs rest\"\n",
    "- **svc_3**: the SVC trained to classify \"label 3 vs rest\"\n",
    "\n",
    "**Criteria**: Accuracy of 70% or better on both public and private test data.\n",
    "\n",
    "**Score**: Solutions that pass the criteria will be scored as follows. The smaller this final score is, the better.\n",
    "1. Each feature map gets transpiled with:\n",
    "    - basis_gates=['u1', 'u2', 'u3', 'cx']\n",
    "    - optimization_level=0\n",
    "2. Calculate the cost for each transpiled circuit:   \n",
    "   cost = 10 * #cx + (#u1 + #u2 + #u3)\n",
    "3. The sum of the costs will be the final score.\n",
    "\n",
    "</div>\n",
    "\n",
    "Again, the prediction you submit should be in the following format.\n",
    "- prediction for the public test data (**sample_test**)\n",
    "- type: numpy.ndarray\n",
    "- shape: (20,)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample prediction: [0 0 0 0 0 0 2 2 2 2 2 2 3 3 3 3 3 3 3 3]\n"
     ]
    }
   ],
   "source": [
    "print(f'Sample prediction: {sample_pred}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submitting your answer for 3c. Please wait...\n",
      "Congratulations 🎉! Your answer is correct and has been submitted.\n",
      "Your score is 500.\n"
     ]
    }
   ],
   "source": [
    "# Check your answer and submit using the following code\n",
    "from qc_grader import grade_ex3c\n",
    "grade_ex3c(pred_test, sample_train, \n",
    "           standard_scaler, pca, min_max_scaler,\n",
    "           pauli_kernel_0, pauli_kernel_2, pauli_kernel_3,\n",
    "           pauli_svc_0, pauli_svc_2, pauli_svc_3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Additional information\n",
    "\n",
    "**Created by:** Shota Nakasuji, Anna Phan\n",
    "\n",
    "**Version:** 1.0.1"
   ]
  }
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